id	sid	tid	token	lemma	pos
ejpam-3338	1	1	can	can	AUX
ejpam-3338	1	2	fractional	fractional	VERB
ejpam-3338	1	3	calculus	calculus	NOUN
ejpam-3338	1	4	be	be	AUX
ejpam-3338	1	5	generalized	generalize	VERB
ejpam-3338	1	6	:	:	PUNCT
ejpam-3338	1	7	problems	problem	NOUN
ejpam-3338	1	8	and	and	CCONJ
ejpam-3338	1	9	efforts	effort	NOUN
ejpam-3338	1	10	european	european	PROPN
ejpam-3338	1	11	journal	journal	PROPN
ejpam-3338	1	12	of	of	ADP
ejpam-3338	1	13	pure	pure	ADJ
ejpam-3338	1	14	and	and	CCONJ
ejpam-3338	1	15	applied	apply	VERB
ejpam-3338	1	16	mathematics	mathematic	NOUN
ejpam-3338	1	17	vol	vol	NOUN
ejpam-3338	1	18	.	.	PUNCT
ejpam-3338	2	1	11	11	NUM
ejpam-3338	2	2	,	,	PUNCT
ejpam-3338	2	3	no	no	INTJ
ejpam-3338	2	4	.	.	NOUN
ejpam-3338	2	5	3	3	NUM
ejpam-3338	2	6	,	,	PUNCT
ejpam-3338	2	7	2018	2018	NUM
ejpam-3338	2	8	,	,	PUNCT
ejpam-3338	2	9	1058	1058	NUM
ejpam-3338	2	10	-	-	SYM
ejpam-3338	2	11	1099	1099	NUM
ejpam-3338	2	12	issn	issn	PROPN
ejpam-3338	2	13	1307	1307	NUM
ejpam-3338	2	14	-	-	SYM
ejpam-3338	2	15	5543	5543	NUM
ejpam-3338	2	16	–	–	PUNCT
ejpam-3338	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3338	2	18	published	publish	VERB
ejpam-3338	2	19	by	by	ADP
ejpam-3338	2	20	new	new	PROPN
ejpam-3338	2	21	york	york	PROPN
ejpam-3338	2	22	business	business	PROPN
ejpam-3338	2	23	global	global	PROPN
ejpam-3338	2	24	can	can	AUX
ejpam-3338	2	25	fractional	fractional	VERB
ejpam-3338	2	26	calculus	calculus	NOUN
ejpam-3338	2	27	be	be	AUX
ejpam-3338	2	28	generalized	generalize	VERB
ejpam-3338	2	29	?	?	PUNCT
ejpam-3338	3	1	problems	problem	NOUN
ejpam-3338	3	2	and	and	CCONJ
ejpam-3338	3	3	efforts	effort	NOUN
ejpam-3338	3	4	syamal	syamal	PROPN
ejpam-3338	3	5	k.sen1,2	k.sen1,2	PROPN
ejpam-3338	3	6	,	,	PUNCT
ejpam-3338	3	7	j.	j.	PROPN
ejpam-3338	3	8	vasundhara	vasundhara	PROPN
ejpam-3338	3	9	devi1,3,∗	devi1,3,∗	PROPN
ejpam-3338	3	10	,	,	PUNCT
ejpam-3338	3	11	r.v.g	r.v.g	NOUN
ejpam-3338	3	12	.	.	PUNCT
ejpam-3338	4	1	ravi	ravi	PROPN
ejpam-3338	4	2	kumar3	kumar3	NOUN
ejpam-3338	4	3	1	1	NUM
ejpam-3338	4	4	gvp-prof.v.lakshmikantham	gvp-prof.v.lakshmikantham	PROPN
ejpam-3338	4	5	institute	institute	VERB
ejpam-3338	4	6	for	for	ADP
ejpam-3338	4	7	advanced	advanced	ADJ
ejpam-3338	4	8	studies	study	NOUN
ejpam-3338	4	9	,	,	PUNCT
ejpam-3338	4	10	gvp	gvp	PROPN
ejpam-3338	4	11	college	college	PROPN
ejpam-3338	4	12	of	of	ADP
ejpam-3338	4	13	engineering	engineering	PROPN
ejpam-3338	4	14	campus	campus	PROPN
ejpam-3338	4	15	,	,	PUNCT
ejpam-3338	4	16	visakhapatnam	visakhapatnam	PROPN
ejpam-3338	4	17	530048	530048	NUM
ejpam-3338	4	18	,	,	PUNCT
ejpam-3338	4	19	india	india	PROPN
ejpam-3338	4	20	2	2	NUM
ejpam-3338	4	21	department	department	NOUN
ejpam-3338	4	22	of	of	ADP
ejpam-3338	4	23	computer	computer	NOUN
ejpam-3338	4	24	science	science	NOUN
ejpam-3338	4	25	and	and	CCONJ
ejpam-3338	4	26	engineering	engineering	NOUN
ejpam-3338	4	27	,	,	PUNCT
ejpam-3338	4	28	gvp	gvp	PROPN
ejpam-3338	4	29	college	college	PROPN
ejpam-3338	4	30	of	of	ADP
ejpam-3338	4	31	engineering	engineering	PROPN
ejpam-3338	4	32	,	,	PUNCT
ejpam-3338	4	33	visakhapatnam	visakhapatnam	PROPN
ejpam-3338	4	34	,	,	PUNCT
ejpam-3338	4	35	ap	ap	PROPN
ejpam-3338	4	36	,	,	PUNCT
ejpam-3338	4	37	india	india	PROPN
ejpam-3338	4	38	3	3	NUM
ejpam-3338	4	39	department	department	PROPN
ejpam-3338	4	40	of	of	ADP
ejpam-3338	4	41	mathematics	mathematic	NOUN
ejpam-3338	4	42	,	,	PUNCT
ejpam-3338	4	43	gvp	gvp	PROPN
ejpam-3338	4	44	college	college	PROPN
ejpam-3338	4	45	of	of	ADP
ejpam-3338	4	46	engineering(a	engineering(a	PROPN
ejpam-3338	4	47	)	)	PUNCT
ejpam-3338	4	48	,	,	PUNCT
ejpam-3338	4	49	visakhapatnam	visakhapatnam	PROPN
ejpam-3338	4	50	,	,	PUNCT
ejpam-3338	4	51	ap	ap	PROPN
ejpam-3338	4	52	,	,	PUNCT
ejpam-3338	4	53	india	india	PROPN
ejpam-3338	4	54	abstract	abstract	NOUN
ejpam-3338	4	55	.	.	PUNCT
ejpam-3338	5	1	fractional	fractional	ADJ
ejpam-3338	5	2	order	order	NOUN
ejpam-3338	5	3	calculus	calculus	NOUN
ejpam-3338	5	4	always	always	ADV
ejpam-3338	5	5	includes	include	VERB
ejpam-3338	5	6	integer	integer	NOUN
ejpam-3338	5	7	-	-	PUNCT
ejpam-3338	5	8	order	order	NOUN
ejpam-3338	5	9	too	too	ADV
ejpam-3338	5	10	.	.	PUNCT
ejpam-3338	6	1	the	the	DET
ejpam-3338	6	2	question	question	NOUN
ejpam-3338	6	3	that	that	PRON
ejpam-3338	6	4	crops	crop	NOUN
ejpam-3338	6	5	up	up	ADP
ejpam-3338	6	6	is	be	AUX
ejpam-3338	6	7	:	:	PUNCT
ejpam-3338	6	8	can	can	AUX
ejpam-3338	6	9	it	it	PRON
ejpam-3338	6	10	be	be	AUX
ejpam-3338	6	11	a	a	DET
ejpam-3338	6	12	widely	widely	ADV
ejpam-3338	6	13	accepted	accept	VERB
ejpam-3338	6	14	generalized	generalized	ADJ
ejpam-3338	6	15	version	version	NOUN
ejpam-3338	6	16	of	of	ADP
ejpam-3338	6	17	classical	classical	ADJ
ejpam-3338	6	18	calculus	calculus	NOUN
ejpam-3338	6	19	?	?	PUNCT
ejpam-3338	7	1	we	we	PRON
ejpam-3338	7	2	attempt	attempt	VERB
ejpam-3338	7	3	to	to	PART
ejpam-3338	7	4	highlight	highlight	VERB
ejpam-3338	7	5	the	the	DET
ejpam-3338	7	6	current	current	ADJ
ejpam-3338	7	7	problems	problem	NOUN
ejpam-3338	7	8	that	that	PRON
ejpam-3338	7	9	come	come	VERB
ejpam-3338	7	10	in	in	ADP
ejpam-3338	7	11	the	the	DET
ejpam-3338	7	12	way	way	NOUN
ejpam-3338	7	13	to	to	PART
ejpam-3338	7	14	define	define	VERB
ejpam-3338	7	15	the	the	DET
ejpam-3338	7	16	fractional	fractional	ADJ
ejpam-3338	7	17	calculus	calculus	NOUN
ejpam-3338	7	18	that	that	PRON
ejpam-3338	7	19	will	will	AUX
ejpam-3338	7	20	be	be	AUX
ejpam-3338	7	21	universally	universally	ADV
ejpam-3338	7	22	accepted	accept	VERB
ejpam-3338	7	23	as	as	ADP
ejpam-3338	7	24	a	a	DET
ejpam-3338	7	25	perfect	perfect	ADJ
ejpam-3338	7	26	generalized	generalized	ADJ
ejpam-3338	7	27	version	version	NOUN
ejpam-3338	7	28	of	of	ADP
ejpam-3338	7	29	integer	integer	NOUN
ejpam-3338	7	30	-	-	PUNCT
ejpam-3338	7	31	order	order	NOUN
ejpam-3338	7	32	calculus	calculus	NOUN
ejpam-3338	7	33	and	and	CCONJ
ejpam-3338	7	34	to	to	PART
ejpam-3338	7	35	point	point	VERB
ejpam-3338	7	36	out	out	ADP
ejpam-3338	7	37	the	the	DET
ejpam-3338	7	38	efforts	effort	NOUN
ejpam-3338	7	39	in	in	ADP
ejpam-3338	7	40	this	this	DET
ejpam-3338	7	41	direction	direction	NOUN
ejpam-3338	7	42	.	.	PUNCT
ejpam-3338	8	1	also	also	ADV
ejpam-3338	8	2	,	,	PUNCT
ejpam-3338	8	3	we	we	PRON
ejpam-3338	8	4	discuss	discuss	VERB
ejpam-3338	8	5	the	the	DET
ejpam-3338	8	6	question	question	NOUN
ejpam-3338	8	7	:	:	PUNCT
ejpam-3338	8	8	given	give	VERB
ejpam-3338	8	9	a	a	DET
ejpam-3338	8	10	non	non	ADJ
ejpam-3338	8	11	-	-	ADJ
ejpam-3338	8	12	integer	integer	ADJ
ejpam-3338	8	13	fractional	fractional	ADJ
ejpam-3338	8	14	order	order	NOUN
ejpam-3338	8	15	differential	differential	NOUN
ejpam-3338	8	16	equation	equation	NOUN
ejpam-3338	8	17	as	as	ADP
ejpam-3338	8	18	a	a	DET
ejpam-3338	8	19	mathematical	mathematical	ADJ
ejpam-3338	8	20	model	model	NOUN
ejpam-3338	8	21	can	can	AUX
ejpam-3338	8	22	we	we	PRON
ejpam-3338	8	23	readily	readily	ADV
ejpam-3338	8	24	write	write	VERB
ejpam-3338	8	25	the	the	DET
ejpam-3338	8	26	corresponding	corresponding	ADJ
ejpam-3338	8	27	physical	physical	ADJ
ejpam-3338	8	28	model	model	NOUN
ejpam-3338	8	29	and	and	CCONJ
ejpam-3338	8	30	vice	vice	ADV
ejpam-3338	8	31	versa	versa	NOUN
ejpam-3338	8	32	in	in	ADP
ejpam-3338	8	33	the	the	DET
ejpam-3338	8	34	same	same	ADJ
ejpam-3338	8	35	way	way	NOUN
ejpam-3338	8	36	as	as	SCONJ
ejpam-3338	8	37	we	we	PRON
ejpam-3338	8	38	traditionally	traditionally	ADV
ejpam-3338	8	39	do	do	VERB
ejpam-3338	8	40	for	for	ADP
ejpam-3338	8	41	classical	classical	ADJ
ejpam-3338	8	42	differential	differential	ADJ
ejpam-3338	8	43	equations	equation	NOUN
ejpam-3338	8	44	?	?	PUNCT
ejpam-3338	9	1	we	we	PRON
ejpam-3338	9	2	demonstrate	demonstrate	VERB
ejpam-3338	9	3	numerically	numerically	ADV
ejpam-3338	9	4	computationally	computationally	ADV
ejpam-3338	9	5	the	the	DET
ejpam-3338	9	6	pros	pro	NOUN
ejpam-3338	9	7	and	and	CCONJ
ejpam-3338	9	8	cons	con	NOUN
ejpam-3338	9	9	while	while	SCONJ
ejpam-3338	9	10	addressing	address	VERB
ejpam-3338	9	11	the	the	DET
ejpam-3338	9	12	questions	question	NOUN
ejpam-3338	9	13	keeping	keep	VERB
ejpam-3338	9	14	in	in	ADP
ejpam-3338	9	15	the	the	DET
ejpam-3338	9	16	background	background	NOUN
ejpam-3338	9	17	the	the	DET
ejpam-3338	9	18	generalization	generalization	NOUN
ejpam-3338	9	19	of	of	ADP
ejpam-3338	9	20	the	the	DET
ejpam-3338	9	21	inverse	inverse	NOUN
ejpam-3338	9	22	of	of	ADP
ejpam-3338	9	23	a	a	DET
ejpam-3338	9	24	matrix	matrix	NOUN
ejpam-3338	9	25	.	.	PUNCT
ejpam-3338	10	1	2010	2010	NUM
ejpam-3338	10	2	mathematics	mathematic	NOUN
ejpam-3338	10	3	subject	subject	NOUN
ejpam-3338	10	4	classifications	classification	NOUN
ejpam-3338	10	5	:	:	PUNCT
ejpam-3338	10	6	26a33	26a33	NUM
ejpam-3338	10	7	,	,	PUNCT
ejpam-3338	10	8	26a36	26a36	NUM
ejpam-3338	10	9	,	,	PUNCT
ejpam-3338	10	10	34a08	34a08	NUM
ejpam-3338	10	11	,	,	PUNCT
ejpam-3338	10	12	44a45	44a45	PRON
ejpam-3338	10	13	key	key	ADJ
ejpam-3338	10	14	words	word	NOUN
ejpam-3338	10	15	and	and	CCONJ
ejpam-3338	10	16	phrases	phrase	NOUN
ejpam-3338	10	17	:	:	PUNCT
ejpam-3338	10	18	differintegrals	differintegral	NOUN
ejpam-3338	10	19	,	,	PUNCT
ejpam-3338	10	20	fractional	fractional	ADJ
ejpam-3338	10	21	calculus	calculus	NOUN
ejpam-3338	10	22	,	,	PUNCT
ejpam-3338	10	23	fractional	fractional	ADJ
ejpam-3338	10	24	differential	differential	ADJ
ejpam-3338	10	25	equations	equation	NOUN
ejpam-3338	10	26	,	,	PUNCT
ejpam-3338	10	27	generalization	generalization	NOUN
ejpam-3338	10	28	of	of	ADP
ejpam-3338	10	29	calculus	calculus	NOUN
ejpam-3338	10	30	,	,	PUNCT
ejpam-3338	10	31	integer	integer	NOUN
ejpam-3338	10	32	order	order	NOUN
ejpam-3338	10	33	calculus	calculus	NOUN
ejpam-3338	10	34	1	1	NUM
ejpam-3338	10	35	.	.	PUNCT
ejpam-3338	11	1	introduction	introduction	NOUN
ejpam-3338	11	2	fractional	fractional	ADJ
ejpam-3338	11	3	calculus	calculus	NOUN
ejpam-3338	11	4	is	be	AUX
ejpam-3338	11	5	the	the	DET
ejpam-3338	11	6	calculus	calculus	NOUN
ejpam-3338	11	7	investigating	investigate	VERB
ejpam-3338	11	8	the	the	DET
ejpam-3338	11	9	properties	property	NOUN
ejpam-3338	11	10	of	of	ADP
ejpam-3338	11	11	derivatives	derivative	NOUN
ejpam-3338	11	12	and	and	CCONJ
ejpam-3338	11	13	integrals	integral	NOUN
ejpam-3338	11	14	of	of	ADP
ejpam-3338	11	15	both	both	PRON
ejpam-3338	11	16	integer	integer	NOUN
ejpam-3338	11	17	order	order	NOUN
ejpam-3338	11	18	and	and	CCONJ
ejpam-3338	11	19	non	non	ADJ
ejpam-3338	11	20	-	-	ADJ
ejpam-3338	11	21	integer	integer	ADJ
ejpam-3338	11	22	fractional	fractional	ADJ
ejpam-3338	11	23	order	order	NOUN
ejpam-3338	11	24	called	call	VERB
ejpam-3338	11	25	fractional	fractional	ADJ
ejpam-3338	11	26	derivatives	derivative	NOUN
ejpam-3338	11	27	and	and	CCONJ
ejpam-3338	11	28	fractional	fractional	ADJ
ejpam-3338	11	29	integrals	integral	NOUN
ejpam-3338	11	30	,	,	PUNCT
ejpam-3338	11	31	in	in	ADP
ejpam-3338	11	32	short	short	ADJ
ejpam-3338	11	33	differintegrals	differintegral	NOUN
ejpam-3338	11	34	.	.	PUNCT
ejpam-3338	12	1	specifically	specifically	ADV
ejpam-3338	12	2	,	,	PUNCT
ejpam-3338	12	3	this	this	DET
ejpam-3338	12	4	discipline	discipline	NOUN
ejpam-3338	12	5	introduces	introduce	VERB
ejpam-3338	12	6	the	the	DET
ejpam-3338	12	7	notion	notion	NOUN
ejpam-3338	12	8	and	and	CCONJ
ejpam-3338	12	9	methods	method	NOUN
ejpam-3338	12	10	of	of	ADP
ejpam-3338	12	11	solving	solve	VERB
ejpam-3338	12	12	differential	differential	ADJ
ejpam-3338	12	13	equations	equation	NOUN
ejpam-3338	12	14	both	both	CCONJ
ejpam-3338	12	15	ordinary	ordinary	ADJ
ejpam-3338	12	16	and	and	CCONJ
ejpam-3338	12	17	partial	partial	ADJ
ejpam-3338	12	18	consisting	consisting	NOUN
ejpam-3338	12	19	of	of	ADP
ejpam-3338	12	20	fractional	fractional	ADJ
ejpam-3338	12	21	derivatives	derivative	NOUN
ejpam-3338	12	22	of	of	ADP
ejpam-3338	12	23	the	the	DET
ejpam-3338	12	24	unknown	unknown	ADJ
ejpam-3338	12	25	function	function	NOUN
ejpam-3338	12	26	(	(	PUNCT
ejpam-3338	12	27	named	name	VERB
ejpam-3338	12	28	as	as	ADP
ejpam-3338	12	29	fractional	fractional	ADJ
ejpam-3338	12	30	differential	differential	ADJ
ejpam-3338	12	31	equations	equation	NOUN
ejpam-3338	12	32	or	or	CCONJ
ejpam-3338	12	33	fdes	fde	NOUN
ejpam-3338	12	34	in	in	ADP
ejpam-3338	12	35	short	short	ADJ
ejpam-3338	12	36	)	)	PUNCT
ejpam-3338	12	37	.	.	PUNCT
ejpam-3338	13	1	the	the	DET
ejpam-3338	13	2	history	history	NOUN
ejpam-3338	13	3	of	of	ADP
ejpam-3338	13	4	fractional	fractional	ADJ
ejpam-3338	13	5	calculus	calculus	NOUN
ejpam-3338	13	6	began	begin	VERB
ejpam-3338	13	7	almost	almost	ADV
ejpam-3338	13	8	at	at	ADP
ejpam-3338	13	9	the	the	DET
ejpam-3338	13	10	same	same	ADJ
ejpam-3338	13	11	time	time	NOUN
ejpam-3338	13	12	(	(	PUNCT
ejpam-3338	13	13	late	late	ADJ
ejpam-3338	13	14	17th	17th	ADJ
ejpam-3338	13	15	century	century	NOUN
ejpam-3338	13	16	a.d	a.d	PROPN
ejpam-3338	13	17	.	.	PUNCT
ejpam-3338	13	18	)	)	PUNCT
ejpam-3338	13	19	when	when	SCONJ
ejpam-3338	13	20	conventional	conventional	ADJ
ejpam-3338	13	21	(	(	PUNCT
ejpam-3338	13	22	classical	classical	ADJ
ejpam-3338	13	23	)	)	PUNCT
ejpam-3338	13	24	calculus	calculus	NOUN
ejpam-3338	13	25	viz	viz	NOUN
ejpam-3338	13	26	.	.	PUNCT
ejpam-3338	14	1	integer	integer	NOUN
ejpam-3338	14	2	-	-	PUNCT
ejpam-3338	14	3	order	order	NOUN
ejpam-3338	14	4	calculus	calculus	NOUN
ejpam-3338	14	5	was	be	AUX
ejpam-3338	14	6	established	establish	VERB
ejpam-3338	14	7	.	.	PUNCT
ejpam-3338	15	1	in	in	ADP
ejpam-3338	15	2	conventional	conventional	ADJ
ejpam-3338	15	3	calculus	calculus	NOUN
ejpam-3338	15	4	,	,	PUNCT
ejpam-3338	15	5	both	both	DET
ejpam-3338	15	6	derivatives	derivative	NOUN
ejpam-3338	15	7	and	and	CCONJ
ejpam-3338	15	8	integrals	integral	NOUN
ejpam-3338	15	9	(	(	PUNCT
ejpam-3338	15	10	anti	anti	ADJ
ejpam-3338	15	11	-	-	ADJ
ejpam-3338	15	12	derivatives	derivative	NOUN
ejpam-3338	15	13	a	a	DET
ejpam-3338	15	14	term	term	NOUN
ejpam-3338	15	15	not	not	PART
ejpam-3338	15	16	widely	widely	ADV
ejpam-3338	15	17	∗corresponding	∗corresponde	VERB
ejpam-3338	15	18	author	author	NOUN
ejpam-3338	15	19	.	.	PUNCT
ejpam-3338	16	1	doi	doi	NOUN
ejpam-3338	16	2	:	:	PUNCT
ejpam-3338	16	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3338	https://doi.org/10.29020/nybg.ejpam.v11i3.3338	NOUN
ejpam-3338	16	4	email	email	NOUN
ejpam-3338	16	5	address	address	NOUN
ejpam-3338	16	6	:	:	PUNCT
ejpam-3338	16	7	jvdevi@gmail.com	jvdevi@gmail.com	X
ejpam-3338	16	8	(	(	PUNCT
ejpam-3338	16	9	j.	j.	PROPN
ejpam-3338	16	10	vasundhara	vasundhara	PROPN
ejpam-3338	16	11	devi	devi	PROPN
ejpam-3338	16	12	)	)	PUNCT
ejpam-3338	16	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3338	16	14	1058	1058	NUM
ejpam-3338	16	15	c	c	NOUN
ejpam-3338	16	16	©	©	PROPN
ejpam-3338	16	17	2018	2018	NUM
ejpam-3338	16	18	ejpam	ejpam	VERB
ejpam-3338	16	19	all	all	DET
ejpam-3338	16	20	rights	right	NOUN
ejpam-3338	16	21	reserved	reserve	VERB
ejpam-3338	16	22	.	.	PUNCT
ejpam-3338	17	1	s.	s.	PROPN
ejpam-3338	17	2	k.sen	k.sen	PROPN
ejpam-3338	17	3	,	,	PUNCT
ejpam-3338	17	4	j.	j.	PROPN
ejpam-3338	17	5	v.	v.	PROPN
ejpam-3338	17	6	devi	devi	PROPN
ejpam-3338	17	7	,	,	PUNCT
ejpam-3338	17	8	r.v.g	r.v.g	NOUN
ejpam-3338	17	9	.	.	PUNCT
ejpam-3338	18	1	r.	r.	PROPN
ejpam-3338	18	2	kumar	kumar	PROPN
ejpam-3338	18	3	/	/	SYM
ejpam-3338	18	4	eur	eur	PROPN
ejpam-3338	18	5	.	.	PUNCT
ejpam-3338	19	1	j.	j.	PROPN
ejpam-3338	19	2	pure	pure	PROPN
ejpam-3338	19	3	appl	appl	PROPN
ejpam-3338	19	4	.	.	PROPN
ejpam-3338	19	5	math	math	PROPN
ejpam-3338	19	6	,	,	PUNCT
ejpam-3338	19	7	11	11	NUM
ejpam-3338	19	8	(	(	PUNCT
ejpam-3338	19	9	3	3	NUM
ejpam-3338	19	10	)	)	PUNCT
ejpam-3338	19	11	(	(	PUNCT
ejpam-3338	19	12	2018	2018	NUM
ejpam-3338	19	13	)	)	PUNCT
ejpam-3338	19	14	,	,	PUNCT
ejpam-3338	19	15	1058	1058	NUM
ejpam-3338	19	16	-	-	SYM
ejpam-3338	19	17	1099	1099	NUM
ejpam-3338	19	18	1059	1059	NUM
ejpam-3338	19	19	used	use	VERB
ejpam-3338	19	20	)	)	PUNCT
ejpam-3338	19	21	are	be	AUX
ejpam-3338	19	22	exactly	exactly	ADV
ejpam-3338	19	23	defined	define	VERB
ejpam-3338	19	24	with	with	ADP
ejpam-3338	19	25	corresponding	corresponding	ADJ
ejpam-3338	19	26	exact	exact	ADJ
ejpam-3338	19	27	physical	physical	ADJ
ejpam-3338	19	28	significance	significance	NOUN
ejpam-3338	19	29	that	that	PRON
ejpam-3338	19	30	is	be	AUX
ejpam-3338	19	31	taught	teach	VERB
ejpam-3338	19	32	in	in	ADP
ejpam-3338	19	33	high	high	ADJ
ejpam-3338	19	34	schools	school	NOUN
ejpam-3338	19	35	/	/	SYM
ejpam-3338	19	36	colleges	college	NOUN
ejpam-3338	19	37	and	and	CCONJ
ejpam-3338	19	38	is	be	AUX
ejpam-3338	19	39	uniquely	uniquely	ADV
ejpam-3338	19	40	and	and	CCONJ
ejpam-3338	19	41	readily	readily	ADV
ejpam-3338	19	42	understood	understand	VERB
ejpam-3338	19	43	.	.	PUNCT
ejpam-3338	20	1	the	the	DET
ejpam-3338	20	2	classical	classical	ADJ
ejpam-3338	20	3	differential	differential	ADJ
ejpam-3338	20	4	equations	equation	NOUN
ejpam-3338	20	5	viz	viz	PROPN
ejpam-3338	20	6	.	.	PUNCT
ejpam-3338	21	1	the	the	DET
ejpam-3338	21	2	integer	integer	NOUN
ejpam-3338	21	3	order	order	NOUN
ejpam-3338	21	4	differential	differential	NOUN
ejpam-3338	21	5	equations	equation	NOUN
ejpam-3338	21	6	both	both	CCONJ
ejpam-3338	21	7	ordinary	ordinary	ADJ
ejpam-3338	21	8	and	and	CCONJ
ejpam-3338	21	9	partial	partial	ADJ
ejpam-3338	21	10	also	also	ADV
ejpam-3338	21	11	pervades	pervade	VERB
ejpam-3338	21	12	not	not	PART
ejpam-3338	21	13	only	only	ADV
ejpam-3338	21	14	almost	almost	ADV
ejpam-3338	21	15	the	the	DET
ejpam-3338	21	16	whole	whole	NOUN
ejpam-3338	21	17	of	of	ADP
ejpam-3338	21	18	science	science	NOUN
ejpam-3338	21	19	and	and	CCONJ
ejpam-3338	21	20	engineering	engineering	NOUN
ejpam-3338	21	21	applications	application	NOUN
ejpam-3338	21	22	but	but	CCONJ
ejpam-3338	21	23	also	also	ADV
ejpam-3338	21	24	the	the	DET
ejpam-3338	21	25	whole	whole	NOUN
ejpam-3338	21	26	of	of	ADP
ejpam-3338	21	27	relatively	relatively	ADV
ejpam-3338	21	28	easily	easily	ADV
ejpam-3338	21	29	understood	understand	VERB
ejpam-3338	21	30	mathematical	mathematical	ADJ
ejpam-3338	21	31	modelling	modelling	NOUN
ejpam-3338	21	32	for	for	ADP
ejpam-3338	21	33	physical	physical	ADJ
ejpam-3338	21	34	problems	problem	NOUN
ejpam-3338	21	35	involving	involve	VERB
ejpam-3338	21	36	derivatives	derivative	NOUN
ejpam-3338	21	37	and	and	CCONJ
ejpam-3338	21	38	integrals	integral	NOUN
ejpam-3338	21	39	.	.	PUNCT
ejpam-3338	22	1	the	the	DET
ejpam-3338	22	2	concerned	concerned	ADJ
ejpam-3338	22	3	scientists	scientist	NOUN
ejpam-3338	22	4	/	/	SYM
ejpam-3338	22	5	modellers	modeller	NOUN
ejpam-3338	22	6	attempted	attempt	VERB
ejpam-3338	22	7	to	to	PART
ejpam-3338	22	8	model	model	VERB
ejpam-3338	22	9	some	some	PRON
ejpam-3338	22	10	of	of	ADP
ejpam-3338	22	11	these	these	DET
ejpam-3338	22	12	physical	physical	ADJ
ejpam-3338	22	13	problems	problem	NOUN
ejpam-3338	22	14	in	in	ADP
ejpam-3338	22	15	terms	term	NOUN
ejpam-3338	22	16	of	of	ADP
ejpam-3338	22	17	non	non	ADJ
ejpam-3338	22	18	-	-	ADJ
ejpam-3338	22	19	integer	integer	ADJ
ejpam-3338	22	20	fractional	fractional	ADJ
ejpam-3338	22	21	order	order	NOUN
ejpam-3338	22	22	differential	differential	ADJ
ejpam-3338	22	23	equations	equation	NOUN
ejpam-3338	22	24	and	and	CCONJ
ejpam-3338	22	25	to	to	PART
ejpam-3338	22	26	demonstrate	demonstrate	VERB
ejpam-3338	22	27	the	the	DET
ejpam-3338	22	28	scope	scope	NOUN
ejpam-3338	22	29	of	of	ADP
ejpam-3338	22	30	fractional	fractional	ADJ
ejpam-3338	22	31	differential	differential	ADJ
ejpam-3338	22	32	equations	equation	NOUN
ejpam-3338	22	33	against	against	ADP
ejpam-3338	22	34	the	the	DET
ejpam-3338	22	35	classical	classical	ADJ
ejpam-3338	22	36	ones	one	NOUN
ejpam-3338	22	37	.	.	PUNCT
ejpam-3338	23	1	their	their	PRON
ejpam-3338	23	2	attempts	attempt	NOUN
ejpam-3338	23	3	mostly	mostly	ADV
ejpam-3338	23	4	were	be	AUX
ejpam-3338	23	5	limited	limit	VERB
ejpam-3338	23	6	to	to	ADP
ejpam-3338	23	7	mathematical	mathematical	ADJ
ejpam-3338	23	8	treatment	treatment	NOUN
ejpam-3338	23	9	rather	rather	ADV
ejpam-3338	23	10	than	than	ADP
ejpam-3338	23	11	a	a	DET
ejpam-3338	23	12	serious	serious	ADJ
ejpam-3338	23	13	computational	computational	ADJ
ejpam-3338	23	14	one	one	NUM
ejpam-3338	23	15	.	.	PUNCT
ejpam-3338	24	1	a	a	DET
ejpam-3338	24	2	rigorous	rigorous	ADJ
ejpam-3338	24	3	computational	computational	ADJ
ejpam-3338	24	4	treatment	treatment	NOUN
ejpam-3338	24	5	both	both	PRON
ejpam-3338	24	6	in	in	ADP
ejpam-3338	24	7	terms	term	NOUN
ejpam-3338	24	8	of	of	ADP
ejpam-3338	24	9	quality	quality	NOUN
ejpam-3338	24	10	of	of	ADP
ejpam-3338	24	11	the	the	DET
ejpam-3338	24	12	numerical	numerical	ADJ
ejpam-3338	24	13	solution	solution	NOUN
ejpam-3338	24	14	(	(	PUNCT
ejpam-3338	24	15	computational	computational	ADJ
ejpam-3338	24	16	relative	relative	ADJ
ejpam-3338	24	17	error	error	NOUN
ejpam-3338	24	18	)	)	PUNCT
ejpam-3338	24	19	and	and	CCONJ
ejpam-3338	24	20	the	the	DET
ejpam-3338	24	21	cost	cost	NOUN
ejpam-3338	24	22	of	of	ADP
ejpam-3338	24	23	the	the	DET
ejpam-3338	24	24	solution	solution	NOUN
ejpam-3338	24	25	(	(	PUNCT
ejpam-3338	24	26	computational	computational	ADJ
ejpam-3338	24	27	complexity	complexity	NOUN
ejpam-3338	24	28	)	)	PUNCT
ejpam-3338	24	29	for	for	ADP
ejpam-3338	24	30	fractional	fractional	ADJ
ejpam-3338	24	31	differential	differential	ADJ
ejpam-3338	24	32	equations	equation	NOUN
ejpam-3338	24	33	were	be	AUX
ejpam-3338	24	34	practically	practically	ADV
ejpam-3338	24	35	not	not	PART
ejpam-3338	24	36	done	do	VERB
ejpam-3338	24	37	and	and	CCONJ
ejpam-3338	24	38	then	then	ADV
ejpam-3338	24	39	compared	compare	VERB
ejpam-3338	24	40	with	with	ADP
ejpam-3338	24	41	the	the	DET
ejpam-3338	24	42	corresponding	corresponding	ADJ
ejpam-3338	24	43	integer	integer	NOUN
ejpam-3338	24	44	order	order	NOUN
ejpam-3338	24	45	differential	differential	ADJ
ejpam-3338	24	46	equations	equation	NOUN
ejpam-3338	24	47	for	for	ADP
ejpam-3338	24	48	a	a	DET
ejpam-3338	24	49	specified	specify	VERB
ejpam-3338	24	50	physical	physical	ADJ
ejpam-3338	24	51	problem	problem	NOUN
ejpam-3338	24	52	,	,	PUNCT
ejpam-3338	24	53	the	the	DET
ejpam-3338	24	54	claim	claim	NOUN
ejpam-3338	24	55	/	/	SYM
ejpam-3338	24	56	statement	statement	NOUN
ejpam-3338	24	57	was	be	AUX
ejpam-3338	24	58	often	often	ADV
ejpam-3338	24	59	in	in	ADP
ejpam-3338	24	60	favour	favour	NOUN
ejpam-3338	24	61	of	of	ADP
ejpam-3338	24	62	fractional	fractional	ADJ
ejpam-3338	24	63	differential	differential	ADJ
ejpam-3338	24	64	equations	equation	NOUN
ejpam-3338	24	65	though	though	SCONJ
ejpam-3338	24	66	in	in	ADP
ejpam-3338	24	67	some	some	DET
ejpam-3338	24	68	sense	sense	NOUN
ejpam-3338	24	69	.	.	PUNCT
ejpam-3338	25	1	in	in	ADP
ejpam-3338	25	2	fractional	fractional	ADJ
ejpam-3338	25	3	calculus	calculus	NOUN
ejpam-3338	25	4	,	,	PUNCT
ejpam-3338	25	5	both	both	CCONJ
ejpam-3338	25	6	derivatives	derivative	NOUN
ejpam-3338	25	7	and	and	CCONJ
ejpam-3338	25	8	integrals	integral	NOUN
ejpam-3338	25	9	are	be	AUX
ejpam-3338	25	10	also	also	ADV
ejpam-3338	25	11	exactly	exactly	ADV
ejpam-3338	25	12	defined	define	VERB
ejpam-3338	25	13	but	but	CCONJ
ejpam-3338	25	14	with	with	ADP
ejpam-3338	25	15	no	no	DET
ejpam-3338	25	16	corresponding	corresponding	ADJ
ejpam-3338	25	17	exact	exact	ADJ
ejpam-3338	25	18	physical	physical	ADJ
ejpam-3338	25	19	significance	significance	NOUN
ejpam-3338	25	20	that	that	PRON
ejpam-3338	25	21	is	be	AUX
ejpam-3338	25	22	readily	readily	ADV
ejpam-3338	25	23	understood	understand	VERB
ejpam-3338	25	24	exactly	exactly	ADV
ejpam-3338	25	25	in	in	ADP
ejpam-3338	25	26	the	the	DET
ejpam-3338	25	27	same	same	ADJ
ejpam-3338	25	28	way	way	NOUN
ejpam-3338	25	29	as	as	ADP
ejpam-3338	25	30	those	those	PRON
ejpam-3338	25	31	in	in	ADP
ejpam-3338	25	32	the	the	DET
ejpam-3338	25	33	conventional	conventional	ADJ
ejpam-3338	25	34	calculus	calculus	NOUN
ejpam-3338	25	35	.	.	PUNCT
ejpam-3338	26	1	for	for	ADP
ejpam-3338	26	2	instance	instance	NOUN
ejpam-3338	26	3	,	,	PUNCT
ejpam-3338	26	4	newtons	newtons	PROPN
ejpam-3338	26	5	1st	1st	PROPN
ejpam-3338	26	6	law	law	NOUN
ejpam-3338	26	7	of	of	ADP
ejpam-3338	26	8	motion	motion	NOUN
ejpam-3338	26	9	viz	viz	PROPN
ejpam-3338	26	10	.	.	PUNCT
ejpam-3338	27	1	every	every	DET
ejpam-3338	27	2	object	object	NOUN
ejpam-3338	27	3	(	(	PUNCT
ejpam-3338	27	4	a	a	DET
ejpam-3338	27	5	point	point	NOUN
ejpam-3338	27	6	mass	mass	NOUN
ejpam-3338	27	7	,	,	PUNCT
ejpam-3338	27	8	say	say	VERB
ejpam-3338	27	9	)	)	PUNCT
ejpam-3338	27	10	either	either	CCONJ
ejpam-3338	27	11	remains	remain	VERB
ejpam-3338	27	12	at	at	ADP
ejpam-3338	27	13	rest	rest	NOUN
ejpam-3338	27	14	eternally	eternally	ADV
ejpam-3338	27	15	or	or	CCONJ
ejpam-3338	27	16	continues	continue	VERB
ejpam-3338	27	17	to	to	PART
ejpam-3338	27	18	move	move	VERB
ejpam-3338	27	19	at	at	ADP
ejpam-3338	27	20	a	a	DET
ejpam-3338	27	21	constant	constant	ADJ
ejpam-3338	27	22	velocity	velocity	NOUN
ejpam-3338	27	23	eternally	eternally	ADV
ejpam-3338	27	24	,	,	PUNCT
ejpam-3338	27	25	unless	unless	SCONJ
ejpam-3338	27	26	acted	act	VERB
ejpam-3338	27	27	upon	upon	SCONJ
ejpam-3338	27	28	by	by	ADP
ejpam-3338	27	29	an	an	DET
ejpam-3338	27	30	external	external	ADJ
ejpam-3338	27	31	impressed	impressed	ADJ
ejpam-3338	27	32	force	force	NOUN
ejpam-3338	27	33	.	.	PUNCT
ejpam-3338	28	1	is	be	AUX
ejpam-3338	28	2	understood	understand	VERB
ejpam-3338	28	3	without	without	ADP
ejpam-3338	28	4	any	any	DET
ejpam-3338	28	5	ambiguity	ambiguity	NOUN
ejpam-3338	28	6	.	.	PUNCT
ejpam-3338	29	1	in	in	ADP
ejpam-3338	29	2	our	our	PRON
ejpam-3338	29	3	physical	physical	ADJ
ejpam-3338	29	4	environment	environment	NOUN
ejpam-3338	29	5	,	,	PUNCT
ejpam-3338	29	6	it	it	PRON
ejpam-3338	29	7	is	be	AUX
ejpam-3338	29	8	not	not	PART
ejpam-3338	29	9	possible	possible	ADJ
ejpam-3338	29	10	to	to	PART
ejpam-3338	29	11	have	have	VERB
ejpam-3338	29	12	external	external	ADJ
ejpam-3338	29	13	impressed	impressed	ADJ
ejpam-3338	29	14	force	force	NOUN
ejpam-3338	29	15	(	(	PUNCT
ejpam-3338	29	16	from	from	ADP
ejpam-3338	29	17	any	any	PRON
ejpam-3338	29	18	of	of	ADP
ejpam-3338	29	19	the	the	DET
ejpam-3338	29	20	infinity	infinity	NOUN
ejpam-3338	29	21	of	of	ADP
ejpam-3338	29	22	possible	possible	ADJ
ejpam-3338	29	23	directions	direction	NOUN
ejpam-3338	29	24	)	)	PUNCT
ejpam-3338	29	25	to	to	PART
ejpam-3338	29	26	have	have	VERB
ejpam-3338	29	27	exact	exact	ADJ
ejpam-3338	29	28	zero	zero	NUM
ejpam-3338	29	29	value	value	NOUN
ejpam-3338	29	30	,	,	PUNCT
ejpam-3338	29	31	we	we	PRON
ejpam-3338	29	32	can	can	AUX
ejpam-3338	29	33	easily	easily	ADV
ejpam-3338	29	34	imagine	imagine	VERB
ejpam-3338	29	35	(	(	PUNCT
ejpam-3338	29	36	the	the	DET
ejpam-3338	29	37	exact	exact	ADJ
ejpam-3338	29	38	zero	zero	NUM
ejpam-3338	29	39	value	value	NOUN
ejpam-3338	29	40	)	)	PUNCT
ejpam-3338	29	41	though	though	ADV
ejpam-3338	29	42	.	.	PUNCT
ejpam-3338	30	1	there	there	PRON
ejpam-3338	30	2	could	could	AUX
ejpam-3338	30	3	be	be	AUX
ejpam-3338	30	4	,	,	PUNCT
ejpam-3338	30	5	for	for	ADP
ejpam-3338	30	6	example	example	NOUN
ejpam-3338	30	7	,	,	PUNCT
ejpam-3338	30	8	air	air	NOUN
ejpam-3338	30	9	resistance	resistance	NOUN
ejpam-3338	30	10	against	against	ADP
ejpam-3338	30	11	the	the	DET
ejpam-3338	30	12	direction	direction	NOUN
ejpam-3338	30	13	of	of	ADP
ejpam-3338	30	14	movement	movement	NOUN
ejpam-3338	30	15	of	of	ADP
ejpam-3338	30	16	the	the	DET
ejpam-3338	30	17	object	object	NOUN
ejpam-3338	30	18	or	or	CCONJ
ejpam-3338	30	19	air	air	NOUN
ejpam-3338	30	20	assistance	assistance	NOUN
ejpam-3338	30	21	/	/	SYM
ejpam-3338	30	22	flow	flow	NOUN
ejpam-3338	30	23	in	in	ADP
ejpam-3338	30	24	the	the	DET
ejpam-3338	30	25	direction	direction	NOUN
ejpam-3338	30	26	of	of	ADP
ejpam-3338	30	27	the	the	DET
ejpam-3338	30	28	movement	movement	NOUN
ejpam-3338	30	29	of	of	ADP
ejpam-3338	30	30	the	the	DET
ejpam-3338	30	31	object	object	NOUN
ejpam-3338	30	32	as	as	ADP
ejpam-3338	30	33	an	an	DET
ejpam-3338	30	34	external	external	ADJ
ejpam-3338	30	35	impressed	impressed	ADJ
ejpam-3338	30	36	force	force	NOUN
ejpam-3338	30	37	over	over	ADP
ejpam-3338	30	38	a	a	DET
ejpam-3338	30	39	finite	finite	NOUN
ejpam-3338	30	40	(	(	PUNCT
ejpam-3338	30	41	not	not	PART
ejpam-3338	30	42	infinite	infinite	ADJ
ejpam-3338	30	43	)	)	PUNCT
ejpam-3338	30	44	period	period	NOUN
ejpam-3338	30	45	of	of	ADP
ejpam-3338	30	46	time	time	NOUN
ejpam-3338	30	47	since	since	SCONJ
ejpam-3338	30	48	we	we	PRON
ejpam-3338	30	49	have	have	AUX
ejpam-3338	30	50	not	not	PART
ejpam-3338	30	51	been	be	AUX
ejpam-3338	30	52	able	able	ADJ
ejpam-3338	30	53	to	to	PART
ejpam-3338	30	54	create	create	VERB
ejpam-3338	30	55	exact	exact	ADJ
ejpam-3338	30	56	vacuum	vacuum	NOUN
ejpam-3338	30	57	in	in	ADP
ejpam-3338	30	58	our	our	PRON
ejpam-3338	30	59	environment	environment	NOUN
ejpam-3338	30	60	nor	nor	CCONJ
ejpam-3338	30	61	possibly	possibly	ADV
ejpam-3338	30	62	does	do	AUX
ejpam-3338	30	63	it	it	PRON
ejpam-3338	30	64	exist	exist	VERB
ejpam-3338	30	65	in	in	ADP
ejpam-3338	30	66	the	the	DET
ejpam-3338	30	67	universe	universe	NOUN
ejpam-3338	30	68	.	.	PUNCT
ejpam-3338	31	1	or	or	CCONJ
ejpam-3338	31	2	/	/	SYM
ejpam-3338	31	3	and	and	CCONJ
ejpam-3338	31	4	there	there	PRON
ejpam-3338	31	5	could	could	AUX
ejpam-3338	31	6	be	be	AUX
ejpam-3338	31	7	any	any	DET
ejpam-3338	31	8	other	other	ADJ
ejpam-3338	31	9	friction	friction	NOUN
ejpam-3338	31	10	(	(	PUNCT
ejpam-3338	31	11	external	external	ADJ
ejpam-3338	31	12	impressed	impressed	ADJ
ejpam-3338	31	13	)	)	PUNCT
ejpam-3338	31	14	force	force	NOUN
ejpam-3338	31	15	such	such	ADJ
ejpam-3338	31	16	as	as	ADP
ejpam-3338	31	17	the	the	DET
ejpam-3338	31	18	one	one	NOUN
ejpam-3338	31	19	created	create	VERB
ejpam-3338	31	20	by	by	ADP
ejpam-3338	31	21	the	the	DET
ejpam-3338	31	22	surface	surface	NOUN
ejpam-3338	31	23	on	on	ADP
ejpam-3338	31	24	/	/	SYM
ejpam-3338	31	25	through	through	ADP
ejpam-3338	31	26	which	which	PRON
ejpam-3338	31	27	the	the	DET
ejpam-3338	31	28	object	object	NOUN
ejpam-3338	31	29	is	be	AUX
ejpam-3338	31	30	moving	move	VERB
ejpam-3338	31	31	.	.	PUNCT
ejpam-3338	32	1	consequently	consequently	ADV
ejpam-3338	32	2	the	the	DET
ejpam-3338	32	3	moving	move	VERB
ejpam-3338	32	4	object	object	NOUN
ejpam-3338	32	5	can	can	AUX
ejpam-3338	32	6	not	not	PART
ejpam-3338	32	7	move	move	VERB
ejpam-3338	32	8	eternally	eternally	ADV
ejpam-3338	32	9	.	.	PUNCT
ejpam-3338	33	1	it	it	PRON
ejpam-3338	33	2	eventually	eventually	ADV
ejpam-3338	33	3	comes	come	VERB
ejpam-3338	33	4	to	to	ADP
ejpam-3338	33	5	a	a	DET
ejpam-3338	33	6	halt	halt	NOUN
ejpam-3338	33	7	based	base	VERB
ejpam-3338	33	8	on	on	ADP
ejpam-3338	33	9	the	the	DET
ejpam-3338	33	10	strength	strength	NOUN
ejpam-3338	33	11	of	of	ADP
ejpam-3338	33	12	the	the	DET
ejpam-3338	33	13	friction	friction	NOUN
ejpam-3338	33	14	forces	force	NOUN
ejpam-3338	33	15	.	.	PUNCT
ejpam-3338	34	1	if	if	SCONJ
ejpam-3338	34	2	the	the	DET
ejpam-3338	34	3	object	object	NOUN
ejpam-3338	34	4	is	be	AUX
ejpam-3338	34	5	stationary	stationary	ADJ
ejpam-3338	34	6	/	/	SYM
ejpam-3338	34	7	static	static	NOUN
ejpam-3338	34	8	,	,	PUNCT
ejpam-3338	34	9	then	then	ADV
ejpam-3338	34	10	,	,	PUNCT
ejpam-3338	34	11	however	however	ADV
ejpam-3338	34	12	,	,	PUNCT
ejpam-3338	34	13	such	such	DET
ejpam-3338	34	14	a	a	DET
ejpam-3338	34	15	friction	friction	NOUN
ejpam-3338	34	16	has	have	VERB
ejpam-3338	34	17	no	no	DET
ejpam-3338	34	18	effect	effect	NOUN
ejpam-3338	34	19	on	on	ADP
ejpam-3338	34	20	the	the	DET
ejpam-3338	34	21	object	object	NOUN
ejpam-3338	34	22	or	or	CCONJ
ejpam-3338	34	23	,	,	PUNCT
ejpam-3338	34	24	equivalently	equivalently	ADV
ejpam-3338	34	25	,	,	PUNCT
ejpam-3338	34	26	a	a	DET
ejpam-3338	34	27	friction	friction	NOUN
ejpam-3338	34	28	simply	simply	ADV
ejpam-3338	34	29	does	do	AUX
ejpam-3338	34	30	not	not	PART
ejpam-3338	34	31	exist	exist	VERB
ejpam-3338	34	32	.	.	PUNCT
ejpam-3338	35	1	mathematicians	mathematician	NOUN
ejpam-3338	35	2	may	may	AUX
ejpam-3338	35	3	consider	consider	VERB
ejpam-3338	35	4	the	the	DET
ejpam-3338	35	5	foregoing	forego	VERB
ejpam-3338	35	6	real	real	ADJ
ejpam-3338	35	7	-	-	PUNCT
ejpam-3338	35	8	world	world	NOUN
ejpam-3338	35	9	situation	situation	NOUN
ejpam-3338	35	10	as	as	ADP
ejpam-3338	35	11	an	an	DET
ejpam-3338	35	12	ideal	ideal	ADJ
ejpam-3338	35	13	example	example	NOUN
ejpam-3338	35	14	of	of	ADP
ejpam-3338	35	15	introducing	introduce	VERB
ejpam-3338	35	16	non	non	ADJ
ejpam-3338	35	17	-	-	ADJ
ejpam-3338	35	18	integer	integer	ADJ
ejpam-3338	35	19	(	(	PUNCT
ejpam-3338	35	20	fractional	fractional	ADJ
ejpam-3338	35	21	)	)	PUNCT
ejpam-3338	35	22	order	order	NOUN
ejpam-3338	35	23	calculus	calculus	NOUN
ejpam-3338	35	24	that	that	PRON
ejpam-3338	35	25	necessarily	necessarily	ADV
ejpam-3338	35	26	brings	bring	VERB
ejpam-3338	35	27	(	(	PUNCT
ejpam-3338	35	28	corresponds	correspond	NOUN
ejpam-3338	35	29	to	to	ADP
ejpam-3338	35	30	)	)	PUNCT
ejpam-3338	35	31	one	one	NUM
ejpam-3338	35	32	or	or	CCONJ
ejpam-3338	35	33	more	more	ADJ
ejpam-3338	35	34	friction	friction	NOUN
ejpam-3338	35	35	forces	force	NOUN
ejpam-3338	35	36	and	and	CCONJ
ejpam-3338	35	37	explains	explain	VERB
ejpam-3338	35	38	rather	rather	ADV
ejpam-3338	35	39	more	more	ADV
ejpam-3338	35	40	conveniently	conveniently	ADV
ejpam-3338	35	41	the	the	DET
ejpam-3338	35	42	real	real	ADJ
ejpam-3338	35	43	-	-	PUNCT
ejpam-3338	35	44	world	world	NOUN
ejpam-3338	35	45	situation	situation	NOUN
ejpam-3338	35	46	for	for	ADP
ejpam-3338	35	47	the	the	DET
ejpam-3338	35	48	object	object	NOUN
ejpam-3338	35	49	in	in	ADP
ejpam-3338	35	50	motion	motion	NOUN
ejpam-3338	35	51	.	.	PUNCT
ejpam-3338	36	1	the	the	DET
ejpam-3338	36	2	question	question	NOUN
ejpam-3338	36	3	is	be	AUX
ejpam-3338	36	4	:	:	PUNCT
ejpam-3338	36	5	can	can	AUX
ejpam-3338	36	6	we	we	PRON
ejpam-3338	36	7	readily	readily	ADV
ejpam-3338	36	8	know	know	VERB
ejpam-3338	36	9	/	/	SYM
ejpam-3338	36	10	find	find	VERB
ejpam-3338	36	11	out	out	ADP
ejpam-3338	36	12	the	the	DET
ejpam-3338	36	13	value	value	NOUN
ejpam-3338	36	14	of	of	ADP
ejpam-3338	36	15	the	the	DET
ejpam-3338	36	16	fraction	fraction	NOUN
ejpam-3338	36	17	that	that	PRON
ejpam-3338	36	18	corresponds	correspond	VERB
ejpam-3338	36	19	precisely	precisely	ADV
ejpam-3338	36	20	to	to	ADP
ejpam-3338	36	21	the	the	DET
ejpam-3338	36	22	friction	friction	NOUN
ejpam-3338	36	23	forces	force	NOUN
ejpam-3338	36	24	in	in	ADP
ejpam-3338	36	25	the	the	DET
ejpam-3338	36	26	same	same	ADJ
ejpam-3338	36	27	way	way	NOUN
ejpam-3338	36	28	as	as	SCONJ
ejpam-3338	36	29	we	we	PRON
ejpam-3338	36	30	do	do	VERB
ejpam-3338	36	31	in	in	ADP
ejpam-3338	36	32	the	the	DET
ejpam-3338	36	33	classical	classical	ADJ
ejpam-3338	36	34	calculus	calculus	NOUN
ejpam-3338	36	35	/	/	SYM
ejpam-3338	36	36	models	model	NOUN
ejpam-3338	36	37	?	?	PUNCT
ejpam-3338	37	1	an	an	DET
ejpam-3338	37	2	ansatz	ansatz	ADJ
ejpam-3338	37	3	(	(	PUNCT
ejpam-3338	37	4	an	an	DET
ejpam-3338	37	5	ansatz	ansatz	NOUN
ejpam-3338	37	6	is	be	AUX
ejpam-3338	37	7	the	the	DET
ejpam-3338	37	8	establishment	establishment	NOUN
ejpam-3338	37	9	of	of	ADP
ejpam-3338	37	10	the	the	DET
ejpam-3338	37	11	starting	start	VERB
ejpam-3338	37	12	equation(s	equation(s	PROPN
ejpam-3338	37	13	)	)	PUNCT
ejpam-3338	37	14	,	,	PUNCT
ejpam-3338	37	15	the	the	DET
ejpam-3338	37	16	theorem(s)/the	theorem(s)/the	PRON
ejpam-3338	37	17	value(s	value(s	NOUN
ejpam-3338	37	18	)	)	PUNCT
ejpam-3338	37	19	describing	describe	VERB
ejpam-3338	37	20	a	a	DET
ejpam-3338	37	21	physical	physical	ADJ
ejpam-3338	37	22	problem	problem	NOUN
ejpam-3338	37	23	or	or	CCONJ
ejpam-3338	37	24	mathematical	mathematical	ADJ
ejpam-3338	37	25	model	model	NOUN
ejpam-3338	37	26	or	or	CCONJ
ejpam-3338	37	27	solution	solution	NOUN
ejpam-3338	37	28	.	.	PUNCT
ejpam-3338	38	1	s.	s.	PROPN
ejpam-3338	38	2	k.sen	k.sen	PROPN
ejpam-3338	38	3	,	,	PUNCT
ejpam-3338	38	4	j.	j.	PROPN
ejpam-3338	38	5	v.	v.	PROPN
ejpam-3338	38	6	devi	devi	PROPN
ejpam-3338	38	7	,	,	PUNCT
ejpam-3338	38	8	r.v.g	r.v.g	NOUN
ejpam-3338	38	9	.	.	PUNCT
ejpam-3338	39	1	r.	r.	PROPN
ejpam-3338	39	2	kumar	kumar	PROPN
ejpam-3338	39	3	/	/	SYM
ejpam-3338	39	4	eur	eur	PROPN
ejpam-3338	39	5	.	.	PUNCT
ejpam-3338	40	1	j.	j.	PROPN
ejpam-3338	40	2	pure	pure	PROPN
ejpam-3338	40	3	appl	appl	PROPN
ejpam-3338	40	4	.	.	PROPN
ejpam-3338	40	5	math	math	PROPN
ejpam-3338	40	6	,	,	PUNCT
ejpam-3338	40	7	11	11	NUM
ejpam-3338	40	8	(	(	PUNCT
ejpam-3338	40	9	3	3	NUM
ejpam-3338	40	10	)	)	PUNCT
ejpam-3338	40	11	(	(	PUNCT
ejpam-3338	40	12	2018	2018	NUM
ejpam-3338	40	13	)	)	PUNCT
ejpam-3338	40	14	,	,	PUNCT
ejpam-3338	40	15	1058	1058	NUM
ejpam-3338	40	16	-	-	SYM
ejpam-3338	40	17	1099	1099	NUM
ejpam-3338	40	18	1060	1060	NUM
ejpam-3338	40	19	it	it	PRON
ejpam-3338	40	20	can	can	AUX
ejpam-3338	40	21	take	take	VERB
ejpam-3338	40	22	into	into	ADP
ejpam-3338	40	23	consideration	consideration	NOUN
ejpam-3338	40	24	boundary	boundary	ADJ
ejpam-3338	40	25	conditions	condition	NOUN
ejpam-3338	40	26	.	.	PUNCT
ejpam-3338	41	1	having	having	AUX
ejpam-3338	41	2	established	establish	VERB
ejpam-3338	41	3	an	an	DET
ejpam-3338	41	4	ansatz	ansatz	ADJ
ejpam-3338	41	5	constituting	constitute	VERB
ejpam-3338	41	6	essentially	essentially	ADV
ejpam-3338	41	7	an	an	DET
ejpam-3338	41	8	assumption	assumption	NOUN
ejpam-3338	41	9	,	,	PUNCT
ejpam-3338	41	10	the	the	DET
ejpam-3338	41	11	equations	equation	NOUN
ejpam-3338	41	12	are	be	AUX
ejpam-3338	41	13	solved	solve	VERB
ejpam-3338	41	14	for	for	ADP
ejpam-3338	41	15	the	the	DET
ejpam-3338	41	16	general	general	ADJ
ejpam-3338	41	17	function	function	NOUN
ejpam-3338	41	18	of	of	ADP
ejpam-3338	41	19	interest	interest	NOUN
ejpam-3338	41	20	constituting	constitute	VERB
ejpam-3338	41	21	a	a	DET
ejpam-3338	41	22	confirmation	confirmation	NOUN
ejpam-3338	41	23	of	of	ADP
ejpam-3338	41	24	the	the	DET
ejpam-3338	41	25	assumption	assumption	NOUN
ejpam-3338	41	26	.	.	PUNCT
ejpam-3338	41	27	)	)	PUNCT
ejpam-3338	42	1	for	for	ADP
ejpam-3338	42	2	friction	friction	NOUN
ejpam-3338	42	3	forces	force	NOUN
ejpam-3338	42	4	fr	fr	NOUN
ejpam-3338	42	5	is	be	AUX
ejpam-3338	42	6	a	a	DET
ejpam-3338	42	7	usually	usually	ADV
ejpam-3338	42	8	followed	follow	VERB
ejpam-3338	42	9	power	power	NOUN
ejpam-3338	42	10	law	law	NOUN
ejpam-3338	43	1	fr	fr	NOUN
ejpam-3338	44	1	=	=	PUNCT
ejpam-3338	45	1	−µ	−µ	ADV
ejpam-3338	45	2	sign(v)|v|α	sign(v)|v|α	NOUN
ejpam-3338	45	3	,	,	PUNCT
ejpam-3338	45	4	(	(	PUNCT
ejpam-3338	45	5	1	1	X
ejpam-3338	45	6	)	)	PUNCT
ejpam-3338	45	7	where	where	SCONJ
ejpam-3338	45	8	µ	µ	NOUN
ejpam-3338	45	9	is	be	AUX
ejpam-3338	45	10	the	the	DET
ejpam-3338	45	11	friction	friction	NOUN
ejpam-3338	45	12	coefficient	coefficient	NOUN
ejpam-3338	45	13	measured	measure	VERB
ejpam-3338	45	14	in	in	ADP
ejpam-3338	45	15	[	[	X
ejpam-3338	45	16	kg	kg	X
ejpam-3338	45	17	/	/	SYM
ejpam-3338	45	18	s(2−α	s(2−α	NOUN
ejpam-3338	45	19	)	)	PUNCT
ejpam-3338	45	20	]	]	PUNCT
ejpam-3338	45	21	in	in	ADP
ejpam-3338	45	22	mks	mks	PROPN
ejpam-3338	45	23	unit	unit	NOUN
ejpam-3338	45	24	system	system	NOUN
ejpam-3338	45	25	,	,	PUNCT
ejpam-3338	45	26	the	the	DET
ejpam-3338	45	27	value	value	NOUN
ejpam-3338	45	28	α	α	NOUN
ejpam-3338	45	29	is	be	AUX
ejpam-3338	45	30	an	an	DET
ejpam-3338	45	31	arbitrarily	arbitrarily	ADV
ejpam-3338	45	32	chosen	choose	VERB
ejpam-3338	45	33	real	real	ADJ
ejpam-3338	45	34	exponent	exponent	NOUN
ejpam-3338	45	35	.	.	PUNCT
ejpam-3338	46	1	in	in	ADP
ejpam-3338	46	2	special	special	ADJ
ejpam-3338	46	3	cases	case	NOUN
ejpam-3338	46	4	,	,	PUNCT
ejpam-3338	46	5	α	α	PROPN
ejpam-3338	46	6	≈	≈	PROPN
ejpam-3338	46	7	0	0	NUM
ejpam-3338	46	8	found	find	VERB
ejpam-3338	46	9	for	for	ADP
ejpam-3338	46	10	static	static	ADJ
ejpam-3338	46	11	and	and	CCONJ
ejpam-3338	46	12	kinetic	kinetic	ADJ
ejpam-3338	46	13	friction	friction	NOUN
ejpam-3338	46	14	for	for	ADP
ejpam-3338	46	15	solids	solid	NOUN
ejpam-3338	46	16	,	,	PUNCT
ejpam-3338	46	17	α=1	α=1	PRON
ejpam-3338	46	18	observed	observe	VERB
ejpam-3338	46	19	for	for	ADP
ejpam-3338	46	20	stokes	stoke	NOUN
ejpam-3338	46	21	friction	friction	NOUN
ejpam-3338	46	22	in	in	ADP
ejpam-3338	46	23	liquids	liquid	NOUN
ejpam-3338	46	24	with	with	ADP
ejpam-3338	46	25	high	high	ADJ
ejpam-3338	46	26	velocity	velocity	NOUN
ejpam-3338	46	27	,	,	PUNCT
ejpam-3338	47	1	α	α	PROPN
ejpam-3338	47	2	≈	≈	PROPN
ejpam-3338	47	3	2	2	NUM
ejpam-3338	47	4	used	use	VERB
ejpam-3338	47	5	as	as	ADP
ejpam-3338	47	6	a	a	DET
ejpam-3338	47	7	general	general	ADJ
ejpam-3338	47	8	trend	trend	NOUN
ejpam-3338	47	9	for	for	ADP
ejpam-3338	47	10	high	high	ADJ
ejpam-3338	47	11	velocity	velocity	NOUN
ejpam-3338	47	12	.	.	PUNCT
ejpam-3338	48	1	the	the	DET
ejpam-3338	48	2	nonlinear	nonlinear	ADJ
ejpam-3338	48	3	ordinary	ordinary	ADJ
ejpam-3338	48	4	differential	differential	ADJ
ejpam-3338	48	5	equation	equation	NOUN
ejpam-3338	48	6	using	use	VERB
ejpam-3338	48	7	newtons	newton	NOUN
ejpam-3338	48	8	2nd	2nd	PROPN
ejpam-3338	48	9	law	law	NOUN
ejpam-3338	48	10	of	of	ADP
ejpam-3338	48	11	motion	motion	NOUN
ejpam-3338	48	12	with	with	ADP
ejpam-3338	48	13	friction	friction	NOUN
ejpam-3338	48	14	forces	force	NOUN
ejpam-3338	48	15	is	be	AUX
ejpam-3338	48	16	m(ẍ	m(ẍ	ADJ
ejpam-3338	48	17	)	)	PUNCT
ejpam-3338	49	1	=	=	SYM
ejpam-3338	50	1	fr	fr	NOUN
ejpam-3338	50	2	=	=	PUNCT
ejpam-3338	50	3	−µ	−µ	ADJ
ejpam-3338	50	4	sign(v)|ẋ|α	sign(v)|ẋ|α	NOUN
ejpam-3338	50	5	,	,	PUNCT
ejpam-3338	50	6	(	(	PUNCT
ejpam-3338	50	7	2	2	X
ejpam-3338	50	8	)	)	PUNCT
ejpam-3338	50	9	where	where	SCONJ
ejpam-3338	50	10	the	the	DET
ejpam-3338	50	11	initial	initial	ADJ
ejpam-3338	50	12	conditions	condition	NOUN
ejpam-3338	50	13	are	be	AUX
ejpam-3338	50	14	x(t	x(t	PROPN
ejpam-3338	50	15	=	=	PUNCT
ejpam-3338	50	16	0	0	NUM
ejpam-3338	50	17	)	)	PUNCT
ejpam-3338	50	18	=	=	SYM
ejpam-3338	51	1	x0	x0	PROPN
ejpam-3338	51	2	(	(	PUNCT
ejpam-3338	51	3	3	3	X
ejpam-3338	51	4	)	)	PUNCT
ejpam-3338	51	5	v(t	v(t	NOUN
ejpam-3338	51	6	=	=	SYM
ejpam-3338	51	7	0	0	NUM
ejpam-3338	51	8	)	)	PUNCT
ejpam-3338	51	9	=	=	SYM
ejpam-3338	52	1	ẋ(t	ẋ(t	NOUN
ejpam-3338	52	2	=	=	SYM
ejpam-3338	52	3	0	0	NUM
ejpam-3338	52	4	)	)	PUNCT
ejpam-3338	52	5	=	=	SYM
ejpam-3338	52	6	v0	v0	NOUN
ejpam-3338	52	7	(	(	PUNCT
ejpam-3338	52	8	4	4	NUM
ejpam-3338	52	9	)	)	PUNCT
ejpam-3338	52	10	the	the	DET
ejpam-3338	52	11	point	point	NOUN
ejpam-3338	52	12	mass	mass	NOUN
ejpam-3338	52	13	m	m	VERB
ejpam-3338	52	14	is	be	AUX
ejpam-3338	52	15	measured	measure	VERB
ejpam-3338	52	16	in	in	ADP
ejpam-3338	52	17	[	[	X
ejpam-3338	52	18	kg	kg	X
ejpam-3338	52	19	]	]	X
ejpam-3338	52	20	.	.	PUNCT
ejpam-3338	53	1	if	if	SCONJ
ejpam-3338	53	2	ẋ	ẋ	PROPN
ejpam-3338	53	3	=	=	SYM
ejpam-3338	53	4	v(t	v(t	NUM
ejpam-3338	53	5	)	)	PUNCT
ejpam-3338	53	6	is	be	AUX
ejpam-3338	53	7	positive	positive	ADJ
ejpam-3338	53	8	,	,	PUNCT
ejpam-3338	53	9	the	the	DET
ejpam-3338	53	10	foregoing	forego	VERB
ejpam-3338	53	11	ordinary	ordinary	ADJ
ejpam-3338	53	12	differential	differential	ADJ
ejpam-3338	53	13	equation	equation	NOUN
ejpam-3338	53	14	(	(	PUNCT
ejpam-3338	53	15	2	2	X
ejpam-3338	53	16	)	)	PUNCT
ejpam-3338	53	17	reduces	reduce	VERB
ejpam-3338	53	18	to	to	ADP
ejpam-3338	53	19	m(ẍ	m(ẍ	PROPN
ejpam-3338	53	20	)	)	PUNCT
ejpam-3338	53	21	=	=	PUNCT
ejpam-3338	54	1	−µ	−µ	ADJ
ejpam-3338	54	2	ẋα	ẋα	PROPN
ejpam-3338	54	3	(	(	PUNCT
ejpam-3338	54	4	5	5	NUM
ejpam-3338	54	5	)	)	PUNCT
ejpam-3338	54	6	when	when	SCONJ
ejpam-3338	54	7	α	α	NOUN
ejpam-3338	54	8	=	=	SYM
ejpam-3338	54	9	1	1	NUM
ejpam-3338	54	10	,	,	PUNCT
ejpam-3338	54	11	the	the	DET
ejpam-3338	54	12	classical	classical	ADJ
ejpam-3338	54	13	force	force	NOUN
ejpam-3338	54	14	and	and	CCONJ
ejpam-3338	54	15	the	the	DET
ejpam-3338	54	16	fractional	fractional	ADJ
ejpam-3338	54	17	friction	friction	NOUN
ejpam-3338	54	18	force	force	NOUN
ejpam-3338	54	19	coincide	coincide	NOUN
ejpam-3338	54	20	.	.	PUNCT
ejpam-3338	55	1	but	but	CCONJ
ejpam-3338	55	2	for	for	ADP
ejpam-3338	55	3	α	α	PRON
ejpam-3338	55	4	6=	6=	ADP
ejpam-3338	55	5	1	1	NUM
ejpam-3338	55	6	i.e.	i.e.	X
ejpam-3338	55	7	for	for	ADP
ejpam-3338	55	8	all	all	DET
ejpam-3338	55	9	other	other	ADJ
ejpam-3338	55	10	real	real	ADJ
ejpam-3338	55	11	α	α	NOUN
ejpam-3338	55	12	except	except	SCONJ
ejpam-3338	55	13	1	1	NUM
ejpam-3338	55	14	,	,	PUNCT
ejpam-3338	55	15	ẋα	ẋα	PROPN
ejpam-3338	55	16	=	=	SYM
ejpam-3338	56	1	(	(	PUNCT
ejpam-3338	56	2	dx	dx	PROPN
ejpam-3338	56	3	dt	dt	X
ejpam-3338	56	4	)	)	PUNCT
ejpam-3338	57	1	α	α	PROPN
ejpam-3338	57	2	6=	6=	ADP
ejpam-3338	57	3	dαx	dαx	PROPN
ejpam-3338	57	4	dtα	dtα	NOUN
ejpam-3338	57	5	(	(	PUNCT
ejpam-3338	57	6	6	6	NUM
ejpam-3338	57	7	)	)	PUNCT
ejpam-3338	57	8	thus	thus	ADV
ejpam-3338	57	9	we	we	PRON
ejpam-3338	57	10	expect	expect	VERB
ejpam-3338	57	11	a	a	DET
ejpam-3338	57	12	dynamic	dynamic	ADJ
ejpam-3338	57	13	behaviour	behaviour	NOUN
ejpam-3338	57	14	different	different	ADJ
ejpam-3338	57	15	from	from	ADP
ejpam-3338	57	16	the	the	DET
ejpam-3338	57	17	classical	classical	ADJ
ejpam-3338	57	18	one	one	NOUN
ejpam-3338	57	19	.	.	PUNCT
ejpam-3338	58	1	the	the	DET
ejpam-3338	58	2	fractional	fractional	ADJ
ejpam-3338	58	3	differential	differential	ADJ
ejpam-3338	58	4	equation	equation	NOUN
ejpam-3338	58	5	m(ẍ	m(ẍ	PROPN
ejpam-3338	58	6	)	)	PUNCT
ejpam-3338	58	7	=	=	SYM
ejpam-3338	58	8	−µ	−µ	NOUN
ejpam-3338	58	9	dαx	dαx	PROPN
ejpam-3338	58	10	dtα	dtα	PROPN
ejpam-3338	58	11	ẋ(t	ẋ(t	PROPN
ejpam-3338	58	12	)	)	PUNCT
ejpam-3338	58	13	>	>	X
ejpam-3338	58	14	0	0	PUNCT
ejpam-3338	58	15	(	(	PUNCT
ejpam-3338	58	16	7	7	NUM
ejpam-3338	58	17	)	)	PUNCT
ejpam-3338	58	18	with	with	ADP
ejpam-3338	58	19	initial	initial	ADJ
ejpam-3338	58	20	conditions	condition	NOUN
ejpam-3338	58	21	(	(	PUNCT
ejpam-3338	58	22	3	3	NUM
ejpam-3338	58	23	)	)	PUNCT
ejpam-3338	58	24	and	and	CCONJ
ejpam-3338	58	25	(	(	PUNCT
ejpam-3338	58	26	4	4	X
ejpam-3338	58	27	)	)	PUNCT
ejpam-3338	58	28	determines	determine	VERB
ejpam-3338	58	29	the	the	DET
ejpam-3338	58	30	dynamical	dynamical	ADJ
ejpam-3338	58	31	behaviour	behaviour	NOUN
ejpam-3338	58	32	of	of	ADP
ejpam-3338	58	33	the	the	DET
ejpam-3338	58	34	classical	classical	ADJ
ejpam-3338	58	35	object	object	NOUN
ejpam-3338	58	36	(	(	PUNCT
ejpam-3338	58	37	point	point	NOUN
ejpam-3338	58	38	mass	mass	PROPN
ejpam-3338	58	39	m	m	PROPN
ejpam-3338	58	40	)	)	PUNCT
ejpam-3338	58	41	to	to	ADP
ejpam-3338	58	42	a	a	DET
ejpam-3338	58	43	fractional	fractional	ADJ
ejpam-3338	58	44	friction	friction	NOUN
ejpam-3338	58	45	force	force	NOUN
ejpam-3338	58	46	.	.	PUNCT
ejpam-3338	59	1	using	use	VERB
ejpam-3338	59	2	the	the	DET
ejpam-3338	59	3	liouvilles	liouville	NOUN
ejpam-3338	59	4	definition	definition	NOUN
ejpam-3338	59	5	of	of	ADP
ejpam-3338	59	6	the	the	DET
ejpam-3338	59	7	fractional	fractional	ADJ
ejpam-3338	59	8	derivative	derivative	NOUN
ejpam-3338	59	9	and	and	CCONJ
ejpam-3338	59	10	using	use	VERB
ejpam-3338	59	11	the	the	DET
ejpam-3338	59	12	ansatz	ansatz	ADJ
ejpam-3338	59	13	x(t	x(t	NOUN
ejpam-3338	59	14	)	)	PUNCT
ejpam-3338	60	1	=	=	SYM
ejpam-3338	60	2	eωt	eωt	NOUN
ejpam-3338	60	3	(	(	PUNCT
ejpam-3338	60	4	8)	8)	NUM
ejpam-3338	60	5	we	we	PRON
ejpam-3338	60	6	obtain	obtain	VERB
ejpam-3338	60	7	the	the	DET
ejpam-3338	60	8	general	general	ADJ
ejpam-3338	60	9	solution	solution	NOUN
ejpam-3338	60	10	consisting	consist	VERB
ejpam-3338	60	11	of	of	ADP
ejpam-3338	60	12	3	3	NUM
ejpam-3338	60	13	different	different	ADJ
ejpam-3338	60	14	constants	constant	NOUN
ejpam-3338	60	15	[	[	X
ejpam-3338	60	16	1	1	NUM
ejpam-3338	60	17	]	]	PUNCT
ejpam-3338	60	18	.	.	PUNCT
ejpam-3338	61	1	we	we	PRON
ejpam-3338	61	2	thus	thus	ADV
ejpam-3338	61	3	need	need	VERB
ejpam-3338	61	4	yet	yet	ADV
ejpam-3338	61	5	1	1	NUM
ejpam-3338	61	6	more	more	ADJ
ejpam-3338	61	7	condition	condition	NOUN
ejpam-3338	61	8	besides	besides	SCONJ
ejpam-3338	61	9	the	the	DET
ejpam-3338	61	10	foregoing	forego	VERB
ejpam-3338	61	11	2	2	NUM
ejpam-3338	61	12	initial	initial	ADJ
ejpam-3338	61	13	conditions	condition	NOUN
ejpam-3338	61	14	.	.	PUNCT
ejpam-3338	62	1	by	by	ADP
ejpam-3338	62	2	choosing	choose	VERB
ejpam-3338	62	3	this	this	DET
ejpam-3338	62	4	1	1	NUM
ejpam-3338	62	5	condition	condition	NOUN
ejpam-3338	62	6	a	a	DET
ejpam-3338	62	7	reasonable	reasonable	ADJ
ejpam-3338	62	8	numerical	numerical	ADJ
ejpam-3338	62	9	value	value	NOUN
ejpam-3338	62	10	,	,	PUNCT
ejpam-3338	62	11	we	we	PRON
ejpam-3338	62	12	get	get	VERB
ejpam-3338	62	13	a	a	DET
ejpam-3338	62	14	solution	solution	NOUN
ejpam-3338	62	15	.	.	PUNCT
ejpam-3338	63	1	since	since	SCONJ
ejpam-3338	63	2	we	we	PRON
ejpam-3338	63	3	can	can	AUX
ejpam-3338	63	4	have	have	VERB
ejpam-3338	63	5	many	many	ADJ
ejpam-3338	63	6	reasonable	reasonable	ADJ
ejpam-3338	63	7	choices	choice	NOUN
ejpam-3338	63	8	,	,	PUNCT
ejpam-3338	63	9	there	there	PRON
ejpam-3338	63	10	will	will	AUX
ejpam-3338	63	11	be	be	AUX
ejpam-3338	63	12	infinitely	infinitely	ADV
ejpam-3338	63	13	many	many	ADJ
ejpam-3338	63	14	(	(	PUNCT
ejpam-3338	63	15	but	but	CCONJ
ejpam-3338	63	16	a	a	DET
ejpam-3338	63	17	finite	finite	ADJ
ejpam-3338	63	18	number	number	NOUN
ejpam-3338	63	19	of	of	ADP
ejpam-3338	63	20	solutions	solution	NOUN
ejpam-3338	63	21	in	in	ADP
ejpam-3338	63	22	a	a	DET
ejpam-3338	63	23	digital	digital	ADJ
ejpam-3338	63	24	computer	computer	NOUN
ejpam-3338	63	25	since	since	SCONJ
ejpam-3338	63	26	it	it	PRON
ejpam-3338	63	27	is	be	AUX
ejpam-3338	63	28	a	a	DET
ejpam-3338	63	29	finite	finite	ADJ
ejpam-3338	63	30	precision	precision	NOUN
ejpam-3338	63	31	machine	machine	NOUN
ejpam-3338	63	32	)	)	PUNCT
ejpam-3338	63	33	numerical	numerical	ADJ
ejpam-3338	63	34	solutions	solution	NOUN
ejpam-3338	63	35	.	.	PUNCT
ejpam-3338	64	1	by	by	ADP
ejpam-3338	64	2	appropriate	appropriate	ADJ
ejpam-3338	64	3	choices	choice	NOUN
ejpam-3338	64	4	of	of	ADP
ejpam-3338	64	5	the	the	DET
ejpam-3338	64	6	condition	condition	NOUN
ejpam-3338	64	7	,	,	PUNCT
ejpam-3338	64	8	we	we	PRON
ejpam-3338	64	9	could	could	AUX
ejpam-3338	64	10	see	see	VERB
ejpam-3338	64	11	that	that	SCONJ
ejpam-3338	64	12	the	the	DET
ejpam-3338	64	13	solutions	solution	NOUN
ejpam-3338	64	14	of	of	ADP
ejpam-3338	64	15	the	the	DET
ejpam-3338	64	16	fractional	fractional	ADJ
ejpam-3338	64	17	differential	differential	NOUN
ejpam-3338	64	18	equation	equation	NOUN
ejpam-3338	64	19	match	match	VERB
ejpam-3338	64	20	up	up	ADP
ejpam-3338	64	21	to	to	ADP
ejpam-3338	64	22	the	the	DET
ejpam-3338	64	23	2nd	2nd	ADJ
ejpam-3338	64	24	order	order	NOUN
ejpam-3338	64	25	term	term	NOUN
ejpam-3338	64	26	in	in	ADP
ejpam-3338	64	27	t	t	PROPN
ejpam-3338	64	28	with	with	ADP
ejpam-3338	64	29	the	the	DET
ejpam-3338	64	30	solutions	solution	NOUN
ejpam-3338	64	31	computed	compute	VERB
ejpam-3338	64	32	for	for	ADP
ejpam-3338	64	33	s.	s.	PROPN
ejpam-3338	64	34	k.sen	k.sen	PROPN
ejpam-3338	64	35	,	,	PUNCT
ejpam-3338	64	36	j.	j.	PROPN
ejpam-3338	64	37	v.	v.	PROPN
ejpam-3338	64	38	devi	devi	PROPN
ejpam-3338	64	39	,	,	PUNCT
ejpam-3338	64	40	r.v.g	r.v.g	NOUN
ejpam-3338	64	41	.	.	PUNCT
ejpam-3338	65	1	r.	r.	PROPN
ejpam-3338	65	2	kumar	kumar	PROPN
ejpam-3338	65	3	/	/	SYM
ejpam-3338	65	4	eur	eur	PROPN
ejpam-3338	65	5	.	.	PUNCT
ejpam-3338	66	1	j.	j.	PROPN
ejpam-3338	66	2	pure	pure	PROPN
ejpam-3338	66	3	appl	appl	PROPN
ejpam-3338	66	4	.	.	PROPN
ejpam-3338	66	5	math	math	PROPN
ejpam-3338	66	6	,	,	PUNCT
ejpam-3338	66	7	11	11	NUM
ejpam-3338	66	8	(	(	PUNCT
ejpam-3338	66	9	3	3	NUM
ejpam-3338	66	10	)	)	PUNCT
ejpam-3338	66	11	(	(	PUNCT
ejpam-3338	66	12	2018	2018	NUM
ejpam-3338	66	13	)	)	PUNCT
ejpam-3338	66	14	,	,	PUNCT
ejpam-3338	66	15	1058	1058	NUM
ejpam-3338	66	16	-	-	SYM
ejpam-3338	66	17	1099	1099	NUM
ejpam-3338	66	18	1061	1061	NUM
ejpam-3338	66	19	the	the	DET
ejpam-3338	66	20	newtonian	newtonian	ADJ
ejpam-3338	66	21	equation	equation	NOUN
ejpam-3338	66	22	of	of	ADP
ejpam-3338	66	23	motion	motion	NOUN
ejpam-3338	66	24	with	with	ADP
ejpam-3338	66	25	the	the	DET
ejpam-3338	66	26	classical	classical	ADJ
ejpam-3338	66	27	friction	friction	NOUN
ejpam-3338	66	28	force	force	NOUN
ejpam-3338	66	29	term	term	NOUN
ejpam-3338	66	30	(	(	PUNCT
ejpam-3338	66	31	1	1	NUM
ejpam-3338	66	32	)	)	PUNCT
ejpam-3338	67	1	[	[	X
ejpam-3338	67	2	1	1	NUM
ejpam-3338	67	3	]	]	PUNCT
ejpam-3338	67	4	.	.	PUNCT
ejpam-3338	68	1	hence	hence	ADV
ejpam-3338	68	2	the	the	DET
ejpam-3338	68	3	difference	difference	NOUN
ejpam-3338	68	4	between	between	ADP
ejpam-3338	68	5	the	the	DET
ejpam-3338	68	6	fractional	fractional	ADJ
ejpam-3338	68	7	solutions	solution	NOUN
ejpam-3338	68	8	and	and	CCONJ
ejpam-3338	68	9	the	the	DET
ejpam-3338	68	10	classical	classical	ADJ
ejpam-3338	68	11	solutions	solution	NOUN
ejpam-3338	68	12	manifests	manifest	NOUN
ejpam-3338	68	13	both	both	CCONJ
ejpam-3338	68	14	numerically	numerically	ADV
ejpam-3338	68	15	and	and	CCONJ
ejpam-3338	68	16	graphically	graphically	ADV
ejpam-3338	68	17	when	when	SCONJ
ejpam-3338	68	18	t	t	PROPN
ejpam-3338	68	19	is	be	AUX
ejpam-3338	68	20	sufficiently	sufficiently	ADV
ejpam-3338	68	21	greater	great	ADJ
ejpam-3338	68	22	than	than	ADP
ejpam-3338	68	23	1[1	1[1	NOUN
ejpam-3338	68	24	]	]	PUNCT
ejpam-3338	68	25	.	.	PUNCT
ejpam-3338	69	1	it	it	PRON
ejpam-3338	69	2	can	can	AUX
ejpam-3338	69	3	be	be	AUX
ejpam-3338	69	4	seen	see	VERB
ejpam-3338	69	5	that	that	SCONJ
ejpam-3338	69	6	there	there	PRON
ejpam-3338	69	7	is	be	VERB
ejpam-3338	69	8	an	an	DET
ejpam-3338	69	9	alternative	alternative	ADJ
ejpam-3338	69	10	choice	choice	NOUN
ejpam-3338	69	11	for	for	ADP
ejpam-3338	69	12	3rd	3rd	ADJ
ejpam-3338	69	13	initial	initial	ADJ
ejpam-3338	69	14	condition	condition	NOUN
ejpam-3338	69	15	.	.	PUNCT
ejpam-3338	70	1	let	let	VERB
ejpam-3338	70	2	the	the	DET
ejpam-3338	70	3	initial	initial	ADJ
ejpam-3338	70	4	(	(	PUNCT
ejpam-3338	70	5	maximum	maximum	ADJ
ejpam-3338	70	6	)	)	PUNCT
ejpam-3338	70	7	velocity	velocity	NOUN
ejpam-3338	70	8	of	of	ADP
ejpam-3338	70	9	the	the	DET
ejpam-3338	70	10	object	object	NOUN
ejpam-3338	70	11	(	(	PUNCT
ejpam-3338	70	12	point	point	NOUN
ejpam-3338	70	13	mass	mass	NOUN
ejpam-3338	70	14	)	)	PUNCT
ejpam-3338	70	15	decrease	decrease	NOUN
ejpam-3338	70	16	through	through	ADP
ejpam-3338	70	17	all	all	DET
ejpam-3338	70	18	stages	stage	NOUN
ejpam-3338	70	19	of	of	ADP
ejpam-3338	70	20	motion	motion	NOUN
ejpam-3338	70	21	due	due	ADP
ejpam-3338	70	22	to	to	ADP
ejpam-3338	70	23	the	the	DET
ejpam-3338	70	24	fractional	fractional	ADJ
ejpam-3338	70	25	friction	friction	NOUN
ejpam-3338	70	26	force	force	NOUN
ejpam-3338	70	27	.	.	PUNCT
ejpam-3338	71	1	hence	hence	ADV
ejpam-3338	71	2	,	,	PUNCT
ejpam-3338	71	3	in	in	ADP
ejpam-3338	71	4	addition	addition	NOUN
ejpam-3338	71	5	to	to	ADP
ejpam-3338	71	6	the	the	DET
ejpam-3338	71	7	initial	initial	ADJ
ejpam-3338	71	8	conditions	condition	NOUN
ejpam-3338	71	9	(	(	PUNCT
ejpam-3338	71	10	3	3	NUM
ejpam-3338	71	11	)	)	PUNCT
ejpam-3338	71	12	and	and	CCONJ
ejpam-3338	71	13	(	(	PUNCT
ejpam-3338	71	14	4	4	NUM
ejpam-3338	71	15	)	)	PUNCT
ejpam-3338	71	16	,	,	PUNCT
ejpam-3338	71	17	we	we	PRON
ejpam-3338	71	18	introduce	introduce	VERB
ejpam-3338	71	19	the	the	DET
ejpam-3338	71	20	3rd	3rd	ADJ
ejpam-3338	71	21	initial	initial	ADJ
ejpam-3338	71	22	condition	condition	NOUN
ejpam-3338	72	1	[	[	X
ejpam-3338	72	2	1	1	NUM
ejpam-3338	72	3	]	]	PUNCT
ejpam-3338	72	4	.	.	PUNCT
ejpam-3338	73	1	v̇(t	v̇(t	ADJ
ejpam-3338	73	2	=	=	NOUN
ejpam-3338	73	3	0	0	NUM
ejpam-3338	73	4	)	)	PUNCT
ejpam-3338	73	5	=	=	SYM
ejpam-3338	73	6	ẍ(t	ẍ(t	PROPN
ejpam-3338	74	1	=	=	PUNCT
ejpam-3338	74	2	0	0	NUM
ejpam-3338	74	3	)	)	PUNCT
ejpam-3338	74	4	=	=	SYM
ejpam-3338	74	5	0	0	PUNCT
ejpam-3338	74	6	(	(	PUNCT
ejpam-3338	74	7	9	9	NUM
ejpam-3338	74	8	)	)	PUNCT
ejpam-3338	74	9	for	for	ADP
ejpam-3338	74	10	the	the	DET
ejpam-3338	74	11	general	general	ADJ
ejpam-3338	74	12	symbolic	symbolic	ADJ
ejpam-3338	74	13	(	(	PUNCT
ejpam-3338	74	14	mathematical	mathematical	ADJ
ejpam-3338	74	15	)	)	PUNCT
ejpam-3338	74	16	solution	solution	NOUN
ejpam-3338	74	17	of	of	ADP
ejpam-3338	74	18	the	the	DET
ejpam-3338	74	19	fde	fde	NOUN
ejpam-3338	74	20	(	(	PUNCT
ejpam-3338	74	21	including	include	VERB
ejpam-3338	74	22	a	a	DET
ejpam-3338	74	23	fractional	fractional	ADJ
ejpam-3338	74	24	friction	friction	NOUN
ejpam-3338	74	25	force	force	NOUN
ejpam-3338	74	26	)	)	PUNCT
ejpam-3338	74	27	valid	valid	ADJ
ejpam-3338	74	28	for	for	ADP
ejpam-3338	74	29	t=0	t=0	PROPN
ejpam-3338	74	30	up	up	ADP
ejpam-3338	74	31	to	to	ADP
ejpam-3338	74	32	t0	t0	NOUN
ejpam-3338	74	33	–	–	PUNCT
ejpam-3338	74	34	the	the	DET
ejpam-3338	74	35	final	final	ADJ
ejpam-3338	74	36	time	time	NOUN
ejpam-3338	74	37	when	when	SCONJ
ejpam-3338	74	38	the	the	DET
ejpam-3338	74	39	object	object	NOUN
ejpam-3338	74	40	halts	halt	VERB
ejpam-3338	74	41	permanently	permanently	ADV
ejpam-3338	74	42	,	,	PUNCT
ejpam-3338	74	43	see	see	VERB
ejpam-3338	74	44	[	[	X
ejpam-3338	74	45	1	1	NUM
ejpam-3338	74	46	,	,	PUNCT
ejpam-3338	74	47	page	page	NOUN
ejpam-3338	74	48	28	28	NUM
ejpam-3338	74	49	]	]	PUNCT
ejpam-3338	74	50	.	.	PUNCT
ejpam-3338	75	1	t0	t0	PROPN
ejpam-3338	75	2	is	be	AUX
ejpam-3338	75	3	obtained	obtain	VERB
ejpam-3338	75	4	as	as	ADP
ejpam-3338	75	5	t0	t0	X
ejpam-3338	75	6	=	=	PROPN
ejpam-3338	75	7	π	π	PROPN
ejpam-3338	75	8	(	(	PUNCT
ejpam-3338	75	9	ᾱ)ϕsin(πᾱ	ᾱ)ϕsin(πᾱ	PROPN
ejpam-3338	75	10	)	)	PUNCT
ejpam-3338	75	11	(	(	PUNCT
ejpam-3338	75	12	10	10	NUM
ejpam-3338	75	13	)	)	PUNCT
ejpam-3338	75	14	where	where	SCONJ
ejpam-3338	75	15	ϕ	ϕ	NOUN
ejpam-3338	75	16	=	=	PUNCT
ejpam-3338	75	17	|	|	ADV
ejpam-3338	75	18	µ	µ	NOUN
ejpam-3338	75	19	m	m	VERB
ejpam-3338	75	20	|	|	ADV
ejpam-3338	75	21	1	1	NUM
ejpam-3338	75	22	ᾱ	ᾱ	NOUN
ejpam-3338	75	23	,	,	PUNCT
ejpam-3338	75	24	ᾱ	ᾱ	NOUN
ejpam-3338	75	25	=	=	SYM
ejpam-3338	75	26	2−	2−	NUM
ejpam-3338	75	27	α	α	NOUN
ejpam-3338	75	28	(	(	PUNCT
ejpam-3338	75	29	11	11	NUM
ejpam-3338	75	30	)	)	PUNCT
ejpam-3338	75	31	the	the	DET
ejpam-3338	75	32	foregoing	forego	VERB
ejpam-3338	75	33	example	example	NOUN
ejpam-3338	75	34	of	of	ADP
ejpam-3338	75	35	an	an	DET
ejpam-3338	75	36	ever	ever	ADV
ejpam-3338	75	37	-	-	PUNCT
ejpam-3338	75	38	existing	exist	VERB
ejpam-3338	75	39	friction	friction	NOUN
ejpam-3338	75	40	force	force	NOUN
ejpam-3338	75	41	can	can	AUX
ejpam-3338	75	42	be	be	AUX
ejpam-3338	75	43	tackled	tackle	VERB
ejpam-3338	75	44	always	always	ADV
ejpam-3338	75	45	by	by	ADP
ejpam-3338	75	46	the	the	DET
ejpam-3338	75	47	integer	integer	NOUN
ejpam-3338	75	48	-	-	PUNCT
ejpam-3338	75	49	order	order	NOUN
ejpam-3338	75	50	(	(	PUNCT
ejpam-3338	75	51	i.e.	i.e.	X
ejpam-3338	75	52	classical	classical	ADJ
ejpam-3338	75	53	)	)	PUNCT
ejpam-3338	75	54	calculus	calculus	NOUN
ejpam-3338	75	55	without	without	ADP
ejpam-3338	75	56	any	any	DET
ejpam-3338	75	57	recourse	recourse	NOUN
ejpam-3338	75	58	to	to	ADP
ejpam-3338	75	59	fractional	fractional	ADJ
ejpam-3338	75	60	calculus	calculus	NOUN
ejpam-3338	75	61	,	,	PUNCT
ejpam-3338	75	62	provided	provided	AUX
ejpam-3338	75	63	we	we	PRON
ejpam-3338	75	64	know	know	VERB
ejpam-3338	75	65	/	/	SYM
ejpam-3338	75	66	determine	determine	VERB
ejpam-3338	75	67	the	the	DET
ejpam-3338	75	68	friction	friction	NOUN
ejpam-3338	75	69	force	force	NOUN
ejpam-3338	75	70	by	by	ADP
ejpam-3338	75	71	an	an	DET
ejpam-3338	75	72	experiment	experiment	NOUN
ejpam-3338	75	73	or	or	CCONJ
ejpam-3338	75	74	otherwise	otherwise	ADV
ejpam-3338	75	75	.	.	PUNCT
ejpam-3338	76	1	hence	hence	ADV
ejpam-3338	76	2	it	it	PRON
ejpam-3338	76	3	is	be	AUX
ejpam-3338	76	4	not	not	PART
ejpam-3338	76	5	absolutely	absolutely	ADV
ejpam-3338	76	6	necessary	necessary	ADJ
ejpam-3338	76	7	to	to	PART
ejpam-3338	76	8	bring	bring	VERB
ejpam-3338	76	9	fractional	fractional	ADJ
ejpam-3338	76	10	calculus	calculus	NOUN
ejpam-3338	76	11	into	into	ADP
ejpam-3338	76	12	picture	picture	NOUN
ejpam-3338	76	13	for	for	ADP
ejpam-3338	76	14	solving	solve	VERB
ejpam-3338	76	15	any	any	DET
ejpam-3338	76	16	physical	physical	ADJ
ejpam-3338	76	17	problem	problem	NOUN
ejpam-3338	76	18	.	.	PUNCT
ejpam-3338	77	1	the	the	DET
ejpam-3338	77	2	solution	solution	NOUN
ejpam-3338	77	3	of	of	ADP
ejpam-3338	77	4	a	a	DET
ejpam-3338	77	5	fractional	fractional	ADJ
ejpam-3338	77	6	differential	differential	ADJ
ejpam-3338	77	7	equation	equation	NOUN
ejpam-3338	77	8	with	with	ADP
ejpam-3338	77	9	appropriate	appropriate	ADJ
ejpam-3338	77	10	initial/	initial/	NUM
ejpam-3338	77	11	boundary	boundary	ADJ
ejpam-3338	77	12	conditions	condition	NOUN
ejpam-3338	77	13	(	(	PUNCT
ejpam-3338	77	14	bcs	bcs	NOUN
ejpam-3338	77	15	)	)	PUNCT
ejpam-3338	77	16	will	will	AUX
ejpam-3338	77	17	be	be	AUX
ejpam-3338	77	18	an	an	DET
ejpam-3338	77	19	analytic	analytic	ADJ
ejpam-3338	77	20	function	function	NOUN
ejpam-3338	77	21	as	as	SCONJ
ejpam-3338	77	22	is	be	AUX
ejpam-3338	77	23	the	the	DET
ejpam-3338	77	24	case	case	NOUN
ejpam-3338	77	25	with	with	ADP
ejpam-3338	77	26	that	that	PRON
ejpam-3338	77	27	of	of	ADP
ejpam-3338	77	28	classical	classical	ADJ
ejpam-3338	77	29	differential	differential	NOUN
ejpam-3338	77	30	equation	equation	NOUN
ejpam-3338	77	31	.	.	PUNCT
ejpam-3338	78	1	numerically	numerically	ADV
ejpam-3338	78	2	,	,	PUNCT
ejpam-3338	78	3	the	the	DET
ejpam-3338	78	4	solution	solution	NOUN
ejpam-3338	78	5	will	will	AUX
ejpam-3338	78	6	be	be	AUX
ejpam-3338	78	7	a	a	DET
ejpam-3338	78	8	(	(	PUNCT
ejpam-3338	78	9	numerical	numerical	ADJ
ejpam-3338	78	10	)	)	PUNCT
ejpam-3338	78	11	table	table	NOUN
ejpam-3338	78	12	consisting	consist	VERB
ejpam-3338	78	13	of	of	ADP
ejpam-3338	78	14	the	the	DET
ejpam-3338	78	15	values	value	NOUN
ejpam-3338	78	16	of	of	ADP
ejpam-3338	78	17	the	the	DET
ejpam-3338	78	18	independent	independent	ADJ
ejpam-3338	78	19	variables	variable	NOUN
ejpam-3338	78	20	and	and	CCONJ
ejpam-3338	78	21	the	the	DET
ejpam-3338	78	22	corresponding	corresponding	ADJ
ejpam-3338	78	23	values	value	NOUN
ejpam-3338	78	24	of	of	ADP
ejpam-3338	78	25	the	the	DET
ejpam-3338	78	26	function	function	NOUN
ejpam-3338	78	27	.	.	PUNCT
ejpam-3338	79	1	the	the	DET
ejpam-3338	79	2	function	function	NOUN
ejpam-3338	79	3	values	value	NOUN
ejpam-3338	79	4	can	can	AUX
ejpam-3338	79	5	be	be	AUX
ejpam-3338	79	6	graphically	graphically	ADV
ejpam-3338	79	7	represented	represent	VERB
ejpam-3338	79	8	for	for	ADP
ejpam-3338	79	9	the	the	DET
ejpam-3338	79	10	function	function	NOUN
ejpam-3338	79	11	of	of	ADP
ejpam-3338	79	12	1	1	NUM
ejpam-3338	79	13	or	or	CCONJ
ejpam-3338	79	14	2	2	NUM
ejpam-3338	79	15	independent	independent	ADJ
ejpam-3338	79	16	variables	variable	NOUN
ejpam-3338	79	17	since	since	SCONJ
ejpam-3338	79	18	we	we	PRON
ejpam-3338	79	19	can	can	AUX
ejpam-3338	79	20	visualize	visualize	VERB
ejpam-3338	79	21	0	0	NUM
ejpam-3338	79	22	,	,	PUNCT
ejpam-3338	79	23	1	1	NUM
ejpam-3338	79	24	,	,	PUNCT
ejpam-3338	79	25	2	2	NUM
ejpam-3338	79	26	,	,	PUNCT
ejpam-3338	79	27	and	and	CCONJ
ejpam-3338	79	28	3	3	NUM
ejpam-3338	79	29	dimensional	dimensional	ADJ
ejpam-3338	79	30	objects	object	NOUN
ejpam-3338	79	31	and	and	CCONJ
ejpam-3338	79	32	not	not	PART
ejpam-3338	79	33	beyond	beyond	ADP
ejpam-3338	79	34	,	,	PUNCT
ejpam-3338	79	35	a	a	DET
ejpam-3338	79	36	mathematical	mathematical	ADJ
ejpam-3338	79	37	extension	extension	NOUN
ejpam-3338	79	38	beyond	beyond	ADP
ejpam-3338	79	39	dimension	dimension	NOUN
ejpam-3338	79	40	3	3	NUM
ejpam-3338	79	41	is	be	AUX
ejpam-3338	79	42	always	always	ADV
ejpam-3338	79	43	possibe	possibe	ADJ
ejpam-3338	79	44	and	and	CCONJ
ejpam-3338	79	45	also	also	ADV
ejpam-3338	79	46	is	be	AUX
ejpam-3338	79	47	required	require	VERB
ejpam-3338	79	48	for	for	ADP
ejpam-3338	79	49	most	most	ADJ
ejpam-3338	79	50	real	real	ADJ
ejpam-3338	79	51	-	-	PUNCT
ejpam-3338	79	52	word	word	NOUN
ejpam-3338	79	53	physical	physical	ADJ
ejpam-3338	79	54	problems	problem	NOUN
ejpam-3338	79	55	though	though	ADV
ejpam-3338	79	56	.	.	PUNCT
ejpam-3338	80	1	the	the	DET
ejpam-3338	80	2	numerical	numerical	ADJ
ejpam-3338	80	3	table	table	NOUN
ejpam-3338	80	4	for	for	ADP
ejpam-3338	80	5	the	the	DET
ejpam-3338	80	6	function	function	NOUN
ejpam-3338	80	7	of	of	ADP
ejpam-3338	80	8	n	n	CCONJ
ejpam-3338	80	9	independent	independent	ADJ
ejpam-3338	80	10	variables	variable	NOUN
ejpam-3338	80	11	(	(	PUNCT
ejpam-3338	80	12	n	n	X
ejpam-3338	80	13	is	be	AUX
ejpam-3338	80	14	a	a	DET
ejpam-3338	80	15	finite	finite	ADJ
ejpam-3338	80	16	integer	integer	NOUN
ejpam-3338	80	17	)	)	PUNCT
ejpam-3338	80	18	can	can	AUX
ejpam-3338	80	19	be	be	AUX
ejpam-3338	80	20	depicted	depict	VERB
ejpam-3338	80	21	,	,	PUNCT
ejpam-3338	80	22	but	but	CCONJ
ejpam-3338	80	23	can	can	AUX
ejpam-3338	80	24	not	not	PART
ejpam-3338	80	25	be	be	AUX
ejpam-3338	80	26	graphically	graphically	ADV
ejpam-3338	80	27	represented	represent	VERB
ejpam-3338	80	28	on	on	ADP
ejpam-3338	80	29	a	a	DET
ejpam-3338	80	30	2	2	NUM
ejpam-3338	80	31	-	-	PUNCT
ejpam-3338	80	32	dimensional	dimensional	ADJ
ejpam-3338	80	33	paper	paper	NOUN
ejpam-3338	80	34	when	when	SCONJ
ejpam-3338	80	35	n	n	PRON
ejpam-3338	80	36	is	be	AUX
ejpam-3338	80	37	greater	great	ADJ
ejpam-3338	80	38	than	than	ADP
ejpam-3338	80	39	2	2	NUM
ejpam-3338	80	40	.	.	PUNCT
ejpam-3338	81	1	it	it	PRON
ejpam-3338	81	2	can	can	AUX
ejpam-3338	81	3	be	be	AUX
ejpam-3338	81	4	seen	see	VERB
ejpam-3338	81	5	that	that	SCONJ
ejpam-3338	81	6	the	the	DET
ejpam-3338	81	7	graph	graph	NOUN
ejpam-3338	81	8	is	be	AUX
ejpam-3338	81	9	a	a	DET
ejpam-3338	81	10	less	less	ADV
ejpam-3338	81	11	accurate	accurate	ADJ
ejpam-3338	81	12	form	form	NOUN
ejpam-3338	81	13	of	of	ADP
ejpam-3338	81	14	the	the	DET
ejpam-3338	81	15	numerical	numerical	ADJ
ejpam-3338	81	16	solution	solution	NOUN
ejpam-3338	81	17	,	,	PUNCT
ejpam-3338	81	18	it	it	PRON
ejpam-3338	81	19	is	be	AUX
ejpam-3338	81	20	visually	visually	ADV
ejpam-3338	81	21	very	very	ADV
ejpam-3338	81	22	useful	useful	ADJ
ejpam-3338	81	23	though	though	ADV
ejpam-3338	81	24	.	.	PUNCT
ejpam-3338	82	1	the	the	DET
ejpam-3338	82	2	recreation	recreation	NOUN
ejpam-3338	82	3	of	of	ADP
ejpam-3338	82	4	the	the	DET
ejpam-3338	82	5	numerical	numerical	ADJ
ejpam-3338	82	6	table	table	NOUN
ejpam-3338	82	7	from	from	ADP
ejpam-3338	82	8	the	the	DET
ejpam-3338	82	9	graph	graph	NOUN
ejpam-3338	82	10	will	will	AUX
ejpam-3338	82	11	have	have	VERB
ejpam-3338	82	12	accuracy	accuracy	NOUN
ejpam-3338	82	13	even	even	ADV
ejpam-3338	82	14	less	less	ADJ
ejpam-3338	82	15	than	than	ADP
ejpam-3338	82	16	(	(	PUNCT
ejpam-3338	82	17	or	or	CCONJ
ejpam-3338	82	18	at	at	ADP
ejpam-3338	82	19	best	well	ADV
ejpam-3338	82	20	equal	equal	ADJ
ejpam-3338	82	21	to	to	ADP
ejpam-3338	82	22	)	)	PUNCT
ejpam-3338	82	23	that	that	PRON
ejpam-3338	82	24	of	of	ADP
ejpam-3338	82	25	the	the	DET
ejpam-3338	82	26	graph	graph	NOUN
ejpam-3338	82	27	.	.	PUNCT
ejpam-3338	83	1	once	once	SCONJ
ejpam-3338	83	2	the	the	DET
ejpam-3338	83	3	foregoing	forego	VERB
ejpam-3338	83	4	analytic	analytic	ADJ
ejpam-3338	83	5	function	function	NOUN
ejpam-3338	83	6	is	be	AUX
ejpam-3338	83	7	known	know	VERB
ejpam-3338	83	8	as	as	ADP
ejpam-3338	83	9	the	the	DET
ejpam-3338	83	10	solution	solution	NOUN
ejpam-3338	83	11	of	of	ADP
ejpam-3338	83	12	the	the	DET
ejpam-3338	83	13	fractional	fractional	ADJ
ejpam-3338	83	14	differential	differential	NOUN
ejpam-3338	83	15	equation	equation	NOUN
ejpam-3338	83	16	,	,	PUNCT
ejpam-3338	83	17	one	one	PRON
ejpam-3338	83	18	can	can	AUX
ejpam-3338	83	19	readily	readily	ADV
ejpam-3338	83	20	determine	determine	VERB
ejpam-3338	83	21	the	the	DET
ejpam-3338	83	22	corresponding	corresponding	ADJ
ejpam-3338	83	23	classical	classical	ADJ
ejpam-3338	83	24	differential	differential	NOUN
ejpam-3338	83	25	equation	equation	NOUN
ejpam-3338	83	26	with	with	ADP
ejpam-3338	83	27	appropriate	appropriate	ADJ
ejpam-3338	83	28	initial	initial	ADJ
ejpam-3338	83	29	conditions	condition	NOUN
ejpam-3338	83	30	.	.	PUNCT
ejpam-3338	84	1	this	this	PRON
ejpam-3338	84	2	implies	imply	VERB
ejpam-3338	84	3	that	that	SCONJ
ejpam-3338	84	4	the	the	DET
ejpam-3338	84	5	fractional	fractional	ADJ
ejpam-3338	84	6	differential	differential	ADJ
ejpam-3338	84	7	equations	equation	NOUN
ejpam-3338	84	8	are	be	AUX
ejpam-3338	84	9	not	not	PART
ejpam-3338	84	10	absolutely	absolutely	ADV
ejpam-3338	84	11	essential	essential	ADJ
ejpam-3338	84	12	to	to	PART
ejpam-3338	84	13	solve	solve	VERB
ejpam-3338	84	14	any	any	DET
ejpam-3338	84	15	physical	physical	ADJ
ejpam-3338	84	16	problem	problem	NOUN
ejpam-3338	84	17	that	that	PRON
ejpam-3338	84	18	can	can	AUX
ejpam-3338	84	19	be	be	AUX
ejpam-3338	84	20	tackled	tackle	VERB
ejpam-3338	84	21	by	by	ADP
ejpam-3338	84	22	the	the	DET
ejpam-3338	84	23	appropriate	appropriate	ADJ
ejpam-3338	84	24	classical	classical	ADJ
ejpam-3338	84	25	differential	differential	NOUN
ejpam-3338	84	26	equations	equation	NOUN
ejpam-3338	84	27	.	.	PUNCT
ejpam-3338	85	1	in	in	ADP
ejpam-3338	85	2	other	other	ADJ
ejpam-3338	85	3	words	word	NOUN
ejpam-3338	85	4	,	,	PUNCT
ejpam-3338	85	5	there	there	PRON
ejpam-3338	85	6	exists	exist	VERB
ejpam-3338	85	7	no	no	DET
ejpam-3338	85	8	physical	physical	ADJ
ejpam-3338	85	9	problem	problem	NOUN
ejpam-3338	85	10	in	in	ADP
ejpam-3338	85	11	nature	nature	NOUN
ejpam-3338	85	12	,	,	PUNCT
ejpam-3338	85	13	which	which	PRON
ejpam-3338	85	14	does	do	AUX
ejpam-3338	85	15	not	not	PART
ejpam-3338	85	16	have	have	VERB
ejpam-3338	85	17	a	a	DET
ejpam-3338	85	18	classical	classical	ADJ
ejpam-3338	85	19	differential	differential	NOUN
ejpam-3338	85	20	equation	equation	NOUN
ejpam-3338	85	21	(	(	PUNCT
ejpam-3338	85	22	cde	cde	PROPN
ejpam-3338	85	23	)	)	PUNCT
ejpam-3338	85	24	model	model	NOUN
ejpam-3338	85	25	but	but	CCONJ
ejpam-3338	85	26	has	have	VERB
ejpam-3338	85	27	a	a	DET
ejpam-3338	85	28	fractional	fractional	ADJ
ejpam-3338	85	29	differential	differential	ADJ
ejpam-3338	85	30	equation	equation	NOUN
ejpam-3338	85	31	(	(	PUNCT
ejpam-3338	85	32	fde	fde	NOUN
ejpam-3338	85	33	)	)	PUNCT
ejpam-3338	85	34	model	model	NOUN
ejpam-3338	85	35	.	.	PUNCT
ejpam-3338	86	1	thus	thus	ADV
ejpam-3338	86	2	the	the	DET
ejpam-3338	86	3	knowledge	knowledge	NOUN
ejpam-3338	86	4	of	of	ADP
ejpam-3338	86	5	fractional	fractional	ADJ
ejpam-3338	86	6	differential	differential	ADJ
ejpam-3338	86	7	equations	equation	NOUN
ejpam-3338	86	8	may	may	AUX
ejpam-3338	86	9	be	be	AUX
ejpam-3338	86	10	considered	consider	VERB
ejpam-3338	86	11	redundant	redundant	ADJ
ejpam-3338	86	12	from	from	ADP
ejpam-3338	86	13	the	the	DET
ejpam-3338	86	14	engineering	engineering	NOUN
ejpam-3338	86	15	and	and	CCONJ
ejpam-3338	86	16	scientific	scientific	ADJ
ejpam-3338	86	17	applications	application	NOUN
ejpam-3338	86	18	point	point	NOUN
ejpam-3338	86	19	of	of	ADP
ejpam-3338	86	20	view	view	NOUN
ejpam-3338	86	21	.	.	PUNCT
ejpam-3338	87	1	but	but	CCONJ
ejpam-3338	87	2	the	the	DET
ejpam-3338	87	3	concerned	concerned	ADJ
ejpam-3338	87	4	quality	quality	NOUN
ejpam-3338	87	5	s.	s.	PROPN
ejpam-3338	87	6	k.sen	k.sen	PROPN
ejpam-3338	87	7	,	,	PUNCT
ejpam-3338	87	8	j.	j.	PROPN
ejpam-3338	87	9	v.	v.	PROPN
ejpam-3338	87	10	devi	devi	PROPN
ejpam-3338	87	11	,	,	PUNCT
ejpam-3338	87	12	r.v.g	r.v.g	NOUN
ejpam-3338	87	13	.	.	PUNCT
ejpam-3338	88	1	r.	r.	PROPN
ejpam-3338	88	2	kumar	kumar	PROPN
ejpam-3338	88	3	/	/	SYM
ejpam-3338	88	4	eur	eur	PROPN
ejpam-3338	88	5	.	.	PUNCT
ejpam-3338	89	1	j.	j.	PROPN
ejpam-3338	89	2	pure	pure	PROPN
ejpam-3338	89	3	appl	appl	PROPN
ejpam-3338	89	4	.	.	PROPN
ejpam-3338	89	5	math	math	PROPN
ejpam-3338	89	6	,	,	PUNCT
ejpam-3338	89	7	11	11	NUM
ejpam-3338	89	8	(	(	PUNCT
ejpam-3338	89	9	3	3	NUM
ejpam-3338	89	10	)	)	PUNCT
ejpam-3338	89	11	(	(	PUNCT
ejpam-3338	89	12	2018	2018	NUM
ejpam-3338	89	13	)	)	PUNCT
ejpam-3338	89	14	,	,	PUNCT
ejpam-3338	89	15	1058	1058	NUM
ejpam-3338	89	16	-	-	SYM
ejpam-3338	89	17	1099	1099	NUM
ejpam-3338	89	18	1062	1062	NUM
ejpam-3338	89	19	(	(	PUNCT
ejpam-3338	89	20	error	error	NOUN
ejpam-3338	89	21	)	)	PUNCT
ejpam-3338	89	22	and	and	CCONJ
ejpam-3338	89	23	cost	cost	NOUN
ejpam-3338	89	24	(	(	PUNCT
ejpam-3338	89	25	complexity	complexity	NOUN
ejpam-3338	89	26	)	)	PUNCT
ejpam-3338	89	27	of	of	ADP
ejpam-3338	89	28	the	the	DET
ejpam-3338	89	29	solution	solution	NOUN
ejpam-3338	89	30	of	of	ADP
ejpam-3338	89	31	fde	fde	PROPN
ejpam-3338	89	32	need	need	VERB
ejpam-3338	89	33	to	to	PART
ejpam-3338	89	34	be	be	AUX
ejpam-3338	89	35	explored	explore	VERB
ejpam-3338	89	36	for	for	ADP
ejpam-3338	89	37	computational	computational	ADJ
ejpam-3338	89	38	competitiveness	competitiveness	NOUN
ejpam-3338	89	39	with	with	ADP
ejpam-3338	89	40	that	that	PRON
ejpam-3338	89	41	of	of	ADP
ejpam-3338	89	42	classical	classical	ADJ
ejpam-3338	89	43	differential	differential	NOUN
ejpam-3338	89	44	equation	equation	NOUN
ejpam-3338	89	45	(	(	PUNCT
ejpam-3338	89	46	cde	cde	PROPN
ejpam-3338	89	47	)	)	PUNCT
ejpam-3338	89	48	for	for	ADP
ejpam-3338	89	49	engineering	engineering	NOUN
ejpam-3338	89	50	applications	application	NOUN
ejpam-3338	89	51	.	.	PUNCT
ejpam-3338	90	1	are	be	AUX
ejpam-3338	90	2	the	the	DET
ejpam-3338	90	3	fde	fde	PROPN
ejpam-3338	90	4	models	model	NOUN
ejpam-3338	90	5	better	well	ADV
ejpam-3338	90	6	than	than	ADP
ejpam-3338	90	7	cde	cde	NOUN
ejpam-3338	90	8	models	model	NOUN
ejpam-3338	90	9	in	in	ADP
ejpam-3338	90	10	terms	term	NOUN
ejpam-3338	90	11	of	of	ADP
ejpam-3338	90	12	quality	quality	NOUN
ejpam-3338	90	13	and	and	CCONJ
ejpam-3338	90	14	cost	cost	NOUN
ejpam-3338	90	15	of	of	ADP
ejpam-3338	90	16	the	the	DET
ejpam-3338	90	17	numerical	numerical	ADJ
ejpam-3338	90	18	solutions	solution	NOUN
ejpam-3338	90	19	always	always	ADV
ejpam-3338	90	20	(	(	PUNCT
ejpam-3338	90	21	for	for	ADP
ejpam-3338	90	22	solving	solve	VERB
ejpam-3338	90	23	a	a	DET
ejpam-3338	90	24	concerned	concerned	ADJ
ejpam-3338	90	25	physical	physical	ADJ
ejpam-3338	90	26	problem	problem	NOUN
ejpam-3338	90	27	)	)	PUNCT
ejpam-3338	90	28	?	?	PUNCT
ejpam-3338	91	1	if	if	SCONJ
ejpam-3338	91	2	the	the	DET
ejpam-3338	91	3	answer	answer	NOUN
ejpam-3338	91	4	is	be	AUX
ejpam-3338	91	5	no	no	DET
ejpam-3338	91	6	implying	imply	VERB
ejpam-3338	91	7	not	not	PART
ejpam-3338	91	8	always	always	ADV
ejpam-3338	91	9	,	,	PUNCT
ejpam-3338	91	10	then	then	ADV
ejpam-3338	91	11	which	which	PRON
ejpam-3338	91	12	are	be	AUX
ejpam-3338	91	13	the	the	DET
ejpam-3338	91	14	practical	practical	ADJ
ejpam-3338	91	15	situations	situation	NOUN
ejpam-3338	91	16	when	when	SCONJ
ejpam-3338	91	17	the	the	DET
ejpam-3338	91	18	fde	fde	PROPN
ejpam-3338	91	19	models	model	NOUN
ejpam-3338	91	20	are	be	AUX
ejpam-3338	91	21	better	well	ADJ
ejpam-3338	91	22	?	?	PUNCT
ejpam-3338	92	1	this	this	DET
ejpam-3338	92	2	issue	issue	NOUN
ejpam-3338	92	3	will	will	AUX
ejpam-3338	92	4	be	be	AUX
ejpam-3338	92	5	discussed	discuss	VERB
ejpam-3338	92	6	elsewhere	elsewhere	ADV
ejpam-3338	92	7	.	.	PUNCT
ejpam-3338	93	1	the	the	DET
ejpam-3338	93	2	interpretation	interpretation	NOUN
ejpam-3338	93	3	of	of	ADP
ejpam-3338	93	4	a	a	DET
ejpam-3338	93	5	fractional	fractional	ADJ
ejpam-3338	93	6	differential	differential	NOUN
ejpam-3338	93	7	equation	equation	NOUN
ejpam-3338	93	8	,	,	PUNCT
ejpam-3338	93	9	more	more	ADV
ejpam-3338	93	10	simply	simply	ADV
ejpam-3338	93	11	a	a	DET
ejpam-3338	93	12	non	non	ADJ
ejpam-3338	93	13	-	-	ADJ
ejpam-3338	93	14	integer	integer	ADJ
ejpam-3338	93	15	fractional	fractional	ADJ
ejpam-3338	93	16	derivative	derivative	NOUN
ejpam-3338	93	17	and	and	CCONJ
ejpam-3338	93	18	that	that	PRON
ejpam-3338	93	19	of	of	ADP
ejpam-3338	93	20	a	a	DET
ejpam-3338	93	21	classical	classical	ADJ
ejpam-3338	93	22	differential	differential	NOUN
ejpam-3338	93	23	equation	equation	NOUN
ejpam-3338	93	24	,	,	PUNCT
ejpam-3338	93	25	more	more	ADV
ejpam-3338	93	26	simply	simply	ADV
ejpam-3338	93	27	an	an	DET
ejpam-3338	93	28	integer	integer	NOUN
ejpam-3338	93	29	-	-	PUNCT
ejpam-3338	93	30	order	order	NOUN
ejpam-3338	93	31	derivative	derivative	NOUN
ejpam-3338	93	32	are	be	AUX
ejpam-3338	93	33	different	different	ADJ
ejpam-3338	93	34	more	more	ADV
ejpam-3338	93	35	specifically	specifically	ADV
ejpam-3338	93	36	from	from	ADP
ejpam-3338	93	37	the	the	DET
ejpam-3338	93	38	exact	exact	ADJ
ejpam-3338	93	39	comprehension	comprehension	NOUN
ejpam-3338	93	40	of	of	ADP
ejpam-3338	93	41	the	the	DET
ejpam-3338	93	42	corresponding	corresponding	ADJ
ejpam-3338	93	43	physical	physical	ADJ
ejpam-3338	93	44	problem	problem	NOUN
ejpam-3338	93	45	point	point	NOUN
ejpam-3338	93	46	in	in	ADP
ejpam-3338	93	47	view	view	NOUN
ejpam-3338	93	48	.	.	PUNCT
ejpam-3338	94	1	the	the	DET
ejpam-3338	94	2	later	later	ADJ
ejpam-3338	94	3	interpretation	interpretation	NOUN
ejpam-3338	94	4	has	have	AUX
ejpam-3338	94	5	been	be	AUX
ejpam-3338	94	6	readily	readily	ADV
ejpam-3338	94	7	exactly	exactly	ADV
ejpam-3338	94	8	comprehended	comprehend	VERB
ejpam-3338	94	9	and	and	CCONJ
ejpam-3338	94	10	easily	easily	ADV
ejpam-3338	94	11	understood	understand	VERB
ejpam-3338	94	12	while	while	SCONJ
ejpam-3338	94	13	the	the	DET
ejpam-3338	94	14	former	former	ADJ
ejpam-3338	94	15	one	one	NOUN
ejpam-3338	94	16	has	have	AUX
ejpam-3338	94	17	not	not	PART
ejpam-3338	94	18	been	be	AUX
ejpam-3338	94	19	.	.	PUNCT
ejpam-3338	95	1	however	however	ADV
ejpam-3338	95	2	,	,	PUNCT
ejpam-3338	95	3	the	the	DET
ejpam-3338	95	4	exact	exact	ADJ
ejpam-3338	95	5	value	value	NOUN
ejpam-3338	95	6	of	of	ADP
ejpam-3338	95	7	the	the	DET
ejpam-3338	95	8	fraction	fraction	NOUN
ejpam-3338	95	9	in	in	ADP
ejpam-3338	95	10	the	the	DET
ejpam-3338	95	11	fractional	fractional	ADJ
ejpam-3338	95	12	order	order	NOUN
ejpam-3338	95	13	can	can	AUX
ejpam-3338	95	14	not	not	PART
ejpam-3338	95	15	be	be	AUX
ejpam-3338	95	16	readily	readily	ADV
ejpam-3338	95	17	known	know	VERB
ejpam-3338	95	18	from	from	ADP
ejpam-3338	95	19	the	the	DET
ejpam-3338	95	20	physical	physical	ADJ
ejpam-3338	95	21	problem	problem	NOUN
ejpam-3338	95	22	except	except	SCONJ
ejpam-3338	95	23	through	through	ADP
ejpam-3338	95	24	a	a	DET
ejpam-3338	95	25	numerical	numerical	ADJ
ejpam-3338	95	26	experiment	experiment	NOUN
ejpam-3338	95	27	or	or	CCONJ
ejpam-3338	95	28	by	by	ADP
ejpam-3338	95	29	some	some	DET
ejpam-3338	95	30	other	other	ADJ
ejpam-3338	95	31	means	mean	NOUN
ejpam-3338	95	32	(	(	PUNCT
ejpam-3338	95	33	say	say	VERB
ejpam-3338	95	34	trial	trial	NOUN
ejpam-3338	95	35	and	and	CCONJ
ejpam-3338	95	36	error	error	NOUN
ejpam-3338	95	37	)	)	PUNCT
ejpam-3338	95	38	.	.	PUNCT
ejpam-3338	96	1	special	special	ADJ
ejpam-3338	96	2	cases	case	NOUN
ejpam-3338	96	3	of	of	ADP
ejpam-3338	96	4	the	the	DET
ejpam-3338	96	5	foregoing	forego	VERB
ejpam-3338	96	6	general	general	ADJ
ejpam-3338	96	7	solution	solution	NOUN
ejpam-3338	96	8	are	be	AUX
ejpam-3338	96	9	the	the	DET
ejpam-3338	96	10	following	follow	VERB
ejpam-3338	96	11	solutions	solution	NOUN
ejpam-3338	96	12	[	[	X
ejpam-3338	96	13	1	1	NUM
ejpam-3338	96	14	]	]	X
ejpam-3338	96	15	:	:	PUNCT
ejpam-3338	96	16	x(t	x(t	PROPN
ejpam-3338	96	17	)	)	PUNCT
ejpam-3338	97	1	=	=	PUNCT
ejpam-3338	98	1	x0	x0	PROPN
ejpam-3338	98	2	+	+	NUM
ejpam-3338	98	3	v0sin(ϕt	v0sin(ϕt	X
ejpam-3338	98	4	)	)	PUNCT
ejpam-3338	98	5	ϕ	ϕ	NOUN
ejpam-3338	98	6	(	(	PUNCT
ejpam-3338	98	7	for	for	ADP
ejpam-3338	98	8	α	α	NOUN
ejpam-3338	98	9	=	=	SYM
ejpam-3338	98	10	0	0	NUM
ejpam-3338	98	11	i.e.	i.e.	X
ejpam-3338	98	12	,	,	PUNCT
ejpam-3338	98	13	for	for	ADP
ejpam-3338	98	14	free	free	ADJ
ejpam-3338	98	15	oscillation	oscillation	NOUN
ejpam-3338	98	16	)	)	PUNCT
ejpam-3338	98	17	(	(	PUNCT
ejpam-3338	98	18	12	12	X
ejpam-3338	98	19	)	)	PUNCT
ejpam-3338	98	20	x(t	x(t	PROPN
ejpam-3338	98	21	)	)	PUNCT
ejpam-3338	99	1	=	=	PUNCT
ejpam-3338	100	1	x0	x0	PROPN
ejpam-3338	101	1	+	+	CCONJ
ejpam-3338	101	2	v0(2−	v0(2−	X
ejpam-3338	101	3	(	(	PUNCT
ejpam-3338	101	4	2	2	NUM
ejpam-3338	101	5	+	+	NUM
ejpam-3338	101	6	ϕt)e−ϕt	ϕt)e−ϕt	NOUN
ejpam-3338	101	7	)	)	PUNCT
ejpam-3338	101	8	(	(	PUNCT
ejpam-3338	101	9	for	for	ADP
ejpam-3338	101	10	α	α	NOUN
ejpam-3338	101	11	=	=	SYM
ejpam-3338	101	12	1	1	NUM
ejpam-3338	101	13	)	)	PUNCT
ejpam-3338	101	14	(	(	PUNCT
ejpam-3338	101	15	13	13	NUM
ejpam-3338	101	16	)	)	PUNCT
ejpam-3338	101	17	this	this	PRON
ejpam-3338	101	18	is	be	AUX
ejpam-3338	101	19	a	a	DET
ejpam-3338	101	20	totally	totally	ADV
ejpam-3338	101	21	new	new	ADJ
ejpam-3338	101	22	function	function	NOUN
ejpam-3338	101	23	type	type	NOUN
ejpam-3338	101	24	.	.	PUNCT
ejpam-3338	102	1	the	the	DET
ejpam-3338	102	2	role	role	NOUN
ejpam-3338	102	3	of	of	ADP
ejpam-3338	102	4	the	the	DET
ejpam-3338	102	5	initial	initial	ADJ
ejpam-3338	102	6	velocity	velocity	NOUN
ejpam-3338	102	7	v0	v0	NOUN
ejpam-3338	102	8	is	be	AUX
ejpam-3338	102	9	not	not	PART
ejpam-3338	102	10	more	more	ADJ
ejpam-3338	102	11	than	than	ADP
ejpam-3338	102	12	just	just	ADV
ejpam-3338	102	13	a	a	DET
ejpam-3338	102	14	scaling	scale	VERB
ejpam-3338	102	15	factor	factor	NOUN
ejpam-3338	102	16	.	.	PUNCT
ejpam-3338	103	1	in	in	ADP
ejpam-3338	103	2	terms	term	NOUN
ejpam-3338	103	3	of	of	ADP
ejpam-3338	103	4	free	free	ADJ
ejpam-3338	103	5	oscillation	oscillation	NOUN
ejpam-3338	103	6	(	(	PUNCT
ejpam-3338	103	7	α	α	NOUN
ejpam-3338	103	8	=	=	NOUN
ejpam-3338	103	9	0	0	NUM
ejpam-3338	103	10	)	)	PUNCT
ejpam-3338	103	11	as	as	ADV
ejpam-3338	103	12	well	well	ADV
ejpam-3338	103	13	as	as	ADP
ejpam-3338	103	14	in	in	ADP
ejpam-3338	103	15	terms	term	NOUN
ejpam-3338	103	16	of	of	ADP
ejpam-3338	103	17	damped	damped	ADJ
ejpam-3338	103	18	oscillation	oscillation	NOUN
ejpam-3338	103	19	(	(	PUNCT
ejpam-3338	103	20	0	0	NUM
ejpam-3338	103	21	<	<	X
ejpam-3338	103	22	α	α	PROPN
ejpam-3338	103	23	≤	≤	NUM
ejpam-3338	103	24	1	1	NUM
ejpam-3338	103	25	)	)	PUNCT
ejpam-3338	103	26	,	,	PUNCT
ejpam-3338	103	27	the	the	DET
ejpam-3338	103	28	time	time	NOUN
ejpam-3338	103	29	variant	variant	ADJ
ejpam-3338	103	30	solutions	solution	NOUN
ejpam-3338	103	31	may	may	AUX
ejpam-3338	103	32	be	be	AUX
ejpam-3338	103	33	better	well	ADV
ejpam-3338	103	34	understood	understand	VERB
ejpam-3338	103	35	when	when	SCONJ
ejpam-3338	103	36	we	we	PRON
ejpam-3338	103	37	consider	consider	VERB
ejpam-3338	103	38	the	the	DET
ejpam-3338	103	39	1st	1st	ADJ
ejpam-3338	103	40	quarter	quarter	NOUN
ejpam-3338	103	41	period	period	NOUN
ejpam-3338	103	42	to	to	PART
ejpam-3338	103	43	describe	describe	VERB
ejpam-3338	103	44	the	the	DET
ejpam-3338	103	45	process	process	NOUN
ejpam-3338	103	46	of	of	ADP
ejpam-3338	103	47	a	a	DET
ejpam-3338	103	48	fractional	fractional	ADJ
ejpam-3338	103	49	friction	friction	NOUN
ejpam-3338	103	50	force	force	NOUN
ejpam-3338	103	51	[	[	X
ejpam-3338	103	52	1	1	NUM
ejpam-3338	103	53	]	]	PUNCT
ejpam-3338	103	54	.	.	PUNCT
ejpam-3338	104	1	the	the	DET
ejpam-3338	104	2	presentation	presentation	NOUN
ejpam-3338	104	3	of	of	ADP
ejpam-3338	104	4	the	the	DET
ejpam-3338	104	5	foregoing	forego	VERB
ejpam-3338	104	6	solutions	solution	NOUN
ejpam-3338	104	7	is	be	AUX
ejpam-3338	104	8	to	to	PART
ejpam-3338	104	9	reveal	reveal	VERB
ejpam-3338	104	10	the	the	DET
ejpam-3338	104	11	effect	effect	NOUN
ejpam-3338	104	12	of	of	ADP
ejpam-3338	104	13	fractional	fractional	ADJ
ejpam-3338	104	14	friction	friction	NOUN
ejpam-3338	104	15	forces	force	NOUN
ejpam-3338	104	16	on	on	ADP
ejpam-3338	104	17	the	the	DET
ejpam-3338	104	18	solution	solution	NOUN
ejpam-3338	104	19	.	.	PUNCT
ejpam-3338	105	1	how	how	SCONJ
ejpam-3338	105	2	do	do	AUX
ejpam-3338	105	3	we	we	PRON
ejpam-3338	105	4	integrate	integrate	VERB
ejpam-3338	105	5	and	and	CCONJ
ejpam-3338	105	6	merge	merge	VERB
ejpam-3338	105	7	these	these	DET
ejpam-3338	105	8	facts	fact	NOUN
ejpam-3338	105	9	so	so	SCONJ
ejpam-3338	105	10	that	that	SCONJ
ejpam-3338	105	11	the	the	DET
ejpam-3338	105	12	classical	classical	ADJ
ejpam-3338	105	13	calculus	calculus	NOUN
ejpam-3338	105	14	becomes	become	VERB
ejpam-3338	105	15	a	a	DET
ejpam-3338	105	16	special	special	ADJ
ejpam-3338	105	17	case	case	NOUN
ejpam-3338	105	18	of	of	ADP
ejpam-3338	105	19	fractional	fractional	ADJ
ejpam-3338	105	20	calculus	calculus	NOUN
ejpam-3338	105	21	?	?	PUNCT
ejpam-3338	106	1	the	the	DET
ejpam-3338	106	2	solutions	solution	NOUN
ejpam-3338	106	3	of	of	ADP
ejpam-3338	106	4	the	the	DET
ejpam-3338	106	5	differential	differential	ADJ
ejpam-3338	106	6	equation	equation	NOUN
ejpam-3338	106	7	mẍ(t	mẍ(t	NOUN
ejpam-3338	106	8	)	)	PUNCT
ejpam-3338	107	1	+	+	CCONJ
ejpam-3338	107	2	γẋ(t	γẋ(t	NUM
ejpam-3338	107	3	)	)	PUNCT
ejpam-3338	107	4	+	+	CCONJ
ejpam-3338	107	5	kx(t	kx(t	X
ejpam-3338	107	6	)	)	PUNCT
ejpam-3338	107	7	=	=	SYM
ejpam-3338	107	8	0	0	NUM
ejpam-3338	107	9	(	(	PUNCT
ejpam-3338	107	10	14	14	NUM
ejpam-3338	107	11	)	)	PUNCT
ejpam-3338	107	12	for	for	ADP
ejpam-3338	107	13	the	the	DET
ejpam-3338	107	14	damped	damped	ADJ
ejpam-3338	107	15	classical	classical	ADJ
ejpam-3338	107	16	harmonic	harmonic	ADJ
ejpam-3338	107	17	oscillator	oscillator	NOUN
ejpam-3338	107	18	will	will	AUX
ejpam-3338	107	19	allow	allow	VERB
ejpam-3338	107	20	us	we	PRON
ejpam-3338	107	21	to	to	PART
ejpam-3338	107	22	investigate	investigate	VERB
ejpam-3338	107	23	and	and	CCONJ
ejpam-3338	107	24	understand	understand	VERB
ejpam-3338	107	25	this	this	DET
ejpam-3338	107	26	aspect	aspect	NOUN
ejpam-3338	107	27	of	of	ADP
ejpam-3338	107	28	fractional	fractional	ADJ
ejpam-3338	107	29	friction	friction	NOUN
ejpam-3338	107	30	,	,	PUNCT
ejpam-3338	107	31	where	where	SCONJ
ejpam-3338	107	32	m	m	VERB
ejpam-3338	107	33	,	,	PUNCT
ejpam-3338	107	34	γ	γ	X
ejpam-3338	107	35	,	,	PUNCT
ejpam-3338	107	36	k	k	X
ejpam-3338	107	37	are	be	AUX
ejpam-3338	107	38	the	the	DET
ejpam-3338	107	39	mass	mass	PROPN
ejpam-3338	107	40	,	,	PUNCT
ejpam-3338	107	41	the	the	DET
ejpam-3338	107	42	damping	damp	VERB
ejpam-3338	107	43	coefficient	coefficient	NOUN
ejpam-3338	107	44	,	,	PUNCT
ejpam-3338	107	45	and	and	CCONJ
ejpam-3338	107	46	the	the	DET
ejpam-3338	107	47	spring	spring	NOUN
ejpam-3338	107	48	constant	constant	NOUN
ejpam-3338	107	49	of	of	ADP
ejpam-3338	107	50	the	the	DET
ejpam-3338	107	51	oscillator	oscillator	NOUN
ejpam-3338	107	52	,	,	PUNCT
ejpam-3338	107	53	respectively	respectively	ADV
ejpam-3338	107	54	[	[	X
ejpam-3338	107	55	1	1	NUM
ejpam-3338	107	56	]	]	PUNCT
ejpam-3338	107	57	.	.	PUNCT
ejpam-3338	108	1	for	for	ADP
ejpam-3338	108	2	every	every	DET
ejpam-3338	108	3	value	value	NOUN
ejpam-3338	108	4	of	of	ADP
ejpam-3338	108	5	the	the	DET
ejpam-3338	108	6	fraction	fraction	NOUN
ejpam-3338	108	7	in	in	ADP
ejpam-3338	108	8	a	a	DET
ejpam-3338	108	9	fractional	fractional	ADJ
ejpam-3338	108	10	mathematical	mathematical	ADJ
ejpam-3338	108	11	model	model	NOUN
ejpam-3338	108	12	usually	usually	ADV
ejpam-3338	108	13	an	an	DET
ejpam-3338	108	14	fde	fde	NOUN
ejpam-3338	108	15	what	what	PRON
ejpam-3338	108	16	will	will	AUX
ejpam-3338	108	17	precisely	precisely	ADV
ejpam-3338	108	18	be	be	AUX
ejpam-3338	108	19	the	the	DET
ejpam-3338	108	20	corresponding	corresponding	ADJ
ejpam-3338	108	21	physical	physical	ADJ
ejpam-3338	108	22	model	model	NOUN
ejpam-3338	108	23	?	?	PUNCT
ejpam-3338	109	1	in	in	ADP
ejpam-3338	109	2	a	a	DET
ejpam-3338	109	3	digital	digital	ADJ
ejpam-3338	109	4	computer	computer	NOUN
ejpam-3338	109	5	(	(	PUNCT
ejpam-3338	109	6	finite	finite	PROPN
ejpam-3338	109	7	precision	precision	NOUN
ejpam-3338	109	8	machine	machine	NOUN
ejpam-3338	109	9	)	)	PUNCT
ejpam-3338	109	10	,	,	PUNCT
ejpam-3338	109	11	concerning	concern	VERB
ejpam-3338	109	12	differential	differential	NOUN
ejpam-3338	109	13	equations	equation	NOUN
ejpam-3338	109	14	,	,	PUNCT
ejpam-3338	109	15	there	there	PRON
ejpam-3338	109	16	will	will	AUX
ejpam-3338	109	17	be	be	AUX
ejpam-3338	109	18	a	a	DET
ejpam-3338	109	19	very	very	ADV
ejpam-3338	109	20	large	large	ADJ
ejpam-3338	109	21	but	but	CCONJ
ejpam-3338	109	22	finite	finite	ADJ
ejpam-3338	109	23	number	number	NOUN
ejpam-3338	109	24	of	of	ADP
ejpam-3338	109	25	physical	physical	ADJ
ejpam-3338	109	26	models	model	NOUN
ejpam-3338	109	27	.	.	PUNCT
ejpam-3338	110	1	corresponding	correspond	VERB
ejpam-3338	110	2	to	to	ADP
ejpam-3338	110	3	each	each	PRON
ejpam-3338	110	4	of	of	ADP
ejpam-3338	110	5	these	these	DET
ejpam-3338	110	6	physical	physical	ADJ
ejpam-3338	110	7	models	model	NOUN
ejpam-3338	110	8	there	there	PRON
ejpam-3338	110	9	will	will	AUX
ejpam-3338	110	10	also	also	ADV
ejpam-3338	110	11	be	be	AUX
ejpam-3338	110	12	an	an	DET
ejpam-3338	110	13	integer	integer	NOUN
ejpam-3338	110	14	-	-	PUNCT
ejpam-3338	110	15	order	order	NOUN
ejpam-3338	110	16	mathematical	mathematical	ADJ
ejpam-3338	110	17	model	model	NOUN
ejpam-3338	110	18	.	.	PUNCT
ejpam-3338	111	1	will	will	AUX
ejpam-3338	111	2	each	each	PRON
ejpam-3338	111	3	of	of	ADP
ejpam-3338	111	4	the	the	DET
ejpam-3338	111	5	integer	integer	NOUN
ejpam-3338	111	6	order	order	NOUN
ejpam-3338	111	7	models	model	NOUN
ejpam-3338	111	8	be	be	AUX
ejpam-3338	111	9	equivalent	equivalent	ADJ
ejpam-3338	111	10	numerically	numerically	ADV
ejpam-3338	111	11	to	to	ADP
ejpam-3338	111	12	the	the	DET
ejpam-3338	111	13	corresponding	corresponding	ADJ
ejpam-3338	111	14	fractional	fractional	ADJ
ejpam-3338	111	15	order	order	NOUN
ejpam-3338	111	16	mathematical	mathematical	ADJ
ejpam-3338	111	17	model	model	NOUN
ejpam-3338	111	18	over	over	ADP
ejpam-3338	111	19	the	the	DET
ejpam-3338	111	20	complete	complete	ADJ
ejpam-3338	111	21	interval	interval	NOUN
ejpam-3338	111	22	(	(	PUNCT
ejpam-3338	111	23	range	range	NOUN
ejpam-3338	111	24	)	)	PUNCT
ejpam-3338	111	25	of	of	ADP
ejpam-3338	111	26	integration	integration	NOUN
ejpam-3338	111	27	?	?	PUNCT
ejpam-3338	112	1	s.	s.	PROPN
ejpam-3338	112	2	k.sen	k.sen	PROPN
ejpam-3338	112	3	,	,	PUNCT
ejpam-3338	112	4	j.	j.	PROPN
ejpam-3338	112	5	v.	v.	PROPN
ejpam-3338	112	6	devi	devi	PROPN
ejpam-3338	112	7	,	,	PUNCT
ejpam-3338	112	8	r.v.g	r.v.g	NOUN
ejpam-3338	112	9	.	.	PUNCT
ejpam-3338	113	1	r.	r.	PROPN
ejpam-3338	113	2	kumar	kumar	PROPN
ejpam-3338	113	3	/	/	SYM
ejpam-3338	113	4	eur	eur	PROPN
ejpam-3338	113	5	.	.	PUNCT
ejpam-3338	114	1	j.	j.	PROPN
ejpam-3338	114	2	pure	pure	PROPN
ejpam-3338	114	3	appl	appl	PROPN
ejpam-3338	114	4	.	.	PROPN
ejpam-3338	114	5	math	math	PROPN
ejpam-3338	114	6	,	,	PUNCT
ejpam-3338	114	7	11	11	NUM
ejpam-3338	114	8	(	(	PUNCT
ejpam-3338	114	9	3	3	NUM
ejpam-3338	114	10	)	)	PUNCT
ejpam-3338	114	11	(	(	PUNCT
ejpam-3338	114	12	2018	2018	NUM
ejpam-3338	114	13	)	)	PUNCT
ejpam-3338	114	14	,	,	PUNCT
ejpam-3338	114	15	1058	1058	NUM
ejpam-3338	114	16	-	-	SYM
ejpam-3338	114	17	1099	1099	NUM
ejpam-3338	114	18	1063	1063	NUM
ejpam-3338	114	19	besides	besides	SCONJ
ejpam-3338	114	20	,	,	PUNCT
ejpam-3338	114	21	quality	quality	NOUN
ejpam-3338	114	22	of	of	ADP
ejpam-3338	114	23	a	a	DET
ejpam-3338	114	24	numerical	numerical	ADJ
ejpam-3338	114	25	solution	solution	NOUN
ejpam-3338	114	26	–	–	PUNCT
ejpam-3338	114	27	a	a	DET
ejpam-3338	114	28	must	must	NOUN
ejpam-3338	114	29	for	for	ADP
ejpam-3338	114	30	any	any	DET
ejpam-3338	114	31	engineering	engineering	NOUN
ejpam-3338	114	32	use	use	NOUN
ejpam-3338	114	33	as	as	ADP
ejpam-3338	114	34	an	an	DET
ejpam-3338	114	35	engineer	engineer	NOUN
ejpam-3338	114	36	needs	need	VERB
ejpam-3338	114	37	a	a	DET
ejpam-3338	114	38	solution	solution	NOUN
ejpam-3338	114	39	in	in	ADP
ejpam-3338	114	40	numbers	number	NOUN
ejpam-3338	114	41	not	not	PART
ejpam-3338	114	42	in	in	ADP
ejpam-3338	114	43	mathematical	mathematical	ADJ
ejpam-3338	114	44	symbols	symbol	NOUN
ejpam-3338	114	45	–	–	PUNCT
ejpam-3338	114	46	implying	imply	VERB
ejpam-3338	114	47	computational	computational	ADJ
ejpam-3338	114	48	relative	relative	ADJ
ejpam-3338	114	49	error	error	NOUN
ejpam-3338	114	50	bounds	bound	NOUN
ejpam-3338	114	51	needs	need	VERB
ejpam-3338	114	52	to	to	PART
ejpam-3338	114	53	be	be	AUX
ejpam-3338	114	54	determined	determine	VERB
ejpam-3338	114	55	.	.	PUNCT
ejpam-3338	115	1	this	this	DET
ejpam-3338	115	2	quality	quality	NOUN
ejpam-3338	115	3	(	(	PUNCT
ejpam-3338	115	4	the	the	DET
ejpam-3338	115	5	error	error	NOUN
ejpam-3338	115	6	bounds	bound	NOUN
ejpam-3338	115	7	)	)	PUNCT
ejpam-3338	115	8	allows	allow	VERB
ejpam-3338	115	9	us	we	PRON
ejpam-3338	115	10	to	to	PART
ejpam-3338	115	11	compare	compare	VERB
ejpam-3338	115	12	relative	relative	ADJ
ejpam-3338	115	13	quality	quality	NOUN
ejpam-3338	115	14	of	of	ADP
ejpam-3338	115	15	2	2	NUM
ejpam-3338	115	16	or	or	CCONJ
ejpam-3338	115	17	more	more	ADV
ejpam-3338	115	18	different	different	ADJ
ejpam-3338	115	19	algorithms	algorithm	NOUN
ejpam-3338	115	20	–	–	PUNCT
ejpam-3338	115	21	both	both	CCONJ
ejpam-3338	115	22	fractional	fractional	ADJ
ejpam-3338	115	23	and	and	CCONJ
ejpam-3338	115	24	corresponding	corresponding	ADJ
ejpam-3338	115	25	integer	integer	NOUN
ejpam-3338	115	26	order	order	NOUN
ejpam-3338	116	1	[	[	X
ejpam-3338	116	2	2	2	NUM
ejpam-3338	116	3	]	]	PUNCT
ejpam-3338	116	4	.	.	PUNCT
ejpam-3338	117	1	cost	cost	NOUN
ejpam-3338	117	2	(	(	PUNCT
ejpam-3338	117	3	computational	computational	ADJ
ejpam-3338	117	4	complexity	complexity	NOUN
ejpam-3338	117	5	)	)	PUNCT
ejpam-3338	117	6	of	of	ADP
ejpam-3338	117	7	the	the	DET
ejpam-3338	117	8	numerical	numerical	ADJ
ejpam-3338	117	9	solution	solution	NOUN
ejpam-3338	117	10	also	also	ADV
ejpam-3338	117	11	needs	need	VERB
ejpam-3338	117	12	to	to	PART
ejpam-3338	117	13	be	be	AUX
ejpam-3338	117	14	obtained	obtain	VERB
ejpam-3338	117	15	.	.	PUNCT
ejpam-3338	118	1	this	this	DET
ejpam-3338	118	2	cost	cost	NOUN
ejpam-3338	118	3	permits	permit	VERB
ejpam-3338	118	4	us	we	PRON
ejpam-3338	118	5	to	to	PART
ejpam-3338	118	6	choose	choose	VERB
ejpam-3338	118	7	that	that	DET
ejpam-3338	118	8	algorithm	algorithm	NOUN
ejpam-3338	118	9	out	out	ADP
ejpam-3338	118	10	of	of	ADP
ejpam-3338	118	11	2	2	NUM
ejpam-3338	118	12	or	or	CCONJ
ejpam-3338	118	13	more	more	ADJ
ejpam-3338	118	14	algorithms	algorithm	NOUN
ejpam-3338	118	15	,	,	PUNCT
ejpam-3338	118	16	which	which	PRON
ejpam-3338	118	17	is	be	AUX
ejpam-3338	118	18	least	least	ADV
ejpam-3338	118	19	expensive	expensive	ADJ
ejpam-3338	118	20	computationally	computationally	ADV
ejpam-3338	118	21	[	[	X
ejpam-3338	118	22	2	2	NUM
ejpam-3338	118	23	]	]	PUNCT
ejpam-3338	118	24	.	.	PUNCT
ejpam-3338	119	1	out	out	ADP
ejpam-3338	119	2	of	of	ADP
ejpam-3338	119	3	the	the	DET
ejpam-3338	119	4	foregoing	forego	VERB
ejpam-3338	119	5	2	2	NUM
ejpam-3338	119	6	parameters	parameter	NOUN
ejpam-3338	119	7	viz	viz	VERB
ejpam-3338	119	8	.	.	PUNCT
ejpam-3338	120	1	quality	quality	NOUN
ejpam-3338	120	2	and	and	CCONJ
ejpam-3338	120	3	cost	cost	NOUN
ejpam-3338	120	4	,	,	PUNCT
ejpam-3338	120	5	usually	usually	ADV
ejpam-3338	120	6	quality	quality	NOUN
ejpam-3338	120	7	is	be	AUX
ejpam-3338	120	8	more	more	ADV
ejpam-3338	120	9	important	important	ADJ
ejpam-3338	120	10	than	than	ADP
ejpam-3338	120	11	cost	cost	NOUN
ejpam-3338	120	12	since	since	SCONJ
ejpam-3338	120	13	most	most	ADJ
ejpam-3338	120	14	of	of	ADP
ejpam-3338	120	15	the	the	DET
ejpam-3338	120	16	differential	differential	ADJ
ejpam-3338	120	17	equation	equation	NOUN
ejpam-3338	120	18	models	model	NOUN
ejpam-3338	120	19	are	be	AUX
ejpam-3338	120	20	not	not	PART
ejpam-3338	120	21	too	too	ADV
ejpam-3338	120	22	large	large	ADJ
ejpam-3338	120	23	.	.	PUNCT
ejpam-3338	121	1	this	this	PRON
ejpam-3338	121	2	is	be	AUX
ejpam-3338	121	3	particularly	particularly	ADV
ejpam-3338	121	4	so	so	ADV
ejpam-3338	121	5	in	in	ADP
ejpam-3338	121	6	the	the	DET
ejpam-3338	121	7	current	current	ADJ
ejpam-3338	121	8	(	(	PUNCT
ejpam-3338	121	9	21st	21st	ADJ
ejpam-3338	121	10	century	century	NOUN
ejpam-3338	121	11	)	)	PUNCT
ejpam-3338	121	12	computational	computational	ADJ
ejpam-3338	121	13	scenario	scenario	NOUN
ejpam-3338	121	14	where	where	SCONJ
ejpam-3338	121	15	the	the	DET
ejpam-3338	121	16	computational	computational	ADJ
ejpam-3338	121	17	power	power	NOUN
ejpam-3338	121	18	has	have	AUX
ejpam-3338	121	19	reached	reach	VERB
ejpam-3338	121	20	/	/	PUNCT
ejpam-3338	121	21	crossed	cross	VERB
ejpam-3338	121	22	1018	1018	NUM
ejpam-3338	121	23	flops	flop	NOUN
ejpam-3338	121	24	(	(	PUNCT
ejpam-3338	121	25	floating	float	VERB
ejpam-3338	121	26	-	-	PUNCT
ejpam-3338	121	27	point	point	NOUN
ejpam-3338	121	28	operations	operation	NOUN
ejpam-3338	121	29	per	per	ADP
ejpam-3338	121	30	second	second	ADJ
ejpam-3338	121	31	)	)	PUNCT
ejpam-3338	121	32	.	.	PUNCT
ejpam-3338	122	1	the	the	DET
ejpam-3338	122	2	fractional	fractional	ADJ
ejpam-3338	122	3	derivative	derivative	NOUN
ejpam-3338	122	4	for	for	ADP
ejpam-3338	122	5	powers	power	NOUN
ejpam-3338	122	6	was	be	AUX
ejpam-3338	122	7	systematically	systematically	ADV
ejpam-3338	122	8	studied	study	VERB
ejpam-3338	122	9	by	by	ADP
ejpam-3338	122	10	riemann	riemann	PROPN
ejpam-3338	122	11	:	:	PUNCT
ejpam-3338	123	1	dα	dα	PROPN
ejpam-3338	123	2	dxα	dxα	ADJ
ejpam-3338	123	3	xk	xk	PROPN
ejpam-3338	123	4	=	=	PUNCT
ejpam-3338	123	5	γ(1	γ(1	PROPN
ejpam-3338	123	6	+	+	NUM
ejpam-3338	123	7	k	k	X
ejpam-3338	123	8	)	)	PUNCT
ejpam-3338	124	1	γ(1	γ(1	PROPN
ejpam-3338	125	1	+	+	CCONJ
ejpam-3338	125	2	k	k	PROPN
ejpam-3338	125	3	−	−	PROPN
ejpam-3338	125	4	α	α	NOUN
ejpam-3338	125	5	)	)	PUNCT
ejpam-3338	125	6	xk−α	xk−α	NOUN
ejpam-3338	125	7	(	(	PUNCT
ejpam-3338	125	8	15	15	NUM
ejpam-3338	125	9	)	)	PUNCT
ejpam-3338	125	10	in	in	ADP
ejpam-3338	125	11	the	the	DET
ejpam-3338	125	12	foregoing	forego	VERB
ejpam-3338	125	13	equation	equation	NOUN
ejpam-3338	125	14	,	,	PUNCT
ejpam-3338	125	15	we	we	PRON
ejpam-3338	125	16	restrict	restrict	VERB
ejpam-3338	125	17	x	x	PUNCT
ejpam-3338	125	18	≥	≥	NOUN
ejpam-3338	125	19	0	0	NUM
ejpam-3338	125	20	,	,	PUNCT
ejpam-3338	125	21	k	k	X
ejpam-3338	125	22	≥	≥	X
ejpam-3338	125	23	0	0	NUM
ejpam-3338	125	24	to	to	PART
ejpam-3338	125	25	ensure	ensure	VERB
ejpam-3338	125	26	the	the	DET
ejpam-3338	125	27	uniqueness	uniqueness	NOUN
ejpam-3338	125	28	of	of	ADP
ejpam-3338	125	29	the	the	DET
ejpam-3338	125	30	fractional	fractional	ADJ
ejpam-3338	125	31	derivative	derivative	ADJ
ejpam-3338	125	32	definition	definition	NOUN
ejpam-3338	125	33	.	.	PUNCT
ejpam-3338	126	1	the	the	DET
ejpam-3338	126	2	fractional	fractional	ADJ
ejpam-3338	126	3	derivative	derivative	NOUN
ejpam-3338	126	4	of	of	ADP
ejpam-3338	126	5	the	the	DET
ejpam-3338	126	6	exponential	exponential	ADJ
ejpam-3338	126	7	function	function	NOUN
ejpam-3338	126	8	was	be	AUX
ejpam-3338	126	9	given	give	VERB
ejpam-3338	126	10	by	by	ADP
ejpam-3338	126	11	liouville	liouville	NOUN
ejpam-3338	126	12	and	and	CCONJ
ejpam-3338	126	13	that	that	PRON
ejpam-3338	126	14	of	of	ADP
ejpam-3338	126	15	trigonometric	trigonometric	ADJ
ejpam-3338	126	16	functions	function	NOUN
ejpam-3338	126	17	was	be	AUX
ejpam-3338	126	18	proposed	propose	VERB
ejpam-3338	126	19	by	by	ADP
ejpam-3338	126	20	fourier	fourier	NOUN
ejpam-3338	126	21	.	.	PUNCT
ejpam-3338	127	1	around	around	ADV
ejpam-3338	127	2	100	100	NUM
ejpam-3338	127	3	years	year	NOUN
ejpam-3338	127	4	earlier	early	ADV
ejpam-3338	127	5	leibniz	leibniz	PROPN
ejpam-3338	127	6	and	and	CCONJ
ejpam-3338	127	7	euler	euler	PROPN
ejpam-3338	127	8	attempted	attempt	VERB
ejpam-3338	127	9	to	to	PART
ejpam-3338	127	10	solve	solve	VERB
ejpam-3338	127	11	this	this	DET
ejpam-3338	127	12	problem	problem	NOUN
ejpam-3338	127	13	of	of	ADP
ejpam-3338	127	14	fractional	fractional	ADJ
ejpam-3338	127	15	derivatives	derivative	NOUN
ejpam-3338	127	16	.	.	PUNCT
ejpam-3338	128	1	according	accord	VERB
ejpam-3338	128	2	to	to	ADP
ejpam-3338	128	3	riemanns	riemanns	ADJ
ejpam-3338	128	4	definition	definition	NOUN
ejpam-3338	128	5	,	,	PUNCT
ejpam-3338	128	6	the	the	DET
ejpam-3338	128	7	fractional	fractional	ADJ
ejpam-3338	128	8	derivative	derivative	NOUN
ejpam-3338	128	9	of	of	ADP
ejpam-3338	128	10	the	the	DET
ejpam-3338	128	11	constant	constant	ADJ
ejpam-3338	128	12	x0	x0	PROPN
ejpam-3338	128	13	is	be	AUX
ejpam-3338	128	14	given	give	VERB
ejpam-3338	128	15	by	by	ADP
ejpam-3338	128	16	dα	dα	PRON
ejpam-3338	128	17	dxα	dxα	ADJ
ejpam-3338	128	18	x0	x0	PROPN
ejpam-3338	128	19	=	=	SYM
ejpam-3338	128	20	1	1	NUM
ejpam-3338	128	21	γ(1−	γ(1−	NOUN
ejpam-3338	128	22	α	α	NUM
ejpam-3338	128	23	)	)	PUNCT
ejpam-3338	128	24	x−α	x−α	PROPN
ejpam-3338	128	25	(	(	PUNCT
ejpam-3338	128	26	16	16	NUM
ejpam-3338	128	27	)	)	PUNCT
ejpam-3338	128	28	which	which	PRON
ejpam-3338	128	29	is	be	AUX
ejpam-3338	128	30	not	not	PART
ejpam-3338	128	31	equal	equal	ADJ
ejpam-3338	128	32	to	to	ADP
ejpam-3338	128	33	0	0	NUM
ejpam-3338	128	34	,	,	PUNCT
ejpam-3338	128	35	the	the	DET
ejpam-3338	128	36	known	know	VERB
ejpam-3338	128	37	behaviour	behaviour	NOUN
ejpam-3338	128	38	in	in	ADP
ejpam-3338	128	39	the	the	DET
ejpam-3338	128	40	integer	integer	NOUN
ejpam-3338	128	41	order	order	NOUN
ejpam-3338	128	42	derivative	derivative	NOUN
ejpam-3338	128	43	.	.	PUNCT
ejpam-3338	129	1	if	if	SCONJ
ejpam-3338	129	2	α	α	PRON
ejpam-3338	129	3	=	=	NOUN
ejpam-3338	129	4	0	0	NUM
ejpam-3338	129	5	or	or	CCONJ
ejpam-3338	129	6	1	1	NUM
ejpam-3338	129	7	,	,	PUNCT
ejpam-3338	129	8	then	then	ADV
ejpam-3338	129	9	the	the	DET
ejpam-3338	129	10	riemann	riemann	PROPN
ejpam-3338	129	11	definition	definition	NOUN
ejpam-3338	129	12	is	be	AUX
ejpam-3338	129	13	compatible	compatible	ADJ
ejpam-3338	129	14	with	with	ADP
ejpam-3338	129	15	the	the	DET
ejpam-3338	129	16	conventional	conventional	ADJ
ejpam-3338	129	17	calculus	calculus	NOUN
ejpam-3338	129	18	definition	definition	NOUN
ejpam-3338	129	19	.	.	PUNCT
ejpam-3338	130	1	consequently	consequently	ADV
ejpam-3338	130	2	as	as	ADP
ejpam-3338	130	3	an	an	DET
ejpam-3338	130	4	additional	additional	ADJ
ejpam-3338	130	5	postulate	postulate	NOUN
ejpam-3338	130	6	caputo	caputo	PROPN
ejpam-3338	130	7	imposed	impose	VERB
ejpam-3338	130	8	dα	dα	PRON
ejpam-3338	130	9	dxα	dxα	ADJ
ejpam-3338	130	10	x0	x0	PROPN
ejpam-3338	130	11	=	=	SYM
ejpam-3338	130	12	0	0	PUNCT
ejpam-3338	131	1	(	(	PUNCT
ejpam-3338	131	2	17	17	NUM
ejpam-3338	131	3	)	)	PUNCT
ejpam-3338	131	4	we	we	PRON
ejpam-3338	131	5	have	have	VERB
ejpam-3338	131	6	thus	thus	ADV
ejpam-3338	131	7	4	4	NUM
ejpam-3338	131	8	different	different	ADJ
ejpam-3338	131	9	definitions	definition	NOUN
ejpam-3338	131	10	of	of	ADP
ejpam-3338	131	11	a	a	DET
ejpam-3338	131	12	fractional	fractional	ADJ
ejpam-3338	131	13	derivative	derivative	NOUN
ejpam-3338	131	14	.	.	PUNCT
ejpam-3338	132	1	the	the	DET
ejpam-3338	132	2	common	common	ADJ
ejpam-3338	132	3	aspects	aspect	NOUN
ejpam-3338	132	4	of	of	ADP
ejpam-3338	132	5	all	all	DET
ejpam-3338	132	6	these	these	DET
ejpam-3338	132	7	definitions	definition	NOUN
ejpam-3338	132	8	satisfy	satisfy	VERB
ejpam-3338	132	9	a	a	DET
ejpam-3338	132	10	correspondence	correspondence	NOUN
ejpam-3338	132	11	principle	principle	NOUN
ejpam-3338	132	12	:	:	PUNCT
ejpam-3338	132	13	limα→n	limα→n	NOUN
ejpam-3338	132	14	dα	dα	PRON
ejpam-3338	132	15	dxα	dxα	ADJ
ejpam-3338	132	16	f(x	f(x	PROPN
ejpam-3338	132	17	)	)	PUNCT
ejpam-3338	133	1	=	=	PRON
ejpam-3338	133	2	dn	dn	PROPN
ejpam-3338	133	3	dxn	dxn	VERB
ejpam-3338	133	4	f(x	f(x	PROPN
ejpam-3338	133	5	)	)	PUNCT
ejpam-3338	133	6	,	,	PUNCT
ejpam-3338	133	7	n	n	NOUN
ejpam-3338	133	8	=	=	SYM
ejpam-3338	133	9	0	0	NUM
ejpam-3338	133	10	,	,	PUNCT
ejpam-3338	133	11	1	1	NUM
ejpam-3338	133	12	,	,	PUNCT
ejpam-3338	133	13	2	2	NUM
ejpam-3338	133	14	,	,	PUNCT
ejpam-3338	133	15	...	...	PUNCT
ejpam-3338	133	16	(	(	PUNCT
ejpam-3338	133	17	18	18	NUM
ejpam-3338	133	18	)	)	PUNCT
ejpam-3338	133	19	and	and	CCONJ
ejpam-3338	133	20	the	the	DET
ejpam-3338	133	21	rules	rule	NOUN
ejpam-3338	133	22	dα	dα	PRON
ejpam-3338	133	23	dxα	dxα	ADJ
ejpam-3338	133	24	cf(x	cf(x	NOUN
ejpam-3338	133	25	)	)	PUNCT
ejpam-3338	133	26	=	=	PUNCT
ejpam-3338	134	1	c	c	X
ejpam-3338	134	2	dα	dα	PRON
ejpam-3338	134	3	dxα	dxα	ADJ
ejpam-3338	134	4	f(x	f(x	PROPN
ejpam-3338	134	5	)	)	PUNCT
ejpam-3338	134	6	(	(	PUNCT
ejpam-3338	134	7	19	19	NUM
ejpam-3338	134	8	)	)	PUNCT
ejpam-3338	134	9	dα	dα	ADJ
ejpam-3338	134	10	dxα	dxα	NOUN
ejpam-3338	134	11	[	[	X
ejpam-3338	134	12	f(x	f(x	PROPN
ejpam-3338	134	13	)	)	PUNCT
ejpam-3338	135	1	+	+	CCONJ
ejpam-3338	135	2	g(x	g(x	NOUN
ejpam-3338	135	3	)	)	PUNCT
ejpam-3338	135	4	]	]	PUNCT
ejpam-3338	136	1	=	=	SYM
ejpam-3338	136	2	dα	dα	PRON
ejpam-3338	136	3	dxα	dxα	ADJ
ejpam-3338	136	4	f(x	f(x	PROPN
ejpam-3338	136	5	)	)	PUNCT
ejpam-3338	137	1	+	+	CCONJ
ejpam-3338	137	2	dα	dα	PRON
ejpam-3338	137	3	dxα	dxα	ADJ
ejpam-3338	137	4	g(x	g(x	NOUN
ejpam-3338	137	5	)	)	PUNCT
ejpam-3338	137	6	(	(	PUNCT
ejpam-3338	137	7	20	20	NUM
ejpam-3338	137	8	)	)	PUNCT
ejpam-3338	137	9	this	this	DET
ejpam-3338	137	10	principle	principle	NOUN
ejpam-3338	137	11	and	and	CCONJ
ejpam-3338	137	12	the	the	DET
ejpam-3338	137	13	rules	rule	NOUN
ejpam-3338	137	14	need	need	VERB
ejpam-3338	137	15	to	to	PART
ejpam-3338	137	16	be	be	AUX
ejpam-3338	137	17	strictly	strictly	ADV
ejpam-3338	137	18	adhered	adhere	VERB
ejpam-3338	137	19	to	to	ADP
ejpam-3338	137	20	by	by	ADP
ejpam-3338	137	21	any	any	DET
ejpam-3338	137	22	other	other	ADJ
ejpam-3338	137	23	definition	definition	NOUN
ejpam-3338	137	24	of	of	ADP
ejpam-3338	137	25	fractional	fractional	ADJ
ejpam-3338	137	26	derivatives	derivative	NOUN
ejpam-3338	137	27	.	.	PUNCT
ejpam-3338	138	1	if	if	SCONJ
ejpam-3338	138	2	these	these	PRON
ejpam-3338	138	3	are	be	AUX
ejpam-3338	138	4	not	not	PART
ejpam-3338	138	5	adhered	adhere	VERB
ejpam-3338	138	6	to	to	ADP
ejpam-3338	138	7	by	by	ADP
ejpam-3338	138	8	a	a	DET
ejpam-3338	138	9	definition	definition	NOUN
ejpam-3338	138	10	,	,	PUNCT
ejpam-3338	138	11	then	then	ADV
ejpam-3338	138	12	such	such	DET
ejpam-3338	138	13	a	a	DET
ejpam-3338	138	14	definition	definition	NOUN
ejpam-3338	138	15	s.	s.	PROPN
ejpam-3338	138	16	k.sen	k.sen	PROPN
ejpam-3338	138	17	,	,	PUNCT
ejpam-3338	138	18	j.	j.	PROPN
ejpam-3338	138	19	v.	v.	PROPN
ejpam-3338	138	20	devi	devi	PROPN
ejpam-3338	138	21	,	,	PUNCT
ejpam-3338	138	22	r.v.g	r.v.g	NOUN
ejpam-3338	138	23	.	.	PUNCT
ejpam-3338	139	1	r.	r.	PROPN
ejpam-3338	139	2	kumar	kumar	PROPN
ejpam-3338	139	3	/	/	SYM
ejpam-3338	139	4	eur	eur	PROPN
ejpam-3338	139	5	.	.	PUNCT
ejpam-3338	140	1	j.	j.	PROPN
ejpam-3338	140	2	pure	pure	PROPN
ejpam-3338	140	3	appl	appl	PROPN
ejpam-3338	140	4	.	.	PROPN
ejpam-3338	140	5	math	math	PROPN
ejpam-3338	140	6	,	,	PUNCT
ejpam-3338	140	7	11	11	NUM
ejpam-3338	140	8	(	(	PUNCT
ejpam-3338	140	9	3	3	NUM
ejpam-3338	140	10	)	)	PUNCT
ejpam-3338	140	11	(	(	PUNCT
ejpam-3338	140	12	2018	2018	NUM
ejpam-3338	140	13	)	)	PUNCT
ejpam-3338	140	14	,	,	PUNCT
ejpam-3338	140	15	1058	1058	NUM
ejpam-3338	140	16	-	-	SYM
ejpam-3338	140	17	1099	1099	NUM
ejpam-3338	140	18	1064	1064	NUM
ejpam-3338	140	19	will	will	AUX
ejpam-3338	140	20	not	not	PART
ejpam-3338	140	21	merit	merit	VERB
ejpam-3338	140	22	in	in	ADP
ejpam-3338	140	23	the	the	DET
ejpam-3338	140	24	first	first	ADJ
ejpam-3338	140	25	place	place	NOUN
ejpam-3338	140	26	as	as	ADP
ejpam-3338	140	27	a	a	DET
ejpam-3338	140	28	possible	possible	ADJ
ejpam-3338	140	29	candidate	candidate	NOUN
ejpam-3338	140	30	for	for	ADP
ejpam-3338	140	31	an	an	DET
ejpam-3338	140	32	attempt	attempt	NOUN
ejpam-3338	140	33	of	of	ADP
ejpam-3338	140	34	fractional	fractional	ADJ
ejpam-3338	140	35	calculus	calculus	NOUN
ejpam-3338	140	36	to	to	PART
ejpam-3338	140	37	be	be	AUX
ejpam-3338	140	38	a	a	DET
ejpam-3338	140	39	generalized	generalized	ADJ
ejpam-3338	140	40	version	version	NOUN
ejpam-3338	140	41	of	of	ADP
ejpam-3338	140	42	conventional	conventional	ADJ
ejpam-3338	140	43	calculus	calculus	NOUN
ejpam-3338	140	44	.	.	PUNCT
ejpam-3338	141	1	further	far	ADV
ejpam-3338	141	2	,	,	PUNCT
ejpam-3338	141	3	we	we	PRON
ejpam-3338	141	4	can	can	AUX
ejpam-3338	141	5	define	define	VERB
ejpam-3338	141	6	,	,	PUNCT
ejpam-3338	141	7	in	in	ADP
ejpam-3338	141	8	analogy	analogy	NOUN
ejpam-3338	141	9	to	to	ADP
ejpam-3338	141	10	the	the	DET
ejpam-3338	141	11	well	well	ADV
ejpam-3338	141	12	-	-	PUNCT
ejpam-3338	141	13	known	know	VERB
ejpam-3338	141	14	taylor	taylor	PROPN
ejpam-3338	141	15	series	series	PROPN
ejpam-3338	141	16	expansion	expansion	PROPN
ejpam-3338	141	17	,	,	PUNCT
ejpam-3338	141	18	series	series	NOUN
ejpam-3338	141	19	on	on	ADP
ejpam-3338	141	20	these	these	DET
ejpam-3338	141	21	4	4	NUM
ejpam-3338	141	22	different	different	ADJ
ejpam-3338	141	23	function	function	NOUN
ejpam-3338	141	24	classes	class	NOUN
ejpam-3338	141	25	and	and	CCONJ
ejpam-3338	141	26	specify	specify	VERB
ejpam-3338	141	27	the	the	DET
ejpam-3338	141	28	corresponding	corresponding	ADJ
ejpam-3338	141	29	fractional	fractional	ADJ
ejpam-3338	141	30	derivatives	derivative	NOUN
ejpam-3338	141	31	according	accord	VERB
ejpam-3338	141	32	to	to	ADP
ejpam-3338	141	33	liouville	liouville	PROPN
ejpam-3338	141	34	,	,	PUNCT
ejpam-3338	141	35	fourier	fourier	NOUN
ejpam-3338	141	36	,	,	PUNCT
ejpam-3338	141	37	riemann	riemann	PROPN
ejpam-3338	141	38	,	,	PUNCT
ejpam-3338	141	39	and	and	CCONJ
ejpam-3338	141	40	caputo	caputo	PROPN
ejpam-3338	141	41	:	:	PUNCT
ejpam-3338	141	42	liouville	liouville	PROPN
ejpam-3338	141	43	:	:	PUNCT
ejpam-3338	141	44	if	if	SCONJ
ejpam-3338	141	45	f(x	f(x	PROPN
ejpam-3338	141	46	)	)	PUNCT
ejpam-3338	142	1	=	=	NOUN
ejpam-3338	142	2	∑∞	∑∞	NOUN
ejpam-3338	142	3	k=0	k=0	PROPN
ejpam-3338	142	4	ake	ake	NOUN
ejpam-3338	142	5	kx	kx	PROPN
ejpam-3338	142	6	,	,	PUNCT
ejpam-3338	142	7	then	then	ADV
ejpam-3338	142	8	dα	dα	DET
ejpam-3338	142	9	dxα	dxα	ADJ
ejpam-3338	142	10	f(x	f(x	PROPN
ejpam-3338	142	11	)	)	PUNCT
ejpam-3338	143	1	=	=	PUNCT
ejpam-3338	144	1	∞∑	∞∑	NUM
ejpam-3338	144	2	k=0	k=0	PROPN
ejpam-3338	144	3	akk	akk	X
ejpam-3338	144	4	αekx	αekx	NOUN
ejpam-3338	144	5	(	(	PUNCT
ejpam-3338	144	6	21	21	NUM
ejpam-3338	144	7	)	)	PUNCT
ejpam-3338	144	8	fourier	fourier	NOUN
ejpam-3338	144	9	:	:	PUNCT
ejpam-3338	144	10	if	if	SCONJ
ejpam-3338	144	11	f(x	f(x	PROPN
ejpam-3338	144	12	)	)	PUNCT
ejpam-3338	144	13	=	=	PROPN
ejpam-3338	144	14	a0	a0	PROPN
ejpam-3338	144	15	+	+	CCONJ
ejpam-3338	144	16	∑∞	∑∞	X
ejpam-3338	144	17	k=1	k=1	X
ejpam-3338	144	18	aksin(kx	aksin(kx	PROPN
ejpam-3338	144	19	)	)	PUNCT
ejpam-3338	144	20	+	+	NUM
ejpam-3338	144	21	∑∞	∑∞	X
ejpam-3338	144	22	k=1	k=1	X
ejpam-3338	144	23	bkcos(kx	bkcos(kx	PROPN
ejpam-3338	144	24	)	)	PUNCT
ejpam-3338	144	25	,	,	PUNCT
ejpam-3338	144	26	then	then	ADV
ejpam-3338	144	27	dα	dα	DET
ejpam-3338	144	28	dxα	dxα	ADJ
ejpam-3338	144	29	f(x	f(x	PROPN
ejpam-3338	144	30	)	)	PUNCT
ejpam-3338	144	31	=	=	PUNCT
ejpam-3338	145	1	∞∑	∞∑	NUM
ejpam-3338	145	2	k=1	k=1	NOUN
ejpam-3338	145	3	akk	akk	VERB
ejpam-3338	145	4	αsin(kx+	αsin(kx+	PROPN
ejpam-3338	145	5	πα	πα	VERB
ejpam-3338	145	6	2	2	NUM
ejpam-3338	145	7	)	)	PUNCT
ejpam-3338	146	1	+	+	CCONJ
ejpam-3338	146	2	∞∑	∞∑	NUM
ejpam-3338	146	3	k=1	k=1	PROPN
ejpam-3338	146	4	bkcos(kx+	bkcos(kx+	NOUN
ejpam-3338	146	5	πα	πα	ADP
ejpam-3338	146	6	2	2	NUM
ejpam-3338	146	7	)	)	PUNCT
ejpam-3338	146	8	(	(	PUNCT
ejpam-3338	146	9	22	22	NUM
ejpam-3338	146	10	)	)	PUNCT
ejpam-3338	146	11	riemann	riemann	PROPN
ejpam-3338	146	12	:	:	PUNCT
ejpam-3338	146	13	if	if	SCONJ
ejpam-3338	146	14	f(x	f(x	PROPN
ejpam-3338	146	15	)	)	PUNCT
ejpam-3338	147	1	=	=	NOUN
ejpam-3338	147	2	∑∞	∑∞	NOUN
ejpam-3338	147	3	k=0	k=0	PUNCT
ejpam-3338	147	4	akx	akx	VERB
ejpam-3338	147	5	kα	kα	PROPN
ejpam-3338	147	6	,	,	PUNCT
ejpam-3338	147	7	then	then	ADV
ejpam-3338	147	8	dα	dα	DET
ejpam-3338	147	9	dxα	dxα	ADJ
ejpam-3338	147	10	f(x	f(x	PROPN
ejpam-3338	147	11	)	)	PUNCT
ejpam-3338	147	12	=	=	PUNCT
ejpam-3338	148	1	∞∑	∞∑	DET
ejpam-3338	148	2	k=0	k=0	PROPN
ejpam-3338	148	3	ak+1	ak+1	VERB
ejpam-3338	148	4	γ((k	γ((k	NOUN
ejpam-3338	148	5	+	+	NUM
ejpam-3338	148	6	2)α	2)α	NUM
ejpam-3338	148	7	)	)	PUNCT
ejpam-3338	148	8	γ((k	γ((k	NOUN
ejpam-3338	149	1	+	+	CCONJ
ejpam-3338	149	2	1)α	1)α	NUM
ejpam-3338	149	3	)	)	PUNCT
ejpam-3338	149	4	xkα	xkα	NOUN
ejpam-3338	150	1	(	(	PUNCT
ejpam-3338	150	2	23	23	NUM
ejpam-3338	150	3	)	)	PUNCT
ejpam-3338	150	4	caputo	caputo	NOUN
ejpam-3338	150	5	:	:	PUNCT
ejpam-3338	150	6	if	if	SCONJ
ejpam-3338	150	7	f(x	f(x	PROPN
ejpam-3338	150	8	)	)	PUNCT
ejpam-3338	150	9	=	=	NOUN
ejpam-3338	151	1	∑∞	∑∞	NOUN
ejpam-3338	151	2	k=0	k=0	PUNCT
ejpam-3338	151	3	akx	akx	VERB
ejpam-3338	151	4	kα	kα	PROPN
ejpam-3338	151	5	,	,	PUNCT
ejpam-3338	151	6	then	then	ADV
ejpam-3338	151	7	dα	dα	DET
ejpam-3338	151	8	dxα	dxα	ADJ
ejpam-3338	151	9	f(x	f(x	PROPN
ejpam-3338	151	10	)	)	PUNCT
ejpam-3338	151	11	=	=	PUNCT
ejpam-3338	152	1	∞∑	∞∑	DET
ejpam-3338	152	2	k=0	k=0	ADV
ejpam-3338	152	3	ak+1	ak+1	VERB
ejpam-3338	152	4	γ(1	γ(1	PROPN
ejpam-3338	153	1	+	+	CCONJ
ejpam-3338	154	1	(	(	PUNCT
ejpam-3338	154	2	k	k	X
ejpam-3338	154	3	+	+	PROPN
ejpam-3338	154	4	1)α	1)α	NUM
ejpam-3338	154	5	)	)	PUNCT
ejpam-3338	155	1	γ(1	γ(1	NOUN
ejpam-3338	155	2	+	+	CCONJ
ejpam-3338	155	3	kα	kα	X
ejpam-3338	155	4	)	)	PUNCT
ejpam-3338	155	5	xkα	xkα	PROPN
ejpam-3338	156	1	(	(	PUNCT
ejpam-3338	156	2	24	24	NUM
ejpam-3338	156	3	)	)	PUNCT
ejpam-3338	156	4	by	by	ADP
ejpam-3338	156	5	considering	consider	VERB
ejpam-3338	156	6	the	the	DET
ejpam-3338	156	7	foregoing	forego	VERB
ejpam-3338	156	8	infinite	infinite	ADJ
ejpam-3338	156	9	series	series	NOUN
ejpam-3338	156	10	/	/	SYM
ejpam-3338	156	11	exponential	exponential	NOUN
ejpam-3338	156	12	functions	function	NOUN
ejpam-3338	156	13	.	.	PUNCT
ejpam-3338	157	1	are	be	AUX
ejpam-3338	157	2	these	these	PRON
ejpam-3338	157	3	4	4	NUM
ejpam-3338	157	4	definitions	definition	NOUN
ejpam-3338	157	5	equivalent	equivalent	ADJ
ejpam-3338	157	6	?	?	PUNCT
ejpam-3338	158	1	the	the	DET
ejpam-3338	158	2	answer	answer	NOUN
ejpam-3338	158	3	is	be	AUX
ejpam-3338	158	4	no	no	PRON
ejpam-3338	158	5	.	.	PUNCT
ejpam-3338	159	1	this	this	PRON
ejpam-3338	159	2	can	can	AUX
ejpam-3338	159	3	be	be	AUX
ejpam-3338	159	4	demonstrated	demonstrate	VERB
ejpam-3338	159	5	by	by	ADP
ejpam-3338	159	6	considering	consider	VERB
ejpam-3338	159	7	the	the	DET
ejpam-3338	159	8	exponential	exponential	ADJ
ejpam-3338	159	9	function	function	NOUN
ejpam-3338	159	10	f(x	f(x	PROPN
ejpam-3338	159	11	)	)	PUNCT
ejpam-3338	160	1	=	=	X
ejpam-3338	160	2	ex	ex	X
ejpam-3338	160	3	as	as	ADP
ejpam-3338	160	4	an	an	DET
ejpam-3338	160	5	example	example	NOUN
ejpam-3338	160	6	.	.	PUNCT
ejpam-3338	161	1	according	accord	VERB
ejpam-3338	161	2	to	to	ADP
ejpam-3338	161	3	caputo	caputo	PROPN
ejpam-3338	161	4	dα	dα	PRON
ejpam-3338	161	5	dxα	dxα	ADJ
ejpam-3338	161	6	f(x	f(x	PROPN
ejpam-3338	161	7	)	)	PUNCT
ejpam-3338	162	1	=	=	X
ejpam-3338	163	1	∞∑	∞∑	NUM
ejpam-3338	163	2	n=1	n=1	PROPN
ejpam-3338	163	3	xn−α	xn−α	PROPN
ejpam-3338	163	4	γ(1	γ(1	PROPN
ejpam-3338	163	5	+	+	CCONJ
ejpam-3338	163	6	n+	n+	NUM
ejpam-3338	163	7	α	α	NOUN
ejpam-3338	163	8	)	)	PUNCT
ejpam-3338	163	9	=	=	SYM
ejpam-3338	164	1	x1−α	x1−α	PROPN
ejpam-3338	164	2	e(1	e(1	PROPN
ejpam-3338	164	3	,	,	PUNCT
ejpam-3338	164	4	2−	2−	NUM
ejpam-3338	164	5	α	α	NOUN
ejpam-3338	164	6	,	,	PUNCT
ejpam-3338	164	7	x	x	NOUN
ejpam-3338	164	8	)	)	PUNCT
ejpam-3338	164	9	(	(	PUNCT
ejpam-3338	164	10	25	25	NUM
ejpam-3338	164	11	)	)	PUNCT
ejpam-3338	164	12	where	where	SCONJ
ejpam-3338	164	13	e(1	e(1	PROPN
ejpam-3338	164	14	,	,	PUNCT
ejpam-3338	164	15	2−α	2−α	NUM
ejpam-3338	164	16	,	,	PUNCT
ejpam-3338	164	17	x	x	X
ejpam-3338	164	18	)	)	PUNCT
ejpam-3338	164	19	is	be	AUX
ejpam-3338	164	20	a	a	DET
ejpam-3338	164	21	generalized	generalized	ADJ
ejpam-3338	164	22	mittag	mittag	ADJ
ejpam-3338	164	23	-	-	PUNCT
ejpam-3338	164	24	leffler	leffler	NOUN
ejpam-3338	164	25	function	function	NOUN
ejpam-3338	164	26	and	and	CCONJ
ejpam-3338	164	27	evidently	evidently	ADV
ejpam-3338	164	28	not	not	PART
ejpam-3338	164	29	an	an	DET
ejpam-3338	164	30	exponential	exponential	ADJ
ejpam-3338	164	31	function	function	NOUN
ejpam-3338	164	32	any	any	PRON
ejpam-3338	164	33	more	more	ADV
ejpam-3338	164	34	.	.	PUNCT
ejpam-3338	165	1	this	this	PRON
ejpam-3338	165	2	is	be	AUX
ejpam-3338	165	3	in	in	ADP
ejpam-3338	165	4	contrast	contrast	NOUN
ejpam-3338	165	5	to	to	ADP
ejpam-3338	165	6	louvilles	louville	NOUN
ejpam-3338	165	7	definition	definition	NOUN
ejpam-3338	165	8	.	.	PUNCT
ejpam-3338	166	1	the	the	DET
ejpam-3338	166	2	non	non	NOUN
ejpam-3338	166	3	-	-	NOUN
ejpam-3338	166	4	equivalence	equivalence	NOUN
ejpam-3338	166	5	of	of	ADP
ejpam-3338	166	6	these	these	DET
ejpam-3338	166	7	definitions	definition	NOUN
ejpam-3338	166	8	is	be	AUX
ejpam-3338	166	9	disturbing	disturbing	ADJ
ejpam-3338	166	10	and	and	CCONJ
ejpam-3338	166	11	an	an	DET
ejpam-3338	166	12	obstacle	obstacle	NOUN
ejpam-3338	166	13	to	to	ADP
ejpam-3338	166	14	the	the	DET
ejpam-3338	166	15	attempt	attempt	NOUN
ejpam-3338	166	16	of	of	ADP
ejpam-3338	166	17	making	make	VERB
ejpam-3338	166	18	fractional	fractional	ADJ
ejpam-3338	166	19	derivatives	derivative	NOUN
ejpam-3338	166	20	a	a	DET
ejpam-3338	166	21	generalized	generalized	ADJ
ejpam-3338	166	22	version	version	NOUN
ejpam-3338	166	23	of	of	ADP
ejpam-3338	166	24	classical	classical	ADJ
ejpam-3338	166	25	derivatives	derivative	NOUN
ejpam-3338	166	26	.	.	PUNCT
ejpam-3338	167	1	however	however	ADV
ejpam-3338	167	2	,	,	PUNCT
ejpam-3338	167	3	not	not	PART
ejpam-3338	167	4	only	only	ADV
ejpam-3338	167	5	such	such	DET
ejpam-3338	167	6	an	an	DET
ejpam-3338	167	7	obstacle	obstacle	NOUN
ejpam-3338	167	8	but	but	CCONJ
ejpam-3338	167	9	also	also	ADV
ejpam-3338	167	10	other	other	ADJ
ejpam-3338	167	11	obstacles	obstacle	NOUN
ejpam-3338	167	12	that	that	PRON
ejpam-3338	167	13	we	we	PRON
ejpam-3338	167	14	could	could	AUX
ejpam-3338	167	15	encounter	encounter	VERB
ejpam-3338	167	16	for	for	ADP
ejpam-3338	167	17	some	some	DET
ejpam-3338	167	18	function	function	NOUN
ejpam-3338	167	19	or	or	CCONJ
ejpam-3338	167	20	the	the	DET
ejpam-3338	167	21	other	other	ADJ
ejpam-3338	167	22	need	need	NOUN
ejpam-3338	167	23	to	to	PART
ejpam-3338	167	24	be	be	AUX
ejpam-3338	167	25	overcome	overcome	VERB
ejpam-3338	167	26	by	by	ADP
ejpam-3338	167	27	more	more	ADV
ejpam-3338	167	28	appropriately	appropriately	ADV
ejpam-3338	167	29	defining	define	VERB
ejpam-3338	167	30	the	the	DET
ejpam-3338	167	31	fractional	fractional	ADJ
ejpam-3338	167	32	derivatives	derivative	NOUN
ejpam-3338	167	33	.	.	PUNCT
ejpam-3338	168	1	once	once	ADV
ejpam-3338	168	2	a	a	DET
ejpam-3338	168	3	generalization	generalization	NOUN
ejpam-3338	168	4	compatible	compatible	ADJ
ejpam-3338	168	5	with	with	ADP
ejpam-3338	168	6	the	the	DET
ejpam-3338	168	7	concerned	concerned	ADJ
ejpam-3338	168	8	physical	physical	ADJ
ejpam-3338	168	9	problems	problem	NOUN
ejpam-3338	168	10	is	be	AUX
ejpam-3338	168	11	achieved	achieve	VERB
ejpam-3338	168	12	,	,	PUNCT
ejpam-3338	168	13	the	the	DET
ejpam-3338	168	14	fractional	fractional	ADJ
ejpam-3338	168	15	calculus	calculus	NOUN
ejpam-3338	168	16	will	will	AUX
ejpam-3338	168	17	be	be	AUX
ejpam-3338	168	18	a	a	DET
ejpam-3338	168	19	part	part	NOUN
ejpam-3338	168	20	of	of	ADP
ejpam-3338	168	21	the	the	DET
ejpam-3338	168	22	regular	regular	ADJ
ejpam-3338	168	23	university	university	NOUN
ejpam-3338	168	24	curriculum	curriculum	NOUN
ejpam-3338	168	25	for	for	ADP
ejpam-3338	168	26	the	the	DET
ejpam-3338	168	27	students	student	NOUN
ejpam-3338	168	28	.	.	PUNCT
ejpam-3338	169	1	there	there	PRON
ejpam-3338	169	2	could	could	AUX
ejpam-3338	169	3	be	be	AUX
ejpam-3338	169	4	many	many	ADJ
ejpam-3338	169	5	problems	problem	NOUN
ejpam-3338	169	6	from	from	ADP
ejpam-3338	169	7	physics	physics	NOUN
ejpam-3338	169	8	which	which	PRON
ejpam-3338	169	9	might	might	AUX
ejpam-3338	169	10	be	be	AUX
ejpam-3338	169	11	beneficially	beneficially	ADV
ejpam-3338	169	12	numerically	numerically	ADV
ejpam-3338	169	13	solved	solve	VERB
ejpam-3338	169	14	using	use	VERB
ejpam-3338	169	15	an	an	DET
ejpam-3338	169	16	appropriate	appropriate	ADJ
ejpam-3338	169	17	mathematical	mathematical	ADJ
ejpam-3338	169	18	model	model	NOUN
ejpam-3338	169	19	based	base	VERB
ejpam-3338	169	20	on	on	ADP
ejpam-3338	169	21	fractional	fractional	ADJ
ejpam-3338	169	22	differential	differential	ADJ
ejpam-3338	169	23	equations	equation	NOUN
ejpam-3338	169	24	.	.	PUNCT
ejpam-3338	170	1	but	but	CCONJ
ejpam-3338	170	2	this	this	PRON
ejpam-3338	170	3	may	may	AUX
ejpam-3338	170	4	not	not	PART
ejpam-3338	170	5	have	have	VERB
ejpam-3338	170	6	direct	direct	ADJ
ejpam-3338	170	7	connection	connection	NOUN
ejpam-3338	170	8	to	to	ADP
ejpam-3338	170	9	the	the	DET
ejpam-3338	170	10	generalized	generalized	ADJ
ejpam-3338	170	11	version	version	NOUN
ejpam-3338	170	12	of	of	ADP
ejpam-3338	170	13	the	the	DET
ejpam-3338	170	14	calculus	calculus	NOUN
ejpam-3338	170	15	.	.	PUNCT
ejpam-3338	171	1	s.	s.	PROPN
ejpam-3338	171	2	k.sen	k.sen	PROPN
ejpam-3338	171	3	,	,	PUNCT
ejpam-3338	171	4	j.	j.	PROPN
ejpam-3338	171	5	v.	v.	PROPN
ejpam-3338	171	6	devi	devi	PROPN
ejpam-3338	171	7	,	,	PUNCT
ejpam-3338	171	8	r.v.g	r.v.g	NOUN
ejpam-3338	171	9	.	.	PUNCT
ejpam-3338	172	1	r.	r.	PROPN
ejpam-3338	172	2	kumar	kumar	PROPN
ejpam-3338	172	3	/	/	SYM
ejpam-3338	172	4	eur	eur	PROPN
ejpam-3338	172	5	.	.	PUNCT
ejpam-3338	173	1	j.	j.	PROPN
ejpam-3338	173	2	pure	pure	PROPN
ejpam-3338	173	3	appl	appl	PROPN
ejpam-3338	173	4	.	.	PROPN
ejpam-3338	173	5	math	math	PROPN
ejpam-3338	173	6	,	,	PUNCT
ejpam-3338	173	7	11	11	NUM
ejpam-3338	173	8	(	(	PUNCT
ejpam-3338	173	9	3	3	NUM
ejpam-3338	173	10	)	)	PUNCT
ejpam-3338	173	11	(	(	PUNCT
ejpam-3338	173	12	2018	2018	NUM
ejpam-3338	173	13	)	)	PUNCT
ejpam-3338	173	14	,	,	PUNCT
ejpam-3338	173	15	1058	1058	NUM
ejpam-3338	173	16	-	-	SYM
ejpam-3338	173	17	1099	1099	NUM
ejpam-3338	173	18	1065	1065	NUM
ejpam-3338	173	19	if	if	SCONJ
ejpam-3338	173	20	a	a	DET
ejpam-3338	173	21	physical	physical	ADJ
ejpam-3338	173	22	frictional	frictional	ADJ
ejpam-3338	173	23	model	model	NOUN
ejpam-3338	173	24	can	can	AUX
ejpam-3338	173	25	be	be	AUX
ejpam-3338	173	26	readily	readily	ADV
ejpam-3338	173	27	converted	convert	VERB
ejpam-3338	173	28	to	to	ADP
ejpam-3338	173	29	a	a	DET
ejpam-3338	173	30	non	non	ADJ
ejpam-3338	173	31	-	-	ADJ
ejpam-3338	173	32	integer	integer	ADJ
ejpam-3338	173	33	fractional	fractional	ADJ
ejpam-3338	173	34	differential	differential	NOUN
ejpam-3338	173	35	equation	equation	NOUN
ejpam-3338	173	36	model	model	NOUN
ejpam-3338	173	37	and	and	CCONJ
ejpam-3338	173	38	vice	vice	NOUN
ejpam-3338	173	39	versa	versa	ADV
ejpam-3338	173	40	exactly	exactly	ADV
ejpam-3338	173	41	in	in	ADP
ejpam-3338	173	42	the	the	DET
ejpam-3338	173	43	same	same	ADJ
ejpam-3338	173	44	way	way	NOUN
ejpam-3338	173	45	as	as	SCONJ
ejpam-3338	173	46	we	we	PRON
ejpam-3338	173	47	could	could	AUX
ejpam-3338	173	48	do	do	VERB
ejpam-3338	173	49	for	for	ADP
ejpam-3338	173	50	integerorder	integerorder	NOUN
ejpam-3338	173	51	differential	differential	PROPN
ejpam-3338	173	52	equation	equation	NOUN
ejpam-3338	173	53	model	model	NOUN
ejpam-3338	173	54	,	,	PUNCT
ejpam-3338	173	55	then	then	ADV
ejpam-3338	173	56	it	it	PRON
ejpam-3338	173	57	would	would	AUX
ejpam-3338	173	58	be	be	AUX
ejpam-3338	173	59	a	a	DET
ejpam-3338	173	60	break	break	NOUN
ejpam-3338	173	61	-	-	PUNCT
ejpam-3338	173	62	through	through	NOUN
ejpam-3338	173	63	in	in	ADP
ejpam-3338	173	64	the	the	DET
ejpam-3338	173	65	process	process	NOUN
ejpam-3338	173	66	of	of	ADP
ejpam-3338	173	67	achieving	achieve	VERB
ejpam-3338	173	68	the	the	DET
ejpam-3338	173	69	desired	desire	VERB
ejpam-3338	173	70	generalization	generalization	NOUN
ejpam-3338	173	71	.	.	PUNCT
ejpam-3338	174	1	the	the	DET
ejpam-3338	174	2	unique	unique	ADJ
ejpam-3338	174	3	generalized	generalized	ADJ
ejpam-3338	174	4	matrix	matrix	NOUN
ejpam-3338	174	5	inverse	inverse	NOUN
ejpam-3338	174	6	(	(	PUNCT
ejpam-3338	174	7	viz	viz	PROPN
ejpam-3338	174	8	.	.	PUNCT
ejpam-3338	175	1	the	the	DET
ejpam-3338	175	2	moore	moore	PROPN
ejpam-3338	175	3	-	-	PUNCT
ejpam-3338	175	4	penrose	penrose	PROPN
ejpam-3338	175	5	matrix	matrix	NOUN
ejpam-3338	175	6	inverse	inverse	NOUN
ejpam-3338	175	7	also	also	ADV
ejpam-3338	175	8	known	know	VERB
ejpam-3338	175	9	as	as	ADP
ejpam-3338	175	10	the	the	DET
ejpam-3338	175	11	minimum	minimum	ADJ
ejpam-3338	175	12	-	-	PUNCT
ejpam-3338	175	13	norm	norm	NOUN
ejpam-3338	175	14	least	least	ADJ
ejpam-3338	175	15	-	-	PUNCT
ejpam-3338	175	16	squares	square	NOUN
ejpam-3338	175	17	inverse	inverse	NOUN
ejpam-3338	175	18	of	of	ADP
ejpam-3338	175	19	the	the	DET
ejpam-3338	175	20	matrix	matrix	NOUN
ejpam-3338	175	21	or	or	CCONJ
ejpam-3338	175	22	as	as	ADP
ejpam-3338	175	23	the	the	DET
ejpam-3338	175	24	pseudo	pseudo	NOUN
ejpam-3338	175	25	-	-	NOUN
ejpam-3338	175	26	inverse	inverse	NOUN
ejpam-3338	175	27	of	of	ADP
ejpam-3338	175	28	the	the	DET
ejpam-3338	175	29	matrix	matrix	NOUN
ejpam-3338	175	30	)	)	PUNCT
ejpam-3338	175	31	out	out	ADP
ejpam-3338	175	32	of	of	ADP
ejpam-3338	175	33	the	the	DET
ejpam-3338	175	34	possible	possible	ADJ
ejpam-3338	175	35	infinity	infinity	NOUN
ejpam-3338	175	36	of	of	ADP
ejpam-3338	175	37	generalized	generalized	ADJ
ejpam-3338	175	38	inverses	inverse	NOUN
ejpam-3338	175	39	of	of	ADP
ejpam-3338	175	40	a	a	DET
ejpam-3338	175	41	matrix	matrix	NOUN
ejpam-3338	175	42	has	have	AUX
ejpam-3338	175	43	been	be	AUX
ejpam-3338	175	44	beautifully	beautifully	ADV
ejpam-3338	175	45	integrated	integrate	VERB
ejpam-3338	175	46	and	and	CCONJ
ejpam-3338	175	47	merged	merge	VERB
ejpam-3338	175	48	with	with	ADP
ejpam-3338	175	49	the	the	DET
ejpam-3338	175	50	true	true	ADJ
ejpam-3338	175	51	matrix	matrix	NOUN
ejpam-3338	175	52	inverse	inverse	NOUN
ejpam-3338	175	53	during	during	ADP
ejpam-3338	175	54	1950	1950	NUM
ejpam-3338	175	55	-	-	SYM
ejpam-3338	175	56	1970s	1970s	NUM
ejpam-3338	175	57	.	.	PUNCT
ejpam-3338	176	1	this	this	DET
ejpam-3338	176	2	integration	integration	NOUN
ejpam-3338	176	3	is	be	AUX
ejpam-3338	176	4	included	include	VERB
ejpam-3338	176	5	in	in	ADP
ejpam-3338	176	6	all	all	DET
ejpam-3338	176	7	university	university	NOUN
ejpam-3338	176	8	science	science	NOUN
ejpam-3338	176	9	and	and	CCONJ
ejpam-3338	176	10	engineering	engineering	NOUN
ejpam-3338	176	11	curricula	curricula	NOUN
ejpam-3338	176	12	.	.	PUNCT
ejpam-3338	177	1	the	the	DET
ejpam-3338	177	2	pseudo	pseudo	NOUN
ejpam-3338	177	3	-	-	NOUN
ejpam-3338	177	4	inverse	inverse	ADJ
ejpam-3338	177	5	[	[	X
ejpam-3338	177	6	3	3	NUM
ejpam-3338	177	7	]	]	PUNCT
ejpam-3338	177	8	(	(	PUNCT
ejpam-3338	177	9	the	the	DET
ejpam-3338	177	10	term	term	NOUN
ejpam-3338	177	11	is	be	AUX
ejpam-3338	177	12	coined	coin	VERB
ejpam-3338	177	13	by	by	ADP
ejpam-3338	177	14	gene	gene	PROPN
ejpam-3338	177	15	h.	h.	PROPN
ejpam-3338	177	16	golub	golub	PROPN
ejpam-3338	177	17	of	of	ADP
ejpam-3338	177	18	stanford	stanford	PROPN
ejpam-3338	177	19	university	university	PROPN
ejpam-3338	177	20	and	and	CCONJ
ejpam-3338	177	21	is	be	AUX
ejpam-3338	177	22	used	use	VERB
ejpam-3338	177	23	widely	widely	ADV
ejpam-3338	177	24	)	)	PUNCT
ejpam-3338	177	25	of	of	ADP
ejpam-3338	177	26	any	any	DET
ejpam-3338	177	27	matrix	matrix	NOUN
ejpam-3338	177	28	square	square	NOUN
ejpam-3338	177	29	,	,	PUNCT
ejpam-3338	177	30	non	non	ADJ
ejpam-3338	177	31	-	-	ADJ
ejpam-3338	177	32	square	square	ADJ
ejpam-3338	177	33	rectangular	rectangular	ADJ
ejpam-3338	177	34	,	,	PUNCT
ejpam-3338	177	35	and	and	CCONJ
ejpam-3338	177	36	singular	singular	ADJ
ejpam-3338	177	37	–	–	PUNCT
ejpam-3338	177	38	is	be	AUX
ejpam-3338	177	39	unique	unique	ADJ
ejpam-3338	177	40	and	and	CCONJ
ejpam-3338	177	41	always	always	ADV
ejpam-3338	177	42	exists	exist	VERB
ejpam-3338	177	43	unlike	unlike	ADP
ejpam-3338	177	44	the	the	DET
ejpam-3338	177	45	true	true	ADJ
ejpam-3338	177	46	inverse	inverse	NOUN
ejpam-3338	177	47	that	that	PRON
ejpam-3338	177	48	exists	exist	VERB
ejpam-3338	177	49	only	only	ADV
ejpam-3338	177	50	for	for	ADP
ejpam-3338	177	51	non	non	ADJ
ejpam-3338	177	52	-	-	ADJ
ejpam-3338	177	53	singular	singular	ADJ
ejpam-3338	177	54	(	(	PUNCT
ejpam-3338	177	55	necessarily	necessarily	ADV
ejpam-3338	177	56	square	square	ADJ
ejpam-3338	177	57	)	)	PUNCT
ejpam-3338	177	58	matrices	matrix	NOUN
ejpam-3338	177	59	.	.	PUNCT
ejpam-3338	178	1	the	the	DET
ejpam-3338	178	2	pseudo	pseudo	NOUN
ejpam-3338	178	3	-	-	NOUN
ejpam-3338	178	4	inverse	inverse	NOUN
ejpam-3338	178	5	is	be	AUX
ejpam-3338	178	6	meant	mean	VERB
ejpam-3338	178	7	for	for	ADP
ejpam-3338	178	8	solving	solve	VERB
ejpam-3338	178	9	non	non	ADJ
ejpam-3338	178	10	-	-	ADJ
ejpam-3338	178	11	square	square	ADJ
ejpam-3338	178	12	rectangular	rectangular	NOUN
ejpam-3338	178	13	as	as	ADV
ejpam-3338	178	14	well	well	ADV
ejpam-3338	178	15	as	as	ADP
ejpam-3338	178	16	square	square	ADJ
ejpam-3338	178	17	linear	linear	NOUN
ejpam-3338	178	18	systems	system	NOUN
ejpam-3338	178	19	and	and	CCONJ
ejpam-3338	178	20	is	be	AUX
ejpam-3338	178	21	extensively	extensively	ADV
ejpam-3338	178	22	used	use	VERB
ejpam-3338	178	23	in	in	ADP
ejpam-3338	178	24	science	science	NOUN
ejpam-3338	178	25	and	and	CCONJ
ejpam-3338	178	26	engineering	engineering	NOUN
ejpam-3338	178	27	applications	application	NOUN
ejpam-3338	178	28	.	.	PUNCT
ejpam-3338	179	1	the	the	DET
ejpam-3338	179	2	pseudo	pseudo	NOUN
ejpam-3338	179	3	-	-	NOUN
ejpam-3338	179	4	inverse	inverse	NOUN
ejpam-3338	179	5	is	be	AUX
ejpam-3338	179	6	non	non	ADJ
ejpam-3338	179	7	-	-	ADJ
ejpam-3338	179	8	redundant	redundant	ADJ
ejpam-3338	179	9	in	in	ADP
ejpam-3338	179	10	the	the	DET
ejpam-3338	179	11	sense	sense	NOUN
ejpam-3338	179	12	that	that	SCONJ
ejpam-3338	179	13	the	the	DET
ejpam-3338	179	14	true	true	ADJ
ejpam-3338	179	15	inverse	inverse	NOUN
ejpam-3338	179	16	can	can	AUX
ejpam-3338	179	17	not	not	PART
ejpam-3338	179	18	take	take	VERB
ejpam-3338	179	19	the	the	DET
ejpam-3338	179	20	place	place	NOUN
ejpam-3338	179	21	of	of	ADP
ejpam-3338	179	22	the	the	DET
ejpam-3338	179	23	pseudo	pseudo	NOUN
ejpam-3338	179	24	-	-	NOUN
ejpam-3338	179	25	inverse	inverse	NOUN
ejpam-3338	179	26	for	for	ADP
ejpam-3338	179	27	solving	solve	VERB
ejpam-3338	179	28	linear	linear	ADJ
ejpam-3338	179	29	equations	equation	NOUN
ejpam-3338	179	30	including	include	VERB
ejpam-3338	179	31	inconsistent	inconsistent	ADJ
ejpam-3338	179	32	equations	equation	NOUN
ejpam-3338	179	33	(	(	PUNCT
ejpam-3338	179	34	for	for	ADP
ejpam-3338	179	35	inconsistent	inconsistent	ADJ
ejpam-3338	179	36	systems	system	NOUN
ejpam-3338	179	37	,	,	PUNCT
ejpam-3338	179	38	the	the	DET
ejpam-3338	179	39	minimum	minimum	ADJ
ejpam-3338	179	40	-	-	PUNCT
ejpam-3338	179	41	norm	norm	NOUN
ejpam-3338	179	42	least	least	ADJ
ejpam-3338	179	43	-	-	PUNCT
ejpam-3338	179	44	squares	square	NOUN
ejpam-3338	179	45	solution	solution	NOUN
ejpam-3338	179	46	is	be	AUX
ejpam-3338	179	47	obtained	obtain	VERB
ejpam-3338	179	48	and	and	CCONJ
ejpam-3338	179	49	is	be	AUX
ejpam-3338	179	50	used	use	VERB
ejpam-3338	179	51	and	and	CCONJ
ejpam-3338	179	52	this	this	DET
ejpam-3338	179	53	solution	solution	NOUN
ejpam-3338	179	54	is	be	AUX
ejpam-3338	179	55	of	of	ADP
ejpam-3338	179	56	paramount	paramount	ADJ
ejpam-3338	179	57	importance	importance	NOUN
ejpam-3338	179	58	in	in	ADP
ejpam-3338	179	59	all	all	DET
ejpam-3338	179	60	our	our	PRON
ejpam-3338	179	61	concerned	concerned	ADJ
ejpam-3338	179	62	physical	physical	ADJ
ejpam-3338	179	63	problems	problem	NOUN
ejpam-3338	179	64	numerically	numerically	ADV
ejpam-3338	179	65	)	)	PUNCT
ejpam-3338	179	66	.	.	PUNCT
ejpam-3338	180	1	if	if	SCONJ
ejpam-3338	180	2	the	the	DET
ejpam-3338	180	3	matrix	matrix	NOUN
ejpam-3338	180	4	is	be	AUX
ejpam-3338	180	5	non	non	ADJ
ejpam-3338	180	6	-	-	ADJ
ejpam-3338	180	7	singular	singular	ADJ
ejpam-3338	180	8	then	then	ADV
ejpam-3338	180	9	the	the	DET
ejpam-3338	180	10	pseudo	pseudo	NOUN
ejpam-3338	180	11	-	-	NOUN
ejpam-3338	180	12	inverse	inverse	NOUN
ejpam-3338	180	13	is	be	AUX
ejpam-3338	180	14	the	the	DET
ejpam-3338	180	15	true	true	ADJ
ejpam-3338	180	16	inverse	inverse	NOUN
ejpam-3338	180	17	of	of	ADP
ejpam-3338	180	18	the	the	DET
ejpam-3338	180	19	matrix	matrix	NOUN
ejpam-3338	180	20	.	.	PUNCT
ejpam-3338	181	1	in	in	ADP
ejpam-3338	181	2	a	a	DET
ejpam-3338	181	3	linear	linear	ADJ
ejpam-3338	181	4	consistent	consistent	ADJ
ejpam-3338	181	5	system	system	NOUN
ejpam-3338	181	6	if	if	SCONJ
ejpam-3338	181	7	the	the	DET
ejpam-3338	181	8	matrix	matrix	NOUN
ejpam-3338	181	9	is	be	AUX
ejpam-3338	181	10	near	near	ADV
ejpam-3338	181	11	-	-	PUNCT
ejpam-3338	181	12	singular	singular	ADJ
ejpam-3338	181	13	then	then	ADV
ejpam-3338	181	14	computational	computational	ADJ
ejpam-3338	181	15	error	error	NOUN
ejpam-3338	181	16	creeps	creep	NOUN
ejpam-3338	181	17	in	in	ADP
ejpam-3338	181	18	the	the	DET
ejpam-3338	181	19	solution	solution	NOUN
ejpam-3338	181	20	irrespective	irrespective	ADV
ejpam-3338	181	21	of	of	ADP
ejpam-3338	181	22	whether	whether	SCONJ
ejpam-3338	181	23	the	the	DET
ejpam-3338	181	24	inverse	inverse	NOUN
ejpam-3338	181	25	is	be	AUX
ejpam-3338	181	26	true	true	ADJ
ejpam-3338	181	27	(	(	PUNCT
ejpam-3338	181	28	when	when	SCONJ
ejpam-3338	181	29	it	it	PRON
ejpam-3338	181	30	exists	exist	VERB
ejpam-3338	181	31	and	and	CCONJ
ejpam-3338	181	32	computable	computable	ADJ
ejpam-3338	181	33	within	within	ADP
ejpam-3338	181	34	the	the	DET
ejpam-3338	181	35	available	available	ADJ
ejpam-3338	181	36	finite	finite	PROPN
ejpam-3338	181	37	precision	precision	NOUN
ejpam-3338	181	38	of	of	ADP
ejpam-3338	181	39	the	the	DET
ejpam-3338	181	40	computer	computer	NOUN
ejpam-3338	181	41	)	)	PUNCT
ejpam-3338	181	42	or	or	CCONJ
ejpam-3338	181	43	pseudo	pseudo	NOUN
ejpam-3338	181	44	.	.	PUNCT
ejpam-3338	182	1	the	the	DET
ejpam-3338	182	2	more	more	ADV
ejpam-3338	182	3	pronounced	pronounce	VERB
ejpam-3338	182	4	the	the	DET
ejpam-3338	182	5	singularity	singularity	NOUN
ejpam-3338	182	6	is	be	AUX
ejpam-3338	182	7	,	,	PUNCT
ejpam-3338	182	8	the	the	DET
ejpam-3338	182	9	more	more	ADJ
ejpam-3338	182	10	will	will	AUX
ejpam-3338	182	11	be	be	AUX
ejpam-3338	182	12	the	the	DET
ejpam-3338	182	13	computational	computational	ADJ
ejpam-3338	182	14	error	error	NOUN
ejpam-3338	182	15	.	.	PUNCT
ejpam-3338	183	1	depending	depend	VERB
ejpam-3338	183	2	on	on	ADP
ejpam-3338	183	3	the	the	DET
ejpam-3338	183	4	context	context	NOUN
ejpam-3338	183	5	,	,	PUNCT
ejpam-3338	183	6	this	this	DET
ejpam-3338	183	7	error	error	NOUN
ejpam-3338	183	8	may	may	AUX
ejpam-3338	183	9	or	or	CCONJ
ejpam-3338	183	10	may	may	AUX
ejpam-3338	183	11	not	not	PART
ejpam-3338	183	12	be	be	AUX
ejpam-3338	183	13	acceptable	acceptable	ADJ
ejpam-3338	183	14	.	.	PUNCT
ejpam-3338	184	1	strictly	strictly	ADV
ejpam-3338	184	2	speaking	speak	VERB
ejpam-3338	184	3	while	while	SCONJ
ejpam-3338	184	4	a	a	DET
ejpam-3338	184	5	singular	singular	ADJ
ejpam-3338	184	6	linear	linear	NOUN
ejpam-3338	184	7	system	system	NOUN
ejpam-3338	184	8	like	like	ADP
ejpam-3338	184	9	a	a	DET
ejpam-3338	184	10	non	non	ADJ
ejpam-3338	184	11	-	-	ADJ
ejpam-3338	184	12	singular	singular	ADJ
ejpam-3338	184	13	one	one	NUM
ejpam-3338	184	14	poses	pose	VERB
ejpam-3338	184	15	no	no	DET
ejpam-3338	184	16	extraordinary	extraordinary	ADJ
ejpam-3338	184	17	error	error	NOUN
ejpam-3338	184	18	problem	problem	NOUN
ejpam-3338	184	19	for	for	ADP
ejpam-3338	184	20	a	a	DET
ejpam-3338	184	21	true	true	ADJ
ejpam-3338	184	22	solution	solution	NOUN
ejpam-3338	184	23	or	or	CCONJ
ejpam-3338	184	24	the	the	DET
ejpam-3338	184	25	minimum	minimum	ADJ
ejpam-3338	184	26	norm	norm	NOUN
ejpam-3338	184	27	least	least	ADJ
ejpam-3338	184	28	-	-	PUNCT
ejpam-3338	184	29	squares	square	NOUN
ejpam-3338	184	30	solution	solution	NOUN
ejpam-3338	184	31	,	,	PUNCT
ejpam-3338	184	32	a	a	DET
ejpam-3338	184	33	near	near	ADV
ejpam-3338	184	34	-	-	PUNCT
ejpam-3338	184	35	singular	singular	NOUN
ejpam-3338	184	36	system	system	NOUN
ejpam-3338	184	37	does	do	VERB
ejpam-3338	184	38	.	.	PUNCT
ejpam-3338	185	1	so	so	ADV
ejpam-3338	185	2	a	a	DET
ejpam-3338	185	3	near	near	ADV
ejpam-3338	185	4	-	-	PUNCT
ejpam-3338	185	5	singular	singular	ADJ
ejpam-3338	185	6	linear	linear	NOUN
ejpam-3338	185	7	system	system	NOUN
ejpam-3338	185	8	may	may	AUX
ejpam-3338	185	9	be	be	AUX
ejpam-3338	185	10	termed	term	VERB
ejpam-3338	185	11	ill	ill	ADV
ejpam-3338	185	12	-	-	PUNCT
ejpam-3338	185	13	conditioned	condition	VERB
ejpam-3338	185	14	with	with	ADP
ejpam-3338	185	15	respect	respect	NOUN
ejpam-3338	185	16	to	to	ADP
ejpam-3338	185	17	its	its	PRON
ejpam-3338	185	18	solution	solution	NOUN
ejpam-3338	185	19	while	while	SCONJ
ejpam-3338	185	20	a	a	DET
ejpam-3338	185	21	strictly	strictly	ADV
ejpam-3338	185	22	singular	singular	ADJ
ejpam-3338	185	23	as	as	ADV
ejpam-3338	185	24	well	well	ADV
ejpam-3338	185	25	as	as	ADP
ejpam-3338	185	26	a	a	DET
ejpam-3338	185	27	non	non	ADJ
ejpam-3338	185	28	-	-	ADJ
ejpam-3338	185	29	singular	singular	ADJ
ejpam-3338	185	30	(	(	PUNCT
ejpam-3338	185	31	sufficiently	sufficiently	ADV
ejpam-3338	185	32	away	away	ADV
ejpam-3338	185	33	from	from	ADP
ejpam-3338	185	34	a	a	DET
ejpam-3338	185	35	near	near	ADV
ejpam-3338	185	36	-	-	PUNCT
ejpam-3338	185	37	singular	singular	NOUN
ejpam-3338	185	38	(	(	PUNCT
ejpam-3338	185	39	depending	depend	VERB
ejpam-3338	185	40	on	on	ADP
ejpam-3338	185	41	the	the	DET
ejpam-3338	185	42	precision	precision	NOUN
ejpam-3338	185	43	/	/	SYM
ejpam-3338	185	44	context	context	NOUN
ejpam-3338	185	45	)	)	PUNCT
ejpam-3338	185	46	)	)	PUNCT
ejpam-3338	186	1	linear	linear	ADJ
ejpam-3338	186	2	system	system	NOUN
ejpam-3338	186	3	may	may	AUX
ejpam-3338	186	4	not	not	PART
ejpam-3338	186	5	be	be	AUX
ejpam-3338	186	6	.	.	PUNCT
ejpam-3338	187	1	if	if	SCONJ
ejpam-3338	187	2	the	the	DET
ejpam-3338	187	3	pseudo	pseudo	NOUN
ejpam-3338	187	4	-	-	NOUN
ejpam-3338	187	5	inverse	inverse	NOUN
ejpam-3338	187	6	of	of	ADP
ejpam-3338	187	7	the	the	DET
ejpam-3338	187	8	rectangular	rectangular	ADJ
ejpam-3338	187	9	matrix	matrix	NOUN
ejpam-3338	187	10	a	a	PRON
ejpam-3338	187	11	is	be	AUX
ejpam-3338	187	12	b	b	NOUN
ejpam-3338	187	13	,	,	PUNCT
ejpam-3338	187	14	then	then	ADV
ejpam-3338	187	15	the	the	DET
ejpam-3338	187	16	pseudo	pseudo	NOUN
ejpam-3338	187	17	inverse	inverse	NOUN
ejpam-3338	187	18	of	of	ADP
ejpam-3338	187	19	the	the	DET
ejpam-3338	187	20	matrix	matrix	NOUN
ejpam-3338	187	21	b	b	NOUN
ejpam-3338	187	22	is	be	AUX
ejpam-3338	187	23	the	the	DET
ejpam-3338	187	24	matrix	matrix	NOUN
ejpam-3338	187	25	a.	a.	NOUN
ejpam-3338	187	26	could	could	AUX
ejpam-3338	187	27	the	the	DET
ejpam-3338	187	28	fractional	fractional	ADJ
ejpam-3338	187	29	calculus	calculus	NOUN
ejpam-3338	187	30	be	be	AUX
ejpam-3338	187	31	made	make	VERB
ejpam-3338	187	32	to	to	PART
ejpam-3338	187	33	have	have	VERB
ejpam-3338	187	34	a	a	DET
ejpam-3338	187	35	similar	similar	ADJ
ejpam-3338	187	36	status	status	NOUN
ejpam-3338	187	37	in	in	ADP
ejpam-3338	187	38	future	future	NOUN
ejpam-3338	187	39	by	by	ADP
ejpam-3338	187	40	appropriate	appropriate	ADJ
ejpam-3338	187	41	definitions	definition	NOUN
ejpam-3338	187	42	and	and	CCONJ
ejpam-3338	187	43	procedures	procedure	NOUN
ejpam-3338	187	44	?	?	PUNCT
ejpam-3338	188	1	in	in	ADP
ejpam-3338	188	2	other	other	ADJ
ejpam-3338	188	3	words	word	NOUN
ejpam-3338	188	4	,	,	PUNCT
ejpam-3338	188	5	once	once	SCONJ
ejpam-3338	188	6	the	the	DET
ejpam-3338	188	7	integer	integer	NOUN
ejpam-3338	188	8	-	-	PUNCT
ejpam-3338	188	9	order	order	NOUN
ejpam-3338	188	10	derivative	derivative	ADJ
ejpam-3338	188	11	/	/	SYM
ejpam-3338	188	12	fractional	fractional	ADJ
ejpam-3338	188	13	derivative	derivative	NOUN
ejpam-3338	188	14	of	of	ADP
ejpam-3338	188	15	a	a	DET
ejpam-3338	188	16	function	function	NOUN
ejpam-3338	188	17	is	be	AUX
ejpam-3338	188	18	known	know	VERB
ejpam-3338	188	19	,	,	PUNCT
ejpam-3338	188	20	can	can	AUX
ejpam-3338	188	21	we	we	PRON
ejpam-3338	188	22	get	get	VERB
ejpam-3338	188	23	back	back	ADV
ejpam-3338	188	24	the	the	DET
ejpam-3338	188	25	original	original	ADJ
ejpam-3338	188	26	function	function	NOUN
ejpam-3338	188	27	using	use	VERB
ejpam-3338	188	28	its	its	PRON
ejpam-3338	188	29	anti	anti	ADJ
ejpam-3338	188	30	-	-	ADJ
ejpam-3338	188	31	derivative	derivative	ADJ
ejpam-3338	188	32	(	(	PUNCT
ejpam-3338	188	33	i.e.	i.e.	X
ejpam-3338	188	34	the	the	DET
ejpam-3338	188	35	integration	integration	NOUN
ejpam-3338	188	36	/	/	SYM
ejpam-3338	188	37	fractional	fractional	ADJ
ejpam-3338	188	38	integration	integration	NOUN
ejpam-3338	188	39	of	of	ADP
ejpam-3338	188	40	the	the	DET
ejpam-3338	188	41	derivative	derivative	NOUN
ejpam-3338	188	42	)	)	PUNCT
ejpam-3338	188	43	by	by	ADP
ejpam-3338	188	44	imposing	impose	VERB
ejpam-3338	188	45	the	the	DET
ejpam-3338	188	46	concerned	concerned	ADJ
ejpam-3338	188	47	condition(s	condition(s	NOUN
ejpam-3338	188	48	)	)	PUNCT
ejpam-3338	188	49	?	?	PUNCT
ejpam-3338	189	1	while	while	SCONJ
ejpam-3338	189	2	computing	compute	VERB
ejpam-3338	189	3	the	the	DET
ejpam-3338	189	4	ever	ever	ADV
ejpam-3338	189	5	-	-	PUNCT
ejpam-3338	189	6	existent	existent	ADJ
ejpam-3338	189	7	pseudo	pseudo	NOUN
ejpam-3338	189	8	-	-	NOUN
ejpam-3338	189	9	inverse	inverse	NOUN
ejpam-3338	189	10	or	or	CCONJ
ejpam-3338	189	11	the	the	DET
ejpam-3338	189	12	non	non	ADJ
ejpam-3338	189	13	-	-	ADJ
ejpam-3338	189	14	ever	ever	ADV
ejpam-3338	189	15	existent	existent	ADJ
ejpam-3338	189	16	true	true	ADJ
ejpam-3338	189	17	inverse	inverse	NOUN
ejpam-3338	189	18	(	(	PUNCT
ejpam-3338	189	19	true	true	ADJ
ejpam-3338	189	20	matrix	matrix	NOUN
ejpam-3338	189	21	inverse	inverse	NOUN
ejpam-3338	189	22	does	do	AUX
ejpam-3338	189	23	not	not	PART
ejpam-3338	189	24	exist	exist	VERB
ejpam-3338	189	25	for	for	ADP
ejpam-3338	189	26	non	non	ADJ
ejpam-3338	189	27	-	-	ADJ
ejpam-3338	189	28	square	square	ADJ
ejpam-3338	189	29	rectangular	rectangular	ADJ
ejpam-3338	189	30	matrices	matrix	NOUN
ejpam-3338	189	31	as	as	ADV
ejpam-3338	189	32	well	well	ADV
ejpam-3338	189	33	as	as	ADP
ejpam-3338	189	34	square	square	ADJ
ejpam-3338	189	35	singular	singular	ADJ
ejpam-3338	189	36	matrices	matrix	NOUN
ejpam-3338	189	37	)	)	PUNCT
ejpam-3338	189	38	of	of	ADP
ejpam-3338	189	39	a	a	DET
ejpam-3338	189	40	matrix	matrix	NOUN
ejpam-3338	189	41	,	,	PUNCT
ejpam-3338	189	42	no	no	DET
ejpam-3338	189	43	fractional	fractional	ADJ
ejpam-3338	189	44	power	power	NOUN
ejpam-3338	189	45	of	of	ADP
ejpam-3338	189	46	the	the	DET
ejpam-3338	189	47	matrix	matrix	NOUN
ejpam-3338	189	48	is	be	AUX
ejpam-3338	189	49	involved	involve	VERB
ejpam-3338	189	50	in	in	ADP
ejpam-3338	189	51	computing	compute	VERB
ejpam-3338	189	52	the	the	DET
ejpam-3338	189	53	pseudo	pseudo	NOUN
ejpam-3338	189	54	-	-	NOUN
ejpam-3338	189	55	inverse	inverse	NOUN
ejpam-3338	189	56	.	.	PUNCT
ejpam-3338	190	1	this	this	PRON
ejpam-3338	190	2	is	be	AUX
ejpam-3338	190	3	quite	quite	ADV
ejpam-3338	190	4	unlike	unlike	ADP
ejpam-3338	190	5	the	the	DET
ejpam-3338	190	6	fractional	fractional	ADJ
ejpam-3338	190	7	calculus	calculus	NOUN
ejpam-3338	190	8	operations	operation	NOUN
ejpam-3338	190	9	.	.	PUNCT
ejpam-3338	191	1	however	however	ADV
ejpam-3338	191	2	,	,	PUNCT
ejpam-3338	191	3	for	for	ADP
ejpam-3338	191	4	a	a	DET
ejpam-3338	191	5	square	square	ADJ
ejpam-3338	191	6	singular	singular	NOUN
ejpam-3338	191	7	or	or	CCONJ
ejpam-3338	191	8	a	a	DET
ejpam-3338	191	9	non	non	ADJ
ejpam-3338	191	10	-	-	ADJ
ejpam-3338	191	11	singular	singular	ADJ
ejpam-3338	191	12	matrix	matrix	NOUN
ejpam-3338	191	13	a	a	PRON
ejpam-3338	191	14	,	,	PUNCT
ejpam-3338	191	15	we	we	PRON
ejpam-3338	191	16	can	can	AUX
ejpam-3338	191	17	find	find	VERB
ejpam-3338	191	18	its	its	PRON
ejpam-3338	191	19	fractional	fractional	ADJ
ejpam-3338	191	20	power	power	NOUN
ejpam-3338	191	21	b	b	PROPN
ejpam-3338	191	22	=	=	SYM
ejpam-3338	191	23	aα	aα	PROPN
ejpam-3338	191	24	.	.	PUNCT
ejpam-3338	192	1	hence	hence	ADV
ejpam-3338	192	2	b(1	b(1	PROPN
ejpam-3338	192	3	/	/	SYM
ejpam-3338	192	4	α	α	NOUN
ejpam-3338	192	5	)	)	PUNCT
ejpam-3338	192	6	=	=	NOUN
ejpam-3338	193	1	a	a	PRON
ejpam-3338	193	2	for	for	ADP
ejpam-3338	193	3	α	α	DET
ejpam-3338	193	4	positive	positive	ADJ
ejpam-3338	193	5	real	real	NOUN
ejpam-3338	193	6	.	.	PUNCT
ejpam-3338	194	1	if	if	SCONJ
ejpam-3338	194	2	α	α	PRON
ejpam-3338	194	3	is	be	AUX
ejpam-3338	194	4	complex	complex	ADJ
ejpam-3338	194	5	with	with	ADP
ejpam-3338	194	6	the	the	DET
ejpam-3338	194	7	imaginary	imaginary	ADJ
ejpam-3338	194	8	part	part	NOUN
ejpam-3338	194	9	6=	6=	ADP
ejpam-3338	194	10	0	0	NUM
ejpam-3338	194	11	,	,	PUNCT
ejpam-3338	194	12	then	then	ADV
ejpam-3338	194	13	the	the	DET
ejpam-3338	194	14	preceding	precede	VERB
ejpam-3338	194	15	rule	rule	NOUN
ejpam-3338	194	16	may	may	AUX
ejpam-3338	194	17	not	not	PART
ejpam-3338	194	18	be	be	AUX
ejpam-3338	194	19	valid	valid	ADJ
ejpam-3338	194	20	for	for	ADP
ejpam-3338	194	21	every	every	DET
ejpam-3338	194	22	matrix	matrix	NOUN
ejpam-3338	194	23	whose	whose	DET
ejpam-3338	194	24	order	order	NOUN
ejpam-3338	194	25	is	be	AUX
ejpam-3338	194	26	greater	great	ADJ
ejpam-3338	194	27	s.	s.	PROPN
ejpam-3338	194	28	k.sen	k.sen	PROPN
ejpam-3338	194	29	,	,	PUNCT
ejpam-3338	194	30	j.	j.	PROPN
ejpam-3338	194	31	v.	v.	PROPN
ejpam-3338	194	32	devi	devi	PROPN
ejpam-3338	194	33	,	,	PUNCT
ejpam-3338	194	34	r.v.g	r.v.g	NOUN
ejpam-3338	194	35	.	.	PUNCT
ejpam-3338	195	1	r.	r.	PROPN
ejpam-3338	195	2	kumar	kumar	PROPN
ejpam-3338	195	3	/	/	SYM
ejpam-3338	195	4	eur	eur	PROPN
ejpam-3338	195	5	.	.	PUNCT
ejpam-3338	196	1	j.	j.	PROPN
ejpam-3338	196	2	pure	pure	PROPN
ejpam-3338	196	3	appl	appl	PROPN
ejpam-3338	196	4	.	.	PROPN
ejpam-3338	196	5	math	math	PROPN
ejpam-3338	196	6	,	,	PUNCT
ejpam-3338	196	7	11	11	NUM
ejpam-3338	196	8	(	(	PUNCT
ejpam-3338	196	9	3	3	NUM
ejpam-3338	196	10	)	)	PUNCT
ejpam-3338	196	11	(	(	PUNCT
ejpam-3338	196	12	2018	2018	NUM
ejpam-3338	196	13	)	)	PUNCT
ejpam-3338	196	14	,	,	PUNCT
ejpam-3338	196	15	1058	1058	NUM
ejpam-3338	196	16	-	-	SYM
ejpam-3338	196	17	1099	1099	NUM
ejpam-3338	196	18	1066	1066	NUM
ejpam-3338	196	19	then	then	ADV
ejpam-3338	196	20	1	1	X
ejpam-3338	196	21	.	.	PUNCT
ejpam-3338	197	1	a	a	DET
ejpam-3338	197	2	fractional	fractional	ADJ
ejpam-3338	197	3	positive	positive	ADJ
ejpam-3338	197	4	real	real	ADJ
ejpam-3338	197	5	power	power	NOUN
ejpam-3338	197	6	α	α	NOUN
ejpam-3338	197	7	of	of	ADP
ejpam-3338	197	8	the	the	DET
ejpam-3338	197	9	matrix	matrix	NOUN
ejpam-3338	197	10	a	a	PRON
ejpam-3338	197	11	could	could	AUX
ejpam-3338	197	12	have	have	VERB
ejpam-3338	197	13	more	more	ADJ
ejpam-3338	197	14	than	than	ADP
ejpam-3338	197	15	one	one	NUM
ejpam-3338	197	16	matrix	matrix	NOUN
ejpam-3338	197	17	.	.	PUNCT
ejpam-3338	198	1	everyone	everyone	PRON
ejpam-3338	198	2	of	of	ADP
ejpam-3338	198	3	these	these	DET
ejpam-3338	198	4	matrices	matrix	NOUN
ejpam-3338	198	5	with	with	ADP
ejpam-3338	198	6	power	power	NOUN
ejpam-3338	198	7	1	1	NUM
ejpam-3338	198	8	α	α	NOUN
ejpam-3338	198	9	will	will	AUX
ejpam-3338	198	10	result	result	VERB
ejpam-3338	198	11	in	in	ADP
ejpam-3338	198	12	the	the	DET
ejpam-3338	198	13	original	original	ADJ
ejpam-3338	198	14	matrix	matrix	NOUN
ejpam-3338	198	15	a.	a.	NOUN
ejpam-3338	198	16	if	if	SCONJ
ejpam-3338	198	17	the	the	DET
ejpam-3338	198	18	matrix	matrix	NOUN
ejpam-3338	198	19	a	a	PRON
ejpam-3338	198	20	is	be	AUX
ejpam-3338	198	21	rectangular	rectangular	ADJ
ejpam-3338	198	22	real	real	ADJ
ejpam-3338	198	23	/	/	SYM
ejpam-3338	198	24	complex	complex	NOUN
ejpam-3338	198	25	,	,	PUNCT
ejpam-3338	198	26	then	then	ADV
ejpam-3338	198	27	appending	append	VERB
ejpam-3338	198	28	0	0	NUM
ejpam-3338	198	29	rows	row	NOUN
ejpam-3338	198	30	or	or	CCONJ
ejpam-3338	198	31	0	0	NUM
ejpam-3338	198	32	columns	column	NOUN
ejpam-3338	198	33	it	it	PRON
ejpam-3338	198	34	can	can	AUX
ejpam-3338	198	35	be	be	AUX
ejpam-3338	198	36	made	make	VERB
ejpam-3338	198	37	square	square	ADJ
ejpam-3338	198	38	.	.	PUNCT
ejpam-3338	199	1	replace	replace	VERB
ejpam-3338	199	2	the	the	DET
ejpam-3338	199	3	original	original	ADJ
ejpam-3338	199	4	rectangular	rectangular	ADJ
ejpam-3338	199	5	matrix	matrix	NOUN
ejpam-3338	199	6	a	a	PRON
ejpam-3338	199	7	by	by	ADP
ejpam-3338	199	8	this	this	DET
ejpam-3338	199	9	new	new	ADJ
ejpam-3338	199	10	square	square	ADJ
ejpam-3338	199	11	matrix	matrix	NOUN
ejpam-3338	199	12	.	.	PUNCT
ejpam-3338	200	1	that	that	PRON
ejpam-3338	200	2	is	be	AUX
ejpam-3338	200	3	,	,	PUNCT
ejpam-3338	200	4	the	the	DET
ejpam-3338	200	5	most	most	ADV
ejpam-3338	200	6	recent	recent	ADJ
ejpam-3338	200	7	matrix	matrix	NOUN
ejpam-3338	200	8	a	a	PRON
ejpam-3338	200	9	is	be	AUX
ejpam-3338	200	10	square	square	ADJ
ejpam-3338	200	11	singular	singular	NOUN
ejpam-3338	200	12	.	.	PUNCT
ejpam-3338	201	1	the	the	DET
ejpam-3338	201	2	foregoing	forego	VERB
ejpam-3338	201	3	fractional	fractional	ADJ
ejpam-3338	201	4	power	power	NOUN
ejpam-3338	201	5	rule	rule	NOUN
ejpam-3338	201	6	in	in	ADP
ejpam-3338	201	7	the	the	DET
ejpam-3338	201	8	preceding	precede	VERB
ejpam-3338	201	9	paragraph	paragraph	NOUN
ejpam-3338	201	10	is	be	AUX
ejpam-3338	201	11	perfectly	perfectly	ADV
ejpam-3338	201	12	valid	valid	ADJ
ejpam-3338	201	13	for	for	ADP
ejpam-3338	201	14	this	this	DET
ejpam-3338	201	15	matrix	matrix	NOUN
ejpam-3338	201	16	a	a	PRON
ejpam-3338	201	17	for	for	ADP
ejpam-3338	201	18	α	α	DET
ejpam-3338	201	19	positive	positive	ADJ
ejpam-3338	201	20	real	real	NOUN
ejpam-3338	201	21	.	.	PUNCT
ejpam-3338	202	1	incidentally	incidentally	ADV
ejpam-3338	202	2	,	,	PUNCT
ejpam-3338	202	3	the	the	DET
ejpam-3338	202	4	identical	identical	ADJ
ejpam-3338	202	5	rule	rule	NOUN
ejpam-3338	202	6	is	be	AUX
ejpam-3338	202	7	always	always	ADV
ejpam-3338	202	8	valid	valid	ADJ
ejpam-3338	202	9	for	for	ADP
ejpam-3338	202	10	a	a	DET
ejpam-3338	202	11	real	real	ADJ
ejpam-3338	202	12	/	/	SYM
ejpam-3338	202	13	complex	complex	ADJ
ejpam-3338	202	14	matrix	matrix	NOUN
ejpam-3338	202	15	of	of	ADP
ejpam-3338	202	16	order	order	NOUN
ejpam-3338	202	17	1	1	NUM
ejpam-3338	202	18	.	.	PUNCT
ejpam-3338	203	1	a	a	DET
ejpam-3338	203	2	real	real	ADJ
ejpam-3338	203	3	/	/	SYM
ejpam-3338	203	4	complex	complex	ADJ
ejpam-3338	203	5	number	number	NOUN
ejpam-3338	203	6	may	may	AUX
ejpam-3338	203	7	be	be	AUX
ejpam-3338	203	8	viewed	view	VERB
ejpam-3338	203	9	as	as	ADP
ejpam-3338	203	10	a	a	DET
ejpam-3338	203	11	real	real	ADJ
ejpam-3338	203	12	/	/	SYM
ejpam-3338	203	13	complex	complex	ADJ
ejpam-3338	203	14	matrix	matrix	NOUN
ejpam-3338	203	15	of	of	ADP
ejpam-3338	203	16	order	order	NOUN
ejpam-3338	203	17	1	1	NUM
ejpam-3338	203	18	and	and	CCONJ
ejpam-3338	203	19	vice	vice	ADV
ejpam-3338	203	20	versa	versa	ADV
ejpam-3338	203	21	.	.	PUNCT
ejpam-3338	204	1	the	the	DET
ejpam-3338	204	2	following	follow	VERB
ejpam-3338	204	3	numerical	numerical	ADJ
ejpam-3338	204	4	examples	example	NOUN
ejpam-3338	204	5	produced	produce	VERB
ejpam-3338	204	6	using	use	VERB
ejpam-3338	204	7	matlab	matlab	PROPN
ejpam-3338	204	8	demonstrate	demonstrate	VERB
ejpam-3338	204	9	the	the	DET
ejpam-3338	204	10	foregoing	forego	VERB
ejpam-3338	204	11	facts	fact	NOUN
ejpam-3338	204	12	.	.	PUNCT
ejpam-3338	205	1	>	>	PUNCT
ejpam-3338	205	2	>	>	X
ejpam-3338	205	3	a	a	X
ejpam-3338	205	4	=	=	PUNCT
ejpam-3338	206	1	[	[	X
ejpam-3338	206	2	1	1	NUM
ejpam-3338	206	3	+	+	NOUN
ejpam-3338	206	4	1i	1i	NOUN
ejpam-3338	206	5	2−2i	2−2i	NUM
ejpam-3338	206	6	3	3	NUM
ejpam-3338	206	7	+	+	NUM
ejpam-3338	206	8	3i	3i	NOUN
ejpam-3338	206	9	;	;	PUNCT
ejpam-3338	206	10	4	4	NUM
ejpam-3338	206	11	+	+	NOUN
ejpam-3338	206	12	4i	4i	NUM
ejpam-3338	206	13	5	5	NUM
ejpam-3338	206	14	+	+	NOUN
ejpam-3338	206	15	5i	5i	NUM
ejpam-3338	206	16	6−6i	6−6i	NUM
ejpam-3338	206	17	;	;	PUNCT
ejpam-3338	206	18	7	7	NUM
ejpam-3338	206	19	+	+	NOUN
ejpam-3338	206	20	7i	7i	NOUN
ejpam-3338	206	21	8−8i	8−8i	NUM
ejpam-3338	206	22	9	9	NUM
ejpam-3338	206	23	+	+	NUM
ejpam-3338	206	24	9i	9i	NOUN
ejpam-3338	206	25	]	]	X
ejpam-3338	206	26	,	,	PUNCT
ejpam-3338	206	27	b	b	X
ejpam-3338	206	28	=	=	SYM
ejpam-3338	206	29	a∧(.4−	a∧(.4−	PROPN
ejpam-3338	206	30	.7i	.7i	PROPN
ejpam-3338	206	31	)	)	PUNCT
ejpam-3338	206	32	,	,	PUNCT
ejpam-3338	206	33	c	c	X
ejpam-3338	206	34	=	=	SYM
ejpam-3338	206	35	b∧(1/(.4−	b∧(1/(.4−	PROPN
ejpam-3338	206	36	.7i	.7i	PROPN
ejpam-3338	206	37	)	)	PUNCT
ejpam-3338	206	38	)	)	PUNCT
ejpam-3338	207	1	(	(	PUNCT
ejpam-3338	207	2	the	the	DET
ejpam-3338	207	3	matrices	matrix	NOUN
ejpam-3338	207	4	a	a	PRON
ejpam-3338	207	5	and	and	CCONJ
ejpam-3338	207	6	c	c	NOUN
ejpam-3338	207	7	will	will	AUX
ejpam-3338	207	8	be	be	AUX
ejpam-3338	207	9	the	the	DET
ejpam-3338	207	10	same	same	ADJ
ejpam-3338	207	11	)	)	PUNCT
ejpam-3338	207	12	a	a	PRON
ejpam-3338	208	1	=	=	NOUN
ejpam-3338	208	2	1.0000	1.0000	NUM
ejpam-3338	208	3	+	+	NUM
ejpam-3338	208	4	1.0000i	1.0000i	PROPN
ejpam-3338	208	5	2.0000	2.0000	NUM
ejpam-3338	208	6	2.0000i	2.0000i	PROPN
ejpam-3338	208	7	3.0000	3.0000	NUM
ejpam-3338	208	8	+	+	CCONJ
ejpam-3338	208	9	3.0000i	3.0000i	NUM
ejpam-3338	208	10	4.0000	4.0000	NUM
ejpam-3338	208	11	+	+	CCONJ
ejpam-3338	208	12	4.0000i	4.0000i	NOUN
ejpam-3338	208	13	5.0000	5.0000	NUM
ejpam-3338	208	14	+	+	CCONJ
ejpam-3338	208	15	5.0000i	5.0000i	NOUN
ejpam-3338	208	16	6.0000	6.0000	NUM
ejpam-3338	208	17	6.0000i	6.0000i	NOUN
ejpam-3338	208	18	7.0000	7.0000	NUM
ejpam-3338	208	19	+	+	CCONJ
ejpam-3338	208	20	7.0000i	7.0000i	PROPN
ejpam-3338	208	21	8.0000	8.0000	NUM
ejpam-3338	208	22	8.0000i	8.0000i	NOUN
ejpam-3338	208	23	9.0000	9.0000	NUM
ejpam-3338	208	24	+	+	CCONJ
ejpam-3338	208	25	9.0000i	9.0000i	NOUN
ejpam-3338	208	26	b	b	NOUN
ejpam-3338	208	27	=	=	SYM
ejpam-3338	208	28	0.0304	0.0304	NUM
ejpam-3338	208	29	0.6891i	0.6891i	NOUN
ejpam-3338	208	30	-0.3652	-0.3652	VERB
ejpam-3338	209	1	+	+	CCONJ
ejpam-3338	209	2	0.8921i	0.8921i	NOUN
ejpam-3338	209	3	-0.1599	-0.1599	PUNCT
ejpam-3338	209	4	1.5749i	1.5749i	NUM
ejpam-3338	210	1	0.9850	0.9850	NUM
ejpam-3338	210	2	0.7253i	0.7253i	NOUN
ejpam-3338	210	3	2.0753	2.0753	NUM
ejpam-3338	210	4	4.7575i	4.7575i	NUM
ejpam-3338	210	5	-2.1730	-2.1730	X
ejpam-3338	211	1	+	+	CCONJ
ejpam-3338	211	2	2.2331i	2.2331i	NOUN
ejpam-3338	211	3	-0.3766	-0.3766	NOUN
ejpam-3338	211	4	1.8286i	1.8286i	NUM
ejpam-3338	211	5	-1.9743	-1.9743	NOUN
ejpam-3338	212	1	+	+	CCONJ
ejpam-3338	213	1	2.9792i	2.9792i	INTJ
ejpam-3338	213	2	i	i	PRON
ejpam-3338	213	3	-0.1007	-0.1007	VERB
ejpam-3338	214	1	5.6070i	5.6070i	PROPN
ejpam-3338	214	2	c	c	NOUN
ejpam-3338	214	3	=	=	SYM
ejpam-3338	214	4	1.0000	1.0000	NUM
ejpam-3338	214	5	+	+	NUM
ejpam-3338	214	6	1.0000i	1.0000i	PROPN
ejpam-3338	214	7	2.0000	2.0000	NUM
ejpam-3338	214	8	2.0000i	2.0000i	PROPN
ejpam-3338	214	9	3.0000	3.0000	NUM
ejpam-3338	214	10	+	+	CCONJ
ejpam-3338	214	11	3.0000i	3.0000i	NUM
ejpam-3338	214	12	4.0000	4.0000	NUM
ejpam-3338	214	13	+	+	CCONJ
ejpam-3338	214	14	4.0000i	4.0000i	NOUN
ejpam-3338	214	15	5.0000	5.0000	NUM
ejpam-3338	215	1	+	+	CCONJ
ejpam-3338	215	2	5.0000i	5.0000i	NOUN
ejpam-3338	215	3	6.0000	6.0000	NUM
ejpam-3338	215	4	6.0000i	6.0000i	NOUN
ejpam-3338	215	5	7.0000	7.0000	NUM
ejpam-3338	215	6	+	+	CCONJ
ejpam-3338	215	7	7.0000i	7.0000i	PROPN
ejpam-3338	215	8	8.0000	8.0000	NUM
ejpam-3338	215	9	8.0000i	8.0000i	NOUN
ejpam-3338	215	10	9.0000	9.0000	NUM
ejpam-3338	215	11	+	+	NUM
ejpam-3338	215	12	9.0000i	9.0000i	NOUN
ejpam-3338	215	13	>	>	PUNCT
ejpam-3338	215	14	>	>	X
ejpam-3338	215	15	clear	clear	PROPN
ejpam-3338	215	16	all	all	PRON
ejpam-3338	215	17	;	;	PUNCT
ejpam-3338	215	18	close	close	VERB
ejpam-3338	215	19	all	all	PRON
ejpam-3338	215	20	>	>	PUNCT
ejpam-3338	215	21	>	>	X
ejpam-3338	216	1	a	a	PRON
ejpam-3338	216	2	=	=	X
ejpam-3338	217	1	[	[	X
ejpam-3338	217	2	1	1	NUM
ejpam-3338	217	3	2	2	NUM
ejpam-3338	217	4	3	3	NUM
ejpam-3338	217	5	4	4	NUM
ejpam-3338	217	6	;	;	PUNCT
ejpam-3338	217	7	5	5	NUM
ejpam-3338	217	8	6	6	NUM
ejpam-3338	217	9	7	7	NUM
ejpam-3338	217	10	8	8	NUM
ejpam-3338	217	11	]	]	PUNCT
ejpam-3338	217	12	,	,	PUNCT
ejpam-3338	217	13	c	c	NOUN
ejpam-3338	217	14	=	=	PUNCT
ejpam-3338	218	1	[	[	X
ejpam-3338	218	2	a	a	X
ejpam-3338	218	3	;	;	PUNCT
ejpam-3338	218	4	zeros(2	zeros(2	NOUN
ejpam-3338	218	5	,	,	PUNCT
ejpam-3338	218	6	4	4	NUM
ejpam-3338	218	7	)	)	PUNCT
ejpam-3338	218	8	]	]	PUNCT
ejpam-3338	218	9	,	,	PUNCT
ejpam-3338	218	10	b	b	X
ejpam-3338	218	11	=	=	SYM
ejpam-3338	218	12	c	c	PROPN
ejpam-3338	218	13	∧	∧	PROPN
ejpam-3338	218	14	(	(	PUNCT
ejpam-3338	218	15	.4−	.4−	PROPN
ejpam-3338	218	16	.7i	.7i	PROPN
ejpam-3338	218	17	)	)	PUNCT
ejpam-3338	218	18	,	,	PUNCT
ejpam-3338	219	1	d	d	X
ejpam-3338	219	2	=	=	SYM
ejpam-3338	219	3	b	b	PROPN
ejpam-3338	219	4	∧	∧	PROPN
ejpam-3338	219	5	(	(	PUNCT
ejpam-3338	219	6	1/(.4−	1/(.4−	NUM
ejpam-3338	219	7	.7i	.7i	NOUN
ejpam-3338	219	8	)	)	PUNCT
ejpam-3338	219	9	)	)	PUNCT
ejpam-3338	220	1	(	(	PUNCT
ejpam-3338	220	2	the	the	DET
ejpam-3338	220	3	matrix	matrix	NOUN
ejpam-3338	220	4	b	b	NOUN
ejpam-3338	220	5	and	and	CCONJ
ejpam-3338	220	6	hence	hence	ADV
ejpam-3338	220	7	the	the	DET
ejpam-3338	220	8	matrix	matrix	NOUN
ejpam-3338	220	9	d	d	AUX
ejpam-3338	220	10	do	do	AUX
ejpam-3338	220	11	not	not	PART
ejpam-3338	220	12	exist	exist	VERB
ejpam-3338	220	13	.	.	PUNCT
ejpam-3338	220	14	)	)	PUNCT
ejpam-3338	221	1	a	a	PRON
ejpam-3338	221	2	=	=	SYM
ejpam-3338	221	3	1	1	NUM
ejpam-3338	221	4	2	2	NUM
ejpam-3338	221	5	3	3	NUM
ejpam-3338	221	6	4	4	NUM
ejpam-3338	221	7	5	5	NUM
ejpam-3338	221	8	6	6	NUM
ejpam-3338	221	9	7	7	NUM
ejpam-3338	221	10	8	8	NUM
ejpam-3338	221	11	c	c	NOUN
ejpam-3338	221	12	=	=	SYM
ejpam-3338	221	13	1	1	NUM
ejpam-3338	221	14	2	2	NUM
ejpam-3338	221	15	3	3	NUM
ejpam-3338	221	16	4	4	NUM
ejpam-3338	221	17	5	5	NUM
ejpam-3338	221	18	6	6	NUM
ejpam-3338	221	19	7	7	NUM
ejpam-3338	221	20	8	8	NUM
ejpam-3338	221	21	0	0	NUM
ejpam-3338	221	22	0	0	NUM
ejpam-3338	221	23	0	0	NUM
ejpam-3338	221	24	0	0	NUM
ejpam-3338	221	25	0	0	NUM
ejpam-3338	221	26	0	0	NUM
ejpam-3338	221	27	0	0	NUM
ejpam-3338	221	28	0	0	NUM
ejpam-3338	221	29	b	b	X
ejpam-3338	221	30	=	=	SYM
ejpam-3338	221	31	nan	nan	PROPN
ejpam-3338	221	32	+	+	PROPN
ejpam-3338	221	33	nani	nani	PROPN
ejpam-3338	221	34	nan	nan	PROPN
ejpam-3338	221	35	+	+	PROPN
ejpam-3338	221	36	nani	nani	PROPN
ejpam-3338	221	37	nan	nan	PROPN
ejpam-3338	221	38	+	+	PROPN
ejpam-3338	221	39	nani	nani	PROPN
ejpam-3338	221	40	nan	nan	PROPN
ejpam-3338	221	41	+	+	PROPN
ejpam-3338	221	42	nani	nani	PROPN
ejpam-3338	221	43	s.	s.	PROPN
ejpam-3338	221	44	k.sen	k.sen	PROPN
ejpam-3338	221	45	,	,	PUNCT
ejpam-3338	221	46	j.	j.	PROPN
ejpam-3338	221	47	v.	v.	PROPN
ejpam-3338	221	48	devi	devi	PROPN
ejpam-3338	221	49	,	,	PUNCT
ejpam-3338	221	50	r.v.g	r.v.g	NOUN
ejpam-3338	221	51	.	.	PUNCT
ejpam-3338	222	1	r.	r.	PROPN
ejpam-3338	222	2	kumar	kumar	PROPN
ejpam-3338	222	3	/	/	SYM
ejpam-3338	222	4	eur	eur	PROPN
ejpam-3338	222	5	.	.	PUNCT
ejpam-3338	223	1	j.	j.	PROPN
ejpam-3338	223	2	pure	pure	PROPN
ejpam-3338	223	3	appl	appl	PROPN
ejpam-3338	223	4	.	.	PROPN
ejpam-3338	223	5	math	math	PROPN
ejpam-3338	223	6	,	,	PUNCT
ejpam-3338	223	7	11	11	NUM
ejpam-3338	223	8	(	(	PUNCT
ejpam-3338	223	9	3	3	NUM
ejpam-3338	223	10	)	)	PUNCT
ejpam-3338	223	11	(	(	PUNCT
ejpam-3338	223	12	2018	2018	NUM
ejpam-3338	223	13	)	)	PUNCT
ejpam-3338	223	14	,	,	PUNCT
ejpam-3338	223	15	1058	1058	NUM
ejpam-3338	223	16	-	-	SYM
ejpam-3338	223	17	1099	1099	NUM
ejpam-3338	223	18	1067	1067	NUM
ejpam-3338	223	19	nan	nan	PROPN
ejpam-3338	223	20	+	+	PROPN
ejpam-3338	223	21	nani	nani	PROPN
ejpam-3338	223	22	nan	nan	PROPN
ejpam-3338	223	23	+	+	PROPN
ejpam-3338	223	24	nani	nani	PROPN
ejpam-3338	223	25	nan	nan	PROPN
ejpam-3338	223	26	+	+	PROPN
ejpam-3338	223	27	nani	nani	PROPN
ejpam-3338	223	28	nan	nan	PROPN
ejpam-3338	223	29	+	+	PROPN
ejpam-3338	223	30	nani	nani	PROPN
ejpam-3338	223	31	nan	nan	PROPN
ejpam-3338	223	32	+	+	PROPN
ejpam-3338	223	33	nani	nani	PROPN
ejpam-3338	223	34	nan	nan	PROPN
ejpam-3338	223	35	+	+	PROPN
ejpam-3338	223	36	nani	nani	PROPN
ejpam-3338	223	37	nan	nan	PROPN
ejpam-3338	223	38	+	+	PROPN
ejpam-3338	223	39	nani	nani	PROPN
ejpam-3338	223	40	nan	nan	PROPN
ejpam-3338	223	41	+	+	PROPN
ejpam-3338	223	42	nani	nani	PROPN
ejpam-3338	223	43	nan	nan	PROPN
ejpam-3338	223	44	+	+	PROPN
ejpam-3338	223	45	nani	nani	PROPN
ejpam-3338	223	46	nan	nan	PROPN
ejpam-3338	223	47	+	+	PROPN
ejpam-3338	223	48	nani	nani	PROPN
ejpam-3338	223	49	nan	nan	PROPN
ejpam-3338	223	50	+	+	PROPN
ejpam-3338	223	51	nani	nani	PROPN
ejpam-3338	223	52	nan	nan	PROPN
ejpam-3338	223	53	+	+	PROPN
ejpam-3338	223	54	nani	nani	PROPN
ejpam-3338	223	55	(	(	PUNCT
ejpam-3338	223	56	nan	nan	PROPN
ejpam-3338	223	57	means	mean	VERB
ejpam-3338	223	58	not	not	PART
ejpam-3338	223	59	a	a	DET
ejpam-3338	223	60	number	number	NOUN
ejpam-3338	223	61	and	and	CCONJ
ejpam-3338	223	62	implies	imply	VERB
ejpam-3338	223	63	usually	usually	ADV
ejpam-3338	223	64	division	division	NOUN
ejpam-3338	223	65	by	by	ADP
ejpam-3338	223	66	0	0	NUM
ejpam-3338	223	67	)	)	PUNCT
ejpam-3338	223	68	?	?	PUNCT
ejpam-3338	223	69	?	?	PUNCT
ejpam-3338	223	70	?	?	PUNCT
ejpam-3338	224	1	error	error	NOUN
ejpam-3338	224	2	using	use	VERB
ejpam-3338	224	3	=	=	NOUN
ejpam-3338	224	4	=	=	PROPN
ejpam-3338	224	5	>	>	X
ejpam-3338	224	6	mpower	mpower	NOUN
ejpam-3338	224	7	input	input	NOUN
ejpam-3338	224	8	to	to	ADP
ejpam-3338	224	9	eig	eig	NOUN
ejpam-3338	224	10	must	must	AUX
ejpam-3338	224	11	not	not	PART
ejpam-3338	224	12	contain	contain	VERB
ejpam-3338	224	13	nan	nan	PROPN
ejpam-3338	224	14	or	or	CCONJ
ejpam-3338	224	15	inf	inf	PROPN
ejpam-3338	224	16	.	.	PUNCT
ejpam-3338	225	1	>	>	PUNCT
ejpam-3338	225	2	>	>	X
ejpam-3338	225	3	a	a	X
ejpam-3338	225	4	=	=	X
ejpam-3338	226	1	[	[	X
ejpam-3338	226	2	1	1	NUM
ejpam-3338	226	3	2	2	NUM
ejpam-3338	226	4	3	3	NUM
ejpam-3338	226	5	4	4	NUM
ejpam-3338	226	6	;	;	PUNCT
ejpam-3338	226	7	5	5	NUM
ejpam-3338	226	8	6	6	NUM
ejpam-3338	226	9	7	7	NUM
ejpam-3338	226	10	8	8	NUM
ejpam-3338	226	11	]	]	PUNCT
ejpam-3338	226	12	,	,	PUNCT
ejpam-3338	226	13	c	c	NOUN
ejpam-3338	226	14	=	=	PUNCT
ejpam-3338	227	1	[	[	X
ejpam-3338	227	2	a	a	X
ejpam-3338	227	3	;	;	PUNCT
ejpam-3338	227	4	zeros(2	zeros(2	NOUN
ejpam-3338	227	5	,	,	PUNCT
ejpam-3338	227	6	4	4	NUM
ejpam-3338	227	7	)	)	PUNCT
ejpam-3338	227	8	]	]	PUNCT
ejpam-3338	227	9	,	,	PUNCT
ejpam-3338	227	10	b	b	X
ejpam-3338	227	11	=	=	SYM
ejpam-3338	227	12	c	c	PROPN
ejpam-3338	227	13	∧	∧	PROPN
ejpam-3338	227	14	.4	.4	PROPN
ejpam-3338	227	15	,	,	PUNCT
ejpam-3338	227	16	d	d	X
ejpam-3338	227	17	=	=	SYM
ejpam-3338	227	18	b	b	PROPN
ejpam-3338	227	19	∧	∧	PROPN
ejpam-3338	227	20	(	(	PUNCT
ejpam-3338	227	21	1/.4	1/.4	NUM
ejpam-3338	227	22	)	)	PUNCT
ejpam-3338	227	23	the	the	DET
ejpam-3338	227	24	matrices	matrix	NOUN
ejpam-3338	227	25	c	c	PROPN
ejpam-3338	227	26	and	and	CCONJ
ejpam-3338	227	27	d	d	NOUN
ejpam-3338	227	28	are	be	AUX
ejpam-3338	227	29	identical	identical	ADJ
ejpam-3338	227	30	.	.	PUNCT
ejpam-3338	227	31	)	)	PUNCT
ejpam-3338	228	1	a	a	PRON
ejpam-3338	228	2	=	=	SYM
ejpam-3338	228	3	1	1	NUM
ejpam-3338	228	4	2	2	NUM
ejpam-3338	228	5	3	3	NUM
ejpam-3338	228	6	4	4	NUM
ejpam-3338	228	7	5	5	NUM
ejpam-3338	228	8	6	6	NUM
ejpam-3338	228	9	7	7	NUM
ejpam-3338	228	10	8	8	NUM
ejpam-3338	228	11	c	c	NOUN
ejpam-3338	228	12	=	=	SYM
ejpam-3338	228	13	1	1	NUM
ejpam-3338	228	14	2	2	NUM
ejpam-3338	228	15	3	3	NUM
ejpam-3338	228	16	4	4	NUM
ejpam-3338	228	17	5	5	NUM
ejpam-3338	228	18	6	6	NUM
ejpam-3338	228	19	7	7	NUM
ejpam-3338	228	20	8	8	NUM
ejpam-3338	228	21	0	0	NUM
ejpam-3338	228	22	0	0	NUM
ejpam-3338	228	23	0	0	NUM
ejpam-3338	228	24	0	0	NUM
ejpam-3338	228	25	0	0	NUM
ejpam-3338	228	26	0	0	NUM
ejpam-3338	228	27	0	0	NUM
ejpam-3338	228	28	0	0	NUM
ejpam-3338	228	29	b	b	X
ejpam-3338	228	30	=	=	SYM
ejpam-3338	228	31	0.6202	0.6202	NUM
ejpam-3338	228	32	+	+	CCONJ
ejpam-3338	228	33	0.5982i	0.5982i	NUM
ejpam-3338	228	34	0.4968	0.4968	NUM
ejpam-3338	228	35	0.1832i	0.1832i	NOUN
ejpam-3338	228	36	0.3733	0.3733	NUM
ejpam-3338	228	37	0.9645i	0.9645i	NOUN
ejpam-3338	229	1	0.2499	0.2499	NUM
ejpam-3338	230	1	1.7458i	1.7458i	NUM
ejpam-3338	230	2	1.2420	1.2420	NUM
ejpam-3338	230	3	0.4579i	0.4579i	NOUN
ejpam-3338	231	1	1.8622	1.8622	NUM
ejpam-3338	231	2	+	+	NOUN
ejpam-3338	231	3	0.1402i	0.1402i	PROPN
ejpam-3338	231	4	2.4825	2.4825	NUM
ejpam-3338	231	5	+	+	CCONJ
ejpam-3338	231	6	0.7384i	0.7384i	PROPN
ejpam-3338	232	1	3.1027	3.1027	NUM
ejpam-3338	232	2	+	+	CCONJ
ejpam-3338	232	3	1.3366i	1.3366i	PROPN
ejpam-3338	232	4	0	0	NUM
ejpam-3338	232	5	0	0	NUM
ejpam-3338	232	6	0	0	NUM
ejpam-3338	232	7	0	0	NUM
ejpam-3338	232	8	0	0	NUM
ejpam-3338	232	9	0	0	NUM
ejpam-3338	232	10	0	0	NUM
ejpam-3338	232	11	0	0	NUM
ejpam-3338	233	1	d	d	NOUN
ejpam-3338	233	2	=	=	NOUN
ejpam-3338	233	3	1.0000	1.0000	NUM
ejpam-3338	233	4	+	+	NUM
ejpam-3338	233	5	0.0000i	0.0000i	NOUN
ejpam-3338	233	6	2.0000	2.0000	NUM
ejpam-3338	233	7	0.0000i	0.0000i	NOUN
ejpam-3338	233	8	3.0000	3.0000	NUM
ejpam-3338	233	9	0.0000i	0.0000i	NOUN
ejpam-3338	233	10	4.0000	4.0000	NUM
ejpam-3338	233	11	0.0000i	0.0000i	NOUN
ejpam-3338	233	12	5.0000	5.0000	NUM
ejpam-3338	233	13	+	+	NUM
ejpam-3338	233	14	0.0000i	0.0000i	NOUN
ejpam-3338	233	15	6.0000	6.0000	NUM
ejpam-3338	233	16	0.0000i	0.0000i	NOUN
ejpam-3338	233	17	7.0000	7.0000	NUM
ejpam-3338	233	18	0.0000i	0.0000i	NOUN
ejpam-3338	233	19	8.0000	8.0000	NUM
ejpam-3338	233	20	0.0000i	0.0000i	NOUN
ejpam-3338	233	21	0	0	NUM
ejpam-3338	233	22	0	0	NUM
ejpam-3338	233	23	0	0	NUM
ejpam-3338	233	24	0	0	NUM
ejpam-3338	233	25	0	0	NUM
ejpam-3338	233	26	0	0	NUM
ejpam-3338	233	27	0	0	NUM
ejpam-3338	233	28	0	0	NUM
ejpam-3338	233	29	>	>	PUNCT
ejpam-3338	233	30	>	>	X
ejpam-3338	233	31	a	a	DET
ejpam-3338	233	32	=	=	SYM
ejpam-3338	233	33	5	5	NUM
ejpam-3338	233	34	+	+	NUM
ejpam-3338	233	35	7i	7i	NUM
ejpam-3338	233	36	,	,	PUNCT
ejpam-3338	233	37	b	b	X
ejpam-3338	233	38	=	=	PUNCT
ejpam-3338	233	39	a	a	DET
ejpam-3338	233	40	∧	∧	PROPN
ejpam-3338	233	41	(	(	PUNCT
ejpam-3338	233	42	.4−	.4−	PROPN
ejpam-3338	233	43	.7i	.7i	PROPN
ejpam-3338	233	44	)	)	PUNCT
ejpam-3338	233	45	,	,	PUNCT
ejpam-3338	233	46	c	c	X
ejpam-3338	234	1	=	=	SYM
ejpam-3338	234	2	b	b	PROPN
ejpam-3338	234	3	∧	∧	PROPN
ejpam-3338	234	4	(	(	PUNCT
ejpam-3338	234	5	1/(.4−	1/(.4−	NUM
ejpam-3338	234	6	.7i	.7i	NOUN
ejpam-3338	234	7	)	)	PUNCT
ejpam-3338	234	8	)	)	PUNCT
ejpam-3338	235	1	(	(	PUNCT
ejpam-3338	235	2	complex	complex	ADJ
ejpam-3338	235	3	power	power	NOUN
ejpam-3338	235	4	of	of	ADP
ejpam-3338	235	5	a	a	DET
ejpam-3338	235	6	complex	complex	ADJ
ejpam-3338	235	7	number	number	NOUN
ejpam-3338	235	8	(	(	PUNCT
ejpam-3338	235	9	1x1	1x1	NUM
ejpam-3338	235	10	matrix	matrix	NOUN
ejpam-3338	235	11	)	)	PUNCT
ejpam-3338	235	12	a	a	PRON
ejpam-3338	236	1	=	=	SYM
ejpam-3338	236	2	5.0000	5.0000	NUM
ejpam-3338	236	3	+	+	CCONJ
ejpam-3338	236	4	7.0000i	7.0000i	NOUN
ejpam-3338	236	5	b	b	NOUN
ejpam-3338	236	6	=	=	SYM
ejpam-3338	236	7	1.9787	1.9787	NUM
ejpam-3338	236	8	4.1534i	4.1534i	NUM
ejpam-3338	236	9	c	c	NOUN
ejpam-3338	236	10	=	=	SYM
ejpam-3338	236	11	5.0000	5.0000	NUM
ejpam-3338	236	12	+	+	NUM
ejpam-3338	236	13	7.0000i	7.0000i	NOUN
ejpam-3338	236	14	(	(	PUNCT
ejpam-3338	236	15	c	c	NOUN
ejpam-3338	236	16	is	be	AUX
ejpam-3338	236	17	the	the	DET
ejpam-3338	236	18	same	same	ADJ
ejpam-3338	236	19	as	as	ADP
ejpam-3338	236	20	a	a	DET
ejpam-3338	236	21	as	as	SCONJ
ejpam-3338	236	22	these	these	PRON
ejpam-3338	236	23	should	should	AUX
ejpam-3338	236	24	be	be	AUX
ejpam-3338	236	25	.	.	PUNCT
ejpam-3338	236	26	)	)	PUNCT
ejpam-3338	237	1	>	>	PUNCT
ejpam-3338	237	2	>	>	X
ejpam-3338	238	1	a	a	X
ejpam-3338	238	2	=	=	PUNCT
ejpam-3338	239	1	[	[	X
ejpam-3338	239	2	1	1	NUM
ejpam-3338	239	3	+	+	NUM
ejpam-3338	239	4	1i	1i	NOUN
ejpam-3338	239	5	2−2i	2−2i	NUM
ejpam-3338	239	6	3	3	NUM
ejpam-3338	239	7	+	+	NOUN
ejpam-3338	239	8	3i	3i	NOUN
ejpam-3338	239	9	;	;	PUNCT
ejpam-3338	239	10	4	4	NUM
ejpam-3338	239	11	+	+	NUM
ejpam-3338	239	12	4i	4i	NUM
ejpam-3338	239	13	5	5	NUM
ejpam-3338	239	14	+	+	NUM
ejpam-3338	239	15	5i	5i	NUM
ejpam-3338	239	16	6−6i	6−6i	NUM
ejpam-3338	239	17	;	;	PUNCT
ejpam-3338	239	18	7	7	NUM
ejpam-3338	239	19	+	+	NUM
ejpam-3338	239	20	7i	7i	NOUN
ejpam-3338	239	21	8−8i	8−8i	NUM
ejpam-3338	239	22	9	9	NUM
ejpam-3338	239	23	+	+	NUM
ejpam-3338	239	24	9i	9i	NUM
ejpam-3338	239	25	]	]	X
ejpam-3338	239	26	,	,	PUNCT
ejpam-3338	239	27	b	b	X
ejpam-3338	239	28	=	=	X
ejpam-3338	239	29	a∧	a∧	NOUN
ejpam-3338	239	30	(	(	PUNCT
ejpam-3338	239	31	.4−	.4−	PROPN
ejpam-3338	239	32	.7i	.7i	PROPN
ejpam-3338	239	33	)	)	PUNCT
ejpam-3338	239	34	,	,	PUNCT
ejpam-3338	239	35	c	c	X
ejpam-3338	239	36	=	=	SYM
ejpam-3338	239	37	b	b	PROPN
ejpam-3338	239	38	∧	∧	PROPN
ejpam-3338	239	39	(	(	PUNCT
ejpam-3338	239	40	1/(.4−	1/(.4−	NUM
ejpam-3338	239	41	.7i	.7i	NOUN
ejpam-3338	239	42	)	)	PUNCT
ejpam-3338	239	43	)	)	PUNCT
ejpam-3338	240	1	(	(	PUNCT
ejpam-3338	240	2	the	the	DET
ejpam-3338	240	3	matrix	matrix	NOUN
ejpam-3338	240	4	c	c	NOUN
ejpam-3338	240	5	is	be	AUX
ejpam-3338	240	6	the	the	DET
ejpam-3338	240	7	same	same	ADJ
ejpam-3338	240	8	as	as	ADP
ejpam-3338	240	9	the	the	DET
ejpam-3338	240	10	matrix	matrix	NOUN
ejpam-3338	240	11	a	a	PRON
ejpam-3338	240	12	as	as	SCONJ
ejpam-3338	240	13	is	be	AUX
ejpam-3338	240	14	expected	expect	VERB
ejpam-3338	240	15	here	here	ADV
ejpam-3338	240	16	.	.	PUNCT
ejpam-3338	240	17	)	)	PUNCT
ejpam-3338	241	1	a	a	DET
ejpam-3338	241	2	=	=	NOUN
ejpam-3338	241	3	1.0000	1.0000	NUM
ejpam-3338	241	4	+	+	NUM
ejpam-3338	241	5	1.0000i	1.0000i	PROPN
ejpam-3338	241	6	2.0000	2.0000	NUM
ejpam-3338	241	7	2.0000i	2.0000i	PROPN
ejpam-3338	241	8	3.0000	3.0000	NUM
ejpam-3338	241	9	+	+	NUM
ejpam-3338	241	10	3.0000i	3.0000i	NUM
ejpam-3338	241	11	s.	s.	PROPN
ejpam-3338	241	12	k.sen	k.sen	PROPN
ejpam-3338	241	13	,	,	PUNCT
ejpam-3338	241	14	j.	j.	PROPN
ejpam-3338	241	15	v.	v.	PROPN
ejpam-3338	241	16	devi	devi	PROPN
ejpam-3338	241	17	,	,	PUNCT
ejpam-3338	241	18	r.v.g	r.v.g	NOUN
ejpam-3338	241	19	.	.	PUNCT
ejpam-3338	242	1	r.	r.	PROPN
ejpam-3338	242	2	kumar	kumar	PROPN
ejpam-3338	242	3	/	/	SYM
ejpam-3338	242	4	eur	eur	PROPN
ejpam-3338	242	5	.	.	PUNCT
ejpam-3338	243	1	j.	j.	PROPN
ejpam-3338	243	2	pure	pure	PROPN
ejpam-3338	243	3	appl	appl	PROPN
ejpam-3338	243	4	.	.	PROPN
ejpam-3338	243	5	math	math	PROPN
ejpam-3338	243	6	,	,	PUNCT
ejpam-3338	243	7	11	11	NUM
ejpam-3338	243	8	(	(	PUNCT
ejpam-3338	243	9	3	3	NUM
ejpam-3338	243	10	)	)	PUNCT
ejpam-3338	243	11	(	(	PUNCT
ejpam-3338	243	12	2018	2018	NUM
ejpam-3338	243	13	)	)	PUNCT
ejpam-3338	243	14	,	,	PUNCT
ejpam-3338	243	15	1058	1058	NUM
ejpam-3338	243	16	-	-	SYM
ejpam-3338	243	17	1099	1099	NUM
ejpam-3338	243	18	1068	1068	NUM
ejpam-3338	243	19	4.0000	4.0000	NUM
ejpam-3338	243	20	+	+	CCONJ
ejpam-3338	243	21	4.0000i	4.0000i	NOUN
ejpam-3338	243	22	5.0000	5.0000	NUM
ejpam-3338	243	23	+	+	CCONJ
ejpam-3338	243	24	5.0000i	5.0000i	NOUN
ejpam-3338	243	25	6.0000	6.0000	NUM
ejpam-3338	243	26	6.0000i	6.0000i	NOUN
ejpam-3338	244	1	7.0000	7.0000	NUM
ejpam-3338	244	2	+	+	CCONJ
ejpam-3338	244	3	7.0000i	7.0000i	PROPN
ejpam-3338	244	4	8.0000	8.0000	NUM
ejpam-3338	244	5	8.0000i	8.0000i	NOUN
ejpam-3338	244	6	9.0000	9.0000	NUM
ejpam-3338	244	7	+	+	CCONJ
ejpam-3338	244	8	9.0000i	9.0000i	NOUN
ejpam-3338	244	9	b	b	NOUN
ejpam-3338	244	10	=	=	SYM
ejpam-3338	244	11	0.0304	0.0304	NUM
ejpam-3338	244	12	0.6891i	0.6891i	NOUN
ejpam-3338	244	13	-0.3652	-0.3652	VERB
ejpam-3338	245	1	+	+	CCONJ
ejpam-3338	245	2	0.8921i	0.8921i	NOUN
ejpam-3338	245	3	-0.1599	-0.1599	PUNCT
ejpam-3338	245	4	1.5749i	1.5749i	NUM
ejpam-3338	246	1	0.9850	0.9850	NUM
ejpam-3338	246	2	0.7253i	0.7253i	NOUN
ejpam-3338	246	3	2.0753	2.0753	NUM
ejpam-3338	246	4	4.7575i	4.7575i	NUM
ejpam-3338	246	5	-2.1730	-2.1730	X
ejpam-3338	247	1	+	+	CCONJ
ejpam-3338	247	2	2.2331i	2.2331i	NOUN
ejpam-3338	247	3	-0.3766	-0.3766	NOUN
ejpam-3338	247	4	1.8286i	1.8286i	NUM
ejpam-3338	247	5	-1.9743	-1.9743	NOUN
ejpam-3338	248	1	+	+	CCONJ
ejpam-3338	249	1	2.9792i	2.9792i	INTJ
ejpam-3338	249	2	i	i	PRON
ejpam-3338	249	3	-0.1007	-0.1007	VERB
ejpam-3338	250	1	5.6070i	5.6070i	PROPN
ejpam-3338	250	2	c	c	NOUN
ejpam-3338	250	3	=	=	SYM
ejpam-3338	250	4	1.0000	1.0000	NUM
ejpam-3338	250	5	+	+	NUM
ejpam-3338	250	6	1.0000i	1.0000i	PROPN
ejpam-3338	250	7	2.0000	2.0000	NUM
ejpam-3338	250	8	2.0000i	2.0000i	PROPN
ejpam-3338	250	9	3.0000	3.0000	NUM
ejpam-3338	250	10	+	+	CCONJ
ejpam-3338	250	11	3.0000i	3.0000i	NUM
ejpam-3338	250	12	4.0000	4.0000	NUM
ejpam-3338	250	13	+	+	CCONJ
ejpam-3338	250	14	4.0000i	4.0000i	NOUN
ejpam-3338	250	15	5.0000	5.0000	NUM
ejpam-3338	251	1	+	+	CCONJ
ejpam-3338	251	2	5.0000i	5.0000i	NOUN
ejpam-3338	251	3	6.0000	6.0000	NUM
ejpam-3338	251	4	6.0000i	6.0000i	NOUN
ejpam-3338	251	5	7.0000	7.0000	NUM
ejpam-3338	251	6	+	+	CCONJ
ejpam-3338	251	7	7.0000i	7.0000i	PROPN
ejpam-3338	251	8	8.0000	8.0000	NUM
ejpam-3338	251	9	8.0000i	8.0000i	NOUN
ejpam-3338	251	10	9.0000	9.0000	NUM
ejpam-3338	251	11	+	+	NUM
ejpam-3338	251	12	9.0000i	9.0000i	NOUN
ejpam-3338	251	13	the	the	DET
ejpam-3338	251	14	matlab	matlab	NOUN
ejpam-3338	251	15	provides	provide	VERB
ejpam-3338	251	16	only	only	ADV
ejpam-3338	251	17	1	1	NUM
ejpam-3338	251	18	of	of	ADP
ejpam-3338	251	19	these	these	DET
ejpam-3338	251	20	possible	possible	ADJ
ejpam-3338	251	21	matrices	matrix	NOUN
ejpam-3338	251	22	(	(	PUNCT
ejpam-3338	251	23	as	as	ADP
ejpam-3338	251	24	answers	answer	NOUN
ejpam-3338	251	25	)	)	PUNCT
ejpam-3338	251	26	and	and	CCONJ
ejpam-3338	251	27	this	this	PRON
ejpam-3338	251	28	serves	serve	VERB
ejpam-3338	251	29	our	our	PRON
ejpam-3338	251	30	purpose	purpose	NOUN
ejpam-3338	251	31	for	for	ADP
ejpam-3338	251	32	solving	solve	VERB
ejpam-3338	251	33	a	a	DET
ejpam-3338	251	34	physical	physical	ADJ
ejpam-3338	251	35	problem	problem	NOUN
ejpam-3338	251	36	well	well	ADV
ejpam-3338	251	37	unless	unless	SCONJ
ejpam-3338	251	38	the	the	DET
ejpam-3338	251	39	context	context	NOUN
ejpam-3338	251	40	demands	demand	VERB
ejpam-3338	251	41	something	something	PRON
ejpam-3338	251	42	different	different	ADJ
ejpam-3338	251	43	from	from	ADP
ejpam-3338	251	44	the	the	DET
ejpam-3338	251	45	usual	usual	ADJ
ejpam-3338	251	46	stuff	stuff	NOUN
ejpam-3338	251	47	.	.	PUNCT
ejpam-3338	252	1	we	we	PRON
ejpam-3338	252	2	provide	provide	VERB
ejpam-3338	252	3	in	in	ADP
ejpam-3338	252	4	section	section	NOUN
ejpam-3338	252	5	2	2	NUM
ejpam-3338	252	6	the	the	DET
ejpam-3338	252	7	problems	problem	NOUN
ejpam-3338	252	8	and	and	CCONJ
ejpam-3338	252	9	efforts	effort	NOUN
ejpam-3338	252	10	toward	toward	ADP
ejpam-3338	252	11	generalizing	generalize	VERB
ejpam-3338	252	12	the	the	DET
ejpam-3338	252	13	calculus	calculus	NOUN
ejpam-3338	252	14	such	such	ADJ
ejpam-3338	252	15	that	that	SCONJ
ejpam-3338	252	16	the	the	DET
ejpam-3338	252	17	integer	integer	NOUN
ejpam-3338	252	18	order	order	NOUN
ejpam-3338	252	19	(	(	PUNCT
ejpam-3338	252	20	classical	classical	ADJ
ejpam-3338	252	21	)	)	PUNCT
ejpam-3338	252	22	calculus	calculus	NOUN
ejpam-3338	252	23	is	be	AUX
ejpam-3338	252	24	integrated	integrate	VERB
ejpam-3338	252	25	/	/	SYM
ejpam-3338	252	26	merged	merge	VERB
ejpam-3338	252	27	with	with	ADP
ejpam-3338	252	28	/	/	SYM
ejpam-3338	252	29	into	into	ADP
ejpam-3338	252	30	the	the	DET
ejpam-3338	252	31	fractional	fractional	ADJ
ejpam-3338	252	32	one	one	NUM
ejpam-3338	252	33	.	.	PUNCT
ejpam-3338	253	1	one	one	NUM
ejpam-3338	253	2	of	of	ADP
ejpam-3338	253	3	the	the	DET
ejpam-3338	253	4	popular	popular	ADJ
ejpam-3338	253	5	fractional	fractional	ADJ
ejpam-3338	253	6	derivative	derivative	ADJ
ejpam-3338	253	7	viz	viz	PROPN
ejpam-3338	253	8	.	.	PUNCT
ejpam-3338	254	1	grunwald	grunwald	NOUN
ejpam-3338	254	2	-	-	PUNCT
ejpam-3338	254	3	letnikov	letnikov	NOUN
ejpam-3338	254	4	derivative	derivative	NOUN
ejpam-3338	254	5	demonstrates	demonstrate	VERB
ejpam-3338	254	6	numerically	numerically	ADV
ejpam-3338	254	7	and	and	CCONJ
ejpam-3338	254	8	also	also	ADV
ejpam-3338	254	9	graphically	graphically	ADV
ejpam-3338	254	10	how	how	SCONJ
ejpam-3338	254	11	the	the	DET
ejpam-3338	254	12	derivatives	derivative	NOUN
ejpam-3338	254	13	behave	behave	VERB
ejpam-3338	254	14	and	and	CCONJ
ejpam-3338	254	15	how	how	SCONJ
ejpam-3338	254	16	well	well	ADV
ejpam-3338	254	17	they	they	PRON
ejpam-3338	254	18	integrate	integrate	VERB
ejpam-3338	254	19	/	/	SYM
ejpam-3338	254	20	merge	merge	VERB
ejpam-3338	254	21	with	with	ADP
ejpam-3338	254	22	the	the	DET
ejpam-3338	254	23	integer	integer	NOUN
ejpam-3338	254	24	order	order	NOUN
ejpam-3338	254	25	ones	one	NOUN
ejpam-3338	254	26	.	.	PUNCT
ejpam-3338	255	1	this	this	PRON
ejpam-3338	255	2	is	be	AUX
ejpam-3338	255	3	essentially	essentially	ADV
ejpam-3338	255	4	an	an	DET
ejpam-3338	255	5	effort	effort	NOUN
ejpam-3338	255	6	by	by	ADP
ejpam-3338	255	7	the	the	DET
ejpam-3338	255	8	mathematicians	mathematician	NOUN
ejpam-3338	255	9	/	/	SYM
ejpam-3338	255	10	physicists	physicist	NOUN
ejpam-3338	255	11	toward	toward	ADP
ejpam-3338	255	12	making	make	VERB
ejpam-3338	255	13	fractional	fractional	ADJ
ejpam-3338	255	14	calculus	calculus	NOUN
ejpam-3338	255	15	a	a	DET
ejpam-3338	255	16	generalized	generalized	ADJ
ejpam-3338	255	17	version	version	NOUN
ejpam-3338	255	18	that	that	PRON
ejpam-3338	255	19	includes	include	VERB
ejpam-3338	255	20	integer	integer	NOUN
ejpam-3338	255	21	-	-	PUNCT
ejpam-3338	255	22	order	order	NOUN
ejpam-3338	255	23	calculus	calculus	NOUN
ejpam-3338	255	24	.	.	PUNCT
ejpam-3338	256	1	also	also	ADV
ejpam-3338	256	2	included	include	VERB
ejpam-3338	256	3	in	in	ADP
ejpam-3338	256	4	this	this	DET
ejpam-3338	256	5	section	section	NOUN
ejpam-3338	256	6	fde	fde	NOUN
ejpam-3338	256	7	and	and	CCONJ
ejpam-3338	256	8	its	its	PRON
ejpam-3338	256	9	integration	integration	NOUN
ejpam-3338	256	10	with	with	ADP
ejpam-3338	256	11	the	the	DET
ejpam-3338	256	12	classical	classical	ADJ
ejpam-3338	256	13	one	one	NOUN
ejpam-3338	256	14	and	and	CCONJ
ejpam-3338	256	15	the	the	DET
ejpam-3338	256	16	interpretation	interpretation	NOUN
ejpam-3338	256	17	.	.	PUNCT
ejpam-3338	257	1	in	in	ADP
ejpam-3338	257	2	section	section	NOUN
ejpam-3338	257	3	3	3	NUM
ejpam-3338	257	4	we	we	PRON
ejpam-3338	257	5	raise	raise	VERB
ejpam-3338	257	6	a	a	DET
ejpam-3338	257	7	few	few	ADJ
ejpam-3338	257	8	of	of	ADP
ejpam-3338	257	9	questions	question	NOUN
ejpam-3338	257	10	on	on	ADP
ejpam-3338	257	11	fractional	fractional	ADJ
ejpam-3338	257	12	odes	ode	NOUN
ejpam-3338	257	13	(	(	PUNCT
ejpam-3338	257	14	fodes	fode	NOUN
ejpam-3338	257	15	)	)	PUNCT
ejpam-3338	257	16	regarding	regard	VERB
ejpam-3338	257	17	how	how	SCONJ
ejpam-3338	257	18	we	we	PRON
ejpam-3338	257	19	convert	convert	VERB
ejpam-3338	257	20	these	these	PRON
ejpam-3338	257	21	to	to	ADP
ejpam-3338	257	22	a	a	DET
ejpam-3338	257	23	system	system	NOUN
ejpam-3338	257	24	of	of	ADP
ejpam-3338	257	25	α	α	NOUN
ejpam-3338	257	26	-	-	PUNCT
ejpam-3338	257	27	th	th	VERB
ejpam-3338	257	28	order	order	NOUN
ejpam-3338	257	29	fodes	fode	NOUN
ejpam-3338	257	30	or	or	CCONJ
ejpam-3338	257	31	/	/	SYM
ejpam-3338	257	32	and	and	CCONJ
ejpam-3338	257	33	1st	1st	ADJ
ejpam-3338	257	34	order	order	NOUN
ejpam-3338	257	35	odes	ode	VERB
ejpam-3338	257	36	,	,	PUNCT
ejpam-3338	257	37	how	how	SCONJ
ejpam-3338	257	38	many	many	ADJ
ejpam-3338	257	39	initial	initial	ADJ
ejpam-3338	257	40	conditions	condition	NOUN
ejpam-3338	257	41	we	we	PRON
ejpam-3338	257	42	would	would	AUX
ejpam-3338	257	43	need	need	VERB
ejpam-3338	257	44	to	to	PART
ejpam-3338	257	45	solve	solve	VERB
ejpam-3338	257	46	these	these	DET
ejpam-3338	257	47	odes	ode	NOUN
ejpam-3338	257	48	,	,	PUNCT
ejpam-3338	257	49	and	and	CCONJ
ejpam-3338	257	50	what	what	DET
ejpam-3338	257	51	procedure(s	procedure(s	NOUN
ejpam-3338	257	52	)	)	PUNCT
ejpam-3338	257	53	we	we	PRON
ejpam-3338	257	54	could	could	AUX
ejpam-3338	257	55	design	design	VERB
ejpam-3338	257	56	and	and	CCONJ
ejpam-3338	257	57	develop	develop	VERB
ejpam-3338	257	58	to	to	PART
ejpam-3338	257	59	numerically	numerically	ADV
ejpam-3338	257	60	solve	solve	VERB
ejpam-3338	257	61	the	the	DET
ejpam-3338	257	62	system	system	NOUN
ejpam-3338	257	63	.	.	PUNCT
ejpam-3338	258	1	also	also	ADV
ejpam-3338	258	2	talked	talk	VERB
ejpam-3338	258	3	about	about	ADP
ejpam-3338	258	4	in	in	ADP
ejpam-3338	258	5	this	this	DET
ejpam-3338	258	6	section	section	NOUN
ejpam-3338	258	7	are	be	AUX
ejpam-3338	258	8	the	the	DET
ejpam-3338	258	9	partial	partial	ADJ
ejpam-3338	258	10	as	as	ADV
ejpam-3338	258	11	well	well	ADV
ejpam-3338	258	12	as	as	ADP
ejpam-3338	258	13	complete	complete	ADJ
ejpam-3338	258	14	generalizations	generalization	NOUN
ejpam-3338	258	15	of	of	ADP
ejpam-3338	258	16	calculus	calculus	NOUN
ejpam-3338	258	17	dealing	deal	VERB
ejpam-3338	258	18	with	with	ADP
ejpam-3338	258	19	both	both	CCONJ
ejpam-3338	258	20	fractional	fractional	ADJ
ejpam-3338	258	21	and	and	CCONJ
ejpam-3338	258	22	integer	integer	NOUN
ejpam-3338	258	23	orders	order	NOUN
ejpam-3338	258	24	.	.	PUNCT
ejpam-3338	259	1	conclusions	conclusion	NOUN
ejpam-3338	259	2	are	be	AUX
ejpam-3338	259	3	included	include	VERB
ejpam-3338	259	4	in	in	ADP
ejpam-3338	259	5	section	section	NOUN
ejpam-3338	259	6	4	4	NUM
ejpam-3338	259	7	.	.	NOUN
ejpam-3338	259	8	2	2	NUM
ejpam-3338	259	9	.	.	NOUN
ejpam-3338	259	10	problems	problem	NOUN
ejpam-3338	259	11	and	and	CCONJ
ejpam-3338	259	12	efforts	effort	NOUN
ejpam-3338	259	13	2.1	2.1	NUM
ejpam-3338	259	14	.	.	PUNCT
ejpam-3338	260	1	leibnitz	leibnitz	PROPN
ejpam-3338	260	2	product	product	NOUN
ejpam-3338	260	3	rule	rule	VERB
ejpam-3338	260	4	the	the	DET
ejpam-3338	260	5	leibniz	leibniz	NOUN
ejpam-3338	260	6	product	product	NOUN
ejpam-3338	260	7	rule	rule	NOUN
ejpam-3338	260	8	(	(	PUNCT
ejpam-3338	260	9	lpr	lpr	PROPN
ejpam-3338	260	10	)	)	PUNCT
ejpam-3338	260	11	for	for	ADP
ejpam-3338	260	12	integer	integer	NOUN
ejpam-3338	260	13	order	order	NOUN
ejpam-3338	260	14	derivatives	derivative	NOUN
ejpam-3338	260	15	(	(	PUNCT
ejpam-3338	260	16	iod	iod	NOUN
ejpam-3338	260	17	)	)	PUNCT
ejpam-3338	260	18	is	be	AUX
ejpam-3338	260	19	d	d	PROPN
ejpam-3338	260	20	dx	dx	PROPN
ejpam-3338	260	21	(	(	PUNCT
ejpam-3338	260	22	f1(x)f2(x	f1(x)f2(x	PROPN
ejpam-3338	260	23	)	)	PUNCT
ejpam-3338	260	24	)	)	PUNCT
ejpam-3338	261	1	=	=	SYM
ejpam-3338	261	2	df1	df1	PROPN
ejpam-3338	261	3	dx	dx	PROPN
ejpam-3338	261	4	f2	f2	PROPN
ejpam-3338	261	5	+	+	CCONJ
ejpam-3338	261	6	f1	f1	PROPN
ejpam-3338	261	7	df2	df2	PROPN
ejpam-3338	261	8	dx	dx	PROPN
ejpam-3338	261	9	(	(	PUNCT
ejpam-3338	261	10	26	26	NUM
ejpam-3338	261	11	)	)	PUNCT
ejpam-3338	261	12	but	but	CCONJ
ejpam-3338	261	13	the	the	DET
ejpam-3338	261	14	lpr	lpr	PROPN
ejpam-3338	261	15	is	be	AUX
ejpam-3338	261	16	not	not	PART
ejpam-3338	261	17	valid	valid	ADJ
ejpam-3338	261	18	for	for	ADP
ejpam-3338	261	19	fractional	fractional	ADJ
ejpam-3338	261	20	order	order	NOUN
ejpam-3338	261	21	derivatives	derivative	NOUN
ejpam-3338	261	22	:	:	PUNCT
ejpam-3338	261	23	dα	dα	PROPN
ejpam-3338	261	24	dx	dx	PROPN
ejpam-3338	261	25	(	(	PUNCT
ejpam-3338	261	26	f1(x)f2(x	f1(x)f2(x	PROPN
ejpam-3338	261	27	)	)	PUNCT
ejpam-3338	261	28	)	)	PUNCT
ejpam-3338	261	29	6=	6=	PRON
ejpam-3338	261	30	dαf1	dαf1	PROPN
ejpam-3338	261	31	dx	dx	PROPN
ejpam-3338	261	32	f2	f2	PROPN
ejpam-3338	261	33	+	+	SYM
ejpam-3338	261	34	f1	f1	PROPN
ejpam-3338	261	35	dαf2	dαf2	PROPN
ejpam-3338	261	36	dx	dx	PROPN
ejpam-3338	261	37	,	,	PUNCT
ejpam-3338	261	38	if(α	if(α	NOUN
ejpam-3338	261	39	6=	6=	PROPN
ejpam-3338	261	40	1	1	NUM
ejpam-3338	261	41	)	)	PUNCT
ejpam-3338	261	42	(	(	PUNCT
ejpam-3338	261	43	27	27	NUM
ejpam-3338	261	44	)	)	PUNCT
ejpam-3338	261	45	the	the	DET
ejpam-3338	261	46	proof	proof	NOUN
ejpam-3338	261	47	follows	follow	VERB
ejpam-3338	261	48	from	from	ADP
ejpam-3338	261	49	the	the	DET
ejpam-3338	261	50	counter	counter	NOUN
ejpam-3338	261	51	-	-	NOUN
ejpam-3338	261	52	example	example	NOUN
ejpam-3338	261	53	where	where	SCONJ
ejpam-3338	261	54	f1(x	f1(x	NOUN
ejpam-3338	261	55	)	)	PUNCT
ejpam-3338	261	56	=	=	SYM
ejpam-3338	261	57	ek1x	ek1x	PROPN
ejpam-3338	261	58	,	,	PUNCT
ejpam-3338	261	59	f2(x	f2(x	PROPN
ejpam-3338	261	60	)	)	PUNCT
ejpam-3338	261	61	=	=	NOUN
ejpam-3338	262	1	ek2x	ek2x	SCONJ
ejpam-3338	262	2	the	the	DET
ejpam-3338	262	3	foregoing	forego	VERB
ejpam-3338	262	4	product	product	NOUN
ejpam-3338	262	5	rule	rule	NOUN
ejpam-3338	262	6	will	will	AUX
ejpam-3338	262	7	be	be	AUX
ejpam-3338	262	8	valid	valid	ADJ
ejpam-3338	262	9	for	for	ADP
ejpam-3338	262	10	the	the	DET
ejpam-3338	262	11	given	give	VERB
ejpam-3338	262	12	problem	problem	NOUN
ejpam-3338	262	13	if	if	SCONJ
ejpam-3338	262	14	kα1	kα1	PROPN
ejpam-3338	262	15	+	+	NUM
ejpam-3338	262	16	kα2	kα2	NOUN
ejpam-3338	263	1	=	=	SYM
ejpam-3338	263	2	(	(	PUNCT
ejpam-3338	263	3	k1	k1	X
ejpam-3338	263	4	+	+	CCONJ
ejpam-3338	263	5	k2)α	k2)α	PROPN
ejpam-3338	263	6	i.e.	i.e.	X
ejpam-3338	263	7	,	,	PUNCT
ejpam-3338	263	8	if	if	SCONJ
ejpam-3338	263	9	k1	k1	PROPN
ejpam-3338	263	10	=	=	SYM
ejpam-3338	263	11	k2	k2	PROPN
ejpam-3338	263	12	s.	s.	PROPN
ejpam-3338	263	13	k.sen	k.sen	PROPN
ejpam-3338	263	14	,	,	PUNCT
ejpam-3338	263	15	j.	j.	PROPN
ejpam-3338	263	16	v.	v.	PROPN
ejpam-3338	263	17	devi	devi	PROPN
ejpam-3338	263	18	,	,	PUNCT
ejpam-3338	263	19	r.v.g	r.v.g	NOUN
ejpam-3338	263	20	.	.	PUNCT
ejpam-3338	264	1	r.	r.	PROPN
ejpam-3338	264	2	kumar	kumar	PROPN
ejpam-3338	264	3	/	/	SYM
ejpam-3338	264	4	eur	eur	PROPN
ejpam-3338	264	5	.	.	PUNCT
ejpam-3338	265	1	j.	j.	PROPN
ejpam-3338	265	2	pure	pure	PROPN
ejpam-3338	265	3	appl	appl	PROPN
ejpam-3338	265	4	.	.	PROPN
ejpam-3338	265	5	math	math	PROPN
ejpam-3338	265	6	,	,	PUNCT
ejpam-3338	265	7	11	11	NUM
ejpam-3338	265	8	(	(	PUNCT
ejpam-3338	265	9	3	3	NUM
ejpam-3338	265	10	)	)	PUNCT
ejpam-3338	265	11	(	(	PUNCT
ejpam-3338	265	12	2018	2018	NUM
ejpam-3338	265	13	)	)	PUNCT
ejpam-3338	265	14	,	,	PUNCT
ejpam-3338	265	15	1058	1058	NUM
ejpam-3338	265	16	-	-	SYM
ejpam-3338	265	17	1099	1099	NUM
ejpam-3338	265	18	1069	1069	NUM
ejpam-3338	265	19	and	and	CCONJ
ejpam-3338	265	20	α	α	NOUN
ejpam-3338	265	21	=	=	PUNCT
ejpam-3338	265	22	any	any	DET
ejpam-3338	265	23	nonnegative	nonnegative	ADJ
ejpam-3338	265	24	integer	integer	NOUN
ejpam-3338	265	25	,	,	PUNCT
ejpam-3338	265	26	or	or	CCONJ
ejpam-3338	265	27	α	α	NOUN
ejpam-3338	265	28	=	=	SYM
ejpam-3338	265	29	1	1	X
ejpam-3338	265	30	.	.	PUNCT
ejpam-3338	266	1	this	this	PRON
ejpam-3338	266	2	is	be	AUX
ejpam-3338	266	3	undesirable	undesirable	ADJ
ejpam-3338	266	4	for	for	ADP
ejpam-3338	266	5	a	a	DET
ejpam-3338	266	6	generalization	generalization	NOUN
ejpam-3338	266	7	of	of	ADP
ejpam-3338	266	8	the	the	DET
ejpam-3338	266	9	rule	rule	NOUN
ejpam-3338	266	10	.	.	PUNCT
ejpam-3338	267	1	is	be	AUX
ejpam-3338	267	2	this	this	DET
ejpam-3338	267	3	problem	problem	NOUN
ejpam-3338	267	4	not	not	PART
ejpam-3338	267	5	surmountable	surmountable	ADJ
ejpam-3338	267	6	by	by	ADP
ejpam-3338	267	7	designing	design	VERB
ejpam-3338	267	8	an	an	DET
ejpam-3338	267	9	appropriate	appropriate	ADJ
ejpam-3338	267	10	procedure	procedure	NOUN
ejpam-3338	267	11	?	?	PUNCT
ejpam-3338	268	1	the	the	DET
ejpam-3338	268	2	answer	answer	NOUN
ejpam-3338	268	3	is	be	AUX
ejpam-3338	268	4	no	no	PRON
ejpam-3338	268	5	.	.	PUNCT
ejpam-3338	269	1	that	that	PRON
ejpam-3338	269	2	is	is	ADV
ejpam-3338	269	3	,	,	PUNCT
ejpam-3338	269	4	the	the	DET
ejpam-3338	269	5	problem	problem	NOUN
ejpam-3338	269	6	is	be	AUX
ejpam-3338	269	7	surmountable	surmountable	ADJ
ejpam-3338	269	8	.	.	PUNCT
ejpam-3338	270	1	the	the	DET
ejpam-3338	270	2	lpr	lpr	PROPN
ejpam-3338	270	3	for	for	ADP
ejpam-3338	270	4	generalized	generalized	ADJ
ejpam-3338	270	5	derivative	derivative	NOUN
ejpam-3338	270	6	(	(	PUNCT
ejpam-3338	270	7	valid	valid	ADJ
ejpam-3338	270	8	for	for	ADP
ejpam-3338	270	9	iod	iod	NOUN
ejpam-3338	270	10	as	as	ADV
ejpam-3338	270	11	well	well	ADV
ejpam-3338	270	12	as	as	ADP
ejpam-3338	270	13	fractional	fractional	ADJ
ejpam-3338	270	14	order	order	NOUN
ejpam-3338	270	15	derivative	derivative	NOUN
ejpam-3338	270	16	(	(	PUNCT
ejpam-3338	270	17	fod	fod	PROPN
ejpam-3338	270	18	)	)	PUNCT
ejpam-3338	270	19	may	may	AUX
ejpam-3338	270	20	be	be	AUX
ejpam-3338	270	21	given	give	VERB
ejpam-3338	270	22	:	:	PUNCT
ejpam-3338	270	23	define	define	VERB
ejpam-3338	270	24	dα	dα	ADJ
ejpam-3338	270	25	dxα	dxα	ADJ
ejpam-3338	270	26	=	=	PUNCT
ejpam-3338	270	27	dα	dα	ADJ
ejpam-3338	270	28	when	when	SCONJ
ejpam-3338	270	29	α	α	NOUN
ejpam-3338	270	30	=	=	SYM
ejpam-3338	270	31	n	n	CCONJ
ejpam-3338	270	32	∈	∈	NOUN
ejpam-3338	270	33	n	n	PRON
ejpam-3338	270	34	is	be	AUX
ejpam-3338	270	35	an	an	DET
ejpam-3338	270	36	arbitrary	arbitrary	ADJ
ejpam-3338	270	37	integer	integer	NOUN
ejpam-3338	270	38	(	(	PUNCT
ejpam-3338	270	39	n	n	X
ejpam-3338	270	40	is	be	AUX
ejpam-3338	270	41	the	the	DET
ejpam-3338	270	42	set	set	NOUN
ejpam-3338	270	43	of	of	ADP
ejpam-3338	270	44	natural	natural	ADJ
ejpam-3338	270	45	numbers	number	NOUN
ejpam-3338	270	46	)	)	PUNCT
ejpam-3338	270	47	,	,	PUNCT
ejpam-3338	270	48	then	then	ADV
ejpam-3338	270	49	dn(f1f2	dn(f1f2	PROPN
ejpam-3338	270	50	)	)	PUNCT
ejpam-3338	270	51	=	=	SYM
ejpam-3338	270	52	n∑	n∑	PROPN
ejpam-3338	270	53	j=0	j=0	PROPN
ejpam-3338	270	54	ncjd	ncjd	NOUN
ejpam-3338	270	55	n−jf1d	n−jf1d	X
ejpam-3338	270	56	jf2	jf2	ADV
ejpam-3338	270	57	(	(	PUNCT
ejpam-3338	270	58	28	28	NUM
ejpam-3338	270	59	)	)	PUNCT
ejpam-3338	270	60	for	for	ADP
ejpam-3338	270	61	arbitrary	arbitrary	ADJ
ejpam-3338	270	62	α	α	NOUN
ejpam-3338	270	63	,	,	PUNCT
ejpam-3338	270	64	dα(f1f2	dα(f1f2	PROPN
ejpam-3338	270	65	)	)	PUNCT
ejpam-3338	270	66	=	=	PROPN
ejpam-3338	271	1	∞∑	∞∑	NUM
ejpam-3338	271	2	j=0	j=0	PROPN
ejpam-3338	271	3	αcjd	αcjd	NOUN
ejpam-3338	271	4	α−jf1d	α−jf1d	NOUN
ejpam-3338	271	5	jf2	jf2	ADV
ejpam-3338	271	6	(	(	PUNCT
ejpam-3338	271	7	29	29	NUM
ejpam-3338	271	8	)	)	PUNCT
ejpam-3338	271	9	where	where	SCONJ
ejpam-3338	271	10	f1	f1	NOUN
ejpam-3338	271	11	,	,	PUNCT
ejpam-3338	271	12	f2	f2	PROPN
ejpam-3338	271	13	are	be	AUX
ejpam-3338	271	14	functions	function	NOUN
ejpam-3338	271	15	of	of	ADP
ejpam-3338	271	16	the	the	DET
ejpam-3338	271	17	independent	independent	ADJ
ejpam-3338	271	18	variable	variable	NOUN
ejpam-3338	271	19	x.	x.	NOUN
ejpam-3338	272	1	the	the	DET
ejpam-3338	272	2	foregoing	forego	VERB
ejpam-3338	272	3	rules	rule	NOUN
ejpam-3338	272	4	(	(	PUNCT
ejpam-3338	272	5	28	28	NUM
ejpam-3338	272	6	)	)	PUNCT
ejpam-3338	272	7	and	and	CCONJ
ejpam-3338	272	8	(	(	PUNCT
ejpam-3338	272	9	29	29	NUM
ejpam-3338	272	10	)	)	PUNCT
ejpam-3338	272	11	,	,	PUNCT
ejpam-3338	272	12	though	though	SCONJ
ejpam-3338	272	13	more	more	ADV
ejpam-3338	272	14	expensive	expensive	ADJ
ejpam-3338	272	15	,	,	PUNCT
ejpam-3338	272	16	in	in	ADP
ejpam-3338	272	17	general	general	ADJ
ejpam-3338	272	18	,	,	PUNCT
ejpam-3338	272	19	from	from	ADP
ejpam-3338	272	20	quality	quality	NOUN
ejpam-3338	272	21	(	(	PUNCT
ejpam-3338	272	22	implying	imply	VERB
ejpam-3338	272	23	more	more	ADV
ejpam-3338	272	24	computational	computational	ADJ
ejpam-3338	272	25	relative	relative	ADJ
ejpam-3338	272	26	error	error	NOUN
ejpam-3338	272	27	)	)	PUNCT
ejpam-3338	272	28	and	and	CCONJ
ejpam-3338	272	29	cost	cost	NOUN
ejpam-3338	272	30	(	(	PUNCT
ejpam-3338	272	31	implying	imply	VERB
ejpam-3338	272	32	more	more	ADV
ejpam-3338	272	33	computational	computational	ADJ
ejpam-3338	272	34	complexity	complexity	NOUN
ejpam-3338	272	35	)	)	PUNCT
ejpam-3338	272	36	points	point	NOUN
ejpam-3338	272	37	of	of	ADP
ejpam-3338	272	38	view	view	NOUN
ejpam-3338	272	39	,	,	PUNCT
ejpam-3338	272	40	are	be	AUX
ejpam-3338	272	41	still	still	ADV
ejpam-3338	272	42	generalized	generalize	VERB
ejpam-3338	272	43	lpr	lpr	PROPN
ejpam-3338	272	44	.	.	PUNCT
ejpam-3338	273	1	however	however	ADV
ejpam-3338	273	2	,	,	PUNCT
ejpam-3338	273	3	a	a	DET
ejpam-3338	273	4	direct	direct	ADJ
ejpam-3338	273	5	transfer	transfer	NOUN
ejpam-3338	273	6	of	of	ADP
ejpam-3338	273	7	any	any	DET
ejpam-3338	273	8	standard	standard	ADJ
ejpam-3338	273	9	rule	rule	NOUN
ejpam-3338	273	10	of	of	ADP
ejpam-3338	273	11	classical	classical	ADJ
ejpam-3338	273	12	calculus	calculus	NOUN
ejpam-3338	273	13	to	to	ADP
ejpam-3338	273	14	fractional	fractional	ADJ
ejpam-3338	273	15	calculus	calculus	NOUN
ejpam-3338	273	16	could	could	AUX
ejpam-3338	273	17	be	be	AUX
ejpam-3338	273	18	hazardous	hazardous	ADJ
ejpam-3338	273	19	.	.	PUNCT
ejpam-3338	274	1	in	in	ADP
ejpam-3338	274	2	every	every	DET
ejpam-3338	274	3	case	case	NOUN
ejpam-3338	274	4	the	the	DET
ejpam-3338	274	5	rule	rule	NOUN
ejpam-3338	274	6	used	use	VERB
ejpam-3338	274	7	in	in	ADP
ejpam-3338	274	8	fractional	fractional	ADJ
ejpam-3338	274	9	calculus	calculus	NOUN
ejpam-3338	274	10	needs	need	NOUN
ejpam-3338	274	11	to	to	PART
ejpam-3338	274	12	be	be	AUX
ejpam-3338	274	13	checked	check	VERB
ejpam-3338	274	14	for	for	ADP
ejpam-3338	274	15	its	its	PRON
ejpam-3338	274	16	validity	validity	NOUN
ejpam-3338	274	17	.	.	PUNCT
ejpam-3338	275	1	a	a	DET
ejpam-3338	275	2	useful	useful	ADJ
ejpam-3338	275	3	strategy	strategy	NOUN
ejpam-3338	275	4	for	for	ADP
ejpam-3338	275	5	a	a	DET
ejpam-3338	275	6	satisfactory	satisfactory	ADJ
ejpam-3338	275	7	generalization	generalization	NOUN
ejpam-3338	275	8	scheme	scheme	NOUN
ejpam-3338	275	9	is	be	AUX
ejpam-3338	275	10	a	a	DET
ejpam-3338	275	11	2	2	NUM
ejpam-3338	275	12	-	-	PUNCT
ejpam-3338	275	13	step	step	NOUN
ejpam-3338	275	14	procedure[1	procedure[1	NOUN
ejpam-3338	275	15	]	]	PUNCT
ejpam-3338	275	16	:	:	PUNCT
ejpam-3338	275	17	step	step	NOUN
ejpam-3338	275	18	1	1	NUM
ejpam-3338	275	19	.	.	PUNCT
ejpam-3338	275	20	derive	derive	VERB
ejpam-3338	275	21	a	a	DET
ejpam-3338	275	22	rule	rule	NOUN
ejpam-3338	275	23	which	which	PRON
ejpam-3338	275	24	is	be	AUX
ejpam-3338	275	25	valid	valid	ADJ
ejpam-3338	275	26	for	for	ADP
ejpam-3338	275	27	all	all	PRON
ejpam-3338	275	28	n	n	PRON
ejpam-3338	275	29	∈	∈	PROPN
ejpam-3338	275	30	n	n	NOUN
ejpam-3338	275	31	.	.	PUNCT
ejpam-3338	276	1	step	step	NOUN
ejpam-3338	276	2	2	2	NUM
ejpam-3338	276	3	.	.	PUNCT
ejpam-3338	276	4	replace	replace	VERB
ejpam-3338	276	5	n	n	NOUN
ejpam-3338	276	6	by	by	ADP
ejpam-3338	276	7	α	α	PROPN
ejpam-3338	276	8	∈	∈	PROPN
ejpam-3338	276	9	c	c	PROPN
ejpam-3338	276	10	and	and	CCONJ
ejpam-3338	276	11	check	check	VERB
ejpam-3338	276	12	the	the	DET
ejpam-3338	276	13	validity	validity	NOUN
ejpam-3338	276	14	,	,	PUNCT
ejpam-3338	276	15	where	where	SCONJ
ejpam-3338	276	16	c	c	PROPN
ejpam-3338	276	17	is	be	AUX
ejpam-3338	276	18	the	the	DET
ejpam-3338	276	19	set	set	NOUN
ejpam-3338	276	20	of	of	ADP
ejpam-3338	276	21	complex	complex	ADJ
ejpam-3338	276	22	numbers	number	NOUN
ejpam-3338	276	23	.	.	PUNCT
ejpam-3338	277	1	computationally	computationally	ADV
ejpam-3338	277	2	,	,	PUNCT
ejpam-3338	277	3	the	the	DET
ejpam-3338	277	4	lpr	lpr	PROPN
ejpam-3338	277	5	is	be	AUX
ejpam-3338	277	6	not	not	PART
ejpam-3338	277	7	an	an	DET
ejpam-3338	277	8	essentially	essentially	ADV
ejpam-3338	277	9	required	require	VERB
ejpam-3338	277	10	rule	rule	NOUN
ejpam-3338	277	11	.	.	PUNCT
ejpam-3338	278	1	computation	computation	NOUN
ejpam-3338	278	2	is	be	AUX
ejpam-3338	278	3	a	a	DET
ejpam-3338	278	4	must	must	NOUN
ejpam-3338	278	5	in	in	ADP
ejpam-3338	278	6	all	all	DET
ejpam-3338	278	7	engineering	engineering	NOUN
ejpam-3338	278	8	and	and	CCONJ
ejpam-3338	278	9	science	science	NOUN
ejpam-3338	278	10	applications	application	NOUN
ejpam-3338	278	11	.	.	PUNCT
ejpam-3338	279	1	nobody	nobody	PRON
ejpam-3338	279	2	can	can	AUX
ejpam-3338	279	3	escape	escape	VERB
ejpam-3338	279	4	computation	computation	NOUN
ejpam-3338	279	5	if	if	SCONJ
ejpam-3338	279	6	he	he	PRON
ejpam-3338	279	7	has	have	VERB
ejpam-3338	279	8	some	some	DET
ejpam-3338	279	9	thing	thing	NOUN
ejpam-3338	279	10	to	to	PART
ejpam-3338	279	11	do	do	VERB
ejpam-3338	279	12	with	with	ADP
ejpam-3338	279	13	a	a	DET
ejpam-3338	279	14	real	real	ADJ
ejpam-3338	279	15	world	world	NOUN
ejpam-3338	279	16	physical	physical	ADJ
ejpam-3338	279	17	problem	problem	NOUN
ejpam-3338	279	18	.	.	PUNCT
ejpam-3338	280	1	consequently	consequently	ADV
ejpam-3338	280	2	,	,	PUNCT
ejpam-3338	280	3	it	it	PRON
ejpam-3338	280	4	is	be	AUX
ejpam-3338	280	5	very	very	ADV
ejpam-3338	280	6	much	much	ADV
ejpam-3338	280	7	more	more	ADV
ejpam-3338	280	8	important	important	ADJ
ejpam-3338	280	9	than	than	ADP
ejpam-3338	280	10	the	the	DET
ejpam-3338	280	11	pure	pure	ADJ
ejpam-3338	280	12	mathematical	mathematical	ADJ
ejpam-3338	280	13	treatment	treatment	NOUN
ejpam-3338	280	14	of	of	ADP
ejpam-3338	280	15	fractional	fractional	ADJ
ejpam-3338	280	16	calculus	calculus	NOUN
ejpam-3338	280	17	/	/	SYM
ejpam-3338	280	18	differential	differential	NOUN
ejpam-3338	280	19	equations	equation	NOUN
ejpam-3338	280	20	.	.	PUNCT
ejpam-3338	281	1	let	let	VERB
ejpam-3338	281	2	x	x	PRON
ejpam-3338	281	3	be	be	AUX
ejpam-3338	281	4	defined	define	VERB
ejpam-3338	281	5	in	in	ADP
ejpam-3338	281	6	a	a	DET
ejpam-3338	281	7	finite	finite	ADJ
ejpam-3338	281	8	interval	interval	NOUN
ejpam-3338	281	9	[	[	X
ejpam-3338	281	10	a	a	X
ejpam-3338	281	11	,	,	PUNCT
ejpam-3338	281	12	b	b	NOUN
ejpam-3338	281	13	]	]	X
ejpam-3338	281	14	,	,	PUNCT
ejpam-3338	281	15	where	where	SCONJ
ejpam-3338	281	16	a	a	DET
ejpam-3338	281	17	,	,	PUNCT
ejpam-3338	281	18	b	b	NOUN
ejpam-3338	281	19	are	be	AUX
ejpam-3338	281	20	numerical	numerical	ADJ
ejpam-3338	281	21	values	value	NOUN
ejpam-3338	281	22	.	.	PUNCT
ejpam-3338	282	1	suppose	suppose	VERB
ejpam-3338	282	2	that	that	SCONJ
ejpam-3338	282	3	f1(x	f1(x	PROPN
ejpam-3338	282	4	)	)	PUNCT
ejpam-3338	282	5	,	,	PUNCT
ejpam-3338	282	6	f2(x	f2(x	PROPN
ejpam-3338	282	7	)	)	PUNCT
ejpam-3338	282	8	,	,	PUNCT
ejpam-3338	282	9	f1(x)f2(x	f1(x)f2(x	PROPN
ejpam-3338	282	10	)	)	PUNCT
ejpam-3338	282	11	are	be	AUX
ejpam-3338	282	12	functions	function	NOUN
ejpam-3338	282	13	defined	define	VERB
ejpam-3338	282	14	by	by	ADP
ejpam-3338	282	15	/	/	SYM
ejpam-3338	282	16	computed	compute	VERB
ejpam-3338	282	17	as	as	ADP
ejpam-3338	282	18	a	a	DET
ejpam-3338	282	19	numerical	numerical	ADJ
ejpam-3338	282	20	table	table	NOUN
ejpam-3338	282	21	having	have	VERB
ejpam-3338	282	22	4	4	NUM
ejpam-3338	282	23	columns	column	NOUN
ejpam-3338	282	24	viz	viz	NOUN
ejpam-3338	282	25	.	.	PUNCT
ejpam-3338	283	1	x	x	PUNCT
ejpam-3338	283	2	f1(x	f1(x	NOUN
ejpam-3338	283	3	)	)	PUNCT
ejpam-3338	283	4	f2(x	f2(x	NOUN
ejpam-3338	283	5	)	)	PUNCT
ejpam-3338	283	6	f1(x)f2(x	f1(x)f2(x	PROPN
ejpam-3338	283	7	)	)	PUNCT
ejpam-3338	284	1	a	a	DET
ejpam-3338	284	2	f1(a	f1(a	PROPN
ejpam-3338	284	3	)	)	PUNCT
ejpam-3338	284	4	f2(a	f2(a	NOUN
ejpam-3338	284	5	)	)	PUNCT
ejpam-3338	284	6	f1(a)f2(a	f1(a)f2(a	NOUN
ejpam-3338	284	7	)	)	PUNCT
ejpam-3338	284	8	.	.	PUNCT
ejpam-3338	285	1	.	.	PUNCT
ejpam-3338	285	2	.	.	PUNCT
ejpam-3338	286	1	s.	s.	PROPN
ejpam-3338	286	2	k.sen	k.sen	PROPN
ejpam-3338	286	3	,	,	PUNCT
ejpam-3338	286	4	j.	j.	PROPN
ejpam-3338	286	5	v.	v.	PROPN
ejpam-3338	286	6	devi	devi	PROPN
ejpam-3338	286	7	,	,	PUNCT
ejpam-3338	286	8	r.v.g	r.v.g	NOUN
ejpam-3338	286	9	.	.	PUNCT
ejpam-3338	287	1	r.	r.	PROPN
ejpam-3338	287	2	kumar	kumar	PROPN
ejpam-3338	287	3	/	/	SYM
ejpam-3338	287	4	eur	eur	PROPN
ejpam-3338	287	5	.	.	PUNCT
ejpam-3338	288	1	j.	j.	PROPN
ejpam-3338	288	2	pure	pure	PROPN
ejpam-3338	288	3	appl	appl	PROPN
ejpam-3338	288	4	.	.	PROPN
ejpam-3338	288	5	math	math	PROPN
ejpam-3338	288	6	,	,	PUNCT
ejpam-3338	288	7	11	11	NUM
ejpam-3338	288	8	(	(	PUNCT
ejpam-3338	288	9	3	3	NUM
ejpam-3338	288	10	)	)	PUNCT
ejpam-3338	288	11	(	(	PUNCT
ejpam-3338	288	12	2018	2018	NUM
ejpam-3338	288	13	)	)	PUNCT
ejpam-3338	288	14	,	,	PUNCT
ejpam-3338	288	15	1058	1058	NUM
ejpam-3338	288	16	-	-	SYM
ejpam-3338	288	17	1099	1099	NUM
ejpam-3338	288	18	1070	1070	NUM
ejpam-3338	288	19	b	b	X
ejpam-3338	288	20	f1(b	f1(b	NOUN
ejpam-3338	288	21	)	)	PUNCT
ejpam-3338	288	22	f2(b	f2(b	NOUN
ejpam-3338	288	23	)	)	PUNCT
ejpam-3338	288	24	f1(b)f2(b	f1(b)f2(b	X
ejpam-3338	288	25	)	)	PUNCT
ejpam-3338	288	26	all	all	DET
ejpam-3338	288	27	the	the	DET
ejpam-3338	288	28	entries	entry	NOUN
ejpam-3338	288	29	from	from	ADP
ejpam-3338	288	30	the	the	DET
ejpam-3338	288	31	2nd	2nd	ADJ
ejpam-3338	288	32	row	row	NOUN
ejpam-3338	288	33	to	to	ADP
ejpam-3338	288	34	the	the	DET
ejpam-3338	288	35	last	last	ADJ
ejpam-3338	288	36	row	row	NOUN
ejpam-3338	288	37	are	be	AUX
ejpam-3338	288	38	all	all	PRON
ejpam-3338	288	39	numerical	numerical	ADJ
ejpam-3338	288	40	elements	element	NOUN
ejpam-3338	288	41	.	.	PUNCT
ejpam-3338	289	1	one	one	PRON
ejpam-3338	289	2	may	may	AUX
ejpam-3338	289	3	use	use	VERB
ejpam-3338	289	4	the	the	DET
ejpam-3338	289	5	1st	1st	NOUN
ejpam-3338	289	6	and	and	CCONJ
ejpam-3338	289	7	the	the	DET
ejpam-3338	289	8	4th	4th	ADJ
ejpam-3338	289	9	columns	column	NOUN
ejpam-3338	289	10	of	of	ADP
ejpam-3338	289	11	the	the	DET
ejpam-3338	289	12	foregoing	forego	VERB
ejpam-3338	289	13	table	table	NOUN
ejpam-3338	289	14	to	to	PART
ejpam-3338	289	15	compute	compute	VERB
ejpam-3338	289	16	a	a	DET
ejpam-3338	289	17	fractional	fractional	ADJ
ejpam-3338	289	18	numerical	numerical	ADJ
ejpam-3338	289	19	derivative	derivative	NOUN
ejpam-3338	289	20	based	base	VERB
ejpam-3338	289	21	on	on	ADP
ejpam-3338	289	22	1	1	NUM
ejpam-3338	289	23	of	of	ADP
ejpam-3338	289	24	the	the	DET
ejpam-3338	289	25	definitions	definition	NOUN
ejpam-3338	289	26	such	such	ADJ
ejpam-3338	289	27	as	as	ADP
ejpam-3338	289	28	the	the	DET
ejpam-3338	289	29	grunwald	grunwald	NOUN
ejpam-3338	289	30	-	-	PUNCT
ejpam-3338	289	31	letnikov	letnikov	NOUN
ejpam-3338	289	32	definition	definition	NOUN
ejpam-3338	289	33	.	.	PUNCT
ejpam-3338	290	1	in	in	ADP
ejpam-3338	290	2	case	case	NOUN
ejpam-3338	290	3	of	of	ADP
ejpam-3338	290	4	3	3	NUM
ejpam-3338	290	5	or	or	CCONJ
ejpam-3338	290	6	more	more	ADJ
ejpam-3338	290	7	functions	function	NOUN
ejpam-3338	290	8	,	,	PUNCT
ejpam-3338	290	9	the	the	DET
ejpam-3338	290	10	product	product	NOUN
ejpam-3338	290	11	rule	rule	NOUN
ejpam-3338	290	12	can	can	AUX
ejpam-3338	290	13	be	be	AUX
ejpam-3338	290	14	obviated	obviate	VERB
ejpam-3338	290	15	similarly	similarly	ADV
ejpam-3338	290	16	.	.	PUNCT
ejpam-3338	291	1	hence	hence	ADV
ejpam-3338	291	2	generalization	generalization	NOUN
ejpam-3338	291	3	problem	problem	NOUN
ejpam-3338	291	4	for	for	ADP
ejpam-3338	291	5	lpr	lpr	PROPN
ejpam-3338	291	6	is	be	AUX
ejpam-3338	291	7	numerically	numerically	ADV
ejpam-3338	291	8	computationally	computationally	ADV
ejpam-3338	291	9	non	non	ADJ
ejpam-3338	291	10	-	-	ADJ
ejpam-3338	291	11	existent	existent	ADJ
ejpam-3338	291	12	.	.	PUNCT
ejpam-3338	292	1	2.2	2.2	NUM
ejpam-3338	292	2	.	.	PUNCT
ejpam-3338	292	3	fractional	fractional	ADJ
ejpam-3338	292	4	derivatives	derivative	NOUN
ejpam-3338	292	5	of	of	ADP
ejpam-3338	292	6	general	general	ADJ
ejpam-3338	292	7	functions	function	NOUN
ejpam-3338	292	8	:	:	PUNCT
ejpam-3338	292	9	values	value	NOUN
ejpam-3338	292	10	and	and	CCONJ
ejpam-3338	292	11	graphs	graph	NOUN
ejpam-3338	292	12	we	we	PRON
ejpam-3338	292	13	present	present	VERB
ejpam-3338	292	14	some	some	PRON
ejpam-3338	292	15	of	of	ADP
ejpam-3338	292	16	the	the	DET
ejpam-3338	292	17	fractional	fractional	ADJ
ejpam-3338	292	18	derivatives	derivative	NOUN
ejpam-3338	292	19	for	for	ADP
ejpam-3338	292	20	a	a	DET
ejpam-3338	292	21	general	general	ADJ
ejpam-3338	292	22	function	function	NOUN
ejpam-3338	292	23	.	.	PUNCT
ejpam-3338	293	1	the	the	DET
ejpam-3338	293	2	presentation	presentation	NOUN
ejpam-3338	293	3	will	will	AUX
ejpam-3338	293	4	help	help	VERB
ejpam-3338	293	5	one	one	NOUN
ejpam-3338	293	6	to	to	PART
ejpam-3338	293	7	get	get	VERB
ejpam-3338	293	8	a	a	DET
ejpam-3338	293	9	feel	feel	NOUN
ejpam-3338	293	10	about	about	ADP
ejpam-3338	293	11	the	the	DET
ejpam-3338	293	12	scope	scope	NOUN
ejpam-3338	293	13	of	of	ADP
ejpam-3338	293	14	each	each	DET
ejpam-3338	293	15	one	one	NUM
ejpam-3338	293	16	of	of	ADP
ejpam-3338	293	17	them	they	PRON
ejpam-3338	293	18	.	.	PUNCT
ejpam-3338	294	1	consequently	consequently	ADV
ejpam-3338	294	2	one	one	PRON
ejpam-3338	294	3	can	can	AUX
ejpam-3338	294	4	decide	decide	VERB
ejpam-3338	294	5	which	which	PRON
ejpam-3338	294	6	of	of	ADP
ejpam-3338	294	7	the	the	DET
ejpam-3338	294	8	definitions	definition	NOUN
ejpam-3338	294	9	would	would	AUX
ejpam-3338	294	10	be	be	AUX
ejpam-3338	294	11	more	more	ADV
ejpam-3338	294	12	desirable	desirable	ADJ
ejpam-3338	294	13	/	/	SYM
ejpam-3338	294	14	suitable	suitable	ADJ
ejpam-3338	294	15	as	as	ADP
ejpam-3338	294	16	an	an	DET
ejpam-3338	294	17	attempt	attempt	NOUN
ejpam-3338	294	18	to	to	PART
ejpam-3338	294	19	generalize	generalize	VERB
ejpam-3338	294	20	the	the	DET
ejpam-3338	294	21	calculus	calculus	NOUN
ejpam-3338	294	22	.	.	PUNCT
ejpam-3338	295	1	it	it	PRON
ejpam-3338	295	2	is	be	AUX
ejpam-3338	295	3	also	also	ADV
ejpam-3338	295	4	possible	possible	ADJ
ejpam-3338	295	5	that	that	SCONJ
ejpam-3338	295	6	a	a	DET
ejpam-3338	295	7	new	new	ADJ
ejpam-3338	295	8	definition	definition	NOUN
ejpam-3338	295	9	for	for	ADP
ejpam-3338	295	10	the	the	DET
ejpam-3338	295	11	fractional	fractional	ADJ
ejpam-3338	295	12	derivative	derivative	NOUN
ejpam-3338	295	13	can	can	AUX
ejpam-3338	295	14	be	be	AUX
ejpam-3338	295	15	proposed	propose	VERB
ejpam-3338	295	16	,	,	PUNCT
ejpam-3338	295	17	which	which	PRON
ejpam-3338	295	18	would	would	AUX
ejpam-3338	295	19	allow	allow	VERB
ejpam-3338	295	20	a	a	DET
ejpam-3338	295	21	better	well	ADJ
ejpam-3338	295	22	generalization	generalization	NOUN
ejpam-3338	295	23	(	(	PUNCT
ejpam-3338	295	24	with	with	ADP
ejpam-3338	295	25	possibly	possibly	ADV
ejpam-3338	295	26	less	less	ADJ
ejpam-3338	295	27	error	error	NOUN
ejpam-3338	295	28	and	and	CCONJ
ejpam-3338	295	29	less	less	ADJ
ejpam-3338	295	30	computation	computation	NOUN
ejpam-3338	295	31	)	)	PUNCT
ejpam-3338	295	32	.	.	PUNCT
ejpam-3338	296	1	grunwald	grunwald	NOUN
ejpam-3338	296	2	-	-	PUNCT
ejpam-3338	296	3	letnikov	letnikov	NOUN
ejpam-3338	296	4	derivative	derivative	NOUN
ejpam-3338	296	5	(	(	PUNCT
ejpam-3338	296	6	reverse	reverse	NOUN
ejpam-3338	296	7	)	)	PUNCT
ejpam-3338	296	8	dαf(x	dαf(x	PROPN
ejpam-3338	296	9	)	)	PUNCT
ejpam-3338	296	10	=	=	PUNCT
ejpam-3338	297	1	limh→0	limh→0	NOUN
ejpam-3338	297	2	1	1	NUM
ejpam-3338	297	3	hα	hα	ADP
ejpam-3338	297	4	∑	∑	PROPN
ejpam-3338	297	5	(	(	PUNCT
ejpam-3338	297	6	0≤m<∞	0≤m<∞	ADV
ejpam-3338	297	7	)	)	PUNCT
ejpam-3338	297	8	(	(	PUNCT
ejpam-3338	297	9	−1)m	−1)m	PROPN
ejpam-3338	297	10	(	(	PUNCT
ejpam-3338	297	11	αcm)f(x+	αcm)f(x+	ADV
ejpam-3338	297	12	(	(	PUNCT
ejpam-3338	297	13	α−m)h	α−m)h	PROPN
ejpam-3338	297	14	)	)	PUNCT
ejpam-3338	297	15	=	=	PUNCT
ejpam-3338	298	1	limh→0	limh→0	NOUN
ejpam-3338	298	2	1	1	NUM
ejpam-3338	298	3	hα	hα	ADP
ejpam-3338	298	4	∑	∑	PROPN
ejpam-3338	298	5	(	(	PUNCT
ejpam-3338	298	6	0≤m<∞	0≤m<∞	ADV
ejpam-3338	298	7	)	)	PUNCT
ejpam-3338	298	8	(	(	PUNCT
ejpam-3338	298	9	−1)m	−1)m	PROPN
ejpam-3338	298	10	γ(1	γ(1	PROPN
ejpam-3338	298	11	+	+	NUM
ejpam-3338	298	12	α	α	X
ejpam-3338	298	13	)	)	PUNCT
ejpam-3338	298	14	γ(1	γ(1	PROPN
ejpam-3338	299	1	+	+	PUNCT
ejpam-3338	299	2	m)γ(1	m)γ(1	PROPN
ejpam-3338	299	3	+	+	CCONJ
ejpam-3338	299	4	α−m	α−m	NOUN
ejpam-3338	299	5	)	)	PUNCT
ejpam-3338	299	6	f(x+	f(x+	NOUN
ejpam-3338	299	7	(	(	PUNCT
ejpam-3338	299	8	α−m)h	α−m)h	PROPN
ejpam-3338	299	9	)	)	PUNCT
ejpam-3338	299	10	(	(	PUNCT
ejpam-3338	299	11	30	30	NUM
ejpam-3338	299	12	)	)	PUNCT
ejpam-3338	299	13	grunwald	grunwald	NOUN
ejpam-3338	299	14	-	-	PUNCT
ejpam-3338	299	15	letnikov	letnikov	NOUN
ejpam-3338	299	16	derivative	derivative	NOUN
ejpam-3338	299	17	(	(	PUNCT
ejpam-3338	299	18	direct	direct	ADJ
ejpam-3338	299	19	)	)	PUNCT
ejpam-3338	299	20	set	set	VERB
ejpam-3338	299	21	h	h	NOUN
ejpam-3338	299	22	=	=	PUNCT
ejpam-3338	299	23	−h	−h	PROPN
ejpam-3338	299	24	dαf(x	dαf(x	PROPN
ejpam-3338	299	25	)	)	PUNCT
ejpam-3338	299	26	=	=	PUNCT
ejpam-3338	299	27	limh→0	limh→0	NOUN
ejpam-3338	299	28	1	1	NUM
ejpam-3338	299	29	hα	hα	ADP
ejpam-3338	299	30	∑	∑	PROPN
ejpam-3338	299	31	(	(	PUNCT
ejpam-3338	299	32	0≤m<∞	0≤m<∞	ADV
ejpam-3338	299	33	)	)	PUNCT
ejpam-3338	299	34	(	(	PUNCT
ejpam-3338	299	35	−1)m	−1)m	PROPN
ejpam-3338	299	36	(	(	PUNCT
ejpam-3338	299	37	αcm)f(x−	αcm)f(x−	PROPN
ejpam-3338	299	38	(	(	PUNCT
ejpam-3338	299	39	α−m)h	α−m)h	PROPN
ejpam-3338	299	40	)	)	PUNCT
ejpam-3338	299	41	=	=	PUNCT
ejpam-3338	300	1	limh→0	limh→0	NOUN
ejpam-3338	300	2	1	1	NUM
ejpam-3338	300	3	hα	hα	ADP
ejpam-3338	300	4	∑	∑	PROPN
ejpam-3338	300	5	(	(	PUNCT
ejpam-3338	300	6	0≤m<∞	0≤m<∞	ADV
ejpam-3338	300	7	)	)	PUNCT
ejpam-3338	300	8	(	(	PUNCT
ejpam-3338	300	9	−1)m	−1)m	PROPN
ejpam-3338	300	10	γ(1	γ(1	PROPN
ejpam-3338	300	11	+	+	NUM
ejpam-3338	300	12	α	α	X
ejpam-3338	300	13	)	)	PUNCT
ejpam-3338	300	14	γ(1	γ(1	PROPN
ejpam-3338	301	1	+	+	PUNCT
ejpam-3338	301	2	m)γ(1	m)γ(1	PROPN
ejpam-3338	301	3	+	+	CCONJ
ejpam-3338	301	4	α−m	α−m	NOUN
ejpam-3338	301	5	)	)	PUNCT
ejpam-3338	301	6	f(x+	f(x+	NOUN
ejpam-3338	301	7	(	(	PUNCT
ejpam-3338	301	8	α−m)h	α−m)h	PROPN
ejpam-3338	301	9	)	)	PUNCT
ejpam-3338	301	10	(	(	PUNCT
ejpam-3338	301	11	31	31	NUM
ejpam-3338	301	12	)	)	PUNCT
ejpam-3338	301	13	we	we	PRON
ejpam-3338	301	14	have	have	AUX
ejpam-3338	301	15	taken	take	VERB
ejpam-3338	301	16	h	h	NOUN
ejpam-3338	301	17	=	=	SYM
ejpam-3338	301	18	.01	.01	NUM
ejpam-3338	301	19	,	,	PUNCT
ejpam-3338	301	20	α	α	NOUN
ejpam-3338	301	21	=	=	SYM
ejpam-3338	301	22	.99	.99	NUM
ejpam-3338	301	23	,	,	PUNCT
ejpam-3338	301	24	m	m	VERB
ejpam-3338	301	25	=	=	NOUN
ejpam-3338	301	26	0	0	NUM
ejpam-3338	301	27	to140	to140	PROPN
ejpam-3338	301	28	.	.	PUNCT
ejpam-3338	301	29	error	error	NOUN
ejpam-3338	301	30	in	in	ADP
ejpam-3338	301	31	computation	computation	NOUN
ejpam-3338	301	32	of	of	ADP
ejpam-3338	301	33	the	the	DET
ejpam-3338	301	34	gamma	gamma	NOUN
ejpam-3338	301	35	function	function	NOUN
ejpam-3338	301	36	is	be	AUX
ejpam-3338	301	37	significant	significant	ADJ
ejpam-3338	301	38	when	when	SCONJ
ejpam-3338	301	39	α	α	PROPN
ejpam-3338	301	40	is	be	AUX
ejpam-3338	301	41	a	a	DET
ejpam-3338	301	42	non	non	ADJ
ejpam-3338	301	43	-	-	ADJ
ejpam-3338	301	44	integer	integer	ADJ
ejpam-3338	301	45	fraction	fraction	NOUN
ejpam-3338	301	46	.	.	PUNCT
ejpam-3338	302	1	if	if	SCONJ
ejpam-3338	302	2	α	α	PRON
ejpam-3338	302	3	is	be	AUX
ejpam-3338	302	4	a	a	DET
ejpam-3338	302	5	positive	positive	ADJ
ejpam-3338	302	6	integer	integer	NOUN
ejpam-3338	302	7	,	,	PUNCT
ejpam-3338	302	8	then	then	ADV
ejpam-3338	302	9	we	we	PRON
ejpam-3338	302	10	can	can	AUX
ejpam-3338	302	11	use	use	VERB
ejpam-3338	302	12	the	the	DET
ejpam-3338	302	13	factorial	factorial	ADJ
ejpam-3338	302	14	function	function	NOUN
ejpam-3338	302	15	(	(	PUNCT
ejpam-3338	302	16	and	and	CCONJ
ejpam-3338	302	17	also	also	ADV
ejpam-3338	302	18	the	the	DET
ejpam-3338	302	19	gamma	gamma	PROPN
ejpam-3338	302	20	function	function	NOUN
ejpam-3338	302	21	)	)	PUNCT
ejpam-3338	302	22	with	with	ADP
ejpam-3338	302	23	many	many	ADJ
ejpam-3338	302	24	terms	term	NOUN
ejpam-3338	302	25	both	both	CCONJ
ejpam-3338	302	26	in	in	ADP
ejpam-3338	302	27	the	the	DET
ejpam-3338	302	28	numerator	numerator	NOUN
ejpam-3338	302	29	and	and	CCONJ
ejpam-3338	302	30	the	the	DET
ejpam-3338	302	31	denominator	denominator	NOUN
ejpam-3338	302	32	cancelling	cancelling	NOUN
ejpam-3338	302	33	.	.	PUNCT
ejpam-3338	303	1	the	the	DET
ejpam-3338	303	2	accuracy	accuracy	NOUN
ejpam-3338	303	3	will	will	AUX
ejpam-3338	303	4	be	be	AUX
ejpam-3338	303	5	significantly	significantly	ADV
ejpam-3338	303	6	more	more	ADJ
ejpam-3338	303	7	.	.	PUNCT
ejpam-3338	304	1	observe	observe	VERB
ejpam-3338	304	2	that	that	SCONJ
ejpam-3338	304	3	in	in	ADP
ejpam-3338	304	4	matlab	matlab	PROPN
ejpam-3338	304	5	,	,	PUNCT
ejpam-3338	304	6	we	we	PRON
ejpam-3338	304	7	can	can	AUX
ejpam-3338	304	8	compute	compute	VERB
ejpam-3338	304	9	(	(	PUNCT
ejpam-3338	304	10	up	up	ADP
ejpam-3338	304	11	to	to	PART
ejpam-3338	304	12	argument	argument	NOUN
ejpam-3338	304	13	17	17	NUM
ejpam-3338	304	14	)	)	PUNCT
ejpam-3338	304	15	exactly	exactly	ADV
ejpam-3338	304	16	factorial(17	factorial(17	NOUN
ejpam-3338	304	17	)	)	PUNCT
ejpam-3338	304	18	=	=	SYM
ejpam-3338	304	19	gamma(18	gamma(18	NOUN
ejpam-3338	304	20	)	)	PUNCT
ejpam-3338	304	21	=	=	SYM
ejpam-3338	304	22	355687428096000	355687428096000	NUM
ejpam-3338	304	23	.	.	PUNCT
ejpam-3338	305	1	beyond	beyond	ADP
ejpam-3338	305	2	the	the	DET
ejpam-3338	305	3	argument	argument	NOUN
ejpam-3338	305	4	17	17	NUM
ejpam-3338	305	5	matlab	matlab	NOUN
ejpam-3338	305	6	provides	provide	VERB
ejpam-3338	305	7	only	only	ADV
ejpam-3338	305	8	approximate	approximate	ADJ
ejpam-3338	305	9	(	(	PUNCT
ejpam-3338	305	10	erroneous	erroneous	ADJ
ejpam-3338	305	11	)	)	PUNCT
ejpam-3338	305	12	integer	integer	NOUN
ejpam-3338	305	13	values	value	NOUN
ejpam-3338	305	14	.	.	PUNCT
ejpam-3338	306	1	the	the	DET
ejpam-3338	306	2	matlab	matlab	PROPN
ejpam-3338	306	3	routine	routine	PROPN
ejpam-3338	306	4	fgl.deriv.m	fgl.deriv.m	PROPN
ejpam-3338	307	1	[	[	X
ejpam-3338	307	2	8	8	NUM
ejpam-3338	307	3	,	,	PUNCT
ejpam-3338	307	4	17	17	NUM
ejpam-3338	307	5	]	]	PUNCT
ejpam-3338	307	6	is	be	AUX
ejpam-3338	307	7	used	use	VERB
ejpam-3338	307	8	to	to	PART
ejpam-3338	307	9	compute	compute	VERB
ejpam-3338	307	10	,	,	PUNCT
ejpam-3338	307	11	in	in	ADP
ejpam-3338	307	12	3	3	NUM
ejpam-3338	307	13	-	-	SYM
ejpam-3338	307	14	d	d	NOUN
ejpam-3338	307	15	,	,	PUNCT
ejpam-3338	307	16	the	the	DET
ejpam-3338	307	17	fractional	fractional	ADJ
ejpam-3338	307	18	derivatives	derivative	NOUN
ejpam-3338	307	19	(	(	PUNCT
ejpam-3338	307	20	including	include	VERB
ejpam-3338	307	21	integer	integer	NOUN
ejpam-3338	307	22	ones	one	NOUN
ejpam-3338	307	23	)	)	PUNCT
ejpam-3338	307	24	for	for	ADP
ejpam-3338	307	25	different	different	ADJ
ejpam-3338	307	26	fractional	fractional	ADJ
ejpam-3338	307	27	orders	order	NOUN
ejpam-3338	307	28	of	of	ADP
ejpam-3338	307	29	an	an	DET
ejpam-3338	307	30	equi	equi	NOUN
ejpam-3338	307	31	-	-	PUNCT
ejpam-3338	307	32	spaced	space	VERB
ejpam-3338	307	33	sampled	sample	VERB
ejpam-3338	307	34	function	function	NOUN
ejpam-3338	307	35	using	use	VERB
ejpam-3338	307	36	grunwald	grunwald	NOUN
ejpam-3338	307	37	-	-	PUNCT
ejpam-3338	307	38	letnikov	letnikov	NOUN
ejpam-3338	307	39	formulation	formulation	NOUN
ejpam-3338	307	40	.	.	PUNCT
ejpam-3338	308	1	the	the	DET
ejpam-3338	308	2	idea	idea	NOUN
ejpam-3338	308	3	is	be	AUX
ejpam-3338	308	4	to	to	PART
ejpam-3338	308	5	demonstrate	demonstrate	VERB
ejpam-3338	308	6	how	how	SCONJ
ejpam-3338	308	7	well	well	ADV
ejpam-3338	308	8	the	the	DET
ejpam-3338	308	9	formulation	formulation	NOUN
ejpam-3338	308	10	integrates	integrate	NOUN
ejpam-3338	308	11	and	and	CCONJ
ejpam-3338	308	12	merges	merge	VERB
ejpam-3338	308	13	the	the	DET
ejpam-3338	308	14	fractional	fractional	ADJ
ejpam-3338	308	15	orders	order	NOUN
ejpam-3338	308	16	with	with	ADP
ejpam-3338	308	17	the	the	DET
ejpam-3338	308	18	integer	integer	NOUN
ejpam-3338	308	19	orders	order	NOUN
ejpam-3338	308	20	.	.	PUNCT
ejpam-3338	309	1	the	the	DET
ejpam-3338	309	2	12line	12line	NUM
ejpam-3338	309	3	matlab	matlab	PROPN
ejpam-3338	309	4	program	program	NOUN
ejpam-3338	309	5	fderiv	fderiv	PROPN
ejpam-3338	309	6	sin1	sin1	PROPN
ejpam-3338	309	7	hp1	hp1	PROPN
ejpam-3338	309	8	,	,	PUNCT
ejpam-3338	309	9	where	where	SCONJ
ejpam-3338	309	10	the	the	DET
ejpam-3338	309	11	sampling	sample	VERB
ejpam-3338	309	12	period	period	NOUN
ejpam-3338	309	13	h=0.1	h=0.1	NOUN
ejpam-3338	309	14	is	be	AUX
ejpam-3338	309	15	as	as	SCONJ
ejpam-3338	309	16	follows	follow	VERB
ejpam-3338	309	17	.	.	PUNCT
ejpam-3338	310	1	s.	s.	PROPN
ejpam-3338	310	2	k.sen	k.sen	PROPN
ejpam-3338	310	3	,	,	PUNCT
ejpam-3338	310	4	j.	j.	PROPN
ejpam-3338	310	5	v.	v.	PROPN
ejpam-3338	310	6	devi	devi	PROPN
ejpam-3338	310	7	,	,	PUNCT
ejpam-3338	310	8	r.v.g	r.v.g	NOUN
ejpam-3338	310	9	.	.	PUNCT
ejpam-3338	311	1	r.	r.	PROPN
ejpam-3338	311	2	kumar	kumar	PROPN
ejpam-3338	311	3	/	/	SYM
ejpam-3338	311	4	eur	eur	PROPN
ejpam-3338	311	5	.	.	PUNCT
ejpam-3338	312	1	j.	j.	PROPN
ejpam-3338	312	2	pure	pure	PROPN
ejpam-3338	312	3	appl	appl	PROPN
ejpam-3338	312	4	.	.	PROPN
ejpam-3338	312	5	math	math	PROPN
ejpam-3338	312	6	,	,	PUNCT
ejpam-3338	312	7	11	11	NUM
ejpam-3338	312	8	(	(	PUNCT
ejpam-3338	312	9	3	3	NUM
ejpam-3338	312	10	)	)	PUNCT
ejpam-3338	312	11	(	(	PUNCT
ejpam-3338	312	12	2018	2018	NUM
ejpam-3338	312	13	)	)	PUNCT
ejpam-3338	312	14	,	,	PUNCT
ejpam-3338	312	15	1058	1058	NUM
ejpam-3338	312	16	-	-	SYM
ejpam-3338	312	17	1099	1099	NUM
ejpam-3338	312	18	1071	1071	NUM
ejpam-3338	312	19	%	%	NOUN
ejpam-3338	312	20	clear	clear	ADJ
ejpam-3338	312	21	all	all	PRON
ejpam-3338	312	22	;	;	PUNCT
ejpam-3338	312	23	close	close	ADV
ejpam-3338	312	24	all	all	PRON
ejpam-3338	312	25	;	;	PUNCT
ejpam-3338	312	26	%	%	X
ejpam-3338	312	27	h=0.1	h=0.1	NOUN
ejpam-3338	312	28	;	;	PUNCT
ejpam-3338	312	29	t=0	t=0	NUM
ejpam-3338	312	30	:	:	PUNCT
ejpam-3338	312	31	h:4*pi	h:4*pi	PRON
ejpam-3338	312	32	;	;	PUNCT
ejpam-3338	312	33	%	%	INTJ
ejpam-3338	312	34	y	y	NOUN
ejpam-3338	312	35	=	=	NOUN
ejpam-3338	312	36	sin(t	sin(t	PROPN
ejpam-3338	312	37	)	)	PUNCT
ejpam-3338	312	38	,	,	PUNCT
ejpam-3338	312	39	%	%	INTJ
ejpam-3338	312	40	order=0:0.1:1	order=0:0.1:1	ADJ
ejpam-3338	312	41	;	;	PUNCT
ejpam-3338	312	42	%	%	NOUN
ejpam-3338	312	43	for	for	ADP
ejpam-3338	312	44	i=1	i=1	PRON
ejpam-3338	312	45	:	:	PUNCT
ejpam-3338	312	46	length(order	length(order	NOUN
ejpam-3338	312	47	)	)	PUNCT
ejpam-3338	312	48	%	%	NOUN
ejpam-3338	312	49	yd(i,:)=fgl	yd(i,:)=fgl	PROPN
ejpam-3338	312	50	deriv(order(i),y	deriv(order(i),y	NOUN
ejpam-3338	312	51	,	,	PUNCT
ejpam-3338	312	52	h	h	NOUN
ejpam-3338	312	53	)	)	PUNCT
ejpam-3338	312	54	;	;	PUNCT
ejpam-3338	312	55	%	%	X
ejpam-3338	312	56	end	end	NOUN
ejpam-3338	312	57	;	;	PUNCT
ejpam-3338	312	58	for	for	ADP
ejpam-3338	312	59	i=1	i=1	X
ejpam-3338	312	60	:	:	PUNCT
ejpam-3338	312	61	length(order	length(order	NOUN
ejpam-3338	312	62	)	)	PUNCT
ejpam-3338	312	63	,	,	PUNCT
ejpam-3338	312	64	%	%	NOUN
ejpam-3338	312	65	’	'	PUNCT
ejpam-3338	312	66	fractional	fractional	ADJ
ejpam-3338	312	67	order	order	NOUN
ejpam-3338	312	68	alpha=’,disp(order(i	alpha=’,disp(order(i	NOUN
ejpam-3338	312	69	)	)	PUNCT
ejpam-3338	312	70	)	)	PUNCT
ejpam-3338	312	71	,	,	PUNCT
ejpam-3338	312	72	%	%	NOUN
ejpam-3338	312	73	’	'	PUNCT
ejpam-3338	312	74	sampled	sample	VERB
ejpam-3338	312	75	derivatives	derivative	NOUN
ejpam-3338	312	76	(	(	PUNCT
ejpam-3338	312	77	omitting	omit	VERB
ejpam-3338	312	78	1st	1st	ADJ
ejpam-3338	312	79	element	element	NOUN
ejpam-3338	312	80	0	0	NUM
ejpam-3338	312	81	)	)	PUNCT
ejpam-3338	312	82	are	be	AUX
ejpam-3338	312	83	’	'	PUNCT
ejpam-3338	312	84	,	,	PUNCT
ejpam-3338	312	85	disp(yd(i	disp(yd(i	PROPN
ejpam-3338	312	86	,	,	PUNCT
ejpam-3338	312	87	:))	:))	PROPN
ejpam-3338	312	88	,	,	PUNCT
ejpam-3338	312	89	end	end	NOUN
ejpam-3338	312	90	;	;	PUNCT
ejpam-3338	312	91	%	%	X
ejpam-3338	312	92	[	[	X
ejpam-3338	312	93	x	x	X
ejpam-3338	312	94	,	,	PUNCT
ejpam-3338	312	95	y]=meshgrid(t	y]=meshgrid(t	NOUN
ejpam-3338	312	96	,	,	PUNCT
ejpam-3338	312	97	order	order	NOUN
ejpam-3338	312	98	)	)	PUNCT
ejpam-3338	312	99	;	;	PUNCT
ejpam-3338	312	100	%	%	X
ejpam-3338	312	101	mesh(x	mesh(x	PROPN
ejpam-3338	312	102	,	,	PUNCT
ejpam-3338	312	103	y	y	PROPN
ejpam-3338	312	104	,	,	PUNCT
ejpam-3338	312	105	yd	yd	NOUN
ejpam-3338	312	106	)	)	PUNCT
ejpam-3338	312	107	%	%	NOUN
ejpam-3338	312	108	xlabel	xlabel	NOUN
ejpam-3338	312	109	(	(	PUNCT
ejpam-3338	312	110	’	'	PUNCT
ejpam-3338	312	111	t	t	NOUN
ejpam-3338	312	112	’	'	PUNCT
ejpam-3338	312	113	)	)	PUNCT
ejpam-3338	312	114	;	;	PUNCT
ejpam-3338	312	115	ylabel	ylabel	NOUN
ejpam-3338	312	116	(	(	PUNCT
ejpam-3338	312	117	’	'	PUNCT
ejpam-3338	312	118	α	α	NOUN
ejpam-3338	312	119	’	'	PUNCT
ejpam-3338	312	120	)	)	PUNCT
ejpam-3338	312	121	;	;	PUNCT
ejpam-3338	312	122	zlabel	zlabel	NOUN
ejpam-3338	312	123	(	(	PUNCT
ejpam-3338	312	124	’	'	PUNCT
ejpam-3338	312	125	y	y	PROPN
ejpam-3338	312	126	’	'	PUNCT
ejpam-3338	312	127	)	)	PUNCT
ejpam-3338	313	1	%	%	NOUN
ejpam-3338	313	2	usage	usage	NOUN
ejpam-3338	313	3	we	we	PRON
ejpam-3338	313	4	call	call	VERB
ejpam-3338	313	5	the	the	DET
ejpam-3338	313	6	following	follow	VERB
ejpam-3338	313	7	12	12	NUM
ejpam-3338	313	8	-	-	PUNCT
ejpam-3338	313	9	line	line	NOUN
ejpam-3338	313	10	matlab	matlab	PROPN
ejpam-3338	313	11	program	program	NOUN
ejpam-3338	313	12	”	"	PUNCT
ejpam-3338	313	13	fderiv	fderiv	PROPN
ejpam-3338	313	14	sin1	sin1	PROPN
ejpam-3338	313	15	hp1	hp1	PROPN
ejpam-3338	313	16	”	"	PUNCT
ejpam-3338	313	17	%	%	NOUN
ejpam-3338	313	18	without	without	ADP
ejpam-3338	313	19	the	the	DET
ejpam-3338	313	20	12	12	NUM
ejpam-3338	313	21	”	"	PUNCT
ejpam-3338	313	22	%	%	NOUN
ejpam-3338	313	23	”	"	PUNCT
ejpam-3338	313	24	symbols	symbol	NOUN
ejpam-3338	313	25	and	and	CCONJ
ejpam-3338	313	26	use	use	VERB
ejpam-3338	313	27	simply	simply	ADV
ejpam-3338	313	28	>	>	PUNCT
ejpam-3338	313	29	>	>	X
ejpam-3338	313	30	fderiv	fderiv	PROPN
ejpam-3338	313	31	sin1	sin1	PROPN
ejpam-3338	313	32	hp1	hp1	PROPN
ejpam-3338	313	33	(	(	PUNCT
ejpam-3338	313	34	in	in	ADP
ejpam-3338	313	35	the	the	DET
ejpam-3338	313	36	command	command	NOUN
ejpam-3338	313	37	%	%	NOUN
ejpam-3338	313	38	window	window	NOUN
ejpam-3338	313	39	)	)	PUNCT
ejpam-3338	313	40	.	.	PUNCT
ejpam-3338	314	1	observe	observe	VERB
ejpam-3338	314	2	that	that	SCONJ
ejpam-3338	314	3	the	the	DET
ejpam-3338	314	4	matlab	matlab	PROPN
ejpam-3338	314	5	program	program	NOUN
ejpam-3338	314	6	uses	use	VERB
ejpam-3338	314	7	the	the	DET
ejpam-3338	314	8	matlab	matlab	PROPN
ejpam-3338	314	9	routine	routine	PROPN
ejpam-3338	314	10	fgl	fgl	PROPN
ejpam-3338	314	11	deriv	deriv	NOUN
ejpam-3338	314	12	which	which	PRON
ejpam-3338	314	13	%	%	NOUN
ejpam-3338	314	14	needs	need	VERB
ejpam-3338	314	15	to	to	PART
ejpam-3338	314	16	be	be	AUX
ejpam-3338	314	17	available	available	ADJ
ejpam-3338	314	18	in	in	ADP
ejpam-3338	314	19	the	the	DET
ejpam-3338	314	20	matlab	matlab	PROPN
ejpam-3338	314	21	machine	machine	NOUN
ejpam-3338	314	22	.	.	PUNCT
ejpam-3338	315	1	we	we	PRON
ejpam-3338	315	2	have	have	AUX
ejpam-3338	315	3	used	use	VERB
ejpam-3338	315	4	the	the	DET
ejpam-3338	315	5	fractional	fractional	ADJ
ejpam-3338	315	6	order	order	NOUN
ejpam-3338	315	7	α	α	NOUN
ejpam-3338	315	8	=	=	SYM
ejpam-3338	315	9	0	0	NUM
ejpam-3338	315	10	,	,	PUNCT
ejpam-3338	315	11	.1	.1	NUM
ejpam-3338	315	12	,	,	PUNCT
ejpam-3338	315	13	.2	.2	NUM
ejpam-3338	315	14	,	,	PUNCT
ejpam-3338	315	15	.3	.3	NUM
ejpam-3338	315	16	,	,	PUNCT
ejpam-3338	315	17	...	...	PUNCT
ejpam-3338	315	18	,	,	PUNCT
ejpam-3338	315	19	1	1	NUM
ejpam-3338	315	20	and	and	CCONJ
ejpam-3338	315	21	computed	compute	VERB
ejpam-3338	315	22	the	the	DET
ejpam-3338	315	23	fractional	fractional	ADJ
ejpam-3338	315	24	(	(	PUNCT
ejpam-3338	315	25	including	include	VERB
ejpam-3338	315	26	integer	integer	NOUN
ejpam-3338	315	27	order	order	NOUN
ejpam-3338	315	28	derivatives	derivative	NOUN
ejpam-3338	315	29	for	for	ADP
ejpam-3338	315	30	x	x	SYM
ejpam-3338	315	31	=	=	SYM
ejpam-3338	315	32	0	0	NUM
ejpam-3338	315	33	,	,	PUNCT
ejpam-3338	315	34	.1	.1	NUM
ejpam-3338	315	35	,	,	PUNCT
ejpam-3338	315	36	.2	.2	NUM
ejpam-3338	315	37	,	,	PUNCT
ejpam-3338	315	38	...	...	PUNCT
ejpam-3338	315	39	,	,	PUNCT
ejpam-3338	315	40	4π	4π	NUM
ejpam-3338	315	41	.	.	PUNCT
ejpam-3338	316	1	one	one	PRON
ejpam-3338	316	2	can	can	AUX
ejpam-3338	316	3	readily	readily	ADV
ejpam-3338	316	4	check	check	VERB
ejpam-3338	316	5	how	how	SCONJ
ejpam-3338	316	6	accurate	accurate	ADJ
ejpam-3338	316	7	the	the	DET
ejpam-3338	316	8	integer	integer	NOUN
ejpam-3338	316	9	order	order	NOUN
ejpam-3338	316	10	derivatives	derivative	NOUN
ejpam-3338	316	11	are	be	AUX
ejpam-3338	316	12	and	and	CCONJ
ejpam-3338	316	13	how	how	SCONJ
ejpam-3338	316	14	the	the	DET
ejpam-3338	316	15	fractional	fractional	ADJ
ejpam-3338	316	16	orders	order	NOUN
ejpam-3338	316	17	merge	merge	VERB
ejpam-3338	316	18	and	and	CCONJ
ejpam-3338	316	19	integrate	integrate	VERB
ejpam-3338	316	20	with	with	ADP
ejpam-3338	316	21	the	the	DET
ejpam-3338	316	22	integer	integer	NOUN
ejpam-3338	316	23	order	order	NOUN
ejpam-3338	316	24	derivatives	derivative	NOUN
ejpam-3338	316	25	.	.	PUNCT
ejpam-3338	317	1	also	also	ADV
ejpam-3338	317	2	see	see	VERB
ejpam-3338	317	3	[	[	X
ejpam-3338	317	4	8	8	NUM
ejpam-3338	317	5	]	]	PUNCT
ejpam-3338	317	6	.	.	PUNCT
ejpam-3338	318	1	the	the	DET
ejpam-3338	318	2	numerical	numerical	ADJ
ejpam-3338	318	3	results	result	NOUN
ejpam-3338	318	4	(	(	PUNCT
ejpam-3338	318	5	only	only	ADV
ejpam-3338	318	6	partially	partially	ADV
ejpam-3338	318	7	produced	produce	VERB
ejpam-3338	318	8	to	to	PART
ejpam-3338	318	9	conserve	conserve	VERB
ejpam-3338	318	10	space	space	NOUN
ejpam-3338	318	11	)	)	PUNCT
ejpam-3338	318	12	and	and	CCONJ
ejpam-3338	318	13	the	the	DET
ejpam-3338	318	14	graph	graph	NOUN
ejpam-3338	318	15	(	(	PUNCT
ejpam-3338	318	16	fig	fig	NOUN
ejpam-3338	318	17	.	.	PUNCT
ejpam-3338	319	1	1a	1a	NOUN
ejpam-3338	319	2	)	)	PUNCT
ejpam-3338	319	3	depicting	depict	VERB
ejpam-3338	319	4	the	the	DET
ejpam-3338	319	5	results	result	NOUN
ejpam-3338	319	6	are	be	AUX
ejpam-3338	319	7	as	as	SCONJ
ejpam-3338	319	8	follows	follow	VERB
ejpam-3338	319	9	.	.	PUNCT
ejpam-3338	320	1	the	the	DET
ejpam-3338	320	2	reader	reader	NOUN
ejpam-3338	320	3	may	may	AUX
ejpam-3338	320	4	view	view	VERB
ejpam-3338	320	5	the	the	DET
ejpam-3338	320	6	complete	complete	ADJ
ejpam-3338	320	7	numerical	numerical	ADJ
ejpam-3338	320	8	result	result	NOUN
ejpam-3338	320	9	along	along	ADP
ejpam-3338	320	10	with	with	ADP
ejpam-3338	320	11	the	the	DET
ejpam-3338	320	12	graph	graph	NOUN
ejpam-3338	320	13	when	when	SCONJ
ejpam-3338	320	14	he	he	PRON
ejpam-3338	320	15	executes	execute	VERB
ejpam-3338	320	16	the	the	DET
ejpam-3338	320	17	foregoing	forego	VERB
ejpam-3338	320	18	matlab	matlab	PROPN
ejpam-3338	320	19	program	program	NOUN
ejpam-3338	320	20	fderiv	fderiv	PROPN
ejpam-3338	320	21	sin1	sin1	PROPN
ejpam-3338	320	22	hp1	hp1	PROPN
ejpam-3338	320	23	.	.	PUNCT
ejpam-3338	321	1	fractional	fractional	ADJ
ejpam-3338	321	2	order	order	NOUN
ejpam-3338	321	3	alpha=	alpha=	SYM
ejpam-3338	321	4	0	0	NUM
ejpam-3338	321	5	sampled	sample	VERB
ejpam-3338	321	6	derivatives	derivative	NOUN
ejpam-3338	321	7	(	(	PUNCT
ejpam-3338	321	8	omitting	omit	VERB
ejpam-3338	321	9	the	the	DET
ejpam-3338	321	10	1st	1st	ADJ
ejpam-3338	321	11	element	element	NOUN
ejpam-3338	321	12	0	0	NUM
ejpam-3338	321	13	)	)	PUNCT
ejpam-3338	321	14	are	be	AUX
ejpam-3338	321	15	0(omit	0(omit	NOUN
ejpam-3338	321	16	)	)	PUNCT
ejpam-3338	321	17	0.0998	0.0998	NUM
ejpam-3338	321	18	0.1987	0.1987	NUM
ejpam-3338	321	19	0.2955	0.2955	NUM
ejpam-3338	321	20	0.3894	0.3894	NUM
ejpam-3338	321	21	0.4794	0.4794	NUM
ejpam-3338	322	1	0.5646	0.5646	NUM
ejpam-3338	322	2	0.6442	0.6442	NUM
ejpam-3338	322	3	0.7174	0.7174	NUM
ejpam-3338	322	4	0.7833	0.7833	NUM
ejpam-3338	322	5	0.8415	0.8415	NUM
ejpam-3338	322	6	0.8912	0.8912	NUM
ejpam-3338	322	7	0.9320	0.9320	NUM
ejpam-3338	322	8	0.9636	0.9636	NUM
ejpam-3338	322	9	0.9854	0.9854	NUM
ejpam-3338	322	10	0.9975	0.9975	NUM
ejpam-3338	322	11	0.9996	0.9996	NUM
ejpam-3338	322	12	0.9917	0.9917	NUM
ejpam-3338	322	13	0.9738	0.9738	NUM
ejpam-3338	322	14	0.9463	0.9463	NUM
ejpam-3338	322	15	0.9093	0.9093	NUM
ejpam-3338	322	16	0.8632	0.8632	NUM
ejpam-3338	322	17	0.8085	0.8085	NUM
ejpam-3338	322	18	0.7457	0.7457	NUM
ejpam-3338	322	19	0.6755	0.6755	NUM
ejpam-3338	322	20	0.5985	0.5985	NUM
ejpam-3338	322	21	0.5155	0.5155	NUM
ejpam-3338	322	22	0.4274	0.4274	NUM
ejpam-3338	322	23	0.3350	0.3350	NUM
ejpam-3338	322	24	0.2392	0.2392	NUM
ejpam-3338	322	25	0.1411	0.1411	NUM
ejpam-3338	322	26	0.0416	0.0416	NUM
ejpam-3338	322	27	-0.0584	-0.0584	NOUN
ejpam-3338	322	28	-0.1577	-0.1577	PROPN
ejpam-3338	322	29	-0.2555	-0.2555	PROPN
ejpam-3338	323	1	-0.3508	-0.3508	PROPN
ejpam-3338	323	2	-0.4425	-0.4425	PROPN
ejpam-3338	323	3	-0.5298	-0.5298	PROPN
ejpam-3338	323	4	-0.6119	-0.6119	PROPN
ejpam-3338	324	1	-0.6878	-0.6878	PROPN
ejpam-3338	324	2	-0.7568	-0.7568	PUNCT
ejpam-3338	324	3	-0.8183	-0.8183	PROPN
ejpam-3338	325	1	-0.8716	-0.8716	PROPN
ejpam-3338	325	2	-0.9162	-0.9162	PUNCT
ejpam-3338	326	1	0.9516	0.9516	NUM
ejpam-3338	326	2	-0.9775	-0.9775	PROPN
ejpam-3338	326	3	-0.9937	-0.9937	PROPN
ejpam-3338	326	4	-0.9999	-0.9999	PROPN
ejpam-3338	326	5	-0.9962	-0.9962	PUNCT
ejpam-3338	326	6	-0.9825	-0.9825	PROPN
ejpam-3338	326	7	-0.9589	-0.9589	PROPN
ejpam-3338	327	1	0.9258	0.9258	NUM
ejpam-3338	327	2	-0.8835	-0.8835	NOUN
ejpam-3338	327	3	-0.8323	-0.8323	NOUN
ejpam-3338	327	4	-0.7728	-0.7728	NOUN
ejpam-3338	327	5	-0.7055	-0.7055	PUNCT
ejpam-3338	327	6	-0.6313	-0.6313	PROPN
ejpam-3338	327	7	-0.5507	-0.5507	PUNCT
ejpam-3338	328	1	0.4646	0.4646	NUM
ejpam-3338	328	2	-0.3739	-0.3739	PROPN
ejpam-3338	328	3	-0.2794	-0.2794	PROPN
ejpam-3338	328	4	-0.1822	-0.1822	PROPN
ejpam-3338	328	5	-0.0831	-0.0831	PUNCT
ejpam-3338	329	1	0.0168	0.0168	NUM
ejpam-3338	329	2	0.1165	0.1165	NUM
ejpam-3338	329	3	0.2151	0.2151	NUM
ejpam-3338	329	4	0.3115	0.3115	NUM
ejpam-3338	329	5	0.4048	0.4048	NUM
ejpam-3338	329	6	0.4941	0.4941	NUM
ejpam-3338	329	7	0.5784	0.5784	NUM
ejpam-3338	329	8	0.6570	0.6570	NUM
ejpam-3338	329	9	0.7290	0.7290	NUM
ejpam-3338	330	1	0.7937	0.7937	NUM
ejpam-3338	330	2	0.8504	0.8504	NUM
ejpam-3338	330	3	0.8987	0.8987	NUM
ejpam-3338	330	4	0.9380	0.9380	NUM
ejpam-3338	330	5	0.9679	0.9679	NUM
ejpam-3338	330	6	0.9882	0.9882	NUM
ejpam-3338	330	7	0.9985	0.9985	NUM
ejpam-3338	330	8	0.9989	0.9989	NUM
ejpam-3338	330	9	0.9894	0.9894	NUM
ejpam-3338	330	10	0.9699	0.9699	NUM
ejpam-3338	330	11	0.9407	0.9407	NUM
ejpam-3338	330	12	0.9022	0.9022	NOUN
ejpam-3338	330	13	0.8546	0.8546	NUM
ejpam-3338	330	14	0.7985	0.7985	NUM
ejpam-3338	330	15	0.7344	0.7344	NUM
ejpam-3338	330	16	0.6630	0.6630	NUM
ejpam-3338	330	17	0.5849	0.5849	NUM
ejpam-3338	330	18	0.5010	0.5010	NUM
ejpam-3338	330	19	0.4121	0.4121	NUM
ejpam-3338	330	20	4	4	NUM
ejpam-3338	330	21	0.3191	0.3191	NUM
ejpam-3338	330	22	0.2229	0.2229	NUM
ejpam-3338	330	23	0.1245	0.1245	NUM
ejpam-3338	330	24	0.0248	0.0248	NUM
ejpam-3338	330	25	−0.0752	−0.0752	VERB
ejpam-3338	330	26	−0.1743	−0.1743	X
ejpam-3338	330	27	−0.2718	−0.2718	X
ejpam-3338	330	28	−0.3665	−0.3665	X
ejpam-3338	330	29	−	−	ADP
ejpam-3338	330	30	0.4575	0.4575	NUM
ejpam-3338	330	31	−	−	PROPN
ejpam-3338	330	32	0.5440	0.5440	NUM
ejpam-3338	330	33	−	−	PROPN
ejpam-3338	330	34	0.6251	0.6251	NUM
ejpam-3338	330	35	−	−	NOUN
ejpam-3338	330	36	0.6999	0.6999	NUM
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ejpam-3338	363	12	(	(	PUNCT
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ejpam-3338	363	14	)	)	PUNCT
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ejpam-3338	371	11	0.3724	0.3724	NUM
ejpam-3338	371	12	0.4631	0.4631	NUM
ejpam-3338	371	13	0.5491	0.5491	NUM
ejpam-3338	371	14	0.6297	0.6297	NUM
ejpam-3338	371	15	0.7038	0.7038	NUM
ejpam-3338	371	16	0.7710	0.7710	NUM
ejpam-3338	371	17	0.8303	0.8303	NUM
ejpam-3338	371	18	0.8814	0.8814	NUM
ejpam-3338	372	1	0.9236	0.9236	NUM
ejpam-3338	372	2	0.9565	0.9565	NUM
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ejpam-3338	373	1	0.9935	0.9935	NUM
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ejpam-3338	374	2	0.9907	0.9907	NUM
ejpam-3338	374	3	0.9743	0.9743	NUM
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ejpam-3338	374	7	s.	s.	PROPN
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ejpam-3338	374	15	.	.	PUNCT
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ejpam-3338	376	6	,	,	PUNCT
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ejpam-3338	376	8	(	(	PUNCT
ejpam-3338	376	9	3	3	NUM
ejpam-3338	376	10	)	)	PUNCT
ejpam-3338	376	11	(	(	PUNCT
ejpam-3338	376	12	2018	2018	NUM
ejpam-3338	376	13	)	)	PUNCT
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ejpam-3338	376	16	-	-	SYM
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ejpam-3338	377	4	0.6078	0.6078	NUM
ejpam-3338	377	5	0.5257	0.5257	NUM
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ejpam-3338	377	11	-0.0456	-0.0456	NOUN
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ejpam-3338	386	19	(	(	PUNCT
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ejpam-3338	386	21	)	)	PUNCT
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ejpam-3338	400	26	(	(	PUNCT
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ejpam-3338	400	31	significant	significant	ADJ
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ejpam-3338	400	35	sine	sine	NOUN
ejpam-3338	400	36	and	and	CCONJ
ejpam-3338	400	37	cosine	cosine	NOUN
ejpam-3338	400	38	functions	function	NOUN
ejpam-3338	400	39	are	be	AUX
ejpam-3338	400	40	having	have	VERB
ejpam-3338	400	41	order	order	NOUN
ejpam-3338	400	42	of	of	ADP
ejpam-3338	400	43	magnitude	magnitude	NOUN
ejpam-3338	400	44	1	1	NUM
ejpam-3338	400	45	)	)	PUNCT
ejpam-3338	400	46	.	.	PUNCT
ejpam-3338	401	1	for	for	ADP
ejpam-3338	401	2	better	well	ADJ
ejpam-3338	401	3	accuracy	accuracy	NOUN
ejpam-3338	401	4	,	,	PUNCT
ejpam-3338	401	5	choose	choose	VERB
ejpam-3338	401	6	the	the	DET
ejpam-3338	401	7	sampling	sample	VERB
ejpam-3338	401	8	period	period	NOUN
ejpam-3338	401	9	h=.01	h=.01	ADJ
ejpam-3338	401	10	(	(	PUNCT
ejpam-3338	401	11	10	10	NUM
ejpam-3338	401	12	times	time	NOUN
ejpam-3338	401	13	higher	high	ADJ
ejpam-3338	401	14	frequency	frequency	NOUN
ejpam-3338	401	15	)	)	PUNCT
ejpam-3338	401	16	.	.	PUNCT
ejpam-3338	402	1	that	that	PRON
ejpam-3338	402	2	is	be	AUX
ejpam-3338	402	3	,	,	PUNCT
ejpam-3338	402	4	replace	replace	VERB
ejpam-3338	402	5	in	in	ADP
ejpam-3338	402	6	the	the	DET
ejpam-3338	402	7	foregoing	forego	VERB
ejpam-3338	402	8	12	12	NUM
ejpam-3338	402	9	-	-	PUNCT
ejpam-3338	402	10	line	line	NOUN
ejpam-3338	402	11	program	program	NOUN
ejpam-3338	402	12	h=0.1	h=0.1	NOUN
ejpam-3338	402	13	by	by	ADP
ejpam-3338	402	14	h=0.01	h=0.01	NOUN
ejpam-3338	402	15	.	.	PUNCT
ejpam-3338	403	1	consequently	consequently	ADV
ejpam-3338	403	2	the	the	DET
ejpam-3338	403	3	numerical	numerical	ADJ
ejpam-3338	403	4	results	result	NOUN
ejpam-3338	403	5	(	(	PUNCT
ejpam-3338	403	6	not	not	PART
ejpam-3338	403	7	depicted	depict	VERB
ejpam-3338	403	8	to	to	PART
ejpam-3338	403	9	conserve	conserve	VERB
ejpam-3338	403	10	space	space	NOUN
ejpam-3338	403	11	)	)	PUNCT
ejpam-3338	403	12	are	be	AUX
ejpam-3338	403	13	correct	correct	ADJ
ejpam-3338	403	14	up	up	ADP
ejpam-3338	403	15	to	to	PART
ejpam-3338	403	16	3	3	NUM
ejpam-3338	403	17	significant	significant	ADJ
ejpam-3338	403	18	digits	digit	NOUN
ejpam-3338	403	19	(	(	PUNCT
ejpam-3338	403	20	enough	enough	ADJ
ejpam-3338	403	21	for	for	ADP
ejpam-3338	403	22	most	most	ADJ
ejpam-3338	403	23	engineering	engineering	NOUN
ejpam-3338	403	24	implementations	implementation	NOUN
ejpam-3338	403	25	)	)	PUNCT
ejpam-3338	403	26	.	.	PUNCT
ejpam-3338	404	1	however	however	ADV
ejpam-3338	404	2	,	,	PUNCT
ejpam-3338	404	3	for	for	ADP
ejpam-3338	404	4	the	the	DET
ejpam-3338	404	5	graph	graph	NOUN
ejpam-3338	404	6	for	for	ADP
ejpam-3338	404	7	h=0.01	h=0.01	NOUN
ejpam-3338	404	8	see	see	VERB
ejpam-3338	404	9	fig	fig	NOUN
ejpam-3338	404	10	.	.	PUNCT
ejpam-3338	405	1	1b	1b	NUM
ejpam-3338	405	2	.	.	PUNCT
ejpam-3338	406	1	it	it	PRON
ejpam-3338	406	2	may	may	AUX
ejpam-3338	406	3	be	be	AUX
ejpam-3338	406	4	seen	see	VERB
ejpam-3338	406	5	how	how	SCONJ
ejpam-3338	406	6	the	the	DET
ejpam-3338	406	7	sampled	sample	VERB
ejpam-3338	406	8	fractional	fractional	ADJ
ejpam-3338	406	9	derivatives	derivative	NOUN
ejpam-3338	406	10	demonstrate	demonstrate	VERB
ejpam-3338	406	11	the	the	DET
ejpam-3338	406	12	curvature	curvature	NOUN
ejpam-3338	406	13	(	(	PUNCT
ejpam-3338	406	14	deviated	deviate	VERB
ejpam-3338	406	15	from	from	ADP
ejpam-3338	406	16	the	the	DET
ejpam-3338	406	17	uniform	uniform	ADJ
ejpam-3338	406	18	behaviour	behaviour	NOUN
ejpam-3338	406	19	as	as	SCONJ
ejpam-3338	406	20	it	it	PRON
ejpam-3338	406	21	should	should	AUX
ejpam-3338	406	22	be	be	AUX
ejpam-3338	406	23	)	)	PUNCT
ejpam-3338	406	24	.	.	PUNCT
ejpam-3338	407	1	as	as	ADP
ejpam-3338	407	2	another	another	DET
ejpam-3338	407	3	example	example	NOUN
ejpam-3338	407	4	we	we	PRON
ejpam-3338	407	5	take	take	VERB
ejpam-3338	407	6	cosine	cosine	NOUN
ejpam-3338	407	7	function	function	NOUN
ejpam-3338	407	8	and	and	CCONJ
ejpam-3338	407	9	demonstrate	demonstrate	VERB
ejpam-3338	407	10	how	how	SCONJ
ejpam-3338	407	11	it	it	PRON
ejpam-3338	407	12	behaves	behave	VERB
ejpam-3338	407	13	for	for	ADP
ejpam-3338	407	14	h	h	NOUN
ejpam-3338	407	15	=	=	SYM
ejpam-3338	407	16	0.1	0.1	NUM
ejpam-3338	407	17	,	,	PUNCT
ejpam-3338	407	18	α	α	NOUN
ejpam-3338	407	19	=	=	SYM
ejpam-3338	407	20	0(.1)14	0(.1)14	PROPN
ejpam-3338	407	21	and	and	CCONJ
ejpam-3338	407	22	the	the	DET
ejpam-3338	407	23	cosine	cosine	NOUN
ejpam-3338	407	24	function	function	NOUN
ejpam-3338	407	25	sampled	sample	VERB
ejpam-3338	407	26	at	at	ADP
ejpam-3338	407	27	points	point	NOUN
ejpam-3338	407	28	−pi2	−pi2	X
ejpam-3338	407	29	(	(	PUNCT
ejpam-3338	407	30	h)6	h)6	PROPN
ejpam-3338	407	31	∗	∗	PROPN
ejpam-3338	407	32	pi	pi	NOUN
ejpam-3338	407	33	.	.	PUNCT
ejpam-3338	408	1	the	the	DET
ejpam-3338	408	2	matlab	matlab	PROPN
ejpam-3338	408	3	program	program	NOUN
ejpam-3338	408	4	fderiv	fderiv	PROPN
ejpam-3338	408	5	cos8.m	cos8.m	PROPN
ejpam-3338	408	6	is	be	AUX
ejpam-3338	408	7	as	as	SCONJ
ejpam-3338	408	8	follows	follow	VERB
ejpam-3338	408	9	clear	clear	ADJ
ejpam-3338	408	10	all	all	PRON
ejpam-3338	408	11	;	;	PUNCT
ejpam-3338	408	12	close	close	ADV
ejpam-3338	408	13	all	all	PRON
ejpam-3338	408	14	;	;	PUNCT
ejpam-3338	408	15	h=0.1	h=0.1	X
ejpam-3338	408	16	;	;	PUNCT
ejpam-3338	408	17	t=-pi/2	t=-pi/2	NOUN
ejpam-3338	408	18	:	:	PUNCT
ejpam-3338	408	19	h:6*pi	h:6*pi	PROPN
ejpam-3338	408	20	;	;	PUNCT
ejpam-3338	408	21	y	y	PROPN
ejpam-3338	408	22	=	=	SYM
ejpam-3338	408	23	cos(t	cos(t	VERB
ejpam-3338	408	24	)	)	PUNCT
ejpam-3338	408	25	,	,	PUNCT
ejpam-3338	408	26	order=0:0.1:1	order=0:0.1:1	NUM
ejpam-3338	408	27	;	;	PUNCT
ejpam-3338	408	28	for	for	ADP
ejpam-3338	408	29	i=1	i=1	X
ejpam-3338	408	30	:	:	PUNCT
ejpam-3338	408	31	length(order	length(order	NOUN
ejpam-3338	408	32	)	)	PUNCT
ejpam-3338	408	33	yd(i,:)=fgl	yd(i,:)=fgl	PROPN
ejpam-3338	408	34	deriv(order(i),y	deriv(order(i),y	NOUN
ejpam-3338	408	35	,	,	PUNCT
ejpam-3338	408	36	h	h	NOUN
ejpam-3338	408	37	)	)	PUNCT
ejpam-3338	408	38	;	;	PUNCT
ejpam-3338	408	39	end	end	NOUN
ejpam-3338	408	40	;	;	PUNCT
ejpam-3338	408	41	for	for	ADP
ejpam-3338	408	42	i=1	i=1	X
ejpam-3338	408	43	:	:	PUNCT
ejpam-3338	408	44	length(order	length(order	NOUN
ejpam-3338	408	45	)	)	PUNCT
ejpam-3338	408	46	,	,	PUNCT
ejpam-3338	408	47	s.	s.	PROPN
ejpam-3338	408	48	k.sen	k.sen	PROPN
ejpam-3338	408	49	,	,	PUNCT
ejpam-3338	408	50	j.	j.	PROPN
ejpam-3338	408	51	v.	v.	PROPN
ejpam-3338	408	52	devi	devi	PROPN
ejpam-3338	408	53	,	,	PUNCT
ejpam-3338	408	54	r.v.g	r.v.g	NOUN
ejpam-3338	408	55	.	.	PUNCT
ejpam-3338	409	1	r.	r.	PROPN
ejpam-3338	409	2	kumar	kumar	PROPN
ejpam-3338	409	3	/	/	SYM
ejpam-3338	409	4	eur	eur	PROPN
ejpam-3338	409	5	.	.	PUNCT
ejpam-3338	410	1	j.	j.	PROPN
ejpam-3338	410	2	pure	pure	PROPN
ejpam-3338	410	3	appl	appl	PROPN
ejpam-3338	410	4	.	.	PROPN
ejpam-3338	410	5	math	math	PROPN
ejpam-3338	410	6	,	,	PUNCT
ejpam-3338	410	7	11	11	NUM
ejpam-3338	410	8	(	(	PUNCT
ejpam-3338	410	9	3	3	NUM
ejpam-3338	410	10	)	)	PUNCT
ejpam-3338	410	11	(	(	PUNCT
ejpam-3338	410	12	2018	2018	NUM
ejpam-3338	410	13	)	)	PUNCT
ejpam-3338	410	14	,	,	PUNCT
ejpam-3338	410	15	1058	1058	NUM
ejpam-3338	410	16	-	-	SYM
ejpam-3338	410	17	1099	1099	NUM
ejpam-3338	410	18	1074	1074	NUM
ejpam-3338	410	19	fig	fig	NOUN
ejpam-3338	410	20	.	.	PUNCT
ejpam-3338	411	1	1a	1a	PROPN
ejpam-3338	411	2	fractional	fractional	ADJ
ejpam-3338	411	3	derivative	derivative	NOUN
ejpam-3338	411	4	of	of	ADP
ejpam-3338	411	5	sin(x)forx	sin(x)forx	NOUN
ejpam-3338	411	6	=	=	NOUN
ejpam-3338	411	7	0(h)4π	0(h)4π	NUM
ejpam-3338	411	8	for	for	ADP
ejpam-3338	411	9	α	α	PROPN
ejpam-3338	411	10	=	=	SYM
ejpam-3338	411	11	0(0.1)1	0(0.1)1	PROPN
ejpam-3338	411	12	,	,	PUNCT
ejpam-3338	411	13	h	h	NOUN
ejpam-3338	411	14	=	=	NOUN
ejpam-3338	411	15	0.1(the	0.1(the	PRON
ejpam-3338	411	16	graph	graph	NOUN
ejpam-3338	411	17	is	be	AUX
ejpam-3338	411	18	slightly	slightly	ADV
ejpam-3338	411	19	different	different	ADJ
ejpam-3338	411	20	in	in	ADP
ejpam-3338	411	21	appearance	appearance	NOUN
ejpam-3338	411	22	from	from	ADP
ejpam-3338	411	23	the	the	DET
ejpam-3338	411	24	original	original	ADJ
ejpam-3338	411	25	graph	graph	NOUN
ejpam-3338	411	26	produced	produce	VERB
ejpam-3338	411	27	by	by	ADP
ejpam-3338	411	28	matlab	matlab	PROPN
ejpam-3338	411	29	due	due	ADP
ejpam-3338	411	30	to	to	PART
ejpam-3338	411	31	copy	copy	VERB
ejpam-3338	411	32	(	(	PUNCT
ejpam-3338	411	33	under	under	ADP
ejpam-3338	411	34	matlab	matlab	PROPN
ejpam-3338	411	35	edit	edit	NOUN
ejpam-3338	411	36	)	)	PUNCT
ejpam-3338	411	37	and	and	CCONJ
ejpam-3338	411	38	paste	paste	NOUN
ejpam-3338	411	39	)	)	PUNCT
ejpam-3338	411	40	’	'	PUNCT
ejpam-3338	411	41	fractional	fractional	ADJ
ejpam-3338	411	42	order	order	NOUN
ejpam-3338	411	43	alpha=’,disp(order(i	alpha=’,disp(order(i	NOUN
ejpam-3338	411	44	)	)	PUNCT
ejpam-3338	411	45	)	)	PUNCT
ejpam-3338	411	46	,	,	PUNCT
ejpam-3338	411	47	’	'	PUNCT
ejpam-3338	411	48	sampled	sample	VERB
ejpam-3338	411	49	derivatives	derivative	NOUN
ejpam-3338	411	50	(	(	PUNCT
ejpam-3338	411	51	omitting	omit	VERB
ejpam-3338	411	52	1st	1st	ADJ
ejpam-3338	411	53	element	element	NOUN
ejpam-3338	411	54	0	0	NUM
ejpam-3338	411	55	)	)	PUNCT
ejpam-3338	411	56	are	be	AUX
ejpam-3338	411	57	’	'	PUNCT
ejpam-3338	411	58	,	,	PUNCT
ejpam-3338	411	59	disp(yd(i	disp(yd(i	PROPN
ejpam-3338	411	60	,	,	PUNCT
ejpam-3338	411	61	:))	:))	PROPN
ejpam-3338	411	62	,	,	PUNCT
ejpam-3338	411	63	end	end	NOUN
ejpam-3338	411	64	;	;	PUNCT
ejpam-3338	411	65	[	[	X
ejpam-3338	411	66	x	x	X
ejpam-3338	411	67	,	,	PUNCT
ejpam-3338	411	68	y]=meshgrid(t	y]=meshgrid(t	NOUN
ejpam-3338	411	69	,	,	PUNCT
ejpam-3338	411	70	order	order	NOUN
ejpam-3338	411	71	)	)	PUNCT
ejpam-3338	411	72	;	;	PUNCT
ejpam-3338	412	1	mesh(x	mesh(x	PROPN
ejpam-3338	412	2	,	,	PUNCT
ejpam-3338	412	3	y	y	PROPN
ejpam-3338	412	4	,	,	PUNCT
ejpam-3338	412	5	yd	yd	NOUN
ejpam-3338	412	6	)	)	PUNCT
ejpam-3338	412	7	xlabel(’t	xlabel(’t	NUM
ejpam-3338	412	8	’	'	PUNCT
ejpam-3338	412	9	)	)	PUNCT
ejpam-3338	412	10	;	;	PUNCT
ejpam-3338	412	11	ylabel(′α′	ylabel(′α′	X
ejpam-3338	412	12	)	)	PUNCT
ejpam-3338	412	13	;	;	PUNCT
ejpam-3338	412	14	zlabel(’y	zlabel(’y	NUM
ejpam-3338	412	15	’	'	PUNCT
ejpam-3338	412	16	)	)	PUNCT
ejpam-3338	412	17	observe	observe	VERB
ejpam-3338	412	18	that	that	SCONJ
ejpam-3338	412	19	there	there	PRON
ejpam-3338	412	20	is	be	VERB
ejpam-3338	412	21	a	a	DET
ejpam-3338	412	22	great	great	ADJ
ejpam-3338	412	23	advantage	advantage	NOUN
ejpam-3338	412	24	in	in	ADP
ejpam-3338	412	25	considering	consider	VERB
ejpam-3338	412	26	an	an	DET
ejpam-3338	412	27	equi	equi	NOUN
ejpam-3338	412	28	-	-	PUNCT
ejpam-3338	412	29	spaced	space	VERB
ejpam-3338	412	30	sampled	sample	VERB
ejpam-3338	412	31	function	function	NOUN
ejpam-3338	412	32	in	in	ADP
ejpam-3338	412	33	numerical	numerical	ADJ
ejpam-3338	412	34	computation	computation	NOUN
ejpam-3338	412	35	.	.	PUNCT
ejpam-3338	413	1	the	the	DET
ejpam-3338	413	2	program	program	NOUN
ejpam-3338	413	3	needs	need	VERB
ejpam-3338	413	4	no	no	DET
ejpam-3338	413	5	change	change	NOUN
ejpam-3338	413	6	except	except	SCONJ
ejpam-3338	413	7	in	in	ADP
ejpam-3338	413	8	the	the	DET
ejpam-3338	413	9	3rd	3rd	ADJ
ejpam-3338	413	10	line	line	NOUN
ejpam-3338	413	11	viz	viz	PROPN
ejpam-3338	413	12	.	.	PUNCT
ejpam-3338	414	1	y	y	PROPN
ejpam-3338	414	2	=	=	PUNCT
ejpam-3338	414	3	cos(t	cos(t	PROPN
ejpam-3338	414	4	)	)	PUNCT
ejpam-3338	414	5	.	.	PUNCT
ejpam-3338	415	1	if	if	SCONJ
ejpam-3338	415	2	we	we	PRON
ejpam-3338	415	3	have	have	VERB
ejpam-3338	415	4	to	to	PART
ejpam-3338	415	5	deal	deal	VERB
ejpam-3338	415	6	with	with	ADP
ejpam-3338	415	7	different	different	ADJ
ejpam-3338	415	8	mathematical	mathematical	ADJ
ejpam-3338	415	9	non	non	ADJ
ejpam-3338	415	10	-	-	ADJ
ejpam-3338	415	11	sampled	sample	VERB
ejpam-3338	415	12	functions	function	NOUN
ejpam-3338	415	13	inside	inside	ADP
ejpam-3338	415	14	the	the	DET
ejpam-3338	415	15	matlab	matlab	PROPN
ejpam-3338	415	16	program	program	NOUN
ejpam-3338	415	17	,	,	PUNCT
ejpam-3338	415	18	then	then	ADV
ejpam-3338	415	19	there	there	PRON
ejpam-3338	415	20	will	will	AUX
ejpam-3338	415	21	be	be	AUX
ejpam-3338	415	22	more	more	ADJ
ejpam-3338	415	23	changes	change	NOUN
ejpam-3338	415	24	in	in	ADP
ejpam-3338	415	25	the	the	DET
ejpam-3338	415	26	program	program	NOUN
ejpam-3338	415	27	.	.	PUNCT
ejpam-3338	416	1	however	however	ADV
ejpam-3338	416	2	,	,	PUNCT
ejpam-3338	416	3	ill	ill	ADV
ejpam-3338	416	4	-	-	PUNCT
ejpam-3338	416	5	conditioned	condition	VERB
ejpam-3338	416	6	functions	function	NOUN
ejpam-3338	416	7	(	(	PUNCT
ejpam-3338	416	8	such	such	ADJ
ejpam-3338	416	9	as	as	ADP
ejpam-3338	416	10	violently	violently	ADV
ejpam-3338	416	11	fluctuating	fluctuate	VERB
ejpam-3338	416	12	continuous	continuous	ADJ
ejpam-3338	416	13	functions	function	NOUN
ejpam-3338	416	14	)	)	PUNCT
ejpam-3338	416	15	would	would	AUX
ejpam-3338	416	16	always	always	ADV
ejpam-3338	416	17	be	be	AUX
ejpam-3338	416	18	needing	need	VERB
ejpam-3338	416	19	very	very	ADV
ejpam-3338	416	20	careful	careful	ADJ
ejpam-3338	416	21	handling	handling	NOUN
ejpam-3338	416	22	/	/	SYM
ejpam-3338	416	23	programming	programming	NOUN
ejpam-3338	416	24	so	so	SCONJ
ejpam-3338	416	25	that	that	SCONJ
ejpam-3338	416	26	we	we	PRON
ejpam-3338	416	27	get	get	VERB
ejpam-3338	416	28	reasonably	reasonably	ADV
ejpam-3338	416	29	good	good	ADJ
ejpam-3338	416	30	usable	usable	ADJ
ejpam-3338	416	31	numerical	numerical	ADJ
ejpam-3338	416	32	results	result	NOUN
ejpam-3338	416	33	.	.	PUNCT
ejpam-3338	417	1	the	the	DET
ejpam-3338	417	2	results	result	NOUN
ejpam-3338	417	3	(	(	PUNCT
ejpam-3338	417	4	produced	produce	VERB
ejpam-3338	417	5	partially	partially	ADV
ejpam-3338	417	6	here	here	ADV
ejpam-3338	417	7	to	to	PART
ejpam-3338	417	8	save	save	VERB
ejpam-3338	417	9	space	space	NOUN
ejpam-3338	417	10	)	)	PUNCT
ejpam-3338	417	11	and	and	CCONJ
ejpam-3338	417	12	the	the	DET
ejpam-3338	417	13	corresponding	corresponding	ADJ
ejpam-3338	417	14	graph	graph	NOUN
ejpam-3338	417	15	(	(	PUNCT
ejpam-3338	417	16	fig	fig	NOUN
ejpam-3338	417	17	.	.	NOUN
ejpam-3338	417	18	2	2	NUM
ejpam-3338	417	19	)	)	PUNCT
ejpam-3338	417	20	are	be	AUX
ejpam-3338	417	21	as	as	SCONJ
ejpam-3338	417	22	follows	follow	VERB
ejpam-3338	417	23	.	.	PUNCT
ejpam-3338	418	1	fractional	fractional	ADJ
ejpam-3338	418	2	order	order	NOUN
ejpam-3338	418	3	alpha=0	alpha=0	AUX
ejpam-3338	418	4	sampled	sample	VERB
ejpam-3338	418	5	derivatives	derivative	NOUN
ejpam-3338	418	6	are	be	AUX
ejpam-3338	418	7	0.0000	0.0000	NUM
ejpam-3338	418	8	0.0998	0.0998	NUM
ejpam-3338	418	9	0.1987	0.1987	NUM
ejpam-3338	418	10	0.2955	0.2955	NUM
ejpam-3338	418	11	0.3894	0.3894	NUM
ejpam-3338	418	12	0.4794	0.4794	NUM
ejpam-3338	419	1	0.5646	0.5646	NUM
ejpam-3338	419	2	0.6442	0.6442	NUM
ejpam-3338	419	3	0.7174	0.7174	NUM
ejpam-3338	419	4	0.7833	0.7833	NUM
ejpam-3338	419	5	0.8415	0.8415	NUM
ejpam-3338	419	6	0.8912	0.8912	NUM
ejpam-3338	419	7	s.	s.	PROPN
ejpam-3338	419	8	k.sen	k.sen	PROPN
ejpam-3338	419	9	,	,	PUNCT
ejpam-3338	419	10	j.	j.	PROPN
ejpam-3338	419	11	v.	v.	PROPN
ejpam-3338	419	12	devi	devi	PROPN
ejpam-3338	419	13	,	,	PUNCT
ejpam-3338	419	14	r.v.g	r.v.g	NOUN
ejpam-3338	419	15	.	.	PUNCT
ejpam-3338	420	1	r.	r.	PROPN
ejpam-3338	420	2	kumar	kumar	PROPN
ejpam-3338	420	3	/	/	SYM
ejpam-3338	420	4	eur	eur	PROPN
ejpam-3338	420	5	.	.	PUNCT
ejpam-3338	421	1	j.	j.	PROPN
ejpam-3338	421	2	pure	pure	PROPN
ejpam-3338	421	3	appl	appl	PROPN
ejpam-3338	421	4	.	.	PROPN
ejpam-3338	421	5	math	math	PROPN
ejpam-3338	421	6	,	,	PUNCT
ejpam-3338	421	7	11	11	NUM
ejpam-3338	421	8	(	(	PUNCT
ejpam-3338	421	9	3	3	NUM
ejpam-3338	421	10	)	)	PUNCT
ejpam-3338	421	11	(	(	PUNCT
ejpam-3338	421	12	2018	2018	NUM
ejpam-3338	421	13	)	)	PUNCT
ejpam-3338	421	14	,	,	PUNCT
ejpam-3338	421	15	1058	1058	NUM
ejpam-3338	421	16	-	-	SYM
ejpam-3338	421	17	1099	1099	NUM
ejpam-3338	421	18	1075	1075	NUM
ejpam-3338	421	19	fig	fig	NOUN
ejpam-3338	421	20	.	.	PUNCT
ejpam-3338	422	1	1b	1b	PROPN
ejpam-3338	422	2	fractional	fractional	ADJ
ejpam-3338	422	3	derivative	derivative	NOUN
ejpam-3338	422	4	of	of	ADP
ejpam-3338	422	5	sin(x)forx	sin(x)forx	NOUN
ejpam-3338	422	6	=	=	NOUN
ejpam-3338	422	7	0(h)4π	0(h)4π	NUM
ejpam-3338	422	8	for	for	ADP
ejpam-3338	422	9	α	α	PROPN
ejpam-3338	422	10	=	=	SYM
ejpam-3338	422	11	0(0.1)1	0(0.1)1	PROPN
ejpam-3338	422	12	,	,	PUNCT
ejpam-3338	422	13	h	h	NOUN
ejpam-3338	423	1	=	=	NOUN
ejpam-3338	423	2	0.01	0.01	NUM
ejpam-3338	423	3	(	(	PUNCT
ejpam-3338	423	4	the	the	DET
ejpam-3338	423	5	graph	graph	NOUN
ejpam-3338	423	6	is	be	AUX
ejpam-3338	423	7	slightly	slightly	ADV
ejpam-3338	423	8	different	different	ADJ
ejpam-3338	423	9	in	in	ADP
ejpam-3338	423	10	appearance	appearance	NOUN
ejpam-3338	423	11	from	from	ADP
ejpam-3338	423	12	the	the	DET
ejpam-3338	423	13	original	original	ADJ
ejpam-3338	423	14	graph	graph	NOUN
ejpam-3338	423	15	produced	produce	VERB
ejpam-3338	423	16	by	by	ADP
ejpam-3338	423	17	matlab	matlab	PROPN
ejpam-3338	423	18	due	due	ADP
ejpam-3338	423	19	to	to	PART
ejpam-3338	423	20	copy	copy	VERB
ejpam-3338	423	21	(	(	PUNCT
ejpam-3338	423	22	under	under	ADP
ejpam-3338	423	23	matlab	matlab	PROPN
ejpam-3338	423	24	edit	edit	NOUN
ejpam-3338	423	25	)	)	PUNCT
ejpam-3338	423	26	and	and	CCONJ
ejpam-3338	423	27	paste	paste	NOUN
ejpam-3338	423	28	)	)	PUNCT
ejpam-3338	423	29	0.9320	0.9320	NUM
ejpam-3338	423	30	0.9636	0.9636	NUM
ejpam-3338	423	31	0.9854	0.9854	NUM
ejpam-3338	423	32	0.9975	0.9975	NUM
ejpam-3338	423	33	0.9996	0.9996	NUM
ejpam-3338	423	34	0.9917	0.9917	NUM
ejpam-3338	423	35	0.9738	0.9738	NUM
ejpam-3338	423	36	0.9463	0.9463	NUM
ejpam-3338	423	37	0.9093	0.9093	NUM
ejpam-3338	423	38	0.8632	0.8632	NUM
ejpam-3338	423	39	0.8085	0.8085	NUM
ejpam-3338	423	40	0.7457	0.7457	NUM
ejpam-3338	423	41	0.6755	0.6755	NUM
ejpam-3338	423	42	0.5985	0.5985	NUM
ejpam-3338	423	43	0.5155	0.5155	NUM
ejpam-3338	423	44	0.4274	0.4274	NUM
ejpam-3338	423	45	0.3350	0.3350	NUM
ejpam-3338	423	46	0.2392	0.2392	NUM
ejpam-3338	423	47	0.1411	0.1411	NUM
ejpam-3338	423	48	0.0416	0.0416	NUM
ejpam-3338	423	49	-0.0584	-0.0584	NOUN
ejpam-3338	423	50	-0.1577	-0.1577	PROPN
ejpam-3338	423	51	-0.2555	-0.2555	PROPN
ejpam-3338	424	1	-0.3508	-0.3508	PROPN
ejpam-3338	424	2	-0.4425	-0.4425	PROPN
ejpam-3338	424	3	-0.5298	-0.5298	PROPN
ejpam-3338	424	4	-0.6119	-0.6119	PROPN
ejpam-3338	425	1	-0.6878	-0.6878	PROPN
ejpam-3338	425	2	-0.7568	-0.7568	PUNCT
ejpam-3338	425	3	-0.8183	-0.8183	PROPN
ejpam-3338	426	1	-0.8716	-0.8716	PROPN
ejpam-3338	426	2	-0.9162	-0.9162	PUNCT
ejpam-3338	427	1	-0.9516	-0.9516	PROPN
ejpam-3338	427	2	-0.9775	-0.9775	PROPN
ejpam-3338	427	3	-0.9937	-0.9937	PROPN
ejpam-3338	427	4	-0.9999	-0.9999	PROPN
ejpam-3338	427	5	-0.9962	-0.9962	PUNCT
ejpam-3338	428	1	-0.9825	-0.9825	PROPN
ejpam-3338	428	2	-0.9589	-0.9589	PROPN
ejpam-3338	428	3	-0.9258	-0.9258	PROPN
ejpam-3338	428	4	-0.8835	-0.8835	PROPN
ejpam-3338	428	5	-0.8323	-0.8323	PROPN
ejpam-3338	428	6	-0.7728	-0.7728	NOUN
ejpam-3338	428	7	-0.7055	-0.7055	PUNCT
ejpam-3338	428	8	-0.6313	-0.6313	PROPN
ejpam-3338	428	9	-0.5507	-0.5507	PUNCT
ejpam-3338	428	10	-0.4646	-0.4646	PROPN
ejpam-3338	428	11	-0.3739	-0.3739	PROPN
ejpam-3338	428	12	-0.2794	-0.2794	PROPN
ejpam-3338	429	1	-0.1822	-0.1822	PROPN
ejpam-3338	429	2	-0.0831	-0.0831	PUNCT
ejpam-3338	430	1	0.0168	0.0168	NUM
ejpam-3338	430	2	0.1165	0.1165	NUM
ejpam-3338	430	3	0.2151	0.2151	NUM
ejpam-3338	430	4	0.3115	0.3115	NUM
ejpam-3338	430	5	0.4048	0.4048	NUM
ejpam-3338	430	6	0.4941	0.4941	NUM
ejpam-3338	430	7	0.5784	0.5784	NUM
ejpam-3338	430	8	0.6570	0.6570	NUM
ejpam-3338	430	9	0.7290	0.7290	NUM
ejpam-3338	431	1	0.7937	0.7937	NUM
ejpam-3338	431	2	0.8504	0.8504	NUM
ejpam-3338	431	3	0.8987	0.8987	NUM
ejpam-3338	431	4	0.9380	0.9380	NUM
ejpam-3338	431	5	0.9679	0.9679	NUM
ejpam-3338	431	6	0.9882	0.9882	NUM
ejpam-3338	431	7	0.9985	0.9985	NUM
ejpam-3338	431	8	0.9989	0.9989	NUM
ejpam-3338	431	9	0.9894	0.9894	NUM
ejpam-3338	431	10	0.9699	0.9699	NUM
ejpam-3338	431	11	0.9407	0.9407	NUM
ejpam-3338	431	12	0.9022	0.9022	NOUN
ejpam-3338	431	13	0.8546	0.8546	NUM
ejpam-3338	431	14	0.7985	0.7985	NUM
ejpam-3338	431	15	0.7344	0.7344	NUM
ejpam-3338	431	16	0.6630	0.6630	NUM
ejpam-3338	431	17	0.5849	0.5849	NUM
ejpam-3338	431	18	0.5010	0.5010	NUM
ejpam-3338	431	19	0.4121	0.4121	NUM
ejpam-3338	431	20	0.3191	0.3191	NUM
ejpam-3338	431	21	0.2229	0.2229	NUM
ejpam-3338	431	22	0.1245	0.1245	NUM
ejpam-3338	431	23	0.0248	0.0248	NUM
ejpam-3338	431	24	-0.0752	-0.0752	PROPN
ejpam-3338	431	25	-0.1743	-0.1743	PROPN
ejpam-3338	431	26	-0.2718	-0.2718	PROPN
ejpam-3338	431	27	-0.3665	-0.3665	PROPN
ejpam-3338	431	28	-0.4575	-0.4575	PROPN
ejpam-3338	431	29	-0.5440	-0.5440	PROPN
ejpam-3338	431	30	-0.6251	-0.6251	PROPN
ejpam-3338	431	31	-0.6999	-0.6999	PROPN
ejpam-3338	431	32	-0.7677	-0.7677	PROPN
ejpam-3338	431	33	-0.8278	-0.8278	PROPN
ejpam-3338	431	34	-0.8797	-0.8797	PROPN
ejpam-3338	431	35	-0.9228	-0.9228	PROPN
ejpam-3338	431	36	-0.9566	-0.9566	PROPN
ejpam-3338	431	37	-0.9809	-0.9809	PROPN
ejpam-3338	431	38	-0.9954	-0.9954	VERB
ejpam-3338	432	1	-1.0000	-1.0000	ADJ
ejpam-3338	432	2	-0.9946	-0.9946	PROPN
ejpam-3338	432	3	-0.9792	-0.9792	PROPN
ejpam-3338	432	4	-0.9540	-0.9540	PROPN
ejpam-3338	433	1	-0.9193	-0.9193	PROPN
ejpam-3338	433	2	-0.8755	-0.8755	PROPN
ejpam-3338	433	3	-0.8228	-0.8228	PROPN
ejpam-3338	434	1	-0.7620	-0.7620	NOUN
ejpam-3338	435	1	0.6935	0.6935	NUM
ejpam-3338	435	2	-0.6181	-0.6181	ADJ
ejpam-3338	435	3	-0.5366	-0.5366	PROPN
ejpam-3338	436	1	-0.4496	-0.4496	PROPN
ejpam-3338	436	2	-0.3582	-0.3582	PROPN
ejpam-3338	436	3	-0.2632	-0.2632	PROPN
ejpam-3338	436	4	-0.1656	-0.1656	PROPN
ejpam-3338	436	5	-0.0663	-0.0663	NOUN
ejpam-3338	436	6	0.0336	0.0336	NUM
ejpam-3338	436	7	0.1332	0.1332	NUM
ejpam-3338	436	8	0.2315	0.2315	NUM
ejpam-3338	436	9	0.3275	0.3275	NUM
ejpam-3338	436	10	0.4202	0.4202	NUM
ejpam-3338	436	11	0.5087	0.5087	NUM
ejpam-3338	437	1	0.5921	0.5921	NUM
ejpam-3338	437	2	0.6696	0.6696	NUM
ejpam-3338	437	3	0.7404	0.7404	NUM
ejpam-3338	437	4	0.8038	0.8038	NUM
ejpam-3338	437	5	0.8592	0.8592	NUM
ejpam-3338	437	6	0.9060	0.9060	NUM
ejpam-3338	437	7	0.9437	0.9437	NUM
ejpam-3338	437	8	0.9720	0.9720	NUM
ejpam-3338	437	9	0.9906	0.9906	NUM
ejpam-3338	437	10	0.9993	0.9993	NUM
ejpam-3338	437	11	0.9980	0.9980	NUM
ejpam-3338	437	12	0.9868	0.9868	NUM
ejpam-3338	437	13	0.9657	0.9657	NUM
ejpam-3338	437	14	0.9349	0.9349	NUM
ejpam-3338	437	15	0.8948	0.8948	NUM
ejpam-3338	437	16	0.8457	0.8457	NUM
ejpam-3338	437	17	0.7883	0.7883	NUM
ejpam-3338	437	18	0.7229	0.7229	NUM
ejpam-3338	437	19	0.6503	0.6503	NUM
ejpam-3338	437	20	0.5712	0.5712	NUM
ejpam-3338	437	21	0.4864	0.4864	NUM
ejpam-3338	438	1	0.3967	0.3967	NUM
ejpam-3338	439	1	0.3031	0.3031	NUM
ejpam-3338	439	2	0.2065	0.2065	NUM
ejpam-3338	439	3	0.1078	0.1078	NUM
ejpam-3338	439	4	0.0080	0.0080	NUM
ejpam-3338	439	5	-0.0919	-0.0919	X
ejpam-3338	439	6	-0.1909	-0.1909	NOUN
ejpam-3338	439	7	-0.2879	-0.2879	PROPN
ejpam-3338	439	8	-0.3821	-0.3821	VERB
ejpam-3338	439	9	-0.4724	-0.4724	PUNCT
ejpam-3338	440	1	-0.5581	-0.5581	PROPN
ejpam-3338	440	2	-0.6381	-0.6381	PROPN
ejpam-3338	440	3	-0.7118	-0.7118	PROPN
ejpam-3338	440	4	-0.7784	-0.7784	VERB
ejpam-3338	441	1	0.8371	0.8371	NUM
ejpam-3338	441	2	-0.8876	-0.8876	NOUN
ejpam-3338	441	3	-0.9291	-0.9291	PROPN
ejpam-3338	441	4	-0.9614	-0.9614	PROPN
ejpam-3338	441	5	-0.9841	-0.9841	PROPN
ejpam-3338	441	6	-0.9969	-0.9969	PROPN
ejpam-3338	441	7	-0.9998	-0.9998	PUNCT
ejpam-3338	442	1	-0.9927	-0.9927	PROPN
ejpam-3338	442	2	-0.9756	-0.9756	PROPN
ejpam-3338	443	1	-0.9488	-0.9488	PROPN
ejpam-3338	443	2	-0.9126	-0.9126	PROPN
ejpam-3338	444	1	-0.8672	-0.8672	PROPN
ejpam-3338	444	2	-0.8132	-0.8132	PROPN
ejpam-3338	444	3	-0.7510	-0.7510	PROPN
ejpam-3338	444	4	-0.6813	-0.6813	PROPN
ejpam-3338	444	5	-0.6048	-0.6048	PROPN
ejpam-3338	444	6	-0.5223	-0.5223	PROPN
ejpam-3338	444	7	-0.4346	-0.4346	PROPN
ejpam-3338	444	8	-0.3425	-0.3425	PROPN
ejpam-3338	444	9	-0.2470	-0.2470	PROPN
ejpam-3338	444	10	-0.1490	-0.1490	PUNCT
ejpam-3338	444	11	-0.0495	-0.0495	VERB
ejpam-3338	444	12	0.0504	0.0504	NUM
ejpam-3338	444	13	0.1499	0.1499	NUM
ejpam-3338	444	14	0.2478	0.2478	NUM
ejpam-3338	444	15	0.3433	0.3433	NUM
ejpam-3338	444	16	0.4354	0.4354	NUM
ejpam-3338	444	17	0.5231	0.5231	NUM
ejpam-3338	445	1	0.6055	0.6055	NUM
ejpam-3338	445	2	0.6820	0.6820	NUM
ejpam-3338	445	3	0.7516	0.7516	NUM
ejpam-3338	445	4	0.8137	0.8137	NUM
ejpam-3338	445	5	0.8676	0.8676	NUM
ejpam-3338	445	6	0.9129	0.9129	NUM
ejpam-3338	445	7	0.9491	0.9491	NUM
ejpam-3338	445	8	0.9758	0.9758	NUM
ejpam-3338	445	9	0.9928	0.9928	NUM
ejpam-3338	445	10	0.9998	0.9998	NUM
ejpam-3338	445	11	s.	s.	PROPN
ejpam-3338	445	12	k.sen	k.sen	PROPN
ejpam-3338	445	13	,	,	PUNCT
ejpam-3338	445	14	j.	j.	PROPN
ejpam-3338	445	15	v.	v.	PROPN
ejpam-3338	445	16	devi	devi	PROPN
ejpam-3338	445	17	,	,	PUNCT
ejpam-3338	445	18	r.v.g	r.v.g	NOUN
ejpam-3338	445	19	.	.	PUNCT
ejpam-3338	446	1	r.	r.	PROPN
ejpam-3338	446	2	kumar	kumar	PROPN
ejpam-3338	446	3	/	/	SYM
ejpam-3338	446	4	eur	eur	PROPN
ejpam-3338	446	5	.	.	PUNCT
ejpam-3338	447	1	j.	j.	PROPN
ejpam-3338	447	2	pure	pure	PROPN
ejpam-3338	447	3	appl	appl	PROPN
ejpam-3338	447	4	.	.	PROPN
ejpam-3338	447	5	math	math	PROPN
ejpam-3338	447	6	,	,	PUNCT
ejpam-3338	447	7	11	11	NUM
ejpam-3338	447	8	(	(	PUNCT
ejpam-3338	447	9	3	3	NUM
ejpam-3338	447	10	)	)	PUNCT
ejpam-3338	447	11	(	(	PUNCT
ejpam-3338	447	12	2018	2018	NUM
ejpam-3338	447	13	)	)	PUNCT
ejpam-3338	447	14	,	,	PUNCT
ejpam-3338	447	15	1058	1058	NUM
ejpam-3338	447	16	-	-	SYM
ejpam-3338	447	17	1099	1099	NUM
ejpam-3338	447	18	1076	1076	NUM
ejpam-3338	447	19	fractional	fractional	ADJ
ejpam-3338	447	20	order	order	NOUN
ejpam-3338	447	21	alpha=	alpha=	NUM
ejpam-3338	447	22	0.1000	0.1000	NUM
ejpam-3338	447	23	sampled	sample	VERB
ejpam-3338	447	24	derivatives	derivative	NOUN
ejpam-3338	447	25	are	be	AUX
ejpam-3338	447	26	0.0000	0.0000	NUM
ejpam-3338	447	27	(	(	PUNCT
ejpam-3338	447	28	omit	omit	ADJ
ejpam-3338	447	29	)	)	PUNCT
ejpam-3338	447	30	0.1257	0.1257	NUM
ejpam-3338	447	31	0.2375	0.2375	NUM
ejpam-3338	448	1	0.3414	0.3414	NUM
ejpam-3338	448	2	0.4382	0.4382	NUM
ejpam-3338	448	3	0.5281	0.5281	NUM
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ejpam-3338	491	13	)	)	PUNCT
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ejpam-3338	491	20	(	(	PUNCT
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ejpam-3338	491	22	)	)	PUNCT
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ejpam-3338	511	24	0.6961	0.6961	NUM
ejpam-3338	511	25	0.6210	0.6210	NUM
ejpam-3338	511	26	0.5397	0.5397	NUM
ejpam-3338	511	27	0.4530	0.4530	NUM
ejpam-3338	511	28	0.3618	0.3618	NUM
ejpam-3338	511	29	0.2670	0.2670	NUM
ejpam-3338	511	30	0.1695	0.1695	NUM
ejpam-3338	511	31	0.0703	0.0703	NUM
ejpam-3338	511	32	as	as	ADP
ejpam-3338	511	33	in	in	ADP
ejpam-3338	511	34	the	the	DET
ejpam-3338	511	35	foregoing	forego	VERB
ejpam-3338	511	36	example	example	NOUN
ejpam-3338	511	37	,	,	PUNCT
ejpam-3338	511	38	here	here	ADV
ejpam-3338	511	39	too	too	ADV
ejpam-3338	511	40	the	the	DET
ejpam-3338	511	41	accuracy	accuracy	NOUN
ejpam-3338	511	42	improves	improve	VERB
ejpam-3338	511	43	when	when	SCONJ
ejpam-3338	511	44	the	the	DET
ejpam-3338	511	45	function	function	NOUN
ejpam-3338	511	46	cos(t	cos(t	NOUN
ejpam-3338	511	47	)	)	PUNCT
ejpam-3338	511	48	is	be	AUX
ejpam-3338	511	49	sampled	sample	VERB
ejpam-3338	511	50	with	with	ADP
ejpam-3338	511	51	higher	high	ADJ
ejpam-3338	511	52	frequency	frequency	NOUN
ejpam-3338	511	53	.	.	PUNCT
ejpam-3338	512	1	if	if	SCONJ
ejpam-3338	512	2	h	h	NOUN
ejpam-3338	512	3	=	=	NOUN
ejpam-3338	512	4	.01	.01	NUM
ejpam-3338	512	5	(	(	PUNCT
ejpam-3338	512	6	implying	imply	VERB
ejpam-3338	512	7	10	10	NUM
ejpam-3338	512	8	times	time	NOUN
ejpam-3338	512	9	higher	high	ADJ
ejpam-3338	512	10	frequency	frequency	NOUN
ejpam-3338	512	11	)	)	PUNCT
ejpam-3338	512	12	,	,	PUNCT
ejpam-3338	512	13	then	then	ADV
ejpam-3338	512	14	the	the	DET
ejpam-3338	512	15	result	result	NOUN
ejpam-3338	512	16	will	will	AUX
ejpam-3338	512	17	be	be	AUX
ejpam-3338	512	18	correct	correct	ADJ
ejpam-3338	512	19	up	up	ADP
ejpam-3338	512	20	to	to	PART
ejpam-3338	512	21	3	3	NUM
ejpam-3338	512	22	significant	significant	ADJ
ejpam-3338	512	23	digits	digit	NOUN
ejpam-3338	512	24	.	.	PUNCT
ejpam-3338	513	1	however	however	ADV
ejpam-3338	513	2	,	,	PUNCT
ejpam-3338	513	3	if	if	SCONJ
ejpam-3338	513	4	the	the	DET
ejpam-3338	513	5	sampling	sampling	NOUN
ejpam-3338	513	6	is	be	AUX
ejpam-3338	513	7	done	do	VERB
ejpam-3338	513	8	with	with	ADP
ejpam-3338	513	9	frequency	frequency	NOUN
ejpam-3338	513	10	increasingly	increasingly	ADV
ejpam-3338	513	11	too	too	ADV
ejpam-3338	513	12	large	large	ADJ
ejpam-3338	513	13	,	,	PUNCT
ejpam-3338	513	14	then	then	ADV
ejpam-3338	513	15	the	the	DET
ejpam-3338	513	16	result	result	NOUN
ejpam-3338	513	17	will	will	AUX
ejpam-3338	513	18	deteriorate	deteriorate	VERB
ejpam-3338	513	19	since	since	SCONJ
ejpam-3338	513	20	the	the	DET
ejpam-3338	513	21	computational	computational	ADJ
ejpam-3338	513	22	error	error	NOUN
ejpam-3338	513	23	starts	start	VERB
ejpam-3338	513	24	creeping	creep	VERB
ejpam-3338	513	25	in	in	ADP
ejpam-3338	513	26	depending	depend	VERB
ejpam-3338	513	27	on	on	ADP
ejpam-3338	513	28	the	the	DET
ejpam-3338	513	29	precision	precision	NOUN
ejpam-3338	513	30	used	use	VERB
ejpam-3338	513	31	.	.	PUNCT
ejpam-3338	514	1	for	for	ADP
ejpam-3338	514	2	most	most	ADJ
ejpam-3338	514	3	practical	practical	ADJ
ejpam-3338	514	4	usage	usage	NOUN
ejpam-3338	514	5	,	,	PUNCT
ejpam-3338	514	6	too	too	ADV
ejpam-3338	514	7	large	large	ADJ
ejpam-3338	514	8	a	a	DET
ejpam-3338	514	9	sampling	sample	VERB
ejpam-3338	514	10	frequency	frequency	NOUN
ejpam-3338	514	11	should	should	AUX
ejpam-3338	514	12	not	not	PART
ejpam-3338	514	13	be	be	AUX
ejpam-3338	514	14	used	use	VERB
ejpam-3338	514	15	since	since	SCONJ
ejpam-3338	514	16	instead	instead	ADV
ejpam-3338	514	17	of	of	ADP
ejpam-3338	514	18	increasingly	increasingly	ADV
ejpam-3338	514	19	improving	improve	VERB
ejpam-3338	514	20	the	the	DET
ejpam-3338	514	21	result	result	NOUN
ejpam-3338	514	22	,	,	PUNCT
ejpam-3338	514	23	it	it	PRON
ejpam-3338	514	24	degenerates	degenerate	NOUN
ejpam-3338	514	25	(	(	PUNCT
ejpam-3338	514	26	worsens	worsens	PROPN
ejpam-3338	514	27	)	)	PUNCT
ejpam-3338	514	28	the	the	DET
ejpam-3338	514	29	result	result	NOUN
ejpam-3338	514	30	.	.	PUNCT
ejpam-3338	515	1	riemann	riemann	PROPN
ejpam-3338	515	2	-	-	PUNCT
ejpam-3338	515	3	liouville	liouville	PROPN
ejpam-3338	515	4	(	(	PUNCT
ejpam-3338	515	5	rl	rl	NOUN
ejpam-3338	515	6	)	)	PUNCT
ejpam-3338	515	7	derivative	derivative	NOUN
ejpam-3338	515	8	the	the	DET
ejpam-3338	515	9	3	3	NUM
ejpam-3338	515	10	most	most	ADV
ejpam-3338	515	11	frequently	frequently	ADV
ejpam-3338	515	12	used	use	VERB
ejpam-3338	515	13	definitions	definition	NOUN
ejpam-3338	515	14	for	for	ADP
ejpam-3338	515	15	the	the	DET
ejpam-3338	515	16	general	general	ADJ
ejpam-3338	515	17	fractional	fractional	ADJ
ejpam-3338	515	18	differintegral	differintegral	NOUN
ejpam-3338	515	19	are	be	AUX
ejpam-3338	515	20	gl	gl	PROPN
ejpam-3338	515	21	,	,	PUNCT
ejpam-3338	515	22	rl	rl	X
ejpam-3338	515	23	(	(	PUNCT
ejpam-3338	515	24	riemann	riemann	PROPN
ejpam-3338	515	25	-	-	PUNCT
ejpam-3338	515	26	liouville	liouville	NOUN
ejpam-3338	515	27	)	)	PUNCT
ejpam-3338	515	28	,	,	PUNCT
ejpam-3338	515	29	and	and	CCONJ
ejpam-3338	515	30	caputo	caputo	PROPN
ejpam-3338	515	31	definitions	definition	NOUN
ejpam-3338	515	32	.	.	PUNCT
ejpam-3338	516	1	we	we	PRON
ejpam-3338	516	2	have	have	AUX
ejpam-3338	516	3	already	already	ADV
ejpam-3338	516	4	discussed	discuss	VERB
ejpam-3338	516	5	gl	gl	NOUN
ejpam-3338	516	6	derivative	derivative	NOUN
ejpam-3338	516	7	in	in	ADP
ejpam-3338	516	8	both	both	CCONJ
ejpam-3338	516	9	reverse	reverse	ADJ
ejpam-3338	516	10	and	and	CCONJ
ejpam-3338	516	11	direct	direct	ADJ
ejpam-3338	516	12	forms	form	NOUN
ejpam-3338	516	13	.	.	PUNCT
ejpam-3338	517	1	in	in	ADP
ejpam-3338	517	2	terms	term	NOUN
ejpam-3338	517	3	of	of	ADP
ejpam-3338	517	4	the	the	DET
ejpam-3338	517	5	fundamental	fundamental	ADJ
ejpam-3338	517	6	continuous	continuous	ADJ
ejpam-3338	517	7	integrodifferential	integrodifferential	ADJ
ejpam-3338	517	8	operator	operator	NOUN
ejpam-3338	517	9	defined	define	VERB
ejpam-3338	517	10	as	as	ADP
ejpam-3338	517	11	dα	dα	PROPN
ejpam-3338	517	12	t	t	PROPN
ejpam-3338	517	13	=	=	PUNCT
ejpam-3338	517	14	dα	dα	PROPN
ejpam-3338	517	15	dtα	dtα	NOUN
ejpam-3338	517	16	:	:	PUNCT
ejpam-3338	517	17	α	α	X
ejpam-3338	517	18	>	>	X
ejpam-3338	517	19	0;dα	0;dα	PUNCT
ejpam-3338	518	1	t	t	X
ejpam-3338	518	2	=	=	SYM
ejpam-3338	518	3	1	1	NUM
ejpam-3338	518	4	:	:	PUNCT
ejpam-3338	518	5	α	α	X
ejpam-3338	518	6	=	=	PUNCT
ejpam-3338	518	7	0;dα	0;dα	NUM
ejpam-3338	519	1	t	t	X
ejpam-3338	519	2	=	=	SYM
ejpam-3338	519	3	∫	∫	PROPN
ejpam-3338	519	4	t	t	PROPN
ejpam-3338	519	5	a	a	DET
ejpam-3338	519	6	dτα	dτα	NOUN
ejpam-3338	519	7	:	:	PUNCT
ejpam-3338	519	8	α	α	X
ejpam-3338	519	9	<	<	X
ejpam-3338	519	10	0	0	NUM
ejpam-3338	520	1	(	(	PUNCT
ejpam-3338	521	1	32	32	NUM
ejpam-3338	521	2	)	)	PUNCT
ejpam-3338	521	3	where	where	SCONJ
ejpam-3338	521	4	a	a	X
ejpam-3338	521	5	,	,	PUNCT
ejpam-3338	521	6	t	t	PROPN
ejpam-3338	521	7	are	be	AUX
ejpam-3338	521	8	bounds	bound	NOUN
ejpam-3338	521	9	of	of	ADP
ejpam-3338	521	10	the	the	DET
ejpam-3338	521	11	operation	operation	NOUN
ejpam-3338	521	12	and	and	CCONJ
ejpam-3338	521	13	α	α	PRON
ejpam-3338	521	14	∈	∈	NOUN
ejpam-3338	521	15	r	r	NOUN
ejpam-3338	521	16	is	be	AUX
ejpam-3338	521	17	a	a	DET
ejpam-3338	521	18	real	real	ADJ
ejpam-3338	521	19	fractional	fractional	NOUN
ejpam-3338	521	20	(	(	PUNCT
ejpam-3338	521	21	including	include	VERB
ejpam-3338	521	22	of	of	ADP
ejpam-3338	521	23	course	course	NOUN
ejpam-3338	521	24	integer	integer	NOUN
ejpam-3338	521	25	)	)	PUNCT
ejpam-3338	521	26	order	order	NOUN
ejpam-3338	522	1	[	[	X
ejpam-3338	522	2	6	6	NUM
ejpam-3338	522	3	,	,	PUNCT
ejpam-3338	522	4	8	8	NUM
ejpam-3338	522	5	]	]	PUNCT
ejpam-3338	522	6	.	.	PUNCT
ejpam-3338	523	1	the	the	DET
ejpam-3338	523	2	rl	rl	PROPN
ejpam-3338	523	3	derivative	derivative	NOUN
ejpam-3338	523	4	for	for	ADP
ejpam-3338	523	5	the	the	DET
ejpam-3338	523	6	general	general	ADJ
ejpam-3338	523	7	function	function	NOUN
ejpam-3338	523	8	f(t	f(t	PROPN
ejpam-3338	523	9	)	)	PUNCT
ejpam-3338	523	10	is	be	AUX
ejpam-3338	523	11	dα	dα	ADP
ejpam-3338	523	12	t	t	PROPN
ejpam-3338	523	13	f(t	f(t	PROPN
ejpam-3338	523	14	)	)	PUNCT
ejpam-3338	523	15	=	=	SYM
ejpam-3338	523	16	1	1	NUM
ejpam-3338	523	17	γ(n−	γ(n−	PROPN
ejpam-3338	523	18	α	α	NOUN
ejpam-3338	523	19	)	)	PUNCT
ejpam-3338	523	20	dn	dn	PROPN
ejpam-3338	523	21	dtn	dtn	PROPN
ejpam-3338	523	22	∫	∫	PROPN
ejpam-3338	523	23	t	t	PROPN
ejpam-3338	523	24	a	a	DET
ejpam-3338	523	25	f(τ	f(τ	NOUN
ejpam-3338	523	26	)	)	PUNCT
ejpam-3338	523	27	(	(	PUNCT
ejpam-3338	523	28	t−	t−	PROPN
ejpam-3338	523	29	τ)α−n+1	τ)α−n+1	PROPN
ejpam-3338	523	30	dτ	dτ	PROPN
ejpam-3338	523	31	,	,	PUNCT
ejpam-3338	523	32	(	(	PUNCT
ejpam-3338	523	33	n−	n−	NOUN
ejpam-3338	523	34	1	1	NUM
ejpam-3338	523	35	<	<	X
ejpam-3338	523	36	α	α	X
ejpam-3338	523	37	<	<	X
ejpam-3338	523	38	n	n	CCONJ
ejpam-3338	523	39	)	)	PUNCT
ejpam-3338	523	40	(	(	PUNCT
ejpam-3338	523	41	33	33	NUM
ejpam-3338	523	42	)	)	PUNCT
ejpam-3338	523	43	the	the	DET
ejpam-3338	523	44	rl	rl	NOUN
ejpam-3338	523	45	definition	definition	NOUN
ejpam-3338	523	46	for	for	ADP
ejpam-3338	523	47	the	the	DET
ejpam-3338	523	48	fractional	fractional	ADJ
ejpam-3338	523	49	derivative	derivative	NOUN
ejpam-3338	523	50	of	of	ADP
ejpam-3338	523	51	f(t	f(t	NOUN
ejpam-3338	523	52	)	)	PUNCT
ejpam-3338	523	53	involves	involve	VERB
ejpam-3338	523	54	both	both	DET
ejpam-3338	523	55	integration	integration	NOUN
ejpam-3338	523	56	and	and	CCONJ
ejpam-3338	523	57	differentiation	differentiation	NOUN
ejpam-3338	523	58	(	(	PUNCT
ejpam-3338	523	59	differintegral	differintegral	ADJ
ejpam-3338	523	60	)	)	PUNCT
ejpam-3338	523	61	unlike	unlike	ADP
ejpam-3338	523	62	the	the	DET
ejpam-3338	523	63	integer	integer	NOUN
ejpam-3338	523	64	order	order	NOUN
ejpam-3338	523	65	derivative	derivative	NOUN
ejpam-3338	523	66	which	which	PRON
ejpam-3338	523	67	is	be	AUX
ejpam-3338	523	68	mathematically	mathematically	ADV
ejpam-3338	523	69	s.	s.	PROPN
ejpam-3338	523	70	k.sen	k.sen	PROPN
ejpam-3338	523	71	,	,	PUNCT
ejpam-3338	523	72	j.	j.	PROPN
ejpam-3338	523	73	v.	v.	PROPN
ejpam-3338	523	74	devi	devi	PROPN
ejpam-3338	523	75	,	,	PUNCT
ejpam-3338	523	76	r.v.g	r.v.g	NOUN
ejpam-3338	523	77	.	.	PUNCT
ejpam-3338	524	1	r.	r.	PROPN
ejpam-3338	524	2	kumar	kumar	PROPN
ejpam-3338	524	3	/	/	SYM
ejpam-3338	524	4	eur	eur	PROPN
ejpam-3338	524	5	.	.	PUNCT
ejpam-3338	525	1	j.	j.	PROPN
ejpam-3338	525	2	pure	pure	PROPN
ejpam-3338	525	3	appl	appl	PROPN
ejpam-3338	525	4	.	.	PROPN
ejpam-3338	525	5	math	math	PROPN
ejpam-3338	525	6	,	,	PUNCT
ejpam-3338	525	7	11	11	NUM
ejpam-3338	525	8	(	(	PUNCT
ejpam-3338	525	9	3	3	NUM
ejpam-3338	525	10	)	)	PUNCT
ejpam-3338	525	11	(	(	PUNCT
ejpam-3338	525	12	2018	2018	NUM
ejpam-3338	525	13	)	)	PUNCT
ejpam-3338	525	14	,	,	PUNCT
ejpam-3338	525	15	1058	1058	NUM
ejpam-3338	525	16	-	-	SYM
ejpam-3338	525	17	1099	1099	NUM
ejpam-3338	525	18	1078	1078	NUM
ejpam-3338	525	19	fig	fig	NOUN
ejpam-3338	525	20	.	.	PUNCT
ejpam-3338	526	1	2	2	NUM
ejpam-3338	526	2	fractional	fractional	ADJ
ejpam-3338	526	3	derivative	derivative	NOUN
ejpam-3338	526	4	of	of	ADP
ejpam-3338	526	5	cos(t	cos(t	NOUN
ejpam-3338	526	6	)	)	PUNCT
ejpam-3338	526	7	for	for	ADP
ejpam-3338	526	8	t	t	NOUN
ejpam-3338	526	9	=	=	SYM
ejpam-3338	527	1	−π	−π	ADP
ejpam-3338	527	2	2	2	NUM
ejpam-3338	527	3	(	(	PUNCT
ejpam-3338	527	4	h)6π	h)6π	VERB
ejpam-3338	527	5	for	for	ADP
ejpam-3338	527	6	=	=	PROPN
ejpam-3338	527	7	0(0.1)1	0(0.1)1	PROPN
ejpam-3338	527	8	,	,	PUNCT
ejpam-3338	527	9	h	h	NOUN
ejpam-3338	528	1	=	=	NOUN
ejpam-3338	528	2	0.1	0.1	NUM
ejpam-3338	528	3	definable	definable	ADJ
ejpam-3338	528	4	exactly	exactly	ADV
ejpam-3338	528	5	for	for	ADP
ejpam-3338	528	6	almost	almost	ADV
ejpam-3338	528	7	all	all	PRON
ejpam-3338	528	8	analytic	analytic	ADJ
ejpam-3338	528	9	functions	function	NOUN
ejpam-3338	528	10	without	without	ADP
ejpam-3338	528	11	any	any	DET
ejpam-3338	528	12	recourse	recourse	NOUN
ejpam-3338	528	13	to	to	ADP
ejpam-3338	528	14	integration	integration	NOUN
ejpam-3338	528	15	.	.	PUNCT
ejpam-3338	529	1	also	also	ADV
ejpam-3338	529	2	,	,	PUNCT
ejpam-3338	529	3	the	the	DET
ejpam-3338	529	4	restriction	restriction	NOUN
ejpam-3338	529	5	on	on	ADP
ejpam-3338	529	6	the	the	DET
ejpam-3338	529	7	fractional	fractional	ADJ
ejpam-3338	529	8	order	order	NOUN
ejpam-3338	529	9	α	α	PROPN
ejpam-3338	529	10	viz	viz	PROPN
ejpam-3338	529	11	.	.	PUNCT
ejpam-3338	530	1	(	(	PUNCT
ejpam-3338	530	2	n−1	n−1	INTJ
ejpam-3338	530	3	<	<	X
ejpam-3338	530	4	α	α	X
ejpam-3338	530	5	<	<	X
ejpam-3338	530	6	n	n	CCONJ
ejpam-3338	530	7	)	)	PUNCT
ejpam-3338	530	8	is	be	AUX
ejpam-3338	530	9	a	a	DET
ejpam-3338	530	10	severe	severe	ADJ
ejpam-3338	530	11	one	one	NUM
ejpam-3338	530	12	in	in	ADP
ejpam-3338	530	13	terms	term	NOUN
ejpam-3338	530	14	of	of	ADP
ejpam-3338	530	15	generalization	generalization	NOUN
ejpam-3338	530	16	.	.	PUNCT
ejpam-3338	531	1	the	the	DET
ejpam-3338	531	2	mathematical	mathematical	ADJ
ejpam-3338	531	3	integration	integration	NOUN
ejpam-3338	531	4	in	in	ADP
ejpam-3338	531	5	the	the	DET
ejpam-3338	531	6	equation	equation	NOUN
ejpam-3338	531	7	(	(	PUNCT
ejpam-3338	531	8	33	33	NUM
ejpam-3338	531	9	)	)	PUNCT
ejpam-3338	531	10	can	can	AUX
ejpam-3338	531	11	not	not	PART
ejpam-3338	531	12	be	be	AUX
ejpam-3338	531	13	obtained	obtain	VERB
ejpam-3338	531	14	in	in	ADP
ejpam-3338	531	15	a	a	DET
ejpam-3338	531	16	closed	closed	ADJ
ejpam-3338	531	17	form	form	NOUN
ejpam-3338	531	18	(	(	PUNCT
ejpam-3338	531	19	unlike	unlike	ADP
ejpam-3338	531	20	the	the	DET
ejpam-3338	531	21	fractional	fractional	ADJ
ejpam-3338	531	22	integration	integration	NOUN
ejpam-3338	531	23	of	of	ADP
ejpam-3338	531	24	functions	function	NOUN
ejpam-3338	531	25	such	such	ADJ
ejpam-3338	531	26	as	as	ADP
ejpam-3338	531	27	sin(x	sin(x	PROPN
ejpam-3338	531	28	)	)	PUNCT
ejpam-3338	531	29	,	,	PUNCT
ejpam-3338	531	30	ex	ex	X
ejpam-3338	531	31	,	,	PUNCT
ejpam-3338	531	32	xk	xk	PROPN
ejpam-3338	531	33	)	)	PUNCT
ejpam-3338	531	34	for	for	ADP
ejpam-3338	531	35	most	most	ADJ
ejpam-3338	531	36	functions	function	NOUN
ejpam-3338	531	37	,	,	PUNCT
ejpam-3338	531	38	a	a	DET
ejpam-3338	531	39	numerical	numerical	ADJ
ejpam-3338	531	40	integration	integration	NOUN
ejpam-3338	531	41	is	be	AUX
ejpam-3338	531	42	always	always	ADV
ejpam-3338	531	43	possible	possible	ADJ
ejpam-3338	531	44	for	for	ADP
ejpam-3338	531	45	all	all	DET
ejpam-3338	531	46	computable	computable	ADJ
ejpam-3338	531	47	mathematical	mathematical	ADJ
ejpam-3338	531	48	analytical	analytical	ADJ
ejpam-3338	531	49	functions	function	NOUN
ejpam-3338	531	50	though	though	ADV
ejpam-3338	531	51	.	.	PUNCT
ejpam-3338	532	1	however	however	ADV
ejpam-3338	532	2	,	,	PUNCT
ejpam-3338	532	3	we	we	PRON
ejpam-3338	532	4	simply	simply	ADV
ejpam-3338	532	5	have	have	VERB
ejpam-3338	532	6	to	to	PART
ejpam-3338	532	7	resort	resort	VERB
ejpam-3338	532	8	to	to	ADP
ejpam-3338	532	9	mathematical	mathematical	ADJ
ejpam-3338	532	10	/	/	SYM
ejpam-3338	532	11	numerical	numerical	ADJ
ejpam-3338	532	12	differentiation	differentiation	NOUN
ejpam-3338	532	13	only	only	ADV
ejpam-3338	532	14	for	for	ADP
ejpam-3338	532	15	derivatives	derivative	NOUN
ejpam-3338	532	16	of	of	ADP
ejpam-3338	532	17	any	any	DET
ejpam-3338	532	18	integer	integer	NOUN
ejpam-3338	532	19	order	order	NOUN
ejpam-3338	532	20	without	without	ADP
ejpam-3338	532	21	any	any	DET
ejpam-3338	532	22	restriction	restriction	NOUN
ejpam-3338	532	23	on	on	ADP
ejpam-3338	532	24	the	the	DET
ejpam-3338	532	25	integer	integer	NOUN
ejpam-3338	532	26	order	order	NOUN
ejpam-3338	532	27	(	(	PUNCT
ejpam-3338	532	28	unlike	unlike	ADP
ejpam-3338	532	29	the	the	DET
ejpam-3338	532	30	fractional	fractional	ADJ
ejpam-3338	532	31	order	order	NOUN
ejpam-3338	532	32	α	α	NOUN
ejpam-3338	532	33	)	)	PUNCT
ejpam-3338	532	34	.	.	PUNCT
ejpam-3338	533	1	computational	computational	ADJ
ejpam-3338	533	2	error	error	NOUN
ejpam-3338	533	3	and	and	CCONJ
ejpam-3338	533	4	computational	computational	ADJ
ejpam-3338	533	5	complexity	complexity	NOUN
ejpam-3338	533	6	in	in	ADP
ejpam-3338	533	7	such	such	ADJ
ejpam-3338	533	8	definitions	definition	NOUN
ejpam-3338	533	9	of	of	ADP
ejpam-3338	533	10	fractional	fractional	ADJ
ejpam-3338	533	11	derivatives	derivative	NOUN
ejpam-3338	533	12	are	be	AUX
ejpam-3338	533	13	usually	usually	ADV
ejpam-3338	533	14	more	more	ADV
ejpam-3338	533	15	dominant	dominant	ADJ
ejpam-3338	533	16	and	and	CCONJ
ejpam-3338	533	17	involved	involved	ADJ
ejpam-3338	533	18	than	than	ADP
ejpam-3338	533	19	those	those	PRON
ejpam-3338	533	20	for	for	ADP
ejpam-3338	533	21	integer	integer	NOUN
ejpam-3338	533	22	order	order	NOUN
ejpam-3338	533	23	derivatives	derivative	NOUN
ejpam-3338	533	24	.	.	PUNCT
ejpam-3338	534	1	can	can	AUX
ejpam-3338	534	2	we	we	PRON
ejpam-3338	534	3	devise	devise	VERB
ejpam-3338	534	4	/	/	PUNCT
ejpam-3338	534	5	innovate	innovate	VERB
ejpam-3338	534	6	a	a	DET
ejpam-3338	534	7	simple	simple	ADJ
ejpam-3338	534	8	procedure	procedure	NOUN
ejpam-3338	534	9	(	(	PUNCT
ejpam-3338	534	10	numerical	numerical	ADJ
ejpam-3338	534	11	or	or	CCONJ
ejpam-3338	534	12	otherwise	otherwise	ADV
ejpam-3338	534	13	)	)	PUNCT
ejpam-3338	534	14	that	that	PRON
ejpam-3338	534	15	will	will	AUX
ejpam-3338	534	16	obviate	obviate	VERB
ejpam-3338	534	17	these	these	DET
ejpam-3338	534	18	problems	problem	NOUN
ejpam-3338	534	19	in	in	ADP
ejpam-3338	534	20	the	the	DET
ejpam-3338	534	21	process	process	NOUN
ejpam-3338	534	22	of	of	ADP
ejpam-3338	534	23	achieving	achieve	VERB
ejpam-3338	534	24	rather	rather	ADV
ejpam-3338	534	25	a	a	DET
ejpam-3338	534	26	straight	straight	ADJ
ejpam-3338	534	27	-	-	PUNCT
ejpam-3338	534	28	forward	forward	NOUN
ejpam-3338	534	29	generalization	generalization	NOUN
ejpam-3338	534	30	for	for	ADP
ejpam-3338	534	31	the	the	DET
ejpam-3338	534	32	derivative	derivative	NOUN
ejpam-3338	534	33	of	of	ADP
ejpam-3338	534	34	any	any	DET
ejpam-3338	534	35	fractional	fractional	ADJ
ejpam-3338	534	36	order	order	NOUN
ejpam-3338	534	37	?	?	PUNCT
ejpam-3338	535	1	there	there	PRON
ejpam-3338	535	2	is	be	VERB
ejpam-3338	535	3	a	a	DET
ejpam-3338	535	4	scope	scope	NOUN
ejpam-3338	535	5	to	to	PART
ejpam-3338	535	6	explore	explore	VERB
ejpam-3338	535	7	this	this	DET
ejpam-3338	535	8	issue	issue	NOUN
ejpam-3338	535	9	and	and	CCONJ
ejpam-3338	535	10	come	come	VERB
ejpam-3338	535	11	out	out	ADP
ejpam-3338	535	12	either	either	CCONJ
ejpam-3338	535	13	defining	define	VERB
ejpam-3338	535	14	a	a	DET
ejpam-3338	535	15	straight	straight	ADJ
ejpam-3338	535	16	-	-	PUNCT
ejpam-3338	535	17	forward	forward	NOUN
ejpam-3338	535	18	generalization	generalization	NOUN
ejpam-3338	535	19	or	or	CCONJ
ejpam-3338	535	20	demonstrating	demonstrating	NOUN
ejpam-3338	535	21	/	/	SYM
ejpam-3338	535	22	proving	prove	VERB
ejpam-3338	535	23	that	that	SCONJ
ejpam-3338	535	24	such	such	DET
ejpam-3338	535	25	a	a	DET
ejpam-3338	535	26	generalization	generalization	NOUN
ejpam-3338	535	27	is	be	AUX
ejpam-3338	535	28	impossible	impossible	ADJ
ejpam-3338	535	29	.	.	PUNCT
ejpam-3338	536	1	we	we	PRON
ejpam-3338	536	2	leave	leave	VERB
ejpam-3338	536	3	the	the	DET
ejpam-3338	536	4	computational	computational	ADJ
ejpam-3338	536	5	exploration	exploration	NOUN
ejpam-3338	536	6	of	of	ADP
ejpam-3338	536	7	the	the	DET
ejpam-3338	536	8	rl	rl	PROPN
ejpam-3338	536	9	fractional	fractional	ADJ
ejpam-3338	536	10	derivative	derivative	ADJ
ejpam-3338	536	11	definition	definition	NOUN
ejpam-3338	536	12	for	for	ADP
ejpam-3338	536	13	the	the	DET
ejpam-3338	536	14	reader	reader	NOUN
ejpam-3338	536	15	so	so	SCONJ
ejpam-3338	536	16	that	that	SCONJ
ejpam-3338	536	17	he	he	PRON
ejpam-3338	536	18	could	could	AUX
ejpam-3338	536	19	find	find	VERB
ejpam-3338	536	20	out	out	ADP
ejpam-3338	536	21	the	the	DET
ejpam-3338	536	22	pros	pro	NOUN
ejpam-3338	536	23	and	and	CCONJ
ejpam-3338	536	24	cons	con	NOUN
ejpam-3338	536	25	of	of	ADP
ejpam-3338	536	26	this	this	DET
ejpam-3338	536	27	definition	definition	NOUN
ejpam-3338	536	28	compared	compare	VERB
ejpam-3338	536	29	with	with	ADP
ejpam-3338	536	30	s.	s.	PROPN
ejpam-3338	536	31	k.sen	k.sen	PROPN
ejpam-3338	536	32	,	,	PUNCT
ejpam-3338	536	33	j.	j.	PROPN
ejpam-3338	536	34	v.	v.	PROPN
ejpam-3338	536	35	devi	devi	PROPN
ejpam-3338	536	36	,	,	PUNCT
ejpam-3338	536	37	r.v.g	r.v.g	NOUN
ejpam-3338	536	38	.	.	PUNCT
ejpam-3338	537	1	r.	r.	PROPN
ejpam-3338	537	2	kumar	kumar	PROPN
ejpam-3338	537	3	/	/	SYM
ejpam-3338	537	4	eur	eur	PROPN
ejpam-3338	537	5	.	.	PUNCT
ejpam-3338	538	1	j.	j.	PROPN
ejpam-3338	538	2	pure	pure	PROPN
ejpam-3338	538	3	appl	appl	PROPN
ejpam-3338	538	4	.	.	PROPN
ejpam-3338	538	5	math	math	PROPN
ejpam-3338	538	6	,	,	PUNCT
ejpam-3338	538	7	11	11	NUM
ejpam-3338	538	8	(	(	PUNCT
ejpam-3338	538	9	3	3	NUM
ejpam-3338	538	10	)	)	PUNCT
ejpam-3338	538	11	(	(	PUNCT
ejpam-3338	538	12	2018	2018	NUM
ejpam-3338	538	13	)	)	PUNCT
ejpam-3338	538	14	,	,	PUNCT
ejpam-3338	538	15	1058	1058	NUM
ejpam-3338	538	16	-	-	SYM
ejpam-3338	538	17	1099	1099	NUM
ejpam-3338	538	18	1079	1079	NUM
ejpam-3338	538	19	those	those	PRON
ejpam-3338	538	20	of	of	ADP
ejpam-3338	538	21	grunwald	grunwald	NOUN
ejpam-3338	538	22	-	-	PUNCT
ejpam-3338	538	23	letnikov	letnikov	PROPN
ejpam-3338	538	24	and	and	CCONJ
ejpam-3338	538	25	caputo	caputo	PROPN
ejpam-3338	538	26	definitions	definition	NOUN
ejpam-3338	538	27	(	(	PUNCT
ejpam-3338	538	28	described	describe	VERB
ejpam-3338	538	29	below	below	ADP
ejpam-3338	538	30	)	)	PUNCT
ejpam-3338	538	31	.	.	PUNCT
ejpam-3338	539	1	caputo	caputo	PROPN
ejpam-3338	539	2	derivative	derivative	PROPN
ejpam-3338	539	3	the	the	DET
ejpam-3338	539	4	caputo	caputo	PROPN
ejpam-3338	539	5	derivative	derivative	NOUN
ejpam-3338	539	6	for	for	ADP
ejpam-3338	539	7	the	the	DET
ejpam-3338	539	8	general	general	ADJ
ejpam-3338	539	9	function	function	NOUN
ejpam-3338	539	10	f(t	f(t	PROPN
ejpam-3338	539	11	)	)	PUNCT
ejpam-3338	539	12	is	be	AUX
ejpam-3338	539	13	dα	dα	ADP
ejpam-3338	539	14	t	t	PROPN
ejpam-3338	539	15	f(t	f(t	PROPN
ejpam-3338	539	16	)	)	PUNCT
ejpam-3338	540	1	=	=	SYM
ejpam-3338	540	2	1	1	NUM
ejpam-3338	540	3	γ(n−	γ(n−	PROPN
ejpam-3338	540	4	α	α	NOUN
ejpam-3338	540	5	)	)	PUNCT
ejpam-3338	540	6	∫	∫	PROPN
ejpam-3338	540	7	t	t	PROPN
ejpam-3338	540	8	a	a	DET
ejpam-3338	540	9	fn(τ	fn(τ	NOUN
ejpam-3338	540	10	)	)	PUNCT
ejpam-3338	540	11	(	(	PUNCT
ejpam-3338	540	12	t−	t−	PROPN
ejpam-3338	540	13	τ)α−n+1	τ)α−n+1	PROPN
ejpam-3338	540	14	dτ	dτ	PROPN
ejpam-3338	540	15	,	,	PUNCT
ejpam-3338	540	16	(	(	PUNCT
ejpam-3338	540	17	n−	n−	NOUN
ejpam-3338	540	18	1	1	NUM
ejpam-3338	540	19	<	<	X
ejpam-3338	540	20	α	α	X
ejpam-3338	540	21	<	<	X
ejpam-3338	540	22	n	n	CCONJ
ejpam-3338	540	23	)	)	PUNCT
ejpam-3338	540	24	(	(	PUNCT
ejpam-3338	540	25	34	34	NUM
ejpam-3338	540	26	)	)	PUNCT
ejpam-3338	540	27	the	the	DET
ejpam-3338	540	28	foregoing	forego	VERB
ejpam-3338	540	29	comments	comment	NOUN
ejpam-3338	540	30	and	and	CCONJ
ejpam-3338	540	31	question	question	NOUN
ejpam-3338	540	32	are	be	AUX
ejpam-3338	540	33	more	more	ADV
ejpam-3338	540	34	or	or	CCONJ
ejpam-3338	540	35	less	less	ADV
ejpam-3338	540	36	valid	valid	ADJ
ejpam-3338	540	37	here	here	ADV
ejpam-3338	540	38	too	too	ADV
ejpam-3338	540	39	.	.	PUNCT
ejpam-3338	541	1	to	to	PART
ejpam-3338	541	2	illustrate	illustrate	VERB
ejpam-3338	541	3	mainly	mainly	ADV
ejpam-3338	541	4	the	the	DET
ejpam-3338	541	5	numerical	numerical	ADJ
ejpam-3338	541	6	computation	computation	NOUN
ejpam-3338	541	7	of	of	ADP
ejpam-3338	541	8	the	the	DET
ejpam-3338	541	9	integration	integration	NOUN
ejpam-3338	541	10	in	in	ADP
ejpam-3338	541	11	equation	equation	NOUN
ejpam-3338	541	12	(	(	PUNCT
ejpam-3338	541	13	34	34	NUM
ejpam-3338	541	14	)	)	PUNCT
ejpam-3338	541	15	,	,	PUNCT
ejpam-3338	541	16	we	we	PRON
ejpam-3338	541	17	consider	consider	VERB
ejpam-3338	541	18	the	the	DET
ejpam-3338	541	19	data	datum	NOUN
ejpam-3338	541	20	n	n	NOUN
ejpam-3338	541	21	=	=	SYM
ejpam-3338	541	22	1	1	NUM
ejpam-3338	541	23	,	,	PUNCT
ejpam-3338	541	24	f(t	f(t	PROPN
ejpam-3338	541	25	)	)	PUNCT
ejpam-3338	542	1	=	=	SYM
ejpam-3338	542	2	sin(t	sin(t	PROPN
ejpam-3338	542	3	)	)	PUNCT
ejpam-3338	542	4	,	,	PUNCT
ejpam-3338	542	5	α	α	X
ejpam-3338	542	6	=	=	SYM
ejpam-3338	542	7	.99	.99	PROPN
ejpam-3338	542	8	,	,	PUNCT
ejpam-3338	542	9	a	a	DET
ejpam-3338	542	10	=	=	SYM
ejpam-3338	542	11	0	0	NUM
ejpam-3338	542	12	,	,	PUNCT
ejpam-3338	542	13	t	t	NOUN
ejpam-3338	543	1	=	=	SYM
ejpam-3338	543	2	π	π	X
ejpam-3338	543	3	.	.	PUNCT
ejpam-3338	544	1	the	the	DET
ejpam-3338	544	2	caputo	caputo	PROPN
ejpam-3338	544	3	fractional	fractional	PROPN
ejpam-3338	544	4	derivative	derivative	NOUN
ejpam-3338	544	5	of	of	ADP
ejpam-3338	544	6	sin(t	sin(t	PROPN
ejpam-3338	544	7	)	)	PUNCT
ejpam-3338	544	8	can	can	AUX
ejpam-3338	544	9	be	be	AUX
ejpam-3338	544	10	written	write	VERB
ejpam-3338	544	11	as	as	ADP
ejpam-3338	544	12	dα	dα	PROPN
ejpam-3338	544	13	t	t	PROPN
ejpam-3338	544	14	sin(t	sin(t	PROPN
ejpam-3338	544	15	)	)	PUNCT
ejpam-3338	544	16	=	=	SYM
ejpam-3338	545	1	1	1	NUM
ejpam-3338	545	2	γ(1−	γ(1−	NOUN
ejpam-3338	545	3	α	α	NUM
ejpam-3338	545	4	)	)	PUNCT
ejpam-3338	545	5	∫	∫	PROPN
ejpam-3338	545	6	t	t	PROPN
ejpam-3338	545	7	a	a	DET
ejpam-3338	545	8	cos(τ	cos(τ	PROPN
ejpam-3338	545	9	)	)	PUNCT
ejpam-3338	545	10	(	(	PUNCT
ejpam-3338	545	11	t−	t−	PROPN
ejpam-3338	545	12	τ)α	τ)α	PUNCT
ejpam-3338	545	13	dτ	dτ	PROPN
ejpam-3338	545	14	,	,	PUNCT
ejpam-3338	545	15	(	(	PUNCT
ejpam-3338	545	16	0	0	X
ejpam-3338	545	17	<	<	X
ejpam-3338	545	18	α	α	X
ejpam-3338	545	19	<	<	X
ejpam-3338	545	20	1	1	NUM
ejpam-3338	545	21	)	)	PUNCT
ejpam-3338	545	22	=	=	SYM
ejpam-3338	545	23	1	1	NUM
ejpam-3338	545	24	γ(0.01	γ(0.01	ADJ
ejpam-3338	545	25	)	)	PUNCT
ejpam-3338	545	26	∫	∫	PROPN
ejpam-3338	546	1	π	π	NOUN
ejpam-3338	546	2	0	0	PUNCT
ejpam-3338	546	3	cos(τ	cos(τ	PROPN
ejpam-3338	546	4	)	)	PUNCT
ejpam-3338	546	5	(	(	PUNCT
ejpam-3338	546	6	t−	t−	PROPN
ejpam-3338	546	7	τ)0.99	τ)0.99	SYM
ejpam-3338	546	8	dτ	dτ	PROPN
ejpam-3338	546	9	.	.	PUNCT
ejpam-3338	547	1	the	the	DET
ejpam-3338	547	2	following	follow	VERB
ejpam-3338	547	3	5	5	NUM
ejpam-3338	547	4	-	-	PUNCT
ejpam-3338	547	5	line	line	NOUN
ejpam-3338	547	6	matlab	matlab	PROPN
ejpam-3338	547	7	program	program	NOUN
ejpam-3338	547	8	is	be	AUX
ejpam-3338	547	9	named	name	VERB
ejpam-3338	547	10	caputo	caputo	PROPN
ejpam-3338	547	11	alp	alp	PROPN
ejpam-3338	547	12	sin.m	sin.m	PROPN
ejpam-3338	547	13	clear	clear	ADJ
ejpam-3338	547	14	all	all	ADV
ejpam-3338	547	15	;	;	PUNCT
ejpam-3338	547	16	close	close	ADV
ejpam-3338	547	17	all	all	PRON
ejpam-3338	547	18	;	;	PUNCT
ejpam-3338	547	19	global	global	ADJ
ejpam-3338	547	20	alp	alp	PROPN
ejpam-3338	547	21	bet	bet	PROPN
ejpam-3338	547	22	;	;	PUNCT
ejpam-3338	547	23	alp=0:.01:1	alp=0:.01:1	PROPN
ejpam-3338	547	24	;	;	PUNCT
ejpam-3338	547	25	for	for	ADP
ejpam-3338	547	26	i=1:101	i=1:101	PROPN
ejpam-3338	547	27	,	,	PUNCT
ejpam-3338	547	28	bet	bet	NOUN
ejpam-3338	547	29	=	=	SYM
ejpam-3338	547	30	alp(i	alp(i	PROPN
ejpam-3338	547	31	)	)	PUNCT
ejpam-3338	547	32	;	;	PUNCT
ejpam-3338	547	33	q(i)=quadgk(@caputo	q(i)=quadgk(@caputo	NOUN
ejpam-3338	547	34	sind	sind	NOUN
ejpam-3338	547	35	,	,	PUNCT
ejpam-3338	547	36	0	0	NUM
ejpam-3338	547	37	,	,	PUNCT
ejpam-3338	547	38	pi)./gamma(1−	pi)./gamma(1−	ADJ
ejpam-3338	547	39	bet	bet	NOUN
ejpam-3338	547	40	)	)	PUNCT
ejpam-3338	547	41	;	;	PUNCT
ejpam-3338	547	42	end	end	NOUN
ejpam-3338	547	43	;	;	PUNCT
ejpam-3338	547	44	disp	disp	X
ejpam-3338	547	45	(	(	PUNCT
ejpam-3338	547	46	’	'	PUNCT
ejpam-3338	547	47	alpha	alpha	NOUN
ejpam-3338	547	48	derivative	derivative	NOUN
ejpam-3338	547	49	’	'	PUNCT
ejpam-3338	547	50	)	)	PUNCT
ejpam-3338	547	51	;	;	PUNCT
ejpam-3338	547	52	disp([alp	disp([alp	PROPN
ejpam-3338	547	53	’	'	PUNCT
ejpam-3338	547	54	’	'	PUNCT
ejpam-3338	547	55	q	q	ADJ
ejpam-3338	547	56	’	'	PUNCT
ejpam-3338	547	57	]	]	PUNCT
ejpam-3338	547	58	)	)	PUNCT
ejpam-3338	547	59	;	;	PUNCT
ejpam-3338	547	60	plot(alp	plot(alp	NOUN
ejpam-3338	547	61	,	,	PUNCT
ejpam-3338	547	62	q	q	NOUN
ejpam-3338	547	63	)	)	PUNCT
ejpam-3338	547	64	;	;	PUNCT
ejpam-3338	547	65	%	%	X
ejpam-3338	547	66	usage	usage	NOUN
ejpam-3338	547	67	%	%	NOUN
ejpam-3338	547	68	>	>	PUNCT
ejpam-3338	547	69	>	>	X
ejpam-3338	547	70	caputo	caputo	PROPN
ejpam-3338	547	71	alp	alp	PROPN
ejpam-3338	547	72	sin	sin	PROPN
ejpam-3338	547	73	%	%	PROPN
ejpam-3338	547	74	uses	use	VERB
ejpam-3338	547	75	function	function	PROPN
ejpam-3338	547	76	caputo	caputo	PROPN
ejpam-3338	547	77	sind	sind	NOUN
ejpam-3338	547	78	;	;	PUNCT
ejpam-3338	547	79	computes	compute	VERB
ejpam-3338	547	80	fractional	fractional	ADJ
ejpam-3338	547	81	derivatives	derivative	NOUN
ejpam-3338	547	82	of	of	ADP
ejpam-3338	547	83	sin(pi	sin(pi	NOUN
ejpam-3338	547	84	)	)	PUNCT
ejpam-3338	548	1	%	%	NOUN
ejpam-3338	548	2	accuracy	accuracy	NOUN
ejpam-3338	548	3	diminishes	diminish	VERB
ejpam-3338	548	4	.	.	PUNCT
ejpam-3338	549	1	function	function	VERB
ejpam-3338	549	2	y	y	PROPN
ejpam-3338	549	3	=	=	PROPN
ejpam-3338	549	4	caputo	caputo	PROPN
ejpam-3338	549	5	sind(x	sind(x	PROPN
ejpam-3338	549	6	)	)	PUNCT
ejpam-3338	549	7	%	%	NOUN
ejpam-3338	549	8	fractional	fractional	ADJ
ejpam-3338	549	9	(	(	PUNCT
ejpam-3338	549	10	0	0	NUM
ejpam-3338	549	11	≤	≤	NUM
ejpam-3338	549	12	alp	alp	NOUN
ejpam-3338	549	13	≤	≤	NUM
ejpam-3338	549	14	1	1	NUM
ejpam-3338	549	15	)	)	PUNCT
ejpam-3338	549	16	derivative	derivative	NOUN
ejpam-3338	549	17	of	of	ADP
ejpam-3338	549	18	sin	sin	NOUN
ejpam-3338	549	19	(	(	PUNCT
ejpam-3338	549	20	pi	pi	NOUN
ejpam-3338	549	21	)	)	PUNCT
ejpam-3338	549	22	global	global	PROPN
ejpam-3338	549	23	alp	alp	PROPN
ejpam-3338	549	24	bet	bet	PROPN
ejpam-3338	549	25	;	;	PUNCT
ejpam-3338	550	1	%	%	X
ejpam-3338	550	2	alp=0:01:.9	alp=0:01:.9	ADV
ejpam-3338	550	3	,	,	PUNCT
ejpam-3338	550	4	bet	bet	NOUN
ejpam-3338	550	5	=	=	SYM
ejpam-3338	550	6	alp(i	alp(i	PROPN
ejpam-3338	550	7	)	)	PUNCT
ejpam-3338	550	8	;	;	PUNCT
ejpam-3338	551	1	y	y	PROPN
ejpam-3338	551	2	=	=	SYM
ejpam-3338	551	3	cos(x)./(pi	cos(x)./(pi	NOUN
ejpam-3338	551	4	-	-	ADJ
ejpam-3338	551	5	x	x	NOUN
ejpam-3338	551	6	)	)	PUNCT
ejpam-3338	551	7	.	.	PUNCT
ejpam-3338	552	1	̂bet	̂bet	PROPN
ejpam-3338	552	2	;	;	PUNCT
ejpam-3338	552	3	%	%	INTJ
ejpam-3338	552	4	(	(	PUNCT
ejpam-3338	552	5	0	0	NUM
ejpam-3338	552	6	<	<	X
ejpam-3338	552	7	=	=	X
ejpam-3338	552	8	alp	alp	NOUN
ejpam-3338	552	9	<	<	X
ejpam-3338	552	10	=	=	NOUN
ejpam-3338	552	11	1	1	NUM
ejpam-3338	552	12	)	)	PUNCT
ejpam-3338	552	13	the	the	DET
ejpam-3338	552	14	results	result	NOUN
ejpam-3338	552	15	(	(	PUNCT
ejpam-3338	552	16	retaining	retain	VERB
ejpam-3338	552	17	only	only	ADV
ejpam-3338	552	18	partially	partially	ADV
ejpam-3338	552	19	to	to	PART
ejpam-3338	552	20	conserve	conserve	VERB
ejpam-3338	552	21	space	space	NOUN
ejpam-3338	552	22	)	)	PUNCT
ejpam-3338	552	23	are	be	AUX
ejpam-3338	552	24	as	as	SCONJ
ejpam-3338	552	25	follows	follow	VERB
ejpam-3338	552	26	.	.	PUNCT
ejpam-3338	553	1	alpha	alpha	NOUN
ejpam-3338	553	2	derivative	derivative	ADJ
ejpam-3338	553	3	0	0	NUM
ejpam-3338	553	4	0.0000	0.0000	NUM
ejpam-3338	553	5	(	(	PUNCT
ejpam-3338	553	6	omit	omit	VERB
ejpam-3338	553	7	this	this	DET
ejpam-3338	553	8	row	row	NOUN
ejpam-3338	553	9	)	)	PUNCT
ejpam-3338	554	1	0.0100	0.0100	NUM
ejpam-3338	554	2	-0.0185	-0.0185	NOUN
ejpam-3338	554	3	0.0200	0.0200	NUM
ejpam-3338	554	4	-0.0368	-0.0368	NOUN
ejpam-3338	554	5	0.0300	0.0300	NUM
ejpam-3338	554	6	-0.0551	-0.0551	NOUN
ejpam-3338	554	7	0.0400	0.0400	NUM
ejpam-3338	554	8	-0.0732	-0.0732	NOUN
ejpam-3338	554	9	.	.	PUNCT
ejpam-3338	554	10	.	.	PUNCT
ejpam-3338	555	1	.	.	PUNCT
ejpam-3338	556	1	0.9600	0.9600	NUM
ejpam-3338	556	2	-0.7603	-0.7603	PROPN
ejpam-3338	556	3	s.	s.	PROPN
ejpam-3338	556	4	k.sen	k.sen	PROPN
ejpam-3338	556	5	,	,	PUNCT
ejpam-3338	556	6	j.	j.	PROPN
ejpam-3338	556	7	v.	v.	PROPN
ejpam-3338	556	8	devi	devi	PROPN
ejpam-3338	556	9	,	,	PUNCT
ejpam-3338	556	10	r.v.g	r.v.g	NOUN
ejpam-3338	556	11	.	.	PUNCT
ejpam-3338	557	1	r.	r.	PROPN
ejpam-3338	557	2	kumar	kumar	PROPN
ejpam-3338	557	3	/	/	SYM
ejpam-3338	557	4	eur	eur	PROPN
ejpam-3338	557	5	.	.	PUNCT
ejpam-3338	558	1	j.	j.	PROPN
ejpam-3338	558	2	pure	pure	PROPN
ejpam-3338	558	3	appl	appl	PROPN
ejpam-3338	558	4	.	.	PROPN
ejpam-3338	558	5	math	math	PROPN
ejpam-3338	558	6	,	,	PUNCT
ejpam-3338	558	7	11	11	NUM
ejpam-3338	558	8	(	(	PUNCT
ejpam-3338	558	9	3	3	NUM
ejpam-3338	558	10	)	)	PUNCT
ejpam-3338	558	11	(	(	PUNCT
ejpam-3338	558	12	2018	2018	NUM
ejpam-3338	558	13	)	)	PUNCT
ejpam-3338	558	14	,	,	PUNCT
ejpam-3338	558	15	1058	1058	NUM
ejpam-3338	558	16	-	-	SYM
ejpam-3338	558	17	1099	1099	NUM
ejpam-3338	558	18	1080	1080	NUM
ejpam-3338	558	19	fig	fig	NOUN
ejpam-3338	558	20	.	.	PUNCT
ejpam-3338	559	1	3	3	NUM
ejpam-3338	559	2	fractional	fractional	ADJ
ejpam-3338	559	3	order	order	NOUN
ejpam-3338	559	4	α	α	NOUN
ejpam-3338	559	5	=	=	SYM
ejpam-3338	559	6	0(.01)1	0(.01)1	NUM
ejpam-3338	559	7	versus	versus	ADP
ejpam-3338	559	8	the	the	DET
ejpam-3338	559	9	caputo	caputo	PROPN
ejpam-3338	559	10	derivative	derivative	NOUN
ejpam-3338	559	11	of	of	ADP
ejpam-3338	559	12	sin(π	sin(π	PROPN
ejpam-3338	559	13	)	)	PUNCT
ejpam-3338	559	14	0.9700	0.9700	NUM
ejpam-3338	559	15	-0.6569	-0.6569	NOUN
ejpam-3338	559	16	0.9800	0.9800	NUM
ejpam-3338	559	17	-0.5094	-0.5094	NOUN
ejpam-3338	559	18	0.9900	0.9900	NUM
ejpam-3338	559	19	-0.2992	-0.2992	NOUN
ejpam-3338	559	20	1.0000	1.0000	NUM
ejpam-3338	559	21	0	0	NUM
ejpam-3338	559	22	the	the	DET
ejpam-3338	559	23	graph	graph	NOUN
ejpam-3338	559	24	(	(	PUNCT
ejpam-3338	559	25	fractional	fractional	ADJ
ejpam-3338	559	26	order	order	NOUN
ejpam-3338	559	27	α	α	NOUN
ejpam-3338	559	28	=	=	SYM
ejpam-3338	559	29	0(.01)1	0(.01)1	NUM
ejpam-3338	559	30	versus	versus	ADP
ejpam-3338	559	31	the	the	DET
ejpam-3338	559	32	derivative	derivative	NOUN
ejpam-3338	559	33	of	of	ADP
ejpam-3338	559	34	sin(π	sin(π	PROPN
ejpam-3338	559	35	)	)	PUNCT
ejpam-3338	559	36	is	be	AUX
ejpam-3338	559	37	as	as	ADP
ejpam-3338	559	38	in	in	ADP
ejpam-3338	559	39	(	(	PUNCT
ejpam-3338	559	40	fig	fig	NOUN
ejpam-3338	559	41	.	.	PUNCT
ejpam-3338	560	1	3	3	NUM
ejpam-3338	560	2	)	)	PUNCT
ejpam-3338	560	3	.	.	PUNCT
ejpam-3338	561	1	it	it	PRON
ejpam-3338	561	2	can	can	AUX
ejpam-3338	561	3	be	be	AUX
ejpam-3338	561	4	seen	see	VERB
ejpam-3338	561	5	both	both	CCONJ
ejpam-3338	561	6	from	from	ADP
ejpam-3338	561	7	the	the	DET
ejpam-3338	561	8	numerical	numerical	ADJ
ejpam-3338	561	9	results	result	NOUN
ejpam-3338	561	10	as	as	ADV
ejpam-3338	561	11	well	well	ADV
ejpam-3338	561	12	as	as	ADP
ejpam-3338	561	13	from	from	ADP
ejpam-3338	561	14	the	the	DET
ejpam-3338	561	15	graph	graph	NOUN
ejpam-3338	561	16	that	that	PRON
ejpam-3338	561	17	the	the	DET
ejpam-3338	561	18	computational	computational	ADJ
ejpam-3338	561	19	error	error	NOUN
ejpam-3338	561	20	is	be	AUX
ejpam-3338	561	21	considerable	considerable	ADJ
ejpam-3338	561	22	.	.	PUNCT
ejpam-3338	562	1	for	for	ADP
ejpam-3338	562	2	α	α	NOUN
ejpam-3338	562	3	close	close	ADV
ejpam-3338	562	4	to	to	ADP
ejpam-3338	562	5	0.9	0.9	NUM
ejpam-3338	562	6	the	the	DET
ejpam-3338	562	7	derivative	derivative	NOUN
ejpam-3338	562	8	of	of	ADP
ejpam-3338	562	9	sin(π	sin(π	PROPN
ejpam-3338	562	10	)	)	PUNCT
ejpam-3338	562	11	is	be	AUX
ejpam-3338	562	12	close	close	ADJ
ejpam-3338	562	13	to	to	PART
ejpam-3338	562	14	-1	-1	VERB
ejpam-3338	562	15	while	while	SCONJ
ejpam-3338	562	16	the	the	DET
ejpam-3338	562	17	derivative	derivative	NOUN
ejpam-3338	562	18	should	should	AUX
ejpam-3338	562	19	be	be	AUX
ejpam-3338	562	20	-1	-1	PUNCT
ejpam-3338	562	21	for	for	ADP
ejpam-3338	562	22	α	α	NOUN
ejpam-3338	562	23	=	=	SYM
ejpam-3338	562	24	1	1	NUM
ejpam-3338	562	25	,	,	PUNCT
ejpam-3338	562	26	however	however	ADV
ejpam-3338	562	27	,	,	PUNCT
ejpam-3338	562	28	a	a	DET
ejpam-3338	562	29	better	well	ADJ
ejpam-3338	562	30	programming	programming	NOUN
ejpam-3338	562	31	skill	skill	NOUN
ejpam-3338	562	32	along	along	ADP
ejpam-3338	562	33	with	with	ADP
ejpam-3338	562	34	an	an	DET
ejpam-3338	562	35	increased	increase	VERB
ejpam-3338	562	36	precision	precision	NOUN
ejpam-3338	562	37	would	would	AUX
ejpam-3338	562	38	produce	produce	VERB
ejpam-3338	562	39	better	well	ADJ
ejpam-3338	562	40	accuracy	accuracy	NOUN
ejpam-3338	562	41	.	.	PUNCT
ejpam-3338	563	1	consider	consider	VERB
ejpam-3338	563	2	the	the	DET
ejpam-3338	563	3	caputo	caputo	PROPN
ejpam-3338	563	4	fractional	fractional	PROPN
ejpam-3338	563	5	derivative	derivative	NOUN
ejpam-3338	563	6	of	of	ADP
ejpam-3338	563	7	sin(pi/2	sin(pi/2	NOUN
ejpam-3338	563	8	)	)	PUNCT
ejpam-3338	563	9	where	where	SCONJ
ejpam-3338	563	10	the	the	DET
ejpam-3338	563	11	fractional	fractional	ADJ
ejpam-3338	563	12	order	order	NOUN
ejpam-3338	563	13	=	=	NOUN
ejpam-3338	563	14	.5,.9	.5,.9	ADJ
ejpam-3338	563	15	,	,	PUNCT
ejpam-3338	563	16	.99,.999,.9999,.99999	.99,.999,.9999,.99999	PROPN
ejpam-3338	563	17	.	.	PUNCT
ejpam-3338	564	1	the	the	DET
ejpam-3338	564	2	matlab	matlab	PROPN
ejpam-3338	564	3	program	program	NOUN
ejpam-3338	564	4	is	be	AUX
ejpam-3338	564	5	function	function	NOUN
ejpam-3338	564	6	y	y	PROPN
ejpam-3338	564	7	=	=	PROPN
ejpam-3338	564	8	caputo	caputo	PROPN
ejpam-3338	564	9	sin(x	sin(x	PROPN
ejpam-3338	564	10	)	)	PUNCT
ejpam-3338	564	11	%	%	NOUN
ejpam-3338	564	12	fractional	fractional	ADJ
ejpam-3338	564	13	(	(	PUNCT
ejpam-3338	564	14	0	0	NUM
ejpam-3338	564	15	≤	≤	NUM
ejpam-3338	564	16	alp	alp	NOUN
ejpam-3338	564	17	≤	≤	NUM
ejpam-3338	564	18	1	1	NUM
ejpam-3338	564	19	)	)	PUNCT
ejpam-3338	564	20	derivative	derivative	NOUN
ejpam-3338	564	21	of	of	ADP
ejpam-3338	564	22	sin	sin	NOUN
ejpam-3338	564	23	(	(	PUNCT
ejpam-3338	564	24	pi	pi	NOUN
ejpam-3338	564	25	)	)	PUNCT
ejpam-3338	564	26	global	global	PROPN
ejpam-3338	564	27	alp	alp	PROPN
ejpam-3338	564	28	bet	bet	PROPN
ejpam-3338	564	29	;	;	PUNCT
ejpam-3338	564	30	%	%	PRON
ejpam-3338	564	31	alp=.999	alp=.999	NOUN
ejpam-3338	564	32	;	;	PUNCT
ejpam-3338	564	33	bet	bet	PROPN
ejpam-3338	564	34	=	=	PROPN
ejpam-3338	564	35	alp	alp	PROPN
ejpam-3338	564	36	;	;	PUNCT
ejpam-3338	564	37	s.	s.	PROPN
ejpam-3338	564	38	k.sen	k.sen	PROPN
ejpam-3338	564	39	,	,	PUNCT
ejpam-3338	564	40	j.	j.	PROPN
ejpam-3338	564	41	v.	v.	PROPN
ejpam-3338	564	42	devi	devi	PROPN
ejpam-3338	564	43	,	,	PUNCT
ejpam-3338	564	44	r.v.g	r.v.g	NOUN
ejpam-3338	564	45	.	.	PUNCT
ejpam-3338	565	1	r.	r.	PROPN
ejpam-3338	565	2	kumar	kumar	PROPN
ejpam-3338	565	3	/	/	SYM
ejpam-3338	565	4	eur	eur	PROPN
ejpam-3338	565	5	.	.	PUNCT
ejpam-3338	566	1	j.	j.	PROPN
ejpam-3338	566	2	pure	pure	PROPN
ejpam-3338	566	3	appl	appl	PROPN
ejpam-3338	566	4	.	.	PROPN
ejpam-3338	566	5	math	math	PROPN
ejpam-3338	566	6	,	,	PUNCT
ejpam-3338	566	7	11	11	NUM
ejpam-3338	566	8	(	(	PUNCT
ejpam-3338	566	9	3	3	NUM
ejpam-3338	566	10	)	)	PUNCT
ejpam-3338	566	11	(	(	PUNCT
ejpam-3338	566	12	2018	2018	NUM
ejpam-3338	566	13	)	)	PUNCT
ejpam-3338	566	14	,	,	PUNCT
ejpam-3338	566	15	1058	1058	NUM
ejpam-3338	566	16	-	-	SYM
ejpam-3338	566	17	1099	1099	NUM
ejpam-3338	566	18	1081	1081	NUM
ejpam-3338	566	19	y	y	SYM
ejpam-3338	566	20	=	=	ADJ
ejpam-3338	566	21	cos(x)./(pi	cos(x)./(pi	NOUN
ejpam-3338	566	22	-	-	ADJ
ejpam-3338	566	23	x).̂alp	x).̂alp	PROPN
ejpam-3338	566	24	;	;	PUNCT
ejpam-3338	566	25	%	%	INTJ
ejpam-3338	566	26	(	(	PUNCT
ejpam-3338	566	27	0	0	NUM
ejpam-3338	566	28	≤	≤	NUM
ejpam-3338	566	29	alp	alp	NOUN
ejpam-3338	566	30	≤	≤	NUM
ejpam-3338	566	31	1	1	NUM
ejpam-3338	566	32	)	)	PUNCT
ejpam-3338	566	33	%	%	NOUN
ejpam-3338	566	34	usage	usage	NOUN
ejpam-3338	566	35	for	for	ADP
ejpam-3338	566	36	caputo	caputo	PROPN
ejpam-3338	566	37	derivative	derivative	PROPN
ejpam-3338	566	38	(	(	PUNCT
ejpam-3338	566	39	0	0	NUM
ejpam-3338	566	40	<	<	X
ejpam-3338	566	41	alp	alp	X
ejpam-3338	566	42	<	<	X
ejpam-3338	566	43	1	1	NUM
ejpam-3338	566	44	)	)	PUNCT
ejpam-3338	566	45	%	%	NOUN
ejpam-3338	566	46	clear	clear	ADJ
ejpam-3338	566	47	all	all	PRON
ejpam-3338	566	48	;	;	PUNCT
ejpam-3338	566	49	close	close	ADV
ejpam-3338	566	50	all	all	PRON
ejpam-3338	566	51	;	;	PUNCT
ejpam-3338	566	52	format	format	NOUN
ejpam-3338	566	53	long	long	ADJ
ejpam-3338	566	54	g	g	NOUN
ejpam-3338	566	55	;	;	PUNCT
ejpam-3338	566	56	global	global	ADJ
ejpam-3338	566	57	alp	alp	PROPN
ejpam-3338	566	58	bet	bet	PROPN
ejpam-3338	566	59	;	;	PUNCT
ejpam-3338	566	60	%	%	PRON
ejpam-3338	566	61	alp=.999	alp=.999	NOUN
ejpam-3338	566	62	;	;	PUNCT
ejpam-3338	567	1	bet	bet	PROPN
ejpam-3338	567	2	=	=	NOUN
ejpam-3338	567	3	alp	alp	PROPN
ejpam-3338	567	4	;	;	PUNCT
ejpam-3338	567	5	q	q	X
ejpam-3338	567	6	=	=	NUM
ejpam-3338	567	7	quadgk(@caputo	quadgk(@caputo	NOUN
ejpam-3338	567	8	sin	sin	NOUN
ejpam-3338	567	9	,	,	PUNCT
ejpam-3338	567	10	0,pi/2)./gamma(1	0,pi/2)./gamma(1	NOUN
ejpam-3338	567	11	-	-	PUNCT
ejpam-3338	567	12	bet	bet	NOUN
ejpam-3338	567	13	)	)	PUNCT
ejpam-3338	567	14	;	;	PUNCT
ejpam-3338	567	15	%	%	INTJ
ejpam-3338	567	16	’	'	PUNCT
ejpam-3338	567	17	alp	alp	PROPN
ejpam-3338	567	18	alp	alp	PROPN
ejpam-3338	567	19	-	-	PUNCT
ejpam-3338	567	20	derivative	derivative	NOUN
ejpam-3338	567	21	of	of	ADP
ejpam-3338	567	22	sin(pi/2	sin(pi/2	NOUN
ejpam-3338	567	23	)	)	PUNCT
ejpam-3338	567	24	’	'	PUNCT
ejpam-3338	567	25	,	,	PUNCT
ejpam-3338	567	26	disp([bet	disp([bet	PROPN
ejpam-3338	567	27	q	q	X
ejpam-3338	567	28	]	]	X
ejpam-3338	567	29	)	)	PUNCT
ejpam-3338	567	30	%	%	INTJ
ejpam-3338	567	31	write	write	NOUN
ejpam-3338	567	32	foregoing	forego	VERB
ejpam-3338	567	33	3	3	NUM
ejpam-3338	567	34	lines	line	NOUN
ejpam-3338	567	35	in	in	ADP
ejpam-3338	567	36	1	1	NUM
ejpam-3338	567	37	line	line	NOUN
ejpam-3338	567	38	in	in	ADP
ejpam-3338	567	39	command	command	NOUN
ejpam-3338	567	40	window	window	NOUN
ejpam-3338	567	41	omitting	omitting	NOUN
ejpam-3338	567	42	%	%	NOUN
ejpam-3338	567	43	%	%	NOUN
ejpam-3338	567	44	and	and	CCONJ
ejpam-3338	567	45	replace	replace	VERB
ejpam-3338	567	46	”	"	PUNCT
ejpam-3338	567	47	alp=.999	alp=.999	NOUN
ejpam-3338	567	48	”	"	PUNCT
ejpam-3338	567	49	by	by	ADP
ejpam-3338	567	50	”	"	PUNCT
ejpam-3338	567	51	alp=.5	alp=.5	NOUN
ejpam-3338	567	52	”	"	PUNCT
ejpam-3338	567	53	when	when	SCONJ
ejpam-3338	567	54	we	we	PRON
ejpam-3338	567	55	wish	wish	VERB
ejpam-3338	567	56	to	to	PART
ejpam-3338	567	57	compute	compute	VERB
ejpam-3338	567	58	%	%	NOUN
ejpam-3338	567	59	the	the	DET
ejpam-3338	567	60	fractional	fractional	ADJ
ejpam-3338	567	61	derivative	derivative	NOUN
ejpam-3338	567	62	of	of	ADP
ejpam-3338	567	63	sin(pi/2	sin(pi/2	NOUN
ejpam-3338	567	64	)	)	PUNCT
ejpam-3338	567	65	at	at	ADP
ejpam-3338	567	66	alp=0.5	alp=0.5	X
ejpam-3338	567	67	.	.	PUNCT
ejpam-3338	568	1	%	%	INTJ
ejpam-3338	568	2	global	global	PROPN
ejpam-3338	568	3	alp	alp	PROPN
ejpam-3338	568	4	bet	bet	PROPN
ejpam-3338	568	5	;	;	PUNCT
ejpam-3338	568	6	alp=.99	alp=.99	NOUN
ejpam-3338	568	7	,	,	PUNCT
ejpam-3338	568	8	bet	bet	PROPN
ejpam-3338	568	9	=	=	NOUN
ejpam-3338	568	10	alp	alp	PROPN
ejpam-3338	568	11	;	;	PUNCT
ejpam-3338	568	12	q	q	X
ejpam-3338	568	13	=	=	NUM
ejpam-3338	568	14	quadgk	quadgk	NOUN
ejpam-3338	568	15	(	(	PUNCT
ejpam-3338	568	16	@	@	ADP
ejpam-3338	568	17	caputo	caputo	PROPN
ejpam-3338	568	18	sin	sin	PROPN
ejpam-3338	568	19	,	,	PUNCT
ejpam-3338	568	20	%	%	INTJ
ejpam-3338	568	21	0,pi/2)./gamma(1	0,pi/2)./gamma(1	NOUN
ejpam-3338	568	22	-	-	PUNCT
ejpam-3338	568	23	bet	bet	NOUN
ejpam-3338	568	24	)	)	PUNCT
ejpam-3338	568	25	;	;	PUNCT
ejpam-3338	568	26	disp([bet	disp([bet	PROPN
ejpam-3338	568	27	q	q	X
ejpam-3338	568	28	]	]	X
ejpam-3338	568	29	)	)	PUNCT
ejpam-3338	568	30	or	or	CCONJ
ejpam-3338	568	31	%	%	INTJ
ejpam-3338	568	32	>	>	X
ejpam-3338	568	33	>	>	X
ejpam-3338	568	34	clear	clear	PROPN
ejpam-3338	568	35	all	all	PRON
ejpam-3338	568	36	;	;	PUNCT
ejpam-3338	568	37	close	close	ADV
ejpam-3338	568	38	all	all	PRON
ejpam-3338	568	39	;	;	PUNCT
ejpam-3338	568	40	global	global	ADJ
ejpam-3338	568	41	alp	alp	PROPN
ejpam-3338	568	42	bet	bet	PROPN
ejpam-3338	568	43	;	;	PUNCT
ejpam-3338	568	44	alp=.99	alp=.99	NOUN
ejpam-3338	568	45	;	;	PUNCT
ejpam-3338	568	46	bet	bet	PROPN
ejpam-3338	568	47	=	=	NOUN
ejpam-3338	568	48	alp	alp	PROPN
ejpam-3338	568	49	;	;	PUNCT
ejpam-3338	568	50	%	%	NOUN
ejpam-3338	568	51	q	q	X
ejpam-3338	569	1	=	=	PRON
ejpam-3338	569	2	quadgk	quadgk	ADJ
ejpam-3338	569	3	(	(	PUNCT
ejpam-3338	569	4	@	@	ADP
ejpam-3338	569	5	caputo	caputo	PROPN
ejpam-3338	569	6	sin	sin	PROPN
ejpam-3338	569	7	,	,	PUNCT
ejpam-3338	569	8	0,pi/2)./gamma(1.-bet	0,pi/2)./gamma(1.-bet	PROPN
ejpam-3338	569	9	)	)	PUNCT
ejpam-3338	569	10	;	;	PUNCT
ejpam-3338	569	11	disp([bet	disp([bet	PROPN
ejpam-3338	569	12	q	q	X
ejpam-3338	569	13	]	]	X
ejpam-3338	569	14	)	)	PUNCT
ejpam-3338	569	15	%	%	NOUN
ejpam-3338	569	16	alp	alp	NOUN
ejpam-3338	570	1	=	=	NOUN
ejpam-3338	570	2	%	%	NOUN
ejpam-3338	570	3	0.9900	0.9900	NUM
ejpam-3338	570	4	%	%	NOUN
ejpam-3338	570	5	0.9900	0.9900	NUM
ejpam-3338	570	6	0.0040	0.0040	NUM
ejpam-3338	570	7	%	%	NOUN
ejpam-3338	570	8	caputo	caputo	PROPN
ejpam-3338	570	9	derivative	derivative	PROPN
ejpam-3338	570	10	viz	viz	PROPN
ejpam-3338	570	11	.	.	PUNCT
ejpam-3338	571	1	d̂alp(sin	d̂alp(sin	PROPN
ejpam-3338	571	2	x	x	X
ejpam-3338	571	3	)	)	PUNCT
ejpam-3338	571	4	for	for	ADP
ejpam-3338	571	5	x=	x=	PROPN
ejpam-3338	571	6	pi/2	pi/2	PROPN
ejpam-3338	571	7	is	be	AUX
ejpam-3338	571	8	.0040	.0040	NUM
ejpam-3338	571	9	%	%	NOUN
ejpam-3338	571	10	when	when	SCONJ
ejpam-3338	571	11	alp	alp	PROPN
ejpam-3338	571	12	=	=	PROPN
ejpam-3338	571	13	.99	.99	PROPN
ejpam-3338	571	14	and	and	CCONJ
ejpam-3338	571	15	3.9892e-004	3.9892e-004	PROPN
ejpam-3338	571	16	when	when	SCONJ
ejpam-3338	571	17	alp	alp	PROPN
ejpam-3338	571	18	=	=	PROPN
ejpam-3338	571	19	.999	.999	NUM
ejpam-3338	571	20	.	.	PUNCT
ejpam-3338	572	1	%	%	INTJ
ejpam-3338	573	1	quadgk	quadgk	NOUN
ejpam-3338	573	2	(	(	PUNCT
ejpam-3338	573	3	@	@	ADP
ejpam-3338	573	4	caputo	caputo	PROPN
ejpam-3338	573	5	sin	sin	PROPN
ejpam-3338	573	6	,	,	PUNCT
ejpam-3338	573	7	0	0	NUM
ejpam-3338	573	8	,	,	PUNCT
ejpam-3338	573	9	pi/2	pi/2	NOUN
ejpam-3338	573	10	)	)	PUNCT
ejpam-3338	574	1	when	when	SCONJ
ejpam-3338	574	2	alp=.99	alp=.99	NOUN
ejpam-3338	575	1	%	%	INTJ
ejpam-3338	575	2	x	x	X
ejpam-3338	575	3	should	should	AUX
ejpam-3338	575	4	not	not	PART
ejpam-3338	575	5	be	be	AUX
ejpam-3338	575	6	pi	pi	ADJ
ejpam-3338	575	7	because	because	SCONJ
ejpam-3338	575	8	of	of	ADP
ejpam-3338	575	9	division	division	NOUN
ejpam-3338	575	10	by	by	ADP
ejpam-3338	575	11	0	0	NUM
ejpam-3338	575	12	%	%	NOUN
ejpam-3338	575	13	and	and	CCONJ
ejpam-3338	575	14	also	also	ADV
ejpam-3338	575	15	it	it	PRON
ejpam-3338	575	16	exceeds	exceed	VERB
ejpam-3338	575	17	max	max	PROPN
ejpam-3338	575	18	no	no	PROPN
ejpam-3338	575	19	of	of	ADP
ejpam-3338	575	20	divns	divns	PROPN
ejpam-3338	575	21	.	.	PUNCT
ejpam-3338	576	1	permitted	permit	VERB
ejpam-3338	576	2	.	.	PUNCT
ejpam-3338	577	1	we	we	PRON
ejpam-3338	577	2	obtain	obtain	VERB
ejpam-3338	577	3	the	the	DET
ejpam-3338	577	4	following	follow	VERB
ejpam-3338	577	5	output	output	NOUN
ejpam-3338	577	6	for	for	ADP
ejpam-3338	577	7	the	the	DET
ejpam-3338	577	8	fractional	fractional	ADJ
ejpam-3338	577	9	derivative	derivative	NOUN
ejpam-3338	577	10	of	of	ADP
ejpam-3338	577	11	sin(pi/2	sin(pi/2	NOUN
ejpam-3338	577	12	)	)	PUNCT
ejpam-3338	577	13	at	at	ADP
ejpam-3338	577	14	the	the	DET
ejpam-3338	577	15	fractional	fractional	ADJ
ejpam-3338	577	16	order	order	NOUN
ejpam-3338	577	17	α=.5,.9,.99,.999	α=.5,.9,.99,.999	NOUN
ejpam-3338	577	18	..	..	PUNCT
ejpam-3338	577	19	9999,.99999	9999,.99999	NUM
ejpam-3338	577	20	α	α	NOUN
ejpam-3338	577	21	α	α	NOUN
ejpam-3338	577	22	order	order	NOUN
ejpam-3338	577	23	derivative	derivative	NOUN
ejpam-3338	577	24	of	of	ADP
ejpam-3338	577	25	sin(π/2	sin(π/2	PROPN
ejpam-3338	577	26	)	)	PUNCT
ejpam-3338	577	27	0.5	0.5	NUM
ejpam-3338	577	28	0.354970157186708	0.354970157186708	NUM
ejpam-3338	577	29	0.9	0.9	NUM
ejpam-3338	577	30	0.0458549655973837	0.0458549655973837	NUM
ejpam-3338	577	31	0.99	0.99	NUM
ejpam-3338	577	32	0.00404259546470162	0.00404259546470162	NUM
ejpam-3338	577	33	0.999	0.999	NUM
ejpam-3338	577	34	0.000398924379050003	0.000398924379050003	NUM
ejpam-3338	577	35	0.9999	0.9999	NUM
ejpam-3338	577	36	3.98391892857323e-005	3.98391892857323e-005	NUM
ejpam-3338	577	37	0.99999	0.99999	NUM
ejpam-3338	577	38	3.98338654632647e-006	3.98338654632647e-006	PROPN
ejpam-3338	577	39	s.	s.	PROPN
ejpam-3338	577	40	k.sen	k.sen	PROPN
ejpam-3338	577	41	,	,	PUNCT
ejpam-3338	577	42	j.	j.	PROPN
ejpam-3338	577	43	v.	v.	PROPN
ejpam-3338	577	44	devi	devi	PROPN
ejpam-3338	577	45	,	,	PUNCT
ejpam-3338	577	46	r.v.g	r.v.g	NOUN
ejpam-3338	577	47	.	.	PUNCT
ejpam-3338	578	1	r.	r.	PROPN
ejpam-3338	578	2	kumar	kumar	PROPN
ejpam-3338	578	3	/	/	SYM
ejpam-3338	578	4	eur	eur	PROPN
ejpam-3338	578	5	.	.	PUNCT
ejpam-3338	579	1	j.	j.	PROPN
ejpam-3338	579	2	pure	pure	PROPN
ejpam-3338	579	3	appl	appl	PROPN
ejpam-3338	579	4	.	.	PROPN
ejpam-3338	579	5	math	math	PROPN
ejpam-3338	579	6	,	,	PUNCT
ejpam-3338	579	7	11	11	NUM
ejpam-3338	579	8	(	(	PUNCT
ejpam-3338	579	9	3	3	NUM
ejpam-3338	579	10	)	)	PUNCT
ejpam-3338	579	11	(	(	PUNCT
ejpam-3338	579	12	2018	2018	NUM
ejpam-3338	579	13	)	)	PUNCT
ejpam-3338	579	14	,	,	PUNCT
ejpam-3338	579	15	1058	1058	NUM
ejpam-3338	579	16	-	-	SYM
ejpam-3338	579	17	1099	1099	NUM
ejpam-3338	579	18	1082	1082	NUM
ejpam-3338	579	19	observe	observe	VERB
ejpam-3338	579	20	that	that	SCONJ
ejpam-3338	579	21	the	the	DET
ejpam-3338	579	22	foregoing	foregoing	NOUN
ejpam-3338	579	23	result	result	NOUN
ejpam-3338	579	24	provides	provide	VERB
ejpam-3338	579	25	some	some	DET
ejpam-3338	579	26	idea	idea	NOUN
ejpam-3338	579	27	about	about	ADP
ejpam-3338	579	28	the	the	DET
ejpam-3338	579	29	accuracy	accuracy	NOUN
ejpam-3338	579	30	of	of	ADP
ejpam-3338	579	31	caputo	caputo	PROPN
ejpam-3338	579	32	fractional	fractional	PROPN
ejpam-3338	579	33	order	order	NOUN
ejpam-3338	579	34	derivative	derivative	NOUN
ejpam-3338	579	35	.	.	PUNCT
ejpam-3338	580	1	specifically	specifically	ADV
ejpam-3338	580	2	one	one	PRON
ejpam-3338	580	3	can	can	AUX
ejpam-3338	580	4	see	see	VERB
ejpam-3338	580	5	how	how	SCONJ
ejpam-3338	580	6	well	well	ADV
ejpam-3338	580	7	the	the	DET
ejpam-3338	580	8	fractional	fractional	ADJ
ejpam-3338	580	9	order	order	NOUN
ejpam-3338	580	10	α	α	NOUN
ejpam-3338	580	11	merges	merge	VERB
ejpam-3338	580	12	with	with	ADP
ejpam-3338	580	13	the	the	DET
ejpam-3338	580	14	integer	integer	NOUN
ejpam-3338	580	15	order	order	NOUN
ejpam-3338	580	16	1	1	X
ejpam-3338	580	17	.	.	PUNCT
ejpam-3338	581	1	here	here	ADV
ejpam-3338	581	2	the	the	DET
ejpam-3338	581	3	generalization	generalization	NOUN
ejpam-3338	581	4	of	of	ADP
ejpam-3338	581	5	the	the	DET
ejpam-3338	581	6	fractional	fractional	ADJ
ejpam-3338	581	7	derivative	derivative	NOUN
ejpam-3338	581	8	through	through	ADP
ejpam-3338	581	9	numerical	numerical	ADJ
ejpam-3338	581	10	integration	integration	NOUN
ejpam-3338	581	11	is	be	AUX
ejpam-3338	581	12	not	not	PART
ejpam-3338	581	13	a	a	DET
ejpam-3338	581	14	straight	straight	ADJ
ejpam-3338	581	15	-	-	PUNCT
ejpam-3338	581	16	forward	forward	NOUN
ejpam-3338	581	17	approach	approach	NOUN
ejpam-3338	581	18	.	.	PUNCT
ejpam-3338	582	1	can	can	AUX
ejpam-3338	582	2	we	we	PRON
ejpam-3338	582	3	have	have	VERB
ejpam-3338	582	4	such	such	DET
ejpam-3338	582	5	an	an	DET
ejpam-3338	582	6	approach	approach	NOUN
ejpam-3338	582	7	with	with	ADP
ejpam-3338	582	8	improved	improved	ADJ
ejpam-3338	582	9	accuracy	accuracy	NOUN
ejpam-3338	582	10	without	without	ADP
ejpam-3338	582	11	limiting	limit	VERB
ejpam-3338	582	12	ourselves	ourselves	PRON
ejpam-3338	582	13	among	among	ADP
ejpam-3338	582	14	several	several	ADJ
ejpam-3338	582	15	definitions	definition	NOUN
ejpam-3338	582	16	of	of	ADP
ejpam-3338	582	17	fractional	fractional	ADJ
ejpam-3338	582	18	derivatives	derivative	NOUN
ejpam-3338	582	19	as	as	SCONJ
ejpam-3338	582	20	mentioned	mention	VERB
ejpam-3338	582	21	above	above	ADV
ejpam-3338	582	22	?	?	PUNCT
ejpam-3338	583	1	as	as	ADP
ejpam-3338	583	2	a	a	DET
ejpam-3338	583	3	matter	matter	NOUN
ejpam-3338	583	4	of	of	ADP
ejpam-3338	583	5	fact	fact	NOUN
ejpam-3338	583	6	,	,	PUNCT
ejpam-3338	583	7	one	one	PRON
ejpam-3338	583	8	may	may	AUX
ejpam-3338	583	9	have	have	VERB
ejpam-3338	583	10	totally	totally	ADV
ejpam-3338	583	11	new	new	ADJ
ejpam-3338	583	12	definition	definition	NOUN
ejpam-3338	583	13	for	for	ADP
ejpam-3338	583	14	fractional	fractional	ADJ
ejpam-3338	583	15	derivatives	derivative	NOUN
ejpam-3338	583	16	and	and	CCONJ
ejpam-3338	583	17	fractional	fractional	ADJ
ejpam-3338	583	18	integrals	integral	NOUN
ejpam-3338	583	19	,	,	PUNCT
ejpam-3338	583	20	that	that	PRON
ejpam-3338	583	21	would	would	AUX
ejpam-3338	583	22	eventually	eventually	ADV
ejpam-3338	583	23	be	be	AUX
ejpam-3338	583	24	widely	widely	ADV
ejpam-3338	583	25	accepted	accept	VERB
ejpam-3338	583	26	as	as	ADP
ejpam-3338	583	27	a	a	DET
ejpam-3338	583	28	generalization	generalization	NOUN
ejpam-3338	583	29	of	of	ADP
ejpam-3338	583	30	classical	classical	ADJ
ejpam-3338	583	31	calculus	calculus	NOUN
ejpam-3338	583	32	.	.	PUNCT
ejpam-3338	584	1	on	on	ADP
ejpam-3338	584	2	the	the	DET
ejpam-3338	584	3	other	other	ADJ
ejpam-3338	584	4	hand	hand	NOUN
ejpam-3338	584	5	,	,	PUNCT
ejpam-3338	584	6	can	can	AUX
ejpam-3338	584	7	we	we	PRON
ejpam-3338	584	8	prove	prove	VERB
ejpam-3338	584	9	that	that	SCONJ
ejpam-3338	584	10	no	no	PRON
ejpam-3338	584	11	more	more	ADJ
ejpam-3338	584	12	definition	definition	NOUN
ejpam-3338	584	13	better	well	ADV
ejpam-3338	584	14	than	than	ADP
ejpam-3338	584	15	the	the	DET
ejpam-3338	584	16	existing	exist	VERB
ejpam-3338	584	17	ones	one	NOUN
ejpam-3338	584	18	is	be	AUX
ejpam-3338	584	19	possible	possible	ADJ
ejpam-3338	584	20	?	?	PUNCT
ejpam-3338	585	1	we	we	PRON
ejpam-3338	585	2	believe	believe	VERB
ejpam-3338	585	3	that	that	SCONJ
ejpam-3338	585	4	we	we	PRON
ejpam-3338	585	5	have	have	AUX
ejpam-3338	585	6	not	not	PART
ejpam-3338	585	7	come	come	VERB
ejpam-3338	585	8	to	to	ADP
ejpam-3338	585	9	a	a	DET
ejpam-3338	585	10	dead	dead	ADJ
ejpam-3338	585	11	end	end	NOUN
ejpam-3338	585	12	;	;	PUNCT
ejpam-3338	585	13	there	there	PRON
ejpam-3338	585	14	is	be	VERB
ejpam-3338	585	15	still	still	ADV
ejpam-3338	585	16	a	a	DET
ejpam-3338	585	17	scope	scope	NOUN
ejpam-3338	585	18	of	of	ADP
ejpam-3338	585	19	deeper	deep	ADJ
ejpam-3338	585	20	exploration	exploration	NOUN
ejpam-3338	585	21	.	.	PUNCT
ejpam-3338	586	1	an	an	DET
ejpam-3338	586	2	important	important	ADJ
ejpam-3338	586	3	point	point	NOUN
ejpam-3338	586	4	is	be	AUX
ejpam-3338	586	5	the	the	DET
ejpam-3338	586	6	readily	readily	ADV
ejpam-3338	586	7	understood	understand	VERB
ejpam-3338	586	8	precise	precise	ADJ
ejpam-3338	586	9	physical	physical	ADJ
ejpam-3338	586	10	interpretation	interpretation	NOUN
ejpam-3338	586	11	of	of	ADP
ejpam-3338	586	12	every	every	DET
ejpam-3338	586	13	fractional	fractional	ADJ
ejpam-3338	586	14	order	order	NOUN
ejpam-3338	586	15	derivative	derivative	NOUN
ejpam-3338	586	16	and	and	CCONJ
ejpam-3338	586	17	every	every	DET
ejpam-3338	586	18	fractional	fractional	ADJ
ejpam-3338	586	19	order	order	NOUN
ejpam-3338	586	20	integral	integral	ADJ
ejpam-3338	586	21	just	just	ADV
ejpam-3338	586	22	like	like	ADP
ejpam-3338	586	23	every	every	DET
ejpam-3338	586	24	integer	integer	NOUN
ejpam-3338	586	25	order	order	NOUN
ejpam-3338	586	26	derivative	derivative	ADJ
ejpam-3338	586	27	and	and	CCONJ
ejpam-3338	586	28	integer	integer	NOUN
ejpam-3338	586	29	order	order	NOUN
ejpam-3338	586	30	integral	integral	ADJ
ejpam-3338	586	31	.	.	PUNCT
ejpam-3338	587	1	a	a	DET
ejpam-3338	587	2	generalization	generalization	NOUN
ejpam-3338	587	3	demands	demand	VERB
ejpam-3338	587	4	such	such	DET
ejpam-3338	587	5	an	an	DET
ejpam-3338	587	6	interpretation	interpretation	NOUN
ejpam-3338	587	7	so	so	SCONJ
ejpam-3338	587	8	that	that	SCONJ
ejpam-3338	587	9	we	we	PRON
ejpam-3338	587	10	need	need	AUX
ejpam-3338	587	11	not	not	PART
ejpam-3338	587	12	worry	worry	VERB
ejpam-3338	587	13	about	about	ADP
ejpam-3338	587	14	whether	whether	SCONJ
ejpam-3338	587	15	the	the	DET
ejpam-3338	587	16	order	order	NOUN
ejpam-3338	587	17	is	be	AUX
ejpam-3338	587	18	an	an	DET
ejpam-3338	587	19	integer	integer	NOUN
ejpam-3338	587	20	or	or	CCONJ
ejpam-3338	587	21	a	a	DET
ejpam-3338	587	22	fraction	fraction	NOUN
ejpam-3338	587	23	.	.	PUNCT
ejpam-3338	588	1	every	every	DET
ejpam-3338	588	2	integer	integer	NOUN
ejpam-3338	588	3	/	/	SYM
ejpam-3338	588	4	fractional	fractional	ADJ
ejpam-3338	588	5	order	order	NOUN
ejpam-3338	588	6	derivative	derivative	ADJ
ejpam-3338	588	7	/	/	SYM
ejpam-3338	588	8	integral	integral	ADJ
ejpam-3338	588	9	carries	carry	VERB
ejpam-3338	588	10	a	a	DET
ejpam-3338	588	11	message	message	NOUN
ejpam-3338	588	12	.	.	PUNCT
ejpam-3338	589	1	every	every	DET
ejpam-3338	589	2	derived	derived	ADJ
ejpam-3338	589	3	step	step	NOUN
ejpam-3338	589	4	in	in	ADP
ejpam-3338	589	5	a	a	DET
ejpam-3338	589	6	procedure	procedure	NOUN
ejpam-3338	589	7	also	also	ADV
ejpam-3338	589	8	gives	give	VERB
ejpam-3338	589	9	us	we	PRON
ejpam-3338	589	10	a	a	DET
ejpam-3338	589	11	distinct	distinct	ADJ
ejpam-3338	589	12	message	message	NOUN
ejpam-3338	589	13	.	.	PUNCT
ejpam-3338	590	1	it	it	PRON
ejpam-3338	590	2	is	be	AUX
ejpam-3338	590	3	a	a	DET
ejpam-3338	590	4	good	good	ADJ
ejpam-3338	590	5	habit	habit	NOUN
ejpam-3338	590	6	to	to	PART
ejpam-3338	590	7	readily	readily	ADV
ejpam-3338	590	8	get	get	VERB
ejpam-3338	590	9	/	/	SYM
ejpam-3338	590	10	understand	understand	VERB
ejpam-3338	590	11	the	the	DET
ejpam-3338	590	12	message	message	NOUN
ejpam-3338	590	13	carried	carry	VERB
ejpam-3338	590	14	by	by	ADP
ejpam-3338	590	15	a	a	DET
ejpam-3338	590	16	step	step	NOUN
ejpam-3338	590	17	/	/	SYM
ejpam-3338	590	18	equation	equation	NOUN
ejpam-3338	590	19	.	.	PUNCT
ejpam-3338	591	1	this	this	PRON
ejpam-3338	591	2	will	will	AUX
ejpam-3338	591	3	immensely	immensely	ADV
ejpam-3338	591	4	help	help	VERB
ejpam-3338	591	5	us	we	PRON
ejpam-3338	591	6	to	to	PART
ejpam-3338	591	7	grasp	grasp	VERB
ejpam-3338	591	8	/	/	PUNCT
ejpam-3338	591	9	to	to	PART
ejpam-3338	591	10	get	get	VERB
ejpam-3338	591	11	a	a	DET
ejpam-3338	591	12	complete	complete	ADJ
ejpam-3338	591	13	feel	feel	NOUN
ejpam-3338	591	14	of	of	ADP
ejpam-3338	591	15	what	what	PRON
ejpam-3338	591	16	is	be	AUX
ejpam-3338	591	17	going	go	VERB
ejpam-3338	591	18	on	on	ADP
ejpam-3338	591	19	in	in	ADP
ejpam-3338	591	20	the	the	DET
ejpam-3338	591	21	process	process	NOUN
ejpam-3338	591	22	/	/	SYM
ejpam-3338	591	23	procedure	procedure	NOUN
ejpam-3338	591	24	.	.	PUNCT
ejpam-3338	592	1	one	one	PRON
ejpam-3338	592	2	should	should	AUX
ejpam-3338	592	3	never	never	ADV
ejpam-3338	592	4	behave	behave	VERB
ejpam-3338	592	5	like	like	ADP
ejpam-3338	592	6	a	a	DET
ejpam-3338	592	7	machine	machine	NOUN
ejpam-3338	592	8	oblivious	oblivious	ADJ
ejpam-3338	592	9	of	of	ADP
ejpam-3338	592	10	what	what	PRON
ejpam-3338	592	11	is	be	AUX
ejpam-3338	592	12	going	go	VERB
ejpam-3338	592	13	around	around	ADP
ejpam-3338	592	14	us	we	PRON
ejpam-3338	592	15	.	.	PUNCT
ejpam-3338	593	1	only	only	ADV
ejpam-3338	593	2	then	then	ADV
ejpam-3338	593	3	we	we	PRON
ejpam-3338	593	4	will	will	AUX
ejpam-3338	593	5	have	have	VERB
ejpam-3338	593	6	the	the	DET
ejpam-3338	593	7	right	right	ADJ
ejpam-3338	593	8	frame	frame	NOUN
ejpam-3338	593	9	of	of	ADP
ejpam-3338	593	10	mind	mind	NOUN
ejpam-3338	593	11	for	for	ADP
ejpam-3338	593	12	the	the	DET
ejpam-3338	593	13	generalization	generalization	NOUN
ejpam-3338	593	14	or	or	CCONJ
ejpam-3338	593	15	for	for	ADP
ejpam-3338	593	16	showing	show	VERB
ejpam-3338	593	17	mathematically	mathematically	ADV
ejpam-3338	593	18	that	that	SCONJ
ejpam-3338	593	19	the	the	DET
ejpam-3338	593	20	desired	desire	VERB
ejpam-3338	593	21	generalization	generalization	NOUN
ejpam-3338	593	22	having	have	VERB
ejpam-3338	593	23	similar	similar	ADJ
ejpam-3338	593	24	applicable	applicable	ADJ
ejpam-3338	593	25	properties	property	NOUN
ejpam-3338	593	26	of	of	ADP
ejpam-3338	593	27	generalized	generalized	ADJ
ejpam-3338	593	28	matrix	matrix	NOUN
ejpam-3338	593	29	inverses	inverse	NOUN
ejpam-3338	593	30	is	be	AUX
ejpam-3338	593	31	impossible	impossible	ADJ
ejpam-3338	593	32	.	.	PUNCT
ejpam-3338	594	1	2.3	2.3	NUM
ejpam-3338	594	2	.	.	PUNCT
ejpam-3338	595	1	fractional	fractional	ADJ
ejpam-3338	595	2	ordinary	ordinary	ADJ
ejpam-3338	595	3	differential	differential	ADJ
ejpam-3338	595	4	equations	equation	NOUN
ejpam-3338	595	5	(	(	PUNCT
ejpam-3338	595	6	fodes	fode	NOUN
ejpam-3338	595	7	)	)	PUNCT
ejpam-3338	595	8	any	any	DET
ejpam-3338	595	9	system	system	NOUN
ejpam-3338	595	10	of	of	ADP
ejpam-3338	595	11	integer	integer	NOUN
ejpam-3338	595	12	order	order	NOUN
ejpam-3338	595	13	ordinary	ordinary	ADJ
ejpam-3338	595	14	differential	differential	ADJ
ejpam-3338	595	15	equations	equation	NOUN
ejpam-3338	595	16	(	(	PUNCT
ejpam-3338	595	17	iodes	iode	NOUN
ejpam-3338	595	18	)	)	PUNCT
ejpam-3338	595	19	with	with	ADP
ejpam-3338	595	20	adequate	adequate	ADJ
ejpam-3338	595	21	initial/2	initial/2	VERB
ejpam-3338	595	22	-	-	PUNCT
ejpam-3338	595	23	point	point	NOUN
ejpam-3338	595	24	boundary	boundary	ADJ
ejpam-3338	595	25	conditions	condition	NOUN
ejpam-3338	595	26	can	can	AUX
ejpam-3338	595	27	always	always	ADV
ejpam-3338	595	28	be	be	AUX
ejpam-3338	595	29	written	write	VERB
ejpam-3338	595	30	as	as	ADP
ejpam-3338	595	31	a	a	DET
ejpam-3338	595	32	system	system	NOUN
ejpam-3338	595	33	of	of	ADP
ejpam-3338	595	34	n	n	PRON
ejpam-3338	595	35	1st	1st	ADJ
ejpam-3338	595	36	order	order	NOUN
ejpam-3338	595	37	odes	ode	VERB
ejpam-3338	595	38	with	with	ADP
ejpam-3338	595	39	n	n	DET
ejpam-3338	595	40	initial/2	initial/2	ADJ
ejpam-3338	595	41	-	-	PUNCT
ejpam-3338	595	42	point	point	NOUN
ejpam-3338	595	43	boundary	boundary	ADJ
ejpam-3338	595	44	conditions	condition	NOUN
ejpam-3338	595	45	.	.	PUNCT
ejpam-3338	596	1	the	the	DET
ejpam-3338	596	2	general	general	ADJ
ejpam-3338	596	3	form	form	NOUN
ejpam-3338	596	4	can	can	AUX
ejpam-3338	596	5	be	be	AUX
ejpam-3338	596	6	written	write	VERB
ejpam-3338	596	7	follows	follow	VERB
ejpam-3338	596	8	.	.	PUNCT
ejpam-3338	597	1	dy1	dy1	NOUN
ejpam-3338	597	2	dt	dt	PROPN
ejpam-3338	597	3	=	=	SYM
ejpam-3338	597	4	f1(t	f1(t	PROPN
ejpam-3338	597	5	,	,	PUNCT
ejpam-3338	597	6	y1	y1	NOUN
ejpam-3338	597	7	,	,	PUNCT
ejpam-3338	597	8	y2	y2	PROPN
ejpam-3338	597	9	,	,	PUNCT
ejpam-3338	597	10	...	...	PUNCT
ejpam-3338	597	11	,	,	PUNCT
ejpam-3338	597	12	yn	yn	PROPN
ejpam-3338	597	13	)	)	PUNCT
ejpam-3338	597	14	dy2	dy2	PROPN
ejpam-3338	597	15	dt	dt	X
ejpam-3338	598	1	=	=	SYM
ejpam-3338	598	2	f2(t	f2(t	PROPN
ejpam-3338	598	3	,	,	PUNCT
ejpam-3338	598	4	y1	y1	NOUN
ejpam-3338	598	5	,	,	PUNCT
ejpam-3338	598	6	y2	y2	PROPN
ejpam-3338	598	7	,	,	PUNCT
ejpam-3338	598	8	...	...	PUNCT
ejpam-3338	598	9	,	,	PUNCT
ejpam-3338	598	10	yn	yn	PROPN
ejpam-3338	598	11	)	)	PUNCT
ejpam-3338	598	12	.	.	PUNCT
ejpam-3338	598	13	.	.	PUNCT
ejpam-3338	598	14	.	.	PUNCT
ejpam-3338	599	1	dyn	dyn	NOUN
ejpam-3338	599	2	dt	dt	NOUN
ejpam-3338	599	3	=	=	SYM
ejpam-3338	599	4	fn(t	fn(t	PROPN
ejpam-3338	599	5	,	,	PUNCT
ejpam-3338	599	6	y1	y1	NOUN
ejpam-3338	599	7	,	,	PUNCT
ejpam-3338	599	8	y2	y2	PROPN
ejpam-3338	599	9	,	,	PUNCT
ejpam-3338	599	10	...	...	PUNCT
ejpam-3338	599	11	,	,	PUNCT
ejpam-3338	599	12	yn	yn	PROPN
ejpam-3338	599	13	)	)	PUNCT
ejpam-3338	599	14	(	(	PUNCT
ejpam-3338	599	15	35	35	NUM
ejpam-3338	599	16	)	)	PUNCT
ejpam-3338	599	17	with	with	ADP
ejpam-3338	599	18	n	n	CCONJ
ejpam-3338	599	19	initial	initial	ADJ
ejpam-3338	599	20	conditions	condition	NOUN
ejpam-3338	599	21	:	:	PUNCT
ejpam-3338	599	22	at	at	ADP
ejpam-3338	599	23	t	t	NOUN
ejpam-3338	599	24	=	=	PUNCT
ejpam-3338	599	25	t0,y1	t0,y1	PROPN
ejpam-3338	599	26	=	=	SYM
ejpam-3338	599	27	α1,y2	α1,y2	PUNCT
ejpam-3338	599	28	=	=	PRON
ejpam-3338	599	29	α2,,yn	α2,,yn	NOUN
ejpam-3338	600	1	=	=	PUNCT
ejpam-3338	600	2	αn	αn	NOUN
ejpam-3338	600	3	or	or	CCONJ
ejpam-3338	600	4	with	with	ADP
ejpam-3338	600	5	n	n	CCONJ
ejpam-3338	600	6	boundary	boundary	ADJ
ejpam-3338	600	7	conditions	condition	NOUN
ejpam-3338	600	8	where	where	SCONJ
ejpam-3338	600	9	some	some	PRON
ejpam-3338	600	10	of	of	ADP
ejpam-3338	600	11	these	these	DET
ejpam-3338	600	12	n	n	CCONJ
ejpam-3338	600	13	conditions	condition	NOUN
ejpam-3338	600	14	are	be	AUX
ejpam-3338	600	15	specified	specify	VERB
ejpam-3338	600	16	at	at	ADP
ejpam-3338	600	17	t	t	NOUN
ejpam-3338	600	18	=	=	SYM
ejpam-3338	600	19	t0	t0	PROPN
ejpam-3338	600	20	while	while	SCONJ
ejpam-3338	600	21	the	the	DET
ejpam-3338	600	22	rest	rest	NOUN
ejpam-3338	600	23	at	at	ADP
ejpam-3338	600	24	t	t	PROPN
ejpam-3338	600	25	=	=	SYM
ejpam-3338	601	1	tf	tf	PROPN
ejpam-3338	601	2	inal	inal	ADJ
ejpam-3338	601	3	.	.	PUNCT
ejpam-3338	602	1	the	the	DET
ejpam-3338	602	2	functions	function	NOUN
ejpam-3338	602	3	f1	f1	NOUN
ejpam-3338	602	4	,	,	PUNCT
ejpam-3338	602	5	f2	f2	PROPN
ejpam-3338	602	6	,	,	PUNCT
ejpam-3338	602	7	...	...	PUNCT
ejpam-3338	602	8	,	,	PUNCT
ejpam-3338	602	9	fn	fn	PROPN
ejpam-3338	602	10	are	be	AUX
ejpam-3338	602	11	written	write	VERB
ejpam-3338	602	12	from	from	ADP
ejpam-3338	602	13	a	a	DET
ejpam-3338	602	14	given	give	VERB
ejpam-3338	602	15	actual	actual	ADJ
ejpam-3338	602	16	system	system	NOUN
ejpam-3338	602	17	of	of	ADP
ejpam-3338	602	18	iodes	iode	NOUN
ejpam-3338	602	19	with	with	ADP
ejpam-3338	602	20	the	the	DET
ejpam-3338	602	21	initial	initial	ADJ
ejpam-3338	602	22	/	/	SYM
ejpam-3338	602	23	boundary	boundary	ADJ
ejpam-3338	602	24	conditions	condition	NOUN
ejpam-3338	602	25	.	.	PUNCT
ejpam-3338	603	1	observe	observe	VERB
ejpam-3338	603	2	that	that	SCONJ
ejpam-3338	603	3	α′is	α′is	PRON
ejpam-3338	603	4	are	be	AUX
ejpam-3338	603	5	specified	specify	VERB
ejpam-3338	603	6	numerical	numerical	ADJ
ejpam-3338	603	7	values	value	NOUN
ejpam-3338	603	8	and	and	CCONJ
ejpam-3338	603	9	are	be	AUX
ejpam-3338	603	10	not	not	PART
ejpam-3338	603	11	connected	connect	VERB
ejpam-3338	603	12	with	with	ADP
ejpam-3338	603	13	the	the	DET
ejpam-3338	603	14	fractional	fractional	ADJ
ejpam-3338	603	15	order	order	NOUN
ejpam-3338	603	16	α	α	NOUN
ejpam-3338	603	17	.	.	PUNCT
ejpam-3338	604	1	s.	s.	PROPN
ejpam-3338	604	2	k.sen	k.sen	PROPN
ejpam-3338	604	3	,	,	PUNCT
ejpam-3338	604	4	j.	j.	PROPN
ejpam-3338	604	5	v.	v.	PROPN
ejpam-3338	604	6	devi	devi	PROPN
ejpam-3338	604	7	,	,	PUNCT
ejpam-3338	604	8	r.v.g	r.v.g	NOUN
ejpam-3338	604	9	.	.	PUNCT
ejpam-3338	605	1	r.	r.	PROPN
ejpam-3338	605	2	kumar	kumar	PROPN
ejpam-3338	605	3	/	/	SYM
ejpam-3338	605	4	eur	eur	PROPN
ejpam-3338	605	5	.	.	PUNCT
ejpam-3338	606	1	j.	j.	PROPN
ejpam-3338	606	2	pure	pure	PROPN
ejpam-3338	606	3	appl	appl	PROPN
ejpam-3338	606	4	.	.	PROPN
ejpam-3338	606	5	math	math	PROPN
ejpam-3338	606	6	,	,	PUNCT
ejpam-3338	606	7	11	11	NUM
ejpam-3338	606	8	(	(	PUNCT
ejpam-3338	606	9	3	3	NUM
ejpam-3338	606	10	)	)	PUNCT
ejpam-3338	606	11	(	(	PUNCT
ejpam-3338	606	12	2018	2018	NUM
ejpam-3338	606	13	)	)	PUNCT
ejpam-3338	606	14	,	,	PUNCT
ejpam-3338	606	15	1058	1058	NUM
ejpam-3338	606	16	-	-	SYM
ejpam-3338	606	17	1099	1099	NUM
ejpam-3338	606	18	1083	1083	NUM
ejpam-3338	606	19	similarly	similarly	ADV
ejpam-3338	606	20	fodes	fode	NOUN
ejpam-3338	606	21	of	of	ADP
ejpam-3338	606	22	fractional	fractional	ADJ
ejpam-3338	606	23	order	order	NOUN
ejpam-3338	606	24	0	0	NUM
ejpam-3338	606	25	<	<	X
ejpam-3338	606	26	α	α	X
ejpam-3338	606	27	<	<	X
ejpam-3338	606	28	1	1	NUM
ejpam-3338	606	29	can	can	AUX
ejpam-3338	606	30	be	be	AUX
ejpam-3338	606	31	written	write	VERB
ejpam-3338	606	32	as	as	ADP
ejpam-3338	606	33	dαy1	dαy1	NOUN
ejpam-3338	606	34	dt	dt	ADP
ejpam-3338	607	1	=	=	SYM
ejpam-3338	607	2	f1(t	f1(t	PROPN
ejpam-3338	607	3	,	,	PUNCT
ejpam-3338	607	4	y1	y1	NOUN
ejpam-3338	607	5	,	,	PUNCT
ejpam-3338	607	6	y2	y2	PROPN
ejpam-3338	607	7	,	,	PUNCT
ejpam-3338	607	8	...	...	PUNCT
ejpam-3338	607	9	,	,	PUNCT
ejpam-3338	607	10	yn	yn	PROPN
ejpam-3338	607	11	)	)	PUNCT
ejpam-3338	607	12	dαy2	dαy2	NOUN
ejpam-3338	607	13	dt	dt	NOUN
ejpam-3338	607	14	=	=	SYM
ejpam-3338	607	15	f2(t	f2(t	PROPN
ejpam-3338	607	16	,	,	PUNCT
ejpam-3338	607	17	y1	y1	NOUN
ejpam-3338	607	18	,	,	PUNCT
ejpam-3338	607	19	y2	y2	PROPN
ejpam-3338	607	20	,	,	PUNCT
ejpam-3338	607	21	...	...	PUNCT
ejpam-3338	607	22	,	,	PUNCT
ejpam-3338	607	23	yn	yn	PROPN
ejpam-3338	607	24	)	)	PUNCT
ejpam-3338	607	25	.	.	PUNCT
ejpam-3338	607	26	.	.	PUNCT
ejpam-3338	608	1	.	.	PUNCT
ejpam-3338	609	1	dαyn	dαyn	VERB
ejpam-3338	609	2	dt	dt	PROPN
ejpam-3338	610	1	=	=	SYM
ejpam-3338	610	2	fn(t	fn(t	PROPN
ejpam-3338	610	3	,	,	PUNCT
ejpam-3338	610	4	y1	y1	NOUN
ejpam-3338	610	5	,	,	PUNCT
ejpam-3338	610	6	y2	y2	PROPN
ejpam-3338	610	7	,	,	PUNCT
ejpam-3338	610	8	...	...	PUNCT
ejpam-3338	610	9	,	,	PUNCT
ejpam-3338	610	10	yn	yn	PROPN
ejpam-3338	610	11	)	)	PUNCT
ejpam-3338	610	12	(	(	PUNCT
ejpam-3338	610	13	36	36	NUM
ejpam-3338	610	14	)	)	PUNCT
ejpam-3338	610	15	with	with	ADP
ejpam-3338	610	16	n	n	CCONJ
ejpam-3338	610	17	initial	initial	ADJ
ejpam-3338	610	18	conditions	condition	NOUN
ejpam-3338	610	19	:	:	PUNCT
ejpam-3338	610	20	at	at	ADP
ejpam-3338	610	21	t	t	NOUN
ejpam-3338	610	22	=	=	PUNCT
ejpam-3338	611	1	t0,y1	t0,y1	PROPN
ejpam-3338	611	2	=	=	SYM
ejpam-3338	611	3	α1,y2	α1,y2	PUNCT
ejpam-3338	611	4	=	=	PRON
ejpam-3338	612	1	α2,,yn	α2,,yn	NOUN
ejpam-3338	613	1	=	=	PUNCT
ejpam-3338	613	2	αn	αn	NOUN
ejpam-3338	613	3	or	or	CCONJ
ejpam-3338	613	4	with	with	ADP
ejpam-3338	613	5	n	n	CCONJ
ejpam-3338	613	6	boundary	boundary	ADJ
ejpam-3338	613	7	conditions	condition	NOUN
ejpam-3338	613	8	where	where	SCONJ
ejpam-3338	613	9	some	some	PRON
ejpam-3338	613	10	of	of	ADP
ejpam-3338	613	11	these	these	DET
ejpam-3338	613	12	n	n	CCONJ
ejpam-3338	613	13	conditions	condition	NOUN
ejpam-3338	613	14	are	be	AUX
ejpam-3338	613	15	specified	specify	VERB
ejpam-3338	613	16	at	at	ADP
ejpam-3338	613	17	t	t	NOUN
ejpam-3338	613	18	=	=	SYM
ejpam-3338	613	19	t0	t0	PROPN
ejpam-3338	613	20	while	while	SCONJ
ejpam-3338	613	21	the	the	DET
ejpam-3338	613	22	rest	rest	NOUN
ejpam-3338	613	23	at	at	ADP
ejpam-3338	613	24	t	t	PROPN
ejpam-3338	613	25	=	=	SYM
ejpam-3338	614	1	tf	tf	PROPN
ejpam-3338	614	2	inal	inal	ADJ
ejpam-3338	614	3	.	.	PUNCT
ejpam-3338	615	1	the	the	DET
ejpam-3338	615	2	functions	function	NOUN
ejpam-3338	615	3	f1	f1	NOUN
ejpam-3338	615	4	,	,	PUNCT
ejpam-3338	615	5	f2	f2	PROPN
ejpam-3338	615	6	,	,	PUNCT
ejpam-3338	615	7	...	...	PUNCT
ejpam-3338	615	8	,	,	PUNCT
ejpam-3338	615	9	fn	fn	PROPN
ejpam-3338	615	10	are	be	AUX
ejpam-3338	615	11	written	write	VERB
ejpam-3338	615	12	from	from	ADP
ejpam-3338	615	13	a	a	DET
ejpam-3338	615	14	given	give	VERB
ejpam-3338	615	15	actual	actual	ADJ
ejpam-3338	615	16	system	system	NOUN
ejpam-3338	615	17	of	of	ADP
ejpam-3338	615	18	iodes	iode	NOUN
ejpam-3338	615	19	with	with	ADP
ejpam-3338	615	20	the	the	DET
ejpam-3338	615	21	initial	initial	ADJ
ejpam-3338	615	22	/	/	SYM
ejpam-3338	615	23	boundary	boundary	ADJ
ejpam-3338	615	24	conditions	condition	NOUN
ejpam-3338	615	25	.	.	PUNCT
ejpam-3338	616	1	consider	consider	VERB
ejpam-3338	616	2	,	,	PUNCT
ejpam-3338	616	3	as	as	ADP
ejpam-3338	616	4	an	an	DET
ejpam-3338	616	5	example	example	NOUN
ejpam-3338	616	6	,	,	PUNCT
ejpam-3338	616	7	the	the	DET
ejpam-3338	616	8	projectile	projectile	NOUN
ejpam-3338	616	9	motion	motion	NOUN
ejpam-3338	616	10	problem	problem	NOUN
ejpam-3338	616	11	.	.	PUNCT
ejpam-3338	617	1	a	a	DET
ejpam-3338	617	2	projectile	projectile	NOUN
ejpam-3338	617	3	of	of	ADP
ejpam-3338	617	4	mass	mass	NOUN
ejpam-3338	617	5	m	m	VERB
ejpam-3338	617	6	is	be	AUX
ejpam-3338	617	7	launched	launch	VERB
ejpam-3338	617	8	with	with	ADP
ejpam-3338	617	9	initial	initial	ADJ
ejpam-3338	617	10	velocity	velocity	NOUN
ejpam-3338	617	11	v0	v0	NOUN
ejpam-3338	617	12	at	at	ADP
ejpam-3338	617	13	an	an	DET
ejpam-3338	617	14	angle	angle	NOUN
ejpam-3338	617	15	θ	θ	NOUN
ejpam-3338	617	16	at	at	ADP
ejpam-3338	617	17	time	time	NOUN
ejpam-3338	618	1	t	t	NOUN
ejpam-3338	618	2	=	=	SYM
ejpam-3338	618	3	0	0	X
ejpam-3338	618	4	.	.	X
ejpam-3338	619	1	atmosphere	atmosphere	NOUN
ejpam-3338	619	2	exerts	exert	VERB
ejpam-3338	619	3	a	a	DET
ejpam-3338	619	4	resistance	resistance	NOUN
ejpam-3338	619	5	force	force	NOUN
ejpam-3338	619	6	r	r	NOUN
ejpam-3338	619	7	on	on	ADP
ejpam-3338	619	8	the	the	DET
ejpam-3338	619	9	mass	mass	NOUN
ejpam-3338	619	10	,	,	PUNCT
ejpam-3338	619	11	proportional	proportional	ADJ
ejpam-3338	619	12	to	to	ADP
ejpam-3338	619	13	the	the	DET
ejpam-3338	619	14	velocity	velocity	NOUN
ejpam-3338	619	15	of	of	ADP
ejpam-3338	619	16	the	the	DET
ejpam-3338	619	17	mass	mass	NOUN
ejpam-3338	619	18	at	at	ADP
ejpam-3338	619	19	time	time	NOUN
ejpam-3338	619	20	t	t	PROPN
ejpam-3338	619	21	,	,	PUNCT
ejpam-3338	619	22	i.e.r	i.e.r	PROPN
ejpam-3338	619	23	=	=	SYM
ejpam-3338	619	24	βv(t	βv(t	NUM
ejpam-3338	619	25	)	)	PUNCT
ejpam-3338	619	26	,	,	PUNCT
ejpam-3338	619	27	where	where	SCONJ
ejpam-3338	619	28	β	β	PROPN
ejpam-3338	619	29	is	be	AUX
ejpam-3338	619	30	a	a	DET
ejpam-3338	619	31	constant	constant	ADJ
ejpam-3338	619	32	and	and	CCONJ
ejpam-3338	619	33	is	be	AUX
ejpam-3338	619	34	opposite	opposite	ADJ
ejpam-3338	619	35	to	to	ADP
ejpam-3338	619	36	the	the	DET
ejpam-3338	619	37	direction	direction	NOUN
ejpam-3338	619	38	of	of	ADP
ejpam-3338	619	39	the	the	DET
ejpam-3338	619	40	velocity	velocity	NOUN
ejpam-3338	619	41	of	of	ADP
ejpam-3338	619	42	the	the	DET
ejpam-3338	619	43	mass	mass	NOUN
ejpam-3338	619	44	.	.	PUNCT
ejpam-3338	620	1	at	at	ADP
ejpam-3338	620	2	time	time	NOUN
ejpam-3338	620	3	t	t	PROPN
ejpam-3338	620	4	,	,	PUNCT
ejpam-3338	620	5	the	the	DET
ejpam-3338	620	6	mass	mass	NOUN
ejpam-3338	620	7	is	be	AUX
ejpam-3338	620	8	at	at	ADP
ejpam-3338	620	9	location	location	NOUN
ejpam-3338	620	10	(	(	PUNCT
ejpam-3338	620	11	x(t	x(t	PROPN
ejpam-3338	620	12	)	)	PUNCT
ejpam-3338	620	13	,	,	PUNCT
ejpam-3338	620	14	y(t	y(t	NOUN
ejpam-3338	620	15	)	)	PUNCT
ejpam-3338	620	16	)	)	PUNCT
ejpam-3338	620	17	;	;	PUNCT
ejpam-3338	620	18	the	the	DET
ejpam-3338	620	19	velocity	velocity	NOUN
ejpam-3338	620	20	of	of	ADP
ejpam-3338	620	21	the	the	DET
ejpam-3338	620	22	mass	mass	NOUN
ejpam-3338	620	23	in	in	ADP
ejpam-3338	620	24	the	the	DET
ejpam-3338	620	25	x	x	NOUN
ejpam-3338	620	26	-	-	NOUN
ejpam-3338	620	27	direction	direction	NOUN
ejpam-3338	620	28	and	and	CCONJ
ejpam-3338	620	29	that	that	SCONJ
ejpam-3338	620	30	in	in	ADP
ejpam-3338	620	31	the	the	DET
ejpam-3338	620	32	y	y	NOUN
ejpam-3338	620	33	-	-	PUNCT
ejpam-3338	620	34	direction	direction	NOUN
ejpam-3338	620	35	are	be	AUX
ejpam-3338	620	36	ẋ(t	ẋ(t	NOUN
ejpam-3338	620	37	)	)	PUNCT
ejpam-3338	620	38	,	,	PUNCT
ejpam-3338	620	39	ẏ(t	ẏ(t	PROPN
ejpam-3338	620	40	)	)	PUNCT
ejpam-3338	620	41	,	,	PUNCT
ejpam-3338	620	42	respectively	respectively	ADV
ejpam-3338	620	43	.	.	PUNCT
ejpam-3338	621	1	thus	thus	ADV
ejpam-3338	621	2	the	the	DET
ejpam-3338	621	3	velocity	velocity	NOUN
ejpam-3338	621	4	of	of	ADP
ejpam-3338	621	5	the	the	DET
ejpam-3338	621	6	mass	mass	NOUN
ejpam-3338	621	7	is	be	AUX
ejpam-3338	621	8	v(t	v(t	VERB
ejpam-3338	621	9	)	)	PUNCT
ejpam-3338	621	10	=	=	SYM
ejpam-3338	622	1	√	√	PROPN
ejpam-3338	622	2	(	(	PUNCT
ejpam-3338	622	3	ẋ2(t	ẋ2(t	PROPN
ejpam-3338	622	4	)	)	PUNCT
ejpam-3338	623	1	+	+	CCONJ
ejpam-3338	623	2	ẏ2(t	ẏ2(t	PROPN
ejpam-3338	623	3	)	)	PUNCT
ejpam-3338	623	4	)	)	PUNCT
ejpam-3338	623	5	at	at	ADP
ejpam-3338	623	6	an	an	DET
ejpam-3338	623	7	angle	angle	NOUN
ejpam-3338	623	8	θ(t	θ(t	NOUN
ejpam-3338	623	9	)	)	PUNCT
ejpam-3338	624	1	=	=	SYM
ejpam-3338	624	2	tan−1	tan−1	PROPN
ejpam-3338	624	3	ẏ(t	ẏ(t	PROPN
ejpam-3338	624	4	)	)	PUNCT
ejpam-3338	624	5	ẋ(t	ẋ(t	PROPN
ejpam-3338	624	6	)	)	PUNCT
ejpam-3338	624	7	.	.	PUNCT
ejpam-3338	625	1	the	the	DET
ejpam-3338	625	2	x	x	NOUN
ejpam-3338	625	3	-	-	NOUN
ejpam-3338	625	4	component	component	NOUN
ejpam-3338	625	5	of	of	ADP
ejpam-3338	625	6	resistance	resistance	NOUN
ejpam-3338	625	7	force	force	NOUN
ejpam-3338	625	8	r	r	NOUN
ejpam-3338	625	9	is	be	AUX
ejpam-3338	625	10	r(t)cosθ(t	r(t)cosθ(t	NOUN
ejpam-3338	625	11	)	)	PUNCT
ejpam-3338	625	12	and	and	CCONJ
ejpam-3338	625	13	y	y	NOUN
ejpam-3338	625	14	-	-	PUNCT
ejpam-3338	625	15	component	component	NOUN
ejpam-3338	625	16	of	of	ADP
ejpam-3338	625	17	r	r	NOUN
ejpam-3338	625	18	is	be	AUX
ejpam-3338	625	19	r(t)sinθ(t	r(t)sinθ(t	NOUN
ejpam-3338	625	20	)	)	PUNCT
ejpam-3338	625	21	.	.	PUNCT
ejpam-3338	626	1	using	use	VERB
ejpam-3338	626	2	newtons	newtons	PROPN
ejpam-3338	626	3	2nd	2nd	PROPN
ejpam-3338	626	4	law	law	NOUN
ejpam-3338	626	5	of	of	ADP
ejpam-3338	626	6	motion	motion	NOUN
ejpam-3338	626	7	,	,	PUNCT
ejpam-3338	626	8	we	we	PRON
ejpam-3338	626	9	can	can	AUX
ejpam-3338	626	10	write	write	VERB
ejpam-3338	626	11	x−	x−	PROPN
ejpam-3338	626	12	direction	direction	NOUN
ejpam-3338	626	13	:	:	PUNCT
ejpam-3338	626	14	mẍ(t	mẍ(t	NOUN
ejpam-3338	626	15	)	)	PUNCT
ejpam-3338	626	16	=	=	SYM
ejpam-3338	626	17	−r(t)cosθ(t	−r(t)cosθ(t	PROPN
ejpam-3338	626	18	)	)	PUNCT
ejpam-3338	626	19	y	y	PROPN
ejpam-3338	626	20	−	−	PROPN
ejpam-3338	626	21	direction	direction	NOUN
ejpam-3338	626	22	:	:	PUNCT
ejpam-3338	626	23	mÿ(t	mÿ(t	NOUN
ejpam-3338	626	24	)	)	PUNCT
ejpam-3338	626	25	=	=	SYM
ejpam-3338	627	1	−mg	−mg	NOUN
ejpam-3338	627	2	−r(t)sinθ(t	−r(t)sinθ(t	NOUN
ejpam-3338	627	3	)	)	PUNCT
ejpam-3338	627	4	(	(	PUNCT
ejpam-3338	627	5	37	37	NUM
ejpam-3338	627	6	)	)	PUNCT
ejpam-3338	627	7	the	the	DET
ejpam-3338	627	8	equation	equation	NOUN
ejpam-3338	627	9	of	of	ADP
ejpam-3338	627	10	motion	motion	NOUN
ejpam-3338	627	11	(	(	PUNCT
ejpam-3338	627	12	mathematical	mathematical	ADJ
ejpam-3338	627	13	model	model	NOUN
ejpam-3338	627	14	)	)	PUNCT
ejpam-3338	627	15	becomes	become	VERB
ejpam-3338	627	16	mẍ(t	mẍ(t	NOUN
ejpam-3338	627	17	)	)	PUNCT
ejpam-3338	628	1	=	=	SYM
ejpam-3338	628	2	−βvcosθ(t	−βvcosθ(t	NUM
ejpam-3338	628	3	)	)	PUNCT
ejpam-3338	628	4	=	=	NOUN
ejpam-3338	629	1	−βv	−βv	X
ejpam-3338	629	2	ẋ√	ẋ√	PROPN
ejpam-3338	629	3	ẋ2	ẋ2	PROPN
ejpam-3338	630	1	+	+	PUNCT
ejpam-3338	630	2	ẏ2	ẏ2	PROPN
ejpam-3338	630	3	i.e.	i.e.	X
ejpam-3338	630	4	,	,	PUNCT
ejpam-3338	630	5	mẍ+	mẍ+	ADJ
ejpam-3338	630	6	βẋ	βẋ	SYM
ejpam-3338	630	7	=	=	SYM
ejpam-3338	630	8	0	0	NUM
ejpam-3338	630	9	mÿ(t	mÿ(t	NOUN
ejpam-3338	630	10	)	)	PUNCT
ejpam-3338	630	11	=	=	PUNCT
ejpam-3338	631	1	−mg	−mg	NOUN
ejpam-3338	632	1	−	−	NOUN
ejpam-3338	632	2	βv	βv	INTJ
ejpam-3338	633	1	ẏ√	ẏ√	PROPN
ejpam-3338	633	2	ẋ2	ẋ2	PROPN
ejpam-3338	634	1	+	+	CCONJ
ejpam-3338	634	2	ẏ2	ẏ2	PROPN
ejpam-3338	634	3	i.e.	i.e.	X
ejpam-3338	634	4	,	,	PUNCT
ejpam-3338	634	5	mÿ	mÿ	NOUN
ejpam-3338	634	6	+	+	PUNCT
ejpam-3338	634	7	βẏ	βẏ	PUNCT
ejpam-3338	634	8	=	=	SYM
ejpam-3338	634	9	−mg	−mg	X
ejpam-3338	634	10	(	(	PUNCT
ejpam-3338	634	11	38	38	NUM
ejpam-3338	634	12	)	)	PUNCT
ejpam-3338	634	13	ic	ic	NOUN
ejpam-3338	634	14	:	:	PUNCT
ejpam-3338	634	15	at	at	ADP
ejpam-3338	634	16	t	t	PROPN
ejpam-3338	634	17	=	=	SYM
ejpam-3338	634	18	0	0	PROPN
ejpam-3338	634	19	,	,	PUNCT
ejpam-3338	634	20	x(0	x(0	PROPN
ejpam-3338	634	21	)	)	PUNCT
ejpam-3338	635	1	=	=	SYM
ejpam-3338	635	2	0	0	NUM
ejpam-3338	635	3	,	,	PUNCT
ejpam-3338	635	4	y(0	y(0	PROPN
ejpam-3338	635	5	)	)	PUNCT
ejpam-3338	635	6	=	=	SYM
ejpam-3338	635	7	0	0	NUM
ejpam-3338	635	8	,	,	PUNCT
ejpam-3338	635	9	ẋ(0	ẋ(0	X
ejpam-3338	635	10	)	)	PUNCT
ejpam-3338	635	11	=	=	SYM
ejpam-3338	635	12	v0cosθ0	v0cosθ0	PROPN
ejpam-3338	635	13	,	,	PUNCT
ejpam-3338	635	14	ẏ(0	ẏ(0	NUM
ejpam-3338	635	15	)	)	PUNCT
ejpam-3338	635	16	=	=	SYM
ejpam-3338	636	1	v0sinθ0	v0sinθ0	NOUN
ejpam-3338	636	2	hence	hence	ADV
ejpam-3338	636	3	the	the	DET
ejpam-3338	636	4	system	system	NOUN
ejpam-3338	636	5	of	of	ADP
ejpam-3338	636	6	4	4	NUM
ejpam-3338	636	7	1st	1st	ADJ
ejpam-3338	636	8	order	order	NOUN
ejpam-3338	636	9	odes	ode	VERB
ejpam-3338	636	10	(	(	PUNCT
ejpam-3338	636	11	computational	computational	ADJ
ejpam-3338	636	12	mathematical	mathematical	ADJ
ejpam-3338	636	13	model	model	NOUN
ejpam-3338	636	14	suitable	suitable	ADJ
ejpam-3338	636	15	for	for	ADP
ejpam-3338	636	16	computer	computer	NOUN
ejpam-3338	636	17	implementation	implementation	NOUN
ejpam-3338	636	18	for	for	ADP
ejpam-3338	636	19	n	n	PROPN
ejpam-3338	636	20	(	(	PUNCT
ejpam-3338	636	21	general	general	ADJ
ejpam-3338	636	22	)	)	PUNCT
ejpam-3338	636	23	1st	1st	ADJ
ejpam-3338	636	24	order	order	NOUN
ejpam-3338	636	25	odes	ode	VERB
ejpam-3338	636	26	)	)	PUNCT
ejpam-3338	636	27	can	can	AUX
ejpam-3338	636	28	be	be	AUX
ejpam-3338	636	29	written	write	VERB
ejpam-3338	636	30	as	as	SCONJ
ejpam-3338	636	31	follows	follow	VERB
ejpam-3338	636	32	.	.	PUNCT
ejpam-3338	637	1	let	let	VERB
ejpam-3338	637	2	x	x	PUNCT
ejpam-3338	637	3	=	=	SYM
ejpam-3338	637	4	x1	x1	PROPN
ejpam-3338	637	5	,	,	PUNCT
ejpam-3338	637	6	y	y	PROPN
ejpam-3338	637	7	=	=	SYM
ejpam-3338	637	8	x2	x2	PROPN
ejpam-3338	637	9	,	,	PUNCT
ejpam-3338	637	10	dx	dx	PROPN
ejpam-3338	637	11	dt	dt	NOUN
ejpam-3338	638	1	=	=	SYM
ejpam-3338	638	2	x3	x3	PROPN
ejpam-3338	638	3	,	,	PUNCT
ejpam-3338	638	4	dy	dy	NOUN
ejpam-3338	638	5	dt	dt	NOUN
ejpam-3338	638	6	=	=	SYM
ejpam-3338	638	7	x4	x4	PROPN
ejpam-3338	638	8	.	.	PUNCT
ejpam-3338	639	1	then	then	ADV
ejpam-3338	639	2	the	the	DET
ejpam-3338	639	3	equation	equation	NOUN
ejpam-3338	639	4	of	of	ADP
ejpam-3338	639	5	motion	motion	NOUN
ejpam-3338	639	6	(	(	PUNCT
ejpam-3338	639	7	mathematical	mathematical	ADJ
ejpam-3338	639	8	model	model	NOUN
ejpam-3338	639	9	)	)	PUNCT
ejpam-3338	639	10	becomes	become	VERB
ejpam-3338	639	11	s.	s.	PROPN
ejpam-3338	639	12	k.sen	k.sen	PROPN
ejpam-3338	639	13	,	,	PUNCT
ejpam-3338	639	14	j.	j.	PROPN
ejpam-3338	639	15	v.	v.	PROPN
ejpam-3338	639	16	devi	devi	PROPN
ejpam-3338	639	17	,	,	PUNCT
ejpam-3338	639	18	r.v.g	r.v.g	NOUN
ejpam-3338	639	19	.	.	PUNCT
ejpam-3338	640	1	r.	r.	PROPN
ejpam-3338	640	2	kumar	kumar	PROPN
ejpam-3338	640	3	/	/	SYM
ejpam-3338	640	4	eur	eur	PROPN
ejpam-3338	640	5	.	.	PUNCT
ejpam-3338	641	1	j.	j.	PROPN
ejpam-3338	641	2	pure	pure	PROPN
ejpam-3338	641	3	appl	appl	PROPN
ejpam-3338	641	4	.	.	PROPN
ejpam-3338	641	5	math	math	PROPN
ejpam-3338	641	6	,	,	PUNCT
ejpam-3338	641	7	11	11	NUM
ejpam-3338	641	8	(	(	PUNCT
ejpam-3338	641	9	3	3	NUM
ejpam-3338	641	10	)	)	PUNCT
ejpam-3338	641	11	(	(	PUNCT
ejpam-3338	641	12	2018	2018	NUM
ejpam-3338	641	13	)	)	PUNCT
ejpam-3338	641	14	,	,	PUNCT
ejpam-3338	641	15	1058	1058	NUM
ejpam-3338	641	16	-	-	SYM
ejpam-3338	641	17	1099	1099	NUM
ejpam-3338	641	18	1084	1084	NUM
ejpam-3338	641	19	dx1	dx1	PROPN
ejpam-3338	641	20	dt	dt	X
ejpam-3338	641	21	=	=	SYM
ejpam-3338	641	22	f1(t	f1(t	PROPN
ejpam-3338	641	23	,	,	PUNCT
ejpam-3338	641	24	x1	x1	PROPN
ejpam-3338	641	25	,	,	PUNCT
ejpam-3338	641	26	x2	x2	PROPN
ejpam-3338	641	27	,	,	PUNCT
ejpam-3338	641	28	x3	x3	ADJ
ejpam-3338	641	29	,	,	PUNCT
ejpam-3338	641	30	x4	x4	PROPN
ejpam-3338	641	31	)	)	PUNCT
ejpam-3338	641	32	=	=	SYM
ejpam-3338	642	1	x3	x3	ADJ
ejpam-3338	642	2	dx2	dx2	NOUN
ejpam-3338	642	3	dt	dt	NOUN
ejpam-3338	642	4	=	=	SYM
ejpam-3338	642	5	f2(t	f2(t	PROPN
ejpam-3338	642	6	,	,	PUNCT
ejpam-3338	642	7	x1	x1	PROPN
ejpam-3338	642	8	,	,	PUNCT
ejpam-3338	642	9	x2	x2	PROPN
ejpam-3338	642	10	,	,	PUNCT
ejpam-3338	642	11	x3	x3	ADJ
ejpam-3338	642	12	,	,	PUNCT
ejpam-3338	642	13	x4	x4	PROPN
ejpam-3338	642	14	)	)	PUNCT
ejpam-3338	642	15	=	=	SYM
ejpam-3338	642	16	x4	x4	PROPN
ejpam-3338	642	17	dx3	dx3	PROPN
ejpam-3338	642	18	dt	dt	X
ejpam-3338	643	1	=	=	SYM
ejpam-3338	643	2	f3(t	f3(t	PROPN
ejpam-3338	643	3	,	,	PUNCT
ejpam-3338	643	4	x1	x1	PROPN
ejpam-3338	643	5	,	,	PUNCT
ejpam-3338	643	6	x2	x2	PROPN
ejpam-3338	643	7	,	,	PUNCT
ejpam-3338	643	8	x3	x3	ADJ
ejpam-3338	643	9	,	,	PUNCT
ejpam-3338	643	10	x4	x4	PROPN
ejpam-3338	643	11	)	)	PUNCT
ejpam-3338	643	12	=	=	PUNCT
ejpam-3338	644	1	−βx3	−βx3	VERB
ejpam-3338	644	2	m	m	VERB
ejpam-3338	644	3	dx4	dx4	INTJ
ejpam-3338	644	4	dt	dt	X
ejpam-3338	644	5	=	=	SYM
ejpam-3338	644	6	f4(t	f4(t	PROPN
ejpam-3338	644	7	,	,	PUNCT
ejpam-3338	644	8	x1	x1	PROPN
ejpam-3338	644	9	,	,	PUNCT
ejpam-3338	644	10	x2	x2	PROPN
ejpam-3338	644	11	,	,	PUNCT
ejpam-3338	644	12	x3	x3	ADJ
ejpam-3338	644	13	,	,	PUNCT
ejpam-3338	644	14	x4	x4	PROPN
ejpam-3338	644	15	)	)	PUNCT
ejpam-3338	644	16	=	=	SYM
ejpam-3338	644	17	(	(	PUNCT
ejpam-3338	644	18	−mg	−mg	X
ejpam-3338	644	19	−	−	PROPN
ejpam-3338	644	20	βx4	βx4	NOUN
ejpam-3338	644	21	)	)	PUNCT
ejpam-3338	644	22	m	m	VERB
ejpam-3338	644	23	(	(	PUNCT
ejpam-3338	644	24	39	39	NUM
ejpam-3338	644	25	)	)	PUNCT
ejpam-3338	644	26	ic	ic	PROPN
ejpam-3338	644	27	:	:	PUNCT
ejpam-3338	644	28	at	at	ADP
ejpam-3338	644	29	t	t	PROPN
ejpam-3338	644	30	=	=	SYM
ejpam-3338	644	31	0	0	PROPN
ejpam-3338	644	32	,	,	PUNCT
ejpam-3338	644	33	x1	x1	PROPN
ejpam-3338	644	34	=	=	SYM
ejpam-3338	644	35	0	0	PROPN
ejpam-3338	644	36	,	,	PUNCT
ejpam-3338	644	37	x2	x2	NOUN
ejpam-3338	644	38	=	=	SYM
ejpam-3338	644	39	0	0	NUM
ejpam-3338	644	40	,	,	PUNCT
ejpam-3338	644	41	x3	x3	NOUN
ejpam-3338	644	42	=	=	SYM
ejpam-3338	644	43	v0cosθ0	v0cosθ0	PROPN
ejpam-3338	644	44	,	,	PUNCT
ejpam-3338	644	45	x4	x4	PROPN
ejpam-3338	644	46	=	=	SYM
ejpam-3338	644	47	v0sinθ0	v0sinθ0	PROPN
ejpam-3338	644	48	.	.	PUNCT
ejpam-3338	644	49	compute	compute	PROPN
ejpam-3338	644	50	:	:	PUNCT
ejpam-3338	644	51	at	at	ADP
ejpam-3338	644	52	t	t	NOUN
ejpam-3338	644	53	=	=	SYM
ejpam-3338	644	54	0(0.1)5	0(0.1)5	NUM
ejpam-3338	644	55	,	,	PUNCT
ejpam-3338	644	56	x1	x1	PROPN
ejpam-3338	644	57	,	,	PUNCT
ejpam-3338	644	58	x2	x2	PROPN
ejpam-3338	644	59	,	,	PUNCT
ejpam-3338	644	60	x3	x3	ADJ
ejpam-3338	644	61	,	,	PUNCT
ejpam-3338	644	62	x4	x4	PROPN
ejpam-3338	644	63	given	give	VERB
ejpam-3338	644	64	v0	v0	NOUN
ejpam-3338	644	65	=	=	SYM
ejpam-3338	644	66	3000meter	3000meter	NUM
ejpam-3338	644	67	/	/	SYM
ejpam-3338	644	68	s	s	PROPN
ejpam-3338	644	69	,	,	PUNCT
ejpam-3338	644	70	β	β	X
ejpam-3338	644	71	=	=	NOUN
ejpam-3338	644	72	0.05	0.05	NUM
ejpam-3338	644	73	,	,	PUNCT
ejpam-3338	644	74	g	g	NOUN
ejpam-3338	644	75	=	=	SYM
ejpam-3338	644	76	9.8meter	9.8meter	NUM
ejpam-3338	644	77	/	/	SYM
ejpam-3338	644	78	s2	s2	PROPN
ejpam-3338	644	79	.	.	PUNCT
ejpam-3338	645	1	introducing	introduce	VERB
ejpam-3338	645	2	the	the	DET
ejpam-3338	645	3	fractional	fractional	ADJ
ejpam-3338	645	4	order	order	NOUN
ejpam-3338	645	5	α	α	PRON
ejpam-3338	645	6	such	such	ADJ
ejpam-3338	645	7	that	that	SCONJ
ejpam-3338	645	8	0	0	NUM
ejpam-3338	645	9	<	<	X
ejpam-3338	645	10	α	α	X
ejpam-3338	645	11	<	<	X
ejpam-3338	645	12	1	1	NUM
ejpam-3338	645	13	in	in	ADP
ejpam-3338	645	14	the	the	DET
ejpam-3338	645	15	foregoing	forego	VERB
ejpam-3338	645	16	system	system	NOUN
ejpam-3338	645	17	of	of	ADP
ejpam-3338	645	18	4	4	NUM
ejpam-3338	645	19	1st	1st	ADJ
ejpam-3338	645	20	order	order	NOUN
ejpam-3338	645	21	odes	ode	VERB
ejpam-3338	645	22	and	and	CCONJ
ejpam-3338	645	23	using	use	VERB
ejpam-3338	645	24	the	the	DET
ejpam-3338	645	25	matlab	matlab	PROPN
ejpam-3338	645	26	routine	routine	NOUN
ejpam-3338	646	1	fde12s	fde12s	PRON
ejpam-3338	646	2	[	[	X
ejpam-3338	646	3	9−	9−	NUM
ejpam-3338	646	4	13	13	NUM
ejpam-3338	646	5	]	]	PUNCT
ejpam-3338	646	6	,	,	PUNCT
ejpam-3338	646	7	we	we	PRON
ejpam-3338	646	8	can	can	AUX
ejpam-3338	646	9	solve	solve	VERB
ejpam-3338	646	10	a	a	DET
ejpam-3338	646	11	system	system	NOUN
ejpam-3338	646	12	of	of	ADP
ejpam-3338	646	13	n	n	CCONJ
ejpam-3338	646	14	fractional	fractional	ADJ
ejpam-3338	646	15	order	order	NOUN
ejpam-3338	646	16	odes	ode	NOUN
ejpam-3338	646	17	(	(	PUNCT
ejpam-3338	646	18	n	n	X
ejpam-3338	646	19	is	be	AUX
ejpam-3338	646	20	a	a	DET
ejpam-3338	646	21	finite	finite	ADJ
ejpam-3338	646	22	positive	positive	ADJ
ejpam-3338	646	23	integer	integer	NOUN
ejpam-3338	646	24	)	)	PUNCT
ejpam-3338	646	25	.	.	PUNCT
ejpam-3338	647	1	refer	refer	VERB
ejpam-3338	647	2	the	the	DET
ejpam-3338	647	3	systems	system	NOUN
ejpam-3338	647	4	(	(	PUNCT
ejpam-3338	647	5	36	36	NUM
ejpam-3338	647	6	)	)	PUNCT
ejpam-3338	647	7	.	.	PUNCT
ejpam-3338	648	1	it	it	PRON
ejpam-3338	648	2	can	can	AUX
ejpam-3338	648	3	be	be	AUX
ejpam-3338	648	4	seen	see	VERB
ejpam-3338	648	5	that	that	SCONJ
ejpam-3338	648	6	when	when	SCONJ
ejpam-3338	648	7	α	α	PROPN
ejpam-3338	648	8	=	=	NOUN
ejpam-3338	648	9	0	0	PROPN
ejpam-3338	648	10	,	,	PUNCT
ejpam-3338	648	11	the	the	DET
ejpam-3338	648	12	differential	differential	ADJ
ejpam-3338	648	13	equations	equation	NOUN
ejpam-3338	648	14	cease	cease	VERB
ejpam-3338	648	15	to	to	PART
ejpam-3338	648	16	exist	exist	VERB
ejpam-3338	648	17	.	.	PUNCT
ejpam-3338	649	1	on	on	ADP
ejpam-3338	649	2	the	the	DET
ejpam-3338	649	3	other	other	ADJ
ejpam-3338	649	4	hand	hand	NOUN
ejpam-3338	649	5	,	,	PUNCT
ejpam-3338	649	6	when	when	SCONJ
ejpam-3338	649	7	α	α	PROPN
ejpam-3338	649	8	=	=	NOUN
ejpam-3338	649	9	1	1	NUM
ejpam-3338	649	10	,	,	PUNCT
ejpam-3338	649	11	the	the	DET
ejpam-3338	649	12	system	system	NOUN
ejpam-3338	649	13	ceases	cease	VERB
ejpam-3338	649	14	to	to	PART
ejpam-3338	649	15	be	be	AUX
ejpam-3338	649	16	fodes	fode	NOUN
ejpam-3338	649	17	.	.	PUNCT
ejpam-3338	650	1	it	it	PRON
ejpam-3338	650	2	becomes	become	VERB
ejpam-3338	650	3	the	the	DET
ejpam-3338	650	4	classical	classical	ADJ
ejpam-3338	650	5	1st	1st	ADJ
ejpam-3338	650	6	order	order	NOUN
ejpam-3338	650	7	odes	ode	VERB
ejpam-3338	650	8	as	as	ADP
ejpam-3338	650	9	in	in	ADP
ejpam-3338	650	10	the	the	DET
ejpam-3338	650	11	system	system	NOUN
ejpam-3338	650	12	(	(	PUNCT
ejpam-3338	650	13	39	39	NUM
ejpam-3338	650	14	)	)	PUNCT
ejpam-3338	650	15	.	.	PUNCT
ejpam-3338	651	1	however	however	ADV
ejpam-3338	651	2	,	,	PUNCT
ejpam-3338	651	3	we	we	PRON
ejpam-3338	651	4	consider	consider	VERB
ejpam-3338	651	5	first	first	ADV
ejpam-3338	651	6	the	the	DET
ejpam-3338	651	7	classical	classical	ADJ
ejpam-3338	651	8	(	(	PUNCT
ejpam-3338	651	9	non	non	ADJ
ejpam-3338	651	10	-	-	ADJ
ejpam-3338	651	11	fractional	fractional	ADJ
ejpam-3338	651	12	)	)	PUNCT
ejpam-3338	651	13	pendulum	pendulum	NOUN
ejpam-3338	651	14	problem	problem	NOUN
ejpam-3338	651	15	where	where	SCONJ
ejpam-3338	651	16	no	no	DET
ejpam-3338	651	17	damping	damp	VERB
ejpam-3338	651	18	exists	exist	VERB
ejpam-3338	651	19	.	.	PUNCT
ejpam-3338	652	1	the	the	DET
ejpam-3338	652	2	matlab	matlab	PROPN
ejpam-3338	652	3	version	version	PROPN
ejpam-3338	652	4	(	(	PUNCT
ejpam-3338	652	5	program	program	NOUN
ejpam-3338	652	6	)	)	PUNCT
ejpam-3338	652	7	of	of	ADP
ejpam-3338	652	8	this	this	DET
ejpam-3338	652	9	problem	problem	NOUN
ejpam-3338	652	10	is	be	AUX
ejpam-3338	652	11	named	name	VERB
ejpam-3338	652	12	as	as	ADP
ejpam-3338	652	13	pendulum	pendulum	NOUN
ejpam-3338	652	14	.	.	PUNCT
ejpam-3338	653	1	then	then	ADV
ejpam-3338	653	2	we	we	PRON
ejpam-3338	653	3	present	present	VERB
ejpam-3338	653	4	the	the	DET
ejpam-3338	653	5	matlab	matlab	PROPN
ejpam-3338	653	6	program	program	NOUN
ejpam-3338	653	7	pendulumfde.m	pendulumfde.m	NOUN
ejpam-3338	653	8	,	,	PUNCT
ejpam-3338	653	9	where	where	SCONJ
ejpam-3338	653	10	α	α	PRON
ejpam-3338	653	11	=	=	SYM
ejpam-3338	653	12	.97	.97	NOUN
ejpam-3338	653	13	,	,	PUNCT
ejpam-3338	653	14	which	which	PRON
ejpam-3338	653	15	uses	use	VERB
ejpam-3338	653	16	the	the	DET
ejpam-3338	653	17	matlab	matlab	PROPN
ejpam-3338	653	18	routine	routine	PROPN
ejpam-3338	653	19	fde12s	fde12s	PROPN
ejpam-3338	653	20	.	.	PUNCT
ejpam-3338	654	1	both	both	CCONJ
ejpam-3338	654	2	the	the	DET
ejpam-3338	654	3	programs	program	NOUN
ejpam-3338	654	4	are	be	AUX
ejpam-3338	654	5	compatible	compatible	ADJ
ejpam-3338	654	6	with	with	ADP
ejpam-3338	654	7	the	the	DET
ejpam-3338	654	8	computational	computational	ADJ
ejpam-3338	654	9	mathematical	mathematical	ADJ
ejpam-3338	654	10	notation	notation	NOUN
ejpam-3338	654	11	and	and	CCONJ
ejpam-3338	654	12	thus	thus	ADV
ejpam-3338	654	13	self	self	NOUN
ejpam-3338	654	14	-	-	PUNCT
ejpam-3338	654	15	explanatory	explanatory	ADJ
ejpam-3338	654	16	.	.	PUNCT
ejpam-3338	655	1	further	far	ADV
ejpam-3338	655	2	both	both	PRON
ejpam-3338	655	3	use	use	VERB
ejpam-3338	655	4	the	the	DET
ejpam-3338	655	5	3	3	NUM
ejpam-3338	655	6	-	-	PUNCT
ejpam-3338	655	7	line	line	NOUN
ejpam-3338	655	8	matlab	matlab	PROPN
ejpam-3338	655	9	function	function	NOUN
ejpam-3338	655	10	sub	sub	NOUN
ejpam-3338	655	11	-	-	ADJ
ejpam-3338	655	12	program	program	ADJ
ejpam-3338	655	13	pend	pend	NOUN
ejpam-3338	655	14	shown	show	VERB
ejpam-3338	655	15	below	below	ADP
ejpam-3338	655	16	both	both	CCONJ
ejpam-3338	655	17	the	the	DET
ejpam-3338	655	18	programs	program	NOUN
ejpam-3338	655	19	pendulum	pendulum	NOUN
ejpam-3338	655	20	and	and	CCONJ
ejpam-3338	655	21	pendulumfde	pendulumfde	VERB
ejpam-3338	655	22	.	.	PUNCT
ejpam-3338	656	1	the	the	DET
ejpam-3338	656	2	2nd	2nd	ADJ
ejpam-3338	656	3	order	order	NOUN
ejpam-3338	656	4	ode	ode	NOUN
ejpam-3338	656	5	representing	represent	VERB
ejpam-3338	656	6	the	the	DET
ejpam-3338	656	7	motion	motion	NOUN
ejpam-3338	656	8	of	of	ADP
ejpam-3338	656	9	a	a	DET
ejpam-3338	656	10	simple	simple	ADJ
ejpam-3338	656	11	gravity	gravity	NOUN
ejpam-3338	656	12	pendulum	pendulum	NOUN
ejpam-3338	656	13	i.e.	i.e.	X
ejpam-3338	656	14	the	the	DET
ejpam-3338	656	15	simple	simple	ADJ
ejpam-3338	656	16	harmonic	harmonic	ADJ
ejpam-3338	656	17	motion	motion	NOUN
ejpam-3338	656	18	is	be	AUX
ejpam-3338	656	19	d2z	d2z	PROPN
ejpam-3338	656	20	dt2	dt2	PROPN
ejpam-3338	657	1	+	+	CCONJ
ejpam-3338	657	2	g	g	PROPN
ejpam-3338	657	3	l	l	NOUN
ejpam-3338	657	4	sinz	sinz	NOUN
ejpam-3338	657	5	=	=	X
ejpam-3338	657	6	0	0	NUM
ejpam-3338	657	7	,	,	PUNCT
ejpam-3338	657	8	i.e.	i.e.	X
ejpam-3338	657	9	,	,	PUNCT
ejpam-3338	657	10	d2z	d2z	X
ejpam-3338	657	11	dt2	dt2	PROPN
ejpam-3338	657	12	=	=	NOUN
ejpam-3338	657	13	−kz	−kz	PROPN
ejpam-3338	657	14	(	(	PUNCT
ejpam-3338	657	15	40	40	NUM
ejpam-3338	657	16	)	)	PUNCT
ejpam-3338	657	17	where	where	SCONJ
ejpam-3338	657	18	z	z	NOUN
ejpam-3338	657	19	=	=	PUNCT
ejpam-3338	657	20	a	a	DET
ejpam-3338	657	21	small	small	ADJ
ejpam-3338	657	22	(	(	PUNCT
ejpam-3338	657	23	≤	≤	NUM
ejpam-3338	657	24	20	20	NUM
ejpam-3338	657	25	degree	degree	NOUN
ejpam-3338	657	26	or	or	CCONJ
ejpam-3338	657	27	0.3491	0.3491	NUM
ejpam-3338	657	28	radian	radian	ADJ
ejpam-3338	657	29	)	)	PUNCT
ejpam-3338	657	30	displacement	displacement	NOUN
ejpam-3338	657	31	,	,	PUNCT
ejpam-3338	657	32	g=	g=	NOUN
ejpam-3338	657	33	acceleration	acceleration	NOUN
ejpam-3338	657	34	due	due	ADP
ejpam-3338	657	35	to	to	ADP
ejpam-3338	657	36	gravity	gravity	NOUN
ejpam-3338	657	37	,	,	PUNCT
ejpam-3338	657	38	l=	l=	ADJ
ejpam-3338	657	39	length	length	NOUN
ejpam-3338	657	40	of	of	ADP
ejpam-3338	657	41	the	the	DET
ejpam-3338	657	42	pendulum	pendulum	NOUN
ejpam-3338	657	43	,	,	PUNCT
ejpam-3338	657	44	k	k	PROPN
ejpam-3338	657	45	=	=	PUNCT
ejpam-3338	657	46	g	g	PROPN
ejpam-3338	657	47	/	/	SYM
ejpam-3338	657	48	l.	l.	NOUN
ejpam-3338	657	49	at	at	ADP
ejpam-3338	657	50	time	time	NOUN
ejpam-3338	657	51	t	t	PROPN
ejpam-3338	657	52	=	=	SYM
ejpam-3338	657	53	0	0	NUM
ejpam-3338	657	54	,	,	PUNCT
ejpam-3338	657	55	z	z	NOUN
ejpam-3338	657	56	=	=	SYM
ejpam-3338	657	57	z0	z0	PROPN
ejpam-3338	657	58	,	,	PUNCT
ejpam-3338	657	59	ż	ż	NOUN
ejpam-3338	657	60	=	=	SYM
ejpam-3338	657	61	v0	v0	PROPN
ejpam-3338	657	62	.	.	PUNCT
ejpam-3338	658	1	expressing	express	VERB
ejpam-3338	658	2	the	the	DET
ejpam-3338	658	3	foregoing	forego	VERB
ejpam-3338	658	4	2nd	2nd	ADJ
ejpam-3338	658	5	order	order	NOUN
ejpam-3338	658	6	ode	ode	VERB
ejpam-3338	658	7	into	into	ADP
ejpam-3338	658	8	2	2	NUM
ejpam-3338	658	9	1st	1st	NOUN
ejpam-3338	658	10	order	order	NOUN
ejpam-3338	658	11	odes	ode	VERB
ejpam-3338	658	12	with	with	ADP
ejpam-3338	658	13	2	2	NUM
ejpam-3338	658	14	initial	initial	ADJ
ejpam-3338	658	15	conditions	condition	NOUN
ejpam-3338	658	16	,	,	PUNCT
ejpam-3338	658	17	one	one	PRON
ejpam-3338	658	18	can	can	AUX
ejpam-3338	658	19	readily	readily	ADV
ejpam-3338	658	20	check	check	VERB
ejpam-3338	658	21	the	the	DET
ejpam-3338	658	22	concerned	concerned	ADJ
ejpam-3338	658	23	pend	pend	PROPN
ejpam-3338	658	24	matlab	matlab	PROPN
ejpam-3338	658	25	function	function	PROPN
ejpam-3338	658	26	sub	sub	NOUN
ejpam-3338	658	27	-	-	NOUN
ejpam-3338	658	28	program	program	NOUN
ejpam-3338	658	29	.	.	PUNCT
ejpam-3338	659	1	pendulum	pendulum	PROPN
ejpam-3338	659	2	non	non	ADJ
ejpam-3338	659	3	-	-	ADJ
ejpam-3338	659	4	fractional	fractional	ADJ
ejpam-3338	659	5	matlab	matlab	PROPN
ejpam-3338	659	6	program	program	NOUN
ejpam-3338	659	7	(	(	PUNCT
ejpam-3338	659	8	main	main	ADJ
ejpam-3338	659	9	)	)	PUNCT
ejpam-3338	659	10	uses	use	VERB
ejpam-3338	659	11	matlab	matlab	PROPN
ejpam-3338	659	12	routine	routine	ADJ
ejpam-3338	659	13	ode23	ode23	PROPN
ejpam-3338	659	14	and	and	CCONJ
ejpam-3338	659	15	the	the	DET
ejpam-3338	659	16	matlab	matlab	PROPN
ejpam-3338	659	17	function	function	PROPN
ejpam-3338	659	18	sub	sub	NOUN
ejpam-3338	659	19	-	-	NOUN
ejpam-3338	659	20	program	program	ADJ
ejpam-3338	660	1	pend.m	pend.m	NOUN
ejpam-3338	660	2	%	%	NOUN
ejpam-3338	660	3	9	9	NUM
ejpam-3338	660	4	-	-	PUNCT
ejpam-3338	660	5	line	line	NOUN
ejpam-3338	660	6	matlab	matlab	PROPN
ejpam-3338	660	7	program	program	NOUN
ejpam-3338	660	8	pendulum	pendulum	NOUN
ejpam-3338	660	9	[	[	X
ejpam-3338	660	10	t	t	NOUN
ejpam-3338	660	11	,	,	PUNCT
ejpam-3338	660	12	z]=ode23(’pend	z]=ode23(’pend	NOUN
ejpam-3338	660	13	’	'	PUNCT
ejpam-3338	660	14	,	,	PUNCT
ejpam-3338	660	15	[	[	X
ejpam-3338	660	16	0,20	0,20	X
ejpam-3338	660	17	]	]	X
ejpam-3338	660	18	,	,	PUNCT
ejpam-3338	660	19	[	[	X
ejpam-3338	660	20	1,0	1,0	NUM
ejpam-3338	660	21	]	]	PUNCT
ejpam-3338	660	22	)	)	PUNCT
ejpam-3338	660	23	;	;	PUNCT
ejpam-3338	660	24	disp	disp	X
ejpam-3338	660	25	(	(	PUNCT
ejpam-3338	660	26	’	'	PUNCT
ejpam-3338	660	27	t	t	PROPN
ejpam-3338	660	28	col	col	PROPN
ejpam-3338	660	29	1	1	NUM
ejpam-3338	660	30	of	of	ADP
ejpam-3338	660	31	z	z	PROPN
ejpam-3338	660	32	col	col	PROPN
ejpam-3338	660	33	2	2	NUM
ejpam-3338	660	34	of	of	ADP
ejpam-3338	660	35	z	z	NOUN
ejpam-3338	660	36	’	'	PUNCT
ejpam-3338	660	37	)	)	PUNCT
ejpam-3338	660	38	;	;	PUNCT
ejpam-3338	660	39	disp	disp	NOUN
ejpam-3338	660	40	(	(	PUNCT
ejpam-3338	660	41	[	[	X
ejpam-3338	660	42	t	t	X
ejpam-3338	660	43	z	z	X
ejpam-3338	660	44	]	]	X
ejpam-3338	660	45	)	)	PUNCT
ejpam-3338	660	46	;	;	PUNCT
ejpam-3338	660	47	plot	plot	NOUN
ejpam-3338	660	48	(	(	PUNCT
ejpam-3338	660	49	t	t	PROPN
ejpam-3338	660	50	,	,	PUNCT
ejpam-3338	660	51	z(:,1	z(:,1	NOUN
ejpam-3338	660	52	)	)	PUNCT
ejpam-3338	660	53	,	,	PUNCT
ejpam-3338	660	54	t	t	PROPN
ejpam-3338	660	55	,	,	PUNCT
ejpam-3338	660	56	z	z	NOUN
ejpam-3338	660	57	(:	(:	NOUN
ejpam-3338	660	58	,	,	PUNCT
ejpam-3338	660	59	2	2	NUM
ejpam-3338	660	60	)	)	PUNCT
ejpam-3338	660	61	)	)	PUNCT
ejpam-3338	660	62	;	;	PUNCT
ejpam-3338	660	63	xlabel(′t′	xlabel(′t′	PROPN
ejpam-3338	660	64	)	)	PUNCT
ejpam-3338	660	65	;	;	PUNCT
ejpam-3338	660	66	ylabel(′col	ylabel(′col	PROPN
ejpam-3338	660	67	1	1	NUM
ejpam-3338	660	68	of	of	ADP
ejpam-3338	660	69	z	z	PROPN
ejpam-3338	660	70	&	&	CCONJ
ejpam-3338	660	71	col	col	PROPN
ejpam-3338	660	72	2	2	NUM
ejpam-3338	660	73	of	of	ADP
ejpam-3338	660	74	z′	z′	NUM
ejpam-3338	660	75	)	)	PUNCT
ejpam-3338	660	76	;	;	PUNCT
ejpam-3338	660	77	s.	s.	PROPN
ejpam-3338	660	78	k.sen	k.sen	PROPN
ejpam-3338	660	79	,	,	PUNCT
ejpam-3338	660	80	j.	j.	PROPN
ejpam-3338	660	81	v.	v.	PROPN
ejpam-3338	660	82	devi	devi	PROPN
ejpam-3338	660	83	,	,	PUNCT
ejpam-3338	660	84	r.v.g	r.v.g	NOUN
ejpam-3338	660	85	.	.	PUNCT
ejpam-3338	661	1	r.	r.	PROPN
ejpam-3338	661	2	kumar	kumar	PROPN
ejpam-3338	661	3	/	/	SYM
ejpam-3338	661	4	eur	eur	PROPN
ejpam-3338	661	5	.	.	PUNCT
ejpam-3338	662	1	j.	j.	PROPN
ejpam-3338	662	2	pure	pure	PROPN
ejpam-3338	662	3	appl	appl	PROPN
ejpam-3338	662	4	.	.	PROPN
ejpam-3338	662	5	math	math	PROPN
ejpam-3338	662	6	,	,	PUNCT
ejpam-3338	662	7	11	11	NUM
ejpam-3338	662	8	(	(	PUNCT
ejpam-3338	662	9	3	3	NUM
ejpam-3338	662	10	)	)	PUNCT
ejpam-3338	662	11	(	(	PUNCT
ejpam-3338	662	12	2018	2018	NUM
ejpam-3338	662	13	)	)	PUNCT
ejpam-3338	662	14	,	,	PUNCT
ejpam-3338	662	15	1058	1058	NUM
ejpam-3338	662	16	-	-	SYM
ejpam-3338	662	17	1099	1099	NUM
ejpam-3338	662	18	1085	1085	NUM
ejpam-3338	662	19	figure	figure	NOUN
ejpam-3338	662	20	(	(	PUNCT
ejpam-3338	662	21	2	2	NUM
ejpam-3338	662	22	)	)	PUNCT
ejpam-3338	662	23	plot(z(:,1),z(:,2	plot(z(:,1),z(:,2	PROPN
ejpam-3338	662	24	)	)	PUNCT
ejpam-3338	662	25	)	)	PUNCT
ejpam-3338	662	26	;	;	PUNCT
ejpam-3338	662	27	xlabel(’displacement’);ylabel(’velocity	xlabel(’displacement’);ylabel(’velocity	PROPN
ejpam-3338	662	28	’	'	PUNCT
ejpam-3338	662	29	)	)	PUNCT
ejpam-3338	662	30	;	;	PUNCT
ejpam-3338	662	31	title(’phase	title(’phase	NUM
ejpam-3338	662	32	plane	plane	NOUN
ejpam-3338	662	33	plot	plot	NOUN
ejpam-3338	662	34	’	'	PUNCT
ejpam-3338	662	35	)	)	PUNCT
ejpam-3338	662	36	;	;	PUNCT
ejpam-3338	663	1	%	%	X
ejpam-3338	663	2	usage	usage	NOUN
ejpam-3338	663	3	type	type	NOUN
ejpam-3338	663	4	pendulum	pendulum	NOUN
ejpam-3338	663	5	in	in	ADP
ejpam-3338	663	6	command	command	NOUN
ejpam-3338	663	7	window	window	NOUN
ejpam-3338	663	8	%	%	INTJ
ejpam-3338	663	9	pend.m	pend.m	NOUN
ejpam-3338	663	10	matlab	matlab	PROPN
ejpam-3338	663	11	function	function	VERB
ejpam-3338	663	12	sub	sub	ADJ
ejpam-3338	663	13	-	-	ADJ
ejpam-3338	663	14	program	program	ADJ
ejpam-3338	663	15	function	function	NOUN
ejpam-3338	663	16	zdot	zdot	NOUN
ejpam-3338	663	17	=	=	NOUN
ejpam-3338	663	18	pend(t	pend(t	NOUN
ejpam-3338	663	19	,	,	PUNCT
ejpam-3338	663	20	z	z	NOUN
ejpam-3338	663	21	)	)	PUNCT
ejpam-3338	663	22	;	;	PUNCT
ejpam-3338	663	23	wsq=1.56	wsq=1.56	NUM
ejpam-3338	663	24	;	;	PUNCT
ejpam-3338	663	25	zdot=[z(2	zdot=[z(2	NUM
ejpam-3338	663	26	)	)	PUNCT
ejpam-3338	663	27	;	;	PUNCT
ejpam-3338	663	28	-wsq*sin(z(1	-wsq*sin(z(1	NUM
ejpam-3338	663	29	)	)	PUNCT
ejpam-3338	663	30	)	)	PUNCT
ejpam-3338	664	1	]	]	PUNCT
ejpam-3338	664	2	;	;	PUNCT
ejpam-3338	664	3	>	>	PUNCT
ejpam-3338	664	4	>	>	X
ejpam-3338	664	5	pendulum	pendulum	NOUN
ejpam-3338	664	6	integer	integer	NOUN
ejpam-3338	664	7	-	-	PUNCT
ejpam-3338	664	8	order	order	NOUN
ejpam-3338	664	9	alpha=1	alpha=1	NOUN
ejpam-3338	664	10	)	)	PUNCT
ejpam-3338	664	11	t	t	PROPN
ejpam-3338	664	12	col	col	PROPN
ejpam-3338	664	13	1	1	NUM
ejpam-3338	664	14	of	of	ADP
ejpam-3338	664	15	z	z	PROPN
ejpam-3338	664	16	col	col	PROPN
ejpam-3338	664	17	2	2	NUM
ejpam-3338	664	18	of	of	ADP
ejpam-3338	664	19	z	z	NOUN
ejpam-3338	664	20	0	0	NUM
ejpam-3338	665	1	1.0000	1.0000	NUM
ejpam-3338	665	2	0	0	NUM
ejpam-3338	665	3	0.0001	0.0001	NUM
ejpam-3338	665	4	1.0000	1.0000	NUM
ejpam-3338	665	5	−	−	PROPN
ejpam-3338	665	6	0.0001	0.0001	NUM
ejpam-3338	665	7	0.0004	0.0004	NUM
ejpam-3338	665	8	1.0000	1.0000	NUM
ejpam-3338	665	9	−	−	NUM
ejpam-3338	665	10	0.0005	0.0005	NUM
ejpam-3338	665	11	0.0019	0.0019	NUM
ejpam-3338	665	12	1.0000	1.0000	NUM
ejpam-3338	665	13	−	−	PROPN
ejpam-3338	665	14	0.0025	0.0025	NUM
ejpam-3338	665	15	0.0095	0.0095	NUM
ejpam-3338	665	16	0.9999	0.9999	NUM
ejpam-3338	665	17	−	−	NUM
ejpam-3338	665	18	0.0125	0.0125	NUM
ejpam-3338	665	19	19.3178	19.3178	NUM
ejpam-3338	665	20	−	−	NOUN
ejpam-3338	665	21	0.7918	0.7918	NUM
ejpam-3338	665	22	0.6916	0.6916	NUM
ejpam-3338	665	23	19.5401	19.5401	NUM
ejpam-3338	665	24	−	−	PROPN
ejpam-3338	665	25	0.6120	0.6120	NUM
ejpam-3338	665	26	0.9163	0.9163	NUM
ejpam-3338	665	27	19.7743	19.7743	NUM
ejpam-3338	665	28	−	−	NOUN
ejpam-3338	665	29	0.3755	0.3755	NUM
ejpam-3338	665	30	1.0899	1.0899	NUM
ejpam-3338	665	31	19.9454	19.9454	NUM
ejpam-3338	665	32	−	−	PROPN
ejpam-3338	665	33	0.1820	0.1820	NUM
ejpam-3338	665	34	1.1634	1.1634	NUM
ejpam-3338	665	35	20.0000	20.0000	NUM
ejpam-3338	665	36	−	−	PROPN
ejpam-3338	665	37	0.1181	0.1181	NUM
ejpam-3338	665	38	1.17614	1.17614	NUM
ejpam-3338	665	39	s.	s.	PROPN
ejpam-3338	665	40	k.sen	k.sen	PROPN
ejpam-3338	665	41	,	,	PUNCT
ejpam-3338	665	42	j.	j.	PROPN
ejpam-3338	665	43	v.	v.	PROPN
ejpam-3338	665	44	devi	devi	PROPN
ejpam-3338	665	45	,	,	PUNCT
ejpam-3338	665	46	r.v.g	r.v.g	NOUN
ejpam-3338	665	47	.	.	PUNCT
ejpam-3338	666	1	r.	r.	PROPN
ejpam-3338	666	2	kumar	kumar	PROPN
ejpam-3338	666	3	/	/	SYM
ejpam-3338	666	4	eur	eur	PROPN
ejpam-3338	666	5	.	.	PUNCT
ejpam-3338	667	1	j.	j.	PROPN
ejpam-3338	667	2	pure	pure	PROPN
ejpam-3338	667	3	appl	appl	PROPN
ejpam-3338	667	4	.	.	PROPN
ejpam-3338	667	5	math	math	PROPN
ejpam-3338	667	6	,	,	PUNCT
ejpam-3338	667	7	11	11	NUM
ejpam-3338	667	8	(	(	PUNCT
ejpam-3338	667	9	3	3	NUM
ejpam-3338	667	10	)	)	PUNCT
ejpam-3338	667	11	(	(	PUNCT
ejpam-3338	667	12	2018	2018	NUM
ejpam-3338	667	13	)	)	PUNCT
ejpam-3338	667	14	,	,	PUNCT
ejpam-3338	667	15	1058	1058	NUM
ejpam-3338	667	16	-	-	SYM
ejpam-3338	667	17	1099	1099	NUM
ejpam-3338	667	18	1086	1086	NUM
ejpam-3338	667	19	fig	fig	NOUN
ejpam-3338	667	20	.	.	PUNCT
ejpam-3338	668	1	4	4	NUM
ejpam-3338	668	2	the	the	DET
ejpam-3338	668	3	graph	graph	NOUN
ejpam-3338	668	4	of	of	ADP
ejpam-3338	668	5	z1	z1	NOUN
ejpam-3338	668	6	,	,	PUNCT
ejpam-3338	668	7	z2	z2	NOUN
ejpam-3338	668	8	for	for	ADP
ejpam-3338	668	9	time	time	NOUN
ejpam-3338	668	10	t=0	t=0	PROPN
ejpam-3338	668	11	to	to	ADP
ejpam-3338	668	12	20	20	NUM
ejpam-3338	668	13	.	.	PUNCT
ejpam-3338	668	14	pendulumfde.m	pendulumfde.m	PROPN
ejpam-3338	668	15	matlab	matlab	PROPN
ejpam-3338	668	16	program	program	NOUN
ejpam-3338	668	17	and	and	CCONJ
ejpam-3338	668	18	the	the	DET
ejpam-3338	668	19	matlab	matlab	PROPN
ejpam-3338	668	20	function	function	PROPN
ejpam-3338	668	21	subprogram	subprogram	PROPN
ejpam-3338	668	22	pend	pend	PROPN
ejpam-3338	668	23	are	be	AUX
ejpam-3338	668	24	as	as	SCONJ
ejpam-3338	668	25	follows	follow	VERB
ejpam-3338	668	26	.	.	PUNCT
ejpam-3338	669	1	one	one	PRON
ejpam-3338	669	2	can	can	AUX
ejpam-3338	669	3	change	change	VERB
ejpam-3338	669	4	/	/	SYM
ejpam-3338	669	5	vary	vary	VERB
ejpam-3338	669	6	the	the	DET
ejpam-3338	669	7	value	value	NOUN
ejpam-3338	669	8	of	of	ADP
ejpam-3338	669	9	alpha	alpha	NOUN
ejpam-3338	669	10	(	(	PUNCT
ejpam-3338	669	11	α	α	NOUN
ejpam-3338	669	12	)	)	PUNCT
ejpam-3338	669	13	in	in	ADP
ejpam-3338	669	14	the	the	DET
ejpam-3338	669	15	program	program	NOUN
ejpam-3338	669	16	and	and	CCONJ
ejpam-3338	669	17	observe	observe	VERB
ejpam-3338	669	18	for	for	ADP
ejpam-3338	669	19	himself	himself	PRON
ejpam-3338	669	20	the	the	DET
ejpam-3338	669	21	damped	damped	ADJ
ejpam-3338	669	22	motion	motion	NOUN
ejpam-3338	669	23	of	of	ADP
ejpam-3338	669	24	the	the	DET
ejpam-3338	669	25	pendulum	pendulum	NOUN
ejpam-3338	669	26	for	for	ADP
ejpam-3338	669	27	each	each	DET
ejpam-3338	669	28	alpha	alpha	NOUN
ejpam-3338	669	29	.	.	PUNCT
ejpam-3338	670	1	global	global	ADJ
ejpam-3338	670	2	h	h	NOUN
ejpam-3338	670	3	y0	y0	PROPN
ejpam-3338	670	4	;	;	PUNCT
ejpam-3338	670	5	%	%	ADP
ejpam-3338	670	6	alpha=1	alpha=1	NUM
ejpam-3338	670	7	%	%	INTJ
ejpam-3338	670	8	alpha=.9	alpha=.9	NOUN
ejpam-3338	670	9	%	%	NOUN
ejpam-3338	670	10	alpha=.99	alpha=.99	NOUN
ejpam-3338	670	11	%	%	NOUN
ejpam-3338	670	12	alpha=.98	alpha=.98	NUM
ejpam-3338	670	13	%	%	NOUN
ejpam-3338	670	14	alpha=.97	alpha=.97	NOUN
ejpam-3338	670	15	h=.1739	h=.1739	PROPN
ejpam-3338	670	16	;	;	PUNCT
ejpam-3338	670	17	y0=[1;0	y0=[1;0	PROPN
ejpam-3338	670	18	]	]	X
ejpam-3338	670	19	;	;	PUNCT
ejpam-3338	670	20	alpha=.97	alpha=.97	NOUN
ejpam-3338	670	21	,	,	PUNCT
ejpam-3338	670	22	[	[	X
ejpam-3338	670	23	t	t	PROPN
ejpam-3338	670	24	,	,	PUNCT
ejpam-3338	670	25	z]=fde12s(alpha,’pend’,0,20	z]=fde12s(alpha,’pend’,0,20	PROPN
ejpam-3338	670	26	)	)	PUNCT
ejpam-3338	670	27	;	;	PUNCT
ejpam-3338	671	1	%	%	X
ejpam-3338	671	2	global	global	ADJ
ejpam-3338	671	3	h	h	NOUN
ejpam-3338	671	4	y0	y0	PROPN
ejpam-3338	671	5	;	;	PUNCT
ejpam-3338	671	6	%	%	X
ejpam-3338	671	7	h=1	h=1	NOUN
ejpam-3338	671	8	;	;	PUNCT
ejpam-3338	671	9	y0=[1;0	y0=[1;0	PROPN
ejpam-3338	671	10	]	]	SYM
ejpam-3338	671	11	disp(alpha	disp(alpha	PROPN
ejpam-3338	671	12	’	'	PUNCT
ejpam-3338	671	13	)	)	PUNCT
ejpam-3338	671	14	;	;	PUNCT
ejpam-3338	671	15	disp	disp	X
ejpam-3338	671	16	(	(	PUNCT
ejpam-3338	671	17	’	'	PUNCT
ejpam-3338	671	18	t	t	PROPN
ejpam-3338	671	19	col	col	PROPN
ejpam-3338	671	20	1	1	NUM
ejpam-3338	671	21	of	of	ADP
ejpam-3338	671	22	z	z	PROPN
ejpam-3338	671	23	col	col	PROPN
ejpam-3338	671	24	2	2	NUM
ejpam-3338	671	25	of	of	ADP
ejpam-3338	671	26	z	z	NOUN
ejpam-3338	671	27	’	'	PUNCT
ejpam-3338	671	28	)	)	PUNCT
ejpam-3338	671	29	;	;	PUNCT
ejpam-3338	671	30	disp	disp	NOUN
ejpam-3338	671	31	(	(	PUNCT
ejpam-3338	671	32	[	[	X
ejpam-3338	671	33	t	t	X
ejpam-3338	671	34	’	'	PUNCT
ejpam-3338	671	35	z	z	NOUN
ejpam-3338	671	36	’	'	PUNCT
ejpam-3338	671	37	]	]	PUNCT
ejpam-3338	671	38	)	)	PUNCT
ejpam-3338	671	39	;	;	PUNCT
ejpam-3338	671	40	plot	plot	NOUN
ejpam-3338	671	41	(	(	PUNCT
ejpam-3338	671	42	t’,z(1	t’,z(1	NOUN
ejpam-3338	671	43	,	,	PUNCT
ejpam-3338	671	44	:)	:)	PRON
ejpam-3338	671	45	’	'	PUNCT
ejpam-3338	671	46	,	,	PUNCT
ejpam-3338	671	47	t	t	PROPN
ejpam-3338	671	48	’	'	PUNCT
ejpam-3338	671	49	,	,	PUNCT
ejpam-3338	671	50	z(2	z(2	PROPN
ejpam-3338	671	51	,	,	PUNCT
ejpam-3338	671	52	:)	:)	NOUN
ejpam-3338	671	53	’	'	PUNCT
ejpam-3338	671	54	)	)	PUNCT
ejpam-3338	671	55	;	;	PUNCT
ejpam-3338	671	56	xlabel(’t	xlabel(’t	NUM
ejpam-3338	671	57	’	'	PUNCT
ejpam-3338	671	58	)	)	PUNCT
ejpam-3338	671	59	;	;	PUNCT
ejpam-3338	671	60	ylabel(’col	ylabel(’col	PROPN
ejpam-3338	671	61	1	1	NUM
ejpam-3338	671	62	of	of	ADP
ejpam-3338	671	63	z	z	PROPN
ejpam-3338	671	64	&	&	CCONJ
ejpam-3338	671	65	col	col	PROPN
ejpam-3338	671	66	2	2	NUM
ejpam-3338	671	67	of	of	ADP
ejpam-3338	671	68	z	z	NOUN
ejpam-3338	671	69	’	'	PUNCT
ejpam-3338	671	70	)	)	PUNCT
ejpam-3338	671	71	;	;	PUNCT
ejpam-3338	671	72	figure	figure	NOUN
ejpam-3338	671	73	(	(	PUNCT
ejpam-3338	671	74	2	2	NUM
ejpam-3338	671	75	)	)	PUNCT
ejpam-3338	671	76	plot(z(1,:),z(2	plot(z(1,:),z(2	NOUN
ejpam-3338	671	77	,	,	PUNCT
ejpam-3338	671	78	:))	:))	PROPN
ejpam-3338	671	79	;	;	PUNCT
ejpam-3338	671	80	xlabel(’displacement’);ylabel(’velocity	xlabel(’displacement’);ylabel(’velocity	PROPN
ejpam-3338	671	81	’	'	PUNCT
ejpam-3338	671	82	)	)	PUNCT
ejpam-3338	671	83	;	;	PUNCT
ejpam-3338	671	84	title(’phase	title(’phase	NUM
ejpam-3338	671	85	plane	plane	NOUN
ejpam-3338	671	86	plot	plot	NOUN
ejpam-3338	671	87	’	'	PUNCT
ejpam-3338	671	88	)	)	PUNCT
ejpam-3338	671	89	;	;	PUNCT
ejpam-3338	671	90	s.	s.	PROPN
ejpam-3338	671	91	k.sen	k.sen	PROPN
ejpam-3338	671	92	,	,	PUNCT
ejpam-3338	671	93	j.	j.	PROPN
ejpam-3338	671	94	v.	v.	PROPN
ejpam-3338	671	95	devi	devi	PROPN
ejpam-3338	671	96	,	,	PUNCT
ejpam-3338	671	97	r.v.g	r.v.g	NOUN
ejpam-3338	671	98	.	.	PUNCT
ejpam-3338	672	1	r.	r.	PROPN
ejpam-3338	672	2	kumar	kumar	PROPN
ejpam-3338	672	3	/	/	SYM
ejpam-3338	672	4	eur	eur	PROPN
ejpam-3338	672	5	.	.	PUNCT
ejpam-3338	673	1	j.	j.	PROPN
ejpam-3338	673	2	pure	pure	PROPN
ejpam-3338	673	3	appl	appl	PROPN
ejpam-3338	673	4	.	.	PROPN
ejpam-3338	673	5	math	math	PROPN
ejpam-3338	673	6	,	,	PUNCT
ejpam-3338	673	7	11	11	NUM
ejpam-3338	673	8	(	(	PUNCT
ejpam-3338	673	9	3	3	NUM
ejpam-3338	673	10	)	)	PUNCT
ejpam-3338	673	11	(	(	PUNCT
ejpam-3338	673	12	2018	2018	NUM
ejpam-3338	673	13	)	)	PUNCT
ejpam-3338	673	14	,	,	PUNCT
ejpam-3338	673	15	1058	1058	NUM
ejpam-3338	673	16	-	-	SYM
ejpam-3338	673	17	1099	1099	NUM
ejpam-3338	673	18	1087	1087	NUM
ejpam-3338	673	19	fig	fig	NOUN
ejpam-3338	673	20	.	.	PUNCT
ejpam-3338	674	1	5	5	NUM
ejpam-3338	674	2	the	the	DET
ejpam-3338	674	3	phase	phase	NOUN
ejpam-3338	674	4	-	-	PUNCT
ejpam-3338	674	5	plane	plane	NOUN
ejpam-3338	674	6	plot	plot	NOUN
ejpam-3338	674	7	displacement	displacement	NOUN
ejpam-3338	674	8	vs.	vs.	ADP
ejpam-3338	674	9	velocity	velocity	NOUN
ejpam-3338	674	10	(	(	PUNCT
ejpam-3338	674	11	observe	observe	VERB
ejpam-3338	674	12	that	that	SCONJ
ejpam-3338	674	13	there	there	PRON
ejpam-3338	674	14	are	be	VERB
ejpam-3338	674	15	rotations	rotation	NOUN
ejpam-3338	674	16	(	(	PUNCT
ejpam-3338	674	17	non	non	ADJ
ejpam-3338	674	18	-	-	ADJ
ejpam-3338	674	19	spiral	spiral	ADJ
ejpam-3338	674	20	)	)	PUNCT
ejpam-3338	674	21	.	.	PUNCT
ejpam-3338	674	22	)	)	PUNCT
ejpam-3338	675	1	%	%	INTJ
ejpam-3338	675	2	usage	usage	NOUN
ejpam-3338	675	3	function	function	NOUN
ejpam-3338	675	4	zdot	zdot	NOUN
ejpam-3338	675	5	=	=	NOUN
ejpam-3338	675	6	pend(t	pend(t	NOUN
ejpam-3338	675	7	,	,	PUNCT
ejpam-3338	675	8	z	z	NOUN
ejpam-3338	675	9	)	)	PUNCT
ejpam-3338	675	10	;	;	PUNCT
ejpam-3338	675	11	wsq=1.56	wsq=1.56	NUM
ejpam-3338	675	12	;	;	PUNCT
ejpam-3338	675	13	zdot=[z(2	zdot=[z(2	NUM
ejpam-3338	675	14	)	)	PUNCT
ejpam-3338	675	15	;	;	PUNCT
ejpam-3338	675	16	-wsq*sin(z(1	-wsq*sin(z(1	NUM
ejpam-3338	675	17	)	)	PUNCT
ejpam-3338	675	18	)	)	PUNCT
ejpam-3338	676	1	]	]	PUNCT
ejpam-3338	676	2	;	;	PUNCT
ejpam-3338	676	3	data	datum	NOUN
ejpam-3338	676	4	and	and	CCONJ
ejpam-3338	676	5	results	result	NOUN
ejpam-3338	676	6	>	>	PUNCT
ejpam-3338	676	7	>	>	X
ejpam-3338	676	8	pendulumfde	pendulumfde	ADJ
ejpam-3338	676	9	alpha	alpha	NOUN
ejpam-3338	676	10	=	=	SYM
ejpam-3338	676	11	1	1	NUM
ejpam-3338	676	12	t	t	NOUN
ejpam-3338	676	13	col	col	NOUN
ejpam-3338	676	14	1	1	NUM
ejpam-3338	676	15	of	of	ADP
ejpam-3338	676	16	z	z	PROPN
ejpam-3338	676	17	col	col	PROPN
ejpam-3338	676	18	2	2	NUM
ejpam-3338	676	19	of	of	ADP
ejpam-3338	676	20	z	z	NOUN
ejpam-3338	676	21	0	0	NUM
ejpam-3338	677	1	1.0000	1.0000	NUM
ejpam-3338	677	2	0	0	NUM
ejpam-3338	677	3	0.1739	0.1739	NUM
ejpam-3338	677	4	0.9802	0.9802	NUM
ejpam-3338	677	5	−	−	NOUN
ejpam-3338	677	6	0.2283	0.2283	NUM
ejpam-3338	677	7	0.3478	0.3478	NUM
ejpam-3338	677	8	0.9209	0.9209	NUM
ejpam-3338	677	9	−	−	NUM
ejpam-3338	677	10	0.4506	0.4506	NUM
ejpam-3338	677	11	0.5217	0.5217	NUM
ejpam-3338	677	12	0.8237	0.8237	NUM
ejpam-3338	677	13	−	−	NUM
ejpam-3338	677	14	0.6602	0.6602	NUM
ejpam-3338	678	1	0.6956	0.6956	NUM
ejpam-3338	678	2	0.6916	0.6916	NUM
ejpam-3338	678	3	−	−	ADP
ejpam-3338	678	4	0.8486	0.8486	NUM
ejpam-3338	678	5	.	.	PUNCT
ejpam-3338	678	6	.	.	PUNCT
ejpam-3338	679	1	.	.	PUNCT
ejpam-3338	680	1	19.4768	19.4768	NUM
ejpam-3338	680	2	−	−	NOUN
ejpam-3338	680	3	0.6150	0.6150	NUM
ejpam-3338	680	4	0.9634	0.9634	NUM
ejpam-3338	680	5	19.6507	19.6507	NUM
ejpam-3338	680	6	−	−	NOUN
ejpam-3338	680	7	0.4338	0.4338	NUM
ejpam-3338	680	8	1.1011	1.1011	NUM
ejpam-3338	680	9	19.8246	19.8246	NUM
ejpam-3338	680	10	−	−	PROPN
ejpam-3338	680	11	0.2324	0.2324	NUM
ejpam-3338	680	12	1.1915	1.1915	NUM
ejpam-3338	680	13	19.9985	19.9985	NUM
ejpam-3338	680	14	−	−	PROPN
ejpam-3338	680	15	0.0198	0.0198	NUM
ejpam-3338	680	16	1.2266	1.2266	NUM
ejpam-3338	680	17	s.	s.	PROPN
ejpam-3338	680	18	k.sen	k.sen	PROPN
ejpam-3338	680	19	,	,	PUNCT
ejpam-3338	680	20	j.	j.	PROPN
ejpam-3338	680	21	v.	v.	PROPN
ejpam-3338	680	22	devi	devi	PROPN
ejpam-3338	680	23	,	,	PUNCT
ejpam-3338	680	24	r.v.g	r.v.g	NOUN
ejpam-3338	680	25	.	.	PUNCT
ejpam-3338	681	1	r.	r.	PROPN
ejpam-3338	681	2	kumar	kumar	PROPN
ejpam-3338	681	3	/	/	SYM
ejpam-3338	681	4	eur	eur	PROPN
ejpam-3338	681	5	.	.	PUNCT
ejpam-3338	682	1	j.	j.	PROPN
ejpam-3338	682	2	pure	pure	PROPN
ejpam-3338	682	3	appl	appl	PROPN
ejpam-3338	682	4	.	.	PROPN
ejpam-3338	682	5	math	math	PROPN
ejpam-3338	682	6	,	,	PUNCT
ejpam-3338	682	7	11	11	NUM
ejpam-3338	682	8	(	(	PUNCT
ejpam-3338	682	9	3	3	NUM
ejpam-3338	682	10	)	)	PUNCT
ejpam-3338	682	11	(	(	PUNCT
ejpam-3338	682	12	2018	2018	NUM
ejpam-3338	682	13	)	)	PUNCT
ejpam-3338	682	14	,	,	PUNCT
ejpam-3338	682	15	1058	1058	NUM
ejpam-3338	682	16	-	-	SYM
ejpam-3338	682	17	1099	1099	NUM
ejpam-3338	682	18	1088	1088	NUM
ejpam-3338	682	19	20.0000	20.0000	NUM
ejpam-3338	682	20	−	−	PROPN
ejpam-3338	682	21	0.0180	0.0180	NUM
ejpam-3338	682	22	1.2264	1.2264	NUM
ejpam-3338	682	23	fig	fig	NOUN
ejpam-3338	682	24	.	.	PUNCT
ejpam-3338	683	1	6	6	NUM
ejpam-3338	683	2	z1	z1	VERB
ejpam-3338	683	3	,	,	PUNCT
ejpam-3338	683	4	z2	z2	NOUN
ejpam-3338	683	5	for	for	ADP
ejpam-3338	683	6	t=[0,20	t=[0,20	NOUN
ejpam-3338	683	7	]	]	PUNCT
ejpam-3338	683	8	.	.	PUNCT
ejpam-3338	684	1	α	α	X
ejpam-3338	684	2	=	=	SYM
ejpam-3338	684	3	1	1	NUM
ejpam-3338	684	4	(	(	PUNCT
ejpam-3338	684	5	non	non	ADJ
ejpam-3338	684	6	-	-	ADJ
ejpam-3338	684	7	fractional	fractional	ADJ
ejpam-3338	684	8	no	no	DET
ejpam-3338	684	9	damping	damping	NOUN
ejpam-3338	684	10	as	as	ADP
ejpam-3338	684	11	in	in	ADP
ejpam-3338	684	12	the	the	DET
ejpam-3338	684	13	foregoing	forego	VERB
ejpam-3338	684	14	simple	simple	ADJ
ejpam-3338	684	15	pendulum	pendulum	NOUN
ejpam-3338	684	16	)	)	PUNCT
ejpam-3338	684	17	fig	fig	NOUN
ejpam-3338	684	18	.	.	PUNCT
ejpam-3338	685	1	7	7	NUM
ejpam-3338	685	2	phase	phase	NOUN
ejpam-3338	685	3	-	-	PUNCT
ejpam-3338	685	4	plane	plane	NOUN
ejpam-3338	685	5	plot	plot	NOUN
ejpam-3338	685	6	for	for	ADP
ejpam-3338	685	7	alpha	alpha	NOUN
ejpam-3338	685	8	=	=	SYM
ejpam-3338	685	9	1	1	NUM
ejpam-3338	685	10	(	(	PUNCT
ejpam-3338	685	11	the	the	DET
ejpam-3338	685	12	graph	graph	NOUN
ejpam-3338	685	13	goes	go	VERB
ejpam-3338	685	14	round	round	ADV
ejpam-3338	685	15	and	and	CCONJ
ejpam-3338	685	16	round	round	VERB
ejpam-3338	685	17	on	on	ADP
ejpam-3338	685	18	the	the	DET
ejpam-3338	685	19	same	same	ADJ
ejpam-3338	685	20	closed	closed	ADJ
ejpam-3338	685	21	curve	curve	NOUN
ejpam-3338	685	22	no	no	DET
ejpam-3338	685	23	spiral	spiral	NOUN
ejpam-3338	685	24	)	)	PUNCT
ejpam-3338	685	25	s.	s.	PROPN
ejpam-3338	685	26	k.sen	k.sen	PROPN
ejpam-3338	685	27	,	,	PUNCT
ejpam-3338	685	28	j.	j.	PROPN
ejpam-3338	685	29	v.	v.	PROPN
ejpam-3338	685	30	devi	devi	PROPN
ejpam-3338	685	31	,	,	PUNCT
ejpam-3338	685	32	r.v.g	r.v.g	NOUN
ejpam-3338	685	33	.	.	PUNCT
ejpam-3338	686	1	r.	r.	PROPN
ejpam-3338	686	2	kumar	kumar	PROPN
ejpam-3338	686	3	/	/	SYM
ejpam-3338	686	4	eur	eur	PROPN
ejpam-3338	686	5	.	.	PUNCT
ejpam-3338	687	1	j.	j.	PROPN
ejpam-3338	687	2	pure	pure	PROPN
ejpam-3338	687	3	appl	appl	PROPN
ejpam-3338	687	4	.	.	PROPN
ejpam-3338	687	5	math	math	PROPN
ejpam-3338	687	6	,	,	PUNCT
ejpam-3338	687	7	11	11	NUM
ejpam-3338	687	8	(	(	PUNCT
ejpam-3338	687	9	3	3	NUM
ejpam-3338	687	10	)	)	PUNCT
ejpam-3338	687	11	(	(	PUNCT
ejpam-3338	687	12	2018	2018	NUM
ejpam-3338	687	13	)	)	PUNCT
ejpam-3338	687	14	,	,	PUNCT
ejpam-3338	687	15	1058	1058	NUM
ejpam-3338	687	16	-	-	SYM
ejpam-3338	687	17	1099	1099	NUM
ejpam-3338	687	18	1089	1089	NUM
ejpam-3338	687	19	alpha	alpha	NOUN
ejpam-3338	687	20	=	=	SYM
ejpam-3338	687	21	0.9900	0.9900	NUM
ejpam-3338	687	22	t	t	NOUN
ejpam-3338	687	23	col	col	NOUN
ejpam-3338	687	24	1	1	NUM
ejpam-3338	687	25	of	of	ADP
ejpam-3338	687	26	z	z	PROPN
ejpam-3338	687	27	col	col	PROPN
ejpam-3338	687	28	2	2	NUM
ejpam-3338	687	29	of	of	ADP
ejpam-3338	687	30	z	z	NOUN
ejpam-3338	687	31	0	0	NUM
ejpam-3338	688	1	1.0000	1.0000	NUM
ejpam-3338	688	2	0	0	NUM
ejpam-3338	688	3	0.1739	0.1739	NUM
ejpam-3338	688	4	0.9792	0.9792	NUM
ejpam-3338	688	5	−	−	NUM
ejpam-3338	688	6	0.2333	0.2333	NUM
ejpam-3338	688	7	0.3478	0.3478	NUM
ejpam-3338	688	8	0.9178	0.9178	NUM
ejpam-3338	688	9	−	−	NOUN
ejpam-3338	688	10	0.4570	0.4570	NUM
ejpam-3338	688	11	0.5217	0.5217	NUM
ejpam-3338	688	12	0.8184	0.8184	NUM
ejpam-3338	688	13	−	−	ADP
ejpam-3338	688	14	0.6661	0.6661	NUM
ejpam-3338	688	15	0.6956	0.6956	NUM
ejpam-3338	688	16	0.6842	0.6842	NUM
ejpam-3338	688	17	−	−	PROPN
ejpam-3338	688	18	0.8525	0.8525	NUM
ejpam-3338	688	19	.	.	PUNCT
ejpam-3338	688	20	.	.	PUNCT
ejpam-3338	688	21	.	.	PUNCT
ejpam-3338	689	1	19.4768	19.4768	NUM
ejpam-3338	690	1	−	−	NOUN
ejpam-3338	690	2	0.0901	0.0901	NUM
ejpam-3338	690	3	0.8556	0.8556	NUM
ejpam-3338	690	4	19.6507	19.6507	NUM
ejpam-3338	690	5	0.0610	0.0610	NUM
ejpam-3338	691	1	0.8569	0.8569	NUM
ejpam-3338	691	2	19.8246	19.8246	NUM
ejpam-3338	691	3	0.2083	0.2083	NUM
ejpam-3338	691	4	0.8173	0.8173	NUM
ejpam-3338	691	5	19.9985	19.9985	NUM
ejpam-3338	691	6	0.3447	0.3447	NUM
ejpam-3338	691	7	0.7395	0.7395	NUM
ejpam-3338	691	8	20.0000	20.0000	NUM
ejpam-3338	691	9	0.3458	0.3458	NUM
ejpam-3338	691	10	0.7386	0.7386	NUM
ejpam-3338	691	11	fig	fig	NOUN
ejpam-3338	691	12	.	.	PUNCT
ejpam-3338	691	13	8	8	NUM
ejpam-3338	691	14	z1	z1	VERB
ejpam-3338	691	15	,	,	PUNCT
ejpam-3338	691	16	z2	z2	PROPN
ejpam-3338	691	17	for	for	ADP
ejpam-3338	691	18	alpha=.99	alpha=.99	PROPN
ejpam-3338	691	19	(	(	PUNCT
ejpam-3338	691	20	observe	observe	VERB
ejpam-3338	691	21	that	that	SCONJ
ejpam-3338	691	22	due	due	ADP
ejpam-3338	691	23	to	to	ADP
ejpam-3338	691	24	slight	slight	ADJ
ejpam-3338	691	25	damping	damp	VERB
ejpam-3338	691	26	(	(	PUNCT
ejpam-3338	691	27	since	since	SCONJ
ejpam-3338	691	28	alpha	alpha	NOUN
ejpam-3338	691	29	slightly	slightly	ADV
ejpam-3338	691	30	reduced	reduce	VERB
ejpam-3338	691	31	)	)	PUNCT
ejpam-3338	691	32	the	the	DET
ejpam-3338	691	33	amplitudes	amplitude	NOUN
ejpam-3338	691	34	decrease	decrease	VERB
ejpam-3338	691	35	gradually	gradually	ADV
ejpam-3338	691	36	)	)	PUNCT
ejpam-3338	691	37	>	>	PUNCT
ejpam-3338	691	38	>	>	X
ejpam-3338	691	39	pendulumfde	pendulumfde	PROPN
ejpam-3338	691	40	fig.9	fig.9	ADJ
ejpam-3338	691	41	phase	phase	NOUN
ejpam-3338	691	42	-	-	PUNCT
ejpam-3338	691	43	plane	plane	NOUN
ejpam-3338	691	44	plot	plot	NOUN
ejpam-3338	691	45	(	(	PUNCT
ejpam-3338	691	46	observe	observe	VERB
ejpam-3338	691	47	that	that	SCONJ
ejpam-3338	691	48	the	the	DET
ejpam-3338	691	49	graph	graph	NOUN
ejpam-3338	691	50	(	(	PUNCT
ejpam-3338	691	51	line	line	NOUN
ejpam-3338	691	52	goes	go	VERB
ejpam-3338	691	53	round	round	ADV
ejpam-3338	691	54	and	and	CCONJ
ejpam-3338	691	55	round	round	ADJ
ejpam-3338	691	56	with	with	ADP
ejpam-3338	691	57	successive	successive	ADJ
ejpam-3338	691	58	decrease	decrease	NOUN
ejpam-3338	691	59	in	in	ADP
ejpam-3338	691	60	radius	radius	NOUN
ejpam-3338	691	61	due	due	ADP
ejpam-3338	691	62	to	to	ADP
ejpam-3338	691	63	slight	slight	ADJ
ejpam-3338	691	64	damping	damp	VERB
ejpam-3338	691	65	spiral	spiral	ADJ
ejpam-3338	691	66	formation	formation	NOUN
ejpam-3338	691	67	)	)	PUNCT
ejpam-3338	692	1	s.	s.	PROPN
ejpam-3338	692	2	k.sen	k.sen	PROPN
ejpam-3338	692	3	,	,	PUNCT
ejpam-3338	692	4	j.	j.	PROPN
ejpam-3338	692	5	v.	v.	PROPN
ejpam-3338	692	6	devi	devi	PROPN
ejpam-3338	692	7	,	,	PUNCT
ejpam-3338	692	8	r.v.g	r.v.g	NOUN
ejpam-3338	692	9	.	.	PUNCT
ejpam-3338	693	1	r.	r.	PROPN
ejpam-3338	693	2	kumar	kumar	PROPN
ejpam-3338	693	3	/	/	SYM
ejpam-3338	693	4	eur	eur	PROPN
ejpam-3338	693	5	.	.	PUNCT
ejpam-3338	694	1	j.	j.	PROPN
ejpam-3338	694	2	pure	pure	PROPN
ejpam-3338	694	3	appl	appl	PROPN
ejpam-3338	694	4	.	.	PROPN
ejpam-3338	694	5	math	math	PROPN
ejpam-3338	694	6	,	,	PUNCT
ejpam-3338	694	7	11	11	NUM
ejpam-3338	694	8	(	(	PUNCT
ejpam-3338	694	9	3	3	NUM
ejpam-3338	694	10	)	)	PUNCT
ejpam-3338	694	11	(	(	PUNCT
ejpam-3338	694	12	2018	2018	NUM
ejpam-3338	694	13	)	)	PUNCT
ejpam-3338	694	14	,	,	PUNCT
ejpam-3338	694	15	1058	1058	NUM
ejpam-3338	694	16	-	-	SYM
ejpam-3338	694	17	1099	1099	NUM
ejpam-3338	694	18	1090	1090	NUM
ejpam-3338	694	19	α=	α=	NUM
ejpam-3338	694	20	0.9800	0.9800	NUM
ejpam-3338	694	21	t	t	NOUN
ejpam-3338	694	22	col	col	NOUN
ejpam-3338	694	23	1	1	NUM
ejpam-3338	694	24	of	of	ADP
ejpam-3338	694	25	z	z	PROPN
ejpam-3338	694	26	col	col	PROPN
ejpam-3338	694	27	2	2	NUM
ejpam-3338	694	28	of	of	ADP
ejpam-3338	694	29	z	z	NOUN
ejpam-3338	694	30	0	0	NUM
ejpam-3338	695	1	1.0000	1.0000	NUM
ejpam-3338	695	2	0	0	NUM
ejpam-3338	695	3	0.1739	0.1739	NUM
ejpam-3338	695	4	0.9781	0.9781	NUM
ejpam-3338	695	5	−	−	NUM
ejpam-3338	695	6	0.2384	0.2384	NUM
ejpam-3338	695	7	0.3478	0.3478	NUM
ejpam-3338	695	8	0.9147	0.9147	NUM
ejpam-3338	695	9	−	−	PROPN
ejpam-3338	695	10	0.4634	0.4634	NUM
ejpam-3338	695	11	0.5217	0.5217	NUM
ejpam-3338	695	12	0.8129	0.8129	NUM
ejpam-3338	695	13	−	−	NUM
ejpam-3338	695	14	0.6720	0.6720	NUM
ejpam-3338	695	15	0.6956	0.6956	NUM
ejpam-3338	695	16	0.6767	0.6767	NUM
ejpam-3338	695	17	−	−	NOUN
ejpam-3338	695	18	0.8563	0.8563	NUM
ejpam-3338	695	19	0.8695	0.8695	NUM
ejpam-3338	695	20	0.5115	0.5115	NUM
ejpam-3338	695	21	−	−	PROPN
ejpam-3338	695	22	1.0069	1.0069	NUM
ejpam-3338	695	23	.	.	PUNCT
ejpam-3338	695	24	.	.	PUNCT
ejpam-3338	696	1	.	.	PUNCT
ejpam-3338	697	1	19.4768	19.4768	NUM
ejpam-3338	698	1	0.1044	0.1044	NUM
ejpam-3338	698	2	0.5781	0.5781	NUM
ejpam-3338	698	3	19.6507	19.6507	NUM
ejpam-3338	698	4	0.2017	0.2017	NUM
ejpam-3338	698	5	0.5322	0.5322	NUM
ejpam-3338	698	6	19.8246	19.8246	NUM
ejpam-3338	698	7	0.2881	0.2881	NUM
ejpam-3338	698	8	0.4619	0.4619	NUM
ejpam-3338	698	9	19.9985	19.9985	NUM
ejpam-3338	698	10	0.3597	0.3597	NUM
ejpam-3338	698	11	0.3713	0.3713	NUM
ejpam-3338	698	12	20.0000	20.0000	NUM
ejpam-3338	698	13	0.3602	0.3602	NUM
ejpam-3338	698	14	0.3704	0.3704	NUM
ejpam-3338	698	15	fig.10	fig.10	DET
ejpam-3338	698	16	z1	z1	VERB
ejpam-3338	698	17	,	,	PUNCT
ejpam-3338	698	18	z2	z2	PROPN
ejpam-3338	698	19	for	for	ADP
ejpam-3338	698	20	alpha=.98	alpha=.98	NOUN
ejpam-3338	698	21	(	(	PUNCT
ejpam-3338	698	22	observe	observe	VERB
ejpam-3338	698	23	that	that	SCONJ
ejpam-3338	698	24	due	due	ADJ
ejpam-3338	698	25	to	to	ADP
ejpam-3338	698	26	further	far	ADV
ejpam-3338	698	27	reduced	reduce	VERB
ejpam-3338	698	28	value	value	NOUN
ejpam-3338	698	29	of	of	ADP
ejpam-3338	698	30	alpha	alpha	NOUN
ejpam-3338	698	31	the	the	DET
ejpam-3338	698	32	amplitudes	amplitude	NOUN
ejpam-3338	698	33	decrease	decrease	VERB
ejpam-3338	698	34	still	still	ADV
ejpam-3338	698	35	further	far	ADV
ejpam-3338	698	36	)	)	PUNCT
ejpam-3338	698	37	fig	fig	NOUN
ejpam-3338	698	38	.	.	PUNCT
ejpam-3338	699	1	11	11	NUM
ejpam-3338	699	2	phase	phase	NOUN
ejpam-3338	699	3	-	-	PUNCT
ejpam-3338	699	4	plane	plane	NOUN
ejpam-3338	699	5	plot	plot	NOUN
ejpam-3338	699	6	for	for	ADP
ejpam-3338	699	7	alpha=.98	alpha=.98	NUM
ejpam-3338	699	8	;	;	PUNCT
ejpam-3338	699	9	a	a	DET
ejpam-3338	699	10	spiral	spiral	ADJ
ejpam-3338	699	11	converging	converging	NOUN
ejpam-3338	699	12	gradually	gradually	ADV
ejpam-3338	699	13	.	.	PUNCT
ejpam-3338	700	1	alpha	alpha	NOUN
ejpam-3338	700	2	=	=	SYM
ejpam-3338	701	1	0.9700	0.9700	NUM
ejpam-3338	701	2	t	t	NOUN
ejpam-3338	701	3	col	col	NOUN
ejpam-3338	701	4	1	1	NUM
ejpam-3338	701	5	of	of	ADP
ejpam-3338	701	6	z	z	PROPN
ejpam-3338	701	7	col	col	PROPN
ejpam-3338	701	8	2	2	NUM
ejpam-3338	701	9	of	of	ADP
ejpam-3338	701	10	z	z	PROPN
ejpam-3338	701	11	s.	s.	PROPN
ejpam-3338	701	12	k.sen	k.sen	PROPN
ejpam-3338	701	13	,	,	PUNCT
ejpam-3338	701	14	j.	j.	PROPN
ejpam-3338	701	15	v.	v.	PROPN
ejpam-3338	701	16	devi	devi	PROPN
ejpam-3338	701	17	,	,	PUNCT
ejpam-3338	701	18	r.v.g	r.v.g	NOUN
ejpam-3338	701	19	.	.	PUNCT
ejpam-3338	702	1	r.	r.	PROPN
ejpam-3338	702	2	kumar	kumar	PROPN
ejpam-3338	702	3	/	/	SYM
ejpam-3338	702	4	eur	eur	PROPN
ejpam-3338	702	5	.	.	PUNCT
ejpam-3338	703	1	j.	j.	PROPN
ejpam-3338	703	2	pure	pure	PROPN
ejpam-3338	703	3	appl	appl	PROPN
ejpam-3338	703	4	.	.	PROPN
ejpam-3338	703	5	math	math	PROPN
ejpam-3338	703	6	,	,	PUNCT
ejpam-3338	703	7	11	11	NUM
ejpam-3338	703	8	(	(	PUNCT
ejpam-3338	703	9	3	3	NUM
ejpam-3338	703	10	)	)	PUNCT
ejpam-3338	703	11	(	(	PUNCT
ejpam-3338	703	12	2018	2018	NUM
ejpam-3338	703	13	)	)	PUNCT
ejpam-3338	703	14	,	,	PUNCT
ejpam-3338	703	15	1058	1058	NUM
ejpam-3338	703	16	-	-	SYM
ejpam-3338	703	17	1099	1099	NUM
ejpam-3338	703	18	1091	1091	NUM
ejpam-3338	703	19	0	0	NUM
ejpam-3338	704	1	1.0000	1.0000	NUM
ejpam-3338	704	2	0	0	NUM
ejpam-3338	704	3	0.1739	0.1739	NUM
ejpam-3338	704	4	0.9771	0.9771	NUM
ejpam-3338	704	5	−	−	NOUN
ejpam-3338	704	6	0.2436	0.2436	NUM
ejpam-3338	704	7	0.1739	0.1739	NUM
ejpam-3338	704	8	0.9771	0.9771	NUM
ejpam-3338	704	9	−	−	NOUN
ejpam-3338	704	10	0.2436	0.2436	NUM
ejpam-3338	704	11	0.3478	0.3478	NUM
ejpam-3338	704	12	0.9114	0.9114	NUM
ejpam-3338	704	13	−	−	NOUN
ejpam-3338	704	14	0.4699	0.4699	NUM
ejpam-3338	704	15	0.5217	0.5217	NUM
ejpam-3338	704	16	0.8073	0.8073	NUM
ejpam-3338	704	17	−	−	NOUN
ejpam-3338	704	18	0.6778	0.6778	NUM
ejpam-3338	704	19	0.6956	0.6956	NUM
ejpam-3338	704	20	0.6691	0.6691	NUM
ejpam-3338	704	21	−	−	ADP
ejpam-3338	704	22	0.8599	0.8599	NUM
ejpam-3338	704	23	.	.	PUNCT
ejpam-3338	704	24	.	.	PUNCT
ejpam-3338	705	1	.	.	PUNCT
ejpam-3338	706	1	19.4768	19.4768	NUM
ejpam-3338	706	2	0.1437	0.1437	NUM
ejpam-3338	706	3	0.3571	0.3571	NUM
ejpam-3338	706	4	19.6507	19.6507	NUM
ejpam-3338	706	5	0.2009	0.2009	NUM
ejpam-3338	706	6	0.3062	0.3062	NUM
ejpam-3338	706	7	19.8246	19.8246	NUM
ejpam-3338	706	8	0.2474	0.2474	NUM
ejpam-3338	706	9	0.2418	0.2418	NUM
ejpam-3338	706	10	19.9985	19.9985	NUM
ejpam-3338	706	11	0.2812	0.2812	NUM
ejpam-3338	706	12	0.1675	0.1675	NUM
ejpam-3338	706	13	20.0000	20.0000	NUM
ejpam-3338	706	14	0.2813	0.2813	NUM
ejpam-3338	706	15	0.1668	0.1668	NUM
ejpam-3338	706	16	fig	fig	NOUN
ejpam-3338	706	17	.	.	PUNCT
ejpam-3338	707	1	12	12	NUM
ejpam-3338	707	2	z1	z1	VERB
ejpam-3338	707	3	,	,	PUNCT
ejpam-3338	707	4	z2	z2	PROPN
ejpam-3338	707	5	for	for	ADP
ejpam-3338	707	6	alpha=.97	alpha=.97	NOUN
ejpam-3338	707	7	(	(	PUNCT
ejpam-3338	707	8	observe	observe	VERB
ejpam-3338	707	9	that	that	SCONJ
ejpam-3338	707	10	the	the	DET
ejpam-3338	707	11	amplitudes	amplitude	NOUN
ejpam-3338	707	12	decrease	decrease	VERB
ejpam-3338	707	13	more	more	ADV
ejpam-3338	707	14	sharply	sharply	ADV
ejpam-3338	707	15	since	since	SCONJ
ejpam-3338	707	16	alpha	alpha	NOUN
ejpam-3338	707	17	is	be	AUX
ejpam-3338	707	18	further	far	ADV
ejpam-3338	707	19	reduced	reduce	VERB
ejpam-3338	707	20	)	)	PUNCT
ejpam-3338	707	21	fig	fig	NOUN
ejpam-3338	707	22	.	.	PUNCT
ejpam-3338	708	1	13	13	NUM
ejpam-3338	708	2	phase	phase	NOUN
ejpam-3338	708	3	-	-	PUNCT
ejpam-3338	708	4	plane	plane	NOUN
ejpam-3338	708	5	plot	plot	NOUN
ejpam-3338	708	6	for	for	ADP
ejpam-3338	708	7	alpha=.97	alpha=.97	NOUN
ejpam-3338	708	8	(	(	PUNCT
ejpam-3338	708	9	the	the	DET
ejpam-3338	708	10	spiral	spiral	NOUN
ejpam-3338	708	11	becomes	become	VERB
ejpam-3338	708	12	shorter	short	ADJ
ejpam-3338	708	13	as	as	SCONJ
ejpam-3338	708	14	alpha	alpha	NOUN
ejpam-3338	708	15	becomes	become	VERB
ejpam-3338	708	16	smaller	small	ADJ
ejpam-3338	708	17	.	.	PUNCT
ejpam-3338	708	18	)	)	PUNCT
ejpam-3338	709	1	alpha	alpha	NOUN
ejpam-3338	709	2	=	=	PUNCT
ejpam-3338	710	1	0.9000	0.9000	NUM
ejpam-3338	710	2	t	t	NOUN
ejpam-3338	710	3	col	col	NOUN
ejpam-3338	710	4	1	1	NUM
ejpam-3338	710	5	of	of	ADP
ejpam-3338	710	6	z	z	PROPN
ejpam-3338	710	7	col	col	PROPN
ejpam-3338	710	8	2	2	NUM
ejpam-3338	710	9	of	of	ADP
ejpam-3338	710	10	z	z	NOUN
ejpam-3338	710	11	0	0	NUM
ejpam-3338	710	12	1.0000	1.0000	NUM
ejpam-3338	710	13	0	0	NUM
ejpam-3338	710	14	s.	s.	PROPN
ejpam-3338	710	15	k.sen	k.sen	PROPN
ejpam-3338	710	16	,	,	PUNCT
ejpam-3338	710	17	j.	j.	PROPN
ejpam-3338	710	18	v.	v.	PROPN
ejpam-3338	710	19	devi	devi	PROPN
ejpam-3338	710	20	,	,	PUNCT
ejpam-3338	710	21	r.v.g	r.v.g	NOUN
ejpam-3338	710	22	.	.	PUNCT
ejpam-3338	710	23	r.	r.	PROPN
ejpam-3338	710	24	kumar	kumar	PROPN
ejpam-3338	710	25	/	/	SYM
ejpam-3338	710	26	eur	eur	PROPN
ejpam-3338	710	27	.	.	PUNCT
ejpam-3338	711	1	j.	j.	PROPN
ejpam-3338	711	2	pure	pure	PROPN
ejpam-3338	711	3	appl	appl	PROPN
ejpam-3338	711	4	.	.	PROPN
ejpam-3338	711	5	math	math	PROPN
ejpam-3338	711	6	,	,	PUNCT
ejpam-3338	711	7	11	11	NUM
ejpam-3338	711	8	(	(	PUNCT
ejpam-3338	711	9	3	3	NUM
ejpam-3338	711	10	)	)	PUNCT
ejpam-3338	711	11	(	(	PUNCT
ejpam-3338	711	12	2018	2018	NUM
ejpam-3338	711	13	)	)	PUNCT
ejpam-3338	711	14	,	,	PUNCT
ejpam-3338	711	15	1058	1058	NUM
ejpam-3338	711	16	-	-	SYM
ejpam-3338	711	17	1099	1099	NUM
ejpam-3338	711	18	1092	1092	NUM
ejpam-3338	712	1	0.1739	0.1739	NUM
ejpam-3338	712	2	0.9680	0.9680	NUM
ejpam-3338	712	3	−	−	NOUN
ejpam-3338	712	4	0.2827	0.2827	NUM
ejpam-3338	712	5	0.3478	0.3478	NUM
ejpam-3338	712	6	0.8854	0.8854	NUM
ejpam-3338	712	7	−	−	NOUN
ejpam-3338	713	1	0.5161	0.5161	NUM
ejpam-3338	713	2	0.5217	0.5217	NUM
ejpam-3338	713	3	0.7644	0.7644	NUM
ejpam-3338	713	4	−	−	NUM
ejpam-3338	713	5	0.7167	0.7167	NUM
ejpam-3338	713	6	0.6956	0.6956	NUM
ejpam-3338	713	7	0.6134	0.6134	NUM
ejpam-3338	713	8	−	−	NOUN
ejpam-3338	713	9	0.8799	0.8799	NUM
ejpam-3338	713	10	0.8695	0.8695	NUM
ejpam-3338	713	11	0.4411	0.4411	NUM
ejpam-3338	713	12	−	−	PROPN
ejpam-3338	713	13	0.9986	0.9986	NUM
ejpam-3338	713	14	.	.	PUNCT
ejpam-3338	713	15	.	.	PUNCT
ejpam-3338	713	16	.	.	PUNCT
ejpam-3338	714	1	19.4768	19.4768	NUM
ejpam-3338	714	2	0.0121	0.0121	NUM
ejpam-3338	714	3	0.0014	0.0014	NUM
ejpam-3338	714	4	19.6507	19.6507	NUM
ejpam-3338	714	5	0.0128	0.0128	NUM
ejpam-3338	714	6	−	−	ADP
ejpam-3338	714	7	0.0024	0.0024	NUM
ejpam-3338	714	8	19.8246	19.8246	NUM
ejpam-3338	714	9	0.0128	0.0128	NUM
ejpam-3338	714	10	−	−	PROPN
ejpam-3338	714	11	0.0062	0.0062	NUM
ejpam-3338	714	12	19.9985	19.9985	NUM
ejpam-3338	714	13	0.0121	0.0121	NUM
ejpam-3338	714	14	−	−	NUM
ejpam-3338	714	15	0.0097	0.0097	NUM
ejpam-3338	714	16	20.0000	20.0000	NUM
ejpam-3338	714	17	0.0121	0.0121	NUM
ejpam-3338	714	18	−	−	NUM
ejpam-3338	714	19	0.0097	0.0097	NUM
ejpam-3338	714	20	fig	fig	NOUN
ejpam-3338	714	21	.	.	PUNCT
ejpam-3338	715	1	14	14	NUM
ejpam-3338	715	2	z	z	NOUN
ejpam-3338	715	3	1,z	1,z	NUM
ejpam-3338	715	4	2	2	NUM
ejpam-3338	715	5	for	for	ADP
ejpam-3338	715	6	alpha=.90	alpha=.90	NOUN
ejpam-3338	715	7	(	(	PUNCT
ejpam-3338	715	8	observe	observe	VERB
ejpam-3338	715	9	that	that	SCONJ
ejpam-3338	715	10	due	due	ADP
ejpam-3338	715	11	to	to	ADP
ejpam-3338	715	12	increased	increase	VERB
ejpam-3338	715	13	damping	damp	VERB
ejpam-3338	715	14	(	(	PUNCT
ejpam-3338	715	15	i.e.	i.e.	X
ejpam-3338	715	16	reduced	reduced	ADJ
ejpam-3338	715	17	alpha	alpha	NOUN
ejpam-3338	715	18	)	)	PUNCT
ejpam-3338	715	19	the	the	DET
ejpam-3338	715	20	amplitudes	amplitude	NOUN
ejpam-3338	715	21	almost	almost	ADV
ejpam-3338	715	22	merge	merge	VERB
ejpam-3338	715	23	as	as	SCONJ
ejpam-3338	715	24	these	these	PRON
ejpam-3338	715	25	should	should	AUX
ejpam-3338	715	26	be	be	AUX
ejpam-3338	715	27	.	.	PUNCT
ejpam-3338	715	28	)	)	PUNCT
ejpam-3338	716	1	fig	fig	NOUN
ejpam-3338	716	2	.	.	PUNCT
ejpam-3338	717	1	15	15	NUM
ejpam-3338	717	2	phase	phase	NOUN
ejpam-3338	717	3	-	-	PUNCT
ejpam-3338	717	4	plane	plane	NOUN
ejpam-3338	717	5	plot	plot	NOUN
ejpam-3338	717	6	looks	look	VERB
ejpam-3338	717	7	like	like	ADP
ejpam-3338	717	8	a	a	DET
ejpam-3338	717	9	snail	snail	NOUN
ejpam-3338	717	10	’s	’s	X
ejpam-3338	717	11	back	back	ADV
ejpam-3338	717	12	i.e.	i.e.	X
ejpam-3338	717	13	the	the	DET
ejpam-3338	717	14	spiral	spiral	ADJ
ejpam-3338	717	15	rapidly	rapidly	ADV
ejpam-3338	717	16	converges	converge	VERB
ejpam-3338	717	17	to	to	ADP
ejpam-3338	717	18	a	a	DET
ejpam-3338	717	19	point	point	NOUN
ejpam-3338	717	20	for	for	ADP
ejpam-3338	717	21	alpha	alpha	NOUN
ejpam-3338	717	22	=	=	NOUN
ejpam-3338	717	23	0.9	0.9	NUM
ejpam-3338	717	24	.	.	PUNCT
ejpam-3338	718	1	remarks	remark	VERB
ejpam-3338	718	2	zero	zero	NUM
ejpam-3338	718	3	friction	friction	NOUN
ejpam-3338	718	4	force	force	NOUN
ejpam-3338	718	5	(	(	PUNCT
ejpam-3338	718	6	ideal	ideal	ADJ
ejpam-3338	718	7	case	case	NOUN
ejpam-3338	718	8	):	):	PUNCT
ejpam-3338	718	9	non	non	ADJ
ejpam-3338	718	10	-	-	ADJ
ejpam-3338	718	11	existent	existent	ADJ
ejpam-3338	718	12	in	in	ADP
ejpam-3338	718	13	nature	nature	NOUN
ejpam-3338	718	14	if	if	SCONJ
ejpam-3338	718	15	alpha	alpha	NOUN
ejpam-3338	718	16	(	(	PUNCT
ejpam-3338	718	17	fractional	fractional	ADJ
ejpam-3338	718	18	order	order	NOUN
ejpam-3338	718	19	,	,	PUNCT
ejpam-3338	718	20	in	in	ADP
ejpam-3338	718	21	general	general	ADJ
ejpam-3338	718	22	)	)	PUNCT
ejpam-3338	718	23	is	be	AUX
ejpam-3338	718	24	1	1	NUM
ejpam-3338	718	25	,	,	PUNCT
ejpam-3338	718	26	then	then	ADV
ejpam-3338	718	27	the	the	DET
ejpam-3338	718	28	pendulum	pendulum	NOUN
ejpam-3338	718	29	will	will	AUX
ejpam-3338	718	30	continue	continue	VERB
ejpam-3338	718	31	simple	simple	ADJ
ejpam-3338	718	32	harmonic	harmonic	ADJ
ejpam-3338	718	33	oscillations	oscillation	NOUN
ejpam-3338	718	34	s.	s.	PROPN
ejpam-3338	718	35	k.sen	k.sen	PROPN
ejpam-3338	718	36	,	,	PUNCT
ejpam-3338	718	37	j.	j.	PROPN
ejpam-3338	718	38	v.	v.	PROPN
ejpam-3338	718	39	devi	devi	PROPN
ejpam-3338	718	40	,	,	PUNCT
ejpam-3338	718	41	r.v.g	r.v.g	NOUN
ejpam-3338	718	42	.	.	PUNCT
ejpam-3338	719	1	r.	r.	PROPN
ejpam-3338	719	2	kumar	kumar	PROPN
ejpam-3338	719	3	/	/	SYM
ejpam-3338	719	4	eur	eur	PROPN
ejpam-3338	719	5	.	.	PUNCT
ejpam-3338	720	1	j.	j.	PROPN
ejpam-3338	720	2	pure	pure	PROPN
ejpam-3338	720	3	appl	appl	PROPN
ejpam-3338	720	4	.	.	PROPN
ejpam-3338	720	5	math	math	PROPN
ejpam-3338	720	6	,	,	PUNCT
ejpam-3338	720	7	11	11	NUM
ejpam-3338	720	8	(	(	PUNCT
ejpam-3338	720	9	3	3	NUM
ejpam-3338	720	10	)	)	PUNCT
ejpam-3338	720	11	(	(	PUNCT
ejpam-3338	720	12	2018	2018	NUM
ejpam-3338	720	13	)	)	PUNCT
ejpam-3338	720	14	,	,	PUNCT
ejpam-3338	720	15	1058	1058	NUM
ejpam-3338	720	16	-	-	SYM
ejpam-3338	720	17	1099	1099	NUM
ejpam-3338	720	18	1093	1093	NUM
ejpam-3338	720	19	without	without	ADP
ejpam-3338	720	20	any	any	DET
ejpam-3338	720	21	damping	damping	NOUN
ejpam-3338	720	22	.	.	PUNCT
ejpam-3338	721	1	the	the	DET
ejpam-3338	721	2	oscillation	oscillation	NOUN
ejpam-3338	721	3	will	will	AUX
ejpam-3338	721	4	have	have	VERB
ejpam-3338	721	5	constant	constant	ADJ
ejpam-3338	721	6	amplitude	amplitude	NOUN
ejpam-3338	721	7	,	,	PUNCT
ejpam-3338	721	8	constant	constant	ADJ
ejpam-3338	721	9	time	time	NOUN
ejpam-3338	721	10	period	period	NOUN
ejpam-3338	721	11	,	,	PUNCT
ejpam-3338	721	12	and	and	CCONJ
ejpam-3338	721	13	will	will	AUX
ejpam-3338	721	14	continue	continue	VERB
ejpam-3338	721	15	the	the	DET
ejpam-3338	721	16	oscillatory	oscillatory	ADJ
ejpam-3338	721	17	motion	motion	NOUN
ejpam-3338	721	18	for	for	ADP
ejpam-3338	721	19	ever	ever	ADV
ejpam-3338	721	20	.	.	PUNCT
ejpam-3338	722	1	the	the	DET
ejpam-3338	722	2	matlab	matlab	PROPN
ejpam-3338	722	3	program	program	NOUN
ejpam-3338	722	4	for	for	ADP
ejpam-3338	722	5	pendulum	pendulum	NOUN
ejpam-3338	722	6	depicts	depict	VERB
ejpam-3338	722	7	the	the	DET
ejpam-3338	722	8	motion	motion	NOUN
ejpam-3338	722	9	(	(	PUNCT
ejpam-3338	722	10	figs	fig	NOUN
ejpam-3338	722	11	.	.	X
ejpam-3338	722	12	4	4	NUM
ejpam-3338	722	13	and	and	CCONJ
ejpam-3338	722	14	5	5	NUM
ejpam-3338	722	15	)	)	PUNCT
ejpam-3338	722	16	.	.	PUNCT
ejpam-3338	723	1	(	(	PUNCT
ejpam-3338	723	2	positive	positive	ADJ
ejpam-3338	723	3	)	)	PUNCT
ejpam-3338	723	4	friction	friction	NOUN
ejpam-3338	723	5	force	force	NOUN
ejpam-3338	723	6	.	.	PUNCT
ejpam-3338	724	1	if	if	SCONJ
ejpam-3338	724	2	alpha<1	alpha<1	NOUN
ejpam-3338	724	3	is	be	AUX
ejpam-3338	724	4	fractional	fractional	ADJ
ejpam-3338	724	5	and	and	CCONJ
ejpam-3338	724	6	assumes	assume	VERB
ejpam-3338	724	7	successively	successively	ADV
ejpam-3338	724	8	the	the	DET
ejpam-3338	724	9	values	value	NOUN
ejpam-3338	724	10	.99	.99	NUM
ejpam-3338	724	11	,	,	PUNCT
ejpam-3338	724	12	.98	.98	NUM
ejpam-3338	724	13	,	,	PUNCT
ejpam-3338	724	14	and	and	CCONJ
ejpam-3338	724	15	.97	.97	NUM
ejpam-3338	724	16	,	,	PUNCT
ejpam-3338	724	17	.90	.90	NUM
ejpam-3338	724	18	,	,	PUNCT
ejpam-3338	724	19	then	then	ADV
ejpam-3338	724	20	the	the	DET
ejpam-3338	724	21	pendulum	pendulum	NOUN
ejpam-3338	724	22	will	will	AUX
ejpam-3338	724	23	continue	continue	VERB
ejpam-3338	724	24	simple	simple	ADJ
ejpam-3338	724	25	harmonic	harmonic	ADJ
ejpam-3338	724	26	oscillations	oscillation	NOUN
ejpam-3338	724	27	/	/	SYM
ejpam-3338	724	28	motion	motion	NOUN
ejpam-3338	724	29	with	with	ADP
ejpam-3338	724	30	progressively	progressively	ADV
ejpam-3338	724	31	increased	increase	VERB
ejpam-3338	724	32	damping	damp	VERB
ejpam-3338	724	33	.	.	PUNCT
ejpam-3338	725	1	while	while	SCONJ
ejpam-3338	725	2	the	the	DET
ejpam-3338	725	3	time	time	NOUN
ejpam-3338	725	4	period	period	NOUN
ejpam-3338	725	5	remains	remain	VERB
ejpam-3338	725	6	unaltered	unaltered	ADJ
ejpam-3338	725	7	,	,	PUNCT
ejpam-3338	725	8	the	the	DET
ejpam-3338	725	9	amplitude	amplitude	NOUN
ejpam-3338	725	10	will	will	AUX
ejpam-3338	725	11	progressively	progressively	ADV
ejpam-3338	725	12	decrease	decrease	VERB
ejpam-3338	725	13	.	.	PUNCT
ejpam-3338	726	1	the	the	DET
ejpam-3338	726	2	matlab	matlab	PROPN
ejpam-3338	726	3	program	program	NOUN
ejpam-3338	726	4	pendulumfde	pendulumfde	NOUN
ejpam-3338	726	5	depicts	depict	VERB
ejpam-3338	726	6	the	the	DET
ejpam-3338	726	7	motion	motion	NOUN
ejpam-3338	726	8	(	(	PUNCT
ejpam-3338	726	9	figs	fig	NOUN
ejpam-3338	726	10	.	.	PUNCT
ejpam-3338	727	1	8	8	NUM
ejpam-3338	727	2	-	-	SYM
ejpam-3338	727	3	15	15	NUM
ejpam-3338	727	4	)	)	PUNCT
ejpam-3338	727	5	.	.	PUNCT
ejpam-3338	728	1	it	it	PRON
ejpam-3338	728	2	can	can	AUX
ejpam-3338	728	3	be	be	AUX
ejpam-3338	728	4	seen	see	VERB
ejpam-3338	728	5	that	that	SCONJ
ejpam-3338	728	6	for	for	ADP
ejpam-3338	728	7	alpha=1	alpha=1	PROPN
ejpam-3338	728	8	both	both	CCONJ
ejpam-3338	728	9	the	the	DET
ejpam-3338	728	10	programs	program	NOUN
ejpam-3338	728	11	pendulum	pendulum	NOUN
ejpam-3338	728	12	and	and	CCONJ
ejpam-3338	728	13	pendulumfde	pendulumfde	VERB
ejpam-3338	728	14	depict	depict	NOUN
ejpam-3338	728	15	beautifully	beautifully	ADV
ejpam-3338	728	16	same	same	ADJ
ejpam-3338	728	17	/	/	SYM
ejpam-3338	728	18	similar	similar	ADJ
ejpam-3338	728	19	graphs	graph	NOUN
ejpam-3338	728	20	.	.	PUNCT
ejpam-3338	729	1	figs	fig	NOUN
ejpam-3338	729	2	.	.	PUNCT
ejpam-3338	730	1	4	4	NUM
ejpam-3338	730	2	and	and	CCONJ
ejpam-3338	730	3	5	5	NUM
ejpam-3338	730	4	output	output	NOUN
ejpam-3338	730	5	by	by	ADP
ejpam-3338	730	6	pendulum	pendulum	NOUN
ejpam-3338	730	7	correspond	correspond	VERB
ejpam-3338	730	8	to	to	ADP
ejpam-3338	730	9	figs	fig	NOUN
ejpam-3338	730	10	.	.	PUNCT
ejpam-3338	731	1	6	6	NUM
ejpam-3338	731	2	and	and	CCONJ
ejpam-3338	731	3	7	7	NUM
ejpam-3338	731	4	produced	produce	VERB
ejpam-3338	731	5	by	by	ADP
ejpam-3338	731	6	pendulumfde	pendulumfde	NOUN
ejpam-3338	731	7	,	,	PUNCT
ejpam-3338	731	8	respectively	respectively	ADV
ejpam-3338	731	9	.	.	PUNCT
ejpam-3338	732	1	for	for	ADP
ejpam-3338	732	2	such	such	DET
ejpam-3338	732	3	a	a	DET
ejpam-3338	732	4	specific	specific	ADJ
ejpam-3338	732	5	type	type	NOUN
ejpam-3338	732	6	of	of	ADP
ejpam-3338	732	7	fodes	fode	NOUN
ejpam-3338	732	8	,	,	PUNCT
ejpam-3338	732	9	both	both	CCONJ
ejpam-3338	732	10	the	the	DET
ejpam-3338	732	11	fractional	fractional	ADJ
ejpam-3338	732	12	order	order	NOUN
ejpam-3338	732	13	and	and	CCONJ
ejpam-3338	732	14	the	the	DET
ejpam-3338	732	15	integer	integer	NOUN
ejpam-3338	732	16	order	order	NOUN
ejpam-3338	732	17	merge	merge	VERB
ejpam-3338	732	18	and	and	CCONJ
ejpam-3338	732	19	integrate	integrate	VERB
ejpam-3338	732	20	well	well	ADV
ejpam-3338	732	21	.	.	PUNCT
ejpam-3338	733	1	consequently	consequently	ADV
ejpam-3338	733	2	the	the	DET
ejpam-3338	733	3	efforts	effort	NOUN
ejpam-3338	733	4	toward	toward	ADP
ejpam-3338	733	5	limited	limited	ADJ
ejpam-3338	733	6	generalization	generalization	NOUN
ejpam-3338	733	7	are	be	AUX
ejpam-3338	733	8	appreciated	appreciate	VERB
ejpam-3338	733	9	.	.	PUNCT
ejpam-3338	734	1	but	but	CCONJ
ejpam-3338	734	2	the	the	DET
ejpam-3338	734	3	physical	physical	ADJ
ejpam-3338	734	4	implication	implication	NOUN
ejpam-3338	734	5	of	of	ADP
ejpam-3338	734	6	alpha	alpha	NOUN
ejpam-3338	734	7	in	in	ADP
ejpam-3338	734	8	terms	term	NOUN
ejpam-3338	734	9	of	of	ADP
ejpam-3338	734	10	friction	friction	NOUN
ejpam-3338	734	11	forces	force	NOUN
ejpam-3338	734	12	and	and	CCONJ
ejpam-3338	734	13	that	that	PRON
ejpam-3338	734	14	of	of	ADP
ejpam-3338	734	15	friction	friction	NOUN
ejpam-3338	734	16	forces	force	NOUN
ejpam-3338	734	17	in	in	ADP
ejpam-3338	734	18	terms	term	NOUN
ejpam-3338	734	19	of	of	ADP
ejpam-3338	734	20	alpha	alpha	NOUN
ejpam-3338	734	21	are	be	AUX
ejpam-3338	734	22	not	not	PART
ejpam-3338	734	23	readily	readily	ADV
ejpam-3338	734	24	known	know	VERB
ejpam-3338	734	25	(	(	PUNCT
ejpam-3338	734	26	as	as	SCONJ
ejpam-3338	734	27	we	we	PRON
ejpam-3338	734	28	do	do	VERB
ejpam-3338	734	29	for	for	ADP
ejpam-3338	734	30	iodes	iode	NOUN
ejpam-3338	734	31	)	)	PUNCT
ejpam-3338	734	32	.	.	PUNCT
ejpam-3338	735	1	implication	implication	NOUN
ejpam-3338	735	2	of	of	ADP
ejpam-3338	735	3	friction	friction	NOUN
ejpam-3338	735	4	forces	force	NOUN
ejpam-3338	735	5	.	.	PUNCT
ejpam-3338	736	1	in	in	ADP
ejpam-3338	736	2	other	other	ADJ
ejpam-3338	736	3	words	word	NOUN
ejpam-3338	736	4	,	,	PUNCT
ejpam-3338	736	5	friction	friction	NOUN
ejpam-3338	736	6	forces	force	NOUN
ejpam-3338	736	7	s	s	VERB
ejpam-3338	736	8	uch	uch	ADJ
ejpam-3338	736	9	as	as	ADP
ejpam-3338	736	10	resistance	resistance	NOUN
ejpam-3338	736	11	due	due	ADP
ejpam-3338	736	12	to	to	ADP
ejpam-3338	736	13	air	air	NOUN
ejpam-3338	736	14	/	/	SYM
ejpam-3338	736	15	wind	wind	NOUN
ejpam-3338	736	16	and	and	CCONJ
ejpam-3338	736	17	that	that	PRON
ejpam-3338	736	18	due	due	ADP
ejpam-3338	736	19	to	to	ADP
ejpam-3338	736	20	various	various	ADJ
ejpam-3338	736	21	parts	part	NOUN
ejpam-3338	736	22	of	of	ADP
ejpam-3338	736	23	the	the	DET
ejpam-3338	736	24	pendulum	pendulum	NOUN
ejpam-3338	736	25	touching	touch	VERB
ejpam-3338	736	26	one	one	NOUN
ejpam-3338	736	27	another	another	PRON
ejpam-3338	736	28	should	should	AUX
ejpam-3338	736	29	determine	determine	VERB
ejpam-3338	736	30	the	the	DET
ejpam-3338	736	31	value	value	NOUN
ejpam-3338	736	32	of	of	ADP
ejpam-3338	736	33	alpha	alpha	PROPN
ejpam-3338	736	34	viz	viz	PROPN
ejpam-3338	736	35	.	.	PUNCT
ejpam-3338	737	1	the	the	DET
ejpam-3338	737	2	value	value	NOUN
ejpam-3338	737	3	of	of	ADP
ejpam-3338	737	4	the	the	DET
ejpam-3338	737	5	fractional	fractional	ADJ
ejpam-3338	737	6	order	order	NOUN
ejpam-3338	737	7	approximately	approximately	ADV
ejpam-3338	737	8	.	.	PUNCT
ejpam-3338	738	1	can	can	AUX
ejpam-3338	738	2	we	we	PRON
ejpam-3338	738	3	still	still	ADV
ejpam-3338	738	4	have	have	VERB
ejpam-3338	738	5	precise	precise	ADJ
ejpam-3338	738	6	magnitude	magnitude	NOUN
ejpam-3338	738	7	of	of	ADP
ejpam-3338	738	8	all	all	DET
ejpam-3338	738	9	the	the	DET
ejpam-3338	738	10	friction	friction	NOUN
ejpam-3338	738	11	forces	force	NOUN
ejpam-3338	738	12	combined	combine	VERB
ejpam-3338	738	13	together	together	ADV
ejpam-3338	738	14	from	from	ADP
ejpam-3338	738	15	the	the	DET
ejpam-3338	738	16	knowledge	knowledge	NOUN
ejpam-3338	738	17	of	of	ADP
ejpam-3338	738	18	alpha	alpha	NOUN
ejpam-3338	738	19	and	and	CCONJ
ejpam-3338	738	20	vice	vice	NOUN
ejpam-3338	738	21	versa	versa	ADV
ejpam-3338	738	22	?	?	PUNCT
ejpam-3338	739	1	a	a	DET
ejpam-3338	739	2	meaningful	meaningful	ADJ
ejpam-3338	739	3	generalization	generalization	NOUN
ejpam-3338	739	4	needs	need	VERB
ejpam-3338	739	5	to	to	PART
ejpam-3338	739	6	sort	sort	VERB
ejpam-3338	739	7	out	out	ADP
ejpam-3338	739	8	this	this	DET
ejpam-3338	739	9	question	question	NOUN
ejpam-3338	739	10	.	.	PUNCT
ejpam-3338	740	1	is	be	AUX
ejpam-3338	740	2	it	it	PRON
ejpam-3338	740	3	possible	possible	ADJ
ejpam-3338	740	4	that	that	SCONJ
ejpam-3338	740	5	throughout	throughout	ADP
ejpam-3338	740	6	the	the	DET
ejpam-3338	740	7	interval	interval	NOUN
ejpam-3338	740	8	of	of	ADP
ejpam-3338	740	9	the	the	DET
ejpam-3338	740	10	independent	independent	ADJ
ejpam-3338	740	11	(	(	PUNCT
ejpam-3338	740	12	time	time	NOUN
ejpam-3338	740	13	)	)	PUNCT
ejpam-3338	740	14	variable	variable	NOUN
ejpam-3338	740	15	t	t	PROPN
ejpam-3338	740	16	,	,	PUNCT
ejpam-3338	740	17	the	the	DET
ejpam-3338	740	18	combination	combination	NOUN
ejpam-3338	740	19	of	of	ADP
ejpam-3338	740	20	friction	friction	NOUN
ejpam-3338	740	21	forces	force	NOUN
ejpam-3338	740	22	and	and	CCONJ
ejpam-3338	740	23	the	the	DET
ejpam-3338	740	24	value	value	NOUN
ejpam-3338	740	25	of	of	ADP
ejpam-3338	740	26	alpha	alpha	PROPN
ejpam-3338	740	27	match	match	NOUN
ejpam-3338	740	28	/	/	PUNCT
ejpam-3338	740	29	are	be	AUX
ejpam-3338	740	30	numerically	numerically	ADV
ejpam-3338	740	31	the	the	DET
ejpam-3338	740	32	same	same	ADJ
ejpam-3338	740	33	at	at	ADP
ejpam-3338	740	34	all	all	DET
ejpam-3338	740	35	equi	equi	NOUN
ejpam-3338	740	36	-	-	PUNCT
ejpam-3338	740	37	spaced	space	VERB
ejpam-3338	740	38	(	(	PUNCT
ejpam-3338	740	39	or	or	CCONJ
ejpam-3338	740	40	non	non	ADJ
ejpam-3338	740	41	-	-	ADJ
ejpam-3338	740	42	equi	equi	NOUN
ejpam-3338	740	43	-	-	PUNCT
ejpam-3338	740	44	spaced	space	VERB
ejpam-3338	740	45	)	)	PUNCT
ejpam-3338	740	46	points	point	NOUN
ejpam-3338	740	47	in	in	ADP
ejpam-3338	740	48	the	the	DET
ejpam-3338	740	49	time	time	NOUN
ejpam-3338	740	50	interval	interval	NOUN
ejpam-3338	740	51	?	?	PUNCT
ejpam-3338	741	1	on	on	ADP
ejpam-3338	741	2	the	the	DET
ejpam-3338	741	3	other	other	ADJ
ejpam-3338	741	4	hand	hand	NOUN
ejpam-3338	741	5	,	,	PUNCT
ejpam-3338	741	6	if	if	SCONJ
ejpam-3338	741	7	we	we	PRON
ejpam-3338	741	8	know	know	VERB
ejpam-3338	741	9	the	the	DET
ejpam-3338	741	10	magnitude	magnitude	NOUN
ejpam-3338	741	11	and	and	CCONJ
ejpam-3338	741	12	direction	direction	NOUN
ejpam-3338	741	13	of	of	ADP
ejpam-3338	741	14	friction	friction	NOUN
ejpam-3338	741	15	forces	force	NOUN
ejpam-3338	741	16	,	,	PUNCT
ejpam-3338	741	17	then	then	ADV
ejpam-3338	741	18	the	the	DET
ejpam-3338	741	19	mathematical	mathematical	ADJ
ejpam-3338	741	20	model	model	NOUN
ejpam-3338	741	21	can	can	AUX
ejpam-3338	741	22	be	be	AUX
ejpam-3338	741	23	written	write	VERB
ejpam-3338	741	24	as	as	ADP
ejpam-3338	741	25	integer	integer	NOUN
ejpam-3338	741	26	-	-	PUNCT
ejpam-3338	741	27	order	order	NOUN
ejpam-3338	741	28	differential	differential	ADJ
ejpam-3338	741	29	equations	equation	NOUN
ejpam-3338	741	30	and	and	CCONJ
ejpam-3338	741	31	then	then	ADV
ejpam-3338	741	32	solved	solve	VERB
ejpam-3338	741	33	without	without	ADP
ejpam-3338	741	34	any	any	DET
ejpam-3338	741	35	need	need	NOUN
ejpam-3338	741	36	of	of	ADP
ejpam-3338	741	37	fractional	fractional	ADJ
ejpam-3338	741	38	order	order	NOUN
ejpam-3338	741	39	model	model	NOUN
ejpam-3338	741	40	.	.	PUNCT
ejpam-3338	742	1	3	3	X
ejpam-3338	742	2	.	.	X
ejpam-3338	742	3	fodes	fode	NOUN
ejpam-3338	742	4	:	:	PUNCT
ejpam-3338	742	5	converting	convert	VERB
ejpam-3338	742	6	to	to	ADP
ejpam-3338	742	7	α−	α−	ADP
ejpam-3338	742	8	th	th	NOUN
ejpam-3338	742	9	or	or	CCONJ
ejpam-3338	742	10	/	/	SYM
ejpam-3338	742	11	and	and	CCONJ
ejpam-3338	742	12	1st	1st	ADJ
ejpam-3338	742	13	order	order	NOUN
ejpam-3338	742	14	odes	ode	VERB
ejpam-3338	742	15	with	with	ADP
ejpam-3338	742	16	generalizations	generalization	NOUN
ejpam-3338	742	17	consider	consider	VERB
ejpam-3338	742	18	,	,	PUNCT
ejpam-3338	742	19	for	for	ADP
ejpam-3338	742	20	instance	instance	NOUN
ejpam-3338	742	21	,	,	PUNCT
ejpam-3338	742	22	the	the	DET
ejpam-3338	742	23	following	follow	VERB
ejpam-3338	742	24	mathematical	mathematical	ADJ
ejpam-3338	742	25	problem	problem	NOUN
ejpam-3338	742	26	involving	involve	VERB
ejpam-3338	742	27	fodes	fode	NOUN
ejpam-3338	742	28	.	.	PUNCT
ejpam-3338	743	1	solve	solve	VERB
ejpam-3338	743	2	numerically	numerically	ADV
ejpam-3338	743	3	the	the	DET
ejpam-3338	743	4	following	follow	VERB
ejpam-3338	743	5	system	system	NOUN
ejpam-3338	743	6	of	of	ADP
ejpam-3338	743	7	2	2	NUM
ejpam-3338	743	8	fodes	fode	NOUN
ejpam-3338	743	9	d3.71y	d3.71y	PROPN
ejpam-3338	743	10	dx3.71	dx3.71	PROPN
ejpam-3338	744	1	+	+	CCONJ
ejpam-3338	744	2	d2.81y	d2.81y	X
ejpam-3338	744	3	dx2.81	dx2.81	PROPN
ejpam-3338	744	4	+	+	CCONJ
ejpam-3338	744	5	dy	dy	VERB
ejpam-3338	744	6	dx	dx	PROPN
ejpam-3338	744	7	+	+	CCONJ
ejpam-3338	744	8	y2	y2	PROPN
ejpam-3338	744	9	=	=	SYM
ejpam-3338	744	10	sint	sint	NOUN
ejpam-3338	744	11	y	y	PROPN
ejpam-3338	744	12	d2.11y	d2.11y	VERB
ejpam-3338	744	13	dx2.11	dx2.11	NOUN
ejpam-3338	744	14	−	−	PROPN
ejpam-3338	744	15	d1.9y	d1.9y	PROPN
ejpam-3338	744	16	dx1.9	dx1.9	PRON
ejpam-3338	744	17	+	+	PUNCT
ejpam-3338	744	18	y0.5	y0.5	NOUN
ejpam-3338	744	19	=	=	NOUN
ejpam-3338	744	20	cost	cost	NOUN
ejpam-3338	744	21	(	(	PUNCT
ejpam-3338	744	22	41	41	NUM
ejpam-3338	744	23	)	)	PUNCT
ejpam-3338	744	24	under	under	ADP
ejpam-3338	744	25	the	the	DET
ejpam-3338	744	26	requisite	requisite	ADJ
ejpam-3338	744	27	number	number	NOUN
ejpam-3338	744	28	of	of	ADP
ejpam-3338	744	29	initial	initial	ADJ
ejpam-3338	744	30	conditions	condition	NOUN
ejpam-3338	744	31	for	for	ADP
ejpam-3338	744	32	t=0(.1)10	t=0(.1)10	NOUN
ejpam-3338	744	33	.	.	PUNCT
ejpam-3338	745	1	the	the	DET
ejpam-3338	745	2	following	follow	VERB
ejpam-3338	745	3	questions	question	NOUN
ejpam-3338	745	4	arise	arise	VERB
ejpam-3338	745	5	:	:	PUNCT
ejpam-3338	745	6	can	can	AUX
ejpam-3338	745	7	we	we	PRON
ejpam-3338	745	8	express	express	VERB
ejpam-3338	745	9	the	the	DET
ejpam-3338	745	10	system	system	NOUN
ejpam-3338	745	11	of	of	ADP
ejpam-3338	745	12	equations	equation	NOUN
ejpam-3338	745	13	(	(	PUNCT
ejpam-3338	745	14	41	41	NUM
ejpam-3338	745	15	)	)	PUNCT
ejpam-3338	745	16	as	as	ADP
ejpam-3338	745	17	a	a	DET
ejpam-3338	745	18	system	system	NOUN
ejpam-3338	745	19	of	of	ADP
ejpam-3338	745	20	k	k	PROPN
ejpam-3338	745	21	1st	1st	ADJ
ejpam-3338	745	22	order	order	NOUN
ejpam-3338	745	23	and/or	and/or	CCONJ
ejpam-3338	745	24	m	m	PROPN
ejpam-3338	745	25	αth	αth	NUM
ejpam-3338	745	26	order	order	NOUN
ejpam-3338	745	27	odes	ode	VERB
ejpam-3338	745	28	?	?	PUNCT
ejpam-3338	746	1	what	what	PRON
ejpam-3338	746	2	will	will	AUX
ejpam-3338	746	3	be	be	AUX
ejpam-3338	746	4	the	the	DET
ejpam-3338	746	5	value	value	NOUN
ejpam-3338	746	6	of	of	ADP
ejpam-3338	746	7	k	k	PROPN
ejpam-3338	746	8	and/or	and/or	CCONJ
ejpam-3338	746	9	the	the	DET
ejpam-3338	746	10	value	value	NOUN
ejpam-3338	746	11	of	of	ADP
ejpam-3338	746	12	m	m	PROPN
ejpam-3338	746	13	?	?	PUNCT
ejpam-3338	747	1	can	can	AUX
ejpam-3338	747	2	we	we	PRON
ejpam-3338	747	3	write	write	VERB
ejpam-3338	747	4	a	a	DET
ejpam-3338	747	5	real	real	ADJ
ejpam-3338	747	6	-	-	PUNCT
ejpam-3338	747	7	world	world	NOUN
ejpam-3338	747	8	physical	physical	ADJ
ejpam-3338	747	9	problem	problem	NOUN
ejpam-3338	747	10	that	that	PRON
ejpam-3338	747	11	corresponds	correspond	VERB
ejpam-3338	747	12	to	to	ADP
ejpam-3338	747	13	the	the	DET
ejpam-3338	747	14	foregoing	forego	VERB
ejpam-3338	747	15	system	system	NOUN
ejpam-3338	747	16	(	(	PUNCT
ejpam-3338	747	17	41	41	NUM
ejpam-3338	747	18	)	)	PUNCT
ejpam-3338	747	19	as	as	ADP
ejpam-3338	747	20	the	the	DET
ejpam-3338	747	21	mathematical	mathematical	ADJ
ejpam-3338	747	22	model	model	NOUN
ejpam-3338	747	23	?	?	PUNCT
ejpam-3338	748	1	or	or	CCONJ
ejpam-3338	748	2	,	,	PUNCT
ejpam-3338	748	3	can	can	AUX
ejpam-3338	748	4	we	we	PRON
ejpam-3338	748	5	have	have	VERB
ejpam-3338	748	6	a	a	DET
ejpam-3338	748	7	real	real	ADJ
ejpam-3338	748	8	-	-	PUNCT
ejpam-3338	748	9	world	world	NOUN
ejpam-3338	748	10	physical	physical	ADJ
ejpam-3338	748	11	problem	problem	NOUN
ejpam-3338	748	12	whose	whose	DET
ejpam-3338	748	13	s.	s.	PROPN
ejpam-3338	748	14	k.sen	k.sen	PROPN
ejpam-3338	748	15	,	,	PUNCT
ejpam-3338	748	16	j.	j.	PROPN
ejpam-3338	748	17	v.	v.	PROPN
ejpam-3338	748	18	devi	devi	PROPN
ejpam-3338	748	19	,	,	PUNCT
ejpam-3338	748	20	r.v.g	r.v.g	NOUN
ejpam-3338	748	21	.	.	PUNCT
ejpam-3338	749	1	r.	r.	PROPN
ejpam-3338	749	2	kumar	kumar	PROPN
ejpam-3338	749	3	/	/	SYM
ejpam-3338	749	4	eur	eur	PROPN
ejpam-3338	749	5	.	.	PUNCT
ejpam-3338	750	1	j.	j.	PROPN
ejpam-3338	750	2	pure	pure	PROPN
ejpam-3338	750	3	appl	appl	PROPN
ejpam-3338	750	4	.	.	PROPN
ejpam-3338	750	5	math	math	PROPN
ejpam-3338	750	6	,	,	PUNCT
ejpam-3338	750	7	11	11	NUM
ejpam-3338	750	8	(	(	PUNCT
ejpam-3338	750	9	3	3	NUM
ejpam-3338	750	10	)	)	PUNCT
ejpam-3338	750	11	(	(	PUNCT
ejpam-3338	750	12	2018	2018	NUM
ejpam-3338	750	13	)	)	PUNCT
ejpam-3338	750	14	,	,	PUNCT
ejpam-3338	750	15	1058	1058	NUM
ejpam-3338	750	16	-	-	SYM
ejpam-3338	750	17	1099	1099	NUM
ejpam-3338	750	18	1094	1094	NUM
ejpam-3338	750	19	mathematical	mathematical	ADJ
ejpam-3338	750	20	model	model	NOUN
ejpam-3338	750	21	will	will	AUX
ejpam-3338	750	22	be	be	AUX
ejpam-3338	750	23	one	one	NUM
ejpam-3338	750	24	similar	similar	ADJ
ejpam-3338	750	25	to	to	ADP
ejpam-3338	750	26	the	the	DET
ejpam-3338	750	27	system	system	NOUN
ejpam-3338	750	28	(	(	PUNCT
ejpam-3338	750	29	41	41	NUM
ejpam-3338	750	30	)	)	PUNCT
ejpam-3338	750	31	?	?	PUNCT
ejpam-3338	751	1	can	can	AUX
ejpam-3338	751	2	we	we	PRON
ejpam-3338	751	3	have	have	VERB
ejpam-3338	751	4	a	a	DET
ejpam-3338	751	5	procedure	procedure	NOUN
ejpam-3338	751	6	to	to	PART
ejpam-3338	751	7	solve	solve	VERB
ejpam-3338	751	8	a	a	DET
ejpam-3338	751	9	corresponding	corresponding	ADJ
ejpam-3338	751	10	system	system	NOUN
ejpam-3338	751	11	of	of	ADP
ejpam-3338	751	12	1st	1st	ADJ
ejpam-3338	751	13	order	order	NOUN
ejpam-3338	751	14	and/or	and/or	CCONJ
ejpam-3338	751	15	αth	αth	NUM
ejpam-3338	751	16	order	order	NOUN
ejpam-3338	751	17	odes	ode	VERB
ejpam-3338	751	18	?	?	PUNCT
ejpam-3338	752	1	a	a	DET
ejpam-3338	752	2	generalization	generalization	NOUN
ejpam-3338	752	3	deserves	deserve	VERB
ejpam-3338	752	4	the	the	DET
ejpam-3338	752	5	answer	answer	NOUN
ejpam-3338	752	6	of	of	ADP
ejpam-3338	752	7	the	the	DET
ejpam-3338	752	8	foregoing	forego	VERB
ejpam-3338	752	9	questions	question	NOUN
ejpam-3338	752	10	.	.	PUNCT
ejpam-3338	753	1	only	only	ADV
ejpam-3338	753	2	after	after	ADP
ejpam-3338	753	3	obtaining	obtain	VERB
ejpam-3338	753	4	the	the	DET
ejpam-3338	753	5	answer	answer	NOUN
ejpam-3338	753	6	,	,	PUNCT
ejpam-3338	753	7	we	we	PRON
ejpam-3338	753	8	may	may	AUX
ejpam-3338	753	9	determine	determine	VERB
ejpam-3338	753	10	if	if	SCONJ
ejpam-3338	753	11	a	a	DET
ejpam-3338	753	12	complete	complete	ADJ
ejpam-3338	753	13	generalization	generalization	NOUN
ejpam-3338	753	14	(	(	PUNCT
ejpam-3338	753	15	i.e.	i.e.	X
ejpam-3338	753	16	a	a	DET
ejpam-3338	753	17	generalization	generalization	NOUN
ejpam-3338	753	18	that	that	PRON
ejpam-3338	753	19	does	do	AUX
ejpam-3338	753	20	not	not	PART
ejpam-3338	753	21	at	at	ADV
ejpam-3338	753	22	all	all	ADV
ejpam-3338	753	23	differentiate	differentiate	VERB
ejpam-3338	753	24	between	between	ADP
ejpam-3338	753	25	an	an	DET
ejpam-3338	753	26	integer	integer	NOUN
ejpam-3338	753	27	-	-	PUNCT
ejpam-3338	753	28	order	order	NOUN
ejpam-3338	753	29	say	say	INTJ
ejpam-3338	753	30	,	,	PUNCT
ejpam-3338	753	31	3	3	NUM
ejpam-3338	753	32	or	or	CCONJ
ejpam-3338	753	33	4	4	NUM
ejpam-3338	753	34	and	and	CCONJ
ejpam-3338	753	35	a	a	DET
ejpam-3338	753	36	fractional	fractional	ADJ
ejpam-3338	753	37	order	order	NOUN
ejpam-3338	753	38	say	say	VERB
ejpam-3338	753	39	2.21	2.21	NUM
ejpam-3338	753	40	and	and	CCONJ
ejpam-3338	753	41	3.78	3.78	NUM
ejpam-3338	753	42	and	and	CCONJ
ejpam-3338	753	43	get	get	VERB
ejpam-3338	753	44	the	the	DET
ejpam-3338	753	45	desired	desire	VERB
ejpam-3338	753	46	numerical	numerical	ADJ
ejpam-3338	753	47	solution	solution	NOUN
ejpam-3338	753	48	)	)	PUNCT
ejpam-3338	753	49	is	be	AUX
ejpam-3338	753	50	achievable	achievable	ADJ
ejpam-3338	753	51	.	.	PUNCT
ejpam-3338	754	1	or	or	CCONJ
ejpam-3338	754	2	,	,	PUNCT
ejpam-3338	754	3	to	to	PART
ejpam-3338	754	4	which	which	DET
ejpam-3338	754	5	extent	extent	NOUN
ejpam-3338	754	6	a	a	DET
ejpam-3338	754	7	generalization	generalization	NOUN
ejpam-3338	754	8	is	be	AUX
ejpam-3338	754	9	feasible	feasible	ADJ
ejpam-3338	754	10	.	.	PUNCT
ejpam-3338	755	1	what	what	PRON
ejpam-3338	755	2	are	be	AUX
ejpam-3338	755	3	the	the	DET
ejpam-3338	755	4	specific	specific	ADJ
ejpam-3338	755	5	procedures	procedure	NOUN
ejpam-3338	755	6	that	that	PRON
ejpam-3338	755	7	need	need	VERB
ejpam-3338	755	8	to	to	PART
ejpam-3338	755	9	be	be	AUX
ejpam-3338	755	10	designed/	designed/	PROPN
ejpam-3338	755	11	innovated	innovate	VERB
ejpam-3338	755	12	to	to	PART
ejpam-3338	755	13	achieve	achieve	VERB
ejpam-3338	755	14	a	a	DET
ejpam-3338	755	15	partial	partial	ADJ
ejpam-3338	755	16	generalization	generalization	NOUN
ejpam-3338	755	17	or	or	CCONJ
ejpam-3338	755	18	a	a	DET
ejpam-3338	755	19	complete	complete	ADJ
ejpam-3338	755	20	one	one	NUM
ejpam-3338	755	21	?	?	PUNCT
ejpam-3338	756	1	then	then	ADV
ejpam-3338	756	2	,	,	PUNCT
ejpam-3338	756	3	of	of	ADP
ejpam-3338	756	4	course	course	NOUN
ejpam-3338	756	5	,	,	PUNCT
ejpam-3338	756	6	comes	come	VERB
ejpam-3338	756	7	the	the	DET
ejpam-3338	756	8	efforts	effort	NOUN
ejpam-3338	756	9	to	to	PART
ejpam-3338	756	10	solve	solve	VERB
ejpam-3338	756	11	numerically	numerically	ADV
ejpam-3338	756	12	computationally	computationally	ADV
ejpam-3338	756	13	the	the	DET
ejpam-3338	756	14	problems	problem	NOUN
ejpam-3338	756	15	for	for	ADP
ejpam-3338	756	16	scientific	scientific	ADJ
ejpam-3338	756	17	/	/	SYM
ejpam-3338	756	18	engineering	engineering	NOUN
ejpam-3338	756	19	implementation	implementation	NOUN
ejpam-3338	756	20	following	follow	VERB
ejpam-3338	756	21	the	the	DET
ejpam-3338	756	22	designed	design	VERB
ejpam-3338	756	23	new	new	ADJ
ejpam-3338	756	24	procedures	procedure	NOUN
ejpam-3338	756	25	.	.	PUNCT
ejpam-3338	757	1	4	4	X
ejpam-3338	757	2	.	.	X
ejpam-3338	757	3	conclusions	conclusion	NOUN
ejpam-3338	757	4	generalizing	generalize	VERB
ejpam-3338	757	5	matrix	matrix	NOUN
ejpam-3338	757	6	inverse	inverse	NOUN
ejpam-3338	757	7	and	and	CCONJ
ejpam-3338	757	8	calculus	calculus	NOUN
ejpam-3338	757	9	:	:	PUNCT
ejpam-3338	757	10	analogy	analogy	NOUN
ejpam-3338	757	11	generalized	generalize	VERB
ejpam-3338	757	12	version	version	NOUN
ejpam-3338	757	13	of	of	ADP
ejpam-3338	757	14	a	a	DET
ejpam-3338	757	15	matrix	matrix	NOUN
ejpam-3338	757	16	inverse	inverse	NOUN
ejpam-3338	757	17	and	and	CCONJ
ejpam-3338	757	18	that	that	PRON
ejpam-3338	757	19	of	of	ADP
ejpam-3338	757	20	the	the	DET
ejpam-3338	757	21	calculus	calculus	NOUN
ejpam-3338	757	22	viz	viz	PROPN
ejpam-3338	757	23	.	.	PUNCT
ejpam-3338	758	1	fractional	fractional	PROPN
ejpam-3338	758	2	calculus	calculus	NOUN
ejpam-3338	758	3	do	do	AUX
ejpam-3338	758	4	not	not	PART
ejpam-3338	758	5	have	have	VERB
ejpam-3338	758	6	one	one	NUM
ejpam-3338	758	7	-	-	PUNCT
ejpam-3338	758	8	to	to	ADP
ejpam-3338	758	9	-	-	PUNCT
ejpam-3338	758	10	one	one	NUM
ejpam-3338	758	11	correspondence	correspondence	NOUN
ejpam-3338	758	12	so	so	ADV
ejpam-3338	758	13	far	far	ADV
ejpam-3338	758	14	as	as	SCONJ
ejpam-3338	758	15	an	an	DET
ejpam-3338	758	16	analogy	analogy	NOUN
ejpam-3338	758	17	is	be	AUX
ejpam-3338	758	18	concerned	concern	VERB
ejpam-3338	758	19	.	.	PUNCT
ejpam-3338	759	1	one	one	NUM
ejpam-3338	759	2	is	be	AUX
ejpam-3338	759	3	fractional	fractional	ADJ
ejpam-3338	759	4	while	while	SCONJ
ejpam-3338	759	5	the	the	DET
ejpam-3338	759	6	other	other	ADJ
ejpam-3338	759	7	is	be	AUX
ejpam-3338	759	8	non	non	ADJ
ejpam-3338	759	9	-	-	ADJ
ejpam-3338	759	10	fractional	fractional	ADJ
ejpam-3338	759	11	.	.	PUNCT
ejpam-3338	760	1	till	till	SCONJ
ejpam-3338	760	2	early	early	ADJ
ejpam-3338	760	3	/	/	SYM
ejpam-3338	760	4	mid20th	mid20th	ADJ
ejpam-3338	760	5	century	century	NOUN
ejpam-3338	760	6	matrix	matrix	NOUN
ejpam-3338	760	7	algebra	algebra	NOUN
ejpam-3338	760	8	was	be	AUX
ejpam-3338	760	9	in	in	ADP
ejpam-3338	760	10	a	a	DET
ejpam-3338	760	11	formative	formative	ADJ
ejpam-3338	760	12	stage	stage	NOUN
ejpam-3338	760	13	.	.	PUNCT
ejpam-3338	761	1	we	we	PRON
ejpam-3338	761	2	knew	know	VERB
ejpam-3338	761	3	how	how	SCONJ
ejpam-3338	761	4	to	to	PART
ejpam-3338	761	5	solve	solve	VERB
ejpam-3338	761	6	linear	linear	PROPN
ejpam-3338	761	7	consistent	consistent	ADJ
ejpam-3338	761	8	square	square	ADJ
ejpam-3338	761	9	full	full	ADJ
ejpam-3338	761	10	-	-	PUNCT
ejpam-3338	761	11	rank	rank	NOUN
ejpam-3338	761	12	system	system	NOUN
ejpam-3338	761	13	using	use	VERB
ejpam-3338	761	14	the	the	DET
ejpam-3338	761	15	true	true	ADJ
ejpam-3338	761	16	matrix	matrix	NOUN
ejpam-3338	761	17	inverse	inverse	NOUN
ejpam-3338	761	18	.	.	PUNCT
ejpam-3338	762	1	or	or	CCONJ
ejpam-3338	762	2	,	,	PUNCT
ejpam-3338	762	3	without	without	ADP
ejpam-3338	762	4	recourse	recourse	NOUN
ejpam-3338	762	5	to	to	PART
ejpam-3338	762	6	matrix	matrix	VERB
ejpam-3338	762	7	algebra	algebra	NOUN
ejpam-3338	762	8	,	,	PUNCT
ejpam-3338	762	9	we	we	PRON
ejpam-3338	762	10	could	could	AUX
ejpam-3338	762	11	solve	solve	VERB
ejpam-3338	762	12	the	the	DET
ejpam-3338	762	13	system	system	NOUN
ejpam-3338	762	14	using	use	VERB
ejpam-3338	762	15	methods	method	NOUN
ejpam-3338	762	16	such	such	ADJ
ejpam-3338	762	17	as	as	ADP
ejpam-3338	762	18	the	the	DET
ejpam-3338	762	19	gauss	gauss	NOUN
ejpam-3338	762	20	reduction	reduction	NOUN
ejpam-3338	762	21	method	method	NOUN
ejpam-3338	762	22	using	use	VERB
ejpam-3338	762	23	partial	partial	ADJ
ejpam-3338	762	24	/	/	SYM
ejpam-3338	762	25	complete	complete	ADJ
ejpam-3338	762	26	pivoting	pivoting	NOUN
ejpam-3338	762	27	(	(	PUNCT
ejpam-3338	762	28	during	during	ADP
ejpam-3338	762	29	19th	19th	ADJ
ejpam-3338	762	30	century	century	NOUN
ejpam-3338	762	31	)	)	PUNCT
ejpam-3338	762	32	.	.	PUNCT
ejpam-3338	763	1	however	however	ADV
ejpam-3338	763	2	,	,	PUNCT
ejpam-3338	763	3	the	the	DET
ejpam-3338	763	4	essence	essence	NOUN
ejpam-3338	763	5	of	of	ADP
ejpam-3338	763	6	the	the	DET
ejpam-3338	763	7	concept	concept	NOUN
ejpam-3338	763	8	of	of	ADP
ejpam-3338	763	9	generalizing	generalize	VERB
ejpam-3338	763	10	the	the	DET
ejpam-3338	763	11	true	true	ADJ
ejpam-3338	763	12	inverse	inverse	NOUN
ejpam-3338	763	13	so	so	SCONJ
ejpam-3338	763	14	that	that	SCONJ
ejpam-3338	763	15	we	we	PRON
ejpam-3338	763	16	can	can	AUX
ejpam-3338	763	17	solve	solve	VERB
ejpam-3338	763	18	any	any	DET
ejpam-3338	763	19	linear	linear	ADJ
ejpam-3338	763	20	system	system	NOUN
ejpam-3338	763	21	written	write	VERB
ejpam-3338	763	22	/	/	PUNCT
ejpam-3338	763	23	given	give	VERB
ejpam-3338	763	24	in	in	ADP
ejpam-3338	763	25	the	the	DET
ejpam-3338	763	26	matrix	matrix	NOUN
ejpam-3338	763	27	-	-	PUNCT
ejpam-3338	763	28	vector	vector	NOUN
ejpam-3338	763	29	form	form	NOUN
ejpam-3338	763	30	consistent	consistent	ADJ
ejpam-3338	763	31	or	or	CCONJ
ejpam-3338	763	32	not	not	PART
ejpam-3338	763	33	,	,	PUNCT
ejpam-3338	763	34	square	square	ADJ
ejpam-3338	763	35	or	or	CCONJ
ejpam-3338	763	36	rectangular	rectangular	ADJ
ejpam-3338	763	37	without	without	ADP
ejpam-3338	763	38	any	any	DET
ejpam-3338	763	39	botheration	botheration	NOUN
ejpam-3338	763	40	about	about	ADP
ejpam-3338	763	41	pruning	prune	VERB
ejpam-3338	763	42	redundant	redundant	ADJ
ejpam-3338	763	43	(	(	PUNCT
ejpam-3338	763	44	linearly	linearly	ADV
ejpam-3338	763	45	dependent	dependent	ADJ
ejpam-3338	763	46	)	)	PUNCT
ejpam-3338	763	47	rows	row	NOUN
ejpam-3338	763	48	of	of	ADP
ejpam-3338	763	49	the	the	DET
ejpam-3338	763	50	system	system	NOUN
ejpam-3338	763	51	was	be	AUX
ejpam-3338	763	52	developed	develop	VERB
ejpam-3338	763	53	during	during	ADP
ejpam-3338	763	54	around	around	ADV
ejpam-3338	763	55	mid-20th	mid-20th	NUM
ejpam-3338	763	56	century	century	NOUN
ejpam-3338	763	57	.	.	PUNCT
ejpam-3338	764	1	for	for	ADP
ejpam-3338	764	2	the	the	DET
ejpam-3338	764	3	inconsistent	inconsistent	ADJ
ejpam-3338	764	4	(	(	PUNCT
ejpam-3338	764	5	contradictory	contradictory	ADJ
ejpam-3338	764	6	linear	linear	PROPN
ejpam-3338	764	7	equations	equation	NOUN
ejpam-3338	764	8	)	)	PUNCT
ejpam-3338	764	9	system	system	NOUN
ejpam-3338	764	10	,	,	PUNCT
ejpam-3338	764	11	we	we	PRON
ejpam-3338	764	12	do	do	AUX
ejpam-3338	764	13	not	not	PART
ejpam-3338	764	14	have	have	VERB
ejpam-3338	764	15	any	any	DET
ejpam-3338	764	16	solution	solution	NOUN
ejpam-3338	764	17	that	that	PRON
ejpam-3338	764	18	satisfies	satisfy	VERB
ejpam-3338	764	19	all	all	DET
ejpam-3338	764	20	the	the	DET
ejpam-3338	764	21	equations	equation	NOUN
ejpam-3338	764	22	.	.	PUNCT
ejpam-3338	765	1	but	but	CCONJ
ejpam-3338	765	2	a	a	DET
ejpam-3338	765	3	specific	specific	ADJ
ejpam-3338	765	4	generalized	generalized	ADJ
ejpam-3338	765	5	inverse	inverse	NOUN
ejpam-3338	765	6	of	of	ADP
ejpam-3338	765	7	the	the	DET
ejpam-3338	765	8	coefficient	coefficient	NOUN
ejpam-3338	765	9	matrix	matrix	NOUN
ejpam-3338	765	10	of	of	ADP
ejpam-3338	765	11	the	the	DET
ejpam-3338	765	12	equation	equation	NOUN
ejpam-3338	765	13	in	in	ADP
ejpam-3338	765	14	matrix	matrix	NOUN
ejpam-3338	765	15	form	form	NOUN
ejpam-3338	765	16	,	,	PUNCT
ejpam-3338	765	17	called	call	VERB
ejpam-3338	765	18	the	the	DET
ejpam-3338	765	19	pseudo	pseudo	NOUN
ejpam-3338	765	20	-	-	NOUN
ejpam-3338	765	21	inverse	inverse	NOUN
ejpam-3338	765	22	,	,	PUNCT
ejpam-3338	765	23	provides	provide	VERB
ejpam-3338	765	24	the	the	DET
ejpam-3338	765	25	minimumnorm	minimumnorm	NOUN
ejpam-3338	765	26	least	least	ADJ
ejpam-3338	765	27	-	-	PUNCT
ejpam-3338	765	28	squares	square	NOUN
ejpam-3338	765	29	inverse	inverse	NOUN
ejpam-3338	765	30	(	(	PUNCT
ejpam-3338	765	31	i.e.	i.e.	X
ejpam-3338	765	32	||x||	||x||	ADV
ejpam-3338	765	33	=	=	SYM
ejpam-3338	765	34	minimum	minimum	ADJ
ejpam-3338	765	35	implying	implying	ADJ
ejpam-3338	765	36	minimum	minimum	ADJ
ejpam-3338	765	37	norm	norm	NOUN
ejpam-3338	765	38	as	as	ADV
ejpam-3338	765	39	well	well	ADV
ejpam-3338	765	40	as	as	ADP
ejpam-3338	765	41	||ax	||ax	ADJ
ejpam-3338	765	42	−	−	PROPN
ejpam-3338	765	43	b||	b||	NOUN
ejpam-3338	766	1	=	=	NUM
ejpam-3338	766	2	minimum	minimum	ADJ
ejpam-3338	766	3	implying	implying	ADJ
ejpam-3338	766	4	least	least	ADJ
ejpam-3338	766	5	squares	square	NOUN
ejpam-3338	766	6	,	,	PUNCT
ejpam-3338	766	7	where	where	SCONJ
ejpam-3338	766	8	x	x	PRON
ejpam-3338	766	9	is	be	AUX
ejpam-3338	766	10	the	the	DET
ejpam-3338	766	11	computed	computed	ADJ
ejpam-3338	766	12	solution	solution	NOUN
ejpam-3338	766	13	of	of	ADP
ejpam-3338	766	14	the	the	DET
ejpam-3338	766	15	linear	linear	ADJ
ejpam-3338	766	16	system	system	NOUN
ejpam-3338	766	17	ax	ax	NOUN
ejpam-3338	766	18	=	=	SYM
ejpam-3338	766	19	b	b	NOUN
ejpam-3338	766	20	,	,	PUNCT
ejpam-3338	766	21	and	and	CCONJ
ejpam-3338	766	22	||.||	||.||	NOUN
ejpam-3338	766	23	is	be	AUX
ejpam-3338	766	24	the	the	DET
ejpam-3338	766	25	euclidian	euclidian	ADJ
ejpam-3338	766	26	matrix	matrix	NOUN
ejpam-3338	766	27	norm	norm	NOUN
ejpam-3338	766	28	)	)	PUNCT
ejpam-3338	766	29	.	.	PUNCT
ejpam-3338	767	1	consequently	consequently	ADV
ejpam-3338	767	2	,	,	PUNCT
ejpam-3338	767	3	we	we	PRON
ejpam-3338	767	4	obtain	obtain	VERB
ejpam-3338	767	5	the	the	DET
ejpam-3338	767	6	minimum	minimum	ADJ
ejpam-3338	767	7	-	-	PUNCT
ejpam-3338	767	8	norm	norm	NOUN
ejpam-3338	767	9	least	least	ADJ
ejpam-3338	767	10	-	-	PUNCT
ejpam-3338	767	11	squares	square	NOUN
ejpam-3338	767	12	solution	solution	NOUN
ejpam-3338	767	13	of	of	ADP
ejpam-3338	767	14	the	the	DET
ejpam-3338	767	15	system	system	NOUN
ejpam-3338	767	16	.	.	PUNCT
ejpam-3338	768	1	this	this	DET
ejpam-3338	768	2	solution	solution	NOUN
ejpam-3338	768	3	is	be	AUX
ejpam-3338	768	4	of	of	ADP
ejpam-3338	768	5	paramount	paramount	ADJ
ejpam-3338	768	6	importance	importance	NOUN
ejpam-3338	768	7	and	and	CCONJ
ejpam-3338	768	8	extensively	extensively	ADV
ejpam-3338	768	9	used	use	VERB
ejpam-3338	768	10	in	in	ADP
ejpam-3338	768	11	whole	whole	NOUN
ejpam-3338	768	12	of	of	ADP
ejpam-3338	768	13	engineering	engineering	NOUN
ejpam-3338	768	14	and	and	CCONJ
ejpam-3338	768	15	science	science	NOUN
ejpam-3338	768	16	as	as	ADV
ejpam-3338	768	17	long	long	ADV
ejpam-3338	768	18	as	as	SCONJ
ejpam-3338	768	19	the	the	DET
ejpam-3338	768	20	degree	degree	NOUN
ejpam-3338	768	21	of	of	ADP
ejpam-3338	768	22	inconsistency	inconsistency	NOUN
ejpam-3338	768	23	(	(	PUNCT
ejpam-3338	768	24	contradiction	contradiction	NOUN
ejpam-3338	768	25	among	among	ADP
ejpam-3338	768	26	the	the	DET
ejpam-3338	768	27	linear	linear	PROPN
ejpam-3338	768	28	equations	equation	NOUN
ejpam-3338	768	29	)	)	PUNCT
ejpam-3338	768	30	is	be	AUX
ejpam-3338	768	31	within	within	ADP
ejpam-3338	768	32	acceptable	acceptable	ADJ
ejpam-3338	768	33	limit	limit	NOUN
ejpam-3338	768	34	depending	depend	VERB
ejpam-3338	768	35	on	on	ADP
ejpam-3338	768	36	the	the	DET
ejpam-3338	768	37	context	context	NOUN
ejpam-3338	768	38	.	.	PUNCT
ejpam-3338	769	1	if	if	SCONJ
ejpam-3338	769	2	there	there	PRON
ejpam-3338	769	3	is	be	VERB
ejpam-3338	769	4	unacceptable	unacceptable	ADJ
ejpam-3338	769	5	inconsistency	inconsistency	NOUN
ejpam-3338	769	6	in	in	ADP
ejpam-3338	769	7	the	the	DET
ejpam-3338	769	8	linear	linear	ADJ
ejpam-3338	769	9	system	system	NOUN
ejpam-3338	769	10	,	,	PUNCT
ejpam-3338	769	11	then	then	ADV
ejpam-3338	769	12	one	one	PRON
ejpam-3338	769	13	should	should	AUX
ejpam-3338	769	14	fall	fall	VERB
ejpam-3338	769	15	back	back	ADV
ejpam-3338	769	16	to	to	ADP
ejpam-3338	769	17	the	the	DET
ejpam-3338	769	18	physical	physical	ADJ
ejpam-3338	769	19	problem	problem	NOUN
ejpam-3338	769	20	,	,	PUNCT
ejpam-3338	769	21	find	find	VERB
ejpam-3338	769	22	out	out	ADP
ejpam-3338	769	23	the	the	DET
ejpam-3338	769	24	cause	cause	NOUN
ejpam-3338	769	25	for	for	ADP
ejpam-3338	769	26	abnormal	abnormal	ADJ
ejpam-3338	769	27	inconsistency	inconsistency	NOUN
ejpam-3338	769	28	and	and	CCONJ
ejpam-3338	769	29	correct	correct	VERB
ejpam-3338	769	30	the	the	DET
ejpam-3338	769	31	error	error	NOUN
ejpam-3338	769	32	/	/	SYM
ejpam-3338	769	33	mistake	mistake	NOUN
ejpam-3338	769	34	.	.	PUNCT
ejpam-3338	770	1	it	it	PRON
ejpam-3338	770	2	can	can	AUX
ejpam-3338	770	3	be	be	AUX
ejpam-3338	770	4	seen	see	VERB
ejpam-3338	770	5	that	that	SCONJ
ejpam-3338	770	6	nature	nature	NOUN
ejpam-3338	770	7	knows	know	VERB
ejpam-3338	770	8	no	no	DET
ejpam-3338	770	9	inconsistency	inconsistency	NOUN
ejpam-3338	770	10	.	.	PUNCT
ejpam-3338	771	1	the	the	DET
ejpam-3338	771	2	inconsistency	inconsistency	NOUN
ejpam-3338	771	3	in	in	ADP
ejpam-3338	771	4	a	a	DET
ejpam-3338	771	5	linear	linear	ADJ
ejpam-3338	771	6	system	system	NOUN
ejpam-3338	771	7	(	(	PUNCT
ejpam-3338	771	8	viz	viz	PROPN
ejpam-3338	771	9	.	.	PUNCT
ejpam-3338	772	1	the	the	DET
ejpam-3338	772	2	mathematical	mathematical	ADJ
ejpam-3338	772	3	model	model	NOUN
ejpam-3338	772	4	corresponding	correspond	VERB
ejpam-3338	772	5	to	to	ADP
ejpam-3338	772	6	a	a	DET
ejpam-3338	772	7	physical	physical	ADJ
ejpam-3338	772	8	problem	problem	NOUN
ejpam-3338	772	9	of	of	ADP
ejpam-3338	772	10	nature	nature	NOUN
ejpam-3338	772	11	)	)	PUNCT
ejpam-3338	772	12	could	could	AUX
ejpam-3338	772	13	result	result	VERB
ejpam-3338	772	14	only	only	ADV
ejpam-3338	772	15	due	due	ADP
ejpam-3338	772	16	to	to	ADP
ejpam-3338	772	17	human	human	ADJ
ejpam-3338	772	18	error	error	NOUN
ejpam-3338	772	19	/	/	SYM
ejpam-3338	772	20	mistake	mistake	NOUN
ejpam-3338	772	21	.	.	PUNCT
ejpam-3338	773	1	since	since	SCONJ
ejpam-3338	773	2	error	error	NOUN
ejpam-3338	773	3	(	(	PUNCT
ejpam-3338	773	4	error	error	NOUN
ejpam-3338	773	5	(	(	PUNCT
ejpam-3338	773	6	not	not	PART
ejpam-3338	773	7	mistake	mistake	NOUN
ejpam-3338	773	8	)	)	PUNCT
ejpam-3338	773	9	in	in	ADP
ejpam-3338	773	10	measurement	measurement	NOUN
ejpam-3338	773	11	and/or	and/or	CCONJ
ejpam-3338	773	12	in	in	ADP
ejpam-3338	773	13	computation	computation	NOUN
ejpam-3338	773	14	)	)	PUNCT
ejpam-3338	773	15	is	be	AUX
ejpam-3338	773	16	ever	ever	ADV
ejpam-3338	773	17	impossible	impossible	ADJ
ejpam-3338	773	18	to	to	PART
ejpam-3338	773	19	be	be	AUX
ejpam-3338	773	20	removed	remove	VERB
ejpam-3338	773	21	,	,	PUNCT
ejpam-3338	773	22	it	it	PRON
ejpam-3338	773	23	could	could	AUX
ejpam-3338	773	24	often	often	ADV
ejpam-3338	773	25	(	(	PUNCT
ejpam-3338	773	26	not	not	PART
ejpam-3338	773	27	always	always	ADV
ejpam-3338	773	28	)	)	PUNCT
ejpam-3338	773	29	result	result	VERB
ejpam-3338	773	30	in	in	ADP
ejpam-3338	773	31	inconsistent	inconsistent	ADJ
ejpam-3338	773	32	/	/	SYM
ejpam-3338	773	33	near	near	ADP
ejpam-3338	773	34	-	-	PUNCT
ejpam-3338	773	35	consistent	consistent	ADJ
ejpam-3338	773	36	system	system	NOUN
ejpam-3338	773	37	.	.	PUNCT
ejpam-3338	774	1	we	we	PRON
ejpam-3338	774	2	need	need	VERB
ejpam-3338	774	3	to	to	PART
ejpam-3338	774	4	deal	deal	VERB
ejpam-3338	774	5	with	with	ADP
ejpam-3338	774	6	such	such	DET
ejpam-3338	774	7	a	a	DET
ejpam-3338	774	8	system	system	NOUN
ejpam-3338	774	9	almost	almost	ADV
ejpam-3338	774	10	always	always	ADV
ejpam-3338	774	11	.	.	PUNCT
ejpam-3338	775	1	so	so	ADV
ejpam-3338	775	2	is	be	AUX
ejpam-3338	775	3	the	the	DET
ejpam-3338	775	4	need	need	NOUN
ejpam-3338	775	5	for	for	ADP
ejpam-3338	775	6	the	the	DET
ejpam-3338	775	7	s.	s.	PROPN
ejpam-3338	775	8	k.sen	k.sen	PROPN
ejpam-3338	775	9	,	,	PUNCT
ejpam-3338	775	10	j.	j.	PROPN
ejpam-3338	775	11	v.	v.	PROPN
ejpam-3338	775	12	devi	devi	PROPN
ejpam-3338	775	13	,	,	PUNCT
ejpam-3338	775	14	r.v.g	r.v.g	NOUN
ejpam-3338	775	15	.	.	PUNCT
ejpam-3338	776	1	r.	r.	PROPN
ejpam-3338	776	2	kumar	kumar	PROPN
ejpam-3338	776	3	/	/	SYM
ejpam-3338	776	4	eur	eur	PROPN
ejpam-3338	776	5	.	.	PUNCT
ejpam-3338	777	1	j.	j.	PROPN
ejpam-3338	777	2	pure	pure	PROPN
ejpam-3338	777	3	appl	appl	PROPN
ejpam-3338	777	4	.	.	PROPN
ejpam-3338	777	5	math	math	PROPN
ejpam-3338	777	6	,	,	PUNCT
ejpam-3338	777	7	11	11	NUM
ejpam-3338	777	8	(	(	PUNCT
ejpam-3338	777	9	3	3	NUM
ejpam-3338	777	10	)	)	PUNCT
ejpam-3338	777	11	(	(	PUNCT
ejpam-3338	777	12	2018	2018	NUM
ejpam-3338	777	13	)	)	PUNCT
ejpam-3338	777	14	,	,	PUNCT
ejpam-3338	777	15	1058	1058	NUM
ejpam-3338	777	16	-	-	SYM
ejpam-3338	777	17	1099	1099	NUM
ejpam-3338	777	18	1095	1095	NUM
ejpam-3338	777	19	minimum	minimum	ADJ
ejpam-3338	777	20	-	-	PUNCT
ejpam-3338	777	21	norm	norm	NOUN
ejpam-3338	777	22	least	least	ADJ
ejpam-3338	777	23	-	-	PUNCT
ejpam-3338	777	24	squares	square	NOUN
ejpam-3338	777	25	inverse	inverse	NOUN
ejpam-3338	777	26	(	(	PUNCT
ejpam-3338	777	27	not	not	PART
ejpam-3338	777	28	the	the	DET
ejpam-3338	777	29	true	true	ADJ
ejpam-3338	777	30	inverse	inverse	NOUN
ejpam-3338	777	31	as	as	SCONJ
ejpam-3338	777	32	it	it	PRON
ejpam-3338	777	33	does	do	AUX
ejpam-3338	777	34	not	not	PART
ejpam-3338	777	35	exist	exist	VERB
ejpam-3338	777	36	for	for	ADP
ejpam-3338	777	37	most	most	ADJ
ejpam-3338	777	38	of	of	ADP
ejpam-3338	777	39	the	the	DET
ejpam-3338	777	40	problems	problem	NOUN
ejpam-3338	777	41	or	or	CCONJ
ejpam-3338	777	42	is	be	AUX
ejpam-3338	777	43	too	too	ADV
ejpam-3338	777	44	erroneous	erroneous	ADJ
ejpam-3338	777	45	due	due	ADJ
ejpam-3338	777	46	to	to	ADP
ejpam-3338	777	47	near	near	ADJ
ejpam-3338	777	48	-	-	PUNCT
ejpam-3338	777	49	singularity	singularity	NOUN
ejpam-3338	777	50	/	/	SYM
ejpam-3338	777	51	non	non	ADJ
ejpam-3338	777	52	-	-	ADJ
ejpam-3338	777	53	square	square	ADJ
ejpam-3338	777	54	rectangularity	rectangularity	NOUN
ejpam-3338	777	55	of	of	ADP
ejpam-3338	777	56	the	the	DET
ejpam-3338	777	57	coefficient	coefficient	NOUN
ejpam-3338	777	58	matrix	matrix	NOUN
ejpam-3338	777	59	a	a	PRON
ejpam-3338	777	60	)	)	PUNCT
ejpam-3338	777	61	almost	almost	ADV
ejpam-3338	777	62	always	always	ADV
ejpam-3338	777	63	in	in	ADP
ejpam-3338	777	64	the	the	DET
ejpam-3338	777	65	physical	physical	ADJ
ejpam-3338	777	66	world	world	NOUN
ejpam-3338	777	67	.	.	PUNCT
ejpam-3338	778	1	one	one	PRON
ejpam-3338	778	2	can	can	AUX
ejpam-3338	778	3	devise	devise	VERB
ejpam-3338	778	4	a	a	DET
ejpam-3338	778	5	row	row	ADV
ejpam-3338	778	6	-	-	PUNCT
ejpam-3338	778	7	pruning	prune	VERB
ejpam-3338	778	8	algorithm	algorithm	NOUN
ejpam-3338	778	9	for	for	ADP
ejpam-3338	778	10	a	a	DET
ejpam-3338	778	11	given	give	VERB
ejpam-3338	778	12	linear	linear	ADJ
ejpam-3338	778	13	system	system	NOUN
ejpam-3338	778	14	ax	ax	NOUN
ejpam-3338	778	15	=	=	NOUN
ejpam-3338	778	16	b	b	NOUN
ejpam-3338	778	17	to	to	PART
ejpam-3338	778	18	remove	remove	VERB
ejpam-3338	778	19	all	all	DET
ejpam-3338	778	20	redundant	redundant	ADJ
ejpam-3338	778	21	rows	row	NOUN
ejpam-3338	778	22	(	(	PUNCT
ejpam-3338	778	23	i.e.	i.e.	X
ejpam-3338	778	24	linearly	linearly	ADV
ejpam-3338	778	25	dependent	dependent	ADJ
ejpam-3338	778	26	rows	row	NOUN
ejpam-3338	778	27	)	)	PUNCT
ejpam-3338	778	28	of	of	ADP
ejpam-3338	778	29	the	the	DET
ejpam-3338	778	30	augmented	augment	VERB
ejpam-3338	778	31	matrix	matrix	NOUN
ejpam-3338	778	32	(	(	PUNCT
ejpam-3338	778	33	a	a	DET
ejpam-3338	778	34	,	,	PUNCT
ejpam-3338	778	35	b	b	NOUN
ejpam-3338	778	36	)	)	PUNCT
ejpam-3338	779	1	[	[	X
ejpam-3338	779	2	14	14	NUM
ejpam-3338	779	3	,	,	PUNCT
ejpam-3338	779	4	15	15	NUM
ejpam-3338	779	5	]	]	PUNCT
ejpam-3338	779	6	.	.	PUNCT
ejpam-3338	780	1	such	such	DET
ejpam-3338	780	2	an	an	DET
ejpam-3338	780	3	algorithm	algorithm	NOUN
ejpam-3338	780	4	will	will	AUX
ejpam-3338	780	5	act	act	VERB
ejpam-3338	780	6	as	as	ADP
ejpam-3338	780	7	a	a	DET
ejpam-3338	780	8	pre	pre	NOUN
ejpam-3338	780	9	-	-	NOUN
ejpam-3338	780	10	processor	processor	NOUN
ejpam-3338	780	11	for	for	ADP
ejpam-3338	780	12	solving	solve	VERB
ejpam-3338	780	13	a	a	DET
ejpam-3338	780	14	linear	linear	ADJ
ejpam-3338	780	15	system	system	NOUN
ejpam-3338	780	16	using	use	VERB
ejpam-3338	780	17	the	the	DET
ejpam-3338	780	18	pseudoinverse	pseudoinverse	NOUN
ejpam-3338	780	19	.	.	PUNCT
ejpam-3338	781	1	the	the	DET
ejpam-3338	781	2	pruning	pruning	NOUN
ejpam-3338	781	3	reduces	reduce	VERB
ejpam-3338	781	4	the	the	DET
ejpam-3338	781	5	computational	computational	ADJ
ejpam-3338	781	6	error	error	NOUN
ejpam-3338	781	7	and	and	CCONJ
ejpam-3338	781	8	also	also	ADV
ejpam-3338	781	9	storage	storage	NOUN
ejpam-3338	781	10	complexity	complexity	NOUN
ejpam-3338	781	11	whenever	whenever	SCONJ
ejpam-3338	781	12	it	it	PRON
ejpam-3338	781	13	occurs	occur	VERB
ejpam-3338	781	14	.	.	PUNCT
ejpam-3338	782	1	however	however	ADV
ejpam-3338	782	2	,	,	PUNCT
ejpam-3338	782	3	this	this	PRON
ejpam-3338	782	4	is	be	AUX
ejpam-3338	782	5	not	not	PART
ejpam-3338	782	6	widely	widely	ADV
ejpam-3338	782	7	used	use	VERB
ejpam-3338	782	8	mainly	mainly	ADV
ejpam-3338	782	9	because	because	SCONJ
ejpam-3338	782	10	it	it	PRON
ejpam-3338	782	11	is	be	AUX
ejpam-3338	782	12	an	an	DET
ejpam-3338	782	13	additional	additional	ADJ
ejpam-3338	782	14	task	task	NOUN
ejpam-3338	782	15	and	and	CCONJ
ejpam-3338	782	16	also	also	ADV
ejpam-3338	782	17	,	,	PUNCT
ejpam-3338	782	18	for	for	ADP
ejpam-3338	782	19	most	most	ADJ
ejpam-3338	782	20	of	of	ADP
ejpam-3338	782	21	the	the	DET
ejpam-3338	782	22	real	real	ADJ
ejpam-3338	782	23	-	-	PUNCT
ejpam-3338	782	24	world	world	NOUN
ejpam-3338	782	25	problems	problem	NOUN
ejpam-3338	782	26	,	,	PUNCT
ejpam-3338	782	27	the	the	DET
ejpam-3338	782	28	current	current	ADJ
ejpam-3338	782	29	(	(	PUNCT
ejpam-3338	782	30	2018	2018	NUM
ejpam-3338	782	31	)	)	PUNCT
ejpam-3338	782	32	computing	compute	VERB
ejpam-3338	782	33	precision	precision	NOUN
ejpam-3338	782	34	and	and	CCONJ
ejpam-3338	782	35	also	also	ADV
ejpam-3338	782	36	storage	storage	NOUN
ejpam-3338	782	37	is	be	AUX
ejpam-3338	782	38	not	not	PART
ejpam-3338	782	39	an	an	DET
ejpam-3338	782	40	issue	issue	NOUN
ejpam-3338	782	41	to	to	PART
ejpam-3338	782	42	obviate	obviate	VERB
ejpam-3338	782	43	the	the	DET
ejpam-3338	782	44	foregoing	forego	VERB
ejpam-3338	782	45	2	2	NUM
ejpam-3338	782	46	problems	problem	NOUN
ejpam-3338	782	47	.	.	PUNCT
ejpam-3338	783	1	thus	thus	ADV
ejpam-3338	783	2	the	the	DET
ejpam-3338	783	3	generalized	generalized	ADJ
ejpam-3338	783	4	inverse	inverse	NOUN
ejpam-3338	783	5	viz	viz	PROPN
ejpam-3338	783	6	.	.	PUNCT
ejpam-3338	784	1	the	the	DET
ejpam-3338	784	2	pseudo	pseudo	NOUN
ejpam-3338	784	3	inverse	inverse	NOUN
ejpam-3338	784	4	of	of	ADP
ejpam-3338	784	5	the	the	DET
ejpam-3338	784	6	matrix	matrix	NOUN
ejpam-3338	784	7	a	a	PRON
ejpam-3338	784	8	is	be	AUX
ejpam-3338	784	9	good	good	ADJ
ejpam-3338	784	10	enough	enough	ADV
ejpam-3338	784	11	for	for	ADP
ejpam-3338	784	12	practically	practically	ADV
ejpam-3338	784	13	all	all	PRON
ejpam-3338	784	14	physical	physical	ADJ
ejpam-3338	784	15	problems	problem	NOUN
ejpam-3338	784	16	.	.	PUNCT
ejpam-3338	785	1	with	with	ADP
ejpam-3338	785	2	the	the	DET
ejpam-3338	785	3	foregoing	forego	VERB
ejpam-3338	785	4	essence	essence	NOUN
ejpam-3338	785	5	of	of	ADP
ejpam-3338	785	6	generalizing	generalize	VERB
ejpam-3338	785	7	the	the	DET
ejpam-3338	785	8	matrix	matrix	NOUN
ejpam-3338	785	9	inverse	inverse	NOUN
ejpam-3338	785	10	in	in	ADP
ejpam-3338	785	11	mind	mind	NOUN
ejpam-3338	785	12	,	,	PUNCT
ejpam-3338	785	13	can	can	AUX
ejpam-3338	785	14	we	we	PRON
ejpam-3338	785	15	have	have	VERB
ejpam-3338	785	16	the	the	DET
ejpam-3338	785	17	similar	similar	ADJ
ejpam-3338	785	18	essence	essence	NOUN
ejpam-3338	785	19	of	of	ADP
ejpam-3338	785	20	generalizing	generalize	VERB
ejpam-3338	785	21	the	the	DET
ejpam-3338	785	22	classical	classical	ADJ
ejpam-3338	785	23	calculus	calculus	NOUN
ejpam-3338	785	24	so	so	SCONJ
ejpam-3338	785	25	that	that	SCONJ
ejpam-3338	785	26	the	the	DET
ejpam-3338	785	27	generalized	generalized	ADJ
ejpam-3338	785	28	calculus	calculus	NOUN
ejpam-3338	785	29	(	(	PUNCT
ejpam-3338	785	30	viz	viz	PROPN
ejpam-3338	785	31	.	.	PUNCT
ejpam-3338	785	32	fractional	fractional	ADJ
ejpam-3338	785	33	calculus	calculus	NOUN
ejpam-3338	785	34	)	)	PUNCT
ejpam-3338	785	35	universally	universally	ADV
ejpam-3338	785	36	serves	serve	VERB
ejpam-3338	785	37	the	the	DET
ejpam-3338	785	38	purpose	purpose	NOUN
ejpam-3338	785	39	for	for	ADP
ejpam-3338	785	40	all	all	DET
ejpam-3338	785	41	calculus	calculus	NOUN
ejpam-3338	785	42	(	(	PUNCT
ejpam-3338	785	43	including	include	VERB
ejpam-3338	785	44	differential	differential	ADJ
ejpam-3338	785	45	equations	equation	NOUN
ejpam-3338	785	46	)	)	PUNCT
ejpam-3338	785	47	problems	problem	NOUN
ejpam-3338	785	48	always	always	ADV
ejpam-3338	785	49	?	?	PUNCT
ejpam-3338	786	1	if	if	SCONJ
ejpam-3338	786	2	we	we	PRON
ejpam-3338	786	3	can	can	AUX
ejpam-3338	786	4	,	,	PUNCT
ejpam-3338	786	5	then	then	ADV
ejpam-3338	786	6	the	the	DET
ejpam-3338	786	7	advantage	advantage	NOUN
ejpam-3338	786	8	of	of	ADP
ejpam-3338	786	9	generalizing	generalize	VERB
ejpam-3338	786	10	the	the	DET
ejpam-3338	786	11	calculus	calculus	NOUN
ejpam-3338	786	12	,	,	PUNCT
ejpam-3338	786	13	of	of	ADP
ejpam-3338	786	14	course	course	NOUN
ejpam-3338	786	15	including	include	VERB
ejpam-3338	786	16	the	the	DET
ejpam-3338	786	17	physical	physical	ADJ
ejpam-3338	786	18	interpretation	interpretation	NOUN
ejpam-3338	786	19	of	of	ADP
ejpam-3338	786	20	fractional	fractional	ADJ
ejpam-3338	786	21	order	order	NOUN
ejpam-3338	786	22	derivative	derivative	ADJ
ejpam-3338	786	23	/	/	SYM
ejpam-3338	786	24	integral	integral	ADJ
ejpam-3338	786	25	,	,	PUNCT
ejpam-3338	786	26	will	will	AUX
ejpam-3338	786	27	be	be	AUX
ejpam-3338	786	28	enormous	enormous	ADJ
ejpam-3338	786	29	in	in	ADP
ejpam-3338	786	30	terms	term	NOUN
ejpam-3338	786	31	of	of	ADP
ejpam-3338	786	32	solving	solve	VERB
ejpam-3338	786	33	numerous	numerous	ADJ
ejpam-3338	786	34	problems	problem	NOUN
ejpam-3338	786	35	in	in	ADP
ejpam-3338	786	36	the	the	DET
ejpam-3338	786	37	physical	physical	ADJ
ejpam-3338	786	38	world	world	NOUN
ejpam-3338	786	39	readily	readily	ADV
ejpam-3338	786	40	and	and	CCONJ
ejpam-3338	786	41	easily	easily	ADV
ejpam-3338	786	42	.	.	PUNCT
ejpam-3338	787	1	classical	classical	ADJ
ejpam-3338	787	2	ode	ode	PROPN
ejpam-3338	787	3	corresponding	corresponding	NOUN
ejpam-3338	787	4	to	to	ADP
ejpam-3338	787	5	any	any	DET
ejpam-3338	787	6	fractional	fractional	ADJ
ejpam-3338	787	7	ode	ode	NOUN
ejpam-3338	787	8	a	a	DET
ejpam-3338	787	9	1	1	NUM
ejpam-3338	787	10	-	-	PUNCT
ejpam-3338	787	11	independent	independent	ADJ
ejpam-3338	787	12	variable	variable	ADJ
ejpam-3338	787	13	fde	fde	NOUN
ejpam-3338	787	14	can	can	AUX
ejpam-3338	787	15	be	be	AUX
ejpam-3338	787	16	written	write	VERB
ejpam-3338	787	17	as	as	ADP
ejpam-3338	787	18	1	1	NUM
ejpam-3338	787	19	or	or	CCONJ
ejpam-3338	787	20	more	more	ADV
ejpam-3338	787	21	distinct	distinct	ADJ
ejpam-3338	787	22	classical	classical	ADJ
ejpam-3338	787	23	odes	ode	NOUN
ejpam-3338	787	24	in	in	ADP
ejpam-3338	787	25	so	so	ADV
ejpam-3338	787	26	far	far	ADV
ejpam-3338	787	27	as	as	SCONJ
ejpam-3338	787	28	its	its	PRON
ejpam-3338	787	29	solution	solution	NOUN
ejpam-3338	787	30	is	be	AUX
ejpam-3338	787	31	concerned	concern	VERB
ejpam-3338	787	32	.	.	PUNCT
ejpam-3338	788	1	consider	consider	VERB
ejpam-3338	788	2	,	,	PUNCT
ejpam-3338	788	3	for	for	ADP
ejpam-3338	788	4	example	example	NOUN
ejpam-3338	788	5	,	,	PUNCT
ejpam-3338	788	6	1	1	NUM
ejpam-3338	788	7	fde	fde	NOUN
ejpam-3338	788	8	where	where	SCONJ
ejpam-3338	788	9	the	the	DET
ejpam-3338	788	10	fraction	fraction	NOUN
ejpam-3338	788	11	α	α	X
ejpam-3338	788	12	<	<	X
ejpam-3338	788	13	1	1	NUM
ejpam-3338	788	14	.	.	PUNCT
ejpam-3338	789	1	its	its	PRON
ejpam-3338	789	2	solution	solution	NOUN
ejpam-3338	789	3	will	will	AUX
ejpam-3338	789	4	correspond	correspond	VERB
ejpam-3338	789	5	to	to	ADP
ejpam-3338	789	6	a	a	DET
ejpam-3338	789	7	continuous	continuous	ADJ
ejpam-3338	789	8	function	function	NOUN
ejpam-3338	789	9	of	of	ADP
ejpam-3338	789	10	1	1	NUM
ejpam-3338	789	11	variable	variable	NOUN
ejpam-3338	789	12	.	.	PUNCT
ejpam-3338	790	1	graphically	graphically	ADV
ejpam-3338	790	2	,	,	PUNCT
ejpam-3338	790	3	this	this	PRON
ejpam-3338	790	4	will	will	AUX
ejpam-3338	790	5	be	be	AUX
ejpam-3338	790	6	a	a	DET
ejpam-3338	790	7	curve	curve	NOUN
ejpam-3338	790	8	(	(	PUNCT
ejpam-3338	790	9	a	a	DET
ejpam-3338	790	10	continuous	continuous	ADJ
ejpam-3338	790	11	line	line	NOUN
ejpam-3338	790	12	)	)	PUNCT
ejpam-3338	790	13	in	in	ADP
ejpam-3338	790	14	the	the	DET
ejpam-3338	790	15	concerned	concerned	ADJ
ejpam-3338	790	16	interval	interval	NOUN
ejpam-3338	790	17	of	of	ADP
ejpam-3338	790	18	the	the	DET
ejpam-3338	790	19	independent	independent	ADJ
ejpam-3338	790	20	variable	variable	NOUN
ejpam-3338	790	21	.	.	PUNCT
ejpam-3338	791	1	corresponding	correspond	VERB
ejpam-3338	791	2	to	to	ADP
ejpam-3338	791	3	this	this	DET
ejpam-3338	791	4	graph	graph	NOUN
ejpam-3338	791	5	,	,	PUNCT
ejpam-3338	791	6	we	we	PRON
ejpam-3338	791	7	can	can	AUX
ejpam-3338	791	8	readily	readily	ADV
ejpam-3338	791	9	produce	produce	VERB
ejpam-3338	791	10	a	a	DET
ejpam-3338	791	11	classical	classical	ADJ
ejpam-3338	791	12	ode	ode	NOUN
ejpam-3338	791	13	of	of	ADP
ejpam-3338	791	14	order	order	NOUN
ejpam-3338	791	15	1	1	NUM
ejpam-3338	791	16	or	or	CCONJ
ejpam-3338	791	17	more	more	ADJ
ejpam-3338	791	18	by	by	ADP
ejpam-3338	791	19	successive	successive	ADJ
ejpam-3338	791	20	differentiation	differentiation	NOUN
ejpam-3338	791	21	.	.	PUNCT
ejpam-3338	792	1	on	on	ADP
ejpam-3338	792	2	the	the	DET
ejpam-3338	792	3	other	other	ADJ
ejpam-3338	792	4	hand	hand	NOUN
ejpam-3338	792	5	,	,	PUNCT
ejpam-3338	792	6	we	we	PRON
ejpam-3338	792	7	may	may	AUX
ejpam-3338	792	8	have	have	VERB
ejpam-3338	792	9	a	a	DET
ejpam-3338	792	10	classical	classical	ADJ
ejpam-3338	792	11	ode	ode	NOUN
ejpam-3338	792	12	(	(	PUNCT
ejpam-3338	792	13	based	base	VERB
ejpam-3338	792	14	,	,	PUNCT
ejpam-3338	792	15	say	say	INTJ
ejpam-3338	792	16	,	,	PUNCT
ejpam-3338	792	17	on	on	ADP
ejpam-3338	792	18	the	the	DET
ejpam-3338	792	19	2nd	2nd	ADJ
ejpam-3338	792	20	law	law	NOUN
ejpam-3338	792	21	of	of	ADP
ejpam-3338	792	22	newton	newton	PROPN
ejpam-3338	792	23	)	)	PUNCT
ejpam-3338	792	24	appended	append	VERB
ejpam-3338	792	25	with	with	ADP
ejpam-3338	792	26	a	a	DET
ejpam-3338	792	27	friction	friction	NOUN
ejpam-3338	792	28	force	force	NOUN
ejpam-3338	792	29	term	term	NOUN
ejpam-3338	792	30	obtained	obtain	VERB
ejpam-3338	792	31	from	from	ADP
ejpam-3338	792	32	a	a	DET
ejpam-3338	792	33	given	give	VERB
ejpam-3338	792	34	physical	physical	ADJ
ejpam-3338	792	35	problem	problem	NOUN
ejpam-3338	792	36	.	.	PUNCT
ejpam-3338	793	1	we	we	PRON
ejpam-3338	793	2	can	can	AUX
ejpam-3338	793	3	easily	easily	ADV
ejpam-3338	793	4	interpret	interpret	VERB
ejpam-3338	793	5	the	the	DET
ejpam-3338	793	6	corresponding	corresponding	ADJ
ejpam-3338	793	7	physical	physical	ADJ
ejpam-3338	793	8	problem	problem	NOUN
ejpam-3338	793	9	for	for	ADP
ejpam-3338	793	10	each	each	PRON
ejpam-3338	793	11	of	of	ADP
ejpam-3338	793	12	the	the	DET
ejpam-3338	793	13	foregoing	forego	VERB
ejpam-3338	793	14	classical	classical	ADJ
ejpam-3338	793	15	odes	ode	NOUN
ejpam-3338	793	16	.	.	PUNCT
ejpam-3338	794	1	these	these	DET
ejpam-3338	794	2	interpretations	interpretation	NOUN
ejpam-3338	794	3	are	be	AUX
ejpam-3338	794	4	distinct	distinct	ADJ
ejpam-3338	794	5	in	in	ADP
ejpam-3338	794	6	the	the	DET
ejpam-3338	794	7	sense	sense	NOUN
ejpam-3338	794	8	that	that	SCONJ
ejpam-3338	794	9	one	one	NUM
ejpam-3338	794	10	physical	physical	ADJ
ejpam-3338	794	11	interpretation	interpretation	NOUN
ejpam-3338	794	12	can	can	AUX
ejpam-3338	794	13	not	not	PART
ejpam-3338	794	14	be	be	AUX
ejpam-3338	794	15	obtained	obtain	VERB
ejpam-3338	794	16	from	from	ADP
ejpam-3338	794	17	other	other	ADJ
ejpam-3338	794	18	and	and	CCONJ
ejpam-3338	794	19	vice	vice	ADV
ejpam-3338	794	20	versa	versa	ADV
ejpam-3338	794	21	,	,	PUNCT
ejpam-3338	794	22	although	although	SCONJ
ejpam-3338	794	23	their	their	PRON
ejpam-3338	794	24	solutions	solution	NOUN
ejpam-3338	794	25	are	be	AUX
ejpam-3338	794	26	the	the	DET
ejpam-3338	794	27	same	same	ADJ
ejpam-3338	794	28	.	.	PUNCT
ejpam-3338	795	1	best	good	ADJ
ejpam-3338	795	2	way	way	NOUN
ejpam-3338	795	3	to	to	PART
ejpam-3338	795	4	compute	compute	VERB
ejpam-3338	795	5	integer	integer	NOUN
ejpam-3338	795	6	order	order	NOUN
ejpam-3338	795	7	derivatives	derivative	NOUN
ejpam-3338	795	8	while	while	SCONJ
ejpam-3338	795	9	computing	compute	VERB
ejpam-3338	795	10	the	the	DET
ejpam-3338	795	11	derivative	derivative	NOUN
ejpam-3338	795	12	of	of	ADP
ejpam-3338	795	13	an	an	DET
ejpam-3338	795	14	analytical	analytical	ADJ
ejpam-3338	795	15	function	function	NOUN
ejpam-3338	795	16	is	be	AUX
ejpam-3338	795	17	not	not	PART
ejpam-3338	795	18	only	only	ADV
ejpam-3338	795	19	easier	easy	ADJ
ejpam-3338	795	20	but	but	CCONJ
ejpam-3338	795	21	also	also	ADV
ejpam-3338	795	22	is	be	AUX
ejpam-3338	795	23	possible	possible	ADJ
ejpam-3338	795	24	for	for	ADP
ejpam-3338	795	25	a	a	DET
ejpam-3338	795	26	much	much	ADV
ejpam-3338	795	27	larger	large	ADJ
ejpam-3338	795	28	set	set	NOUN
ejpam-3338	795	29	of	of	ADP
ejpam-3338	795	30	functions	function	NOUN
ejpam-3338	795	31	by	by	ADP
ejpam-3338	795	32	a	a	DET
ejpam-3338	795	33	concerned	concerned	ADJ
ejpam-3338	795	34	person	person	NOUN
ejpam-3338	795	35	.	.	PUNCT
ejpam-3338	796	1	this	this	PRON
ejpam-3338	796	2	is	be	AUX
ejpam-3338	796	3	unlike	unlike	ADP
ejpam-3338	796	4	analytical	analytical	ADJ
ejpam-3338	796	5	(	(	PUNCT
ejpam-3338	796	6	not	not	PART
ejpam-3338	796	7	computational	computational	ADJ
ejpam-3338	796	8	)	)	PUNCT
ejpam-3338	796	9	integration	integration	NOUN
ejpam-3338	796	10	of	of	ADP
ejpam-3338	796	11	an	an	DET
ejpam-3338	796	12	analytical	analytical	ADJ
ejpam-3338	796	13	function	function	NOUN
ejpam-3338	796	14	.	.	PUNCT
ejpam-3338	797	1	most	most	ADJ
ejpam-3338	797	2	of	of	ADP
ejpam-3338	797	3	the	the	DET
ejpam-3338	797	4	functions	function	NOUN
ejpam-3338	797	5	can	can	AUX
ejpam-3338	797	6	not	not	PART
ejpam-3338	797	7	be	be	AUX
ejpam-3338	797	8	analytically	analytically	ADV
ejpam-3338	797	9	integrated	integrate	VERB
ejpam-3338	797	10	in	in	ADP
ejpam-3338	797	11	a	a	DET
ejpam-3338	797	12	closed	closed	ADJ
ejpam-3338	797	13	form	form	NOUN
ejpam-3338	797	14	.	.	PUNCT
ejpam-3338	798	1	a	a	DET
ejpam-3338	798	2	famous	famous	ADJ
ejpam-3338	798	3	example	example	NOUN
ejpam-3338	798	4	is	be	AUX
ejpam-3338	798	5	the	the	DET
ejpam-3338	798	6	normal	normal	ADJ
ejpam-3338	798	7	distribution	distribution	NOUN
ejpam-3338	798	8	function	function	NOUN
ejpam-3338	798	9	φ(z	φ(z	PROPN
ejpam-3338	798	10	)	)	PUNCT
ejpam-3338	799	1	=	=	SYM
ejpam-3338	799	2	1√	1√	NUM
ejpam-3338	799	3	2	2	NUM
ejpam-3338	799	4	∫	∫	NOUN
ejpam-3338	799	5	z	z	NOUN
ejpam-3338	799	6	0	0	NUM
ejpam-3338	799	7	e−x	e−x	PROPN
ejpam-3338	799	8	2	2	NUM
ejpam-3338	799	9	dx	dx	NOUN
ejpam-3338	799	10	=	=	SYM
ejpam-3338	799	11	erf	erf	PROPN
ejpam-3338	799	12	(	(	PUNCT
ejpam-3338	799	13	z√	z√	PROPN
ejpam-3338	799	14	2	2	NUM
ejpam-3338	799	15	)	)	PUNCT
ejpam-3338	799	16	(	(	PUNCT
ejpam-3338	799	17	42	42	NUM
ejpam-3338	799	18	)	)	PUNCT
ejpam-3338	799	19	where	where	SCONJ
ejpam-3338	799	20	erf=	erf=	X
ejpam-3338	799	21	error	error	NOUN
ejpam-3338	799	22	function	function	NOUN
ejpam-3338	799	23	,	,	PUNCT
ejpam-3338	799	24	gives	give	VERB
ejpam-3338	799	25	the	the	DET
ejpam-3338	799	26	probability	probability	NOUN
ejpam-3338	799	27	that	that	SCONJ
ejpam-3338	799	28	a	a	DET
ejpam-3338	799	29	standard	standard	ADJ
ejpam-3338	799	30	normal	normal	ADJ
ejpam-3338	799	31	variate	variate	NOUN
ejpam-3338	799	32	assumes	assume	VERB
ejpam-3338	799	33	a	a	DET
ejpam-3338	799	34	value	value	NOUN
ejpam-3338	799	35	in	in	ADP
ejpam-3338	799	36	the	the	DET
ejpam-3338	799	37	interval	interval	NOUN
ejpam-3338	799	38	[	[	X
ejpam-3338	799	39	0	0	NUM
ejpam-3338	799	40	,	,	PUNCT
ejpam-3338	799	41	z	z	NOUN
ejpam-3338	799	42	]	]	X
ejpam-3338	799	43	.	.	PUNCT
ejpam-3338	800	1	neither	neither	PRON
ejpam-3338	800	2	φ(z	φ(z	PROPN
ejpam-3338	800	3	)	)	PUNCT
ejpam-3338	800	4	nor	nor	CCONJ
ejpam-3338	800	5	erf	erf	NOUN
ejpam-3338	800	6	can	can	AUX
ejpam-3338	800	7	be	be	AUX
ejpam-3338	800	8	expressed	express	VERB
ejpam-3338	800	9	exactly	exactly	ADV
ejpam-3338	800	10	in	in	ADP
ejpam-3338	800	11	terms	term	NOUN
ejpam-3338	800	12	of	of	ADP
ejpam-3338	800	13	a	a	DET
ejpam-3338	800	14	finite	finite	ADJ
ejpam-3338	800	15	number	number	NOUN
ejpam-3338	800	16	of	of	ADP
ejpam-3338	800	17	add	add	NOUN
ejpam-3338	800	18	,	,	PUNCT
ejpam-3338	800	19	subtract	subtract	ADJ
ejpam-3338	800	20	,	,	PUNCT
ejpam-3338	800	21	multiply	multiply	NOUN
ejpam-3338	800	22	,	,	PUNCT
ejpam-3338	800	23	square	square	ADJ
ejpam-3338	800	24	-	-	PUNCT
ejpam-3338	800	25	root	root	NOUN
ejpam-3338	800	26	operations	operation	NOUN
ejpam-3338	800	27	.	.	PUNCT
ejpam-3338	801	1	so	so	ADV
ejpam-3338	801	2	both	both	PRON
ejpam-3338	801	3	must	must	AUX
ejpam-3338	801	4	be	be	AUX
ejpam-3338	801	5	either	either	DET
ejpam-3338	801	6	s.	s.	PROPN
ejpam-3338	801	7	k.sen	k.sen	PROPN
ejpam-3338	801	8	,	,	PUNCT
ejpam-3338	801	9	j.	j.	PROPN
ejpam-3338	801	10	v.	v.	PROPN
ejpam-3338	801	11	devi	devi	PROPN
ejpam-3338	801	12	,	,	PUNCT
ejpam-3338	801	13	r.v.g	r.v.g	NOUN
ejpam-3338	801	14	.	.	PUNCT
ejpam-3338	802	1	r.	r.	PROPN
ejpam-3338	802	2	kumar	kumar	PROPN
ejpam-3338	802	3	/	/	SYM
ejpam-3338	802	4	eur	eur	PROPN
ejpam-3338	802	5	.	.	PUNCT
ejpam-3338	803	1	j.	j.	PROPN
ejpam-3338	803	2	pure	pure	PROPN
ejpam-3338	803	3	appl	appl	PROPN
ejpam-3338	803	4	.	.	PROPN
ejpam-3338	803	5	math	math	PROPN
ejpam-3338	803	6	,	,	PUNCT
ejpam-3338	803	7	11	11	NUM
ejpam-3338	803	8	(	(	PUNCT
ejpam-3338	803	9	3	3	NUM
ejpam-3338	803	10	)	)	PUNCT
ejpam-3338	803	11	(	(	PUNCT
ejpam-3338	803	12	2018	2018	NUM
ejpam-3338	803	13	)	)	PUNCT
ejpam-3338	803	14	,	,	PUNCT
ejpam-3338	803	15	1058	1058	NUM
ejpam-3338	803	16	-	-	SYM
ejpam-3338	803	17	1099	1099	NUM
ejpam-3338	803	18	1096	1096	NUM
ejpam-3338	803	19	computed	compute	VERB
ejpam-3338	803	20	numerically	numerically	ADV
ejpam-3338	803	21	or	or	CCONJ
ejpam-3338	803	22	approximated	approximate	VERB
ejpam-3338	803	23	(	(	PUNCT
ejpam-3338	803	24	to	to	ADP
ejpam-3338	803	25	a	a	DET
ejpam-3338	803	26	finite	finite	ADJ
ejpam-3338	803	27	number	number	NOUN
ejpam-3338	803	28	of	of	ADP
ejpam-3338	803	29	terms	term	NOUN
ejpam-3338	803	30	)	)	PUNCT
ejpam-3338	803	31	.	.	PUNCT
ejpam-3338	804	1	in	in	ADP
ejpam-3338	804	2	either	either	DET
ejpam-3338	804	3	case	case	NOUN
ejpam-3338	804	4	we	we	PRON
ejpam-3338	804	5	get	get	VERB
ejpam-3338	804	6	only	only	ADV
ejpam-3338	804	7	erroneous	erroneous	ADJ
ejpam-3338	804	8	(	(	PUNCT
ejpam-3338	804	9	acceptable	acceptable	ADJ
ejpam-3338	804	10	or	or	CCONJ
ejpam-3338	804	11	not	not	PART
ejpam-3338	804	12	depending	depend	VERB
ejpam-3338	804	13	on	on	ADP
ejpam-3338	804	14	the	the	DET
ejpam-3338	804	15	context	context	NOUN
ejpam-3338	804	16	)	)	PUNCT
ejpam-3338	804	17	values	value	NOUN
ejpam-3338	804	18	(	(	PUNCT
ejpam-3338	804	19	numerical	numerical	ADJ
ejpam-3338	804	20	or	or	CCONJ
ejpam-3338	804	21	mathematical	mathematical	ADJ
ejpam-3338	804	22	)	)	PUNCT
ejpam-3338	804	23	.	.	PUNCT
ejpam-3338	805	1	however	however	ADV
ejpam-3338	805	2	,	,	PUNCT
ejpam-3338	805	3	numerical	numerical	ADJ
ejpam-3338	805	4	computation	computation	NOUN
ejpam-3338	805	5	of	of	ADP
ejpam-3338	805	6	a	a	DET
ejpam-3338	805	7	derivative	derivative	NOUN
ejpam-3338	805	8	and	and	CCONJ
ejpam-3338	805	9	of	of	ADP
ejpam-3338	805	10	an	an	DET
ejpam-3338	805	11	integral	integral	ADJ
ejpam-3338	805	12	with	with	ADP
ejpam-3338	805	13	specified	specify	VERB
ejpam-3338	805	14	numerical	numerical	ADJ
ejpam-3338	805	15	bounds	bound	NOUN
ejpam-3338	805	16	(	(	PUNCT
ejpam-3338	805	17	limits	limit	NOUN
ejpam-3338	805	18	of	of	ADP
ejpam-3338	805	19	integration	integration	NOUN
ejpam-3338	805	20	)	)	PUNCT
ejpam-3338	805	21	is	be	AUX
ejpam-3338	805	22	not	not	PART
ejpam-3338	805	23	only	only	ADV
ejpam-3338	805	24	always	always	ADV
ejpam-3338	805	25	possible	possible	ADJ
ejpam-3338	805	26	but	but	CCONJ
ejpam-3338	805	27	also	also	ADV
ejpam-3338	805	28	absolutely	absolutely	ADV
ejpam-3338	805	29	required	require	VERB
ejpam-3338	805	30	in	in	ADP
ejpam-3338	805	31	every	every	DET
ejpam-3338	805	32	engineering	engineering	NOUN
ejpam-3338	805	33	/	/	SYM
ejpam-3338	805	34	science	science	NOUN
ejpam-3338	805	35	application	application	NOUN
ejpam-3338	805	36	.	.	PUNCT
ejpam-3338	806	1	the	the	DET
ejpam-3338	806	2	numerical	numerical	ADJ
ejpam-3338	806	3	computation	computation	NOUN
ejpam-3338	806	4	of	of	ADP
ejpam-3338	806	5	a	a	DET
ejpam-3338	806	6	derivative	derivative	NOUN
ejpam-3338	806	7	of	of	ADP
ejpam-3338	806	8	higher	high	ADJ
ejpam-3338	806	9	integer	integer	NOUN
ejpam-3338	806	10	order	order	NOUN
ejpam-3338	806	11	(	(	PUNCT
ejpam-3338	806	12	order	order	NOUN
ejpam-3338	806	13	2	2	NUM
ejpam-3338	806	14	or	or	CCONJ
ejpam-3338	806	15	more	more	ADJ
ejpam-3338	806	16	)	)	PUNCT
ejpam-3338	806	17	does	do	AUX
ejpam-3338	806	18	involve	involve	VERB
ejpam-3338	806	19	increasingly	increasingly	ADV
ejpam-3338	806	20	more	more	ADV
ejpam-3338	806	21	pronounced	pronounce	VERB
ejpam-3338	806	22	error	error	NOUN
ejpam-3338	806	23	.	.	PUNCT
ejpam-3338	807	1	successive	successive	ADJ
ejpam-3338	807	2	numerical	numerical	ADJ
ejpam-3338	807	3	derivatives	derivative	NOUN
ejpam-3338	807	4	are	be	AUX
ejpam-3338	807	5	successively	successively	ADV
ejpam-3338	807	6	more	more	ADV
ejpam-3338	807	7	erroneous	erroneous	ADJ
ejpam-3338	807	8	since	since	SCONJ
ejpam-3338	807	9	a	a	DET
ejpam-3338	807	10	higher	high	ADJ
ejpam-3338	807	11	order	order	NOUN
ejpam-3338	807	12	numerical	numerical	ADJ
ejpam-3338	807	13	derivative	derivative	NOUN
ejpam-3338	807	14	is	be	AUX
ejpam-3338	807	15	computed	compute	VERB
ejpam-3338	807	16	based	base	VERB
ejpam-3338	807	17	on	on	ADP
ejpam-3338	807	18	already	already	ADV
ejpam-3338	807	19	computed	compute	VERB
ejpam-3338	807	20	lower	low	ADJ
ejpam-3338	807	21	order	order	NOUN
ejpam-3338	807	22	derivative	derivative	NOUN
ejpam-3338	807	23	having	have	VERB
ejpam-3338	807	24	inherent	inherent	ADJ
ejpam-3338	807	25	computational	computational	ADJ
ejpam-3338	807	26	error	error	NOUN
ejpam-3338	807	27	.	.	PUNCT
ejpam-3338	808	1	like	like	ADP
ejpam-3338	808	2	entropy	entropy	PROPN
ejpam-3338	808	3	,	,	PUNCT
ejpam-3338	808	4	errors	error	NOUN
ejpam-3338	808	5	go	go	VERB
ejpam-3338	808	6	on	on	ADP
ejpam-3338	808	7	increasing	increase	VERB
ejpam-3338	808	8	successively	successively	ADV
ejpam-3338	808	9	the	the	PRON
ejpam-3338	808	10	higher	high	ADJ
ejpam-3338	808	11	the	the	DET
ejpam-3338	808	12	derivatives	derivative	NOUN
ejpam-3338	808	13	we	we	PRON
ejpam-3338	808	14	compute	compute	VERB
ejpam-3338	808	15	.	.	PUNCT
ejpam-3338	809	1	under	under	ADP
ejpam-3338	809	2	these	these	DET
ejpam-3338	809	3	circumstances	circumstance	NOUN
ejpam-3338	809	4	,	,	PUNCT
ejpam-3338	809	5	a	a	DET
ejpam-3338	809	6	best	good	ADJ
ejpam-3338	809	7	way	way	NOUN
ejpam-3338	809	8	to	to	PART
ejpam-3338	809	9	compute	compute	VERB
ejpam-3338	809	10	integer	integer	NOUN
ejpam-3338	809	11	order	order	NOUN
ejpam-3338	809	12	derivatives	derivative	NOUN
ejpam-3338	809	13	would	would	AUX
ejpam-3338	809	14	be	be	AUX
ejpam-3338	809	15	to	to	PART
ejpam-3338	809	16	use	use	VERB
ejpam-3338	809	17	(	(	PUNCT
ejpam-3338	809	18	successive	successive	ADJ
ejpam-3338	809	19	)	)	PUNCT
ejpam-3338	809	20	symbolic	symbolic	ADJ
ejpam-3338	809	21	derivative	derivative	ADJ
ejpam-3338	809	22	computations	computation	NOUN
ejpam-3338	809	23	followed	follow	VERB
ejpam-3338	809	24	by	by	ADP
ejpam-3338	809	25	the	the	DET
ejpam-3338	809	26	numerical	numerical	ADJ
ejpam-3338	809	27	derivative	derivative	ADJ
ejpam-3338	809	28	computation	computation	NOUN
ejpam-3338	809	29	at	at	ADP
ejpam-3338	809	30	the	the	DET
ejpam-3338	809	31	final	final	ADJ
ejpam-3338	809	32	step	step	NOUN
ejpam-3338	809	33	.	.	PUNCT
ejpam-3338	810	1	the	the	DET
ejpam-3338	810	2	successive	successive	ADJ
ejpam-3338	810	3	symbolic	symbolic	ADJ
ejpam-3338	810	4	computations	computation	NOUN
ejpam-3338	810	5	can	can	AUX
ejpam-3338	810	6	be	be	AUX
ejpam-3338	810	7	carried	carry	VERB
ejpam-3338	810	8	out	out	ADP
ejpam-3338	810	9	exactly	exactly	ADV
ejpam-3338	810	10	in	in	ADP
ejpam-3338	810	11	matlab	matlab	PROPN
ejpam-3338	810	12	for	for	ADP
ejpam-3338	810	13	most	most	ADJ
ejpam-3338	810	14	(	(	PUNCT
ejpam-3338	810	15	not	not	PART
ejpam-3338	810	16	all	all	PRON
ejpam-3338	810	17	)	)	PUNCT
ejpam-3338	810	18	of	of	ADP
ejpam-3338	810	19	the	the	DET
ejpam-3338	810	20	analytic	analytic	ADJ
ejpam-3338	810	21	functions	function	NOUN
ejpam-3338	810	22	and/or	and/or	CCONJ
ejpam-3338	810	23	for	for	ADP
ejpam-3338	810	24	a	a	DET
ejpam-3338	810	25	combination	combination	NOUN
ejpam-3338	810	26	of	of	ADP
ejpam-3338	810	27	this	this	DET
ejpam-3338	810	28	functions	function	NOUN
ejpam-3338	810	29	.	.	PUNCT
ejpam-3338	811	1	the	the	DET
ejpam-3338	811	2	foregoing	forego	VERB
ejpam-3338	811	3	best	good	ADJ
ejpam-3338	811	4	way	way	NOUN
ejpam-3338	811	5	will	will	AUX
ejpam-3338	811	6	provide	provide	VERB
ejpam-3338	811	7	least	least	ADJ
ejpam-3338	811	8	computational	computational	ADJ
ejpam-3338	811	9	error	error	NOUN
ejpam-3338	811	10	(	(	PUNCT
ejpam-3338	811	11	for	for	ADP
ejpam-3338	811	12	a	a	DET
ejpam-3338	811	13	given	give	VERB
ejpam-3338	811	14	precision	precision	NOUN
ejpam-3338	811	15	of	of	ADP
ejpam-3338	811	16	the	the	DET
ejpam-3338	811	17	computer	computer	NOUN
ejpam-3338	811	18	)	)	PUNCT
ejpam-3338	811	19	which	which	PRON
ejpam-3338	811	20	is	be	AUX
ejpam-3338	811	21	most	most	ADV
ejpam-3338	811	22	desired	desire	VERB
ejpam-3338	811	23	in	in	ADP
ejpam-3338	811	24	all	all	DET
ejpam-3338	811	25	forms	form	NOUN
ejpam-3338	811	26	of	of	ADP
ejpam-3338	811	27	computations	computation	NOUN
ejpam-3338	811	28	.	.	PUNCT
ejpam-3338	812	1	sometimes	sometimes	ADV
ejpam-3338	812	2	the	the	DET
ejpam-3338	812	3	successive	successive	ADJ
ejpam-3338	812	4	integer	integer	NOUN
ejpam-3338	812	5	-	-	PUNCT
ejpam-3338	812	6	order	order	NOUN
ejpam-3338	812	7	derivative	derivative	NOUN
ejpam-3338	812	8	of	of	ADP
ejpam-3338	812	9	a	a	DET
ejpam-3338	812	10	non	non	ADJ
ejpam-3338	812	11	-	-	ADJ
ejpam-3338	812	12	polynomial	polynomial	ADJ
ejpam-3338	812	13	function	function	NOUN
ejpam-3338	812	14	or	or	CCONJ
ejpam-3338	812	15	a	a	DET
ejpam-3338	812	16	combination	combination	NOUN
ejpam-3338	812	17	of	of	ADP
ejpam-3338	812	18	non	non	ADJ
ejpam-3338	812	19	-	-	ADJ
ejpam-3338	812	20	polynomial	polynomial	ADJ
ejpam-3338	812	21	and	and	CCONJ
ejpam-3338	812	22	polynomial	polynomial	ADJ
ejpam-3338	812	23	functions	function	NOUN
ejpam-3338	812	24	could	could	AUX
ejpam-3338	812	25	result	result	VERB
ejpam-3338	812	26	in	in	ADP
ejpam-3338	812	27	a	a	DET
ejpam-3338	812	28	much	much	ADV
ejpam-3338	812	29	larger	large	ADJ
ejpam-3338	812	30	analytical	analytical	ADJ
ejpam-3338	812	31	function	function	NOUN
ejpam-3338	812	32	implying	imply	VERB
ejpam-3338	812	33	much	much	ADV
ejpam-3338	812	34	more	more	ADJ
ejpam-3338	812	35	numerical	numerical	ADJ
ejpam-3338	812	36	computation	computation	NOUN
ejpam-3338	812	37	.	.	PUNCT
ejpam-3338	813	1	in	in	ADP
ejpam-3338	813	2	such	such	DET
ejpam-3338	813	3	a	a	DET
ejpam-3338	813	4	case	case	NOUN
ejpam-3338	813	5	,	,	PUNCT
ejpam-3338	813	6	one	one	PRON
ejpam-3338	813	7	may	may	AUX
ejpam-3338	813	8	follow	follow	VERB
ejpam-3338	813	9	one	one	NUM
ejpam-3338	813	10	of	of	ADP
ejpam-3338	813	11	the	the	DET
ejpam-3338	813	12	2	2	NUM
ejpam-3338	813	13	ways	way	NOUN
ejpam-3338	813	14	viz	viz	NUM
ejpam-3338	813	15	.	.	PUNCT
ejpam-3338	814	1	the	the	DET
ejpam-3338	814	2	foregoing	foregoing	NOUN
ejpam-3338	814	3	”	"	PUNCT
ejpam-3338	814	4	a	a	DET
ejpam-3338	814	5	best	good	ADJ
ejpam-3338	814	6	way	way	NOUN
ejpam-3338	814	7	”	"	PUNCT
ejpam-3338	814	8	and	and	CCONJ
ejpam-3338	814	9	the	the	DET
ejpam-3338	814	10	straight	straight	ADJ
ejpam-3338	814	11	-	-	PUNCT
ejpam-3338	814	12	forward	forward	NOUN
ejpam-3338	814	13	(	(	PUNCT
ejpam-3338	814	14	usual	usual	ADJ
ejpam-3338	814	15	)	)	PUNCT
ejpam-3338	814	16	successive	successive	ADJ
ejpam-3338	814	17	numerical	numerical	ADJ
ejpam-3338	814	18	computation	computation	NOUN
ejpam-3338	814	19	way	way	NOUN
ejpam-3338	814	20	(	(	PUNCT
ejpam-3338	814	21	from	from	ADP
ejpam-3338	814	22	the	the	DET
ejpam-3338	814	23	very	very	ADV
ejpam-3338	814	24	1st	1st	ADJ
ejpam-3338	814	25	step	step	NOUN
ejpam-3338	814	26	)	)	PUNCT
ejpam-3338	814	27	for	for	ADP
ejpam-3338	814	28	the	the	DET
ejpam-3338	814	29	given	give	VERB
ejpam-3338	814	30	function	function	NOUN
ejpam-3338	814	31	and	and	CCONJ
ejpam-3338	814	32	decide	decide	VERB
ejpam-3338	814	33	one	one	NUM
ejpam-3338	814	34	of	of	ADP
ejpam-3338	814	35	the	the	DET
ejpam-3338	814	36	ways	way	NOUN
ejpam-3338	814	37	,	,	PUNCT
ejpam-3338	814	38	that	that	PRON
ejpam-3338	814	39	produces	produce	VERB
ejpam-3338	814	40	less	less	ADV
ejpam-3338	814	41	computational	computational	ADJ
ejpam-3338	814	42	error	error	NOUN
ejpam-3338	814	43	.	.	PUNCT
ejpam-3338	815	1	the	the	DET
ejpam-3338	815	2	computational	computational	ADJ
ejpam-3338	815	3	complexity	complexity	NOUN
ejpam-3338	815	4	(	(	PUNCT
ejpam-3338	815	5	cost	cost	NOUN
ejpam-3338	815	6	of	of	ADP
ejpam-3338	815	7	computation	computation	NOUN
ejpam-3338	815	8	)	)	PUNCT
ejpam-3338	815	9	issue	issue	NOUN
ejpam-3338	815	10	is	be	AUX
ejpam-3338	815	11	mostly	mostly	ADV
ejpam-3338	815	12	a	a	DET
ejpam-3338	815	13	minor	minor	ADJ
ejpam-3338	815	14	/	/	SYM
ejpam-3338	815	15	trivial	trivial	ADJ
ejpam-3338	815	16	issue	issue	NOUN
ejpam-3338	815	17	in	in	ADP
ejpam-3338	815	18	this	this	DET
ejpam-3338	815	19	hyper	hyper	NOUN
ejpam-3338	815	20	-	-	ADJ
ejpam-3338	815	21	computing	computing	ADJ
ejpam-3338	815	22	(	(	PUNCT
ejpam-3338	815	23	over	over	ADP
ejpam-3338	815	24	1018	1018	NUM
ejpam-3338	815	25	floating	float	VERB
ejpam-3338	815	26	-	-	PUNCT
ejpam-3338	815	27	point	point	NOUN
ejpam-3338	815	28	operations	operation	NOUN
ejpam-3338	815	29	per	per	ADP
ejpam-3338	815	30	sec	sec	PROPN
ejpam-3338	815	31	)	)	PUNCT
ejpam-3338	815	32	era	era	NOUN
ejpam-3338	815	33	.	.	PUNCT
ejpam-3338	816	1	the	the	DET
ejpam-3338	816	2	difficulty	difficulty	NOUN
ejpam-3338	816	3	of	of	ADP
ejpam-3338	816	4	determining	determine	VERB
ejpam-3338	816	5	symbolic	symbolic	ADJ
ejpam-3338	816	6	derivative	derivative	NOUN
ejpam-3338	816	7	for	for	ADP
ejpam-3338	816	8	a	a	DET
ejpam-3338	816	9	long	long	ADV
ejpam-3338	816	10	involved	involved	ADJ
ejpam-3338	816	11	function	function	NOUN
ejpam-3338	816	12	(	(	PUNCT
ejpam-3338	816	13	not	not	PART
ejpam-3338	816	14	being	be	AUX
ejpam-3338	816	15	able	able	ADJ
ejpam-3338	816	16	to	to	PART
ejpam-3338	816	17	write	write	VERB
ejpam-3338	816	18	/	/	SYM
ejpam-3338	816	19	automate	automate	NOUN
ejpam-3338	816	20	the	the	DET
ejpam-3338	816	21	symbolic	symbolic	ADJ
ejpam-3338	816	22	derivative	derivative	ADJ
ejpam-3338	816	23	computation	computation	NOUN
ejpam-3338	816	24	for	for	ADP
ejpam-3338	816	25	all	all	DET
ejpam-3338	816	26	highly	highly	ADV
ejpam-3338	816	27	involved	involved	ADJ
ejpam-3338	816	28	/	/	SYM
ejpam-3338	816	29	lengthy	lengthy	ADJ
ejpam-3338	816	30	analytic	analytic	ADJ
ejpam-3338	816	31	functions	function	NOUN
ejpam-3338	816	32	)	)	PUNCT
ejpam-3338	816	33	is	be	AUX
ejpam-3338	816	34	due	due	ADJ
ejpam-3338	816	35	to	to	ADP
ejpam-3338	816	36	the	the	DET
ejpam-3338	816	37	programmers	programmer	NOUN
ejpam-3338	816	38	limitations	limitation	NOUN
ejpam-3338	816	39	in	in	ADP
ejpam-3338	816	40	his	his	PRON
ejpam-3338	816	41	comprehension	comprehension	NOUN
ejpam-3338	816	42	(	(	PUNCT
ejpam-3338	816	43	a	a	DET
ejpam-3338	816	44	common	common	ADJ
ejpam-3338	816	45	human	human	ADJ
ejpam-3338	816	46	being	being	NOUN
ejpam-3338	816	47	can	can	AUX
ejpam-3338	816	48	comprehend	comprehend	VERB
ejpam-3338	816	49	5	5	NUM
ejpam-3338	816	50	to	to	PART
ejpam-3338	816	51	9	9	NUM
ejpam-3338	816	52	things	thing	NOUN
ejpam-3338	816	53	at	at	ADP
ejpam-3338	816	54	a	a	DET
ejpam-3338	816	55	time	time	NOUN
ejpam-3338	816	56	.	.	PUNCT
ejpam-3338	816	57	)	)	PUNCT
ejpam-3338	817	1	and	and	CCONJ
ejpam-3338	817	2	his	his	PRON
ejpam-3338	817	3	programming	programming	NOUN
ejpam-3338	817	4	skill	skill	NOUN
ejpam-3338	817	5	involving	involve	VERB
ejpam-3338	817	6	differentiation	differentiation	NOUN
ejpam-3338	817	7	of	of	ADP
ejpam-3338	817	8	a	a	DET
ejpam-3338	817	9	general	general	ADJ
ejpam-3338	817	10	function	function	NOUN
ejpam-3338	817	11	.	.	PUNCT
ejpam-3338	818	1	such	such	ADJ
ejpam-3338	818	2	limitations	limitation	NOUN
ejpam-3338	818	3	may	may	AUX
ejpam-3338	818	4	not	not	PART
ejpam-3338	818	5	come	come	VERB
ejpam-3338	818	6	into	into	ADP
ejpam-3338	818	7	picture	picture	NOUN
ejpam-3338	818	8	for	for	ADP
ejpam-3338	818	9	a	a	DET
ejpam-3338	818	10	person	person	NOUN
ejpam-3338	818	11	/	/	SYM
ejpam-3338	818	12	programmer	programmer	NOUN
ejpam-3338	818	13	when	when	SCONJ
ejpam-3338	818	14	he	he	PRON
ejpam-3338	818	15	uses	use	VERB
ejpam-3338	818	16	the	the	DET
ejpam-3338	818	17	rules	rule	NOUN
ejpam-3338	818	18	of	of	ADP
ejpam-3338	818	19	symbolic	symbolic	ADJ
ejpam-3338	818	20	derivation	derivation	NOUN
ejpam-3338	818	21	with	with	ADP
ejpam-3338	818	22	sufficient	sufficient	ADJ
ejpam-3338	818	23	care	care	NOUN
ejpam-3338	818	24	and	and	CCONJ
ejpam-3338	818	25	concentration	concentration	NOUN
ejpam-3338	818	26	for	for	ADP
ejpam-3338	818	27	a	a	DET
ejpam-3338	818	28	specific	specific	ADJ
ejpam-3338	818	29	function	function	NOUN
ejpam-3338	818	30	or	or	CCONJ
ejpam-3338	818	31	a	a	DET
ejpam-3338	818	32	combination	combination	NOUN
ejpam-3338	818	33	of	of	ADP
ejpam-3338	818	34	functions	function	NOUN
ejpam-3338	818	35	.	.	PUNCT
ejpam-3338	819	1	however	however	ADV
ejpam-3338	819	2	,	,	PUNCT
ejpam-3338	819	3	a	a	DET
ejpam-3338	819	4	mistake	mistake	NOUN
ejpam-3338	819	5	,	,	PUNCT
ejpam-3338	819	6	though	though	SCONJ
ejpam-3338	819	7	rare	rare	ADJ
ejpam-3338	819	8	,	,	PUNCT
ejpam-3338	819	9	can	can	AUX
ejpam-3338	819	10	not	not	PART
ejpam-3338	819	11	be	be	AUX
ejpam-3338	819	12	ruled	rule	VERB
ejpam-3338	819	13	out	out	ADP
ejpam-3338	819	14	for	for	ADP
ejpam-3338	819	15	any	any	DET
ejpam-3338	819	16	living	live	VERB
ejpam-3338	819	17	being	being	NOUN
ejpam-3338	819	18	including	include	VERB
ejpam-3338	819	19	a	a	DET
ejpam-3338	819	20	mathematical	mathematical	ADJ
ejpam-3338	819	21	/	/	SYM
ejpam-3338	819	22	computational	computational	ADJ
ejpam-3338	819	23	prodigy	prodigy	NOUN
ejpam-3338	819	24	(	(	PUNCT
ejpam-3338	819	25	as	as	SCONJ
ejpam-3338	819	26	to	to	PART
ejpam-3338	819	27	err	err	NOUN
ejpam-3338	819	28	(	(	PUNCT
ejpam-3338	819	29	mistake	mistake	NOUN
ejpam-3338	819	30	)	)	PUNCT
ejpam-3338	819	31	is	be	AUX
ejpam-3338	819	32	human	human	ADJ
ejpam-3338	819	33	(	(	PUNCT
ejpam-3338	819	34	living	live	VERB
ejpam-3338	819	35	being	being	NOUN
ejpam-3338	819	36	)	)	PUNCT
ejpam-3338	819	37	is	be	AUX
ejpam-3338	819	38	eternally	eternally	ADV
ejpam-3338	819	39	true	true	ADJ
ejpam-3338	819	40	without	without	ADP
ejpam-3338	819	41	any	any	DET
ejpam-3338	819	42	exception	exception	NOUN
ejpam-3338	819	43	.	.	PUNCT
ejpam-3338	820	1	in	in	ADP
ejpam-3338	820	2	this	this	DET
ejpam-3338	820	3	context	context	NOUN
ejpam-3338	820	4	,	,	PUNCT
ejpam-3338	820	5	not	not	PART
ejpam-3338	820	6	to	to	PART
ejpam-3338	820	7	err	err	VERB
ejpam-3338	820	8	is	be	AUX
ejpam-3338	820	9	computer	computer	NOUN
ejpam-3338	820	10	(	(	PUNCT
ejpam-3338	820	11	non	non	ADJ
ejpam-3338	820	12	-	-	ADJ
ejpam-3338	820	13	living	living	ADJ
ejpam-3338	820	14	being	being	NOUN
ejpam-3338	820	15	)	)	PUNCT
ejpam-3338	820	16	may	may	AUX
ejpam-3338	820	17	be	be	AUX
ejpam-3338	820	18	considered	consider	VERB
ejpam-3338	820	19	equally	equally	ADV
ejpam-3338	820	20	true	true	ADJ
ejpam-3338	820	21	)	)	PUNCT
ejpam-3338	820	22	.	.	PUNCT
ejpam-3338	821	1	for	for	ADP
ejpam-3338	821	2	computing	compute	VERB
ejpam-3338	821	3	a	a	DET
ejpam-3338	821	4	fractional	fractional	ADJ
ejpam-3338	821	5	order	order	NOUN
ejpam-3338	821	6	derivative	derivative	NOUN
ejpam-3338	821	7	of	of	ADP
ejpam-3338	821	8	a	a	DET
ejpam-3338	821	9	function	function	NOUN
ejpam-3338	821	10	where	where	SCONJ
ejpam-3338	821	11	the	the	DET
ejpam-3338	821	12	order	order	NOUN
ejpam-3338	821	13	α	α	X
ejpam-3338	821	14	=	=	SYM
ejpam-3338	821	15	n.f	n.f	PROPN
ejpam-3338	821	16	,	,	PUNCT
ejpam-3338	821	17	n	n	PRON
ejpam-3338	821	18	being	be	AUX
ejpam-3338	821	19	a	a	DET
ejpam-3338	821	20	positive	positive	ADJ
ejpam-3338	821	21	integer	integer	NOUN
ejpam-3338	821	22	and	and	CCONJ
ejpam-3338	821	23	(	(	PUNCT
ejpam-3338	821	24	.f	.f	PROPN
ejpam-3338	821	25	)	)	PUNCT
ejpam-3338	821	26	the	the	DET
ejpam-3338	821	27	fractional	fractional	ADJ
ejpam-3338	821	28	part	part	NOUN
ejpam-3338	821	29	,	,	PUNCT
ejpam-3338	821	30	successive	successive	ADJ
ejpam-3338	821	31	integer	integer	NOUN
ejpam-3338	821	32	order	order	NOUN
ejpam-3338	821	33	derivatives	derivative	NOUN
ejpam-3338	821	34	can	can	AUX
ejpam-3338	821	35	be	be	AUX
ejpam-3338	821	36	obtained	obtain	VERB
ejpam-3338	821	37	as	as	ADP
ejpam-3338	821	38	in	in	ADP
ejpam-3338	821	39	the	the	DET
ejpam-3338	821	40	foregoing	forego	VERB
ejpam-3338	821	41	case	case	NOUN
ejpam-3338	821	42	and	and	CCONJ
ejpam-3338	821	43	then	then	ADV
ejpam-3338	821	44	the	the	DET
ejpam-3338	821	45	fractional	fractional	ADJ
ejpam-3338	821	46	part	part	NOUN
ejpam-3338	821	47	(	(	PUNCT
ejpam-3338	821	48	.f	.f	PROPN
ejpam-3338	821	49	)	)	PUNCT
ejpam-3338	821	50	could	could	AUX
ejpam-3338	821	51	be	be	AUX
ejpam-3338	821	52	computed	compute	VERB
ejpam-3338	821	53	according	accord	VERB
ejpam-3338	821	54	to	to	ADP
ejpam-3338	821	55	one	one	NUM
ejpam-3338	821	56	of	of	ADP
ejpam-3338	821	57	the	the	DET
ejpam-3338	821	58	most	most	ADV
ejpam-3338	821	59	appropriate	appropriate	ADJ
ejpam-3338	821	60	definitions	definition	NOUN
ejpam-3338	821	61	such	such	ADJ
ejpam-3338	821	62	as	as	ADP
ejpam-3338	821	63	the	the	DET
ejpam-3338	821	64	grunwald	grunwald	NOUN
ejpam-3338	821	65	-	-	PUNCT
ejpam-3338	821	66	letnikov	letnikov	NOUN
ejpam-3338	821	67	definition	definition	NOUN
ejpam-3338	821	68	.	.	PUNCT
ejpam-3338	822	1	here	here	ADV
ejpam-3338	822	2	a	a	DET
ejpam-3338	822	3	generalization	generalization	NOUN
ejpam-3338	822	4	procedure	procedure	NOUN
ejpam-3338	822	5	that	that	PRON
ejpam-3338	822	6	could	could	AUX
ejpam-3338	822	7	be	be	AUX
ejpam-3338	822	8	considered	consider	VERB
ejpam-3338	822	9	a	a	DET
ejpam-3338	822	10	straight	straight	ADJ
ejpam-3338	822	11	-	-	PUNCT
ejpam-3338	822	12	forward	forward	NOUN
ejpam-3338	822	13	extension	extension	NOUN
ejpam-3338	822	14	of	of	ADP
ejpam-3338	822	15	the	the	DET
ejpam-3338	822	16	integer	integer	NOUN
ejpam-3338	822	17	order	order	NOUN
ejpam-3338	822	18	derivatives	derivative	NOUN
ejpam-3338	822	19	deserves	deserve	VERB
ejpam-3338	822	20	to	to	PART
ejpam-3338	822	21	be	be	AUX
ejpam-3338	822	22	devised	devise	VERB
ejpam-3338	822	23	/	/	SYM
ejpam-3338	822	24	designed	design	VERB
ejpam-3338	822	25	for	for	ADP
ejpam-3338	822	26	a	a	DET
ejpam-3338	822	27	widely	widely	ADV
ejpam-3338	822	28	accepted	accept	VERB
ejpam-3338	822	29	integration	integration	NOUN
ejpam-3338	822	30	/	/	SYM
ejpam-3338	822	31	merger	merger	NOUN
ejpam-3338	822	32	.	.	PUNCT
ejpam-3338	823	1	s.	s.	PROPN
ejpam-3338	823	2	k.sen	k.sen	PROPN
ejpam-3338	823	3	,	,	PUNCT
ejpam-3338	823	4	j.	j.	PROPN
ejpam-3338	823	5	v.	v.	PROPN
ejpam-3338	823	6	devi	devi	PROPN
ejpam-3338	823	7	,	,	PUNCT
ejpam-3338	823	8	r.v.g	r.v.g	NOUN
ejpam-3338	823	9	.	.	PUNCT
ejpam-3338	824	1	r.	r.	PROPN
ejpam-3338	824	2	kumar	kumar	PROPN
ejpam-3338	824	3	/	/	SYM
ejpam-3338	824	4	eur	eur	PROPN
ejpam-3338	824	5	.	.	PUNCT
ejpam-3338	825	1	j.	j.	PROPN
ejpam-3338	825	2	pure	pure	PROPN
ejpam-3338	825	3	appl	appl	PROPN
ejpam-3338	825	4	.	.	PROPN
ejpam-3338	825	5	math	math	PROPN
ejpam-3338	825	6	,	,	PUNCT
ejpam-3338	825	7	11	11	NUM
ejpam-3338	825	8	(	(	PUNCT
ejpam-3338	825	9	3	3	NUM
ejpam-3338	825	10	)	)	PUNCT
ejpam-3338	825	11	(	(	PUNCT
ejpam-3338	825	12	2018	2018	NUM
ejpam-3338	825	13	)	)	PUNCT
ejpam-3338	825	14	,	,	PUNCT
ejpam-3338	825	15	1058	1058	NUM
ejpam-3338	825	16	-	-	SYM
ejpam-3338	825	17	1099	1099	NUM
ejpam-3338	825	18	1097	1097	NUM
ejpam-3338	825	19	when	when	SCONJ
ejpam-3338	825	20	the	the	DET
ejpam-3338	825	21	function	function	NOUN
ejpam-3338	825	22	is	be	AUX
ejpam-3338	825	23	known	know	VERB
ejpam-3338	825	24	as	as	ADP
ejpam-3338	825	25	equi	equi	NOUN
ejpam-3338	825	26	-	-	PUNCT
ejpam-3338	825	27	spaced	space	VERB
ejpam-3338	825	28	sampled	sample	VERB
ejpam-3338	825	29	numbers	number	NOUN
ejpam-3338	825	30	or	or	CCONJ
ejpam-3338	825	31	non	non	ADJ
ejpam-3338	825	32	-	-	ADJ
ejpam-3338	825	33	equi	equi	NOUN
ejpam-3338	825	34	-	-	PUNCT
ejpam-3338	825	35	spaced	space	VERB
ejpam-3338	825	36	sampled	sample	VERB
ejpam-3338	825	37	numbers	number	NOUN
ejpam-3338	825	38	,	,	PUNCT
ejpam-3338	825	39	then	then	ADV
ejpam-3338	825	40	the	the	DET
ejpam-3338	825	41	problem	problem	NOUN
ejpam-3338	825	42	of	of	ADP
ejpam-3338	825	43	computing	compute	VERB
ejpam-3338	825	44	derivative	derivative	NOUN
ejpam-3338	825	45	is	be	AUX
ejpam-3338	825	46	usually	usually	ADV
ejpam-3338	825	47	completely	completely	ADV
ejpam-3338	825	48	numerical	numerical	ADJ
ejpam-3338	825	49	.	.	PUNCT
ejpam-3338	826	1	the	the	DET
ejpam-3338	826	2	symbolic	symbolic	ADJ
ejpam-3338	826	3	derivation	derivation	NOUN
ejpam-3338	826	4	successive	successive	ADJ
ejpam-3338	826	5	or	or	CCONJ
ejpam-3338	826	6	not	not	PART
ejpam-3338	826	7	that	that	SCONJ
ejpam-3338	826	8	either	either	CCONJ
ejpam-3338	826	9	physically	physically	ADV
ejpam-3338	826	10	inflates	inflate	VERB
ejpam-3338	826	11	the	the	DET
ejpam-3338	826	12	function	function	NOUN
ejpam-3338	826	13	or	or	CCONJ
ejpam-3338	826	14	deflates	deflate	VERB
ejpam-3338	826	15	the	the	DET
ejpam-3338	826	16	function	function	NOUN
ejpam-3338	826	17	usually	usually	ADV
ejpam-3338	826	18	will	will	AUX
ejpam-3338	826	19	not	not	PART
ejpam-3338	826	20	figure	figure	VERB
ejpam-3338	826	21	here	here	ADV
ejpam-3338	826	22	.	.	PUNCT
ejpam-3338	827	1	numerical	numerical	ADJ
ejpam-3338	827	2	input	input	PROPN
ejpam-3338	827	3	functions	function	NOUN
ejpam-3338	827	4	.	.	PUNCT
ejpam-3338	828	1	it	it	PRON
ejpam-3338	828	2	is	be	AUX
ejpam-3338	828	3	possible	possible	ADJ
ejpam-3338	828	4	that	that	SCONJ
ejpam-3338	828	5	we	we	PRON
ejpam-3338	828	6	may	may	AUX
ejpam-3338	828	7	deal	deal	VERB
ejpam-3338	828	8	with	with	ADP
ejpam-3338	828	9	functions	function	NOUN
ejpam-3338	828	10	which	which	PRON
ejpam-3338	828	11	are	be	AUX
ejpam-3338	828	12	known	know	VERB
ejpam-3338	828	13	through	through	ADP
ejpam-3338	828	14	tables	table	NOUN
ejpam-3338	828	15	of	of	ADP
ejpam-3338	828	16	numbers	number	NOUN
ejpam-3338	828	17	.	.	PUNCT
ejpam-3338	829	1	after	after	ADV
ejpam-3338	829	2	all	all	ADV
ejpam-3338	829	3	,	,	PUNCT
ejpam-3338	829	4	everything	everything	PRON
ejpam-3338	829	5	has	have	VERB
ejpam-3338	829	6	to	to	PART
ejpam-3338	829	7	be	be	AUX
ejpam-3338	829	8	in	in	ADP
ejpam-3338	829	9	numbers	number	NOUN
ejpam-3338	829	10	for	for	ADP
ejpam-3338	829	11	every	every	DET
ejpam-3338	829	12	practical	practical	ADJ
ejpam-3338	829	13	/	/	SYM
ejpam-3338	829	14	real	real	ADJ
ejpam-3338	829	15	-	-	PUNCT
ejpam-3338	829	16	world	world	NOUN
ejpam-3338	829	17	application	application	NOUN
ejpam-3338	829	18	.	.	PUNCT
ejpam-3338	830	1	the	the	DET
ejpam-3338	830	2	problem	problem	NOUN
ejpam-3338	830	3	of	of	ADP
ejpam-3338	830	4	generalization	generalization	NOUN
ejpam-3338	830	5	seems	seem	VERB
ejpam-3338	830	6	to	to	PART
ejpam-3338	830	7	be	be	AUX
ejpam-3338	830	8	comparatively	comparatively	ADV
ejpam-3338	830	9	easy	easy	ADJ
ejpam-3338	830	10	(	(	PUNCT
ejpam-3338	830	11	if	if	SCONJ
ejpam-3338	830	12	it	it	PRON
ejpam-3338	830	13	is	be	AUX
ejpam-3338	830	14	possible	possible	ADJ
ejpam-3338	830	15	)	)	PUNCT
ejpam-3338	830	16	since	since	SCONJ
ejpam-3338	830	17	we	we	PRON
ejpam-3338	830	18	may	may	AUX
ejpam-3338	830	19	not	not	PART
ejpam-3338	830	20	have	have	VERB
ejpam-3338	830	21	to	to	PART
ejpam-3338	830	22	worry	worry	VERB
ejpam-3338	830	23	too	too	ADV
ejpam-3338	830	24	much	much	ADJ
ejpam-3338	830	25	about	about	ADP
ejpam-3338	830	26	a	a	DET
ejpam-3338	830	27	large	large	ADJ
ejpam-3338	830	28	array	array	NOUN
ejpam-3338	830	29	of	of	ADP
ejpam-3338	830	30	mathematical	mathematical	ADJ
ejpam-3338	830	31	functions	function	NOUN
ejpam-3338	830	32	and	and	CCONJ
ejpam-3338	830	33	their	their	PRON
ejpam-3338	830	34	varying	vary	VERB
ejpam-3338	830	35	properties	property	NOUN
ejpam-3338	830	36	over	over	ADP
ejpam-3338	830	37	the	the	DET
ejpam-3338	830	38	concerned	concerned	ADJ
ejpam-3338	830	39	domain	domain	NOUN
ejpam-3338	830	40	.	.	PUNCT
ejpam-3338	831	1	all	all	PRON
ejpam-3338	831	2	we	we	PRON
ejpam-3338	831	3	need	need	VERB
ejpam-3338	831	4	to	to	PART
ejpam-3338	831	5	worry	worry	VERB
ejpam-3338	831	6	is	be	AUX
ejpam-3338	831	7	about	about	ADP
ejpam-3338	831	8	computational	computational	ADJ
ejpam-3338	831	9	error	error	NOUN
ejpam-3338	831	10	and	and	CCONJ
ejpam-3338	831	11	occasionally	occasionally	ADV
ejpam-3338	831	12	computational	computational	ADJ
ejpam-3338	831	13	complexity	complexity	NOUN
ejpam-3338	831	14	subject	subject	NOUN
ejpam-3338	831	15	,	,	PUNCT
ejpam-3338	831	16	however	however	ADV
ejpam-3338	831	17	,	,	PUNCT
ejpam-3338	831	18	to	to	ADP
ejpam-3338	831	19	continuity	continuity	NOUN
ejpam-3338	831	20	/	/	SYM
ejpam-3338	831	21	analyticity	analyticity	NOUN
ejpam-3338	831	22	of	of	ADP
ejpam-3338	831	23	the	the	DET
ejpam-3338	831	24	functions	function	NOUN
ejpam-3338	831	25	.	.	PUNCT
ejpam-3338	832	1	for	for	ADP
ejpam-3338	832	2	the	the	DET
ejpam-3338	832	3	differential	differential	ADJ
ejpam-3338	832	4	equations	equation	NOUN
ejpam-3338	832	5	integer	integer	NOUN
ejpam-3338	832	6	-	-	PUNCT
ejpam-3338	832	7	order	order	NOUN
ejpam-3338	832	8	as	as	ADV
ejpam-3338	832	9	well	well	ADV
ejpam-3338	832	10	as	as	ADP
ejpam-3338	832	11	fractional	fractional	ADJ
ejpam-3338	832	12	order	order	NOUN
ejpam-3338	832	13	we	we	PRON
ejpam-3338	832	14	would	would	AUX
ejpam-3338	832	15	get	get	VERB
ejpam-3338	832	16	the	the	DET
ejpam-3338	832	17	solution	solution	NOUN
ejpam-3338	832	18	viz	viz	NOUN
ejpam-3338	832	19	.	.	PUNCT
ejpam-3338	833	1	the	the	DET
ejpam-3338	833	2	function	function	NOUN
ejpam-3338	833	3	not	not	PART
ejpam-3338	833	4	in	in	ADP
ejpam-3338	833	5	terms	term	NOUN
ejpam-3338	833	6	of	of	ADP
ejpam-3338	833	7	a	a	DET
ejpam-3338	833	8	mathematical	mathematical	ADJ
ejpam-3338	833	9	function	function	NOUN
ejpam-3338	833	10	but	but	CCONJ
ejpam-3338	833	11	in	in	ADP
ejpam-3338	833	12	terms	term	NOUN
ejpam-3338	833	13	of	of	ADP
ejpam-3338	833	14	a	a	DET
ejpam-3338	833	15	numerical	numerical	ADJ
ejpam-3338	833	16	table	table	NOUN
ejpam-3338	833	17	containing	contain	VERB
ejpam-3338	833	18	a	a	DET
ejpam-3338	833	19	number	number	NOUN
ejpam-3338	833	20	of	of	ADP
ejpam-3338	833	21	rows	row	NOUN
ejpam-3338	833	22	,	,	PUNCT
ejpam-3338	833	23	every	every	DET
ejpam-3338	833	24	row	row	NOUN
ejpam-3338	833	25	consists	consist	VERB
ejpam-3338	833	26	of	of	ADP
ejpam-3338	833	27	values	value	NOUN
ejpam-3338	833	28	of	of	ADP
ejpam-3338	833	29	independent	independent	ADJ
ejpam-3338	833	30	variables	variable	NOUN
ejpam-3338	833	31	and	and	CCONJ
ejpam-3338	833	32	the	the	DET
ejpam-3338	833	33	corresponding	corresponding	ADJ
ejpam-3338	833	34	function	function	NOUN
ejpam-3338	833	35	value	value	NOUN
ejpam-3338	833	36	.	.	PUNCT
ejpam-3338	834	1	here	here	ADV
ejpam-3338	834	2	too	too	ADV
ejpam-3338	834	3	the	the	DET
ejpam-3338	834	4	problem	problem	NOUN
ejpam-3338	834	5	of	of	ADP
ejpam-3338	834	6	generalization	generalization	NOUN
ejpam-3338	834	7	appears	appear	VERB
ejpam-3338	834	8	to	to	PART
ejpam-3338	834	9	be	be	AUX
ejpam-3338	834	10	relatively	relatively	ADV
ejpam-3338	834	11	simple	simple	ADJ
ejpam-3338	834	12	.	.	PUNCT
ejpam-3338	835	1	however	however	ADV
ejpam-3338	835	2	,	,	PUNCT
ejpam-3338	835	3	the	the	DET
ejpam-3338	835	4	background	background	NOUN
ejpam-3338	835	5	mathematical	mathematical	ADJ
ejpam-3338	835	6	knowledge	knowledge	NOUN
ejpam-3338	835	7	in	in	ADP
ejpam-3338	835	8	this	this	DET
ejpam-3338	835	9	subject	subject	ADJ
ejpam-3338	835	10	area	area	NOUN
ejpam-3338	835	11	is	be	AUX
ejpam-3338	835	12	extremely	extremely	ADV
ejpam-3338	835	13	(	(	PUNCT
ejpam-3338	835	14	sometimes	sometimes	ADV
ejpam-3338	835	15	critically	critically	ADV
ejpam-3338	835	16	)	)	PUNCT
ejpam-3338	835	17	helpful	helpful	ADJ
ejpam-3338	835	18	to	to	ADP
ejpam-3338	835	19	completely	completely	ADV
ejpam-3338	835	20	and	and	CCONJ
ejpam-3338	835	21	confidently	confidently	ADV
ejpam-3338	835	22	rely	rely	VERB
ejpam-3338	835	23	on	on	ADP
ejpam-3338	835	24	the	the	DET
ejpam-3338	835	25	numerical	numerical	ADJ
ejpam-3338	835	26	results	result	NOUN
ejpam-3338	835	27	and	and	CCONJ
ejpam-3338	835	28	the	the	DET
ejpam-3338	835	29	concerned	concerned	ADJ
ejpam-3338	835	30	graphs	graph	NOUN
ejpam-3338	835	31	.	.	PUNCT
ejpam-3338	836	1	blindly	blindly	ADV
ejpam-3338	836	2	/	/	PUNCT
ejpam-3338	836	3	mechanically	mechanically	ADV
ejpam-3338	836	4	doing	do	VERB
ejpam-3338	836	5	computations	computation	NOUN
ejpam-3338	836	6	without	without	ADP
ejpam-3338	836	7	getting	get	VERB
ejpam-3338	836	8	a	a	DET
ejpam-3338	836	9	feel	feel	NOUN
ejpam-3338	836	10	/	/	SYM
ejpam-3338	836	11	an	an	DET
ejpam-3338	836	12	understanding	understanding	NOUN
ejpam-3338	836	13	about	about	ADP
ejpam-3338	836	14	what	what	PRON
ejpam-3338	836	15	the	the	DET
ejpam-3338	836	16	numbers	number	NOUN
ejpam-3338	836	17	are	be	AUX
ejpam-3338	836	18	saying	say	VERB
ejpam-3338	836	19	(	(	PUNCT
ejpam-3338	836	20	or	or	CCONJ
ejpam-3338	836	21	giving	give	VERB
ejpam-3338	836	22	us	we	PRON
ejpam-3338	836	23	message	message	NOUN
ejpam-3338	836	24	)	)	PUNCT
ejpam-3338	836	25	is	be	AUX
ejpam-3338	836	26	unacceptable	unacceptable	ADJ
ejpam-3338	836	27	.	.	PUNCT
ejpam-3338	837	1	problems	problem	NOUN
ejpam-3338	837	2	and	and	CCONJ
ejpam-3338	837	3	efforts	effort	NOUN
ejpam-3338	837	4	toward	toward	ADP
ejpam-3338	837	5	generalization	generalization	NOUN
ejpam-3338	837	6	.	.	PUNCT
ejpam-3338	838	1	we	we	PRON
ejpam-3338	838	2	have	have	AUX
ejpam-3338	838	3	mentioned	mention	VERB
ejpam-3338	838	4	the	the	DET
ejpam-3338	838	5	various	various	ADJ
ejpam-3338	838	6	problems	problem	NOUN
ejpam-3338	838	7	and	and	CCONJ
ejpam-3338	838	8	innovative	innovative	ADJ
ejpam-3338	838	9	efforts	effort	NOUN
ejpam-3338	838	10	toward	toward	ADP
ejpam-3338	838	11	generalization	generalization	NOUN
ejpam-3338	838	12	of	of	ADP
ejpam-3338	838	13	fractional	fractional	ADJ
ejpam-3338	838	14	calculus	calculus	NOUN
ejpam-3338	838	15	not	not	PART
ejpam-3338	838	16	only	only	ADV
ejpam-3338	838	17	in	in	ADP
ejpam-3338	838	18	section	section	NOUN
ejpam-3338	838	19	2	2	NUM
ejpam-3338	838	20	(	(	PUNCT
ejpam-3338	838	21	problems	problem	NOUN
ejpam-3338	838	22	and	and	CCONJ
ejpam-3338	838	23	efforts	effort	NOUN
ejpam-3338	838	24	)	)	PUNCT
ejpam-3338	838	25	,	,	PUNCT
ejpam-3338	838	26	but	but	CCONJ
ejpam-3338	838	27	also	also	ADV
ejpam-3338	838	28	in	in	ADP
ejpam-3338	838	29	section	section	NOUN
ejpam-3338	838	30	1	1	NUM
ejpam-3338	838	31	(	(	PUNCT
ejpam-3338	838	32	introduction	introduction	NOUN
ejpam-3338	838	33	)	)	PUNCT
ejpam-3338	838	34	.	.	PUNCT
ejpam-3338	839	1	section	section	NOUN
ejpam-3338	839	2	3	3	NUM
ejpam-3338	839	3	that	that	PRON
ejpam-3338	839	4	deals	deal	VERB
ejpam-3338	839	5	with	with	ADP
ejpam-3338	839	6	fractional	fractional	ADJ
ejpam-3338	839	7	ordinary	ordinary	ADJ
ejpam-3338	839	8	differential	differential	ADJ
ejpam-3338	839	9	equation	equation	NOUN
ejpam-3338	839	10	may	may	AUX
ejpam-3338	839	11	be	be	AUX
ejpam-3338	839	12	considered	consider	VERB
ejpam-3338	839	13	as	as	ADP
ejpam-3338	839	14	a	a	DET
ejpam-3338	839	15	good	good	ADJ
ejpam-3338	839	16	effort	effort	NOUN
ejpam-3338	839	17	toward	toward	ADP
ejpam-3338	839	18	generalization	generalization	NOUN
ejpam-3338	839	19	.	.	PUNCT
ejpam-3338	840	1	the	the	DET
ejpam-3338	840	2	pain	pain	NOUN
ejpam-3338	840	3	-	-	PUNCT
ejpam-3338	840	4	staking	stake	VERB
ejpam-3338	840	5	effort	effort	NOUN
ejpam-3338	840	6	of	of	ADP
ejpam-3338	840	7	the	the	DET
ejpam-3338	840	8	author	author	NOUN
ejpam-3338	840	9	in	in	ADP
ejpam-3338	840	10	writing	write	VERB
ejpam-3338	840	11	a	a	DET
ejpam-3338	840	12	detailed	detailed	ADJ
ejpam-3338	840	13	matlab	matlab	NOUN
ejpam-3338	840	14	program	program	NOUN
ejpam-3338	840	15	that	that	PRON
ejpam-3338	840	16	works	work	VERB
ejpam-3338	840	17	well	well	ADV
ejpam-3338	840	18	for	for	ADP
ejpam-3338	840	19	odes	ode	NOUN
ejpam-3338	840	20	with	with	ADP
ejpam-3338	840	21	,	,	PUNCT
ejpam-3338	840	22	of	of	ADP
ejpam-3338	840	23	course	course	NOUN
ejpam-3338	840	24	,	,	PUNCT
ejpam-3338	840	25	restricted	restrict	VERB
ejpam-3338	840	26	fractional	fractional	ADJ
ejpam-3338	840	27	order	order	NOUN
ejpam-3338	840	28	is	be	AUX
ejpam-3338	840	29	remarkable	remarkable	ADJ
ejpam-3338	840	30	.	.	PUNCT
ejpam-3338	841	1	however	however	ADV
ejpam-3338	841	2	,	,	PUNCT
ejpam-3338	841	3	the	the	DET
ejpam-3338	841	4	restriction	restriction	NOUN
ejpam-3338	841	5	on	on	ADP
ejpam-3338	841	6	the	the	DET
ejpam-3338	841	7	fractional	fractional	ADJ
ejpam-3338	841	8	order	order	NOUN
ejpam-3338	841	9	is	be	AUX
ejpam-3338	841	10	an	an	DET
ejpam-3338	841	11	important	important	ADJ
ejpam-3338	841	12	issue	issue	NOUN
ejpam-3338	841	13	that	that	PRON
ejpam-3338	841	14	needs	need	VERB
ejpam-3338	841	15	to	to	PART
ejpam-3338	841	16	be	be	AUX
ejpam-3338	841	17	sorted	sort	VERB
ejpam-3338	841	18	out	out	ADP
ejpam-3338	841	19	for	for	ADP
ejpam-3338	841	20	a	a	DET
ejpam-3338	841	21	possible	possible	ADJ
ejpam-3338	841	22	usable	usable	ADJ
ejpam-3338	841	23	generalization	generalization	NOUN
ejpam-3338	841	24	.	.	PUNCT
ejpam-3338	842	1	any	any	DET
ejpam-3338	842	2	system	system	NOUN
ejpam-3338	842	3	of	of	ADP
ejpam-3338	842	4	odes	ode	NOUN
ejpam-3338	842	5	can	can	AUX
ejpam-3338	842	6	always	always	ADV
ejpam-3338	842	7	be	be	AUX
ejpam-3338	842	8	written	write	VERB
ejpam-3338	842	9	as	as	ADP
ejpam-3338	842	10	a	a	DET
ejpam-3338	842	11	system	system	NOUN
ejpam-3338	842	12	of	of	ADP
ejpam-3338	842	13	n	n	PRON
ejpam-3338	842	14	1st	1st	ADJ
ejpam-3338	842	15	order	order	NOUN
ejpam-3338	842	16	odes	ode	VERB
ejpam-3338	842	17	with	with	ADP
ejpam-3338	842	18	n	n	CCONJ
ejpam-3338	842	19	initial	initial	ADJ
ejpam-3338	842	20	conditions	condition	NOUN
ejpam-3338	842	21	or	or	CCONJ
ejpam-3338	842	22	n	n	DET
ejpam-3338	842	23	2	2	NUM
ejpam-3338	842	24	-	-	PUNCT
ejpam-3338	842	25	point	point	NOUN
ejpam-3338	842	26	boundary	boundary	ADJ
ejpam-3338	842	27	conditions	condition	NOUN
ejpam-3338	842	28	.	.	PUNCT
ejpam-3338	843	1	a	a	DET
ejpam-3338	843	2	general	general	ADJ
ejpam-3338	843	3	computer	computer	NOUN
ejpam-3338	843	4	(	(	PUNCT
ejpam-3338	843	5	matlab	matlab	PROPN
ejpam-3338	843	6	,	,	PUNCT
ejpam-3338	843	7	say	say	INTJ
ejpam-3338	843	8	)	)	PUNCT
ejpam-3338	843	9	program	program	NOUN
ejpam-3338	843	10	for	for	ADP
ejpam-3338	843	11	the	the	DET
ejpam-3338	843	12	system	system	NOUN
ejpam-3338	843	13	of	of	ADP
ejpam-3338	843	14	n	n	PRON
ejpam-3338	843	15	1st	1st	ADJ
ejpam-3338	843	16	order	order	NOUN
ejpam-3338	843	17	odes	ode	NOUN
ejpam-3338	843	18	can	can	AUX
ejpam-3338	843	19	always	always	ADV
ejpam-3338	843	20	be	be	AUX
ejpam-3338	843	21	written	write	VERB
ejpam-3338	843	22	[	[	X
ejpam-3338	843	23	16	16	NUM
ejpam-3338	843	24	]	]	PUNCT
ejpam-3338	843	25	.	.	PUNCT
ejpam-3338	844	1	the	the	DET
ejpam-3338	844	2	widely	widely	ADV
ejpam-3338	844	3	used	use	VERB
ejpam-3338	844	4	matlab	matlab	NOUN
ejpam-3338	844	5	provides	provide	VERB
ejpam-3338	844	6	such	such	DET
ejpam-3338	844	7	a	a	DET
ejpam-3338	844	8	program	program	NOUN
ejpam-3338	844	9	for	for	ADP
ejpam-3338	844	10	n	n	PRON
ejpam-3338	844	11	1st	1st	ADJ
ejpam-3338	844	12	order	order	NOUN
ejpam-3338	844	13	odes	ode	VERB
ejpam-3338	844	14	with	with	ADP
ejpam-3338	844	15	n	n	CCONJ
ejpam-3338	844	16	initial	initial	ADJ
ejpam-3338	844	17	conditions	condition	NOUN
ejpam-3338	844	18	.	.	PUNCT
ejpam-3338	845	1	such	such	DET
ejpam-3338	845	2	a	a	DET
ejpam-3338	845	3	general	general	ADJ
ejpam-3338	845	4	computer	computer	NOUN
ejpam-3338	845	5	program	program	NOUN
ejpam-3338	845	6	can	can	AUX
ejpam-3338	845	7	not	not	PART
ejpam-3338	845	8	be	be	AUX
ejpam-3338	845	9	written	write	VERB
ejpam-3338	845	10	for	for	ADP
ejpam-3338	845	11	a	a	DET
ejpam-3338	845	12	system	system	NOUN
ejpam-3338	845	13	of	of	ADP
ejpam-3338	845	14	integer	integer	NOUN
ejpam-3338	845	15	order	order	NOUN
ejpam-3338	845	16	partial	partial	ADJ
ejpam-3338	845	17	differential	differential	NOUN
ejpam-3338	845	18	equations	equation	NOUN
ejpam-3338	845	19	(	(	PUNCT
ejpam-3338	845	20	pdes	pde	NOUN
ejpam-3338	845	21	)	)	PUNCT
ejpam-3338	845	22	.	.	PUNCT
ejpam-3338	846	1	fractional	fractional	ADJ
ejpam-3338	846	2	partial	partial	ADJ
ejpam-3338	846	3	differential	differential	NOUN
ejpam-3338	846	4	equations	equation	NOUN
ejpam-3338	846	5	are	be	AUX
ejpam-3338	846	6	no	no	DET
ejpam-3338	846	7	exceptions	exception	NOUN
ejpam-3338	846	8	.	.	PUNCT
ejpam-3338	847	1	however	however	ADV
ejpam-3338	847	2	,	,	PUNCT
ejpam-3338	847	3	we	we	PRON
ejpam-3338	847	4	are	be	AUX
ejpam-3338	847	5	not	not	PART
ejpam-3338	847	6	much	much	ADV
ejpam-3338	847	7	concerned	concerned	ADJ
ejpam-3338	847	8	with	with	ADP
ejpam-3338	847	9	this	this	DET
ejpam-3338	847	10	issue	issue	NOUN
ejpam-3338	847	11	in	in	ADP
ejpam-3338	847	12	this	this	DET
ejpam-3338	847	13	context	context	NOUN
ejpam-3338	847	14	.	.	PUNCT
ejpam-3338	848	1	quality	quality	NOUN
ejpam-3338	848	2	and	and	CCONJ
ejpam-3338	848	3	cost	cost	NOUN
ejpam-3338	848	4	of	of	ADP
ejpam-3338	848	5	the	the	DET
ejpam-3338	848	6	solution	solution	NOUN
ejpam-3338	848	7	.	.	PUNCT
ejpam-3338	849	1	how	how	SCONJ
ejpam-3338	849	2	do	do	AUX
ejpam-3338	849	3	the	the	DET
ejpam-3338	849	4	quality	quality	NOUN
ejpam-3338	849	5	(	(	PUNCT
ejpam-3338	849	6	relative	relative	ADJ
ejpam-3338	849	7	computational	computational	ADJ
ejpam-3338	849	8	error	error	NOUN
ejpam-3338	849	9	)	)	PUNCT
ejpam-3338	849	10	and	and	CCONJ
ejpam-3338	849	11	the	the	DET
ejpam-3338	849	12	cost	cost	NOUN
ejpam-3338	849	13	(	(	PUNCT
ejpam-3338	849	14	computational	computational	ADJ
ejpam-3338	849	15	complexity	complexity	NOUN
ejpam-3338	849	16	)	)	PUNCT
ejpam-3338	849	17	of	of	ADP
ejpam-3338	849	18	the	the	DET
ejpam-3338	849	19	solution	solution	NOUN
ejpam-3338	849	20	of	of	ADP
ejpam-3338	849	21	a	a	DET
ejpam-3338	849	22	system	system	NOUN
ejpam-3338	849	23	of	of	ADP
ejpam-3338	849	24	fdes	fde	NOUN
ejpam-3338	849	25	differ	differ	VERB
ejpam-3338	849	26	from	from	ADP
ejpam-3338	849	27	that	that	PRON
ejpam-3338	849	28	of	of	ADP
ejpam-3338	849	29	the	the	DET
ejpam-3338	849	30	equivalent	equivalent	ADJ
ejpam-3338	849	31	system	system	NOUN
ejpam-3338	849	32	of	of	ADP
ejpam-3338	849	33	integer	integer	NOUN
ejpam-3338	849	34	order	order	NOUN
ejpam-3338	849	35	differential	differential	ADJ
ejpam-3338	849	36	equations	equation	NOUN
ejpam-3338	849	37	?	?	PUNCT
ejpam-3338	850	1	which	which	DET
ejpam-3338	850	2	solution	solution	NOUN
ejpam-3338	850	3	will	will	AUX
ejpam-3338	850	4	be	be	AUX
ejpam-3338	850	5	better	well	ADJ
ejpam-3338	850	6	?	?	PUNCT
ejpam-3338	851	1	these	these	DET
ejpam-3338	851	2	questions	question	NOUN
ejpam-3338	851	3	,	,	PUNCT
ejpam-3338	851	4	though	though	SCONJ
ejpam-3338	851	5	appear	appear	VERB
ejpam-3338	851	6	to	to	PART
ejpam-3338	851	7	be	be	AUX
ejpam-3338	851	8	out	out	ADP
ejpam-3338	851	9	of	of	ADP
ejpam-3338	851	10	context	context	NOUN
ejpam-3338	851	11	for	for	ADP
ejpam-3338	851	12	generalization	generalization	NOUN
ejpam-3338	851	13	,	,	PUNCT
ejpam-3338	851	14	are	be	AUX
ejpam-3338	851	15	still	still	ADV
ejpam-3338	851	16	important	important	ADJ
ejpam-3338	851	17	to	to	PART
ejpam-3338	851	18	support	support	VERB
ejpam-3338	851	19	the	the	DET
ejpam-3338	851	20	scope	scope	NOUN
ejpam-3338	851	21	of	of	ADP
ejpam-3338	851	22	fractional	fractional	ADJ
ejpam-3338	851	23	order	order	NOUN
ejpam-3338	851	24	systems	system	NOUN
ejpam-3338	851	25	in	in	ADP
ejpam-3338	851	26	calculus	calculus	NOUN
ejpam-3338	851	27	and	and	CCONJ
ejpam-3338	851	28	to	to	PART
ejpam-3338	851	29	make	make	VERB
ejpam-3338	851	30	it	it	PRON
ejpam-3338	851	31	an	an	DET
ejpam-3338	851	32	integral	integral	ADJ
ejpam-3338	851	33	part	part	NOUN
ejpam-3338	851	34	of	of	ADP
ejpam-3338	851	35	the	the	DET
ejpam-3338	851	36	current	current	ADJ
ejpam-3338	851	37	calculus	calculus	NOUN
ejpam-3338	851	38	that	that	PRON
ejpam-3338	851	39	we	we	PRON
ejpam-3338	851	40	are	be	AUX
ejpam-3338	851	41	taught	teach	VERB
ejpam-3338	851	42	globally	globally	ADV
ejpam-3338	851	43	.	.	PUNCT
ejpam-3338	852	1	references	reference	NOUN
ejpam-3338	852	2	1098	1098	NUM
ejpam-3338	852	3	acknowledgements	acknowledgement	NOUN
ejpam-3338	852	4	the	the	DET
ejpam-3338	852	5	authors	author	NOUN
ejpam-3338	852	6	thank	thank	VERB
ejpam-3338	852	7	the	the	DET
ejpam-3338	852	8	science	science	NOUN
ejpam-3338	852	9	and	and	CCONJ
ejpam-3338	852	10	engineering	engineering	NOUN
ejpam-3338	852	11	research	research	NOUN
ejpam-3338	852	12	board	board	NOUN
ejpam-3338	852	13	(	(	PUNCT
ejpam-3338	852	14	serb	serb	NOUN
ejpam-3338	852	15	)	)	PUNCT
ejpam-3338	852	16	of	of	ADP
ejpam-3338	852	17	the	the	DET
ejpam-3338	852	18	department	department	NOUN
ejpam-3338	852	19	of	of	ADP
ejpam-3338	852	20	science	science	NOUN
ejpam-3338	852	21	and	and	CCONJ
ejpam-3338	852	22	technology	technology	NOUN
ejpam-3338	852	23	(	(	PUNCT
ejpam-3338	852	24	dst	dst	PROPN
ejpam-3338	852	25	)	)	PUNCT
ejpam-3338	852	26	,	,	PUNCT
ejpam-3338	852	27	government	government	NOUN
ejpam-3338	852	28	of	of	ADP
ejpam-3338	852	29	india	india	PROPN
ejpam-3338	852	30	for	for	ADP
ejpam-3338	852	31	their	their	PRON
ejpam-3338	852	32	support	support	NOUN
ejpam-3338	852	33	of	of	ADP
ejpam-3338	852	34	the	the	DET
ejpam-3338	852	35	reported	report	VERB
ejpam-3338	852	36	work	work	NOUN
ejpam-3338	852	37	under	under	ADP
ejpam-3338	852	38	the	the	DET
ejpam-3338	852	39	project	project	NOUN
ejpam-3338	852	40	dst	dst	PROPN
ejpam-3338	852	41	serb	serb	PROPN
ejpam-3338	852	42	emr/2016/003572	emr/2016/003572	PROPN
ejpam-3338	852	43	dated	date	VERB
ejpam-3338	852	44	feb	feb	PROPN
ejpam-3338	852	45	06	06	NUM
ejpam-3338	852	46	,	,	PUNCT
ejpam-3338	852	47	2017	2017	NUM
ejpam-3338	852	48	.	.	PUNCT
ejpam-3338	853	1	references	reference	NOUN
ejpam-3338	853	2	[	[	X
ejpam-3338	853	3	1	1	NUM
ejpam-3338	853	4	]	]	PUNCT
ejpam-3338	853	5	r.	r.	PROPN
ejpam-3338	853	6	herrmann	herrmann	PROPN
ejpam-3338	853	7	,	,	PUNCT
ejpam-3338	853	8	fractional	fractional	ADJ
ejpam-3338	853	9	calculus	calculus	NOUN
ejpam-3338	853	10	:	:	PUNCT
ejpam-3338	853	11	an	an	DET
ejpam-3338	853	12	introduction	introduction	NOUN
ejpam-3338	853	13	for	for	ADP
ejpam-3338	853	14	physicists	physicist	NOUN
ejpam-3338	853	15	,	,	PUNCT
ejpam-3338	853	16	world	world	NOUN
ejpam-3338	853	17	scientific	scientific	ADJ
ejpam-3338	853	18	,	,	PUNCT
ejpam-3338	853	19	new	new	PROPN
ejpam-3338	853	20	jersey	jersey	PROPN
ejpam-3338	853	21	,	,	PUNCT
ejpam-3338	853	22	2010	2010	NUM
ejpam-3338	853	23	.	.	PUNCT
ejpam-3338	854	1	[	[	X
ejpam-3338	854	2	2	2	X
ejpam-3338	854	3	]	]	PUNCT
ejpam-3338	854	4	v.	v.	CCONJ
ejpam-3338	854	5	lakshmikantham	lakshmikantham	NOUN
ejpam-3338	854	6	and	and	CCONJ
ejpam-3338	854	7	s.k	s.k	PROPN
ejpam-3338	854	8	.	.	PROPN
ejpam-3338	854	9	sen	sen	PROPN
ejpam-3338	854	10	,	,	PUNCT
ejpam-3338	854	11	computational	computational	ADJ
ejpam-3338	854	12	error	error	NOUN
ejpam-3338	854	13	and	and	CCONJ
ejpam-3338	854	14	complexity	complexity	NOUN
ejpam-3338	854	15	in	in	ADP
ejpam-3338	854	16	sience	sience	NOUN
ejpam-3338	854	17	and	and	CCONJ
ejpam-3338	854	18	engineering	engineering	NOUN
ejpam-3338	854	19	,	,	PUNCT
ejpam-3338	854	20	elsevier	elsevier	NOUN
ejpam-3338	854	21	,	,	PUNCT
ejpam-3338	854	22	amsterdam	amsterdam	PROPN
ejpam-3338	854	23	,	,	PUNCT
ejpam-3338	854	24	2005	2005	NUM
ejpam-3338	854	25	.	.	PUNCT
ejpam-3338	855	1	[	[	X
ejpam-3338	855	2	3	3	X
ejpam-3338	855	3	]	]	X
ejpam-3338	855	4	c.	c.	PROPN
ejpam-3338	855	5	r.	r.	PROPN
ejpam-3338	855	6	rao	rao	PROPN
ejpam-3338	855	7	and	and	CCONJ
ejpam-3338	855	8	s.	s.	PROPN
ejpam-3338	855	9	k.	k.	PROPN
ejpam-3338	855	10	mitra	mitra	PROPN
ejpam-3338	855	11	,	,	PUNCT
ejpam-3338	855	12	generatized	generatize	VERB
ejpam-3338	855	13	inverse	inverse	NOUN
ejpam-3338	855	14	of	of	ADP
ejpam-3338	855	15	matrices	matrix	NOUN
ejpam-3338	855	16	and	and	CCONJ
ejpam-3338	855	17	its	its	PRON
ejpam-3338	855	18	applications	application	NOUN
ejpam-3338	855	19	,	,	PUNCT
ejpam-3338	855	20	wiley	wiley	NOUN
ejpam-3338	855	21	,	,	PUNCT
ejpam-3338	855	22	1972	1972	NUM
ejpam-3338	855	23	.	.	PUNCT
ejpam-3338	856	1	[	[	X
ejpam-3338	856	2	4	4	X
ejpam-3338	856	3	]	]	X
ejpam-3338	856	4	g.	g.	PROPN
ejpam-3338	856	5	h.	h.	PROPN
ejpam-3338	856	6	golub	golub	PROPN
ejpam-3338	856	7	,	,	PUNCT
ejpam-3338	856	8	van	van	PROPN
ejpam-3338	856	9	loan	loan	NOUN
ejpam-3338	856	10	,	,	PUNCT
ejpam-3338	856	11	and	and	CCONJ
ejpam-3338	856	12	f.	f.	PROPN
ejpam-3338	856	13	charles	charles	PROPN
ejpam-3338	856	14	,	,	PUNCT
ejpam-3338	856	15	it	it	PRON
ejpam-3338	856	16	matrix	matrix	VERB
ejpam-3338	856	17	computations	computation	NOUN
ejpam-3338	856	18	(	(	PUNCT
ejpam-3338	856	19	3rd	3rd	ADJ
ejpam-3338	856	20	ed	ed	NOUN
ejpam-3338	856	21	.	.	PUNCT
ejpam-3338	856	22	)	)	PUNCT
ejpam-3338	856	23	,	,	PUNCT
ejpam-3338	856	24	johns	johns	PROPN
ejpam-3338	856	25	hopkins	hopkins	PROPN
ejpam-3338	856	26	university	university	PROPN
ejpam-3338	856	27	press	press	NOUN
ejpam-3338	856	28	,	,	PUNCT
ejpam-3338	856	29	1996	1996	NUM
ejpam-3338	856	30	.	.	PUNCT
ejpam-3338	857	1	[	[	X
ejpam-3338	857	2	5	5	X
ejpam-3338	857	3	]	]	PUNCT
ejpam-3338	857	4	k.	k.	PROPN
ejpam-3338	857	5	b.	b.	PROPN
ejpam-3338	857	6	oldham	oldham	PROPN
ejpam-3338	857	7	and	and	CCONJ
ejpam-3338	857	8	j.	j.	PROPN
ejpam-3338	857	9	spanier	spanier	PROPN
ejpam-3338	857	10	,	,	PUNCT
ejpam-3338	857	11	the	the	DET
ejpam-3338	857	12	fractional	fractional	ADJ
ejpam-3338	857	13	calculus	calculus	NOUN
ejpam-3338	857	14	,	,	PUNCT
ejpam-3338	857	15	academic	academic	ADJ
ejpam-3338	857	16	press	press	NOUN
ejpam-3338	857	17	,	,	PUNCT
ejpam-3338	857	18	1974	1974	NUM
ejpam-3338	857	19	.	.	PUNCT
ejpam-3338	858	1	[	[	X
ejpam-3338	858	2	6	6	NUM
ejpam-3338	858	3	]	]	PUNCT
ejpam-3338	858	4	k.	k.	PROPN
ejpam-3338	858	5	s.	s.	PROPN
ejpam-3338	858	6	miller	miller	PROPN
ejpam-3338	858	7	and	and	CCONJ
ejpam-3338	858	8	b.	b.	PROPN
ejpam-3338	858	9	ross	ross	PROPN
ejpam-3338	858	10	,	,	PUNCT
ejpam-3338	858	11	an	an	DET
ejpam-3338	858	12	introduction	introduction	NOUN
ejpam-3338	858	13	to	to	ADP
ejpam-3338	858	14	the	the	DET
ejpam-3338	858	15	fractional	fractional	ADJ
ejpam-3338	858	16	calculus	calculus	NOUN
ejpam-3338	858	17	and	and	CCONJ
ejpam-3338	858	18	fractional	fractional	ADJ
ejpam-3338	858	19	differential	differential	ADJ
ejpam-3338	858	20	equations	equation	NOUN
ejpam-3338	858	21	,	,	PUNCT
ejpam-3338	858	22	wiley	wiley	NOUN
ejpam-3338	858	23	,	,	PUNCT
ejpam-3338	858	24	new	new	PROPN
ejpam-3338	858	25	york	york	PROPN
ejpam-3338	858	26	,	,	PUNCT
ejpam-3338	858	27	1993	1993	NUM
ejpam-3338	858	28	.	.	PUNCT
ejpam-3338	859	1	[	[	X
ejpam-3338	859	2	7	7	NUM
ejpam-3338	859	3	]	]	X
ejpam-3338	859	4	i.	i.	NOUN
ejpam-3338	859	5	podlubny	podlubny	PROPN
ejpam-3338	859	6	,	,	PUNCT
ejpam-3338	859	7	fractioal	fractioal	NOUN
ejpam-3338	859	8	differential	differential	NOUN
ejpam-3338	859	9	equations	equation	NOUN
ejpam-3338	859	10	,	,	PUNCT
ejpam-3338	859	11	academic	academic	ADJ
ejpam-3338	859	12	press	press	NOUN
ejpam-3338	859	13	,	,	PUNCT
ejpam-3338	859	14	san	san	PROPN
ejpam-3338	859	15	diago	diago	PROPN
ejpam-3338	859	16	,	,	PUNCT
ejpam-3338	859	17	1999	1999	NUM
ejpam-3338	859	18	.	.	PUNCT
ejpam-3338	860	1	[	[	X
ejpam-3338	860	2	8	8	NUM
ejpam-3338	860	3	]	]	X
ejpam-3338	860	4	i.	i.	PROPN
ejpam-3338	860	5	petras	petras	PROPN
ejpam-3338	860	6	,	,	PUNCT
ejpam-3338	860	7	fractional	fractional	ADJ
ejpam-3338	860	8	derivatives	derivative	NOUN
ejpam-3338	860	9	,	,	PUNCT
ejpam-3338	860	10	fractional	fractional	ADJ
ejpam-3338	860	11	integrals	integral	NOUN
ejpam-3338	860	12	,	,	PUNCT
ejpam-3338	860	13	and	and	CCONJ
ejpam-3338	860	14	fractional	fractional	ADJ
ejpam-3338	860	15	differential	differential	ADJ
ejpam-3338	860	16	equations	equation	NOUN
ejpam-3338	860	17	in	in	ADP
ejpam-3338	860	18	matlab	matlab	PROPN
ejpam-3338	860	19	,	,	PUNCT
ejpam-3338	860	20	239	239	NUM
ejpam-3338	860	21	-	-	SYM
ejpam-3338	860	22	264	264	NUM
ejpam-3338	860	23	,	,	PUNCT
ejpam-3338	860	24	in	in	ADP
ejpam-3338	860	25	:	:	PUNCT
ejpam-3338	860	26	engineering	engineer	VERB
ejpam-3338	860	27	education	education	NOUN
ejpam-3338	860	28	and	and	CCONJ
ejpam-3338	860	29	research	research	NOUN
ejpam-3338	860	30	using	use	VERB
ejpam-3338	860	31	matlab	matlab	PROPN
ejpam-3338	860	32	,	,	PUNCT
ejpam-3338	860	33	ed	ed	NOUN
ejpam-3338	860	34	.	.	PUNCT
ejpam-3338	860	35	:	:	PUNCT
ejpam-3338	860	36	ali	ali	PROPN
ejpam-3338	860	37	assi	assi	PROPN
ejpam-3338	860	38	,	,	PUNCT
ejpam-3338	860	39	intech	intech	PROPN
ejpam-3338	860	40	,	,	PUNCT
ejpam-3338	860	41	480	480	NUM
ejpam-3338	860	42	pages	page	NOUN
ejpam-3338	860	43	,	,	PUNCT
ejpam-3338	860	44	2011	2011	NUM
ejpam-3338	860	45	.	.	PUNCT
ejpam-3338	861	1	[	[	X
ejpam-3338	861	2	9	9	NUM
ejpam-3338	861	3	]	]	PUNCT
ejpam-3338	861	4	k.	k.	PROPN
ejpam-3338	861	5	diethelm	diethelm	PROPN
ejpam-3338	861	6	,	,	PUNCT
ejpam-3338	861	7	a.d	a.d	PROPN
ejpam-3338	861	8	.	.	PROPN
ejpam-3338	861	9	freed	freed	PROPN
ejpam-3338	861	10	,	,	PUNCT
ejpam-3338	861	11	the	the	DET
ejpam-3338	861	12	frac	frac	PROPN
ejpam-3338	861	13	pece	pece	PROPN
ejpam-3338	861	14	subroutine	subroutine	NOUN
ejpam-3338	861	15	for	for	ADP
ejpam-3338	861	16	the	the	DET
ejpam-3338	861	17	numerical	numerical	ADJ
ejpam-3338	861	18	solution	solution	NOUN
ejpam-3338	861	19	of	of	ADP
ejpam-3338	861	20	differential	differential	ADJ
ejpam-3338	861	21	equations	equation	NOUN
ejpam-3338	861	22	of	of	ADP
ejpam-3338	861	23	fractional	fractional	ADJ
ejpam-3338	861	24	order	order	NOUN
ejpam-3338	861	25	,	,	PUNCT
ejpam-3338	861	26	in	in	ADP
ejpam-3338	861	27	:	:	PUNCT
ejpam-3338	861	28	s.	s.	PROPN
ejpam-3338	861	29	heinzel	heinzel	PROPN
ejpam-3338	861	30	,	,	PUNCT
ejpam-3338	861	31	t.	t.	NOUN
ejpam-3338	861	32	plesser	plesser	NOUN
ejpam-3338	861	33	(	(	PUNCT
ejpam-3338	861	34	eds	ed	NOUN
ejpam-3338	861	35	.	.	PUNCT
ejpam-3338	861	36	)	)	PUNCT
ejpam-3338	861	37	,	,	PUNCT
ejpam-3338	861	38	forschung	forschung	VERB
ejpam-3338	861	39	und	und	PROPN
ejpam-3338	861	40	wissenschaftliches	wissenschaftliche	VERB
ejpam-3338	861	41	rechnen	rechnen	PROPN
ejpam-3338	861	42	1998	1998	NUM
ejpam-3338	861	43	,	,	PUNCT
ejpam-3338	861	44	gessellschaft	gessellschaft	PROPN
ejpam-3338	861	45	fur	fur	PROPN
ejpam-3338	861	46	wissenschaftliche	wissenschaftliche	PROPN
ejpam-3338	861	47	datenverarbeitung	datenverarbeitung	PROPN
ejpam-3338	861	48	,	,	PUNCT
ejpam-3338	861	49	gottingen	gottingen	NOUN
ejpam-3338	861	50	,	,	PUNCT
ejpam-3338	861	51	1999	1999	NUM
ejpam-3338	861	52	,	,	PUNCT
ejpam-3338	861	53	pp	pp	ADJ
ejpam-3338	861	54	.	.	PUNCT
ejpam-3338	862	1	57	57	NUM
ejpam-3338	862	2	-	-	SYM
ejpam-3338	862	3	71	71	NUM
ejpam-3338	862	4	.	.	PUNCT
ejpam-3338	863	1	[	[	X
ejpam-3338	863	2	10	10	NUM
ejpam-3338	863	3	]	]	PUNCT
ejpam-3338	863	4	k.	k.	PROPN
ejpam-3338	863	5	diethelm	diethelm	PROPN
ejpam-3338	863	6	,	,	PUNCT
ejpam-3338	863	7	n.j	n.j	PROPN
ejpam-3338	863	8	.	.	PROPN
ejpam-3338	863	9	ford	ford	PROPN
ejpam-3338	863	10	,	,	PUNCT
ejpam-3338	863	11	a.d	a.d	PROPN
ejpam-3338	863	12	.	.	PROPN
ejpam-3338	863	13	freed	free	VERB
ejpam-3338	863	14	,	,	PUNCT
ejpam-3338	863	15	detailed	detailed	ADJ
ejpam-3338	863	16	error	error	NOUN
ejpam-3338	863	17	analysis	analysis	NOUN
ejpam-3338	863	18	for	for	ADP
ejpam-3338	863	19	a	a	DET
ejpam-3338	863	20	fractional	fractional	ADJ
ejpam-3338	863	21	adams	adams	PROPN
ejpam-3338	863	22	method	method	NOUN
ejpam-3338	863	23	,	,	PUNCT
ejpam-3338	863	24	numer	numer	NOUN
ejpam-3338	863	25	.	.	PROPN
ejpam-3338	863	26	algorithms	algorithms	PROPN
ejpam-3338	863	27	,	,	PUNCT
ejpam-3338	863	28	36	36	NUM
ejpam-3338	863	29	(	(	PUNCT
ejpam-3338	863	30	1	1	NUM
ejpam-3338	863	31	)	)	PUNCT
ejpam-3338	863	32	(	(	PUNCT
ejpam-3338	863	33	2004	2004	NUM
ejpam-3338	863	34	)	)	PUNCT
ejpam-3338	863	35	31	31	NUM
ejpam-3338	863	36	-	-	SYM
ejpam-3338	863	37	52	52	NUM
ejpam-3338	863	38	.	.	PUNCT
ejpam-3338	864	1	[	[	X
ejpam-3338	864	2	11	11	NUM
ejpam-3338	864	3	]	]	PUNCT
ejpam-3338	864	4	k.	k.	PROPN
ejpam-3338	864	5	diethelm	diethelm	PROPN
ejpam-3338	864	6	,	,	PUNCT
ejpam-3338	864	7	efficient	efficient	ADJ
ejpam-3338	864	8	solution	solution	NOUN
ejpam-3338	864	9	of	of	ADP
ejpam-3338	864	10	multi	multi	ADJ
ejpam-3338	864	11	-	-	ADJ
ejpam-3338	864	12	term	term	ADJ
ejpam-3338	864	13	fractional	fractional	ADJ
ejpam-3338	864	14	differential	differential	NOUN
ejpam-3338	864	15	equations	equation	NOUN
ejpam-3338	864	16	using	use	VERB
ejpam-3338	864	17	p(ec)me	p(ec)me	VERB
ejpam-3338	864	18	methods	method	NOUN
ejpam-3338	864	19	,	,	PUNCT
ejpam-3338	864	20	computing	compute	VERB
ejpam-3338	864	21	71	71	NUM
ejpam-3338	864	22	(	(	PUNCT
ejpam-3338	864	23	2003	2003	NUM
ejpam-3338	864	24	)	)	PUNCT
ejpam-3338	864	25	,	,	PUNCT
ejpam-3338	864	26	pp	pp	ADJ
ejpam-3338	864	27	.	.	PUNCT
ejpam-3338	865	1	305	305	NUM
ejpam-3338	865	2	-	-	SYM
ejpam-3338	865	3	319	319	NUM
ejpam-3338	865	4	.	.	PUNCT
ejpam-3338	866	1	[	[	X
ejpam-3338	866	2	12	12	NUM
ejpam-3338	866	3	]	]	X
ejpam-3338	866	4	e.	e.	PROPN
ejpam-3338	866	5	hairer	hairer	PROPN
ejpam-3338	866	6	,	,	PUNCT
ejpam-3338	866	7	c.	c.	PROPN
ejpam-3338	866	8	lubich	lubich	PROPN
ejpam-3338	866	9	,	,	PUNCT
ejpam-3338	866	10	m.	m.	PROPN
ejpam-3338	866	11	schlichte	schlichte	PROPN
ejpam-3338	866	12	,	,	PUNCT
ejpam-3338	866	13	fast	fast	ADJ
ejpam-3338	866	14	numerical	numerical	ADJ
ejpam-3338	866	15	solution	solution	NOUN
ejpam-3338	866	16	of	of	ADP
ejpam-3338	866	17	nonlinear	nonlinear	PROPN
ejpam-3338	866	18	volterra	volterra	PROPN
ejpam-3338	866	19	convolution	convolution	PROPN
ejpam-3338	866	20	equations	equation	NOUN
ejpam-3338	866	21	,	,	PUNCT
ejpam-3338	866	22	siam	siam	PROPN
ejpam-3338	866	23	,	,	PUNCT
ejpam-3338	866	24	j.	j.	PROPN
ejpam-3338	866	25	sci	sci	PROPN
ejpam-3338	866	26	.	.	PROPN
ejpam-3338	866	27	statist	statist	PROPN
ejpam-3338	866	28	.	.	PUNCT
ejpam-3338	867	1	comput	comput	NOUN
ejpam-3338	867	2	.	.	PUNCT
ejpam-3338	868	1	6	6	NUM
ejpam-3338	868	2	(	(	PUNCT
ejpam-3338	868	3	3	3	NUM
ejpam-3338	868	4	)	)	PUNCT
ejpam-3338	868	5	(	(	PUNCT
ejpam-3338	868	6	1985	1985	NUM
ejpam-3338	868	7	)	)	PUNCT
ejpam-3338	868	8	532	532	NUM
ejpam-3338	868	9	-	-	SYM
ejpam-3338	868	10	541	541	NUM
ejpam-3338	868	11	.	.	PUNCT
ejpam-3338	869	1	[	[	X
ejpam-3338	869	2	13	13	NUM
ejpam-3338	869	3	]	]	X
ejpam-3338	869	4	r.	r.	PROPN
ejpam-3338	869	5	garrappa	garrappa	PROPN
ejpam-3338	869	6	,	,	PUNCT
ejpam-3338	869	7	on	on	ADP
ejpam-3338	869	8	linear	linear	ADJ
ejpam-3338	869	9	stability	stability	NOUN
ejpam-3338	869	10	of	of	ADP
ejpam-3338	869	11	predictor	predictor	NOUN
ejpam-3338	869	12	-	-	PUNCT
ejpam-3338	869	13	corrector	corrector	NOUN
ejpam-3338	869	14	algorithms	algorithm	NOUN
ejpam-3338	869	15	for	for	ADP
ejpam-3338	869	16	fractional	fractional	ADJ
ejpam-3338	869	17	differential	differential	ADJ
ejpam-3338	869	18	equations	equation	NOUN
ejpam-3338	869	19	,	,	PUNCT
ejpam-3338	869	20	internat	internat	PROPN
ejpam-3338	869	21	.	.	PUNCT
ejpam-3338	870	1	j.	j.	PROPN
ejpam-3338	870	2	comput	comput	PROPN
ejpam-3338	870	3	.	.	PUNCT
ejpam-3338	871	1	math	math	NOUN
ejpam-3338	871	2	.	.	PUNCT
ejpam-3338	872	1	87	87	NUM
ejpam-3338	872	2	(	(	PUNCT
ejpam-3338	872	3	10	10	NUM
ejpam-3338	872	4	)	)	PUNCT
ejpam-3338	872	5	(	(	PUNCT
ejpam-3338	872	6	2010	2010	NUM
ejpam-3338	872	7	)	)	PUNCT
ejpam-3338	872	8	2281	2281	NUM
ejpam-3338	872	9	-	-	SYM
ejpam-3338	872	10	2290	2290	NUM
ejpam-3338	872	11	.	.	PUNCT
ejpam-3338	873	1	copyright	copyright	NOUN
ejpam-3338	873	2	references	reference	NOUN
ejpam-3338	873	3	1099	1099	NUM
ejpam-3338	873	4	(	(	PUNCT
ejpam-3338	873	5	c	c	NOUN
ejpam-3338	873	6	)	)	PUNCT
ejpam-3338	873	7	2011	2011	NUM
ejpam-3338	873	8	-	-	SYM
ejpam-3338	873	9	2012	2012	NUM
ejpam-3338	873	10	,	,	PUNCT
ejpam-3338	873	11	roberto	roberto	PROPN
ejpam-3338	873	12	garrappa	garrappa	PROPN
ejpam-3338	873	13	,	,	PUNCT
ejpam-3338	873	14	university	university	NOUN
ejpam-3338	873	15	of	of	ADP
ejpam-3338	873	16	bari	bari	NOUN
ejpam-3338	873	17	,	,	PUNCT
ejpam-3338	873	18	italy	italy	PROPN
ejpam-3338	873	19	,	,	PUNCT
ejpam-3338	873	20	garrappa	garrappa	NOUN
ejpam-3338	873	21	at	at	ADP
ejpam-3338	873	22	dm	dm	NOUN
ejpam-3338	873	23	dot	dot	NOUN
ejpam-3338	873	24	uniba	uniba	NOUN
ejpam-3338	873	25	dot	dot	NOUN
ejpam-3338	873	26	it	it	PRON
ejpam-3338	873	27	,	,	PUNCT
ejpam-3338	873	28	revision	revision	NOUN
ejpam-3338	873	29	:	:	PUNCT
ejpam-3338	873	30	1.2	1.2	NUM
ejpam-3338	873	31	date	date	NOUN
ejpam-3338	873	32	:	:	PUNCT
ejpam-3338	873	33	july	july	PROPN
ejpam-3338	873	34	,	,	PUNCT
ejpam-3338	873	35	6	6	NUM
ejpam-3338	873	36	2012	2012	NUM
ejpam-3338	873	37	.	.	PUNCT
ejpam-3338	874	1	[	[	X
ejpam-3338	874	2	14	14	NUM
ejpam-3338	874	3	]	]	X
ejpam-3338	874	4	s.k	s.k	PROPN
ejpam-3338	874	5	.	.	PROPN
ejpam-3338	874	6	sen	sen	PROPN
ejpam-3338	874	7	,	,	PUNCT
ejpam-3338	874	8	a	a	DET
ejpam-3338	874	9	row	row	NOUN
ejpam-3338	874	10	-	-	PUNCT
ejpam-3338	874	11	pruning	prune	VERB
ejpam-3338	874	12	algorithm	algorithm	NOUN
ejpam-3338	874	13	to	to	PART
ejpam-3338	874	14	compute	compute	VERB
ejpam-3338	874	15	a	a	DET
ejpam-3338	874	16	generalized	generalized	ADJ
ejpam-3338	874	17	inverse	inverse	NOUN
ejpam-3338	874	18	,	,	PUNCT
ejpam-3338	874	19	37th	37th	ADJ
ejpam-3338	874	20	congress	congress	NOUN
ejpam-3338	874	21	of	of	ADP
ejpam-3338	874	22	istam	istam	NOUN
ejpam-3338	874	23	and	and	CCONJ
ejpam-3338	874	24	symp	symp	NOUN
ejpam-3338	874	25	.	.	PUNCT
ejpam-3338	875	1	on	on	ADP
ejpam-3338	875	2	rheology	rheology	NOUN
ejpam-3338	875	3	of	of	ADP
ejpam-3338	875	4	biological	biological	ADJ
ejpam-3338	875	5	materials	material	NOUN
ejpam-3338	875	6	,	,	PUNCT
ejpam-3338	875	7	january	january	PROPN
ejpam-3338	875	8	14	14	NUM
ejpam-3338	875	9	-	-	SYM
ejpam-3338	875	10	17	17	NUM
ejpam-3338	875	11	,	,	PUNCT
ejpam-3338	875	12	1993	1993	NUM
ejpam-3338	875	13	,	,	PUNCT
ejpam-3338	875	14	g.b	g.b	PROPN
ejpam-3338	875	15	.	.	PROPN
ejpam-3338	875	16	pant	pant	PROPN
ejpam-3338	875	17	univ	univ	PROPN
ejpam-3338	875	18	.	.	PROPN
ejpam-3338	876	1	of	of	ADP
ejpam-3338	876	2	agriculture	agriculture	NOUN
ejpam-3338	876	3	and	and	CCONJ
ejpam-3338	876	4	technology	technology	NOUN
ejpam-3338	876	5	,	,	PUNCT
ejpam-3338	876	6	pantnagar	pantnagar	NOUN
ejpam-3338	876	7	,	,	PUNCT
ejpam-3338	876	8	india	india	PROPN
ejpam-3338	876	9	,	,	PUNCT
ejpam-3338	876	10	99	99	NUM
ejpam-3338	876	11	-	-	SYM
ejpam-3338	876	12	100	100	NUM
ejpam-3338	876	13	(	(	PUNCT
ejpam-3338	876	14	abstract	abstract	ADJ
ejpam-3338	876	15	)	)	PUNCT
ejpam-3338	876	16	.	.	PUNCT
ejpam-3338	877	1	[	[	X
ejpam-3338	877	2	15	15	X
ejpam-3338	877	3	]	]	X
ejpam-3338	877	4	v.	v.	CCONJ
ejpam-3338	877	5	lakshmikantham	lakshmikantham	ADJ
ejpam-3338	877	6	,	,	PUNCT
ejpam-3338	877	7	s.k	s.k	PROPN
ejpam-3338	877	8	.	.	PROPN
ejpam-3338	877	9	sen	sen	PROPN
ejpam-3338	877	10	,	,	PUNCT
ejpam-3338	877	11	and	and	CCONJ
ejpam-3338	877	12	s.	s.	PROPN
ejpam-3338	877	13	sivasundaram	sivasundaram	PROPN
ejpam-3338	877	14	,	,	PUNCT
ejpam-3338	877	15	concise	concise	ADJ
ejpam-3338	877	16	row	row	NOUN
ejpam-3338	877	17	-	-	PUNCT
ejpam-3338	877	18	pruning	prune	VERB
ejpam-3338	877	19	algorithm	algorithm	NOUN
ejpam-3338	877	20	to	to	PART
ejpam-3338	877	21	invert	invert	VERB
ejpam-3338	877	22	a	a	DET
ejpam-3338	877	23	matrix	matrix	NOUN
ejpam-3338	877	24	,	,	PUNCT
ejpam-3338	877	25	applied	apply	VERB
ejpam-3338	877	26	mathematics	mathematic	NOUN
ejpam-3338	877	27	and	and	CCONJ
ejpam-3338	877	28	computation	computation	NOUN
ejpam-3338	877	29	,	,	PUNCT
ejpam-3338	877	30	(	(	PUNCT
ejpam-3338	877	31	elsevier	elsevier	NOUN
ejpam-3338	877	32	science	science	NOUN
ejpam-3338	877	33	pub	pub	PROPN
ejpam-3338	877	34	.	.	PUNCT
ejpam-3338	878	1	co.	co.	PROPN
ejpam-3338	878	2	,	,	PUNCT
ejpam-3338	878	3	new	new	PROPN
ejpam-3338	878	4	york	york	PROPN
ejpam-3338	878	5	)	)	PUNCT
ejpam-3338	878	6	,	,	PUNCT
ejpam-3338	878	7	60	60	NUM
ejpam-3338	878	8	,	,	PUNCT
ejpam-3338	878	9	1994	1994	NUM
ejpam-3338	878	10	,	,	PUNCT
ejpam-3338	878	11	17	17	NUM
ejpam-3338	878	12	-	-	SYM
ejpam-3338	878	13	24	24	NUM
ejpam-3338	878	14	.	.	PUNCT
ejpam-3338	879	1	[	[	X
ejpam-3338	879	2	16	16	NUM
ejpam-3338	879	3	]	]	X
ejpam-3338	879	4	s.k	s.k	PROPN
ejpam-3338	879	5	.	.	PROPN
ejpam-3338	879	6	sen	sen	PROPN
ejpam-3338	879	7	and	and	CCONJ
ejpam-3338	879	8	m.	m.	PROPN
ejpam-3338	879	9	chanda	chanda	PROPN
ejpam-3338	879	10	,	,	PUNCT
ejpam-3338	879	11	a	a	DET
ejpam-3338	879	12	general	general	ADJ
ejpam-3338	879	13	scheme	scheme	NOUN
ejpam-3338	879	14	for	for	ADP
ejpam-3338	879	15	solving	solve	VERB
ejpam-3338	879	16	ordinary	ordinary	ADJ
ejpam-3338	879	17	differential	differential	ADJ
ejpam-3338	879	18	equations	equation	NOUN
ejpam-3338	879	19	under	under	ADP
ejpam-3338	879	20	two	two	NUM
ejpam-3338	879	21	-	-	PUNCT
ejpam-3338	879	22	point	point	NOUN
ejpam-3338	879	23	boundary	boundary	ADJ
ejpam-3338	879	24	conditions	condition	NOUN
ejpam-3338	879	25	,	,	PUNCT
ejpam-3338	879	26	j.	j.	PROPN
ejpam-3338	879	27	ind	ind	PROPN
ejpam-3338	879	28	.	.	PUNCT
ejpam-3338	879	29	inst	inst	PROPN
ejpam-3338	879	30	.	.	PUNCT
ejpam-3338	880	1	sci	sci	PROPN
ejpam-3338	880	2	.	.	PROPN
ejpam-3338	880	3	,	,	PUNCT
ejpam-3338	880	4	54	54	NUM
ejpam-3338	880	5	,	,	PUNCT
ejpam-3338	880	6	3	3	NUM
ejpam-3338	880	7	,	,	PUNCT
ejpam-3338	880	8	1972	1972	NUM
ejpam-3338	880	9	,	,	PUNCT
ejpam-3338	880	10	139	139	NUM
ejpam-3338	880	11	145	145	NUM
ejpam-3338	880	12	.	.	PUNCT
ejpam-3338	881	1	[	[	X
ejpam-3338	881	2	17	17	NUM
ejpam-3338	881	3	]	]	X
ejpam-3338	881	4	f.m	f.m	PROPN
ejpam-3338	881	5	.	.	PROPN
ejpam-3338	881	6	bayat	bayat	PROPN
ejpam-3338	881	7	,	,	PUNCT
ejpam-3338	881	8	fractional	fractional	ADJ
ejpam-3338	881	9	differentiator	differentiator	NOUN
ejpam-3338	881	10	,	,	PUNCT
ejpam-3338	881	11	mathworks	mathworks	PROPN
ejpam-3338	881	12	,	,	PUNCT
ejpam-3338	881	13	inc	inc	PROPN
ejpam-3338	881	14	.	.	PROPN
ejpam-3338	881	15	matlab	matlab	PROPN
ejpam-3338	881	16	central	central	ADJ
ejpam-3338	881	17	file	file	NOUN
ejpam-3338	881	18	exchange	exchange	NOUN
ejpam-3338	881	19	,	,	PUNCT
ejpam-3338	881	20	2007	2007	NUM
ejpam-3338	881	21	,	,	PUNCT
ejpam-3338	881	22	url	url	PROPN
ejpam-3338	881	23	:	:	PUNCT
ejpam-3338	881	24	www.mathworks.com/matlabcentral/fileexchange/13858	www.mathworks.com/matlabcentral/fileexchange/13858	NOUN