id	sid	tid	token	lemma	pos
ejpam-3609	1	1	european	european	PROPN
ejpam-3609	1	2	journal	journal	PROPN
ejpam-3609	1	3	of	of	ADP
ejpam-3609	1	4	pure	pure	ADJ
ejpam-3609	1	5	and	and	CCONJ
ejpam-3609	1	6	applied	apply	VERB
ejpam-3609	1	7	mathematics	mathematic	NOUN
ejpam-3609	1	8	vol	vol	NOUN
ejpam-3609	1	9	.	.	PROPN
ejpam-3609	2	1	13	13	NUM
ejpam-3609	2	2	,	,	PUNCT
ejpam-3609	2	3	no	no	INTJ
ejpam-3609	2	4	.	.	NOUN
ejpam-3609	2	5	1	1	NUM
ejpam-3609	2	6	,	,	PUNCT
ejpam-3609	2	7	2020	2020	NUM
ejpam-3609	2	8	,	,	PUNCT
ejpam-3609	2	9	19	19	NUM
ejpam-3609	2	10	-	-	SYM
ejpam-3609	2	11	32	32	NUM
ejpam-3609	2	12	issn	issn	PROPN
ejpam-3609	2	13	1307	1307	NUM
ejpam-3609	2	14	-	-	SYM
ejpam-3609	2	15	5543	5543	NUM
ejpam-3609	2	16	–	–	PUNCT
ejpam-3609	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3609	2	18	published	publish	VERB
ejpam-3609	2	19	by	by	ADP
ejpam-3609	2	20	new	new	PROPN
ejpam-3609	2	21	york	york	PROPN
ejpam-3609	2	22	business	business	PROPN
ejpam-3609	2	23	global	global	ADJ
ejpam-3609	2	24	using	use	VERB
ejpam-3609	2	25	fractal	fractal	ADJ
ejpam-3609	2	26	calculus	calculus	NOUN
ejpam-3609	2	27	to	to	PART
ejpam-3609	2	28	express	express	VERB
ejpam-3609	2	29	electric	electric	ADJ
ejpam-3609	2	30	potential	potential	ADJ
ejpam-3609	2	31	and	and	CCONJ
ejpam-3609	2	32	electric	electric	ADJ
ejpam-3609	2	33	field	field	NOUN
ejpam-3609	2	34	in	in	ADP
ejpam-3609	2	35	terms	term	NOUN
ejpam-3609	2	36	of	of	ADP
ejpam-3609	2	37	staircase	staircase	NOUN
ejpam-3609	2	38	and	and	CCONJ
ejpam-3609	2	39	characteristic	characteristic	ADJ
ejpam-3609	2	40	functions	function	NOUN
ejpam-3609	2	41	nasibeh	nasibeh	NOUN
ejpam-3609	2	42	delfan1	delfan1	PROPN
ejpam-3609	2	43	,	,	PUNCT
ejpam-3609	2	44	amir	amir	PROPN
ejpam-3609	2	45	pishkoo2,∗	pishkoo2,∗	PROPN
ejpam-3609	2	46	,	,	PUNCT
ejpam-3609	2	47	mahdi	mahdi	PROPN
ejpam-3609	2	48	azhini1	azhini1	PROPN
ejpam-3609	2	49	,	,	PUNCT
ejpam-3609	2	50	maslina	maslina	NOUN
ejpam-3609	2	51	darus3	darus3	NOUN
ejpam-3609	2	52	1	1	NUM
ejpam-3609	2	53	department	department	NOUN
ejpam-3609	2	54	of	of	ADP
ejpam-3609	2	55	mathematics	mathematic	NOUN
ejpam-3609	2	56	,	,	PUNCT
ejpam-3609	2	57	islamic	islamic	PROPN
ejpam-3609	2	58	azad	azad	PROPN
ejpam-3609	2	59	university	university	PROPN
ejpam-3609	2	60	,	,	PUNCT
ejpam-3609	2	61	science	science	NOUN
ejpam-3609	2	62	and	and	CCONJ
ejpam-3609	2	63	research	research	NOUN
ejpam-3609	2	64	branch	branch	NOUN
ejpam-3609	2	65	,	,	PUNCT
ejpam-3609	2	66	tehran	tehran	PROPN
ejpam-3609	2	67	,	,	PUNCT
ejpam-3609	2	68	iran	iran	PROPN
ejpam-3609	2	69	.	.	PUNCT
ejpam-3609	3	1	2	2	NUM
ejpam-3609	3	2	physics	physics	NOUN
ejpam-3609	3	3	and	and	CCONJ
ejpam-3609	3	4	accelerators	accelerator	NOUN
ejpam-3609	3	5	research	research	NOUN
ejpam-3609	3	6	school	school	NOUN
ejpam-3609	3	7	,	,	PUNCT
ejpam-3609	3	8	nuclear	nuclear	ADJ
ejpam-3609	3	9	science	science	NOUN
ejpam-3609	3	10	and	and	CCONJ
ejpam-3609	3	11	technology	technology	NOUN
ejpam-3609	3	12	research	research	PROPN
ejpam-3609	3	13	institute	institute	PROPN
ejpam-3609	3	14	,	,	PUNCT
ejpam-3609	3	15	p.o	p.o	PROPN
ejpam-3609	3	16	.	.	PROPN
ejpam-3609	3	17	box	box	PROPN
ejpam-3609	3	18	14395	14395	PROPN
ejpam-3609	3	19	-	-	SYM
ejpam-3609	3	20	836	836	NUM
ejpam-3609	3	21	,	,	PUNCT
ejpam-3609	3	22	tehran	tehran	PROPN
ejpam-3609	3	23	,	,	PUNCT
ejpam-3609	3	24	iran	iran	PROPN
ejpam-3609	3	25	3	3	NUM
ejpam-3609	3	26	department	department	PROPN
ejpam-3609	3	27	of	of	ADP
ejpam-3609	3	28	mathematical	mathematical	ADJ
ejpam-3609	3	29	sciences	science	NOUN
ejpam-3609	3	30	,	,	PUNCT
ejpam-3609	3	31	faculty	faculty	NOUN
ejpam-3609	3	32	of	of	ADP
ejpam-3609	3	33	science	science	NOUN
ejpam-3609	3	34	and	and	CCONJ
ejpam-3609	3	35	technology	technology	NOUN
ejpam-3609	3	36	,	,	PUNCT
ejpam-3609	3	37	universiti	universiti	PROPN
ejpam-3609	3	38	kebangsaan	kebangsaan	PROPN
ejpam-3609	3	39	malaysia	malaysia	PROPN
ejpam-3609	3	40	,	,	PUNCT
ejpam-3609	3	41	bangi	bangi	VERB
ejpam-3609	3	42	43600	43600	NUM
ejpam-3609	3	43	,	,	PUNCT
ejpam-3609	3	44	malaysia	malaysia	PROPN
ejpam-3609	3	45	abstract	abstract	NOUN
ejpam-3609	3	46	.	.	PUNCT
ejpam-3609	4	1	the	the	DET
ejpam-3609	4	2	dirac	dirac	PROPN
ejpam-3609	4	3	delta	delta	NOUN
ejpam-3609	4	4	function	function	NOUN
ejpam-3609	4	5	is	be	AUX
ejpam-3609	4	6	usually	usually	ADV
ejpam-3609	4	7	used	use	VERB
ejpam-3609	4	8	to	to	PART
ejpam-3609	4	9	express	express	VERB
ejpam-3609	4	10	the	the	DET
ejpam-3609	4	11	discrete	discrete	ADJ
ejpam-3609	4	12	distribution	distribution	NOUN
ejpam-3609	4	13	of	of	ADP
ejpam-3609	4	14	electric	electric	ADJ
ejpam-3609	4	15	charges	charge	NOUN
ejpam-3609	4	16	in	in	ADP
ejpam-3609	4	17	electrostatic	electrostatic	ADJ
ejpam-3609	4	18	problems	problem	NOUN
ejpam-3609	4	19	.	.	PUNCT
ejpam-3609	5	1	the	the	DET
ejpam-3609	5	2	integration	integration	NOUN
ejpam-3609	5	3	of	of	ADP
ejpam-3609	5	4	the	the	DET
ejpam-3609	5	5	product	product	NOUN
ejpam-3609	5	6	of	of	ADP
ejpam-3609	5	7	the	the	DET
ejpam-3609	5	8	dirac	dirac	PROPN
ejpam-3609	5	9	delta	delta	PROPN
ejpam-3609	5	10	function	function	NOUN
ejpam-3609	5	11	and	and	CCONJ
ejpam-3609	5	12	the	the	DET
ejpam-3609	5	13	green	green	ADJ
ejpam-3609	5	14	functions	function	NOUN
ejpam-3609	5	15	can	can	AUX
ejpam-3609	5	16	calculate	calculate	VERB
ejpam-3609	5	17	the	the	DET
ejpam-3609	5	18	electric	electric	ADJ
ejpam-3609	5	19	potential	potential	NOUN
ejpam-3609	5	20	and	and	CCONJ
ejpam-3609	5	21	the	the	DET
ejpam-3609	5	22	electric	electric	ADJ
ejpam-3609	5	23	field	field	NOUN
ejpam-3609	5	24	.	.	PUNCT
ejpam-3609	6	1	using	use	VERB
ejpam-3609	6	2	fractal	fractal	ADJ
ejpam-3609	6	3	calculus	calculus	NOUN
ejpam-3609	6	4	,	,	PUNCT
ejpam-3609	6	5	characteristic	characteristic	ADJ
ejpam-3609	6	6	function	function	NOUN
ejpam-3609	6	7	,	,	PUNCT
ejpam-3609	6	8	χcn(x	χcn(x	PROPN
ejpam-3609	6	9	)	)	PUNCT
ejpam-3609	6	10	,	,	PUNCT
ejpam-3609	6	11	as	as	SCONJ
ejpam-3609	6	12	an	an	DET
ejpam-3609	6	13	alternative	alternative	NOUN
ejpam-3609	6	14	for	for	ADP
ejpam-3609	6	15	dirac	dirac	NOUN
ejpam-3609	6	16	delta	delta	NOUN
ejpam-3609	6	17	function	function	NOUN
ejpam-3609	6	18	is	be	AUX
ejpam-3609	6	19	used	use	VERB
ejpam-3609	6	20	to	to	PART
ejpam-3609	6	21	describe	describe	VERB
ejpam-3609	6	22	cantor	cantor	NOUN
ejpam-3609	6	23	set	set	NOUN
ejpam-3609	6	24	charge	charge	NOUN
ejpam-3609	6	25	distribution	distribution	NOUN
ejpam-3609	6	26	which	which	PRON
ejpam-3609	6	27	is	be	AUX
ejpam-3609	6	28	typical	typical	ADJ
ejpam-3609	6	29	example	example	NOUN
ejpam-3609	6	30	of	of	ADP
ejpam-3609	6	31	a	a	DET
ejpam-3609	6	32	discrete	discrete	ADJ
ejpam-3609	6	33	set	set	NOUN
ejpam-3609	6	34	.	.	PUNCT
ejpam-3609	7	1	in	in	ADP
ejpam-3609	7	2	these	these	DET
ejpam-3609	7	3	cases	case	NOUN
ejpam-3609	7	4	we	we	PRON
ejpam-3609	7	5	deal	deal	VERB
ejpam-3609	7	6	with	with	ADP
ejpam-3609	7	7	fα	fα	NOUN
ejpam-3609	7	8	-	-	PUNCT
ejpam-3609	7	9	integration	integration	NOUN
ejpam-3609	7	10	and	and	CCONJ
ejpam-3609	7	11	fα	fα	NOUN
ejpam-3609	7	12	-	-	PUNCT
ejpam-3609	7	13	derivative	derivative	NOUN
ejpam-3609	7	14	of	of	ADP
ejpam-3609	7	15	the	the	DET
ejpam-3609	7	16	product	product	NOUN
ejpam-3609	7	17	of	of	ADP
ejpam-3609	7	18	characteristic	characteristic	ADJ
ejpam-3609	7	19	function	function	NOUN
ejpam-3609	7	20	and	and	CCONJ
ejpam-3609	7	21	function	function	NOUN
ejpam-3609	7	22	of	of	ADP
ejpam-3609	7	23	staircase	staircase	NOUN
ejpam-3609	7	24	function	function	NOUN
ejpam-3609	7	25	,	,	PUNCT
ejpam-3609	7	26	namely	namely	ADV
ejpam-3609	7	27	f(sαcn	f(sαcn	NOUN
ejpam-3609	7	28	(	(	PUNCT
ejpam-3609	7	29	x	x	NOUN
ejpam-3609	7	30	)	)	PUNCT
ejpam-3609	7	31	)	)	PUNCT
ejpam-3609	7	32	,	,	PUNCT
ejpam-3609	7	33	which	which	PRON
ejpam-3609	7	34	lead	lead	VERB
ejpam-3609	7	35	to	to	ADP
ejpam-3609	7	36	calculation	calculation	NOUN
ejpam-3609	7	37	of	of	ADP
ejpam-3609	7	38	electric	electric	ADJ
ejpam-3609	7	39	potential	potential	ADJ
ejpam-3609	7	40	and	and	CCONJ
ejpam-3609	7	41	electric	electric	ADJ
ejpam-3609	7	42	field	field	NOUN
ejpam-3609	7	43	.	.	PUNCT
ejpam-3609	8	1	recently	recently	ADV
ejpam-3609	8	2	,	,	PUNCT
ejpam-3609	8	3	a	a	DET
ejpam-3609	8	4	calculus	calculus	NOUN
ejpam-3609	8	5	based	base	VERB
ejpam-3609	8	6	fractals	fractal	NOUN
ejpam-3609	8	7	,	,	PUNCT
ejpam-3609	8	8	called	call	VERB
ejpam-3609	8	9	fα	fα	NOUN
ejpam-3609	8	10	-	-	PUNCT
ejpam-3609	8	11	calculus	calculus	NOUN
ejpam-3609	8	12	,	,	PUNCT
ejpam-3609	8	13	has	have	AUX
ejpam-3609	8	14	been	be	AUX
ejpam-3609	8	15	developed	develop	VERB
ejpam-3609	8	16	which	which	PRON
ejpam-3609	8	17	involve	involve	VERB
ejpam-3609	8	18	fα	fα	ADV
ejpam-3609	8	19	-	-	ADJ
ejpam-3609	8	20	integral	integral	ADJ
ejpam-3609	8	21	and	and	CCONJ
ejpam-3609	8	22	fα	fα	NOUN
ejpam-3609	8	23	-	-	PUNCT
ejpam-3609	8	24	derivative	derivative	ADJ
ejpam-3609	8	25	,	,	PUNCT
ejpam-3609	8	26	of	of	ADP
ejpam-3609	8	27	orders	order	NOUN
ejpam-3609	8	28	α	α	NOUN
ejpam-3609	8	29	,	,	PUNCT
ejpam-3609	8	30	0	0	NUM
ejpam-3609	8	31	<	<	X
ejpam-3609	8	32	α	α	X
ejpam-3609	8	33	<	<	X
ejpam-3609	8	34	1	1	NUM
ejpam-3609	8	35	,	,	PUNCT
ejpam-3609	8	36	where	where	SCONJ
ejpam-3609	8	37	α	α	NOUN
ejpam-3609	8	38	is	be	AUX
ejpam-3609	8	39	dimension	dimension	NOUN
ejpam-3609	8	40	of	of	ADP
ejpam-3609	8	41	f	f	PROPN
ejpam-3609	8	42	.	.	PUNCT
ejpam-3609	9	1	in	in	ADP
ejpam-3609	9	2	fα	fα	NOUN
ejpam-3609	9	3	-	-	PUNCT
ejpam-3609	9	4	calculus	calculus	NOUN
ejpam-3609	9	5	the	the	DET
ejpam-3609	9	6	staircase	staircase	NOUN
ejpam-3609	9	7	function	function	NOUN
ejpam-3609	9	8	and	and	CCONJ
ejpam-3609	9	9	characteristic	characteristic	ADJ
ejpam-3609	9	10	function	function	NOUN
ejpam-3609	9	11	have	have	VERB
ejpam-3609	9	12	special	special	ADJ
ejpam-3609	9	13	roles	role	NOUN
ejpam-3609	9	14	.	.	PUNCT
ejpam-3609	10	1	finally	finally	ADV
ejpam-3609	10	2	,	,	PUNCT
ejpam-3609	10	3	using	use	VERB
ejpam-3609	10	4	comsol	comsol	NOUN
ejpam-3609	10	5	multiphysics	multiphysics	PROPN
ejpam-3609	10	6	software	software	NOUN
ejpam-3609	10	7	we	we	PRON
ejpam-3609	10	8	solve	solve	VERB
ejpam-3609	10	9	ordinary	ordinary	ADJ
ejpam-3609	10	10	laplace	laplace	NOUN
ejpam-3609	10	11	’s	’s	PART
ejpam-3609	10	12	equation	equation	NOUN
ejpam-3609	10	13	(	(	PUNCT
ejpam-3609	10	14	not	not	PART
ejpam-3609	10	15	fractional	fractional	ADJ
ejpam-3609	10	16	)	)	PUNCT
ejpam-3609	10	17	in	in	ADP
ejpam-3609	10	18	the	the	DET
ejpam-3609	10	19	fractal	fractal	ADJ
ejpam-3609	10	20	region	region	NOUN
ejpam-3609	10	21	with	with	ADP
ejpam-3609	10	22	koch	koch	PROPN
ejpam-3609	10	23	snowflake	snowflake	PROPN
ejpam-3609	10	24	boundary	boundary	NOUN
ejpam-3609	10	25	which	which	PRON
ejpam-3609	10	26	is	be	AUX
ejpam-3609	10	27	non	non	ADJ
ejpam-3609	10	28	-	-	ADJ
ejpam-3609	10	29	differentiable	differentiable	ADJ
ejpam-3609	10	30	fractal	fractal	NOUN
ejpam-3609	10	31	,	,	PUNCT
ejpam-3609	10	32	and	and	CCONJ
ejpam-3609	10	33	give	give	VERB
ejpam-3609	10	34	their	their	PRON
ejpam-3609	10	35	graphs	graph	NOUN
ejpam-3609	10	36	for	for	ADP
ejpam-3609	10	37	the	the	DET
ejpam-3609	10	38	three	three	NUM
ejpam-3609	10	39	first	first	ADJ
ejpam-3609	10	40	iterations	iteration	NOUN
ejpam-3609	10	41	.	.	PUNCT
ejpam-3609	11	1	2020	2020	NUM
ejpam-3609	11	2	mathematics	mathematic	NOUN
ejpam-3609	11	3	subject	subject	NOUN
ejpam-3609	11	4	classifications	classification	NOUN
ejpam-3609	11	5	:	:	PUNCT
ejpam-3609	11	6	26a33	26a33	NUM
ejpam-3609	11	7	,	,	PUNCT
ejpam-3609	11	8	28a80	28a80	NUM
ejpam-3609	11	9	,	,	PUNCT
ejpam-3609	11	10	31c20	31c20	NUM
ejpam-3609	11	11	key	key	ADJ
ejpam-3609	11	12	words	word	NOUN
ejpam-3609	11	13	and	and	CCONJ
ejpam-3609	11	14	phrases	phrase	NOUN
ejpam-3609	11	15	:	:	PUNCT
ejpam-3609	11	16	cantor	cantor	PROPN
ejpam-3609	11	17	set	set	PROPN
ejpam-3609	11	18	,	,	PUNCT
ejpam-3609	11	19	fractal	fractal	ADJ
ejpam-3609	11	20	calculus	calculus	NOUN
ejpam-3609	11	21	,	,	PUNCT
ejpam-3609	11	22	fα	fα	NOUN
ejpam-3609	11	23	-	-	PUNCT
ejpam-3609	11	24	integral	integral	ADJ
ejpam-3609	11	25	,	,	PUNCT
ejpam-3609	11	26	fα	fα	NOUN
ejpam-3609	11	27	-	-	PUNCT
ejpam-3609	11	28	derivative	derivative	ADJ
ejpam-3609	11	29	,	,	PUNCT
ejpam-3609	11	30	potential	potential	ADJ
ejpam-3609	11	31	theory	theory	NOUN
ejpam-3609	11	32	,	,	PUNCT
ejpam-3609	11	33	discrete	discrete	ADJ
ejpam-3609	11	34	distribution	distribution	NOUN
ejpam-3609	11	35	1	1	NUM
ejpam-3609	11	36	.	.	PUNCT
ejpam-3609	12	1	introduction	introduction	NOUN
ejpam-3609	12	2	different	different	ADJ
ejpam-3609	12	3	types	type	NOUN
ejpam-3609	12	4	of	of	ADP
ejpam-3609	12	5	charge	charge	NOUN
ejpam-3609	12	6	distributions	distribution	NOUN
ejpam-3609	12	7	can	can	AUX
ejpam-3609	12	8	be	be	AUX
ejpam-3609	12	9	expressed	express	VERB
ejpam-3609	12	10	by	by	ADP
ejpam-3609	12	11	using	use	VERB
ejpam-3609	12	12	dirac	dirac	NOUN
ejpam-3609	12	13	delta	delta	NOUN
ejpam-3609	12	14	functions	function	NOUN
ejpam-3609	12	15	.	.	PUNCT
ejpam-3609	13	1	dirac	dirac	PROPN
ejpam-3609	13	2	delta	delta	PROPN
ejpam-3609	13	3	function	function	NOUN
ejpam-3609	13	4	is	be	AUX
ejpam-3609	13	5	in	in	ADP
ejpam-3609	13	6	fact	fact	NOUN
ejpam-3609	13	7	one	one	NUM
ejpam-3609	13	8	kind	kind	NOUN
ejpam-3609	13	9	of	of	ADP
ejpam-3609	13	10	distribution	distribution	NOUN
ejpam-3609	13	11	that	that	SCONJ
ejpam-3609	13	12	in	in	ADP
ejpam-3609	13	13	one	one	NUM
ejpam-3609	13	14	dimension	dimension	NOUN
ejpam-3609	13	15	,	,	PUNCT
ejpam-3609	13	16	it	it	PRON
ejpam-3609	13	17	is	be	AUX
ejpam-3609	13	18	written	write	VERB
ejpam-3609	13	19	as	as	ADP
ejpam-3609	13	20	δ(x	δ(x	PROPN
ejpam-3609	13	21	−	−	PROPN
ejpam-3609	13	22	a	a	X
ejpam-3609	13	23	)	)	PUNCT
ejpam-3609	13	24	which	which	PRON
ejpam-3609	13	25	mathematically	mathematically	ADV
ejpam-3609	13	26	is	be	AUX
ejpam-3609	13	27	improper	improper	ADJ
ejpam-3609	13	28	function	function	NOUN
ejpam-3609	13	29	having	have	VERB
ejpam-3609	13	30	the	the	DET
ejpam-3609	13	31	following	follow	VERB
ejpam-3609	13	32	properties	property	NOUN
ejpam-3609	13	33	∗corresponding	∗corresponde	VERB
ejpam-3609	13	34	author	author	NOUN
ejpam-3609	13	35	.	.	PUNCT
ejpam-3609	14	1	doi	doi	NOUN
ejpam-3609	14	2	:	:	PUNCT
ejpam-3609	14	3	https://doi.org/10.29020/nybg.ejpam.v13i1.3609	https://doi.org/10.29020/nybg.ejpam.v13i1.3609	PROPN
ejpam-3609	14	4	email	email	NOUN
ejpam-3609	14	5	addresses	address	NOUN
ejpam-3609	14	6	:	:	PUNCT
ejpam-3609	14	7	apishkoo@gmail.com	apishkoo@gmail.com	X
ejpam-3609	14	8	(	(	PUNCT
ejpam-3609	14	9	a.	a.	NOUN
ejpam-3609	14	10	pishkoo	pishkoo	NOUN
ejpam-3609	14	11	)	)	PUNCT
ejpam-3609	14	12	,	,	PUNCT
ejpam-3609	14	13	maslina@ukm.edu.my	maslina@ukm.edu.my	X
ejpam-3609	14	14	(	(	PUNCT
ejpam-3609	14	15	m.	m.	NOUN
ejpam-3609	14	16	darus	darus	PROPN
ejpam-3609	14	17	)	)	PUNCT
ejpam-3609	14	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3609	15	1	19	19	NUM
ejpam-3609	15	2	c	c	X
ejpam-3609	15	3	©	©	NOUN
ejpam-3609	15	4	2020	2020	NUM
ejpam-3609	15	5	ejpam	ejpam	VERB
ejpam-3609	15	6	all	all	DET
ejpam-3609	15	7	rights	right	NOUN
ejpam-3609	15	8	reserved	reserve	VERB
ejpam-3609	15	9	.	.	PUNCT
ejpam-3609	16	1	a.	a.	NOUN
ejpam-3609	16	2	pishkoo	pishkoo	PROPN
ejpam-3609	16	3	et	et	PROPN
ejpam-3609	16	4	al	al	PROPN
ejpam-3609	16	5	.	.	PUNCT
ejpam-3609	16	6	/	/	SYM
ejpam-3609	16	7	eur	eur	PROPN
ejpam-3609	16	8	.	.	PUNCT
ejpam-3609	17	1	j.	j.	PROPN
ejpam-3609	17	2	pure	pure	PROPN
ejpam-3609	17	3	appl	appl	PROPN
ejpam-3609	17	4	.	.	PROPN
ejpam-3609	17	5	math	math	PROPN
ejpam-3609	17	6	,	,	PUNCT
ejpam-3609	17	7	13	13	NUM
ejpam-3609	17	8	(	(	PUNCT
ejpam-3609	17	9	1	1	NUM
ejpam-3609	17	10	)	)	PUNCT
ejpam-3609	17	11	(	(	PUNCT
ejpam-3609	17	12	2020	2020	NUM
ejpam-3609	17	13	)	)	PUNCT
ejpam-3609	17	14	,	,	PUNCT
ejpam-3609	17	15	19	19	NUM
ejpam-3609	17	16	-	-	SYM
ejpam-3609	17	17	32	32	NUM
ejpam-3609	17	18	20	20	NUM
ejpam-3609	18	1	[	[	SYM
ejpam-3609	18	2	16	16	NUM
ejpam-3609	18	3	,	,	PUNCT
ejpam-3609	18	4	18	18	NUM
ejpam-3609	18	5	]	]	SYM
ejpam-3609	18	6	:	:	PUNCT
ejpam-3609	18	7	1δ(x−	1δ(x−	NUM
ejpam-3609	18	8	a	a	NOUN
ejpam-3609	18	9	)	)	PUNCT
ejpam-3609	18	10	=	=	SYM
ejpam-3609	18	11	0	0	NUM
ejpam-3609	19	1	for	for	ADP
ejpam-3609	19	2	x	x	SYM
ejpam-3609	19	3	6=	6=	ADP
ejpam-3609	19	4	a.	a.	NOUN
ejpam-3609	19	5	2∫	2∫	NUM
ejpam-3609	19	6	δ(x−	δ(x−	NOUN
ejpam-3609	19	7	a)dx	a)dx	PROPN
ejpam-3609	19	8	=	=	PUNCT
ejpam-3609	19	9	1	1	NUM
ejpam-3609	19	10	if	if	SCONJ
ejpam-3609	19	11	the	the	DET
ejpam-3609	19	12	region	region	NOUN
ejpam-3609	19	13	of	of	ADP
ejpam-3609	19	14	integration	integration	NOUN
ejpam-3609	19	15	includes	include	VERB
ejpam-3609	19	16	x	x	X
ejpam-3609	19	17	=	=	SYM
ejpam-3609	19	18	a	a	NOUN
ejpam-3609	19	19	,	,	PUNCT
ejpam-3609	19	20	and	and	CCONJ
ejpam-3609	19	21	otherwise	otherwise	ADV
ejpam-3609	19	22	0	0	X
ejpam-3609	19	23	.	.	PUNCT
ejpam-3609	20	1	in	in	ADP
ejpam-3609	20	2	more	more	ADJ
ejpam-3609	20	3	than	than	ADP
ejpam-3609	20	4	one	one	NUM
ejpam-3609	20	5	dimension	dimension	NOUN
ejpam-3609	20	6	,	,	PUNCT
ejpam-3609	20	7	we	we	PRON
ejpam-3609	20	8	merely	merely	ADV
ejpam-3609	20	9	take	take	VERB
ejpam-3609	20	10	products	product	NOUN
ejpam-3609	20	11	of	of	ADP
ejpam-3609	20	12	delta	delta	NOUN
ejpam-3609	20	13	functions	function	NOUN
ejpam-3609	20	14	in	in	ADP
ejpam-3609	20	15	each	each	DET
ejpam-3609	20	16	dimension	dimension	NOUN
ejpam-3609	20	17	.	.	PUNCT
ejpam-3609	21	1	example	example	NOUN
ejpam-3609	22	1	1	1	NUM
ejpam-3609	22	2	.	.	NOUN
ejpam-3609	22	3	1	1	NUM
ejpam-3609	22	4	in	in	ADP
ejpam-3609	22	5	spherical	spherical	ADJ
ejpam-3609	22	6	coordinates	coordinate	NOUN
ejpam-3609	22	7	,	,	PUNCT
ejpam-3609	22	8	a	a	DET
ejpam-3609	22	9	charge	charge	NOUN
ejpam-3609	22	10	q	q	AUX
ejpam-3609	22	11	uniformly	uniformly	ADV
ejpam-3609	22	12	distributed	distribute	VERB
ejpam-3609	22	13	over	over	ADP
ejpam-3609	22	14	a	a	DET
ejpam-3609	22	15	spherical	spherical	ADJ
ejpam-3609	22	16	shell	shell	NOUN
ejpam-3609	22	17	of	of	ADP
ejpam-3609	22	18	radius	radius	NOUN
ejpam-3609	22	19	r0	r0	NOUN
ejpam-3609	22	20	is	be	AUX
ejpam-3609	22	21	ρ(r	ρ(r	PROPN
ejpam-3609	22	22	)	)	PUNCT
ejpam-3609	22	23	=	=	PUNCT
ejpam-3609	22	24	qδ(r	qδ(r	X
ejpam-3609	22	25	−r0	−r0	NOUN
ejpam-3609	22	26	)	)	PUNCT
ejpam-3609	22	27	4πr2	4πr2	NOUN
ejpam-3609	22	28	.	.	PUNCT
ejpam-3609	22	29	example	example	NOUN
ejpam-3609	23	1	2	2	NUM
ejpam-3609	23	2	.	.	NOUN
ejpam-3609	23	3	2	2	NUM
ejpam-3609	23	4	in	in	ADP
ejpam-3609	23	5	cylindrical	cylindrical	ADJ
ejpam-3609	23	6	coordinates	coordinate	NOUN
ejpam-3609	23	7	,	,	PUNCT
ejpam-3609	23	8	a	a	DET
ejpam-3609	23	9	ring	ring	NOUN
ejpam-3609	23	10	of	of	ADP
ejpam-3609	23	11	charge	charge	NOUN
ejpam-3609	23	12	q	q	PROPN
ejpam-3609	23	13	with	with	ADP
ejpam-3609	23	14	radius	radius	NOUN
ejpam-3609	23	15	a	a	DET
ejpam-3609	23	16	laying	laying	NOUN
ejpam-3609	23	17	in	in	ADP
ejpam-3609	23	18	the	the	DET
ejpam-3609	23	19	xy	xy	PROPN
ejpam-3609	23	20	plane	plane	NOUN
ejpam-3609	23	21	with	with	ADP
ejpam-3609	23	22	its	its	PRON
ejpam-3609	23	23	center	center	NOUN
ejpam-3609	23	24	at	at	ADP
ejpam-3609	23	25	the	the	DET
ejpam-3609	23	26	origin	origin	NOUN
ejpam-3609	23	27	is	be	AUX
ejpam-3609	23	28	described	describe	VERB
ejpam-3609	23	29	with	with	ADP
ejpam-3609	23	30	λ(ρ	λ(ρ	PROPN
ejpam-3609	23	31	,	,	PUNCT
ejpam-3609	23	32	z	z	NOUN
ejpam-3609	23	33	)	)	PUNCT
ejpam-3609	24	1	=	=	SYM
ejpam-3609	24	2	qδ(ρ−	qδ(ρ−	PART
ejpam-3609	24	3	a)δ(z	a)δ(z	NOUN
ejpam-3609	24	4	)	)	PUNCT
ejpam-3609	24	5	2πρ	2πρ	NOUN
ejpam-3609	24	6	.	.	PUNCT
ejpam-3609	25	1	example	example	NOUN
ejpam-3609	26	1	3	3	NUM
ejpam-3609	26	2	.	.	X
ejpam-3609	26	3	3the	3the	NUM
ejpam-3609	26	4	same	same	ADJ
ejpam-3609	26	5	ring	ring	NOUN
ejpam-3609	26	6	of	of	ADP
ejpam-3609	26	7	charge	charge	NOUN
ejpam-3609	26	8	q	q	PROPN
ejpam-3609	26	9	with	with	ADP
ejpam-3609	26	10	radius	radius	NOUN
ejpam-3609	26	11	a	a	PRON
ejpam-3609	26	12	in	in	ADP
ejpam-3609	26	13	spherical	spherical	ADJ
ejpam-3609	26	14	coordinates	coordinate	NOUN
ejpam-3609	26	15	is	be	AUX
ejpam-3609	26	16	described	describe	VERB
ejpam-3609	26	17	by	by	ADP
ejpam-3609	26	18	λ(r	λ(r	PROPN
ejpam-3609	26	19	,	,	PUNCT
ejpam-3609	26	20	θ	θ	NOUN
ejpam-3609	26	21	)	)	PUNCT
ejpam-3609	26	22	=	=	SYM
ejpam-3609	26	23	qδ(r	qδ(r	NOUN
ejpam-3609	26	24	−	−	NOUN
ejpam-3609	26	25	a)δ(θ	a)δ(θ	ADJ
ejpam-3609	26	26	−	−	PROPN
ejpam-3609	26	27	π	π	PROPN
ejpam-3609	26	28	2	2	NUM
ejpam-3609	26	29	)	)	PUNCT
ejpam-3609	26	30	2πr2	2πr2	NUM
ejpam-3609	26	31	sin	sin	NOUN
ejpam-3609	26	32	θ	θ	NOUN
ejpam-3609	26	33	.	.	PUNCT
ejpam-3609	27	1	in	in	ADP
ejpam-3609	27	2	ordinary	ordinary	ADJ
ejpam-3609	27	3	calculus	calculus	NOUN
ejpam-3609	27	4	,	,	PUNCT
ejpam-3609	27	5	we	we	PRON
ejpam-3609	27	6	deal	deal	VERB
ejpam-3609	27	7	with	with	ADP
ejpam-3609	27	8	discontinuity	discontinuity	NOUN
ejpam-3609	27	9	,	,	PUNCT
ejpam-3609	27	10	lack	lack	NOUN
ejpam-3609	27	11	of	of	ADP
ejpam-3609	27	12	continuity	continuity	NOUN
ejpam-3609	27	13	,	,	PUNCT
ejpam-3609	27	14	in	in	ADP
ejpam-3609	27	15	some	some	DET
ejpam-3609	27	16	points	point	NOUN
ejpam-3609	27	17	or	or	CCONJ
ejpam-3609	27	18	intervals	interval	NOUN
ejpam-3609	27	19	.	.	PUNCT
ejpam-3609	28	1	there	there	PRON
ejpam-3609	28	2	are	be	VERB
ejpam-3609	28	3	also	also	ADV
ejpam-3609	28	4	some	some	DET
ejpam-3609	28	5	situations	situation	NOUN
ejpam-3609	28	6	where	where	SCONJ
ejpam-3609	28	7	a	a	DET
ejpam-3609	28	8	derivative	derivative	NOUN
ejpam-3609	28	9	of	of	ADP
ejpam-3609	28	10	a	a	DET
ejpam-3609	28	11	function	function	NOUN
ejpam-3609	28	12	fails	fail	VERB
ejpam-3609	28	13	to	to	PART
ejpam-3609	28	14	exist	exist	VERB
ejpam-3609	28	15	.	.	PUNCT
ejpam-3609	29	1	discontinuity	discontinuity	NOUN
ejpam-3609	29	2	and	and	CCONJ
ejpam-3609	29	3	non	non	ADJ
ejpam-3609	29	4	-	-	ADJ
ejpam-3609	29	5	differentiability	differentiability	NOUN
ejpam-3609	29	6	are	be	AUX
ejpam-3609	29	7	two	two	NUM
ejpam-3609	29	8	common	common	ADJ
ejpam-3609	29	9	problems	problem	NOUN
ejpam-3609	29	10	in	in	ADP
ejpam-3609	29	11	ordinary	ordinary	ADJ
ejpam-3609	29	12	calculus	calculus	NOUN
ejpam-3609	29	13	.	.	PUNCT
ejpam-3609	30	1	on	on	ADP
ejpam-3609	30	2	the	the	DET
ejpam-3609	30	3	other	other	ADJ
ejpam-3609	30	4	hand	hand	NOUN
ejpam-3609	30	5	,	,	PUNCT
ejpam-3609	30	6	we	we	PRON
ejpam-3609	30	7	observe	observe	VERB
ejpam-3609	30	8	fractals	fractal	NOUN
ejpam-3609	30	9	[	[	X
ejpam-3609	30	10	15	15	NUM
ejpam-3609	30	11	,	,	PUNCT
ejpam-3609	30	12	19	19	NUM
ejpam-3609	30	13	]	]	PUNCT
ejpam-3609	30	14	which	which	PRON
ejpam-3609	30	15	are	be	AUX
ejpam-3609	30	16	continuous	continuous	ADJ
ejpam-3609	30	17	or	or	CCONJ
ejpam-3609	30	18	discontinuous	discontinuous	ADJ
ejpam-3609	30	19	,	,	PUNCT
ejpam-3609	30	20	and	and	CCONJ
ejpam-3609	30	21	usually	usually	ADV
ejpam-3609	30	22	nowhere	nowhere	ADV
ejpam-3609	30	23	differentiable	differentiable	ADJ
ejpam-3609	30	24	.	.	PUNCT
ejpam-3609	31	1	fractals	fractal	NOUN
ejpam-3609	31	2	are	be	AUX
ejpam-3609	31	3	often	often	ADV
ejpam-3609	31	4	so	so	ADV
ejpam-3609	31	5	irregular	irregular	ADJ
ejpam-3609	31	6	that	that	SCONJ
ejpam-3609	31	7	defining	define	VERB
ejpam-3609	31	8	smooth	smooth	ADJ
ejpam-3609	31	9	,	,	PUNCT
ejpam-3609	31	10	differentiable	differentiable	ADJ
ejpam-3609	31	11	structures	structure	NOUN
ejpam-3609	31	12	on	on	ADP
ejpam-3609	31	13	them	they	PRON
ejpam-3609	31	14	seem	seem	VERB
ejpam-3609	31	15	very	very	ADV
ejpam-3609	31	16	difficult	difficult	ADJ
ejpam-3609	31	17	.	.	PUNCT
ejpam-3609	32	1	in	in	ADP
ejpam-3609	32	2	the	the	DET
ejpam-3609	32	3	past	past	ADJ
ejpam-3609	32	4	few	few	ADJ
ejpam-3609	32	5	years	year	NOUN
ejpam-3609	32	6	,	,	PUNCT
ejpam-3609	32	7	the	the	DET
ejpam-3609	32	8	new	new	ADJ
ejpam-3609	32	9	calculus	calculus	NOUN
ejpam-3609	32	10	called	call	VERB
ejpam-3609	32	11	fα	fα	NOUN
ejpam-3609	32	12	-	-	PUNCT
ejpam-3609	32	13	calculus	calculus	NOUN
ejpam-3609	32	14	or	or	CCONJ
ejpam-3609	32	15	fractal	fractal	ADJ
ejpam-3609	32	16	calculus	calculus	NOUN
ejpam-3609	32	17	[	[	X
ejpam-3609	32	18	10–12	10–12	NUM
ejpam-3609	32	19	]	]	PUNCT
ejpam-3609	32	20	have	have	AUX
ejpam-3609	32	21	been	be	AUX
ejpam-3609	32	22	introduced	introduce	VERB
ejpam-3609	32	23	by	by	ADP
ejpam-3609	32	24	gangal	gangal	ADJ
ejpam-3609	32	25	,	,	PUNCT
ejpam-3609	32	26	parvate	parvate	ADJ
ejpam-3609	32	27	,	,	PUNCT
ejpam-3609	32	28	and	and	CCONJ
ejpam-3609	32	29	satin	satin	NOUN
ejpam-3609	32	30	.	.	PUNCT
ejpam-3609	33	1	unfortunately	unfortunately	ADV
ejpam-3609	33	2	,	,	PUNCT
ejpam-3609	33	3	applying	apply	VERB
ejpam-3609	33	4	the	the	DET
ejpam-3609	33	5	methods	method	NOUN
ejpam-3609	33	6	of	of	ADP
ejpam-3609	33	7	ordinary	ordinary	ADJ
ejpam-3609	33	8	calculus	calculus	NOUN
ejpam-3609	33	9	on	on	ADP
ejpam-3609	33	10	fractals	fractal	NOUN
ejpam-3609	33	11	are	be	AUX
ejpam-3609	33	12	powerless	powerless	ADJ
ejpam-3609	33	13	.	.	PUNCT
ejpam-3609	34	1	they	they	PRON
ejpam-3609	34	2	study	study	VERB
ejpam-3609	34	3	“	"	PUNCT
ejpam-3609	34	4	fokkerplanck	fokkerplanck	NOUN
ejpam-3609	34	5	equation	equation	NOUN
ejpam-3609	34	6	”	"	PUNCT
ejpam-3609	34	7	,	,	PUNCT
ejpam-3609	34	8	“	"	PUNCT
ejpam-3609	34	9	langevin	langevin	ADJ
ejpam-3609	34	10	equation	equation	NOUN
ejpam-3609	34	11	”	"	PUNCT
ejpam-3609	34	12	on	on	ADP
ejpam-3609	34	13	fractal	fractal	ADJ
ejpam-3609	34	14	curves	curve	NOUN
ejpam-3609	34	15	[	[	X
ejpam-3609	34	16	21	21	NUM
ejpam-3609	34	17	,	,	PUNCT
ejpam-3609	34	18	22	22	NUM
ejpam-3609	34	19	]	]	PUNCT
ejpam-3609	34	20	.	.	PUNCT
ejpam-3609	35	1	using	use	VERB
ejpam-3609	35	2	fα	fα	NOUN
ejpam-3609	35	3	-	-	PUNCT
ejpam-3609	35	4	calculus	calculus	NOUN
ejpam-3609	35	5	,	,	PUNCT
ejpam-3609	35	6	golmankhaneh	golmankhaneh	NOUN
ejpam-3609	35	7	and	and	CCONJ
ejpam-3609	35	8	fernandez	fernandez	PROPN
ejpam-3609	35	9	define	define	VERB
ejpam-3609	35	10	integrals	integral	NOUN
ejpam-3609	35	11	and	and	CCONJ
ejpam-3609	35	12	derivatives	derivative	NOUN
ejpam-3609	35	13	of	of	ADP
ejpam-3609	35	14	functions	function	NOUN
ejpam-3609	35	15	on	on	ADP
ejpam-3609	35	16	cantor	cantor	PROPN
ejpam-3609	35	17	tartan	tartan	PROPN
ejpam-3609	35	18	spaces	space	NOUN
ejpam-3609	35	19	with	with	ADP
ejpam-3609	35	20	different	different	ADJ
ejpam-3609	35	21	dimensions	dimension	NOUN
ejpam-3609	35	22	among	among	ADP
ejpam-3609	35	23	with	with	ADP
ejpam-3609	35	24	their	their	PRON
ejpam-3609	35	25	related	relate	VERB
ejpam-3609	35	26	differential	differential	ADJ
ejpam-3609	35	27	equations	equation	NOUN
ejpam-3609	36	1	[	[	X
ejpam-3609	36	2	1	1	NUM
ejpam-3609	36	3	]	]	PUNCT
ejpam-3609	36	4	.	.	PUNCT
ejpam-3609	37	1	for	for	ADP
ejpam-3609	37	2	example	example	NOUN
ejpam-3609	37	3	suband	suband	NOUN
ejpam-3609	37	4	superdiffusion	superdiffusion	NOUN
ejpam-3609	37	5	on	on	ADP
ejpam-3609	37	6	cantor	cantor	PROPN
ejpam-3609	37	7	sets	set	NOUN
ejpam-3609	37	8	which	which	PRON
ejpam-3609	37	9	are	be	AUX
ejpam-3609	37	10	totally	totally	ADV
ejpam-3609	37	11	disconnected	disconnected	ADJ
ejpam-3609	37	12	fractals	fractal	NOUN
ejpam-3609	37	13	are	be	AUX
ejpam-3609	37	14	appeared	appear	VERB
ejpam-3609	37	15	when	when	SCONJ
ejpam-3609	37	16	one	one	PRON
ejpam-3609	37	17	needs	need	VERB
ejpam-3609	37	18	to	to	PART
ejpam-3609	37	19	relax	relax	VERB
ejpam-3609	37	20	the	the	DET
ejpam-3609	37	21	continuum	continuum	ADJ
ejpam-3609	37	22	requirement	requirement	NOUN
ejpam-3609	37	23	[	[	X
ejpam-3609	37	24	4	4	NUM
ejpam-3609	37	25	]	]	PUNCT
ejpam-3609	37	26	.	.	PUNCT
ejpam-3609	38	1	in	in	ADP
ejpam-3609	38	2	[	[	X
ejpam-3609	38	3	10	10	NUM
ejpam-3609	38	4	,	,	PUNCT
ejpam-3609	38	5	11	11	NUM
ejpam-3609	38	6	]	]	PUNCT
ejpam-3609	38	7	a	a	DET
ejpam-3609	38	8	new	new	ADJ
ejpam-3609	38	9	calculus	calculus	NOUN
ejpam-3609	38	10	based	base	VERB
ejpam-3609	38	11	on	on	ADP
ejpam-3609	38	12	fractal	fractal	ADJ
ejpam-3609	38	13	subsets	subset	NOUN
ejpam-3609	38	14	of	of	ADP
ejpam-3609	38	15	the	the	DET
ejpam-3609	38	16	real	real	ADJ
ejpam-3609	38	17	line	line	NOUN
ejpam-3609	38	18	is	be	AUX
ejpam-3609	38	19	formulated	formulate	VERB
ejpam-3609	38	20	which	which	PRON
ejpam-3609	38	21	involves	involve	VERB
ejpam-3609	38	22	an	an	DET
ejpam-3609	38	23	integral	integral	NOUN
ejpam-3609	38	24	of	of	ADP
ejpam-3609	38	25	order	order	NOUN
ejpam-3609	38	26	α	α	NOUN
ejpam-3609	38	27	,	,	PUNCT
ejpam-3609	38	28	0	0	NUM
ejpam-3609	38	29	<	<	X
ejpam-3609	38	30	α	α	X
ejpam-3609	38	31	<	<	X
ejpam-3609	38	32	1	1	NUM
ejpam-3609	38	33	,	,	PUNCT
ejpam-3609	38	34	called	call	VERB
ejpam-3609	38	35	fα	fα	ADV
ejpam-3609	38	36	-	-	PUNCT
ejpam-3609	38	37	integral	integral	ADJ
ejpam-3609	38	38	and	and	CCONJ
ejpam-3609	38	39	a	a	DET
ejpam-3609	38	40	derivative	derivative	NOUN
ejpam-3609	38	41	of	of	ADP
ejpam-3609	38	42	order	order	NOUN
ejpam-3609	38	43	α	α	NOUN
ejpam-3609	38	44	,	,	PUNCT
ejpam-3609	38	45	0	0	NUM
ejpam-3609	38	46	<	<	X
ejpam-3609	38	47	α	α	X
ejpam-3609	38	48	<	<	X
ejpam-3609	38	49	1	1	NUM
ejpam-3609	38	50	,	,	PUNCT
ejpam-3609	38	51	called	call	VERB
ejpam-3609	38	52	fα	fα	ADV
ejpam-3609	38	53	-	-	PUNCT
ejpam-3609	38	54	derivative	derivative	NOUN
ejpam-3609	38	55	.	.	PUNCT
ejpam-3609	39	1	this	this	PRON
ejpam-3609	39	2	enables	enable	VERB
ejpam-3609	39	3	us	we	PRON
ejpam-3609	39	4	to	to	PART
ejpam-3609	39	5	differentiate	differentiate	VERB
ejpam-3609	39	6	functions	function	NOUN
ejpam-3609	39	7	,	,	PUNCT
ejpam-3609	39	8	like	like	ADP
ejpam-3609	39	9	the	the	DET
ejpam-3609	39	10	cantor	cantor	PROPN
ejpam-3609	39	11	staircase	staircase	NOUN
ejpam-3609	39	12	,	,	PUNCT
ejpam-3609	39	13	“	"	PUNCT
ejpam-3609	39	14	changing	change	VERB
ejpam-3609	39	15	”	"	PUNCT
ejpam-3609	39	16	only	only	ADV
ejpam-3609	39	17	on	on	ADP
ejpam-3609	39	18	a	a	DET
ejpam-3609	39	19	fractal	fractal	ADJ
ejpam-3609	39	20	set	set	NOUN
ejpam-3609	39	21	.	.	PUNCT
ejpam-3609	40	1	the	the	DET
ejpam-3609	40	2	fα	fα	NOUN
ejpam-3609	40	3	-	-	PUNCT
ejpam-3609	40	4	derivative	derivative	NOUN
ejpam-3609	40	5	is	be	AUX
ejpam-3609	40	6	local	local	ADJ
ejpam-3609	40	7	unlike	unlike	ADP
ejpam-3609	40	8	the	the	DET
ejpam-3609	40	9	classical	classical	ADJ
ejpam-3609	40	10	fractional	fractional	ADJ
ejpam-3609	40	11	derivative	derivative	NOUN
ejpam-3609	40	12	.	.	PUNCT
ejpam-3609	41	1	they	they	PRON
ejpam-3609	41	2	generalize	generalize	VERB
ejpam-3609	41	3	their	their	PRON
ejpam-3609	41	4	work	work	NOUN
ejpam-3609	41	5	in	in	ADP
ejpam-3609	41	6	rn	rn	PROPN
ejpam-3609	42	1	[	[	X
ejpam-3609	42	2	12	12	NUM
ejpam-3609	42	3	]	]	PUNCT
ejpam-3609	42	4	so	so	SCONJ
ejpam-3609	42	5	that	that	SCONJ
ejpam-3609	42	6	this	this	DET
ejpam-3609	42	7	time	time	NOUN
ejpam-3609	42	8	a	a	DET
ejpam-3609	42	9	new	new	ADJ
ejpam-3609	42	10	calculus	calculus	NOUN
ejpam-3609	42	11	on	on	ADP
ejpam-3609	42	12	fractal	fractal	ADJ
ejpam-3609	42	13	curves	curve	NOUN
ejpam-3609	42	14	,	,	PUNCT
ejpam-3609	42	15	such	such	ADJ
ejpam-3609	42	16	as	as	ADP
ejpam-3609	42	17	the	the	DET
ejpam-3609	42	18	von	von	PROPN
ejpam-3609	42	19	koch	koch	PROPN
ejpam-3609	42	20	curve	curve	PROPN
ejpam-3609	42	21	,	,	PUNCT
ejpam-3609	42	22	is	be	AUX
ejpam-3609	42	23	formulated	formulate	VERB
ejpam-3609	42	24	.	.	PUNCT
ejpam-3609	43	1	a	a	DET
ejpam-3609	43	2	riemann	riemann	PROPN
ejpam-3609	43	3	-	-	PUNCT
ejpam-3609	43	4	like	like	ADJ
ejpam-3609	43	5	integral	integral	ADJ
ejpam-3609	43	6	along	along	ADP
ejpam-3609	43	7	a	a	DET
ejpam-3609	43	8	fractal	fractal	ADJ
ejpam-3609	43	9	curve	curve	NOUN
ejpam-3609	43	10	f	f	PROPN
ejpam-3609	43	11	,	,	PUNCT
ejpam-3609	43	12	called	call	VERB
ejpam-3609	43	13	fα	fα	ADV
ejpam-3609	43	14	-	-	PUNCT
ejpam-3609	43	15	integral	integral	ADJ
ejpam-3609	43	16	,	,	PUNCT
ejpam-3609	43	17	is	be	AUX
ejpam-3609	43	18	defined	define	VERB
ejpam-3609	43	19	where	where	SCONJ
ejpam-3609	43	20	α	α	NOUN
ejpam-3609	43	21	is	be	AUX
ejpam-3609	43	22	the	the	DET
ejpam-3609	43	23	dimension	dimension	NOUN
ejpam-3609	43	24	of	of	ADP
ejpam-3609	43	25	f	f	PROPN
ejpam-3609	43	26	.	.	PUNCT
ejpam-3609	44	1	a	a	DET
ejpam-3609	44	2	derivative	derivative	NOUN
ejpam-3609	44	3	along	along	ADP
ejpam-3609	44	4	the	the	DET
ejpam-3609	44	5	fractal	fractal	ADJ
ejpam-3609	44	6	curve	curve	NOUN
ejpam-3609	44	7	called	call	VERB
ejpam-3609	44	8	fα	fα	NOUN
ejpam-3609	44	9	-	-	PUNCT
ejpam-3609	44	10	derivative	derivative	NOUN
ejpam-3609	44	11	,	,	PUNCT
ejpam-3609	44	12	is	be	AUX
ejpam-3609	44	13	also	also	ADV
ejpam-3609	44	14	defined	define	VERB
ejpam-3609	44	15	.	.	PUNCT
ejpam-3609	45	1	fractal	fractal	ADJ
ejpam-3609	45	2	calculus	calculus	PROPN
ejpam-3609	45	3	has	have	AUX
ejpam-3609	45	4	found	find	VERB
ejpam-3609	45	5	many	many	ADJ
ejpam-3609	45	6	applications	application	NOUN
ejpam-3609	45	7	in	in	ADP
ejpam-3609	45	8	physics	physics	NOUN
ejpam-3609	45	9	and	and	CCONJ
ejpam-3609	45	10	engineering	engineering	NOUN
ejpam-3609	45	11	[	[	X
ejpam-3609	45	12	2	2	NUM
ejpam-3609	45	13	,	,	PUNCT
ejpam-3609	45	14	3	3	NUM
ejpam-3609	45	15	,	,	PUNCT
ejpam-3609	45	16	5–9	5–9	NUM
ejpam-3609	45	17	,	,	PUNCT
ejpam-3609	45	18	13	13	NUM
ejpam-3609	45	19	,	,	PUNCT
ejpam-3609	45	20	14	14	NUM
ejpam-3609	45	21	,	,	PUNCT
ejpam-3609	45	22	17	17	NUM
ejpam-3609	45	23	,	,	PUNCT
ejpam-3609	45	24	20	20	NUM
ejpam-3609	45	25	]	]	PUNCT
ejpam-3609	45	26	.	.	PUNCT
ejpam-3609	46	1	a.	a.	NOUN
ejpam-3609	46	2	pishkoo	pishkoo	PROPN
ejpam-3609	46	3	et	et	PROPN
ejpam-3609	46	4	al	al	PROPN
ejpam-3609	46	5	.	.	PUNCT
ejpam-3609	46	6	/	/	SYM
ejpam-3609	46	7	eur	eur	PROPN
ejpam-3609	46	8	.	.	PUNCT
ejpam-3609	47	1	j.	j.	PROPN
ejpam-3609	47	2	pure	pure	PROPN
ejpam-3609	47	3	appl	appl	PROPN
ejpam-3609	47	4	.	.	PROPN
ejpam-3609	47	5	math	math	PROPN
ejpam-3609	47	6	,	,	PUNCT
ejpam-3609	47	7	13	13	NUM
ejpam-3609	47	8	(	(	PUNCT
ejpam-3609	47	9	1	1	NUM
ejpam-3609	47	10	)	)	PUNCT
ejpam-3609	47	11	(	(	PUNCT
ejpam-3609	47	12	2020	2020	NUM
ejpam-3609	47	13	)	)	PUNCT
ejpam-3609	47	14	,	,	PUNCT
ejpam-3609	47	15	19	19	NUM
ejpam-3609	47	16	-	-	SYM
ejpam-3609	47	17	32	32	NUM
ejpam-3609	47	18	21	21	NUM
ejpam-3609	47	19	definition	definition	NOUN
ejpam-3609	47	20	1	1	NUM
ejpam-3609	47	21	.	.	PUNCT
ejpam-3609	48	1	[	[	X
ejpam-3609	48	2	10	10	NUM
ejpam-3609	48	3	]	]	X
ejpam-3609	48	4	if	if	SCONJ
ejpam-3609	48	5	f	f	PROPN
ejpam-3609	48	6	is	be	AUX
ejpam-3609	48	7	an	an	DET
ejpam-3609	48	8	α	α	NOUN
ejpam-3609	48	9	-	-	ADJ
ejpam-3609	48	10	perfect	perfect	ADJ
ejpam-3609	48	11	set	set	NOUN
ejpam-3609	48	12	then	then	ADV
ejpam-3609	48	13	the	the	DET
ejpam-3609	48	14	fα	fα	NOUN
ejpam-3609	48	15	-	-	PUNCT
ejpam-3609	48	16	derivative	derivative	NOUN
ejpam-3609	48	17	of	of	ADP
ejpam-3609	48	18	f	f	PROPN
ejpam-3609	48	19	at	at	ADP
ejpam-3609	48	20	x	x	PROPN
ejpam-3609	48	21	is	be	AUX
ejpam-3609	48	22	dαf	dαf	NOUN
ejpam-3609	48	23	(	(	PUNCT
ejpam-3609	48	24	f(x	f(x	PROPN
ejpam-3609	48	25	)	)	PUNCT
ejpam-3609	48	26	)	)	PUNCT
ejpam-3609	49	1	=	=	PRON
ejpam-3609	49	2	{	{	PUNCT
ejpam-3609	49	3	f	f	X
ejpam-3609	49	4	−	−	PROPN
ejpam-3609	49	5	limy→x	limy→x	PROPN
ejpam-3609	49	6	f(y)−f(x	f(y)−f(x	PROPN
ejpam-3609	49	7	)	)	PUNCT
ejpam-3609	49	8	sαf	sαf	NOUN
ejpam-3609	49	9	(	(	PUNCT
ejpam-3609	49	10	y)−sαf	y)−sαf	NOUN
ejpam-3609	49	11	(	(	PUNCT
ejpam-3609	49	12	x	x	NOUN
ejpam-3609	49	13	)	)	PUNCT
ejpam-3609	49	14	if	if	SCONJ
ejpam-3609	49	15	x	x	SYM
ejpam-3609	49	16	∈	∈	PROPN
ejpam-3609	49	17	f	f	X
ejpam-3609	49	18	0	0	NUM
ejpam-3609	49	19	othervise	othervise	NOUN
ejpam-3609	49	20	,	,	PUNCT
ejpam-3609	49	21	}	}	PUNCT
ejpam-3609	49	22	(	(	PUNCT
ejpam-3609	49	23	1	1	X
ejpam-3609	49	24	)	)	PUNCT
ejpam-3609	49	25	if	if	SCONJ
ejpam-3609	49	26	limit	limit	NOUN
ejpam-3609	49	27	exist	exist	VERB
ejpam-3609	49	28	.	.	PUNCT
ejpam-3609	50	1	the	the	DET
ejpam-3609	50	2	α	α	NOUN
ejpam-3609	50	3	-	-	ADJ
ejpam-3609	50	4	perfect	perfect	ADJ
ejpam-3609	50	5	sets	set	NOUN
ejpam-3609	50	6	are	be	AUX
ejpam-3609	50	7	sets	set	NOUN
ejpam-3609	50	8	having	have	VERB
ejpam-3609	50	9	properties	property	NOUN
ejpam-3609	50	10	necessary	necessary	ADJ
ejpam-3609	50	11	to	to	PART
ejpam-3609	50	12	define	define	VERB
ejpam-3609	50	13	fαderivative	fαderivative	ADJ
ejpam-3609	50	14	.	.	PUNCT
ejpam-3609	51	1	like	like	ADP
ejpam-3609	51	2	the	the	DET
ejpam-3609	51	3	first	first	ADJ
ejpam-3609	51	4	order	order	NOUN
ejpam-3609	51	5	derivative	derivative	NOUN
ejpam-3609	51	6	,	,	PUNCT
ejpam-3609	51	7	the	the	DET
ejpam-3609	51	8	fα	fα	NOUN
ejpam-3609	51	9	-	-	PUNCT
ejpam-3609	51	10	derivative	derivative	NOUN
ejpam-3609	51	11	is	be	AUX
ejpam-3609	51	12	a	a	DET
ejpam-3609	51	13	limit	limit	NOUN
ejpam-3609	51	14	of	of	ADP
ejpam-3609	51	15	a	a	DET
ejpam-3609	51	16	quotient	quotient	NOUN
ejpam-3609	51	17	.	.	PUNCT
ejpam-3609	52	1	but	but	CCONJ
ejpam-3609	52	2	here	here	ADV
ejpam-3609	52	3	the	the	DET
ejpam-3609	52	4	limit	limit	NOUN
ejpam-3609	52	5	is	be	AUX
ejpam-3609	52	6	f	f	PROPN
ejpam-3609	52	7	-limit	-limit	PROPN
ejpam-3609	52	8	,	,	PUNCT
ejpam-3609	52	9	and	and	CCONJ
ejpam-3609	52	10	the	the	DET
ejpam-3609	52	11	denominator	denominator	NOUN
ejpam-3609	52	12	is	be	AUX
ejpam-3609	52	13	the	the	DET
ejpam-3609	52	14	difference	difference	NOUN
ejpam-3609	52	15	in	in	ADP
ejpam-3609	52	16	the	the	DET
ejpam-3609	52	17	values	value	NOUN
ejpam-3609	52	18	of	of	ADP
ejpam-3609	52	19	the	the	DET
ejpam-3609	52	20	staircase	staircase	NOUN
ejpam-3609	52	21	function	function	NOUN
ejpam-3609	52	22	sαf	sαf	NOUN
ejpam-3609	52	23	at	at	ADP
ejpam-3609	52	24	two	two	NUM
ejpam-3609	52	25	points	point	NOUN
ejpam-3609	52	26	.	.	PUNCT
ejpam-3609	53	1	moreover	moreover	ADV
ejpam-3609	53	2	,	,	PUNCT
ejpam-3609	53	3	intuitively	intuitively	ADV
ejpam-3609	53	4	speaking	speak	VERB
ejpam-3609	53	5	,	,	PUNCT
ejpam-3609	53	6	f	f	PROPN
ejpam-3609	53	7	is	be	AUX
ejpam-3609	53	8	typically	typically	ADV
ejpam-3609	53	9	the	the	DET
ejpam-3609	53	10	set	set	NOUN
ejpam-3609	53	11	of	of	ADP
ejpam-3609	53	12	change	change	NOUN
ejpam-3609	53	13	of	of	ADP
ejpam-3609	53	14	the	the	DET
ejpam-3609	53	15	function	function	NOUN
ejpam-3609	53	16	,	,	PUNCT
ejpam-3609	53	17	and	and	CCONJ
ejpam-3609	53	18	α	α	PRON
ejpam-3609	53	19	is	be	AUX
ejpam-3609	53	20	typically	typically	ADV
ejpam-3609	53	21	the	the	DET
ejpam-3609	53	22	γ	γ	NOUN
ejpam-3609	53	23	-	-	NOUN
ejpam-3609	53	24	dimension	dimension	NOUN
ejpam-3609	53	25	of	of	ADP
ejpam-3609	53	26	f	f	PROPN
ejpam-3609	53	27	.	.	PUNCT
ejpam-3609	54	1	theorem	theorem	NOUN
ejpam-3609	54	2	1	1	NUM
ejpam-3609	54	3	.	.	PUNCT
ejpam-3609	55	1	[	[	X
ejpam-3609	55	2	10	10	NUM
ejpam-3609	55	3	]	]	PUNCT
ejpam-3609	55	4	let	let	VERB
ejpam-3609	55	5	f	f	PRON
ejpam-3609	55	6	be	be	AUX
ejpam-3609	55	7	such	such	ADJ
ejpam-3609	55	8	that	that	SCONJ
ejpam-3609	55	9	f	f	PROPN
ejpam-3609	55	10	∩	∩	PROPN
ejpam-3609	55	11	[	[	X
ejpam-3609	55	12	a	a	X
ejpam-3609	55	13	,	,	PUNCT
ejpam-3609	55	14	b	b	NOUN
ejpam-3609	55	15	]	]	PUNCT
ejpam-3609	55	16	is	be	AUX
ejpam-3609	55	17	compact	compact	ADJ
ejpam-3609	55	18	and	and	CCONJ
ejpam-3609	55	19	sαf	sαf	NOUN
ejpam-3609	55	20	is	be	AUX
ejpam-3609	55	21	finite	finite	ADJ
ejpam-3609	55	22	on	on	ADP
ejpam-3609	55	23	[	[	X
ejpam-3609	55	24	a	a	X
ejpam-3609	55	25	,	,	PUNCT
ejpam-3609	55	26	b	b	NOUN
ejpam-3609	55	27	]	]	PUNCT
ejpam-3609	55	28	.	.	PUNCT
ejpam-3609	56	1	let	let	VERB
ejpam-3609	56	2	f	f	PROPN
ejpam-3609	56	3	∈	∈	PROPN
ejpam-3609	56	4	b(f	b(f	PROPN
ejpam-3609	56	5	)	)	PUNCT
ejpam-3609	56	6	,	,	PUNCT
ejpam-3609	56	7	and	and	CCONJ
ejpam-3609	56	8	b	b	X
ejpam-3609	56	9	>	>	X
ejpam-3609	56	10	a.	a.	NOUN
ejpam-3609	56	11	if	if	SCONJ
ejpam-3609	56	12	f	f	PROPN
ejpam-3609	56	13	is	be	AUX
ejpam-3609	56	14	f	f	PROPN
ejpam-3609	56	15	-continuous	-continuous	ADJ
ejpam-3609	56	16	on	on	ADP
ejpam-3609	56	17	f	f	PROPN
ejpam-3609	56	18	∩	∩	PROPN
ejpam-3609	56	19	[	[	X
ejpam-3609	56	20	a	a	X
ejpam-3609	56	21	,	,	PUNCT
ejpam-3609	56	22	b	b	NOUN
ejpam-3609	56	23	]	]	X
ejpam-3609	56	24	,	,	PUNCT
ejpam-3609	56	25	then	then	ADV
ejpam-3609	56	26	f	f	PROPN
ejpam-3609	56	27	is	be	AUX
ejpam-3609	56	28	fα	fα	ADV
ejpam-3609	56	29	-	-	PUNCT
ejpam-3609	56	30	integrable	integrable	ADJ
ejpam-3609	56	31	on	on	ADP
ejpam-3609	56	32	[	[	X
ejpam-3609	56	33	a	a	X
ejpam-3609	56	34	,	,	PUNCT
ejpam-3609	56	35	b	b	NOUN
ejpam-3609	56	36	]	]	X
ejpam-3609	56	37	if	if	SCONJ
ejpam-3609	56	38	supremum	supremum	ADJ
ejpam-3609	56	39	and	and	CCONJ
ejpam-3609	56	40	infimum	infimum	ADJ
ejpam-3609	56	41	∫	∫	PROPN
ejpam-3609	56	42	b	b	PROPN
ejpam-3609	56	43	a	a	DET
ejpam-3609	56	44	f(x	f(x	PROPN
ejpam-3609	56	45	)	)	PUNCT
ejpam-3609	56	46	dαfx	dαfx	NOUN
ejpam-3609	57	1	=	=	SYM
ejpam-3609	57	2	∫	∫	PROPN
ejpam-3609	57	3	b	b	PROPN
ejpam-3609	57	4	a	a	DET
ejpam-3609	57	5	f(x	f(x	PROPN
ejpam-3609	57	6	)	)	PUNCT
ejpam-3609	57	7	dαfx	dαfx	NOUN
ejpam-3609	57	8	.	.	PUNCT
ejpam-3609	58	1	(	(	PUNCT
ejpam-3609	58	2	2	2	X
ejpam-3609	58	3	)	)	PUNCT
ejpam-3609	58	4	in	in	ADP
ejpam-3609	58	5	that	that	DET
ejpam-3609	58	6	case	case	NOUN
ejpam-3609	58	7	the	the	DET
ejpam-3609	58	8	fα	fα	ADV
ejpam-3609	58	9	-	-	ADJ
ejpam-3609	58	10	integral	integral	ADJ
ejpam-3609	58	11	of	of	ADP
ejpam-3609	58	12	f	f	PROPN
ejpam-3609	58	13	on	on	ADP
ejpam-3609	58	14	[	[	X
ejpam-3609	58	15	a	a	X
ejpam-3609	58	16	,	,	PUNCT
ejpam-3609	58	17	b	b	NOUN
ejpam-3609	58	18	]	]	X
ejpam-3609	58	19	,	,	PUNCT
ejpam-3609	58	20	denoted	denote	VERB
ejpam-3609	58	21	by	by	ADP
ejpam-3609	58	22	∫	∫	PROPN
ejpam-3609	58	23	b	b	PROPN
ejpam-3609	58	24	a	a	DET
ejpam-3609	58	25	f(x	f(x	PROPN
ejpam-3609	58	26	)	)	PUNCT
ejpam-3609	58	27	dαfx	dαfx	NOUN
ejpam-3609	58	28	is	be	AUX
ejpam-3609	58	29	given	give	VERB
ejpam-3609	58	30	by	by	ADP
ejpam-3609	58	31	the	the	DET
ejpam-3609	58	32	common	common	ADJ
ejpam-3609	58	33	value	value	NOUN
ejpam-3609	58	34	.	.	PUNCT
ejpam-3609	59	1	2	2	X
ejpam-3609	59	2	.	.	X
ejpam-3609	59	3	main	main	ADJ
ejpam-3609	59	4	results	result	NOUN
ejpam-3609	59	5	the	the	DET
ejpam-3609	59	6	forms	form	NOUN
ejpam-3609	59	7	of	of	ADP
ejpam-3609	59	8	functions	function	NOUN
ejpam-3609	59	9	in	in	ADP
ejpam-3609	59	10	r	r	NOUN
ejpam-3609	59	11	and	and	CCONJ
ejpam-3609	59	12	fα	fα	NOUN
ejpam-3609	59	13	-	-	PUNCT
ejpam-3609	59	14	space	space	NOUN
ejpam-3609	59	15	are	be	AUX
ejpam-3609	59	16	different	different	ADJ
ejpam-3609	59	17	.	.	PUNCT
ejpam-3609	60	1	for	for	ADP
ejpam-3609	60	2	instance	instance	NOUN
ejpam-3609	60	3	we	we	PRON
ejpam-3609	60	4	consider	consider	VERB
ejpam-3609	60	5	g(x	g(x	NOUN
ejpam-3609	60	6	)	)	PUNCT
ejpam-3609	61	1	=	=	SYM
ejpam-3609	61	2	x2	x2	PROPN
ejpam-3609	61	3	and	and	CCONJ
ejpam-3609	61	4	f(x	f(x	PROPN
ejpam-3609	61	5	)	)	PUNCT
ejpam-3609	62	1	=	=	PUNCT
ejpam-3609	62	2	(	(	PUNCT
ejpam-3609	62	3	sαc(x))2	sαc(x))2	X
ejpam-3609	62	4	(	(	PUNCT
ejpam-3609	62	5	see	see	VERB
ejpam-3609	62	6	fig.1	fig.1	PROPN
ejpam-3609	62	7	)	)	PUNCT
ejpam-3609	62	8	.	.	PUNCT
ejpam-3609	63	1	using	use	VERB
ejpam-3609	63	2	eq	eq	ADP
ejpam-3609	63	3	.	.	PROPN
ejpam-3609	63	4	1	1	NUM
ejpam-3609	63	5	,	,	PUNCT
ejpam-3609	63	6	their	their	PRON
ejpam-3609	63	7	standard	standard	NOUN
ejpam-3609	63	8	and	and	CCONJ
ejpam-3609	63	9	fα	fα	NOUN
ejpam-3609	63	10	-	-	PUNCT
ejpam-3609	63	11	derivatives	derivative	NOUN
ejpam-3609	63	12	can	can	AUX
ejpam-3609	63	13	be	be	AUX
ejpam-3609	63	14	compared	compare	VERB
ejpam-3609	63	15	(	(	PUNCT
ejpam-3609	63	16	fig	fig	NOUN
ejpam-3609	63	17	.	.	PUNCT
ejpam-3609	64	1	2	2	NUM
ejpam-3609	64	2	)	)	PUNCT
ejpam-3609	64	3	.	.	PUNCT
ejpam-3609	65	1	after	after	ADP
ejpam-3609	65	2	defining	define	VERB
ejpam-3609	65	3	fα	fα	NOUN
ejpam-3609	65	4	-	-	NOUN
ejpam-3609	65	5	derivative	derivative	ADJ
ejpam-3609	65	6	,	,	PUNCT
ejpam-3609	65	7	fα	fα	NOUN
ejpam-3609	65	8	-	-	ADJ
ejpam-3609	65	9	integral	integral	ADJ
ejpam-3609	65	10	is	be	AUX
ejpam-3609	65	11	defined	define	VERB
ejpam-3609	65	12	.	.	PUNCT
ejpam-3609	66	1	in	in	ADP
ejpam-3609	66	2	the	the	DET
ejpam-3609	66	3	definition	definition	NOUN
ejpam-3609	66	4	of	of	ADP
ejpam-3609	66	5	fα	fα	ADV
ejpam-3609	66	6	-	-	PUNCT
ejpam-3609	66	7	integral	integral	ADJ
ejpam-3609	66	8	,	,	PUNCT
ejpam-3609	66	9	just	just	ADV
ejpam-3609	66	10	the	the	DET
ejpam-3609	66	11	values	value	NOUN
ejpam-3609	66	12	of	of	ADP
ejpam-3609	66	13	the	the	DET
ejpam-3609	66	14	function	function	NOUN
ejpam-3609	66	15	at	at	ADP
ejpam-3609	66	16	points	point	NOUN
ejpam-3609	66	17	belonging	belong	VERB
ejpam-3609	66	18	to	to	ADP
ejpam-3609	66	19	the	the	DET
ejpam-3609	66	20	set	set	NOUN
ejpam-3609	66	21	f	f	PROPN
ejpam-3609	66	22	are	be	AUX
ejpam-3609	66	23	considered	consider	VERB
ejpam-3609	66	24	.	.	PUNCT
ejpam-3609	67	1	in	in	ADP
ejpam-3609	67	2	this	this	DET
ejpam-3609	67	3	type	type	NOUN
ejpam-3609	67	4	of	of	ADP
ejpam-3609	67	5	integral	integral	ADJ
ejpam-3609	67	6	,	,	PUNCT
ejpam-3609	67	7	instead	instead	ADV
ejpam-3609	67	8	of	of	ADP
ejpam-3609	67	9	the	the	DET
ejpam-3609	67	10	length	length	NOUN
ejpam-3609	67	11	of	of	ADP
ejpam-3609	67	12	subintervals	subinterval	NOUN
ejpam-3609	67	13	(	(	PUNCT
ejpam-3609	67	14	xi+1	xi+1	NOUN
ejpam-3609	67	15	−	−	NOUN
ejpam-3609	67	16	xi	xi	NOUN
ejpam-3609	67	17	)	)	PUNCT
ejpam-3609	67	18	the	the	DET
ejpam-3609	67	19	difference	difference	NOUN
ejpam-3609	67	20	between	between	ADP
ejpam-3609	67	21	their	their	PRON
ejpam-3609	67	22	values	value	NOUN
ejpam-3609	67	23	of	of	ADP
ejpam-3609	67	24	the	the	DET
ejpam-3609	67	25	integral	integral	ADJ
ejpam-3609	67	26	staircase	staircase	NOUN
ejpam-3609	67	27	function	function	NOUN
ejpam-3609	67	28	sαf	sαf	NOUN
ejpam-3609	67	29	(	(	PUNCT
ejpam-3609	67	30	xi+1)−sαf	xi+1)−sαf	X
ejpam-3609	67	31	(	(	PUNCT
ejpam-3609	67	32	xi	xi	X
ejpam-3609	67	33	)	)	PUNCT
ejpam-3609	67	34	are	be	AUX
ejpam-3609	67	35	inserted	insert	VERB
ejpam-3609	67	36	(	(	PUNCT
ejpam-3609	67	37	fig	fig	NOUN
ejpam-3609	67	38	.	.	PUNCT
ejpam-3609	68	1	3	3	NUM
ejpam-3609	68	2	)	)	PUNCT
ejpam-3609	68	3	.	.	PUNCT
ejpam-3609	69	1	fα	fα	NOUN
ejpam-3609	69	2	-	-	PUNCT
ejpam-3609	69	3	integration	integration	NOUN
ejpam-3609	69	4	of	of	ADP
ejpam-3609	69	5	staircase	staircase	NOUN
ejpam-3609	69	6	and	and	CCONJ
ejpam-3609	69	7	characteristic	characteristic	ADJ
ejpam-3609	69	8	functions	function	NOUN
ejpam-3609	69	9	indefinite	indefinite	ADJ
ejpam-3609	69	10	integral	integral	ADJ
ejpam-3609	69	11	of	of	ADP
ejpam-3609	69	12	characteristic	characteristic	ADJ
ejpam-3609	69	13	function	function	NOUN
ejpam-3609	69	14	is	be	AUX
ejpam-3609	69	15	defined	define	VERB
ejpam-3609	69	16	as∫	as∫	PROPN
ejpam-3609	69	17	x́	x́	PROPN
ejpam-3609	70	1	a	a	DET
ejpam-3609	70	2	χf	χf	PROPN
ejpam-3609	70	3	(	(	PUNCT
ejpam-3609	70	4	x	x	NOUN
ejpam-3609	70	5	)	)	PUNCT
ejpam-3609	70	6	dαfx	dαfx	NOUN
ejpam-3609	70	7	=	=	SYM
ejpam-3609	70	8	sαf	sαf	NOUN
ejpam-3609	70	9	(	(	PUNCT
ejpam-3609	70	10	x́	x́	PROPN
ejpam-3609	70	11	)	)	PUNCT
ejpam-3609	70	12	,	,	PUNCT
ejpam-3609	70	13	assume	assume	VERB
ejpam-3609	70	14	for	for	ADP
ejpam-3609	70	15	the	the	DET
ejpam-3609	70	16	simplicity	simplicity	NOUN
ejpam-3609	70	17	sαf	sαf	NOUN
ejpam-3609	70	18	(	(	PUNCT
ejpam-3609	70	19	a	a	X
ejpam-3609	70	20	)	)	PUNCT
ejpam-3609	70	21	=	=	SYM
ejpam-3609	71	1	0	0	X
ejpam-3609	71	2	.	.	PUNCT
ejpam-3609	72	1	indefinite	indefinite	ADJ
ejpam-3609	72	2	integral	integral	ADJ
ejpam-3609	72	3	of	of	ADP
ejpam-3609	72	4	staircase	staircase	NOUN
ejpam-3609	72	5	function	function	PROPN
ejpam-3609	72	6	is∫	is∫	PROPN
ejpam-3609	72	7	x́	x́	PROPN
ejpam-3609	73	1	a	a	DET
ejpam-3609	73	2	sαf	sαf	NOUN
ejpam-3609	73	3	(	(	PUNCT
ejpam-3609	73	4	x	x	NOUN
ejpam-3609	73	5	)	)	PUNCT
ejpam-3609	73	6	dαfx	dαfx	NOUN
ejpam-3609	73	7	=	=	PUNCT
ejpam-3609	74	1	[	[	X
ejpam-3609	74	2	sαf	sαf	NOUN
ejpam-3609	74	3	(	(	PUNCT
ejpam-3609	74	4	x́)]2	x́)]2	PROPN
ejpam-3609	74	5	2	2	NUM
ejpam-3609	74	6	.	.	PUNCT
ejpam-3609	74	7	a.	a.	NOUN
ejpam-3609	74	8	pishkoo	pishkoo	PROPN
ejpam-3609	74	9	et	et	PROPN
ejpam-3609	74	10	al	al	PROPN
ejpam-3609	74	11	.	.	PUNCT
ejpam-3609	74	12	/	/	SYM
ejpam-3609	74	13	eur	eur	PROPN
ejpam-3609	74	14	.	.	PUNCT
ejpam-3609	75	1	j.	j.	PROPN
ejpam-3609	75	2	pure	pure	PROPN
ejpam-3609	75	3	appl	appl	PROPN
ejpam-3609	75	4	.	.	PROPN
ejpam-3609	75	5	math	math	PROPN
ejpam-3609	75	6	,	,	PUNCT
ejpam-3609	75	7	13	13	NUM
ejpam-3609	75	8	(	(	PUNCT
ejpam-3609	75	9	1	1	NUM
ejpam-3609	75	10	)	)	PUNCT
ejpam-3609	75	11	(	(	PUNCT
ejpam-3609	75	12	2020	2020	NUM
ejpam-3609	75	13	)	)	PUNCT
ejpam-3609	75	14	,	,	PUNCT
ejpam-3609	75	15	19	19	NUM
ejpam-3609	75	16	-	-	SYM
ejpam-3609	75	17	32	32	NUM
ejpam-3609	75	18	22	22	NUM
ejpam-3609	75	19	figure	figure	NOUN
ejpam-3609	75	20	1	1	NUM
ejpam-3609	75	21	:	:	PUNCT
ejpam-3609	75	22	comparing	compare	VERB
ejpam-3609	75	23	graph	graph	NOUN
ejpam-3609	75	24	of	of	ADP
ejpam-3609	75	25	functions	function	NOUN
ejpam-3609	75	26	g(x	g(x	NOUN
ejpam-3609	75	27	)	)	PUNCT
ejpam-3609	76	1	=	=	SYM
ejpam-3609	76	2	x2	x2	PROPN
ejpam-3609	76	3	and	and	CCONJ
ejpam-3609	76	4	f(x	f(x	PROPN
ejpam-3609	76	5	)	)	PUNCT
ejpam-3609	77	1	=	=	PRON
ejpam-3609	77	2	(	(	PUNCT
ejpam-3609	77	3	sαc(x))2	sαc(x))2	NOUN
ejpam-3609	77	4	in	in	ADP
ejpam-3609	77	5	r	r	NOUN
ejpam-3609	77	6	and	and	CCONJ
ejpam-3609	77	7	fα	fα	NOUN
ejpam-3609	77	8	-	-	PUNCT
ejpam-3609	77	9	space	space	NOUN
ejpam-3609	77	10	,	,	PUNCT
ejpam-3609	77	11	respectively	respectively	ADV
ejpam-3609	77	12	on	on	ADP
ejpam-3609	77	13	the	the	DET
ejpam-3609	77	14	interval	interval	NOUN
ejpam-3609	77	15	[	[	X
ejpam-3609	77	16	0,1	0,1	NUM
ejpam-3609	77	17	]	]	PUNCT
ejpam-3609	77	18	figure	figure	NOUN
ejpam-3609	77	19	2	2	NUM
ejpam-3609	77	20	:	:	PUNCT
ejpam-3609	77	21	comparing	compare	VERB
ejpam-3609	77	22	derivative	derivative	NOUN
ejpam-3609	77	23	of	of	ADP
ejpam-3609	77	24	functions	function	NOUN
ejpam-3609	77	25	g(x	g(x	NOUN
ejpam-3609	77	26	)	)	PUNCT
ejpam-3609	78	1	=	=	SYM
ejpam-3609	78	2	x2	x2	PROPN
ejpam-3609	78	3	and	and	CCONJ
ejpam-3609	78	4	f(x	f(x	PROPN
ejpam-3609	78	5	)	)	PUNCT
ejpam-3609	79	1	=	=	PRON
ejpam-3609	79	2	(	(	PUNCT
ejpam-3609	79	3	sαc(x))2	sαc(x))2	NOUN
ejpam-3609	79	4	in	in	ADP
ejpam-3609	79	5	r	r	NOUN
ejpam-3609	79	6	and	and	CCONJ
ejpam-3609	79	7	fα	fα	NOUN
ejpam-3609	79	8	-	-	PUNCT
ejpam-3609	79	9	space	space	NOUN
ejpam-3609	79	10	,	,	PUNCT
ejpam-3609	79	11	respectively	respectively	ADV
ejpam-3609	79	12	on	on	ADP
ejpam-3609	79	13	the	the	DET
ejpam-3609	79	14	interval	interval	NOUN
ejpam-3609	79	15	[	[	X
ejpam-3609	79	16	0,1	0,1	X
ejpam-3609	79	17	]	]	PUNCT
ejpam-3609	79	18	in	in	ADP
ejpam-3609	79	19	other	other	ADJ
ejpam-3609	79	20	words	word	NOUN
ejpam-3609	79	21	,	,	PUNCT
ejpam-3609	79	22	consecutive	consecutive	ADJ
ejpam-3609	79	23	double	double	ADJ
ejpam-3609	79	24	integration	integration	NOUN
ejpam-3609	79	25	of	of	ADP
ejpam-3609	79	26	characteristic	characteristic	ADJ
ejpam-3609	79	27	function	function	NOUN
ejpam-3609	79	28	give	give	VERB
ejpam-3609	79	29	us∫	us∫	PROPN
ejpam-3609	79	30	x́	x́	PROPN
ejpam-3609	80	1	a	a	DET
ejpam-3609	80	2	dαf	dαf	NOUN
ejpam-3609	80	3	x́	x́	PROPN
ejpam-3609	81	1	∫	∫	PROPN
ejpam-3609	81	2	x́	x́	PROPN
ejpam-3609	82	1	a	a	DET
ejpam-3609	82	2	χf	χf	PROPN
ejpam-3609	82	3	(	(	PUNCT
ejpam-3609	82	4	x	x	NOUN
ejpam-3609	82	5	)	)	PUNCT
ejpam-3609	82	6	dαfx	dαfx	NOUN
ejpam-3609	82	7	=	=	PUNCT
ejpam-3609	83	1	[	[	X
ejpam-3609	83	2	sαf	sαf	NOUN
ejpam-3609	83	3	(	(	PUNCT
ejpam-3609	83	4	x́)]2	x́)]2	PROPN
ejpam-3609	83	5	2	2	NUM
ejpam-3609	83	6	.	.	PUNCT
ejpam-3609	84	1	n	n	PRON
ejpam-3609	84	2	-times	-time	NOUN
ejpam-3609	84	3	fα	fα	NOUN
ejpam-3609	84	4	-	-	PUNCT
ejpam-3609	84	5	integration	integration	NOUN
ejpam-3609	84	6	of	of	ADP
ejpam-3609	84	7	characteristic	characteristic	ADJ
ejpam-3609	84	8	function	function	NOUN
ejpam-3609	84	9	give	give	VERB
ejpam-3609	84	10	the	the	DET
ejpam-3609	84	11	following	follow	VERB
ejpam-3609	84	12	formula	formula	NOUN
ejpam-3609	84	13	(	(	PUNCT
ejpam-3609	84	14	n	n	CCONJ
ejpam-3609	84	15	−	−	PROPN
ejpam-3609	84	16	times	time	NOUN
ejpam-3609	84	17	integration	integration	NOUN
ejpam-3609	84	18	)	)	PUNCT
ejpam-3609	84	19	∫	∫	PROPN
ejpam-3609	84	20	x́	x́	PROPN
ejpam-3609	85	1	a	a	DET
ejpam-3609	85	2	dαf	dαf	NOUN
ejpam-3609	85	3	x́	x́	PROPN
ejpam-3609	85	4	...	...	PUNCT
ejpam-3609	86	1	∫	∫	PROPN
ejpam-3609	86	2	x́	x́	PROPN
ejpam-3609	87	1	a	a	DET
ejpam-3609	87	2	χf	χf	PROPN
ejpam-3609	87	3	(	(	PUNCT
ejpam-3609	87	4	x	x	NOUN
ejpam-3609	87	5	)	)	PUNCT
ejpam-3609	87	6	dαfx	dαfx	NOUN
ejpam-3609	87	7	=	=	PUNCT
ejpam-3609	88	1	[	[	X
ejpam-3609	88	2	sαf	sαf	NOUN
ejpam-3609	88	3	(	(	PUNCT
ejpam-3609	88	4	x́)]n	x́)]n	PROPN
ejpam-3609	88	5	n	n	PROPN
ejpam-3609	88	6	.	.	PUNCT
ejpam-3609	89	1	fα	fα	NOUN
ejpam-3609	89	2	-	-	PUNCT
ejpam-3609	89	3	integration	integration	NOUN
ejpam-3609	89	4	for	for	ADP
ejpam-3609	89	5	product	product	NOUN
ejpam-3609	89	6	of	of	ADP
ejpam-3609	89	7	sαf	sαf	NOUN
ejpam-3609	89	8	and	and	CCONJ
ejpam-3609	89	9	χf	χf	VERB
ejpam-3609	89	10	let	let	VERB
ejpam-3609	89	11	f	f	PROPN
ejpam-3609	89	12	=	=	PROPN
ejpam-3609	89	13	c1	c1	PROPN
ejpam-3609	89	14	and	and	CCONJ
ejpam-3609	89	15	α	α	NOUN
ejpam-3609	89	16	=	=	SYM
ejpam-3609	89	17	ln	ln	PROPN
ejpam-3609	89	18	2	2	NUM
ejpam-3609	89	19	ln	ln	NOUN
ejpam-3609	89	20	3	3	NUM
ejpam-3609	89	21	=	=	SYM
ejpam-3609	89	22	0.63	0.63	NUM
ejpam-3609	89	23	,	,	PUNCT
ejpam-3609	89	24	namely	namely	ADV
ejpam-3609	89	25	cantor	cantor	NOUN
ejpam-3609	89	26	set	set	NOUN
ejpam-3609	89	27	in	in	ADP
ejpam-3609	89	28	the	the	DET
ejpam-3609	89	29	first	first	ADJ
ejpam-3609	89	30	iteration	iteration	NOUN
ejpam-3609	89	31	,	,	PUNCT
ejpam-3609	89	32	we	we	PRON
ejpam-3609	89	33	calculate	calculate	VERB
ejpam-3609	89	34	the	the	DET
ejpam-3609	89	35	following	follow	VERB
ejpam-3609	89	36	integral	integral	ADJ
ejpam-3609	89	37	:	:	PUNCT
ejpam-3609	89	38	a.	a.	NOUN
ejpam-3609	89	39	pishkoo	pishkoo	NOUN
ejpam-3609	89	40	et	et	PROPN
ejpam-3609	89	41	al	al	PROPN
ejpam-3609	89	42	.	.	PUNCT
ejpam-3609	89	43	/	/	SYM
ejpam-3609	89	44	eur	eur	PROPN
ejpam-3609	89	45	.	.	PUNCT
ejpam-3609	90	1	j.	j.	PROPN
ejpam-3609	90	2	pure	pure	PROPN
ejpam-3609	90	3	appl	appl	PROPN
ejpam-3609	90	4	.	.	PROPN
ejpam-3609	90	5	math	math	PROPN
ejpam-3609	90	6	,	,	PUNCT
ejpam-3609	90	7	13	13	NUM
ejpam-3609	90	8	(	(	PUNCT
ejpam-3609	90	9	1	1	NUM
ejpam-3609	90	10	)	)	PUNCT
ejpam-3609	90	11	(	(	PUNCT
ejpam-3609	90	12	2020	2020	NUM
ejpam-3609	90	13	)	)	PUNCT
ejpam-3609	90	14	,	,	PUNCT
ejpam-3609	90	15	19	19	NUM
ejpam-3609	90	16	-	-	SYM
ejpam-3609	90	17	32	32	NUM
ejpam-3609	90	18	23	23	NUM
ejpam-3609	90	19	figure	figure	NOUN
ejpam-3609	90	20	3	3	NUM
ejpam-3609	90	21	:	:	PUNCT
ejpam-3609	90	22	comparing	compare	VERB
ejpam-3609	90	23	an	an	DET
ejpam-3609	90	24	integral	integral	ADJ
ejpam-3609	90	25	of	of	ADP
ejpam-3609	90	26	functions	function	NOUN
ejpam-3609	90	27	g(x	g(x	NOUN
ejpam-3609	90	28	)	)	PUNCT
ejpam-3609	91	1	=	=	SYM
ejpam-3609	91	2	x2	x2	PROPN
ejpam-3609	91	3	and	and	CCONJ
ejpam-3609	91	4	f(x	f(x	PROPN
ejpam-3609	91	5	)	)	PUNCT
ejpam-3609	92	1	=	=	PRON
ejpam-3609	92	2	(	(	PUNCT
ejpam-3609	92	3	sαc(x))2	sαc(x))2	NOUN
ejpam-3609	92	4	in	in	ADP
ejpam-3609	92	5	r	r	NOUN
ejpam-3609	92	6	and	and	CCONJ
ejpam-3609	92	7	fα	fα	NOUN
ejpam-3609	92	8	-	-	PUNCT
ejpam-3609	92	9	space	space	NOUN
ejpam-3609	92	10	,	,	PUNCT
ejpam-3609	92	11	respectively	respectively	ADV
ejpam-3609	92	12	on	on	ADP
ejpam-3609	92	13	the	the	DET
ejpam-3609	92	14	interval	interval	NOUN
ejpam-3609	92	15	[	[	X
ejpam-3609	92	16	0,1	0,1	NUM
ejpam-3609	92	17	]	]	PUNCT
ejpam-3609	92	18	∫	∫	PROPN
ejpam-3609	92	19	1	1	NUM
ejpam-3609	92	20	0	0	NUM
ejpam-3609	92	21	sαc1	sαc1	NOUN
ejpam-3609	92	22	(	(	PUNCT
ejpam-3609	92	23	x)χc1(x	x)χc1(x	PROPN
ejpam-3609	92	24	)	)	PUNCT
ejpam-3609	92	25	dαc1	dαc1	NOUN
ejpam-3609	92	26	x	x	X
ejpam-3609	93	1	=	=	SYM
ejpam-3609	93	2	∫	∫	PROPN
ejpam-3609	93	3	1	1	NUM
ejpam-3609	93	4	3	3	NUM
ejpam-3609	93	5	0	0	NUM
ejpam-3609	93	6	sαc1	sαc1	NOUN
ejpam-3609	93	7	(	(	PUNCT
ejpam-3609	93	8	x	x	NOUN
ejpam-3609	93	9	)	)	PUNCT
ejpam-3609	93	10	dαc1	dαc1	ADJ
ejpam-3609	93	11	x+	x+	X
ejpam-3609	93	12	0	0	PUNCT
ejpam-3609	94	1	+	+	NUM
ejpam-3609	94	2	∫	∫	PROPN
ejpam-3609	94	3	1	1	NUM
ejpam-3609	94	4	2	2	NUM
ejpam-3609	94	5	3	3	NUM
ejpam-3609	94	6	sαc1	sαc1	NOUN
ejpam-3609	94	7	(	(	PUNCT
ejpam-3609	94	8	x	x	NOUN
ejpam-3609	94	9	)	)	PUNCT
ejpam-3609	94	10	dαc1	dαc1	NOUN
ejpam-3609	94	11	x	x	X
ejpam-3609	95	1	=	=	SYM
ejpam-3609	95	2	∫	∫	PROPN
ejpam-3609	95	3	1	1	NUM
ejpam-3609	95	4	0	0	NUM
ejpam-3609	95	5	sαc1	sαc1	NOUN
ejpam-3609	95	6	(	(	PUNCT
ejpam-3609	95	7	x	x	NOUN
ejpam-3609	95	8	)	)	PUNCT
ejpam-3609	95	9	dαc1	dαc1	NOUN
ejpam-3609	95	10	x	x	X
ejpam-3609	96	1	=	=	PUNCT
ejpam-3609	97	1	[	[	X
ejpam-3609	97	2	sαc1	sαc1	NOUN
ejpam-3609	97	3	(	(	PUNCT
ejpam-3609	97	4	1)]2	1)]2	NUM
ejpam-3609	97	5	2	2	NUM
ejpam-3609	97	6	−	−	NOUN
ejpam-3609	98	1	[	[	X
ejpam-3609	98	2	sαc1	sαc1	NOUN
ejpam-3609	98	3	(	(	PUNCT
ejpam-3609	98	4	0)]2	0)]2	NOUN
ejpam-3609	98	5	2	2	NUM
ejpam-3609	98	6	=	=	SYM
ejpam-3609	98	7	1	1	NUM
ejpam-3609	98	8	2	2	NUM
ejpam-3609	98	9	−	−	NOUN
ejpam-3609	98	10	0	0	NUM
ejpam-3609	98	11	,	,	PUNCT
ejpam-3609	98	12	in	in	ADP
ejpam-3609	98	13	which	which	PRON
ejpam-3609	98	14	we	we	PRON
ejpam-3609	98	15	have	have	AUX
ejpam-3609	98	16	used	use	VERB
ejpam-3609	98	17	sαc1	sαc1	NOUN
ejpam-3609	98	18	(	(	PUNCT
ejpam-3609	98	19	1	1	NUM
ejpam-3609	98	20	3	3	NUM
ejpam-3609	98	21	)	)	PUNCT
ejpam-3609	98	22	=	=	VERB
ejpam-3609	98	23	sαc1	sαc1	NOUN
ejpam-3609	98	24	(	(	PUNCT
ejpam-3609	98	25	2	2	NUM
ejpam-3609	98	26	3	3	NUM
ejpam-3609	98	27	)	)	PUNCT
ejpam-3609	98	28	.	.	PUNCT
ejpam-3609	99	1	let	let	VERB
ejpam-3609	99	2	f	f	NOUN
ejpam-3609	99	3	=	=	PROPN
ejpam-3609	99	4	c2	c2	PROPN
ejpam-3609	99	5	then	then	ADV
ejpam-3609	99	6	the	the	DET
ejpam-3609	99	7	integral	integral	ADJ
ejpam-3609	99	8	will	will	AUX
ejpam-3609	99	9	be∫	be∫	PROPN
ejpam-3609	99	10	1	1	NUM
ejpam-3609	99	11	0	0	NUM
ejpam-3609	99	12	sαc2	sαc2	PROPN
ejpam-3609	99	13	(	(	PUNCT
ejpam-3609	99	14	x)χc2(x	x)χc2(x	PROPN
ejpam-3609	99	15	)	)	PUNCT
ejpam-3609	99	16	dαc2	dαc2	PROPN
ejpam-3609	99	17	x	x	PUNCT
ejpam-3609	100	1	=	=	PUNCT
ejpam-3609	100	2	∫	∫	PROPN
ejpam-3609	100	3	1	1	NUM
ejpam-3609	100	4	9	9	NUM
ejpam-3609	100	5	0	0	NUM
ejpam-3609	100	6	sαc2	sαc2	PROPN
ejpam-3609	100	7	(	(	PUNCT
ejpam-3609	100	8	x	x	NOUN
ejpam-3609	100	9	)	)	PUNCT
ejpam-3609	100	10	dαc2	dαc2	PROPN
ejpam-3609	100	11	x+	x+	X
ejpam-3609	100	12	0	0	PUNCT
ejpam-3609	101	1	+	+	NUM
ejpam-3609	101	2	∫	∫	PROPN
ejpam-3609	101	3	1	1	NUM
ejpam-3609	101	4	3	3	NUM
ejpam-3609	101	5	2	2	NUM
ejpam-3609	101	6	9	9	NUM
ejpam-3609	101	7	sαc2	sαc2	NOUN
ejpam-3609	101	8	(	(	PUNCT
ejpam-3609	101	9	x	x	NOUN
ejpam-3609	101	10	)	)	PUNCT
ejpam-3609	101	11	dαc2	dαc2	PROPN
ejpam-3609	101	12	x+	x+	X
ejpam-3609	101	13	0	0	PUNCT
ejpam-3609	102	1	+	+	CCONJ
ejpam-3609	102	2	∫	∫	PROPN
ejpam-3609	102	3	7	7	NUM
ejpam-3609	102	4	9	9	NUM
ejpam-3609	102	5	6	6	NUM
ejpam-3609	102	6	9	9	NUM
ejpam-3609	102	7	sαc2	sαc2	NOUN
ejpam-3609	102	8	(	(	PUNCT
ejpam-3609	102	9	x	x	NOUN
ejpam-3609	102	10	)	)	PUNCT
ejpam-3609	102	11	dαc2	dαc2	PROPN
ejpam-3609	102	12	x+	x+	X
ejpam-3609	102	13	0	0	PUNCT
ejpam-3609	103	1	+	+	NUM
ejpam-3609	103	2	∫	∫	PROPN
ejpam-3609	103	3	9	9	NUM
ejpam-3609	103	4	9	9	NUM
ejpam-3609	103	5	8	8	NUM
ejpam-3609	103	6	9	9	NUM
ejpam-3609	103	7	sαc2	sαc2	NOUN
ejpam-3609	103	8	(	(	PUNCT
ejpam-3609	103	9	x	x	NOUN
ejpam-3609	103	10	)	)	PUNCT
ejpam-3609	103	11	dαc2	dαc2	PROPN
ejpam-3609	103	12	x	x	PUNCT
ejpam-3609	104	1	=	=	PUNCT
ejpam-3609	104	2	∫	∫	PROPN
ejpam-3609	104	3	1	1	NUM
ejpam-3609	104	4	0	0	NUM
ejpam-3609	104	5	sαc2	sαc2	PROPN
ejpam-3609	104	6	(	(	PUNCT
ejpam-3609	104	7	x	x	NOUN
ejpam-3609	104	8	)	)	PUNCT
ejpam-3609	104	9	dαc2	dαc2	PROPN
ejpam-3609	104	10	x	x	X
ejpam-3609	105	1	=	=	PUNCT
ejpam-3609	106	1	[	[	X
ejpam-3609	106	2	sαc2	sαc2	PROPN
ejpam-3609	106	3	(	(	PUNCT
ejpam-3609	106	4	1)]2	1)]2	NUM
ejpam-3609	106	5	2	2	NUM
ejpam-3609	106	6	−	−	PROPN
ejpam-3609	107	1	[	[	X
ejpam-3609	107	2	sαc2	sαc2	PROPN
ejpam-3609	107	3	(	(	PUNCT
ejpam-3609	107	4	0)]2	0)]2	NOUN
ejpam-3609	107	5	2	2	NUM
ejpam-3609	107	6	=	=	SYM
ejpam-3609	107	7	1	1	NUM
ejpam-3609	107	8	2	2	NUM
ejpam-3609	107	9	−	−	NOUN
ejpam-3609	107	10	0	0	NUM
ejpam-3609	107	11	,	,	PUNCT
ejpam-3609	107	12	in	in	ADP
ejpam-3609	107	13	which	which	PRON
ejpam-3609	107	14	we	we	PRON
ejpam-3609	107	15	have	have	AUX
ejpam-3609	107	16	used	use	VERB
ejpam-3609	107	17	sαc2	sαc2	PROPN
ejpam-3609	107	18	(	(	PUNCT
ejpam-3609	107	19	1	1	NUM
ejpam-3609	107	20	9	9	NUM
ejpam-3609	107	21	)	)	PUNCT
ejpam-3609	107	22	=	=	SYM
ejpam-3609	108	1	sαc2	sαc2	PROPN
ejpam-3609	108	2	(	(	PUNCT
ejpam-3609	108	3	2	2	NUM
ejpam-3609	108	4	9	9	NUM
ejpam-3609	108	5	)	)	PUNCT
ejpam-3609	108	6	,	,	PUNCT
ejpam-3609	108	7	sαc2	sαc2	PROPN
ejpam-3609	108	8	(	(	PUNCT
ejpam-3609	108	9	1	1	NUM
ejpam-3609	108	10	3	3	NUM
ejpam-3609	108	11	)	)	PUNCT
ejpam-3609	108	12	=	=	SYM
ejpam-3609	108	13	sαc2	sαc2	PROPN
ejpam-3609	108	14	(	(	PUNCT
ejpam-3609	108	15	6	6	NUM
ejpam-3609	108	16	9	9	NUM
ejpam-3609	108	17	)	)	PUNCT
ejpam-3609	108	18	,	,	PUNCT
ejpam-3609	108	19	and	and	CCONJ
ejpam-3609	108	20	sαc2	sαc2	PROPN
ejpam-3609	108	21	(	(	PUNCT
ejpam-3609	108	22	7	7	NUM
ejpam-3609	108	23	9	9	NUM
ejpam-3609	108	24	)	)	PUNCT
ejpam-3609	108	25	=	=	SYM
ejpam-3609	108	26	sαc2	sαc2	PROPN
ejpam-3609	108	27	(	(	PUNCT
ejpam-3609	108	28	8	8	NUM
ejpam-3609	108	29	9	9	NUM
ejpam-3609	108	30	)	)	PUNCT
ejpam-3609	108	31	.	.	PUNCT
ejpam-3609	109	1	it	it	PRON
ejpam-3609	109	2	can	can	AUX
ejpam-3609	109	3	be	be	AUX
ejpam-3609	109	4	expected	expect	VERB
ejpam-3609	109	5	that	that	SCONJ
ejpam-3609	109	6	for	for	ADP
ejpam-3609	109	7	the	the	DET
ejpam-3609	109	8	nth	nth	ADJ
ejpam-3609	109	9	iteration	iteration	NOUN
ejpam-3609	109	10	we	we	PRON
ejpam-3609	109	11	have∫	have∫	VERB
ejpam-3609	109	12	1	1	NUM
ejpam-3609	109	13	0	0	NUM
ejpam-3609	109	14	sαcn(x)χcn(x	sαcn(x)χcn(x	NUM
ejpam-3609	109	15	)	)	PUNCT
ejpam-3609	109	16	dαcnx	dαcnx	NOUN
ejpam-3609	109	17	=	=	NOUN
ejpam-3609	109	18	1	1	NUM
ejpam-3609	109	19	2	2	NUM
ejpam-3609	109	20	.	.	PUNCT
ejpam-3609	110	1	(	(	PUNCT
ejpam-3609	110	2	3	3	X
ejpam-3609	110	3	)	)	PUNCT
ejpam-3609	110	4	a.	a.	NOUN
ejpam-3609	110	5	pishkoo	pishkoo	NOUN
ejpam-3609	110	6	et	et	PROPN
ejpam-3609	110	7	al	al	PROPN
ejpam-3609	110	8	.	.	PUNCT
ejpam-3609	110	9	/	/	SYM
ejpam-3609	110	10	eur	eur	PROPN
ejpam-3609	110	11	.	.	PUNCT
ejpam-3609	111	1	j.	j.	PROPN
ejpam-3609	111	2	pure	pure	PROPN
ejpam-3609	111	3	appl	appl	PROPN
ejpam-3609	111	4	.	.	PROPN
ejpam-3609	111	5	math	math	PROPN
ejpam-3609	111	6	,	,	PUNCT
ejpam-3609	111	7	13	13	NUM
ejpam-3609	111	8	(	(	PUNCT
ejpam-3609	111	9	1	1	NUM
ejpam-3609	111	10	)	)	PUNCT
ejpam-3609	111	11	(	(	PUNCT
ejpam-3609	111	12	2020	2020	NUM
ejpam-3609	111	13	)	)	PUNCT
ejpam-3609	111	14	,	,	PUNCT
ejpam-3609	111	15	19	19	NUM
ejpam-3609	111	16	-	-	SYM
ejpam-3609	111	17	32	32	NUM
ejpam-3609	111	18	24	24	NUM
ejpam-3609	111	19	electric	electric	ADJ
ejpam-3609	111	20	charge	charge	NOUN
ejpam-3609	111	21	distributed	distribute	VERB
ejpam-3609	111	22	on	on	ADP
ejpam-3609	111	23	cantor	cantor	PROPN
ejpam-3609	111	24	set	set	PROPN
ejpam-3609	111	25	and	and	CCONJ
ejpam-3609	111	26	electric	electric	ADJ
ejpam-3609	111	27	potential	potential	NOUN
ejpam-3609	111	28	let	let	VERB
ejpam-3609	111	29	the	the	DET
ejpam-3609	111	30	electric	electric	ADJ
ejpam-3609	111	31	charge	charge	NOUN
ejpam-3609	111	32	q	q	PUNCT
ejpam-3609	111	33	is	be	AUX
ejpam-3609	111	34	uniformly	uniformly	ADV
ejpam-3609	111	35	distributed	distribute	VERB
ejpam-3609	111	36	over	over	ADP
ejpam-3609	111	37	the	the	DET
ejpam-3609	111	38	cantor	cantor	NOUN
ejpam-3609	111	39	set	set	NOUN
ejpam-3609	111	40	.	.	PUNCT
ejpam-3609	112	1	at	at	ADP
ejpam-3609	112	2	each	each	DET
ejpam-3609	112	3	stage	stage	NOUN
ejpam-3609	112	4	of	of	ADP
ejpam-3609	112	5	process	process	NOUN
ejpam-3609	112	6	of	of	ADP
ejpam-3609	112	7	iteration	iteration	NOUN
ejpam-3609	112	8	:	:	PUNCT
ejpam-3609	112	9	zero	zero	NUM
ejpam-3609	112	10	iteration	iteration	NOUN
ejpam-3609	112	11	,	,	PUNCT
ejpam-3609	112	12	first	first	ADJ
ejpam-3609	112	13	iteration	iteration	NOUN
ejpam-3609	112	14	,	,	PUNCT
ejpam-3609	112	15	second	second	ADJ
ejpam-3609	112	16	iteration	iteration	NOUN
ejpam-3609	112	17	etc	etc	X
ejpam-3609	112	18	.	.	PUNCT
ejpam-3609	113	1	the	the	DET
ejpam-3609	113	2	electric	electric	ADJ
ejpam-3609	113	3	charge	charge	NOUN
ejpam-3609	113	4	density	density	NOUN
ejpam-3609	113	5	increases	increase	VERB
ejpam-3609	113	6	with	with	ADP
ejpam-3609	113	7	the	the	DET
ejpam-3609	113	8	certain	certain	ADJ
ejpam-3609	113	9	ratio	ratio	NOUN
ejpam-3609	113	10	,	,	PUNCT
ejpam-3609	113	11	respectively	respectively	ADV
ejpam-3609	113	12	(	(	PUNCT
ejpam-3609	113	13	see	see	VERB
ejpam-3609	113	14	fig	fig	NOUN
ejpam-3609	113	15	.	.	PUNCT
ejpam-3609	114	1	4	4	NUM
ejpam-3609	114	2	)	)	PUNCT
ejpam-3609	114	3	.	.	PUNCT
ejpam-3609	115	1	since	since	SCONJ
ejpam-3609	115	2	the	the	DET
ejpam-3609	115	3	charge	charge	NOUN
ejpam-3609	115	4	distribution	distribution	NOUN
ejpam-3609	115	5	is	be	AUX
ejpam-3609	115	6	discrete	discrete	ADJ
ejpam-3609	115	7	,	,	PUNCT
ejpam-3609	115	8	the	the	DET
ejpam-3609	115	9	characteristic	characteristic	ADJ
ejpam-3609	115	10	function	function	NOUN
ejpam-3609	115	11	χc(x	χc(x	PUNCT
ejpam-3609	115	12	)	)	PUNCT
ejpam-3609	115	13	can	can	AUX
ejpam-3609	115	14	be	be	AUX
ejpam-3609	115	15	used	use	VERB
ejpam-3609	115	16	to	to	PART
ejpam-3609	115	17	figure	figure	VERB
ejpam-3609	115	18	4	4	NUM
ejpam-3609	115	19	:	:	PUNCT
ejpam-3609	115	20	distributed	distribute	VERB
ejpam-3609	115	21	charge	charge	NOUN
ejpam-3609	115	22	q	q	PROPN
ejpam-3609	115	23	on	on	ADP
ejpam-3609	115	24	cantor	cantor	PROPN
ejpam-3609	115	25	set	set	NOUN
ejpam-3609	115	26	describe	describe	VERB
ejpam-3609	115	27	it	it	PRON
ejpam-3609	115	28	as	as	ADP
ejpam-3609	115	29	charge	charge	NOUN
ejpam-3609	115	30	density	density	NOUN
ejpam-3609	115	31	function	function	NOUN
ejpam-3609	115	32	.	.	PUNCT
ejpam-3609	116	1	at	at	ADP
ejpam-3609	116	2	first	first	ADV
ejpam-3609	116	3	,	,	PUNCT
ejpam-3609	116	4	assume	assume	VERB
ejpam-3609	116	5	that	that	SCONJ
ejpam-3609	116	6	the	the	DET
ejpam-3609	116	7	unit	unit	NOUN
ejpam-3609	116	8	charge	charge	NOUN
ejpam-3609	116	9	(	(	PUNCT
ejpam-3609	116	10	qtotal	qtotal	ADJ
ejpam-3609	116	11	=	=	SYM
ejpam-3609	116	12	1	1	NUM
ejpam-3609	116	13	)	)	PUNCT
ejpam-3609	116	14	is	be	AUX
ejpam-3609	116	15	uniformly	uniformly	ADV
ejpam-3609	116	16	distributed	distribute	VERB
ejpam-3609	116	17	over	over	ADP
ejpam-3609	116	18	the	the	DET
ejpam-3609	116	19	set	set	NOUN
ejpam-3609	116	20	c0	c0	NOUN
ejpam-3609	116	21	=	=	PUNCT
ejpam-3609	117	1	[	[	X
ejpam-3609	117	2	0	0	NUM
ejpam-3609	117	3	,	,	PUNCT
ejpam-3609	117	4	1	1	NUM
ejpam-3609	117	5	]	]	PUNCT
ejpam-3609	117	6	while	while	SCONJ
ejpam-3609	117	7	χc0(x	χc0(x	PROPN
ejpam-3609	117	8	)	)	PUNCT
ejpam-3609	117	9	=	=	PUNCT
ejpam-3609	117	10	1	1	NUM
ejpam-3609	117	11	for	for	ADP
ejpam-3609	117	12	all	all	DET
ejpam-3609	117	13	values	value	NOUN
ejpam-3609	117	14	of	of	ADP
ejpam-3609	117	15	x	x	X
ejpam-3609	117	16	∈	∈	PROPN
ejpam-3609	117	17	[	[	X
ejpam-3609	117	18	0	0	NUM
ejpam-3609	117	19	,	,	PUNCT
ejpam-3609	117	20	1	1	NUM
ejpam-3609	117	21	]	]	PUNCT
ejpam-3609	117	22	.	.	PUNCT
ejpam-3609	118	1	now	now	ADV
ejpam-3609	118	2	we	we	PRON
ejpam-3609	118	3	obtain	obtain	VERB
ejpam-3609	118	4	the	the	DET
ejpam-3609	118	5	constant	constant	ADJ
ejpam-3609	118	6	k.	k.	NOUN
ejpam-3609	118	7	q	q	PUNCT
ejpam-3609	119	1	=	=	PUNCT
ejpam-3609	119	2	∫	∫	PROPN
ejpam-3609	119	3	b=1	b=1	PROPN
ejpam-3609	119	4	a=0	a=0	PROPN
ejpam-3609	119	5	χc0(x	χc0(x	PROPN
ejpam-3609	119	6	)	)	PUNCT
ejpam-3609	119	7	dαc0	dαc0	NOUN
ejpam-3609	119	8	x	x	X
ejpam-3609	119	9	=	=	SYM
ejpam-3609	119	10	k[sαc0	k[sαc0	PROPN
ejpam-3609	119	11	(	(	PUNCT
ejpam-3609	119	12	1)−	1)−	PROPN
ejpam-3609	119	13	sαc0	sαc0	PROPN
ejpam-3609	119	14	(	(	PUNCT
ejpam-3609	119	15	0	0	NUM
ejpam-3609	119	16	)	)	PUNCT
ejpam-3609	119	17	]	]	PUNCT
ejpam-3609	119	18	.	.	PUNCT
ejpam-3609	120	1	(	(	PUNCT
ejpam-3609	120	2	4	4	NUM
ejpam-3609	120	3	)	)	PUNCT
ejpam-3609	120	4	so	so	ADV
ejpam-3609	120	5	k	k	X
ejpam-3609	121	1	=	=	PUNCT
ejpam-3609	121	2	1	1	X
ejpam-3609	121	3	.	.	PUNCT
ejpam-3609	122	1	if	if	SCONJ
ejpam-3609	122	2	0	0	NUM
ejpam-3609	122	3	<	<	X
ejpam-3609	122	4	a	a	DET
ejpam-3609	122	5	<	<	X
ejpam-3609	122	6	b	b	X
ejpam-3609	122	7	<	<	X
ejpam-3609	122	8	1	1	NUM
ejpam-3609	122	9	then	then	ADV
ejpam-3609	122	10	q	q	X
ejpam-3609	122	11	6=	6=	ADV
ejpam-3609	122	12	qtot	qtot	ADJ
ejpam-3609	122	13	and	and	CCONJ
ejpam-3609	122	14	for	for	ADP
ejpam-3609	122	15	it	it	PRON
ejpam-3609	122	16	we	we	PRON
ejpam-3609	122	17	have	have	AUX
ejpam-3609	122	18	(	(	PUNCT
ejpam-3609	122	19	see	see	VERB
ejpam-3609	122	20	fig	fig	NOUN
ejpam-3609	122	21	.	.	PUNCT
ejpam-3609	123	1	5	5	NUM
ejpam-3609	123	2	)	)	PUNCT
ejpam-3609	123	3	q	q	NOUN
ejpam-3609	123	4	=	=	NOUN
ejpam-3609	123	5	sαc0	sαc0	PROPN
ejpam-3609	123	6	(	(	PUNCT
ejpam-3609	123	7	b)−	b)−	PROPN
ejpam-3609	123	8	sαc0	sαc0	PROPN
ejpam-3609	123	9	(	(	PUNCT
ejpam-3609	123	10	a	a	NOUN
ejpam-3609	123	11	)	)	PUNCT
ejpam-3609	123	12	.	.	PUNCT
ejpam-3609	124	1	(	(	PUNCT
ejpam-3609	124	2	5	5	X
ejpam-3609	124	3	)	)	PUNCT
ejpam-3609	124	4	example1	example1	AUX
ejpam-3609	124	5	let	let	VERB
ejpam-3609	124	6	a	a	DET
ejpam-3609	124	7	=	=	SYM
ejpam-3609	124	8	0.2	0.2	NUM
ejpam-3609	124	9	and	and	CCONJ
ejpam-3609	124	10	b	b	X
ejpam-3609	125	1	=	=	NOUN
ejpam-3609	125	2	0.7	0.7	NUM
ejpam-3609	125	3	then	then	ADV
ejpam-3609	125	4	the	the	DET
ejpam-3609	125	5	charge	charge	NOUN
ejpam-3609	125	6	q	q	NOUN
ejpam-3609	125	7	in	in	ADP
ejpam-3609	125	8	the	the	DET
ejpam-3609	125	9	interval	interval	NOUN
ejpam-3609	125	10	[	[	X
ejpam-3609	125	11	a	a	X
ejpam-3609	125	12	,	,	PUNCT
ejpam-3609	125	13	b	b	X
ejpam-3609	125	14	]	]	X
ejpam-3609	125	15	is	be	AUX
ejpam-3609	125	16	q	q	NOUN
ejpam-3609	125	17	=	=	PUNCT
ejpam-3609	125	18	0.7−	0.7−	NOUN
ejpam-3609	125	19	0.2	0.2	NUM
ejpam-3609	125	20	=	=	SYM
ejpam-3609	125	21	0.5	0.5	NUM
ejpam-3609	125	22	(	(	PUNCT
ejpam-3609	125	23	coulomb	coulomb	NOUN
ejpam-3609	125	24	)	)	PUNCT
ejpam-3609	125	25	.	.	PUNCT
ejpam-3609	126	1	now	now	ADV
ejpam-3609	126	2	suppose	suppose	VERB
ejpam-3609	126	3	the	the	DET
ejpam-3609	126	4	charge	charge	NOUN
ejpam-3609	126	5	is	be	AUX
ejpam-3609	126	6	uniformly	uniformly	ADV
ejpam-3609	126	7	distributed	distribute	VERB
ejpam-3609	126	8	on	on	ADP
ejpam-3609	126	9	c1	c1	PROPN
ejpam-3609	126	10	=	=	PUNCT
ejpam-3609	127	1	[	[	X
ejpam-3609	127	2	0	0	NUM
ejpam-3609	127	3	,	,	PUNCT
ejpam-3609	127	4	1	1	NUM
ejpam-3609	127	5	3	3	NUM
ejpam-3609	127	6	]	]	PUNCT
ejpam-3609	127	7	∪	∪	ADP
ejpam-3609	127	8	[	[	PUNCT
ejpam-3609	127	9	2	2	NUM
ejpam-3609	127	10	3	3	NUM
ejpam-3609	127	11	,	,	PUNCT
ejpam-3609	127	12	1	1	NUM
ejpam-3609	127	13	]	]	PUNCT
ejpam-3609	127	14	(	(	PUNCT
ejpam-3609	127	15	fig	fig	NOUN
ejpam-3609	127	16	.	.	PUNCT
ejpam-3609	128	1	6	6	NUM
ejpam-3609	128	2	)	)	PUNCT
ejpam-3609	128	3	.	.	PUNCT
ejpam-3609	129	1	while	while	SCONJ
ejpam-3609	129	2	χc1(x	χc1(x	NUM
ejpam-3609	129	3	)	)	PUNCT
ejpam-3609	130	1	=	=	SYM
ejpam-3609	130	2	1	1	NUM
ejpam-3609	130	3	for	for	ADP
ejpam-3609	130	4	x	x	PROPN
ejpam-3609	130	5	∈	∈	PROPN
ejpam-3609	130	6	c1	c1	NOUN
ejpam-3609	130	7	and	and	CCONJ
ejpam-3609	130	8	otherwise	otherwise	ADV
ejpam-3609	130	9	χc1(x	χc1(x	NUM
ejpam-3609	130	10	)	)	PUNCT
ejpam-3609	130	11	=	=	SYM
ejpam-3609	130	12	0	0	PUNCT
ejpam-3609	131	1	(	(	PUNCT
ejpam-3609	131	2	see	see	VERB
ejpam-3609	131	3	fig	fig	NOUN
ejpam-3609	131	4	.	.	PUNCT
ejpam-3609	132	1	7	7	NUM
ejpam-3609	132	2	)	)	PUNCT
ejpam-3609	132	3	.	.	PUNCT
ejpam-3609	133	1	example2	example2	PROPN
ejpam-3609	133	2	let	let	VERB
ejpam-3609	133	3	a	a	DET
ejpam-3609	133	4	=	=	NOUN
ejpam-3609	133	5	0.25	0.25	NUM
ejpam-3609	133	6	and	and	CCONJ
ejpam-3609	133	7	b	b	X
ejpam-3609	133	8	=	=	SYM
ejpam-3609	133	9	0.6	0.6	NUM
ejpam-3609	133	10	then	then	ADV
ejpam-3609	133	11	the	the	DET
ejpam-3609	133	12	charge	charge	NOUN
ejpam-3609	133	13	q	q	NOUN
ejpam-3609	133	14	in	in	ADP
ejpam-3609	133	15	the	the	DET
ejpam-3609	133	16	interval	interval	NOUN
ejpam-3609	133	17	[	[	X
ejpam-3609	133	18	a	a	X
ejpam-3609	133	19	,	,	PUNCT
ejpam-3609	133	20	b	b	X
ejpam-3609	133	21	]	]	X
ejpam-3609	133	22	is	be	AUX
ejpam-3609	133	23	q	q	NOUN
ejpam-3609	133	24	=	=	ADJ
ejpam-3609	133	25	sαc1	sαc1	NOUN
ejpam-3609	133	26	(	(	PUNCT
ejpam-3609	133	27	0.6)−	0.6)−	NUM
ejpam-3609	133	28	sαc1	sαc1	NOUN
ejpam-3609	133	29	(	(	PUNCT
ejpam-3609	133	30	0.25	0.25	NUM
ejpam-3609	133	31	)	)	PUNCT
ejpam-3609	133	32	=	=	PUNCT
ejpam-3609	134	1	0.5−	0.5−	NUM
ejpam-3609	134	2	0.375	0.375	NUM
ejpam-3609	134	3	=	=	SYM
ejpam-3609	134	4	0.125	0.125	NUM
ejpam-3609	134	5	(	(	PUNCT
ejpam-3609	134	6	coulomb	coulomb	NOUN
ejpam-3609	134	7	)	)	PUNCT
ejpam-3609	134	8	.	.	PUNCT
ejpam-3609	135	1	then	then	ADV
ejpam-3609	135	2	,	,	PUNCT
ejpam-3609	135	3	this	this	DET
ejpam-3609	135	4	time	time	NOUN
ejpam-3609	135	5	suppose	suppose	VERB
ejpam-3609	135	6	the	the	DET
ejpam-3609	135	7	charge	charge	NOUN
ejpam-3609	135	8	is	be	AUX
ejpam-3609	135	9	uniformly	uniformly	ADV
ejpam-3609	135	10	distributed	distribute	VERB
ejpam-3609	135	11	on	on	ADP
ejpam-3609	135	12	c2	c2	PROPN
ejpam-3609	135	13	=	=	PUNCT
ejpam-3609	136	1	[	[	X
ejpam-3609	136	2	0	0	NUM
ejpam-3609	136	3	,	,	PUNCT
ejpam-3609	136	4	1	1	NUM
ejpam-3609	136	5	9	9	NUM
ejpam-3609	136	6	]	]	PUNCT
ejpam-3609	136	7	∪	∪	X
ejpam-3609	136	8	[	[	PUNCT
ejpam-3609	136	9	2	2	NUM
ejpam-3609	136	10	9	9	NUM
ejpam-3609	136	11	,	,	PUNCT
ejpam-3609	136	12	3	3	NUM
ejpam-3609	136	13	9	9	NUM
ejpam-3609	136	14	]	]	PUNCT
ejpam-3609	136	15	∪	∪	X
ejpam-3609	136	16	[	[	PUNCT
ejpam-3609	136	17	6	6	NUM
ejpam-3609	136	18	9	9	NUM
ejpam-3609	136	19	,	,	PUNCT
ejpam-3609	136	20	7	7	NUM
ejpam-3609	136	21	9	9	NUM
ejpam-3609	136	22	]	]	PUNCT
ejpam-3609	136	23	∪	∪	X
ejpam-3609	136	24	[	[	X
ejpam-3609	136	25	8	8	NUM
ejpam-3609	136	26	9	9	NUM
ejpam-3609	136	27	,	,	PUNCT
ejpam-3609	136	28	1	1	NUM
ejpam-3609	136	29	]	]	PUNCT
ejpam-3609	136	30	,	,	PUNCT
ejpam-3609	136	31	while	while	SCONJ
ejpam-3609	136	32	χc2(x	χc2(x	PROPN
ejpam-3609	136	33	)	)	PUNCT
ejpam-3609	136	34	=	=	SYM
ejpam-3609	136	35	1	1	NUM
ejpam-3609	136	36	for	for	ADP
ejpam-3609	136	37	x	x	PROPN
ejpam-3609	136	38	∈	∈	PROPN
ejpam-3609	136	39	c2	c2	PROPN
ejpam-3609	136	40	and	and	CCONJ
ejpam-3609	136	41	otherwise	otherwise	ADV
ejpam-3609	136	42	χc2(x	χc2(x	PROPN
ejpam-3609	136	43	)	)	PUNCT
ejpam-3609	136	44	=	=	SYM
ejpam-3609	136	45	0	0	PUNCT
ejpam-3609	136	46	(	(	PUNCT
ejpam-3609	136	47	see	see	VERB
ejpam-3609	136	48	fig	fig	NOUN
ejpam-3609	136	49	.	.	PUNCT
ejpam-3609	137	1	8)	8)	NUM
ejpam-3609	137	2	.	.	PUNCT
ejpam-3609	138	1	the	the	DET
ejpam-3609	138	2	amount	amount	NOUN
ejpam-3609	138	3	of	of	ADP
ejpam-3609	138	4	distributed	distribute	VERB
ejpam-3609	138	5	charge	charge	NOUN
ejpam-3609	138	6	from	from	ADP
ejpam-3609	138	7	0	0	NUM
ejpam-3609	138	8	to	to	PART
ejpam-3609	138	9	x	x	PRON
ejpam-3609	138	10	can	can	AUX
ejpam-3609	138	11	be	be	AUX
ejpam-3609	138	12	obtained	obtain	VERB
ejpam-3609	138	13	from	from	ADP
ejpam-3609	138	14	the	the	DET
ejpam-3609	138	15	graph	graph	NOUN
ejpam-3609	138	16	of	of	ADP
ejpam-3609	138	17	staircase	staircase	NOUN
ejpam-3609	138	18	a.	a.	NOUN
ejpam-3609	138	19	pishkoo	pishkoo	PROPN
ejpam-3609	138	20	et	et	PROPN
ejpam-3609	138	21	al	al	PROPN
ejpam-3609	138	22	.	.	PUNCT
ejpam-3609	138	23	/	/	SYM
ejpam-3609	138	24	eur	eur	PROPN
ejpam-3609	138	25	.	.	PUNCT
ejpam-3609	139	1	j.	j.	PROPN
ejpam-3609	139	2	pure	pure	PROPN
ejpam-3609	139	3	appl	appl	PROPN
ejpam-3609	139	4	.	.	PROPN
ejpam-3609	139	5	math	math	PROPN
ejpam-3609	139	6	,	,	PUNCT
ejpam-3609	139	7	13	13	NUM
ejpam-3609	139	8	(	(	PUNCT
ejpam-3609	139	9	1	1	NUM
ejpam-3609	139	10	)	)	PUNCT
ejpam-3609	139	11	(	(	PUNCT
ejpam-3609	139	12	2020	2020	NUM
ejpam-3609	139	13	)	)	PUNCT
ejpam-3609	139	14	,	,	PUNCT
ejpam-3609	139	15	19	19	NUM
ejpam-3609	139	16	-	-	SYM
ejpam-3609	139	17	32	32	NUM
ejpam-3609	139	18	25	25	NUM
ejpam-3609	139	19	figure	figure	NOUN
ejpam-3609	139	20	5	5	NUM
ejpam-3609	139	21	:	:	PUNCT
ejpam-3609	139	22	qtot	qtot	VERB
ejpam-3609	139	23	from	from	ADP
ejpam-3609	139	24	0	0	NUM
ejpam-3609	139	25	to	to	PART
ejpam-3609	139	26	x	x	PRON
ejpam-3609	139	27	at	at	ADP
ejpam-3609	139	28	continuous	continuous	ADJ
ejpam-3609	139	29	state	state	NOUN
ejpam-3609	139	30	(	(	PUNCT
ejpam-3609	139	31	zero	zero	NUM
ejpam-3609	139	32	iteration	iteration	NOUN
ejpam-3609	139	33	)	)	PUNCT
ejpam-3609	139	34	figure	figure	NOUN
ejpam-3609	139	35	6	6	NUM
ejpam-3609	139	36	:	:	PUNCT
ejpam-3609	139	37	qtot	qtot	ADJ
ejpam-3609	139	38	from	from	ADP
ejpam-3609	139	39	0	0	NUM
ejpam-3609	139	40	to	to	PART
ejpam-3609	139	41	x	x	PROPN
ejpam-3609	139	42	is	be	AUX
ejpam-3609	139	43	changed	change	VERB
ejpam-3609	139	44	as	as	ADP
ejpam-3609	139	45	staircase	staircase	NOUN
ejpam-3609	139	46	function	function	NOUN
ejpam-3609	139	47	(	(	PUNCT
ejpam-3609	139	48	at	at	ADP
ejpam-3609	139	49	first	first	ADJ
ejpam-3609	139	50	iteration	iteration	NOUN
ejpam-3609	139	51	)	)	PUNCT
ejpam-3609	139	52	function	function	NOUN
ejpam-3609	139	53	at	at	ADP
ejpam-3609	139	54	second	second	ADJ
ejpam-3609	139	55	iteration	iteration	NOUN
ejpam-3609	139	56	(	(	PUNCT
ejpam-3609	139	57	fig	fig	NOUN
ejpam-3609	139	58	.	.	PUNCT
ejpam-3609	140	1	9	9	NUM
ejpam-3609	140	2	)	)	PUNCT
ejpam-3609	140	3	.	.	PUNCT
ejpam-3609	141	1	example3	example3	PROPN
ejpam-3609	142	1	let	let	VERB
ejpam-3609	142	2	a	a	DET
ejpam-3609	142	3	=	=	SYM
ejpam-3609	142	4	0.32	0.32	NUM
ejpam-3609	142	5	and	and	CCONJ
ejpam-3609	142	6	b	b	X
ejpam-3609	142	7	=	=	SYM
ejpam-3609	142	8	5	5	NUM
ejpam-3609	142	9	6	6	NUM
ejpam-3609	142	10	then	then	ADV
ejpam-3609	142	11	the	the	DET
ejpam-3609	142	12	charge	charge	NOUN
ejpam-3609	142	13	q	q	NOUN
ejpam-3609	142	14	in	in	ADP
ejpam-3609	142	15	the	the	DET
ejpam-3609	142	16	interval	interval	NOUN
ejpam-3609	142	17	[	[	X
ejpam-3609	142	18	a	a	X
ejpam-3609	142	19	,	,	PUNCT
ejpam-3609	142	20	b	b	X
ejpam-3609	142	21	]	]	X
ejpam-3609	142	22	is	be	AUX
ejpam-3609	142	23	q	q	NOUN
ejpam-3609	142	24	=	=	PUNCT
ejpam-3609	142	25	sαc2	sαc2	PROPN
ejpam-3609	142	26	(	(	PUNCT
ejpam-3609	142	27	5	5	NUM
ejpam-3609	142	28	6	6	NUM
ejpam-3609	142	29	)	)	PUNCT
ejpam-3609	143	1	−	−	PROPN
ejpam-3609	144	1	sαc2	sαc2	PROPN
ejpam-3609	144	2	(	(	PUNCT
ejpam-3609	144	3	0.32	0.32	NUM
ejpam-3609	144	4	)	)	PUNCT
ejpam-3609	144	5	=	=	PUNCT
ejpam-3609	144	6	0.75−	0.75−	NOUN
ejpam-3609	144	7	0.475	0.475	NUM
ejpam-3609	144	8	=	=	SYM
ejpam-3609	144	9	0.28	0.28	NUM
ejpam-3609	144	10	(	(	PUNCT
ejpam-3609	144	11	coulomb	coulomb	NOUN
ejpam-3609	144	12	)	)	PUNCT
ejpam-3609	144	13	.	.	PUNCT
ejpam-3609	145	1	electric	electric	ADJ
ejpam-3609	145	2	charge	charge	NOUN
ejpam-3609	145	3	density	density	NOUN
ejpam-3609	145	4	for	for	ADP
ejpam-3609	145	5	cantor	cantor	PROPN
ejpam-3609	145	6	set	set	NOUN
ejpam-3609	145	7	charge	charge	NOUN
ejpam-3609	145	8	distribution	distribution	NOUN
ejpam-3609	145	9	in	in	ADP
ejpam-3609	145	10	this	this	DET
ejpam-3609	145	11	section	section	NOUN
ejpam-3609	145	12	the	the	DET
ejpam-3609	145	13	linear	linear	ADJ
ejpam-3609	145	14	charge	charge	NOUN
ejpam-3609	145	15	density	density	NOUN
ejpam-3609	145	16	in	in	ADP
ejpam-3609	145	17	the	the	DET
ejpam-3609	145	18	fractal	fractal	ADJ
ejpam-3609	145	19	space	space	NOUN
ejpam-3609	145	20	for	for	ADP
ejpam-3609	145	21	the	the	DET
ejpam-3609	145	22	cantor	cantor	PROPN
ejpam-3609	145	23	set	set	NOUN
ejpam-3609	145	24	is	be	AUX
ejpam-3609	145	25	obtained	obtain	VERB
ejpam-3609	145	26	.	.	PUNCT
ejpam-3609	146	1	in	in	ADP
ejpam-3609	146	2	the	the	DET
ejpam-3609	146	3	first	first	ADJ
ejpam-3609	146	4	iteration	iteration	NOUN
ejpam-3609	146	5	,	,	PUNCT
ejpam-3609	146	6	it	it	PRON
ejpam-3609	146	7	is	be	AUX
ejpam-3609	146	8	equal	equal	ADJ
ejpam-3609	146	9	to	to	ADP
ejpam-3609	146	10	λc1	λc1	VERB
ejpam-3609	146	11	=	=	SYM
ejpam-3609	146	12	q	q	PROPN
ejpam-3609	146	13	2	2	NUM
ejpam-3609	146	14	3	3	NUM
ejpam-3609	146	15	χc1(x	χc1(x	NOUN
ejpam-3609	146	16	)	)	PUNCT
ejpam-3609	147	1	=	=	SYM
ejpam-3609	147	2	3q	3q	NUM
ejpam-3609	147	3	2	2	NUM
ejpam-3609	147	4	χc1(x	χc1(x	NOUN
ejpam-3609	147	5	)	)	PUNCT
ejpam-3609	147	6	.	.	PUNCT
ejpam-3609	148	1	(	(	PUNCT
ejpam-3609	148	2	6	6	X
ejpam-3609	148	3	)	)	PUNCT
ejpam-3609	148	4	a.	a.	NOUN
ejpam-3609	148	5	pishkoo	pishkoo	NOUN
ejpam-3609	148	6	et	et	PROPN
ejpam-3609	148	7	al	al	PROPN
ejpam-3609	148	8	.	.	PUNCT
ejpam-3609	148	9	/	/	SYM
ejpam-3609	148	10	eur	eur	PROPN
ejpam-3609	148	11	.	.	PUNCT
ejpam-3609	149	1	j.	j.	PROPN
ejpam-3609	149	2	pure	pure	PROPN
ejpam-3609	149	3	appl	appl	PROPN
ejpam-3609	149	4	.	.	PROPN
ejpam-3609	149	5	math	math	PROPN
ejpam-3609	149	6	,	,	PUNCT
ejpam-3609	149	7	13	13	NUM
ejpam-3609	149	8	(	(	PUNCT
ejpam-3609	149	9	1	1	NUM
ejpam-3609	149	10	)	)	PUNCT
ejpam-3609	149	11	(	(	PUNCT
ejpam-3609	149	12	2020	2020	NUM
ejpam-3609	149	13	)	)	PUNCT
ejpam-3609	149	14	,	,	PUNCT
ejpam-3609	149	15	19	19	NUM
ejpam-3609	149	16	-	-	SYM
ejpam-3609	149	17	32	32	NUM
ejpam-3609	149	18	26	26	NUM
ejpam-3609	149	19	figure	figure	NOUN
ejpam-3609	149	20	7	7	NUM
ejpam-3609	149	21	:	:	PUNCT
ejpam-3609	149	22	density	density	NOUN
ejpam-3609	149	23	function	function	NOUN
ejpam-3609	149	24	λ	λ	PROPN
ejpam-3609	149	25	is	be	AUX
ejpam-3609	149	26	changed	change	VERB
ejpam-3609	149	27	as	as	ADP
ejpam-3609	149	28	characteristic	characteristic	ADJ
ejpam-3609	149	29	function	function	NOUN
ejpam-3609	149	30	(	(	PUNCT
ejpam-3609	149	31	at	at	ADP
ejpam-3609	149	32	first	first	ADJ
ejpam-3609	149	33	iteration	iteration	NOUN
ejpam-3609	149	34	)	)	PUNCT
ejpam-3609	149	35	figure	figure	NOUN
ejpam-3609	149	36	8	8	NUM
ejpam-3609	149	37	:	:	PUNCT
ejpam-3609	149	38	density	density	NOUN
ejpam-3609	149	39	function	function	NOUN
ejpam-3609	149	40	λ	λ	PROPN
ejpam-3609	149	41	is	be	AUX
ejpam-3609	149	42	changed	change	VERB
ejpam-3609	149	43	as	as	ADP
ejpam-3609	149	44	characteristic	characteristic	ADJ
ejpam-3609	149	45	function	function	NOUN
ejpam-3609	149	46	(	(	PUNCT
ejpam-3609	149	47	at	at	ADP
ejpam-3609	149	48	second	second	ADJ
ejpam-3609	149	49	iteration	iteration	NOUN
ejpam-3609	149	50	)	)	PUNCT
ejpam-3609	149	51	for	for	ADP
ejpam-3609	149	52	the	the	DET
ejpam-3609	149	53	second	second	ADJ
ejpam-3609	149	54	iteration	iteration	NOUN
ejpam-3609	149	55	we	we	PRON
ejpam-3609	149	56	have	have	VERB
ejpam-3609	149	57	λc2	λc2	NOUN
ejpam-3609	149	58	=	=	SYM
ejpam-3609	149	59	q	q	X
ejpam-3609	149	60	(	(	PUNCT
ejpam-3609	149	61	2	2	NUM
ejpam-3609	149	62	3)2	3)2	NUM
ejpam-3609	149	63	χc2(x	χc2(x	PROPN
ejpam-3609	149	64	)	)	PUNCT
ejpam-3609	149	65	=	=	PRON
ejpam-3609	150	1	(	(	PUNCT
ejpam-3609	150	2	3	3	NUM
ejpam-3609	150	3	2	2	NUM
ejpam-3609	150	4	)	)	PUNCT
ejpam-3609	150	5	2qχc2(x	2qχc2(x	NUM
ejpam-3609	150	6	)	)	PUNCT
ejpam-3609	150	7	.	.	PUNCT
ejpam-3609	151	1	(	(	PUNCT
ejpam-3609	151	2	7	7	X
ejpam-3609	151	3	)	)	PUNCT
ejpam-3609	151	4	finally	finally	ADV
ejpam-3609	151	5	at	at	ADP
ejpam-3609	151	6	nth	nth	PROPN
ejpam-3609	151	7	iteration	iteration	NOUN
ejpam-3609	151	8	we	we	PRON
ejpam-3609	151	9	obtain	obtain	VERB
ejpam-3609	151	10	(	(	PUNCT
ejpam-3609	151	11	fig	fig	NOUN
ejpam-3609	151	12	.	.	PUNCT
ejpam-3609	152	1	10	10	NUM
ejpam-3609	152	2	)	)	PUNCT
ejpam-3609	152	3	λcn	λcn	NOUN
ejpam-3609	153	1	=	=	SYM
ejpam-3609	153	2	q	q	X
ejpam-3609	153	3	(	(	PUNCT
ejpam-3609	153	4	2	2	NUM
ejpam-3609	153	5	3)n	3)n	NUM
ejpam-3609	153	6	χcn(x	χcn(x	PROPN
ejpam-3609	153	7	)	)	PUNCT
ejpam-3609	153	8	=	=	PUNCT
ejpam-3609	153	9	(	(	PUNCT
ejpam-3609	153	10	3	3	NUM
ejpam-3609	153	11	2	2	NUM
ejpam-3609	153	12	)	)	PUNCT
ejpam-3609	153	13	nqχcn(x	nqχcn(x	NUM
ejpam-3609	153	14	)	)	PUNCT
ejpam-3609	153	15	.	.	PUNCT
ejpam-3609	154	1	(	(	PUNCT
ejpam-3609	154	2	8)	8)	NUM
ejpam-3609	154	3	a.	a.	NOUN
ejpam-3609	154	4	pishkoo	pishkoo	NOUN
ejpam-3609	154	5	et	et	PROPN
ejpam-3609	154	6	al	al	PROPN
ejpam-3609	154	7	.	.	PUNCT
ejpam-3609	154	8	/	/	SYM
ejpam-3609	154	9	eur	eur	PROPN
ejpam-3609	154	10	.	.	PUNCT
ejpam-3609	155	1	j.	j.	PROPN
ejpam-3609	155	2	pure	pure	PROPN
ejpam-3609	155	3	appl	appl	PROPN
ejpam-3609	155	4	.	.	PROPN
ejpam-3609	155	5	math	math	PROPN
ejpam-3609	155	6	,	,	PUNCT
ejpam-3609	155	7	13	13	NUM
ejpam-3609	155	8	(	(	PUNCT
ejpam-3609	155	9	1	1	NUM
ejpam-3609	155	10	)	)	PUNCT
ejpam-3609	155	11	(	(	PUNCT
ejpam-3609	155	12	2020	2020	NUM
ejpam-3609	155	13	)	)	PUNCT
ejpam-3609	155	14	,	,	PUNCT
ejpam-3609	155	15	19	19	NUM
ejpam-3609	155	16	-	-	SYM
ejpam-3609	155	17	32	32	NUM
ejpam-3609	155	18	27	27	NUM
ejpam-3609	155	19	figure	figure	NOUN
ejpam-3609	155	20	9	9	NUM
ejpam-3609	155	21	:	:	PUNCT
ejpam-3609	155	22	qtot	qtot	VERB
ejpam-3609	155	23	from	from	ADP
ejpam-3609	155	24	0	0	NUM
ejpam-3609	155	25	to	to	PART
ejpam-3609	155	26	x	x	PROPN
ejpam-3609	155	27	is	be	AUX
ejpam-3609	155	28	changed	change	VERB
ejpam-3609	155	29	as	as	ADP
ejpam-3609	155	30	staircase	staircase	NOUN
ejpam-3609	155	31	function	function	NOUN
ejpam-3609	155	32	(	(	PUNCT
ejpam-3609	155	33	at	at	ADP
ejpam-3609	155	34	second	second	ADJ
ejpam-3609	155	35	iteration	iteration	NOUN
ejpam-3609	155	36	)	)	PUNCT
ejpam-3609	155	37	figure	figure	NOUN
ejpam-3609	155	38	10	10	NUM
ejpam-3609	155	39	:	:	PUNCT
ejpam-3609	155	40	to	to	PART
ejpam-3609	155	41	express	express	VERB
ejpam-3609	155	42	density	density	NOUN
ejpam-3609	155	43	function	function	NOUN
ejpam-3609	155	44	in	in	ADP
ejpam-3609	155	45	terms	term	NOUN
ejpam-3609	155	46	of	of	ADP
ejpam-3609	155	47	characteristic	characteristic	ADJ
ejpam-3609	155	48	function	function	NOUN
ejpam-3609	155	49	when	when	SCONJ
ejpam-3609	155	50	n→∞	n→∞	PRON
ejpam-3609	155	51	charge	charge	NOUN
ejpam-3609	155	52	density	density	NOUN
ejpam-3609	155	53	goes	go	VERB
ejpam-3609	155	54	to	to	ADP
ejpam-3609	155	55	infinity	infinity	NOUN
ejpam-3609	155	56	.	.	PUNCT
ejpam-3609	156	1	given	give	VERB
ejpam-3609	156	2	charge	charge	NOUN
ejpam-3609	156	3	density	density	NOUN
ejpam-3609	156	4	function	function	NOUN
ejpam-3609	156	5	,	,	PUNCT
ejpam-3609	156	6	in	in	ADP
ejpam-3609	156	7	electrostatic	electrostatic	ADJ
ejpam-3609	156	8	problems	problem	NOUN
ejpam-3609	156	9	we	we	PRON
ejpam-3609	156	10	can	can	AUX
ejpam-3609	156	11	calculate	calculate	VERB
ejpam-3609	156	12	the	the	DET
ejpam-3609	156	13	electric	electric	ADJ
ejpam-3609	156	14	potential	potential	NOUN
ejpam-3609	156	15	by	by	ADP
ejpam-3609	156	16	the	the	DET
ejpam-3609	156	17	following	follow	VERB
ejpam-3609	156	18	integral	integral	ADJ
ejpam-3609	156	19	(	(	PUNCT
ejpam-3609	156	20	cgs	cgs	NOUN
ejpam-3609	156	21	system	system	NOUN
ejpam-3609	156	22	):	):	PUNCT
ejpam-3609	156	23	u(sαc2	u(sαc2	PROPN
ejpam-3609	156	24	(	(	PUNCT
ejpam-3609	156	25	x	x	NOUN
ejpam-3609	156	26	)	)	PUNCT
ejpam-3609	156	27	)	)	PUNCT
ejpam-3609	157	1	=	=	PUNCT
ejpam-3609	157	2	∫	∫	PROPN
ejpam-3609	158	1	1	1	NUM
ejpam-3609	158	2	0	0	NUM
ejpam-3609	158	3	9	9	NUM
ejpam-3609	158	4	4qχc2(x́	4qχc2(x́	PRON
ejpam-3609	158	5	)	)	PUNCT
ejpam-3609	158	6	sαc2	sαc2	PROPN
ejpam-3609	158	7	(	(	PUNCT
ejpam-3609	158	8	x)−	x)−	PROPN
ejpam-3609	158	9	sαc2	sαc2	PROPN
ejpam-3609	158	10	(	(	PUNCT
ejpam-3609	158	11	x́	x́	PROPN
ejpam-3609	158	12	)	)	PUNCT
ejpam-3609	158	13	dαc2	dαc2	PROPN
ejpam-3609	158	14	x́	x́	PROPN
ejpam-3609	158	15	,	,	PUNCT
ejpam-3609	158	16	=	=	SYM
ejpam-3609	158	17	∫	∫	PROPN
ejpam-3609	158	18	1	1	NUM
ejpam-3609	158	19	9	9	NUM
ejpam-3609	158	20	0	0	NUM
ejpam-3609	158	21	9	9	NUM
ejpam-3609	158	22	4q	4q	NOUN
ejpam-3609	158	23	sαc2	sαc2	PROPN
ejpam-3609	158	24	(	(	PUNCT
ejpam-3609	158	25	x)−	x)−	PROPN
ejpam-3609	158	26	sαc2	sαc2	PROPN
ejpam-3609	158	27	(	(	PUNCT
ejpam-3609	158	28	x́	x́	PROPN
ejpam-3609	158	29	)	)	PUNCT
ejpam-3609	158	30	dαc2	dαc2	PROPN
ejpam-3609	158	31	x́+	x́+	NUM
ejpam-3609	158	32	∫	∫	PROPN
ejpam-3609	158	33	3	3	NUM
ejpam-3609	158	34	9	9	NUM
ejpam-3609	158	35	2	2	NUM
ejpam-3609	158	36	9	9	NUM
ejpam-3609	158	37	9	9	NUM
ejpam-3609	158	38	4q	4q	NOUN
ejpam-3609	158	39	sαc2	sαc2	PROPN
ejpam-3609	158	40	(	(	PUNCT
ejpam-3609	158	41	x)−	x)−	PROPN
ejpam-3609	158	42	sαc2	sαc2	PROPN
ejpam-3609	158	43	(	(	PUNCT
ejpam-3609	158	44	x́	x́	PROPN
ejpam-3609	158	45	)	)	PUNCT
ejpam-3609	158	46	dαc2	dαc2	PROPN
ejpam-3609	158	47	x́+	x́+	NUM
ejpam-3609	158	48	∫	∫	PROPN
ejpam-3609	158	49	7	7	NUM
ejpam-3609	158	50	9	9	NUM
ejpam-3609	158	51	6	6	NUM
ejpam-3609	158	52	9	9	NUM
ejpam-3609	158	53	9	9	NUM
ejpam-3609	158	54	4q	4q	NOUN
ejpam-3609	158	55	sαc2	sαc2	PROPN
ejpam-3609	158	56	(	(	PUNCT
ejpam-3609	158	57	x)−	x)−	PROPN
ejpam-3609	158	58	sαc2	sαc2	PROPN
ejpam-3609	158	59	(	(	PUNCT
ejpam-3609	158	60	x́	x́	PROPN
ejpam-3609	158	61	)	)	PUNCT
ejpam-3609	158	62	dαc2	dαc2	PROPN
ejpam-3609	158	63	x́	x́	PROPN
ejpam-3609	159	1	+	+	CCONJ
ejpam-3609	159	2	∫	∫	PROPN
ejpam-3609	159	3	9	9	NUM
ejpam-3609	159	4	9	9	NUM
ejpam-3609	159	5	8	8	NUM
ejpam-3609	159	6	9	9	NUM
ejpam-3609	159	7	9	9	NUM
ejpam-3609	159	8	4q	4q	NOUN
ejpam-3609	159	9	sαc2	sαc2	PROPN
ejpam-3609	159	10	(	(	PUNCT
ejpam-3609	159	11	x)−	x)−	PROPN
ejpam-3609	159	12	sαc2	sαc2	PROPN
ejpam-3609	159	13	(	(	PUNCT
ejpam-3609	159	14	x́	x́	PROPN
ejpam-3609	159	15	)	)	PUNCT
ejpam-3609	159	16	dαc2	dαc2	PROPN
ejpam-3609	160	1	x́.	x́.	PROPN
ejpam-3609	160	2	regarding	regard	VERB
ejpam-3609	160	3	different	different	ADJ
ejpam-3609	160	4	values	value	NOUN
ejpam-3609	160	5	of	of	ADP
ejpam-3609	160	6	staircase	staircase	NOUN
ejpam-3609	160	7	function	function	NOUN
ejpam-3609	160	8	sαc2	sαc2	PROPN
ejpam-3609	160	9	(	(	PUNCT
ejpam-3609	160	10	1	1	NUM
ejpam-3609	160	11	9	9	NUM
ejpam-3609	160	12	)	)	PUNCT
ejpam-3609	161	1	=	=	SYM
ejpam-3609	161	2	sαc2	sαc2	PROPN
ejpam-3609	161	3	(	(	PUNCT
ejpam-3609	161	4	2	2	NUM
ejpam-3609	161	5	9	9	NUM
ejpam-3609	161	6	)	)	PUNCT
ejpam-3609	161	7	=	=	SYM
ejpam-3609	161	8	0.25	0.25	NUM
ejpam-3609	161	9	;	;	PUNCT
ejpam-3609	161	10	sαc2	sαc2	PROPN
ejpam-3609	161	11	(	(	PUNCT
ejpam-3609	161	12	3	3	NUM
ejpam-3609	161	13	9	9	NUM
ejpam-3609	161	14	)	)	PUNCT
ejpam-3609	161	15	=	=	SYM
ejpam-3609	161	16	sαc2	sαc2	PROPN
ejpam-3609	161	17	(	(	PUNCT
ejpam-3609	161	18	6	6	NUM
ejpam-3609	161	19	9	9	NUM
ejpam-3609	161	20	)	)	PUNCT
ejpam-3609	161	21	=	=	SYM
ejpam-3609	161	22	0.5	0.5	NUM
ejpam-3609	161	23	a.	a.	NOUN
ejpam-3609	161	24	pishkoo	pishkoo	NOUN
ejpam-3609	161	25	et	et	PROPN
ejpam-3609	161	26	al	al	PROPN
ejpam-3609	161	27	.	.	PUNCT
ejpam-3609	161	28	/	/	SYM
ejpam-3609	161	29	eur	eur	PROPN
ejpam-3609	161	30	.	.	PUNCT
ejpam-3609	162	1	j.	j.	PROPN
ejpam-3609	162	2	pure	pure	PROPN
ejpam-3609	162	3	appl	appl	PROPN
ejpam-3609	162	4	.	.	PROPN
ejpam-3609	162	5	math	math	PROPN
ejpam-3609	162	6	,	,	PUNCT
ejpam-3609	162	7	13	13	NUM
ejpam-3609	162	8	(	(	PUNCT
ejpam-3609	162	9	1	1	NUM
ejpam-3609	162	10	)	)	PUNCT
ejpam-3609	162	11	(	(	PUNCT
ejpam-3609	162	12	2020	2020	NUM
ejpam-3609	162	13	)	)	PUNCT
ejpam-3609	162	14	,	,	PUNCT
ejpam-3609	162	15	19	19	NUM
ejpam-3609	162	16	-	-	SYM
ejpam-3609	162	17	32	32	NUM
ejpam-3609	162	18	28	28	NUM
ejpam-3609	162	19	figure	figure	NOUN
ejpam-3609	162	20	11	11	NUM
ejpam-3609	162	21	:	:	PUNCT
ejpam-3609	162	22	instead	instead	ADV
ejpam-3609	162	23	of	of	ADP
ejpam-3609	162	24	variables	variable	NOUN
ejpam-3609	162	25	x	x	PUNCT
ejpam-3609	162	26	and	and	CCONJ
ejpam-3609	162	27	x́	x́	PROPN
ejpam-3609	163	1	we	we	PRON
ejpam-3609	163	2	consider	consider	VERB
ejpam-3609	163	3	sαc2	sαc2	PROPN
ejpam-3609	163	4	(	(	PUNCT
ejpam-3609	163	5	x	x	NOUN
ejpam-3609	163	6	)	)	PUNCT
ejpam-3609	163	7	and	and	CCONJ
ejpam-3609	163	8	sαc2	sαc2	PROPN
ejpam-3609	163	9	(	(	PUNCT
ejpam-3609	163	10	x́	x́	PROPN
ejpam-3609	163	11	)	)	PUNCT
ejpam-3609	163	12	sαc2	sαc2	PROPN
ejpam-3609	163	13	(	(	PUNCT
ejpam-3609	163	14	7	7	NUM
ejpam-3609	163	15	9	9	NUM
ejpam-3609	163	16	)	)	PUNCT
ejpam-3609	164	1	=	=	SYM
ejpam-3609	164	2	sαc2	sαc2	PROPN
ejpam-3609	164	3	(	(	PUNCT
ejpam-3609	164	4	8	8	NUM
ejpam-3609	164	5	9	9	NUM
ejpam-3609	164	6	)	)	PUNCT
ejpam-3609	164	7	=	=	SYM
ejpam-3609	164	8	0.75	0.75	NUM
ejpam-3609	164	9	;	;	PUNCT
ejpam-3609	164	10	sαc2	sαc2	PROPN
ejpam-3609	164	11	(	(	PUNCT
ejpam-3609	164	12	0	0	NUM
ejpam-3609	164	13	)	)	PUNCT
ejpam-3609	164	14	=	=	SYM
ejpam-3609	164	15	0	0	NUM
ejpam-3609	164	16	;	;	PUNCT
ejpam-3609	164	17	sαc2	sαc2	PROPN
ejpam-3609	164	18	(	(	PUNCT
ejpam-3609	164	19	1	1	X
ejpam-3609	164	20	)	)	PUNCT
ejpam-3609	164	21	=	=	SYM
ejpam-3609	164	22	1	1	NUM
ejpam-3609	164	23	we	we	PRON
ejpam-3609	164	24	have	have	VERB
ejpam-3609	164	25	u(sαc2	u(sαc2	PROPN
ejpam-3609	164	26	(	(	PUNCT
ejpam-3609	164	27	x	x	NOUN
ejpam-3609	164	28	)	)	PUNCT
ejpam-3609	164	29	)	)	PUNCT
ejpam-3609	165	1	=	=	SYM
ejpam-3609	165	2	9	9	NUM
ejpam-3609	165	3	4	4	NUM
ejpam-3609	165	4	q	q	NOUN
ejpam-3609	166	1	ln	ln	ADJ
ejpam-3609	167	1	|	|	ADV
ejpam-3609	167	2	sαc2	sαc2	PROPN
ejpam-3609	167	3	(	(	PUNCT
ejpam-3609	167	4	x	x	X
ejpam-3609	167	5	)	)	PUNCT
ejpam-3609	167	6	sαc2	sαc2	PROPN
ejpam-3609	167	7	(	(	PUNCT
ejpam-3609	167	8	x)−	x)−	PROPN
ejpam-3609	167	9	1	1	NUM
ejpam-3609	167	10	|	|	ADV
ejpam-3609	167	11	.	.	PUNCT
ejpam-3609	168	1	(	(	PUNCT
ejpam-3609	168	2	9	9	NUM
ejpam-3609	168	3	)	)	PUNCT
ejpam-3609	168	4	example3	example3	NOUN
ejpam-3609	168	5	calculate	calculate	VERB
ejpam-3609	168	6	the	the	DET
ejpam-3609	168	7	values	value	NOUN
ejpam-3609	168	8	of	of	ADP
ejpam-3609	168	9	electric	electric	ADJ
ejpam-3609	168	10	potential	potential	NOUN
ejpam-3609	168	11	at	at	ADP
ejpam-3609	168	12	xp	xp	PROPN
ejpam-3609	168	13	=	=	SYM
ejpam-3609	168	14	1	1	NUM
ejpam-3609	168	15	6	6	NUM
ejpam-3609	168	16	,	,	PUNCT
ejpam-3609	168	17	0.4	0.4	NUM
ejpam-3609	168	18	,	,	PUNCT
ejpam-3609	168	19	0.5	0.5	NUM
ejpam-3609	168	20	,	,	PUNCT
ejpam-3609	168	21	0.6	0.6	NUM
ejpam-3609	168	22	,	,	PUNCT
ejpam-3609	168	23	5	5	NUM
ejpam-3609	168	24	6	6	NUM
ejpam-3609	168	25	.	.	PUNCT
ejpam-3609	169	1	u(sαc2	u(sαc2	PROPN
ejpam-3609	169	2	(	(	PUNCT
ejpam-3609	169	3	1	1	NUM
ejpam-3609	169	4	6	6	NUM
ejpam-3609	169	5	)	)	PUNCT
ejpam-3609	169	6	)	)	PUNCT
ejpam-3609	170	1	=	=	PRON
ejpam-3609	170	2	9q	9q	NOUN
ejpam-3609	170	3	4	4	NUM
ejpam-3609	170	4	(	(	PUNCT
ejpam-3609	170	5	−1.098	−1.098	PROPN
ejpam-3609	170	6	)	)	PUNCT
ejpam-3609	170	7	;	;	PUNCT
ejpam-3609	170	8	u(sαc2	u(sαc2	PROPN
ejpam-3609	170	9	(	(	PUNCT
ejpam-3609	170	10	0.4	0.4	NUM
ejpam-3609	170	11	)	)	PUNCT
ejpam-3609	170	12	)	)	PUNCT
ejpam-3609	171	1	=	=	SYM
ejpam-3609	171	2	0;u(sαc2	0;u(sαc2	PROPN
ejpam-3609	171	3	(	(	PUNCT
ejpam-3609	171	4	0.5	0.5	NUM
ejpam-3609	171	5	)	)	PUNCT
ejpam-3609	171	6	)	)	PUNCT
ejpam-3609	172	1	=	=	SYM
ejpam-3609	172	2	0	0	NUM
ejpam-3609	172	3	;	;	PUNCT
ejpam-3609	172	4	u(sαc2	u(sαc2	PROPN
ejpam-3609	172	5	(	(	PUNCT
ejpam-3609	172	6	0.6	0.6	NUM
ejpam-3609	172	7	)	)	PUNCT
ejpam-3609	172	8	)	)	PUNCT
ejpam-3609	173	1	=	=	PUNCT
ejpam-3609	173	2	0	0	NUM
ejpam-3609	173	3	;	;	PUNCT
ejpam-3609	173	4	u(sαc2	u(sαc2	PROPN
ejpam-3609	173	5	(	(	PUNCT
ejpam-3609	173	6	5	5	NUM
ejpam-3609	173	7	6	6	NUM
ejpam-3609	173	8	)	)	PUNCT
ejpam-3609	173	9	)	)	PUNCT
ejpam-3609	174	1	=	=	PRON
ejpam-3609	174	2	9q	9q	NOUN
ejpam-3609	174	3	4	4	NUM
ejpam-3609	174	4	(	(	PUNCT
ejpam-3609	174	5	1.098	1.098	NUM
ejpam-3609	174	6	)	)	PUNCT
ejpam-3609	174	7	.	.	PUNCT
ejpam-3609	175	1	if	if	SCONJ
ejpam-3609	175	2	instead	instead	ADV
ejpam-3609	175	3	of	of	ADP
ejpam-3609	175	4	charge	charge	NOUN
ejpam-3609	175	5	distribution	distribution	NOUN
ejpam-3609	175	6	at	at	ADP
ejpam-3609	175	7	second	second	ADJ
ejpam-3609	175	8	iteration	iteration	NOUN
ejpam-3609	175	9	we	we	PRON
ejpam-3609	175	10	have	have	VERB
ejpam-3609	175	11	charge	charge	NOUN
ejpam-3609	175	12	distribution	distribution	NOUN
ejpam-3609	175	13	at	at	ADP
ejpam-3609	175	14	nth	nth	NOUN
ejpam-3609	175	15	iteration	iteration	NOUN
ejpam-3609	175	16	we	we	PRON
ejpam-3609	175	17	deduce	deduce	VERB
ejpam-3609	175	18	the	the	DET
ejpam-3609	175	19	following	follow	VERB
ejpam-3609	175	20	formula	formula	NOUN
ejpam-3609	175	21	u(sαcn(x	u(sαcn(x	NOUN
ejpam-3609	175	22	)	)	PUNCT
ejpam-3609	175	23	)	)	PUNCT
ejpam-3609	176	1	=	=	PUNCT
ejpam-3609	176	2	(	(	PUNCT
ejpam-3609	176	3	3	3	NUM
ejpam-3609	176	4	2	2	NUM
ejpam-3609	176	5	)	)	PUNCT
ejpam-3609	176	6	nq	nq	PROPN
ejpam-3609	176	7	ln	ln	ADV
ejpam-3609	176	8	|	|	ADV
ejpam-3609	176	9	sαcn(x	sαcn(x	VERB
ejpam-3609	176	10	)	)	PUNCT
ejpam-3609	176	11	sαcn(x)−	sαcn(x)−	NOUN
ejpam-3609	176	12	1	1	NUM
ejpam-3609	176	13	|	|	ADV
ejpam-3609	176	14	.	.	PUNCT
ejpam-3609	177	1	(	(	PUNCT
ejpam-3609	177	2	10	10	NUM
ejpam-3609	177	3	)	)	PUNCT
ejpam-3609	177	4	now	now	ADV
ejpam-3609	177	5	by	by	ADP
ejpam-3609	177	6	using	use	VERB
ejpam-3609	177	7	the	the	DET
ejpam-3609	177	8	operator	operator	NOUN
ejpam-3609	177	9	dα	dα	PART
ejpam-3609	177	10	cn	cn	PROPN
ejpam-3609	177	11	on	on	ADP
ejpam-3609	177	12	electric	electric	ADJ
ejpam-3609	177	13	potential	potential	NOUN
ejpam-3609	177	14	,	,	PUNCT
ejpam-3609	177	15	electric	electric	ADJ
ejpam-3609	177	16	field	field	NOUN
ejpam-3609	177	17	can	can	AUX
ejpam-3609	177	18	be	be	AUX
ejpam-3609	177	19	deduced	deduce	VERB
ejpam-3609	177	20	.	.	PUNCT
ejpam-3609	178	1	using	use	VERB
ejpam-3609	178	2	the	the	DET
ejpam-3609	178	3	following	follow	VERB
ejpam-3609	178	4	formula	formula	NOUN
ejpam-3609	178	5	dα	dα	INTJ
ejpam-3609	178	6	cn	cn	PROPN
ejpam-3609	178	7	ln	ln	PROPN
ejpam-3609	179	1	|f(sαcn(x))|	|f(sαcn(x))|	PROPN
ejpam-3609	179	2	=	=	PRON
ejpam-3609	179	3	dα	dα	PROPN
ejpam-3609	179	4	cn	cn	NOUN
ejpam-3609	179	5	f(sαcn(x	f(sαcn(x	PROPN
ejpam-3609	179	6	)	)	PUNCT
ejpam-3609	179	7	)	)	PUNCT
ejpam-3609	179	8	f(sαcn(x	f(sαcn(x	X
ejpam-3609	179	9	)	)	PUNCT
ejpam-3609	179	10	)	)	PUNCT
ejpam-3609	179	11	,	,	PUNCT
ejpam-3609	179	12	(	(	PUNCT
ejpam-3609	179	13	11	11	X
ejpam-3609	179	14	)	)	PUNCT
ejpam-3609	179	15	we	we	PRON
ejpam-3609	179	16	have	have	VERB
ejpam-3609	179	17	dα	dα	PRON
ejpam-3609	179	18	cn	cn	PROPN
ejpam-3609	179	19	sαcn(x)[sαcn(x)−	sαcn(x)[sαcn(x)−	PROPN
ejpam-3609	179	20	1]−	1]−	NUM
ejpam-3609	179	21	sαcn(x)dα	sαcn(x)dα	NOUN
ejpam-3609	180	1	cn	cn	PROPN
ejpam-3609	181	1	[	[	X
ejpam-3609	181	2	sαcn(x)−	sαcn(x)−	PROPN
ejpam-3609	181	3	1	1	NUM
ejpam-3609	181	4	]	]	PUNCT
ejpam-3609	181	5	(	(	PUNCT
ejpam-3609	181	6	sαcn(x)−	sαcn(x)−	PROPN
ejpam-3609	181	7	1)2	1)2	NUM
ejpam-3609	181	8	,	,	PUNCT
ejpam-3609	181	9	(	(	PUNCT
ejpam-3609	181	10	12	12	NUM
ejpam-3609	181	11	)	)	PUNCT
ejpam-3609	181	12	a.	a.	NOUN
ejpam-3609	181	13	pishkoo	pishkoo	NOUN
ejpam-3609	181	14	et	et	PROPN
ejpam-3609	181	15	al	al	PROPN
ejpam-3609	181	16	.	.	PUNCT
ejpam-3609	181	17	/	/	SYM
ejpam-3609	181	18	eur	eur	PROPN
ejpam-3609	181	19	.	.	PUNCT
ejpam-3609	182	1	j.	j.	PROPN
ejpam-3609	182	2	pure	pure	PROPN
ejpam-3609	182	3	appl	appl	PROPN
ejpam-3609	182	4	.	.	PROPN
ejpam-3609	182	5	math	math	PROPN
ejpam-3609	182	6	,	,	PUNCT
ejpam-3609	182	7	13	13	NUM
ejpam-3609	182	8	(	(	PUNCT
ejpam-3609	182	9	1	1	NUM
ejpam-3609	182	10	)	)	PUNCT
ejpam-3609	182	11	(	(	PUNCT
ejpam-3609	182	12	2020	2020	NUM
ejpam-3609	182	13	)	)	PUNCT
ejpam-3609	182	14	,	,	PUNCT
ejpam-3609	182	15	19	19	NUM
ejpam-3609	182	16	-	-	SYM
ejpam-3609	182	17	32	32	NUM
ejpam-3609	182	18	29	29	NUM
ejpam-3609	182	19	while	while	SCONJ
ejpam-3609	182	20	dα	dα	PRON
ejpam-3609	182	21	cn	cn	PROPN
ejpam-3609	182	22	sαcn(x	sαcn(x	PROPN
ejpam-3609	182	23	)	)	PUNCT
ejpam-3609	182	24	=	=	SYM
ejpam-3609	182	25	χαcn(x	χαcn(x	PROPN
ejpam-3609	182	26	)	)	PUNCT
ejpam-3609	182	27	,	,	PUNCT
ejpam-3609	182	28	and	and	CCONJ
ejpam-3609	182	29	e(sαcn(x	e(sαcn(x	X
ejpam-3609	182	30	)	)	PUNCT
ejpam-3609	182	31	)	)	PUNCT
ejpam-3609	183	1	=	=	PUNCT
ejpam-3609	183	2	−dα	−dα	X
ejpam-3609	183	3	cn	cn	PROPN
ejpam-3609	184	1	[	[	X
ejpam-3609	184	2	u(sαcn(x	u(sαcn(x	X
ejpam-3609	184	3	)	)	PUNCT
ejpam-3609	184	4	)	)	PUNCT
ejpam-3609	184	5	]	]	PUNCT
ejpam-3609	184	6	.	.	PUNCT
ejpam-3609	185	1	finally	finally	ADV
ejpam-3609	185	2	,	,	PUNCT
ejpam-3609	185	3	we	we	PRON
ejpam-3609	185	4	obtain	obtain	VERB
ejpam-3609	185	5	electric	electric	ADJ
ejpam-3609	185	6	field	field	NOUN
ejpam-3609	185	7	e(sαcn(x	e(sαcn(x	PROPN
ejpam-3609	185	8	)	)	PUNCT
ejpam-3609	185	9	)	)	PUNCT
ejpam-3609	186	1	=	=	PRON
ejpam-3609	186	2	χαcn	χαcn	X
ejpam-3609	186	3	(	(	PUNCT
ejpam-3609	186	4	x	x	NOUN
ejpam-3609	186	5	)	)	PUNCT
ejpam-3609	186	6	(	(	PUNCT
ejpam-3609	186	7	sαcn	sαcn	X
ejpam-3609	186	8	(	(	PUNCT
ejpam-3609	186	9	x)−1)2	x)−1)2	PROPN
ejpam-3609	186	10	sαcn	sαcn	NOUN
ejpam-3609	186	11	(	(	PUNCT
ejpam-3609	186	12	x	x	NOUN
ejpam-3609	186	13	)	)	PUNCT
ejpam-3609	186	14	sαcn	sαcn	NOUN
ejpam-3609	186	15	(	(	PUNCT
ejpam-3609	186	16	x)−1	x)−1	X
ejpam-3609	186	17	=	=	SYM
ejpam-3609	186	18	χαcn(x	χαcn(x	PROPN
ejpam-3609	186	19	)	)	PUNCT
ejpam-3609	186	20	sαcn(x)(sαcn(x)−	sαcn(x)(sαcn(x)−	PROPN
ejpam-3609	186	21	1	1	NUM
ejpam-3609	186	22	)	)	PUNCT
ejpam-3609	186	23	.	.	PUNCT
ejpam-3609	187	1	(	(	PUNCT
ejpam-3609	187	2	13	13	NUM
ejpam-3609	187	3	)	)	SYM
ejpam-3609	187	4	3	3	NUM
ejpam-3609	187	5	.	.	PUNCT
ejpam-3609	187	6	electric	electric	ADJ
ejpam-3609	187	7	potential	potential	NOUN
ejpam-3609	187	8	for	for	ADP
ejpam-3609	187	9	koch	koch	PROPN
ejpam-3609	187	10	snowflake	snowflake	PROPN
ejpam-3609	187	11	boundary	boundary	ADV
ejpam-3609	187	12	in	in	ADP
ejpam-3609	187	13	comsol	comsol	NOUN
ejpam-3609	187	14	multiphysics	multiphysics	PROPN
ejpam-3609	187	15	one	one	NUM
ejpam-3609	187	16	deal	deal	NOUN
ejpam-3609	187	17	with	with	ADP
ejpam-3609	187	18	two	two	NUM
ejpam-3609	187	19	different	different	ADJ
ejpam-3609	187	20	environment	environment	NOUN
ejpam-3609	187	21	:	:	PUNCT
ejpam-3609	187	22	“	"	PUNCT
ejpam-3609	187	23	model	model	NOUN
ejpam-3609	187	24	builder	builder	NOUN
ejpam-3609	187	25	desktop	desktop	NOUN
ejpam-3609	187	26	”	"	PUNCT
ejpam-3609	187	27	and	and	CCONJ
ejpam-3609	187	28	“	"	PUNCT
ejpam-3609	187	29	application	application	NOUN
ejpam-3609	187	30	builder	builder	NOUN
ejpam-3609	187	31	desktop	desktop	NOUN
ejpam-3609	187	32	”	"	PUNCT
ejpam-3609	187	33	.	.	PUNCT
ejpam-3609	188	1	the	the	DET
ejpam-3609	188	2	application	application	NOUN
ejpam-3609	188	3	builder	builder	NOUN
ejpam-3609	188	4	desktop	desktop	NOUN
ejpam-3609	188	5	environment	environment	NOUN
ejpam-3609	188	6	show	show	NOUN
ejpam-3609	188	7	ones	one	NOUN
ejpam-3609	188	8	how	how	SCONJ
ejpam-3609	188	9	to	to	PART
ejpam-3609	188	10	use	use	VERB
ejpam-3609	188	11	the	the	DET
ejpam-3609	188	12	form	form	NOUN
ejpam-3609	188	13	editor	editor	NOUN
ejpam-3609	188	14	and	and	CCONJ
ejpam-3609	188	15	the	the	DET
ejpam-3609	188	16	method	method	NOUN
ejpam-3609	188	17	editor	editor	NOUN
ejpam-3609	188	18	.	.	PUNCT
ejpam-3609	189	1	note	note	VERB
ejpam-3609	189	2	that	that	SCONJ
ejpam-3609	189	3	we	we	PRON
ejpam-3609	189	4	can	can	AUX
ejpam-3609	189	5	switch	switch	VERB
ejpam-3609	189	6	between	between	ADP
ejpam-3609	189	7	the	the	DET
ejpam-3609	189	8	model	model	NOUN
ejpam-3609	189	9	builder	builder	NOUN
ejpam-3609	189	10	and	and	CCONJ
ejpam-3609	189	11	application	application	NOUN
ejpam-3609	189	12	builder	builder	NOUN
ejpam-3609	189	13	by	by	ADP
ejpam-3609	189	14	clicking	click	VERB
ejpam-3609	189	15	on	on	ADP
ejpam-3609	189	16	their	their	PRON
ejpam-3609	189	17	buttons	button	NOUN
ejpam-3609	189	18	.	.	PUNCT
ejpam-3609	190	1	this	this	DET
ejpam-3609	190	2	software	software	NOUN
ejpam-3609	190	3	uses	use	VERB
ejpam-3609	190	4	finite	finite	ADJ
ejpam-3609	190	5	element	element	NOUN
ejpam-3609	190	6	method	method	NOUN
ejpam-3609	190	7	(	(	PUNCT
ejpam-3609	190	8	fem	fem	NOUN
ejpam-3609	190	9	)	)	PUNCT
ejpam-3609	190	10	to	to	PART
ejpam-3609	190	11	solve	solve	VERB
ejpam-3609	190	12	different	different	ADJ
ejpam-3609	190	13	types	type	NOUN
ejpam-3609	190	14	of	of	ADP
ejpam-3609	190	15	problems	problem	NOUN
ejpam-3609	190	16	numerically	numerically	ADV
ejpam-3609	190	17	.	.	PUNCT
ejpam-3609	191	1	for	for	ADP
ejpam-3609	191	2	koch	koch	PROPN
ejpam-3609	191	3	snowflake	snowflake	PROPN
ejpam-3609	191	4	boundary	boundary	NOUN
ejpam-3609	191	5	,	,	PUNCT
ejpam-3609	191	6	laplace	laplace	NOUN
ejpam-3609	191	7	equation	equation	NOUN
ejpam-3609	191	8	interface	interface	NOUN
ejpam-3609	191	9	is	be	AUX
ejpam-3609	191	10	used	use	VERB
ejpam-3609	191	11	to	to	PART
ejpam-3609	191	12	compute	compute	VERB
ejpam-3609	191	13	electric	electric	ADJ
ejpam-3609	191	14	potential	potential	NOUN
ejpam-3609	191	15	.	.	PUNCT
ejpam-3609	192	1	choosing	choose	VERB
ejpam-3609	192	2	normal	normal	ADJ
ejpam-3609	192	3	mesh	mesh	NOUN
ejpam-3609	192	4	,	,	PUNCT
ejpam-3609	192	5	one	one	PRON
ejpam-3609	192	6	may	may	AUX
ejpam-3609	192	7	compute	compute	VERB
ejpam-3609	192	8	electric	electric	ADJ
ejpam-3609	192	9	potential	potential	NOUN
ejpam-3609	192	10	.	.	PUNCT
ejpam-3609	193	1	our	our	PRON
ejpam-3609	193	2	results	result	NOUN
ejpam-3609	193	3	have	have	AUX
ejpam-3609	193	4	been	be	AUX
ejpam-3609	193	5	summarized	summarize	VERB
ejpam-3609	193	6	in	in	ADP
ejpam-3609	193	7	fig	fig	NOUN
ejpam-3609	193	8	.	.	PUNCT
ejpam-3609	194	1	12	12	NUM
ejpam-3609	194	2	,	,	PUNCT
ejpam-3609	194	3	fig	fig	NOUN
ejpam-3609	194	4	.	.	PUNCT
ejpam-3609	195	1	13	13	NUM
ejpam-3609	195	2	,	,	PUNCT
ejpam-3609	195	3	fig	fig	NOUN
ejpam-3609	195	4	.	.	PUNCT
ejpam-3609	195	5	15	15	NUM
ejpam-3609	195	6	,	,	PUNCT
ejpam-3609	195	7	and	and	CCONJ
ejpam-3609	195	8	fig	fig	NOUN
ejpam-3609	195	9	.	.	PUNCT
ejpam-3609	196	1	16	16	NUM
ejpam-3609	196	2	for	for	ADP
ejpam-3609	196	3	the	the	DET
ejpam-3609	196	4	zero	zero	NUM
ejpam-3609	196	5	,	,	PUNCT
ejpam-3609	196	6	first	first	ADJ
ejpam-3609	196	7	,	,	PUNCT
ejpam-3609	196	8	second	second	ADJ
ejpam-3609	196	9	,	,	PUNCT
ejpam-3609	196	10	and	and	CCONJ
ejpam-3609	196	11	third	third	ADJ
ejpam-3609	196	12	iteration	iteration	NOUN
ejpam-3609	196	13	,	,	PUNCT
ejpam-3609	196	14	respectively	respectively	ADV
ejpam-3609	196	15	(	(	PUNCT
ejpam-3609	196	16	see	see	VERB
ejpam-3609	196	17	also	also	ADV
ejpam-3609	196	18	mp4	mp4	VERB
ejpam-3609	196	19	file	file	NOUN
ejpam-3609	196	20	)	)	PUNCT
ejpam-3609	196	21	.	.	PUNCT
ejpam-3609	197	1	figure	figure	NOUN
ejpam-3609	197	2	12	12	NUM
ejpam-3609	197	3	:	:	PUNCT
ejpam-3609	197	4	to	to	PART
ejpam-3609	197	5	create	create	VERB
ejpam-3609	197	6	koch	koch	PROPN
ejpam-3609	197	7	snowflake	snowflake	NOUN
ejpam-3609	197	8	,	,	PUNCT
ejpam-3609	197	9	to	to	PART
ejpam-3609	197	10	plot	plot	VERB
ejpam-3609	197	11	mesh	mesh	NOUN
ejpam-3609	197	12	,	,	PUNCT
ejpam-3609	197	13	and	and	CCONJ
ejpam-3609	197	14	to	to	PART
ejpam-3609	197	15	compute	compute	VERB
ejpam-3609	197	16	electric	electric	ADJ
ejpam-3609	197	17	field	field	NOUN
ejpam-3609	197	18	at	at	ADP
ejpam-3609	197	19	zero	zero	NUM
ejpam-3609	197	20	iteration	iteration	NOUN
ejpam-3609	197	21	4	4	NUM
ejpam-3609	197	22	.	.	PUNCT
ejpam-3609	198	1	conclusions	conclusion	NOUN
ejpam-3609	198	2	and	and	CCONJ
ejpam-3609	198	3	future	future	ADJ
ejpam-3609	198	4	works	work	NOUN
ejpam-3609	198	5	in	in	ADP
ejpam-3609	198	6	this	this	DET
ejpam-3609	198	7	paper	paper	NOUN
ejpam-3609	198	8	,	,	PUNCT
ejpam-3609	198	9	fractal	fractal	ADJ
ejpam-3609	198	10	calculus	calculus	NOUN
ejpam-3609	198	11	as	as	ADP
ejpam-3609	198	12	a	a	DET
ejpam-3609	198	13	new	new	ADJ
ejpam-3609	198	14	mathematical	mathematical	ADJ
ejpam-3609	198	15	language	language	NOUN
ejpam-3609	198	16	tool	tool	NOUN
ejpam-3609	198	17	is	be	AUX
ejpam-3609	198	18	used	use	VERB
ejpam-3609	198	19	in	in	ADP
ejpam-3609	198	20	physics	physics	NOUN
ejpam-3609	198	21	(	(	PUNCT
ejpam-3609	198	22	electrostatics	electrostatics	PROPN
ejpam-3609	198	23	)	)	PUNCT
ejpam-3609	198	24	to	to	PART
ejpam-3609	198	25	calculate	calculate	VERB
ejpam-3609	198	26	and	and	CCONJ
ejpam-3609	198	27	express	express	VERB
ejpam-3609	198	28	the	the	DET
ejpam-3609	198	29	electric	electric	ADJ
ejpam-3609	198	30	potential	potential	ADJ
ejpam-3609	198	31	and	and	CCONJ
ejpam-3609	198	32	electric	electric	ADJ
ejpam-3609	198	33	field	field	NOUN
ejpam-3609	198	34	.	.	PUNCT
ejpam-3609	199	1	if	if	SCONJ
ejpam-3609	199	2	charge	charge	NOUN
ejpam-3609	199	3	distribution	distribution	NOUN
ejpam-3609	199	4	is	be	AUX
ejpam-3609	199	5	of	of	ADP
ejpam-3609	199	6	type	type	NOUN
ejpam-3609	199	7	discrete	discrete	ADJ
ejpam-3609	199	8	and	and	CCONJ
ejpam-3609	199	9	fractal	fractal	ADJ
ejpam-3609	199	10	,	,	PUNCT
ejpam-3609	199	11	then	then	ADV
ejpam-3609	199	12	we	we	PRON
ejpam-3609	199	13	can	can	AUX
ejpam-3609	199	14	solve	solve	VERB
ejpam-3609	199	15	one	one	NUM
ejpam-3609	199	16	problem	problem	NOUN
ejpam-3609	199	17	with	with	ADP
ejpam-3609	199	18	many	many	ADJ
ejpam-3609	199	19	different	different	ADJ
ejpam-3609	199	20	distributions	distribution	NOUN
ejpam-3609	199	21	that	that	PRON
ejpam-3609	199	22	each	each	PRON
ejpam-3609	199	23	of	of	ADP
ejpam-3609	199	24	them	they	PRON
ejpam-3609	199	25	is	be	AUX
ejpam-3609	199	26	ith	ith	PROPN
ejpam-3609	199	27	iteration	iteration	NOUN
ejpam-3609	199	28	,	,	PUNCT
ejpam-3609	199	29	i	i	PRON
ejpam-3609	199	30	=	=	NOUN
ejpam-3609	199	31	0	0	NUM
ejpam-3609	199	32	,	,	PUNCT
ejpam-3609	199	33	1	1	NUM
ejpam-3609	199	34	,	,	PUNCT
ejpam-3609	199	35	2,etc	2,etc	NUM
ejpam-3609	199	36	.	.	X
ejpam-3609	200	1	we	we	PRON
ejpam-3609	200	2	solve	solve	VERB
ejpam-3609	200	3	the	the	DET
ejpam-3609	200	4	problem	problem	NOUN
ejpam-3609	200	5	with	with	ADP
ejpam-3609	200	6	cantor	cantor	PROPN
ejpam-3609	200	7	set	set	VERB
ejpam-3609	200	8	fractal	fractal	ADJ
ejpam-3609	200	9	charge	charge	NOUN
ejpam-3609	200	10	distribution	distribution	NOUN
ejpam-3609	200	11	while	while	SCONJ
ejpam-3609	200	12	for	for	ADP
ejpam-3609	200	13	other	other	ADJ
ejpam-3609	200	14	kind	kind	NOUN
ejpam-3609	200	15	of	of	ADP
ejpam-3609	200	16	discrete	discrete	ADJ
ejpam-3609	200	17	fractal	fractal	ADJ
ejpam-3609	200	18	distributions	distribution	NOUN
ejpam-3609	200	19	this	this	DET
ejpam-3609	200	20	work	work	NOUN
ejpam-3609	200	21	can	can	AUX
ejpam-3609	200	22	be	be	AUX
ejpam-3609	200	23	continue	continue	VERB
ejpam-3609	200	24	in	in	ADP
ejpam-3609	200	25	future	future	NOUN
ejpam-3609	200	26	.	.	PUNCT
ejpam-3609	201	1	we	we	PRON
ejpam-3609	201	2	have	have	AUX
ejpam-3609	201	3	also	also	ADV
ejpam-3609	201	4	studied	study	VERB
ejpam-3609	201	5	the	the	DET
ejpam-3609	201	6	same	same	ADJ
ejpam-3609	201	7	problem	problem	NOUN
ejpam-3609	201	8	but	but	CCONJ
ejpam-3609	201	9	with	with	ADP
ejpam-3609	201	10	different	different	ADJ
ejpam-3609	201	11	boundaries	boundary	NOUN
ejpam-3609	201	12	which	which	PRON
ejpam-3609	201	13	are	be	AUX
ejpam-3609	201	14	ith	ith	PROPN
ejpam-3609	201	15	iteration	iteration	NOUN
ejpam-3609	201	16	,	,	PUNCT
ejpam-3609	201	17	i	i	PRON
ejpam-3609	201	18	=	=	NOUN
ejpam-3609	201	19	0	0	NUM
ejpam-3609	201	20	,	,	PUNCT
ejpam-3609	201	21	1	1	NUM
ejpam-3609	201	22	,	,	PUNCT
ejpam-3609	201	23	2,etc	2,etc	NUM
ejpam-3609	201	24	in	in	ADP
ejpam-3609	201	25	comsol	comsol	NOUN
ejpam-3609	201	26	multiphysics	multiphysics	PROPN
ejpam-3609	201	27	a.	a.	NOUN
ejpam-3609	201	28	pishkoo	pishkoo	PROPN
ejpam-3609	201	29	et	et	PROPN
ejpam-3609	201	30	al	al	PROPN
ejpam-3609	201	31	.	.	PUNCT
ejpam-3609	201	32	/	/	SYM
ejpam-3609	201	33	eur	eur	PROPN
ejpam-3609	201	34	.	.	PUNCT
ejpam-3609	202	1	j.	j.	PROPN
ejpam-3609	202	2	pure	pure	PROPN
ejpam-3609	202	3	appl	appl	PROPN
ejpam-3609	202	4	.	.	PROPN
ejpam-3609	202	5	math	math	PROPN
ejpam-3609	202	6	,	,	PUNCT
ejpam-3609	202	7	13	13	NUM
ejpam-3609	202	8	(	(	PUNCT
ejpam-3609	202	9	1	1	NUM
ejpam-3609	202	10	)	)	PUNCT
ejpam-3609	202	11	(	(	PUNCT
ejpam-3609	202	12	2020	2020	NUM
ejpam-3609	202	13	)	)	PUNCT
ejpam-3609	202	14	,	,	PUNCT
ejpam-3609	202	15	19	19	NUM
ejpam-3609	202	16	-	-	SYM
ejpam-3609	202	17	32	32	NUM
ejpam-3609	202	18	30	30	NUM
ejpam-3609	202	19	figure	figure	NOUN
ejpam-3609	202	20	13	13	NUM
ejpam-3609	202	21	:	:	PUNCT
ejpam-3609	202	22	to	to	PART
ejpam-3609	202	23	create	create	VERB
ejpam-3609	202	24	koch	koch	PROPN
ejpam-3609	202	25	snowflake	snowflake	NOUN
ejpam-3609	202	26	,	,	PUNCT
ejpam-3609	202	27	to	to	PART
ejpam-3609	202	28	plot	plot	VERB
ejpam-3609	202	29	mesh	mesh	NOUN
ejpam-3609	202	30	,	,	PUNCT
ejpam-3609	202	31	and	and	CCONJ
ejpam-3609	202	32	to	to	PART
ejpam-3609	202	33	compute	compute	VERB
ejpam-3609	202	34	electric	electric	ADJ
ejpam-3609	202	35	field	field	NOUN
ejpam-3609	202	36	at	at	ADP
ejpam-3609	202	37	first	first	ADJ
ejpam-3609	202	38	iteration	iteration	NOUN
ejpam-3609	202	39	figure	figure	NOUN
ejpam-3609	202	40	14	14	NUM
ejpam-3609	202	41	:	:	PUNCT
ejpam-3609	202	42	to	to	PART
ejpam-3609	202	43	create	create	VERB
ejpam-3609	202	44	koch	koch	PROPN
ejpam-3609	202	45	snowflake	snowflake	NOUN
ejpam-3609	202	46	,	,	PUNCT
ejpam-3609	202	47	to	to	PART
ejpam-3609	202	48	plot	plot	VERB
ejpam-3609	202	49	mesh	mesh	NOUN
ejpam-3609	202	50	,	,	PUNCT
ejpam-3609	202	51	and	and	CCONJ
ejpam-3609	202	52	to	to	PART
ejpam-3609	202	53	compute	compute	VERB
ejpam-3609	202	54	electric	electric	ADJ
ejpam-3609	202	55	field	field	NOUN
ejpam-3609	202	56	at	at	ADP
ejpam-3609	202	57	second	second	ADJ
ejpam-3609	202	58	iteration	iteration	NOUN
ejpam-3609	202	59	figure	figure	NOUN
ejpam-3609	202	60	15	15	NUM
ejpam-3609	202	61	:	:	PUNCT
ejpam-3609	202	62	to	to	PART
ejpam-3609	202	63	create	create	VERB
ejpam-3609	202	64	koch	koch	PROPN
ejpam-3609	202	65	snowflake	snowflake	NOUN
ejpam-3609	202	66	,	,	PUNCT
ejpam-3609	202	67	to	to	PART
ejpam-3609	202	68	plot	plot	VERB
ejpam-3609	202	69	mesh	mesh	NOUN
ejpam-3609	202	70	,	,	PUNCT
ejpam-3609	202	71	and	and	CCONJ
ejpam-3609	202	72	to	to	PART
ejpam-3609	202	73	compute	compute	VERB
ejpam-3609	202	74	electric	electric	ADJ
ejpam-3609	202	75	field	field	NOUN
ejpam-3609	202	76	at	at	ADP
ejpam-3609	202	77	third	third	ADJ
ejpam-3609	202	78	iteration	iteration	NOUN
ejpam-3609	202	79	references	reference	NOUN
ejpam-3609	202	80	31	31	NUM
ejpam-3609	202	81	software	software	NOUN
ejpam-3609	202	82	numerically	numerically	ADV
ejpam-3609	202	83	by	by	ADP
ejpam-3609	202	84	using	use	VERB
ejpam-3609	202	85	finite	finite	ADJ
ejpam-3609	202	86	element	element	NOUN
ejpam-3609	202	87	method	method	NOUN
ejpam-3609	202	88	(	(	PUNCT
ejpam-3609	202	89	fem	fem	NOUN
ejpam-3609	202	90	)	)	PUNCT
ejpam-3609	202	91	.	.	PUNCT
ejpam-3609	203	1	acknowledgments	acknowledgment	NOUN
ejpam-3609	203	2	the	the	DET
ejpam-3609	203	3	authors	author	NOUN
ejpam-3609	203	4	are	be	AUX
ejpam-3609	203	5	grateful	grateful	ADJ
ejpam-3609	203	6	to	to	ADP
ejpam-3609	203	7	the	the	DET
ejpam-3609	203	8	referees	referee	NOUN
ejpam-3609	203	9	and	and	CCONJ
ejpam-3609	203	10	the	the	DET
ejpam-3609	203	11	editor	editor	NOUN
ejpam-3609	203	12	for	for	ADP
ejpam-3609	203	13	valuable	valuable	ADJ
ejpam-3609	203	14	remarks	remark	NOUN
ejpam-3609	203	15	which	which	PRON
ejpam-3609	203	16	contributed	contribute	VERB
ejpam-3609	203	17	to	to	ADP
ejpam-3609	203	18	the	the	DET
ejpam-3609	203	19	improvement	improvement	NOUN
ejpam-3609	203	20	of	of	ADP
ejpam-3609	203	21	the	the	DET
ejpam-3609	203	22	paper	paper	NOUN
ejpam-3609	203	23	.	.	PUNCT
ejpam-3609	204	1	the	the	DET
ejpam-3609	204	2	fourth	fourth	ADJ
ejpam-3609	204	3	author	author	NOUN
ejpam-3609	204	4	was	be	AUX
ejpam-3609	204	5	supported	support	VERB
ejpam-3609	204	6	by	by	ADP
ejpam-3609	204	7	frgs	frgs	PROPN
ejpam-3609	204	8	grant	grant	PROPN
ejpam-3609	204	9	number	number	NOUN
ejpam-3609	204	10	stated	state	VERB
ejpam-3609	204	11	:	:	PUNCT
ejpam-3609	204	12	frgs/1/2019	frgs/1/2019	PROPN
ejpam-3609	204	13	/	/	SYM
ejpam-3609	204	14	stg06	stg06	NOUN
ejpam-3609	204	15	/	/	SYM
ejpam-3609	204	16	ukm/01/1	ukm/01/1	NOUN
ejpam-3609	204	17	.	.	PUNCT
ejpam-3609	205	1	5	5	X
ejpam-3609	205	2	.	.	X
ejpam-3609	205	3	conflicts	conflict	NOUN
ejpam-3609	205	4	of	of	ADP
ejpam-3609	205	5	interest	interest	NOUN
ejpam-3609	205	6	the	the	DET
ejpam-3609	205	7	authors	author	NOUN
ejpam-3609	205	8	declare	declare	VERB
ejpam-3609	205	9	that	that	SCONJ
ejpam-3609	205	10	there	there	PRON
ejpam-3609	205	11	are	be	VERB
ejpam-3609	205	12	no	no	DET
ejpam-3609	205	13	conflicts	conflict	NOUN
ejpam-3609	205	14	of	of	ADP
ejpam-3609	205	15	interest	interest	NOUN
ejpam-3609	205	16	regarding	regard	VERB
ejpam-3609	205	17	the	the	DET
ejpam-3609	205	18	publication	publication	NOUN
ejpam-3609	205	19	of	of	ADP
ejpam-3609	205	20	this	this	DET
ejpam-3609	205	21	paper	paper	NOUN
ejpam-3609	205	22	.	.	PUNCT
ejpam-3609	206	1	references	reference	NOUN
ejpam-3609	206	2	[	[	X
ejpam-3609	206	3	1	1	X
ejpam-3609	206	4	]	]	PUNCT
ejpam-3609	206	5	a	a	DET
ejpam-3609	206	6	fernandez	fernandez	PROPN
ejpam-3609	206	7	a	a	DET
ejpam-3609	206	8	k	k	PROPN
ejpam-3609	206	9	golmankhaneh	golmankhaneh	PROPN
ejpam-3609	206	10	.	.	PUNCT
ejpam-3609	207	1	fractal	fractal	ADJ
ejpam-3609	207	2	calculus	calculus	NOUN
ejpam-3609	207	3	of	of	ADP
ejpam-3609	207	4	functions	function	NOUN
ejpam-3609	207	5	on	on	ADP
ejpam-3609	207	6	cantor	cantor	PROPN
ejpam-3609	207	7	tartan	tartan	PROPN
ejpam-3609	207	8	spaces	space	NOUN
ejpam-3609	207	9	.	.	PUNCT
ejpam-3609	208	1	fractal	fractal	ADJ
ejpam-3609	208	2	fract	fract	PROPN
ejpam-3609	208	3	,	,	PUNCT
ejpam-3609	208	4	2:1–13	2:1–13	NUM
ejpam-3609	208	5	,	,	PUNCT
ejpam-3609	208	6	2018	2018	NUM
ejpam-3609	208	7	.	.	PUNCT
ejpam-3609	209	1	[	[	X
ejpam-3609	209	2	2	2	X
ejpam-3609	209	3	]	]	PUNCT
ejpam-3609	209	4	a	a	DET
ejpam-3609	209	5	fernandez	fernandez	PROPN
ejpam-3609	209	6	a	a	DET
ejpam-3609	209	7	k	k	PROPN
ejpam-3609	209	8	golmankhaneh	golmankhaneh	NOUN
ejpam-3609	209	9	.	.	PUNCT
ejpam-3609	210	1	random	random	ADJ
ejpam-3609	210	2	variables	variable	NOUN
ejpam-3609	210	3	and	and	CCONJ
ejpam-3609	210	4	stable	stable	ADJ
ejpam-3609	210	5	distributions	distribution	NOUN
ejpam-3609	210	6	on	on	ADP
ejpam-3609	210	7	fractal	fractal	ADJ
ejpam-3609	210	8	cantor	cantor	NOUN
ejpam-3609	210	9	sets	set	NOUN
ejpam-3609	210	10	.	.	PUNCT
ejpam-3609	211	1	fractal	fractal	ADJ
ejpam-3609	211	2	fract	fract	NOUN
ejpam-3609	211	3	,	,	PUNCT
ejpam-3609	211	4	3	3	NUM
ejpam-3609	211	5	,	,	PUNCT
ejpam-3609	211	6	2019	2019	NUM
ejpam-3609	211	7	.	.	PUNCT
ejpam-3609	212	1	[	[	X
ejpam-3609	212	2	3	3	X
ejpam-3609	212	3	]	]	PUNCT
ejpam-3609	212	4	a	a	DET
ejpam-3609	212	5	k	k	PROPN
ejpam-3609	212	6	golmankhaneh	golmankhaneh	PROPN
ejpam-3609	212	7	d	d	PROPN
ejpam-3609	212	8	baleanu	baleanu	VERB
ejpam-3609	212	9	a	a	DET
ejpam-3609	212	10	k	k	PROPN
ejpam-3609	212	11	golmankhaneh	golmankhaneh	NOUN
ejpam-3609	212	12	,	,	PUNCT
ejpam-3609	212	13	a	a	DET
ejpam-3609	212	14	fernandez	fernandez	NOUN
ejpam-3609	212	15	.	.	PUNCT
ejpam-3609	213	1	diffusion	diffusion	NOUN
ejpam-3609	213	2	on	on	ADP
ejpam-3609	213	3	middle	middle	ADJ
ejpam-3609	213	4	-	-	PUNCT
ejpam-3609	213	5	ξ	ξ	PROPN
ejpam-3609	213	6	cantor	cantor	NOUN
ejpam-3609	213	7	sets	set	NOUN
ejpam-3609	213	8	.	.	PUNCT
ejpam-3609	214	1	entropy	entropy	PROPN
ejpam-3609	214	2	,	,	PUNCT
ejpam-3609	214	3	2	2	NUM
ejpam-3609	214	4	,	,	PUNCT
ejpam-3609	214	5	2018	2018	NUM
ejpam-3609	214	6	.	.	PUNCT
ejpam-3609	215	1	[	[	X
ejpam-3609	215	2	4	4	X
ejpam-3609	215	3	]	]	X
ejpam-3609	215	4	a	a	DET
ejpam-3609	215	5	s	s	X
ejpam-3609	215	6	balankin	balankin	NOUN
ejpam-3609	215	7	a	a	DET
ejpam-3609	215	8	k	k	PROPN
ejpam-3609	215	9	golmankhaneh	golmankhaneh	PROPN
ejpam-3609	215	10	.	.	PUNCT
ejpam-3609	216	1	suband	suband	PROPN
ejpam-3609	216	2	super	super	NOUN
ejpam-3609	216	3	-	-	NOUN
ejpam-3609	216	4	diffusion	diffusion	NOUN
ejpam-3609	216	5	on	on	ADP
ejpam-3609	216	6	cantor	cantor	PROPN
ejpam-3609	216	7	sets	set	NOUN
ejpam-3609	216	8	:	:	PUNCT
ejpam-3609	216	9	beyond	beyond	ADP
ejpam-3609	216	10	the	the	DET
ejpam-3609	216	11	paradox	paradox	NOUN
ejpam-3609	216	12	.	.	PUNCT
ejpam-3609	217	1	physics	physics	NOUN
ejpam-3609	217	2	letters	letter	NOUN
ejpam-3609	217	3	a	a	PRON
ejpam-3609	217	4	,	,	PUNCT
ejpam-3609	217	5	382:960–967	382:960–967	NUM
ejpam-3609	217	6	,	,	PUNCT
ejpam-3609	217	7	2018	2018	NUM
ejpam-3609	217	8	.	.	PUNCT
ejpam-3609	218	1	[	[	X
ejpam-3609	218	2	5	5	NUM
ejpam-3609	218	3	]	]	X
ejpam-3609	218	4	c	c	PROPN
ejpam-3609	218	5	cattani	cattani	VERB
ejpam-3609	218	6	a	a	DET
ejpam-3609	218	7	k	k	PROPN
ejpam-3609	218	8	golmankhaneh	golmankhaneh	PROPN
ejpam-3609	218	9	.	.	PUNCT
ejpam-3609	219	1	fractal	fractal	ADJ
ejpam-3609	219	2	logistic	logistic	ADJ
ejpam-3609	219	3	equation	equation	NOUN
ejpam-3609	219	4	.	.	PUNCT
ejpam-3609	220	1	fractal	fractal	ADJ
ejpam-3609	220	2	fract	fract	NOUN
ejpam-3609	220	3	,	,	PUNCT
ejpam-3609	220	4	3	3	NUM
ejpam-3609	220	5	,	,	PUNCT
ejpam-3609	220	6	2019	2019	NUM
ejpam-3609	220	7	.	.	PUNCT
ejpam-3609	221	1	[	[	X
ejpam-3609	221	2	6	6	NUM
ejpam-3609	221	3	]	]	PUNCT
ejpam-3609	221	4	c	c	X
ejpam-3609	221	5	tunç	tunç	VERB
ejpam-3609	221	6	a	a	DET
ejpam-3609	221	7	k	k	PROPN
ejpam-3609	221	8	golmankhaneh	golmankhaneh	PROPN
ejpam-3609	221	9	.	.	PUNCT
ejpam-3609	222	1	sumudu	sumudu	NOUN
ejpam-3609	222	2	transform	transform	NOUN
ejpam-3609	222	3	in	in	ADP
ejpam-3609	222	4	fractal	fractal	ADJ
ejpam-3609	222	5	calculus	calculus	NOUN
ejpam-3609	222	6	.	.	PUNCT
ejpam-3609	223	1	applied	apply	VERB
ejpam-3609	223	2	mathematics	mathematic	NOUN
ejpam-3609	223	3	and	and	CCONJ
ejpam-3609	223	4	computation	computation	NOUN
ejpam-3609	223	5	,	,	PUNCT
ejpam-3609	223	6	350:386–401	350:386–401	NUM
ejpam-3609	223	7	,	,	PUNCT
ejpam-3609	223	8	2019	2019	NUM
ejpam-3609	223	9	.	.	PUNCT
ejpam-3609	224	1	[	[	X
ejpam-3609	224	2	7	7	NUM
ejpam-3609	224	3	]	]	X
ejpam-3609	224	4	d	d	NOUN
ejpam-3609	224	5	baleanu	baleanu	VERB
ejpam-3609	224	6	a	a	DET
ejpam-3609	224	7	k	k	PROPN
ejpam-3609	224	8	golmankhaneh	golmankhaneh	NOUN
ejpam-3609	224	9	.	.	PUNCT
ejpam-3609	225	1	fractional	fractional	ADJ
ejpam-3609	225	2	dynamics	dynamic	NOUN
ejpam-3609	225	3	.	.	PUNCT
ejpam-3609	226	1	sciendo	sciendo	PROPN
ejpam-3609	226	2	migration	migration	PROPN
ejpam-3609	226	3	,	,	PUNCT
ejpam-3609	226	4	chapter:307	chapter:307	NOUN
ejpam-3609	226	5	-	-	PUNCT
ejpam-3609	226	6	332	332	NUM
ejpam-3609	226	7	,	,	PUNCT
ejpam-3609	226	8	2015	2015	NUM
ejpam-3609	226	9	.	.	PUNCT
ejpam-3609	227	1	[	[	X
ejpam-3609	227	2	8	8	NUM
ejpam-3609	227	3	]	]	X
ejpam-3609	227	4	d	d	NOUN
ejpam-3609	227	5	baleanu	baleanu	VERB
ejpam-3609	227	6	a	a	DET
ejpam-3609	227	7	k	k	PROPN
ejpam-3609	227	8	golmankhaneh	golmankhaneh	NOUN
ejpam-3609	227	9	.	.	PUNCT
ejpam-3609	228	1	diffraction	diffraction	NOUN
ejpam-3609	228	2	from	from	ADP
ejpam-3609	228	3	fractal	fractal	ADJ
ejpam-3609	228	4	grating	grate	VERB
ejpam-3609	228	5	cantor	cantor	NOUN
ejpam-3609	228	6	sets	set	NOUN
ejpam-3609	228	7	.	.	PUNCT
ejpam-3609	229	1	journal	journal	NOUN
ejpam-3609	229	2	of	of	ADP
ejpam-3609	229	3	modern	modern	ADJ
ejpam-3609	229	4	optics	optic	NOUN
ejpam-3609	229	5	,	,	PUNCT
ejpam-3609	229	6	63:1364–1369	63:1364–1369	NUM
ejpam-3609	229	7	,	,	PUNCT
ejpam-3609	229	8	2016	2016	NUM
ejpam-3609	229	9	.	.	PUNCT
ejpam-3609	230	1	[	[	X
ejpam-3609	230	2	9	9	NUM
ejpam-3609	230	3	]	]	X
ejpam-3609	230	4	d	d	NOUN
ejpam-3609	230	5	baleanu	baleanu	VERB
ejpam-3609	230	6	a	a	DET
ejpam-3609	230	7	k	k	PROPN
ejpam-3609	230	8	golmankhaneh	golmankhaneh	NOUN
ejpam-3609	230	9	.	.	PUNCT
ejpam-3609	231	1	heat	heat	NOUN
ejpam-3609	231	2	and	and	CCONJ
ejpam-3609	231	3	maxwells	maxwell	NOUN
ejpam-3609	231	4	equations	equation	NOUN
ejpam-3609	231	5	on	on	ADP
ejpam-3609	231	6	cantor	cantor	NOUN
ejpam-3609	231	7	cubes	cube	NOUN
ejpam-3609	231	8	.	.	PUNCT
ejpam-3609	232	1	rom	rom	PROPN
ejpam-3609	232	2	.	.	PUNCT
ejpam-3609	233	1	rep	rep	PROPN
ejpam-3609	233	2	.	.	PROPN
ejpam-3609	233	3	phys	phys	PROPN
ejpam-3609	233	4	,	,	PUNCT
ejpam-3609	233	5	69:1–11	69:1–11	NUM
ejpam-3609	233	6	,	,	PUNCT
ejpam-3609	233	7	2017	2017	NUM
ejpam-3609	233	8	.	.	PUNCT
ejpam-3609	234	1	[	[	X
ejpam-3609	234	2	10	10	NUM
ejpam-3609	234	3	]	]	SYM
ejpam-3609	234	4	a	a	DET
ejpam-3609	234	5	d	d	PROPN
ejpam-3609	234	6	gangal	gangal	NOUN
ejpam-3609	234	7	a	a	DET
ejpam-3609	234	8	parvate	parvate	NOUN
ejpam-3609	234	9	.	.	PUNCT
ejpam-3609	234	10	calculus	calculus	NOUN
ejpam-3609	234	11	on	on	ADP
ejpam-3609	234	12	fractal	fractal	ADJ
ejpam-3609	234	13	subsets	subset	NOUN
ejpam-3609	234	14	of	of	ADP
ejpam-3609	234	15	real	real	ADJ
ejpam-3609	234	16	line	line	NOUN
ejpam-3609	235	1	i	i	PRON
ejpam-3609	235	2	:	:	PUNCT
ejpam-3609	235	3	formulation	formulation	NOUN
ejpam-3609	235	4	.	.	PUNCT
ejpam-3609	236	1	fractals	fractal	NOUN
ejpam-3609	236	2	,	,	PUNCT
ejpam-3609	236	3	17:53–81	17:53–81	NUM
ejpam-3609	236	4	,	,	PUNCT
ejpam-3609	236	5	2009	2009	NUM
ejpam-3609	236	6	.	.	PUNCT
ejpam-3609	237	1	[	[	X
ejpam-3609	237	2	11	11	NUM
ejpam-3609	237	3	]	]	PUNCT
ejpam-3609	237	4	a	a	DET
ejpam-3609	237	5	d	d	PROPN
ejpam-3609	237	6	gangal	gangal	NOUN
ejpam-3609	237	7	a	a	DET
ejpam-3609	237	8	parvate	parvate	NOUN
ejpam-3609	237	9	.	.	PUNCT
ejpam-3609	237	10	calculus	calculus	NOUN
ejpam-3609	237	11	on	on	ADP
ejpam-3609	237	12	fractal	fractal	ADJ
ejpam-3609	237	13	subsets	subset	NOUN
ejpam-3609	237	14	of	of	ADP
ejpam-3609	237	15	real	real	ADJ
ejpam-3609	237	16	line	line	NOUN
ejpam-3609	237	17	ii	ii	PROPN
ejpam-3609	237	18	:	:	PUNCT
ejpam-3609	237	19	conjugacy	conjugacy	VERB
ejpam-3609	237	20	with	with	ADP
ejpam-3609	237	21	ordinary	ordinary	ADJ
ejpam-3609	237	22	calculus	calculus	NOUN
ejpam-3609	237	23	.	.	PUNCT
ejpam-3609	238	1	fractals	fractal	NOUN
ejpam-3609	238	2	,	,	PUNCT
ejpam-3609	238	3	19:271–290	19:271–290	NUM
ejpam-3609	238	4	,	,	PUNCT
ejpam-3609	238	5	2011	2011	NUM
ejpam-3609	238	6	.	.	PUNCT
ejpam-3609	239	1	references	reference	NOUN
ejpam-3609	239	2	32	32	NUM
ejpam-3609	240	1	[	[	X
ejpam-3609	240	2	12	12	NUM
ejpam-3609	240	3	]	]	PUNCT
ejpam-3609	240	4	a	a	DET
ejpam-3609	240	5	d	d	PROPN
ejpam-3609	240	6	gangal	gangal	NOUN
ejpam-3609	240	7	a	a	DET
ejpam-3609	240	8	parvate	parvate	NOUN
ejpam-3609	240	9	,	,	PUNCT
ejpam-3609	240	10	s	s	NOUN
ejpam-3609	240	11	satin	satin	NOUN
ejpam-3609	240	12	.	.	PUNCT
ejpam-3609	240	13	caclulus	caclulus	NOUN
ejpam-3609	240	14	on	on	ADP
ejpam-3609	240	15	fractal	fractal	ADJ
ejpam-3609	240	16	curves	curve	NOUN
ejpam-3609	240	17	in	in	ADP
ejpam-3609	240	18	rn	rn	PROPN
ejpam-3609	240	19	.	.	PROPN
ejpam-3609	240	20	fractals	fractal	NOUN
ejpam-3609	240	21	,	,	PUNCT
ejpam-3609	240	22	19:15–27	19:15–27	NUM
ejpam-3609	240	23	,	,	PUNCT
ejpam-3609	240	24	2011	2011	NUM
ejpam-3609	240	25	.	.	PUNCT
ejpam-3609	241	1	[	[	X
ejpam-3609	241	2	13	13	NUM
ejpam-3609	241	3	]	]	PUNCT
ejpam-3609	241	4	a	a	DET
ejpam-3609	241	5	pishkoo	pishkoo	NOUN
ejpam-3609	241	6	f	f	PROPN
ejpam-3609	241	7	k	k	PROPN
ejpam-3609	241	8	jafari	jafari	PROPN
ejpam-3609	241	9	,	,	PUNCT
ejpam-3609	241	10	m	m	VERB
ejpam-3609	241	11	r	r	NOUN
ejpam-3609	241	12	madanbeigi	madanbeigi	NOUN
ejpam-3609	241	13	.	.	PUNCT
ejpam-3609	242	1	conformable	conformable	VERB
ejpam-3609	242	2	derivative	derivative	ADJ
ejpam-3609	242	3	and	and	CCONJ
ejpam-3609	242	4	fractal	fractal	ADJ
ejpam-3609	242	5	derivative	derivative	NOUN
ejpam-3609	242	6	of	of	ADP
ejpam-3609	242	7	functions	function	NOUN
ejpam-3609	242	8	on	on	ADP
ejpam-3609	242	9	the	the	DET
ejpam-3609	242	10	interval	interval	NOUN
ejpam-3609	242	11	[	[	X
ejpam-3609	242	12	0,1	0,1	NOUN
ejpam-3609	242	13	]	]	PUNCT
ejpam-3609	242	14	.	.	PUNCT
ejpam-3609	243	1	to	to	ADP
ejpam-3609	243	2	physics	physics	PROPN
ejpam-3609	243	3	journal	journal	PROPN
ejpam-3609	243	4	,	,	PUNCT
ejpam-3609	243	5	4:82–90	4:82–90	NUM
ejpam-3609	243	6	,	,	PUNCT
ejpam-3609	243	7	2019	2019	NUM
ejpam-3609	243	8	.	.	PUNCT
ejpam-3609	244	1	[	[	X
ejpam-3609	244	2	14	14	NUM
ejpam-3609	244	3	]	]	X
ejpam-3609	244	4	a	a	DET
ejpam-3609	244	5	pishkoo	pishkoo	NOUN
ejpam-3609	244	6	f	f	PROPN
ejpam-3609	244	7	k	k	PROPN
ejpam-3609	244	8	jafari	jafari	PROPN
ejpam-3609	244	9	,	,	PUNCT
ejpam-3609	244	10	m	m	PROPN
ejpam-3609	244	11	s	s	PROPN
ejpam-3609	244	12	asgari	asgari	ADJ
ejpam-3609	244	13	.	.	PUNCT
ejpam-3609	245	1	fractal	fractal	ADJ
ejpam-3609	245	2	calculus	calculus	NOUN
ejpam-3609	245	3	for	for	ADP
ejpam-3609	245	4	fractal	fractal	ADJ
ejpam-3609	245	5	materials	material	NOUN
ejpam-3609	245	6	.	.	PUNCT
ejpam-3609	246	1	fractal	fractal	ADJ
ejpam-3609	246	2	fract	fract	PROPN
ejpam-3609	246	3	,	,	PUNCT
ejpam-3609	246	4	3:3010008	3:3010008	NUM
ejpam-3609	246	5	,	,	PUNCT
ejpam-3609	246	6	2019	2019	NUM
ejpam-3609	246	7	.	.	PUNCT
ejpam-3609	247	1	[	[	X
ejpam-3609	247	2	15	15	NUM
ejpam-3609	247	3	]	]	X
ejpam-3609	247	4	k	k	PROPN
ejpam-3609	247	5	falconer	falconer	NOUN
ejpam-3609	247	6	.	.	PUNCT
ejpam-3609	247	7	fractal	fractal	PROPN
ejpam-3609	247	8	geometry	geometry	NOUN
ejpam-3609	247	9	:	:	PUNCT
ejpam-3609	247	10	mathematical	mathematical	ADJ
ejpam-3609	247	11	foundations	foundation	NOUN
ejpam-3609	247	12	and	and	CCONJ
ejpam-3609	247	13	applications	application	NOUN
ejpam-3609	247	14	.	.	PUNCT
ejpam-3609	248	1	second	second	ADJ
ejpam-3609	248	2	edition	edition	PROPN
ejpam-3609	248	3	,	,	PUNCT
ejpam-3609	248	4	wiley	wiley	PROPN
ejpam-3609	248	5	,	,	PUNCT
ejpam-3609	248	6	new	new	PROPN
ejpam-3609	248	7	york	york	PROPN
ejpam-3609	248	8	,	,	PUNCT
ejpam-3609	248	9	2007	2007	NUM
ejpam-3609	248	10	.	.	PUNCT
ejpam-3609	249	1	[	[	X
ejpam-3609	249	2	16	16	NUM
ejpam-3609	249	3	]	]	X
ejpam-3609	249	4	f	f	PROPN
ejpam-3609	249	5	e	e	PROPN
ejpam-3609	249	6	harris	harris	PROPN
ejpam-3609	249	7	g	g	PROPN
ejpam-3609	249	8	b	b	PROPN
ejpam-3609	249	9	arfken	arfken	PROPN
ejpam-3609	249	10	,	,	PUNCT
ejpam-3609	249	11	h	h	PROPN
ejpam-3609	249	12	j	j	PROPN
ejpam-3609	249	13	weber	weber	PROPN
ejpam-3609	249	14	.	.	PUNCT
ejpam-3609	250	1	mathematical	mathematical	ADJ
ejpam-3609	250	2	methods	method	NOUN
ejpam-3609	250	3	for	for	ADP
ejpam-3609	250	4	physicists	physicist	NOUN
ejpam-3609	250	5	.	.	PUNCT
ejpam-3609	251	1	7th	7th	ADJ
ejpam-3609	251	2	edition	edition	NOUN
ejpam-3609	251	3	,	,	PUNCT
ejpam-3609	251	4	academic	academic	PROPN
ejpam-3609	251	5	press	press	PROPN
ejpam-3609	251	6	inc	inc	PROPN
ejpam-3609	251	7	.	.	PROPN
ejpam-3609	251	8	,	,	PUNCT
ejpam-3609	251	9	orlando	orlando	PROPN
ejpam-3609	251	10	,	,	PUNCT
ejpam-3609	251	11	florida	florida	PROPN
ejpam-3609	251	12	,	,	PUNCT
ejpam-3609	251	13	2012	2012	NUM
ejpam-3609	251	14	.	.	PUNCT
ejpam-3609	252	1	[	[	X
ejpam-3609	252	2	17	17	NUM
ejpam-3609	252	3	]	]	PUNCT
ejpam-3609	252	4	a	a	DET
ejpam-3609	252	5	k	k	PROPN
ejpam-3609	252	6	golmankhaneh	golmankhaneh	NOUN
ejpam-3609	252	7	.	.	PUNCT
ejpam-3609	253	1	statistical	statistical	ADJ
ejpam-3609	253	2	mechanics	mechanic	NOUN
ejpam-3609	253	3	involving	involve	VERB
ejpam-3609	253	4	fractal	fractal	ADJ
ejpam-3609	253	5	temperature	temperature	NOUN
ejpam-3609	253	6	.	.	PUNCT
ejpam-3609	254	1	fractal	fractal	ADJ
ejpam-3609	254	2	fract	fract	PROPN
ejpam-3609	254	3	,	,	PUNCT
ejpam-3609	254	4	3:3020020	3:3020020	NUM
ejpam-3609	254	5	,	,	PUNCT
ejpam-3609	254	6	2019	2019	NUM
ejpam-3609	254	7	.	.	PUNCT
ejpam-3609	255	1	[	[	X
ejpam-3609	255	2	18	18	NUM
ejpam-3609	255	3	]	]	X
ejpam-3609	255	4	j	j	PROPN
ejpam-3609	255	5	d	d	PROPN
ejpam-3609	255	6	jackson	jackson	PROPN
ejpam-3609	255	7	.	.	PUNCT
ejpam-3609	256	1	classical	classical	ADJ
ejpam-3609	256	2	electrodynamics	electrodynamic	NOUN
ejpam-3609	256	3	.	.	PUNCT
ejpam-3609	257	1	third	third	PROPN
ejpam-3609	257	2	edition	edition	PROPN
ejpam-3609	257	3	,	,	PUNCT
ejpam-3609	257	4	wiley	wiley	PROPN
ejpam-3609	257	5	,	,	PUNCT
ejpam-3609	257	6	new	new	PROPN
ejpam-3609	257	7	york	york	PROPN
ejpam-3609	257	8	,	,	PUNCT
ejpam-3609	257	9	1998	1998	NUM
ejpam-3609	257	10	.	.	PUNCT
ejpam-3609	258	1	[	[	X
ejpam-3609	258	2	19	19	NUM
ejpam-3609	258	3	]	]	SYM
ejpam-3609	258	4	b	b	PROPN
ejpam-3609	258	5	b	b	X
ejpam-3609	258	6	mandelbrot	mandelbrot	PROPN
ejpam-3609	258	7	.	.	PUNCT
ejpam-3609	259	1	the	the	DET
ejpam-3609	259	2	fractal	fractal	ADJ
ejpam-3609	259	3	geometry	geometry	NOUN
ejpam-3609	259	4	of	of	ADP
ejpam-3609	259	5	nature	nature	NOUN
ejpam-3609	259	6	.	.	PUNCT
ejpam-3609	260	1	w.	w.	PROPN
ejpam-3609	260	2	h.	h.	PROPN
ejpam-3609	260	3	freeman	freeman	PROPN
ejpam-3609	260	4	and	and	CCONJ
ejpam-3609	260	5	company	company	NOUN
ejpam-3609	260	6	,	,	PUNCT
ejpam-3609	260	7	united	united	PROPN
ejpam-3609	260	8	states	states	PROPN
ejpam-3609	260	9	,	,	PUNCT
ejpam-3609	260	10	1977	1977	NUM
ejpam-3609	260	11	.	.	PUNCT
ejpam-3609	261	1	[	[	X
ejpam-3609	261	2	20	20	NUM
ejpam-3609	261	3	]	]	X
ejpam-3609	261	4	m	m	VERB
ejpam-3609	261	5	azhini	azhini	NOUN
ejpam-3609	261	6	n	n	X
ejpam-3609	261	7	delfan	delfan	NOUN
ejpam-3609	261	8	,	,	PUNCT
ejpam-3609	261	9	a	a	DET
ejpam-3609	261	10	pishkoo	pishkoo	NOUN
ejpam-3609	261	11	.	.	PUNCT
ejpam-3609	262	1	using	use	VERB
ejpam-3609	262	2	comsol	comsol	NOUN
ejpam-3609	262	3	multiphysics	multiphysic	NOUN
ejpam-3609	262	4	to	to	PART
ejpam-3609	262	5	simulate	simulate	VERB
ejpam-3609	262	6	adiation	adiation	NOUN
ejpam-3609	262	7	from	from	ADP
ejpam-3609	262	8	dipole	dipole	NOUN
ejpam-3609	262	9	antenna	antenna	NOUN
ejpam-3609	262	10	and	and	CCONJ
ejpam-3609	262	11	first	first	ADJ
ejpam-3609	262	12	iteration	iteration	NOUN
ejpam-3609	262	13	cantor	cantor	NOUN
ejpam-3609	262	14	set	set	VERB
ejpam-3609	262	15	shape	shape	NOUN
ejpam-3609	262	16	antenna	antenna	NOUN
ejpam-3609	262	17	.	.	PUNCT
ejpam-3609	263	1	to	to	ADP
ejpam-3609	263	2	physics	physics	PROPN
ejpam-3609	263	3	journal	journal	PROPN
ejpam-3609	263	4	,	,	PUNCT
ejpam-3609	263	5	4:48–54	4:48–54	NUM
ejpam-3609	263	6	,	,	PUNCT
ejpam-3609	263	7	2019	2019	NUM
ejpam-3609	263	8	.	.	PUNCT
ejpam-3609	264	1	[	[	X
ejpam-3609	264	2	21	21	NUM
ejpam-3609	264	3	]	]	PUNCT
ejpam-3609	264	4	a	a	DET
ejpam-3609	264	5	d	d	PROPN
ejpam-3609	264	6	gangal	gangal	NOUN
ejpam-3609	264	7	s	s	PART
ejpam-3609	264	8	satin	satin	NOUN
ejpam-3609	264	9	.	.	PUNCT
ejpam-3609	265	1	langevin	langevin	ADJ
ejpam-3609	265	2	equation	equation	NOUN
ejpam-3609	265	3	on	on	ADP
ejpam-3609	265	4	fractal	fractal	ADJ
ejpam-3609	265	5	curves	curve	NOUN
ejpam-3609	265	6	.	.	PUNCT
ejpam-3609	266	1	fractals	fractal	NOUN
ejpam-3609	266	2	,	,	PUNCT
ejpam-3609	266	3	24:1650028	24:1650028	NUM
ejpam-3609	266	4	,	,	PUNCT
ejpam-3609	266	5	2016	2016	NUM
ejpam-3609	266	6	.	.	PUNCT
ejpam-3609	267	1	[	[	X
ejpam-3609	267	2	22	22	NUM
ejpam-3609	267	3	]	]	PUNCT
ejpam-3609	267	4	a	a	DET
ejpam-3609	267	5	d	d	PROPN
ejpam-3609	267	6	gangal	gangal	NOUN
ejpam-3609	267	7	s	s	PART
ejpam-3609	267	8	satin	satin	NOUN
ejpam-3609	267	9	,	,	PUNCT
ejpam-3609	267	10	a	a	DET
ejpam-3609	267	11	parvate	parvate	NOUN
ejpam-3609	267	12	.	.	PUNCT
ejpam-3609	267	13	fokker	fokker	NOUN
ejpam-3609	267	14	-	-	PUNCT
ejpam-3609	267	15	planck	planck	NOUN
ejpam-3609	267	16	equation	equation	NOUN
ejpam-3609	267	17	on	on	ADP
ejpam-3609	267	18	fractal	fractal	ADJ
ejpam-3609	267	19	curves	curve	NOUN
ejpam-3609	267	20	.	.	PUNCT
ejpam-3609	268	1	chaos	chaos	NOUN
ejpam-3609	268	2	,	,	PUNCT
ejpam-3609	268	3	solitons	soliton	NOUN
ejpam-3609	268	4	&	&	CCONJ
ejpam-3609	268	5	fractals	fractal	NOUN
ejpam-3609	268	6	,	,	PUNCT
ejpam-3609	268	7	5:30–35	5:30–35	NUM
ejpam-3609	268	8	,	,	PUNCT
ejpam-3609	268	9	2013	2013	NUM
ejpam-3609	268	10	.	.	PUNCT