id	sid	tid	token	lemma	pos
stem-5222	1	1	295	295	NUM
stem-5222	1	2	american	american	ADJ
stem-5222	1	3	journal	journal	PROPN
stem-5222	1	4	of	of	ADP
stem-5222	1	5	language	language	NOUN
stem-5222	1	6	,	,	PUNCT
stem-5222	1	7	literacy	literacy	NOUN
stem-5222	1	8	and	and	CCONJ
stem-5222	1	9	learning	learn	VERB
stem-5222	1	10	in	in	ADP
stem-5222	1	11	stem	stem	NOUN
stem-5222	1	12	education	education	NOUN
stem-5222	1	13	www	www	PROPN
stem-5222	1	14	.	.	PROPN
stem-5222	2	1	grnjournal.us	grnjournal.us	PROPN
stem-5222	2	2	american	american	PROPN
stem-5222	2	3	journal	journal	PROPN
stem-5222	2	4	of	of	ADP
stem-5222	2	5	language	language	NOUN
stem-5222	2	6	,	,	PUNCT
stem-5222	2	7	literacy	literacy	NOUN
stem-5222	2	8	and	and	CCONJ
stem-5222	2	9	learning	learn	VERB
stem-5222	2	10	in	in	ADP
stem-5222	2	11	stem	stem	NOUN
stem-5222	2	12	education	education	NOUN
stem-5222	2	13	volume	volume	NOUN
stem-5222	2	14	02	02	NUM
stem-5222	2	15	,	,	PUNCT
stem-5222	2	16	issue	issue	NOUN
stem-5222	2	17	06	06	NUM
stem-5222	2	18	,	,	PUNCT
stem-5222	2	19	2024	2024	NUM
stem-5222	2	20	issn	issn	X
stem-5222	2	21	(	(	PUNCT
stem-5222	2	22	e	e	NOUN
stem-5222	2	23	):	):	PUNCT
stem-5222	2	24	2993	2993	NUM
stem-5222	2	25	-	-	SYM
stem-5222	2	26	2769	2769	NUM
stem-5222	2	27	analyzing	analyze	VERB
stem-5222	2	28	complex	complex	ADJ
stem-5222	2	29	numbers	number	NOUN
stem-5222	2	30	using	use	VERB
stem-5222	2	31	numerical	numerical	ADJ
stem-5222	2	32	theory	theory	PROPN
stem-5222	2	33	aseel	aseel	PROPN
stem-5222	2	34	najeh	najeh	PROPN
stem-5222	2	35	abbas	abbas	PROPN
stem-5222	2	36	researcher	researcher	PROPN
stem-5222	2	37	,	,	PUNCT
stem-5222	2	38	al	al	PROPN
stem-5222	2	39	-	-	PUNCT
stem-5222	2	40	mustansiriya	mustansiriya	PROPN
stem-5222	2	41	university	university	PROPN
stem-5222	2	42	/	/	SYM
stem-5222	2	43	college	college	PROPN
stem-5222	2	44	of	of	ADP
stem-5222	2	45	administration	administration	NOUN
stem-5222	2	46	and	and	CCONJ
stem-5222	2	47	economics	economics	NOUN
stem-5222	2	48	/	/	SYM
stem-5222	2	49	information	information	NOUN
stem-5222	2	50	technology	technology	NOUN
stem-5222	2	51	division	division	NOUN
stem-5222	2	52	abstract	abstract	NOUN
stem-5222	2	53	.	.	PUNCT
stem-5222	3	1	complex	complex	ADJ
stem-5222	3	2	numbers	number	NOUN
stem-5222	3	3	,	,	PUNCT
stem-5222	3	4	which	which	PRON
stem-5222	3	5	are	be	AUX
stem-5222	3	6	essential	essential	ADJ
stem-5222	3	7	in	in	ADP
stem-5222	3	8	several	several	ADJ
stem-5222	3	9	branches	branch	NOUN
stem-5222	3	10	of	of	ADP
stem-5222	3	11	mathematics	mathematic	NOUN
stem-5222	3	12	and	and	CCONJ
stem-5222	3	13	engineering	engineering	NOUN
stem-5222	3	14	,	,	PUNCT
stem-5222	3	15	provide	provide	VERB
stem-5222	3	16	distinctive	distinctive	ADJ
stem-5222	3	17	difficulties	difficulty	NOUN
stem-5222	3	18	and	and	CCONJ
stem-5222	3	19	possibilities	possibility	NOUN
stem-5222	3	20	for	for	ADP
stem-5222	3	21	study	study	NOUN
stem-5222	3	22	.	.	PUNCT
stem-5222	4	1	this	this	DET
stem-5222	4	2	study	study	NOUN
stem-5222	4	3	examines	examine	VERB
stem-5222	4	4	the	the	DET
stem-5222	4	5	use	use	NOUN
stem-5222	4	6	of	of	ADP
stem-5222	4	7	numerical	numerical	ADJ
stem-5222	4	8	theory	theory	NOUN
stem-5222	4	9	in	in	ADP
stem-5222	4	10	analysing	analyse	VERB
stem-5222	4	11	complicated	complicated	ADJ
stem-5222	4	12	numbers	number	NOUN
stem-5222	4	13	,	,	PUNCT
stem-5222	4	14	offering	offer	VERB
stem-5222	4	15	valuable	valuable	ADJ
stem-5222	4	16	insights	insight	NOUN
stem-5222	4	17	into	into	ADP
stem-5222	4	18	their	their	PRON
stem-5222	4	19	characteristics	characteristic	NOUN
stem-5222	4	20	and	and	CCONJ
stem-5222	4	21	behaviours	behaviour	NOUN
stem-5222	4	22	across	across	ADP
stem-5222	4	23	many	many	ADJ
stem-5222	4	24	situations	situation	NOUN
stem-5222	4	25	.	.	PUNCT
stem-5222	5	1	through	through	ADP
stem-5222	5	2	the	the	DET
stem-5222	5	3	use	use	NOUN
stem-5222	5	4	of	of	ADP
stem-5222	5	5	numerical	numerical	ADJ
stem-5222	5	6	techniques	technique	NOUN
stem-5222	5	7	,	,	PUNCT
stem-5222	5	8	our	our	PRON
stem-5222	5	9	objective	objective	NOUN
stem-5222	5	10	is	be	AUX
stem-5222	5	11	to	to	PART
stem-5222	5	12	enhance	enhance	VERB
stem-5222	5	13	comprehension	comprehension	NOUN
stem-5222	5	14	of	of	ADP
stem-5222	5	15	intricate	intricate	ADJ
stem-5222	5	16	number	number	NOUN
stem-5222	5	17	systems	system	NOUN
stem-5222	5	18	,	,	PUNCT
stem-5222	5	19	namely	namely	ADV
stem-5222	5	20	in	in	ADP
stem-5222	5	21	the	the	DET
stem-5222	5	22	resolution	resolution	NOUN
stem-5222	5	23	of	of	ADP
stem-5222	5	24	equations	equation	NOUN
stem-5222	5	25	,	,	PUNCT
stem-5222	5	26	examination	examination	NOUN
stem-5222	5	27	of	of	ADP
stem-5222	5	28	functions	function	NOUN
stem-5222	5	29	,	,	PUNCT
stem-5222	5	30	and	and	CCONJ
stem-5222	5	31	representation	representation	NOUN
stem-5222	5	32	of	of	ADP
stem-5222	5	33	real	real	ADJ
stem-5222	5	34	-	-	PUNCT
stem-5222	5	35	world	world	NOUN
stem-5222	5	36	occurrences	occurrence	NOUN
stem-5222	5	37	.	.	PUNCT
stem-5222	6	1	first	first	ADV
stem-5222	6	2	,	,	PUNCT
stem-5222	6	3	we	we	PRON
stem-5222	6	4	will	will	AUX
stem-5222	6	5	examine	examine	VERB
stem-5222	6	6	the	the	DET
stem-5222	6	7	fundamental	fundamental	ADJ
stem-5222	6	8	characteristics	characteristic	NOUN
stem-5222	6	9	of	of	ADP
stem-5222	6	10	complex	complex	ADJ
stem-5222	6	11	numbers	number	NOUN
stem-5222	6	12	,	,	PUNCT
stem-5222	6	13	which	which	PRON
stem-5222	6	14	include	include	VERB
stem-5222	6	15	their	their	PRON
stem-5222	6	16	depiction	depiction	NOUN
stem-5222	6	17	in	in	ADP
stem-5222	6	18	cartesian	cartesian	ADJ
stem-5222	6	19	and	and	CCONJ
stem-5222	6	20	polar	polar	ADJ
stem-5222	6	21	forms	form	NOUN
stem-5222	6	22	,	,	PUNCT
stem-5222	6	23	as	as	ADV
stem-5222	6	24	well	well	ADV
stem-5222	6	25	as	as	ADP
stem-5222	6	26	their	their	PRON
stem-5222	6	27	operations	operation	NOUN
stem-5222	6	28	,	,	PUNCT
stem-5222	6	29	such	such	ADJ
stem-5222	6	30	as	as	ADP
stem-5222	6	31	addition	addition	NOUN
stem-5222	6	32	,	,	PUNCT
stem-5222	6	33	multiplication	multiplication	NOUN
stem-5222	6	34	,	,	PUNCT
stem-5222	6	35	and	and	CCONJ
stem-5222	6	36	complex	complex	ADJ
stem-5222	6	37	conjugation	conjugation	NOUN
stem-5222	6	38	.	.	PUNCT
stem-5222	7	1	the	the	DET
stem-5222	7	2	study	study	NOUN
stem-5222	7	3	subsequently	subsequently	ADV
stem-5222	7	4	explores	explore	VERB
stem-5222	7	5	more	more	ADV
stem-5222	7	6	sophisticated	sophisticated	ADJ
stem-5222	7	7	subjects	subject	NOUN
stem-5222	7	8	,	,	PUNCT
stem-5222	7	9	such	such	ADJ
stem-5222	7	10	as	as	ADP
stem-5222	7	11	the	the	DET
stem-5222	7	12	origins	origin	NOUN
stem-5222	7	13	of	of	ADP
stem-5222	7	14	complex	complex	ADJ
stem-5222	7	15	numbers	number	NOUN
stem-5222	7	16	,	,	PUNCT
stem-5222	7	17	and	and	CCONJ
stem-5222	7	18	the	the	DET
stem-5222	7	19	use	use	NOUN
stem-5222	7	20	of	of	ADP
stem-5222	7	21	numerical	numerical	ADJ
stem-5222	7	22	methods	method	NOUN
stem-5222	7	23	to	to	PART
stem-5222	7	24	estimate	estimate	VERB
stem-5222	7	25	these	these	DET
stem-5222	7	26	origins	origin	NOUN
stem-5222	7	27	.	.	PUNCT
stem-5222	8	1	this	this	DET
stem-5222	8	2	research	research	NOUN
stem-5222	8	3	mostly	mostly	ADV
stem-5222	8	4	centres	centre	VERB
stem-5222	8	5	on	on	ADP
stem-5222	8	6	using	use	VERB
stem-5222	8	7	numerical	numerical	ADJ
stem-5222	8	8	methods	method	NOUN
stem-5222	8	9	to	to	PART
stem-5222	8	10	solve	solve	VERB
stem-5222	8	11	intricate	intricate	ADJ
stem-5222	8	12	problems	problem	NOUN
stem-5222	8	13	.	.	PUNCT
stem-5222	9	1	we	we	PRON
stem-5222	9	2	analyse	analyse	VERB
stem-5222	9	3	the	the	DET
stem-5222	9	4	convergence	convergence	NOUN
stem-5222	9	5	qualities	quality	NOUN
stem-5222	9	6	and	and	CCONJ
stem-5222	9	7	computing	computing	NOUN
stem-5222	9	8	efficiency	efficiency	NOUN
stem-5222	9	9	of	of	ADP
stem-5222	9	10	approaches	approach	NOUN
stem-5222	9	11	such	such	ADJ
stem-5222	9	12	as	as	ADP
stem-5222	9	13	the	the	DET
stem-5222	9	14	newton	newton	PROPN
stem-5222	9	15	-	-	PUNCT
stem-5222	9	16	raphson	raphson	PROPN
stem-5222	9	17	method	method	NOUN
stem-5222	9	18	,	,	PUNCT
stem-5222	9	19	iterative	iterative	NOUN
stem-5222	9	20	refinement	refinement	NOUN
stem-5222	9	21	,	,	PUNCT
stem-5222	9	22	and	and	CCONJ
stem-5222	9	23	the	the	DET
stem-5222	9	24	durand	durand	PROPN
stem-5222	9	25	-	-	PUNCT
stem-5222	9	26	kerner	kerner	PROPN
stem-5222	9	27	method	method	PROPN
stem-5222	9	28	.	.	PUNCT
stem-5222	10	1	the	the	DET
stem-5222	10	2	study	study	NOUN
stem-5222	10	3	also	also	ADV
stem-5222	10	4	examines	examine	VERB
stem-5222	10	5	the	the	DET
stem-5222	10	6	use	use	NOUN
stem-5222	10	7	of	of	ADP
stem-5222	10	8	these	these	DET
stem-5222	10	9	techniques	technique	NOUN
stem-5222	10	10	using	use	VERB
stem-5222	10	11	contemporary	contemporary	ADJ
stem-5222	10	12	computer	computer	NOUN
stem-5222	10	13	tools	tool	NOUN
stem-5222	10	14	and	and	CCONJ
stem-5222	10	15	software	software	NOUN
stem-5222	10	16	,	,	PUNCT
stem-5222	10	17	emphasising	emphasise	VERB
stem-5222	10	18	its	its	PRON
stem-5222	10	19	tangible	tangible	ADJ
stem-5222	10	20	applications	application	NOUN
stem-5222	10	21	in	in	ADP
stem-5222	10	22	the	the	DET
stem-5222	10	23	fields	field	NOUN
stem-5222	10	24	of	of	ADP
stem-5222	10	25	engineering	engineering	NOUN
stem-5222	10	26	and	and	CCONJ
stem-5222	10	27	physics	physics	NOUN
stem-5222	10	28	.	.	PUNCT
stem-5222	11	1	in	in	ADP
stem-5222	11	2	addition	addition	NOUN
stem-5222	11	3	,	,	PUNCT
stem-5222	11	4	we	we	PRON
stem-5222	11	5	examine	examine	VERB
stem-5222	11	6	the	the	DET
stem-5222	11	7	numerical	numerical	ADJ
stem-5222	11	8	stability	stability	NOUN
stem-5222	11	9	and	and	CCONJ
stem-5222	11	10	error	error	NOUN
stem-5222	11	11	analysis	analysis	NOUN
stem-5222	11	12	in	in	ADP
stem-5222	11	13	the	the	DET
stem-5222	11	14	realm	realm	NOUN
stem-5222	11	15	of	of	ADP
stem-5222	11	16	complex	complex	ADJ
stem-5222	11	17	number	number	NOUN
stem-5222	11	18	calculations	calculation	NOUN
stem-5222	11	19	.	.	PUNCT
stem-5222	12	1	this	this	PRON
stem-5222	12	2	is	be	AUX
stem-5222	12	3	an	an	DET
stem-5222	12	4	examination	examination	NOUN
stem-5222	12	5	of	of	ADP
stem-5222	12	6	problems	problem	NOUN
stem-5222	12	7	related	relate	VERB
stem-5222	12	8	to	to	ADP
stem-5222	12	9	floating	float	VERB
stem-5222	12	10	-	-	PUNCT
stem-5222	12	11	point	point	NOUN
stem-5222	12	12	arithmetic	arithmetic	ADJ
stem-5222	12	13	and	and	CCONJ
stem-5222	12	14	the	the	DET
stem-5222	12	15	techniques	technique	NOUN
stem-5222	12	16	used	use	VERB
stem-5222	12	17	to	to	PART
stem-5222	12	18	reduce	reduce	VERB
stem-5222	12	19	numerical	numerical	ADJ
stem-5222	12	20	imprecisions	imprecision	NOUN
stem-5222	12	21	.	.	PUNCT
stem-5222	13	1	emphasis	emphasis	NOUN
stem-5222	13	2	is	be	AUX
stem-5222	13	3	placed	place	VERB
stem-5222	13	4	on	on	ADP
stem-5222	13	5	the	the	DET
stem-5222	13	6	condition	condition	NOUN
stem-5222	13	7	numbers	number	NOUN
stem-5222	13	8	of	of	ADP
stem-5222	13	9	complex	complex	ADJ
stem-5222	13	10	functions	function	NOUN
stem-5222	13	11	and	and	CCONJ
stem-5222	13	12	their	their	PRON
stem-5222	13	13	influence	influence	NOUN
stem-5222	13	14	on	on	ADP
stem-5222	13	15	the	the	DET
stem-5222	13	16	resilience	resilience	NOUN
stem-5222	13	17	of	of	ADP
stem-5222	13	18	numerical	numerical	ADJ
stem-5222	13	19	solutions	solution	NOUN
stem-5222	13	20	.	.	PUNCT
stem-5222	14	1	the	the	DET
stem-5222	14	2	practical	practical	ADJ
stem-5222	14	3	importance	importance	NOUN
stem-5222	14	4	of	of	ADP
stem-5222	14	5	numerical	numerical	ADJ
stem-5222	14	6	analysis	analysis	NOUN
stem-5222	14	7	of	of	ADP
stem-5222	14	8	complex	complex	ADJ
stem-5222	14	9	numbers	number	NOUN
stem-5222	14	10	is	be	AUX
stem-5222	14	11	shown	show	VERB
stem-5222	14	12	by	by	ADP
stem-5222	14	13	examining	examine	VERB
stem-5222	14	14	applications	application	NOUN
stem-5222	14	15	in	in	ADP
stem-5222	14	16	engineering	engineering	NOUN
stem-5222	14	17	,	,	PUNCT
stem-5222	14	18	such	such	ADJ
stem-5222	14	19	as	as	ADP
stem-5222	14	20	signal	signal	NOUN
stem-5222	14	21	processing	processing	NOUN
stem-5222	14	22	and	and	CCONJ
stem-5222	14	23	control	control	NOUN
stem-5222	14	24	systems	system	NOUN
stem-5222	14	25	.	.	PUNCT
stem-5222	15	1	case	case	NOUN
stem-5222	15	2	studies	study	NOUN
stem-5222	15	3	exemplify	exemplify	VERB
stem-5222	15	4	the	the	DET
stem-5222	15	5	use	use	NOUN
stem-5222	15	6	of	of	ADP
stem-5222	15	7	numerical	numerical	ADJ
stem-5222	15	8	approaches	approach	NOUN
stem-5222	15	9	in	in	ADP
stem-5222	15	10	solving	solve	VERB
stem-5222	15	11	real	real	ADJ
stem-5222	15	12	-	-	PUNCT
stem-5222	15	13	world	world	NOUN
stem-5222	15	14	situations	situation	NOUN
stem-5222	15	15	that	that	PRON
stem-5222	15	16	include	include	VERB
stem-5222	15	17	intricate	intricate	ADJ
stem-5222	15	18	variables	variable	NOUN
stem-5222	15	19	,	,	PUNCT
stem-5222	15	20	highlighting	highlight	VERB
stem-5222	15	21	the	the	DET
stem-5222	15	22	adaptability	adaptability	NOUN
stem-5222	15	23	and	and	CCONJ
stem-5222	15	24	efficacy	efficacy	NOUN
stem-5222	15	25	of	of	ADP
stem-5222	15	26	these	these	DET
stem-5222	15	27	techniques	technique	NOUN
stem-5222	15	28	.	.	PUNCT
stem-5222	16	1	key	key	ADJ
stem-5222	16	2	words	word	NOUN
stem-5222	16	3	:	:	PUNCT
stem-5222	16	4	analyzing	analyze	VERB
stem-5222	16	5	,	,	PUNCT
stem-5222	16	6	complex	complex	ADJ
stem-5222	16	7	numbers	number	NOUN
stem-5222	16	8	,	,	PUNCT
stem-5222	16	9	numerical	numerical	ADJ
stem-5222	16	10	theory	theory	NOUN
stem-5222	16	11	.	.	PUNCT
stem-5222	17	1	introduction	introduction	NOUN
stem-5222	17	2	:	:	PUNCT
stem-5222	17	3	the	the	DET
stem-5222	17	4	subject	subject	ADJ
stem-5222	17	5	matter	matter	NOUN
stem-5222	17	6	of	of	ADP
stem-5222	17	7	these	these	DET
stem-5222	17	8	notes	note	NOUN
stem-5222	17	9	pertains	pertain	VERB
stem-5222	17	10	to	to	PART
stem-5222	17	11	complex	complex	ADJ
stem-5222	17	12	analysis	analysis	NOUN
stem-5222	17	13	,	,	PUNCT
stem-5222	17	14	a	a	DET
stem-5222	17	15	branch	branch	NOUN
stem-5222	17	16	of	of	ADP
stem-5222	17	17	mathematics	mathematic	NOUN
stem-5222	17	18	that	that	PRON
stem-5222	17	19	focuses	focus	VERB
stem-5222	17	20	on	on	ADP
stem-5222	17	21	the	the	DET
stem-5222	17	22	study	study	NOUN
stem-5222	17	23	of	of	ADP
stem-5222	17	24	analytic	analytic	ADJ
stem-5222	17	25	functions	function	NOUN
stem-5222	17	26	of	of	ADP
stem-5222	17	27	a	a	DET
stem-5222	17	28	complex	complex	ADJ
stem-5222	17	29	variable	variable	NOUN
stem-5222	17	30	and	and	CCONJ
stem-5222	17	31	their	their	PRON
stem-5222	17	32	corresponding	corresponding	ADJ
stem-5222	17	33	features	feature	NOUN
stem-5222	17	34	.	.	PUNCT
stem-5222	18	1	although	although	SCONJ
stem-5222	18	2	it	it	PRON
stem-5222	18	3	may	may	AUX
stem-5222	18	4	seem	seem	VERB
stem-5222	18	5	niche	niche	NOUN
stem-5222	18	6	,	,	PUNCT
stem-5222	18	7	there	there	PRON
stem-5222	18	8	are	be	VERB
stem-5222	18	9	at	at	ADV
stem-5222	18	10	least	least	ADJ
stem-5222	18	11	two	two	NUM
stem-5222	18	12	compelling	compelling	ADJ
stem-5222	18	13	justifications	justification	NOUN
stem-5222	18	14	for	for	ADP
stem-5222	18	15	why	why	SCONJ
stem-5222	18	16	all	all	DET
stem-5222	18	17	mathematicians	mathematician	NOUN
stem-5222	18	18	should	should	AUX
stem-5222	18	19	acquire	acquire	VERB
stem-5222	18	20	knowledge	knowledge	NOUN
stem-5222	18	21	in	in	ADP
stem-5222	18	22	complicated	complicated	ADJ
stem-5222	18	23	analysis	analysis	NOUN
stem-5222	18	24	.	.	PUNCT
stem-5222	19	1	in	in	ADP
stem-5222	19	2	my	my	PRON
stem-5222	19	3	humble	humble	ADJ
stem-5222	19	4	view	view	NOUN
stem-5222	19	5	,	,	PUNCT
stem-5222	19	6	it	it	PRON
stem-5222	19	7	is	be	AUX
stem-5222	19	8	one	one	NUM
stem-5222	19	9	of	of	ADP
stem-5222	19	10	the	the	DET
stem-5222	19	11	most	most	ADV
stem-5222	19	12	aesthetically	aesthetically	ADV
stem-5222	19	13	pleasing	pleasing	ADJ
stem-5222	19	14	domains	domain	NOUN
stem-5222	19	15	in	in	ADP
stem-5222	19	16	mathematics	mathematic	NOUN
stem-5222	19	17	.	.	PUNCT
stem-5222	20	1	a	a	DET
stem-5222	20	2	possible	possible	ADJ
stem-5222	20	3	interpretation	interpretation	NOUN
stem-5222	20	4	is	be	AUX
stem-5222	20	5	that	that	SCONJ
stem-5222	20	6	complex	complex	ADJ
stem-5222	20	7	analysis	analysis	NOUN
stem-5222	20	8	exhibits	exhibit	VERB
stem-5222	20	9	a	a	DET
stem-5222	20	10	large	large	ADJ
stem-5222	20	11	proportion	proportion	NOUN
stem-5222	20	12	of	of	ADP
stem-5222	20	13	theorems	theorem	NOUN
stem-5222	20	14	relative	relative	ADJ
stem-5222	20	15	to	to	ADP
stem-5222	20	16	definitions	definition	NOUN
stem-5222	20	17	,	,	PUNCT
stem-5222	20	18	resulting	result	VERB
stem-5222	20	19	in	in	ADP
stem-5222	20	20	a	a	DET
stem-5222	20	21	low	low	ADJ
stem-5222	20	22	level	level	NOUN
stem-5222	20	23	of	of	ADP
stem-5222	20	24	"	"	PUNCT
stem-5222	20	25	entropy	entropy	NOUN
stem-5222	20	26	"	"	PUNCT
stem-5222	20	27	.	.	PUNCT
stem-5222	21	1	in	in	ADP
stem-5222	21	2	other	other	ADJ
stem-5222	21	3	words	word	NOUN
stem-5222	21	4	,	,	PUNCT
stem-5222	21	5	the	the	DET
stem-5222	21	6	amount	amount	NOUN
stem-5222	21	7	of	of	ADP
stem-5222	21	8	output	output	NOUN
stem-5222	21	9	obtained	obtain	VERB
stem-5222	21	10	exceeds	exceed	VERB
stem-5222	21	11	the	the	DET
stem-5222	21	12	amount	amount	NOUN
stem-5222	21	13	of	of	ADP
stem-5222	21	14	input	input	NOUN
stem-5222	21	15	provided	provide	VERB
stem-5222	21	16	.	.	PUNCT
stem-5222	22	1	another	another	DET
stem-5222	22	2	reason	reason	NOUN
stem-5222	22	3	is	be	AUX
stem-5222	22	4	that	that	SCONJ
stem-5222	22	5	complex	complex	ADJ
stem-5222	22	6	analysis	analysis	NOUN
stem-5222	22	7	has	have	VERB
stem-5222	22	8	a	a	DET
stem-5222	22	9	multitude	multitude	NOUN
stem-5222	22	10	of	of	ADP
stem-5222	22	11	applications	application	NOUN
stem-5222	22	12	,	,	PUNCT
stem-5222	22	13	both	both	CCONJ
stem-5222	22	14	in	in	ADP
stem-5222	22	15	pure	pure	ADJ
stem-5222	22	16	mathematics	mathematic	NOUN
stem-5222	22	17	and	and	CCONJ
stem-5222	22	18	practical	practical	ADJ
stem-5222	22	19	mathematics	mathematic	NOUN
stem-5222	22	20	,	,	PUNCT
stem-5222	22	21	to	to	ADP
stem-5222	22	22	areas	area	NOUN
stem-5222	22	23	that	that	PRON
stem-5222	22	24	may	may	AUX
stem-5222	22	25	not	not	PART
stem-5222	22	26	first	first	ADV
stem-5222	22	27	seem	seem	VERB
stem-5222	22	28	to	to	PART
stem-5222	22	29	be	be	AUX
stem-5222	22	30	related	relate	VERB
stem-5222	22	31	to	to	ADP
stem-5222	22	32	complex	complex	ADJ
stem-5222	22	33	numbers	number	NOUN
stem-5222	22	34	.	.	PUNCT
stem-5222	23	1	as	as	ADP
stem-5222	23	2	an	an	DET
stem-5222	23	3	illustration	illustration	NOUN
stem-5222	23	4	:	:	PUNCT
stem-5222	23	5	•	•	ADP
stem-5222	23	6	the	the	DET
stem-5222	23	7	introduction	introduction	NOUN
stem-5222	23	8	of	of	ADP
stem-5222	23	9	296	296	NUM
stem-5222	23	10	american	american	ADJ
stem-5222	23	11	journal	journal	NOUN
stem-5222	23	12	of	of	ADP
stem-5222	23	13	language	language	NOUN
stem-5222	23	14	,	,	PUNCT
stem-5222	23	15	literacy	literacy	NOUN
stem-5222	23	16	and	and	CCONJ
stem-5222	23	17	learning	learn	VERB
stem-5222	23	18	in	in	ADP
stem-5222	23	19	stem	stem	NOUN
stem-5222	23	20	education	education	NOUN
stem-5222	23	21	www	www	PROPN
stem-5222	23	22	.	.	PUNCT
stem-5222	24	1	grnjournal.us	grnjournal.us	X
stem-5222	24	2	complex	complex	ADJ
stem-5222	24	3	numbers	number	NOUN
stem-5222	24	4	by	by	ADP
stem-5222	24	5	cardano	cardano	PROPN
stem-5222	24	6	was	be	AUX
stem-5222	24	7	motivated	motivate	VERB
stem-5222	24	8	by	by	ADP
stem-5222	24	9	the	the	DET
stem-5222	24	10	need	need	NOUN
stem-5222	24	11	to	to	PART
stem-5222	24	12	solve	solve	VERB
stem-5222	24	13	polynomial	polynomial	ADJ
stem-5222	24	14	equations	equation	NOUN
stem-5222	24	15	.	.	PUNCT
stem-5222	25	1	in	in	ADP
stem-5222	25	2	1543	1543	NUM
stem-5222	25	3	,	,	PUNCT
stem-5222	25	4	cardano	cardano	PROPN
stem-5222	25	5	published	publish	VERB
stem-5222	25	6	the	the	DET
stem-5222	25	7	well	well	ADV
stem-5222	25	8	-	-	PUNCT
stem-5222	25	9	known	know	VERB
stem-5222	25	10	method	method	NOUN
stem-5222	25	11	for	for	ADP
stem-5222	25	12	solving	solve	VERB
stem-5222	25	13	cubic	cubic	ADJ
stem-5222	25	14	equations	equation	NOUN
stem-5222	25	15	,	,	PUNCT
stem-5222	25	16	which	which	PRON
stem-5222	25	17	he	he	PRON
stem-5222	25	18	learned	learn	VERB
stem-5222	25	19	about	about	ADP
stem-5222	25	20	via	via	ADP
stem-5222	25	21	scipione	scipione	NOUN
stem-5222	25	22	del	del	X
stem-5222	25	23	ferro	ferro	NOUN
stem-5222	25	24	's	's	PART
stem-5222	25	25	earlier	early	ADJ
stem-5222	25	26	solution	solution	NOUN
stem-5222	25	27	.	.	PUNCT
stem-5222	26	1	it	it	PRON
stem-5222	26	2	is	be	AUX
stem-5222	26	3	crucial	crucial	ADJ
stem-5222	26	4	to	to	PART
stem-5222	26	5	remember	remember	VERB
stem-5222	26	6	that	that	SCONJ
stem-5222	26	7	cardano	cardano	PROPN
stem-5222	26	8	's	's	PART
stem-5222	26	9	method	method	NOUN
stem-5222	26	10	may	may	AUX
stem-5222	26	11	include	include	VERB
stem-5222	26	12	performing	perform	VERB
stem-5222	26	13	operations	operation	NOUN
stem-5222	26	14	in	in	ADP
stem-5222	26	15	the	the	DET
stem-5222	26	16	complex	complex	ADJ
stem-5222	26	17	plane	plane	NOUN
stem-5222	26	18	as	as	ADP
stem-5222	26	19	an	an	DET
stem-5222	26	20	intermediary	intermediary	ADJ
stem-5222	26	21	step	step	NOUN
stem-5222	26	22	,	,	PUNCT
stem-5222	26	23	even	even	ADV
stem-5222	26	24	if	if	SCONJ
stem-5222	26	25	the	the	DET
stem-5222	26	26	cubic	cubic	ADJ
stem-5222	26	27	equation	equation	NOUN
stem-5222	26	28	being	be	AUX
stem-5222	26	29	solved	solve	VERB
stem-5222	26	30	has	have	VERB
stem-5222	26	31	only	only	ADV
stem-5222	26	32	real	real	ADJ
stem-5222	26	33	roots	root	NOUN
stem-5222	26	34	.	.	PUNCT
stem-5222	26	35	example	example	NOUN
stem-5222	27	1	1	1	NUM
stem-5222	27	2	.	.	PUNCT
stem-5222	27	3	using	use	VERB
stem-5222	27	4	cardano	cardano	PROPN
stem-5222	27	5	’s	’s	PART
stem-5222	27	6	formula	formula	NOUN
stem-5222	27	7	,	,	PUNCT
stem-5222	27	8	it	it	PRON
stem-5222	27	9	can	can	AUX
stem-5222	27	10	be	be	AUX
stem-5222	27	11	found	find	VERB
stem-5222	27	12	that	that	SCONJ
stem-5222	27	13	the	the	DET
stem-5222	27	14	solutions	solution	NOUN
stem-5222	27	15	to	to	ADP
stem-5222	27	16	the	the	DET
stem-5222	27	17	cubic	cubic	ADJ
stem-5222	27	18	equation	equation	NOUN
stem-5222	27	19	z	z	NOUN
stem-5222	27	20	3	3	NUM
stem-5222	27	21	+	+	CCONJ
stem-5222	27	22	6z	6z	NOUN
stem-5222	27	23	2	2	NUM
stem-5222	27	24	+	+	NUM
stem-5222	27	25	9z	9z	NUM
stem-5222	27	26	+	+	CCONJ
stem-5222	27	27	3	3	NUM
stem-5222	27	28	=	=	SYM
stem-5222	27	29	0	0	NUM
stem-5222	27	30	are	be	AUX
stem-5222	27	31	z1	z1	ADJ
stem-5222	27	32	=	=	SYM
stem-5222	27	33	2	2	NUM
stem-5222	27	34	cos(2π/9	cos(2π/9	NOUN
stem-5222	27	35	)	)	PUNCT
stem-5222	27	36	−	−	PROPN
stem-5222	27	37	2	2	NUM
stem-5222	27	38	,	,	PUNCT
stem-5222	27	39	z2	z2	NOUN
stem-5222	27	40	=	=	SYM
stem-5222	27	41	2	2	NUM
stem-5222	27	42	cos(8π/9	cos(8π/9	NOUN
stem-5222	27	43	)	)	PUNCT
stem-5222	27	44	−	−	ADP
stem-5222	27	45	2	2	NUM
stem-5222	27	46	,	,	PUNCT
stem-5222	27	47	z3	z3	PROPN
stem-5222	27	48	=	=	SYM
stem-5222	27	49	2	2	NUM
stem-5222	27	50	sin(π/18	sin(π/18	PROPN
stem-5222	27	51	)	)	PUNCT
stem-5222	27	52	−	−	PROPN
stem-5222	28	1	2	2	NUM
stem-5222	28	2	.	.	NOUN
stem-5222	28	3	•	•	NUM
stem-5222	28	4	proving	prove	VERB
stem-5222	28	5	stirling	stirling	NOUN
stem-5222	28	6	’s	’s	PART
stem-5222	28	7	formula	formula	NOUN
stem-5222	28	8	:	:	PUNCT
stem-5222	28	9	n	n	X
stem-5222	28	10	!	!	PUNCT
stem-5222	29	1	∼	∼	NOUN
stem-5222	29	2	√	√	NUM
stem-5222	29	3	2πn(n	2πn(n	NUM
stem-5222	29	4	/	/	SYM
stem-5222	29	5	e	e	NOUN
stem-5222	29	6	)	)	PUNCT
stem-5222	29	7	n	n	CCONJ
stem-5222	29	8	here	here	ADV
stem-5222	29	9	,	,	PUNCT
stem-5222	29	10	an	an	DET
stem-5222	29	11	∼	∼	NOUN
stem-5222	29	12	bn	bn	NOUN
stem-5222	29	13	is	be	AUX
stem-5222	29	14	the	the	DET
stem-5222	29	15	standard	standard	ADJ
stem-5222	29	16	“	"	PUNCT
stem-5222	29	17	asymptotic	asymptotic	ADJ
stem-5222	29	18	to	to	ADP
stem-5222	29	19	”	"	PUNCT
stem-5222	29	20	relation	relation	NOUN
stem-5222	29	21	,	,	PUNCT
stem-5222	29	22	defined	define	VERB
stem-5222	29	23	to	to	PART
stem-5222	29	24	mean	mean	VERB
stem-5222	29	25	limn→∞	limn→∞	PROPN
stem-5222	29	26	an	an	DET
stem-5222	29	27	/	/	SYM
stem-5222	29	28	bn	bn	NOUN
stem-5222	29	29	=	=	NOUN
stem-5222	29	30	1	1	NUM
stem-5222	29	31	.	.	PUNCT
stem-5222	30	1	the	the	DET
stem-5222	30	2	prime	prime	ADJ
stem-5222	30	3	number	number	NOUN
stem-5222	30	4	theorem	theorem	VERB
stem-5222	30	5	states	state	NOUN
stem-5222	30	6	that	that	SCONJ
stem-5222	30	7	the	the	DET
stem-5222	30	8	function	function	NOUN
stem-5222	30	9	π(n	π(n	PROPN
stem-5222	30	10	)	)	PUNCT
stem-5222	30	11	,	,	PUNCT
stem-5222	30	12	which	which	PRON
stem-5222	30	13	represents	represent	VERB
stem-5222	30	14	the	the	DET
stem-5222	30	15	number	number	NOUN
stem-5222	30	16	of	of	ADP
stem-5222	30	17	prime	prime	ADJ
stem-5222	30	18	numbers	number	NOUN
stem-5222	30	19	less	less	ADJ
stem-5222	30	20	than	than	ADP
stem-5222	30	21	or	or	CCONJ
stem-5222	30	22	equal	equal	ADJ
stem-5222	30	23	to	to	ADP
stem-5222	30	24	n	n	CCONJ
stem-5222	30	25	,	,	PUNCT
stem-5222	30	26	is	be	AUX
stem-5222	30	27	approximately	approximately	ADV
stem-5222	30	28	equal	equal	ADJ
stem-5222	30	29	to	to	ADP
stem-5222	30	30	n	n	NUM
stem-5222	30	31	times	time	NOUN
stem-5222	30	32	the	the	DET
stem-5222	30	33	natural	natural	ADJ
stem-5222	30	34	logarithm	logarithm	NOUN
stem-5222	30	35	of	of	ADP
stem-5222	30	36	n.	n.	NOUN
stem-5222	30	37	•	•	NOUN
stem-5222	30	38	demonstrating	demonstrate	VERB
stem-5222	30	39	many	many	ADJ
stem-5222	30	40	asymptotic	asymptotic	ADJ
stem-5222	30	41	formulae	formulae	NOUN
stem-5222	30	42	in	in	ADP
stem-5222	30	43	number	number	NOUN
stem-5222	30	44	theory	theory	NOUN
stem-5222	30	45	and	and	CCONJ
stem-5222	30	46	combinatorics	combinatoric	NOUN
stem-5222	30	47	,	,	PUNCT
stem-5222	30	48	such	such	ADJ
stem-5222	30	49	as	as	ADP
stem-5222	30	50	the	the	DET
stem-5222	30	51	hardy	hardy	ADJ
stem-5222	30	52	ramanujan	ramanujan	NOUN
stem-5222	30	53	formula	formula	NOUN
stem-5222	30	54	p(n	p(n	NOUN
stem-5222	30	55	)	)	PUNCT
stem-5222	30	56	∼	∼	NOUN
stem-5222	30	57	1	1	NUM
stem-5222	30	58	4	4	NUM
stem-5222	30	59	√	√	NUM
stem-5222	30	60	3n	3n	NUM
stem-5222	30	61	e	e	NOUN
stem-5222	30	62	π	π	NOUN
stem-5222	30	63	√	√	ADP
stem-5222	30	64	2n/3	2n/3	NUM
stem-5222	30	65	.	.	PUNCT
stem-5222	31	1	this	this	DET
stem-5222	31	2	formula	formula	NOUN
stem-5222	31	3	calculates	calculate	VERB
stem-5222	31	4	the	the	DET
stem-5222	31	5	approximate	approximate	ADJ
stem-5222	31	6	number	number	NOUN
stem-5222	31	7	of	of	ADP
stem-5222	31	8	integer	integer	NOUN
stem-5222	31	9	divisions	division	NOUN
stem-5222	31	10	of	of	ADP
stem-5222	31	11	n.	n.	NOUN
stem-5222	31	12	•	•	NOUN
stem-5222	31	13	assessment	assessment	NOUN
stem-5222	31	14	of	of	ADP
stem-5222	31	15	complex	complex	ADJ
stem-5222	31	16	definite	definite	ADJ
stem-5222	31	17	integrals	integral	NOUN
stem-5222	31	18	,	,	PUNCT
stem-5222	31	19	such	such	ADJ
stem-5222	31	20	as	as	ADP
stem-5222	31	21	the	the	DET
stem-5222	31	22	evaluation	evaluation	NOUN
stem-5222	31	23	of	of	ADP
stem-5222	31	24	z	z	PROPN
stem-5222	31	25	∞	∞	NOUN
stem-5222	31	26	0	0	NUM
stem-5222	32	1	sin(t	sin(t	NOUN
stem-5222	32	2	2	2	NUM
stem-5222	32	3	)	)	PUNCT
stem-5222	32	4	dt	dt	NOUN
stem-5222	33	1	=	=	NOUN
stem-5222	33	2	1	1	NUM
stem-5222	33	3	2	2	NUM
stem-5222	33	4	r	r	NOUN
stem-5222	33	5	π	π	NOUN
stem-5222	33	6	2	2	NUM
stem-5222	33	7	.	.	PUNCT
stem-5222	34	1	(	(	PUNCT
stem-5222	34	2	this	this	DET
stem-5222	34	3	application	application	NOUN
stem-5222	34	4	is	be	AUX
stem-5222	34	5	prominently	prominently	ADV
stem-5222	34	6	highlighted	highlight	VERB
stem-5222	34	7	in	in	ADP
stem-5222	34	8	earlier	early	ADJ
stem-5222	34	9	textbooks	textbook	NOUN
stem-5222	34	10	and	and	CCONJ
stem-5222	34	11	has	have	AUX
stem-5222	34	12	been	be	AUX
stem-5222	34	13	seen	see	VERB
stem-5222	34	14	to	to	PART
stem-5222	34	15	lead	lead	VERB
stem-5222	34	16	to	to	ADP
stem-5222	34	17	a	a	DET
stem-5222	34	18	modest	modest	ADJ
stem-5222	34	19	occurrence	occurrence	NOUN
stem-5222	34	20	of	of	ADP
stem-5222	34	21	post	post	ADJ
stem-5222	34	22	-	-	ADJ
stem-5222	34	23	traumatic	traumatic	ADJ
stem-5222	34	24	stress	stress	NOUN
stem-5222	34	25	disorder	disorder	NOUN
stem-5222	34	26	.	.	PUNCT
stem-5222	34	27	)	)	PUNCT
stem-5222	35	1	•	•	ADP
stem-5222	35	2	resolving	resolve	VERB
stem-5222	35	3	physics	physics	NOUN
stem-5222	35	4	issues	issue	NOUN
stem-5222	35	5	including	include	VERB
stem-5222	35	6	hydrodynamics	hydrodynamic	NOUN
stem-5222	35	7	,	,	PUNCT
stem-5222	35	8	heat	heat	NOUN
stem-5222	35	9	conduction	conduction	NOUN
stem-5222	35	10	,	,	PUNCT
stem-5222	35	11	electrostatics	electrostatic	NOUN
stem-5222	35	12	,	,	PUNCT
stem-5222	35	13	and	and	CCONJ
stem-5222	35	14	other	other	ADJ
stem-5222	35	15	related	related	ADJ
stem-5222	35	16	topics	topic	NOUN
stem-5222	35	17	.	.	PUNCT
stem-5222	36	1	examining	examine	VERB
stem-5222	36	2	alternating	alternate	VERB
stem-5222	36	3	current	current	ADJ
stem-5222	36	4	electrical	electrical	ADJ
stem-5222	36	5	networks	network	NOUN
stem-5222	36	6	by	by	ADP
stem-5222	36	7	using	use	VERB
stem-5222	36	8	ohm	ohm	NOUN
stem-5222	36	9	's	's	PART
stem-5222	36	10	law	law	NOUN
stem-5222	36	11	to	to	ADP
stem-5222	36	12	electrical	electrical	ADJ
stem-5222	36	13	impedance	impedance	NOUN
stem-5222	36	14	.	.	PUNCT
stem-5222	37	1	complex	complex	ADJ
stem-5222	37	2	analysis	analysis	NOUN
stem-5222	37	3	is	be	AUX
stem-5222	37	4	also	also	ADV
stem-5222	37	5	used	use	VERB
stem-5222	37	6	in	in	ADP
stem-5222	37	7	several	several	ADJ
stem-5222	37	8	significant	significant	ADJ
stem-5222	37	9	applications	application	NOUN
stem-5222	37	10	within	within	ADP
stem-5222	37	11	the	the	DET
stem-5222	37	12	fields	field	NOUN
stem-5222	37	13	of	of	ADP
stem-5222	37	14	electrical	electrical	ADJ
stem-5222	37	15	engineering	engineering	NOUN
stem-5222	37	16	,	,	PUNCT
stem-5222	37	17	signals	signal	VERB
stem-5222	37	18	processing	processing	NOUN
stem-5222	37	19	,	,	PUNCT
stem-5222	37	20	and	and	CCONJ
stem-5222	37	21	control	control	NOUN
stem-5222	37	22	theory	theory	NOUN
stem-5222	37	23	.	.	PUNCT
stem-5222	38	1	•	•	NUM
stem-5222	38	2	the	the	DET
stem-5222	38	3	study	study	NOUN
stem-5222	38	4	of	of	ADP
stem-5222	38	5	probability	probability	NOUN
stem-5222	38	6	and	and	CCONJ
stem-5222	38	7	combinatorics	combinatoric	NOUN
stem-5222	38	8	involves	involve	VERB
stem-5222	38	9	analysing	analyse	VERB
stem-5222	38	10	mathematical	mathematical	ADJ
stem-5222	38	11	formulas	formula	NOUN
stem-5222	38	12	such	such	ADJ
stem-5222	38	13	as	as	ADP
stem-5222	38	14	the	the	DET
stem-5222	38	15	cardy	cardy	NOUN
stem-5222	38	16	-	-	PUNCT
stem-5222	38	17	smirnov	smirnov	ADJ
stem-5222	38	18	formula	formula	NOUN
stem-5222	38	19	in	in	ADP
stem-5222	38	20	percolation	percolation	NOUN
stem-5222	38	21	theory	theory	NOUN
stem-5222	38	22	and	and	CCONJ
stem-5222	38	23	the	the	DET
stem-5222	38	24	connective	connective	ADJ
stem-5222	38	25	constant	constant	NOUN
stem-5222	38	26	for	for	ADP
stem-5222	38	27	self	self	NOUN
stem-5222	38	28	-	-	PUNCT
stem-5222	38	29	avoiding	avoid	VERB
stem-5222	38	30	walks	walk	NOUN
stem-5222	38	31	on	on	ADP
stem-5222	38	32	the	the	DET
stem-5222	38	33	hexagonal	hexagonal	ADJ
stem-5222	38	34	lattice	lattice	NOUN
stem-5222	38	35	.	.	PUNCT
stem-5222	39	1	•	•	NUM
stem-5222	39	2	in	in	ADP
stem-5222	39	3	2016	2016	NUM
stem-5222	39	4	,	,	PUNCT
stem-5222	39	5	it	it	PRON
stem-5222	39	6	was	be	AUX
stem-5222	39	7	shown	show	VERB
stem-5222	39	8	that	that	SCONJ
stem-5222	39	9	the	the	DET
stem-5222	39	10	most	most	ADV
stem-5222	39	11	efficient	efficient	ADJ
stem-5222	39	12	densities	density	NOUN
stem-5222	39	13	for	for	ADP
stem-5222	39	14	packing	pack	VERB
stem-5222	39	15	spheres	sphere	NOUN
stem-5222	39	16	in	in	ADP
stem-5222	39	17	8	8	NUM
stem-5222	39	18	and	and	CCONJ
stem-5222	39	19	24	24	NUM
stem-5222	39	20	dimensions	dimension	NOUN
stem-5222	39	21	are	be	AUX
stem-5222	39	22	π	π	PROPN
stem-5222	39	23	4/384	4/384	NUM
stem-5222	39	24	and	and	CCONJ
stem-5222	39	25	π	π	PROPN
stem-5222	39	26	12/12	12/12	NUM
stem-5222	39	27	!	!	PUNCT
stem-5222	39	28	,	,	PUNCT
stem-5222	39	29	respectively	respectively	ADV
stem-5222	39	30	.	.	PUNCT
stem-5222	40	1	the	the	DET
stem-5222	40	2	proofs	proof	NOUN
stem-5222	40	3	use	use	VERB
stem-5222	40	4	complicated	complicated	ADJ
stem-5222	40	5	analysis	analysis	NOUN
stem-5222	40	6	,	,	PUNCT
stem-5222	40	7	particularly	particularly	ADV
stem-5222	40	8	the	the	DET
stem-5222	40	9	branch	branch	NOUN
stem-5222	40	10	that	that	PRON
stem-5222	40	11	examines	examine	VERB
stem-5222	40	12	certain	certain	ADJ
stem-5222	40	13	special	special	ADJ
stem-5222	40	14	functions	function	NOUN
stem-5222	40	15	called	call	VERB
stem-5222	40	16	modular	modular	ADJ
stem-5222	40	17	forms	form	NOUN
stem-5222	40	18	,	,	PUNCT
stem-5222	40	19	in	in	ADP
stem-5222	40	20	a	a	DET
stem-5222	40	21	remarkable	remarkable	ADJ
stem-5222	40	22	manner	manner	NOUN
stem-5222	40	23	.	.	PUNCT
stem-5222	41	1	•	•	NUM
stem-5222	41	2	complex	complex	ADJ
stem-5222	41	3	numbers	number	NOUN
stem-5222	41	4	are	be	AUX
stem-5222	41	5	used	use	VERB
stem-5222	41	6	by	by	ADP
stem-5222	41	7	nature	nature	NOUN
stem-5222	41	8	in	in	ADP
stem-5222	41	9	schrödinger	schrödinger	NOUN
stem-5222	41	10	's	's	PART
stem-5222	41	11	equation	equation	NOUN
stem-5222	41	12	and	and	CCONJ
stem-5222	41	13	quantum	quantum	NOUN
stem-5222	41	14	field	field	NOUN
stem-5222	41	15	theory	theory	NOUN
stem-5222	41	16	.	.	PUNCT
stem-5222	42	1	this	this	DET
stem-5222	42	2	phenomenon	phenomenon	NOUN
stem-5222	42	3	is	be	AUX
stem-5222	42	4	not	not	PART
stem-5222	42	5	just	just	ADV
stem-5222	42	6	a	a	DET
stem-5222	42	7	mathematical	mathematical	ADJ
stem-5222	42	8	convenience	convenience	NOUN
stem-5222	42	9	or	or	CCONJ
stem-5222	42	10	trickery	trickery	NOUN
stem-5222	42	11	,	,	PUNCT
stem-5222	42	12	but	but	CCONJ
stem-5222	42	13	rather	rather	ADV
stem-5222	42	14	seems	seem	VERB
stem-5222	42	15	to	to	PART
stem-5222	42	16	be	be	AUX
stem-5222	42	17	an	an	DET
stem-5222	42	18	inherent	inherent	ADJ
stem-5222	42	19	characteristic	characteristic	NOUN
stem-5222	42	20	of	of	ADP
stem-5222	42	21	the	the	DET
stem-5222	42	22	fundamental	fundamental	ADJ
stem-5222	42	23	equations	equation	NOUN
stem-5222	42	24	that	that	PRON
stem-5222	42	25	describe	describe	VERB
stem-5222	42	26	our	our	PRON
stem-5222	42	27	physical	physical	ADJ
stem-5222	42	28	world	world	NOUN
stem-5222	42	29	.	.	PUNCT
stem-5222	43	1	for	for	ADP
stem-5222	43	2	what	what	DET
stem-5222	43	3	reason	reason	NOUN
stem-5222	43	4	?	?	PUNCT
stem-5222	44	1	the	the	DET
stem-5222	44	2	answer	answer	NOUN
stem-5222	44	3	remains	remain	VERB
stem-5222	44	4	unknown	unknown	ADJ
stem-5222	44	5	.	.	PUNCT
stem-5222	45	1	•	•	NUM
stem-5222	45	2	conformal	conformal	NOUN
stem-5222	45	3	maps	map	NOUN
stem-5222	45	4	,	,	PUNCT
stem-5222	45	5	often	often	ADV
stem-5222	45	6	used	use	VERB
stem-5222	45	7	in	in	ADP
stem-5222	45	8	geometric	geometric	ADJ
stem-5222	45	9	applications	application	NOUN
stem-5222	45	10	where	where	SCONJ
stem-5222	45	11	the	the	DET
stem-5222	45	12	algebraic	algebraic	ADJ
stem-5222	45	13	or	or	CCONJ
stem-5222	45	14	analytic	analytic	ADJ
stem-5222	45	15	properties	property	NOUN
stem-5222	45	16	of	of	ADP
stem-5222	45	17	complex	complex	ADJ
stem-5222	45	18	numbers	number	NOUN
stem-5222	45	19	may	may	AUX
stem-5222	45	20	seem	seem	VERB
stem-5222	45	21	unimportant	unimportant	ADJ
stem-5222	45	22	,	,	PUNCT
stem-5222	45	23	are	be	AUX
stem-5222	45	24	really	really	ADV
stem-5222	45	25	closely	closely	ADV
stem-5222	45	26	connected	connect	VERB
stem-5222	45	27	to	to	ADP
stem-5222	45	28	complex	complex	ADJ
stem-5222	45	29	analysis	analysis	NOUN
stem-5222	45	30	.	.	PUNCT
stem-5222	46	1	conformal	conformal	ADJ
stem-5222	46	2	maps	map	NOUN
stem-5222	46	3	were	be	AUX
stem-5222	46	4	used	use	VERB
stem-5222	46	5	by	by	ADP
stem-5222	46	6	the	the	DET
stem-5222	46	7	dutch	dutch	PROPN
stem-5222	46	8	artist	artist	NOUN
stem-5222	46	9	m.c	m.c	PROPN
stem-5222	46	10	.	.	PROPN
stem-5222	46	11	escher	escher	PROPN
stem-5222	46	12	,	,	PUNCT
stem-5222	46	13	despite	despite	SCONJ
stem-5222	46	14	lacking	lack	VERB
stem-5222	46	15	mathematical	mathematical	ADJ
stem-5222	46	16	knowledge	knowledge	NOUN
stem-5222	46	17	,	,	PUNCT
stem-5222	46	18	to	to	PART
stem-5222	46	19	produce	produce	VERB
stem-5222	46	20	awe	awe	ADV
stem-5222	46	21	-	-	PUNCT
stem-5222	46	22	inspiring	inspire	VERB
stem-5222	46	23	artwork	artwork	NOUN
stem-5222	46	24	.	.	PUNCT
stem-5222	47	1	additionally	additionally	ADV
stem-5222	47	2	,	,	PUNCT
stem-5222	47	3	these	these	DET
stem-5222	47	4	maps	map	NOUN
stem-5222	47	5	have	have	AUX
stem-5222	47	6	been	be	AUX
stem-5222	47	7	utilised	utilise	VERB
stem-5222	47	8	by	by	ADP
stem-5222	47	9	others	other	NOUN
stem-5222	47	10	to	to	PART
stem-5222	47	11	get	get	VERB
stem-5222	47	12	a	a	DET
stem-5222	47	13	deeper	deep	ADJ
stem-5222	47	14	comprehension	comprehension	NOUN
stem-5222	47	15	of	of	ADP
stem-5222	47	16	escher	escher	PROPN
stem-5222	47	17	's	's	PART
stem-5222	47	18	work	work	NOUN
stem-5222	47	19	and	and	CCONJ
stem-5222	47	20	even	even	ADV
stem-5222	47	21	enhance	enhance	VERB
stem-5222	47	22	it	it	PRON
stem-5222	47	23	.	.	PUNCT
stem-5222	48	1	numerical	numerical	PROPN
stem-5222	48	2	theory	theory	PROPN
stem-5222	48	3	numerical	numerical	PROPN
stem-5222	48	4	theory	theory	PROPN
stem-5222	48	5	,	,	PUNCT
stem-5222	48	6	a	a	DET
stem-5222	48	7	crucial	crucial	ADJ
stem-5222	48	8	subdivision	subdivision	NOUN
stem-5222	48	9	of	of	ADP
stem-5222	48	10	computational	computational	ADJ
stem-5222	48	11	mathematics	mathematic	NOUN
stem-5222	48	12	,	,	PUNCT
stem-5222	48	13	offers	offer	VERB
stem-5222	48	14	important	important	ADJ
stem-5222	48	15	methods	method	NOUN
stem-5222	48	16	for	for	ADP
stem-5222	48	17	the	the	DET
stem-5222	48	18	accurate	accurate	ADJ
stem-5222	48	19	and	and	CCONJ
stem-5222	48	20	effective	effective	ADJ
stem-5222	48	21	examination	examination	NOUN
stem-5222	48	22	of	of	ADP
stem-5222	48	23	complex	complex	ADJ
stem-5222	48	24	numbers	number	NOUN
stem-5222	48	25	.	.	PUNCT
stem-5222	49	1	this	this	DET
stem-5222	49	2	study	study	NOUN
stem-5222	49	3	explores	explore	VERB
stem-5222	49	4	the	the	DET
stem-5222	49	5	use	use	NOUN
stem-5222	49	6	of	of	ADP
stem-5222	49	7	numerical	numerical	ADJ
stem-5222	49	8	297	297	NUM
stem-5222	49	9	american	american	ADJ
stem-5222	49	10	journal	journal	PROPN
stem-5222	49	11	of	of	ADP
stem-5222	49	12	language	language	NOUN
stem-5222	49	13	,	,	PUNCT
stem-5222	49	14	literacy	literacy	NOUN
stem-5222	49	15	and	and	CCONJ
stem-5222	49	16	learning	learn	VERB
stem-5222	49	17	in	in	ADP
stem-5222	49	18	stem	stem	NOUN
stem-5222	49	19	education	education	NOUN
stem-5222	49	20	www	www	PROPN
stem-5222	49	21	.	.	PUNCT
stem-5222	50	1	grnjournal.us	grnjournal.us	PROPN
stem-5222	50	2	theory	theory	NOUN
stem-5222	50	3	to	to	PART
stem-5222	50	4	improve	improve	VERB
stem-5222	50	5	the	the	DET
stem-5222	50	6	comprehension	comprehension	NOUN
stem-5222	50	7	and	and	CCONJ
stem-5222	50	8	practical	practical	ADJ
stem-5222	50	9	use	use	NOUN
stem-5222	50	10	of	of	ADP
stem-5222	50	11	complex	complex	ADJ
stem-5222	50	12	numbers	number	NOUN
stem-5222	50	13	in	in	ADP
stem-5222	50	14	different	different	ADJ
stem-5222	50	15	scientific	scientific	ADJ
stem-5222	50	16	and	and	CCONJ
stem-5222	50	17	engineering	engineering	NOUN
stem-5222	50	18	situations	situation	NOUN
stem-5222	50	19	.	.	PUNCT
stem-5222	51	1	the	the	DET
stem-5222	51	2	primary	primary	ADJ
stem-5222	51	3	objective	objective	NOUN
stem-5222	51	4	is	be	AUX
stem-5222	51	5	to	to	PART
stem-5222	51	6	provide	provide	VERB
stem-5222	51	7	reliable	reliable	ADJ
stem-5222	51	8	numerical	numerical	ADJ
stem-5222	51	9	techniques	technique	NOUN
stem-5222	51	10	for	for	ADP
stem-5222	51	11	solving	solve	VERB
stem-5222	51	12	intricate	intricate	ADJ
stem-5222	51	13	equations	equation	NOUN
stem-5222	51	14	,	,	PUNCT
stem-5222	51	15	examining	examine	VERB
stem-5222	51	16	functions	function	NOUN
stem-5222	51	17	,	,	PUNCT
stem-5222	51	18	and	and	CCONJ
stem-5222	51	19	addressing	address	VERB
stem-5222	51	20	real	real	ADJ
stem-5222	51	21	-	-	PUNCT
stem-5222	51	22	world	world	NOUN
stem-5222	51	23	computing	computing	NOUN
stem-5222	51	24	obstacles	obstacle	NOUN
stem-5222	51	25	.	.	PUNCT
stem-5222	52	1	first	first	ADV
stem-5222	52	2	,	,	PUNCT
stem-5222	52	3	we	we	PRON
stem-5222	52	4	will	will	AUX
stem-5222	52	5	examine	examine	VERB
stem-5222	52	6	the	the	DET
stem-5222	52	7	fundamental	fundamental	ADJ
stem-5222	52	8	characteristics	characteristic	NOUN
stem-5222	52	9	and	and	CCONJ
stem-5222	52	10	ways	way	NOUN
stem-5222	52	11	to	to	PART
stem-5222	52	12	represent	represent	VERB
stem-5222	52	13	complex	complex	ADJ
stem-5222	52	14	numbers	number	NOUN
stem-5222	52	15	,	,	PUNCT
stem-5222	52	16	such	such	ADJ
stem-5222	52	17	as	as	ADP
stem-5222	52	18	cartesian	cartesian	ADJ
stem-5222	52	19	and	and	CCONJ
stem-5222	52	20	polar	polar	ADJ
stem-5222	52	21	forms	form	NOUN
stem-5222	52	22	.	.	PUNCT
stem-5222	53	1	we	we	PRON
stem-5222	53	2	will	will	AUX
stem-5222	53	3	also	also	ADV
stem-5222	53	4	explore	explore	VERB
stem-5222	53	5	operations	operation	NOUN
stem-5222	53	6	like	like	ADP
stem-5222	53	7	addition	addition	NOUN
stem-5222	53	8	,	,	PUNCT
stem-5222	53	9	multiplication	multiplication	NOUN
stem-5222	53	10	,	,	PUNCT
stem-5222	53	11	and	and	CCONJ
stem-5222	53	12	conjugation	conjugation	NOUN
stem-5222	53	13	.	.	PUNCT
stem-5222	54	1	this	this	DET
stem-5222	54	2	foundation	foundation	NOUN
stem-5222	54	3	provides	provide	VERB
stem-5222	54	4	the	the	DET
stem-5222	54	5	groundwork	groundwork	NOUN
stem-5222	54	6	for	for	ADP
stem-5222	54	7	investigating	investigate	VERB
stem-5222	54	8	sophisticated	sophisticated	ADJ
stem-5222	54	9	numerical	numerical	ADJ
stem-5222	54	10	techniques	technique	NOUN
stem-5222	54	11	specifically	specifically	ADV
stem-5222	54	12	designed	design	VERB
stem-5222	54	13	for	for	ADP
stem-5222	54	14	complex	complex	ADJ
stem-5222	54	15	numbers	number	NOUN
stem-5222	54	16	.	.	PUNCT
stem-5222	55	1	crucial	crucial	ADJ
stem-5222	55	2	areas	area	NOUN
stem-5222	55	3	of	of	ADP
stem-5222	55	4	examination	examination	NOUN
stem-5222	55	5	encompass	encompass	NOUN
stem-5222	55	6	:	:	PUNCT
stem-5222	55	7	1	1	X
stem-5222	55	8	.	.	X
stem-5222	55	9	algorithms	algorithm	NOUN
stem-5222	55	10	for	for	ADP
stem-5222	55	11	finding	find	VERB
stem-5222	55	12	the	the	DET
stem-5222	55	13	roots	root	NOUN
stem-5222	55	14	of	of	ADP
stem-5222	55	15	equations	equation	NOUN
stem-5222	55	16	:	:	PUNCT
stem-5222	55	17	the	the	DET
stem-5222	55	18	newton	newton	PROPN
stem-5222	55	19	-	-	PUNCT
stem-5222	55	20	raphson	raphson	PROPN
stem-5222	55	21	method	method	NOUN
stem-5222	55	22	is	be	AUX
stem-5222	55	23	a	a	DET
stem-5222	55	24	mathematical	mathematical	ADJ
stem-5222	55	25	technique	technique	NOUN
stem-5222	55	26	that	that	PRON
stem-5222	55	27	is	be	AUX
stem-5222	55	28	specifically	specifically	ADV
stem-5222	55	29	designed	design	VERB
stem-5222	55	30	to	to	PART
stem-5222	55	31	handle	handle	VERB
stem-5222	55	32	complicated	complicated	ADJ
stem-5222	55	33	functions	function	NOUN
stem-5222	55	34	.	.	PUNCT
stem-5222	56	1	it	it	PRON
stem-5222	56	2	involves	involve	VERB
stem-5222	56	3	analysing	analyse	VERB
stem-5222	56	4	the	the	DET
stem-5222	56	5	convergence	convergence	NOUN
stem-5222	56	6	criteria	criterion	NOUN
stem-5222	56	7	and	and	CCONJ
stem-5222	56	8	effectiveness	effectiveness	NOUN
stem-5222	56	9	of	of	ADP
stem-5222	56	10	the	the	DET
stem-5222	56	11	method	method	NOUN
stem-5222	56	12	.	.	PUNCT
stem-5222	57	1	the	the	DET
stem-5222	57	2	durand	durand	PROPN
stem-5222	57	3	-	-	PUNCT
stem-5222	57	4	kerner	kerner	PROPN
stem-5222	57	5	method	method	NOUN
stem-5222	57	6	is	be	AUX
stem-5222	57	7	a	a	DET
stem-5222	57	8	reliable	reliable	ADJ
stem-5222	57	9	technique	technique	NOUN
stem-5222	57	10	for	for	ADP
stem-5222	57	11	concurrently	concurrently	ADV
stem-5222	57	12	determining	determine	VERB
stem-5222	57	13	all	all	DET
stem-5222	57	14	the	the	DET
stem-5222	57	15	roots	root	NOUN
stem-5222	57	16	of	of	ADP
stem-5222	57	17	complex	complex	ADJ
stem-5222	57	18	polynomials	polynomial	NOUN
stem-5222	57	19	.	.	PUNCT
stem-5222	58	1	iterative	iterative	NOUN
stem-5222	58	2	refinement	refinement	NOUN
stem-5222	58	3	techniques	technique	NOUN
stem-5222	58	4	are	be	AUX
stem-5222	58	5	used	use	VERB
stem-5222	58	6	to	to	PART
stem-5222	58	7	improve	improve	VERB
stem-5222	58	8	the	the	DET
stem-5222	58	9	accuracy	accuracy	NOUN
stem-5222	58	10	and	and	CCONJ
stem-5222	58	11	stability	stability	NOUN
stem-5222	58	12	of	of	ADP
stem-5222	58	13	root	root	NOUN
stem-5222	58	14	-	-	PUNCT
stem-5222	58	15	finding	find	VERB
stem-5222	58	16	methods	method	NOUN
stem-5222	58	17	.	.	PUNCT
stem-5222	59	1	2	2	X
stem-5222	59	2	.	.	X
stem-5222	59	3	numerical	numerical	ADJ
stem-5222	59	4	solutions	solution	NOUN
stem-5222	59	5	of	of	ADP
stem-5222	59	6	complex	complex	ADJ
stem-5222	59	7	equations	equation	NOUN
stem-5222	59	8	:	:	PUNCT
stem-5222	59	9	•	•	NUM
stem-5222	59	10	methods	method	NOUN
stem-5222	59	11	for	for	ADP
stem-5222	59	12	solving	solve	VERB
stem-5222	59	13	linear	linear	NOUN
stem-5222	59	14	and	and	CCONJ
stem-5222	59	15	nonlinear	nonlinear	ADJ
stem-5222	59	16	systems	system	NOUN
stem-5222	59	17	that	that	PRON
stem-5222	59	18	include	include	VERB
stem-5222	59	19	complex	complex	ADJ
stem-5222	59	20	variables	variable	NOUN
stem-5222	59	21	.	.	PUNCT
stem-5222	60	1			ADJ
stem-5222	60	2	utilisation	utilisation	NOUN
stem-5222	60	3	of	of	ADP
stem-5222	60	4	iterative	iterative	ADJ
stem-5222	60	5	techniques	technique	NOUN
stem-5222	60	6	like	like	ADP
stem-5222	60	7	as	as	ADP
stem-5222	60	8	jacobi	jacobi	PROPN
stem-5222	60	9	,	,	PUNCT
stem-5222	60	10	gauss	gauss	NOUN
stem-5222	60	11	-	-	PUNCT
stem-5222	60	12	seidel	seidel	NOUN
stem-5222	60	13	,	,	PUNCT
stem-5222	60	14	and	and	CCONJ
stem-5222	60	15	conjugate	conjugate	VERB
stem-5222	60	16	gradient	gradient	ADJ
stem-5222	60	17	methods	method	NOUN
stem-5222	60	18	in	in	ADP
stem-5222	60	19	the	the	DET
stem-5222	60	20	realm	realm	NOUN
stem-5222	60	21	of	of	ADP
stem-5222	60	22	complex	complex	ADJ
stem-5222	60	23	numbers	number	NOUN
stem-5222	60	24	.	.	PUNCT
stem-5222	61	1	3	3	X
stem-5222	61	2	.	.	X
stem-5222	61	3	analysis	analysis	NOUN
stem-5222	61	4	of	of	ADP
stem-5222	61	5	complex	complex	ADJ
stem-5222	61	6	functions	function	NOUN
stem-5222	61	7	:	:	PUNCT
stem-5222	61	8	•	•	NUM
stem-5222	61	9	calculation	calculation	NOUN
stem-5222	61	10	of	of	ADP
stem-5222	61	11	derivatives	derivative	NOUN
stem-5222	61	12	and	and	CCONJ
stem-5222	61	13	integrals	integral	NOUN
stem-5222	61	14	of	of	ADP
stem-5222	61	15	complex	complex	ADJ
stem-5222	61	16	functions	function	NOUN
stem-5222	61	17	using	use	VERB
stem-5222	61	18	numerical	numerical	ADJ
stem-5222	61	19	methods	method	NOUN
stem-5222	61	20	.	.	PUNCT
stem-5222	62	1			VERB
stem-5222	62	2	the	the	DET
stem-5222	62	3	study	study	NOUN
stem-5222	62	4	of	of	ADP
stem-5222	62	5	conformal	conformal	NOUN
stem-5222	62	6	maps	map	NOUN
stem-5222	62	7	and	and	CCONJ
stem-5222	62	8	associated	associated	ADJ
stem-5222	62	9	numerical	numerical	ADJ
stem-5222	62	10	approximations	approximation	NOUN
stem-5222	62	11	.	.	PUNCT
stem-5222	63	1			ADJ
stem-5222	63	2	applying	apply	VERB
stem-5222	63	3	finite	finite	ADJ
stem-5222	63	4	difference	difference	NOUN
stem-5222	63	5	and	and	CCONJ
stem-5222	63	6	finite	finite	ADJ
stem-5222	63	7	element	element	NOUN
stem-5222	63	8	techniques	technique	NOUN
stem-5222	63	9	to	to	PART
stem-5222	63	10	solve	solve	VERB
stem-5222	63	11	intricate	intricate	ADJ
stem-5222	63	12	ordinary	ordinary	ADJ
stem-5222	63	13	and	and	CCONJ
stem-5222	63	14	partial	partial	ADJ
stem-5222	63	15	differential	differential	NOUN
stem-5222	63	16	equations	equation	NOUN
stem-5222	63	17	.	.	PUNCT
stem-5222	64	1	4	4	X
stem-5222	64	2	.	.	X
stem-5222	64	3	analysis	analysis	NOUN
stem-5222	64	4	of	of	ADP
stem-5222	64	5	errors	error	NOUN
stem-5222	64	6	and	and	CCONJ
stem-5222	64	7	stability	stability	NOUN
stem-5222	64	8	:	:	PUNCT
stem-5222	64	9			ADJ
stem-5222	64	10	complex	complex	ADJ
stem-5222	64	11	numbers	number	NOUN
stem-5222	64	12	provide	provide	VERB
stem-5222	64	13	unique	unique	ADJ
stem-5222	64	14	challenges	challenge	NOUN
stem-5222	64	15	related	relate	VERB
stem-5222	64	16	to	to	ADP
stem-5222	64	17	floating	float	VERB
stem-5222	64	18	-	-	PUNCT
stem-5222	64	19	point	point	NOUN
stem-5222	64	20	arithmetic	arithmetic	ADJ
stem-5222	64	21	.	.	PUNCT
stem-5222	65	1			ADJ
stem-5222	65	2	dissemination	dissemination	NOUN
stem-5222	65	3	of	of	ADP
stem-5222	65	4	computational	computational	ADJ
stem-5222	65	5	inaccuracies	inaccuracy	NOUN
stem-5222	65	6	and	and	CCONJ
stem-5222	65	7	methods	method	NOUN
stem-5222	65	8	to	to	PART
stem-5222	65	9	mitigate	mitigate	VERB
stem-5222	65	10	their	their	PRON
stem-5222	65	11	influence	influence	NOUN
stem-5222	65	12	.	.	PUNCT
stem-5222	66	1			ADJ
stem-5222	66	2	calculation	calculation	NOUN
stem-5222	66	3	of	of	ADP
stem-5222	66	4	condition	condition	NOUN
stem-5222	66	5	numbers	number	NOUN
stem-5222	66	6	and	and	CCONJ
stem-5222	66	7	doing	do	VERB
stem-5222	66	8	sensitivity	sensitivity	NOUN
stem-5222	66	9	analysis	analysis	NOUN
stem-5222	66	10	for	for	ADP
stem-5222	66	11	complicated	complicated	ADJ
stem-5222	66	12	functions	function	NOUN
stem-5222	66	13	.	.	PUNCT
stem-5222	67	1	5	5	X
stem-5222	67	2	.	.	X
stem-5222	67	3	applications	application	NOUN
stem-5222	67	4	in	in	ADP
stem-5222	67	5	the	the	DET
stem-5222	67	6	fields	field	NOUN
stem-5222	67	7	of	of	ADP
stem-5222	67	8	science	science	NOUN
stem-5222	67	9	and	and	CCONJ
stem-5222	67	10	engineering	engineering	NOUN
stem-5222	67	11	:	:	PUNCT
stem-5222	67	12			ADJ
stem-5222	67	13	signal	signal	NOUN
stem-5222	67	14	processing	processing	NOUN
stem-5222	67	15	involves	involve	VERB
stem-5222	67	16	the	the	DET
stem-5222	67	17	use	use	NOUN
stem-5222	67	18	of	of	ADP
stem-5222	67	19	fourier	fourier	NOUN
stem-5222	67	20	and	and	CCONJ
stem-5222	67	21	laplace	laplace	NOUN
stem-5222	67	22	transforms	transform	VERB
stem-5222	67	23	in	in	ADP
stem-5222	67	24	the	the	DET
stem-5222	67	25	complex	complex	ADJ
stem-5222	67	26	domain	domain	NOUN
stem-5222	67	27	.	.	PUNCT
stem-5222	68	1			ADJ
stem-5222	68	2	analyzing	analyze	VERB
stem-5222	68	3	control	control	NOUN
stem-5222	68	4	systems	system	NOUN
stem-5222	68	5	utilising	utilise	VERB
stem-5222	68	6	intricate	intricate	ADJ
stem-5222	68	7	poles	pole	NOUN
stem-5222	68	8	and	and	CCONJ
stem-5222	68	9	zeros	zero	NOUN
stem-5222	68	10	.	.	PUNCT
stem-5222	69	1			VERB
stem-5222	69	2	simulations	simulation	NOUN
stem-5222	69	3	of	of	ADP
stem-5222	69	4	electromagnetic	electromagnetic	ADJ
stem-5222	69	5	fields	field	NOUN
stem-5222	69	6	with	with	ADP
stem-5222	69	7	intricate	intricate	ADJ
stem-5222	69	8	permittivity	permittivity	NOUN
stem-5222	69	9	and	and	CCONJ
stem-5222	69	10	permeability	permeability	NOUN
stem-5222	69	11	.	.	PUNCT
stem-5222	70	1	we	we	PRON
stem-5222	70	2	showcase	showcase	VERB
stem-5222	70	3	the	the	DET
stem-5222	70	4	practical	practical	ADJ
stem-5222	70	5	applications	application	NOUN
stem-5222	70	6	of	of	ADP
stem-5222	70	7	numerical	numerical	ADJ
stem-5222	70	8	techniques	technique	NOUN
stem-5222	70	9	for	for	ADP
stem-5222	70	10	complex	complex	ADJ
stem-5222	70	11	numbers	number	NOUN
stem-5222	70	12	by	by	ADP
stem-5222	70	13	presenting	present	VERB
stem-5222	70	14	in	in	ADP
stem-5222	70	15	-	-	PUNCT
stem-5222	70	16	depth	depth	NOUN
stem-5222	70	17	case	case	NOUN
stem-5222	70	18	studies	study	NOUN
stem-5222	70	19	.	.	PUNCT
stem-5222	71	1	these	these	DET
stem-5222	71	2	case	case	NOUN
stem-5222	71	3	studies	study	NOUN
stem-5222	71	4	highlight	highlight	VERB
stem-5222	71	5	the	the	DET
stem-5222	71	6	efficiency	efficiency	NOUN
stem-5222	71	7	of	of	ADP
stem-5222	71	8	these	these	DET
stem-5222	71	9	approaches	approach	NOUN
stem-5222	71	10	in	in	ADP
stem-5222	71	11	addressing	address	VERB
stem-5222	71	12	real	real	ADJ
stem-5222	71	13	-	-	PUNCT
stem-5222	71	14	world	world	NOUN
stem-5222	71	15	situations	situation	NOUN
stem-5222	71	16	.	.	PUNCT
stem-5222	72	1	these	these	DET
stem-5222	72	2	examples	example	NOUN
stem-5222	72	3	highlight	highlight	VERB
stem-5222	72	4	the	the	DET
stem-5222	72	5	adaptability	adaptability	NOUN
stem-5222	72	6	and	and	CCONJ
stem-5222	72	7	indispensability	indispensability	NOUN
stem-5222	72	8	of	of	ADP
stem-5222	72	9	numerical	numerical	ADJ
stem-5222	72	10	theory	theory	NOUN
stem-5222	72	11	in	in	ADP
stem-5222	72	12	contemporary	contemporary	ADJ
stem-5222	72	13	scientific	scientific	ADJ
stem-5222	72	14	and	and	CCONJ
stem-5222	72	15	engineering	engineering	NOUN
stem-5222	72	16	applications	application	NOUN
stem-5222	72	17	.	.	PUNCT
stem-5222	73	1	the	the	DET
stem-5222	73	2	fundamental	fundamental	ADJ
stem-5222	73	3	theorem	theorem	NOUN
stem-5222	73	4	of	of	ADP
stem-5222	73	5	algebra	algebra	NOUN
stem-5222	73	6	the	the	DET
stem-5222	73	7	fundamental	fundamental	ADJ
stem-5222	73	8	theorem	theorem	NOUN
stem-5222	73	9	of	of	ADP
stem-5222	73	10	algebra	algebra	PROPN
stem-5222	73	11	is	be	AUX
stem-5222	73	12	a	a	DET
stem-5222	73	13	renowned	renowned	ADJ
stem-5222	73	14	theorem	theorem	NOUN
stem-5222	73	15	in	in	ADP
stem-5222	73	16	the	the	DET
stem-5222	73	17	field	field	NOUN
stem-5222	73	18	of	of	ADP
stem-5222	73	19	complex	complex	ADJ
stem-5222	73	20	analysis	analysis	NOUN
stem-5222	73	21	,	,	PUNCT
stem-5222	73	22	despite	despite	SCONJ
stem-5222	73	23	its	its	PRON
stem-5222	73	24	rather	rather	ADV
stem-5222	73	25	misleading	misleading	ADJ
stem-5222	73	26	name	name	NOUN
stem-5222	73	27	.	.	PUNCT
stem-5222	74	1	this	this	PRON
stem-5222	74	2	seems	seem	VERB
stem-5222	74	3	to	to	PART
stem-5222	74	4	be	be	AUX
stem-5222	74	5	an	an	DET
stem-5222	74	6	appropriate	appropriate	ADJ
stem-5222	74	7	location	location	NOUN
stem-5222	74	8	to	to	PART
stem-5222	74	9	start	start	VERB
stem-5222	74	10	our	our	PRON
stem-5222	74	11	exploration	exploration	NOUN
stem-5222	74	12	of	of	ADP
stem-5222	74	13	the	the	DET
stem-5222	74	14	hypothesis	hypothesis	NOUN
stem-5222	74	15	.	.	PUNCT
stem-5222	75	1	theorem	theorem	NOUN
stem-5222	75	2	1	1	NUM
stem-5222	75	3	(	(	PUNCT
stem-5222	75	4	the	the	DET
stem-5222	75	5	fundamental	fundamental	ADJ
stem-5222	75	6	theorem	theorem	NOUN
stem-5222	75	7	of	of	ADP
stem-5222	75	8	algebra	algebra	NOUN
stem-5222	75	9	):	):	PUNCT
stem-5222	75	10	every	every	DET
stem-5222	75	11	polynomial	polynomial	ADJ
stem-5222	75	12	p(z	p(z	NOUN
stem-5222	75	13	)	)	PUNCT
stem-5222	75	14	that	that	PRON
stem-5222	75	15	is	be	AUX
stem-5222	75	16	not	not	PART
stem-5222	75	17	constant	constant	ADJ
stem-5222	75	18	over	over	ADP
stem-5222	75	19	the	the	DET
stem-5222	75	20	complex	complex	ADJ
stem-5222	75	21	numbers	number	NOUN
stem-5222	75	22	has	have	VERB
stem-5222	75	23	at	at	ADV
stem-5222	75	24	least	least	ADJ
stem-5222	75	25	one	one	NUM
stem-5222	75	26	root	root	NOUN
stem-5222	75	27	.	.	PUNCT
stem-5222	76	1	the	the	DET
stem-5222	76	2	basic	basic	ADJ
stem-5222	76	3	theorem	theorem	NOUN
stem-5222	76	4	of	of	ADP
stem-5222	76	5	algebra	algebra	PROPN
stem-5222	76	6	is	be	AUX
stem-5222	76	7	an	an	DET
stem-5222	76	8	intricate	intricate	ADJ
stem-5222	76	9	outcome	outcome	NOUN
stem-5222	76	10	that	that	PRON
stem-5222	76	11	has	have	VERB
stem-5222	76	12	several	several	ADJ
stem-5222	76	13	elegant	elegant	ADJ
stem-5222	76	14	demonstrations	demonstration	NOUN
stem-5222	76	15	.	.	PUNCT
stem-5222	77	1	i	i	PRON
stem-5222	77	2	will	will	AUX
stem-5222	77	3	demonstrate	demonstrate	VERB
stem-5222	77	4	three	three	NUM
stem-5222	77	5	of	of	ADP
stem-5222	77	6	these	these	PRON
stem-5222	77	7	.	.	PUNCT
stem-5222	78	1	please	please	INTJ
stem-5222	78	2	inform	inform	VERB
stem-5222	78	3	me	i	PRON
stem-5222	78	4	if	if	SCONJ
stem-5222	78	5	you	you	PRON
stem-5222	78	6	come	come	VERB
stem-5222	78	7	across	across	ADP
stem-5222	78	8	any	any	DET
stem-5222	78	9	instances	instance	NOUN
stem-5222	78	10	of	of	ADP
stem-5222	78	11	"	"	PUNCT
stem-5222	78	12	algebra	algebra	NOUN
stem-5222	78	13	"	"	PUNCT
stem-5222	78	14	.	.	PUNCT
stem-5222	78	15	.	.	PUNCT
stem-5222	79	1	.	.	PUNCT
stem-5222	80	1	298	298	NUM
stem-5222	80	2	american	american	ADJ
stem-5222	80	3	journal	journal	PROPN
stem-5222	80	4	of	of	ADP
stem-5222	80	5	language	language	NOUN
stem-5222	80	6	,	,	PUNCT
stem-5222	80	7	literacy	literacy	NOUN
stem-5222	80	8	and	and	CCONJ
stem-5222	80	9	learning	learn	VERB
stem-5222	80	10	in	in	ADP
stem-5222	80	11	stem	stem	NOUN
stem-5222	80	12	education	education	NOUN
stem-5222	80	13	www	www	PROPN
stem-5222	80	14	.	.	PUNCT
stem-5222	81	1	grnjournal.us	grnjournal.us	X
stem-5222	81	2	initial	initial	ADJ
stem-5222	81	3	demonstration	demonstration	NOUN
stem-5222	81	4	:	:	PUNCT
stem-5222	81	5	analytic	analytic	ADJ
stem-5222	81	6	demonstration	demonstration	NOUN
stem-5222	81	7	.	.	PUNCT
stem-5222	82	1	allow	allow	VERB
stem-5222	82	2	p(z	p(z	NOUN
stem-5222	82	3	)	)	PUNCT
stem-5222	82	4	=	=	SYM
stem-5222	82	5	anz	anz	PROPN
stem-5222	82	6	n	n	PROPN
stem-5222	82	7	+	+	CCONJ
stem-5222	82	8	an−1z	an−1z	PROPN
stem-5222	82	9	n−1	n−1	PROPN
stem-5222	83	1	+	+	NUM
stem-5222	83	2	.	.	PUNCT
stem-5222	83	3	.	.	PUNCT
stem-5222	84	1	.	.	PUNCT
stem-5222	85	1	+	+	CCONJ
stem-5222	85	2	a0	a0	PROPN
stem-5222	85	3	be	be	VERB
stem-5222	85	4	a	a	DET
stem-5222	85	5	polynomial	polynomial	NOUN
stem-5222	85	6	of	of	ADP
stem-5222	85	7	degree	degree	NOUN
stem-5222	85	8	n	n	PRON
stem-5222	85	9	≥	≥	NOUN
stem-5222	85	10	1	1	NUM
stem-5222	85	11	,	,	PUNCT
stem-5222	85	12	and	and	CCONJ
stem-5222	85	13	consider	consider	VERB
stem-5222	85	14	where	where	SCONJ
stem-5222	85	15	|p(z)|	|p(z)|	NOUN
stem-5222	85	16	attains	attain	VERB
stem-5222	85	17	its	its	PRON
stem-5222	85	18	infimum	infimum	NOUN
stem-5222	85	19	.	.	PUNCT
stem-5222	86	1	first	first	ADV
stem-5222	86	2	,	,	PUNCT
stem-5222	86	3	note	note	VERB
stem-5222	86	4	that	that	SCONJ
stem-5222	86	5	it	it	PRON
stem-5222	86	6	ca	can	AUX
stem-5222	86	7	n’t	not	PART
stem-5222	86	8	happen	happen	VERB
stem-5222	86	9	as	as	ADP
stem-5222	86	10	|z|	|z|	NOUN
stem-5222	86	11	→	→	SYM
stem-5222	86	12	∞	∞	PROPN
stem-5222	86	13	,	,	PUNCT
stem-5222	86	14	since	since	SCONJ
stem-5222	86	15	|p(z)|	|p(z)|	PROPN
stem-5222	86	16	=	=	SYM
stem-5222	86	17	|z|	|z|	PROPN
stem-5222	86	18	n	n	X
stem-5222	86	19	·	·	PUNCT
stem-5222	86	20	(	(	PUNCT
stem-5222	86	21	|an	|an	X
stem-5222	86	22	+	+	X
stem-5222	86	23	an−1z	an−1z	NUM
stem-5222	86	24	−1	−1	NOUN
stem-5222	86	25	+	+	CCONJ
stem-5222	86	26	an−2z	an−2z	NUM
stem-5222	86	27	−2	−2	NOUN
stem-5222	86	28	+	+	X
stem-5222	86	29	.	.	PUNCT
stem-5222	86	30	.	.	PUNCT
stem-5222	86	31	.	.	PUNCT
stem-5222	87	1	+	+	CCONJ
stem-5222	87	2	a0z	a0z	ADJ
stem-5222	87	3	−n	−n	ADJ
stem-5222	87	4	|	|	NOUN
stem-5222	87	5	)	)	PUNCT
stem-5222	87	6	,	,	PUNCT
stem-5222	87	7	and	and	CCONJ
stem-5222	87	8	in	in	ADP
stem-5222	87	9	particular	particular	ADJ
stem-5222	87	10	lim|z|→∞	lim|z|→∞	NOUN
stem-5222	87	11	|p(z)|	|p(z)|	PROPN
stem-5222	87	12	|z|n	|z|n	NOUN
stem-5222	87	13	=	=	SYM
stem-5222	87	14	|an|	|an|	PROPN
stem-5222	87	15	,	,	PUNCT
stem-5222	87	16	so	so	ADV
stem-5222	87	17	for	for	ADP
stem-5222	87	18	large	large	ADJ
stem-5222	87	19	|z|	|z|	NOUN
stem-5222	87	20	it	it	PRON
stem-5222	87	21	is	be	AUX
stem-5222	87	22	guaranteed	guarantee	VERB
stem-5222	87	23	that	that	SCONJ
stem-5222	87	24	|p(z)|	|p(z)|	ADJ
stem-5222	87	25	≥	≥	NUM
stem-5222	87	26	|p(0)|	|p(0)|	NOUN
stem-5222	87	27	=	=	PUNCT
stem-5222	87	28	|a0|	|a0|	NOUN
stem-5222	87	29	.	.	PUNCT
stem-5222	88	1	fixing	fix	VERB
stem-5222	88	2	some	some	DET
stem-5222	88	3	radius	radius	NOUN
stem-5222	88	4	r	r	NOUN
stem-5222	88	5	>	>	X
stem-5222	88	6	0	0	NUM
stem-5222	88	7	for	for	ADP
stem-5222	88	8	which	which	PRON
stem-5222	88	9	|z|	|z|	VERB
stem-5222	88	10	>	>	X
stem-5222	88	11	r	r	NOUN
stem-5222	88	12	implies	imply	VERB
stem-5222	88	13	|p(z)|	|p(z)|	NOUN
stem-5222	88	14	≥	≥	NOUN
stem-5222	88	15	|a0|	|a0|	VERB
stem-5222	88	16	,	,	PUNCT
stem-5222	88	17	we	we	PRON
stem-5222	88	18	therefore	therefore	ADV
stem-5222	88	19	have	have	VERB
stem-5222	88	20	that	that	DET
stem-5222	88	21	m0	m0	NOUN
stem-5222	88	22	:	:	PUNCT
stem-5222	88	23	=	=	SYM
stem-5222	88	24	inf	inf	ADJ
stem-5222	88	25	z∈c	z∈c	VERB
stem-5222	88	26	|p(z)|	|p(z)|	PROPN
stem-5222	88	27	=	=	SYM
stem-5222	88	28	inf	inf	NOUN
stem-5222	88	29	|z|≤r	|z|≤r	PROPN
stem-5222	88	30	|p(z)|	|p(z)|	PROPN
stem-5222	88	31	=	=	SYM
stem-5222	88	32	min	min	NOUN
stem-5222	88	33	|z|≤r	|z|≤r	PROPN
stem-5222	88	34	|p(z)|	|p(z)|	PROPN
stem-5222	88	35	=	=	SYM
stem-5222	88	36	|p(z0)|	|p(z0)|	NOUN
stem-5222	88	37	where	where	SCONJ
stem-5222	88	38	z0	z0	PROPN
stem-5222	88	39	=	=	PROPN
stem-5222	88	40	arg	arg	NOUN
stem-5222	88	41	min	min	NOUN
stem-5222	88	42	|z|≤r	|z|≤r	PROPN
stem-5222	88	43	|p(z)|	|p(z)|	PROPN
stem-5222	88	44	,	,	PUNCT
stem-5222	88	45	and	and	CCONJ
stem-5222	88	46	the	the	DET
stem-5222	88	47	minimum	minimum	NOUN
stem-5222	88	48	exists	exist	VERB
stem-5222	88	49	because	because	SCONJ
stem-5222	88	50	p(z	p(z	NOUN
stem-5222	88	51	)	)	PUNCT
stem-5222	88	52	is	be	AUX
stem-5222	88	53	a	a	DET
stem-5222	88	54	continuous	continuous	ADJ
stem-5222	88	55	function	function	NOUN
stem-5222	88	56	on	on	ADP
stem-5222	88	57	the	the	DET
stem-5222	88	58	disc	disc	NOUN
stem-5222	88	59	dr(0	dr(0	NOUN
stem-5222	88	60	)	)	PUNCT
stem-5222	88	61	.	.	PUNCT
stem-5222	89	1	denote	denote	PROPN
stem-5222	89	2	w0	w0	PROPN
stem-5222	89	3	=	=	PUNCT
stem-5222	89	4	p(z0	p(z0	NOUN
stem-5222	89	5	)	)	PUNCT
stem-5222	89	6	,	,	PUNCT
stem-5222	89	7	so	so	SCONJ
stem-5222	89	8	that	that	SCONJ
stem-5222	89	9	m0	m0	NOUN
stem-5222	89	10	=	=	PUNCT
stem-5222	89	11	|w0|	|w0|	VERB
stem-5222	89	12	.	.	PUNCT
stem-5222	90	1	we	we	PRON
stem-5222	90	2	now	now	ADV
stem-5222	90	3	claim	claim	VERB
stem-5222	90	4	that	that	SCONJ
stem-5222	90	5	m0	m0	NOUN
stem-5222	90	6	=	=	PUNCT
stem-5222	90	7	0	0	X
stem-5222	90	8	.	.	PUNCT
stem-5222	90	9	assume	assume	VERB
stem-5222	90	10	by	by	ADP
stem-5222	90	11	contradiction	contradiction	NOUN
stem-5222	90	12	that	that	SCONJ
stem-5222	90	13	it	it	PRON
stem-5222	90	14	does	do	AUX
stem-5222	90	15	n’t	not	PART
stem-5222	90	16	,	,	PUNCT
stem-5222	90	17	and	and	CCONJ
stem-5222	90	18	examine	examine	VERB
stem-5222	90	19	the	the	DET
stem-5222	90	20	local	local	ADJ
stem-5222	90	21	behavior	behavior	NOUN
stem-5222	90	22	of	of	ADP
stem-5222	90	23	p(z	p(z	NOUN
stem-5222	90	24	)	)	PUNCT
stem-5222	90	25	around	around	ADP
stem-5222	90	26	z0	z0	PROPN
stem-5222	90	27	;	;	PUNCT
stem-5222	90	28	more	more	ADV
stem-5222	90	29	precisely	precisely	ADV
stem-5222	90	30	,	,	PUNCT
stem-5222	90	31	expanding	expand	VERB
stem-5222	90	32	p(z	p(z	NOUN
stem-5222	90	33	)	)	PUNCT
stem-5222	90	34	in	in	ADP
stem-5222	90	35	powers	power	NOUN
stem-5222	90	36	of	of	ADP
stem-5222	90	37	z	z	NOUN
stem-5222	90	38	−	−	PROPN
stem-5222	90	39	z0	z0	PROPN
stem-5222	91	1	we	we	PRON
stem-5222	91	2	can	can	AUX
stem-5222	91	3	write	write	VERB
stem-5222	91	4	p(z	p(z	NOUN
stem-5222	91	5	)	)	PUNCT
stem-5222	92	1	=	=	SYM
stem-5222	92	2	w0	w0	PROPN
stem-5222	92	3	+	+	CCONJ
stem-5222	92	4	xn	xn	PUNCT
stem-5222	93	1	j=1	j=1	ADJ
stem-5222	93	2	cj	cj	PROPN
stem-5222	94	1	(	(	PUNCT
stem-5222	94	2	z	z	NOUN
stem-5222	94	3	−	−	PROPN
stem-5222	94	4	z0	z0	PROPN
stem-5222	94	5	)	)	PUNCT
stem-5222	94	6	j	j	PROPN
stem-5222	94	7	=	=	PROPN
stem-5222	94	8	w0	w0	PROPN
stem-5222	94	9	+	+	CCONJ
stem-5222	94	10	ck(z	ck(z	NUM
stem-5222	94	11	−	−	PROPN
stem-5222	94	12	z0	z0	PROPN
stem-5222	94	13	)	)	PUNCT
stem-5222	94	14	k	k	PROPN
stem-5222	95	1	+	+	PROPN
stem-5222	95	2	.	.	PUNCT
stem-5222	95	3	.	.	PUNCT
stem-5222	95	4	.	.	PUNCT
stem-5222	96	1	+	+	CCONJ
stem-5222	96	2	cn(z	cn(z	PUNCT
stem-5222	96	3	−	−	PROPN
stem-5222	96	4	z0	z0	PROPN
stem-5222	96	5	)	)	PUNCT
stem-5222	96	6	n	n	CCONJ
stem-5222	96	7	,	,	PUNCT
stem-5222	96	8	299	299	NUM
stem-5222	96	9	american	american	ADJ
stem-5222	96	10	journal	journal	PROPN
stem-5222	96	11	of	of	ADP
stem-5222	96	12	language	language	NOUN
stem-5222	96	13	,	,	PUNCT
stem-5222	96	14	literacy	literacy	NOUN
stem-5222	96	15	and	and	CCONJ
stem-5222	96	16	learning	learn	VERB
stem-5222	96	17	in	in	ADP
stem-5222	96	18	stem	stem	NOUN
stem-5222	96	19	education	education	NOUN
stem-5222	96	20	www	www	NOUN
stem-5222	96	21	.	.	PUNCT
stem-5222	97	1	grnjournal.us	grnjournal.us	X
stem-5222	97	2	the	the	DET
stem-5222	97	3	value	value	NOUN
stem-5222	97	4	of	of	ADP
stem-5222	97	5	k	k	PROPN
stem-5222	97	6	is	be	AUX
stem-5222	97	7	the	the	DET
stem-5222	97	8	smallest	small	ADJ
stem-5222	97	9	positive	positive	ADJ
stem-5222	97	10	index	index	NOUN
stem-5222	97	11	at	at	ADP
stem-5222	97	12	which	which	PRON
stem-5222	97	13	cj	cj	NOUN
stem-5222	97	14	is	be	AUX
stem-5222	97	15	not	not	PART
stem-5222	97	16	equal	equal	ADJ
stem-5222	97	17	to	to	ADP
stem-5222	97	18	zero	zero	NUM
stem-5222	97	19	.	.	PUNCT
stem-5222	98	1	(	(	PUNCT
stem-5222	98	2	exercise	exercise	NOUN
stem-5222	98	3	:	:	PUNCT
stem-5222	98	4	what	what	PRON
stem-5222	98	5	is	be	AUX
stem-5222	98	6	the	the	DET
stem-5222	98	7	reason	reason	NOUN
stem-5222	98	8	for	for	ADP
stem-5222	98	9	being	be	AUX
stem-5222	98	10	able	able	ADJ
stem-5222	98	11	to	to	PART
stem-5222	98	12	grow	grow	VERB
stem-5222	98	13	p(z	p(z	VERB
stem-5222	98	14	)	)	PUNCT
stem-5222	98	15	in	in	ADP
stem-5222	98	16	this	this	DET
stem-5222	98	17	manner	manner	NOUN
stem-5222	98	18	?	?	PUNCT
stem-5222	98	19	)	)	PUNCT
stem-5222	99	1	consider	consider	VERB
stem-5222	99	2	starting	start	VERB
stem-5222	99	3	the	the	DET
stem-5222	99	4	process	process	NOUN
stem-5222	99	5	with	with	ADP
stem-5222	99	6	an	an	DET
stem-5222	99	7	initial	initial	ADJ
stem-5222	99	8	value	value	NOUN
stem-5222	99	9	of	of	ADP
stem-5222	99	10	z	z	NOUN
stem-5222	99	11	=	=	SYM
stem-5222	99	12	z0	z0	PROPN
stem-5222	99	13	and	and	CCONJ
stem-5222	99	14	proceeding	proceeding	NOUN
stem-5222	99	15	in	in	ADP
stem-5222	99	16	a	a	DET
stem-5222	99	17	certain	certain	ADJ
stem-5222	99	18	direction	direction	NOUN
stem-5222	100	1	e	e	NOUN
stem-5222	100	2	iθ	iθ	ADV
stem-5222	100	3	away	away	ADV
stem-5222	100	4	from	from	ADP
stem-5222	100	5	z0	z0	PROPN
stem-5222	100	6	.	.	PUNCT
stem-5222	101	1	what	what	PRON
stem-5222	101	2	is	be	AUX
stem-5222	101	3	the	the	DET
stem-5222	101	4	outcome	outcome	NOUN
stem-5222	101	5	or	or	CCONJ
stem-5222	101	6	result	result	VERB
stem-5222	101	7	of	of	ADP
stem-5222	101	8	p(z	p(z	NOUN
stem-5222	101	9	)	)	PUNCT
stem-5222	101	10	?	?	PUNCT
stem-5222	102	1	the	the	DET
stem-5222	102	2	expansion	expansion	NOUN
stem-5222	102	3	provides	provide	VERB
stem-5222	102	4	p(z0	p(z0	NOUN
stem-5222	102	5	+	+	X
stem-5222	102	6	reiθ	reiθ	ADJ
stem-5222	102	7	)	)	PUNCT
stem-5222	102	8	=	=	PUNCT
stem-5222	102	9	w0	w0	PROPN
stem-5222	102	10	+	+	CCONJ
stem-5222	102	11	ckr	ckr	PROPN
stem-5222	102	12	k	k	X
stem-5222	102	13	e	e	NOUN
stem-5222	102	14	ikθ	ikθ	NOUN
stem-5222	102	15	+	+	CCONJ
stem-5222	102	16	ck+1r	ck+1r	VERB
stem-5222	102	17	k+1e	k+1e	PROPN
stem-5222	102	18	i(k+1)θ	i(k+1)θ	PROPN
stem-5222	102	19	+	+	PROPN
stem-5222	102	20	.	.	PUNCT
stem-5222	102	21	.	.	PUNCT
stem-5222	102	22	.	.	PUNCT
stem-5222	103	1	+	+	CCONJ
stem-5222	103	2	cnr	cnr	PROPN
stem-5222	103	3	n	n	CCONJ
stem-5222	103	4	e	e	NOUN
stem-5222	103	5	inθ	inθ	VERB
stem-5222	103	6	.	.	PUNCT
stem-5222	104	1	when	when	SCONJ
stem-5222	104	2	r	r	NOUN
stem-5222	104	3	is	be	AUX
stem-5222	104	4	very	very	ADV
stem-5222	104	5	small	small	ADJ
stem-5222	104	6	,	,	PUNCT
stem-5222	104	7	the	the	DET
stem-5222	104	8	power	power	NOUN
stem-5222	104	9	r	r	NOUN
stem-5222	104	10	k	k	PROPN
stem-5222	104	11	dominates	dominate	VERB
stem-5222	104	12	the	the	DET
stem-5222	104	13	other	other	ADJ
stem-5222	104	14	terms	term	NOUN
stem-5222	104	15	r	r	VERB
stem-5222	104	16	j	j	PROPN
stem-5222	104	17	with	with	ADP
stem-5222	104	18	k	k	PROPN
stem-5222	104	19	<	<	X
stem-5222	104	20	j	j	PROPN
stem-5222	104	21	≤	≤	PROPN
stem-5222	104	22	n	n	CCONJ
stem-5222	104	23	,	,	PUNCT
stem-5222	104	24	i.e.	i.e.	X
stem-5222	104	25	,	,	PUNCT
stem-5222	104	26	p(z0	p(z0	NOUN
stem-5222	104	27	+	+	X
stem-5222	104	28	reiθ	reiθ	ADJ
stem-5222	104	29	)	)	PUNCT
stem-5222	104	30	=	=	PUNCT
stem-5222	104	31	w0	w0	PROPN
stem-5222	104	32	+	+	CCONJ
stem-5222	104	33	r	r	NOUN
stem-5222	104	34	k	k	X
stem-5222	104	35	(	(	PUNCT
stem-5222	104	36	cke	cke	NOUN
stem-5222	104	37	ikθ	ikθ	NOUN
stem-5222	104	38	+	+	X
stem-5222	104	39	ck+1rei(k+1)θ	ck+1rei(k+1)θ	ADV
stem-5222	104	40	+	+	PUNCT
stem-5222	104	41	.	.	PUNCT
stem-5222	104	42	.	.	PUNCT
stem-5222	104	43	.	.	PUNCT
stem-5222	105	1	+	+	CCONJ
stem-5222	105	2	cnr	cnr	ADJ
stem-5222	105	3	n−k	n−k	NOUN
stem-5222	105	4	e	e	NOUN
stem-5222	105	5	inθ	inθ	X
stem-5222	105	6	)	)	PUNCT
stem-5222	105	7	=	=	SYM
stem-5222	105	8	w0	w0	PROPN
stem-5222	105	9	+	+	CCONJ
stem-5222	105	10	ckr	ckr	PROPN
stem-5222	105	11	k	k	PROPN
stem-5222	105	12	e	e	PROPN
stem-5222	105	13	ikθ(1	ikθ(1	NOUN
stem-5222	105	14	+	+	CCONJ
stem-5222	105	15	g(r	g(r	PROPN
stem-5222	105	16	,	,	PUNCT
stem-5222	105	17	θ	θ	NOUN
stem-5222	105	18	)	)	PUNCT
stem-5222	105	19	)	)	PUNCT
stem-5222	105	20	,	,	PUNCT
stem-5222	105	21	where	where	SCONJ
stem-5222	105	22	limr→0	limr→0	PROPN
stem-5222	105	23	|g(r	|g(r	PROPN
stem-5222	105	24	,	,	PUNCT
stem-5222	105	25	θ)|	θ)|	NOUN
stem-5222	105	26	=	=	PUNCT
stem-5222	105	27	0	0	PROPN
stem-5222	105	28	.	.	PUNCT
stem-5222	106	1	to	to	PART
stem-5222	106	2	reach	reach	VERB
stem-5222	106	3	a	a	DET
stem-5222	106	4	contradiction	contradiction	NOUN
stem-5222	106	5	,	,	PUNCT
stem-5222	106	6	it	it	PRON
stem-5222	106	7	is	be	AUX
stem-5222	106	8	now	now	ADV
stem-5222	106	9	enough	enough	ADJ
stem-5222	106	10	to	to	PART
stem-5222	106	11	choose	choose	VERB
stem-5222	106	12	θ	θ	PROPN
stem-5222	106	13	so	so	SCONJ
stem-5222	106	14	that	that	SCONJ
stem-5222	106	15	the	the	DET
stem-5222	106	16	vector	vector	NOUN
stem-5222	106	17	ckr	ckr	PROPN
stem-5222	106	18	k	k	PROPN
stem-5222	106	19	e	e	PROPN
stem-5222	106	20	ikθ	ikθ	NOUN
stem-5222	106	21	“	"	PUNCT
stem-5222	106	22	points	point	NOUN
stem-5222	106	23	in	in	ADP
stem-5222	106	24	the	the	DET
stem-5222	106	25	opposite	opposite	ADJ
stem-5222	106	26	direction	direction	NOUN
stem-5222	106	27	”	"	PUNCT
stem-5222	106	28	from	from	ADP
stem-5222	106	29	w0	w0	PROPN
stem-5222	106	30	,	,	PUNCT
stem-5222	106	31	that	that	ADV
stem-5222	106	32	is	is	ADV
stem-5222	106	33	,	,	PUNCT
stem-5222	106	34	such	such	ADJ
stem-5222	106	35	that	that	SCONJ
stem-5222	106	36	ckr	ckr	PROPN
stem-5222	106	37	k	k	PROPN
stem-5222	106	38	e	e	PROPN
stem-5222	106	39	ikθ	ikθ	NOUN
stem-5222	106	40	300	300	NUM
stem-5222	106	41	american	american	ADJ
stem-5222	106	42	journal	journal	NOUN
stem-5222	106	43	of	of	ADP
stem-5222	106	44	language	language	NOUN
stem-5222	106	45	,	,	PUNCT
stem-5222	106	46	literacy	literacy	NOUN
stem-5222	106	47	and	and	CCONJ
stem-5222	106	48	learning	learn	VERB
stem-5222	106	49	in	in	ADP
stem-5222	106	50	stem	stem	NOUN
stem-5222	106	51	education	education	NOUN
stem-5222	106	52	www	www	PROPN
stem-5222	106	53	.	.	PUNCT
stem-5222	107	1	grnjournal.us	grnjournal.us	X
stem-5222	107	2	w0	w0	PROPN
stem-5222	107	3	∈	∈	PROPN
stem-5222	107	4	(	(	PUNCT
stem-5222	107	5	−∞	−∞	NOUN
stem-5222	107	6	,	,	PUNCT
stem-5222	107	7	0	0	NUM
stem-5222	107	8	)	)	PUNCT
stem-5222	107	9	.	.	PUNCT
stem-5222	108	1	obviously	obviously	ADV
stem-5222	108	2	this	this	PRON
stem-5222	108	3	is	be	AUX
stem-5222	108	4	possible	possible	ADJ
stem-5222	108	5	:	:	PUNCT
stem-5222	108	6	take	take	VERB
stem-5222	108	7	θ	θ	NOUN
stem-5222	108	8	=	=	SYM
stem-5222	108	9	1	1	NUM
stem-5222	108	10	k	k	NOUN
stem-5222	108	11	(	(	PUNCT
stem-5222	108	12	arg	arg	PROPN
stem-5222	108	13	w0	w0	PROPN
stem-5222	108	14	−	−	PROPN
stem-5222	108	15	arg(ck	arg(ck	ADJ
stem-5222	108	16	)	)	PUNCT
stem-5222	109	1	+	+	CCONJ
stem-5222	109	2	π	π	X
stem-5222	109	3	)	)	PUNCT
stem-5222	109	4	.	.	PUNCT
stem-5222	110	1	it	it	PRON
stem-5222	110	2	follows	follow	VERB
stem-5222	110	3	that	that	SCONJ
stem-5222	110	4	,	,	PUNCT
stem-5222	110	5	for	for	ADP
stem-5222	110	6	r	r	NOUN
stem-5222	110	7	small	small	ADJ
stem-5222	110	8	enough	enough	ADV
stem-5222	110	9	,	,	PUNCT
stem-5222	110	10	|w0	|w0	ADJ
stem-5222	111	1	+	+	CCONJ
stem-5222	111	2	ckr	ckr	PROPN
stem-5222	111	3	k	k	PROPN
stem-5222	111	4	e	e	PROPN
stem-5222	111	5	ikθ|	ikθ|	NOUN
stem-5222	111	6	<	<	X
stem-5222	111	7	|w0|	|w0|	NOUN
stem-5222	111	8	and	and	CCONJ
stem-5222	111	9	for	for	ADP
stem-5222	111	10	r	r	NOUN
stem-5222	111	11	small	small	ADJ
stem-5222	111	12	enough	enough	ADV
stem-5222	111	13	(	(	PUNCT
stem-5222	111	14	possibly	possibly	ADV
stem-5222	111	15	even	even	ADV
stem-5222	111	16	smaller	small	ADJ
stem-5222	111	17	than	than	ADP
stem-5222	111	18	the	the	DET
stem-5222	111	19	previous	previous	ADJ
stem-5222	111	20	small	small	ADJ
stem-5222	111	21	r	r	NOUN
stem-5222	111	22	)	)	PUNCT
stem-5222	111	23	|p(z0	|p(z0	NOUN
stem-5222	111	24	+	+	CCONJ
stem-5222	111	25	reiθ)|	reiθ)|	NOUN
stem-5222	111	26	=	=	SYM
stem-5222	111	27	|w0	|w0	PROPN
stem-5222	111	28	+	+	CCONJ
stem-5222	111	29	ckr	ckr	PROPN
stem-5222	111	30	k	k	PROPN
stem-5222	111	31	e	e	PROPN
stem-5222	111	32	ikθ(1	ikθ(1	NOUN
stem-5222	111	33	+	+	CCONJ
stem-5222	111	34	g(r	g(r	PROPN
stem-5222	111	35	,	,	PUNCT
stem-5222	111	36	θ))|	θ))|	PROPN
stem-5222	111	37	<	<	X
stem-5222	111	38	|w0|	|w0|	PROPN
stem-5222	111	39	,	,	PUNCT
stem-5222	111	40	numerical	numerical	ADJ
stem-5222	111	41	solutions	solution	NOUN
stem-5222	111	42	of	of	ADP
stem-5222	111	43	complex	complex	ADJ
stem-5222	111	44	numerical	numerical	ADJ
stem-5222	111	45	solutions	solution	NOUN
stem-5222	111	46	of	of	ADP
stem-5222	111	47	complicated	complicated	ADJ
stem-5222	111	48	equations	equation	NOUN
stem-5222	111	49	play	play	VERB
stem-5222	111	50	a	a	DET
stem-5222	111	51	crucial	crucial	ADJ
stem-5222	111	52	role	role	NOUN
stem-5222	111	53	in	in	ADP
stem-5222	111	54	many	many	ADJ
stem-5222	111	55	scientific	scientific	ADJ
stem-5222	111	56	and	and	CCONJ
stem-5222	111	57	technical	technical	ADJ
stem-5222	111	58	fields	field	NOUN
stem-5222	111	59	,	,	PUNCT
stem-5222	111	60	particularly	particularly	ADV
stem-5222	111	61	when	when	SCONJ
stem-5222	111	62	analytical	analytical	ADJ
stem-5222	111	63	solutions	solution	NOUN
stem-5222	111	64	are	be	AUX
stem-5222	111	65	impractical	impractical	ADJ
stem-5222	111	66	or	or	CCONJ
stem-5222	111	67	unattainable	unattainable	ADJ
stem-5222	111	68	.	.	PUNCT
stem-5222	112	1	this	this	DET
stem-5222	112	2	work	work	NOUN
stem-5222	112	3	aims	aim	VERB
stem-5222	112	4	to	to	PART
stem-5222	112	5	create	create	VERB
stem-5222	112	6	and	and	CCONJ
stem-5222	112	7	analyse	analyse	VERB
stem-5222	112	8	numerical	numerical	ADJ
stem-5222	112	9	techniques	technique	NOUN
stem-5222	112	10	for	for	ADP
stem-5222	112	11	solving	solve	VERB
stem-5222	112	12	both	both	CCONJ
stem-5222	112	13	linear	linear	ADJ
stem-5222	112	14	and	and	CCONJ
stem-5222	112	15	nonlinear	nonlinear	ADJ
stem-5222	112	16	complex	complex	ADJ
stem-5222	112	17	equations	equation	NOUN
stem-5222	112	18	,	,	PUNCT
stem-5222	112	19	using	use	VERB
stem-5222	112	20	the	the	DET
stem-5222	112	21	extensive	extensive	ADJ
stem-5222	112	22	area	area	NOUN
stem-5222	112	23	of	of	ADP
stem-5222	112	24	numerical	numerical	ADJ
stem-5222	112	25	theory	theory	NOUN
stem-5222	112	26	.	.	PUNCT
stem-5222	113	1	first	first	ADV
stem-5222	113	2	,	,	PUNCT
stem-5222	113	3	we	we	PRON
stem-5222	113	4	analyse	analyse	VERB
stem-5222	113	5	the	the	DET
stem-5222	113	6	fundamental	fundamental	ADJ
stem-5222	113	7	ideas	idea	NOUN
stem-5222	113	8	that	that	PRON
stem-5222	113	9	form	form	VERB
stem-5222	113	10	the	the	DET
stem-5222	113	11	basis	basis	NOUN
stem-5222	113	12	of	of	ADP
stem-5222	113	13	numerical	numerical	ADJ
stem-5222	113	14	solutions	solution	NOUN
stem-5222	113	15	for	for	ADP
stem-5222	113	16	complex	complex	ADJ
stem-5222	113	17	equations	equation	NOUN
stem-5222	113	18	.	.	PUNCT
stem-5222	114	1	this	this	PRON
stem-5222	114	2	includes	include	VERB
stem-5222	114	3	studying	study	VERB
stem-5222	114	4	the	the	DET
stem-5222	114	5	representation	representation	NOUN
stem-5222	114	6	of	of	ADP
stem-5222	114	7	complex	complex	ADJ
stem-5222	114	8	numbers	number	NOUN
stem-5222	114	9	and	and	CCONJ
stem-5222	114	10	their	their	PRON
stem-5222	114	11	basic	basic	ADJ
stem-5222	114	12	operations	operation	NOUN
stem-5222	114	13	.	.	PUNCT
stem-5222	115	1	having	have	VERB
stem-5222	115	2	a	a	DET
stem-5222	115	3	solid	solid	ADJ
stem-5222	115	4	grasp	grasp	NOUN
stem-5222	115	5	of	of	ADP
stem-5222	115	6	this	this	DET
stem-5222	115	7	fundamental	fundamental	ADJ
stem-5222	115	8	knowledge	knowledge	NOUN
stem-5222	115	9	is	be	AUX
stem-5222	115	10	essential	essential	ADJ
stem-5222	115	11	for	for	ADP
stem-5222	115	12	efficiently	efficiently	ADV
stem-5222	115	13	executing	execute	VERB
stem-5222	115	14	and	and	CCONJ
stem-5222	115	15	comprehending	comprehending	ADJ
stem-5222	115	16	numerical	numerical	ADJ
stem-5222	115	17	algorithms	algorithm	NOUN
stem-5222	115	18	.	.	PUNCT
stem-5222	116	1	crucial	crucial	ADJ
stem-5222	116	2	topics	topic	NOUN
stem-5222	116	3	of	of	ADP
stem-5222	116	4	inquiry	inquiry	NOUN
stem-5222	116	5	encompass	encompass	NOUN
stem-5222	116	6	:	:	PUNCT
stem-5222	116	7	1	1	X
stem-5222	116	8	.	.	PUNCT
stem-5222	116	9	linear	linear	ADJ
stem-5222	116	10	complex	complex	ADJ
stem-5222	116	11	equations	equation	NOUN
stem-5222	116	12	:	:	PUNCT
stem-5222	116	13			VERB
stem-5222	116	14	direct	direct	ADJ
stem-5222	116	15	methods	method	NOUN
stem-5222	116	16	:	:	PUNCT
stem-5222	116	17	adaptations	adaptation	NOUN
stem-5222	116	18	of	of	ADP
stem-5222	116	19	classical	classical	ADJ
stem-5222	116	20	algorithms	algorithm	NOUN
stem-5222	116	21	such	such	ADJ
stem-5222	116	22	as	as	ADP
stem-5222	116	23	gaussian	gaussian	ADJ
stem-5222	116	24	elimination	elimination	NOUN
stem-5222	116	25	and	and	CCONJ
stem-5222	116	26	lu	lu	NOUN
stem-5222	116	27	decomposition	decomposition	NOUN
stem-5222	116	28	for	for	ADP
stem-5222	116	29	solving	solve	VERB
stem-5222	116	30	systems	system	NOUN
stem-5222	116	31	of	of	ADP
stem-5222	116	32	linear	linear	PROPN
stem-5222	116	33	equations	equation	NOUN
stem-5222	116	34	with	with	ADP
stem-5222	116	35	complex	complex	ADJ
stem-5222	116	36	coefficients	coefficient	NOUN
stem-5222	116	37	.	.	PUNCT
stem-5222	117	1	we	we	PRON
stem-5222	117	2	analyze	analyze	VERB
stem-5222	117	3	the	the	DET
stem-5222	117	4	computational	computational	ADJ
stem-5222	117	5	complexity	complexity	NOUN
stem-5222	117	6	and	and	CCONJ
stem-5222	117	7	stability	stability	NOUN
stem-5222	117	8	of	of	ADP
stem-5222	117	9	these	these	DET
stem-5222	117	10	methods	method	NOUN
stem-5222	117	11	in	in	ADP
stem-5222	117	12	the	the	DET
stem-5222	117	13	complex	complex	ADJ
stem-5222	117	14	domain	domain	NOUN
stem-5222	117	15	.	.	PUNCT
stem-5222	118	1			ADJ
stem-5222	118	2	iterative	iterative	NOUN
stem-5222	118	3	methods	method	NOUN
stem-5222	118	4	:	:	PUNCT
stem-5222	118	5	techniques	technique	NOUN
stem-5222	118	6	such	such	ADJ
stem-5222	118	7	as	as	ADP
stem-5222	118	8	jacobi	jacobi	PROPN
stem-5222	118	9	,	,	PUNCT
stem-5222	118	10	gauss	gauss	NOUN
stem-5222	118	11	-	-	PUNCT
stem-5222	118	12	seidel	seidel	NOUN
stem-5222	118	13	,	,	PUNCT
stem-5222	118	14	and	and	CCONJ
stem-5222	118	15	successive	successive	ADJ
stem-5222	118	16	over	over	ADP
stem-5222	118	17	-	-	PUNCT
stem-5222	118	18	relaxation	relaxation	NOUN
stem-5222	118	19	(	(	PUNCT
stem-5222	118	20	sor	sor	NOUN
stem-5222	118	21	)	)	PUNCT
stem-5222	118	22	methods	method	NOUN
stem-5222	118	23	,	,	PUNCT
stem-5222	118	24	and	and	CCONJ
stem-5222	118	25	their	their	PRON
stem-5222	118	26	convergence	convergence	NOUN
stem-5222	118	27	properties	property	NOUN
stem-5222	118	28	when	when	SCONJ
stem-5222	118	29	applied	apply	VERB
stem-5222	118	30	to	to	ADP
stem-5222	118	31	complex	complex	ADJ
stem-5222	118	32	systems	system	NOUN
stem-5222	118	33	.	.	PUNCT
stem-5222	119	1	the	the	DET
stem-5222	119	2	application	application	NOUN
stem-5222	119	3	of	of	ADP
stem-5222	119	4	the	the	DET
stem-5222	119	5	conjugate	conjugate	ADJ
stem-5222	119	6	gradient	gradient	NOUN
stem-5222	119	7	method	method	NOUN
stem-5222	119	8	for	for	ADP
stem-5222	119	9	large	large	ADJ
stem-5222	119	10	,	,	PUNCT
stem-5222	119	11	sparse	sparse	ADJ
stem-5222	119	12	complex	complex	ADJ
stem-5222	119	13	systems	system	NOUN
stem-5222	119	14	is	be	AUX
stem-5222	119	15	also	also	ADV
stem-5222	119	16	explored	explore	VERB
stem-5222	119	17	.	.	PUNCT
stem-5222	120	1	2	2	X
stem-5222	120	2	.	.	X
stem-5222	120	3	nonlinear	nonlinear	ADJ
stem-5222	120	4	complex	complex	ADJ
stem-5222	120	5	equations	equation	NOUN
stem-5222	120	6	:	:	PUNCT
stem-5222	120	7			PROPN
stem-5222	120	8	newton	newton	PROPN
stem-5222	120	9	-	-	PUNCT
stem-5222	120	10	raphson	raphson	NOUN
stem-5222	120	11	method	method	NOUN
stem-5222	120	12	:	:	PUNCT
stem-5222	120	13	extension	extension	NOUN
stem-5222	120	14	to	to	ADP
stem-5222	120	15	complex	complex	ADJ
stem-5222	120	16	functions	function	NOUN
stem-5222	120	17	,	,	PUNCT
stem-5222	120	18	including	include	VERB
stem-5222	120	19	derivation	derivation	NOUN
stem-5222	120	20	and	and	CCONJ
stem-5222	120	21	implementation	implementation	NOUN
stem-5222	120	22	details	detail	NOUN
stem-5222	120	23	.	.	PUNCT
stem-5222	121	1	we	we	PRON
stem-5222	121	2	study	study	VERB
stem-5222	121	3	the	the	DET
stem-5222	121	4	method	method	NOUN
stem-5222	121	5	's	's	PART
stem-5222	121	6	local	local	ADJ
stem-5222	121	7	and	and	CCONJ
stem-5222	121	8	global	global	ADJ
stem-5222	121	9	convergence	convergence	NOUN
stem-5222	121	10	behavior	behavior	NOUN
stem-5222	121	11	in	in	ADP
stem-5222	121	12	the	the	DET
stem-5222	121	13	context	context	NOUN
stem-5222	121	14	of	of	ADP
stem-5222	121	15	complex	complex	ADJ
stem-5222	121	16	-	-	PUNCT
stem-5222	121	17	valued	value	VERB
stem-5222	121	18	functions	function	NOUN
stem-5222	121	19	.	.	PUNCT
stem-5222	122	1			VERB
stem-5222	122	2	broyden	broyden	PROPN
stem-5222	122	3	’s	’s	PART
stem-5222	122	4	method	method	NOUN
stem-5222	122	5	:	:	PUNCT
stem-5222	122	6	a	a	DET
stem-5222	122	7	quasi	quasi	NOUN
stem-5222	122	8	-	-	ADJ
stem-5222	122	9	newton	newton	PROPN
stem-5222	122	10	method	method	NOUN
stem-5222	122	11	adapted	adapt	VERB
stem-5222	122	12	for	for	ADP
stem-5222	122	13	solving	solve	VERB
stem-5222	122	14	systems	system	NOUN
stem-5222	122	15	of	of	ADP
stem-5222	122	16	nonlinear	nonlinear	ADJ
stem-5222	122	17	complex	complex	ADJ
stem-5222	122	18	equations	equation	NOUN
stem-5222	122	19	,	,	PUNCT
stem-5222	122	20	providing	provide	VERB
stem-5222	122	21	a	a	DET
stem-5222	122	22	trade	trade	NOUN
stem-5222	122	23	-	-	PUNCT
stem-5222	122	24	off	off	NOUN
stem-5222	122	25	between	between	ADP
stem-5222	122	26	computational	computational	ADJ
stem-5222	122	27	efficiency	efficiency	NOUN
stem-5222	122	28	and	and	CCONJ
stem-5222	122	29	convergence	convergence	NOUN
stem-5222	122	30	speed	speed	NOUN
stem-5222	122	31	.	.	PUNCT
stem-5222	123	1			VERB
stem-5222	123	2	durand	durand	PROPN
stem-5222	123	3	-	-	PUNCT
stem-5222	123	4	kerner	kerner	PROPN
stem-5222	123	5	method	method	PROPN
stem-5222	123	6	:	:	PUNCT
stem-5222	123	7	specifically	specifically	ADV
stem-5222	123	8	for	for	ADP
stem-5222	123	9	finding	find	VERB
stem-5222	123	10	all	all	DET
stem-5222	123	11	roots	root	NOUN
stem-5222	123	12	of	of	ADP
stem-5222	123	13	a	a	DET
stem-5222	123	14	complex	complex	ADJ
stem-5222	123	15	polynomial	polynomial	NOUN
stem-5222	123	16	simultaneously	simultaneously	ADV
stem-5222	123	17	,	,	PUNCT
stem-5222	123	18	we	we	PRON
stem-5222	123	19	discuss	discuss	VERB
stem-5222	123	20	its	its	PRON
stem-5222	123	21	algorithmic	algorithmic	ADJ
stem-5222	123	22	structure	structure	NOUN
stem-5222	123	23	,	,	PUNCT
stem-5222	123	24	convergence	convergence	NOUN
stem-5222	123	25	properties	property	NOUN
stem-5222	123	26	,	,	PUNCT
stem-5222	123	27	and	and	CCONJ
stem-5222	123	28	practical	practical	ADJ
stem-5222	123	29	implementation	implementation	NOUN
stem-5222	123	30	issues	issue	NOUN
stem-5222	123	31	.	.	PUNCT
stem-5222	124	1	301	301	NUM
stem-5222	124	2	american	american	ADJ
stem-5222	124	3	journal	journal	PROPN
stem-5222	124	4	of	of	ADP
stem-5222	124	5	language	language	NOUN
stem-5222	124	6	,	,	PUNCT
stem-5222	124	7	literacy	literacy	NOUN
stem-5222	124	8	and	and	CCONJ
stem-5222	124	9	learning	learn	VERB
stem-5222	124	10	in	in	ADP
stem-5222	124	11	stem	stem	NOUN
stem-5222	124	12	education	education	NOUN
stem-5222	124	13	www	www	PROPN
stem-5222	124	14	.	.	PROPN
stem-5222	125	1	grnjournal.us	grnjournal.us	X
stem-5222	125	2	3	3	X
stem-5222	125	3	.	.	PUNCT
stem-5222	125	4	hybrid	hybrid	ADJ
stem-5222	125	5	methods	method	NOUN
stem-5222	125	6	:	:	PUNCT
stem-5222	125	7			ADJ
stem-5222	125	8	combination	combination	NOUN
stem-5222	125	9	of	of	ADP
stem-5222	125	10	direct	direct	ADJ
stem-5222	125	11	and	and	CCONJ
stem-5222	125	12	iterative	iterative	ADJ
stem-5222	125	13	approaches	approach	NOUN
stem-5222	125	14	:	:	PUNCT
stem-5222	125	15	strategies	strategy	NOUN
stem-5222	125	16	for	for	ADP
stem-5222	125	17	leveraging	leverage	VERB
stem-5222	125	18	the	the	DET
stem-5222	125	19	strengths	strength	NOUN
stem-5222	125	20	of	of	ADP
stem-5222	125	21	both	both	DET
stem-5222	125	22	methods	method	NOUN
stem-5222	125	23	to	to	PART
stem-5222	125	24	improve	improve	VERB
stem-5222	125	25	convergence	convergence	NOUN
stem-5222	125	26	rates	rate	NOUN
stem-5222	125	27	and	and	CCONJ
stem-5222	125	28	stability	stability	NOUN
stem-5222	125	29	in	in	ADP
stem-5222	125	30	solving	solve	VERB
stem-5222	125	31	complex	complex	ADJ
stem-5222	125	32	equations	equation	NOUN
stem-5222	125	33	.	.	PUNCT
stem-5222	126	1			VERB
stem-5222	126	2	adaptive	adaptive	ADJ
stem-5222	126	3	algorithms	algorithm	NOUN
stem-5222	126	4	:	:	PUNCT
stem-5222	126	5	development	development	NOUN
stem-5222	126	6	of	of	ADP
stem-5222	126	7	algorithms	algorithm	NOUN
stem-5222	126	8	that	that	PRON
stem-5222	126	9	adjust	adjust	VERB
stem-5222	126	10	their	their	PRON
stem-5222	126	11	parameters	parameter	NOUN
stem-5222	126	12	dynamically	dynamically	ADV
stem-5222	126	13	based	base	VERB
stem-5222	126	14	on	on	ADP
stem-5222	126	15	the	the	DET
stem-5222	126	16	behavior	behavior	NOUN
stem-5222	126	17	of	of	ADP
stem-5222	126	18	the	the	DET
stem-5222	126	19	solution	solution	NOUN
stem-5222	126	20	process	process	NOUN
stem-5222	126	21	,	,	PUNCT
stem-5222	126	22	enhancing	enhance	VERB
stem-5222	126	23	robustness	robustness	NOUN
stem-5222	126	24	and	and	CCONJ
stem-5222	126	25	efficiency	efficiency	NOUN
stem-5222	126	26	.	.	PUNCT
stem-5222	127	1	4	4	X
stem-5222	127	2	.	.	NOUN
stem-5222	127	3	error	error	NOUN
stem-5222	127	4	analysis	analysis	NOUN
stem-5222	127	5	and	and	CCONJ
stem-5222	127	6	stability	stability	NOUN
stem-5222	127	7	:	:	PUNCT
stem-5222	127	8			ADJ
stem-5222	127	9	floating	float	VERB
stem-5222	127	10	-	-	PUNCT
stem-5222	127	11	point	point	NOUN
stem-5222	127	12	arithmetic	arithmetic	NOUN
stem-5222	127	13	:	:	PUNCT
stem-5222	127	14	issues	issue	NOUN
stem-5222	127	15	specific	specific	ADJ
stem-5222	127	16	to	to	ADP
stem-5222	127	17	complex	complex	ADJ
stem-5222	127	18	numbers	number	NOUN
stem-5222	127	19	,	,	PUNCT
stem-5222	127	20	including	include	VERB
stem-5222	127	21	round	round	NOUN
stem-5222	127	22	-	-	PUNCT
stem-5222	127	23	off	off	ADP
stem-5222	127	24	errors	error	NOUN
stem-5222	127	25	and	and	CCONJ
stem-5222	127	26	their	their	PRON
stem-5222	127	27	propagation	propagation	NOUN
stem-5222	127	28	through	through	ADP
stem-5222	127	29	numerical	numerical	ADJ
stem-5222	127	30	algorithms	algorithm	NOUN
stem-5222	127	31	.	.	PUNCT
stem-5222	128	1			ADJ
stem-5222	128	2	condition	condition	NOUN
stem-5222	128	3	number	number	NOUN
stem-5222	128	4	analysis	analysis	NOUN
stem-5222	128	5	:	:	PUNCT
stem-5222	128	6	evaluating	evaluate	VERB
stem-5222	128	7	the	the	DET
stem-5222	128	8	sensitivity	sensitivity	NOUN
stem-5222	128	9	of	of	ADP
stem-5222	128	10	complex	complex	ADJ
stem-5222	128	11	systems	system	NOUN
stem-5222	128	12	to	to	ADP
stem-5222	128	13	perturbations	perturbation	NOUN
stem-5222	128	14	in	in	ADP
stem-5222	128	15	input	input	NOUN
stem-5222	128	16	data	datum	NOUN
stem-5222	128	17	and	and	CCONJ
stem-5222	128	18	initial	initial	ADJ
stem-5222	128	19	guesses	guess	NOUN
stem-5222	128	20	,	,	PUNCT
stem-5222	128	21	crucial	crucial	ADJ
stem-5222	128	22	for	for	ADP
stem-5222	128	23	understanding	understand	VERB
stem-5222	128	24	the	the	DET
stem-5222	128	25	reliability	reliability	NOUN
stem-5222	128	26	of	of	ADP
stem-5222	128	27	numerical	numerical	ADJ
stem-5222	128	28	solutions	solution	NOUN
stem-5222	128	29	.	.	PUNCT
stem-5222	129	1	5	5	X
stem-5222	129	2	.	.	X
stem-5222	129	3	practical	practical	ADJ
stem-5222	129	4	applications	application	NOUN
stem-5222	129	5	:	:	PUNCT
stem-5222	129	6			ADJ
stem-5222	129	7	signal	signal	NOUN
stem-5222	129	8	processing	processing	NOUN
stem-5222	129	9	:	:	PUNCT
stem-5222	129	10	solving	solve	VERB
stem-5222	129	11	complex	complex	ADJ
stem-5222	129	12	equations	equation	NOUN
stem-5222	129	13	arising	arise	VERB
stem-5222	129	14	in	in	ADP
stem-5222	129	15	filter	filter	NOUN
stem-5222	129	16	design	design	NOUN
stem-5222	129	17	and	and	CCONJ
stem-5222	129	18	spectral	spectral	ADJ
stem-5222	129	19	analysis	analysis	NOUN
stem-5222	129	20	.	.	PUNCT
stem-5222	130	1			ADJ
stem-5222	130	2	control	control	NOUN
stem-5222	130	3	systems	system	NOUN
stem-5222	130	4	:	:	PUNCT
stem-5222	130	5	application	application	NOUN
stem-5222	130	6	in	in	ADP
stem-5222	130	7	stability	stability	NOUN
stem-5222	130	8	analysis	analysis	NOUN
stem-5222	130	9	and	and	CCONJ
stem-5222	130	10	controller	controller	NOUN
stem-5222	130	11	design	design	NOUN
stem-5222	130	12	using	use	VERB
stem-5222	130	13	complex	complex	ADJ
stem-5222	130	14	poles	pole	NOUN
stem-5222	130	15	and	and	CCONJ
stem-5222	130	16	zeros	zero	NOUN
stem-5222	130	17	.	.	PUNCT
stem-5222	131	1			ADJ
stem-5222	131	2	electromagnetic	electromagnetic	ADJ
stem-5222	131	3	field	field	NOUN
stem-5222	131	4	problems	problem	NOUN
stem-5222	131	5	:	:	PUNCT
stem-5222	131	6	modeling	modeling	NOUN
stem-5222	131	7	and	and	CCONJ
stem-5222	131	8	simulation	simulation	NOUN
stem-5222	131	9	involving	involve	VERB
stem-5222	131	10	complex	complex	ADJ
stem-5222	131	11	permittivity	permittivity	NOUN
stem-5222	131	12	and	and	CCONJ
stem-5222	131	13	permeability	permeability	NOUN
stem-5222	131	14	,	,	PUNCT
stem-5222	131	15	where	where	SCONJ
stem-5222	131	16	solving	solve	VERB
stem-5222	131	17	maxwell	maxwell	PROPN
stem-5222	131	18	's	's	PART
stem-5222	131	19	equations	equation	NOUN
stem-5222	131	20	in	in	ADP
stem-5222	131	21	the	the	DET
stem-5222	131	22	complex	complex	ADJ
stem-5222	131	23	domain	domain	NOUN
stem-5222	131	24	is	be	AUX
stem-5222	131	25	essential	essential	ADJ
stem-5222	131	26	.	.	PUNCT
stem-5222	132	1	by	by	ADP
stem-5222	132	2	presenting	present	VERB
stem-5222	132	3	detailed	detailed	ADJ
stem-5222	132	4	case	case	NOUN
stem-5222	132	5	studies	study	NOUN
stem-5222	132	6	and	and	CCONJ
stem-5222	132	7	numerical	numerical	ADJ
stem-5222	132	8	experiments	experiment	NOUN
stem-5222	132	9	,	,	PUNCT
stem-5222	132	10	we	we	PRON
stem-5222	132	11	illustrate	illustrate	VERB
stem-5222	132	12	the	the	DET
stem-5222	132	13	effectiveness	effectiveness	NOUN
stem-5222	132	14	of	of	ADP
stem-5222	132	15	these	these	DET
stem-5222	132	16	methods	method	NOUN
stem-5222	132	17	in	in	ADP
stem-5222	132	18	real	real	ADJ
stem-5222	132	19	-	-	PUNCT
stem-5222	132	20	world	world	NOUN
stem-5222	132	21	scenarios	scenario	NOUN
stem-5222	132	22	.	.	PUNCT
stem-5222	133	1	these	these	DET
stem-5222	133	2	examples	example	NOUN
stem-5222	133	3	demonstrate	demonstrate	VERB
stem-5222	133	4	the	the	DET
stem-5222	133	5	practical	practical	ADJ
stem-5222	133	6	benefits	benefit	NOUN
stem-5222	133	7	and	and	CCONJ
stem-5222	133	8	challenges	challenge	NOUN
stem-5222	133	9	of	of	ADP
stem-5222	133	10	applying	apply	VERB
stem-5222	133	11	numerical	numerical	ADJ
stem-5222	133	12	solutions	solution	NOUN
stem-5222	133	13	to	to	ADP
stem-5222	133	14	complex	complex	ADJ
stem-5222	133	15	equations	equation	NOUN
stem-5222	133	16	,	,	PUNCT
stem-5222	133	17	highlighting	highlight	VERB
stem-5222	133	18	areas	area	NOUN
stem-5222	133	19	for	for	ADP
stem-5222	133	20	further	further	ADJ
stem-5222	133	21	research	research	NOUN
stem-5222	133	22	and	and	CCONJ
stem-5222	133	23	development	development	NOUN
stem-5222	133	24	.	.	PUNCT
stem-5222	134	1	conclusion	conclusion	NOUN
stem-5222	134	2	analyzing	analyze	VERB
stem-5222	134	3	complex	complex	ADJ
stem-5222	134	4	numbers	number	NOUN
stem-5222	134	5	through	through	ADP
stem-5222	134	6	numerical	numerical	ADJ
stem-5222	134	7	theory	theory	NOUN
stem-5222	134	8	offers	offer	VERB
stem-5222	134	9	profound	profound	ADJ
stem-5222	134	10	insights	insight	NOUN
stem-5222	134	11	and	and	CCONJ
stem-5222	134	12	practical	practical	ADJ
stem-5222	134	13	tools	tool	NOUN
stem-5222	134	14	for	for	ADP
stem-5222	134	15	various	various	ADJ
stem-5222	134	16	fields	field	NOUN
stem-5222	134	17	in	in	ADP
stem-5222	134	18	mathematics	mathematic	NOUN
stem-5222	134	19	and	and	CCONJ
stem-5222	134	20	engineering	engineering	NOUN
stem-5222	134	21	.	.	PUNCT
stem-5222	135	1	here	here	ADV
stem-5222	135	2	are	be	AUX
stem-5222	135	3	key	key	ADJ
stem-5222	135	4	takeaways	takeaway	NOUN
stem-5222	135	5	and	and	CCONJ
stem-5222	135	6	conclusions	conclusion	NOUN
stem-5222	135	7	:	:	PUNCT
stem-5222	135	8	1	1	X
stem-5222	135	9	.	.	PUNCT
stem-5222	135	10	enhanced	enhance	VERB
stem-5222	135	11	understanding	understanding	NOUN
stem-5222	135	12	of	of	ADP
stem-5222	135	13	complex	complex	ADJ
stem-5222	135	14	functions	function	NOUN
stem-5222	135	15	:	:	PUNCT
stem-5222	135	16			ADJ
stem-5222	135	17	numerical	numerical	ADJ
stem-5222	135	18	methods	method	NOUN
stem-5222	135	19	provide	provide	VERB
stem-5222	135	20	a	a	DET
stem-5222	135	21	robust	robust	ADJ
stem-5222	135	22	framework	framework	NOUN
stem-5222	135	23	for	for	ADP
stem-5222	135	24	evaluating	evaluate	VERB
stem-5222	135	25	complex	complex	ADJ
stem-5222	135	26	functions	function	NOUN
stem-5222	135	27	,	,	PUNCT
stem-5222	135	28	particularly	particularly	ADV
stem-5222	135	29	when	when	SCONJ
stem-5222	135	30	analytical	analytical	ADJ
stem-5222	135	31	solutions	solution	NOUN
stem-5222	135	32	are	be	AUX
stem-5222	135	33	intractable	intractable	ADJ
stem-5222	135	34	.	.	PUNCT
stem-5222	136	1	techniques	technique	NOUN
stem-5222	136	2	such	such	ADJ
stem-5222	136	3	as	as	ADP
stem-5222	136	4	numerical	numerical	ADJ
stem-5222	136	5	integration	integration	NOUN
stem-5222	136	6	and	and	CCONJ
stem-5222	136	7	differentiation	differentiation	NOUN
stem-5222	136	8	are	be	AUX
stem-5222	136	9	essential	essential	ADJ
stem-5222	136	10	for	for	ADP
stem-5222	136	11	understanding	understand	VERB
stem-5222	136	12	the	the	DET
stem-5222	136	13	behavior	behavior	NOUN
stem-5222	136	14	of	of	ADP
stem-5222	136	15	complex	complex	ADJ
stem-5222	136	16	functions	function	NOUN
stem-5222	136	17	in	in	ADP
stem-5222	136	18	applied	applied	ADJ
stem-5222	136	19	contexts	contexts	NOUN
stem-5222	136	20	.	.	PUNCT
stem-5222	137	1	2	2	X
stem-5222	137	2	.	.	X
stem-5222	137	3	applications	application	NOUN
stem-5222	137	4	in	in	ADP
stem-5222	137	5	engineering	engineering	NOUN
stem-5222	137	6	and	and	CCONJ
stem-5222	137	7	physics	physics	PROPN
stem-5222	137	8	:	:	PUNCT
stem-5222	137	9			ADJ
stem-5222	137	10	complex	complex	ADJ
stem-5222	137	11	numbers	number	NOUN
stem-5222	137	12	are	be	AUX
stem-5222	137	13	pivotal	pivotal	ADJ
stem-5222	137	14	in	in	ADP
stem-5222	137	15	solving	solve	VERB
stem-5222	137	16	differential	differential	ADJ
stem-5222	137	17	equations	equation	NOUN
stem-5222	137	18	,	,	PUNCT
stem-5222	137	19	particularly	particularly	ADV
stem-5222	137	20	in	in	ADP
stem-5222	137	21	electrical	electrical	ADJ
stem-5222	137	22	engineering	engineering	NOUN
stem-5222	137	23	(	(	PUNCT
stem-5222	137	24	e.g.	e.g.	ADV
stem-5222	137	25	,	,	PUNCT
stem-5222	137	26	analyzing	analyze	VERB
stem-5222	137	27	ac	ac	ADJ
stem-5222	137	28	circuits	circuit	NOUN
stem-5222	137	29	using	use	VERB
stem-5222	137	30	phasors	phasor	NOUN
stem-5222	137	31	)	)	PUNCT
stem-5222	137	32	and	and	CCONJ
stem-5222	137	33	quantum	quantum	PROPN
stem-5222	137	34	physics	physics	NOUN
stem-5222	137	35	.	.	PUNCT
stem-5222	138	1	numerical	numerical	PROPN
stem-5222	138	2	approaches	approach	NOUN
stem-5222	138	3	allow	allow	VERB
stem-5222	138	4	for	for	ADP
stem-5222	138	5	the	the	DET
stem-5222	138	6	modeling	modeling	NOUN
stem-5222	138	7	of	of	ADP
stem-5222	138	8	waveforms	waveform	NOUN
stem-5222	138	9	,	,	PUNCT
stem-5222	138	10	signal	signal	ADJ
stem-5222	138	11	processing	processing	NOUN
stem-5222	138	12	,	,	PUNCT
stem-5222	138	13	and	and	CCONJ
stem-5222	138	14	system	system	NOUN
stem-5222	138	15	dynamics	dynamic	NOUN
stem-5222	138	16	where	where	SCONJ
stem-5222	138	17	complex	complex	ADJ
stem-5222	138	18	functions	function	NOUN
stem-5222	138	19	are	be	AUX
stem-5222	138	20	prevalent	prevalent	ADJ
stem-5222	138	21	.	.	PUNCT
stem-5222	139	1	3	3	X
stem-5222	139	2	.	.	X
stem-5222	139	3	algorithm	algorithm	NOUN
stem-5222	139	4	development	development	NOUN
stem-5222	139	5	and	and	CCONJ
stem-5222	139	6	computational	computational	ADJ
stem-5222	139	7	efficiency	efficiency	NOUN
stem-5222	139	8	:	:	PUNCT
stem-5222	139	9			PROPN
stem-5222	139	10	numerical	numerical	PROPN
stem-5222	139	11	theory	theory	NOUN
stem-5222	139	12	aids	aid	NOUN
stem-5222	139	13	in	in	ADP
stem-5222	139	14	the	the	DET
stem-5222	139	15	development	development	NOUN
stem-5222	139	16	of	of	ADP
stem-5222	139	17	algorithms	algorithm	NOUN
stem-5222	139	18	for	for	ADP
stem-5222	139	19	efficient	efficient	ADJ
stem-5222	139	20	computation	computation	NOUN
stem-5222	139	21	with	with	ADP
stem-5222	139	22	complex	complex	ADJ
stem-5222	139	23	numbers	number	NOUN
stem-5222	139	24	.	.	PUNCT
stem-5222	140	1	techniques	technique	NOUN
stem-5222	140	2	like	like	ADP
stem-5222	140	3	the	the	DET
stem-5222	140	4	fast	fast	ADJ
stem-5222	140	5	fourier	fourier	NOUN
stem-5222	140	6	transform	transform	NOUN
stem-5222	140	7	(	(	PUNCT
stem-5222	140	8	fft	fft	PROPN
stem-5222	140	9	)	)	PUNCT
stem-5222	140	10	rely	rely	VERB
stem-5222	140	11	heavily	heavily	ADV
stem-5222	140	12	on	on	ADP
stem-5222	140	13	complex	complex	ADJ
stem-5222	140	14	number	number	NOUN
stem-5222	140	15	arithmetic	arithmetic	ADJ
stem-5222	140	16	,	,	PUNCT
stem-5222	140	17	demonstrating	demonstrate	VERB
stem-5222	140	18	the	the	DET
stem-5222	140	19	importance	importance	NOUN
stem-5222	140	20	of	of	ADP
stem-5222	140	21	numerical	numerical	ADJ
stem-5222	140	22	methods	method	NOUN
stem-5222	140	23	in	in	ADP
stem-5222	140	24	handling	handle	VERB
stem-5222	140	25	large	large	ADJ
stem-5222	140	26	-	-	PUNCT
stem-5222	140	27	scale	scale	NOUN
stem-5222	140	28	computations	computation	NOUN
stem-5222	140	29	efficiently	efficiently	ADV
stem-5222	140	30	.	.	PUNCT
stem-5222	141	1	4	4	X
stem-5222	141	2	.	.	X
stem-5222	141	3	stability	stability	NOUN
stem-5222	141	4	and	and	CCONJ
stem-5222	141	5	convergence	convergence	NOUN
stem-5222	141	6	of	of	ADP
stem-5222	141	7	numerical	numerical	ADJ
stem-5222	141	8	methods	method	NOUN
stem-5222	141	9	:	:	PUNCT
stem-5222	141	10			VERB
stem-5222	141	11	analyzing	analyze	VERB
stem-5222	141	12	the	the	DET
stem-5222	141	13	stability	stability	NOUN
stem-5222	141	14	and	and	CCONJ
stem-5222	141	15	convergence	convergence	NOUN
stem-5222	141	16	of	of	ADP
stem-5222	141	17	numerical	numerical	ADJ
stem-5222	141	18	methods	method	NOUN
stem-5222	141	19	when	when	SCONJ
stem-5222	141	20	applied	apply	VERB
stem-5222	141	21	to	to	ADP
stem-5222	141	22	complex	complex	ADJ
stem-5222	141	23	functions	function	NOUN
stem-5222	141	24	is	be	AUX
stem-5222	141	25	crucial	crucial	ADJ
stem-5222	141	26	.	.	PUNCT
stem-5222	142	1	ensuring	ensure	VERB
stem-5222	142	2	that	that	SCONJ
stem-5222	142	3	algorithms	algorithm	NOUN
stem-5222	142	4	produce	produce	VERB
stem-5222	142	5	accurate	accurate	ADJ
stem-5222	142	6	and	and	CCONJ
stem-5222	142	7	reliable	reliable	ADJ
stem-5222	142	8	results	result	NOUN
stem-5222	142	9	requires	require	VERB
stem-5222	142	10	a	a	DET
stem-5222	142	11	deep	deep	ADJ
stem-5222	142	12	understanding	understanding	NOUN
stem-5222	142	13	of	of	ADP
stem-5222	142	14	how	how	SCONJ
stem-5222	142	15	numerical	numerical	ADJ
stem-5222	142	16	errors	error	NOUN
stem-5222	142	17	propagate	propagate	VERB
stem-5222	142	18	in	in	ADP
stem-5222	142	19	the	the	DET
stem-5222	142	20	complex	complex	ADJ
stem-5222	142	21	plane	plane	NOUN
stem-5222	142	22	.	.	PUNCT
stem-5222	143	1	5	5	NUM
stem-5222	143	2	.	.	X
stem-5222	143	3	visualization	visualization	NOUN
stem-5222	143	4	and	and	CCONJ
stem-5222	143	5	geometric	geometric	ADJ
stem-5222	143	6	interpretation	interpretation	NOUN
stem-5222	143	7	:	:	PUNCT
stem-5222	143	8	302	302	NUM
stem-5222	143	9	american	american	ADJ
stem-5222	143	10	journal	journal	NOUN
stem-5222	143	11	of	of	ADP
stem-5222	143	12	language	language	NOUN
stem-5222	143	13	,	,	PUNCT
stem-5222	143	14	literacy	literacy	NOUN
stem-5222	143	15	and	and	CCONJ
stem-5222	143	16	learning	learn	VERB
stem-5222	143	17	in	in	ADP
stem-5222	143	18	stem	stem	NOUN
stem-5222	143	19	education	education	NOUN
stem-5222	143	20	www	www	PROPN
stem-5222	143	21	.	.	PUNCT
stem-5222	144	1	grnjournal.us	grnjournal.us	X
stem-5222	144	2			VERB
stem-5222	144	3	numerical	numerical	ADJ
stem-5222	144	4	techniques	technique	NOUN
stem-5222	144	5	allow	allow	VERB
stem-5222	144	6	for	for	ADP
stem-5222	144	7	the	the	DET
stem-5222	144	8	visualization	visualization	NOUN
stem-5222	144	9	of	of	ADP
stem-5222	144	10	complex	complex	ADJ
stem-5222	144	11	functions	function	NOUN
stem-5222	144	12	and	and	CCONJ
stem-5222	144	13	transformations	transformation	NOUN
stem-5222	144	14	,	,	PUNCT
stem-5222	144	15	aiding	aid	VERB
stem-5222	144	16	in	in	ADP
stem-5222	144	17	the	the	DET
stem-5222	144	18	geometric	geometric	ADJ
stem-5222	144	19	interpretation	interpretation	NOUN
stem-5222	144	20	of	of	ADP
stem-5222	144	21	complex	complex	ADJ
stem-5222	144	22	analysis	analysis	NOUN
stem-5222	144	23	concepts	concept	NOUN
stem-5222	144	24	.	.	PUNCT
stem-5222	145	1	this	this	PRON
stem-5222	145	2	can	can	AUX
stem-5222	145	3	be	be	AUX
stem-5222	145	4	particularly	particularly	ADV
stem-5222	145	5	helpful	helpful	ADJ
stem-5222	145	6	in	in	ADP
stem-5222	145	7	educational	educational	ADJ
stem-5222	145	8	contexts	context	NOUN
stem-5222	145	9	and	and	CCONJ
stem-5222	145	10	in	in	ADP
stem-5222	145	11	the	the	DET
stem-5222	145	12	development	development	NOUN
stem-5222	145	13	of	of	ADP
stem-5222	145	14	intuition	intuition	NOUN
stem-5222	145	15	about	about	ADP
stem-5222	145	16	complex	complex	ADJ
stem-5222	145	17	systems	system	NOUN
stem-5222	145	18	.	.	PUNCT
stem-5222	146	1	6	6	NUM
stem-5222	146	2	.	.	X
stem-5222	146	3	real	real	ADJ
stem-5222	146	4	-	-	PUNCT
stem-5222	146	5	world	world	NOUN
stem-5222	146	6	problem	problem	NOUN
stem-5222	146	7	solving	solving	NOUN
stem-5222	146	8	:	:	PUNCT
stem-5222	146	9			ADJ
stem-5222	146	10	practical	practical	ADJ
stem-5222	146	11	problems	problem	NOUN
stem-5222	146	12	in	in	ADP
stem-5222	146	13	science	science	NOUN
stem-5222	146	14	and	and	CCONJ
stem-5222	146	15	engineering	engineering	NOUN
stem-5222	146	16	often	often	ADV
stem-5222	146	17	require	require	VERB
stem-5222	146	18	the	the	DET
stem-5222	146	19	numerical	numerical	ADJ
stem-5222	146	20	solution	solution	NOUN
stem-5222	146	21	of	of	ADP
stem-5222	146	22	equations	equation	NOUN
stem-5222	146	23	involving	involve	VERB
stem-5222	146	24	complex	complex	ADJ
stem-5222	146	25	numbers	number	NOUN
stem-5222	146	26	.	.	PUNCT
stem-5222	147	1	numerical	numerical	PROPN
stem-5222	147	2	theory	theory	NOUN
stem-5222	147	3	equips	equip	VERB
stem-5222	147	4	practitioners	practitioner	NOUN
stem-5222	147	5	with	with	ADP
stem-5222	147	6	the	the	DET
stem-5222	147	7	tools	tool	NOUN
stem-5222	147	8	to	to	PART
stem-5222	147	9	tackle	tackle	VERB
stem-5222	147	10	such	such	ADJ
stem-5222	147	11	problems	problem	NOUN
stem-5222	147	12	effectively	effectively	ADV
stem-5222	147	13	,	,	PUNCT
stem-5222	147	14	bridging	bridge	VERB
stem-5222	147	15	the	the	DET
stem-5222	147	16	gap	gap	NOUN
stem-5222	147	17	between	between	ADP
stem-5222	147	18	theoretical	theoretical	ADJ
stem-5222	147	19	mathematics	mathematic	NOUN
stem-5222	147	20	and	and	CCONJ
stem-5222	147	21	practical	practical	ADJ
stem-5222	147	22	application	application	NOUN
stem-5222	147	23	.	.	PUNCT
stem-5222	148	1	7	7	X
stem-5222	148	2	.	.	X
stem-5222	148	3	interdisciplinary	interdisciplinary	ADJ
stem-5222	148	4	impact	impact	NOUN
stem-5222	148	5	:	:	PUNCT
stem-5222	148	6			VERB
stem-5222	148	7	the	the	DET
stem-5222	148	8	application	application	NOUN
stem-5222	148	9	of	of	ADP
stem-5222	148	10	numerical	numerical	ADJ
stem-5222	148	11	methods	method	NOUN
stem-5222	148	12	to	to	ADP
stem-5222	148	13	complex	complex	ADJ
stem-5222	148	14	numbers	number	NOUN
stem-5222	148	15	spans	span	VERB
stem-5222	148	16	multiple	multiple	ADJ
stem-5222	148	17	disciplines	discipline	NOUN
stem-5222	148	18	,	,	PUNCT
stem-5222	148	19	fostering	foster	VERB
stem-5222	148	20	interdisciplinary	interdisciplinary	ADJ
stem-5222	148	21	research	research	NOUN
stem-5222	148	22	and	and	CCONJ
stem-5222	148	23	collaboration	collaboration	NOUN
stem-5222	148	24	.	.	PUNCT
stem-5222	149	1	fields	field	NOUN
stem-5222	149	2	such	such	ADJ
stem-5222	149	3	as	as	ADP
stem-5222	149	4	fluid	fluid	ADJ
stem-5222	149	5	dynamics	dynamic	NOUN
stem-5222	149	6	,	,	PUNCT
stem-5222	149	7	control	control	NOUN
stem-5222	149	8	theory	theory	NOUN
stem-5222	149	9	,	,	PUNCT
stem-5222	149	10	and	and	CCONJ
stem-5222	149	11	telecommunications	telecommunications	NOUN
stem-5222	149	12	benefit	benefit	NOUN
stem-5222	149	13	from	from	ADP
stem-5222	149	14	these	these	DET
stem-5222	149	15	techniques	technique	NOUN
stem-5222	149	16	,	,	PUNCT
stem-5222	149	17	illustrating	illustrate	VERB
stem-5222	149	18	their	their	PRON
stem-5222	149	19	broad	broad	ADJ
stem-5222	149	20	impact	impact	NOUN
stem-5222	149	21	.	.	PUNCT
stem-5222	150	1	in	in	ADP
stem-5222	150	2	summary	summary	NOUN
stem-5222	150	3	,	,	PUNCT
stem-5222	150	4	the	the	DET
stem-5222	150	5	intersection	intersection	NOUN
stem-5222	150	6	of	of	ADP
stem-5222	150	7	complex	complex	ADJ
stem-5222	150	8	numbers	number	NOUN
stem-5222	150	9	and	and	CCONJ
stem-5222	150	10	numerical	numerical	ADJ
stem-5222	150	11	theory	theory	NOUN
stem-5222	150	12	is	be	AUX
stem-5222	150	13	a	a	DET
stem-5222	150	14	rich	rich	ADJ
stem-5222	150	15	area	area	NOUN
stem-5222	150	16	of	of	ADP
stem-5222	150	17	study	study	NOUN
stem-5222	150	18	that	that	PRON
stem-5222	150	19	enhances	enhance	VERB
stem-5222	150	20	our	our	PRON
stem-5222	150	21	ability	ability	NOUN
stem-5222	150	22	to	to	PART
stem-5222	150	23	solve	solve	VERB
stem-5222	150	24	complex	complex	ADJ
stem-5222	150	25	problems	problem	NOUN
stem-5222	150	26	,	,	PUNCT
stem-5222	150	27	develop	develop	VERB
stem-5222	150	28	efficient	efficient	ADJ
stem-5222	150	29	computational	computational	ADJ
stem-5222	150	30	tools	tool	NOUN
stem-5222	150	31	,	,	PUNCT
stem-5222	150	32	and	and	CCONJ
stem-5222	150	33	deepen	deepen	VERB
stem-5222	150	34	our	our	PRON
stem-5222	150	35	understanding	understanding	NOUN
stem-5222	150	36	of	of	ADP
stem-5222	150	37	mathematical	mathematical	ADJ
stem-5222	150	38	phenomena	phenomenon	NOUN
stem-5222	150	39	.	.	PUNCT
stem-5222	151	1	through	through	ADP
stem-5222	151	2	numerical	numerical	ADJ
stem-5222	151	3	analysis	analysis	NOUN
stem-5222	151	4	,	,	PUNCT
stem-5222	151	5	we	we	PRON
stem-5222	151	6	can	can	AUX
stem-5222	151	7	extend	extend	VERB
stem-5222	151	8	the	the	DET
stem-5222	151	9	reach	reach	NOUN
stem-5222	151	10	of	of	ADP
stem-5222	151	11	complex	complex	ADJ
stem-5222	151	12	analysis	analysis	NOUN
stem-5222	151	13	into	into	ADP
stem-5222	151	14	practical	practical	ADJ
stem-5222	151	15	and	and	CCONJ
stem-5222	151	16	applied	applied	ADJ
stem-5222	151	17	realms	realm	NOUN
stem-5222	151	18	,	,	PUNCT
stem-5222	151	19	driving	drive	VERB
stem-5222	151	20	innovation	innovation	NOUN
stem-5222	151	21	and	and	CCONJ
stem-5222	151	22	discovery	discovery	NOUN
stem-5222	151	23	across	across	ADP
stem-5222	151	24	various	various	ADJ
stem-5222	151	25	scientific	scientific	ADJ
stem-5222	151	26	and	and	CCONJ
stem-5222	151	27	engineering	engineering	NOUN
stem-5222	151	28	domains	domain	NOUN
stem-5222	151	29	.	.	PUNCT
stem-5222	152	1	references	reference	NOUN
stem-5222	152	2	1	1	NUM
stem-5222	152	3	.	.	PUNCT
stem-5222	152	4	altmann	altmann	PROPN
stem-5222	152	5	,	,	PUNCT
stem-5222	152	6	simon	simon	PROPN
stem-5222	152	7	l.	l.	PROPN
stem-5222	152	8	(	(	PUNCT
stem-5222	152	9	1989	1989	NUM
stem-5222	152	10	)	)	PUNCT
stem-5222	152	11	,	,	PUNCT
stem-5222	152	12	"	"	PUNCT
stem-5222	152	13	hamilton	hamilton	PROPN
stem-5222	152	14	,	,	PUNCT
stem-5222	152	15	rodrigues	rodrigue	NOUN
stem-5222	152	16	,	,	PUNCT
stem-5222	152	17	and	and	CCONJ
stem-5222	152	18	the	the	DET
stem-5222	152	19	quaternion	quaternion	NOUN
stem-5222	152	20	scandal	scandal	NOUN
stem-5222	152	21	,	,	PUNCT
stem-5222	152	22	"	"	PUNCT
stem-5222	152	23	math	math	NOUN
stem-5222	152	24	.	.	PUNCT
stem-5222	153	1	mag	mag	INTJ
stem-5222	153	2	.	.	PROPN
stem-5222	153	3	,	,	PUNCT
stem-5222	153	4	v.	v.	ADP
stem-5222	153	5	62	62	NUM
stem-5222	153	6	,	,	PUNCT
stem-5222	153	7	no	no	INTJ
stem-5222	153	8	.	.	NOUN
stem-5222	153	9	5	5	NUM
stem-5222	153	10	.	.	NUM
stem-5222	153	11	,	,	PUNCT
stem-5222	153	12	pp	pp	PROPN
stem-5222	153	13	.	.	PUNCT
stem-5222	154	1	291	291	NUM
stem-5222	154	2	-	-	SYM
stem-5222	154	3	307	307	NUM
stem-5222	154	4	.	.	PUNCT
stem-5222	155	1	2	2	NUM
stem-5222	155	2	.	.	X
stem-5222	155	3	axler	axler	PROPN
stem-5222	155	4	,	,	PUNCT
stem-5222	155	5	sheldon	sheldon	PROPN
stem-5222	155	6	(	(	PUNCT
stem-5222	155	7	1986	1986	NUM
stem-5222	155	8	)	)	PUNCT
stem-5222	155	9	,	,	PUNCT
stem-5222	155	10	"	"	PUNCT
stem-5222	155	11	harmonic	harmonic	ADJ
stem-5222	155	12	functions	function	NOUN
stem-5222	155	13	from	from	ADP
stem-5222	155	14	a	a	DET
stem-5222	155	15	complex	complex	ADJ
stem-5222	155	16	analysis	analysis	NOUN
stem-5222	155	17	viewpoint	viewpoint	NOUN
stem-5222	155	18	,	,	PUNCT
stem-5222	155	19	"	"	PUNCT
stem-5222	155	20	am	be	AUX
stem-5222	155	21	.	.	PUNCT
stem-5222	156	1	math	math	NOUN
stem-5222	156	2	.	.	PUNCT
stem-5222	157	1	m.	m.	NOUN
stem-5222	157	2	,	,	PUNCT
stem-5222	157	3	v.	v.	ADP
stem-5222	157	4	93	93	NUM
stem-5222	157	5	,	,	PUNCT
stem-5222	157	6	no	no	INTJ
stem-5222	157	7	.	.	NOUN
stem-5222	157	8	4	4	NUM
stem-5222	157	9	,	,	PUNCT
stem-5222	157	10	pp	pp	ADJ
stem-5222	157	11	.	.	PUNCT
stem-5222	158	1	246	246	NUM
stem-5222	158	2	-	-	SYM
stem-5222	158	3	258	258	NUM
stem-5222	158	4	.	.	PUNCT
stem-5222	159	1	3	3	NUM
stem-5222	159	2	.	.	X
stem-5222	159	3	azarnia	azarnia	PROPN
stem-5222	159	4	,	,	PUNCT
stem-5222	159	5	nozar	nozar	NOUN
stem-5222	159	6	(	(	PUNCT
stem-5222	159	7	1987	1987	NUM
stem-5222	159	8	)	)	PUNCT
stem-5222	159	9	,	,	PUNCT
stem-5222	159	10	"	"	PUNCT
stem-5222	159	11	a	a	DET
stem-5222	159	12	classroom	classroom	NOUN
stem-5222	159	13	note	note	NOUN
stem-5222	159	14	:	:	PUNCT
stem-5222	159	15	on	on	ADP
stem-5222	159	16	elementary	elementary	ADJ
stem-5222	159	17	use	use	NOUN
stem-5222	159	18	of	of	ADP
stem-5222	159	19	complex	complex	ADJ
stem-5222	159	20	numbers	number	NOUN
stem-5222	159	21	,	,	PUNCT
stem-5222	159	22	"	"	PUNCT
stem-5222	159	23	math	math	NOUN
stem-5222	159	24	,	,	PUNCT
stem-5222	159	25	and	and	CCONJ
stem-5222	159	26	comp	comp	NOUN
stem-5222	159	27	.	.	PUNCT
stem-5222	160	1	ed	ed	NOUN
stem-5222	160	2	.	.	PROPN
stem-5222	160	3	,	,	PUNCT
stem-5222	160	4	vol	vol	NOUN
stem-5222	160	5	21	21	NUM
stem-5222	160	6	,	,	PUNCT
stem-5222	160	7	no	no	INTJ
stem-5222	160	8	.	.	NOUN
stem-5222	160	9	2	2	NUM
stem-5222	160	10	,	,	PUNCT
stem-5222	160	11	pp	pp	ADJ
stem-5222	160	12	.	.	PUNCT
stem-5222	161	1	135	135	NUM
stem-5222	161	2	-	-	SYM
stem-5222	161	3	136	136	NUM
stem-5222	161	4	.	.	PUNCT
stem-5222	162	1	4	4	X
stem-5222	162	2	.	.	X
stem-5222	162	3	bak	bak	PROPN
stem-5222	162	4	,	,	PUNCT
stem-5222	162	5	joseph	joseph	PROPN
stem-5222	162	6	,	,	PUNCT
stem-5222	162	7	and	and	CCONJ
stem-5222	162	8	donald	donald	PROPN
stem-5222	162	9	j.	j.	PROPN
stem-5222	162	10	newman	newman	PROPN
stem-5222	162	11	(	(	PUNCT
stem-5222	162	12	1982	1982	NUM
stem-5222	162	13	)	)	PUNCT
stem-5222	162	14	,	,	PUNCT
stem-5222	162	15	complex	complex	ADJ
stem-5222	162	16	analysis	analysis	NOUN
stem-5222	162	17	,	,	PUNCT
stem-5222	162	18	new	new	PROPN
stem-5222	162	19	york	york	PROPN
stem-5222	162	20	:	:	PUNCT
stem-5222	162	21	springerverlag	springerverlag	PROPN
stem-5222	162	22	.	.	PUNCT
stem-5222	163	1	5	5	X
stem-5222	163	2	.	.	X
stem-5222	163	3	baker	baker	PROPN
stem-5222	163	4	,	,	PUNCT
stem-5222	163	5	i.	i.	PROPN
stem-5222	163	6	n.	n.	PROPN
stem-5222	163	7	,	,	PUNCT
stem-5222	163	8	and	and	CCONJ
stem-5222	163	9	p.	p.	PROPN
stem-5222	163	10	j.	j.	PROPN
stem-5222	163	11	rippon	rippon	PROPN
stem-5222	163	12	(	(	PUNCT
stem-5222	163	13	1985	1985	NUM
stem-5222	163	14	)	)	PUNCT
stem-5222	163	15	,	,	PUNCT
stem-5222	163	16	"	"	PUNCT
stem-5222	163	17	a	a	DET
stem-5222	163	18	note	note	NOUN
stem-5222	163	19	on	on	ADP
stem-5222	163	20	complex	complex	ADJ
stem-5222	163	21	integration	integration	NOUN
stem-5222	163	22	,	,	PUNCT
stem-5222	163	23	"	"	PUNCT
stem-5222	163	24	am	be	AUX
stem-5222	163	25	.	.	PUNCT
stem-5222	163	26	math	math	NOUN
stem-5222	163	27	.	.	PUNCT
stem-5222	164	1	m.	m.	NOUN
stem-5222	164	2	,v	,v	PROPN
stem-5222	164	3	.	.	PUNCT
stem-5222	165	1	92	92	NUM
stem-5222	165	2	,	,	PUNCT
stem-5222	165	3	no	no	INTJ
stem-5222	165	4	.	.	NOUN
stem-5222	165	5	7	7	NUM
stem-5222	165	6	,	,	PUNCT
stem-5222	165	7	pp	pp	ADJ
stem-5222	165	8	.	.	PUNCT
stem-5222	166	1	501	501	NUM
stem-5222	166	2	-	-	SYM
stem-5222	166	3	504	504	NUM
stem-5222	166	4	.	.	PUNCT
stem-5222	167	1	6	6	NUM
stem-5222	167	2	.	.	X
stem-5222	167	3	baker	baker	PROPN
stem-5222	167	4	,	,	PUNCT
stem-5222	167	5	john	john	PROPN
stem-5222	167	6	a.	a.	PROPN
stem-5222	167	7	(	(	PUNCT
stem-5222	167	8	1991	1991	NUM
stem-5222	167	9	)	)	PUNCT
stem-5222	167	10	,	,	PUNCT
stem-5222	167	11	"	"	PUNCT
stem-5222	167	12	plane	plane	NOUN
stem-5222	167	13	curves	curve	NOUN
stem-5222	167	14	,	,	PUNCT
stem-5222	167	15	polar	polar	ADJ
stem-5222	167	16	coordinates	coordinate	NOUN
stem-5222	167	17	and	and	CCONJ
stem-5222	167	18	winding	wind	VERB
stem-5222	167	19	numbers	number	NOUN
stem-5222	167	20	,	,	PUNCT
stem-5222	167	21	"	"	PUNCT
stem-5222	167	22	math	math	NOUN
stem-5222	167	23	.	.	PUNCT
stem-5222	168	1	mag	mag	INTJ
stem-5222	168	2	.	.	PROPN
stem-5222	168	3	,	,	PUNCT
stem-5222	168	4	v.	v.	ADP
stem-5222	168	5	64	64	NUM
stem-5222	168	6	,	,	PUNCT
stem-5222	168	7	no	no	INTJ
stem-5222	168	8	.	.	NOUN
stem-5222	168	9	2	2	NUM
stem-5222	168	10	,	,	PUNCT
stem-5222	168	11	pp	pp	ADJ
stem-5222	168	12	.	.	PUNCT
stem-5222	169	1	75	75	NUM
stem-5222	169	2	-	-	SYM
stem-5222	169	3	91	91	NUM
stem-5222	169	4	.	.	PUNCT
stem-5222	170	1	7	7	X
stem-5222	170	2	.	.	X
stem-5222	170	3	bannon	bannon	PROPN
stem-5222	170	4	,	,	PUNCT
stem-5222	170	5	thomas	thomas	PROPN
stem-5222	170	6	j.	j.	PROPN
stem-5222	170	7	(	(	PUNCT
stem-5222	170	8	1991	1991	NUM
stem-5222	170	9	)	)	PUNCT
stem-5222	170	10	,	,	PUNCT
stem-5222	170	11	"	"	PUNCT
stem-5222	170	12	fractals	fractal	NOUN
stem-5222	170	13	and	and	CCONJ
stem-5222	170	14	transformations	transformation	NOUN
stem-5222	170	15	,	,	PUNCT
stem-5222	170	16	"	"	PUNCT
stem-5222	170	17	math	math	NOUN
stem-5222	170	18	.	.	PUNCT
stem-5222	171	1	teach	teach	VERB
stem-5222	171	2	.	.	PUNCT
stem-5222	171	3	,	,	PUNCT
stem-5222	172	1	v.	v.	ADP
stem-5222	172	2	81	81	NUM
stem-5222	172	3	,	,	PUNCT
stem-5222	172	4	no	no	INTJ
stem-5222	172	5	.	.	NOUN
stem-5222	172	6	3	3	NUM
stem-5222	172	7	,	,	PUNCT
stem-5222	172	8	pp	pp	ADJ
stem-5222	172	9	.	.	PUNCT
stem-5222	172	10	178185	178185	NUM
stem-5222	172	11	.	.	PUNCT
stem-5222	173	1	8	8	X
stem-5222	173	2	.	.	X
stem-5222	174	1	barcellos	barcello	NOUN
stem-5222	174	2	,	,	PUNCT
stem-5222	174	3	anthony	anthony	PROPN
stem-5222	174	4	(	(	PUNCT
stem-5222	174	5	1984	1984	NUM
stem-5222	174	6	)	)	PUNCT
stem-5222	174	7	,	,	PUNCT
stem-5222	174	8	"	"	PUNCT
stem-5222	174	9	the	the	DET
stem-5222	174	10	fractal	fractal	ADJ
stem-5222	174	11	geometry	geometry	NOUN
stem-5222	174	12	of	of	ADP
stem-5222	174	13	mandelbrot	mandelbrot	NOUN
stem-5222	174	14	,	,	PUNCT
stem-5222	174	15	"	"	PUNCT
stem-5222	174	16	t.	t.	PROPN
stem-5222	174	17	y.	y.	PROPN
stem-5222	174	18	c.	c.	PROPN
stem-5222	174	19	math	math	PROPN
stem-5222	174	20	.	.	PUNCT
stem-5222	175	1	j.	j.	PROPN
stem-5222	175	2	,	,	PUNCT
stem-5222	175	3	v.	v.	ADP
stem-5222	175	4	15	15	NUM
stem-5222	175	5	,	,	PUNCT
stem-5222	175	6	no	no	INTJ
stem-5222	175	7	.	.	NOUN
stem-5222	175	8	2	2	NUM
stem-5222	175	9	,	,	PUNCT
stem-5222	175	10	pp	pp	ADJ
stem-5222	175	11	.	.	PUNCT
stem-5222	176	1	98	98	NUM
stem-5222	176	2	-	-	SYM
stem-5222	176	3	114	114	NUM
stem-5222	176	4	.	.	PUNCT
stem-5222	177	1	9	9	X
stem-5222	177	2	.	.	X
stem-5222	177	3	barnsley	barnsley	NOUN
stem-5222	177	4	,	,	PUNCT
stem-5222	177	5	michael	michael	PROPN
stem-5222	177	6	fielding	field	VERB
stem-5222	177	7	(	(	PUNCT
stem-5222	177	8	1988	1988	NUM
stem-5222	177	9	)	)	PUNCT
stem-5222	177	10	,	,	PUNCT
stem-5222	177	11	fractals	fractal	NOUN
stem-5222	177	12	everywhere	everywhere	ADV
stem-5222	177	13	,	,	PUNCT
stem-5222	177	14	boston	boston	PROPN
stem-5222	177	15	:	:	PUNCT
stem-5222	177	16	academic	academic	ADJ
stem-5222	177	17	press	press	NOUN
stem-5222	177	18	.	.	PUNCT
stem-5222	178	1	10	10	NUM
stem-5222	178	2	.	.	X
stem-5222	178	3	barry	barry	PROPN
stem-5222	178	4	,	,	PUNCT
stem-5222	178	5	p.	p.	PROPN
stem-5222	178	6	d.	d.	PROPN
stem-5222	178	7	,	,	PUNCT
stem-5222	178	8	and	and	CCONJ
stem-5222	178	9	d.	d.	PROPN
stem-5222	178	10	j.	j.	PROPN
stem-5222	178	11	hurley	hurley	PROPN
stem-5222	178	12	(	(	PUNCT
stem-5222	178	13	1991	1991	NUM
stem-5222	178	14	)	)	PUNCT
stem-5222	178	15	,	,	PUNCT
stem-5222	178	16	"	"	PUNCT
stem-5222	178	17	on	on	ADP
stem-5222	178	18	series	series	NOUN
stem-5222	178	19	of	of	ADP
stem-5222	178	20	partial	partial	ADJ
stem-5222	178	21	fractions	fraction	NOUN
stem-5222	178	22	,	,	PUNCT
stem-5222	178	23	"	"	PUNCT
stem-5222	178	24	am	be	AUX
stem-5222	178	25	.	.	PUNCT
stem-5222	179	1	math	math	NOUN
stem-5222	179	2	.	.	PUNCT
stem-5222	180	1	m.	m.	NOUN
stem-5222	180	2	,	,	PUNCT
stem-5222	180	3	v.	v.	ADP
stem-5222	180	4	98	98	NUM
stem-5222	180	5	,	,	PUNCT
stem-5222	180	6	no	no	INTJ
stem-5222	180	7	.	.	NOUN
stem-5222	180	8	3	3	NUM
stem-5222	180	9	,	,	PUNCT
stem-5222	180	10	pp	pp	ADJ
stem-5222	180	11	.	.	PUNCT
stem-5222	181	1	240	240	NUM
stem-5222	181	2	-	-	SYM
stem-5222	181	3	242	242	NUM
stem-5222	181	4	.	.	PUNCT
stem-5222	182	1	11	11	NUM
stem-5222	182	2	.	.	PUNCT
stem-5222	183	1	barton	barton	PROPN
stem-5222	183	2	,	,	PUNCT
stem-5222	183	3	ray	ray	PROPN
stem-5222	183	4	(	(	PUNCT
stem-5222	183	5	1990	1990	NUM
stem-5222	183	6	)	)	PUNCT
stem-5222	183	7	,	,	PUNCT
stem-5222	183	8	"	"	PUNCT
stem-5222	183	9	chaos	chaos	NOUN
stem-5222	183	10	and	and	CCONJ
stem-5222	183	11	fractals	fractal	NOUN
stem-5222	183	12	,	,	PUNCT
stem-5222	183	13	"	"	PUNCT
stem-5222	183	14	math	math	NOUN
stem-5222	183	15	.	.	PUNCT
stem-5222	184	1	teach	teach	VERB
stem-5222	184	2	.	.	PUNCT
stem-5222	184	3	,	,	PUNCT
stem-5222	185	1	v.	v.	ADP
stem-5222	185	2	83	83	NUM
stem-5222	185	3	,	,	PUNCT
stem-5222	185	4	no	no	INTJ
stem-5222	185	5	.	.	NOUN
stem-5222	185	6	7	7	NUM
stem-5222	185	7	,	,	PUNCT
stem-5222	185	8	pp	pp	ADJ
stem-5222	185	9	.	.	PUNCT
stem-5222	186	1	524	524	NUM
stem-5222	186	2	-	-	SYM
stem-5222	186	3	529	529	NUM
stem-5222	186	4	.	.	PUNCT
stem-5222	187	1	12	12	NUM
stem-5222	187	2	.	.	PUNCT
stem-5222	188	1	beardon	beardon	PROPN
stem-5222	188	2	,	,	PUNCT
stem-5222	188	3	alan	alan	PROPN
stem-5222	188	4	f.	f.	PROPN
stem-5222	188	5	(	(	PUNCT
stem-5222	188	6	1987	1987	NUM
stem-5222	188	7	)	)	PUNCT
stem-5222	188	8	,	,	PUNCT
stem-5222	188	9	"	"	PUNCT
stem-5222	188	10	curvature	curvature	NOUN
stem-5222	188	11	,	,	PUNCT
stem-5222	188	12	circles	circle	NOUN
stem-5222	188	13	and	and	CCONJ
stem-5222	188	14	conformal	conformal	NOUN
stem-5222	188	15	maps	map	NOUN
stem-5222	188	16	,	,	PUNCT
stem-5222	188	17	"	"	PUNCT
stem-5222	188	18	am	be	AUX
stem-5222	188	19	.	.	PUNCT
stem-5222	189	1	math	math	NOUN
stem-5222	189	2	.	.	PUNCT
stem-5222	190	1	m.	m.	NOUN
stem-5222	190	2	,	,	PUNCT
stem-5222	190	3	v	v	NOUN
stem-5222	190	4	,	,	PUNCT
stem-5222	190	5	94	94	NUM
stem-5222	190	6	,	,	PUNCT
stem-5222	190	7	no	no	INTJ
stem-5222	190	8	.	.	NOUN
stem-5222	190	9	1	1	NUM
stem-5222	190	10	,	,	PUNCT
stem-5222	190	11	pp	pp	ADJ
stem-5222	190	12	.	.	PUNCT
stem-5222	191	1	48	48	NUM
stem-5222	191	2	-	-	SYM
stem-5222	191	3	53	53	NUM
stem-5222	191	4	.	.	NOUN
stem-5222	192	1	13	13	NUM
stem-5222	192	2	.	.	PUNCT
stem-5222	192	3	berresford	berresford	PROPN
stem-5222	192	4	,	,	PUNCT
stem-5222	192	5	geoffrey	geoffrey	PROPN
stem-5222	192	6	c.	c.	PROPN
stem-5222	192	7	(	(	PUNCT
stem-5222	192	8	1981	1981	NUM
stem-5222	192	9	)	)	PUNCT
stem-5222	192	10	,	,	PUNCT
stem-5222	192	11	"	"	PUNCT
stem-5222	192	12	cauchy	cauchy	PROPN
stem-5222	192	13	's	's	PART
stem-5222	192	14	theorem	theorem	NOUN
stem-5222	192	15	,	,	PUNCT
stem-5222	192	16	"	"	PUNCT
stem-5222	192	17	am	be	AUX
stem-5222	192	18	.	.	PUNCT
stem-5222	193	1	math	math	NOUN
stem-5222	193	2	.	.	PUNCT
stem-5222	194	1	m.	m.	NOUN
stem-5222	194	2	,	,	PUNCT
stem-5222	194	3	v.	v.	ADP
stem-5222	194	4	88	88	NUM
stem-5222	194	5	,	,	PUNCT
stem-5222	194	6	no	no	INTJ
stem-5222	194	7	.	.	NOUN
stem-5222	194	8	10	10	NUM
stem-5222	194	9	,	,	PUNCT
stem-5222	194	10	pp	pp	ADJ
stem-5222	194	11	.	.	PUNCT
stem-5222	195	1	741	741	NUM
stem-5222	195	2	-	-	SYM
stem-5222	195	3	742	742	NUM
stem-5222	195	4	.	.	PUNCT
stem-5222	196	1	14	14	NUM
stem-5222	196	2	.	.	PUNCT
stem-5222	197	1	bivens	bivens	PROPN
stem-5222	197	2	,	,	PUNCT
stem-5222	197	3	irl	irl	PROPN
stem-5222	197	4	c.	c.	NOUN
stem-5222	197	5	(	(	PUNCT
stem-5222	197	6	1992	1992	NUM
stem-5222	197	7	)	)	PUNCT
stem-5222	197	8	,	,	PUNCT
stem-5222	197	9	"	"	PUNCT
stem-5222	197	10	when	when	SCONJ
stem-5222	197	11	do	do	AUX
stem-5222	197	12	orthogonal	orthogonal	ADJ
stem-5222	197	13	families	family	NOUN
stem-5222	197	14	of	of	ADP
stem-5222	197	15	curves	curve	NOUN
stem-5222	197	16	possess	possess	VERB
stem-5222	197	17	a	a	DET
stem-5222	197	18	complex	complex	ADJ
stem-5222	197	19	potential	potential	NOUN
stem-5222	197	20	?	?	PUNCT
stem-5222	197	21	"	"	PUNCT
stem-5222	197	22	math	math	NOUN
stem-5222	197	23	.	.	PUNCT
stem-5222	198	1	mag	mag	INTJ
stem-5222	198	2	.	.	PROPN
stem-5222	198	3	,	,	PUNCT
stem-5222	199	1	v.	v.	ADP
stem-5222	199	2	65	65	NUM
stem-5222	199	3	,	,	PUNCT
stem-5222	199	4	no	no	INTJ
stem-5222	199	5	.	.	NOUN
stem-5222	199	6	4	4	NUM
stem-5222	199	7	,	,	PUNCT
stem-5222	199	8	pp	pp	ADJ
stem-5222	199	9	.	.	PUNCT
stem-5222	200	1	226	226	NUM
stem-5222	200	2	-	-	SYM
stem-5222	200	3	235	235	NUM
stem-5222	200	4	.	.	NOUN
stem-5222	200	5	15	15	NUM
stem-5222	200	6	.	.	PUNCT
stem-5222	201	1	bleick	bleick	NOUN
stem-5222	201	2	,	,	PUNCT
stem-5222	201	3	w.	w.	PROPN
stem-5222	201	4	e.	e.	PROPN
stem-5222	201	5	(	(	PUNCT
stem-5222	201	6	1956	1956	NUM
stem-5222	201	7	)	)	PUNCT
stem-5222	201	8	,	,	PUNCT
stem-5222	201	9	"	"	PUNCT
stem-5222	201	10	fourier	fouri	ADJ
stem-5222	201	11	analysis	analysis	NOUN
stem-5222	201	12	of	of	ADP
stem-5222	201	13	engine	engine	NOUN
stem-5222	201	14	unbalance	unbalance	NOUN
stem-5222	201	15	by	by	ADP
stem-5222	201	16	contour	contour	NOUN
stem-5222	201	17	integration	integration	NOUN
stem-5222	201	18	,	,	PUNCT
stem-5222	201	19	"	"	PUNCT
stem-5222	201	20	am	be	AUX
stem-5222	201	21	.	.	PUNCT
stem-5222	202	1	math	math	NOUN
stem-5222	202	2	.	.	PUNCT
stem-5222	203	1	m.	m.	NOUN
stem-5222	203	2	,	,	PUNCT
stem-5222	203	3	v.	v.	ADP
stem-5222	203	4	63	63	NUM
stem-5222	203	5	,	,	PUNCT
stem-5222	203	6	no	no	INTJ
stem-5222	203	7	.	.	NOUN
stem-5222	203	8	7	7	NUM
stem-5222	203	9	,	,	PUNCT
stem-5222	203	10	pp	pp	ADJ
stem-5222	203	11	.	.	PUNCT
stem-5222	204	1	466	466	NUM
stem-5222	204	2	-	-	SYM
stem-5222	204	3	472	472	NUM
stem-5222	204	4	.	.	PUNCT