id	sid	tid	token	lemma	pos
biomedich-48	1	1	biology	biology	NOUN
biomedich-48	1	2	,	,	PUNCT
biomedich-48	1	3	medicine	medicine	NOUN
biomedich-48	1	4	,	,	PUNCT
biomedich-48	1	5	&	&	CCONJ
biomedich-48	1	6	natural	natural	ADJ
biomedich-48	1	7	product	product	NOUN
biomedich-48	1	8	chemistry	chemistry	NOUN
biomedich-48	1	9	issn	issn	VERB
biomedich-48	1	10	2089	2089	NUM
biomedich-48	1	11	-	-	SYM
biomedich-48	1	12	6514	6514	NUM
biomedich-48	1	13	(	(	PUNCT
biomedich-48	1	14	paper	paper	NOUN
biomedich-48	1	15	)	)	PUNCT
biomedich-48	1	16	volume	volume	NOUN
biomedich-48	1	17	6	6	NUM
biomedich-48	1	18	,	,	PUNCT
biomedich-48	1	19	number	number	NOUN
biomedich-48	1	20	2	2	NUM
biomedich-48	1	21	,	,	PUNCT
biomedich-48	1	22	2017	2017	NUM
biomedich-48	2	1	|	|	ADV
biomedich-48	2	2	pages	page	NOUN
biomedich-48	2	3	:	:	PUNCT
biomedich-48	2	4	37	37	NUM
biomedich-48	2	5	-	-	SYM
biomedich-48	2	6	45	45	NUM
biomedich-48	2	7	|	|	ADV
biomedich-48	2	8	doi	doi	NOUN
biomedich-48	2	9	:	:	PUNCT
biomedich-48	2	10	10.14421	10.14421	NUM
biomedich-48	2	11	/	/	SYM
biomedich-48	2	12	biomedich.2017.62.37	biomedich.2017.62.37	PROPN
biomedich-48	2	13	-	-	PUNCT
biomedich-48	2	14	45	45	NUM
biomedich-48	2	15	issn	issn	PROPN
biomedich-48	2	16	2540	2540	NUM
biomedich-48	2	17	-	-	SYM
biomedich-48	2	18	9328	9328	NUM
biomedich-48	2	19	(	(	PUNCT
biomedich-48	2	20	online	online	ADV
biomedich-48	2	21	)	)	PUNCT
biomedich-48	2	22	the	the	DET
biomedich-48	2	23	female	female	ADJ
biomedich-48	2	24	population	population	NOUN
biomedich-48	2	25	growth	growth	NOUN
biomedich-48	2	26	projection	projection	NOUN
biomedich-48	2	27	year	year	NOUN
biomedich-48	2	28	2021	2021	NUM
biomedich-48	2	29	in	in	ADP
biomedich-48	2	30	trenggalek	trenggalek	NOUN
biomedich-48	2	31	regency	regency	PROPN
biomedich-48	2	32	by	by	ADP
biomedich-48	2	33	leslie	leslie	PROPN
biomedich-48	2	34	matrix	matrix	NOUN
biomedich-48	2	35	model	model	NOUN
biomedich-48	2	36	on	on	ADP
biomedich-48	2	37	the	the	DET
biomedich-48	2	38	birth	birth	NOUN
biomedich-48	2	39	rate	rate	NOUN
biomedich-48	2	40	and	and	CCONJ
biomedich-48	2	41	life	life	NOUN
biomedich-48	2	42	expectancy	expectancy	NOUN
biomedich-48	2	43	dewi	dewi	PROPN
biomedich-48	2	44	anggreini	anggreini	PROPN
biomedich-48	2	45	mathematics	mathematics	PROPN
biomedich-48	2	46	education	education	PROPN
biomedich-48	2	47	department	department	NOUN
biomedich-48	2	48	stkip	stkip	VERB
biomedich-48	2	49	pgri	pgri	NOUN
biomedich-48	2	50	tulungagung	tulungagung	PROPN
biomedich-48	2	51	,	,	PUNCT
biomedich-48	2	52	jl	jl	PROPN
biomedich-48	2	53	.	.	PROPN
biomedich-48	2	54	mayor	mayor	PROPN
biomedich-48	2	55	sujadi	sujadi	PROPN
biomedich-48	2	56	east	east	PROPN
biomedich-48	2	57	street	street	PROPN
biomedich-48	2	58	,	,	PUNCT
biomedich-48	2	59	no.7	no.7	PROPN
biomedich-48	2	60	,	,	PUNCT
biomedich-48	2	61	tulungagung	tulungagung	PROPN
biomedich-48	2	62	,	,	PUNCT
biomedich-48	2	63	66221	66221	NUM
biomedich-48	2	64	,	,	PUNCT
biomedich-48	2	65	indonesia	indonesia	PROPN
biomedich-48	2	66	author	author	NOUN
biomedich-48	2	67	correspondency	correspondency	NOUN
biomedich-48	2	68	:	:	PUNCT
biomedich-48	2	69	anggreini_004@yahoo.com	anggreini_004@yahoo.com	PROPN
biomedich-48	2	70	abstract	abstract	VERB
biomedich-48	2	71	this	this	DET
biomedich-48	2	72	research	research	NOUN
biomedich-48	2	73	aims	aim	VERB
biomedich-48	2	74	to	to	PART
biomedich-48	2	75	determine	determine	VERB
biomedich-48	2	76	the	the	DET
biomedich-48	2	77	number	number	NOUN
biomedich-48	2	78	of	of	ADP
biomedich-48	2	79	female	female	ADJ
biomedich-48	2	80	residents	resident	NOUN
biomedich-48	2	81	in	in	ADP
biomedich-48	2	82	trenggalek	trenggalek	NOUN
biomedich-48	2	83	regency	regency	PROPN
biomedich-48	2	84	in	in	ADP
biomedich-48	2	85	2021	2021	NUM
biomedich-48	2	86	based	base	VERB
biomedich-48	2	87	on	on	ADP
biomedich-48	2	88	data	datum	NOUN
biomedich-48	2	89	on	on	ADP
biomedich-48	2	90	birth	birth	NOUN
biomedich-48	2	91	rate	rate	NOUN
biomedich-48	2	92	and	and	CCONJ
biomedich-48	2	93	life	life	NOUN
biomedich-48	2	94	expectancy	expectancy	NOUN
biomedich-48	2	95	.	.	PUNCT
biomedich-48	3	1	the	the	DET
biomedich-48	3	2	use	use	NOUN
biomedich-48	3	3	of	of	ADP
biomedich-48	3	4	eigenvalues	eigenvalue	NOUN
biomedich-48	3	5	and	and	CCONJ
biomedich-48	3	6	eigenvectors	eigenvector	NOUN
biomedich-48	3	7	aims	aim	VERB
biomedich-48	3	8	to	to	PART
biomedich-48	3	9	determine	determine	VERB
biomedich-48	3	10	the	the	DET
biomedich-48	3	11	dividing	dividing	NOUN
biomedich-48	3	12	age	age	NOUN
biomedich-48	3	13	distribution	distribution	NOUN
biomedich-48	3	14	by	by	ADP
biomedich-48	3	15	leslie	leslie	PROPN
biomedich-48	3	16	matrix	matrix	NOUN
biomedich-48	3	17	model	model	NOUN
biomedich-48	3	18	.	.	PUNCT
biomedich-48	4	1	the	the	DET
biomedich-48	4	2	eigenvectors	eigenvector	NOUN
biomedich-48	4	3	are	be	AUX
biomedich-48	4	4	used	use	VERB
biomedich-48	4	5	to	to	PART
biomedich-48	4	6	determine	determine	VERB
biomedich-48	4	7	the	the	DET
biomedich-48	4	8	number	number	NOUN
biomedich-48	4	9	of	of	ADP
biomedich-48	4	10	female	female	ADJ
biomedich-48	4	11	populations	population	NOUN
biomedich-48	4	12	of	of	ADP
biomedich-48	4	13	each	each	DET
biomedich-48	4	14	age	age	NOUN
biomedich-48	4	15	interval	interval	NOUN
biomedich-48	4	16	,	,	PUNCT
biomedich-48	4	17	while	while	SCONJ
biomedich-48	4	18	the	the	DET
biomedich-48	4	19	eigenvalues	eigenvalue	NOUN
biomedich-48	4	20	are	be	AUX
biomedich-48	4	21	used	use	VERB
biomedich-48	4	22	to	to	PART
biomedich-48	4	23	determine	determine	VERB
biomedich-48	4	24	population	population	NOUN
biomedich-48	4	25	growth	growth	NOUN
biomedich-48	4	26	rates	rate	NOUN
biomedich-48	4	27	.	.	PUNCT
biomedich-48	5	1	the	the	DET
biomedich-48	5	2	research	research	NOUN
biomedich-48	5	3	method	method	NOUN
biomedich-48	5	4	used	use	VERB
biomedich-48	5	5	is	be	AUX
biomedich-48	5	6	to	to	PART
biomedich-48	5	7	determine	determine	VERB
biomedich-48	5	8	the	the	DET
biomedich-48	5	9	subject	subject	NOUN
biomedich-48	5	10	of	of	ADP
biomedich-48	5	11	research	research	NOUN
biomedich-48	5	12	.	.	PUNCT
biomedich-48	6	1	the	the	DET
biomedich-48	6	2	next	next	ADJ
biomedich-48	6	3	stage	stage	NOUN
biomedich-48	6	4	is	be	AUX
biomedich-48	6	5	to	to	PART
biomedich-48	6	6	collect	collect	VERB
biomedich-48	6	7	research	research	NOUN
biomedich-48	6	8	data	datum	NOUN
biomedich-48	6	9	,	,	PUNCT
biomedich-48	6	10	then	then	ADV
biomedich-48	6	11	analyze	analyze	VERB
biomedich-48	6	12	the	the	DET
biomedich-48	6	13	data	datum	NOUN
biomedich-48	6	14	and	and	CCONJ
biomedich-48	6	15	last	last	ADJ
biomedich-48	6	16	draw	draw	NOUN
biomedich-48	6	17	conclusions	conclusion	NOUN
biomedich-48	6	18	.	.	PUNCT
biomedich-48	7	1	the	the	DET
biomedich-48	7	2	research	research	NOUN
biomedich-48	7	3	data	datum	NOUN
biomedich-48	7	4	is	be	AUX
biomedich-48	7	5	obtained	obtain	VERB
biomedich-48	7	6	from	from	ADP
biomedich-48	7	7	bps	bps	NOUN
biomedich-48	7	8	kabupaten	kabupaten	PROPN
biomedich-48	7	9	trenggalek	trenggalek	NOUN
biomedich-48	7	10	and	and	CCONJ
biomedich-48	7	11	bps	bps	PROPN
biomedich-48	7	12	east	east	PROPN
biomedich-48	7	13	java	java	PROPN
biomedich-48	7	14	province	province	PROPN
biomedich-48	7	15	that	that	PRON
biomedich-48	7	16	is	be	AUX
biomedich-48	7	17	data	datum	NOUN
biomedich-48	7	18	of	of	ADP
biomedich-48	7	19	woman	woman	NOUN
biomedich-48	7	20	population	population	NOUN
biomedich-48	7	21	from	from	ADP
biomedich-48	7	22	year	year	NOUN
biomedich-48	7	23	2010	2010	NUM
biomedich-48	7	24	-	-	SYM
biomedich-48	7	25	2015	2015	NUM
biomedich-48	7	26	.	.	PUNCT
biomedich-48	8	1	the	the	DET
biomedich-48	8	2	result	result	NOUN
biomedich-48	8	3	of	of	ADP
biomedich-48	8	4	this	this	DET
biomedich-48	8	5	research	research	NOUN
biomedich-48	8	6	using	use	VERB
biomedich-48	8	7	leslie	leslie	PROPN
biomedich-48	8	8	matrix	matrix	NOUN
biomedich-48	8	9	model	model	NOUN
biomedich-48	8	10	for	for	ADP
biomedich-48	8	11	female	female	ADJ
biomedich-48	8	12	population	population	NOUN
biomedich-48	8	13	in	in	ADP
biomedich-48	8	14	trenggalek	trenggalek	NOUN
biomedich-48	8	15	regency	regency	PROPN
biomedich-48	8	16	that	that	PRON
biomedich-48	8	17	is	be	AUX
biomedich-48	8	18	discrete	discrete	ADJ
biomedich-48	8	19	model	model	NOUN
biomedich-48	8	20	.	.	PUNCT
biomedich-48	9	1	the	the	DET
biomedich-48	9	2	discrete	discrete	ADJ
biomedich-48	9	3	model	model	NOUN
biomedich-48	9	4	is	be	AUX
biomedich-48	9	5	divided	divide	VERB
biomedich-48	9	6	into	into	ADP
biomedich-48	9	7	fourteen	fourteen	NUM
biomedich-48	9	8	age	age	NOUN
biomedich-48	9	9	intervals	interval	NOUN
biomedich-48	9	10	constructed	construct	VERB
biomedich-48	9	11	using	use	VERB
biomedich-48	9	12	the	the	DET
biomedich-48	9	13	birthrate	birthrate	ADJ
biomedich-48	9	14	and	and	CCONJ
biomedich-48	9	15	life	life	NOUN
biomedich-48	9	16	expectancy	expectancy	NOUN
biomedich-48	9	17	.	.	PUNCT
biomedich-48	10	1	the	the	DET
biomedich-48	10	2	conclusions	conclusion	NOUN
biomedich-48	10	3	of	of	ADP
biomedich-48	10	4	the	the	DET
biomedich-48	10	5	study	study	NOUN
biomedich-48	10	6	showed	show	VERB
biomedich-48	10	7	that	that	SCONJ
biomedich-48	10	8	the	the	DET
biomedich-48	10	9	number	number	NOUN
biomedich-48	10	10	of	of	ADP
biomedich-48	10	11	female	female	ADJ
biomedich-48	10	12	population	population	NOUN
biomedich-48	10	13	in	in	ADP
biomedich-48	10	14	trenggalek	trenggalek	NOUN
biomedich-48	10	15	regency	regency	PROPN
biomedich-48	10	16	tended	tend	VERB
biomedich-48	10	17	to	to	PART
biomedich-48	10	18	increase	increase	VERB
biomedich-48	10	19	with	with	ADP
biomedich-48	10	20	positive	positive	ADJ
biomedich-48	10	21	eigen	eigen	NOUN
biomedich-48	10	22	value	value	NOUN
biomedich-48	10	23	greater	great	ADJ
biomedich-48	10	24	than	than	ADP
biomedich-48	10	25	one	one	NUM
biomedich-48	10	26	.	.	PUNCT
biomedich-48	11	1	in	in	ADP
biomedich-48	11	2	other	other	ADJ
biomedich-48	11	3	words	word	NOUN
biomedich-48	11	4	,	,	PUNCT
biomedich-48	11	5	the	the	DET
biomedich-48	11	6	growth	growth	NOUN
biomedich-48	11	7	rate	rate	NOUN
biomedich-48	11	8	of	of	ADP
biomedich-48	11	9	female	female	ADJ
biomedich-48	11	10	population	population	NOUN
biomedich-48	11	11	in	in	ADP
biomedich-48	11	12	trenggalek	trenggalek	NOUN
biomedich-48	11	13	regency	regency	PROPN
biomedich-48	11	14	tends	tend	VERB
biomedich-48	11	15	to	to	PART
biomedich-48	11	16	be	be	AUX
biomedich-48	11	17	positive	positive	ADJ
biomedich-48	11	18	.	.	PUNCT
biomedich-48	12	1	the	the	DET
biomedich-48	12	2	success	success	NOUN
biomedich-48	12	3	of	of	ADP
biomedich-48	12	4	leslie	leslie	PROPN
biomedich-48	12	5	's	's	PART
biomedich-48	12	6	matrix	matrix	NOUN
biomedich-48	12	7	model	model	NOUN
biomedich-48	12	8	is	be	AUX
biomedich-48	12	9	the	the	DET
biomedich-48	12	10	application	application	NOUN
biomedich-48	12	11	of	of	ADP
biomedich-48	12	12	case	case	NOUN
biomedich-48	12	13	studies	study	NOUN
biomedich-48	12	14	in	in	ADP
biomedich-48	12	15	predicting	predict	VERB
biomedich-48	12	16	the	the	DET
biomedich-48	12	17	number	number	NOUN
biomedich-48	12	18	of	of	ADP
biomedich-48	12	19	female	female	ADJ
biomedich-48	12	20	populations	population	NOUN
biomedich-48	12	21	in	in	ADP
biomedich-48	12	22	trenggalek	trenggalek	NOUN
biomedich-48	12	23	district	district	NOUN
biomedich-48	12	24	by	by	ADP
biomedich-48	12	25	2021	2021	NUM
biomedich-48	12	26	using	use	VERB
biomedich-48	12	27	the	the	DET
biomedich-48	12	28	maple	maple	NOUN
biomedich-48	12	29	16	16	NUM
biomedich-48	12	30	program	program	NOUN
biomedich-48	12	31	.	.	PUNCT
biomedich-48	13	1	keywords	keyword	NOUN
biomedich-48	13	2	:	:	PUNCT
biomedich-48	13	3	eigen	eigen	PROPN
biomedich-48	13	4	value	value	NOUN
biomedich-48	13	5	;	;	PUNCT
biomedich-48	13	6	eigenvector	eigenvector	PROPN
biomedich-48	13	7	;	;	PUNCT
biomedich-48	13	8	leslie	leslie	PROPN
biomedich-48	13	9	matrix	matrix	NOUN
biomedich-48	13	10	.	.	PUNCT
biomedich-48	14	1	introduction	introduction	NOUN
biomedich-48	14	2	trenggalek	trenggalek	PROPN
biomedich-48	14	3	regency	regency	PROPN
biomedich-48	14	4	is	be	AUX
biomedich-48	14	5	a	a	DET
biomedich-48	14	6	regency	regency	NOUN
biomedich-48	14	7	in	in	ADP
biomedich-48	14	8	east	east	PROPN
biomedich-48	14	9	java	java	PROPN
biomedich-48	14	10	province	province	PROPN
biomedich-48	14	11	which	which	PRON
biomedich-48	14	12	is	be	AUX
biomedich-48	14	13	located	locate	VERB
biomedich-48	14	14	in	in	ADP
biomedich-48	14	15	the	the	DET
biomedich-48	14	16	southern	southern	ADJ
biomedich-48	14	17	part	part	NOUN
biomedich-48	14	18	of	of	ADP
biomedich-48	14	19	the	the	DET
biomedich-48	14	20	province	province	NOUN
biomedich-48	14	21	of	of	ADP
biomedich-48	14	22	east	east	PROPN
biomedich-48	14	23	java	java	PROPN
biomedich-48	14	24	with	with	ADP
biomedich-48	14	25	an	an	DET
biomedich-48	14	26	area	area	NOUN
biomedich-48	14	27	of	of	ADP
biomedich-48	14	28	1,261.40	1,261.40	NUM
biomedich-48	14	29	km²	km²	NOUN
biomedich-48	14	30	.	.	PUNCT
biomedich-48	15	1	trenggalek	trenggalek	PROPN
biomedich-48	15	2	regency	regency	PROPN
biomedich-48	15	3	largely	largely	ADV
biomedich-48	15	4	made	make	VERB
biomedich-48	15	5	up	up	ADP
biomedich-48	15	6	of	of	ADP
biomedich-48	15	7	mountainous	mountainous	ADJ
biomedich-48	15	8	land	land	NOUN
biomedich-48	15	9	with	with	ADP
biomedich-48	15	10	an	an	DET
biomedich-48	15	11	area	area	NOUN
biomedich-48	15	12	of	of	ADP
biomedich-48	15	13	2/3	2/3	NUM
biomedich-48	15	14	covers	cover	VERB
biomedich-48	15	15	part	part	NOUN
biomedich-48	15	16	of	of	ADP
biomedich-48	15	17	the	the	DET
biomedich-48	15	18	area	area	NOUN
biomedich-48	15	19	.	.	PUNCT
biomedich-48	16	1	while	while	SCONJ
biomedich-48	16	2	the	the	DET
biomedich-48	16	3	rest	rest	NOUN
biomedich-48	16	4	of	of	ADP
biomedich-48	16	5	his	his	PRON
biomedich-48	16	6	(	(	PUNCT
biomedich-48	16	7	1/3	1/3	NUM
biomedich-48	16	8	part	part	NOUN
biomedich-48	16	9	)	)	PUNCT
biomedich-48	16	10	is	be	AUX
biomedich-48	16	11	the	the	DET
biomedich-48	16	12	land	land	NOUN
biomedich-48	16	13	of	of	ADP
biomedich-48	16	14	the	the	DET
biomedich-48	16	15	lowlands	lowland	NOUN
biomedich-48	16	16	.	.	PUNCT
biomedich-48	17	1	trenggalek	trenggalek	PROPN
biomedich-48	17	2	regency	regency	PROPN
biomedich-48	17	3	is	be	AUX
biomedich-48	17	4	subdivided	subdivide	VERB
biomedich-48	17	5	into	into	ADP
biomedich-48	17	6	14	14	NUM
biomedich-48	17	7	subdistricts	subdistrict	NOUN
biomedich-48	17	8	da	da	NOUN
biomedich-48	17	9	157	157	NUM
biomedich-48	17	10	villages	village	NOUN
biomedich-48	17	11	.	.	PUNCT
biomedich-48	18	1	only	only	ADV
biomedich-48	18	2	about	about	ADV
biomedich-48	18	3	4	4	NUM
biomedich-48	18	4	subdistricts	subdistrict	NOUN
biomedich-48	18	5	which	which	PRON
biomedich-48	18	6	are	be	AUX
biomedich-48	18	7	the	the	DET
biomedich-48	18	8	majority	majority	NOUN
biomedich-48	18	9	of	of	ADP
biomedich-48	18	10	the	the	DET
biomedich-48	18	11	village	village	NOUN
biomedich-48	18	12	of	of	ADP
biomedich-48	18	13	plains	plain	NOUN
biomedich-48	18	14	,	,	PUNCT
biomedich-48	18	15	which	which	PRON
biomedich-48	18	16	are	be	AUX
biomedich-48	18	17	:	:	PUNCT
biomedich-48	18	18	pogalan	pogalan	NOUN
biomedich-48	18	19	,	,	PUNCT
biomedich-48	18	20	trenggalek	trenggalek	NOUN
biomedich-48	18	21	subdistrict	subdistrict	PROPN
biomedich-48	18	22	,	,	PUNCT
biomedich-48	18	23	district	district	NOUN
biomedich-48	18	24	and	and	CCONJ
biomedich-48	18	25	sub	sub	ADJ
biomedich-48	18	26	-	-	ADJ
biomedich-48	18	27	district	district	ADJ
biomedich-48	18	28	durenan	durenan	PROPN
biomedich-48	18	29	monument	monument	PROPN
biomedich-48	18	30	.	.	PUNCT
biomedich-48	19	1	while	while	SCONJ
biomedich-48	19	2	the	the	DET
biomedich-48	19	3	majority	majority	NOUN
biomedich-48	19	4	of	of	ADP
biomedich-48	19	5	other	other	ADJ
biomedich-48	19	6	sub	sub	NOUN
biomedich-48	19	7	10	10	NUM
biomedich-48	19	8	village	village	NOUN
biomedich-48	19	9	mountains	mountain	NOUN
biomedich-48	19	10	.	.	PUNCT
biomedich-48	20	1	a	a	DET
biomedich-48	20	2	large	large	ADJ
biomedich-48	20	3	number	number	NOUN
biomedich-48	20	4	of	of	ADP
biomedich-48	20	5	trenggalek	trenggalek	NOUN
biomedich-48	20	6	regency	regency	PROPN
biomedich-48	20	7	year	year	NOUN
biomedich-48	20	8	2015	2015	NUM
biomedich-48	20	9	as	as	ADV
biomedich-48	20	10	much	much	ADV
biomedich-48	20	11	689,200	689,200	NUM
biomedich-48	20	12	inhabitants	inhabitant	NOUN
biomedich-48	20	13	.	.	PUNCT
biomedich-48	21	1	number	number	NOUN
biomedich-48	21	2	of	of	ADP
biomedich-48	21	3	changes	change	NOUN
biomedich-48	21	4	in	in	ADP
biomedich-48	21	5	the	the	DET
biomedich-48	21	6	populations	population	NOUN
biomedich-48	21	7	affected	affect	VERB
biomedich-48	21	8	by	by	ADP
biomedich-48	21	9	the	the	DET
biomedich-48	21	10	internal	internal	ADJ
biomedich-48	21	11	state	state	NOUN
biomedich-48	21	12	of	of	ADP
biomedich-48	21	13	the	the	DET
biomedich-48	21	14	population	population	NOUN
biomedich-48	21	15	is	be	AUX
biomedich-48	21	16	birth	birth	NOUN
biomedich-48	21	17	,	,	PUNCT
biomedich-48	21	18	death	death	NOUN
biomedich-48	21	19	,	,	PUNCT
biomedich-48	21	20	and	and	CCONJ
biomedich-48	21	21	survival	survival	NOUN
biomedich-48	21	22	.	.	PUNCT
biomedich-48	22	1	the	the	DET
biomedich-48	22	2	existence	existence	NOUN
biomedich-48	22	3	of	of	ADP
biomedich-48	22	4	a	a	DET
biomedich-48	22	5	number	number	NOUN
biomedich-48	22	6	of	of	ADP
biomedich-48	22	7	changes	change	NOUN
biomedich-48	22	8	of	of	ADP
biomedich-48	22	9	a	a	DET
biomedich-48	22	10	population	population	NOUN
biomedich-48	22	11	called	call	VERB
biomedich-48	22	12	the	the	DET
biomedich-48	22	13	growth	growth	NOUN
biomedich-48	22	14	of	of	ADP
biomedich-48	22	15	population	population	NOUN
biomedich-48	22	16	.	.	PUNCT
biomedich-48	23	1	population	population	NOUN
biomedich-48	23	2	growth	growth	NOUN
biomedich-48	23	3	can	can	AUX
biomedich-48	23	4	provide	provide	VERB
biomedich-48	23	5	information	information	NOUN
biomedich-48	23	6	as	as	ADP
biomedich-48	23	7	to	to	ADP
biomedich-48	23	8	whether	whether	SCONJ
biomedich-48	23	9	changes	change	NOUN
biomedich-48	23	10	in	in	ADP
biomedich-48	23	11	population	population	NOUN
biomedich-48	23	12	numbers	number	NOUN
biomedich-48	23	13	for	for	ADP
biomedich-48	23	14	next	next	ADJ
biomedich-48	23	15	year	year	NOUN
biomedich-48	23	16	is	be	AUX
biomedich-48	23	17	always	always	ADV
biomedich-48	23	18	increasing	increase	VERB
biomedich-48	23	19	,	,	PUNCT
biomedich-48	23	20	decreasing	decrease	VERB
biomedich-48	23	21	or	or	CCONJ
biomedich-48	23	22	constant	constant	ADJ
biomedich-48	23	23	.	.	PUNCT
biomedich-48	24	1	(	(	PUNCT
biomedich-48	24	2	pratama	pratama	NOUN
biomedich-48	24	3	,	,	PUNCT
biomedich-48	24	4	prihandono	prihandono	NOUN
biomedich-48	24	5	and	and	CCONJ
biomedich-48	24	6	kusumastuti	kusumastuti	PROPN
biomedich-48	24	7	,	,	PUNCT
biomedich-48	24	8	2013	2013	NUM
biomedich-48	24	9	,	,	PUNCT
biomedich-48	24	10	p.	p.	NOUN
biomedich-48	24	11	163	163	NUM
biomedich-48	24	12	)	)	PUNCT
biomedich-48	24	13	.	.	PUNCT
biomedich-48	25	1	population	population	NOUN
biomedich-48	25	2	projection	projection	NOUN
biomedich-48	25	3	is	be	AUX
biomedich-48	25	4	not	not	PART
biomedich-48	25	5	a	a	DET
biomedich-48	25	6	forecast	forecast	NOUN
biomedich-48	25	7	but	but	CCONJ
biomedich-48	25	8	a	a	DET
biomedich-48	25	9	population	population	NOUN
biomedich-48	25	10	of	of	ADP
biomedich-48	25	11	scientific	scientific	ADJ
biomedich-48	25	12	calculations	calculation	NOUN
biomedich-48	25	13	based	base	VERB
biomedich-48	25	14	on	on	ADP
biomedich-48	25	15	the	the	DET
biomedich-48	25	16	assumption	assumption	NOUN
biomedich-48	25	17	of	of	ADP
biomedich-48	25	18	the	the	DET
biomedich-48	25	19	components	component	NOUN
biomedich-48	25	20	of	of	ADP
biomedich-48	25	21	population	population	NOUN
biomedich-48	25	22	growth	growth	NOUN
biomedich-48	25	23	rate	rate	NOUN
biomedich-48	25	24	,	,	PUNCT
biomedich-48	25	25	i.e.	i.e.	X
biomedich-48	25	26	,	,	PUNCT
biomedich-48	25	27	birth	birth	NOUN
biomedich-48	25	28	,	,	PUNCT
biomedich-48	25	29	death	death	NOUN
biomedich-48	25	30	,	,	PUNCT
biomedich-48	25	31	and	and	CCONJ
biomedich-48	25	32	displacement	displacement	NOUN
biomedich-48	25	33	.	.	PUNCT
biomedich-48	26	1	the	the	DET
biomedich-48	26	2	third	third	ADJ
biomedich-48	26	3	component	component	NOUN
biomedich-48	26	4	is	be	AUX
biomedich-48	26	5	what	what	PRON
biomedich-48	26	6	determines	determine	VERB
biomedich-48	26	7	the	the	DET
biomedich-48	26	8	magnitude	magnitude	NOUN
biomedich-48	26	9	of	of	ADP
biomedich-48	26	10	the	the	DET
biomedich-48	26	11	age	age	NOUN
biomedich-48	26	12	structure	structure	NOUN
biomedich-48	26	13	of	of	ADP
biomedich-48	26	14	the	the	DET
biomedich-48	26	15	population	population	NOUN
biomedich-48	26	16	and	and	CCONJ
biomedich-48	26	17	the	the	DET
biomedich-48	26	18	population	population	NOUN
biomedich-48	26	19	in	in	ADP
biomedich-48	26	20	the	the	DET
biomedich-48	26	21	future	future	NOUN
biomedich-48	26	22	.	.	PUNCT
biomedich-48	27	1	to	to	PART
biomedich-48	27	2	determine	determine	VERB
biomedich-48	27	3	each	each	DET
biomedich-48	27	4	assumption	assumption	NOUN
biomedich-48	27	5	needed	need	VERB
biomedich-48	27	6	data	datum	NOUN
biomedich-48	27	7	that	that	PRON
biomedich-48	27	8	illustrates	illustrate	VERB
biomedich-48	27	9	the	the	DET
biomedich-48	27	10	trend	trend	NOUN
biomedich-48	27	11	in	in	ADP
biomedich-48	27	12	the	the	DET
biomedich-48	27	13	past	past	NOUN
biomedich-48	27	14	to	to	ADP
biomedich-48	27	15	the	the	DET
biomedich-48	27	16	present	present	NOUN
biomedich-48	27	17	,	,	PUNCT
biomedich-48	27	18	factors	factor	NOUN
biomedich-48	27	19	that	that	PRON
biomedich-48	27	20	affect	affect	VERB
biomedich-48	27	21	the	the	DET
biomedich-48	27	22	relationship	relationship	NOUN
biomedich-48	27	23	between	between	ADP
biomedich-48	27	24	a	a	DET
biomedich-48	27	25	component	component	NOUN
biomedich-48	27	26	and	and	CCONJ
biomedich-48	27	27	a	a	DET
biomedich-48	27	28	component	component	NOUN
biomedich-48	27	29	with	with	ADP
biomedich-48	27	30	another	another	PRON
biomedich-48	27	31	as	as	ADV
biomedich-48	27	32	well	well	ADV
biomedich-48	27	33	as	as	ADP
biomedich-48	27	34	the	the	DET
biomedich-48	27	35	expected	expect	VERB
biomedich-48	27	36	target	target	NOUN
biomedich-48	27	37	is	be	AUX
biomedich-48	27	38	reached	reach	VERB
biomedich-48	27	39	on	on	ADP
biomedich-48	27	40	the	the	DET
biomedich-48	27	41	future	future	NOUN
biomedich-48	27	42	come	come	NOUN
biomedich-48	27	43	.	.	PUNCT
biomedich-48	28	1	science	science	NOUN
biomedich-48	28	2	many	many	ADJ
biomedich-48	28	3	rapidly	rapidly	ADV
biomedich-48	28	4	developing	develop	VERB
biomedich-48	28	5	lately	lately	ADV
biomedich-48	28	6	,	,	PUNCT
biomedich-48	28	7	including	include	VERB
biomedich-48	28	8	mathematical	mathematical	ADJ
biomedich-48	28	9	modeling	modeling	NOUN
biomedich-48	28	10	.	.	PUNCT
biomedich-48	29	1	according	accord	VERB
biomedich-48	29	2	to	to	ADP
biomedich-48	29	3	iswanto	iswanto	NOUN
biomedich-48	29	4	(	(	PUNCT
biomedich-48	29	5	2012	2012	NUM
biomedich-48	29	6	,	,	PUNCT
biomedich-48	29	7	p.	p.	NOUN
biomedich-48	29	8	19	19	NUM
biomedich-48	29	9	)	)	PUNCT
biomedich-48	29	10	in	in	ADP
biomedich-48	29	11	its	its	PRON
biomedich-48	29	12	development	development	NOUN
biomedich-48	29	13	of	of	ADP
biomedich-48	29	14	mathematical	mathematical	ADJ
biomedich-48	29	15	models	model	NOUN
biomedich-48	29	16	can	can	AUX
biomedich-48	29	17	be	be	AUX
biomedich-48	29	18	represented	represent	VERB
biomedich-48	29	19	on	on	ADP
biomedich-48	29	20	the	the	DET
biomedich-48	29	21	problems	problem	NOUN
biomedich-48	29	22	that	that	PRON
biomedich-48	29	23	occur	occur	VERB
biomedich-48	29	24	in	in	ADP
biomedich-48	29	25	everyday	everyday	ADJ
biomedich-48	29	26	life	life	NOUN
biomedich-48	29	27	.	.	PUNCT
biomedich-48	30	1	so	so	ADV
biomedich-48	30	2	there	there	PRON
biomedich-48	30	3	is	be	VERB
biomedich-48	30	4	a	a	DET
biomedich-48	30	5	strong	strong	ADJ
biomedich-48	30	6	relationship	relationship	NOUN
biomedich-48	30	7	between	between	ADP
biomedich-48	30	8	applied	apply	VERB
biomedich-48	30	9	science	science	NOUN
biomedich-48	30	10	and	and	CCONJ
biomedich-48	30	11	mathematics	mathematic	NOUN
biomedich-48	30	12	are	be	AUX
biomedich-48	30	13	represented	represent	VERB
biomedich-48	30	14	by	by	ADP
biomedich-48	30	15	mathematical	mathematical	ADJ
biomedich-48	30	16	models	model	NOUN
biomedich-48	30	17	that	that	PRON
biomedich-48	30	18	are	be	AUX
biomedich-48	30	19	designed	design	VERB
biomedich-48	30	20	and	and	CCONJ
biomedich-48	30	21	implemented	implement	VERB
biomedich-48	30	22	with	with	ADP
biomedich-48	30	23	the	the	DET
biomedich-48	30	24	help	help	NOUN
biomedich-48	30	25	of	of	ADP
biomedich-48	30	26	computer	computer	NOUN
biomedich-48	30	27	science	science	NOUN
biomedich-48	30	28	,	,	PUNCT
biomedich-48	30	29	to	to	PART
biomedich-48	30	30	facilitate	facilitate	VERB
biomedich-48	30	31	the	the	DET
biomedich-48	30	32	simulation	simulation	NOUN
biomedich-48	30	33	of	of	ADP
biomedich-48	30	34	realworld	realworld	PROPN
biomedich-48	30	35	systems	systems	PROPN
biomedich-48	30	36	.	.	PUNCT
biomedich-48	31	1	population	population	NOUN
biomedich-48	31	2	growth	growth	NOUN
biomedich-48	31	3	is	be	AUX
biomedich-48	31	4	one	one	NUM
biomedich-48	31	5	of	of	ADP
biomedich-48	31	6	the	the	DET
biomedich-48	31	7	examples	example	NOUN
biomedich-48	31	8	of	of	ADP
biomedich-48	31	9	the	the	DET
biomedich-48	31	10	application	application	NOUN
biomedich-48	31	11	of	of	ADP
biomedich-48	31	12	the	the	DET
biomedich-48	31	13	linear	linear	ADJ
biomedich-48	31	14	algebra	algebra	NOUN
biomedich-48	31	15	in	in	ADP
biomedich-48	31	16	field	field	NOUN
biomedich-48	31	17	biology	biology	NOUN
biomedich-48	31	18	and	and	CCONJ
biomedich-48	31	19	ecology	ecology	NOUN
biomedich-48	31	20	specifically	specifically	ADV
biomedich-48	31	21	quantitatively	quantitatively	ADV
biomedich-48	31	22	.	.	PUNCT
biomedich-48	32	1	population	population	NOUN
biomedich-48	32	2	growth	growth	NOUN
biomedich-48	32	3	in	in	ADP
biomedich-48	32	4	ecology	ecology	NOUN
biomedich-48	32	5	is	be	AUX
biomedich-48	32	6	often	often	ADV
biomedich-48	32	7	referred	refer	VERB
biomedich-48	32	8	to	to	ADP
biomedich-48	32	9	as	as	ADP
biomedich-48	32	10	the	the	DET
biomedich-48	32	11	"	"	PUNCT
biomedich-48	32	12	population	population	NOUN
biomedich-48	32	13	dynamics	dynamic	NOUN
biomedich-48	32	14	"	"	PUNCT
biomedich-48	32	15	.	.	PUNCT
biomedich-48	33	1	ecology	ecology	NOUN
biomedich-48	33	2	is	be	AUX
biomedich-48	33	3	usually	usually	ADV
biomedich-48	33	4	defined	define	VERB
biomedich-48	33	5	as	as	ADP
biomedich-48	33	6	the	the	DET
biomedich-48	33	7	relationship	relationship	NOUN
biomedich-48	33	8	between	between	ADP
biomedich-48	33	9	living	live	VERB
biomedich-48	33	10	beings	being	NOUN
biomedich-48	33	11	with	with	ADP
biomedich-48	33	12	their	their	PRON
biomedich-48	33	13	environment	environment	NOUN
biomedich-48	33	14	(	(	PUNCT
biomedich-48	33	15	tarumingkeng	tarumingkeng	X
biomedich-48	33	16	,	,	PUNCT
biomedich-48	33	17	1994	1994	NUM
biomedich-48	33	18	,	,	PUNCT
biomedich-48	33	19	p.	p.	NOUN
biomedich-48	33	20	6	6	NUM
biomedich-48	33	21	)	)	PUNCT
biomedich-48	33	22	.	.	PUNCT
biomedich-48	34	1	many	many	ADJ
biomedich-48	34	2	models	model	NOUN
biomedich-48	34	3	that	that	PRON
biomedich-48	34	4	can	can	AUX
biomedich-48	34	5	be	be	AUX
biomedich-48	34	6	used	use	VERB
biomedich-48	34	7	to	to	PART
biomedich-48	34	8	explain	explain	VERB
biomedich-48	34	9	the	the	DET
biomedich-48	34	10	growth	growth	NOUN
biomedich-48	34	11	of	of	ADP
biomedich-48	34	12	the	the	DET
biomedich-48	34	13	population	population	NOUN
biomedich-48	34	14	.	.	PUNCT
biomedich-48	35	1	one	one	NUM
biomedich-48	35	2	of	of	ADP
biomedich-48	35	3	the	the	DET
biomedich-48	35	4	models	model	NOUN
biomedich-48	35	5	used	use	VERB
biomedich-48	35	6	by	by	ADP
biomedich-48	35	7	demographers	demographer	NOUN
biomedich-48	35	8	is	be	AUX
biomedich-48	35	9	the	the	DET
biomedich-48	35	10	model	model	NOUN
biomedich-48	35	11	leslie	leslie	PROPN
biomedich-48	35	12	.	.	PUNCT
biomedich-48	36	1	where	where	SCONJ
biomedich-48	36	2	the	the	DET
biomedich-48	36	3	model	model	NOUN
biomedich-48	36	4	using	use	VERB
biomedich-48	36	5	a	a	DET
biomedich-48	36	6	mathematical	mathematical	ADJ
biomedich-48	36	7	approach	approach	NOUN
biomedich-48	36	8	,	,	PUNCT
biomedich-48	36	9	i.e.	i.e.	X
biomedich-48	36	10	the	the	DET
biomedich-48	36	11	matrix	matrix	NOUN
biomedich-48	36	12	.	.	PUNCT
biomedich-48	37	1	in	in	ADP
biomedich-48	37	2	the	the	DET
biomedich-48	37	3	model	model	NOUN
biomedich-48	37	4	leslie	leslie	PROPN
biomedich-48	37	5	that	that	DET
biomedich-48	37	6	birth	birth	NOUN
biomedich-48	37	7	and	and	CCONJ
biomedich-48	37	8	death	death	NOUN
biomedich-48	37	9	processes	process	NOUN
biomedich-48	37	10	depending	depend	VERB
biomedich-48	37	11	on	on	ADP
biomedich-48	37	12	the	the	DET
biomedich-48	37	13	age	age	NOUN
biomedich-48	37	14	and	and	CCONJ
biomedich-48	37	15	become	become	VERB
biomedich-48	37	16	an	an	DET
biomedich-48	37	17	important	important	ADJ
biomedich-48	37	18	part	part	NOUN
biomedich-48	37	19	in	in	ADP
biomedich-48	37	20	the	the	DET
biomedich-48	37	21	growth	growth	NOUN
biomedich-48	37	22	of	of	ADP
biomedich-48	37	23	the	the	DET
biomedich-48	37	24	population	population	NOUN
biomedich-48	37	25	.	.	PUNCT
biomedich-48	38	1	in	in	ADP
biomedich-48	38	2	general	general	ADJ
biomedich-48	38	3	,	,	PUNCT
biomedich-48	38	4	the	the	DET
biomedich-48	38	5	growth	growth	NOUN
biomedich-48	38	6	of	of	ADP
biomedich-48	38	7	a	a	DET
biomedich-48	38	8	living	live	VERB
biomedich-48	38	9	http://dx.doi.org/10.14421/biomedich.2017.62.37-45	http://dx.doi.org/10.14421/biomedich.2017.62.37-45	NOUN
biomedich-48	38	10	38	38	NUM
biomedich-48	38	11	biology	biology	NOUN
biomedich-48	38	12	,	,	PUNCT
biomedich-48	38	13	medicine	medicine	NOUN
biomedich-48	38	14	,	,	PUNCT
biomedich-48	38	15	&	&	CCONJ
biomedich-48	38	16	natural	natural	ADJ
biomedich-48	38	17	product	product	NOUN
biomedich-48	38	18	chemistry	chemistry	NOUN
biomedich-48	38	19	6	6	NUM
biomedich-48	38	20	(	(	PUNCT
biomedich-48	38	21	2	2	NUM
biomedich-48	38	22	)	)	PUNCT
biomedich-48	38	23	,	,	PUNCT
biomedich-48	38	24	2017	2017	NUM
biomedich-48	38	25	:	:	PUNCT
biomedich-48	38	26	37	37	NUM
biomedich-48	38	27	-	-	SYM
biomedich-48	38	28	45	45	NUM
biomedich-48	38	29	creature	creature	NOUN
biomedich-48	38	30	is	be	AUX
biomedich-48	38	31	a	a	DET
biomedich-48	38	32	process	process	NOUN
biomedich-48	38	33	of	of	ADP
biomedich-48	38	34	continuous	continuous	ADJ
biomedich-48	38	35	or	or	CCONJ
biomedich-48	38	36	ongoing	ongoing	ADJ
biomedich-48	38	37	process	process	NOUN
biomedich-48	38	38	taking	take	VERB
biomedich-48	38	39	place	place	NOUN
biomedich-48	38	40	.	.	PUNCT
biomedich-48	39	1	however	however	ADV
biomedich-48	39	2	,	,	PUNCT
biomedich-48	39	3	the	the	DET
biomedich-48	39	4	study	study	NOUN
biomedich-48	39	5	population	population	NOUN
biomedich-48	39	6	should	should	AUX
biomedich-48	39	7	be	be	AUX
biomedich-48	39	8	also	also	ADV
biomedich-48	39	9	approached	approach	VERB
biomedich-48	39	10	from	from	ADP
biomedich-48	39	11	a	a	DET
biomedich-48	39	12	discrete	discrete	ADJ
biomedich-48	39	13	time	time	NOUN
biomedich-48	39	14	review	review	NOUN
biomedich-48	39	15	.	.	PUNCT
biomedich-48	40	1	the	the	DET
biomedich-48	40	2	use	use	NOUN
biomedich-48	40	3	of	of	ADP
biomedich-48	40	4	discrete	discrete	ADJ
biomedich-48	40	5	pattern	pattern	NOUN
biomedich-48	40	6	based	base	VERB
biomedich-48	40	7	also	also	ADV
biomedich-48	40	8	upon	upon	SCONJ
biomedich-48	40	9	the	the	DET
biomedich-48	40	10	observations	observation	NOUN
biomedich-48	40	11	of	of	ADP
biomedich-48	40	12	the	the	DET
biomedich-48	40	13	population	population	NOUN
biomedich-48	40	14	that	that	PRON
biomedich-48	40	15	is	be	AUX
biomedich-48	40	16	generally	generally	ADV
biomedich-48	40	17	done	do	VERB
biomedich-48	40	18	interval	interval	NOUN
biomedich-48	40	19	-	-	PUNCT
biomedich-48	40	20	the	the	DET
biomedich-48	40	21	interval	interval	NOUN
biomedich-48	40	22	period	period	NOUN
biomedich-48	40	23	such	such	ADJ
biomedich-48	40	24	as	as	ADP
biomedich-48	40	25	a	a	DET
biomedich-48	40	26	day	day	NOUN
biomedich-48	40	27	,	,	PUNCT
biomedich-48	40	28	a	a	DET
biomedich-48	40	29	week	week	NOUN
biomedich-48	40	30	,	,	PUNCT
biomedich-48	40	31	and	and	CCONJ
biomedich-48	40	32	the	the	DET
biomedich-48	40	33	units	unit	NOUN
biomedich-48	40	34	of	of	ADP
biomedich-48	40	35	time	time	NOUN
biomedich-48	40	36	according	accord	VERB
biomedich-48	40	37	to	to	ADP
biomedich-48	40	38	a	a	DET
biomedich-48	40	39	draft	draft	NOUN
biomedich-48	40	40	of	of	ADP
biomedich-48	40	41	the	the	DET
biomedich-48	40	42	researchers	researcher	NOUN
biomedich-48	40	43	concerned	concern	VERB
biomedich-48	40	44	.	.	PUNCT
biomedich-48	41	1	based	base	VERB
biomedich-48	41	2	on	on	ADP
biomedich-48	41	3	these	these	DET
biomedich-48	41	4	considerations	consideration	NOUN
biomedich-48	41	5	,	,	PUNCT
biomedich-48	41	6	in	in	ADP
biomedich-48	41	7	addition	addition	NOUN
biomedich-48	41	8	to	to	ADP
biomedich-48	41	9	growth	growth	NOUN
biomedich-48	41	10	models	model	NOUN
biomedich-48	41	11	based	base	VERB
biomedich-48	41	12	on	on	ADP
biomedich-48	41	13	the	the	DET
biomedich-48	41	14	continuous	continuous	ADJ
biomedich-48	41	15	solutions	solution	NOUN
biomedich-48	41	16	need	need	VERB
biomedich-48	41	17	to	to	PART
biomedich-48	41	18	be	be	AUX
biomedich-48	41	19	evaluated	evaluate	VERB
biomedich-48	41	20	more	more	ADV
biomedich-48	41	21	thoroughly	thoroughly	ADV
biomedich-48	41	22	with	with	ADP
biomedich-48	41	23	the	the	DET
biomedich-48	41	24	solution	solution	NOUN
biomedich-48	41	25	of	of	ADP
biomedich-48	41	26	the	the	DET
biomedich-48	41	27	discrete	discrete	ADJ
biomedich-48	41	28	basis	basis	NOUN
biomedich-48	41	29	.	.	PUNCT
biomedich-48	42	1	(	(	PUNCT
biomedich-48	42	2	tarumingkeng	tarumingkeng	X
biomedich-48	42	3	,	,	PUNCT
biomedich-48	42	4	1994	1994	NUM
biomedich-48	42	5	,	,	PUNCT
biomedich-48	42	6	p.	p.	NOUN
biomedich-48	42	7	27	27	NUM
biomedich-48	42	8	)	)	PUNCT
biomedich-48	42	9	.	.	PUNCT
biomedich-48	43	1	in	in	ADP
biomedich-48	43	2	addition	addition	NOUN
biomedich-48	43	3	,	,	PUNCT
biomedich-48	43	4	the	the	DET
biomedich-48	43	5	existence	existence	NOUN
biomedich-48	43	6	of	of	ADP
biomedich-48	43	7	significant	significant	ADJ
biomedich-48	43	8	size	size	NOUN
biomedich-48	43	9	have	have	VERB
biomedich-48	43	10	yet	yet	ADV
biomedich-48	43	11	to	to	PART
biomedich-48	43	12	know	know	VERB
biomedich-48	43	13	the	the	DET
biomedich-48	43	14	growth	growth	NOUN
biomedich-48	43	15	of	of	ADP
biomedich-48	43	16	female	female	ADJ
biomedich-48	43	17	population	population	NOUN
biomedich-48	43	18	in	in	ADP
biomedich-48	43	19	trenggalek	trenggalek	NOUN
biomedich-48	43	20	based	base	VERB
biomedich-48	43	21	on	on	ADP
biomedich-48	43	22	birth	birth	NOUN
biomedich-48	43	23	rate	rate	NOUN
biomedich-48	43	24	and	and	CCONJ
biomedich-48	43	25	life	life	NOUN
biomedich-48	43	26	expectancy	expectancy	NOUN
biomedich-48	43	27	for	for	ADP
biomedich-48	43	28	the	the	DET
biomedich-48	43	29	coming	come	VERB
biomedich-48	43	30	year	year	NOUN
biomedich-48	43	31	as	as	ADV
biomedich-48	43	32	well	well	ADV
biomedich-48	43	33	as	as	ADP
biomedich-48	43	34	the	the	DET
biomedich-48	43	35	limiting	limit	VERB
biomedich-48	43	36	distribution	distribution	NOUN
biomedich-48	43	37	of	of	ADP
biomedich-48	43	38	unknown	unknown	ADJ
biomedich-48	43	39	age	age	NOUN
biomedich-48	43	40	by	by	ADP
biomedich-48	43	41	using	use	VERB
biomedich-48	43	42	model	model	NOUN
biomedich-48	43	43	the	the	DET
biomedich-48	43	44	leslie	leslie	PROPN
biomedich-48	43	45	matrix	matrix	NOUN
biomedich-48	43	46	.	.	PUNCT
biomedich-48	44	1	there	there	PRON
biomedich-48	44	2	is	be	VERB
biomedich-48	44	3	some	some	DET
biomedich-48	44	4	research	research	NOUN
biomedich-48	44	5	on	on	ADP
biomedich-48	44	6	matrix	matrix	NOUN
biomedich-48	44	7	leslie	leslie	PROPN
biomedich-48	44	8	i.e.	i.e.	X
biomedich-48	44	9	research	research	PROPN
biomedich-48	44	10	corazon	corazon	PROPN
biomedich-48	44	11	,	,	PUNCT
biomedich-48	44	12	nurul	nurul	NOUN
biomedich-48	44	13	,	,	PUNCT
biomedich-48	44	14	h.	h.	PROPN
biomedich-48	44	15	and	and	CCONJ
biomedich-48	44	16	yusienta	yusienta	NOUN
biomedich-48	44	17	,	,	PUNCT
biomedich-48	44	18	m.	m.	NOUN
biomedich-48	44	19	,	,	PUNCT
biomedich-48	44	20	(	(	PUNCT
biomedich-48	44	21	2016	2016	NUM
biomedich-48	44	22	,	,	PUNCT
biomedich-48	44	23	p.	p.	NOUN
biomedich-48	44	24	6	6	NUM
biomedich-48	44	25	)	)	PUNCT
biomedich-48	44	26	which	which	PRON
biomedich-48	44	27	uses	use	VERB
biomedich-48	44	28	a	a	DET
biomedich-48	44	29	matrix	matrix	NOUN
biomedich-48	44	30	of	of	ADP
biomedich-48	44	31	leslie	leslie	PROPN
biomedich-48	44	32	to	to	PART
biomedich-48	44	33	predict	predict	VERB
biomedich-48	44	34	the	the	DET
biomedich-48	44	35	number	number	NOUN
biomedich-48	44	36	and	and	CCONJ
biomedich-48	44	37	pace	pace	NOUN
biomedich-48	44	38	of	of	ADP
biomedich-48	44	39	growth	growth	NOUN
biomedich-48	44	40	in	in	ADP
biomedich-48	44	41	the	the	DET
biomedich-48	44	42	province	province	NOUN
biomedich-48	44	43	of	of	ADP
biomedich-48	44	44	riau	riau	NOUN
biomedich-48	44	45	in	in	ADP
biomedich-48	44	46	the	the	DET
biomedich-48	44	47	year	year	NOUN
biomedich-48	44	48	2017	2017	NUM
biomedich-48	44	49	.	.	PUNCT
biomedich-48	45	1	so	so	ADV
biomedich-48	45	2	the	the	DET
biomedich-48	45	3	obtained	obtain	VERB
biomedich-48	45	4	results	result	NOUN
biomedich-48	45	5	of	of	ADP
biomedich-48	45	6	the	the	DET
biomedich-48	45	7	total	total	ADJ
biomedich-48	45	8	population	population	NOUN
biomedich-48	45	9	of	of	ADP
biomedich-48	45	10	women	woman	NOUN
biomedich-48	45	11	in	in	ADP
biomedich-48	45	12	riau	riau	PROPN
biomedich-48	45	13	province	province	PROPN
biomedich-48	45	14	tend	tend	VERB
biomedich-48	45	15	to	to	PART
biomedich-48	45	16	experience	experience	VERB
biomedich-48	45	17	increased	increase	VERB
biomedich-48	45	18	.	.	PUNCT
biomedich-48	46	1	in	in	ADP
biomedich-48	46	2	addition	addition	NOUN
biomedich-48	46	3	the	the	DET
biomedich-48	46	4	results	result	NOUN
biomedich-48	46	5	of	of	ADP
biomedich-48	46	6	research	research	NOUN
biomedich-48	46	7	conducted	conduct	VERB
biomedich-48	46	8	by	by	ADP
biomedich-48	46	9	pratama	pratama	NOUN
biomedich-48	46	10	,	,	PUNCT
biomedich-48	46	11	prihandon	prihandon	PROPN
biomedich-48	46	12	.	.	PUNCT
biomedich-48	47	1	from	from	ADP
biomedich-48	47	2	the	the	DET
biomedich-48	47	3	description	description	NOUN
biomedich-48	47	4	it	it	PRON
biomedich-48	47	5	is	be	AUX
biomedich-48	47	6	necessary	necessary	ADJ
biomedich-48	47	7	to	to	PART
biomedich-48	47	8	determine	determine	VERB
biomedich-48	47	9	the	the	DET
biomedich-48	47	10	abundance	abundance	NOUN
biomedich-48	47	11	of	of	ADP
biomedich-48	47	12	female	female	ADJ
biomedich-48	47	13	population	population	NOUN
biomedich-48	47	14	and	and	CCONJ
biomedich-48	47	15	knowing	know	VERB
biomedich-48	47	16	the	the	DET
biomedich-48	47	17	limiting	limit	VERB
biomedich-48	47	18	age	age	NOUN
biomedich-48	47	19	distribution	distribution	NOUN
biomedich-48	47	20	of	of	ADP
biomedich-48	47	21	the	the	DET
biomedich-48	47	22	female	female	ADJ
biomedich-48	47	23	population	population	NOUN
biomedich-48	47	24	in	in	ADP
biomedich-48	47	25	trenggalek	trenggalek	NOUN
biomedich-48	47	26	based	base	VERB
biomedich-48	47	27	on	on	ADP
biomedich-48	47	28	birth	birth	NOUN
biomedich-48	47	29	rate	rate	NOUN
biomedich-48	47	30	and	and	CCONJ
biomedich-48	47	31	life	life	NOUN
biomedich-48	47	32	expectancy	expectancy	NOUN
biomedich-48	47	33	using	use	VERB
biomedich-48	47	34	the	the	DET
biomedich-48	47	35	eigen	eigen	PROPN
biomedich-48	47	36	values	value	NOUN
biomedich-48	47	37	and	and	CCONJ
biomedich-48	47	38	eigen	eigen	PROPN
biomedich-48	47	39	vectors	vector	NOUN
biomedich-48	47	40	matrix	matrix	NOUN
biomedich-48	47	41	of	of	ADP
biomedich-48	47	42	leslie	leslie	PROPN
biomedich-48	47	43	.	.	PUNCT
biomedich-48	48	1	materials	material	NOUN
biomedich-48	48	2	and	and	CCONJ
biomedich-48	48	3	methods	method	NOUN
biomedich-48	48	4	this	this	DET
biomedich-48	48	5	research	research	NOUN
biomedich-48	48	6	is	be	AUX
biomedich-48	48	7	research	research	NOUN
biomedich-48	48	8	with	with	ADP
biomedich-48	48	9	quantitative	quantitative	ADJ
biomedich-48	48	10	approach	approach	NOUN
biomedich-48	48	11	with	with	ADP
biomedich-48	48	12	the	the	DET
biomedich-48	48	13	types	type	NOUN
biomedich-48	48	14	of	of	ADP
biomedich-48	48	15	descriptive	descriptive	ADJ
biomedich-48	48	16	research	research	NOUN
biomedich-48	48	17	.	.	PUNCT
biomedich-48	49	1	this	this	DET
biomedich-48	49	2	research	research	NOUN
biomedich-48	49	3	is	be	AUX
biomedich-48	49	4	done	do	VERB
biomedich-48	49	5	by	by	ADP
biomedich-48	49	6	taking	take	VERB
biomedich-48	49	7	a	a	DET
biomedich-48	49	8	secondary	secondary	ADJ
biomedich-48	49	9	data	datum	NOUN
biomedich-48	49	10	in	in	ADP
biomedich-48	49	11	some	some	PRON
biomedich-48	49	12	of	of	ADP
biomedich-48	49	13	the	the	DET
biomedich-48	49	14	central	central	ADJ
biomedich-48	49	15	bureau	bureau	NOUN
biomedich-48	49	16	of	of	ADP
biomedich-48	49	17	statistics	statistic	NOUN
biomedich-48	49	18	in	in	ADP
biomedich-48	49	19	east	east	PROPN
biomedich-48	49	20	java	java	PROPN
biomedich-48	49	21	province	province	PROPN
biomedich-48	49	22	and	and	CCONJ
biomedich-48	49	23	trenggalek	trenggalek	NOUN
biomedich-48	49	24	regency	regency	PROPN
biomedich-48	49	25	bps	bps	PROPN
biomedich-48	49	26	.	.	PUNCT
biomedich-48	50	1	the	the	DET
biomedich-48	50	2	sample	sample	NOUN
biomedich-48	50	3	in	in	ADP
biomedich-48	50	4	this	this	DET
biomedich-48	50	5	study	study	NOUN
biomedich-48	50	6	is	be	AUX
biomedich-48	50	7	a	a	DET
biomedich-48	50	8	population	population	NOUN
biomedich-48	50	9	of	of	ADP
biomedich-48	50	10	women	woman	NOUN
biomedich-48	50	11	of	of	ADP
biomedich-48	50	12	the	the	DET
biomedich-48	50	13	years	year	NOUN
biomedich-48	50	14	2010	2010	NUM
biomedich-48	50	15	to	to	ADP
biomedich-48	50	16	2015	2015	NUM
biomedich-48	50	17	,	,	PUNCT
biomedich-48	50	18	by	by	ADP
biomedich-48	50	19	comparison	comparison	NOUN
biomedich-48	50	20	with	with	ADP
biomedich-48	50	21	the	the	DET
biomedich-48	50	22	number	number	NOUN
biomedich-48	50	23	of	of	ADP
biomedich-48	50	24	child	child	NOUN
biomedich-48	50	25	birth	birth	NOUN
biomedich-48	50	26	from	from	ADP
biomedich-48	50	27	the	the	DET
biomedich-48	50	28	year	year	NOUN
biomedich-48	50	29	2010	2010	NUM
biomedich-48	50	30	to	to	ADP
biomedich-48	50	31	the	the	DET
biomedich-48	50	32	year	year	NOUN
biomedich-48	50	33	2015	2015	NUM
biomedich-48	50	34	.	.	PUNCT
biomedich-48	51	1	from	from	ADP
biomedich-48	51	2	the	the	DET
biomedich-48	51	3	results	result	NOUN
biomedich-48	51	4	of	of	ADP
biomedich-48	51	5	the	the	DET
biomedich-48	51	6	data	datum	NOUN
biomedich-48	51	7	then	then	ADV
biomedich-48	51	8	diplikasikan	diplikasikan	VERB
biomedich-48	51	9	by	by	ADP
biomedich-48	51	10	applying	apply	VERB
biomedich-48	51	11	the	the	DET
biomedich-48	51	12	matrix	matrix	NOUN
biomedich-48	51	13	model	model	NOUN
biomedich-48	51	14	leslie	leslie	PROPN
biomedich-48	51	15	to	to	PART
biomedich-48	51	16	look	look	VERB
biomedich-48	51	17	for	for	ADP
biomedich-48	51	18	population	population	NOUN
biomedich-48	51	19	,	,	PUNCT
biomedich-48	51	20	the	the	DET
biomedich-48	51	21	value	value	NOUN
biomedich-48	51	22	of	of	ADP
biomedich-48	51	23	the	the	DET
biomedich-48	51	24	eigenvalues	eigenvalues	PROPN
biomedich-48	51	25	and	and	CCONJ
biomedich-48	51	26	eigen	eigen	PROPN
biomedich-48	51	27	vectors	vector	NOUN
biomedich-48	51	28	.	.	PUNCT
biomedich-48	52	1	procedure	procedure	NOUN
biomedich-48	52	2	research	research	NOUN
biomedich-48	52	3	the	the	DET
biomedich-48	52	4	research	research	NOUN
biomedich-48	52	5	methods	method	NOUN
biomedich-48	52	6	used	use	VERB
biomedich-48	52	7	in	in	ADP
biomedich-48	52	8	this	this	DET
biomedich-48	52	9	research	research	NOUN
biomedich-48	52	10	are	be	AUX
biomedich-48	52	11	:	:	PUNCT
biomedich-48	52	12	the	the	DET
biomedich-48	52	13	first	first	ADJ
biomedich-48	52	14	stage	stage	NOUN
biomedich-48	52	15	is	be	AUX
biomedich-48	52	16	to	to	PART
biomedich-48	52	17	determine	determine	VERB
biomedich-48	52	18	the	the	DET
biomedich-48	52	19	subject	subject	NOUN
biomedich-48	52	20	of	of	ADP
biomedich-48	52	21	the	the	DET
biomedich-48	52	22	research	research	NOUN
biomedich-48	52	23	,	,	PUNCT
biomedich-48	52	24	as	as	ADP
biomedich-48	52	25	for	for	ADP
biomedich-48	52	26	the	the	DET
biomedich-48	52	27	subject	subject	NOUN
biomedich-48	52	28	of	of	ADP
biomedich-48	52	29	his	his	PRON
biomedich-48	52	30	research	research	NOUN
biomedich-48	52	31	is	be	AUX
biomedich-48	52	32	the	the	DET
biomedich-48	52	33	female	female	ADJ
biomedich-48	52	34	population	population	NOUN
biomedich-48	52	35	on	on	ADP
biomedich-48	52	36	the	the	DET
biomedich-48	52	37	birth	birth	NOUN
biomedich-48	52	38	rate	rate	NOUN
biomedich-48	52	39	and	and	CCONJ
biomedich-48	52	40	life	life	NOUN
biomedich-48	52	41	expectancy	expectancy	NOUN
biomedich-48	52	42	in	in	ADP
biomedich-48	52	43	east	east	PROPN
biomedich-48	52	44	java	java	PROPN
biomedich-48	52	45	province	province	PROPN
biomedich-48	52	46	and	and	CCONJ
biomedich-48	52	47	the	the	DET
biomedich-48	52	48	second	second	ADJ
biomedich-48	52	49	stage	stage	NOUN
biomedich-48	52	50	is	be	AUX
biomedich-48	52	51	to	to	PART
biomedich-48	52	52	(	(	PUNCT
biomedich-48	52	53	1	1	X
biomedich-48	52	54	)	)	PUNCT
biomedich-48	52	55	collect	collect	VERB
biomedich-48	52	56	research	research	NOUN
biomedich-48	52	57	data	datum	NOUN
biomedich-48	52	58	,	,	PUNCT
biomedich-48	52	59	with	with	ADP
biomedich-48	52	60	regard	regard	NOUN
biomedich-48	52	61	to	to	ADP
biomedich-48	52	62	the	the	DET
biomedich-48	52	63	collection	collection	NOUN
biomedich-48	52	64	of	of	ADP
biomedich-48	52	65	research	research	NOUN
biomedich-48	52	66	data	datum	NOUN
biomedich-48	52	67	obtained	obtain	VERB
biomedich-48	52	68	from	from	ADP
biomedich-48	52	69	secondary	secondary	ADJ
biomedich-48	52	70	data	datum	NOUN
biomedich-48	52	71	in	in	ADP
biomedich-48	52	72	the	the	DET
biomedich-48	52	73	central	central	ADJ
biomedich-48	52	74	bureau	bureau	NOUN
biomedich-48	52	75	of	of	ADP
biomedich-48	52	76	statistics	statistic	NOUN
biomedich-48	52	77	of	of	ADP
biomedich-48	52	78	east	east	PROPN
biomedich-48	52	79	java	java	PROPN
biomedich-48	52	80	province	province	PROPN
biomedich-48	52	81	and	and	CCONJ
biomedich-48	52	82	trenggalek	trenggalek	NOUN
biomedich-48	52	83	regency	regency	PROPN
biomedich-48	52	84	bps	bps	PROPN
biomedich-48	52	85	(	(	PUNCT
biomedich-48	52	86	2	2	NUM
biomedich-48	52	87	)	)	PUNCT
biomedich-48	52	88	data	datum	NOUN
biomedich-48	52	89	analysis	analysis	NOUN
biomedich-48	52	90	and	and	CCONJ
biomedich-48	52	91	the	the	DET
biomedich-48	52	92	last	last	ADJ
biomedich-48	52	93	is	be	AUX
biomedich-48	52	94	an	an	DET
biomedich-48	52	95	interesting	interesting	ADJ
biomedich-48	52	96	conclusion	conclusion	NOUN
biomedich-48	52	97	.	.	PUNCT
biomedich-48	53	1	observed	observed	ADJ
biomedich-48	53	2	variables	variable	NOUN
biomedich-48	53	3	observed	observe	VERB
biomedich-48	53	4	variables	variable	NOUN
biomedich-48	53	5	in	in	ADP
biomedich-48	53	6	this	this	DET
biomedich-48	53	7	study	study	NOUN
biomedich-48	53	8	was	be	AUX
biomedich-48	53	9	the	the	DET
biomedich-48	53	10	value	value	NOUN
biomedich-48	53	11	of	of	ADP
biomedich-48	53	12	eigen	eigen	PROPN
biomedich-48	53	13	and	and	CCONJ
biomedich-48	53	14	eigen	eigen	PROPN
biomedich-48	53	15	vectors	vector	NOUN
biomedich-48	53	16	of	of	ADP
biomedich-48	53	17	the	the	DET
biomedich-48	53	18	matrix	matrix	NOUN
biomedich-48	53	19	leslie	leslie	PROPN
biomedich-48	53	20	.	.	PUNCT
biomedich-48	54	1	eigen	eigen	PROPN
biomedich-48	54	2	values	value	NOUN
biomedich-48	54	3	of	of	ADP
biomedich-48	54	4	l	l	NOUN
biomedich-48	54	5	are	be	AUX
biomedich-48	54	6	the	the	DET
biomedich-48	54	7	roots	root	NOUN
biomedich-48	54	8	of	of	ADP
biomedich-48	54	9	polynomials	polynomial	NOUN
biomedich-48	54	10	of	of	ADP
biomedich-48	54	11	its	its	PRON
biomedich-48	54	12	characteristics	characteristic	NOUN
biomedich-48	54	13	.	.	PUNCT
biomedich-48	55	1	the	the	DET
biomedich-48	55	2	observed	observed	ADJ
biomedich-48	55	3	variables	variable	NOUN
biomedich-48	55	4	in	in	ADP
biomedich-48	55	5	this	this	DET
biomedich-48	55	6	study	study	NOUN
biomedich-48	55	7	was	be	AUX
biomedich-48	55	8	the	the	DET
biomedich-48	55	9	value	value	NOUN
biomedich-48	55	10	of	of	ADP
biomedich-48	55	11	eigen	eigen	PROPN
biomedich-48	55	12	and	and	CCONJ
biomedich-48	55	13	eigen	eigen	PROPN
biomedich-48	55	14	vectors	vector	NOUN
biomedich-48	55	15	of	of	ADP
biomedich-48	55	16	the	the	DET
biomedich-48	55	17	matrix	matrix	NOUN
biomedich-48	55	18	leslie	leslie	PROPN
biomedich-48	55	19	.	.	PUNCT
biomedich-48	56	1	eigen	eigen	PROPN
biomedich-48	56	2	values	value	NOUN
biomedich-48	56	3	of	of	ADP
biomedich-48	56	4	l	l	NOUN
biomedich-48	56	5	are	be	AUX
biomedich-48	56	6	the	the	DET
biomedich-48	56	7	roots	root	NOUN
biomedich-48	56	8	of	of	ADP
biomedich-48	56	9	polynomials	polynomial	NOUN
biomedich-48	56	10	of	of	ADP
biomedich-48	56	11	its	its	PRON
biomedich-48	56	12	characteristics	characteristic	NOUN
biomedich-48	56	13	.	.	PUNCT
biomedich-48	57	1	polynomial	polynomial	ADJ
biomedich-48	57	2	matrix	matrix	NOUN
biomedich-48	57	3	characteristics	characteristic	NOUN
biomedich-48	57	4	of	of	ADP
biomedich-48	57	5	leslie	leslie	PROPN
biomedich-48	57	6	are	be	AUX
biomedich-48	57	7	:	:	PUNCT
biomedich-48	57	8	𝑝(𝜆	𝑝(𝜆	X
biomedich-48	57	9	)	)	PUNCT
biomedich-48	57	10	=	=	SYM
biomedich-48	58	1	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	58	2	−	−	NOUN
biomedich-48	58	3	𝑎1𝜆	𝑎1𝜆	PROPN
biomedich-48	58	4	𝑛−1	𝑛−1	PROPN
biomedich-48	58	5	−	−	NOUN
biomedich-48	58	6	𝑎2𝑏1𝜆	𝑎2𝑏1𝜆	NOUN
biomedich-48	59	1	𝑛−2	𝑛−2	PROPN
biomedich-48	59	2	−	−	NOUN
biomedich-48	59	3	𝑎3𝑏1𝑏2𝜆	𝑎3𝑏1𝑏2𝜆	PROPN
biomedich-48	59	4	𝑛−3	𝑛−3	PROPN
biomedich-48	59	5	⋯−	⋯−	ADV
biomedich-48	59	6	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	PROPN
biomedich-48	59	7	⋯𝑏𝑛−1	⋯𝑏𝑛−1	NOUN
biomedich-48	59	8	𝐱	𝐱	NOUN
biomedich-48	59	9	=	=	SYM
biomedich-48	59	10	[	[	PUNCT
biomedich-48	59	11	𝑥1	𝑥1	NOUN
biomedich-48	59	12	𝑥2	𝑥2	NOUN
biomedich-48	59	13	𝑥3	𝑥3	NOUN
biomedich-48	59	14	⋮	⋮	NOUN
biomedich-48	59	15	𝑥𝑛	𝑥𝑛	PROPN
biomedich-48	59	16	]	]	X
biomedich-48	59	17	a	a	DET
biomedich-48	59	18	vector	vector	NOUN
biomedich-48	59	19	of	of	ADP
biomedich-48	59	20	eigenvalues	eigenvalue	NOUN
biomedich-48	59	21	of	of	ADP
biomedich-48	59	22	a	a	DET
biomedich-48	59	23	leslie	leslie	PROPN
biomedich-48	59	24	matrix	matrix	NOUN
biomedich-48	59	25	l	l	NOUN
biomedich-48	59	26	related	relate	VERB
biomedich-48	59	27	𝜆1	𝜆1	NOUN
biomedich-48	60	1	if	if	SCONJ
biomedich-48	60	2	and	and	CCONJ
biomedich-48	60	3	only	only	ADV
biomedich-48	60	4	if	if	SCONJ
biomedich-48	60	5	x	x	PRON
biomedich-48	60	6	is	be	AUX
biomedich-48	60	7	a	a	DET
biomedich-48	60	8	non	non	ADJ
biomedich-48	60	9	-	-	ADJ
biomedich-48	60	10	trivial	trivial	ADJ
biomedich-48	60	11	solution	solution	NOUN
biomedich-48	60	12	of	of	ADP
biomedich-48	60	13	(	(	PUNCT
biomedich-48	60	14	𝜆𝐼	𝜆𝐼	NOUN
biomedich-48	60	15	−	−	NOUN
biomedich-48	60	16	𝐿)𝐱	𝐿)𝐱	NOUN
biomedich-48	61	1	=	=	SYM
biomedich-48	61	2	0	0	X
biomedich-48	61	3	.	.	PUNCT
biomedich-48	62	1	data	datum	NOUN
biomedich-48	62	2	analysis	analysis	NOUN
biomedich-48	62	3	technique	technique	NOUN
biomedich-48	62	4	in	in	ADP
biomedich-48	62	5	doing	do	VERB
biomedich-48	62	6	data	datum	NOUN
biomedich-48	62	7	analysis	analysis	NOUN
biomedich-48	62	8	techniques	technique	NOUN
biomedich-48	62	9	after	after	SCONJ
biomedich-48	62	10	the	the	DET
biomedich-48	62	11	data	data	NOUN
biomedich-48	62	12	is	be	AUX
biomedich-48	62	13	finished	finish	VERB
biomedich-48	62	14	being	be	AUX
biomedich-48	62	15	processed	process	VERB
biomedich-48	62	16	which	which	PRON
biomedich-48	62	17	do	do	VERB
biomedich-48	62	18	first	first	ADV
biomedich-48	62	19	is	be	AUX
biomedich-48	62	20	find	find	VERB
biomedich-48	62	21	the	the	DET
biomedich-48	62	22	values	value	NOUN
biomedich-48	62	23	of	of	ADP
biomedich-48	62	24	ai	ai	PROPN
biomedich-48	62	25	(	(	PUNCT
biomedich-48	62	26	a	a	DET
biomedich-48	62	27	fertility	fertility	NOUN
biomedich-48	62	28	figure	figure	NOUN
biomedich-48	62	29	female	female	ADJ
biomedich-48	62	30	population	population	NOUN
biomedich-48	62	31	)	)	PUNCT
biomedich-48	62	32	obtained	obtain	VERB
biomedich-48	62	33	from	from	ADP
biomedich-48	62	34	the	the	DET
biomedich-48	62	35	quotient	quotient	NOUN
biomedich-48	62	36	between	between	ADP
biomedich-48	62	37	the	the	DET
biomedich-48	62	38	average	average	ADJ
biomedich-48	62	39	number	number	NOUN
biomedich-48	62	40	of	of	ADP
biomedich-48	62	41	births	birth	NOUN
biomedich-48	62	42	born	bear	VERB
biomedich-48	62	43	son	son	NOUN
biomedich-48	62	44	a	a	DET
biomedich-48	62	45	mom	mom	NOUN
biomedich-48	62	46	on	on	ADP
biomedich-48	62	47	2010	2010	NUM
biomedich-48	62	48	-	-	SYM
biomedich-48	62	49	2015	2015	NUM
biomedich-48	62	50	year	year	NOUN
biomedich-48	62	51	divided	divide	VERB
biomedich-48	62	52	by	by	ADP
biomedich-48	62	53	the	the	DET
biomedich-48	62	54	number	number	NOUN
biomedich-48	62	55	of	of	ADP
biomedich-48	62	56	female	female	ADJ
biomedich-48	62	57	population	population	NOUN
biomedich-48	62	58	in	in	ADP
biomedich-48	62	59	the	the	DET
biomedich-48	62	60	year	year	NOUN
biomedich-48	62	61	2010	2010	NUM
biomedich-48	62	62	and	and	CCONJ
biomedich-48	62	63	bi	bi	NOUN
biomedich-48	62	64	(	(	PUNCT
biomedich-48	62	65	life	life	NOUN
biomedich-48	62	66	expectancy	expectancy	NOUN
biomedich-48	62	67	female	female	ADJ
biomedich-48	62	68	population	population	NOUN
biomedich-48	62	69	)	)	PUNCT
biomedich-48	62	70	are	be	AUX
biomedich-48	62	71	obtained	obtain	VERB
biomedich-48	62	72	from	from	ADP
biomedich-48	62	73	the	the	DET
biomedich-48	62	74	results	result	NOUN
biomedich-48	62	75	of	of	ADP
biomedich-48	62	76	the	the	DET
biomedich-48	62	77	women	woman	NOUN
biomedich-48	62	78	's	's	PART
biomedich-48	62	79	division	division	NOUN
biomedich-48	62	80	of	of	ADP
biomedich-48	62	81	the	the	DET
biomedich-48	62	82	population	population	NOUN
biomedich-48	62	83	the	the	DET
biomedich-48	62	84	year	year	NOUN
biomedich-48	62	85	2015	2015	NUM
biomedich-48	62	86	with	with	ADP
biomedich-48	62	87	total	total	ADJ
biomedich-48	62	88	population	population	NOUN
biomedich-48	62	89	of	of	ADP
biomedich-48	62	90	woman	woman	NOUN
biomedich-48	62	91	of	of	ADP
biomedich-48	62	92	the	the	DET
biomedich-48	62	93	year	year	NOUN
biomedich-48	62	94	2010	2010	NUM
biomedich-48	62	95	.	.	PUNCT
biomedich-48	63	1	second	second	ADJ
biomedich-48	63	2	,	,	PUNCT
biomedich-48	63	3	the	the	DET
biomedich-48	63	4	mengkontruksi	mengkontruksi	PROPN
biomedich-48	63	5	model	model	NOUN
biomedich-48	63	6	matrix	matrix	NOUN
biomedich-48	63	7	of	of	ADP
biomedich-48	63	8	leslie	leslie	PROPN
biomedich-48	63	9	on	on	ADP
biomedich-48	63	10	the	the	DET
biomedich-48	63	11	growth	growth	NOUN
biomedich-48	63	12	of	of	ADP
biomedich-48	63	13	the	the	DET
biomedich-48	63	14	population	population	NOUN
biomedich-48	63	15	.	.	PUNCT
biomedich-48	64	1	third	third	ADV
biomedich-48	64	2	after	after	SCONJ
biomedich-48	64	3	matric	matric	PROPN
biomedich-48	64	4	leslie	leslie	PROPN
biomedich-48	64	5	was	be	AUX
biomedich-48	64	6	formed	form	VERB
biomedich-48	64	7	later	later	ADV
biomedich-48	64	8	enter	enter	VERB
biomedich-48	64	9	the	the	DET
biomedich-48	64	10	data	datum	NOUN
biomedich-48	64	11	the	the	DET
biomedich-48	64	12	number	number	NOUN
biomedich-48	64	13	of	of	ADP
biomedich-48	64	14	female	female	ADJ
biomedich-48	64	15	population	population	NOUN
biomedich-48	64	16	in	in	ADP
biomedich-48	64	17	2015	2015	NUM
biomedich-48	64	18	to	to	PART
biomedich-48	64	19	generate	generate	VERB
biomedich-48	64	20	predictions	prediction	NOUN
biomedich-48	64	21	of	of	ADP
biomedich-48	64	22	the	the	DET
biomedich-48	64	23	total	total	ADJ
biomedich-48	64	24	population	population	NOUN
biomedich-48	64	25	of	of	ADP
biomedich-48	64	26	women	woman	NOUN
biomedich-48	64	27	in	in	ADP
biomedich-48	64	28	the	the	DET
biomedich-48	64	29	year	year	NOUN
biomedich-48	64	30	2021	2021	NUM
biomedich-48	64	31	.	.	PUNCT
biomedich-48	65	1	third	third	ADJ
biomedich-48	65	2	,	,	PUNCT
biomedich-48	65	3	find	find	VERB
biomedich-48	65	4	the	the	DET
biomedich-48	65	5	value	value	NOUN
biomedich-48	65	6	of	of	ADP
biomedich-48	65	7	a	a	DET
biomedich-48	65	8	positive	positive	ADJ
biomedich-48	65	9	eigenvalues	eigenvalue	NOUN
biomedich-48	65	10	in	in	ADP
biomedich-48	65	11	the	the	DET
biomedich-48	65	12	matrix	matrix	NOUN
biomedich-48	65	13	.	.	PUNCT
biomedich-48	66	1	fifth	fifth	ADJ
biomedich-48	66	2	,	,	PUNCT
biomedich-48	66	3	determine	determine	VERB
biomedich-48	66	4	the	the	DET
biomedich-48	66	5	value	value	NOUN
biomedich-48	66	6	of	of	ADP
biomedich-48	66	7	the	the	DET
biomedich-48	66	8	eigen	eigen	PROPN
biomedich-48	66	9	vectors	vectors	PROPN
biomedich-48	66	10	eigen	eigen	PROPN
biomedich-48	66	11	were	be	AUX
biomedich-48	66	12	positive	positive	ADJ
biomedich-48	66	13	.	.	PUNCT
biomedich-48	67	1	sixth	sixth	ADV
biomedich-48	67	2	,	,	PUNCT
biomedich-48	67	3	using	use	VERB
biomedich-48	67	4	equation	equation	NOUN
biomedich-48	67	5	approach	approach	NOUN
biomedich-48	67	6	to	to	PART
biomedich-48	67	7	determine	determine	VERB
biomedich-48	67	8	the	the	DET
biomedich-48	67	9	limiting	limit	VERB
biomedich-48	67	10	age	age	NOUN
biomedich-48	67	11	distribution	distribution	NOUN
biomedich-48	67	12	.	.	PUNCT
biomedich-48	68	1	the	the	DET
biomedich-48	68	2	seventh	seventh	ADJ
biomedich-48	68	3	note	note	NOUN
biomedich-48	68	4	the	the	DET
biomedich-48	68	5	abundance	abundance	NOUN
biomedich-48	68	6	of	of	ADP
biomedich-48	68	7	female	female	ADJ
biomedich-48	68	8	population	population	NOUN
biomedich-48	68	9	for	for	ADP
biomedich-48	68	10	a	a	DET
biomedich-48	68	11	long	long	ADJ
biomedich-48	68	12	period	period	NOUN
biomedich-48	68	13	to	to	PART
biomedich-48	68	14	come	come	VERB
biomedich-48	68	15	.	.	PUNCT
biomedich-48	69	1	the	the	DET
biomedich-48	69	2	eighth	eighth	ADJ
biomedich-48	69	3	research	research	NOUN
biomedich-48	69	4	report	report	NOUN
biomedich-48	69	5	compiled	compile	VERB
biomedich-48	69	6	and	and	CCONJ
biomedich-48	69	7	processed	process	VERB
biomedich-48	69	8	data	datum	NOUN
biomedich-48	69	9	through	through	ADP
biomedich-48	69	10	the	the	DET
biomedich-48	69	11	application	application	NOUN
biomedich-48	69	12	of	of	ADP
biomedich-48	69	13	maple	maple	NOUN
biomedich-48	69	14	16	16	NUM
biomedich-48	69	15	.	.	PUNCT
biomedich-48	69	16	matrix	matrix	NOUN
biomedich-48	69	17	according	accord	VERB
biomedich-48	69	18	to	to	ADP
biomedich-48	69	19	kariadinata	kariadinata	PROPN
biomedich-48	69	20	(	(	PUNCT
biomedich-48	69	21	2013	2013	NUM
biomedich-48	69	22	,	,	PUNCT
biomedich-48	69	23	p.11	p.11	NOUN
biomedich-48	69	24	)	)	PUNCT
biomedich-48	69	25	matrix	matrix	NOUN
biomedich-48	69	26	is	be	AUX
biomedich-48	69	27	the	the	DET
biomedich-48	69	28	arrangement	arrangement	NOUN
biomedich-48	69	29	of	of	ADP
biomedich-48	69	30	a	a	DET
biomedich-48	69	31	group	group	NOUN
biomedich-48	69	32	of	of	ADP
biomedich-48	69	33	numbers	number	NOUN
biomedich-48	69	34	in	in	ADP
biomedich-48	69	35	a	a	DET
biomedich-48	69	36	rectangular	rectangular	ADJ
biomedich-48	69	37	shaped	shape	VERB
biomedich-48	69	38	ranks	rank	NOUN
biomedich-48	69	39	arranged	arrange	VERB
biomedich-48	69	40	based	base	VERB
biomedich-48	69	41	on	on	ADP
biomedich-48	69	42	row	row	NOUN
biomedich-48	69	43	and	and	CCONJ
biomedich-48	69	44	column	column	NOUN
biomedich-48	69	45	,	,	PUNCT
biomedich-48	69	46	and	and	CCONJ
biomedich-48	69	47	placed	place	VERB
biomedich-48	69	48	between	between	ADP
biomedich-48	69	49	two	two	NUM
biomedich-48	69	50	brackets	bracket	NOUN
biomedich-48	69	51	.	.	PUNCT
biomedich-48	70	1	meanwhile	meanwhile	ADV
biomedich-48	70	2	,	,	PUNCT
biomedich-48	70	3	according	accord	VERB
biomedich-48	70	4	to	to	ADP
biomedich-48	70	5	anton	anton	PROPN
biomedich-48	70	6	,	,	PUNCT
biomedich-48	70	7	h.	h.	PROPN
biomedich-48	70	8	&	&	CCONJ
biomedich-48	70	9	rorres	rorres	PROPN
biomedich-48	70	10	,	,	PUNCT
biomedich-48	70	11	c.	c.	PROPN
biomedich-48	70	12	(	(	PUNCT
biomedich-48	70	13	2004	2004	NUM
biomedich-48	70	14	,	,	PUNCT
biomedich-48	70	15	p.	p.	NOUN
biomedich-48	70	16	23	23	NUM
biomedich-48	70	17	)	)	PUNCT
biomedich-48	70	18	a	a	DET
biomedich-48	70	19	matrix	matrix	NOUN
biomedich-48	70	20	with	with	ADP
biomedich-48	70	21	n	n	NOUN
biomedich-48	70	22	rows	row	NOUN
biomedich-48	70	23	and	and	CCONJ
biomedich-48	70	24	n	n	DET
biomedich-48	70	25	columns	column	NOUN
biomedich-48	70	26	is	be	AUX
biomedich-48	70	27	called	call	VERB
biomedich-48	70	28	an	an	DET
biomedich-48	70	29	n	n	NUM
biomedich-48	70	30	order	order	NOUN
biomedich-48	70	31	square	square	ADJ
biomedich-48	70	32	matrix	matrix	NOUN
biomedich-48	70	33	(	(	PUNCT
biomedich-48	70	34	in	in	ADP
biomedich-48	70	35	square	square	ADJ
biomedich-48	70	36	matrices	matrix	NOUN
biomedich-48	70	37	of	of	ADP
biomedich-48	70	38	order	order	NOUN
biomedich-48	70	39	n	n	CCONJ
biomedich-48	70	40	)	)	PUNCT
biomedich-48	70	41	,	,	PUNCT
biomedich-48	70	42	and	and	CCONJ
biomedich-48	70	43	the	the	DET
biomedich-48	70	44	entries	entry	NOUN
biomedich-48	70	45	𝑎11	𝑎11	VERB
biomedich-48	70	46	,	,	PUNCT
biomedich-48	70	47	𝑎22	𝑎22	NOUN
biomedich-48	70	48	,	,	PUNCT
biomedich-48	70	49	…	…	PUNCT
biomedich-48	70	50	,	,	PUNCT
biomedich-48	70	51	𝑎𝑛𝑛	𝑎𝑛𝑛	ADP
biomedich-48	70	52	on	on	ADP
biomedich-48	70	53	the	the	DET
biomedich-48	70	54	main	main	ADJ
biomedich-48	70	55	diagonal	diagonal	NOUN
biomedich-48	70	56	is	be	AUX
biomedich-48	70	57	said	say	VERB
biomedich-48	70	58	to	to	PART
biomedich-48	70	59	be	be	AUX
biomedich-48	70	60	from	from	ADP
biomedich-48	70	61	a.	a.	NOUN
biomedich-48	70	62	when	when	SCONJ
biomedich-48	70	63	a	a	PRON
biomedich-48	70	64	is	be	AUX
biomedich-48	70	65	the	the	DET
biomedich-48	70	66	matrix	matrix	NOUN
biomedich-48	70	67	has	have	VERB
biomedich-48	70	68	n	n	NUM
biomedich-48	70	69	rows	row	NOUN
biomedich-48	70	70	and	and	CCONJ
biomedich-48	70	71	n	n	DET
biomedich-48	70	72	column	column	NOUN
biomedich-48	70	73	(	(	PUNCT
biomedich-48	70	74	type	type	NOUN
biomedich-48	70	75	n	n	NOUN
biomedich-48	70	76	x	x	NOUN
biomedich-48	70	77	n	n	CCONJ
biomedich-48	70	78	)	)	PUNCT
biomedich-48	70	79	,	,	PUNCT
biomedich-48	70	80	then	then	ADV
biomedich-48	70	81	a	a	PRON
biomedich-48	70	82	can	can	AUX
biomedich-48	70	83	be	be	AUX
biomedich-48	70	84	written	write	VERB
biomedich-48	70	85	as	as	ADP
biomedich-48	70	86	:	:	PUNCT
biomedich-48	70	87	[	[	PUNCT
biomedich-48	70	88	𝑎11	𝑎11	ADJ
biomedich-48	70	89	𝑎21	𝑎21	NOUN
biomedich-48	70	90	⋮	⋮	NOUN
biomedich-48	70	91	𝑎𝑛1	𝑎𝑛1	VERB
biomedich-48	70	92	𝑎12	𝑎12	NOUN
biomedich-48	70	93	𝑎22	𝑎22	NOUN
biomedich-48	70	94	⋮	⋮	NOUN
biomedich-48	71	1	𝑎𝑛2	𝑎𝑛2	PROPN
biomedich-48	71	2	⋯	⋯	PROPN
biomedich-48	71	3	⋯	⋯	PROPN
biomedich-48	71	4	⋯	⋯	PROPN
biomedich-48	71	5	𝑎1𝑛	𝑎1𝑛	PROPN
biomedich-48	71	6	𝑎2𝑛	𝑎2𝑛	PROPN
biomedich-48	71	7	⋮	⋮	NOUN
biomedich-48	71	8	𝑎𝑛𝑛	𝑎𝑛𝑛	ADV
biomedich-48	71	9	]	]	PUNCT
biomedich-48	71	10	anggreini	anggreini	ADV
biomedich-48	71	11	–	–	PUNCT
biomedich-48	71	12	the	the	DET
biomedich-48	71	13	female	female	ADJ
biomedich-48	71	14	population	population	NOUN
biomedich-48	71	15	growth	growth	NOUN
biomedich-48	71	16	projection	projection	NOUN
biomedich-48	71	17	year	year	NOUN
biomedich-48	71	18	2021	2021	NUM
biomedich-48	71	19	in	in	ADP
biomedich-48	71	20	trenggalek	trenggalek	NOUN
biomedich-48	71	21	…	…	PUNCT
biomedich-48	71	22	39	39	NUM
biomedich-48	71	23	inverse	inverse	NOUN
biomedich-48	71	24	of	of	ADP
biomedich-48	71	25	a	a	DET
biomedich-48	71	26	matrix	matrix	NOUN
biomedich-48	71	27	according	accord	VERB
biomedich-48	71	28	to	to	ADP
biomedich-48	71	29	adiwijaya	adiwijaya	NOUN
biomedich-48	71	30	(	(	PUNCT
biomedich-48	71	31	2014	2014	NUM
biomedich-48	71	32	,	,	PUNCT
biomedich-48	71	33	p.	p.	NOUN
biomedich-48	71	34	10	10	NUM
biomedich-48	71	35	)	)	PUNCT
biomedich-48	71	36	suppose	suppose	VERB
biomedich-48	71	37	a	a	PRON
biomedich-48	71	38	and	and	CCONJ
biomedich-48	71	39	b	b	NOUN
biomedich-48	71	40	are	be	AUX
biomedich-48	71	41	square	square	ADJ
biomedich-48	71	42	matrices	matrix	NOUN
biomedich-48	71	43	of	of	ADP
biomedich-48	71	44	the	the	DET
biomedich-48	71	45	same	same	ADJ
biomedich-48	71	46	size	size	NOUN
biomedich-48	71	47	are	be	AUX
biomedich-48	71	48	and	and	CCONJ
biomedich-48	71	49	i	i	PRON
biomedich-48	71	50	is	be	AUX
biomedich-48	71	51	the	the	DET
biomedich-48	71	52	identity	identity	NOUN
biomedich-48	71	53	matrix	matrix	NOUN
biomedich-48	71	54	.	.	PUNCT
biomedich-48	72	1	if	if	SCONJ
biomedich-48	72	2	a.b	a.b	PROPN
biomedich-48	72	3	=	=	NOUN
biomedich-48	72	4	i	i	PROPN
biomedich-48	72	5	then	then	ADV
biomedich-48	72	6	b	b	PROPN
biomedich-48	72	7	is	be	AUX
biomedich-48	72	8	called	call	VERB
biomedich-48	72	9	the	the	DET
biomedich-48	72	10	inverse	inverse	NOUN
biomedich-48	72	11	of	of	ADP
biomedich-48	72	12	matrix	matrix	NOUN
biomedich-48	72	13	a	a	PRON
biomedich-48	72	14	(	(	PUNCT
biomedich-48	72	15	on	on	ADP
biomedich-48	72	16	the	the	DET
biomedich-48	72	17	contrary	contrary	NOUN
biomedich-48	72	18	,	,	PUNCT
biomedich-48	72	19	a	a	PRON
biomedich-48	72	20	is	be	AUX
biomedich-48	72	21	the	the	DET
biomedich-48	72	22	inverse	inverse	NOUN
biomedich-48	72	23	of	of	ADP
biomedich-48	72	24	matrix	matrix	NOUN
biomedich-48	72	25	b	b	NOUN
biomedich-48	72	26	)	)	PUNCT
biomedich-48	72	27	.	.	PUNCT
biomedich-48	73	1	notation	notation	NOUN
biomedich-48	73	2	that	that	SCONJ
biomedich-48	73	3	the	the	DET
biomedich-48	73	4	inverse	inverse	NOUN
biomedich-48	73	5	of	of	ADP
biomedich-48	73	6	matrix	matrix	NOUN
biomedich-48	73	7	b	b	NOUN
biomedich-48	73	8	is	be	AUX
biomedich-48	73	9	a	a	PRON
biomedich-48	73	10	is	be	AUX
biomedich-48	73	11	b=	b=	NOUN
biomedich-48	73	12	a-1	a-1	NOUN
biomedich-48	73	13	and	and	CCONJ
biomedich-48	73	14	vice	vice	PROPN
biomedich-48	73	15	versa	versa	PROPN
biomedich-48	73	16	a=	a=	PROPN
biomedich-48	73	17	b-1	b-1	PROPN
biomedich-48	73	18	matriks	matriks	PROPN
biomedich-48	73	19	elementer	elementer	PROPN
biomedich-48	73	20	according	accord	VERB
biomedich-48	73	21	to	to	ADP
biomedich-48	73	22	anton	anton	PROPN
biomedich-48	73	23	,	,	PUNCT
biomedich-48	73	24	h	h	PROPN
biomedich-48	73	25	&	&	CCONJ
biomedich-48	73	26	rorres	rorre	NOUN
biomedich-48	73	27	,	,	PUNCT
biomedich-48	73	28	c	c	PROPN
biomedich-48	73	29	(	(	PUNCT
biomedich-48	73	30	2004	2004	NUM
biomedich-48	73	31	,	,	PUNCT
biomedich-48	73	32	p.56	p.56	NOUN
biomedich-48	73	33	)	)	PUNCT
biomedich-48	73	34	an	an	DET
biomedich-48	73	35	n	n	NOUN
biomedich-48	73	36	x	x	SYM
biomedich-48	74	1	n	n	DET
biomedich-48	74	2	matrix	matrix	NOUN
biomedich-48	74	3	is	be	AUX
biomedich-48	74	4	called	call	VERB
biomedich-48	74	5	elementary	elementary	ADJ
biomedich-48	74	6	matrix	matrix	NOUN
biomedich-48	74	7	if	if	SCONJ
biomedich-48	74	8	the	the	DET
biomedich-48	74	9	matrix	matrix	NOUN
biomedich-48	74	10	can	can	AUX
biomedich-48	74	11	be	be	AUX
biomedich-48	74	12	derived	derive	VERB
biomedich-48	74	13	from	from	ADP
biomedich-48	74	14	in	in	ADP
biomedich-48	74	15	n	n	NOUN
biomedich-48	74	16	x	x	NOUN
biomedich-48	74	17	n	n	PRON
biomedich-48	74	18	identity	identity	NOUN
biomedich-48	74	19	matrix	matrix	NOUN
biomedich-48	74	20	by	by	ADP
biomedich-48	74	21	performing	perform	VERB
biomedich-48	74	22	a	a	DET
biomedich-48	74	23	single	single	ADJ
biomedich-48	74	24	elementary	elementary	NOUN
biomedich-48	74	25	row	row	NOUN
biomedich-48	74	26	operation	operation	NOUN
biomedich-48	74	27	.	.	PUNCT
biomedich-48	75	1	each	each	DET
biomedich-48	75	2	elementary	elementary	ADJ
biomedich-48	75	3	matrix	matrix	NOUN
biomedich-48	75	4	can	can	AUX
biomedich-48	75	5	be	be	AUX
biomedich-48	75	6	reversed	reverse	VERB
biomedich-48	75	7	,	,	PUNCT
biomedich-48	75	8	and	and	CCONJ
biomedich-48	75	9	its	its	PRON
biomedich-48	75	10	inverse	inverse	NOUN
biomedich-48	75	11	is	be	AUX
biomedich-48	75	12	also	also	ADV
biomedich-48	75	13	an	an	DET
biomedich-48	75	14	elementary	elementary	ADJ
biomedich-48	75	15	matrix	matrix	NOUN
biomedich-48	75	16	.	.	PUNCT
biomedich-48	76	1	if	if	SCONJ
biomedich-48	76	2	a	a	PRON
biomedich-48	76	3	is	be	AUX
biomedich-48	76	4	an	an	DET
biomedich-48	76	5	n	n	NOUN
biomedich-48	76	6	x	x	SYM
biomedich-48	76	7	n	n	CCONJ
biomedich-48	76	8	,	,	PUNCT
biomedich-48	76	9	matrix	matrix	NOUN
biomedich-48	76	10	,	,	PUNCT
biomedich-48	76	11	then	then	ADV
biomedich-48	76	12	the	the	DET
biomedich-48	76	13	following	following	ADJ
biomedich-48	76	14	statements	statement	NOUN
biomedich-48	76	15	are	be	AUX
biomedich-48	76	16	equivalent	equivalent	ADJ
biomedich-48	76	17	,	,	PUNCT
biomedich-48	76	18	they	they	PRON
biomedich-48	76	19	are	be	AUX
biomedich-48	76	20	all	all	ADV
biomedich-48	76	21	true	true	ADJ
biomedich-48	76	22	or	or	CCONJ
biomedich-48	76	23	all	all	PRON
biomedich-48	76	24	wrong	wrong	ADJ
biomedich-48	76	25	:	:	PUNCT
biomedich-48	76	26	a	a	X
biomedich-48	76	27	)	)	PUNCT
biomedich-48	76	28	a	a	PRON
biomedich-48	76	29	is	be	AUX
biomedich-48	76	30	invertible	invertible	ADJ
biomedich-48	76	31	,	,	PUNCT
biomedich-48	76	32	b	b	NOUN
biomedich-48	76	33	)	)	PUNCT
biomedich-48	76	34	a	a	DET
biomedich-48	76	35	x	x	SYM
biomedich-48	76	36	=	=	SYM
biomedich-48	76	37	0	0	NUM
biomedich-48	76	38	has	have	VERB
biomedich-48	76	39	only	only	ADV
biomedich-48	76	40	a	a	DET
biomedich-48	76	41	trivial	trivial	ADJ
biomedich-48	76	42	solution	solution	NOUN
biomedich-48	76	43	,	,	PUNCT
biomedich-48	76	44	c	c	NOUN
biomedich-48	76	45	)	)	PUNCT
biomedich-48	76	46	a	a	DET
biomedich-48	76	47	row	row	NOUN
biomedich-48	76	48	equivalent	equivalent	ADJ
biomedich-48	76	49	to	to	ADP
biomedich-48	76	50	in	in	ADP
biomedich-48	76	51	or	or	CCONJ
biomedich-48	76	52	reduced	reduce	VERB
biomedich-48	76	53	rowechelon	rowechelon	NOUN
biomedich-48	76	54	form	form	NOUN
biomedich-48	76	55	a	a	PRON
biomedich-48	76	56	is	be	AUX
biomedich-48	76	57	in	in	ADP
biomedich-48	76	58	..	..	PUNCT
biomedich-48	76	59	determinants	determinant	NOUN
biomedich-48	76	60	according	accord	VERB
biomedich-48	76	61	to	to	ADP
biomedich-48	76	62	anton	anton	PROPN
biomedich-48	76	63	,	,	PUNCT
biomedich-48	76	64	h	h	PROPN
biomedich-48	76	65	&	&	CCONJ
biomedich-48	76	66	rorres	rorre	NOUN
biomedich-48	76	67	,	,	PUNCT
biomedich-48	76	68	c	c	PROPN
biomedich-48	76	69	(	(	PUNCT
biomedich-48	76	70	2004	2004	NUM
biomedich-48	76	71	,	,	PUNCT
biomedich-48	76	72	p.92	p.92	NOUN
biomedich-48	76	73	)	)	PUNCT
biomedich-48	76	74	an	an	DET
biomedich-48	76	75	elementary	elementary	ADJ
biomedich-48	76	76	product	product	NOUN
biomedich-48	76	77	of	of	ADP
biomedich-48	76	78	a	a	DET
biomedich-48	76	79	matrix	matrix	NOUN
biomedich-48	76	80	a	a	PRON
biomedich-48	76	81	,	,	PUNCT
biomedich-48	76	82	a	a	PRON
biomedich-48	76	83	,	,	PUNCT
biomedich-48	76	84	nn	nn	X
biomedich-48	76	85	x	x	X
biomedich-48	76	86	,	,	PUNCT
biomedich-48	76	87	is	be	AUX
biomedich-48	76	88	a	a	DET
biomedich-48	76	89	product	product	NOUN
biomedich-48	76	90	of	of	ADP
biomedich-48	76	91	entries	entry	NOUN
biomedich-48	76	92	of	of	ADP
biomedich-48	76	93	,	,	PUNCT
biomedich-48	76	94	none	none	NOUN
biomedich-48	76	95	of	of	ADP
biomedich-48	76	96	which	which	PRON
biomedich-48	76	97	come	come	VERB
biomedich-48	76	98	from	from	ADP
biomedich-48	76	99	the	the	DET
biomedich-48	76	100	same	same	ADJ
biomedich-48	76	101	row	row	NOUN
biomedich-48	76	102	or	or	CCONJ
biomedich-48	76	103	column	column	NOUN
biomedich-48	76	104	.	.	PUNCT
biomedich-48	77	1	eigenvalues	eigenvalue	NOUN
biomedich-48	77	2	and	and	CCONJ
biomedich-48	77	3	eigenvectors	eigenvector	NOUN
biomedich-48	77	4	according	accord	VERB
biomedich-48	77	5	to	to	ADP
biomedich-48	77	6	kariadinata	kariadinata	NOUN
biomedich-48	77	7	(	(	PUNCT
biomedich-48	77	8	2013	2013	NUM
biomedich-48	77	9	,	,	PUNCT
biomedich-48	77	10	p.209	p.209	NOUN
biomedich-48	77	11	)	)	PUNCT
biomedich-48	77	12	if	if	SCONJ
biomedich-48	77	13	a	a	PRON
biomedich-48	77	14	is	be	AUX
biomedich-48	77	15	an	an	DET
biomedich-48	77	16	n	n	NOUN
biomedich-48	77	17	x	x	SYM
biomedich-48	77	18	n	n	NOUN
biomedich-48	77	19	size	size	NOUN
biomedich-48	77	20	matrix	matrix	NOUN
biomedich-48	77	21	,	,	PUNCT
biomedich-48	77	22	then	then	ADV
biomedich-48	77	23	the	the	DET
biomedich-48	77	24	nonzero	nonzero	PROPN
biomedich-48	77	25	vector	vector	NOUN
biomedich-48	77	26	x	x	PUNCT
biomedich-48	77	27	in	in	ADP
biomedich-48	77	28	rn	rn	PROPN
biomedich-48	77	29	is	be	AUX
biomedich-48	77	30	called	call	VERB
biomedich-48	77	31	an	an	DET
biomedich-48	77	32	eigenvector	eigenvector	NOUN
biomedich-48	77	33	of	of	ADP
biomedich-48	77	34	a	a	DET
biomedich-48	77	35	if	if	SCONJ
biomedich-48	77	36	a	a	PRON
biomedich-48	77	37	x	x	PUNCT
biomedich-48	77	38	is	be	AUX
biomedich-48	77	39	a	a	DET
biomedich-48	77	40	scalar	scalar	ADJ
biomedich-48	77	41	multiple	multiple	NOUN
biomedich-48	77	42	of	of	ADP
biomedich-48	77	43	x	x	PRON
biomedich-48	77	44	;	;	PUNCT
biomedich-48	77	45	ie	ie	X
biomedich-48	77	46	,	,	PUNCT
biomedich-48	77	47	𝐴𝒙	𝐴𝒙	PROPN
biomedich-48	77	48	=	=	PUNCT
biomedich-48	77	49	𝜆𝒙	𝜆𝒙	NOUN
biomedich-48	77	50	for	for	ADP
biomedich-48	77	51	any	any	DET
biomedich-48	77	52	scalar	scalar	ADJ
biomedich-48	77	53	λ	λ	NOUN
biomedich-48	77	54	.	.	PUNCT
biomedich-48	78	1	the	the	DET
biomedich-48	78	2	scalar	scalar	ADJ
biomedich-48	78	3	λ	λ	PROPN
biomedich-48	78	4	is	be	AUX
biomedich-48	78	5	called	call	VERB
biomedich-48	78	6	the	the	DET
biomedich-48	78	7	eigenvalue	eigenvalue	NOUN
biomedich-48	78	8	of	of	ADP
biomedich-48	78	9	a	a	PRON
biomedich-48	78	10	and	and	CCONJ
biomedich-48	78	11	x	x	ADJ
biomedich-48	78	12	is	be	AUX
biomedich-48	78	13	said	say	VERB
biomedich-48	78	14	to	to	PART
biomedich-48	78	15	be	be	AUX
biomedich-48	78	16	the	the	DET
biomedich-48	78	17	eigenvector	eigenvector	NOUN
biomedich-48	78	18	corresponding	corresponding	ADJ
biomedich-48	78	19	to	to	PART
biomedich-48	78	20	𝜆.	𝜆.	VERB
biomedich-48	78	21	to	to	PART
biomedich-48	78	22	find	find	VERB
biomedich-48	78	23	the	the	DET
biomedich-48	78	24	eigenvalue	eigenvalue	NOUN
biomedich-48	78	25	of	of	ADP
biomedich-48	78	26	the	the	DET
biomedich-48	78	27	matrix	matrix	NOUN
biomedich-48	78	28	a	a	PRON
biomedich-48	78	29	of	of	ADP
biomedich-48	78	30	nxn	nxn	PROPN
biomedich-48	78	31	size	size	NOUN
biomedich-48	78	32	then	then	ADV
biomedich-48	78	33	𝐴𝒙	𝐴𝒙	PROPN
biomedich-48	78	34	=	=	PUNCT
biomedich-48	78	35	𝜆𝒙	𝜆𝒙	NOUN
biomedich-48	78	36	can	can	AUX
biomedich-48	78	37	be	be	AUX
biomedich-48	78	38	rewritten	rewrite	VERB
biomedich-48	78	39	as	as	ADP
biomedich-48	78	40	𝐴𝒙	𝐴𝒙	PROPN
biomedich-48	78	41	=	=	PUNCT
biomedich-48	78	42	𝜆𝐼𝒙	𝜆𝐼𝒙	NOUN
biomedich-48	78	43	or	or	CCONJ
biomedich-48	78	44	equivalent	equivalent	ADJ
biomedich-48	78	45	to	to	ADP
biomedich-48	78	46	(	(	PUNCT
biomedich-48	78	47	𝜆𝐼	𝜆𝐼	NOUN
biomedich-48	78	48	−	−	NOUN
biomedich-48	78	49	𝐴)𝐱	𝐴)𝐱	NOUN
biomedich-48	79	1	=	=	NOUN
biomedich-48	79	2	0	0	X
biomedich-48	79	3	.	.	PUNCT
biomedich-48	80	1	to	to	PART
biomedich-48	80	2	be	be	AUX
biomedich-48	80	3	an	an	DET
biomedich-48	80	4	eigenvalue	eigenvalue	NOUN
biomedich-48	80	5	,	,	PUNCT
biomedich-48	80	6	there	there	PRON
biomedich-48	80	7	must	must	AUX
biomedich-48	80	8	be	be	AUX
biomedich-48	80	9	a	a	DET
biomedich-48	80	10	nonzero	nonzero	ADJ
biomedich-48	80	11	solution	solution	NOUN
biomedich-48	80	12	of	of	ADP
biomedich-48	80	13	the	the	DET
biomedich-48	80	14	equation	equation	NOUN
biomedich-48	80	15	(	(	PUNCT
biomedich-48	80	16	𝜆𝐼	𝜆𝐼	NOUN
biomedich-48	80	17	−	−	NOUN
biomedich-48	80	18	𝐴)𝐱	𝐴)𝐱	NOUN
biomedich-48	81	1	=	=	SYM
biomedich-48	81	2	0	0	NUM
biomedich-48	81	3	,	,	PUNCT
biomedich-48	81	4	obtained	obtain	VERB
biomedich-48	81	5	if	if	SCONJ
biomedich-48	81	6	and	and	CCONJ
biomedich-48	82	1	only	only	ADV
biomedich-48	82	2	if	if	SCONJ
biomedich-48	82	3	det	det	PROPN
biomedich-48	82	4	(	(	PUNCT
biomedich-48	82	5	𝜆𝐼	𝜆𝐼	NOUN
biomedich-48	82	6	−	−	NOUN
biomedich-48	82	7	𝐴)𝐱	𝐴)𝐱	NOUN
biomedich-48	82	8	=	=	NOUN
biomedich-48	82	9	0	0	NUM
biomedich-48	82	10	.	.	PUNCT
biomedich-48	83	1	the	the	DET
biomedich-48	83	2	equation	equation	NOUN
biomedich-48	83	3	of	of	ADP
biomedich-48	83	4	det	det	PROPN
biomedich-48	83	5	(	(	PUNCT
biomedich-48	83	6	𝜆𝐼	𝜆𝐼	NOUN
biomedich-48	83	7	−	−	NOUN
biomedich-48	83	8	𝐴)𝐱	𝐴)𝐱	NOUN
biomedich-48	84	1	=	=	SYM
biomedich-48	84	2	0	0	NUM
biomedich-48	84	3	is	be	AUX
biomedich-48	84	4	called	call	VERB
biomedich-48	84	5	the	the	DET
biomedich-48	84	6	characteristic	characteristic	ADJ
biomedich-48	84	7	equation	equation	NOUN
biomedich-48	84	8	of	of	ADP
biomedich-48	84	9	a	a	PRON
biomedich-48	84	10	;	;	PUNCT
biomedich-48	84	11	the	the	DET
biomedich-48	84	12	scalar	scalar	NOUN
biomedich-48	84	13	that	that	PRON
biomedich-48	84	14	satisfies	satisfy	VERB
biomedich-48	84	15	this	this	DET
biomedich-48	84	16	equation	equation	NOUN
biomedich-48	84	17	is	be	AUX
biomedich-48	84	18	the	the	DET
biomedich-48	84	19	eigenvalue	eigenvalue	NOUN
biomedich-48	84	20	of	of	ADP
biomedich-48	84	21	a.	a.	NOUN
biomedich-48	84	22	when	when	SCONJ
biomedich-48	84	23	expanded	expand	VERB
biomedich-48	84	24	,	,	PUNCT
biomedich-48	84	25	then	then	ADV
biomedich-48	84	26	det	det	PROPN
biomedich-48	84	27	(	(	PUNCT
biomedich-48	84	28	λi	λi	NOUN
biomedich-48	84	29	-	-	PUNCT
biomedich-48	84	30	a	a	PRON
biomedich-48	84	31	)	)	PUNCT
biomedich-48	84	32	is	be	AUX
biomedich-48	84	33	a	a	DET
biomedich-48	84	34	polynomial	polynomial	ADJ
biomedich-48	84	35	p	p	NOUN
biomedich-48	84	36	in	in	ADP
biomedich-48	84	37	a	a	DET
biomedich-48	84	38	variable	variable	NOUN
biomedich-48	84	39	called	call	VERB
biomedich-48	84	40	characteristic	characteristic	ADJ
biomedich-48	84	41	polynomial	polynomial	NOUN
biomedich-48	84	42	of	of	ADP
biomedich-48	84	43	a.	a.	NOUN
biomedich-48	84	44	the	the	DET
biomedich-48	84	45	characteristic	characteristic	ADJ
biomedich-48	84	46	polynomial	polynomial	ADJ
biomedich-48	84	47	𝑝(𝑥	𝑝(𝑥	NOUN
biomedich-48	84	48	)	)	PUNCT
biomedich-48	84	49	of	of	ADP
biomedich-48	84	50	an	an	DET
biomedich-48	84	51	nxn	nxn	NOUN
biomedich-48	84	52	matrix	matrix	NOUN
biomedich-48	84	53	has	have	VERB
biomedich-48	84	54	the	the	DET
biomedich-48	84	55	form	form	NOUN
biomedich-48	84	56	:	:	PUNCT
biomedich-48	84	57	𝑝(𝜆	𝑝(𝜆	NOUN
biomedich-48	84	58	)	)	PUNCT
biomedich-48	84	59	=	=	SYM
biomedich-48	84	60	det(𝜆𝐼	det(𝜆𝐼	NOUN
biomedich-48	84	61	−	−	PROPN
biomedich-48	84	62	𝐴	𝐴	PROPN
biomedich-48	84	63	)	)	PUNCT
biomedich-48	84	64	=	=	PUNCT
biomedich-48	85	1	𝜆𝑛	𝜆𝑛	PROPN
biomedich-48	85	2	+	+	NUM
biomedich-48	85	3	𝐶1𝜆	𝐶1𝜆	PROPN
biomedich-48	85	4	𝑛−1	𝑛−1	PROPN
biomedich-48	85	5	+	+	NUM
biomedich-48	85	6	⋯+	⋯+	NOUN
biomedich-48	86	1	𝐶𝑛	𝐶𝑛	DET
biomedich-48	86	2	diagonalization	diagonalization	NOUN
biomedich-48	86	3	of	of	ADP
biomedich-48	86	4	the	the	DET
biomedich-48	86	5	matrix	matrix	NOUN
biomedich-48	86	6	according	accord	VERB
biomedich-48	86	7	to	to	ADP
biomedich-48	86	8	anton	anton	PROPN
biomedich-48	86	9	,	,	PUNCT
biomedich-48	86	10	h	h	PROPN
biomedich-48	86	11	&	&	CCONJ
biomedich-48	86	12	rorres	rorre	NOUN
biomedich-48	86	13	,	,	PUNCT
biomedich-48	86	14	c	c	PROPN
biomedich-48	86	15	(	(	PUNCT
biomedich-48	86	16	2004	2004	NUM
biomedich-48	86	17	,	,	PUNCT
biomedich-48	86	18	p.74	p.74	PROPN
biomedich-48	86	19	)	)	PUNCT
biomedich-48	86	20	the	the	DET
biomedich-48	86	21	diagonal	diagonal	ADJ
biomedich-48	86	22	matrix	matrix	NOUN
biomedich-48	86	23	of	of	ADP
biomedich-48	86	24	a	a	DET
biomedich-48	86	25	square	square	ADJ
biomedich-48	86	26	matrix	matrix	NOUN
biomedich-48	86	27	whose	whose	DET
biomedich-48	86	28	entry	entry	NOUN
biomedich-48	86	29	does	do	AUX
biomedich-48	86	30	not	not	PART
biomedich-48	86	31	lie	lie	VERB
biomedich-48	86	32	in	in	ADP
biomedich-48	86	33	the	the	DET
biomedich-48	86	34	main	main	ADJ
biomedich-48	86	35	diagonal	diagonal	NOUN
biomedich-48	86	36	is	be	AUX
biomedich-48	86	37	zero	zero	NUM
biomedich-48	86	38	is	be	AUX
biomedich-48	86	39	called	call	VERB
biomedich-48	86	40	the	the	DET
biomedich-48	86	41	diagonal	diagonal	ADJ
biomedich-48	86	42	matrix	matrix	NOUN
biomedich-48	86	43	.	.	PUNCT
biomedich-48	87	1	a	a	DET
biomedich-48	87	2	common	common	ADJ
biomedich-48	87	3	diagonal	diagonal	ADJ
biomedich-48	87	4	matrix	matrix	NOUN
biomedich-48	87	5	d	d	NOUN
biomedich-48	87	6	,	,	PUNCT
biomedich-48	87	7	n	n	NOUN
biomedich-48	87	8	x	x	SYM
biomedich-48	87	9	n	n	PRON
biomedich-48	87	10	can	can	AUX
biomedich-48	87	11	be	be	AUX
biomedich-48	87	12	written	write	VERB
biomedich-48	87	13	[	[	PUNCT
biomedich-48	87	14	𝑑1	𝑑1	NOUN
biomedich-48	87	15	0	0	PUNCT
biomedich-48	87	16	⋮	⋮	NOUN
biomedich-48	87	17	0	0	NUM
biomedich-48	87	18	0	0	NUM
biomedich-48	87	19	𝑑2	𝑑2	NOUN
biomedich-48	87	20	⋮	⋮	NOUN
biomedich-48	87	21	0	0	NUM
biomedich-48	88	1	⋯	⋯	NOUN
biomedich-48	89	1	⋯	⋯	PROPN
biomedich-48	89	2	⋯	⋯	ADP
biomedich-48	89	3	0	0	NOUN
biomedich-48	89	4	0	0	NUM
biomedich-48	89	5	⋮	⋮	NOUN
biomedich-48	89	6	𝑑𝑛	𝑑𝑛	X
biomedich-48	89	7	]	]	PUNCT
biomedich-48	89	8	a	a	DET
biomedich-48	89	9	diagonal	diagonal	ADJ
biomedich-48	89	10	matrix	matrix	NOUN
biomedich-48	89	11	can	can	AUX
biomedich-48	89	12	be	be	AUX
biomedich-48	89	13	reversed	reverse	VERB
biomedich-48	89	14	,	,	PUNCT
biomedich-48	89	15	if	if	SCONJ
biomedich-48	89	16	and	and	CCONJ
biomedich-48	89	17	only	only	ADV
biomedich-48	89	18	if	if	SCONJ
biomedich-48	89	19	all	all	DET
biomedich-48	89	20	entries	entry	NOUN
biomedich-48	89	21	in	in	ADP
biomedich-48	89	22	the	the	DET
biomedich-48	89	23	main	main	ADJ
biomedich-48	89	24	diagonal	diagonal	ADJ
biomedich-48	89	25	position	position	NOUN
biomedich-48	89	26	are	be	AUX
biomedich-48	89	27	non	non	ADJ
biomedich-48	89	28	-	-	ADJ
biomedich-48	89	29	zero	zero	NUM
biomedich-48	89	30	;	;	PUNCT
biomedich-48	89	31	in	in	ADP
biomedich-48	89	32	this	this	DET
biomedich-48	89	33	case	case	NOUN
biomedich-48	89	34	the	the	DET
biomedich-48	89	35	inverse	inverse	NOUN
biomedich-48	89	36	of	of	ADP
biomedich-48	89	37	d	d	PROPN
biomedich-48	89	38	is	be	AUX
biomedich-48	89	39	𝐷−1	𝐷−1	ADJ
biomedich-48	89	40	=	=	PUNCT
biomedich-48	89	41	[	[	PUNCT
biomedich-48	89	42	1	1	NUM
biomedich-48	89	43	𝑑1⁄	𝑑1⁄	PROPN
biomedich-48	89	44	0	0	NUM
biomedich-48	89	45	⋮	⋮	NOUN
biomedich-48	89	46	0	0	NUM
biomedich-48	89	47	0	0	NUM
biomedich-48	89	48	1	1	NUM
biomedich-48	89	49	𝑑2⁄	𝑑2⁄	PROPN
biomedich-48	89	50	⋮	⋮	NOUN
biomedich-48	89	51	0	0	NUM
biomedich-48	90	1	⋯	⋯	NOUN
biomedich-48	90	2	⋯	⋯	PROPN
biomedich-48	90	3	⋯	⋯	ADP
biomedich-48	90	4	0	0	NOUN
biomedich-48	90	5	0	0	NUM
biomedich-48	90	6	⋮	⋮	NOUN
biomedich-48	90	7	1	1	NUM
biomedich-48	90	8	𝑑𝑛⁄	𝑑𝑛⁄	SYM
biomedich-48	90	9	]	]	PUNCT
biomedich-48	91	1	so	so	ADV
biomedich-48	91	2	,	,	PUNCT
biomedich-48	91	3	𝐷𝐷−1	𝐷𝐷−1	ADJ
biomedich-48	91	4	=	=	PUNCT
biomedich-48	91	5	𝐷−1𝐷	𝐷−1𝐷	PROPN
biomedich-48	91	6	=	=	SYM
biomedich-48	91	7	𝐼.	𝐼.	PROPN
biomedich-48	91	8	results	result	VERB
biomedich-48	91	9	and	and	CCONJ
biomedich-48	91	10	discussion	discussion	NOUN
biomedich-48	91	11	leslie	leslie	PROPN
biomedich-48	91	12	matrix	matrix	NOUN
biomedich-48	91	13	model	model	NOUN
biomedich-48	91	14	in	in	ADP
biomedich-48	91	15	population	population	NOUN
biomedich-48	91	16	growth	growth	NOUN
biomedich-48	91	17	in	in	ADP
biomedich-48	91	18	leslie	leslie	PROPN
biomedich-48	91	19	's	's	PART
biomedich-48	91	20	model	model	NOUN
biomedich-48	91	21	,	,	PUNCT
biomedich-48	91	22	women	woman	NOUN
biomedich-48	91	23	or	or	CCONJ
biomedich-48	91	24	females	female	NOUN
biomedich-48	91	25	are	be	AUX
biomedich-48	91	26	divided	divide	VERB
biomedich-48	91	27	over	over	ADP
biomedich-48	91	28	age	age	NOUN
biomedich-48	91	29	groups	group	NOUN
biomedich-48	91	30	that	that	PRON
biomedich-48	91	31	are	be	AUX
biomedich-48	91	32	timed	time	VERB
biomedich-48	91	33	together	together	ADV
biomedich-48	91	34	.	.	PUNCT
biomedich-48	92	1	specifically	specifically	ADV
biomedich-48	92	2	,	,	PUNCT
biomedich-48	92	3	uppose	uppose	VERB
biomedich-48	92	4	that	that	SCONJ
biomedich-48	92	5	the	the	DET
biomedich-48	92	6	maximum	maximum	ADJ
biomedich-48	92	7	age	age	NOUN
biomedich-48	92	8	reached	reach	VERB
biomedich-48	92	9	by	by	ADP
biomedich-48	92	10	any	any	DET
biomedich-48	92	11	woman	woman	NOUN
biomedich-48	92	12	or	or	CCONJ
biomedich-48	92	13	female	female	NOUN
biomedich-48	92	14	in	in	ADP
biomedich-48	92	15	the	the	DET
biomedich-48	92	16	population	population	NOUN
biomedich-48	92	17	is	be	AUX
biomedich-48	92	18	m	m	NOUN
biomedich-48	92	19	years	year	NOUN
biomedich-48	92	20	(	(	PUNCT
biomedich-48	92	21	or	or	CCONJ
biomedich-48	92	22	expressed	express	VERB
biomedich-48	92	23	in	in	ADP
biomedich-48	92	24	other	other	ADJ
biomedich-48	92	25	units	unit	NOUN
biomedich-48	92	26	of	of	ADP
biomedich-48	92	27	time	time	NOUN
biomedich-48	92	28	)	)	PUNCT
biomedich-48	92	29	and	and	CCONJ
biomedich-48	92	30	then	then	ADV
biomedich-48	92	31	the	the	DET
biomedich-48	92	32	population	population	NOUN
biomedich-48	92	33	is	be	AUX
biomedich-48	92	34	divided	divide	VERB
biomedich-48	92	35	over	over	ADP
biomedich-48	92	36	n	n	PRON
biomedich-48	92	37	the	the	DET
biomedich-48	92	38	age	age	NOUN
biomedich-48	92	39	group	group	NOUN
biomedich-48	92	40	.	.	PUNCT
biomedich-48	93	1	so	so	ADV
biomedich-48	93	2	the	the	DET
biomedich-48	93	3	time	time	NOUN
biomedich-48	93	4	period	period	NOUN
biomedich-48	93	5	in	in	ADP
biomedich-48	93	6	each	each	DET
biomedich-48	93	7	group	group	NOUN
biomedich-48	93	8	m	m	PROPN
biomedich-48	93	9	/	/	SYM
biomedich-48	93	10	n	n	NUM
biomedich-48	93	11	years	year	NOUN
biomedich-48	93	12	.	.	PUNCT
biomedich-48	94	1	the	the	DET
biomedich-48	94	2	age	age	NOUN
biomedich-48	94	3	group	group	NOUN
biomedich-48	94	4	will	will	AUX
biomedich-48	94	5	be	be	AUX
biomedich-48	94	6	explained	explain	VERB
biomedich-48	94	7	by	by	ADP
biomedich-48	94	8	the	the	DET
biomedich-48	94	9	following	follow	VERB
biomedich-48	94	10	table	table	NOUN
biomedich-48	94	11	:	:	PUNCT
biomedich-48	94	12	table	table	NOUN
biomedich-48	94	13	1	1	NUM
biomedich-48	94	14	.	.	PUNCT
biomedich-48	94	15	age	age	NOUN
biomedich-48	94	16	group	group	NOUN
biomedich-48	94	17	of	of	ADP
biomedich-48	94	18	leslie	leslie	PROPN
biomedich-48	94	19	matrix	matrix	NOUN
biomedich-48	94	20	model	model	NOUN
biomedich-48	94	21	.	.	PUNCT
biomedich-48	95	1	age	age	NOUN
biomedich-48	95	2	group	group	NOUN
biomedich-48	95	3	age	age	NOUN
biomedich-48	95	4	interval	interval	NOUN
biomedich-48	95	5	1	1	NUM
biomedich-48	96	1	[	[	X
biomedich-48	96	2	0,m	0,m	NOUN
biomedich-48	96	3	/	/	SYM
biomedich-48	96	4	n	n	CCONJ
biomedich-48	96	5	]	]	SYM
biomedich-48	96	6	2	2	NUM
biomedich-48	96	7	[	[	X
biomedich-48	96	8	m	m	NOUN
biomedich-48	96	9	/	/	SYM
biomedich-48	96	10	n,2m	n,2m	PROPN
biomedich-48	96	11	/	/	SYM
biomedich-48	96	12	n	n	CCONJ
biomedich-48	96	13	]	]	X
biomedich-48	96	14	3	3	NUM
biomedich-48	97	1	[	[	X
biomedich-48	97	2	2m	2m	NUM
biomedich-48	97	3	/	/	SYM
biomedich-48	97	4	n,3m	n,3m	PROPN
biomedich-48	97	5	/	/	SYM
biomedich-48	97	6	n	n	CCONJ
biomedich-48	97	7	]	]	PUNCT
biomedich-48	97	8	:	:	PUNCT
biomedich-48	97	9	:	:	PUNCT
biomedich-48	97	10	:	:	PUNCT
biomedich-48	97	11	:	:	PUNCT
biomedich-48	97	12	(	(	PUNCT
biomedich-48	97	13	n-1	n-1	NUM
biomedich-48	97	14	)	)	PUNCT
biomedich-48	98	1	[	[	X
biomedich-48	98	2	(	(	PUNCT
biomedich-48	98	3	n-2)2m	n-2)2m	ADJ
biomedich-48	98	4	/	/	SYM
biomedich-48	98	5	n,(n-1)m	n,(n-1)m	NOUN
biomedich-48	98	6	/	/	SYM
biomedich-48	98	7	n	n	CCONJ
biomedich-48	98	8	]	]	PUNCT
biomedich-48	98	9	n	n	PRON
biomedich-48	98	10	[	[	X
biomedich-48	98	11	(	(	PUNCT
biomedich-48	98	12	n-1)m	n-1)m	PROPN
biomedich-48	98	13	/	/	SYM
biomedich-48	98	14	n	n	CCONJ
biomedich-48	98	15	,	,	PUNCT
biomedich-48	98	16	m	m	VERB
biomedich-48	98	17	]	]	AUX
biomedich-48	98	18	for	for	ADP
biomedich-48	98	19	example	example	NOUN
biomedich-48	98	20	known	know	VERB
biomedich-48	98	21	to	to	ADP
biomedich-48	98	22	the	the	DET
biomedich-48	98	23	number	number	NOUN
biomedich-48	98	24	of	of	ADP
biomedich-48	98	25	women	woman	NOUN
biomedich-48	98	26	or	or	CCONJ
biomedich-48	98	27	females	female	NOUN
biomedich-48	98	28	in	in	ADP
biomedich-48	98	29	each	each	DET
biomedich-48	98	30	group	group	NOUN
biomedich-48	98	31	of	of	ADP
biomedich-48	98	32	to	to	ADP
biomedich-48	98	33	-	-	PUNCT
biomedich-48	98	34	n	n	NOUN
biomedich-48	98	35	group	group	NOUN
biomedich-48	98	36	at	at	ADP
biomedich-48	98	37	time	time	NOUN
biomedich-48	98	38	t	t	PROPN
biomedich-48	98	39	=	=	SYM
biomedich-48	98	40	0	0	X
biomedich-48	98	41	.	.	PUNCT
biomedich-48	98	42	specifically	specifically	ADV
biomedich-48	98	43	,	,	PUNCT
biomedich-48	98	44	for	for	ADP
biomedich-48	98	45	example	example	NOUN
biomedich-48	98	46	,	,	PUNCT
biomedich-48	98	47	there	there	PRON
biomedich-48	98	48	are	be	VERB
biomedich-48	98	49	x1	x1	PROPN
biomedich-48	98	50	(	(	PUNCT
biomedich-48	98	51	0	0	NUM
biomedich-48	98	52	)	)	PUNCT
biomedich-48	98	53	women	woman	NOUN
biomedich-48	98	54	or	or	CCONJ
biomedich-48	98	55	females	female	NOUN
biomedich-48	98	56	in	in	ADP
biomedich-48	98	57	the	the	DET
biomedich-48	98	58	first	first	ADJ
biomedich-48	98	59	group	group	NOUN
biomedich-48	98	60	,	,	PUNCT
biomedich-48	98	61	x2	x2	PROPN
biomedich-48	98	62	(	(	PUNCT
biomedich-48	98	63	0	0	NUM
biomedich-48	98	64	)	)	PUNCT
biomedich-48	98	65	woman	woman	NOUN
biomedich-48	98	66	or	or	CCONJ
biomedich-48	98	67	female	female	ADJ
biomedich-48	98	68	in	in	ADP
biomedich-48	98	69	second	second	ADJ
biomedich-48	98	70	group	group	NOUN
biomedich-48	98	71	,	,	PUNCT
biomedich-48	98	72	x3	x3	PROPN
biomedich-48	98	73	(	(	PUNCT
biomedich-48	98	74	0	0	NUM
biomedich-48	98	75	)	)	PUNCT
biomedich-48	98	76	woman	woman	NOUN
biomedich-48	98	77	or	or	CCONJ
biomedich-48	98	78	female	female	ADJ
biomedich-48	98	79	in	in	ADP
biomedich-48	98	80	the	the	DET
biomedich-48	98	81	third	third	ADJ
biomedich-48	98	82	group	group	NOUN
biomedich-48	98	83	,	,	PUNCT
biomedich-48	98	84	and	and	CCONJ
biomedich-48	98	85	so	so	ADV
biomedich-48	98	86	on	on	ADV
biomedich-48	98	87	.	.	PUNCT
biomedich-48	99	1	with	with	ADP
biomedich-48	99	2	the	the	DET
biomedich-48	99	3	number	number	NOUN
biomedich-48	99	4	ke	ke	NOUN
biomedich-48	99	5	-	-	PUNCT
biomedich-48	99	6	n	n	NOUN
biomedich-48	99	7	will	will	AUX
biomedich-48	99	8	be	be	AUX
biomedich-48	99	9	formed	form	VERB
biomedich-48	99	10	a	a	DET
biomedich-48	99	11	column	column	NOUN
biomedich-48	99	12	vector	vector	NOUN
biomedich-48	99	13	x(0	x(0	PROPN
biomedich-48	99	14	)	)	PUNCT
biomedich-48	99	15	that	that	PRON
biomedich-48	99	16	is	be	AUX
biomedich-48	99	17	:	:	PUNCT
biomedich-48	99	18	𝐱(0	𝐱(0	ADJ
biomedich-48	99	19	)	)	PUNCT
biomedich-48	99	20	=	=	PROPN
biomedich-48	100	1	[	[	PUNCT
biomedich-48	100	2	𝑥1	𝑥1	NOUN
biomedich-48	100	3	(	(	PUNCT
biomedich-48	100	4	0	0	NUM
biomedich-48	100	5	)	)	PUNCT
biomedich-48	100	6	𝑥2	𝑥2	NOUN
biomedich-48	100	7	(	(	PUNCT
biomedich-48	100	8	0	0	NUM
biomedich-48	100	9	)	)	PUNCT
biomedich-48	100	10	⋮	⋮	NOUN
biomedich-48	100	11	𝑥(0	𝑥(0	PROPN
biomedich-48	100	12	)	)	PUNCT
biomedich-48	100	13	]	]	PUNCT
biomedich-48	101	1	this	this	DET
biomedich-48	101	2	vector	vector	NOUN
biomedich-48	101	3	is	be	AUX
biomedich-48	101	4	called	call	VERB
biomedich-48	101	5	the	the	DET
biomedich-48	101	6	age	age	NOUN
biomedich-48	101	7	distribution	distribution	NOUN
biomedich-48	101	8	vector	vector	NOUN
biomedich-48	101	9	of	of	ADP
biomedich-48	101	10	the	the	DET
biomedich-48	101	11	origin	origin	NOUN
biomedich-48	101	12	(	(	PUNCT
biomedich-48	101	13	initial	initial	ADJ
biomedich-48	101	14	age	age	NOUN
biomedich-48	101	15	distribution	distribution	NOUN
biomedich-48	101	16	vector	vector	NOUN
biomedich-48	101	17	)	)	PUNCT
biomedich-48	101	18	.	.	PUNCT
biomedich-48	102	1	over	over	ADP
biomedich-48	102	2	time	time	NOUN
biomedich-48	102	3	,	,	PUNCT
biomedich-48	102	4	the	the	DET
biomedich-48	102	5	number	number	NOUN
biomedich-48	102	6	of	of	ADP
biomedich-48	102	7	women	woman	NOUN
biomedich-48	102	8	or	or	CCONJ
biomedich-48	102	9	females	female	NOUN
biomedich-48	102	10	in	in	ADP
biomedich-48	102	11	each	each	DET
biomedich-48	102	12	group	group	NOUN
biomedich-48	102	13	of	of	ADP
biomedich-48	102	14	to	to	ADP
biomedich-48	102	15	–	–	PUNCT
biomedich-48	102	16	n	n	CCONJ
biomedich-48	102	17	the	the	DET
biomedich-48	102	18	group	group	NOUN
biomedich-48	102	19	will	will	AUX
biomedich-48	102	20	change	change	VERB
biomedich-48	102	21	due	due	ADP
biomedich-48	102	22	to	to	ADP
biomedich-48	102	23	three	three	NUM
biomedich-48	102	24	biological	biological	ADJ
biomedich-48	102	25	processes	process	NOUN
biomedich-48	102	26	,	,	PUNCT
biomedich-48	102	27	namely	namely	ADV
biomedich-48	102	28	:	:	PUNCT
biomedich-48	102	29	birth	birth	NOUN
biomedich-48	102	30	,	,	PUNCT
biomedich-48	102	31	death	death	NOUN
biomedich-48	102	32	and	and	CCONJ
biomedich-48	102	33	aging	aging	NOUN
biomedich-48	102	34	.	.	PUNCT
biomedich-48	103	1	by	by	ADP
biomedich-48	103	2	explaining	explain	VERB
biomedich-48	103	3	these	these	DET
biomedich-48	103	4	three	three	NUM
biomedich-48	103	5	processes	process	NOUN
biomedich-48	103	6	quantitatively	quantitatively	ADV
biomedich-48	103	7	,	,	PUNCT
biomedich-48	103	8	it	it	PRON
biomedich-48	103	9	can	can	AUX
biomedich-48	103	10	be	be	AUX
biomedich-48	103	11	seen	see	VERB
biomedich-48	103	12	how	how	SCONJ
biomedich-48	103	13	to	to	PART
biomedich-48	103	14	project	project	VERB
biomedich-48	103	15	the	the	DET
biomedich-48	103	16	vector	vector	NOUN
biomedich-48	103	17	of	of	ADP
biomedich-48	103	18	early	early	ADJ
biomedich-48	103	19	age	age	NOUN
biomedich-48	103	20	distribution	distribution	NOUN
biomedich-48	103	21	into	into	ADP
biomedich-48	103	22	the	the	DET
biomedich-48	103	23	future	future	NOUN
biomedich-48	103	24	.	.	PUNCT
biomedich-48	104	1	the	the	DET
biomedich-48	104	2	easiest	easy	ADJ
biomedich-48	104	3	way	way	NOUN
biomedich-48	104	4	to	to	PART
biomedich-48	104	5	learn	learn	VERB
biomedich-48	104	6	about	about	ADP
biomedich-48	104	7	the	the	DET
biomedich-48	104	8	aging	age	VERB
biomedich-48	104	9	process	process	NOUN
biomedich-48	104	10	is	be	AUX
biomedich-48	104	11	to	to	PART
biomedich-48	104	12	observe	observe	VERB
biomedich-48	104	13	the	the	DET
biomedich-48	104	14	population	population	NOUN
biomedich-48	104	15	at	at	ADP
biomedich-48	104	16	discrete	discrete	ADJ
biomedich-48	104	17	times	time	NOUN
biomedich-48	104	18	,	,	PUNCT
biomedich-48	104	19	say	say	VERB
biomedich-48	104	20	𝑡0	𝑡0	NOUN
biomedich-48	104	21	,	,	PUNCT
biomedich-48	104	22	𝑡1	𝑡1	NOUN
biomedich-48	104	23	,	,	PUNCT
biomedich-48	104	24	.	.	PUNCT
biomedich-48	104	25	.	.	PUNCT
biomedich-48	105	1	.	.	PUNCT
biomedich-48	106	1	,	,	PUNCT
biomedich-48	106	2	𝑡𝑘	𝑡𝑘	ADV
biomedich-48	106	3	,	,	PUNCT
biomedich-48	106	4	.	.	PUNCT
biomedich-48	106	5	...	...	PUNCT
biomedich-48	107	1	leslie	leslie	PROPN
biomedich-48	107	2	's	's	PART
biomedich-48	107	3	model	model	NOUN
biomedich-48	107	4	requires	require	VERB
biomedich-48	107	5	that	that	SCONJ
biomedich-48	107	6	the	the	DET
biomedich-48	107	7	time	time	NOUN
biomedich-48	107	8	span	span	NOUN
biomedich-48	107	9	between	between	ADP
biomedich-48	107	10	two	two	NUM
biomedich-48	107	11	consecutive	consecutive	ADJ
biomedich-48	107	12	observation	observation	NOUN
biomedich-48	107	13	times	time	NOUN
biomedich-48	107	14	is	be	AUX
biomedich-48	107	15	the	the	DET
biomedich-48	107	16	40	40	NUM
biomedich-48	107	17	biology	biology	NOUN
biomedich-48	107	18	,	,	PUNCT
biomedich-48	107	19	medicine	medicine	NOUN
biomedich-48	107	20	,	,	PUNCT
biomedich-48	107	21	&	&	CCONJ
biomedich-48	107	22	natural	natural	ADJ
biomedich-48	107	23	product	product	NOUN
biomedich-48	107	24	chemistry	chemistry	NOUN
biomedich-48	107	25	6	6	NUM
biomedich-48	107	26	(	(	PUNCT
biomedich-48	107	27	2	2	NUM
biomedich-48	107	28	)	)	PUNCT
biomedich-48	107	29	,	,	PUNCT
biomedich-48	107	30	2017	2017	NUM
biomedich-48	107	31	:	:	PUNCT
biomedich-48	107	32	37	37	NUM
biomedich-48	107	33	-	-	SYM
biomedich-48	107	34	45	45	NUM
biomedich-48	107	35	same	same	ADJ
biomedich-48	107	36	as	as	ADP
biomedich-48	107	37	the	the	DET
biomedich-48	107	38	time	time	NOUN
biomedich-48	107	39	period	period	NOUN
biomedich-48	107	40	of	of	ADP
biomedich-48	107	41	the	the	DET
biomedich-48	107	42	hose	hose	NOUN
biomedich-48	107	43	(	(	PUNCT
biomedich-48	107	44	interval	interval	NOUN
biomedich-48	107	45	)	)	PUNCT
biomedich-48	107	46	age	age	NOUN
biomedich-48	107	47	,	,	PUNCT
biomedich-48	107	48	and	and	CCONJ
biomedich-48	107	49	is	be	AUX
biomedich-48	107	50	written	write	VERB
biomedich-48	107	51	as	as	SCONJ
biomedich-48	107	52	follows	follow	VERB
biomedich-48	107	53	:	:	PUNCT
biomedich-48	107	54	𝑡0	𝑡0	PROPN
biomedich-48	107	55	=	=	SYM
biomedich-48	107	56	0	0	NUM
biomedich-48	107	57	,	,	PUNCT
biomedich-48	107	58	𝑡1	𝑡1	NOUN
biomedich-48	107	59	=	=	SYM
biomedich-48	107	60	𝑀	𝑀	PROPN
biomedich-48	107	61	𝑛⁄	𝑛⁄	PROPN
biomedich-48	107	62	,	,	PUNCT
biomedich-48	107	63	𝑡2	𝑡2	NOUN
biomedich-48	107	64	=	=	PUNCT
biomedich-48	107	65	2𝑀	2𝑀	PROPN
biomedich-48	107	66	𝑛⁄	𝑛⁄	PROPN
biomedich-48	107	67	,	,	PUNCT
biomedich-48	107	68	to	to	ADP
biomedich-48	107	69	𝑡𝑘	𝑡𝑘	ADV
biomedich-48	108	1	=	=	PUNCT
biomedich-48	108	2	𝑘𝑀	𝑘𝑀	NOUN
biomedich-48	108	3	𝑛⁄	𝑛⁄	NOUN
biomedich-48	108	4	with	with	ADP
biomedich-48	108	5	this	this	DET
biomedich-48	108	6	assumption	assumption	NOUN
biomedich-48	108	7	,	,	PUNCT
biomedich-48	108	8	all	all	DET
biomedich-48	108	9	women	woman	NOUN
biomedich-48	108	10	or	or	CCONJ
biomedich-48	108	11	females	female	NOUN
biomedich-48	108	12	in	in	ADP
biomedich-48	108	13	the	the	DET
biomedich-48	108	14	group-(𝑖	group-(𝑖	PROPN
biomedich-48	108	15	+	+	NOUN
biomedich-48	108	16	1	1	NUM
biomedich-48	108	17	)	)	PUNCT
biomedich-48	108	18	at	at	ADP
biomedich-48	108	19	𝑡𝑘+1	𝑡𝑘+1	NOUN
biomedich-48	108	20	time	time	NOUN
biomedich-48	108	21	have	have	AUX
biomedich-48	108	22	been	be	AUX
biomedich-48	108	23	in	in	ADP
biomedich-48	108	24	group	group	NOUN
biomedich-48	108	25	to	to	ADP
biomedich-48	108	26	-	-	PUNCT
biomedich-48	108	27	i	i	PRON
biomedich-48	108	28	at	at	ADP
biomedich-48	108	29	time	time	NOUN
biomedich-48	108	30	𝑡𝑘.	𝑡𝑘.	VERB
biomedich-48	108	31	the	the	DET
biomedich-48	108	32	process	process	NOUN
biomedich-48	108	33	of	of	ADP
biomedich-48	108	34	birth	birth	NOUN
biomedich-48	108	35	and	and	CCONJ
biomedich-48	108	36	death	death	NOUN
biomedich-48	108	37	processes	process	NOUN
biomedich-48	108	38	between	between	ADP
biomedich-48	108	39	two	two	NUM
biomedich-48	108	40	consecutive	consecutive	ADJ
biomedich-48	108	41	observation	observation	NOUN
biomedich-48	108	42	times	time	NOUN
biomedich-48	108	43	can	can	AUX
biomedich-48	108	44	be	be	AUX
biomedich-48	108	45	explained	explain	VERB
biomedich-48	108	46	using	use	VERB
biomedich-48	108	47	demographic	demographic	ADJ
biomedich-48	108	48	parameters	parameter	NOUN
biomedich-48	108	49	.	.	PUNCT
biomedich-48	109	1	as	as	SCONJ
biomedich-48	109	2	follows	follow	VERB
biomedich-48	109	3	:	:	PUNCT
biomedich-48	109	4	table	table	NOUN
biomedich-48	109	5	2	2	NUM
biomedich-48	109	6	.	.	PUNCT
biomedich-48	110	1	parameters	parameter	NOUN
biomedich-48	110	2	in	in	ADP
biomedich-48	110	3	leslie	leslie	PROPN
biomedich-48	110	4	matrix	matrix	NOUN
biomedich-48	110	5	model	model	NOUN
biomedich-48	110	6	.	.	PUNCT
biomedich-48	111	1	parameter	parameter	PROPN
biomedich-48	111	2	model	model	NOUN
biomedich-48	111	3	information	information	NOUN
biomedich-48	111	4	𝑎𝑖	𝑎𝑖	ADP
biomedich-48	111	5	𝑖	𝑖	NOUN
biomedich-48	111	6	=	=	SYM
biomedich-48	111	7	1,2	1,2	NUM
biomedich-48	111	8	,	,	PUNCT
biomedich-48	111	9	…	…	PUNCT
biomedich-48	111	10	,	,	PUNCT
biomedich-48	111	11	𝑛	𝑛	DET
biomedich-48	111	12	average	average	ADJ
biomedich-48	111	13	number	number	NOUN
biomedich-48	111	14	of	of	ADP
biomedich-48	111	15	girls	girl	NOUN
biomedich-48	111	16	who	who	PRON
biomedich-48	111	17	was	be	AUX
biomedich-48	111	18	born	bear	VERB
biomedich-48	111	19	by	by	ADP
biomedich-48	111	20	a	a	DET
biomedich-48	111	21	woman	woman	NOUN
biomedich-48	111	22	during	during	ADP
biomedich-48	111	23	her	her	PRON
biomedich-48	111	24	time	time	NOUN
biomedich-48	111	25	in	in	ADP
biomedich-48	111	26	the	the	DET
biomedich-48	111	27	age	age	NOUN
biomedich-48	111	28	group	group	NOUN
biomedich-48	111	29	i.	i.	NOUN
biomedich-48	111	30	𝑏𝑖	𝑏𝑖	PROPN
biomedich-48	111	31	𝑖	𝑖	PROPN
biomedich-48	111	32	=	=	SYM
biomedich-48	111	33	1,2	1,2	NUM
biomedich-48	111	34	,	,	PUNCT
biomedich-48	111	35	…	…	PUNCT
biomedich-48	111	36	,	,	PUNCT
biomedich-48	111	37	𝑛	𝑛	DET
biomedich-48	111	38	the	the	DET
biomedich-48	111	39	number	number	NOUN
biomedich-48	111	40	of	of	ADP
biomedich-48	111	41	women	woman	NOUN
biomedich-48	111	42	in	in	ADP
biomedich-48	111	43	the	the	DET
biomedich-48	111	44	i	i	NOUN
biomedich-48	111	45	-	-	PUNCT
biomedich-48	111	46	age	age	NOUN
biomedich-48	111	47	group	group	NOUN
biomedich-48	111	48	who	who	PRON
biomedich-48	111	49	can	can	AUX
biomedich-48	111	50	be	be	AUX
biomedich-48	111	51	expected	expect	VERB
biomedich-48	111	52	is	be	AUX
biomedich-48	111	53	still	still	ADV
biomedich-48	111	54	alive	alive	ADJ
biomedich-48	111	55	and	and	CCONJ
biomedich-48	111	56	up	up	ADP
biomedich-48	111	57	to	to	ADP
biomedich-48	111	58	age	age	NOUN
biomedich-48	111	59	group	group	PROPN
biomedich-48	111	60	i.	i.	PROPN
biomedich-48	111	61	by	by	ADP
biomedich-48	111	62	defition	defition	NOUN
biomedich-48	111	63	,	,	PUNCT
biomedich-48	111	64	it	it	PRON
biomedich-48	111	65	will	will	AUX
biomedich-48	111	66	be	be	AUX
biomedich-48	111	67	obtained	obtain	VERB
biomedich-48	111	68	that	that	SCONJ
biomedich-48	111	69	(	(	PUNCT
biomedich-48	111	70	i	i	NOUN
biomedich-48	111	71	)	)	PUNCT
biomedich-48	111	72	𝑎𝑖	𝑎𝑖	ADP
biomedich-48	111	73	≥	≥	NOUN
biomedich-48	111	74	0	0	NUM
biomedich-48	111	75	for	for	ADP
biomedich-48	111	76	𝑖	𝑖	PRON
biomedich-48	111	77	=	=	SYM
biomedich-48	111	78	1,2	1,2	NUM
biomedich-48	111	79	,	,	PUNCT
biomedich-48	111	80	.	.	PUNCT
biomedich-48	111	81	.	.	PUNCT
biomedich-48	112	1	.	.	PUNCT
biomedich-48	113	1	,	,	PUNCT
biomedich-48	113	2	𝑛	𝑛	PROPN
biomedich-48	113	3	and	and	CCONJ
biomedich-48	113	4	(	(	PUNCT
biomedich-48	113	5	ii	ii	NOUN
biomedich-48	113	6	)	)	PUNCT
biomedich-48	113	7	0	0	PUNCT
biomedich-48	114	1	<	<	X
biomedich-48	114	2	𝑏𝑖	𝑏𝑖	ADP
biomedich-48	114	3	≤	≤	NUM
biomedich-48	114	4	1	1	NUM
biomedich-48	114	5	for	for	ADP
biomedich-48	114	6	𝑖	𝑖	PRON
biomedich-48	114	7	=	=	SYM
biomedich-48	114	8	1,2	1,2	NUM
biomedich-48	114	9	,	,	PUNCT
biomedich-48	114	10	.	.	PUNCT
biomedich-48	114	11	.	.	PUNCT
biomedich-48	115	1	.	.	PUNCT
biomedich-48	116	1	,	,	PUNCT
biomedich-48	116	2	𝑛	𝑛	DET
biomedich-48	116	3	−	−	NOUN
biomedich-48	116	4	1.can	1.can	AUX
biomedich-48	116	5	be	be	AUX
biomedich-48	116	6	seen	see	VERB
biomedich-48	116	7	that	that	SCONJ
biomedich-48	116	8	,	,	PUNCT
biomedich-48	116	9	should	should	AUX
biomedich-48	116	10	not	not	PART
biomedich-48	116	11	allow	allow	VERB
biomedich-48	116	12	for	for	ADP
biomedich-48	116	13	𝑏𝑖	𝑏𝑖	ADP
biomedich-48	116	14	which	which	PRON
biomedich-48	116	15	is	be	AUX
biomedich-48	116	16	equal	equal	ADJ
biomedich-48	116	17	to	to	ADP
biomedich-48	116	18	zero	zero	NUM
biomedich-48	116	19	,	,	PUNCT
biomedich-48	116	20	because	because	SCONJ
biomedich-48	116	21	if	if	SCONJ
biomedich-48	116	22	this	this	PRON
biomedich-48	116	23	happens	happen	VERB
biomedich-48	116	24	then	then	ADV
biomedich-48	116	25	there	there	PRON
biomedich-48	116	26	will	will	AUX
biomedich-48	116	27	be	be	AUX
biomedich-48	116	28	no	no	DET
biomedich-48	116	29	female	female	ADJ
biomedich-48	116	30	or	or	CCONJ
biomedich-48	116	31	female	female	ADJ
biomedich-48	116	32	alive	alive	ADJ
biomedich-48	116	33	after	after	ADP
biomedich-48	116	34	the	the	DET
biomedich-48	116	35	age	age	NOUN
biomedich-48	116	36	group	group	NOUN
biomedich-48	116	37	to	to	ADP
biomedich-48	116	38	-	-	PUNCT
biomedich-48	116	39	i.	i.	NOUN
biomedich-48	116	40	and	and	CCONJ
biomedich-48	116	41	also	also	ADV
biomedich-48	116	42	considered	consider	VERB
biomedich-48	116	43	that	that	SCONJ
biomedich-48	116	44	at	at	ADP
biomedich-48	116	45	least	least	ADJ
biomedich-48	116	46	there	there	PRON
biomedich-48	116	47	is	be	VERB
biomedich-48	116	48	one	one	NUM
biomedich-48	116	49	𝑎𝑖	𝑎𝑖	ADP
biomedich-48	116	50	positive	positive	ADJ
biomedich-48	116	51	that	that	PRON
biomedich-48	116	52	will	will	AUX
biomedich-48	116	53	occur	occur	VERB
biomedich-48	116	54	birth	birth	NOUN
biomedich-48	116	55	.	.	PUNCT
biomedich-48	117	1	each	each	DET
biomedich-48	117	2	age	age	NOUN
biomedich-48	117	3	group	group	NOUN
biomedich-48	117	4	in	in	ADP
biomedich-48	117	5	which	which	PRON
biomedich-48	117	6	the	the	DET
biomedich-48	117	7	corresponding	correspond	VERB
biomedich-48	117	8	value	value	NOUN
biomedich-48	117	9	𝑎𝑖	𝑎𝑖	PRON
biomedich-48	117	10	is	be	AUX
biomedich-48	117	11	positive	positive	ADJ
biomedich-48	117	12	is	be	AUX
biomedich-48	117	13	called	call	VERB
biomedich-48	117	14	the	the	DET
biomedich-48	117	15	fertile	fertile	ADJ
biomedich-48	117	16	age	age	NOUN
biomedich-48	117	17	group	group	NOUN
biomedich-48	117	18	(	(	PUNCT
biomedich-48	117	19	fertile	fertile	ADJ
biomedich-48	117	20	age	age	NOUN
biomedich-48	117	21	class	class	NOUN
biomedich-48	117	22	)	)	PUNCT
biomedich-48	117	23	.	.	PUNCT
biomedich-48	118	1	next	next	ADV
biomedich-48	118	2	we	we	PRON
biomedich-48	118	3	will	will	AUX
biomedich-48	118	4	define	define	VERB
biomedich-48	118	5	the	the	DET
biomedich-48	118	6	age	age	NOUN
biomedich-48	118	7	distribution	distribution	NOUN
biomedich-48	118	8	vector	vector	NOUN
biomedich-48	118	9	𝑥(𝑘	𝑥(𝑘	NOUN
biomedich-48	118	10	)	)	PUNCT
biomedich-48	118	11	at	at	ADP
biomedich-48	118	12	the	the	DET
biomedich-48	118	13	time	time	NOUN
biomedich-48	118	14	𝑡𝑘	𝑡𝑘	ADV
biomedich-48	118	15	with	with	ADP
biomedich-48	118	16	:	:	PUNCT
biomedich-48	118	17	𝐱(𝑘	𝐱(𝑘	VERB
biomedich-48	118	18	)	)	PUNCT
biomedich-48	119	1	=	=	PUNCT
biomedich-48	119	2	[	[	PUNCT
biomedich-48	119	3	𝑥1	𝑥1	NOUN
biomedich-48	119	4	(	(	PUNCT
biomedich-48	119	5	𝑘	𝑘	NOUN
biomedich-48	119	6	)	)	PUNCT
biomedich-48	119	7	𝑥2	𝑥2	NOUN
biomedich-48	119	8	(	(	PUNCT
biomedich-48	119	9	𝑘	𝑘	NOUN
biomedich-48	119	10	)	)	PUNCT
biomedich-48	119	11	⋮	⋮	NOUN
biomedich-48	119	12	𝑥(𝑘	𝑥(𝑘	NOUN
biomedich-48	119	13	)	)	PUNCT
biomedich-48	119	14	]	]	PUNCT
biomedich-48	119	15	where	where	SCONJ
biomedich-48	119	16	𝑥𝑖	𝑥𝑖	PROPN
biomedich-48	119	17	(	(	PUNCT
biomedich-48	119	18	𝑘	𝑘	NOUN
biomedich-48	119	19	)	)	PUNCT
biomedich-48	119	20	is	be	AUX
biomedich-48	119	21	the	the	DET
biomedich-48	119	22	number	number	NOUN
biomedich-48	119	23	of	of	ADP
biomedich-48	119	24	women	woman	NOUN
biomedich-48	119	25	or	or	CCONJ
biomedich-48	119	26	females	female	NOUN
biomedich-48	119	27	in	in	ADP
biomedich-48	119	28	the	the	DET
biomedich-48	119	29	i	i	NOUN
biomedich-48	119	30	-	-	PUNCT
biomedich-48	119	31	age	age	NOUN
biomedich-48	119	32	group	group	NOUN
biomedich-48	119	33	at	at	ADP
biomedich-48	119	34	the	the	DET
biomedich-48	119	35	time	time	NOUN
biomedich-48	119	36	𝑡𝑘.	𝑡𝑘.	NOUN
biomedich-48	119	37	at	at	ADP
biomedich-48	119	38	times	time	NOUN
biomedich-48	119	39	,	,	PUNCT
biomedich-48	119	40	women	woman	NOUN
biomedich-48	119	41	in	in	ADP
biomedich-48	119	42	the	the	DET
biomedich-48	119	43	first	first	ADJ
biomedich-48	119	44	age	age	NOUN
biomedich-48	119	45	group	group	NOUN
biomedich-48	119	46	are	be	AUX
biomedich-48	119	47	daughters	daughter	NOUN
biomedich-48	119	48	of	of	ADP
biomedich-48	119	49	women	woman	NOUN
biomedich-48	119	50	born	bear	VERB
biomedich-48	119	51	between	between	ADP
biomedich-48	119	52	time	time	NOUN
biomedich-48	119	53	𝑡𝑘−1	𝑡𝑘−1	PROPN
biomedich-48	119	54	and	and	CCONJ
biomedich-48	119	55	time	time	NOUN
biomedich-48	119	56	𝑡𝑘.	𝑡𝑘.	NOUN
biomedich-48	119	57	so	so	ADV
biomedich-48	119	58	,	,	PUNCT
biomedich-48	119	59	it	it	PRON
biomedich-48	119	60	can	can	AUX
biomedich-48	119	61	be	be	AUX
biomedich-48	119	62	written	write	VERB
biomedich-48	119	63	or	or	CCONJ
biomedich-48	119	64	mathematically	mathematically	ADV
biomedich-48	119	65	,	,	PUNCT
biomedich-48	119	66	𝑥1	𝑥1	NOUN
biomedich-48	119	67	(	(	PUNCT
biomedich-48	119	68	𝑘	𝑘	NOUN
biomedich-48	119	69	)	)	PUNCT
biomedich-48	119	70	=	=	SYM
biomedich-48	119	71	𝑎1𝑥1	𝑎1𝑥1	PROPN
biomedich-48	119	72	(	(	PUNCT
biomedich-48	119	73	𝑘−1	𝑘−1	PROPN
biomedich-48	119	74	)	)	PUNCT
biomedich-48	120	1	+	+	CCONJ
biomedich-48	121	1	𝑎2𝑥2	𝑎2𝑥2	VERB
biomedich-48	121	2	(	(	PUNCT
biomedich-48	121	3	𝑘−1	𝑘−1	PROPN
biomedich-48	121	4	)	)	PUNCT
biomedich-48	121	5	+	+	NUM
biomedich-48	121	6	⋯+	⋯+	NOUN
biomedich-48	121	7	𝑎𝑛𝑥𝑛	𝑎𝑛𝑥𝑛	NOUN
biomedich-48	121	8	(	(	PUNCT
biomedich-48	121	9	𝑘−1	𝑘−1	PROPN
biomedich-48	121	10	)	)	PUNCT
biomedich-48	121	11	(	(	PUNCT
biomedich-48	121	12	1	1	X
biomedich-48	121	13	)	)	PUNCT
biomedich-48	121	14	number	number	NOUN
biomedich-48	121	15	of	of	ADP
biomedich-48	121	16	women	woman	NOUN
biomedich-48	121	17	in	in	ADP
biomedich-48	121	18	the	the	DET
biomedich-48	121	19	age	age	NOUN
biomedich-48	121	20	group	group	NOUN
biomedich-48	121	21	to	to	ADP
biomedich-48	121	22	−(𝑖	−(𝑖	PROPN
biomedich-48	121	23	+	+	CCONJ
biomedich-48	121	24	1	1	X
biomedich-48	121	25	)	)	PUNCT
biomedich-48	121	26	(	(	PUNCT
biomedich-48	121	27	𝑖	𝑖	SYM
biomedich-48	121	28	=	=	SYM
biomedich-48	121	29	1	1	NUM
biomedich-48	121	30	,	,	PUNCT
biomedich-48	121	31	2	2	NUM
biomedich-48	121	32	,	,	PUNCT
biomedich-48	121	33	.	.	PUNCT
biomedich-48	121	34	.	.	PUNCT
biomedich-48	121	35	.	.	PUNCT
biomedich-48	122	1	,	,	PUNCT
biomedich-48	122	2	𝑛	𝑛	DET
biomedich-48	122	3	−	−	NOUN
biomedich-48	122	4	1	1	NUM
biomedich-48	122	5	)	)	PUNCT
biomedich-48	122	6	at	at	ADP
biomedich-48	122	7	the	the	DET
biomedich-48	122	8	time	time	NOUN
biomedich-48	122	9	𝑡𝑘	𝑡𝑘	ADV
biomedich-48	122	10	are	be	AUX
biomedich-48	122	11	women	woman	NOUN
biomedich-48	122	12	in	in	ADP
biomedich-48	122	13	groups	group	NOUN
biomedich-48	122	14	to	to	ADP
biomedich-48	122	15	−𝑖	−𝑖	VERB
biomedich-48	122	16	at	at	ADP
biomedich-48	122	17	the	the	DET
biomedich-48	122	18	time	time	NOUN
biomedich-48	122	19	𝑡𝑘−1	𝑡𝑘−1	PROPN
biomedich-48	122	20	who	who	PRON
biomedich-48	122	21	are	be	AUX
biomedich-48	122	22	still	still	ADV
biomedich-48	122	23	alive	alive	ADJ
biomedich-48	122	24	at	at	ADP
biomedich-48	122	25	the	the	DET
biomedich-48	122	26	time	time	NOUN
biomedich-48	122	27	𝑡𝑘.or	𝑡𝑘.or	ADJ
biomedich-48	122	28	mathematically	mathematically	ADV
biomedich-48	122	29	𝑥𝑖+1	𝑥𝑖+1	PROPN
biomedich-48	122	30	(	(	PUNCT
biomedich-48	122	31	𝑘	𝑘	NOUN
biomedich-48	122	32	)	)	PUNCT
biomedich-48	122	33	=	=	SYM
biomedich-48	123	1	𝑏𝑖𝑥𝑖	𝑏𝑖𝑥𝑖	NOUN
biomedich-48	123	2	(	(	PUNCT
biomedich-48	123	3	𝑘−1	𝑘−1	PROPN
biomedich-48	123	4	)	)	PUNCT
biomedich-48	123	5	,	,	PUNCT
biomedich-48	123	6	𝑖	𝑖	X
biomedich-48	123	7	=	=	SYM
biomedich-48	123	8	1,2	1,2	NUM
biomedich-48	123	9	,	,	PUNCT
biomedich-48	123	10	…	…	PUNCT
biomedich-48	123	11	,	,	PUNCT
biomedich-48	123	12	𝑛	𝑛	PRON
biomedich-48	123	13	−	−	NUM
biomedich-48	123	14	1	1	NUM
biomedich-48	123	15	(	(	PUNCT
biomedich-48	123	16	2	2	NUM
biomedich-48	123	17	)	)	PUNCT
biomedich-48	123	18	by	by	ADP
biomedich-48	123	19	using	use	VERB
biomedich-48	123	20	matrix	matrix	NOUN
biomedich-48	123	21	notation	notation	NOUN
biomedich-48	123	22	,	,	PUNCT
biomedich-48	123	23	equations	equation	NOUN
biomedich-48	123	24	(	(	PUNCT
biomedich-48	123	25	1	1	NUM
biomedich-48	123	26	)	)	PUNCT
biomedich-48	123	27	and	and	CCONJ
biomedich-48	123	28	(	(	PUNCT
biomedich-48	123	29	2	2	X
biomedich-48	123	30	)	)	PUNCT
biomedich-48	123	31	can	can	AUX
biomedich-48	123	32	be	be	AUX
biomedich-48	123	33	written	write	VERB
biomedich-48	123	34	in	in	ADP
biomedich-48	123	35	the	the	DET
biomedich-48	123	36	form	form	NOUN
biomedich-48	123	37	[	[	PUNCT
biomedich-48	123	38	𝑥1	𝑥1	NOUN
biomedich-48	123	39	(	(	PUNCT
biomedich-48	123	40	𝑘	𝑘	NOUN
biomedich-48	123	41	)	)	PUNCT
biomedich-48	123	42	𝑥2	𝑥2	NOUN
biomedich-48	123	43	(	(	PUNCT
biomedich-48	123	44	𝑘	𝑘	NOUN
biomedich-48	123	45	)	)	PUNCT
biomedich-48	123	46	𝑥3	𝑥3	NOUN
biomedich-48	123	47	(	(	PUNCT
biomedich-48	123	48	𝑘	𝑘	NOUN
biomedich-48	123	49	)	)	PUNCT
biomedich-48	123	50	⋮	⋮	NOUN
biomedich-48	123	51	𝑥𝑛	𝑥𝑛	PROPN
biomedich-48	123	52	(	(	PUNCT
biomedich-48	123	53	𝑘	𝑘	NOUN
biomedich-48	123	54	)	)	PUNCT
biomedich-48	123	55	]	]	PUNCT
biomedich-48	124	1	=	=	PUNCT
biomedich-48	124	2	[	[	PUNCT
biomedich-48	124	3	𝑎1	𝑎1	SCONJ
biomedich-48	124	4	𝑏1	𝑏1	ADJ
biomedich-48	124	5	0	0	NUM
biomedich-48	124	6	⋮	⋮	NOUN
biomedich-48	124	7	0	0	X
biomedich-48	125	1	𝑎2	𝑎2	NOUN
biomedich-48	125	2	0	0	NUM
biomedich-48	125	3	𝑏2	𝑏2	PROPN
biomedich-48	125	4	⋮	⋮	NOUN
biomedich-48	125	5	0	0	NUM
biomedich-48	126	1	𝑎3	𝑎3	ADJ
biomedich-48	126	2	0	0	SYM
biomedich-48	126	3	0	0	NUM
biomedich-48	126	4	⋮	⋮	NOUN
biomedich-48	126	5	0	0	NUM
biomedich-48	127	1	⋯	⋯	NOUN
biomedich-48	127	2	⋯	⋯	PROPN
biomedich-48	127	3	⋯	⋯	NOUN
biomedich-48	127	4	⋮	⋮	NOUN
biomedich-48	127	5	0	0	X
biomedich-48	128	1	𝑎𝑛−1	𝑎𝑛−1	PROPN
biomedich-48	128	2	0	0	NUM
biomedich-48	128	3	0	0	NUM
biomedich-48	128	4	⋮	⋮	NOUN
biomedich-48	128	5	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	128	6	𝑎𝑛	𝑎𝑛	VERB
biomedich-48	128	7	0	0	NUM
biomedich-48	128	8	0	0	NUM
biomedich-48	128	9	⋮	⋮	NOUN
biomedich-48	128	10	0	0	NUM
biomedich-48	128	11	]	]	PUNCT
biomedich-48	129	1	[	[	PUNCT
biomedich-48	129	2	𝑥1	𝑥1	NOUN
biomedich-48	129	3	(	(	PUNCT
biomedich-48	129	4	𝑘−1	𝑘−1	PROPN
biomedich-48	129	5	)	)	PUNCT
biomedich-48	129	6	𝑥2	𝑥2	NOUN
biomedich-48	129	7	(	(	PUNCT
biomedich-48	129	8	𝑘−1	𝑘−1	PROPN
biomedich-48	129	9	)	)	PUNCT
biomedich-48	129	10	𝑥3	𝑥3	NOUN
biomedich-48	129	11	(	(	PUNCT
biomedich-48	129	12	𝑘−1	𝑘−1	PROPN
biomedich-48	129	13	)	)	PUNCT
biomedich-48	129	14	⋮	⋮	NOUN
biomedich-48	129	15	𝑥𝑛	𝑥𝑛	PROPN
biomedich-48	130	1	(	(	PUNCT
biomedich-48	130	2	𝑘−1	𝑘−1	PROPN
biomedich-48	130	3	)	)	PUNCT
biomedich-48	130	4	]	]	PUNCT
biomedich-48	130	5	or	or	CCONJ
biomedich-48	130	6	more	more	ADV
biomedich-48	130	7	succinctly	succinctly	ADV
biomedich-48	130	8	𝐱(𝑘	𝐱(𝑘	VERB
biomedich-48	130	9	)	)	PUNCT
biomedich-48	130	10	=	=	SYM
biomedich-48	130	11	𝐿𝐱(𝑘−1	𝐿𝐱(𝑘−1	PROPN
biomedich-48	130	12	)	)	PUNCT
biomedich-48	130	13	,	,	PUNCT
biomedich-48	130	14	with	with	ADP
biomedich-48	130	15	𝑘	𝑘	PRON
biomedich-48	130	16	=	=	SYM
biomedich-48	130	17	1,2	1,2	NUM
biomedich-48	130	18	,	,	PUNCT
biomedich-48	130	19	…	…	PUNCT
biomedich-48	130	20	(	(	PUNCT
biomedich-48	130	21	3	3	X
biomedich-48	130	22	)	)	PUNCT
biomedich-48	130	23	where	where	SCONJ
biomedich-48	130	24	l	l	NOUN
biomedich-48	130	25	is	be	AUX
biomedich-48	130	26	leslie	leslie	PROPN
biomedich-48	130	27	matrix	matrix	NOUN
biomedich-48	130	28	𝐿	𝐿	NOUN
biomedich-48	130	29	=	=	SYM
biomedich-48	130	30	[	[	PUNCT
biomedich-48	130	31	𝑎1	𝑎1	SCONJ
biomedich-48	130	32	𝑏1	𝑏1	ADJ
biomedich-48	130	33	0	0	NUM
biomedich-48	130	34	⋮	⋮	NOUN
biomedich-48	130	35	0	0	X
biomedich-48	131	1	𝑎2	𝑎2	NOUN
biomedich-48	131	2	0	0	NUM
biomedich-48	131	3	𝑏2	𝑏2	PROPN
biomedich-48	131	4	⋮	⋮	NOUN
biomedich-48	131	5	0	0	NUM
biomedich-48	132	1	𝑎3	𝑎3	ADJ
biomedich-48	132	2	0	0	SYM
biomedich-48	132	3	0	0	NUM
biomedich-48	132	4	⋮	⋮	NOUN
biomedich-48	132	5	0	0	NUM
biomedich-48	133	1	⋯	⋯	NOUN
biomedich-48	133	2	⋯	⋯	PROPN
biomedich-48	133	3	⋯	⋯	NOUN
biomedich-48	133	4	⋮	⋮	NOUN
biomedich-48	133	5	0	0	X
biomedich-48	134	1	𝑎𝑛−1	𝑎𝑛−1	PROPN
biomedich-48	134	2	0	0	NUM
biomedich-48	134	3	0	0	NUM
biomedich-48	134	4	⋮	⋮	NOUN
biomedich-48	134	5	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	134	6	𝑎𝑛	𝑎𝑛	VERB
biomedich-48	134	7	0	0	NUM
biomedich-48	134	8	0	0	NUM
biomedich-48	134	9	⋮	⋮	NOUN
biomedich-48	134	10	0	0	NUM
biomedich-48	134	11	]	]	PUNCT
biomedich-48	134	12	(	(	PUNCT
biomedich-48	134	13	4	4	NUM
biomedich-48	134	14	)	)	PUNCT
biomedich-48	134	15	from	from	ADP
biomedich-48	134	16	the	the	DET
biomedich-48	134	17	equation	equation	NOUN
biomedich-48	134	18	(	(	PUNCT
biomedich-48	134	19	3	3	X
biomedich-48	134	20	)	)	PUNCT
biomedich-48	134	21	is	be	AUX
biomedich-48	134	22	found	find	VERB
biomedich-48	134	23	that	that	SCONJ
biomedich-48	134	24	𝐱(1	𝐱(1	PROPN
biomedich-48	134	25	)	)	PUNCT
biomedich-48	134	26	=	=	SYM
biomedich-48	134	27	𝐿𝐱(1	𝐿𝐱(1	PROPN
biomedich-48	134	28	)	)	PUNCT
biomedich-48	134	29	𝐱(2	𝐱(2	PROPN
biomedich-48	134	30	)	)	PUNCT
biomedich-48	134	31	=	=	SYM
biomedich-48	134	32	𝐿𝐱(1	𝐿𝐱(1	PROPN
biomedich-48	134	33	)	)	PUNCT
biomedich-48	134	34	=	=	SYM
biomedich-48	134	35	𝐿(2)𝐱(0	𝐿(2)𝐱(0	PROPN
biomedich-48	134	36	)	)	PUNCT
biomedich-48	134	37	𝐱(3	𝐱(3	PROPN
biomedich-48	134	38	)	)	PUNCT
biomedich-48	134	39	=	=	SYM
biomedich-48	134	40	𝐿𝐱(2	𝐿𝐱(2	NOUN
biomedich-48	134	41	)	)	PUNCT
biomedich-48	134	42	=	=	SYM
biomedich-48	134	43	𝐿(3)𝐱(0	𝐿(3)𝐱(0	ADJ
biomedich-48	134	44	)	)	PUNCT
biomedich-48	134	45	⋮	⋮	NOUN
biomedich-48	134	46	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	134	47	)	)	PUNCT
biomedich-48	134	48	=	=	SYM
biomedich-48	134	49	𝐿𝐱(𝑘−1	𝐿𝐱(𝑘−1	PROPN
biomedich-48	134	50	)	)	PUNCT
biomedich-48	135	1	=	=	SYM
biomedich-48	135	2	𝐿(𝑘)𝐱(0	𝐿(𝑘)𝐱(0	PROPN
biomedich-48	135	3	)	)	PUNCT
biomedich-48	135	4	(	(	PUNCT
biomedich-48	135	5	5	5	NUM
biomedich-48	135	6	)	)	PUNCT
biomedich-48	135	7	thus	thus	ADV
biomedich-48	135	8	,	,	PUNCT
biomedich-48	135	9	if	if	SCONJ
biomedich-48	135	10	we	we	PRON
biomedich-48	135	11	know	know	VERB
biomedich-48	135	12	the	the	DET
biomedich-48	135	13	start	start	NOUN
biomedich-48	135	14	age	age	NOUN
biomedich-48	135	15	distribution	distribution	NOUN
biomedich-48	135	16	𝐱(0	𝐱(0	PROPN
biomedich-48	135	17	)	)	PUNCT
biomedich-48	135	18	and	and	CCONJ
biomedich-48	135	19	leslie	leslie	PROPN
biomedich-48	135	20	matrix	matrix	NOUN
biomedich-48	135	21	l	l	NOUN
biomedich-48	135	22	,	,	PUNCT
biomedich-48	135	23	then	then	ADV
biomedich-48	135	24	we	we	PRON
biomedich-48	135	25	can	can	AUX
biomedich-48	135	26	determine	determine	VERB
biomedich-48	135	27	the	the	DET
biomedich-48	135	28	age	age	NOUN
biomedich-48	135	29	distribution	distribution	NOUN
biomedich-48	135	30	of	of	ADP
biomedich-48	135	31	women	woman	NOUN
biomedich-48	135	32	or	or	CCONJ
biomedich-48	135	33	females	female	NOUN
biomedich-48	135	34	at	at	ADP
biomedich-48	135	35	any	any	DET
biomedich-48	135	36	later	later	ADJ
biomedich-48	135	37	time	time	NOUN
biomedich-48	135	38	.	.	PUNCT
biomedich-48	136	1	limited	limited	ADJ
biomedich-48	136	2	age	age	NOUN
biomedich-48	136	3	distribution	distribution	NOUN
biomedich-48	136	4	although	although	SCONJ
biomedich-48	136	5	the	the	DET
biomedich-48	136	6	equation	equation	NOUN
biomedich-48	136	7	(	(	PUNCT
biomedich-48	136	8	5	5	X
biomedich-48	136	9	)	)	PUNCT
biomedich-48	136	10	gives	give	VERB
biomedich-48	136	11	the	the	DET
biomedich-48	136	12	age	age	NOUN
biomedich-48	136	13	distribution	distribution	NOUN
biomedich-48	136	14	of	of	ADP
biomedich-48	136	15	the	the	DET
biomedich-48	136	16	population	population	NOUN
biomedich-48	136	17	at	at	ADP
biomedich-48	136	18	any	any	DET
biomedich-48	136	19	given	give	VERB
biomedich-48	136	20	time	time	NOUN
biomedich-48	136	21	,	,	PUNCT
biomedich-48	136	22	it	it	PRON
biomedich-48	136	23	does	do	AUX
biomedich-48	136	24	not	not	PART
biomedich-48	136	25	immediately	immediately	ADV
biomedich-48	136	26	provide	provide	VERB
biomedich-48	136	27	an	an	DET
biomedich-48	136	28	overview	overview	NOUN
biomedich-48	136	29	of	of	ADP
biomedich-48	136	30	the	the	DET
biomedich-48	136	31	dynamics	dynamic	NOUN
biomedich-48	136	32	of	of	ADP
biomedich-48	136	33	the	the	DET
biomedich-48	136	34	anggreini	anggreini	NOUN
biomedich-48	136	35	–	–	PUNCT
biomedich-48	136	36	the	the	DET
biomedich-48	136	37	female	female	ADJ
biomedich-48	136	38	population	population	NOUN
biomedich-48	136	39	growth	growth	NOUN
biomedich-48	136	40	projection	projection	NOUN
biomedich-48	136	41	year	year	NOUN
biomedich-48	136	42	2021	2021	NUM
biomedich-48	136	43	in	in	ADP
biomedich-48	136	44	trenggalek	trenggalek	NOUN
biomedich-48	136	45	…	…	PUNCT
biomedich-48	136	46	41	41	NUM
biomedich-48	136	47	growth	growth	NOUN
biomedich-48	136	48	process	process	NOUN
biomedich-48	136	49	.	.	PUNCT
biomedich-48	137	1	it	it	PRON
biomedich-48	137	2	is	be	AUX
biomedich-48	137	3	necessary	necessary	ADJ
biomedich-48	137	4	to	to	PART
biomedich-48	137	5	investigate	investigate	VERB
biomedich-48	137	6	the	the	DET
biomedich-48	137	7	eigenvalues	eigenvalue	NOUN
biomedich-48	137	8	and	and	CCONJ
biomedich-48	137	9	eigenvectors	eigenvector	NOUN
biomedich-48	137	10	of	of	ADP
biomedich-48	137	11	leslie	leslie	PROPN
biomedich-48	137	12	's	's	PART
biomedich-48	137	13	matrix	matrix	NOUN
biomedich-48	137	14	.	.	PUNCT
biomedich-48	138	1	the	the	DET
biomedich-48	138	2	eigenvalues	eigenvalue	NOUN
biomedich-48	138	3	of	of	ADP
biomedich-48	138	4	l	l	NOUN
biomedich-48	138	5	are	be	AUX
biomedich-48	138	6	the	the	DET
biomedich-48	138	7	roots	root	NOUN
biomedich-48	138	8	of	of	ADP
biomedich-48	138	9	the	the	DET
biomedich-48	138	10	characteristic	characteristic	ADJ
biomedich-48	138	11	polynomial	polynomial	NOUN
biomedich-48	138	12	.	.	PUNCT
biomedich-48	139	1	the	the	DET
biomedich-48	139	2	characteristic	characteristic	ADJ
biomedich-48	139	3	polynomial	polynomial	NOUN
biomedich-48	139	4	of	of	ADP
biomedich-48	139	5	leslie	leslie	PROPN
biomedich-48	139	6	's	's	PART
biomedich-48	139	7	matrix	matrix	NOUN
biomedich-48	139	8	is	be	AUX
biomedich-48	139	9	𝑝(𝜆	𝑝(𝜆	PROPN
biomedich-48	139	10	)	)	PUNCT
biomedich-48	139	11	=	=	SYM
biomedich-48	140	1	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	140	2	−	−	NOUN
biomedich-48	140	3	𝑎1𝜆	𝑎1𝜆	PROPN
biomedich-48	140	4	𝑛−1	𝑛−1	PROPN
biomedich-48	140	5	−	−	NOUN
biomedich-48	140	6	𝑎2𝑏1𝜆	𝑎2𝑏1𝜆	NOUN
biomedich-48	141	1	𝑛−2	𝑛−2	PROPN
biomedich-48	141	2	−	−	NOUN
biomedich-48	141	3	𝑎3𝑏1𝑏2𝜆	𝑎3𝑏1𝑏2𝜆	PROPN
biomedich-48	141	4	𝑛−3	𝑛−3	PROPN
biomedich-48	141	5	⋯−	⋯−	PRON
biomedich-48	141	6	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	PROPN
biomedich-48	141	7	⋯𝑏𝑛−1	⋯𝑏𝑛−1	NOUN
biomedich-48	141	8	will	will	AUX
biomedich-48	141	9	be	be	AUX
biomedich-48	141	10	given	give	VERB
biomedich-48	141	11	the	the	DET
biomedich-48	141	12	theorems	theorem	NOUN
biomedich-48	141	13	related	relate	VERB
biomedich-48	141	14	to	to	ADP
biomedich-48	141	15	leslie	leslie	PROPN
biomedich-48	141	16	's	's	PART
biomedich-48	141	17	matrix	matrix	NOUN
biomedich-48	141	18	,	,	PUNCT
biomedich-48	141	19	as	as	SCONJ
biomedich-48	141	20	follows	follow	VERB
biomedich-48	141	21	:	:	PUNCT
biomedich-48	141	22	theorem	theorem	VERB
biomedich-48	141	23	1	1	NUM
biomedich-48	141	24	a	a	DET
biomedich-48	141	25	leslie	leslie	PROPN
biomedich-48	141	26	matrix	matrix	NOUN
biomedich-48	141	27	l	l	NOUN
biomedich-48	141	28	has	have	VERB
biomedich-48	141	29	a	a	DET
biomedich-48	141	30	unique	unique	ADJ
biomedich-48	141	31	positive	positive	ADJ
biomedich-48	141	32	eigen	eigen	NOUN
biomedich-48	141	33	value	value	NOUN
biomedich-48	141	34	𝜆1	𝜆1	NOUN
biomedich-48	141	35	.	.	PUNCT
biomedich-48	142	1	this	this	DET
biomedich-48	142	2	eigenvalue	eigenvalue	PROPN
biomedich-48	142	3	has	have	VERB
biomedich-48	142	4	a	a	DET
biomedich-48	142	5	multiplicity	multiplicity	NOUN
biomedich-48	142	6	of	of	ADP
biomedich-48	142	7	1	1	NUM
biomedich-48	142	8	and	and	CCONJ
biomedich-48	142	9	has	have	VERB
biomedich-48	142	10	an	an	DET
biomedich-48	142	11	eigenvector	eigenvector	NOUN
biomedich-48	142	12	𝐱1	𝐱1	NOUN
biomedich-48	142	13	that	that	PRON
biomedich-48	142	14	all	all	DET
biomedich-48	142	15	entries	entry	NOUN
biomedich-48	142	16	are	be	AUX
biomedich-48	142	17	positive	positive	ADJ
biomedich-48	142	18	.	.	PUNCT
biomedich-48	143	1	evidence	evidence	NOUN
biomedich-48	143	2	:	:	PUNCT
biomedich-48	143	3	(	(	PUNCT
biomedich-48	143	4	i	i	NOUN
biomedich-48	143	5	)	)	PUNCT
biomedich-48	143	6	the	the	DET
biomedich-48	143	7	leslie	leslie	PROPN
biomedich-48	143	8	matrix	matrix	NOUN
biomedich-48	143	9	l	l	NOUN
biomedich-48	143	10	has	have	VERB
biomedich-48	143	11	a	a	DET
biomedich-48	143	12	positive	positive	ADJ
biomedich-48	143	13	eigenvalue	eigenvalue	NOUN
biomedich-48	143	14	𝜆1	𝜆1	NOUN
biomedich-48	143	15	.	.	PUNCT
biomedich-48	144	1	the	the	DET
biomedich-48	144	2	eigenvalue	eigenvalue	PROPN
biomedich-48	144	3	is	be	AUX
biomedich-48	144	4	the	the	DET
biomedich-48	144	5	root	root	NOUN
biomedich-48	144	6	of	of	ADP
biomedich-48	144	7	the	the	DET
biomedich-48	144	8	characteristic	characteristic	ADJ
biomedich-48	144	9	equation	equation	NOUN
biomedich-48	144	10	,	,	PUNCT
biomedich-48	144	11	that	that	PRON
biomedich-48	144	12	is	be	AUX
biomedich-48	144	13	𝑝(𝜆	𝑝(𝜆	PROPN
biomedich-48	144	14	)	)	PUNCT
biomedich-48	144	15	=	=	SYM
biomedich-48	144	16	|𝜆𝐼	|𝜆𝐼	NOUN
biomedich-48	145	1	−	−	PROPN
biomedich-48	145	2	𝐿|	𝐿|	NOUN
biomedich-48	145	3	=	=	SYM
biomedich-48	145	4	0	0	NUM
biomedich-48	145	5	𝑝(𝜆	𝑝(𝜆	PROPN
biomedich-48	145	6	)	)	PUNCT
biomedich-48	145	7	=	=	SYM
biomedich-48	146	1	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	146	2	−	−	NOUN
biomedich-48	146	3	𝑎1𝜆	𝑎1𝜆	PROPN
biomedich-48	146	4	𝑛−1	𝑛−1	PROPN
biomedich-48	146	5	−	−	NOUN
biomedich-48	146	6	𝑎2𝑏1𝜆	𝑎2𝑏1𝜆	NOUN
biomedich-48	147	1	𝑛−2	𝑛−2	PROPN
biomedich-48	147	2	−	−	NOUN
biomedich-48	147	3	𝑎3𝑏1𝑏2𝜆	𝑎3𝑏1𝑏2𝜆	PROPN
biomedich-48	147	4	𝑛−3	𝑛−3	PROPN
biomedich-48	147	5	⋯−	⋯−	DET
biomedich-48	147	6	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	PROPN
biomedich-48	147	7	⋯𝑏𝑛−1	⋯𝑏𝑛−1	NOUN
biomedich-48	147	8	if	if	SCONJ
biomedich-48	147	9	𝑝(𝜆	𝑝(𝜆	NOUN
biomedich-48	147	10	)	)	PUNCT
biomedich-48	147	11	=	=	SYM
biomedich-48	147	12	0	0	NUM
biomedich-48	147	13	,	,	PUNCT
biomedich-48	147	14	so	so	ADV
biomedich-48	147	15	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	147	16	−	−	NUM
biomedich-48	147	17	𝑎1𝜆	𝑎1𝜆	PROPN
biomedich-48	147	18	𝑛−1	𝑛−1	PROPN
biomedich-48	147	19	−	−	NOUN
biomedich-48	147	20	𝑎2𝑏1𝜆	𝑎2𝑏1𝜆	NOUN
biomedich-48	147	21	𝑛−2	𝑛−2	PROPN
biomedich-48	147	22	−	−	NOUN
biomedich-48	147	23	𝑎3𝑏1𝑏2𝜆	𝑎3𝑏1𝑏2𝜆	PROPN
biomedich-48	147	24	𝑛−3	𝑛−3	PROPN
biomedich-48	147	25	⋯−	⋯−	DET
biomedich-48	147	26	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	147	27	⋯𝑏𝑛−1	⋯𝑏𝑛−1	NOUN
biomedich-48	147	28	=	=	SYM
biomedich-48	147	29	0	0	NUM
biomedich-48	147	30	(	(	PUNCT
biomedich-48	147	31	6	6	NUM
biomedich-48	147	32	)	)	PUNCT
biomedich-48	147	33	because	because	SCONJ
biomedich-48	147	34	one	one	NUM
biomedich-48	147	35	of	of	ADP
biomedich-48	147	36	the	the	DET
biomedich-48	147	37	roots	root	NOUN
biomedich-48	147	38	of	of	ADP
biomedich-48	147	39	the	the	DET
biomedich-48	147	40	equation	equation	NOUN
biomedich-48	147	41	(	(	PUNCT
biomedich-48	147	42	6	6	NUM
biomedich-48	147	43	)	)	PUNCT
biomedich-48	147	44	must	must	AUX
biomedich-48	147	45	be	be	AUX
biomedich-48	147	46	the	the	DET
biomedich-48	147	47	dividing	divide	VERB
biomedich-48	147	48	factor	factor	NOUN
biomedich-48	147	49	of	of	ADP
biomedich-48	147	50	the	the	DET
biomedich-48	147	51	coefficient	coefficient	NOUN
biomedich-48	147	52	𝑎𝑛𝑏1𝑏2⋯𝑏𝑛−1	𝑎𝑛𝑏1𝑏2⋯𝑏𝑛−1	NOUN
biomedich-48	147	53	,	,	PUNCT
biomedich-48	147	54	i.e	i.e	PROPN
biomedich-48	147	55	±𝑎𝑛	±𝑎𝑛	NOUN
biomedich-48	147	56	,	,	PUNCT
biomedich-48	147	57	±𝑏1	±𝑏1	PROPN
biomedich-48	147	58	,	,	PUNCT
biomedich-48	147	59	±𝑏2,⋯	±𝑏2,⋯	VERB
biomedich-48	147	60	,	,	PUNCT
biomedich-48	147	61	±𝑏𝑛−1	±𝑏𝑛−1	PROPN
biomedich-48	147	62	suppose	suppose	VERB
biomedich-48	147	63	that	that	SCONJ
biomedich-48	147	64	the	the	DET
biomedich-48	147	65	solution	solution	NOUN
biomedich-48	147	66	of	of	ADP
biomedich-48	147	67	one	one	NUM
biomedich-48	147	68	of	of	ADP
biomedich-48	147	69	the	the	DET
biomedich-48	147	70	divider	divid	ADJ
biomedich-48	147	71	factors	factor	NOUN
biomedich-48	147	72	,	,	PUNCT
biomedich-48	147	73	for	for	ADP
biomedich-48	147	74	example	example	NOUN
biomedich-48	147	75	,	,	PUNCT
biomedich-48	147	76	is	be	AUX
biomedich-48	147	77	taken	take	VERB
biomedich-48	147	78	𝑏1	𝑏1	NOUN
biomedich-48	147	79	>	>	X
biomedich-48	147	80	0	0	PUNCT
biomedich-48	148	1	as	as	ADP
biomedich-48	148	2	a	a	DET
biomedich-48	148	3	solution	solution	NOUN
biomedich-48	148	4	or	or	CCONJ
biomedich-48	148	5	𝑏1	𝑏1	NOUN
biomedich-48	148	6	as	as	ADP
biomedich-48	148	7	its	its	PRON
biomedich-48	148	8	root	root	NOUN
biomedich-48	148	9	,	,	PUNCT
biomedich-48	148	10	so	so	SCONJ
biomedich-48	148	11	the	the	DET
biomedich-48	148	12	equation	equation	NOUN
biomedich-48	148	13	(	(	PUNCT
biomedich-48	148	14	6	6	NUM
biomedich-48	148	15	)	)	PUNCT
biomedich-48	148	16	becomes	become	VERB
biomedich-48	148	17	𝑝(𝜆	𝑝(𝜆	NOUN
biomedich-48	148	18	)	)	PUNCT
biomedich-48	149	1	=	=	SYM
biomedich-48	150	1	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	150	2	−	−	NOUN
biomedich-48	150	3	𝑎1𝜆	𝑎1𝜆	PROPN
biomedich-48	150	4	𝑛−1	𝑛−1	PROPN
biomedich-48	150	5	−	−	NOUN
biomedich-48	150	6	𝑎2𝑏1𝜆	𝑎2𝑏1𝜆	NOUN
biomedich-48	151	1	𝑛−2	𝑛−2	PROPN
biomedich-48	151	2	−	−	NOUN
biomedich-48	151	3	𝑎3𝑏1𝑏2𝜆	𝑎3𝑏1𝑏2𝜆	PROPN
biomedich-48	151	4	𝑛−3	𝑛−3	PROPN
biomedich-48	151	5	⋯−	⋯−	DET
biomedich-48	151	6	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	151	7	⋯𝑏𝑛−1	⋯𝑏𝑛−1	NOUN
biomedich-48	151	8	=	=	NOUN
biomedich-48	151	9	0	0	NUM
biomedich-48	151	10	𝜆𝑛	𝜆𝑛	NOUN
biomedich-48	151	11	=	=	SYM
biomedich-48	151	12	𝑎1𝜆	𝑎1𝜆	PROPN
biomedich-48	151	13	𝑛−1	𝑛−1	PROPN
biomedich-48	151	14	+	+	CCONJ
biomedich-48	151	15	𝑎2𝑏1𝜆	𝑎2𝑏1𝜆	NUM
biomedich-48	151	16	𝑛−2	𝑛−2	PROPN
biomedich-48	151	17	+	+	CCONJ
biomedich-48	151	18	𝑎3𝑏1𝑏2𝜆	𝑎3𝑏1𝑏2𝜆	PROPN
biomedich-48	151	19	𝑛−3	𝑛−3	PROPN
biomedich-48	151	20	⋯+	⋯+	PUNCT
biomedich-48	151	21	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	PROPN
biomedich-48	151	22	⋯𝑏𝑛−1	⋯𝑏𝑛−1	NOUN
biomedich-48	151	23	(	(	PUNCT
biomedich-48	151	24	𝜆	𝜆	ADP
biomedich-48	151	25	−	−	PROPN
biomedich-48	151	26	𝑏1)(𝑎1𝜆	𝑏1)(𝑎1𝜆	PROPN
biomedich-48	151	27	𝑛−1	𝑛−1	PROPN
biomedich-48	151	28	+	+	CCONJ
biomedich-48	151	29	𝑎2𝑏1𝜆	𝑎2𝑏1𝜆	NUM
biomedich-48	151	30	𝑛−2	𝑛−2	PROPN
biomedich-48	151	31	+	+	NUM
biomedich-48	151	32	𝑎3𝑏1𝑏2𝜆	𝑎3𝑏1𝑏2𝜆	PROPN
biomedich-48	151	33	𝑛−3	𝑛−3	PROPN
biomedich-48	151	34	+	+	CCONJ
biomedich-48	151	35	⋯	⋯	PROPN
biomedich-48	151	36	+	+	PROPN
biomedich-48	151	37	𝑎𝑛𝑏2	𝑎𝑛𝑏2	NOUN
biomedich-48	151	38	⋯𝑏𝑛−1	⋯𝑏𝑛−1	NOUN
biomedich-48	151	39	)	)	PUNCT
biomedich-48	151	40	=	=	SYM
biomedich-48	151	41	𝜆𝑛	𝜆𝑛	NUM
biomedich-48	151	42	means	mean	NOUN
biomedich-48	151	43	obtained	obtain	VERB
biomedich-48	151	44	a	a	DET
biomedich-48	151	45	positive	positive	ADJ
biomedich-48	151	46	eigen	eigen	PROPN
biomedich-48	151	47	value	value	NOUN
biomedich-48	151	48	𝜆1	𝜆1	NOUN
biomedich-48	151	49	,	,	PUNCT
biomedich-48	151	50	that	that	PRON
biomedich-48	151	51	is	is	ADV
biomedich-48	151	52	𝜆1	𝜆1	ADJ
biomedich-48	151	53	=	=	SYM
biomedich-48	151	54	𝑏1	𝑏1	NOUN
biomedich-48	151	55	.	.	PUNCT
biomedich-48	152	1	it	it	PRON
biomedich-48	152	2	will	will	AUX
biomedich-48	152	3	then	then	ADV
biomedich-48	152	4	be	be	AUX
biomedich-48	152	5	proven	prove	VERB
biomedich-48	152	6	that	that	SCONJ
biomedich-48	152	7	leslie	leslie	PROPN
biomedich-48	152	8	matrix	matrix	NOUN
biomedich-48	152	9	l	l	NOUN
biomedich-48	152	10	has	have	VERB
biomedich-48	152	11	a	a	DET
biomedich-48	152	12	𝜆1	𝜆1	ADJ
biomedich-48	152	13	single	single	ADJ
biomedich-48	152	14	eigenvalue	eigenvalue	PROPN
biomedich-48	152	15	that	that	SCONJ
biomedich-48	152	16	single	single	ADJ
biomedich-48	152	17	,	,	PUNCT
biomedich-48	152	18	that	that	ADV
biomedich-48	152	19	is	is	ADV
biomedich-48	152	20	𝜆1	𝜆1	ADJ
biomedich-48	152	21	=	=	SYM
biomedich-48	152	22	𝑏1	𝑏1	NOUN
biomedich-48	152	23	.	.	PUNCT
biomedich-48	153	1	it	it	PRON
biomedich-48	153	2	will	will	AUX
biomedich-48	153	3	be	be	AUX
biomedich-48	153	4	assumed	assume	VERB
biomedich-48	153	5	that	that	SCONJ
biomedich-48	153	6	leslie	leslie	PROPN
biomedich-48	153	7	's	's	PART
biomedich-48	153	8	matrix	matrix	NOUN
biomedich-48	153	9	has	have	VERB
biomedich-48	153	10	another	another	DET
biomedich-48	153	11	positive	positive	ADJ
biomedich-48	153	12	eigenvalue	eigenvalue	NOUN
biomedich-48	153	13	.	.	PUNCT
biomedich-48	154	1	so	so	ADV
biomedich-48	154	2	to	to	PART
biomedich-48	154	3	prove	prove	VERB
biomedich-48	154	4	it	it	PRON
biomedich-48	154	5	used	use	VERB
biomedich-48	154	6	a	a	DET
biomedich-48	154	7	way	way	NOUN
biomedich-48	154	8	of	of	ADP
biomedich-48	154	9	contradiction	contradiction	NOUN
biomedich-48	154	10	.	.	PUNCT
biomedich-48	155	1	an	an	DET
biomedich-48	155	2	example	example	NOUN
biomedich-48	155	3	𝜆2	𝜆2	NOUN
biomedich-48	155	4	is	be	AUX
biomedich-48	155	5	another	another	DET
biomedich-48	155	6	positive	positive	ADJ
biomedich-48	155	7	eigenvalue	eigenvalue	NOUN
biomedich-48	155	8	assuming	assume	VERB
biomedich-48	155	9	𝜆1	𝜆1	NOUN
biomedich-48	155	10	≠	≠	PROPN
biomedich-48	155	11	𝜆2	𝜆2	NOUN
biomedich-48	155	12	or	or	CCONJ
biomedich-48	155	13	𝜆2	𝜆2	NOUN
biomedich-48	155	14	≠	≠	ADJ
biomedich-48	155	15	𝑏1	𝑏1	NOUN
biomedich-48	155	16	.	.	PUNCT
biomedich-48	156	1	is	be	AUX
biomedich-48	156	2	known	know	VERB
biomedich-48	156	3	𝑝(𝜆	𝑝(𝜆	PROPN
biomedich-48	156	4	)	)	PUNCT
biomedich-48	156	5	=	=	SYM
biomedich-48	157	1	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	157	2	−	−	NOUN
biomedich-48	157	3	𝑎1𝜆	𝑎1𝜆	PROPN
biomedich-48	157	4	𝑛−1	𝑛−1	PROPN
biomedich-48	157	5	−	−	NOUN
biomedich-48	157	6	𝑎2𝑏1𝜆	𝑎2𝑏1𝜆	NOUN
biomedich-48	158	1	𝑛−2	𝑛−2	PROPN
biomedich-48	158	2	−	−	NOUN
biomedich-48	158	3	𝑎3𝑏1𝑏2𝜆	𝑎3𝑏1𝑏2𝜆	PROPN
biomedich-48	158	4	𝑛−3	𝑛−3	PROPN
biomedich-48	158	5	⋯−	⋯−	DET
biomedich-48	158	6	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	PROPN
biomedich-48	158	7	⋯𝑏𝑛−1	⋯𝑏𝑛−1	NOUN
biomedich-48	158	8	if	if	SCONJ
biomedich-48	158	9	𝑝(𝜆	𝑝(𝜆	NOUN
biomedich-48	158	10	)	)	PUNCT
biomedich-48	158	11	=	=	SYM
biomedich-48	158	12	0	0	NUM
biomedich-48	158	13	,	,	PUNCT
biomedich-48	158	14	then	then	ADV
biomedich-48	158	15	,	,	PUNCT
biomedich-48	158	16	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	158	17	−	−	NUM
biomedich-48	158	18	𝑎1𝜆	𝑎1𝜆	PROPN
biomedich-48	158	19	𝑛−1	𝑛−1	PROPN
biomedich-48	158	20	−	−	NOUN
biomedich-48	158	21	𝑎2𝑏1𝜆	𝑎2𝑏1𝜆	NOUN
biomedich-48	159	1	𝑛−2	𝑛−2	PROPN
biomedich-48	159	2	−	−	NOUN
biomedich-48	159	3	𝑎3𝑏1𝑏2𝜆	𝑎3𝑏1𝑏2𝜆	PROPN
biomedich-48	159	4	𝑛−3	𝑛−3	PROPN
biomedich-48	159	5	⋯−	⋯−	DET
biomedich-48	159	6	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	159	7	⋯𝑏𝑛−1	⋯𝑏𝑛−1	NOUN
biomedich-48	159	8	=	=	NOUN
biomedich-48	159	9	0	0	SYM
biomedich-48	159	10	the	the	DET
biomedich-48	159	11	two	two	NUM
biomedich-48	159	12	segments	segment	NOUN
biomedich-48	159	13	are	be	AUX
biomedich-48	159	14	divided	divide	VERB
biomedich-48	159	15	by	by	ADP
biomedich-48	159	16	𝜆𝑛	𝜆𝑛	NOUN
biomedich-48	159	17	,	,	PUNCT
biomedich-48	159	18	be	be	VERB
biomedich-48	159	19	1	1	NUM
biomedich-48	159	20	=	=	SYM
biomedich-48	159	21	𝑎1	𝑎1	ADP
biomedich-48	159	22	𝜆	𝜆	PRON
biomedich-48	159	23	+	+	PROPN
biomedich-48	159	24	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	159	25	𝜆2	𝜆2	NOUN
biomedich-48	159	26	+	+	CCONJ
biomedich-48	159	27	𝑎3𝑏1𝑏2	𝑎3𝑏1𝑏2	PROPN
biomedich-48	159	28	𝜆3	𝜆3	NOUN
biomedich-48	159	29	+	+	CCONJ
biomedich-48	159	30	⋯+	⋯+	NOUN
biomedich-48	159	31	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	159	32	…	…	SYM
biomedich-48	159	33	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	159	34	𝜆𝑛	𝜆𝑛	NOUN
biomedich-48	159	35	so	so	ADV
biomedich-48	159	36	𝑞(𝜆	𝑞(𝜆	ADV
biomedich-48	159	37	)	)	PUNCT
biomedich-48	159	38	=	=	SYM
biomedich-48	159	39	1	1	NUM
biomedich-48	159	40	,	,	PUNCT
biomedich-48	159	41	for	for	ADP
biomedich-48	159	42	𝜆	𝜆	DET
biomedich-48	159	43	≠	≠	PROPN
biomedich-48	159	44	0	0	NUM
biomedich-48	159	45	or	or	CCONJ
biomedich-48	159	46	𝑞(𝜆	𝑞(𝜆	NUM
biomedich-48	159	47	)	)	PUNCT
biomedich-48	160	1	=	=	PUNCT
biomedich-48	160	2	𝑎1	𝑎1	ADP
biomedich-48	160	3	𝜆	𝜆	PRON
biomedich-48	160	4	+	+	PROPN
biomedich-48	160	5	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	160	6	𝜆2	𝜆2	NOUN
biomedich-48	160	7	+	+	CCONJ
biomedich-48	160	8	𝑎3𝑏1𝑏2	𝑎3𝑏1𝑏2	PROPN
biomedich-48	160	9	𝜆3	𝜆3	NOUN
biomedich-48	160	10	+	+	CCONJ
biomedich-48	160	11	⋯+	⋯+	NOUN
biomedich-48	160	12	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	160	13	…	…	SYM
biomedich-48	160	14	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	160	15	𝜆𝑛	𝜆𝑛	NOUN
biomedich-48	160	16	(	(	PUNCT
biomedich-48	160	17	7	7	X
biomedich-48	160	18	)	)	PUNCT
biomedich-48	160	19	proven	prove	VERB
biomedich-48	160	20	that	that	SCONJ
biomedich-48	160	21	𝜆1	𝜆1	NOUN
biomedich-48	160	22	and	and	CCONJ
biomedich-48	160	23	𝜆2	𝜆2	NOUN
biomedich-48	160	24	is	be	AUX
biomedich-48	160	25	the	the	DET
biomedich-48	160	26	solution	solution	NOUN
biomedich-48	160	27	of	of	ADP
biomedich-48	160	28	the	the	DET
biomedich-48	160	29	system	system	NOUN
biomedich-48	160	30	of	of	ADP
biomedich-48	160	31	equations	equation	NOUN
biomedich-48	160	32	𝑞(𝜆	𝑞(𝜆	ADV
biomedich-48	160	33	)	)	PUNCT
biomedich-48	160	34	=	=	SYM
biomedich-48	161	1	1	1	X
biomedich-48	161	2	.	.	PUNCT
biomedich-48	162	1	so	so	ADV
biomedich-48	162	2	get	get	VERB
biomedich-48	162	3	it	it	PRON
biomedich-48	162	4	𝑞(𝜆1	𝑞(𝜆1	NOUN
biomedich-48	162	5	)	)	PUNCT
biomedich-48	162	6	=	=	SYM
biomedich-48	162	7	1	1	NUM
biomedich-48	162	8	and	and	CCONJ
biomedich-48	162	9	𝑞(𝜆2	𝑞(𝜆2	ADJ
biomedich-48	162	10	)	)	PUNCT
biomedich-48	162	11	=	=	SYM
biomedich-48	162	12	1	1	NUM
biomedich-48	162	13	or	or	CCONJ
biomedich-48	162	14	𝑞(𝜆1	𝑞(𝜆1	NOUN
biomedich-48	162	15	)	)	PUNCT
biomedich-48	162	16	=	=	SYM
biomedich-48	162	17	𝑞(𝜆2	𝑞(𝜆2	ADJ
biomedich-48	162	18	)	)	PUNCT
biomedich-48	162	19	.	.	PUNCT
biomedich-48	163	1	then	then	ADV
biomedich-48	163	2	by	by	ADP
biomedich-48	163	3	using	use	VERB
biomedich-48	163	4	the	the	DET
biomedich-48	163	5	equation	equation	NOUN
biomedich-48	163	6	(	(	PUNCT
biomedich-48	163	7	7	7	NUM
biomedich-48	163	8	)	)	PUNCT
biomedich-48	163	9	,	,	PUNCT
biomedich-48	163	10	and	and	CCONJ
biomedich-48	163	11	if	if	SCONJ
biomedich-48	163	12	𝑞(𝜆1	𝑞(𝜆1	ADJ
biomedich-48	163	13	)	)	PUNCT
biomedich-48	163	14	=	=	SYM
biomedich-48	163	15	𝑞(𝜆2	𝑞(𝜆2	X
biomedich-48	163	16	)	)	PUNCT
biomedich-48	163	17	𝑎1	𝑎1	NOUN
biomedich-48	163	18	𝜆1	𝜆1	NOUN
biomedich-48	163	19	+	+	CCONJ
biomedich-48	163	20	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	163	21	𝜆1	𝜆1	NOUN
biomedich-48	163	22	2	2	NUM
biomedich-48	163	23	+	+	CCONJ
biomedich-48	163	24	𝑎3𝑏1𝑏2	𝑎3𝑏1𝑏2	NOUN
biomedich-48	163	25	𝜆1	𝜆1	NOUN
biomedich-48	163	26	3	3	NUM
biomedich-48	163	27	+	+	NUM
biomedich-48	163	28	⋯+	⋯+	NOUN
biomedich-48	163	29	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	163	30	…	…	PUNCT
biomedich-48	163	31	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	163	32	𝜆1	𝜆1	NOUN
biomedich-48	163	33	𝑛	𝑛	PRON
biomedich-48	164	1	=	=	PUNCT
biomedich-48	164	2	𝑎1	𝑎1	NOUN
biomedich-48	164	3	𝜆2	𝜆2	NOUN
biomedich-48	164	4	+	+	CCONJ
biomedich-48	164	5	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	164	6	𝜆2	𝜆2	NOUN
biomedich-48	164	7	2	2	NUM
biomedich-48	164	8	+	+	SYM
biomedich-48	164	9	𝑎3𝑏1𝑏2	𝑎3𝑏1𝑏2	PROPN
biomedich-48	164	10	𝜆2	𝜆2	NOUN
biomedich-48	164	11	3	3	NUM
biomedich-48	164	12	+	+	NOUN
biomedich-48	164	13	⋯+	⋯+	NOUN
biomedich-48	164	14	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	164	15	…	…	SYM
biomedich-48	164	16	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	164	17	𝜆2	𝜆2	NOUN
biomedich-48	164	18	𝑛	𝑛	NOUN
biomedich-48	164	19	if	if	SCONJ
biomedich-48	164	20	𝑞(𝜆1	𝑞(𝜆1	NOUN
biomedich-48	164	21	)	)	PUNCT
biomedich-48	164	22	deducted	deduct	VERB
biomedich-48	164	23	by	by	ADP
biomedich-48	164	24	𝑞(𝜆2	𝑞(𝜆2	ADJ
biomedich-48	164	25	)	)	PUNCT
biomedich-48	164	26	then	then	ADV
biomedich-48	164	27	𝑎1	𝑎1	INTJ
biomedich-48	164	28	(	(	PUNCT
biomedich-48	164	29	1	1	NUM
biomedich-48	164	30	𝜆1	𝜆1	NOUN
biomedich-48	164	31	−	−	PROPN
biomedich-48	164	32	1	1	NUM
biomedich-48	164	33	𝜆2	𝜆2	NOUN
biomedich-48	164	34	)	)	PUNCT
biomedich-48	164	35	+	+	PUNCT
biomedich-48	165	1	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	165	2	(	(	PUNCT
biomedich-48	165	3	1	1	NUM
biomedich-48	165	4	𝜆1	𝜆1	NOUN
biomedich-48	165	5	2	2	NUM
biomedich-48	165	6	−	−	NOUN
biomedich-48	165	7	1	1	NUM
biomedich-48	165	8	𝜆2	𝜆2	NOUN
biomedich-48	165	9	2	2	NUM
biomedich-48	165	10	)	)	PUNCT
biomedich-48	165	11	+	+	CCONJ
biomedich-48	165	12	𝑎2𝑏1𝑏2	𝑎2𝑏1𝑏2	ADJ
biomedich-48	165	13	(	(	PUNCT
biomedich-48	165	14	1	1	NUM
biomedich-48	165	15	𝜆1	𝜆1	NOUN
biomedich-48	165	16	3	3	NUM
biomedich-48	165	17	−	−	NOUN
biomedich-48	165	18	1	1	NUM
biomedich-48	165	19	𝜆2	𝜆2	NOUN
biomedich-48	165	20	3	3	NUM
biomedich-48	165	21	)	)	PUNCT
biomedich-48	165	22	+	+	NUM
biomedich-48	165	23	…	…	PUNCT
biomedich-48	165	24	+	+	NUM
biomedich-48	165	25	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	165	26	…	…	PUNCT
biomedich-48	165	27	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	165	28	(	(	PUNCT
biomedich-48	165	29	1	1	NUM
biomedich-48	165	30	𝜆1	𝜆1	NOUN
biomedich-48	165	31	𝑛	𝑛	DET
biomedich-48	165	32	−	−	NUM
biomedich-48	165	33	1	1	NUM
biomedich-48	165	34	𝜆2	𝜆2	NOUN
biomedich-48	165	35	𝑛	𝑛	NOUN
biomedich-48	165	36	)	)	PUNCT
biomedich-48	165	37	=	=	SYM
biomedich-48	165	38	0	0	X
biomedich-48	165	39	be	be	VERB
biomedich-48	165	40	𝑎1	𝑎1	PRON
biomedich-48	165	41	(	(	PUNCT
biomedich-48	165	42	𝜆2−𝜆1	𝜆2−𝜆1	NOUN
biomedich-48	165	43	𝜆1𝜆2	𝜆1𝜆2	X
biomedich-48	165	44	)	)	PUNCT
biomedich-48	166	1	+	+	CCONJ
biomedich-48	166	2	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	166	3	(	(	PUNCT
biomedich-48	166	4	𝜆2	𝜆2	NOUN
biomedich-48	166	5	2−𝜆1	2−𝜆1	NUM
biomedich-48	166	6	2	2	NUM
biomedich-48	166	7	𝜆1	𝜆1	NOUN
biomedich-48	166	8	2𝜆2	2𝜆2	NUM
biomedich-48	166	9	2	2	NUM
biomedich-48	166	10	)	)	PUNCT
biomedich-48	166	11	+	+	CCONJ
biomedich-48	166	12	𝑎2𝑏1𝑏2	𝑎2𝑏1𝑏2	ADJ
biomedich-48	166	13	(	(	PUNCT
biomedich-48	166	14	𝜆2	𝜆2	NOUN
biomedich-48	166	15	3−𝜆1	3−𝜆1	NUM
biomedich-48	166	16	3	3	NUM
biomedich-48	166	17	𝜆1	𝜆1	NOUN
biomedich-48	166	18	3𝜆2	3𝜆2	NUM
biomedich-48	166	19	3	3	NUM
biomedich-48	166	20	)	)	PUNCT
biomedich-48	166	21	+	+	CCONJ
biomedich-48	166	22	…	…	PUNCT
biomedich-48	166	23	+	+	NUM
biomedich-48	166	24	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	166	25	…	…	PUNCT
biomedich-48	166	26	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	166	27	(	(	PUNCT
biomedich-48	166	28	𝜆2	𝜆2	NOUN
biomedich-48	166	29	𝑛−𝜆1	𝑛−𝜆1	NOUN
biomedich-48	167	1	𝑛	𝑛	PRON
biomedich-48	167	2	𝜆1	𝜆1	VERB
biomedich-48	167	3	𝑛𝜆2	𝑛𝜆2	VERB
biomedich-48	167	4	𝑛	𝑛	ADP
biomedich-48	167	5	)	)	PUNCT
biomedich-48	168	1	=	=	SYM
biomedich-48	168	2	0	0	NUM
biomedich-48	169	1	or	or	CCONJ
biomedich-48	169	2	𝑎1	𝑎1	INTJ
biomedich-48	169	3	𝜆1𝜆2	𝜆1𝜆2	PROPN
biomedich-48	169	4	(	(	PUNCT
biomedich-48	169	5	𝜆2	𝜆2	NOUN
biomedich-48	169	6	−	−	PROPN
biomedich-48	169	7	𝜆1	𝜆1	PROPN
biomedich-48	169	8	)	)	PUNCT
biomedich-48	170	1	+	+	CCONJ
biomedich-48	170	2	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	170	3	𝜆1	𝜆1	NOUN
biomedich-48	170	4	2𝜆2	2𝜆2	NUM
biomedich-48	170	5	2	2	NUM
biomedich-48	170	6	(	(	PUNCT
biomedich-48	170	7	𝜆2	𝜆2	NOUN
biomedich-48	170	8	2	2	NUM
biomedich-48	170	9	−	−	NOUN
biomedich-48	170	10	𝜆1	𝜆1	NOUN
biomedich-48	170	11	2	2	NUM
biomedich-48	170	12	)	)	PUNCT
biomedich-48	170	13	+	+	CCONJ
biomedich-48	170	14	𝑎2𝑏1𝑏2	𝑎2𝑏1𝑏2	PROPN
biomedich-48	170	15	𝜆1	𝜆1	NOUN
biomedich-48	170	16	3𝜆2	3𝜆2	NUM
biomedich-48	170	17	3	3	NUM
biomedich-48	170	18	(	(	PUNCT
biomedich-48	170	19	𝜆2	𝜆2	NOUN
biomedich-48	170	20	3	3	NUM
biomedich-48	170	21	−	−	PROPN
biomedich-48	170	22	𝜆1	𝜆1	NOUN
biomedich-48	170	23	3	3	X
biomedich-48	170	24	)	)	PUNCT
biomedich-48	171	1	+	+	NOUN
biomedich-48	171	2	⋯+	⋯+	NOUN
biomedich-48	171	3	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	171	4	…	…	PUNCT
biomedich-48	171	5	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	171	6	𝜆1	𝜆1	NOUN
biomedich-48	171	7	𝑛𝜆2	𝑛𝜆2	VERB
biomedich-48	171	8	𝑛	𝑛	PROPN
biomedich-48	171	9	(	(	PUNCT
biomedich-48	171	10	𝜆2	𝜆2	NOUN
biomedich-48	171	11	𝑛	𝑛	PRON
biomedich-48	171	12	−	−	PROPN
biomedich-48	171	13	𝜆1	𝜆1	NOUN
biomedich-48	171	14	𝑛	𝑛	NOUN
biomedich-48	171	15	)	)	PUNCT
biomedich-48	171	16	=	=	SYM
biomedich-48	171	17	0	0	PUNCT
biomedich-48	172	1	(	(	PUNCT
biomedich-48	172	2	8)	8)	NUM
biomedich-48	172	3	the	the	DET
biomedich-48	172	4	equation	equation	NOUN
biomedich-48	172	5	(	(	PUNCT
biomedich-48	172	6	8)	8)	NUM
biomedich-48	172	7	will	will	AUX
biomedich-48	172	8	be	be	AUX
biomedich-48	172	9	valid	valid	ADJ
biomedich-48	172	10	if	if	SCONJ
biomedich-48	172	11	,	,	PUNCT
biomedich-48	172	12	𝜆1	𝜆1	NOUN
biomedich-48	172	13	=	=	SYM
biomedich-48	172	14	𝜆2	𝜆2	NOUN
biomedich-48	172	15	,	,	PUNCT
biomedich-48	172	16	or	or	CCONJ
biomedich-48	172	17	contradictory	contradictory	ADJ
biomedich-48	172	18	to	to	ADP
biomedich-48	172	19	,	,	PUNCT
biomedich-48	172	20	the	the	DET
biomedich-48	172	21	assumption	assumption	NOUN
biomedich-48	172	22	stating	state	VERB
biomedich-48	172	23	.	.	PUNCT
biomedich-48	173	1	𝜆1	𝜆1	VERB
biomedich-48	173	2	≠	≠	PROPN
biomedich-48	173	3	𝜆2	𝜆2	NOUN
biomedich-48	173	4	.	.	PUNCT
biomedich-48	174	1	so	so	ADV
biomedich-48	174	2	the	the	DET
biomedich-48	174	3	true	true	ADJ
biomedich-48	174	4	is	be	AUX
biomedich-48	174	5	the	the	DET
biomedich-48	174	6	positive	positive	ADJ
biomedich-48	174	7	eigenvalue	eigenvalue	NOUN
biomedich-48	174	8	of	of	ADP
biomedich-48	174	9	leslie	leslie	PROPN
biomedich-48	174	10	's	's	PART
biomedich-48	174	11	matrix	matrix	NOUN
biomedich-48	174	12	is	be	AUX
biomedich-48	174	13	singular	singular	ADJ
biomedich-48	174	14	,	,	PUNCT
biomedich-48	174	15	that	that	PRON
biomedich-48	174	16	is	be	AUX
biomedich-48	174	17	𝜆1	𝜆1	NOUN
biomedich-48	174	18	=	=	PUNCT
biomedich-48	174	19	𝜆2	𝜆2	NOUN
biomedich-48	174	20	=	=	SYM
biomedich-48	174	21	𝑏1	𝑏1	NOUN
biomedich-48	174	22	.	.	PUNCT
biomedich-48	175	1	(	(	PUNCT
biomedich-48	175	2	ii	ii	NOUN
biomedich-48	175	3	)	)	PUNCT
biomedich-48	175	4	positive	positive	ADJ
biomedich-48	175	5	eigenvalues	eigenvalue	NOUN
biomedich-48	175	6	have	have	VERB
biomedich-48	175	7	a	a	DET
biomedich-48	175	8	multiplicity	multiplicity	NOUN
biomedich-48	175	9	of	of	ADP
biomedich-48	175	10	1	1	NUM
biomedich-48	175	11	𝜆1𝑥4	𝜆1𝑥4	X
biomedich-48	176	1	=	=	SYM
biomedich-48	176	2	𝑏3𝑥3	𝑏3𝑥3	PROPN
biomedich-48	176	3	𝑥4	𝑥4	NOUN
biomedich-48	176	4	=	=	SYM
biomedich-48	176	5	𝑏3	𝑏3	NOUN
biomedich-48	176	6	𝜆1	𝜆1	VERB
biomedich-48	176	7	𝑥3	𝑥3	NOUN
biomedich-48	176	8	→	→	SYM
biomedich-48	176	9	𝑥4	𝑥4	ADJ
biomedich-48	176	10	=	=	SYM
biomedich-48	176	11	𝑏3	𝑏3	NOUN
biomedich-48	176	12	𝜆1	𝜆1	NOUN
biomedich-48	176	13	(	(	PUNCT
biomedich-48	176	14	𝑏1𝑏2	𝑏1𝑏2	NOUN
biomedich-48	176	15	𝜆1	𝜆1	NOUN
biomedich-48	176	16	2	2	NUM
biomedich-48	176	17	𝑥1	𝑥1	NOUN
biomedich-48	176	18	)	)	PUNCT
biomedich-48	176	19	−𝑏𝑛−1𝑥𝑛−1	−𝑏𝑛−1𝑥𝑛−1	PUNCT
biomedich-48	177	1	+	+	CCONJ
biomedich-48	177	2	𝜆1𝑥𝑛	𝜆1𝑥𝑛	X
biomedich-48	177	3	=	=	SYM
biomedich-48	177	4	0	0	NUM
biomedich-48	177	5	42	42	NUM
biomedich-48	177	6	biology	biology	NOUN
biomedich-48	177	7	,	,	PUNCT
biomedich-48	177	8	medicine	medicine	NOUN
biomedich-48	177	9	,	,	PUNCT
biomedich-48	177	10	&	&	CCONJ
biomedich-48	177	11	natural	natural	ADJ
biomedich-48	177	12	product	product	NOUN
biomedich-48	177	13	chemistry	chemistry	NOUN
biomedich-48	177	14	6	6	NUM
biomedich-48	177	15	(	(	PUNCT
biomedich-48	177	16	2	2	NUM
biomedich-48	177	17	)	)	PUNCT
biomedich-48	177	18	,	,	PUNCT
biomedich-48	177	19	2017	2017	NUM
biomedich-48	177	20	:	:	PUNCT
biomedich-48	177	21	37	37	NUM
biomedich-48	177	22	-	-	SYM
biomedich-48	177	23	45	45	NUM
biomedich-48	177	24	𝜆1𝑥𝑛	𝜆1𝑥𝑛	PUNCT
biomedich-48	177	25	=	=	SYM
biomedich-48	177	26	𝑏𝑛−1𝑥𝑛−1	𝑏𝑛−1𝑥𝑛−1	NOUN
biomedich-48	177	27	𝑥𝑛	𝑥𝑛	PROPN
biomedich-48	177	28	=	=	SYM
biomedich-48	177	29	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	177	30	𝜆1	𝜆1	NOUN
biomedich-48	177	31	𝑥𝑛−1	𝑥𝑛−1	NOUN
biomedich-48	177	32	𝑥𝑛	𝑥𝑛	PROPN
biomedich-48	177	33	=	=	SYM
biomedich-48	177	34	𝑏1𝑏2	𝑏1𝑏2	PROPN
biomedich-48	177	35	…	…	PUNCT
biomedich-48	177	36	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	177	37	𝜆1	𝜆1	NOUN
biomedich-48	177	38	𝑥𝑛−1	𝑥𝑛−1	PROPN
biomedich-48	177	39	so	so	ADV
biomedich-48	177	40	obtained	obtain	VERB
biomedich-48	177	41	𝑥2	𝑥2	NOUN
biomedich-48	177	42	=	=	SYM
biomedich-48	177	43	𝑏1	𝑏1	ADJ
biomedich-48	177	44	𝜆1	𝜆1	NOUN
biomedich-48	177	45	𝑥1	𝑥1	NOUN
biomedich-48	177	46	𝑥3	𝑥3	NOUN
biomedich-48	177	47	=	=	PROPN
biomedich-48	177	48	𝑏2	𝑏2	PROPN
biomedich-48	177	49	𝜆1	𝜆1	NOUN
biomedich-48	177	50	𝑥2	𝑥2	NOUN
biomedich-48	177	51	=	=	SYM
biomedich-48	177	52	𝑏1𝑏2	𝑏1𝑏2	NOUN
biomedich-48	177	53	𝜆1	𝜆1	NOUN
biomedich-48	177	54	2	2	NUM
biomedich-48	177	55	𝑥1	𝑥1	NOUN
biomedich-48	177	56	𝑥4	𝑥4	NOUN
biomedich-48	177	57	=	=	SYM
biomedich-48	177	58	𝑏3	𝑏3	NOUN
biomedich-48	177	59	𝜆1	𝜆1	VERB
biomedich-48	177	60	𝑥3	𝑥3	NOUN
biomedich-48	177	61	=	=	SYM
biomedich-48	177	62	𝑏1𝑏2𝑏3	𝑏1𝑏2𝑏3	PROPN
biomedich-48	177	63	𝜆1	𝜆1	NOUN
biomedich-48	177	64	3	3	NUM
biomedich-48	177	65	𝑥1	𝑥1	NOUN
biomedich-48	177	66	⋮	⋮	NOUN
biomedich-48	177	67	𝑥𝑛	𝑥𝑛	VERB
biomedich-48	177	68	=	=	SYM
biomedich-48	177	69	𝑏1𝑏2	𝑏1𝑏2	NOUN
biomedich-48	177	70	…	…	PUNCT
biomedich-48	177	71	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	177	72	𝜆1	𝜆1	NOUN
biomedich-48	177	73	𝑥𝑛−1	𝑥𝑛−1	NOUN
biomedich-48	177	74	=	=	SYM
biomedich-48	177	75	𝑏1𝑏2	𝑏1𝑏2	NOUN
biomedich-48	177	76	…	…	PUNCT
biomedich-48	177	77	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	177	78	𝜆1	𝜆1	NOUN
biomedich-48	177	79	𝑛−1	𝑛−1	PROPN
biomedich-48	177	80	𝑥1	𝑥1	NOUN
biomedich-48	177	81	if	if	SCONJ
biomedich-48	177	82	for	for	ADP
biomedich-48	177	83	example	example	NOUN
biomedich-48	177	84	taken	take	VERB
biomedich-48	177	85	𝑥1	𝑥1	NOUN
biomedich-48	177	86	=	=	SYM
biomedich-48	177	87	1	1	NUM
biomedich-48	177	88	,	,	PUNCT
biomedich-48	177	89	then	then	ADV
biomedich-48	177	90	eigenvector	eigenvector	VERB
biomedich-48	177	91	𝐱	𝐱	PROPN
biomedich-48	177	92	corresponds	correspond	NOUN
biomedich-48	177	93	to	to	PART
biomedich-48	177	94	𝜆1	𝜆1	VERB
biomedich-48	177	95	that	that	PRON
biomedich-48	177	96	is	be	AUX
biomedich-48	177	97	𝐱1	𝐱1	NOUN
biomedich-48	177	98	=	=	PUNCT
biomedich-48	177	99	[	[	PUNCT
biomedich-48	177	100	𝑥1	𝑥1	NOUN
biomedich-48	177	101	𝑥2	𝑥2	NOUN
biomedich-48	177	102	𝑥3	𝑥3	ADJ
biomedich-48	177	103	𝑥4	𝑥4	NOUN
biomedich-48	177	104	⋮	⋮	NOUN
biomedich-48	177	105	𝑥𝑛	𝑥𝑛	VERB
biomedich-48	177	106	]	]	X
biomedich-48	177	107	=	=	PUNCT
biomedich-48	177	108	[	[	PUNCT
biomedich-48	177	109	1	1	NUM
biomedich-48	177	110	𝑏1	𝑏1	ADJ
biomedich-48	177	111	𝜆1⁄	𝜆1⁄	SYM
biomedich-48	177	112	𝑏1𝑏2	𝑏1𝑏2	NOUN
biomedich-48	177	113	𝜆1	𝜆1	NOUN
biomedich-48	177	114	2⁄	2⁄	NUM
biomedich-48	177	115	𝑏1𝑏2𝑏3	𝑏1𝑏2𝑏3	PROPN
biomedich-48	177	116	𝜆1	𝜆1	NOUN
biomedich-48	177	117	3⁄	3⁄	NUM
biomedich-48	177	118	⋮	⋮	NOUN
biomedich-48	177	119	𝑏1𝑏2	𝑏1𝑏2	ADP
biomedich-48	177	120	…	…	PUNCT
biomedich-48	177	121	𝜆1	𝜆1	NOUN
biomedich-48	178	1	𝑛−1⁄	𝑛−1⁄	X
biomedich-48	178	2	]	]	X
biomedich-48	179	1	it	it	PRON
biomedich-48	179	2	is	be	AUX
biomedich-48	179	3	proven	prove	VERB
biomedich-48	179	4	that	that	SCONJ
biomedich-48	179	5	leslie	leslie	PROPN
biomedich-48	179	6	's	's	PART
biomedich-48	179	7	matrix	matrix	NOUN
biomedich-48	179	8	eigenvect	eigenvect	NOUN
biomedich-48	179	9	or	or	CCONJ
biomedich-48	179	10	of	of	ADP
biomedich-48	179	11	all	all	DET
biomedich-48	179	12	elements	element	NOUN
biomedich-48	179	13	is	be	AUX
biomedich-48	179	14	positive	positive	ADJ
biomedich-48	179	15	.	.	PUNCT
biomedich-48	180	1	theorem	theorem	ADJ
biomedich-48	180	2	2	2	NUM
biomedich-48	180	3	if	if	SCONJ
biomedich-48	180	4	𝜆1	𝜆1	NOUN
biomedich-48	180	5	is	be	AUX
biomedich-48	180	6	the	the	DET
biomedich-48	180	7	unique	unique	ADJ
biomedich-48	180	8	positive	positive	ADJ
biomedich-48	180	9	eigenvalue	eigenvalue	NOUN
biomedich-48	180	10	of	of	ADP
biomedich-48	180	11	a	a	DET
biomedich-48	180	12	leslie	leslie	PROPN
biomedich-48	180	13	matrix	matrix	NOUN
biomedich-48	180	14	l	l	NOUN
biomedich-48	180	15	and	and	CCONJ
biomedich-48	180	16	if	if	SCONJ
biomedich-48	180	17	𝜆𝑖	𝜆𝑖	PROPN
biomedich-48	180	18	is	be	AUX
biomedich-48	180	19	any	any	DET
biomedich-48	180	20	real	real	ADJ
biomedich-48	180	21	eigenvalues	eigenvalue	NOUN
biomedich-48	180	22	or	or	CCONJ
biomedich-48	180	23	complex	complex	NOUN
biomedich-48	180	24	of	of	ADP
biomedich-48	180	25	𝐿	𝐿	PROPN
biomedich-48	180	26	,	,	PUNCT
biomedich-48	180	27	then	then	ADV
biomedich-48	180	28	|𝜆𝑘|	|𝜆𝑘|	VERB
biomedich-48	180	29	≤	≤	NOUN
biomedich-48	180	30	𝜆1	𝜆1	NOUN
biomedich-48	180	31	.	.	PUNCT
biomedich-48	181	1	evidence	evidence	NOUN
biomedich-48	181	2	:	:	PUNCT
biomedich-48	181	3	it	it	PRON
biomedich-48	181	4	has	have	AUX
biomedich-48	181	5	been	be	AUX
biomedich-48	181	6	proved	prove	VERB
biomedich-48	181	7	that	that	SCONJ
biomedich-48	181	8	𝜆1	𝜆1	NOUN
biomedich-48	181	9	is	be	AUX
biomedich-48	181	10	a	a	DET
biomedich-48	181	11	single	single	ADJ
biomedich-48	181	12	positive	positive	ADJ
biomedich-48	181	13	eigenvalue	eigenvalue	NOUN
biomedich-48	181	14	,	,	PUNCT
biomedich-48	181	15	then	then	ADV
biomedich-48	181	16	𝜆1	𝜆1	NOUN
biomedich-48	181	17	is	be	AUX
biomedich-48	181	18	an	an	DET
biomedich-48	181	19	eigenvalue	eigenvalue	NOUN
biomedich-48	181	20	that	that	PRON
biomedich-48	181	21	can	can	AUX
biomedich-48	181	22	be	be	AUX
biomedich-48	181	23	a	a	DET
biomedich-48	181	24	real	real	ADJ
biomedich-48	181	25	or	or	CCONJ
biomedich-48	181	26	complex	complex	ADJ
biomedich-48	181	27	number	number	NOUN
biomedich-48	181	28	.	.	PUNCT
biomedich-48	182	1	if	if	SCONJ
biomedich-48	182	2	for	for	ADP
biomedich-48	182	3	example	example	NOUN
biomedich-48	182	4	𝜆𝑘	𝜆𝑘	NOUN
biomedich-48	182	5	=	=	NOUN
biomedich-48	182	6	0	0	NUM
biomedich-48	183	1	it	it	PRON
biomedich-48	183	2	proves	prove	VERB
biomedich-48	183	3	that	that	SCONJ
biomedich-48	183	4	|𝜆𝑘|	|𝜆𝑘|	VERB
biomedich-48	183	5	≤	≤	NOUN
biomedich-48	183	6	𝜆1.then	𝜆1.then	PROPN
biomedich-48	183	7	taken	take	VERB
biomedich-48	183	8	any	any	DET
biomedich-48	183	9	𝜆𝑘	𝜆𝑘	NOUN
biomedich-48	183	10	=	=	NOUN
biomedich-48	183	11	𝑟𝑒𝑖𝜃	𝑟𝑒𝑖𝜃	NOUN
biomedich-48	183	12	with	with	ADP
biomedich-48	183	13	,	,	PUNCT
biomedich-48	183	14	𝑖	𝑖	NOUN
biomedich-48	183	15	=	=	PUNCT
biomedich-48	183	16	√−1	√−1	PROPN
biomedich-48	183	17	,	,	PUNCT
biomedich-48	183	18	to	to	PART
biomedich-48	183	19	prove	prove	VERB
biomedich-48	183	20	the	the	DET
biomedich-48	183	21	same	same	ADJ
biomedich-48	183	22	as	as	ADP
biomedich-48	183	23	showing	show	VERB
biomedich-48	183	24	|𝑟|	|𝑟|	ADP
biomedich-48	183	25	≤	≤	NOUN
biomedich-48	183	26	𝜆1	𝜆1	NOUN
biomedich-48	183	27	.	.	PUNCT
biomedich-48	184	1	the	the	DET
biomedich-48	184	2	necessary	necessary	ADJ
biomedich-48	184	3	conditions	condition	NOUN
biomedich-48	184	4	and	and	CCONJ
biomedich-48	184	5	sufficient	sufficient	ADJ
biomedich-48	184	6	conditions	condition	NOUN
biomedich-48	184	7	𝜆𝑘	𝜆𝑘	VERB
biomedich-48	184	8	to	to	PART
biomedich-48	184	9	be	be	AUX
biomedich-48	184	10	an	an	DET
biomedich-48	184	11	eigenvalue	eigenvalue	NOUN
biomedich-48	184	12	,	,	PUNCT
biomedich-48	184	13	𝜆𝑘	𝜆𝑘	PRON
biomedich-48	184	14	must	must	AUX
biomedich-48	184	15	be	be	AUX
biomedich-48	184	16	the	the	DET
biomedich-48	184	17	solution	solution	NOUN
biomedich-48	184	18	of	of	ADP
biomedich-48	184	19	the	the	DET
biomedich-48	184	20	system	system	NOUN
biomedich-48	184	21	of	of	ADP
biomedich-48	184	22	equations	equation	NOUN
biomedich-48	184	23	𝑞(𝜆	𝑞(𝜆	ADV
biomedich-48	184	24	)	)	PUNCT
biomedich-48	185	1	=	=	VERB
biomedich-48	186	1	𝑎1	𝑎1	INTJ
biomedich-48	186	2	𝜆𝑘	𝜆𝑘	NOUN
biomedich-48	187	1	+	+	ADJ
biomedich-48	187	2	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	187	3	𝜆𝑘	𝜆𝑘	NUM
biomedich-48	187	4	2	2	NUM
biomedich-48	187	5	+	+	NUM
biomedich-48	187	6	⋯+	⋯+	NOUN
biomedich-48	187	7	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	187	8	…	…	SYM
biomedich-48	187	9	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	187	10	𝜆𝑘	𝜆𝑘	NOUN
biomedich-48	187	11	𝑛	𝑛	NOUN
biomedich-48	187	12	=	=	SYM
biomedich-48	187	13	1	1	NUM
biomedich-48	187	14	,	,	PUNCT
biomedich-48	187	15	𝑞(𝜆	𝑞(𝜆	PROPN
biomedich-48	187	16	)	)	PUNCT
biomedich-48	187	17	=	=	SYM
biomedich-48	187	18	1	1	NUM
biomedich-48	187	19	for	for	ADP
biomedich-48	187	20	𝜆	𝜆	DET
biomedich-48	187	21	≠	≠	PROPN
biomedich-48	187	22	0	0	NUM
biomedich-48	187	23	𝑞(𝜆	𝑞(𝜆	PROPN
biomedich-48	187	24	)	)	PUNCT
biomedich-48	188	1	=	=	SYM
biomedich-48	188	2	𝑎1	𝑎1	ADP
biomedich-48	188	3	𝑟𝑒𝑖𝜃	𝑟𝑒𝑖𝜃	VERB
biomedich-48	188	4	+	+	X
biomedich-48	188	5	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	188	6	(	(	PUNCT
biomedich-48	188	7	𝑟𝑖𝜃	𝑟𝑖𝜃	NOUN
biomedich-48	188	8	)	)	PUNCT
biomedich-48	188	9	2	2	NUM
biomedich-48	188	10	+	+	NUM
biomedich-48	188	11	⋯+	⋯+	NOUN
biomedich-48	188	12	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	188	13	…	…	SYM
biomedich-48	188	14	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	188	15	(	(	PUNCT
biomedich-48	188	16	𝑟𝑖𝜃	𝑟𝑖𝜃	NOUN
biomedich-48	188	17	)	)	PUNCT
biomedich-48	188	18	𝑛	𝑛	NOUN
biomedich-48	189	1	=	=	SYM
biomedich-48	189	2	1	1	NUM
biomedich-48	189	3	𝑎1	𝑎1	NOUN
biomedich-48	189	4	𝑟	𝑟	X
biomedich-48	189	5	(	(	PUNCT
biomedich-48	189	6	𝑒−𝑖𝜃	𝑒−𝑖𝜃	PROPN
biomedich-48	189	7	)	)	PUNCT
biomedich-48	189	8	+	+	NUM
biomedich-48	189	9	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	189	10	𝑟2	𝑟2	NOUN
biomedich-48	189	11	(	(	PUNCT
biomedich-48	189	12	𝑒−2𝑖𝜃	𝑒−2𝑖𝜃	NOUN
biomedich-48	189	13	)	)	PUNCT
biomedich-48	190	1	+	+	NUM
biomedich-48	190	2	⋯+	⋯+	NOUN
biomedich-48	190	3	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	190	4	…	…	SYM
biomedich-48	190	5	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	190	6	𝑟𝑛	𝑟𝑛	ADJ
biomedich-48	190	7	(	(	PUNCT
biomedich-48	190	8	𝑒−𝑛𝑖𝜃	𝑒−𝑛𝑖𝜃	ADJ
biomedich-48	190	9	)	)	PUNCT
biomedich-48	190	10	=	=	SYM
biomedich-48	191	1	1	1	NUM
biomedich-48	191	2	𝑎1	𝑎1	NOUN
biomedich-48	191	3	𝑟	𝑟	X
biomedich-48	191	4	(	(	PUNCT
biomedich-48	191	5	cos(−𝜃	cos(−𝜃	PROPN
biomedich-48	191	6	)	)	PUNCT
biomedich-48	191	7	+	+	NUM
biomedich-48	191	8	𝑖	𝑖	SYM
biomedich-48	191	9	sin(−𝜃	sin(−𝜃	PROPN
biomedich-48	191	10	)	)	PUNCT
biomedich-48	191	11	)	)	PUNCT
biomedich-48	192	1	+	+	PUNCT
biomedich-48	192	2	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	192	3	𝑟2	𝑟2	NOUN
biomedich-48	192	4	(	(	PUNCT
biomedich-48	192	5	cos(−2𝜃	cos(−2𝜃	NOUN
biomedich-48	192	6	)	)	PUNCT
biomedich-48	192	7	(	(	PUNCT
biomedich-48	192	8	…	…	PUNCT
biomedich-48	192	9	+	+	NUM
biomedich-48	192	10	𝑖	𝑖	SYM
biomedich-48	192	11	sin(−2𝜃))−2	sin(−2𝜃))−2	NOUN
biomedich-48	193	1	+	+	X
biomedich-48	193	2	⋯	⋯	NOUN
biomedich-48	193	3	…	…	PUNCT
biomedich-48	193	4	+	+	NUM
biomedich-48	193	5	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	193	6	…	…	SYM
biomedich-48	193	7	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	193	8	𝑟𝑛	𝑟𝑛	X
biomedich-48	193	9	(	(	PUNCT
biomedich-48	193	10	cos(−𝑛𝜃	cos(−𝑛𝜃	PROPN
biomedich-48	193	11	)	)	PUNCT
biomedich-48	193	12	+	+	NUM
biomedich-48	193	13	𝑖	𝑖	PROPN
biomedich-48	193	14	sin(−𝑛𝜃	sin(−𝑛𝜃	PROPN
biomedich-48	193	15	)	)	PUNCT
biomedich-48	193	16	)	)	PUNCT
biomedich-48	194	1	=	=	PUNCT
biomedich-48	195	1	1	1	NUM
biomedich-48	195	2	𝑎1	𝑎1	NOUN
biomedich-48	195	3	𝑟	𝑟	X
biomedich-48	195	4	(	(	PUNCT
biomedich-48	195	5	cos𝜃	cos𝜃	NOUN
biomedich-48	195	6	−	−	PROPN
biomedich-48	195	7	𝑖	𝑖	SYM
biomedich-48	195	8	sin	sin	NOUN
biomedich-48	195	9	𝜃	𝜃	NOUN
biomedich-48	195	10	)	)	PUNCT
biomedich-48	195	11	+	+	PUNCT
biomedich-48	195	12	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	195	13	𝑟2	𝑟2	NOUN
biomedich-48	195	14	(	(	PUNCT
biomedich-48	195	15	cos2𝜃	cos2𝜃	X
biomedich-48	195	16	−	−	NOUN
biomedich-48	195	17	𝑖	𝑖	SYM
biomedich-48	195	18	sin	sin	NOUN
biomedich-48	195	19	2𝜃	2𝜃	NUM
biomedich-48	195	20	)	)	PUNCT
biomedich-48	196	1	+	+	CCONJ
biomedich-48	197	1	+	+	ADJ
biomedich-48	197	2	⋯+	⋯+	NOUN
biomedich-48	197	3	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	197	4	…	…	SYM
biomedich-48	197	5	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	197	6	𝑟𝑛	𝑟𝑛	INTJ
biomedich-48	197	7	(	(	PUNCT
biomedich-48	197	8	cos𝑛𝜃	cos𝑛𝜃	ADJ
biomedich-48	197	9	−	−	PROPN
biomedich-48	197	10	𝑖	𝑖	SYM
biomedich-48	197	11	sin	sin	NOUN
biomedich-48	197	12	𝑛𝜃	𝑛𝜃	AUX
biomedich-48	197	13	)	)	PUNCT
biomedich-48	197	14	=	=	SYM
biomedich-48	198	1	1	1	NUM
biomedich-48	198	2	it	it	PRON
biomedich-48	198	3	means	mean	VERB
biomedich-48	198	4	𝑎1	𝑎1	PROPN
biomedich-48	198	5	𝑟	𝑟	X
biomedich-48	198	6	(	(	PUNCT
biomedich-48	198	7	cos𝜃	cos𝜃	NOUN
biomedich-48	198	8	)	)	PUNCT
biomedich-48	198	9	+	+	PUNCT
biomedich-48	198	10	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	198	11	𝑟2	𝑟2	NOUN
biomedich-48	198	12	(	(	PUNCT
biomedich-48	198	13	cos2𝜃	cos2𝜃	PUNCT
biomedich-48	198	14	)	)	PUNCT
biomedich-48	199	1	+	+	CCONJ
biomedich-48	199	2	⋯	⋯	PROPN
biomedich-48	199	3	…	…	PUNCT
biomedich-48	199	4	+	+	NUM
biomedich-48	199	5	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	199	6	…	…	SYM
biomedich-48	199	7	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	199	8	𝑟𝑛	𝑟𝑛	INTJ
biomedich-48	199	9	(	(	PUNCT
biomedich-48	199	10	cos𝑛𝜃	cos𝑛𝜃	NOUN
biomedich-48	199	11	)	)	PUNCT
biomedich-48	199	12	=	=	SYM
biomedich-48	199	13	1	1	NUM
biomedich-48	199	14	and	and	CCONJ
biomedich-48	199	15	𝑎1	𝑎1	ADJ
biomedich-48	199	16	𝑟	𝑟	X
biomedich-48	199	17	(	(	PUNCT
biomedich-48	199	18	sin	sin	NOUN
biomedich-48	199	19	𝜃	𝜃	NOUN
biomedich-48	199	20	)	)	PUNCT
biomedich-48	200	1	+	+	CCONJ
biomedich-48	200	2	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	200	3	𝑟2	𝑟2	NOUN
biomedich-48	200	4	(	(	PUNCT
biomedich-48	200	5	sin	sin	NOUN
biomedich-48	200	6	2𝜃	2𝜃	NUM
biomedich-48	200	7	)	)	PUNCT
biomedich-48	201	1	+	+	CCONJ
biomedich-48	201	2	⋯	⋯	ADP
biomedich-48	201	3	…	…	PUNCT
biomedich-48	201	4	+	+	NUM
biomedich-48	201	5	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	201	6	…	…	SYM
biomedich-48	201	7	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	201	8	𝑟𝑛	𝑟𝑛	INTJ
biomedich-48	201	9	(	(	PUNCT
biomedich-48	201	10	sin	sin	NOUN
biomedich-48	201	11	𝜃	𝜃	NOUN
biomedich-48	201	12	)	)	PUNCT
biomedich-48	201	13	=	=	SYM
biomedich-48	201	14	0	0	PUNCT
biomedich-48	201	15	if	if	SCONJ
biomedich-48	201	16	taken	take	VERB
biomedich-48	201	17	only	only	ADV
biomedich-48	201	18	the	the	DET
biomedich-48	201	19	real	real	ADJ
biomedich-48	201	20	part	part	NOUN
biomedich-48	201	21	is	be	AUX
biomedich-48	201	22	𝑎1	𝑎1	ADP
biomedich-48	201	23	𝑟	𝑟	X
biomedich-48	201	24	(	(	PUNCT
biomedich-48	201	25	cos𝜃	cos𝜃	NOUN
biomedich-48	201	26	)	)	PUNCT
biomedich-48	202	1	+	+	PUNCT
biomedich-48	202	2	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	202	3	𝑟2	𝑟2	NOUN
biomedich-48	202	4	(	(	PUNCT
biomedich-48	202	5	cos2𝜃	cos2𝜃	PUNCT
biomedich-48	202	6	)	)	PUNCT
biomedich-48	203	1	+	+	CCONJ
biomedich-48	203	2	⋯	⋯	PROPN
biomedich-48	203	3	…	…	PUNCT
biomedich-48	203	4	+	+	NUM
biomedich-48	203	5	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	203	6	…	…	SYM
biomedich-48	203	7	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	203	8	𝑟𝑛	𝑟𝑛	INTJ
biomedich-48	203	9	(	(	PUNCT
biomedich-48	203	10	cos𝑛𝜃	cos𝑛𝜃	NOUN
biomedich-48	203	11	)	)	PUNCT
biomedich-48	203	12	=	=	SYM
biomedich-48	203	13	1	1	NUM
biomedich-48	203	14	because	because	SCONJ
biomedich-48	203	15	𝜆1	𝜆1	NOUN
biomedich-48	203	16	is	be	AUX
biomedich-48	203	17	an	an	DET
biomedich-48	203	18	eigenvalue	eigenvalue	NOUN
biomedich-48	203	19	so	so	ADV
biomedich-48	203	20	𝜆1	𝜆1	PROPN
biomedich-48	203	21	satisfies	satisfy	VERB
biomedich-48	203	22	the	the	DET
biomedich-48	203	23	equation	equation	NOUN
biomedich-48	203	24	𝑞(𝜆	𝑞(𝜆	ADV
biomedich-48	203	25	)	)	PUNCT
biomedich-48	204	1	=	=	SYM
biomedich-48	204	2	1	1	NUM
biomedich-48	204	3	so	so	ADV
biomedich-48	204	4	𝑞(𝜆	𝑞(𝜆	ADV
biomedich-48	204	5	)	)	PUNCT
biomedich-48	204	6	=	=	SYM
biomedich-48	205	1	𝑎1	𝑎1	ADP
biomedich-48	205	2	𝜆1	𝜆1	NOUN
biomedich-48	205	3	+	+	CCONJ
biomedich-48	205	4	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	205	5	𝜆1	𝜆1	NOUN
biomedich-48	205	6	2	2	NUM
biomedich-48	205	7	+	+	NUM
biomedich-48	205	8	⋯+	⋯+	NOUN
biomedich-48	205	9	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	205	10	…	…	PUNCT
biomedich-48	205	11	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	205	12	𝜆1	𝜆1	NOUN
biomedich-48	205	13	𝑛	𝑛	NOUN
biomedich-48	206	1	=	=	SYM
biomedich-48	207	1	1	1	NUM
biomedich-48	208	1	if	if	SCONJ
biomedich-48	208	2	𝑎1	𝑎1	VERB
biomedich-48	208	3	𝑟	𝑟	X
biomedich-48	208	4	(	(	PUNCT
biomedich-48	208	5	𝑐𝑜𝑠𝜃	𝑐𝑜𝑠𝜃	NOUN
biomedich-48	208	6	)	)	PUNCT
biomedich-48	208	7	+	+	CCONJ
biomedich-48	208	8	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	208	9	𝑟2	𝑟2	NOUN
biomedich-48	208	10	(	(	PUNCT
biomedich-48	208	11	𝑐𝑜𝑠2𝜃	𝑐𝑜𝑠2𝜃	NUM
biomedich-48	208	12	)	)	PUNCT
biomedich-48	209	1	+	+	NUM
biomedich-48	209	2	⋯+	⋯+	NOUN
biomedich-48	209	3	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	209	4	…	…	SYM
biomedich-48	209	5	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	209	6	𝑟𝑛	𝑟𝑛	X
biomedich-48	209	7	(	(	PUNCT
biomedich-48	209	8	𝑐𝑜𝑠𝑛𝜃	𝑐𝑜𝑠𝑛𝜃	PROPN
biomedich-48	209	9	)	)	PUNCT
biomedich-48	210	1	=	=	PUNCT
biomedich-48	211	1	𝑎1	𝑎1	ADP
biomedich-48	211	2	𝜆1	𝜆1	NOUN
biomedich-48	211	3	+	+	CCONJ
biomedich-48	211	4	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	211	5	𝜆1	𝜆1	NOUN
biomedich-48	211	6	2	2	NUM
biomedich-48	211	7	+	+	NUM
biomedich-48	211	8	⋯+	⋯+	NOUN
biomedich-48	211	9	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	211	10	…	…	PUNCT
biomedich-48	211	11	𝑏𝑛−1	𝑏𝑛−1	NOUN
biomedich-48	211	12	𝜆1	𝜆1	NOUN
biomedich-48	211	13	𝑛	𝑛	PROPN
biomedich-48	211	14	(	(	PUNCT
biomedich-48	211	15	9	9	X
biomedich-48	211	16	)	)	PUNCT
biomedich-48	211	17	this	this	DET
biomedich-48	211	18	equation	equation	NOUN
biomedich-48	211	19	is	be	AUX
biomedich-48	211	20	subtracted	subtract	VERB
biomedich-48	211	21	into	into	ADP
biomedich-48	211	22	𝑎1	𝑎1	PROPN
biomedich-48	211	23	(	(	PUNCT
biomedich-48	211	24	cos𝜃	cos𝜃	NOUN
biomedich-48	211	25	𝑟	𝑟	NOUN
biomedich-48	211	26	−	−	PROPN
biomedich-48	211	27	1	1	NUM
biomedich-48	211	28	𝜆1	𝜆1	NOUN
biomedich-48	211	29	)	)	PUNCT
biomedich-48	212	1	+	+	CCONJ
biomedich-48	212	2	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	212	3	(	(	PUNCT
biomedich-48	212	4	cos2𝜃	cos2𝜃	NOUN
biomedich-48	212	5	𝑟2	𝑟2	NOUN
biomedich-48	212	6	−	−	PROPN
biomedich-48	212	7	1	1	NUM
biomedich-48	212	8	𝜆1	𝜆1	NOUN
biomedich-48	212	9	2	2	NUM
biomedich-48	212	10	)	)	PUNCT
biomedich-48	213	1	+	+	CCONJ
biomedich-48	213	2	⋯	⋯	ADP
biomedich-48	213	3	…	…	PUNCT
biomedich-48	213	4	+	+	NUM
biomedich-48	213	5	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	213	6	…	…	PUNCT
biomedich-48	213	7	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	213	8	(	(	PUNCT
biomedich-48	213	9	cos𝑛𝜃	cos𝑛𝜃	ADJ
biomedich-48	213	10	𝑟𝑛	𝑟𝑛	ADP
biomedich-48	213	11	−	−	NUM
biomedich-48	213	12	1	1	NUM
biomedich-48	213	13	𝜆1	𝜆1	NOUN
biomedich-48	213	14	𝑛	𝑛	NOUN
biomedich-48	213	15	)	)	PUNCT
biomedich-48	213	16	=	=	SYM
biomedich-48	213	17	0	0	PUNCT
biomedich-48	214	1	𝑎1	𝑎1	INTJ
biomedich-48	214	2	(	(	PUNCT
biomedich-48	214	3	𝜆1	𝜆1	VERB
biomedich-48	214	4	cos𝜃−𝑟	cos𝜃−𝑟	NOUN
biomedich-48	214	5	𝑟𝜆1	𝑟𝜆1	PROPN
biomedich-48	214	6	)	)	PUNCT
biomedich-48	215	1	+	+	CCONJ
biomedich-48	215	2	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	215	3	(	(	PUNCT
biomedich-48	215	4	𝜆1	𝜆1	NOUN
biomedich-48	215	5	2	2	NUM
biomedich-48	215	6	cos2𝜃−𝑟2	cos2𝜃−𝑟2	NOUN
biomedich-48	215	7	𝑟2𝜆1	𝑟2𝜆1	X
biomedich-48	215	8	2	2	NUM
biomedich-48	215	9	)	)	PUNCT
biomedich-48	216	1	+	+	CCONJ
biomedich-48	216	2	⋯	⋯	ADP
biomedich-48	216	3	…	…	PUNCT
biomedich-48	216	4	+	+	NUM
biomedich-48	216	5	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	216	6	…	…	PUNCT
biomedich-48	216	7	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	216	8	(	(	PUNCT
biomedich-48	216	9	𝜆1	𝜆1	VERB
biomedich-48	216	10	𝑛	𝑛	DET
biomedich-48	216	11	cos𝑛𝜃𝑟𝑛	cos𝑛𝜃𝑟𝑛	VERB
biomedich-48	216	12	𝑟𝑛𝜆1	𝑟𝑛𝜆1	NOUN
biomedich-48	216	13	𝑛	𝑛	ADP
biomedich-48	216	14	)	)	PUNCT
biomedich-48	216	15	=	=	SYM
biomedich-48	216	16	0	0	NUM
biomedich-48	216	17	equations	equation	NOUN
biomedich-48	216	18	(	(	PUNCT
biomedich-48	216	19	9	9	NUM
biomedich-48	216	20	)	)	PUNCT
biomedich-48	216	21	apply	apply	VERB
biomedich-48	216	22	if	if	SCONJ
biomedich-48	216	23	𝜆1	𝜆1	PROPN
biomedich-48	216	24	cos	cos	PROPN
biomedich-48	216	25	𝜃	𝜃	NUM
biomedich-48	216	26	−	−	NOUN
biomedich-48	216	27	𝑟	𝑟	NOUN
biomedich-48	216	28	=	=	SYM
biomedich-48	216	29	0	0	NUM
biomedich-48	216	30	obtained	obtain	VERB
biomedich-48	216	31	𝑟	𝑟	NOUN
biomedich-48	216	32	=	=	SYM
biomedich-48	216	33	𝜆1	𝜆1	PROPN
biomedich-48	216	34	cos𝜃.	cos𝜃.	NOUN
biomedich-48	216	35	because	because	SCONJ
biomedich-48	216	36	−1	−1	NOUN
biomedich-48	216	37	≤	≤	NUM
biomedich-48	216	38	cos𝜃	cos𝜃	NOUN
biomedich-48	216	39	≤	≤	NOUN
biomedich-48	216	40	1	1	NUM
biomedich-48	216	41	→	→	SYM
biomedich-48	216	42	−𝜆1	−𝜆1	NOUN
biomedich-48	216	43	≤	≤	PROPN
biomedich-48	216	44	𝑟	𝑟	PRON
biomedich-48	216	45	≤	≤	NOUN
biomedich-48	216	46	𝜆1	𝜆1	NOUN
biomedich-48	216	47	,	,	PUNCT
biomedich-48	216	48	it	it	PRON
biomedich-48	216	49	means	mean	VERB
biomedich-48	216	50	|𝑟|	|𝑟|	ADP
biomedich-48	216	51	≤	≤	PROPN
biomedich-48	216	52	𝜆1	𝜆1	NOUN
biomedich-48	216	53	.	.	PUNCT
biomedich-48	217	1	if	if	SCONJ
biomedich-48	217	2	𝜆1	𝜆1	NOUN
biomedich-48	217	3	meet	meet	VERB
biomedich-48	217	4	|𝜆𝑘|	|𝜆𝑘|	NOUN
biomedich-48	217	5	<	<	X
biomedich-48	217	6	𝜆1	𝜆1	PROPN
biomedich-48	217	7	is	be	AUX
biomedich-48	217	8	said	say	VERB
biomedich-48	217	9	that	that	SCONJ
biomedich-48	217	10	𝜆1	𝜆1	PROPN
biomedich-48	217	11	is	be	AUX
biomedich-48	217	12	a	a	DET
biomedich-48	217	13	dominant	dominant	ADJ
biomedich-48	217	14	eigen	eigen	NOUN
biomedich-48	217	15	value	value	NOUN
biomedich-48	217	16	of	of	ADP
biomedich-48	217	17	𝐿.	𝐿.	PROPN
biomedich-48	217	18	therefore	therefore	ADV
biomedich-48	217	19	the	the	DET
biomedich-48	217	20	condition	condition	NOUN
biomedich-48	217	21	of	of	ADP
biomedich-48	217	22	theorem	theorem	ADJ
biomedich-48	217	23	2	2	NUM
biomedich-48	217	24	is	be	AUX
biomedich-48	217	25	not	not	PART
biomedich-48	217	26	strong	strong	ADJ
biomedich-48	217	27	enough	enough	ADV
biomedich-48	217	28	to	to	PART
biomedich-48	217	29	prove	prove	VERB
biomedich-48	217	30	that	that	SCONJ
biomedich-48	217	31	the	the	DET
biomedich-48	217	32	eigenvalues	eigenvalue	NOUN
biomedich-48	217	33	of	of	ADP
biomedich-48	217	34	leslie	leslie	PROPN
biomedich-48	217	35	's	's	PART
biomedich-48	217	36	matrix	matrix	NOUN
biomedich-48	217	37	are	be	AUX
biomedich-48	217	38	dominant	dominant	ADJ
biomedich-48	217	39	.	.	PUNCT
biomedich-48	218	1	theorem	theorem	VERB
biomedich-48	218	2	3	3	NUM
biomedich-48	218	3	if	if	SCONJ
biomedich-48	218	4	two	two	NUM
biomedich-48	218	5	consecutive	consecutive	ADJ
biomedich-48	218	6	entries	entry	NOUN
biomedich-48	218	7	𝑎𝑖	𝑎𝑖	ADP
biomedich-48	218	8	and	and	CCONJ
biomedich-48	218	9	𝑎𝑖+1	𝑎𝑖+1	NUM
biomedich-48	218	10	in	in	ADP
biomedich-48	218	11	the	the	DET
biomedich-48	218	12	first	first	ADJ
biomedich-48	218	13	row	row	NOUN
biomedich-48	218	14	of	of	ADP
biomedich-48	218	15	a	a	DET
biomedich-48	218	16	leslie	leslie	PROPN
biomedich-48	218	17	matrix	matrix	NOUN
biomedich-48	218	18	𝐿	𝐿	PROPN
biomedich-48	218	19	are	be	AUX
biomedich-48	218	20	not	not	PART
biomedich-48	218	21	equal	equal	ADJ
biomedich-48	218	22	to	to	ADP
biomedich-48	218	23	zero	zero	NUM
biomedich-48	218	24	then	then	ADV
biomedich-48	218	25	the	the	DET
biomedich-48	218	26	positive	positive	ADJ
biomedich-48	218	27	eigenvalue	eigenvalue	NOUN
biomedich-48	218	28	of	of	ADP
biomedich-48	218	29	𝐿	𝐿	PROPN
biomedich-48	218	30	is	be	AUX
biomedich-48	218	31	dominant	dominant	ADJ
biomedich-48	218	32	.	.	PUNCT
biomedich-48	219	1	it	it	PRON
biomedich-48	219	2	is	be	AUX
biomedich-48	219	3	called	call	VERB
biomedich-48	219	4	the	the	DET
biomedich-48	219	5	dominant	dominant	PROPN
biomedich-48	219	6	eigenvalue	eigenvalue	PROPN
biomedich-48	219	7	j.	j.	PROPN
biomedich-48	219	8	|𝜆𝑘|	|𝜆𝑘|	PROPN
biomedich-48	219	9	<	<	X
biomedich-48	219	10	𝜆1	𝜆1	PROPN
biomedich-48	219	11	should	should	AUX
biomedich-48	219	12	not	not	PART
biomedich-48	219	13	|𝜆𝑘|	|𝜆𝑘|	VERB
biomedich-48	219	14	=	=	PUNCT
biomedich-48	219	15	𝜆1	𝜆1	NOUN
biomedich-48	219	16	or	or	CCONJ
biomedich-48	219	17	indicated	indicate	VERB
biomedich-48	219	18	|𝜆𝑘|	|𝜆𝑘|	NOUN
biomedich-48	219	19	≠	≠	NOUN
biomedich-48	219	20	𝜆1	𝜆1	NOUN
biomedich-48	219	21	.	.	PUNCT
biomedich-48	220	1	by	by	ADP
biomedich-48	220	2	definition	definition	NOUN
biomedich-48	220	3	𝑎𝑖	𝑎𝑖	ADP
biomedich-48	220	4	>	>	X
biomedich-48	220	5	0	0	NUM
biomedich-48	220	6	and	and	CCONJ
biomedich-48	220	7	𝑎𝑖+1	𝑎𝑖+1	NUM
biomedich-48	220	8	>	>	PUNCT
biomedich-48	220	9	0	0	X
biomedich-48	220	10	.	.	PUNCT
biomedich-48	221	1	with	with	ADP
biomedich-48	221	2	𝑖	𝑖	NOUN
biomedich-48	221	3	=	=	SYM
biomedich-48	221	4	1,2	1,2	NUM
biomedich-48	221	5	,	,	PUNCT
biomedich-48	221	6	…	…	PUNCT
biomedich-48	221	7	,	,	PUNCT
biomedich-48	221	8	𝑛	𝑛	PROPN
biomedich-48	221	9	,	,	PUNCT
biomedich-48	221	10	without	without	ADP
biomedich-48	221	11	prejudice	prejudice	NOUN
biomedich-48	221	12	generaly	generaly	NOUN
biomedich-48	221	13	theorem	theorem	NOUN
biomedich-48	221	14	be	be	AUX
biomedich-48	221	15	understood	understand	VERB
biomedich-48	221	16	𝑖	𝑖	X
biomedich-48	221	17	=	=	NOUN
biomedich-48	222	1	1	1	X
biomedich-48	222	2	.	.	PUNCT
biomedich-48	223	1	so	so	ADV
biomedich-48	223	2	𝑎1	𝑎1	VERB
biomedich-48	223	3	>	>	X
biomedich-48	223	4	0	0	PUNCT
biomedich-48	224	1	and	and	CCONJ
biomedich-48	224	2	𝑎2	𝑎2	PROPN
biomedich-48	224	3	>	>	X
biomedich-48	224	4	0	0	PROPN
biomedich-48	224	5	,	,	PUNCT
biomedich-48	224	6	so	so	SCONJ
biomedich-48	224	7	it	it	PRON
biomedich-48	224	8	will	will	AUX
biomedich-48	224	9	be	be	AUX
biomedich-48	224	10	shown	show	VERB
biomedich-48	224	11	|𝜆𝑘|	|𝜆𝑘|	ADP
biomedich-48	224	12	≠	≠	NOUN
biomedich-48	224	13	𝜆1	𝜆1	NOUN
biomedich-48	224	14	with	with	ADP
biomedich-48	224	15	𝑘	𝑘	PROPN
biomedich-48	224	16	=	=	SYM
biomedich-48	224	17	2,3	2,3	NUM
biomedich-48	224	18	,	,	PUNCT
biomedich-48	224	19	…	…	PUNCT
biomedich-48	224	20	,	,	PUNCT
biomedich-48	224	21	𝑛	𝑛	NOUN
biomedich-48	224	22	,	,	PUNCT
biomedich-48	224	23	where	where	SCONJ
biomedich-48	224	24	𝜆1	𝜆1	NOUN
biomedich-48	224	25	is	be	AUX
biomedich-48	224	26	positif	positif	NOUN
biomedich-48	224	27	.	.	PUNCT
biomedich-48	225	1	to	to	PART
biomedich-48	225	2	prove	prove	VERB
biomedich-48	225	3	it	it	PRON
biomedich-48	225	4	is	be	AUX
biomedich-48	225	5	done	do	VERB
biomedich-48	225	6	way	way	NOUN
biomedich-48	225	7	of	of	ADP
biomedich-48	225	8	contradiction	contradiction	NOUN
biomedich-48	225	9	.	.	PUNCT
biomedich-48	226	1	that	that	PRON
biomedich-48	226	2	is	is	ADV
biomedich-48	226	3	,	,	PUNCT
biomedich-48	226	4	it	it	PRON
biomedich-48	226	5	will	will	AUX
biomedich-48	226	6	be	be	AUX
biomedich-48	226	7	assumed	assume	VERB
biomedich-48	226	8	that	that	SCONJ
biomedich-48	226	9	𝜆𝑘	𝜆𝑘	ADV
biomedich-48	226	10	=	=	NOUN
biomedich-48	226	11	𝜆1	𝜆1	PROPN
biomedich-48	226	12	.	.	PUNCT
biomedich-48	227	1	if	if	SCONJ
biomedich-48	227	2	𝜆𝑘	𝜆𝑘	VERB
biomedich-48	227	3	=	=	NOUN
biomedich-48	227	4	𝜆1	𝜆1	PROPN
biomedich-48	227	5	then	then	ADV
biomedich-48	227	6	𝑟𝑒𝑖𝜃	𝑟𝑒𝑖𝜃	VERB
biomedich-48	227	7	=	=	SYM
biomedich-48	227	8	𝜆1	𝜆1	PROPN
biomedich-48	227	9	,	,	PUNCT
biomedich-48	227	10	so	so	SCONJ
biomedich-48	227	11	𝑟(𝑐𝑜𝑠𝜃	𝑟(𝑐𝑜𝑠𝜃	NOUN
biomedich-48	227	12	+	+	CCONJ
biomedich-48	227	13	𝑠𝑖𝑛𝜃	𝑠𝑖𝑛𝜃	NOUN
biomedich-48	227	14	)	)	PUNCT
biomedich-48	227	15	=	=	SYM
biomedich-48	227	16	𝜆1	𝜆1	PROPN
biomedich-48	227	17	.	.	PUNCT
biomedich-48	228	1	𝑟𝑐𝑜𝑠𝜃	𝑟𝑐𝑜𝑠𝜃	PROPN
biomedich-48	228	2	+	+	CCONJ
biomedich-48	228	3	𝑖𝑟𝑠𝑖𝑛𝜃	𝑖𝑟𝑠𝑖𝑛𝜃	NOUN
biomedich-48	228	4	=	=	SYM
biomedich-48	228	5	𝜆1	𝜆1	NOUN
biomedich-48	228	6	+	+	CCONJ
biomedich-48	228	7	𝑖0	𝑖0	NOUN
biomedich-48	228	8	.	.	PUNCT
biomedich-48	228	9	obtained	obtain	VERB
biomedich-48	228	10	𝑟𝑐𝑜𝑠𝜃	𝑟𝑐𝑜𝑠𝜃	NOUN
biomedich-48	228	11	=	=	SYM
biomedich-48	228	12	𝜆1	𝜆1	PROPN
biomedich-48	228	13	and	and	CCONJ
biomedich-48	228	14	𝑟𝑠𝑖𝑛𝜃	𝑟𝑠𝑖𝑛𝜃	NOUN
biomedich-48	228	15	=	=	SYM
biomedich-48	228	16	0	0	X
biomedich-48	228	17	.	.	PUNCT
biomedich-48	229	1	anggreini	anggreini	NOUN
biomedich-48	229	2	–	–	PUNCT
biomedich-48	229	3	the	the	DET
biomedich-48	229	4	female	female	ADJ
biomedich-48	229	5	population	population	NOUN
biomedich-48	229	6	growth	growth	NOUN
biomedich-48	229	7	projection	projection	NOUN
biomedich-48	229	8	year	year	NOUN
biomedich-48	229	9	2021	2021	NUM
biomedich-48	229	10	in	in	ADP
biomedich-48	229	11	trenggalek	trenggalek	NOUN
biomedich-48	229	12	…	…	PUNCT
biomedich-48	229	13	43	43	NUM
biomedich-48	229	14	if	if	SCONJ
biomedich-48	229	15	the	the	DET
biomedich-48	229	16	equation	equation	NOUN
biomedich-48	229	17	𝑟𝑐𝑜𝑠𝜃	𝑟𝑐𝑜𝑠𝜃	NOUN
biomedich-48	229	18	=	=	SYM
biomedich-48	229	19	𝜆1	𝜆1	PROPN
biomedich-48	229	20	multiplied	multiply	VERB
biomedich-48	229	21	by	by	ADP
biomedich-48	229	22	𝑐𝑜𝑠𝜃	𝑐𝑜𝑠𝜃	NOUN
biomedich-48	229	23	be	be	AUX
biomedich-48	229	24	𝑟𝑐𝑜𝑠2𝜃	𝑟𝑐𝑜𝑠2𝜃	VERB
biomedich-48	229	25	=	=	PUNCT
biomedich-48	230	1	𝜆1𝑐𝑜𝑠𝜃.	𝜆1𝑐𝑜𝑠𝜃.	PUNCT
biomedich-48	230	2	it	it	PRON
biomedich-48	230	3	means	mean	VERB
biomedich-48	230	4	𝜆1𝑐𝑜𝑠𝜃	𝜆1𝑐𝑜𝑠𝜃	NOUN
biomedich-48	230	5	≠	≠	PROPN
biomedich-48	230	6	𝑟	𝑟	NOUN
biomedich-48	230	7	or	or	CCONJ
biomedich-48	230	8	𝜆1𝑐𝑜𝑠𝜃	𝜆1𝑐𝑜𝑠𝜃	NOUN
biomedich-48	230	9	−	−	VERB
biomedich-48	230	10	𝑟	𝑟	NOUN
biomedich-48	230	11	≠	≠	PROPN
biomedich-48	230	12	0	0	NUM
biomedich-48	230	13	based	base	VERB
biomedich-48	230	14	on	on	ADP
biomedich-48	230	15	the	the	DET
biomedich-48	230	16	equation	equation	NOUN
biomedich-48	230	17	(	(	PUNCT
biomedich-48	230	18	9	9	NUM
biomedich-48	230	19	)	)	PUNCT
biomedich-48	230	20	that	that	PRON
biomedich-48	230	21	is	be	AUX
biomedich-48	230	22	𝑎1	𝑎1	PRON
biomedich-48	230	23	(	(	PUNCT
biomedich-48	230	24	𝜆1𝑐𝑜𝑠𝜃−𝑟	𝜆1𝑐𝑜𝑠𝜃−𝑟	NOUN
biomedich-48	230	25	𝑟𝜆1	𝑟𝜆1	PROPN
biomedich-48	230	26	)	)	PUNCT
biomedich-48	231	1	+	+	CCONJ
biomedich-48	232	1	𝑎2𝑏1	𝑎2𝑏1	NOUN
biomedich-48	232	2	(	(	PUNCT
biomedich-48	232	3	𝜆1	𝜆1	VERB
biomedich-48	232	4	2𝑐𝑜𝑠2𝜃−𝑟2	2𝑐𝑜𝑠2𝜃−𝑟2	PROPN
biomedich-48	232	5	𝑟2𝜆1	𝑟2𝜆1	PROPN
biomedich-48	232	6	2	2	NUM
biomedich-48	232	7	)	)	PUNCT
biomedich-48	233	1	+	+	CCONJ
biomedich-48	233	2	⋯	⋯	NOUN
biomedich-48	233	3	⋯+	⋯+	NOUN
biomedich-48	233	4	𝑎𝑛𝑏1𝑏2	𝑎𝑛𝑏1𝑏2	NOUN
biomedich-48	233	5	…	…	PUNCT
biomedich-48	233	6	𝑏𝑛−1	𝑏𝑛−1	PROPN
biomedich-48	233	7	(	(	PUNCT
biomedich-48	233	8	𝜆1	𝜆1	VERB
biomedich-48	233	9	𝑛𝑐𝑜𝑠𝑛𝜃−𝑟𝑛	𝑛𝑐𝑜𝑠𝑛𝜃−𝑟𝑛	NUM
biomedich-48	233	10	𝑟𝑛𝜆1	𝑟𝑛𝜆1	NOUN
biomedich-48	233	11	𝑛	𝑛	ADP
biomedich-48	233	12	)	)	PUNCT
biomedich-48	233	13	=	=	SYM
biomedich-48	233	14	0	0	NUM
biomedich-48	233	15	earned	earn	VERB
biomedich-48	233	16	value	value	NOUN
biomedich-48	233	17	𝑎1	𝑎1	NOUN
biomedich-48	233	18	=	=	SYM
biomedich-48	233	19	0	0	NUM
biomedich-48	233	20	and	and	CCONJ
biomedich-48	233	21	𝑎2	𝑎2	NOUN
biomedich-48	233	22	=	=	SYM
biomedich-48	233	23	0	0	X
biomedich-48	233	24	.	.	PUNCT
biomedich-48	234	1	the	the	DET
biomedich-48	234	2	statement	statement	NOUN
biomedich-48	234	3	is	be	AUX
biomedich-48	234	4	contrary	contrary	ADJ
biomedich-48	234	5	to	to	ADP
biomedich-48	234	6	the	the	DET
biomedich-48	234	7	assumption	assumption	NOUN
biomedich-48	234	8	that	that	PRON
biomedich-48	234	9	states	state	VERB
biomedich-48	234	10	𝑎1	𝑎1	NOUN
biomedich-48	234	11	>	>	X
biomedich-48	234	12	0	0	PUNCT
biomedich-48	235	1	and	and	CCONJ
biomedich-48	235	2	𝑎2	𝑎2	PROPN
biomedich-48	235	3	>	>	X
biomedich-48	235	4	0	0	X
biomedich-48	235	5	.	.	PUNCT
biomedich-48	236	1	meaning	mean	VERB
biomedich-48	236	2	the	the	DET
biomedich-48	236	3	wrong	wrong	ADJ
biomedich-48	236	4	supposition	supposition	NOUN
biomedich-48	236	5	|𝜆𝑘|	|𝜆𝑘|	NOUN
biomedich-48	236	6	≠	≠	NOUN
biomedich-48	236	7	𝜆1	𝜆1	NOUN
biomedich-48	236	8	.	.	PUNCT
biomedich-48	237	1	in	in	ADP
biomedich-48	237	2	the	the	DET
biomedich-48	237	3	next	next	ADJ
biomedich-48	237	4	section	section	NOUN
biomedich-48	237	5	it	it	PRON
biomedich-48	237	6	will	will	AUX
biomedich-48	237	7	always	always	ADV
biomedich-48	237	8	be	be	AUX
biomedich-48	237	9	assumed	assume	VERB
biomedich-48	237	10	that	that	SCONJ
biomedich-48	237	11	the	the	DET
biomedich-48	237	12	requirements	requirement	NOUN
biomedich-48	237	13	of	of	ADP
biomedich-48	237	14	theorem	theorem	ADJ
biomedich-48	237	15	3	3	NUM
biomedich-48	237	16	are	be	AUX
biomedich-48	237	17	met	meet	VERB
biomedich-48	237	18	.	.	PUNCT
biomedich-48	238	1	it	it	PRON
biomedich-48	238	2	will	will	AUX
biomedich-48	238	3	be	be	AUX
biomedich-48	238	4	assumed	assume	VERB
biomedich-48	238	5	that	that	SCONJ
biomedich-48	238	6	l	l	NOUN
biomedich-48	238	7	can	can	AUX
biomedich-48	238	8	be	be	AUX
biomedich-48	238	9	diagonalized	diagonalize	VERB
biomedich-48	238	10	.	.	PUNCT
biomedich-48	239	1	it	it	PRON
biomedich-48	239	2	is	be	AUX
biomedich-48	239	3	not	not	PART
biomedich-48	239	4	necessary	necessary	ADJ
biomedich-48	239	5	for	for	SCONJ
biomedich-48	239	6	the	the	DET
biomedich-48	239	7	conclusions	conclusion	NOUN
biomedich-48	239	8	to	to	PART
biomedich-48	239	9	be	be	AUX
biomedich-48	239	10	taken	take	VERB
biomedich-48	239	11	,	,	PUNCT
biomedich-48	239	12	but	but	CCONJ
biomedich-48	239	13	this	this	PRON
biomedich-48	239	14	will	will	AUX
biomedich-48	239	15	simplify	simplify	VERB
biomedich-48	239	16	the	the	DET
biomedich-48	239	17	argument	argument	NOUN
biomedich-48	239	18	.	.	PUNCT
biomedich-48	240	1	in	in	ADP
biomedich-48	240	2	this	this	DET
biomedich-48	240	3	case	case	NOUN
biomedich-48	240	4	,	,	PUNCT
biomedich-48	240	5	l	l	NOUN
biomedich-48	240	6	has	have	VERB
biomedich-48	240	7	n	n	PRON
biomedich-48	240	8	eigenvalues	eigenvalue	NOUN
biomedich-48	240	9	,	,	PUNCT
biomedich-48	240	10	𝜆1	𝜆1	NOUN
biomedich-48	240	11	,	,	PUNCT
biomedich-48	240	12	𝜆2	𝜆2	PROPN
biomedich-48	240	13	,	,	PUNCT
biomedich-48	240	14	...	...	PUNCT
biomedich-48	240	15	,	,	PUNCT
biomedich-48	240	16	𝜆𝑛	𝜆𝑛	NOUN
biomedich-48	240	17	,	,	PUNCT
biomedich-48	240	18	which	which	PRON
biomedich-48	240	19	need	need	AUX
biomedich-48	240	20	not	not	PART
biomedich-48	240	21	be	be	AUX
biomedich-48	240	22	different	different	ADJ
biomedich-48	240	23	from	from	ADP
biomedich-48	240	24	each	each	DET
biomedich-48	240	25	other	other	ADJ
biomedich-48	240	26	,	,	PUNCT
biomedich-48	240	27	and	and	CCONJ
biomedich-48	240	28	n	n	CCONJ
biomedich-48	240	29	linearly	linearly	ADV
biomedich-48	240	30	independent	independent	ADJ
biomedich-48	240	31	eigenvectors	eigenvector	NOUN
biomedich-48	240	32	𝐱1	𝐱1	NOUN
biomedich-48	240	33	,	,	PUNCT
biomedich-48	240	34	𝐱2	𝐱2	PROPN
biomedich-48	240	35	,	,	PUNCT
biomedich-48	240	36	...	...	PUNCT
biomedich-48	240	37	,	,	PUNCT
biomedich-48	240	38	𝐱𝑛	𝐱𝑛	INTJ
biomedich-48	240	39	,	,	PUNCT
biomedich-48	240	40	which	which	PRON
biomedich-48	240	41	corresponds	correspond	VERB
biomedich-48	240	42	to	to	ADP
biomedich-48	240	43	the	the	DET
biomedich-48	240	44	eigenvalue	eigenvalue	NOUN
biomedich-48	240	45	.	.	PUNCT
biomedich-48	241	1	in	in	ADP
biomedich-48	241	2	this	this	DET
biomedich-48	241	3	list	list	NOUN
biomedich-48	241	4	will	will	AUX
biomedich-48	241	5	be	be	AUX
biomedich-48	241	6	placed	place	VERB
biomedich-48	241	7	eigenvalues	eigenvalue	NOUN
biomedich-48	241	8	𝜆1	𝜆1	VERB
biomedich-48	241	9	the	the	DET
biomedich-48	241	10	dominant	dominant	ADJ
biomedich-48	241	11	first	first	ADV
biomedich-48	241	12	.	.	PUNCT
biomedich-48	242	1	a	a	DET
biomedich-48	242	2	matrix	matrix	NOUN
biomedich-48	242	3	p	p	NOUN
biomedich-48	242	4	will	will	AUX
biomedich-48	242	5	be	be	AUX
biomedich-48	242	6	formed	form	VERB
biomedich-48	242	7	whose	whose	DET
biomedich-48	242	8	columns	column	NOUN
biomedich-48	242	9	are	be	AUX
biomedich-48	242	10	eigenvectors	eigenvector	NOUN
biomedich-48	242	11	of	of	ADP
biomedich-48	242	12	l.	l.	PROPN
biomedich-48	242	13	𝑃	𝑃	PROPN
biomedich-48	242	14	=	=	SYM
biomedich-48	243	1	[	[	X
biomedich-48	243	2	𝐱1|𝐱2|𝐱3|⋯	𝐱1|𝐱2|𝐱3|⋯	NOUN
biomedich-48	243	3	|𝐱𝑛	|𝐱𝑛	X
biomedich-48	243	4	]	]	X
biomedich-48	243	5	𝐿𝑃	𝐿𝑃	PROPN
biomedich-48	243	6	=	=	SYM
biomedich-48	243	7	𝐿[𝐱1|𝐱2|𝐱3|⋯	𝐿[𝐱1|𝐱2|𝐱3|⋯	PUNCT
biomedich-48	243	8	|𝐱𝑛	|𝐱𝑛	X
biomedich-48	243	9	]	]	X
biomedich-48	243	10	=	=	PUNCT
biomedich-48	244	1	[	[	X
biomedich-48	244	2	𝐿𝐱1|𝐿𝐱2|𝐿𝐱3|⋯	𝐿𝐱1|𝐿𝐱2|𝐿𝐱3|⋯	PROPN
biomedich-48	244	3	|𝐿𝐱𝑛	|𝐿𝐱𝑛	NOUN
biomedich-48	244	4	]	]	X
biomedich-48	244	5	=	=	SYM
biomedich-48	245	1	[	[	X
biomedich-48	245	2	𝜆1𝐱1|𝜆2𝐱2|𝜆3𝐱3|⋯	𝜆1𝐱1|𝜆2𝐱2|𝜆3𝐱3|⋯	PROPN
biomedich-48	245	3	|𝜆𝑛𝐱𝑛	|𝜆𝑛𝐱𝑛	PROPN
biomedich-48	245	4	]	]	X
biomedich-48	245	5	=	=	SYM
biomedich-48	246	1	[	[	X
biomedich-48	246	2	𝐱1|𝐱2|𝐱3|⋯	𝐱1|𝐱2|𝐱3|⋯	NOUN
biomedich-48	246	3	|𝐱𝑛	|𝐱𝑛	X
biomedich-48	246	4	]	]	X
biomedich-48	246	5	[	[	PUNCT
biomedich-48	246	6	𝜆1	𝜆1	NOUN
biomedich-48	246	7	0	0	NUM
biomedich-48	246	8	⋮	⋮	NOUN
biomedich-48	246	9	0	0	NUM
biomedich-48	246	10	0	0	NUM
biomedich-48	246	11	𝜆2	𝜆2	NOUN
biomedich-48	246	12	⋮	⋮	NOUN
biomedich-48	246	13	0	0	NUM
biomedich-48	247	1	⋯	⋯	NOUN
biomedich-48	247	2	⋯	⋯	PROPN
biomedich-48	247	3	⋯	⋯	ADP
biomedich-48	247	4	0	0	NOUN
biomedich-48	247	5	0	0	NUM
biomedich-48	247	6	⋮	⋮	NOUN
biomedich-48	247	7	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	247	8	]	]	PUNCT
biomedich-48	247	9	=	=	PUNCT
biomedich-48	247	10	𝑃𝐷	𝑃𝐷	PROPN
biomedich-48	247	11	because	because	SCONJ
biomedich-48	247	12	column	column	NOUN
biomedich-48	247	13	vectors	vector	NOUN
biomedich-48	247	14	of	of	ADP
biomedich-48	247	15	the	the	DET
biomedich-48	247	16	linear	linear	ADJ
biomedich-48	247	17	matrices	matrix	NOUN
biomedich-48	247	18	p	p	NOUN
biomedich-48	247	19	are	be	AUX
biomedich-48	247	20	linearly	linearly	ADV
biomedich-48	247	21	independent	independent	ADJ
biomedich-48	247	22	,	,	PUNCT
biomedich-48	247	23	and	and	CCONJ
biomedich-48	247	24	p	p	NOUN
biomedich-48	247	25	is	be	AUX
biomedich-48	247	26	reversible	reversible	ADJ
biomedich-48	247	27	so	so	SCONJ
biomedich-48	247	28	that	that	SCONJ
biomedich-48	247	29	the	the	DET
biomedich-48	247	30	matrix	matrix	NOUN
biomedich-48	247	31	l	l	NOUN
biomedich-48	247	32	can	can	AUX
biomedich-48	247	33	be	be	AUX
biomedich-48	247	34	diagonalized	diagonalize	VERB
biomedich-48	247	35	.	.	PUNCT
biomedich-48	248	1	the	the	DET
biomedich-48	248	2	diagonalization	diagonalization	NOUN
biomedich-48	248	3	of	of	ADP
biomedich-48	248	4	l	l	NOUN
biomedich-48	248	5	will	will	AUX
biomedich-48	248	6	be	be	AUX
biomedich-48	248	7	given	give	VERB
biomedich-48	248	8	by	by	ADP
biomedich-48	248	9	the	the	DET
biomedich-48	248	10	equation	equation	NOUN
biomedich-48	248	11	𝐿	𝐿	NOUN
biomedich-48	248	12	=	=	PUNCT
biomedich-48	248	13	𝑃𝐷𝑃−1	𝑃𝐷𝑃−1	VERB
biomedich-48	248	14	𝐿	𝐿	PROPN
biomedich-48	248	15	=	=	SYM
biomedich-48	248	16	𝑃	𝑃	PROPN
biomedich-48	248	17	[	[	PUNCT
biomedich-48	248	18	𝜆1	𝜆1	NOUN
biomedich-48	248	19	0	0	NUM
biomedich-48	248	20	⋮	⋮	NOUN
biomedich-48	248	21	0	0	NUM
biomedich-48	248	22	0	0	NUM
biomedich-48	248	23	𝜆2	𝜆2	NOUN
biomedich-48	248	24	⋮	⋮	NOUN
biomedich-48	248	25	0	0	NUM
biomedich-48	249	1	⋯	⋯	NOUN
biomedich-48	249	2	⋯	⋯	PROPN
biomedich-48	249	3	⋯	⋯	ADP
biomedich-48	249	4	0	0	NOUN
biomedich-48	249	5	0	0	NUM
biomedich-48	249	6	⋮	⋮	NOUN
biomedich-48	249	7	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	250	1	]	]	X
biomedich-48	250	2	𝑃−1	𝑃−1	X
biomedich-48	250	3	from	from	ADP
biomedich-48	250	4	this	this	DET
biomedich-48	250	5	equation	equation	NOUN
biomedich-48	250	6	is	be	AUX
biomedich-48	250	7	obtained	obtain	VERB
biomedich-48	250	8	𝐿𝑘	𝐿𝑘	PROPN
biomedich-48	250	9	=	=	PUNCT
biomedich-48	250	10	𝑃	𝑃	PROPN
biomedich-48	250	11	[	[	PUNCT
biomedich-48	250	12	𝜆1	𝜆1	NOUN
biomedich-48	250	13	𝑘	𝑘	PRON
biomedich-48	250	14	0	0	NUM
biomedich-48	250	15	⋮	⋮	NOUN
biomedich-48	250	16	0	0	NUM
biomedich-48	250	17	0	0	NUM
biomedich-48	250	18	𝜆2	𝜆2	NOUN
biomedich-48	250	19	𝑘	𝑘	DET
biomedich-48	250	20	⋮	⋮	NOUN
biomedich-48	250	21	0	0	SYM
biomedich-48	251	1	⋯	⋯	NOUN
biomedich-48	251	2	⋯	⋯	PROPN
biomedich-48	251	3	⋯	⋯	ADP
biomedich-48	251	4	0	0	NOUN
biomedich-48	251	5	0	0	NUM
biomedich-48	251	6	⋮	⋮	NOUN
biomedich-48	251	7	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	251	8	𝑘	𝑘	X
biomedich-48	251	9	]	]	X
biomedich-48	251	10	𝑃−1	𝑃−1	X
biomedich-48	251	11	for	for	ADP
biomedich-48	251	12	𝑘	𝑘	X
biomedich-48	251	13	=	=	SYM
biomedich-48	251	14	1,2	1,2	NUM
biomedich-48	251	15	,	,	PUNCT
biomedich-48	251	16	…	…	PUNCT
biomedich-48	251	17	for	for	ADP
biomedich-48	251	18	any	any	DET
biomedich-48	251	19	vector	vector	NOUN
biomedich-48	251	20	of	of	ADP
biomedich-48	251	21	age	age	NOUN
biomedich-48	251	22	distribution	distribution	NOUN
biomedich-48	251	23	it	it	PRON
biomedich-48	251	24	will	will	AUX
biomedich-48	251	25	first	first	ADV
biomedich-48	251	26	𝐱(0	𝐱(0	PROPN
biomedich-48	251	27	)	)	PUNCT
biomedich-48	251	28	be	be	AUX
biomedich-48	251	29	obtained	obtain	VERB
biomedich-48	251	30	𝐿𝑘𝐱(0	𝐿𝑘𝐱(0	PROPN
biomedich-48	251	31	)	)	PUNCT
biomedich-48	251	32	=	=	PUNCT
biomedich-48	251	33	𝑃	𝑃	PROPN
biomedich-48	251	34	[	[	PUNCT
biomedich-48	251	35	𝜆1	𝜆1	NOUN
biomedich-48	251	36	𝑘	𝑘	PRON
biomedich-48	251	37	0	0	NUM
biomedich-48	251	38	⋮	⋮	NOUN
biomedich-48	251	39	0	0	NUM
biomedich-48	251	40	0	0	NUM
biomedich-48	251	41	𝜆2	𝜆2	NOUN
biomedich-48	251	42	𝑘	𝑘	DET
biomedich-48	251	43	⋮	⋮	NOUN
biomedich-48	251	44	0	0	SYM
biomedich-48	252	1	⋯	⋯	NOUN
biomedich-48	252	2	⋯	⋯	PROPN
biomedich-48	252	3	⋯	⋯	ADP
biomedich-48	252	4	0	0	NOUN
biomedich-48	252	5	0	0	NUM
biomedich-48	252	6	⋮	⋮	NOUN
biomedich-48	252	7	𝜆𝑛	𝜆𝑛	ADP
biomedich-48	252	8	𝑘	𝑘	X
biomedich-48	252	9	]	]	X
biomedich-48	252	10	𝑃−1𝐱(0	𝑃−1𝐱(0	X
biomedich-48	252	11	)	)	PUNCT
biomedich-48	252	12	for	for	ADP
biomedich-48	252	13	𝑘	𝑘	NOUN
biomedich-48	252	14	=	=	SYM
biomedich-48	252	15	1,2	1,2	NUM
biomedich-48	252	16	,	,	PUNCT
biomedich-48	252	17	…	…	PUNCT
biomedich-48	252	18	by	by	ADP
biomedich-48	252	19	dividing	divide	VERB
biomedich-48	252	20	two	two	NUM
biomedich-48	252	21	sections	section	NOUN
biomedich-48	252	22	of	of	ADP
biomedich-48	252	23	this	this	DET
biomedich-48	252	24	equation	equation	NOUN
biomedich-48	252	25	by	by	ADP
biomedich-48	252	26	𝜆1	𝜆1	NOUN
biomedich-48	252	27	𝑘	𝑘	PRON
biomedich-48	252	28	and	and	CCONJ
biomedich-48	252	29	using	use	VERB
biomedich-48	252	30	the	the	DET
biomedich-48	252	31	fact	fact	NOUN
biomedich-48	252	32	that	that	SCONJ
biomedich-48	252	33	𝐱(𝑘	𝐱(𝑘	VERB
biomedich-48	252	34	)	)	PUNCT
biomedich-48	252	35	=	=	SYM
biomedich-48	252	36	𝐿(𝑘)𝐱(0	𝐿(𝑘)𝐱(0	PROPN
biomedich-48	252	37	)	)	PUNCT
biomedich-48	252	38	,	,	PUNCT
biomedich-48	252	39	it	it	PRON
biomedich-48	252	40	will	will	AUX
biomedich-48	252	41	be	be	AUX
biomedich-48	252	42	obtained	obtain	VERB
biomedich-48	252	43	1	1	NUM
biomedich-48	252	44	𝜆1	𝜆1	NOUN
biomedich-48	252	45	𝑘	𝑘	PRON
biomedich-48	252	46	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	252	47	)	)	PUNCT
biomedich-48	252	48	=	=	PUNCT
biomedich-48	252	49	𝑃	𝑃	NOUN
biomedich-48	252	50	[	[	PUNCT
biomedich-48	252	51	1	1	NUM
biomedich-48	252	52	0	0	NUM
biomedich-48	252	53	⋮	⋮	NOUN
biomedich-48	252	54	0	0	X
biomedich-48	252	55	0	0	PUNCT
biomedich-48	253	1	(	(	PUNCT
biomedich-48	253	2	𝜆2	𝜆2	NOUN
biomedich-48	253	3	𝜆1⁄	𝜆1⁄	PROPN
biomedich-48	253	4	)	)	PUNCT
biomedich-48	253	5	𝑘	𝑘	DET
biomedich-48	253	6	⋮	⋮	NOUN
biomedich-48	253	7	0	0	SYM
biomedich-48	254	1	⋯	⋯	NOUN
biomedich-48	254	2	⋯	⋯	PROPN
biomedich-48	254	3	⋯	⋯	ADP
biomedich-48	254	4	0	0	NOUN
biomedich-48	254	5	0	0	NUM
biomedich-48	254	6	⋮	⋮	NOUN
biomedich-48	254	7	(	(	PUNCT
biomedich-48	254	8	𝜆𝑛	𝜆𝑛	NOUN
biomedich-48	254	9	𝜆1⁄	𝜆1⁄	SYM
biomedich-48	254	10	)	)	PUNCT
biomedich-48	254	11	𝑘	𝑘	X
biomedich-48	254	12	]	]	X
biomedich-48	254	13	𝑃−1𝐱(0	𝑃−1𝐱(0	X
biomedich-48	254	14	)	)	PUNCT
biomedich-48	254	15	(	(	PUNCT
biomedich-48	254	16	10	10	NUM
biomedich-48	254	17	)	)	PUNCT
biomedich-48	254	18	because	because	SCONJ
biomedich-48	254	19	𝜆1	𝜆1	NOUN
biomedich-48	254	20	is	be	AUX
biomedich-48	254	21	the	the	DET
biomedich-48	254	22	dominant	dominant	ADJ
biomedich-48	254	23	eigen	eigen	PROPN
biomedich-48	254	24	value	value	NOUN
biomedich-48	254	25	that	that	PRON
biomedich-48	254	26	is	be	AUX
biomedich-48	254	27	|𝜆1|	|𝜆1|	NOUN
biomedich-48	254	28	>	>	X
biomedich-48	254	29	|𝜆𝑖|	|𝜆𝑖|	PROPN
biomedich-48	254	30	,	,	PUNCT
biomedich-48	254	31	then	then	ADV
biomedich-48	254	32	|𝜆𝑖	|𝜆𝑖	PROPN
biomedich-48	254	33	𝜆1⁄	𝜆1⁄	PROPN
biomedich-48	254	34	|	|	ADV
biomedich-48	254	35	<	<	X
biomedich-48	254	36	1	1	NUM
biomedich-48	254	37	for	for	ADP
biomedich-48	254	38	𝑖	𝑖	NOUN
biomedich-48	254	39	=	=	SYM
biomedich-48	254	40	2,3	2,3	NUM
biomedich-48	254	41	,	,	PUNCT
biomedich-48	254	42	…	…	PUNCT
biomedich-48	254	43	,	,	PUNCT
biomedich-48	254	44	𝑛.	𝑛.	NOUN
biomedich-48	254	45	it	it	PRON
biomedich-48	254	46	is	be	AUX
biomedich-48	254	47	clear	clear	ADJ
biomedich-48	254	48	that	that	SCONJ
biomedich-48	254	49	(	(	PUNCT
biomedich-48	254	50	𝜆𝑖	𝜆𝑖	PROPN
biomedich-48	254	51	𝜆1⁄	𝜆1⁄	PROPN
biomedich-48	254	52	)	)	PUNCT
biomedich-48	254	53	𝑘	𝑘	PROPN
biomedich-48	254	54	→	→	SYM
biomedich-48	254	55	0	0	PROPN
biomedich-48	254	56	if	if	SCONJ
biomedich-48	254	57	𝑘	𝑘	PRON
biomedich-48	254	58	→	→	SYM
biomedich-48	254	59	∞	∞	NUM
biomedich-48	254	60	for	for	ADP
biomedich-48	254	61	𝑖	𝑖	NOUN
biomedich-48	254	62	=	=	SYM
biomedich-48	254	63	2,3	2,3	NUM
biomedich-48	254	64	,	,	PUNCT
biomedich-48	254	65	…	…	PUNCT
biomedich-48	254	66	,	,	PUNCT
biomedich-48	254	67	𝑛.	𝑛.	NOUN
biomedich-48	254	68	using	use	VERB
biomedich-48	254	69	this	this	DET
biomedich-48	254	70	fact	fact	NOUN
biomedich-48	254	71	,	,	PUNCT
biomedich-48	254	72	it	it	PRON
biomedich-48	254	73	can	can	AUX
biomedich-48	254	74	take	take	VERB
biomedich-48	254	75	limits	limit	NOUN
biomedich-48	254	76	from	from	ADP
biomedich-48	254	77	both	both	DET
biomedich-48	254	78	sides	side	NOUN
biomedich-48	254	79	of	of	ADP
biomedich-48	254	80	(	(	PUNCT
biomedich-48	254	81	10	10	NUM
biomedich-48	254	82	)	)	PUNCT
biomedich-48	254	83	to	to	PART
biomedich-48	254	84	get	get	VERB
biomedich-48	254	85	lim	lim	PROPN
biomedich-48	254	86	𝑘→∞	𝑘→∞	PUNCT
biomedich-48	254	87	{	{	PUNCT
biomedich-48	254	88	1	1	NUM
biomedich-48	254	89	𝜆1	𝜆1	NOUN
biomedich-48	254	90	𝑘	𝑘	DET
biomedich-48	254	91	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	254	92	)	)	PUNCT
biomedich-48	254	93	}	}	PUNCT
biomedich-48	254	94	=	=	SYM
biomedich-48	254	95	𝑝	𝑝	PROPN
biomedich-48	254	96	[	[	PUNCT
biomedich-48	254	97	1	1	NUM
biomedich-48	254	98	0	0	NUM
biomedich-48	254	99	0	0	NUM
biomedich-48	254	100	⋯	⋯	ADP
biomedich-48	254	101	0	0	NUM
biomedich-48	254	102	0	0	NUM
biomedich-48	254	103	0	0	NUM
biomedich-48	254	104	0	0	NUM
biomedich-48	254	105	⋯	⋯	NOUN
biomedich-48	254	106	0	0	NUM
biomedich-48	254	107	⋮	⋮	NOUN
biomedich-48	254	108	⋮	⋮	ADJ
biomedich-48	254	109	⋮	⋮	ADJ
biomedich-48	254	110	⋮	⋮	NOUN
biomedich-48	254	111	0	0	NUM
biomedich-48	254	112	0	0	NUM
biomedich-48	254	113	0	0	NUM
biomedich-48	254	114	⋯	⋯	NOUN
biomedich-48	254	115	0	0	NUM
biomedich-48	254	116	]	]	PUNCT
biomedich-48	254	117	𝑃−1𝐱(𝟎	𝑃−1𝐱(𝟎	X
biomedich-48	254	118	)	)	PUNCT
biomedich-48	254	119	(	(	PUNCT
biomedich-48	254	120	11	11	X
biomedich-48	254	121	)	)	PUNCT
biomedich-48	254	122	it	it	PRON
biomedich-48	254	123	will	will	AUX
biomedich-48	254	124	then	then	ADV
biomedich-48	254	125	be	be	AUX
biomedich-48	254	126	declared	declare	VERB
biomedich-48	254	127	the	the	DET
biomedich-48	254	128	first	first	ADJ
biomedich-48	254	129	entry	entry	NOUN
biomedich-48	254	130	of	of	ADP
biomedich-48	254	131	the	the	DET
biomedich-48	254	132	column	column	NOUN
biomedich-48	254	133	vector	vector	NOUN
biomedich-48	254	134	𝑃−1𝐱(𝟎	𝑃−1𝐱(𝟎	PUNCT
biomedich-48	254	135	)	)	PUNCT
biomedich-48	254	136	with	with	ADP
biomedich-48	254	137	the	the	DET
biomedich-48	254	138	constants	constant	NOUN
biomedich-48	254	139	𝑐	𝑐	NOUN
biomedich-48	254	140	,	,	PUNCT
biomedich-48	254	141	then	then	ADV
biomedich-48	254	142	𝑃−1𝐱(𝟎	𝑃−1𝐱(𝟎	PUNCT
biomedich-48	254	143	)	)	PUNCT
biomedich-48	255	1	=	=	PUNCT
biomedich-48	255	2	[	[	PUNCT
biomedich-48	255	3	𝑐	𝑐	PROPN
biomedich-48	255	4	𝑐1	𝑐1	NOUN
biomedich-48	255	5	⋮	⋮	NOUN
biomedich-48	255	6	𝑐𝑛−1	𝑐𝑛−1	VERB
biomedich-48	255	7	]	]	X
biomedich-48	255	8	.	.	PUNCT
biomedich-48	256	1	this	this	DET
biomedich-48	256	2	result	result	NOUN
biomedich-48	256	3	is	be	AUX
biomedich-48	256	4	entered	enter	VERB
biomedich-48	256	5	into	into	ADP
biomedich-48	256	6	the	the	DET
biomedich-48	256	7	equation	equation	NOUN
biomedich-48	256	8	(	(	PUNCT
biomedich-48	256	9	11	11	NUM
biomedich-48	256	10	)	)	PUNCT
biomedich-48	256	11	lim	lim	NOUN
biomedich-48	256	12	𝑘→∞	𝑘→∞	PUNCT
biomedich-48	256	13	{	{	PUNCT
biomedich-48	256	14	1	1	NUM
biomedich-48	256	15	𝜆1	𝜆1	NOUN
biomedich-48	256	16	𝑘	𝑘	DET
biomedich-48	256	17	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	256	18	)	)	PUNCT
biomedich-48	256	19	}	}	PUNCT
biomedich-48	257	1	=	=	SYM
biomedich-48	257	2	𝑝	𝑝	PROPN
biomedich-48	257	3	[	[	PUNCT
biomedich-48	257	4	1	1	NUM
biomedich-48	257	5	0	0	NUM
biomedich-48	257	6	0	0	NUM
biomedich-48	257	7	⋯	⋯	ADP
biomedich-48	257	8	0	0	NUM
biomedich-48	257	9	0	0	NUM
biomedich-48	257	10	0	0	NUM
biomedich-48	257	11	0	0	NUM
biomedich-48	257	12	⋯	⋯	NOUN
biomedich-48	257	13	0	0	NUM
biomedich-48	257	14	⋮	⋮	NOUN
biomedich-48	257	15	⋮	⋮	ADJ
biomedich-48	257	16	⋮	⋮	ADJ
biomedich-48	257	17	⋮	⋮	NOUN
biomedich-48	257	18	0	0	NUM
biomedich-48	257	19	0	0	NUM
biomedich-48	257	20	0	0	NUM
biomedich-48	257	21	⋯	⋯	NOUN
biomedich-48	257	22	0	0	NUM
biomedich-48	257	23	]	]	PUNCT
biomedich-48	258	1	[	[	PUNCT
biomedich-48	258	2	𝑐	𝑐	PROPN
biomedich-48	258	3	𝑐1	𝑐1	NOUN
biomedich-48	258	4	⋮	⋮	NOUN
biomedich-48	258	5	𝑐𝑛−1	𝑐𝑛−1	VERB
biomedich-48	258	6	]	]	X
biomedich-48	258	7	=	=	PUNCT
biomedich-48	259	1	[	[	X
biomedich-48	259	2	𝐱1|𝐱2|𝐱3|⋯	𝐱1|𝐱2|𝐱3|⋯	NOUN
biomedich-48	259	3	|𝐱𝑛	|𝐱𝑛	X
biomedich-48	259	4	]	]	X
biomedich-48	259	5	[	[	PUNCT
biomedich-48	259	6	1	1	NUM
biomedich-48	259	7	0	0	NUM
biomedich-48	259	8	0	0	NUM
biomedich-48	259	9	⋯	⋯	ADP
biomedich-48	259	10	0	0	NUM
biomedich-48	259	11	0	0	NUM
biomedich-48	259	12	0	0	NUM
biomedich-48	259	13	0	0	NUM
biomedich-48	259	14	⋯	⋯	NOUN
biomedich-48	259	15	0	0	NUM
biomedich-48	259	16	⋮	⋮	NOUN
biomedich-48	259	17	⋮	⋮	ADJ
biomedich-48	259	18	⋮	⋮	ADJ
biomedich-48	259	19	⋮	⋮	NOUN
biomedich-48	259	20	0	0	NUM
biomedich-48	259	21	0	0	NUM
biomedich-48	259	22	0	0	NUM
biomedich-48	259	23	⋯	⋯	NOUN
biomedich-48	259	24	0	0	NUM
biomedich-48	259	25	]	]	PUNCT
biomedich-48	260	1	[	[	PUNCT
biomedich-48	260	2	𝑐	𝑐	PROPN
biomedich-48	260	3	𝑐1	𝑐1	NOUN
biomedich-48	260	4	⋮	⋮	NOUN
biomedich-48	260	5	𝑐𝑛−1	𝑐𝑛−1	VERB
biomedich-48	260	6	]	]	X
biomedich-48	260	7	=	=	PUNCT
biomedich-48	261	1	[	[	X
biomedich-48	261	2	𝐱1|𝐱2|𝐱3|⋯	𝐱1|𝐱2|𝐱3|⋯	NOUN
biomedich-48	261	3	|𝐱𝑛	|𝐱𝑛	X
biomedich-48	261	4	]	]	X
biomedich-48	261	5	[	[	PUNCT
biomedich-48	261	6	𝑐	𝑐	NOUN
biomedich-48	261	7	0	0	NUM
biomedich-48	261	8	⋮	⋮	NOUN
biomedich-48	261	9	0	0	NUM
biomedich-48	261	10	]	]	PUNCT
biomedich-48	262	1	=	=	PUNCT
biomedich-48	262	2	𝑐𝐱1	𝑐𝐱1	INTJ
biomedich-48	262	3	so	so	SCONJ
biomedich-48	262	4	that	that	SCONJ
biomedich-48	262	5	the	the	DET
biomedich-48	262	6	right	right	ADJ
biomedich-48	262	7	-	-	PUNCT
biomedich-48	262	8	hand	hand	NOUN
biomedich-48	262	9	side	side	NOUN
biomedich-48	262	10	of	of	ADP
biomedich-48	262	11	(	(	PUNCT
biomedich-48	262	12	11	11	NUM
biomedich-48	262	13	)	)	PUNCT
biomedich-48	262	14	can	can	AUX
biomedich-48	262	15	be	be	AUX
biomedich-48	262	16	written	write	VERB
biomedich-48	262	17	as	as	ADP
biomedich-48	262	18	𝑐𝐱𝟏	𝑐𝐱𝟏	PROPN
biomedich-48	262	19	,	,	PUNCT
biomedich-48	262	20	where	where	SCONJ
biomedich-48	262	21	𝑐	𝑐	PROPN
biomedich-48	262	22	is	be	AUX
biomedich-48	262	23	a	a	DET
biomedich-48	262	24	positive	positive	ADJ
biomedich-48	262	25	controw	controw	NOUN
biomedich-48	262	26	that	that	PRON
biomedich-48	262	27	depends	depend	VERB
biomedich-48	262	28	only	only	ADV
biomedich-48	262	29	on	on	ADP
biomedich-48	262	30	the	the	DET
biomedich-48	262	31	vector	vector	NOUN
biomedich-48	262	32	of	of	ADP
biomedich-48	262	33	age	age	NOUN
biomedich-48	262	34	distribution	distribution	NOUN
biomedich-48	262	35	first	first	ADV
biomedich-48	262	36	𝐱(0).so	𝐱(0).so	X
biomedich-48	262	37	(	(	PUNCT
biomedich-48	262	38	11	11	NUM
biomedich-48	262	39	)	)	PUNCT
biomedich-48	263	1	be	be	AUX
biomedich-48	263	2	lim	lim	PROPN
biomedich-48	263	3	𝑘→∞	𝑘→∞	PUNCT
biomedich-48	263	4	{	{	PUNCT
biomedich-48	263	5	1	1	NUM
biomedich-48	263	6	𝜆1	𝜆1	NOUN
biomedich-48	263	7	𝑘	𝑘	DET
biomedich-48	263	8	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	263	9	)	)	PUNCT
biomedich-48	263	10	}	}	PUNCT
biomedich-48	263	11	=	=	PUNCT
biomedich-48	263	12	𝑐𝐱𝟏	𝑐𝐱𝟏	NOUN
biomedich-48	263	13	(	(	PUNCT
biomedich-48	263	14	12	12	NUM
biomedich-48	263	15	)	)	PUNCT
biomedich-48	263	16	the	the	DET
biomedich-48	263	17	equation	equation	NOUN
biomedich-48	263	18	(	(	PUNCT
biomedich-48	263	19	12	12	NUM
biomedich-48	263	20	)	)	PUNCT
biomedich-48	263	21	gives	give	VERB
biomedich-48	263	22	an	an	DET
biomedich-48	263	23	approximation	approximation	NOUN
biomedich-48	263	24	𝐱(𝑘)~𝑐𝜆1	𝐱(𝑘)~𝑐𝜆1	PROPN
biomedich-48	263	25	𝑘𝐱𝟏	𝑘𝐱𝟏	NOUN
biomedich-48	263	26	(	(	PUNCT
biomedich-48	263	27	13	13	NUM
biomedich-48	263	28	)	)	PUNCT
biomedich-48	263	29	for	for	ADP
biomedich-48	263	30	large	large	ADJ
biomedich-48	263	31	k	k	PROPN
biomedich-48	263	32	values	value	NOUN
biomedich-48	263	33	.	.	PUNCT
biomedich-48	264	1	from	from	ADP
biomedich-48	264	2	(	(	PUNCT
biomedich-48	264	3	13	13	NUM
biomedich-48	264	4	)	)	PUNCT
biomedich-48	264	5	also	also	ADV
biomedich-48	264	6	obtain	obtain	VERB
biomedich-48	264	7	𝐱(𝑘−1	𝐱(𝑘−1	NOUN
biomedich-48	264	8	)	)	PUNCT
biomedich-48	264	9	≃	≃	NOUN
biomedich-48	264	10	𝑐𝜆1	𝑐𝜆1	VERB
biomedich-48	264	11	𝑘−1𝐱𝟏	𝑘−1𝐱𝟏	X
biomedich-48	264	12	(	(	PUNCT
biomedich-48	264	13	14	14	NUM
biomedich-48	264	14	)	)	PUNCT
biomedich-48	264	15	by	by	ADP
biomedich-48	264	16	comparing	compare	VERB
biomedich-48	264	17	equations	equation	NOUN
biomedich-48	264	18	(	(	PUNCT
biomedich-48	264	19	13	13	NUM
biomedich-48	264	20	)	)	PUNCT
biomedich-48	264	21	and	and	CCONJ
biomedich-48	264	22	equations	equation	NOUN
biomedich-48	264	23	(	(	PUNCT
biomedich-48	264	24	14	14	NUM
biomedich-48	264	25	)	)	PUNCT
biomedich-48	264	26	obtained	obtain	VERB
biomedich-48	264	27	44	44	NUM
biomedich-48	264	28	biology	biology	NOUN
biomedich-48	264	29	,	,	PUNCT
biomedich-48	264	30	medicine	medicine	NOUN
biomedich-48	264	31	,	,	PUNCT
biomedich-48	264	32	&	&	CCONJ
biomedich-48	264	33	natural	natural	ADJ
biomedich-48	264	34	product	product	NOUN
biomedich-48	264	35	chemistry	chemistry	NOUN
biomedich-48	264	36	6	6	NUM
biomedich-48	264	37	(	(	PUNCT
biomedich-48	264	38	2	2	NUM
biomedich-48	264	39	)	)	PUNCT
biomedich-48	264	40	,	,	PUNCT
biomedich-48	264	41	2017	2017	NUM
biomedich-48	264	42	:	:	PUNCT
biomedich-48	264	43	37	37	NUM
biomedich-48	264	44	-	-	SYM
biomedich-48	264	45	45	45	NUM
biomedich-48	264	46	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	264	47	)	)	PUNCT
biomedich-48	264	48	≃	≃	NOUN
biomedich-48	264	49	𝜆1𝐱	𝜆1𝐱	PUNCT
biomedich-48	264	50	(	(	PUNCT
biomedich-48	264	51	𝑘−1	𝑘−1	PROPN
biomedich-48	264	52	)	)	PUNCT
biomedich-48	264	53	(	(	PUNCT
biomedich-48	264	54	15	15	NUM
biomedich-48	264	55	)	)	PUNCT
biomedich-48	264	56	for	for	ADP
biomedich-48	264	57	large	large	ADJ
biomedich-48	264	58	𝑘	𝑘	DET
biomedich-48	264	59	values	value	NOUN
biomedich-48	264	60	.	.	PUNCT
biomedich-48	265	1	this	this	PRON
biomedich-48	265	2	means	mean	VERB
biomedich-48	265	3	that	that	SCONJ
biomedich-48	265	4	for	for	ADP
biomedich-48	265	5	large	large	ADJ
biomedich-48	265	6	time	time	NOUN
biomedich-48	265	7	values	value	NOUN
biomedich-48	265	8	each	each	DET
biomedich-48	265	9	age	age	NOUN
biomedich-48	265	10	distribution	distribution	NOUN
biomedich-48	265	11	vector	vector	NOUN
biomedich-48	265	12	is	be	AUX
biomedich-48	265	13	a	a	DET
biomedich-48	265	14	scalar	scalar	ADJ
biomedich-48	265	15	multiple	multiple	NOUN
biomedich-48	265	16	of	of	ADP
biomedich-48	265	17	the	the	DET
biomedich-48	265	18	previous	previous	ADJ
biomedich-48	265	19	age	age	NOUN
biomedich-48	265	20	distribution	distribution	NOUN
biomedich-48	265	21	vector	vector	NOUN
biomedich-48	265	22	,	,	PUNCT
biomedich-48	265	23	and	and	CCONJ
biomedich-48	265	24	the	the	DET
biomedich-48	265	25	scalar	scalar	NOUN
biomedich-48	265	26	is	be	AUX
biomedich-48	265	27	the	the	DET
biomedich-48	265	28	positive	positive	ADJ
biomedich-48	265	29	eigenvalue	eigenvalue	NOUN
biomedich-48	265	30	of	of	ADP
biomedich-48	265	31	leslie	leslie	PROPN
biomedich-48	265	32	's	's	PART
biomedich-48	265	33	matrix	matrix	NOUN
biomedich-48	265	34	.	.	PUNCT
biomedich-48	266	1	consequently	consequently	ADV
biomedich-48	266	2	,	,	PUNCT
biomedich-48	266	3	the	the	DET
biomedich-48	266	4	proportion	proportion	NOUN
biomedich-48	266	5	of	of	ADP
biomedich-48	266	6	females	female	NOUN
biomedich-48	266	7	in	in	ADP
biomedich-48	266	8	each	each	DET
biomedich-48	266	9	group	group	NOUN
biomedich-48	266	10	of	of	ADP
biomedich-48	266	11	age	age	NOUN
biomedich-48	266	12	groups	group	NOUN
biomedich-48	266	13	will	will	AUX
biomedich-48	266	14	be	be	AUX
biomedich-48	266	15	constant.then	constant.then	PROPN
biomedich-48	266	16	we	we	PRON
biomedich-48	266	17	will	will	AUX
biomedich-48	266	18	review	review	VERB
biomedich-48	266	19	the	the	DET
biomedich-48	266	20	equations	equation	NOUN
biomedich-48	266	21	(	(	PUNCT
biomedich-48	266	22	13	13	NUM
biomedich-48	266	23	)	)	PUNCT
biomedich-48	266	24	that	that	PRON
biomedich-48	266	25	give	give	VERB
biomedich-48	266	26	the	the	DET
biomedich-48	266	27	age	age	NOUN
biomedich-48	266	28	distribution	distribution	NOUN
biomedich-48	266	29	vector	vector	NOUN
biomedich-48	266	30	of	of	ADP
biomedich-48	266	31	the	the	DET
biomedich-48	266	32	population	population	NOUN
biomedich-48	266	33	for	for	ADP
biomedich-48	266	34	a	a	DET
biomedich-48	266	35	long	long	ADJ
biomedich-48	266	36	time	time	NOUN
biomedich-48	266	37	:	:	PUNCT
biomedich-48	266	38	)	)	PUNCT
biomedich-48	267	1	(	(	PUNCT
biomedich-48	267	2	k	k	NOUN
biomedich-48	267	3	x	x	PUNCT
biomedich-48	267	4	~	~	PUNCT
biomedich-48	267	5	kc	kc	PROPN
biomedich-48	267	6	1	1	NUM
biomedich-48	267	7	1x	1x	NUM
biomedich-48	267	8	(	(	PUNCT
biomedich-48	267	9	16	16	NUM
biomedich-48	267	10	)	)	PUNCT
biomedich-48	267	11	three	three	NUM
biomedich-48	267	12	cases	case	NOUN
biomedich-48	267	13	will	will	AUX
biomedich-48	267	14	appear	appear	VERB
biomedich-48	267	15	in	in	ADP
biomedich-48	267	16	accordance	accordance	NOUN
biomedich-48	267	17	with	with	ADP
biomedich-48	267	18	eigenvalues	eigenvalue	NOUN
biomedich-48	267	19	𝜆1	𝜆1	NOUN
biomedich-48	267	20	:	:	PUNCT
biomedich-48	267	21	(	(	PUNCT
biomedich-48	267	22	i	i	NOUN
biomedich-48	267	23	)	)	PUNCT
biomedich-48	267	24	the	the	DET
biomedich-48	267	25	total	total	ADJ
biomedich-48	267	26	population	population	NOUN
biomedich-48	267	27	will	will	AUX
biomedich-48	267	28	eventually	eventually	ADV
biomedich-48	267	29	tend	tend	VERB
biomedich-48	267	30	to	to	PART
biomedich-48	267	31	increase	increase	VERB
biomedich-48	267	32	/	/	SYM
biomedich-48	267	33	increase	increase	NOUN
biomedich-48	267	34	if	if	SCONJ
biomedich-48	267	35	𝜆1	𝜆1	VERB
biomedich-48	267	36	>	>	X
biomedich-48	267	37	1	1	NUM
biomedich-48	267	38	,	,	PUNCT
biomedich-48	267	39	(	(	PUNCT
biomedich-48	267	40	ii	ii	NOUN
biomedich-48	267	41	)	)	PUNCT
biomedich-48	267	42	the	the	DET
biomedich-48	267	43	total	total	ADJ
biomedich-48	267	44	population	population	NOUN
biomedich-48	267	45	will	will	AUX
biomedich-48	267	46	eventually	eventually	ADV
biomedich-48	267	47	tend	tend	VERB
biomedich-48	267	48	to	to	PART
biomedich-48	267	49	decrease	decrease	VERB
biomedich-48	267	50	/	/	SYM
biomedich-48	267	51	decrease	decrease	NOUN
biomedich-48	267	52	if	if	SCONJ
biomedich-48	267	53	𝜆1	𝜆1	VERB
biomedich-48	267	54	<	<	X
biomedich-48	267	55	1	1	NUM
biomedich-48	267	56	,	,	PUNCT
biomedich-48	267	57	(	(	PUNCT
biomedich-48	267	58	iii	iii	X
biomedich-48	267	59	)	)	PUNCT
biomedich-48	267	60	population	population	NOUN
biomedich-48	267	61	will	will	AUX
biomedich-48	267	62	tend	tend	VERB
biomedich-48	267	63	to	to	PART
biomedich-48	267	64	be	be	AUX
biomedich-48	267	65	stable	stable	ADJ
biomedich-48	267	66	/	/	SYM
biomedich-48	267	67	fixed	fix	VERB
biomedich-48	267	68	if	if	SCONJ
biomedich-48	267	69	𝜆1	𝜆1	NOUN
biomedich-48	267	70	=	=	PUNCT
biomedich-48	268	1	1	1	X
biomedich-48	268	2	.	.	PUNCT
biomedich-48	268	3	if	if	SCONJ
biomedich-48	268	4	the	the	DET
biomedich-48	268	5	population	population	NOUN
biomedich-48	268	6	tends	tend	VERB
biomedich-48	268	7	to	to	PART
biomedich-48	268	8	decline	decline	VERB
biomedich-48	268	9	then	then	ADV
biomedich-48	268	10	it	it	PRON
biomedich-48	268	11	can	can	AUX
biomedich-48	268	12	be	be	AUX
biomedich-48	268	13	said	say	VERB
biomedich-48	268	14	also	also	ADV
biomedich-48	268	15	that	that	SCONJ
biomedich-48	268	16	the	the	DET
biomedich-48	268	17	population	population	NOUN
biomedich-48	268	18	growth	growth	NOUN
biomedich-48	268	19	rate	rate	NOUN
biomedich-48	268	20	is	be	AUX
biomedich-48	268	21	negative	negative	ADJ
biomedich-48	268	22	,	,	PUNCT
biomedich-48	268	23	where	where	SCONJ
biomedich-48	268	24	as	as	SCONJ
biomedich-48	268	25	if	if	SCONJ
biomedich-48	268	26	the	the	DET
biomedich-48	268	27	population	population	NOUN
biomedich-48	268	28	number	number	NOUN
biomedich-48	268	29	increases	increase	VERB
biomedich-48	268	30	it	it	PRON
biomedich-48	268	31	can	can	AUX
biomedich-48	268	32	be	be	AUX
biomedich-48	268	33	said	say	VERB
biomedich-48	268	34	also	also	ADV
biomedich-48	268	35	that	that	SCONJ
biomedich-48	268	36	the	the	DET
biomedich-48	268	37	population	population	NOUN
biomedich-48	268	38	growth	growth	NOUN
biomedich-48	268	39	rate	rate	NOUN
biomedich-48	268	40	is	be	AUX
biomedich-48	268	41	positive	positive	ADJ
biomedich-48	268	42	.	.	PUNCT
biomedich-48	269	1	data	datum	NOUN
biomedich-48	269	2	on	on	ADP
biomedich-48	269	3	population	population	NOUN
biomedich-48	269	4	of	of	ADP
biomedich-48	269	5	women	woman	NOUN
biomedich-48	269	6	and	and	CCONJ
biomedich-48	269	7	number	number	NOUN
biomedich-48	269	8	of	of	ADP
biomedich-48	269	9	children	child	NOUN
biomedich-48	269	10	born	bear	VERB
biomedich-48	269	11	in	in	ADP
biomedich-48	269	12	2010	2010	NUM
biomedich-48	269	13	and	and	CCONJ
biomedich-48	269	14	year	year	NOUN
biomedich-48	269	15	2015	2015	NUM
biomedich-48	269	16	in	in	ADP
biomedich-48	269	17	trenggalek	trenggalek	NOUN
biomedich-48	269	18	regency	regency	PROPN
biomedich-48	269	19	the	the	DET
biomedich-48	269	20	following	follow	VERB
biomedich-48	269	21	data	datum	NOUN
biomedich-48	269	22	on	on	ADP
biomedich-48	269	23	the	the	DET
biomedich-48	269	24	number	number	NOUN
biomedich-48	269	25	of	of	ADP
biomedich-48	269	26	female	female	ADJ
biomedich-48	269	27	population	population	NOUN
biomedich-48	269	28	from	from	ADP
biomedich-48	269	29	2010	2010	NUM
biomedich-48	269	30	-	-	SYM
biomedich-48	269	31	2015	2015	NUM
biomedich-48	269	32	in	in	ADP
biomedich-48	269	33	trenggalek	trenggalek	NOUN
biomedich-48	269	34	regency	regency	PROPN
biomedich-48	269	35	that	that	PRON
biomedich-48	269	36	has	have	AUX
biomedich-48	269	37	been	be	AUX
biomedich-48	269	38	studied	study	VERB
biomedich-48	269	39	in	in	ADP
biomedich-48	269	40	the	the	DET
biomedich-48	269	41	research	research	NOUN
biomedich-48	269	42	.	.	PUNCT
biomedich-48	270	1	because	because	SCONJ
biomedich-48	270	2	only	only	ADV
biomedich-48	270	3	a	a	DET
biomedich-48	270	4	few	few	ADJ
biomedich-48	270	5	women	woman	NOUN
biomedich-48	270	6	over	over	ADP
biomedich-48	270	7	45	45	NUM
biomedich-48	270	8	years	year	NOUN
biomedich-48	270	9	old	old	ADJ
biomedich-48	270	10	who	who	PRON
biomedich-48	270	11	gave	give	VERB
biomedich-48	270	12	birth	birth	NOUN
biomedich-48	270	13	to	to	ADP
biomedich-48	270	14	a	a	DET
biomedich-48	270	15	child	child	NOUN
biomedich-48	270	16	,	,	PUNCT
biomedich-48	270	17	it	it	PRON
biomedich-48	270	18	will	will	AUX
biomedich-48	270	19	be	be	AUX
biomedich-48	270	20	limited	limit	VERB
biomedich-48	270	21	from	from	ADP
biomedich-48	270	22	the	the	DET
biomedich-48	270	23	population	population	NOUN
biomedich-48	270	24	of	of	ADP
biomedich-48	270	25	women	woman	NOUN
biomedich-48	270	26	aged	age	VERB
biomedich-48	270	27	between	between	ADP
biomedich-48	270	28	15	15	NUM
biomedich-48	270	29	and	and	CCONJ
biomedich-48	270	30	49	49	NUM
biomedich-48	270	31	years	year	NOUN
biomedich-48	270	32	this	this	PRON
biomedich-48	270	33	is	be	AUX
biomedich-48	270	34	due	due	ADJ
biomedich-48	270	35	to	to	ADP
biomedich-48	270	36	the	the	DET
biomedich-48	270	37	age	age	NOUN
biomedich-48	270	38	of	of	ADP
biomedich-48	270	39	female	female	ADJ
biomedich-48	270	40	fertility	fertility	NOUN
biomedich-48	270	41	interval	interval	NOUN
biomedich-48	270	42	of	of	ADP
biomedich-48	270	43	15	15	NUM
biomedich-48	270	44	-	-	SYM
biomedich-48	270	45	49	49	NUM
biomedich-48	270	46	years	year	NOUN
biomedich-48	270	47	.	.	PUNCT
biomedich-48	271	1	this	this	DET
biomedich-48	271	2	data	data	NOUN
biomedich-48	271	3	is	be	AUX
biomedich-48	271	4	for	for	ADP
biomedich-48	271	5	the	the	DET
biomedich-48	271	6	age	age	NOUN
biomedich-48	271	7	group	group	NOUN
biomedich-48	271	8	with	with	ADP
biomedich-48	271	9	the	the	DET
biomedich-48	271	10	period	period	NOUN
biomedich-48	271	11	of	of	ADP
biomedich-48	271	12	5	5	NUM
biomedich-48	271	13	years	year	NOUN
biomedich-48	271	14	,	,	PUNCT
biomedich-48	271	15	so	so	CCONJ
biomedich-48	271	16	the	the	DET
biomedich-48	271	17	total	total	ADJ
biomedich-48	271	18	number	number	NOUN
biomedich-48	271	19	is	be	AUX
biomedich-48	271	20	14	14	NUM
biomedich-48	271	21	age	age	NOUN
biomedich-48	271	22	groups	group	NOUN
biomedich-48	271	23	.	.	PUNCT
biomedich-48	272	1	from	from	ADP
biomedich-48	272	2	table	table	NOUN
biomedich-48	272	3	3	3	NUM
biomedich-48	272	4	data	datum	NOUN
biomedich-48	272	5	will	will	AUX
biomedich-48	272	6	be	be	AUX
biomedich-48	272	7	analyzed	analyze	VERB
biomedich-48	272	8	by	by	ADP
biomedich-48	272	9	looking	look	VERB
biomedich-48	272	10	for	for	ADP
biomedich-48	272	11	parameter	parameter	NOUN
biomedich-48	272	12	𝑎𝑖	𝑎𝑖	PROPN
biomedich-48	272	13	(	(	PUNCT
biomedich-48	272	14	fertility	fertility	NOUN
biomedich-48	272	15	number	number	NOUN
biomedich-48	272	16	)	)	PUNCT
biomedich-48	272	17	and	and	CCONJ
biomedich-48	272	18	𝑏𝑖	𝑏𝑖	ADP
biomedich-48	272	19	parameter	parameter	NOUN
biomedich-48	272	20	(	(	PUNCT
biomedich-48	272	21	life	life	NOUN
biomedich-48	272	22	expectancy	expectancy	NOUN
biomedich-48	272	23	)	)	PUNCT
biomedich-48	272	24	.	.	PUNCT
biomedich-48	273	1	leslie	leslie	PROPN
biomedich-48	273	2	matrix	matrix	NOUN
biomedich-48	273	3	model	model	NOUN
biomedich-48	273	4	can	can	AUX
biomedich-48	273	5	be	be	AUX
biomedich-48	273	6	used	use	VERB
biomedich-48	273	7	to	to	PART
biomedich-48	273	8	determine	determine	VERB
biomedich-48	273	9	the	the	DET
biomedich-48	273	10	number	number	NOUN
biomedich-48	273	11	of	of	ADP
biomedich-48	273	12	female	female	ADJ
biomedich-48	273	13	population	population	NOUN
biomedich-48	273	14	the	the	DET
biomedich-48	273	15	next	next	ADJ
biomedich-48	273	16	6	6	NUM
biomedich-48	273	17	years	year	NOUN
biomedich-48	273	18	.	.	PUNCT
biomedich-48	274	1	using	use	VERB
biomedich-48	274	2	leslie	leslie	PROPN
biomedich-48	274	3	's	's	PART
biomedich-48	274	4	matrix	matrix	NOUN
biomedich-48	274	5	,	,	PUNCT
biomedich-48	274	6	according	accord	VERB
biomedich-48	274	7	to	to	ADP
biomedich-48	274	8	table	table	NOUN
biomedich-48	274	9	4	4	NUM
biomedich-48	274	10	.	.	PUNCT
biomedich-48	275	1	the	the	DET
biomedich-48	275	2	female	female	ADJ
biomedich-48	275	3	population	population	NOUN
biomedich-48	275	4	is	be	AUX
biomedich-48	275	5	divided	divide	VERB
biomedich-48	275	6	into	into	ADP
biomedich-48	275	7	several	several	ADJ
biomedich-48	275	8	age	age	NOUN
biomedich-48	275	9	-	-	PUNCT
biomedich-48	275	10	class	class	NOUN
biomedich-48	275	11	intervals	interval	NOUN
biomedich-48	275	12	,	,	PUNCT
biomedich-48	275	13	with	with	ADP
biomedich-48	275	14	the	the	DET
biomedich-48	275	15	interval	interval	NOUN
biomedich-48	275	16	of	of	ADP
biomedich-48	275	17	female	female	ADJ
biomedich-48	275	18	fertility	fertility	NOUN
biomedich-48	275	19	15	15	NUM
biomedich-48	275	20	-	-	SYM
biomedich-48	275	21	49	49	NUM
biomedich-48	275	22	years	year	NOUN
biomedich-48	275	23	.	.	PUNCT
biomedich-48	276	1	to	to	PART
biomedich-48	276	2	calculate	calculate	VERB
biomedich-48	276	3	the	the	DET
biomedich-48	276	4	number	number	NOUN
biomedich-48	276	5	of	of	ADP
biomedich-48	276	6	female	female	ADJ
biomedich-48	276	7	population	population	NOUN
biomedich-48	276	8	by	by	ADP
biomedich-48	276	9	matrix	matrix	NOUN
biomedich-48	276	10	method	method	PROPN
biomedich-48	276	11	leslie	leslie	PROPN
biomedich-48	276	12	influenced	influence	VERB
biomedich-48	276	13	by	by	ADP
biomedich-48	276	14	fertility	fertility	NOUN
biomedich-48	276	15	rate	rate	NOUN
biomedich-48	276	16	(	(	PUNCT
biomedich-48	276	17	𝑎𝑖	𝑎𝑖	NOUN
biomedich-48	276	18	)	)	PUNCT
biomedich-48	276	19	life	life	NOUN
biomedich-48	276	20	expectancy	expectancy	NOUN
biomedich-48	276	21	(	(	PUNCT
biomedich-48	276	22	𝑏𝑖	𝑏𝑖	NOUN
biomedich-48	276	23	)	)	PUNCT
biomedich-48	276	24	.	.	PUNCT
biomedich-48	277	1	here	here	ADV
biomedich-48	277	2	is	be	AUX
biomedich-48	277	3	a	a	DET
biomedich-48	277	4	settlement	settlement	NOUN
biomedich-48	277	5	step	step	NOUN
biomedich-48	277	6	to	to	PART
biomedich-48	277	7	predict	predict	VERB
biomedich-48	277	8	the	the	DET
biomedich-48	277	9	number	number	NOUN
biomedich-48	277	10	and	and	CCONJ
biomedich-48	277	11	growth	growth	NOUN
biomedich-48	277	12	rate	rate	NOUN
biomedich-48	277	13	in	in	ADP
biomedich-48	277	14	trenggalek	trenggalek	NOUN
biomedich-48	277	15	regency	regency	PROPN
biomedich-48	277	16	in	in	ADP
biomedich-48	277	17	2021	2021	NUM
biomedich-48	277	18	.	.	PUNCT
biomedich-48	278	1	table	table	NOUN
biomedich-48	278	2	3	3	NUM
biomedich-48	278	3	.	.	X
biomedich-48	278	4	number	number	NOUN
biomedich-48	278	5	of	of	ADP
biomedich-48	278	6	female	female	ADJ
biomedich-48	278	7	population	population	NOUN
biomedich-48	278	8	year	year	NOUN
biomedich-48	278	9	2010	2010	NUM
biomedich-48	278	10	-	-	SYM
biomedich-48	278	11	2015	2015	NUM
biomedich-48	278	12	.	.	PUNCT
biomedich-48	279	1	age	age	NOUN
biomedich-48	279	2	class	class	NOUN
biomedich-48	279	3	number	number	NOUN
biomedich-48	279	4	of	of	ADP
biomedich-48	279	5	female	female	ADJ
biomedich-48	279	6	2010	2010	NUM
biomedich-48	279	7	number	number	NOUN
biomedich-48	279	8	of	of	ADP
biomedich-48	279	9	female	female	ADJ
biomedich-48	279	10	2015	2015	NUM
biomedich-48	279	11	ai	ai	VERB
biomedich-48	279	12	bi	bi	PROPN
biomedich-48	279	13	0	0	PROPN
biomedich-48	279	14	-	-	SYM
biomedich-48	279	15	4	4	NUM
biomedich-48	279	16	24,284	24,284	NUM
biomedich-48	279	17	22,860	22,860	NUM
biomedich-48	279	18	0	0	NUM
biomedich-48	279	19	0.978257	0.978257	NUM
biomedich-48	279	20	5	5	NUM
biomedich-48	279	21	-	-	SYM
biomedich-48	279	22	9	9	NUM
biomedich-48	279	23	24,529	24,529	NUM
biomedich-48	279	24	23,756	23,756	NUM
biomedich-48	279	25	0	0	NUM
biomedich-48	279	26	1.019365	1.019365	NUM
biomedich-48	279	27	10	10	NUM
biomedich-48	279	28	-	-	SYM
biomedich-48	279	29	14	14	NUM
biomedich-48	279	30	26,129	26,129	NUM
biomedich-48	279	31	25,004	25,004	NUM
biomedich-48	279	32	0	0	NUM
biomedich-48	280	1	0.933752	0.933752	NUM
biomedich-48	280	2	15	15	NUM
biomedich-48	280	3	-	-	SYM
biomedich-48	280	4	19	19	NUM
biomedich-48	280	5	24,704	24,704	NUM
biomedich-48	280	6	24,398	24,398	NUM
biomedich-48	280	7	0.0099	0.0099	NUM
biomedich-48	280	8	0.903538	0.903538	NUM
biomedich-48	280	9	20	20	NUM
biomedich-48	280	10	-	-	SYM
biomedich-48	280	11	24	24	NUM
biomedich-48	280	12	22,592	22,592	NUM
biomedich-48	280	13	22,321	22,321	NUM
biomedich-48	280	14	0.2599	0.2599	NUM
biomedich-48	280	15	1.018900	1.018900	NUM
biomedich-48	280	16	25	25	NUM
biomedich-48	280	17	-	-	SYM
biomedich-48	280	18	29	29	NUM
biomedich-48	280	19	24,790	24,790	NUM
biomedich-48	280	20	23,019	23,019	NUM
biomedich-48	280	21	0.2688	0.2688	NUM
biomedich-48	280	22	0.943687	0.943687	NUM
biomedich-48	280	23	30	30	NUM
biomedich-48	280	24	-	-	SYM
biomedich-48	280	25	34	34	NUM
biomedich-48	280	26	24,627	24,627	NUM
biomedich-48	280	27	23,394	23,394	NUM
biomedich-48	280	28	0.2698	0.2698	NUM
biomedich-48	280	29	1.055955	1.055955	NUM
biomedich-48	280	30	35	35	NUM
biomedich-48	280	31	-	-	SYM
biomedich-48	280	32	39	39	NUM
biomedich-48	280	33	26,632	26,632	NUM
biomedich-48	280	34	26,005	26,005	NUM
biomedich-48	280	35	0.2599	0.2599	NUM
biomedich-48	280	36	1.052418	1.052418	NUM
biomedich-48	280	37	40	40	NUM
biomedich-48	280	38	-	-	SYM
biomedich-48	280	39	44	44	NUM
biomedich-48	280	40	28,185	28,185	NUM
biomedich-48	280	41	28,028	28,028	NUM
biomedich-48	280	42	0.0795	0.0795	NUM
biomedich-48	280	43	0.969700	0.969700	NUM
biomedich-48	280	44	45	45	NUM
biomedich-48	280	45	-	-	SYM
biomedich-48	280	46	49	49	NUM
biomedich-48	280	47	25,671	25,671	NUM
biomedich-48	280	48	27,331	27,331	NUM
biomedich-48	280	49	0.0374	0.0374	NUM
biomedich-48	281	1	0.994313	0.994313	NUM
biomedich-48	281	2	50	50	NUM
biomedich-48	281	3	-	-	SYM
biomedich-48	281	4	54	54	NUM
biomedich-48	281	5	21,950	21,950	NUM
biomedich-48	281	6	25,525	25,525	NUM
biomedich-48	281	7	0	0	NUM
biomedich-48	281	8	0.987198	0.987198	NUM
biomedich-48	281	9	55	55	NUM
biomedich-48	281	10	-	-	SYM
biomedich-48	281	11	59	59	NUM
biomedich-48	281	12	17,401	17,401	NUM
biomedich-48	281	13	21,669	21,669	NUM
biomedich-48	281	14	0	0	NUM
biomedich-48	281	15	0.925694	0.925694	NUM
biomedich-48	281	16	60	60	NUM
biomedich-48	281	17	-	-	SYM
biomedich-48	281	18	64	64	NUM
biomedich-48	281	19	13,651	13,651	NUM
biomedich-48	281	20	16,108	16,108	NUM
biomedich-48	281	21	0	0	NUM
biomedich-48	281	22	2.738627	2.738627	NUM
biomedich-48	281	23	65	65	NUM
biomedich-48	281	24	+	+	NUM
biomedich-48	281	25	35,320	35,320	NUM
biomedich-48	281	26	37,385	37,385	NUM
biomedich-48	281	27	0	0	SYM
biomedich-48	281	28	0	0	NUM
biomedich-48	281	29	total	total	NOUN
biomedich-48	281	30	340,465	340,465	NUM
biomedich-48	281	31	346,803	346,803	NUM
biomedich-48	281	32	next	next	ADJ
biomedich-48	281	33	will	will	AUX
biomedich-48	281	34	be	be	AUX
biomedich-48	281	35	analyzed	analyze	VERB
biomedich-48	281	36	using	use	VERB
biomedich-48	281	37	the	the	DET
biomedich-48	281	38	maple	maple	NOUN
biomedich-48	281	39	16	16	NUM
biomedich-48	281	40	program	program	NOUN
biomedich-48	281	41	to	to	PART
biomedich-48	281	42	determine	determine	VERB
biomedich-48	281	43	the	the	DET
biomedich-48	281	44	dynamics	dynamic	NOUN
biomedich-48	281	45	of	of	ADP
biomedich-48	281	46	the	the	DET
biomedich-48	281	47	growth	growth	NOUN
biomedich-48	281	48	process	process	NOUN
biomedich-48	281	49	based	base	VERB
biomedich-48	281	50	on	on	ADP
biomedich-48	281	51	the	the	DET
biomedich-48	281	52	eigenvalues	eigenvalue	NOUN
biomedich-48	281	53	and	and	CCONJ
biomedich-48	281	54	eigenvectors	eigenvector	NOUN
biomedich-48	281	55	of	of	ADP
biomedich-48	281	56	leslie	leslie	PROPN
biomedich-48	281	57	matrix	matrix	NOUN
biomedich-48	281	58	.	.	PUNCT
biomedich-48	282	1	then	then	ADV
biomedich-48	282	2	using	use	VERB
biomedich-48	282	3	the	the	DET
biomedich-48	282	4	equation	equation	NOUN
biomedich-48	282	5	approach	approach	NOUN
biomedich-48	282	6	for	for	ADP
biomedich-48	282	7	the	the	DET
biomedich-48	282	8	age	age	NOUN
biomedich-48	282	9	limited	limit	VERB
biomedich-48	282	10	distribution	distribution	NOUN
biomedich-48	282	11	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	282	12	)	)	PUNCT
biomedich-48	282	13	≃	≃	NOUN
biomedich-48	282	14	𝜆1𝐱	𝜆1𝐱	PUNCT
biomedich-48	282	15	(	(	PUNCT
biomedich-48	282	16	𝑘−1	𝑘−1	PROPN
biomedich-48	282	17	)	)	PUNCT
biomedich-48	282	18	~	~	PUNCT
biomedich-48	282	19	will	will	AUX
biomedich-48	282	20	find	find	VERB
biomedich-48	282	21	the	the	DET
biomedich-48	282	22	rate	rate	NOUN
biomedich-48	282	23	growth	growth	NOUN
biomedich-48	282	24	of	of	ADP
biomedich-48	282	25	female	female	ADJ
biomedich-48	282	26	population	population	NOUN
biomedich-48	282	27	in	in	ADP
biomedich-48	282	28	trenggalek	trenggalek	NOUN
biomedich-48	282	29	regency	regency	PROPN
biomedich-48	282	30	.	.	PUNCT
biomedich-48	283	1	having	having	AUX
biomedich-48	283	2	formed	form	VERB
biomedich-48	283	3	leslie	leslie	PROPN
biomedich-48	283	4	's	's	PART
biomedich-48	283	5	matrix	matrix	NOUN
biomedich-48	283	6	,	,	PUNCT
biomedich-48	283	7	based	base	VERB
biomedich-48	283	8	on	on	ADP
biomedich-48	283	9	equation	equation	NOUN
biomedich-48	283	10	(	(	PUNCT
biomedich-48	283	11	3	3	NUM
biomedich-48	283	12	)	)	PUNCT
biomedich-48	283	13	,	,	PUNCT
biomedich-48	283	14	that	that	PRON
biomedich-48	283	15	is	is	ADV
biomedich-48	283	16	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	283	17	)	)	PUNCT
biomedich-48	283	18	=	=	SYM
biomedich-48	283	19	𝐿𝐱(𝑘−1	𝐿𝐱(𝑘−1	PROPN
biomedich-48	283	20	)	)	PUNCT
biomedich-48	283	21	with	with	ADP
biomedich-48	283	22	𝑘	𝑘	NOUN
biomedich-48	283	23	=	=	SYM
biomedich-48	283	24	1,2	1,2	NUM
biomedich-48	283	25	,	,	PUNCT
biomedich-48	283	26	…	…	PUNCT
biomedich-48	283	27	to	to	PART
biomedich-48	283	28	predict	predict	VERB
biomedich-48	283	29	the	the	DET
biomedich-48	283	30	number	number	NOUN
biomedich-48	283	31	of	of	ADP
biomedich-48	283	32	women	woman	NOUN
biomedich-48	283	33	in	in	ADP
biomedich-48	283	34	2021	2021	NUM
biomedich-48	283	35	.	.	PUNCT
biomedich-48	284	1	based	base	VERB
biomedich-48	284	2	on	on	ADP
biomedich-48	284	3	table	table	NOUN
biomedich-48	284	4	.	.	PUNCT
biomedich-48	285	1	3	3	NUM
biomedich-48	285	2	we	we	PRON
biomedich-48	285	3	obtain	obtain	VERB
biomedich-48	285	4	the	the	DET
biomedich-48	285	5	following	follow	VERB
biomedich-48	285	6	leslie	leslie	PROPN
biomedich-48	285	7	matrix	matrix	NOUN
biomedich-48	285	8	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	285	9	)	)	PUNCT
biomedich-48	285	10	=	=	SYM
biomedich-48	285	11	𝐿𝐱(𝑘−1	𝐿𝐱(𝑘−1	PROPN
biomedich-48	285	12	)	)	PUNCT
biomedich-48	285	13	=	=	PUNCT
biomedich-48	286	1			PROPN
biomedich-48	286	2			NOUN
biomedich-48	286	3			PUNCT
biomedich-48	287	1			PUNCT
biomedich-48	288	1			PUNCT
biomedich-48	289	1			PUNCT
biomedich-48	290	1			PUNCT
biomedich-48	291	1			PUNCT
biomedich-48	292	1			PUNCT
biomedich-48	293	1			PUNCT
biomedich-48	294	1			PUNCT
biomedich-48	295	1			NOUN
biomedich-48	296	1			PUNCT
biomedich-48	297	1			NOUN
biomedich-48	297	2			PROPN
biomedich-48	297	3			PROPN
biomedich-48	297	4			X
biomedich-48	297	5			NOUN
biomedich-48	297	6			NOUN
biomedich-48	297	7			NOUN
biomedich-48	297	8			NOUN
biomedich-48	297	9			NOUN
biomedich-48	297	10			NOUN
biomedich-48	297	11			NOUN
biomedich-48	297	12			NOUN
biomedich-48	297	13			NOUN
biomedich-48	297	14			NOUN
biomedich-48	297	15			NOUN
biomedich-48	297	16			NOUN
biomedich-48	297	17			NOUN
biomedich-48	297	18			NOUN
biomedich-48	297	19			NOUN
biomedich-48	297	20			NOUN
biomedich-48	297	21			PROPN
biomedich-48	298	1			ADJ
biomedich-48	298	2			PROPN
biomedich-48	298	3			PROPN
biomedich-48	299	1			PUNCT
biomedich-48	300	1			PUNCT
biomedich-48	301	1			PUNCT
biomedich-48	302	1			PUNCT
biomedich-48	303	1			PUNCT
biomedich-48	304	1			PUNCT
biomedich-48	305	1			NOUN
biomedich-48	306	1			PUNCT
biomedich-48	307	1			NOUN
biomedich-48	307	2			PROPN
biomedich-48	307	3			PROPN
biomedich-48	307	4			X
biomedich-48	307	5			NOUN
biomedich-48	307	6			NOUN
biomedich-48	307	7			NOUN
biomedich-48	307	8			NOUN
biomedich-48	307	9			NOUN
biomedich-48	307	10			NOUN
biomedich-48	307	11			NOUN
biomedich-48	307	12			NOUN
biomedich-48	307	13			NOUN
biomedich-48	307	14			NOUN
biomedich-48	307	15			NOUN
biomedich-48	307	16			NOUN
biomedich-48	307	17			VERB
biomedich-48	307	18			NOUN
biomedich-48	307	19			NOUN
biomedich-48	307	20			PROPN
biomedich-48	307	21			PUNCT
biomedich-48	308	1			PUNCT
biomedich-48	309	1			PUNCT
biomedich-48	310	1			PUNCT
biomedich-48	311	1			PUNCT
biomedich-48	312	1			PUNCT
biomedich-48	313	1			PUNCT
biomedich-48	314	1			PUNCT
biomedich-48	315	1			PUNCT
biomedich-48	316	1			NOUN
biomedich-48	317	1			PUNCT
biomedich-48	318	1			NOUN
biomedich-48	318	2			PROPN
biomedich-48	318	3			PROPN
biomedich-48	318	4			X
biomedich-48	318	5			NOUN
biomedich-48	318	6			NOUN
biomedich-48	318	7			NOUN
biomedich-48	318	8			NOUN
biomedich-48	318	9			NOUN
biomedich-48	318	10			NOUN
biomedich-48	318	11			NOUN
biomedich-48	318	12			NOUN
biomedich-48	318	13			NOUN
biomedich-48	318	14			NOUN
biomedich-48	318	15			NOUN
biomedich-48	318	16			NOUN
biomedich-48	318	17			NOUN
biomedich-48	318	18			NOUN
biomedich-48	318	19			NOUN
biomedich-48	318	20			VERB
biomedich-48	318	21			PROPN
biomedich-48	318	22	343.39	343.39	NUM
biomedich-48	318	23	058,20	058,20	NUM
biomedich-48	318	24	198,25	198,25	NOUN
biomedich-48	318	25	175,27	175,27	NUM
biomedich-48	318	26	178.27	178.27	NUM
biomedich-48	318	27	368,27	368,27	NUM
biomedich-48	318	28	702,24	702,24	NOUN
biomedich-48	319	1	722,21	722,21	NUM
biomedich-48	319	2	742,22	742,22	NUM
biomedich-48	319	3	044,22	044,22	NOUN
biomedich-48	319	4	347,23	347,23	NUM
biomedich-48	319	5	216,24	216,24	NUM
biomedich-48	319	6	361,22	361,22	NUM
biomedich-48	319	7	553,28	553,28	NUM
biomedich-48	319	8	37,385	37,385	NUM
biomedich-48	319	9	16,108	16,108	NUM
biomedich-48	319	10	21,669	21,669	NUM
biomedich-48	319	11	25,525	25,525	NUM
biomedich-48	319	12	27,331	27,331	NUM
biomedich-48	319	13	28,028	28,028	NUM
biomedich-48	319	14	26,005	26,005	NUM
biomedich-48	319	15	23,394	23,394	NUM
biomedich-48	319	16	23,019	23,019	NUM
biomedich-48	319	17	22,321	22,321	NUM
biomedich-48	319	18	24,398	24,398	NUM
biomedich-48	319	19	25,004	25,004	NUM
biomedich-48	319	20	23,756	23,756	NUM
biomedich-48	319	21	22,860	22,860	NUM
biomedich-48	319	22	02.7386000000000000	02.7386000000000000	NUM
biomedich-48	319	23	000.925600000000000	000.925600000000000	NUM
biomedich-48	319	24	0000.98710000000000	0000.98710000000000	NUM
biomedich-48	320	1	00000.9943000000000	00000.9943000000000	NUM
biomedich-48	320	2	000000.969700000000	000000.969700000000	INTJ
biomedich-48	321	1	0000001.05240000000	0000001.05240000000	VERB
biomedich-48	321	2	00000001.0559000000	00000001.0559000000	NUM
biomedich-48	322	1	000000000.943600000	000000000.943600000	NUM
biomedich-48	323	1	0000000001.01890000	0000000001.01890000	NUM
biomedich-48	324	1	00000000000.9035000	00000000000.9035000	NUM
biomedich-48	325	1	000000000000.933700	000000000000.933700	INTJ
biomedich-48	326	1	0000000000001.01930	0000000000001.01930	NOUN
biomedich-48	326	2	00000000000000.9782	00000000000000.9782	PUNCT
biomedich-48	327	1	00000.03740.07950.25990.26980.26880.25990.0099000	00000.03740.07950.25990.26980.26880.25990.0099000	NUM
biomedich-48	327	2	anggreini	anggreini	NOUN
biomedich-48	327	3	–	–	PUNCT
biomedich-48	327	4	the	the	DET
biomedich-48	327	5	female	female	ADJ
biomedich-48	327	6	population	population	NOUN
biomedich-48	327	7	growth	growth	NOUN
biomedich-48	327	8	projection	projection	NOUN
biomedich-48	327	9	year	year	NOUN
biomedich-48	327	10	2021	2021	NUM
biomedich-48	327	11	in	in	ADP
biomedich-48	327	12	trenggalek	trenggalek	NOUN
biomedich-48	327	13	…	…	PUNCT
biomedich-48	327	14	45	45	NUM
biomedich-48	327	15	then	then	ADV
biomedich-48	327	16	by	by	ADP
biomedich-48	327	17	using	use	VERB
biomedich-48	327	18	the	the	DET
biomedich-48	327	19	equation	equation	NOUN
biomedich-48	327	20	approach	approach	NOUN
biomedich-48	327	21	for	for	ADP
biomedich-48	327	22	limited	limited	ADJ
biomedich-48	327	23	age	age	NOUN
biomedich-48	327	24	distribution	distribution	NOUN
biomedich-48	327	25	:	:	PUNCT
biomedich-48	327	26	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	327	27	)	)	PUNCT
biomedich-48	327	28	≃	≃	NOUN
biomedich-48	327	29	𝜆1𝐱	𝜆1𝐱	PUNCT
biomedich-48	327	30	(	(	PUNCT
biomedich-48	327	31	𝑘−1	𝑘−1	PROPN
biomedich-48	327	32	)	)	PUNCT
biomedich-48	328	1	so	so	SCONJ
biomedich-48	328	2	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	328	3	)	)	PUNCT
biomedich-48	328	4	≃	≃	NOUN
biomedich-48	328	5	1,000391𝐱(𝑘−1	1,000391𝐱(𝑘−1	NUM
biomedich-48	328	6	)	)	PUNCT
biomedich-48	328	7	.	.	PUNCT
biomedich-48	329	1	from	from	ADP
biomedich-48	329	2	the	the	DET
biomedich-48	329	3	eigen	eigen	PROPN
biomedich-48	329	4	value	value	NOUN
biomedich-48	329	5	obtained	obtain	VERB
biomedich-48	329	6	𝜆1	𝜆1	PROPN
biomedich-48	329	7	>	>	X
biomedich-48	330	1	1	1	NUM
biomedich-48	331	1	so	so	SCONJ
biomedich-48	331	2	that	that	SCONJ
biomedich-48	331	3	every	every	DET
biomedich-48	331	4	five	five	NUM
biomedich-48	331	5	years	year	NOUN
biomedich-48	331	6	of	of	ADP
biomedich-48	331	7	female	female	ADJ
biomedich-48	331	8	population	population	NOUN
biomedich-48	331	9	in	in	ADP
biomedich-48	331	10	trenggalek	trenggalek	NOUN
biomedich-48	331	11	regency	regency	PROPN
biomedich-48	331	12	will	will	AUX
biomedich-48	331	13	tend	tend	VERB
biomedich-48	331	14	to	to	PART
biomedich-48	331	15	increase	increase	VERB
biomedich-48	331	16	or	or	CCONJ
biomedich-48	331	17	in	in	ADP
biomedich-48	331	18	other	other	ADJ
biomedich-48	331	19	words	word	NOUN
biomedich-48	331	20	growth	growth	NOUN
biomedich-48	331	21	rate	rate	NOUN
biomedich-48	331	22	of	of	ADP
biomedich-48	331	23	woman	woman	NOUN
biomedich-48	331	24	population	population	NOUN
biomedich-48	331	25	in	in	ADP
biomedich-48	331	26	trenggalek	trenggalek	NOUN
biomedich-48	331	27	regency	regency	PROPN
biomedich-48	331	28	tends	tend	VERB
biomedich-48	331	29	to	to	PART
biomedich-48	331	30	be	be	AUX
biomedich-48	331	31	positive	positive	ADJ
biomedich-48	331	32	value	value	NOUN
biomedich-48	331	33	.	.	PUNCT
biomedich-48	332	1	table	table	NOUN
biomedich-48	332	2	4	4	NUM
biomedich-48	332	3	.	.	PUNCT
biomedich-48	332	4	number	number	NOUN
biomedich-48	332	5	of	of	ADP
biomedich-48	332	6	women	woman	NOUN
biomedich-48	332	7	year	year	NOUN
biomedich-48	332	8	2010	2010	NUM
biomedich-48	332	9	and	and	CCONJ
biomedich-48	332	10	2015	2015	NUM
biomedich-48	332	11	&	&	CCONJ
biomedich-48	332	12	women	woman	NOUN
biomedich-48	332	13	's	's	PART
biomedich-48	332	14	prediction	prediction	NOUN
biomedich-48	332	15	year	year	NOUN
biomedich-48	332	16	2021	2021	NUM
biomedich-48	332	17	.	.	PUNCT
biomedich-48	333	1	age	age	NOUN
biomedich-48	333	2	class	class	NOUN
biomedich-48	333	3	number	number	NOUN
biomedich-48	333	4	of	of	ADP
biomedich-48	333	5	female	female	ADJ
biomedich-48	333	6	2010	2010	NUM
biomedich-48	333	7	number	number	NOUN
biomedich-48	333	8	of	of	ADP
biomedich-48	333	9	female	female	ADJ
biomedich-48	333	10	2015	2015	NUM
biomedich-48	333	11	number	number	NOUN
biomedich-48	333	12	of	of	ADP
biomedich-48	333	13	female	female	ADJ
biomedich-48	333	14	2021	2021	NUM
biomedich-48	333	15	0	0	NUM
biomedich-48	333	16	-	-	SYM
biomedich-48	333	17	4	4	NUM
biomedich-48	333	18	24,284	24,284	NUM
biomedich-48	333	19	22,860	22,860	NUM
biomedich-48	333	20	28,553	28,553	NUM
biomedich-48	333	21	5	5	NUM
biomedich-48	333	22	-	-	SYM
biomedich-48	333	23	9	9	NUM
biomedich-48	333	24	24,529	24,529	NUM
biomedich-48	333	25	23,756	23,756	NUM
biomedich-48	333	26	22,361	22,361	NUM
biomedich-48	333	27	10	10	NUM
biomedich-48	333	28	-	-	SYM
biomedich-48	333	29	14	14	NUM
biomedich-48	333	30	26,129	26,129	NUM
biomedich-48	333	31	25,004	25,004	NUM
biomedich-48	333	32	24,216	24,216	NUM
biomedich-48	333	33	15	15	NUM
biomedich-48	333	34	-	-	SYM
biomedich-48	333	35	19	19	NUM
biomedich-48	333	36	24,704	24,704	NUM
biomedich-48	333	37	24,398	24,398	NUM
biomedich-48	333	38	23,347	23,347	NUM
biomedich-48	333	39	20	20	NUM
biomedich-48	333	40	-	-	SYM
biomedich-48	333	41	24	24	NUM
biomedich-48	333	42	22,592	22,592	NUM
biomedich-48	333	43	22,321	22,321	NUM
biomedich-48	333	44	22,044	22,044	NUM
biomedich-48	333	45	25	25	NUM
biomedich-48	333	46	-	-	SYM
biomedich-48	333	47	29	29	NUM
biomedich-48	333	48	24,790	24,790	NUM
biomedich-48	333	49	23,019	23,019	NUM
biomedich-48	333	50	22,742	22,742	NUM
biomedich-48	333	51	30	30	NUM
biomedich-48	333	52	-	-	SYM
biomedich-48	333	53	34	34	NUM
biomedich-48	333	54	24,627	24,627	NUM
biomedich-48	333	55	23,394	23,394	NUM
biomedich-48	333	56	21,722	21,722	NUM
biomedich-48	333	57	35	35	NUM
biomedich-48	333	58	-	-	SYM
biomedich-48	333	59	39	39	NUM
biomedich-48	333	60	26,632	26,632	NUM
biomedich-48	333	61	26,005	26,005	NUM
biomedich-48	333	62	24,702	24,702	NUM
biomedich-48	333	63	40	40	NUM
biomedich-48	333	64	-	-	SYM
biomedich-48	333	65	44	44	NUM
biomedich-48	333	66	28,185	28,185	NUM
biomedich-48	333	67	28,028	28,028	NUM
biomedich-48	333	68	27,368	27,368	NUM
biomedich-48	333	69	45	45	NUM
biomedich-48	333	70	-	-	SYM
biomedich-48	333	71	49	49	NUM
biomedich-48	333	72	25,671	25,671	NUM
biomedich-48	333	73	27,331	27,331	NUM
biomedich-48	333	74	27,178	27,178	NUM
biomedich-48	333	75	50	50	NUM
biomedich-48	333	76	-	-	SYM
biomedich-48	333	77	54	54	NUM
biomedich-48	333	78	21,950	21,950	NUM
biomedich-48	333	79	25,525	25,525	NUM
biomedich-48	333	80	27,175	27,175	NUM
biomedich-48	333	81	55	55	NUM
biomedich-48	333	82	-	-	SYM
biomedich-48	333	83	59	59	NUM
biomedich-48	333	84	17,401	17,401	NUM
biomedich-48	333	85	21,669	21,669	NUM
biomedich-48	333	86	25,198	25,198	NUM
biomedich-48	333	87	60	60	NUM
biomedich-48	333	88	-	-	SYM
biomedich-48	333	89	64	64	NUM
biomedich-48	333	90	13,651	13,651	NUM
biomedich-48	333	91	16,108	16,108	NUM
biomedich-48	333	92	20,058	20,058	NUM
biomedich-48	333	93	65	65	NUM
biomedich-48	333	94	+	+	SYM
biomedich-48	333	95	35,320	35,320	NUM
biomedich-48	333	96	37,385	37,385	NUM
biomedich-48	333	97	39,343	39,343	NUM
biomedich-48	333	98	total	total	NOUN
biomedich-48	333	99	340,465	340,465	NUM
biomedich-48	333	100	346,803	346,803	NUM
biomedich-48	333	101	356,007	356,007	NUM
biomedich-48	333	102	conclusion	conclusion	NOUN
biomedich-48	333	103	based	base	VERB
biomedich-48	333	104	on	on	ADP
biomedich-48	333	105	the	the	DET
biomedich-48	333	106	data	data	NOUN
biomedich-48	333	107	analysis	analysis	NOUN
biomedich-48	333	108	of	of	ADP
biomedich-48	333	109	leslie	leslie	PROPN
biomedich-48	333	110	matrix	matrix	NOUN
biomedich-48	333	111	in	in	ADP
biomedich-48	333	112	female	female	ADJ
biomedich-48	333	113	population	population	NOUN
biomedich-48	333	114	in	in	ADP
biomedich-48	333	115	trenggalek	trenggalek	NOUN
biomedich-48	333	116	regency	regency	PROPN
biomedich-48	333	117	,	,	PUNCT
biomedich-48	333	118	it	it	PRON
biomedich-48	333	119	can	can	AUX
biomedich-48	333	120	be	be	AUX
biomedich-48	333	121	concluded	conclude	VERB
biomedich-48	333	122	that	that	SCONJ
biomedich-48	333	123	eigen	eigen	PROPN
biomedich-48	333	124	value	value	NOUN
biomedich-48	333	125	for	for	ADP
biomedich-48	333	126	the	the	DET
biomedich-48	333	127	total	total	ADJ
biomedich-48	333	128	population	population	NOUN
biomedich-48	333	129	of	of	ADP
biomedich-48	333	130	women	woman	NOUN
biomedich-48	333	131	in	in	ADP
biomedich-48	333	132	trenggalek	trenggalek	NOUN
biomedich-48	333	133	regency	regency	PROPN
biomedich-48	333	134	in	in	ADP
biomedich-48	333	135	year	year	NOUN
biomedich-48	333	136	2021	2021	NUM
biomedich-48	333	137	amounted	amount	VERB
biomedich-48	333	138	to	to	ADP
biomedich-48	333	139	356.007	356.007	NUM
biomedich-48	333	140	.	.	PUNCT
biomedich-48	334	1	distribution	distribution	NOUN
biomedich-48	334	2	age	age	NOUN
biomedich-48	334	3	limit	limit	NOUN
biomedich-48	334	4	for	for	ADP
biomedich-48	334	5	female	female	ADJ
biomedich-48	334	6	population	population	NOUN
biomedich-48	334	7	in	in	ADP
biomedich-48	334	8	trengggalek	trengggalek	PROPN
biomedich-48	334	9	regency	regency	PROPN
biomedich-48	334	10	is	be	AUX
biomedich-48	334	11	𝐱(𝑘	𝐱(𝑘	NOUN
biomedich-48	334	12	)	)	PUNCT
biomedich-48	334	13	≃	≃	NOUN
biomedich-48	334	14	𝜆1𝐱	𝜆1𝐱	PUNCT
biomedich-48	334	15	(	(	PUNCT
biomedich-48	334	16	𝑘−1	𝑘−1	PROPN
biomedich-48	334	17	)	)	PUNCT
biomedich-48	334	18	with	with	ADP
biomedich-48	334	19	positive	positive	ADJ
biomedich-48	334	20	eigen	eigen	NOUN
biomedich-48	334	21	value	value	NOUN
biomedich-48	334	22	𝜆1	𝜆1	NOUN
biomedich-48	334	23	>	>	X
biomedich-48	334	24	1	1	NUM
biomedich-48	334	25	is	be	AUX
biomedich-48	334	26	greater	great	ADJ
biomedich-48	334	27	than	than	ADP
biomedich-48	334	28	one	one	NUM
biomedich-48	334	29	that	that	PRON
biomedich-48	334	30	is	be	AUX
biomedich-48	334	31	equal	equal	ADJ
biomedich-48	334	32	to	to	ADP
biomedich-48	334	33	1,000391	1,000391	NUM
biomedich-48	334	34	so	so	SCONJ
biomedich-48	334	35	that	that	SCONJ
biomedich-48	334	36	the	the	DET
biomedich-48	334	37	number	number	NOUN
biomedich-48	334	38	of	of	ADP
biomedich-48	334	39	female	female	ADJ
biomedich-48	334	40	population	population	NOUN
biomedich-48	334	41	in	in	ADP
biomedich-48	334	42	trenggalek	trenggalek	NOUN
biomedich-48	334	43	regency	regency	PROPN
biomedich-48	334	44	in	in	ADP
biomedich-48	334	45	year	year	NOUN
biomedich-48	334	46	2021	2021	NUM
biomedich-48	334	47	tend	tend	VERB
biomedich-48	334	48	to	to	PART
biomedich-48	334	49	increase	increase	VERB
biomedich-48	334	50	or	or	CCONJ
biomedich-48	334	51	can	can	AUX
biomedich-48	334	52	be	be	AUX
biomedich-48	334	53	said	say	VERB
biomedich-48	334	54	growth	growth	NOUN
biomedich-48	334	55	rate	rate	NOUN
biomedich-48	334	56	of	of	ADP
biomedich-48	334	57	population	population	NOUN
biomedich-48	334	58	tends	tend	VERB
biomedich-48	334	59	to	to	PART
biomedich-48	334	60	be	be	AUX
biomedich-48	334	61	positive	positive	ADJ
biomedich-48	334	62	value	value	NOUN
biomedich-48	334	63	.	.	PUNCT
biomedich-48	335	1	references	reference	NOUN
biomedich-48	335	2	adiwijaya	adiwijaya	NOUN
biomedich-48	335	3	.	.	PUNCT
biomedich-48	336	1	2014	2014	NUM
biomedich-48	336	2	.	.	PUNCT
biomedich-48	337	1	application	application	NOUN
biomedich-48	337	2	of	of	ADP
biomedich-48	337	3	matrices	matrix	NOUN
biomedich-48	337	4	and	and	CCONJ
biomedich-48	337	5	vector	vector	NOUN
biomedich-48	337	6	spaces	space	NOUN
biomedich-48	337	7	.	.	PUNCT
biomedich-48	338	1	yogyakarta	yogyakarta	PROPN
biomedich-48	338	2	:	:	PUNCT
biomedich-48	339	1	graha	graha	PROPN
biomedich-48	339	2	ilmu	ilmu	PROPN
biomedich-48	339	3	.	.	PUNCT
biomedich-48	340	1	anton	anton	PROPN
biomedich-48	340	2	,	,	PUNCT
biomedich-48	340	3	h.	h.	PROPN
biomedich-48	340	4	&	&	CCONJ
biomedich-48	340	5	rorres	rorres	PROPN
biomedich-48	340	6	,	,	PUNCT
biomedich-48	340	7	c.	c.	PROPN
biomedich-48	340	8	1988	1988	NUM
biomedich-48	340	9	.	.	PUNCT
biomedich-48	341	1	application	application	NOUN
biomedich-48	341	2	of	of	ADP
biomedich-48	341	3	linear	linear	PROPN
biomedich-48	341	4	algebra	algebra	PROPN
biomedich-48	341	5	.	.	PUNCT
biomedich-48	342	1	jakarta	jakarta	PROPN
biomedich-48	342	2	:	:	PUNCT
biomedich-48	342	3	erland	erland	PROPN
biomedich-48	342	4	.	.	PUNCT
biomedich-48	343	1	anton	anton	PROPN
biomedich-48	343	2	,	,	PUNCT
biomedich-48	343	3	h	h	PROPN
biomedich-48	343	4	&	&	CCONJ
biomedich-48	343	5	rorres	rorre	NOUN
biomedich-48	343	6	,	,	PUNCT
biomedich-48	343	7	c.	c.	PROPN
biomedich-48	343	8	2004	2004	NUM
biomedich-48	343	9	.	.	PUNCT
biomedich-48	344	1	linear	linear	PROPN
biomedich-48	344	2	elementary	elementary	PROPN
biomedich-48	344	3	algebra	algebra	PROPN
biomedich-48	344	4	(	(	PUNCT
biomedich-48	344	5	app	app	NOUN
biomedich-48	344	6	version	version	NOUN
biomedich-48	344	7	)	)	PUNCT
biomedich-48	344	8	.	.	PUNCT
biomedich-48	345	1	jakarta	jakarta	PROPN
biomedich-48	345	2	:	:	PUNCT
biomedich-48	345	3	erland	erland	PROPN
biomedich-48	345	4	.	.	PUNCT
biomedich-48	346	1	central	central	ADJ
biomedich-48	346	2	bureau	bureau	PROPN
biomedich-48	346	3	of	of	ADP
biomedich-48	346	4	statistics	statistic	NOUN
biomedich-48	346	5	.	.	PUNCT
biomedich-48	347	1	2013	2013	NUM
biomedich-48	347	2	.	.	PUNCT
biomedich-48	348	1	projection	projection	NOUN
biomedich-48	348	2	of	of	ADP
biomedich-48	348	3	indonesian	indonesian	ADJ
biomedich-48	348	4	population	population	NOUN
biomedich-48	348	5	(	(	PUNCT
biomedich-48	348	6	indonesian	indonesian	ADJ
biomedich-48	348	7	population	population	NOUN
biomedich-48	348	8	projection	projection	NOUN
biomedich-48	348	9	)	)	PUNCT
biomedich-48	348	10	2010	2010	NUM
biomedich-48	348	11	-	-	SYM
biomedich-48	348	12	2035	2035	NUM
biomedich-48	348	13	,	,	PUNCT
biomedich-48	348	14	jakarta	jakarta	PROPN
biomedich-48	348	15	.	.	PUNCT
biomedich-48	349	1	corazon	corazon	PROPN
biomedich-48	349	2	,	,	PUNCT
biomedich-48	349	3	nurul	nurul	NOUN
biomedich-48	349	4	,	,	PUNCT
biomedich-48	349	5	h	h	NOUN
biomedich-48	349	6	and	and	CCONJ
biomedich-48	349	7	yusianta	yusianta	PROPN
biomedich-48	349	8	,	,	PUNCT
biomedich-48	349	9	m	m	PROPN
biomedich-48	349	10	,	,	PUNCT
biomedich-48	349	11	2016	2016	NUM
biomedich-48	349	12	.	.	PUNCT
biomedich-48	350	1	leslie	leslie	PROPN
biomedich-48	350	2	's	's	PART
biomedich-48	350	3	matrix	matrix	NOUN
biomedich-48	350	4	application	application	NOUN
biomedich-48	350	5	to	to	PART
biomedich-48	350	6	predict	predict	VERB
biomedich-48	350	7	the	the	DET
biomedich-48	350	8	number	number	NOUN
biomedich-48	350	9	and	and	CCONJ
biomedich-48	350	10	growth	growth	NOUN
biomedich-48	350	11	rate	rate	NOUN
biomedich-48	350	12	of	of	ADP
biomedich-48	350	13	women	woman	NOUN
biomedich-48	350	14	in	in	ADP
biomedich-48	350	15	riau	riau	PROPN
biomedich-48	350	16	province	province	NOUN
biomedich-48	350	17	by	by	ADP
biomedich-48	350	18	2017	2017	NUM
biomedich-48	350	19	.	.	PUNCT
biomedich-48	351	1	journal	journal	PROPN
biomedich-48	351	2	of	of	ADP
biomedich-48	351	3	mathematical	mathematical	ADJ
biomedich-48	351	4	and	and	CCONJ
biomedich-48	351	5	statistical	statistical	ADJ
biomedich-48	351	6	science	science	NOUN
biomedich-48	351	7	(	(	PUNCT
biomedich-48	351	8	jsms	jsms	PROPN
biomedich-48	351	9	)	)	PUNCT
biomedich-48	351	10	,	,	PUNCT
biomedich-48	351	11	2	2	NUM
biomedich-48	351	12	(	(	PUNCT
biomedich-48	351	13	3	3	NUM
biomedich-48	351	14	)	)	PUNCT
biomedich-48	351	15	,	,	PUNCT
biomedich-48	351	16	1	1	NUM
biomedich-48	351	17	-	-	SYM
biomedich-48	351	18	11	11	NUM
biomedich-48	351	19	,	,	PUNCT
biomedich-48	351	20	ejournal.uinsuska.ac.id/index.php/jsms/article	ejournal.uinsuska.ac.id/index.php/jsms/article	NOUN
biomedich-48	351	21	/	/	SYM
biomedich-48	351	22	download	download	NOUN
biomedich-48	351	23	/	/	SYM
biomedich-48	351	24	3098	3098	NUM
biomedich-48	351	25	/	/	SYM
biomedich-48	351	26	iswanto	iswanto	NOUN
biomedich-48	351	27	,	,	PUNCT
biomedich-48	351	28	r.j	r.j	PROPN
biomedich-48	351	29	.	.	PROPN
biomedich-48	351	30	2012	2012	NUM
biomedich-48	351	31	.	.	PUNCT
biomedich-48	352	1	applied	apply	VERB
biomedich-48	352	2	and	and	CCONJ
biomedich-48	352	3	applied	apply	VERB
biomedich-48	352	4	mathematical	mathematical	ADJ
biomedich-48	352	5	modeling	modeling	NOUN
biomedich-48	352	6	.	.	PUNCT
biomedich-48	353	1	yogyakarta	yogyakarta	PROPN
biomedich-48	353	2	:	:	PUNCT
biomedich-48	354	1	graha	graha	PROPN
biomedich-48	354	2	ilmu	ilmu	PROPN
biomedich-48	354	3	.	.	PUNCT
biomedich-48	355	1	kariadinata	kariadinata	PROPN
biomedich-48	355	2	,	,	PUNCT
biomedich-48	355	3	r.	r.	PROPN
biomedich-48	355	4	2013	2013	NUM
biomedich-48	355	5	.	.	PUNCT
biomedich-48	356	1	algebra	algebra	NOUN
biomedich-48	356	2	of	of	ADP
biomedich-48	356	3	elementary	elementary	ADJ
biomedich-48	356	4	matrices	matrix	NOUN
biomedich-48	356	5	.	.	PUNCT
biomedich-48	357	1	bandung	bandung	PROPN
biomedich-48	357	2	:	:	PUNCT
biomedich-48	357	3	cv	cv	PROPN
biomedich-48	357	4	pustaka	pustaka	ADJ
biomedich-48	357	5	setia	setia	PROPN
biomedich-48	357	6	.	.	PUNCT
biomedich-48	357	7	pratama	pratama	PROPN
biomedich-48	357	8	,	,	PUNCT
biomedich-48	357	9	prihandono	prihandono	NOUN
biomedich-48	357	10	and	and	CCONJ
biomedich-48	357	11	kusumastuti	kusumastuti	PROPN
biomedich-48	357	12	2013	2013	NUM
biomedich-48	357	13	.	.	PUNCT
biomedich-48	358	1	leslie	leslie	PROPN
biomedich-48	358	2	's	's	PART
biomedich-48	358	3	matrix	matrix	NOUN
biomedich-48	358	4	application	application	NOUN
biomedich-48	358	5	to	to	PART
biomedich-48	358	6	predict	predict	VERB
biomedich-48	358	7	the	the	DET
biomedich-48	358	8	number	number	NOUN
biomedich-48	358	9	and	and	CCONJ
biomedich-48	358	10	rate	rate	NOUN
biomedich-48	358	11	of	of	ADP
biomedich-48	358	12	growth	growth	NOUN
biomedich-48	358	13	of	of	ADP
biomedich-48	358	14	a	a	DET
biomedich-48	358	15	population	population	NOUN
biomedich-48	358	16	.	.	PUNCT
biomedich-48	359	1	bimaster	bimaster	NOUN
biomedich-48	359	2	:	:	PUNCT
biomedich-48	359	3	math	math	NOUN
biomedich-48	359	4	scientific	scientific	ADJ
biomedich-48	359	5	bulletin	bulletin	NOUN
biomedich-48	359	6	.	.	PUNCT
biomedich-48	360	1	stat	stat	PROPN
biomedich-48	360	2	.	.	PUNCT
biomedich-48	361	1	and	and	CCONJ
biomedich-48	361	2	applied	apply	VERB
biomedich-48	361	3	,	,	PUNCT
biomedich-48	361	4	2	2	NUM
biomedich-48	361	5	(	(	PUNCT
biomedich-48	361	6	3	3	NUM
biomedich-48	361	7	)	)	PUNCT
biomedich-48	361	8	,	,	PUNCT
biomedich-48	361	9	163	163	NUM
biomedich-48	361	10	-	-	SYM
biomedich-48	361	11	172	172	NUM
biomedich-48	361	12	.	.	PUNCT
biomedich-48	361	13	http://jurnal.untan.ac.id/index.php/jbmstr/article/view/3859	http://jurnal.untan.ac.id/index.php/jbmstr/article/view/3859	PROPN
biomedich-48	361	14	.	.	PUNCT
biomedich-48	362	1	tarumingkeng	tarumingkeng	PROPN
biomedich-48	362	2	,	,	PUNCT
biomedich-48	362	3	r.c	r.c	PROPN
biomedich-48	362	4	.	.	PROPN
biomedich-48	362	5	1994	1994	NUM
biomedich-48	362	6	,	,	PUNCT
biomedich-48	362	7	population	population	NOUN
biomedich-48	362	8	dynamics	dynamic	NOUN
biomedich-48	362	9	(	(	PUNCT
biomedich-48	362	10	quantitative	quantitative	ADJ
biomedich-48	362	11	ecological	ecological	ADJ
biomedich-48	362	12	studies	study	NOUN
biomedich-48	362	13	)	)	PUNCT
biomedich-48	362	14	,	,	PUNCT
biomedich-48	362	15	pustaka	pustaka	ADJ
biomedich-48	362	16	sinar	sinar	PROPN
biomedich-48	362	17	harapan	harapan	PROPN
biomedich-48	362	18	,	,	PUNCT
biomedich-48	362	19	jakarta	jakarta	PROPN
biomedich-48	362	20	this	this	DET
biomedich-48	362	21	page	page	NOUN
biomedich-48	362	22	intentionally	intentionally	ADV
biomedich-48	362	23	left	leave	VERB
biomedich-48	362	24	blank	blank	ADP
biomedich-48	362	25	the	the	DET
biomedich-48	362	26	female	female	ADJ
biomedich-48	362	27	population	population	NOUN
biomedich-48	362	28	growth	growth	NOUN
biomedich-48	362	29	projection	projection	NOUN
biomedich-48	362	30	year	year	NOUN
biomedich-48	362	31	2021	2021	NUM
biomedich-48	362	32	in	in	ADP
biomedich-48	362	33	trenggalek	trenggalek	NOUN
biomedich-48	362	34	regency	regency	PROPN
biomedich-48	362	35	by	by	ADP
biomedich-48	362	36	leslie	leslie	PROPN
biomedich-48	362	37	matrix	matrix	NOUN
biomedich-48	362	38	model	model	NOUN
biomedich-48	362	39	on	on	ADP
biomedich-48	362	40	the	the	DET
biomedich-48	362	41	birth	birth	NOUN
biomedich-48	362	42	rate	rate	NOUN
biomedich-48	362	43	and	and	CCONJ
biomedich-48	362	44	life	life	NOUN
biomedich-48	362	45	expectancy	expectancy	NOUN