id	sid	tid	token	lemma	pos
ijassa-429	1	1	advances	advance	NOUN
ijassa-429	1	2	in	in	ADP
ijassa-429	1	3	systems	system	NOUN
ijassa-429	1	4	science	science	NOUN
ijassa-429	1	5	and	and	CCONJ
ijassa-429	1	6	applications	application	NOUN
ijassa-429	1	7	(	(	PUNCT
ijassa-429	1	8	2013	2013	NUM
ijassa-429	1	9	)	)	PUNCT
ijassa-429	1	10	vol.13	vol.13	NOUN
ijassa-429	1	11	no.1	no.1	VERB
ijassa-429	1	12	80	80	NUM
ijassa-429	1	13	-	-	SYM
ijassa-429	1	14	99	99	NUM
ijassa-429	1	15	an	an	DET
ijassa-429	1	16	extension	extension	NOUN
ijassa-429	1	17	of	of	ADP
ijassa-429	1	18	a	a	DET
ijassa-429	1	19	logistic	logistic	ADJ
ijassa-429	1	20	model	model	NOUN
ijassa-429	1	21	for	for	ADP
ijassa-429	1	22	microbial	microbial	ADJ
ijassa-429	1	23	kinetics	kinetic	NOUN
ijassa-429	1	24	anne	anne	PROPN
ijassa-429	1	25	talkington1	talkington1	PROPN
ijassa-429	1	26	,	,	PUNCT
ijassa-429	1	27	floyd	floyd	PROPN
ijassa-429	1	28	inman	inman	PROPN
ijassa-429	1	29	iii2	iii2	PROPN
ijassa-429	1	30	,	,	PUNCT
ijassa-429	1	31	leonard	leonard	PROPN
ijassa-429	1	32	d.	d.	PROPN
ijassa-429	1	33	holmes2	holmes2	PROPN
ijassa-429	1	34	and	and	CCONJ
ijassa-429	1	35	guo	guo	PROPN
ijassa-429	1	36	wei2	wei2	PROPN
ijassa-429	1	37	1duke	1duke	PROPN
ijassa-429	1	38	university	university	NOUN
ijassa-429	1	39	,	,	PUNCT
ijassa-429	1	40	durham	durham	PROPN
ijassa-429	1	41	,	,	PUNCT
ijassa-429	1	42	nc	nc	PROPN
ijassa-429	1	43	27708	27708	NUM
ijassa-429	1	44	,	,	PUNCT
ijassa-429	1	45	usa	usa	PROPN
ijassa-429	1	46	2university	2university	PROPN
ijassa-429	1	47	of	of	ADP
ijassa-429	1	48	north	north	PROPN
ijassa-429	1	49	carolina	carolina	PROPN
ijassa-429	1	50	at	at	ADP
ijassa-429	1	51	pembroke	pembroke	PROPN
ijassa-429	1	52	,	,	PUNCT
ijassa-429	1	53	pembroke	pembroke	PROPN
ijassa-429	1	54	,	,	PUNCT
ijassa-429	1	55	nc	nc	PROPN
ijassa-429	1	56	28372	28372	NUM
ijassa-429	1	57	,	,	PUNCT
ijassa-429	1	58	usa	usa	PROPN
ijassa-429	1	59	abstract	abstract	NOUN
ijassa-429	1	60	in	in	ADP
ijassa-429	1	61	contrast	contrast	NOUN
ijassa-429	1	62	to	to	ADP
ijassa-429	1	63	the	the	DET
ijassa-429	1	64	traditional	traditional	ADJ
ijassa-429	1	65	logistic	logistic	ADJ
ijassa-429	1	66	model	model	NOUN
ijassa-429	1	67	,	,	PUNCT
ijassa-429	1	68	a	a	DET
ijassa-429	1	69	series	series	NOUN
ijassa-429	1	70	of	of	ADP
ijassa-429	1	71	asymmetrical	asymmetrical	ADJ
ijassa-429	1	72	models	model	NOUN
ijassa-429	1	73	have	have	AUX
ijassa-429	1	74	been	be	AUX
ijassa-429	1	75	proposed	propose	VERB
ijassa-429	1	76	for	for	ADP
ijassa-429	1	77	modeling	model	VERB
ijassa-429	1	78	bacterial	bacterial	ADJ
ijassa-429	1	79	growth	growth	NOUN
ijassa-429	1	80	.	.	PUNCT
ijassa-429	2	1	these	these	DET
ijassa-429	2	2	models	model	NOUN
ijassa-429	2	3	are	be	AUX
ijassa-429	2	4	similar	similar	ADJ
ijassa-429	2	5	to	to	ADP
ijassa-429	2	6	the	the	DET
ijassa-429	2	7	logistic	logistic	ADJ
ijassa-429	2	8	model	model	NOUN
ijassa-429	2	9	for	for	ADP
ijassa-429	2	10	the	the	DET
ijassa-429	2	11	lag	lag	NOUN
ijassa-429	2	12	-	-	PUNCT
ijassa-429	2	13	phase	phase	NOUN
ijassa-429	2	14	and	and	CCONJ
ijassa-429	2	15	exponential	exponential	ADJ
ijassa-429	2	16	phase	phase	NOUN
ijassa-429	2	17	of	of	ADP
ijassa-429	2	18	the	the	DET
ijassa-429	2	19	population	population	NOUN
ijassa-429	2	20	growth	growth	NOUN
ijassa-429	2	21	,	,	PUNCT
ijassa-429	2	22	but	but	CCONJ
ijassa-429	2	23	quite	quite	ADV
ijassa-429	2	24	different	different	ADJ
ijassa-429	2	25	in	in	ADP
ijassa-429	2	26	the	the	DET
ijassa-429	2	27	stationary	stationary	ADJ
ijassa-429	2	28	phase	phase	NOUN
ijassa-429	2	29	−	−	PROPN
ijassa-429	3	1	the	the	DET
ijassa-429	3	2	growth	growth	NOUN
ijassa-429	3	3	becomes	become	VERB
ijassa-429	3	4	remarkably	remarkably	ADV
ijassa-429	3	5	slower	slow	ADJ
ijassa-429	3	6	after	after	ADP
ijassa-429	3	7	the	the	DET
ijassa-429	3	8	inflection	inflection	NOUN
ijassa-429	3	9	point	point	NOUN
ijassa-429	3	10	.	.	PUNCT
ijassa-429	4	1	at	at	ADP
ijassa-429	4	2	this	this	DET
ijassa-429	4	3	point	point	NOUN
ijassa-429	4	4	,	,	PUNCT
ijassa-429	4	5	limiting	limit	VERB
ijassa-429	4	6	factors	factor	NOUN
ijassa-429	4	7	within	within	ADP
ijassa-429	4	8	the	the	DET
ijassa-429	4	9	population	population	NOUN
ijassa-429	4	10	such	such	ADJ
ijassa-429	4	11	as	as	ADP
ijassa-429	4	12	competition	competition	NOUN
ijassa-429	4	13	or	or	CCONJ
ijassa-429	4	14	environmental	environmental	ADJ
ijassa-429	4	15	stress	stress	NOUN
ijassa-429	4	16	inhibit	inhibit	VERB
ijassa-429	4	17	further	further	ADJ
ijassa-429	4	18	exponential	exponential	ADJ
ijassa-429	4	19	growth	growth	NOUN
ijassa-429	4	20	.	.	PUNCT
ijassa-429	5	1	moreover	moreover	ADV
ijassa-429	5	2	,	,	PUNCT
ijassa-429	5	3	models	model	NOUN
ijassa-429	5	4	as	as	ADP
ijassa-429	5	5	variations	variation	NOUN
ijassa-429	5	6	of	of	ADP
ijassa-429	5	7	the	the	DET
ijassa-429	5	8	traditional	traditional	ADJ
ijassa-429	5	9	exponential	exponential	ADJ
ijassa-429	5	10	model	model	NOUN
ijassa-429	5	11	are	be	AUX
ijassa-429	5	12	also	also	ADV
ijassa-429	5	13	proposed	propose	VERB
ijassa-429	5	14	.	.	PUNCT
ijassa-429	6	1	the	the	DET
ijassa-429	6	2	models	model	NOUN
ijassa-429	6	3	presented	present	VERB
ijassa-429	6	4	demonstrate	demonstrate	VERB
ijassa-429	6	5	more	more	ADJ
ijassa-429	6	6	general	general	ADJ
ijassa-429	6	7	patterns	pattern	NOUN
ijassa-429	6	8	and	and	CCONJ
ijassa-429	6	9	representative	representative	ADJ
ijassa-429	6	10	properties	property	NOUN
ijassa-429	6	11	,	,	PUNCT
ijassa-429	6	12	from	from	ADP
ijassa-429	6	13	which	which	PRON
ijassa-429	6	14	relevant	relevant	ADJ
ijassa-429	6	15	algorithms	algorithm	NOUN
ijassa-429	6	16	can	can	AUX
ijassa-429	6	17	be	be	AUX
ijassa-429	6	18	developed	develop	VERB
ijassa-429	6	19	for	for	ADP
ijassa-429	6	20	calculating	calculate	VERB
ijassa-429	6	21	the	the	DET
ijassa-429	6	22	population	population	NOUN
ijassa-429	6	23	specific	specific	ADJ
ijassa-429	6	24	growth	growth	NOUN
ijassa-429	6	25	rate	rate	NOUN
ijassa-429	6	26	occurring	occur	VERB
ijassa-429	6	27	in	in	ADP
ijassa-429	6	28	the	the	DET
ijassa-429	6	29	exponential	exponential	ADJ
ijassa-429	6	30	phase	phase	NOUN
ijassa-429	6	31	.	.	PUNCT
ijassa-429	7	1	keywords	keyword	VERB
ijassa-429	7	2	maclaurin	maclaurin	NOUN
ijassa-429	7	3	series	series	NOUN
ijassa-429	7	4	,	,	PUNCT
ijassa-429	7	5	logistic	logistic	ADJ
ijassa-429	7	6	growth	growth	NOUN
ijassa-429	7	7	,	,	PUNCT
ijassa-429	7	8	exponential	exponential	ADJ
ijassa-429	7	9	growth	growth	NOUN
ijassa-429	7	10	,	,	PUNCT
ijassa-429	7	11	point	point	NOUN
ijassa-429	7	12	of	of	ADP
ijassa-429	7	13	inflection	inflection	NOUN
ijassa-429	7	14	,	,	PUNCT
ijassa-429	7	15	carrying	carry	VERB
ijassa-429	7	16	capacity	capacity	NOUN
ijassa-429	7	17	,	,	PUNCT
ijassa-429	7	18	specific	specific	ADJ
ijassa-429	7	19	growth	growth	NOUN
ijassa-429	7	20	rate	rate	NOUN
ijassa-429	7	21	1	1	NUM
ijassa-429	7	22	introduction	introduction	NOUN
ijassa-429	7	23	the	the	DET
ijassa-429	7	24	study	study	NOUN
ijassa-429	7	25	of	of	ADP
ijassa-429	7	26	microbial	microbial	ADJ
ijassa-429	7	27	kinetics	kinetic	NOUN
ijassa-429	7	28	is	be	AUX
ijassa-429	7	29	of	of	ADP
ijassa-429	7	30	particular	particular	ADJ
ijassa-429	7	31	significance	significance	NOUN
ijassa-429	7	32	to	to	ADP
ijassa-429	7	33	research	research	NOUN
ijassa-429	7	34	in	in	ADP
ijassa-429	7	35	the	the	DET
ijassa-429	7	36	fields	field	NOUN
ijassa-429	7	37	of	of	ADP
ijassa-429	7	38	microbiology	microbiology	NOUN
ijassa-429	7	39	and	and	CCONJ
ijassa-429	7	40	biotechnology	biotechnology	NOUN
ijassa-429	8	1	[	[	X
ijassa-429	8	2	1	1	NUM
ijassa-429	8	3	]	]	PUNCT
ijassa-429	8	4	.	.	PUNCT
ijassa-429	9	1	although	although	SCONJ
ijassa-429	9	2	existing	exist	VERB
ijassa-429	9	3	models	model	NOUN
ijassa-429	9	4	and	and	CCONJ
ijassa-429	9	5	methods	method	NOUN
ijassa-429	9	6	have	have	AUX
ijassa-429	9	7	been	be	AUX
ijassa-429	9	8	developed	develop	VERB
ijassa-429	9	9	,	,	PUNCT
ijassa-429	9	10	an	an	DET
ijassa-429	9	11	issue	issue	NOUN
ijassa-429	9	12	arises	arise	VERB
ijassa-429	9	13	over	over	ADP
ijassa-429	9	14	the	the	DET
ijassa-429	9	15	precision	precision	NOUN
ijassa-429	9	16	of	of	ADP
ijassa-429	9	17	potentially	potentially	ADV
ijassa-429	9	18	subjective	subjective	ADJ
ijassa-429	9	19	,	,	PUNCT
ijassa-429	9	20	traditional	traditional	ADJ
ijassa-429	9	21	methods	method	NOUN
ijassa-429	9	22	of	of	ADP
ijassa-429	9	23	culture	culture	NOUN
ijassa-429	9	24	analysis	analysis	NOUN
ijassa-429	9	25	.	.	PUNCT
ijassa-429	10	1	calculating	calculate	VERB
ijassa-429	10	2	population	population	NOUN
ijassa-429	10	3	growth	growth	NOUN
ijassa-429	10	4	rate	rate	NOUN
ijassa-429	10	5	is	be	AUX
ijassa-429	10	6	essential	essential	ADJ
ijassa-429	10	7	to	to	ADP
ijassa-429	10	8	microbial	microbial	ADJ
ijassa-429	10	9	kinetic	kinetic	ADJ
ijassa-429	10	10	studies	study	NOUN
ijassa-429	10	11	of	of	ADP
ijassa-429	10	12	substrate	substrate	NOUN
ijassa-429	10	13	-	-	PUNCT
ijassa-429	10	14	culture	culture	NOUN
ijassa-429	10	15	interactions	interaction	NOUN
ijassa-429	10	16	,	,	PUNCT
ijassa-429	10	17	and	and	CCONJ
ijassa-429	10	18	the	the	DET
ijassa-429	10	19	introduction	introduction	NOUN
ijassa-429	10	20	of	of	ADP
ijassa-429	10	21	a	a	DET
ijassa-429	10	22	new	new	ADJ
ijassa-429	10	23	model	model	NOUN
ijassa-429	10	24	for	for	ADP
ijassa-429	10	25	population	population	NOUN
ijassa-429	10	26	growth	growth	NOUN
ijassa-429	10	27	increases	increase	VERB
ijassa-429	10	28	the	the	DET
ijassa-429	10	29	precision	precision	NOUN
ijassa-429	10	30	of	of	ADP
ijassa-429	10	31	the	the	DET
ijassa-429	10	32	method	method	NOUN
ijassa-429	10	33	.	.	PUNCT
ijassa-429	11	1	pinpointing	pinpoint	VERB
ijassa-429	11	2	this	this	DET
ijassa-429	11	3	microbial	microbial	ADJ
ijassa-429	11	4	specific	specific	ADJ
ijassa-429	11	5	growth	growth	NOUN
ijassa-429	11	6	rate	rate	NOUN
ijassa-429	11	7	,	,	PUNCT
ijassa-429	11	8	represented	represent	VERB
ijassa-429	11	9	as	as	ADP
ijassa-429	11	10	µ	µ	NOUN
ijassa-429	11	11	or	or	CCONJ
ijassa-429	11	12	r	r	NOUN
ijassa-429	11	13	,	,	PUNCT
ijassa-429	11	14	with	with	SCONJ
ijassa-429	11	15	accuracy	accuracy	NOUN
ijassa-429	11	16	and	and	CCONJ
ijassa-429	11	17	precision	precision	NOUN
ijassa-429	11	18	is	be	AUX
ijassa-429	11	19	at	at	ADP
ijassa-429	11	20	the	the	DET
ijassa-429	11	21	heart	heart	NOUN
ijassa-429	11	22	of	of	ADP
ijassa-429	11	23	consistency	consistency	NOUN
ijassa-429	11	24	in	in	ADP
ijassa-429	11	25	understanding	understand	VERB
ijassa-429	11	26	laboratory	laboratory	NOUN
ijassa-429	11	27	results	result	NOUN
ijassa-429	11	28	.	.	PUNCT
ijassa-429	12	1	furthermore	furthermore	ADV
ijassa-429	12	2	,	,	PUNCT
ijassa-429	12	3	extending	extend	VERB
ijassa-429	12	4	calculations	calculation	NOUN
ijassa-429	12	5	to	to	PART
ijassa-429	12	6	model	model	VERB
ijassa-429	12	7	the	the	DET
ijassa-429	12	8	data	datum	NOUN
ijassa-429	12	9	uses	use	VERB
ijassa-429	12	10	growth	growth	NOUN
ijassa-429	12	11	patterns	pattern	NOUN
ijassa-429	12	12	to	to	PART
ijassa-429	12	13	provide	provide	VERB
ijassa-429	12	14	insight	insight	NOUN
ijassa-429	12	15	into	into	ADP
ijassa-429	12	16	characteristics	characteristic	NOUN
ijassa-429	12	17	of	of	ADP
ijassa-429	12	18	the	the	DET
ijassa-429	12	19	microbe	microbe	NOUN
ijassa-429	12	20	.	.	PUNCT
ijassa-429	13	1	an	an	DET
ijassa-429	13	2	exploration	exploration	NOUN
ijassa-429	13	3	of	of	ADP
ijassa-429	13	4	four	four	NUM
ijassa-429	13	5	models	model	NOUN
ijassa-429	13	6	incorporates	incorporate	VERB
ijassa-429	13	7	a	a	DET
ijassa-429	13	8	review	review	NOUN
ijassa-429	13	9	and	and	CCONJ
ijassa-429	13	10	extension	extension	NOUN
ijassa-429	13	11	of	of	ADP
ijassa-429	13	12	the	the	DET
ijassa-429	13	13	traditional	traditional	ADJ
ijassa-429	13	14	exponential	exponential	ADJ
ijassa-429	13	15	and	and	CCONJ
ijassa-429	13	16	logistic	logistic	ADJ
ijassa-429	13	17	growth	growth	NOUN
ijassa-429	13	18	function	function	NOUN
ijassa-429	13	19	,	,	PUNCT
ijassa-429	13	20	and	and	CCONJ
ijassa-429	13	21	introduces	introduce	VERB
ijassa-429	13	22	the	the	DET
ijassa-429	13	23	potential	potential	NOUN
ijassa-429	13	24	for	for	ADP
ijassa-429	13	25	exponential	exponential	NOUN
ijassa-429	13	26	-	-	PUNCT
ijassa-429	13	27	like	like	ADJ
ijassa-429	13	28	and	and	CCONJ
ijassa-429	13	29	logistic	logistic	ADJ
ijassa-429	13	30	-	-	PUNCT
ijassa-429	13	31	like	like	ADJ
ijassa-429	13	32	functions	function	NOUN
ijassa-429	13	33	using	use	VERB
ijassa-429	13	34	a	a	DET
ijassa-429	13	35	modified	modify	VERB
ijassa-429	13	36	form	form	NOUN
ijassa-429	13	37	of	of	ADP
ijassa-429	13	38	the	the	DET
ijassa-429	13	39	exponential	exponential	ADJ
ijassa-429	13	40	maclaurin	maclaurin	NOUN
ijassa-429	13	41	series	series	NOUN
ijassa-429	13	42	.	.	PUNCT
ijassa-429	14	1	several	several	ADJ
ijassa-429	14	2	models	model	NOUN
ijassa-429	14	3	have	have	AUX
ijassa-429	14	4	been	be	AUX
ijassa-429	14	5	fit	fit	ADJ
ijassa-429	14	6	for	for	ADP
ijassa-429	14	7	microbial	microbial	ADJ
ijassa-429	14	8	growth	growth	NOUN
ijassa-429	14	9	curves	curve	NOUN
ijassa-429	14	10	,	,	PUNCT
ijassa-429	14	11	modifications	modification	NOUN
ijassa-429	14	12	of	of	ADP
ijassa-429	14	13	the	the	DET
ijassa-429	14	14	idealized	idealized	ADJ
ijassa-429	14	15	exponential	exponential	NOUN
ijassa-429	14	16	(	(	PUNCT
ijassa-429	14	17	malthusian	malthusian	NOUN
ijassa-429	14	18	)	)	PUNCT
ijassa-429	14	19	and	and	CCONJ
ijassa-429	14	20	logistic	logistic	ADJ
ijassa-429	14	21	(	(	PUNCT
ijassa-429	14	22	limited	limited	ADJ
ijassa-429	14	23	)	)	PUNCT
ijassa-429	14	24	growth	growth	NOUN
ijassa-429	14	25	to	to	PART
ijassa-429	14	26	fit	fit	VERB
ijassa-429	14	27	the	the	DET
ijassa-429	14	28	reality	reality	NOUN
ijassa-429	14	29	of	of	ADP
ijassa-429	14	30	microbial	microbial	ADJ
ijassa-429	14	31	patterns	pattern	NOUN
ijassa-429	14	32	.	.	PUNCT
ijassa-429	15	1	among	among	ADP
ijassa-429	15	2	growth	growth	NOUN
ijassa-429	15	3	models	model	NOUN
ijassa-429	15	4	,	,	PUNCT
ijassa-429	15	5	competition	competition	NOUN
ijassa-429	15	6	models	model	NOUN
ijassa-429	15	7	,	,	PUNCT
ijassa-429	15	8	and	and	CCONJ
ijassa-429	15	9	nutrient	nutrient	ADJ
ijassa-429	15	10	uptake	uptake	ADJ
ijassa-429	15	11	models	model	NOUN
ijassa-429	15	12	are	be	AUX
ijassa-429	15	13	included	include	VERB
ijassa-429	15	14	theta	theta	NOUN
ijassa-429	15	15	logistic	logistic	ADJ
ijassa-429	15	16	functions	function	NOUN
ijassa-429	15	17	,	,	PUNCT
ijassa-429	15	18	trans	trans	ADJ
ijassa-429	15	19	-	-	ADJ
ijassa-429	15	20	theta	theta	ADJ
ijassa-429	15	21	logistic	logistic	ADJ
ijassa-429	15	22	functions	function	NOUN
ijassa-429	15	23	,	,	PUNCT
ijassa-429	15	24	time	time	NOUN
ijassa-429	15	25	-	-	PUNCT
ijassa-429	15	26	delay	delay	NOUN
ijassa-429	15	27	logistic	logistic	ADJ
ijassa-429	15	28	functions	function	NOUN
ijassa-429	15	29	,	,	PUNCT
ijassa-429	15	30	general	general	ADJ
ijassa-429	15	31	logistic	logistic	ADJ
ijassa-429	15	32	functions	function	NOUN
ijassa-429	15	33	.	.	PUNCT
ijassa-429	16	1	michaelis	michaeli	NOUN
ijassa-429	16	2	-	-	PUNCT
ijassa-429	16	3	menten	menten	VERB
ijassa-429	16	4	kinetics	kinetic	NOUN
ijassa-429	16	5	,	,	PUNCT
ijassa-429	16	6	gompertz	gompertz	NOUN
ijassa-429	16	7	,	,	PUNCT
ijassa-429	16	8	von	von	PROPN
ijassa-429	16	9	bertalanffy	bertalanffy	PROPN
ijassa-429	16	10	and	and	CCONJ
ijassa-429	16	11	general	general	PROPN
ijassa-429	16	12	von	von	PROPN
ijassa-429	16	13	bertalanffy	bertalanffy	PROPN
ijassa-429	16	14	,	,	PUNCT
ijassa-429	16	15	verhlust	verhlust	PROPN
ijassa-429	16	16	,	,	PUNCT
ijassa-429	16	17	and	and	CCONJ
ijassa-429	16	18	advances	advance	NOUN
ijassa-429	16	19	in	in	ADP
ijassa-429	16	20	systems	system	NOUN
ijassa-429	16	21	science	science	NOUN
ijassa-429	16	22	and	and	CCONJ
ijassa-429	16	23	applications	application	NOUN
ijassa-429	16	24	(	(	PUNCT
ijassa-429	16	25	2013	2013	NUM
ijassa-429	16	26	)	)	PUNCT
ijassa-429	16	27	vol.13	vol.13	NOUN
ijassa-429	16	28	no.1	no.1	VERB
ijassa-429	16	29	81	81	NUM
ijassa-429	16	30	lotka	lotka	PROPN
ijassa-429	16	31	-	-	PUNCT
ijassa-429	16	32	volterra	volterra	PROPN
ijassa-429	16	33	are	be	AUX
ijassa-429	16	34	specific	specific	ADJ
ijassa-429	16	35	cases	case	NOUN
ijassa-429	16	36	of	of	ADP
ijassa-429	16	37	these	these	DET
ijassa-429	16	38	models	model	NOUN
ijassa-429	16	39	[	[	X
ijassa-429	16	40	2	2	NUM
ijassa-429	16	41	-	-	SYM
ijassa-429	16	42	11	11	NUM
ijassa-429	16	43	]	]	PUNCT
ijassa-429	16	44	.	.	PUNCT
ijassa-429	17	1	exponential	exponential	ADJ
ijassa-429	17	2	growth	growth	NOUN
ijassa-429	17	3	,	,	PUNCT
ijassa-429	17	4	or	or	CCONJ
ijassa-429	17	5	unlimited	unlimited	ADJ
ijassa-429	17	6	and	and	CCONJ
ijassa-429	17	7	ever	ever	ADV
ijassa-429	17	8	-	-	PUNCT
ijassa-429	17	9	increasing	increase	VERB
ijassa-429	17	10	growth	growth	NOUN
ijassa-429	17	11	,	,	PUNCT
ijassa-429	17	12	is	be	AUX
ijassa-429	17	13	represented	represent	VERB
ijassa-429	17	14	by	by	ADP
ijassa-429	17	15	the	the	DET
ijassa-429	17	16	general	general	ADJ
ijassa-429	17	17	differential	differential	NOUN
ijassa-429	17	18	form	form	NOUN
ijassa-429	17	19	dp	dp	NOUN
ijassa-429	17	20	dt	dt	NOUN
ijassa-429	17	21	=	=	PUNCT
ijassa-429	17	22	rp	rp	NOUN
ijassa-429	17	23	,	,	PUNCT
ijassa-429	17	24	and	and	CCONJ
ijassa-429	17	25	its	its	PRON
ijassa-429	17	26	solution	solution	NOUN
ijassa-429	17	27	p	p	X
ijassa-429	17	28	(	(	PUNCT
ijassa-429	17	29	t	t	NOUN
ijassa-429	17	30	)	)	PUNCT
ijassa-429	17	31	=	=	NOUN
ijassa-429	18	1	p0e	p0e	NOUN
ijassa-429	18	2	rt[8	rt[8	PROPN
ijassa-429	18	3	]	]	PUNCT
ijassa-429	18	4	.	.	PUNCT
ijassa-429	19	1	logistic	logistic	ADJ
ijassa-429	19	2	growth	growth	NOUN
ijassa-429	19	3	is	be	AUX
ijassa-429	19	4	sigmoidal	sigmoidal	NOUN
ijassa-429	19	5	and	and	CCONJ
ijassa-429	19	6	limited	limited	ADJ
ijassa-429	19	7	.	.	PUNCT
ijassa-429	20	1	it	it	PRON
ijassa-429	20	2	is	be	AUX
ijassa-429	20	3	represented	represent	VERB
ijassa-429	20	4	by	by	ADP
ijassa-429	20	5	the	the	DET
ijassa-429	20	6	general	general	ADJ
ijassa-429	20	7	differential	differential	NOUN
ijassa-429	20	8	form	form	NOUN
ijassa-429	20	9	dp	dp	NOUN
ijassa-429	20	10	dt	dt	NOUN
ijassa-429	20	11	=	=	PUNCT
ijassa-429	20	12	rp	rp	NOUN
ijassa-429	20	13	(	(	PUNCT
ijassa-429	20	14	1	1	NUM
ijassa-429	20	15	−	−	PROPN
ijassa-429	20	16	p	p	NOUN
ijassa-429	20	17	m	m	PROPN
ijassa-429	20	18	)	)	PUNCT
ijassa-429	20	19	,	,	PUNCT
ijassa-429	20	20	and	and	CCONJ
ijassa-429	20	21	its	its	PRON
ijassa-429	20	22	solution	solution	NOUN
ijassa-429	20	23	p	p	X
ijassa-429	20	24	(	(	PUNCT
ijassa-429	20	25	t	t	NOUN
ijassa-429	20	26	)	)	PUNCT
ijassa-429	20	27	=	=	PROPN
ijassa-429	20	28	mp0ert	mp0ert	PROPN
ijassa-429	20	29	m+p0(ert−1	m+p0(ert−1	PROPN
ijassa-429	20	30	)	)	PUNCT
ijassa-429	21	1	[	[	X
ijassa-429	21	2	8	8	NUM
ijassa-429	21	3	]	]	PUNCT
ijassa-429	21	4	.	.	PUNCT
ijassa-429	22	1	previous	previous	ADJ
ijassa-429	22	2	extensions	extension	NOUN
ijassa-429	22	3	to	to	ADP
ijassa-429	22	4	the	the	DET
ijassa-429	22	5	logistic	logistic	ADJ
ijassa-429	22	6	model	model	NOUN
ijassa-429	22	7	involve	involve	VERB
ijassa-429	22	8	the	the	DET
ijassa-429	22	9	general	general	ADJ
ijassa-429	22	10	logistic	logistic	ADJ
ijassa-429	22	11	model	model	NOUN
ijassa-429	22	12	and	and	CCONJ
ijassa-429	22	13	the	the	DET
ijassa-429	22	14	time	time	NOUN
ijassa-429	22	15	-	-	PUNCT
ijassa-429	22	16	sensitive	sensitive	ADJ
ijassa-429	22	17	carrying	carrying	NOUN
ijassa-429	22	18	capacity	capacity	NOUN
ijassa-429	22	19	logistic	logistic	ADJ
ijassa-429	22	20	model	model	NOUN
ijassa-429	22	21	[	[	X
ijassa-429	22	22	8	8	NUM
ijassa-429	22	23	-	-	SYM
ijassa-429	22	24	11	11	NUM
ijassa-429	22	25	]	]	PUNCT
ijassa-429	22	26	.	.	PUNCT
ijassa-429	23	1	the	the	DET
ijassa-429	23	2	general	general	ADJ
ijassa-429	23	3	logistic	logistic	ADJ
ijassa-429	23	4	model	model	NOUN
ijassa-429	23	5	takes	take	VERB
ijassa-429	23	6	the	the	DET
ijassa-429	23	7	differential	differential	ADJ
ijassa-429	23	8	form	form	NOUN
ijassa-429	23	9	dp	dp	NOUN
ijassa-429	23	10	dt	dt	NOUN
ijassa-429	23	11	=	=	SYM
ijassa-429	23	12	rpα[1	rpα[1	NUM
ijassa-429	23	13	−	−	PROPN
ijassa-429	24	1	(	(	PUNCT
ijassa-429	24	2	p	p	NOUN
ijassa-429	24	3	m	m	NOUN
ijassa-429	24	4	)	)	PUNCT
ijassa-429	25	1	ν	ν	X
ijassa-429	25	2	]	]	X
ijassa-429	25	3	γ	γ	X
ijassa-429	25	4	,	,	PUNCT
ijassa-429	25	5	which	which	PRON
ijassa-429	25	6	is	be	AUX
ijassa-429	25	7	simplified	simplify	VERB
ijassa-429	25	8	to	to	ADP
ijassa-429	25	9	p	p	PROPN
ijassa-429	25	10	(	(	PUNCT
ijassa-429	25	11	t	t	NOUN
ijassa-429	25	12	)	)	PUNCT
ijassa-429	25	13	=	=	SYM
ijassa-429	25	14	m	m	VERB
ijassa-429	26	1	[	[	X
ijassa-429	26	2	1+[(γ−1)βrm(α−1)t+	1+[(γ−1)βrm(α−1)t+	NUM
ijassa-429	26	3	[	[	PUNCT
ijassa-429	26	4	(	(	PUNCT
ijassa-429	26	5	m	m	VERB
ijassa-429	26	6	p0	p0	NOUN
ijassa-429	26	7	)	)	PUNCT
ijassa-429	26	8	β−1](1−γ)]1/(1−γ)]1	β−1](1−γ)]1/(1−γ)]1	NOUN
ijassa-429	26	9	/	/	SYM
ijassa-429	26	10	β	β	NOUN
ijassa-429	26	11	or	or	CCONJ
ijassa-429	26	12	p	p	PROPN
ijassa-429	26	13	(	(	PUNCT
ijassa-429	26	14	t	t	PROPN
ijassa-429	26	15	)	)	PUNCT
ijassa-429	26	16	=	=	PUNCT
ijassa-429	27	1	a	a	DET
ijassa-429	27	2	+	+	NUM
ijassa-429	27	3	m−a	m−a	PROPN
ijassa-429	27	4	(	(	PUNCT
ijassa-429	27	5	1+qe−r(t−t1))1	1+qe−r(t−t1))1	NUM
ijassa-429	27	6	/	/	SYM
ijassa-429	27	7	ν	ν	NOUN
ijassa-429	27	8	,	,	PUNCT
ijassa-429	27	9	(	(	PUNCT
ijassa-429	27	10	t1	t1	NOUN
ijassa-429	27	11	is	be	AUX
ijassa-429	27	12	defined	define	VERB
ijassa-429	27	13	as	as	ADP
ijassa-429	27	14	time	time	NOUN
ijassa-429	27	15	of	of	ADP
ijassa-429	27	16	maximum	maximum	ADJ
ijassa-429	27	17	growth	growth	NOUN
ijassa-429	27	18	,	,	PUNCT
ijassa-429	27	19	a	a	PRON
ijassa-429	27	20	is	be	AUX
ijassa-429	27	21	the	the	DET
ijassa-429	27	22	value	value	NOUN
ijassa-429	27	23	of	of	ADP
ijassa-429	27	24	the	the	DET
ijassa-429	27	25	lower	low	ADJ
ijassa-429	27	26	asymptote	asymptote	NOUN
ijassa-429	27	27	,	,	PUNCT
ijassa-429	27	28	q	q	PUNCT
ijassa-429	27	29	is	be	AUX
ijassa-429	27	30	an	an	DET
ijassa-429	27	31	initial	initial	ADJ
ijassa-429	27	32	condition	condition	NOUN
ijassa-429	27	33	constant	constant	ADJ
ijassa-429	27	34	,	,	PUNCT
ijassa-429	27	35	ν	ν	NOUN
ijassa-429	27	36	is	be	AUX
ijassa-429	27	37	a	a	DET
ijassa-429	27	38	constant	constant	ADJ
ijassa-429	27	39	determining	determine	VERB
ijassa-429	27	40	the	the	DET
ijassa-429	27	41	point	point	NOUN
ijassa-429	27	42	of	of	ADP
ijassa-429	27	43	inflection	inflection	NOUN
ijassa-429	27	44	,	,	PUNCT
ijassa-429	27	45	and	and	CCONJ
ijassa-429	27	46	α	α	NOUN
ijassa-429	27	47	and	and	CCONJ
ijassa-429	27	48	γ	γ	PROPN
ijassa-429	27	49	represent	represent	VERB
ijassa-429	27	50	constant	constant	ADJ
ijassa-429	27	51	inflection	inflection	NOUN
ijassa-429	27	52	value	value	NOUN
ijassa-429	27	53	parameters	parameter	NOUN
ijassa-429	27	54	)	)	PUNCT
ijassa-429	28	1	[	[	X
ijassa-429	28	2	8	8	NUM
ijassa-429	28	3	]	]	PUNCT
ijassa-429	28	4	.	.	PUNCT
ijassa-429	29	1	this	this	PRON
ijassa-429	29	2	introduces	introduce	VERB
ijassa-429	29	3	new	new	ADJ
ijassa-429	29	4	parameters	parameter	NOUN
ijassa-429	29	5	so	so	SCONJ
ijassa-429	29	6	that	that	SCONJ
ijassa-429	29	7	the	the	DET
ijassa-429	29	8	curve	curve	NOUN
ijassa-429	29	9	can	can	AUX
ijassa-429	29	10	idealize	idealize	VERB
ijassa-429	29	11	scenarios	scenario	NOUN
ijassa-429	29	12	previously	previously	ADV
ijassa-429	29	13	considered	consider	VERB
ijassa-429	29	14	“	"	PUNCT
ijassa-429	29	15	less	less	ADV
ijassa-429	29	16	ideal	ideal	ADJ
ijassa-429	29	17	”	"	PUNCT
ijassa-429	29	18	by	by	ADP
ijassa-429	29	19	existing	exist	VERB
ijassa-429	29	20	models	model	NOUN
ijassa-429	29	21	.	.	PUNCT
ijassa-429	30	1	the	the	DET
ijassa-429	30	2	time	time	NOUN
ijassa-429	30	3	-	-	PUNCT
ijassa-429	30	4	varying	vary	VERB
ijassa-429	30	5	model	model	NOUN
ijassa-429	30	6	introduces	introduce	VERB
ijassa-429	30	7	the	the	DET
ijassa-429	30	8	upper	upper	ADJ
ijassa-429	30	9	bound	bind	VERB
ijassa-429	30	10	itself	itself	PRON
ijassa-429	30	11	as	as	ADP
ijassa-429	30	12	a	a	DET
ijassa-429	30	13	function	function	NOUN
ijassa-429	30	14	of	of	ADP
ijassa-429	30	15	time	time	NOUN
ijassa-429	30	16	,	,	PUNCT
ijassa-429	30	17	and	and	CCONJ
ijassa-429	30	18	it	it	PRON
ijassa-429	30	19	therefore	therefore	ADV
ijassa-429	30	20	can	can	AUX
ijassa-429	30	21	not	not	PART
ijassa-429	30	22	be	be	AUX
ijassa-429	30	23	definitely	definitely	ADV
ijassa-429	30	24	determined	determined	ADJ
ijassa-429	30	25	as	as	ADP
ijassa-429	30	26	an	an	DET
ijassa-429	30	27	analytical	analytical	ADJ
ijassa-429	30	28	solution	solution	NOUN
ijassa-429	30	29	.	.	PUNCT
ijassa-429	31	1	this	this	DET
ijassa-429	31	2	model	model	NOUN
ijassa-429	31	3	further	far	ADV
ijassa-429	31	4	complicates	complicate	VERB
ijassa-429	31	5	the	the	DET
ijassa-429	31	6	function	function	NOUN
ijassa-429	31	7	with	with	ADP
ijassa-429	31	8	the	the	DET
ijassa-429	31	9	introduction	introduction	NOUN
ijassa-429	31	10	of	of	ADP
ijassa-429	31	11	a	a	DET
ijassa-429	31	12	variable	variable	ADJ
ijassa-429	31	13	parameter	parameter	NOUN
ijassa-429	31	14	.	.	PUNCT
ijassa-429	32	1	it	it	PRON
ijassa-429	32	2	is	be	AUX
ijassa-429	32	3	represented	represent	VERB
ijassa-429	32	4	as	as	ADP
ijassa-429	32	5	dp	dp	NOUN
ijassa-429	32	6	dt	dt	NOUN
ijassa-429	32	7	=	=	PUNCT
ijassa-429	32	8	rp	rp	NOUN
ijassa-429	32	9	(	(	PUNCT
ijassa-429	32	10	1−	1−	NUM
ijassa-429	32	11	p	p	NOUN
ijassa-429	32	12	m(t))[11	m(t))[11	NOUN
ijassa-429	32	13	]	]	PUNCT
ijassa-429	32	14	.	.	PUNCT
ijassa-429	33	1	the	the	DET
ijassa-429	33	2	introduction	introduction	NOUN
ijassa-429	33	3	of	of	ADP
ijassa-429	33	4	a	a	DET
ijassa-429	33	5	series	series	NOUN
ijassa-429	33	6	incorporates	incorporate	VERB
ijassa-429	33	7	the	the	DET
ijassa-429	33	8	concept	concept	NOUN
ijassa-429	33	9	of	of	ADP
ijassa-429	33	10	a	a	DET
ijassa-429	33	11	traditional	traditional	ADJ
ijassa-429	33	12	model	model	NOUN
ijassa-429	33	13	modified	modify	VERB
ijassa-429	33	14	through	through	ADP
ijassa-429	33	15	extension	extension	NOUN
ijassa-429	33	16	.	.	PUNCT
ijassa-429	34	1	this	this	DET
ijassa-429	34	2	new	new	ADJ
ijassa-429	34	3	function	function	NOUN
ijassa-429	34	4	is	be	AUX
ijassa-429	34	5	explored	explore	VERB
ijassa-429	34	6	as	as	ADP
ijassa-429	34	7	a	a	DET
ijassa-429	34	8	differential	differential	NOUN
ijassa-429	34	9	,	,	PUNCT
ijassa-429	34	10	and	and	CCONJ
ijassa-429	34	11	characterized	characterize	VERB
ijassa-429	34	12	by	by	ADP
ijassa-429	34	13	its	its	PRON
ijassa-429	34	14	non	non	ADJ
ijassa-429	34	15	-	-	ADJ
ijassa-429	34	16	integrable	integrable	ADJ
ijassa-429	34	17	form	form	NOUN
ijassa-429	34	18	.	.	PUNCT
ijassa-429	35	1	the	the	DET
ijassa-429	35	2	exponential	exponential	ADJ
ijassa-429	35	3	and	and	CCONJ
ijassa-429	35	4	logistic	logistic	ADJ
ijassa-429	35	5	models	model	NOUN
ijassa-429	35	6	represent	represent	VERB
ijassa-429	35	7	the	the	DET
ijassa-429	35	8	first	first	ADJ
ijassa-429	35	9	two	two	NUM
ijassa-429	35	10	terms	term	NOUN
ijassa-429	35	11	of	of	ADP
ijassa-429	35	12	a	a	DET
ijassa-429	35	13	maclaurin	maclaurin	NOUN
ijassa-429	35	14	series	series	NOUN
ijassa-429	35	15	.	.	PUNCT
ijassa-429	36	1	previously	previously	ADV
ijassa-429	36	2	,	,	PUNCT
ijassa-429	36	3	the	the	DET
ijassa-429	36	4	remaining	remain	VERB
ijassa-429	36	5	terms	term	NOUN
ijassa-429	36	6	were	be	AUX
ijassa-429	36	7	not	not	PART
ijassa-429	36	8	considered	consider	VERB
ijassa-429	36	9	significant	significant	ADJ
ijassa-429	36	10	,	,	PUNCT
ijassa-429	36	11	and	and	CCONJ
ijassa-429	36	12	the	the	DET
ijassa-429	36	13	use	use	NOUN
ijassa-429	36	14	of	of	ADP
ijassa-429	36	15	a	a	DET
ijassa-429	36	16	series	series	NOUN
ijassa-429	36	17	was	be	AUX
ijassa-429	36	18	disregarded	disregard	VERB
ijassa-429	36	19	[	[	X
ijassa-429	36	20	8	8	NUM
ijassa-429	36	21	]	]	PUNCT
ijassa-429	36	22	.	.	PUNCT
ijassa-429	37	1	however	however	ADV
ijassa-429	37	2	,	,	PUNCT
ijassa-429	37	3	discovering	discover	VERB
ijassa-429	37	4	and	and	CCONJ
ijassa-429	37	5	incorporating	incorporate	VERB
ijassa-429	37	6	the	the	DET
ijassa-429	37	7	terms	term	NOUN
ijassa-429	37	8	as	as	SCONJ
ijassa-429	37	9	an	an	DET
ijassa-429	37	10	expanded	expand	VERB
ijassa-429	37	11	series	series	NOUN
ijassa-429	37	12	removes	remove	VERB
ijassa-429	37	13	inconsistencies	inconsistency	NOUN
ijassa-429	37	14	between	between	ADP
ijassa-429	37	15	methods	method	NOUN
ijassa-429	37	16	of	of	ADP
ijassa-429	37	17	calculation	calculation	NOUN
ijassa-429	37	18	for	for	ADP
ijassa-429	37	19	parameters	parameter	NOUN
ijassa-429	37	20	,	,	PUNCT
ijassa-429	37	21	such	such	ADJ
ijassa-429	37	22	as	as	ADP
ijassa-429	37	23	rate	rate	NOUN
ijassa-429	37	24	of	of	ADP
ijassa-429	37	25	increase	increase	NOUN
ijassa-429	37	26	.	.	PUNCT
ijassa-429	38	1	the	the	DET
ijassa-429	38	2	convergence	convergence	NOUN
ijassa-429	38	3	of	of	ADP
ijassa-429	38	4	the	the	DET
ijassa-429	38	5	series	series	NOUN
ijassa-429	38	6	represents	represent	VERB
ijassa-429	38	7	an	an	DET
ijassa-429	38	8	ideal	ideal	ADJ
ijassa-429	38	9	model	model	NOUN
ijassa-429	38	10	,	,	PUNCT
ijassa-429	38	11	that	that	PRON
ijassa-429	38	12	can	can	AUX
ijassa-429	38	13	be	be	AUX
ijassa-429	38	14	characterized	characterize	VERB
ijassa-429	38	15	by	by	ADP
ijassa-429	38	16	the	the	DET
ijassa-429	38	17	properties	property	NOUN
ijassa-429	38	18	of	of	ADP
ijassa-429	38	19	several	several	ADJ
ijassa-429	38	20	functions	function	NOUN
ijassa-429	38	21	,	,	PUNCT
ijassa-429	38	22	and	and	CCONJ
ijassa-429	38	23	to	to	PART
ijassa-429	38	24	which	which	PRON
ijassa-429	38	25	these	these	DET
ijassa-429	38	26	functions	function	NOUN
ijassa-429	38	27	converge	converge	VERB
ijassa-429	38	28	.	.	PUNCT
ijassa-429	39	1	the	the	DET
ijassa-429	39	2	first	first	ADJ
ijassa-429	39	3	terms	term	NOUN
ijassa-429	39	4	reflect	reflect	VERB
ijassa-429	39	5	its	its	PRON
ijassa-429	39	6	most	most	ADV
ijassa-429	39	7	basic	basic	ADJ
ijassa-429	39	8	exponential	exponential	ADJ
ijassa-429	39	9	and	and	CCONJ
ijassa-429	39	10	logistic	logistic	ADJ
ijassa-429	39	11	properties	property	NOUN
ijassa-429	39	12	.	.	PUNCT
ijassa-429	40	1	as	as	SCONJ
ijassa-429	40	2	it	it	PRON
ijassa-429	40	3	continues	continue	VERB
ijassa-429	40	4	to	to	PART
ijassa-429	40	5	expand	expand	VERB
ijassa-429	40	6	and	and	CCONJ
ijassa-429	40	7	the	the	DET
ijassa-429	40	8	series	series	NOUN
ijassa-429	40	9	converges	converge	VERB
ijassa-429	40	10	,	,	PUNCT
ijassa-429	40	11	truncation	truncation	NOUN
ijassa-429	40	12	produces	produce	VERB
ijassa-429	40	13	a	a	DET
ijassa-429	40	14	series	series	NOUN
ijassa-429	40	15	of	of	ADP
ijassa-429	40	16	polynomial	polynomial	ADJ
ijassa-429	40	17	functions	function	NOUN
ijassa-429	40	18	with	with	ADP
ijassa-429	40	19	exponential	exponential	ADJ
ijassa-429	40	20	and	and	CCONJ
ijassa-429	40	21	logistic	logistic	ADJ
ijassa-429	40	22	-	-	PUNCT
ijassa-429	40	23	like	like	ADJ
ijassa-429	40	24	(	(	PUNCT
ijassa-429	40	25	sigmoidal	sigmoidal	NOUN
ijassa-429	40	26	)	)	PUNCT
ijassa-429	40	27	growth	growth	NOUN
ijassa-429	40	28	patterns	pattern	NOUN
ijassa-429	40	29	.	.	PUNCT
ijassa-429	41	1	the	the	DET
ijassa-429	41	2	final	final	ADJ
ijassa-429	41	3	closed	closed	ADJ
ijassa-429	41	4	model	model	NOUN
ijassa-429	41	5	itself	itself	PRON
ijassa-429	41	6	appears	appear	VERB
ijassa-429	41	7	to	to	PART
ijassa-429	41	8	grow	grow	VERB
ijassa-429	41	9	infinitely	infinitely	ADV
ijassa-429	41	10	,	,	PUNCT
ijassa-429	41	11	like	like	ADP
ijassa-429	41	12	an	an	DET
ijassa-429	41	13	exponential	exponential	ADJ
ijassa-429	41	14	function	function	NOUN
ijassa-429	41	15	,	,	PUNCT
ijassa-429	41	16	but	but	CCONJ
ijassa-429	41	17	at	at	ADP
ijassa-429	41	18	a	a	DET
ijassa-429	41	19	slower	slow	ADJ
ijassa-429	41	20	rate	rate	NOUN
ijassa-429	41	21	,	,	PUNCT
ijassa-429	41	22	like	like	ADP
ijassa-429	41	23	a	a	DET
ijassa-429	41	24	hyperbolic	hyperbolic	ADJ
ijassa-429	41	25	pattern	pattern	NOUN
ijassa-429	41	26	.	.	PUNCT
ijassa-429	42	1	indeed	indeed	ADV
ijassa-429	42	2	,	,	PUNCT
ijassa-429	42	3	elements	element	NOUN
ijassa-429	42	4	of	of	ADP
ijassa-429	42	5	the	the	DET
ijassa-429	42	6	series	series	NOUN
ijassa-429	42	7	resemble	resemble	VERB
ijassa-429	42	8	the	the	DET
ijassa-429	42	9	taylor	taylor	PROPN
ijassa-429	42	10	series	series	NOUN
ijassa-429	42	11	expansions	expansion	NOUN
ijassa-429	42	12	for	for	ADP
ijassa-429	42	13	the	the	DET
ijassa-429	42	14	hyperbolic	hyperbolic	ADJ
ijassa-429	42	15	sine	sine	NOUN
ijassa-429	42	16	(	(	PUNCT
ijassa-429	42	17	sinh	sinh	NOUN
ijassa-429	42	18	)	)	PUNCT
ijassa-429	42	19	and	and	CCONJ
ijassa-429	42	20	cosine	cosine	NOUN
ijassa-429	42	21	(	(	PUNCT
ijassa-429	42	22	cosh	cosh	NOUN
ijassa-429	42	23	)	)	PUNCT
ijassa-429	42	24	functions	function	NOUN
ijassa-429	42	25	,	,	PUNCT
ijassa-429	42	26	and	and	CCONJ
ijassa-429	42	27	the	the	DET
ijassa-429	42	28	geometric	geometric	ADJ
ijassa-429	42	29	series	series	NOUN
ijassa-429	42	30	hyperbolic	hyperbolic	ADJ
ijassa-429	42	31	expansion	expansion	NOUN
ijassa-429	42	32	,	,	PUNCT
ijassa-429	42	33	in	in	ADP
ijassa-429	42	34	addition	addition	NOUN
ijassa-429	42	35	to	to	ADP
ijassa-429	42	36	the	the	DET
ijassa-429	42	37	inherently	inherently	ADV
ijassa-429	42	38	exponential	exponential	ADJ
ijassa-429	42	39	elements	element	NOUN
ijassa-429	42	40	.	.	PUNCT
ijassa-429	43	1	the	the	DET
ijassa-429	43	2	potentially	potentially	ADV
ijassa-429	43	3	hyperbolic	hyperbolic	ADJ
ijassa-429	43	4	properties	property	NOUN
ijassa-429	43	5	connect	connect	VERB
ijassa-429	43	6	this	this	DET
ijassa-429	43	7	model	model	NOUN
ijassa-429	43	8	to	to	ADP
ijassa-429	43	9	the	the	DET
ijassa-429	43	10	monod	monod	NOUN
ijassa-429	43	11	and	and	CCONJ
ijassa-429	43	12	michaelis	michaeli	NOUN
ijassa-429	43	13	-	-	PUNCT
ijassa-429	43	14	menten	menten	ADJ
ijassa-429	43	15	models	model	NOUN
ijassa-429	43	16	[	[	X
ijassa-429	43	17	2	2	NUM
ijassa-429	43	18	]	]	PUNCT
ijassa-429	43	19	,	,	PUNCT
ijassa-429	43	20	while	while	SCONJ
ijassa-429	43	21	they	they	PRON
ijassa-429	43	22	provide	provide	VERB
ijassa-429	43	23	a	a	DET
ijassa-429	43	24	basis	basis	NOUN
ijassa-429	43	25	for	for	ADP
ijassa-429	43	26	parametric	parametric	ADJ
ijassa-429	43	27	data	datum	NOUN
ijassa-429	43	28	analysis	analysis	NOUN
ijassa-429	43	29	through	through	ADP
ijassa-429	43	30	the	the	DET
ijassa-429	43	31	function	function	NOUN
ijassa-429	43	32	.	.	PUNCT
ijassa-429	44	1	however	however	ADV
ijassa-429	44	2	,	,	PUNCT
ijassa-429	44	3	it	it	PRON
ijassa-429	44	4	is	be	AUX
ijassa-429	44	5	not	not	PART
ijassa-429	44	6	a	a	DET
ijassa-429	44	7	distinct	distinct	ADJ
ijassa-429	44	8	hyperbola	hyperbola	NOUN
ijassa-429	44	9	because	because	SCONJ
ijassa-429	44	10	the	the	DET
ijassa-429	44	11	values	value	NOUN
ijassa-429	44	12	of	of	ADP
ijassa-429	44	13	dp	dp	NOUN
ijassa-429	44	14	dt	dt	NOUN
ijassa-429	44	15	approach	approach	NOUN
ijassa-429	44	16	infinity	infinity	NOUN
ijassa-429	44	17	as	as	ADP
ijassa-429	44	18	p	p	NOUN
ijassa-429	44	19	approaches	approach	NOUN
ijassa-429	44	20	infinity	infinity	NOUN
ijassa-429	44	21	,	,	PUNCT
ijassa-429	44	22	without	without	ADP
ijassa-429	44	23	any	any	DET
ijassa-429	44	24	distinct	distinct	ADJ
ijassa-429	44	25	limit	limit	NOUN
ijassa-429	44	26	or	or	CCONJ
ijassa-429	44	27	asymptote	asymptote	VERB
ijassa-429	44	28	.	.	PUNCT
ijassa-429	45	1	this	this	DET
ijassa-429	45	2	new	new	ADJ
ijassa-429	45	3	series	series	NOUN
ijassa-429	45	4	relies	rely	VERB
ijassa-429	45	5	on	on	ADP
ijassa-429	45	6	the	the	DET
ijassa-429	45	7	parameters	parameter	NOUN
ijassa-429	45	8	of	of	ADP
ijassa-429	45	9	growth	growth	NOUN
ijassa-429	45	10	limit	limit	NOUN
ijassa-429	45	11	,	,	PUNCT
ijassa-429	45	12	rate	rate	NOUN
ijassa-429	45	13	of	of	ADP
ijassa-429	45	14	increase	increase	NOUN
ijassa-429	45	15	,	,	PUNCT
ijassa-429	45	16	and	and	CCONJ
ijassa-429	45	17	82	82	NUM
ijassa-429	45	18	anne	anne	PROPN
ijassa-429	45	19	talkington	talkington	NOUN
ijassa-429	45	20	:	:	PUNCT
ijassa-429	45	21	an	an	DET
ijassa-429	45	22	extension	extension	NOUN
ijassa-429	45	23	of	of	ADP
ijassa-429	45	24	a	a	DET
ijassa-429	45	25	logistic	logistic	ADJ
ijassa-429	45	26	model	model	NOUN
ijassa-429	45	27	for	for	ADP
ijassa-429	45	28	microbial	microbial	ADJ
ijassa-429	45	29	kinetics	kinetic	NOUN
ijassa-429	45	30	population	population	NOUN
ijassa-429	45	31	size	size	NOUN
ijassa-429	45	32	related	relate	VERB
ijassa-429	45	33	through	through	ADP
ijassa-429	45	34	time	time	NOUN
ijassa-429	45	35	.	.	PUNCT
ijassa-429	46	1	it	it	PRON
ijassa-429	46	2	is	be	AUX
ijassa-429	46	3	unique	unique	ADJ
ijassa-429	46	4	in	in	ADP
ijassa-429	46	5	that	that	SCONJ
ijassa-429	46	6	it	it	PRON
ijassa-429	46	7	does	do	AUX
ijassa-429	46	8	not	not	PART
ijassa-429	46	9	introduce	introduce	VERB
ijassa-429	46	10	new	new	ADJ
ijassa-429	46	11	factors	factor	NOUN
ijassa-429	46	12	or	or	CCONJ
ijassa-429	46	13	parameters	parameter	NOUN
ijassa-429	46	14	with	with	ADP
ijassa-429	46	15	each	each	DET
ijassa-429	46	16	additional	additional	ADJ
ijassa-429	46	17	term	term	NOUN
ijassa-429	46	18	,	,	PUNCT
ijassa-429	46	19	but	but	CCONJ
ijassa-429	46	20	builds	build	VERB
ijassa-429	46	21	upon	upon	SCONJ
ijassa-429	46	22	known	know	VERB
ijassa-429	46	23	parameters	parameter	NOUN
ijassa-429	46	24	.	.	PUNCT
ijassa-429	47	1	manipulation	manipulation	NOUN
ijassa-429	47	2	of	of	ADP
ijassa-429	47	3	the	the	DET
ijassa-429	47	4	series	series	NOUN
ijassa-429	47	5	model	model	NOUN
ijassa-429	47	6	over	over	ADP
ijassa-429	47	7	its	its	PRON
ijassa-429	47	8	interval	interval	NOUN
ijassa-429	47	9	of	of	ADP
ijassa-429	47	10	convergence	convergence	NOUN
ijassa-429	47	11	opens	open	VERB
ijassa-429	47	12	applications	application	NOUN
ijassa-429	47	13	in	in	ADP
ijassa-429	47	14	both	both	CCONJ
ijassa-429	47	15	symmetrical	symmetrical	ADJ
ijassa-429	47	16	and	and	CCONJ
ijassa-429	47	17	asymmetrical	asymmetrical	ADJ
ijassa-429	47	18	(	(	PUNCT
ijassa-429	47	19	semi	semi	ADJ
ijassa-429	47	20	-	-	ADJ
ijassa-429	47	21	logistic	logistic	ADJ
ijassa-429	47	22	)	)	PUNCT
ijassa-429	47	23	growth	growth	NOUN
ijassa-429	47	24	patterns	pattern	NOUN
ijassa-429	47	25	.	.	PUNCT
ijassa-429	48	1	analysis	analysis	NOUN
ijassa-429	48	2	of	of	ADP
ijassa-429	48	3	the	the	DET
ijassa-429	48	4	curve	curve	NOUN
ijassa-429	48	5	to	to	ADP
ijassa-429	48	6	the	the	DET
ijassa-429	48	7	upper	upper	ADJ
ijassa-429	48	8	bound	bind	VERB
ijassa-429	48	9	of	of	ADP
ijassa-429	48	10	its	its	PRON
ijassa-429	48	11	convergence	convergence	NOUN
ijassa-429	48	12	(	(	PUNCT
ijassa-429	48	13	below	below	ADV
ijassa-429	48	14	and	and	CCONJ
ijassa-429	48	15	including	include	VERB
ijassa-429	48	16	the	the	DET
ijassa-429	48	17	inflection	inflection	NOUN
ijassa-429	48	18	point	point	NOUN
ijassa-429	48	19	)	)	PUNCT
ijassa-429	48	20	produces	produce	VERB
ijassa-429	48	21	a	a	DET
ijassa-429	48	22	precise	precise	ADJ
ijassa-429	48	23	estimate	estimate	NOUN
ijassa-429	48	24	for	for	ADP
ijassa-429	48	25	the	the	DET
ijassa-429	48	26	initial	initial	ADJ
ijassa-429	48	27	takeoff	takeoff	NOUN
ijassa-429	48	28	of	of	ADP
ijassa-429	48	29	the	the	DET
ijassa-429	48	30	microbe	microbe	NOUN
ijassa-429	48	31	;	;	PUNCT
ijassa-429	48	32	the	the	DET
ijassa-429	48	33	rotation	rotation	NOUN
ijassa-429	48	34	of	of	ADP
ijassa-429	48	35	the	the	DET
ijassa-429	48	36	existing	exist	VERB
ijassa-429	48	37	curve	curve	NOUN
ijassa-429	48	38	and	and	CCONJ
ijassa-429	48	39	intersection	intersection	NOUN
ijassa-429	48	40	of	of	ADP
ijassa-429	48	41	another	another	DET
ijassa-429	48	42	curve	curve	NOUN
ijassa-429	48	43	are	be	AUX
ijassa-429	48	44	two	two	NUM
ijassa-429	48	45	approaches	approach	NOUN
ijassa-429	48	46	for	for	ADP
ijassa-429	48	47	determining	determine	VERB
ijassa-429	48	48	the	the	DET
ijassa-429	48	49	upper	upper	ADJ
ijassa-429	48	50	bound	bind	VERB
ijassa-429	48	51	.	.	PUNCT
ijassa-429	49	1	evaluating	evaluate	VERB
ijassa-429	49	2	the	the	DET
ijassa-429	49	3	series	series	NOUN
ijassa-429	49	4	as	as	ADP
ijassa-429	49	5	a	a	DET
ijassa-429	49	6	whole	whole	NOUN
ijassa-429	49	7	,	,	PUNCT
ijassa-429	49	8	or	or	CCONJ
ijassa-429	49	9	as	as	ADP
ijassa-429	49	10	an	an	DET
ijassa-429	49	11	individual	individual	ADJ
ijassa-429	49	12	polynomial	polynomial	ADJ
ijassa-429	49	13	function	function	NOUN
ijassa-429	49	14	at	at	ADP
ijassa-429	49	15	any	any	DET
ijassa-429	49	16	point	point	NOUN
ijassa-429	49	17	of	of	ADP
ijassa-429	49	18	truncation	truncation	NOUN
ijassa-429	49	19	,	,	PUNCT
ijassa-429	49	20	allows	allow	VERB
ijassa-429	49	21	for	for	ADP
ijassa-429	49	22	the	the	DET
ijassa-429	49	23	ability	ability	NOUN
ijassa-429	49	24	to	to	PART
ijassa-429	49	25	fit	fit	VERB
ijassa-429	49	26	both	both	CCONJ
ijassa-429	49	27	limited	limited	ADJ
ijassa-429	49	28	and	and	CCONJ
ijassa-429	49	29	unlimited	unlimited	ADJ
ijassa-429	49	30	growth	growth	NOUN
ijassa-429	49	31	patterns	pattern	NOUN
ijassa-429	49	32	.	.	PUNCT
ijassa-429	50	1	the	the	DET
ijassa-429	50	2	models	model	NOUN
ijassa-429	50	3	,	,	PUNCT
ijassa-429	50	4	likewise	likewise	ADV
ijassa-429	50	5	,	,	PUNCT
ijassa-429	50	6	are	be	AUX
ijassa-429	50	7	consistent	consistent	ADJ
ijassa-429	50	8	with	with	ADP
ijassa-429	50	9	numerical	numerical	ADJ
ijassa-429	50	10	(	(	PUNCT
ijassa-429	50	11	nonparametric	nonparametric	NOUN
ijassa-429	50	12	)	)	PUNCT
ijassa-429	50	13	methods	method	NOUN
ijassa-429	50	14	for	for	ADP
ijassa-429	50	15	determining	determine	VERB
ijassa-429	50	16	microbial	microbial	ADJ
ijassa-429	50	17	specific	specific	ADJ
ijassa-429	50	18	growth	growth	NOUN
ijassa-429	50	19	rate	rate	NOUN
ijassa-429	51	1	[	[	X
ijassa-429	51	2	12	12	NUM
ijassa-429	51	3	-	-	SYM
ijassa-429	51	4	13	13	NUM
ijassa-429	51	5	]	]	PUNCT
ijassa-429	51	6	.	.	PUNCT
ijassa-429	52	1	numerical	numerical	ADJ
ijassa-429	52	2	methods	method	NOUN
ijassa-429	52	3	analyze	analyze	VERB
ijassa-429	52	4	the	the	DET
ijassa-429	52	5	data	datum	NOUN
ijassa-429	52	6	without	without	ADP
ijassa-429	52	7	assumption	assumption	NOUN
ijassa-429	52	8	,	,	PUNCT
ijassa-429	52	9	whereas	whereas	SCONJ
ijassa-429	52	10	the	the	DET
ijassa-429	52	11	models	model	NOUN
ijassa-429	52	12	provide	provide	VERB
ijassa-429	52	13	a	a	DET
ijassa-429	52	14	framework	framework	NOUN
ijassa-429	52	15	for	for	ADP
ijassa-429	52	16	the	the	DET
ijassa-429	52	17	data	datum	NOUN
ijassa-429	52	18	.	.	PUNCT
ijassa-429	53	1	each	each	PRON
ijassa-429	53	2	introduces	introduce	VERB
ijassa-429	53	3	a	a	DET
ijassa-429	53	4	degree	degree	NOUN
ijassa-429	53	5	of	of	ADP
ijassa-429	53	6	precision	precision	NOUN
ijassa-429	53	7	and	and	CCONJ
ijassa-429	53	8	understanding	understanding	NOUN
ijassa-429	53	9	of	of	ADP
ijassa-429	53	10	the	the	DET
ijassa-429	53	11	data	datum	NOUN
ijassa-429	53	12	.	.	PUNCT
ijassa-429	54	1	2	2	NUM
ijassa-429	54	2	procedure	procedure	NOUN
ijassa-429	54	3	to	to	PART
ijassa-429	54	4	determine	determine	VERB
ijassa-429	54	5	the	the	DET
ijassa-429	54	6	value	value	NOUN
ijassa-429	54	7	of	of	ADP
ijassa-429	54	8	the	the	DET
ijassa-429	54	9	specific	specific	ADJ
ijassa-429	54	10	growth	growth	NOUN
ijassa-429	54	11	rate	rate	NOUN
ijassa-429	54	12	numerically	numerically	ADV
ijassa-429	54	13	,	,	PUNCT
ijassa-429	54	14	an	an	DET
ijassa-429	54	15	algorithm	algorithm	NOUN
ijassa-429	54	16	was	be	AUX
ijassa-429	54	17	developed	develop	VERB
ijassa-429	54	18	to	to	PART
ijassa-429	54	19	analyze	analyze	VERB
ijassa-429	54	20	the	the	DET
ijassa-429	54	21	data	datum	NOUN
ijassa-429	54	22	through	through	ADP
ijassa-429	54	23	elimination	elimination	NOUN
ijassa-429	54	24	.	.	PUNCT
ijassa-429	55	1	it	it	PRON
ijassa-429	55	2	removes	remove	VERB
ijassa-429	55	3	all	all	DET
ijassa-429	55	4	subjectivity	subjectivity	NOUN
ijassa-429	55	5	and	and	CCONJ
ijassa-429	55	6	assumptions	assumption	NOUN
ijassa-429	55	7	found	find	VERB
ijassa-429	55	8	in	in	ADP
ijassa-429	55	9	previous	previous	ADJ
ijassa-429	55	10	methods	method	NOUN
ijassa-429	55	11	.	.	PUNCT
ijassa-429	56	1	the	the	DET
ijassa-429	56	2	new	new	ADJ
ijassa-429	56	3	algorithm	algorithm	NOUN
ijassa-429	56	4	focuses	focus	VERB
ijassa-429	56	5	on	on	ADP
ijassa-429	56	6	eliminating	eliminate	VERB
ijassa-429	56	7	non	non	ADJ
ijassa-429	56	8	-	-	ADJ
ijassa-429	56	9	significant	significant	ADJ
ijassa-429	56	10	data	datum	NOUN
ijassa-429	56	11	points	point	NOUN
ijassa-429	56	12	.	.	PUNCT
ijassa-429	57	1	initially	initially	ADV
ijassa-429	57	2	,	,	PUNCT
ijassa-429	57	3	all	all	DET
ijassa-429	57	4	points	point	NOUN
ijassa-429	57	5	past	past	ADP
ijassa-429	57	6	the	the	DET
ijassa-429	57	7	point	point	NOUN
ijassa-429	57	8	of	of	ADP
ijassa-429	57	9	inflection	inflection	NOUN
ijassa-429	57	10	are	be	AUX
ijassa-429	57	11	eliminated	eliminate	VERB
ijassa-429	57	12	.	.	PUNCT
ijassa-429	58	1	this	this	PRON
ijassa-429	58	2	is	be	AUX
ijassa-429	58	3	defined	define	VERB
ijassa-429	58	4	as	as	ADP
ijassa-429	58	5	the	the	DET
ijassa-429	58	6	point	point	NOUN
ijassa-429	58	7	at	at	ADP
ijassa-429	58	8	which	which	PRON
ijassa-429	58	9	the	the	DET
ijassa-429	58	10	concavity	concavity	NOUN
ijassa-429	58	11	of	of	ADP
ijassa-429	58	12	the	the	DET
ijassa-429	58	13	data	data	NOUN
ijassa-429	58	14	changes	change	NOUN
ijassa-429	58	15	from	from	ADP
ijassa-429	58	16	up	up	ADP
ijassa-429	58	17	to	to	ADP
ijassa-429	58	18	down	down	ADV
ijassa-429	58	19	,	,	PUNCT
ijassa-429	58	20	or	or	CCONJ
ijassa-429	58	21	the	the	DET
ijassa-429	58	22	second	second	ADJ
ijassa-429	58	23	derivative	derivative	ADJ
ijassa-429	58	24	changes	change	NOUN
ijassa-429	58	25	from	from	ADP
ijassa-429	58	26	positive	positive	ADJ
ijassa-429	58	27	to	to	PART
ijassa-429	58	28	negative	negative	VERB
ijassa-429	58	29	.	.	PUNCT
ijassa-429	59	1	thus	thus	ADV
ijassa-429	59	2	,	,	PUNCT
ijassa-429	59	3	the	the	DET
ijassa-429	59	4	deceleration	deceleration	NOUN
ijassa-429	59	5	phase	phase	NOUN
ijassa-429	59	6	is	be	AUX
ijassa-429	59	7	disregarded	disregard	VERB
ijassa-429	59	8	in	in	ADP
ijassa-429	59	9	analyzing	analyze	VERB
ijassa-429	59	10	growth	growth	NOUN
ijassa-429	59	11	.	.	PUNCT
ijassa-429	60	1	the	the	DET
ijassa-429	60	2	next	next	ADJ
ijassa-429	60	3	step	step	NOUN
ijassa-429	60	4	is	be	AUX
ijassa-429	60	5	to	to	PART
ijassa-429	60	6	isolate	isolate	VERB
ijassa-429	60	7	the	the	DET
ijassa-429	60	8	growth	growth	NOUN
ijassa-429	60	9	phase	phase	NOUN
ijassa-429	60	10	from	from	ADP
ijassa-429	60	11	the	the	DET
ijassa-429	60	12	lag	lag	NOUN
ijassa-429	60	13	and	and	CCONJ
ijassa-429	60	14	acceleration	acceleration	NOUN
ijassa-429	60	15	phases	phase	NOUN
ijassa-429	60	16	.	.	PUNCT
ijassa-429	61	1	further	further	ADJ
ijassa-429	61	2	elimination	elimination	NOUN
ijassa-429	61	3	is	be	AUX
ijassa-429	61	4	accomplished	accomplish	VERB
ijassa-429	61	5	through	through	ADP
ijassa-429	61	6	regression	regression	NOUN
ijassa-429	61	7	.	.	PUNCT
ijassa-429	62	1	the	the	DET
ijassa-429	62	2	natural	natural	ADJ
ijassa-429	62	3	logarithm	logarithm	NOUN
ijassa-429	62	4	of	of	ADP
ijassa-429	62	5	the	the	DET
ijassa-429	62	6	function	function	NOUN
ijassa-429	62	7	is	be	AUX
ijassa-429	62	8	taken	take	VERB
ijassa-429	62	9	,	,	PUNCT
ijassa-429	62	10	and	and	CCONJ
ijassa-429	62	11	the	the	DET
ijassa-429	62	12	slope	slope	NOUN
ijassa-429	62	13	of	of	ADP
ijassa-429	62	14	the	the	DET
ijassa-429	62	15	linearized	linearize	VERB
ijassa-429	62	16	function	function	NOUN
ijassa-429	62	17	is	be	AUX
ijassa-429	62	18	determined	determine	VERB
ijassa-429	62	19	from	from	ADP
ijassa-429	62	20	the	the	DET
ijassa-429	62	21	line	line	NOUN
ijassa-429	62	22	of	of	ADP
ijassa-429	62	23	best	good	ADJ
ijassa-429	62	24	fit	fit	ADJ
ijassa-429	62	25	.	.	PUNCT
ijassa-429	63	1	points	point	NOUN
ijassa-429	63	2	from	from	ADP
ijassa-429	63	3	the	the	DET
ijassa-429	63	4	left	left	NOUN
ijassa-429	63	5	that	that	PRON
ijassa-429	63	6	lower	low	ADJ
ijassa-429	63	7	the	the	DET
ijassa-429	63	8	slope	slope	NOUN
ijassa-429	63	9	are	be	AUX
ijassa-429	63	10	eliminated	eliminate	VERB
ijassa-429	63	11	,	,	PUNCT
ijassa-429	63	12	and	and	CCONJ
ijassa-429	63	13	another	another	DET
ijassa-429	63	14	regression	regression	NOUN
ijassa-429	63	15	line	line	NOUN
ijassa-429	63	16	is	be	AUX
ijassa-429	63	17	fitted	fit	VERB
ijassa-429	63	18	to	to	ADP
ijassa-429	63	19	the	the	DET
ijassa-429	63	20	remaining	remain	VERB
ijassa-429	63	21	points	point	NOUN
ijassa-429	63	22	.	.	PUNCT
ijassa-429	64	1	the	the	DET
ijassa-429	64	2	process	process	NOUN
ijassa-429	64	3	is	be	AUX
ijassa-429	64	4	repeated	repeat	VERB
ijassa-429	64	5	as	as	SCONJ
ijassa-429	64	6	the	the	DET
ijassa-429	64	7	slope	slope	NOUN
ijassa-429	64	8	increases	increase	NOUN
ijassa-429	64	9	and	and	CCONJ
ijassa-429	64	10	iterations	iteration	NOUN
ijassa-429	64	11	continue	continue	VERB
ijassa-429	64	12	until	until	SCONJ
ijassa-429	64	13	either	either	CCONJ
ijassa-429	64	14	the	the	DET
ijassa-429	64	15	change	change	NOUN
ijassa-429	64	16	in	in	ADP
ijassa-429	64	17	slope	slope	NOUN
ijassa-429	64	18	(	(	PUNCT
ijassa-429	64	19	indicative	indicative	ADJ
ijassa-429	64	20	of	of	ADP
ijassa-429	64	21	growth	growth	NOUN
ijassa-429	64	22	rate	rate	NOUN
ijassa-429	64	23	)	)	PUNCT
ijassa-429	64	24	is	be	AUX
ijassa-429	64	25	not	not	PART
ijassa-429	64	26	statistically	statistically	ADV
ijassa-429	64	27	significant	significant	ADJ
ijassa-429	64	28	,	,	PUNCT
ijassa-429	64	29	or	or	CCONJ
ijassa-429	64	30	until	until	SCONJ
ijassa-429	64	31	the	the	DET
ijassa-429	64	32	number	number	NOUN
ijassa-429	64	33	of	of	ADP
ijassa-429	64	34	remaining	remain	VERB
ijassa-429	64	35	points	point	NOUN
ijassa-429	64	36	becomes	become	VERB
ijassa-429	64	37	too	too	ADV
ijassa-429	64	38	small	small	ADJ
ijassa-429	64	39	.	.	PUNCT
ijassa-429	65	1	the	the	DET
ijassa-429	65	2	slope	slope	NOUN
ijassa-429	65	3	of	of	ADP
ijassa-429	65	4	the	the	DET
ijassa-429	65	5	regression	regression	NOUN
ijassa-429	65	6	line	line	NOUN
ijassa-429	65	7	for	for	ADP
ijassa-429	65	8	the	the	DET
ijassa-429	65	9	final	final	ADJ
ijassa-429	65	10	remaining	remaining	ADJ
ijassa-429	65	11	points	point	NOUN
ijassa-429	65	12	is	be	AUX
ijassa-429	65	13	the	the	DET
ijassa-429	65	14	specific	specific	ADJ
ijassa-429	65	15	growth	growth	NOUN
ijassa-429	65	16	rate	rate	NOUN
ijassa-429	65	17	.	.	PUNCT
ijassa-429	66	1	3	3	NUM
ijassa-429	66	2	cases	case	NOUN
ijassa-429	66	3	of	of	ADP
ijassa-429	66	4	the	the	DET
ijassa-429	66	5	series	series	NOUN
ijassa-429	66	6	discussion	discussion	NOUN
ijassa-429	66	7	there	there	PRON
ijassa-429	66	8	are	be	VERB
ijassa-429	66	9	four	four	NUM
ijassa-429	66	10	notable	notable	ADJ
ijassa-429	66	11	models	model	NOUN
ijassa-429	66	12	that	that	PRON
ijassa-429	66	13	serve	serve	VERB
ijassa-429	66	14	appropriate	appropriate	ADJ
ijassa-429	66	15	data	datum	NOUN
ijassa-429	66	16	set	set	VERB
ijassa-429	66	17	fit	fit	ADJ
ijassa-429	66	18	.	.	PUNCT
ijassa-429	67	1	fitting	fit	VERB
ijassa-429	67	2	an	an	DET
ijassa-429	67	3	appropriate	appropriate	ADJ
ijassa-429	67	4	model	model	NOUN
ijassa-429	67	5	to	to	ADP
ijassa-429	67	6	the	the	DET
ijassa-429	67	7	data	datum	NOUN
ijassa-429	67	8	set	set	VERB
ijassa-429	67	9	is	be	AUX
ijassa-429	67	10	critical	critical	ADJ
ijassa-429	67	11	for	for	ADP
ijassa-429	67	12	the	the	DET
ijassa-429	67	13	most	most	ADV
ijassa-429	67	14	accurate	accurate	ADJ
ijassa-429	67	15	approximations	approximation	NOUN
ijassa-429	67	16	of	of	ADP
ijassa-429	67	17	data	datum	NOUN
ijassa-429	67	18	parameters	parameter	NOUN
ijassa-429	67	19	and	and	CCONJ
ijassa-429	67	20	descriptions	description	NOUN
ijassa-429	67	21	of	of	ADP
ijassa-429	67	22	the	the	DET
ijassa-429	67	23	populations	population	NOUN
ijassa-429	67	24	.	.	PUNCT
ijassa-429	68	1	the	the	DET
ijassa-429	68	2	most	most	ADV
ijassa-429	68	3	basic	basic	ADJ
ijassa-429	68	4	is	be	AUX
ijassa-429	68	5	the	the	DET
ijassa-429	68	6	exponential	exponential	ADJ
ijassa-429	68	7	model	model	NOUN
ijassa-429	68	8	[	[	X
ijassa-429	68	9	8	8	NUM
ijassa-429	68	10	,	,	PUNCT
ijassa-429	68	11	14	14	NUM
ijassa-429	68	12	-	-	SYM
ijassa-429	68	13	15	15	NUM
ijassa-429	68	14	]	]	PUNCT
ijassa-429	68	15	.	.	PUNCT
ijassa-429	69	1	also	also	ADV
ijassa-429	69	2	known	know	VERB
ijassa-429	69	3	as	as	ADP
ijassa-429	69	4	the	the	DET
ijassa-429	69	5	malthusian	malthusian	ADJ
ijassa-429	69	6	model	model	NOUN
ijassa-429	69	7	,	,	PUNCT
ijassa-429	69	8	it	it	PRON
ijassa-429	69	9	depicts	depict	VERB
ijassa-429	69	10	unlimited	unlimited	ADJ
ijassa-429	69	11	growth	growth	NOUN
ijassa-429	69	12	.	.	PUNCT
ijassa-429	70	1	biologically	biologically	ADV
ijassa-429	70	2	,	,	PUNCT
ijassa-429	70	3	there	there	PRON
ijassa-429	70	4	is	be	VERB
ijassa-429	70	5	no	no	DET
ijassa-429	70	6	carrying	carry	VERB
ijassa-429	70	7	capacity	capacity	NOUN
ijassa-429	70	8	of	of	ADP
ijassa-429	70	9	the	the	DET
ijassa-429	70	10	population	population	NOUN
ijassa-429	70	11	,	,	PUNCT
ijassa-429	70	12	and	and	CCONJ
ijassa-429	70	13	it	it	PRON
ijassa-429	70	14	therefore	therefore	ADV
ijassa-429	70	15	multiplies	multiply	VERB
ijassa-429	70	16	infinitely	infinitely	ADV
ijassa-429	70	17	.	.	PUNCT
ijassa-429	71	1	mathematically	mathematically	ADV
ijassa-429	71	2	,	,	PUNCT
ijassa-429	71	3	there	there	PRON
ijassa-429	71	4	is	be	VERB
ijassa-429	71	5	advances	advance	NOUN
ijassa-429	71	6	in	in	ADP
ijassa-429	71	7	systems	system	NOUN
ijassa-429	71	8	science	science	NOUN
ijassa-429	71	9	and	and	CCONJ
ijassa-429	71	10	applications	application	NOUN
ijassa-429	71	11	(	(	PUNCT
ijassa-429	71	12	2013	2013	NUM
ijassa-429	71	13	)	)	PUNCT
ijassa-429	71	14	vol.13	vol.13	NOUN
ijassa-429	71	15	no.1	no.1	VERB
ijassa-429	71	16	83	83	NUM
ijassa-429	71	17	no	no	DET
ijassa-429	71	18	asymptote	asymptote	NOUN
ijassa-429	71	19	to	to	PART
ijassa-429	71	20	describe	describe	VERB
ijassa-429	71	21	limiting	limit	VERB
ijassa-429	71	22	factors	factor	NOUN
ijassa-429	71	23	.	.	PUNCT
ijassa-429	72	1	these	these	PRON
ijassa-429	72	2	may	may	AUX
ijassa-429	72	3	include	include	VERB
ijassa-429	72	4	competition	competition	NOUN
ijassa-429	72	5	,	,	PUNCT
ijassa-429	72	6	lack	lack	NOUN
ijassa-429	72	7	of	of	ADP
ijassa-429	72	8	nutrients	nutrient	NOUN
ijassa-429	72	9	,	,	PUNCT
ijassa-429	72	10	or	or	CCONJ
ijassa-429	72	11	density	density	NOUN
ijassa-429	72	12	-	-	PUNCT
ijassa-429	72	13	dependent	dependent	ADJ
ijassa-429	72	14	inhibition	inhibition	NOUN
ijassa-429	72	15	in	in	ADP
ijassa-429	72	16	the	the	DET
ijassa-429	72	17	microbial	microbial	ADJ
ijassa-429	72	18	population	population	NOUN
ijassa-429	73	1	[	[	X
ijassa-429	73	2	16	16	NUM
ijassa-429	73	3	]	]	PUNCT
ijassa-429	73	4	.	.	PUNCT
ijassa-429	74	1	the	the	DET
ijassa-429	74	2	model	model	NOUN
ijassa-429	74	3	is	be	AUX
ijassa-429	74	4	represented	represent	VERB
ijassa-429	74	5	as	as	ADP
ijassa-429	74	6	a	a	DET
ijassa-429	74	7	direct	direct	ADJ
ijassa-429	74	8	proportion	proportion	NOUN
ijassa-429	74	9	between	between	ADP
ijassa-429	74	10	the	the	DET
ijassa-429	74	11	rate	rate	NOUN
ijassa-429	74	12	of	of	ADP
ijassa-429	74	13	population	population	NOUN
ijassa-429	74	14	change	change	NOUN
ijassa-429	74	15	and	and	CCONJ
ijassa-429	74	16	population	population	NOUN
ijassa-429	74	17	size	size	NOUN
ijassa-429	74	18	(	(	PUNCT
ijassa-429	74	19	equation	equation	NOUN
ijassa-429	74	20	1	1	NUM
ijassa-429	74	21	,	,	PUNCT
ijassa-429	74	22	fig.1	fig.1	PROPN
ijassa-429	74	23	)	)	PUNCT
ijassa-429	74	24	.	.	PUNCT
ijassa-429	75	1	dp	dp	NOUN
ijassa-429	76	1	dt	dt	NOUN
ijassa-429	76	2	=	=	PUNCT
ijassa-429	76	3	rp	rp	NOUN
ijassa-429	76	4	(	(	PUNCT
ijassa-429	76	5	1	1	X
ijassa-429	76	6	)	)	PUNCT
ijassa-429	76	7	fig.1	fig.1	ADJ
ijassa-429	76	8	graphical	graphical	ADJ
ijassa-429	76	9	representation	representation	NOUN
ijassa-429	76	10	of	of	ADP
ijassa-429	76	11	the	the	DET
ijassa-429	76	12	exponential	exponential	ADJ
ijassa-429	76	13	model	model	NOUN
ijassa-429	76	14	for	for	ADP
ijassa-429	76	15	microbial	microbial	ADJ
ijassa-429	76	16	population	population	NOUN
ijassa-429	76	17	growth	growth	NOUN
ijassa-429	76	18	of	of	ADP
ijassa-429	76	19	course	course	NOUN
ijassa-429	76	20	,	,	PUNCT
ijassa-429	76	21	the	the	DET
ijassa-429	76	22	simplest	simple	ADJ
ijassa-429	76	23	model	model	NOUN
ijassa-429	76	24	given	give	VERB
ijassa-429	76	25	above	above	ADV
ijassa-429	76	26	does	do	AUX
ijassa-429	76	27	not	not	PART
ijassa-429	76	28	reflect	reflect	VERB
ijassa-429	76	29	most	most	ADJ
ijassa-429	76	30	biological	biological	ADJ
ijassa-429	76	31	growth	growth	NOUN
ijassa-429	76	32	systems	system	NOUN
ijassa-429	76	33	.	.	PUNCT
ijassa-429	77	1	more	more	ADV
ijassa-429	77	2	appropriate	appropriate	ADJ
ijassa-429	77	3	models	model	NOUN
ijassa-429	77	4	were	be	AUX
ijassa-429	77	5	thus	thus	ADV
ijassa-429	77	6	explored	explore	VERB
ijassa-429	77	7	by	by	ADP
ijassa-429	77	8	researcher	researcher	NOUN
ijassa-429	77	9	,	,	PUNCT
ijassa-429	77	10	as	as	SCONJ
ijassa-429	77	11	stated	state	VERB
ijassa-429	77	12	below	below	ADV
ijassa-429	77	13	.	.	PUNCT
ijassa-429	78	1	microbial	microbial	ADJ
ijassa-429	78	2	growth	growth	NOUN
ijassa-429	78	3	may	may	AUX
ijassa-429	78	4	be	be	AUX
ijassa-429	78	5	logistic	logistic	ADJ
ijassa-429	78	6	[	[	X
ijassa-429	78	7	17	17	NUM
ijassa-429	78	8	]	]	PUNCT
ijassa-429	78	9	.	.	PUNCT
ijassa-429	79	1	this	this	DET
ijassa-429	79	2	model	model	NOUN
ijassa-429	79	3	is	be	AUX
ijassa-429	79	4	a	a	DET
ijassa-429	79	5	special	special	ADJ
ijassa-429	79	6	case	case	NOUN
ijassa-429	79	7	of	of	ADP
ijassa-429	79	8	limited	limited	ADJ
ijassa-429	79	9	growth	growth	NOUN
ijassa-429	79	10	in	in	ADP
ijassa-429	79	11	which	which	DET
ijassa-429	79	12	rate	rate	NOUN
ijassa-429	79	13	of	of	ADP
ijassa-429	79	14	population	population	NOUN
ijassa-429	79	15	decrease	decrease	NOUN
ijassa-429	79	16	mirrors	mirror	NOUN
ijassa-429	79	17	rate	rate	NOUN
ijassa-429	79	18	of	of	ADP
ijassa-429	79	19	increase	increase	NOUN
ijassa-429	79	20	.	.	PUNCT
ijassa-429	80	1	the	the	DET
ijassa-429	80	2	population	population	NOUN
ijassa-429	80	3	grows	grow	VERB
ijassa-429	80	4	exponentially	exponentially	ADV
ijassa-429	80	5	but	but	CCONJ
ijassa-429	80	6	encounters	encounter	VERB
ijassa-429	80	7	one	one	NUM
ijassa-429	80	8	or	or	CCONJ
ijassa-429	80	9	more	more	ADJ
ijassa-429	80	10	obstacles	obstacle	NOUN
ijassa-429	80	11	that	that	PRON
ijassa-429	80	12	prohibit	prohibit	VERB
ijassa-429	80	13	it	it	PRON
ijassa-429	80	14	from	from	ADP
ijassa-429	80	15	increasing	increase	VERB
ijassa-429	80	16	indefinitely	indefinitely	ADV
ijassa-429	80	17	.	.	PUNCT
ijassa-429	81	1	as	as	SCONJ
ijassa-429	81	2	the	the	DET
ijassa-429	81	3	definite	definite	ADJ
ijassa-429	81	4	limit	limit	NOUN
ijassa-429	81	5	m	m	VERB
ijassa-429	81	6	approaches	approach	VERB
ijassa-429	81	7	infinity	infinity	NOUN
ijassa-429	81	8	,	,	PUNCT
ijassa-429	81	9	growth	growth	NOUN
ijassa-429	81	10	patterns	pattern	NOUN
ijassa-429	81	11	approach	approach	VERB
ijassa-429	81	12	the	the	DET
ijassa-429	81	13	exponential	exponential	ADJ
ijassa-429	81	14	model	model	NOUN
ijassa-429	81	15	.	.	PUNCT
ijassa-429	82	1	logistic	logistic	ADJ
ijassa-429	82	2	growth	growth	NOUN
ijassa-429	82	3	,	,	PUNCT
ijassa-429	82	4	often	often	ADV
ijassa-429	82	5	used	use	VERB
ijassa-429	82	6	as	as	ADP
ijassa-429	82	7	a	a	DET
ijassa-429	82	8	standard	standard	NOUN
ijassa-429	82	9	in	in	ADP
ijassa-429	82	10	population	population	NOUN
ijassa-429	82	11	studies	study	NOUN
ijassa-429	82	12	,	,	PUNCT
ijassa-429	82	13	is	be	AUX
ijassa-429	82	14	represented	represent	VERB
ijassa-429	82	15	by	by	ADP
ijassa-429	82	16	the	the	DET
ijassa-429	82	17	differential	differential	ADJ
ijassa-429	82	18	equation	equation	NOUN
ijassa-429	82	19	2	2	NUM
ijassa-429	82	20	(	(	PUNCT
ijassa-429	82	21	see	see	VERB
ijassa-429	82	22	also	also	ADV
ijassa-429	82	23	fig.2	fig.2	PROPN
ijassa-429	82	24	)	)	PUNCT
ijassa-429	82	25	.	.	PUNCT
ijassa-429	83	1	dp	dp	NOUN
ijassa-429	84	1	dt	dt	NOUN
ijassa-429	84	2	=	=	PUNCT
ijassa-429	84	3	rp	rp	NOUN
ijassa-429	84	4	(	(	PUNCT
ijassa-429	84	5	1−	1−	NUM
ijassa-429	84	6	p	p	NOUN
ijassa-429	84	7	m	m	NOUN
ijassa-429	84	8	)	)	PUNCT
ijassa-429	84	9	(	(	PUNCT
ijassa-429	84	10	2	2	X
ijassa-429	84	11	)	)	PUNCT
ijassa-429	84	12	the	the	DET
ijassa-429	84	13	logistic	logistic	ADJ
ijassa-429	84	14	growth	growth	NOUN
ijassa-429	84	15	model	model	NOUN
ijassa-429	84	16	introduces	introduce	VERB
ijassa-429	84	17	the	the	DET
ijassa-429	84	18	first	first	ADJ
ijassa-429	84	19	two	two	NUM
ijassa-429	84	20	terms	term	NOUN
ijassa-429	84	21	of	of	ADP
ijassa-429	84	22	a	a	DET
ijassa-429	84	23	maclaurin	maclaurin	NOUN
ijassa-429	84	24	series	series	NOUN
ijassa-429	84	25	that	that	PRON
ijassa-429	84	26	can	can	AUX
ijassa-429	84	27	be	be	AUX
ijassa-429	84	28	used	use	VERB
ijassa-429	84	29	to	to	PART
ijassa-429	84	30	model	model	VERB
ijassa-429	84	31	microbial	microbial	ADJ
ijassa-429	84	32	growth	growth	NOUN
ijassa-429	84	33	.	.	PUNCT
ijassa-429	85	1	limiting	limit	VERB
ijassa-429	85	2	the	the	DET
ijassa-429	85	3	series	series	NOUN
ijassa-429	85	4	to	to	ADP
ijassa-429	85	5	two	two	NUM
ijassa-429	85	6	terms	term	NOUN
ijassa-429	85	7	introduces	introduce	VERB
ijassa-429	85	8	truncation	truncation	NOUN
ijassa-429	85	9	error	error	NOUN
ijassa-429	85	10	[	[	X
ijassa-429	85	11	14	14	NUM
ijassa-429	85	12	-	-	SYM
ijassa-429	85	13	15	15	NUM
ijassa-429	85	14	]	]	PUNCT
ijassa-429	85	15	.	.	PUNCT
ijassa-429	86	1	this	this	DET
ijassa-429	86	2	error	error	NOUN
ijassa-429	86	3	can	can	AUX
ijassa-429	86	4	be	be	AUX
ijassa-429	86	5	reduced	reduce	VERB
ijassa-429	86	6	with	with	ADP
ijassa-429	86	7	the	the	DET
ijassa-429	86	8	introduction	introduction	NOUN
ijassa-429	86	9	of	of	ADP
ijassa-429	86	10	additional	additional	ADJ
ijassa-429	86	11	terms	term	NOUN
ijassa-429	86	12	.	.	PUNCT
ijassa-429	87	1	successive	successive	ADJ
ijassa-429	87	2	terms	term	NOUN
ijassa-429	87	3	alternate	alternate	VERB
ijassa-429	87	4	in	in	ADP
ijassa-429	87	5	sign	sign	NOUN
ijassa-429	87	6	,	,	PUNCT
ijassa-429	87	7	and	and	CCONJ
ijassa-429	87	8	each	each	PRON
ijassa-429	87	9	is	be	AUX
ijassa-429	87	10	smaller	small	ADJ
ijassa-429	87	11	in	in	ADP
ijassa-429	87	12	value	value	NOUN
ijassa-429	87	13	than	than	ADP
ijassa-429	87	14	the	the	DET
ijassa-429	87	15	term	term	NOUN
ijassa-429	87	16	it	it	PRON
ijassa-429	87	17	follows	follow	VERB
ijassa-429	87	18	[	[	X
ijassa-429	87	19	14	14	NUM
ijassa-429	87	20	-	-	SYM
ijassa-429	87	21	15	15	NUM
ijassa-429	87	22	]	]	PUNCT
ijassa-429	87	23	.	.	PUNCT
ijassa-429	88	1	extending	extend	VERB
ijassa-429	88	2	the	the	DET
ijassa-429	88	3	series	series	NOUN
ijassa-429	88	4	another	another	DET
ijassa-429	88	5	step	step	NOUN
ijassa-429	88	6	produces	produce	VERB
ijassa-429	88	7	a	a	DET
ijassa-429	88	8	differential	differential	ADJ
ijassa-429	88	9	function	function	NOUN
ijassa-429	88	10	to	to	ADP
ijassa-429	88	11	the	the	DET
ijassa-429	88	12	fourth	fourth	ADJ
ijassa-429	88	13	power	power	NOUN
ijassa-429	88	14	of	of	ADP
ijassa-429	88	15	p	p	PROPN
ijassa-429	88	16	.	.	PUNCT
ijassa-429	89	1	this	this	DET
ijassa-429	89	2	function	function	NOUN
ijassa-429	89	3	is	be	AUX
ijassa-429	89	4	similar	similar	ADJ
ijassa-429	89	5	to	to	ADP
ijassa-429	89	6	logistic	logistic	ADJ
ijassa-429	89	7	growth	growth	NOUN
ijassa-429	89	8	in	in	ADP
ijassa-429	89	9	the	the	DET
ijassa-429	89	10	lower	low	ADJ
ijassa-429	89	11	portion	portion	NOUN
ijassa-429	89	12	of	of	ADP
ijassa-429	89	13	the	the	DET
ijassa-429	89	14	curve	curve	NOUN
ijassa-429	89	15	,	,	PUNCT
ijassa-429	89	16	up	up	ADP
ijassa-429	89	17	to	to	ADP
ijassa-429	89	18	the	the	DET
ijassa-429	89	19	point	point	NOUN
ijassa-429	89	20	of	of	ADP
ijassa-429	89	21	84	84	NUM
ijassa-429	89	22	anne	anne	PROPN
ijassa-429	89	23	talkington	talkington	NOUN
ijassa-429	89	24	:	:	PUNCT
ijassa-429	89	25	an	an	DET
ijassa-429	89	26	extension	extension	NOUN
ijassa-429	89	27	of	of	ADP
ijassa-429	89	28	a	a	DET
ijassa-429	89	29	logistic	logistic	ADJ
ijassa-429	89	30	model	model	NOUN
ijassa-429	89	31	for	for	ADP
ijassa-429	89	32	microbial	microbial	ADJ
ijassa-429	89	33	kinetics	kinetic	NOUN
ijassa-429	89	34	fig.2	fig.2	NOUN
ijassa-429	89	35	graphical	graphical	ADJ
ijassa-429	89	36	representation	representation	NOUN
ijassa-429	89	37	of	of	ADP
ijassa-429	89	38	the	the	DET
ijassa-429	89	39	logistic	logistic	ADJ
ijassa-429	89	40	growth	growth	NOUN
ijassa-429	89	41	model	model	NOUN
ijassa-429	89	42	inflection	inflection	NOUN
ijassa-429	89	43	.	.	PUNCT
ijassa-429	90	1	however	however	ADV
ijassa-429	90	2	,	,	PUNCT
ijassa-429	90	3	the	the	DET
ijassa-429	90	4	point	point	NOUN
ijassa-429	90	5	of	of	ADP
ijassa-429	90	6	inflection	inflection	NOUN
ijassa-429	90	7	is	be	AUX
ijassa-429	90	8	no	no	ADV
ijassa-429	90	9	longer	long	ADV
ijassa-429	90	10	the	the	DET
ijassa-429	90	11	midpoint	midpoint	NOUN
ijassa-429	90	12	between	between	ADP
ijassa-429	90	13	the	the	DET
ijassa-429	90	14	upper	upper	ADJ
ijassa-429	90	15	and	and	CCONJ
ijassa-429	90	16	lower	low	ADJ
ijassa-429	90	17	limits	limit	NOUN
ijassa-429	90	18	of	of	ADP
ijassa-429	90	19	growth	growth	NOUN
ijassa-429	90	20	.	.	PUNCT
ijassa-429	91	1	beyond	beyond	ADP
ijassa-429	91	2	the	the	DET
ijassa-429	91	3	point	point	NOUN
ijassa-429	91	4	of	of	ADP
ijassa-429	91	5	inflection	inflection	NOUN
ijassa-429	91	6	,	,	PUNCT
ijassa-429	91	7	growth	growth	NOUN
ijassa-429	91	8	reduces	reduce	VERB
ijassa-429	91	9	rapidly	rapidly	ADV
ijassa-429	91	10	and	and	CCONJ
ijassa-429	91	11	tapers	taper	NOUN
ijassa-429	91	12	until	until	SCONJ
ijassa-429	91	13	it	it	PRON
ijassa-429	91	14	reaches	reach	VERB
ijassa-429	91	15	its	its	PRON
ijassa-429	91	16	actual	actual	ADJ
ijassa-429	91	17	limit	limit	NOUN
ijassa-429	91	18	.	.	PUNCT
ijassa-429	92	1	the	the	DET
ijassa-429	92	2	population	population	NOUN
ijassa-429	92	3	may	may	AUX
ijassa-429	92	4	have	have	AUX
ijassa-429	92	5	been	be	AUX
ijassa-429	92	6	subjected	subject	VERB
ijassa-429	92	7	to	to	ADP
ijassa-429	92	8	extreme	extreme	ADJ
ijassa-429	92	9	pressure	pressure	NOUN
ijassa-429	92	10	over	over	ADP
ijassa-429	92	11	a	a	DET
ijassa-429	92	12	short	short	ADJ
ijassa-429	92	13	period	period	NOUN
ijassa-429	92	14	of	of	ADP
ijassa-429	92	15	time	time	NOUN
ijassa-429	92	16	,	,	PUNCT
ijassa-429	92	17	so	so	ADV
ijassa-429	92	18	realized	realize	VERB
ijassa-429	92	19	growth	growth	NOUN
ijassa-429	92	20	does	do	AUX
ijassa-429	92	21	not	not	PART
ijassa-429	92	22	reach	reach	VERB
ijassa-429	92	23	the	the	DET
ijassa-429	92	24	theoretical	theoretical	ADJ
ijassa-429	92	25	,	,	PUNCT
ijassa-429	92	26	ideal	ideal	ADJ
ijassa-429	92	27	estimate	estimate	NOUN
ijassa-429	92	28	of	of	ADP
ijassa-429	92	29	m	m	PROPN
ijassa-429	92	30	.	.	PUNCT
ijassa-429	93	1	this	this	DET
ijassa-429	93	2	reduced	reduce	VERB
ijassa-429	93	3	upper	upper	ADJ
ijassa-429	93	4	bound	bind	VERB
ijassa-429	93	5	is	be	AUX
ijassa-429	93	6	characteristic	characteristic	ADJ
ijassa-429	93	7	of	of	ADP
ijassa-429	93	8	higher	high	ADJ
ijassa-429	93	9	even	even	ADJ
ijassa-429	93	10	degrees	degree	NOUN
ijassa-429	93	11	of	of	ADP
ijassa-429	93	12	p	p	NOUN
ijassa-429	93	13	in	in	ADP
ijassa-429	93	14	the	the	DET
ijassa-429	93	15	extension	extension	NOUN
ijassa-429	93	16	of	of	ADP
ijassa-429	93	17	the	the	DET
ijassa-429	93	18	formula	formula	NOUN
ijassa-429	93	19	due	due	ADP
ijassa-429	93	20	to	to	ADP
ijassa-429	93	21	factorial	factorial	ADJ
ijassa-429	93	22	growth	growth	NOUN
ijassa-429	93	23	in	in	ADP
ijassa-429	93	24	the	the	DET
ijassa-429	93	25	denominator	denominator	NOUN
ijassa-429	93	26	.	.	PUNCT
ijassa-429	94	1	the	the	DET
ijassa-429	94	2	end	end	NOUN
ijassa-429	94	3	behavior	behavior	NOUN
ijassa-429	94	4	of	of	ADP
ijassa-429	94	5	odd	odd	ADJ
ijassa-429	94	6	degrees	degree	NOUN
ijassa-429	94	7	of	of	ADP
ijassa-429	94	8	p	p	NOUN
ijassa-429	94	9	mimics	mimic	VERB
ijassa-429	94	10	exponential	exponential	ADJ
ijassa-429	94	11	-	-	PUNCT
ijassa-429	94	12	like	like	ADJ
ijassa-429	94	13	growth	growth	NOUN
ijassa-429	94	14	.	.	PUNCT
ijassa-429	95	1	the	the	DET
ijassa-429	95	2	fourth	fourth	ADJ
ijassa-429	95	3	-	-	PUNCT
ijassa-429	95	4	degree	degree	NOUN
ijassa-429	95	5	formula	formula	NOUN
ijassa-429	95	6	is	be	AUX
ijassa-429	95	7	represented	represent	VERB
ijassa-429	95	8	as	as	ADP
ijassa-429	95	9	equation	equation	NOUN
ijassa-429	95	10	3	3	NUM
ijassa-429	95	11	,	,	PUNCT
ijassa-429	95	12	and	and	CCONJ
ijassa-429	95	13	its	its	PRON
ijassa-429	95	14	graphical	graphical	ADJ
ijassa-429	95	15	interpretation	interpretation	NOUN
ijassa-429	95	16	as	as	ADP
ijassa-429	95	17	fig.3	fig.3	PROPN
ijassa-429	95	18	.	.	PUNCT
ijassa-429	96	1	dp	dp	NOUN
ijassa-429	96	2	dt	dt	NOUN
ijassa-429	96	3	=	=	PUNCT
ijassa-429	96	4	rp	rp	NOUN
ijassa-429	96	5	−	−	NOUN
ijassa-429	96	6	2rp	2rp	ADJ
ijassa-429	96	7	2	2	NUM
ijassa-429	96	8	m(2	m(2	NOUN
ijassa-429	96	9	!	!	PUNCT
ijassa-429	96	10	)	)	PUNCT
ijassa-429	97	1	+	+	CCONJ
ijassa-429	97	2	8rp	8rp	ADJ
ijassa-429	97	3	3	3	NUM
ijassa-429	97	4	m2(3	m2(3	NOUN
ijassa-429	97	5	!	!	PUNCT
ijassa-429	97	6	)	)	PUNCT
ijassa-429	98	1	−	−	PROPN
ijassa-429	98	2	48rp	48rp	ADJ
ijassa-429	98	3	4	4	NUM
ijassa-429	98	4	m3(4	m3(4	NOUN
ijassa-429	98	5	!	!	PUNCT
ijassa-429	98	6	)	)	PUNCT
ijassa-429	99	1	(	(	PUNCT
ijassa-429	99	2	3	3	X
ijassa-429	99	3	)	)	PUNCT
ijassa-429	99	4	fig.3	fig.3	PROPN
ijassa-429	99	5	graphical	graphical	ADJ
ijassa-429	99	6	representation	representation	NOUN
ijassa-429	99	7	of	of	ADP
ijassa-429	99	8	the	the	DET
ijassa-429	99	9	fourth	fourth	ADJ
ijassa-429	99	10	-	-	PUNCT
ijassa-429	99	11	degree	degree	NOUN
ijassa-429	99	12	model	model	NOUN
ijassa-429	99	13	the	the	DET
ijassa-429	99	14	most	most	ADV
ijassa-429	99	15	idealized	idealized	ADJ
ijassa-429	99	16	model	model	NOUN
ijassa-429	99	17	is	be	AUX
ijassa-429	99	18	the	the	DET
ijassa-429	99	19	use	use	NOUN
ijassa-429	99	20	of	of	ADP
ijassa-429	99	21	the	the	DET
ijassa-429	99	22	full	full	ADJ
ijassa-429	99	23	infinite	infinite	ADJ
ijassa-429	99	24	series	series	NOUN
ijassa-429	99	25	,	,	PUNCT
ijassa-429	99	26	represented	represent	VERB
ijassa-429	99	27	in	in	ADP
ijassa-429	99	28	advances	advance	NOUN
ijassa-429	99	29	in	in	ADP
ijassa-429	99	30	systems	system	NOUN
ijassa-429	99	31	science	science	NOUN
ijassa-429	99	32	and	and	CCONJ
ijassa-429	99	33	applications	application	NOUN
ijassa-429	99	34	(	(	PUNCT
ijassa-429	99	35	2013	2013	NUM
ijassa-429	99	36	)	)	PUNCT
ijassa-429	99	37	vol.13	vol.13	NOUN
ijassa-429	99	38	no.1	no.1	X
ijassa-429	99	39	85	85	NUM
ijassa-429	99	40	its	its	PRON
ijassa-429	99	41	closed	closed	ADJ
ijassa-429	99	42	form	form	NOUN
ijassa-429	99	43	for	for	ADP
ijassa-429	99	44	precision	precision	NOUN
ijassa-429	99	45	.	.	PUNCT
ijassa-429	100	1	it	it	PRON
ijassa-429	100	2	states	state	VERB
ijassa-429	100	3	that	that	SCONJ
ijassa-429	100	4	the	the	DET
ijassa-429	100	5	rate	rate	NOUN
ijassa-429	100	6	of	of	ADP
ijassa-429	100	7	change	change	NOUN
ijassa-429	100	8	of	of	ADP
ijassa-429	100	9	the	the	DET
ijassa-429	100	10	population	population	NOUN
ijassa-429	100	11	and	and	CCONJ
ijassa-429	100	12	a	a	DET
ijassa-429	100	13	function	function	NOUN
ijassa-429	100	14	of	of	ADP
ijassa-429	100	15	the	the	DET
ijassa-429	100	16	population	population	NOUN
ijassa-429	100	17	size	size	NOUN
ijassa-429	100	18	are	be	AUX
ijassa-429	100	19	directly	directly	ADV
ijassa-429	100	20	proportional	proportional	ADJ
ijassa-429	100	21	.	.	PUNCT
ijassa-429	101	1	the	the	DET
ijassa-429	101	2	function	function	NOUN
ijassa-429	101	3	of	of	ADP
ijassa-429	101	4	population	population	NOUN
ijassa-429	101	5	size	size	NOUN
ijassa-429	101	6	is	be	AUX
ijassa-429	101	7	the	the	DET
ijassa-429	101	8	maclaurin	maclaurin	PROPN
ijassa-429	101	9	series	series	NOUN
ijassa-429	101	10	.	.	PUNCT
ijassa-429	102	1	the	the	DET
ijassa-429	102	2	function	function	NOUN
ijassa-429	102	3	,	,	PUNCT
ijassa-429	102	4	or	or	CCONJ
ijassa-429	102	5	the	the	DET
ijassa-429	102	6	series	series	NOUN
ijassa-429	102	7	,	,	PUNCT
ijassa-429	102	8	incorporates	incorporate	VERB
ijassa-429	102	9	the	the	DET
ijassa-429	102	10	exponential	exponential	ADJ
ijassa-429	102	11	model	model	NOUN
ijassa-429	102	12	when	when	SCONJ
ijassa-429	102	13	m	m	PROPN
ijassa-429	102	14	(	(	PUNCT
ijassa-429	102	15	the	the	DET
ijassa-429	102	16	upper	upper	ADJ
ijassa-429	102	17	limit	limit	NOUN
ijassa-429	102	18	)	)	PUNCT
ijassa-429	102	19	approaches	approach	VERB
ijassa-429	102	20	infinity	infinity	NOUN
ijassa-429	102	21	.	.	PUNCT
ijassa-429	103	1	it	it	PRON
ijassa-429	103	2	incorporates	incorporate	VERB
ijassa-429	103	3	the	the	DET
ijassa-429	103	4	logistic	logistic	ADJ
ijassa-429	103	5	model	model	NOUN
ijassa-429	103	6	as	as	ADP
ijassa-429	103	7	the	the	DET
ijassa-429	103	8	ideal	ideal	ADJ
ijassa-429	103	9	symmetrical	symmetrical	ADJ
ijassa-429	103	10	case	case	NOUN
ijassa-429	103	11	in	in	ADP
ijassa-429	103	12	which	which	PRON
ijassa-429	103	13	the	the	DET
ijassa-429	103	14	point	point	NOUN
ijassa-429	103	15	of	of	ADP
ijassa-429	103	16	inflection	inflection	NOUN
ijassa-429	103	17	is	be	AUX
ijassa-429	103	18	the	the	DET
ijassa-429	103	19	midpoint	midpoint	NOUN
ijassa-429	103	20	between	between	ADP
ijassa-429	103	21	the	the	DET
ijassa-429	103	22	upper	upper	ADJ
ijassa-429	103	23	and	and	CCONJ
ijassa-429	103	24	lower	low	ADJ
ijassa-429	103	25	limits	limit	NOUN
ijassa-429	103	26	of	of	ADP
ijassa-429	103	27	growth	growth	NOUN
ijassa-429	103	28	.	.	PUNCT
ijassa-429	104	1	if	if	SCONJ
ijassa-429	104	2	the	the	DET
ijassa-429	104	3	lower	low	ADJ
ijassa-429	104	4	limit	limit	NOUN
ijassa-429	104	5	is	be	AUX
ijassa-429	104	6	0	0	NUM
ijassa-429	104	7	,	,	PUNCT
ijassa-429	104	8	p	p	NOUN
ijassa-429	104	9	represents	represent	VERB
ijassa-429	104	10	population	population	NOUN
ijassa-429	104	11	size	size	NOUN
ijassa-429	104	12	at	at	ADP
ijassa-429	104	13	the	the	DET
ijassa-429	104	14	point	point	NOUN
ijassa-429	104	15	of	of	ADP
ijassa-429	104	16	inflection	inflection	NOUN
ijassa-429	104	17	,	,	PUNCT
ijassa-429	104	18	and	and	CCONJ
ijassa-429	104	19	m	m	PROPN
ijassa-429	104	20	represents	represent	VERB
ijassa-429	104	21	the	the	DET
ijassa-429	104	22	upper	upper	ADJ
ijassa-429	104	23	growth	growth	NOUN
ijassa-429	104	24	limit	limit	NOUN
ijassa-429	104	25	,	,	PUNCT
ijassa-429	104	26	then	then	ADV
ijassa-429	104	27	this	this	PRON
ijassa-429	104	28	is	be	AUX
ijassa-429	104	29	represented	represent	VERB
ijassa-429	104	30	as	as	ADP
ijassa-429	104	31	2p	2p	NUM
ijassa-429	104	32	=	=	SYM
ijassa-429	104	33	m	m	NOUN
ijassa-429	104	34	.	.	PUNCT
ijassa-429	105	1	all	all	PRON
ijassa-429	105	2	of	of	ADP
ijassa-429	105	3	the	the	DET
ijassa-429	105	4	previous	previous	ADJ
ijassa-429	105	5	models	model	NOUN
ijassa-429	105	6	converge	converge	VERB
ijassa-429	105	7	,	,	PUNCT
ijassa-429	105	8	as	as	ADP
ijassa-429	105	9	a	a	DET
ijassa-429	105	10	series	series	NOUN
ijassa-429	105	11	of	of	ADP
ijassa-429	105	12	overestimates	overestimate	NOUN
ijassa-429	105	13	and	and	CCONJ
ijassa-429	105	14	underestimates	underestimate	VERB
ijassa-429	105	15	,	,	PUNCT
ijassa-429	105	16	to	to	ADP
ijassa-429	105	17	the	the	DET
ijassa-429	105	18	model	model	NOUN
ijassa-429	105	19	presented	present	VERB
ijassa-429	105	20	by	by	ADP
ijassa-429	105	21	the	the	DET
ijassa-429	105	22	complete	complete	ADJ
ijassa-429	105	23	series	series	NOUN
ijassa-429	105	24	.	.	PUNCT
ijassa-429	106	1	it	it	PRON
ijassa-429	106	2	is	be	AUX
ijassa-429	106	3	an	an	DET
ijassa-429	106	4	exponential	exponential	ADJ
ijassa-429	106	5	-	-	PUNCT
ijassa-429	106	6	like	like	ADJ
ijassa-429	106	7	function	function	NOUN
ijassa-429	106	8	,	,	PUNCT
ijassa-429	106	9	but	but	CCONJ
ijassa-429	106	10	its	its	PRON
ijassa-429	106	11	predictions	prediction	NOUN
ijassa-429	106	12	for	for	ADP
ijassa-429	106	13	population	population	NOUN
ijassa-429	106	14	(	(	PUNCT
ijassa-429	106	15	p	p	X
ijassa-429	106	16	(	(	PUNCT
ijassa-429	106	17	t	t	PROPN
ijassa-429	106	18	)	)	PUNCT
ijassa-429	106	19	)	)	PUNCT
ijassa-429	106	20	lie	lie	NOUN
ijassa-429	106	21	between	between	ADP
ijassa-429	106	22	the	the	DET
ijassa-429	106	23	exponential	exponential	ADJ
ijassa-429	106	24	and	and	CCONJ
ijassa-429	106	25	logistic	logistic	ADJ
ijassa-429	106	26	predictions	prediction	NOUN
ijassa-429	106	27	.	.	PUNCT
ijassa-429	107	1	the	the	DET
ijassa-429	107	2	modified	modify	VERB
ijassa-429	107	3	alternating	alternate	VERB
ijassa-429	107	4	maclaurin	maclaurin	NOUN
ijassa-429	107	5	series	series	NOUN
ijassa-429	107	6	is	be	AUX
ijassa-429	107	7	convergent	convergent	ADJ
ijassa-429	107	8	for	for	ADP
ijassa-429	107	9	all	all	DET
ijassa-429	107	10	points	point	NOUN
ijassa-429	107	11	up	up	ADP
ijassa-429	107	12	to	to	ADP
ijassa-429	107	13	and	and	CCONJ
ijassa-429	107	14	including	include	VERB
ijassa-429	107	15	the	the	DET
ijassa-429	107	16	point	point	NOUN
ijassa-429	107	17	of	of	ADP
ijassa-429	107	18	inflection	inflection	NOUN
ijassa-429	107	19	.	.	PUNCT
ijassa-429	108	1	it	it	PRON
ijassa-429	108	2	satisfies	satisfy	VERB
ijassa-429	108	3	the	the	DET
ijassa-429	108	4	conditions	condition	NOUN
ijassa-429	108	5	of	of	ADP
ijassa-429	108	6	the	the	DET
ijassa-429	108	7	ratio	ratio	NOUN
ijassa-429	108	8	test	test	NOUN
ijassa-429	108	9	and	and	CCONJ
ijassa-429	108	10	leibniz	leibniz	PROPN
ijassa-429	108	11	’s	’s	PART
ijassa-429	108	12	theorem	theorem	NOUN
ijassa-429	108	13	for	for	ADP
ijassa-429	108	14	this	this	DET
ijassa-429	108	15	domain	domain	NOUN
ijassa-429	108	16	and	and	CCONJ
ijassa-429	108	17	range	range	NOUN
ijassa-429	108	18	[	[	X
ijassa-429	108	19	14	14	NUM
ijassa-429	108	20	-	-	SYM
ijassa-429	108	21	15	15	NUM
ijassa-429	108	22	]	]	PUNCT
ijassa-429	108	23	.	.	PUNCT
ijassa-429	109	1	past	past	ADP
ijassa-429	109	2	the	the	DET
ijassa-429	109	3	point	point	NOUN
ijassa-429	109	4	of	of	ADP
ijassa-429	109	5	inflection	inflection	NOUN
ijassa-429	109	6	,	,	PUNCT
ijassa-429	109	7	divergence	divergence	NOUN
ijassa-429	109	8	becomes	become	VERB
ijassa-429	109	9	more	more	ADV
ijassa-429	109	10	extreme	extreme	ADJ
ijassa-429	109	11	with	with	ADP
ijassa-429	109	12	additional	additional	ADJ
ijassa-429	109	13	terms	term	NOUN
ijassa-429	109	14	.	.	PUNCT
ijassa-429	110	1	as	as	ADP
ijassa-429	110	2	a	a	DET
ijassa-429	110	3	model	model	NOUN
ijassa-429	110	4	,	,	PUNCT
ijassa-429	110	5	therefore	therefore	ADV
ijassa-429	110	6	,	,	PUNCT
ijassa-429	110	7	it	it	PRON
ijassa-429	110	8	accurately	accurately	ADV
ijassa-429	110	9	produces	produce	VERB
ijassa-429	110	10	the	the	DET
ijassa-429	110	11	lower	low	ADJ
ijassa-429	110	12	portion	portion	NOUN
ijassa-429	110	13	of	of	ADP
ijassa-429	110	14	the	the	DET
ijassa-429	110	15	curve	curve	NOUN
ijassa-429	110	16	.	.	PUNCT
ijassa-429	111	1	if	if	SCONJ
ijassa-429	111	2	the	the	DET
ijassa-429	111	3	growth	growth	NOUN
ijassa-429	111	4	pattern	pattern	NOUN
ijassa-429	111	5	is	be	AUX
ijassa-429	111	6	symmetrical	symmetrical	ADJ
ijassa-429	111	7	,	,	PUNCT
ijassa-429	111	8	a	a	DET
ijassa-429	111	9	180o	180o	PROPN
ijassa-429	111	10	rotation	rotation	NOUN
ijassa-429	111	11	about	about	ADP
ijassa-429	111	12	the	the	DET
ijassa-429	111	13	point	point	NOUN
ijassa-429	111	14	of	of	ADP
ijassa-429	111	15	inflection	inflection	NOUN
ijassa-429	111	16	projects	project	VERB
ijassa-429	111	17	the	the	DET
ijassa-429	111	18	upper	upper	ADJ
ijassa-429	111	19	portion	portion	NOUN
ijassa-429	111	20	.	.	PUNCT
ijassa-429	112	1	if	if	SCONJ
ijassa-429	112	2	the	the	DET
ijassa-429	112	3	growth	growth	NOUN
ijassa-429	112	4	is	be	AUX
ijassa-429	112	5	semi	semi	ADJ
ijassa-429	112	6	-	-	ADJ
ijassa-429	112	7	logistic	logistic	ADJ
ijassa-429	112	8	,	,	PUNCT
ijassa-429	112	9	it	it	PRON
ijassa-429	112	10	appears	appear	VERB
ijassa-429	112	11	as	as	ADP
ijassa-429	112	12	portions	portion	NOUN
ijassa-429	112	13	of	of	ADP
ijassa-429	112	14	intersecting	intersect	VERB
ijassa-429	112	15	logistic	logistic	ADJ
ijassa-429	112	16	curves	curve	NOUN
ijassa-429	112	17	,	,	PUNCT
ijassa-429	112	18	and	and	CCONJ
ijassa-429	112	19	the	the	DET
ijassa-429	112	20	point	point	NOUN
ijassa-429	112	21	of	of	ADP
ijassa-429	112	22	intersection	intersection	NOUN
ijassa-429	112	23	is	be	AUX
ijassa-429	112	24	the	the	DET
ijassa-429	112	25	point	point	NOUN
ijassa-429	112	26	of	of	ADP
ijassa-429	112	27	inflection	inflection	NOUN
ijassa-429	112	28	.	.	PUNCT
ijassa-429	113	1	in	in	ADP
ijassa-429	113	2	this	this	DET
ijassa-429	113	3	scenario	scenario	NOUN
ijassa-429	113	4	,	,	PUNCT
ijassa-429	113	5	the	the	DET
ijassa-429	113	6	bottom	bottom	ADJ
ijassa-429	113	7	portion	portion	NOUN
ijassa-429	113	8	of	of	ADP
ijassa-429	113	9	the	the	DET
ijassa-429	113	10	curve	curve	NOUN
ijassa-429	113	11	is	be	AUX
ijassa-429	113	12	accurately	accurately	ADV
ijassa-429	113	13	described	describe	VERB
ijassa-429	113	14	by	by	ADP
ijassa-429	113	15	the	the	DET
ijassa-429	113	16	model	model	NOUN
ijassa-429	113	17	(	(	PUNCT
ijassa-429	113	18	equation	equation	NOUN
ijassa-429	113	19	4	4	NUM
ijassa-429	113	20	,	,	PUNCT
ijassa-429	113	21	fig.4	fig.4	PROPN
ijassa-429	113	22	)	)	PUNCT
ijassa-429	113	23	.	.	PUNCT
ijassa-429	114	1	fig.4	fig.4	PRON
ijassa-429	114	2	graphical	graphical	ADJ
ijassa-429	114	3	depiction	depiction	NOUN
ijassa-429	114	4	of	of	ADP
ijassa-429	114	5	the	the	DET
ijassa-429	114	6	modified	modify	VERB
ijassa-429	114	7	alternating	alternate	VERB
ijassa-429	114	8	maclaurin	maclaurin	PROPN
ijassa-429	114	9	series	series	PROPN
ijassa-429	114	10	model	model	NOUN
ijassa-429	114	11	dp	dp	NOUN
ijassa-429	114	12	dt	dt	NOUN
ijassa-429	114	13	=	=	SYM
ijassa-429	114	14	∞∑	∞∑	PROPN
ijassa-429	114	15	n=0	n=0	PROPN
ijassa-429	114	16	(	(	PUNCT
ijassa-429	114	17	−1)n(2nn!)rpn+1	−1)n(2nn!)rpn+1	NOUN
ijassa-429	114	18	mn(n+	mn(n+	NOUN
ijassa-429	114	19	1	1	NUM
ijassa-429	114	20	)	)	PUNCT
ijassa-429	114	21	!	!	PUNCT
ijassa-429	115	1	(	(	PUNCT
ijassa-429	115	2	4	4	X
ijassa-429	115	3	)	)	PUNCT
ijassa-429	115	4	its	its	PRON
ijassa-429	115	5	expanded	expand	VERB
ijassa-429	115	6	form	form	NOUN
ijassa-429	115	7	appears	appear	VERB
ijassa-429	115	8	as	as	ADP
ijassa-429	115	9	equation	equation	NOUN
ijassa-429	115	10	5	5	NUM
ijassa-429	115	11	.	.	NOUN
ijassa-429	115	12	86	86	NUM
ijassa-429	115	13	anne	anne	PROPN
ijassa-429	115	14	talkington	talkington	NOUN
ijassa-429	115	15	:	:	PUNCT
ijassa-429	115	16	an	an	DET
ijassa-429	115	17	extension	extension	NOUN
ijassa-429	115	18	of	of	ADP
ijassa-429	115	19	a	a	DET
ijassa-429	115	20	logistic	logistic	ADJ
ijassa-429	115	21	model	model	NOUN
ijassa-429	115	22	for	for	ADP
ijassa-429	115	23	microbial	microbial	ADJ
ijassa-429	115	24	kinetics	kinetic	NOUN
ijassa-429	115	25	dp	dp	NOUN
ijassa-429	115	26	dt	dt	NOUN
ijassa-429	116	1	=	=	NOUN
ijassa-429	116	2	rp	rp	NOUN
ijassa-429	116	3	−	−	NOUN
ijassa-429	116	4	2rp	2rp	ADJ
ijassa-429	116	5	2	2	NUM
ijassa-429	116	6	m(2	m(2	NOUN
ijassa-429	116	7	!	!	PUNCT
ijassa-429	116	8	)	)	PUNCT
ijassa-429	117	1	+	+	CCONJ
ijassa-429	117	2	8rp	8rp	ADJ
ijassa-429	117	3	3	3	NUM
ijassa-429	117	4	m2(3	m2(3	NOUN
ijassa-429	117	5	!	!	PUNCT
ijassa-429	117	6	)	)	PUNCT
ijassa-429	118	1	−	−	PROPN
ijassa-429	118	2	48rp	48rp	ADJ
ijassa-429	119	1	4	4	NUM
ijassa-429	119	2	m3(4	m3(4	NOUN
ijassa-429	119	3	!	!	PUNCT
ijassa-429	119	4	)	)	PUNCT
ijassa-429	120	1	+	+	CCONJ
ijassa-429	120	2	384rp	384rp	NOUN
ijassa-429	120	3	5	5	NUM
ijassa-429	120	4	m4(5	m4(5	PROPN
ijassa-429	120	5	!	!	PUNCT
ijassa-429	120	6	)	)	PUNCT
ijassa-429	121	1	−	−	PROPN
ijassa-429	122	1	3840rp	3840rp	PROPN
ijassa-429	122	2	6	6	NUM
ijassa-429	122	3	m5(6	m5(6	NOUN
ijassa-429	122	4	!	!	PUNCT
ijassa-429	122	5	)	)	PUNCT
ijassa-429	123	1	+	+	CCONJ
ijassa-429	123	2	...	...	PUNCT
ijassa-429	123	3	+	+	CCONJ
ijassa-429	123	4	(	(	PUNCT
ijassa-429	123	5	−1)n(2nn!)rpn+1	−1)n(2nn!)rpn+1	VERB
ijassa-429	123	6	mn(n+	mn(n+	NOUN
ijassa-429	123	7	1	1	NUM
ijassa-429	123	8	)	)	PUNCT
ijassa-429	123	9	!	!	PUNCT
ijassa-429	124	1	(	(	PUNCT
ijassa-429	124	2	5	5	X
ijassa-429	124	3	)	)	PUNCT
ijassa-429	124	4	its	its	PRON
ijassa-429	124	5	simplified	simplified	ADJ
ijassa-429	124	6	form	form	NOUN
ijassa-429	124	7	appears	appear	VERB
ijassa-429	124	8	as	as	ADP
ijassa-429	124	9	equation	equation	NOUN
ijassa-429	124	10	6	6	NUM
ijassa-429	124	11	.	.	PUNCT
ijassa-429	125	1	dp	dp	NOUN
ijassa-429	125	2	dt	dt	NOUN
ijassa-429	125	3	=	=	PUNCT
ijassa-429	125	4	rp	rp	NOUN
ijassa-429	125	5	∞∑	∞∑	PROPN
ijassa-429	125	6	n=0	n=0	NUM
ijassa-429	125	7	(	(	PUNCT
ijassa-429	125	8	−1)n	−1)n	X
ijassa-429	125	9	(	(	PUNCT
ijassa-429	125	10	n+	n+	NOUN
ijassa-429	125	11	1	1	NUM
ijassa-429	125	12	)	)	PUNCT
ijassa-429	125	13	×	×	NOUN
ijassa-429	125	14	(	(	PUNCT
ijassa-429	125	15	2p	2p	NUM
ijassa-429	125	16	m	m	NOUN
ijassa-429	125	17	)	)	PUNCT
ijassa-429	125	18	n	n	CCONJ
ijassa-429	125	19	(	(	PUNCT
ijassa-429	125	20	6	6	X
ijassa-429	125	21	)	)	PUNCT
ijassa-429	125	22	its	its	PRON
ijassa-429	125	23	closed	closed	ADJ
ijassa-429	125	24	form	form	NOUN
ijassa-429	125	25	appears	appear	VERB
ijassa-429	125	26	as	as	ADP
ijassa-429	125	27	equation	equation	NOUN
ijassa-429	125	28	7	7	NUM
ijassa-429	125	29	.	.	PUNCT
ijassa-429	126	1	dp	dp	NOUN
ijassa-429	126	2	dt	dt	NOUN
ijassa-429	126	3	=	=	PUNCT
ijassa-429	126	4	rln(1	rln(1	X
ijassa-429	127	1	+	+	CCONJ
ijassa-429	127	2	p	p	X
ijassa-429	127	3	m	m	VERB
ijassa-429	127	4	2	2	NUM
ijassa-429	127	5	)	)	PUNCT
ijassa-429	127	6	m	m	VERB
ijassa-429	127	7	2	2	NUM
ijassa-429	127	8	(	(	PUNCT
ijassa-429	127	9	7	7	NUM
ijassa-429	127	10	)	)	PUNCT
ijassa-429	127	11	the	the	DET
ijassa-429	127	12	similarities	similarity	NOUN
ijassa-429	127	13	of	of	ADP
ijassa-429	127	14	the	the	DET
ijassa-429	127	15	function	function	NOUN
ijassa-429	127	16	to	to	ADP
ijassa-429	127	17	the	the	DET
ijassa-429	127	18	exponential	exponential	ADJ
ijassa-429	127	19	function	function	NOUN
ijassa-429	127	20	are	be	AUX
ijassa-429	127	21	evident	evident	ADJ
ijassa-429	127	22	in	in	ADP
ijassa-429	127	23	the	the	DET
ijassa-429	127	24	simplified	simplified	ADJ
ijassa-429	127	25	form	form	NOUN
ijassa-429	127	26	of	of	ADP
ijassa-429	127	27	the	the	DET
ijassa-429	127	28	model	model	NOUN
ijassa-429	127	29	.	.	PUNCT
ijassa-429	128	1	the	the	DET
ijassa-429	128	2	factor	factor	NOUN
ijassa-429	128	3	rp	rp	NOUN
ijassa-429	128	4	represents	represent	VERB
ijassa-429	128	5	exponential	exponential	ADJ
ijassa-429	128	6	growth	growth	NOUN
ijassa-429	128	7	.	.	PUNCT
ijassa-429	129	1	in	in	ADP
ijassa-429	129	2	addition	addition	NOUN
ijassa-429	129	3	,	,	PUNCT
ijassa-429	129	4	the	the	DET
ijassa-429	129	5	behavior	behavior	NOUN
ijassa-429	129	6	of	of	ADP
ijassa-429	129	7	the	the	DET
ijassa-429	129	8	series	series	NOUN
ijassa-429	129	9	is	be	AUX
ijassa-429	129	10	similar	similar	ADJ
ijassa-429	129	11	to	to	ADP
ijassa-429	129	12	that	that	PRON
ijassa-429	129	13	of	of	ADP
ijassa-429	129	14	exponential	exponential	ADJ
ijassa-429	129	15	growth	growth	NOUN
ijassa-429	129	16	for	for	ADP
ijassa-429	129	17	sufficiently	sufficiently	ADV
ijassa-429	129	18	small	small	ADJ
ijassa-429	129	19	values	value	NOUN
ijassa-429	129	20	of	of	ADP
ijassa-429	129	21	p	p	NOUN
ijassa-429	129	22	(	(	PUNCT
ijassa-429	129	23	p	p	X
ijassa-429	129	24	<	<	X
ijassa-429	129	25	<	<	X
ijassa-429	129	26	1	1	NUM
ijassa-429	129	27	)	)	PUNCT
ijassa-429	129	28	.	.	PUNCT
ijassa-429	130	1	dp	dp	NOUN
ijassa-429	131	1	dt	dt	NOUN
ijassa-429	131	2	=	=	PUNCT
ijassa-429	131	3	rln(1	rln(1	X
ijassa-429	132	1	+	+	CCONJ
ijassa-429	132	2	p	p	X
ijassa-429	132	3	m	m	VERB
ijassa-429	132	4	2	2	NUM
ijassa-429	132	5	)	)	PUNCT
ijassa-429	132	6	m	m	VERB
ijassa-429	132	7	2	2	NUM
ijassa-429	132	8	dp	dp	NOUN
ijassa-429	132	9	dt	dt	NOUN
ijassa-429	132	10	=	=	SYM
ijassa-429	132	11	r	r	NOUN
ijassa-429	132	12	×	×	NOUN
ijassa-429	132	13	m	m	NOUN
ijassa-429	132	14	2	2	NUM
ijassa-429	132	15	×	×	NOUN
ijassa-429	132	16	ln(1	ln(1	NOUN
ijassa-429	132	17	+	+	CCONJ
ijassa-429	132	18	2p	2p	NUM
ijassa-429	132	19	m	m	NOUN
ijassa-429	132	20	)	)	PUNCT
ijassa-429	133	1	ln(1	ln(1	ADP
ijassa-429	133	2	+	+	NUM
ijassa-429	133	3	2p	2p	NUM
ijassa-429	133	4	m	m	NOUN
ijassa-429	133	5	)	)	PUNCT
ijassa-429	134	1	≈	≈	PROPN
ijassa-429	134	2	2p	2p	NUM
ijassa-429	134	3	m	m	VERB
ijassa-429	134	4	dp	dp	NOUN
ijassa-429	135	1	dt	dt	NOUN
ijassa-429	135	2	=	=	SYM
ijassa-429	136	1	r	r	NOUN
ijassa-429	136	2	×	×	NOUN
ijassa-429	136	3	m	m	VERB
ijassa-429	136	4	2	2	NUM
ijassa-429	136	5	×	×	NOUN
ijassa-429	136	6	2p	2p	NUM
ijassa-429	136	7	m	m	NOUN
ijassa-429	136	8	=	=	NOUN
ijassa-429	136	9	rp	rp	NOUN
ijassa-429	136	10	this	this	DET
ijassa-429	136	11	property	property	NOUN
ijassa-429	136	12	does	do	AUX
ijassa-429	136	13	not	not	PART
ijassa-429	136	14	apply	apply	VERB
ijassa-429	136	15	when	when	SCONJ
ijassa-429	136	16	2p	2p	NUM
ijassa-429	136	17	m	m	NOUN
ijassa-429	136	18	is	be	AUX
ijassa-429	136	19	greater	great	ADJ
ijassa-429	136	20	than	than	ADP
ijassa-429	136	21	1	1	NUM
ijassa-429	136	22	,	,	PUNCT
ijassa-429	136	23	because	because	SCONJ
ijassa-429	136	24	ln(1	ln(1	NOUN
ijassa-429	136	25	+	+	NUM
ijassa-429	136	26	x	x	X
ijassa-429	136	27	)	)	PUNCT
ijassa-429	136	28	=	=	SYM
ijassa-429	136	29	x−	x−	PROPN
ijassa-429	136	30	1	1	NUM
ijassa-429	136	31	2x	2x	NUM
ijassa-429	136	32	2	2	NUM
ijassa-429	136	33	+	+	CCONJ
ijassa-429	136	34	1	1	NUM
ijassa-429	136	35	3x	3x	NUM
ijassa-429	136	36	3	3	NUM
ijassa-429	136	37	−	−	NOUN
ijassa-429	136	38	1	1	NUM
ijassa-429	136	39	4x	4x	NUM
ijassa-429	136	40	4	4	NUM
ijassa-429	136	41	+	+	CCONJ
ijassa-429	136	42	...	...	PUNCT
ijassa-429	136	43	holds	hold	VERB
ijassa-429	136	44	only	only	ADV
ijassa-429	136	45	for	for	ADP
ijassa-429	136	46	−1	−1	NOUN
ijassa-429	136	47	<	<	X
ijassa-429	136	48	x	x	SYM
ijassa-429	136	49	≤	≤	NUM
ijassa-429	136	50	1	1	NUM
ijassa-429	136	51	.	.	PUNCT
ijassa-429	136	52	also	also	ADV
ijassa-429	136	53	like	like	ADP
ijassa-429	136	54	an	an	DET
ijassa-429	136	55	exponential	exponential	ADJ
ijassa-429	136	56	function	function	NOUN
ijassa-429	136	57	,	,	PUNCT
ijassa-429	136	58	the	the	DET
ijassa-429	136	59	graph	graph	NOUN
ijassa-429	136	60	of	of	ADP
ijassa-429	136	61	the	the	DET
ijassa-429	136	62	population	population	NOUN
ijassa-429	136	63	p	p	NOUN
ijassa-429	136	64	over	over	ADP
ijassa-429	136	65	time	time	NOUN
ijassa-429	136	66	is	be	AUX
ijassa-429	136	67	concave	concave	VERB
ijassa-429	136	68	up	up	ADP
ijassa-429	136	69	,	,	PUNCT
ijassa-429	136	70	as	as	SCONJ
ijassa-429	136	71	justified	justify	VERB
ijassa-429	136	72	by	by	ADP
ijassa-429	136	73	the	the	DET
ijassa-429	136	74	always	always	ADV
ijassa-429	136	75	positive	positive	ADJ
ijassa-429	136	76	second	second	ADJ
ijassa-429	136	77	derivative	derivative	NOUN
ijassa-429	136	78	:	:	PUNCT
ijassa-429	136	79	d2p	d2p	NOUN
ijassa-429	136	80	dt2	dt2	NOUN
ijassa-429	136	81	=	=	NOUN
ijassa-429	136	82	r	r	NOUN
ijassa-429	136	83	m	m	NOUN
ijassa-429	136	84	2	2	NUM
ijassa-429	136	85	1	1	NUM
ijassa-429	136	86	1	1	NUM
ijassa-429	136	87	+	+	CCONJ
ijassa-429	136	88	p	p	NOUN
ijassa-429	136	89	m	m	VERB
ijassa-429	136	90	2	2	NUM
ijassa-429	136	91	(	(	PUNCT
ijassa-429	136	92	1	1	NUM
ijassa-429	136	93	+	+	CCONJ
ijassa-429	136	94	p	p	NOUN
ijassa-429	136	95	m	m	VERB
ijassa-429	136	96	2	2	NUM
ijassa-429	136	97	)	)	PUNCT
ijassa-429	136	98	′	′	NUM
ijassa-429	136	99	t	t	NOUN
ijassa-429	137	1	=	=	PUNCT
ijassa-429	137	2	r	r	NOUN
ijassa-429	137	3	m	m	VERB
ijassa-429	137	4	2	2	NUM
ijassa-429	137	5	1	1	NUM
ijassa-429	137	6	1	1	NUM
ijassa-429	137	7	+	+	CCONJ
ijassa-429	137	8	p	p	NOUN
ijassa-429	137	9	m	m	PROPN
ijassa-429	137	10	2	2	NUM
ijassa-429	137	11	1	1	NUM
ijassa-429	137	12	m	m	NUM
ijassa-429	137	13	2	2	NUM
ijassa-429	137	14	dp	dp	NOUN
ijassa-429	137	15	dt	dt	NOUN
ijassa-429	137	16	=	=	SYM
ijassa-429	137	17	r2	r2	PROPN
ijassa-429	137	18	m	m	VERB
ijassa-429	137	19	2	2	NUM
ijassa-429	137	20	1	1	NUM
ijassa-429	137	21	1	1	NUM
ijassa-429	137	22	+	+	CCONJ
ijassa-429	137	23	p	p	NOUN
ijassa-429	137	24	m	m	VERB
ijassa-429	137	25	2	2	NUM
ijassa-429	138	1	ln(1	ln(1	NOUN
ijassa-429	138	2	+	+	NOUN
ijassa-429	138	3	p	p	NOUN
ijassa-429	138	4	m	m	VERB
ijassa-429	138	5	2	2	NUM
ijassa-429	138	6	)	)	PUNCT
ijassa-429	138	7	>	>	X
ijassa-429	138	8	0	0	PUNCT
ijassa-429	139	1	however	however	ADV
ijassa-429	139	2	,	,	PUNCT
ijassa-429	139	3	the	the	DET
ijassa-429	139	4	rate	rate	NOUN
ijassa-429	139	5	of	of	ADP
ijassa-429	139	6	growth	growth	NOUN
ijassa-429	139	7	as	as	ADP
ijassa-429	139	8	p	p	NOUN
ijassa-429	139	9	approaches	approach	NOUN
ijassa-429	139	10	infinity	infinity	NOUN
ijassa-429	139	11	is	be	AUX
ijassa-429	139	12	much	much	ADV
ijassa-429	139	13	slower	slow	ADJ
ijassa-429	139	14	than	than	ADP
ijassa-429	139	15	that	that	PRON
ijassa-429	139	16	of	of	ADP
ijassa-429	139	17	an	an	DET
ijassa-429	139	18	exponential	exponential	ADJ
ijassa-429	139	19	function	function	NOUN
ijassa-429	139	20	since	since	SCONJ
ijassa-429	139	21	by	by	ADP
ijassa-429	139	22	limit	limit	NOUN
ijassa-429	139	23	comparison	comparison	NOUN
ijassa-429	139	24	:	:	PUNCT
ijassa-429	139	25	lim	lim	PROPN
ijassa-429	139	26	p→∞	p→∞	PROPN
ijassa-429	140	1	rp	rp	NOUN
ijassa-429	140	2	r	r	NOUN
ijassa-429	140	3	×	×	PROPN
ijassa-429	140	4	m	m	NOUN
ijassa-429	140	5	2	2	NUM
ijassa-429	140	6	×	×	NOUN
ijassa-429	141	1	ln(1	ln(1	NOUN
ijassa-429	141	2	+	+	CCONJ
ijassa-429	141	3	p	p	NOUN
ijassa-429	141	4	m	m	NOUN
ijassa-429	141	5	)	)	PUNCT
ijassa-429	142	1	=	=	SYM
ijassa-429	142	2	lim	lim	PROPN
ijassa-429	142	3	p→∞	p→∞	ADV
ijassa-429	142	4	2p	2p	NUM
ijassa-429	142	5	m	m	NOUN
ijassa-429	142	6	×	×	NOUN
ijassa-429	143	1	ln(1	ln(1	NOUN
ijassa-429	143	2	+	+	CCONJ
ijassa-429	143	3	p	p	NOUN
ijassa-429	143	4	m	m	NOUN
ijassa-429	143	5	)	)	PUNCT
ijassa-429	144	1	=	=	SYM
ijassa-429	144	2	∞	∞	NUM
ijassa-429	144	3	advances	advance	NOUN
ijassa-429	144	4	in	in	ADP
ijassa-429	144	5	systems	system	NOUN
ijassa-429	144	6	science	science	NOUN
ijassa-429	144	7	and	and	CCONJ
ijassa-429	144	8	applications	application	NOUN
ijassa-429	144	9	(	(	PUNCT
ijassa-429	144	10	2013	2013	NUM
ijassa-429	144	11	)	)	PUNCT
ijassa-429	144	12	vol.13	vol.13	NOUN
ijassa-429	144	13	no.1	no.1	VERB
ijassa-429	144	14	87	87	NUM
ijassa-429	145	1	it	it	PRON
ijassa-429	145	2	is	be	AUX
ijassa-429	145	3	known	know	VERB
ijassa-429	145	4	that	that	SCONJ
ijassa-429	145	5	the	the	DET
ijassa-429	145	6	numerator	numerator	NOUN
ijassa-429	145	7	becomes	become	VERB
ijassa-429	145	8	infinitely	infinitely	ADV
ijassa-429	145	9	large	large	ADJ
ijassa-429	145	10	at	at	ADP
ijassa-429	145	11	a	a	DET
ijassa-429	145	12	faster	fast	ADJ
ijassa-429	145	13	rate	rate	NOUN
ijassa-429	145	14	than	than	ADP
ijassa-429	145	15	the	the	DET
ijassa-429	145	16	denominator	denominator	NOUN
ijassa-429	145	17	.	.	PUNCT
ijassa-429	146	1	l′hôpital′s	l′hôpital′s	ADV
ijassa-429	146	2	rule	rule	NOUN
ijassa-429	146	3	confirms	confirm	VERB
ijassa-429	146	4	this	this	DET
ijassa-429	146	5	assertion	assertion	NOUN
ijassa-429	146	6	by	by	ADP
ijassa-429	146	7	removing	remove	VERB
ijassa-429	146	8	the	the	DET
ijassa-429	146	9	infinite	infinite	ADJ
ijassa-429	146	10	term	term	NOUN
ijassa-429	146	11	from	from	ADP
ijassa-429	146	12	the	the	DET
ijassa-429	146	13	function	function	NOUN
ijassa-429	146	14	,	,	PUNCT
ijassa-429	146	15	to	to	PART
ijassa-429	146	16	arrive	arrive	VERB
ijassa-429	146	17	at	at	ADP
ijassa-429	146	18	the	the	DET
ijassa-429	146	19	definite	definite	ADJ
ijassa-429	146	20	conclusion	conclusion	NOUN
ijassa-429	146	21	:	:	PUNCT
ijassa-429	146	22	lim	lim	PROPN
ijassa-429	146	23	p→∞	p→∞	PROPN
ijassa-429	147	1	rp	rp	NOUN
ijassa-429	147	2	r	r	NOUN
ijassa-429	147	3	×	×	PROPN
ijassa-429	147	4	m	m	NOUN
ijassa-429	147	5	2	2	NUM
ijassa-429	147	6	×	×	NOUN
ijassa-429	148	1	ln(1	ln(1	NOUN
ijassa-429	148	2	+	+	CCONJ
ijassa-429	148	3	p	p	NOUN
ijassa-429	148	4	m	m	NOUN
ijassa-429	148	5	)	)	PUNCT
ijassa-429	149	1	=	=	SYM
ijassa-429	149	2	lim	lim	PROPN
ijassa-429	149	3	p→∞	p→∞	PROPN
ijassa-429	149	4	(	(	PUNCT
ijassa-429	149	5	rp	rp	NOUN
ijassa-429	149	6	)	)	PUNCT
ijassa-429	149	7	′	′	NUM
ijassa-429	150	1	lim	lim	PROPN
ijassa-429	150	2	p→∞	p→∞	PROPN
ijassa-429	150	3	(	(	PUNCT
ijassa-429	150	4	r	r	NOUN
ijassa-429	150	5	×	×	PROPN
ijassa-429	150	6	m	m	NOUN
ijassa-429	150	7	2	2	NUM
ijassa-429	150	8	×	×	NOUN
ijassa-429	150	9	ln(1	ln(1	NOUN
ijassa-429	150	10	+	+	CCONJ
ijassa-429	150	11	p	p	NOUN
ijassa-429	150	12	m	m	NOUN
ijassa-429	150	13	)	)	PUNCT
ijassa-429	150	14	)	)	PUNCT
ijassa-429	150	15	′	′	NUM
ijassa-429	151	1	=	=	PUNCT
ijassa-429	151	2	r	r	NOUN
ijassa-429	151	3	lim	lim	PROPN
ijassa-429	151	4	p→∞	p→∞	PROPN
ijassa-429	151	5	(	(	PUNCT
ijassa-429	151	6	r	r	NOUN
ijassa-429	151	7	×	×	PROPN
ijassa-429	151	8	m	m	NOUN
ijassa-429	151	9	2	2	NUM
ijassa-429	151	10	×	×	NOUN
ijassa-429	151	11	1	1	NUM
ijassa-429	151	12	m	m	NOUN
ijassa-429	151	13	1	1	NUM
ijassa-429	151	14	+	+	SYM
ijassa-429	151	15	p	p	NOUN
ijassa-429	151	16	m	m	NOUN
ijassa-429	151	17	)	)	PUNCT
ijassa-429	152	1	=	=	SYM
ijassa-429	152	2	∞	∞	NOUN
ijassa-429	152	3	this	this	DET
ijassa-429	152	4	property	property	NOUN
ijassa-429	152	5	is	be	AUX
ijassa-429	152	6	the	the	DET
ijassa-429	152	7	result	result	NOUN
ijassa-429	152	8	of	of	ADP
ijassa-429	152	9	the	the	DET
ijassa-429	152	10	alternating	alternate	VERB
ijassa-429	152	11	series	series	NOUN
ijassa-429	152	12	succession	succession	NOUN
ijassa-429	152	13	of	of	ADP
ijassa-429	152	14	positive	positive	ADJ
ijassa-429	152	15	and	and	CCONJ
ijassa-429	152	16	negative	negative	ADJ
ijassa-429	152	17	terms	term	NOUN
ijassa-429	152	18	.	.	PUNCT
ijassa-429	153	1	the	the	DET
ijassa-429	153	2	positive	positive	ADJ
ijassa-429	153	3	and	and	CCONJ
ijassa-429	153	4	negative	negative	ADJ
ijassa-429	153	5	terms	term	NOUN
ijassa-429	153	6	indicate	indicate	VERB
ijassa-429	153	7	the	the	DET
ijassa-429	153	8	properties	property	NOUN
ijassa-429	153	9	of	of	ADP
ijassa-429	153	10	the	the	DET
ijassa-429	153	11	series	series	NOUN
ijassa-429	153	12	at	at	ADP
ijassa-429	153	13	any	any	DET
ijassa-429	153	14	point	point	NOUN
ijassa-429	153	15	of	of	ADP
ijassa-429	153	16	truncation	truncation	NOUN
ijassa-429	153	17	.	.	PUNCT
ijassa-429	154	1	if	if	SCONJ
ijassa-429	154	2	truncated	truncate	VERB
ijassa-429	154	3	up	up	ADP
ijassa-429	154	4	to	to	ADP
ijassa-429	154	5	an	an	DET
ijassa-429	154	6	even	even	ADJ
ijassa-429	154	7	degree	degree	NOUN
ijassa-429	154	8	of	of	ADP
ijassa-429	154	9	p	p	NOUN
ijassa-429	154	10	(	(	PUNCT
ijassa-429	154	11	say	say	INTJ
ijassa-429	154	12	up	up	ADP
ijassa-429	154	13	to	to	PART
ijassa-429	154	14	pn+1	pn+1	VERB
ijassa-429	154	15	where	where	SCONJ
ijassa-429	154	16	n	n	PRON
ijassa-429	154	17	is	be	AUX
ijassa-429	154	18	odd	odd	ADJ
ijassa-429	154	19	)	)	PUNCT
ijassa-429	154	20	,	,	PUNCT
ijassa-429	154	21	then	then	ADV
ijassa-429	154	22	the	the	DET
ijassa-429	154	23	solution	solution	NOUN
ijassa-429	154	24	p	p	NOUN
ijassa-429	154	25	has	have	VERB
ijassa-429	154	26	an	an	DET
ijassa-429	154	27	upper	upper	ADJ
ijassa-429	154	28	bound	bind	VERB
ijassa-429	154	29	,	,	PUNCT
ijassa-429	154	30	and	and	CCONJ
ijassa-429	154	31	an	an	DET
ijassa-429	154	32	inflection	inflection	NOUN
ijassa-429	154	33	point	point	NOUN
ijassa-429	154	34	(	(	PUNCT
ijassa-429	154	35	see	see	VERB
ijassa-429	154	36	theorem	theorem	NOUN
ijassa-429	154	37	2	2	NUM
ijassa-429	154	38	)	)	PUNCT
ijassa-429	154	39	.	.	PUNCT
ijassa-429	155	1	the	the	DET
ijassa-429	155	2	inflection	inflection	NOUN
ijassa-429	155	3	point	point	NOUN
ijassa-429	155	4	will	will	AUX
ijassa-429	155	5	always	always	ADV
ijassa-429	155	6	occur	occur	VERB
ijassa-429	155	7	when	when	SCONJ
ijassa-429	155	8	p	p	PROPN
ijassa-429	155	9	=	=	NOUN
ijassa-429	155	10	m	m	VERB
ijassa-429	155	11	2	2	NUM
ijassa-429	155	12	as	as	SCONJ
ijassa-429	155	13	justified	justify	VERB
ijassa-429	155	14	by	by	ADP
ijassa-429	155	15	the	the	DET
ijassa-429	155	16	second	second	ADJ
ijassa-429	155	17	derivative	derivative	NOUN
ijassa-429	155	18	of	of	ADP
ijassa-429	155	19	p	p	PROPN
ijassa-429	155	20	(	(	PUNCT
ijassa-429	155	21	t	t	PROPN
ijassa-429	155	22	)	)	PUNCT
ijassa-429	155	23	as	as	SCONJ
ijassa-429	155	24	follows	follow	VERB
ijassa-429	155	25	.	.	PUNCT
ijassa-429	156	1	dp	dp	NOUN
ijassa-429	157	1	dt	dt	NOUN
ijassa-429	157	2	=	=	SYM
ijassa-429	157	3	n∑	n∑	PROPN
ijassa-429	157	4	n=0	n=0	PROPN
ijassa-429	157	5	(	(	PUNCT
ijassa-429	157	6	−1)n2nrpn+1	−1)n2nrpn+1	ADJ
ijassa-429	157	7	mn(n+	mn(n+	NOUN
ijassa-429	157	8	1	1	NUM
ijassa-429	157	9	)	)	PUNCT
ijassa-429	157	10	(	(	PUNCT
ijassa-429	157	11	8)	8)	NUM
ijassa-429	157	12	d2p	d2p	NOUN
ijassa-429	157	13	dt2	dt2	NOUN
ijassa-429	157	14	=	=	SYM
ijassa-429	157	15	n∑	n∑	NOUN
ijassa-429	157	16	n=0	n=0	PROPN
ijassa-429	157	17	(	(	PUNCT
ijassa-429	157	18	−1)n2nr(n+	−1)n2nr(n+	PROPN
ijassa-429	157	19	1)pn	1)pn	NUM
ijassa-429	157	20	mn(n+	mn(n+	PROPN
ijassa-429	157	21	1	1	NUM
ijassa-429	157	22	)	)	PUNCT
ijassa-429	157	23	(	(	PUNCT
ijassa-429	157	24	dp	dp	NOUN
ijassa-429	157	25	dt	dt	NOUN
ijassa-429	157	26	)	)	PUNCT
ijassa-429	158	1	=	=	SYM
ijassa-429	158	2	r	r	X
ijassa-429	158	3	(	(	PUNCT
ijassa-429	158	4	dp	dp	NOUN
ijassa-429	158	5	dt	dt	NOUN
ijassa-429	158	6	)	)	PUNCT
ijassa-429	158	7	n∑	n∑	NOUN
ijassa-429	159	1	n=0	n=0	NUM
ijassa-429	159	2	(	(	PUNCT
ijassa-429	159	3	−1)n	−1)n	PROPN
ijassa-429	159	4	(	(	PUNCT
ijassa-429	159	5	2p	2p	NUM
ijassa-429	159	6	m	m	NOUN
ijassa-429	159	7	)	)	PUNCT
ijassa-429	159	8	n	n	CCONJ
ijassa-429	159	9	(	(	PUNCT
ijassa-429	159	10	9	9	NUM
ijassa-429	159	11	)	)	PUNCT
ijassa-429	159	12	in	in	ADP
ijassa-429	159	13	the	the	DET
ijassa-429	159	14	case	case	NOUN
ijassa-429	159	15	2p	2p	NUM
ijassa-429	159	16	=	=	SYM
ijassa-429	159	17	m	m	NOUN
ijassa-429	159	18	,	,	PUNCT
ijassa-429	159	19	we	we	PRON
ijassa-429	159	20	have	have	VERB
ijassa-429	159	21	d2p	d2p	NOUN
ijassa-429	160	1	dt2	dt2	NOUN
ijassa-429	160	2	=	=	SYM
ijassa-429	160	3	r	r	NOUN
ijassa-429	160	4	(	(	PUNCT
ijassa-429	160	5	dp	dp	NOUN
ijassa-429	160	6	dt	dt	NOUN
ijassa-429	160	7	)	)	PUNCT
ijassa-429	160	8	n∑	n∑	CCONJ
ijassa-429	160	9	n=0	n=0	PROPN
ijassa-429	160	10	(	(	PUNCT
ijassa-429	160	11	−1)n	−1)n	PROPN
ijassa-429	160	12	hence	hence	ADV
ijassa-429	160	13	,	,	PUNCT
ijassa-429	160	14	when	when	SCONJ
ijassa-429	160	15	n	n	X
ijassa-429	160	16	is	be	AUX
ijassa-429	160	17	odd	odd	ADJ
ijassa-429	160	18	,	,	PUNCT
ijassa-429	160	19	it	it	PRON
ijassa-429	160	20	holds	hold	VERB
ijassa-429	160	21	that	that	SCONJ
ijassa-429	160	22	d2p	d2p	NOUN
ijassa-429	160	23	dt2	dt2	PROPN
ijassa-429	160	24	|p	|p	PROPN
ijassa-429	160	25	=	=	NOUN
ijassa-429	160	26	m	m	VERB
ijassa-429	160	27	2	2	NUM
ijassa-429	160	28	=	=	SYM
ijassa-429	160	29	0	0	NUM
ijassa-429	160	30	it	it	PRON
ijassa-429	160	31	follows	follow	VERB
ijassa-429	160	32	from	from	ADP
ijassa-429	160	33	the	the	DET
ijassa-429	160	34	chain	chain	NOUN
ijassa-429	160	35	rule	rule	NOUN
ijassa-429	160	36	of	of	ADP
ijassa-429	160	37	derivatives	derivative	NOUN
ijassa-429	160	38	[	[	X
ijassa-429	160	39	14	14	NUM
ijassa-429	160	40	-	-	SYM
ijassa-429	160	41	15	15	NUM
ijassa-429	160	42	]	]	PUNCT
ijassa-429	160	43	:	:	PUNCT
ijassa-429	161	1	d	d	X
ijassa-429	161	2	dt	dt	X
ijassa-429	161	3	(	(	PUNCT
ijassa-429	161	4	dp	dp	NOUN
ijassa-429	161	5	dt	dt	NOUN
ijassa-429	161	6	)	)	PUNCT
ijassa-429	161	7	=	=	PUNCT
ijassa-429	162	1	d	d	NUM
ijassa-429	162	2	dp	dp	NOUN
ijassa-429	162	3	(	(	PUNCT
ijassa-429	162	4	dp	dp	NOUN
ijassa-429	162	5	dt	dt	NOUN
ijassa-429	162	6	)	)	PUNCT
ijassa-429	162	7	×	×	NOUN
ijassa-429	162	8	dp	dp	NOUN
ijassa-429	162	9	dt	dt	NOUN
ijassa-429	162	10	that	that	SCONJ
ijassa-429	162	11	the	the	DET
ijassa-429	162	12	derivative	derivative	NOUN
ijassa-429	162	13	of	of	ADP
ijassa-429	162	14	dp	dp	NOUN
ijassa-429	162	15	dt	dt	PROPN
ijassa-429	162	16	with	with	ADP
ijassa-429	162	17	respect	respect	NOUN
ijassa-429	162	18	to	to	ADP
ijassa-429	162	19	t	t	PROPN
ijassa-429	162	20	is	be	AUX
ijassa-429	162	21	equal	equal	ADJ
ijassa-429	162	22	to	to	ADP
ijassa-429	162	23	the	the	DET
ijassa-429	162	24	derivative	derivative	NOUN
ijassa-429	162	25	of	of	ADP
ijassa-429	162	26	dp	dp	NOUN
ijassa-429	162	27	dt	dt	PROPN
ijassa-429	162	28	with	with	ADP
ijassa-429	162	29	respect	respect	NOUN
ijassa-429	162	30	to	to	ADP
ijassa-429	162	31	p	p	NOUN
ijassa-429	162	32	.	.	PUNCT
ijassa-429	163	1	the	the	DET
ijassa-429	163	2	value	value	NOUN
ijassa-429	163	3	for	for	ADP
ijassa-429	163	4	dp	dp	NOUN
ijassa-429	163	5	dt	dt	NOUN
ijassa-429	163	6	decreases	decrease	VERB
ijassa-429	163	7	at	at	ADP
ijassa-429	163	8	it	it	PRON
ijassa-429	163	9	nears	near	VERB
ijassa-429	163	10	its	its	PRON
ijassa-429	163	11	upper	upper	ADJ
ijassa-429	163	12	bound	bind	VERB
ijassa-429	163	13	but	but	CCONJ
ijassa-429	163	14	never	never	ADV
ijassa-429	163	15	becomes	become	VERB
ijassa-429	163	16	0	0	NUM
ijassa-429	163	17	.	.	PUNCT
ijassa-429	164	1	it	it	PRON
ijassa-429	164	2	is	be	AUX
ijassa-429	164	3	always	always	ADV
ijassa-429	164	4	positive	positive	ADJ
ijassa-429	164	5	(	(	PUNCT
ijassa-429	164	6	theorem	theorem	NOUN
ijassa-429	164	7	3	3	NUM
ijassa-429	164	8	)	)	PUNCT
ijassa-429	164	9	.	.	PUNCT
ijassa-429	165	1	continued	continue	VERB
ijassa-429	165	2	simplification	simplification	NOUN
ijassa-429	165	3	of	of	ADP
ijassa-429	165	4	the	the	DET
ijassa-429	165	5	modified	modify	VERB
ijassa-429	165	6	alternating	alternate	VERB
ijassa-429	165	7	maclaurin	maclaurin	NOUN
ijassa-429	165	8	series	series	NOUN
ijassa-429	165	9	and	and	CCONJ
ijassa-429	165	10	its	its	PRON
ijassa-429	165	11	truncations	truncation	NOUN
ijassa-429	165	12	,	,	PUNCT
ijassa-429	165	13	as	as	SCONJ
ijassa-429	165	14	shown	show	VERB
ijassa-429	165	15	below	below	ADV
ijassa-429	165	16	,	,	PUNCT
ijassa-429	165	17	reveals	reveal	VERB
ijassa-429	165	18	its	its	PRON
ijassa-429	165	19	properties	property	NOUN
ijassa-429	165	20	and	and	CCONJ
ijassa-429	165	21	its	its	PRON
ijassa-429	165	22	relationship	relationship	NOUN
ijassa-429	165	23	to	to	ADP
ijassa-429	165	24	the	the	DET
ijassa-429	165	25	form	form	NOUN
ijassa-429	165	26	of	of	ADP
ijassa-429	165	27	a	a	DET
ijassa-429	165	28	transcritical	transcritical	ADJ
ijassa-429	165	29	bifurcation	bifurcation	NOUN
ijassa-429	165	30	.	.	PUNCT
ijassa-429	166	1	88	88	NUM
ijassa-429	166	2	anne	anne	PROPN
ijassa-429	166	3	talkington	talkington	NOUN
ijassa-429	166	4	:	:	PUNCT
ijassa-429	166	5	an	an	DET
ijassa-429	166	6	extension	extension	NOUN
ijassa-429	166	7	of	of	ADP
ijassa-429	166	8	a	a	DET
ijassa-429	166	9	logistic	logistic	ADJ
ijassa-429	166	10	model	model	NOUN
ijassa-429	166	11	for	for	ADP
ijassa-429	166	12	microbial	microbial	ADJ
ijassa-429	166	13	kinetics	kinetic	NOUN
ijassa-429	166	14	4	4	NUM
ijassa-429	166	15	simplified	simplify	VERB
ijassa-429	166	16	series	series	NOUN
ijassa-429	166	17	dp	dp	NOUN
ijassa-429	166	18	dt	dt	NOUN
ijassa-429	166	19	=	=	PUNCT
ijassa-429	166	20	rp	rp	NOUN
ijassa-429	166	21	∞∑	∞∑	PROPN
ijassa-429	166	22	n=0	n=0	NUM
ijassa-429	166	23	(	(	PUNCT
ijassa-429	166	24	−1)n	−1)n	X
ijassa-429	166	25	n+	n+	ADP
ijassa-429	166	26	1	1	NUM
ijassa-429	166	27	(	(	PUNCT
ijassa-429	166	28	2p	2p	NUM
ijassa-429	166	29	m	m	NOUN
ijassa-429	166	30	)	)	PUNCT
ijassa-429	166	31	n	n	NOUN
ijassa-429	166	32	=	=	SYM
ijassa-429	166	33	rp	rp	NOUN
ijassa-429	167	1	[	[	X
ijassa-429	167	2	1−	1−	NUM
ijassa-429	167	3	1	1	NUM
ijassa-429	167	4	2	2	NUM
ijassa-429	167	5	(	(	PUNCT
ijassa-429	167	6	2p	2p	NUM
ijassa-429	167	7	m	m	NOUN
ijassa-429	167	8	)	)	PUNCT
ijassa-429	168	1	+	+	CCONJ
ijassa-429	168	2	1	1	NUM
ijassa-429	168	3	3	3	NUM
ijassa-429	168	4	(	(	PUNCT
ijassa-429	168	5	2p	2p	NUM
ijassa-429	168	6	m	m	NOUN
ijassa-429	168	7	)	)	PUNCT
ijassa-429	168	8	2	2	NUM
ijassa-429	168	9	−	−	NOUN
ijassa-429	168	10	1	1	NUM
ijassa-429	168	11	4	4	NUM
ijassa-429	168	12	(	(	PUNCT
ijassa-429	168	13	2p	2p	NUM
ijassa-429	168	14	m	m	NOUN
ijassa-429	168	15	)	)	PUNCT
ijassa-429	168	16	3	3	NUM
ijassa-429	169	1	+	+	CCONJ
ijassa-429	169	2	1	1	NUM
ijassa-429	169	3	5	5	NUM
ijassa-429	169	4	(	(	PUNCT
ijassa-429	169	5	2p	2p	NUM
ijassa-429	169	6	m	m	NOUN
ijassa-429	169	7	)	)	PUNCT
ijassa-429	169	8	4	4	NUM
ijassa-429	169	9	−	−	NOUN
ijassa-429	169	10	1	1	NUM
ijassa-429	169	11	6	6	NUM
ijassa-429	169	12	(	(	PUNCT
ijassa-429	169	13	2p	2p	NUM
ijassa-429	169	14	m	m	NOUN
ijassa-429	169	15	)	)	PUNCT
ijassa-429	169	16	5	5	NUM
ijassa-429	170	1	+	+	CCONJ
ijassa-429	170	2	...	...	PUNCT
ijassa-429	170	3	]	]	X
ijassa-429	170	4	(	(	PUNCT
ijassa-429	170	5	10	10	NUM
ijassa-429	170	6	)	)	PUNCT
ijassa-429	170	7	theorem	theorem	NOUN
ijassa-429	170	8	1	1	NUM
ijassa-429	170	9	for	for	ADP
ijassa-429	170	10	equation	equation	NOUN
ijassa-429	170	11	(	(	PUNCT
ijassa-429	170	12	10	10	NUM
ijassa-429	170	13	)	)	PUNCT
ijassa-429	170	14	,	,	PUNCT
ijassa-429	170	15	(	(	PUNCT
ijassa-429	170	16	i	i	NOUN
ijassa-429	170	17	)	)	PUNCT
ijassa-429	170	18	the	the	DET
ijassa-429	170	19	closed	closed	ADJ
ijassa-429	170	20	form	form	NOUN
ijassa-429	170	21	of	of	ADP
ijassa-429	170	22	the	the	DET
ijassa-429	170	23	series	series	NOUN
ijassa-429	170	24	on	on	ADP
ijassa-429	170	25	the	the	DET
ijassa-429	170	26	right	right	ADJ
ijassa-429	170	27	-	-	PUNCT
ijassa-429	170	28	hand	hand	NOUN
ijassa-429	170	29	side	side	NOUN
ijassa-429	170	30	is	be	AUX
ijassa-429	170	31	dp	dp	NOUN
ijassa-429	170	32	dt	dt	NOUN
ijassa-429	170	33	=	=	PUNCT
ijassa-429	170	34	rln(1	rln(1	X
ijassa-429	171	1	+	+	CCONJ
ijassa-429	171	2	p	p	X
ijassa-429	171	3	m	m	VERB
ijassa-429	171	4	2	2	NUM
ijassa-429	171	5	)	)	PUNCT
ijassa-429	171	6	m	m	VERB
ijassa-429	171	7	2	2	NUM
ijassa-429	171	8	;	;	PUNCT
ijassa-429	171	9	(	(	PUNCT
ijassa-429	171	10	ii	ii	NOUN
ijassa-429	171	11	)	)	PUNCT
ijassa-429	171	12	it	it	PRON
ijassa-429	171	13	holds	hold	VERB
ijassa-429	171	14	that	that	SCONJ
ijassa-429	171	15	dp	dp	NOUN
ijassa-429	171	16	dt	dt	X
ijassa-429	171	17	>	>	X
ijassa-429	171	18	0	0	PUNCT
ijassa-429	172	1	at	at	ADP
ijassa-429	172	2	any	any	DET
ijassa-429	172	3	time	time	NOUN
ijassa-429	172	4	t.	t.	NOUN
ijassa-429	172	5	proof	proof	NOUN
ijassa-429	172	6	(	(	PUNCT
ijassa-429	172	7	i	i	NOUN
ijassa-429	172	8	)	)	PUNCT
ijassa-429	172	9	equation	equation	NOUN
ijassa-429	172	10	(	(	PUNCT
ijassa-429	172	11	10	10	NUM
ijassa-429	172	12	)	)	PUNCT
ijassa-429	172	13	is	be	AUX
ijassa-429	172	14	simplified	simplify	VERB
ijassa-429	172	15	to	to	ADP
ijassa-429	172	16	dp	dp	NOUN
ijassa-429	172	17	dt	dt	NOUN
ijassa-429	172	18	=	=	SYM
ijassa-429	172	19	r	r	NOUN
ijassa-429	172	20	∑∞	∑∞	NOUN
ijassa-429	172	21	n=0	n=0	NUM
ijassa-429	172	22	(	(	PUNCT
ijassa-429	172	23	−1)n2npn+1	−1)n2npn+1	NOUN
ijassa-429	172	24	mn(n+1	mn(n+1	NOUN
ijassa-429	172	25	)	)	PUNCT
ijassa-429	172	26	(	(	PUNCT
ijassa-429	172	27	by	by	ADP
ijassa-429	172	28	cancelling	cancel	VERB
ijassa-429	172	29	n	n	PRON
ijassa-429	172	30	!	!	PUNCT
ijassa-429	172	31	)	)	PUNCT
ijassa-429	172	32	.	.	PUNCT
ijassa-429	173	1	then	then	ADV
ijassa-429	173	2	we	we	PRON
ijassa-429	173	3	have	have	VERB
ijassa-429	173	4	dp	dp	NOUN
ijassa-429	173	5	dt	dt	NOUN
ijassa-429	173	6	=	=	SYM
ijassa-429	173	7	r	r	NOUN
ijassa-429	173	8	∞∑	∞∑	PROPN
ijassa-429	173	9	n=0	n=0	NUM
ijassa-429	173	10	(	(	PUNCT
ijassa-429	173	11	−1)n2npn+1	−1)n2npn+1	ADJ
ijassa-429	173	12	mn+1(n+	mn+1(n+	NOUN
ijassa-429	173	13	1	1	X
ijassa-429	173	14	)	)	PUNCT
ijassa-429	173	15	=	=	SYM
ijassa-429	174	1	rp	rp	ADP
ijassa-429	174	2	∞∑	∞∑	PROPN
ijassa-429	174	3	n=0	n=0	NUM
ijassa-429	174	4	(	(	PUNCT
ijassa-429	174	5	−1)n	−1)n	X
ijassa-429	174	6	(	(	PUNCT
ijassa-429	174	7	2	2	NUM
ijassa-429	174	8	pm	pm	NOUN
ijassa-429	174	9	)	)	PUNCT
ijassa-429	174	10	n	n	X
ijassa-429	174	11	n+	n+	ADP
ijassa-429	174	12	1	1	X
ijassa-429	174	13	=	=	SYM
ijassa-429	174	14	rp	rp	NOUN
ijassa-429	174	15	∞∑	∞∑	NOUN
ijassa-429	174	16	n=0	n=0	NUM
ijassa-429	174	17	(	(	PUNCT
ijassa-429	174	18	−2p	−2p	PROPN
ijassa-429	174	19	m	m	PROPN
ijassa-429	174	20	)	)	PUNCT
ijassa-429	174	21	n	n	X
ijassa-429	174	22	n+	n+	ADP
ijassa-429	175	1	1	1	NUM
ijassa-429	175	2	=	=	SYM
ijassa-429	175	3	rp	rp	NOUN
ijassa-429	176	1	[	[	X
ijassa-429	176	2	1	1	NUM
ijassa-429	176	3	+	+	NOUN
ijassa-429	176	4	x	x	SYM
ijassa-429	176	5	2	2	NUM
ijassa-429	176	6	+	+	NUM
ijassa-429	176	7	x2	x2	PROPN
ijassa-429	176	8	3	3	NUM
ijassa-429	176	9	+	+	CCONJ
ijassa-429	176	10	x3	x3	ADJ
ijassa-429	176	11	4	4	NUM
ijassa-429	176	12	+	+	CCONJ
ijassa-429	176	13	...	...	PUNCT
ijassa-429	177	1	+	+	NUM
ijassa-429	177	2	xn	xn	NOUN
ijassa-429	177	3	n+	n+	ADP
ijassa-429	177	4	1	1	NUM
ijassa-429	177	5	+	+	CCONJ
ijassa-429	177	6	...	...	PUNCT
ijassa-429	177	7	]	]	X
ijassa-429	177	8	(	(	PUNCT
ijassa-429	177	9	for	for	ADP
ijassa-429	177	10	x	x	X
ijassa-429	177	11	=	=	SYM
ijassa-429	177	12	−2p	−2p	NUM
ijassa-429	177	13	m	m	NOUN
ijassa-429	177	14	)	)	PUNCT
ijassa-429	178	1	=	=	PUNCT
ijassa-429	179	1	rp	rp	NOUN
ijassa-429	179	2	x	x	PUNCT
ijassa-429	180	1	[	[	X
ijassa-429	180	2	x+	x+	ADJ
ijassa-429	180	3	x2	x2	NOUN
ijassa-429	180	4	2	2	NUM
ijassa-429	180	5	+	+	CCONJ
ijassa-429	180	6	x3	x3	ADJ
ijassa-429	180	7	3	3	NUM
ijassa-429	180	8	+	+	CCONJ
ijassa-429	180	9	x4	x4	PROPN
ijassa-429	180	10	4	4	NUM
ijassa-429	180	11	+	+	CCONJ
ijassa-429	180	12	...	...	PUNCT
ijassa-429	181	1	+	+	CCONJ
ijassa-429	181	2	xn+1	xn+1	NUM
ijassa-429	181	3	n+	n+	NUM
ijassa-429	181	4	1	1	NUM
ijassa-429	181	5	+	+	CCONJ
ijassa-429	181	6	...	...	PUNCT
ijassa-429	181	7	]	]	PUNCT
ijassa-429	182	1	=	=	PUNCT
ijassa-429	182	2	rp	rp	NOUN
ijassa-429	182	3	x	x	X
ijassa-429	182	4	(	(	PUNCT
ijassa-429	182	5	−1)ln(1−	−1)ln(1−	NOUN
ijassa-429	182	6	x	x	X
ijassa-429	182	7	)	)	PUNCT
ijassa-429	183	1	=	=	SYM
ijassa-429	183	2	r	r	NOUN
ijassa-429	183	3	m	m	VERB
ijassa-429	183	4	2	2	NUM
ijassa-429	183	5	ln(1	ln(1	NOUN
ijassa-429	183	6	+	+	NUM
ijassa-429	183	7	2p	2p	NUM
ijassa-429	183	8	m	m	NOUN
ijassa-429	183	9	)	)	PUNCT
ijassa-429	183	10	by	by	ADP
ijassa-429	183	11	the	the	DET
ijassa-429	183	12	taylor	taylor	PROPN
ijassa-429	183	13	expansion	expansion	NOUN
ijassa-429	183	14	of	of	ADP
ijassa-429	183	15	natural	natural	ADJ
ijassa-429	183	16	logarithm	logarithm	NOUN
ijassa-429	183	17	:	:	PUNCT
ijassa-429	184	1	ln(1	ln(1	NOUN
ijassa-429	184	2	−	−	PROPN
ijassa-429	184	3	x	x	SYM
ijassa-429	184	4	)	)	PUNCT
ijassa-429	184	5	=	=	NOUN
ijassa-429	184	6	∑∞	∑∞	NOUN
ijassa-429	185	1	n=0	n=0	NUM
ijassa-429	185	2	xn	xn	PROPN
ijassa-429	185	3	n	n	PROPN
ijassa-429	185	4	for	for	ADP
ijassa-429	185	5	−1	−1	NOUN
ijassa-429	185	6	≤	≤	NUM
ijassa-429	185	7	x	x	PUNCT
ijassa-429	185	8	<	<	X
ijassa-429	185	9	1	1	NUM
ijassa-429	185	10	.	.	PUNCT
ijassa-429	186	1	hence	hence	ADV
ijassa-429	186	2	,	,	PUNCT
ijassa-429	186	3	we	we	PRON
ijassa-429	186	4	have	have	VERB
ijassa-429	186	5	r	r	NOUN
ijassa-429	186	6	=	=	SYM
ijassa-429	186	7	dp	dp	NOUN
ijassa-429	186	8	dt	dt	X
ijassa-429	186	9	ln(1	ln(1	PROPN
ijassa-429	186	10	+	+	NOUN
ijassa-429	186	11	p	p	NOUN
ijassa-429	186	12	m	m	VERB
ijassa-429	186	13	2	2	NUM
ijassa-429	186	14	)	)	PUNCT
ijassa-429	186	15	m	m	VERB
ijassa-429	186	16	2	2	NUM
ijassa-429	186	17	,	,	PUNCT
ijassa-429	186	18	and	and	CCONJ
ijassa-429	186	19	this	this	PRON
ijassa-429	186	20	holds	hold	VERB
ijassa-429	186	21	whenever	whenever	SCONJ
ijassa-429	186	22	−1	−1	NOUN
ijassa-429	186	23	≤	≤	ADV
ijassa-429	186	24	−2p	−2p	PROPN
ijassa-429	186	25	m	m	VERB
ijassa-429	186	26	<	<	X
ijassa-429	186	27	1	1	NUM
ijassa-429	186	28	,	,	PUNCT
ijassa-429	186	29	i.e.	i.e.	X
ijassa-429	186	30	,	,	PUNCT
ijassa-429	186	31	p	p	PROPN
ijassa-429	186	32	≤	≤	NUM
ijassa-429	186	33	m	m	VERB
ijassa-429	186	34	2	2	NUM
ijassa-429	186	35	.	.	PUNCT
ijassa-429	187	1	thus	thus	ADV
ijassa-429	187	2	,	,	PUNCT
ijassa-429	187	3	the	the	DET
ijassa-429	187	4	closed	closed	ADJ
ijassa-429	187	5	form	form	NOUN
ijassa-429	187	6	of	of	ADP
ijassa-429	187	7	the	the	DET
ijassa-429	187	8	series	series	NOUN
ijassa-429	187	9	is	be	AUX
ijassa-429	187	10	given	give	VERB
ijassa-429	187	11	by	by	ADP
ijassa-429	187	12	dp	dp	NOUN
ijassa-429	187	13	dt	dt	NOUN
ijassa-429	187	14	=	=	PUNCT
ijassa-429	187	15	rln(1	rln(1	X
ijassa-429	187	16	+	+	CCONJ
ijassa-429	187	17	p	p	X
ijassa-429	187	18	m	m	VERB
ijassa-429	187	19	2	2	NUM
ijassa-429	187	20	)	)	PUNCT
ijassa-429	187	21	m	m	VERB
ijassa-429	187	22	2	2	NUM
ijassa-429	187	23	.	.	PUNCT
ijassa-429	188	1	(	(	PUNCT
ijassa-429	188	2	11	11	NUM
ijassa-429	188	3	)	)	PUNCT
ijassa-429	188	4	(	(	PUNCT
ijassa-429	188	5	ii	ii	NOUN
ijassa-429	188	6	)	)	PUNCT
ijassa-429	188	7	this	this	PRON
ijassa-429	188	8	is	be	AUX
ijassa-429	188	9	implied	imply	VERB
ijassa-429	188	10	by	by	ADP
ijassa-429	188	11	the	the	DET
ijassa-429	188	12	closed	closed	ADJ
ijassa-429	188	13	form	form	NOUN
ijassa-429	188	14	given	give	VERB
ijassa-429	188	15	in	in	ADP
ijassa-429	188	16	(	(	PUNCT
ijassa-429	188	17	i	i	NOUN
ijassa-429	188	18	)	)	PUNCT
ijassa-429	188	19	.	.	PUNCT
ijassa-429	189	1	theorem	theorem	ADJ
ijassa-429	189	2	2	2	NUM
ijassa-429	189	3	:	:	PUNCT
ijassa-429	189	4	for	for	ADP
ijassa-429	189	5	the	the	DET
ijassa-429	189	6	following	follow	VERB
ijassa-429	189	7	tail	tail	NOUN
ijassa-429	189	8	-	-	PUNCT
ijassa-429	189	9	truncated	truncate	VERB
ijassa-429	189	10	equation	equation	NOUN
ijassa-429	189	11	dp	dp	NOUN
ijassa-429	189	12	dt	dt	NOUN
ijassa-429	189	13	=	=	SYM
ijassa-429	189	14	rp	rp	PROPN
ijassa-429	189	15	n∑	n∑	PROPN
ijassa-429	189	16	n=0	n=0	PROPN
ijassa-429	189	17	(	(	PUNCT
ijassa-429	189	18	−1)n	−1)n	PROPN
ijassa-429	189	19	n+	n+	ADP
ijassa-429	189	20	1	1	NUM
ijassa-429	189	21	(	(	PUNCT
ijassa-429	189	22	2p	2p	NUM
ijassa-429	189	23	m	m	NOUN
ijassa-429	189	24	)	)	PUNCT
ijassa-429	189	25	n	n	CCONJ
ijassa-429	189	26	(	(	PUNCT
ijassa-429	189	27	12	12	NUM
ijassa-429	189	28	)	)	PUNCT
ijassa-429	189	29	advances	advance	NOUN
ijassa-429	189	30	in	in	ADP
ijassa-429	189	31	systems	system	NOUN
ijassa-429	189	32	science	science	NOUN
ijassa-429	189	33	and	and	CCONJ
ijassa-429	189	34	applications	application	NOUN
ijassa-429	189	35	(	(	PUNCT
ijassa-429	189	36	2013	2013	NUM
ijassa-429	189	37	)	)	PUNCT
ijassa-429	189	38	vol.13	vol.13	NOUN
ijassa-429	189	39	no.1	no.1	VERB
ijassa-429	189	40	89	89	NUM
ijassa-429	189	41	(	(	PUNCT
ijassa-429	189	42	i	i	NOUN
ijassa-429	189	43	)	)	PUNCT
ijassa-429	189	44	if	if	SCONJ
ijassa-429	189	45	n	n	PRON
ijassa-429	189	46	is	be	AUX
ijassa-429	189	47	odd	odd	ADJ
ijassa-429	189	48	(	(	PUNCT
ijassa-429	189	49	so	so	ADV
ijassa-429	189	50	the	the	DET
ijassa-429	189	51	highest	high	ADJ
ijassa-429	189	52	power	power	NOUN
ijassa-429	189	53	of	of	ADP
ijassa-429	189	54	p	p	NOUN
ijassa-429	189	55	is	be	AUX
ijassa-429	189	56	even	even	ADV
ijassa-429	189	57	)	)	PUNCT
ijassa-429	189	58	,	,	PUNCT
ijassa-429	189	59	then	then	ADV
ijassa-429	189	60	d2p	d2p	VERB
ijassa-429	189	61	dt2	dt2	PROPN
ijassa-429	189	62	is	be	AUX
ijassa-429	189	63	positive	positive	ADJ
ijassa-429	189	64	when	when	SCONJ
ijassa-429	189	65	p	p	PROPN
ijassa-429	189	66	<	<	X
ijassa-429	189	67	m	m	VERB
ijassa-429	189	68	2	2	NUM
ijassa-429	189	69	,	,	PUNCT
ijassa-429	189	70	is	be	AUX
ijassa-429	189	71	zero	zero	NUM
ijassa-429	189	72	when	when	SCONJ
ijassa-429	189	73	p	p	PROPN
ijassa-429	189	74	=	=	NOUN
ijassa-429	189	75	m	m	NOUN
ijassa-429	189	76	2	2	NUM
ijassa-429	189	77	,	,	PUNCT
ijassa-429	189	78	and	and	CCONJ
ijassa-429	189	79	is	be	AUX
ijassa-429	189	80	negative	negative	ADJ
ijassa-429	189	81	when	when	SCONJ
ijassa-429	189	82	p	p	PROPN
ijassa-429	189	83	>	>	X
ijassa-429	189	84	m	m	PROPN
ijassa-429	189	85	2	2	NUM
ijassa-429	189	86	.	.	PUNCT
ijassa-429	190	1	this	this	PRON
ijassa-429	190	2	is	be	AUX
ijassa-429	190	3	an	an	DET
ijassa-429	190	4	asymmetrical	asymmetrical	ADJ
ijassa-429	190	5	model	model	NOUN
ijassa-429	190	6	.	.	PUNCT
ijassa-429	191	1	(	(	PUNCT
ijassa-429	191	2	ii	ii	NOUN
ijassa-429	191	3	)	)	PUNCT
ijassa-429	191	4	if	if	SCONJ
ijassa-429	191	5	n	n	PRON
ijassa-429	191	6	is	be	AUX
ijassa-429	191	7	even	even	ADV
ijassa-429	191	8	(	(	PUNCT
ijassa-429	191	9	so	so	ADV
ijassa-429	191	10	the	the	DET
ijassa-429	191	11	highest	high	ADJ
ijassa-429	191	12	power	power	NOUN
ijassa-429	191	13	of	of	ADP
ijassa-429	191	14	p	p	NOUN
ijassa-429	191	15	is	be	AUX
ijassa-429	191	16	odd	odd	ADJ
ijassa-429	191	17	)	)	PUNCT
ijassa-429	191	18	,	,	PUNCT
ijassa-429	191	19	then	then	ADV
ijassa-429	191	20	d2p	d2p	NOUN
ijassa-429	191	21	dt2	dt2	PROPN
ijassa-429	191	22	is	be	AUX
ijassa-429	191	23	always	always	ADV
ijassa-429	191	24	positive	positive	ADJ
ijassa-429	191	25	.	.	PUNCT
ijassa-429	192	1	since	since	SCONJ
ijassa-429	192	2	the	the	DET
ijassa-429	192	3	second	second	ADJ
ijassa-429	192	4	derivative	derivative	NOUN
ijassa-429	192	5	is	be	AUX
ijassa-429	192	6	always	always	ADV
ijassa-429	192	7	positive	positive	ADJ
ijassa-429	192	8	,	,	PUNCT
ijassa-429	192	9	the	the	DET
ijassa-429	192	10	first	first	ADJ
ijassa-429	192	11	derivative	derivative	NOUN
ijassa-429	192	12	is	be	AUX
ijassa-429	192	13	always	always	ADV
ijassa-429	192	14	increasing	increase	VERB
ijassa-429	192	15	.	.	PUNCT
ijassa-429	193	1	therefore	therefore	ADV
ijassa-429	193	2	,	,	PUNCT
ijassa-429	193	3	if	if	SCONJ
ijassa-429	193	4	the	the	DET
ijassa-429	193	5	first	first	ADJ
ijassa-429	193	6	derivative	derivative	NOUN
ijassa-429	193	7	is	be	AUX
ijassa-429	193	8	positive	positive	ADJ
ijassa-429	193	9	initially	initially	ADV
ijassa-429	193	10	,	,	PUNCT
ijassa-429	193	11	the	the	DET
ijassa-429	193	12	first	first	ADJ
ijassa-429	193	13	derivative	derivative	NOUN
ijassa-429	193	14	is	be	AUX
ijassa-429	193	15	never	never	ADV
ijassa-429	193	16	zero	zero	NUM
ijassa-429	193	17	or	or	CCONJ
ijassa-429	193	18	negative	negative	ADJ
ijassa-429	193	19	.	.	PUNCT
ijassa-429	194	1	(	(	PUNCT
ijassa-429	194	2	the	the	DET
ijassa-429	194	3	least	least	ADV
ijassa-429	194	4	upper	upper	ADJ
ijassa-429	194	5	bound	bind	VERB
ijassa-429	194	6	of	of	ADP
ijassa-429	194	7	p	p	PROPN
ijassa-429	194	8	is	be	AUX
ijassa-429	194	9	finite	finite	ADJ
ijassa-429	194	10	and	and	CCONJ
ijassa-429	194	11	determined	determine	VERB
ijassa-429	194	12	as	as	SCONJ
ijassa-429	194	13	described	describe	VERB
ijassa-429	194	14	in	in	ADP
ijassa-429	194	15	theorem	theorem	ADJ
ijassa-429	194	16	3	3	NUM
ijassa-429	194	17	.	.	PUNCT
ijassa-429	194	18	)	)	PUNCT
ijassa-429	195	1	proof	proof	NOUN
ijassa-429	195	2	it	it	PRON
ijassa-429	195	3	has	have	AUX
ijassa-429	195	4	been	be	AUX
ijassa-429	195	5	established	establish	VERB
ijassa-429	195	6	above	above	ADP
ijassa-429	195	7	that	that	PRON
ijassa-429	195	8	in	in	ADP
ijassa-429	195	9	the	the	DET
ijassa-429	195	10	case	case	NOUN
ijassa-429	195	11	2p	2p	NUM
ijassa-429	195	12	=	=	SYM
ijassa-429	195	13	m	m	NOUN
ijassa-429	195	14	d2p	d2p	NOUN
ijassa-429	196	1	dt2	dt2	NOUN
ijassa-429	196	2	=	=	SYM
ijassa-429	196	3	r	r	NOUN
ijassa-429	196	4	(	(	PUNCT
ijassa-429	196	5	dp	dp	NOUN
ijassa-429	196	6	dt	dt	NOUN
ijassa-429	196	7	)	)	PUNCT
ijassa-429	197	1	∞∑	∞∑	PROPN
ijassa-429	197	2	n=0	n=0	NUM
ijassa-429	197	3	(	(	PUNCT
ijassa-429	197	4	−1)n	−1)n	PROPN
ijassa-429	197	5	=	=	SYM
ijassa-429	197	6	r	r	NOUN
ijassa-429	197	7	(	(	PUNCT
ijassa-429	197	8	dp	dp	NOUN
ijassa-429	197	9	dt	dt	NOUN
ijassa-429	197	10	)	)	PUNCT
ijassa-429	198	1	[	[	X
ijassa-429	198	2	1−	1−	NUM
ijassa-429	198	3	1	1	NUM
ijassa-429	198	4	+	+	CCONJ
ijassa-429	198	5	1−	1−	NUM
ijassa-429	198	6	1	1	NUM
ijassa-429	198	7	+	+	CCONJ
ijassa-429	198	8	...	...	PUNCT
ijassa-429	198	9	]	]	PUNCT
ijassa-429	198	10	for	for	ADP
ijassa-429	198	11	an	an	DET
ijassa-429	198	12	even	even	ADJ
ijassa-429	198	13	number	number	NOUN
ijassa-429	198	14	of	of	ADP
ijassa-429	198	15	terms	term	NOUN
ijassa-429	198	16	,	,	PUNCT
ijassa-429	198	17	or	or	CCONJ
ijassa-429	198	18	odd	odd	ADJ
ijassa-429	198	19	n	n	NOUN
ijassa-429	198	20	:	:	PUNCT
ijassa-429	198	21	case	case	NOUN
ijassa-429	198	22	2p	2p	NUM
ijassa-429	198	23	=	=	NOUN
ijassa-429	198	24	m	m	NOUN
ijassa-429	198	25	.	.	PUNCT
ijassa-429	199	1	the	the	DET
ijassa-429	199	2	truncation	truncation	NOUN
ijassa-429	199	3	of	of	ADP
ijassa-429	199	4	the	the	DET
ijassa-429	199	5	above	above	ADJ
ijassa-429	199	6	equation	equation	NOUN
ijassa-429	199	7	results	result	NOUN
ijassa-429	199	8	in	in	ADP
ijassa-429	199	9	an	an	DET
ijassa-429	199	10	even	even	ADV
ijassa-429	199	11	pairing	pairing	NOUN
ijassa-429	199	12	of	of	ADP
ijassa-429	199	13	terms	term	NOUN
ijassa-429	199	14	that	that	PRON
ijassa-429	199	15	cancel	cancel	VERB
ijassa-429	199	16	out	out	ADP
ijassa-429	199	17	,	,	PUNCT
ijassa-429	199	18	and	and	CCONJ
ijassa-429	199	19	the	the	DET
ijassa-429	199	20	derivative	derivative	NOUN
ijassa-429	199	21	is	be	AUX
ijassa-429	199	22	equal	equal	ADJ
ijassa-429	199	23	to	to	ADP
ijassa-429	199	24	0	0	NUM
ijassa-429	199	25	.	.	PUNCT
ijassa-429	199	26	case	case	NOUN
ijassa-429	199	27	2p	2p	NOUN
ijassa-429	199	28	<	<	X
ijassa-429	199	29	m	m	NOUN
ijassa-429	199	30	.	.	PUNCT
ijassa-429	200	1	d2p	d2p	NOUN
ijassa-429	200	2	dt2	dt2	NOUN
ijassa-429	200	3	=	=	SYM
ijassa-429	200	4	r	r	NOUN
ijassa-429	200	5	(	(	PUNCT
ijassa-429	200	6	dp	dp	NOUN
ijassa-429	200	7	dt	dt	NOUN
ijassa-429	200	8	)	)	PUNCT
ijassa-429	201	1	∞∑	∞∑	PROPN
ijassa-429	201	2	n=0	n=0	NUM
ijassa-429	201	3	(	(	PUNCT
ijassa-429	201	4	−1)n	−1)n	PROPN
ijassa-429	201	5	=	=	SYM
ijassa-429	201	6	r	r	NOUN
ijassa-429	201	7	(	(	PUNCT
ijassa-429	201	8	dp	dp	NOUN
ijassa-429	201	9	dt	dt	NOUN
ijassa-429	201	10	)	)	PUNCT
ijassa-429	202	1	[	[	X
ijassa-429	202	2	1−	1−	NUM
ijassa-429	202	3	(	(	PUNCT
ijassa-429	202	4	2p	2p	NUM
ijassa-429	202	5	m	m	NOUN
ijassa-429	202	6	)	)	PUNCT
ijassa-429	203	1	+	+	ADJ
ijassa-429	203	2	(	(	PUNCT
ijassa-429	203	3	2p	2p	NUM
ijassa-429	203	4	m	m	NOUN
ijassa-429	203	5	)	)	PUNCT
ijassa-429	203	6	2−	2−	NUM
ijassa-429	203	7	(	(	PUNCT
ijassa-429	203	8	2p	2p	NUM
ijassa-429	203	9	m	m	NOUN
ijassa-429	203	10	)	)	PUNCT
ijassa-429	203	11	3	3	X
ijassa-429	203	12	+	+	NOUN
ijassa-429	203	13	(	(	PUNCT
ijassa-429	203	14	2p	2p	NUM
ijassa-429	203	15	m	m	NOUN
ijassa-429	203	16	)	)	PUNCT
ijassa-429	203	17	4−	4−	PROPN
ijassa-429	203	18	(	(	PUNCT
ijassa-429	203	19	2p	2p	NUM
ijassa-429	203	20	m	m	NOUN
ijassa-429	203	21	)	)	PUNCT
ijassa-429	203	22	5	5	NUM
ijassa-429	203	23	+	+	CCONJ
ijassa-429	203	24	...	...	PUNCT
ijassa-429	203	25	]	]	PUNCT
ijassa-429	203	26	a	a	DET
ijassa-429	203	27	grouping	grouping	NOUN
ijassa-429	203	28	of	of	ADP
ijassa-429	203	29	the	the	DET
ijassa-429	203	30	first	first	ADJ
ijassa-429	203	31	6	6	NUM
ijassa-429	203	32	terms	term	NOUN
ijassa-429	203	33	of	of	ADP
ijassa-429	203	34	the	the	DET
ijassa-429	203	35	second	second	ADJ
ijassa-429	203	36	derivative	derivative	ADJ
ijassa-429	203	37	results	result	NOUN
ijassa-429	203	38	in	in	ADP
ijassa-429	203	39	d2p	d2p	NOUN
ijassa-429	203	40	dt2	dt2	NOUN
ijassa-429	203	41	=	=	SYM
ijassa-429	203	42	r	r	NOUN
ijassa-429	203	43	(	(	PUNCT
ijassa-429	203	44	dp	dp	NOUN
ijassa-429	203	45	dt	dt	NOUN
ijassa-429	203	46	)	)	PUNCT
ijassa-429	204	1	[	[	PUNCT
ijassa-429	204	2	[	[	X
ijassa-429	204	3	1−	1−	NUM
ijassa-429	204	4	(	(	PUNCT
ijassa-429	204	5	2p	2p	NUM
ijassa-429	204	6	m	m	NOUN
ijassa-429	204	7	)	)	PUNCT
ijassa-429	204	8	]	]	PUNCT
ijassa-429	205	1	+	+	CCONJ
ijassa-429	205	2	[	[	X
ijassa-429	205	3	(	(	PUNCT
ijassa-429	205	4	2p	2p	NUM
ijassa-429	205	5	m	m	NOUN
ijassa-429	205	6	)	)	PUNCT
ijassa-429	205	7	2	2	NUM
ijassa-429	205	8	−	−	PROPN
ijassa-429	205	9	(	(	PUNCT
ijassa-429	205	10	2p	2p	NUM
ijassa-429	205	11	m	m	NOUN
ijassa-429	205	12	)	)	PUNCT
ijassa-429	205	13	3	3	NUM
ijassa-429	205	14	]	]	PUNCT
ijassa-429	205	15	+	+	CCONJ
ijassa-429	206	1	[	[	X
ijassa-429	206	2	(	(	PUNCT
ijassa-429	206	3	2p	2p	NUM
ijassa-429	206	4	m	m	NOUN
ijassa-429	206	5	)	)	PUNCT
ijassa-429	206	6	4	4	NUM
ijassa-429	206	7	−	−	PROPN
ijassa-429	206	8	(	(	PUNCT
ijassa-429	206	9	2p	2p	NUM
ijassa-429	206	10	m	m	NOUN
ijassa-429	206	11	)	)	PUNCT
ijassa-429	206	12	5	5	NUM
ijassa-429	206	13	]	]	PUNCT
ijassa-429	206	14	]	]	PUNCT
ijassa-429	206	15	>	>	X
ijassa-429	206	16	0	0	X
ijassa-429	206	17	.	.	PUNCT
ijassa-429	206	18	case	case	NOUN
ijassa-429	206	19	2p	2p	NOUN
ijassa-429	206	20	>	>	X
ijassa-429	206	21	m	m	NOUN
ijassa-429	206	22	.	.	PUNCT
ijassa-429	207	1	d2p	d2p	NOUN
ijassa-429	207	2	dt2	dt2	NOUN
ijassa-429	207	3	=	=	SYM
ijassa-429	207	4	r	r	NOUN
ijassa-429	207	5	(	(	PUNCT
ijassa-429	207	6	dp	dp	NOUN
ijassa-429	207	7	dt	dt	NOUN
ijassa-429	207	8	)	)	PUNCT
ijassa-429	208	1	∞∑	∞∑	PROPN
ijassa-429	208	2	n=0	n=0	NUM
ijassa-429	208	3	(	(	PUNCT
ijassa-429	208	4	−1)n	−1)n	PROPN
ijassa-429	208	5	=	=	SYM
ijassa-429	208	6	r	r	NOUN
ijassa-429	208	7	(	(	PUNCT
ijassa-429	208	8	dp	dp	NOUN
ijassa-429	208	9	dt	dt	NOUN
ijassa-429	208	10	)	)	PUNCT
ijassa-429	208	11	[	[	PUNCT
ijassa-429	208	12	1−	1−	NUM
ijassa-429	208	13	(	(	PUNCT
ijassa-429	208	14	2p	2p	NUM
ijassa-429	208	15	m	m	NOUN
ijassa-429	208	16	)	)	PUNCT
ijassa-429	209	1	+	+	ADJ
ijassa-429	209	2	(	(	PUNCT
ijassa-429	209	3	2p	2p	NUM
ijassa-429	209	4	m	m	NOUN
ijassa-429	209	5	)	)	PUNCT
ijassa-429	209	6	2−	2−	NUM
ijassa-429	209	7	(	(	PUNCT
ijassa-429	209	8	2p	2p	NUM
ijassa-429	209	9	m	m	NOUN
ijassa-429	209	10	)	)	PUNCT
ijassa-429	209	11	3	3	X
ijassa-429	209	12	+	+	NOUN
ijassa-429	209	13	(	(	PUNCT
ijassa-429	209	14	2p	2p	NUM
ijassa-429	209	15	m	m	NOUN
ijassa-429	209	16	)	)	PUNCT
ijassa-429	209	17	4−	4−	PROPN
ijassa-429	209	18	(	(	PUNCT
ijassa-429	209	19	2p	2p	NUM
ijassa-429	209	20	m	m	NOUN
ijassa-429	209	21	)	)	PUNCT
ijassa-429	209	22	5	5	NUM
ijassa-429	209	23	+	+	NOUN
ijassa-429	209	24	...	...	PUNCT
ijassa-429	209	25	]	]	PUNCT
ijassa-429	209	26	a	a	DET
ijassa-429	209	27	grouping	grouping	NOUN
ijassa-429	209	28	of	of	ADP
ijassa-429	209	29	the	the	DET
ijassa-429	209	30	first	first	ADJ
ijassa-429	209	31	6	6	NUM
ijassa-429	209	32	terms	term	NOUN
ijassa-429	209	33	results	result	VERB
ijassa-429	209	34	in	in	ADP
ijassa-429	209	35	[	[	PUNCT
ijassa-429	209	36	[	[	X
ijassa-429	209	37	1−	1−	NUM
ijassa-429	209	38	(	(	PUNCT
ijassa-429	209	39	2p	2p	NUM
ijassa-429	209	40	m	m	NOUN
ijassa-429	209	41	)	)	PUNCT
ijassa-429	209	42	]	]	PUNCT
ijassa-429	210	1	+	+	PUNCT
ijassa-429	211	1	[	[	X
ijassa-429	211	2	(	(	PUNCT
ijassa-429	211	3	2p	2p	NUM
ijassa-429	211	4	m	m	NOUN
ijassa-429	211	5	)	)	PUNCT
ijassa-429	211	6	2−	2−	NUM
ijassa-429	211	7	(	(	PUNCT
ijassa-429	211	8	2p	2p	NUM
ijassa-429	211	9	m	m	NOUN
ijassa-429	211	10	)	)	PUNCT
ijassa-429	211	11	3]+	3]+	NUM
ijassa-429	212	1	[	[	X
ijassa-429	212	2	(	(	PUNCT
ijassa-429	212	3	2p	2p	NUM
ijassa-429	212	4	m	m	NOUN
ijassa-429	212	5	)	)	PUNCT
ijassa-429	212	6	4−	4−	PROPN
ijassa-429	212	7	(	(	PUNCT
ijassa-429	212	8	2p	2p	NUM
ijassa-429	212	9	m	m	NOUN
ijassa-429	212	10	)	)	PUNCT
ijassa-429	212	11	5	5	NUM
ijassa-429	212	12	]	]	PUNCT
ijassa-429	212	13	]	]	PUNCT
ijassa-429	212	14	<	<	X
ijassa-429	212	15	0	0	X
ijassa-429	212	16	.	.	PUNCT
ijassa-429	213	1	(	(	PUNCT
ijassa-429	213	2	each	each	DET
ijassa-429	213	3	bracket	bracket	NOUN
ijassa-429	213	4	is	be	AUX
ijassa-429	213	5	negative	negative	ADJ
ijassa-429	213	6	.	.	PUNCT
ijassa-429	213	7	)	)	PUNCT
ijassa-429	214	1	for	for	ADP
ijassa-429	214	2	an	an	DET
ijassa-429	214	3	odd	odd	ADJ
ijassa-429	214	4	number	number	NOUN
ijassa-429	214	5	of	of	ADP
ijassa-429	214	6	terms	term	NOUN
ijassa-429	214	7	,	,	PUNCT
ijassa-429	214	8	or	or	CCONJ
ijassa-429	214	9	even	even	ADV
ijassa-429	214	10	n	n	PRON
ijassa-429	214	11	:	:	PUNCT
ijassa-429	214	12	the	the	DET
ijassa-429	214	13	truncation	truncation	NOUN
ijassa-429	214	14	of	of	ADP
ijassa-429	214	15	d2p	d2p	NOUN
ijassa-429	214	16	dt2	dt2	NOUN
ijassa-429	214	17	=	=	SYM
ijassa-429	214	18	r	r	NOUN
ijassa-429	214	19	(	(	PUNCT
ijassa-429	214	20	dp	dp	NOUN
ijassa-429	214	21	dt	dt	NOUN
ijassa-429	214	22	)	)	PUNCT
ijassa-429	214	23	∞∑	∞∑	PROPN
ijassa-429	214	24	n=0	n=0	NUM
ijassa-429	214	25	(	(	PUNCT
ijassa-429	214	26	−1)n	−1)n	PROPN
ijassa-429	214	27	=	=	SYM
ijassa-429	214	28	r	r	NOUN
ijassa-429	214	29	(	(	PUNCT
ijassa-429	214	30	dp	dp	NOUN
ijassa-429	214	31	dt	dt	NOUN
ijassa-429	214	32	)	)	PUNCT
ijassa-429	215	1	[	[	X
ijassa-429	215	2	1−	1−	NUM
ijassa-429	215	3	1	1	NUM
ijassa-429	215	4	+	+	CCONJ
ijassa-429	215	5	1−	1−	NUM
ijassa-429	215	6	1	1	NUM
ijassa-429	215	7	+	+	CCONJ
ijassa-429	215	8	1−	1−	NUM
ijassa-429	215	9	1	1	NUM
ijassa-429	215	10	+	+	CCONJ
ijassa-429	215	11	...	...	PUNCT
ijassa-429	215	12	]	]	PUNCT
ijassa-429	215	13	90	90	NUM
ijassa-429	215	14	anne	anne	PROPN
ijassa-429	215	15	talkington	talkington	NOUN
ijassa-429	215	16	:	:	PUNCT
ijassa-429	215	17	an	an	DET
ijassa-429	215	18	extension	extension	NOUN
ijassa-429	215	19	of	of	ADP
ijassa-429	215	20	a	a	DET
ijassa-429	215	21	logistic	logistic	ADJ
ijassa-429	215	22	model	model	NOUN
ijassa-429	215	23	for	for	ADP
ijassa-429	215	24	microbial	microbial	ADJ
ijassa-429	215	25	kinetics	kinetic	NOUN
ijassa-429	215	26	results	result	NOUN
ijassa-429	215	27	in	in	ADP
ijassa-429	215	28	a	a	DET
ijassa-429	215	29	pairing	pairing	NOUN
ijassa-429	215	30	with	with	ADP
ijassa-429	215	31	an	an	DET
ijassa-429	215	32	additional	additional	ADJ
ijassa-429	215	33	positive	positive	ADJ
ijassa-429	215	34	term	term	NOUN
ijassa-429	215	35	that	that	PRON
ijassa-429	215	36	is	be	AUX
ijassa-429	215	37	not	not	PART
ijassa-429	215	38	cancelled	cancel	VERB
ijassa-429	215	39	.	.	PUNCT
ijassa-429	216	1	so	so	ADV
ijassa-429	216	2	this	this	DET
ijassa-429	216	3	second	second	ADJ
ijassa-429	216	4	derivative	derivative	NOUN
ijassa-429	216	5	is	be	AUX
ijassa-429	216	6	positive	positive	ADJ
ijassa-429	216	7	.	.	PUNCT
ijassa-429	217	1	case	case	NOUN
ijassa-429	217	2	2p	2p	NOUN
ijassa-429	217	3	<	<	X
ijassa-429	217	4	m	m	NOUN
ijassa-429	217	5	.	.	PUNCT
ijassa-429	218	1	d2p	d2p	NOUN
ijassa-429	218	2	dt2	dt2	NOUN
ijassa-429	218	3	=	=	SYM
ijassa-429	218	4	r	r	NOUN
ijassa-429	218	5	(	(	PUNCT
ijassa-429	218	6	dp	dp	NOUN
ijassa-429	218	7	dt	dt	NOUN
ijassa-429	218	8	)	)	PUNCT
ijassa-429	219	1	∞∑	∞∑	PROPN
ijassa-429	219	2	n=0	n=0	NUM
ijassa-429	219	3	(	(	PUNCT
ijassa-429	219	4	−1)n	−1)n	PROPN
ijassa-429	219	5	=	=	SYM
ijassa-429	219	6	r	r	NOUN
ijassa-429	219	7	(	(	PUNCT
ijassa-429	219	8	dp	dp	NOUN
ijassa-429	219	9	dt	dt	NOUN
ijassa-429	219	10	)	)	PUNCT
ijassa-429	219	11	[	[	PUNCT
ijassa-429	219	12	1−	1−	NUM
ijassa-429	219	13	(	(	PUNCT
ijassa-429	219	14	2p	2p	NUM
ijassa-429	219	15	m	m	NOUN
ijassa-429	219	16	)	)	PUNCT
ijassa-429	220	1	+	+	ADJ
ijassa-429	220	2	(	(	PUNCT
ijassa-429	220	3	2p	2p	NUM
ijassa-429	220	4	m	m	NOUN
ijassa-429	220	5	)	)	PUNCT
ijassa-429	220	6	2−	2−	NUM
ijassa-429	220	7	(	(	PUNCT
ijassa-429	220	8	2p	2p	NUM
ijassa-429	220	9	m	m	NOUN
ijassa-429	220	10	)	)	PUNCT
ijassa-429	220	11	3	3	X
ijassa-429	220	12	+	+	NOUN
ijassa-429	220	13	(	(	PUNCT
ijassa-429	220	14	2p	2p	NUM
ijassa-429	220	15	m	m	NOUN
ijassa-429	220	16	)	)	PUNCT
ijassa-429	220	17	4−	4−	PROPN
ijassa-429	220	18	(	(	PUNCT
ijassa-429	220	19	2p	2p	NUM
ijassa-429	220	20	m	m	NOUN
ijassa-429	220	21	)	)	PUNCT
ijassa-429	220	22	5	5	NUM
ijassa-429	220	23	+	+	NOUN
ijassa-429	220	24	...	...	PUNCT
ijassa-429	220	25	]	]	PUNCT
ijassa-429	220	26	a	a	DET
ijassa-429	220	27	grouping	grouping	NOUN
ijassa-429	220	28	of	of	ADP
ijassa-429	220	29	the	the	DET
ijassa-429	220	30	first	first	ADJ
ijassa-429	220	31	5	5	NUM
ijassa-429	220	32	terms	term	NOUN
ijassa-429	220	33	of	of	ADP
ijassa-429	220	34	the	the	DET
ijassa-429	220	35	second	second	ADJ
ijassa-429	220	36	derivative	derivative	ADJ
ijassa-429	220	37	results	result	NOUN
ijassa-429	220	38	in	in	ADP
ijassa-429	220	39	[	[	PUNCT
ijassa-429	220	40	[	[	X
ijassa-429	220	41	1−	1−	NUM
ijassa-429	220	42	(	(	PUNCT
ijassa-429	220	43	2p	2p	NUM
ijassa-429	220	44	m	m	NOUN
ijassa-429	220	45	)	)	PUNCT
ijassa-429	220	46	]	]	PUNCT
ijassa-429	221	1	+	+	CCONJ
ijassa-429	222	1	[	[	X
ijassa-429	222	2	(	(	PUNCT
ijassa-429	222	3	2p	2p	NUM
ijassa-429	222	4	m	m	NOUN
ijassa-429	222	5	)	)	PUNCT
ijassa-429	222	6	2	2	NUM
ijassa-429	222	7	−	−	PROPN
ijassa-429	222	8	(	(	PUNCT
ijassa-429	222	9	2p	2p	NUM
ijassa-429	222	10	m	m	NOUN
ijassa-429	222	11	)	)	PUNCT
ijassa-429	222	12	3	3	NUM
ijassa-429	222	13	]	]	PUNCT
ijassa-429	222	14	+	+	CCONJ
ijassa-429	222	15	(	(	PUNCT
ijassa-429	222	16	2p	2p	NUM
ijassa-429	222	17	m	m	NOUN
ijassa-429	222	18	)	)	PUNCT
ijassa-429	222	19	4	4	NUM
ijassa-429	222	20	]	]	PUNCT
ijassa-429	222	21	>	>	X
ijassa-429	222	22	0	0	X
ijassa-429	222	23	.	.	PUNCT
ijassa-429	222	24	case	case	NOUN
ijassa-429	222	25	2p	2p	NOUN
ijassa-429	222	26	>	>	X
ijassa-429	222	27	m	m	NOUN
ijassa-429	222	28	.	.	PUNCT
ijassa-429	223	1	d2p	d2p	NOUN
ijassa-429	223	2	dt2	dt2	NOUN
ijassa-429	223	3	=	=	SYM
ijassa-429	223	4	r	r	NOUN
ijassa-429	223	5	(	(	PUNCT
ijassa-429	223	6	dp	dp	NOUN
ijassa-429	223	7	dt	dt	NOUN
ijassa-429	223	8	)	)	PUNCT
ijassa-429	224	1	∞∑	∞∑	PROPN
ijassa-429	224	2	n=0	n=0	NUM
ijassa-429	224	3	(	(	PUNCT
ijassa-429	224	4	−1)n	−1)n	PROPN
ijassa-429	224	5	=	=	SYM
ijassa-429	224	6	r	r	NOUN
ijassa-429	224	7	(	(	PUNCT
ijassa-429	224	8	dp	dp	NOUN
ijassa-429	224	9	dt	dt	NOUN
ijassa-429	224	10	)	)	PUNCT
ijassa-429	224	11	[	[	PUNCT
ijassa-429	224	12	1−	1−	NUM
ijassa-429	224	13	(	(	PUNCT
ijassa-429	224	14	2p	2p	NUM
ijassa-429	224	15	m	m	NOUN
ijassa-429	224	16	)	)	PUNCT
ijassa-429	225	1	+	+	ADJ
ijassa-429	225	2	(	(	PUNCT
ijassa-429	225	3	2p	2p	NUM
ijassa-429	225	4	m	m	NOUN
ijassa-429	225	5	)	)	PUNCT
ijassa-429	225	6	2−	2−	NUM
ijassa-429	225	7	(	(	PUNCT
ijassa-429	225	8	2p	2p	NUM
ijassa-429	225	9	m	m	NOUN
ijassa-429	225	10	)	)	PUNCT
ijassa-429	225	11	3	3	X
ijassa-429	225	12	+	+	NOUN
ijassa-429	225	13	(	(	PUNCT
ijassa-429	225	14	2p	2p	NUM
ijassa-429	225	15	m	m	NOUN
ijassa-429	225	16	)	)	PUNCT
ijassa-429	225	17	4−	4−	PROPN
ijassa-429	225	18	(	(	PUNCT
ijassa-429	225	19	2p	2p	NUM
ijassa-429	225	20	m	m	NOUN
ijassa-429	225	21	)	)	PUNCT
ijassa-429	225	22	5	5	NUM
ijassa-429	225	23	+	+	NOUN
ijassa-429	225	24	...	...	PUNCT
ijassa-429	225	25	]	]	PUNCT
ijassa-429	225	26	a	a	DET
ijassa-429	225	27	grouping	grouping	NOUN
ijassa-429	225	28	of	of	ADP
ijassa-429	225	29	the	the	DET
ijassa-429	225	30	first	first	ADJ
ijassa-429	225	31	5	5	NUM
ijassa-429	225	32	terms	term	NOUN
ijassa-429	225	33	results	result	VERB
ijassa-429	225	34	in	in	ADP
ijassa-429	225	35	[	[	PUNCT
ijassa-429	225	36	1	1	NUM
ijassa-429	225	37	+	+	CCONJ
ijassa-429	225	38	[	[	X
ijassa-429	225	39	−	−	X
ijassa-429	225	40	(	(	PUNCT
ijassa-429	225	41	2p	2p	NUM
ijassa-429	225	42	m	m	NOUN
ijassa-429	225	43	)	)	PUNCT
ijassa-429	226	1	+	+	CCONJ
ijassa-429	226	2	(	(	PUNCT
ijassa-429	226	3	2p	2p	NUM
ijassa-429	226	4	m	m	NOUN
ijassa-429	226	5	)	)	PUNCT
ijassa-429	226	6	2	2	NUM
ijassa-429	226	7	]	]	PUNCT
ijassa-429	226	8	+	+	CCONJ
ijassa-429	226	9	[	[	X
ijassa-429	226	10	−	−	X
ijassa-429	226	11	(	(	PUNCT
ijassa-429	226	12	2p	2p	NUM
ijassa-429	226	13	m	m	NOUN
ijassa-429	226	14	)	)	PUNCT
ijassa-429	226	15	3	3	NUM
ijassa-429	226	16	+	+	CCONJ
ijassa-429	226	17	(	(	PUNCT
ijassa-429	226	18	2p	2p	NUM
ijassa-429	226	19	m	m	NOUN
ijassa-429	226	20	)	)	PUNCT
ijassa-429	226	21	4	4	NUM
ijassa-429	226	22	]	]	PUNCT
ijassa-429	226	23	]	]	PUNCT
ijassa-429	226	24	>	>	X
ijassa-429	226	25	0	0	X
ijassa-429	226	26	.	.	PUNCT
ijassa-429	226	27	theorem	theorem	NOUN
ijassa-429	226	28	3	3	NUM
ijassa-429	226	29	:	:	PUNCT
ijassa-429	226	30	for	for	ADP
ijassa-429	226	31	the	the	DET
ijassa-429	226	32	above	above	ADJ
ijassa-429	226	33	tail	tail	NOUN
ijassa-429	226	34	-	-	PUNCT
ijassa-429	226	35	truncated	truncate	VERB
ijassa-429	226	36	equation	equation	NOUN
ijassa-429	226	37	(	(	PUNCT
ijassa-429	226	38	12	12	NUM
ijassa-429	226	39	)	)	PUNCT
ijassa-429	226	40	,	,	PUNCT
ijassa-429	227	1	(	(	PUNCT
ijassa-429	227	2	i	i	NOUN
ijassa-429	227	3	)	)	PUNCT
ijassa-429	227	4	dp	dp	PROPN
ijassa-429	227	5	dt	dt	NOUN
ijassa-429	227	6	is	be	AUX
ijassa-429	227	7	always	always	ADV
ijassa-429	227	8	positive	positive	ADJ
ijassa-429	227	9	(	(	PUNCT
ijassa-429	227	10	i.e.	i.e.	X
ijassa-429	227	11	,	,	PUNCT
ijassa-429	227	12	the	the	DET
ijassa-429	227	13	right	right	ADJ
ijassa-429	227	14	-	-	PUNCT
ijassa-429	227	15	hand	hand	NOUN
ijassa-429	227	16	side	side	NOUN
ijassa-429	227	17	is	be	AUX
ijassa-429	227	18	always	always	ADV
ijassa-429	227	19	positive	positive	ADJ
ijassa-429	227	20	)	)	PUNCT
ijassa-429	227	21	.	.	PUNCT
ijassa-429	228	1	(	(	PUNCT
ijassa-429	228	2	ii	ii	NOUN
ijassa-429	228	3	)	)	PUNCT
ijassa-429	228	4	when	when	SCONJ
ijassa-429	228	5	n	n	X
ijassa-429	228	6	is	be	AUX
ijassa-429	228	7	odd	odd	ADJ
ijassa-429	228	8	(	(	PUNCT
ijassa-429	228	9	i.e.	i.e.	X
ijassa-429	228	10	,	,	PUNCT
ijassa-429	228	11	including	include	VERB
ijassa-429	228	12	up	up	ADP
ijassa-429	228	13	to	to	ADP
ijassa-429	228	14	an	an	DET
ijassa-429	228	15	even	even	ADJ
ijassa-429	228	16	power	power	NOUN
ijassa-429	228	17	of	of	ADP
ijassa-429	228	18	p	p	NOUN
ijassa-429	228	19	in	in	ADP
ijassa-429	228	20	the	the	DET
ijassa-429	228	21	partial	partial	ADJ
ijassa-429	228	22	sum	sum	NOUN
ijassa-429	228	23	)	)	PUNCT
ijassa-429	228	24	,	,	PUNCT
ijassa-429	228	25	the	the	DET
ijassa-429	228	26	equation	equation	NOUN
ijassa-429	228	27	rp	rp	ADP
ijassa-429	228	28	∑n	∑n	PROPN
ijassa-429	228	29	n=0	n=0	NUM
ijassa-429	228	30	(	(	PUNCT
ijassa-429	228	31	−1)n	−1)n	PROPN
ijassa-429	228	32	n+1	n+1	NUM
ijassa-429	228	33	(	(	PUNCT
ijassa-429	228	34	2	2	NUM
ijassa-429	228	35	pm	pm	NOUN
ijassa-429	228	36	)	)	PUNCT
ijassa-429	228	37	n	n	NOUN
ijassa-429	228	38	=	=	SYM
ijassa-429	228	39	0	0	PROPN
ijassa-429	228	40	has	have	VERB
ijassa-429	228	41	a	a	DET
ijassa-429	228	42	unique	unique	ADJ
ijassa-429	228	43	positive	positive	ADJ
ijassa-429	228	44	solution	solution	NOUN
ijassa-429	228	45	and	and	CCONJ
ijassa-429	228	46	the	the	DET
ijassa-429	228	47	supremum	supremum	ADJ
ijassa-429	228	48	value	value	NOUN
ijassa-429	228	49	of	of	ADP
ijassa-429	228	50	p	p	NOUN
ijassa-429	228	51	is	be	AUX
ijassa-429	228	52	determined	determine	VERB
ijassa-429	228	53	by	by	ADP
ijassa-429	228	54	this	this	DET
ijassa-429	228	55	positive	positive	ADJ
ijassa-429	228	56	zero	zero	NUM
ijassa-429	228	57	of	of	ADP
ijassa-429	228	58	the	the	DET
ijassa-429	228	59	equation	equation	NOUN
ijassa-429	228	60	.	.	PUNCT
ijassa-429	229	1	moreover	moreover	ADV
ijassa-429	229	2	,	,	PUNCT
ijassa-429	229	3	it	it	PRON
ijassa-429	229	4	holds	hold	VERB
ijassa-429	229	5	that	that	SCONJ
ijassa-429	229	6	rp	rp	NOUN
ijassa-429	229	7	∑n	∑n	PROPN
ijassa-429	229	8	n=0	n=0	NUM
ijassa-429	229	9	(	(	PUNCT
ijassa-429	229	10	−1)n	−1)n	PROPN
ijassa-429	229	11	n+1	n+1	NUM
ijassa-429	229	12	(	(	PUNCT
ijassa-429	229	13	2	2	NUM
ijassa-429	229	14	pm	pm	NOUN
ijassa-429	229	15	)	)	PUNCT
ijassa-429	229	16	n	n	NOUN
ijassa-429	229	17	=	=	SYM
ijassa-429	229	18	rm	rm	NOUN
ijassa-429	229	19	2	2	NUM
ijassa-429	229	20	∫	∫	PROPN
ijassa-429	229	21	2p	2p	NUM
ijassa-429	229	22	m	m	PROPN
ijassa-429	229	23	0	0	NUM
ijassa-429	229	24	1−xn+1	1−xn+1	NUM
ijassa-429	229	25	1+x	1+x	NUM
ijassa-429	229	26	dx	dx	PROPN
ijassa-429	229	27	.	.	PUNCT
ijassa-429	230	1	these	these	DET
ijassa-429	230	2	models	model	NOUN
ijassa-429	230	3	are	be	AUX
ijassa-429	230	4	all	all	ADV
ijassa-429	230	5	asymmetrical	asymmetrical	ADJ
ijassa-429	230	6	.	.	PUNCT
ijassa-429	231	1	proof	proof	NOUN
ijassa-429	231	2	(	(	PUNCT
ijassa-429	231	3	i	i	NOUN
ijassa-429	231	4	)	)	PUNCT
ijassa-429	231	5	if	if	SCONJ
ijassa-429	231	6	n	n	PRON
ijassa-429	231	7	is	be	AUX
ijassa-429	231	8	even	even	ADV
ijassa-429	231	9	,	,	PUNCT
ijassa-429	231	10	this	this	PRON
ijassa-429	231	11	is	be	AUX
ijassa-429	231	12	clearly	clearly	ADV
ijassa-429	231	13	true	true	ADJ
ijassa-429	231	14	.	.	PUNCT
ijassa-429	232	1	let	let	VERB
ijassa-429	232	2	gn	gn	INTJ
ijassa-429	232	3	(	(	PUNCT
ijassa-429	232	4	x	x	NOUN
ijassa-429	232	5	)	)	PUNCT
ijassa-429	232	6	=	=	SYM
ijassa-429	233	1	n∑	n∑	NOUN
ijassa-429	233	2	n=0	n=0	NUM
ijassa-429	233	3	(	(	PUNCT
ijassa-429	233	4	−1)n	−1)n	PROPN
ijassa-429	233	5	n+	n+	ADP
ijassa-429	233	6	1	1	NUM
ijassa-429	233	7	xn	xn	X
ijassa-429	233	8	.	.	PUNCT
ijassa-429	234	1	then	then	ADV
ijassa-429	234	2	dp	dp	VERB
ijassa-429	234	3	dt	dt	NOUN
ijassa-429	234	4	=	=	PUNCT
ijassa-429	234	5	rp	rp	PROPN
ijassa-429	234	6	n∑	n∑	PROPN
ijassa-429	234	7	n=0	n=0	PROPN
ijassa-429	234	8	(	(	PUNCT
ijassa-429	234	9	−1)n	−1)n	PROPN
ijassa-429	234	10	n+	n+	ADP
ijassa-429	234	11	1	1	NUM
ijassa-429	234	12	(	(	PUNCT
ijassa-429	234	13	2p	2p	NUM
ijassa-429	234	14	m	m	NOUN
ijassa-429	234	15	)	)	PUNCT
ijassa-429	234	16	n	n	NOUN
ijassa-429	234	17	=	=	PRON
ijassa-429	234	18	rpgn	rpgn	NOUN
ijassa-429	234	19	(	(	PUNCT
ijassa-429	234	20	2p	2p	NUM
ijassa-429	234	21	m	m	NOUN
ijassa-429	234	22	)	)	PUNCT
ijassa-429	234	23	.	.	PUNCT
ijassa-429	235	1	since	since	SCONJ
ijassa-429	235	2	xgn	xgn	PROPN
ijassa-429	235	3	(	(	PUNCT
ijassa-429	235	4	x	x	X
ijassa-429	235	5	)	)	PUNCT
ijassa-429	235	6	=	=	SYM
ijassa-429	235	7	∑n	∑n	PROPN
ijassa-429	235	8	n=0	n=0	NUM
ijassa-429	235	9	(	(	PUNCT
ijassa-429	235	10	−1)n	−1)n	X
ijassa-429	235	11	n+1	n+1	PROPN
ijassa-429	235	12	xn+1	xn+1	PROPN
ijassa-429	235	13	,	,	PUNCT
ijassa-429	235	14	we	we	PRON
ijassa-429	235	15	have	have	VERB
ijassa-429	235	16	(	(	PUNCT
ijassa-429	235	17	xgn	xgn	X
ijassa-429	235	18	(	(	PUNCT
ijassa-429	235	19	x	x	NOUN
ijassa-429	235	20	)	)	PUNCT
ijassa-429	235	21	)	)	PUNCT
ijassa-429	236	1	′	′	NUM
ijassa-429	237	1	=	=	PUNCT
ijassa-429	238	1	∑n	∑n	NUM
ijassa-429	238	2	n=0(−x)n	n=0(−x)n	NOUN
ijassa-429	238	3	=	=	SYM
ijassa-429	238	4	1−(−x)n+1	1−(−x)n+1	PROPN
ijassa-429	238	5	1+x	1+x	NUM
ijassa-429	238	6	,	,	PUNCT
ijassa-429	238	7	and	and	CCONJ
ijassa-429	238	8	hence	hence	ADV
ijassa-429	238	9	it	it	PRON
ijassa-429	238	10	holds	hold	VERB
ijassa-429	238	11	that	that	SCONJ
ijassa-429	238	12	[	[	PUNCT
ijassa-429	238	13	xgn	xgn	PROPN
ijassa-429	238	14	(	(	PUNCT
ijassa-429	238	15	x	x	X
ijassa-429	238	16	)	)	PUNCT
ijassa-429	238	17	]	]	PUNCT
ijassa-429	239	1	|	|	ADV
ijassa-429	239	2	2p	2p	NUM
ijassa-429	239	3	m	m	NOUN
ijassa-429	239	4	0	0	NUM
ijassa-429	240	1	=	=	SYM
ijassa-429	240	2	∫	∫	PROPN
ijassa-429	240	3	2p	2p	NUM
ijassa-429	240	4	m	m	VERB
ijassa-429	240	5	0	0	NUM
ijassa-429	241	1	(	(	PUNCT
ijassa-429	241	2	xgn	xgn	X
ijassa-429	241	3	(	(	PUNCT
ijassa-429	241	4	x	x	NOUN
ijassa-429	241	5	)	)	PUNCT
ijassa-429	241	6	)	)	PUNCT
ijassa-429	241	7	′	′	NUM
ijassa-429	241	8	dx	dx	PROPN
ijassa-429	242	1	=	=	SYM
ijassa-429	242	2	∫	∫	PROPN
ijassa-429	242	3	2p	2p	NUM
ijassa-429	242	4	m	m	PROPN
ijassa-429	242	5	0	0	NUM
ijassa-429	242	6	1−	1−	NUM
ijassa-429	242	7	(	(	PUNCT
ijassa-429	242	8	−x)n+1	−x)n+1	NOUN
ijassa-429	242	9	1	1	NUM
ijassa-429	243	1	+	+	CCONJ
ijassa-429	243	2	x	x	SYM
ijassa-429	243	3	dx	dx	PROPN
ijassa-429	243	4	,	,	PUNCT
ijassa-429	243	5	advances	advance	NOUN
ijassa-429	243	6	in	in	ADP
ijassa-429	243	7	systems	system	NOUN
ijassa-429	243	8	science	science	NOUN
ijassa-429	243	9	and	and	CCONJ
ijassa-429	243	10	applications	application	NOUN
ijassa-429	243	11	(	(	PUNCT
ijassa-429	243	12	2013	2013	NUM
ijassa-429	243	13	)	)	PUNCT
ijassa-429	243	14	vol.13	vol.13	NOUN
ijassa-429	243	15	no.1	no.1	VERB
ijassa-429	243	16	91	91	NUM
ijassa-429	243	17	implying	imply	VERB
ijassa-429	243	18	2p	2p	NUM
ijassa-429	243	19	m	m	NOUN
ijassa-429	243	20	gn	gn	INTJ
ijassa-429	244	1	(	(	PUNCT
ijassa-429	244	2	2p	2p	NUM
ijassa-429	244	3	m	m	NOUN
ijassa-429	244	4	)	)	PUNCT
ijassa-429	245	1	−	−	NOUN
ijassa-429	245	2	0	0	NUM
ijassa-429	246	1	=	=	SYM
ijassa-429	246	2			PROPN
ijassa-429	246	3	∫	∫	PROPN
ijassa-429	246	4	2p	2p	NUM
ijassa-429	246	5	m	m	VERB
ijassa-429	246	6	0	0	NUM
ijassa-429	246	7	1−xn+1	1−xn+1	NUM
ijassa-429	246	8	1+x	1+x	NUM
ijassa-429	246	9	dx	dx	PROPN
ijassa-429	246	10	,	,	PUNCT
ijassa-429	246	11	if	if	SCONJ
ijassa-429	246	12	n	n	PROPN
ijassa-429	246	13	+	+	CCONJ
ijassa-429	246	14	1	1	NUM
ijassa-429	246	15	even,∫	even,∫	ADJ
ijassa-429	246	16	2p	2p	NUM
ijassa-429	246	17	m	m	VERB
ijassa-429	246	18	0	0	NUM
ijassa-429	246	19	1+xn+1	1+xn+1	NUM
ijassa-429	246	20	1+x	1+x	NUM
ijassa-429	246	21	dx	dx	PROPN
ijassa-429	246	22	,	,	PUNCT
ijassa-429	246	23	if	if	SCONJ
ijassa-429	246	24	n	n	PROPN
ijassa-429	246	25	+	+	CCONJ
ijassa-429	246	26	1	1	NUM
ijassa-429	246	27	odd	odd	ADJ
ijassa-429	246	28	.	.	PUNCT
ijassa-429	247	1	therefore	therefore	ADV
ijassa-429	247	2	,	,	PUNCT
ijassa-429	247	3	dp	dp	NOUN
ijassa-429	247	4	dt	dt	NOUN
ijassa-429	247	5	=	=	NOUN
ijassa-429	247	6	rpgn	rpgn	NOUN
ijassa-429	247	7	(	(	PUNCT
ijassa-429	247	8	2p	2p	NUM
ijassa-429	247	9	m	m	NOUN
ijassa-429	247	10	)	)	PUNCT
ijassa-429	248	1	=	=	SYM
ijassa-429	248	2	rp×m	rp×m	ADJ
ijassa-429	248	3	2p	2p	NUM
ijassa-429	248	4	×2p	×2p	NOUN
ijassa-429	248	5	m	m	VERB
ijassa-429	248	6	gn	gn	INTJ
ijassa-429	248	7	(	(	PUNCT
ijassa-429	248	8	2p	2p	NUM
ijassa-429	248	9	m	m	NOUN
ijassa-429	248	10	)	)	PUNCT
ijassa-429	249	1	=	=	SYM
ijassa-429	249	2	rm	rm	NOUN
ijassa-429	249	3	2	2	NUM
ijassa-429	249	4			NOUN
ijassa-429	249	5	∫	∫	PROPN
ijassa-429	249	6	2p	2p	NUM
ijassa-429	249	7	m	m	VERB
ijassa-429	249	8	0	0	NUM
ijassa-429	249	9	1−xn+1	1−xn+1	NUM
ijassa-429	249	10	1+x	1+x	NUM
ijassa-429	249	11	dx	dx	PROPN
ijassa-429	249	12	,	,	PUNCT
ijassa-429	249	13	if	if	SCONJ
ijassa-429	249	14	n	n	PROPN
ijassa-429	249	15	+	+	CCONJ
ijassa-429	249	16	1	1	NUM
ijassa-429	249	17	even,∫	even,∫	ADJ
ijassa-429	249	18	2p	2p	NUM
ijassa-429	249	19	m	m	VERB
ijassa-429	249	20	0	0	NUM
ijassa-429	249	21	1+xn+1	1+xn+1	NUM
ijassa-429	249	22	1+x	1+x	NUM
ijassa-429	249	23	dx	dx	PROPN
ijassa-429	249	24	,	,	PUNCT
ijassa-429	249	25	if	if	SCONJ
ijassa-429	249	26	n	n	PROPN
ijassa-429	249	27	+	+	CCONJ
ijassa-429	249	28	1	1	NUM
ijassa-429	249	29	odd	odd	ADJ
ijassa-429	249	30	.	.	PUNCT
ijassa-429	250	1	it	it	PRON
ijassa-429	250	2	is	be	AUX
ijassa-429	250	3	obvious	obvious	ADJ
ijassa-429	250	4	that	that	SCONJ
ijassa-429	250	5	dp	dp	NOUN
ijassa-429	250	6	dt	dt	NOUN
ijassa-429	250	7	=	=	SYM
ijassa-429	250	8	rm	rm	PROPN
ijassa-429	250	9	2	2	NUM
ijassa-429	250	10	∫	∫	PROPN
ijassa-429	250	11	2p	2p	NUM
ijassa-429	250	12	m	m	VERB
ijassa-429	250	13	0	0	NUM
ijassa-429	250	14	1+xn+1	1+xn+1	NUM
ijassa-429	250	15	1+x	1+x	NUM
ijassa-429	250	16	dx	dx	PROPN
ijassa-429	250	17	>	>	X
ijassa-429	250	18	0	0	PUNCT
ijassa-429	250	19	when	when	SCONJ
ijassa-429	250	20	n	n	X
ijassa-429	250	21	is	be	AUX
ijassa-429	250	22	even	even	ADV
ijassa-429	250	23	(	(	PUNCT
ijassa-429	250	24	n	n	X
ijassa-429	250	25	+	+	CCONJ
ijassa-429	250	26	1	1	NUM
ijassa-429	250	27	is	be	AUX
ijassa-429	250	28	odd	odd	ADJ
ijassa-429	250	29	)	)	PUNCT
ijassa-429	250	30	.	.	PUNCT
ijassa-429	251	1	next	next	ADV
ijassa-429	251	2	we	we	PRON
ijassa-429	251	3	consider	consider	VERB
ijassa-429	251	4	the	the	DET
ijassa-429	251	5	case	case	NOUN
ijassa-429	251	6	that	that	SCONJ
ijassa-429	251	7	n	n	PRON
ijassa-429	251	8	is	be	AUX
ijassa-429	251	9	odd	odd	ADJ
ijassa-429	251	10	(	(	PUNCT
ijassa-429	251	11	or	or	CCONJ
ijassa-429	251	12	n	n	PRON
ijassa-429	251	13	+	+	PRON
ijassa-429	251	14	1	1	NUM
ijassa-429	251	15	is	be	AUX
ijassa-429	251	16	even	even	ADV
ijassa-429	251	17	)	)	PUNCT
ijassa-429	251	18	.	.	PUNCT
ijassa-429	252	1	it	it	PRON
ijassa-429	252	2	follows	follow	VERB
ijassa-429	252	3	from	from	ADP
ijassa-429	252	4	the	the	DET
ijassa-429	252	5	above	above	ADJ
ijassa-429	252	6	proof	proof	NOUN
ijassa-429	252	7	that	that	SCONJ
ijassa-429	252	8	dp	dp	NOUN
ijassa-429	252	9	dt	dt	NOUN
ijassa-429	252	10	=	=	SYM
ijassa-429	252	11	rm	rm	PROPN
ijassa-429	252	12	2	2	NUM
ijassa-429	252	13	∫	∫	PROPN
ijassa-429	252	14	2p	2p	NUM
ijassa-429	252	15	m	m	PROPN
ijassa-429	252	16	0	0	NUM
ijassa-429	252	17	1−xn+1	1−xn+1	NUM
ijassa-429	252	18	1+x	1+x	NUM
ijassa-429	252	19	dx	dx	PROPN
ijassa-429	252	20	.	.	PUNCT
ijassa-429	253	1	when	when	SCONJ
ijassa-429	253	2	p	p	PRON
ijassa-429	253	3	≤	≤	NUM
ijassa-429	253	4	m	m	VERB
ijassa-429	253	5	2	2	NUM
ijassa-429	253	6	(	(	PUNCT
ijassa-429	253	7	2	2	NUM
ijassa-429	253	8	pm	pm	NOUN
ijassa-429	253	9	≤	≤	NUM
ijassa-429	253	10	1	1	NUM
ijassa-429	253	11	)	)	PUNCT
ijassa-429	253	12	,	,	PUNCT
ijassa-429	253	13	dp	dp	NOUN
ijassa-429	253	14	dt	dt	NOUN
ijassa-429	253	15	is	be	AUX
ijassa-429	253	16	positive	positive	ADJ
ijassa-429	253	17	because	because	SCONJ
ijassa-429	253	18	1	1	NUM
ijassa-429	253	19	−	−	NOUN
ijassa-429	253	20	xn+1	xn+1	NUM
ijassa-429	253	21	is	be	AUX
ijassa-429	253	22	always	always	ADV
ijassa-429	253	23	positive	positive	ADJ
ijassa-429	253	24	except	except	SCONJ
ijassa-429	253	25	at	at	ADP
ijassa-429	253	26	the	the	DET
ijassa-429	253	27	single	single	ADJ
ijassa-429	253	28	point	point	NOUN
ijassa-429	253	29	x	x	X
ijassa-429	254	1	=	=	PUNCT
ijassa-429	254	2	2p	2p	NUM
ijassa-429	254	3	m	m	VERB
ijassa-429	254	4	,	,	PUNCT
ijassa-429	254	5	at	at	ADP
ijassa-429	254	6	which	which	PRON
ijassa-429	254	7	1	1	NUM
ijassa-429	254	8	−	−	NOUN
ijassa-429	254	9	xn+1	xn+1	NUM
ijassa-429	254	10	is	be	AUX
ijassa-429	254	11	zero	zero	NUM
ijassa-429	254	12	.	.	PUNCT
ijassa-429	255	1	we	we	PRON
ijassa-429	255	2	claim	claim	VERB
ijassa-429	255	3	that	that	SCONJ
ijassa-429	255	4	dp	dp	NOUN
ijassa-429	255	5	dt	dt	NOUN
ijassa-429	255	6	never	never	ADV
ijassa-429	255	7	becomes	become	VERB
ijassa-429	255	8	0	0	NUM
ijassa-429	255	9	.	.	PUNCT
ijassa-429	256	1	in	in	ADP
ijassa-429	256	2	fact	fact	NOUN
ijassa-429	256	3	,	,	PUNCT
ijassa-429	256	4	if	if	SCONJ
ijassa-429	256	5	dp	dp	NOUN
ijassa-429	256	6	dt	dt	NOUN
ijassa-429	256	7	becomes	become	VERB
ijassa-429	256	8	0	0	NUM
ijassa-429	256	9	at	at	ADP
ijassa-429	256	10	some	some	DET
ijassa-429	256	11	infimum	infimum	ADJ
ijassa-429	256	12	time	time	NOUN
ijassa-429	256	13	t0	t0	PROPN
ijassa-429	256	14	,	,	PUNCT
ijassa-429	256	15	it	it	PRON
ijassa-429	256	16	must	must	AUX
ijassa-429	256	17	strictly	strictly	ADV
ijassa-429	256	18	be	be	AUX
ijassa-429	256	19	after	after	ADP
ijassa-429	256	20	the	the	DET
ijassa-429	256	21	time	time	NOUN
ijassa-429	256	22	at	at	ADP
ijassa-429	256	23	which	which	PRON
ijassa-429	256	24	the	the	DET
ijassa-429	256	25	inflection	inflection	NOUN
ijassa-429	256	26	point	point	NOUN
ijassa-429	256	27	occurs	occur	VERB
ijassa-429	256	28	.	.	PUNCT
ijassa-429	257	1	(	(	PUNCT
ijassa-429	257	2	at	at	ADP
ijassa-429	257	3	this	this	DET
ijassa-429	257	4	point	point	NOUN
ijassa-429	257	5	,	,	PUNCT
ijassa-429	257	6	dp	dp	NOUN
ijassa-429	257	7	dt	dt	NOUN
ijassa-429	257	8	changes	change	NOUN
ijassa-429	257	9	from	from	ADP
ijassa-429	257	10	positive	positive	ADJ
ijassa-429	257	11	with	with	ADP
ijassa-429	257	12	upward	upward	ADJ
ijassa-429	257	13	concavity	concavity	NOUN
ijassa-429	257	14	and	and	CCONJ
ijassa-429	257	15	begins	begin	VERB
ijassa-429	257	16	to	to	PART
ijassa-429	257	17	decrease	decrease	VERB
ijassa-429	257	18	.	.	PUNCT
ijassa-429	258	1	the	the	DET
ijassa-429	258	2	value	value	NOUN
ijassa-429	258	3	of	of	ADP
ijassa-429	258	4	the	the	DET
ijassa-429	258	5	integral	integral	ADJ
ijassa-429	258	6	,	,	PUNCT
ijassa-429	258	7	likewise	likewise	ADV
ijassa-429	258	8	,	,	PUNCT
ijassa-429	258	9	begins	begin	VERB
ijassa-429	258	10	to	to	PART
ijassa-429	258	11	decrease	decrease	VERB
ijassa-429	258	12	after	after	ADP
ijassa-429	258	13	the	the	DET
ijassa-429	258	14	shift	shift	NOUN
ijassa-429	258	15	in	in	ADP
ijassa-429	258	16	dp	dp	NOUN
ijassa-429	258	17	dt	dt	NOUN
ijassa-429	258	18	at	at	ADP
ijassa-429	258	19	this	this	DET
ijassa-429	258	20	point	point	NOUN
ijassa-429	258	21	,	,	PUNCT
ijassa-429	258	22	corresponding	correspond	VERB
ijassa-429	258	23	to	to	ADP
ijassa-429	258	24	the	the	DET
ijassa-429	258	25	concavity	concavity	NOUN
ijassa-429	258	26	,	,	PUNCT
ijassa-429	258	27	but	but	CCONJ
ijassa-429	258	28	the	the	DET
ijassa-429	258	29	value	value	NOUN
ijassa-429	258	30	still	still	ADV
ijassa-429	258	31	must	must	AUX
ijassa-429	258	32	be	be	AUX
ijassa-429	258	33	positive	positive	ADJ
ijassa-429	258	34	.	.	PUNCT
ijassa-429	259	1	it	it	PRON
ijassa-429	259	2	follows	follow	VERB
ijassa-429	259	3	that	that	SCONJ
ijassa-429	259	4	dp	dp	NOUN
ijassa-429	259	5	dt	dt	NOUN
ijassa-429	259	6	can	can	AUX
ijassa-429	259	7	not	not	PART
ijassa-429	259	8	be	be	AUX
ijassa-429	259	9	0	0	NUM
ijassa-429	259	10	at	at	ADP
ijassa-429	259	11	the	the	DET
ijassa-429	259	12	inflection	inflection	NOUN
ijassa-429	259	13	point	point	NOUN
ijassa-429	259	14	.	.	PUNCT
ijassa-429	259	15	)	)	PUNCT
ijassa-429	260	1	since	since	SCONJ
ijassa-429	260	2	d2p	d2p	NOUN
ijassa-429	260	3	dt2	dt2	PROPN
ijassa-429	260	4	is	be	AUX
ijassa-429	260	5	still	still	ADV
ijassa-429	260	6	negative	negative	ADJ
ijassa-429	260	7	at	at	ADP
ijassa-429	260	8	t0	t0	NOUN
ijassa-429	260	9	,	,	PUNCT
ijassa-429	260	10	p	p	X
ijassa-429	260	11	(	(	PUNCT
ijassa-429	260	12	t	t	PROPN
ijassa-429	260	13	)	)	PUNCT
ijassa-429	260	14	by	by	ADP
ijassa-429	260	15	definition	definition	NOUN
ijassa-429	260	16	would	would	AUX
ijassa-429	260	17	have	have	AUX
ijassa-429	260	18	attained	attain	VERB
ijassa-429	260	19	its	its	PRON
ijassa-429	260	20	local	local	ADJ
ijassa-429	260	21	maximum	maximum	NOUN
ijassa-429	260	22	p	p	X
ijassa-429	260	23	(	(	PUNCT
ijassa-429	260	24	t0	t0	PROPN
ijassa-429	260	25	)	)	PUNCT
ijassa-429	260	26	(	(	PUNCT
ijassa-429	260	27	at	at	ADP
ijassa-429	260	28	a	a	DET
ijassa-429	260	29	specific	specific	ADJ
ijassa-429	260	30	p	p	X
ijassa-429	260	31	(	(	PUNCT
ijassa-429	260	32	t0	t0	PROPN
ijassa-429	260	33	)	)	PUNCT
ijassa-429	260	34	>	>	X
ijassa-429	260	35	m	m	PROPN
ijassa-429	260	36	2	2	NUM
ijassa-429	260	37	)	)	PUNCT
ijassa-429	260	38	.	.	PUNCT
ijassa-429	261	1	now	now	ADV
ijassa-429	261	2	,	,	PUNCT
ijassa-429	261	3	let	let	VERB
ijassa-429	261	4	t1	t1	NOUN
ijassa-429	261	5	be	be	AUX
ijassa-429	261	6	a	a	DET
ijassa-429	261	7	nearby	nearby	ADJ
ijassa-429	261	8	point	point	NOUN
ijassa-429	261	9	of	of	ADP
ijassa-429	261	10	t0	t0	NOUN
ijassa-429	261	11	,	,	PUNCT
ijassa-429	261	12	on	on	ADP
ijassa-429	261	13	the	the	DET
ijassa-429	261	14	right	right	NOUN
ijassa-429	261	15	of	of	ADP
ijassa-429	261	16	t0	t0	PRON
ijassa-429	262	1	such	such	ADJ
ijassa-429	262	2	that	that	SCONJ
ijassa-429	262	3	m	m	VERB
ijassa-429	262	4	2	2	NUM
ijassa-429	262	5	<	<	X
ijassa-429	262	6	p	p	X
ijassa-429	262	7	(	(	PUNCT
ijassa-429	262	8	t1	t1	NOUN
ijassa-429	262	9	)	)	PUNCT
ijassa-429	262	10	<	<	X
ijassa-429	262	11	p	p	X
ijassa-429	262	12	(	(	PUNCT
ijassa-429	262	13	t0	t0	PROPN
ijassa-429	262	14	)	)	PUNCT
ijassa-429	262	15	.	.	PUNCT
ijassa-429	263	1	(	(	PUNCT
ijassa-429	263	2	since	since	SCONJ
ijassa-429	263	3	dp	dp	NOUN
ijassa-429	263	4	dt	dt	X
ijassa-429	263	5	|t	|t	NOUN
ijassa-429	263	6	=	=	SYM
ijassa-429	263	7	t0	t0	PROPN
ijassa-429	263	8	=	=	SYM
ijassa-429	263	9	0	0	PUNCT
ijassa-429	263	10	and	and	CCONJ
ijassa-429	263	11	d2p	d2p	PROPN
ijassa-429	263	12	dt2	dt2	PROPN
ijassa-429	263	13	<	<	X
ijassa-429	263	14	0	0	PUNCT
ijassa-429	263	15	after	after	ADP
ijassa-429	263	16	t	t	PROPN
ijassa-429	263	17	=	=	SYM
ijassa-429	263	18	t0	t0	PROPN
ijassa-429	263	19	,	,	PUNCT
ijassa-429	263	20	dp	dp	NOUN
ijassa-429	263	21	dt	dt	NOUN
ijassa-429	263	22	is	be	AUX
ijassa-429	263	23	negative	negative	ADJ
ijassa-429	263	24	after	after	ADP
ijassa-429	263	25	t	t	PROPN
ijassa-429	263	26	=	=	SYM
ijassa-429	263	27	t0	t0	PROPN
ijassa-429	263	28	)	)	PUNCT
ijassa-429	263	29	.	.	PUNCT
ijassa-429	264	1	then	then	ADV
ijassa-429	264	2	the	the	DET
ijassa-429	264	3	result	result	NOUN
ijassa-429	264	4	would	would	AUX
ijassa-429	264	5	become	become	VERB
ijassa-429	264	6	0	0	NUM
ijassa-429	264	7	=	=	SYM
ijassa-429	264	8	dp	dp	NOUN
ijassa-429	264	9	dt	dt	X
ijassa-429	264	10	|t	|t	NOUN
ijassa-429	264	11	=	=	SYM
ijassa-429	264	12	t0	t0	PROPN
ijassa-429	264	13	=	=	SYM
ijassa-429	264	14	rm	rm	PROPN
ijassa-429	264	15	2	2	NUM
ijassa-429	264	16	∫	∫	PROPN
ijassa-429	264	17	2p	2p	NUM
ijassa-429	264	18	(	(	PUNCT
ijassa-429	264	19	t0	t0	NOUN
ijassa-429	264	20	)	)	PUNCT
ijassa-429	264	21	m	m	VERB
ijassa-429	264	22	0	0	NUM
ijassa-429	264	23	1−xn+1	1−xn+1	NUM
ijassa-429	264	24	1+x	1+x	NUM
ijassa-429	264	25	dx	dx	PROPN
ijassa-429	264	26	<	<	X
ijassa-429	264	27	rm	rm	PROPN
ijassa-429	264	28	2	2	NUM
ijassa-429	264	29	∫	∫	PROPN
ijassa-429	264	30	2p	2p	NUM
ijassa-429	264	31	(	(	PUNCT
ijassa-429	264	32	t1	t1	NOUN
ijassa-429	264	33	)	)	PUNCT
ijassa-429	264	34	m	m	VERB
ijassa-429	264	35	0	0	NUM
ijassa-429	264	36	1−xn+1	1−xn+1	NUM
ijassa-429	264	37	1+x	1+x	NUM
ijassa-429	264	38	dx	dx	NOUN
ijassa-429	264	39	=	=	PUNCT
ijassa-429	264	40	dp	dp	PROPN
ijassa-429	265	1	dt	dt	X
ijassa-429	265	2	|t	|t	PROPN
ijassa-429	265	3	=	=	PROPN
ijassa-429	265	4	t1	t1	NOUN
ijassa-429	265	5	,	,	PUNCT
ijassa-429	265	6	a	a	DET
ijassa-429	265	7	contradiction	contradiction	NOUN
ijassa-429	265	8	.	.	PUNCT
ijassa-429	266	1	because	because	SCONJ
ijassa-429	266	2	the	the	DET
ijassa-429	266	3	value	value	NOUN
ijassa-429	266	4	of	of	ADP
ijassa-429	266	5	p	p	NOUN
ijassa-429	266	6	(	(	PUNCT
ijassa-429	266	7	t1	t1	NOUN
ijassa-429	266	8	)	)	PUNCT
ijassa-429	266	9	is	be	AUX
ijassa-429	266	10	less	less	ADJ
ijassa-429	266	11	than	than	ADP
ijassa-429	266	12	the	the	DET
ijassa-429	266	13	value	value	NOUN
ijassa-429	266	14	of	of	ADP
ijassa-429	266	15	p	p	PROPN
ijassa-429	266	16	(	(	PUNCT
ijassa-429	266	17	t0	t0	PROPN
ijassa-429	266	18	)	)	PUNCT
ijassa-429	266	19	,	,	PUNCT
ijassa-429	266	20	the	the	DET
ijassa-429	266	21	inequality	inequality	NOUN
ijassa-429	266	22	is	be	AUX
ijassa-429	266	23	inconsistent	inconsistent	ADJ
ijassa-429	266	24	with	with	ADP
ijassa-429	266	25	the	the	DET
ijassa-429	266	26	fact	fact	NOUN
ijassa-429	266	27	that	that	SCONJ
ijassa-429	266	28	dp	dp	NOUN
ijassa-429	266	29	dt	dt	NOUN
ijassa-429	266	30	at	at	ADP
ijassa-429	266	31	t1	t1	PROPN
ijassa-429	266	32	must	must	AUX
ijassa-429	266	33	be	be	AUX
ijassa-429	266	34	negative	negative	ADJ
ijassa-429	266	35	.	.	PUNCT
ijassa-429	267	1	hence	hence	ADV
ijassa-429	267	2	,	,	PUNCT
ijassa-429	267	3	dp	dp	NOUN
ijassa-429	267	4	dt	dt	NOUN
ijassa-429	267	5	never	never	ADV
ijassa-429	267	6	reaches	reach	VERB
ijassa-429	267	7	0	0	NUM
ijassa-429	267	8	,	,	PUNCT
ijassa-429	267	9	and	and	CCONJ
ijassa-429	267	10	it	it	PRON
ijassa-429	267	11	follows	follow	VERB
ijassa-429	267	12	from	from	ADP
ijassa-429	267	13	the	the	DET
ijassa-429	267	14	continuity	continuity	NOUN
ijassa-429	267	15	of	of	ADP
ijassa-429	267	16	dp	dp	NOUN
ijassa-429	267	17	dt	dt	NOUN
ijassa-429	267	18	that	that	PRON
ijassa-429	267	19	dp	dp	NOUN
ijassa-429	268	1	dt	dt	NOUN
ijassa-429	268	2	can	can	AUX
ijassa-429	268	3	never	never	ADV
ijassa-429	268	4	be	be	AUX
ijassa-429	268	5	negative	negative	ADJ
ijassa-429	268	6	.	.	PUNCT
ijassa-429	269	1	therefore	therefore	ADV
ijassa-429	269	2	,	,	PUNCT
ijassa-429	269	3	dp	dp	NOUN
ijassa-429	269	4	dt	dt	NOUN
ijassa-429	269	5	is	be	AUX
ijassa-429	269	6	always	always	ADV
ijassa-429	269	7	positive	positive	ADJ
ijassa-429	269	8	.	.	PUNCT
ijassa-429	270	1	proof	proof	NOUN
ijassa-429	270	2	of	of	ADP
ijassa-429	270	3	(	(	PUNCT
ijassa-429	270	4	ii	ii	NOUN
ijassa-429	270	5	)	)	PUNCT
ijassa-429	270	6	method	method	NOUN
ijassa-429	270	7	for	for	ADP
ijassa-429	270	8	determining	determine	VERB
ijassa-429	270	9	the	the	DET
ijassa-429	270	10	supremum	supremum	NOUN
ijassa-429	270	11	of	of	ADP
ijassa-429	270	12	p	p	NOUN
ijassa-429	270	13	:	:	PUNCT
ijassa-429	270	14	let	let	VERB
ijassa-429	270	15	us	we	PRON
ijassa-429	270	16	illustrate	illustrate	VERB
ijassa-429	270	17	the	the	DET
ijassa-429	270	18	method	method	NOUN
ijassa-429	270	19	using	use	VERB
ijassa-429	270	20	two	two	NUM
ijassa-429	270	21	(	(	PUNCT
ijassa-429	270	22	logistic	logistic	NOUN
ijassa-429	270	23	)	)	PUNCT
ijassa-429	270	24	,	,	PUNCT
ijassa-429	270	25	four	four	NUM
ijassa-429	270	26	,	,	PUNCT
ijassa-429	270	27	or	or	CCONJ
ijassa-429	270	28	six	six	NUM
ijassa-429	270	29	terms	term	NOUN
ijassa-429	270	30	.	.	PUNCT
ijassa-429	271	1	if	if	SCONJ
ijassa-429	271	2	n	n	NOUN
ijassa-429	271	3	=	=	SYM
ijassa-429	271	4	1	1	NUM
ijassa-429	271	5	,	,	PUNCT
ijassa-429	271	6	n+1	n+1	PROPN
ijassa-429	271	7	=	=	SYM
ijassa-429	271	8	2	2	NUM
ijassa-429	271	9	(	(	PUNCT
ijassa-429	271	10	the	the	DET
ijassa-429	271	11	traditional	traditional	ADJ
ijassa-429	271	12	logistic	logistic	ADJ
ijassa-429	271	13	model	model	NOUN
ijassa-429	271	14	)	)	PUNCT
ijassa-429	272	1	,	,	PUNCT
ijassa-429	272	2	then	then	ADV
ijassa-429	272	3	dp	dp	VERB
ijassa-429	272	4	dt	dt	NOUN
ijassa-429	273	1	=	=	PUNCT
ijassa-429	273	2	...	...	PUNCT
ijassa-429	274	1	=	=	SYM
ijassa-429	274	2	rp	rp	NOUN
ijassa-429	274	3	(	(	PUNCT
ijassa-429	274	4	1−	1−	NUM
ijassa-429	274	5	p	p	NOUN
ijassa-429	274	6	m	m	PROPN
ijassa-429	274	7	)	)	PUNCT
ijassa-429	274	8	.	.	PUNCT
ijassa-429	275	1	hence	hence	ADV
ijassa-429	275	2	,	,	PUNCT
ijassa-429	275	3	dp	dp	NOUN
ijassa-429	275	4	dt	dt	NOUN
ijassa-429	275	5	>	>	X
ijassa-429	275	6	0	0	PUNCT
ijassa-429	276	1	if	if	SCONJ
ijassa-429	276	2	and	and	CCONJ
ijassa-429	276	3	only	only	ADV
ijassa-429	276	4	if	if	SCONJ
ijassa-429	276	5	p	p	X
ijassa-429	276	6	<	<	X
ijassa-429	276	7	m	m	VERB
ijassa-429	276	8	.	.	PUNCT
ijassa-429	277	1	observe	observe	VERB
ijassa-429	277	2	that	that	SCONJ
ijassa-429	277	3	if	if	SCONJ
ijassa-429	277	4	p	p	PRON
ijassa-429	277	5	could	could	AUX
ijassa-429	277	6	exceed	exceed	VERB
ijassa-429	277	7	m	m	PRON
ijassa-429	277	8	,	,	PUNCT
ijassa-429	277	9	then	then	ADV
ijassa-429	277	10	dp	dp	NOUN
ijassa-429	277	11	dt	dt	NOUN
ijassa-429	277	12	would	would	AUX
ijassa-429	277	13	become	become	VERB
ijassa-429	277	14	negative	negative	ADJ
ijassa-429	277	15	and	and	CCONJ
ijassa-429	277	16	consequently	consequently	ADV
ijassa-429	277	17	p	p	X
ijassa-429	277	18	would	would	AUX
ijassa-429	277	19	be	be	AUX
ijassa-429	277	20	immediately	immediately	ADV
ijassa-429	277	21	lowered	lower	VERB
ijassa-429	277	22	making	make	VERB
ijassa-429	277	23	dp	dp	NOUN
ijassa-429	277	24	dt	dt	NOUN
ijassa-429	277	25	positive	positive	ADJ
ijassa-429	277	26	.	.	PUNCT
ijassa-429	278	1	therefore	therefore	ADV
ijassa-429	278	2	,	,	PUNCT
ijassa-429	278	3	dp	dp	NOUN
ijassa-429	278	4	dt	dt	NOUN
ijassa-429	278	5	is	be	AUX
ijassa-429	278	6	always	always	ADV
ijassa-429	278	7	positive	positive	ADJ
ijassa-429	278	8	.	.	PUNCT
ijassa-429	279	1	again	again	ADV
ijassa-429	279	2	,	,	PUNCT
ijassa-429	279	3	continuity	continuity	NOUN
ijassa-429	279	4	indicates	indicate	VERB
ijassa-429	279	5	that	that	SCONJ
ijassa-429	279	6	dp	dp	NOUN
ijassa-429	279	7	dt	dt	NOUN
ijassa-429	279	8	must	must	AUX
ijassa-429	279	9	reach	reach	VERB
ijassa-429	279	10	and	and	CCONJ
ijassa-429	279	11	cross	cross	VERB
ijassa-429	279	12	through	through	ADP
ijassa-429	279	13	a	a	DET
ijassa-429	279	14	point	point	NOUN
ijassa-429	279	15	of	of	ADP
ijassa-429	279	16	0	0	NUM
ijassa-429	279	17	slope	slope	NOUN
ijassa-429	279	18	to	to	PART
ijassa-429	279	19	become	become	VERB
ijassa-429	279	20	negative	negative	ADJ
ijassa-429	279	21	,	,	PUNCT
ijassa-429	279	22	which	which	PRON
ijassa-429	279	23	is	be	AUX
ijassa-429	279	24	impossible	impossible	ADJ
ijassa-429	279	25	.	.	PUNCT
ijassa-429	280	1	92	92	NUM
ijassa-429	280	2	anne	anne	PROPN
ijassa-429	280	3	talkington	talkington	NOUN
ijassa-429	280	4	:	:	PUNCT
ijassa-429	280	5	an	an	DET
ijassa-429	280	6	extension	extension	NOUN
ijassa-429	280	7	of	of	ADP
ijassa-429	280	8	a	a	DET
ijassa-429	280	9	logistic	logistic	ADJ
ijassa-429	280	10	model	model	NOUN
ijassa-429	280	11	for	for	ADP
ijassa-429	280	12	microbial	microbial	ADJ
ijassa-429	280	13	kinetics	kinetic	NOUN
ijassa-429	280	14	if	if	SCONJ
ijassa-429	280	15	n	n	X
ijassa-429	280	16	=	=	SYM
ijassa-429	280	17	3	3	NUM
ijassa-429	280	18	,	,	PUNCT
ijassa-429	280	19	n	n	PROPN
ijassa-429	280	20	+	+	CCONJ
ijassa-429	280	21	1	1	NUM
ijassa-429	280	22	=	=	SYM
ijassa-429	280	23	4	4	NUM
ijassa-429	280	24	(	(	PUNCT
ijassa-429	280	25	four	four	NUM
ijassa-429	280	26	terms	term	NOUN
ijassa-429	280	27	)	)	PUNCT
ijassa-429	280	28	,	,	PUNCT
ijassa-429	280	29	then	then	ADV
ijassa-429	280	30	dp	dp	NOUN
ijassa-429	280	31	dt	dt	NOUN
ijassa-429	280	32	=	=	SYM
ijassa-429	280	33	rm	rm	PROPN
ijassa-429	280	34	2	2	NUM
ijassa-429	280	35	∫	∫	PROPN
ijassa-429	280	36	2p	2p	NUM
ijassa-429	280	37	m	m	VERB
ijassa-429	280	38	0	0	NUM
ijassa-429	280	39	1−x4	1−x4	NUM
ijassa-429	280	40	1+x	1+x	NUM
ijassa-429	280	41	dx	dx	NOUN
ijassa-429	280	42	=	=	SYM
ijassa-429	280	43	rp	rp	PROPN
ijassa-429	280	44	(	(	PUNCT
ijassa-429	280	45	1−	1−	NUM
ijassa-429	280	46	1	1	NUM
ijassa-429	280	47	2	2	NUM
ijassa-429	280	48	2p	2p	NUM
ijassa-429	280	49	m	m	NOUN
ijassa-429	280	50	+	+	NOUN
ijassa-429	280	51	1	1	NUM
ijassa-429	280	52	3	3	NUM
ijassa-429	280	53	(	(	PUNCT
ijassa-429	280	54	2p	2p	NUM
ijassa-429	280	55	m	m	NOUN
ijassa-429	280	56	)	)	PUNCT
ijassa-429	280	57	2−	2−	NUM
ijassa-429	280	58	1	1	NUM
ijassa-429	280	59	4	4	NUM
ijassa-429	280	60	(	(	PUNCT
ijassa-429	280	61	2p	2p	NUM
ijassa-429	280	62	m	m	NOUN
ijassa-429	280	63	)	)	PUNCT
ijassa-429	280	64	3	3	NUM
ijassa-429	280	65	)	)	PUNCT
ijassa-429	280	66	.	.	PUNCT
ijassa-429	281	1	the	the	DET
ijassa-429	281	2	equation	equation	NOUN
ijassa-429	281	3	1−	1−	NUM
ijassa-429	281	4	1	1	NUM
ijassa-429	281	5	2x+	2x+	NUM
ijassa-429	281	6	1	1	NUM
ijassa-429	281	7	3x	3x	NUM
ijassa-429	281	8	2−	2−	NUM
ijassa-429	281	9	1	1	NUM
ijassa-429	281	10	4x	4x	NOUN
ijassa-429	281	11	3	3	NUM
ijassa-429	281	12	=	=	SYM
ijassa-429	281	13	0	0	PROPN
ijassa-429	281	14	has	have	VERB
ijassa-429	281	15	a	a	DET
ijassa-429	281	16	real	real	ADJ
ijassa-429	281	17	solution	solution	NOUN
ijassa-429	281	18	1.621	1.621	NUM
ijassa-429	281	19	.	.	PUNCT
ijassa-429	282	1	for	for	ADP
ijassa-429	282	2	example	example	NOUN
ijassa-429	282	3	,	,	PUNCT
ijassa-429	282	4	this	this	PRON
ijassa-429	282	5	gives	give	VERB
ijassa-429	282	6	the	the	DET
ijassa-429	282	7	maximum	maximum	NOUN
ijassa-429	282	8	of	of	ADP
ijassa-429	282	9	p	p	NOUN
ijassa-429	282	10	as	as	ADP
ijassa-429	282	11	81.05	81.05	NUM
ijassa-429	282	12	,	,	PUNCT
ijassa-429	282	13	assuming	assume	VERB
ijassa-429	282	14	m	m	PROPN
ijassa-429	282	15	=	=	NOUN
ijassa-429	282	16	100	100	NUM
ijassa-429	282	17	.	.	PUNCT
ijassa-429	283	1	if	if	SCONJ
ijassa-429	283	2	n	n	NOUN
ijassa-429	283	3	=	=	SYM
ijassa-429	283	4	5	5	NUM
ijassa-429	283	5	,	,	PUNCT
ijassa-429	283	6	n	n	PROPN
ijassa-429	283	7	+	+	CCONJ
ijassa-429	283	8	1	1	NUM
ijassa-429	283	9	=	=	SYM
ijassa-429	283	10	6	6	NUM
ijassa-429	283	11	(	(	PUNCT
ijassa-429	283	12	six	six	NUM
ijassa-429	283	13	terms	term	NOUN
ijassa-429	283	14	)	)	PUNCT
ijassa-429	283	15	,	,	PUNCT
ijassa-429	283	16	then	then	ADV
ijassa-429	283	17	dp	dp	NOUN
ijassa-429	283	18	dt	dt	NOUN
ijassa-429	283	19	=	=	SYM
ijassa-429	283	20	rm	rm	PROPN
ijassa-429	283	21	2	2	NUM
ijassa-429	283	22	∫	∫	PROPN
ijassa-429	283	23	2p	2p	NUM
ijassa-429	283	24	m	m	VERB
ijassa-429	283	25	0	0	NUM
ijassa-429	283	26	1−x6	1−x6	NUM
ijassa-429	284	1	1+x	1+x	NUM
ijassa-429	284	2	dx	dx	NOUN
ijassa-429	284	3	=	=	SYM
ijassa-429	284	4	rp	rp	PROPN
ijassa-429	284	5	(	(	PUNCT
ijassa-429	284	6	1−	1−	NUM
ijassa-429	284	7	1	1	NUM
ijassa-429	284	8	2	2	NUM
ijassa-429	284	9	2p	2p	NUM
ijassa-429	284	10	m	m	NOUN
ijassa-429	284	11	+	+	NOUN
ijassa-429	284	12	1	1	NUM
ijassa-429	284	13	3	3	NUM
ijassa-429	284	14	(	(	PUNCT
ijassa-429	284	15	2p	2p	NUM
ijassa-429	284	16	m	m	NOUN
ijassa-429	284	17	)	)	PUNCT
ijassa-429	284	18	2−	2−	NUM
ijassa-429	284	19	1	1	NUM
ijassa-429	284	20	4	4	NUM
ijassa-429	284	21	(	(	PUNCT
ijassa-429	284	22	2p	2p	NUM
ijassa-429	284	23	m	m	NOUN
ijassa-429	284	24	)	)	PUNCT
ijassa-429	284	25	3	3	NUM
ijassa-429	284	26	+	+	NUM
ijassa-429	284	27	1	1	NUM
ijassa-429	284	28	5	5	NUM
ijassa-429	284	29	(	(	PUNCT
ijassa-429	284	30	2p	2p	NUM
ijassa-429	284	31	m	m	NOUN
ijassa-429	284	32	)	)	PUNCT
ijassa-429	284	33	4−	4−	NOUN
ijassa-429	284	34	1	1	NUM
ijassa-429	284	35	6	6	NUM
ijassa-429	284	36	(	(	PUNCT
ijassa-429	284	37	2p	2p	NUM
ijassa-429	284	38	m	m	NOUN
ijassa-429	284	39	)	)	PUNCT
ijassa-429	284	40	5	5	NUM
ijassa-429	284	41	)	)	PUNCT
ijassa-429	284	42	.	.	PUNCT
ijassa-429	285	1	the	the	DET
ijassa-429	285	2	equation	equation	NOUN
ijassa-429	285	3	1−	1−	NUM
ijassa-429	285	4	1	1	NUM
ijassa-429	285	5	2x+	2x+	NUM
ijassa-429	285	6	1	1	NUM
ijassa-429	285	7	3x	3x	NUM
ijassa-429	285	8	2−	2−	NUM
ijassa-429	285	9	1	1	NUM
ijassa-429	285	10	4x	4x	NOUN
ijassa-429	285	11	3	3	NUM
ijassa-429	285	12	+	+	SYM
ijassa-429	285	13	1	1	NUM
ijassa-429	285	14	5x	5x	NOUN
ijassa-429	285	15	4−	4−	NOUN
ijassa-429	285	16	1	1	NUM
ijassa-429	285	17	6x	6x	NUM
ijassa-429	285	18	5	5	NUM
ijassa-429	285	19	=	=	SYM
ijassa-429	285	20	0	0	PROPN
ijassa-429	285	21	has	have	VERB
ijassa-429	285	22	a	a	DET
ijassa-429	285	23	real	real	ADJ
ijassa-429	285	24	solution	solution	NOUN
ijassa-429	285	25	1.462	1.462	NUM
ijassa-429	285	26	.	.	PUNCT
ijassa-429	286	1	this	this	PRON
ijassa-429	286	2	gives	give	VERB
ijassa-429	286	3	the	the	DET
ijassa-429	286	4	maximum	maximum	NOUN
ijassa-429	286	5	of	of	ADP
ijassa-429	286	6	p	p	NOUN
ijassa-429	286	7	as	as	ADP
ijassa-429	286	8	73.1	73.1	NUM
ijassa-429	286	9	,	,	PUNCT
ijassa-429	286	10	assuming	assume	VERB
ijassa-429	286	11	m	m	PROPN
ijassa-429	286	12	=	=	ADJ
ijassa-429	286	13	100	100	NUM
ijassa-429	286	14	.	.	PUNCT
ijassa-429	287	1	generally	generally	ADV
ijassa-429	287	2	,	,	PUNCT
ijassa-429	287	3	for	for	ADP
ijassa-429	287	4	any	any	DET
ijassa-429	287	5	odd	odd	ADJ
ijassa-429	287	6	n	n	NOUN
ijassa-429	287	7	,	,	PUNCT
ijassa-429	287	8	dp	dp	NOUN
ijassa-429	287	9	dt	dt	NOUN
ijassa-429	287	10	is	be	AUX
ijassa-429	287	11	always	always	ADV
ijassa-429	287	12	positive	positive	ADJ
ijassa-429	287	13	,	,	PUNCT
ijassa-429	287	14	and	and	CCONJ
ijassa-429	287	15	the	the	DET
ijassa-429	287	16	supremum	supremum	ADJ
ijassa-429	287	17	value	value	NOUN
ijassa-429	287	18	of	of	ADP
ijassa-429	287	19	p	p	NOUN
ijassa-429	287	20	is	be	AUX
ijassa-429	287	21	determined	determine	VERB
ijassa-429	287	22	by	by	ADP
ijassa-429	287	23	a	a	DET
ijassa-429	287	24	positive	positive	ADJ
ijassa-429	287	25	real	real	ADJ
ijassa-429	287	26	solution	solution	NOUN
ijassa-429	287	27	(	(	PUNCT
ijassa-429	287	28	that	that	PRON
ijassa-429	287	29	exists	exist	VERB
ijassa-429	287	30	uniquely	uniquely	ADV
ijassa-429	287	31	)	)	PUNCT
ijassa-429	287	32	of	of	ADP
ijassa-429	287	33	the	the	DET
ijassa-429	287	34	equation	equation	NOUN
ijassa-429	287	35	dp	dp	NOUN
ijassa-429	287	36	dt	dt	NOUN
ijassa-429	287	37	=	=	SYM
ijassa-429	287	38	rm	rm	PROPN
ijassa-429	287	39	2	2	NUM
ijassa-429	287	40	∫	∫	PROPN
ijassa-429	287	41	2p	2p	NUM
ijassa-429	287	42	m	m	PROPN
ijassa-429	287	43	0	0	NUM
ijassa-429	287	44	1−xn+1	1−xn+1	NUM
ijassa-429	287	45	1+x	1+x	NUM
ijassa-429	287	46	dx	dx	NOUN
ijassa-429	288	1	=	=	SYM
ijassa-429	288	2	rp	rp	PROPN
ijassa-429	288	3	∑n	∑n	PROPN
ijassa-429	288	4	n=0	n=0	NUM
ijassa-429	288	5	(	(	PUNCT
ijassa-429	288	6	−1)n	−1)n	PROPN
ijassa-429	288	7	n+1	n+1	NUM
ijassa-429	288	8	(	(	PUNCT
ijassa-429	288	9	2	2	NUM
ijassa-429	288	10	pm	pm	NOUN
ijassa-429	288	11	)	)	PUNCT
ijassa-429	288	12	n.	n.	NOUN
ijassa-429	288	13	the	the	DET
ijassa-429	288	14	supremum	supremum	ADJ
ijassa-429	288	15	values	value	NOUN
ijassa-429	288	16	decrease	decrease	NOUN
ijassa-429	288	17	as	as	SCONJ
ijassa-429	288	18	n	n	NUM
ijassa-429	288	19	is	be	AUX
ijassa-429	288	20	increased	increase	VERB
ijassa-429	288	21	.	.	PUNCT
ijassa-429	289	1	rp	rp	NOUN
ijassa-429	289	2	∑n	∑n	PROPN
ijassa-429	289	3	n=0	n=0	NUM
ijassa-429	289	4	(	(	PUNCT
ijassa-429	289	5	−1)n	−1)n	PROPN
ijassa-429	289	6	n+1	n+1	NUM
ijassa-429	289	7	(	(	PUNCT
ijassa-429	289	8	2	2	NUM
ijassa-429	289	9	pm	pm	NOUN
ijassa-429	289	10	)	)	PUNCT
ijassa-429	289	11	n	n	NOUN
ijassa-429	289	12	=	=	SYM
ijassa-429	289	13	rm	rm	NOUN
ijassa-429	289	14	2	2	NUM
ijassa-429	289	15	∫	∫	PROPN
ijassa-429	289	16	2p	2p	NUM
ijassa-429	289	17	m	m	PROPN
ijassa-429	289	18	0	0	NUM
ijassa-429	289	19	1−xn+1	1−xn+1	NUM
ijassa-429	289	20	1+x	1+x	NUM
ijassa-429	289	21	dx	dx	PROPN
ijassa-429	289	22	can	can	AUX
ijassa-429	289	23	not	not	PART
ijassa-429	289	24	be	be	AUX
ijassa-429	289	25	zero	zero	NUM
ijassa-429	289	26	when	when	SCONJ
ijassa-429	289	27	p	p	PROPN
ijassa-429	289	28	≤	≤	NUM
ijassa-429	289	29	m	m	VERB
ijassa-429	289	30	2	2	NUM
ijassa-429	289	31	;	;	PUNCT
ijassa-429	289	32	the	the	DET
ijassa-429	289	33	equation	equation	NOUN
ijassa-429	289	34	∑n	∑n	PROPN
ijassa-429	289	35	n=0	n=0	NUM
ijassa-429	289	36	(	(	PUNCT
ijassa-429	289	37	−1)n	−1)n	X
ijassa-429	289	38	n+1	n+1	X
ijassa-429	289	39	xn	xn	PUNCT
ijassa-429	289	40	=	=	SYM
ijassa-429	289	41	0	0	PROPN
ijassa-429	289	42	does	do	AUX
ijassa-429	289	43	not	not	PART
ijassa-429	289	44	have	have	VERB
ijassa-429	289	45	a	a	DET
ijassa-429	289	46	solution	solution	NOUN
ijassa-429	289	47	less	less	ADJ
ijassa-429	289	48	than	than	ADP
ijassa-429	289	49	1	1	NUM
ijassa-429	289	50	(	(	PUNCT
ijassa-429	289	51	hence	hence	ADV
ijassa-429	289	52	divergence	divergence	NOUN
ijassa-429	289	53	as	as	SCONJ
ijassa-429	289	54	the	the	DET
ijassa-429	289	55	partial	partial	ADJ
ijassa-429	289	56	series	series	NOUN
ijassa-429	289	57	extends	extend	VERB
ijassa-429	289	58	to	to	PART
ijassa-429	289	59	infinite	infinite	VERB
ijassa-429	289	60	form	form	NOUN
ijassa-429	289	61	)	)	PUNCT
ijassa-429	289	62	.	.	PUNCT
ijassa-429	290	1	∫	∫	PROPN
ijassa-429	291	1	α	α	NOUN
ijassa-429	291	2	0	0	NUM
ijassa-429	291	3	1−xn+1	1−xn+1	NUM
ijassa-429	291	4	1+x	1+x	NUM
ijassa-429	291	5	dx	dx	PROPN
ijassa-429	291	6	>	>	X
ijassa-429	291	7	0	0	PUNCT
ijassa-429	292	1	if	if	SCONJ
ijassa-429	292	2	α	α	PRON
ijassa-429	292	3	≤	≤	NOUN
ijassa-429	292	4	1	1	NUM
ijassa-429	292	5	and	and	CCONJ
ijassa-429	292	6	∫	∫	PROPN
ijassa-429	292	7	β	β	X
ijassa-429	292	8	0	0	NUM
ijassa-429	292	9	1−xn+1	1−xn+1	NUM
ijassa-429	292	10	1+x	1+x	NUM
ijassa-429	292	11	dx	dx	PROPN
ijassa-429	292	12	<	<	X
ijassa-429	292	13	0	0	PUNCT
ijassa-429	293	1	if	if	SCONJ
ijassa-429	293	2	β	β	X
ijassa-429	293	3	is	be	AUX
ijassa-429	293	4	(	(	PUNCT
ijassa-429	293	5	sufficiently	sufficiently	ADV
ijassa-429	293	6	)	)	PUNCT
ijassa-429	293	7	large	large	ADJ
ijassa-429	293	8	.	.	PUNCT
ijassa-429	294	1	there	there	PRON
ijassa-429	294	2	exists	exist	VERB
ijassa-429	294	3	γ	γ	X
ijassa-429	294	4	between	between	ADP
ijassa-429	294	5	α	α	PROPN
ijassa-429	294	6	and	and	CCONJ
ijassa-429	294	7	β	β	PRON
ijassa-429	294	8	such	such	ADJ
ijassa-429	294	9	that	that	DET
ijassa-429	294	10	∫	∫	PROPN
ijassa-429	294	11	γ	γ	X
ijassa-429	294	12	0	0	PROPN
ijassa-429	294	13	1−xn+1	1−xn+1	NUM
ijassa-429	294	14	1+x	1+x	NUM
ijassa-429	294	15	dx	dx	NOUN
ijassa-429	294	16	=	=	SYM
ijassa-429	294	17	0	0	NUM
ijassa-429	294	18	;	;	PUNCT
ijassa-429	294	19	∫	∫	PROPN
ijassa-429	294	20	α	α	NOUN
ijassa-429	294	21	0	0	NUM
ijassa-429	294	22	1−xn+1	1−xn+1	NUM
ijassa-429	294	23	1+x	1+x	NUM
ijassa-429	294	24	dx	dx	PROPN
ijassa-429	294	25	>	>	X
ijassa-429	294	26	∫	∫	PROPN
ijassa-429	294	27	β	β	X
ijassa-429	294	28	0	0	NUM
ijassa-429	294	29	1−xn+1	1−xn+1	NUM
ijassa-429	294	30	1+x	1+x	NUM
ijassa-429	294	31	dx	dx	PROPN
ijassa-429	294	32	for	for	ADP
ijassa-429	294	33	α	α	PRON
ijassa-429	294	34	≤	≤	ADJ
ijassa-429	294	35	1	1	NUM
ijassa-429	294	36	<	<	X
ijassa-429	294	37	β	β	NOUN
ijassa-429	294	38	.	.	PUNCT
ijassa-429	295	1	more	more	ADV
ijassa-429	295	2	precisely	precisely	ADV
ijassa-429	295	3	,	,	PUNCT
ijassa-429	295	4	an	an	DET
ijassa-429	295	5	arbitrary	arbitrary	ADJ
ijassa-429	295	6	α	α	NOUN
ijassa-429	295	7	beyond	beyond	ADP
ijassa-429	295	8	the	the	DET
ijassa-429	295	9	point	point	NOUN
ijassa-429	295	10	of	of	ADP
ijassa-429	295	11	inflection	inflection	NOUN
ijassa-429	295	12	presents	present	VERB
ijassa-429	295	13	a	a	DET
ijassa-429	295	14	scenario	scenario	NOUN
ijassa-429	295	15	that	that	PRON
ijassa-429	295	16	is	be	AUX
ijassa-429	295	17	consistent	consistent	ADJ
ijassa-429	295	18	with	with	ADP
ijassa-429	295	19	the	the	DET
ijassa-429	295	20	definition	definition	NOUN
ijassa-429	295	21	of	of	ADP
ijassa-429	295	22	a	a	DET
ijassa-429	295	23	maximum	maximum	ADJ
ijassa-429	295	24	point	point	NOUN
ijassa-429	295	25	and	and	CCONJ
ijassa-429	295	26	downward	downward	ADJ
ijassa-429	295	27	concavity	concavity	NOUN
ijassa-429	295	28	in	in	ADP
ijassa-429	295	29	this	this	DET
ijassa-429	295	30	domain	domain	NOUN
ijassa-429	295	31	.	.	PUNCT
ijassa-429	296	1	hence	hence	ADV
ijassa-429	296	2	,	,	PUNCT
ijassa-429	296	3	the	the	DET
ijassa-429	296	4	equation	equation	NOUN
ijassa-429	296	5	n∑	n∑	PROPN
ijassa-429	296	6	n=0	n=0	NUM
ijassa-429	296	7	(	(	PUNCT
ijassa-429	296	8	−1)n	−1)n	PROPN
ijassa-429	296	9	n+	n+	ADP
ijassa-429	296	10	1	1	NUM
ijassa-429	296	11	xn	xn	X
ijassa-429	296	12	=	=	SYM
ijassa-429	296	13	0	0	NUM
ijassa-429	296	14	(	(	PUNCT
ijassa-429	296	15	13	13	NUM
ijassa-429	296	16	)	)	PUNCT
ijassa-429	296	17	has	have	VERB
ijassa-429	296	18	a	a	DET
ijassa-429	296	19	unique	unique	ADJ
ijassa-429	296	20	positive	positive	ADJ
ijassa-429	296	21	solution	solution	NOUN
ijassa-429	296	22	x0	x0	PROPN
ijassa-429	296	23	.	.	PUNCT
ijassa-429	297	1	the	the	DET
ijassa-429	297	2	formula	formula	NOUN
ijassa-429	297	3	for	for	ADP
ijassa-429	297	4	calculating	calculate	VERB
ijassa-429	297	5	the	the	DET
ijassa-429	297	6	supremum	supremum	NOUN
ijassa-429	297	7	of	of	ADP
ijassa-429	297	8	p	p	PROPN
ijassa-429	297	9	is	be	AUX
ijassa-429	297	10	psup	psup	ADJ
ijassa-429	297	11	=	=	PUNCT
ijassa-429	297	12	x0p	x0p	PUNCT
ijassa-429	297	13	=	=	PUNCT
ijassa-429	298	1	x0	x0	PROPN
ijassa-429	298	2	m	m	VERB
ijassa-429	298	3	2	2	NUM
ijassa-429	298	4	.	.	PUNCT
ijassa-429	299	1	in	in	ADP
ijassa-429	299	2	summary	summary	NOUN
ijassa-429	299	3	,	,	PUNCT
ijassa-429	299	4	each	each	DET
ijassa-429	299	5	term	term	NOUN
ijassa-429	299	6	is	be	AUX
ijassa-429	299	7	smaller	small	ADJ
ijassa-429	299	8	than	than	ADP
ijassa-429	299	9	the	the	DET
ijassa-429	299	10	term	term	NOUN
ijassa-429	299	11	preceding	precede	VERB
ijassa-429	299	12	it	it	PRON
ijassa-429	299	13	until	until	SCONJ
ijassa-429	299	14	p	p	NOUN
ijassa-429	299	15	is	be	AUX
ijassa-429	299	16	equal	equal	ADJ
ijassa-429	299	17	to	to	ADP
ijassa-429	299	18	the	the	DET
ijassa-429	299	19	least	least	ADJ
ijassa-429	299	20	upper	upper	ADJ
ijassa-429	299	21	bound	bind	VERB
ijassa-429	299	22	.	.	PUNCT
ijassa-429	300	1	at	at	ADP
ijassa-429	300	2	p	p	PROPN
ijassa-429	300	3	=	=	PROPN
ijassa-429	300	4	m	m	PROPN
ijassa-429	300	5	2	2	NUM
ijassa-429	300	6	,	,	PUNCT
ijassa-429	300	7	dp	dp	NOUN
ijassa-429	300	8	dt	dt	NOUN
ijassa-429	300	9	has	have	AUX
ijassa-429	300	10	reached	reach	VERB
ijassa-429	300	11	its	its	PRON
ijassa-429	300	12	maximum	maximum	ADJ
ijassa-429	300	13	value	value	NOUN
ijassa-429	300	14	and	and	CCONJ
ijassa-429	300	15	will	will	AUX
ijassa-429	300	16	decrease	decrease	VERB
ijassa-429	300	17	but	but	CCONJ
ijassa-429	300	18	will	will	AUX
ijassa-429	300	19	still	still	ADV
ijassa-429	300	20	be	be	AUX
ijassa-429	300	21	positive	positive	ADJ
ijassa-429	300	22	,	,	PUNCT
ijassa-429	300	23	so	so	CCONJ
ijassa-429	300	24	the	the	DET
ijassa-429	300	25	negative	negative	ADJ
ijassa-429	300	26	terms	term	NOUN
ijassa-429	300	27	can	can	AUX
ijassa-429	300	28	not	not	PART
ijassa-429	300	29	be	be	AUX
ijassa-429	300	30	larger	large	ADJ
ijassa-429	300	31	than	than	ADP
ijassa-429	300	32	the	the	DET
ijassa-429	300	33	positive	positive	ADJ
ijassa-429	300	34	terms	term	NOUN
ijassa-429	300	35	before	before	ADP
ijassa-429	300	36	them	they	PRON
ijassa-429	300	37	.	.	PUNCT
ijassa-429	301	1	the	the	DET
ijassa-429	301	2	slopes	slope	NOUN
ijassa-429	301	3	remain	remain	VERB
ijassa-429	301	4	positive	positive	ADJ
ijassa-429	301	5	and	and	CCONJ
ijassa-429	301	6	decrease	decrease	NOUN
ijassa-429	301	7	as	as	SCONJ
ijassa-429	301	8	dp	dp	NOUN
ijassa-429	301	9	dt	dt	NOUN
ijassa-429	301	10	approaches	approach	VERB
ijassa-429	301	11	0	0	NUM
ijassa-429	301	12	at	at	ADP
ijassa-429	301	13	the	the	DET
ijassa-429	301	14	least	least	ADJ
ijassa-429	301	15	upper	upper	ADJ
ijassa-429	301	16	bound	bind	VERB
ijassa-429	301	17	without	without	ADP
ijassa-429	301	18	ever	ever	ADV
ijassa-429	301	19	reaching	reach	VERB
ijassa-429	301	20	it	it	PRON
ijassa-429	301	21	.	.	PUNCT
ijassa-429	302	1	therefore	therefore	ADV
ijassa-429	302	2	,	,	PUNCT
ijassa-429	302	3	dp	dp	NOUN
ijassa-429	302	4	dt	dt	NOUN
ijassa-429	302	5	will	will	AUX
ijassa-429	302	6	always	always	ADV
ijassa-429	302	7	be	be	AUX
ijassa-429	302	8	positive	positive	ADJ
ijassa-429	302	9	despite	despite	SCONJ
ijassa-429	302	10	negative	negative	ADJ
ijassa-429	302	11	concavity	concavity	NOUN
ijassa-429	302	12	(	(	PUNCT
ijassa-429	302	13	reduction	reduction	NOUN
ijassa-429	302	14	in	in	ADP
ijassa-429	302	15	value	value	NOUN
ijassa-429	302	16	)	)	PUNCT
ijassa-429	302	17	past	past	ADP
ijassa-429	302	18	the	the	DET
ijassa-429	302	19	point	point	NOUN
ijassa-429	302	20	of	of	ADP
ijassa-429	302	21	inflection	inflection	NOUN
ijassa-429	302	22	,	,	PUNCT
ijassa-429	302	23	and	and	CCONJ
ijassa-429	302	24	the	the	DET
ijassa-429	302	25	limit	limit	NOUN
ijassa-429	302	26	of	of	ADP
ijassa-429	302	27	dp	dp	NOUN
ijassa-429	302	28	dt	dt	NOUN
ijassa-429	302	29	as	as	SCONJ
ijassa-429	302	30	p	p	PROPN
ijassa-429	302	31	approaches	approach	VERB
ijassa-429	302	32	a	a	DET
ijassa-429	302	33	set	set	NOUN
ijassa-429	302	34	of	of	ADP
ijassa-429	302	35	arbitrary	arbitrary	ADJ
ijassa-429	302	36	values	value	NOUN
ijassa-429	302	37	reveals	reveal	VERB
ijassa-429	302	38	an	an	DET
ijassa-429	302	39	approximation	approximation	NOUN
ijassa-429	302	40	of	of	ADP
ijassa-429	302	41	the	the	DET
ijassa-429	302	42	least	least	ADJ
ijassa-429	302	43	upper	upper	ADJ
ijassa-429	302	44	bound	bind	VERB
ijassa-429	302	45	of	of	ADP
ijassa-429	302	46	the	the	DET
ijassa-429	302	47	function	function	NOUN
ijassa-429	302	48	.	.	PUNCT
ijassa-429	303	1	if	if	SCONJ
ijassa-429	303	2	the	the	DET
ijassa-429	303	3	limit	limit	NOUN
ijassa-429	303	4	reveals	reveal	VERB
ijassa-429	303	5	that	that	SCONJ
ijassa-429	303	6	dp	dp	NOUN
ijassa-429	303	7	dt	dt	NOUN
ijassa-429	303	8	is	be	AUX
ijassa-429	303	9	less	less	ADJ
ijassa-429	303	10	than	than	ADP
ijassa-429	303	11	0	0	NUM
ijassa-429	303	12	at	at	ADP
ijassa-429	303	13	a	a	DET
ijassa-429	303	14	particular	particular	ADJ
ijassa-429	303	15	value	value	NOUN
ijassa-429	303	16	of	of	ADP
ijassa-429	303	17	p	p	NOUN
ijassa-429	303	18	,	,	PUNCT
ijassa-429	303	19	then	then	ADV
ijassa-429	303	20	the	the	DET
ijassa-429	303	21	least	least	ADV
ijassa-429	303	22	upper	upper	ADJ
ijassa-429	303	23	bound	bind	VERB
ijassa-429	303	24	is	be	AUX
ijassa-429	303	25	below	below	ADP
ijassa-429	303	26	that	that	DET
ijassa-429	303	27	value	value	NOUN
ijassa-429	303	28	;	;	PUNCT
ijassa-429	303	29	the	the	DET
ijassa-429	303	30	value	value	NOUN
ijassa-429	303	31	can	can	AUX
ijassa-429	303	32	never	never	ADV
ijassa-429	303	33	be	be	AUX
ijassa-429	303	34	reached	reach	VERB
ijassa-429	303	35	.	.	PUNCT
ijassa-429	304	1	at	at	ADP
ijassa-429	304	2	the	the	DET
ijassa-429	304	3	upper	upper	ADJ
ijassa-429	304	4	limit	limit	NOUN
ijassa-429	304	5	,	,	PUNCT
ijassa-429	304	6	a	a	DET
ijassa-429	304	7	horizontal	horizontal	ADJ
ijassa-429	304	8	asymptote	asymptote	NOUN
ijassa-429	304	9	,	,	PUNCT
ijassa-429	304	10	dp	dp	NOUN
ijassa-429	304	11	dt	dt	NOUN
ijassa-429	304	12	is	be	AUX
ijassa-429	304	13	0	0	PROPN
ijassa-429	304	14	.	.	PUNCT
ijassa-429	305	1	therefore	therefore	ADV
ijassa-429	305	2	,	,	PUNCT
ijassa-429	305	3	dp	dp	NOUN
ijassa-429	305	4	dt	dt	NOUN
ijassa-429	305	5	approaches	approach	VERB
ijassa-429	305	6	this	this	DET
ijassa-429	305	7	value	value	NOUN
ijassa-429	305	8	at	at	ADP
ijassa-429	305	9	the	the	DET
ijassa-429	305	10	transition	transition	NOUN
ijassa-429	305	11	from	from	ADP
ijassa-429	305	12	a	a	DET
ijassa-429	305	13	small	small	ADJ
ijassa-429	305	14	positive	positive	ADJ
ijassa-429	305	15	value	value	NOUN
ijassa-429	305	16	to	to	ADP
ijassa-429	305	17	a	a	DET
ijassa-429	305	18	small	small	ADJ
ijassa-429	305	19	negative	negative	ADJ
ijassa-429	305	20	value	value	NOUN
ijassa-429	305	21	.	.	PUNCT
ijassa-429	306	1	when	when	SCONJ
ijassa-429	306	2	limit	limit	VERB
ijassa-429	306	3	comparison	comparison	NOUN
ijassa-429	306	4	reveals	reveal	VERB
ijassa-429	306	5	that	that	SCONJ
ijassa-429	306	6	one	one	NUM
ijassa-429	306	7	value	value	NOUN
ijassa-429	306	8	results	result	VERB
ijassa-429	306	9	in	in	ADP
ijassa-429	306	10	a	a	DET
ijassa-429	306	11	positive	positive	ADJ
ijassa-429	306	12	dp	dp	NOUN
ijassa-429	306	13	dt	dt	NOUN
ijassa-429	306	14	and	and	CCONJ
ijassa-429	306	15	the	the	DET
ijassa-429	306	16	next	next	ADJ
ijassa-429	306	17	value	value	NOUN
ijassa-429	306	18	for	for	ADP
ijassa-429	306	19	p	p	NOUN
ijassa-429	306	20	results	result	NOUN
ijassa-429	306	21	in	in	ADP
ijassa-429	306	22	a	a	DET
ijassa-429	306	23	negative	negative	ADJ
ijassa-429	306	24	dp	dp	NOUN
ijassa-429	306	25	dt	dt	NOUN
ijassa-429	306	26	,	,	PUNCT
ijassa-429	306	27	the	the	DET
ijassa-429	306	28	bound	bind	VERB
ijassa-429	306	29	must	must	AUX
ijassa-429	306	30	lie	lie	VERB
ijassa-429	306	31	between	between	ADP
ijassa-429	306	32	these	these	DET
ijassa-429	306	33	two	two	NUM
ijassa-429	306	34	points	point	NOUN
ijassa-429	306	35	.	.	PUNCT
ijassa-429	307	1	in	in	ADP
ijassa-429	307	2	the	the	DET
ijassa-429	307	3	advances	advance	NOUN
ijassa-429	307	4	in	in	ADP
ijassa-429	307	5	systems	system	NOUN
ijassa-429	307	6	science	science	NOUN
ijassa-429	307	7	and	and	CCONJ
ijassa-429	307	8	applications	application	NOUN
ijassa-429	307	9	(	(	PUNCT
ijassa-429	307	10	2013	2013	NUM
ijassa-429	307	11	)	)	PUNCT
ijassa-429	307	12	vol.13	vol.13	NOUN
ijassa-429	307	13	no.1	no.1	VERB
ijassa-429	307	14	93	93	NUM
ijassa-429	307	15	logistic	logistic	ADJ
ijassa-429	307	16	case	case	NOUN
ijassa-429	307	17	,	,	PUNCT
ijassa-429	307	18	this	this	DET
ijassa-429	307	19	limit	limit	NOUN
ijassa-429	307	20	is	be	AUX
ijassa-429	307	21	m	m	PRON
ijassa-429	307	22	.	.	PUNCT
ijassa-429	308	1	by	by	ADP
ijassa-429	308	2	contrast	contrast	NOUN
ijassa-429	308	3	,	,	PUNCT
ijassa-429	308	4	a	a	DET
ijassa-429	308	5	function	function	NOUN
ijassa-429	308	6	with	with	ADP
ijassa-429	308	7	an	an	DET
ijassa-429	308	8	odd	odd	ADJ
ijassa-429	308	9	degree	degree	NOUN
ijassa-429	308	10	of	of	ADP
ijassa-429	308	11	p	p	NOUN
ijassa-429	308	12	resembles	resemble	VERB
ijassa-429	308	13	the	the	DET
ijassa-429	308	14	properties	property	NOUN
ijassa-429	308	15	of	of	ADP
ijassa-429	308	16	an	an	DET
ijassa-429	308	17	exponential	exponential	ADJ
ijassa-429	308	18	function	function	NOUN
ijassa-429	308	19	.	.	PUNCT
ijassa-429	309	1	it	it	PRON
ijassa-429	309	2	is	be	AUX
ijassa-429	309	3	concave	concave	VERB
ijassa-429	309	4	up	up	ADP
ijassa-429	309	5	as	as	ADV
ijassa-429	309	6	well	well	ADV
ijassa-429	309	7	as	as	ADP
ijassa-429	309	8	always	always	ADV
ijassa-429	309	9	increasing	increase	VERB
ijassa-429	309	10	;	;	PUNCT
ijassa-429	309	11	the	the	DET
ijassa-429	309	12	sum	sum	NOUN
ijassa-429	309	13	of	of	ADP
ijassa-429	309	14	the	the	DET
ijassa-429	309	15	alternating	alternate	VERB
ijassa-429	309	16	terms	term	NOUN
ijassa-429	309	17	is	be	AUX
ijassa-429	309	18	positive	positive	ADJ
ijassa-429	309	19	,	,	PUNCT
ijassa-429	309	20	plus	plus	CCONJ
ijassa-429	309	21	the	the	DET
ijassa-429	309	22	addition	addition	NOUN
ijassa-429	309	23	of	of	ADP
ijassa-429	309	24	a	a	DET
ijassa-429	309	25	positive	positive	ADJ
ijassa-429	309	26	term	term	NOUN
ijassa-429	309	27	.	.	PUNCT
ijassa-429	310	1	it	it	PRON
ijassa-429	310	2	has	have	VERB
ijassa-429	310	3	neither	neither	CCONJ
ijassa-429	310	4	a	a	DET
ijassa-429	310	5	point	point	NOUN
ijassa-429	310	6	of	of	ADP
ijassa-429	310	7	inflection	inflection	NOUN
ijassa-429	310	8	nor	nor	CCONJ
ijassa-429	310	9	an	an	DET
ijassa-429	310	10	upper	upper	ADJ
ijassa-429	310	11	bound	bind	VERB
ijassa-429	310	12	.	.	PUNCT
ijassa-429	311	1	in	in	ADP
ijassa-429	311	2	terms	term	NOUN
ijassa-429	311	3	of	of	ADP
ijassa-429	311	4	the	the	DET
ijassa-429	311	5	second	second	ADJ
ijassa-429	311	6	derivative	derivative	NOUN
ijassa-429	311	7	defined	define	VERB
ijassa-429	311	8	above	above	ADV
ijassa-429	311	9	,	,	PUNCT
ijassa-429	311	10	the	the	DET
ijassa-429	311	11	incomplete	incomplete	ADJ
ijassa-429	311	12	pairings	pairing	NOUN
ijassa-429	311	13	ensure	ensure	VERB
ijassa-429	311	14	positive	positive	ADJ
ijassa-429	311	15	concavity	concavity	NOUN
ijassa-429	311	16	(	(	PUNCT
ijassa-429	311	17	theorem	theorem	NOUN
ijassa-429	311	18	2	2	NUM
ijassa-429	311	19	)	)	PUNCT
ijassa-429	311	20	.	.	PUNCT
ijassa-429	312	1	the	the	DET
ijassa-429	312	2	series	series	NOUN
ijassa-429	312	3	and	and	CCONJ
ijassa-429	312	4	its	its	PRON
ijassa-429	312	5	truncations	truncation	NOUN
ijassa-429	312	6	can	can	AUX
ijassa-429	312	7	be	be	AUX
ijassa-429	312	8	analyzed	analyze	VERB
ijassa-429	312	9	as	as	ADP
ijassa-429	312	10	a	a	DET
ijassa-429	312	11	transcritical	transcritical	ADJ
ijassa-429	312	12	bifurcation	bifurcation	NOUN
ijassa-429	312	13	[	[	X
ijassa-429	312	14	18	18	NUM
ijassa-429	312	15	]	]	PUNCT
ijassa-429	312	16	.	.	PUNCT
ijassa-429	313	1	the	the	DET
ijassa-429	313	2	concept	concept	NOUN
ijassa-429	313	3	of	of	ADP
ijassa-429	313	4	“	"	PUNCT
ijassa-429	313	5	harvesting	harvesting	NOUN
ijassa-429	313	6	”	"	PUNCT
ijassa-429	313	7	,	,	PUNCT
ijassa-429	313	8	initially	initially	ADV
ijassa-429	313	9	applied	apply	VERB
ijassa-429	313	10	to	to	ADP
ijassa-429	313	11	logistic	logistic	ADJ
ijassa-429	313	12	growth	growth	NOUN
ijassa-429	313	13	,	,	PUNCT
ijassa-429	313	14	remains	remain	VERB
ijassa-429	313	15	.	.	PUNCT
ijassa-429	314	1	for	for	ADP
ijassa-429	314	2	even	even	ADJ
ijassa-429	314	3	degrees	degree	NOUN
ijassa-429	314	4	of	of	ADP
ijassa-429	314	5	p	p	NOUN
ijassa-429	314	6	,	,	PUNCT
ijassa-429	314	7	the	the	DET
ijassa-429	314	8	model	model	NOUN
ijassa-429	314	9	exhibits	exhibit	VERB
ijassa-429	314	10	logistic	logistic	ADJ
ijassa-429	314	11	-	-	PUNCT
ijassa-429	314	12	like	like	ADJ
ijassa-429	314	13	properties	property	NOUN
ijassa-429	314	14	and	and	CCONJ
ijassa-429	314	15	therefore	therefore	ADV
ijassa-429	314	16	the	the	DET
ijassa-429	314	17	potential	potential	NOUN
ijassa-429	314	18	for	for	ADP
ijassa-429	314	19	two	two	NUM
ijassa-429	314	20	positive	positive	ADJ
ijassa-429	314	21	zeros	zero	NOUN
ijassa-429	314	22	.	.	PUNCT
ijassa-429	315	1	in	in	ADP
ijassa-429	315	2	logistic	logistic	ADJ
ijassa-429	315	3	growth	growth	NOUN
ijassa-429	315	4	(	(	PUNCT
ijassa-429	315	5	power	power	NOUN
ijassa-429	315	6	of	of	ADP
ijassa-429	315	7	p	p	NOUN
ijassa-429	315	8	is	be	AUX
ijassa-429	315	9	2	2	NUM
ijassa-429	315	10	)	)	PUNCT
ijassa-429	315	11	,	,	PUNCT
ijassa-429	315	12	zeros	zero	NOUN
ijassa-429	315	13	are	be	AUX
ijassa-429	315	14	found	find	VERB
ijassa-429	315	15	as	as	ADP
ijassa-429	315	16	the	the	DET
ijassa-429	315	17	solutions	solution	NOUN
ijassa-429	315	18	to	to	ADP
ijassa-429	315	19	a	a	DET
ijassa-429	315	20	simplified	simplified	ADJ
ijassa-429	315	21	,	,	PUNCT
ijassa-429	315	22	basic	basic	ADJ
ijassa-429	315	23	quadratic	quadratic	ADJ
ijassa-429	315	24	form	form	NOUN
ijassa-429	315	25	of	of	ADP
ijassa-429	315	26	the	the	DET
ijassa-429	315	27	equation	equation	NOUN
ijassa-429	315	28	.	.	PUNCT
ijassa-429	316	1	in	in	ADP
ijassa-429	316	2	the	the	DET
ijassa-429	316	3	general	general	ADJ
ijassa-429	316	4	situation	situation	NOUN
ijassa-429	316	5	(	(	PUNCT
ijassa-429	316	6	power	power	NOUN
ijassa-429	316	7	of	of	ADP
ijassa-429	316	8	p	p	NOUN
ijassa-429	316	9	is	be	AUX
ijassa-429	316	10	even	even	ADV
ijassa-429	316	11	and	and	CCONJ
ijassa-429	316	12	larger	large	ADJ
ijassa-429	316	13	than	than	ADP
ijassa-429	316	14	or	or	CCONJ
ijassa-429	316	15	equal	equal	ADJ
ijassa-429	316	16	to	to	ADP
ijassa-429	316	17	4	4	NUM
ijassa-429	316	18	)	)	PUNCT
ijassa-429	316	19	,	,	PUNCT
ijassa-429	316	20	by	by	ADP
ijassa-429	316	21	the	the	DET
ijassa-429	316	22	integral	integral	ADJ
ijassa-429	316	23	representation	representation	NOUN
ijassa-429	316	24	given	give	VERB
ijassa-429	316	25	in	in	ADP
ijassa-429	316	26	theorem	theorem	ADJ
ijassa-429	316	27	3	3	NUM
ijassa-429	316	28	(	(	PUNCT
ijassa-429	316	29	ii	ii	NOUN
ijassa-429	316	30	)	)	PUNCT
ijassa-429	316	31	,	,	PUNCT
ijassa-429	316	32	dp	dp	NOUN
ijassa-429	316	33	dt	dt	NOUN
ijassa-429	316	34	=	=	SYM
ijassa-429	316	35	0	0	PROPN
ijassa-429	316	36	has	have	VERB
ijassa-429	316	37	two	two	NUM
ijassa-429	316	38	positive	positive	ADJ
ijassa-429	316	39	zeros	zero	NOUN
ijassa-429	316	40	,	,	PUNCT
ijassa-429	316	41	one	one	NUM
ijassa-429	316	42	positive	positive	ADJ
ijassa-429	316	43	zero	zero	NUM
ijassa-429	316	44	,	,	PUNCT
ijassa-429	316	45	or	or	CCONJ
ijassa-429	316	46	no	no	DET
ijassa-429	316	47	positive	positive	ADJ
ijassa-429	316	48	(	(	PUNCT
ijassa-429	316	49	real	real	ADJ
ijassa-429	316	50	)	)	PUNCT
ijassa-429	316	51	zeros	zero	NOUN
ijassa-429	316	52	.	.	PUNCT
ijassa-429	317	1	such	such	ADJ
ijassa-429	317	2	zeros	zero	NOUN
ijassa-429	317	3	in	in	ADP
ijassa-429	317	4	the	the	DET
ijassa-429	317	5	forms	form	NOUN
ijassa-429	317	6	of	of	ADP
ijassa-429	317	7	the	the	DET
ijassa-429	317	8	series	series	NOUN
ijassa-429	317	9	can	can	AUX
ijassa-429	317	10	be	be	AUX
ijassa-429	317	11	determined	determine	VERB
ijassa-429	317	12	by	by	ADP
ijassa-429	317	13	utilizing	utilize	VERB
ijassa-429	317	14	numerical	numerical	ADJ
ijassa-429	317	15	methods	method	NOUN
ijassa-429	317	16	.	.	PUNCT
ijassa-429	318	1	as	as	ADP
ijassa-429	318	2	the	the	DET
ijassa-429	318	3	degree	degree	NOUN
ijassa-429	318	4	increases	increase	NOUN
ijassa-429	318	5	,	,	PUNCT
ijassa-429	318	6	the	the	DET
ijassa-429	318	7	amount	amount	NOUN
ijassa-429	318	8	of	of	ADP
ijassa-429	318	9	symmetry	symmetry	NOUN
ijassa-429	318	10	as	as	SCONJ
ijassa-429	318	11	found	find	VERB
ijassa-429	318	12	in	in	ADP
ijassa-429	318	13	logistic	logistic	ADJ
ijassa-429	318	14	models	model	NOUN
ijassa-429	318	15	decreases	decrease	VERB
ijassa-429	318	16	.	.	PUNCT
ijassa-429	319	1	as	as	ADP
ijassa-429	319	2	the	the	DET
ijassa-429	319	3	number	number	NOUN
ijassa-429	319	4	of	of	ADP
ijassa-429	319	5	terms	term	NOUN
ijassa-429	319	6	in	in	ADP
ijassa-429	319	7	the	the	DET
ijassa-429	319	8	polynomial	polynomial	ADJ
ijassa-429	319	9	increases	increase	NOUN
ijassa-429	319	10	,	,	PUNCT
ijassa-429	319	11	and	and	CCONJ
ijassa-429	319	12	approaches	approach	VERB
ijassa-429	319	13	the	the	DET
ijassa-429	319	14	closed	closed	ADJ
ijassa-429	319	15	form	form	NOUN
ijassa-429	319	16	of	of	ADP
ijassa-429	319	17	the	the	DET
ijassa-429	319	18	series	series	NOUN
ijassa-429	319	19	,	,	PUNCT
ijassa-429	319	20	the	the	DET
ijassa-429	319	21	equation	equation	NOUN
ijassa-429	319	22	becomes	become	VERB
ijassa-429	319	23	increasingly	increasingly	ADV
ijassa-429	319	24	complex	complex	ADJ
ijassa-429	319	25	to	to	PART
ijassa-429	319	26	solve	solve	VERB
ijassa-429	319	27	.	.	PUNCT
ijassa-429	320	1	in	in	ADP
ijassa-429	320	2	this	this	DET
ijassa-429	320	3	parametric	parametric	ADJ
ijassa-429	320	4	approach	approach	NOUN
ijassa-429	320	5	,	,	PUNCT
ijassa-429	320	6	fixed	fix	VERB
ijassa-429	320	7	points	point	NOUN
ijassa-429	320	8	are	be	AUX
ijassa-429	320	9	determined	determine	VERB
ijassa-429	320	10	as	as	ADP
ijassa-429	320	11	the	the	DET
ijassa-429	320	12	variable	variable	ADJ
ijassa-429	320	13	values	value	NOUN
ijassa-429	320	14	that	that	PRON
ijassa-429	320	15	set	set	VERB
ijassa-429	320	16	the	the	DET
ijassa-429	320	17	equation	equation	NOUN
ijassa-429	320	18	at	at	ADP
ijassa-429	320	19	equilibrium	equilibrium	NOUN
ijassa-429	320	20	.	.	PUNCT
ijassa-429	321	1	a	a	DET
ijassa-429	321	2	harvesting	harvesting	NOUN
ijassa-429	321	3	term	term	NOUN
ijassa-429	321	4	introduces	introduce	VERB
ijassa-429	321	5	a	a	DET
ijassa-429	321	6	parameter	parameter	NOUN
ijassa-429	321	7	that	that	PRON
ijassa-429	321	8	affects	affect	VERB
ijassa-429	321	9	the	the	DET
ijassa-429	321	10	location	location	NOUN
ijassa-429	321	11	of	of	ADP
ijassa-429	321	12	such	such	ADJ
ijassa-429	321	13	points	point	NOUN
ijassa-429	321	14	,	,	PUNCT
ijassa-429	321	15	and	and	CCONJ
ijassa-429	321	16	their	their	PRON
ijassa-429	321	17	position	position	NOUN
ijassa-429	321	18	for	for	ADP
ijassa-429	321	19	approaching	approach	VERB
ijassa-429	321	20	or	or	CCONJ
ijassa-429	321	21	separating	separate	VERB
ijassa-429	321	22	from	from	ADP
ijassa-429	321	23	one	one	NUM
ijassa-429	321	24	another	another	DET
ijassa-429	321	25	as	as	ADP
ijassa-429	321	26	the	the	DET
ijassa-429	321	27	differential	differential	ADJ
ijassa-429	321	28	increases	increase	NOUN
ijassa-429	321	29	or	or	CCONJ
ijassa-429	321	30	decreases	decrease	NOUN
ijassa-429	321	31	.	.	PUNCT
ijassa-429	322	1	the	the	DET
ijassa-429	322	2	equation	equation	NOUN
ijassa-429	322	3	for	for	ADP
ijassa-429	322	4	transcritical	transcritical	ADJ
ijassa-429	322	5	bifurcation	bifurcation	NOUN
ijassa-429	322	6	is	be	AUX
ijassa-429	322	7	as	as	SCONJ
ijassa-429	322	8	follows	follow	VERB
ijassa-429	322	9	(	(	PUNCT
ijassa-429	322	10	equation	equation	NOUN
ijassa-429	322	11	14	14	NUM
ijassa-429	322	12	):	):	PUNCT
ijassa-429	323	1	dp	dp	NOUN
ijassa-429	323	2	dt	dt	NOUN
ijassa-429	323	3	=	=	PUNCT
ijassa-429	323	4	rp	rp	NOUN
ijassa-429	323	5	∞∑	∞∑	PROPN
ijassa-429	323	6	n=0	n=0	NUM
ijassa-429	323	7	(	(	PUNCT
ijassa-429	323	8	−1)n	−1)n	X
ijassa-429	323	9	n+	n+	ADP
ijassa-429	323	10	1	1	NUM
ijassa-429	323	11	×	×	NOUN
ijassa-429	323	12	(	(	PUNCT
ijassa-429	323	13	2p	2p	NUM
ijassa-429	323	14	m	m	NOUN
ijassa-429	323	15	)	)	PUNCT
ijassa-429	323	16	n	n	X
ijassa-429	323	17	−h	−h	ADJ
ijassa-429	323	18	(	(	PUNCT
ijassa-429	323	19	14	14	NUM
ijassa-429	323	20	)	)	PUNCT
ijassa-429	323	21	because	because	SCONJ
ijassa-429	323	22	the	the	DET
ijassa-429	323	23	model	model	NOUN
ijassa-429	323	24	is	be	AUX
ijassa-429	323	25	idealized	idealize	VERB
ijassa-429	323	26	,	,	PUNCT
ijassa-429	323	27	it	it	PRON
ijassa-429	323	28	can	can	AUX
ijassa-429	323	29	be	be	AUX
ijassa-429	323	30	used	use	VERB
ijassa-429	323	31	as	as	ADP
ijassa-429	323	32	a	a	DET
ijassa-429	323	33	method	method	NOUN
ijassa-429	323	34	to	to	PART
ijassa-429	323	35	solve	solve	VERB
ijassa-429	323	36	for	for	ADP
ijassa-429	323	37	rate	rate	NOUN
ijassa-429	323	38	of	of	ADP
ijassa-429	323	39	growth	growth	NOUN
ijassa-429	323	40	.	.	PUNCT
ijassa-429	324	1	such	such	ADJ
ijassa-429	324	2	calculations	calculation	NOUN
ijassa-429	324	3	are	be	AUX
ijassa-429	324	4	consistent	consistent	ADJ
ijassa-429	324	5	with	with	ADP
ijassa-429	324	6	the	the	DET
ijassa-429	324	7	numerical	numerical	ADJ
ijassa-429	324	8	estimates	estimate	NOUN
ijassa-429	324	9	.	.	PUNCT
ijassa-429	325	1	like	like	ADP
ijassa-429	325	2	theta	theta	NOUN
ijassa-429	325	3	logistic	logistic	ADJ
ijassa-429	325	4	models	model	NOUN
ijassa-429	325	5	,	,	PUNCT
ijassa-429	325	6	this	this	DET
ijassa-429	325	7	model	model	NOUN
ijassa-429	325	8	introduces	introduce	VERB
ijassa-429	325	9	precision	precision	NOUN
ijassa-429	325	10	through	through	ADP
ijassa-429	325	11	specific	specific	ADJ
ijassa-429	325	12	terms	term	NOUN
ijassa-429	325	13	added	add	VERB
ijassa-429	325	14	to	to	ADP
ijassa-429	325	15	the	the	DET
ijassa-429	325	16	traditional	traditional	ADJ
ijassa-429	325	17	logistic	logistic	ADJ
ijassa-429	325	18	model	model	NOUN
ijassa-429	325	19	.	.	PUNCT
ijassa-429	326	1	it	it	PRON
ijassa-429	326	2	is	be	AUX
ijassa-429	326	3	unique	unique	ADJ
ijassa-429	326	4	in	in	ADP
ijassa-429	326	5	that	that	SCONJ
ijassa-429	326	6	it	it	PRON
ijassa-429	326	7	achieves	achieve	VERB
ijassa-429	326	8	this	this	DET
ijassa-429	326	9	precision	precision	NOUN
ijassa-429	326	10	without	without	ADP
ijassa-429	326	11	the	the	DET
ijassa-429	326	12	introduction	introduction	NOUN
ijassa-429	326	13	of	of	ADP
ijassa-429	326	14	new	new	ADJ
ijassa-429	326	15	parameters	parameter	NOUN
ijassa-429	326	16	and	and	CCONJ
ijassa-429	326	17	accounts	account	NOUN
ijassa-429	326	18	for	for	ADP
ijassa-429	326	19	lack	lack	NOUN
ijassa-429	326	20	of	of	ADP
ijassa-429	326	21	symmetry	symmetry	NOUN
ijassa-429	326	22	(	(	PUNCT
ijassa-429	326	23	semi	semi	ADJ
ijassa-429	326	24	-	-	ADJ
ijassa-429	326	25	logistic	logistic	ADJ
ijassa-429	326	26	scenarios	scenario	NOUN
ijassa-429	326	27	)	)	PUNCT
ijassa-429	326	28	through	through	ADP
ijassa-429	326	29	the	the	DET
ijassa-429	326	30	model	model	NOUN
ijassa-429	326	31	itself	itself	PRON
ijassa-429	326	32	rather	rather	ADV
ijassa-429	326	33	than	than	ADP
ijassa-429	326	34	a	a	DET
ijassa-429	326	35	term	term	NOUN
ijassa-429	326	36	in	in	ADP
ijassa-429	326	37	the	the	DET
ijassa-429	326	38	formula	formula	NOUN
ijassa-429	326	39	.	.	PUNCT
ijassa-429	327	1	this	this	DET
ijassa-429	327	2	form	form	NOUN
ijassa-429	327	3	of	of	ADP
ijassa-429	327	4	the	the	DET
ijassa-429	327	5	series	series	NOUN
ijassa-429	327	6	is	be	AUX
ijassa-429	327	7	appropriate	appropriate	ADJ
ijassa-429	327	8	to	to	PART
ijassa-429	327	9	solve	solve	VERB
ijassa-429	327	10	for	for	ADP
ijassa-429	327	11	growth	growth	NOUN
ijassa-429	327	12	rate	rate	NOUN
ijassa-429	327	13	of	of	ADP
ijassa-429	327	14	any	any	DET
ijassa-429	327	15	indicator	indicator	NOUN
ijassa-429	327	16	(	(	PUNCT
ijassa-429	327	17	equation	equation	NOUN
ijassa-429	327	18	15	15	NUM
ijassa-429	327	19	):	):	PUNCT
ijassa-429	327	20	µ	µ	NOUN
ijassa-429	327	21	=	=	SYM
ijassa-429	327	22	r	r	NOUN
ijassa-429	327	23	=	=	NOUN
ijassa-429	327	24	dp	dp	NOUN
ijassa-429	327	25	dt∑∞	dt∑∞	NOUN
ijassa-429	327	26	n=0	n=0	PUNCT
ijassa-429	327	27	(	(	PUNCT
ijassa-429	327	28	−1)n(n!2n)pn+1	−1)n(n!2n)pn+1	NOUN
ijassa-429	327	29	mn(n+1	mn(n+1	ADJ
ijassa-429	327	30	)	)	PUNCT
ijassa-429	327	31	!	!	PUNCT
ijassa-429	328	1	(	(	PUNCT
ijassa-429	328	2	15	15	NUM
ijassa-429	328	3	)	)	PUNCT
ijassa-429	328	4	94	94	NUM
ijassa-429	328	5	anne	anne	PROPN
ijassa-429	328	6	talkington	talkington	NOUN
ijassa-429	328	7	:	:	PUNCT
ijassa-429	328	8	an	an	DET
ijassa-429	328	9	extension	extension	NOUN
ijassa-429	328	10	of	of	ADP
ijassa-429	328	11	a	a	DET
ijassa-429	328	12	logistic	logistic	ADJ
ijassa-429	328	13	model	model	NOUN
ijassa-429	328	14	for	for	ADP
ijassa-429	328	15	microbial	microbial	ADJ
ijassa-429	328	16	kinetics	kinetic	NOUN
ijassa-429	328	17	closed	close	VERB
ijassa-429	328	18	form	form	NOUN
ijassa-429	328	19	of	of	ADP
ijassa-429	328	20	the	the	DET
ijassa-429	328	21	series	series	NOUN
ijassa-429	328	22	(	(	PUNCT
ijassa-429	328	23	equation	equation	NOUN
ijassa-429	328	24	16	16	NUM
ijassa-429	328	25	):	):	PUNCT
ijassa-429	329	1	r	r	NOUN
ijassa-429	329	2	=	=	SYM
ijassa-429	329	3	dp	dp	NOUN
ijassa-429	329	4	dt	dt	NOUN
ijassa-429	329	5	m	m	VERB
ijassa-429	329	6	2	2	NUM
ijassa-429	330	1	ln(1	ln(1	NOUN
ijassa-429	330	2	+	+	NUM
ijassa-429	330	3	2p	2p	NUM
ijassa-429	330	4	m	m	NOUN
ijassa-429	330	5	)	)	PUNCT
ijassa-429	330	6	.	.	PUNCT
ijassa-429	331	1	(	(	PUNCT
ijassa-429	331	2	16	16	X
ijassa-429	331	3	)	)	PUNCT
ijassa-429	331	4	consider	consider	VERB
ijassa-429	331	5	that	that	PRON
ijassa-429	331	6	:	:	PUNCT
ijassa-429	332	1	ln(1	ln(1	NOUN
ijassa-429	332	2	+	+	NUM
ijassa-429	332	3	2p	2p	NUM
ijassa-429	332	4	m	m	NOUN
ijassa-429	332	5	)	)	PUNCT
ijassa-429	333	1	=	=	PUNCT
ijassa-429	333	2	ln(2	ln(2	PROPN
ijassa-429	333	3	)	)	PUNCT
ijassa-429	333	4	when	when	SCONJ
ijassa-429	333	5	m	m	VERB
ijassa-429	333	6	=	=	VERB
ijassa-429	333	7	2p	2p	NOUN
ijassa-429	333	8	.	.	PUNCT
ijassa-429	334	1	the	the	DET
ijassa-429	334	2	modified	modify	VERB
ijassa-429	334	3	alternating	alternate	VERB
ijassa-429	334	4	maclaurin	maclaurin	NOUN
ijassa-429	334	5	series	series	NOUN
ijassa-429	334	6	accurately	accurately	ADV
ijassa-429	334	7	models	model	VERB
ijassa-429	334	8	the	the	DET
ijassa-429	334	9	data	datum	NOUN
ijassa-429	334	10	as	as	SCONJ
ijassa-429	334	11	it	it	PRON
ijassa-429	334	12	converges	converge	VERB
ijassa-429	334	13	,	,	PUNCT
ijassa-429	334	14	over	over	ADP
ijassa-429	334	15	the	the	DET
ijassa-429	334	16	domain	domain	NOUN
ijassa-429	334	17	of	of	ADP
ijassa-429	334	18	initial	initial	ADJ
ijassa-429	334	19	data	datum	NOUN
ijassa-429	334	20	collection	collection	NOUN
ijassa-429	334	21	to	to	ADP
ijassa-429	334	22	the	the	DET
ijassa-429	334	23	point	point	NOUN
ijassa-429	334	24	of	of	ADP
ijassa-429	334	25	inflection	inflection	NOUN
ijassa-429	334	26	p	p	NOUN
ijassa-429	334	27	.	.	PUNCT
ijassa-429	335	1	the	the	DET
ijassa-429	335	2	model	model	NOUN
ijassa-429	335	3	converges	converge	VERB
ijassa-429	335	4	with	with	ADP
ijassa-429	335	5	the	the	DET
ijassa-429	335	6	condition	condition	NOUN
ijassa-429	335	7	that	that	SCONJ
ijassa-429	335	8	p	p	PROPN
ijassa-429	335	9	≤	≤	NUM
ijassa-429	335	10	m	m	VERB
ijassa-429	335	11	2	2	NUM
ijassa-429	335	12	.	.	PUNCT
ijassa-429	336	1	the	the	DET
ijassa-429	336	2	applicability	applicability	NOUN
ijassa-429	336	3	of	of	ADP
ijassa-429	336	4	the	the	DET
ijassa-429	336	5	maclaurin	maclaurin	NOUN
ijassa-429	336	6	series	series	NOUN
ijassa-429	336	7	as	as	ADP
ijassa-429	336	8	a	a	DET
ijassa-429	336	9	method	method	NOUN
ijassa-429	336	10	for	for	ADP
ijassa-429	336	11	determining	determine	VERB
ijassa-429	336	12	growth	growth	NOUN
ijassa-429	336	13	rate	rate	NOUN
ijassa-429	336	14	is	be	AUX
ijassa-429	336	15	categorized	categorize	VERB
ijassa-429	336	16	as	as	ADP
ijassa-429	336	17	one	one	NUM
ijassa-429	336	18	of	of	ADP
ijassa-429	336	19	three	three	NUM
ijassa-429	336	20	cases	case	NOUN
ijassa-429	336	21	,	,	PUNCT
ijassa-429	336	22	based	base	VERB
ijassa-429	336	23	on	on	ADP
ijassa-429	336	24	the	the	DET
ijassa-429	336	25	relationship	relationship	NOUN
ijassa-429	336	26	between	between	ADP
ijassa-429	336	27	p	p	PROPN
ijassa-429	336	28	and	and	CCONJ
ijassa-429	336	29	m	m	NOUN
ijassa-429	336	30	.	.	PUNCT
ijassa-429	337	1	the	the	DET
ijassa-429	337	2	following	follow	VERB
ijassa-429	337	3	procedure	procedure	NOUN
ijassa-429	337	4	applies	apply	VERB
ijassa-429	337	5	for	for	ADP
ijassa-429	337	6	the	the	DET
ijassa-429	337	7	first	first	ADJ
ijassa-429	337	8	case	case	NOUN
ijassa-429	337	9	of	of	ADP
ijassa-429	337	10	the	the	DET
ijassa-429	337	11	modified	modify	VERB
ijassa-429	337	12	alternating	alternate	VERB
ijassa-429	337	13	maclaurin	maclaurin	NOUN
ijassa-429	337	14	series	series	NOUN
ijassa-429	337	15	:	:	PUNCT
ijassa-429	337	16	if	if	SCONJ
ijassa-429	337	17	data	datum	NOUN
ijassa-429	337	18	is	be	AUX
ijassa-429	337	19	symmetrical	symmetrical	ADJ
ijassa-429	337	20	(	(	PUNCT
ijassa-429	337	21	ideally	ideally	ADV
ijassa-429	337	22	logistic	logistic	ADJ
ijassa-429	337	23	)	)	PUNCT
ijassa-429	337	24	and	and	CCONJ
ijassa-429	337	25	p	p	X
ijassa-429	337	26	=	=	NOUN
ijassa-429	337	27	m	m	PROPN
ijassa-429	337	28	2	2	NUM
ijassa-429	337	29	.	.	NOUN
ijassa-429	338	1	1	1	X
ijassa-429	338	2	)	)	PUNCT
ijassa-429	338	3	the	the	DET
ijassa-429	338	4	y	y	NOUN
ijassa-429	338	5	-	-	PUNCT
ijassa-429	338	6	coordinate	coordinate	NOUN
ijassa-429	338	7	of	of	ADP
ijassa-429	338	8	the	the	DET
ijassa-429	338	9	point	point	NOUN
ijassa-429	338	10	of	of	ADP
ijassa-429	338	11	inflection	inflection	NOUN
ijassa-429	338	12	(	(	PUNCT
ijassa-429	338	13	value	value	NOUN
ijassa-429	338	14	substituted	substitute	VERB
ijassa-429	338	15	for	for	ADP
ijassa-429	338	16	p	p	NOUN
ijassa-429	338	17	)	)	PUNCT
ijassa-429	338	18	is	be	AUX
ijassa-429	338	19	the	the	DET
ijassa-429	338	20	midpoint	midpoint	NOUN
ijassa-429	338	21	between	between	ADP
ijassa-429	338	22	the	the	DET
ijassa-429	338	23	upper	upper	ADJ
ijassa-429	338	24	and	and	CCONJ
ijassa-429	338	25	lower	low	ADJ
ijassa-429	338	26	limits	limit	NOUN
ijassa-429	338	27	of	of	ADP
ijassa-429	338	28	growth	growth	NOUN
ijassa-429	338	29	(	(	PUNCT
ijassa-429	338	30	asymptotes	asymptote	NOUN
ijassa-429	338	31	)	)	PUNCT
ijassa-429	338	32	.	.	PUNCT
ijassa-429	339	1	it	it	PRON
ijassa-429	339	2	is	be	AUX
ijassa-429	339	3	calculated	calculate	VERB
ijassa-429	339	4	as	as	ADP
ijassa-429	339	5	lower	low	ADJ
ijassa-429	339	6	limit	limit	NOUN
ijassa-429	339	7	+	+	CCONJ
ijassa-429	339	8	(	(	PUNCT
ijassa-429	339	9	1/2	1/2	NUM
ijassa-429	339	10	)	)	PUNCT
ijassa-429	339	11	(	(	PUNCT
ijassa-429	339	12	upper	upper	ADJ
ijassa-429	339	13	limit	limit	NOUN
ijassa-429	339	14	lower	low	ADJ
ijassa-429	339	15	limit	limit	NOUN
ijassa-429	339	16	)	)	PUNCT
ijassa-429	339	17	.	.	PUNCT
ijassa-429	340	1	2	2	X
ijassa-429	340	2	)	)	PUNCT
ijassa-429	340	3	dp	dp	NOUN
ijassa-429	340	4	dt	dt	NOUN
ijassa-429	340	5	represents	represent	VERB
ijassa-429	340	6	change	change	NOUN
ijassa-429	340	7	in	in	ADP
ijassa-429	340	8	population	population	NOUN
ijassa-429	340	9	(	(	PUNCT
ijassa-429	340	10	growth	growth	NOUN
ijassa-429	340	11	)	)	PUNCT
ijassa-429	340	12	over	over	ADP
ijassa-429	340	13	time	time	NOUN
ijassa-429	340	14	.	.	PUNCT
ijassa-429	341	1	it	it	PRON
ijassa-429	341	2	should	should	AUX
ijassa-429	341	3	reach	reach	VERB
ijassa-429	341	4	its	its	PRON
ijassa-429	341	5	maximum	maximum	ADJ
ijassa-429	341	6	value	value	NOUN
ijassa-429	341	7	at	at	ADP
ijassa-429	341	8	the	the	DET
ijassa-429	341	9	point	point	NOUN
ijassa-429	341	10	of	of	ADP
ijassa-429	341	11	inflection	inflection	NOUN
ijassa-429	341	12	.	.	PUNCT
ijassa-429	342	1	dp	dp	NOUN
ijassa-429	343	1	dt	dt	NOUN
ijassa-429	343	2	should	should	AUX
ijassa-429	343	3	therefore	therefore	ADV
ijassa-429	343	4	reflect	reflect	VERB
ijassa-429	343	5	the	the	DET
ijassa-429	343	6	change	change	NOUN
ijassa-429	343	7	at	at	ADP
ijassa-429	343	8	the	the	DET
ijassa-429	343	9	point	point	NOUN
ijassa-429	343	10	of	of	ADP
ijassa-429	343	11	inflection	inflection	NOUN
ijassa-429	343	12	as	as	ADP
ijassa-429	343	13	a	a	DET
ijassa-429	343	14	tangent	tangent	ADJ
ijassa-429	343	15	line	line	NOUN
ijassa-429	343	16	.	.	PUNCT
ijassa-429	344	1	it	it	PRON
ijassa-429	344	2	is	be	AUX
ijassa-429	344	3	determined	determine	VERB
ijassa-429	344	4	more	more	ADV
ijassa-429	344	5	precisely	precisely	ADV
ijassa-429	344	6	as	as	ADP
ijassa-429	344	7	the	the	DET
ijassa-429	344	8	mean	mean	ADJ
ijassa-429	344	9	value	value	NOUN
ijassa-429	344	10	of	of	ADP
ijassa-429	344	11	the	the	DET
ijassa-429	344	12	rates	rate	NOUN
ijassa-429	344	13	of	of	ADP
ijassa-429	344	14	change	change	NOUN
ijassa-429	344	15	surrounding	surround	VERB
ijassa-429	344	16	the	the	DET
ijassa-429	344	17	point	point	NOUN
ijassa-429	344	18	of	of	ADP
ijassa-429	344	19	inflection	inflection	NOUN
ijassa-429	344	20	.	.	PUNCT
ijassa-429	345	1	for	for	ADP
ijassa-429	345	2	even	even	ADV
ijassa-429	345	3	greater	great	ADJ
ijassa-429	345	4	precision	precision	NOUN
ijassa-429	345	5	,	,	PUNCT
ijassa-429	345	6	arbitrary	arbitrary	ADJ
ijassa-429	345	7	ranges	range	NOUN
ijassa-429	345	8	chosen	choose	VERB
ijassa-429	345	9	to	to	PART
ijassa-429	345	10	include	include	VERB
ijassa-429	345	11	the	the	DET
ijassa-429	345	12	point	point	NOUN
ijassa-429	345	13	of	of	ADP
ijassa-429	345	14	inflection	inflection	NOUN
ijassa-429	345	15	can	can	AUX
ijassa-429	345	16	be	be	AUX
ijassa-429	345	17	averaged	average	VERB
ijassa-429	345	18	and	and	CCONJ
ijassa-429	345	19	compared	compare	VERB
ijassa-429	345	20	;	;	PUNCT
ijassa-429	345	21	the	the	DET
ijassa-429	345	22	greatest	great	ADJ
ijassa-429	345	23	value	value	NOUN
ijassa-429	345	24	among	among	ADP
ijassa-429	345	25	these	these	PRON
ijassa-429	345	26	is	be	AUX
ijassa-429	345	27	taken	take	VERB
ijassa-429	345	28	as	as	ADP
ijassa-429	345	29	dp	dp	NOUN
ijassa-429	345	30	dt	dt	NOUN
ijassa-429	345	31	.	.	PUNCT
ijassa-429	346	1	3	3	X
ijassa-429	346	2	)	)	PUNCT
ijassa-429	346	3	m	m	VERB
ijassa-429	346	4	is	be	AUX
ijassa-429	346	5	the	the	DET
ijassa-429	346	6	upper	upper	ADJ
ijassa-429	346	7	limit	limit	NOUN
ijassa-429	346	8	of	of	ADP
ijassa-429	346	9	growth	growth	NOUN
ijassa-429	346	10	.	.	PUNCT
ijassa-429	347	1	it	it	PRON
ijassa-429	347	2	is	be	AUX
ijassa-429	347	3	identified	identify	VERB
ijassa-429	347	4	as	as	ADP
ijassa-429	347	5	a	a	DET
ijassa-429	347	6	horizontal	horizontal	ADJ
ijassa-429	347	7	asymptote	asymptote	NOUN
ijassa-429	347	8	.	.	PUNCT
ijassa-429	348	1	4	4	X
ijassa-429	348	2	)	)	PUNCT
ijassa-429	348	3	values	value	NOUN
ijassa-429	348	4	for	for	ADP
ijassa-429	348	5	p	p	NOUN
ijassa-429	348	6	,	,	PUNCT
ijassa-429	348	7	dp	dp	NOUN
ijassa-429	348	8	dt	dt	NOUN
ijassa-429	348	9	and	and	CCONJ
ijassa-429	348	10	m	m	PROPN
ijassa-429	348	11	are	be	AUX
ijassa-429	348	12	substituted	substitute	VERB
ijassa-429	348	13	into	into	ADP
ijassa-429	348	14	the	the	DET
ijassa-429	348	15	series	series	NOUN
ijassa-429	348	16	to	to	PART
ijassa-429	348	17	solve	solve	VERB
ijassa-429	348	18	for	for	ADP
ijassa-429	348	19	r	r	NOUN
ijassa-429	348	20	(	(	PUNCT
ijassa-429	348	21	µ	µ	NOUN
ijassa-429	348	22	)	)	PUNCT
ijassa-429	348	23	.	.	PUNCT
ijassa-429	349	1	example	example	NOUN
ijassa-429	349	2	of	of	ADP
ijassa-429	349	3	the	the	DET
ijassa-429	349	4	first	first	ADJ
ijassa-429	349	5	case	case	NOUN
ijassa-429	349	6	:	:	PUNCT
ijassa-429	349	7	fig.5	fig.5	VERB
ijassa-429	349	8	graphical	graphical	ADJ
ijassa-429	349	9	traditional	traditional	ADJ
ijassa-429	349	10	method	method	NOUN
ijassa-429	349	11	:	:	PUNCT
ijassa-429	349	12	µ=1.0374	µ=1.0374	ADP
ijassa-429	349	13	advances	advance	NOUN
ijassa-429	349	14	in	in	ADP
ijassa-429	349	15	systems	system	NOUN
ijassa-429	349	16	science	science	NOUN
ijassa-429	349	17	and	and	CCONJ
ijassa-429	349	18	applications	application	NOUN
ijassa-429	349	19	(	(	PUNCT
ijassa-429	349	20	2013	2013	NUM
ijassa-429	349	21	)	)	PUNCT
ijassa-429	349	22	vol.13	vol.13	NOUN
ijassa-429	349	23	no.1	no.1	VERB
ijassa-429	349	24	95	95	NUM
ijassa-429	349	25	graphical	graphical	ADJ
ijassa-429	349	26	traditional	traditional	ADJ
ijassa-429	349	27	method	method	NOUN
ijassa-429	349	28	:	:	PUNCT
ijassa-429	349	29	µ=1.0374	µ=1.0374	PRON
ijassa-429	349	30	maclaurin	maclaurin	NOUN
ijassa-429	349	31	series	series	NOUN
ijassa-429	349	32	method	method	NOUN
ijassa-429	349	33	:	:	PUNCT
ijassa-429	349	34	p	p	X
ijassa-429	349	35	=	=	SYM
ijassa-429	349	36	3	3	NUM
ijassa-429	349	37	;	;	PUNCT
ijassa-429	349	38	dpdt	dpdt	NOUN
ijassa-429	349	39	=	=	SYM
ijassa-429	349	40	2.2;m	2.2;m	NUM
ijassa-429	349	41	=	=	SYM
ijassa-429	350	1	6	6	NUM
ijassa-429	350	2	µ	µ	X
ijassa-429	350	3	=	=	SYM
ijassa-429	350	4	1.0580	1.0580	NUM
ijassa-429	350	5	error	error	NOUN
ijassa-429	350	6	(	(	PUNCT
ijassa-429	350	7	disparity	disparity	NOUN
ijassa-429	350	8	between	between	ADP
ijassa-429	350	9	the	the	DET
ijassa-429	350	10	methods	method	NOUN
ijassa-429	350	11	):	):	PUNCT
ijassa-429	350	12	1.99	1.99	NUM
ijassa-429	350	13	%	%	NOUN
ijassa-429	350	14	the	the	DET
ijassa-429	350	15	following	follow	VERB
ijassa-429	350	16	procedure	procedure	NOUN
ijassa-429	350	17	applies	apply	VERB
ijassa-429	350	18	for	for	ADP
ijassa-429	350	19	the	the	DET
ijassa-429	350	20	second	second	ADJ
ijassa-429	350	21	case	case	NOUN
ijassa-429	350	22	of	of	ADP
ijassa-429	350	23	the	the	DET
ijassa-429	350	24	modified	modify	VERB
ijassa-429	350	25	alternating	alternate	VERB
ijassa-429	350	26	maclaurin	maclaurin	NOUN
ijassa-429	350	27	series	series	NOUN
ijassa-429	350	28	:	:	PUNCT
ijassa-429	350	29	if	if	SCONJ
ijassa-429	350	30	the	the	DET
ijassa-429	350	31	point	point	NOUN
ijassa-429	350	32	of	of	ADP
ijassa-429	350	33	inflection	inflection	NOUN
ijassa-429	350	34	is	be	AUX
ijassa-429	350	35	less	less	ADJ
ijassa-429	350	36	than	than	ADP
ijassa-429	350	37	half	half	NOUN
ijassa-429	350	38	of	of	ADP
ijassa-429	350	39	the	the	DET
ijassa-429	350	40	carrying	carrying	NOUN
ijassa-429	350	41	capacity	capacity	NOUN
ijassa-429	350	42	,	,	PUNCT
ijassa-429	350	43	or	or	CCONJ
ijassa-429	350	44	p	p	X
ijassa-429	350	45	<	<	X
ijassa-429	350	46	m	m	PROPN
ijassa-429	350	47	2	2	NUM
ijassa-429	350	48	.	.	NOUN
ijassa-429	350	49	1	1	X
ijassa-429	350	50	)	)	PUNCT
ijassa-429	350	51	the	the	DET
ijassa-429	350	52	y	y	NOUN
ijassa-429	350	53	-	-	PUNCT
ijassa-429	350	54	coordinate	coordinate	NOUN
ijassa-429	350	55	of	of	ADP
ijassa-429	350	56	the	the	DET
ijassa-429	350	57	point	point	NOUN
ijassa-429	350	58	of	of	ADP
ijassa-429	350	59	inflection	inflection	NOUN
ijassa-429	350	60	(	(	PUNCT
ijassa-429	350	61	value	value	NOUN
ijassa-429	350	62	substituted	substitute	VERB
ijassa-429	350	63	for	for	ADP
ijassa-429	350	64	p	p	NOUN
ijassa-429	350	65	)	)	PUNCT
ijassa-429	350	66	is	be	AUX
ijassa-429	350	67	less	less	ADJ
ijassa-429	350	68	than	than	ADP
ijassa-429	350	69	the	the	DET
ijassa-429	350	70	midpoint	midpoint	NOUN
ijassa-429	350	71	between	between	ADP
ijassa-429	350	72	the	the	DET
ijassa-429	350	73	upper	upper	ADJ
ijassa-429	350	74	and	and	CCONJ
ijassa-429	350	75	lower	low	ADJ
ijassa-429	350	76	limits	limit	NOUN
ijassa-429	350	77	of	of	ADP
ijassa-429	350	78	growth	growth	NOUN
ijassa-429	350	79	(	(	PUNCT
ijassa-429	350	80	asymptotes	asymptote	NOUN
ijassa-429	350	81	)	)	PUNCT
ijassa-429	350	82	.	.	PUNCT
ijassa-429	351	1	it	it	PRON
ijassa-429	351	2	is	be	AUX
ijassa-429	351	3	calculated	calculate	VERB
ijassa-429	351	4	as	as	ADP
ijassa-429	351	5	the	the	DET
ijassa-429	351	6	point	point	NOUN
ijassa-429	351	7	in	in	ADP
ijassa-429	351	8	the	the	DET
ijassa-429	351	9	center	center	NOUN
ijassa-429	351	10	of	of	ADP
ijassa-429	351	11	the	the	DET
ijassa-429	351	12	range	range	NOUN
ijassa-429	351	13	of	of	ADP
ijassa-429	351	14	maximum	maximum	ADJ
ijassa-429	351	15	change	change	NOUN
ijassa-429	351	16	in	in	ADP
ijassa-429	351	17	population	population	NOUN
ijassa-429	351	18	over	over	ADP
ijassa-429	351	19	time	time	NOUN
ijassa-429	351	20	(	(	PUNCT
ijassa-429	351	21	largest	large	ADJ
ijassa-429	351	22	values	value	NOUN
ijassa-429	351	23	of	of	ADP
ijassa-429	351	24	dp	dp	NOUN
ijassa-429	351	25	dt	dt	NOUN
ijassa-429	351	26	)	)	PUNCT
ijassa-429	351	27	.	.	PUNCT
ijassa-429	352	1	when	when	SCONJ
ijassa-429	352	2	averages	average	NOUN
ijassa-429	352	3	are	be	AUX
ijassa-429	352	4	taken	take	VERB
ijassa-429	352	5	for	for	ADP
ijassa-429	352	6	dp	dp	NOUN
ijassa-429	352	7	dt	dt	NOUN
ijassa-429	352	8	,	,	PUNCT
ijassa-429	352	9	p	p	PRON
ijassa-429	352	10	should	should	AUX
ijassa-429	352	11	be	be	AUX
ijassa-429	352	12	at	at	ADP
ijassa-429	352	13	or	or	CCONJ
ijassa-429	352	14	near	near	ADP
ijassa-429	352	15	the	the	DET
ijassa-429	352	16	center	center	NOUN
ijassa-429	352	17	of	of	ADP
ijassa-429	352	18	the	the	DET
ijassa-429	352	19	range	range	NOUN
ijassa-429	352	20	.	.	PUNCT
ijassa-429	353	1	2	2	X
ijassa-429	353	2	)	)	PUNCT
ijassa-429	353	3	dp	dp	NOUN
ijassa-429	353	4	dt	dt	NOUN
ijassa-429	353	5	represents	represent	VERB
ijassa-429	353	6	change	change	NOUN
ijassa-429	353	7	in	in	ADP
ijassa-429	353	8	population	population	NOUN
ijassa-429	353	9	(	(	PUNCT
ijassa-429	353	10	growth	growth	NOUN
ijassa-429	353	11	)	)	PUNCT
ijassa-429	353	12	over	over	ADP
ijassa-429	353	13	time	time	NOUN
ijassa-429	353	14	.	.	PUNCT
ijassa-429	354	1	it	it	PRON
ijassa-429	354	2	should	should	AUX
ijassa-429	354	3	reach	reach	VERB
ijassa-429	354	4	its	its	PRON
ijassa-429	354	5	maximum	maximum	ADJ
ijassa-429	354	6	value	value	NOUN
ijassa-429	354	7	at	at	ADP
ijassa-429	354	8	the	the	DET
ijassa-429	354	9	point	point	NOUN
ijassa-429	354	10	of	of	ADP
ijassa-429	354	11	inflection	inflection	NOUN
ijassa-429	354	12	.	.	PUNCT
ijassa-429	355	1	dp	dp	NOUN
ijassa-429	356	1	dt	dt	NOUN
ijassa-429	356	2	should	should	AUX
ijassa-429	356	3	therefore	therefore	ADV
ijassa-429	356	4	reflect	reflect	VERB
ijassa-429	356	5	the	the	DET
ijassa-429	356	6	change	change	NOUN
ijassa-429	356	7	at	at	ADP
ijassa-429	356	8	the	the	DET
ijassa-429	356	9	point	point	NOUN
ijassa-429	356	10	of	of	ADP
ijassa-429	356	11	inflection	inflection	NOUN
ijassa-429	356	12	as	as	ADP
ijassa-429	356	13	a	a	DET
ijassa-429	356	14	tangent	tangent	ADJ
ijassa-429	356	15	line	line	NOUN
ijassa-429	356	16	.	.	PUNCT
ijassa-429	357	1	it	it	PRON
ijassa-429	357	2	is	be	AUX
ijassa-429	357	3	determined	determine	VERB
ijassa-429	357	4	more	more	ADV
ijassa-429	357	5	precisely	precisely	ADV
ijassa-429	357	6	as	as	ADP
ijassa-429	357	7	the	the	DET
ijassa-429	357	8	mean	mean	ADJ
ijassa-429	357	9	value	value	NOUN
ijassa-429	357	10	of	of	ADP
ijassa-429	357	11	the	the	DET
ijassa-429	357	12	rates	rate	NOUN
ijassa-429	357	13	of	of	ADP
ijassa-429	357	14	change	change	NOUN
ijassa-429	357	15	surrounding	surround	VERB
ijassa-429	357	16	the	the	DET
ijassa-429	357	17	point	point	NOUN
ijassa-429	357	18	of	of	ADP
ijassa-429	357	19	inflection	inflection	NOUN
ijassa-429	357	20	.	.	PUNCT
ijassa-429	358	1	for	for	ADP
ijassa-429	358	2	even	even	ADV
ijassa-429	358	3	greater	great	ADJ
ijassa-429	358	4	precision	precision	NOUN
ijassa-429	358	5	,	,	PUNCT
ijassa-429	358	6	arbitrary	arbitrary	ADJ
ijassa-429	358	7	ranges	range	NOUN
ijassa-429	358	8	chosen	choose	VERB
ijassa-429	358	9	to	to	PART
ijassa-429	358	10	include	include	VERB
ijassa-429	358	11	the	the	DET
ijassa-429	358	12	point	point	NOUN
ijassa-429	358	13	of	of	ADP
ijassa-429	358	14	inflection	inflection	NOUN
ijassa-429	358	15	can	can	AUX
ijassa-429	358	16	be	be	AUX
ijassa-429	358	17	averaged	average	VERB
ijassa-429	358	18	and	and	CCONJ
ijassa-429	358	19	compared	compare	VERB
ijassa-429	358	20	;	;	PUNCT
ijassa-429	358	21	the	the	DET
ijassa-429	358	22	greatest	great	ADJ
ijassa-429	358	23	value	value	NOUN
ijassa-429	358	24	among	among	ADP
ijassa-429	358	25	these	these	PRON
ijassa-429	358	26	is	be	AUX
ijassa-429	358	27	taken	take	VERB
ijassa-429	358	28	as	as	ADP
ijassa-429	358	29	dp	dp	NOUN
ijassa-429	358	30	dt	dt	NOUN
ijassa-429	358	31	.	.	PUNCT
ijassa-429	359	1	3	3	X
ijassa-429	359	2	)	)	PUNCT
ijassa-429	359	3	m	m	VERB
ijassa-429	359	4	is	be	AUX
ijassa-429	359	5	the	the	DET
ijassa-429	359	6	upper	upper	ADJ
ijassa-429	359	7	limit	limit	NOUN
ijassa-429	359	8	of	of	ADP
ijassa-429	359	9	growth	growth	NOUN
ijassa-429	359	10	.	.	PUNCT
ijassa-429	360	1	it	it	PRON
ijassa-429	360	2	is	be	AUX
ijassa-429	360	3	identified	identify	VERB
ijassa-429	360	4	as	as	ADP
ijassa-429	360	5	a	a	DET
ijassa-429	360	6	horizontal	horizontal	ADJ
ijassa-429	360	7	asymptote	asymptote	NOUN
ijassa-429	360	8	.	.	PUNCT
ijassa-429	361	1	4	4	X
ijassa-429	361	2	)	)	PUNCT
ijassa-429	361	3	values	value	NOUN
ijassa-429	361	4	for	for	ADP
ijassa-429	361	5	p	p	NOUN
ijassa-429	361	6	,	,	PUNCT
ijassa-429	361	7	dp	dp	NOUN
ijassa-429	361	8	dt	dt	NOUN
ijassa-429	361	9	,	,	PUNCT
ijassa-429	361	10	and	and	CCONJ
ijassa-429	361	11	m	m	PROPN
ijassa-429	361	12	are	be	AUX
ijassa-429	361	13	substituted	substitute	VERB
ijassa-429	361	14	into	into	ADP
ijassa-429	361	15	the	the	DET
ijassa-429	361	16	series	series	NOUN
ijassa-429	361	17	to	to	PART
ijassa-429	361	18	solve	solve	VERB
ijassa-429	361	19	for	for	ADP
ijassa-429	361	20	r	r	NOUN
ijassa-429	361	21	(	(	PUNCT
ijassa-429	361	22	µ	µ	NOUN
ijassa-429	361	23	)	)	PUNCT
ijassa-429	361	24	.	.	PUNCT
ijassa-429	362	1	5	5	NUM
ijassa-429	362	2	)	)	PUNCT
ijassa-429	362	3	because	because	SCONJ
ijassa-429	362	4	p	p	NOUN
ijassa-429	362	5	is	be	AUX
ijassa-429	362	6	low	low	ADJ
ijassa-429	362	7	with	with	ADP
ijassa-429	362	8	respect	respect	NOUN
ijassa-429	362	9	to	to	ADP
ijassa-429	362	10	m	m	PROPN
ijassa-429	362	11	,	,	PUNCT
ijassa-429	362	12	convergence	convergence	NOUN
ijassa-429	362	13	of	of	ADP
ijassa-429	362	14	the	the	DET
ijassa-429	362	15	series	series	NOUN
ijassa-429	362	16	occurs	occur	VERB
ijassa-429	362	17	more	more	ADV
ijassa-429	362	18	rapidly	rapidly	ADV
ijassa-429	362	19	than	than	ADP
ijassa-429	362	20	in	in	ADP
ijassa-429	362	21	the	the	DET
ijassa-429	362	22	symmetrical	symmetrical	ADJ
ijassa-429	362	23	first	first	ADJ
ijassa-429	362	24	case	case	NOUN
ijassa-429	362	25	.	.	PUNCT
ijassa-429	363	1	the	the	DET
ijassa-429	363	2	result	result	NOUN
ijassa-429	363	3	is	be	AUX
ijassa-429	363	4	more	more	ADV
ijassa-429	363	5	precise	precise	ADJ
ijassa-429	363	6	at	at	ADP
ijassa-429	363	7	a	a	DET
ijassa-429	363	8	smaller	small	ADJ
ijassa-429	363	9	number	number	NOUN
ijassa-429	363	10	of	of	ADP
ijassa-429	363	11	terms	term	NOUN
ijassa-429	363	12	.	.	PUNCT
ijassa-429	364	1	example	example	NOUN
ijassa-429	364	2	of	of	ADP
ijassa-429	364	3	the	the	DET
ijassa-429	364	4	second	second	ADJ
ijassa-429	364	5	case	case	NOUN
ijassa-429	364	6	:	:	PUNCT
ijassa-429	364	7	fig.6	fig.6	VERB
ijassa-429	364	8	graphical	graphical	ADJ
ijassa-429	364	9	traditional	traditional	ADJ
ijassa-429	364	10	method	method	NOUN
ijassa-429	364	11	:	:	PUNCT
ijassa-429	364	12	µ=0.2817	µ=0.2817	VERB
ijassa-429	364	13	graphical	graphical	ADJ
ijassa-429	364	14	traditional	traditional	ADJ
ijassa-429	364	15	method	method	NOUN
ijassa-429	364	16	:	:	PUNCT
ijassa-429	364	17	µ=0.2817	µ=0.2817	PROPN
ijassa-429	364	18	96	96	NUM
ijassa-429	364	19	anne	anne	PROPN
ijassa-429	364	20	talkington	talkington	NOUN
ijassa-429	364	21	:	:	PUNCT
ijassa-429	364	22	an	an	DET
ijassa-429	364	23	extension	extension	NOUN
ijassa-429	364	24	of	of	ADP
ijassa-429	364	25	a	a	DET
ijassa-429	364	26	logistic	logistic	ADJ
ijassa-429	364	27	model	model	NOUN
ijassa-429	364	28	for	for	ADP
ijassa-429	364	29	microbial	microbial	ADJ
ijassa-429	364	30	kinetics	kinetic	NOUN
ijassa-429	364	31	maclaurin	maclaurin	NOUN
ijassa-429	364	32	series	series	NOUN
ijassa-429	364	33	method	method	NOUN
ijassa-429	364	34	:	:	PUNCT
ijassa-429	364	35	p	p	X
ijassa-429	364	36	=	=	PROPN
ijassa-429	364	37	0.15	0.15	NUM
ijassa-429	364	38	;	;	PUNCT
ijassa-429	364	39	dpdt	dpdt	NOUN
ijassa-429	364	40	=	=	SYM
ijassa-429	364	41	0.04;m	0.04;m	NOUN
ijassa-429	365	1	=	=	SYM
ijassa-429	365	2	1.3	1.3	NUM
ijassa-429	365	3	µ	µ	NOUN
ijassa-429	365	4	=	=	SYM
ijassa-429	365	5	0.2964	0.2964	NUM
ijassa-429	365	6	error	error	NOUN
ijassa-429	365	7	(	(	PUNCT
ijassa-429	365	8	disparity	disparity	NOUN
ijassa-429	365	9	between	between	ADP
ijassa-429	365	10	the	the	DET
ijassa-429	365	11	methods	method	NOUN
ijassa-429	365	12	):	):	PUNCT
ijassa-429	365	13	5.22	5.22	NUM
ijassa-429	365	14	%	%	NOUN
ijassa-429	365	15	the	the	DET
ijassa-429	365	16	following	follow	VERB
ijassa-429	365	17	procedure	procedure	NOUN
ijassa-429	365	18	applies	apply	VERB
ijassa-429	365	19	for	for	ADP
ijassa-429	365	20	the	the	DET
ijassa-429	365	21	third	third	ADJ
ijassa-429	365	22	case	case	NOUN
ijassa-429	365	23	of	of	ADP
ijassa-429	365	24	the	the	DET
ijassa-429	365	25	modified	modify	VERB
ijassa-429	365	26	alternating	alternate	VERB
ijassa-429	365	27	maclaurin	maclaurin	NOUN
ijassa-429	365	28	series	series	NOUN
ijassa-429	365	29	:	:	PUNCT
ijassa-429	365	30	if	if	SCONJ
ijassa-429	365	31	the	the	DET
ijassa-429	365	32	point	point	NOUN
ijassa-429	365	33	of	of	ADP
ijassa-429	365	34	inflection	inflection	NOUN
ijassa-429	365	35	is	be	AUX
ijassa-429	365	36	greater	great	ADJ
ijassa-429	365	37	than	than	ADP
ijassa-429	365	38	half	half	NOUN
ijassa-429	365	39	of	of	ADP
ijassa-429	365	40	the	the	DET
ijassa-429	365	41	carrying	carrying	NOUN
ijassa-429	365	42	capacity	capacity	NOUN
ijassa-429	365	43	,	,	PUNCT
ijassa-429	365	44	or	or	CCONJ
ijassa-429	365	45	p	p	X
ijassa-429	365	46	>	>	X
ijassa-429	365	47	m	m	PROPN
ijassa-429	365	48	2	2	NUM
ijassa-429	365	49	.	.	NOUN
ijassa-429	365	50	1	1	X
ijassa-429	365	51	)	)	PUNCT
ijassa-429	365	52	the	the	DET
ijassa-429	365	53	y	y	NOUN
ijassa-429	365	54	-	-	PUNCT
ijassa-429	365	55	coordinate	coordinate	NOUN
ijassa-429	365	56	of	of	ADP
ijassa-429	365	57	the	the	DET
ijassa-429	365	58	point	point	NOUN
ijassa-429	365	59	of	of	ADP
ijassa-429	365	60	inflection	inflection	NOUN
ijassa-429	365	61	(	(	PUNCT
ijassa-429	365	62	value	value	NOUN
ijassa-429	365	63	substituted	substitute	VERB
ijassa-429	365	64	for	for	ADP
ijassa-429	365	65	p	p	NOUN
ijassa-429	365	66	)	)	PUNCT
ijassa-429	365	67	is	be	AUX
ijassa-429	365	68	greater	great	ADJ
ijassa-429	365	69	than	than	ADP
ijassa-429	365	70	the	the	DET
ijassa-429	365	71	midpoint	midpoint	NOUN
ijassa-429	365	72	between	between	ADP
ijassa-429	365	73	the	the	DET
ijassa-429	365	74	upper	upper	ADJ
ijassa-429	365	75	and	and	CCONJ
ijassa-429	365	76	lower	low	ADJ
ijassa-429	365	77	limits	limit	NOUN
ijassa-429	365	78	of	of	ADP
ijassa-429	365	79	growth	growth	NOUN
ijassa-429	365	80	(	(	PUNCT
ijassa-429	365	81	asymptotes	asymptote	NOUN
ijassa-429	365	82	)	)	PUNCT
ijassa-429	365	83	.	.	PUNCT
ijassa-429	366	1	it	it	PRON
ijassa-429	366	2	is	be	AUX
ijassa-429	366	3	calculated	calculate	VERB
ijassa-429	366	4	as	as	ADP
ijassa-429	366	5	the	the	DET
ijassa-429	366	6	point	point	NOUN
ijassa-429	366	7	in	in	ADP
ijassa-429	366	8	the	the	DET
ijassa-429	366	9	center	center	NOUN
ijassa-429	366	10	of	of	ADP
ijassa-429	366	11	the	the	DET
ijassa-429	366	12	range	range	NOUN
ijassa-429	366	13	of	of	ADP
ijassa-429	366	14	maximum	maximum	ADJ
ijassa-429	366	15	change	change	NOUN
ijassa-429	366	16	in	in	ADP
ijassa-429	366	17	population	population	NOUN
ijassa-429	366	18	over	over	ADP
ijassa-429	366	19	time	time	NOUN
ijassa-429	366	20	(	(	PUNCT
ijassa-429	366	21	largest	large	ADJ
ijassa-429	366	22	values	value	NOUN
ijassa-429	366	23	of	of	ADP
ijassa-429	366	24	dp	dp	NOUN
ijassa-429	366	25	dt	dt	NOUN
ijassa-429	366	26	)	)	PUNCT
ijassa-429	366	27	.	.	PUNCT
ijassa-429	367	1	when	when	SCONJ
ijassa-429	367	2	averages	average	NOUN
ijassa-429	367	3	are	be	AUX
ijassa-429	367	4	taken	take	VERB
ijassa-429	367	5	for	for	ADP
ijassa-429	367	6	dp	dp	NOUN
ijassa-429	367	7	dt	dt	NOUN
ijassa-429	367	8	,	,	PUNCT
ijassa-429	367	9	p	p	PRON
ijassa-429	367	10	should	should	AUX
ijassa-429	367	11	be	be	AUX
ijassa-429	367	12	at	at	ADP
ijassa-429	367	13	or	or	CCONJ
ijassa-429	367	14	near	near	ADP
ijassa-429	367	15	the	the	DET
ijassa-429	367	16	center	center	NOUN
ijassa-429	367	17	of	of	ADP
ijassa-429	367	18	the	the	DET
ijassa-429	367	19	range	range	NOUN
ijassa-429	367	20	.	.	PUNCT
ijassa-429	368	1	2	2	X
ijassa-429	368	2	)	)	PUNCT
ijassa-429	368	3	dp	dp	NOUN
ijassa-429	368	4	dt	dt	NOUN
ijassa-429	368	5	represents	represent	VERB
ijassa-429	368	6	change	change	NOUN
ijassa-429	368	7	in	in	ADP
ijassa-429	368	8	population	population	NOUN
ijassa-429	368	9	(	(	PUNCT
ijassa-429	368	10	growth	growth	NOUN
ijassa-429	368	11	)	)	PUNCT
ijassa-429	368	12	over	over	ADP
ijassa-429	368	13	time	time	NOUN
ijassa-429	368	14	.	.	PUNCT
ijassa-429	369	1	it	it	PRON
ijassa-429	369	2	should	should	AUX
ijassa-429	369	3	reach	reach	VERB
ijassa-429	369	4	its	its	PRON
ijassa-429	369	5	maximum	maximum	ADJ
ijassa-429	369	6	value	value	NOUN
ijassa-429	369	7	at	at	ADP
ijassa-429	369	8	the	the	DET
ijassa-429	369	9	point	point	NOUN
ijassa-429	369	10	of	of	ADP
ijassa-429	369	11	inflection	inflection	NOUN
ijassa-429	369	12	.	.	PUNCT
ijassa-429	370	1	dp	dp	NOUN
ijassa-429	371	1	dt	dt	NOUN
ijassa-429	371	2	should	should	AUX
ijassa-429	371	3	therefore	therefore	ADV
ijassa-429	371	4	reflect	reflect	VERB
ijassa-429	371	5	the	the	DET
ijassa-429	371	6	change	change	NOUN
ijassa-429	371	7	at	at	ADP
ijassa-429	371	8	the	the	DET
ijassa-429	371	9	point	point	NOUN
ijassa-429	371	10	of	of	ADP
ijassa-429	371	11	inflection	inflection	NOUN
ijassa-429	371	12	as	as	ADP
ijassa-429	371	13	a	a	DET
ijassa-429	371	14	tangent	tangent	ADJ
ijassa-429	371	15	line	line	NOUN
ijassa-429	371	16	.	.	PUNCT
ijassa-429	372	1	it	it	PRON
ijassa-429	372	2	is	be	AUX
ijassa-429	372	3	determined	determine	VERB
ijassa-429	372	4	more	more	ADV
ijassa-429	372	5	precisely	precisely	ADV
ijassa-429	372	6	as	as	ADP
ijassa-429	372	7	the	the	DET
ijassa-429	372	8	mean	mean	ADJ
ijassa-429	372	9	value	value	NOUN
ijassa-429	372	10	of	of	ADP
ijassa-429	372	11	the	the	DET
ijassa-429	372	12	rates	rate	NOUN
ijassa-429	372	13	of	of	ADP
ijassa-429	372	14	change	change	NOUN
ijassa-429	372	15	surrounding	surround	VERB
ijassa-429	372	16	the	the	DET
ijassa-429	372	17	point	point	NOUN
ijassa-429	372	18	of	of	ADP
ijassa-429	372	19	inflection	inflection	NOUN
ijassa-429	372	20	.	.	PUNCT
ijassa-429	373	1	for	for	ADP
ijassa-429	373	2	even	even	ADV
ijassa-429	373	3	greater	great	ADJ
ijassa-429	373	4	precision	precision	NOUN
ijassa-429	373	5	,	,	PUNCT
ijassa-429	373	6	arbitrary	arbitrary	ADJ
ijassa-429	373	7	ranges	range	NOUN
ijassa-429	373	8	chosen	choose	VERB
ijassa-429	373	9	to	to	PART
ijassa-429	373	10	include	include	VERB
ijassa-429	373	11	the	the	DET
ijassa-429	373	12	point	point	NOUN
ijassa-429	373	13	of	of	ADP
ijassa-429	373	14	inflection	inflection	NOUN
ijassa-429	373	15	can	can	AUX
ijassa-429	373	16	be	be	AUX
ijassa-429	373	17	averaged	average	VERB
ijassa-429	373	18	and	and	CCONJ
ijassa-429	373	19	compared	compare	VERB
ijassa-429	373	20	;	;	PUNCT
ijassa-429	373	21	the	the	DET
ijassa-429	373	22	greatest	great	ADJ
ijassa-429	373	23	value	value	NOUN
ijassa-429	373	24	among	among	ADP
ijassa-429	373	25	these	these	PRON
ijassa-429	373	26	is	be	AUX
ijassa-429	373	27	taken	take	VERB
ijassa-429	373	28	as	as	ADP
ijassa-429	373	29	dp	dp	NOUN
ijassa-429	373	30	dt	dt	NOUN
ijassa-429	373	31	.	.	PUNCT
ijassa-429	374	1	furthermore	furthermore	ADV
ijassa-429	374	2	,	,	PUNCT
ijassa-429	374	3	the	the	DET
ijassa-429	374	4	use	use	NOUN
ijassa-429	374	5	of	of	ADP
ijassa-429	374	6	means	mean	NOUN
ijassa-429	374	7	contributes	contribute	VERB
ijassa-429	374	8	to	to	ADP
ijassa-429	374	9	the	the	DET
ijassa-429	374	10	robustness	robustness	NOUN
ijassa-429	374	11	and	and	CCONJ
ijassa-429	374	12	applicability	applicability	NOUN
ijassa-429	374	13	of	of	ADP
ijassa-429	374	14	the	the	DET
ijassa-429	374	15	symmetrical	symmetrical	ADJ
ijassa-429	374	16	case	case	NOUN
ijassa-429	374	17	.	.	PUNCT
ijassa-429	375	1	3	3	X
ijassa-429	375	2	)	)	PUNCT
ijassa-429	375	3	m	m	VERB
ijassa-429	375	4	is	be	AUX
ijassa-429	375	5	the	the	DET
ijassa-429	375	6	upper	upper	ADJ
ijassa-429	375	7	limit	limit	NOUN
ijassa-429	375	8	of	of	ADP
ijassa-429	375	9	growth	growth	NOUN
ijassa-429	375	10	.	.	PUNCT
ijassa-429	376	1	it	it	PRON
ijassa-429	376	2	is	be	AUX
ijassa-429	376	3	identified	identify	VERB
ijassa-429	376	4	as	as	ADP
ijassa-429	376	5	a	a	DET
ijassa-429	376	6	horizontal	horizontal	ADJ
ijassa-429	376	7	asymptote	asymptote	NOUN
ijassa-429	376	8	.	.	PUNCT
ijassa-429	377	1	in	in	ADP
ijassa-429	377	2	this	this	DET
ijassa-429	377	3	case	case	NOUN
ijassa-429	377	4	,	,	PUNCT
ijassa-429	377	5	use	use	NOUN
ijassa-429	377	6	of	of	ADP
ijassa-429	377	7	the	the	DET
ijassa-429	377	8	horizontal	horizontal	ADJ
ijassa-429	377	9	asymptote	asymptote	ADJ
ijassa-429	377	10	results	result	NOUN
ijassa-429	377	11	in	in	ADP
ijassa-429	377	12	divergence	divergence	NOUN
ijassa-429	377	13	of	of	ADP
ijassa-429	377	14	the	the	DET
ijassa-429	377	15	series	series	NOUN
ijassa-429	377	16	.	.	PUNCT
ijassa-429	378	1	therefore	therefore	ADV
ijassa-429	378	2	,	,	PUNCT
ijassa-429	378	3	ratios	ratio	NOUN
ijassa-429	378	4	are	be	AUX
ijassa-429	378	5	implemented	implement	VERB
ijassa-429	378	6	to	to	PART
ijassa-429	378	7	calculate	calculate	VERB
ijassa-429	378	8	r	r	NOUN
ijassa-429	378	9	or	or	CCONJ
ijassa-429	378	10	µ.	µ.	NOUN
ijassa-429	378	11	let	let	VERB
ijassa-429	378	12	the	the	DET
ijassa-429	378	13	horizontal	horizontal	ADJ
ijassa-429	378	14	asymptote	asymptote	NOUN
ijassa-429	378	15	be	be	AUX
ijassa-429	378	16	denoted	denote	VERB
ijassa-429	378	17	as	as	ADP
ijassa-429	378	18	m0	m0	NOUN
ijassa-429	378	19	.	.	PUNCT
ijassa-429	379	1	set	set	PROPN
ijassa-429	379	2	m1	m1	PROPN
ijassa-429	379	3	,	,	PUNCT
ijassa-429	379	4	an	an	DET
ijassa-429	379	5	alternate	alternate	ADJ
ijassa-429	379	6	limit	limit	NOUN
ijassa-429	379	7	,	,	PUNCT
ijassa-429	379	8	as	as	ADV
ijassa-429	379	9	equal	equal	ADJ
ijassa-429	379	10	to	to	ADP
ijassa-429	379	11	2p	2p	NUM
ijassa-429	379	12	.	.	PUNCT
ijassa-429	380	1	4	4	X
ijassa-429	380	2	)	)	PUNCT
ijassa-429	380	3	values	value	NOUN
ijassa-429	380	4	for	for	ADP
ijassa-429	380	5	p	p	NOUN
ijassa-429	380	6	,	,	PUNCT
ijassa-429	380	7	dp	dp	NOUN
ijassa-429	380	8	dt	dt	NOUN
ijassa-429	380	9	,	,	PUNCT
ijassa-429	380	10	and	and	CCONJ
ijassa-429	380	11	m1	m1	PROPN
ijassa-429	380	12	are	be	AUX
ijassa-429	380	13	substituted	substitute	VERB
ijassa-429	380	14	into	into	ADP
ijassa-429	380	15	the	the	DET
ijassa-429	380	16	series	series	NOUN
ijassa-429	380	17	to	to	PART
ijassa-429	380	18	solve	solve	VERB
ijassa-429	380	19	for	for	ADP
ijassa-429	380	20	r	r	NOUN
ijassa-429	380	21	(	(	PUNCT
ijassa-429	380	22	µ	µ	NOUN
ijassa-429	380	23	)	)	PUNCT
ijassa-429	380	24	.	.	PUNCT
ijassa-429	381	1	the	the	DET
ijassa-429	381	2	series	series	NOUN
ijassa-429	381	3	converges	converge	VERB
ijassa-429	381	4	as	as	ADP
ijassa-429	381	5	in	in	ADP
ijassa-429	381	6	the	the	DET
ijassa-429	381	7	symmetrical	symmetrical	ADJ
ijassa-429	381	8	first	first	ADJ
ijassa-429	381	9	case	case	NOUN
ijassa-429	381	10	.	.	PUNCT
ijassa-429	382	1	5	5	X
ijassa-429	382	2	)	)	PUNCT
ijassa-429	382	3	the	the	DET
ijassa-429	382	4	use	use	NOUN
ijassa-429	382	5	of	of	ADP
ijassa-429	382	6	m1	m1	PROPN
ijassa-429	382	7	results	result	NOUN
ijassa-429	382	8	in	in	ADP
ijassa-429	382	9	an	an	DET
ijassa-429	382	10	inflated	inflated	ADJ
ijassa-429	382	11	value	value	NOUN
ijassa-429	382	12	for	for	ADP
ijassa-429	382	13	r	r	NOUN
ijassa-429	382	14	(	(	PUNCT
ijassa-429	382	15	µ	µ	NOUN
ijassa-429	382	16	)	)	PUNCT
ijassa-429	382	17	.	.	PUNCT
ijassa-429	383	1	to	to	PART
ijassa-429	383	2	account	account	VERB
ijassa-429	383	3	for	for	ADP
ijassa-429	383	4	the	the	DET
ijassa-429	383	5	substitution	substitution	NOUN
ijassa-429	383	6	of	of	ADP
ijassa-429	383	7	m1	m1	NOUN
ijassa-429	383	8	,	,	PUNCT
ijassa-429	383	9	the	the	DET
ijassa-429	383	10	result	result	NOUN
ijassa-429	383	11	of	of	ADP
ijassa-429	383	12	the	the	DET
ijassa-429	383	13	series	series	NOUN
ijassa-429	383	14	is	be	AUX
ijassa-429	383	15	divided	divide	VERB
ijassa-429	383	16	by	by	ADP
ijassa-429	383	17	the	the	DET
ijassa-429	383	18	value	value	NOUN
ijassa-429	383	19	of	of	ADP
ijassa-429	383	20	m1	m1	PROPN
ijassa-429	383	21	m0	m0	PROPN
ijassa-429	383	22	.	.	PUNCT
ijassa-429	384	1	example	example	NOUN
ijassa-429	384	2	of	of	ADP
ijassa-429	384	3	the	the	DET
ijassa-429	384	4	third	third	ADJ
ijassa-429	384	5	case	case	NOUN
ijassa-429	384	6	:	:	PUNCT
ijassa-429	384	7	graphical	graphical	ADJ
ijassa-429	384	8	traditional	traditional	ADJ
ijassa-429	384	9	method	method	NOUN
ijassa-429	384	10	:	:	PUNCT
ijassa-429	384	11	µ=0.1704	µ=0.1704	PROPN
ijassa-429	384	12	maclaurin	maclaurin	PROPN
ijassa-429	384	13	series	series	PROPN
ijassa-429	384	14	method	method	NOUN
ijassa-429	384	15	:	:	PUNCT
ijassa-429	384	16	p	p	X
ijassa-429	384	17	=	=	NOUN
ijassa-429	384	18	0.38	0.38	NUM
ijassa-429	384	19	;	;	PUNCT
ijassa-429	384	20	dpdt	dpdt	NOUN
ijassa-429	384	21	=	=	SYM
ijassa-429	384	22	0.05;m0	0.05;m0	X
ijassa-429	385	1	=	=	PUNCT
ijassa-429	385	2	0.61;m1	0.61;m1	NUM
ijassa-429	385	3	=	=	PUNCT
ijassa-429	385	4	0.76	0.76	NUM
ijassa-429	385	5	µ	µ	X
ijassa-429	385	6	=	=	SYM
ijassa-429	385	7	0.1523	0.1523	NUM
ijassa-429	385	8	error	error	NOUN
ijassa-429	385	9	(	(	PUNCT
ijassa-429	385	10	disparity	disparity	NOUN
ijassa-429	385	11	between	between	ADP
ijassa-429	385	12	the	the	DET
ijassa-429	385	13	methods	method	NOUN
ijassa-429	385	14	):	):	PUNCT
ijassa-429	385	15	10.62	10.62	NUM
ijassa-429	385	16	%	%	NOUN
ijassa-429	385	17	5	5	NUM
ijassa-429	385	18	limitations	limitation	NOUN
ijassa-429	385	19	irregular	irregular	ADJ
ijassa-429	385	20	data	datum	NOUN
ijassa-429	385	21	is	be	AUX
ijassa-429	385	22	the	the	DET
ijassa-429	385	23	greatest	great	ADJ
ijassa-429	385	24	limitation	limitation	NOUN
ijassa-429	385	25	to	to	ADP
ijassa-429	385	26	any	any	DET
ijassa-429	385	27	method	method	NOUN
ijassa-429	385	28	of	of	ADP
ijassa-429	385	29	determining	determine	VERB
ijassa-429	385	30	microbial	microbial	ADJ
ijassa-429	385	31	kinetics	kinetic	NOUN
ijassa-429	385	32	.	.	PUNCT
ijassa-429	386	1	environmental	environmental	ADJ
ijassa-429	386	2	factors	factor	NOUN
ijassa-429	386	3	such	such	ADJ
ijassa-429	386	4	as	as	ADP
ijassa-429	386	5	ph	ph	ADJ
ijassa-429	386	6	inconsistency	inconsistency	NOUN
ijassa-429	386	7	,	,	PUNCT
ijassa-429	386	8	culture	culture	NOUN
ijassa-429	386	9	contamination	contamination	NOUN
ijassa-429	386	10	,	,	PUNCT
ijassa-429	386	11	advances	advance	NOUN
ijassa-429	386	12	in	in	ADP
ijassa-429	386	13	systems	system	NOUN
ijassa-429	386	14	science	science	NOUN
ijassa-429	386	15	and	and	CCONJ
ijassa-429	386	16	applications	application	NOUN
ijassa-429	386	17	(	(	PUNCT
ijassa-429	386	18	2013	2013	NUM
ijassa-429	386	19	)	)	PUNCT
ijassa-429	386	20	vol.13	vol.13	NOUN
ijassa-429	386	21	no.1	no.1	VERB
ijassa-429	386	22	97	97	NUM
ijassa-429	386	23	fig.7	fig.7	ADJ
ijassa-429	386	24	graphical	graphical	ADJ
ijassa-429	386	25	traditional	traditional	ADJ
ijassa-429	386	26	method	method	NOUN
ijassa-429	386	27	:	:	PUNCT
ijassa-429	386	28	µ=0.1704	µ=0.1704	NOUN
ijassa-429	386	29	or	or	CCONJ
ijassa-429	386	30	other	other	ADJ
ijassa-429	386	31	laboratory	laboratory	NOUN
ijassa-429	386	32	error	error	NOUN
ijassa-429	386	33	introduce	introduce	VERB
ijassa-429	386	34	complications	complication	NOUN
ijassa-429	386	35	to	to	ADP
ijassa-429	386	36	the	the	DET
ijassa-429	386	37	data	datum	NOUN
ijassa-429	386	38	[	[	X
ijassa-429	386	39	16	16	NUM
ijassa-429	386	40	]	]	PUNCT
ijassa-429	386	41	.	.	PUNCT
ijassa-429	387	1	furthermore	furthermore	ADV
ijassa-429	387	2	,	,	PUNCT
ijassa-429	387	3	microbial	microbial	ADJ
ijassa-429	387	4	cultures	culture	NOUN
ijassa-429	387	5	are	be	AUX
ijassa-429	387	6	inherently	inherently	ADV
ijassa-429	387	7	not	not	PART
ijassa-429	387	8	ideal	ideal	ADJ
ijassa-429	387	9	.	.	PUNCT
ijassa-429	388	1	the	the	DET
ijassa-429	388	2	use	use	NOUN
ijassa-429	388	3	of	of	ADP
ijassa-429	388	4	an	an	DET
ijassa-429	388	5	ideal	ideal	ADJ
ijassa-429	388	6	model	model	NOUN
ijassa-429	388	7	provides	provide	VERB
ijassa-429	388	8	a	a	DET
ijassa-429	388	9	basis	basis	NOUN
ijassa-429	388	10	of	of	ADP
ijassa-429	388	11	comparison	comparison	NOUN
ijassa-429	388	12	by	by	ADP
ijassa-429	388	13	which	which	PRON
ijassa-429	388	14	inconsistencies	inconsistency	NOUN
ijassa-429	388	15	may	may	AUX
ijassa-429	388	16	be	be	AUX
ijassa-429	388	17	determined	determine	VERB
ijassa-429	388	18	.	.	PUNCT
ijassa-429	389	1	a	a	DET
ijassa-429	389	2	numerical	numerical	ADJ
ijassa-429	389	3	method	method	NOUN
ijassa-429	389	4	strictly	strictly	ADV
ijassa-429	389	5	relies	rely	VERB
ijassa-429	389	6	upon	upon	SCONJ
ijassa-429	389	7	the	the	DET
ijassa-429	389	8	data	datum	NOUN
ijassa-429	389	9	.	.	PUNCT
ijassa-429	390	1	however	however	ADV
ijassa-429	390	2	,	,	PUNCT
ijassa-429	390	3	irregular	irregular	ADJ
ijassa-429	390	4	data	datum	NOUN
ijassa-429	390	5	will	will	AUX
ijassa-429	390	6	produce	produce	VERB
ijassa-429	390	7	an	an	DET
ijassa-429	390	8	irregular	irregular	ADJ
ijassa-429	390	9	result	result	NOUN
ijassa-429	390	10	.	.	PUNCT
ijassa-429	391	1	neither	neither	DET
ijassa-429	391	2	method	method	NOUN
ijassa-429	391	3	will	will	AUX
ijassa-429	391	4	produce	produce	VERB
ijassa-429	391	5	an	an	DET
ijassa-429	391	6	accurate	accurate	ADJ
ijassa-429	391	7	or	or	CCONJ
ijassa-429	391	8	precise	precise	ADJ
ijassa-429	391	9	estimate	estimate	NOUN
ijassa-429	391	10	.	.	PUNCT
ijassa-429	392	1	the	the	DET
ijassa-429	392	2	expansion	expansion	NOUN
ijassa-429	392	3	of	of	ADP
ijassa-429	392	4	the	the	DET
ijassa-429	392	5	maclaurin	maclaurin	NOUN
ijassa-429	392	6	series	series	NOUN
ijassa-429	392	7	is	be	AUX
ijassa-429	392	8	currently	currently	ADV
ijassa-429	392	9	under	under	ADP
ijassa-429	392	10	investigation	investigation	NOUN
ijassa-429	392	11	to	to	PART
ijassa-429	392	12	extend	extend	VERB
ijassa-429	392	13	the	the	DET
ijassa-429	392	14	model	model	NOUN
ijassa-429	392	15	beyond	beyond	ADP
ijassa-429	392	16	the	the	DET
ijassa-429	392	17	point	point	NOUN
ijassa-429	392	18	of	of	ADP
ijassa-429	392	19	inflection	inflection	NOUN
ijassa-429	392	20	.	.	PUNCT
ijassa-429	393	1	successful	successful	ADJ
ijassa-429	393	2	extension	extension	NOUN
ijassa-429	393	3	would	would	AUX
ijassa-429	393	4	eliminate	eliminate	VERB
ijassa-429	393	5	divergence	divergence	NOUN
ijassa-429	393	6	as	as	ADP
ijassa-429	393	7	a	a	DET
ijassa-429	393	8	limitation	limitation	NOUN
ijassa-429	393	9	to	to	ADP
ijassa-429	393	10	the	the	DET
ijassa-429	393	11	microbial	microbial	ADJ
ijassa-429	393	12	growth	growth	NOUN
ijassa-429	393	13	model	model	NOUN
ijassa-429	393	14	and	and	CCONJ
ijassa-429	393	15	its	its	PRON
ijassa-429	393	16	applications	application	NOUN
ijassa-429	393	17	.	.	PUNCT
ijassa-429	394	1	6	6	NUM
ijassa-429	394	2	conclusion	conclusion	NOUN
ijassa-429	394	3	microbial	microbial	ADJ
ijassa-429	394	4	growth	growth	NOUN
ijassa-429	394	5	kinetics	kinetic	NOUN
ijassa-429	394	6	is	be	AUX
ijassa-429	394	7	the	the	DET
ijassa-429	394	8	numerical	numerical	ADJ
ijassa-429	394	9	analysis	analysis	NOUN
ijassa-429	394	10	of	of	ADP
ijassa-429	394	11	a	a	DET
ijassa-429	394	12	complex	complex	ADJ
ijassa-429	394	13	living	living	NOUN
ijassa-429	394	14	system	system	NOUN
ijassa-429	394	15	.	.	PUNCT
ijassa-429	395	1	a	a	DET
ijassa-429	395	2	data	data	NOUN
ijassa-429	395	3	-	-	PUNCT
ijassa-429	395	4	based	base	VERB
ijassa-429	395	5	approach	approach	NOUN
ijassa-429	395	6	is	be	AUX
ijassa-429	395	7	significant	significant	ADJ
ijassa-429	395	8	as	as	SCONJ
ijassa-429	395	9	it	it	PRON
ijassa-429	395	10	determines	determine	VERB
ijassa-429	395	11	microbial	microbial	ADJ
ijassa-429	395	12	growth	growth	NOUN
ijassa-429	395	13	rate	rate	NOUN
ijassa-429	395	14	through	through	ADP
ijassa-429	395	15	a	a	DET
ijassa-429	395	16	procedure	procedure	NOUN
ijassa-429	395	17	designed	design	VERB
ijassa-429	395	18	to	to	PART
ijassa-429	395	19	fit	fit	VERB
ijassa-429	395	20	the	the	DET
ijassa-429	395	21	data	datum	NOUN
ijassa-429	395	22	exactly	exactly	ADV
ijassa-429	395	23	.	.	PUNCT
ijassa-429	396	1	the	the	DET
ijassa-429	396	2	use	use	NOUN
ijassa-429	396	3	of	of	ADP
ijassa-429	396	4	models	model	NOUN
ijassa-429	396	5	is	be	AUX
ijassa-429	396	6	essential	essential	ADJ
ijassa-429	396	7	to	to	ADP
ijassa-429	396	8	understanding	understand	VERB
ijassa-429	396	9	the	the	DET
ijassa-429	396	10	population	population	NOUN
ijassa-429	396	11	structure	structure	NOUN
ijassa-429	396	12	through	through	ADP
ijassa-429	396	13	the	the	DET
ijassa-429	396	14	relationship	relationship	NOUN
ijassa-429	396	15	of	of	ADP
ijassa-429	396	16	population	population	NOUN
ijassa-429	396	17	,	,	PUNCT
ijassa-429	396	18	population	population	NOUN
ijassa-429	396	19	growth	growth	NOUN
ijassa-429	396	20	rate	rate	NOUN
ijassa-429	396	21	,	,	PUNCT
ijassa-429	396	22	carrying	carry	VERB
ijassa-429	396	23	capacity	capacity	NOUN
ijassa-429	396	24	,	,	PUNCT
ijassa-429	396	25	and	and	CCONJ
ijassa-429	396	26	time	time	NOUN
ijassa-429	396	27	.	.	PUNCT
ijassa-429	397	1	population	population	NOUN
ijassa-429	397	2	,	,	PUNCT
ijassa-429	397	3	and	and	CCONJ
ijassa-429	397	4	the	the	DET
ijassa-429	397	5	population	population	NOUN
ijassa-429	397	6	growth	growth	NOUN
ijassa-429	397	7	rate	rate	NOUN
ijassa-429	397	8	,	,	PUNCT
ijassa-429	397	9	change	change	NOUN
ijassa-429	397	10	as	as	ADP
ijassa-429	397	11	a	a	DET
ijassa-429	397	12	function	function	NOUN
ijassa-429	397	13	of	of	ADP
ijassa-429	397	14	time	time	NOUN
ijassa-429	397	15	.	.	PUNCT
ijassa-429	398	1	the	the	DET
ijassa-429	398	2	models	model	NOUN
ijassa-429	398	3	relate	relate	VERB
ijassa-429	398	4	this	this	PRON
ijassa-429	398	5	through	through	ADP
ijassa-429	398	6	direct	direct	ADJ
ijassa-429	398	7	variation	variation	NOUN
ijassa-429	398	8	and	and	CCONJ
ijassa-429	398	9	a	a	DET
ijassa-429	398	10	more	more	ADV
ijassa-429	398	11	complex	complex	ADJ
ijassa-429	398	12	function	function	NOUN
ijassa-429	398	13	.	.	PUNCT
ijassa-429	399	1	the	the	DET
ijassa-429	399	2	explored	explore	VERB
ijassa-429	399	3	models	model	NOUN
ijassa-429	399	4	are	be	AUX
ijassa-429	399	5	built	build	VERB
ijassa-429	399	6	upon	upon	SCONJ
ijassa-429	399	7	exponential	exponential	ADJ
ijassa-429	399	8	and	and	CCONJ
ijassa-429	399	9	logistic	logistic	ADJ
ijassa-429	399	10	growth	growth	NOUN
ijassa-429	399	11	,	,	PUNCT
ijassa-429	399	12	and	and	CCONJ
ijassa-429	399	13	related	relate	VERB
ijassa-429	399	14	through	through	ADP
ijassa-429	399	15	the	the	DET
ijassa-429	399	16	transcritical	transcritical	ADJ
ijassa-429	399	17	bifurcation	bifurcation	NOUN
ijassa-429	399	18	.	.	PUNCT
ijassa-429	400	1	each	each	DET
ijassa-429	400	2	model	model	NOUN
ijassa-429	400	3	is	be	AUX
ijassa-429	400	4	unique	unique	ADJ
ijassa-429	400	5	in	in	ADP
ijassa-429	400	6	its	its	PRON
ijassa-429	400	7	ability	ability	NOUN
ijassa-429	400	8	to	to	PART
ijassa-429	400	9	predict	predict	VERB
ijassa-429	400	10	and	and	CCONJ
ijassa-429	400	11	determine	determine	VERB
ijassa-429	400	12	the	the	DET
ijassa-429	400	13	growth	growth	NOUN
ijassa-429	400	14	of	of	ADP
ijassa-429	400	15	a	a	DET
ijassa-429	400	16	particular	particular	ADJ
ijassa-429	400	17	microbe	microbe	NOUN
ijassa-429	400	18	.	.	PUNCT
ijassa-429	401	1	culturing	culture	VERB
ijassa-429	401	2	technique	technique	NOUN
ijassa-429	401	3	is	be	AUX
ijassa-429	401	4	also	also	ADV
ijassa-429	401	5	a	a	DET
ijassa-429	401	6	factor	factor	NOUN
ijassa-429	401	7	in	in	ADP
ijassa-429	401	8	that	that	SCONJ
ijassa-429	401	9	it	it	PRON
ijassa-429	401	10	imposes	impose	VERB
ijassa-429	401	11	or	or	CCONJ
ijassa-429	401	12	prevents	prevent	VERB
ijassa-429	401	13	natural	natural	ADJ
ijassa-429	401	14	limiting	limiting	NOUN
ijassa-429	401	15	factors	factor	NOUN
ijassa-429	401	16	.	.	PUNCT
ijassa-429	402	1	batch	batch	NOUN
ijassa-429	402	2	cultures	culture	NOUN
ijassa-429	402	3	,	,	PUNCT
ijassa-429	402	4	and	and	CCONJ
ijassa-429	402	5	secondary	secondary	ADJ
ijassa-429	402	6	metabolite	metabolite	NOUN
ijassa-429	402	7	fed	feed	VERB
ijassa-429	402	8	batch	batch	NOUN
ijassa-429	402	9	,	,	PUNCT
ijassa-429	402	10	for	for	ADP
ijassa-429	402	11	example	example	NOUN
ijassa-429	402	12	,	,	PUNCT
ijassa-429	402	13	display	display	VERB
ijassa-429	402	14	a	a	DET
ijassa-429	402	15	pattern	pattern	NOUN
ijassa-429	402	16	that	that	PRON
ijassa-429	402	17	may	may	AUX
ijassa-429	402	18	fall	fall	VERB
ijassa-429	402	19	into	into	ADP
ijassa-429	402	20	the	the	DET
ijassa-429	402	21	logistic	logistic	NOUN
ijassa-429	402	22	,	,	PUNCT
ijassa-429	402	23	the	the	DET
ijassa-429	402	24	symmetrical	symmetrical	ADJ
ijassa-429	402	25	series	series	NOUN
ijassa-429	402	26	,	,	PUNCT
ijassa-429	402	27	or	or	CCONJ
ijassa-429	402	28	the	the	DET
ijassa-429	402	29	fourth	fourth	ADJ
ijassa-429	402	30	-	-	PUNCT
ijassa-429	402	31	degree	degree	NOUN
ijassa-429	402	32	model	model	NOUN
ijassa-429	402	33	.	.	PUNCT
ijassa-429	403	1	primary	primary	ADJ
ijassa-429	403	2	metabolite	metabolite	NOUN
ijassa-429	403	3	and	and	CCONJ
ijassa-429	403	4	continuous	continuous	ADJ
ijassa-429	403	5	cultures	culture	NOUN
ijassa-429	403	6	tend	tend	VERB
ijassa-429	403	7	towards	towards	ADP
ijassa-429	403	8	exponential	exponential	ADJ
ijassa-429	403	9	-	-	PUNCT
ijassa-429	403	10	like	like	ADJ
ijassa-429	403	11	growth	growth	NOUN
ijassa-429	403	12	patterns	pattern	NOUN
ijassa-429	403	13	,	,	PUNCT
ijassa-429	403	14	as	as	SCONJ
ijassa-429	403	15	modeled	model	VERB
ijassa-429	403	16	by	by	ADP
ijassa-429	403	17	exponential	exponential	ADJ
ijassa-429	403	18	growth	growth	NOUN
ijassa-429	403	19	or	or	CCONJ
ijassa-429	403	20	the	the	DET
ijassa-429	403	21	closed	closed	ADJ
ijassa-429	403	22	form	form	NOUN
ijassa-429	403	23	of	of	ADP
ijassa-429	403	24	the	the	DET
ijassa-429	403	25	modified	modify	VERB
ijassa-429	403	26	alternating	alternate	VERB
ijassa-429	403	27	maclaurin	maclaurin	NOUN
ijassa-429	403	28	series	series	NOUN
ijassa-429	403	29	.	.	PUNCT
ijassa-429	404	1	for	for	ADP
ijassa-429	404	2	calculations	calculation	NOUN
ijassa-429	404	3	using	use	VERB
ijassa-429	404	4	these	these	DET
ijassa-429	404	5	models	model	NOUN
ijassa-429	404	6	,	,	PUNCT
ijassa-429	404	7	the	the	DET
ijassa-429	404	8	point	point	NOUN
ijassa-429	404	9	of	of	ADP
ijassa-429	404	10	manipulation	manipulation	NOUN
ijassa-429	404	11	of	of	ADP
ijassa-429	404	12	culture	culture	NOUN
ijassa-429	404	13	conditions	condition	NOUN
ijassa-429	404	14	98	98	NUM
ijassa-429	404	15	anne	anne	PROPN
ijassa-429	404	16	talkington	talkington	NOUN
ijassa-429	404	17	:	:	PUNCT
ijassa-429	404	18	an	an	DET
ijassa-429	404	19	extension	extension	NOUN
ijassa-429	404	20	of	of	ADP
ijassa-429	404	21	a	a	DET
ijassa-429	404	22	logistic	logistic	ADJ
ijassa-429	404	23	model	model	NOUN
ijassa-429	404	24	for	for	ADP
ijassa-429	404	25	microbial	microbial	ADJ
ijassa-429	404	26	kinetics	kinetic	NOUN
ijassa-429	404	27	represents	represent	VERB
ijassa-429	404	28	the	the	DET
ijassa-429	404	29	point	point	NOUN
ijassa-429	404	30	of	of	ADP
ijassa-429	404	31	environmental	environmental	ADJ
ijassa-429	404	32	change	change	NOUN
ijassa-429	404	33	,	,	PUNCT
ijassa-429	404	34	indicated	indicate	VERB
ijassa-429	404	35	graphically	graphically	ADV
ijassa-429	404	36	as	as	ADP
ijassa-429	404	37	the	the	DET
ijassa-429	404	38	point	point	NOUN
ijassa-429	404	39	of	of	ADP
ijassa-429	404	40	inflection	inflection	NOUN
ijassa-429	404	41	.	.	PUNCT
ijassa-429	405	1	in	in	ADP
ijassa-429	405	2	full	full	ADJ
ijassa-429	405	3	expansion	expansion	NOUN
ijassa-429	405	4	,	,	PUNCT
ijassa-429	405	5	the	the	DET
ijassa-429	405	6	discussed	discuss	VERB
ijassa-429	405	7	models	model	NOUN
ijassa-429	405	8	converge	converge	VERB
ijassa-429	405	9	to	to	ADP
ijassa-429	405	10	the	the	DET
ijassa-429	405	11	curve	curve	NOUN
ijassa-429	405	12	of	of	ADP
ijassa-429	405	13	the	the	DET
ijassa-429	405	14	modified	modify	VERB
ijassa-429	405	15	alternating	alternate	VERB
ijassa-429	405	16	maclaurin	maclaurin	NOUN
ijassa-429	405	17	series	series	NOUN
ijassa-429	405	18	,	,	PUNCT
ijassa-429	405	19	up	up	ADP
ijassa-429	405	20	to	to	ADP
ijassa-429	405	21	the	the	DET
ijassa-429	405	22	point	point	NOUN
ijassa-429	405	23	of	of	ADP
ijassa-429	405	24	inflection	inflection	NOUN
ijassa-429	405	25	.	.	PUNCT
ijassa-429	406	1	the	the	DET
ijassa-429	406	2	partial	partial	ADJ
ijassa-429	406	3	curve	curve	NOUN
ijassa-429	406	4	is	be	AUX
ijassa-429	406	5	precise	precise	ADJ
ijassa-429	406	6	for	for	ADP
ijassa-429	406	7	this	this	DET
ijassa-429	406	8	domain	domain	NOUN
ijassa-429	406	9	and	and	CCONJ
ijassa-429	406	10	range	range	NOUN
ijassa-429	406	11	,	,	PUNCT
ijassa-429	406	12	and	and	CCONJ
ijassa-429	406	13	presents	present	VERB
ijassa-429	406	14	a	a	DET
ijassa-429	406	15	scenario	scenario	NOUN
ijassa-429	406	16	of	of	ADP
ijassa-429	406	17	semi	semi	ADJ
ijassa-429	406	18	-	-	ADJ
ijassa-429	406	19	logistic	logistic	ADJ
ijassa-429	406	20	analysis	analysis	NOUN
ijassa-429	406	21	viewing	view	VERB
ijassa-429	406	22	the	the	DET
ijassa-429	406	23	growth	growth	NOUN
ijassa-429	406	24	curve	curve	NOUN
ijassa-429	406	25	as	as	ADP
ijassa-429	406	26	the	the	DET
ijassa-429	406	27	intersection	intersection	NOUN
ijassa-429	406	28	of	of	ADP
ijassa-429	406	29	separate	separate	ADJ
ijassa-429	406	30	curves	curve	NOUN
ijassa-429	406	31	.	.	PUNCT
ijassa-429	407	1	in	in	ADP
ijassa-429	407	2	all	all	DET
ijassa-429	407	3	cases	case	NOUN
ijassa-429	407	4	,	,	PUNCT
ijassa-429	407	5	the	the	DET
ijassa-429	407	6	models	model	NOUN
ijassa-429	407	7	can	can	AUX
ijassa-429	407	8	be	be	AUX
ijassa-429	407	9	solved	solve	VERB
ijassa-429	407	10	for	for	ADP
ijassa-429	407	11	the	the	DET
ijassa-429	407	12	microbial	microbial	ADJ
ijassa-429	407	13	specific	specific	ADJ
ijassa-429	407	14	growth	growth	NOUN
ijassa-429	407	15	rate	rate	NOUN
ijassa-429	407	16	,	,	PUNCT
ijassa-429	407	17	and	and	CCONJ
ijassa-429	407	18	yield	yield	VERB
ijassa-429	407	19	precise	precise	ADJ
ijassa-429	407	20	results	result	NOUN
ijassa-429	407	21	consistent	consistent	ADJ
ijassa-429	407	22	with	with	ADP
ijassa-429	407	23	traditional	traditional	ADJ
ijassa-429	407	24	methods	method	NOUN
ijassa-429	407	25	of	of	ADP
ijassa-429	407	26	analysis	analysis	NOUN
ijassa-429	407	27	.	.	PUNCT
ijassa-429	408	1	acknowledgements	acknowledgement	NOUN
ijassa-429	408	2	the	the	DET
ijassa-429	408	3	authors	author	NOUN
ijassa-429	408	4	would	would	AUX
ijassa-429	408	5	like	like	VERB
ijassa-429	408	6	to	to	PART
ijassa-429	408	7	thank	thank	VERB
ijassa-429	408	8	farm	farm	PROPN
ijassa-429	408	9	bureau	bureau	PROPN
ijassa-429	408	10	robeson	robeson	PROPN
ijassa-429	408	11	for	for	ADP
ijassa-429	408	12	their	their	PRON
ijassa-429	408	13	support	support	NOUN
ijassa-429	408	14	.	.	PUNCT
ijassa-429	409	1	references	reference	NOUN
ijassa-429	409	2	[	[	X
ijassa-429	409	3	1	1	NUM
ijassa-429	409	4	]	]	PUNCT
ijassa-429	409	5	brock	brock	PROPN
ijassa-429	409	6	td	td	PROPN
ijassa-429	409	7	.	.	PUNCT
ijassa-429	410	1	(	(	PUNCT
ijassa-429	410	2	1971	1971	NUM
ijassa-429	410	3	)	)	PUNCT
ijassa-429	410	4	,	,	PUNCT
ijassa-429	410	5	“	"	PUNCT
ijassa-429	410	6	microbial	microbial	ADJ
ijassa-429	410	7	growth	growth	NOUN
ijassa-429	410	8	rates	rate	NOUN
ijassa-429	410	9	in	in	ADP
ijassa-429	410	10	nature	nature	NOUN
ijassa-429	410	11	”	"	PUNCT
ijassa-429	410	12	,	,	PUNCT
ijassa-429	410	13	bacteriol	bacteriol	NOUN
ijassa-429	410	14	rev	rev	PROPN
ijassa-429	410	15	,	,	PUNCT
ijassa-429	410	16	vol.35	vol.35	NOUN
ijassa-429	410	17	,	,	PUNCT
ijassa-429	410	18	no.1	no.1	NUM
ijassa-429	410	19	,	,	PUNCT
ijassa-429	410	20	pp.39	pp.39	NOUN
ijassa-429	410	21	-	-	NOUN
ijassa-429	410	22	58	58	NUM
ijassa-429	410	23	.	.	PUNCT
ijassa-429	411	1	[	[	X
ijassa-429	411	2	2	2	X
ijassa-429	411	3	]	]	PUNCT
ijassa-429	411	4	monod	monod	PROPN
ijassa-429	411	5	j.	j.	PROPN
ijassa-429	411	6	(	(	PUNCT
ijassa-429	411	7	1949	1949	NUM
ijassa-429	411	8	)	)	PUNCT
ijassa-429	411	9	,	,	PUNCT
ijassa-429	411	10	“	"	PUNCT
ijassa-429	411	11	the	the	DET
ijassa-429	411	12	growth	growth	NOUN
ijassa-429	411	13	of	of	ADP
ijassa-429	411	14	bacterial	bacterial	ADJ
ijassa-429	411	15	cultures	culture	NOUN
ijassa-429	411	16	”	"	PUNCT
ijassa-429	411	17	,	,	PUNCT
ijassa-429	411	18	ann	ann	PROPN
ijassa-429	411	19	rev	rev	PROPN
ijassa-429	411	20	microbiol	microbiol	PROPN
ijassa-429	411	21	,	,	PUNCT
ijassa-429	411	22	vol.3	vol.3	PROPN
ijassa-429	411	23	,	,	PUNCT
ijassa-429	411	24	pp.371	pp.371	NOUN
ijassa-429	411	25	-	-	PUNCT
ijassa-429	411	26	394	394	NUM
ijassa-429	411	27	.	.	PUNCT
ijassa-429	412	1	[	[	X
ijassa-429	412	2	3	3	X
ijassa-429	412	3	]	]	X
ijassa-429	412	4	zwietering	zwietering	PROPN
ijassa-429	412	5	mh	mh	PROPN
ijassa-429	412	6	,	,	PUNCT
ijassa-429	412	7	jongenburger	jongenburger	PROPN
ijassa-429	412	8	i	i	PROPN
ijassa-429	412	9	,	,	PUNCT
ijassa-429	412	10	rombouts	rombouts	PROPN
ijassa-429	412	11	fm	fm	PROPN
ijassa-429	412	12	,	,	PUNCT
ijassa-429	412	13	riet	riet	PROPN
ijassa-429	412	14	kv	kv	PROPN
ijassa-429	412	15	.	.	PUNCT
ijassa-429	413	1	(	(	PUNCT
ijassa-429	413	2	1990	1990	NUM
ijassa-429	413	3	)	)	PUNCT
ijassa-429	413	4	,	,	PUNCT
ijassa-429	413	5	“	"	PUNCT
ijassa-429	413	6	modeling	modeling	NOUN
ijassa-429	413	7	of	of	ADP
ijassa-429	413	8	the	the	DET
ijassa-429	413	9	bacterial	bacterial	ADJ
ijassa-429	413	10	growth	growth	NOUN
ijassa-429	413	11	curve	curve	NOUN
ijassa-429	413	12	”	"	PUNCT
ijassa-429	413	13	,	,	PUNCT
ijassa-429	413	14	app	app	PROPN
ijassa-429	413	15	env	env	PROPN
ijassa-429	413	16	microbiol	microbiol	PROPN
ijassa-429	413	17	,	,	PUNCT
ijassa-429	413	18	vol.56	vol.56	ADV
ijassa-429	413	19	,	,	PUNCT
ijassa-429	413	20	no.6	no.6	PROPN
ijassa-429	413	21	,	,	PUNCT
ijassa-429	413	22	pp.18751881	pp.18751881	NOUN
ijassa-429	413	23	.	.	PUNCT
ijassa-429	414	1	[	[	X
ijassa-429	414	2	4	4	X
ijassa-429	414	3	]	]	X
ijassa-429	414	4	contois	contois	NOUN
ijassa-429	414	5	de	de	X
ijassa-429	414	6	.	.	PROPN
ijassa-429	414	7	(	(	PUNCT
ijassa-429	414	8	1959	1959	NUM
ijassa-429	414	9	)	)	PUNCT
ijassa-429	414	10	,	,	PUNCT
ijassa-429	414	11	“	"	PUNCT
ijassa-429	414	12	kinetics	kinetic	NOUN
ijassa-429	414	13	of	of	ADP
ijassa-429	414	14	bacterial	bacterial	ADJ
ijassa-429	414	15	growth	growth	NOUN
ijassa-429	414	16	:	:	PUNCT
ijassa-429	414	17	relationship	relationship	NOUN
ijassa-429	414	18	between	between	ADP
ijassa-429	414	19	population	population	NOUN
ijassa-429	414	20	density	density	NOUN
ijassa-429	414	21	and	and	CCONJ
ijassa-429	414	22	specific	specific	ADJ
ijassa-429	414	23	growth	growth	NOUN
ijassa-429	414	24	rate	rate	NOUN
ijassa-429	414	25	of	of	ADP
ijassa-429	414	26	continuous	continuous	ADJ
ijassa-429	414	27	cultures	culture	NOUN
ijassa-429	414	28	”	"	PUNCT
ijassa-429	414	29	,	,	PUNCT
ijassa-429	414	30	j	j	PROPN
ijassa-429	414	31	gen	gen	PROPN
ijassa-429	414	32	microbiol	microbiol	PROPN
ijassa-429	414	33	,	,	PUNCT
ijassa-429	414	34	vol.21	vol.21	NOUN
ijassa-429	414	35	,	,	PUNCT
ijassa-429	414	36	no.1	no.1	NUM
ijassa-429	414	37	,	,	PUNCT
ijassa-429	414	38	pp.40	pp.40	NOUN
ijassa-429	414	39	-	-	PUNCT
ijassa-429	414	40	50	50	NUM
ijassa-429	414	41	.	.	PUNCT
ijassa-429	415	1	[	[	X
ijassa-429	415	2	5	5	NUM
ijassa-429	415	3	]	]	X
ijassa-429	415	4	grijspeerdt	grijspeerdt	PROPN
ijassa-429	415	5	k	k	PROPN
ijassa-429	415	6	,	,	PUNCT
ijassa-429	415	7	vanrolleghem	vanrolleghem	PROPN
ijassa-429	415	8	p.	p.	NOUN
ijassa-429	415	9	(	(	PUNCT
ijassa-429	415	10	1999	1999	NUM
ijassa-429	415	11	)	)	PUNCT
ijassa-429	415	12	,	,	PUNCT
ijassa-429	415	13	“	"	PUNCT
ijassa-429	415	14	estimating	estimate	VERB
ijassa-429	415	15	the	the	DET
ijassa-429	415	16	parameters	parameter	NOUN
ijassa-429	415	17	of	of	ADP
ijassa-429	415	18	the	the	DET
ijassa-429	415	19	baranyi	baranyi	PROPN
ijassa-429	415	20	model	model	NOUN
ijassa-429	415	21	for	for	ADP
ijassa-429	415	22	bacterial	bacterial	ADJ
ijassa-429	415	23	growth	growth	NOUN
ijassa-429	415	24	”	"	PUNCT
ijassa-429	415	25	,	,	PUNCT
ijassa-429	415	26	food	food	NOUN
ijassa-429	415	27	microbiol	microbiol	PROPN
ijassa-429	415	28	,	,	PUNCT
ijassa-429	415	29	vol.16	vol.16	PROPN
ijassa-429	415	30	,	,	PUNCT
ijassa-429	415	31	no.6	no.6	PROPN
ijassa-429	415	32	,	,	PUNCT
ijassa-429	415	33	pp.593605	pp.593605	PROPN
ijassa-429	415	34	.	.	PUNCT
ijassa-429	416	1	[	[	X
ijassa-429	416	2	6	6	NUM
ijassa-429	416	3	]	]	PUNCT
ijassa-429	416	4	gilpin	gilpin	NOUN
ijassa-429	416	5	michael	michael	PROPN
ijassa-429	416	6	,	,	PUNCT
ijassa-429	416	7	e	e	PROPN
ijassa-429	416	8	ayala	ayala	PROPN
ijassa-429	416	9	,	,	PUNCT
ijassa-429	416	10	francisco	francisco	PROPN
ijassa-429	416	11	j.	j.	PROPN
ijassa-429	416	12	(	(	PUNCT
ijassa-429	416	13	1973	1973	NUM
ijassa-429	416	14	)	)	PUNCT
ijassa-429	416	15	,	,	PUNCT
ijassa-429	416	16	“	"	PUNCT
ijassa-429	416	17	global	global	ADJ
ijassa-429	416	18	models	model	NOUN
ijassa-429	416	19	of	of	ADP
ijassa-429	416	20	growth	growth	NOUN
ijassa-429	416	21	and	and	CCONJ
ijassa-429	416	22	competition	competition	NOUN
ijassa-429	416	23	”	"	PUNCT
ijassa-429	416	24	,	,	PUNCT
ijassa-429	416	25	proceedings	proceeding	NOUN
ijassa-429	416	26	of	of	ADP
ijassa-429	416	27	the	the	DET
ijassa-429	416	28	national	national	PROPN
ijassa-429	416	29	academy	academy	PROPN
ijassa-429	416	30	of	of	ADP
ijassa-429	416	31	sciences	sciences	PROPN
ijassa-429	416	32	of	of	ADP
ijassa-429	416	33	the	the	DET
ijassa-429	416	34	united	united	PROPN
ijassa-429	416	35	states	states	PROPN
ijassa-429	416	36	of	of	ADP
ijassa-429	416	37	america	america	PROPN
ijassa-429	416	38	,	,	PUNCT
ijassa-429	416	39	vol.70	vol.70	NOUN
ijassa-429	416	40	,	,	PUNCT
ijassa-429	416	41	no.12	no.12	NOUN
ijassa-429	416	42	,	,	PUNCT
ijassa-429	416	43	pp.3590	pp.3590	NOUN
ijassa-429	416	44	-	-	PUNCT
ijassa-429	416	45	3593	3593	NUM
ijassa-429	416	46	.	.	PUNCT
ijassa-429	417	1	[	[	X
ijassa-429	417	2	7	7	X
ijassa-429	417	3	]	]	X
ijassa-429	417	4	kozusko	kozusko	PROPN
ijassa-429	417	5	f	f	PROPN
ijassa-429	417	6	,	,	PUNCT
ijassa-429	417	7	bourdeau	bourdeau	ADJ
ijassa-429	417	8	m.	m.	NOUN
ijassa-429	417	9	(	(	PUNCT
ijassa-429	417	10	2011	2011	NUM
ijassa-429	417	11	)	)	PUNCT
ijassa-429	417	12	,	,	PUNCT
ijassa-429	417	13	“	"	PUNCT
ijassa-429	417	14	trans	trans	ADJ
ijassa-429	417	15	-	-	ADJ
ijassa-429	417	16	theta	theta	ADJ
ijassa-429	417	17	logistics	logistic	NOUN
ijassa-429	417	18	:	:	PUNCT
ijassa-429	417	19	a	a	DET
ijassa-429	417	20	new	new	ADJ
ijassa-429	417	21	family	family	NOUN
ijassa-429	417	22	of	of	ADP
ijassa-429	417	23	population	population	NOUN
ijassa-429	417	24	growth	growth	NOUN
ijassa-429	417	25	sigmoid	sigmoid	NOUN
ijassa-429	417	26	functions	function	NOUN
ijassa-429	417	27	”	"	PUNCT
ijassa-429	417	28	,	,	PUNCT
ijassa-429	417	29	acta	acta	PROPN
ijassa-429	417	30	biotheor	biotheor	PROPN
ijassa-429	417	31	,	,	PUNCT
ijassa-429	417	32	vol.59	vol.59	PRON
ijassa-429	417	33	,	,	PUNCT
ijassa-429	417	34	no.3	no.3	NOUN
ijassa-429	417	35	-	-	PUNCT
ijassa-429	417	36	4	4	NUM
ijassa-429	417	37	,	,	PUNCT
ijassa-429	417	38	pp.273289	pp.273289	PROPN
ijassa-429	417	39	.	.	PUNCT
ijassa-429	417	40	doi	doi	NOUN
ijassa-429	417	41	10.1007	10.1007	NUM
ijassa-429	417	42	/	/	SYM
ijassa-429	417	43	s10441	s10441	ADJ
ijassa-429	417	44	-	-	PUNCT
ijassa-429	417	45	011	011	NUM
ijassa-429	417	46	-	-	PUNCT
ijassa-429	417	47	9131	9131	NUM
ijassa-429	417	48	-	-	SYM
ijassa-429	417	49	3	3	NUM
ijassa-429	417	50	.	.	PUNCT
ijassa-429	418	1	[	[	X
ijassa-429	418	2	8	8	NUM
ijassa-429	418	3	]	]	X
ijassa-429	418	4	tsoularis	tsoularis	NOUN
ijassa-429	418	5	a.	a.	NOUN
ijassa-429	418	6	(	(	PUNCT
ijassa-429	418	7	2001	2001	NUM
ijassa-429	418	8	)	)	PUNCT
ijassa-429	418	9	,	,	PUNCT
ijassa-429	418	10	“	"	PUNCT
ijassa-429	418	11	analysis	analysis	NOUN
ijassa-429	418	12	of	of	ADP
ijassa-429	418	13	logistic	logistic	ADJ
ijassa-429	418	14	growth	growth	NOUN
ijassa-429	418	15	models	model	NOUN
ijassa-429	418	16	”	"	PUNCT
ijassa-429	418	17	,	,	PUNCT
ijassa-429	418	18	res	re	NOUN
ijassa-429	418	19	.	.	PUNCT
ijassa-429	419	1	lett	lett	PROPN
ijassa-429	419	2	.	.	PUNCT
ijassa-429	419	3	inf	inf	PROPN
ijassa-429	419	4	.	.	PROPN
ijassa-429	419	5	math	math	PROPN
ijassa-429	419	6	.	.	PUNCT
ijassa-429	420	1	sci	sci	PROPN
ijassa-429	420	2	.	.	PROPN
ijassa-429	420	3	,	,	PUNCT
ijassa-429	420	4	vol.2	vol.2	PROPN
ijassa-429	420	5	,	,	PUNCT
ijassa-429	420	6	pp.23	pp.23	PROPN
ijassa-429	420	7	-	-	PUNCT
ijassa-429	420	8	46	46	NUM
ijassa-429	420	9	.	.	PUNCT
ijassa-429	421	1	[	[	X
ijassa-429	421	2	9	9	NUM
ijassa-429	421	3	]	]	PUNCT
ijassa-429	421	4	birch	birch	NOUN
ijassa-429	421	5	c.p.d	c.p.d	NOUN
ijassa-429	421	6	.	.	PUNCT
ijassa-429	422	1	(	(	PUNCT
ijassa-429	422	2	1999	1999	NUM
ijassa-429	422	3	)	)	PUNCT
ijassa-429	422	4	,	,	PUNCT
ijassa-429	422	5	“	"	PUNCT
ijassa-429	422	6	a	a	DET
ijassa-429	422	7	new	new	ADJ
ijassa-429	422	8	generalized	generalized	ADJ
ijassa-429	422	9	logistic	logistic	ADJ
ijassa-429	422	10	sigmoid	sigmoid	NOUN
ijassa-429	422	11	growth	growth	NOUN
ijassa-429	422	12	equation	equation	NOUN
ijassa-429	422	13	compared	compare	VERB
ijassa-429	422	14	with	with	ADP
ijassa-429	422	15	the	the	DET
ijassa-429	422	16	richards	richard	NOUN
ijassa-429	422	17	growth	growth	NOUN
ijassa-429	422	18	equation	equation	NOUN
ijassa-429	422	19	”	"	PUNCT
ijassa-429	422	20	,	,	PUNCT
ijassa-429	422	21	annals	annals	NOUN
ijassa-429	422	22	of	of	ADP
ijassa-429	422	23	botany	botany	NOUN
ijassa-429	422	24	,	,	PUNCT
ijassa-429	422	25	vol.83	vol.83	PROPN
ijassa-429	422	26	,	,	PUNCT
ijassa-429	422	27	no.6	no.6	PROPN
ijassa-429	422	28	,	,	PUNCT
ijassa-429	422	29	pp.713	pp.713	PROPN
ijassa-429	422	30	-	-	PUNCT
ijassa-429	422	31	723	723	NUM
ijassa-429	422	32	advances	advance	NOUN
ijassa-429	422	33	in	in	ADP
ijassa-429	422	34	systems	system	NOUN
ijassa-429	422	35	science	science	NOUN
ijassa-429	422	36	and	and	CCONJ
ijassa-429	422	37	applications	application	NOUN
ijassa-429	422	38	(	(	PUNCT
ijassa-429	422	39	2013	2013	NUM
ijassa-429	422	40	)	)	PUNCT
ijassa-429	422	41	vol.13	vol.13	NOUN
ijassa-429	422	42	no.1	no.1	X
ijassa-429	422	43	99	99	NUM
ijassa-429	423	1	[	[	SYM
ijassa-429	423	2	10	10	NUM
ijassa-429	423	3	]	]	X
ijassa-429	423	4	yin	yin	PROPN
ijassa-429	423	5	x	x	X
ijassa-429	423	6	,	,	PUNCT
ijassa-429	423	7	goudriaan	goudriaan	PROPN
ijassa-429	423	8	j	j	PROPN
ijassa-429	423	9	,	,	PUNCT
ijassa-429	423	10	lantinga	lantinga	PROPN
ijassa-429	423	11	e.a	e.a	PROPN
ijassa-429	423	12	,	,	PUNCT
ijassa-429	423	13	spiertz	spiertz	PROPN
ijassa-429	423	14	h.j	h.j	PROPN
ijassa-429	423	15	.	.	PROPN
ijassa-429	423	16	(	(	PUNCT
ijassa-429	423	17	2003	2003	NUM
ijassa-429	423	18	)	)	PUNCT
ijassa-429	423	19	,	,	PUNCT
ijassa-429	423	20	“	"	PUNCT
ijassa-429	423	21	a	a	DET
ijassa-429	423	22	flexible	flexible	ADJ
ijassa-429	423	23	sigmoid	sigmoid	NOUN
ijassa-429	423	24	function	function	NOUN
ijassa-429	423	25	of	of	ADP
ijassa-429	423	26	determinate	determinate	ADJ
ijassa-429	423	27	growth	growth	NOUN
ijassa-429	423	28	”	"	PUNCT
ijassa-429	423	29	,	,	PUNCT
ijassa-429	423	30	annals	annals	NOUN
ijassa-429	423	31	of	of	ADP
ijassa-429	423	32	botany	botany	NOUN
ijassa-429	423	33	,	,	PUNCT
ijassa-429	423	34	vol.91	vol.91	NOUN
ijassa-429	423	35	,	,	PUNCT
ijassa-429	423	36	no.3	no.3	NOUN
ijassa-429	423	37	,	,	PUNCT
ijassa-429	423	38	pp.361371	pp.361371	PROPN
ijassa-429	423	39	.	.	PUNCT
ijassa-429	424	1	[	[	X
ijassa-429	424	2	11	11	NUM
ijassa-429	424	3	]	]	X
ijassa-429	424	4	yukalov	yukalov	PROPN
ijassa-429	424	5	v.i	v.i	PROPN
ijassa-429	424	6	,	,	PUNCT
ijassa-429	424	7	yukalova	yukalova	PROPN
ijassa-429	424	8	e.p	e.p	PROPN
ijassa-429	424	9	,	,	PUNCT
ijassa-429	424	10	sornette	sornette	PROPN
ijassa-429	424	11	d.	d.	PROPN
ijassa-429	424	12	(	(	PUNCT
ijassa-429	424	13	2009	2009	NUM
ijassa-429	424	14	)	)	PUNCT
ijassa-429	424	15	,	,	PUNCT
ijassa-429	424	16	“	"	PUNCT
ijassa-429	424	17	punctuated	punctuate	VERB
ijassa-429	424	18	evolution	evolution	NOUN
ijassa-429	424	19	due	due	ADP
ijassa-429	424	20	to	to	ADP
ijassa-429	424	21	delayed	delay	VERB
ijassa-429	424	22	carrying	carrying	NOUN
ijassa-429	424	23	capacity	capacity	NOUN
ijassa-429	424	24	”	"	PUNCT
ijassa-429	424	25	,	,	PUNCT
ijassa-429	424	26	physica	physica	NOUN
ijassa-429	424	27	d	d	PROPN
ijassa-429	424	28	,	,	PUNCT
ijassa-429	424	29	vol.238	vol.238	NOUN
ijassa-429	424	30	,	,	PUNCT
ijassa-429	424	31	no.17	no.17	NOUN
ijassa-429	424	32	,	,	PUNCT
ijassa-429	424	33	pp.1752	pp.1752	PROPN
ijassa-429	424	34	-	-	SYM
ijassa-429	424	35	1767	1767	NUM
ijassa-429	424	36	.	.	PUNCT
ijassa-429	425	1	[	[	X
ijassa-429	425	2	12	12	NUM
ijassa-429	425	3	]	]	X
ijassa-429	425	4	panikov	panikov	NOUN
ijassa-429	425	5	ns	ns	INTJ
ijassa-429	425	6	.	.	PUNCT
ijassa-429	425	7	(	(	PUNCT
ijassa-429	425	8	1995	1995	NUM
ijassa-429	425	9	)	)	PUNCT
ijassa-429	425	10	,	,	PUNCT
ijassa-429	425	11	microbial	microbial	ADJ
ijassa-429	425	12	growth	growth	NOUN
ijassa-429	425	13	kinetics	kinetic	NOUN
ijassa-429	425	14	,	,	PUNCT
ijassa-429	425	15	chapman	chapman	PROPN
ijassa-429	425	16	&	&	CCONJ
ijassa-429	425	17	hall	hall	PROPN
ijassa-429	425	18	,	,	PUNCT
ijassa-429	425	19	london	london	PROPN
ijassa-429	425	20	.	.	PUNCT
ijassa-429	426	1	[	[	X
ijassa-429	426	2	13	13	NUM
ijassa-429	426	3	]	]	X
ijassa-429	426	4	perni	perni	PROPN
ijassa-429	426	5	s	s	PROPN
ijassa-429	426	6	,	,	PUNCT
ijassa-429	426	7	andrew	andrew	PROPN
ijassa-429	426	8	pw	pw	PROPN
ijassa-429	426	9	,	,	PUNCT
ijassa-429	426	10	shama	shama	NOUN
ijassa-429	426	11	g.	g.	PROPN
ijassa-429	426	12	(	(	PUNCT
ijassa-429	426	13	2005	2005	NUM
ijassa-429	426	14	)	)	PUNCT
ijassa-429	426	15	,	,	PUNCT
ijassa-429	426	16	“	"	PUNCT
ijassa-429	426	17	estimating	estimate	VERB
ijassa-429	426	18	the	the	DET
ijassa-429	426	19	maximum	maximum	ADJ
ijassa-429	426	20	specific	specific	ADJ
ijassa-429	426	21	growth	growth	NOUN
ijassa-429	426	22	rate	rate	NOUN
ijassa-429	426	23	from	from	ADP
ijassa-429	426	24	microbial	microbial	ADJ
ijassa-429	426	25	growth	growth	NOUN
ijassa-429	426	26	curves	curve	NOUN
ijassa-429	426	27	:	:	PUNCT
ijassa-429	426	28	definition	definition	NOUN
ijassa-429	426	29	is	be	AUX
ijassa-429	426	30	everything	everything	PRON
ijassa-429	426	31	”	"	PUNCT
ijassa-429	426	32	,	,	PUNCT
ijassa-429	426	33	food	food	NOUN
ijassa-429	426	34	microbiol	microbiol	PROPN
ijassa-429	426	35	,	,	PUNCT
ijassa-429	426	36	vol.22	vol.22	NOUN
ijassa-429	426	37	,	,	PUNCT
ijassa-429	426	38	no.6	no.6	PROPN
ijassa-429	426	39	,	,	PUNCT
ijassa-429	426	40	pp.491	pp.491	NOUN
ijassa-429	426	41	-	-	SYM
ijassa-429	426	42	495	495	NUM
ijassa-429	426	43	.	.	PUNCT
ijassa-429	427	1	doi	doi	NOUN
ijassa-429	427	2	:	:	PUNCT
ijassa-429	427	3	10.1016	10.1016	NUM
ijassa-429	427	4	/	/	SYM
ijassa-429	427	5	j.fm.2004.11.014	j.fm.2004.11.014	PROPN
ijassa-429	428	1	[	[	X
ijassa-429	428	2	14	14	NUM
ijassa-429	428	3	]	]	X
ijassa-429	428	4	stewart	stewart	PROPN
ijassa-429	428	5	,	,	PUNCT
ijassa-429	428	6	j.	j.	PROPN
ijassa-429	428	7	(	(	PUNCT
ijassa-429	428	8	2008	2008	NUM
ijassa-429	428	9	)	)	PUNCT
ijassa-429	428	10	,	,	PUNCT
ijassa-429	428	11	calculus	calculus	NOUN
ijassa-429	428	12	,	,	PUNCT
ijassa-429	428	13	early	early	ADJ
ijassa-429	428	14	transcendentals(6th	transcendentals(6th	NOUN
ijassa-429	428	15	ed	ed	NOUN
ijassa-429	428	16	.	.	PUNCT
ijassa-429	428	17	)	)	PUNCT
ijassa-429	428	18	,	,	PUNCT
ijassa-429	428	19	belmont	belmont	PROPN
ijassa-429	428	20	,	,	PUNCT
ijassa-429	428	21	california	california	PROPN
ijassa-429	428	22	:	:	PUNCT
ijassa-429	428	23	thomson	thomson	PROPN
ijassa-429	428	24	learning	learning	NOUN
ijassa-429	428	25	.	.	PUNCT
ijassa-429	429	1	[	[	X
ijassa-429	429	2	15	15	NUM
ijassa-429	429	3	]	]	PUNCT
ijassa-429	429	4	demana	demana	PROPN
ijassa-429	429	5	f.	f.	PROPN
ijassa-429	429	6	d	d	PROPN
ijassa-429	429	7	,	,	PUNCT
ijassa-429	429	8	finney	finney	PROPN
ijassa-429	429	9	r.	r.	PROPN
ijassa-429	429	10	l	l	PROPN
ijassa-429	429	11	,	,	PUNCT
ijassa-429	429	12	kennedy	kennedy	PROPN
ijassa-429	429	13	d	d	PROPN
ijassa-429	429	14	,	,	PUNCT
ijassa-429	429	15	&	&	CCONJ
ijassa-429	429	16	waits	wait	VERB
ijassa-429	429	17	b.	b.	PROPN
ijassa-429	429	18	k.	k.	PROPN
ijassa-429	429	19	(	(	PUNCT
ijassa-429	429	20	2003	2003	NUM
ijassa-429	429	21	)	)	PUNCT
ijassa-429	429	22	,	,	PUNCT
ijassa-429	429	23	calculus	calculus	NOUN
ijassa-429	429	24	:	:	PUNCT
ijassa-429	429	25	graphical	graphical	ADJ
ijassa-429	429	26	,	,	PUNCT
ijassa-429	429	27	numerical	numerical	ADJ
ijassa-429	429	28	,	,	PUNCT
ijassa-429	429	29	algebraic	algebraic	ADJ
ijassa-429	429	30	,	,	PUNCT
ijassa-429	429	31	upper	upper	ADJ
ijassa-429	429	32	saddle	saddle	NOUN
ijassa-429	429	33	river	river	NOUN
ijassa-429	429	34	,	,	PUNCT
ijassa-429	429	35	new	new	PROPN
ijassa-429	429	36	jersey	jersey	PROPN
ijassa-429	429	37	:	:	PUNCT
ijassa-429	429	38	prentice	prentice	PROPN
ijassa-429	429	39	hall	hall	PROPN
ijassa-429	429	40	.	.	PUNCT
ijassa-429	430	1	[	[	X
ijassa-429	430	2	16	16	NUM
ijassa-429	430	3	]	]	X
ijassa-429	430	4	gause	gause	PROPN
ijassa-429	430	5	g.	g.	PROPN
ijassa-429	430	6	f.	f.	PROPN
ijassa-429	430	7	(	(	PUNCT
ijassa-429	430	8	1934	1934	NUM
ijassa-429	430	9	)	)	PUNCT
ijassa-429	430	10	,	,	PUNCT
ijassa-429	430	11	struggle	struggle	VERB
ijassa-429	430	12	for	for	ADP
ijassa-429	430	13	existence	existence	NOUN
ijassa-429	430	14	,	,	PUNCT
ijassa-429	430	15	hafner	hafner	PROPN
ijassa-429	430	16	,	,	PUNCT
ijassa-429	430	17	new	new	PROPN
ijassa-429	430	18	york	york	PROPN
ijassa-429	430	19	.	.	PUNCT
ijassa-429	431	1	[	[	X
ijassa-429	431	2	17	17	NUM
ijassa-429	431	3	]	]	PUNCT
ijassa-429	431	4	gause	gause	PROPN
ijassa-429	431	5	g.	g.	PROPN
ijassa-429	431	6	f.	f.	PROPN
ijassa-429	431	7	(	(	PUNCT
ijassa-429	431	8	1932	1932	NUM
ijassa-429	431	9	)	)	PUNCT
ijassa-429	431	10	,	,	PUNCT
ijassa-429	431	11	“	"	PUNCT
ijassa-429	431	12	experimental	experimental	ADJ
ijassa-429	431	13	studies	study	NOUN
ijassa-429	431	14	on	on	ADP
ijassa-429	431	15	the	the	DET
ijassa-429	431	16	struggle	struggle	NOUN
ijassa-429	431	17	for	for	ADP
ijassa-429	431	18	existence	existence	NOUN
ijassa-429	431	19	.	.	PUNCT
ijassa-429	432	1	i.	i.	PROPN
ijassa-429	432	2	mixed	mix	VERB
ijassa-429	432	3	populations	population	NOUN
ijassa-429	432	4	of	of	ADP
ijassa-429	432	5	two	two	NUM
ijassa-429	432	6	species	specie	NOUN
ijassa-429	432	7	of	of	ADP
ijassa-429	432	8	yeast	yeast	NOUN
ijassa-429	432	9	”	"	PUNCT
ijassa-429	432	10	,	,	PUNCT
ijassa-429	432	11	j.	j.	PROPN
ijassa-429	432	12	exp	exp	PROPN
ijassa-429	432	13	.	.	PUNCT
ijassa-429	433	1	biol	biol	PROPN
ijassa-429	433	2	.	.	PUNCT
ijassa-429	433	3	,	,	PUNCT
ijassa-429	434	1	vol.9	vol.9	PROPN
ijassa-429	434	2	,	,	PUNCT
ijassa-429	434	3	no.4	no.4	PROPN
ijassa-429	434	4	,	,	PUNCT
ijassa-429	434	5	pp.389	pp.389	NOUN
ijassa-429	434	6	-	-	PUNCT
ijassa-429	434	7	402	402	NUM
ijassa-429	434	8	.	.	PUNCT
ijassa-429	435	1	[	[	X
ijassa-429	435	2	18	18	NUM
ijassa-429	435	3	]	]	X
ijassa-429	435	4	guckenheimer	guckenheimer	PROPN
ijassa-429	435	5	j.	j.	PROPN
ijassa-429	435	6	and	and	CCONJ
ijassa-429	435	7	holmes	holmes	PROPN
ijassa-429	435	8	p.	p.	PROPN
ijassa-429	435	9	(	(	PUNCT
ijassa-429	435	10	1997	1997	NUM
ijassa-429	435	11	)	)	PUNCT
ijassa-429	435	12	,	,	PUNCT
ijassa-429	435	13	nonlinear	nonlinear	ADJ
ijassa-429	435	14	oscillations	oscillation	NOUN
ijassa-429	435	15	,	,	PUNCT
ijassa-429	435	16	dynamical	dynamical	ADJ
ijassa-429	435	17	systems	system	NOUN
ijassa-429	435	18	,	,	PUNCT
ijassa-429	435	19	and	and	CCONJ
ijassa-429	435	20	bifurcations	bifurcation	NOUN
ijassa-429	435	21	of	of	ADP
ijassa-429	435	22	vector	vector	NOUN
ijassa-429	435	23	fields	field	NOUN
ijassa-429	435	24	,	,	PUNCT
ijassa-429	435	25	3rd	3rd	ADJ
ijassa-429	435	26	ed	ed	NOUN
ijassa-429	435	27	.	.	PUNCT
ijassa-429	436	1	new	new	PROPN
ijassa-429	436	2	york	york	PROPN
ijassa-429	436	3	:	:	PUNCT
ijassa-429	436	4	springerverlag	springerverlag	PROPN
ijassa-429	436	5	.	.	PUNCT
ijassa-429	437	1	corresponding	correspond	VERB
ijassa-429	437	2	author	author	NOUN
ijassa-429	437	3	guo	guo	PROPN
ijassa-429	437	4	wei	wei	PROPN
ijassa-429	437	5	can	can	AUX
ijassa-429	437	6	be	be	AUX
ijassa-429	437	7	contacted	contact	VERB
ijassa-429	437	8	at	at	ADP
ijassa-429	437	9	:	:	PUNCT
ijassa-429	437	10	guo.wei@uncp.edu	guo.wei@uncp.edu	PROPN
ijassa-429	437	11	.	.	PUNCT