id	sid	tid	token	lemma	pos
iajs-880	1	1	ibn	ibn	PROPN
iajs-880	1	2	alhaitham	alhaitham	NOUN
iajs-880	1	3	j.	j.	PROPN
iajs-880	1	4	for	for	ADP
iajs-880	1	5	pure	pure	ADJ
iajs-880	1	6	&	&	CCONJ
iajs-880	1	7	appl	appl	PROPN
iajs-880	1	8	.	.	PUNCT
iajs-880	2	1	sci	sci	PROPN
iajs-880	2	2	.	.	PROPN
iajs-880	3	1	vo	vo	INTJ
iajs-880	3	2	l.24	l.24	PROPN
iajs-880	3	3	(	(	PUNCT
iajs-880	3	4	1	1	NUM
iajs-880	3	5	)	)	PUNCT
iajs-880	3	6	2011	2011	NUM
iajs-880	3	7	existence	existence	NOUN
iajs-880	3	8	of	of	ADP
iajs-880	3	9	positive	positive	ADJ
iajs-880	3	10	solution	solution	NOUN
iajs-880	3	11	for	for	ADP
iajs-880	3	12	boundary	boundary	ADJ
iajs-880	3	13	value	value	NOUN
iajs-880	3	14	problems	problem	NOUN
iajs-880	3	15	s.	s.	PROPN
iajs-880	3	16	m	m	PROPN
iajs-880	3	17	.	.	PUNCT
iajs-880	4	1	hussein	hussein	PROPN
iajs-880	4	2	department	department	PROPN
iajs-880	4	3	of	of	ADP
iajs-880	4	4	mathematics	mathematics	PROPN
iajs-880	4	5	,	,	PUNCT
iajs-880	4	6	education	education	NOUN
iajs-880	4	7	college	college	NOUN
iajs-880	4	8	for	for	ADP
iajs-880	4	9	pure	pure	ADJ
iajs-880	4	10	sciences	science	NOUN
iajs-880	4	11	,	,	PUNCT
iajs-880	4	12	university	university	NOUN
iajs-880	4	13	of	of	ADP
iajs-880	4	14	anbar	anbar	PROPN
iajs-880	4	15	received	receive	VERB
iajs-880	4	16	in	in	ADP
iajs-880	4	17	june,1,2010	june,1,2010	PROPN
iajs-880	4	18	accepted	accept	VERB
iajs-880	4	19	in	in	ADP
iajs-880	4	20	oct,19,2010	oct,19,2010	PROPN
iajs-880	4	21	abstract	abstract	ADV
iajs-880	4	22	this	this	DET
iajs-880	4	23	paper	paper	NOUN
iajs-880	4	24	studies	study	NOUN
iajs-880	4	25	the	the	DET
iajs-880	4	26	existence	existence	NOUN
iajs-880	4	27	of	of	ADP
iajs-880	4	28	positive	positive	ADJ
iajs-880	4	29	solutions	solution	NOUN
iajs-880	4	30	for	for	ADP
iajs-880	4	31	the	the	DET
iajs-880	4	32	following	follow	VERB
iajs-880	4	33	boundary	boundary	ADJ
iajs-880	4	34	value	value	NOUN
iajs-880	4	35	problem	problem	NOUN
iajs-880	4	36	:	:	PUNCT
iajs-880	4	37	0	0	NUM
iajs-880	4	38	y(b	y(b	NOUN
iajs-880	4	39	)	)	PUNCT
iajs-880	5	1	0(a)y	0(a)y	X
iajs-880	5	2	β	β	X
iajs-880	5	3	y(a	y(a	PROPN
iajs-880	5	4	)	)	PUNCT
iajs-880	5	5	α	α	PROPN
iajs-880	5	6	bta	bta	NOUN
iajs-880	5	7	f(y	f(y	NOUN
iajs-880	5	8	)	)	PUNCT
iajs-880	5	9	g(t	g(t	PROPN
iajs-880	5	10	)	)	PUNCT
iajs-880	6	1	λy	λy	PROPN
iajs-880	6	2			NUM
iajs-880	6	3			NOUN
iajs-880	6	4			PUNCT
iajs-880	7	1	the	the	DET
iajs-880	7	2	solution	solution	NOUN
iajs-880	7	3	procedure	procedure	NOUN
iajs-880	7	4	follows	follow	VERB
iajs-880	7	5	using	use	VERB
iajs-880	7	6	the	the	DET
iajs-880	7	7	fixed	fix	VERB
iajs-880	7	8	point	point	NOUN
iajs-880	7	9	theorem	theorem	NOUN
iajs-880	7	10	and	and	CCONJ
iajs-880	7	11	obtains	obtain	VERB
iajs-880	7	12	that	that	SCONJ
iajs-880	7	13	this	this	DET
iajs-880	7	14	problem	problem	NOUN
iajs-880	7	15	has	have	VERB
iajs-880	7	16	at	at	ADV
iajs-880	7	17	least	least	ADV
iajs-880	7	18	one	one	NUM
iajs-880	7	19	positive	positive	ADJ
iajs-880	7	20	solution	solution	NOUN
iajs-880	7	21	.also	.also	PUNCT
iajs-880	7	22	,	,	PUNCT
iajs-880	7	23	it	it	PRON
iajs-880	7	24	determines	determine	VERB
iajs-880	7	25	(	(	PUNCT
iajs-880	7	26			X
iajs-880	7	27	)	)	PUNCT
iajs-880	7	28	eigenvalue	eigenvalue	NOUN
iajs-880	7	29	which	which	PRON
iajs-880	7	30	would	would	AUX
iajs-880	7	31	be	be	AUX
iajs-880	7	32	needed	need	VERB
iajs-880	7	33	to	to	PART
iajs-880	7	34	find	find	VERB
iajs-880	7	35	the	the	DET
iajs-880	7	36	positive	positive	ADJ
iajs-880	7	37	solution	solution	NOUN
iajs-880	7	38	.	.	PUNCT
iajs-880	8	1	keywords	keyword	NOUN
iajs-880	8	2	:	:	PUNCT
iajs-880	8	3	positive	positive	ADJ
iajs-880	8	4	solution	solution	NOUN
iajs-880	8	5	,	,	PUNCT
iajs-880	8	6	boundary	boundary	ADJ
iajs-880	8	7	value	value	NOUN
iajs-880	8	8	problem	problem	NOUN
iajs-880	8	9	,	,	PUNCT
iajs-880	8	10	fixed	fix	VERB
iajs-880	8	11	point	point	NOUN
iajs-880	8	12	theorem	theorem	NOUN
iajs-880	8	13	.	.	PUNCT
iajs-880	9	1	introduction	introduction	NOUN
iajs-880	9	2	in	in	ADP
iajs-880	9	3	this	this	DET
iajs-880	9	4	paper	paper	NOUN
iajs-880	9	5	we	we	PRON
iajs-880	9	6	shall	shall	AUX
iajs-880	9	7	consider	consider	VERB
iajs-880	9	8	the	the	DET
iajs-880	9	9	second	second	ADJ
iajs-880	9	10	order	order	NOUN
iajs-880	9	11	boundary	boundary	ADJ
iajs-880	9	12	value	value	NOUN
iajs-880	9	13	problem	problem	NOUN
iajs-880	9	14	(	(	PUNCT
iajs-880	9	15	bvp	bvp	PROPN
iajs-880	9	16	)	)	PUNCT
iajs-880	9	17	the	the	DET
iajs-880	9	18	following	follow	VERB
iajs-880	9	19	conditions	condition	NOUN
iajs-880	9	20	will	will	AUX
iajs-880	9	21	be	be	AUX
iajs-880	9	22	assumed	assume	VERB
iajs-880	9	23	throughout	throughout	ADP
iajs-880	9	24	:	:	PUNCT
iajs-880	9	25	a	a	DET
iajs-880	9	26	f	f	X
iajs-880	9	27	:	:	PUNCT
iajs-880	10	1	[	[	X
iajs-880	10	2	0	0	NUM
iajs-880	10	3	,	,	PUNCT
iajs-880	10	4			NOUN
iajs-880	10	5	)	)	PUNCT
iajs-880	10	6			PUNCT
iajs-880	11	1	[	[	X
iajs-880	11	2	0	0	NUM
iajs-880	11	3	,	,	PUNCT
iajs-880	11	4			PROPN
iajs-880	11	5	)	)	PUNCT
iajs-880	11	6	is	be	AUX
iajs-880	11	7	continuous	continuous	ADJ
iajs-880	11	8	,	,	PUNCT
iajs-880	11	9	b	b	X
iajs-880	11	10	g	g	NOUN
iajs-880	11	11	:	:	PUNCT
iajs-880	11	12	[	[	X
iajs-880	11	13	0	0	NUM
iajs-880	11	14	,	,	PUNCT
iajs-880	11	15	1	1	NUM
iajs-880	11	16	]	]	PUNCT
iajs-880	11	17			PUNCT
iajs-880	12	1	[	[	X
iajs-880	12	2	0	0	NUM
iajs-880	12	3	,	,	PUNCT
iajs-880	12	4			PROPN
iajs-880	12	5	)	)	PUNCT
iajs-880	12	6	is	be	AUX
iajs-880	12	7	continuous	continuous	ADJ
iajs-880	12	8	and	and	CCONJ
iajs-880	12	9	does	do	AUX
iajs-880	12	10	not	not	PART
iajs-880	12	11	vanish	vanish	VERB
iajs-880	12	12	identically	identically	ADV
iajs-880	12	13	on	on	ADP
iajs-880	12	14	any	any	DET
iajs-880	12	15	subinterval	subinterval	NOUN
iajs-880	12	16	,	,	PUNCT
iajs-880	13	1	c	c	PROPN
iajs-880	13	2	x	x	SYM
iajs-880	13	3	f(x	f(x	PROPN
iajs-880	13	4	)	)	PUNCT
iajs-880	13	5	limf	limf	PROPN
iajs-880	13	6	0x	0x	NOUN
iajs-880	13	7	0	0	NUM
iajs-880	13	8			PUNCT
iajs-880	13	9			PROPN
iajs-880	14	1			NUM
iajs-880	14	2	and	and	CCONJ
iajs-880	14	3	x	x	SYM
iajs-880	14	4	f(x	f(x	PROPN
iajs-880	14	5	)	)	PUNCT
iajs-880	14	6	limf	limf	PROPN
iajs-880	14	7	x	x	AUX
iajs-880	14	8			AUX
iajs-880	14	9			VERB
iajs-880	14	10			PRON
iajs-880	14	11	exist	exist	VERB
iajs-880	14	12	,	,	PUNCT
iajs-880	14	13	d	d	ADP
iajs-880	14	14			X
iajs-880	14	15	,	,	PUNCT
iajs-880	14	16			VERB
iajs-880	14	17	such	such	ADJ
iajs-880	14	18	that	that	SCONJ
iajs-880	14	19			NOUN
iajs-880	14	20	and	and	CCONJ
iajs-880	14	21			NOUN
iajs-880	14	22	are	be	AUX
iajs-880	14	23	not	not	PART
iajs-880	14	24	both	both	DET
iajs-880	14	25	zero	zero	NUM
iajs-880	14	26	and	and	CCONJ
iajs-880	14	27	z	z	NOUN
iajs-880	14	28	=	=	NOUN
iajs-880	14	29			PROPN
iajs-880	14	30			ADV
iajs-880	14	31			PROPN
iajs-880	14	32	>	>	X
iajs-880	14	33	0	0	PUNCT
iajs-880	14	34	,	,	PUNCT
iajs-880	14	35	and	and	CCONJ
iajs-880	14	36	e	e	X
iajs-880	14	37	a	a	DET
iajs-880	14	38	≥	≥	NOUN
iajs-880	14	39	0	0	NUM
iajs-880	14	40	,	,	PUNCT
iajs-880	14	41	b	b	PROPN
iajs-880	14	42	≤1	≤1	PROPN
iajs-880	14	43	.	.	PUNCT
iajs-880	15	1	the	the	DET
iajs-880	15	2	boundary	boundary	ADJ
iajs-880	15	3	value	value	NOUN
iajs-880	15	4	problem	problem	NOUN
iajs-880	15	5	(	(	PUNCT
iajs-880	15	6	1.1	1.1	NUM
iajs-880	15	7	)	)	PUNCT
iajs-880	15	8	arises	arise	VERB
iajs-880	15	9	in	in	ADP
iajs-880	15	10	the	the	DET
iajs-880	15	11	applied	apply	VERB
iajs-880	15	12	mathematical	mathematical	ADJ
iajs-880	15	13	sciences	science	NOUN
iajs-880	15	14	such	such	ADJ
iajs-880	15	15	as	as	ADP
iajs-880	15	16	nonlinear	nonlinear	ADJ
iajs-880	15	17	diffusion	diffusion	NOUN
iajs-880	15	18	generated	generate	VERB
iajs-880	15	19	by	by	ADP
iajs-880	15	20	nonlinear	nonlinear	ADJ
iajs-880	15	21	sources	source	NOUN
iajs-880	15	22	,	,	PUNCT
iajs-880	15	23	thermal	thermal	ADJ
iajs-880	15	24	ignition	ignition	NOUN
iajs-880	15	25	of	of	ADP
iajs-880	15	26	gases	gas	NOUN
iajs-880	15	27	and	and	CCONJ
iajs-880	15	28	chemical	chemical	NOUN
iajs-880	15	29	concentrations	concentration	NOUN
iajs-880	15	30	in	in	ADP
iajs-880	15	31	biological	biological	ADJ
iajs-880	15	32	problems	problem	NOUN
iajs-880	15	33	;	;	PUNCT
iajs-880	15	34	for	for	ADP
iajs-880	15	35	example	example	NOUN
iajs-880	15	36	see	see	VERB
iajs-880	15	37	[	[	X
iajs-880	15	38	1	1	X
iajs-880	15	39	]	]	PUNCT
iajs-880	15	40	,	,	PUNCT
iajs-880	15	41	[	[	X
iajs-880	15	42	2	2	NUM
iajs-880	15	43	]	]	PUNCT
iajs-880	15	44	,	,	PUNCT
iajs-880	15	45	[	[	X
iajs-880	15	46	3	3	NUM
iajs-880	15	47	]	]	PUNCT
iajs-880	15	48	.	.	PUNCT
iajs-880	16	1	when	when	SCONJ
iajs-880	16	2	=1	=1	PROPN
iajs-880	16	3	and	and	CCONJ
iajs-880	16	4	f	f	PROPN
iajs-880	16	5	is	be	AUX
iajs-880	16	6	either	either	DET
iajs-880	16	7	superlinear	superlinear	NOUN
iajs-880	16	8	that	that	PRON
iajs-880	16	9	is	be	AUX
iajs-880	16	10	(	(	PUNCT
iajs-880	16	11	f	f	NOUN
iajs-880	16	12	0	0	NUM
iajs-880	17	1	=	=	SYM
iajs-880	17	2	0	0	NUM
iajs-880	17	3	and	and	CCONJ
iajs-880	17	4	f	f	PROPN
iajs-880	17	5			NOUN
iajs-880	17	6	=	=	SYM
iajs-880	17	7			PROPN
iajs-880	17	8	)	)	PUNCT
iajs-880	17	9	or	or	CCONJ
iajs-880	17	10	f	f	PROPN
iajs-880	17	11	is	be	AUX
iajs-880	17	12	sublinear	sublinear	NOUN
iajs-880	17	13	that	that	PRON
iajs-880	17	14	is	be	AUX
iajs-880	17	15	(	(	PUNCT
iajs-880	17	16	f	f	NOUN
iajs-880	17	17	0	0	NUM
iajs-880	18	1	=	=	SYM
iajs-880	18	2			VERB
iajs-880	18	3	and	and	CCONJ
iajs-880	18	4	f	f	NOUN
iajs-880	18	5			PROPN
iajs-880	18	6	=	=	SYM
iajs-880	18	7	0	0	NUM
iajs-880	18	8	)	)	PUNCT
iajs-880	18	9	,	,	PUNCT
iajs-880	18	10	1.1	1.1	NUM
iajs-880	18	11	)	)	PUNCT
iajs-880	18	12	.........	.........	PUNCT
iajs-880	19	1	(	(	PUNCT
iajs-880	19	2	0	0	NUM
iajs-880	19	3	y(b	y(b	NOUN
iajs-880	19	4	)	)	PUNCT
iajs-880	20	1	0(a)y	0(a)y	X
iajs-880	20	2	β	β	X
iajs-880	20	3	y(a	y(a	PROPN
iajs-880	20	4	)	)	PUNCT
iajs-880	20	5	α	α	PROPN
iajs-880	20	6	bta	bta	NOUN
iajs-880	20	7	f(y	f(y	NOUN
iajs-880	20	8	)	)	PUNCT
iajs-880	20	9	g(t	g(t	PROPN
iajs-880	20	10	)	)	PUNCT
iajs-880	21	1	λy	λy	ADP
iajs-880	21	2			NUM
iajs-880	21	3			PROPN
iajs-880	21	4			NUM
iajs-880	21	5			NOUN
iajs-880	21	6			NUM
iajs-880	21	7			NUM
iajs-880	21	8			PROPN
iajs-880	21	9			ADJ
iajs-880	21	10	ibn	ibn	PROPN
iajs-880	21	11	alhaitham	alhaitham	NOUN
iajs-880	22	1	j.	j.	PROPN
iajs-880	23	1	fo	fo	ADP
iajs-880	23	2	r	r	NOUN
iajs-880	23	3	pure	pure	ADJ
iajs-880	23	4	&	&	CCONJ
iajs-880	23	5	appl	appl	PROPN
iajs-880	23	6	.	.	PUNCT
iajs-880	24	1	sc	sc	PROPN
iajs-880	24	2	i.	i.	PROPN
iajs-880	24	3	vo	vo	PROPN
iajs-880	24	4	l.24	l.24	PROPN
iajs-880	24	5	(	(	PUNCT
iajs-880	24	6	1	1	NUM
iajs-880	24	7	)	)	PUNCT
iajs-880	24	8	2011	2011	NUM
iajs-880	24	9	erbe	erbe	NOUN
iajs-880	24	10	and	and	CCONJ
iajs-880	24	11	wang	wang	PROPN
iajs-880	25	1	[	[	X
iajs-880	25	2	5	5	NUM
iajs-880	25	3	]	]	PUNCT
iajs-880	25	4	obtained	obtain	VERB
iajs-880	25	5	solutions	solution	NOUN
iajs-880	25	6	that	that	PRON
iajs-880	25	7	are	be	AUX
iajs-880	25	8	positive	positive	ADJ
iajs-880	25	9	with	with	ADP
iajs-880	25	10	respect	respect	NOUN
iajs-880	25	11	to	to	ADP
iajs-880	25	12	a	a	DET
iajs-880	25	13	cone	cone	NOUN
iajs-880	25	14	which	which	PRON
iajs-880	25	15	lies	lie	VERB
iajs-880	25	16	in	in	ADP
iajs-880	25	17	an	an	DET
iajs-880	25	18	annular	annular	ADJ
iajs-880	25	19	type	type	NOUN
iajs-880	25	20	region	region	NOUN
iajs-880	25	21	.the	.the	PUNCT
iajs-880	26	1	methods	method	NOUN
iajs-880	26	2	of	of	ADP
iajs-880	26	3	[	[	X
iajs-880	26	4	5	5	NUM
iajs-880	26	5	]	]	PUNCT
iajs-880	26	6	were	be	AUX
iajs-880	26	7	then	then	ADV
iajs-880	26	8	extended	extend	VERB
iajs-880	26	9	to	to	ADP
iajs-880	26	10	higher	high	ADJ
iajs-880	26	11	order	order	NOUN
iajs-880	26	12	bvp	bvp	NOUN
iajs-880	26	13	in	in	ADP
iajs-880	26	14	[	[	X
iajs-880	26	15	4	4	NUM
iajs-880	26	16	]	]	PUNCT
iajs-880	26	17	.	.	PUNCT
iajs-880	27	1	for	for	ADP
iajs-880	27	2	the	the	DET
iajs-880	27	3	case	case	NOUN
iajs-880	27	4			X
iajs-880	27	5	=	=	X
iajs-880	27	6	1,	1,	NUM
iajs-880	27	7	=	=	SYM
iajs-880	27	8	0,	0,	PUNCT
iajs-880	28	1	=	=	NOUN
iajs-880	28	2	1	1	NUM
iajs-880	28	3	,	,	PUNCT
iajs-880	28	4			NUM
iajs-880	28	5	=	=	SYM
iajs-880	28	6	0	0	NUM
iajs-880	28	7	,	,	PUNCT
iajs-880	28	8	johnny	johnny	PROPN
iajs-880	28	9	henderson	henderson	PROPN
iajs-880	28	10	and	and	CCONJ
iajs-880	28	11	haiyan	haiyan	PROPN
iajs-880	28	12	wang	wang	PROPN
iajs-880	29	1	[	[	X
iajs-880	29	2	7	7	NUM
iajs-880	29	3	]	]	PUNCT
iajs-880	29	4	obtained	obtain	VERB
iajs-880	29	5	solutions	solution	NOUN
iajs-880	29	6	that	that	PRON
iajs-880	29	7	are	be	AUX
iajs-880	29	8	positive	positive	ADJ
iajs-880	29	9	for	for	ADP
iajs-880	29	10	an	an	DET
iajs-880	29	11	open	open	ADJ
iajs-880	29	12	interval	interval	NOUN
iajs-880	29	13	of	of	ADP
iajs-880	29	14	eigenvalues	eigenvalue	NOUN
iajs-880	29	15	.	.	PUNCT
iajs-880	30	1	not	not	PART
iajs-880	30	2	required	require	VERB
iajs-880	30	3	in	in	ADP
iajs-880	30	4	this	this	DET
iajs-880	30	5	work	work	NOUN
iajs-880	30	6	that	that	PRON
iajs-880	30	7	f	f	PROPN
iajs-880	30	8	would	would	AUX
iajs-880	30	9	be	be	AUX
iajs-880	30	10	either	either	CCONJ
iajs-880	30	11	superlinear	superlinear	NOUN
iajs-880	30	12	or	or	CCONJ
iajs-880	30	13	sublinear	sublinear	NOUN
iajs-880	30	14	,	,	PUNCT
iajs-880	30	15	yet	yet	ADV
iajs-880	30	16	,	,	PUNCT
iajs-880	30	17	as	as	ADP
iajs-880	30	18	in	in	ADP
iajs-880	30	19	[	[	X
iajs-880	30	20	4	4	NUM
iajs-880	30	21	]	]	PUNCT
iajs-880	30	22	,	,	PUNCT
iajs-880	31	1	[	[	X
iajs-880	31	2	5	5	NUM
iajs-880	31	3	]	]	PUNCT
iajs-880	31	4	but	but	CCONJ
iajs-880	31	5	as	as	ADP
iajs-880	31	6	in	in	ADP
iajs-880	31	7	[	[	X
iajs-880	31	8	7	7	NUM
iajs-880	31	9	]	]	PUNCT
iajs-880	31	10	,	,	PUNCT
iajs-880	31	11	the	the	DET
iajs-880	31	12	arguments	argument	NOUN
iajs-880	31	13	presented	present	VERB
iajs-880	31	14	here	here	ADV
iajs-880	31	15	for	for	ADP
iajs-880	31	16	obtaining	obtain	VERB
iajs-880	31	17	solutions	solution	NOUN
iajs-880	31	18	of(1.1)for	of(1.1)for	ADP
iajs-880	31	19	certain	certain	VERB
iajs-880	31	20	involve	involve	VERB
iajs-880	31	21	concavity	concavity	NOUN
iajs-880	31	22	properties	property	NOUN
iajs-880	31	23	of	of	ADP
iajs-880	31	24	solutions	solution	NOUN
iajs-880	31	25	,	,	PUNCT
iajs-880	31	26	which	which	PRON
iajs-880	31	27	are	be	AUX
iajs-880	31	28	employed	employ	VERB
iajs-880	31	29	in	in	ADP
iajs-880	31	30	defining	define	VERB
iajs-880	31	31	a	a	DET
iajs-880	31	32	cone	cone	NOUN
iajs-880	31	33	on	on	ADP
iajs-880	31	34	which	which	PRON
iajs-880	31	35	a	a	DET
iajs-880	31	36	positive	positive	ADJ
iajs-880	31	37	integral	integral	ADJ
iajs-880	31	38	operator	operator	NOUN
iajs-880	31	39	is	be	AUX
iajs-880	31	40	defined	define	VERB
iajs-880	31	41	.	.	PUNCT
iajs-880	32	1	a	a	DET
iajs-880	32	2	krasnosel’skii	krasnosel’skii	ADJ
iajs-880	32	3	fixed	fix	VERB
iajs-880	32	4	point	point	NOUN
iajs-880	32	5	theorem	theorem	ADJ
iajs-880	32	6	[	[	X
iajs-880	32	7	8	8	NUM
iajs-880	32	8	]	]	PUNCT
iajs-880	32	9	is	be	AUX
iajs-880	32	10	applied	apply	VERB
iajs-880	32	11	to	to	PART
iajs-880	32	12	yield	yield	VERB
iajs-880	32	13	positive	positive	ADJ
iajs-880	32	14	solutions	solution	NOUN
iajs-880	32	15	of	of	ADP
iajs-880	32	16	(	(	PUNCT
iajs-880	32	17	1.1	1.1	NUM
iajs-880	32	18	)	)	PUNCT
iajs-880	32	19	,	,	PUNCT
iajs-880	32	20	for	for	ADP
iajs-880	32	21			X
iajs-880	32	22	belongs	belong	VERB
iajs-880	32	23	to	to	ADP
iajs-880	32	24	an	an	DET
iajs-880	32	25	open	open	ADJ
iajs-880	32	26	interval	interval	NOUN
iajs-880	32	27	.	.	PUNCT
iajs-880	33	1	section	section	NOUN
iajs-880	33	2	2	2	NUM
iajs-880	33	3	,	,	PUNCT
iajs-880	33	4	presents	present	VERB
iajs-880	33	5	some	some	DET
iajs-880	33	6	properties	property	NOUN
iajs-880	33	7	of	of	ADP
iajs-880	33	8	green	green	PROPN
iajs-880	33	9	’s	’s	PART
iajs-880	33	10	functions	function	NOUN
iajs-880	33	11	that	that	PRON
iajs-880	33	12	are	be	AUX
iajs-880	33	13	used	use	VERB
iajs-880	33	14	in	in	ADP
iajs-880	33	15	defining	define	VERB
iajs-880	33	16	a	a	DET
iajs-880	33	17	positive	positive	ADJ
iajs-880	33	18	operator	operator	NOUN
iajs-880	33	19	,	,	PUNCT
iajs-880	33	20	also	also	ADV
iajs-880	33	21	states	state	VERB
iajs-880	33	22	the	the	DET
iajs-880	33	23	krasnosel’skii	krasnosel’skii	PROPN
iajs-880	33	24	fixed	fix	VERB
iajs-880	33	25	point	point	NOUN
iajs-880	33	26	theorem	theorem	NOUN
iajs-880	33	27	.	.	PUNCT
iajs-880	34	1	section	section	NOUN
iajs-880	34	2	3	3	NUM
iajs-880	34	3	,	,	PUNCT
iajs-880	34	4	gives	give	VERB
iajs-880	34	5	an	an	DET
iajs-880	34	6	appropriate	appropriate	ADJ
iajs-880	34	7	banach	banach	NOUN
iajs-880	34	8	space	space	NOUN
iajs-880	34	9	and	and	CCONJ
iajs-880	34	10	constructs	construct	VERB
iajs-880	34	11	a	a	DET
iajs-880	34	12	cone	cone	NOUN
iajs-880	34	13	to	to	PART
iajs-880	34	14	which	which	PRON
iajs-880	34	15	we	we	PRON
iajs-880	34	16	apply	apply	VERB
iajs-880	34	17	the	the	DET
iajs-880	34	18	fixed	fix	VERB
iajs-880	34	19	point	point	NOUN
iajs-880	34	20	theorem	theorem	VERB
iajs-880	34	21	yielding	yield	VERB
iajs-880	34	22	solutions	solution	NOUN
iajs-880	34	23	of	of	ADP
iajs-880	34	24	1	1	NUM
iajs-880	34	25	.1	.1	NUM
iajs-880	34	26	,	,	PUNCT
iajs-880	34	27	for	for	ADP
iajs-880	34	28	an	an	DET
iajs-880	34	29	open	open	ADJ
iajs-880	34	30	interval	interval	NOUN
iajs-880	34	31	of	of	ADP
iajs-880	34	32	eigenvalues	eigenvalue	NOUN
iajs-880	34	33	.	.	PUNCT
iajs-880	35	1	2some	2some	NUM
iajs-880	35	2	preliminaries	preliminary	NOUN
iajs-880	35	3	in	in	ADP
iajs-880	35	4	this	this	DET
iajs-880	35	5	section	section	NOUN
iajs-880	35	6	,	,	PUNCT
iajs-880	35	7	we	we	PRON
iajs-880	35	8	state	state	VERB
iajs-880	35	9	the	the	DET
iajs-880	35	10	above	above	ADJ
iajs-880	35	11	mentioned	mention	VERB
iajs-880	35	12	krasnosel’skii	krasnosel’skii	PROPN
iajs-880	35	13	fixed	fix	VERB
iajs-880	35	14	point	point	NOUN
iajs-880	35	15	theorem	theorem	VERB
iajs-880	35	16	.	.	PUNCT
iajs-880	36	1	we	we	PRON
iajs-880	36	2	will	will	AUX
iajs-880	36	3	apply	apply	VERB
iajs-880	36	4	this	this	DET
iajs-880	36	5	fixed	fix	VERB
iajs-880	36	6	point	point	NOUN
iajs-880	36	7	theorem	theorem	VERB
iajs-880	36	8	to	to	ADP
iajs-880	36	9	completely	completely	ADV
iajs-880	36	10	continuous	continuous	ADJ
iajs-880	36	11	integral	integral	ADJ
iajs-880	36	12	operator	operator	NOUN
iajs-880	36	13	,	,	PUNCT
iajs-880	36	14	whose	whose	DET
iajs-880	36	15	kernal	kernal	ADJ
iajs-880	36	16	,	,	PUNCT
iajs-880	36	17	g	g	PROPN
iajs-880	36	18	(	(	PUNCT
iajs-880	36	19	t	t	PROPN
iajs-880	36	20	,	,	PUNCT
iajs-880	36	21	s	s	PART
iajs-880	36	22	)	)	PUNCT
iajs-880	36	23	,	,	PUNCT
iajs-880	36	24	is	be	AUX
iajs-880	36	25	the	the	DET
iajs-880	36	26	green	green	PROPN
iajs-880	36	27	’s	’s	PART
iajs-880	36	28	function	function	NOUN
iajs-880	36	29	for	for	ADP
iajs-880	36	30	y	y	NOUN
iajs-880	36	31	=	=	SYM
iajs-880	36	32	0	0	NUM
iajs-880	36	33			X
iajs-880	36	34	y(a	y(a	X
iajs-880	36	35	)	)	PUNCT
iajs-880	36	36			PROPN
iajs-880	36	37	y	y	PROPN
iajs-880	36	38	(a	(a	PROPN
iajs-880	36	39	)	)	PUNCT
iajs-880	36	40	=	=	PUNCT
iajs-880	37	1	0	0	PUNCT
iajs-880	37	2	0	0	NUM
iajs-880	37	3	y(b	y(b	NOUN
iajs-880	37	4	)	)	PUNCT
iajs-880	38	1			PRON
iajs-880	38	2	is	be	AUX
iajs-880	38	3	…	…	PUNCT
iajs-880	38	4	…	…	PUNCT
iajs-880	38	5	…	…	PUNCT
iajs-880	38	6	..	..	PUNCT
iajs-880	38	7	(	(	PUNCT
iajs-880	38	8	2.1	2.1	NUM
iajs-880	38	9	)	)	PUNCT
iajs-880	38	10			NUM
iajs-880	38	11			NUM
iajs-880	38	12			NUM
iajs-880	38	13			NOUN
iajs-880	39	1			NOUN
iajs-880	39	2			ADV
iajs-880	40	1			ADJ
iajs-880	40	2			ADV
iajs-880	41	1			NOUN
iajs-880	41	2	btsa	btsa	NOUN
iajs-880	41	3	)	)	PUNCT
iajs-880	41	4	t	t	NOUN
iajs-880	41	5	-1	-1	PUNCT
iajs-880	41	6	(	(	PUNCT
iajs-880	41	7	)	)	PUNCT
iajs-880	41	8	βαs	βαs	NOUN
iajs-880	42	1	(	(	PUNCT
iajs-880	42	2	z	z	NOUN
iajs-880	42	3	1	1	NUM
iajs-880	42	4	bsta	bsta	NOUN
iajs-880	42	5	)	)	PUNCT
iajs-880	42	6	s-1	s-1	NOUN
iajs-880	42	7	(	(	PUNCT
iajs-880	42	8	)	)	PUNCT
iajs-880	42	9	βαt	βαt	NOUN
iajs-880	42	10	(	(	PUNCT
iajs-880	42	11	z	z	NOUN
iajs-880	42	12	1	1	NUM
iajs-880	42	13	s)g(t	s)g(t	PROPN
iajs-880	42	14	,	,	PUNCT
iajs-880	42	15	from	from	ADP
iajs-880	42	16	which	which	PRON
iajs-880	42	17	g(t	g(t	PROPN
iajs-880	42	18	,	,	PUNCT
iajs-880	42	19	s	s	PROPN
iajs-880	42	20	)	)	PUNCT
iajs-880	42	21	>	>	X
iajs-880	42	22	0	0	PUNCT
iajs-880	43	1	on	on	ADP
iajs-880	43	2	(	(	PUNCT
iajs-880	43	3	0	0	NUM
iajs-880	43	4	,	,	PUNCT
iajs-880	43	5	1	1	NUM
iajs-880	43	6	)	)	PUNCT
iajs-880	43	7			NOUN
iajs-880	43	8	(	(	PUNCT
iajs-880	43	9	0	0	NUM
iajs-880	43	10	,	,	PUNCT
iajs-880	43	11	1	1	NUM
iajs-880	43	12	)	)	PUNCT
iajs-880	43	13	,	,	PUNCT
iajs-880	43	14	…	…	PUNCT
iajs-880	43	15	…	…	PUNCT
iajs-880	43	16	…	…	SYM
iajs-880	43	17	.(2.2	.(2.2	NUM
iajs-880	43	18	)	)	PUNCT
iajs-880	43	19	g(t	g(t	PROPN
iajs-880	43	20	,	,	PUNCT
iajs-880	43	21	s	s	PROPN
iajs-880	43	22	)	)	PUNCT
iajs-880	43	23			NOUN
iajs-880	43	24	g(s	g(s	PROPN
iajs-880	43	25	,	,	PUNCT
iajs-880	43	26	s	s	X
iajs-880	43	27	)	)	PUNCT
iajs-880	43	28	=	=	SYM
iajs-880	43	29	)	)	PUNCT
iajs-880	43	30	s	s	PART
iajs-880	43	31	-1	-1	PRON
iajs-880	43	32	(	(	PUNCT
iajs-880	43	33	)	)	PUNCT
iajs-880	43	34	βs	βs	X
iajs-880	43	35	α	α	PRON
iajs-880	43	36	(	(	PUNCT
iajs-880	43	37	z	z	PROPN
iajs-880	43	38	1	1	NUM
iajs-880	43	39			PUNCT
iajs-880	43	40	,	,	PUNCT
iajs-880	43	41	a	a	DET
iajs-880	43	42			NUM
iajs-880	43	43	t	t	NOUN
iajs-880	43	44			NUM
iajs-880	43	45	b	b	NOUN
iajs-880	43	46	,	,	PUNCT
iajs-880	43	47	a	a	DET
iajs-880	43	48			NUM
iajs-880	43	49	s	s	PART
iajs-880	43	50			NUM
iajs-880	43	51	b	b	NOUN
iajs-880	43	52	,	,	PUNCT
iajs-880	43	53	…	…	PUNCT
iajs-880	43	54	…	…	PUNCT
iajs-880	43	55	(	(	PUNCT
iajs-880	43	56	2.3	2.3	NUM
iajs-880	43	57	)	)	PUNCT
iajs-880	44	1	and	and	CCONJ
iajs-880	44	2	it	it	PRON
iajs-880	44	3	is	be	AUX
iajs-880	44	4	shown	show	VERB
iajs-880	44	5	in	in	ADP
iajs-880	44	6	[	[	X
iajs-880	44	7	5	5	NUM
iajs-880	44	8	]	]	PUNCT
iajs-880	44	9	that	that	SCONJ
iajs-880	44	10	:	:	PUNCT
iajs-880	44	11	g(t	g(t	PROPN
iajs-880	44	12	,	,	PUNCT
iajs-880	44	13	s	s	PROPN
iajs-880	44	14	)	)	PUNCT
iajs-880	44	15			NUM
iajs-880	44	16	m	m	NOUN
iajs-880	44	17	g(s	g(s	PROPN
iajs-880	44	18	,	,	PUNCT
iajs-880	44	19	s	s	X
iajs-880	44	20	)	)	PUNCT
iajs-880	44	21	=	=	SYM
iajs-880	44	22	m	m	PROPN
iajs-880	44	23	)	)	PUNCT
iajs-880	44	24	s	s	PART
iajs-880	44	25	-1	-1	PUNCT
iajs-880	44	26	(	(	PUNCT
iajs-880	44	27	)	)	PUNCT
iajs-880	44	28	βs	βs	X
iajs-880	45	1	α	α	PRON
iajs-880	45	2	(	(	PUNCT
iajs-880	45	3	z	z	PROPN
iajs-880	45	4	1	1	NUM
iajs-880	45	5			PUNCT
iajs-880	45	6	,	,	PUNCT
iajs-880	45	7	4	4	NUM
iajs-880	45	8	12b	12b	NOUN
iajs-880	45	9	t	t	PROPN
iajs-880	45	10	4	4	NUM
iajs-880	45	11	12a	12a	NOUN
iajs-880	45	12			ADP
iajs-880	45	13			PROPN
iajs-880	45	14			PROPN
iajs-880	45	15	,	,	PUNCT
iajs-880	45	16	a	a	DET
iajs-880	45	17			NUM
iajs-880	45	18	s	s	PART
iajs-880	45	19			NUM
iajs-880	45	20	b	b	NOUN
iajs-880	45	21	,	,	PUNCT
iajs-880	45	22	…	…	PUNCT
iajs-880	45	23	(	(	PUNCT
iajs-880	45	24	2.4	2.4	NUM
iajs-880	45	25	)	)	PUNCT
iajs-880	45	26	where	where	SCONJ
iajs-880	45	27			PROPN
iajs-880	45	28			X
iajs-880	45	29			PROPN
iajs-880	45	30			PROPN
iajs-880	45	31			NUM
iajs-880	45	32			ADV
iajs-880	45	33			ADV
iajs-880	45	34			PROPN
iajs-880	45	35			PROPN
iajs-880	45	36	β)4(α	β)4(α	NUM
iajs-880	45	37	4βα	4βα	NOUN
iajs-880	45	38	,	,	PUNCT
iajs-880	45	39	4	4	NUM
iajs-880	45	40	1	1	NUM
iajs-880	45	41	minm	minm	NOUN
iajs-880	45	42	we	we	PRON
iajs-880	45	43	shall	shall	AUX
iajs-880	45	44	apply	apply	VERB
iajs-880	45	45	the	the	DET
iajs-880	45	46	following	following	ADJ
iajs-880	45	47	fixed	fix	VERB
iajs-880	45	48	point	point	NOUN
iajs-880	45	49	theorem	theorem	VERB
iajs-880	45	50	to	to	PART
iajs-880	45	51	obtain	obtain	VERB
iajs-880	45	52	solutions	solution	NOUN
iajs-880	45	53	of	of	ADP
iajs-880	45	54	(	(	PUNCT
iajs-880	45	55	1.1	1.1	NUM
iajs-880	45	56	)	)	PUNCT
iajs-880	45	57	,	,	PUNCT
iajs-880	45	58	for	for	ADP
iajs-880	45	59	certain	certain	ADJ
iajs-880	45	60			ADJ
iajs-880	45	61	theorem	theorem	ADJ
iajs-880	45	62	1	1	NUM
iajs-880	45	63	[	[	NOUN
iajs-880	45	64	8	8	NUM
iajs-880	45	65	]	]	PUNCT
iajs-880	45	66	.	.	PUNCT
iajs-880	46	1	let	let	VERB
iajs-880	46	2	b	b	NOUN
iajs-880	46	3	a	a	DET
iajs-880	46	4	banach	banach	NOUN
iajs-880	46	5	space	space	NOUN
iajs-880	46	6	,	,	PUNCT
iajs-880	46	7	and	and	CCONJ
iajs-880	46	8	let	let	VERB
iajs-880	46	9	p	p	PRON
iajs-880	46	10	be	be	AUX
iajs-880	46	11	a	a	DET
iajs-880	46	12	cone	cone	NOUN
iajs-880	46	13	in	in	ADP
iajs-880	46	14	b	b	PROPN
iajs-880	46	15	.	.	PUNCT
iajs-880	47	1	assume	assume	VERB
iajs-880	47	2	n	n	X
iajs-880	47	3	,	,	PUNCT
iajs-880	47	4	k	k	PROPN
iajs-880	47	5	are	be	AUX
iajs-880	47	6	be	be	VERB
iajs-880	47	7	knn0	knn0	NOUN
iajs-880	47	8			NOUN
iajs-880	47	9	,	,	PUNCT
iajs-880	47	10	and	and	CCONJ
iajs-880	47	11	let	let	VERB
iajs-880	47	12	pn)\k(p	pn)\k(p	PROPN
iajs-880	47	13	:	:	PUNCT
iajs-880	47	14	t	t	X
iajs-880	48	1			ADV
iajs-880	48	2	open	open	ADJ
iajs-880	48	3	subsets	subset	NOUN
iajs-880	48	4	of	of	ADP
iajs-880	48	5	b	b	NOUN
iajs-880	48	6	with	with	ADP
iajs-880	48	7	a	a	DET
iajs-880	48	8	completely	completely	ADV
iajs-880	48	9	continuous	continuous	ADJ
iajs-880	48	10	operator	operator	NOUN
iajs-880	48	11	such	such	ADJ
iajs-880	48	12	that	that	PRON
iajs-880	48	13	,	,	PUNCT
iajs-880	48	14	either	either	CCONJ
iajs-880	48	15	1	1	NUM
iajs-880	48	16	tu	tu	PROPN
iajs-880	48	17			VERB
iajs-880	48	18			NOUN
iajs-880	48	19			VERB
iajs-880	48	20	u	u	NOUN
iajs-880	48	21			VERB
iajs-880	48	22	,	,	PUNCT
iajs-880	48	23	u	u	NOUN
iajs-880	48	24			NOUN
iajs-880	48	25	p	p	X
iajs-880	48	26			PUNCT
iajs-880	48	27	n	n	NOUN
iajs-880	48	28	,	,	PUNCT
iajs-880	48	29	and	and	CCONJ
iajs-880	48	30			VERB
iajs-880	48	31	tu	tu	PROPN
iajs-880	48	32			PROPN
iajs-880	48	33			NUM
iajs-880	48	34			VERB
iajs-880	48	35	u	u	NOUN
iajs-880	48	36			ADJ
iajs-880	48	37	,	,	PUNCT
iajs-880	48	38	u	u	NOUN
iajs-880	48	39			NOUN
iajs-880	48	40	p	p	NOUN
iajs-880	48	41			PUNCT
iajs-880	48	42	k	k	NOUN
iajs-880	48	43	,	,	PUNCT
iajs-880	48	44	or	or	CCONJ
iajs-880	48	45	2	2	NUM
iajs-880	48	46	tu	tu	PROPN
iajs-880	48	47			PROPN
iajs-880	48	48			NUM
iajs-880	48	49			VERB
iajs-880	48	50	u	u	NOUN
iajs-880	48	51			ADJ
iajs-880	48	52	,	,	PUNCT
iajs-880	48	53	u	u	NOUN
iajs-880	48	54			NOUN
iajs-880	48	55	p	p	X
iajs-880	48	56			PUNCT
iajs-880	48	57	n	n	NOUN
iajs-880	48	58	,	,	PUNCT
iajs-880	48	59	and	and	CCONJ
iajs-880	48	60			VERB
iajs-880	48	61	tu	tu	PROPN
iajs-880	48	62			VERB
iajs-880	48	63			NOUN
iajs-880	48	64			VERB
iajs-880	48	65	u	u	NOUN
iajs-880	48	66			VERB
iajs-880	48	67	,	,	PUNCT
iajs-880	48	68	u	u	NOUN
iajs-880	48	69			NOUN
iajs-880	48	70	p	p	NOUN
iajs-880	48	71			PUNCT
iajs-880	48	72	k	k	NOUN
iajs-880	48	73	ibn	ibn	PROPN
iajs-880	48	74	alhaitham	alhaitham	NOUN
iajs-880	49	1	j.	j.	PROPN
iajs-880	50	1	fo	fo	ADP
iajs-880	50	2	r	r	NOUN
iajs-880	50	3	pure	pure	ADJ
iajs-880	50	4	&	&	CCONJ
iajs-880	50	5	appl	appl	PROPN
iajs-880	50	6	.	.	PUNCT
iajs-880	51	1	sc	sc	PROPN
iajs-880	51	2	i.	i.	PROPN
iajs-880	51	3	vo	vo	PROPN
iajs-880	51	4	l.24	l.24	PROPN
iajs-880	51	5	(	(	PUNCT
iajs-880	51	6	1	1	NUM
iajs-880	51	7	)	)	PUNCT
iajs-880	51	8	2011	2011	NUM
iajs-880	51	9	.	.	PUNCT
iajs-880	52	1	n)\k(p	n)\k(p	PROPN
iajs-880	52	2	then	then	ADV
iajs-880	52	3	t	t	PROPN
iajs-880	52	4	has	have	VERB
iajs-880	52	5	a	a	DET
iajs-880	52	6	fixed	fix	VERB
iajs-880	52	7	point	point	NOUN
iajs-880	52	8	in	in	ADP
iajs-880	52	9	3	3	NUM
iajs-880	52	10	.	.	PUNCT
iajs-880	53	1	solutions	solution	NOUN
iajs-880	53	2	in	in	ADP
iajs-880	53	3	the	the	DET
iajs-880	53	4	cone	cone	NOUN
iajs-880	53	5	in	in	ADP
iajs-880	53	6	this	this	DET
iajs-880	53	7	section	section	NOUN
iajs-880	53	8	,	,	PUNCT
iajs-880	53	9	apply	apply	VERB
iajs-880	53	10	theorem	theorem	NOUN
iajs-880	53	11	1	1	NUM
iajs-880	53	12	to	to	ADP
iajs-880	53	13	the	the	DET
iajs-880	53	14	eigenvalue	eigenvalue	PROPN
iajs-880	53	15	problem	problem	NOUN
iajs-880	53	16	(	(	PUNCT
iajs-880	53	17	1.1	1.1	NUM
iajs-880	53	18	)	)	PUNCT
iajs-880	53	19	.	.	PUNCT
iajs-880	54	1	note	note	VERB
iajs-880	54	2	that	that	SCONJ
iajs-880	54	3	y(t	y(t	PROPN
iajs-880	54	4	)	)	PUNCT
iajs-880	54	5	is	be	AUX
iajs-880	54	6	a	a	DET
iajs-880	54	7	solution	solution	NOUN
iajs-880	54	8	of	of	ADP
iajs-880	54	9	(	(	PUNCT
iajs-880	54	10	1.1	1.1	NUM
iajs-880	54	11	)	)	PUNCT
iajs-880	54	12	if	if	SCONJ
iajs-880	54	13	,	,	PUNCT
iajs-880	54	14	and	and	CCONJ
iajs-880	54	15	only	only	ADV
iajs-880	54	16	if	if	SCONJ
iajs-880	54	17	,	,	PUNCT
iajs-880	54	18	y(t	y(t	PROPN
iajs-880	54	19	)	)	PUNCT
iajs-880	54	20	=	=	SYM
iajs-880	54	21			X
iajs-880	54	22	ds	ds	X
iajs-880	54	23	f(y(s	f(y(s	NOUN
iajs-880	54	24	)	)	PUNCT
iajs-880	54	25	)	)	PUNCT
iajs-880	54	26	g(s	g(s	PROPN
iajs-880	54	27	)	)	PUNCT
iajs-880	54	28	s	s	PART
iajs-880	54	29	)	)	PUNCT
iajs-880	54	30	,	,	PUNCT
iajs-880	54	31	(	(	PUNCT
iajs-880	54	32	t	t	PROPN
iajs-880	54	33	g	g	PROPN
iajs-880	54	34	b	b	PROPN
iajs-880	54	35	a	a	PRON
iajs-880	54	36			X
iajs-880	54	37	,	,	PUNCT
iajs-880	54	38	a	a	DET
iajs-880	54	39			NUM
iajs-880	54	40	t	t	NOUN
iajs-880	54	41			NUM
iajs-880	54	42	b	b	NOUN
iajs-880	54	43	for	for	ADP
iajs-880	54	44	our	our	PRON
iajs-880	54	45	construction	construction	NOUN
iajs-880	54	46	,	,	PUNCT
iajs-880	54	47	let	let	VERB
iajs-880	54	48	b	b	NOUN
iajs-880	54	49	=	=	PUNCT
iajs-880	54	50	c[a	c[a	PROPN
iajs-880	54	51	,	,	PUNCT
iajs-880	54	52	b	b	X
iajs-880	54	53	]	]	PUNCT
iajs-880	54	54	,	,	PUNCT
iajs-880	54	55	with	with	ADP
iajs-880	54	56	norm	norm	NOUN
iajs-880	54	57	,	,	PUNCT
iajs-880	54	58	x(t)supx	x(t)supx	PROPN
iajs-880	54	59	bt	bt	PROPN
iajs-880	54	60	a	a	DET
iajs-880	54	61			PROPN
iajs-880	54	62			PROPN
iajs-880	54	63	define	define	VERB
iajs-880	54	64	a	a	DET
iajs-880	54	65	cone	cone	NOUN
iajs-880	54	66	p	p	NOUN
iajs-880	54	67	by	by	ADP
iajs-880	54	68	:	:	PUNCT
iajs-880	54	69			NUM
iajs-880	54	70			NUM
iajs-880	54	71			PROPN
iajs-880	54	72			PROPN
iajs-880	54	73			NOUN
iajs-880	54	74			NUM
iajs-880	54	75			NUM
iajs-880	54	76			ADP
iajs-880	54	77			NOUN
iajs-880	54	78			VERB
iajs-880	54	79			PROPN
iajs-880	54	80			PUNCT
iajs-880	54	81	xmx(t)min	xmx(t)min	PROPN
iajs-880	54	82	,	,	PUNCT
iajs-880	54	83	b][a	b][a	ADJ
iajs-880	54	84	,	,	PUNCT
iajs-880	54	85	on	on	ADP
iajs-880	54	86	0	0	NUM
iajs-880	54	87	x(t	x(t	PROPN
iajs-880	54	88	):	):	PUNCT
iajs-880	54	89	bxp	bxp	NOUN
iajs-880	54	90	4	4	NUM
iajs-880	54	91	12b	12b	NOUN
iajs-880	54	92	t	t	PROPN
iajs-880	54	93	4	4	NUM
iajs-880	54	94	12a	12a	NOUN
iajs-880	55	1			PROPN
iajs-880	56	1			PROPN
iajs-880	57	1			PROPN
iajs-880	57	2			PROPN
iajs-880	57	3			NUM
iajs-880	57	4			ADV
iajs-880	57	5			ADV
iajs-880	58	1			PROPN
iajs-880	59	1			PROPN
iajs-880	60	1	β)4(α	β)4(α	NUM
iajs-880	60	2	4βα	4βα	NOUN
iajs-880	60	3	,	,	PUNCT
iajs-880	60	4	4	4	NUM
iajs-880	60	5	1	1	NUM
iajs-880	60	6	minm	minm	NOUN
iajs-880	60	7	where	where	SCONJ
iajs-880	60	8	also	also	ADV
iajs-880	60	9	,	,	PUNCT
iajs-880	60	10	let	let	VERB
iajs-880	60	11	the	the	DET
iajs-880	60	12	number	number	NOUN
iajs-880	60	13	h[a	h[a	PROPN
iajs-880	60	14	,	,	PUNCT
iajs-880	60	15	b	b	AUX
iajs-880	60	16	]	]	PUNCT
iajs-880	60	17	be	be	AUX
iajs-880	60	18	defined	define	VERB
iajs-880	60	19	by	by	ADP
iajs-880	60	20	...	...	PUNCT
iajs-880	60	21	(	(	PUNCT
iajs-880	60	22	3.1	3.1	NUM
iajs-880	60	23	)	)	PUNCT
iajs-880	60	24	..........	..........	PUNCT
iajs-880	61	1	ds	ds	PRON
iajs-880	61	2	g(s	g(s	NOUN
iajs-880	61	3	)	)	PUNCT
iajs-880	61	4	s)g(t	s)g(t	PROPN
iajs-880	61	5	,	,	PUNCT
iajs-880	61	6	maxds	maxds	NOUN
iajs-880	61	7	g(s	g(s	PROPN
iajs-880	61	8	)	)	PUNCT
iajs-880	61	9	s)g(h	s)g(h	NUM
iajs-880	61	10	,	,	PUNCT
iajs-880	61	11	4	4	NUM
iajs-880	61	12	12b	12b	NOUN
iajs-880	61	13	4	4	NUM
iajs-880	61	14	12a	12a	NOUN
iajs-880	61	15	4	4	NUM
iajs-880	61	16	12b	12b	NOUN
iajs-880	61	17	4	4	NUM
iajs-880	61	18	12a	12a	NOUN
iajs-880	61	19			X
iajs-880	61	20			PRON
iajs-880	61	21			PROPN
iajs-880	61	22			VERB
iajs-880	61	23			PUNCT
iajs-880	61	24			PROPN
iajs-880	61	25	theorem	theorem	ADJ
iajs-880	61	26	2	2	NUM
iajs-880	61	27	.	.	X
iajs-880	61	28	assume	assume	VERB
iajs-880	61	29	that	that	SCONJ
iajs-880	61	30	conditions	condition	NOUN
iajs-880	61	31	(	(	PUNCT
iajs-880	61	32	a),(b),(c	a),(b),(c	NOUN
iajs-880	61	33	)	)	PUNCT
iajs-880	61	34	and	and	CCONJ
iajs-880	61	35	(	(	PUNCT
iajs-880	61	36	d	d	X
iajs-880	61	37	)	)	PUNCT
iajs-880	61	38	are	be	AUX
iajs-880	61	39	satisfied	satisfied	ADJ
iajs-880	61	40	.then	.then	ADV
iajs-880	61	41	,	,	PUNCT
iajs-880	61	42	for	for	ADP
iajs-880	61	43	each	each	DET
iajs-880	61	44			ADJ
iajs-880	61	45	satisfying	satisfying	NOUN
iajs-880	61	46	...	...	PUNCT
iajs-880	61	47	(	(	PUNCT
iajs-880	61	48	3.2	3.2	NUM
iajs-880	61	49	)	)	PUNCT
iajs-880	61	50	……	……	NOUN
iajs-880	61	51	.	.	PUNCT
iajs-880	62	1			PROPN
iajs-880	62	2			NUM
iajs-880	62	3			ADV
iajs-880	62	4			PUNCT
iajs-880	62	5			VERB
iajs-880	62	6	b	b	PROPN
iajs-880	62	7	a	a	DET
iajs-880	62	8	0	0	NUM
iajs-880	62	9	4	4	NUM
iajs-880	62	10	1)(2b	1)(2b	NUM
iajs-880	62	11	4	4	NUM
iajs-880	62	12	1)(2a	1)(2a	NUM
iajs-880	62	13	ds)f	ds)f	PROPN
iajs-880	62	14	g(s	g(s	PROPN
iajs-880	62	15	)	)	PUNCT
iajs-880	62	16	s)g(s	s)g(s	NOUN
iajs-880	62	17	,	,	PUNCT
iajs-880	62	18	(	(	PUNCT
iajs-880	62	19	1	1	NUM
iajs-880	62	20	λ	λ	PROPN
iajs-880	62	21	ds)f	ds)f	PROPN
iajs-880	62	22	g(s	g(s	PROPN
iajs-880	62	23	)	)	PUNCT
iajs-880	63	1	s)g(h,(m	s)g(h,(m	VERB
iajs-880	63	2	4	4	NUM
iajs-880	63	3	there	there	ADV
iajs-880	63	4	exists	exist	VERB
iajs-880	63	5	at	at	ADP
iajs-880	63	6	least	least	ADV
iajs-880	63	7	one	one	NUM
iajs-880	63	8	solution	solution	NOUN
iajs-880	63	9	of	of	ADP
iajs-880	63	10	(	(	PUNCT
iajs-880	63	11	1.1	1.1	NUM
iajs-880	63	12	)	)	PUNCT
iajs-880	63	13	in	in	ADP
iajs-880	63	14	p	p	NOUN
iajs-880	63	15	.	.	PUNCT
iajs-880	64	1	proof	proof	NOUN
iajs-880	64	2	.	.	PUNCT
iajs-880	65	1	let	let	VERB
iajs-880	65	2			ADJ
iajs-880	65	3	be	be	AUX
iajs-880	65	4	given	give	VERB
iajs-880	65	5	as	as	ADP
iajs-880	65	6	in	in	ADP
iajs-880	65	7	(	(	PUNCT
iajs-880	65	8	3.2	3.2	NUM
iajs-880	65	9	)	)	PUNCT
iajs-880	65	10	.	.	PUNCT
iajs-880	66	1	now	now	ADV
iajs-880	66	2	,	,	PUNCT
iajs-880	66	3	let	let	VERB
iajs-880	66	4			PROPN
iajs-880	66	5	>	>	X
iajs-880	66	6	0	0	PUNCT
iajs-880	66	7	be	be	AUX
iajs-880	66	8	chosen	choose	VERB
iajs-880	66	9	such	such	ADJ
iajs-880	66	10	that	that	SCONJ
iajs-880	66	11	.(3.3	.(3.3	NUM
iajs-880	66	12	)	)	PUNCT
iajs-880	66	13	..........	..........	PUNCT
iajs-880	67	1	ε)ds)(f	ε)ds)(f	NUM
iajs-880	67	2	g(s	g(s	PROPN
iajs-880	67	3	)	)	PUNCT
iajs-880	67	4	s)g(s	s)g(s	NOUN
iajs-880	67	5	,	,	PUNCT
iajs-880	67	6	(	(	PUNCT
iajs-880	67	7	1	1	NUM
iajs-880	67	8	λ	λ	PROPN
iajs-880	67	9	ε)ds)(f	ε)ds)(f	PROPN
iajs-880	67	10	g(s	g(s	PROPN
iajs-880	67	11	)	)	PUNCT
iajs-880	67	12	s)g(h,(m	s)g(h,(m	VERB
iajs-880	67	13	4	4	NUM
iajs-880	67	14	b	b	NOUN
iajs-880	67	15	a	a	DET
iajs-880	67	16	0	0	NUM
iajs-880	67	17	4	4	NUM
iajs-880	67	18	1)(2b	1)(2b	NUM
iajs-880	67	19	4	4	NUM
iajs-880	67	20	1)(2a	1)(2a	NUM
iajs-880	67	21			ADJ
iajs-880	67	22			X
iajs-880	67	23			PUNCT
iajs-880	67	24			PROPN
iajs-880	67	25			CCONJ
iajs-880	67	26			ADV
iajs-880	67	27			VERB
iajs-880	67	28	define	define	VERB
iajs-880	67	29	an	an	DET
iajs-880	67	30	integral	integral	ADJ
iajs-880	67	31	operator	operator	NOUN
iajs-880	67	32	t	t	NOUN
iajs-880	67	33	:	:	PUNCT
iajs-880	67	34	p	p	X
iajs-880	67	35			X
iajs-880	67	36	b	b	NOUN
iajs-880	67	37	by	by	ADP
iajs-880	67	38	ty(t	ty(t	NUM
iajs-880	67	39	)	)	PUNCT
iajs-880	67	40	=	=	NOUN
iajs-880	67	41			X
iajs-880	67	42	ds	ds	ADJ
iajs-880	67	43	f(y(s	f(y(s	NOUN
iajs-880	67	44	)	)	PUNCT
iajs-880	67	45	)	)	PUNCT
iajs-880	67	46	g(s	g(s	PROPN
iajs-880	67	47	)	)	PUNCT
iajs-880	67	48	s	s	PART
iajs-880	67	49	)	)	PUNCT
iajs-880	67	50	,	,	PUNCT
iajs-880	67	51	(	(	PUNCT
iajs-880	67	52	t	t	PROPN
iajs-880	67	53	g	g	PROPN
iajs-880	67	54	b	b	PROPN
iajs-880	67	55	a	a	PRON
iajs-880	67	56			X
iajs-880	67	57	,	,	PUNCT
iajs-880	67	58	y	y	PROPN
iajs-880	67	59			NOUN
iajs-880	67	60	p	p	X
iajs-880	67	61	…	…	PUNCT
iajs-880	67	62	…	…	PUNCT
iajs-880	67	63	…	…	PUNCT
iajs-880	67	64	(	(	PUNCT
iajs-880	67	65	3.4	3.4	NUM
iajs-880	67	66	)	)	PUNCT
iajs-880	67	67	we	we	PRON
iajs-880	67	68	seek	seek	VERB
iajs-880	67	69	a	a	DET
iajs-880	67	70	fixed	fix	VERB
iajs-880	67	71	point	point	NOUN
iajs-880	67	72	of	of	ADP
iajs-880	67	73	t	t	PROPN
iajs-880	67	74	in	in	ADP
iajs-880	67	75	the	the	DET
iajs-880	67	76	cone	cone	NOUN
iajs-880	67	77	p.	p.	NOUN
iajs-880	67	78	from	from	ADP
iajs-880	67	79	(	(	PUNCT
iajs-880	67	80	2.2	2.2	NUM
iajs-880	67	81	)	)	PUNCT
iajs-880	67	82	,	,	PUNCT
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iajs-880	67	84	note	note	VERB
iajs-880	67	85	that	that	SCONJ
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iajs-880	67	88	y	y	PROPN
iajs-880	67	89			PROPN
iajs-880	67	90	p	p	PROPN
iajs-880	67	91	,	,	PUNCT
iajs-880	67	92	ty(t	ty(t	NUM
iajs-880	67	93	)	)	PUNCT
iajs-880	67	94			NUM
iajs-880	67	95	0	0	NUM
iajs-880	67	96	on	on	ADP
iajs-880	67	97	[	[	X
iajs-880	67	98	a	a	DET
iajs-880	67	99	,	,	PUNCT
iajs-880	67	100	b	b	NOUN
iajs-880	67	101	]	]	PUNCT
iajs-880	67	102	.	.	PUNCT
iajs-880	68	1	also	also	ADV
iajs-880	68	2	,	,	PUNCT
iajs-880	68	3	for	for	ADP
iajs-880	68	4	y	y	PROPN
iajs-880	68	5			PROPN
iajs-880	68	6	p	p	X
iajs-880	68	7	,	,	PUNCT
iajs-880	68	8	we	we	PRON
iajs-880	68	9	have	have	VERB
iajs-880	68	10	from	from	ADP
iajs-880	68	11	(	(	PUNCT
iajs-880	68	12	2.3	2.3	NUM
iajs-880	68	13	)	)	PUNCT
iajs-880	68	14	that	that	PRON
iajs-880	68	15	ty(t	ty(t	PUNCT
iajs-880	68	16	)	)	PUNCT
iajs-880	69	1	=	=	PUNCT
iajs-880	69	2			X
iajs-880	69	3	ds	ds	X
iajs-880	69	4	f(y(s	f(y(s	NOUN
iajs-880	69	5	)	)	PUNCT
iajs-880	69	6	)	)	PUNCT
iajs-880	69	7	g(s	g(s	PROPN
iajs-880	69	8	)	)	PUNCT
iajs-880	69	9	s	s	PART
iajs-880	69	10	)	)	PUNCT
iajs-880	69	11	,	,	PUNCT
iajs-880	69	12	(	(	PUNCT
iajs-880	70	1	t	t	PROPN
iajs-880	70	2	g	g	PROPN
iajs-880	70	3	b	b	PROPN
iajs-880	70	4	a	a	DET
iajs-880	70	5			X
iajs-880	70	6	ibn	ibn	PROPN
iajs-880	70	7	alhaitham	alhaitham	NOUN
iajs-880	70	8	j.	j.	PROPN
iajs-880	71	1	fo	fo	ADP
iajs-880	71	2	r	r	NOUN
iajs-880	71	3	pure	pure	ADJ
iajs-880	71	4	&	&	CCONJ
iajs-880	71	5	appl	appl	PROPN
iajs-880	71	6	.	.	PUNCT
iajs-880	72	1	sc	sc	PROPN
iajs-880	72	2	i.	i.	PROPN
iajs-880	72	3	vo	vo	PROPN
iajs-880	73	1	l.24	l.24	PROPN
iajs-880	73	2	(	(	PUNCT
iajs-880	73	3	1	1	NUM
iajs-880	73	4	)	)	PUNCT
iajs-880	73	5	2011	2011	NUM
iajs-880	73	6	ty	ty	NOUN
iajs-880	73	7			VERB
iajs-880	73	8			NOUN
iajs-880	73	9			X
iajs-880	73	10	ds	ds	X
iajs-880	73	11	f(y(s	f(y(s	NOUN
iajs-880	73	12	)	)	PUNCT
iajs-880	73	13	)	)	PUNCT
iajs-880	73	14	g(s	g(s	PROPN
iajs-880	73	15	)	)	PUNCT
iajs-880	73	16	s	s	PART
iajs-880	73	17	)	)	PUNCT
iajs-880	73	18	,	,	PUNCT
iajs-880	73	19	(	(	PUNCT
iajs-880	73	20	sg	sg	PROPN
iajs-880	73	21	b	b	PROPN
iajs-880	73	22	a	a	PRON
iajs-880	73	23			X
iajs-880	73	24	…	…	PUNCT
iajs-880	73	25	…	…	PUNCT
iajs-880	73	26	…	…	PUNCT
iajs-880	73	27	(	(	PUNCT
iajs-880	73	28	3.5	3.5	NUM
iajs-880	73	29	)	)	PUNCT
iajs-880	73	30	now	now	ADV
iajs-880	73	31	,	,	PUNCT
iajs-880	73	32	if	if	SCONJ
iajs-880	73	33	y	y	PROPN
iajs-880	73	34			PROPN
iajs-880	73	35	p	p	X
iajs-880	73	36	,	,	PUNCT
iajs-880	73	37	we	we	PRON
iajs-880	73	38	have	have	AUX
iajs-880	73	39	by	by	ADP
iajs-880	73	40	(	(	PUNCT
iajs-880	73	41	2.4	2.4	NUM
iajs-880	73	42	)	)	PUNCT
iajs-880	73	43	and	and	CCONJ
iajs-880	73	44	(	(	PUNCT
iajs-880	73	45	3.5	3.5	NUM
iajs-880	73	46	)	)	PUNCT
iajs-880	73	47	,	,	PUNCT
iajs-880	73	48	tym	tym	VERB
iajs-880	73	49	ds	ds	ADJ
iajs-880	73	50	f(y(s	f(y(s	PROPN
iajs-880	73	51	)	)	PUNCT
iajs-880	73	52	)	)	PUNCT
iajs-880	73	53	g(s	g(s	PROPN
iajs-880	73	54	)	)	PUNCT
iajs-880	73	55	s	s	PART
iajs-880	73	56	)	)	PUNCT
iajs-880	73	57	,	,	PUNCT
iajs-880	73	58	(	(	PUNCT
iajs-880	73	59	sgλ	sgλ	NOUN
iajs-880	73	60	m	m	VERB
iajs-880	73	61	ds	ds	ADJ
iajs-880	73	62	f(y(s	f(y(s	NOUN
iajs-880	73	63	)	)	PUNCT
iajs-880	73	64	)	)	PUNCT
iajs-880	73	65	g(s	g(s	PROPN
iajs-880	73	66	)	)	PUNCT
iajs-880	73	67	s	s	PART
iajs-880	73	68	)	)	PUNCT
iajs-880	73	69	,	,	PUNCT
iajs-880	73	70	(	(	PUNCT
iajs-880	73	71	t	t	PROPN
iajs-880	73	72	gλminty(t)min	gλminty(t)min	PROPN
iajs-880	73	73	b	b	PROPN
iajs-880	73	74	a	a	DET
iajs-880	73	75	b	b	NOUN
iajs-880	73	76	a4	a4	NOUN
iajs-880	73	77	12b	12b	NOUN
iajs-880	73	78	t	t	PROPN
iajs-880	73	79	4	4	NUM
iajs-880	73	80	12a	12a	NOUN
iajs-880	73	81	4	4	NUM
iajs-880	73	82	12b	12b	NOUN
iajs-880	73	83	t	t	PROPN
iajs-880	73	84	4	4	NUM
iajs-880	73	85	12a	12a	NOUN
iajs-880	73	86			NUM
iajs-880	73	87			NUM
iajs-880	73	88			NOUN
iajs-880	74	1			PUNCT
iajs-880	74	2			NOUN
iajs-880	74	3			PROPN
iajs-880	74	4			PROPN
iajs-880	74	5			PROPN
iajs-880	74	6			ADV
iajs-880	74	7			PROPN
iajs-880	75	1	p	p	X
iajs-880	75	2	.	.	PUNCT
iajs-880	76	1	in	in	ADP
iajs-880	76	2	addition	addition	NOUN
iajs-880	76	3	,	,	PUNCT
iajs-880	76	4	standard	standard	ADJ
iajs-880	76	5	arguments	argument	NOUN
iajs-880	76	6	show	show	VERB
iajs-880	76	7	that	that	SCONJ
iajs-880	76	8	t	t	PROPN
iajs-880	76	9	is	be	AUX
iajs-880	76	10	as	as	ADP
iajs-880	76	11	a	a	DET
iajs-880	76	12	consequence	consequence	NOUN
iajs-880	76	13	,	,	PUNCT
iajs-880	76	14	t	t	X
iajs-880	76	15	:	:	PUNCT
iajs-880	76	16	p	p	X
iajs-880	76	17	completely	completely	ADV
iajs-880	76	18	continuous	continuous	ADJ
iajs-880	76	19	.	.	PUNCT
iajs-880	77	1	now	now	ADV
iajs-880	77	2	,	,	PUNCT
iajs-880	77	3	turning	turn	VERB
iajs-880	77	4	to	to	ADP
iajs-880	77	5	f0	f0	PROPN
iajs-880	77	6	,	,	PUNCT
iajs-880	77	7	there	there	PRON
iajs-880	77	8	exist	exist	VERB
iajs-880	77	9	an	an	DET
iajs-880	77	10	k	k	PROPN
iajs-880	77	11	1	1	NUM
iajs-880	77	12	>	>	SYM
iajs-880	77	13	0	0	NUM
iajs-880	77	14	such	such	ADJ
iajs-880	77	15	that	that	SCONJ
iajs-880	77	16	f(x	f(x	PROPN
iajs-880	77	17	)	)	PUNCT
iajs-880	77	18			NOUN
iajs-880	77	19	(	(	PUNCT
iajs-880	77	20	f0	f0	PROPN
iajs-880	77	21	+	+	PROPN
iajs-880	77	22			PROPN
iajs-880	77	23	)	)	PUNCT
iajs-880	77	24	x	x	PUNCT
iajs-880	77	25	,	,	PUNCT
iajs-880	77	26	for	for	ADP
iajs-880	77	27	0	0	NUM
iajs-880	77	28	<	<	X
iajs-880	77	29	x	x	SYM
iajs-880	77	30			NUM
iajs-880	77	31	k1	k1	NOUN
iajs-880	77	32	.	.	PUNCT
iajs-880	78	1	y	y	PROPN
iajs-880	78	2			PROPN
iajs-880	78	3	p	p	PRON
iajs-880	78	4	such	such	ADJ
iajs-880	78	5	that	that	DET
iajs-880	78	6			VERB
iajs-880	78	7	y	y	PROPN
iajs-880	78	8			NOUN
iajs-880	78	9	=	=	PROPN
iajs-880	78	10	k1	k1	NOUN
iajs-880	78	11	,	,	PUNCT
iajs-880	78	12	we	we	PRON
iajs-880	78	13	have	have	VERB
iajs-880	78	14	from	from	ADP
iajs-880	78	15	(	(	PUNCT
iajs-880	78	16	2.3	2.3	NUM
iajs-880	78	17	)	)	PUNCT
iajs-880	78	18	and	and	CCONJ
iajs-880	78	19	(	(	PUNCT
iajs-880	78	20	3.3	3.3	NUM
iajs-880	78	21	)	)	PUNCT
iajs-880	78	22	so	so	ADV
iajs-880	78	23	,	,	PUNCT
iajs-880	78	24	by	by	ADP
iajs-880	78	25	choosing	choose	VERB
iajs-880	78	26	y	y	PROPN
iajs-880	78	27	y	y	PROPN
iajs-880	78	28	y(s	y(s	PROPN
iajs-880	78	29	)	)	PUNCT
iajs-880	78	30	ε)(f	ε)(f	VERB
iajs-880	78	31	ds	ds	PRON
iajs-880	78	32	g(s	g(s	NOUN
iajs-880	78	33	)	)	PUNCT
iajs-880	78	34	s)g(s	s)g(s	NOUN
iajs-880	78	35	,	,	PUNCT
iajs-880	78	36	λ	λ	X
iajs-880	78	37	ds	ds	ADJ
iajs-880	78	38	y(s	y(s	PROPN
iajs-880	78	39	)	)	PUNCT
iajs-880	78	40	ε)(f	ε)(f	NOUN
iajs-880	79	1	g(s	g(	NOUN
iajs-880	79	2	)	)	PUNCT
iajs-880	79	3	s)g(s	s)g(s	NOUN
iajs-880	79	4	,	,	PUNCT
iajs-880	79	5	λ	λ	X
iajs-880	79	6	ds	ds	ADJ
iajs-880	79	7	f(y(s	f(y(s	NOUN
iajs-880	79	8	)	)	PUNCT
iajs-880	79	9	)	)	PUNCT
iajs-880	79	10	g(s	g(s	PROPN
iajs-880	79	11	)	)	PUNCT
iajs-880	79	12	s)g(s	s)g(s	NOUN
iajs-880	79	13	,	,	PUNCT
iajs-880	79	14	λty(t	λty(t	PROPN
iajs-880	79	15	)	)	PUNCT
iajs-880	79	16	b	b	NOUN
iajs-880	79	17	a	a	DET
iajs-880	79	18	0	0	NUM
iajs-880	79	19	b	b	NOUN
iajs-880	79	20	a	a	DET
iajs-880	79	21	0	0	NUM
iajs-880	79	22	b	b	NOUN
iajs-880	79	23	a	a	DET
iajs-880	79	24			NUM
iajs-880	79	25			PROPN
iajs-880	79	26			NOUN
iajs-880	79	27			NOUN
iajs-880	79	28			PUNCT
iajs-880	79	29			X
iajs-880	79	30			PUNCT
iajs-880	79	31	consequently	consequently	ADV
iajs-880	79	32	,	,	PUNCT
iajs-880	79	33	yty	yty	VERB
iajs-880	79	34			NOUN
iajs-880	79	35	.	.	PUNCT
iajs-880	80	1	so	so	ADV
iajs-880	80	2	,	,	PUNCT
iajs-880	80	3	if	if	SCONJ
iajs-880	80	4	we	we	PRON
iajs-880	80	5	set	set	VERB
iajs-880	80	6	1	1	PUNCT
iajs-880	80	7	=	=	PUNCT
iajs-880	80	8	{	{	PUNCT
iajs-880	80	9	x	x	PROPN
iajs-880	80	10			NOUN
iajs-880	80	11	b	b	VERB
iajs-880	80	12	x	x	PUNCT
iajs-880	80	13	<	<	X
iajs-880	80	14	k1	k1	PROPN
iajs-880	80	15	}	}	PUNCT
iajs-880	80	16	then	then	ADV
iajs-880	80	17	ty	ty	PROPN
iajs-880	80	18			VERB
iajs-880	80	19			NOUN
iajs-880	80	20	y	y	NOUN
iajs-880	80	21			VERB
iajs-880	80	22	,	,	PUNCT
iajs-880	80	23	for	for	ADP
iajs-880	80	24	y	y	PROPN
iajs-880	80	25	p	p	NOUN
iajs-880	80	26			VERB
iajs-880	80	27	1	1	PROPN
iajs-880	80	28	.	.	PUNCT
iajs-880	81	1	…	…	PUNCT
iajs-880	81	2	…	…	PUNCT
iajs-880	81	3	…	…	PUNCT
iajs-880	81	4	.(3.6	.(3.6	NUM
iajs-880	81	5	)	)	PUNCT
iajs-880	81	6	next	next	ADV
iajs-880	81	7	,	,	PUNCT
iajs-880	81	8	considering	consider	VERB
iajs-880	81	9	f	f	NOUN
iajs-880	81	10	,	,	PUNCT
iajs-880	81	11	there	there	PRON
iajs-880	81	12	exist	exist	VERB
iajs-880	81	13	an	an	DET
iajs-880	81	14	k2	k2	NOUN
iajs-880	81	15	>	>	X
iajs-880	81	16	0	0	NUM
iajs-880	81	17	such	such	ADJ
iajs-880	81	18	that	that	SCONJ
iajs-880	81	19	f	f	PROPN
iajs-880	81	20	(	(	PUNCT
iajs-880	81	21	x	x	NOUN
iajs-880	81	22	)	)	PUNCT
iajs-880	81	23			NUM
iajs-880	81	24	(	(	PUNCT
iajs-880	81	25	f	f	PROPN
iajs-880	81	26			PROPN
iajs-880	81	27	)	)	PUNCT
iajs-880	81	28	x	x	PUNCT
iajs-880	81	29	,	,	PUNCT
iajs-880	81	30	for	for	ADP
iajs-880	81	31	all	all	DET
iajs-880	81	32	x	x	SYM
iajs-880	81	33	>	>	X
iajs-880	81	34	k2	k2	PROPN
iajs-880	81	35	.	.	PUNCT
iajs-880	82	1	let	let	VERB
iajs-880	82	2	k3	k3	PROPN
iajs-880	82	3	=	=	PROPN
iajs-880	82	4	max	max	X
iajs-880	82	5	{	{	PUNCT
iajs-880	82	6	2k1	2k1	NUM
iajs-880	82	7	,	,	PUNCT
iajs-880	82	8	}	}	PUNCT
iajs-880	82	9	m	m	VERB
iajs-880	82	10	k	k	NOUN
iajs-880	82	11	2	2	NUM
iajs-880	82	12	and	and	CCONJ
iajs-880	82	13	let	let	VERB
iajs-880	82	14	2	2	ADJ
iajs-880	82	15	=	=	SYM
iajs-880	82	16	{	{	PUNCT
iajs-880	82	17	x	x	PROPN
iajs-880	82	18			NOUN
iajs-880	82	19	b	b	PROPN
iajs-880	82	20			PROPN
iajs-880	82	21	x	x	PUNCT
iajs-880	82	22	<	<	X
iajs-880	82	23	k3	k3	X
iajs-880	82	24	}	}	PUNCT
iajs-880	82	25	if	if	SCONJ
iajs-880	82	26	y	y	PROPN
iajs-880	82	27			NOUN
iajs-880	82	28	p	p	NOUN
iajs-880	82	29	with	with	ADP
iajs-880	82	30	y	y	NOUN
iajs-880	82	31			VERB
iajs-880	82	32	=	=	SYM
iajs-880	82	33	k3	k3	PROPN
iajs-880	82	34	,	,	PUNCT
iajs-880	82	35	then	then	ADV
iajs-880	82	36	23	23	NUM
iajs-880	82	37	4	4	NUM
iajs-880	82	38	12b	12b	NOUN
iajs-880	82	39	t	t	PROPN
iajs-880	82	40	4	4	NUM
iajs-880	82	41	12a	12a	NOUN
iajs-880	82	42	kmkymy(t)min	kmkymy(t)min	X
iajs-880	82	43			PROPN
iajs-880	82	44			PROPN
iajs-880	82	45			PROPN
iajs-880	82	46			ADV
iajs-880	82	47	,	,	PUNCT
iajs-880	82	48	and	and	CCONJ
iajs-880	82	49	we	we	PRON
iajs-880	82	50	have	have	VERB
iajs-880	82	51	from	from	ADP
iajs-880	82	52	(	(	PUNCT
iajs-880	82	53	3.1	3.1	NUM
iajs-880	82	54	)	)	PUNCT
iajs-880	82	55	and	and	CCONJ
iajs-880	82	56	(	(	PUNCT
iajs-880	82	57	3.3	3.3	NUM
iajs-880	82	58	)	)	PUNCT
iajs-880	82	59	that	that	PRON
iajs-880	82	60	y	y	PROPN
iajs-880	82	61	y	y	PROPN
iajs-880	82	62	ε)(f	ε)(f	VERB
iajs-880	82	63	ds	ds	PRON
iajs-880	82	64	g(s	g(s	NOUN
iajs-880	82	65	)	)	PUNCT
iajs-880	82	66	s)g(h	s)g(h	X
iajs-880	82	67	,	,	PUNCT
iajs-880	82	68	m	m	VERB
iajs-880	82	69	λ	λ	X
iajs-880	82	70	ds	ds	ADJ
iajs-880	82	71	y(s	y(s	PROPN
iajs-880	82	72	)	)	PUNCT
iajs-880	82	73	ε)(f	ε)(f	NOUN
iajs-880	82	74	g(s	g(	NOUN
iajs-880	82	75	)	)	PUNCT
iajs-880	82	76	s)g(h	s)g(h	X
iajs-880	82	77	,	,	PUNCT
iajs-880	82	78	λ	λ	X
iajs-880	82	79	ds	ds	ADJ
iajs-880	82	80	f(y(s	f(y(s	NOUN
iajs-880	82	81	)	)	PUNCT
iajs-880	82	82	)	)	PUNCT
iajs-880	82	83	g(s	g(s	PROPN
iajs-880	82	84	)	)	PUNCT
iajs-880	82	85	s)g(h	s)g(h	X
iajs-880	82	86	,	,	PUNCT
iajs-880	82	87	λ	λ	X
iajs-880	82	88	ds	ds	ADJ
iajs-880	82	89	f(y(s	f(y(s	NOUN
iajs-880	82	90	)	)	PUNCT
iajs-880	82	91	)	)	PUNCT
iajs-880	82	92	g(s	g(s	PROPN
iajs-880	82	93	)	)	PUNCT
iajs-880	82	94	s)g(h	s)g(h	X
iajs-880	82	95	,	,	PUNCT
iajs-880	82	96	λty(h	λty(h	PROPN
iajs-880	82	97	)	)	PUNCT
iajs-880	82	98	4	4	NUM
iajs-880	82	99	1)(2b	1)(2b	NOUN
iajs-880	82	100	4	4	NUM
iajs-880	82	101	1)(2a	1)(2a	NUM
iajs-880	82	102	4	4	NUM
iajs-880	82	103	1)(2b	1)(2b	NUM
iajs-880	82	104	4	4	NUM
iajs-880	82	105	1)(2a	1)(2a	NUM
iajs-880	82	106	4	4	NUM
iajs-880	82	107	1)(2b	1)(2b	NUM
iajs-880	82	108	4	4	NUM
iajs-880	82	109	1)(2a	1)(2a	NUM
iajs-880	82	110	b	b	NOUN
iajs-880	82	111	a	a	DET
iajs-880	82	112			NUM
iajs-880	82	113			PROPN
iajs-880	82	114			PROPN
iajs-880	82	115			PROPN
iajs-880	82	116			NUM
iajs-880	82	117			ADP
iajs-880	82	118			X
iajs-880	82	119			PROPN
iajs-880	82	120			PUNCT
iajs-880	82	121			PROPN
iajs-880	82	122			PROPN
iajs-880	82	123			PROPN
iajs-880	82	124			ADV
iajs-880	82	125			PUNCT
iajs-880	82	126			PROPN
iajs-880	82	127			PUNCT
iajs-880	82	128			PUNCT
iajs-880	82	129	ibn	ibn	PROPN
iajs-880	82	130	alhaitham	alhaitham	NOUN
iajs-880	83	1	j.	j.	PROPN
iajs-880	84	1	fo	fo	ADP
iajs-880	84	2	r	r	NOUN
iajs-880	84	3	pure	pure	ADJ
iajs-880	84	4	&	&	CCONJ
iajs-880	84	5	appl	appl	PROPN
iajs-880	84	6	.	.	PUNCT
iajs-880	85	1	sc	sc	PROPN
iajs-880	85	2	i.	i.	PROPN
iajs-880	85	3	vo	vo	PROPN
iajs-880	85	4	l.24	l.24	PROPN
iajs-880	85	5	(	(	PUNCT
iajs-880	85	6	1	1	NUM
iajs-880	85	7	)	)	PUNCT
iajs-880	85	8	2011	2011	NUM
iajs-880	85	9	thus	thus	ADV
iajs-880	85	10	,	,	PUNCT
iajs-880	85	11	yty	yty	NOUN
iajs-880	85	12			NUM
iajs-880	85	13	.	.	PUNCT
iajs-880	86	1	hence	hence	ADV
iajs-880	86	2	,	,	PUNCT
iajs-880	86	3	ty	ty	PROPN
iajs-880	86	4			VERB
iajs-880	86	5			PROPN
iajs-880	86	6	y	y	NOUN
iajs-880	86	7			VERB
iajs-880	86	8	,	,	PUNCT
iajs-880	86	9	for	for	ADP
iajs-880	86	10	y	y	PROPN
iajs-880	86	11			PROPN
iajs-880	86	12	p	p	NOUN
iajs-880	86	13			PROPN
iajs-880	86	14	2	2	NUM
iajs-880	86	15	…	…	PUNCT
iajs-880	86	16	…	…	PUNCT
iajs-880	86	17	…	…	SYM
iajs-880	86	18	.(3.7	.(3.7	NOUN
iajs-880	86	19	)	)	PUNCT
iajs-880	86	20	applying	apply	VERB
iajs-880	86	21	(	(	PUNCT
iajs-880	86	22	1	1	NUM
iajs-880	86	23	)	)	PUNCT
iajs-880	86	24	of	of	ADP
iajs-880	86	25	theorem	theorem	NOUN
iajs-880	86	26	1	1	NUM
iajs-880	86	27	to	to	ADP
iajs-880	86	28	(	(	PUNCT
iajs-880	86	29	3.6	3.6	NUM
iajs-880	86	30	)	)	PUNCT
iajs-880	86	31	and	and	CCONJ
iajs-880	86	32	(	(	PUNCT
iajs-880	86	33	3.7	3.7	NUM
iajs-880	86	34	)	)	PUNCT
iajs-880	86	35	yields	yield	NOUN
iajs-880	86	36	that	that	PRON
iajs-880	86	37	t	t	PROPN
iajs-880	86	38	has	have	VERB
iajs-880	86	39	a	a	DET
iajs-880	86	40	fixed	fix	VERB
iajs-880	86	41	point	point	NOUN
iajs-880	86	42	y(t	y(t	NUM
iajs-880	86	43	)	)	PUNCT
iajs-880	86	44			NOUN
iajs-880	86	45	)	)	PUNCT
iajs-880	86	46	\(p	\(p	PROPN
iajs-880	86	47	12	12	NUM
iajs-880	86	48			NOUN
iajs-880	86	49	.	.	PUNCT
iajs-880	87	1	as	as	ADP
iajs-880	87	2	such	such	ADJ
iajs-880	87	3	,	,	PUNCT
iajs-880	87	4	y(t	y(t	PROPN
iajs-880	87	5	)	)	PUNCT
iajs-880	87	6	is	be	AUX
iajs-880	87	7	a	a	DET
iajs-880	87	8	desired	desire	VERB
iajs-880	87	9	solution	solution	NOUN
iajs-880	87	10	of	of	ADP
iajs-880	87	11	1.1	1.1	NUM
iajs-880	87	12	for	for	ADP
iajs-880	87	13	the	the	DET
iajs-880	87	14	given	give	VERB
iajs-880	87	15			NOUN
iajs-880	87	16	.	.	PUNCT
iajs-880	88	1	further	far	ADV
iajs-880	88	2	,	,	PUNCT
iajs-880	88	3	since	since	SCONJ
iajs-880	88	4	g	g	PROPN
iajs-880	88	5	(	(	PUNCT
iajs-880	88	6	t	t	PROPN
iajs-880	88	7	,	,	PUNCT
iajs-880	88	8	s	s	PROPN
iajs-880	88	9	)	)	PUNCT
iajs-880	88	10	>	>	X
iajs-880	88	11	0	0	PUNCT
iajs-880	88	12	,	,	PUNCT
iajs-880	88	13	it	it	PRON
iajs-880	88	14	follows	follow	VERB
iajs-880	88	15	that	that	SCONJ
iajs-880	88	16	y	y	PROPN
iajs-880	88	17	(	(	PUNCT
iajs-880	88	18	t	t	PROPN
iajs-880	88	19	)	)	PUNCT
iajs-880	88	20	>	>	X
iajs-880	88	21	0	0	PUNCT
iajs-880	88	22	for	for	ADP
iajs-880	88	23	a	a	DET
iajs-880	88	24	<	<	X
iajs-880	88	25	t	t	X
iajs-880	88	26	<	<	X
iajs-880	88	27	b	b	PROPN
iajs-880	88	28	.	.	PUNCT
iajs-880	89	1	this	this	PRON
iajs-880	89	2	completes	complete	VERB
iajs-880	89	3	the	the	DET
iajs-880	89	4	proof	proof	NOUN
iajs-880	89	5	of	of	ADP
iajs-880	89	6	the	the	DET
iajs-880	89	7	theorem	theorem	NOUN
iajs-880	89	8	.	.	PUNCT
iajs-880	90	1	theorem	theorem	NOUN
iajs-880	90	2	3	3	NUM
iajs-880	90	3	.	.	PUNCT
iajs-880	91	1	assume	assume	VERB
iajs-880	91	2	that	that	SCONJ
iajs-880	91	3	condition	condition	NOUN
iajs-880	91	4	(	(	PUNCT
iajs-880	91	5	a),(b),(c	a),(b),(c	NOUN
iajs-880	91	6	)	)	PUNCT
iajs-880	91	7	,	,	PUNCT
iajs-880	91	8	(	(	PUNCT
iajs-880	91	9	d	d	X
iajs-880	91	10	)	)	PUNCT
iajs-880	91	11	and	and	CCONJ
iajs-880	91	12	(	(	PUNCT
iajs-880	91	13	e	e	NOUN
iajs-880	91	14	)	)	PUNCT
iajs-880	91	15	are	be	AUX
iajs-880	91	16	satisfied	satisfied	ADJ
iajs-880	91	17	.	.	PUNCT
iajs-880	92	1	then	then	ADV
iajs-880	92	2	,	,	PUNCT
iajs-880	92	3	for	for	ADP
iajs-880	92	4	each	each	DET
iajs-880	92	5			ADJ
iajs-880	92	6	satisfying	satisfying	ADJ
iajs-880	92	7			ADJ
iajs-880	92	8			PROPN
iajs-880	92	9			PUNCT
iajs-880	92	10			PUNCT
iajs-880	92	11			PUNCT
iajs-880	92	12	b	b	NOUN
iajs-880	92	13	a	a	DET
iajs-880	92	14	4	4	NUM
iajs-880	92	15	1)(2b	1)(2b	NOUN
iajs-880	92	16	4	4	NUM
iajs-880	92	17	1)(2a	1)(2a	NUM
iajs-880	92	18	0	0	NUM
iajs-880	92	19	ds)f	ds)f	PROPN
iajs-880	92	20	g(s	g(s	PROPN
iajs-880	92	21	)	)	PUNCT
iajs-880	92	22	s)g(s	s)g(s	NOUN
iajs-880	92	23	,	,	PUNCT
iajs-880	92	24	(	(	PUNCT
iajs-880	92	25	1	1	NUM
iajs-880	92	26	λ	λ	PROPN
iajs-880	92	27	ds)f	ds)f	PROPN
iajs-880	92	28	g(s	g(s	PROPN
iajs-880	92	29	)	)	PUNCT
iajs-880	92	30	s)g(h,(m	s)g(h,(m	PROPN
iajs-880	92	31	4	4	NUM
iajs-880	92	32	…	…	SYM
iajs-880	92	33	…	…	PUNCT
iajs-880	92	34	…	…	PUNCT
iajs-880	92	35	.(3.8	.(3.8	NUM
iajs-880	92	36	)	)	PUNCT
iajs-880	93	1	there	there	PRON
iajs-880	93	2	exists	exist	VERB
iajs-880	93	3	at	at	ADP
iajs-880	93	4	least	least	ADV
iajs-880	93	5	one	one	NUM
iajs-880	93	6	solution	solution	NOUN
iajs-880	93	7	of	of	ADP
iajs-880	93	8	1.1	1.1	NUM
iajs-880	93	9	in	in	ADP
iajs-880	93	10	p	p	NOUN
iajs-880	93	11	.	.	PUNCT
iajs-880	94	1	proof	proof	NOUN
iajs-880	94	2	.	.	PUNCT
iajs-880	95	1	let	let	VERB
iajs-880	95	2			ADJ
iajs-880	95	3	be	be	AUX
iajs-880	95	4	given	give	VERB
iajs-880	95	5	as	as	ADP
iajs-880	95	6	in	in	ADP
iajs-880	95	7	(	(	PUNCT
iajs-880	95	8	3.8	3.8	NUM
iajs-880	95	9	)	)	PUNCT
iajs-880	95	10	.	.	PUNCT
iajs-880	96	1	now	now	ADV
iajs-880	96	2	,	,	PUNCT
iajs-880	96	3	let	let	VERB
iajs-880	96	4			PROPN
iajs-880	96	5	>	>	X
iajs-880	96	6	0	0	PUNCT
iajs-880	96	7	be	be	AUX
iajs-880	96	8	chosen	choose	VERB
iajs-880	96	9	such	such	ADJ
iajs-880	96	10	that	that	DET
iajs-880	96	11	3.9	3.9	NUM
iajs-880	96	12	)	)	PUNCT
iajs-880	96	13	.........	.........	PUNCT
iajs-880	97	1	(	(	PUNCT
iajs-880	97	2	ε)ds)(f	ε)ds)(f	NUM
iajs-880	97	3	s)g(s)g(s	s)g(s)g(s	NUM
iajs-880	97	4	,	,	PUNCT
iajs-880	97	5	(	(	PUNCT
iajs-880	97	6	1	1	NUM
iajs-880	97	7	λ	λ	PROPN
iajs-880	97	8	ε)ds)(f	ε)ds)(f	PROPN
iajs-880	97	9	g(s	g(s	PROPN
iajs-880	97	10	)	)	PUNCT
iajs-880	97	11	s)g(h,(m	s)g(h,(m	VERB
iajs-880	97	12	1	1	NUM
iajs-880	97	13	b	b	NOUN
iajs-880	97	14	a	a	DET
iajs-880	97	15	4	4	NUM
iajs-880	97	16	1)(2b	1)(2b	NOUN
iajs-880	97	17	4	4	NUM
iajs-880	97	18	1)(2a	1)(2a	NUM
iajs-880	97	19	0	0	NUM
iajs-880	97	20			ADJ
iajs-880	97	21			X
iajs-880	97	22			PUNCT
iajs-880	97	23			NOUN
iajs-880	97	24			PROPN
iajs-880	97	25			PUNCT
iajs-880	97	26			PUNCT
iajs-880	97	27	let	let	VERB
iajs-880	97	28	t	t	PROPN
iajs-880	97	29	be	be	AUX
iajs-880	97	30	the	the	DET
iajs-880	97	31	cone	cone	NOUN
iajs-880	97	32	preserving	preserve	VERB
iajs-880	97	33	,	,	PUNCT
iajs-880	97	34	completely	completely	ADV
iajs-880	97	35	continuous	continuous	ADJ
iajs-880	97	36	operator	operator	NOUN
iajs-880	97	37	that	that	PRON
iajs-880	97	38	was	be	AUX
iajs-880	97	39	defined	define	VERB
iajs-880	97	40	by(3.4	by(3.4	NOUN
iajs-880	97	41	)	)	PUNCT
iajs-880	97	42	.	.	PUNCT
iajs-880	98	1	beginning	begin	VERB
iajs-880	98	2	with	with	ADP
iajs-880	98	3	f0	f0	PROPN
iajs-880	98	4	,	,	PUNCT
iajs-880	98	5	there	there	PRON
iajs-880	98	6	exists	exist	VERB
iajs-880	98	7	an	an	DET
iajs-880	98	8	k	k	PROPN
iajs-880	98	9	4	4	NUM
iajs-880	98	10	>	>	SYM
iajs-880	98	11	0	0	NUM
iajs-880	98	12	such	such	ADJ
iajs-880	98	13	that	that	SCONJ
iajs-880	98	14	f(x	f(x	PROPN
iajs-880	98	15	)	)	PUNCT
iajs-880	98	16			PROPN
iajs-880	98	17	(	(	PUNCT
iajs-880	98	18	f0	f0	PROPN
iajs-880	98	19			PROPN
iajs-880	98	20	)	)	PUNCT
iajs-880	98	21	x	x	PUNCT
iajs-880	98	22	,	,	PUNCT
iajs-880	98	23	for	for	ADP
iajs-880	98	24	0	0	NUM
iajs-880	98	25	<	<	X
iajs-880	98	26	x	x	SYM
iajs-880	98	27			NUM
iajs-880	98	28	k4	k4	NOUN
iajs-880	98	29	.	.	PUNCT
iajs-880	99	1	y	y	PROPN
iajs-880	99	2			NOUN
iajs-880	99	3	p	p	PRON
iajs-880	99	4	such	such	ADJ
iajs-880	99	5	that	that	DET
iajs-880	99	6			VERB
iajs-880	99	7	y	y	PROPN
iajs-880	99	8			NOUN
iajs-880	99	9	=	=	PROPN
iajs-880	99	10	k4	k4	NOUN
iajs-880	99	11	,	,	PUNCT
iajs-880	99	12	we	we	PRON
iajs-880	99	13	have	have	VERB
iajs-880	99	14	from	from	ADP
iajs-880	99	15	(	(	PUNCT
iajs-880	99	16	3.1	3.1	NUM
iajs-880	99	17	)	)	PUNCT
iajs-880	99	18	and	and	CCONJ
iajs-880	99	19	(	(	PUNCT
iajs-880	99	20	3.9	3.9	NUM
iajs-880	99	21	)	)	PUNCT
iajs-880	99	22	so	so	ADV
iajs-880	99	23	,	,	PUNCT
iajs-880	99	24	for	for	SCONJ
iajs-880	99	25	so	so	ADV
iajs-880	99	26	y	y	PROPN
iajs-880	99	27	y	y	PROPN
iajs-880	99	28	ε)(f	ε)(f	VERB
iajs-880	99	29	ds	ds	PRON
iajs-880	99	30	g(s	g(s	NOUN
iajs-880	99	31	)	)	PUNCT
iajs-880	99	32	s),g(h	s),g(h	PUNCT
iajs-880	100	1	λ	λ	INTJ
iajs-880	100	2	m	m	VERB
iajs-880	100	3	ds	ds	PROPN
iajs-880	100	4	y(s	y(s	PROPN
iajs-880	100	5	)	)	PUNCT
iajs-880	100	6	ε)(f	ε)(f	NOUN
iajs-880	100	7	g(s	g(	NOUN
iajs-880	100	8	)	)	PUNCT
iajs-880	100	9	s),g(h	s),g(h	PUNCT
iajs-880	101	1	λ	λ	X
iajs-880	101	2	ds	ds	ADJ
iajs-880	101	3	f(y(s	f(y(s	PROPN
iajs-880	101	4	)	)	PUNCT
iajs-880	101	5	)	)	PUNCT
iajs-880	101	6	g(s	g(s	PROPN
iajs-880	101	7	)	)	PUNCT
iajs-880	101	8	s),g(h	s),g(h	PUNCT
iajs-880	102	1	λ	λ	X
iajs-880	102	2	ds	ds	ADJ
iajs-880	102	3	f(y(s	f(y(s	PROPN
iajs-880	102	4	)	)	PUNCT
iajs-880	102	5	)	)	PUNCT
iajs-880	102	6	g(s	g(s	PROPN
iajs-880	102	7	)	)	PUNCT
iajs-880	102	8	s)g(h	s)g(h	X
iajs-880	102	9	,	,	PUNCT
iajs-880	102	10	λty(h	λty(h	PROPN
iajs-880	102	11	)	)	PUNCT
iajs-880	102	12	4	4	NUM
iajs-880	102	13	1)(2b	1)(2b	NOUN
iajs-880	102	14	4	4	NUM
iajs-880	102	15	1)(2a	1)(2a	NUM
iajs-880	102	16	0	0	NUM
iajs-880	102	17	4	4	NUM
iajs-880	102	18	1)(2b	1)(2b	NUM
iajs-880	102	19	4	4	NUM
iajs-880	102	20	1)(2a	1)(2a	NUM
iajs-880	102	21	0	0	NUM
iajs-880	102	22	4	4	NUM
iajs-880	102	23	1)(2b	1)(2b	NUM
iajs-880	102	24	4	4	NUM
iajs-880	102	25	1)(2a	1)(2a	NUM
iajs-880	102	26	b	b	NOUN
iajs-880	102	27	a	a	DET
iajs-880	102	28			NUM
iajs-880	102	29			PROPN
iajs-880	102	30			PROPN
iajs-880	102	31			PROPN
iajs-880	102	32			NUM
iajs-880	102	33			ADP
iajs-880	102	34			X
iajs-880	102	35			PROPN
iajs-880	102	36			PUNCT
iajs-880	103	1			PROPN
iajs-880	103	2			PROPN
iajs-880	103	3			PROPN
iajs-880	103	4			PROPN
iajs-880	103	5			PUNCT
iajs-880	103	6			VERB
iajs-880	103	7	thus	thus	ADV
iajs-880	103	8	,	,	PUNCT
iajs-880	103	9	yty	yty	ADJ
iajs-880	103	10			NUM
iajs-880	103	11	.	.	PUNCT
iajs-880	104	1	so	so	ADV
iajs-880	104	2	,	,	PUNCT
iajs-880	104	3	if	if	SCONJ
iajs-880	104	4	we	we	PRON
iajs-880	104	5	let	let	VERB
iajs-880	104	6	3	3	NOUN
iajs-880	104	7	=	=	PUNCT
iajs-880	104	8	{	{	PUNCT
iajs-880	104	9	x	x	PROPN
iajs-880	104	10			NOUN
iajs-880	104	11	b	b	VERB
iajs-880	104	12	x	x	PUNCT
iajs-880	104	13	<	<	X
iajs-880	104	14	k4	k4	PROPN
iajs-880	104	15	}	}	PUNCT
iajs-880	104	16	then	then	ADV
iajs-880	104	17	ty	ty	PROPN
iajs-880	104	18			PROPN
iajs-880	104	19			PROPN
iajs-880	104	20	y	y	NOUN
iajs-880	104	21			VERB
iajs-880	104	22	for	for	ADP
iajs-880	104	23	y	y	PROPN
iajs-880	104	24			PROPN
iajs-880	104	25	p3	p3	PROPN
iajs-880	104	26	…	…	PUNCT
iajs-880	104	27	…	…	PUNCT
iajs-880	104	28	.	.	PUNCT
iajs-880	105	1	(	(	PUNCT
iajs-880	105	2	3.10	3.10	NUM
iajs-880	105	3	)	)	PUNCT
iajs-880	105	4	it	it	PRON
iajs-880	105	5	remains	remain	VERB
iajs-880	105	6	to	to	PART
iajs-880	105	7	consider	consider	VERB
iajs-880	105	8	f	f	NOUN
iajs-880	105	9	,	,	PUNCT
iajs-880	105	10	there	there	PRON
iajs-880	105	11	exists	exist	VERB
iajs-880	105	12	an	an	DET
iajs-880	105	13	k5	k5	PROPN
iajs-880	105	14	>	>	X
iajs-880	105	15	0	0	NUM
iajs-880	106	1	such	such	ADJ
iajs-880	106	2	that	that	SCONJ
iajs-880	106	3	f	f	PROPN
iajs-880	106	4	(	(	PUNCT
iajs-880	106	5	x	x	X
iajs-880	106	6	)	)	PUNCT
iajs-880	106	7			NOUN
iajs-880	106	8	(	(	PUNCT
iajs-880	106	9	f	f	PROPN
iajs-880	106	10	+	+	SYM
iajs-880	106	11			PROPN
iajs-880	106	12	)	)	PUNCT
iajs-880	106	13	x	x	NOUN
iajs-880	106	14	,	,	PUNCT
iajs-880	106	15	for	for	ADP
iajs-880	106	16	all	all	DET
iajs-880	106	17	x	x	PUNCT
iajs-880	106	18	>	>	X
iajs-880	106	19	k5	k5	PROPN
iajs-880	106	20	.	.	PUNCT
iajs-880	107	1	there	there	PRON
iajs-880	107	2	are	be	VERB
iajs-880	107	3	the	the	DET
iajs-880	107	4	two	two	NUM
iajs-880	107	5	cases	case	NOUN
iajs-880	107	6	,	,	PUNCT
iajs-880	107	7	(	(	PUNCT
iajs-880	107	8	a	a	X
iajs-880	107	9	)	)	PUNCT
iajs-880	107	10	f	f	PROPN
iajs-880	107	11	is	be	AUX
iajs-880	107	12	bounded	bound	VERB
iajs-880	107	13	,	,	PUNCT
iajs-880	107	14	and	and	CCONJ
iajs-880	107	15	(	(	PUNCT
iajs-880	107	16	b	b	X
iajs-880	107	17	)	)	PUNCT
iajs-880	107	18	f	f	PROPN
iajs-880	107	19	is	be	AUX
iajs-880	107	20	unbounded	unbounded	ADJ
iajs-880	107	21	.	.	PUNCT
iajs-880	108	1	for	for	ADP
iajs-880	108	2	case	case	NOUN
iajs-880	108	3	(	(	PUNCT
iajs-880	108	4	a	a	NOUN
iajs-880	108	5	)	)	PUNCT
iajs-880	108	6	,	,	PUNCT
iajs-880	108	7	suppose	suppose	VERB
iajs-880	108	8	k6	k6	PROPN
iajs-880	108	9	>	>	X
iajs-880	108	10	0	0	NUM
iajs-880	108	11	is	be	AUX
iajs-880	108	12	such	such	ADJ
iajs-880	108	13	that	that	SCONJ
iajs-880	108	14	f(x	f(x	NOUN
iajs-880	108	15	)	)	PUNCT
iajs-880	108	16			NOUN
iajs-880	108	17	k6	k6	NOUN
iajs-880	108	18	,	,	PUNCT
iajs-880	108	19	for	for	ADP
iajs-880	108	20	all	all	PRON
iajs-880	108	21	0	0	NUM
iajs-880	108	22	<	<	X
iajs-880	108	23	x	x	X
iajs-880	108	24	<	<	X
iajs-880	108	25			X
iajs-880	108	26	.	.	PUNCT
iajs-880	109	1	ibn	ibn	PROPN
iajs-880	109	2	alhaitham	alhaitham	NOUN
iajs-880	110	1	j.	j.	PROPN
iajs-880	111	1	fo	fo	ADP
iajs-880	111	2	r	r	NOUN
iajs-880	111	3	pure	pure	ADJ
iajs-880	111	4	&	&	CCONJ
iajs-880	111	5	appl	appl	PROPN
iajs-880	111	6	.	.	PUNCT
iajs-880	112	1	sc	sc	PROPN
iajs-880	112	2	i.	i.	PROPN
iajs-880	112	3	vo	vo	PROPN
iajs-880	112	4	l.24	l.24	PROPN
iajs-880	112	5	(	(	PUNCT
iajs-880	112	6	1	1	NUM
iajs-880	112	7	)	)	PUNCT
iajs-880	112	8	2011	2011	NUM
iajs-880	112	9	let	let	VERB
iajs-880	112	10	k7	k7	PROPN
iajs-880	112	11	=	=	PROPN
iajs-880	112	12	max	max	PROPN
iajs-880	112	13	{	{	PUNCT
iajs-880	112	14	2k4	2k4	NUM
iajs-880	112	15	,	,	PUNCT
iajs-880	112	16	k6	k6	NOUN
iajs-880	112	17			SYM
iajs-880	112	18	b	b	PROPN
iajs-880	112	19	a	a	DET
iajs-880	112	20	ds	ds	ADJ
iajs-880	112	21	}	}	PUNCT
iajs-880	112	22	f(y(s	f(y(s	PROPN
iajs-880	112	23	)	)	PUNCT
iajs-880	112	24	)	)	PUNCT
iajs-880	112	25	g(s	g(s	PROPN
iajs-880	112	26	)	)	PUNCT
iajs-880	112	27	s)g(s	s)g(s	NOUN
iajs-880	112	28	,	,	PUNCT
iajs-880	112	29	λ	λ	INTJ
iajs-880	112	30	.	.	PUNCT
iajs-880	113	1	then	then	ADV
iajs-880	113	2	,	,	PUNCT
iajs-880	113	3	for	for	ADP
iajs-880	113	4	y	y	PROPN
iajs-880	113	5			PROPN
iajs-880	113	6	p	p	NOUN
iajs-880	113	7	with	with	ADP
iajs-880	113	8	y	y	NOUN
iajs-880	113	9			VERB
iajs-880	113	10	=	=	SYM
iajs-880	113	11	k7	k7	PROPN
iajs-880	113	12	we	we	PRON
iajs-880	113	13	have	have	VERB
iajs-880	113	14	from	from	ADP
iajs-880	113	15	(	(	PUNCT
iajs-880	113	16	2.3	2.3	NUM
iajs-880	113	17	)	)	PUNCT
iajs-880	113	18	and	and	CCONJ
iajs-880	113	19	(	(	PUNCT
iajs-880	113	20	3.2	3.2	NUM
iajs-880	113	21	)	)	PUNCT
iajs-880	113	22	so	so	SCONJ
iajs-880	113	23	that	that	SCONJ
iajs-880	113	24	yty	yty	VERB
iajs-880	113	25			NOUN
iajs-880	113	26	.	.	PUNCT
iajs-880	114	1	so	so	ADV
iajs-880	114	2	if	if	SCONJ
iajs-880	114	3	4	4	VERB
iajs-880	114	4	=	=	SYM
iajs-880	114	5	{	{	PUNCT
iajs-880	114	6	x	x	PROPN
iajs-880	114	7			NOUN
iajs-880	114	8	b	b	VERB
iajs-880	114	9	x	x	PUNCT
iajs-880	114	10	<	<	X
iajs-880	114	11	k7	k7	PROPN
iajs-880	114	12	}	}	PUNCT
iajs-880	114	13	then	then	ADV
iajs-880	114	14	ty	ty	PROPN
iajs-880	114	15			VERB
iajs-880	114	16			NOUN
iajs-880	114	17	y	y	NOUN
iajs-880	114	18			VERB
iajs-880	114	19	,	,	PUNCT
iajs-880	114	20	for	for	ADP
iajs-880	114	21	y	y	PROPN
iajs-880	114	22			NOUN
iajs-880	114	23	p	p	X
iajs-880	114	24	4	4	PROPN
iajs-880	114	25	…	…	PUNCT
iajs-880	114	26	…	…	PUNCT
iajs-880	114	27	…	…	PUNCT
iajs-880	114	28	.(3.11	.(3.11	PUNCT
iajs-880	114	29	)	)	PUNCT
iajs-880	115	1	for	for	ADP
iajs-880	115	2	case	case	NOUN
iajs-880	115	3	(	(	PUNCT
iajs-880	115	4	b	b	NOUN
iajs-880	115	5	)	)	PUNCT
iajs-880	115	6	,	,	PUNCT
iajs-880	115	7	let	let	VERB
iajs-880	115	8	k8	k8	PROPN
iajs-880	115	9	>	>	X
iajs-880	115	10	max	max	PROPN
iajs-880	115	11	{	{	PUNCT
iajs-880	115	12	2k4	2k4	NUM
iajs-880	115	13	,	,	PUNCT
iajs-880	115	14	k5	k5	PROPN
iajs-880	115	15	}	}	PUNCT
iajs-880	115	16	be	be	AUX
iajs-880	115	17	such	such	ADJ
iajs-880	115	18	that	that	SCONJ
iajs-880	115	19	f(x	f(x	PROPN
iajs-880	115	20	)	)	PUNCT
iajs-880	115	21			NOUN
iajs-880	115	22	f(k8	f(k8	NOUN
iajs-880	115	23	)	)	PUNCT
iajs-880	115	24	,	,	PUNCT
iajs-880	115	25	for	for	ADP
iajs-880	115	26	0	0	NUM
iajs-880	115	27	<	<	X
iajs-880	115	28	x	x	SYM
iajs-880	115	29			NUM
iajs-880	115	30	k8	k8	NOUN
iajs-880	115	31	.	.	PUNCT
iajs-880	116	1	by	by	ADP
iajs-880	116	2	choosing	choose	VERB
iajs-880	116	3	y	y	PROPN
iajs-880	116	4			PROPN
iajs-880	116	5	p	p	NOUN
iajs-880	116	6	such	such	ADJ
iajs-880	116	7	that	that	SCONJ
iajs-880	116	8	y	y	NOUN
iajs-880	116	9			VERB
iajs-880	116	10	=	=	SYM
iajs-880	116	11	k8	k8	NOUN
iajs-880	116	12	and	and	CCONJ
iajs-880	116	13	we	we	PRON
iajs-880	116	14	have	have	VERB
iajs-880	116	15	from	from	ADP
iajs-880	116	16	(	(	PUNCT
iajs-880	116	17	2.3	2.3	NUM
iajs-880	116	18	)	)	PUNCT
iajs-880	116	19	,	,	PUNCT
iajs-880	116	20	(	(	PUNCT
iajs-880	116	21	3.2	3.2	NUM
iajs-880	116	22	)	)	PUNCT
iajs-880	116	23	and	and	CCONJ
iajs-880	116	24	(	(	PUNCT
iajs-880	116	25	3.9	3.9	NUM
iajs-880	116	26	)	)	PUNCT
iajs-880	116	27	but	but	CCONJ
iajs-880	116	28			PROPN
iajs-880	116	29			PROPN
iajs-880	116	30			PROPN
iajs-880	116	31	b	b	PROPN
iajs-880	116	32	a	a	DET
iajs-880	116	33	b	b	NOUN
iajs-880	116	34	a	a	DET
iajs-880	116	35	8	8	NUM
iajs-880	116	36	yε)(f	yε)(f	NOUN
iajs-880	116	37	ds	ds	ADJ
iajs-880	116	38	g(s	g(s	PROPN
iajs-880	116	39	)	)	PUNCT
iajs-880	116	40	s)g(s	s)g(s	NOUN
iajs-880	116	41	,	,	PUNCT
iajs-880	116	42	λε)k(f	λε)k(f	AUX
iajs-880	116	43	ds	ds	PRON
iajs-880	116	44	g(s	g(s	NOUN
iajs-880	116	45	)	)	PUNCT
iajs-880	116	46	s)g(s	s)g(s	NOUN
iajs-880	116	47	,	,	PUNCT
iajs-880	116	48	λ	λ	PROPN
iajs-880	116	49	therefore	therefore	ADV
iajs-880	116	50			PUNCT
iajs-880	116	51			PROPN
iajs-880	116	52			VERB
iajs-880	116	53	b	b	PRON
iajs-880	116	54	a	a	DET
iajs-880	116	55	yε)(f	yε)(f	NOUN
iajs-880	116	56	ds	ds	ADJ
iajs-880	116	57	g(s	g(s	PROPN
iajs-880	116	58	)	)	PUNCT
iajs-880	116	59	s)g(s	s)g(s	NOUN
iajs-880	116	60	,	,	PUNCT
iajs-880	116	61	λ	λ	NOUN
iajs-880	116	62	ty(t	ty(t	NUM
iajs-880	116	63	)	)	PUNCT
iajs-880	116	64	and	and	CCONJ
iajs-880	116	65	so	so	ADV
iajs-880	116	66	yty	yty	VERB
iajs-880	116	67			NOUN
iajs-880	116	68	.	.	PUNCT
iajs-880	117	1	for	for	ADP
iajs-880	117	2	this	this	DET
iajs-880	117	3	case	case	NOUN
iajs-880	117	4	,	,	PUNCT
iajs-880	117	5	if	if	SCONJ
iajs-880	117	6	we	we	PRON
iajs-880	117	7	let	let	VERB
iajs-880	117	8	4	4	NOUN
iajs-880	117	9	=	=	PRON
iajs-880	117	10	{	{	PUNCT
iajs-880	117	11	x	x	PROPN
iajs-880	117	12			NOUN
iajs-880	117	13	b	b	VERB
iajs-880	117	14	x	x	PUNCT
iajs-880	117	15	<	<	X
iajs-880	117	16	k8	k8	X
iajs-880	117	17	}	}	PUNCT
iajs-880	117	18	then	then	ADV
iajs-880	117	19	ty	ty	PROPN
iajs-880	117	20			VERB
iajs-880	117	21			NOUN
iajs-880	117	22	y	y	NOUN
iajs-880	117	23			VERB
iajs-880	117	24	,	,	PUNCT
iajs-880	117	25	for	for	ADP
iajs-880	117	26	y	y	PROPN
iajs-880	117	27			NOUN
iajs-880	117	28	p	p	X
iajs-880	117	29	4	4	PROPN
iajs-880	117	30	…	…	PUNCT
iajs-880	117	31	…	…	PUNCT
iajs-880	117	32	…	…	PUNCT
iajs-880	117	33	.(3.12	.(3.12	X
iajs-880	117	34	)	)	PUNCT
iajs-880	117	35	thus	thus	ADV
iajs-880	117	36	,	,	PUNCT
iajs-880	117	37	in	in	ADP
iajs-880	117	38	both	both	DET
iajs-880	117	39	cases	case	NOUN
iajs-880	117	40	,	,	PUNCT
iajs-880	117	41	an	an	DET
iajs-880	117	42	applying	applying	NOUN
iajs-880	117	43	of	of	ADP
iajs-880	117	44	part	part	NOUN
iajs-880	117	45	(	(	PUNCT
iajs-880	117	46	2	2	NUM
iajs-880	117	47	)	)	PUNCT
iajs-880	117	48	of	of	ADP
iajs-880	117	49	theorem	theorem	NOUN
iajs-880	117	50	1	1	NUM
iajs-880	117	51	to	to	ADP
iajs-880	117	52	(	(	PUNCT
iajs-880	117	53	3.10),(3.11	3.10),(3.11	NUM
iajs-880	117	54	)	)	PUNCT
iajs-880	117	55	and	and	CCONJ
iajs-880	117	56	(	(	PUNCT
iajs-880	117	57	3.12	3.12	NUM
iajs-880	117	58	)	)	PUNCT
iajs-880	117	59	yields	yield	NOUN
iajs-880	117	60	that	that	PRON
iajs-880	117	61	t	t	PROPN
iajs-880	117	62	has	have	VERB
iajs-880	117	63	a	a	DET
iajs-880	117	64	fixed	fix	VERB
iajs-880	117	65	point	point	NOUN
iajs-880	117	66	y(t	y(t	NUM
iajs-880	117	67	)	)	PUNCT
iajs-880	117	68			NOUN
iajs-880	117	69	)	)	PUNCT
iajs-880	117	70	\(p	\(p	PROPN
iajs-880	117	71	34	34	NUM
iajs-880	117	72			NOUN
iajs-880	117	73	.	.	PUNCT
iajs-880	118	1	as	as	ADP
iajs-880	118	2	such	such	ADJ
iajs-880	118	3	,	,	PUNCT
iajs-880	118	4	y(t	y(t	PROPN
iajs-880	118	5	)	)	PUNCT
iajs-880	118	6	is	be	AUX
iajs-880	118	7	a	a	DET
iajs-880	118	8	desired	desire	VERB
iajs-880	118	9	solution	solution	NOUN
iajs-880	118	10	of	of	ADP
iajs-880	118	11	1.1	1.1	NUM
iajs-880	118	12	for	for	ADP
iajs-880	118	13	the	the	DET
iajs-880	118	14	given	give	VERB
iajs-880	118	15			NOUN
iajs-880	118	16	.	.	PUNCT
iajs-880	119	1	further	far	ADV
iajs-880	119	2	,	,	PUNCT
iajs-880	119	3	since	since	SCONJ
iajs-880	119	4	g	g	PROPN
iajs-880	119	5	(	(	PUNCT
iajs-880	119	6	t	t	PROPN
iajs-880	119	7	,	,	PUNCT
iajs-880	119	8	s	s	PROPN
iajs-880	119	9	)	)	PUNCT
iajs-880	119	10	>	>	X
iajs-880	119	11	0	0	PUNCT
iajs-880	119	12	,	,	PUNCT
iajs-880	119	13	it	it	PRON
iajs-880	119	14	follows	follow	VERB
iajs-880	119	15	that	that	SCONJ
iajs-880	119	16	y	y	PROPN
iajs-880	119	17	(	(	PUNCT
iajs-880	119	18	t	t	PROPN
iajs-880	119	19	)	)	PUNCT
iajs-880	119	20	>	>	X
iajs-880	119	21	0	0	PUNCT
iajs-880	119	22	for	for	ADP
iajs-880	119	23	a	a	DET
iajs-880	119	24	<	<	X
iajs-880	119	25	t	t	X
iajs-880	119	26	<	<	X
iajs-880	119	27	b	b	PROPN
iajs-880	119	28	.	.	PUNCT
iajs-880	120	1	this	this	PRON
iajs-880	120	2	completes	complete	VERB
iajs-880	120	3	the	the	DET
iajs-880	120	4	proof	proof	NOUN
iajs-880	120	5	of	of	ADP
iajs-880	120	6	the	the	DET
iajs-880	120	7	theorem	theorem	NOUN
iajs-880	120	8	.	.	PUNCT
iajs-880	121	1			X
iajs-880	122	1			X
iajs-880	122	2			X
iajs-880	122	3			PUNCT
iajs-880	122	4			PROPN
iajs-880	122	5			NOUN
iajs-880	122	6			NOUN
iajs-880	122	7			NUM
iajs-880	122	8			PROPN
iajs-880	122	9	b	b	NOUN
iajs-880	122	10	a	a	DET
iajs-880	122	11	8	8	NUM
iajs-880	122	12	b	b	NOUN
iajs-880	122	13	a	a	DET
iajs-880	122	14	8	8	NUM
iajs-880	122	15	b	b	NOUN
iajs-880	122	16	a	a	DET
iajs-880	122	17	b	b	NOUN
iajs-880	122	18	a	a	DET
iajs-880	122	19	ε)k(f	ε)k(f	X
iajs-880	122	20	ds	ds	PRON
iajs-880	122	21	g(s	g(s	PROPN
iajs-880	122	22	)	)	PUNCT
iajs-880	122	23	s)g(s	s)g(s	NOUN
iajs-880	122	24	,	,	PUNCT
iajs-880	122	25	λ	λ	NOUN
iajs-880	122	26	ds	ds	ADJ
iajs-880	122	27	)	)	PUNCT
iajs-880	122	28	f(k	f(k	ADJ
iajs-880	122	29	g(s	g(s	NOUN
iajs-880	122	30	)	)	PUNCT
iajs-880	122	31	s)g(s	s)g(s	NOUN
iajs-880	122	32	,	,	PUNCT
iajs-880	122	33	λ	λ	X
iajs-880	122	34	ds	ds	ADJ
iajs-880	122	35	f(y(s	f(y(s	NOUN
iajs-880	122	36	)	)	PUNCT
iajs-880	122	37	)	)	PUNCT
iajs-880	122	38	g(s	g(s	PROPN
iajs-880	122	39	)	)	PUNCT
iajs-880	122	40	s)g(s	s)g(s	NOUN
iajs-880	122	41	,	,	PUNCT
iajs-880	122	42	λ	λ	X
iajs-880	122	43	ds	ds	ADJ
iajs-880	122	44	f(y(s	f(y(s	NOUN
iajs-880	122	45	)	)	PUNCT
iajs-880	122	46	)	)	PUNCT
iajs-880	122	47	g(s	g(s	PROPN
iajs-880	122	48	)	)	PUNCT
iajs-880	122	49	s)g(t	s)g(t	PROPN
iajs-880	122	50	,	,	PUNCT
iajs-880	122	51	λ	λ	PROPN
iajs-880	122	52	ty(t	ty(t	PUNCT
iajs-880	122	53	)	)	PUNCT
iajs-880	122	54	y	y	PROPN
iajs-880	122	55	ds	ds	ADJ
iajs-880	122	56	g(s	g(s	PROPN
iajs-880	122	57	)	)	PUNCT
iajs-880	122	58	s)g(s	s)g(s	NOUN
iajs-880	122	59	,	,	PUNCT
iajs-880	122	60	k	k	PROPN
iajs-880	122	61	λ	λ	X
iajs-880	122	62	ds	ds	PROPN
iajs-880	122	63	}	}	PUNCT
iajs-880	122	64	f(y(s	f(y(s	PROPN
iajs-880	122	65	)	)	PUNCT
iajs-880	122	66	)	)	PUNCT
iajs-880	122	67	g(s	g(s	PROPN
iajs-880	122	68	)	)	PUNCT
iajs-880	122	69	s)g(t	s)g(t	PROPN
iajs-880	122	70	,	,	PUNCT
iajs-880	122	71	λ	λ	PROPN
iajs-880	122	72	ty(t	ty(t	NUM
iajs-880	122	73	)	)	PUNCT
iajs-880	122	74	b	b	NOUN
iajs-880	122	75	a	a	DET
iajs-880	122	76	6	6	NUM
iajs-880	122	77	b	b	NOUN
iajs-880	122	78	a	a	DET
iajs-880	122	79			NUM
iajs-880	122	80			NOUN
iajs-880	122	81			NUM
iajs-880	122	82			ADP
iajs-880	122	83			PUNCT
iajs-880	122	84	ibn	ibn	PROPN
iajs-880	122	85	alhaitham	alhaitham	NOUN
iajs-880	123	1	j.	j.	PROPN
iajs-880	124	1	fo	fo	ADP
iajs-880	124	2	r	r	NOUN
iajs-880	124	3	pure	pure	ADJ
iajs-880	124	4	&	&	CCONJ
iajs-880	124	5	appl	appl	PROPN
iajs-880	124	6	.	.	PUNCT
iajs-880	125	1	sc	sc	PROPN
iajs-880	125	2	i.	i.	PROPN
iajs-880	125	3	vo	vo	PROPN
iajs-880	125	4	l.24	l.24	PROPN
iajs-880	125	5	(	(	PUNCT
iajs-880	125	6	1	1	NUM
iajs-880	125	7	)	)	PUNCT
iajs-880	125	8	2011	2011	NUM
iajs-880	125	9	references	reference	NOUN
iajs-880	125	10	1	1	NUM
iajs-880	125	11	.	.	PUNCT
iajs-880	126	1	kuiper	kuiper	PROPN
iajs-880	126	2	,	,	PUNCT
iajs-880	126	3	h.	h.	PROPN
iajs-880	126	4	j.	j.	PROPN
iajs-880	126	5	(	(	PUNCT
iajs-880	126	6	1979	1979	NUM
iajs-880	126	7	)	)	PUNCT
iajs-880	126	8	.	.	PUNCT
iajs-880	127	1	on	on	ADP
iajs-880	127	2	positive	positive	ADJ
iajs-880	127	3	solution	solution	NOUN
iajs-880	127	4	of	of	ADP
iajs-880	127	5	nonlinear	nonlinear	ADJ
iajs-880	127	6	elliptic	elliptic	ADJ
iajs-880	127	7	eigenvalue	eigenvalue	NOUN
iajs-880	127	8	problems	problem	NOUN
iajs-880	127	9	,	,	PUNCT
iajs-880	127	10	rend	rend	VERB
iajs-880	127	11	.	.	PUNCT
iajs-880	128	1	math	math	PROPN
iajs-880	128	2	.	.	PUNCT
iajs-880	129	1	cire	cire	PROPN
iajs-880	129	2	.	.	PUNCT
iajs-880	130	1	palermo	palermo	PROPN
iajs-880	130	2	,	,	PUNCT
iajs-880	130	3	serie	serie	PROPN
iajs-880	130	4	ii	ii	PROPN
iajs-880	130	5	,	,	PUNCT
iajs-880	130	6	tom	tom	PROPN
iajs-880	130	7	.	.	PROPN
iajs-880	130	8	xx	xx	PROPN
iajs-880	130	9	113	113	NUM
iajs-880	130	10	-	-	SYM
iajs-880	130	11	138	138	NUM
iajs-880	130	12	.	.	PUNCT
iajs-880	131	1	2	2	X
iajs-880	131	2	.	.	X
iajs-880	131	3	erbe	erbe	PROPN
iajs-880	131	4	,	,	PUNCT
iajs-880	131	5	l.	l.	PROPN
iajs-880	131	6	h.	h.	PROPN
iajs-880	131	7	;	;	PUNCT
iajs-880	131	8	hu	hu	PROPN
iajs-880	131	9	,	,	PUNCT
iajs-880	131	10	s.	s.	PROPN
iajs-880	131	11	and	and	CCONJ
iajs-880	131	12	wang	wang	PROPN
iajs-880	131	13	,	,	PUNCT
iajs-880	131	14	h.	h.	PROPN
iajs-880	131	15	(	(	PUNCT
iajs-880	131	16	1994	1994	NUM
iajs-880	131	17	)	)	PUNCT
iajs-880	131	18	multiple	multiple	ADJ
iajs-880	131	19	positive	positive	ADJ
iajs-880	131	20	solutions	solution	NOUN
iajs-880	131	21	of	of	ADP
iajs-880	131	22	some	some	DET
iajs-880	131	23	boundary	boundary	ADJ
iajs-880	131	24	value	value	NOUN
iajs-880	131	25	problems	problem	NOUN
iajs-880	131	26	,	,	PUNCT
iajs-880	131	27	j.	j.	PROPN
iajs-880	131	28	m	m	PROPN
iajs-880	131	29	ath	ath	PROPN
iajs-880	131	30	.	.	PUNCT
iajs-880	132	1	anal.appl.184	anal.appl.184	NOUN
iajs-880	132	2	:	:	PUNCT
iajs-880	132	3	640–748	640–748	NUM
iajs-880	132	4	.	.	PUNCT
iajs-880	133	1	3	3	X
iajs-880	133	2	.	.	X
iajs-880	133	3	eloe	eloe	PROPN
iajs-880	133	4	,	,	PUNCT
iajs-880	133	5	p.w	p.w	PROPN
iajs-880	133	6	.	.	PROPN
iajs-880	133	7	;	;	PUNCT
iajs-880	133	8	henderson	henderson	PROPN
iajs-880	133	9	,	,	PUNCT
iajs-880	133	10	j.	j.	PROPN
iajs-880	133	11	and	and	CCONJ
iajs-880	133	12	wong	wong	PROPN
iajs-880	133	13	,	,	PUNCT
iajs-880	133	14	p.j.y	p.j.y	PROPN
iajs-880	133	15	.	.	PUNCT
iajs-880	133	16	positive	positive	ADJ
iajs-880	133	17	solutions	solution	NOUN
iajs-880	133	18	for	for	ADP
iajs-880	133	19	two	two	NUM
iajs-880	133	20	–	–	PUNCT
iajs-880	133	21	point	point	NOUN
iajs-880	133	22	boundary	boundary	ADJ
iajs-880	133	23	value	value	NOUN
iajs-880	133	24	problems	problem	NOUN
iajs-880	133	25	,	,	PUNCT
iajs-880	133	26	dyn	dyn	NOUN
iajs-880	133	27	.	.	PUNCT
iajs-880	134	1	sys	sys	PROPN
iajs-880	134	2	.	.	PUNCT
iajs-880	134	3	appl	appl	PROPN
iajs-880	134	4	.	.	PROPN
iajs-880	135	1	,	,	PUNCT
iajs-880	135	2	in	in	ADP
iajs-880	135	3	press	press	NOUN
iajs-880	135	4	.	.	PUNCT
iajs-880	136	1	4	4	X
iajs-880	136	2	.	.	X
iajs-880	136	3	eloe	eloe	PROPN
iajs-880	136	4	,	,	PUNCT
iajs-880	136	5	p.	p.	PROPN
iajs-880	136	6	w.	w.	PROPN
iajs-880	136	7	and	and	CCONJ
iajs-880	136	8	henderson	henderson	PROPN
iajs-880	136	9	,	,	PUNCT
iajs-880	136	10	j.	j.	PROPN
iajs-880	136	11	(	(	PUNCT
iajs-880	136	12	1995	1995	NUM
iajs-880	136	13	)	)	PUNCT
iajs-880	136	14	.	.	PUNCT
iajs-880	137	1	positive	positive	ADJ
iajs-880	137	2	solutions	solution	NOUN
iajs-880	137	3	for	for	ADP
iajs-880	137	4	higher	high	ADJ
iajs-880	137	5	order	order	NOUN
iajs-880	137	6	differential	differential	ADJ
iajs-880	137	7	equations	equation	NOUN
iajs-880	137	8	,	,	PUNCT
iajs-880	137	9	elec	elec	PROPN
iajs-880	137	10	.	.	PUNCT
iajs-880	138	1	j.	j.	PROPN
iajs-880	138	2	diff	diff	PROPN
iajs-880	138	3	.	.	PUNCT
iajs-880	139	1	equ	equ	PROPN
iajs-880	139	2	.	.	PROPN
iajs-880	139	3	3	3	NUM
iajs-880	139	4	:1	:1	PUNCT
iajs-880	139	5	–	–	PUNCT
iajs-880	139	6	8	8	NUM
iajs-880	139	7	.	.	X
iajs-880	139	8	5	5	X
iajs-880	139	9	.	.	X
iajs-880	139	10	erbe	erbe	PROPN
iajs-880	139	11	,	,	PUNCT
iajs-880	139	12	l.	l.	PROPN
iajs-880	139	13	h.	h.	PROPN
iajs-880	139	14	and	and	CCONJ
iajs-880	139	15	wang	wang	PROPN
iajs-880	139	16	,	,	PUNCT
iajs-880	139	17	h.	h.	PROPN
iajs-880	139	18	(	(	PUNCT
iajs-880	139	19	1994	1994	NUM
iajs-880	139	20	)	)	PUNCT
iajs-880	139	21	.	.	PUNCT
iajs-880	140	1	on	on	ADP
iajs-880	140	2	the	the	DET
iajs-880	140	3	existence	existence	NOUN
iajs-880	140	4	of	of	ADP
iajs-880	140	5	positive	positive	ADJ
iajs-880	140	6	solution	solution	NOUN
iajs-880	140	7	of	of	ADP
iajs-880	140	8	ordinary	ordinary	ADJ
iajs-880	140	9	differential	differential	ADJ
iajs-880	140	10	equations	equation	NOUN
iajs-880	140	11	,	,	PUNCT
iajs-880	140	12	proc	proc	PROPN
iajs-880	140	13	.	.	PUNCT
iajs-880	141	1	amer	amer	PROPN
iajs-880	141	2	.	.	PUNCT
iajs-880	141	3	math	math	PROPN
iajs-880	141	4	.	.	PUNCT
iajs-880	142	1	soc	soc	PROPN
iajs-880	142	2	.	.	PUNCT
iajs-880	143	1	120	120	NUM
iajs-880	143	2	:	:	SYM
iajs-880	143	3	743	743	NUM
iajs-880	143	4	–	–	SYM
iajs-880	143	5	748	748	NUM
iajs-880	143	6	.	.	X
iajs-880	144	1	6	6	X
iajs-880	144	2	.	.	X
iajs-880	144	3	garaizar	garaizar	NOUN
iajs-880	144	4	,	,	PUNCT
iajs-880	144	5	x.	x.	NOUN
iajs-880	144	6	(	(	PUNCT
iajs-880	144	7	1987	1987	NUM
iajs-880	144	8	)	)	PUNCT
iajs-880	144	9	.	.	PUNCT
iajs-880	145	1	existence	existence	NOUN
iajs-880	145	2	of	of	ADP
iajs-880	145	3	positive	positive	ADJ
iajs-880	145	4	radial	radial	ADJ
iajs-880	145	5	solutions	solution	NOUN
iajs-880	145	6	for	for	ADP
iajs-880	145	7	semilinear	semilinear	ADJ
iajs-880	145	8	elliptic	elliptic	ADJ
iajs-880	145	9	problems	problem	NOUN
iajs-880	145	10	in	in	ADP
iajs-880	145	11	the	the	DET
iajs-880	145	12	annulus	annulus	NOUN
iajs-880	145	13	,	,	PUNCT
iajs-880	145	14	j.	j.	PROPN
iajs-880	145	15	diff	diff	PROPN
iajs-880	145	16	.	.	PUNCT
iajs-880	146	1	equ	equ	PROPN
iajs-880	146	2	.	.	PROPN
iajs-880	147	1	70	70	NUM
iajs-880	147	2	:	:	SYM
iajs-880	147	3	69	69	NUM
iajs-880	147	4	–	–	SYM
iajs-880	147	5	72	72	NUM
iajs-880	147	6	.	.	PUNCT
iajs-880	148	1	7	7	X
iajs-880	148	2	.	.	X
iajs-880	148	3	henderson	henderson	PROPN
iajs-880	148	4	,	,	PUNCT
iajs-880	148	5	j.	j.	PROPN
iajs-880	148	6	and	and	CCONJ
iajs-880	148	7	wang	wang	PROPN
iajs-880	148	8	,	,	PUNCT
iajs-880	148	9	h.	h.	PROPN
iajs-880	148	10	(	(	PUNCT
iajs-880	148	11	1997	1997	NUM
iajs-880	148	12	)	)	PUNCT
iajs-880	148	13	.	.	PUNCT
iajs-880	149	1	positive	positive	ADJ
iajs-880	149	2	solutions	solution	NOUN
iajs-880	149	3	for	for	ADP
iajs-880	149	4	nonlinear	nonlinear	ADJ
iajs-880	149	5	eigenvalue	eigenvalue	ADJ
iajs-880	149	6	problems	problem	NOUN
iajs-880	149	7	,	,	PUNCT
iajs-880	149	8	j.	j.	PROPN
iajs-880	149	9	m	m	PROPN
iajs-880	149	10	ath	ath	PROPN
iajs-880	149	11	.	.	PUNCT
iajs-880	150	1	anal	anal	PROPN
iajs-880	150	2	.	.	PUNCT
iajs-880	150	3	appl	appl	PROPN
iajs-880	150	4	.	.	PUNCT
iajs-880	151	1	208	208	NUM
iajs-880	151	2	:	:	PUNCT
iajs-880	151	3	252	252	NUM
iajs-880	151	4	–	–	PUNCT
iajs-880	151	5	259	259	NUM
iajs-880	151	6	.	.	X
iajs-880	152	1	8	8	X
iajs-880	152	2	.	.	X
iajs-880	153	1	krasnoseelskii	krasnoseelskii	PROPN
iajs-880	153	2	,	,	PUNCT
iajs-880	153	3	m.	m.	NOUN
iajs-880	153	4	a.(1964	a.(1964	PROPN
iajs-880	153	5	)	)	PUNCT
iajs-880	153	6	.	.	PUNCT
iajs-880	154	1	positive	positive	ADJ
iajs-880	154	2	solutions	solution	NOUN
iajs-880	154	3	of	of	ADP
iajs-880	154	4	operator	operator	NOUN
iajs-880	154	5	equations	equation	NOUN
iajs-880	154	6	,	,	PUNCT
iajs-880	154	7	noordhoff	noordhoff	NOUN
iajs-880	154	8	,	,	PUNCT
iajs-880	154	9	groning	groning	NOUN
iajs-880	154	10	.	.	PUNCT
iajs-880	154	11	2011	2011	NUM
iajs-880	154	12	)	)	PUNCT
iajs-880	154	13	1	1	NUM
iajs-880	154	14	(	(	PUNCT
iajs-880	154	15	24مجلة	24مجلة	NUM
iajs-880	154	16	ابن	ابن	VERB
iajs-880	154	17	الهیثم	الهیثم	ADJ
iajs-880	154	18	للعلوم	للعلوم	PROPN
iajs-880	154	19	الصرفة	الصرفة	PROPN
iajs-880	154	20	والتطبیقیة	والتطبیقیة	PROPN
iajs-880	154	21	المجلد	المجلد	PROPN
iajs-880	154	22	وجود	وجود	VERB
iajs-880	154	23	الحلول	الحلول	PROPN
iajs-880	154	24	الموجبة	الموجبة	PROPN
iajs-880	154	25	لمسائل	لمسائل	PROPN
iajs-880	154	26	القیم	القیم	PROPN
iajs-880	154	27	الحدودیة	الحدودیة	PROPN
iajs-880	154	28	صالح	صالح	PROPN
iajs-880	154	29	محمد	محمد	PROPN
iajs-880	154	30	حسین	حسین	ADJ
iajs-880	154	31	جامعة	جامعة	PROPN
iajs-880	154	32	االنبار،كلیة	االنبار،كلیة	PUNCT
iajs-880	154	33	التربیة	التربیة	PROPN
iajs-880	154	34	للعلوم	للعلوم	PROPN
iajs-880	154	35	الصرفة	الصرفة	PROPN
iajs-880	154	36	،	،	PROPN
iajs-880	154	37	قسم	قسم	PROPN
iajs-880	154	38	الریاضیات	الریاضیات	VERB
iajs-880	154	39	2010حزیران	2010حزیران	NUM
iajs-880	154	40	1استلم	1استلم	NUM
iajs-880	154	41	البحث	البحث	NOUN
iajs-880	154	42	في	في	SCONJ
iajs-880	154	43	2010تشرین	2010تشرین	NUM
iajs-880	154	44	االول	االول	NOUN
iajs-880	154	45	19قبل	19قبل	NUM
iajs-880	154	46	البحث	البحث	VERB
iajs-880	154	47	في	في	ADP
iajs-880	154	48	الخالصة	الخالصة	NOUN
iajs-880	154	49	-	-	PUNCT
iajs-880	154	50	:	:	PUNCT
iajs-880	154	51	االتیةالحلول	االتیةالحلول	PROPN
iajs-880	154	52	الموجبة	الموجبة	PROPN
iajs-880	154	53	للمسألة	للمسألة	PROPN
iajs-880	154	54	الحدودیة	الحدودیة	VERB
iajs-880	154	55	وجوددرس	وجوددرس	PROPN
iajs-880	154	56	هذا	هذا	NOUN
iajs-880	154	57	البحث	البحث	NOUN
iajs-880	154	58	0	0	NUM
iajs-880	154	59	y(b	y(b	NOUN
iajs-880	154	60	)	)	PUNCT
iajs-880	154	61	0(a)y	0(a)y	PUNCT
iajs-880	155	1	β	β	X
iajs-880	155	2	y(a	y(a	PROPN
iajs-880	155	3	)	)	PUNCT
iajs-880	155	4	α	α	PROPN
iajs-880	155	5	bta	bta	NOUN
iajs-880	155	6	f(y	f(y	NOUN
iajs-880	155	7	)	)	PUNCT
iajs-880	155	8	g(t	g(t	PROPN
iajs-880	155	9	)	)	PUNCT
iajs-880	156	1	λy	λy	PROPN
iajs-880	156	2			NUM
iajs-880	156	3			PROPN
iajs-880	156	4			ADJ
iajs-880	156	5			X
iajs-880	156	6	)	)	PUNCT
iajs-880	156	7	قـیم	قـیم	PROPN
iajs-880	157	1	المعلمـة	المعلمـة	PROPN
iajs-880	157	2	تـم	تـم	VERB
iajs-880	157	3	تحدیـدو	تحدیـدو	PROPN
iajs-880	157	4	اموجبـ	اموجبـ	PROPN
iajs-880	157	5	اواحد	اواحد	PROPN
iajs-880	157	6	حال	حال	PROPN
iajs-880	157	7	األقلأن	األقلأن	PROPN
iajs-880	157	8	هذه	هذه	PROPN
iajs-880	157	9	المسألة	المسألة	PROPN
iajs-880	157	10	تمتلك	تمتلك	PROPN
iajs-880	157	11	على	على	PROPN
iajs-880	157	12	ت	ت	PROPN
iajs-880	157	13	إلىنظریة	إلىنظریة	PROPN
iajs-880	157	14	النقطة	النقطة	PROPN
iajs-880	157	15	الثابتة	الثابتة	PROPN
iajs-880	157	16	وتوصل	وتوصل	PROPN
iajs-880	157	17	استخدمم	استخدمم	NOUN
iajs-880	157	18	.	.	PUNCT
iajs-880	158	1	لمسألة	لمسألة	PROPN
iajs-880	158	2	الحدودیةل	الحدودیةل	PROPN
iajs-880	158	3	حلول	حلول	PROPN
iajs-880	158	4	موجبة	موجبة	PROPN
iajs-880	158	5	وجدتعندها	وجدتعندها	PROPN
iajs-880	158	6	التي	التي	PROPN
iajs-880	158	7	(	(	PUNCT