id	sid	tid	token	lemma	pos
iajs-551	1	1	mathematics	mathematic	NOUN
iajs-551	1	2	333	333	NUM
iajs-551	1	3	مجلة	مجلة	NOUN
iajs-551	1	4	إبن	إبن	VERB
iajs-551	1	5	الهيثم	الهيثم	ADJ
iajs-551	1	6	للعلوم	للعلوم	NOUN
iajs-551	1	7	الصرفة	الصرفة	NOUN
iajs-551	2	1	و	و	PRON
iajs-551	2	2	التطبيقية	التطبيقية	ADJ
iajs-551	2	3	2012	2012	NUM
iajs-551	2	4	السنة	السنة	NOUN
iajs-551	2	5	25	25	NUM
iajs-551	2	6	المجلد	المجلد	NOUN
iajs-551	2	7	3	3	NUM
iajs-551	2	8	العدد	العدد	PROPN
iajs-551	2	9	ibn	ibn	PROPN
iajs-551	2	10	al	al	PROPN
iajs-551	2	11	-	-	PUNCT
iajs-551	2	12	haitham	haitham	PROPN
iajs-551	2	13	journal	journal	PROPN
iajs-551	2	14	for	for	ADP
iajs-551	2	15	pure	pure	ADJ
iajs-551	2	16	and	and	CCONJ
iajs-551	2	17	applied	apply	VERB
iajs-551	2	18	science	science	NOUN
iajs-551	2	19	no	no	NOUN
iajs-551	2	20	.	.	NOUN
iajs-551	2	21	3	3	NUM
iajs-551	2	22	vol	vol	NOUN
iajs-551	2	23	.	.	PUNCT
iajs-551	3	1	25	25	NUM
iajs-551	3	2	year	year	NOUN
iajs-551	3	3	2012	2012	NUM
iajs-551	3	4	degree	degree	NOUN
iajs-551	3	5	of	of	ADP
iajs-551	3	6	monotone	monotone	ADJ
iajs-551	3	7	approximation	approximation	NOUN
iajs-551	3	8	in	in	ADP
iajs-551	3	9	,	,	PUNCT
iajs-551	3	10	pl	pl	PROPN
iajs-551	3	11	α	α	PROPN
iajs-551	3	12	spaces	space	NOUN
iajs-551	3	13	s.	s.	PROPN
iajs-551	3	14	k.	k.	PROPN
iajs-551	3	15	jassim	jassim	PROPN
iajs-551	3	16	and	and	CCONJ
iajs-551	3	17	i.	i.	PROPN
iajs-551	3	18	z.	z.	PROPN
iajs-551	3	19	shamkhi	shamkhi	PROPN
iajs-551	3	20	department	department	PROPN
iajs-551	3	21	of	of	ADP
iajs-551	3	22	mathematics	mathematics	PROPN
iajs-551	3	23	,	,	PUNCT
iajs-551	3	24	college	college	NOUN
iajs-551	3	25	of	of	ADP
iajs-551	3	26	science	science	NOUN
iajs-551	3	27	–	–	PUNCT
iajs-551	3	28	al	al	PROPN
iajs-551	3	29	-	-	PUNCT
iajs-551	3	30	mustansiriya	mustansiriya	PROPN
iajs-551	3	31	university	university	NOUN
iajs-551	3	32	received	receive	VERB
iajs-551	3	33	in	in	ADP
iajs-551	3	34	:	:	PUNCT
iajs-551	3	35	18	18	NUM
iajs-551	3	36	february	february	NOUN
iajs-551	3	37	2011	2011	NUM
iajs-551	3	38	accepted	accept	VERB
iajs-551	3	39	in	in	ADP
iajs-551	3	40	:	:	PUNCT
iajs-551	3	41	18	18	NUM
iajs-551	3	42	march	march	NOUN
iajs-551	3	43	2012	2012	NUM
iajs-551	3	44	abstract	abstract	NOUN
iajs-551	3	45	the	the	DET
iajs-551	3	46	aim	aim	NOUN
iajs-551	3	47	of	of	ADP
iajs-551	3	48	this	this	DET
iajs-551	3	49	paper	paper	NOUN
iajs-551	3	50	is	be	AUX
iajs-551	3	51	to	to	PART
iajs-551	3	52	study	study	VERB
iajs-551	3	53	the	the	DET
iajs-551	3	54	best	good	ADJ
iajs-551	3	55	approximation	approximation	NOUN
iajs-551	3	56	of	of	ADP
iajs-551	3	57	unbounded	unbounded	ADJ
iajs-551	3	58	functions	function	NOUN
iajs-551	3	59	in	in	ADP
iajs-551	3	60	the	the	DET
iajs-551	3	61	weighted	weight	VERB
iajs-551	3	62	spaces	space	NOUN
iajs-551	3	63	,	,	PUNCT
iajs-551	3	64	1	1	NUM
iajs-551	3	65	,	,	PUNCT
iajs-551	3	66	0,p	0,p	PUNCT
iajs-551	4	1	pl	pl	PROPN
iajs-551	4	2	α	α	NUM
iajs-551	4	3	α≥	α≥	PROPN
iajs-551	4	4	>	>	X
iajs-551	4	5	.	.	PUNCT
iajs-551	5	1	key	key	ADJ
iajs-551	5	2	words	word	NOUN
iajs-551	5	3	:	:	PUNCT
iajs-551	5	4	weighted	weighted	ADJ
iajs-551	5	5	space	space	NOUN
iajs-551	5	6	,	,	PUNCT
iajs-551	5	7	unbounded	unbounded	ADJ
iajs-551	5	8	functions	function	NOUN
iajs-551	5	9	,	,	PUNCT
iajs-551	5	10	monotone	monotone	ADJ
iajs-551	5	11	approximation	approximation	NOUN
iajs-551	5	12	introduction	introduction	NOUN
iajs-551	5	13	with	with	ADP
iajs-551	5	14	a	a	DET
iajs-551	5	15	great	great	ADJ
iajs-551	5	16	potential	potential	NOUN
iajs-551	5	17	for	for	ADP
iajs-551	5	18	applications	application	NOUN
iajs-551	5	19	to	to	ADP
iajs-551	5	20	a	a	DET
iajs-551	5	21	wide	wide	ADJ
iajs-551	5	22	variety	variety	NOUN
iajs-551	5	23	of	of	ADP
iajs-551	5	24	problems	problem	NOUN
iajs-551	5	25	,	,	PUNCT
iajs-551	5	26	approximation	approximation	NOUN
iajs-551	5	27	theory	theory	NOUN
iajs-551	5	28	represents	represent	VERB
iajs-551	5	29	on	on	ADP
iajs-551	5	30	old	old	ADJ
iajs-551	5	31	field	field	NOUN
iajs-551	5	32	of	of	ADP
iajs-551	5	33	mathematical	mathematical	ADJ
iajs-551	5	34	research	research	NOUN
iajs-551	5	35	.	.	PUNCT
iajs-551	6	1	in	in	ADP
iajs-551	6	2	the	the	DET
iajs-551	6	3	fifties	fifty	NOUN
iajs-551	6	4	a	a	DET
iajs-551	6	5	new	new	ADJ
iajs-551	6	6	breath	breath	NOUN
iajs-551	6	7	over	over	ADP
iajs-551	6	8	it	it	PRON
iajs-551	6	9	has	have	AUX
iajs-551	6	10	been	be	AUX
iajs-551	6	11	brought	bring	VERB
iajs-551	6	12	by	by	ADP
iajs-551	6	13	a	a	DET
iajs-551	6	14	systematic	systematic	ADJ
iajs-551	6	15	study	study	NOUN
iajs-551	6	16	of	of	ADP
iajs-551	6	17	the	the	DET
iajs-551	6	18	linear	linear	ADJ
iajs-551	6	19	methods	method	NOUN
iajs-551	6	20	of	of	ADP
iajs-551	6	21	approximation	approximation	NOUN
iajs-551	6	22	which	which	PRON
iajs-551	6	23	are	be	AUX
iajs-551	6	24	given	give	VERB
iajs-551	6	25	by	by	ADP
iajs-551	6	26	sequences	sequence	NOUN
iajs-551	6	27	of	of	ADP
iajs-551	6	28	linear	linear	PROPN
iajs-551	6	29	operators	operator	NOUN
iajs-551	6	30	.these	.these	VERB
iajs-551	6	31	methods	method	NOUN
iajs-551	6	32	became	become	VERB
iajs-551	6	33	a	a	DET
iajs-551	6	34	firmly	firmly	ADV
iajs-551	6	35	entrenched	entrenched	ADJ
iajs-551	6	36	part	part	NOUN
iajs-551	6	37	of	of	ADP
iajs-551	6	38	approximation	approximation	NOUN
iajs-551	6	39	theory	theory	NOUN
iajs-551	6	40	.	.	PUNCT
iajs-551	7	1	the	the	DET
iajs-551	7	2	problem	problem	NOUN
iajs-551	7	3	of	of	ADP
iajs-551	7	4	function	function	NOUN
iajs-551	7	5	connected	connect	VERB
iajs-551	7	6	with	with	ADP
iajs-551	7	7	different	different	ADJ
iajs-551	7	8	polynomials	polynomial	NOUN
iajs-551	7	9	was	be	AUX
iajs-551	7	10	examined	examine	VERB
iajs-551	7	11	in	in	ADP
iajs-551	7	12	many	many	ADJ
iajs-551	7	13	paper	paper	NOUN
iajs-551	7	14	like[1	like[1	PROPN
iajs-551	7	15	]	]	PUNCT
iajs-551	7	16	and	and	CCONJ
iajs-551	7	17	[	[	X
iajs-551	7	18	2	2	NUM
iajs-551	7	19	]	]	PUNCT
iajs-551	7	20	.	.	PUNCT
iajs-551	8	1	in	in	ADP
iajs-551	8	2	this	this	DET
iajs-551	8	3	paper	paper	NOUN
iajs-551	8	4	we	we	PRON
iajs-551	8	5	studied	study	VERB
iajs-551	8	6	the	the	DET
iajs-551	8	7	degree	degree	NOUN
iajs-551	8	8	of	of	ADP
iajs-551	8	9	approximation	approximation	NOUN
iajs-551	8	10	of	of	ADP
iajs-551	8	11	unbound	unbound	NOUN
iajs-551	8	12	functions	function	NOUN
iajs-551	8	13	by	by	ADP
iajs-551	8	14	using	use	VERB
iajs-551	8	15	piecewise	piecewise	NOUN
iajs-551	8	16	monotone	monotone	ADJ
iajs-551	8	17	polynomials	polynomial	NOUN
iajs-551	8	18	in	in	ADP
iajs-551	8	19	the	the	DET
iajs-551	8	20	weighted	weight	VERB
iajs-551	8	21	spaces	space	NOUN
iajs-551	8	22	,	,	PUNCT
iajs-551	8	23	pl	pl	PROPN
iajs-551	8	24	α	α	NOUN
iajs-551	8	25	.	.	PUNCT
iajs-551	9	1	definitions	definition	NOUN
iajs-551	9	2	and	and	CCONJ
iajs-551	9	3	notations	notation	NOUN
iajs-551	9	4	let	let	VERB
iajs-551	9	5	f	f	PRON
iajs-551	9	6	be	be	AUX
iajs-551	9	7	any	any	DET
iajs-551	9	8	function	function	NOUN
iajs-551	9	9	such	such	ADJ
iajs-551	9	10	that	that	SCONJ
iajs-551	9	11	(	(	PUNCT
iajs-551	9	12	)	)	PUNCT
iajs-551	10	1	[	[	PUNCT
iajs-551	10	2	]	]	X
iajs-551	10	3	,	,	PUNCT
iajs-551	10	4	0	0	NUM
iajs-551	10	5	,	,	PUNCT
iajs-551	10	6	,	,	PUNCT
iajs-551	10	7	,	,	PUNCT
iajs-551	10	8	xf	xf	PROPN
iajs-551	10	9	x	x	PROPN
iajs-551	10	10	me	i	PRON
iajs-551	10	11	m	m	VERB
iajs-551	10	12	r	r	NOUN
iajs-551	10	13	x	x	PUNCT
iajs-551	10	14	a	a	DET
iajs-551	10	15	bα	bα	NOUN
iajs-551	10	16	α≤	α≤	NOUN
iajs-551	10	17	>	>	PUNCT
iajs-551	10	18	∈	∈	PROPN
iajs-551	10	19	∈	∈	NOUN
iajs-551	10	20	we	we	PRON
iajs-551	10	21	denote	denote	VERB
iajs-551	10	22	by	by	ADP
iajs-551	10	23	,	,	PUNCT
iajs-551	10	24	pl	pl	PROPN
iajs-551	10	25	α	α	NOUN
iajs-551	10	26	,	,	PUNCT
iajs-551	10	27	the	the	DET
iajs-551	10	28	spaces	space	NOUN
iajs-551	10	29	of	of	ADP
iajs-551	10	30	all	all	DET
iajs-551	10	31	functions	function	NOUN
iajs-551	10	32	such	such	ADJ
iajs-551	10	33	that	that	SCONJ
iajs-551	10	34	(	(	PUNCT
iajs-551	10	35	)	)	PUNCT
iajs-551	10	36	1	1	NUM
iajs-551	10	37	,	,	PUNCT
iajs-551	10	38	d	d	X
iajs-551	10	39	,	,	PUNCT
iajs-551	10	40	1α	1α	NUM
iajs-551	10	41	α	α	PRON
iajs-551	10	42	−	−	PROPN
iajs-551	10	43			VERB
iajs-551	10	44			NUM
iajs-551	10	45			ADJ
iajs-551	10	46	∫	∫	NOUN
iajs-551	10	47			ADJ
iajs-551	10	48			NOUN
iajs-551	10	49	=	=	SYM
iajs-551	10	50	<	<	X
iajs-551	10	51	∞	∞	PROPN
iajs-551	10	52	≤	≤	PUNCT
iajs-551	10	53	<	<	X
iajs-551	10	54	∞x	∞x	NOUN
iajs-551	11	1	pa	pa	PROPN
iajs-551	11	2	p	p	PROPN
iajs-551	11	3	p	p	PROPN
iajs-551	11	4	b	b	X
iajs-551	11	5	f	f	X
iajs-551	11	6	f	f	NOUN
iajs-551	11	7	x	x	PUNCT
iajs-551	11	8	e	e	NOUN
iajs-551	11	9	x	x	X
iajs-551	11	10	p	p	X
iajs-551	11	11	…	…	PUNCT
iajs-551	11	12	(	(	PUNCT
iajs-551	11	13	2.1	2.1	NUM
iajs-551	11	14	)	)	PUNCT
iajs-551	11	15	see	see	VERB
iajs-551	11	16	[	[	X
iajs-551	11	17	7	7	NUM
iajs-551	11	18	]	]	PUNCT
iajs-551	11	19	.	.	PUNCT
iajs-551	12	1	we	we	PRON
iajs-551	12	2	approximated	approximate	VERB
iajs-551	12	3	f	f	PROPN
iajs-551	12	4	by	by	ADP
iajs-551	12	5	a	a	DET
iajs-551	12	6	piecewise	piecewise	NOUN
iajs-551	12	7	polynomial	polynomial	NOUN
iajs-551	12	8	of	of	ADP
iajs-551	12	9	degree	degree	NOUN
iajs-551	12	10	at	at	ADP
iajs-551	12	11	most	most	ADJ
iajs-551	12	12	n	n	NOUN
iajs-551	12	13	.	.	PUNCT
iajs-551	13	1	definition	definition	NOUN
iajs-551	13	2	1	1	NUM
iajs-551	13	3	let	let	VERB
iajs-551	13	4	1	1	NUM
iajs-551	13	5	2	2	NUM
iajs-551	13	6	1	1	NUM
iajs-551	13	7	0	0	NUM
iajs-551	13	8	1	1	NUM
iajs-551	13	9	1	1	NUM
iajs-551	13	10	2	2	NUM
iajs-551	13	11	1	1	NUM
iajs-551	13	12	1s	1	NOUN
iajs-551	13	13	(	(	PUNCT
iajs-551	13	14	x	x	X
iajs-551	13	15	,	,	PUNCT
iajs-551	13	16	x	x	INTJ
iajs-551	13	17	,	,	PUNCT
iajs-551	13	18	....	....	PUNCT
iajs-551	13	19	,	,	PUNCT
iajs-551	13	20	x	x	X
iajs-551	13	21	)	)	PUNCT
iajs-551	13	22	=	=	PRON
iajs-551	13	23	{	{	PUNCT
iajs-551	13	24	s	s	X
iajs-551	13	25	[	[	X
iajs-551	13	26	a	a	DET
iajs-551	13	27	,	,	PUNCT
iajs-551	13	28	b	b	NOUN
iajs-551	13	29	]	]	PUNCT
iajs-551	13	30	;	;	PUNCT
iajs-551	13	31	s	s	X
iajs-551	13	32	(	(	PUNCT
iajs-551	13	33	x	x	INTJ
iajs-551	13	34	,	,	PUNCT
iajs-551	13	35	x	x	PROPN
iajs-551	13	36	)	)	PUNCT
iajs-551	13	37	,	,	PUNCT
iajs-551	13	38	1	1	NUM
iajs-551	13	39	,	,	PUNCT
iajs-551	13	40	2	2	NUM
iajs-551	13	41	,	,	PUNCT
iajs-551	13	42	...	...	PUNCT
iajs-551	14	1	1}where	1}where	NUM
iajs-551	14	2	(	(	PUNCT
iajs-551	14	3	,	,	PUNCT
iajs-551	14	4	)	)	PUNCT
iajs-551	14	5	(	(	PUNCT
iajs-551	14	6	,	,	PUNCT
iajs-551	14	7	)	)	PUNCT
iajs-551	14	8	(	(	PUNCT
iajs-551	14	9	,	,	PUNCT
iajs-551	14	10	)	)	PUNCT
iajs-551	14	11	...	...	PUNCT
iajs-551	14	12	(	(	PUNCT
iajs-551	14	13	,	,	PUNCT
iajs-551	14	14	)	)	PUNCT
iajs-551	14	15	i-1	i-1	NOUN
iajs-551	14	16	ik	ik	PROPN
iajs-551	14	17	n	n	PROPN
iajs-551	15	1	i	i	PRON
iajs-551	16	1	i	i	VERB
iajs-551	16	2	k	k	PROPN
iajs-551	17	1	k	k	PROPN
iajs-551	17	2	nc	nc	PROPN
iajs-551	18	1	i	i	PRON
iajs-551	18	2	k	k	PROPN
iajs-551	19	1	x	x	PUNCT
iajs-551	19	2	x	x	PUNCT
iajs-551	19	3	x	x	PUNCT
iajs-551	19	4	x	x	PUNCT
iajs-551	19	5	x	x	PUNCT
iajs-551	19	6	x	x	PUNCT
iajs-551	19	7	x	x	SYM
iajs-551	19	8	xn	xn	PROPN
iajs-551	19	9	n	n	NUM
iajs-551	19	10	−	−	PROPN
iajs-551	19	11	−	−	PROPN
iajs-551	19	12	−∈	−∈	PROPN
iajs-551	19	13	∈π	∈π	PROPN
iajs-551	19	14	=	=	PUNCT
iajs-551	20	1	+	+	NUM
iajs-551	20	2	π	π	X
iajs-551	20	3	=	=	PUNCT
iajs-551	20	4	,	,	PUNCT
iajs-551	20	5	{	{	PUNCT
iajs-551	20	6	x	x	NOUN
iajs-551	20	7	,	,	PUNCT
iajs-551	20	8	x	x	INTJ
iajs-551	20	9	,	,	PUNCT
iajs-551	20	10	....	....	PUNCT
iajs-551	20	11	,	,	PUNCT
iajs-551	20	12	x	x	X
iajs-551	20	13	}	}	SYM
iajs-551	20	14	1	1	NUM
iajs-551	20	15	2	2	NUM
iajs-551	20	16	k	k	NOUN
iajs-551	20	17	is	be	AUX
iajs-551	20	18	a	a	DET
iajs-551	20	19	space	space	NOUN
iajs-551	20	20	of	of	ADP
iajs-551	20	21	spline	spline	NOUN
iajs-551	20	22	with	with	ADP
iajs-551	20	23	simple	simple	ADJ
iajs-551	20	24	knots	knot	NOUN
iajs-551	20	25	(	(	PUNCT
iajs-551	20	26	x	x	X
iajs-551	20	27	,	,	PUNCT
iajs-551	20	28	x	x	INTJ
iajs-551	20	29	,	,	PUNCT
iajs-551	20	30	....	....	PUNCT
iajs-551	20	31	,	,	PUNCT
iajs-551	20	32	x	x	X
iajs-551	20	33	)	)	PUNCT
iajs-551	20	34	1	1	NUM
iajs-551	20	35	2	2	NUM
iajs-551	20	36	k	k	NOUN
iajs-551	20	37	,	,	PUNCT
iajs-551	20	38	consider	consider	VERB
iajs-551	20	39	0	0	NUM
iajs-551	20	40	1	1	NUM
iajs-551	20	41	1a	1a	NOUN
iajs-551	20	42	=	=	PUNCT
iajs-551	21	1	x	x	PUNCT
iajs-551	21	2	x	x	PUNCT
iajs-551	21	3	x	x	PUNCT
iajs-551	21	4	x	x	X
iajs-551	21	5	=	=	X
iajs-551	21	6	bk	bk	NOUN
iajs-551	21	7	k	k	PUNCT
iajs-551	22	1	+	+	ADP
iajs-551	22	2	<	<	X
iajs-551	22	3	<	<	X
iajs-551	22	4	....	....	PUNCT
iajs-551	22	5	<	<	X
iajs-551	22	6	apartition	apartition	NOUN
iajs-551	22	7	on	on	ADP
iajs-551	22	8	interval	interval	NOUN
iajs-551	22	9	[	[	X
iajs-551	22	10	a	a	X
iajs-551	22	11	,	,	PUNCT
iajs-551	22	12	b	b	NOUN
iajs-551	22	13	]	]	PUNCT
iajs-551	22	14	.for	.for	ADP
iajs-551	22	15	k=1,2,	k=1,2,	PROPN
iajs-551	22	16	…	…	PUNCT
iajs-551	22	17	let	let	VERB
iajs-551	22	18	1	1	NUM
iajs-551	22	19	2(x	2(x	NUM
iajs-551	22	20	,	,	PUNCT
iajs-551	22	21	x	x	INTJ
iajs-551	22	22	,	,	PUNCT
iajs-551	22	23	...	...	PUNCT
iajs-551	22	24	,	,	PUNCT
iajs-551	22	25	x	x	X
iajs-551	22	26	)	)	PUNCT
iajs-551	22	27	k	k	PROPN
iajs-551	22	28	k	k	PROPN
iajs-551	22	29	k	k	PROPN
iajs-551	22	30	ks	ks	PROPN
iajs-551	22	31	sk	sk	VERB
iajs-551	22	32	n=	n=	ADJ
iajs-551	22	33	,	,	PUNCT
iajs-551	22	34	for	for	ADP
iajs-551	22	35	some	some	DET
iajs-551	22	36	k	k	PROPN
iajs-551	22	37	knot	knot	NOUN
iajs-551	22	38	such	such	ADJ
iajs-551	22	39	that	that	DET
iajs-551	22	40	end	end	NOUN
iajs-551	22	41	points	point	NOUN
iajs-551	22	42	[	[	X
iajs-551	22	43	bounded	bound	VERB
iajs-551	22	44	]	]	X
iajs-551	22	45	,	,	PUNCT
iajs-551	22	46	0	0	NUM
iajs-551	22	47	1a	1a	X
iajs-551	22	48	=	=	PUNCT
iajs-551	22	49	x	x	X
iajs-551	22	50	and	and	CCONJ
iajs-551	22	51	b	b	X
iajs-551	22	52	=	=	NOUN
iajs-551	22	53	x	x	VERB
iajs-551	22	54	for	for	ADP
iajs-551	22	55	each	each	DET
iajs-551	22	56	kk	kk	PROPN
iajs-551	22	57	k	k	PROPN
iajs-551	22	58	k	k	PROPN
iajs-551	23	1	+	+	CCONJ
iajs-551	23	2	.	.	PUNCT
iajs-551	24	1	the	the	DET
iajs-551	24	2	mesh	mesh	NOUN
iajs-551	24	3	is	be	AUX
iajs-551	24	4	denoted	denote	VERB
iajs-551	24	5	by	by	ADP
iajs-551	24	6	(	(	PUNCT
iajs-551	24	7	)	)	PUNCT
iajs-551	24	8	10,1	10,1	NUM
iajs-551	24	9	,	,	PUNCT
iajs-551	24	10	...	...	PUNCT
iajs-551	24	11	,	,	PUNCT
iajs-551	24	12	k	k	PROPN
iajs-551	24	13	k	k	PROPN
iajs-551	25	1	i	i	PRON
iajs-551	25	2	ii	ii	VERB
iajs-551	26	1	k	k	NOUN
iajs-551	26	2	m	m	VERB
iajs-551	26	3	max	max	PROPN
iajs-551	26	4	x	x	PUNCT
iajs-551	26	5	xk	xk	PROPN
iajs-551	26	6	+	+	PROPN
iajs-551	26	7	=	=	SYM
iajs-551	26	8	=	=	SYM
iajs-551	26	9	−	−	PROPN
iajs-551	26	10	denote	denote	NOUN
iajs-551	26	11	,	,	PUNCT
iajs-551	26	12	1	1	NUM
iajs-551	26	13	,	,	PUNCT
iajs-551	26	14	2,	2,	NUM
iajs-551	26	15	....	....	PUNCT
iajs-551	26	16	,s	,s	SYM
iajs-551	26	17	s	s	PART
iajs-551	26	18	ny	ny	NOUN
iajs-551	26	19	=	=	PUNCT
iajs-551	26	20	the	the	DET
iajs-551	26	21	collection	collection	NOUN
iajs-551	26	22	of	of	ADP
iajs-551	26	23	all	all	DET
iajs-551	26	24	set	set	ADJ
iajs-551	26	25	mathematics	mathematic	NOUN
iajs-551	26	26	334	334	NUM
iajs-551	26	27	مجلة	مجلة	VERB
iajs-551	26	28	إبن	إبن	VERB
iajs-551	26	29	الهيثم	الهيثم	ADJ
iajs-551	26	30	للعلوم	للعلوم	NOUN
iajs-551	26	31	الصرفة	الصرفة	NOUN
iajs-551	27	1	و	و	PRON
iajs-551	27	2	التطبيقية	التطبيقية	ADJ
iajs-551	27	3	2012	2012	NUM
iajs-551	27	4	السنة	السنة	NOUN
iajs-551	27	5	25	25	NUM
iajs-551	27	6	المجلد	المجلد	NOUN
iajs-551	27	7	3	3	NUM
iajs-551	27	8	العدد	العدد	PROPN
iajs-551	27	9	ibn	ibn	PROPN
iajs-551	27	10	al	al	PROPN
iajs-551	27	11	-	-	PUNCT
iajs-551	27	12	haitham	haitham	PROPN
iajs-551	27	13	journal	journal	PROPN
iajs-551	27	14	for	for	ADP
iajs-551	27	15	pure	pure	ADJ
iajs-551	27	16	and	and	CCONJ
iajs-551	27	17	applied	apply	VERB
iajs-551	27	18	science	science	NOUN
iajs-551	27	19	no	no	NOUN
iajs-551	27	20	.	.	NOUN
iajs-551	27	21	3	3	NUM
iajs-551	27	22	vol	vol	NOUN
iajs-551	27	23	.	.	PUNCT
iajs-551	28	1	25	25	NUM
iajs-551	28	2	year	year	NOUN
iajs-551	28	3	2012	2012	NUM
iajs-551	28	4	{	{	PUNCT
iajs-551	28	5	}	}	PUNCT
iajs-551	28	6	,	,	PUNCT
iajs-551	28	7	0	0	NUM
iajs-551	28	8	...	...	PUNCT
iajs-551	28	9	1s	1s	NUM
iajs-551	28	10	sy	sy	INTJ
iajs-551	28	11	y	y	PROPN
iajs-551	29	1	y=	y=	X
iajs-551	29	2	<	<	X
iajs-551	29	3	<	<	X
iajs-551	29	4	<	<	X
iajs-551	29	5	,	,	PUNCT
iajs-551	29	6	and	and	CCONJ
iajs-551	29	7	(	(	PUNCT
iajs-551	29	8	)	)	PUNCT
iajs-551	29	9	(	(	PUNCT
iajs-551	29	10	1	1	X
iajs-551	29	11	)	)	PUNCT
iajs-551	29	12	y∆	y∆	NOUN
iajs-551	29	13	be	be	VERB
iajs-551	29	14	the	the	DET
iajs-551	29	15	collection	collection	NOUN
iajs-551	29	16	of	of	ADP
iajs-551	29	17	all	all	DET
iajs-551	29	18	functions	function	NOUN
iajs-551	29	19	[	[	PUNCT
iajs-551	29	20	]	]	X
iajs-551	29	21	,	,	PUNCT
iajs-551	29	22	0,1,f	0,1,f	NOUN
iajs-551	29	23	f	f	PROPN
iajs-551	29	24	lp	lp	NOUN
iajs-551	29	25	α′∈	α′∈	NOUN
iajs-551	29	26	which	which	PRON
iajs-551	29	27	change	change	VERB
iajs-551	29	28	monotonicity	monotonicity	NOUN
iajs-551	29	29	at	at	ADP
iajs-551	29	30	the	the	DET
iajs-551	29	31	points	point	NOUN
iajs-551	29	32	of	of	ADP
iajs-551	29	33	sy	sy	PROPN
iajs-551	29	34	.	.	PUNCT
iajs-551	30	1	set	set	PROPN
iajs-551	30	2	(	(	PUNCT
iajs-551	30	3	)	)	PUNCT
iajs-551	30	4	(	(	PUNCT
iajs-551	30	5	)	)	PUNCT
iajs-551	30	6	1	1	NUM
iajs-551	30	7	s	s	VERB
iajs-551	30	8	ix	ix	NOUN
iajs-551	30	9	x	x	INTJ
iajs-551	30	10	yi=∏	yi=∏	NOUN
iajs-551	30	11	=	=	SYM
iajs-551	30	12	∏	∏	PROPN
iajs-551	30	13	−	−	NOUN
iajs-551	30	14	…	…	PUNCT
iajs-551	30	15	(	(	PUNCT
iajs-551	30	16	2.2	2.2	NUM
iajs-551	30	17	)	)	PUNCT
iajs-551	30	18	the	the	DET
iajs-551	30	19	differentiable	differentiable	ADJ
iajs-551	30	20	function	function	NOUN
iajs-551	30	21	in	in	ADP
iajs-551	30	22	[	[	X
iajs-551	30	23	0,1],lp	0,1],lp	X
iajs-551	30	24	α	α	NOUN
iajs-551	30	25	is	be	AUX
iajs-551	30	26	in	in	ADP
iajs-551	30	27	(	(	PUNCT
iajs-551	30	28	)	)	PUNCT
iajs-551	30	29	(	(	PUNCT
iajs-551	30	30	1	1	X
iajs-551	30	31	)	)	PUNCT
iajs-551	30	32	y∆	y∆	PROPN
iajs-551	30	33	if	if	SCONJ
iajs-551	30	34	(	(	PUNCT
iajs-551	30	35	)	)	PUNCT
iajs-551	30	36	(	(	PUNCT
iajs-551	30	37	)	)	PUNCT
iajs-551	30	38	0	0	NUM
iajs-551	30	39	,	,	PUNCT
iajs-551	30	40	0,1	0,1	NUM
iajs-551	30	41	,	,	PUNCT
iajs-551	30	42	f	f	PROPN
iajs-551	30	43	x	x	PUNCT
iajs-551	30	44	x	x	PUNCT
iajs-551	30	45	x	x	SYM
iajs-551	30	46			PROPN
iajs-551	30	47			NOUN
iajs-551	30	48	′	′	VERB
iajs-551	30	49	∏	∏	NUM
iajs-551	30	50	≥	≥	NOUN
iajs-551	31	1	∈	∈	NOUN
iajs-551	32	1	[	[	X
iajs-551	32	2	4	4	NUM
iajs-551	32	3	]	]	PUNCT
iajs-551	32	4	.	.	PUNCT
iajs-551	33	1	definition	definition	NOUN
iajs-551	33	2	2	2	NUM
iajs-551	33	3	:	:	PUNCT
iajs-551	33	4	[	[	X
iajs-551	33	5	7	7	X
iajs-551	33	6	]	]	PUNCT
iajs-551	33	7	the	the	DET
iajs-551	33	8	degree	degree	NOUN
iajs-551	33	9	of	of	ADP
iajs-551	33	10	monotone	monotone	ADJ
iajs-551	33	11	approximation	approximation	NOUN
iajs-551	33	12	by	by	ADP
iajs-551	33	13	polynomials	polynomial	NOUN
iajs-551	33	14	np	np	ADP
iajs-551	33	15	of	of	ADP
iajs-551	33	16	degree	degree	NOUN
iajs-551	33	17	not	not	PART
iajs-551	33	18	exceeding	exceed	VERB
iajs-551	33	19	n	n	PRON
iajs-551	33	20	will	will	AUX
iajs-551	33	21	be	be	AUX
iajs-551	33	22	denoted	denote	VERB
iajs-551	33	23	by	by	ADP
iajs-551	33	24	(	(	PUNCT
iajs-551	33	25	)	)	PUNCT
iajs-551	33	26	(	(	PUNCT
iajs-551	33	27	1	1	X
iajs-551	33	28	)	)	PUNCT
iajs-551	33	29	(	(	PUNCT
iajs-551	33	30	)	)	PUNCT
iajs-551	33	31	,	,	PUNCT
iajs-551	33	32	(	(	PUNCT
iajs-551	33	33	1	1	NUM
iajs-551	33	34	)	)	PUNCT
iajs-551	33	35	,	,	PUNCT
iajs-551	33	36	,	,	PUNCT
iajs-551	33	37	,	,	PUNCT
iajs-551	34	1	inf	inf	NOUN
iajs-551	34	2	p	p	PROPN
iajs-551	34	3	y	y	PROPN
iajs-551	34	4	ln	ln	NOUN
iajs-551	34	5	p	p	PROPN
iajs-551	34	6	e	e	PROPN
iajs-551	34	7	f	f	PROPN
iajs-551	34	8	y	y	PROPN
iajs-551	34	9	f	f	PROPN
iajs-551	34	10	pnp	pnp	PROPN
iajs-551	35	1	pn	pn	PROPN
iajs-551	35	2	α	α	PROPN
iajs-551	35	3	α	α	PROPN
iajs-551	35	4	α	α	NOUN
iajs-551	35	5	∈∆	∈∆	NOUN
iajs-551	36	1	=	=	SYM
iajs-551	36	2	−	−	PROPN
iajs-551	36	3			NOUN
iajs-551	36	4	…	…	PUNCT
iajs-551	36	5	(	(	PUNCT
iajs-551	36	6	2.3	2.3	NUM
iajs-551	36	7	)	)	PUNCT
iajs-551	36	8	for	for	ADP
iajs-551	36	9	p	p	NOUN
iajs-551	36	10	=	=	SYM
iajs-551	36	11	∞	∞	NUM
iajs-551	36	12	then	then	ADV
iajs-551	36	13	(	(	PUNCT
iajs-551	36	14	)	)	PUNCT
iajs-551	36	15	(	(	PUNCT
iajs-551	36	16	)	)	PUNCT
iajs-551	36	17	[	[	PUNCT
iajs-551	36	18	]	]	X
iajs-551	36	19	(	(	PUNCT
iajs-551	36	20	1	1	NUM
iajs-551	36	21	)	)	PUNCT
iajs-551	36	22	,	,	PUNCT
iajs-551	36	23	,	,	PUNCT
iajs-551	36	24	,	,	PUNCT
iajs-551	36	25	inf	inf	PROPN
iajs-551	36	26	,	,	PUNCT
iajs-551	36	27	0,1n	0,1n	NUM
iajs-551	36	28	ne	ne	PROPN
iajs-551	37	1	f	f	PROPN
iajs-551	37	2	y	y	PROPN
iajs-551	37	3	f	f	PROPN
iajs-551	38	1	x	x	X
iajs-551	38	2	p	p	X
iajs-551	38	3	xα	xα	ADP
iajs-551	38	4	α	α	NOUN
iajs-551	38	5	∞	∞	NOUN
iajs-551	38	6	∞	∞	NUM
iajs-551	38	7	=	=	PUNCT
iajs-551	39	1	−	−	PROPN
iajs-551	39	2	∈	∈	NOUN
iajs-551	39	3	let	let	VERB
iajs-551	39	4	(	(	PUNCT
iajs-551	39	5	)	)	PUNCT
iajs-551	39	6	(	(	PUNCT
iajs-551	39	7	)	)	PUNCT
iajs-551	39	8	xxx	xxx	PROPN
iajs-551	39	9	−=	−=	NOUN
iajs-551	39	10	1ϕ	1ϕ	ADJ
iajs-551	39	11	,	,	PUNCT
iajs-551	39	12	x∈[0,1	x∈[0,1	PROPN
iajs-551	39	13	]	]	X
iajs-551	39	14	…	…	PUNCT
iajs-551	39	15	(	(	PUNCT
iajs-551	39	16	2.4	2.4	NUM
iajs-551	39	17	)	)	PUNCT
iajs-551	39	18	the	the	DET
iajs-551	39	19	spaces	space	NOUN
iajs-551	39	20	,	,	PUNCT
iajs-551	39	21	,	,	PUNCT
iajs-551	39	22	p	p	X
iajs-551	39	23	rl	rl	ADP
iajs-551	39	24	α	α	PROPN
iajs-551	39	25	ϕ	ϕ	PROPN
iajs-551	39	26	,	,	PUNCT
iajs-551	39	27	r∈n	r∈n	PROPN
iajs-551	39	28	are	be	AUX
iajs-551	39	29	the	the	DET
iajs-551	39	30	spaces	space	NOUN
iajs-551	39	31	of	of	ADP
iajs-551	39	32	all	all	DET
iajs-551	39	33	functions	function	NOUN
iajs-551	39	34	such	such	ADJ
iajs-551	39	35	that	that	PRON
iajs-551	39	36	(	(	PUNCT
iajs-551	39	37	)	)	PUNCT
iajs-551	39	38	(	(	PUNCT
iajs-551	39	39	)	)	PUNCT
iajs-551	39	40	1	1	NUM
iajs-551	39	41	1	1	NUM
iajs-551	39	42	0	0	NUM
iajs-551	39	43	ppr	ppr	NOUN
iajs-551	39	44	xx	xx	NUM
iajs-551	40	1	f	f	NOUN
iajs-551	40	2	x	x	PUNCT
iajs-551	40	3	e	e	X
iajs-551	40	4	dxα−	dxα−	X
iajs-551	40	5			PROPN
iajs-551	40	6			ADJ
iajs-551	40	7			PROPN
iajs-551	40	8			X
iajs-551	40	9			PROPN
iajs-551	40	10	<	<	X
iajs-551	40	11	∞∫	∞∫	PROPN
iajs-551	40	12	…	…	PUNCT
iajs-551	40	13	(	(	PUNCT
iajs-551	40	14	2.5	2.5	NUM
iajs-551	40	15	)	)	PUNCT
iajs-551	40	16	where	where	SCONJ
iajs-551	40	17	(	(	PUNCT
iajs-551	40	18	)	)	PUNCT
iajs-551	40	19	(	(	PUNCT
iajs-551	40	20	)	)	PUNCT
iajs-551	40	21	(	(	PUNCT
iajs-551	40	22	)	)	PUNCT
iajs-551	40	23	(	(	PUNCT
iajs-551	40	24	)	)	PUNCT
iajs-551	40	25	x	x	SYM
iajs-551	40	26	rrf	rrf	PROPN
iajs-551	40	27	f	f	X
iajs-551	40	28	x	x	PUNCT
iajs-551	40	29	e	e	PROPN
iajs-551	40	30	α−=	α−=	X
iajs-551	40	31	and	and	CCONJ
iajs-551	40	32	(	(	PUNCT
iajs-551	40	33	)	)	PUNCT
iajs-551	40	34	(	(	PUNCT
iajs-551	40	35	)	)	PUNCT
iajs-551	40	36	1	1	NUM
iajs-551	40	37	2	2	NUM
iajs-551	40	38	lim	lim	NOUN
iajs-551	40	39	0r	0r	X
iajs-551	41	1	r	r	NOUN
iajs-551	41	2	x	x	X
iajs-551	41	3	x	x	X
iajs-551	41	4	f	f	PROPN
iajs-551	41	5	xϕ	xϕ	PUNCT
iajs-551	41	6	→	→	PUNCT
iajs-551	41	7	=	=	SYM
iajs-551	41	8	.	.	PUNCT
iajs-551	42	1	definition	definition	NOUN
iajs-551	42	2	3	3	NUM
iajs-551	42	3	:	:	PUNCT
iajs-551	43	1	[	[	X
iajs-551	43	2	3	3	X
iajs-551	43	3	]	]	PUNCT
iajs-551	43	4	for	for	ADP
iajs-551	43	5	1k	1k	NUM
iajs-551	43	6	≥	≥	NOUN
iajs-551	43	7	the	the	DET
iajs-551	43	8	ditizian	ditizian	ADJ
iajs-551	43	9	–	–	PUNCT
iajs-551	43	10	totik	totik	NOUN
iajs-551	43	11	modules	module	NOUN
iajs-551	43	12	of	of	ADP
iajs-551	43	13	smoothness	smoothness	NOUN
iajs-551	43	14	is	be	AUX
iajs-551	43	15	defined	define	VERB
iajs-551	43	16	by	by	ADP
iajs-551	43	17	(	(	PUNCT
iajs-551	43	18	)	)	PUNCT
iajs-551	43	19	(	(	PUNCT
iajs-551	43	20	)	)	PUNCT
iajs-551	43	21	(	(	PUNCT
iajs-551	43	22	)	)	PUNCT
iajs-551	43	23	(	(	PUNCT
iajs-551	43	24	)	)	PUNCT
iajs-551	43	25	(	(	PUNCT
iajs-551	43	26	)	)	PUNCT
iajs-551	43	27	(	(	PUNCT
iajs-551	43	28	)	)	PUNCT
iajs-551	43	29	,	,	PUNCT
iajs-551	43	30	,	,	PUNCT
iajs-551	43	31	sup	sup	INTJ
iajs-551	43	32	,	,	PUNCT
iajs-551	43	33	0r	0r	PROPN
iajs-551	43	34	rr	rr	PROPN
iajs-551	44	1	k	k	PROPN
iajs-551	44	2	k	k	PROPN
iajs-551	44	3	r	r	PROPN
iajs-551	44	4	kh	kh	PROPN
iajs-551	44	5	h	h	PROPN
iajs-551	44	6	xp	xp	PROPN
iajs-551	45	1	p	p	X
iajs-551	45	2	f	f	PROPN
iajs-551	45	3	t	t	PROPN
iajs-551	45	4	x	x	SYM
iajs-551	45	5	f	f	NOUN
iajs-551	45	6	x	x	SYM
iajs-551	45	7	tϕ	tϕ	INTJ
iajs-551	45	8	ϕω	ϕω	INTJ
iajs-551	45	9	ϕ=	ϕ=	PRON
iajs-551	45	10	∆	∆	PROPN
iajs-551	45	11	≥	≥	NOUN
iajs-551	45	12	and	and	CCONJ
iajs-551	45	13	(	(	PUNCT
iajs-551	45	14	)	)	PUNCT
iajs-551	45	15	(	(	PUNCT
iajs-551	45	16	)	)	PUNCT
iajs-551	45	17	(	(	PUNCT
iajs-551	45	18	)	)	PUNCT
iajs-551	45	19	(	(	PUNCT
iajs-551	45	20	)	)	PUNCT
iajs-551	45	21	(	(	PUNCT
iajs-551	45	22	)	)	PUNCT
iajs-551	45	23	(	(	PUNCT
iajs-551	45	24	)	)	PUNCT
iajs-551	45	25	,	,	PUNCT
iajs-551	45	26	,	,	PUNCT
iajs-551	45	27	,	,	PUNCT
iajs-551	45	28	,	,	PUNCT
iajs-551	45	29	sup	sup	INTJ
iajs-551	45	30	,	,	PUNCT
iajs-551	45	31	0r	0r	PROPN
iajs-551	45	32	rr	rr	PROPN
iajs-551	46	1	k	k	PROPN
iajs-551	46	2	k	k	PROPN
iajs-551	46	3	r	r	PROPN
iajs-551	46	4	kh	kh	PROPN
iajs-551	46	5	h	h	PROPN
iajs-551	46	6	xp	xp	PROPN
iajs-551	47	1	p	p	X
iajs-551	47	2	f	f	PROPN
iajs-551	47	3	t	t	PROPN
iajs-551	47	4	x	x	SYM
iajs-551	47	5	f	f	NOUN
iajs-551	47	6	x	x	SYM
iajs-551	47	7	tϕ	tϕ	PROPN
iajs-551	47	8	ϕα	ϕα	ADV
iajs-551	47	9	α	α	PROPN
iajs-551	47	10	ω	ω	NOUN
iajs-551	47	11	ϕ=	ϕ=	NOUN
iajs-551	47	12	∆	∆	PROPN
iajs-551	47	13	≥	≥	NOUN
iajs-551	48	1	[	[	X
iajs-551	48	2	7	7	NUM
iajs-551	48	3	]	]	SYM
iajs-551	48	4	…	…	PUNCT
iajs-551	48	5	(	(	PUNCT
iajs-551	48	6	2.6	2.6	NUM
iajs-551	48	7	)	)	PUNCT
iajs-551	48	8	where	where	SCONJ
iajs-551	48	9	k	k	PROPN
iajs-551	48	10	th	th	X
iajs-551	48	11	symmetric	symmetric	ADJ
iajs-551	48	12	difference	difference	NOUN
iajs-551	48	13	is	be	AUX
iajs-551	48	14	defined	define	VERB
iajs-551	48	15	by	by	ADP
iajs-551	48	16	(	(	PUNCT
iajs-551	48	17	)	)	PUNCT
iajs-551	48	18	(	(	PUNCT
iajs-551	48	19	)	)	PUNCT
iajs-551	48	20	(	(	PUNCT
iajs-551	48	21	)	)	PUNCT
iajs-551	48	22	(	(	PUNCT
iajs-551	48	23	)	)	PUNCT
iajs-551	48	24	(	(	PUNCT
iajs-551	48	25	)	)	PUNCT
iajs-551	48	26	0	0	NUM
iajs-551	48	27	1	1	NUM
iajs-551	48	28	2	2	NUM
iajs-551	48	29	k	k	NOUN
iajs-551	48	30	kk	kk	PROPN
iajs-551	48	31	jk	jk	PROPN
iajs-551	48	32	h	h	PROPN
iajs-551	48	33	x	x	PROPN
iajs-551	48	34	jj	jj	PROPN
iajs-551	48	35	k	k	PROPN
iajs-551	48	36	j	j	PROPN
iajs-551	48	37	h	h	NOUN
iajs-551	49	1	x	x	NOUN
iajs-551	49	2	g	g	NOUN
iajs-551	49	3	x	x	X
iajs-551	49	4	g	g	PROPN
iajs-551	49	5	xϕ	xϕ	PROPN
iajs-551	50	1	ϕ+	ϕ+	PUNCT
iajs-551	50	2	=	=	NOUN
iajs-551	50	3	−	−	VERB
iajs-551	50	4			PUNCT
iajs-551	50	5	∆	∆	NOUN
iajs-551	50	6	=	=	SYM
iajs-551	51	1	−	−	PROPN
iajs-551	52	1	−	−	PROPN
iajs-551	52	2			VERB
iajs-551	52	3			ADJ
iajs-551	52	4			NOUN
iajs-551	52	5			NOUN
iajs-551	52	6			PUNCT
iajs-551	52	7	∑	∑	ADV
iajs-551	52	8	is	be	AUX
iajs-551	52	9	…	…	PUNCT
iajs-551	52	10	(	(	PUNCT
iajs-551	52	11	2.7	2.7	NUM
iajs-551	52	12	)	)	PUNCT
iajs-551	52	13	and	and	CCONJ
iajs-551	52	14	the	the	DET
iajs-551	52	15	supermum	supermum	NOUN
iajs-551	52	16	is	be	AUX
iajs-551	52	17	taken	take	VERB
iajs-551	52	18	over	over	ADP
iajs-551	52	19	all	all	PRON
iajs-551	52	20	(	(	PUNCT
iajs-551	52	21	)	)	PUNCT
iajs-551	52	22	(	(	PUNCT
iajs-551	52	23	)	)	PUNCT
iajs-551	52	24	1,0	1,0	NUM
iajs-551	52	25	2	2	NUM
iajs-551	52	26	,	,	PUNCT
iajs-551	52	27	∈xhkxx	∈xhkxx	PROPN
iajs-551	52	28	ϕ	ϕ	X
iajs-551	52	29	.	.	PUNCT
iajs-551	53	1	note	note	VERB
iajs-551	53	2	that	that	SCONJ
iajs-551	53	3	for	for	ADP
iajs-551	53	4	[	[	PUNCT
iajs-551	53	5	]	]	X
iajs-551	53	6	,	,	PUNCT
iajs-551	53	7	0,1pf	0,1pf	NUM
iajs-551	53	8	l	l	NOUN
iajs-551	53	9	α∈	α∈	NOUN
iajs-551	53	10	then	then	ADV
iajs-551	53	11	(	(	PUNCT
iajs-551	53	12	)	)	PUNCT
iajs-551	53	13	(	(	PUNCT
iajs-551	53	14	)	)	PUNCT
iajs-551	53	15	,	,	PUNCT
iajs-551	53	16	0	0	NUM
iajs-551	53	17	,	,	PUNCT
iajs-551	53	18	,	,	PUNCT
iajs-551	53	19	,	,	PUNCT
iajs-551	53	20	,	,	PUNCT
iajs-551	53	21	k	k	PROPN
iajs-551	53	22	kp	kp	PROPN
iajs-551	54	1	p	p	PROPN
iajs-551	54	2	f	f	PROPN
iajs-551	54	3	t	t	PROPN
iajs-551	54	4	f	f	PROPN
iajs-551	55	1	tϕ	tϕ	PROPN
iajs-551	55	2	ϕ	ϕ	PROPN
iajs-551	55	3	α	α	PROPN
iajs-551	55	4	α	α	PROPN
iajs-551	55	5	ω	ω	NUM
iajs-551	55	6	ω=	ω=	X
iajs-551	55	7	.	.	PUNCT
iajs-551	56	1	mathematics	mathematic	NOUN
iajs-551	56	2	335	335	NUM
iajs-551	56	3	مجلة	مجلة	VERB
iajs-551	56	4	إبن	إبن	NOUN
iajs-551	56	5	الهيثم	الهيثم	ADJ
iajs-551	56	6	للعلوم	للعلوم	NOUN
iajs-551	56	7	الصرفة	الصرفة	NOUN
iajs-551	56	8	و	و	PRON
iajs-551	56	9	التطبيقية	التطبيقية	ADJ
iajs-551	56	10	2012	2012	NUM
iajs-551	56	11	السنة	السنة	NOUN
iajs-551	57	1	25	25	NUM
iajs-551	57	2	المجلد	المجلد	NOUN
iajs-551	57	3	3	3	NUM
iajs-551	57	4	العدد	العدد	PROPN
iajs-551	57	5	ibn	ibn	PROPN
iajs-551	57	6	al	al	PROPN
iajs-551	57	7	-	-	PUNCT
iajs-551	57	8	haitham	haitham	PROPN
iajs-551	57	9	journal	journal	PROPN
iajs-551	57	10	for	for	ADP
iajs-551	57	11	pure	pure	ADJ
iajs-551	57	12	and	and	CCONJ
iajs-551	57	13	applied	apply	VERB
iajs-551	57	14	science	science	NOUN
iajs-551	57	15	no	no	NOUN
iajs-551	57	16	.	.	NOUN
iajs-551	57	17	3	3	NUM
iajs-551	57	18	vol	vol	NOUN
iajs-551	57	19	.	.	PUNCT
iajs-551	57	20	25	25	NUM
iajs-551	57	21	year	year	NOUN
iajs-551	57	22	2012	2012	NUM
iajs-551	57	23	definition	definition	NOUN
iajs-551	57	24	4	4	NUM
iajs-551	57	25	:	:	PUNCT
iajs-551	57	26	[	[	X
iajs-551	57	27	6	6	NUM
iajs-551	57	28	]	]	PUNCT
iajs-551	57	29	at	at	ADP
iajs-551	57	30	the	the	DET
iajs-551	57	31	points	point	NOUN
iajs-551	57	32	0	0	NUM
iajs-551	57	33	1	1	NUM
iajs-551	57	34	,	,	PUNCT
iajs-551	57	35	,	,	PUNCT
iajs-551	57	36	..	..	PUNCT
iajs-551	57	37	,	,	PUNCT
iajs-551	57	38	nx	nx	X
iajs-551	57	39	x	x	PUNCT
iajs-551	57	40	x	x	VERB
iajs-551	57	41	are	be	AUX
iajs-551	57	42	defined	define	VERB
iajs-551	57	43	by	by	ADP
iajs-551	57	44	0	0	NUM
iajs-551	57	45	1	1	NUM
iajs-551	57	46	0	0	NUM
iajs-551	57	47	0	0	NUM
iajs-551	57	48	(	(	PUNCT
iajs-551	57	49	)	)	PUNCT
iajs-551	57	50	[	[	PUNCT
iajs-551	57	51	,	,	PUNCT
iajs-551	57	52	,	,	PUNCT
iajs-551	57	53	..	..	PUNCT
iajs-551	57	54	,	,	PUNCT
iajs-551	57	55	;	;	PUNCT
iajs-551	57	56	]	]	PUNCT
iajs-551	57	57	(	(	PUNCT
iajs-551	57	58	)	)	PUNCT
iajs-551	58	1	n	n	PRON
iajs-551	58	2	j	j	PROPN
iajs-551	58	3	n	n	CCONJ
iajs-551	58	4	j	j	PROPN
iajs-551	59	1	j	j	PROPN
iajs-551	60	1	i	i	PRON
iajs-551	61	1	i	i	PRON
iajs-551	62	1	i	i	PRON
iajs-551	62	2	j	j	NOUN
iajs-551	63	1	f	f	NOUN
iajs-551	63	2	x	x	PUNCT
iajs-551	64	1	x	x	PUNCT
iajs-551	64	2	x	x	PUNCT
iajs-551	64	3	x	x	X
iajs-551	64	4	f	f	NOUN
iajs-551	64	5	x	x	X
iajs-551	64	6	x=	x=	PUNCT
iajs-551	64	7	=	=	SYM
iajs-551	64	8	≠	≠	PROPN
iajs-551	64	9	=	=	PUNCT
iajs-551	64	10	−∑∏	−∑∏	NOUN
iajs-551	64	11	then	then	ADV
iajs-551	64	12	[	[	PUNCT
iajs-551	64	13	]	]	X
iajs-551	64	14	gzz	gzz	NOUN
iajs-551	64	15	;	;	PUNCT
iajs-551	64	16	,	,	PUNCT
iajs-551	64	17	10	10	NUM
iajs-551	64	18	stands	stand	VERB
iajs-551	64	19	for	for	ADP
iajs-551	64	20	the	the	DET
iajs-551	64	21	first	first	ADJ
iajs-551	64	22	divided	divide	VERB
iajs-551	64	23	difference	difference	NOUN
iajs-551	64	24	of	of	ADP
iajs-551	64	25	function	function	NOUN
iajs-551	64	26	g	g	NOUN
iajs-551	64	27	at	at	ADP
iajs-551	64	28	the	the	DET
iajs-551	64	29	knots	knot	NOUN
iajs-551	64	30	0z	0z	NOUN
iajs-551	64	31	and	and	CCONJ
iajs-551	64	32	1z	1z	NUM
iajs-551	64	33	,	,	PUNCT
iajs-551	64	34	and	and	CCONJ
iajs-551	64	35	[	[	PUNCT
iajs-551	64	36	]	]	X
iajs-551	64	37	gzzz	gzzz	NOUN
iajs-551	64	38	;	;	PUNCT
iajs-551	64	39	,	,	PUNCT
iajs-551	64	40	,	,	PUNCT
iajs-551	64	41	210	210	NUM
iajs-551	64	42	denotes	denote	VERB
iajs-551	64	43	the	the	DET
iajs-551	64	44	second	second	ADJ
iajs-551	64	45	divided	divide	VERB
iajs-551	64	46	difference	difference	NOUN
iajs-551	64	47	at	at	ADP
iajs-551	64	48	the	the	DET
iajs-551	64	49	knots	knot	NOUN
iajs-551	64	50	10	10	NUM
iajs-551	64	51	,	,	PUNCT
iajs-551	64	52	zz	zz	PROPN
iajs-551	64	53	and	and	CCONJ
iajs-551	64	54	2z	2z	NUM
iajs-551	64	55	.	.	PUNCT
iajs-551	65	1	the	the	DET
iajs-551	65	2	main	main	ADJ
iajs-551	65	3	result	result	NOUN
iajs-551	65	4	:	:	PUNCT
iajs-551	65	5	in	in	ADP
iajs-551	65	6	[	[	X
iajs-551	65	7	5	5	NUM
iajs-551	65	8	]	]	X
iajs-551	65	9	leviatan	leviatan	ADJ
iajs-551	65	10	and	and	CCONJ
iajs-551	65	11	shevchuk	shevchuk	NOUN
iajs-551	65	12	proved	prove	VERB
iajs-551	65	13	that	that	SCONJ
iajs-551	65	14	for	for	SCONJ
iajs-551	65	15	every	every	PRON
iajs-551	65	16	(	(	PUNCT
iajs-551	65	17	)	)	PUNCT
iajs-551	65	18	(	(	PUNCT
iajs-551	65	19	)	)	PUNCT
iajs-551	65	20	1	1	NUM
iajs-551	65	21	rf	rf	NOUN
iajs-551	65	22	y	y	NOUN
iajs-551	65	23	cϕ∈∆	cϕ∈∆	NOUN
iajs-551	65	24			PROPN
iajs-551	65	25	then	then	ADV
iajs-551	65	26	:	:	PUNCT
iajs-551	65	27	(	(	PUNCT
iajs-551	65	28	)	)	PUNCT
iajs-551	65	29	(	(	PUNCT
iajs-551	65	30	)	)	PUNCT
iajs-551	65	31	1	1	NUM
iajs-551	65	32	(	(	PUNCT
iajs-551	65	33	)	)	PUNCT
iajs-551	65	34	,	,	PUNCT
iajs-551	65	35	1	1	NUM
iajs-551	65	36	,	,	PUNCT
iajs-551	65	37	,	,	PUNCT
iajs-551	65	38	r	r	NOUN
iajs-551	65	39	n	n	PROPN
iajs-551	65	40	k	k	PROPN
iajs-551	65	41	rr	rr	PROPN
iajs-551	65	42	ce	ce	PROPN
iajs-551	65	43	f	f	PROPN
iajs-551	65	44	y	y	PROPN
iajs-551	65	45	f	f	PROPN
iajs-551	65	46	n	n	CCONJ
iajs-551	65	47	n	n	ADV
iajs-551	65	48	ϕω	ϕω	X
iajs-551	65	49			PROPN
iajs-551	65	50	≤	≤	PUNCT
iajs-551	65	51			NOUN
iajs-551	65	52			VERB
iajs-551	65	53			PRON
iajs-551	65	54			PUNCT
iajs-551	65	55	…	…	PUNCT
iajs-551	65	56	(	(	PUNCT
iajs-551	65	57	3.1	3.1	NUM
iajs-551	65	58	)	)	PUNCT
iajs-551	65	59	where	where	SCONJ
iajs-551	65	60	c	c	NOUN
iajs-551	65	61	is	be	AUX
iajs-551	65	62	a	a	DET
iajs-551	65	63	constant	constant	ADJ
iajs-551	65	64	independent	independent	NOUN
iajs-551	65	65	of	of	ADP
iajs-551	65	66	n	n	PROPN
iajs-551	65	67	and	and	CCONJ
iajs-551	65	68	f	f	PROPN
iajs-551	65	69	.	.	PUNCT
iajs-551	66	1	also	also	ADV
iajs-551	66	2	they	they	PRON
iajs-551	66	3	showed	show	VERB
iajs-551	66	4	that	that	SCONJ
iajs-551	66	5	theorem	theorem	NOUN
iajs-551	66	6	1	1	NUM
iajs-551	66	7	:	:	PUNCT
iajs-551	66	8	[	[	X
iajs-551	66	9	5	5	X
iajs-551	66	10	]	]	PUNCT
iajs-551	66	11	if	if	SCONJ
iajs-551	66	12	(	(	PUNCT
iajs-551	66	13	)	)	PUNCT
iajs-551	66	14	(	(	PUNCT
iajs-551	66	15	)	)	PUNCT
iajs-551	66	16	rrf	rrf	PROPN
iajs-551	67	1	c	c	PROPN
iajs-551	67	2	yϕ∈	yϕ∈	PROPN
iajs-551	67	3	∆	∆	ADJ
iajs-551	67	4	with	with	ADP
iajs-551	67	5	r	r	NOUN
iajs-551	67	6	>	>	X
iajs-551	67	7	2	2	NUM
iajs-551	67	8	,	,	PUNCT
iajs-551	67	9	then	then	ADV
iajs-551	67	10	(	(	PUNCT
iajs-551	67	11	)	)	PUNCT
iajs-551	67	12	(	(	PUNCT
iajs-551	67	13	)	)	PUNCT
iajs-551	67	14	(	(	PUNCT
iajs-551	67	15	)	)	PUNCT
iajs-551	67	16	(	(	PUNCT
iajs-551	67	17	1	1	NUM
iajs-551	67	18	)	)	PUNCT
iajs-551	67	19	,	,	PUNCT
iajs-551	67	20	,	,	PUNCT
iajs-551	67	21	,	,	PUNCT
iajs-551	67	22	1	1	NUM
iajs-551	67	23	,	,	PUNCT
iajs-551	67	24	,	,	PUNCT
iajs-551	67	25	,	,	PUNCT
iajs-551	67	26	r	r	NOUN
iajs-551	67	27	n	n	PROPN
iajs-551	67	28	k	k	PROPN
iajs-551	67	29	rr	rr	PROPN
iajs-551	67	30	c	c	PROPN
iajs-551	68	1	k	k	NOUN
iajs-551	68	2	r	r	NOUN
iajs-551	68	3	y	y	PROPN
iajs-551	68	4	e	e	PROPN
iajs-551	68	5	f	f	PROPN
iajs-551	68	6	y	y	PROPN
iajs-551	68	7	f	f	PROPN
iajs-551	68	8	n	n	CCONJ
iajs-551	68	9	k	k	NOUN
iajs-551	68	10	r	r	NOUN
iajs-551	68	11	n	n	NOUN
iajs-551	68	12	n	n	ADJ
iajs-551	68	13	ϕω	ϕω	X
iajs-551	68	14			PROPN
iajs-551	68	15	≤	≤	NOUN
iajs-551	68	16	≥	≥	NOUN
iajs-551	69	1	+	+	NOUN
iajs-551	69	2			NOUN
iajs-551	69	3			VERB
iajs-551	69	4			PRON
iajs-551	69	5			PUNCT
iajs-551	69	6	…	…	PUNCT
iajs-551	69	7	(	(	PUNCT
iajs-551	69	8	3.2	3.2	NUM
iajs-551	69	9	)	)	PUNCT
iajs-551	69	10	where	where	SCONJ
iajs-551	69	11	,	,	PUNCT
iajs-551	69	12	rc	rc	PROPN
iajs-551	69	13	r	r	PROPN
iajs-551	69	14	nϕ	nϕ	PROPN
iajs-551	69	15	∈	∈	PROPN
iajs-551	69	16	is	be	AUX
iajs-551	69	17	the	the	DET
iajs-551	69	18	space	space	NOUN
iajs-551	69	19	of	of	ADP
iajs-551	69	20	functions	function	NOUN
iajs-551	69	21	(	(	PUNCT
iajs-551	69	22	)	)	PUNCT
iajs-551	69	23	(	(	PUNCT
iajs-551	69	24	)	)	PUNCT
iajs-551	69	25	,	,	PUNCT
iajs-551	69	26	0,1r	0,1r	NUM
iajs-551	69	27	rf	rf	PROPN
iajs-551	69	28	f	f	PROPN
iajs-551	69	29	c∈	c∈	NOUN
iajs-551	69	30	for	for	ADP
iajs-551	69	31	which	which	PRON
iajs-551	69	32	(	(	PUNCT
iajs-551	69	33	)	)	PUNCT
iajs-551	69	34	(	(	PUNCT
iajs-551	69	35	)	)	PUNCT
iajs-551	69	36	1	1	NUM
iajs-551	69	37	2	2	NUM
iajs-551	69	38	lim	lim	NOUN
iajs-551	69	39	(	(	PUNCT
iajs-551	69	40	)	)	PUNCT
iajs-551	69	41	0rr	0rr	X
iajs-551	70	1	x	x	PUNCT
iajs-551	70	2	x	x	X
iajs-551	70	3	f	f	PROPN
iajs-551	70	4	xϕ	xϕ	PUNCT
iajs-551	70	5	→	→	SYM
iajs-551	70	6	=	=	X
iajs-551	70	7	and	and	CCONJ
iajs-551	70	8	[	[	PUNCT
iajs-551	70	9	]	]	X
iajs-551	70	10	0	0	NUM
iajs-551	70	11	0,1c	0,1c	NOUN
iajs-551	70	12	cϕ	cϕ	ADP
iajs-551	70	13	=	=	X
iajs-551	70	14	.	.	PUNCT
iajs-551	71	1	now	now	ADV
iajs-551	71	2	we	we	PRON
iajs-551	71	3	prove	prove	VERB
iajs-551	71	4	the	the	DET
iajs-551	71	5	following	following	NOUN
iajs-551	71	6	theorem	theorem	NOUN
iajs-551	71	7	when	when	SCONJ
iajs-551	71	8	r	r	NOUN
iajs-551	71	9	≤	≤	ADV
iajs-551	71	10	2	2	NUM
iajs-551	71	11	by	by	ADP
iajs-551	71	12	c(s	c(	NOUN
iajs-551	71	13	)	)	PUNCT
iajs-551	71	14	denote	denote	VERB
iajs-551	71	15	the	the	DET
iajs-551	71	16	different	different	ADJ
iajs-551	71	17	constants	constant	NOUN
iajs-551	71	18	which	which	PRON
iajs-551	71	19	are	be	AUX
iajs-551	71	20	constants	constant	NOUN
iajs-551	71	21	depend	depend	VERB
iajs-551	71	22	only	only	ADV
iajs-551	71	23	on	on	ADP
iajs-551	71	24	s	s	NOUN
iajs-551	71	25	,	,	PUNCT
iajs-551	71	26	while	while	SCONJ
iajs-551	71	27	n(y	n(y	PROPN
iajs-551	71	28	)	)	PUNCT
iajs-551	71	29	the	the	DET
iajs-551	71	30	constants	constant	NOUN
iajs-551	71	31	which	which	PRON
iajs-551	71	32	depend	depend	VERB
iajs-551	71	33	on	on	ADP
iajs-551	71	34	y.	y.	PROPN
iajs-551	71	35	theorem	theorem	VERB
iajs-551	71	36	2	2	NUM
iajs-551	71	37	:	:	PUNCT
iajs-551	71	38	[	[	X
iajs-551	71	39	7	7	X
iajs-551	71	40	]	]	X
iajs-551	71	41	if	if	SCONJ
iajs-551	71	42	1	1	NUM
iajs-551	71	43	(	(	PUNCT
iajs-551	71	44	1	1	NUM
iajs-551	71	45	)	)	PUNCT
iajs-551	71	46	,	,	PUNCT
iajs-551	71	47	,	,	PUNCT
iajs-551	71	48	(	(	PUNCT
iajs-551	71	49	)	)	PUNCT
iajs-551	71	50	pf	pf	PROPN
iajs-551	71	51	l	l	NOUN
iajs-551	71	52	yα	yα	NOUN
iajs-551	71	53	ϕ∈	ϕ∈	NOUN
iajs-551	71	54	∆	∆	VERB
iajs-551	71	55	then	then	ADV
iajs-551	71	56	(	(	PUNCT
iajs-551	71	57	)	)	PUNCT
iajs-551	71	58	(	(	PUNCT
iajs-551	71	59	)	)	PUNCT
iajs-551	71	60	1	1	NUM
iajs-551	71	61	2,1	2,1	NUM
iajs-551	71	62	,	,	PUNCT
iajs-551	71	63	,	,	PUNCT
iajs-551	71	64	1	1	NUM
iajs-551	71	65	,	,	PUNCT
iajs-551	71	66	,	,	PUNCT
iajs-551	71	67	n	n	PROPN
iajs-551	71	68	p	p	PROPN
iajs-551	71	69	p	p	X
iajs-551	71	70	ce	ce	PROPN
iajs-551	72	1	f	f	PROPN
iajs-551	72	2	y	y	PROPN
iajs-551	72	3	f	f	PROPN
iajs-551	72	4	n	n	CCONJ
iajs-551	72	5	n	n	PROPN
iajs-551	72	6	ϕ	ϕ	PROPN
iajs-551	72	7	α	α	PROPN
iajs-551	72	8	α	α	PROPN
iajs-551	72	9	ω	ω	PROPN
iajs-551	72	10			PROPN
iajs-551	72	11	′≤	′≤	NOUN
iajs-551	72	12			NOUN
iajs-551	72	13			VERB
iajs-551	72	14			PRON
iajs-551	72	15			NOUN
iajs-551	72	16	,	,	PUNCT
iajs-551	72	17	n	n	CCONJ
iajs-551	72	18	≥	≥	NOUN
iajs-551	72	19	n(y	n(y	NUM
iajs-551	72	20	)	)	PUNCT
iajs-551	72	21	…	…	PUNCT
iajs-551	72	22	(	(	PUNCT
iajs-551	72	23	3.3	3.3	NUM
iajs-551	72	24	)	)	PUNCT
iajs-551	72	25	an	an	DET
iajs-551	72	26	immediate	immediate	ADJ
iajs-551	72	27	consequence	consequence	NOUN
iajs-551	72	28	of	of	ADP
iajs-551	72	29	this	this	DET
iajs-551	72	30	theorem	theorem	NOUN
iajs-551	72	31	is	be	AUX
iajs-551	72	32	that	that	SCONJ
iajs-551	72	33	:	:	PUNCT
iajs-551	72	34	corollary	corollary	ADJ
iajs-551	72	35	1	1	NUM
iajs-551	72	36	:	:	PUNCT
iajs-551	72	37	[	[	X
iajs-551	72	38	7	7	X
iajs-551	72	39	]	]	X
iajs-551	72	40	if	if	SCONJ
iajs-551	72	41	2	2	NUM
iajs-551	72	42	(	(	PUNCT
iajs-551	72	43	1	1	NUM
iajs-551	72	44	)	)	PUNCT
iajs-551	72	45	,	,	PUNCT
iajs-551	72	46	,	,	PUNCT
iajs-551	72	47	(	(	PUNCT
iajs-551	72	48	)	)	PUNCT
iajs-551	72	49	pf	pf	PROPN
iajs-551	72	50	l	l	NOUN
iajs-551	72	51	yα	yα	NOUN
iajs-551	72	52	ϕ∈	ϕ∈	NOUN
iajs-551	72	53	∆	∆	ADV
iajs-551	72	54	,	,	PUNCT
iajs-551	72	55	then	then	ADV
iajs-551	72	56	(	(	PUNCT
iajs-551	72	57	)	)	PUNCT
iajs-551	72	58	(	(	PUNCT
iajs-551	72	59	)	)	PUNCT
iajs-551	72	60	1	1	NUM
iajs-551	72	61	1,22	1,22	NUM
iajs-551	72	62	,	,	PUNCT
iajs-551	72	63	,	,	PUNCT
iajs-551	72	64	1	1	NUM
iajs-551	72	65	,	,	PUNCT
iajs-551	72	66	,	,	PUNCT
iajs-551	72	67	n	n	PROPN
iajs-551	72	68	p	p	PROPN
iajs-551	72	69	p	p	X
iajs-551	72	70	ce	ce	PROPN
iajs-551	73	1	f	f	PROPN
iajs-551	73	2	y	y	PROPN
iajs-551	73	3	f	f	PROPN
iajs-551	73	4	n	n	CCONJ
iajs-551	73	5	n	n	PROPN
iajs-551	73	6	ϕ	ϕ	PROPN
iajs-551	73	7	α	α	PROPN
iajs-551	73	8	α	α	PROPN
iajs-551	73	9	ω	ω	PROPN
iajs-551	73	10			PROPN
iajs-551	73	11	′≤	′≤	NOUN
iajs-551	73	12			NOUN
iajs-551	73	13			VERB
iajs-551	73	14			PRON
iajs-551	73	15			NOUN
iajs-551	73	16	,	,	PUNCT
iajs-551	73	17	n	n	CCONJ
iajs-551	73	18	≥	≥	NOUN
iajs-551	73	19	n(y	n(y	NUM
iajs-551	73	20	)	)	PUNCT
iajs-551	73	21	…	…	PUNCT
iajs-551	73	22	(	(	PUNCT
iajs-551	73	23	3.4	3.4	NUM
iajs-551	73	24	)	)	PUNCT
iajs-551	73	25	mathematics	mathematic	NOUN
iajs-551	73	26	336	336	NUM
iajs-551	73	27	مجلة	مجلة	VERB
iajs-551	73	28	إبن	إبن	VERB
iajs-551	73	29	الهيثم	الهيثم	ADJ
iajs-551	73	30	للعلوم	للعلوم	NOUN
iajs-551	73	31	الصرفة	الصرفة	NOUN
iajs-551	73	32	و	و	PRON
iajs-551	73	33	التطبيقية	التطبيقية	ADJ
iajs-551	73	34	2012	2012	NUM
iajs-551	73	35	السنة	السنة	NOUN
iajs-551	74	1	25	25	NUM
iajs-551	74	2	المجلد	المجلد	NOUN
iajs-551	74	3	3	3	NUM
iajs-551	74	4	العدد	العدد	PROPN
iajs-551	74	5	ibn	ibn	PROPN
iajs-551	74	6	al	al	PROPN
iajs-551	74	7	-	-	PUNCT
iajs-551	74	8	haitham	haitham	PROPN
iajs-551	74	9	journal	journal	PROPN
iajs-551	74	10	for	for	ADP
iajs-551	74	11	pure	pure	ADJ
iajs-551	74	12	and	and	CCONJ
iajs-551	74	13	applied	apply	VERB
iajs-551	74	14	science	science	NOUN
iajs-551	74	15	no	no	NOUN
iajs-551	74	16	.	.	NOUN
iajs-551	74	17	3	3	NUM
iajs-551	74	18	vol	vol	NOUN
iajs-551	74	19	.	.	PUNCT
iajs-551	74	20	25	25	NUM
iajs-551	74	21	year	year	NOUN
iajs-551	74	22	2012	2012	NUM
iajs-551	74	23	remark	remark	NOUN
iajs-551	74	24	:	:	PUNCT
iajs-551	74	25	it	it	PRON
iajs-551	74	26	should	should	AUX
iajs-551	74	27	be	be	AUX
iajs-551	74	28	noted	note	VERB
iajs-551	74	29	that	that	SCONJ
iajs-551	74	30	in	in	ADP
iajs-551	74	31	the	the	DET
iajs-551	74	32	case	case	NOUN
iajs-551	74	33	r=1	r=1	NOUN
iajs-551	74	34	,	,	PUNCT
iajs-551	74	35	k=2	k=2	PROPN
iajs-551	74	36	and	and	CCONJ
iajs-551	74	37	r=2	r=2	PROPN
iajs-551	74	38	,	,	PUNCT
iajs-551	74	39	k=1	k=1	PROPN
iajs-551	74	40	the	the	DET
iajs-551	74	41	estimates	estimate	NOUN
iajs-551	74	42	of	of	ADP
iajs-551	74	43	form	form	NOUN
iajs-551	74	44	(	(	PUNCT
iajs-551	74	45	3.3	3.3	NUM
iajs-551	74	46	)	)	PUNCT
iajs-551	74	47	and	and	CCONJ
iajs-551	74	48	(	(	PUNCT
iajs-551	74	49	3.4	3.4	NUM
iajs-551	74	50	)	)	PUNCT
iajs-551	74	51	in	in	ADP
iajs-551	74	52	the	the	DET
iajs-551	74	53	case	case	NOUN
iajs-551	74	54	1	1	NUM
iajs-551	74	55	rc	rc	PROPN
iajs-551	74	56	(	(	PUNCT
iajs-551	74	57	1	1	NUM
iajs-551	74	58	)	)	PUNCT
iajs-551	74	59	(	(	PUNCT
iajs-551	74	60	)	)	PUNCT
iajs-551	74	61	y∆	y∆	PROPN
iajs-551	74	62	.	.	PUNCT
iajs-551	75	1	corollary	corollary	ADJ
iajs-551	75	2	2	2	NUM
iajs-551	75	3	:	:	PUNCT
iajs-551	75	4	[	[	X
iajs-551	75	5	7	7	X
iajs-551	75	6	]	]	PUNCT
iajs-551	75	7	for	for	ADP
iajs-551	75	8	each	each	DET
iajs-551	75	9	,	,	PUNCT
iajs-551	75	10	sy	sy	PROPN
iajs-551	75	11	y∈	y∈	NOUN
iajs-551	75	12	there	there	PRON
iajs-551	75	13	is	be	VERB
iajs-551	75	14	a	a	DET
iajs-551	75	15	function	function	NOUN
iajs-551	75	16	(	(	PUNCT
iajs-551	75	17	)	)	PUNCT
iajs-551	75	18	(	(	PUNCT
iajs-551	75	19	)	)	PUNCT
iajs-551	75	20	yf	yf	NOUN
iajs-551	75	21	1∆∈	1∆∈	NOUN
iajs-551	75	22	with	with	ADP
iajs-551	75	23	(	(	PUNCT
iajs-551	75	24	)	)	PUNCT
iajs-551	75	25	2	2	NUM
iajs-551	75	26	,	,	PUNCT
iajs-551	75	27	1	1	NUM
iajs-551	75	28	,	,	PUNCT
iajs-551	75	29	3n	3n	NUM
iajs-551	76	1	p	p	X
iajs-551	76	2	e	e	PROPN
iajs-551	76	3	f	f	PROPN
iajs-551	76	4	n	n	ADV
iajs-551	76	5	nα	nα	VERB
iajs-551	76	6	≤	≤	NUM
iajs-551	76	7	≥	≥	NOUN
iajs-551	76	8	(	(	PUNCT
iajs-551	76	9	)	)	PUNCT
iajs-551	76	10	(	(	PUNCT
iajs-551	76	11	)	)	SYM
iajs-551	76	12	1	1	NUM
iajs-551	76	13	2,n	2,n	NUM
iajs-551	76	14	ce	ce	PROPN
iajs-551	76	15	f	f	PROPN
iajs-551	76	16	y	y	PROPN
iajs-551	76	17	n	n	ADV
iajs-551	76	18	≤	≤	NUM
iajs-551	76	19	,	,	PUNCT
iajs-551	76	20	n	n	PRON
iajs-551	76	21	≥	≥	NOUN
iajs-551	76	22	n(y	n(y	NUM
iajs-551	76	23	)	)	PUNCT
iajs-551	76	24	…	…	PUNCT
iajs-551	76	25	(	(	PUNCT
iajs-551	76	26	3.5	3.5	NUM
iajs-551	76	27	)	)	PUNCT
iajs-551	76	28	where	where	SCONJ
iajs-551	76	29	(	(	PUNCT
iajs-551	76	30	)	)	PUNCT
iajs-551	76	31	,	,	PUNCT
iajs-551	76	32	n	n	NOUN
iajs-551	76	33	p	p	NOUN
iajs-551	76	34	e	e	X
iajs-551	76	35	f	f	PROPN
iajs-551	76	36	α	α	PROPN
iajs-551	76	37	is	be	AUX
iajs-551	76	38	the	the	DET
iajs-551	76	39	degree	degree	NOUN
iajs-551	76	40	of	of	ADP
iajs-551	76	41	unconstrained	unconstrained	ADJ
iajs-551	76	42	approximation	approximation	NOUN
iajs-551	76	43	.	.	PUNCT
iajs-551	77	1	now	now	ADV
iajs-551	77	2	,	,	PUNCT
iajs-551	77	3	let	let	VERB
iajs-551	77	4	[	[	PUNCT
iajs-551	77	5	]	]	X
iajs-551	77	6	1,0	1,0	NUM
iajs-551	77	7	=	=	SYM
iajs-551	77	8	i	i	PRON
iajs-551	77	9	and	and	CCONJ
iajs-551	77	10	put	put	VERB
iajs-551	77	11	.,	.,	NOUN
iajs-551	77	12	...	...	PUNCT
iajs-551	77	13	,1,0,11	,1,0,11	PUNCT
iajs-551	77	14	nj	nj	PROPN
iajs-551	78	1	n	n	PROPN
iajs-551	78	2	jcos	jcos	PROPN
iajs-551	78	3	n	n	PROPN
iajs-551	78	4	xj	xj	PROPN
iajs-551	78	5	=	=	SYM
iajs-551	78	6			PROPN
iajs-551	78	7			NUM
iajs-551	78	8			ADJ
iajs-551	78	9			NOUN
iajs-551	78	10	∏	∏	PROPN
iajs-551	78	11	−=	−=	NOUN
iajs-551	78	12	we	we	PRON
iajs-551	78	13	denote	denote	VERB
iajs-551	78	14	by	by	ADP
iajs-551	78	15	ns	ns	NUM
iajs-551	78	16	the	the	DET
iajs-551	78	17	set	set	NOUN
iajs-551	78	18	of	of	ADP
iajs-551	78	19	continuous	continuous	ADJ
iajs-551	78	20	piecewise	piecewise	NOUN
iajs-551	78	21	polynomials	polynomial	NOUN
iajs-551	78	22	in	in	ADP
iajs-551	78	23	[	[	PUNCT
iajs-551	78	24	]	]	X
iajs-551	78	25	,	,	PUNCT
iajs-551	78	26	0,1pl	0,1pl	NUM
iajs-551	78	27	α	α	NOUN
iajs-551	78	28	.	.	PUNCT
iajs-551	79	1	we	we	PRON
iajs-551	79	2	put	put	VERB
iajs-551	79	3	[	[	PUNCT
iajs-551	79	4	]	]	X
iajs-551	79	5	00	00	NUM
iajs-551	79	6	,	,	PUNCT
iajs-551	79	7	0	0	NUM
iajs-551	79	8	xi	xi	X
iajs-551	80	1	=	=	PUNCT
iajs-551	81	1	and	and	CCONJ
iajs-551	81	2	[	[	PUNCT
iajs-551	81	3	]	]	X
iajs-551	81	4	nnn	nnn	NOUN
iajs-551	81	5	xxi	xxi	PROPN
iajs-551	81	6	,	,	PUNCT
iajs-551	81	7	1−=	1−=	PROPN
iajs-551	81	8	let	let	VERB
iajs-551	81	9	(	(	PUNCT
iajs-551	81	10	)	)	PUNCT
iajs-551	81	11	(	(	PUNCT
iajs-551	81	12	)	)	PUNCT
iajs-551	81	13	(	(	PUNCT
iajs-551	81	14	)	)	PUNCT
iajs-551	81	15	[	[	PUNCT
iajs-551	81	16	]	]	SYM
iajs-551	81	17	1	1	NUM
iajs-551	81	18	1	1	NUM
iajs-551	81	19	1	1	NUM
iajs-551	81	20	1	1	NUM
iajs-551	81	21	1	1	NUM
iajs-551	81	22	,	,	PUNCT
iajs-551	81	23	2	2	NUM
iajs-551	81	24	,	,	PUNCT
iajs-551	81	25	l	l	NOUN
iajs-551	81	26	x	x	X
iajs-551	82	1	f	f	PUNCT
iajs-551	82	2	x	x	PUNCT
iajs-551	82	3	x	x	PUNCT
iajs-551	82	4	x	x	PUNCT
iajs-551	82	5	x	x	X
iajs-551	82	6	x	x	X
iajs-551	82	7	f′	f′	PROPN
iajs-551	82	8	′=	′=	PROPN
iajs-551	82	9	+	+	CCONJ
iajs-551	82	10	−	−	PROPN
iajs-551	82	11	be	be	AUX
iajs-551	82	12	the	the	DET
iajs-551	82	13	linear	linear	ADJ
iajs-551	82	14	polynomials	polynomial	NOUN
iajs-551	82	15	which	which	PRON
iajs-551	82	16	interpolates	interpolate	VERB
iajs-551	82	17	f	f	NOUN
iajs-551	82	18	′	′	NUM
iajs-551	82	19	at	at	ADP
iajs-551	82	20	1x	1x	NUM
iajs-551	82	21	and	and	CCONJ
iajs-551	82	22	12x	12x	PROPN
iajs-551	82	23	.	.	PUNCT
iajs-551	83	1	we	we	PRON
iajs-551	83	2	set	set	VERB
iajs-551	83	3	(	(	PUNCT
iajs-551	83	4	)	)	PUNCT
iajs-551	83	5	(	(	PUNCT
iajs-551	83	6	)	)	PUNCT
iajs-551	83	7	(	(	PUNCT
iajs-551	83	8	)	)	PUNCT
iajs-551	83	9	(	(	PUNCT
iajs-551	83	10	)	)	SYM
iajs-551	83	11	1	1	NUM
iajs-551	83	12	1	1	NUM
iajs-551	83	13	1	1	NUM
iajs-551	83	14	1	1	NUM
iajs-551	83	15	11	11	NUM
iajs-551	83	16	,	,	PUNCT
iajs-551	83	17	;	;	PUNCT
iajs-551	83	18	n	n	CCONJ
iajs-551	83	19	n	n	CCONJ
iajs-551	83	20	n	n	CCONJ
iajs-551	83	21	n	n	CCONJ
iajs-551	83	22	n	n	CCONJ
iajs-551	83	23	nl	nl	NOUN
iajs-551	83	24	x	x	PROPN
iajs-551	83	25	f	f	NOUN
iajs-551	83	26	x	x	PUNCT
iajs-551	83	27	x	x	PUNCT
iajs-551	83	28	x	x	PUNCT
iajs-551	83	29	x	x	PUNCT
iajs-551	83	30	x	x	PUNCT
iajs-551	83	31	x	x	PUNCT
iajs-551	83	32	f−	f−	NOUN
iajs-551	83	33	−	−	PROPN
iajs-551	83	34	−	−	PROPN
iajs-551	83	35	−	−	PROPN
iajs-551	83	36	−′	−′	PROPN
iajs-551	83	37	′=	′=	PROPN
iajs-551	83	38	+	+	CCONJ
iajs-551	83	39	−	−	PROPN
iajs-551	83	40	−	−	NOUN
iajs-551	83	41	−	−	NOUN
iajs-551	83	42			NOUN
iajs-551	83	43			PROPN
iajs-551	83	44	lemma	lemma	PROPN
iajs-551	83	45	1	1	NUM
iajs-551	83	46	:	:	PUNCT
iajs-551	84	1	[	[	X
iajs-551	84	2	4	4	NUM
iajs-551	84	3	,	,	PUNCT
iajs-551	84	4	lemma	lemma	PROPN
iajs-551	84	5	2	2	NUM
iajs-551	84	6	]	]	PUNCT
iajs-551	84	7	if	if	SCONJ
iajs-551	84	8	(	(	PUNCT
iajs-551	84	9	1)1	1)1	NUM
iajs-551	84	10	,	,	PUNCT
iajs-551	84	11	(	(	PUNCT
iajs-551	84	12	)	)	PUNCT
iajs-551	84	13	p	p	NOUN
iajs-551	84	14	yf	yf	NOUN
iajs-551	84	15	l	l	NOUN
iajs-551	84	16	ϕ∈	ϕ∈	NOUN
iajs-551	84	17	∆	∆	ADV
iajs-551	84	18	then	then	ADV
iajs-551	84	19	there	there	PRON
iajs-551	84	20	is	be	VERB
iajs-551	84	21	a	a	DET
iajs-551	84	22	continuous	continuous	ADJ
iajs-551	84	23	piecewise	piecewise	NOUN
iajs-551	84	24	polynomials	polynomial	NOUN
iajs-551	84	25	n	n	PRON
iajs-551	84	26	ns	ns	VERB
iajs-551	84	27	s∈	s∈	NOUN
iajs-551	84	28	such	such	ADJ
iajs-551	84	29	that	that	SCONJ
iajs-551	84	30	(	(	PUNCT
iajs-551	84	31	)	)	PUNCT
iajs-551	84	32	(	(	PUNCT
iajs-551	84	33	)	)	PUNCT
iajs-551	84	34	2,1	2,1	NUM
iajs-551	84	35	1	1	NUM
iajs-551	84	36	1	1	NUM
iajs-551	84	37	1	1	NUM
iajs-551	84	38	,	,	PUNCT
iajs-551	84	39	0	0	NUM
iajs-551	84	40	,	,	PUNCT
iajs-551	84	41	,	,	PUNCT
iajs-551	84	42	(	(	PUNCT
iajs-551	84	43	)	)	PUNCT
iajs-551	84	44	(	(	PUNCT
iajs-551	84	45	)	)	PUNCT
iajs-551	84	46	,	,	PUNCT
iajs-551	84	47	ϕω	ϕω	PROPN
iajs-551	84	48			PROPN
iajs-551	84	49			PROPN
iajs-551	84	50			NOUN
iajs-551	84	51			NOUN
iajs-551	84	52			NOUN
iajs-551	84	53			NOUN
iajs-551	84	54			PRON
iajs-551	84	55			PUNCT
iajs-551	85	1			PROPN
iajs-551	85	2			PROPN
iajs-551	85	3			PROPN
iajs-551	85	4			PROPN
iajs-551	85	5			PROPN
iajs-551	85	6			PROPN
iajs-551	85	7	−	−	X
iajs-551	85	8			NOUN
iajs-551	85	9			PROPN
iajs-551	85	10			PROPN
iajs-551	85	11			PROPN
iajs-551	85	12			PROPN
iajs-551	85	13	′≤	′≤	NOUN
iajs-551	85	14	′∏	′∏	AUX
iajs-551	85	15	≥	≥	NOUN
iajs-551	85	16	∈	∈	PROPN
iajs-551	86	1	′	′	NOUN
iajs-551	87	1	−	−	NOUN
iajs-551	87	2	=	=	SYM
iajs-551	87	3	∈	∈	PROPN
iajs-551	87	4			NOUN
iajs-551	87	5			PROPN
iajs-551	87	6			NOUN
iajs-551	87	7	n	n	CCONJ
iajs-551	87	8	p	p	PROPN
iajs-551	87	9	p	p	PROPN
iajs-551	87	10	n	n	CCONJ
iajs-551	87	11	n	n	CCONJ
iajs-551	87	12	n	n	CCONJ
iajs-551	87	13	n	n	CCONJ
iajs-551	87	14	n	n	NOUN
iajs-551	87	15	c	c	NOUN
iajs-551	87	16	fn	fn	NOUN
iajs-551	87	17	n	n	ADV
iajs-551	87	18	x	x	SYM
iajs-551	87	19	s	s	NOUN
iajs-551	87	20	x	x	X
iajs-551	87	21	x	x	PUNCT
iajs-551	87	22	x	x	PUNCT
iajs-551	87	23	x	x	X
iajs-551	87	24	s	s	X
iajs-551	87	25	f	f	X
iajs-551	87	26	s	s	NOUN
iajs-551	87	27	x	x	NOUN
iajs-551	87	28	l	l	NOUN
iajs-551	87	29	x	x	PUNCT
iajs-551	87	30	x	x	SYM
iajs-551	87	31	i	i	PRON
iajs-551	87	32	…	…	PUNCT
iajs-551	87	33	(	(	PUNCT
iajs-551	87	34	3.6	3.6	NUM
iajs-551	87	35	)	)	PUNCT
iajs-551	87	36	lemma	lemma	PROPN
iajs-551	87	37	2	2	NUM
iajs-551	87	38	if	if	SCONJ
iajs-551	87	39	(	(	PUNCT
iajs-551	87	40	1)1	1)1	NUM
iajs-551	87	41	,	,	PUNCT
iajs-551	87	42	,	,	PUNCT
iajs-551	87	43	(	(	PUNCT
iajs-551	87	44	)	)	PUNCT
iajs-551	87	45	p	p	NOUN
iajs-551	87	46	yf	yf	NOUN
iajs-551	87	47	l	l	NOUN
iajs-551	87	48	α	α	PROPN
iajs-551	88	1	ϕ∈	ϕ∈	NOUN
iajs-551	88	2	∆	∆	ADV
iajs-551	88	3	then	then	ADV
iajs-551	88	4	there	there	PRON
iajs-551	88	5	is	be	VERB
iajs-551	88	6	a	a	DET
iajs-551	88	7	continuous	continuous	ADJ
iajs-551	88	8	piecewise	piecewise	NOUN
iajs-551	88	9	polynomials	polynomial	NOUN
iajs-551	88	10	ns	ns	ADJ
iajs-551	88	11	sn∈	sn∈	NOUN
iajs-551	89	1	such	such	ADJ
iajs-551	89	2	that	that	DET
iajs-551	89	3	mathematics	mathematic	NOUN
iajs-551	89	4	337	337	NUM
iajs-551	89	5	مجلة	مجلة	NOUN
iajs-551	89	6	إبن	إبن	VERB
iajs-551	89	7	الهيثم	الهيثم	ADJ
iajs-551	89	8	للعلوم	للعلوم	NOUN
iajs-551	89	9	الصرفة	الصرفة	NOUN
iajs-551	90	1	و	و	PRON
iajs-551	90	2	التطبيقية	التطبيقية	ADJ
iajs-551	90	3	2012	2012	NUM
iajs-551	90	4	السنة	السنة	NOUN
iajs-551	90	5	25	25	NUM
iajs-551	90	6	المجلد	المجلد	NOUN
iajs-551	90	7	3	3	NUM
iajs-551	90	8	العدد	العدد	PROPN
iajs-551	90	9	ibn	ibn	PROPN
iajs-551	90	10	al	al	PROPN
iajs-551	90	11	-	-	PUNCT
iajs-551	90	12	haitham	haitham	PROPN
iajs-551	90	13	journal	journal	PROPN
iajs-551	90	14	for	for	ADP
iajs-551	90	15	pure	pure	ADJ
iajs-551	90	16	and	and	CCONJ
iajs-551	90	17	applied	apply	VERB
iajs-551	90	18	science	science	NOUN
iajs-551	90	19	no	no	NOUN
iajs-551	90	20	.	.	NOUN
iajs-551	90	21	3	3	NUM
iajs-551	90	22	vol	vol	NOUN
iajs-551	90	23	.	.	PUNCT
iajs-551	91	1	25	25	NUM
iajs-551	91	2	year	year	NOUN
iajs-551	91	3	2012	2012	NUM
iajs-551	91	4	2,1	2,1	NUM
iajs-551	91	5	,	,	PUNCT
iajs-551	91	6	,	,	PUNCT
iajs-551	91	7	1	1	NUM
iajs-551	91	8	1	1	NUM
iajs-551	91	9	(	(	PUNCT
iajs-551	91	10	,	,	PUNCT
iajs-551	91	11	(	(	PUNCT
iajs-551	91	12	)	)	PUNCT
iajs-551	91	13	0	0	NUM
iajs-551	91	14	,	,	PUNCT
iajs-551	91	15	[	[	PUNCT
iajs-551	91	16	1	1	NUM
iajs-551	91	17	)	)	PUNCT
iajs-551	91	18	,	,	PUNCT
iajs-551	91	19	]	]	PUNCT
iajs-551	91	20	(	(	PUNCT
iajs-551	91	21	)	)	PUNCT
iajs-551	91	22	(	(	PUNCT
iajs-551	91	23	)	)	PUNCT
iajs-551	91	24	,	,	PUNCT
iajs-551	91	25	ϕ	ϕ	X
iajs-551	91	26	αα	αα	PROPN
iajs-551	91	27	ω	ω	PROPN
iajs-551	91	28			PROPN
iajs-551	91	29			PROPN
iajs-551	91	30			PROPN
iajs-551	91	31			PROPN
iajs-551	91	32			PROPN
iajs-551	91	33			PROPN
iajs-551	91	34	−	−	NUM
iajs-551	91	35			X
iajs-551	91	36			PROPN
iajs-551	91	37			PROPN
iajs-551	91	38			PROPN
iajs-551	91	39			PROPN
iajs-551	91	40			PROPN
iajs-551	91	41	′≤	′≤	NOUN
iajs-551	91	42	′∏	′∏	AUX
iajs-551	91	43	≥	≥	NOUN
iajs-551	91	44	∈	∈	PROPN
iajs-551	92	1	′	′	NOUN
iajs-551	93	1	−	−	NOUN
iajs-551	93	2	=	=	SYM
iajs-551	93	3	∈	∈	PROPN
iajs-551	93	4			NOUN
iajs-551	93	5			PROPN
iajs-551	93	6			PROPN
iajs-551	93	7	n	n	CCONJ
iajs-551	93	8	pp	pp	CCONJ
iajs-551	93	9	n	n	CCONJ
iajs-551	93	10	n	n	CCONJ
iajs-551	93	11	n	n	CCONJ
iajs-551	93	12	n	n	CCONJ
iajs-551	93	13	n	n	NOUN
iajs-551	93	14	c	c	NOUN
iajs-551	93	15	fn	fn	NOUN
iajs-551	93	16	x	x	X
iajs-551	93	17	s	s	NOUN
iajs-551	93	18	x	x	X
iajs-551	93	19	x	x	X
iajs-551	93	20	s	s	PRON
iajs-551	93	21	f	f	X
iajs-551	93	22	s	s	PART
iajs-551	93	23	n	n	NOUN
iajs-551	93	24	x	x	NOUN
iajs-551	93	25	x	x	PUNCT
iajs-551	94	1	l	l	NOUN
iajs-551	94	2	x	x	PUNCT
iajs-551	94	3	x	x	SYM
iajs-551	94	4	i	i	PRON
iajs-551	94	5	…	…	PUNCT
iajs-551	94	6	(	(	PUNCT
iajs-551	94	7	3.7	3.7	NUM
iajs-551	94	8	)	)	PUNCT
iajs-551	94	9	proof	proof	NOUN
iajs-551	94	10	of	of	ADP
iajs-551	94	11	lemma	lemma	PROPN
iajs-551	94	12	2	2	NUM
iajs-551	94	13	0	0	NUM
iajs-551	94	14	1	1	NUM
iajs-551	94	15	11	11	NUM
iajs-551	94	16	1	1	NUM
iajs-551	94	17	,	,	PUNCT
iajs-551	94	18	0	0	NUM
iajs-551	95	1	ppp	ppp	NOUN
iajs-551	95	2	p	p	NOUN
iajs-551	95	3	x	x	PROPN
iajs-551	95	4	xx	xx	NUM
iajs-551	96	1	np	np	INTJ
iajs-551	96	2	f	f	PROPN
iajs-551	96	3	s	s	PROPN
iajs-551	96	4	f	f	PROPN
iajs-551	96	5	s	s	X
iajs-551	96	6	e	e	NOUN
iajs-551	96	7	dxn	dxn	PROPN
iajs-551	96	8	n	n	NUM
iajs-551	96	9	fe	fe	X
iajs-551	96	10	s	s	X
iajs-551	96	11	e	e	X
iajs-551	96	12	dxα	dxα	NOUN
iajs-551	96	13	αα	αα	PROPN
iajs-551	96	14	α	α	PROPN
iajs-551	96	15			PROPN
iajs-551	96	16			PUNCT
iajs-551	97	1	−	−	PROPN
iajs-551	97	2	−−	−−	NOUN
iajs-551	97	3			NOUN
iajs-551	98	1			NOUN
iajs-551	98	2			VERB
iajs-551	98	3			PRON
iajs-551	98	4			PUNCT
iajs-551	99	1	−	−	PUNCT
iajs-551	99	2	=	=	PUNCT
iajs-551	99	3	−∫	−∫	NOUN
iajs-551	99	4			NOUN
iajs-551	99	5	=	=	X
iajs-551	99	6	−∫	−∫	PUNCT
iajs-551	100	1			PROPN
iajs-551	100	2			NOUN
iajs-551	100	3			NOUN
iajs-551	100	4			NOUN
iajs-551	100	5			NOUN
iajs-551	100	6			NOUN
iajs-551	100	7	=	=	SYM
iajs-551	100	8	1	1	NUM
iajs-551	100	9	0	0	NUM
iajs-551	100	10	1	1	NUM
iajs-551	100	11	(	(	PUNCT
iajs-551	100	12	)	)	PUNCT
iajs-551	100	13	(	(	PUNCT
iajs-551	100	14	)	)	PUNCT
iajs-551	101	1	p	p	X
iajs-551	101	2	p	p	X
iajs-551	101	3	g	g	NOUN
iajs-551	101	4	x	x	PUNCT
iajs-551	101	5	g	g	PROPN
iajs-551	101	6	dxn	dxn	VERB
iajs-551	101	7	x	x	PROPN
iajs-551	101	8			PROPN
iajs-551	101	9			NOUN
iajs-551	101	10			NOUN
iajs-551	101	11			NOUN
iajs-551	101	12			NOUN
iajs-551	101	13			PRON
iajs-551	101	14			PUNCT
iajs-551	101	15	−∫	−∫	VERB
iajs-551	101	16			NOUN
iajs-551	101	17	=	=	SYM
iajs-551	101	18	(	(	PUNCT
iajs-551	101	19	)	)	PUNCT
iajs-551	101	20	(	(	PUNCT
iajs-551	101	21	)	)	PUNCT
iajs-551	102	1	p	p	X
iajs-551	102	2	g	g	PROPN
iajs-551	102	3	x	x	PROPN
iajs-551	102	4	gn	gn	PROPN
iajs-551	102	5	x−	x−	PROPN
iajs-551	102	6			PROPN
iajs-551	102	7	such	such	ADJ
iajs-551	102	8	that	that	SCONJ
iajs-551	102	9	(	(	PUNCT
iajs-551	102	10	)	)	PUNCT
iajs-551	102	11	(	(	PUNCT
iajs-551	102	12	)	)	PUNCT
iajs-551	102	13	xg	xg	NOUN
iajs-551	103	1	x	x	PUNCT
iajs-551	103	2	f	f	X
iajs-551	103	3	x	x	PUNCT
iajs-551	103	4	e	e	NOUN
iajs-551	103	5	α−=	α−=	X
iajs-551	103	6	and	and	CCONJ
iajs-551	103	7	(	(	PUNCT
iajs-551	103	8	)	)	PUNCT
iajs-551	103	9	x	x	SYM
iajs-551	103	10	n	n	X
iajs-551	103	11	ng	ng	PROPN
iajs-551	103	12	s	s	PART
iajs-551	103	13	ex	ex	NOUN
iajs-551	103	14	α−=	α−=	ADJ
iajs-551	103	15			NOUN
iajs-551	103	16	where	where	SCONJ
iajs-551	103	17	(	(	PUNCT
iajs-551	103	18	)	)	PUNCT
iajs-551	103	19	1	1	NUM
iajs-551	103	20	,	,	PUNCT
iajs-551	103	21	(	(	PUNCT
iajs-551	103	22	)	)	PUNCT
iajs-551	103	23	pg	pg	INTJ
iajs-551	103	24	x	x	X
iajs-551	103	25	l	l	NOUN
iajs-551	103	26	yα∈	yα∈	PROPN
iajs-551	103	27	and	and	CCONJ
iajs-551	103	28	(	(	PUNCT
iajs-551	103	29	)	)	PUNCT
iajs-551	103	30	gn	gn	PROPN
iajs-551	104	1	x	x	PROPN
iajs-551	104	2	is	be	AUX
iajs-551	104	3	the	the	DET
iajs-551	104	4	continuous	continuous	ADJ
iajs-551	104	5	piecewise	piecewise	NOUN
iajs-551	104	6	polynomial	polynomial	NOUN
iajs-551	104	7	in	in	ADP
iajs-551	104	8	sn	sn	PROPN
iajs-551	104	9	.	.	PUNCT
iajs-551	105	1	then	then	ADV
iajs-551	105	2	by	by	ADP
iajs-551	105	3	lemma	lemma	PROPN
iajs-551	105	4	1	1	NUM
iajs-551	105	5	2,1	2,1	NUM
iajs-551	105	6	,	,	PUNCT
iajs-551	105	7	1	1	NUM
iajs-551	105	8	,	,	PUNCT
iajs-551	105	9	p	p	X
iajs-551	105	10	p	p	X
iajs-551	105	11	p	p	NOUN
iajs-551	105	12	cf	cf	NOUN
iajs-551	105	13	s	s	PROPN
iajs-551	105	14	g	g	NOUN
iajs-551	105	15	g	g	PROPN
iajs-551	105	16	gn	gn	PROPN
iajs-551	105	17	n	n	CCONJ
iajs-551	105	18	n	n	PROPN
iajs-551	105	19	n	n	ADV
iajs-551	105	20	ϕ	ϕ	PROPN
iajs-551	105	21	α	α	PROPN
iajs-551	105	22	ω	ω	PROPN
iajs-551	105	23			PROPN
iajs-551	105	24			PROPN
iajs-551	105	25			NOUN
iajs-551	105	26			VERB
iajs-551	105	27			NOUN
iajs-551	105	28			PUNCT
iajs-551	106	1	′−	′−	NOUN
iajs-551	106	2	=	=	PUNCT
iajs-551	107	1	−	−	PROPN
iajs-551	107	2	≤	≤	PROPN
iajs-551	107	3			NOUN
iajs-551	107	4	2,1	2,1	NUM
iajs-551	107	5	,	,	PUNCT
iajs-551	107	6	1	1	NUM
iajs-551	107	7	,	,	PUNCT
iajs-551	108	1	p	p	NOUN
iajs-551	108	2	c	c	NOUN
iajs-551	108	3	fn	fn	NOUN
iajs-551	108	4	n	n	ADV
iajs-551	108	5	ϕ	ϕ	PROPN
iajs-551	108	6	α	α	PROPN
iajs-551	108	7	ω	ω	PROPN
iajs-551	108	8			PROPN
iajs-551	108	9			PROPN
iajs-551	108	10			NOUN
iajs-551	108	11			VERB
iajs-551	108	12			NOUN
iajs-551	108	13			PUNCT
iajs-551	109	1	′=	′=	PROPN
iajs-551	109	2	therefore	therefore	ADV
iajs-551	109	3	2,1	2,1	NUM
iajs-551	109	4	,	,	PUNCT
iajs-551	109	5	,	,	PUNCT
iajs-551	109	6	1	1	NUM
iajs-551	109	7	,	,	PUNCT
iajs-551	109	8	p	p	X
iajs-551	109	9	p	p	X
iajs-551	109	10	cf	cf	NOUN
iajs-551	109	11	s	s	NOUN
iajs-551	109	12	fn	fn	NOUN
iajs-551	109	13	n	n	CCONJ
iajs-551	109	14	n	n	NOUN
iajs-551	109	15	ϕ	ϕ	PROPN
iajs-551	109	16	α	α	PROPN
iajs-551	109	17	α	α	PROPN
iajs-551	109	18	ω	ω	PROPN
iajs-551	109	19			PROPN
iajs-551	109	20			PROPN
iajs-551	109	21			NOUN
iajs-551	109	22			VERB
iajs-551	109	23			NOUN
iajs-551	109	24			PUNCT
iajs-551	110	1	′−	′−	PROPN
iajs-551	110	2	≤	≤	PROPN
iajs-551	110	3	.	.	PUNCT
iajs-551	111	1	proof	proof	NOUN
iajs-551	111	2	of	of	ADP
iajs-551	111	3	theorem	theorem	NOUN
iajs-551	111	4	(	(	PUNCT
iajs-551	111	5	2	2	NUM
iajs-551	111	6	)	)	PUNCT
iajs-551	111	7	we	we	PRON
iajs-551	111	8	first	first	ADV
iajs-551	111	9	take	take	VERB
iajs-551	111	10	n	n	ADV
iajs-551	111	11	sufficiently	sufficiently	ADV
iajs-551	111	12	large	large	ADJ
iajs-551	111	13	so	so	SCONJ
iajs-551	111	14	that	that	SCONJ
iajs-551	111	15	f	f	PROPN
iajs-551	111	16	monotone	monotone	NOUN
iajs-551	111	17	in	in	ADP
iajs-551	111	18	1i	1i	NOUN
iajs-551	111	19	and	and	CCONJ
iajs-551	111	20	ni	ni	PROPN
iajs-551	111	21	.	.	PUNCT
iajs-551	112	1	then	then	ADV
iajs-551	112	2	in	in	ADP
iajs-551	112	3	view	view	NOUN
iajs-551	112	4	of	of	ADP
iajs-551	112	5	lemma	lemma	PROPN
iajs-551	112	6	2	2	NUM
iajs-551	112	7	at	at	ADP
iajs-551	112	8	most	most	ADJ
iajs-551	112	9	what	what	PRON
iajs-551	112	10	we	we	PRON
iajs-551	112	11	have	have	AUX
iajs-551	112	12	to	to	PART
iajs-551	112	13	correct	correct	VERB
iajs-551	112	14	the	the	DET
iajs-551	112	15	behavior	behavior	NOUN
iajs-551	112	16	of	of	ADP
iajs-551	112	17	ns	ns	NUM
iajs-551	112	18	on	on	ADP
iajs-551	112	19	1i	1i	NOUN
iajs-551	112	20	and	and	CCONJ
iajs-551	112	21	ni	ni	NOUN
iajs-551	112	22	while	while	SCONJ
iajs-551	112	23	keeping	keep	VERB
iajs-551	112	24	it	it	PRON
iajs-551	112	25	close	close	ADV
iajs-551	112	26	to	to	ADP
iajs-551	112	27	the	the	DET
iajs-551	112	28	original	original	ADJ
iajs-551	112	29	function	function	NOUN
iajs-551	112	30	.	.	PUNCT
iajs-551	113	1	a	a	DET
iajs-551	113	2	spline	spline	ADJ
iajs-551	113	3	polynomial	polynomial	ADJ
iajs-551	113	4	ns	ns	NUM
iajs-551	113	5	satisfying	satisfying	NOUN
iajs-551	113	6	.	.	PUNCT
iajs-551	114	1	2,1	2,1	NUM
iajs-551	114	2	1	1	NUM
iajs-551	114	3	1	1	NUM
iajs-551	114	4	,	,	PUNCT
iajs-551	114	5	,	,	PUNCT
iajs-551	114	6	(	(	PUNCT
iajs-551	114	7	)	)	PUNCT
iajs-551	114	8	1	1	NUM
iajs-551	114	9	(	(	PUNCT
iajs-551	114	10	)	)	PUNCT
iajs-551	114	11	(	(	PUNCT
iajs-551	114	12	)	)	PUNCT
iajs-551	114	13	,	,	PUNCT
iajs-551	114	14	[	[	PUNCT
iajs-551	114	15	(	(	PUNCT
iajs-551	114	16	0	0	NUM
iajs-551	114	17	)	)	PUNCT
iajs-551	114	18	0	0	NUM
iajs-551	115	1	(	(	PUNCT
iajs-551	115	2	1	1	NUM
iajs-551	115	3	)	)	PUNCT
iajs-551	115	4	0	0	NUM
iajs-551	115	5	,	,	PUNCT
iajs-551	115	6	]	]	PUNCT
iajs-551	115	7	(	(	PUNCT
iajs-551	115	8	0	0	NUM
iajs-551	115	9	)	)	PUNCT
iajs-551	115	10	(	(	PUNCT
iajs-551	115	11	1	1	X
iajs-551	115	12	)	)	PUNCT
iajs-551	115	13	1	1	NUM
iajs-551	115	14	(	(	PUNCT
iajs-551	115	15	,	,	PUNCT
iajs-551	115	16	)	)	PUNCT
iajs-551	115	17	ϕ	ϕ	PROPN
iajs-551	115	18	αα	αα	PROPN
iajs-551	115	19	ω	ω	PROPN
iajs-551	115	20			PROPN
iajs-551	115	21	−	−	PROPN
iajs-551	115	22			PROPN
iajs-551	115	23			PROPN
iajs-551	115	24			PROPN
iajs-551	115	25			PROPN
iajs-551	115	26			PROPN
iajs-551	115	27			PROPN
iajs-551	115	28			PROPN
iajs-551	115	29			PROPN
iajs-551	115	30			X
iajs-551	116	1	=	=	SYM
iajs-551	116	2	∈	∈	PROPN
iajs-551	116	3	≥	≥	NOUN
iajs-551	116	4	≥	≥	NOUN
iajs-551	116	5	∏	∏	PROPN
iajs-551	116	6	∏	∏	PROPN
iajs-551	116	7	′	′	NOUN
iajs-551	116	8	′	′	NUM
iajs-551	117	1	′−	′−	NOUN
iajs-551	117	2	≤	≤	NUM
iajs-551	117	3			PRON
iajs-551	117	4			NOUN
iajs-551	117	5			X
iajs-551	117	6			PROPN
iajs-551	117	7			PROPN
iajs-551	117	8	n	n	CCONJ
iajs-551	117	9	n	n	CCONJ
iajs-551	117	10	n	n	CCONJ
iajs-551	117	11	n	n	CCONJ
iajs-551	117	12	n	n	CCONJ
iajs-551	117	13	n	n	CCONJ
iajs-551	117	14	n	n	CCONJ
iajs-551	117	15	n	n	ADV
iajs-551	117	16	plp	plp	VERB
iajs-551	118	1	i	i	PRON
iajs-551	118	2	i	i	PRON
iajs-551	118	3	n	n	VERB
iajs-551	118	4	s	s	NOUN
iajs-551	118	5	x	x	X
iajs-551	118	6	s	s	NOUN
iajs-551	118	7	x	x	X
iajs-551	118	8	x	x	PUNCT
iajs-551	118	9	x	x	X
iajs-551	118	10	s	s	X
iajs-551	118	11	s	s	X
iajs-551	118	12	x	x	X
iajs-551	118	13	s	s	X
iajs-551	118	14	s	s	X
iajs-551	118	15	c	c	NOUN
iajs-551	118	16	f	f	PROPN
iajs-551	118	17	n	n	PROPN
iajs-551	118	18	…	…	PUNCT
iajs-551	118	19	(	(	PUNCT
iajs-551	118	20	4.1	4.1	NUM
iajs-551	118	21	)	)	PUNCT
iajs-551	118	22	indeed	indeed	ADV
iajs-551	118	23	since	since	SCONJ
iajs-551	118	24	1	1	NUM
iajs-551	118	25	2	2	NUM
iajs-551	118	26	,	,	PUNCT
iajs-551	118	27	n	n	PRON
iajs-551	118	28	ci	ci	NOUN
iajs-551	119	1	i	i	PRON
iajs-551	119	2	n	n	VERB
iajs-551	119	3	≤	≤	NOUN
iajs-551	119	4	then	then	ADV
iajs-551	119	5	mathematics	mathematic	NOUN
iajs-551	119	6	338	338	NUM
iajs-551	119	7	مجلة	مجلة	NOUN
iajs-551	119	8	إبن	إبن	VERB
iajs-551	119	9	الهيثم	الهيثم	ADJ
iajs-551	119	10	للعلوم	للعلوم	NOUN
iajs-551	119	11	الصرفة	الصرفة	NOUN
iajs-551	119	12	و	و	PRON
iajs-551	119	13	التطبيقية	التطبيقية	ADJ
iajs-551	119	14	2012	2012	NUM
iajs-551	119	15	السنة	السنة	NOUN
iajs-551	119	16	25	25	NUM
iajs-551	119	17	المجلد	المجلد	NOUN
iajs-551	119	18	3	3	NUM
iajs-551	119	19	العدد	العدد	PROPN
iajs-551	119	20	ibn	ibn	PROPN
iajs-551	119	21	al	al	PROPN
iajs-551	119	22	-	-	PUNCT
iajs-551	119	23	haitham	haitham	PROPN
iajs-551	119	24	journal	journal	PROPN
iajs-551	119	25	for	for	ADP
iajs-551	119	26	pure	pure	ADJ
iajs-551	119	27	and	and	CCONJ
iajs-551	119	28	applied	apply	VERB
iajs-551	119	29	science	science	NOUN
iajs-551	119	30	no	no	NOUN
iajs-551	119	31	.	.	NOUN
iajs-551	119	32	3	3	NUM
iajs-551	119	33	vol	vol	NOUN
iajs-551	119	34	.	.	PUNCT
iajs-551	120	1	25	25	NUM
iajs-551	120	2	year	year	NOUN
iajs-551	120	3	2012	2012	NUM
iajs-551	120	4	1	1	NUM
iajs-551	120	5	,	,	PUNCT
iajs-551	120	6	(	(	PUNCT
iajs-551	120	7	)	)	PUNCT
iajs-551	120	8	111	111	NUM
iajs-551	120	9	[	[	PUNCT
iajs-551	120	10	(	(	PUNCT
iajs-551	120	11	(	(	PUNCT
iajs-551	120	12	)	)	PUNCT
iajs-551	120	13	(	(	PUNCT
iajs-551	120	14	)	)	PUNCT
iajs-551	120	15	)	)	PUNCT
iajs-551	121	1	]	]	PUNCT
iajs-551	121	2	x	x	X
iajs-551	121	3	p	p	X
iajs-551	121	4	p	p	PROPN
iajs-551	121	5	n	n	CCONJ
iajs-551	121	6	n	n	CCONJ
iajs-551	121	7	n	n	CCONJ
iajs-551	121	8	n	n	NOUN
iajs-551	121	9	i	i	NOUN
iajs-551	121	10	ii	ii	PROPN
iajs-551	121	11	ilp	ilp	ADJ
iajs-551	121	12	i	i	PRON
iajs-551	122	1	i	i	PRON
iajs-551	122	2	nnn	nnn	VERB
iajs-551	122	3	s	s	PROPN
iajs-551	122	4	s	s	NOUN
iajs-551	122	5	s	s	X
iajs-551	122	6	t	t	PROPN
iajs-551	122	7	s	s	PROPN
iajs-551	122	8	t	t	NOUN
iajs-551	122	9	e	e	X
iajs-551	122	10	dt	dt	ADP
iajs-551	122	11	dxα	dxα	PROPN
iajs-551	122	12	α	α	NOUN
iajs-551	122	13	−′	−′	NOUN
iajs-551	122	14	′	′	NUM
iajs-551	122	15	′	′	NUM
iajs-551	123	1	′−	′−	PROPN
iajs-551	123	2	≤	≤	NUM
iajs-551	123	3	−∫∫	−∫∫	PROPN
iajs-551	123	4			PROPN
iajs-551	123	5			NOUN
iajs-551	123	6			NOUN
iajs-551	123	7	=	=	SYM
iajs-551	123	8	1	1	NUM
iajs-551	123	9	11	11	NUM
iajs-551	123	10	[	[	PUNCT
iajs-551	123	11	(	(	PUNCT
iajs-551	123	12	)	)	PUNCT
iajs-551	124	1	]	]	PUNCT
iajs-551	124	2	p	p	X
iajs-551	125	1	p	p	X
iajs-551	126	1	i	i	PRON
iajs-551	126	2	ii	ii	VERB
iajs-551	127	1	i	i	INTJ
iajs-551	127	2	nn	nn	INTJ
iajs-551	127	3	g	g	PROPN
iajs-551	127	4	g	g	PROPN
iajs-551	127	5	dt	dt	X
iajs-551	127	6	dx−∫∫	dx−∫∫	NOUN
iajs-551	128	1			X
iajs-551	128	2	…	…	PUNCT
iajs-551	128	3	(	(	PUNCT
iajs-551	128	4	4.2	4.2	NUM
iajs-551	128	5	)	)	PUNCT
iajs-551	128	6	then	then	ADV
iajs-551	128	7	by	by	ADP
iajs-551	128	8	holder	holder	NOUN
iajs-551	128	9	's	's	PART
iajs-551	128	10	inequality	inequality	NOUN
iajs-551	128	11	we	we	PRON
iajs-551	128	12	have	have	VERB
iajs-551	128	13	1	1	NUM
iajs-551	128	14	1	1	NUM
iajs-551	128	15	2	2	NUM
iajs-551	128	16	(	(	PUNCT
iajs-551	128	17	)	)	PUNCT
iajs-551	128	18	1	1	NUM
iajs-551	128	19	,	,	PUNCT
iajs-551	128	20	(	(	PUNCT
iajs-551	128	21	)	)	PUNCT
iajs-551	128	22	(	(	PUNCT
iajs-551	128	23	)	)	SYM
iajs-551	128	24	1	1	NUM
iajs-551	128	25	1	1	NUM
iajs-551	128	26	1	1	NUM
iajs-551	128	27	p	p	NOUN
iajs-551	128	28	q	q	X
iajs-551	128	29	p	p	PROPN
iajs-551	129	1	n	n	CCONJ
iajs-551	130	1	n	n	ADV
iajs-551	131	1	lp	lp	NOUN
iajs-551	132	1	i	i	PRON
iajs-551	132	2	i	i	PRON
iajs-551	132	3	nlp	nlp	VERB
iajs-551	133	1	i	i	PRON
iajs-551	133	2	i	i	PRON
iajs-551	133	3	i	i	PRON
iajs-551	133	4	in	in	ADP
iajs-551	133	5	n	n	PRON
iajs-551	133	6	s	s	NOUN
iajs-551	133	7	s	s	NOUN
iajs-551	133	8	g	g	PROPN
iajs-551	133	9	g	g	PROPN
iajs-551	133	10	dx	dx	PROPN
iajs-551	133	11	nα	nα	ADP
iajs-551	133	12			PROPN
iajs-551	133	13			PROPN
iajs-551	133	14	′	′	PROPN
iajs-551	133	15	′	′	NUM
iajs-551	133	16			ADJ
iajs-551	133	17	−	−	ADJ
iajs-551	133	18	≤	≤	NOUN
iajs-551	133	19	−∫	−∫	PUNCT
iajs-551	134	1			PROPN
iajs-551	134	2			ADJ
iajs-551	134	3			ADJ
iajs-551	134	4			NOUN
iajs-551	134	5			NOUN
iajs-551	134	6			PROPN
iajs-551	134	7			ADJ
iajs-551	134	8			ADJ
iajs-551	134	9			NOUN
iajs-551	134	10	1	1	NUM
iajs-551	134	11	1	1	NUM
iajs-551	134	12	2	2	NUM
iajs-551	134	13	(	(	PUNCT
iajs-551	134	14	)	)	PUNCT
iajs-551	134	15	1	1	NUM
iajs-551	134	16	1	1	NUM
iajs-551	134	17	q	q	NOUN
iajs-551	134	18	p	p	X
iajs-551	135	1	p	p	X
iajs-551	136	1	lp	lp	INTJ
iajs-551	137	1	i	i	PRON
iajs-551	138	1	i	i	PRON
iajs-551	138	2	n	n	VERB
iajs-551	138	3	g	g	PROPN
iajs-551	138	4	g	g	PROPN
iajs-551	138	5	n	n	PROPN
iajs-551	138	6	+	+	NUM
iajs-551	138	7			PROPN
iajs-551	138	8	≤	≤	PROPN
iajs-551	138	9	−	−	PUNCT
iajs-551	138	10			PROPN
iajs-551	138	11			X
iajs-551	139	1			PUNCT
iajs-551	139	2			ADJ
iajs-551	139	3	1	1	NUM
iajs-551	139	4	1	1	NUM
iajs-551	139	5	2	2	NUM
iajs-551	139	6	,	,	PUNCT
iajs-551	139	7	(	(	PUNCT
iajs-551	139	8	)	)	PUNCT
iajs-551	139	9	1	1	NUM
iajs-551	139	10	1	1	NUM
iajs-551	139	11	q	q	NOUN
iajs-551	139	12	p	p	X
iajs-551	139	13	p	p	PROPN
iajs-551	139	14	n	n	CCONJ
iajs-551	139	15	n	n	ADV
iajs-551	139	16	lp	lp	NOUN
iajs-551	140	1	i	i	PRON
iajs-551	140	2	i	i	PRON
iajs-551	141	1	n	n	VERB
iajs-551	141	2	s	s	NOUN
iajs-551	141	3	s	s	X
iajs-551	141	4	n	n	PRON
iajs-551	142	1	α	α	NOUN
iajs-551	142	2	+	+	CCONJ
iajs-551	142	3	=	=	NOUN
iajs-551	142	4			NOUN
iajs-551	142	5			NUM
iajs-551	142	6	′	′	NUM
iajs-551	142	7	′−	′−	NOUN
iajs-551	142	8			ADJ
iajs-551	142	9			NOUN
iajs-551	142	10			ADJ
iajs-551	142	11			NOUN
iajs-551	142	12	2	2	NUM
iajs-551	142	13	1	1	NUM
iajs-551	142	14	,	,	PUNCT
iajs-551	142	15	(	(	PUNCT
iajs-551	142	16	)	)	PUNCT
iajs-551	142	17	1α	1α	NUM
iajs-551	142	18	≤	≤	NOUN
iajs-551	142	19	′	′	NUM
iajs-551	142	20	′−	′−	NOUN
iajs-551	142	21			ADJ
iajs-551	142	22			NOUN
iajs-551	142	23	n	n	CCONJ
iajs-551	142	24	nn	nn	INTJ
iajs-551	142	25	lp	lp	NOUN
iajs-551	143	1	i	i	PRON
iajs-551	143	2	i	i	PRON
iajs-551	143	3	n	n	VERB
iajs-551	143	4	s	s	NOUN
iajs-551	143	5	s	s	X
iajs-551	143	6	from	from	ADP
iajs-551	143	7	(	(	PUNCT
iajs-551	143	8	4.1	4.1	NUM
iajs-551	143	9	)	)	PUNCT
iajs-551	143	10	and	and	CCONJ
iajs-551	143	11	(	(	PUNCT
iajs-551	143	12	4.2	4.2	NUM
iajs-551	143	13	)	)	PUNCT
iajs-551	143	14	we	we	PRON
iajs-551	143	15	get	get	VERB
iajs-551	143	16	2,1	2,1	NUM
iajs-551	143	17	2,1	2,1	NUM
iajs-551	143	18	,	,	PUNCT
iajs-551	143	19	2	2	NUM
iajs-551	143	20	,	,	PUNCT
iajs-551	143	21	,	,	PUNCT
iajs-551	143	22	1	1	NUM
iajs-551	143	23	(	(	PUNCT
iajs-551	143	24	,	,	PUNCT
iajs-551	143	25	)	)	PUNCT
iajs-551	143	26	1	1	NUM
iajs-551	143	27	(	(	PUNCT
iajs-551	143	28	,	,	PUNCT
iajs-551	143	29	)	)	PUNCT
iajs-551	143	30	n	n	CCONJ
iajs-551	144	1	n	n	CCONJ
iajs-551	145	1	pp	pp	ADV
iajs-551	145	2	p	p	PROPN
iajs-551	145	3	cs	cs	PROPN
iajs-551	145	4	s	s	PROPN
iajs-551	145	5	n	n	NOUN
iajs-551	145	6	f	f	PROPN
iajs-551	145	7	nn	nn	PROPN
iajs-551	145	8	c	c	PROPN
iajs-551	145	9	f	f	PROPN
iajs-551	145	10	n	n	PROPN
iajs-551	145	11	n	n	PROPN
iajs-551	145	12	ϕ	ϕ	PROPN
iajs-551	145	13	ϕ	ϕ	X
iajs-551	145	14	αα	αα	ADP
iajs-551	145	15	α	α	PROPN
iajs-551	145	16	ω	ω	NOUN
iajs-551	145	17	ω=	ω=	X
iajs-551	145	18	′−	′−	PROPN
iajs-551	145	19	≤	≤	NUM
iajs-551	145	20	′	′	NUM
iajs-551	145	21			NOUN
iajs-551	145	22	which	which	PRON
iajs-551	145	23	combined	combine	VERB
iajs-551	145	24	with	with	ADP
iajs-551	145	25	(	(	PUNCT
iajs-551	145	26	3.6	3.6	NUM
iajs-551	145	27	)	)	PUNCT
iajs-551	145	28	and	and	CCONJ
iajs-551	145	29	(	(	PUNCT
iajs-551	145	30	4.3	4.3	NUM
iajs-551	145	31	)	)	PUNCT
iajs-551	145	32	implies	imply	VERB
iajs-551	145	33	.	.	PUNCT
iajs-551	146	1	(	(	PUNCT
iajs-551	146	2	)	)	PUNCT
iajs-551	146	3	2,1	2,1	NUM
iajs-551	146	4	2,1	2,1	NUM
iajs-551	146	5	2,1	2,1	NUM
iajs-551	146	6	(	(	PUNCT
iajs-551	146	7	1	1	NUM
iajs-551	146	8	)	)	PUNCT
iajs-551	146	9	,	,	PUNCT
iajs-551	146	10	,	,	PUNCT
iajs-551	146	11	,	,	PUNCT
iajs-551	146	12	,	,	PUNCT
iajs-551	146	13	,	,	PUNCT
iajs-551	146	14	(	(	PUNCT
iajs-551	146	15	)	)	PUNCT
iajs-551	146	16	,	,	PUNCT
iajs-551	146	17	[	[	PUNCT
iajs-551	146	18	,	,	PUNCT
iajs-551	146	19	]	]	SYM
iajs-551	146	20	1	1	NUM
iajs-551	146	21	2	2	NUM
iajs-551	146	22	1	1	NUM
iajs-551	146	23	1	1	NUM
iajs-551	146	24	,	,	PUNCT
iajs-551	146	25	,	,	PUNCT
iajs-551	146	26	,	,	PUNCT
iajs-551	146	27	,	,	PUNCT
iajs-551	146	28	,	,	PUNCT
iajs-551	146	29	1	1	NUM
iajs-551	146	30	1	1	NUM
iajs-551	146	31	(	(	PUNCT
iajs-551	146	32	,	,	PUNCT
iajs-551	146	33	)	)	PUNCT
iajs-551	146	34	0	0	NUM
iajs-551	147	1	(	(	PUNCT
iajs-551	147	2	,	,	PUNCT
iajs-551	147	3	)	)	PUNCT
iajs-551	147	4	1	1	NUM
iajs-551	147	5	(	(	PUNCT
iajs-551	147	6	,	,	PUNCT
iajs-551	147	7	)	)	PUNCT
iajs-551	147	8	n	n	CCONJ
iajs-551	147	9	n	n	CCONJ
iajs-551	147	10	nn	nn	PROPN
iajs-551	147	11	n	n	CCONJ
iajs-551	147	12	p	p	PROPN
iajs-551	147	13	p	p	PROPN
iajs-551	147	14	p	p	PROPN
iajs-551	147	15	n	n	CCONJ
iajs-551	147	16	n	n	CCONJ
iajs-551	147	17	n	n	CCONJ
iajs-551	147	18	n	n	CCONJ
iajs-551	147	19	n	n	NOUN
iajs-551	147	20	p	p	NOUN
iajs-551	147	21	lp	lp	PROPN
iajs-551	147	22	l	l	NOUN
iajs-551	147	23	l	l	NOUN
iajs-551	148	1	lp	lp	NOUN
iajs-551	148	2	x	x	NOUN
iajs-551	148	3	x	x	PUNCT
iajs-551	148	4	n	n	ADP
iajs-551	148	5	p	p	NOUN
iajs-551	148	6	p	p	X
iajs-551	149	1	p	p	X
iajs-551	149	2	f	f	X
iajs-551	149	3	y	y	PROPN
iajs-551	149	4	pe	pe	PROPN
iajs-551	150	1	f	f	PROPN
iajs-551	150	2	s	s	AUX
iajs-551	150	3	f	f	PROPN
iajs-551	150	4	s	s	X
iajs-551	150	5	s	s	X
iajs-551	150	6	s	s	X
iajs-551	150	7	f	f	X
iajs-551	150	8	s	s	X
iajs-551	150	9	s	s	X
iajs-551	150	10	s	s	X
iajs-551	150	11	s	s	X
iajs-551	150	12	s	s	X
iajs-551	150	13	c	c	NOUN
iajs-551	150	14	cf	cf	NOUN
iajs-551	150	15	f	f	PROPN
iajs-551	150	16	n	n	CCONJ
iajs-551	150	17	n	n	CCONJ
iajs-551	150	18	n	n	CCONJ
iajs-551	150	19	n	n	PROPN
iajs-551	150	20	c	c	NOUN
iajs-551	150	21	f	f	PROPN
iajs-551	150	22	n	n	PROPN
iajs-551	150	23	n	n	PROPN
iajs-551	150	24	ϕ	ϕ	PROPN
iajs-551	150	25	ϕ	ϕ	X
iajs-551	150	26	ϕ	ϕ	X
iajs-551	150	27	α	α	NOUN
iajs-551	150	28	α	α	NOUN
iajs-551	150	29	α	α	NOUN
iajs-551	150	30	α	α	NOUN
iajs-551	150	31	α	α	NOUN
iajs-551	150	32	α	α	NOUN
iajs-551	150	33	α	α	NOUN
iajs-551	150	34	α	α	NOUN
iajs-551	150	35	α	α	NOUN
iajs-551	150	36	α	α	PROPN
iajs-551	150	37	ω	ω	PROPN
iajs-551	150	38	ω	ω	PROPN
iajs-551	150	39	ω	ω	PROPN
iajs-551	150	40	=	=	SYM
iajs-551	150	41	−	−	PROPN
iajs-551	150	42	≤	≤	NUM
iajs-551	150	43	−	−	NOUN
iajs-551	150	44	≤	≤	NUM
iajs-551	150	45	−	−	PROPN
iajs-551	150	46	+	+	CCONJ
iajs-551	150	47	−	−	PROPN
iajs-551	150	48	≤	≤	NUM
iajs-551	150	49	−	−	PROPN
iajs-551	151	1	+	+	CCONJ
iajs-551	151	2	−	−	PROPN
iajs-551	151	3	+	+	CCONJ
iajs-551	151	4	−	−	NUM
iajs-551	152	1	′	′	NUM
iajs-551	152	2	′+	′+	PUNCT
iajs-551	153	1	+	+	CCONJ
iajs-551	153	2	′=	′=	PROPN
iajs-551	153	3			PRON
iajs-551	153	4			NOUN
iajs-551	153	5			PROPN
iajs-551	153	6			PROPN
iajs-551	153	7			PROPN
iajs-551	153	8			PROPN
iajs-551	153	9	references	reference	NOUN
iajs-551	153	10	1	1	NUM
iajs-551	153	11	.	.	PUNCT
iajs-551	153	12	rempulska	rempulska	PROPN
iajs-551	153	13	,	,	PUNCT
iajs-551	153	14	l.	l.	PROPN
iajs-551	153	15	and	and	CCONJ
iajs-551	153	16	skorupka	skorupka	NOUN
iajs-551	153	17	,	,	PUNCT
iajs-551	153	18	(	(	PUNCT
iajs-551	153	19	2004	2004	NUM
iajs-551	153	20	)	)	PUNCT
iajs-551	153	21	,	,	PUNCT
iajs-551	153	22	on	on	ADP
iajs-551	153	23	strong	strong	ADJ
iajs-551	153	24	approximation	approximation	NOUN
iajs-551	153	25	of	of	ADP
iajs-551	153	26	function	function	NOUN
iajs-551	153	27	by	by	ADP
iajs-551	153	28	certain	certain	ADJ
iajs-551	153	29	operators	operator	NOUN
iajs-551	153	30	,	,	PUNCT
iajs-551	153	31	math	math	PROPN
iajs-551	153	32	.j	.j	PROPN
iajs-551	153	33	.	.	PUNCT
iajs-551	154	1	okayama	okayama	PROPN
iajs-551	154	2	,	,	PUNCT
iajs-551	154	3	univ	univ	PROPN
iajs-551	154	4	.	.	PROPN
iajs-551	154	5	,	,	PUNCT
iajs-551	154	6	46	46	NUM
iajs-551	154	7	,	,	PUNCT
iajs-551	154	8	153	153	NUM
iajs-551	154	9	-	-	SYM
iajs-551	154	10	161	161	NUM
iajs-551	154	11	.	.	PUNCT
iajs-551	155	1	2	2	X
iajs-551	155	2	.	.	X
iajs-551	155	3	miller	miller	PROPN
iajs-551	155	4	,	,	PUNCT
iajs-551	155	5	h.	h.	PROPN
iajs-551	155	6	and	and	CCONJ
iajs-551	155	7	orhan	orhan	PROPN
iajs-551	155	8	,	,	PUNCT
iajs-551	155	9	c.	c.	PROPN
iajs-551	155	10	,	,	PUNCT
iajs-551	155	11	(	(	PUNCT
iajs-551	155	12	2001	2001	NUM
iajs-551	155	13	)	)	PUNCT
iajs-551	155	14	,	,	PUNCT
iajs-551	155	15	on	on	ADP
iajs-551	155	16	almost	almost	ADV
iajs-551	155	17	convergent	convergent	ADJ
iajs-551	155	18	subsequences	subsequence	NOUN
iajs-551	155	19	and	and	CCONJ
iajs-551	155	20	statistically	statistically	ADV
iajs-551	155	21	convergent	convergent	ADJ
iajs-551	155	22	subsequences	subsequence	NOUN
iajs-551	155	23	,	,	PUNCT
iajs-551	155	24	acta	acta	PROPN
iajs-551	155	25	math	math	PROPN
iajs-551	155	26	.	.	PUNCT
iajs-551	156	1	hungar	hungar	NOUN
iajs-551	156	2	,	,	PUNCT
iajs-551	156	3	93	93	NUM
iajs-551	156	4	,	,	PUNCT
iajs-551	156	5	135	135	NUM
iajs-551	156	6	-	-	SYM
iajs-551	156	7	151	151	NUM
iajs-551	156	8	.	.	PUNCT
iajs-551	157	1	3	3	NUM
iajs-551	157	2	.	.	X
iajs-551	157	3	ditizian	ditizian	ADJ
iajs-551	157	4	,	,	PUNCT
iajs-551	157	5	z.	z.	PROPN
iajs-551	157	6	and	and	CCONJ
iajs-551	157	7	totik	totik	PROPN
iajs-551	157	8	,	,	PUNCT
iajs-551	157	9	v.	v.	ADV
iajs-551	157	10	,	,	PUNCT
iajs-551	157	11	(	(	PUNCT
iajs-551	157	12	1987	1987	NUM
iajs-551	157	13	)	)	PUNCT
iajs-551	157	14	,	,	PUNCT
iajs-551	157	15	moduli	modulus	NOUN
iajs-551	157	16	of	of	ADP
iajs-551	157	17	smoothness	smoothness	NOUN
iajs-551	157	18	,	,	PUNCT
iajs-551	157	19	springer	springer	NOUN
iajs-551	157	20	series	series	NOUN
iajs-551	157	21	in	in	ADP
iajs-551	157	22	computational	computational	ADJ
iajs-551	157	23	mathematics	mathematic	NOUN
iajs-551	157	24	,	,	PUNCT
iajs-551	157	25	springer	springer	NOUN
iajs-551	157	26	verlage	verlage	NOUN
iajs-551	157	27	,	,	PUNCT
iajs-551	157	28	new	new	PROPN
iajs-551	157	29	york	york	PROPN
iajs-551	157	30	.	.	PUNCT
iajs-551	158	1	mathematics	mathematic	NOUN
iajs-551	158	2	339	339	NUM
iajs-551	158	3	مجلة	مجلة	NOUN
iajs-551	158	4	إبن	إبن	VERB
iajs-551	158	5	الهيثم	الهيثم	ADJ
iajs-551	158	6	للعلوم	للعلوم	NOUN
iajs-551	158	7	الصرفة	الصرفة	NOUN
iajs-551	159	1	و	و	PRON
iajs-551	159	2	التطبيقية	التطبيقية	ADJ
iajs-551	159	3	2012	2012	NUM
iajs-551	159	4	السنة	السنة	NOUN
iajs-551	159	5	25	25	NUM
iajs-551	159	6	المجلد	المجلد	NOUN
iajs-551	159	7	3	3	NUM
iajs-551	159	8	العدد	العدد	PROPN
iajs-551	159	9	ibn	ibn	PROPN
iajs-551	159	10	al	al	PROPN
iajs-551	159	11	-	-	PUNCT
iajs-551	159	12	haitham	haitham	PROPN
iajs-551	159	13	journal	journal	PROPN
iajs-551	159	14	for	for	ADP
iajs-551	159	15	pure	pure	ADJ
iajs-551	159	16	and	and	CCONJ
iajs-551	159	17	applied	apply	VERB
iajs-551	159	18	science	science	NOUN
iajs-551	159	19	no	no	NOUN
iajs-551	159	20	.	.	NOUN
iajs-551	159	21	3	3	NUM
iajs-551	159	22	vol	vol	NOUN
iajs-551	159	23	.	.	PUNCT
iajs-551	160	1	25	25	NUM
iajs-551	160	2	year	year	NOUN
iajs-551	160	3	2012	2012	NUM
iajs-551	160	4	4	4	NUM
iajs-551	160	5	.	.	PUNCT
iajs-551	160	6	leviatan	leviatan	PROPN
iajs-551	160	7	d.	d.	PROPN
iajs-551	160	8	and	and	CCONJ
iajs-551	160	9	shevchuk	shevchuk	PROPN
iajs-551	160	10	,	,	PUNCT
iajs-551	160	11	i.a	i.a	PROPN
iajs-551	160	12	.	.	PROPN
iajs-551	160	13	,	,	PUNCT
iajs-551	160	14	(	(	PUNCT
iajs-551	160	15	1998	1998	NUM
iajs-551	160	16	)	)	PUNCT
iajs-551	160	17	,	,	PUNCT
iajs-551	160	18	nearly	nearly	ADV
iajs-551	160	19	comonotone	comonotone	NOUN
iajs-551	160	20	approximation	approximation	NOUN
iajs-551	160	21	,	,	PUNCT
iajs-551	160	22	j	j	PROPN
iajs-551	160	23	approx	approx	PROPN
iajs-551	160	24	.	.	PUNCT
iajs-551	161	1	theory	theory	NOUN
iajs-551	161	2	,	,	PUNCT
iajs-551	161	3	53	53	NUM
iajs-551	161	4	-	-	SYM
iajs-551	161	5	81	81	NUM
iajs-551	161	6	.	.	PUNCT
iajs-551	162	1	5	5	NUM
iajs-551	162	2	.	.	X
iajs-551	162	3	leviatan	leviatan	PROPN
iajs-551	162	4	,	,	PUNCT
iajs-551	162	5	d.	d.	PROPN
iajs-551	162	6	and	and	CCONJ
iajs-551	162	7	shevchuk	shevchuk	PROPN
iajs-551	162	8	,	,	PUNCT
iajs-551	162	9	i.a	i.a	PROPN
iajs-551	162	10	.	.	PROPN
iajs-551	162	11	,	,	PUNCT
iajs-551	162	12	(	(	PUNCT
iajs-551	162	13	1999	1999	NUM
iajs-551	162	14	)	)	PUNCT
iajs-551	162	15	,	,	PUNCT
iajs-551	162	16	some	some	DET
iajs-551	162	17	positive	positive	ADJ
iajs-551	162	18	results	result	NOUN
iajs-551	162	19	and	and	CCONJ
iajs-551	162	20	couterexamples	couterexample	VERB
iajs-551	162	21	in	in	ADP
iajs-551	162	22	comonotone	comonotone	NOUN
iajs-551	162	23	approximation	approximation	NOUN
iajs-551	162	24	ii	ii	PROPN
iajs-551	162	25	,	,	PUNCT
iajs-551	162	26	j	j	PROPN
iajs-551	162	27	.approx	.approx	PROPN
iajs-551	162	28	.	.	PUNCT
iajs-551	163	1	theorey	theorey	NOUN
iajs-551	163	2	,	,	PUNCT
iajs-551	163	3	195	195	NUM
iajs-551	163	4	-	-	SYM
iajs-551	163	5	206	206	NUM
iajs-551	163	6	.	.	PUNCT
iajs-551	164	1	6	6	NUM
iajs-551	164	2	.	.	X
iajs-551	165	1	r.k	r.k	PROPN
iajs-551	165	2	.	.	PROPN
iajs-551	165	3	beston	beston	PROPN
iajs-551	165	4	and	and	CCONJ
iajs-551	165	5	d.	d.	PROPN
iajs-551	165	6	leviatan	leviatan	PROPN
iajs-551	165	7	(	(	PUNCT
iajs-551	165	8	1993	1993	NUM
iajs-551	165	9	):	):	PUNCT
iajs-551	165	10	"	"	PUNCT
iajs-551	165	11	on	on	ADP
iajs-551	165	12	comonotone	comonotone	NOUN
iajs-551	165	13	approximation	approximation	NOUN
iajs-551	165	14	"	"	PUNCT
iajs-551	165	15	.	.	PUNCT
iajs-551	166	1	canada	canada	PROPN
iajs-551	166	2	.	.	PUNCT
iajs-551	167	1	math	math	PROPN
iajs-551	167	2	.bull	.bull	NOUN
iajs-551	167	3	,	,	PUNCT
iajs-551	167	4	26,220	26,220	NUM
iajs-551	167	5	-	-	SYM
iajs-551	167	6	224	224	NUM
iajs-551	167	7	.	.	PUNCT
iajs-551	168	1	7	7	X
iajs-551	168	2	.	.	X
iajs-551	168	3	husain	husain	PROPN
iajs-551	168	4	,	,	PUNCT
iajs-551	168	5	l.a	l.a	PROPN
iajs-551	168	6	.	.	PROPN
iajs-551	168	7	,	,	PUNCT
iajs-551	168	8	(	(	PUNCT
iajs-551	168	9	2010	2010	NUM
iajs-551	168	10	)	)	PUNCT
iajs-551	168	11	,	,	PUNCT
iajs-551	168	12	unbounded	unbounded	ADJ
iajs-551	168	13	function	function	NOUN
iajs-551	168	14	approximation	approximation	NOUN
iajs-551	168	15	in	in	ADP
iajs-551	168	16	some	some	PRON
iajs-551	168	17	,	,	PUNCT
iajs-551	168	18	pl	pl	PROPN
iajs-551	168	19	α	α	PROPN
iajs-551	168	20	spaces	space	NOUN
iajs-551	168	21	,	,	PUNCT
iajs-551	168	22	m.sc	m.sc	PROPN
iajs-551	168	23	thesis	thesis	NOUN
iajs-551	168	24	,	,	PUNCT
iajs-551	168	25	mustansirya	mustansirya	NOUN
iajs-551	168	26	university	university	NOUN
iajs-551	168	27	,	,	PUNCT
iajs-551	168	28	department	department	NOUN
iajs-551	168	29	of	of	ADP
iajs-551	168	30	mathematics	mathematics	PROPN
iajs-551	168	31	,	,	PUNCT
iajs-551	168	32	college	college	NOUN
iajs-551	168	33	of	of	ADP
iajs-551	168	34	science	science	NOUN
iajs-551	168	35	.	.	PUNCT
iajs-551	169	1	mathematics	mathematic	NOUN
iajs-551	169	2	340	340	NUM
iajs-551	169	3	مجلة	مجلة	NOUN
iajs-551	169	4	إبن	إبن	VERB
iajs-551	169	5	الهيثم	الهيثم	ADJ
iajs-551	169	6	للعلوم	للعلوم	NOUN
iajs-551	169	7	الصرفة	الصرفة	NOUN
iajs-551	169	8	و	و	PRON
iajs-551	169	9	التطبيقية	التطبيقية	ADJ
iajs-551	169	10	2012	2012	NUM
iajs-551	169	11	السنة	السنة	NOUN
iajs-551	170	1	25	25	NUM
iajs-551	170	2	المجلد	المجلد	NOUN
iajs-551	170	3	3	3	NUM
iajs-551	170	4	العدد	العدد	PROPN
iajs-551	170	5	ibn	ibn	PROPN
iajs-551	170	6	al	al	PROPN
iajs-551	170	7	-	-	PUNCT
iajs-551	170	8	haitham	haitham	PROPN
iajs-551	170	9	journal	journal	PROPN
iajs-551	170	10	for	for	ADP
iajs-551	170	11	pure	pure	ADJ
iajs-551	170	12	and	and	CCONJ
iajs-551	170	13	applied	apply	VERB
iajs-551	170	14	science	science	NOUN
iajs-551	170	15	no	no	NOUN
iajs-551	170	16	.	.	NOUN
iajs-551	170	17	3	3	NUM
iajs-551	170	18	vol	vol	NOUN
iajs-551	170	19	.	.	PUNCT
iajs-551	170	20	25	25	NUM
iajs-551	170	21	year	year	NOUN
iajs-551	170	22	2012	2012	NUM
iajs-551	170	23	pl	pl	PROPN
iajs-551	170	24	,	,	PUNCT
iajs-551	170	25	التقريب	التقريب	NOUN
iajs-551	170	26	الرتيب	الرتيب	ADJ
iajs-551	170	27	في	في	SCONJ
iajs-551	170	28	الفضاء	الفضاء	NOUN
iajs-551	170	29	α	α	PROPN
iajs-551	170	30	صاحب	صاحب	NOUN
iajs-551	170	31	كحيط	كحيط	VERB
iajs-551	170	32	جاسم	جاسم	PROPN
iajs-551	170	33	،	،	X
iajs-551	170	34	إسراء	إسراء	PROPN
iajs-551	170	35	زايد	زايد	NOUN
iajs-551	170	36	شمخي	شمخي	ADJ
iajs-551	170	37	الجامعة	الجامعة	NOUN
iajs-551	170	38	المستنصرية	المستنصرية	NOUN
iajs-551	170	39	–	–	PUNCT
iajs-551	170	40	كلية	كلية	NOUN
iajs-551	170	41	العلوم	العلوم	NOUN
iajs-551	170	42	–	–	PUNCT
iajs-551	170	43	قسم	قسم	DET
iajs-551	170	44	الرياضيات	الرياضيات	NOUN
iajs-551	170	45	2012اذار	2012اذار	PROPN
iajs-551	170	46	18قبل	18قبل	PROPN
iajs-551	170	47	البحث	البحث	PROPN
iajs-551	170	48	في	في	PROPN
iajs-551	170	49	:	:	PUNCT
iajs-551	170	50	2011شباط	2011شباط	NUM
iajs-551	170	51	18استلم	18استلم	NUM
iajs-551	170	52	البحث	البحث	VERB
iajs-551	170	53	في	في	PROPN
iajs-551	170	54	:	:	PUNCT
iajs-551	170	55	الخالصة	الخالصة	PROPN
iajs-551	170	56	أفضل	أفضل	PROPN
iajs-551	170	57	تقريب	تقريب	PROPN
iajs-551	170	58	للدوال	للدوال	ADP
iajs-551	170	59	الغير	الغير	ADV
iajs-551	170	60	مقيدة	مقيدة	VERB
iajs-551	170	61	في	في	PRON
iajs-551	170	62	فضاء	فضاء	ADJ
iajs-551	170	63	الوزن	الوزن	PROPN
iajs-551	170	64	الغرض	الغرض	PROPN
iajs-551	170	65	من	من	PROPN
iajs-551	170	66	هذا	هذا	NOUN
iajs-551	170	67	البحث	البحث	NOUN
iajs-551	170	68	هو	هو	PROPN
iajs-551	170	69	دراسة	دراسة	PROPN
iajs-551	170	70	درجة	درجة	PROPN
iajs-551	170	71	,	,	PUNCT
iajs-551	170	72	(	(	PUNCT
iajs-551	170	73	1	1	NUM
iajs-551	170	74	)	)	PUNCT
iajs-551	170	75	,	,	PUNCT
iajs-551	170	76	0,α	0,α	PROPN
iajs-551	171	1	α≤	α≤	NOUN
iajs-551	171	2	≤	≤	NOUN
iajs-551	172	1	∞	∞	PROPN
iajs-551	172	2	>	>	PUNCT
iajs-551	172	3	p	p	PROPN
iajs-551	172	4	pl	pl	PROPN
iajs-551	172	5	.	.	PROPN
iajs-551	172	6	فضاء	فضاء	PROPN
iajs-551	172	7	الوزن	الوزن	PROPN
iajs-551	172	8	،	،	PROPN
iajs-551	172	9	الدوال	الدوال	PROPN
iajs-551	172	10	غير	غير	PROPN
iajs-551	172	11	المقيدة	المقيدة	PROPN
iajs-551	172	12	،	،	PROPN
iajs-551	172	13	التقريب	التقريب	PROPN
iajs-551	172	14	الرتيب	الرتيب	PROPN
iajs-551	172	15	.	.	PUNCT
iajs-551	173	1	:	:	PUNCT
iajs-551	173	2	الكلمات	الكلمات	VERB
iajs-551	173	3	المفتاحية	المفتاحية	NOUN
iajs-551	173	4	received	receive	VERB
iajs-551	173	5	in	in	ADP
iajs-551	173	6	:	:	PUNCT
iajs-551	173	7	18	18	NUM
iajs-551	173	8	february	february	NOUN
iajs-551	173	9	2011	2011	NUM
iajs-551	173	10	accepted	accept	VERB
iajs-551	173	11	in	in	ADP
iajs-551	173	12	:	:	PUNCT
iajs-551	173	13	18	18	NUM
iajs-551	173	14	march	march	NOUN
iajs-551	173	15	2012	2012	NUM