id	sid	tid	token	lemma	pos
iajs-116	1	1	microsoft	microsoft	PROPN
iajs-116	1	2	word	word	NOUN
iajs-116	1	3	271	271	NUM
iajs-116	1	4	-	-	SYM
iajs-116	1	5	281	281	NUM
iajs-116	1	6	mathematics	mathematic	NOUN
iajs-116	1	7	|	|	ADV
iajs-116	1	8	271	271	NUM
iajs-116	1	9	2016	2016	NUM
iajs-116	1	10	)	)	PUNCT
iajs-116	1	11	عام	عام	ADP
iajs-116	1	12	2العدد	2العدد	NUM
iajs-116	1	13	(	(	PUNCT
iajs-116	1	14	29مجلة	29مجلة	NUM
iajs-116	1	15	إبن	إبن	VERB
iajs-116	1	16	الهيثم	الهيثم	ADJ
iajs-116	1	17	للعلوم	للعلوم	NOUN
iajs-116	1	18	الصرفة	الصرفة	NOUN
iajs-116	2	1	و	و	PRON
iajs-116	2	2	التطبيقية	التطبيقية	ADV
iajs-116	2	3	المجلد	المجلد	VERB
iajs-116	2	4	ibn	ibn	PROPN
iajs-116	2	5	al	al	PROPN
iajs-116	2	6	-	-	PUNCT
iajs-116	2	7	haitham	haitham	PROPN
iajs-116	2	8	jour	jour	X
iajs-116	2	9	.	.	PROPN
iajs-116	3	1	for	for	ADP
iajs-116	3	2	pure	pure	ADJ
iajs-116	3	3	&	&	CCONJ
iajs-116	3	4	appl	appl	PROPN
iajs-116	3	5	.	.	PUNCT
iajs-116	4	1	sci	sci	PROPN
iajs-116	4	2	.	.	PUNCT
iajs-116	4	3	vol	vol	NOUN
iajs-116	4	4	.	.	PROPN
iajs-116	4	5	29	29	NUM
iajs-116	4	6	(	(	PUNCT
iajs-116	4	7	2	2	NUM
iajs-116	4	8	)	)	PUNCT
iajs-116	4	9	2016	2016	NUM
iajs-116	4	10	on	on	ADP
iajs-116	4	11	the	the	DET
iajs-116	4	12	degree	degree	NOUN
iajs-116	4	13	of	of	ADP
iajs-116	4	14	best	good	ADJ
iajs-116	4	15	approximation	approximation	NOUN
iajs-116	4	16	of	of	ADP
iajs-116	4	17	unbounded	unbounded	ADJ
iajs-116	4	18	functions	function	NOUN
iajs-116	4	19	by	by	ADP
iajs-116	4	20	algebraic	algebraic	PROPN
iajs-116	4	21	polynomial	polynomial	PROPN
iajs-116	4	22	alaa	alaa	PROPN
iajs-116	4	23	a.	a.	PROPN
iajs-116	4	24	auad	auad	PROPN
iajs-116	4	25	dept	dept	PROPN
iajs-116	4	26	.	.	PROPN
iajs-116	5	1	of	of	ADP
iajs-116	5	2	mathematics	mathematics	PROPN
iajs-116	5	3	/	/	SYM
iajs-116	5	4	college	college	NOUN
iajs-116	5	5	of	of	ADP
iajs-116	5	6	education	education	NOUN
iajs-116	5	7	for	for	ADP
iajs-116	5	8	pure	pure	ADJ
iajs-116	5	9	science	science	NOUN
iajs-116	5	10	/	/	SYM
iajs-116	5	11	university	university	NOUN
iajs-116	5	12	of	of	ADP
iajs-116	5	13	alanbar	alanbar	NOUN
iajs-116	5	14	received	receive	VERB
iajs-116	5	15	in:27	in:27	PROPN
iajs-116	5	16	/	/	SYM
iajs-116	5	17	march/2016,accepted	march/2016,accepte	VERB
iajs-116	5	18	in:22	in:22	PROPN
iajs-116	5	19	/	/	SYM
iajs-116	5	20	may/2016	may/2016	NOUN
iajs-116	5	21	abstract	abstract	NOUN
iajs-116	5	22	in	in	ADP
iajs-116	5	23	this	this	DET
iajs-116	5	24	paper	paper	NOUN
iajs-116	5	25	we	we	PRON
iajs-116	5	26	introduce	introduce	VERB
iajs-116	5	27	a	a	DET
iajs-116	5	28	new	new	ADJ
iajs-116	5	29	class	class	NOUN
iajs-116	5	30	of	of	ADP
iajs-116	5	31	degree	degree	NOUN
iajs-116	5	32	of	of	ADP
iajs-116	5	33	best	good	ADJ
iajs-116	5	34	algebraic	algebraic	ADJ
iajs-116	5	35	approximation	approximation	NOUN
iajs-116	5	36	polynomial	polynomial	ADJ
iajs-116	5	37	α	α	PROPN
iajs-116	5	38	,	,	PUNCT
iajs-116	5	39	,	,	PUNCT
iajs-116	5	40	for	for	ADP
iajs-116	5	41	unbounded	unbounded	ADJ
iajs-116	5	42	functions	function	NOUN
iajs-116	5	43	in	in	ADP
iajs-116	5	44	weighted	weight	VERB
iajs-116	5	45	space	space	NOUN
iajs-116	5	46	lp	lp	PROPN
iajs-116	5	47	,	,	PUNCT
iajs-116	5	48	α(x	α(x	NOUN
iajs-116	5	49	)	)	PUNCT
iajs-116	5	50	,	,	PUNCT
iajs-116	5	51	1	1	NUM
iajs-116	5	52	∞	∞	NUM
iajs-116	5	53	.we	.we	PUNCT
iajs-116	6	1	shall	shall	AUX
iajs-116	6	2	prove	prove	VERB
iajs-116	6	3	direct	direct	ADJ
iajs-116	6	4	and	and	CCONJ
iajs-116	6	5	converse	converse	NOUN
iajs-116	6	6	theorems	theorem	NOUN
iajs-116	6	7	for	for	ADP
iajs-116	6	8	best	good	ADJ
iajs-116	6	9	algebraic	algebraic	ADJ
iajs-116	6	10	approximation	approximation	NOUN
iajs-116	6	11	in	in	ADP
iajs-116	6	12	terms	term	NOUN
iajs-116	6	13	modulus	modulus	NOUN
iajs-116	6	14	of	of	ADP
iajs-116	6	15	smoothness	smoothness	NOUN
iajs-116	6	16	in	in	ADP
iajs-116	6	17	weighted	weighted	ADJ
iajs-116	6	18	space	space	NOUN
iajs-116	6	19	.	.	PUNCT
iajs-116	7	1	keyword	keyword	NOUN
iajs-116	7	2	:	:	PUNCT
iajs-116	7	3	degree	degree	NOUN
iajs-116	7	4	of	of	ADP
iajs-116	7	5	best	good	ADJ
iajs-116	7	6	approximation	approximation	NOUN
iajs-116	7	7	,	,	PUNCT
iajs-116	7	8	unbounded	unbounded	ADJ
iajs-116	7	9	functions	function	NOUN
iajs-116	7	10	,	,	PUNCT
iajs-116	7	11	weight	weight	NOUN
iajs-116	7	12	space	space	NOUN
iajs-116	7	13	,	,	PUNCT
iajs-116	7	14	modulus	modulus	NOUN
iajs-116	7	15	of	of	ADP
iajs-116	7	16	smoothness	smoothness	NOUN
iajs-116	7	17	.	.	PUNCT
iajs-116	8	1	mathematics	mathematic	NOUN
iajs-116	8	2	|	|	ADV
iajs-116	8	3	272	272	NUM
iajs-116	8	4	2016	2016	NUM
iajs-116	8	5	)	)	PUNCT
iajs-116	8	6	عام	عام	ADP
iajs-116	8	7	2العدد	2العدد	NUM
iajs-116	8	8	(	(	PUNCT
iajs-116	8	9	29لمجلد	29لمجلد	NUM
iajs-116	8	10	ا	ا	X
iajs-116	8	11	مجلة	مجلة	NOUN
iajs-116	8	12	إبن	إبن	VERB
iajs-116	8	13	الهيثم	الهيثم	ADJ
iajs-116	8	14	للعلوم	للعلوم	NOUN
iajs-116	8	15	الصرفة	الصرفة	NOUN
iajs-116	9	1	و	و	PRON
iajs-116	9	2	التطبيقية	التطبيقية	ADJ
iajs-116	9	3	ibn	ibn	PROPN
iajs-116	9	4	al	al	PROPN
iajs-116	9	5	-	-	PUNCT
iajs-116	9	6	haitham	haitham	PROPN
iajs-116	9	7	jour	jour	X
iajs-116	9	8	.	.	PROPN
iajs-116	9	9	for	for	ADP
iajs-116	9	10	pure	pure	ADJ
iajs-116	9	11	&	&	CCONJ
iajs-116	9	12	appl	appl	PROPN
iajs-116	9	13	.	.	PUNCT
iajs-116	10	1	sci	sci	PROPN
iajs-116	10	2	.	.	PUNCT
iajs-116	10	3	vol	vol	NOUN
iajs-116	10	4	.	.	PROPN
iajs-116	10	5	29	29	NUM
iajs-116	10	6	(	(	PUNCT
iajs-116	10	7	2	2	NUM
iajs-116	10	8	)	)	PUNCT
iajs-116	10	9	2016	2016	NUM
iajs-116	10	10	1	1	NUM
iajs-116	10	11	.	.	PUNCT
iajs-116	11	1	introduction	introduction	NOUN
iajs-116	11	2	many	many	ADJ
iajs-116	11	3	papers	paper	NOUN
iajs-116	11	4	have	have	AUX
iajs-116	11	5	recently	recently	ADV
iajs-116	11	6	appeared	appear	VERB
iajs-116	11	7	connected	connect	VERB
iajs-116	11	8	with	with	ADP
iajs-116	11	9	best	good	ADJ
iajs-116	11	10	approximation	approximation	NOUN
iajs-116	11	11	to	to	ADP
iajs-116	11	12	functions	function	NOUN
iajs-116	11	13	of	of	ADP
iajs-116	11	14	one	one	NUM
iajs-116	11	15	variable	variable	NOUN
iajs-116	11	16	see	see	VERB
iajs-116	11	17	[	[	X
iajs-116	11	18	1,2,3	1,2,3	NOUN
iajs-116	11	19	]	]	PUNCT
iajs-116	11	20	and	and	CCONJ
iajs-116	11	21	the	the	DET
iajs-116	11	22	references	reference	NOUN
iajs-116	11	23	there	there	ADV
iajs-116	11	24	.	.	PUNCT
iajs-116	12	1	in	in	ADP
iajs-116	12	2	this	this	DET
iajs-116	12	3	paper	paper	NOUN
iajs-116	12	4	we	we	PRON
iajs-116	12	5	shall	shall	AUX
iajs-116	12	6	consider	consider	VERB
iajs-116	12	7	the	the	DET
iajs-116	12	8	degree	degree	NOUN
iajs-116	12	9	of	of	ADP
iajs-116	12	10	best	good	ADJ
iajs-116	12	11	algebraic	algebraic	ADJ
iajs-116	12	12	approximation	approximation	NOUN
iajs-116	12	13	of	of	ADP
iajs-116	12	14	unbounded	unbounded	ADJ
iajs-116	12	15	functions	function	NOUN
iajs-116	12	16	.	.	PUNCT
iajs-116	13	1	indeed	indeed	ADV
iajs-116	13	2	,	,	PUNCT
iajs-116	13	3	in	in	ADP
iajs-116	13	4	terms	term	NOUN
iajs-116	13	5	of	of	ADP
iajs-116	13	6	the	the	DET
iajs-116	13	7	modulus	modulus	NOUN
iajs-116	13	8	of	of	ADP
iajs-116	13	9	smoothness	smoothness	ADJ
iajs-116	13	10	direct	direct	NOUN
iajs-116	13	11	(	(	PUNCT
iajs-116	13	12	jackson	jackson	PROPN
iajs-116	13	13	–	–	PUNCT
iajs-116	13	14	type	type	NOUN
iajs-116	13	15	)	)	PUNCT
iajs-116	13	16	as	as	ADV
iajs-116	13	17	well	well	ADV
iajs-116	13	18	as	as	ADP
iajs-116	13	19	inverse	inverse	NOUN
iajs-116	13	20	(	(	PUNCT
iajs-116	13	21	bernstein	bernstein	PROPN
iajs-116	13	22	–	–	PUNCT
iajs-116	13	23	type	type	NOUN
iajs-116	13	24	)	)	PUNCT
iajs-116	13	25	theorems	theorem	NOUN
iajs-116	13	26	are	be	AUX
iajs-116	13	27	established	establish	VERB
iajs-116	13	28	so	so	SCONJ
iajs-116	13	29	that	that	SCONJ
iajs-116	13	30	a	a	DET
iajs-116	13	31	constructive	constructive	ADJ
iajs-116	13	32	theory	theory	NOUN
iajs-116	13	33	of	of	ADP
iajs-116	13	34	unbounded	unbounded	ADJ
iajs-116	13	35	functions	function	NOUN
iajs-116	13	36	may	may	AUX
iajs-116	13	37	developed	develop	VERB
iajs-116	13	38	in	in	ADP
iajs-116	13	39	weighted	weight	VERB
iajs-116	13	40	space	space	NOUN
iajs-116	13	41	lp	lp	PROPN
iajs-116	13	42	,	,	PUNCT
iajs-116	13	43	α(x	α(x	NOUN
iajs-116	13	44	)	)	PUNCT
iajs-116	13	45	.	.	PUNCT
iajs-116	14	1	let	let	VERB
iajs-116	14	2	∞,∞	∞,∞	NOUN
iajs-116	14	3	,	,	PUNCT
iajs-116	14	4	by‖.	by‖.	PROPN
iajs-116	14	5	‖	‖	PROPN
iajs-116	14	6	we	we	PRON
iajs-116	14	7	denote	denote	VERB
iajs-116	14	8	the	the	DET
iajs-116	14	9	lp(x)norm	lp(x)norm	NOUN
iajs-116	14	10	,	,	PUNCT
iajs-116	14	11	1	1	NUM
iajs-116	14	12	p	p	NOUN
iajs-116	14	13	˂	˂	PROPN
iajs-116	14	14	∞	∞	PROPN
iajs-116	14	15	and	and	CCONJ
iajs-116	14	16	‖	‖	PROPN
iajs-116	14	17	‖	‖	PROPN
iajs-116	15	1	|	|	ADV
iajs-116	15	2	|	|	ADV
iajs-116	15	3	∞	∞	NUM
iajs-116	15	4	…	…	PUNCT
iajs-116	15	5	…	…	PUNCT
iajs-116	15	6	…	…	PUNCT
iajs-116	15	7	…	…	PUNCT
iajs-116	15	8	…	…	PUNCT
iajs-116	15	9	…	…	PUNCT
iajs-116	15	10	…	…	PUNCT
iajs-116	15	11	…	…	PUNCT
iajs-116	15	12	…	…	PUNCT
iajs-116	15	13	…	…	PUNCT
iajs-116	15	14	.(1	.(1	NUM
iajs-116	15	15	)	)	PUNCT
iajs-116	15	16	and	and	CCONJ
iajs-116	15	17	define	define	VERB
iajs-116	15	18	for	for	ADP
iajs-116	15	19	a	a	DET
iajs-116	15	20	suitable	suitable	ADJ
iajs-116	15	21	set	set	NOUN
iajs-116	15	22	,	,	PUNCT
iajs-116	15	23	of	of	ADP
iajs-116	15	24	all	all	DET
iajs-116	15	25	weight	weight	NOUN
iajs-116	15	26	functions	function	NOUN
iajs-116	15	27	on	on	ADP
iajs-116	15	28	open	open	ADJ
iajs-116	15	29	interval	interval	NOUN
iajs-116	15	30	,	,	PUNCT
iajs-116	15	31	such	such	ADJ
iajs-116	15	32	that	that	SCONJ
iajs-116	15	33	|	|	ADV
iajs-116	15	34	|	|	ADV
iajs-116	15	35	,	,	PUNCT
iajs-116	15	36	where	where	SCONJ
iajs-116	15	37	m	m	NOUN
iajs-116	15	38	is	be	AUX
iajs-116	15	39	positive	positive	ADJ
iajs-116	15	40	real	real	ADJ
iajs-116	15	41	number	number	NOUN
iajs-116	15	42	and	and	CCONJ
iajs-116	15	43	:	:	PUNCT
iajs-116	15	44	→	→	SYM
iajs-116	15	45	weight	weight	NOUN
iajs-116	15	46	function	function	NOUN
iajs-116	15	47	.	.	PUNCT
iajs-116	16	1	we	we	PRON
iajs-116	16	2	shall	shall	AUX
iajs-116	16	3	denote	denote	VERB
iajs-116	16	4	by	by	ADP
iajs-116	16	5	lp	lp	PROPN
iajs-116	16	6	,	,	PUNCT
iajs-116	16	7	α(x	α(x	NOUN
iajs-116	16	8	)	)	PUNCT
iajs-116	16	9	the	the	DET
iajs-116	16	10	space	space	NOUN
iajs-116	16	11	of	of	ADP
iajs-116	16	12	all	all	DET
iajs-116	16	13	unbounded	unbounded	ADJ
iajs-116	16	14	functions	function	NOUN
iajs-116	16	15	on	on	ADP
iajs-116	16	16	,	,	PUNCT
iajs-116	16	17	which	which	PRON
iajs-116	16	18	are	be	AUX
iajs-116	16	19	equipped	equip	VERB
iajs-116	16	20	with	with	ADP
iajs-116	16	21	the	the	DET
iajs-116	16	22	following	follow	VERB
iajs-116	16	23	norm	norm	NOUN
iajs-116	16	24	‖	‖	PROPN
iajs-116	16	25	‖	‖	PROPN
iajs-116	16	26	,	,	PUNCT
iajs-116	16	27	|	|	ADV
iajs-116	17	1	|	|	ADV
iajs-116	17	2	∞.	∞.	PROPN
iajs-116	17	3	…	…	PUNCT
iajs-116	17	4	…	…	PUNCT
iajs-116	17	5	..	..	PUNCT
iajs-116	17	6	(	(	PUNCT
iajs-116	17	7	2	2	X
iajs-116	17	8	)	)	PUNCT
iajs-116	18	1	for	for	ADP
iajs-116	18	2	∈	∈	PROPN
iajs-116	18	3	,	,	PUNCT
iajs-116	18	4	and	and	CCONJ
iajs-116	18	5	∈	∈	PROPN
iajs-116	18	6	,	,	PUNCT
iajs-116	18	7	we	we	PRON
iajs-116	18	8	define	define	VERB
iajs-116	18	9	the	the	DET
iajs-116	18	10	local	local	ADJ
iajs-116	18	11	modulus	modulus	NOUN
iajs-116	18	12	of	of	ADP
iajs-116	18	13	order	order	NOUN
iajs-116	18	14	of	of	ADP
iajs-116	18	15	in	in	ADP
iajs-116	18	16	point	point	NOUN
iajs-116	18	17	as	as	SCONJ
iajs-116	18	18	follows	follow	VERB
iajs-116	18	19	,	,	PUNCT
iajs-116	18	20	,	,	PUNCT
iajs-116	18	21	,	,	PUNCT
iajs-116	18	22	|	|	ADV
iajs-116	18	23	|	|	ADV
iajs-116	18	24	∆	∆	PROPN
iajs-116	18	25	∶	∶	NOUN
iajs-116	18	26	,	,	PUNCT
iajs-116	18	27	∈	∈	PROPN
iajs-116	18	28	,	,	PUNCT
iajs-116	18	29	∩	∩	NOUN
iajs-116	18	30	…	…	PUNCT
iajs-116	18	31	…	…	PUNCT
iajs-116	18	32	…	…	PUNCT
iajs-116	18	33	...	...	PUNCT
iajs-116	18	34	(	(	PUNCT
iajs-116	18	35	3	3	X
iajs-116	18	36	)	)	PUNCT
iajs-116	18	37	where	where	SCONJ
iajs-116	18	38	∆	∆	PROPN
iajs-116	18	39	∑	∑	PROPN
iajs-116	18	40	1	1	NUM
iajs-116	18	41	,	,	PUNCT
iajs-116	18	42	∈	∈	PROPN
iajs-116	18	43	0	0	NUM
iajs-116	18	44	…	…	PUNCT
iajs-116	18	45	…	…	PUNCT
iajs-116	18	46	…	…	PUNCT
iajs-116	18	47	.(4	.(4	NUM
iajs-116	18	48	)	)	PUNCT
iajs-116	18	49	.	.	PUNCT
iajs-116	19	1	also	also	ADV
iajs-116	19	2	the	the	DET
iajs-116	19	3	modulus	modulus	NOUN
iajs-116	19	4	of	of	ADP
iajs-116	19	5	smoothness	smoothness	NOUN
iajs-116	19	6	of	of	ADP
iajs-116	19	7	order	order	NOUN
iajs-116	19	8	of	of	ADP
iajs-116	19	9	function	function	NOUN
iajs-116	19	10	is	be	AUX
iajs-116	19	11	the	the	DET
iajs-116	19	12	following	follow	VERB
iajs-116	19	13	function	function	NOUN
iajs-116	19	14	of	of	ADP
iajs-116	19	15	:	:	PUNCT
iajs-116	19	16	,	,	PUNCT
iajs-116	19	17	,	,	PUNCT
iajs-116	19	18	|	|	ADV
iajs-116	19	19	|	|	ADV
iajs-116	19	20	∆	∆	PROPN
iajs-116	19	21	.	.	PUNCT
iajs-116	20	1	,	,	PUNCT
iajs-116	20	2	…	…	PUNCT
iajs-116	20	3	…	…	PUNCT
iajs-116	20	4	…	…	PUNCT
iajs-116	20	5	…	…	PUNCT
iajs-116	20	6	…	…	PUNCT
iajs-116	20	7	…	…	PUNCT
iajs-116	20	8	…	…	PUNCT
iajs-116	20	9	…	…	PUNCT
iajs-116	20	10	…	…	PUNCT
iajs-116	20	11	…	…	PUNCT
iajs-116	20	12	…	…	SYM
iajs-116	20	13	.	.	PUNCT
iajs-116	20	14	…	…	PUNCT
iajs-116	20	15	(5	(5	X
iajs-116	20	16	)	)	PUNCT
iajs-116	20	17	.	.	PUNCT
iajs-116	21	1	let	let	AUX
iajs-116	21	2	be	be	AUX
iajs-116	21	3	the	the	DET
iajs-116	21	4	set	set	NOUN
iajs-116	21	5	of	of	ADP
iajs-116	21	6	natural	natural	ADJ
iajs-116	21	7	numbers	number	NOUN
iajs-116	21	8	and	and	CCONJ
iajs-116	21	9	ℙ	ℙ	PRON
iajs-116	21	10	the	the	DET
iajs-116	21	11	set	set	NOUN
iajs-116	21	12	of	of	ADP
iajs-116	21	13	all	all	DET
iajs-116	21	14	algebraic	algebraic	ADJ
iajs-116	21	15	polynomials	polynomial	NOUN
iajs-116	21	16	of	of	ADP
iajs-116	21	17	degree	degree	NOUN
iajs-116	21	18	less	less	ADJ
iajs-116	21	19	than	than	ADP
iajs-116	21	20	or	or	CCONJ
iajs-116	21	21	equal	equal	ADJ
iajs-116	21	22	to	to	ADP
iajs-116	21	23	∈	∈	PROPN
iajs-116	21	24	.	.	PUNCT
iajs-116	22	1	the	the	DET
iajs-116	22	2	degree	degree	NOUN
iajs-116	22	3	of	of	ADP
iajs-116	22	4	best	good	ADJ
iajs-116	22	5	algebraic	algebraic	ADJ
iajs-116	22	6	approximation	approximation	NOUN
iajs-116	22	7	of	of	ADP
iajs-116	22	8	order	order	NOUN
iajs-116	22	9	of	of	ADP
iajs-116	22	10	the	the	DET
iajs-116	22	11	function	function	NOUN
iajs-116	22	12	∈	∈	PROPN
iajs-116	22	13	,	,	PUNCT
iajs-116	22	14	is	be	AUX
iajs-116	22	15	given	give	VERB
iajs-116	22	16	by	by	ADP
iajs-116	22	17	,	,	PUNCT
iajs-116	22	18	‖	‖	PROPN
iajs-116	22	19	‖	‖	PROPN
iajs-116	22	20	,	,	PUNCT
iajs-116	22	21	;	;	PUNCT
iajs-116	22	22	∈	∈	PROPN
iajs-116	22	23	ℙ	ℙ	PROPN
iajs-116	22	24	…	…	PUNCT
iajs-116	22	25	…	…	PUNCT
iajs-116	22	26	…	…	PUNCT
iajs-116	22	27	…	…	PUNCT
iajs-116	22	28	…	…	PUNCT
iajs-116	22	29	…	…	PUNCT
iajs-116	22	30	…	…	PUNCT
iajs-116	22	31	…	…	SYM
iajs-116	22	32	.	.	NUM
iajs-116	22	33	…	…	PUNCT
iajs-116	22	34	…	…	PUNCT
iajs-116	22	35	..	..	PUNCT
iajs-116	22	36	(6	(6	PROPN
iajs-116	22	37	)	)	PUNCT
iajs-116	22	38	.	.	PUNCT
iajs-116	23	1	the	the	DET
iajs-116	23	2	most	most	ADV
iajs-116	23	3	essential	essential	ADJ
iajs-116	23	4	consequence	consequence	NOUN
iajs-116	23	5	of	of	ADP
iajs-116	23	6	the	the	DET
iajs-116	23	7	proved	prove	VERB
iajs-116	23	8	here	here	ADV
iajs-116	23	9	is	be	AUX
iajs-116	23	10	corollary	corollary	ADJ
iajs-116	23	11	:	:	PUNCT
iajs-116	23	12	for	for	ADP
iajs-116	23	13	0	0	NUM
iajs-116	23	14	and	and	CCONJ
iajs-116	23	15	1	1	NUM
iajs-116	23	16	∞	∞	NUM
iajs-116	23	17	,	,	PUNCT
iajs-116	23	18	we	we	PRON
iajs-116	23	19	have	have	VERB
iajs-116	23	20	,	,	PUNCT
iajs-116	23	21	,	,	PUNCT
iajs-116	23	22	ο	ο	NOUN
iajs-116	24	1	if	if	SCONJ
iajs-116	25	1	and	and	CCONJ
iajs-116	25	2	only	only	ADV
iajs-116	25	3	if	if	SCONJ
iajs-116	25	4	,	,	PUNCT
iajs-116	25	5	ο	ο	NOUN
iajs-116	25	6	.	.	PUNCT
iajs-116	26	1	mathematics	mathematic	NOUN
iajs-116	26	2	|	|	ADV
iajs-116	26	3	273	273	NUM
iajs-116	26	4	2016	2016	NUM
iajs-116	26	5	)	)	PUNCT
iajs-116	26	6	عام	عام	ADP
iajs-116	26	7	2العدد	2العدد	NUM
iajs-116	26	8	(	(	PUNCT
iajs-116	26	9	29لمجلد	29لمجلد	NUM
iajs-116	26	10	ا	ا	X
iajs-116	26	11	مجلة	مجلة	NOUN
iajs-116	26	12	إبن	إبن	VERB
iajs-116	26	13	الهيثم	الهيثم	ADJ
iajs-116	26	14	للعلوم	للعلوم	NOUN
iajs-116	26	15	الصرفة	الصرفة	NOUN
iajs-116	27	1	و	و	PRON
iajs-116	27	2	التطبيقية	التطبيقية	ADJ
iajs-116	27	3	ibn	ibn	PROPN
iajs-116	27	4	al	al	PROPN
iajs-116	27	5	-	-	PUNCT
iajs-116	27	6	haitham	haitham	PROPN
iajs-116	27	7	jour	jour	X
iajs-116	27	8	.	.	PROPN
iajs-116	27	9	for	for	ADP
iajs-116	27	10	pure	pure	ADJ
iajs-116	27	11	&	&	CCONJ
iajs-116	27	12	appl	appl	PROPN
iajs-116	27	13	.	.	PUNCT
iajs-116	28	1	sci	sci	PROPN
iajs-116	28	2	.	.	PUNCT
iajs-116	28	3	vol	vol	NOUN
iajs-116	28	4	.	.	PROPN
iajs-116	28	5	29	29	NUM
iajs-116	28	6	(	(	PUNCT
iajs-116	28	7	2	2	NUM
iajs-116	28	8	)	)	PUNCT
iajs-116	28	9	2016	2016	NUM
iajs-116	28	10	if	if	SCONJ
iajs-116	28	11	and	and	CCONJ
iajs-116	28	12	,	,	PUNCT
iajs-116	28	13	are	be	AUX
iajs-116	28	14	positive	positive	ADJ
iajs-116	28	15	integer	integer	NOUN
iajs-116	28	16	and	and	CCONJ
iajs-116	28	17	0	0	NUM
iajs-116	28	18	,	,	PUNCT
iajs-116	28	19	then	then	ADV
iajs-116	28	20	,	,	PUNCT
iajs-116	28	21	ο	ο	NOUN
iajs-116	28	22	equivalently	equivalently	ADV
iajs-116	28	23	,	,	PUNCT
iajs-116	28	24	,	,	PUNCT
iajs-116	28	25	ο	ο	NOUN
iajs-116	28	26	is	be	AUX
iajs-116	28	27	valid	valid	ADJ
iajs-116	28	28	if	if	SCONJ
iajs-116	28	29	and	and	CCONJ
iajs-116	28	30	only	only	ADV
iajs-116	28	31	if	if	SCONJ
iajs-116	28	32	has	have	VERB
iajs-116	28	33	a	a	DET
iajs-116	28	34	derivative	derivative	NOUN
iajs-116	28	35	of	of	ADP
iajs-116	28	36	order	order	NOUN
iajs-116	28	37	satisfying	satisfying	ADJ
iajs-116	28	38	,	,	PUNCT
iajs-116	28	39	∞	∞	PROPN
iajs-116	28	40	and	and	CCONJ
iajs-116	28	41	,	,	PUNCT
iajs-116	28	42	,	,	PUNCT
iajs-116	28	43	ο	ο	INTJ
iajs-116	28	44	.	.	PUNCT
iajs-116	29	1	further	further	ADJ
iajs-116	29	2	details	detail	NOUN
iajs-116	29	3	and	and	CCONJ
iajs-116	29	4	elementary	elementary	ADJ
iajs-116	29	5	properties	property	NOUN
iajs-116	29	6	of	of	ADP
iajs-116	29	7	,	,	PUNCT
iajs-116	29	8	,	,	PUNCT
iajs-116	29	9	see	see	VERB
iajs-116	29	10	[	[	X
iajs-116	29	11	4,5	4,5	NUM
iajs-116	29	12	]	]	PUNCT
iajs-116	29	13	.	.	PUNCT
iajs-116	30	1	with	with	ADP
iajs-116	30	2	the	the	DET
iajs-116	30	3	aid	aid	NOUN
iajs-116	30	4	of	of	ADP
iajs-116	30	5	these	these	DET
iajs-116	30	6	concepts	concept	NOUN
iajs-116	30	7	one	one	PRON
iajs-116	30	8	may	may	AUX
iajs-116	30	9	now	now	ADV
iajs-116	30	10	work	work	VERB
iajs-116	30	11	out	out	ADP
iajs-116	30	12	a	a	DET
iajs-116	30	13	constructive	constructive	ADJ
iajs-116	30	14	theory	theory	NOUN
iajs-116	30	15	of	of	ADP
iajs-116	30	16	functions	function	NOUN
iajs-116	30	17	for	for	ADP
iajs-116	30	18	the	the	DET
iajs-116	30	19	weight	weight	NOUN
iajs-116	30	20	space	space	NOUN
iajs-116	30	21	,	,	PUNCT
iajs-116	30	22	,	,	PUNCT
iajs-116	30	23	parallel	parallel	ADJ
iajs-116	30	24	to	to	ADP
iajs-116	30	25	classical	classical	ADJ
iajs-116	30	26	theory	theory	NOUN
iajs-116	30	27	of	of	ADP
iajs-116	30	28	jackson	jackson	PROPN
iajs-116	30	29	-	-	PUNCT
iajs-116	30	30	bernstein	bernstein	PROPN
iajs-116	30	31	for	for	ADP
iajs-116	30	32	,	,	PUNCT
iajs-116	30	33	,	,	PUNCT
iajs-116	30	34	see	see	VERB
iajs-116	30	35	sections	section	NOUN
iajs-116	30	36	2	2	NUM
iajs-116	30	37	and	and	CCONJ
iajs-116	30	38	3	3	NUM
iajs-116	30	39	for	for	ADP
iajs-116	30	40	detail	detail	NOUN
iajs-116	30	41	.	.	PUNCT
iajs-116	31	1	we	we	PRON
iajs-116	31	2	formulate	formulate	VERB
iajs-116	31	3	and	and	CCONJ
iajs-116	31	4	prove	prove	VERB
iajs-116	31	5	our	our	PRON
iajs-116	31	6	jackson	jackson	PROPN
iajs-116	31	7	-	-	PUNCT
iajs-116	31	8	type	type	NOUN
iajs-116	31	9	theorem	theorem	NOUN
iajs-116	31	10	and	and	CCONJ
iajs-116	31	11	in	in	ADP
iajs-116	31	12	section	section	NOUN
iajs-116	31	13	3	3	NUM
iajs-116	31	14	,	,	PUNCT
iajs-116	31	15	we	we	PRON
iajs-116	31	16	formulate	formulate	VERB
iajs-116	31	17	and	and	CCONJ
iajs-116	31	18	prove	prove	VERB
iajs-116	31	19	our	our	PRON
iajs-116	31	20	bernstein	bernstein	NOUN
iajs-116	31	21	-	-	PUNCT
iajs-116	31	22	type	type	NOUN
iajs-116	31	23	theorem	theorem	NOUN
iajs-116	31	24	.	.	PUNCT
iajs-116	32	1	the	the	DET
iajs-116	32	2	corollary	corollary	NOUN
iajs-116	32	3	announced	announce	VERB
iajs-116	32	4	above	above	ADV
iajs-116	32	5	follows	follow	VERB
iajs-116	32	6	from	from	ADP
iajs-116	32	7	direct	direct	ADJ
iajs-116	32	8	theorem	theorem	NOUN
iajs-116	32	9	(	(	PUNCT
iajs-116	32	10	1	1	NUM
iajs-116	32	11	)	)	PUNCT
iajs-116	32	12	of	of	ADP
iajs-116	32	13	section	section	NOUN
iajs-116	32	14	2	2	NUM
iajs-116	32	15	combined	combine	VERB
iajs-116	32	16	with	with	ADP
iajs-116	32	17	converse	converse	NOUN
iajs-116	32	18	theorem	theorem	NOUN
iajs-116	32	19	(	(	PUNCT
iajs-116	32	20	2	2	NUM
iajs-116	32	21	)	)	PUNCT
iajs-116	32	22	of	of	ADP
iajs-116	32	23	section	section	NOUN
iajs-116	32	24	3	3	NUM
iajs-116	32	25	.	.	NOUN
iajs-116	32	26	2	2	NUM
iajs-116	32	27	.	.	PUNCT
iajs-116	33	1	the	the	DET
iajs-116	33	2	direct	direct	ADJ
iajs-116	33	3	algebraic	algebraic	PROPN
iajs-116	33	4	approximation	approximation	NOUN
iajs-116	33	5	theorem	theorem	NOUN
iajs-116	33	6	:	:	PUNCT
iajs-116	33	7	let	let	VERB
iajs-116	33	8	∈	∈	PROPN
iajs-116	33	9	,	,	PUNCT
iajs-116	33	10	,	,	PUNCT
iajs-116	33	11	1	1	NUM
iajs-116	33	12	∞	∞	NOUN
iajs-116	33	13	,	,	PUNCT
iajs-116	33	14	natural	natural	ADJ
iajs-116	33	15	number	number	NOUN
iajs-116	33	16	and	and	CCONJ
iajs-116	33	17	0	0	NUM
iajs-116	33	18	.	.	PUNCT
iajs-116	34	1	we	we	PRON
iajs-116	34	2	define	define	VERB
iajs-116	34	3	α	α	PRON
iajs-116	34	4	,	,	PUNCT
iajs-116	34	5	∑	∑	PROPN
iajs-116	34	6	1	1	NUM
iajs-116	34	7	…	…	SYM
iajs-116	34	8	…	…	PUNCT
iajs-116	34	9	…	…	PUNCT
iajs-116	34	10	…	…	PUNCT
iajs-116	34	11	…	…	PUNCT
iajs-116	34	12	…	…	PUNCT
iajs-116	34	13	…	…	SYM
iajs-116	34	14	.	.	PUNCT
iajs-116	34	15	…	…	PUNCT
iajs-116	34	16	(7	(7	NOUN
iajs-116	34	17	)	)	PUNCT
iajs-116	34	18	.	.	PUNCT
iajs-116	35	1	we	we	PRON
iajs-116	35	2	set	set	VERB
iajs-116	35	3	|	|	ADV
iajs-116	35	4	|	|	ADV
iajs-116	35	5	√	√	INTJ
iajs-116	35	6	0	0	NUM
iajs-116	36	1	|	|	CCONJ
iajs-116	36	2	|	|	ADV
iajs-116	36	3	√	√	INTJ
iajs-116	36	4	and	and	CCONJ
iajs-116	36	5	√	√	PROPN
iajs-116	36	6	,	,	PUNCT
iajs-116	36	7	α	α	X
iajs-116	36	8	,	,	PUNCT
iajs-116	36	9	,	,	PUNCT
iajs-116	36	10	.	.	PUNCT
iajs-116	37	1	it	it	PRON
iajs-116	37	2	is	be	AUX
iajs-116	37	3	clear	clear	ADJ
iajs-116	37	4	that	that	SCONJ
iajs-116	37	5	∈	∈	PROPN
iajs-116	37	6	ℙ	ℙ	PROPN
iajs-116	37	7	.	.	PUNCT
iajs-116	38	1	lemma	lemma	PROPN
iajs-116	38	2	1	1	NUM
iajs-116	39	1	[	[	X
iajs-116	39	2	4	4	NUM
iajs-116	39	3	]	]	PUNCT
iajs-116	39	4	:	:	PUNCT
iajs-116	39	5	we	we	PRON
iajs-116	39	6	have	have	VERB
iajs-116	39	7	for	for	ADP
iajs-116	39	8	every	every	DET
iajs-116	39	9	1	1	NUM
iajs-116	39	10	∞	∞	NUM
iajs-116	39	11	,	,	PUNCT
iajs-116	39	12	0	0	NUM
iajs-116	39	13	1	1	NUM
iajs-116	39	14	and	and	CCONJ
iajs-116	39	15	every	every	DET
iajs-116	39	16	positive	positive	ADJ
iajs-116	39	17	function	function	NOUN
iajs-116	39	18	α	α	NOUN
iajs-116	39	19	,	,	PUNCT
iajs-116	39	20	∆	∆	PROPN
iajs-116	39	21	and	and	CCONJ
iajs-116	39	22	α	α	NOUN
iajs-116	39	23	,	,	PUNCT
iajs-116	39	24	,	,	PUNCT
iajs-116	39	25	|	|	ADV
iajs-116	39	26	|	|	ADV
iajs-116	39	27	∆	∆	PROPN
iajs-116	39	28	,	,	PUNCT
iajs-116	39	29	1,2	1,2	NUM
iajs-116	39	30	,	,	PUNCT
iajs-116	39	31	…	…	PUNCT
iajs-116	39	32	,	,	PUNCT
iajs-116	39	33	.	.	PUNCT
iajs-116	40	1	prove	prove	VERB
iajs-116	40	2	of	of	ADP
iajs-116	40	3	this	this	PRON
iajs-116	40	4	lemma	lemma	PROPN
iajs-116	40	5	see	see	VERB
iajs-116	40	6	[	[	X
iajs-116	40	7	4	4	NUM
iajs-116	40	8	]	]	PUNCT
iajs-116	40	9	.	.	PUNCT
iajs-116	41	1	lemma	lemma	PROPN
iajs-116	41	2	2	2	NUM
iajs-116	41	3	:	:	PUNCT
iajs-116	41	4	for	for	ADP
iajs-116	41	5	every	every	DET
iajs-116	41	6	∈	∈	PROPN
iajs-116	41	7	,	,	PUNCT
iajs-116	41	8	and	and	CCONJ
iajs-116	41	9	1	1	NUM
iajs-116	41	10	∞	∞	NUM
iajs-116	41	11	,	,	PUNCT
iajs-116	41	12	we	we	PRON
iajs-116	41	13	have	have	VERB
iajs-116	41	14	mathematics	mathematic	NOUN
iajs-116	41	15	|	|	ADV
iajs-116	41	16	274	274	NUM
iajs-116	41	17	2016	2016	NUM
iajs-116	41	18	)	)	PUNCT
iajs-116	41	19	عام	عام	ADP
iajs-116	41	20	2العدد	2العدد	NUM
iajs-116	41	21	(	(	PUNCT
iajs-116	41	22	29لمجلد	29لمجلد	NUM
iajs-116	41	23	ا	ا	X
iajs-116	41	24	مجلة	مجلة	NOUN
iajs-116	41	25	إبن	إبن	VERB
iajs-116	41	26	الهيثم	الهيثم	ADJ
iajs-116	41	27	للعلوم	للعلوم	NOUN
iajs-116	41	28	الصرفة	الصرفة	NOUN
iajs-116	42	1	و	و	PRON
iajs-116	42	2	التطبيقية	التطبيقية	ADJ
iajs-116	42	3	ibn	ibn	PROPN
iajs-116	42	4	al	al	PROPN
iajs-116	42	5	-	-	PUNCT
iajs-116	42	6	haitham	haitham	PROPN
iajs-116	42	7	jour	jour	X
iajs-116	42	8	.	.	PROPN
iajs-116	42	9	for	for	ADP
iajs-116	42	10	pure	pure	ADJ
iajs-116	42	11	&	&	CCONJ
iajs-116	42	12	appl	appl	PROPN
iajs-116	42	13	.	.	PUNCT
iajs-116	43	1	sci	sci	PROPN
iajs-116	43	2	.	.	PUNCT
iajs-116	43	3	vol	vol	NOUN
iajs-116	43	4	.	.	PROPN
iajs-116	43	5	29	29	NUM
iajs-116	43	6	(	(	PUNCT
iajs-116	43	7	2	2	NUM
iajs-116	43	8	)	)	PUNCT
iajs-116	43	9	2016	2016	NUM
iajs-116	43	10	‖	‖	PROPN
iajs-116	43	11	‖	‖	PROPN
iajs-116	43	12	,	,	PUNCT
iajs-116	43	13	,	,	PUNCT
iajs-116	43	14	√	√	INTJ
iajs-116	43	15	,	,	PUNCT
iajs-116	43	16	and	and	CCONJ
iajs-116	43	17	,	,	PUNCT
iajs-116	43	18	,	,	PUNCT
iajs-116	43	19	√	√	INTJ
iajs-116	43	20	,	,	PUNCT
iajs-116	43	21	.	.	PUNCT
iajs-116	44	1	proof	proof	NOUN
iajs-116	44	2	:	:	PUNCT
iajs-116	44	3	from	from	ADP
iajs-116	44	4	theorem	theorem	NOUN
iajs-116	44	5	of	of	ADP
iajs-116	44	6	marchoud	marchoud	NOUN
iajs-116	44	7	see	see	VERB
iajs-116	44	8	[	[	X
iajs-116	44	9	5	5	NUM
iajs-116	44	10	]	]	PUNCT
iajs-116	44	11	,	,	PUNCT
iajs-116	44	12	we	we	PRON
iajs-116	44	13	have	have	VERB
iajs-116	44	14	,	,	PUNCT
iajs-116	44	15	,	,	PUNCT
iajs-116	44	16	‖	‖	PROPN
iajs-116	44	17	‖	‖	PROPN
iajs-116	44	18	,	,	PUNCT
iajs-116	44	19	,	,	PUNCT
iajs-116	44	20	,	,	PUNCT
iajs-116	44	21	since	since	SCONJ
iajs-116	44	22	for	for	ADP
iajs-116	44	23	|	|	ADV
iajs-116	44	24	|	|	ADV
iajs-116	44	25	√	√	INTJ
iajs-116	44	26	,	,	PUNCT
iajs-116	44	27	we	we	PRON
iajs-116	44	28	obtain	obtain	VERB
iajs-116	44	29	|	|	ADV
iajs-116	44	30	|	|	ADV
iajs-116	44	31	for	for	SCONJ
iajs-116	44	32	∈	∈	PROPN
iajs-116	44	33	∞,∞	∞,∞	PROPN
iajs-116	44	34	.	.	PUNCT
iajs-116	45	1	consequently	consequently	ADV
iajs-116	45	2	‖	‖	PROPN
iajs-116	45	3	‖	‖	ADJ
iajs-116	45	4	,	,	PUNCT
iajs-116	45	5	|	|	ADV
iajs-116	45	6	|	|	ADV
iajs-116	45	7	∆	∆	PROPN
iajs-116	45	8	∆	∆	PROPN
iajs-116	45	9	.	.	PUNCT
iajs-116	46	1	,	,	PUNCT
iajs-116	46	2	,	,	PUNCT
iajs-116	46	3	√	√	INTJ
iajs-116	46	4	,	,	PUNCT
iajs-116	46	5	;	;	PUNCT
iajs-116	46	6	√	√	INTJ
iajs-116	46	7	.	.	PUNCT
iajs-116	47	1	now	now	ADV
iajs-116	47	2	‖	‖	ADJ
iajs-116	47	3	‖	‖	PROPN
iajs-116	47	4	,	,	PUNCT
iajs-116	47	5	‖	‖	PROPN
iajs-116	47	6	‖	‖	PROPN
iajs-116	47	7	,	,	PUNCT
iajs-116	47	8	∆	∆	PROPN
iajs-116	47	9	.	.	PUNCT
iajs-116	48	1	,	,	PUNCT
iajs-116	48	2	‖	‖	PROPN
iajs-116	48	3	‖	‖	PROPN
iajs-116	48	4	,	,	PUNCT
iajs-116	48	5	,	,	PUNCT
iajs-116	48	6	√	√	INTJ
iajs-116	48	7	,	,	PUNCT
iajs-116	48	8	since	since	SCONJ
iajs-116	48	9	‖	‖	PROPN
iajs-116	48	10	‖	‖	PROPN
iajs-116	48	11	,	,	PUNCT
iajs-116	48	12	,	,	PUNCT
iajs-116	48	13	√	√	NUM
iajs-116	48	14	,	,	PUNCT
iajs-116	48	15	so	so	ADV
iajs-116	48	16	‖	‖	PROPN
iajs-116	48	17	‖	‖	PROPN
iajs-116	48	18	,	,	PUNCT
iajs-116	48	19	,	,	PUNCT
iajs-116	48	20	√	√	INTJ
iajs-116	48	21	,	,	PUNCT
iajs-116	48	22	.	.	PUNCT
iajs-116	49	1	we	we	PRON
iajs-116	49	2	have	have	VERB
iajs-116	49	3	α	α	PRON
iajs-116	49	4	,	,	PUNCT
iajs-116	49	5	,	,	PUNCT
iajs-116	49	6	,	,	PUNCT
iajs-116	49	7	for	for	ADP
iajs-116	49	8	∈	∈	PROPN
iajs-116	49	9	and	and	CCONJ
iajs-116	49	10	by	by	ADP
iajs-116	49	11	lemma	lemma	PROPN
iajs-116	49	12	1	1	NUM
iajs-116	49	13	,	,	PUNCT
iajs-116	49	14	,	,	PUNCT
iajs-116	49	15	∑	∑	PROPN
iajs-116	49	16	α	α	X
iajs-116	49	17	,	,	PUNCT
iajs-116	49	18	,	,	PUNCT
iajs-116	49	19	mathematics	mathematic	NOUN
iajs-116	49	20	|	|	ADV
iajs-116	49	21	275	275	NUM
iajs-116	49	22	2016	2016	NUM
iajs-116	49	23	)	)	PUNCT
iajs-116	49	24	عام	عام	ADP
iajs-116	49	25	2العدد	2العدد	NUM
iajs-116	49	26	(	(	PUNCT
iajs-116	49	27	29لمجلد	29لمجلد	NUM
iajs-116	49	28	ا	ا	X
iajs-116	49	29	مجلة	مجلة	NOUN
iajs-116	49	30	إبن	إبن	VERB
iajs-116	49	31	الهيثم	الهيثم	ADJ
iajs-116	49	32	للعلوم	للعلوم	NOUN
iajs-116	49	33	الصرفة	الصرفة	NOUN
iajs-116	50	1	و	و	PRON
iajs-116	50	2	التطبيقية	التطبيقية	ADJ
iajs-116	50	3	ibn	ibn	PROPN
iajs-116	50	4	al	al	PROPN
iajs-116	50	5	-	-	PUNCT
iajs-116	50	6	haitham	haitham	PROPN
iajs-116	50	7	jour	jour	X
iajs-116	50	8	.	.	PROPN
iajs-116	50	9	for	for	ADP
iajs-116	50	10	pure	pure	ADJ
iajs-116	50	11	&	&	CCONJ
iajs-116	50	12	appl	appl	PROPN
iajs-116	50	13	.	.	PUNCT
iajs-116	51	1	sci	sci	PROPN
iajs-116	51	2	.	.	PUNCT
iajs-116	51	3	vol	vol	NOUN
iajs-116	51	4	.	.	PROPN
iajs-116	51	5	29	29	NUM
iajs-116	51	6	(	(	PUNCT
iajs-116	51	7	2	2	NUM
iajs-116	51	8	)	)	PUNCT
iajs-116	51	9	2016	2016	NUM
iajs-116	51	10	∑	∑	ADP
iajs-116	51	11	∆	∆	PROPN
iajs-116	51	12	,	,	PUNCT
iajs-116	51	13	.	.	PUNCT
iajs-116	52	1	as	as	ADP
iajs-116	52	2	consequence	consequence	NOUN
iajs-116	52	3	of	of	ADP
iajs-116	52	4	0	0	NUM
iajs-116	52	5	for	for	ADP
iajs-116	52	6	|	|	ADV
iajs-116	52	7	|	|	ADV
iajs-116	52	8	√	√	INTJ
iajs-116	52	9	,	,	PUNCT
iajs-116	52	10	hence	hence	ADV
iajs-116	52	11	∆	∆	X
iajs-116	52	12	0	0	PUNCT
iajs-116	53	1	for	for	ADP
iajs-116	53	2	|	|	ADV
iajs-116	53	3	|	|	ADV
iajs-116	53	4	√	√	INTJ
iajs-116	53	5	,	,	PUNCT
iajs-116	53	6	so	so	CCONJ
iajs-116	53	7	,	,	PUNCT
iajs-116	53	8	,	,	PUNCT
iajs-116	53	9	√	√	INTJ
iajs-116	53	10	,	,	PUNCT
iajs-116	53	11	;	;	PUNCT
iajs-116	53	12	√	√	INTJ
iajs-116	53	13	.	.	PUNCT
iajs-116	54	1	■	■	PUNCT
iajs-116	54	2	theorem	theorem	ADJ
iajs-116	54	3	1	1	NUM
iajs-116	54	4	:	:	PUNCT
iajs-116	54	5	let	let	VERB
iajs-116	54	6	∈	∈	PROPN
iajs-116	54	7	,	,	PUNCT
iajs-116	54	8	and	and	CCONJ
iajs-116	54	9	1	1	NUM
iajs-116	54	10	∞.	∞.	PROPN
iajs-116	54	11	for	for	ADP
iajs-116	54	12	every	every	DET
iajs-116	54	13	natural	natural	ADJ
iajs-116	54	14	there	there	PRON
iajs-116	54	15	exists	exist	VERB
iajs-116	54	16	constant	constant	ADJ
iajs-116	54	17	depending	depend	VERB
iajs-116	54	18	on	on	ADP
iajs-116	54	19	,	,	PUNCT
iajs-116	54	20	such	such	ADJ
iajs-116	54	21	that	that	PRON
iajs-116	54	22	,	,	PUNCT
iajs-116	54	23	,	,	PUNCT
iajs-116	54	24	√	√	INTJ
iajs-116	54	25	,	,	PUNCT
iajs-116	54	26	.	.	PUNCT
iajs-116	55	1	proof	proof	NOUN
iajs-116	55	2	:	:	PUNCT
iajs-116	55	3	from	from	ADP
iajs-116	55	4	definition	definition	NOUN
iajs-116	55	5	of	of	ADP
iajs-116	55	6	degree	degree	NOUN
iajs-116	55	7	of	of	ADP
iajs-116	55	8	best	good	ADJ
iajs-116	55	9	algebraic	algebraic	ADJ
iajs-116	55	10	approximation	approximation	NOUN
iajs-116	55	11	,	,	PUNCT
iajs-116	55	12	we	we	PRON
iajs-116	55	13	have	have	VERB
iajs-116	55	14	,	,	PUNCT
iajs-116	55	15	α	α	PROPN
iajs-116	55	16	,	,	PUNCT
iajs-116	55	17	,	,	PUNCT
iajs-116	55	18	.	.	PUNCT
iajs-116	56	1	,	,	PUNCT
iajs-116	56	2	,	,	PUNCT
iajs-116	56	3	where	where	SCONJ
iajs-116	56	4	α	α	NOUN
iajs-116	56	5	,	,	PUNCT
iajs-116	56	6	∈	∈	PROPN
iajs-116	56	7	ℙ	ℙ	PROPN
iajs-116	56	8	.	.	PUNCT
iajs-116	57	1	hence	hence	ADV
iajs-116	57	2	from	from	ADP
iajs-116	57	3	lemma	lemma	PROPN
iajs-116	57	4	2	2	NUM
iajs-116	57	5	,	,	PUNCT
iajs-116	57	6	we	we	PRON
iajs-116	57	7	obtain	obtain	VERB
iajs-116	57	8	,	,	PUNCT
iajs-116	57	9	,	,	PUNCT
iajs-116	57	10	√	√	INTJ
iajs-116	57	11	,	,	PUNCT
iajs-116	57	12	■	■	PUNCT
iajs-116	57	13	3	3	X
iajs-116	57	14	.	.	PUNCT
iajs-116	58	1	the	the	DET
iajs-116	58	2	converse	converse	NOUN
iajs-116	58	3	approximation	approximation	NOUN
iajs-116	58	4	theorem	theorem	NOUN
iajs-116	58	5	:	:	PUNCT
iajs-116	58	6	we	we	PRON
iajs-116	58	7	need	need	VERB
iajs-116	58	8	the	the	DET
iajs-116	58	9	following	following	NOUN
iajs-116	58	10	lemmas	lemma	NOUN
iajs-116	58	11	to	to	PART
iajs-116	58	12	prove	prove	VERB
iajs-116	58	13	converse	converse	NOUN
iajs-116	58	14	theorem	theorem	NOUN
iajs-116	58	15	lemma	lemma	PROPN
iajs-116	58	16	3	3	NUM
iajs-116	59	1	[	[	X
iajs-116	59	2	6	6	NUM
iajs-116	59	3	]	]	PUNCT
iajs-116	59	4	:	:	PUNCT
iajs-116	59	5	we	we	PRON
iajs-116	59	6	have	have	VERB
iajs-116	59	7	for	for	ADP
iajs-116	59	8	every	every	DET
iajs-116	59	9	∈	∈	PROPN
iajs-116	59	10	ℙ	ℙ	NOUN
iajs-116	59	11	,	,	PUNCT
iajs-116	59	12	1	1	NUM
iajs-116	59	13	∞	∞	NUM
iajs-116	59	14	and	and	CCONJ
iajs-116	59	15	n=1,2	n=1,2	ADJ
iajs-116	59	16	,	,	PUNCT
iajs-116	59	17	…	…	PUNCT
iajs-116	59	18	/	/	PUNCT
iajs-116	59	19	.	.	PUNCT
iajs-116	60	1	lemma	lemma	PROPN
iajs-116	60	2	4	4	NUM
iajs-116	61	1	[	[	X
iajs-116	61	2	7	7	NUM
iajs-116	61	3	]	]	PUNCT
iajs-116	61	4	:	:	PUNCT
iajs-116	61	5	we	we	PRON
iajs-116	61	6	have	have	VERB
iajs-116	61	7	for	for	ADP
iajs-116	61	8	every	every	DET
iajs-116	61	9	∈	∈	PROPN
iajs-116	61	10	ℙ	ℙ	NOUN
iajs-116	61	11	,	,	PUNCT
iajs-116	61	12	1	1	NUM
iajs-116	61	13	∞	∞	NUM
iajs-116	61	14	and	and	CCONJ
iajs-116	61	15	n=1,2	n=1,2	ADJ
iajs-116	61	16	,	,	PUNCT
iajs-116	61	17	…	…	PUNCT
iajs-116	61	18	,	,	PUNCT
iajs-116	61	19	‖	‖	PROPN
iajs-116	61	20	‖	‖	PROPN
iajs-116	61	21	,	,	PUNCT
iajs-116	61	22	.	.	PUNCT
iajs-116	62	1	lemma	lemma	PROPN
iajs-116	62	2	5	5	NUM
iajs-116	62	3	:	:	PUNCT
iajs-116	62	4	let	let	VERB
iajs-116	62	5	∈	∈	PROPN
iajs-116	62	6	,	,	PUNCT
iajs-116	62	7	,	,	PUNCT
iajs-116	62	8	1	1	NUM
iajs-116	62	9	∞	∞	NUM
iajs-116	62	10	,	,	PUNCT
iajs-116	62	11	∈	∈	PROPN
iajs-116	62	12	ℙ	ℙ	PROPN
iajs-116	62	13	and	and	CCONJ
iajs-116	62	14	‖	‖	PROPN
iajs-116	62	15	‖	‖	PROPN
iajs-116	62	16	,	,	PUNCT
iajs-116	62	17	.	.	PUNCT
iajs-116	63	1	mathematics	mathematic	NOUN
iajs-116	63	2	|	|	ADV
iajs-116	63	3	276	276	NUM
iajs-116	63	4	2016	2016	NUM
iajs-116	63	5	)	)	PUNCT
iajs-116	63	6	عام	عام	ADP
iajs-116	63	7	2العدد	2العدد	NUM
iajs-116	63	8	(	(	PUNCT
iajs-116	63	9	29لمجلد	29لمجلد	NUM
iajs-116	63	10	ا	ا	X
iajs-116	63	11	مجلة	مجلة	NOUN
iajs-116	63	12	إبن	إبن	VERB
iajs-116	63	13	الهيثم	الهيثم	ADJ
iajs-116	63	14	للعلوم	للعلوم	NOUN
iajs-116	63	15	الصرفة	الصرفة	NOUN
iajs-116	64	1	و	و	PRON
iajs-116	64	2	التطبيقية	التطبيقية	ADJ
iajs-116	64	3	ibn	ibn	PROPN
iajs-116	64	4	al	al	PROPN
iajs-116	64	5	-	-	PUNCT
iajs-116	64	6	haitham	haitham	PROPN
iajs-116	64	7	jour	jour	X
iajs-116	64	8	.	.	PROPN
iajs-116	64	9	for	for	ADP
iajs-116	64	10	pure	pure	ADJ
iajs-116	64	11	&	&	CCONJ
iajs-116	64	12	appl	appl	PROPN
iajs-116	64	13	.	.	PUNCT
iajs-116	65	1	sci	sci	PROPN
iajs-116	65	2	.	.	PUNCT
iajs-116	65	3	vol	vol	NOUN
iajs-116	65	4	.	.	PROPN
iajs-116	65	5	29	29	NUM
iajs-116	65	6	(	(	PUNCT
iajs-116	65	7	2	2	NUM
iajs-116	65	8	)	)	PUNCT
iajs-116	65	9	2016	2016	NUM
iajs-116	65	10	we	we	PRON
iajs-116	65	11	have	have	VERB
iajs-116	65	12	,	,	PUNCT
iajs-116	65	13	√	√	INTJ
iajs-116	65	14	,	,	PUNCT
iajs-116	65	15	‖	‖	PROPN
iajs-116	65	16	‖	‖	PROPN
iajs-116	65	17	,	,	PUNCT
iajs-116	65	18	∑	∑	PROPN
iajs-116	65	19	1	1	NUM
iajs-116	65	20	,	,	PUNCT
iajs-116	65	21	.	.	PUNCT
iajs-116	66	1	proof	proof	NOUN
iajs-116	66	2	:	:	PUNCT
iajs-116	66	3	let	let	VERB
iajs-116	66	4	∈	∈	PROPN
iajs-116	66	5	ℙ	ℙ	PROPN
iajs-116	66	6	be	be	AUX
iajs-116	66	7	a	a	DET
iajs-116	66	8	polynomial	polynomial	ADJ
iajs-116	66	9	satisfying	satisfying	NOUN
iajs-116	66	10	‖	‖	PROPN
iajs-116	66	11	‖	‖	PROPN
iajs-116	66	12	,	,	PUNCT
iajs-116	66	13	2	2	NUM
iajs-116	66	14	,	,	PUNCT
iajs-116	66	15	.	.	PUNCT
iajs-116	67	1	by	by	ADP
iajs-116	67	2	using	use	VERB
iajs-116	67	3	lemma	lemma	PROPN
iajs-116	67	4	4	4	NUM
iajs-116	67	5	,	,	PUNCT
iajs-116	67	6	we	we	PRON
iajs-116	67	7	obtain	obtain	VERB
iajs-116	67	8	,	,	PUNCT
iajs-116	67	9	,	,	PUNCT
iajs-116	67	10	‖	‖	PROPN
iajs-116	67	11	‖	‖	PROPN
iajs-116	67	12	,	,	PUNCT
iajs-116	67	13	|	|	ADV
iajs-116	67	14	|	|	ADV
iajs-116	67	15	,	,	PUNCT
iajs-116	67	16	,	,	PUNCT
iajs-116	67	17	,	,	PUNCT
iajs-116	67	18	we	we	PRON
iajs-116	67	19	have	have	VERB
iajs-116	67	20	,	,	PUNCT
iajs-116	67	21	from	from	ADP
iajs-116	67	22	properties	property	NOUN
iajs-116	67	23	of	of	ADP
iajs-116	67	24	modulus	modulus	NOUN
iajs-116	67	25	of	of	ADP
iajs-116	67	26	continuity	continuity	NOUN
iajs-116	67	27	and	and	CCONJ
iajs-116	67	28	lemma	lemma	PROPN
iajs-116	67	29	4	4	NUM
iajs-116	67	30	,	,	PUNCT
iajs-116	67	31	,	,	PUNCT
iajs-116	67	32	,	,	PUNCT
iajs-116	67	33	,	,	PUNCT
iajs-116	67	34	,	,	PUNCT
iajs-116	67	35	,	,	PUNCT
iajs-116	68	1	‖	‖	PROPN
iajs-116	68	2	‖	‖	PROPN
iajs-116	68	3	,	,	PUNCT
iajs-116	68	4	‖	‖	PROPN
iajs-116	68	5	‖	‖	ADJ
iajs-116	68	6	,	,	PUNCT
iajs-116	69	1	|	|	ADV
iajs-116	69	2	|	|	ADV
iajs-116	69	3	|	|	ADV
iajs-116	69	4	|	|	ADV
iajs-116	69	5	‖	‖	ADJ
iajs-116	69	6	‖	‖	PROPN
iajs-116	69	7	,	,	PUNCT
iajs-116	69	8	2‖	2‖	PROPN
iajs-116	69	9	‖	‖	PROPN
iajs-116	69	10	,	,	PUNCT
iajs-116	69	11	‖	‖	PROPN
iajs-116	69	12	‖	‖	PROPN
iajs-116	69	13	,	,	PUNCT
iajs-116	69	14	,	,	PUNCT
iajs-116	69	15	‖	‖	PROPN
iajs-116	69	16	‖	‖	PROPN
iajs-116	69	17	,	,	PUNCT
iajs-116	69	18	so	so	ADV
iajs-116	69	19	,	,	PUNCT
iajs-116	69	20	,	,	PUNCT
iajs-116	69	21	,	,	PUNCT
iajs-116	69	22	,	,	PUNCT
iajs-116	69	23	‖	‖	PROPN
iajs-116	69	24	‖	‖	PROPN
iajs-116	69	25	,	,	PUNCT
iajs-116	69	26	also	also	ADV
iajs-116	69	27	,	,	PUNCT
iajs-116	69	28	we	we	PRON
iajs-116	69	29	can	can	AUX
iajs-116	69	30	prove	prove	VERB
iajs-116	69	31	mathematics	mathematic	NOUN
iajs-116	69	32	|	|	ADV
iajs-116	69	33	277	277	NUM
iajs-116	69	34	2016	2016	NUM
iajs-116	69	35	)	)	PUNCT
iajs-116	69	36	عام	عام	ADP
iajs-116	69	37	2العدد	2العدد	NUM
iajs-116	69	38	(	(	PUNCT
iajs-116	69	39	29لمجلد	29لمجلد	NUM
iajs-116	69	40	ا	ا	X
iajs-116	69	41	مجلة	مجلة	NOUN
iajs-116	69	42	إبن	إبن	VERB
iajs-116	69	43	الهيثم	الهيثم	ADJ
iajs-116	69	44	للعلوم	للعلوم	NOUN
iajs-116	69	45	الصرفة	الصرفة	NOUN
iajs-116	70	1	و	و	PRON
iajs-116	70	2	التطبيقية	التطبيقية	ADJ
iajs-116	70	3	ibn	ibn	PROPN
iajs-116	70	4	al	al	PROPN
iajs-116	70	5	-	-	PUNCT
iajs-116	70	6	haitham	haitham	PROPN
iajs-116	70	7	jour	jour	X
iajs-116	70	8	.	.	PROPN
iajs-116	70	9	for	for	ADP
iajs-116	70	10	pure	pure	ADJ
iajs-116	70	11	&	&	CCONJ
iajs-116	70	12	appl	appl	PROPN
iajs-116	70	13	.	.	PUNCT
iajs-116	71	1	sci	sci	PROPN
iajs-116	71	2	.	.	PUNCT
iajs-116	71	3	vol	vol	NOUN
iajs-116	71	4	.	.	PROPN
iajs-116	71	5	29	29	NUM
iajs-116	71	6	(	(	PUNCT
iajs-116	71	7	2	2	NUM
iajs-116	71	8	)	)	PUNCT
iajs-116	71	9	2016	2016	NUM
iajs-116	71	10	,	,	PUNCT
iajs-116	71	11	,	,	PUNCT
iajs-116	71	12	,	,	PUNCT
iajs-116	71	13	2	2	X
iajs-116	71	14	/	/	SYM
iajs-116	71	15	,	,	PUNCT
iajs-116	71	16	‖	‖	PROPN
iajs-116	71	17	‖	‖	PROPN
iajs-116	71	18	,	,	PUNCT
iajs-116	71	19	∑	∑	PROPN
iajs-116	71	20	1	1	NUM
iajs-116	71	21	,	,	PUNCT
iajs-116	71	22	‖	‖	PROPN
iajs-116	71	23	‖	‖	PROPN
iajs-116	71	24	,	,	PUNCT
iajs-116	71	25	…	…	PUNCT
iajs-116	71	26	(	(	PUNCT
iajs-116	71	27	8)	8)	NUM
iajs-116	71	28	.	.	PUNCT
iajs-116	71	29	let	let	VERB
iajs-116	71	30	2	2	NUM
iajs-116	71	31	2	2	NUM
iajs-116	71	32	,	,	PUNCT
iajs-116	71	33	,	,	PUNCT
iajs-116	71	34	‖	‖	PROPN
iajs-116	71	35	‖	‖	PROPN
iajs-116	71	36	,	,	PUNCT
iajs-116	72	1	|	|	ADV
iajs-116	72	2	|	|	ADV
iajs-116	72	3	|	|	ADV
iajs-116	72	4	|	|	ADV
iajs-116	72	5	‖	‖	ADJ
iajs-116	72	6	‖	‖	PROPN
iajs-116	72	7	,	,	PUNCT
iajs-116	72	8	‖	‖	PROPN
iajs-116	72	9	‖	‖	PROPN
iajs-116	72	10	,	,	PUNCT
iajs-116	72	11	…	…	PUNCT
iajs-116	72	12	…	…	PUNCT
iajs-116	72	13	…	…	PUNCT
iajs-116	72	14	…	…	PUNCT
iajs-116	72	15	…	…	PUNCT
iajs-116	72	16	…	…	PUNCT
iajs-116	72	17	…	…	PUNCT
iajs-116	72	18	..	..	PUNCT
iajs-116	72	19	(	(	PUNCT
iajs-116	72	20	9	9	NUM
iajs-116	72	21	)	)	PUNCT
iajs-116	72	22	from	from	ADP
iajs-116	72	23	(	(	PUNCT
iajs-116	72	24	8)	8)	NUM
iajs-116	72	25	and	and	CCONJ
iajs-116	72	26	(	(	PUNCT
iajs-116	72	27	9	9	NUM
iajs-116	72	28	)	)	PUNCT
iajs-116	72	29	,	,	PUNCT
iajs-116	72	30	we	we	PRON
iajs-116	72	31	get	get	VERB
iajs-116	72	32	,	,	PUNCT
iajs-116	72	33	√	√	INTJ
iajs-116	72	34	,	,	PUNCT
iajs-116	72	35	‖	‖	PROPN
iajs-116	72	36	‖	‖	PROPN
iajs-116	72	37	,	,	PUNCT
iajs-116	72	38	∑	∑	PROPN
iajs-116	72	39	1	1	NUM
iajs-116	72	40	,	,	PUNCT
iajs-116	72	41	.	.	PUNCT
iajs-116	73	1	■	■	PUNCT
iajs-116	73	2	theorem	theorem	ADJ
iajs-116	73	3	2	2	NUM
iajs-116	73	4	:	:	PUNCT
iajs-116	73	5	let	let	VERB
iajs-116	73	6	∈	∈	PROPN
iajs-116	73	7	,	,	PUNCT
iajs-116	73	8	,	,	PUNCT
iajs-116	73	9	1	1	NUM
iajs-116	73	10	∞.	∞.	PROPN
iajs-116	73	11	for	for	ADP
iajs-116	73	12	every	every	DET
iajs-116	73	13	natural	natural	ADJ
iajs-116	73	14	number	number	NOUN
iajs-116	73	15	there	there	ADV
iajs-116	73	16	exist	exist	VERB
iajs-116	73	17	a	a	DET
iajs-116	73	18	constant	constant	ADJ
iajs-116	73	19	depending	depend	VERB
iajs-116	73	20	on	on	ADP
iajs-116	73	21	,	,	PUNCT
iajs-116	73	22	such	such	ADJ
iajs-116	73	23	that	that	PRON
iajs-116	73	24	,	,	PUNCT
iajs-116	73	25	√	√	NUM
iajs-116	73	26	,	,	PUNCT
iajs-116	73	27	√	√	PROPN
iajs-116	73	28	‖	‖	PROPN
iajs-116	73	29	‖	‖	PROPN
iajs-116	73	30	,	,	PUNCT
iajs-116	73	31	∑	∑	PROPN
iajs-116	73	32	1	1	NUM
iajs-116	73	33	,	,	PUNCT
iajs-116	73	34	,	,	PUNCT
iajs-116	73	35	1,2	1,2	NUM
iajs-116	73	36	,	,	PUNCT
iajs-116	73	37	…	…	PUNCT
iajs-116	73	38	.	.	PUNCT
iajs-116	73	39	.	.	PUNCT
iajs-116	74	1	proof	proof	NOUN
iajs-116	74	2	:	:	PUNCT
iajs-116	74	3	we	we	PRON
iajs-116	74	4	insert	insert	VERB
iajs-116	74	5	in	in	ADP
iajs-116	74	6	lemma	lemma	PROPN
iajs-116	74	7	5	5	NUM
iajs-116	74	8	,	,	PUNCT
iajs-116	74	9	,	,	PUNCT
iajs-116	74	10	√	√	NUM
iajs-116	74	11	and	and	CCONJ
iajs-116	74	12	take	take	VERB
iajs-116	74	13	in	in	ADP
iajs-116	74	14	consideration	consideration	NOUN
iajs-116	74	15	that	that	SCONJ
iajs-116	74	16	by	by	ADP
iajs-116	74	17	the	the	DET
iajs-116	74	18	monotony	monotony	NOUN
iajs-116	74	19	of	of	ADP
iajs-116	74	20	,	,	PUNCT
iajs-116	74	21	,	,	PUNCT
iajs-116	74	22	∑	∑	ADV
iajs-116	74	23	,	,	PUNCT
iajs-116	74	24	so	so	ADV
iajs-116	74	25	,	,	PUNCT
iajs-116	74	26	,	,	PUNCT
iajs-116	74	27	√	√	INTJ
iajs-116	74	28	,	,	PUNCT
iajs-116	74	29	√	√	PROPN
iajs-116	74	30	‖	‖	PROPN
iajs-116	74	31	‖	‖	PROPN
iajs-116	74	32	,	,	PUNCT
iajs-116	74	33	∑	∑	PROPN
iajs-116	74	34	1	1	NUM
iajs-116	74	35	,	,	PUNCT
iajs-116	74	36	√	√	PROPN
iajs-116	74	37	‖	‖	PROPN
iajs-116	74	38	‖	‖	PROPN
iajs-116	74	39	,	,	PUNCT
iajs-116	74	40	∑	∑	PROPN
iajs-116	74	41	1	1	NUM
iajs-116	74	42	,	,	PUNCT
iajs-116	74	43	.	.	PUNCT
iajs-116	75	1	■	■	PUNCT
iajs-116	75	2	mathematics	mathematic	NOUN
iajs-116	75	3	|	|	ADV
iajs-116	75	4	278	278	NUM
iajs-116	75	5	2016	2016	NUM
iajs-116	75	6	)	)	PUNCT
iajs-116	75	7	عام	عام	ADP
iajs-116	75	8	2العدد	2العدد	NUM
iajs-116	75	9	(	(	PUNCT
iajs-116	75	10	29لمجلد	29لمجلد	NUM
iajs-116	75	11	ا	ا	X
iajs-116	75	12	مجلة	مجلة	NOUN
iajs-116	75	13	إبن	إبن	VERB
iajs-116	75	14	الهيثم	الهيثم	ADJ
iajs-116	75	15	للعلوم	للعلوم	NOUN
iajs-116	75	16	الصرفة	الصرفة	NOUN
iajs-116	76	1	و	و	PRON
iajs-116	76	2	التطبيقية	التطبيقية	ADJ
iajs-116	76	3	ibn	ibn	PROPN
iajs-116	76	4	al	al	PROPN
iajs-116	76	5	-	-	PUNCT
iajs-116	76	6	haitham	haitham	PROPN
iajs-116	76	7	jour	jour	X
iajs-116	76	8	.	.	PROPN
iajs-116	76	9	for	for	ADP
iajs-116	76	10	pure	pure	ADJ
iajs-116	76	11	&	&	CCONJ
iajs-116	76	12	appl	appl	PROPN
iajs-116	76	13	.	.	PUNCT
iajs-116	77	1	sci	sci	PROPN
iajs-116	77	2	.	.	PUNCT
iajs-116	77	3	vol	vol	NOUN
iajs-116	77	4	.	.	PROPN
iajs-116	77	5	29	29	NUM
iajs-116	77	6	(	(	PUNCT
iajs-116	77	7	2	2	NUM
iajs-116	77	8	)	)	PUNCT
iajs-116	77	9	2016	2016	NUM
iajs-116	77	10	theorem	theorem	VERB
iajs-116	77	11	3	3	NUM
iajs-116	77	12	:	:	PUNCT
iajs-116	77	13	let	let	VERB
iajs-116	77	14	∈	∈	PROPN
iajs-116	77	15	,	,	PUNCT
iajs-116	77	16	,	,	PUNCT
iajs-116	77	17	1	1	NUM
iajs-116	77	18	∞	∞	NUM
iajs-116	77	19	and	and	CCONJ
iajs-116	77	20	∑	∑	PROPN
iajs-116	77	21	1	1	NUM
iajs-116	77	22	,	,	PUNCT
iajs-116	77	23	∞.	∞.	PROPN
iajs-116	77	24	then	then	ADV
iajs-116	77	25	has	have	AUX
iajs-116	77	26	derivative	derivative	NOUN
iajs-116	77	27	of	of	ADP
iajs-116	77	28	order	order	NOUN
iajs-116	77	29	,	,	PUNCT
iajs-116	77	30	∈	∈	PROPN
iajs-116	77	31	,	,	PUNCT
iajs-116	77	32	and	and	CCONJ
iajs-116	77	33	,	,	PUNCT
iajs-116	77	34	,	,	PUNCT
iajs-116	77	35	∑	∑	PROPN
iajs-116	77	36	1	1	NUM
iajs-116	77	37	,	,	PUNCT
iajs-116	77	38	proof	proof	NOUN
iajs-116	77	39	:	:	PUNCT
iajs-116	77	40	let	let	VERB
iajs-116	77	41	∈	∈	PROPN
iajs-116	77	42	ℙ	ℙ	NOUN
iajs-116	77	43	satisfy	satisfy	NOUN
iajs-116	77	44	‖	‖	ADJ
iajs-116	77	45	‖	‖	PROPN
iajs-116	77	46	,	,	PUNCT
iajs-116	77	47	2	2	NUM
iajs-116	77	48	,	,	PUNCT
iajs-116	77	49	,	,	PUNCT
iajs-116	77	50	we	we	PRON
iajs-116	77	51	have	have	VERB
iajs-116	77	52	in	in	ADP
iajs-116	77	53	consequence	consequence	NOUN
iajs-116	77	54	of	of	ADP
iajs-116	77	55	lemma	lemma	PROPN
iajs-116	77	56	3	3	NUM
iajs-116	77	57	,	,	PUNCT
iajs-116	77	58	,	,	PUNCT
iajs-116	77	59	,	,	PUNCT
iajs-116	77	60	,	,	PUNCT
iajs-116	77	61	,	,	PUNCT
iajs-116	77	62	the	the	DET
iajs-116	77	63	sequence	sequence	NOUN
iajs-116	77	64	is	be	AUX
iajs-116	77	65	convergent	convergent	ADJ
iajs-116	77	66	in	in	ADP
iajs-116	77	67	weighted	weight	VERB
iajs-116	77	68	space	space	NOUN
iajs-116	77	69	,	,	PUNCT
iajs-116	77	70	,	,	PUNCT
iajs-116	77	71	we	we	PRON
iajs-116	77	72	denote	denote	VERB
iajs-116	77	73	it	it	PRON
iajs-116	77	74	is	be	AUX
iajs-116	77	75	limit	limit	NOUN
iajs-116	77	76	by	by	ADP
iajs-116	77	77	∈	∈	PROPN
iajs-116	77	78	,	,	PUNCT
iajs-116	77	79	.	.	PUNCT
iajs-116	78	1	since	since	SCONJ
iajs-116	78	2	,	,	PUNCT
iajs-116	78	3	→	→	SYM
iajs-116	78	4	0	0	NUM
iajs-116	78	5	,	,	PUNCT
iajs-116	78	6	is	be	AUX
iajs-116	78	7	derivative	derivative	ADJ
iajs-116	78	8	of	of	ADP
iajs-116	78	9	order	order	NOUN
iajs-116	78	10	of	of	ADP
iajs-116	78	11	.	.	PUNCT
iajs-116	79	1	moreover	moreover	ADV
iajs-116	79	2	,	,	PUNCT
iajs-116	79	3	we	we	PRON
iajs-116	79	4	have	have	AUX
iajs-116	79	5	,	,	PUNCT
iajs-116	79	6	,	,	PUNCT
iajs-116	79	7	∑	∑	PROPN
iajs-116	79	8	2	2	NUM
iajs-116	79	9	/	/	SYM
iajs-116	79	10	,	,	PUNCT
iajs-116	79	11	2	2	NUM
iajs-116	79	12	/	/	SYM
iajs-116	79	13	,	,	PUNCT
iajs-116	79	14	∑	∑	PROPN
iajs-116	79	15	1	1	NUM
iajs-116	79	16	,	,	PUNCT
iajs-116	79	17	…	…	PUNCT
iajs-116	79	18	…	…	PUNCT
iajs-116	79	19	(	(	PUNCT
iajs-116	79	20	10	10	NUM
iajs-116	79	21	)	)	PUNCT
iajs-116	79	22	let	let	VERB
iajs-116	79	23	2	2	NUM
iajs-116	79	24	2	2	NUM
iajs-116	79	25	,	,	PUNCT
iajs-116	79	26	form	form	VERB
iajs-116	79	27	lemma	lemma	PROPN
iajs-116	79	28	3	3	NUM
iajs-116	79	29	we	we	PRON
iajs-116	79	30	have	have	VERB
iajs-116	79	31	,	,	PUNCT
iajs-116	79	32	‖	‖	PROPN
iajs-116	79	33	‖	‖	PROPN
iajs-116	79	34	,	,	PUNCT
iajs-116	79	35	,	,	PUNCT
iajs-116	79	36	…	…	PUNCT
iajs-116	79	37	…	…	PUNCT
iajs-116	79	38	…	…	PUNCT
iajs-116	79	39	…	…	PUNCT
iajs-116	79	40	…	…	PUNCT
iajs-116	79	41	…	…	PUNCT
iajs-116	79	42	…	…	PUNCT
iajs-116	79	43	..	..	PUNCT
iajs-116	79	44	(	(	PUNCT
iajs-116	79	45	11	11	NUM
iajs-116	79	46	)	)	PUNCT
iajs-116	79	47	from	from	ADP
iajs-116	79	48	(	(	PUNCT
iajs-116	79	49	10	10	NUM
iajs-116	79	50	)	)	PUNCT
iajs-116	79	51	and	and	CCONJ
iajs-116	79	52	(	(	PUNCT
iajs-116	79	53	11	11	NUM
iajs-116	79	54	)	)	PUNCT
iajs-116	79	55	,	,	PUNCT
iajs-116	79	56	we	we	PRON
iajs-116	79	57	obtain	obtain	AUX
iajs-116	79	58	,	,	PUNCT
iajs-116	79	59	,	,	PUNCT
iajs-116	79	60	,	,	PUNCT
iajs-116	79	61	∑	∑	PROPN
iajs-116	79	62	1	1	NUM
iajs-116	79	63	,	,	PUNCT
iajs-116	79	64	■	■	PUNCT
iajs-116	79	65	theorem	theorem	ADJ
iajs-116	79	66	4	4	NUM
iajs-116	79	67	:	:	PUNCT
iajs-116	79	68	we	we	PRON
iajs-116	79	69	have	have	VERB
iajs-116	79	70	for	for	ADP
iajs-116	79	71	every	every	DET
iajs-116	79	72	natural	natural	ADJ
iajs-116	79	73	and	and	CCONJ
iajs-116	79	74	m	m	VERB
iajs-116	79	75	every	every	DET
iajs-116	79	76	∈	∈	PROPN
iajs-116	79	77	,	,	PUNCT
iajs-116	79	78	mathematics	mathematic	NOUN
iajs-116	79	79	|	|	ADV
iajs-116	79	80	279	279	NUM
iajs-116	79	81	2016	2016	NUM
iajs-116	79	82	)	)	PUNCT
iajs-116	79	83	عام	عام	ADP
iajs-116	79	84	2العدد	2العدد	NUM
iajs-116	79	85	(	(	PUNCT
iajs-116	79	86	29لمجلد	29لمجلد	NUM
iajs-116	79	87	ا	ا	X
iajs-116	79	88	مجلة	مجلة	NOUN
iajs-116	79	89	إبن	إبن	VERB
iajs-116	79	90	الهيثم	الهيثم	ADJ
iajs-116	79	91	للعلوم	للعلوم	NOUN
iajs-116	79	92	الصرفة	الصرفة	NOUN
iajs-116	80	1	و	و	PRON
iajs-116	80	2	التطبيقية	التطبيقية	ADJ
iajs-116	80	3	ibn	ibn	PROPN
iajs-116	80	4	al	al	PROPN
iajs-116	80	5	-	-	PUNCT
iajs-116	80	6	haitham	haitham	PROPN
iajs-116	80	7	jour	jour	X
iajs-116	80	8	.	.	PROPN
iajs-116	80	9	for	for	ADP
iajs-116	80	10	pure	pure	ADJ
iajs-116	80	11	&	&	CCONJ
iajs-116	80	12	appl	appl	PROPN
iajs-116	80	13	.	.	PUNCT
iajs-116	81	1	sci	sci	PROPN
iajs-116	81	2	.	.	PUNCT
iajs-116	81	3	vol	vol	NOUN
iajs-116	81	4	.	.	PROPN
iajs-116	81	5	29	29	NUM
iajs-116	81	6	(	(	PUNCT
iajs-116	81	7	2	2	NUM
iajs-116	81	8	)	)	PUNCT
iajs-116	81	9	2016	2016	NUM
iajs-116	81	10	,	,	PUNCT
iajs-116	81	11	√	√	NUM
iajs-116	81	12	,	,	PUNCT
iajs-116	81	13	,	,	PUNCT
iajs-116	81	14	√	√	ADP
iajs-116	81	15	∑	∑	ADP
iajs-116	81	16	1	1	NUM
iajs-116	81	17	,	,	PUNCT
iajs-116	81	18	∑	∑	PROPN
iajs-116	81	19	1∞	1∞	NUM
iajs-116	81	20	,	,	PUNCT
iajs-116	81	21	.	.	PUNCT
iajs-116	82	1	proof	proof	NOUN
iajs-116	82	2	:	:	PUNCT
iajs-116	82	3	from	from	ADP
iajs-116	82	4	theorem	theorem	ADJ
iajs-116	82	5	2	2	NUM
iajs-116	82	6	and	and	CCONJ
iajs-116	82	7	theorem	theorem	VERB
iajs-116	82	8	3	3	NUM
iajs-116	82	9	,	,	PUNCT
iajs-116	82	10	we	we	PRON
iajs-116	82	11	have	have	VERB
iajs-116	82	12	,	,	PUNCT
iajs-116	82	13	√	√	INTJ
iajs-116	82	14	,	,	PUNCT
iajs-116	82	15	,	,	PUNCT
iajs-116	82	16	√	√	INTJ
iajs-116	82	17	,	,	PUNCT
iajs-116	82	18	∑	∑	PROPN
iajs-116	82	19	1	1	NUM
iajs-116	82	20	,	,	PUNCT
iajs-116	82	21	,	,	PUNCT
iajs-116	82	22	,	,	PUNCT
iajs-116	82	23	∑	∑	PROPN
iajs-116	82	24	1	1	NUM
iajs-116	82	25	,	,	PUNCT
iajs-116	82	26	..	..	PUNCT
iajs-116	82	27	(	(	PUNCT
iajs-116	82	28	12	12	NUM
iajs-116	82	29	)	)	PUNCT
iajs-116	82	30	as	as	ADV
iajs-116	82	31	well	well	ADV
iajs-116	82	32	as	as	ADP
iajs-116	82	33	from	from	ADP
iajs-116	82	34	(	(	PUNCT
iajs-116	82	35	10	10	NUM
iajs-116	82	36	)	)	PUNCT
iajs-116	82	37	and	and	CCONJ
iajs-116	82	38	take	take	VERB
iajs-116	82	39	0	0	NUM
iajs-116	82	40	,	,	PUNCT
iajs-116	82	41	∑	∑	PROPN
iajs-116	82	42	1	1	NUM
iajs-116	82	43	,	,	PUNCT
iajs-116	82	44	…	…	PUNCT
iajs-116	82	45	…	…	PUNCT
iajs-116	82	46	…	…	PUNCT
iajs-116	82	47	…	…	PUNCT
iajs-116	82	48	…	…	PUNCT
iajs-116	82	49	…	…	PUNCT
iajs-116	82	50	…	…	PUNCT
iajs-116	82	51	…	…	PUNCT
iajs-116	82	52	…	…	SYM
iajs-116	82	53	.(13	.(13	SYM
iajs-116	82	54	)	)	PUNCT
iajs-116	82	55	new	new	ADJ
iajs-116	82	56	,	,	PUNCT
iajs-116	82	57	from	from	ADP
iajs-116	82	58	(	(	PUNCT
iajs-116	82	59	12	12	NUM
iajs-116	82	60	)	)	PUNCT
iajs-116	82	61	and	and	CCONJ
iajs-116	82	62	(	(	PUNCT
iajs-116	82	63	13	13	NUM
iajs-116	82	64	)	)	PUNCT
iajs-116	82	65	,	,	PUNCT
iajs-116	82	66	we	we	PRON
iajs-116	82	67	obtain	obtain	VERB
iajs-116	82	68	,	,	PUNCT
iajs-116	82	69	√	√	INTJ
iajs-116	82	70	,	,	PUNCT
iajs-116	82	71	,	,	PUNCT
iajs-116	82	72	√	√	ADP
iajs-116	82	73	∑	∑	ADP
iajs-116	82	74	1	1	NUM
iajs-116	82	75	,	,	PUNCT
iajs-116	82	76	∑	∑	PROPN
iajs-116	82	77	1	1	NUM
iajs-116	82	78	,	,	PUNCT
iajs-116	82	79	∑	∑	PROPN
iajs-116	82	80	1	1	NUM
iajs-116	82	81	,	,	PUNCT
iajs-116	82	82	,	,	PUNCT
iajs-116	82	83	√	√	ADP
iajs-116	82	84	∑	∑	ADP
iajs-116	82	85	1	1	NUM
iajs-116	82	86	,	,	PUNCT
iajs-116	82	87	∑	∑	PROPN
iajs-116	82	88	1	1	NUM
iajs-116	82	89	,	,	PUNCT
iajs-116	82	90	∑	∑	PROPN
iajs-116	82	91	1	1	NUM
iajs-116	82	92	∑	∑	SYM
iajs-116	82	93	1	1	NUM
iajs-116	82	94	,	,	PUNCT
iajs-116	82	95	,	,	PUNCT
iajs-116	82	96	√	√	ADP
iajs-116	82	97	∑	∑	ADP
iajs-116	82	98	1	1	NUM
iajs-116	82	99	,	,	PUNCT
iajs-116	82	100	∑	∑	ADP
iajs-116	82	101	∑	∑	PROPN
iajs-116	82	102	1	1	NUM
iajs-116	82	103	1	1	NUM
iajs-116	82	104	,	,	PUNCT
iajs-116	82	105	,	,	PUNCT
iajs-116	82	106	√	√	ADP
iajs-116	82	107	∑	∑	ADP
iajs-116	82	108	1	1	NUM
iajs-116	82	109	,	,	PUNCT
iajs-116	82	110	∑	∑	PROPN
iajs-116	82	111	1	1	NUM
iajs-116	82	112	,	,	PUNCT
iajs-116	82	113	■	■	PUNCT
iajs-116	82	114	acknowledgments	acknowledgment	NOUN
iajs-116	82	115	i	i	PRON
iajs-116	82	116	am	be	AUX
iajs-116	82	117	grateful	grateful	ADJ
iajs-116	82	118	to	to	PART
iajs-116	82	119	prof	prof	VERB
iajs-116	82	120	.	.	PUNCT
iajs-116	83	1	s.	s.	PROPN
iajs-116	83	2	jassim	jassim	PROPN
iajs-116	83	3	,	,	PUNCT
iajs-116	83	4	from	from	ADP
iajs-116	83	5	whom	whom	PRON
iajs-116	83	6	i	i	PRON
iajs-116	83	7	learnt	learn	VERB
iajs-116	83	8	the	the	DET
iajs-116	83	9	approximation	approximation	NOUN
iajs-116	83	10	of	of	ADP
iajs-116	83	11	unbounded	unbounded	ADJ
iajs-116	83	12	functions	function	NOUN
iajs-116	83	13	played	play	VERB
iajs-116	83	14	in	in	ADP
iajs-116	83	15	development	development	NOUN
iajs-116	83	16	of	of	ADP
iajs-116	83	17	the	the	DET
iajs-116	83	18	nation	nation	NOUN
iajs-116	83	19	of	of	ADP
iajs-116	83	20	weighted	weight	VERB
iajs-116	83	21	spaces	space	NOUN
iajs-116	83	22	.	.	PUNCT
iajs-116	84	1	mathematics	mathematic	NOUN
iajs-116	84	2	|	|	ADV
iajs-116	84	3	280	280	NUM
iajs-116	84	4	2016	2016	NUM
iajs-116	84	5	)	)	PUNCT
iajs-116	84	6	عام	عام	ADP
iajs-116	84	7	2العدد	2العدد	NUM
iajs-116	84	8	(	(	PUNCT
iajs-116	84	9	29لمجلد	29لمجلد	NUM
iajs-116	84	10	ا	ا	X
iajs-116	84	11	مجلة	مجلة	NOUN
iajs-116	84	12	إبن	إبن	VERB
iajs-116	84	13	الهيثم	الهيثم	ADJ
iajs-116	84	14	للعلوم	للعلوم	NOUN
iajs-116	84	15	الصرفة	الصرفة	NOUN
iajs-116	85	1	و	و	PRON
iajs-116	85	2	التطبيقية	التطبيقية	ADJ
iajs-116	85	3	ibn	ibn	PROPN
iajs-116	85	4	al	al	PROPN
iajs-116	85	5	-	-	PUNCT
iajs-116	85	6	haitham	haitham	PROPN
iajs-116	85	7	jour	jour	X
iajs-116	85	8	.	.	PROPN
iajs-116	85	9	for	for	ADP
iajs-116	85	10	pure	pure	ADJ
iajs-116	85	11	&	&	CCONJ
iajs-116	85	12	appl	appl	PROPN
iajs-116	85	13	.	.	PUNCT
iajs-116	86	1	sci	sci	PROPN
iajs-116	86	2	.	.	PUNCT
iajs-116	86	3	vol	vol	NOUN
iajs-116	86	4	.	.	PROPN
iajs-116	86	5	29	29	NUM
iajs-116	86	6	(	(	PUNCT
iajs-116	86	7	2	2	NUM
iajs-116	86	8	)	)	SYM
iajs-116	86	9	2016	2016	NUM
iajs-116	86	10	references	reference	NOUN
iajs-116	86	11	1	1	NUM
iajs-116	86	12	.	.	PUNCT
iajs-116	87	1	adell	adell	PROPN
iajs-116	87	2	,	,	PUNCT
iajs-116	87	3	a.	a.	PROPN
iajs-116	87	4	,	,	PUNCT
iajs-116	87	5	and	and	CCONJ
iajs-116	87	6	bustamante	bustamante	PROPN
iajs-116	87	7	j.	j.	PROPN
iajs-116	87	8	,(2014	,(2014	PROPN
iajs-116	87	9	)	)	PUNCT
iajs-116	87	10	,	,	PUNCT
iajs-116	87	11	polynomial	polynomial	ADJ
iajs-116	87	12	operators	operator	NOUN
iajs-116	87	13	for	for	ADP
iajs-116	87	14	one	one	NUM
iajs-116	87	15	-	-	PUNCT
iajs-116	87	16	sided	sided	ADJ
iajs-116	87	17	lpapproximation	lpapproximation	NOUN
iajs-116	87	18	to	to	ADP
iajs-116	87	19	riemann	riemann	PROPN
iajs-116	87	20	integrable	integrable	ADJ
iajs-116	87	21	functions	function	NOUN
iajs-116	87	22	,	,	PUNCT
iajs-116	87	23	journal	journal	NOUN
iajs-116	87	24	of	of	ADP
iajs-116	87	25	inequalities	inequality	NOUN
iajs-116	87	26	and	and	CCONJ
iajs-116	87	27	applications	application	NOUN
iajs-116	87	28	,	,	PUNCT
iajs-116	87	29	2014/1/494	2014/1/494	NUM
iajs-116	87	30	.	.	NOUN
iajs-116	87	31	2	2	NUM
iajs-116	87	32	.	.	X
iajs-116	87	33	draganov	draganov	PROPN
iajs-116	87	34	,	,	PUNCT
iajs-116	87	35	r.	r.	PROPN
iajs-116	87	36	,	,	PUNCT
iajs-116	87	37	(	(	PUNCT
iajs-116	87	38	2011),on	2011),on	NUM
iajs-116	87	39	the	the	DET
iajs-116	87	40	approximation	approximation	NOUN
iajs-116	87	41	by	by	ADP
iajs-116	87	42	convolution	convolution	NOUN
iajs-116	87	43	operators	operator	NOUN
iajs-116	87	44	in	in	ADP
iajs-116	87	45	homogeneous	homogeneous	ADJ
iajs-116	87	46	banach	banach	NOUN
iajs-116	87	47	spaces	space	NOUN
iajs-116	87	48	of	of	ADP
iajs-116	87	49	periodic	periodic	ADJ
iajs-116	87	50	functions	function	NOUN
iajs-116	87	51	,	,	PUNCT
iajs-116	87	52	mathematica	mathematica	PROPN
iajs-116	87	53	balkanica	balkanica	PROPN
iajs-116	87	54	,	,	PUNCT
iajs-116	87	55	new	new	ADJ
iajs-116	87	56	series	series	NOUN
iajs-116	87	57	,	,	PUNCT
iajs-116	87	58	vol	vol	NOUN
iajs-116	87	59	.	.	PROPN
iajs-116	87	60	25	25	NUM
iajs-116	87	61	,	,	PUNCT
iajs-116	87	62	fasc	fasc	PROPN
iajs-116	87	63	.	.	PROPN
iajs-116	87	64	,	,	PUNCT
iajs-116	87	65	1	1	NUM
iajs-116	87	66	-	-	SYM
iajs-116	87	67	2	2	NUM
iajs-116	87	68	,	,	PUNCT
iajs-116	87	69	39	39	NUM
iajs-116	87	70	-	-	SYM
iajs-116	87	71	59	59	NUM
iajs-116	87	72	.	.	PUNCT
iajs-116	88	1	3	3	X
iajs-116	88	2	.	.	X
iajs-116	88	3	jassim	jassim	PROPN
iajs-116	88	4	s.	s.	PROPN
iajs-116	88	5	and	and	CCONJ
iajs-116	88	6	alaa	alaa	PROPN
iajs-116	88	7	a.	a.	PROPN
iajs-116	88	8	,(2014	,(2014	PROPN
iajs-116	88	9	)	)	PUNCT
iajs-116	88	10	,	,	PUNCT
iajs-116	88	11	direct	direct	ADJ
iajs-116	88	12	and	and	CCONJ
iajs-116	88	13	inverse	inverse	ADJ
iajs-116	88	14	theorems	theorem	NOUN
iajs-116	88	15	in	in	ADP
iajs-116	88	16	weighted	weight	VERB
iajs-116	88	17	space	space	NOUN
iajs-116	88	18	lp	lp	PROPN
iajs-116	88	19	,	,	PUNCT
iajs-116	88	20	w(x	w(x	NOUN
iajs-116	88	21	)	)	PUNCT
iajs-116	88	22	”	"	PUNCT
iajs-116	88	23	,	,	PUNCT
iajs-116	88	24	international	international	ADJ
iajs-116	88	25	journal	journal	NOUN
iajs-116	88	26	of	of	ADP
iajs-116	88	27	scientific	scientific	ADJ
iajs-116	88	28	and	and	CCONJ
iajs-116	88	29	engineering	engineering	NOUN
iajs-116	88	30	research	research	NOUN
iajs-116	88	31	,	,	PUNCT
iajs-116	88	32	vol	vol	NOUN
iajs-116	88	33	.	.	PROPN
iajs-116	88	34	5	5	NUM
iajs-116	88	35	,	,	PUNCT
iajs-116	88	36	iss	iss	PROPN
iajs-116	88	37	.	.	PROPN
iajs-116	88	38	4	4	NUM
iajs-116	88	39	,	,	PUNCT
iajs-116	88	40	833	833	NUM
iajs-116	88	41	-	-	SYM
iajs-116	88	42	839	839	NUM
iajs-116	88	43	.	.	PUNCT
iajs-116	89	1	4	4	X
iajs-116	89	2	.	.	X
iajs-116	90	1	popov	popov	PROPN
iajs-116	90	2	v.	v.	ADP
iajs-116	90	3	a.	a.	PROPN
iajs-116	90	4	,	,	PUNCT
iajs-116	90	5	(	(	PUNCT
iajs-116	90	6	1983	1983	NUM
iajs-116	90	7	)	)	PUNCT
iajs-116	90	8	,	,	PUNCT
iajs-116	90	9	the	the	DET
iajs-116	90	10	averaged	average	VERB
iajs-116	90	11	modli	modli	NOUN
iajs-116	90	12	and	and	CCONJ
iajs-116	90	13	their	their	PRON
iajs-116	90	14	function	function	NOUN
iajs-116	90	15	spaces	space	NOUN
iajs-116	90	16	,	,	PUNCT
iajs-116	90	17	in	in	ADP
iajs-116	90	18	.	.	PUNCT
iajs-116	91	1	constructive	constructive	ADJ
iajs-116	91	2	function	function	PROPN
iajs-116	91	3	theory	theory	NOUN
iajs-116	91	4	81,published	81,published	PROPN
iajs-116	91	5	house	house	PROPN
iajs-116	91	6	bulg	bulg	PROPN
iajs-116	91	7	.	.	PUNCT
iajs-116	92	1	acad	acad	PROPN
iajs-116	92	2	.	.	PUNCT
iajs-116	93	1	sci	sci	PROPN
iajs-116	93	2	.	.	PROPN
iajs-116	93	3	,	,	PUNCT
iajs-116	93	4	sofia	sofia	PROPN
iajs-116	93	5	.	.	PUNCT
iajs-116	94	1	5	5	NUM
iajs-116	94	2	.	.	X
iajs-116	94	3	sendov	sendov	PROPN
iajs-116	94	4	b.	b.	PROPN
iajs-116	94	5	and	and	CCONJ
iajs-116	94	6	popov	popov	PROPN
iajs-116	94	7	v.	v.	ADP
iajs-116	94	8	a.	a.	PROPN
iajs-116	94	9	,	,	PUNCT
iajs-116	94	10	(	(	PUNCT
iajs-116	94	11	1988	1988	NUM
iajs-116	94	12	)	)	PUNCT
iajs-116	94	13	,	,	PUNCT
iajs-116	94	14	the	the	DET
iajs-116	94	15	averaged	average	VERB
iajs-116	94	16	modli	modli	NOUN
iajs-116	94	17	of	of	ADP
iajs-116	94	18	smoothness	smoothness	PROPN
iajs-116	94	19	,	,	PUNCT
iajs-116	94	20	wiley	wiley	PROPN
iajs-116	94	21	,	,	PUNCT
iajs-116	94	22	new	new	PROPN
iajs-116	94	23	york	york	PROPN
iajs-116	94	24	.	.	PUNCT
iajs-116	95	1	6	6	X
iajs-116	95	2	.	.	X
iajs-116	95	3	freud	freud	PROPN
iajs-116	95	4	g.	g.	PROPN
iajs-116	95	5	,(1972	,(1972	PROPN
iajs-116	95	6	)	)	PUNCT
iajs-116	95	7	,	,	PUNCT
iajs-116	95	8	on	on	ADP
iajs-116	95	9	direct	direct	ADJ
iajs-116	95	10	and	and	CCONJ
iajs-116	95	11	converse	converse	NOUN
iajs-116	95	12	theorems	theorem	NOUN
iajs-116	95	13	in	in	ADP
iajs-116	95	14	the	the	DET
iajs-116	95	15	theory	theory	NOUN
iajs-116	95	16	of	of	ADP
iajs-116	95	17	weighted	weight	VERB
iajs-116	95	18	polynomial	polynomial	ADJ
iajs-116	95	19	approximation	approximation	NOUN
iajs-116	95	20	,	,	PUNCT
iajs-116	95	21	published	publish	VERB
iajs-116	95	22	by	by	ADP
iajs-116	95	23	springerverlag	springerverlag	NOUN
iajs-116	95	24	,	,	PUNCT
iajs-116	95	25	math	math	NOUN
iajs-116	95	26	.	.	PUNCT
iajs-116	96	1	z.	z.	PROPN
iajs-116	96	2	,	,	PUNCT
iajs-116	96	3	126	126	NUM
iajs-116	96	4	,	,	PUNCT
iajs-116	96	5	123	123	NUM
iajs-116	96	6	-	-	SYM
iajs-116	96	7	136	136	NUM
iajs-116	96	8	.	.	PUNCT
iajs-116	97	1	7	7	X
iajs-116	97	2	.	.	X
iajs-116	97	3	devore	devore	ADJ
iajs-116	97	4	a.	a.	NOUN
iajs-116	97	5	and	and	CCONJ
iajs-116	97	6	lornentz	lornentz	PROPN
iajs-116	97	7	g.	g.	PROPN
iajs-116	97	8	,	,	PUNCT
iajs-116	97	9	(	(	PUNCT
iajs-116	97	10	1993	1993	NUM
iajs-116	97	11	)	)	PUNCT
iajs-116	97	12	,	,	PUNCT
iajs-116	97	13	constructive	constructive	ADJ
iajs-116	97	14	approximation	approximation	NOUN
iajs-116	97	15	,	,	PUNCT
iajs-116	97	16	springer	springer	NOUN
iajs-116	97	17	-	-	PUNCT
iajs-116	97	18	verlag	verlag	PROPN
iajs-116	97	19	,	,	PUNCT
iajs-116	97	20	new	new	PROPN
iajs-116	97	21	york	york	PROPN
iajs-116	97	22	.	.	PUNCT
iajs-116	98	1	mathematics	mathematic	NOUN
iajs-116	98	2	|	|	ADV
iajs-116	98	3	281	281	NUM
iajs-116	98	4	2016	2016	NUM
iajs-116	98	5	)	)	PUNCT
iajs-116	98	6	عام	عام	ADP
iajs-116	98	7	2العدد	2العدد	NUM
iajs-116	98	8	(	(	PUNCT
iajs-116	98	9	29لمجلد	29لمجلد	NUM
iajs-116	98	10	ا	ا	X
iajs-116	98	11	مجلة	مجلة	NOUN
iajs-116	98	12	إبن	إبن	VERB
iajs-116	98	13	الهيثم	الهيثم	ADJ
iajs-116	98	14	للعلوم	للعلوم	NOUN
iajs-116	98	15	الصرفة	الصرفة	NOUN
iajs-116	99	1	و	و	PRON
iajs-116	99	2	التطبيقية	التطبيقية	ADJ
iajs-116	99	3	ibn	ibn	PROPN
iajs-116	99	4	al	al	PROPN
iajs-116	99	5	-	-	PUNCT
iajs-116	99	6	haitham	haitham	PROPN
iajs-116	99	7	jour	jour	X
iajs-116	99	8	.	.	PROPN
iajs-116	99	9	for	for	ADP
iajs-116	99	10	pure	pure	ADJ
iajs-116	99	11	&	&	CCONJ
iajs-116	99	12	appl	appl	PROPN
iajs-116	99	13	.	.	PUNCT
iajs-116	100	1	sci	sci	PROPN
iajs-116	100	2	.	.	PUNCT
iajs-116	100	3	vol	vol	NOUN
iajs-116	100	4	.	.	PROPN
iajs-116	100	5	29	29	NUM
iajs-116	100	6	(	(	PUNCT
iajs-116	100	7	2	2	NUM
iajs-116	100	8	)	)	SYM
iajs-116	100	9	2016	2016	NUM
iajs-116	100	10	دراسة	دراسة	PROPN
iajs-116	100	11	درجة	درجة	ADJ
iajs-116	100	12	أفضل	أفضل	PROPN
iajs-116	100	13	تقريب	تقريب	PROPN
iajs-116	100	14	للدوال	للدوال	ADP
iajs-116	100	15	الغير	الغير	ADV
iajs-116	100	16	مقيدة	مقيدة	NOUN
iajs-116	100	17	بواسطة	بواسطة	ADJ
iajs-116	100	18	متعددات	متعددات	NOUN
iajs-116	100	19	الحدود	الحدود	NOUN
iajs-116	100	20	الجبرية	الجبرية	VERB
iajs-116	100	21	عالء	عالء	PROPN
iajs-116	100	22	عدنان	عدنان	VERB
iajs-116	100	23	عواد	عواد	PROPN
iajs-116	100	24	جامعة	جامعة	PROPN
iajs-116	100	25	االنبارقسم	االنبارقسم	PROPN
iajs-116	100	26	الرياضيات	الرياضيات	PROPN
iajs-116	100	27	/	/	SYM
iajs-116	100	28	كلية	كلية	NOUN
iajs-116	100	29	التربية	التربية	NOUN
iajs-116	100	30	للعلوم	للعلوم	NOUN
iajs-116	100	31	الصرفة/	الصرفة/	NUM
iajs-116	100	32	2016أيار//22،قبل	2016أيار//22،قبل	NOUN
iajs-116	100	33	في:2016اذار//27استلم	في:2016اذار//27استلم	PROPN
iajs-116	100	34	في	في	PROPN
iajs-116	100	35	:	:	PUNCT
iajs-116	100	36	الخالصة	الخالصة	PROPN
iajs-116	100	37	افضل	افضل	PROPN
iajs-116	100	38	تقريب	تقريب	PROPN
iajs-116	100	39	للدوال	للدوال	ADP
iajs-116	100	40	الغير	الغير	ADV
iajs-116	100	41	مقيدة	مقيدة	NOUN
iajs-116	100	42	بواسطة	بواسطة	ADJ
iajs-116	100	43	متعددات	متعددات	NOUN
iajs-116	100	44	الحدود	الحدود	NOUN
iajs-116	100	45	الجبرية	الجبرية	VERB
iajs-116	100	46	في	في	ADP
iajs-116	100	47	في	في	PRON
iajs-116	100	48	هذا	هذا	NOUN
iajs-116	100	49	البحث	البحث	PROPN
iajs-116	100	50	عرضنا	عرضنا	PROPN
iajs-116	100	51	نوع	نوع	PROPN
iajs-116	100	52	جديد	جديد	PROPN
iajs-116	100	53	من	من	PROPN
iajs-116	100	54	درجة	درجة	ADJ
iajs-116	100	55	)	)	PUNCT
iajs-116	100	56	فضاء	فضاء	ADJ
iajs-116	100	57	الوزن	الوزن	NOUN
iajs-116	100	58	,	,	PUNCT
iajs-116	100	59	1)و	1)و	PROPN
iajs-116	100	60	(	(	PUNCT
iajs-116	100	61	.	.	PUNCT
iajs-116	101	1	سوف	سوف	PRON
iajs-116	101	2	نبرهن	نبرهن	PROPN
iajs-116	101	3	المبرهنات	المبرهنات	ADJ
iajs-116	101	4	المباشرة	المباشرة	NOUN
iajs-116	101	5	والمعكوسة	والمعكوسة	PROPN
iajs-116	101	6	ألفضل	ألفضل	PROPN
iajs-116	101	7	تقريب	تقريب	PROPN
iajs-116	101	8	لهذه	لهذه	PROPN
iajs-116	101	9	الدوال	الدوال	PROPN
iajs-116	101	10	∞	∞	PROPN
iajs-116	101	11	بواسطة	بواسطة	NOUN
iajs-116	101	12	متعددات	متعددات	NOUN
iajs-116	101	13	الحدود	الحدود	NOUN
iajs-116	101	14	الجبرية	الجبرية	VERB
iajs-116	101	15	بشروط	بشروط	VERB
iajs-116	101	16	مقياس	مقياس	ADJ
iajs-116	101	17	النعومة	النعومة	PROPN
iajs-116	101	18	في	في	ADP
iajs-116	101	19	فضاء	فضاء	ADJ
iajs-116	101	20	الوزن	الوزن	NOUN
iajs-116	101	21	.	.	PUNCT
iajs-116	102	1	:	:	PUNCT
iajs-116	102	2	درجة	درجة	ADJ
iajs-116	102	3	أفضل	أفضل	PROPN
iajs-116	102	4	تقريب	تقريب	PROPN
iajs-116	102	5	,	,	PUNCT
iajs-116	102	6	الدوال	الدوال	ADP
iajs-116	102	7	الغير	الغير	ADV
iajs-116	102	8	مقيدة	مقيدة	NOUN
iajs-116	102	9	,	,	PUNCT
iajs-116	102	10	فضاء	فضاء	X
iajs-116	102	11	الوزن	الوزن	NOUN
iajs-116	102	12	,	,	PUNCT
iajs-116	102	13	مقياس	مقياس	ADJ
iajs-116	102	14	النعومة	النعومة	NOUN
iajs-116	102	15	.	.	PUNCT
iajs-116	103	1	الكلمات	الكلمات	VERB
iajs-116	103	2	المفتاحية	المفتاحية	NOUN