id	sid	tid	token	lemma	pos
iajs-878	1	1	2011	2011	NUM
iajs-878	1	2	)	)	PUNCT
iajs-878	1	3	1	1	NUM
iajs-878	1	4	(	(	PUNCT
iajs-878	1	5	24مجلة	24مجلة	NUM
iajs-878	1	6	ابن	ابن	VERB
iajs-878	1	7	الهیثم	الهیثم	ADJ
iajs-878	1	8	للعلوم	للعلوم	PROPN
iajs-878	1	9	الصرفة	الصرفة	PROPN
iajs-878	1	10	والتطبیقیة	والتطبیقیة	PROPN
iajs-878	1	11	المجلد	المجلد	VERB
iajs-878	1	12	iaxax	iaxax	PROPN
iajs-878	1	13	ةالحظات	ةالحظات	PROPN
iajs-878	1	14	حول	حول	VERB
iajs-878	1	15	معادلة	معادلة	PROPN
iajs-878	1	16	المؤثرالالخطیم	المؤثرالالخطیم	PROPN
iajs-878	1	17	n	n	ADV
iajs-878	1	18			VERB
iajs-878	1	19			PROPN
iajs-878	1	20	*	*	SYM
iajs-878	1	21	مي	مي	ADP
iajs-878	1	22	محمد	محمد	PROPN
iajs-878	1	23	هاللو	هاللو	VERB
iajs-878	1	24	بثینه	بثینه	PROPN
iajs-878	1	25	عبد	عبد	PROPN
iajs-878	1	26	الحسن	الحسن	PROPN
iajs-878	1	27	احمد	احمد	PROPN
iajs-878	1	28	د	د	PROPN
iajs-878	1	29	،	،	X
iajs-878	1	30	كلیة	كلیة	PROPN
iajs-878	1	31	العلوم،قسم	العلوم،قسم	PROPN
iajs-878	1	32	الریاضیات	الریاضیات	VERB
iajs-878	1	33	جامعة	جامعة	PROPN
iajs-878	1	34	بغدا	بغدا	PROPN
iajs-878	1	35	دادجامعة	دادجامعة	PROPN
iajs-878	1	36	بغ،ابن	بغ،ابن	PROPN
iajs-878	1	37	الهیثم	الهیثم	VERB
iajs-878	1	38	ةكلیة	ةكلیة	PROPN
iajs-878	1	39	التربی	التربی	PROPN
iajs-878	1	40	،	،	PROPN
iajs-878	1	41	قسم	قسم	PROPN
iajs-878	1	42	الریاضیات	الریاضیات	VERB
iajs-878	1	43	2009	2009	NUM
iajs-878	1	44	نیسان	نیسان	NOUN
iajs-878	1	45	13استلم	13استلم	X
iajs-878	1	46	البحث	البحث	VERB
iajs-878	1	47	في	في	ADP
iajs-878	1	48	2009تموز	2009تموز	PROPN
iajs-878	1	49	7قبل	7قبل	PROPN
iajs-878	1	50	البحث	البحث	VERB
iajs-878	1	51	في	في	ADP
iajs-878	1	52	ةالخالص	ةالخالص	NOUN
iajs-878	1	53	ــة	ــة	PROPN
iajs-878	1	54	لمعادلــة	لمعادلــة	PROPN
iajs-878	1	55	المــؤثر	المــؤثر	PROPN
iajs-878	1	56	ةوریالشــروط	ةوریالشــروط	PROPN
iajs-878	1	57	الضــر	الضــر	PROPN
iajs-878	1	58	iaxaxوالكافیـ	iaxaxوالكافیـ	PROPN
iajs-878	1	59	n	n	CCONJ
iajs-878	1	60			VERB
iajs-878	1	61			PROPN
iajs-878	1	62	*	*	SYM
iajs-878	1	63	،	،	NOUN
iajs-878	1	64	ــق	ــق	PROPN
iajs-878	1	65	حقیقــي	حقیقــي	PROPN
iajs-878	1	66	للحصـــول	للحصـــول	PROPN
iajs-878	1	67	علــى	علــى	PROPN
iajs-878	1	68	حــل	حــل	PROPN
iajs-878	1	69	موجـــب	موجـــب	PROPN
iajs-878	1	70	ذاتــي	ذاتــي	PROPN
iajs-878	1	71	الترافـ	الترافـ	PROPN
iajs-878	1	72	xـاد	xـاد	PROPN
iajs-878	1	73	علــى	علــى	PROPN
iajs-878	1	74	هــذه	هــذه	PROPN
iajs-878	1	75	الشــروط	الشــروط	PROPN
iajs-878	1	76	وبعــض	وبعــض	PROPN
iajs-878	1	77	الخصــائص	الخصــائص	PROPN
iajs-878	1	78	للمـؤثر	للمـؤثر	PROPN
iajs-878	1	79	قـد	قـد	VERB
iajs-878	1	80	اعطیــت	اعطیــت	PROPN
iajs-878	1	81	ـهوكــذ	ـهوكــذ	PROPN
iajs-878	1	82	،	،	PROPN
iajs-878	1	83	باالعتمـ	باالعتمـ	PROPN
iajs-878	1	84	قــد	قــد	PROPN
iajs-878	1	85	اعطیــت	اعطیــت	PROPN
iajs-878	1	86	aوxلبــین	aوxلبــین	PROPN
iajs-878	1	87	الحــ	الحــ	PROPN
iajs-878	1	88	لك	لك	PROPN
iajs-878	2	1	العــال	العــال	PROPN
iajs-878	2	2	قـ	قـ	PROPN
iajs-878	3	1	.أیضا	.أیضا	PRON
iajs-878	3	2	مؤثر	مؤثر	PROPN
iajs-878	3	3	موجب	موجب	PROPN
iajs-878	3	4	ذاتي	ذاتي	ADV
iajs-878	3	5	الترافق	الترافق	ADJ
iajs-878	3	6	،	،	NOUN
iajs-878	3	7	القطر	القطر	PROPN
iajs-878	3	8	الطیفي،معادلة	الطیفي،معادلة	PROPN
iajs-878	3	9	المؤثر	المؤثر	PROPN
iajs-878	3	10	الالخطیة	الالخطیة	PROPN
iajs-878	3	11	:	:	PUNCT
iajs-878	3	12	الكلمات	الكلمات	VERB
iajs-878	3	13	المفتاحیة	المفتاحیة	ADJ
iajs-878	3	14	ibn	ibn	PROPN
iajs-878	3	15	alhaitham	alhaitham	PROPN
iajs-878	3	16	j.	j.	PROPN
iajs-878	3	17	for	for	ADP
iajs-878	3	18	pure	pure	ADJ
iajs-878	3	19	&	&	CCONJ
iajs-878	3	20	appl	appl	PROPN
iajs-878	3	21	.	.	PUNCT
iajs-878	4	1	sci	sci	PROPN
iajs-878	4	2	.	.	PUNCT
iajs-878	4	3	vol.24	vol.24	NOUN
iajs-878	4	4	(	(	PUNCT
iajs-878	4	5	1	1	NUM
iajs-878	4	6	)	)	PUNCT
iajs-878	4	7	2011	2011	NUM
iajs-878	4	8	notes	note	NOUN
iajs-878	4	9	on	on	ADP
iajs-878	4	10	the	the	DET
iajs-878	4	11	non	non	ADJ
iajs-878	4	12	linear	linear	PROPN
iajs-878	4	13	operator	operator	NOUN
iajs-878	4	14	equation	equation	NOUN
iajs-878	4	15	iaxax	iaxax	NOUN
iajs-878	4	16	n	n	CCONJ
iajs-878	4	17			X
iajs-878	4	18			PROPN
iajs-878	4	19	*	*	SYM
iajs-878	4	20	b.a	b.a	PROPN
iajs-878	4	21	.	.	PROPN
iajs-878	4	22	ahmed	ahmed	PROPN
iajs-878	4	23	and	and	CCONJ
iajs-878	4	24	m.m	m.m	PROPN
iajs-878	4	25	.	.	PROPN
iajs-878	4	26	hilal	hilal	PROPN
iajs-878	4	27	department	department	PROPN
iajs-878	4	28	of	of	ADP
iajs-878	4	29	mathematics	mathematics	PROPN
iajs-878	4	30	,	,	PUNCT
iajs-878	4	31	college	college	NOUN
iajs-878	4	32	of	of	ADP
iajs-878	4	33	science	science	NOUN
iajs-878	4	34	,	,	PUNCT
iajs-878	4	35	university	university	NOUN
iajs-878	4	36	of	of	ADP
iajs-878	4	37	baghdad	baghdad	PROPN
iajs-878	4	38	department	department	PROPN
iajs-878	4	39	of	of	ADP
iajs-878	4	40	mathematics	mathematics	PROPN
iajs-878	4	41	,	,	PUNCT
iajs-878	4	42	college	college	NOUN
iajs-878	4	43	of	of	ADP
iajs-878	4	44	education	education	PROPN
iajs-878	4	45	ibn	ibn	PROPN
iajs-878	4	46	al	al	PROPN
iajs-878	4	47	-	-	PUNCT
iajs-878	4	48	haitham	haitham	PROPN
iajs-878	4	49	,	,	PUNCT
iajs-878	4	50	university	university	PROPN
iajs-878	4	51	of	of	ADP
iajs-878	4	52	baghdad	baghdad	PROPN
iajs-878	4	53	received	receive	VERB
iajs-878	4	54	in	in	ADP
iajs-878	4	55	april,13,2009	april,13,2009	NOUN
iajs-878	4	56	accepted	accept	VERB
iajs-878	4	57	in	in	ADP
iajs-878	4	58	july,7,2009	july,7,2009	PROPN
iajs-878	4	59	abstract	abstract	ADJ
iajs-878	4	60	necessary	necessary	ADJ
iajs-878	4	61	and	and	CCONJ
iajs-878	4	62	sufficient	sufficient	ADJ
iajs-878	4	63	conditions	condition	NOUN
iajs-878	4	64	for	for	ADP
iajs-878	4	65	the	the	DET
iajs-878	4	66	operator	operator	NOUN
iajs-878	4	67	equation	equation	NOUN
iajs-878	4	68	iaxax	iaxax	NOUN
iajs-878	4	69	n	n	CCONJ
iajs-878	4	70			X
iajs-878	4	71			PROPN
iajs-878	4	72	*	*	PUNCT
iajs-878	4	73	,	,	PUNCT
iajs-878	4	74	to	to	PART
iajs-878	4	75	have	have	AUX
iajs-878	4	76	a	a	DET
iajs-878	4	77	real	real	ADJ
iajs-878	4	78	positive	positive	ADJ
iajs-878	4	79	definite	definite	ADJ
iajs-878	4	80	solution	solution	NOUN
iajs-878	4	81	x	x	PRON
iajs-878	4	82	are	be	AUX
iajs-878	4	83	given	give	VERB
iajs-878	4	84	.	.	PUNCT
iajs-878	5	1	based	base	VERB
iajs-878	5	2	on	on	ADP
iajs-878	5	3	these	these	DET
iajs-878	5	4	conditions	condition	NOUN
iajs-878	5	5	,	,	PUNCT
iajs-878	5	6	some	some	DET
iajs-878	5	7	properties	property	NOUN
iajs-878	5	8	of	of	ADP
iajs-878	5	9	the	the	DET
iajs-878	5	10	operator	operator	NOUN
iajs-878	5	11	a	a	PRON
iajs-878	5	12	as	as	ADV
iajs-878	5	13	well	well	ADV
iajs-878	5	14	as	as	ADP
iajs-878	5	15	relation	relation	NOUN
iajs-878	5	16	between	between	ADP
iajs-878	5	17	the	the	DET
iajs-878	5	18	solutions	solution	NOUN
iajs-878	5	19	x	x	PUNCT
iajs-878	5	20	and	and	CCONJ
iajs-878	5	21	a	a	PRON
iajs-878	5	22	are	be	AUX
iajs-878	5	23	given	give	VERB
iajs-878	5	24	.	.	PUNCT
iajs-878	6	1	key	key	ADJ
iajs-878	6	2	words	word	NOUN
iajs-878	6	3	:	:	PUNCT
iajs-878	6	4	non	non	ADJ
iajs-878	6	5	-	-	ADJ
iajs-878	6	6	linear	linear	ADJ
iajs-878	6	7	operator	operator	NOUN
iajs-878	6	8	equation	equation	NOUN
iajs-878	6	9	;	;	PUNCT
iajs-878	6	10	spectral	spectral	ADJ
iajs-878	6	11	radius	radius	NOUN
iajs-878	6	12	;	;	PUNCT
iajs-878	6	13	positive	positive	ADJ
iajs-878	6	14	definite	definite	ADJ
iajs-878	6	15	operator	operator	NOUN
iajs-878	6	16	.	.	PUNCT
iajs-878	7	1	ams	am	NOUN
iajs-878	7	2	classification	classification	NOUN
iajs-878	7	3	:	:	PUNCT
iajs-878	7	4	39b42	39b42	NUM
iajs-878	7	5	.	.	PUNCT
iajs-878	8	1	introduction	introduction	NOUN
iajs-878	8	2	consider	consider	VERB
iajs-878	8	3	the	the	DET
iajs-878	8	4	non	non	ADJ
iajs-878	8	5	-	-	ADJ
iajs-878	8	6	linear	linear	ADJ
iajs-878	8	7	operator	operator	NOUN
iajs-878	8	8	equation	equation	NOUN
iajs-878	8	9	)	)	PUNCT
iajs-878	8	10	1	1	NUM
iajs-878	8	11	(	(	PUNCT
iajs-878	8	12	*	*	PUNCT
iajs-878	8	13	iaxax	iaxax	NOUN
iajs-878	8	14	n	n	CCONJ
iajs-878	8	15			X
iajs-878	8	16			NOUN
iajs-878	8	17	where	where	SCONJ
iajs-878	8	18	i	i	PRON
iajs-878	8	19	is	be	AUX
iajs-878	8	20	identity	identity	NOUN
iajs-878	8	21	operator	operator	NOUN
iajs-878	8	22	,	,	PUNCT
iajs-878	8	23	and	and	CCONJ
iajs-878	8	24			PROPN
iajs-878	8	25	hbxaa	hbxaa	PROPN
iajs-878	8	26			NOUN
iajs-878	8	27	,	,	PUNCT
iajs-878	8	28	,	,	PUNCT
iajs-878	8	29	*	*	PUNCT
iajs-878	8	30	;	;	PUNCT
iajs-878	8	31	where	where	SCONJ
iajs-878	8	32			PROPN
iajs-878	8	33	hb	hb	PROPN
iajs-878	8	34	denotes	denote	VERB
iajs-878	8	35	the	the	DET
iajs-878	8	36	banach	banach	NOUN
iajs-878	8	37	algebra	algebra	NOUN
iajs-878	8	38	of	of	ADP
iajs-878	8	39	all	all	DET
iajs-878	8	40	bounded	bound	VERB
iajs-878	8	41	linear	linear	PROPN
iajs-878	8	42	operators	operator	NOUN
iajs-878	8	43	on	on	ADP
iajs-878	8	44	h	h	NOUN
iajs-878	8	45	;	;	PUNCT
iajs-878	8	46	h	h	NOUN
iajs-878	8	47	is	be	AUX
iajs-878	8	48	an	an	DET
iajs-878	8	49	infinite	infinite	ADJ
iajs-878	8	50	dimensional	dimensional	ADJ
iajs-878	8	51	complex	complex	ADJ
iajs-878	8	52	hilbert	hilbert	NOUN
iajs-878	8	53	space	space	NOUN
iajs-878	8	54	.	.	PUNCT
iajs-878	9	1	several	several	ADJ
iajs-878	9	2	authors	author	NOUN
iajs-878	9	3	have	have	AUX
iajs-878	9	4	studied	study	VERB
iajs-878	9	5	the	the	DET
iajs-878	9	6	above	above	ADJ
iajs-878	9	7	equation	equation	NOUN
iajs-878	9	8	when	when	SCONJ
iajs-878	9	9	xa	xa	PROPN
iajs-878	9	10	,	,	PUNCT
iajs-878	9	11	are	be	AUX
iajs-878	9	12	matrices	matrix	NOUN
iajs-878	9	13	and	and	CCONJ
iajs-878	9	14	2,1	2,1	NUM
iajs-878	9	15			NUM
iajs-878	9	16	nn	nn	NOUN
iajs-878	9	17	and	and	CCONJ
iajs-878	9	18	they	they	PRON
iajs-878	9	19	have	have	AUX
iajs-878	9	20	obtained	obtain	VERB
iajs-878	9	21	theoretical	theoretical	ADJ
iajs-878	9	22	properties	property	NOUN
iajs-878	9	23	of	of	ADP
iajs-878	9	24	these	these	DET
iajs-878	9	25	equations	equation	NOUN
iajs-878	9	26	.	.	PUNCT
iajs-878	10	1	in	in	ADP
iajs-878	10	2	[	[	X
iajs-878	10	3	1	1	NUM
iajs-878	10	4	]	]	X
iajs-878	10	5	equation	equation	NOUN
iajs-878	10	6	(	(	PUNCT
iajs-878	10	7	1	1	X
iajs-878	10	8	)	)	PUNCT
iajs-878	10	9	was	be	AUX
iajs-878	10	10	studied	study	VERB
iajs-878	10	11	in	in	ADP
iajs-878	10	12	the	the	DET
iajs-878	10	13	case	case	NOUN
iajs-878	10	14	x	x	PUNCT
iajs-878	10	15	is	be	AUX
iajs-878	10	16	a	a	DET
iajs-878	10	17	self_adjoint	self_adjoint	NOUN
iajs-878	10	18	positive	positive	ADJ
iajs-878	10	19	operator	operator	NOUN
iajs-878	10	20	,	,	PUNCT
iajs-878	10	21	which	which	PRON
iajs-878	10	22	arises	arise	VERB
iajs-878	10	23	in	in	ADP
iajs-878	10	24	many	many	ADJ
iajs-878	10	25	applications	application	NOUN
iajs-878	10	26	such	such	ADJ
iajs-878	10	27	as	as	ADP
iajs-878	10	28	in	in	ADP
iajs-878	10	29	control	control	NOUN
iajs-878	10	30	theory	theory	NOUN
iajs-878	10	31	and	and	CCONJ
iajs-878	10	32	statistics	statistic	NOUN
iajs-878	10	33	and	and	CCONJ
iajs-878	10	34	in	in	ADP
iajs-878	10	35	dynamic	dynamic	ADJ
iajs-878	10	36	programming	programming	NOUN
iajs-878	10	37	in	in	ADP
iajs-878	10	38	this	this	DET
iajs-878	10	39	paper	paper	NOUN
iajs-878	10	40	,	,	PUNCT
iajs-878	10	41	we	we	PRON
iajs-878	10	42	study	study	VERB
iajs-878	10	43	equation	equation	NOUN
iajs-878	10	44	(	(	PUNCT
iajs-878	10	45	1	1	NUM
iajs-878	10	46	)	)	PUNCT
iajs-878	10	47	where	where	SCONJ
iajs-878	10	48	x	x	PRON
iajs-878	10	49	belongs	belong	VERB
iajs-878	10	50	to	to	ADP
iajs-878	10	51	the	the	DET
iajs-878	10	52	set	set	NOUN
iajs-878	10	53	;	;	PUNCT
iajs-878	11	1	where	where	SCONJ
iajs-878	11	2			NOUN
iajs-878	11	3			SYM
iajs-878	11	4			NOUN
iajs-878	11	5			NOUN
iajs-878	11	6	ttrhbtttaac	ttrhbtttaac	PROPN
iajs-878	11	7			PROPN
iajs-878	11	8	;	;	PUNCT
iajs-878	11	9	,	,	PUNCT
iajs-878	11	10	:	:	PUNCT
iajs-878	12	1	*	*	PUNCT
iajs-878	12	2	.	.	PUNCT
iajs-878	13	1	where	where	SCONJ
iajs-878	13	2			PROPN
iajs-878	13	3	tr	tr	PROPN
iajs-878	13	4	is	be	AUX
iajs-878	13	5	the	the	DET
iajs-878	13	6	spectral	spectral	ADJ
iajs-878	13	7	radius	radius	NOUN
iajs-878	13	8	of	of	ADP
iajs-878	13	9	t	t	PROPN
iajs-878	13	10	1	1	NUM
iajs-878	13	11	-	-	PUNCT
iajs-878	13	12	preliminaries	preliminary	NOUN
iajs-878	13	13	in	in	ADP
iajs-878	13	14	this	this	DET
iajs-878	13	15	section	section	NOUN
iajs-878	13	16	we	we	PRON
iajs-878	13	17	present	present	VERB
iajs-878	13	18	notation	notation	NOUN
iajs-878	13	19	,	,	PUNCT
iajs-878	13	20	lemma	lemma	PROPN
iajs-878	13	21	and	and	CCONJ
iajs-878	13	22	theorem	theorem	NOUN
iajs-878	13	23	which	which	PRON
iajs-878	13	24	will	will	AUX
iajs-878	13	25	be	be	AUX
iajs-878	13	26	used	use	VERB
iajs-878	13	27	in	in	ADP
iajs-878	13	28	the	the	DET
iajs-878	13	29	remainder	remainder	NOUN
iajs-878	13	30	of	of	ADP
iajs-878	13	31	the	the	DET
iajs-878	13	32	paper	paper	NOUN
iajs-878	13	33	.	.	PUNCT
iajs-878	14	1	the	the	DET
iajs-878	14	2	notation	notation	PROPN
iajs-878	14	3			PROPN
iajs-878	14	4	00	00	PUNCT
iajs-878	15	1			NUM
iajs-878	15	2	aa	aa	NOUN
iajs-878	15	3	means	mean	VERB
iajs-878	15	4	that	that	SCONJ
iajs-878	15	5	a	a	PRON
iajs-878	15	6	is	be	AUX
iajs-878	15	7	positive	positive	ADJ
iajs-878	15	8	operator	operator	NOUN
iajs-878	15	9	,	,	PUNCT
iajs-878	15	10	and	and	CCONJ
iajs-878	15	11	ba	ba	PROPN
iajs-878	15	12			PROPN
iajs-878	15	13	is	be	AUX
iajs-878	15	14	used	use	VERB
iajs-878	15	15	as	as	ADP
iajs-878	15	16	an	an	DET
iajs-878	15	17	alternative	alternative	ADJ
iajs-878	15	18	notation	notation	NOUN
iajs-878	15	19	for	for	ADP
iajs-878	15	20	0	0	NUM
iajs-878	15	21	ba	ba	PROPN
iajs-878	15	22	.it	.it	PUNCT
iajs-878	15	23	is	be	AUX
iajs-878	15	24	well	well	ADV
iajs-878	15	25	-	-	PUNCT
iajs-878	15	26	known	know	VERB
iajs-878	15	27	for	for	ADP
iajs-878	15	28	any	any	DET
iajs-878	15	29	operator	operator	NOUN
iajs-878	15	30			NOUN
iajs-878	15	31			PROPN
iajs-878	15	32	tthbt	tthbt	NOUN
iajs-878	15	33	*	*	PUNCT
iajs-878	15	34	,	,	PUNCT
iajs-878	15	35			NOUN
iajs-878	15	36	is	be	AUX
iajs-878	15	37	positive	positive	ADJ
iajs-878	15	38	operator	operator	NOUN
iajs-878	15	39			NOUN
iajs-878	16	1	22.,2	22.,2	PROPN
iajs-878	16	2	p	p	NOUN
iajs-878	16	3	,	,	PUNCT
iajs-878	16	4	let	let	VERB
iajs-878	16	5	spec	spec	VERB
iajs-878	16	6	a	a	DET
iajs-878	16	7	denotes	denote	NOUN
iajs-878	16	8	the	the	DET
iajs-878	16	9	spectrum	spectrum	NOUN
iajs-878	16	10	of	of	ADP
iajs-878	16	11	a.	a.	PROPN
iajs-878	16	12	lemma	lemma	PROPN
iajs-878	16	13	1.1[3	1.1[3	NUM
iajs-878	16	14	,	,	PUNCT
iajs-878	16	15	p.	p.	NOUN
iajs-878	16	16	866	866	NUM
iajs-878	17	1	]	]	X
iajs-878	17	2	:	:	PUNCT
iajs-878	17	3	let	let	VERB
iajs-878	17	4	m	m	PRON
iajs-878	17	5	and	and	CCONJ
iajs-878	17	6	n	n	CCONJ
iajs-878	17	7	be	be	VERB
iajs-878	17	8	two	two	NUM
iajs-878	17	9	arbitrary	arbitrary	ADJ
iajs-878	17	10	operators	operator	NOUN
iajs-878	17	11	then	then	ADV
iajs-878	17	12	:	:	PUNCT
iajs-878	17	13			NOUN
iajs-878	17	14			SYM
iajs-878	17	15			NOUN
iajs-878	18	1	nnmmrmnnmr	nnmmrmnnmr	NOUN
iajs-878	19	1	*	*	PUNCT
iajs-878	19	2	*	*	PUNCT
iajs-878	19	3	*	*	PUNCT
iajs-878	19	4	*	*	PUNCT
iajs-878	19	5			NUM
iajs-878	19	6	proof	proof	NOUN
iajs-878	19	7	:	:	PUNCT
iajs-878	19	8	by	by	ADP
iajs-878	19	9	elementary	elementary	ADJ
iajs-878	19	10	calculus	calculus	NOUN
iajs-878	19	11	,	,	PUNCT
iajs-878	19	12	we	we	PRON
iajs-878	19	13	have	have	AUX
iajs-878	19	14	that	that	DET
iajs-878	19	15			NOUN
iajs-878	19	16			PUNCT
iajs-878	19	17			ADJ
iajs-878	19	18			PROPN
iajs-878	19	19			NOUN
iajs-878	19	20			NOUN
iajs-878	19	21			PROPN
iajs-878	19	22			NOUN
iajs-878	19	23			PROPN
iajs-878	19	24			NOUN
iajs-878	19	25			NOUN
iajs-878	19	26			NOUN
iajs-878	19	27			PROPN
iajs-878	19	28			NOUN
iajs-878	19	29			PROPN
iajs-878	19	30			NOUN
iajs-878	20	1			PROPN
iajs-878	20	2			PROPN
iajs-878	20	3			PRON
iajs-878	20	4			NOUN
iajs-878	20	5			VERB
iajs-878	20	6			PROPN
iajs-878	20	7			PROPN
iajs-878	20	8			PROPN
iajs-878	20	9	n	n	INTJ
iajs-878	20	10	m	m	VERB
iajs-878	20	11	oi	oi	INTJ
iajs-878	20	12	i	i	PRON
iajs-878	20	13	nmrmnnmr	nmrmnnmr	VERB
iajs-878	20	14	0	0	PUNCT
iajs-878	21	1	*	*	PUNCT
iajs-878	21	2	*	*	PUNCT
iajs-878	21	3	*	*	PUNCT
iajs-878	21	4	*	*	PUNCT
iajs-878	21	5	since	since	SCONJ
iajs-878	21	6	the	the	DET
iajs-878	21	7	non	non	ADJ
iajs-878	21	8	-	-	ADJ
iajs-878	21	9	zero	zero	NUM
iajs-878	21	10	elements	element	NOUN
iajs-878	21	11	of	of	ADP
iajs-878	21	12	specmn	specmn	NOUN
iajs-878	21	13	and	and	CCONJ
iajs-878	21	14	specnm	specnm	NOUN
iajs-878	21	15	are	be	AUX
iajs-878	21	16	the	the	DET
iajs-878	21	17	same	same	ADJ
iajs-878	21	18	[	[	X
iajs-878	21	19	4	4	NUM
iajs-878	21	20	,	,	PUNCT
iajs-878	21	21	p.43	p.43	NOUN
iajs-878	21	22	]	]	X
iajs-878	21	23	;	;	PUNCT
iajs-878	21	24	so	so	CCONJ
iajs-878	21	25	for	for	ADP
iajs-878	21	26	any	any	DET
iajs-878	21	27	two	two	NUM
iajs-878	21	28	operators	operator	NOUN
iajs-878	21	29	,	,	PUNCT
iajs-878	21	30	we	we	PRON
iajs-878	21	31	have	have	VERB
iajs-878	21	32	:	:	PUNCT
iajs-878	21	33	ibn	ibn	PROPN
iajs-878	21	34	alhaitham	alhaitham	NOUN
iajs-878	21	35	j.	j.	PROPN
iajs-878	21	36	for	for	ADP
iajs-878	21	37	pure	pure	ADJ
iajs-878	21	38	&	&	CCONJ
iajs-878	21	39	appl	appl	PROPN
iajs-878	21	40	.	.	PUNCT
iajs-878	22	1	sci	sci	PROPN
iajs-878	22	2	.	.	PUNCT
iajs-878	22	3	vol.24	vol.24	NOUN
iajs-878	22	4	(	(	PUNCT
iajs-878	22	5	1	1	NUM
iajs-878	22	6	)	)	PUNCT
iajs-878	22	7	2011	2011	NUM
iajs-878	22	8			ADJ
iajs-878	22	9			ADP
iajs-878	22	10			PROPN
iajs-878	22	11			NOUN
iajs-878	22	12			NUM
iajs-878	22	13			PROPN
iajs-878	22	14			NOUN
iajs-878	22	15			PROPN
iajs-878	22	16			NOUN
iajs-878	22	17			NOUN
iajs-878	22	18			NOUN
iajs-878	22	19			PROPN
iajs-878	22	20			NOUN
iajs-878	22	21			PROPN
iajs-878	22	22			NOUN
iajs-878	22	23			PROPN
iajs-878	22	24			PROPN
iajs-878	22	25			PRON
iajs-878	22	26			NOUN
iajs-878	22	27			VERB
iajs-878	22	28			PROPN
iajs-878	22	29			NOUN
iajs-878	22	30			NUM
iajs-878	22	31			NOUN
iajs-878	22	32			PROPN
iajs-878	22	33			NOUN
iajs-878	22	34			PROPN
iajs-878	22	35			NOUN
iajs-878	22	36			PROPN
iajs-878	23	1			PROPN
iajs-878	23	2			PRON
iajs-878	23	3			NOUN
iajs-878	23	4			VERB
iajs-878	23	5			PROPN
iajs-878	23	6			PROPN
iajs-878	23	7			PROPN
iajs-878	23	8			X
iajs-878	23	9			NOUN
iajs-878	23	10			VERB
iajs-878	23	11			PRON
iajs-878	23	12			NOUN
iajs-878	23	13	*	*	PUNCT
iajs-878	23	14	*	*	PUNCT
iajs-878	23	15	*	*	PUNCT
iajs-878	23	16	*	*	NOUN
iajs-878	23	17	0	0	NUM
iajs-878	23	18	0	0	NUM
iajs-878	23	19	nm	nm	NOUN
iajs-878	23	20	n	n	ADV
iajs-878	23	21	m	m	VERB
iajs-878	23	22	i	i	INTJ
iajs-878	23	23	i	i	PRON
iajs-878	23	24	r	r	VERB
iajs-878	23	25	n	n	VERB
iajs-878	23	26	m	m	VERB
iajs-878	23	27	oi	oi	PROPN
iajs-878	23	28	io	io	X
iajs-878	23	29	nmr	nmr	NOUN
iajs-878	23	30	now	now	ADV
iajs-878	23	31	,	,	PUNCT
iajs-878	23	32			PROPN
iajs-878	23	33			PROPN
iajs-878	23	34	aar	aar	NOUN
iajs-878	23	35			NOUN
iajs-878	23	36	,	,	PUNCT
iajs-878	23	37	where	where	SCONJ
iajs-878	23	38	denotes	denote	VERB
iajs-878	23	39	the	the	DET
iajs-878	23	40	operator	operator	NOUN
iajs-878	23	41	norm	norm	NOUN
iajs-878	23	42	.	.	PUNCT
iajs-878	24	1	so	so	ADV
iajs-878	24	2			NOUN
iajs-878	24	3			SYM
iajs-878	24	4			NOUN
iajs-878	24	5			PROPN
iajs-878	24	6			ADJ
iajs-878	24	7			ADP
iajs-878	24	8			ADJ
iajs-878	24	9			ADP
iajs-878	24	10			ADJ
iajs-878	24	11			NOUN
iajs-878	24	12			NOUN
iajs-878	24	13	nnmmr	nnmmr	ADV
iajs-878	24	14	n	n	PRON
iajs-878	24	15	m	m	VERB
iajs-878	24	16	nmr	nmr	NOUN
iajs-878	24	17	nm	nm	ADP
iajs-878	24	18	n	n	ADV
iajs-878	24	19	m	m	VERB
iajs-878	24	20	r	r	NOUN
iajs-878	24	21	nm	nm	NOUN
iajs-878	25	1	n	n	ADV
iajs-878	25	2	m	m	VERB
iajs-878	25	3	oi	oi	NOUN
iajs-878	25	4	io	io	X
iajs-878	25	5	nm	nm	INTJ
iajs-878	25	6	n	n	ADV
iajs-878	25	7	m	m	VERB
iajs-878	25	8	oi	oi	INTJ
iajs-878	25	9	i	i	PRON
iajs-878	25	10	rnm	rnm	VERB
iajs-878	26	1	n	n	PRON
iajs-878	26	2	m	m	VERB
iajs-878	26	3	oi	oi	NOUN
iajs-878	26	4	io	io	X
iajs-878	26	5	r	r	NOUN
iajs-878	26	6	*	*	PUNCT
iajs-878	26	7	*	*	PUNCT
iajs-878	27	1	*	*	PUNCT
iajs-878	27	2	*	*	PUNCT
iajs-878	28	1	*	*	PUNCT
iajs-878	28	2	*	*	PUNCT
iajs-878	29	1	*	*	PUNCT
iajs-878	29	2	*	*	PUNCT
iajs-878	29	3	*	*	PUNCT
iajs-878	29	4	*	*	PUNCT
iajs-878	29	5	*	*	PUNCT
iajs-878	29	6	*	*	SYM
iajs-878	29	7	1	1	NUM
iajs-878	29	8	0	0	NUM
iajs-878	29	9			PROPN
iajs-878	29	10			NOUN
iajs-878	29	11			NOUN
iajs-878	29	12			PROPN
iajs-878	29	13			NOUN
iajs-878	29	14			PROPN
iajs-878	29	15			NOUN
iajs-878	29	16			PROPN
iajs-878	29	17			PROPN
iajs-878	29	18			PRON
iajs-878	29	19			NOUN
iajs-878	29	20			VERB
iajs-878	29	21			PROPN
iajs-878	29	22			NOUN
iajs-878	29	23			NOUN
iajs-878	29	24			NOUN
iajs-878	30	1			PROPN
iajs-878	30	2			NOUN
iajs-878	30	3			PROPN
iajs-878	30	4			NOUN
iajs-878	30	5			PROPN
iajs-878	30	6			PROPN
iajs-878	30	7			PRON
iajs-878	30	8			NOUN
iajs-878	30	9			VERB
iajs-878	30	10			PROPN
iajs-878	30	11			NOUN
iajs-878	30	12			NOUN
iajs-878	30	13			PROPN
iajs-878	30	14			X
iajs-878	30	15			NOUN
iajs-878	30	16			VERB
iajs-878	30	17			PROPN
iajs-878	30	18			PROPN
iajs-878	30	19			PROPN
iajs-878	30	20			X
iajs-878	30	21			NOUN
iajs-878	30	22			VERB
iajs-878	30	23			PROPN
iajs-878	30	24			PROPN
iajs-878	30	25			NOUN
iajs-878	30	26			NOUN
iajs-878	30	27			NOUN
iajs-878	30	28			PROPN
iajs-878	30	29			NOUN
iajs-878	30	30			PROPN
iajs-878	30	31			NOUN
iajs-878	30	32			NOUN
iajs-878	30	33			NOUN
iajs-878	30	34			PROPN
iajs-878	30	35			PROPN
iajs-878	30	36			PROPN
iajs-878	30	37			NOUN
iajs-878	30	38			NOUN
iajs-878	30	39			NOUN
iajs-878	30	40			NOUN
iajs-878	30	41			PROPN
iajs-878	30	42			NOUN
iajs-878	30	43			PROPN
iajs-878	30	44			NOUN
iajs-878	30	45			NOUN
iajs-878	30	46			NOUN
iajs-878	30	47			PROPN
iajs-878	30	48			NOUN
iajs-878	30	49			PROPN
iajs-878	30	50			NOUN
iajs-878	30	51			PROPN
iajs-878	31	1			PROPN
iajs-878	31	2			PRON
iajs-878	31	3			NOUN
iajs-878	31	4			VERB
iajs-878	31	5			PROPN
iajs-878	31	6			NOUN
iajs-878	31	7	which	which	PRON
iajs-878	31	8	completes	complete	VERB
iajs-878	31	9	the	the	DET
iajs-878	31	10	proof	proof	NOUN
iajs-878	31	11	.	.	PUNCT
iajs-878	32	1	2necessary	2necessary	NUM
iajs-878	32	2	and	and	CCONJ
iajs-878	32	3	sufficient	sufficient	ADJ
iajs-878	32	4	conditions	condition	NOUN
iajs-878	32	5	of	of	ADP
iajs-878	32	6	the	the	DET
iajs-878	32	7	solution	solution	NOUN
iajs-878	32	8	of	of	ADP
iajs-878	32	9	the	the	DET
iajs-878	32	10	equation	equation	NOUN
iajs-878	32	11	we	we	PRON
iajs-878	32	12	study	study	VERB
iajs-878	32	13	the	the	DET
iajs-878	32	14	existence	existence	NOUN
iajs-878	32	15	of	of	ADP
iajs-878	32	16	the	the	DET
iajs-878	32	17	solution	solution	NOUN
iajs-878	32	18	of	of	ADP
iajs-878	32	19	equation	equation	NOUN
iajs-878	32	20	(	(	PUNCT
iajs-878	32	21	1	1	NUM
iajs-878	32	22	)	)	PUNCT
iajs-878	32	23	by	by	ADP
iajs-878	32	24	the	the	DET
iajs-878	32	25	following	follow	VERB
iajs-878	32	26	theorem	theorem	NOUN
iajs-878	32	27	:	:	PUNCT
iajs-878	32	28	theorem	theorem	NOUN
iajs-878	32	29	2.1	2.1	NUM
iajs-878	32	30	:	:	PUNCT
iajs-878	32	31	the	the	DET
iajs-878	32	32	operator	operator	NOUN
iajs-878	32	33	equation	equation	NOUN
iajs-878	32	34	(	(	PUNCT
iajs-878	32	35	1	1	X
iajs-878	32	36	)	)	PUNCT
iajs-878	32	37	has	have	VERB
iajs-878	32	38	a	a	DET
iajs-878	32	39	solution	solution	NOUN
iajs-878	32	40	x	x	PUNCT
iajs-878	32	41	positive	positive	ADJ
iajs-878	32	42	operator	operator	NOUN
iajs-878	32	43	if	if	SCONJ
iajs-878	32	44	and	and	CCONJ
iajs-878	32	45	only	only	ADV
iajs-878	32	46	if	if	SCONJ
iajs-878	32	47	the	the	DET
iajs-878	32	48	operator	operator	NOUN
iajs-878	32	49	a	a	PRON
iajs-878	32	50	takes	take	VERB
iajs-878	32	51	the	the	DET
iajs-878	32	52	following	follow	VERB
iajs-878	32	53	factorization	factorization	NOUN
iajs-878	32	54	form	form	NOUN
iajs-878	32	55			NOUN
iajs-878	32	56			SYM
iajs-878	32	57			NOUN
iajs-878	32	58			NUM
iajs-878	32	59	)	)	PUNCT
iajs-878	32	60	2	2	NUM
iajs-878	32	61	(	(	PUNCT
iajs-878	32	62	2	2	NUM
iajs-878	32	63	*	*	PUNCT
iajs-878	32	64	*	*	SYM
iajs-878	32	65	2	2	NUM
iajs-878	32	66	1	1	NUM
iajs-878	32	67	*	*	SYM
iajs-878	32	68			NUM
iajs-878	32	69			PROPN
iajs-878	32	70			NUM
iajs-878	32	71			NUM
iajs-878	32	72			ADP
iajs-878	32	73			NUM
iajs-878	32	74			PROPN
iajs-878	32	75	evenisnifzww	evenisnifzww	PROPN
iajs-878	32	76	oddisnifzwww	oddisnifzwww	PROPN
iajs-878	32	77	a	a	DET
iajs-878	32	78	n	n	CCONJ
iajs-878	32	79	n	n	NOUN
iajs-878	33	1			NUM
iajs-878	34	1			NUM
iajs-878	34	2	where	where	SCONJ
iajs-878	34	3	w	w	NOUN
iajs-878	34	4	is	be	AUX
iajs-878	34	5	an	an	DET
iajs-878	34	6	invertible	invertible	ADJ
iajs-878	34	7	operator	operator	NOUN
iajs-878	34	8	and	and	CCONJ
iajs-878	34	9	izzww	izzww	NOUN
iajs-878	35	1			NOUN
iajs-878	35	2	*	*	PUNCT
iajs-878	35	3	*	*	NOUN
iajs-878	35	4	.	.	PUNCT
iajs-878	36	1	proof	proof	NOUN
iajs-878	36	2	:	:	PUNCT
iajs-878	36	3	suppose	suppose	VERB
iajs-878	36	4	that	that	SCONJ
iajs-878	36	5	equation	equation	NOUN
iajs-878	36	6	(	(	PUNCT
iajs-878	36	7	1	1	X
iajs-878	36	8	)	)	PUNCT
iajs-878	36	9	has	have	VERB
iajs-878	36	10	a	a	DET
iajs-878	36	11	solution	solution	NOUN
iajs-878	36	12	x	x	X
iajs-878	36	13	.	.	PUNCT
iajs-878	37	1	then	then	ADV
iajs-878	37	2	,	,	PUNCT
iajs-878	37	3	using	use	VERB
iajs-878	37	4	the	the	DET
iajs-878	37	5	set	set	NOUN
iajs-878	37	6	c	c	NOUN
iajs-878	37	7	we	we	PRON
iajs-878	37	8	can	can	AUX
iajs-878	37	9	write	write	VERB
iajs-878	37	10	x	x	PUNCT
iajs-878	37	11	as	as	ADP
iajs-878	37	12	wwx	wwx	NOUN
iajs-878	37	13	*	*	NOUN
iajs-878	37	14			NOUN
iajs-878	37	15	.	.	PUNCT
iajs-878	38	1	equation	equation	NOUN
iajs-878	38	2	(	(	PUNCT
iajs-878	38	3	1	1	X
iajs-878	38	4	)	)	PUNCT
iajs-878	38	5	can	can	AUX
iajs-878	38	6	be	be	AUX
iajs-878	38	7	written	write	VERB
iajs-878	38	8	as	as	ADP
iajs-878	38	9			NOUN
iajs-878	38	10			PROPN
iajs-878	38	11	iawwaww	iawwaww	NOUN
iajs-878	38	12	n	n	CCONJ
iajs-878	38	13			X
iajs-878	38	14			NOUN
iajs-878	38	15	*	*	NOUN
iajs-878	38	16	*	*	PUNCT
iajs-878	38	17	*	*	PUNCT
iajs-878	38	18	the	the	DET
iajs-878	38	19	prove	prove	NOUN
iajs-878	38	20	using	use	VERB
iajs-878	38	21	mathematical	mathematical	ADJ
iajs-878	38	22	induction	induction	NOUN
iajs-878	38	23	:	:	PUNCT
iajs-878	38	24			PRON
iajs-878	38	25	suppose	suppose	VERB
iajs-878	38	26	1n	1n	NUM
iajs-878	38	27	,	,	PUNCT
iajs-878	38	28	then	then	ADV
iajs-878	38	29			NOUN
iajs-878	38	30			SYM
iajs-878	38	31			NOUN
iajs-878	39	1			PROPN
iajs-878	39	2	iawwaww	iawwaww	NOUN
iajs-878	39	3	iawwaww	iawwaww	NOUN
iajs-878	39	4			X
iajs-878	39	5			X
iajs-878	39	6			NOUN
iajs-878	39	7			VERB
iajs-878	39	8	1	1	NUM
iajs-878	39	9	*	*	SYM
iajs-878	39	10	1	1	NUM
iajs-878	39	11	*	*	PUNCT
iajs-878	39	12	*	*	PUNCT
iajs-878	39	13	1	1	NUM
iajs-878	39	14	*	*	PUNCT
iajs-878	39	15	*	*	PUNCT
iajs-878	39	16	*	*	PUNCT
iajs-878	39	17	further	far	ADV
iajs-878	39	18	,	,	PUNCT
iajs-878	39	19	we	we	PRON
iajs-878	39	20	can	can	AUX
iajs-878	39	21	rewrite	rewrite	VERB
iajs-878	39	22	the	the	DET
iajs-878	39	23	last	last	ADJ
iajs-878	39	24	equations	equation	NOUN
iajs-878	39	25	as	as	ADP
iajs-878	39	26	:	:	PUNCT
iajs-878	39	27			PROPN
iajs-878	39	28			NOUN
iajs-878	39	29			PROPN
iajs-878	39	30			NOUN
iajs-878	39	31			NUM
iajs-878	39	32	)	)	PUNCT
iajs-878	39	33	3	3	NUM
iajs-878	39	34	(	(	PUNCT
iajs-878	39	35	1	1	NUM
iajs-878	39	36	*	*	PUNCT
iajs-878	39	37	*	*	PUNCT
iajs-878	39	38	*	*	PUNCT
iajs-878	39	39	1	1	NUM
iajs-878	39	40	*	*	SYM
iajs-878	39	41	iawawww	iawawww	ADJ
iajs-878	39	42			X
iajs-878	39	43			PROPN
iajs-878	39	44	ibn	ibn	PROPN
iajs-878	39	45	alhaitham	alhaitham	NOUN
iajs-878	39	46	j.	j.	PROPN
iajs-878	39	47	for	for	ADP
iajs-878	39	48	pure	pure	ADJ
iajs-878	39	49	&	&	CCONJ
iajs-878	39	50	appl	appl	PROPN
iajs-878	39	51	.	.	PUNCT
iajs-878	40	1	sci	sci	PROPN
iajs-878	40	2	.	.	PUNCT
iajs-878	40	3	vol.24	vol.24	NOUN
iajs-878	40	4	(	(	PUNCT
iajs-878	40	5	1	1	NUM
iajs-878	40	6	)	)	PUNCT
iajs-878	40	7	2011	2011	NUM
iajs-878	40	8	equation	equation	NOUN
iajs-878	40	9			NOUN
iajs-878	40	10	3	3	PROPN
iajs-878	40	11	can	can	AUX
iajs-878	40	12	be	be	AUX
iajs-878	40	13	rewritten	rewrite	VERB
iajs-878	40	14	in	in	ADP
iajs-878	40	15	the	the	DET
iajs-878	40	16	equivalent	equivalent	ADJ
iajs-878	40	17	form	form	NOUN
iajs-878	40	18	[	[	X
iajs-878	40	19	5	5	NUM
iajs-878	40	20	,	,	PUNCT
iajs-878	40	21	p.171	p.171	VERB
iajs-878	40	22	]	]	PUNCT
iajs-878	40	23	:	:	PUNCT
iajs-878	40	24	)	)	PUNCT
iajs-878	41	1	4	4	NUM
iajs-878	41	2	(	(	PUNCT
iajs-878	41	3	*	*	PUNCT
iajs-878	41	4	*	*	PUNCT
iajs-878	41	5	*	*	PUNCT
iajs-878	42	1	i	i	PRON
iajs-878	42	2	aw	aw	INTJ
iajs-878	43	1	w	w	INTJ
iajs-878	43	2	aw	aw	INTJ
iajs-878	43	3	w	w	PROPN
iajs-878	43	4			PROPN
iajs-878	43	5			PROPN
iajs-878	43	6			NOUN
iajs-878	43	7			NOUN
iajs-878	43	8			VERB
iajs-878	43	9			PROPN
iajs-878	43	10			PROPN
iajs-878	43	11			PROPN
iajs-878	43	12			X
iajs-878	43	13			NOUN
iajs-878	43	14			VERB
iajs-878	43	15			PROPN
iajs-878	43	16			PROPN
iajs-878	43	17	now	now	ADV
iajs-878	43	18	,	,	PUNCT
iajs-878	43	19	set	set	VERB
iajs-878	43	20	awz	awz	ADJ
iajs-878	43	21	*	*	PUNCT
iajs-878	43	22			ADJ
iajs-878	43	23	;	;	PUNCT
iajs-878	43	24	then	then	ADV
iajs-878	43	25	zwa	zwa	X
iajs-878	43	26	*	*	PUNCT
iajs-878	43	27			NOUN
iajs-878	43	28	as	as	SCONJ
iajs-878	43	29	desired	desire	VERB
iajs-878	43	30	,	,	PUNCT
iajs-878	43	31			PRON
iajs-878	43	32	suppose	suppose	VERB
iajs-878	43	33	it	it	PRON
iajs-878	43	34	is	be	AUX
iajs-878	43	35	true	true	ADJ
iajs-878	43	36	when	when	SCONJ
iajs-878	43	37	pn	pn	PROPN
iajs-878	43	38			PROPN
iajs-878	43	39	to	to	PART
iajs-878	43	40	show	show	VERB
iajs-878	43	41	that	that	SCONJ
iajs-878	43	42	it	it	PRON
iajs-878	43	43	is	be	AUX
iajs-878	43	44	true	true	ADJ
iajs-878	43	45	when	when	SCONJ
iajs-878	43	46	1	1	NUM
iajs-878	43	47	pn	pn	PROPN
iajs-878	43	48			NOUN
iajs-878	43	49			SYM
iajs-878	43	50			NOUN
iajs-878	44	1			SYM
iajs-878	44	2			NOUN
iajs-878	44	3			SYM
iajs-878	44	4			NOUN
iajs-878	44	5			PROPN
iajs-878	44	6	iawwwwaww	iawwwwaww	PROPN
iajs-878	44	7	iawwaww	iawwaww	NOUN
iajs-878	44	8	p	p	PROPN
iajs-878	44	9	p	p	NOUN
iajs-878	44	10			X
iajs-878	44	11			X
iajs-878	44	12			NOUN
iajs-878	45	1			NOUN
iajs-878	45	2	1	1	NUM
iajs-878	45	3	*	*	PUNCT
iajs-878	45	4	*	*	PUNCT
iajs-878	45	5	*	*	PUNCT
iajs-878	45	6	*	*	PUNCT
iajs-878	45	7	1	1	NUM
iajs-878	45	8	*	*	PUNCT
iajs-878	45	9	*	*	PUNCT
iajs-878	45	10	*	*	PUNCT
iajs-878	45	11	if	if	SCONJ
iajs-878	45	12	p	p	NOUN
iajs-878	45	13	is	be	AUX
iajs-878	45	14	odd	odd	ADJ
iajs-878	45	15	,	,	PUNCT
iajs-878	45	16	then	then	ADV
iajs-878	45	17			NOUN
iajs-878	45	18			SYM
iajs-878	45	19			NOUN
iajs-878	45	20			SYM
iajs-878	45	21			NOUN
iajs-878	45	22			SYM
iajs-878	45	23			NOUN
iajs-878	45	24			SYM
iajs-878	45	25			NOUN
iajs-878	45	26			SYM
iajs-878	45	27			NOUN
iajs-878	45	28			SYM
iajs-878	45	29			NOUN
iajs-878	45	30			NUM
iajs-878	45	31	)	)	PUNCT
iajs-878	45	32	5(**1***1	5(**1***1	NUM
iajs-878	45	33	*	*	SYM
iajs-878	45	34	1	1	NUM
iajs-878	45	35	*	*	PUNCT
iajs-878	45	36	*	*	PUNCT
iajs-878	45	37	*	*	PUNCT
iajs-878	45	38	1	1	NUM
iajs-878	45	39	*	*	SYM
iajs-878	45	40	11	11	NUM
iajs-878	45	41	*	*	SYM
iajs-878	45	42	1	1	NUM
iajs-878	45	43	*	*	PUNCT
iajs-878	45	44	*	*	NOUN
iajs-878	45	45	1	1	NUM
iajs-878	45	46	*	*	SYM
iajs-878	45	47	1	1	NUM
iajs-878	45	48	*	*	SYM
iajs-878	45	49	1	1	NUM
iajs-878	45	50	*	*	SYM
iajs-878	45	51	1	1	NUM
iajs-878	45	52	*	*	SYM
iajs-878	45	53	1	1	NUM
iajs-878	45	54	*	*	PUNCT
iajs-878	45	55	*	*	PUNCT
iajs-878	45	56	*	*	PUNCT
iajs-878	45	57	iawwwwawwwwwww	iawwwwawwwwwww	PROPN
iajs-878	45	58	iawwwwwwwaww	iawwwwwwwaww	PROPN
iajs-878	45	59	iawwwwwwwwwwaww	iawwwwwwwwwwaww	PROPN
iajs-878	45	60			X
iajs-878	45	61			NOUN
iajs-878	45	62			X
iajs-878	45	63			PROPN
iajs-878	45	64			NOUN
iajs-878	45	65			NOUN
iajs-878	45	66			PRON
iajs-878	45	67			NUM
iajs-878	45	68			NUM
iajs-878	45	69	equation	equation	NOUN
iajs-878	45	70	(	(	PUNCT
iajs-878	45	71	5	5	X
iajs-878	45	72	)	)	PUNCT
iajs-878	45	73	can	can	AUX
iajs-878	45	74	be	be	AUX
iajs-878	45	75	rewritten	rewrite	VERB
iajs-878	45	76	in	in	ADP
iajs-878	45	77	the	the	DET
iajs-878	45	78	equivalent	equivalent	ADJ
iajs-878	45	79	form	form	NOUN
iajs-878	45	80	:	:	PUNCT
iajs-878	45	81			PROPN
iajs-878	45	82			PROPN
iajs-878	45	83			X
iajs-878	45	84			NOUN
iajs-878	45	85			VERB
iajs-878	45	86			PROPN
iajs-878	45	87			PROPN
iajs-878	45	88			PROPN
iajs-878	45	89			X
iajs-878	45	90			NOUN
iajs-878	45	91			VERB
iajs-878	45	92			PROPN
iajs-878	45	93			PROPN
iajs-878	45	94	awwww	awwww	PROPN
iajs-878	45	95	w	w	PROPN
iajs-878	45	96	awwww	awwww	PROPN
iajs-878	45	97	w	w	PROPN
iajs-878	45	98	*	*	PROPN
iajs-878	45	99	*	*	PROPN
iajs-878	45	100	1	1	NUM
iajs-878	45	101	*	*	PUNCT
iajs-878	45	102	*	*	PUNCT
iajs-878	46	1	*	*	PUNCT
iajs-878	46	2	*	*	PUNCT
iajs-878	46	3	1	1	NUM
iajs-878	46	4	*	*	SYM
iajs-878	46	5			PRON
iajs-878	46	6	now	now	ADV
iajs-878	46	7	,	,	PUNCT
iajs-878	46	8	set	set	VERB
iajs-878	46	9	awwwwz	awwwwz	NOUN
iajs-878	46	10	*	*	PUNCT
iajs-878	46	11	*	*	PUNCT
iajs-878	46	12	1	1	NUM
iajs-878	46	13	*	*	NUM
iajs-878	46	14			NOUN
iajs-878	46	15			NUM
iajs-878	46	16	,	,	PUNCT
iajs-878	46	17	then	then	ADV
iajs-878	46	18	zwwwwwa	zwwwwwa	X
iajs-878	47	1	*	*	PUNCT
iajs-878	47	2	*	*	PUNCT
iajs-878	47	3	*	*	PUNCT
iajs-878	47	4			X
iajs-878	47	5	,	,	PUNCT
iajs-878	47	6	as	as	SCONJ
iajs-878	47	7	form	form	NOUN
iajs-878	47	8			NOUN
iajs-878	47	9			PUNCT
iajs-878	47	10	zwww	zwww	NOUN
iajs-878	48	1	p	p	PROPN
iajs-878	48	2	*	*	PROPN
iajs-878	48	3	2	2	NUM
iajs-878	48	4	1	1	NUM
iajs-878	48	5	*	*	PUNCT
iajs-878	48	6			NOUN
iajs-878	48	7	if	if	SCONJ
iajs-878	48	8	p	p	NOUN
iajs-878	48	9	is	be	AUX
iajs-878	48	10	even	even	ADV
iajs-878	48	11	,	,	PUNCT
iajs-878	48	12	then	then	ADV
iajs-878	48	13	:	:	PUNCT
iajs-878	48	14			NOUN
iajs-878	48	15			SYM
iajs-878	48	16			NOUN
iajs-878	49	1			SYM
iajs-878	49	2			NOUN
iajs-878	49	3			SYM
iajs-878	49	4			NOUN
iajs-878	49	5			SYM
iajs-878	49	6			NOUN
iajs-878	49	7			SYM
iajs-878	49	8			NOUN
iajs-878	49	9			PROPN
iajs-878	49	10	)	)	PUNCT
iajs-878	49	11	6(*1	6(*1	NOUN
iajs-878	49	12	*	*	PUNCT
iajs-878	49	13	1**1	1**1	NUM
iajs-878	49	14	*	*	SYM
iajs-878	49	15	1	1	NUM
iajs-878	49	16	*	*	PUNCT
iajs-878	49	17	*	*	PUNCT
iajs-878	49	18	1	1	NUM
iajs-878	49	19	*	*	SYM
iajs-878	49	20	1	1	NUM
iajs-878	49	21	*	*	SYM
iajs-878	49	22	1	1	NUM
iajs-878	49	23	*	*	SYM
iajs-878	49	24	1	1	NUM
iajs-878	49	25	*	*	PUNCT
iajs-878	49	26	*	*	NOUN
iajs-878	49	27	1	1	NUM
iajs-878	49	28	*	*	SYM
iajs-878	49	29	1	1	NUM
iajs-878	49	30	*	*	SYM
iajs-878	49	31	1	1	NUM
iajs-878	49	32	*	*	SYM
iajs-878	49	33	1	1	NUM
iajs-878	49	34	*	*	PUNCT
iajs-878	49	35	*	*	PUNCT
iajs-878	49	36	*	*	PUNCT
iajs-878	49	37	iawwwwawwwwww	iawwwwawwwwww	PROPN
iajs-878	49	38	iawwwwwwwwaww	iawwwwwwwwaww	ADJ
iajs-878	49	39	iawwwwwwwwaww	iawwwwwwwwaww	ADJ
iajs-878	49	40			NOUN
iajs-878	49	41			NOUN
iajs-878	49	42			NOUN
iajs-878	49	43			NOUN
iajs-878	49	44			NOUN
iajs-878	49	45			NOUN
iajs-878	49	46			PUNCT
iajs-878	49	47			NUM
iajs-878	49	48			NUM
iajs-878	49	49	equation	equation	NOUN
iajs-878	49	50	(	(	PUNCT
iajs-878	49	51	6	6	NUM
iajs-878	49	52	)	)	PUNCT
iajs-878	49	53	can	can	AUX
iajs-878	49	54	be	be	AUX
iajs-878	49	55	rewritten	rewrite	VERB
iajs-878	49	56	in	in	ADP
iajs-878	49	57	the	the	DET
iajs-878	49	58	equivalent	equivalent	ADJ
iajs-878	49	59	form	form	NOUN
iajs-878	49	60	:	:	PUNCT
iajs-878	49	61	i	i	PROPN
iajs-878	49	62	awwww	awwww	PROPN
iajs-878	49	63	w	w	PROPN
iajs-878	49	64	awwww	awwww	PROPN
iajs-878	49	65	w	w	PROPN
iajs-878	49	66			PROPN
iajs-878	49	67			PROPN
iajs-878	49	68			NOUN
iajs-878	49	69			NOUN
iajs-878	49	70			VERB
iajs-878	49	71			PROPN
iajs-878	49	72			PROPN
iajs-878	49	73			PROPN
iajs-878	49	74			X
iajs-878	49	75			NOUN
iajs-878	49	76			VERB
iajs-878	49	77			PROPN
iajs-878	49	78			NOUN
iajs-878	49	79	*	*	PUNCT
iajs-878	49	80	1	1	NUM
iajs-878	49	81	*	*	SYM
iajs-878	49	82	1	1	NUM
iajs-878	49	83	*	*	PUNCT
iajs-878	49	84	*	*	PUNCT
iajs-878	49	85	1	1	NUM
iajs-878	49	86	*	*	SYM
iajs-878	49	87	1	1	NUM
iajs-878	49	88			X
iajs-878	49	89	new	new	ADJ
iajs-878	49	90	,	,	PUNCT
iajs-878	49	91	set	set	VERB
iajs-878	49	92	awwwwz	awwwwz	NOUN
iajs-878	49	93	*	*	PUNCT
iajs-878	49	94	1	1	NUM
iajs-878	49	95	*	*	SYM
iajs-878	49	96	1	1	NUM
iajs-878	49	97			NOUN
iajs-878	49	98			NUM
iajs-878	49	99	;	;	PUNCT
iajs-878	49	100	then	then	ADV
iajs-878	49	101			NOUN
iajs-878	50	1	zwwwwwwwwa	zwwwwwwwwa	PUNCT
iajs-878	51	1	*	*	PUNCT
iajs-878	51	2	*	*	PUNCT
iajs-878	51	3	*	*	PUNCT
iajs-878	51	4	*	*	X
iajs-878	51	5			X
iajs-878	51	6	,	,	PUNCT
iajs-878	51	7	as	as	SCONJ
iajs-878	51	8	form	form	NOUN
iajs-878	51	9			NOUN
iajs-878	51	10			PROPN
iajs-878	51	11	zww	zww	NOUN
iajs-878	52	1	p	p	VERB
iajs-878	52	2	2	2	NUM
iajs-878	52	3	*	*	PUNCT
iajs-878	52	4	conversely	conversely	ADV
iajs-878	52	5	,	,	PUNCT
iajs-878	52	6	assume	assume	VERB
iajs-878	52	7	that	that	SCONJ
iajs-878	52	8	the	the	DET
iajs-878	52	9	operator	operator	NOUN
iajs-878	52	10	a	a	DET
iajs-878	52	11	admits	admit	VERB
iajs-878	52	12	the	the	DET
iajs-878	52	13	factorization	factorization	NOUN
iajs-878	52	14			NOUN
iajs-878	52	15	zwwwwwa	zwwwwwa	PUNCT
iajs-878	53	1	*	*	PUNCT
iajs-878	53	2	*	*	PUNCT
iajs-878	53	3	*	*	PUNCT
iajs-878	53	4			X
iajs-878	53	5	,	,	PUNCT
iajs-878	53	6	if	if	SCONJ
iajs-878	53	7	n	n	PRON
iajs-878	53	8	is	be	AUX
iajs-878	53	9	odd	odd	ADJ
iajs-878	53	10	,	,	PUNCT
iajs-878	53	11	and	and	CCONJ
iajs-878	53	12	set	set	VERB
iajs-878	53	13	wwx	wwx	NOUN
iajs-878	53	14	*	*	NOUN
iajs-878	53	15			NUM
iajs-878	53	16	,	,	PUNCT
iajs-878	53	17	we	we	PRON
iajs-878	53	18	then	then	ADV
iajs-878	53	19	need	need	VERB
iajs-878	53	20	to	to	PART
iajs-878	53	21	show	show	VERB
iajs-878	53	22	that	that	SCONJ
iajs-878	53	23	x	x	X
iajs-878	53	24	(	(	PUNCT
iajs-878	53	25	which	which	PRON
iajs-878	53	26	is	be	AUX
iajs-878	53	27	positive	positive	ADJ
iajs-878	53	28	operator	operator	NOUN
iajs-878	53	29	)	)	PUNCT
iajs-878	53	30	is	be	AUX
iajs-878	53	31	a	a	DET
iajs-878	53	32	solution	solution	NOUN
iajs-878	53	33	to	to	ADP
iajs-878	53	34	the	the	DET
iajs-878	53	35	operator	operator	NOUN
iajs-878	53	36	equation	equation	NOUN
iajs-878	53	37	(	(	PUNCT
iajs-878	53	38	1	1	NUM
iajs-878	53	39	)	)	PUNCT
iajs-878	53	40	,	,	PUNCT
iajs-878	53	41	we	we	PRON
iajs-878	53	42	have	have	VERB
iajs-878	53	43	:	:	PUNCT
iajs-878	53	44			NOUN
iajs-878	53	45			PROPN
iajs-878	53	46			NOUN
iajs-878	53	47			SYM
iajs-878	53	48			NOUN
iajs-878	53	49			SYM
iajs-878	53	50			NOUN
iajs-878	53	51			SYM
iajs-878	53	52			NOUN
iajs-878	53	53			SYM
iajs-878	53	54			NOUN
iajs-878	53	55			PUNCT
iajs-878	54	1	i	i	PRON
iajs-878	54	2	z	z	VERB
iajs-878	54	3	w	w	PROPN
iajs-878	54	4	z	z	PROPN
iajs-878	54	5	w	w	PROPN
iajs-878	54	6	zzww	zzww	PROPN
iajs-878	54	7	zwwwwwwwwwwwwzww	zwwwwwwwwwwwwzww	PROPN
iajs-878	54	8	zwwwwwwwwwwwwwzww	zwwwwwwwwwwwwwzww	PROPN
iajs-878	54	9	zwwwwwwwzwwwwwwwaxax	zwwwwwwwzwwwwwwwaxax	PROPN
iajs-878	54	10	nn	nn	PROPN
iajs-878	54	11			PROPN
iajs-878	54	12			PROPN
iajs-878	54	13			PROPN
iajs-878	54	14			PRON
iajs-878	54	15			NOUN
iajs-878	54	16			VERB
iajs-878	54	17			PROPN
iajs-878	54	18			PROPN
iajs-878	54	19			PROPN
iajs-878	54	20			X
iajs-878	54	21			NOUN
iajs-878	54	22			VERB
iajs-878	54	23			PROPN
iajs-878	55	1			ADJ
iajs-878	55	2			ADJ
iajs-878	55	3			ADJ
iajs-878	55	4			ADJ
iajs-878	55	5			PROPN
iajs-878	55	6			PROPN
iajs-878	55	7			SYM
iajs-878	55	8			PROPN
iajs-878	55	9	*	*	PUNCT
iajs-878	56	1	*	*	PUNCT
iajs-878	56	2	*	*	PUNCT
iajs-878	57	1	*	*	PUNCT
iajs-878	57	2	*	*	PUNCT
iajs-878	57	3	*	*	PUNCT
iajs-878	57	4	*	*	PUNCT
iajs-878	57	5	1	1	NUM
iajs-878	57	6	*	*	SYM
iajs-878	57	7	1	1	NUM
iajs-878	57	8	*	*	PUNCT
iajs-878	57	9	*	*	PUNCT
iajs-878	57	10	*	*	PUNCT
iajs-878	58	1	*	*	PUNCT
iajs-878	58	2	*	*	PUNCT
iajs-878	58	3	*	*	PUNCT
iajs-878	58	4	1	1	NUM
iajs-878	58	5	*	*	SYM
iajs-878	58	6	1	1	NUM
iajs-878	58	7	*	*	PUNCT
iajs-878	58	8	*	*	PUNCT
iajs-878	58	9	*	*	PUNCT
iajs-878	58	10	*	*	PUNCT
iajs-878	58	11	*	*	PUNCT
iajs-878	59	1	*	*	PUNCT
iajs-878	59	2	*	*	PUNCT
iajs-878	59	3	*	*	PUNCT
iajs-878	59	4	*	*	PUNCT
iajs-878	59	5	*	*	PUNCT
iajs-878	59	6	*	*	PUNCT
iajs-878	59	7	*	*	PUNCT
iajs-878	59	8	*	*	PUNCT
iajs-878	59	9	*	*	PUNCT
iajs-878	59	10	*	*	PUNCT
iajs-878	59	11			PROPN
iajs-878	59	12			PROPN
iajs-878	59	13			X
iajs-878	59	14	when	when	SCONJ
iajs-878	59	15	n	n	X
iajs-878	59	16	is	be	AUX
iajs-878	59	17	even	even	ADV
iajs-878	59	18	,	,	PUNCT
iajs-878	59	19	then	then	ADV
iajs-878	59	20	zwwwwwwwa	zwwwwwwwa	VERB
iajs-878	60	1	*	*	PUNCT
iajs-878	61	1	*	*	PUNCT
iajs-878	61	2	*	*	X
iajs-878	61	3			PUNCT
iajs-878	61	4	,	,	PUNCT
iajs-878	61	5	and	and	CCONJ
iajs-878	61	6	set	set	VERB
iajs-878	61	7	wwx	wwx	NOUN
iajs-878	62	1	*	*	NOUN
iajs-878	62	2			NUM
iajs-878	62	3	,	,	PUNCT
iajs-878	62	4	we	we	PRON
iajs-878	62	5	then	then	ADV
iajs-878	62	6	need	need	VERB
iajs-878	62	7	to	to	PART
iajs-878	62	8	show	show	VERB
iajs-878	62	9	that	that	SCONJ
iajs-878	62	10	x	x	X
iajs-878	62	11	(	(	PUNCT
iajs-878	62	12	which	which	PRON
iajs-878	62	13	is	be	AUX
iajs-878	62	14	positive	positive	ADJ
iajs-878	62	15	definite	definite	ADJ
iajs-878	62	16	)	)	PUNCT
iajs-878	62	17	is	be	AUX
iajs-878	62	18	a	a	DET
iajs-878	62	19	solution	solution	NOUN
iajs-878	62	20	to	to	ADP
iajs-878	62	21	the	the	DET
iajs-878	62	22	operator	operator	NOUN
iajs-878	62	23	equation	equation	NOUN
iajs-878	62	24	(	(	PUNCT
iajs-878	62	25	1	1	NUM
iajs-878	62	26	)	)	PUNCT
iajs-878	62	27	.we	.we	PUNCT
iajs-878	63	1	have	have	VERB
iajs-878	63	2	.	.	PUNCT
iajs-878	64	1	ibn	ibn	PROPN
iajs-878	64	2	alhaitham	alhaitham	PROPN
iajs-878	65	1	j.	j.	PROPN
iajs-878	66	1	fo	fo	ADP
iajs-878	66	2	r	r	NOUN
iajs-878	66	3	pure	pure	ADJ
iajs-878	66	4	&	&	CCONJ
iajs-878	66	5	appl	appl	PROPN
iajs-878	66	6	.	.	PUNCT
iajs-878	67	1	sc	sc	PROPN
iajs-878	67	2	i.	i.	PROPN
iajs-878	67	3	vo	vo	PROPN
iajs-878	68	1	l.24	l.24	PROPN
iajs-878	68	2	(	(	PUNCT
iajs-878	68	3	1	1	NUM
iajs-878	68	4	)	)	PUNCT
iajs-878	68	5	2011	2011	NUM
iajs-878	68	6			NOUN
iajs-878	68	7			SYM
iajs-878	68	8			NOUN
iajs-878	68	9			SYM
iajs-878	68	10			NOUN
iajs-878	68	11			SYM
iajs-878	68	12			NOUN
iajs-878	68	13			SYM
iajs-878	68	14			NOUN
iajs-878	68	15			SYM
iajs-878	68	16			NOUN
iajs-878	68	17			SYM
iajs-878	68	18			NOUN
iajs-878	68	19			SYM
iajs-878	68	20			NOUN
iajs-878	68	21			PUNCT
iajs-878	69	1	i	i	PRON
iajs-878	69	2	z	z	VERB
iajs-878	69	3	w	w	PROPN
iajs-878	69	4	z	z	PROPN
iajs-878	69	5	w	w	PROPN
iajs-878	69	6	zzww	zzww	PROPN
iajs-878	69	7	wzwwwwwwwwwwwwwwwzww	wzwwwwwwwwwwwwwwwzww	PROPN
iajs-878	69	8	zwwwwwwwwwwwwwwwwwwzww	zwwwwwwwwwwwwwwwwwwzww	PROPN
iajs-878	69	9	zwwwwwwwwzwwwwwwwwaxax	zwwwwwwwwzwwwwwwwwaxax	PROPN
iajs-878	69	10	nn	nn	PROPN
iajs-878	69	11			PROPN
iajs-878	69	12			PROPN
iajs-878	69	13			PROPN
iajs-878	69	14			PRON
iajs-878	69	15			NOUN
iajs-878	69	16			VERB
iajs-878	69	17			PROPN
iajs-878	69	18			PROPN
iajs-878	69	19			PROPN
iajs-878	69	20			X
iajs-878	69	21			NOUN
iajs-878	69	22			VERB
iajs-878	69	23			PROPN
iajs-878	70	1			ADJ
iajs-878	70	2			ADJ
iajs-878	70	3			ADJ
iajs-878	70	4			PROPN
iajs-878	70	5			PROPN
iajs-878	70	6			PROPN
iajs-878	70	7			NOUN
iajs-878	70	8			NOUN
iajs-878	70	9	*	*	PUNCT
iajs-878	71	1	*	*	PUNCT
iajs-878	71	2	*	*	PUNCT
iajs-878	72	1	*	*	PUNCT
iajs-878	72	2	*	*	PUNCT
iajs-878	72	3	*	*	PUNCT
iajs-878	72	4	*	*	PUNCT
iajs-878	72	5	1	1	NUM
iajs-878	72	6	*	*	SYM
iajs-878	72	7	1	1	NUM
iajs-878	72	8	*	*	PUNCT
iajs-878	72	9	*	*	PUNCT
iajs-878	72	10	*	*	PUNCT
iajs-878	72	11	*	*	PUNCT
iajs-878	72	12	*	*	PUNCT
iajs-878	73	1	*	*	PUNCT
iajs-878	73	2	*	*	PUNCT
iajs-878	73	3	*	*	PUNCT
iajs-878	73	4	11	11	NUM
iajs-878	73	5	*	*	SYM
iajs-878	73	6	1	1	NUM
iajs-878	73	7	*	*	PUNCT
iajs-878	73	8	*	*	PUNCT
iajs-878	73	9	*	*	PUNCT
iajs-878	73	10	*	*	PUNCT
iajs-878	73	11	*	*	PUNCT
iajs-878	73	12	*	*	PUNCT
iajs-878	74	1	*	*	PUNCT
iajs-878	74	2	*	*	PUNCT
iajs-878	74	3	*	*	PUNCT
iajs-878	74	4	*	*	PUNCT
iajs-878	74	5	*	*	PUNCT
iajs-878	74	6	*	*	PUNCT
iajs-878	74	7	*	*	PUNCT
iajs-878	74	8	*	*	PUNCT
iajs-878	74	9	*	*	PUNCT
iajs-878	74	10	*	*	PUNCT
iajs-878	75	1			PROPN
iajs-878	75	2			PROPN
iajs-878	75	3			PRON
iajs-878	75	4	which	which	PRON
iajs-878	75	5	completes	complete	VERB
iajs-878	75	6	the	the	DET
iajs-878	75	7	proof	proof	NOUN
iajs-878	75	8	of	of	ADP
iajs-878	75	9	the	the	DET
iajs-878	75	10	theorem	theorem	NOUN
iajs-878	75	11	.	.	PUNCT
iajs-878	76	1	3relation	3relation	NUM
iajs-878	76	2	between	between	ADP
iajs-878	76	3	solution	solution	NOUN
iajs-878	76	4	x	x	PUNCT
iajs-878	76	5	and	and	CCONJ
iajs-878	76	6	operator	operator	NOUN
iajs-878	76	7	a	a	PRON
iajs-878	76	8	:	:	PUNCT
iajs-878	76	9	in	in	ADP
iajs-878	76	10	this	this	DET
iajs-878	76	11	section	section	NOUN
iajs-878	76	12	,	,	PUNCT
iajs-878	76	13	we	we	PRON
iajs-878	76	14	will	will	AUX
iajs-878	76	15	study	study	VERB
iajs-878	76	16	the	the	DET
iajs-878	76	17	relations	relation	NOUN
iajs-878	76	18	between	between	ADP
iajs-878	76	19	x	x	PUNCT
iajs-878	76	20	and	and	CCONJ
iajs-878	76	21	a	a	PRON
iajs-878	76	22	in	in	ADP
iajs-878	76	23	equation	equation	NOUN
iajs-878	76	24	(	(	PUNCT
iajs-878	76	25	1	1	X
iajs-878	76	26	)	)	PUNCT
iajs-878	76	27	theorem	theorem	VERB
iajs-878	76	28	3.1	3.1	NUM
iajs-878	76	29	:	:	PUNCT
iajs-878	76	30	if	if	SCONJ
iajs-878	76	31	equation	equation	NOUN
iajs-878	76	32	(	(	PUNCT
iajs-878	76	33	1	1	X
iajs-878	76	34	)	)	PUNCT
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iajs-878	76	39	,	,	PUNCT
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iajs-878	76	42	all	all	DET
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iajs-878	76	49	i	i	NOUN
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iajs-878	76	51	12	12	NUM
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iajs-878	76	55	2	2	NUM
iajs-878	76	56	1	1	NUM
iajs-878	76	57	2	2	NUM
iajs-878	76	58			NOUN
iajs-878	76	59			PROPN
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iajs-878	77	1			PROPN
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iajs-878	78	1			PROPN
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iajs-878	78	4			VERB
iajs-878	78	5			PROPN
iajs-878	78	6			VERB
iajs-878	78	7			PROPN
iajs-878	78	8	nn	nn	PROPN
iajs-878	78	9	xaaxr	xaaxr	PROPN
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iajs-878	79	2	ii	ii	NOUN
iajs-878	79	3	)	)	PUNCT
iajs-878	79	4			NOUN
iajs-878	79	5			PUNCT
iajs-878	79	6			NOUN
iajs-878	79	7			PUNCT
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iajs-878	79	9	2	2	NUM
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iajs-878	80	2	:	:	PUNCT
iajs-878	80	3	(	(	PUNCT
iajs-878	80	4	i	i	NOUN
iajs-878	80	5	)	)	PUNCT
iajs-878	80	6	using	use	VERB
iajs-878	80	7	theorem	theorem	NOUN
iajs-878	80	8	(	(	PUNCT
iajs-878	80	9	2.1	2.1	NUM
iajs-878	80	10	)	)	PUNCT
iajs-878	80	11	,	,	PUNCT
iajs-878	80	12	when	when	SCONJ
iajs-878	80	13	n	n	X
iajs-878	80	14	is	be	AUX
iajs-878	80	15	even	even	ADV
iajs-878	80	16	.	.	PUNCT
iajs-878	81	1	we	we	PRON
iajs-878	81	2	obtain	obtain	VERB
iajs-878	81	3	:	:	PUNCT
iajs-878	81	4			NOUN
iajs-878	81	5			SYM
iajs-878	81	6			NOUN
iajs-878	81	7			SYM
iajs-878	81	8			NOUN
iajs-878	81	9			SYM
iajs-878	81	10			NOUN
iajs-878	81	11			SYM
iajs-878	81	12			NOUN
iajs-878	81	13			SYM
iajs-878	81	14			NOUN
iajs-878	81	15			PUNCT
iajs-878	81	16			PROPN
iajs-878	81	17			NUM
iajs-878	81	18			PRON
iajs-878	81	19			PROPN
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iajs-878	81	21			NOUN
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iajs-878	81	23			PROPN
iajs-878	81	24			NUM
iajs-878	81	25			PRON
iajs-878	81	26			PROPN
iajs-878	81	27			PROPN
iajs-878	81	28			NOUN
iajs-878	81	29			PROPN
iajs-878	81	30			PROPN
iajs-878	81	31			NOUN
iajs-878	82	1			PROPN
iajs-878	82	2			PROPN
iajs-878	82	3			PROPN
iajs-878	83	1			PROPN
iajs-878	83	2			PROPN
iajs-878	83	3			PROPN
iajs-878	83	4			VERB
iajs-878	83	5			PROPN
iajs-878	83	6			PUNCT
iajs-878	83	7			PROPN
iajs-878	83	8			PROPN
iajs-878	83	9			VERB
iajs-878	83	10			NOUN
iajs-878	83	11	2	2	NUM
iajs-878	83	12	1	1	NUM
iajs-878	83	13	*	*	PUNCT
iajs-878	83	14	*	*	SYM
iajs-878	83	15	2	2	NUM
iajs-878	83	16	1	1	NUM
iajs-878	83	17	*	*	SYM
iajs-878	83	18	2	2	NUM
iajs-878	83	19	1	1	NUM
iajs-878	83	20	2	2	NUM
iajs-878	83	21	*	*	SYM
iajs-878	83	22	2**2	2**2	NUM
iajs-878	83	23	*	*	SYM
iajs-878	83	24	2	2	NUM
iajs-878	83	25	1	1	NUM
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iajs-878	83	29	1	1	NUM
iajs-878	83	30	2	2	NUM
iajs-878	83	31	*	*	SYM
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iajs-878	83	42	1	1	NUM
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iajs-878	83	50	lemma	lemma	PROPN
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iajs-878	83	52	1.1	1.1	NUM
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iajs-878	83	58			NOUN
iajs-878	83	59			SYM
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iajs-878	84	10			NUM
iajs-878	84	11			PROPN
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iajs-878	85	1			PROPN
iajs-878	85	2			PROPN
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iajs-878	86	1			PROPN
iajs-878	86	2			PROPN
iajs-878	86	3			PROPN
iajs-878	86	4			VERB
iajs-878	86	5			PROPN
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iajs-878	86	7			PROPN
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iajs-878	86	9	zzmmr	zzmmr	PROPN
iajs-878	86	10	mzzmrxaaxr	mzzmrxaaxr	PROPN
iajs-878	86	11	nn	nn	PROPN
iajs-878	87	1	now	now	ADV
iajs-878	87	2	,	,	PUNCT
iajs-878	87	3	when	when	SCONJ
iajs-878	87	4	n	n	X
iajs-878	87	5	is	be	AUX
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iajs-878	87	7	;	;	PUNCT
iajs-878	87	8	we	we	PRON
iajs-878	87	9	obtain	obtain	VERB
iajs-878	87	10			NOUN
iajs-878	87	11			PUNCT
iajs-878	87	12			NOUN
iajs-878	87	13			SYM
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iajs-878	87	17			PUNCT
iajs-878	87	18			NOUN
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iajs-878	88	7	1	1	NUM
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iajs-878	88	17	*	*	SYM
iajs-878	88	18	2	2	NUM
iajs-878	88	19	1	1	NUM
iajs-878	88	20	2	2	NUM
iajs-878	88	21	*	*	SYM
iajs-878	88	22	2	2	NUM
iajs-878	88	23	1	1	NUM
iajs-878	88	24	2	2	NUM
iajs-878	88	25	*	*	SYM
iajs-878	88	26	2	2	NUM
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iajs-878	88	29			NOUN
iajs-878	88	30			PROPN
iajs-878	88	31			NUM
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iajs-878	91	1			PROPN
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iajs-878	91	4			VERB
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iajs-878	91	6			VERB
iajs-878	91	7			PROPN
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iajs-878	91	9			VERB
iajs-878	91	10			PROPN
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iajs-878	92	1	j.	j.	PROPN
iajs-878	93	1	fo	fo	ADP
iajs-878	93	2	r	r	NOUN
iajs-878	93	3	pure	pure	ADJ
iajs-878	93	4	&	&	CCONJ
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iajs-878	94	18			NOUN
iajs-878	94	19			SYM
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iajs-878	94	21			PUNCT
iajs-878	94	22			NOUN
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iajs-878	96	1			PROPN
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iajs-878	97	1			PROPN
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iajs-878	97	26	,	,	PUNCT
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iajs-878	97	29			NOUN
iajs-878	97	30			PUNCT
iajs-878	97	31			NOUN
iajs-878	97	32			SYM
iajs-878	97	33			NOUN
iajs-878	97	34			SYM
iajs-878	97	35			NOUN
iajs-878	97	36			SYM
iajs-878	97	37			NOUN
iajs-878	97	38			SYM
iajs-878	97	39			NOUN
iajs-878	97	40			SYM
iajs-878	97	41			NOUN
iajs-878	97	42			PUNCT
iajs-878	97	43			NOUN
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iajs-878	99	1			NUM
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iajs-878	99	3	,	,	PUNCT
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iajs-878	100	1			NOUN
iajs-878	100	2			PROPN
iajs-878	100	3	02**2	02**2	PROPN
iajs-878	100	4	*	*	PUNCT
iajs-878	100	5			PROPN
iajs-878	100	6	nn	nn	PROPN
iajs-878	100	7	wwzziww	wwzziww	NOUN
iajs-878	100	8	.	.	PUNCT
iajs-878	101	1	if	if	SCONJ
iajs-878	101	2	n	n	NOUN
iajs-878	101	3	is	be	AUX
iajs-878	101	4	odd	odd	ADJ
iajs-878	101	5	,	,	PUNCT
iajs-878	101	6	then	then	ADV
iajs-878	101	7	.	.	PUNCT
iajs-878	102	1	from	from	ADP
iajs-878	102	2	theorem	theorem	NOUN
iajs-878	102	3	(	(	PUNCT
iajs-878	102	4	2.1	2.1	NUM
iajs-878	102	5	)	)	PUNCT
iajs-878	102	6	,	,	PUNCT
iajs-878	102	7	we	we	PRON
iajs-878	102	8	have	have	VERB
iajs-878	102	9			NOUN
iajs-878	103	1			PUNCT
iajs-878	103	2			NOUN
iajs-878	103	3			SYM
iajs-878	103	4			NOUN
iajs-878	103	5			SYM
iajs-878	103	6			NOUN
iajs-878	103	7			SYM
iajs-878	103	8			NOUN
iajs-878	103	9			SYM
iajs-878	103	10			NOUN
iajs-878	103	11			SYM
iajs-878	103	12			NOUN
iajs-878	103	13			SYM
iajs-878	103	14			NOUN
iajs-878	103	15			SYM
iajs-878	103	16			NOUN
iajs-878	103	17			SYM
iajs-878	103	18			NOUN
iajs-878	103	19			SYM
iajs-878	103	20			NOUN
iajs-878	103	21			PROPN
iajs-878	103	22			ADJ
iajs-878	103	23			VERB
iajs-878	103	24			PROPN
iajs-878	103	25			NOUN
iajs-878	103	26			PROPN
iajs-878	103	27			NOUN
iajs-878	103	28			NOUN
iajs-878	103	29			PROPN
iajs-878	103	30	wwwzziwww	wwwzziwww	PROPN
iajs-878	103	31	wwwzzwwwww	wwwzzwwwww	PROPN
iajs-878	103	32	wwwzzwwwwwww	wwwzzwwwwwww	PROPN
iajs-878	103	33	wwwzzwwwwwwwaaxx	wwwzzwwwwwwwaaxx	PROPN
iajs-878	103	34	nn	nn	PROPN
iajs-878	103	35	nn	nn	PROPN
iajs-878	103	36	nn	nn	PROPN
iajs-878	103	37	nnnnnn	nnnnnn	PROPN
iajs-878	103	38	2	2	NUM
iajs-878	103	39	1	1	NUM
iajs-878	103	40	*	*	PUNCT
iajs-878	103	41	*	*	PUNCT
iajs-878	103	42	*	*	SYM
iajs-878	103	43	2	2	NUM
iajs-878	103	44	1	1	NUM
iajs-878	103	45	*	*	SYM
iajs-878	103	46	2	2	NUM
iajs-878	103	47	1	1	NUM
iajs-878	103	48	*	*	PUNCT
iajs-878	103	49	*	*	PUNCT
iajs-878	103	50	*	*	PUNCT
iajs-878	103	51	*	*	PUNCT
iajs-878	103	52	2	2	NUM
iajs-878	103	53	1	1	NUM
iajs-878	103	54	*	*	SYM
iajs-878	103	55	2	2	NUM
iajs-878	103	56	1	1	NUM
iajs-878	103	57	*	*	PUNCT
iajs-878	103	58	*	*	PUNCT
iajs-878	103	59	*	*	SYM
iajs-878	103	60	2	2	NUM
iajs-878	103	61	1	1	NUM
iajs-878	103	62	*	*	SYM
iajs-878	103	63	2	2	NUM
iajs-878	103	64	1	1	NUM
iajs-878	103	65	*	*	SYM
iajs-878	103	66	2	2	NUM
iajs-878	103	67	1	1	NUM
iajs-878	103	68	*	*	SYM
iajs-878	103	69	2	2	NUM
iajs-878	103	70	1	1	NUM
iajs-878	103	71	*	*	PUNCT
iajs-878	103	72	*	*	PUNCT
iajs-878	103	73	*	*	SYM
iajs-878	103	74	2	2	NUM
iajs-878	103	75	1	1	NUM
iajs-878	103	76	*	*	SYM
iajs-878	103	77	2	2	NUM
iajs-878	103	78	*	*	SYM
iajs-878	103	79	2**2	2**2	NUM
iajs-878	103	80	*	*	SYM
iajs-878	103	81	2	2	NUM
iajs-878	103	82			NUM
iajs-878	103	83			NUM
iajs-878	103	84			NUM
iajs-878	103	85			NUM
iajs-878	103	86			PROPN
iajs-878	103	87			NOUN
iajs-878	103	88			PROPN
iajs-878	103	89			NUM
iajs-878	103	90			PRON
iajs-878	103	91			PROPN
iajs-878	103	92			PROPN
iajs-878	103	93			NOUN
iajs-878	103	94			PROPN
iajs-878	103	95			PROPN
iajs-878	103	96	since	since	SCONJ
iajs-878	103	97	izzww	izzww	NOUN
iajs-878	103	98			NOUN
iajs-878	103	99	*	*	PUNCT
iajs-878	103	100	*	*	PUNCT
iajs-878	103	101	and	and	CCONJ
iajs-878	103	102			NOUN
iajs-878	103	103			SYM
iajs-878	103	104			NOUN
iajs-878	103	105			PROPN
iajs-878	103	106	0	0	NUM
iajs-878	103	107	,	,	PUNCT
iajs-878	103	108	*	*	PUNCT
iajs-878	103	109	*	*	PUNCT
iajs-878	103	110	*	*	PUNCT
iajs-878	103	111	*	*	PUNCT
iajs-878	103	112			PROPN
iajs-878	103	113	wwzzizzspeczzspec	wwzzizzspeczzspec	ADJ
iajs-878	103	114	,	,	PUNCT
iajs-878	103	115	and	and	CCONJ
iajs-878	103	116	thus	thus	ADV
iajs-878	103	117	,	,	PUNCT
iajs-878	103	118	,	,	PUNCT
iajs-878	103	119	0	0	PROPN
iajs-878	103	120	*	*	PROPN
iajs-878	103	121			PROPN
iajs-878	103	122	zzi	zzi	NOUN
iajs-878	103	123	,	,	PUNCT
iajs-878	103	124	therefore	therefore	ADV
iajs-878	103	125	,	,	PUNCT
iajs-878	103	126	,	,	PUNCT
iajs-878	103	127			NOUN
iajs-878	103	128			SYM
iajs-878	103	129			PROPN
iajs-878	103	130			NOUN
iajs-878	104	1			PROPN
iajs-878	104	2	02**2	02**2	PROPN
iajs-878	104	3	*	*	PUNCT
iajs-878	104	4			PROPN
iajs-878	104	5	nn	nn	PROPN
iajs-878	104	6	wwzziww	wwzziww	PROPN
iajs-878	104	7	references	reference	NOUN
iajs-878	104	8	1	1	NUM
iajs-878	104	9	.	.	PUNCT
iajs-878	105	1	ahmed	ahmed	PROPN
iajs-878	105	2	,	,	PUNCT
iajs-878	105	3	b.a	b.a	PROPN
iajs-878	105	4	.	.	PROPN
iajs-878	105	5	and	and	CCONJ
iajs-878	105	6	hilal	hilal	PROPN
iajs-878	105	7	,	,	PUNCT
iajs-878	105	8	m.m	m.m	PROPN
iajs-878	105	9	.	.	PROPN
iajs-878	105	10	,	,	PUNCT
iajs-878	105	11	(	(	PUNCT
iajs-878	105	12	2008	2008	NUM
iajs-878	105	13	)	)	PUNCT
iajs-878	105	14	,	,	PUNCT
iajs-878	105	15	on	on	ADP
iajs-878	105	16	solvability	solvability	NOUN
iajs-878	105	17	of	of	ADP
iajs-878	105	18	an	an	DET
iajs-878	105	19	operator	operator	NOUN
iajs-878	105	20	equation	equation	NOUN
iajs-878	105	21	,	,	PUNCT
iajs-878	105	22	proceeding	proceed	VERB
iajs-878	105	23	of	of	ADP
iajs-878	105	24	the	the	DET
iajs-878	105	25	3rd	3rd	ADJ
iajs-878	105	26	conference	conference	NOUN
iajs-878	105	27	on	on	ADP
iajs-878	105	28	mathematical	mathematical	ADJ
iajs-878	105	29	science	science	NOUN
iajs-878	105	30	in	in	ADP
iajs-878	105	31	united	united	PROPN
iajs-878	105	32	arab	arab	PROPN
iajs-878	105	33	emirates	emirates	PROPN
iajs-878	105	34	university	university	PROPN
iajs-878	105	35	,	,	PUNCT
iajs-878	105	36	in	in	ADP
iajs-878	105	37	the	the	DET
iajs-878	105	38	icm	icm	NOUN
iajs-878	105	39	,	,	PUNCT
iajs-878	105	40	2	2	NUM
iajs-878	105	41	.	.	X
iajs-878	105	42	feintuch	feintuch	ADJ
iajs-878	105	43	,	,	PUNCT
iajs-878	105	44	a.	a.	NOUN
iajs-878	105	45	(	(	PUNCT
iajs-878	105	46	1998	1998	NUM
iajs-878	105	47	)	)	PUNCT
iajs-878	105	48	,	,	PUNCT
iajs-878	105	49	robust	robust	ADJ
iajs-878	105	50	control	control	NOUN
iajs-878	105	51	theory	theory	NOUN
iajs-878	105	52	in	in	ADP
iajs-878	105	53	hilbert	hilbert	PROPN
iajs-878	105	54	space	space	NOUN
iajs-878	105	55	,	,	PUNCT
iajs-878	105	56	springer	springer	NOUN
iajs-878	105	57	-	-	PUNCT
iajs-878	105	58	verlag	verlag	PROPN
iajs-878	105	59	,	,	PUNCT
iajs-878	105	60	new	new	PROPN
iajs-878	105	61	york	york	PROPN
iajs-878	105	62	,	,	PUNCT
iajs-878	105	63	inc	inc	PROPN
iajs-878	105	64	.	.	PROPN
iajs-878	105	65	3	3	X
iajs-878	105	66	.	.	X
iajs-878	105	67	ramadan	ramadan	PROPN
iajs-878	105	68	,	,	PUNCT
iajs-878	105	69	m.	m.	NOUN
iajs-878	105	70	a.	a.	PROPN
iajs-878	105	71	(	(	PUNCT
iajs-878	105	72	2007),necessary	2007),necessary	ADJ
iajs-878	105	73	and	and	CCONJ
iajs-878	105	74	sufficient	sufficient	ADJ
iajs-878	105	75	conditions	condition	NOUN
iajs-878	105	76	for	for	ADP
iajs-878	105	77	the	the	DET
iajs-878	105	78	existence	existence	NOUN
iajs-878	105	79	of	of	ADP
iajs-878	105	80	positive	positive	ADJ
iajs-878	105	81	definite	definite	ADJ
iajs-878	105	82	solution	solution	NOUN
iajs-878	105	83	of	of	ADP
iajs-878	105	84	the	the	DET
iajs-878	105	85	matrix	matrix	NOUN
iajs-878	105	86	equation	equation	NOUN
iajs-878	105	87	,	,	PUNCT
iajs-878	105	88	nanyang	nanyang	PROPN
iajs-878	105	89	university	university	PROPN
iajs-878	105	90	of	of	ADP
iajs-878	105	91	technology	technology	NOUN
iajs-878	105	92	.	.	PUNCT
iajs-878	106	1	4	4	X
iajs-878	106	2	.	.	X
iajs-878	106	3	halmos	halmos	NOUN
iajs-878	106	4	,	,	PUNCT
iajs-878	106	5	p.	p.	PROPN
iajs-878	106	6	r.	r.	PROPN
iajs-878	106	7	(	(	PUNCT
iajs-878	106	8	1982	1982	NUM
iajs-878	106	9	)	)	PUNCT
iajs-878	106	10	,	,	PUNCT
iajs-878	106	11	a	a	DET
iajs-878	106	12	hilbert	hilbert	NOUN
iajs-878	106	13	space	space	NOUN
iajs-878	106	14	problem	problem	NOUN
iajs-878	106	15	book	book	NOUN
iajs-878	106	16	,	,	PUNCT
iajs-878	106	17	springer	springer	NOUN
iajs-878	106	18	-	-	PUNCT
iajs-878	106	19	verlag	verlag	PROPN
iajs-878	106	20	,	,	PUNCT
iajs-878	106	21	new	new	PROPN
iajs-878	106	22	york	york	PROPN
iajs-878	106	23	,	,	PUNCT
iajs-878	106	24	heidelberg	heidelberg	PROPN
iajs-878	106	25	,	,	PUNCT
iajs-878	106	26	new	new	PROPN
iajs-878	106	27	york	york	PROPN
iajs-878	106	28	,	,	PUNCT
iajs-878	106	29	berlin	berlin	PROPN
iajs-878	106	30	,	,	PUNCT
iajs-878	106	31	.	.	PUNCT
iajs-878	107	1	5	5	X
iajs-878	107	2	.	.	X
iajs-878	107	3	conway	conway	PROPN
iajs-878	107	4	,	,	PUNCT
iajs-878	107	5	j.b	j.b	PROPN
iajs-878	107	6	.	.	PUNCT
iajs-878	107	7	(	(	PUNCT
iajs-878	107	8	1985	1985	NUM
iajs-878	107	9	)	)	PUNCT
iajs-878	107	10	,	,	PUNCT
iajs-878	107	11	a	a	DET
iajs-878	107	12	course	course	NOUN
iajs-878	107	13	in	in	ADP
iajs-878	107	14	functional	functional	ADJ
iajs-878	107	15	analysis	analysis	NOUN
iajs-878	107	16	,	,	PUNCT
iajs-878	107	17	springerverlage	springerverlage	NOUN
iajs-878	107	18	,	,	PUNCT
iajs-878	107	19	berlin	berlin	PROPN
iajs-878	107	20	heidelberg	heidelberg	PROPN
iajs-878	107	21	,	,	PUNCT
iajs-878	107	22	new	new	PROPN
iajs-878	107	23	york	york	PROPN
iajs-878	107	24	.	.	PUNCT