id	sid	tid	token	lemma	pos
cana-535	1	1	communications	communication	NOUN
cana-535	1	2	on	on	ADP
cana-535	1	3	applied	apply	VERB
cana-535	1	4	nonlinear	nonlinear	ADJ
cana-535	1	5	analysis	analysis	NOUN
cana-535	1	6	issn	issn	NOUN
cana-535	1	7	:	:	PUNCT
cana-535	1	8	1074	1074	NUM
cana-535	1	9	-	-	PUNCT
cana-535	1	10	133x	133x	NUM
cana-535	1	11	vol	vol	NOUN
cana-535	1	12	31	31	NUM
cana-535	1	13	no	no	NOUN
cana-535	1	14	.	.	NOUN
cana-535	1	15	2	2	NUM
cana-535	1	16	(	(	PUNCT
cana-535	1	17	2024	2024	NUM
cana-535	1	18	)	)	PUNCT
cana-535	1	19	205	205	NUM
cana-535	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-535	1	21	a	a	DET
cana-535	1	22	note	note	NOUN
cana-535	1	23	on	on	ADP
cana-535	1	24	hybrid	hybrid	ADJ
cana-535	1	25	coset	coset	NOUN
cana-535	1	26	of	of	ADP
cana-535	1	27	a	a	DET
cana-535	1	28	nearring	nearre	VERB
cana-535	1	29	p.	p.	NOUN
cana-535	1	30	narasimha	narasimha	PROPN
cana-535	1	31	swamy	swamy	PROPN
cana-535	1	32	1a	1a	NOUN
cana-535	1	33	,	,	PUNCT
cana-535	1	34	bhurgula	bhurgula	VERB
cana-535	1	35	harika	harika	NOUN
cana-535	1	36	1b	1b	NUM
cana-535	1	37	,	,	PUNCT
cana-535	1	38	k.	k.	PROPN
cana-535	1	39	vijay	vijay	PROPN
cana-535	1	40	kumar2c	kumar2c	PROPN
cana-535	1	41	,	,	PUNCT
cana-535	1	42	b.	b.	PROPN
cana-535	1	43	jyothi3d	jyothi3d	PROPN
cana-535	1	44	and	and	CCONJ
cana-535	1	45	k.	k.	PROPN
cana-535	1	46	rajani1e	rajani1e	PROPN
cana-535	1	47	1department	1department	NUM
cana-535	1	48	of	of	ADP
cana-535	1	49	mathematics	mathematic	NOUN
cana-535	1	50	,	,	PUNCT
cana-535	1	51	school	school	NOUN
cana-535	1	52	of	of	ADP
cana-535	1	53	science	science	NOUN
cana-535	1	54	,	,	PUNCT
cana-535	1	55	gitam	gitam	NOUN
cana-535	1	56	deemed	deem	VERB
cana-535	1	57	to	to	PART
cana-535	1	58	be	be	AUX
cana-535	1	59	university	university	NOUN
cana-535	1	60	,	,	PUNCT
cana-535	1	61	hyderabad	hyderabad	PROPN
cana-535	1	62	campus502329	campus502329	PROPN
cana-535	1	63	,	,	PUNCT
cana-535	1	64	india	india	PROPN
cana-535	1	65	2department	2department	PROPN
cana-535	1	66	of	of	ADP
cana-535	1	67	mathematics	mathematic	NOUN
cana-535	1	68	,	,	PUNCT
cana-535	1	69	ku	ku	PROPN
cana-535	1	70	college	college	PROPN
cana-535	1	71	of	of	ADP
cana-535	1	72	engineering	engineering	NOUN
cana-535	1	73	and	and	CCONJ
cana-535	1	74	technology	technology	NOUN
cana-535	1	75	,	,	PUNCT
cana-535	1	76	kakatiya	kakatiya	PROPN
cana-535	1	77	university	university	PROPN
cana-535	1	78	,	,	PUNCT
cana-535	1	79	warangal506009	warangal506009	PROPN
cana-535	1	80	,	,	PUNCT
cana-535	1	81	india	india	PROPN
cana-535	1	82	3department	3department	PROPN
cana-535	1	83	of	of	ADP
cana-535	1	84	mathematics	mathematic	NOUN
cana-535	1	85	,	,	PUNCT
cana-535	1	86	telangana	telangana	PROPN
cana-535	1	87	mahila	mahila	PROPN
cana-535	1	88	vishwavidyalayam	vishwavidyalayam	PROPN
cana-535	1	89	,	,	PUNCT
cana-535	1	90	koti	koti	PROPN
cana-535	1	91	,	,	PUNCT
cana-535	1	92	hyderabad-500095	hyderabad-500095	NOUN
cana-535	1	93	,	,	PUNCT
cana-535	1	94	india	india	PROPN
cana-535	1	95	email	email	NOUN
cana-535	1	96	:	:	PUNCT
cana-535	1	97	a	a	DET
cana-535	1	98	swamy.pasham@gmail.com	swamy.pasham@gmail.com	NUM
cana-535	1	99	b	b	NOUN
cana-535	1	100	harika.burgula84@gmail.com	harika.burgula84@gmail.com	X
cana-535	1	101	c	c	NOUN
cana-535	1	102	vijay.kntm@gmail.com	vijay.kntm@gmail.com	X
cana-535	2	1	d	d	NOUN
cana-535	2	2	jyothireddydumbala@gmail.com	jyothireddydumbala@gmail.com	X
cana-535	3	1	e	e	NOUN
cana-535	3	2	rajanireddy2u@gmail.com	rajanireddy2u@gmail.com	PROPN
cana-535	3	3	article	article	PROPN
cana-535	3	4	history	history	NOUN
cana-535	3	5	:	:	PUNCT
cana-535	3	6	received	receive	VERB
cana-535	3	7	:	:	PUNCT
cana-535	3	8	30	30	NUM
cana-535	3	9	-	-	SYM
cana-535	3	10	01	01	NUM
cana-535	3	11	-	-	PUNCT
cana-535	3	12	2024	2024	NUM
cana-535	3	13	revised	revise	VERB
cana-535	3	14	:	:	PUNCT
cana-535	3	15	14	14	NUM
cana-535	3	16	-	-	PUNCT
cana-535	3	17	04	04	NUM
cana-535	3	18	-	-	PUNCT
cana-535	3	19	2024	2024	NUM
cana-535	3	20	accepted	accept	VERB
cana-535	3	21	:	:	PUNCT
cana-535	3	22	24	24	NUM
cana-535	3	23	-	-	PUNCT
cana-535	3	24	04	04	NUM
cana-535	3	25	-	-	PUNCT
cana-535	3	26	2024	2024	NUM
cana-535	3	27	abstract	abstract	NOUN
cana-535	3	28	:	:	PUNCT
cana-535	3	29	the	the	DET
cana-535	3	30	present	present	ADJ
cana-535	3	31	study	study	NOUN
cana-535	3	32	intends	intend	VERB
cana-535	3	33	to	to	PART
cana-535	3	34	learn	learn	VERB
cana-535	3	35	hybrid	hybrid	ADJ
cana-535	3	36	coset	coset	NOUN
cana-535	3	37	of	of	ADP
cana-535	3	38	a	a	DET
cana-535	3	39	nearring	nearring	NOUN
cana-535	3	40	.	.	PUNCT
cana-535	4	1	it	it	PRON
cana-535	4	2	is	be	AUX
cana-535	4	3	explained	explain	VERB
cana-535	4	4	with	with	ADP
cana-535	4	5	the	the	DET
cana-535	4	6	adequate	adequate	ADJ
cana-535	4	7	definitions	definition	NOUN
cana-535	4	8	and	and	CCONJ
cana-535	4	9	theorems	theorem	NOUN
cana-535	4	10	of	of	ADP
cana-535	4	11	the	the	DET
cana-535	4	12	hybrid	hybrid	ADJ
cana-535	4	13	coset	coset	NOUN
cana-535	4	14	of	of	ADP
cana-535	4	15	a	a	DET
cana-535	4	16	nearing	nearing	NOUN
cana-535	4	17	and	and	CCONJ
cana-535	4	18	near	near	ADP
cana-535	4	19	ring	ring	NOUN
cana-535	4	20	homomorphism	homomorphism	NOUN
cana-535	4	21	.	.	PUNCT
cana-535	5	1	it	it	PRON
cana-535	5	2	has	have	AUX
cana-535	5	3	been	be	AUX
cana-535	5	4	demonstrated	demonstrate	VERB
cana-535	5	5	that	that	SCONJ
cana-535	5	6	hybrid	hybrid	ADJ
cana-535	5	7	coset	coset	NOUN
cana-535	5	8	of	of	ADP
cana-535	5	9	a	a	DET
cana-535	5	10	nearring	nearring	NOUN
cana-535	5	11	is	be	AUX
cana-535	5	12	a	a	DET
cana-535	5	13	nearring	nearre	VERB
cana-535	5	14	epimorphism	epimorphism	NOUN
cana-535	5	15	with	with	ADP
cana-535	5	16	kernel	kernel	PROPN
cana-535	5	17	.	.	PUNCT
cana-535	6	1	further	far	ADV
cana-535	6	2	,	,	PUNCT
cana-535	6	3	we	we	PRON
cana-535	6	4	established	establish	VERB
cana-535	6	5	some	some	DET
cana-535	6	6	important	important	ADJ
cana-535	6	7	fundamental	fundamental	ADJ
cana-535	6	8	results	result	NOUN
cana-535	6	9	in	in	ADP
cana-535	6	10	terms	term	NOUN
cana-535	6	11	of	of	ADP
cana-535	6	12	hybrid	hybrid	ADJ
cana-535	6	13	structure	structure	NOUN
cana-535	6	14	corresponding	correspond	VERB
cana-535	6	15	to	to	ADP
cana-535	6	16	the	the	DET
cana-535	6	17	nearrings	nearring	NOUN
cana-535	6	18	.	.	PUNCT
cana-535	7	1	keywords	keyword	NOUN
cana-535	7	2	:	:	PUNCT
cana-535	7	3	hybrid	hybrid	ADJ
cana-535	7	4	structure	structure	NOUN
cana-535	7	5	,	,	PUNCT
cana-535	7	6	near	near	ADP
cana-535	7	7	ring	ring	NOUN
cana-535	7	8	,	,	PUNCT
cana-535	7	9	coset	coset	NOUN
cana-535	7	10	,	,	PUNCT
cana-535	7	11	hybrid	hybrid	ADJ
cana-535	7	12	coset	coset	NOUN
cana-535	7	13	1	1	NUM
cana-535	7	14	.	.	X
cana-535	7	15	introduction	introduction	NOUN
cana-535	7	16	a	a	DET
cana-535	7	17	nearring	nearring	NOUN
cana-535	7	18	is	be	AUX
cana-535	7	19	an	an	DET
cana-535	7	20	algebraic	algebraic	ADJ
cana-535	7	21	system	system	NOUN
cana-535	7	22	connected	connect	VERB
cana-535	7	23	to	to	ADP
cana-535	7	24	two	two	NUM
cana-535	7	25	binary	binary	ADJ
cana-535	7	26	operations	operation	NOUN
cana-535	7	27	,	,	PUNCT
cana-535	7	28	which	which	PRON
cana-535	7	29	gratifies	gratify	VERB
cana-535	7	30	all	all	PRON
cana-535	7	31	of	of	ADP
cana-535	7	32	a	a	DET
cana-535	7	33	ring	ring	NOUN
cana-535	7	34	's	's	PART
cana-535	7	35	axioms	axiom	NOUN
cana-535	7	36	,	,	PUNCT
cana-535	7	37	with	with	ADP
cana-535	7	38	the	the	DET
cana-535	7	39	conceivable	conceivable	ADJ
cana-535	7	40	exception	exception	NOUN
cana-535	7	41	of	of	ADP
cana-535	7	42	one	one	NUM
cana-535	7	43	distributive	distributive	ADJ
cana-535	7	44	law	law	NOUN
cana-535	7	45	.	.	PUNCT
cana-535	8	1	the	the	DET
cana-535	8	2	very	very	ADJ
cana-535	8	3	idea	idea	NOUN
cana-535	8	4	of	of	ADP
cana-535	8	5	nearring	nearring	NOUN
cana-535	8	6	was	be	AUX
cana-535	8	7	first	first	ADV
cana-535	8	8	adapted	adapt	VERB
cana-535	8	9	by	by	ADP
cana-535	8	10	g.	g.	PROPN
cana-535	8	11	pilz	pilz	PROPN
cana-535	9	1	[	[	X
cana-535	9	2	1	1	NUM
cana-535	9	3	]	]	PUNCT
cana-535	9	4	.	.	PUNCT
cana-535	10	1	nearrings	nearring	NOUN
cana-535	10	2	have	have	AUX
cana-535	10	3	been	be	AUX
cana-535	10	4	the	the	DET
cana-535	10	5	subject	subject	NOUN
cana-535	10	6	of	of	ADP
cana-535	10	7	investigation	investigation	NOUN
cana-535	10	8	by	by	ADP
cana-535	10	9	nobusawa[2	nobusawa[2	PROPN
cana-535	10	10	]	]	PUNCT
cana-535	10	11	,	,	PUNCT
cana-535	10	12	bh	bh	PROPN
cana-535	10	13	satyanarayana	satyanarayana	PROPN
cana-535	11	1	[	[	X
cana-535	11	2	3	3	NUM
cana-535	11	3	]	]	PUNCT
cana-535	11	4	and	and	CCONJ
cana-535	11	5	t.	t.	PROPN
cana-535	11	6	srinivas	srinivas	PROPN
cana-535	12	1	[	[	X
cana-535	12	2	4	4	NUM
cana-535	12	3	]	]	PUNCT
cana-535	12	4	.	.	PUNCT
cana-535	13	1	in	in	ADP
cana-535	13	2	1965	1965	NUM
cana-535	13	3	,	,	PUNCT
cana-535	13	4	l.a	l.a	PROPN
cana-535	13	5	.	.	PROPN
cana-535	13	6	zadeh	zadeh	PROPN
cana-535	14	1	[	[	X
cana-535	14	2	5	5	NUM
cana-535	14	3	]	]	PUNCT
cana-535	14	4	introduced	introduce	VERB
cana-535	14	5	new	new	ADJ
cana-535	14	6	concept	concept	NOUN
cana-535	14	7	about	about	ADP
cana-535	14	8	fuzzy	fuzzy	ADJ
cana-535	14	9	set	set	NOUN
cana-535	14	10	.	.	PUNCT
cana-535	15	1	this	this	DET
cana-535	15	2	concept	concept	NOUN
cana-535	15	3	highlighting	highlight	VERB
cana-535	15	4	the	the	DET
cana-535	15	5	membership	membership	NOUN
cana-535	15	6	status	status	NOUN
cana-535	15	7	of	of	ADP
cana-535	15	8	an	an	DET
cana-535	15	9	indeterminate	indeterminate	ADJ
cana-535	15	10	or	or	CCONJ
cana-535	15	11	fuzzy	fuzzy	ADJ
cana-535	15	12	set	set	NOUN
cana-535	15	13	.	.	PUNCT
cana-535	16	1	in	in	ADP
cana-535	16	2	this	this	DET
cana-535	16	3	concept	concept	NOUN
cana-535	16	4	,	,	PUNCT
cana-535	16	5	membership	membership	NOUN
cana-535	16	6	status	status	NOUN
cana-535	16	7	is	be	AUX
cana-535	16	8	defined	define	VERB
cana-535	16	9	as	as	ADP
cana-535	16	10	a	a	DET
cana-535	16	11	function	function	NOUN
cana-535	16	12	whose	whose	DET
cana-535	16	13	value	value	NOUN
cana-535	16	14	is	be	AUX
cana-535	16	15	in	in	ADP
cana-535	16	16	the	the	DET
cana-535	16	17	interval	interval	NOUN
cana-535	16	18	[	[	X
cana-535	16	19	0	0	NUM
cana-535	16	20	,	,	PUNCT
cana-535	16	21	1	1	NUM
cana-535	16	22	]	]	PUNCT
cana-535	16	23	.	.	PUNCT
cana-535	17	1	fuzzy	fuzzy	ADJ
cana-535	17	2	set	set	NOUN
cana-535	17	3	theory	theory	NOUN
cana-535	17	4	is	be	AUX
cana-535	17	5	established	establish	VERB
cana-535	17	6	in	in	ADP
cana-535	17	7	many	many	ADJ
cana-535	17	8	directions	direction	NOUN
cana-535	17	9	by	by	ADP
cana-535	17	10	many	many	ADJ
cana-535	17	11	scholars	scholar	NOUN
cana-535	17	12	and	and	CCONJ
cana-535	17	13	has	have	AUX
cana-535	17	14	got	got	AUX
cana-535	17	15	evoked	evoke	VERB
cana-535	17	16	great	great	ADJ
cana-535	17	17	interest	interest	NOUN
cana-535	17	18	in	in	ADP
cana-535	17	19	the	the	DET
cana-535	17	20	minds	mind	NOUN
cana-535	17	21	of	of	ADP
cana-535	17	22	many	many	ADJ
cana-535	17	23	researchers	researcher	NOUN
cana-535	17	24	who	who	PRON
cana-535	17	25	are	be	AUX
cana-535	17	26	working	work	VERB
cana-535	17	27	in	in	ADP
cana-535	17	28	different	different	ADJ
cana-535	17	29	fields	field	NOUN
cana-535	17	30	of	of	ADP
cana-535	17	31	mathematics	mathematic	NOUN
cana-535	17	32	.	.	PUNCT
cana-535	18	1	the	the	DET
cana-535	18	2	theory	theory	NOUN
cana-535	18	3	of	of	ADP
cana-535	18	4	fuzzy	fuzzy	ADJ
cana-535	18	5	sets	set	NOUN
cana-535	18	6	has	have	AUX
cana-535	18	7	found	find	VERB
cana-535	18	8	many	many	ADJ
cana-535	18	9	applications	application	NOUN
cana-535	18	10	,	,	PUNCT
cana-535	18	11	including	include	VERB
cana-535	18	12	engineering	engineering	NOUN
cana-535	18	13	,	,	PUNCT
cana-535	18	14	robotics	robotic	NOUN
cana-535	18	15	design	design	NOUN
cana-535	18	16	,	,	PUNCT
cana-535	18	17	computer	computer	NOUN
cana-535	18	18	modelling	modelling	NOUN
cana-535	18	19	,	,	PUNCT
cana-535	18	20	and	and	CCONJ
cana-535	18	21	water	water	NOUN
cana-535	18	22	resource	resource	NOUN
cana-535	18	23	planning	planning	NOUN
cana-535	18	24	.	.	PUNCT
cana-535	19	1	a	a	DET
cana-535	19	2	hesitant	hesitant	ADJ
cana-535	19	3	fuzzy	fuzzy	ADJ
cana-535	19	4	set	set	NOUN
cana-535	19	5	is	be	AUX
cana-535	19	6	an	an	DET
cana-535	19	7	extraordinary	extraordinary	ADJ
cana-535	19	8	tool	tool	NOUN
cana-535	19	9	for	for	ADP
cana-535	19	10	disclosing	disclose	VERB
cana-535	19	11	people	people	NOUN
cana-535	19	12	's	's	PART
cana-535	19	13	hesitancy	hesitancy	NOUN
cana-535	19	14	in	in	ADP
cana-535	19	15	every	every	DET
cana-535	19	16	life	life	NOUN
cana-535	19	17	and	and	CCONJ
cana-535	19	18	for	for	ADP
cana-535	19	19	handling	handle	VERB
cana-535	19	20	with	with	ADP
cana-535	19	21	uncertainty	uncertainty	NOUN
cana-535	19	22	,	,	PUNCT
cana-535	19	23	which	which	PRON
cana-535	19	24	could	could	AUX
cana-535	19	25	be	be	AUX
cana-535	19	26	suitably	suitably	ADV
cana-535	19	27	and	and	CCONJ
cana-535	19	28	matching	match	VERB
cana-535	19	29	way	way	NOUN
cana-535	19	30	labelled	label	VERB
cana-535	19	31	in	in	ADP
cana-535	19	32	terms	term	NOUN
cana-535	19	33	of	of	ADP
cana-535	19	34	the	the	DET
cana-535	19	35	decision	decision	NOUN
cana-535	19	36	makers	maker	NOUN
cana-535	19	37	’	’	PART
cana-535	19	38	opinions	opinion	NOUN
cana-535	19	39	.	.	PUNCT
cana-535	20	1	an	an	DET
cana-535	20	2	extensive	extensive	ADJ
cana-535	20	3	range	range	NOUN
cana-535	20	4	of	of	ADP
cana-535	20	5	existing	exist	VERB
cana-535	20	6	theories	theory	NOUN
cana-535	20	7	,	,	PUNCT
cana-535	20	8	like	like	ADP
cana-535	20	9	the	the	DET
cana-535	20	10	probability	probability	NOUN
cana-535	20	11	theory	theory	NOUN
cana-535	20	12	,	,	PUNCT
cana-535	20	13	theory	theory	NOUN
cana-535	20	14	of	of	ADP
cana-535	20	15	fuzzy	fuzzy	ADJ
cana-535	20	16	set	set	NOUN
cana-535	20	17	,	,	PUNCT
cana-535	20	18	vague	vague	ADJ
cana-535	20	19	sets	set	NOUN
cana-535	20	20	,	,	PUNCT
cana-535	20	21	interval	interval	NOUN
cana-535	20	22	mathematics	mathematic	NOUN
cana-535	20	23	theory	theory	NOUN
cana-535	20	24	,	,	PUNCT
cana-535	20	25	theory	theory	NOUN
cana-535	20	26	of	of	ADP
cana-535	20	27	rough	rough	ADJ
cana-535	20	28	set	set	NOUN
cana-535	20	29	,	,	PUNCT
cana-535	20	30	etc	etc	X
cana-535	20	31	.	.	X
cana-535	20	32	,	,	PUNCT
cana-535	20	33	are	be	AUX
cana-535	20	34	observed	observe	VERB
cana-535	20	35	to	to	PART
cana-535	20	36	deal	deal	VERB
cana-535	20	37	a	a	DET
cana-535	20	38	variety	variety	NOUN
cana-535	20	39	of	of	ADP
cana-535	20	40	problems	problem	NOUN
cana-535	20	41	in	in	ADP
cana-535	20	42	many	many	ADJ
cana-535	20	43	domains	domain	NOUN
cana-535	20	44	that	that	PRON
cana-535	20	45	which	which	PRON
cana-535	20	46	require	require	VERB
cana-535	20	47	data	datum	NOUN
cana-535	20	48	with	with	ADP
cana-535	20	49	uncertainties	uncertainty	NOUN
cana-535	20	50	.	.	PUNCT
cana-535	21	1	v.	v.	ADP
cana-535	21	2	torra	torra	VERB
cana-535	22	1	[	[	X
cana-535	22	2	6	6	NUM
cana-535	22	3	]	]	PUNCT
cana-535	22	4	established	establish	VERB
cana-535	22	5	the	the	DET
cana-535	22	6	perception	perception	NOUN
cana-535	22	7	of	of	ADP
cana-535	22	8	hesitant	hesitant	ADJ
cana-535	22	9	fuzzy	fuzzy	ADJ
cana-535	22	10	sets	set	NOUN
cana-535	22	11	.	.	PUNCT
cana-535	23	1	all	all	DET
cana-535	23	2	these	these	DET
cana-535	23	3	theories	theory	NOUN
cana-535	23	4	communications	communication	NOUN
cana-535	23	5	on	on	ADP
cana-535	23	6	applied	apply	VERB
cana-535	23	7	nonlinear	nonlinear	ADJ
cana-535	23	8	analysis	analysis	NOUN
cana-535	23	9	issn	issn	NOUN
cana-535	23	10	:	:	PUNCT
cana-535	23	11	1074	1074	NUM
cana-535	23	12	-	-	PUNCT
cana-535	23	13	133x	133x	NUM
cana-535	23	14	vol	vol	NOUN
cana-535	23	15	31	31	NUM
cana-535	23	16	no	no	NOUN
cana-535	23	17	.	.	NOUN
cana-535	23	18	2	2	NUM
cana-535	23	19	(	(	PUNCT
cana-535	23	20	2024	2024	NUM
cana-535	23	21	)	)	PUNCT
cana-535	23	22	206	206	NUM
cana-535	23	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-535	23	24	have	have	VERB
cana-535	23	25	their	their	PRON
cana-535	23	26	own	own	ADJ
cana-535	23	27	limitations	limitation	NOUN
cana-535	23	28	and	and	CCONJ
cana-535	23	29	difficulties	difficulty	NOUN
cana-535	23	30	which	which	PRON
cana-535	23	31	are	be	AUX
cana-535	23	32	elevated	elevate	VERB
cana-535	23	33	already	already	ADV
cana-535	23	34	[	[	X
cana-535	23	35	7	7	NUM
cana-535	23	36	]	]	PUNCT
cana-535	23	37	.	.	PUNCT
cana-535	24	1	to	to	PART
cana-535	24	2	be	be	AUX
cana-535	24	3	free	free	ADJ
cana-535	24	4	from	from	ADP
cana-535	24	5	these	these	DET
cana-535	24	6	difficulties	difficulty	NOUN
cana-535	24	7	,	,	PUNCT
cana-535	24	8	d.	d.	PROPN
cana-535	24	9	molodtsov	molodtsov	PROPN
cana-535	25	1	[	[	X
cana-535	25	2	7	7	NUM
cana-535	25	3	]	]	PUNCT
cana-535	25	4	familiarized	familiarize	VERB
cana-535	25	5	the	the	DET
cana-535	25	6	soft	soft	ADJ
cana-535	25	7	set	set	NOUN
cana-535	25	8	theory	theory	NOUN
cana-535	25	9	as	as	ADP
cana-535	25	10	a	a	DET
cana-535	25	11	new	new	ADJ
cana-535	25	12	mathematical	mathematical	ADJ
cana-535	25	13	tool	tool	NOUN
cana-535	25	14	for	for	ADP
cana-535	25	15	handling	handle	VERB
cana-535	25	16	with	with	ADP
cana-535	25	17	uncertainties	uncertainty	NOUN
cana-535	25	18	that	that	PRON
cana-535	25	19	is	be	AUX
cana-535	25	20	free	free	ADJ
cana-535	25	21	from	from	ADP
cana-535	25	22	the	the	DET
cana-535	25	23	difficulties	difficulty	NOUN
cana-535	25	24	.	.	PUNCT
cana-535	26	1	molodtsov	molodtsov	PROPN
cana-535	26	2	effectively	effectively	ADV
cana-535	26	3	applied	apply	VERB
cana-535	26	4	the	the	DET
cana-535	26	5	theory	theory	NOUN
cana-535	26	6	of	of	ADP
cana-535	26	7	soft	soft	ADJ
cana-535	26	8	set	set	NOUN
cana-535	26	9	in	in	ADP
cana-535	26	10	many	many	ADJ
cana-535	26	11	directions	direction	NOUN
cana-535	26	12	,	,	PUNCT
cana-535	26	13	such	such	ADJ
cana-535	26	14	as	as	ADP
cana-535	26	15	functions	function	NOUN
cana-535	26	16	’	'	PUNCT
cana-535	26	17	smoothness	smoothness	NOUN
cana-535	26	18	,	,	PUNCT
cana-535	26	19	theory	theory	NOUN
cana-535	26	20	of	of	ADP
cana-535	26	21	game	game	NOUN
cana-535	26	22	,	,	PUNCT
cana-535	26	23	riemann	riemann	PROPN
cana-535	26	24	integration	integration	PROPN
cana-535	26	25	,	,	PUNCT
cana-535	26	26	perron	perron	PROPN
cana-535	26	27	integration	integration	NOUN
cana-535	26	28	operations	operation	NOUN
cana-535	26	29	research	research	NOUN
cana-535	26	30	,	,	PUNCT
cana-535	26	31	probability	probability	NOUN
cana-535	26	32	,	,	PUNCT
cana-535	26	33	measurement	measurement	NOUN
cana-535	26	34	theory	theory	NOUN
cana-535	26	35	and	and	CCONJ
cana-535	26	36	many	many	ADJ
cana-535	26	37	other	other	ADJ
cana-535	26	38	.	.	PUNCT
cana-535	27	1	as	as	ADP
cana-535	27	2	a	a	DET
cana-535	27	3	parallel	parallel	ADJ
cana-535	27	4	circuit	circuit	NOUN
cana-535	27	5	of	of	ADP
cana-535	27	6	fuzzy	fuzzy	ADJ
cana-535	27	7	sets	set	NOUN
cana-535	27	8	and	and	CCONJ
cana-535	27	9	soft	soft	ADJ
cana-535	27	10	sets	set	NOUN
cana-535	27	11	(	(	PUNCT
cana-535	27	12	or	or	CCONJ
cana-535	27	13	,	,	PUNCT
cana-535	27	14	hesitant	hesitant	ADJ
cana-535	27	15	fuzzy	fuzzy	ADJ
cana-535	27	16	sets	set	NOUN
cana-535	27	17	)	)	PUNCT
cana-535	27	18	,	,	PUNCT
cana-535	27	19	jun	jun	PROPN
cana-535	27	20	,	,	PUNCT
cana-535	27	21	song	song	NOUN
cana-535	27	22	and	and	CCONJ
cana-535	27	23	muhiuddin	muhiuddin	VERB
cana-535	27	24	[	[	X
cana-535	27	25	8	8	NUM
cana-535	27	26	]	]	PUNCT
cana-535	27	27	proposed	propose	VERB
cana-535	27	28	the	the	DET
cana-535	27	29	idea	idea	NOUN
cana-535	27	30	of	of	ADP
cana-535	27	31	hybrid	hybrid	ADJ
cana-535	27	32	structures	structure	NOUN
cana-535	27	33	in	in	ADP
cana-535	27	34	a	a	DET
cana-535	27	35	set	set	NOUN
cana-535	27	36	of	of	ADP
cana-535	27	37	parameters	parameter	NOUN
cana-535	27	38	over	over	ADP
cana-535	27	39	an	an	DET
cana-535	27	40	initial	initial	ADJ
cana-535	27	41	universe	universe	NOUN
cana-535	27	42	set	set	NOUN
cana-535	27	43	,	,	PUNCT
cana-535	27	44	and	and	CCONJ
cana-535	27	45	illustrating	illustrate	VERB
cana-535	27	46	numerous	numerous	ADJ
cana-535	27	47	properties	property	NOUN
cana-535	27	48	.	.	PUNCT
cana-535	28	1	using	use	VERB
cana-535	28	2	this	this	DET
cana-535	28	3	idea	idea	NOUN
cana-535	28	4	,	,	PUNCT
cana-535	28	5	they	they	PRON
cana-535	28	6	initiated	initiate	VERB
cana-535	28	7	the	the	DET
cana-535	28	8	idea	idea	NOUN
cana-535	28	9	of	of	ADP
cana-535	28	10	a	a	DET
cana-535	28	11	hybrid	hybrid	ADJ
cana-535	28	12	gamma	gamma	NOUN
cana-535	28	13	near	near	ADP
cana-535	28	14	ring	ring	PROPN
cana-535	28	15	,	,	PUNCT
cana-535	28	16	hybrid	hybrid	ADJ
cana-535	28	17	ideal	ideal	NOUN
cana-535	28	18	of	of	ADP
cana-535	28	19	a	a	DET
cana-535	28	20	gamma	gamma	NOUN
cana-535	28	21	near	near	ADP
cana-535	28	22	ring	ring	PROPN
cana-535	28	23	.	.	PUNCT
cana-535	29	1	b.	b.	PROPN
cana-535	29	2	elavarasan	elavarasan	PROPN
cana-535	29	3	[	[	X
cana-535	29	4	9	9	NUM
cana-535	29	5	]	]	PUNCT
cana-535	29	6	deliberated	deliberate	VERB
cana-535	29	7	hybrid	hybrid	ADJ
cana-535	29	8	structures	structure	NOUN
cana-535	29	9	applied	apply	VERB
cana-535	29	10	to	to	ADP
cana-535	29	11	ideals	ideal	NOUN
cana-535	29	12	in	in	ADP
cana-535	29	13	near	near	ADJ
cana-535	29	14	-	-	PUNCT
cana-535	29	15	rings	ring	NOUN
cana-535	29	16	.	.	PUNCT
cana-535	30	1	saima	saima	PROPN
cana-535	30	2	anis	anis	PROPN
cana-535	31	1	[	[	X
cana-535	31	2	10	10	NUM
cana-535	31	3	]	]	PUNCT
cana-535	31	4	has	have	AUX
cana-535	31	5	explored	explore	VERB
cana-535	31	6	hybrid	hybrid	ADJ
cana-535	31	7	ideals	ideal	NOUN
cana-535	31	8	in	in	ADP
cana-535	31	9	semigroups	semigroup	NOUN
cana-535	31	10	.	.	PUNCT
cana-535	32	1	m.	m.	NOUN
cana-535	32	2	himaya	himaya	PROPN
cana-535	32	3	jaleela	jaleela	PROPN
cana-535	32	4	begum	begum	VERB
cana-535	32	5	[	[	X
cana-535	32	6	11	11	NUM
cana-535	32	7	]	]	PUNCT
cana-535	32	8	explored	explore	VERB
cana-535	32	9	hybrid	hybrid	ADJ
cana-535	32	10	fuzzy	fuzzy	ADJ
cana-535	32	11	bi	bi	NOUN
cana-535	32	12	-	-	NOUN
cana-535	32	13	ideals	ideal	NOUN
cana-535	32	14	in	in	ADP
cana-535	32	15	near	near	ADJ
cana-535	32	16	-	-	PUNCT
cana-535	32	17	rings	ring	NOUN
cana-535	32	18	.	.	PUNCT
cana-535	33	1	s.	s.	PROPN
cana-535	33	2	abou	abou	PROPN
cana-535	33	3	-	-	PROPN
cana-535	33	4	zaid	zaid	PROPN
cana-535	34	1	[	[	X
cana-535	34	2	12	12	NUM
cana-535	34	3	]	]	PUNCT
cana-535	34	4	and	and	CCONJ
cana-535	34	5	s.d	s.d	PROPN
cana-535	34	6	.	.	PROPN
cana-535	34	7	kim	kim	PROPN
cana-535	35	1	[	[	X
cana-535	35	2	13	13	NUM
cana-535	35	3	]	]	PUNCT
cana-535	35	4	were	be	AUX
cana-535	35	5	developed	develop	VERB
cana-535	35	6	fuzzy	fuzzy	ADJ
cana-535	35	7	ideals	ideal	NOUN
cana-535	35	8	of	of	ADP
cana-535	35	9	near	near	ADJ
cana-535	35	10	rings	ring	NOUN
cana-535	35	11	.	.	PUNCT
cana-535	36	1	p.	p.	NOUN
cana-535	36	2	narasimha	narasimha	PROPN
cana-535	36	3	swamy	swamy	PROPN
cana-535	36	4	[	[	X
cana-535	36	5	14	14	NUM
cana-535	36	6	]	]	PUNCT
cana-535	36	7	has	have	AUX
cana-535	36	8	developed	develop	VERB
cana-535	36	9	sim	sim	NOUN
cana-535	36	10	of	of	ADP
cana-535	36	11	fuzzy	fuzzy	ADJ
cana-535	36	12	ideals	ideal	NOUN
cana-535	36	13	of	of	ADP
cana-535	36	14	γ	γ	X
cana-535	36	15	-	-	PUNCT
cana-535	36	16	near	near	ADP
cana-535	36	17	-	-	PUNCT
cana-535	36	18	rings	ring	NOUN
cana-535	36	19	.	.	PUNCT
cana-535	37	1	k.	k.	PROPN
cana-535	37	2	vijay	vijay	PROPN
cana-535	37	3	kumar	kumar	PROPN
cana-535	37	4	[	[	X
cana-535	37	5	15	15	NUM
cana-535	37	6	]	]	PUNCT
cana-535	37	7	has	have	AUX
cana-535	37	8	proposed	propose	VERB
cana-535	37	9	the	the	DET
cana-535	37	10	idea	idea	NOUN
cana-535	37	11	on	on	ADP
cana-535	37	12	bipolar	bipolar	ADJ
cana-535	37	13	fuzzy	fuzzy	ADJ
cana-535	37	14	quasi	quasi	NOUN
cana-535	37	15	ideals	ideal	NOUN
cana-535	37	16	and	and	CCONJ
cana-535	37	17	bipolar	bipolar	ADJ
cana-535	37	18	n	n	CCONJ
cana-535	37	19	-	-	NOUN
cana-535	37	20	subgroups	subgroup	NOUN
cana-535	37	21	of	of	ADP
cana-535	37	22	near	near	ADJ
cana-535	37	23	rings	ring	NOUN
cana-535	37	24	.	.	PUNCT
cana-535	38	1	satyanarayana	satyanarayana	PROPN
cana-535	38	2	bhavanari	bhavanari	PROPN
cana-535	39	1	[	[	X
cana-535	39	2	16	16	NUM
cana-535	39	3	]	]	PUNCT
cana-535	39	4	has	have	AUX
cana-535	39	5	explored	explore	VERB
cana-535	39	6	on	on	ADP
cana-535	39	7	fuzzy	fuzzy	ADJ
cana-535	39	8	cosets	coset	NOUN
cana-535	39	9	of	of	ADP
cana-535	39	10	gamma	gamma	NOUN
cana-535	39	11	near	near	ADP
cana-535	39	12	rings	ring	NOUN
cana-535	39	13	.	.	PUNCT
cana-535	40	1	t.	t.	PROPN
cana-535	40	2	srinivas	srinivas	PROPN
cana-535	41	1	[	[	X
cana-535	41	2	17	17	NUM
cana-535	41	3	]	]	PUNCT
cana-535	41	4	,	,	PUNCT
cana-535	41	5	harika	harika	X
cana-535	41	6	bhurgula	bhurgula	VERB
cana-535	42	1	[	[	X
cana-535	42	2	18	18	NUM
cana-535	42	3	]	]	PUNCT
cana-535	42	4	and	and	CCONJ
cana-535	42	5	b.	b.	PROPN
cana-535	42	6	jyothi	jyothi	PROPN
cana-535	43	1	[	[	X
cana-535	43	2	19,20	19,20	X
cana-535	43	3	]	]	PUNCT
cana-535	43	4	have	have	AUX
cana-535	43	5	established	establish	VERB
cana-535	43	6	the	the	DET
cana-535	43	7	concepts	concept	NOUN
cana-535	43	8	on	on	ADP
cana-535	43	9	near	near	ADP
cana-535	43	10	algebra	algebra	NOUN
cana-535	43	11	.	.	PUNCT
cana-535	44	1	in	in	ADP
cana-535	44	2	which	which	PRON
cana-535	44	3	i	i	PRON
cana-535	44	4	have	have	AUX
cana-535	44	5	inspired	inspire	VERB
cana-535	44	6	to	to	PART
cana-535	44	7	study	study	VERB
cana-535	44	8	on	on	ADP
cana-535	44	9	near	near	ADP
cana-535	44	10	ring	ring	NOUN
cana-535	44	11	concepts	concept	NOUN
cana-535	44	12	.	.	PUNCT
cana-535	45	1	in	in	ADP
cana-535	45	2	the	the	DET
cana-535	45	3	current	current	ADJ
cana-535	45	4	study	study	NOUN
cana-535	45	5	,	,	PUNCT
cana-535	45	6	we	we	PRON
cana-535	45	7	acquaint	acquaint	VERB
cana-535	45	8	with	with	ADP
cana-535	45	9	the	the	DET
cana-535	45	10	conception	conception	NOUN
cana-535	45	11	of	of	ADP
cana-535	45	12	hybrid	hybrid	ADJ
cana-535	45	13	coset	coset	NOUN
cana-535	45	14	of	of	ADP
cana-535	45	15	a	a	DET
cana-535	45	16	near	near	ADJ
cana-535	45	17	ring	ring	NOUN
cana-535	45	18	and	and	CCONJ
cana-535	45	19	hybrid	hybrid	ADJ
cana-535	45	20	structure	structure	NOUN
cana-535	45	21	is	be	AUX
cana-535	45	22	used	use	VERB
cana-535	45	23	to	to	PART
cana-535	45	24	analyze	analyze	VERB
cana-535	45	25	the	the	DET
cana-535	45	26	structural	structural	ADJ
cana-535	45	27	statements	statement	NOUN
cana-535	45	28	of	of	ADP
cana-535	45	29	near	near	ADJ
cana-535	45	30	rings	ring	NOUN
cana-535	45	31	.	.	PUNCT
cana-535	46	1	all	all	ADV
cana-535	46	2	over	over	ADP
cana-535	46	3	this	this	DET
cana-535	46	4	paper	paper	NOUN
cana-535	46	5	𝑁	𝑁	PROPN
cana-535	46	6	means	mean	VERB
cana-535	46	7	a	a	DET
cana-535	46	8	(	(	PUNCT
cana-535	46	9	right	right	NOUN
cana-535	46	10	)	)	PUNCT
cana-535	46	11	near	near	ADP
cana-535	46	12	ring	ring	NOUN
cana-535	46	13	.	.	PUNCT
cana-535	47	1	2	2	X
cana-535	47	2	.	.	X
cana-535	47	3	preliminaries	preliminary	NOUN
cana-535	47	4	definition	definition	NOUN
cana-535	47	5	2.1	2.1	NUM
cana-535	47	6	:	:	PUNCT
cana-535	48	1	[	[	X
cana-535	48	2	8	8	NUM
cana-535	48	3	]	]	PUNCT
cana-535	48	4	let	let	VERB
cana-535	48	5	𝑈	𝑈	PROPN
cana-535	48	6	be	be	AUX
cana-535	48	7	a	a	DET
cana-535	48	8	universal	universal	ADJ
cana-535	48	9	set	set	NOUN
cana-535	48	10	,	,	PUNCT
cana-535	48	11	𝑃(𝑈	𝑃(𝑈	NOUN
cana-535	48	12	)	)	PUNCT
cana-535	48	13	be	be	AUX
cana-535	48	14	the	the	DET
cana-535	48	15	power	power	NOUN
cana-535	48	16	set	set	NOUN
cana-535	48	17	,	,	PUNCT
cana-535	48	18	𝐿	𝐿	PROPN
cana-535	48	19	be	be	VERB
cana-535	48	20	the	the	DET
cana-535	48	21	set	set	NOUN
cana-535	48	22	of	of	ADP
cana-535	48	23	parameters	parameter	NOUN
cana-535	48	24	and	and	CCONJ
cana-535	48	25	𝐼	𝐼	PROPN
cana-535	48	26	be	be	VERB
cana-535	48	27	the	the	DET
cana-535	48	28	unit	unit	NOUN
cana-535	48	29	interval	interval	NOUN
cana-535	48	30	.	.	PUNCT
cana-535	49	1	a	a	DET
cana-535	49	2	mapping	mapping	NOUN
cana-535	49	3	𝜉𝜆	𝜉𝜆	NOUN
cana-535	49	4	≔	≔	NOUN
cana-535	49	5	(	(	PUNCT
cana-535	49	6	𝜉	𝜉	NOUN
cana-535	49	7	̃	̃	PROPN
cana-535	49	8	,	,	PUNCT
cana-535	49	9	𝜆	𝜆	NOUN
cana-535	49	10	):	):	PUNCT
cana-535	49	11	𝐿	𝐿	PROPN
cana-535	49	12	→	→	SYM
cana-535	49	13	𝑃(𝑈	𝑃(𝑈	NOUN
cana-535	49	14	)	)	PUNCT
cana-535	49	15	𝑋	𝑋	PROPN
cana-535	49	16	𝐼	𝐼	PROPN
cana-535	49	17	,	,	PUNCT
cana-535	49	18	𝑞	𝑞	X
cana-535	49	19	→	→	PUNCT
cana-535	49	20	(	(	PUNCT
cana-535	49	21	𝜉(𝑞	𝜉(𝑞	PROPN
cana-535	49	22	)	)	PUNCT
cana-535	49	23	,	,	PUNCT
cana-535	49	24	𝜆(𝑞	𝜆(𝑞	NOUN
cana-535	49	25	)	)	PUNCT
cana-535	49	26	)	)	PUNCT
cana-535	50	1	i.e.	i.e.	X
cana-535	50	2	,	,	PUNCT
cana-535	50	3	the	the	DET
cana-535	50	4	image	image	NOUN
cana-535	50	5	of	of	ADP
cana-535	50	6	𝑞	𝑞	PROPN
cana-535	50	7	is	be	AUX
cana-535	50	8	chosen	choose	VERB
cana-535	50	9	by	by	ADP
cana-535	50	10	(	(	PUNCT
cana-535	50	11	𝜉(𝑞	𝜉(𝑞	PROPN
cana-535	50	12	)	)	PUNCT
cana-535	50	13	,	,	PUNCT
cana-535	50	14	𝜆(𝑞	𝜆(𝑞	NOUN
cana-535	50	15	)	)	PUNCT
cana-535	50	16	)	)	PUNCT
cana-535	50	17	is	be	AUX
cana-535	50	18	entitled	entitle	VERB
cana-535	50	19	a	a	DET
cana-535	50	20	hybrid	hybrid	ADJ
cana-535	50	21	structure	structure	NOUN
cana-535	50	22	(	(	PUNCT
cana-535	50	23	hs	hs	X
cana-535	50	24	)	)	PUNCT
cana-535	50	25	in	in	ADP
cana-535	50	26	𝐿	𝐿	PROPN
cana-535	50	27	over	over	ADP
cana-535	50	28	𝑈	𝑈	PROPN
cana-535	50	29	,	,	PUNCT
cana-535	50	30	where	where	SCONJ
cana-535	50	31	𝜉	𝜉	X
cana-535	50	32	:	:	PUNCT
cana-535	50	33	𝐿	𝐿	PROPN
cana-535	50	34	→	→	SYM
cana-535	50	35	𝑃(𝑈	𝑃(𝑈	NOUN
cana-535	50	36	)	)	PUNCT
cana-535	50	37	and	and	CCONJ
cana-535	50	38	𝜆	𝜆	PRON
cana-535	50	39	∶	∶	PROPN
cana-535	50	40	𝐿	𝐿	PROPN
cana-535	50	41	→	→	SYM
cana-535	50	42	𝐼	𝐼	PROPN
cana-535	50	43	are	be	AUX
cana-535	50	44	the	the	DET
cana-535	50	45	mappings	mapping	NOUN
cana-535	50	46	.	.	PUNCT
cana-535	51	1	definition	definition	NOUN
cana-535	51	2	2.2	2.2	NUM
cana-535	51	3	:	:	PUNCT
cana-535	52	1	[	[	X
cana-535	52	2	8	8	NUM
cana-535	52	3	]	]	PUNCT
cana-535	52	4	let	let	VERB
cana-535	52	5	𝜉𝜆	𝜉𝜆	PRON
cana-535	52	6	be	be	AUX
cana-535	52	7	a	a	DET
cana-535	52	8	hs	hs	PROPN
cana-535	52	9	in	in	ADP
cana-535	52	10	𝐿	𝐿	PROPN
cana-535	52	11	over	over	ADP
cana-535	52	12	𝑈.	𝑈.	PROPN
cana-535	52	13	then	then	ADV
cana-535	52	14	the	the	DET
cana-535	52	15	sets	set	NOUN
cana-535	52	16	𝜉𝜆[𝛼	𝜉𝜆[𝛼	NOUN
cana-535	52	17	,	,	PUNCT
cana-535	52	18	𝑡	𝑡	X
cana-535	52	19	]	]	PUNCT
cana-535	52	20	=	=	X
cana-535	52	21	{	{	PUNCT
cana-535	52	22	𝑞	𝑞	PROPN
cana-535	52	23	∈	∈	PROPN
cana-535	52	24	𝐿	𝐿	PROPN
cana-535	52	25	𝜉(𝑞)⁄	𝜉(𝑞)⁄	PROPN
cana-535	52	26	⊇	⊇	NOUN
cana-535	52	27	𝛼	𝛼	NOUN
cana-535	52	28	,	,	PUNCT
cana-535	52	29	𝜆(𝑞	𝜆(𝑞	NOUN
cana-535	52	30	)	)	PUNCT
cana-535	52	31	≤	≤	NUM
cana-535	52	32	𝑡	𝑡	X
cana-535	52	33	}	}	PUNCT
cana-535	52	34	,	,	PUNCT
cana-535	52	35	𝜉𝜆(𝛼	𝜉𝜆(𝛼	X
cana-535	52	36	,	,	PUNCT
cana-535	52	37	𝑡	𝑡	X
cana-535	52	38	]	]	PUNCT
cana-535	52	39	=	=	X
cana-535	52	40	{	{	PUNCT
cana-535	52	41	𝑞	𝑞	PROPN
cana-535	52	42	∈	∈	PROPN
cana-535	52	43	𝐿	𝐿	PROPN
cana-535	52	44	𝜉(𝑞)⁄	𝜉(𝑞)⁄	PROPN
cana-535	52	45	⊋	⊋	NOUN
cana-535	52	46	𝛼	𝛼	NOUN
cana-535	52	47	,	,	PUNCT
cana-535	52	48	𝜆(𝑞	𝜆(𝑞	NOUN
cana-535	52	49	)	)	PUNCT
cana-535	52	50	≤	≤	NUM
cana-535	52	51	𝑡	𝑡	X
cana-535	52	52	}	}	PUNCT
cana-535	52	53	,	,	PUNCT
cana-535	52	54	𝜉𝜆[𝛼	𝜉𝜆[𝛼	NOUN
cana-535	52	55	,	,	PUNCT
cana-535	52	56	𝑡	𝑡	NOUN
cana-535	52	57	)	)	PUNCT
cana-535	52	58	=	=	SYM
cana-535	52	59	{	{	PUNCT
cana-535	52	60	𝑞	𝑞	PROPN
cana-535	52	61	∈	∈	PROPN
cana-535	52	62	𝐿	𝐿	PROPN
cana-535	52	63	𝜉(𝑞)⁄	𝜉(𝑞)⁄	PROPN
cana-535	52	64	⊇	⊇	NOUN
cana-535	52	65	𝛼	𝛼	NOUN
cana-535	52	66	,	,	PUNCT
cana-535	52	67	𝜆(𝑞	𝜆(𝑞	NOUN
cana-535	52	68	)	)	PUNCT
cana-535	52	69	<	<	X
cana-535	52	70	𝑡	𝑡	X
cana-535	52	71	}	}	PUNCT
cana-535	52	72	,	,	PUNCT
cana-535	52	73	𝜉𝜆(𝛼	𝜉𝜆(𝛼	X
cana-535	52	74	,	,	PUNCT
cana-535	52	75	𝑡	𝑡	X
cana-535	52	76	)	)	PUNCT
cana-535	52	77	=	=	SYM
cana-535	52	78	{	{	PUNCT
cana-535	52	79	𝑞	𝑞	PROPN
cana-535	52	80	∈	∈	PROPN
cana-535	52	81	𝐿	𝐿	PROPN
cana-535	52	82	𝜉(𝑞)⁄	𝜉(𝑞)⁄	PROPN
cana-535	52	83	⊋	⊋	NOUN
cana-535	52	84	𝛼	𝛼	NOUN
cana-535	52	85	,	,	PUNCT
cana-535	52	86	𝜆(𝑞	𝜆(𝑞	NOUN
cana-535	52	87	)	)	PUNCT
cana-535	52	88	<	<	X
cana-535	52	89	𝑡	𝑡	X
cana-535	52	90	}	}	PUNCT
cana-535	52	91	are	be	AUX
cana-535	52	92	entitled	entitle	VERB
cana-535	52	93	the	the	DET
cana-535	52	94	[	[	X
cana-535	52	95	𝛼	𝛼	NOUN
cana-535	52	96	,	,	PUNCT
cana-535	52	97	𝑡	𝑡	X
cana-535	52	98	]	]	PUNCT
cana-535	52	99	–	–	PUNCT
cana-535	52	100	hybrid	hybrid	ADJ
cana-535	52	101	cut	cut	NOUN
cana-535	52	102	(	(	PUNCT
cana-535	52	103	hc	hc	NOUN
cana-535	52	104	)	)	PUNCT
cana-535	52	105	,	,	PUNCT
cana-535	52	106	(	(	PUNCT
cana-535	52	107	𝛼	𝛼	X
cana-535	52	108	,	,	PUNCT
cana-535	52	109	𝑡	𝑡	X
cana-535	52	110	]	]	PUNCT
cana-535	52	111	–	–	PUNCT
cana-535	52	112	hc	hc	NOUN
cana-535	52	113	,	,	PUNCT
cana-535	52	114	[	[	X
cana-535	52	115	𝛼	𝛼	X
cana-535	52	116	,	,	PUNCT
cana-535	52	117	𝑡	𝑡	NOUN
cana-535	52	118	)	)	PUNCT
cana-535	52	119	–	–	PUNCT
cana-535	52	120	hc	hc	NOUN
cana-535	52	121	,	,	PUNCT
cana-535	52	122	and	and	CCONJ
cana-535	52	123	(	(	PUNCT
cana-535	52	124	𝛼	𝛼	NOUN
cana-535	52	125	,	,	PUNCT
cana-535	52	126	𝑡	𝑡	NOUN
cana-535	52	127	)	)	PUNCT
cana-535	52	128	–	–	PUNCT
cana-535	52	129	hc	hc	NOUN
cana-535	52	130	of	of	ADP
cana-535	52	131	𝜉𝜆	𝜉𝜆	PRON
cana-535	52	132	respectively	respectively	ADV
cana-535	52	133	,	,	PUNCT
cana-535	52	134	where	where	SCONJ
cana-535	52	135	𝛼	𝛼	X
cana-535	52	136	∈	∈	PROPN
cana-535	52	137	𝑃(𝑈	𝑃(𝑈	NOUN
cana-535	52	138	)	)	PUNCT
cana-535	52	139	,	,	PUNCT
cana-535	52	140	𝑡	𝑡	PROPN
cana-535	52	141	∈	∈	PROPN
cana-535	52	142	𝐼.	𝐼.	PROPN
cana-535	52	143	obviously	obviously	ADV
cana-535	52	144	,	,	PUNCT
cana-535	52	145	𝜉𝜆(𝛼	𝜉𝜆(𝛼	PROPN
cana-535	52	146	,	,	PUNCT
cana-535	52	147	𝑡	𝑡	X
cana-535	52	148	)	)	PUNCT
cana-535	52	149	⊆	⊆	NUM
cana-535	52	150	𝜉𝜆(𝛼	𝜉𝜆(𝛼	NOUN
cana-535	52	151	,	,	PUNCT
cana-535	52	152	𝑡	𝑡	X
cana-535	52	153	]	]	PUNCT
cana-535	52	154	⊆	⊆	NUM
cana-535	52	155	𝜉𝜆[𝛼	𝜉𝜆[𝛼	NOUN
cana-535	52	156	,	,	PUNCT
cana-535	52	157	𝑡	𝑡	X
cana-535	52	158	]	]	PUNCT
cana-535	52	159	and	and	CCONJ
cana-535	52	160	𝜉𝜆(𝛼	𝜉𝜆(𝛼	NOUN
cana-535	52	161	,	,	PUNCT
cana-535	52	162	𝑡	𝑡	X
cana-535	52	163	)	)	PUNCT
cana-535	52	164	⊆	⊆	NUM
cana-535	52	165	𝜉𝜆[𝛼	𝜉𝜆[𝛼	NOUN
cana-535	52	166	,	,	PUNCT
cana-535	52	167	𝑡	𝑡	NOUN
cana-535	52	168	)	)	PUNCT
cana-535	52	169	⊆	⊆	NUM
cana-535	52	170	𝜉𝜆[𝛼	𝜉𝜆[𝛼	NOUN
cana-535	52	171	,	,	PUNCT
cana-535	52	172	𝑡	𝑡	X
cana-535	52	173	]	]	PUNCT
cana-535	52	174	.	.	PUNCT
cana-535	53	1	communications	communication	NOUN
cana-535	53	2	on	on	ADP
cana-535	53	3	applied	apply	VERB
cana-535	53	4	nonlinear	nonlinear	ADJ
cana-535	53	5	analysis	analysis	NOUN
cana-535	53	6	issn	issn	NOUN
cana-535	53	7	:	:	PUNCT
cana-535	53	8	1074	1074	NUM
cana-535	53	9	-	-	PUNCT
cana-535	53	10	133x	133x	NUM
cana-535	53	11	vol	vol	NOUN
cana-535	53	12	31	31	NUM
cana-535	53	13	no	no	NOUN
cana-535	53	14	.	.	NOUN
cana-535	53	15	2	2	NUM
cana-535	53	16	(	(	PUNCT
cana-535	53	17	2024	2024	NUM
cana-535	53	18	)	)	PUNCT
cana-535	53	19	207	207	NUM
cana-535	53	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-535	53	21	definition	definition	NOUN
cana-535	53	22	2.3	2.3	NUM
cana-535	53	23	:	:	PUNCT
cana-535	54	1	[	[	X
cana-535	54	2	9	9	NUM
cana-535	54	3	]	]	PUNCT
cana-535	54	4	let	let	VERB
cana-535	54	5	�	�	PROPN
cana-535	54	6	̃	̃	PROPN
cana-535	54	7	�	�	PROPN
cana-535	54	8	𝛾	𝛾	AUX
cana-535	54	9	be	be	VERB
cana-535	54	10	a	a	DET
cana-535	54	11	hs	hs	NOUN
cana-535	54	12	of	of	ADP
cana-535	54	13	a	a	DET
cana-535	54	14	nearring	nearre	VERB
cana-535	54	15	𝑁	𝑁	PROPN
cana-535	54	16	,	,	PUNCT
cana-535	54	17	�	�	PROPN
cana-535	54	18	̃	̃	PROPN
cana-535	54	19	�	�	NOUN
cana-535	54	20	𝛾	𝛾	PROPN
cana-535	54	21	is	be	AUX
cana-535	54	22	called	call	VERB
cana-535	54	23	a	a	DET
cana-535	54	24	hybrid	hybrid	ADJ
cana-535	54	25	nearring	nearring	NOUN
cana-535	54	26	of	of	ADP
cana-535	54	27	𝑁	𝑁	PROPN
cana-535	54	28	over	over	ADP
cana-535	54	29	𝑈	𝑈	PROPN
cana-535	54	30	if	if	SCONJ
cana-535	54	31	the	the	DET
cana-535	54	32	following	follow	VERB
cana-535	54	33	conditions	condition	NOUN
cana-535	54	34	clutch	clutch	VERB
cana-535	54	35	:	:	PUNCT
cana-535	54	36	(	(	PUNCT
cana-535	54	37	𝑖)	𝑖)	NUM
cana-535	54	38	�	�	SYM
cana-535	54	39	̃	̃	PROPN
cana-535	54	40	�	�	PROPN
cana-535	54	41	(𝑞	(𝑞	NOUN
cana-535	54	42	−	−	NOUN
cana-535	54	43	𝜍	𝜍	NOUN
cana-535	54	44	)	)	PUNCT
cana-535	54	45	⊇	⊇	PROPN
cana-535	54	46	�	�	PROPN
cana-535	54	47	̃	̃	PROPN
cana-535	54	48	�	�	NOUN
cana-535	54	49	(𝑞	(𝑞	NOUN
cana-535	54	50	)	)	PUNCT
cana-535	54	51	∩	∩	PROPN
cana-535	54	52	�	�	PROPN
cana-535	54	53	̃	̃	PROPN
cana-535	54	54	�	�	PROPN
cana-535	54	55	(𝜍	(𝜍	NOUN
cana-535	54	56	)	)	PUNCT
cana-535	54	57	,	,	PUNCT
cana-535	54	58	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	54	59	−	−	PROPN
cana-535	54	60	𝜍	𝜍	NOUN
cana-535	54	61	)	)	PUNCT
cana-535	54	62	≤	≤	NUM
cana-535	54	63	⋁{𝛾(𝑞	⋁{𝛾(𝑞	NUM
cana-535	54	64	)	)	PUNCT
cana-535	54	65	,	,	PUNCT
cana-535	54	66	𝛾(𝜍	𝛾(𝜍	PROPN
cana-535	54	67	)	)	PUNCT
cana-535	54	68	}	}	PUNCT
cana-535	54	69	∀	∀	PUNCT
cana-535	55	1	𝑞	𝑞	NOUN
cana-535	55	2	,	,	PUNCT
cana-535	55	3	𝜍	𝜍	PRON
cana-535	55	4	∈	∈	ADJ
cana-535	55	5	𝑁	𝑁	PROPN
cana-535	55	6	(	(	PUNCT
cana-535	55	7	𝑖𝑖)	𝑖𝑖)	PROPN
cana-535	55	8	�	�	PROPN
cana-535	55	9	̃	̃	NOUN
cana-535	55	10	�	�	NOUN
cana-535	55	11	(𝑞𝜍	(𝑞𝜍	PUNCT
cana-535	55	12	)	)	PUNCT
cana-535	55	13	⊇	⊇	PROPN
cana-535	55	14	�	�	PROPN
cana-535	55	15	̃	̃	PROPN
cana-535	55	16	�	�	NOUN
cana-535	55	17	(𝑞	(𝑞	NOUN
cana-535	55	18	)	)	PUNCT
cana-535	55	19	∩	∩	PROPN
cana-535	55	20	�	�	PROPN
cana-535	55	21	̃	̃	PROPN
cana-535	55	22	�	�	PROPN
cana-535	55	23	(𝜍	(𝜍	NOUN
cana-535	55	24	)	)	PUNCT
cana-535	55	25	,	,	PUNCT
cana-535	55	26	𝛾(𝑞𝜍	𝛾(𝑞𝜍	NOUN
cana-535	55	27	)	)	PUNCT
cana-535	55	28	≤	≤	NUM
cana-535	55	29	⋁{𝛾(𝑞	⋁{𝛾(𝑞	NUM
cana-535	55	30	)	)	PUNCT
cana-535	55	31	,	,	PUNCT
cana-535	55	32	𝛾(𝜍	𝛾(𝜍	PROPN
cana-535	55	33	)	)	PUNCT
cana-535	55	34	}	}	PUNCT
cana-535	55	35	∀	∀	PUNCT
cana-535	56	1	𝑞	𝑞	NOUN
cana-535	56	2	,	,	PUNCT
cana-535	56	3	𝜍	𝜍	ADP
cana-535	56	4	∈	∈	NOUN
cana-535	56	5	𝑁.	𝑁.	PROPN
cana-535	56	6	3	3	NUM
cana-535	56	7	.	.	PUNCT
cana-535	56	8	main	main	ADJ
cana-535	56	9	results	result	NOUN
cana-535	56	10	in	in	ADP
cana-535	56	11	this	this	PRON
cana-535	56	12	,	,	PUNCT
cana-535	56	13	we	we	PRON
cana-535	56	14	introduce	introduce	VERB
cana-535	56	15	hybrid	hybrid	ADJ
cana-535	56	16	coset	coset	NOUN
cana-535	56	17	of	of	ADP
cana-535	56	18	a	a	DET
cana-535	56	19	nearring	nearre	VERB
cana-535	56	20	(	(	PUNCT
cana-535	56	21	hcnr	hcnr	NOUN
cana-535	56	22	)	)	PUNCT
cana-535	56	23	and	and	CCONJ
cana-535	56	24	attain	attain	VERB
cana-535	56	25	some	some	PRON
cana-535	56	26	of	of	ADP
cana-535	56	27	the	the	DET
cana-535	56	28	properties	property	NOUN
cana-535	56	29	of	of	ADP
cana-535	56	30	hybrid	hybrid	ADJ
cana-535	56	31	coset	coset	NOUN
cana-535	56	32	of	of	ADP
cana-535	56	33	a	a	DET
cana-535	56	34	nearring	nearring	NOUN
cana-535	56	35	.	.	PUNCT
cana-535	57	1	definition	definition	NOUN
cana-535	57	2	3.1	3.1	NUM
cana-535	57	3	:	:	PUNCT
cana-535	57	4	let	let	VERB
cana-535	57	5	n	n	PRON
cana-535	57	6	be	be	AUX
cana-535	57	7	a	a	DET
cana-535	57	8	nr	nr	NOUN
cana-535	57	9	.	.	PUNCT
cana-535	58	1	a	a	DET
cana-535	58	2	hs	hs	PROPN
cana-535	58	3	�	�	PROPN
cana-535	58	4	̃	̃	PROPN
cana-535	58	5	�	�	PROPN
cana-535	58	6	𝛾	𝛾	NOUN
cana-535	58	7	in	in	ADP
cana-535	58	8	𝑁	𝑁	PROPN
cana-535	58	9	over	over	ADP
cana-535	58	10	𝑈	𝑈	PROPN
cana-535	58	11	is	be	AUX
cana-535	58	12	entitled	entitle	VERB
cana-535	58	13	a	a	DET
cana-535	58	14	hinr	hinr	ADJ
cana-535	58	15	if	if	SCONJ
cana-535	58	16	the	the	DET
cana-535	58	17	following	follow	VERB
cana-535	58	18	conditions	condition	NOUN
cana-535	58	19	clutch	clutch	VERB
cana-535	58	20	.	.	PUNCT
cana-535	59	1	(	(	PUNCT
cana-535	59	2	𝑖	𝑖	X
cana-535	59	3	)	)	PUNCT
cana-535	59	4	�	�	PROPN
cana-535	59	5	̃	̃	PROPN
cana-535	59	6	�	�	PROPN
cana-535	59	7	(𝑞	(𝑞	NOUN
cana-535	59	8	−	−	NOUN
cana-535	59	9	𝜍	𝜍	NOUN
cana-535	59	10	)	)	PUNCT
cana-535	59	11	⊇	⊇	PROPN
cana-535	59	12	�	�	PROPN
cana-535	59	13	̃	̃	PROPN
cana-535	59	14	�	�	NOUN
cana-535	59	15	(𝑞	(𝑞	NOUN
cana-535	59	16	)	)	PUNCT
cana-535	59	17	∩	∩	PROPN
cana-535	59	18	�	�	PROPN
cana-535	59	19	̃	̃	PROPN
cana-535	59	20	�	�	PROPN
cana-535	59	21	(𝜍	(𝜍	NOUN
cana-535	59	22	)	)	PUNCT
cana-535	59	23	,	,	PUNCT
cana-535	59	24	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	59	25	−	−	PROPN
cana-535	59	26	𝜍	𝜍	NOUN
cana-535	59	27	)	)	PUNCT
cana-535	59	28	≤	≤	NUM
cana-535	59	29	⋁{𝛾(𝑞	⋁{𝛾(𝑞	NUM
cana-535	59	30	)	)	PUNCT
cana-535	59	31	,	,	PUNCT
cana-535	59	32	𝛾(𝜍	𝛾(𝜍	PROPN
cana-535	59	33	)	)	PUNCT
cana-535	59	34	}	}	PUNCT
cana-535	59	35	∀	∀	PUNCT
cana-535	60	1	𝑞	𝑞	NOUN
cana-535	60	2	,	,	PUNCT
cana-535	60	3	𝜍	𝜍	PRON
cana-535	60	4	∈	∈	ADJ
cana-535	60	5	𝑁	𝑁	PROPN
cana-535	60	6	(	(	PUNCT
cana-535	60	7	𝑖𝑖	𝑖𝑖	ADJ
cana-535	60	8	)	)	PUNCT
cana-535	60	9	�	�	PROPN
cana-535	60	10	̃	̃	PROPN
cana-535	60	11	�	�	NOUN
cana-535	60	12	(𝑞𝜍	(𝑞𝜍	SYM
cana-535	60	13	)	)	PUNCT
cana-535	60	14	⊇	⊇	PROPN
cana-535	60	15	�	�	PROPN
cana-535	60	16	̃	̃	PROPN
cana-535	60	17	�	�	NOUN
cana-535	60	18	(𝑞	(𝑞	NOUN
cana-535	60	19	)	)	PUNCT
cana-535	60	20	∩	∩	PROPN
cana-535	60	21	�	�	PROPN
cana-535	60	22	̃	̃	PROPN
cana-535	60	23	�	�	PROPN
cana-535	60	24	(𝜍	(𝜍	NOUN
cana-535	60	25	)	)	PUNCT
cana-535	60	26	,	,	PUNCT
cana-535	60	27	𝛾(𝑞𝜍	𝛾(𝑞𝜍	NOUN
cana-535	60	28	)	)	PUNCT
cana-535	60	29	≤	≤	NUM
cana-535	60	30	⋁{𝛾(𝑞	⋁{𝛾(𝑞	NUM
cana-535	60	31	)	)	PUNCT
cana-535	60	32	,	,	PUNCT
cana-535	60	33	𝛾(𝜍	𝛾(𝜍	PROPN
cana-535	60	34	)	)	PUNCT
cana-535	60	35	}	}	PUNCT
cana-535	60	36	∀	∀	PUNCT
cana-535	61	1	𝑞	𝑞	NOUN
cana-535	61	2	,	,	PUNCT
cana-535	61	3	𝜍	𝜍	PRON
cana-535	61	4	∈	∈	ADJ
cana-535	61	5	𝑁	𝑁	PROPN
cana-535	61	6	(	(	PUNCT
cana-535	61	7	𝑖𝑖𝑖)	𝑖𝑖𝑖)	PROPN
cana-535	61	8	�	�	PROPN
cana-535	61	9	̃	̃	PROPN
cana-535	61	10	�	�	NOUN
cana-535	61	11	(𝑞	(𝑞	NOUN
cana-535	61	12	+	+	CCONJ
cana-535	61	13	𝜍	𝜍	ADP
cana-535	61	14	−	−	DET
cana-535	61	15	𝑞	𝑞	PROPN
cana-535	61	16	)	)	PUNCT
cana-535	61	17	⊇	⊇	PROPN
cana-535	61	18	�	�	PROPN
cana-535	61	19	̃	̃	PROPN
cana-535	61	20	�	�	PROPN
cana-535	61	21	(𝜍	(𝜍	NOUN
cana-535	61	22	)	)	PUNCT
cana-535	61	23	,	,	PUNCT
cana-535	61	24	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	61	25	+	+	CCONJ
cana-535	61	26	𝜍	𝜍	ADP
cana-535	61	27	−	−	PRON
cana-535	61	28	𝑞	𝑞	NOUN
cana-535	61	29	)	)	PUNCT
cana-535	61	30	≤	≤	ADJ
cana-535	61	31	𝛾(𝜍	𝛾(𝜍	NOUN
cana-535	61	32	)	)	PUNCT
cana-535	61	33	∀	∀	PUNCT
cana-535	62	1	𝑞	𝑞	NOUN
cana-535	62	2	,	,	PUNCT
cana-535	62	3	𝜍	𝜍	PRON
cana-535	62	4	∈	∈	ADJ
cana-535	62	5	𝑁	𝑁	PROPN
cana-535	62	6	(	(	PUNCT
cana-535	62	7	𝑖𝑣)	𝑖𝑣)	PROPN
cana-535	62	8	�	�	PROPN
cana-535	62	9	̃	̃	PROPN
cana-535	62	10	�	�	NOUN
cana-535	62	11	(𝑞𝜍	(𝑞𝜍	PUNCT
cana-535	62	12	)	)	PUNCT
cana-535	62	13	⊇	⊇	PROPN
cana-535	62	14	�	�	PROPN
cana-535	62	15	̃	̃	PROPN
cana-535	62	16	�	�	PROPN
cana-535	62	17	(𝑞	(𝑞	NOUN
cana-535	62	18	)	)	PUNCT
cana-535	62	19	,	,	PUNCT
cana-535	62	20	𝛾(𝑞𝜍	𝛾(𝑞𝜍	NOUN
cana-535	62	21	)	)	PUNCT
cana-535	62	22	≤	≤	NOUN
cana-535	62	23	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	62	24	)	)	PUNCT
cana-535	62	25	∀	∀	PUNCT
cana-535	63	1	𝑞	𝑞	NOUN
cana-535	63	2	,	,	PUNCT
cana-535	63	3	𝜍	𝜍	PRON
cana-535	63	4	∈	∈	ADJ
cana-535	63	5	𝑁	𝑁	PROPN
cana-535	63	6	(	(	PUNCT
cana-535	63	7	𝑣)	𝑣)	NUM
cana-535	63	8	�	�	PROPN
cana-535	63	9	̃	̃	NOUN
cana-535	63	10	�	�	NOUN
cana-535	63	11	(𝜍(𝑞	(𝜍(𝑞	SYM
cana-535	63	12	+	+	NOUN
cana-535	63	13	𝑖	𝑖	X
cana-535	63	14	)	)	PUNCT
cana-535	63	15	−	−	PROPN
cana-535	63	16	𝜍𝑞	𝜍𝑞	PROPN
cana-535	63	17	)	)	PUNCT
cana-535	63	18	⊇	⊇	PROPN
cana-535	63	19	�	�	PROPN
cana-535	63	20	̃	̃	PROPN
cana-535	63	21	�	�	PROPN
cana-535	63	22	(𝑖	(𝑖	NOUN
cana-535	63	23	)	)	PUNCT
cana-535	63	24	,	,	PUNCT
cana-535	63	25	𝛾(𝜍(𝑞	𝛾(𝜍(𝑞	VERB
cana-535	63	26	+	+	SYM
cana-535	63	27	𝑖	𝑖	X
cana-535	63	28	)	)	PUNCT
cana-535	63	29	−	−	PROPN
cana-535	63	30	𝜍𝑞	𝜍𝑞	SYM
cana-535	63	31	)	)	PUNCT
cana-535	63	32	≤	≤	NOUN
cana-535	63	33	𝛾(𝑖	𝛾(𝑖	NOUN
cana-535	63	34	)	)	PUNCT
cana-535	63	35	∀	∀	PUNCT
cana-535	64	1	𝑞	𝑞	NOUN
cana-535	64	2	,	,	PUNCT
cana-535	64	3	𝜍	𝜍	PROPN
cana-535	64	4	,	,	PUNCT
cana-535	64	5	𝑖	𝑖	ADP
cana-535	64	6	∈	∈	PROPN
cana-535	64	7	𝑁.	𝑁.	PROPN
cana-535	65	1	if	if	SCONJ
cana-535	65	2	�	�	PROPN
cana-535	65	3	̃	̃	PROPN
cana-535	65	4	�	�	PROPN
cana-535	65	5	𝛾	𝛾	PROPN
cana-535	65	6	gratifies	gratify	VERB
cana-535	65	7	(	(	PUNCT
cana-535	65	8	𝑖	𝑖	NOUN
cana-535	65	9	)	)	PUNCT
cana-535	65	10	,	,	PUNCT
cana-535	65	11	(	(	PUNCT
cana-535	65	12	𝑖𝑖	𝑖𝑖	NOUN
cana-535	65	13	)	)	PUNCT
cana-535	65	14	,	,	PUNCT
cana-535	65	15	(	(	PUNCT
cana-535	65	16	𝑖𝑖𝑖	𝑖𝑖𝑖	NOUN
cana-535	65	17	)	)	PUNCT
cana-535	65	18	and	and	CCONJ
cana-535	65	19	(	(	PUNCT
cana-535	65	20	𝑖𝑣	𝑖𝑣	X
cana-535	65	21	)	)	PUNCT
cana-535	65	22	then	then	ADV
cana-535	65	23	�	�	PROPN
cana-535	65	24	̃	̃	PROPN
cana-535	65	25	�	�	NOUN
cana-535	65	26	𝛾	𝛾	NOUN
cana-535	65	27	is	be	AUX
cana-535	65	28	entitled	entitle	VERB
cana-535	65	29	a	a	DET
cana-535	65	30	right	right	ADJ
cana-535	65	31	hinr	hinr	NOUN
cana-535	65	32	of	of	ADP
cana-535	65	33	𝑁.	𝑁.	PROPN
cana-535	65	34	if	if	SCONJ
cana-535	65	35	�	�	PROPN
cana-535	65	36	̃	̃	PROPN
cana-535	65	37	�	�	PROPN
cana-535	65	38	𝛾	𝛾	PROPN
cana-535	65	39	gratifies	gratify	VERB
cana-535	65	40	(	(	PUNCT
cana-535	65	41	𝑖	𝑖	NOUN
cana-535	65	42	)	)	PUNCT
cana-535	65	43	,	,	PUNCT
cana-535	65	44	(	(	PUNCT
cana-535	65	45	𝑖𝑖	𝑖𝑖	NOUN
cana-535	65	46	)	)	PUNCT
cana-535	65	47	,	,	PUNCT
cana-535	65	48	(	(	PUNCT
cana-535	65	49	𝑖𝑖𝑖	𝑖𝑖𝑖	NOUN
cana-535	65	50	)	)	PUNCT
cana-535	65	51	and	and	CCONJ
cana-535	65	52	(	(	PUNCT
cana-535	65	53	𝑣	𝑣	X
cana-535	65	54	)	)	PUNCT
cana-535	65	55	then	then	ADV
cana-535	65	56	�	�	PROPN
cana-535	65	57	̃	̃	PROPN
cana-535	65	58	�	�	NOUN
cana-535	65	59	𝛾	𝛾	NOUN
cana-535	65	60	is	be	AUX
cana-535	65	61	entitled	entitle	VERB
cana-535	65	62	a	a	DET
cana-535	65	63	left	left	ADJ
cana-535	65	64	hinr	hinr	NOUN
cana-535	65	65	of	of	ADP
cana-535	65	66	𝑁.	𝑁.	PROPN
cana-535	65	67	example	example	NOUN
cana-535	65	68	3.2	3.2	NUM
cana-535	65	69	:	:	PUNCT
cana-535	65	70	let	let	VERB
cana-535	65	71	𝑁	𝑁	PROPN
cana-535	65	72	=	=	SYM
cana-535	65	73	{	{	PUNCT
cana-535	65	74	0	0	NUM
cana-535	65	75	,	,	PUNCT
cana-535	65	76	𝑎𝜏	𝑎𝜏	PROPN
cana-535	65	77	,	,	PUNCT
cana-535	65	78	𝑏𝜏	𝑏𝜏	PROPN
cana-535	65	79	,	,	PUNCT
cana-535	65	80	𝑐𝜏	𝑐𝜏	AUX
cana-535	65	81	}	}	PUNCT
cana-535	65	82	be	be	AUX
cana-535	65	83	a	a	DET
cana-535	65	84	set	set	NOUN
cana-535	65	85	with	with	ADP
cana-535	65	86	two	two	NUM
cana-535	65	87	binary	binary	ADJ
cana-535	65	88	operations	operation	NOUN
cana-535	65	89	‘	'	PUNCT
cana-535	65	90	+	+	ADJ
cana-535	65	91	’	'	PUNCT
cana-535	65	92	,	,	PUNCT
cana-535	65	93	‘	'	PUNCT
cana-535	65	94	.	.	PUNCT
cana-535	65	95	’	'	PUNCT
cana-535	66	1	as	as	SCONJ
cana-535	66	2	follows	follow	VERB
cana-535	66	3	+	+	X
cana-535	66	4	0	0	NUM
cana-535	66	5	𝑎𝜏	𝑎𝜏	VERB
cana-535	66	6	𝑏𝜏	𝑏𝜏	NOUN
cana-535	67	1	𝑐𝜏	𝑐𝜏	ADV
cana-535	67	2	0	0	NUM
cana-535	67	3	0	0	NUM
cana-535	67	4	𝑎𝜏	𝑎𝜏	VERB
cana-535	67	5	𝑏𝜏	𝑏𝜏	INTJ
cana-535	67	6	𝑐𝜏	𝑐𝜏	INTJ
cana-535	67	7	𝑎𝜏	𝑎𝜏	INTJ
cana-535	67	8	𝑎𝜏	𝑎𝜏	ADV
cana-535	67	9	0	0	NUM
cana-535	68	1	𝑐𝜏	𝑐𝜏	NOUN
cana-535	69	1	𝑏𝜏	𝑏𝜏	PRON
cana-535	70	1	𝑏𝜏	𝑏𝜏	INTJ
cana-535	71	1	𝑏𝜏	𝑏𝜏	INTJ
cana-535	72	1	𝑐𝜏	𝑐𝜏	INTJ
cana-535	72	2	0	0	NUM
cana-535	72	3	𝑎𝜏	𝑎𝜏	VERB
cana-535	72	4	𝑐𝜏	𝑐𝜏	INTJ
cana-535	72	5	𝑐𝜏	𝑐𝜏	INTJ
cana-535	72	6	𝑏𝜏	𝑏𝜏	NOUN
cana-535	72	7	𝑎𝜏	𝑎𝜏	ADJ
cana-535	72	8	0	0	NUM
cana-535	73	1	then	then	ADV
cana-535	73	2	(	(	PUNCT
cana-535	73	3	𝑁	𝑁	PROPN
cana-535	73	4	,	,	PUNCT
cana-535	73	5	+	+	NOUN
cana-535	73	6	,	,	PUNCT
cana-535	73	7	.	.	PUNCT
cana-535	73	8	)	)	PUNCT
cana-535	73	9	is	be	AUX
cana-535	73	10	a	a	DET
cana-535	73	11	nearring	nearring	NOUN
cana-535	73	12	.	.	PUNCT
cana-535	74	1	then	then	ADV
cana-535	74	2	the	the	DET
cana-535	74	3	hybrid	hybrid	ADJ
cana-535	74	4	structure	structure	NOUN
cana-535	74	5	�	�	PROPN
cana-535	74	6	̃	̃	PROPN
cana-535	74	7	�	�	NOUN
cana-535	74	8	𝛾	𝛾	NOUN
cana-535	74	9	in	in	ADP
cana-535	74	10	𝑁	𝑁	PROPN
cana-535	74	11	over	over	ADP
cana-535	74	12	𝑈	𝑈	NOUN
cana-535	74	13	=	=	SYM
cana-535	74	14	{	{	PUNCT
cana-535	74	15	𝑢1	𝑢1	PROPN
cana-535	74	16	,	,	PUNCT
cana-535	74	17	𝑢2	𝑢2	PROPN
cana-535	74	18	,	,	PUNCT
cana-535	74	19	𝑢3	𝑢3	PROPN
cana-535	74	20	,	,	PUNCT
cana-535	74	21	𝑢4	𝑢4	NOUN
cana-535	74	22	,	,	PUNCT
cana-535	74	23	𝑢5	𝑢5	PROPN
cana-535	74	24	}	}	PUNCT
cana-535	74	25	which	which	PRON
cana-535	74	26	is	be	AUX
cana-535	74	27	given	give	VERB
cana-535	74	28	below	below	ADP
cana-535	74	29	therefore	therefore	ADV
cana-535	74	30	(	(	PUNCT
cana-535	74	31	�	�	PROPN
cana-535	74	32	̃	̃	NOUN
cana-535	74	33	�	�	NOUN
cana-535	74	34	𝛾	𝛾	NOUN
cana-535	74	35	,	,	PUNCT
cana-535	74	36	𝑁	𝑁	NOUN
cana-535	74	37	)	)	PUNCT
cana-535	74	38	is	be	AUX
cana-535	74	39	a	a	DET
cana-535	74	40	hinr	hinr	NOUN
cana-535	74	41	.	.	PUNCT
cana-535	74	42	.	.	PUNCT
cana-535	75	1	0	0	PUNCT
cana-535	76	1	𝑎𝜏	𝑎𝜏	VERB
cana-535	76	2	𝑏𝜏	𝑏𝜏	PRON
cana-535	76	3	𝑐𝜏	𝑐𝜏	ADV
cana-535	76	4	0	0	NUM
cana-535	76	5	0	0	NUM
cana-535	76	6	0	0	NUM
cana-535	76	7	0	0	NUM
cana-535	76	8	0	0	NUM
cana-535	76	9	𝑎𝜏	𝑎𝜏	NOUN
cana-535	76	10	𝑎𝜏	𝑎𝜏	INTJ
cana-535	76	11	𝑎𝜏	𝑎𝜏	INTJ
cana-535	76	12	𝑎𝜏	𝑎𝜏	INTJ
cana-535	76	13	𝑎𝜏	𝑎𝜏	ADP
cana-535	76	14	𝑏𝜏	𝑏𝜏	INTJ
cana-535	77	1	𝑏𝜏	𝑏𝜏	INTJ
cana-535	78	1	𝑏𝜏	𝑏𝜏	INTJ
cana-535	79	1	𝑏𝜏	𝑏𝜏	INTJ
cana-535	80	1	𝑏𝜏	𝑏𝜏	INTJ
cana-535	81	1	𝑐𝜏	𝑐𝜏	INTJ
cana-535	82	1	𝑐𝜏	𝑐𝜏	INTJ
cana-535	83	1	𝑐𝜏	𝑐𝜏	INTJ
cana-535	84	1	𝑐𝜏	𝑐𝜏	INTJ
cana-535	84	2	𝑐𝜏	𝑐𝜏	ADP
cana-535	84	3	𝑁	𝑁	PROPN
cana-535	84	4	�	�	PROPN
cana-535	84	5	̃	̃	PROPN
cana-535	84	6	�	�	PROPN
cana-535	85	1	𝛾	𝛾	ADP
cana-535	85	2	0	0	NUM
cana-535	85	3	{	{	PUNCT
cana-535	85	4	𝑢1	𝑢1	PROPN
cana-535	85	5	,	,	PUNCT
cana-535	85	6	𝑢2	𝑢2	PROPN
cana-535	85	7	,	,	PUNCT
cana-535	85	8	𝑢3	𝑢3	PROPN
cana-535	85	9	,	,	PUNCT
cana-535	85	10	𝑢4	𝑢4	NOUN
cana-535	85	11	,	,	PUNCT
cana-535	85	12	𝑢5	𝑢5	NOUN
cana-535	85	13	}	}	PUNCT
cana-535	85	14	0.5	0.5	NUM
cana-535	85	15	𝑎𝜏	𝑎𝜏	NOUN
cana-535	85	16	{	{	PUNCT
cana-535	85	17	𝑢1	𝑢1	PROPN
cana-535	85	18	,	,	PUNCT
cana-535	85	19	𝑢5	𝑢5	PROPN
cana-535	85	20	}	}	PUNCT
cana-535	85	21	0.6	0.6	NUM
cana-535	85	22	𝑏𝜏	𝑏𝜏	PROPN
cana-535	85	23	{	{	PUNCT
cana-535	85	24	𝑢2	𝑢2	PROPN
cana-535	85	25	,	,	PUNCT
cana-535	85	26	𝑢3	𝑢3	PROPN
cana-535	85	27	,	,	PUNCT
cana-535	85	28	𝑢5	𝑢5	PROPN
cana-535	85	29	}	}	PUNCT
cana-535	85	30	0.7	0.7	NUM
cana-535	85	31	𝑐𝜏	𝑐𝜏	PROPN
cana-535	85	32	{	{	PUNCT
cana-535	85	33	𝑢2	𝑢2	PROPN
cana-535	85	34	,	,	PUNCT
cana-535	85	35	𝑢4	𝑢4	PROPN
cana-535	85	36	,	,	PUNCT
cana-535	85	37	𝑢5	𝑢5	NOUN
cana-535	85	38	}	}	PUNCT
cana-535	85	39	0.8	0.8	NUM
cana-535	85	40	communications	communication	NOUN
cana-535	85	41	on	on	ADP
cana-535	85	42	applied	apply	VERB
cana-535	85	43	nonlinear	nonlinear	ADJ
cana-535	85	44	analysis	analysis	NOUN
cana-535	85	45	issn	issn	NOUN
cana-535	85	46	:	:	PUNCT
cana-535	85	47	1074	1074	NUM
cana-535	85	48	-	-	PUNCT
cana-535	85	49	133x	133x	NUM
cana-535	85	50	vol	vol	NOUN
cana-535	85	51	31	31	NUM
cana-535	85	52	no	no	NOUN
cana-535	85	53	.	.	NOUN
cana-535	85	54	2	2	NUM
cana-535	85	55	(	(	PUNCT
cana-535	85	56	2024	2024	NUM
cana-535	85	57	)	)	PUNCT
cana-535	85	58	208	208	NUM
cana-535	85	59	https://internationalpubls.com	https://internationalpubls.com	X
cana-535	85	60	definition	definition	NOUN
cana-535	85	61	3.3	3.3	NUM
cana-535	85	62	:	:	PUNCT
cana-535	85	63	let	let	VERB
cana-535	85	64	�	�	PROPN
cana-535	85	65	̃	̃	PROPN
cana-535	85	66	�	�	PROPN
cana-535	85	67	𝛾	𝛾	NOUN
cana-535	85	68	be	be	AUX
cana-535	85	69	a	a	DET
cana-535	85	70	hinr	hinr	NOUN
cana-535	85	71	of	of	ADP
cana-535	85	72	𝑁	𝑁	PROPN
cana-535	85	73	over	over	ADP
cana-535	85	74	𝑈	𝑈	PROPN
cana-535	85	75	and	and	CCONJ
cana-535	85	76	𝜍	𝜍	ADP
cana-535	85	77	∈	∈	PROPN
cana-535	85	78	𝑁.	𝑁.	PROPN
cana-535	85	79	then	then	ADV
cana-535	85	80	the	the	DET
cana-535	85	81	hybrid	hybrid	ADJ
cana-535	85	82	coset	coset	NOUN
cana-535	85	83	(	(	PUNCT
cana-535	85	84	or	or	CCONJ
cana-535	85	85	coset	coset	VERB
cana-535	85	86	)	)	PUNCT
cana-535	85	87	of	of	ADP
cana-535	85	88	�	�	PROPN
cana-535	85	89	̃	̃	PROPN
cana-535	85	90	�	�	NOUN
cana-535	85	91	𝛾	𝛾	NOUN
cana-535	85	92	is	be	AUX
cana-535	85	93	denoted	denote	VERB
cana-535	85	94	by	by	ADP
cana-535	85	95	𝜍	𝜍	PRON
cana-535	85	96	+	+	PROPN
cana-535	85	97	�	�	PROPN
cana-535	85	98	̃	̃	PROPN
cana-535	85	99	�	�	NOUN
cana-535	85	100	𝛾	𝛾	NOUN
cana-535	85	101	and	and	CCONJ
cana-535	85	102	is	be	AUX
cana-535	85	103	demarcated	demarcate	VERB
cana-535	85	104	by	by	ADP
cana-535	85	105	(	(	PUNCT
cana-535	85	106	𝜍	𝜍	PROPN
cana-535	85	107	+	+	PROPN
cana-535	85	108	�	�	PROPN
cana-535	85	109	̃	̃	PROPN
cana-535	85	110	�	�	NOUN
cana-535	85	111	)(𝑞	)(𝑞	NOUN
cana-535	85	112	)	)	PUNCT
cana-535	85	113	=	=	SYM
cana-535	85	114	�	�	PROPN
cana-535	85	115	̃	̃	PROPN
cana-535	85	116	�	�	PROPN
cana-535	85	117	(𝑞	(𝑞	NOUN
cana-535	85	118	−	−	NOUN
cana-535	85	119	𝜍	𝜍	NOUN
cana-535	85	120	)	)	PUNCT
cana-535	85	121	and	and	CCONJ
cana-535	85	122	(	(	PUNCT
cana-535	85	123	𝜍	𝜍	X
cana-535	85	124	+	+	X
cana-535	85	125	𝛾)(𝑞	𝛾)(𝑞	X
cana-535	85	126	)	)	PUNCT
cana-535	85	127	=	=	SYM
cana-535	85	128	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	85	129	−	−	PROPN
cana-535	85	130	𝜍	𝜍	NOUN
cana-535	85	131	)	)	PUNCT
cana-535	85	132	∀	∀	X
cana-535	86	1	𝑞	𝑞	X
cana-535	86	2	∈	∈	PROPN
cana-535	86	3	𝑁.	𝑁.	PROPN
cana-535	86	4	theorem	theorem	VERB
cana-535	86	5	3.4	3.4	NUM
cana-535	86	6	:	:	PUNCT
cana-535	86	7	let	let	VERB
cana-535	86	8	�	�	PROPN
cana-535	86	9	̃	̃	PROPN
cana-535	86	10	�	�	PROPN
cana-535	86	11	𝛾	𝛾	NOUN
cana-535	86	12	be	be	AUX
cana-535	86	13	a	a	DET
cana-535	86	14	hinr	hinr	NOUN
cana-535	86	15	of	of	ADP
cana-535	86	16	𝑁	𝑁	PROPN
cana-535	86	17	over	over	ADP
cana-535	86	18	𝑈	𝑈	PROPN
cana-535	86	19	and	and	CCONJ
cana-535	86	20	𝑞	𝑞	PROPN
cana-535	86	21	,	,	PUNCT
cana-535	86	22	𝜍	𝜍	ADP
cana-535	86	23	∈	∈	PROPN
cana-535	86	24	𝑁.	𝑁.	PROPN
cana-535	86	25	then	then	ADV
cana-535	86	26	𝑞	𝑞	PROPN
cana-535	86	27	+	+	PROPN
cana-535	86	28	�	�	PROPN
cana-535	86	29	̃	̃	PROPN
cana-535	86	30	�	�	NOUN
cana-535	86	31	𝛾	𝛾	NOUN
cana-535	86	32	=	=	SYM
cana-535	86	33	𝜍	𝜍	X
cana-535	86	34	+	+	PROPN
cana-535	86	35	�	�	PROPN
cana-535	86	36	̃	̃	PROPN
cana-535	86	37	�	�	NOUN
cana-535	86	38	𝛾	𝛾	NOUN
cana-535	86	39	if	if	SCONJ
cana-535	86	40	and	and	CCONJ
cana-535	86	41	only	only	ADV
cana-535	86	42	if	if	SCONJ
cana-535	86	43	�	�	PROPN
cana-535	86	44	̃	̃	PROPN
cana-535	86	45	�	�	PROPN
cana-535	86	46	(𝑞	(𝑞	NOUN
cana-535	86	47	−	−	NOUN
cana-535	86	48	𝜍	𝜍	NOUN
cana-535	86	49	)	)	PUNCT
cana-535	86	50	=	=	SYM
cana-535	86	51	�	�	PROPN
cana-535	86	52	̃	̃	PROPN
cana-535	86	53	�	�	PROPN
cana-535	86	54	(0	(0	X
cana-535	86	55	)	)	PUNCT
cana-535	86	56	and	and	CCONJ
cana-535	86	57	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	86	58	−	−	PROPN
cana-535	86	59	𝜍	𝜍	NOUN
cana-535	86	60	)	)	PUNCT
cana-535	86	61	=	=	PUNCT
cana-535	86	62	𝛾(0	𝛾(0	PROPN
cana-535	86	63	)	)	PUNCT
cana-535	86	64	.	.	PUNCT
cana-535	87	1	proof	proof	NOUN
cana-535	87	2	:	:	PUNCT
cana-535	87	3	let	let	VERB
cana-535	87	4	𝑞	𝑞	PRON
cana-535	87	5	,	,	PUNCT
cana-535	87	6	𝜍	𝜍	ADP
cana-535	87	7	∈	∈	PROPN
cana-535	87	8	𝑁.	𝑁.	PROPN
cana-535	87	9	suppose	suppose	VERB
cana-535	87	10	that	that	SCONJ
cana-535	87	11	𝑞	𝑞	PROPN
cana-535	87	12	+	+	PROPN
cana-535	87	13	�	�	PROPN
cana-535	87	14	̃	̃	PROPN
cana-535	87	15	�	�	NOUN
cana-535	87	16	𝛾	𝛾	NOUN
cana-535	87	17	=	=	SYM
cana-535	87	18	𝜍	𝜍	X
cana-535	87	19	+	+	PROPN
cana-535	87	20	�	�	PROPN
cana-535	87	21	̃	̃	PROPN
cana-535	87	22	�	�	NOUN
cana-535	87	23	𝛾.	𝛾.	NOUN
cana-535	87	24	then	then	ADV
cana-535	87	25	�	�	PROPN
cana-535	87	26	̃	̃	PROPN
cana-535	87	27	�	�	PROPN
cana-535	87	28	(𝑞	(𝑞	NOUN
cana-535	87	29	−	−	NOUN
cana-535	87	30	𝜍	𝜍	NOUN
cana-535	87	31	)	)	PUNCT
cana-535	87	32	=	=	SYM
cana-535	87	33	(	(	PUNCT
cana-535	87	34	𝜍	𝜍	ADP
cana-535	87	35	+	+	PROPN
cana-535	87	36	�	�	PROPN
cana-535	87	37	̃	̃	PROPN
cana-535	87	38	�	�	NOUN
cana-535	87	39	)(𝑞	)(𝑞	NOUN
cana-535	87	40	)	)	PUNCT
cana-535	88	1	=	=	PRON
cana-535	88	2	(	(	PUNCT
cana-535	88	3	𝑞	𝑞	PROPN
cana-535	88	4	+	+	PROPN
cana-535	88	5	�	�	PROPN
cana-535	88	6	̃	̃	PROPN
cana-535	88	7	�	�	NOUN
cana-535	88	8	)(𝑞	)(𝑞	NOUN
cana-535	88	9	)	)	PUNCT
cana-535	88	10	=	=	SYM
cana-535	88	11	�	�	PROPN
cana-535	88	12	̃	̃	PROPN
cana-535	88	13	�	�	PROPN
cana-535	88	14	(𝑞	(𝑞	NOUN
cana-535	88	15	−	−	NOUN
cana-535	88	16	𝑞	𝑞	NOUN
cana-535	88	17	)	)	PUNCT
cana-535	88	18	=	=	SYM
cana-535	88	19	�	�	PROPN
cana-535	88	20	̃	̃	PROPN
cana-535	88	21	�	�	PROPN
cana-535	88	22	(0	(0	X
cana-535	88	23	)	)	PUNCT
cana-535	88	24	and	and	CCONJ
cana-535	88	25	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	88	26	−	−	PROPN
cana-535	88	27	𝜍	𝜍	NOUN
cana-535	88	28	)	)	PUNCT
cana-535	88	29	=	=	SYM
cana-535	88	30	(	(	PUNCT
cana-535	88	31	𝜍	𝜍	X
cana-535	88	32	+	+	X
cana-535	88	33	𝛾)(𝑞	𝛾)(𝑞	NOUN
cana-535	88	34	)	)	PUNCT
cana-535	88	35	=	=	SYM
cana-535	88	36	(	(	PUNCT
cana-535	88	37	𝑞	𝑞	X
cana-535	88	38	+	+	CCONJ
cana-535	88	39	𝛾)(𝑞	𝛾)(𝑞	X
cana-535	88	40	)	)	PUNCT
cana-535	88	41	=	=	SYM
cana-535	88	42	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	88	43	−	−	ADP
cana-535	88	44	𝑞	𝑞	NOUN
cana-535	88	45	)	)	PUNCT
cana-535	88	46	=	=	PUNCT
cana-535	88	47	𝛾(0	𝛾(0	PROPN
cana-535	88	48	)	)	PUNCT
cana-535	88	49	.	.	PUNCT
cana-535	89	1	conversely	conversely	ADV
cana-535	89	2	,	,	PUNCT
cana-535	89	3	suppose	suppose	VERB
cana-535	89	4	that	that	SCONJ
cana-535	89	5	�	�	PROPN
cana-535	89	6	̃	̃	PROPN
cana-535	89	7	�	�	PROPN
cana-535	89	8	(𝑞	(𝑞	NOUN
cana-535	89	9	−	−	NOUN
cana-535	89	10	𝜍	𝜍	NOUN
cana-535	89	11	)	)	PUNCT
cana-535	89	12	=	=	SYM
cana-535	89	13	�	�	PROPN
cana-535	89	14	̃	̃	PROPN
cana-535	89	15	�	�	PROPN
cana-535	89	16	(0	(0	X
cana-535	89	17	)	)	PUNCT
cana-535	89	18	and	and	CCONJ
cana-535	89	19	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	89	20	−	−	PROPN
cana-535	89	21	𝜍	𝜍	NOUN
cana-535	89	22	)	)	PUNCT
cana-535	89	23	=	=	PUNCT
cana-535	89	24	𝛾(0	𝛾(0	PROPN
cana-535	89	25	)	)	PUNCT
cana-535	89	26	.	.	PUNCT
cana-535	90	1	for	for	ADP
cana-535	90	2	every	every	DET
cana-535	90	3	𝜅	𝜅	PRON
cana-535	90	4	∈	∈	PROPN
cana-535	90	5	𝑁	𝑁	PROPN
cana-535	90	6	,	,	PUNCT
cana-535	90	7	we	we	PRON
cana-535	90	8	have	have	VERB
cana-535	90	9	(	(	PUNCT
cana-535	90	10	𝑞	𝑞	PROPN
cana-535	90	11	+	+	PROPN
cana-535	90	12	�	�	PROPN
cana-535	90	13	̃	̃	PROPN
cana-535	90	14	�	�	NOUN
cana-535	90	15	)(𝜅	)(𝜅	PUNCT
cana-535	90	16	)	)	PUNCT
cana-535	90	17	=	=	PUNCT
cana-535	90	18	�	�	PROPN
cana-535	90	19	̃	̃	PROPN
cana-535	90	20	�	�	PROPN
cana-535	90	21	(𝜅	(𝜅	PROPN
cana-535	90	22	−	−	PROPN
cana-535	90	23	𝑞	𝑞	NOUN
cana-535	90	24	)	)	PUNCT
cana-535	90	25	=	=	SYM
cana-535	90	26	�	�	PROPN
cana-535	90	27	̃	̃	PROPN
cana-535	90	28	�	�	PROPN
cana-535	90	29	(𝜅	(𝜅	PROPN
cana-535	90	30	−	−	NOUN
cana-535	90	31	𝜍	𝜍	PROPN
cana-535	91	1	+	+	X
cana-535	91	2	𝜍	𝜍	ADP
cana-535	91	3	−	−	PRON
cana-535	91	4	𝑞	𝑞	NOUN
cana-535	91	5	)	)	PUNCT
cana-535	91	6	=	=	SYM
cana-535	91	7	�	�	PROPN
cana-535	91	8	̃	̃	PROPN
cana-535	91	9	�	�	PROPN
cana-535	91	10	[(𝜅	[(𝜅	X
cana-535	91	11	−	−	PROPN
cana-535	91	12	𝜍	𝜍	X
cana-535	91	13	)	)	PUNCT
cana-535	92	1	+	+	CCONJ
cana-535	92	2	(	(	PUNCT
cana-535	92	3	𝜍	𝜍	PART
cana-535	92	4	−	−	PROPN
cana-535	92	5	𝑞	𝑞	PROPN
cana-535	92	6	)	)	PUNCT
cana-535	92	7	]	]	PUNCT
cana-535	92	8	⊇	⊇	PROPN
cana-535	92	9	�	�	PROPN
cana-535	92	10	̃	̃	PROPN
cana-535	92	11	�	�	PROPN
cana-535	92	12	(𝜅	(𝜅	PROPN
cana-535	92	13	−	−	PROPN
cana-535	92	14	𝜍	𝜍	NOUN
cana-535	92	15	)	)	PUNCT
cana-535	92	16	∩	∩	ADJ
cana-535	92	17	�	�	PROPN
cana-535	92	18	̃	̃	PROPN
cana-535	92	19	�	�	PROPN
cana-535	92	20	(𝜍	(𝜍	NOUN
cana-535	92	21	−	−	PUNCT
cana-535	92	22	𝑞	𝑞	NOUN
cana-535	92	23	)	)	PUNCT
cana-535	92	24	=	=	SYM
cana-535	92	25	�	�	PROPN
cana-535	92	26	̃	̃	PROPN
cana-535	92	27	�	�	PROPN
cana-535	92	28	(𝜅	(𝜅	PROPN
cana-535	92	29	−	−	PROPN
cana-535	92	30	𝜍	𝜍	NOUN
cana-535	92	31	)	)	PUNCT
cana-535	92	32	∩	∩	ADJ
cana-535	92	33	�	�	PROPN
cana-535	92	34	̃	̃	PROPN
cana-535	92	35	�	�	PROPN
cana-535	92	36	(𝑞	(𝑞	NOUN
cana-535	92	37	−	−	NOUN
cana-535	92	38	𝜍	𝜍	NOUN
cana-535	92	39	)	)	PUNCT
cana-535	92	40	=	=	SYM
cana-535	92	41	�	�	PROPN
cana-535	92	42	̃	̃	PROPN
cana-535	92	43	�	�	PROPN
cana-535	92	44	(𝜅	(𝜅	PROPN
cana-535	92	45	−	−	PROPN
cana-535	92	46	𝜍	𝜍	NOUN
cana-535	92	47	)	)	PUNCT
cana-535	92	48	∩	∩	ADJ
cana-535	92	49	�	�	PROPN
cana-535	92	50	̃	̃	PROPN
cana-535	92	51	�	�	PROPN
cana-535	92	52	(0	(0	X
cana-535	92	53	)	)	PUNCT
cana-535	92	54	=	=	SYM
cana-535	92	55	�	�	PROPN
cana-535	92	56	̃	̃	PROPN
cana-535	92	57	�	�	PROPN
cana-535	92	58	(𝜅	(𝜅	PROPN
cana-535	92	59	−	−	PROPN
cana-535	92	60	𝜍	𝜍	NOUN
cana-535	92	61	)	)	PUNCT
cana-535	92	62	=	=	SYM
cana-535	92	63	(	(	PUNCT
cana-535	92	64	𝜍	𝜍	ADP
cana-535	92	65	+	+	PROPN
cana-535	92	66	�	�	PROPN
cana-535	92	67	̃	̃	PROPN
cana-535	92	68	�	�	NOUN
cana-535	92	69	)(𝜅	)(𝜅	NUM
cana-535	92	70	)	)	PUNCT
cana-535	93	1	and	and	CCONJ
cana-535	93	2	(	(	PUNCT
cana-535	93	3	𝑞	𝑞	X
cana-535	93	4	+	+	ADJ
cana-535	93	5	𝛾)(𝜅	𝛾)(𝜅	PUNCT
cana-535	93	6	)	)	PUNCT
cana-535	94	1	=	=	SYM
cana-535	94	2	𝛾(𝜅	𝛾(𝜅	PROPN
cana-535	94	3	−	−	PROPN
cana-535	94	4	𝑞	𝑞	NOUN
cana-535	94	5	)	)	PUNCT
cana-535	94	6	=	=	SYM
cana-535	94	7	𝛾(𝜅	𝛾(𝜅	PROPN
cana-535	94	8	−	−	X
cana-535	94	9	𝜍	𝜍	PROPN
cana-535	94	10	+	+	X
cana-535	94	11	𝜍	𝜍	ADP
cana-535	94	12	−	−	PRON
cana-535	94	13	𝑞	𝑞	SYM
cana-535	94	14	)	)	PUNCT
cana-535	94	15	=	=	SYM
cana-535	94	16	𝛾[(𝜅	𝛾[(𝜅	NOUN
cana-535	94	17	−	−	PROPN
cana-535	94	18	𝜍	𝜍	X
cana-535	94	19	)	)	PUNCT
cana-535	94	20	+	+	CCONJ
cana-535	94	21	(	(	PUNCT
cana-535	94	22	𝜍	𝜍	PART
cana-535	94	23	−	−	PROPN
cana-535	94	24	𝑞	𝑞	PROPN
cana-535	94	25	)	)	PUNCT
cana-535	94	26	]	]	PUNCT
cana-535	94	27	≤∨	≤∨	VERB
cana-535	94	28	{	{	PUNCT
cana-535	94	29	𝛾(𝜅	𝛾(𝜅	PROPN
cana-535	94	30	−	−	PROPN
cana-535	94	31	𝜍	𝜍	X
cana-535	94	32	)	)	PUNCT
cana-535	94	33	,	,	PUNCT
cana-535	94	34	𝛾(𝜍	𝛾(𝜍	PROPN
cana-535	94	35	−	−	PROPN
cana-535	94	36	𝑞	𝑞	NOUN
cana-535	94	37	)	)	PUNCT
cana-535	94	38	}	}	PUNCT
cana-535	94	39	=	=	X
cana-535	94	40	∨	∨	X
cana-535	94	41	{	{	PUNCT
cana-535	94	42	𝛾(𝜅	𝛾(𝜅	PROPN
cana-535	94	43	−	−	PROPN
cana-535	94	44	𝜍	𝜍	NOUN
cana-535	94	45	)	)	PUNCT
cana-535	94	46	,	,	PUNCT
cana-535	94	47	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	94	48	−	−	PROPN
cana-535	94	49	𝜍	𝜍	NOUN
cana-535	94	50	)	)	PUNCT
cana-535	94	51	}	}	PUNCT
cana-535	94	52	=	=	X
cana-535	94	53	∨	∨	X
cana-535	94	54	{	{	PUNCT
cana-535	94	55	𝛾(𝜅	𝛾(𝜅	PROPN
cana-535	94	56	−	−	PROPN
cana-535	94	57	𝜍	𝜍	NOUN
cana-535	94	58	)	)	PUNCT
cana-535	94	59	,	,	PUNCT
cana-535	94	60	𝛾(0	𝛾(0	PROPN
cana-535	94	61	)	)	PUNCT
cana-535	94	62	}	}	PUNCT
cana-535	95	1	=	=	SYM
cana-535	95	2	𝛾(𝜅	𝛾(𝜅	PROPN
cana-535	95	3	−	−	PROPN
cana-535	95	4	𝜍	𝜍	NOUN
cana-535	95	5	)	)	PUNCT
cana-535	95	6	=	=	SYM
cana-535	95	7	(	(	PUNCT
cana-535	95	8	𝜍	𝜍	X
cana-535	95	9	+	+	ADJ
cana-535	95	10	𝛾)(𝜅	𝛾)(𝜅	NOUN
cana-535	95	11	)	)	PUNCT
cana-535	95	12	.	.	PUNCT
cana-535	96	1	thus	thus	ADV
cana-535	96	2	𝑞	𝑞	X
cana-535	96	3	+	+	PROPN
cana-535	96	4	�	�	PROPN
cana-535	96	5	̃	̃	PROPN
cana-535	96	6	�	�	PROPN
cana-535	96	7	⊇	⊇	PROPN
cana-535	96	8	𝜍	𝜍	PROPN
cana-535	96	9	+	+	PROPN
cana-535	96	10	�	�	PROPN
cana-535	96	11	̃	̃	PROPN
cana-535	96	12	�	�	PROPN
cana-535	96	13	and	and	CCONJ
cana-535	96	14	(	(	PUNCT
cana-535	96	15	𝑞	𝑞	X
cana-535	96	16	+	+	NOUN
cana-535	96	17	𝛾	𝛾	NOUN
cana-535	96	18	)	)	PUNCT
cana-535	96	19	≤	≤	NOUN
cana-535	96	20	(	(	PUNCT
cana-535	96	21	𝜍	𝜍	X
cana-535	96	22	+	+	ADJ
cana-535	96	23	𝛾	𝛾	NOUN
cana-535	96	24	)	)	PUNCT
cana-535	96	25	.	.	PUNCT
cana-535	97	1	now	now	ADV
cana-535	97	2	,	,	PUNCT
cana-535	97	3	(	(	PUNCT
cana-535	97	4	𝜍	𝜍	X
cana-535	97	5	+	+	PROPN
cana-535	97	6	�	�	PROPN
cana-535	97	7	̃	̃	PROPN
cana-535	97	8	�	�	NOUN
cana-535	97	9	)(𝜅	)(𝜅	PUNCT
cana-535	97	10	)	)	PUNCT
cana-535	97	11	=	=	PUNCT
cana-535	97	12	�	�	PROPN
cana-535	97	13	̃	̃	PROPN
cana-535	97	14	�	�	PROPN
cana-535	97	15	(𝜅	(𝜅	PROPN
cana-535	97	16	−	−	PROPN
cana-535	97	17	𝜍	𝜍	NOUN
cana-535	97	18	)	)	PUNCT
cana-535	97	19	=	=	SYM
cana-535	97	20	�	�	PROPN
cana-535	97	21	̃	̃	PROPN
cana-535	97	22	�	�	PROPN
cana-535	97	23	(𝜅	(𝜅	PROPN
cana-535	97	24	−	−	PROPN
cana-535	97	25	𝑞	𝑞	X
cana-535	97	26	+	+	NOUN
cana-535	97	27	𝑞	𝑞	X
cana-535	97	28	−	−	NOUN
cana-535	97	29	𝜍	𝜍	NOUN
cana-535	97	30	)	)	PUNCT
cana-535	97	31	=	=	SYM
cana-535	97	32	�	�	PROPN
cana-535	97	33	̃	̃	PROPN
cana-535	97	34	�	�	PROPN
cana-535	97	35	[(𝜅	[(𝜅	X
cana-535	97	36	−	−	X
cana-535	97	37	𝑞	𝑞	SYM
cana-535	97	38	)	)	PUNCT
cana-535	98	1	+	+	CCONJ
cana-535	98	2	(	(	PUNCT
cana-535	98	3	𝑞	𝑞	X
cana-535	98	4	−	−	PROPN
cana-535	98	5	𝜍	𝜍	X
cana-535	98	6	)	)	PUNCT
cana-535	98	7	]	]	PUNCT
cana-535	98	8	⊇	⊇	PROPN
cana-535	98	9	�	�	PROPN
cana-535	98	10	̃	̃	PROPN
cana-535	98	11	�	�	PROPN
cana-535	98	12	(𝜅	(𝜅	PROPN
cana-535	98	13	−	−	PROPN
cana-535	98	14	𝑞	𝑞	NOUN
cana-535	98	15	)	)	PUNCT
cana-535	98	16	∩	∩	ADJ
cana-535	98	17	�	�	PROPN
cana-535	98	18	̃	̃	PROPN
cana-535	98	19	�	�	PROPN
cana-535	98	20	(𝑞	(𝑞	NOUN
cana-535	98	21	−	−	NOUN
cana-535	98	22	𝜍	𝜍	NOUN
cana-535	98	23	)	)	PUNCT
cana-535	98	24	=	=	SYM
cana-535	98	25	�	�	PROPN
cana-535	98	26	̃	̃	PROPN
cana-535	98	27	�	�	PROPN
cana-535	98	28	(𝜅	(𝜅	PROPN
cana-535	98	29	−	−	PROPN
cana-535	98	30	𝑞	𝑞	NOUN
cana-535	98	31	)	)	PUNCT
cana-535	98	32	∩	∩	ADJ
cana-535	98	33	�	�	PROPN
cana-535	98	34	̃	̃	PROPN
cana-535	98	35	�	�	PROPN
cana-535	98	36	(𝑞	(𝑞	NOUN
cana-535	98	37	−	−	NOUN
cana-535	98	38	𝜍	𝜍	NOUN
cana-535	98	39	)	)	PUNCT
cana-535	98	40	=	=	SYM
cana-535	98	41	�	�	PROPN
cana-535	98	42	̃	̃	PROPN
cana-535	98	43	�	�	PROPN
cana-535	98	44	(𝜅	(𝜅	PROPN
cana-535	98	45	−	−	PROPN
cana-535	98	46	𝑞	𝑞	NOUN
cana-535	98	47	)	)	PUNCT
cana-535	98	48	∩	∩	ADJ
cana-535	98	49	�	�	PROPN
cana-535	98	50	̃	̃	PROPN
cana-535	98	51	�	�	PROPN
cana-535	98	52	(0	(0	X
cana-535	98	53	)	)	PUNCT
cana-535	98	54	=	=	SYM
cana-535	98	55	�	�	PROPN
cana-535	98	56	̃	̃	PROPN
cana-535	98	57	�	�	PROPN
cana-535	98	58	(𝜅	(𝜅	PROPN
cana-535	98	59	−	−	PROPN
cana-535	98	60	𝑞	𝑞	NOUN
cana-535	98	61	)	)	PUNCT
cana-535	98	62	=	=	SYM
cana-535	98	63	(	(	PUNCT
cana-535	98	64	𝑞	𝑞	PROPN
cana-535	98	65	+	+	PROPN
cana-535	98	66	�	�	PROPN
cana-535	98	67	̃	̃	PROPN
cana-535	98	68	�	�	NOUN
cana-535	98	69	)(𝜅	)(𝜅	NUM
cana-535	98	70	)	)	PUNCT
cana-535	99	1	and	and	CCONJ
cana-535	99	2	(	(	PUNCT
cana-535	99	3	𝜍	𝜍	X
cana-535	99	4	+	+	ADJ
cana-535	99	5	𝛾)(𝜅	𝛾)(𝜅	PUNCT
cana-535	99	6	)	)	PUNCT
cana-535	99	7	=	=	SYM
cana-535	100	1	𝛾(𝜅	𝛾(𝜅	PROPN
cana-535	100	2	−	−	PROPN
cana-535	100	3	𝜍	𝜍	X
cana-535	100	4	)	)	PUNCT
cana-535	100	5	=	=	SYM
cana-535	101	1	𝛾(𝜅	𝛾(𝜅	ADJ
cana-535	101	2	−	−	PUNCT
cana-535	101	3	𝑞	𝑞	PROPN
cana-535	101	4	+	+	NOUN
cana-535	101	5	𝑞	𝑞	X
cana-535	101	6	−	−	NOUN
cana-535	101	7	𝜍	𝜍	X
cana-535	101	8	)	)	PUNCT
cana-535	101	9	=	=	SYM
cana-535	101	10	𝛾[(𝜅	𝛾[(𝜅	NOUN
cana-535	101	11	−	−	PROPN
cana-535	101	12	𝑞	𝑞	PROPN
cana-535	101	13	)	)	PUNCT
cana-535	101	14	+	+	CCONJ
cana-535	101	15	(	(	PUNCT
cana-535	101	16	𝑞	𝑞	X
cana-535	101	17	−	−	PROPN
cana-535	101	18	𝜍	𝜍	NOUN
cana-535	101	19	)	)	PUNCT
cana-535	101	20	]	]	PUNCT
cana-535	101	21	≤	≤	NUM
cana-535	101	22	∨	∨	NUM
cana-535	101	23	{	{	PUNCT
cana-535	101	24	𝛾(𝜅	𝛾(𝜅	PROPN
cana-535	101	25	−	−	PROPN
cana-535	101	26	𝑞	𝑞	PROPN
cana-535	101	27	)	)	PUNCT
cana-535	101	28	,	,	PUNCT
cana-535	101	29	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	101	30	−	−	PROPN
cana-535	101	31	𝜍	𝜍	NOUN
cana-535	101	32	)	)	PUNCT
cana-535	101	33	}	}	PUNCT
cana-535	102	1	=	=	X
cana-535	102	2	∨	∨	X
cana-535	102	3	{	{	PUNCT
cana-535	102	4	𝛾(𝜅	𝛾(𝜅	PROPN
cana-535	102	5	−	−	PROPN
cana-535	102	6	𝑞	𝑞	PROPN
cana-535	102	7	)	)	PUNCT
cana-535	102	8	,	,	PUNCT
cana-535	102	9	𝛾(0	𝛾(0	PROPN
cana-535	102	10	)	)	PUNCT
cana-535	102	11	}	}	PUNCT
cana-535	102	12	=	=	SYM
cana-535	103	1	𝛾(𝜅	𝛾(𝜅	PROPN
cana-535	103	2	−	−	PROPN
cana-535	103	3	𝑞	𝑞	NOUN
cana-535	103	4	)	)	PUNCT
cana-535	103	5	=	=	SYM
cana-535	103	6	(	(	PUNCT
cana-535	103	7	𝑞	𝑞	X
cana-535	103	8	+	+	ADJ
cana-535	103	9	𝛾)(𝜅	𝛾)(𝜅	NOUN
cana-535	103	10	)	)	PUNCT
cana-535	103	11	.	.	PUNCT
cana-535	104	1	thus	thus	ADV
cana-535	104	2	𝜍	𝜍	X
cana-535	104	3	+	+	ADJ
cana-535	104	4	�	�	PROPN
cana-535	104	5	̃	̃	PROPN
cana-535	104	6	�	�	PROPN
cana-535	104	7	⊇	⊇	PROPN
cana-535	104	8	𝑞	𝑞	PROPN
cana-535	104	9	+	+	PROPN
cana-535	104	10	�	�	PROPN
cana-535	104	11	̃	̃	PROPN
cana-535	104	12	�	�	PROPN
cana-535	104	13	and	and	CCONJ
cana-535	104	14	(	(	PUNCT
cana-535	104	15	𝜍	𝜍	X
cana-535	104	16	+	+	CCONJ
cana-535	104	17	𝛾	𝛾	NOUN
cana-535	104	18	)	)	PUNCT
cana-535	104	19	≤	≤	NOUN
cana-535	104	20	(	(	PUNCT
cana-535	104	21	𝑞	𝑞	X
cana-535	104	22	+	+	NOUN
cana-535	104	23	𝛾	𝛾	NOUN
cana-535	104	24	)	)	PUNCT
cana-535	104	25	.	.	PUNCT
cana-535	105	1	hence	hence	ADV
cana-535	105	2	𝑞	𝑞	PROPN
cana-535	105	3	+	+	PROPN
cana-535	105	4	�	�	PROPN
cana-535	105	5	̃	̃	NOUN
cana-535	105	6	�	�	NOUN
cana-535	105	7	=	=	SYM
cana-535	105	8	𝜍	𝜍	PROPN
cana-535	105	9	+	+	PROPN
cana-535	105	10	�	�	PROPN
cana-535	105	11	̃	̃	PROPN
cana-535	105	12	�	�	PROPN
cana-535	105	13	and	and	CCONJ
cana-535	105	14	𝑞	𝑞	X
cana-535	105	15	+	+	NOUN
cana-535	105	16	𝛾	𝛾	AUX
cana-535	105	17	=	=	SYM
cana-535	105	18	𝜍	𝜍	X
cana-535	105	19	+	+	CCONJ
cana-535	105	20	𝛾.	𝛾.	ADV
cana-535	105	21	theorem	theorem	ADJ
cana-535	105	22	3.5	3.5	NUM
cana-535	105	23	:	:	PUNCT
cana-535	105	24	let	let	VERB
cana-535	105	25	�	�	PROPN
cana-535	105	26	̃	̃	PROPN
cana-535	105	27	�	�	PROPN
cana-535	105	28	𝛾	𝛾	NOUN
cana-535	105	29	be	be	AUX
cana-535	105	30	a	a	DET
cana-535	105	31	hinr	hinr	NOUN
cana-535	105	32	of	of	ADP
cana-535	105	33	𝑁	𝑁	PROPN
cana-535	105	34	over	over	ADP
cana-535	105	35	𝑈.	𝑈.	PROPN
cana-535	105	36	then	then	ADV
cana-535	105	37	the	the	DET
cana-535	105	38	following	follow	VERB
cana-535	105	39	two	two	NUM
cana-535	105	40	statements	statement	NOUN
cana-535	105	41	hold	hold	VERB
cana-535	105	42	:	:	PUNCT
cana-535	105	43	if	if	SCONJ
cana-535	105	44	𝑞	𝑞	X
cana-535	105	45	+	+	PROPN
cana-535	105	46	�	�	PROPN
cana-535	105	47	̃	̃	NOUN
cana-535	105	48	�	�	NOUN
cana-535	105	49	=	=	SYM
cana-535	105	50	𝑛	𝑛	PROPN
cana-535	105	51	+	+	PROPN
cana-535	105	52	�	�	PROPN
cana-535	105	53	̃	̃	PROPN
cana-535	105	54	�	�	PROPN
cana-535	105	55	,	,	PUNCT
cana-535	105	56	𝜍	𝜍	PROPN
cana-535	105	57	+	+	PROPN
cana-535	105	58	�	�	PROPN
cana-535	105	59	̃	̃	NOUN
cana-535	105	60	�	�	NOUN
cana-535	105	61	=	=	SYM
cana-535	105	62	𝑣	𝑣	PROPN
cana-535	105	63	+	+	PROPN
cana-535	105	64	�	�	PROPN
cana-535	105	65	̃	̃	PROPN
cana-535	105	66	�	�	PROPN
cana-535	105	67	then	then	ADV
cana-535	105	68	(	(	PUNCT
cana-535	105	69	𝑞	𝑞	X
cana-535	105	70	+	+	X
cana-535	105	71	𝜍	𝜍	X
cana-535	105	72	)	)	PUNCT
cana-535	105	73	+	+	CCONJ
cana-535	105	74	�	�	PROPN
cana-535	105	75	̃	̃	NOUN
cana-535	105	76	�	�	NOUN
cana-535	105	77	=	=	SYM
cana-535	105	78	(	(	PUNCT
cana-535	105	79	𝑛	𝑛	PROPN
cana-535	105	80	+	+	NUM
cana-535	105	81	𝑣	𝑣	X
cana-535	105	82	)	)	PUNCT
cana-535	106	1	+	+	CCONJ
cana-535	106	2	�	�	PROPN
cana-535	106	3	̃	̃	PROPN
cana-535	106	4	�	�	PROPN
cana-535	106	5	,	,	PUNCT
cana-535	106	6	𝑞𝜍	𝑞𝜍	NOUN
cana-535	106	7	+	+	CCONJ
cana-535	106	8	�	�	PROPN
cana-535	106	9	̃	̃	PROPN
cana-535	106	10	�	�	NOUN
cana-535	106	11	=	=	SYM
cana-535	106	12	𝑛𝑣	𝑛𝑣	PROPN
cana-535	106	13	+	+	PROPN
cana-535	106	14	�	�	PROPN
cana-535	106	15	̃	̃	PROPN
cana-535	106	16	�	�	PROPN
cana-535	106	17	and	and	CCONJ
cana-535	106	18	if	if	SCONJ
cana-535	106	19	𝑞	𝑞	X
cana-535	106	20	+	+	NOUN
cana-535	106	21	𝛾	𝛾	NOUN
cana-535	106	22	=	=	SYM
cana-535	106	23	𝑛	𝑛	PROPN
cana-535	106	24	+	+	CCONJ
cana-535	106	25	𝛾	𝛾	X
cana-535	106	26	,	,	PUNCT
cana-535	106	27	𝜍	𝜍	X
cana-535	106	28	+	+	X
cana-535	106	29	𝛾	𝛾	NOUN
cana-535	106	30	=	=	SYM
cana-535	106	31	𝑣	𝑣	X
cana-535	107	1	+	+	CCONJ
cana-535	107	2	𝛾	𝛾	ADP
cana-535	107	3	then	then	ADV
cana-535	107	4	(	(	PUNCT
cana-535	107	5	𝑞	𝑞	X
cana-535	107	6	+	+	X
cana-535	107	7	𝜍	𝜍	X
cana-535	107	8	)	)	PUNCT
cana-535	107	9	+	+	NUM
cana-535	107	10	𝛾	𝛾	X
cana-535	107	11	=	=	SYM
cana-535	107	12	(	(	PUNCT
cana-535	107	13	𝑛	𝑛	PROPN
cana-535	107	14	+	+	SYM
cana-535	107	15	𝑣	𝑣	X
cana-535	107	16	)	)	PUNCT
cana-535	107	17	+	+	CCONJ
cana-535	107	18	𝛾	𝛾	NOUN
cana-535	107	19	,	,	PUNCT
cana-535	107	20	𝑞𝜍	𝑞𝜍	NOUN
cana-535	107	21	+	+	CCONJ
cana-535	107	22	𝛾	𝛾	NOUN
cana-535	107	23	=	=	SYM
cana-535	107	24	𝑛𝑣	𝑛𝑣	NOUN
cana-535	107	25	+	+	CCONJ
cana-535	107	26	𝛾	𝛾	X
cana-535	107	27	∀	∀	X
cana-535	107	28	𝑞	𝑞	NOUN
cana-535	107	29	,	,	PUNCT
cana-535	107	30	𝜍	𝜍	PROPN
cana-535	107	31	,	,	PUNCT
cana-535	107	32	𝑛	𝑛	PROPN
cana-535	107	33	,	,	PUNCT
cana-535	107	34	𝑣	𝑣	PRON
cana-535	107	35	∈	∈	NOUN
cana-535	107	36	𝑁.	𝑁.	PROPN
cana-535	107	37	proof	proof	NOUN
cana-535	107	38	:	:	PUNCT
cana-535	107	39	suppose	suppose	VERB
cana-535	107	40	that	that	SCONJ
cana-535	107	41	𝑞	𝑞	PROPN
cana-535	107	42	+	+	PROPN
cana-535	107	43	�	�	PROPN
cana-535	107	44	̃	̃	NOUN
cana-535	107	45	�	�	NOUN
cana-535	107	46	=	=	SYM
cana-535	107	47	𝑛	𝑛	PROPN
cana-535	107	48	+	+	PROPN
cana-535	107	49	�	�	PROPN
cana-535	107	50	̃	̃	PROPN
cana-535	107	51	�	�	PROPN
cana-535	107	52	,	,	PUNCT
cana-535	107	53	𝜍	𝜍	PROPN
cana-535	107	54	+	+	PROPN
cana-535	107	55	�	�	PROPN
cana-535	107	56	̃	̃	NOUN
cana-535	107	57	�	�	NOUN
cana-535	107	58	=	=	SYM
cana-535	107	59	𝑣	𝑣	PROPN
cana-535	107	60	+	+	PROPN
cana-535	107	61	�	�	PROPN
cana-535	107	62	̃	̃	PROPN
cana-535	107	63	�	�	PROPN
cana-535	107	64	and	and	CCONJ
cana-535	107	65	𝑞	𝑞	X
cana-535	107	66	+	+	PROPN
cana-535	107	67	𝛾	𝛾	NOUN
cana-535	107	68	=	=	SYM
cana-535	107	69	𝑛	𝑛	PROPN
cana-535	107	70	+	+	CCONJ
cana-535	107	71	𝛾	𝛾	X
cana-535	107	72	,	,	PUNCT
cana-535	107	73	𝜍	𝜍	X
cana-535	107	74	+	+	X
cana-535	107	75	𝛾	𝛾	NOUN
cana-535	107	76	=	=	SYM
cana-535	107	77	𝑣	𝑣	X
cana-535	107	78	+	+	CCONJ
cana-535	107	79	𝛾.	𝛾.	ADJ
cana-535	107	80	then	then	ADV
cana-535	107	81	�	�	PROPN
cana-535	107	82	̃	̃	PROPN
cana-535	107	83	�	�	PROPN
cana-535	107	84	(𝑞	(𝑞	NOUN
cana-535	107	85	−	−	NOUN
cana-535	107	86	𝑛	𝑛	NOUN
cana-535	107	87	)	)	PUNCT
cana-535	107	88	=	=	SYM
cana-535	107	89	�	�	PROPN
cana-535	107	90	̃	̃	PROPN
cana-535	107	91	�	�	PROPN
cana-535	107	92	(0	(0	PUNCT
cana-535	107	93	)	)	PUNCT
cana-535	107	94	,	,	PUNCT
cana-535	107	95	�	�	PROPN
cana-535	107	96	̃	̃	PROPN
cana-535	107	97	�	�	PROPN
cana-535	107	98	(𝜍	(𝜍	NOUN
cana-535	107	99	−	−	NOUN
cana-535	107	100	𝑣	𝑣	NOUN
cana-535	107	101	)	)	PUNCT
cana-535	107	102	=	=	SYM
cana-535	107	103	�	�	PROPN
cana-535	107	104	̃	̃	PROPN
cana-535	107	105	�	�	PROPN
cana-535	107	106	(0	(0	X
cana-535	107	107	)	)	PUNCT
cana-535	107	108	and	and	CCONJ
cana-535	107	109	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	107	110	−	−	PUNCT
cana-535	107	111	𝑛	𝑛	NOUN
cana-535	107	112	)	)	PUNCT
cana-535	107	113	=	=	PUNCT
cana-535	107	114	𝛾(0	𝛾(0	PROPN
cana-535	107	115	)	)	PUNCT
cana-535	107	116	,	,	PUNCT
cana-535	107	117	𝛾(𝜍	𝛾(𝜍	PROPN
cana-535	107	118	−	−	PROPN
cana-535	107	119	𝑣	𝑣	NOUN
cana-535	107	120	)	)	PUNCT
cana-535	107	121	=	=	PUNCT
cana-535	108	1	𝛾(0	𝛾(0	PROPN
cana-535	108	2	)	)	PUNCT
cana-535	108	3	.	.	PUNCT
cana-535	109	1	consider	consider	VERB
cana-535	109	2	�	�	PROPN
cana-535	109	3	̃	̃	NOUN
cana-535	109	4	�	�	NOUN
cana-535	109	5	[(𝑞	[(𝑞	X
cana-535	109	6	+	+	X
cana-535	109	7	𝜍	𝜍	X
cana-535	109	8	)	)	PUNCT
cana-535	109	9	−	−	PROPN
cana-535	110	1	(	(	PUNCT
cana-535	110	2	𝑛	𝑛	PROPN
cana-535	110	3	+	+	X
cana-535	110	4	𝑣	𝑣	X
cana-535	110	5	)	)	PUNCT
cana-535	110	6	]	]	PUNCT
cana-535	110	7	=	=	PUNCT
cana-535	110	8	�	�	PROPN
cana-535	110	9	̃	̃	PROPN
cana-535	110	10	�	�	PROPN
cana-535	110	11	[(𝑞	[(𝑞	NOUN
cana-535	110	12	−	−	PROPN
cana-535	110	13	𝑛	𝑛	NOUN
cana-535	110	14	)	)	PUNCT
cana-535	111	1	+	+	CCONJ
cana-535	111	2	(	(	PUNCT
cana-535	111	3	𝜍	𝜍	PART
cana-535	111	4	−	−	PROPN
cana-535	111	5	𝑣	𝑣	NOUN
cana-535	111	6	)	)	PUNCT
cana-535	111	7	]	]	PUNCT
cana-535	111	8	⊇	⊇	PROPN
cana-535	111	9	�	�	PROPN
cana-535	111	10	̃	̃	PROPN
cana-535	111	11	�	�	PROPN
cana-535	111	12	(𝑞	(𝑞	NOUN
cana-535	111	13	−	−	NOUN
cana-535	111	14	𝑛	𝑛	NOUN
cana-535	111	15	)	)	PUNCT
cana-535	111	16	∩	∩	ADJ
cana-535	111	17	�	�	PROPN
cana-535	111	18	̃	̃	PROPN
cana-535	111	19	�	�	PROPN
cana-535	111	20	(𝜍	(𝜍	NOUN
cana-535	111	21	−	−	NOUN
cana-535	111	22	𝑣	𝑣	NOUN
cana-535	111	23	)	)	PUNCT
cana-535	111	24	=	=	SYM
cana-535	111	25	�	�	PROPN
cana-535	111	26	̃	̃	PROPN
cana-535	111	27	�	�	PROPN
cana-535	111	28	(0	(0	NOUN
cana-535	111	29	)	)	PUNCT
cana-535	111	30	∩	∩	PROPN
cana-535	111	31	�	�	PROPN
cana-535	111	32	̃	̃	PROPN
cana-535	111	33	�	�	PROPN
cana-535	111	34	(0	(0	X
cana-535	111	35	)	)	PUNCT
cana-535	111	36	=	=	SYM
cana-535	111	37	�	�	PROPN
cana-535	111	38	̃	̃	PROPN
cana-535	111	39	�	�	PROPN
cana-535	111	40	(0	(0	X
cana-535	111	41	)	)	PUNCT
cana-535	111	42	and	and	CCONJ
cana-535	111	43	𝛾[(𝑞	𝛾[(𝑞	VERB
cana-535	111	44	+	+	CCONJ
cana-535	111	45	𝜍	𝜍	X
cana-535	111	46	)	)	PUNCT
cana-535	111	47	−	−	PROPN
cana-535	111	48	(	(	PUNCT
cana-535	111	49	𝑛	𝑛	PROPN
cana-535	111	50	+	+	X
cana-535	111	51	𝑣	𝑣	X
cana-535	111	52	)	)	PUNCT
cana-535	111	53	]	]	PUNCT
cana-535	112	1	=	=	PUNCT
cana-535	112	2	𝛾[(𝑞	𝛾[(𝑞	PROPN
cana-535	112	3	−	−	PROPN
cana-535	112	4	𝑛	𝑛	NOUN
cana-535	112	5	)	)	PUNCT
cana-535	113	1	+	+	CCONJ
cana-535	113	2	(	(	PUNCT
cana-535	113	3	𝜍	𝜍	PART
cana-535	113	4	−	−	PROPN
cana-535	113	5	𝑣	𝑣	NOUN
cana-535	113	6	)	)	PUNCT
cana-535	113	7	]	]	PUNCT
cana-535	113	8	≤	≤	NUM
cana-535	113	9	∨	∨	NUM
cana-535	113	10	{	{	PUNCT
cana-535	113	11	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	113	12	−	−	PROPN
cana-535	113	13	𝑛	𝑛	PROPN
cana-535	113	14	)	)	PUNCT
cana-535	113	15	,	,	PUNCT
cana-535	113	16	𝛾(𝜍	𝛾(𝜍	PROPN
cana-535	113	17	−	−	PROPN
cana-535	113	18	𝑣	𝑣	NOUN
cana-535	113	19	)	)	PUNCT
cana-535	113	20	}	}	PUNCT
cana-535	114	1	=	=	NUM
cana-535	114	2	∨	∨	NOUN
cana-535	114	3	{	{	PUNCT
cana-535	114	4	𝛾(0	𝛾(0	PROPN
cana-535	114	5	)	)	PUNCT
cana-535	114	6	,	,	PUNCT
cana-535	114	7	𝛾(0	𝛾(0	PROPN
cana-535	114	8	)	)	PUNCT
cana-535	114	9	}	}	PUNCT
cana-535	114	10	=	=	PUNCT
cana-535	114	11	𝛾(0	𝛾(0	PROPN
cana-535	114	12	)	)	PUNCT
cana-535	114	13	.	.	PUNCT
cana-535	115	1	but	but	CCONJ
cana-535	115	2	�	�	PROPN
cana-535	115	3	̃	̃	PROPN
cana-535	115	4	�	�	PROPN
cana-535	115	5	(0	(0	X
cana-535	115	6	)	)	PUNCT
cana-535	115	7	⊇	⊇	PROPN
cana-535	115	8	�	�	PROPN
cana-535	115	9	̃	̃	PROPN
cana-535	115	10	�	�	NOUN
cana-535	115	11	[(𝑞	[(𝑞	X
cana-535	115	12	+	+	X
cana-535	115	13	𝜍	𝜍	X
cana-535	115	14	)	)	PUNCT
cana-535	115	15	−	−	PROPN
cana-535	115	16	(	(	PUNCT
cana-535	115	17	𝑛	𝑛	PROPN
cana-535	115	18	+	+	X
cana-535	115	19	𝑣	𝑣	X
cana-535	115	20	)	)	PUNCT
cana-535	115	21	]	]	PUNCT
cana-535	115	22	and	and	CCONJ
cana-535	115	23	𝛾(0	𝛾(0	NOUN
cana-535	115	24	)	)	PUNCT
cana-535	115	25	≤	≤	NUM
cana-535	115	26	𝛾[(𝑞	𝛾[(𝑞	NOUN
cana-535	115	27	+	+	CCONJ
cana-535	115	28	𝜍	𝜍	X
cana-535	115	29	)	)	PUNCT
cana-535	115	30	−	−	PROPN
cana-535	115	31	(	(	PUNCT
cana-535	115	32	𝑛	𝑛	PROPN
cana-535	115	33	+	+	X
cana-535	115	34	𝑣	𝑣	X
cana-535	115	35	)	)	PUNCT
cana-535	115	36	]	]	PUNCT
cana-535	115	37	.	.	PUNCT
cana-535	116	1	therefore	therefore	ADV
cana-535	116	2	�	�	PROPN
cana-535	116	3	̃	̃	PROPN
cana-535	116	4	�	�	NOUN
cana-535	116	5	[(𝑞	[(𝑞	X
cana-535	116	6	+	+	X
cana-535	116	7	𝜍	𝜍	X
cana-535	116	8	)	)	PUNCT
cana-535	116	9	−	−	PROPN
cana-535	116	10	(	(	PUNCT
cana-535	116	11	𝑛	𝑛	PROPN
cana-535	116	12	+	+	X
cana-535	116	13	𝑣	𝑣	X
cana-535	116	14	)	)	PUNCT
cana-535	116	15	]	]	PUNCT
cana-535	116	16	=	=	PUNCT
cana-535	116	17	�	�	PROPN
cana-535	116	18	̃	̃	PROPN
cana-535	116	19	�	�	PROPN
cana-535	116	20	(0	(0	X
cana-535	116	21	)	)	PUNCT
cana-535	116	22	and	and	CCONJ
cana-535	116	23	𝛾[(𝑞	𝛾[(𝑞	VERB
cana-535	116	24	+	+	CCONJ
cana-535	116	25	𝜍	𝜍	X
cana-535	116	26	)	)	PUNCT
cana-535	116	27	−	−	PROPN
cana-535	116	28	(	(	PUNCT
cana-535	116	29	𝑛	𝑛	PROPN
cana-535	116	30	+	+	X
cana-535	116	31	𝑣	𝑣	X
cana-535	116	32	)	)	PUNCT
cana-535	116	33	]	]	PUNCT
cana-535	116	34	=	=	PUNCT
cana-535	116	35	𝛾(0	𝛾(0	PROPN
cana-535	116	36	)	)	PUNCT
cana-535	116	37	.	.	PUNCT
cana-535	117	1	thus	thus	ADV
cana-535	117	2	(	(	PUNCT
cana-535	117	3	𝑞	𝑞	X
cana-535	117	4	+	+	X
cana-535	117	5	𝜍	𝜍	X
cana-535	117	6	)	)	PUNCT
cana-535	117	7	+	+	CCONJ
cana-535	117	8	�	�	PROPN
cana-535	117	9	̃	̃	NOUN
cana-535	117	10	�	�	NOUN
cana-535	117	11	=	=	SYM
cana-535	117	12	(	(	PUNCT
cana-535	117	13	𝑛	𝑛	PROPN
cana-535	117	14	+	+	NUM
cana-535	117	15	𝑣	𝑣	X
cana-535	117	16	)	)	PUNCT
cana-535	117	17	+	+	CCONJ
cana-535	117	18	�	�	PROPN
cana-535	117	19	̃	̃	PROPN
cana-535	117	20	�	�	PROPN
cana-535	117	21	,	,	PUNCT
cana-535	117	22	𝑞𝜍	𝑞𝜍	NOUN
cana-535	117	23	+	+	CCONJ
cana-535	117	24	�	�	PROPN
cana-535	117	25	̃	̃	PROPN
cana-535	117	26	�	�	NOUN
cana-535	117	27	=	=	SYM
cana-535	117	28	𝑛𝑣	𝑛𝑣	PROPN
cana-535	117	29	+	+	PROPN
cana-535	117	30	�	�	PROPN
cana-535	117	31	̃	̃	PROPN
cana-535	117	32	�	�	PROPN
cana-535	117	33	and	and	CCONJ
cana-535	117	34	(	(	PUNCT
cana-535	117	35	𝑞	𝑞	PROPN
cana-535	117	36	+	+	X
cana-535	117	37	𝜍	𝜍	X
cana-535	117	38	)	)	PUNCT
cana-535	117	39	+	+	NUM
cana-535	117	40	𝛾	𝛾	X
cana-535	117	41	=	=	SYM
cana-535	117	42	(	(	PUNCT
cana-535	117	43	𝑛	𝑛	PROPN
cana-535	117	44	+	+	SYM
cana-535	117	45	𝑣	𝑣	X
cana-535	117	46	)	)	PUNCT
cana-535	117	47	+	+	CCONJ
cana-535	117	48	𝛾.	𝛾.	ADV
cana-535	117	49	again	again	ADV
cana-535	117	50	�	�	PROPN
cana-535	117	51	̃	̃	PROPN
cana-535	117	52	�	�	PROPN
cana-535	117	53	[𝑞𝜍	[𝑞𝜍	X
cana-535	117	54	−	−	NUM
cana-535	117	55	𝑛𝑣	𝑛𝑣	NOUN
cana-535	117	56	]	]	X
cana-535	117	57	=	=	PUNCT
cana-535	117	58	�	�	PROPN
cana-535	117	59	̃	̃	PROPN
cana-535	117	60	�	�	PROPN
cana-535	117	61	[𝑛𝑣	[𝑛𝑣	NOUN
cana-535	117	62	−	−	PROPN
cana-535	117	63	𝑞𝜍	𝑞𝜍	NOUN
cana-535	117	64	]	]	X
cana-535	117	65	=	=	PUNCT
cana-535	117	66	�	�	PROPN
cana-535	117	67	̃	̃	PROPN
cana-535	117	68	�	�	PROPN
cana-535	117	69	𝑟(𝑛𝑣	𝑟(𝑛𝑣	NUM
cana-535	117	70	−	−	PROPN
cana-535	117	71	𝑞𝑣	𝑞𝑣	NOUN
cana-535	117	72	+	+	CCONJ
cana-535	117	73	𝑞𝑣	𝑞𝑣	X
cana-535	117	74	−	−	PROPN
cana-535	117	75	𝑞𝜍	𝑞𝜍	NOUN
cana-535	117	76	)	)	PUNCT
cana-535	117	77	=	=	SYM
cana-535	117	78	�	�	PROPN
cana-535	117	79	̃	̃	PROPN
cana-535	117	80	�	�	PROPN
cana-535	117	81	[(𝑛	[(𝑛	X
cana-535	117	82	−	−	NOUN
cana-535	117	83	𝑞)𝑣	𝑞)𝑣	ADJ
cana-535	118	1	+	+	PROPN
cana-535	118	2	𝑞(𝜍	𝑞(𝜍	PROPN
cana-535	118	3	+	+	CCONJ
cana-535	118	4	(	(	PUNCT
cana-535	118	5	−𝜍	−𝜍	ADV
cana-535	118	6	+	+	CCONJ
cana-535	118	7	𝑣	𝑣	X
cana-535	118	8	)	)	PUNCT
cana-535	118	9	)	)	PUNCT
cana-535	119	1	−	−	ADP
cana-535	119	2	𝑞𝜍	𝑞𝜍	NOUN
cana-535	119	3	]	]	X
cana-535	119	4	⊇	⊇	PROPN
cana-535	119	5	�	�	PROPN
cana-535	119	6	̃	̃	PROPN
cana-535	119	7	�	�	PROPN
cana-535	119	8	((𝑛	((𝑛	PROPN
cana-535	119	9	−	−	PROPN
cana-535	119	10	𝑞)𝑣	𝑞)𝑣	ADJ
cana-535	119	11	)	)	PUNCT
cana-535	119	12	∩	∩	PROPN
cana-535	119	13	�	�	PROPN
cana-535	119	14	̃	̃	PROPN
cana-535	119	15	�	�	PROPN
cana-535	119	16	(𝑞(𝜍	(𝑞(𝜍	NOUN
cana-535	119	17	+	+	CCONJ
cana-535	119	18	(	(	PUNCT
cana-535	119	19	−𝜍	−𝜍	ADV
cana-535	119	20	+	+	CCONJ
cana-535	119	21	𝑣	𝑣	X
cana-535	119	22	)	)	PUNCT
cana-535	119	23	)	)	PUNCT
cana-535	120	1	−	−	ADP
cana-535	120	2	𝑞𝜍	𝑞𝜍	NOUN
cana-535	120	3	)	)	PUNCT
cana-535	120	4	communications	communication	NOUN
cana-535	120	5	on	on	ADP
cana-535	120	6	applied	apply	VERB
cana-535	120	7	nonlinear	nonlinear	ADJ
cana-535	120	8	analysis	analysis	NOUN
cana-535	120	9	issn	issn	NOUN
cana-535	120	10	:	:	PUNCT
cana-535	120	11	1074	1074	NUM
cana-535	120	12	-	-	PUNCT
cana-535	120	13	133x	133x	NUM
cana-535	120	14	vol	vol	NOUN
cana-535	120	15	31	31	NUM
cana-535	120	16	no	no	NOUN
cana-535	120	17	.	.	NOUN
cana-535	120	18	2	2	NUM
cana-535	120	19	(	(	PUNCT
cana-535	120	20	2024	2024	NUM
cana-535	120	21	)	)	PUNCT
cana-535	120	22	209	209	NUM
cana-535	120	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-535	120	24	⊇	⊇	PROPN
cana-535	120	25	�	�	PROPN
cana-535	120	26	̃	̃	PROPN
cana-535	120	27	�	�	PROPN
cana-535	120	28	(𝑛	(𝑛	NOUN
cana-535	120	29	−	−	NOUN
cana-535	120	30	𝑞	𝑞	NOUN
cana-535	120	31	)	)	PUNCT
cana-535	120	32	∩	∩	ADJ
cana-535	120	33	�	�	PROPN
cana-535	120	34	̃	̃	PROPN
cana-535	120	35	�	�	NOUN
cana-535	120	36	(−𝜍	(−𝜍	PROPN
cana-535	120	37	+	+	CCONJ
cana-535	120	38	𝑣	𝑣	X
cana-535	120	39	)	)	PUNCT
cana-535	120	40	=	=	SYM
cana-535	120	41	�	�	PROPN
cana-535	120	42	̃	̃	PROPN
cana-535	120	43	�	�	PROPN
cana-535	120	44	(𝑛	(𝑛	NOUN
cana-535	120	45	−	−	NOUN
cana-535	120	46	𝑞	𝑞	NOUN
cana-535	120	47	)	)	PUNCT
cana-535	120	48	∩	∩	ADJ
cana-535	120	49	�	�	PROPN
cana-535	120	50	̃	̃	PROPN
cana-535	120	51	�	�	PROPN
cana-535	120	52	(𝜍	(𝜍	NOUN
cana-535	120	53	−	−	NOUN
cana-535	120	54	𝑣	𝑣	NOUN
cana-535	120	55	)	)	PUNCT
cana-535	120	56	=	=	SYM
cana-535	120	57	�	�	PROPN
cana-535	120	58	̃	̃	PROPN
cana-535	120	59	�	�	PROPN
cana-535	120	60	(0	(0	NOUN
cana-535	120	61	)	)	PUNCT
cana-535	120	62	∩	∩	PROPN
cana-535	120	63	�	�	PROPN
cana-535	120	64	̃	̃	PROPN
cana-535	120	65	�	�	PROPN
cana-535	120	66	(0	(0	X
cana-535	120	67	)	)	PUNCT
cana-535	120	68	=	=	SYM
cana-535	120	69	�	�	PROPN
cana-535	120	70	̃	̃	PROPN
cana-535	120	71	�	�	PROPN
cana-535	120	72	(0	(0	X
cana-535	120	73	)	)	PUNCT
cana-535	120	74	and	and	CCONJ
cana-535	120	75	𝛾[𝑞𝜍	𝛾[𝑞𝜍	PROPN
cana-535	120	76	−	−	PROPN
cana-535	120	77	𝑛𝑣	𝑛𝑣	NOUN
cana-535	120	78	]	]	X
cana-535	120	79	=	=	PUNCT
cana-535	120	80	𝛾[𝑛𝑣	𝛾[𝑛𝑣	NOUN
cana-535	120	81	−	−	PROPN
cana-535	120	82	𝑞𝜍	𝑞𝜍	NOUN
cana-535	120	83	]	]	X
cana-535	120	84	=	=	X
cana-535	120	85	𝛾(𝑛𝑣	𝛾(𝑛𝑣	PRON
cana-535	120	86	−	−	PROPN
cana-535	120	87	𝑞𝑣	𝑞𝑣	NOUN
cana-535	120	88	+	+	CCONJ
cana-535	120	89	𝑞𝑣	𝑞𝑣	X
cana-535	120	90	−	−	PROPN
cana-535	120	91	𝑞𝜍	𝑞𝜍	NOUN
cana-535	120	92	)	)	PUNCT
cana-535	120	93	=	=	NOUN
cana-535	121	1	𝛾[(𝑛	𝛾[(𝑛	NOUN
cana-535	121	2	−	−	PROPN
cana-535	121	3	𝑞)𝑣	𝑞)𝑣	PROPN
cana-535	122	1	+	+	PROPN
cana-535	122	2	𝑞(𝜍	𝑞(𝜍	PROPN
cana-535	122	3	+	+	CCONJ
cana-535	122	4	(	(	PUNCT
cana-535	122	5	−𝜍	−𝜍	ADV
cana-535	122	6	+	+	CCONJ
cana-535	122	7	𝑣	𝑣	X
cana-535	122	8	)	)	PUNCT
cana-535	122	9	)	)	PUNCT
cana-535	123	1	−	−	ADP
cana-535	123	2	𝑞𝜍	𝑞𝜍	NOUN
cana-535	123	3	]	]	PUNCT
cana-535	123	4	≤	≤	NUM
cana-535	123	5	∨	∨	NUM
cana-535	123	6	{	{	PUNCT
cana-535	123	7	𝛾((𝑛	𝛾((𝑛	VERB
cana-535	123	8	−	−	NOUN
cana-535	123	9	𝑞)𝑣	𝑞)𝑣	ADJ
cana-535	123	10	)	)	PUNCT
cana-535	123	11	,	,	PUNCT
cana-535	123	12	𝛾(𝑞(𝜍	𝛾(𝑞(𝜍	PROPN
cana-535	123	13	+	+	CCONJ
cana-535	123	14	(	(	PUNCT
cana-535	123	15	−𝜍	−𝜍	ADV
cana-535	123	16	+	+	CCONJ
cana-535	123	17	𝑣	𝑣	X
cana-535	123	18	)	)	PUNCT
cana-535	123	19	)	)	PUNCT
cana-535	124	1	−	−	PROPN
cana-535	124	2	𝑞𝜍	𝑞𝜍	NOUN
cana-535	124	3	)	)	PUNCT
cana-535	124	4	}	}	PUNCT
cana-535	124	5	≤	≤	NUM
cana-535	124	6	∨	∨	NUM
cana-535	124	7	{	{	PUNCT
cana-535	124	8	𝛾(𝑛	𝛾(𝑛	PROPN
cana-535	124	9	−	−	PROPN
cana-535	124	10	𝑞	𝑞	NOUN
cana-535	124	11	)	)	PUNCT
cana-535	124	12	,	,	PUNCT
cana-535	124	13	𝛾(−𝜍	𝛾(−𝜍	VERB
cana-535	124	14	+	+	CCONJ
cana-535	124	15	𝑣	𝑣	X
cana-535	124	16	)	)	PUNCT
cana-535	124	17	}	}	PUNCT
cana-535	124	18	=	=	SYM
cana-535	124	19	∨	∨	X
cana-535	124	20	{	{	PUNCT
cana-535	124	21	𝛾(𝑢	𝛾(𝑢	ADJ
cana-535	124	22	−	−	PRON
cana-535	124	23	𝑞	𝑞	NOUN
cana-535	124	24	)	)	PUNCT
cana-535	124	25	,	,	PUNCT
cana-535	124	26	𝛾(𝜍	𝛾(𝜍	PROPN
cana-535	124	27	−	−	PROPN
cana-535	124	28	𝑣	𝑣	NOUN
cana-535	124	29	)	)	PUNCT
cana-535	124	30	}	}	PUNCT
cana-535	124	31	=	=	PUNCT
cana-535	124	32	∨	∨	X
cana-535	124	33	{	{	PUNCT
cana-535	124	34	𝛾(0	𝛾(0	PROPN
cana-535	124	35	)	)	PUNCT
cana-535	124	36	,	,	PUNCT
cana-535	124	37	𝛾(0	𝛾(0	PROPN
cana-535	124	38	)	)	PUNCT
cana-535	124	39	}	}	PUNCT
cana-535	124	40	=	=	PUNCT
cana-535	124	41	𝛾(0	𝛾(0	PROPN
cana-535	124	42	)	)	PUNCT
cana-535	124	43	.	.	PUNCT
cana-535	125	1	but	but	CCONJ
cana-535	125	2	�	�	PROPN
cana-535	125	3	̃	̃	PROPN
cana-535	125	4	�	�	PROPN
cana-535	125	5	(0	(0	X
cana-535	125	6	)	)	PUNCT
cana-535	125	7	⊇	⊇	PROPN
cana-535	125	8	�	�	PROPN
cana-535	125	9	̃	̃	PROPN
cana-535	125	10	�	�	PROPN
cana-535	125	11	(𝑞𝜍	(𝑞𝜍	PUNCT
cana-535	125	12	−	−	NUM
cana-535	125	13	𝑛𝑣	𝑛𝑣	NOUN
cana-535	125	14	)	)	PUNCT
cana-535	125	15	and	and	CCONJ
cana-535	125	16	𝛾(0	𝛾(0	NOUN
cana-535	125	17	)	)	PUNCT
cana-535	125	18	≤	≤	NOUN
cana-535	126	1	𝛾(𝑞𝜍	𝛾(𝑞𝜍	ADJ
cana-535	126	2	−	−	NUM
cana-535	126	3	𝑛𝑣	𝑛𝑣	NOUN
cana-535	126	4	)	)	PUNCT
cana-535	126	5	.	.	PUNCT
cana-535	127	1	therefore	therefore	ADV
cana-535	127	2	�	�	PROPN
cana-535	127	3	̃	̃	PROPN
cana-535	127	4	�	�	PROPN
cana-535	127	5	(𝑞𝜍	(𝑞𝜍	PUNCT
cana-535	127	6	−	−	NUM
cana-535	127	7	𝑛𝑣	𝑛𝑣	NOUN
cana-535	127	8	)	)	PUNCT
cana-535	127	9	=	=	SYM
cana-535	127	10	�	�	PROPN
cana-535	127	11	̃	̃	PROPN
cana-535	127	12	�	�	PROPN
cana-535	127	13	(0	(0	X
cana-535	127	14	)	)	PUNCT
cana-535	127	15	and	and	CCONJ
cana-535	127	16	𝛾(𝑞𝜍	𝛾(𝑞𝜍	NUM
cana-535	127	17	−	−	PROPN
cana-535	127	18	𝑛𝑣	𝑛𝑣	NOUN
cana-535	127	19	)	)	PUNCT
cana-535	127	20	=	=	PUNCT
cana-535	127	21	𝛾(0	𝛾(0	PROPN
cana-535	127	22	)	)	PUNCT
cana-535	127	23	.	.	PUNCT
cana-535	128	1	thus	thus	ADV
cana-535	128	2	𝑞𝜍	𝑞𝜍	X
cana-535	128	3	+	+	CCONJ
cana-535	128	4	�	�	PROPN
cana-535	128	5	̃	̃	PROPN
cana-535	128	6	�	�	NOUN
cana-535	128	7	=	=	SYM
cana-535	128	8	𝑛𝑣	𝑛𝑣	PROPN
cana-535	128	9	+	+	PROPN
cana-535	128	10	�	�	PROPN
cana-535	128	11	̃	̃	PROPN
cana-535	128	12	�	�	PROPN
cana-535	128	13	and	and	CCONJ
cana-535	128	14	𝑞𝜍	𝑞𝜍	NOUN
cana-535	128	15	+	+	CCONJ
cana-535	128	16	𝛾	𝛾	NOUN
cana-535	128	17	=	=	SYM
cana-535	128	18	𝑛𝑣	𝑛𝑣	NOUN
cana-535	128	19	+	+	CCONJ
cana-535	128	20	𝛾.	𝛾.	ADJ
cana-535	128	21	notation	notation	NOUN
cana-535	128	22	3.6	3.6	NUM
cana-535	128	23	:	:	PUNCT
cana-535	128	24	let	let	VERB
cana-535	128	25	�	�	PROPN
cana-535	128	26	̃	̃	PROPN
cana-535	128	27	�	�	PROPN
cana-535	128	28	𝛾	𝛾	AUX
cana-535	128	29	be	be	AUX
cana-535	128	30	a	a	DET
cana-535	128	31	hinr	hinr	NOUN
cana-535	128	32	of	of	ADP
cana-535	128	33	𝑁	𝑁	PROPN
cana-535	128	34	over	over	ADP
cana-535	128	35	𝑈.	𝑈.	PROPN
cana-535	128	36	then	then	ADV
cana-535	128	37	the	the	DET
cana-535	128	38	set	set	NOUN
cana-535	128	39	of	of	ADP
cana-535	128	40	all	all	DET
cana-535	128	41	cosets	coset	NOUN
cana-535	128	42	of	of	ADP
cana-535	128	43	�	�	PROPN
cana-535	128	44	̃	̃	PROPN
cana-535	128	45	�	�	NOUN
cana-535	128	46	𝛾	𝛾	NOUN
cana-535	128	47	is	be	AUX
cana-535	128	48	𝑁	𝑁	PROPN
cana-535	128	49	�	�	PROPN
cana-535	128	50	̃	̃	PROPN
cana-535	128	51	�	�	PROPN
cana-535	128	52	𝛾	𝛾	NOUN
cana-535	128	53	⁄	⁄	NOUN
cana-535	128	54	=	=	PUNCT
cana-535	128	55	{	{	PUNCT
cana-535	128	56	𝜍	𝜍	X
cana-535	128	57	+	+	PROPN
cana-535	128	58	�	�	PROPN
cana-535	128	59	̃	̃	PROPN
cana-535	128	60	�	�	NOUN
cana-535	128	61	𝛾	𝛾	NOUN
cana-535	128	62	:	:	PUNCT
cana-535	128	63	𝜍	𝜍	X
cana-535	128	64	∈	∈	PROPN
cana-535	128	65	𝑁	𝑁	PROPN
cana-535	128	66	}	}	PUNCT
cana-535	128	67	,	,	PUNCT
cana-535	128	68	where	where	SCONJ
cana-535	128	69	𝑁	𝑁	PROPN
cana-535	128	70	�	�	PROPN
cana-535	128	71	̃	̃	PROPN
cana-535	128	72	�	�	PROPN
cana-535	128	73	⁄	⁄	NOUN
cana-535	128	74	=	=	PUNCT
cana-535	128	75	{	{	PUNCT
cana-535	128	76	𝜍	𝜍	X
cana-535	128	77	+	+	PROPN
cana-535	128	78	�	�	PROPN
cana-535	128	79	̃	̃	PROPN
cana-535	128	80	�	�	PROPN
cana-535	128	81	:	:	PUNCT
cana-535	128	82	𝜍	𝜍	ADP
cana-535	128	83	∈	∈	PROPN
cana-535	128	84	𝑁	𝑁	PROPN
cana-535	128	85	}	}	PUNCT
cana-535	128	86	and	and	CCONJ
cana-535	128	87	𝑁	𝑁	PROPN
cana-535	128	88	𝛾⁄	𝛾⁄	PROPN
cana-535	128	89	=	=	PUNCT
cana-535	128	90	{	{	PUNCT
cana-535	128	91	𝜍	𝜍	X
cana-535	129	1	+	+	X
cana-535	129	2	𝛾	𝛾	NOUN
cana-535	129	3	:	:	PUNCT
cana-535	129	4	𝜍	𝜍	PRON
cana-535	129	5	∈	∈	PROPN
cana-535	129	6	𝑁	𝑁	PROPN
cana-535	129	7	}	}	PUNCT
cana-535	129	8	.	.	PUNCT
cana-535	130	1	theorem	theorem	VERB
cana-535	130	2	3.7	3.7	NUM
cana-535	130	3	:	:	PUNCT
cana-535	130	4	let	let	VERB
cana-535	130	5	�	�	PROPN
cana-535	130	6	̃	̃	PROPN
cana-535	130	7	�	�	PROPN
cana-535	130	8	𝛾	𝛾	NOUN
cana-535	130	9	be	be	AUX
cana-535	130	10	a	a	DET
cana-535	130	11	hinr	hinr	NOUN
cana-535	130	12	of	of	ADP
cana-535	130	13	𝑁	𝑁	PROPN
cana-535	130	14	over	over	ADP
cana-535	130	15	𝑈.	𝑈.	PROPN
cana-535	130	16	then	then	ADV
cana-535	130	17	𝑁	𝑁	PROPN
cana-535	130	18	�	�	PROPN
cana-535	130	19	̃	̃	PROPN
cana-535	130	20	�	�	PROPN
cana-535	130	21	𝛾	𝛾	NOUN
cana-535	130	22	⁄	⁄	PROPN
cana-535	130	23	is	be	AUX
cana-535	130	24	a	a	DET
cana-535	130	25	near	near	ADJ
cana-535	130	26	ring	ring	NOUN
cana-535	130	27	with	with	ADP
cana-535	130	28	respect	respect	NOUN
cana-535	130	29	to	to	ADP
cana-535	130	30	the	the	DET
cana-535	130	31	operations	operation	NOUN
cana-535	130	32	defined	define	VERB
cana-535	130	33	by	by	ADP
cana-535	130	34	(	(	PUNCT
cana-535	130	35	𝑞	𝑞	PROPN
cana-535	130	36	+	+	PROPN
cana-535	130	37	�	�	PROPN
cana-535	130	38	̃	̃	PROPN
cana-535	130	39	�	�	PROPN
cana-535	130	40	)	)	PUNCT
cana-535	130	41	+	+	CCONJ
cana-535	130	42	(	(	PUNCT
cana-535	130	43	𝜍	𝜍	PART
cana-535	130	44	+	+	PROPN
cana-535	130	45	�	�	PROPN
cana-535	130	46	̃	̃	PROPN
cana-535	130	47	�	�	PROPN
cana-535	130	48	)	)	PUNCT
cana-535	130	49	=	=	PUNCT
cana-535	130	50	(	(	PUNCT
cana-535	130	51	𝑞	𝑞	X
cana-535	130	52	+	+	X
cana-535	130	53	𝜍	𝜍	X
cana-535	130	54	)	)	PUNCT
cana-535	130	55	+	+	CCONJ
cana-535	130	56	�	�	PROPN
cana-535	130	57	̃	̃	PROPN
cana-535	130	58	�	�	PROPN
cana-535	130	59	,	,	PUNCT
cana-535	130	60	(	(	PUNCT
cana-535	130	61	𝑞	𝑞	PROPN
cana-535	130	62	+	+	PROPN
cana-535	130	63	�	�	PROPN
cana-535	130	64	̃	̃	PROPN
cana-535	130	65	�	�	NOUN
cana-535	130	66	)(𝜍	)(𝜍	ADJ
cana-535	130	67	+	+	X
cana-535	130	68	�	�	PROPN
cana-535	130	69	̃	̃	NOUN
cana-535	130	70	�	�	PROPN
cana-535	130	71	)	)	PUNCT
cana-535	130	72	=	=	PUNCT
cana-535	130	73	(	(	PUNCT
cana-535	130	74	𝑞𝜍	𝑞𝜍	NOUN
cana-535	130	75	)	)	PUNCT
cana-535	131	1	+	+	CCONJ
cana-535	131	2	�	�	PROPN
cana-535	131	3	̃	̃	PROPN
cana-535	131	4	�	�	PROPN
cana-535	131	5	and	and	CCONJ
cana-535	131	6	(	(	PUNCT
cana-535	131	7	𝑞	𝑞	X
cana-535	131	8	+	+	NOUN
cana-535	131	9	𝛾	𝛾	PROPN
cana-535	131	10	)	)	PUNCT
cana-535	132	1	+	+	CCONJ
cana-535	132	2	(	(	PUNCT
cana-535	132	3	𝜍	𝜍	X
cana-535	132	4	+	+	ADJ
cana-535	132	5	𝛾	𝛾	NOUN
cana-535	132	6	)	)	PUNCT
cana-535	132	7	=	=	SYM
cana-535	132	8	(	(	PUNCT
cana-535	132	9	𝑞	𝑞	X
cana-535	132	10	+	+	X
cana-535	132	11	𝜍	𝜍	X
cana-535	132	12	)	)	PUNCT
cana-535	133	1	+	+	CCONJ
cana-535	133	2	𝛾	𝛾	ADP
cana-535	133	3	,	,	PUNCT
cana-535	133	4	(	(	PUNCT
cana-535	133	5	𝑞	𝑞	NOUN
cana-535	133	6	+	+	X
cana-535	133	7	𝛾)(𝜍	𝛾)(𝜍	NOUN
cana-535	133	8	+	+	CCONJ
cana-535	133	9	𝛾	𝛾	NOUN
cana-535	133	10	)	)	PUNCT
cana-535	133	11	=	=	SYM
cana-535	133	12	(	(	PUNCT
cana-535	133	13	𝑞𝜍	𝑞𝜍	NOUN
cana-535	133	14	)	)	PUNCT
cana-535	133	15	+	+	CCONJ
cana-535	133	16	𝛾	𝛾	X
cana-535	133	17	∀	∀	X
cana-535	133	18	𝑞	𝑞	NOUN
cana-535	133	19	,	,	PUNCT
cana-535	133	20	𝜍	𝜍	ADP
cana-535	133	21	∈	∈	ADJ
cana-535	133	22	𝑁.	𝑁.	PROPN
cana-535	133	23	proof	proof	NOUN
cana-535	133	24	:	:	PUNCT
cana-535	133	25	a	a	DET
cana-535	133	26	direct	direct	ADJ
cana-535	133	27	verification	verification	NOUN
cana-535	133	28	shows	show	VERB
cana-535	133	29	that	that	SCONJ
cana-535	133	30	(	(	PUNCT
cana-535	133	31	𝑁	𝑁	PROPN
cana-535	133	32	�	�	PROPN
cana-535	133	33	̃	̃	PROPN
cana-535	133	34	�	�	PROPN
cana-535	133	35	𝛾	𝛾	NOUN
cana-535	133	36	⁄	⁄	PROPN
cana-535	133	37	,	,	PUNCT
cana-535	133	38	+	+	PUNCT
cana-535	133	39	)	)	PUNCT
cana-535	133	40	is	be	AUX
cana-535	133	41	a	a	DET
cana-535	133	42	group	group	NOUN
cana-535	133	43	.	.	PUNCT
cana-535	134	1	let	let	VERB
cana-535	134	2	𝑞	𝑞	PRON
cana-535	134	3	+	+	PROPN
cana-535	134	4	�	�	PROPN
cana-535	134	5	̃	̃	PROPN
cana-535	134	6	�	�	PROPN
cana-535	134	7	,	,	PUNCT
cana-535	134	8	𝜍	𝜍	PROPN
cana-535	134	9	+	+	PROPN
cana-535	134	10	�	�	PROPN
cana-535	134	11	̃	̃	PROPN
cana-535	134	12	�	�	PROPN
cana-535	134	13	,	,	PUNCT
cana-535	134	14	𝑗	𝑗	PROPN
cana-535	134	15	+	+	NUM
cana-535	134	16	�	�	PROPN
cana-535	134	17	̃	̃	PROPN
cana-535	134	18	�	�	PROPN
cana-535	134	19	∈	∈	PROPN
cana-535	134	20	𝑁	𝑁	PROPN
cana-535	134	21	�	�	PROPN
cana-535	134	22	̃	̃	PROPN
cana-535	134	23	�	�	PROPN
cana-535	134	24	𝛾	𝛾	NOUN
cana-535	134	25	⁄	⁄	ADJ
cana-535	134	26	and	and	CCONJ
cana-535	134	27	+	+	NOUN
cana-535	134	28	𝛾	𝛾	NOUN
cana-535	134	29	,	,	PUNCT
cana-535	134	30	𝜍	𝜍	X
cana-535	134	31	+	+	CCONJ
cana-535	134	32	𝛾	𝛾	PROPN
cana-535	134	33	,	,	PUNCT
cana-535	134	34	𝑗	𝑗	PROPN
cana-535	134	35	+	+	X
cana-535	134	36	𝛾	𝛾	NOUN
cana-535	134	37	∈	∈	NOUN
cana-535	134	38	𝑁	𝑁	PROPN
cana-535	134	39	�	�	PROPN
cana-535	134	40	̃	̃	PROPN
cana-535	134	41	�	�	PROPN
cana-535	134	42	𝛾	𝛾	NOUN
cana-535	134	43	⁄	⁄	PROPN
cana-535	134	44	,	,	PUNCT
cana-535	134	45	where	where	SCONJ
cana-535	134	46	𝑞	𝑞	PROPN
cana-535	134	47	,	,	PUNCT
cana-535	134	48	𝜍	𝜍	PROPN
cana-535	134	49	,	,	PUNCT
cana-535	134	50	𝑗	𝑗	PROPN
cana-535	134	51	∈	∈	NOUN
cana-535	134	52	𝑁.	𝑁.	PROPN
cana-535	135	1	then	then	ADV
cana-535	135	2	[	[	X
cana-535	135	3	(	(	PUNCT
cana-535	135	4	𝑞	𝑞	PROPN
cana-535	135	5	+	+	PROPN
cana-535	135	6	�	�	PROPN
cana-535	135	7	̃	̃	PROPN
cana-535	135	8	�	�	NOUN
cana-535	135	9	)(𝜍	)(𝜍	ADJ
cana-535	135	10	+	+	X
cana-535	135	11	�	�	PROPN
cana-535	135	12	̃	̃	PROPN
cana-535	135	13	�	�	PROPN
cana-535	135	14	)](𝑗	)](𝑗	ADJ
cana-535	135	15	+	+	CCONJ
cana-535	135	16	�	�	PROPN
cana-535	135	17	̃	̃	PROPN
cana-535	135	18	�	�	PROPN
cana-535	135	19	)	)	PUNCT
cana-535	135	20	=	=	PUNCT
cana-535	135	21	(	(	PUNCT
cana-535	135	22	𝑞𝜍	𝑞𝜍	NOUN
cana-535	135	23	+	+	CCONJ
cana-535	135	24	�	�	PROPN
cana-535	135	25	̃	̃	PROPN
cana-535	135	26	�	�	PROPN
cana-535	135	27	)(𝑗	)(𝑗	VERB
cana-535	135	28	+	+	ADJ
cana-535	135	29	�	�	PROPN
cana-535	135	30	̃	̃	NOUN
cana-535	135	31	�	�	PROPN
cana-535	135	32	)	)	PUNCT
cana-535	135	33	=	=	PUNCT
cana-535	136	1	(	(	PUNCT
cana-535	136	2	𝑞𝜍)𝑗	𝑞𝜍)𝑗	PROPN
cana-535	136	3	+	+	PROPN
cana-535	136	4	�	�	PROPN
cana-535	136	5	̃	̃	PROPN
cana-535	136	6	�	�	NOUN
cana-535	136	7	=	=	PUNCT
cana-535	136	8	𝑞(𝜍𝑗	𝑞(𝜍𝑗	NOUN
cana-535	136	9	)	)	PUNCT
cana-535	137	1	+	+	NUM
cana-535	137	2	�	�	PROPN
cana-535	137	3	̃	̃	NOUN
cana-535	137	4	�	�	NOUN
cana-535	137	5	=	=	SYM
cana-535	137	6	(	(	PUNCT
cana-535	137	7	𝑞	𝑞	PROPN
cana-535	137	8	+	+	PROPN
cana-535	137	9	�	�	PROPN
cana-535	137	10	̃	̃	PROPN
cana-535	137	11	�	�	PROPN
cana-535	137	12	)[(𝜍	)[(𝜍	ADJ
cana-535	137	13	+	+	NUM
cana-535	137	14	�	�	PROPN
cana-535	137	15	̃	̃	PROPN
cana-535	137	16	�	�	PROPN
cana-535	137	17	)(𝑗	)(𝑗	VERB
cana-535	137	18	+	+	PROPN
cana-535	137	19	�	�	PROPN
cana-535	137	20	̃	̃	PROPN
cana-535	137	21	�	�	PROPN
cana-535	137	22	)	)	PUNCT
cana-535	137	23	]	]	PUNCT
cana-535	137	24	and	and	CCONJ
cana-535	137	25	[	[	X
cana-535	137	26	(	(	PUNCT
cana-535	137	27	𝑞	𝑞	X
cana-535	137	28	+	+	NOUN
cana-535	137	29	𝛾)(𝜍	𝛾)(𝜍	NOUN
cana-535	137	30	+	+	CCONJ
cana-535	137	31	𝛾)](𝑗	𝛾)](𝑗	NOUN
cana-535	137	32	+	+	CCONJ
cana-535	137	33	𝛾	𝛾	X
cana-535	137	34	)	)	PUNCT
cana-535	137	35	=	=	SYM
cana-535	137	36	(	(	PUNCT
cana-535	137	37	𝑞𝜍	𝑞𝜍	NOUN
cana-535	137	38	+	+	X
cana-535	137	39	𝛾)(𝑗	𝛾)(𝑗	NOUN
cana-535	137	40	+	+	CCONJ
cana-535	137	41	𝛾	𝛾	X
cana-535	137	42	)	)	PUNCT
cana-535	137	43	=	=	SYM
cana-535	137	44	(	(	PUNCT
cana-535	137	45	𝑞𝜍)𝑗	𝑞𝜍)𝑗	PROPN
cana-535	137	46	+	+	NUM
cana-535	137	47	𝛾	𝛾	NOUN
cana-535	137	48	=	=	SYM
cana-535	137	49	𝑞(𝜍𝑗	𝑞(𝜍𝑗	NOUN
cana-535	137	50	)	)	PUNCT
cana-535	137	51	+	+	CCONJ
cana-535	137	52	𝛾	𝛾	X
cana-535	137	53	=	=	SYM
cana-535	137	54	(	(	PUNCT
cana-535	137	55	𝑞	𝑞	X
cana-535	137	56	+	+	X
cana-535	137	57	𝛾)[(𝜍	𝛾)[(𝜍	PRON
cana-535	137	58	+	+	CCONJ
cana-535	137	59	𝛾)(𝑗	𝛾)(𝑗	NOUN
cana-535	137	60	+	+	CCONJ
cana-535	137	61	𝛾	𝛾	NOUN
cana-535	137	62	)	)	PUNCT
cana-535	137	63	]	]	PUNCT
cana-535	137	64	.	.	PUNCT
cana-535	138	1	this	this	PRON
cana-535	138	2	shows	show	VERB
cana-535	138	3	that	that	SCONJ
cana-535	138	4	𝑁	𝑁	PROPN
cana-535	138	5	�	�	PROPN
cana-535	138	6	̃	̃	PROPN
cana-535	138	7	�	�	PROPN
cana-535	138	8	𝛾	𝛾	NOUN
cana-535	138	9	⁄	⁄	PROPN
cana-535	138	10	is	be	AUX
cana-535	138	11	a	a	DET
cana-535	138	12	semi	semi	ADJ
cana-535	138	13	group	group	NOUN
cana-535	138	14	under	under	ADP
cana-535	138	15	multiplication	multiplication	NOUN
cana-535	138	16	.	.	PUNCT
cana-535	139	1	consider	consider	VERB
cana-535	139	2	[	[	X
cana-535	139	3	(	(	PUNCT
cana-535	139	4	𝑞	𝑞	PROPN
cana-535	139	5	+	+	PROPN
cana-535	139	6	�	�	PROPN
cana-535	139	7	̃	̃	PROPN
cana-535	139	8	�	�	PROPN
cana-535	139	9	)	)	PUNCT
cana-535	140	1	+	+	CCONJ
cana-535	140	2	(	(	PUNCT
cana-535	140	3	𝜍	𝜍	PART
cana-535	140	4	+	+	PROPN
cana-535	140	5	�	�	PROPN
cana-535	140	6	̃	̃	PROPN
cana-535	140	7	�	�	PROPN
cana-535	140	8	)](𝑗	)](𝑗	ADJ
cana-535	140	9	+	+	CCONJ
cana-535	140	10	�	�	PROPN
cana-535	140	11	̃	̃	PROPN
cana-535	140	12	�	�	PROPN
cana-535	140	13	)	)	PUNCT
cana-535	141	1	=	=	PUNCT
cana-535	141	2	(	(	PUNCT
cana-535	141	3	(	(	PUNCT
cana-535	141	4	𝑞	𝑞	X
cana-535	141	5	+	+	NOUN
cana-535	141	6	𝜍	𝜍	X
cana-535	141	7	)	)	PUNCT
cana-535	141	8	+	+	CCONJ
cana-535	141	9	�	�	PROPN
cana-535	141	10	̃	̃	NOUN
cana-535	141	11	�	�	PROPN
cana-535	141	12	)(𝑗	)(𝑗	VERB
cana-535	141	13	+	+	ADJ
cana-535	141	14	�	�	PROPN
cana-535	141	15	̃	̃	NOUN
cana-535	141	16	�	�	PROPN
cana-535	141	17	)	)	PUNCT
cana-535	141	18	=	=	PUNCT
cana-535	141	19	(	(	PUNCT
cana-535	141	20	𝑞	𝑞	NOUN
cana-535	141	21	+	+	CCONJ
cana-535	141	22	𝜍)𝑗	𝜍)𝑗	NOUN
cana-535	141	23	+	+	CCONJ
cana-535	141	24	�	�	PROPN
cana-535	141	25	̃	̃	NOUN
cana-535	141	26	�	�	NOUN
cana-535	141	27	=	=	PUNCT
cana-535	141	28	(	(	PUNCT
cana-535	141	29	𝑞𝑗	𝑞𝑗	ADP
cana-535	141	30	+	+	CCONJ
cana-535	141	31	𝜍𝑗	𝜍𝑗	ADJ
cana-535	141	32	)	)	PUNCT
cana-535	141	33	+	+	CCONJ
cana-535	141	34	�	�	PROPN
cana-535	141	35	̃	̃	NOUN
cana-535	141	36	�	�	NOUN
cana-535	141	37	=	=	PUNCT
cana-535	141	38	(	(	PUNCT
cana-535	141	39	𝑞𝑗	𝑞𝑗	PROPN
cana-535	141	40	+	+	NUM
cana-535	141	41	�	�	PROPN
cana-535	141	42	̃	̃	PROPN
cana-535	141	43	�	�	PROPN
cana-535	141	44	)	)	PUNCT
cana-535	141	45	+	+	CCONJ
cana-535	141	46	(	(	PUNCT
cana-535	141	47	𝜍𝑗	𝜍𝑗	ADP
cana-535	141	48	+	+	CCONJ
cana-535	141	49	�	�	PROPN
cana-535	141	50	̃	̃	PROPN
cana-535	141	51	�	�	PROPN
cana-535	141	52	)	)	PUNCT
cana-535	141	53	=	=	PUNCT
cana-535	141	54	(	(	PUNCT
cana-535	141	55	𝑞	𝑞	PROPN
cana-535	141	56	+	+	PROPN
cana-535	141	57	�	�	PROPN
cana-535	141	58	̃	̃	PROPN
cana-535	141	59	�	�	PROPN
cana-535	141	60	)(𝑗	)(𝑗	VERB
cana-535	141	61	+	+	ADJ
cana-535	141	62	�	�	PROPN
cana-535	141	63	̃	̃	PROPN
cana-535	141	64	�	�	PROPN
cana-535	141	65	)	)	PUNCT
cana-535	142	1	+	+	CCONJ
cana-535	142	2	(	(	PUNCT
cana-535	142	3	𝜍	𝜍	PART
cana-535	142	4	+	+	PROPN
cana-535	142	5	�	�	PROPN
cana-535	142	6	̃	̃	PROPN
cana-535	142	7	�	�	PROPN
cana-535	142	8	)(𝑗	)(𝑗	VERB
cana-535	142	9	+	+	PROPN
cana-535	142	10	�	�	PROPN
cana-535	142	11	̃	̃	PROPN
cana-535	142	12	�	�	PROPN
cana-535	142	13	)	)	PUNCT
cana-535	142	14	,	,	PUNCT
cana-535	143	1	[	[	X
cana-535	143	2	(	(	PUNCT
cana-535	143	3	𝑞	𝑞	X
cana-535	143	4	+	+	NOUN
cana-535	143	5	𝛾	𝛾	PROPN
cana-535	143	6	)	)	PUNCT
cana-535	143	7	+	+	CCONJ
cana-535	143	8	(	(	PUNCT
cana-535	143	9	𝜍	𝜍	X
cana-535	143	10	+	+	X
cana-535	143	11	𝛾)](𝑗	𝛾)](𝑗	NOUN
cana-535	143	12	+	+	CCONJ
cana-535	143	13	𝛾	𝛾	X
cana-535	143	14	)	)	PUNCT
cana-535	144	1	=	=	SYM
cana-535	144	2	(	(	PUNCT
cana-535	144	3	(	(	PUNCT
cana-535	144	4	𝑞	𝑞	X
cana-535	144	5	+	+	X
cana-535	144	6	𝜍	𝜍	X
cana-535	144	7	)	)	PUNCT
cana-535	144	8	+	+	NUM
cana-535	144	9	𝛾)(𝑗	𝛾)(𝑗	NOUN
cana-535	144	10	+	+	CCONJ
cana-535	144	11	𝛾	𝛾	X
cana-535	144	12	)	)	PUNCT
cana-535	144	13	=	=	SYM
cana-535	144	14	(	(	PUNCT
cana-535	144	15	𝑞	𝑞	NOUN
cana-535	144	16	+	+	X
cana-535	144	17	𝜍)𝑗	𝜍)𝑗	NOUN
cana-535	144	18	+	+	CCONJ
cana-535	144	19	𝛾	𝛾	X
cana-535	144	20	=	=	PUNCT
cana-535	144	21	(	(	PUNCT
cana-535	144	22	𝑞𝑗	𝑞𝑗	ADP
cana-535	144	23	+	+	CCONJ
cana-535	144	24	𝜍𝑗	𝜍𝑗	ADJ
cana-535	144	25	)	)	PUNCT
cana-535	144	26	+	+	CCONJ
cana-535	144	27	𝛾	𝛾	X
cana-535	144	28	=	=	SYM
cana-535	144	29	(	(	PUNCT
cana-535	144	30	𝑞𝑗	𝑞𝑗	VERB
cana-535	144	31	+	+	CCONJ
cana-535	144	32	𝛾	𝛾	NOUN
cana-535	144	33	)	)	PUNCT
cana-535	144	34	+	+	CCONJ
cana-535	144	35	(	(	PUNCT
cana-535	144	36	𝜍𝑗	𝜍𝑗	ADP
cana-535	144	37	+	+	CCONJ
cana-535	144	38	𝛾	𝛾	X
cana-535	144	39	)	)	PUNCT
cana-535	144	40	=	=	SYM
cana-535	144	41	(	(	PUNCT
cana-535	144	42	𝑞	𝑞	X
cana-535	144	43	+	+	X
cana-535	144	44	𝛾)(𝑗	𝛾)(𝑗	PROPN
cana-535	144	45	+	+	CCONJ
cana-535	144	46	𝛾	𝛾	X
cana-535	144	47	)	)	PUNCT
cana-535	144	48	+	+	CCONJ
cana-535	144	49	(	(	PUNCT
cana-535	144	50	𝜍	𝜍	PART
cana-535	144	51	+	+	NOUN
cana-535	144	52	𝛾)(𝑗	𝛾)(𝑗	NOUN
cana-535	144	53	+	+	CCONJ
cana-535	144	54	𝛾	𝛾	NOUN
cana-535	144	55	)	)	PUNCT
cana-535	144	56	.	.	PUNCT
cana-535	145	1	hence	hence	ADV
cana-535	145	2	𝑁	𝑁	PROPN
cana-535	145	3	�	�	PROPN
cana-535	145	4	̃	̃	PROPN
cana-535	145	5	�	�	PROPN
cana-535	145	6	𝛾	𝛾	NOUN
cana-535	145	7	⁄	⁄	PROPN
cana-535	145	8	is	be	AUX
cana-535	145	9	a	a	DET
cana-535	145	10	nearring	nearring	NOUN
cana-535	145	11	.	.	PUNCT
cana-535	146	1	communications	communication	NOUN
cana-535	146	2	on	on	ADP
cana-535	146	3	applied	apply	VERB
cana-535	146	4	nonlinear	nonlinear	ADJ
cana-535	146	5	analysis	analysis	NOUN
cana-535	146	6	issn	issn	NOUN
cana-535	146	7	:	:	PUNCT
cana-535	146	8	1074	1074	NUM
cana-535	146	9	-	-	PUNCT
cana-535	146	10	133x	133x	NUM
cana-535	146	11	vol	vol	NOUN
cana-535	146	12	31	31	NUM
cana-535	146	13	no	no	NOUN
cana-535	146	14	.	.	NOUN
cana-535	146	15	2	2	NUM
cana-535	146	16	(	(	PUNCT
cana-535	146	17	2024	2024	NUM
cana-535	146	18	)	)	PUNCT
cana-535	146	19	210	210	NUM
cana-535	146	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-535	146	21	definition	definition	NOUN
cana-535	146	22	3.8	3.8	NUM
cana-535	146	23	:	:	PUNCT
cana-535	146	24	let	let	VERB
cana-535	146	25	�	�	PROPN
cana-535	146	26	̃	̃	PROPN
cana-535	146	27	�	�	PROPN
cana-535	146	28	𝛾	𝛾	NOUN
cana-535	146	29	be	be	AUX
cana-535	146	30	a	a	DET
cana-535	146	31	hinr	hinr	NOUN
cana-535	146	32	of	of	ADP
cana-535	146	33	𝑁.	𝑁.	PROPN
cana-535	146	34	then	then	ADV
cana-535	146	35	𝑁	𝑁	PROPN
cana-535	146	36	�	�	PROPN
cana-535	146	37	̃	̃	PROPN
cana-535	146	38	�	�	PROPN
cana-535	146	39	𝛾	𝛾	NOUN
cana-535	146	40	⁄	⁄	PROPN
cana-535	146	41	,	,	PUNCT
cana-535	146	42	the	the	DET
cana-535	146	43	set	set	NOUN
cana-535	146	44	of	of	ADP
cana-535	146	45	all	all	DET
cana-535	146	46	cosets	coset	NOUN
cana-535	146	47	of	of	ADP
cana-535	146	48	�	�	PROPN
cana-535	146	49	̃	̃	PROPN
cana-535	146	50	�	�	NOUN
cana-535	146	51	𝛾	𝛾	PROPN
cana-535	146	52	is	be	AUX
cana-535	146	53	called	call	VERB
cana-535	146	54	a	a	DET
cana-535	146	55	hybrid	hybrid	ADJ
cana-535	146	56	quotient	quotient	NOUN
cana-535	146	57	nearring	nearre	VERB
cana-535	146	58	of	of	ADP
cana-535	146	59	𝑁	𝑁	PROPN
cana-535	146	60	by	by	ADP
cana-535	146	61	�	�	PROPN
cana-535	146	62	̃	̃	PROPN
cana-535	146	63	�	�	PROPN
cana-535	146	64	𝛾	𝛾	NOUN
cana-535	146	65	with	with	ADP
cana-535	146	66	respect	respect	NOUN
cana-535	146	67	to	to	ADP
cana-535	146	68	the	the	DET
cana-535	146	69	following	follow	VERB
cana-535	146	70	operations	operation	NOUN
cana-535	146	71	:	:	PUNCT
cana-535	146	72	(	(	PUNCT
cana-535	146	73	𝑞	𝑞	X
cana-535	146	74	+	+	PROPN
cana-535	146	75	�	�	PROPN
cana-535	146	76	̃	̃	PROPN
cana-535	146	77	�	�	PROPN
cana-535	146	78	)	)	PUNCT
cana-535	147	1	+	+	CCONJ
cana-535	147	2	(	(	PUNCT
cana-535	147	3	𝜍	𝜍	PART
cana-535	147	4	+	+	PROPN
cana-535	147	5	�	�	PROPN
cana-535	147	6	̃	̃	PROPN
cana-535	147	7	�	�	PROPN
cana-535	147	8	)	)	PUNCT
cana-535	148	1	=	=	PUNCT
cana-535	148	2	(	(	PUNCT
cana-535	148	3	𝑞	𝑞	X
cana-535	148	4	+	+	X
cana-535	148	5	𝜍	𝜍	X
cana-535	148	6	)	)	PUNCT
cana-535	148	7	+	+	CCONJ
cana-535	148	8	�	�	PROPN
cana-535	148	9	̃	̃	PROPN
cana-535	148	10	�	�	PROPN
cana-535	148	11	and	and	CCONJ
cana-535	148	12	(	(	PUNCT
cana-535	148	13	𝑞	𝑞	X
cana-535	148	14	+	+	NOUN
cana-535	148	15	𝛾	𝛾	PROPN
cana-535	148	16	)	)	PUNCT
cana-535	148	17	+	+	CCONJ
cana-535	148	18	(	(	PUNCT
cana-535	148	19	𝜍	𝜍	X
cana-535	148	20	+	+	ADJ
cana-535	148	21	𝛾	𝛾	NOUN
cana-535	148	22	)	)	PUNCT
cana-535	148	23	=	=	SYM
cana-535	148	24	(	(	PUNCT
cana-535	148	25	𝑞	𝑞	X
cana-535	148	26	+	+	X
cana-535	148	27	𝜍	𝜍	X
cana-535	148	28	)	)	PUNCT
cana-535	149	1	+	+	CCONJ
cana-535	149	2	𝛾	𝛾	ADP
cana-535	149	3	,	,	PUNCT
cana-535	149	4	(	(	PUNCT
cana-535	149	5	𝑞	𝑞	PROPN
cana-535	149	6	+	+	PROPN
cana-535	149	7	�	�	PROPN
cana-535	149	8	̃	̃	PROPN
cana-535	149	9	�	�	NOUN
cana-535	149	10	)(𝜍	)(𝜍	ADJ
cana-535	149	11	+	+	X
cana-535	149	12	�	�	PROPN
cana-535	149	13	̃	̃	NOUN
cana-535	149	14	�	�	PROPN
cana-535	149	15	)	)	PUNCT
cana-535	150	1	=	=	PUNCT
cana-535	150	2	(	(	PUNCT
cana-535	150	3	𝑞𝜍	𝑞𝜍	NOUN
cana-535	150	4	)	)	PUNCT
cana-535	150	5	+	+	CCONJ
cana-535	150	6	�	�	PROPN
cana-535	150	7	̃	̃	PROPN
cana-535	150	8	�	�	PROPN
cana-535	150	9	and	and	CCONJ
cana-535	150	10	(	(	PUNCT
cana-535	150	11	𝑞	𝑞	X
cana-535	150	12	+	+	X
cana-535	150	13	𝛾)(𝜍	𝛾)(𝜍	NOUN
cana-535	150	14	+	+	CCONJ
cana-535	150	15	𝛾	𝛾	NOUN
cana-535	150	16	)	)	PUNCT
cana-535	150	17	=	=	SYM
cana-535	150	18	(	(	PUNCT
cana-535	150	19	𝑞𝜍	𝑞𝜍	NOUN
cana-535	150	20	)	)	PUNCT
cana-535	150	21	+	+	CCONJ
cana-535	150	22	𝛾	𝛾	NOUN
cana-535	150	23	for	for	ADP
cana-535	150	24	every	every	DET
cana-535	150	25	𝑞	𝑞	PROPN
cana-535	150	26	,	,	PUNCT
cana-535	150	27	𝜍	𝜍	ADP
cana-535	150	28	∈	∈	PROPN
cana-535	150	29	𝑁.	𝑁.	PROPN
cana-535	150	30	theorem	theorem	VERB
cana-535	150	31	3.9	3.9	NUM
cana-535	150	32	:	:	PUNCT
cana-535	150	33	let	let	VERB
cana-535	150	34	�	�	PROPN
cana-535	150	35	̃	̃	PROPN
cana-535	150	36	�	�	PROPN
cana-535	150	37	𝛾	𝛾	NOUN
cana-535	150	38	be	be	AUX
cana-535	150	39	a	a	DET
cana-535	150	40	hinr	hinr	NOUN
cana-535	150	41	of	of	ADP
cana-535	150	42	𝑁.	𝑁.	PROPN
cana-535	150	43	define	define	NOUN
cana-535	150	44	∅	∅	NOUN
cana-535	150	45	:	:	PUNCT
cana-535	150	46	𝑁	𝑁	PROPN
cana-535	150	47	�	�	PROPN
cana-535	150	48	̃	̃	PROPN
cana-535	150	49	�	�	PROPN
cana-535	151	1	𝛾	𝛾	NOUN
cana-535	151	2	⁄	⁄	PROPN
cana-535	151	3	→	→	SYM
cana-535	151	4	𝑃(𝑈)𝑋𝐼	𝑃(𝑈)𝑋𝐼	NOUN
cana-535	151	5	by	by	ADP
cana-535	151	6	∅(𝑞	∅(𝑞	PROPN
cana-535	151	7	+	+	CCONJ
cana-535	151	8	�	�	PROPN
cana-535	151	9	̃	̃	PROPN
cana-535	151	10	�	�	NOUN
cana-535	151	11	𝛾	𝛾	NOUN
cana-535	151	12	)	)	PUNCT
cana-535	151	13	=	=	SYM
cana-535	151	14	�	�	PROPN
cana-535	151	15	̃	̃	PROPN
cana-535	151	16	�	�	NOUN
cana-535	151	17	𝛾(𝑞	𝛾(𝑞	NOUN
cana-535	151	18	)	)	PUNCT
cana-535	151	19	i.e.	i.e.	X
cana-535	151	20	,	,	PUNCT
cana-535	151	21	∅(𝑞	∅(𝑞	PROPN
cana-535	151	22	+	+	SYM
cana-535	151	23	�	�	PROPN
cana-535	151	24	̃	̃	NOUN
cana-535	151	25	�	�	PROPN
cana-535	151	26	)	)	PUNCT
cana-535	151	27	=	=	SYM
cana-535	151	28	�	�	PROPN
cana-535	151	29	̃	̃	PROPN
cana-535	151	30	�	�	NOUN
cana-535	151	31	(𝑞	(𝑞	NOUN
cana-535	151	32	)	)	PUNCT
cana-535	151	33	and	and	CCONJ
cana-535	151	34	∅(𝑞	∅(𝑞	PROPN
cana-535	151	35	+	+	CCONJ
cana-535	151	36	𝛾	𝛾	X
cana-535	151	37	)	)	PUNCT
cana-535	151	38	=	=	SYM
cana-535	151	39	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	151	40	)	)	PUNCT
cana-535	151	41	∀	∀	PUNCT
cana-535	152	1	𝑞	𝑞	X
cana-535	152	2	∈	∈	PROPN
cana-535	152	3	𝑁.	𝑁.	PROPN
cana-535	152	4	then	then	ADV
cana-535	152	5	∅	∅	NOUN
cana-535	152	6	is	be	AUX
cana-535	152	7	a	a	DET
cana-535	152	8	hybrid	hybrid	ADJ
cana-535	152	9	ideal	ideal	NOUN
cana-535	152	10	of	of	ADP
cana-535	152	11	𝑁	𝑁	PROPN
cana-535	152	12	�	�	PROPN
cana-535	152	13	̃	̃	PROPN
cana-535	152	14	�	�	PROPN
cana-535	152	15	𝛾	𝛾	NOUN
cana-535	152	16	⁄	⁄	PROPN
cana-535	152	17	.	.	PUNCT
cana-535	153	1	proof	proof	NOUN
cana-535	153	2	:	:	PUNCT
cana-535	153	3	suppose	suppose	VERB
cana-535	153	4	that	that	SCONJ
cana-535	153	5	𝑞	𝑞	PROPN
cana-535	153	6	+	+	PROPN
cana-535	153	7	�	�	PROPN
cana-535	153	8	̃	̃	NOUN
cana-535	153	9	�	�	NOUN
cana-535	153	10	=	=	SYM
cana-535	153	11	𝜍	𝜍	PROPN
cana-535	153	12	+	+	PROPN
cana-535	153	13	�	�	PROPN
cana-535	153	14	̃	̃	PROPN
cana-535	153	15	�	�	PROPN
cana-535	153	16	and	and	CCONJ
cana-535	153	17	𝑞	𝑞	X
cana-535	153	18	+	+	NOUN
cana-535	153	19	𝛾	𝛾	NOUN
cana-535	153	20	=	=	SYM
cana-535	153	21	𝜍	𝜍	X
cana-535	153	22	+	+	CCONJ
cana-535	153	23	𝛾.	𝛾.	PROPN
cana-535	153	24	then	then	ADV
cana-535	153	25	�	�	PROPN
cana-535	153	26	̃	̃	PROPN
cana-535	153	27	�	�	PROPN
cana-535	153	28	(𝑞	(𝑞	NOUN
cana-535	153	29	−	−	NOUN
cana-535	153	30	𝜍	𝜍	NOUN
cana-535	153	31	)	)	PUNCT
cana-535	153	32	=	=	SYM
cana-535	153	33	�	�	PROPN
cana-535	153	34	̃	̃	PROPN
cana-535	153	35	�	�	PROPN
cana-535	153	36	(0	(0	X
cana-535	153	37	)	)	PUNCT
cana-535	153	38	and	and	CCONJ
cana-535	153	39	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	153	40	−	−	PROPN
cana-535	153	41	𝜍	𝜍	NOUN
cana-535	153	42	)	)	PUNCT
cana-535	153	43	=	=	PUNCT
cana-535	153	44	𝛾(0	𝛾(0	PROPN
cana-535	153	45	)	)	PUNCT
cana-535	153	46	.	.	PUNCT
cana-535	154	1	this	this	PRON
cana-535	154	2	implies	imply	VERB
cana-535	154	3	that	that	SCONJ
cana-535	154	4	�	�	PROPN
cana-535	154	5	̃	̃	PROPN
cana-535	154	6	�	�	NOUN
cana-535	154	7	(𝑞	(𝑞	NOUN
cana-535	154	8	)	)	PUNCT
cana-535	154	9	=	=	SYM
cana-535	154	10	�	�	PROPN
cana-535	154	11	̃	̃	PROPN
cana-535	154	12	�	�	PROPN
cana-535	154	13	(𝜍	(𝜍	NOUN
cana-535	154	14	)	)	PUNCT
cana-535	154	15	and	and	CCONJ
cana-535	154	16	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	154	17	)	)	PUNCT
cana-535	154	18	=	=	SYM
cana-535	154	19	𝛾(𝜍	𝛾(𝜍	NOUN
cana-535	154	20	)	)	PUNCT
cana-535	154	21	i.e.	i.e.	X
cana-535	154	22	,	,	PUNCT
cana-535	154	23	∅(𝑞	∅(𝑞	PROPN
cana-535	154	24	+	+	SYM
cana-535	154	25	�	�	PROPN
cana-535	154	26	̃	̃	NOUN
cana-535	154	27	�	�	PROPN
cana-535	154	28	)	)	PUNCT
cana-535	154	29	=	=	NOUN
cana-535	154	30	∅(𝜍	∅(𝜍	NOUN
cana-535	154	31	+	+	SYM
cana-535	154	32	�	�	PROPN
cana-535	154	33	̃	̃	PROPN
cana-535	154	34	�	�	PROPN
cana-535	154	35	)	)	PUNCT
cana-535	154	36	and	and	CCONJ
cana-535	154	37	∅(𝑞	∅(𝑞	PROPN
cana-535	154	38	+	+	CCONJ
cana-535	154	39	𝛾	𝛾	X
cana-535	154	40	)	)	PUNCT
cana-535	154	41	=	=	NOUN
cana-535	154	42	∅(𝜍	∅(𝜍	NOUN
cana-535	154	43	+	+	SYM
cana-535	154	44	𝛾	𝛾	NOUN
cana-535	154	45	)	)	PUNCT
cana-535	154	46	.	.	PUNCT
cana-535	155	1	therefore	therefore	ADV
cana-535	155	2	∅	∅	NOUN
cana-535	155	3	is	be	AUX
cana-535	155	4	well	well	ADV
cana-535	155	5	defined	define	VERB
cana-535	155	6	.	.	PUNCT
cana-535	156	1	we	we	PRON
cana-535	156	2	verify	verify	VERB
cana-535	156	3	that	that	SCONJ
cana-535	156	4	∅	∅	NOUN
cana-535	156	5	is	be	AUX
cana-535	156	6	a	a	DET
cana-535	156	7	hybrid	hybrid	ADJ
cana-535	156	8	ideal	ideal	NOUN
cana-535	156	9	of	of	ADP
cana-535	156	10	𝑁	𝑁	PROPN
cana-535	156	11	�	�	PROPN
cana-535	156	12	̃	̃	PROPN
cana-535	156	13	�	�	PROPN
cana-535	156	14	𝛾	𝛾	NOUN
cana-535	156	15	⁄	⁄	PROPN
cana-535	156	16	.	.	PUNCT
cana-535	157	1	let	let	VERB
cana-535	157	2	𝑞	𝑞	PRON
cana-535	157	3	+	+	PROPN
cana-535	157	4	�	�	PROPN
cana-535	157	5	̃	̃	PROPN
cana-535	157	6	�	�	NOUN
cana-535	157	7	𝛾	𝛾	NOUN
cana-535	157	8	,	,	PUNCT
cana-535	157	9	𝜍	𝜍	PROPN
cana-535	157	10	+	+	PROPN
cana-535	157	11	�	�	PROPN
cana-535	157	12	̃	̃	PROPN
cana-535	157	13	�	�	PROPN
cana-535	157	14	𝛾	𝛾	NOUN
cana-535	157	15	,	,	PUNCT
cana-535	157	16	𝑗	𝑗	PROPN
cana-535	157	17	+	+	NUM
cana-535	157	18	�	�	PROPN
cana-535	157	19	̃	̃	PROPN
cana-535	157	20	�	�	PROPN
cana-535	157	21	𝛾	𝛾	NOUN
cana-535	157	22	∈	∈	NOUN
cana-535	157	23	𝑁	𝑁	PROPN
cana-535	157	24	�	�	PROPN
cana-535	157	25	̃	̃	PROPN
cana-535	157	26	�	�	PROPN
cana-535	157	27	𝛾	𝛾	NOUN
cana-535	157	28	⁄	⁄	PROPN
cana-535	157	29	.	.	PUNCT
cana-535	158	1	(	(	PUNCT
cana-535	158	2	𝑖	𝑖	X
cana-535	158	3	)	)	PUNCT
cana-535	158	4	∅((𝑞	∅((𝑞	PROPN
cana-535	158	5	+	+	SYM
cana-535	158	6	�	�	PROPN
cana-535	158	7	̃	̃	PROPN
cana-535	158	8	�	�	PROPN
cana-535	158	9	)	)	PUNCT
cana-535	159	1	+	+	CCONJ
cana-535	159	2	(	(	PUNCT
cana-535	159	3	𝜍	𝜍	PART
cana-535	159	4	+	+	PROPN
cana-535	159	5	�	�	PROPN
cana-535	159	6	̃	̃	PROPN
cana-535	159	7	�	�	PROPN
cana-535	159	8	)	)	PUNCT
cana-535	159	9	)	)	PUNCT
cana-535	160	1	=	=	PUNCT
cana-535	161	1	∅((𝑞	∅((𝑞	PROPN
cana-535	161	2	+	+	CCONJ
cana-535	161	3	𝜍	𝜍	X
cana-535	161	4	)	)	PUNCT
cana-535	161	5	+	+	CCONJ
cana-535	161	6	�	�	PROPN
cana-535	161	7	̃	̃	NOUN
cana-535	161	8	�	�	PROPN
cana-535	161	9	)	)	PUNCT
cana-535	161	10	=	=	SYM
cana-535	161	11	�	�	PROPN
cana-535	161	12	̃	̃	PROPN
cana-535	161	13	�	�	PROPN
cana-535	161	14	(𝑞	(𝑞	NOUN
cana-535	161	15	+	+	CCONJ
cana-535	161	16	𝜍	𝜍	X
cana-535	161	17	)	)	PUNCT
cana-535	161	18	⊇	⊇	PROPN
cana-535	161	19	�	�	PROPN
cana-535	161	20	̃	̃	PROPN
cana-535	161	21	�	�	NOUN
cana-535	161	22	(𝑞	(𝑞	NOUN
cana-535	161	23	)	)	PUNCT
cana-535	161	24	∩	∩	PROPN
cana-535	161	25	�	�	PROPN
cana-535	161	26	̃	̃	PROPN
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cana-535	161	28	(𝜍	(𝜍	NOUN
cana-535	161	29	)	)	PUNCT
cana-535	161	30	=	=	PUNCT
cana-535	162	1	∅(𝑞	∅(𝑞	PROPN
cana-535	162	2	+	+	CCONJ
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cana-535	162	4	̃	̃	PROPN
cana-535	162	5	�	�	PROPN
cana-535	162	6	)	)	PUNCT
cana-535	162	7	∩	∩	NOUN
cana-535	162	8	∅(𝜍	∅(𝜍	NOUN
cana-535	162	9	+	+	SYM
cana-535	162	10	�	�	PROPN
cana-535	162	11	̃	̃	PROPN
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cana-535	162	13	)	)	PUNCT
cana-535	162	14	,	,	PUNCT
cana-535	162	15	and	and	CCONJ
cana-535	162	16	∅((𝑞	∅((𝑞	NOUN
cana-535	162	17	+	+	CCONJ
cana-535	162	18	𝛾	𝛾	X
cana-535	162	19	)	)	PUNCT
cana-535	163	1	+	+	CCONJ
cana-535	163	2	(	(	PUNCT
cana-535	163	3	𝜍	𝜍	X
cana-535	163	4	+	+	ADJ
cana-535	163	5	𝛾	𝛾	NOUN
cana-535	163	6	)	)	PUNCT
cana-535	163	7	)	)	PUNCT
cana-535	164	1	=	=	PUNCT
cana-535	165	1	∅((𝑞	∅((𝑞	PROPN
cana-535	165	2	+	+	CCONJ
cana-535	165	3	𝜍	𝜍	X
cana-535	165	4	)	)	PUNCT
cana-535	165	5	+	+	NUM
cana-535	165	6	𝛾	𝛾	X
cana-535	165	7	)	)	PUNCT
cana-535	165	8	=	=	SYM
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cana-535	165	10	+	+	CCONJ
cana-535	165	11	𝜍	𝜍	X
cana-535	165	12	)	)	PUNCT
cana-535	165	13	≤	≤	NUM
cana-535	165	14	⋁{𝛾(𝑞	⋁{𝛾(𝑞	NUM
cana-535	165	15	)	)	PUNCT
cana-535	165	16	,	,	PUNCT
cana-535	165	17	𝛾(𝜍	𝛾(𝜍	PROPN
cana-535	165	18	)	)	PUNCT
cana-535	165	19	}	}	PUNCT
cana-535	166	1	=	=	SYM
cana-535	166	2	⋁{∅(𝑞	⋁{∅(𝑞	PROPN
cana-535	166	3	+	+	CCONJ
cana-535	166	4	𝛾	𝛾	PROPN
cana-535	166	5	)	)	PUNCT
cana-535	166	6	,	,	PUNCT
cana-535	166	7	∅(𝜍	∅(𝜍	NOUN
cana-535	166	8	+	+	CCONJ
cana-535	166	9	𝛾	𝛾	NOUN
cana-535	166	10	)	)	PUNCT
cana-535	166	11	}	}	PUNCT
cana-535	166	12	.	.	PUNCT
cana-535	167	1	(	(	PUNCT
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cana-535	167	3	)	)	PUNCT
cana-535	167	4	∅(𝑞	∅(𝑞	PROPN
cana-535	167	5	+	+	CCONJ
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cana-535	167	7	̃	̃	NOUN
cana-535	167	8	�	�	PROPN
cana-535	167	9	)	)	PUNCT
cana-535	167	10	=	=	SYM
cana-535	167	11	�	�	PROPN
cana-535	167	12	̃	̃	PROPN
cana-535	167	13	�	�	NOUN
cana-535	167	14	(𝑞	(𝑞	NOUN
cana-535	167	15	)	)	PUNCT
cana-535	167	16	=	=	SYM
cana-535	167	17	�	�	PROPN
cana-535	167	18	̃	̃	PROPN
cana-535	167	19	�	�	PROPN
cana-535	167	20	(−𝑞	(−𝑞	PROPN
cana-535	167	21	)	)	PUNCT
cana-535	168	1	=	=	SYM
cana-535	168	2	∅(−𝑞	∅(−𝑞	NUM
cana-535	168	3	+	+	NUM
cana-535	168	4	�	�	PROPN
cana-535	168	5	̃	̃	PROPN
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cana-535	168	7	)	)	PUNCT
cana-535	169	1	and	and	CCONJ
cana-535	169	2	∅(𝑞	∅(𝑞	PROPN
cana-535	169	3	+	+	CCONJ
cana-535	169	4	𝛾	𝛾	X
cana-535	169	5	)	)	PUNCT
cana-535	169	6	=	=	SYM
cana-535	169	7	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	169	8	)	)	PUNCT
cana-535	169	9	=	=	PUNCT
cana-535	169	10	𝛾(−𝑞	𝛾(−𝑞	X
cana-535	169	11	)	)	PUNCT
cana-535	170	1	=	=	SYM
cana-535	170	2	∅(−𝑞	∅(−𝑞	NUM
cana-535	170	3	+	+	SYM
cana-535	170	4	𝛾	𝛾	NOUN
cana-535	170	5	)	)	PUNCT
cana-535	170	6	.	.	PUNCT
cana-535	171	1	(	(	PUNCT
cana-535	171	2	𝑖𝑖𝑖	𝑖𝑖𝑖	NOUN
cana-535	171	3	)	)	PUNCT
cana-535	171	4	∅	∅	NOUN
cana-535	171	5	(	(	PUNCT
cana-535	171	6	(	(	PUNCT
cana-535	171	7	𝜍	𝜍	PART
cana-535	171	8	+	+	PROPN
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cana-535	171	10	̃	̃	PROPN
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cana-535	171	12	)	)	PUNCT
cana-535	171	13	+	+	CCONJ
cana-535	171	14	(	(	PUNCT
cana-535	171	15	𝑞	𝑞	PROPN
cana-535	171	16	+	+	PROPN
cana-535	171	17	�	�	PROPN
cana-535	171	18	̃	̃	PROPN
cana-535	171	19	�	�	PROPN
cana-535	171	20	)	)	PUNCT
cana-535	171	21	−	−	PROPN
cana-535	172	1	(	(	PUNCT
cana-535	172	2	𝜍	𝜍	PROPN
cana-535	172	3	+	+	PROPN
cana-535	172	4	�	�	PROPN
cana-535	172	5	̃	̃	PROPN
cana-535	172	6	�	�	PROPN
cana-535	172	7	)	)	PUNCT
cana-535	172	8	)	)	PUNCT
cana-535	173	1	=	=	SYM
cana-535	173	2	∅((𝜍	∅((𝜍	PROPN
cana-535	173	3	+	+	CCONJ
cana-535	173	4	𝑞	𝑞	X
cana-535	173	5	−	−	PROPN
cana-535	173	6	𝜍	𝜍	X
cana-535	173	7	)	)	PUNCT
cana-535	173	8	+	+	CCONJ
cana-535	173	9	�	�	PROPN
cana-535	173	10	̃	̃	NOUN
cana-535	173	11	�	�	PROPN
cana-535	173	12	)	)	PUNCT
cana-535	173	13	=	=	SYM
cana-535	173	14	�	�	PROPN
cana-535	173	15	̃	̃	PROPN
cana-535	173	16	�	�	PROPN
cana-535	173	17	(𝜍	(𝜍	NOUN
cana-535	173	18	+	+	NOUN
cana-535	173	19	𝑞	𝑞	X
cana-535	173	20	−	−	NOUN
cana-535	173	21	𝜍	𝜍	NOUN
cana-535	173	22	)	)	PUNCT
cana-535	173	23	=	=	SYM
cana-535	173	24	�	�	PROPN
cana-535	173	25	̃	̃	PROPN
cana-535	173	26	�	�	NOUN
cana-535	173	27	(𝑞	(𝑞	NOUN
cana-535	173	28	)	)	PUNCT
cana-535	173	29	=	=	PUNCT
cana-535	173	30	∅(𝑞	∅(𝑞	PROPN
cana-535	173	31	+	+	CCONJ
cana-535	173	32	�	�	PROPN
cana-535	173	33	̃	̃	PROPN
cana-535	173	34	�	�	PROPN
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cana-535	173	36	and	and	CCONJ
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cana-535	173	38	(	(	PUNCT
cana-535	173	39	(	(	PUNCT
cana-535	173	40	𝜍	𝜍	X
cana-535	173	41	+	+	X
cana-535	173	42	𝛾	𝛾	X
cana-535	173	43	)	)	PUNCT
cana-535	173	44	+	+	CCONJ
cana-535	173	45	(	(	PUNCT
cana-535	173	46	𝑞	𝑞	X
cana-535	173	47	+	+	NOUN
cana-535	173	48	𝛾	𝛾	NOUN
cana-535	173	49	)	)	PUNCT
cana-535	173	50	−	−	PROPN
cana-535	173	51	(	(	PUNCT
cana-535	173	52	𝜍	𝜍	X
cana-535	173	53	+	+	CCONJ
cana-535	173	54	𝛾	𝛾	NOUN
cana-535	173	55	)	)	PUNCT
cana-535	173	56	)	)	PUNCT
cana-535	174	1	=	=	SYM
cana-535	174	2	∅((𝜍	∅((𝜍	PROPN
cana-535	174	3	+	+	CCONJ
cana-535	174	4	𝑞	𝑞	X
cana-535	174	5	−	−	PROPN
cana-535	174	6	𝜍	𝜍	X
cana-535	174	7	)	)	PUNCT
cana-535	174	8	+	+	NUM
cana-535	174	9	𝛾	𝛾	X
cana-535	174	10	)	)	PUNCT
cana-535	174	11	=	=	SYM
cana-535	174	12	𝛾(𝜍	𝛾(𝜍	NOUN
cana-535	174	13	+	+	CCONJ
cana-535	174	14	𝑞	𝑞	X
cana-535	174	15	−	−	NOUN
cana-535	174	16	𝜍	𝜍	NOUN
cana-535	174	17	)	)	PUNCT
cana-535	174	18	=	=	SYM
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cana-535	174	20	)	)	PUNCT
cana-535	174	21	=	=	VERB
cana-535	174	22	∅(𝑞	∅(𝑞	PROPN
cana-535	174	23	+	+	CCONJ
cana-535	174	24	𝛾	𝛾	NOUN
cana-535	174	25	)	)	PUNCT
cana-535	174	26	.	.	PUNCT
cana-535	175	1	(	(	PUNCT
cana-535	175	2	𝑖𝑣	𝑖𝑣	X
cana-535	175	3	)	)	PUNCT
cana-535	175	4	∅	∅	NOUN
cana-535	175	5	(	(	PUNCT
cana-535	175	6	(	(	PUNCT
cana-535	175	7	𝜍	𝜍	PART
cana-535	175	8	+	+	PROPN
cana-535	175	9	�	�	PROPN
cana-535	175	10	̃	̃	PROPN
cana-535	175	11	�	�	PROPN
cana-535	175	12	)((𝑞	)((𝑞	PUNCT
cana-535	175	13	+	+	PROPN
cana-535	175	14	�	�	PROPN
cana-535	175	15	̃	̃	PROPN
cana-535	175	16	�	�	PROPN
cana-535	175	17	)	)	PUNCT
cana-535	175	18	+	+	CCONJ
cana-535	175	19	(	(	PUNCT
cana-535	175	20	𝑗	𝑗	PROPN
cana-535	175	21	+	+	NUM
cana-535	175	22	�	�	PROPN
cana-535	175	23	̃	̃	PROPN
cana-535	175	24	�	�	PROPN
cana-535	175	25	)	)	PUNCT
cana-535	175	26	−	−	PROPN
cana-535	176	1	(	(	PUNCT
cana-535	176	2	𝜍	𝜍	PROPN
cana-535	176	3	+	+	PROPN
cana-535	176	4	�	�	PROPN
cana-535	176	5	̃	̃	PROPN
cana-535	176	6	�	�	PROPN
cana-535	176	7	)(𝑞	)(𝑞	PRON
cana-535	176	8	+	+	PROPN
cana-535	176	9	�	�	PROPN
cana-535	176	10	̃	̃	PROPN
cana-535	176	11	�	�	PROPN
cana-535	176	12	)	)	PUNCT
cana-535	176	13	)	)	PUNCT
cana-535	177	1	=	=	NOUN
cana-535	177	2	∅	∅	NOUN
cana-535	177	3	(	(	PUNCT
cana-535	177	4	(	(	PUNCT
cana-535	177	5	𝜍	𝜍	PART
cana-535	177	6	+	+	PROPN
cana-535	177	7	�	�	PROPN
cana-535	177	8	̃	̃	PROPN
cana-535	177	9	�	�	PROPN
cana-535	177	10	)((𝑞	)((𝑞	PUNCT
cana-535	177	11	+	+	NUM
cana-535	177	12	𝑗	𝑗	X
cana-535	177	13	)	)	PUNCT
cana-535	177	14	+	+	CCONJ
cana-535	177	15	�	�	PROPN
cana-535	177	16	̃	̃	PROPN
cana-535	177	17	�	�	PROPN
cana-535	177	18	)	)	PUNCT
cana-535	177	19	−	−	PROPN
cana-535	177	20	(	(	PUNCT
cana-535	177	21	𝜍𝑞	𝜍𝑞	X
cana-535	177	22	+	+	CCONJ
cana-535	177	23	�	�	PROPN
cana-535	177	24	̃	̃	PROPN
cana-535	177	25	�	�	NOUN
cana-535	177	26	)	)	PUNCT
cana-535	177	27	)	)	PUNCT
cana-535	178	1	=	=	PUNCT
cana-535	178	2	∅((𝜍(𝑞	∅((𝜍(𝑞	NOUN
cana-535	178	3	+	+	CCONJ
cana-535	178	4	𝑗	𝑗	X
cana-535	178	5	)	)	PUNCT
cana-535	178	6	+	+	CCONJ
cana-535	178	7	�	�	PROPN
cana-535	178	8	̃	̃	PROPN
cana-535	178	9	�	�	PROPN
cana-535	178	10	)	)	PUNCT
cana-535	178	11	−	−	PROPN
cana-535	178	12	(	(	PUNCT
cana-535	178	13	𝜍𝑞	𝜍𝑞	X
cana-535	178	14	+	+	CCONJ
cana-535	178	15	�	�	PROPN
cana-535	178	16	̃	̃	PROPN
cana-535	178	17	�	�	NOUN
cana-535	178	18	)	)	PUNCT
cana-535	178	19	)	)	PUNCT
cana-535	179	1	=	=	PUNCT
cana-535	179	2	∅((𝜍(𝑞	∅((𝜍(𝑞	NOUN
cana-535	179	3	+	+	CCONJ
cana-535	179	4	𝑗	𝑗	NOUN
cana-535	179	5	)	)	PUNCT
cana-535	179	6	−	−	PROPN
cana-535	179	7	𝜍𝑞	𝜍𝑞	PROPN
cana-535	179	8	)	)	PUNCT
cana-535	179	9	+	+	NUM
cana-535	179	10	�	�	PROPN
cana-535	179	11	̃	̃	NOUN
cana-535	179	12	�	�	PROPN
cana-535	179	13	)	)	PUNCT
cana-535	179	14	=	=	SYM
cana-535	179	15	�	�	PROPN
cana-535	179	16	̃	̃	PROPN
cana-535	179	17	�	�	PROPN
cana-535	179	18	(𝜍(𝑞	(𝜍(𝑞	X
cana-535	179	19	+	+	NOUN
cana-535	179	20	𝑗	𝑗	NOUN
cana-535	179	21	)	)	PUNCT
cana-535	179	22	−	−	PROPN
cana-535	179	23	𝜍𝑞	𝜍𝑞	NOUN
cana-535	179	24	)	)	PUNCT
cana-535	179	25	=	=	SYM
cana-535	179	26	�	�	PROPN
cana-535	179	27	̃	̃	PROPN
cana-535	179	28	�	�	PROPN
cana-535	179	29	(𝑗	(𝑗	NUM
cana-535	179	30	)	)	PUNCT
cana-535	179	31	=	=	SYM
cana-535	179	32	∅(𝑗	∅(𝑗	PROPN
cana-535	179	33	+	+	PROPN
cana-535	179	34	�	�	PROPN
cana-535	179	35	̃	̃	PROPN
cana-535	179	36	�	�	PROPN
cana-535	179	37	)	)	PUNCT
cana-535	179	38	and	and	CCONJ
cana-535	179	39	∅	∅	NOUN
cana-535	179	40	(	(	PUNCT
cana-535	179	41	(	(	PUNCT
cana-535	179	42	𝜍	𝜍	X
cana-535	179	43	+	+	CCONJ
cana-535	179	44	𝛾)((𝑞	𝛾)((𝑞	NOUN
cana-535	179	45	+	+	CCONJ
cana-535	179	46	𝛾	𝛾	X
cana-535	179	47	)	)	PUNCT
cana-535	179	48	+	+	CCONJ
cana-535	179	49	(	(	PUNCT
cana-535	179	50	𝑗	𝑗	X
cana-535	179	51	+	+	NUM
cana-535	179	52	𝛾	𝛾	NOUN
cana-535	179	53	)	)	PUNCT
cana-535	179	54	−	−	PROPN
cana-535	179	55	(	(	PUNCT
cana-535	179	56	𝜍	𝜍	PROPN
cana-535	179	57	+	+	NOUN
cana-535	179	58	𝛾)(𝑞	𝛾)(𝑞	PUNCT
cana-535	179	59	+	+	CCONJ
cana-535	179	60	𝛾	𝛾	NOUN
cana-535	179	61	)	)	PUNCT
cana-535	179	62	)	)	PUNCT
cana-535	180	1	=	=	NOUN
cana-535	180	2	∅	∅	NOUN
cana-535	180	3	(	(	PUNCT
cana-535	180	4	(	(	PUNCT
cana-535	180	5	𝜍	𝜍	X
cana-535	180	6	+	+	CCONJ
cana-535	180	7	𝛾)((𝑞	𝛾)((𝑞	PROPN
cana-535	180	8	+	+	CCONJ
cana-535	180	9	𝑗	𝑗	NOUN
cana-535	180	10	)	)	PUNCT
cana-535	180	11	+	+	NUM
cana-535	180	12	𝛾	𝛾	NOUN
cana-535	180	13	)	)	PUNCT
cana-535	180	14	−	−	PROPN
cana-535	180	15	(	(	PUNCT
cana-535	180	16	𝜍𝑞	𝜍𝑞	NOUN
cana-535	180	17	+	+	CCONJ
cana-535	180	18	𝛾	𝛾	NOUN
cana-535	180	19	)	)	PUNCT
cana-535	180	20	)	)	PUNCT
cana-535	181	1	=	=	PUNCT
cana-535	181	2	∅((𝜍(𝑞	∅((𝜍(𝑞	NOUN
cana-535	181	3	+	+	CCONJ
cana-535	181	4	𝑗	𝑗	X
cana-535	181	5	)	)	PUNCT
cana-535	181	6	+	+	NUM
cana-535	181	7	𝛾	𝛾	NOUN
cana-535	181	8	)	)	PUNCT
cana-535	181	9	−	−	PROPN
cana-535	181	10	(	(	PUNCT
cana-535	181	11	𝜍𝑞	𝜍𝑞	NOUN
cana-535	181	12	+	+	CCONJ
cana-535	181	13	𝛾	𝛾	NOUN
cana-535	181	14	)	)	PUNCT
cana-535	181	15	)	)	PUNCT
cana-535	182	1	=	=	PUNCT
cana-535	182	2	∅((𝜍(𝑞	∅((𝜍(𝑞	NOUN
cana-535	182	3	+	+	CCONJ
cana-535	182	4	𝑗	𝑗	NOUN
cana-535	182	5	)	)	PUNCT
cana-535	182	6	−	−	PROPN
cana-535	182	7	𝜍𝑞	𝜍𝑞	NOUN
cana-535	182	8	)	)	PUNCT
cana-535	182	9	+	+	NUM
cana-535	182	10	𝛾	𝛾	X
cana-535	182	11	)	)	PUNCT
cana-535	182	12	=	=	SYM
cana-535	182	13	𝛾(𝜍(𝑞	𝛾(𝜍(𝑞	PROPN
cana-535	182	14	+	+	CCONJ
cana-535	182	15	𝑗	𝑗	NOUN
cana-535	182	16	)	)	PUNCT
cana-535	182	17	−	−	PROPN
cana-535	182	18	𝜍𝑞	𝜍𝑞	NOUN
cana-535	182	19	)	)	PUNCT
cana-535	182	20	=	=	SYM
cana-535	182	21	𝛾(𝑗	𝛾(𝑗	PROPN
cana-535	182	22	)	)	PUNCT
cana-535	182	23	=	=	PUNCT
cana-535	182	24	∅(𝑗	∅(𝑗	PROPN
cana-535	182	25	+	+	CCONJ
cana-535	182	26	𝛾	𝛾	PROPN
cana-535	182	27	)	)	PUNCT
cana-535	182	28	.	.	PUNCT
cana-535	183	1	hence	hence	ADV
cana-535	183	2	∅	∅	NOUN
cana-535	183	3	is	be	AUX
cana-535	183	4	a	a	DET
cana-535	183	5	hybrid	hybrid	ADJ
cana-535	183	6	ideal	ideal	NOUN
cana-535	183	7	of	of	ADP
cana-535	183	8	𝑁	𝑁	PROPN
cana-535	183	9	�	�	PROPN
cana-535	183	10	̃	̃	PROPN
cana-535	183	11	�	�	PROPN
cana-535	183	12	𝛾	𝛾	NOUN
cana-535	183	13	⁄	⁄	PROPN
cana-535	183	14	.	.	PUNCT
cana-535	184	1	communications	communication	NOUN
cana-535	184	2	on	on	ADP
cana-535	184	3	applied	apply	VERB
cana-535	184	4	nonlinear	nonlinear	ADJ
cana-535	184	5	analysis	analysis	NOUN
cana-535	184	6	issn	issn	NOUN
cana-535	184	7	:	:	PUNCT
cana-535	184	8	1074	1074	NUM
cana-535	184	9	-	-	PUNCT
cana-535	184	10	133x	133x	NUM
cana-535	184	11	vol	vol	NOUN
cana-535	184	12	31	31	NUM
cana-535	184	13	no	no	NOUN
cana-535	184	14	.	.	NOUN
cana-535	184	15	2	2	NUM
cana-535	184	16	(	(	PUNCT
cana-535	184	17	2024	2024	NUM
cana-535	184	18	)	)	PUNCT
cana-535	184	19	211	211	NUM
cana-535	184	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-535	184	21	definition	definition	NOUN
cana-535	184	22	3.10	3.10	NUM
cana-535	184	23	:	:	PUNCT
cana-535	184	24	let	let	VERB
cana-535	184	25	𝑁1	𝑁1	NOUN
cana-535	184	26	,	,	PUNCT
cana-535	184	27	𝑁2	𝑁2	NOUN
cana-535	184	28	be	be	AUX
cana-535	184	29	near	near	ADP
cana-535	184	30	rings	ring	NOUN
cana-535	184	31	.	.	PUNCT
cana-535	185	1	a	a	DET
cana-535	185	2	mapping	mapping	NOUN
cana-535	185	3	∅	∅	NOUN
cana-535	185	4	:	:	PUNCT
cana-535	185	5	𝑁1	𝑁1	PROPN
cana-535	185	6	→	→	SYM
cana-535	185	7	𝑁2	𝑁2	NOUN
cana-535	185	8	is	be	AUX
cana-535	185	9	called	call	VERB
cana-535	185	10	a	a	DET
cana-535	185	11	nearing	near	VERB
cana-535	185	12	homomorphism	homomorphism	NOUN
cana-535	185	13	if	if	SCONJ
cana-535	185	14	∅(𝑞	∅(𝑞	PROPN
cana-535	185	15	+	+	CCONJ
cana-535	185	16	𝜍	𝜍	X
cana-535	185	17	)	)	PUNCT
cana-535	185	18	=	=	NOUN
cana-535	185	19	∅(𝑞	∅(𝑞	VERB
cana-535	185	20	)	)	PUNCT
cana-535	185	21	+	+	NUM
cana-535	185	22	∅(𝜍	∅(𝜍	NOUN
cana-535	185	23	)	)	PUNCT
cana-535	185	24	and	and	CCONJ
cana-535	185	25	∅(𝑞𝜍	∅(𝑞𝜍	ADJ
cana-535	185	26	)	)	PUNCT
cana-535	185	27	=	=	SYM
cana-535	185	28	∅(𝑞)∅(𝜍	∅(𝑞)∅(𝜍	NOUN
cana-535	185	29	)	)	PUNCT
cana-535	185	30	∀	∀	PUNCT
cana-535	186	1	𝑞	𝑞	NOUN
cana-535	186	2	,	,	PUNCT
cana-535	186	3	𝜍	𝜍	PROPN
cana-535	186	4	∈	∈	PROPN
cana-535	186	5	𝑁1	𝑁1	PROPN
cana-535	186	6	.	.	PUNCT
cana-535	187	1	moreover	moreover	ADV
cana-535	187	2	if	if	SCONJ
cana-535	187	3	∅	∅	NOUN
cana-535	187	4	is	be	AUX
cana-535	187	5	one	one	NUM
cana-535	187	6	-	-	PUNCT
cana-535	187	7	one	one	NUM
cana-535	187	8	then	then	ADV
cana-535	187	9	∅	∅	NOUN
cana-535	187	10	is	be	AUX
cana-535	187	11	called	call	VERB
cana-535	187	12	as	as	ADP
cana-535	187	13	monomorphism	monomorphism	NOUN
cana-535	187	14	,	,	PUNCT
cana-535	187	15	if	if	SCONJ
cana-535	187	16	∅	∅	NOUN
cana-535	187	17	is	be	AUX
cana-535	187	18	onto	onto	ADP
cana-535	187	19	then	then	ADV
cana-535	187	20	∅	∅	NOUN
cana-535	187	21	is	be	AUX
cana-535	187	22	called	call	VERB
cana-535	187	23	epimorphism	epimorphism	NOUN
cana-535	187	24	,	,	PUNCT
cana-535	187	25	if	if	SCONJ
cana-535	187	26	∅	∅	NOUN
cana-535	187	27	is	be	AUX
cana-535	187	28	bijective	bijective	ADJ
cana-535	187	29	then	then	ADV
cana-535	187	30	∅	∅	NOUN
cana-535	187	31	is	be	AUX
cana-535	187	32	called	call	VERB
cana-535	187	33	an	an	DET
cana-535	187	34	isomorphism	isomorphism	NOUN
cana-535	187	35	.	.	PUNCT
cana-535	188	1	theorem	theorem	VERB
cana-535	188	2	3.11	3.11	NUM
cana-535	188	3	:	:	PUNCT
cana-535	188	4	if	if	SCONJ
cana-535	188	5	�	�	PROPN
cana-535	188	6	̃	̃	PROPN
cana-535	188	7	�	�	NOUN
cana-535	188	8	𝛾	𝛾	NOUN
cana-535	188	9	is	be	AUX
cana-535	188	10	a	a	DET
cana-535	188	11	hinr	hinr	ADJ
cana-535	188	12	𝑁	𝑁	NOUN
cana-535	188	13	then	then	ADV
cana-535	188	14	the	the	DET
cana-535	188	15	mapping	mapping	NOUN
cana-535	188	16	∅	∅	NOUN
cana-535	188	17	:	:	PUNCT
cana-535	188	18	𝑁	𝑁	PROPN
cana-535	188	19	→	→	SYM
cana-535	188	20	𝑁/	𝑁/	NUM
cana-535	188	21	�	�	NOUN
cana-535	188	22	̃	̃	NOUN
cana-535	188	23	�	�	PROPN
cana-535	188	24	𝛾	𝛾	NOUN
cana-535	188	25	defined	define	VERB
cana-535	188	26	by	by	ADP
cana-535	188	27	∅(𝑞	∅(𝑞	NOUN
cana-535	188	28	)	)	PUNCT
cana-535	188	29	=	=	SYM
cana-535	188	30	𝑞	𝑞	PROPN
cana-535	188	31	+	+	PROPN
cana-535	188	32	�	�	PROPN
cana-535	188	33	̃	̃	PROPN
cana-535	188	34	�	�	PROPN
cana-535	188	35	𝛾	𝛾	PART
cana-535	188	36	∀	∀	NOUN
cana-535	188	37	𝑞	𝑞	X
cana-535	188	38	∈	∈	NOUN
cana-535	188	39	𝑁	𝑁	PROPN
cana-535	188	40	where	where	SCONJ
cana-535	188	41	∅(𝑞	∅(𝑞	VERB
cana-535	188	42	)	)	PUNCT
cana-535	188	43	=	=	SYM
cana-535	188	44	𝑞	𝑞	PROPN
cana-535	188	45	+	+	PROPN
cana-535	188	46	�	�	PROPN
cana-535	188	47	̃	̃	PROPN
cana-535	188	48	�	�	PROPN
cana-535	188	49	and	and	CCONJ
cana-535	188	50	∅(𝑞	∅(𝑞	PROPN
cana-535	188	51	)	)	PUNCT
cana-535	188	52	=	=	SYM
cana-535	188	53	𝑞	𝑞	PROPN
cana-535	188	54	+	+	CCONJ
cana-535	188	55	𝛾	𝛾	PROPN
cana-535	188	56	,	,	PUNCT
cana-535	188	57	is	be	AUX
cana-535	188	58	a	a	DET
cana-535	188	59	near	near	ADJ
cana-535	188	60	ring	ring	NOUN
cana-535	188	61	epimorphism	epimorphism	NOUN
cana-535	188	62	with	with	ADP
cana-535	188	63	kernal	kernal	ADJ
cana-535	188	64	�	�	PROPN
cana-535	188	65	̃	̃	PROPN
cana-535	188	66	�	�	NOUN
cana-535	188	67	𝛾∗	𝛾∗	NOUN
cana-535	188	68	where	where	SCONJ
cana-535	188	69	�	�	PROPN
cana-535	188	70	̃	̃	PROPN
cana-535	188	71	�	�	NOUN
cana-535	188	72	𝛾∗	𝛾∗	NOUN
cana-535	188	73	=	=	SYM
cana-535	188	74	{	{	PUNCT
cana-535	188	75	𝑞	𝑞	X
cana-535	188	76	∈	∈	PROPN
cana-535	188	77	𝑁	𝑁	PROPN
cana-535	188	78	:	:	PUNCT
cana-535	188	79	�	�	PROPN
cana-535	188	80	̃	̃	PROPN
cana-535	188	81	�	�	NOUN
cana-535	188	82	𝛾(𝑞	𝛾(𝑞	NOUN
cana-535	188	83	)	)	PUNCT
cana-535	188	84	=	=	SYM
cana-535	188	85	�	�	PROPN
cana-535	188	86	̃	̃	PROPN
cana-535	188	87	�	�	NOUN
cana-535	188	88	𝛾(0	𝛾(0	NOUN
cana-535	188	89	)	)	PUNCT
cana-535	188	90	}	}	PUNCT
cana-535	188	91	ie	ie	PROPN
cana-535	188	92	.	.	PROPN
cana-535	188	93	,	,	PUNCT
cana-535	188	94	�	�	PROPN
cana-535	188	95	̃	̃	PROPN
cana-535	188	96	�	�	NOUN
cana-535	188	97	𝛾∗	𝛾∗	NOUN
cana-535	188	98	=	=	SYM
cana-535	188	99	{	{	PUNCT
cana-535	188	100	𝑞	𝑞	X
cana-535	188	101	∈	∈	PROPN
cana-535	188	102	𝑁	𝑁	PROPN
cana-535	188	103	:	:	PUNCT
cana-535	188	104	�	�	PROPN
cana-535	188	105	̃	̃	PROPN
cana-535	188	106	�	�	NOUN
cana-535	188	107	(𝑞	(𝑞	NOUN
cana-535	188	108	)	)	PUNCT
cana-535	188	109	=	=	SYM
cana-535	188	110	�	�	PROPN
cana-535	188	111	̃	̃	PROPN
cana-535	188	112	�	�	PROPN
cana-535	188	113	(0	(0	NOUN
cana-535	188	114	)	)	PUNCT
cana-535	188	115	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-535	188	116	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	188	117	)	)	PUNCT
cana-535	188	118	=	=	PUNCT
cana-535	188	119	𝛾(0	𝛾(0	PROPN
cana-535	188	120	)	)	PUNCT
cana-535	188	121	}	}	PUNCT
cana-535	188	122	.	.	PUNCT
cana-535	189	1	proof	proof	NOUN
cana-535	189	2	:	:	PUNCT
cana-535	189	3	let	let	VERB
cana-535	189	4	𝑞	𝑞	PRON
cana-535	189	5	,	,	PUNCT
cana-535	189	6	𝑦	𝑦	NOUN
cana-535	189	7	∈	∈	NOUN
cana-535	189	8	𝑁.	𝑁.	PROPN
cana-535	189	9	suppose	suppose	VERB
cana-535	189	10	that	that	SCONJ
cana-535	189	11	𝑞	𝑞	PROPN
cana-535	189	12	=	=	X
cana-535	189	13	𝜍.	𝜍.	PROPN
cana-535	189	14	then	then	ADV
cana-535	189	15	𝑞	𝑞	PROPN
cana-535	189	16	+	+	PROPN
cana-535	189	17	�	�	PROPN
cana-535	189	18	̃	̃	NOUN
cana-535	189	19	�	�	NOUN
cana-535	189	20	=	=	SYM
cana-535	189	21	𝜍	𝜍	PROPN
cana-535	189	22	+	+	PROPN
cana-535	189	23	�	�	PROPN
cana-535	189	24	̃	̃	PROPN
cana-535	189	25	�	�	PROPN
cana-535	189	26	and	and	CCONJ
cana-535	189	27	𝑞	𝑞	X
cana-535	189	28	+	+	NOUN
cana-535	189	29	𝛾	𝛾	AUX
cana-535	189	30	=	=	SYM
cana-535	189	31	𝜍	𝜍	X
cana-535	189	32	+	+	CCONJ
cana-535	189	33	𝛾.	𝛾.	ADJ
cana-535	189	34	this	this	PRON
cana-535	189	35	implies	imply	VERB
cana-535	189	36	that	that	SCONJ
cana-535	189	37	∅(𝑞	∅(𝑞	ADJ
cana-535	189	38	)	)	PUNCT
cana-535	189	39	=	=	SYM
cana-535	189	40	∅(𝜍	∅(𝜍	NOUN
cana-535	189	41	)	)	PUNCT
cana-535	189	42	.	.	PUNCT
cana-535	190	1	therefore	therefore	ADV
cana-535	190	2	∅	∅	NOUN
cana-535	190	3	is	be	AUX
cana-535	190	4	well	well	ADV
cana-535	190	5	defined	define	VERB
cana-535	190	6	.	.	PUNCT
cana-535	191	1	now	now	ADV
cana-535	191	2	∅(𝑞	∅(𝑞	VERB
cana-535	191	3	+	+	CCONJ
cana-535	191	4	𝜍	𝜍	X
cana-535	191	5	)	)	PUNCT
cana-535	191	6	=	=	SYM
cana-535	191	7	(	(	PUNCT
cana-535	191	8	𝑞	𝑞	X
cana-535	191	9	+	+	X
cana-535	191	10	𝜍	𝜍	X
cana-535	191	11	)	)	PUNCT
cana-535	191	12	+	+	CCONJ
cana-535	191	13	�	�	PROPN
cana-535	191	14	̃	̃	NOUN
cana-535	191	15	�	�	NOUN
cana-535	191	16	=	=	SYM
cana-535	191	17	(	(	PUNCT
cana-535	191	18	𝑞	𝑞	PROPN
cana-535	191	19	+	+	PROPN
cana-535	191	20	�	�	PROPN
cana-535	191	21	̃	̃	PROPN
cana-535	191	22	�	�	PROPN
cana-535	191	23	)	)	PUNCT
cana-535	191	24	+	+	CCONJ
cana-535	192	1	(	(	PUNCT
cana-535	192	2	𝜍	𝜍	PART
cana-535	192	3	+	+	PROPN
cana-535	192	4	�	�	PROPN
cana-535	192	5	̃	̃	PROPN
cana-535	192	6	�	�	PROPN
cana-535	192	7	)	)	PUNCT
cana-535	192	8	=	=	PUNCT
cana-535	192	9	∅(𝑞	∅(𝑞	VERB
cana-535	192	10	)	)	PUNCT
cana-535	192	11	+	+	NUM
cana-535	192	12	∅(𝜍	∅(𝜍	NOUN
cana-535	192	13	)	)	PUNCT
cana-535	192	14	and	and	CCONJ
cana-535	192	15	∅(𝑞	∅(𝑞	VERB
cana-535	192	16	+	+	CCONJ
cana-535	192	17	𝜍	𝜍	X
cana-535	192	18	)	)	PUNCT
cana-535	192	19	=	=	SYM
cana-535	192	20	(	(	PUNCT
cana-535	192	21	𝑞	𝑞	X
cana-535	192	22	+	+	X
cana-535	192	23	𝜍	𝜍	X
cana-535	192	24	)	)	PUNCT
cana-535	193	1	+	+	NUM
cana-535	193	2	𝛾	𝛾	X
cana-535	193	3	=	=	SYM
cana-535	193	4	(	(	PUNCT
cana-535	193	5	𝑞	𝑞	X
cana-535	193	6	+	+	NOUN
cana-535	193	7	𝛾	𝛾	PROPN
cana-535	193	8	)	)	PUNCT
cana-535	194	1	+	+	CCONJ
cana-535	194	2	(	(	PUNCT
cana-535	194	3	𝜍	𝜍	X
cana-535	194	4	+	+	ADJ
cana-535	194	5	𝛾	𝛾	NOUN
cana-535	194	6	)	)	PUNCT
cana-535	194	7	=	=	NOUN
cana-535	194	8	∅(𝑞	∅(𝑞	VERB
cana-535	194	9	)	)	PUNCT
cana-535	194	10	+	+	NUM
cana-535	194	11	∅(𝜍	∅(𝜍	NOUN
cana-535	194	12	)	)	PUNCT
cana-535	194	13	,	,	PUNCT
cana-535	194	14	∅(𝑞𝜍	∅(𝑞𝜍	NOUN
cana-535	194	15	)	)	PUNCT
cana-535	194	16	=	=	SYM
cana-535	194	17	(	(	PUNCT
cana-535	194	18	𝑞𝜍	𝑞𝜍	NOUN
cana-535	194	19	)	)	PUNCT
cana-535	195	1	+	+	CCONJ
cana-535	195	2	�	�	PROPN
cana-535	195	3	̃	̃	NOUN
cana-535	195	4	�	�	NOUN
cana-535	195	5	=	=	SYM
cana-535	195	6	(	(	PUNCT
cana-535	195	7	𝑞	𝑞	PROPN
cana-535	195	8	+	+	PROPN
cana-535	195	9	�	�	PROPN
cana-535	195	10	̃	̃	PROPN
cana-535	195	11	�	�	NOUN
cana-535	195	12	)(𝜍	)(𝜍	ADJ
cana-535	195	13	+	+	X
cana-535	195	14	�	�	PROPN
cana-535	195	15	̃	̃	NOUN
cana-535	195	16	�	�	PROPN
cana-535	195	17	)	)	PUNCT
cana-535	195	18	=	=	SYM
cana-535	195	19	∅(𝑞)∅(𝜍	∅(𝑞)∅(𝜍	NOUN
cana-535	195	20	)	)	PUNCT
cana-535	195	21	and	and	CCONJ
cana-535	195	22	∅(𝑞𝜍	∅(𝑞𝜍	NOUN
cana-535	195	23	)	)	PUNCT
cana-535	195	24	=	=	SYM
cana-535	195	25	(	(	PUNCT
cana-535	195	26	𝑞𝜍	𝑞𝜍	NOUN
cana-535	195	27	)	)	PUNCT
cana-535	195	28	+	+	CCONJ
cana-535	195	29	𝛾	𝛾	X
cana-535	195	30	=	=	SYM
cana-535	195	31	(	(	PUNCT
cana-535	195	32	𝑞	𝑞	X
cana-535	195	33	+	+	X
cana-535	195	34	𝛾)(𝜍	𝛾)(𝜍	NOUN
cana-535	195	35	+	+	CCONJ
cana-535	195	36	𝛾	𝛾	NOUN
cana-535	195	37	)	)	PUNCT
cana-535	195	38	=	=	SYM
cana-535	195	39	∅(𝑞)∅(𝜍	∅(𝑞)∅(𝜍	PROPN
cana-535	195	40	)	)	PUNCT
cana-535	195	41	.	.	PUNCT
cana-535	196	1	therefore	therefore	ADV
cana-535	196	2	∅	∅	NOUN
cana-535	196	3	is	be	AUX
cana-535	196	4	a	a	DET
cana-535	196	5	homomorphism	homomorphism	NOUN
cana-535	196	6	.	.	PUNCT
cana-535	197	1	let	let	VERB
cana-535	197	2	𝑞	𝑞	PRON
cana-535	197	3	+	+	PROPN
cana-535	197	4	�	�	PROPN
cana-535	197	5	̃	̃	PROPN
cana-535	197	6	�	�	PROPN
cana-535	197	7	𝛾	𝛾	NOUN
cana-535	197	8	∈	∈	NOUN
cana-535	197	9	𝑁	𝑁	PROPN
cana-535	197	10	�	�	PROPN
cana-535	197	11	̃	̃	PROPN
cana-535	197	12	�	�	PROPN
cana-535	197	13	𝛾	𝛾	NOUN
cana-535	197	14	⁄	⁄	PROPN
cana-535	197	15	.	.	PUNCT
cana-535	198	1	then	then	ADV
cana-535	198	2	𝑞	𝑞	X
cana-535	198	3	∈	∈	PROPN
cana-535	198	4	𝑁.	𝑁.	PROPN
cana-535	198	5	for	for	ADP
cana-535	198	6	this	this	DET
cana-535	198	7	𝑞	𝑞	PROPN
cana-535	198	8	∈	∈	PROPN
cana-535	198	9	𝑁	𝑁	PROPN
cana-535	198	10	,	,	PUNCT
cana-535	198	11	we	we	PRON
cana-535	198	12	have	have	AUX
cana-535	198	13	∅(𝑞	∅(𝑞	VERB
cana-535	198	14	)	)	PUNCT
cana-535	198	15	=	=	SYM
cana-535	198	16	𝑞	𝑞	PROPN
cana-535	198	17	+	+	PROPN
cana-535	198	18	�	�	PROPN
cana-535	198	19	̃	̃	PROPN
cana-535	198	20	�	�	PROPN
cana-535	198	21	𝛾.	𝛾.	NOUN
cana-535	198	22	therefore	therefore	ADV
cana-535	198	23	∅	∅	NOUN
cana-535	198	24	is	be	AUX
cana-535	198	25	a	a	DET
cana-535	198	26	near	near	ADJ
cana-535	198	27	ring	ring	NOUN
cana-535	198	28	epimorphism	epimorphism	NOUN
cana-535	198	29	.	.	PUNCT
cana-535	199	1	and	and	CCONJ
cana-535	199	2	now	now	ADV
cana-535	199	3	𝑞	𝑞	X
cana-535	199	4	∈	∈	PROPN
cana-535	199	5	ker∅	ker∅	NOUN
cana-535	199	6	⇔	⇔	PROPN
cana-535	199	7	∅(𝑞	∅(𝑞	PROPN
cana-535	199	8	)	)	PUNCT
cana-535	199	9	=	=	SYM
cana-535	199	10	0	0	PUNCT
cana-535	200	1	=	=	SYM
cana-535	200	2	0	0	PUNCT
cana-535	200	3	+	+	NUM
cana-535	200	4	�	�	PROPN
cana-535	200	5	̃	̃	NOUN
cana-535	200	6	�	�	NOUN
cana-535	200	7	=	=	SYM
cana-535	200	8	0	0	NUM
cana-535	201	1	+	+	CCONJ
cana-535	201	2	𝛾	𝛾	VERB
cana-535	201	3	⇔	⇔	X
cana-535	201	4	𝑞	𝑞	PROPN
cana-535	201	5	+	+	PROPN
cana-535	201	6	�	�	PROPN
cana-535	201	7	̃	̃	NOUN
cana-535	201	8	�	�	NOUN
cana-535	201	9	=	=	SYM
cana-535	201	10	0	0	PUNCT
cana-535	201	11	+	+	NUM
cana-535	201	12	�	�	PROPN
cana-535	201	13	̃	̃	PROPN
cana-535	201	14	�	�	PROPN
cana-535	201	15	and	and	CCONJ
cana-535	201	16	𝑞	𝑞	X
cana-535	201	17	+	+	PROPN
cana-535	201	18	𝛾	𝛾	NOUN
cana-535	201	19	=	=	SYM
cana-535	201	20	0	0	PUNCT
cana-535	202	1	+	+	CCONJ
cana-535	202	2	𝛾	𝛾	PROPN
cana-535	202	3	⇔	⇔	PROPN
cana-535	202	4	�	�	PROPN
cana-535	202	5	̃	̃	PROPN
cana-535	202	6	�	�	PROPN
cana-535	202	7	(𝑞	(𝑞	NOUN
cana-535	202	8	−	−	NOUN
cana-535	202	9	0	0	NUM
cana-535	202	10	)	)	PUNCT
cana-535	202	11	=	=	SYM
cana-535	202	12	�	�	PROPN
cana-535	202	13	̃	̃	PROPN
cana-535	202	14	�	�	PROPN
cana-535	202	15	(0	(0	X
cana-535	202	16	)	)	PUNCT
cana-535	202	17	and	and	CCONJ
cana-535	202	18	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	202	19	−	−	PROPN
cana-535	202	20	0	0	NUM
cana-535	202	21	)	)	PUNCT
cana-535	202	22	=	=	SYM
cana-535	203	1	𝛾(0	𝛾(0	PROPN
cana-535	203	2	)	)	PUNCT
cana-535	203	3	⇔	⇔	PROPN
cana-535	203	4	�	�	PROPN
cana-535	203	5	̃	̃	PROPN
cana-535	203	6	�	�	NOUN
cana-535	203	7	(𝑞	(𝑞	NOUN
cana-535	203	8	)	)	PUNCT
cana-535	203	9	=	=	SYM
cana-535	203	10	�	�	PROPN
cana-535	203	11	̃	̃	PROPN
cana-535	203	12	�	�	PROPN
cana-535	203	13	(0	(0	X
cana-535	203	14	)	)	PUNCT
cana-535	203	15	and	and	CCONJ
cana-535	203	16	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	203	17	)	)	PUNCT
cana-535	203	18	=	=	SYM
cana-535	203	19	𝛾(0	𝛾(0	PROPN
cana-535	203	20	)	)	PUNCT
cana-535	203	21	⇔	⇔	PROPN
cana-535	203	22	𝑞	𝑞	PROPN
cana-535	203	23	∈	∈	PROPN
cana-535	203	24	�	�	PROPN
cana-535	203	25	̃	̃	PROPN
cana-535	203	26	�	�	NOUN
cana-535	203	27	𝛾∗	𝛾∗	NOUN
cana-535	203	28	.	.	PUNCT
cana-535	204	1	this	this	PRON
cana-535	204	2	shows	show	VERB
cana-535	204	3	that	that	SCONJ
cana-535	204	4	kernal	kernal	ADJ
cana-535	204	5	∅	∅	NOUN
cana-535	204	6	=	=	SYM
cana-535	204	7	�	�	PROPN
cana-535	204	8	̃	̃	PROPN
cana-535	204	9	�	�	NOUN
cana-535	204	10	𝛾∗	𝛾∗	NOUN
cana-535	204	11	.	.	PUNCT
cana-535	205	1	theorem	theorem	VERB
cana-535	205	2	3.12	3.12	NUM
cana-535	205	3	:	:	PUNCT
cana-535	205	4	if	if	SCONJ
cana-535	205	5	�	�	PROPN
cana-535	205	6	̃	̃	PROPN
cana-535	205	7	�	�	NOUN
cana-535	205	8	𝛾	𝛾	NOUN
cana-535	205	9	is	be	AUX
cana-535	205	10	a	a	DET
cana-535	205	11	hinr	hinr	ADJ
cana-535	205	12	𝑁.	𝑁.	NOUN
cana-535	205	13	then	then	ADV
cana-535	205	14	𝑁	𝑁	PROPN
cana-535	205	15	�	�	PROPN
cana-535	205	16	̃	̃	PROPN
cana-535	205	17	�	�	PROPN
cana-535	205	18	𝛾	𝛾	NOUN
cana-535	205	19	⁄	⁄	PROPN
cana-535	205	20	is	be	AUX
cana-535	205	21	isomorphic	isomorphic	ADJ
cana-535	205	22	to	to	ADP
cana-535	205	23	𝑁	𝑁	PROPN
cana-535	205	24	�	�	PROPN
cana-535	205	25	̃	̃	PROPN
cana-535	205	26	�	�	PROPN
cana-535	205	27	𝛾∗	𝛾∗	NOUN
cana-535	205	28	⁄	⁄	PROPN
cana-535	205	29	,	,	PUNCT
cana-535	205	30	where	where	SCONJ
cana-535	205	31	�	�	PROPN
cana-535	205	32	̃	̃	PROPN
cana-535	205	33	�	�	NOUN
cana-535	205	34	𝛾∗	𝛾∗	NOUN
cana-535	205	35	=	=	SYM
cana-535	205	36	{	{	PUNCT
cana-535	205	37	𝑞	𝑞	X
cana-535	205	38	∈	∈	PROPN
cana-535	205	39	𝑁	𝑁	PROPN
cana-535	205	40	:	:	PUNCT
cana-535	205	41	�	�	PROPN
cana-535	205	42	̃	̃	PROPN
cana-535	205	43	�	�	NOUN
cana-535	205	44	(𝑞	(𝑞	NOUN
cana-535	205	45	)	)	PUNCT
cana-535	205	46	=	=	SYM
cana-535	205	47	�	�	PROPN
cana-535	205	48	̃	̃	PROPN
cana-535	205	49	�	�	PROPN
cana-535	205	50	(0	(0	NOUN
cana-535	205	51	)	)	PUNCT
cana-535	205	52	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-535	205	53	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	205	54	)	)	PUNCT
cana-535	205	55	=	=	PUNCT
cana-535	205	56	𝛾(0	𝛾(0	PROPN
cana-535	205	57	)	)	PUNCT
cana-535	205	58	}	}	PUNCT
cana-535	205	59	.	.	PUNCT
cana-535	206	1	proof	proof	NOUN
cana-535	206	2	:	:	PUNCT
cana-535	206	3	we	we	PRON
cana-535	206	4	have	have	VERB
cana-535	206	5	that	that	DET
cana-535	206	6	�	�	PROPN
cana-535	206	7	̃	̃	PROPN
cana-535	206	8	�	�	NOUN
cana-535	206	9	𝛾∗	𝛾∗	NOUN
cana-535	206	10	is	be	AUX
cana-535	206	11	an	an	DET
cana-535	206	12	ideal(kernal	ideal(kernal	ADJ
cana-535	206	13	)	)	PUNCT
cana-535	206	14	of	of	ADP
cana-535	206	15	𝑁.	𝑁.	PROPN
cana-535	206	16	we	we	PRON
cana-535	206	17	know	know	VERB
cana-535	206	18	that	that	SCONJ
cana-535	206	19	𝑁	𝑁	PROPN
cana-535	206	20	�	�	PROPN
cana-535	206	21	̃	̃	PROPN
cana-535	206	22	�	�	PROPN
cana-535	206	23	𝛾	𝛾	NOUN
cana-535	206	24	⁄	⁄	NOUN
cana-535	206	25	=	=	PUNCT
cana-535	206	26	{	{	PUNCT
cana-535	206	27	𝑞	𝑞	PROPN
cana-535	206	28	+	+	PROPN
cana-535	206	29	�	�	PROPN
cana-535	206	30	̃	̃	PROPN
cana-535	206	31	�	�	NOUN
cana-535	206	32	𝛾	𝛾	NOUN
cana-535	206	33	:	:	PUNCT
cana-535	206	34	𝑞	𝑞	X
cana-535	206	35	∈	∈	PROPN
cana-535	206	36	𝑁	𝑁	PROPN
cana-535	206	37	}	}	PUNCT
cana-535	206	38	and	and	CCONJ
cana-535	206	39	𝑁	𝑁	PROPN
cana-535	206	40	�	�	PROPN
cana-535	206	41	̃	̃	PROPN
cana-535	206	42	�	�	PROPN
cana-535	206	43	𝛾∗	𝛾∗	NOUN
cana-535	206	44	⁄	⁄	PROPN
cana-535	207	1	=	=	PUNCT
cana-535	207	2	{	{	PUNCT
cana-535	207	3	𝑞	𝑞	PROPN
cana-535	207	4	+	+	PROPN
cana-535	207	5	�	�	PROPN
cana-535	207	6	̃	̃	PROPN
cana-535	207	7	�	�	NOUN
cana-535	207	8	𝛾∗	𝛾∗	NOUN
cana-535	207	9	:	:	PUNCT
cana-535	207	10	𝑞	𝑞	X
cana-535	207	11	∈	∈	PROPN
cana-535	207	12	𝑁	𝑁	PROPN
cana-535	207	13	}	}	PUNCT
cana-535	207	14	.	.	PUNCT
cana-535	208	1	define	define	VERB
cana-535	208	2	a	a	DET
cana-535	208	3	mapping	mapping	NOUN
cana-535	208	4	∅	∅	NOUN
cana-535	208	5	:	:	PUNCT
cana-535	208	6	𝑁	𝑁	PROPN
cana-535	208	7	�	�	PROPN
cana-535	208	8	̃	̃	PROPN
cana-535	208	9	�	�	PROPN
cana-535	208	10	𝛾	𝛾	NOUN
cana-535	208	11	⁄	⁄	PROPN
cana-535	208	12	→	→	SYM
cana-535	208	13	𝑁	𝑁	PROPN
cana-535	208	14	�	�	PROPN
cana-535	208	15	̃	̃	PROPN
cana-535	208	16	�	�	PROPN
cana-535	208	17	𝛾∗	𝛾∗	NOUN
cana-535	208	18	⁄	⁄	PROPN
cana-535	208	19	by	by	ADP
cana-535	208	20	∅(𝑞	∅(𝑞	PROPN
cana-535	208	21	+	+	CCONJ
cana-535	208	22	�	�	PROPN
cana-535	208	23	̃	̃	NOUN
cana-535	208	24	�	�	PROPN
cana-535	208	25	)	)	PUNCT
cana-535	208	26	=	=	SYM
cana-535	208	27	𝑞	𝑞	PROPN
cana-535	208	28	+	+	PROPN
cana-535	208	29	�	�	PROPN
cana-535	208	30	̃	̃	PROPN
cana-535	208	31	�	�	NOUN
cana-535	208	32	∗	∗	NOUN
cana-535	208	33	and	and	CCONJ
cana-535	208	34	∅(𝑞	∅(𝑞	PROPN
cana-535	208	35	+	+	CCONJ
cana-535	208	36	𝛾	𝛾	X
cana-535	208	37	)	)	PUNCT
cana-535	208	38	=	=	SYM
cana-535	209	1	𝑞	𝑞	PROPN
cana-535	209	2	+	+	ADJ
cana-535	209	3	𝛾∗	𝛾∗	NOUN
cana-535	209	4	for	for	ADP
cana-535	209	5	every	every	DET
cana-535	209	6	𝑞	𝑞	PROPN
cana-535	209	7	+	+	PROPN
cana-535	209	8	�	�	PROPN
cana-535	209	9	̃	̃	PROPN
cana-535	209	10	�	�	PROPN
cana-535	209	11	,	,	PUNCT
cana-535	209	12	𝑞	𝑞	X
cana-535	209	13	+	+	NOUN
cana-535	209	14	𝛾	𝛾	NOUN
cana-535	209	15	∈	∈	NOUN
cana-535	209	16	𝑁	𝑁	PROPN
cana-535	209	17	�	�	PROPN
cana-535	209	18	̃	̃	PROPN
cana-535	209	19	�	�	PROPN
cana-535	209	20	𝛾	𝛾	NOUN
cana-535	209	21	⁄	⁄	PROPN
cana-535	209	22	.	.	PUNCT
cana-535	210	1	to	to	PART
cana-535	210	2	prove	prove	VERB
cana-535	210	3	that	that	SCONJ
cana-535	210	4	𝑁	𝑁	PROPN
cana-535	210	5	�	�	PROPN
cana-535	210	6	̃	̃	PROPN
cana-535	210	7	�	�	PROPN
cana-535	210	8	𝛾	𝛾	NOUN
cana-535	210	9	⁄	⁄	PROPN
cana-535	210	10	is	be	AUX
cana-535	210	11	isomorphic	isomorphic	ADJ
cana-535	210	12	to	to	ADP
cana-535	210	13	𝑁	𝑁	PROPN
cana-535	210	14	�	�	PROPN
cana-535	210	15	̃	̃	PROPN
cana-535	210	16	�	�	PROPN
cana-535	210	17	𝛾∗	𝛾∗	NOUN
cana-535	210	18	⁄	⁄	PROPN
cana-535	210	19	,	,	PUNCT
cana-535	210	20	it	it	PRON
cana-535	210	21	is	be	AUX
cana-535	210	22	sufficient	sufficient	ADJ
cana-535	210	23	to	to	PART
cana-535	210	24	prove	prove	VERB
cana-535	210	25	that	that	SCONJ
cana-535	210	26	∅	∅	NOUN
cana-535	210	27	is	be	AUX
cana-535	210	28	well	well	ADV
cana-535	210	29	defined	define	VERB
cana-535	210	30	,	,	PUNCT
cana-535	210	31	one	one	NUM
cana-535	210	32	-	-	PUNCT
cana-535	210	33	one	one	NUM
cana-535	210	34	,	,	PUNCT
cana-535	210	35	onto	onto	ADP
cana-535	210	36	and	and	CCONJ
cana-535	210	37	homomorphism	homomorphism	NOUN
cana-535	210	38	.	.	PUNCT
cana-535	211	1	let	let	VERB
cana-535	211	2	𝑞	𝑞	PRON
cana-535	211	3	+	+	PROPN
cana-535	211	4	�	�	PROPN
cana-535	211	5	̃	̃	PROPN
cana-535	211	6	�	�	NOUN
cana-535	211	7	𝛾	𝛾	NOUN
cana-535	211	8	,	,	PUNCT
cana-535	211	9	𝜍	𝜍	PROPN
cana-535	211	10	+	+	PROPN
cana-535	211	11	�	�	PROPN
cana-535	211	12	̃	̃	PROPN
cana-535	211	13	�	�	PROPN
cana-535	211	14	𝛾	𝛾	NOUN
cana-535	211	15	∈	∈	NOUN
cana-535	211	16	𝑁	𝑁	PROPN
cana-535	211	17	�	�	PROPN
cana-535	211	18	̃	̃	PROPN
cana-535	211	19	�	�	PROPN
cana-535	211	20	𝛾	𝛾	NOUN
cana-535	211	21	⁄	⁄	PROPN
cana-535	211	22	,	,	PUNCT
cana-535	211	23	where	where	SCONJ
cana-535	211	24	𝑞	𝑞	NOUN
cana-535	211	25	,	,	PUNCT
cana-535	211	26	𝛾	𝛾	ADP
cana-535	211	27	∈	∈	NOUN
cana-535	211	28	𝑁.	𝑁.	PROPN
cana-535	211	29	communications	communication	NOUN
cana-535	211	30	on	on	ADP
cana-535	211	31	applied	apply	VERB
cana-535	211	32	nonlinear	nonlinear	ADJ
cana-535	211	33	analysis	analysis	NOUN
cana-535	211	34	issn	issn	NOUN
cana-535	211	35	:	:	PUNCT
cana-535	211	36	1074	1074	NUM
cana-535	211	37	-	-	PUNCT
cana-535	211	38	133x	133x	NUM
cana-535	211	39	vol	vol	NOUN
cana-535	211	40	31	31	NUM
cana-535	211	41	no	no	NOUN
cana-535	211	42	.	.	NOUN
cana-535	211	43	2	2	NUM
cana-535	211	44	(	(	PUNCT
cana-535	211	45	2024	2024	NUM
cana-535	211	46	)	)	PUNCT
cana-535	211	47	212	212	NUM
cana-535	211	48	https://internationalpubls.com	https://internationalpubls.com	X
cana-535	211	49	then	then	ADV
cana-535	211	50	𝑞	𝑞	PROPN
cana-535	211	51	+	+	PROPN
cana-535	211	52	�	�	PROPN
cana-535	211	53	̃	̃	NOUN
cana-535	211	54	�	�	NOUN
cana-535	211	55	=	=	SYM
cana-535	211	56	𝜍	𝜍	PROPN
cana-535	211	57	+	+	PROPN
cana-535	211	58	�	�	PROPN
cana-535	211	59	̃	̃	PROPN
cana-535	211	60	�	�	PROPN
cana-535	211	61	⇔	⇔	PROPN
cana-535	211	62	�	�	PROPN
cana-535	211	63	̃	̃	PROPN
cana-535	211	64	�	�	PROPN
cana-535	211	65	(𝑞	(𝑞	NOUN
cana-535	211	66	−	−	NOUN
cana-535	211	67	𝜍	𝜍	NOUN
cana-535	211	68	)	)	PUNCT
cana-535	211	69	=	=	SYM
cana-535	211	70	�	�	PROPN
cana-535	211	71	̃	̃	PROPN
cana-535	211	72	�	�	PROPN
cana-535	211	73	(0	(0	X
cana-535	211	74	)	)	PUNCT
cana-535	211	75	⇔	⇔	PROPN
cana-535	211	76	𝑞	𝑞	X
cana-535	211	77	−	−	PROPN
cana-535	211	78	𝜍	𝜍	ADP
cana-535	211	79	∈	∈	PROPN
cana-535	211	80	�	�	PROPN
cana-535	211	81	̃	̃	PROPN
cana-535	211	82	�	�	PROPN
cana-535	211	83	∗	∗	NOUN
cana-535	211	84	⇔	⇔	X
cana-535	211	85	𝑞	𝑞	PROPN
cana-535	211	86	+	+	PROPN
cana-535	211	87	�	�	PROPN
cana-535	211	88	̃	̃	PROPN
cana-535	211	89	�	�	NOUN
cana-535	211	90	∗	∗	NOUN
cana-535	211	91	=	=	SYM
cana-535	211	92	𝜍	𝜍	PROPN
cana-535	211	93	+	+	PROPN
cana-535	211	94	�	�	PROPN
cana-535	211	95	̃	̃	PROPN
cana-535	211	96	�	�	PROPN
cana-535	211	97	∗	∗	NOUN
cana-535	211	98	⇔	⇔	NOUN
cana-535	211	99	∅(𝑞	∅(𝑞	PROPN
cana-535	211	100	+	+	SYM
cana-535	211	101	�	�	PROPN
cana-535	211	102	̃	̃	NOUN
cana-535	211	103	�	�	PROPN
cana-535	211	104	)	)	PUNCT
cana-535	211	105	=	=	NOUN
cana-535	211	106	∅(𝜍	∅(𝜍	NOUN
cana-535	211	107	+	+	SYM
cana-535	211	108	�	�	PROPN
cana-535	211	109	̃	̃	PROPN
cana-535	211	110	�	�	PROPN
cana-535	211	111	)	)	PUNCT
cana-535	211	112	and	and	CCONJ
cana-535	211	113	𝑞	𝑞	X
cana-535	211	114	+	+	NOUN
cana-535	211	115	𝛾	𝛾	NOUN
cana-535	211	116	=	=	SYM
cana-535	211	117	𝜍	𝜍	X
cana-535	212	1	+	+	CCONJ
cana-535	212	2	𝛾	𝛾	PROPN
cana-535	212	3	⇔	⇔	X
cana-535	212	4	𝛾(𝑞	𝛾(𝑞	PROPN
cana-535	212	5	−	−	PROPN
cana-535	212	6	𝜍	𝜍	NOUN
cana-535	212	7	)	)	PUNCT
cana-535	212	8	=	=	SYM
cana-535	212	9	𝛾(0	𝛾(0	PROPN
cana-535	212	10	)	)	PUNCT
cana-535	212	11	⇔	⇔	PROPN
cana-535	212	12	𝑞	𝑞	X
cana-535	212	13	−	−	PROPN
cana-535	212	14	𝜍	𝜍	ADP
cana-535	212	15	∈	∈	PROPN
cana-535	212	16	𝛾∗	𝛾∗	NOUN
cana-535	212	17	⇔	⇔	PROPN
cana-535	212	18	𝑞	𝑞	PROPN
cana-535	212	19	+	+	PROPN
cana-535	212	20	𝛾∗	𝛾∗	NOUN
cana-535	212	21	=	=	SYM
cana-535	212	22	𝜍	𝜍	X
cana-535	212	23	+	+	X
cana-535	212	24	𝛾∗	𝛾∗	PROPN
cana-535	212	25	⇔	⇔	PROPN
cana-535	212	26	∅(𝑞	∅(𝑞	PROPN
cana-535	212	27	+	+	CCONJ
cana-535	212	28	𝛾	𝛾	X
cana-535	212	29	)	)	PUNCT
cana-535	212	30	=	=	NOUN
cana-535	212	31	∅(𝜍	∅(𝜍	NOUN
cana-535	212	32	+	+	SYM
cana-535	212	33	𝛾	𝛾	NOUN
cana-535	212	34	)	)	PUNCT
cana-535	212	35	.	.	PUNCT
cana-535	213	1	therefore	therefore	ADV
cana-535	213	2	∅	∅	NOUN
cana-535	213	3	is	be	AUX
cana-535	213	4	well	well	ADV
cana-535	213	5	defined	define	VERB
cana-535	213	6	and	and	CCONJ
cana-535	213	7	one	one	NUM
cana-535	213	8	-	-	PUNCT
cana-535	213	9	one	one	NUM
cana-535	213	10	.	.	PUNCT
cana-535	214	1	let	let	VERB
cana-535	214	2	𝜍	𝜍	PRON
cana-535	214	3	+	+	ADJ
cana-535	214	4	�	�	PROPN
cana-535	214	5	̃	̃	NOUN
cana-535	214	6	�	�	NOUN
cana-535	214	7	𝛾∗	𝛾∗	NOUN
cana-535	214	8	∈	∈	PROPN
cana-535	214	9	𝑁	𝑁	PROPN
cana-535	214	10	�	�	PROPN
cana-535	214	11	̃	̃	PROPN
cana-535	214	12	�	�	PROPN
cana-535	214	13	𝛾∗	𝛾∗	NOUN
cana-535	214	14	⁄	⁄	PROPN
cana-535	214	15	.	.	PUNCT
cana-535	215	1	then	then	ADV
cana-535	215	2	𝜍	𝜍	ADP
cana-535	215	3	∈	∈	PROPN
cana-535	215	4	𝑁.	𝑁.	PROPN
cana-535	215	5	for	for	ADP
cana-535	215	6	this	this	PRON
cana-535	215	7	𝜍	𝜍	ADP
cana-535	215	8	∈	∈	PROPN
cana-535	215	9	𝑁	𝑁	PROPN
cana-535	215	10	,	,	PUNCT
cana-535	215	11	we	we	PRON
cana-535	215	12	have	have	VERB
cana-535	215	13	𝑞	𝑞	X
cana-535	215	14	+	+	ADJ
cana-535	215	15	�	�	PROPN
cana-535	215	16	̃	̃	PROPN
cana-535	215	17	�	�	PROPN
cana-535	215	18	𝛾	𝛾	NOUN
cana-535	215	19	∈	∈	NOUN
cana-535	215	20	𝑁	𝑁	PROPN
cana-535	215	21	�	�	PROPN
cana-535	215	22	̃	̃	PROPN
cana-535	215	23	�	�	PROPN
cana-535	215	24	𝛾	𝛾	NOUN
cana-535	215	25	⁄	⁄	PROPN
cana-535	215	26	and	and	CCONJ
cana-535	215	27	∅(𝜍	∅(𝜍	NOUN
cana-535	216	1	+	+	CCONJ
cana-535	216	2	�	�	PROPN
cana-535	216	3	̃	̃	NOUN
cana-535	216	4	�	�	PROPN
cana-535	216	5	)	)	PUNCT
cana-535	216	6	=	=	SYM
cana-535	216	7	𝜍	𝜍	PROPN
cana-535	216	8	+	+	PROPN
cana-535	216	9	�	�	PROPN
cana-535	216	10	̃	̃	PROPN
cana-535	216	11	�	�	NOUN
cana-535	216	12	∗	∗	NOUN
cana-535	216	13	and	and	CCONJ
cana-535	216	14	∅(𝜍	∅(𝜍	NOUN
cana-535	216	15	+	+	CCONJ
cana-535	216	16	𝛾	𝛾	X
cana-535	216	17	)	)	PUNCT
cana-535	216	18	=	=	SYM
cana-535	217	1	𝜍	𝜍	X
cana-535	218	1	+	+	X
cana-535	218	2	𝛾∗.	𝛾∗.	ADP
cana-535	218	3	that	that	PRON
cana-535	218	4	is	be	AUX
cana-535	218	5	for	for	ADP
cana-535	218	6	each	each	PRON
cana-535	218	7	𝜍	𝜍	X
cana-535	218	8	+	+	PROPN
cana-535	218	9	�	�	PROPN
cana-535	218	10	̃	̃	PROPN
cana-535	218	11	�	�	NOUN
cana-535	218	12	𝛾∗	𝛾∗	NOUN
cana-535	218	13	∈	∈	PROPN
cana-535	218	14	𝑁	𝑁	PROPN
cana-535	218	15	�	�	PROPN
cana-535	218	16	̃	̃	PROPN
cana-535	218	17	�	�	PROPN
cana-535	218	18	𝛾∗	𝛾∗	VERB
cana-535	218	19	⁄	⁄	PROPN
cana-535	218	20	there	there	PRON
cana-535	218	21	exists	exist	VERB
cana-535	218	22	𝜍	𝜍	ADP
cana-535	218	23	+	+	ADJ
cana-535	218	24	�	�	PROPN
cana-535	218	25	̃	̃	PROPN
cana-535	218	26	�	�	PROPN
cana-535	218	27	𝛾	𝛾	NOUN
cana-535	218	28	∈	∈	NOUN
cana-535	218	29	𝑁	𝑁	PROPN
cana-535	218	30	�	�	PROPN
cana-535	218	31	̃	̃	PROPN
cana-535	218	32	�	�	PROPN
cana-535	218	33	𝛾	𝛾	NOUN
cana-535	218	34	⁄	⁄	ADP
cana-535	218	35	such	such	ADJ
cana-535	218	36	that	that	DET
cana-535	218	37	∅(𝜍	∅(𝜍	NOUN
cana-535	218	38	+	+	SYM
cana-535	218	39	�	�	PROPN
cana-535	218	40	̃	̃	NOUN
cana-535	218	41	�	�	PROPN
cana-535	218	42	)	)	PUNCT
cana-535	218	43	=	=	SYM
cana-535	218	44	𝜍	𝜍	PROPN
cana-535	218	45	+	+	PROPN
cana-535	218	46	�	�	PROPN
cana-535	218	47	̃	̃	PROPN
cana-535	218	48	�	�	NOUN
cana-535	218	49	∗	∗	NOUN
cana-535	218	50	and	and	CCONJ
cana-535	218	51	∅(𝜍	∅(𝜍	NOUN
cana-535	218	52	+	+	CCONJ
cana-535	218	53	𝛾	𝛾	X
cana-535	218	54	)	)	PUNCT
cana-535	218	55	=	=	SYM
cana-535	219	1	𝜍	𝜍	X
cana-535	219	2	+	+	CCONJ
cana-535	219	3	𝛾∗.	𝛾∗.	ADP
cana-535	219	4	therefore	therefore	ADV
cana-535	219	5	∅	∅	NOUN
cana-535	219	6	is	be	AUX
cana-535	219	7	onto	onto	ADP
cana-535	219	8	.	.	PUNCT
cana-535	220	1	let	let	VERB
cana-535	220	2	𝑞	𝑞	PROPN
cana-535	220	3	+	+	PROPN
cana-535	220	4	�	�	PROPN
cana-535	220	5	̃	̃	PROPN
cana-535	220	6	�	�	NOUN
cana-535	220	7	𝛾	𝛾	NOUN
cana-535	220	8	,	,	PUNCT
cana-535	220	9	𝜍	𝜍	PROPN
cana-535	220	10	+	+	PROPN
cana-535	220	11	�	�	PROPN
cana-535	220	12	̃	̃	PROPN
cana-535	220	13	�	�	PROPN
cana-535	220	14	𝛾	𝛾	NOUN
cana-535	220	15	∈	∈	NOUN
cana-535	220	16	𝑁	𝑁	PROPN
cana-535	220	17	�	�	PROPN
cana-535	220	18	̃	̃	PROPN
cana-535	220	19	�	�	PROPN
cana-535	220	20	𝛾	𝛾	NOUN
cana-535	220	21	⁄	⁄	PROPN
cana-535	220	22	,	,	PUNCT
cana-535	220	23	𝑞	𝑞	X
cana-535	220	24	,	,	PUNCT
cana-535	220	25	𝛾	𝛾	ADP
cana-535	220	26	∈	∈	PROPN
cana-535	220	27	𝑁.	𝑁.	PROPN
cana-535	220	28	then	then	ADV
cana-535	220	29	∅((𝑞	∅((𝑞	PROPN
cana-535	220	30	+	+	SYM
cana-535	220	31	�	�	PROPN
cana-535	220	32	̃	̃	PROPN
cana-535	220	33	�	�	PROPN
cana-535	220	34	)	)	PUNCT
cana-535	221	1	+	+	CCONJ
cana-535	221	2	(	(	PUNCT
cana-535	221	3	𝜍	𝜍	PART
cana-535	221	4	+	+	PROPN
cana-535	221	5	�	�	PROPN
cana-535	221	6	̃	̃	PROPN
cana-535	221	7	�	�	PROPN
cana-535	221	8	)	)	PUNCT
cana-535	221	9	)	)	PUNCT
cana-535	222	1	=	=	PUNCT
cana-535	223	1	∅((𝑞	∅((𝑞	PROPN
cana-535	223	2	+	+	CCONJ
cana-535	223	3	𝜍	𝜍	X
cana-535	223	4	)	)	PUNCT
cana-535	223	5	+	+	CCONJ
cana-535	223	6	�	�	PROPN
cana-535	223	7	̃	̃	NOUN
cana-535	223	8	�	�	PROPN
cana-535	223	9	)	)	PUNCT
cana-535	223	10	=	=	PUNCT
cana-535	223	11	(	(	PUNCT
cana-535	223	12	𝑞	𝑞	X
cana-535	223	13	+	+	X
cana-535	223	14	𝜍	𝜍	X
cana-535	223	15	)	)	PUNCT
cana-535	223	16	+	+	CCONJ
cana-535	223	17	�	�	PROPN
cana-535	223	18	̃	̃	PROPN
cana-535	223	19	�	�	NOUN
cana-535	223	20	∗	∗	NOUN
cana-535	223	21	=	=	SYM
cana-535	223	22	(	(	PUNCT
cana-535	223	23	𝑞	𝑞	PROPN
cana-535	223	24	+	+	PROPN
cana-535	223	25	�	�	PROPN
cana-535	223	26	̃	̃	PROPN
cana-535	223	27	�	�	NOUN
cana-535	223	28	∗	∗	NOUN
cana-535	223	29	)	)	PUNCT
cana-535	224	1	+	+	CCONJ
cana-535	224	2	(	(	PUNCT
cana-535	224	3	𝜍	𝜍	PART
cana-535	224	4	+	+	PROPN
cana-535	224	5	�	�	PROPN
cana-535	224	6	̃	̃	PROPN
cana-535	224	7	�	�	NOUN
cana-535	224	8	∗	∗	NOUN
cana-535	224	9	)	)	PUNCT
cana-535	225	1	=	=	PUNCT
cana-535	225	2	∅(𝑞	∅(𝑞	PROPN
cana-535	225	3	+	+	CCONJ
cana-535	225	4	�	�	PROPN
cana-535	225	5	̃	̃	PROPN
cana-535	225	6	�	�	PROPN
cana-535	225	7	)	)	PUNCT
cana-535	225	8	+	+	NUM
cana-535	225	9	∅(𝜍	∅(𝜍	NOUN
cana-535	225	10	+	+	SYM
cana-535	225	11	�	�	PROPN
cana-535	225	12	̃	̃	PROPN
cana-535	225	13	�	�	PROPN
cana-535	225	14	)	)	PUNCT
cana-535	225	15	and	and	CCONJ
cana-535	225	16	∅((𝑞	∅((𝑞	PROPN
cana-535	225	17	+	+	CCONJ
cana-535	225	18	𝛾	𝛾	X
cana-535	225	19	)	)	PUNCT
cana-535	225	20	+	+	CCONJ
cana-535	225	21	(	(	PUNCT
cana-535	225	22	𝜍	𝜍	X
cana-535	225	23	+	+	ADJ
cana-535	225	24	𝛾	𝛾	NOUN
cana-535	225	25	)	)	PUNCT
cana-535	225	26	)	)	PUNCT
cana-535	226	1	=	=	PUNCT
cana-535	227	1	∅((𝑞	∅((𝑞	PROPN
cana-535	227	2	+	+	CCONJ
cana-535	227	3	𝜍	𝜍	X
cana-535	227	4	)	)	PUNCT
cana-535	227	5	+	+	CCONJ
cana-535	227	6	𝛾	𝛾	X
cana-535	227	7	)	)	PUNCT
cana-535	227	8	=	=	SYM
cana-535	227	9	(	(	PUNCT
cana-535	227	10	𝑞	𝑞	X
cana-535	227	11	+	+	X
cana-535	227	12	𝜍	𝜍	X
cana-535	227	13	)	)	PUNCT
cana-535	228	1	+	+	NUM
cana-535	228	2	𝛾∗	𝛾∗	NOUN
cana-535	228	3	=	=	SYM
cana-535	228	4	(	(	PUNCT
cana-535	228	5	𝑞	𝑞	X
cana-535	228	6	+	+	X
cana-535	228	7	𝛾∗	𝛾∗	NOUN
cana-535	228	8	)	)	PUNCT
cana-535	228	9	+	+	CCONJ
cana-535	228	10	(	(	PUNCT
cana-535	228	11	𝜍	𝜍	X
cana-535	228	12	+	+	X
cana-535	228	13	𝛾∗	𝛾∗	NOUN
cana-535	228	14	)	)	PUNCT
cana-535	228	15	=	=	PUNCT
cana-535	228	16	∅(𝑞	∅(𝑞	PROPN
cana-535	228	17	+	+	CCONJ
cana-535	228	18	𝛾	𝛾	X
cana-535	228	19	)	)	PUNCT
cana-535	228	20	+	+	NUM
cana-535	228	21	∅(𝜍	∅(𝜍	NOUN
cana-535	228	22	+	+	CCONJ
cana-535	228	23	𝛾	𝛾	NOUN
cana-535	228	24	)	)	PUNCT
cana-535	228	25	,	,	PUNCT
cana-535	228	26	∅((𝑞	∅((𝑞	PROPN
cana-535	228	27	+	+	SYM
cana-535	228	28	�	�	PROPN
cana-535	228	29	̃	̃	PROPN
cana-535	228	30	�	�	NOUN
cana-535	228	31	)(𝜍	)(𝜍	ADJ
cana-535	228	32	+	+	X
cana-535	228	33	�	�	PROPN
cana-535	228	34	̃	̃	PROPN
cana-535	228	35	�	�	PROPN
cana-535	228	36	)	)	PUNCT
cana-535	228	37	)	)	PUNCT
cana-535	229	1	=	=	PUNCT
cana-535	229	2	∅((𝑞𝜍	∅((𝑞𝜍	X
cana-535	229	3	)	)	PUNCT
cana-535	229	4	+	+	CCONJ
cana-535	229	5	�	�	PROPN
cana-535	229	6	̃	̃	NOUN
cana-535	229	7	�	�	PROPN
cana-535	229	8	)	)	PUNCT
cana-535	229	9	=	=	PUNCT
cana-535	229	10	(	(	PUNCT
cana-535	229	11	𝑞𝜍	𝑞𝜍	NOUN
cana-535	229	12	)	)	PUNCT
cana-535	230	1	+	+	CCONJ
cana-535	230	2	�	�	PROPN
cana-535	230	3	̃	̃	PROPN
cana-535	230	4	�	�	NOUN
cana-535	230	5	∗	∗	NOUN
cana-535	230	6	=	=	SYM
cana-535	230	7	(	(	PUNCT
cana-535	230	8	𝑞	𝑞	PROPN
cana-535	230	9	+	+	PROPN
cana-535	230	10	�	�	PROPN
cana-535	230	11	̃	̃	PROPN
cana-535	230	12	�	�	PROPN
cana-535	230	13	∗)(𝜍	∗)(𝜍	NOUN
cana-535	230	14	+	+	SYM
cana-535	230	15	�	�	PROPN
cana-535	230	16	̃	̃	PROPN
cana-535	230	17	�	�	NOUN
cana-535	230	18	∗	∗	NOUN
cana-535	230	19	)	)	PUNCT
cana-535	231	1	=	=	PUNCT
cana-535	231	2	∅(𝑞	∅(𝑞	PROPN
cana-535	231	3	+	+	CCONJ
cana-535	231	4	�	�	PROPN
cana-535	231	5	̃	̃	NOUN
cana-535	231	6	�	�	PROPN
cana-535	231	7	)∅(𝜍	)∅(𝜍	PUNCT
cana-535	231	8	+	+	NUM
cana-535	231	9	�	�	PROPN
cana-535	231	10	̃	̃	PROPN
cana-535	231	11	�	�	PROPN
cana-535	231	12	)	)	PUNCT
cana-535	231	13	and	and	CCONJ
cana-535	231	14	∅((𝑞	∅((𝑞	NOUN
cana-535	231	15	+	+	CCONJ
cana-535	231	16	𝛾)(𝜍	𝛾)(𝜍	NOUN
cana-535	231	17	+	+	CCONJ
cana-535	231	18	𝛾	𝛾	NOUN
cana-535	231	19	)	)	PUNCT
cana-535	231	20	)	)	PUNCT
cana-535	232	1	=	=	PUNCT
cana-535	232	2	∅((𝑞𝜍	∅((𝑞𝜍	X
cana-535	232	3	)	)	PUNCT
cana-535	233	1	+	+	CCONJ
cana-535	233	2	𝛾	𝛾	X
cana-535	233	3	)	)	PUNCT
cana-535	233	4	=	=	SYM
cana-535	233	5	(	(	PUNCT
cana-535	233	6	𝑞𝜍	𝑞𝜍	NOUN
cana-535	233	7	)	)	PUNCT
cana-535	233	8	+	+	CCONJ
cana-535	233	9	𝛾∗	𝛾∗	NOUN
cana-535	233	10	=	=	SYM
cana-535	233	11	(	(	PUNCT
cana-535	233	12	𝑞	𝑞	X
cana-535	233	13	+	+	X
cana-535	233	14	𝛾∗)(𝜍	𝛾∗)(𝜍	NOUN
cana-535	233	15	+	+	CCONJ
cana-535	233	16	𝛾∗	𝛾∗	NOUN
cana-535	233	17	)	)	PUNCT
cana-535	233	18	=	=	PUNCT
cana-535	233	19	∅(𝑞	∅(𝑞	VERB
cana-535	233	20	+	+	CCONJ
cana-535	233	21	𝛾)∅(𝜍	𝛾)∅(𝜍	X
cana-535	233	22	+	+	CCONJ
cana-535	233	23	𝛾.	𝛾.	ADJ
cana-535	233	24	)	)	PUNCT
cana-535	233	25	therefore	therefore	ADV
cana-535	233	26	∅	∅	NOUN
cana-535	233	27	is	be	AUX
cana-535	233	28	a	a	DET
cana-535	233	29	homomorphism	homomorphism	NOUN
cana-535	233	30	.	.	PUNCT
cana-535	234	1	hence	hence	ADV
cana-535	234	2	𝑁	𝑁	PROPN
cana-535	234	3	�	�	PROPN
cana-535	234	4	̃	̃	PROPN
cana-535	234	5	�	�	PROPN
cana-535	234	6	𝛾	𝛾	NOUN
cana-535	234	7	⁄	⁄	PROPN
cana-535	234	8	is	be	AUX
cana-535	234	9	isomorphic	isomorphic	ADJ
cana-535	234	10	to	to	ADP
cana-535	234	11	𝑁	𝑁	PROPN
cana-535	234	12	�	�	PROPN
cana-535	234	13	̃	̃	PROPN
cana-535	234	14	�	�	PROPN
cana-535	234	15	𝛾∗	𝛾∗	NOUN
cana-535	234	16	⁄	⁄	PROPN
cana-535	234	17	.	.	PUNCT
cana-535	235	1	4	4	X
cana-535	235	2	.	.	X
cana-535	235	3	conclusion	conclusion	NOUN
cana-535	235	4	in	in	ADP
cana-535	235	5	this	this	DET
cana-535	235	6	study	study	NOUN
cana-535	235	7	,	,	PUNCT
cana-535	235	8	we	we	PRON
cana-535	235	9	familiarized	familiarize	VERB
cana-535	235	10	the	the	DET
cana-535	235	11	idea	idea	NOUN
cana-535	235	12	of	of	ADP
cana-535	235	13	hybrid	hybrid	ADJ
cana-535	235	14	coset	coset	NOUN
cana-535	235	15	of	of	ADP
cana-535	235	16	a	a	DET
cana-535	235	17	nearring	nearre	VERB
cana-535	235	18	and	and	CCONJ
cana-535	235	19	explored	explore	VERB
cana-535	235	20	numerous	numerous	ADJ
cana-535	235	21	properties	property	NOUN
cana-535	235	22	.	.	PUNCT
cana-535	236	1	using	use	VERB
cana-535	236	2	these	these	DET
cana-535	236	3	ideas	idea	NOUN
cana-535	236	4	,	,	PUNCT
cana-535	236	5	we	we	PRON
cana-535	236	6	familiarized	familiarize	VERB
cana-535	236	7	the	the	DET
cana-535	236	8	ideas	idea	NOUN
cana-535	236	9	of	of	ADP
cana-535	236	10	nearring	nearre	VERB
cana-535	236	11	homomorphism	homomorphism	NOUN
cana-535	236	12	and	and	CCONJ
cana-535	236	13	isomorphism	isomorphism	NOUN
cana-535	236	14	.	.	PUNCT
cana-535	237	1	research	research	NOUN
cana-535	237	2	can	can	AUX
cana-535	237	3	be	be	AUX
cana-535	237	4	prolonged	prolong	VERB
cana-535	237	5	to	to	ADP
cana-535	237	6	the	the	DET
cana-535	237	7	hybrid	hybrid	ADJ
cana-535	237	8	ideal	ideal	NOUN
cana-535	237	9	of	of	ADP
cana-535	237	10	a	a	DET
cana-535	237	11	gamma	gamma	NOUN
cana-535	237	12	near	near	ADP
cana-535	237	13	algebra	algebra	PROPN
cana-535	237	14	,	,	PUNCT
cana-535	237	15	sum	sum	NOUN
cana-535	237	16	of	of	ADP
cana-535	237	17	hybrid	hybrid	ADJ
cana-535	237	18	ideals	ideal	NOUN
cana-535	237	19	of	of	ADP
cana-535	237	20	a	a	DET
cana-535	237	21	near	near	ADJ
cana-535	237	22	algebra	algebra	NOUN
cana-535	237	23	and	and	CCONJ
cana-535	237	24	sum	sum	NOUN
cana-535	237	25	of	of	ADP
cana-535	237	26	hybrid	hybrid	ADJ
cana-535	237	27	ideals	ideal	NOUN
cana-535	237	28	of	of	ADP
cana-535	237	29	a	a	DET
cana-535	237	30	gamma	gamma	NOUN
cana-535	237	31	near	near	ADP
cana-535	237	32	algebra	algebra	PROPN
cana-535	237	33	.	.	PUNCT
cana-535	238	1	5	5	X
cana-535	238	2	.	.	X
cana-535	238	3	acknowledgements	acknowledgement	VERB
cana-535	238	4	the	the	DET
cana-535	238	5	authors	author	NOUN
cana-535	238	6	outspread	outspread	VERB
cana-535	238	7	their	their	PRON
cana-535	238	8	appreciation	appreciation	NOUN
cana-535	238	9	to	to	ADP
cana-535	238	10	gitam	gitam	PROPN
cana-535	238	11	deemed	deem	VERB
cana-535	238	12	to	to	PART
cana-535	238	13	be	be	AUX
cana-535	238	14	university	university	NOUN
cana-535	238	15	,	,	PUNCT
cana-535	238	16	india	india	PROPN
cana-535	238	17	for	for	ADP
cana-535	238	18	funding	fund	VERB
cana-535	238	19	this	this	DET
cana-535	238	20	research	research	NOUN
cana-535	238	21	under	under	ADP
cana-535	238	22	gitam	gitam	NOUN
cana-535	238	23	seed	seed	NOUN
cana-535	238	24	grant	grant	NOUN
cana-535	238	25	file	file	NOUN
cana-535	238	26	number	number	NOUN
cana-535	238	27	2021/0104	2021/0104	NUM
cana-535	238	28	.	.	PUNCT
cana-535	239	1	references	reference	NOUN
cana-535	239	2	[	[	X
cana-535	239	3	1	1	NUM
cana-535	239	4	]	]	X
cana-535	239	5	g.	g.	PROPN
cana-535	239	6	pilz	pilz	PROPN
cana-535	239	7	,	,	PUNCT
cana-535	239	8	“	"	PUNCT
cana-535	239	9	near	near	ADP
cana-535	239	10	-	-	PUNCT
cana-535	239	11	ring	ring	NOUN
cana-535	239	12	,	,	PUNCT
cana-535	239	13	”	"	PUNCT
cana-535	239	14	north	north	NOUN
cana-535	239	15	holland	holland	PROPN
cana-535	239	16	publishers	publisher	NOUN
cana-535	239	17	,	,	PUNCT
cana-535	239	18	amsterdam	amsterdam	PROPN
cana-535	239	19	(	(	PUNCT
cana-535	239	20	1983	1983	NUM
cana-535	239	21	)	)	PUNCT
cana-535	239	22	.	.	PUNCT
cana-535	240	1	[	[	X
cana-535	240	2	2	2	NUM
cana-535	240	3	]	]	PUNCT
cana-535	240	4	nobusawa	nobusawa	NOUN
cana-535	240	5	,	,	PUNCT
cana-535	240	6	“	"	PUNCT
cana-535	240	7	on	on	ADP
cana-535	240	8	a	a	DET
cana-535	240	9	generalization	generalization	NOUN
cana-535	240	10	of	of	ADP
cana-535	240	11	the	the	DET
cana-535	240	12	ring	ring	NOUN
cana-535	240	13	theory	theory	NOUN
cana-535	240	14	”	"	PUNCT
cana-535	240	15	,	,	PUNCT
cana-535	240	16	osaka	osaka	PROPN
cana-535	240	17	journal	journal	PROPN
cana-535	240	18	of	of	ADP
cana-535	240	19	mathematics	mathematic	NOUN
cana-535	240	20	,	,	PUNCT
cana-535	240	21	1(1964	1(1964	NUM
cana-535	240	22	)	)	PUNCT
cana-535	240	23	,	,	PUNCT
cana-535	240	24	81	81	NUM
cana-535	240	25	-	-	SYM
cana-535	240	26	89	89	NUM
cana-535	240	27	.	.	PUNCT
cana-535	241	1	[	[	X
cana-535	241	2	3	3	X
cana-535	241	3	]	]	X
cana-535	241	4	bh	bh	NOUN
cana-535	241	5	.	.	PROPN
cana-535	241	6	satyanarayana	satyanarayana	PROPN
cana-535	241	7	,	,	PUNCT
cana-535	241	8	contribution	contribution	NOUN
cana-535	241	9	to	to	ADP
cana-535	241	10	near	near	ADJ
cana-535	241	11	-	-	PUNCT
cana-535	241	12	ring	ring	NOUN
cana-535	241	13	theory	theory	NOUN
cana-535	241	14	,	,	PUNCT
cana-535	241	15	doctoral	doctoral	ADJ
cana-535	241	16	dissertation	dissertation	NOUN
cana-535	241	17	,	,	PUNCT
cana-535	241	18	acharya	acharya	PROPN
cana-535	241	19	nagarjuna	nagarjuna	PROPN
cana-535	241	20	university	university	PROPN
cana-535	241	21	,	,	PUNCT
cana-535	241	22	1984	1984	NUM
cana-535	241	23	.	.	PUNCT
cana-535	242	1	[	[	X
cana-535	242	2	4	4	X
cana-535	242	3	]	]	PUNCT
cana-535	242	4	t.	t.	PROPN
cana-535	242	5	srinivas	srinivas	PROPN
cana-535	242	6	,	,	PUNCT
cana-535	242	7	near	near	ADP
cana-535	242	8	-	-	PUNCT
cana-535	242	9	rings	ring	NOUN
cana-535	242	10	and	and	CCONJ
cana-535	242	11	application	application	NOUN
cana-535	242	12	to	to	ADP
cana-535	242	13	function	function	NOUN
cana-535	242	14	spaces	space	NOUN
cana-535	242	15	,	,	PUNCT
cana-535	242	16	doctoral	doctoral	ADJ
cana-535	242	17	dissertation	dissertation	NOUN
cana-535	242	18	,	,	PUNCT
cana-535	242	19	kakatiya	kakatiya	PROPN
cana-535	242	20	university	university	NOUN
cana-535	242	21	,	,	PUNCT
cana-535	242	22	1996	1996	NUM
cana-535	242	23	.	.	PUNCT
cana-535	243	1	[	[	X
cana-535	243	2	5	5	X
cana-535	243	3	]	]	PUNCT
cana-535	243	4	l.	l.	PROPN
cana-535	243	5	a.	a.	PROPN
cana-535	243	6	zadeh	zadeh	PROPN
cana-535	243	7	,	,	PUNCT
cana-535	243	8	fuzzy	fuzzy	ADJ
cana-535	243	9	sets	set	NOUN
cana-535	243	10	,	,	PUNCT
cana-535	243	11	inform	inform	NOUN
cana-535	243	12	.	.	PUNCT
cana-535	244	1	control	control	NOUN
cana-535	244	2	.	.	PUNCT
cana-535	244	3	,	,	PUNCT
cana-535	245	1	vol.8	vol.8	PROPN
cana-535	245	2	(	(	PUNCT
cana-535	245	3	1965	1965	NUM
cana-535	245	4	)	)	PUNCT
cana-535	245	5	,	,	PUNCT
cana-535	245	6	338	338	NUM
cana-535	245	7	-	-	SYM
cana-535	245	8	353	353	NUM
cana-535	245	9	.	.	PUNCT
cana-535	246	1	[	[	X
cana-535	246	2	6	6	NUM
cana-535	246	3	]	]	PUNCT
cana-535	246	4	v.	v.	CCONJ
cana-535	246	5	torra	torra	PROPN
cana-535	246	6	,	,	PUNCT
cana-535	246	7	“	"	PUNCT
cana-535	246	8	hesitant	hesitant	ADJ
cana-535	246	9	fuzzy	fuzzy	ADJ
cana-535	246	10	sets	set	NOUN
cana-535	246	11	”	"	PUNCT
cana-535	246	12	,	,	PUNCT
cana-535	246	13	international	international	ADJ
cana-535	246	14	journal	journal	NOUN
cana-535	246	15	of	of	ADP
cana-535	246	16	intelligent	intelligent	ADJ
cana-535	246	17	systems	system	NOUN
cana-535	246	18	,	,	PUNCT
cana-535	246	19	vol	vol	NOUN
cana-535	246	20	.	.	PROPN
cana-535	247	1	25	25	NUM
cana-535	247	2	(	(	PUNCT
cana-535	247	3	2010	2010	NUM
cana-535	247	4	)	)	PUNCT
cana-535	247	5	,	,	PUNCT
cana-535	247	6	529	529	NUM
cana-535	247	7	-	-	SYM
cana-535	247	8	539	539	NUM
cana-535	247	9	.	.	PUNCT
cana-535	248	1	[	[	X
cana-535	248	2	7	7	X
cana-535	248	3	]	]	X
cana-535	248	4	d.	d.	PROPN
cana-535	248	5	molodtsov	molodtsov	PROPN
cana-535	248	6	,	,	PUNCT
cana-535	248	7	“	"	PUNCT
cana-535	248	8	soft	soft	ADJ
cana-535	248	9	set	set	ADJ
cana-535	248	10	theoryfirst	theoryfirst	NOUN
cana-535	248	11	results	result	NOUN
cana-535	248	12	”	"	PUNCT
cana-535	248	13	,	,	PUNCT
cana-535	248	14	computers	computer	NOUN
cana-535	248	15	and	and	CCONJ
cana-535	248	16	mathematics	mathematic	NOUN
cana-535	248	17	with	with	ADP
cana-535	248	18	applications	application	NOUN
cana-535	248	19	,	,	PUNCT
cana-535	248	20	37(1999),1931	37(1999),1931	NUM
cana-535	248	21	.	.	PUNCT
cana-535	249	1	[	[	X
cana-535	249	2	8	8	NUM
cana-535	249	3	]	]	X
cana-535	249	4	young	young	ADJ
cana-535	249	5	bae	bae	PROPN
cana-535	249	6	jun	jun	PROPN
cana-535	249	7	,	,	PUNCT
cana-535	249	8	seok	seok	PROPN
cana-535	249	9	zun	zun	PROPN
cana-535	249	10	song	song	NOUN
cana-535	249	11	and	and	CCONJ
cana-535	249	12	g.	g.	PROPN
cana-535	249	13	muhiuddin	muhiuddin	PROPN
cana-535	249	14	,	,	PUNCT
cana-535	249	15	“	"	PUNCT
cana-535	249	16	hybrid	hybrid	ADJ
cana-535	249	17	structures	structure	NOUN
cana-535	249	18	and	and	CCONJ
cana-535	249	19	applications	application	NOUN
cana-535	249	20	”	"	PUNCT
cana-535	249	21	,	,	PUNCT
cana-535	249	22	annals	annal	NOUN
cana-535	249	23	of	of	ADP
cana-535	249	24	communications	communication	NOUN
cana-535	249	25	in	in	ADP
cana-535	249	26	mathematics	mathematic	NOUN
cana-535	249	27	,	,	PUNCT
cana-535	249	28	vol.1(1	vol.1(1	NOUN
cana-535	249	29	)	)	PUNCT
cana-535	249	30	(	(	PUNCT
cana-535	249	31	2018	2018	NUM
cana-535	249	32	)	)	PUNCT
cana-535	249	33	,	,	PUNCT
cana-535	249	34	11	11	NUM
cana-535	249	35	-	-	SYM
cana-535	249	36	25	25	NUM
cana-535	249	37	.	.	PUNCT
cana-535	250	1	[	[	X
cana-535	250	2	9	9	NUM
cana-535	250	3	]	]	PUNCT
cana-535	250	4	b.	b.	PROPN
cana-535	250	5	elavarasan	elavarasan	PROPN
cana-535	250	6	,	,	PUNCT
cana-535	250	7	g.	g.	PROPN
cana-535	250	8	muhiuddin	muhiuddin	PROPN
cana-535	250	9	,	,	PUNCT
cana-535	250	10	k.	k.	PROPN
cana-535	250	11	porselvi	porselvi	PROPN
cana-535	250	12	and	and	CCONJ
cana-535	250	13	y	y	PROPN
cana-535	250	14	b	b	PROPN
cana-535	250	15	jun	jun	PROPN
cana-535	250	16	,	,	PUNCT
cana-535	250	17	“	"	PUNCT
cana-535	250	18	hybrid	hybrid	ADJ
cana-535	250	19	structures	structure	NOUN
cana-535	250	20	applied	apply	VERB
cana-535	250	21	to	to	ADP
cana-535	250	22	ideals	ideal	NOUN
cana-535	250	23	in	in	ADP
cana-535	250	24	near	near	ADJ
cana-535	250	25	-	-	PUNCT
cana-535	250	26	rings	ring	NOUN
cana-535	250	27	”	"	PUNCT
cana-535	250	28	,	,	PUNCT
cana-535	250	29	complex	complex	ADJ
cana-535	250	30	&	&	CCONJ
cana-535	250	31	intelligent	intelligent	ADJ
cana-535	250	32	systems	system	NOUN
cana-535	250	33	,	,	PUNCT
cana-535	250	34	vol	vol	NOUN
cana-535	250	35	(	(	PUNCT
cana-535	250	36	7	7	NUM
cana-535	250	37	)	)	PUNCT
cana-535	250	38	(	(	PUNCT
cana-535	250	39	2021	2021	NUM
cana-535	250	40	)	)	PUNCT
cana-535	250	41	,	,	PUNCT
cana-535	250	42	1489	1489	NUM
cana-535	250	43	-	-	SYM
cana-535	250	44	1498	1498	NUM
cana-535	250	45	.	.	PUNCT
cana-535	251	1	[	[	X
cana-535	251	2	10	10	NUM
cana-535	251	3	]	]	X
cana-535	251	4	saima	saima	PROPN
cana-535	251	5	anis	anis	PROPN
cana-535	251	6	,	,	PUNCT
cana-535	251	7	m	m	PROPN
cana-535	251	8	khan	khan	PROPN
cana-535	251	9	,	,	PUNCT
cana-535	251	10	yb	yb	PROPN
cana-535	251	11	jun	jun	PROPN
cana-535	251	12	,	,	PUNCT
cana-535	251	13	“	"	PUNCT
cana-535	251	14	hybrid	hybrid	ADJ
cana-535	251	15	ideals	ideal	NOUN
cana-535	251	16	in	in	ADP
cana-535	251	17	semi	semi	ADJ
cana-535	251	18	groups	group	NOUN
cana-535	251	19	”	"	PUNCT
cana-535	251	20	,	,	PUNCT
cana-535	251	21	cogent	cogent	NOUN
cana-535	251	22	mathematics	mathematic	NOUN
cana-535	251	23	,	,	PUNCT
cana-535	251	24	(	(	PUNCT
cana-535	251	25	2017	2017	NUM
cana-535	251	26	)	)	PUNCT
cana-535	251	27	,	,	PUNCT
cana-535	251	28	4:1352117	4:1352117	X
cana-535	251	29	.	.	PUNCT
cana-535	252	1	[	[	X
cana-535	252	2	11	11	NUM
cana-535	252	3	]	]	PUNCT
cana-535	252	4	m.	m.	NOUN
cana-535	252	5	himaya	himaya	PROPN
cana-535	252	6	jaleela	jaleela	PROPN
cana-535	252	7	begum	begum	PROPN
cana-535	252	8	,	,	PUNCT
cana-535	252	9	g.	g.	PROPN
cana-535	252	10	rama	rama	PROPN
cana-535	252	11	,	,	PUNCT
cana-535	252	12	“	"	PUNCT
cana-535	252	13	hybrid	hybrid	ADJ
cana-535	252	14	fuzzy	fuzzy	ADJ
cana-535	252	15	bi	bi	NOUN
cana-535	252	16	-	-	NOUN
cana-535	252	17	ideals	ideal	NOUN
cana-535	252	18	in	in	ADP
cana-535	252	19	near	near	ADJ
cana-535	252	20	rings	ring	NOUN
cana-535	252	21	”	"	PUNCT
cana-535	252	22	,	,	PUNCT
cana-535	252	23	turkish	turkish	ADJ
cana-535	252	24	journal	journal	NOUN
cana-535	252	25	of	of	ADP
cana-535	252	26	computer	computer	NOUN
cana-535	252	27	and	and	CCONJ
cana-535	252	28	mathematics	mathematic	NOUN
cana-535	252	29	education	education	NOUN
cana-535	252	30	,	,	PUNCT
cana-535	252	31	vol.12	vol.12	NOUN
cana-535	252	32	(	(	PUNCT
cana-535	252	33	7	7	NUM
cana-535	252	34	)	)	PUNCT
cana-535	252	35	(	(	PUNCT
cana-535	252	36	2021	2021	NUM
cana-535	252	37	)	)	PUNCT
cana-535	252	38	,	,	PUNCT
cana-535	252	39	3291	3291	NUM
cana-535	252	40	-	-	SYM
cana-535	252	41	3295	3295	NUM
cana-535	252	42	.	.	PUNCT
cana-535	253	1	communications	communication	NOUN
cana-535	253	2	on	on	ADP
cana-535	253	3	applied	apply	VERB
cana-535	253	4	nonlinear	nonlinear	ADJ
cana-535	253	5	analysis	analysis	NOUN
cana-535	253	6	issn	issn	NOUN
cana-535	253	7	:	:	PUNCT
cana-535	253	8	1074	1074	NUM
cana-535	253	9	-	-	PUNCT
cana-535	253	10	133x	133x	NUM
cana-535	253	11	vol	vol	NOUN
cana-535	253	12	31	31	NUM
cana-535	253	13	no	no	NOUN
cana-535	253	14	.	.	NOUN
cana-535	253	15	2	2	NUM
cana-535	253	16	(	(	PUNCT
cana-535	253	17	2024	2024	NUM
cana-535	253	18	)	)	PUNCT
cana-535	253	19	213	213	NUM
cana-535	253	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-535	254	1	[	[	X
cana-535	254	2	12	12	NUM
cana-535	254	3	]	]	PUNCT
cana-535	254	4	s.	s.	PROPN
cana-535	254	5	abou	abou	PROPN
cana-535	254	6	zaid	zaid	PROPN
cana-535	254	7	,	,	PUNCT
cana-535	254	8	on	on	ADP
cana-535	254	9	fuzzy	fuzzy	ADJ
cana-535	254	10	sub	sub	NOUN
cana-535	254	11	near	near	ADP
cana-535	254	12	rings	ring	NOUN
cana-535	254	13	and	and	CCONJ
cana-535	254	14	ideals	ideal	NOUN
cana-535	254	15	,	,	PUNCT
cana-535	254	16	fuzzy	fuzzy	ADJ
cana-535	254	17	sets	set	NOUN
cana-535	254	18	and	and	CCONJ
cana-535	254	19	systems	system	NOUN
cana-535	254	20	,	,	PUNCT
cana-535	254	21	(	(	PUNCT
cana-535	254	22	1991),44(1	1991),44(1	NUM
cana-535	254	23	)	)	PUNCT
cana-535	254	24	,	,	PUNCT
cana-535	254	25	139	139	NUM
cana-535	254	26	-	-	SYM
cana-535	254	27	146	146	NUM
cana-535	254	28	.	.	PUNCT
cana-535	255	1	[	[	X
cana-535	255	2	13	13	NUM
cana-535	255	3	]	]	X
cana-535	255	4	s.d	s.d	PROPN
cana-535	255	5	.	.	PROPN
cana-535	255	6	kim	kim	PROPN
cana-535	255	7	and	and	CCONJ
cana-535	255	8	h.s	h.s	PROPN
cana-535	255	9	.	.	PROPN
cana-535	255	10	kim	kim	PROPN
cana-535	255	11	,	,	PUNCT
cana-535	255	12	“	"	PUNCT
cana-535	255	13	on	on	ADP
cana-535	255	14	fuzzy	fuzzy	ADJ
cana-535	255	15	ideals	ideal	NOUN
cana-535	255	16	of	of	ADP
cana-535	255	17	near	near	ADJ
cana-535	255	18	rings	ring	NOUN
cana-535	255	19	”	"	PUNCT
cana-535	255	20	,	,	PUNCT
cana-535	255	21	bulletin	bulletin	NOUN
cana-535	255	22	of	of	ADP
cana-535	255	23	the	the	DET
cana-535	255	24	korean	korean	PROPN
cana-535	255	25	mathematical	mathematical	ADJ
cana-535	255	26	society	society	NOUN
cana-535	255	27	,	,	PUNCT
cana-535	255	28	(	(	PUNCT
cana-535	255	29	1996	1996	NUM
cana-535	255	30	)	)	PUNCT
cana-535	255	31	33(4	33(4	NUM
cana-535	255	32	)	)	PUNCT
cana-535	255	33	,	,	PUNCT
cana-535	255	34	593	593	NUM
cana-535	255	35	-	-	SYM
cana-535	255	36	601	601	NUM
cana-535	255	37	.	.	PUNCT
cana-535	256	1	[	[	X
cana-535	256	2	14	14	NUM
cana-535	256	3	]	]	X
cana-535	256	4	p.	p.	PROPN
cana-535	256	5	narasimha	narasimha	PROPN
cana-535	256	6	swamy	swamy	PROPN
cana-535	256	7	,	,	PUNCT
cana-535	256	8	k.	k.	PROPN
cana-535	256	9	vijay	vijay	PROPN
cana-535	256	10	kumar	kumar	PROPN
cana-535	256	11	,	,	PUNCT
cana-535	256	12	t.	t.	PROPN
cana-535	256	13	nagaiah	nagaiah	PROPN
cana-535	256	14	and	and	CCONJ
cana-535	256	15	t.	t.	PROPN
cana-535	256	16	srinivas	srinivas	PROPN
cana-535	256	17	,	,	PUNCT
cana-535	256	18	“	"	PUNCT
cana-535	256	19	sum	sum	NOUN
cana-535	256	20	of	of	ADP
cana-535	256	21	fuzzy	fuzzy	ADJ
cana-535	256	22	ideals	ideal	NOUN
cana-535	256	23	of	of	ADP
cana-535	256	24	γ	γ	X
cana-535	256	25	-	-	PUNCT
cana-535	256	26	near	near	ADP
cana-535	256	27	-	-	PUNCT
cana-535	256	28	rings	ring	NOUN
cana-535	256	29	”	"	PUNCT
cana-535	256	30	,	,	PUNCT
cana-535	256	31	annals	annal	NOUN
cana-535	256	32	of	of	ADP
cana-535	256	33	fuzzy	fuzzy	ADJ
cana-535	256	34	mathematics	mathematic	NOUN
cana-535	256	35	and	and	CCONJ
cana-535	256	36	informatics	informatic	NOUN
cana-535	256	37	,	,	PUNCT
cana-535	256	38	vol	vol	NOUN
cana-535	256	39	9	9	NUM
cana-535	256	40	(	(	PUNCT
cana-535	256	41	4	4	NUM
cana-535	256	42	)	)	PUNCT
cana-535	256	43	,	,	PUNCT
cana-535	256	44	(	(	PUNCT
cana-535	256	45	april	april	PROPN
cana-535	256	46	2015	2015	NUM
cana-535	256	47	)	)	PUNCT
cana-535	256	48	,	,	PUNCT
cana-535	256	49	665	665	NUM
cana-535	256	50	-	-	SYM
cana-535	256	51	675	675	NUM
cana-535	256	52	.	.	PUNCT
cana-535	257	1	[	[	X
cana-535	257	2	15	15	NUM
cana-535	257	3	]	]	X
cana-535	257	4	k.	k.	PROPN
cana-535	257	5	vijay	vijay	PROPN
cana-535	257	6	kumar	kumar	PROPN
cana-535	257	7	,	,	PUNCT
cana-535	257	8	b.	b.	PROPN
cana-535	257	9	jyothi	jyothi	PROPN
cana-535	257	10	,	,	PUNCT
cana-535	257	11	p.	p.	PROPN
cana-535	257	12	narasimha	narasimha	PROPN
cana-535	257	13	swamy	swamy	PROPN
cana-535	257	14	,	,	PUNCT
cana-535	257	15	t.	t.	PROPN
cana-535	257	16	nagaiah	nagaiah	PROPN
cana-535	257	17	,	,	PUNCT
cana-535	257	18	g.	g.	PROPN
cana-535	257	19	omprakasham	omprakasham	PROPN
cana-535	257	20	,	,	PUNCT
cana-535	257	21	“	"	PUNCT
cana-535	257	22	characterization	characterization	NOUN
cana-535	257	23	on	on	ADP
cana-535	257	24	bipolar	bipolar	ADJ
cana-535	257	25	fuzzy	fuzzy	ADJ
cana-535	257	26	quasi	quasi	NOUN
cana-535	257	27	ideals	ideal	NOUN
cana-535	257	28	and	and	CCONJ
cana-535	257	29	bipolar	bipolar	ADJ
cana-535	257	30	n	n	CCONJ
cana-535	257	31	-	-	NOUN
cana-535	257	32	subgroups	subgroup	NOUN
cana-535	257	33	of	of	ADP
cana-535	257	34	near	near	ADJ
cana-535	257	35	rings	ring	NOUN
cana-535	257	36	”	"	PUNCT
cana-535	257	37	.	.	PUNCT
cana-535	258	1	aipcp	aipcp	PROPN
cana-535	258	2	,	,	PUNCT
cana-535	258	3	(	(	PUNCT
cana-535	258	4	2020	2020	NUM
cana-535	258	5	)	)	PUNCT
cana-535	258	6	,	,	PUNCT
cana-535	258	7	2246	2246	NUM
cana-535	258	8	,	,	PUNCT
cana-535	258	9	020053	020053	NUM
cana-535	258	10	-	-	SYM
cana-535	258	11	1	1	NUM
cana-535	258	12	to	to	ADP
cana-535	258	13	020053	020053	NUM
cana-535	258	14	-	-	SYM
cana-535	258	15	4	4	NUM
cana-535	258	16	.	.	PUNCT
cana-535	259	1	[	[	X
cana-535	259	2	16	16	NUM
cana-535	259	3	]	]	X
cana-535	259	4	satyanarayana	satyanarayana	PROPN
cana-535	259	5	bhavanari	bhavanari	PROPN
cana-535	259	6	and	and	CCONJ
cana-535	259	7	syam	syam	PROPN
cana-535	259	8	prasad	prasad	PROPN
cana-535	259	9	kuncham	kuncham	PROPN
cana-535	259	10	,	,	PUNCT
cana-535	259	11	“	"	PUNCT
cana-535	259	12	on	on	ADP
cana-535	259	13	fuzzy	fuzzy	ADJ
cana-535	259	14	cosets	coset	NOUN
cana-535	259	15	of	of	ADP
cana-535	259	16	gamma	gamma	NOUN
cana-535	259	17	nearrings	nearring	NOUN
cana-535	259	18	”	"	PUNCT
cana-535	259	19	,	,	PUNCT
cana-535	259	20	turk	turk	PROPN
cana-535	259	21	journal	journal	PROPN
cana-535	259	22	of	of	ADP
cana-535	259	23	math	math	NOUN
cana-535	259	24	,	,	PUNCT
cana-535	259	25	vol	vol	NOUN
cana-535	259	26	.	.	PROPN
cana-535	259	27	29	29	NUM
cana-535	259	28	,	,	PUNCT
cana-535	259	29	1(2005	1(2005	NUM
cana-535	259	30	)	)	PUNCT
cana-535	259	31	,	,	PUNCT
cana-535	259	32	11	11	NUM
cana-535	259	33	-	-	SYM
cana-535	259	34	22	22	NUM
cana-535	259	35	.	.	PUNCT
cana-535	260	1	[	[	X
cana-535	260	2	17	17	NUM
cana-535	260	3	]	]	PUNCT
cana-535	260	4	t.	t.	PROPN
cana-535	260	5	srinivas	srinivas	PROPN
cana-535	260	6	and	and	CCONJ
cana-535	260	7	p.	p.	PROPN
cana-535	260	8	narasimha	narasimha	PROPN
cana-535	260	9	swamy	swamy	PROPN
cana-535	260	10	,	,	PUNCT
cana-535	260	11	a	a	DET
cana-535	260	12	note	note	NOUN
cana-535	260	13	on	on	ADP
cana-535	260	14	fuzzy	fuzzy	ADJ
cana-535	260	15	near	near	NOUN
cana-535	260	16	-	-	PUNCT
cana-535	260	17	algebras	algebra	NOUN
cana-535	260	18	,	,	PUNCT
cana-535	260	19	international	international	ADJ
cana-535	260	20	journal	journal	NOUN
cana-535	260	21	of	of	ADP
cana-535	260	22	algebra	algebra	PROPN
cana-535	260	23	5	5	NUM
cana-535	260	24	,	,	PUNCT
cana-535	260	25	22	22	NUM
cana-535	260	26	(	(	PUNCT
cana-535	260	27	2011	2011	NUM
cana-535	260	28	)	)	PUNCT
cana-535	260	29	1085–1098	1085–1098	NOUN
cana-535	260	30	.	.	PUNCT
cana-535	261	1	[	[	X
cana-535	261	2	18	18	NUM
cana-535	261	3	]	]	PUNCT
cana-535	261	4	harika	harika	X
cana-535	261	5	bhurgula	bhurgula	NOUN
cana-535	261	6	,	,	PUNCT
cana-535	261	7	narasimha	narasimha	PROPN
cana-535	261	8	swamy	swamy	PROPN
cana-535	261	9	pasham	pasham	PROPN
cana-535	261	10	,	,	PUNCT
cana-535	261	11	ravikumar	ravikumar	PROPN
cana-535	261	12	bandaru	bandaru	PROPN
cana-535	261	13	and	and	CCONJ
cana-535	261	14	amal	amal	PROPN
cana-535	261	15	s.alali	s.alali	PROPN
cana-535	261	16	,	,	PUNCT
cana-535	261	17	hybrid	hybrid	NOUN
cana-535	261	18	near	near	ADP
cana-535	261	19	algebra	algebra	NOUN
cana-535	261	20	,	,	PUNCT
cana-535	261	21	axioms	axiom	NOUN
cana-535	261	22	,	,	PUNCT
cana-535	261	23	(	(	PUNCT
cana-535	261	24	2023),12	2023),12	NUM
cana-535	261	25	,	,	PUNCT
cana-535	261	26	877	877	NUM
cana-535	261	27	.	.	PUNCT
cana-535	262	1	[	[	X
cana-535	262	2	19	19	NUM
cana-535	262	3	]	]	PUNCT
cana-535	262	4	b.	b.	PROPN
cana-535	262	5	jyothi	jyothi	PROPN
cana-535	262	6	,	,	PUNCT
cana-535	262	7	p.	p.	PROPN
cana-535	262	8	narasimha	narasimha	PROPN
cana-535	262	9	swamy	swamy	PROPN
cana-535	262	10	,	,	PUNCT
cana-535	262	11	rakshita	rakshita	PROPN
cana-535	262	12	deshmukh	deshmukh	PROPN
cana-535	262	13	.	.	PROPN
cana-535	262	14	,	,	PUNCT
cana-535	262	15	b.	b.	PROPN
cana-535	262	16	satyanarayana	satyanarayana	PROPN
cana-535	262	17	,	,	PUNCT
cana-535	262	18	“	"	PUNCT
cana-535	262	19	prime	prime	ADJ
cana-535	262	20	bi	bi	NOUN
cana-535	262	21	-	-	NOUN
cana-535	262	22	ideals	ideal	NOUN
cana-535	262	23	of	of	ADP
cana-535	262	24	a	a	DET
cana-535	262	25	near	near	ADJ
cana-535	262	26	algebra	algebra	NOUN
cana-535	262	27	”	"	PUNCT
cana-535	262	28	,	,	PUNCT
cana-535	262	29	international	international	ADJ
cana-535	262	30	journal	journal	NOUN
cana-535	262	31	of	of	ADP
cana-535	262	32	latest	late	ADJ
cana-535	262	33	trends	trend	NOUN
cana-535	262	34	in	in	ADP
cana-535	262	35	engineering	engineering	NOUN
cana-535	262	36	and	and	CCONJ
cana-535	262	37	technology	technology	NOUN
cana-535	262	38	,	,	PUNCT
cana-535	262	39	(	(	PUNCT
cana-535	262	40	2019	2019	NUM
cana-535	262	41	)	)	PUNCT
cana-535	262	42	14(4	14(4	NOUN
cana-535	262	43	)	)	PUNCT
cana-535	262	44	,	,	PUNCT
cana-535	262	45	001	001	NUM
cana-535	262	46	-	-	SYM
cana-535	262	47	003	003	NUM
cana-535	262	48	.	.	PUNCT
cana-535	263	1	[	[	X
cana-535	263	2	20	20	NUM
cana-535	263	3	]	]	PUNCT
cana-535	263	4	b.	b.	PROPN
cana-535	263	5	jyothi	jyothi	PROPN
cana-535	263	6	,	,	PUNCT
cana-535	263	7	p.	p.	PROPN
cana-535	263	8	narasimha	narasimha	PROPN
cana-535	263	9	swamy	swamy	PROPN
cana-535	263	10	,	,	PUNCT
cana-535	263	11	k.	k.	PROPN
cana-535	263	12	vijay	vijay	PROPN
cana-535	263	13	kumar	kumar	PROPN
cana-535	263	14	,	,	PUNCT
cana-535	263	15	t.	t.	PROPN
cana-535	263	16	srinivas	srinivas	PROPN
cana-535	263	17	,	,	PUNCT
cana-535	263	18	“	"	PUNCT
cana-535	263	19	fuzzy	fuzzy	ADJ
cana-535	263	20	bi	bi	NOUN
cana-535	263	21	-	-	NOUN
cana-535	263	22	ideal	ideal	NOUN
cana-535	263	23	of	of	ADP
cana-535	263	24	a	a	DET
cana-535	263	25	near	near	ADJ
cana-535	263	26	algebra	algebra	NOUN
cana-535	263	27	”	"	PUNCT
cana-535	263	28	,	,	PUNCT
cana-535	263	29	aipcp	aipcp	NOUN
cana-535	263	30	,	,	PUNCT
cana-535	263	31	(	(	PUNCT
cana-535	263	32	2020	2020	NUM
cana-535	263	33	)	)	PUNCT
cana-535	263	34	2246	2246	NUM
cana-535	263	35	,	,	PUNCT
cana-535	263	36	020080	020080	NUM
cana-535	263	37	-	-	SYM
cana-535	263	38	1	1	NUM
cana-535	263	39	to	to	ADP
cana-535	263	40	020080	020080	NUM
cana-535	263	41	-	-	SYM
cana-535	263	42	5	5	NUM
cana-535	263	43	.	.	PUNCT