id	sid	tid	token	lemma	pos
iajs-2801	1	1	ibn	ibn	PROPN
iajs-2801	1	2	al	al	PROPN
iajs-2801	1	3	-	-	PUNCT
iajs-2801	1	4	haitham	haitham	PROPN
iajs-2801	1	5	jour	jour	X
iajs-2801	1	6	.	.	PROPN
iajs-2801	1	7	for	for	ADP
iajs-2801	1	8	pure	pure	ADJ
iajs-2801	1	9	&	&	CCONJ
iajs-2801	1	10	appl	appl	PROPN
iajs-2801	1	11	.	.	PUNCT
iajs-2801	2	1	sci	sci	PROPN
iajs-2801	2	2	.	.	PUNCT
iajs-2801	3	1	35(1)2022	35(1)2022	NUM
iajs-2801	3	2	73	73	NUM
iajs-2801	4	1	this	this	DET
iajs-2801	4	2	work	work	NOUN
iajs-2801	4	3	is	be	AUX
iajs-2801	4	4	licensed	license	VERB
iajs-2801	4	5	under	under	ADP
iajs-2801	4	6	a	a	DET
iajs-2801	4	7	creative	creative	ADJ
iajs-2801	4	8	commons	common	NOUN
iajs-2801	4	9	attribution	attribution	NOUN
iajs-2801	4	10	4.0	4.0	NUM
iajs-2801	4	11	international	international	ADJ
iajs-2801	4	12	license	license	NOUN
iajs-2801	4	13	.	.	PUNCT
iajs-2801	5	1	the	the	DET
iajs-2801	5	2	homomorphism	homomorphism	NOUN
iajs-2801	5	3	of	of	ADP
iajs-2801	5	4	cubic	cubic	ADJ
iajs-2801	5	5	bipolar	bipolar	ADJ
iajs-2801	5	6	ideals	ideal	NOUN
iajs-2801	5	7	of	of	ADP
iajs-2801	5	8	a	a	DET
iajs-2801	5	9	ku	ku	PROPN
iajs-2801	5	10	-	-	PUNCT
iajs-2801	5	11	semigroup	semigroup	PROPN
iajs-2801	5	12	abstract	abstract	NOUN
iajs-2801	5	13	the	the	DET
iajs-2801	5	14	idea	idea	NOUN
iajs-2801	5	15	of	of	ADP
iajs-2801	5	16	a	a	DET
iajs-2801	5	17	homomorphism	homomorphism	NOUN
iajs-2801	5	18	of	of	ADP
iajs-2801	5	19	a	a	DET
iajs-2801	5	20	cubic	cubic	ADJ
iajs-2801	5	21	set	set	NOUN
iajs-2801	5	22	of	of	ADP
iajs-2801	5	23	a	a	DET
iajs-2801	5	24	ku	ku	PROPN
iajs-2801	5	25	-	-	PUNCT
iajs-2801	5	26	semigroup	semigroup	PROPN
iajs-2801	5	27	is	be	AUX
iajs-2801	5	28	studied	study	VERB
iajs-2801	5	29	and	and	CCONJ
iajs-2801	5	30	the	the	DET
iajs-2801	5	31	concept	concept	NOUN
iajs-2801	5	32	of	of	ADP
iajs-2801	5	33	the	the	DET
iajs-2801	5	34	product	product	NOUN
iajs-2801	5	35	between	between	ADP
iajs-2801	5	36	two	two	NUM
iajs-2801	5	37	cubic	cubic	ADJ
iajs-2801	5	38	sets	set	NOUN
iajs-2801	5	39	is	be	AUX
iajs-2801	5	40	defined	define	VERB
iajs-2801	5	41	.	.	PUNCT
iajs-2801	6	1	and	and	CCONJ
iajs-2801	6	2	then	then	ADV
iajs-2801	6	3	,	,	PUNCT
iajs-2801	6	4	a	a	DET
iajs-2801	6	5	new	new	ADJ
iajs-2801	6	6	cubic	cubic	ADJ
iajs-2801	6	7	bipolar	bipolar	ADJ
iajs-2801	6	8	fuzzy	fuzzy	ADJ
iajs-2801	6	9	set	set	NOUN
iajs-2801	6	10	in	in	ADP
iajs-2801	6	11	this	this	DET
iajs-2801	6	12	structure	structure	NOUN
iajs-2801	6	13	is	be	AUX
iajs-2801	6	14	discussed	discuss	VERB
iajs-2801	6	15	,	,	PUNCT
iajs-2801	6	16	and	and	CCONJ
iajs-2801	6	17	some	some	DET
iajs-2801	6	18	important	important	ADJ
iajs-2801	6	19	results	result	NOUN
iajs-2801	6	20	are	be	AUX
iajs-2801	6	21	achieved	achieve	VERB
iajs-2801	6	22	.	.	PUNCT
iajs-2801	7	1	also	also	ADV
iajs-2801	7	2	,	,	PUNCT
iajs-2801	7	3	the	the	DET
iajs-2801	7	4	product	product	NOUN
iajs-2801	7	5	of	of	ADP
iajs-2801	7	6	cubic	cubic	ADJ
iajs-2801	7	7	subsets	subset	NOUN
iajs-2801	7	8	is	be	AUX
iajs-2801	7	9	discussed	discuss	VERB
iajs-2801	7	10	and	and	CCONJ
iajs-2801	7	11	some	some	DET
iajs-2801	7	12	theorems	theorem	NOUN
iajs-2801	7	13	are	be	AUX
iajs-2801	7	14	proved	prove	VERB
iajs-2801	7	15	.	.	PUNCT
iajs-2801	8	1	2010	2010	NUM
iajs-2801	8	2	ams	am	NOUN
iajs-2801	8	3	classification	classification	NOUN
iajs-2801	8	4	:	:	PUNCT
iajs-2801	8	5	06f35	06f35	NUM
iajs-2801	8	6	,	,	PUNCT
iajs-2801	8	7	03g25	03g25	NUM
iajs-2801	8	8	,	,	PUNCT
iajs-2801	8	9	08a72	08a72	NUM
iajs-2801	8	10	.	.	PUNCT
iajs-2801	9	1	key	key	ADJ
iajs-2801	9	2	words	word	NOUN
iajs-2801	9	3	:	:	PUNCT
iajs-2801	9	4	a	a	DET
iajs-2801	9	5	ku	ku	PROPN
iajs-2801	9	6	-	-	PUNCT
iajs-2801	9	7	semigroup	semigroup	PROPN
iajs-2801	9	8	,	,	PUNCT
iajs-2801	9	9	a	a	DET
iajs-2801	9	10	cubic	cubic	ADJ
iajs-2801	9	11	sub	sub	NOUN
iajs-2801	9	12	ku	ku	PROPN
iajs-2801	9	13	-	-	PUNCT
iajs-2801	9	14	semigroup	semigroup	PROPN
iajs-2801	9	15	,	,	PUNCT
iajs-2801	9	16	a	a	DET
iajs-2801	9	17	cubic	cubic	ADJ
iajs-2801	9	18	bipolar	bipolar	ADJ
iajs-2801	9	19	k	k	NOUN
iajs-2801	9	20	-	-	NOUN
iajs-2801	9	21	ideal	ideal	ADJ
iajs-2801	9	22	,	,	PUNCT
iajs-2801	9	23	homomorphism	homomorphism	NOUN
iajs-2801	9	24	.	.	PUNCT
iajs-2801	10	1	1.introduction	1.introduction	NUM
iajs-2801	10	2	in	in	ADP
iajs-2801	10	3	2009	2009	NUM
iajs-2801	10	4	,	,	PUNCT
iajs-2801	10	5	prabpayak	prabpayak	NOUN
iajs-2801	10	6	and	and	CCONJ
iajs-2801	10	7	leerawat	leerawat	VERB
iajs-2801	11	1	[	[	X
iajs-2801	11	2	1,2	1,2	NUM
iajs-2801	11	3	]	]	PUNCT
iajs-2801	11	4	studied	study	VERB
iajs-2801	11	5	a	a	DET
iajs-2801	11	6	new	new	ADJ
iajs-2801	11	7	algebra	algebra	NOUN
iajs-2801	11	8	called	call	VERB
iajs-2801	11	9	a	a	DET
iajs-2801	11	10	ku	ku	NOUN
iajs-2801	11	11	-	-	PUNCT
iajs-2801	11	12	algebra	algebra	NOUN
iajs-2801	11	13	.	.	PUNCT
iajs-2801	12	1	they	they	PRON
iajs-2801	12	2	introduced	introduce	VERB
iajs-2801	12	3	homomorphism	homomorphism	NOUN
iajs-2801	12	4	in	in	ADP
iajs-2801	12	5	a	a	DET
iajs-2801	12	6	ku	ku	NOUN
iajs-2801	12	7	-	-	PUNCT
iajs-2801	12	8	algebra	algebra	PROPN
iajs-2801	12	9	and	and	CCONJ
iajs-2801	12	10	discussed	discuss	VERB
iajs-2801	12	11	some	some	DET
iajs-2801	12	12	recent	recent	ADJ
iajs-2801	12	13	results	result	NOUN
iajs-2801	12	14	.	.	PUNCT
iajs-2801	13	1	after	after	ADP
iajs-2801	13	2	that	that	PRON
iajs-2801	13	3	,	,	PUNCT
iajs-2801	13	4	mostafa	mostafa	PROPN
iajs-2801	13	5	et	et	PROPN
iajs-2801	13	6	al	al	PROPN
iajs-2801	13	7	.	.	PUNCT
iajs-2801	14	1	[	[	X
iajs-2801	14	2	3	3	NUM
iajs-2801	14	3	,	,	PUNCT
iajs-2801	14	4	4	4	NUM
iajs-2801	14	5	]	]	PUNCT
iajs-2801	14	6	studied	study	VERB
iajs-2801	14	7	the	the	DET
iajs-2801	14	8	concepts	concept	NOUN
iajs-2801	14	9	of	of	ADP
iajs-2801	14	10	fuzzy	fuzzy	ADJ
iajs-2801	14	11	ku	ku	NOUN
iajs-2801	14	12	-	-	PUNCT
iajs-2801	14	13	ideals	ideal	NOUN
iajs-2801	14	14	and	and	CCONJ
iajs-2801	14	15	an	an	DET
iajs-2801	14	16	interval	interval	NOUN
iajs-2801	14	17	value	value	NOUN
iajs-2801	14	18	fuzzy	fuzzy	ADJ
iajs-2801	14	19	kuideals	kuideal	NOUN
iajs-2801	14	20	.	.	PUNCT
iajs-2801	15	1	in	in	ADP
iajs-2801	15	2	[	[	X
iajs-2801	15	3	5	5	NUM
iajs-2801	15	4	]	]	X
iajs-2801	15	5	kareem	kareem	PROPN
iajs-2801	15	6	and	and	CCONJ
iajs-2801	15	7	hasan	hasan	PROPN
iajs-2801	15	8	presented	present	VERB
iajs-2801	15	9	the	the	DET
iajs-2801	15	10	structure	structure	NOUN
iajs-2801	15	11	of	of	ADP
iajs-2801	15	12	a	a	DET
iajs-2801	15	13	ku	ku	PROPN
iajs-2801	15	14	-	-	PUNCT
iajs-2801	15	15	semigroup	semigroup	PROPN
iajs-2801	15	16	and	and	CCONJ
iajs-2801	15	17	introduced	introduce	VERB
iajs-2801	15	18	some	some	DET
iajs-2801	15	19	ideals	ideal	NOUN
iajs-2801	15	20	of	of	ADP
iajs-2801	15	21	this	this	DET
iajs-2801	15	22	structure	structure	NOUN
iajs-2801	15	23	.	.	PUNCT
iajs-2801	16	1	after	after	ADP
iajs-2801	16	2	that	that	PRON
iajs-2801	16	3	,	,	PUNCT
iajs-2801	16	4	they	they	PRON
iajs-2801	16	5	introduced	introduce	VERB
iajs-2801	16	6	the	the	DET
iajs-2801	16	7	fuzzy	fuzzy	ADJ
iajs-2801	16	8	ideals	ideal	NOUN
iajs-2801	16	9	of	of	ADP
iajs-2801	16	10	this	this	DET
iajs-2801	16	11	structure	structure	NOUN
iajs-2801	16	12	in	in	ADP
iajs-2801	16	13	[	[	X
iajs-2801	16	14	6	6	NUM
iajs-2801	16	15	]	]	PUNCT
iajs-2801	16	16	.	.	PUNCT
iajs-2801	17	1	in	in	ADP
iajs-2801	17	2	[	[	X
iajs-2801	17	3	7	7	NUM
iajs-2801	17	4	]	]	X
iajs-2801	17	5	kareem	kareem	PROPN
iajs-2801	17	6	and	and	CCONJ
iajs-2801	17	7	talib	talib	PROPN
iajs-2801	17	8	gave	give	VERB
iajs-2801	17	9	the	the	DET
iajs-2801	17	10	concept	concept	NOUN
iajs-2801	17	11	of	of	ADP
iajs-2801	17	12	an	an	DET
iajs-2801	17	13	interval	interval	NOUN
iajs-2801	17	14	value	value	NOUN
iajs-2801	17	15	fuzzy	fuzzy	ADJ
iajs-2801	17	16	some	some	DET
iajs-2801	17	17	ideal	ideal	NOUN
iajs-2801	17	18	in	in	ADP
iajs-2801	17	19	kusemigroup	kusemigroup	NOUN
iajs-2801	17	20	.	.	PUNCT
iajs-2801	18	1	jun	jun	PROPN
iajs-2801	18	2	et	et	PROPN
iajs-2801	18	3	al	al	PROPN
iajs-2801	18	4	.	.	PUNCT
iajs-2801	19	1	[	[	X
iajs-2801	19	2	8	8	NUM
iajs-2801	19	3	,	,	PUNCT
iajs-2801	19	4	9	9	NUM
iajs-2801	19	5	]	]	PUNCT
iajs-2801	19	6	introduced	introduce	VERB
iajs-2801	19	7	the	the	DET
iajs-2801	19	8	concept	concept	NOUN
iajs-2801	19	9	of	of	ADP
iajs-2801	19	10	cubic	cubic	ADJ
iajs-2801	19	11	subalgebras	subalgebra	NOUN
iajs-2801	19	12	/	/	SYM
iajs-2801	19	13	ideals	ideal	NOUN
iajs-2801	19	14	in	in	ADP
iajs-2801	19	15	bck	bck	PROPN
iajs-2801	19	16	/	/	SYM
iajs-2801	19	17	bci	bci	NOUN
iajs-2801	19	18	-	-	PUNCT
iajs-2801	19	19	algebras	algebras	X
iajs-2801	19	20	.	.	PUNCT
iajs-2801	20	1	yaqoob	yaqoob	VERB
iajs-2801	20	2	et	et	NOUN
iajs-2801	21	1	al	al	PROPN
iajs-2801	22	1	[	[	X
iajs-2801	22	2	10	10	NUM
iajs-2801	22	3	]	]	PUNCT
iajs-2801	22	4	presented	present	VERB
iajs-2801	22	5	a	a	DET
iajs-2801	22	6	cubic	cubic	ADJ
iajs-2801	22	7	ku	ku	NOUN
iajs-2801	22	8	-	-	PUNCT
iajs-2801	22	9	algebra	algebra	PROPN
iajs-2801	22	10	and	and	CCONJ
iajs-2801	22	11	discussed	discuss	VERB
iajs-2801	22	12	a	a	DET
iajs-2801	22	13	few	few	ADJ
iajs-2801	22	14	interesting	interesting	ADJ
iajs-2801	22	15	theorems	theorem	NOUN
iajs-2801	22	16	.	.	PUNCT
iajs-2801	23	1	this	this	DET
iajs-2801	23	2	work	work	NOUN
iajs-2801	23	3	studied	study	VERB
iajs-2801	23	4	the	the	DET
iajs-2801	23	5	idea	idea	NOUN
iajs-2801	23	6	of	of	ADP
iajs-2801	23	7	a	a	DET
iajs-2801	23	8	homomorphism	homomorphism	NOUN
iajs-2801	23	9	of	of	ADP
iajs-2801	23	10	a	a	DET
iajs-2801	23	11	cubic	cubic	ADJ
iajs-2801	23	12	set	set	NOUN
iajs-2801	23	13	of	of	ADP
iajs-2801	23	14	a	a	DET
iajs-2801	23	15	ku	ku	PROPN
iajs-2801	23	16	-	-	PUNCT
iajs-2801	23	17	semigroup	semigroup	PROPN
iajs-2801	23	18	,	,	PUNCT
iajs-2801	23	19	and	and	CCONJ
iajs-2801	23	20	a	a	DET
iajs-2801	23	21	new	new	ADJ
iajs-2801	23	22	cubic	cubic	ADJ
iajs-2801	23	23	bipolar	bipolar	ADJ
iajs-2801	23	24	fuzzy	fuzzy	ADJ
iajs-2801	23	25	set	set	NOUN
iajs-2801	23	26	in	in	ADP
iajs-2801	23	27	this	this	DET
iajs-2801	23	28	structure	structure	NOUN
iajs-2801	23	29	is	be	AUX
iajs-2801	23	30	defined	define	VERB
iajs-2801	23	31	,	,	PUNCT
iajs-2801	23	32	and	and	CCONJ
iajs-2801	23	33	some	some	DET
iajs-2801	23	34	important	important	ADJ
iajs-2801	23	35	results	result	NOUN
iajs-2801	23	36	are	be	AUX
iajs-2801	23	37	achieved	achieve	VERB
iajs-2801	23	38	.	.	PUNCT
iajs-2801	24	1	also	also	ADV
iajs-2801	24	2	,	,	PUNCT
iajs-2801	24	3	the	the	DET
iajs-2801	24	4	product	product	NOUN
iajs-2801	24	5	of	of	ADP
iajs-2801	24	6	cubic	cubic	ADJ
iajs-2801	24	7	subsets	subset	NOUN
iajs-2801	24	8	was	be	AUX
iajs-2801	24	9	discussed	discuss	VERB
iajs-2801	24	10	,	,	PUNCT
iajs-2801	24	11	and	and	CCONJ
iajs-2801	24	12	a	a	DET
iajs-2801	24	13	few	few	ADJ
iajs-2801	24	14	theorems	theorem	NOUN
iajs-2801	24	15	were	be	AUX
iajs-2801	24	16	proved	prove	VERB
iajs-2801	24	17	.	.	PUNCT
iajs-2801	25	1	ibn	ibn	PROPN
iajs-2801	25	2	al	al	PROPN
iajs-2801	25	3	haitham	haitham	PROPN
iajs-2801	25	4	journal	journal	PROPN
iajs-2801	25	5	for	for	ADP
iajs-2801	25	6	pure	pure	ADJ
iajs-2801	25	7	and	and	CCONJ
iajs-2801	25	8	applied	apply	VERB
iajs-2801	25	9	science	science	NOUN
iajs-2801	25	10	journal	journal	PROPN
iajs-2801	25	11	homepage	homepage	NOUN
iajs-2801	25	12	:	:	PUNCT
iajs-2801	25	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2801	25	14	doi	doi	NOUN
iajs-2801	25	15	:	:	PUNCT
iajs-2801	25	16	10.30526/35.1.2801	10.30526/35.1.2801	NUM
iajs-2801	25	17	article	article	NOUN
iajs-2801	25	18	history	history	NOUN
iajs-2801	25	19	:	:	PUNCT
iajs-2801	25	20	received	receive	VERB
iajs-2801	25	21	22	22	NUM
iajs-2801	25	22	,	,	PUNCT
iajs-2801	25	23	june	june	PROPN
iajs-2801	25	24	2021	2021	NUM
iajs-2801	25	25	,	,	PUNCT
iajs-2801	25	26	accepted	accept	VERB
iajs-2801	25	27	4,october	4,october	NUM
iajs-2801	25	28	2021	2021	NUM
iajs-2801	25	29	,	,	PUNCT
iajs-2801	25	30	published	publish	VERB
iajs-2801	25	31	in	in	ADP
iajs-2801	25	32	january	january	PROPN
iajs-2801	25	33	2022	2022	NUM
iajs-2801	25	34	.	.	PUNCT
iajs-2801	26	1	wisam	wisam	PROPN
iajs-2801	26	2	k.	k.	PROPN
iajs-2801	26	3	awad	awad	PROPN
iajs-2801	26	4	aa.ww21@yahoo.com	aa.ww21@yahoo.com	PROPN
iajs-2801	26	5	department	department	PROPN
iajs-2801	26	6	of	of	ADP
iajs-2801	26	7	mathematics	mathematic	NOUN
iajs-2801	26	8	,	,	PUNCT
iajs-2801	26	9	ibnal	ibnal	ADJ
iajs-2801	26	10	-	-	PUNCT
iajs-2801	26	11	haitham	haitham	PROPN
iajs-2801	26	12	college	college	PROPN
iajs-2801	26	13	of	of	ADP
iajs-2801	26	14	education	education	NOUN
iajs-2801	26	15	,	,	PUNCT
iajs-2801	26	16	university	university	NOUN
iajs-2801	26	17	of	of	ADP
iajs-2801	26	18	baghdad	baghdad	PROPN
iajs-2801	26	19	.	.	PUNCT
iajs-2801	27	1	fatema	fatema	PROPN
iajs-2801	27	2	f.	f.	PROPN
iajs-2801	27	3	kareem	kareem	PROPN
iajs-2801	27	4	fa_sa20072000@yahoo.com	fa_sa20072000@yahoo.com	PROPN
iajs-2801	27	5	department	department	PROPN
iajs-2801	27	6	of	of	ADP
iajs-2801	27	7	mathematics	mathematics	PROPN
iajs-2801	27	8	,	,	PUNCT
iajs-2801	27	9	ibn	ibn	NOUN
iajs-2801	27	10	-	-	PUNCT
iajs-2801	27	11	alhaitham	alhaitham	NOUN
iajs-2801	27	12	college	college	NOUN
iajs-2801	27	13	of	of	ADP
iajs-2801	27	14	education	education	NOUN
iajs-2801	27	15	,	,	PUNCT
iajs-2801	27	16	university	university	NOUN
iajs-2801	27	17	of	of	ADP
iajs-2801	27	18	baghdad	baghdad	PROPN
iajs-2801	27	19	.	.	PUNCT
iajs-2801	28	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2801	28	2	mailto:aa.ww21@yahoo.com	mailto:aa.ww21@yahoo.com	X
iajs-2801	29	1	mailto:fa_sa20072000@yahoo.com	mailto:fa_sa20072000@yahoo.com	X
iajs-2801	29	2	ibn	ibn	PROPN
iajs-2801	29	3	al	al	PROPN
iajs-2801	29	4	-	-	PUNCT
iajs-2801	29	5	haitham	haitham	PROPN
iajs-2801	29	6	jour	jour	X
iajs-2801	29	7	.	.	PROPN
iajs-2801	29	8	for	for	ADP
iajs-2801	29	9	pure	pure	ADJ
iajs-2801	29	10	&	&	CCONJ
iajs-2801	29	11	appl	appl	PROPN
iajs-2801	29	12	.	.	PUNCT
iajs-2801	30	1	sci	sci	PROPN
iajs-2801	30	2	.	.	PUNCT
iajs-2801	31	1	35(1)2022	35(1)2022	NUM
iajs-2801	31	2	74	74	NUM
iajs-2801	31	3	2	2	NUM
iajs-2801	31	4	.	.	PUNCT
iajs-2801	31	5	basic	basic	ADJ
iajs-2801	31	6	concepts	concept	NOUN
iajs-2801	31	7	we	we	PRON
iajs-2801	31	8	introduce	introduce	VERB
iajs-2801	31	9	some	some	DET
iajs-2801	31	10	definitions	definition	NOUN
iajs-2801	31	11	,	,	PUNCT
iajs-2801	31	12	propositions	proposition	NOUN
iajs-2801	31	13	and	and	CCONJ
iajs-2801	31	14	theorems	theorem	NOUN
iajs-2801	31	15	of	of	ADP
iajs-2801	31	16	ku	ku	PROPN
iajs-2801	31	17	-	-	PUNCT
iajs-2801	31	18	algebra	algebra	PROPN
iajs-2801	31	19	and	and	CCONJ
iajs-2801	31	20	kusemigroup	kusemigroup	NOUN
iajs-2801	31	21	in	in	ADP
iajs-2801	31	22	this	this	DET
iajs-2801	31	23	part	part	NOUN
iajs-2801	31	24	.	.	PUNCT
iajs-2801	32	1	definition2.1[1	definition2.1[1	X
iajs-2801	32	2	]	]	X
iajs-2801	32	3	.	.	PUNCT
iajs-2801	33	1	a	a	DET
iajs-2801	33	2	ku	ku	PROPN
iajs-2801	33	3	-	-	PUNCT
iajs-2801	33	4	algebra	algebra	PROPN
iajs-2801	33	5	(	(	PUNCT
iajs-2801	33	6	ℵ,∗	ℵ,∗	PROPN
iajs-2801	33	7	,	,	PUNCT
iajs-2801	33	8	0	0	NUM
iajs-2801	33	9	)	)	PUNCT
iajs-2801	33	10	is	be	AUX
iajs-2801	33	11	satisfied	satisfied	ADJ
iajs-2801	33	12	the	the	DET
iajs-2801	33	13	following	follow	VERB
iajs-2801	33	14	conditions	condition	NOUN
iajs-2801	33	15	,	,	PUNCT
iajs-2801	33	16	for	for	ADP
iajs-2801	33	17	allα	allα	PROPN
iajs-2801	33	18	,	,	PUNCT
iajs-2801	33	19	β	β	X
iajs-2801	33	20	,	,	PUNCT
iajs-2801	33	21	δ	δ	PROPN
iajs-2801	33	22	∈	∈	PROPN
iajs-2801	33	23	ℵ	ℵ	NOUN
iajs-2801	33	24	,	,	PUNCT
iajs-2801	33	25	(	(	PUNCT
iajs-2801	33	26	ku1	ku1	NOUN
iajs-2801	33	27	)	)	PUNCT
iajs-2801	33	28	(	(	PUNCT
iajs-2801	33	29	𝛼	𝛼	X
iajs-2801	33	30	∗	∗	NOUN
iajs-2801	33	31	𝛽	𝛽	NOUN
iajs-2801	33	32	)	)	PUNCT
iajs-2801	33	33	∗	∗	NOUN
iajs-2801	34	1	[	[	X
iajs-2801	34	2	(	(	PUNCT
iajs-2801	34	3	𝛽	𝛽	PROPN
iajs-2801	34	4	∗	∗	X
iajs-2801	34	5	δ	δ	PROPN
iajs-2801	34	6	)	)	PUNCT
iajs-2801	34	7	∗	∗	NOUN
iajs-2801	34	8	(	(	PUNCT
iajs-2801	34	9	𝛼	𝛼	X
iajs-2801	34	10	∗	∗	X
iajs-2801	34	11	δ	δ	PROPN
iajs-2801	34	12	)	)	PUNCT
iajs-2801	34	13	]	]	PUNCT
iajs-2801	35	1	=	=	PUNCT
iajs-2801	35	2	0	0	PUNCT
iajs-2801	35	3	(	(	PUNCT
iajs-2801	35	4	ku2)𝛼	ku2)𝛼	PROPN
iajs-2801	35	5	∗	∗	NOUN
iajs-2801	35	6	0	0	NUM
iajs-2801	36	1	=	=	SYM
iajs-2801	36	2	0	0	NUM
iajs-2801	36	3	(	(	PUNCT
iajs-2801	36	4	ku3	ku3	X
iajs-2801	36	5	)	)	PUNCT
iajs-2801	36	6	0∗	0∗	PUNCT
iajs-2801	37	1	𝛼	𝛼	X
iajs-2801	37	2	=	=	ADJ
iajs-2801	37	3	𝛼	𝛼	X
iajs-2801	37	4	(	(	PUNCT
iajs-2801	37	5	ku4)𝛼	ku4)𝛼	PROPN
iajs-2801	37	6	∗	∗	NOUN
iajs-2801	37	7	𝛽	𝛽	NOUN
iajs-2801	37	8	=	=	SYM
iajs-2801	37	9	0	0	PROPN
iajs-2801	37	10	and𝛽	and𝛽	PROPN
iajs-2801	37	11	∗	∗	NOUN
iajs-2801	37	12	𝛼	𝛼	PROPN
iajs-2801	37	13	implies	imply	VERB
iajs-2801	37	14	𝛼	𝛼	PROPN
iajs-2801	37	15	=	=	SYM
iajs-2801	37	16	𝛽	𝛽	PROPN
iajs-2801	37	17	and	and	CCONJ
iajs-2801	37	18	(	(	PUNCT
iajs-2801	37	19	ku5)𝛼	ku5)𝛼	PROPN
iajs-2801	37	20	∗	∗	NOUN
iajs-2801	37	21	𝛼	𝛼	NOUN
iajs-2801	38	1	=	=	NOUN
iajs-2801	38	2	0	0	NUM
iajs-2801	39	1	the	the	DET
iajs-2801	39	2	relation	relation	NOUN
iajs-2801	39	3	≤	≤	NUM
iajs-2801	39	4	on	on	ADP
iajs-2801	39	5	a	a	DET
iajs-2801	39	6	ku	ku	NOUN
iajs-2801	39	7	-	-	PUNCT
iajs-2801	39	8	algebra	algebra	PROPN
iajs-2801	39	9	ℵ	ℵ	NOUN
iajs-2801	39	10	is	be	AUX
iajs-2801	39	11	define	define	VERB
iajs-2801	39	12	𝛼	𝛼	PRON
iajs-2801	39	13	≤	≤	NUM
iajs-2801	39	14	𝛽	𝛽	PROPN
iajs-2801	39	15	⟺	⟺	PRON
iajs-2801	39	16	𝛽	𝛽	PROPN
iajs-2801	39	17	∗	∗	X
iajs-2801	39	18	𝛼	𝛼	NOUN
iajs-2801	39	19	=	=	NOUN
iajs-2801	39	20	0	0	PROPN
iajs-2801	39	21	.	.	PUNCT
iajs-2801	39	22	example	example	NOUN
iajs-2801	39	23	2.2	2.2	NUM
iajs-2801	39	24	[	[	SYM
iajs-2801	39	25	1].the	1].the	DET
iajs-2801	39	26	following	follow	VERB
iajs-2801	39	27	table	table	NOUN
iajs-2801	39	28	define	define	VERB
iajs-2801	39	29	the	the	DET
iajs-2801	39	30	binary	binary	PROPN
iajs-2801	39	31	operation	operation	NOUN
iajs-2801	39	32	∗	∗	NOUN
iajs-2801	39	33	on	on	ADP
iajs-2801	39	34	the	the	DET
iajs-2801	39	35	set	set	NOUN
iajs-2801	39	36	ℵ	ℵ	NOUN
iajs-2801	39	37	=	=	SYM
iajs-2801	39	38	{	{	PUNCT
iajs-2801	39	39	0	0	NUM
iajs-2801	39	40	,	,	PUNCT
iajs-2801	39	41	𝑎	𝑎	NOUN
iajs-2801	39	42	,	,	PUNCT
iajs-2801	39	43	𝑏	𝑏	NOUN
iajs-2801	39	44	,	,	PUNCT
iajs-2801	39	45	𝑐	𝑐	NOUN
iajs-2801	39	46	}	}	PUNCT
iajs-2801	39	47	then	then	ADV
iajs-2801	39	48	(	(	PUNCT
iajs-2801	39	49	ℵ,∗	ℵ,∗	PROPN
iajs-2801	39	50	,	,	PUNCT
iajs-2801	39	51	0	0	NUM
iajs-2801	39	52	)	)	PUNCT
iajs-2801	39	53	is	be	AUX
iajs-2801	39	54	a	a	DET
iajs-2801	39	55	ku	ku	NOUN
iajs-2801	39	56	-	-	PUNCT
iajs-2801	39	57	algebra	algebra	PROPN
iajs-2801	39	58	.	.	PUNCT
iajs-2801	40	1	theorem2.3[2	theorem2.3[2	X
iajs-2801	41	1	]	]	X
iajs-2801	41	2	.	.	PUNCT
iajs-2801	42	1	the	the	DET
iajs-2801	42	2	following	follow	VERB
iajs-2801	42	3	axioms	axiom	NOUN
iajs-2801	42	4	are	be	AUX
iajs-2801	42	5	satisfying	satisfying	ADJ
iajs-2801	42	6	,	,	PUNCT
iajs-2801	42	7	in	in	ADP
iajs-2801	42	8	a	a	DET
iajs-2801	42	9	ku	ku	NOUN
iajs-2801	42	10	-	-	PUNCT
iajs-2801	42	11	algebraℵ.	algebraℵ.	NOUN
iajs-2801	42	12	for	for	ADP
iajs-2801	42	13	all	all	DET
iajs-2801	42	14	α	α	PROPN
iajs-2801	42	15	,	,	PUNCT
iajs-2801	42	16	β	β	X
iajs-2801	42	17	,	,	PUNCT
iajs-2801	42	18	δ	δ	PROPN
iajs-2801	42	19	∈	∈	PROPN
iajs-2801	42	20	ℵ	ℵ	NOUN
iajs-2801	42	21	,	,	PUNCT
iajs-2801	42	22	(	(	PUNCT
iajs-2801	42	23	1	1	X
iajs-2801	42	24	)	)	PUNCT
iajs-2801	42	25	if	if	SCONJ
iajs-2801	42	26	𝛼	𝛼	PRON
iajs-2801	42	27	≤	≤	NOUN
iajs-2801	42	28	𝛽	𝛽	PRON
iajs-2801	42	29	imply𝛽	imply𝛽	NOUN
iajs-2801	42	30	∗	∗	NOUN
iajs-2801	42	31	δ	δ	PROPN
iajs-2801	42	32	≤	≤	X
iajs-2801	42	33	𝛼	𝛼	PROPN
iajs-2801	42	34	∗	∗	X
iajs-2801	42	35	δ	δ	PROPN
iajs-2801	42	36	(	(	PUNCT
iajs-2801	42	37	2)𝛼	2)𝛼	PROPN
iajs-2801	42	38	∗	∗	NOUN
iajs-2801	42	39	(	(	PUNCT
iajs-2801	42	40	𝛽	𝛽	PROPN
iajs-2801	42	41	∗	∗	X
iajs-2801	42	42	δ	δ	PROPN
iajs-2801	42	43	)	)	PUNCT
iajs-2801	43	1	=	=	SYM
iajs-2801	43	2	𝛽	𝛽	NOUN
iajs-2801	43	3	∗	∗	NOUN
iajs-2801	43	4	(	(	PUNCT
iajs-2801	43	5	𝛼	𝛼	X
iajs-2801	43	6	∗	∗	X
iajs-2801	43	7	δ	δ	PROPN
iajs-2801	43	8	)	)	PUNCT
iajs-2801	43	9	(	(	PUNCT
iajs-2801	43	10	3)((𝛽	3)((𝛽	NUM
iajs-2801	43	11	∗	∗	NOUN
iajs-2801	43	12	𝛼	𝛼	NOUN
iajs-2801	43	13	)	)	PUNCT
iajs-2801	43	14	∗	∗	NOUN
iajs-2801	43	15	𝛼	𝛼	NOUN
iajs-2801	43	16	)	)	PUNCT
iajs-2801	43	17	≤	≤	NOUN
iajs-2801	43	18	𝛽	𝛽	DET
iajs-2801	43	19	definition2.4[5	definition2.4[5	NOUN
iajs-2801	43	20	]	]	PUNCT
iajs-2801	43	21	.	.	PUNCT
iajs-2801	44	1	the	the	DET
iajs-2801	44	2	set	set	NOUN
iajs-2801	44	3	ℵ	ℵ	ADP
iajs-2801	44	4	≠	≠	PROPN
iajs-2801	44	5	𝜑	𝜑	NOUN
iajs-2801	44	6	and	and	CCONJ
iajs-2801	44	7	two	two	NUM
iajs-2801	44	8	binary	binary	ADJ
iajs-2801	44	9	operations	operation	NOUN
iajs-2801	44	10	∗,∘	∗,∘	PROPN
iajs-2801	44	11	with	with	ADP
iajs-2801	44	12	a	a	DET
iajs-2801	44	13	constant~0	constant~0	NOUN
iajs-2801	44	14	is	be	AUX
iajs-2801	44	15	named	name	VERB
iajs-2801	44	16	a	a	DET
iajs-2801	44	17	ku	ku	PROPN
iajs-2801	44	18	-	-	PUNCT
iajs-2801	44	19	semigroup	semigroup	PROPN
iajs-2801	44	20	if	if	SCONJ
iajs-2801	44	21	~~	~~	NUM
iajs-2801	44	22	(	(	PUNCT
iajs-2801	44	23	i	i	NOUN
iajs-2801	44	24	)	)	PUNCT
iajs-2801	44	25	the	the	DET
iajs-2801	44	26	triple	triple	ADJ
iajs-2801	44	27	(	(	PUNCT
iajs-2801	44	28	ℵ,∗	ℵ,∗	PROPN
iajs-2801	44	29	,	,	PUNCT
iajs-2801	44	30	0)isˑa	0)isˑa	ADP
iajs-2801	44	31	ku	ku	PROPN
iajs-2801	44	32	-	-	PUNCT
iajs-2801	44	33	algebra	algebra	PROPN
iajs-2801	44	34	(	(	PUNCT
iajs-2801	44	35	ii	ii	NOUN
iajs-2801	44	36	)	)	PUNCT
iajs-2801	44	37	the	the	DET
iajs-2801	44	38	ordered	order	VERB
iajs-2801	44	39	pair	pair	NOUN
iajs-2801	44	40	(	(	PUNCT
iajs-2801	44	41	ℵ,∘)is	ℵ,∘)is	ADJ
iajs-2801	44	42	aˑsemigroup	aˑsemigroup	NOUN
iajs-2801	44	43	(	(	PUNCT
iajs-2801	44	44	iii	iii	NOUN
iajs-2801	44	45	)	)	PUNCT
iajs-2801	44	46	α	α	PROPN
iajs-2801	44	47	,	,	PUNCT
iajs-2801	44	48	β	β	X
iajs-2801	44	49	,	,	PUNCT
iajs-2801	44	50	δ	δ	PROPN
iajs-2801	44	51	∈	∈	PROPN
iajs-2801	44	52	ℵ	ℵ	NOUN
iajs-2801	44	53	,	,	PUNCT
iajs-2801	44	54	,	,	PUNCT
iajs-2801	44	55	α	α	PROPN
iajs-2801	44	56	∘	∘	X
iajs-2801	44	57	(	(	PUNCT
iajs-2801	44	58	β	β	X
iajs-2801	44	59	∗	∗	X
iajs-2801	44	60	δ	δ	PROPN
iajs-2801	44	61	)	)	PUNCT
iajs-2801	44	62	=	=	PUNCT
iajs-2801	45	1	(	(	PUNCT
iajs-2801	45	2	α	α	X
iajs-2801	45	3	∘	∘	X
iajs-2801	45	4	β	β	NOUN
iajs-2801	45	5	)	)	PUNCT
iajs-2801	45	6	∗	∗	NOUN
iajs-2801	45	7	(	(	PUNCT
iajs-2801	45	8	α	α	PROPN
iajs-2801	45	9	∘	∘	PROPN
iajs-2801	45	10	δ)and(α	δ)and(α	PROPN
iajs-2801	45	11	∗	∗	NOUN
iajs-2801	45	12	β	β	NOUN
iajs-2801	45	13	)	)	PUNCT
iajs-2801	45	14	∘	∘	PROPN
iajs-2801	45	15	δ	δ	X
iajs-2801	45	16	=	=	PUNCT
iajs-2801	45	17	(	(	PUNCT
iajs-2801	45	18	α	α	PROPN
iajs-2801	45	19	∘	∘	PROPN
iajs-2801	45	20	δ	δ	PROPN
iajs-2801	45	21	)	)	PUNCT
iajs-2801	45	22	∗	∗	NOUN
iajs-2801	45	23	(	(	PUNCT
iajs-2801	45	24	β	β	X
iajs-2801	45	25	∘	∘	X
iajs-2801	45	26	δ	δ	PROPN
iajs-2801	45	27	)	)	PUNCT
iajs-2801	45	28	.	.	PUNCT
iajs-2801	46	1	example	example	NOUN
iajs-2801	47	1	2.5[5	2.5[5	NUM
iajs-2801	47	2	]	]	PUNCT
iajs-2801	47	3	.	.	PUNCT
iajs-2801	48	1	if	if	SCONJ
iajs-2801	48	2	ℵ	ℵ	NOUN
iajs-2801	48	3	=	=	SYM
iajs-2801	48	4	{	{	PUNCT
iajs-2801	48	5	0,1,2,3	0,1,2,3	NOUN
iajs-2801	48	6	}	}	PUNCT
iajs-2801	48	7	is	be	AUX
iajs-2801	48	8	ˑa	ˑa	ADV
iajs-2801	48	9	set	set	VERB
iajs-2801	48	10	and	and	CCONJ
iajs-2801	48	11	two	two	NUM
iajs-2801	48	12	binary	binary	ADJ
iajs-2801	48	13	operations	operation	NOUN
iajs-2801	48	14	∗	∗	NOUN
iajs-2801	48	15	and	and	CCONJ
iajs-2801	48	16	∘	∘	NOUN
iajs-2801	48	17	are	be	AUX
iajs-2801	48	18	defined	define	VERB
iajs-2801	48	19	by	by	ADP
iajs-2801	48	20	the	the	DET
iajs-2801	48	21	following	following	NOUN
iajs-2801	48	22	.	.	PUNCT
iajs-2801	49	1	thenˑ(ℵ,∗,∘	thenˑ(ℵ,∗,∘	PROPN
iajs-2801	49	2	,	,	PUNCT
iajs-2801	49	3	0	0	NUM
iajs-2801	49	4	)	)	PUNCT
iajs-2801	49	5	is	be	AUX
iajs-2801	49	6	aˑku	aˑku	NOUN
iajs-2801	49	7	-	-	PUNCT
iajs-2801	49	8	semigroup	semigroup	NOUN
iajs-2801	49	9	.	.	PUNCT
iajs-2801	49	10	"	"	PUNCT
iajs-2801	50	1	definition	definition	NOUN
iajs-2801	50	2	2.6[5	2.6[5	NUM
iajs-2801	50	3	]	]	PUNCT
iajs-2801	50	4	.	.	PUNCT
iajs-2801	51	1	a	a	DET
iajs-2801	51	2	non	non	ADJ
iajs-2801	51	3	-	-	ADJ
iajs-2801	51	4	empty	empty	ADJ
iajs-2801	51	5	subset	subset	NOUN
iajs-2801	51	6	a	a	PRON
iajs-2801	51	7	of	of	ADP
iajs-2801	51	8	ℵ	ℵ	NOUN
iajs-2801	51	9	is	be	AUX
iajs-2801	51	10	named	name	VERB
iajs-2801	51	11	aˑsubku	aˑsubku	NOUN
iajs-2801	51	12	-	-	PUNCT
iajs-2801	51	13	semigroup	semigroup	NOUN
iajs-2801	51	14	if	if	SCONJ
iajs-2801	51	15	it	it	PRON
iajs-2801	51	16	is	be	AUX
iajs-2801	51	17	satisfied	satisfied	ADJ
iajs-2801	51	18	𝛼	𝛼	ADP
iajs-2801	51	19	∗	∗	NOUN
iajs-2801	51	20	𝛽	𝛽	PROPN
iajs-2801	51	21	,	,	PUNCT
iajs-2801	51	22	𝛼	𝛼	PROPN
iajs-2801	51	23	∘	∘	NOUN
iajs-2801	51	24	𝛽	𝛽	NOUN
iajs-2801	51	25	∈	∈	PROPN
iajs-2801	51	26	𝛢	𝛢	NOUN
iajs-2801	51	27	,	,	PUNCT
iajs-2801	51	28	for	for	ADP
iajs-2801	51	29	all𝛼,𝛽	all𝛼,𝛽	PROPN
iajs-2801	51	30	∈	∈	PROPN
iajs-2801	51	31	𝛢.	𝛢.	PROPN
iajs-2801	51	32	definition2.7[5	definition2.7[5	ADJ
iajs-2801	51	33	]	]	X
iajs-2801	51	34	.	.	PUNCT
iajs-2801	52	1	a	a	DET
iajs-2801	52	2	non	non	ADJ
iajs-2801	52	3	-	-	ADJ
iajs-2801	52	4	empty	empty	ADJ
iajs-2801	52	5	subset	subset	NOUN
iajs-2801	52	6	𝐼ℵ	𝐼ℵ	NOUN
iajs-2801	52	7	is	be	AUX
iajs-2801	52	8	called	call	VERB
iajs-2801	52	9	an	an	DET
iajs-2801	52	10	s	s	NOUN
iajs-2801	52	11	-	-	NOUN
iajs-2801	52	12	ideal	ideal	NOUN
iajs-2801	52	13	of	of	ADP
iajs-2801	52	14	ℵ	ℵ	NOUN
iajs-2801	52	15	,	,	PUNCT
iajs-2801	52	16	if	if	SCONJ
iajs-2801	52	17	(	(	PUNCT
iajs-2801	52	18	i	i	NOUN
iajs-2801	52	19	)	)	PUNCT
iajs-2801	52	20	0	0	PUNCT
iajs-2801	53	1	∈	∈	PROPN
iajs-2801	53	2	𝛪	𝛪	PROPN
iajs-2801	53	3	ibn	ibn	PROPN
iajs-2801	53	4	al	al	PROPN
iajs-2801	53	5	-	-	PUNCT
iajs-2801	53	6	haitham	haitham	PROPN
iajs-2801	53	7	jour	jour	X
iajs-2801	53	8	.	.	PROPN
iajs-2801	53	9	for	for	ADP
iajs-2801	53	10	pure	pure	ADJ
iajs-2801	53	11	&	&	CCONJ
iajs-2801	53	12	appl	appl	PROPN
iajs-2801	53	13	.	.	PUNCT
iajs-2801	54	1	sci	sci	PROPN
iajs-2801	54	2	.	.	PUNCT
iajs-2801	55	1	35(1)2022	35(1)2022	NUM
iajs-2801	55	2	75	75	NUM
iajs-2801	55	3	(	(	PUNCT
iajs-2801	55	4	ii	ii	NOUN
iajs-2801	55	5	)	)	PUNCT
iajs-2801	55	6	𝛼	𝛼	PROPN
iajs-2801	55	7	∗	∗	NOUN
iajs-2801	55	8	𝛽	𝛽	NOUN
iajs-2801	55	9	∈	∈	PROPN
iajs-2801	55	10	𝛪	𝛪	PROPN
iajs-2801	55	11	and	and	CCONJ
iajs-2801	55	12	𝛼	𝛼	PRON
iajs-2801	55	13	∈	∈	NOUN
iajs-2801	55	14	𝛪	𝛪	PROPN
iajs-2801	55	15	imply	imply	VERB
iajs-2801	55	16	𝛽	𝛽	PRON
iajs-2801	55	17	∈	∈	PRON
iajs-2801	55	18	𝛪.ˑˑ	𝛪.ˑˑ	INTJ
iajs-2801	55	19	(	(	PUNCT
iajs-2801	55	20	iii)∀𝛼	iii)∀𝛼	PUNCT
iajs-2801	55	21	∈	∈	NOUN
iajs-2801	55	22	ℵ	ℵ	NOUN
iajs-2801	55	23	,	,	PUNCT
iajs-2801	55	24	𝒆	𝒆	PROPN
iajs-2801	55	25	∈	∈	PROPN
iajs-2801	55	26	𝐼	𝐼	PROPN
iajs-2801	55	27	,	,	PUNCT
iajs-2801	55	28	we	we	PRON
iajs-2801	55	29	have	have	VERB
iajs-2801	55	30	𝛼	𝛼	SYM
iajs-2801	55	31	∘	∘	NOUN
iajs-2801	55	32	𝒆	𝒆	X
iajs-2801	55	33	∈	∈	PROPN
iajs-2801	55	34	𝐼	𝐼	PROPN
iajs-2801	55	35	and	and	CCONJ
iajs-2801	55	36	𝒆	𝒆	X
iajs-2801	55	37	∘	∘	NOUN
iajs-2801	55	38	𝛼	𝛼	PROPN
iajs-2801	55	39	∈	∈	PROPN
iajs-2801	55	40	𝐼.	𝐼.	PROPN
iajs-2801	55	41	definition2.8[5	definition2.8[5	NOUN
iajs-2801	55	42	]	]	PUNCT
iajs-2801	55	43	.	.	PUNCT
iajs-2801	56	1	the	the	DET
iajs-2801	56	2	set	set	NOUN
iajs-2801	56	3	𝜑	𝜑	NOUN
iajs-2801	56	4	≠	≠	PROPN
iajs-2801	56	5	𝐴ℵ	𝐴ℵ	PROPN
iajs-2801	56	6	is	be	AUX
iajs-2801	56	7	named	name	VERB
iajs-2801	56	8	a	a	DET
iajs-2801	56	9	k	k	ADJ
iajs-2801	56	10	-	-	PUNCT
iajs-2801	56	11	ideal	ideal	ADJ
iajs-2801	56	12	ofℵ	ofℵ	NOUN
iajs-2801	56	13	,	,	PUNCT
iajs-2801	56	14	if~	if~	PROPN
iajs-2801	56	15	i	i	PRON
iajs-2801	56	16	)	)	PUNCT
iajs-2801	56	17	0	0	PUNCT
iajs-2801	57	1	∈	∈	PROPN
iajs-2801	57	2	𝛪	𝛪	PROPN
iajs-2801	57	3	ii	ii	PROPN
iajs-2801	57	4	)	)	PUNCT
iajs-2801	57	5	∀𝛼,𝛽	∀𝛼,𝛽	X
iajs-2801	57	6	,	,	PUNCT
iajs-2801	57	7	δ	δ	PROPN
iajs-2801	57	8	∈	∈	PROPN
iajs-2801	57	9	ℵ	ℵ	NOUN
iajs-2801	57	10	,	,	PUNCT
iajs-2801	57	11	(	(	PUNCT
iajs-2801	57	12	𝛼	𝛼	NOUN
iajs-2801	57	13	∗	∗	NOUN
iajs-2801	57	14	(	(	PUNCT
iajs-2801	57	15	𝛽	𝛽	PROPN
iajs-2801	57	16	∗	∗	X
iajs-2801	57	17	δ	δ	PROPN
iajs-2801	57	18	)	)	PUNCT
iajs-2801	57	19	)	)	PUNCT
iajs-2801	58	1	∈	∈	PROPN
iajs-2801	58	2	𝐼	𝐼	PROPN
iajs-2801	58	3	,	,	PUNCT
iajs-2801	58	4	𝛽	𝛽	PROPN
iajs-2801	58	5	∈	∈	PROPN
iajs-2801	58	6	𝛪imply𝛼	𝛪imply𝛼	PROPN
iajs-2801	58	7	∗	∗	VERB
iajs-2801	58	8	δ	δ	PROPN
iajs-2801	58	9	∈	∈	PROPN
iajs-2801	58	10	𝛪.	𝛪.	PROPN
iajs-2801	58	11	iii	iii	PROPN
iajs-2801	58	12	)	)	PUNCT
iajs-2801	58	13	∀𝛼	∀𝛼	PROPN
iajs-2801	58	14	∈	∈	PROPN
iajs-2801	58	15	ℵ~,𝒆	ℵ~,𝒆	NUM
iajs-2801	58	16	∈	∈	PROPN
iajs-2801	58	17	α,~we	α,~we	NOUN
iajs-2801	58	18	have~𝛼	have~𝛼	NOUN
iajs-2801	58	19	∘	∘	NOUN
iajs-2801	58	20	𝒆	𝒆	PROPN
iajs-2801	58	21	∈	∈	PROPN
iajs-2801	58	22	α	α	NOUN
iajs-2801	58	23	and	and	CCONJ
iajs-2801	58	24	𝒆	𝒆	ADJ
iajs-2801	58	25	∘	∘	NOUN
iajs-2801	58	26	𝛼	𝛼	PROPN
iajs-2801	58	27	∈	∈	PROPN
iajs-2801	58	28	α~.	α~.	NUM
iajs-2801	58	29	definition2.9[5	definition2.9[5	NOUN
iajs-2801	58	30	]	]	PUNCT
iajs-2801	58	31	.	.	PUNCT
iajs-2801	59	1	letˑℵ	letˑℵ	PROPN
iajs-2801	59	2	and	and	CCONJ
iajs-2801	59	3	ℵ′be	ℵ′be	NOUN
iajs-2801	59	4	two	two	NUM
iajs-2801	59	5	ku	ku	PROPN
iajs-2801	59	6	-	-	PUNCT
iajs-2801	59	7	semigroups	semigroup	NOUN
iajs-2801	59	8	.	.	PUNCT
iajs-2801	60	1	a	a	DET
iajs-2801	60	2	mapping	mapping	NOUN
iajs-2801	60	3	ˑ𝑓	ˑ𝑓	NOUN
iajs-2801	60	4	:	:	PUNCT
iajs-2801	60	5	ℵ	ℵ	X
iajs-2801	60	6	→	→	SYM
iajs-2801	60	7	ℵ′is	ℵ′is	NOUN
iajs-2801	60	8	called	call	VERB
iajs-2801	60	9	a	a	DET
iajs-2801	60	10	kusemigroup	kusemigroup	NOUN
iajs-2801	60	11	homomorphism	homomorphism	PROPN
iajs-2801	60	12	if𝑓(𝛼	if𝑓(𝛼	PROPN
iajs-2801	60	13	∗	∗	NOUN
iajs-2801	60	14	𝛽	𝛽	NOUN
iajs-2801	60	15	)	)	PUNCT
iajs-2801	60	16	=	=	PUNCT
iajs-2801	60	17	𝑓𝛼	𝑓𝛼	NUM
iajs-2801	60	18	∗	∗	NOUN
iajs-2801	60	19	𝑓(𝛽)and𝑓(𝛼	𝑓(𝛽)and𝑓(𝛼	PROPN
iajs-2801	60	20	𝛽	𝛽	NOUN
iajs-2801	60	21	)	)	PUNCT
iajs-2801	60	22	=	=	SYM
iajs-2801	60	23	𝑓(𝛼	𝑓(𝛼	PROPN
iajs-2801	60	24	)	)	PUNCT
iajs-2801	60	25	𝑓(𝛽	𝑓(𝛽	NOUN
iajs-2801	60	26	)	)	PUNCT
iajs-2801	60	27	for	for	ADP
iajs-2801	60	28	all𝛼	all𝛼	NOUN
iajs-2801	60	29	,	,	PUNCT
iajs-2801	60	30	𝛽	𝛽	PROPN
iajs-2801	60	31	∈	∈	PRON
iajs-2801	60	32	ℵ.	ℵ.	NOUN
iajs-2801	61	1	the	the	DET
iajs-2801	61	2	set	set	NOUN
iajs-2801	61	3	{	{	PUNCT
iajs-2801	61	4	𝛼	𝛼	NOUN
iajs-2801	61	5	∈	∈	ADJ
iajs-2801	61	6	ℵ	ℵ	NOUN
iajs-2801	61	7	:	:	PUNCT
iajs-2801	61	8	𝑓(𝛼	𝑓(𝛼	ADJ
iajs-2801	61	9	)	)	PUNCT
iajs-2801	61	10	=	=	SYM
iajs-2801	61	11	0}is	0}is	NOUN
iajs-2801	61	12	called	call	VERB
iajs-2801	61	13	the	the	DET
iajs-2801	61	14	kernel	kernel	PROPN
iajs-2801	61	15	of𝑓	of𝑓	PROPN
iajs-2801	61	16	and	and	CCONJ
iajs-2801	61	17	denoted	denote	VERB
iajs-2801	61	18	by𝑘𝑒𝑟𝑓	by𝑘𝑒𝑟𝑓	NOUN
iajs-2801	61	19	moreover	moreover	ADV
iajs-2801	61	20	,	,	PUNCT
iajs-2801	61	21	the	the	DET
iajs-2801	61	22	set	set	NOUN
iajs-2801	61	23	{	{	PUNCT
iajs-2801	61	24	𝑓(𝛼	𝑓(𝛼	PROPN
iajs-2801	61	25	)	)	PUNCT
iajs-2801	61	26	∈	∈	PROPN
iajs-2801	61	27	ℵ′	ℵ′	PART
iajs-2801	61	28	∶	∶	NOUN
iajs-2801	61	29	𝛼	𝛼	ADP
iajs-2801	61	30	∈	∈	NOUN
iajs-2801	61	31	ℵ	ℵ	NOUN
iajs-2801	61	32	}	}	PUNCT
iajs-2801	61	33	is	be	AUX
iajs-2801	61	34	called	call	VERB
iajs-2801	61	35	the	the	DET
iajs-2801	61	36	image	image	NOUN
iajs-2801	61	37	of	of	ADP
iajs-2801	61	38	𝑓	𝑓	PRON
iajs-2801	61	39	and	and	CCONJ
iajs-2801	61	40	denoted	denote	VERB
iajs-2801	61	41	by	by	ADP
iajs-2801	61	42	𝑖𝑚𝑓.	𝑖𝑚𝑓.	NOUN
iajs-2801	61	43	we	we	PRON
iajs-2801	61	44	recall	recall	VERB
iajs-2801	61	45	that	that	SCONJ
iajs-2801	61	46	a	a	DET
iajs-2801	61	47	cubic	cubic	ADJ
iajs-2801	61	48	bipolar	bipolar	ADJ
iajs-2801	61	49	valued	value	VERB
iajs-2801	61	50	fuzzy	fuzzy	ADJ
iajs-2801	61	51	subset	subset	NOUN
iajs-2801	61	52	in	in	ADP
iajs-2801	61	53	[	[	X
iajs-2801	61	54	11	11	NUM
iajs-2801	61	55	]	]	PUNCT
iajs-2801	61	56	as	as	SCONJ
iajs-2801	61	57	follows	follow	VERB
iajs-2801	61	58	:	:	PUNCT
iajs-2801	61	59	definition	definition	NOUN
iajs-2801	61	60	2.10[11	2.10[11	NUM
iajs-2801	61	61	]	]	PUNCT
iajs-2801	61	62	.	.	PUNCT
iajs-2801	62	1	let	let	VERB
iajs-2801	62	2	ℵ	ℵ	PRON
iajs-2801	62	3	be	be	AUX
iajs-2801	62	4	a	a	DET
iajs-2801	62	5	non	non	ADJ
iajs-2801	62	6	-	-	ADJ
iajs-2801	62	7	empty	empty	ADJ
iajs-2801	62	8	set	set	NOUN
iajs-2801	62	9	.	.	PUNCT
iajs-2801	63	1	a	a	DET
iajs-2801	63	2	cubic	cubic	ADJ
iajs-2801	63	3	bipolar	bipolar	ADJ
iajs-2801	63	4	set	set	VERB
iajs-2801	63	5	in	in	ADP
iajs-2801	63	6	a	a	DET
iajs-2801	63	7	set	set	NOUN
iajs-2801	63	8	ℵ	ℵ	NOUN
iajs-2801	63	9	is	be	AUX
iajs-2801	63	10	the	the	DET
iajs-2801	63	11	structureω	structureω	NOUN
iajs-2801	63	12	=	=	PUNCT
iajs-2801	63	13	{	{	PUNCT
iajs-2801	63	14	〈	〈	NOUN
iajs-2801	63	15	𝛼	𝛼	NOUN
iajs-2801	63	16	,	,	PUNCT
iajs-2801	63	17	𝜇ω	𝜇ω	ADP
iajs-2801	63	18	+	+	ADJ
iajs-2801	63	19	(	(	PUNCT
iajs-2801	63	20	𝛼	𝛼	NOUN
iajs-2801	63	21	)	)	PUNCT
iajs-2801	63	22	,	,	PUNCT
iajs-2801	63	23	𝜇ω	𝜇ω	NOUN
iajs-2801	63	24	−(𝛼	−(𝛼	NOUN
iajs-2801	63	25	)	)	PUNCT
iajs-2801	63	26	,	,	PUNCT
iajs-2801	63	27	𝜆ω	𝜆ω	X
iajs-2801	63	28	+	+	ADJ
iajs-2801	63	29	(	(	PUNCT
iajs-2801	63	30	𝛼	𝛼	NOUN
iajs-2801	63	31	)	)	PUNCT
iajs-2801	63	32	,	,	PUNCT
iajs-2801	63	33	𝜆ω	𝜆ω	ADP
iajs-2801	63	34	−(𝛼	−(𝛼	NOUN
iajs-2801	63	35	):	):	PUNCT
iajs-2801	63	36	𝛼	𝛼	PROPN
iajs-2801	63	37	∈	∈	PROPN
iajs-2801	63	38	ℵ	ℵ	NOUN
iajs-2801	63	39	〉	〉	NOUN
iajs-2801	63	40	}	}	PUNCT
iajs-2801	63	41	where	where	SCONJ
iajs-2801	63	42	𝑁(𝛼	𝑁(𝛼	VERB
iajs-2801	63	43	)	)	PUNCT
iajs-2801	63	44	=	=	SYM
iajs-2801	63	45	{	{	PUNCT
iajs-2801	63	46	�	�	PROPN
iajs-2801	63	47	̃	̃	PROPN
iajs-2801	63	48	�	�	PROPN
iajs-2801	63	49	ω	ω	NOUN
iajs-2801	63	50	+	+	PROPN
iajs-2801	63	51	(	(	PUNCT
iajs-2801	63	52	𝛼	𝛼	NOUN
iajs-2801	63	53	)	)	PUNCT
iajs-2801	63	54	,	,	PUNCT
iajs-2801	63	55	𝜇ω	𝜇ω	ADP
iajs-2801	63	56	−(𝛼	−(𝛼	NOUN
iajs-2801	63	57	)	)	PUNCT
iajs-2801	63	58	}	}	PUNCT
iajs-2801	63	59	is	be	AUX
iajs-2801	63	60	calledinterval	calledinterval	ADJ
iajs-2801	63	61	valued	value	VERB
iajs-2801	63	62	bipolar	bipolar	ADJ
iajs-2801	63	63	fuzzy	fuzzy	ADJ
iajs-2801	63	64	set	set	NOUN
iajs-2801	63	65	and	and	CCONJ
iajs-2801	63	66	𝐾(𝛼	𝐾(𝛼	NUM
iajs-2801	63	67	)	)	PUNCT
iajs-2801	63	68	=	=	NOUN
iajs-2801	63	69	{	{	PUNCT
iajs-2801	63	70	𝜆ω	𝜆ω	X
iajs-2801	63	71	+	+	ADJ
iajs-2801	63	72	(	(	PUNCT
iajs-2801	63	73	𝛼	𝛼	NOUN
iajs-2801	63	74	)	)	PUNCT
iajs-2801	63	75	,	,	PUNCT
iajs-2801	63	76	𝜆ω	𝜆ω	ADP
iajs-2801	63	77	−(𝛼	−(𝛼	NOUN
iajs-2801	63	78	)	)	PUNCT
iajs-2801	63	79	}	}	PUNCT
iajs-2801	63	80	is	be	AUX
iajs-2801	63	81	a	a	DET
iajs-2801	63	82	bipolar	bipolar	ADJ
iajs-2801	63	83	fuzzy	fuzzy	ADJ
iajs-2801	63	84	set	set	NOUN
iajs-2801	63	85	.	.	PUNCT
iajs-2801	64	1	consider	consider	VERB
iajs-2801	64	2	𝜇ω	𝜇ω	PRON
iajs-2801	64	3	+	+	ADJ
iajs-2801	64	4	:	:	PUNCT
iajs-2801	64	5	ℵ	ℵ	PROPN
iajs-2801	64	6	→	→	SYM
iajs-2801	64	7	𝐷[0,1	𝐷[0,1	NOUN
iajs-2801	64	8	]	]	X
iajs-2801	64	9	such	such	ADJ
iajs-2801	64	10	that	that	SCONJ
iajs-2801	64	11	𝜇ω	𝜇ω	NOUN
iajs-2801	64	12	+	+	NOUN
iajs-2801	64	13	(	(	PUNCT
iajs-2801	64	14	𝛼	𝛼	NOUN
iajs-2801	64	15	)	)	PUNCT
iajs-2801	64	16	=	=	PUNCT
iajs-2801	65	1	[	[	X
iajs-2801	65	2	𝛿ωl	𝛿ωl	X
iajs-2801	65	3	+	+	CCONJ
iajs-2801	65	4	(	(	PUNCT
iajs-2801	65	5	𝛼	𝛼	NOUN
iajs-2801	65	6	)	)	PUNCT
iajs-2801	65	7	,	,	PUNCT
iajs-2801	65	8	𝛿ωu	𝛿ωu	NOUN
iajs-2801	65	9	+	+	CCONJ
iajs-2801	65	10	(	(	PUNCT
iajs-2801	65	11	𝛼	𝛼	NOUN
iajs-2801	65	12	)	)	PUNCT
iajs-2801	65	13	]	]	PUNCT
iajs-2801	65	14	and	and	CCONJ
iajs-2801	65	15	𝜇ω	𝜇ω	ADP
iajs-2801	65	16	−	−	NOUN
iajs-2801	65	17	:	:	PUNCT
iajs-2801	65	18	ℵ	ℵ	X
iajs-2801	65	19	→	→	SYM
iajs-2801	65	20	𝐷[−1,0	𝐷[−1,0	NOUN
iajs-2801	65	21	]	]	PUNCT
iajs-2801	65	22	such	such	ADJ
iajs-2801	65	23	that	that	SCONJ
iajs-2801	65	24	𝜇ω	𝜇ω	NOUN
iajs-2801	65	25	−(𝛼	−(𝛼	NOUN
iajs-2801	65	26	)	)	PUNCT
iajs-2801	65	27	=	=	PUNCT
iajs-2801	66	1	[	[	X
iajs-2801	66	2	𝛿ωl	𝛿ωl	NOUN
iajs-2801	66	3	−	−	PROPN
iajs-2801	66	4	(	(	PUNCT
iajs-2801	66	5	𝛼	𝛼	NOUN
iajs-2801	66	6	)	)	PUNCT
iajs-2801	66	7	,	,	PUNCT
iajs-2801	66	8	𝛿ωu	𝛿ωu	VERB
iajs-2801	66	9	−	−	PROPN
iajs-2801	66	10	(	(	PUNCT
iajs-2801	66	11	𝛼	𝛼	NOUN
iajs-2801	66	12	)	)	PUNCT
iajs-2801	66	13	]	]	PUNCT
iajs-2801	66	14	,	,	PUNCT
iajs-2801	66	15	also	also	ADV
iajs-2801	66	16	𝜆ω	𝜆ω	ADP
iajs-2801	67	1	+	+	ADJ
iajs-2801	67	2	:	:	PUNCT
iajs-2801	67	3	ℵ	ℵ	ADJ
iajs-2801	67	4	→	→	SYM
iajs-2801	67	5	[	[	X
iajs-2801	67	6	0,1	0,1	NUM
iajs-2801	67	7	]	]	PUNCT
iajs-2801	67	8	,	,	PUNCT
iajs-2801	67	9	and	and	CCONJ
iajs-2801	67	10	𝜆ω	𝜆ω	ADP
iajs-2801	67	11	−	−	NOUN
iajs-2801	67	12	:	:	PUNCT
iajs-2801	67	13	ℵ	ℵ	X
iajs-2801	67	14	→	→	NOUN
iajs-2801	67	15	[	[	X
iajs-2801	67	16	−1,0]it	−1,0]it	NOUN
iajs-2801	67	17	follows	follow	VERB
iajs-2801	67	18	that	that	SCONJ
iajs-2801	67	19	ω	ω	PROPN
iajs-2801	67	20	=	=	SYM
iajs-2801	67	21	{	{	PUNCT
iajs-2801	67	22	<	<	X
iajs-2801	67	23	𝛼	𝛼	X
iajs-2801	67	24	,	,	PUNCT
iajs-2801	67	25	{	{	PUNCT
iajs-2801	67	26	[	[	X
iajs-2801	67	27	𝛿ωl	𝛿ωl	NOUN
iajs-2801	67	28	+	+	CCONJ
iajs-2801	67	29	(	(	PUNCT
iajs-2801	67	30	𝛼	𝛼	NOUN
iajs-2801	67	31	)	)	PUNCT
iajs-2801	67	32	,	,	PUNCT
iajs-2801	67	33	𝛿ωu	𝛿ωu	NOUN
iajs-2801	67	34	+	+	CCONJ
iajs-2801	67	35	(	(	PUNCT
iajs-2801	67	36	𝛼	𝛼	NOUN
iajs-2801	67	37	)	)	PUNCT
iajs-2801	67	38	]	]	PUNCT
iajs-2801	67	39	,	,	PUNCT
iajs-2801	67	40	[	[	X
iajs-2801	67	41	𝛿ωl	𝛿ωl	NOUN
iajs-2801	67	42	−	−	PROPN
iajs-2801	67	43	(	(	PUNCT
iajs-2801	67	44	𝛼	𝛼	NOUN
iajs-2801	67	45	)	)	PUNCT
iajs-2801	67	46	,	,	PUNCT
iajs-2801	67	47	𝛿ωu	𝛿ωu	VERB
iajs-2801	67	48	−	−	PROPN
iajs-2801	67	49	(	(	PUNCT
iajs-2801	67	50	𝛼	𝛼	NOUN
iajs-2801	67	51	)	)	PUNCT
iajs-2801	67	52	]	]	PUNCT
iajs-2801	67	53	}	}	PUNCT
iajs-2801	67	54	,	,	PUNCT
iajs-2801	67	55	𝜆ω	𝜆ω	ADP
iajs-2801	67	56	+	+	ADJ
iajs-2801	67	57	(	(	PUNCT
iajs-2801	67	58	𝛼	𝛼	NOUN
iajs-2801	67	59	)	)	PUNCT
iajs-2801	67	60	,	,	PUNCT
iajs-2801	67	61	𝜆ω	𝜆ω	ADP
iajs-2801	67	62	−(𝛼	−(𝛼	NOUN
iajs-2801	67	63	)	)	PUNCT
iajs-2801	67	64	}	}	PUNCT
iajs-2801	67	65	>	>	PUNCT
iajs-2801	67	66	:	:	PUNCT
iajs-2801	67	67	𝛼	𝛼	X
iajs-2801	67	68	∈	∈	ADJ
iajs-2801	67	69	ℵ	ℵ	NOUN
iajs-2801	67	70	}	}	PUNCT
iajs-2801	67	71	it	it	PRON
iajs-2801	67	72	is	be	AUX
iajs-2801	67	73	a	a	DET
iajs-2801	67	74	cubicbipolar	cubicbipolar	NOUN
iajs-2801	67	75	set	set	NOUN
iajs-2801	67	76	and	and	CCONJ
iajs-2801	67	77	can	can	AUX
iajs-2801	67	78	be	be	AUX
iajs-2801	67	79	denoted	denote	VERB
iajs-2801	67	80	by	by	ADP
iajs-2801	67	81	ω	ω	PROPN
iajs-2801	67	82	=	=	SYM
iajs-2801	67	83	〈	〈	PROPN
iajs-2801	67	84	𝑁	𝑁	PROPN
iajs-2801	67	85	,	,	PUNCT
iajs-2801	67	86	𝐾	𝐾	PROPN
iajs-2801	67	87	〉	〉	NOUN
iajs-2801	67	88	.	.	PUNCT
iajs-2801	67	89	definition2.11[11	definition2.11[11	NOUN
iajs-2801	67	90	]	]	PUNCT
iajs-2801	67	91	.	.	PUNCT
iajs-2801	68	1	a	a	DET
iajs-2801	68	2	cubic	cubic	ADJ
iajs-2801	68	3	bipolar	bipolar	ADJ
iajs-2801	68	4	set	set	VERB
iajs-2801	68	5	ω	ω	PROPN
iajs-2801	68	6	=	=	PUNCT
iajs-2801	68	7	〈	〈	PROPN
iajs-2801	68	8	𝑁	𝑁	PROPN
iajs-2801	68	9	,	,	PUNCT
iajs-2801	68	10	𝐾	𝐾	NOUN
iajs-2801	68	11	〉	〉	NOUN
iajs-2801	68	12	is	be	AUX
iajs-2801	68	13	named	name	VERB
iajs-2801	68	14	a	a	DET
iajs-2801	68	15	cubic	cubic	ADJ
iajs-2801	68	16	bipolar	bipolar	ADJ
iajs-2801	68	17	sub	sub	NOUN
iajs-2801	68	18	kusemigroup	kusemigroup	NOUN
iajs-2801	68	19	if	if	SCONJ
iajs-2801	68	20	:	:	PUNCT
iajs-2801	68	21	∀𝛼	∀𝛼	NUM
iajs-2801	68	22	,	,	PUNCT
iajs-2801	68	23	𝛽	𝛽	PROPN
iajs-2801	68	24	∈	∈	PROPN
iajs-2801	68	25	ℵ	ℵ	NOUN
iajs-2801	68	26	,	,	PUNCT
iajs-2801	68	27	(	(	PUNCT
iajs-2801	68	28	1	1	X
iajs-2801	68	29	)	)	PUNCT
iajs-2801	69	1	𝜇ω	𝜇ω	NOUN
iajs-2801	70	1	+	+	PROPN
iajs-2801	70	2	(	(	PUNCT
iajs-2801	70	3	𝛼	𝛼	PROPN
iajs-2801	70	4	∗	∗	NOUN
iajs-2801	70	5	𝛽	𝛽	NOUN
iajs-2801	70	6	)	)	PUNCT
iajs-2801	70	7	≥	≥	PROPN
iajs-2801	70	8	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	70	9	{	{	PUNCT
iajs-2801	70	10	𝜇ω	𝜇ω	X
iajs-2801	70	11	+	+	NOUN
iajs-2801	70	12	(	(	PUNCT
iajs-2801	70	13	𝛼)ˑ	𝛼)ˑ	ADJ
iajs-2801	70	14	,	,	PUNCT
iajs-2801	71	1	𝜇ω	𝜇ω	ADP
iajs-2801	71	2	+	+	PROPN
iajs-2801	71	3	(	(	PUNCT
iajs-2801	71	4	𝛽	𝛽	NOUN
iajs-2801	71	5	)	)	PUNCT
iajs-2801	71	6	}	}	PUNCT
iajs-2801	71	7	,	,	PUNCT
iajs-2801	71	8	𝜇ω	𝜇ω	NOUN
iajs-2801	71	9	−(𝛼	−(𝛼	NOUN
iajs-2801	71	10	∗	∗	NOUN
iajs-2801	71	11	𝛽	𝛽	NOUN
iajs-2801	71	12	)	)	PUNCT
iajs-2801	71	13	≤	≤	NOUN
iajs-2801	71	14	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	71	15	{	{	PUNCT
iajs-2801	71	16	𝜇ω	𝜇ω	NOUN
iajs-2801	71	17	−(𝛼)ˑ	−(𝛼)ˑ	PROPN
iajs-2801	71	18	,	,	PUNCT
iajs-2801	71	19	𝜇ω	𝜇ω	NOUN
iajs-2801	71	20	−(𝛽	−(𝛽	NOUN
iajs-2801	71	21	)	)	PUNCT
iajs-2801	71	22	}	}	PUNCT
iajs-2801	71	23	𝜆ω	𝜆ω	PUNCT
iajs-2801	72	1	+	+	ADJ
iajs-2801	72	2	(	(	PUNCT
iajs-2801	72	3	𝛼	𝛼	PROPN
iajs-2801	72	4	∗	∗	NOUN
iajs-2801	72	5	𝛽	𝛽	NOUN
iajs-2801	72	6	)	)	PUNCT
iajs-2801	72	7	≥	≥	NOUN
iajs-2801	72	8	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	72	9	{	{	PUNCT
iajs-2801	72	10	𝜆ω	𝜆ω	X
iajs-2801	72	11	+	+	ADJ
iajs-2801	72	12	(	(	PUNCT
iajs-2801	72	13	𝛼)ˑ	𝛼)ˑ	ADJ
iajs-2801	72	14	,	,	PUNCT
iajs-2801	72	15	𝜆ω	𝜆ω	X
iajs-2801	72	16	+	+	ADJ
iajs-2801	72	17	(	(	PUNCT
iajs-2801	72	18	𝛽	𝛽	NOUN
iajs-2801	72	19	)	)	PUNCT
iajs-2801	72	20	}	}	PUNCT
iajs-2801	72	21	,	,	PUNCT
iajs-2801	72	22	𝜆ω	𝜆ω	ADP
iajs-2801	72	23	−(𝛼	−(𝛼	NOUN
iajs-2801	72	24	∗	∗	NOUN
iajs-2801	72	25	𝛽	𝛽	NOUN
iajs-2801	72	26	)	)	PUNCT
iajs-2801	72	27	≤	≤	NUM
iajs-2801	72	28	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	72	29	{	{	PUNCT
iajs-2801	72	30	𝜆ω	𝜆ω	NOUN
iajs-2801	72	31	−(𝛼)ˑ	−(𝛼)ˑ	PROPN
iajs-2801	72	32	,	,	PUNCT
iajs-2801	72	33	𝜆ω	𝜆ω	DET
iajs-2801	72	34	−(𝛽	−(𝛽	NOUN
iajs-2801	72	35	)	)	PUNCT
iajs-2801	72	36	}	}	PUNCT
iajs-2801	72	37	,	,	PUNCT
iajs-2801	72	38	(	(	PUNCT
iajs-2801	72	39	2	2	X
iajs-2801	72	40	)	)	PUNCT
iajs-2801	72	41	𝜇ω	𝜇ω	NOUN
iajs-2801	72	42	+	+	PROPN
iajs-2801	72	43	(	(	PUNCT
iajs-2801	72	44	𝛼	𝛼	PROPN
iajs-2801	72	45	∘	∘	PROPN
iajs-2801	72	46	𝛽	𝛽	NOUN
iajs-2801	72	47	)	)	PUNCT
iajs-2801	72	48	≥	≥	PROPN
iajs-2801	72	49	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	72	50	{	{	PUNCT
iajs-2801	72	51	𝜇ω	𝜇ω	X
iajs-2801	72	52	+	+	NOUN
iajs-2801	72	53	(	(	PUNCT
iajs-2801	72	54	𝛼)ˑ	𝛼)ˑ	ADJ
iajs-2801	72	55	,	,	PUNCT
iajs-2801	73	1	𝜇ω	𝜇ω	ADP
iajs-2801	73	2	+	+	PROPN
iajs-2801	73	3	(	(	PUNCT
iajs-2801	73	4	𝛽	𝛽	NOUN
iajs-2801	73	5	)	)	PUNCT
iajs-2801	73	6	}	}	PUNCT
iajs-2801	73	7	,	,	PUNCT
iajs-2801	73	8	𝜇ω	𝜇ω	NOUN
iajs-2801	73	9	−(𝛼	−(𝛼	NOUN
iajs-2801	73	10	∘	∘	NOUN
iajs-2801	73	11	𝛽	𝛽	NOUN
iajs-2801	73	12	)	)	PUNCT
iajs-2801	73	13	≤	≤	NOUN
iajs-2801	73	14	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	73	15	{	{	PUNCT
iajs-2801	73	16	𝜇ω	𝜇ω	NOUN
iajs-2801	73	17	−(𝛼)ˑ	−(𝛼)ˑ	PROPN
iajs-2801	73	18	,	,	PUNCT
iajs-2801	73	19	𝜇ω	𝜇ω	NOUN
iajs-2801	73	20	−(𝛽	−(𝛽	NOUN
iajs-2801	73	21	)	)	PUNCT
iajs-2801	73	22	}	}	PUNCT
iajs-2801	73	23	𝜆ω	𝜆ω	PUNCT
iajs-2801	74	1	+	+	ADJ
iajs-2801	74	2	(	(	PUNCT
iajs-2801	74	3	𝛼	𝛼	PROPN
iajs-2801	74	4	∘	∘	PROPN
iajs-2801	74	5	𝛽	𝛽	NOUN
iajs-2801	74	6	)	)	PUNCT
iajs-2801	74	7	≥	≥	NOUN
iajs-2801	74	8	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	74	9	{	{	PUNCT
iajs-2801	74	10	𝜆ω	𝜆ω	X
iajs-2801	74	11	+	+	ADJ
iajs-2801	74	12	(	(	PUNCT
iajs-2801	74	13	𝛼)ˑ	𝛼)ˑ	ADJ
iajs-2801	74	14	,	,	PUNCT
iajs-2801	74	15	𝜆ω	𝜆ω	X
iajs-2801	74	16	+	+	ADJ
iajs-2801	74	17	(	(	PUNCT
iajs-2801	74	18	𝛽	𝛽	NOUN
iajs-2801	74	19	)	)	PUNCT
iajs-2801	74	20	}	}	PUNCT
iajs-2801	74	21	,	,	PUNCT
iajs-2801	74	22	𝜆ω	𝜆ω	ADP
iajs-2801	74	23	−(𝛼	−(𝛼	NOUN
iajs-2801	74	24	∘	∘	NOUN
iajs-2801	74	25	𝛽	𝛽	NOUN
iajs-2801	74	26	)	)	PUNCT
iajs-2801	74	27	≤	≤	NUM
iajs-2801	74	28	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	74	29	{	{	PUNCT
iajs-2801	74	30	𝜆ω	𝜆ω	NOUN
iajs-2801	74	31	−(𝛼)ˑ	−(𝛼)ˑ	PROPN
iajs-2801	74	32	,	,	PUNCT
iajs-2801	74	33	𝜆ω	𝜆ω	DET
iajs-2801	74	34	−(𝛽	−(𝛽	NOUN
iajs-2801	74	35	)	)	PUNCT
iajs-2801	74	36	}	}	PUNCT
iajs-2801	74	37	,	,	PUNCT
iajs-2801	74	38	example2.12[11	example2.12[11	PROPN
iajs-2801	74	39	]	]	PUNCT
iajs-2801	74	40	.	.	PUNCT
iajs-2801	75	1	if	if	SCONJ
iajs-2801	75	2	ℵ	ℵ	NOUN
iajs-2801	75	3	=	=	SYM
iajs-2801	75	4	{	{	PUNCT
iajs-2801	75	5	0,1,2,3	0,1,2,3	NOUN
iajs-2801	75	6	}	}	PUNCT
iajs-2801	75	7	is	be	AUX
iajs-2801	75	8	ˑa	ˑa	ADV
iajs-2801	75	9	set	set	VERB
iajs-2801	75	10	and	and	CCONJ
iajs-2801	75	11	two	two	NUM
iajs-2801	75	12	binary	binary	ADJ
iajs-2801	75	13	operations	operation	NOUN
iajs-2801	75	14	∗	∗	NOUN
iajs-2801	75	15	and	and	CCONJ
iajs-2801	75	16	∘	∘	PROPN
iajs-2801	75	17	are	be	AUX
iajs-2801	75	18	define	define	ADJ
iajs-2801	75	19	by	by	ADP
iajs-2801	75	20	the	the	DET
iajs-2801	75	21	following	following	NOUN
iajs-2801	75	22	.	.	PUNCT
iajs-2801	76	1	then(ℵ,∗,∘	then(ℵ,∗,∘	NOUN
iajs-2801	76	2	,	,	PUNCT
iajs-2801	76	3	0	0	NUM
iajs-2801	76	4	)	)	PUNCT
iajs-2801	76	5	ˑis	ˑis	VERB
iajs-2801	76	6	a	a	DET
iajs-2801	76	7	ku	ku	PROPN
iajs-2801	76	8	-	-	PUNCT
iajs-2801	76	9	semigroup	semigroup	PROPN
iajs-2801	76	10	.	.	PUNCT
iajs-2801	77	1	defineω	defineω	PROPN
iajs-2801	77	2	=	=	PUNCT
iajs-2801	77	3	〈	〈	PROPN
iajs-2801	77	4	𝑁	𝑁	PROPN
iajs-2801	77	5	,	,	PUNCT
iajs-2801	77	6	𝐾	𝐾	PROPN
iajs-2801	77	7	〉	〉	NOUN
iajs-2801	77	8	as	as	SCONJ
iajs-2801	77	9	follows	follow	VERB
iajs-2801	77	10	𝑁(𝛼	𝑁(𝛼	PRON
iajs-2801	77	11	)	)	PUNCT
iajs-2801	77	12	=	=	PRON
iajs-2801	77	13	{	{	PUNCT
iajs-2801	77	14	{	{	PUNCT
iajs-2801	78	1	[	[	X
iajs-2801	78	2	−0.2	−0.2	PROPN
iajs-2801	78	3	,	,	PUNCT
iajs-2801	78	4	−0.5	−0.5	PROPN
iajs-2801	78	5	]	]	PUNCT
iajs-2801	78	6	,	,	PUNCT
iajs-2801	79	1	[	[	X
iajs-2801	79	2	0.1,0.9	0.1,0.9	X
iajs-2801	79	3	]	]	X
iajs-2801	79	4	}	}	PUNCT
iajs-2801	79	5	𝑖𝑓	𝑖𝑓	ADP
iajs-2801	79	6	𝛼	𝛼	VERB
iajs-2801	79	7	=	=	SYM
iajs-2801	79	8	{	{	PUNCT
iajs-2801	79	9	0,1	0,1	NOUN
iajs-2801	79	10	}	}	PUNCT
iajs-2801	79	11	{	{	PUNCT
iajs-2801	80	1	[	[	X
iajs-2801	80	2	−0.6	−0.6	PROPN
iajs-2801	80	3	,	,	PUNCT
iajs-2801	80	4	−0.2	−0.2	PROPN
iajs-2801	80	5	]	]	PUNCT
iajs-2801	80	6	,	,	PUNCT
iajs-2801	80	7	[	[	X
iajs-2801	80	8	0.2,0.5	0.2,0.5	NUM
iajs-2801	80	9	]	]	X
iajs-2801	80	10	}	}	PUNCT
iajs-2801	80	11	𝑖𝑓	𝑖𝑓	ADP
iajs-2801	80	12	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	NOUN
iajs-2801	80	13	,	,	PUNCT
iajs-2801	80	14	𝜆ω	𝜆ω	X
iajs-2801	80	15	+	+	ADJ
iajs-2801	80	16	(	(	PUNCT
iajs-2801	80	17	𝛼	𝛼	NOUN
iajs-2801	80	18	)	)	PUNCT
iajs-2801	80	19	=	=	SYM
iajs-2801	80	20	{	{	PUNCT
iajs-2801	80	21	0.5	0.5	NUM
iajs-2801	80	22	𝑖𝑓	𝑖𝑓	NUM
iajs-2801	80	23	𝛼	𝛼	NOUN
iajs-2801	80	24	=	=	NOUN
iajs-2801	80	25	{	{	PUNCT
iajs-2801	80	26	0,1	0,1	NOUN
iajs-2801	80	27	}	}	PUNCT
iajs-2801	80	28	0.3	0.3	NUM
iajs-2801	80	29	𝑖𝑓	𝑖𝑓	NOUN
iajs-2801	80	30	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	NOUN
iajs-2801	80	31	𝜆ω	𝜆ω	ADP
iajs-2801	80	32	−(𝛼	−(𝛼	NOUN
iajs-2801	80	33	)	)	PUNCT
iajs-2801	81	1	=	=	PRON
iajs-2801	81	2	{	{	PUNCT
iajs-2801	81	3	−0.6	−0.6	PROPN
iajs-2801	81	4	𝑖𝑓	𝑖𝑓	ADP
iajs-2801	81	5	𝛼	𝛼	NOUN
iajs-2801	81	6	=	=	SYM
iajs-2801	81	7	{	{	PUNCT
iajs-2801	81	8	0,1	0,1	NOUN
iajs-2801	81	9	}	}	PUNCT
iajs-2801	81	10	−0.3	−0.3	PROPN
iajs-2801	81	11	𝑖𝑓	𝑖𝑓	ADP
iajs-2801	81	12	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	PROPN
iajs-2801	81	13	then	then	ADV
iajs-2801	81	14	ω	ω	PROPN
iajs-2801	81	15	=	=	PUNCT
iajs-2801	81	16	〈	〈	PROPN
iajs-2801	81	17	𝑁	𝑁	PROPN
iajs-2801	81	18	,	,	PUNCT
iajs-2801	81	19	𝐾〉is	𝐾〉is	PROPN
iajs-2801	81	20	a	a	DET
iajs-2801	81	21	cubic	cubic	ADJ
iajs-2801	81	22	bipolar	bipolar	ADJ
iajs-2801	81	23	sub	sub	NOUN
iajs-2801	81	24	ku	ku	PROPN
iajs-2801	81	25	-	-	PUNCT
iajs-2801	81	26	semigroup	semigroup	PROPN
iajs-2801	81	27	ofℵˑ.	ofℵˑ.	PROPN
iajs-2801	81	28	definition	definition	NOUN
iajs-2801	81	29	2.13[11	2.13[11	NUM
iajs-2801	81	30	]	]	PUNCT
iajs-2801	81	31	.	.	PUNCT
iajs-2801	82	1	a	a	DET
iajs-2801	82	2	cubic	cubic	ADJ
iajs-2801	82	3	bipolar	bipolar	ADJ
iajs-2801	82	4	set	set	VERB
iajs-2801	82	5	ω	ω	PROPN
iajs-2801	82	6	=	=	PUNCT
iajs-2801	82	7	〈	〈	PROPN
iajs-2801	82	8	𝑁	𝑁	PROPN
iajs-2801	82	9	,	,	PUNCT
iajs-2801	82	10	𝐾〉in	𝐾〉in	NOUN
iajs-2801	82	11	ℵis	ℵis	NOUN
iajs-2801	82	12	called	call	VERB
iajs-2801	82	13	a	a	DET
iajs-2801	82	14	cubic	cubic	ADJ
iajs-2801	82	15	bipolar	bipolar	ADJ
iajs-2801	82	16	ideal	ideal	NOUN
iajs-2801	82	17	of	of	ADP
iajs-2801	82	18	ℵif	ℵif	PROPN
iajs-2801	82	19	,	,	PUNCT
iajs-2801	82	20	∀𝛼	∀𝛼	PRON
iajs-2801	82	21	,	,	PUNCT
iajs-2801	82	22	𝛽	𝛽	PROPN
iajs-2801	82	23	∈	∈	PROPN
iajs-2801	82	24	ℵ	ℵ	X
iajs-2801	82	25	(	(	PUNCT
iajs-2801	82	26	bc1	bc1	NOUN
iajs-2801	82	27	)	)	PUNCT
iajs-2801	82	28	𝜇ω	𝜇ω	ADP
iajs-2801	83	1	+	+	NOUN
iajs-2801	83	2	(	(	PUNCT
iajs-2801	83	3	0	0	NUM
iajs-2801	83	4	)	)	PUNCT
iajs-2801	83	5	≥	≥	NOUN
iajs-2801	83	6	𝜇ω	𝜇ω	ADP
iajs-2801	83	7	+	+	NOUN
iajs-2801	83	8	(	(	PUNCT
iajs-2801	83	9	𝛼	𝛼	NOUN
iajs-2801	83	10	)	)	PUNCT
iajs-2801	83	11	,	,	PUNCT
iajs-2801	83	12	𝜆ω	𝜆ω	X
iajs-2801	84	1	+	+	ADJ
iajs-2801	84	2	(	(	PUNCT
iajs-2801	84	3	0	0	NUM
iajs-2801	84	4	)	)	PUNCT
iajs-2801	84	5	≥	≥	NOUN
iajs-2801	84	6	𝜆ω	𝜆ω	X
iajs-2801	84	7	+	+	ADJ
iajs-2801	84	8	(	(	PUNCT
iajs-2801	84	9	𝛼	𝛼	NOUN
iajs-2801	84	10	)	)	PUNCT
iajs-2801	84	11	and	and	CCONJ
iajs-2801	84	12	𝜇ω	𝜇ω	ADP
iajs-2801	84	13	−(0	−(0	NOUN
iajs-2801	84	14	)	)	PUNCT
iajs-2801	84	15	≤	≤	NOUN
iajs-2801	84	16	𝜇ω	𝜇ω	ADP
iajs-2801	84	17	−(𝛼	−(𝛼	NOUN
iajs-2801	84	18	)	)	PUNCT
iajs-2801	84	19	,	,	PUNCT
iajs-2801	84	20	𝜆ω	𝜆ω	ADP
iajs-2801	84	21	−(0	−(0	NOUN
iajs-2801	84	22	)	)	PUNCT
iajs-2801	84	23	≤	≤	NOUN
iajs-2801	84	24	𝜆ω	𝜆ω	ADP
iajs-2801	84	25	−(𝛼	−(𝛼	NOUN
iajs-2801	84	26	)	)	PUNCT
iajs-2801	84	27			PROPN
iajs-2801	84	28			PROPN
iajs-2801	84	29	ibn	ibn	PROPN
iajs-2801	84	30	al	al	PROPN
iajs-2801	84	31	-	-	PUNCT
iajs-2801	84	32	haitham	haitham	PROPN
iajs-2801	84	33	jour	jour	X
iajs-2801	84	34	.	.	PROPN
iajs-2801	85	1	for	for	ADP
iajs-2801	85	2	pure	pure	ADJ
iajs-2801	85	3	&	&	CCONJ
iajs-2801	85	4	appl	appl	PROPN
iajs-2801	85	5	.	.	PUNCT
iajs-2801	86	1	sci	sci	PROPN
iajs-2801	86	2	.	.	PROPN
iajs-2801	87	1	35(1)2022	35(1)2022	NUM
iajs-2801	87	2	76	76	NUM
iajs-2801	87	3	(	(	PUNCT
iajs-2801	87	4	bc2	bc2	NOUN
iajs-2801	87	5	)	)	PUNCT
iajs-2801	87	6	𝜇ω	𝜇ω	ADP
iajs-2801	87	7	+	+	NOUN
iajs-2801	87	8	(	(	PUNCT
iajs-2801	87	9	𝛽	𝛽	NOUN
iajs-2801	87	10	)	)	PUNCT
iajs-2801	87	11	≥	≥	NOUN
iajs-2801	87	12	𝑟𝑚𝑖𝑛{𝜇ω	𝑟𝑚𝑖𝑛{𝜇ω	NUM
iajs-2801	88	1	+	+	PROPN
iajs-2801	88	2	(	(	PUNCT
iajs-2801	88	3	𝛼	𝛼	PROPN
iajs-2801	88	4	∗	∗	NOUN
iajs-2801	88	5	𝛽	𝛽	NOUN
iajs-2801	88	6	)	)	PUNCT
iajs-2801	88	7	,	,	PUNCT
iajs-2801	88	8	𝜇ω	𝜇ω	ADP
iajs-2801	88	9	+	+	ADJ
iajs-2801	88	10	(	(	PUNCT
iajs-2801	88	11	𝛼	𝛼	NOUN
iajs-2801	88	12	)	)	PUNCT
iajs-2801	88	13	}	}	PUNCT
iajs-2801	88	14	,	,	PUNCT
iajs-2801	88	15	𝜇ω	𝜇ω	NOUN
iajs-2801	88	16	−(𝛽	−(𝛽	NOUN
iajs-2801	88	17	)	)	PUNCT
iajs-2801	88	18	≤	≤	NOUN
iajs-2801	88	19	𝑟𝑚𝑎𝑥{𝜇ω	𝑟𝑚𝑎𝑥{𝜇ω	NUM
iajs-2801	88	20	−(𝛼	−(𝛼	NOUN
iajs-2801	88	21	∗	∗	ADP
iajs-2801	88	22	𝛽	𝛽	NOUN
iajs-2801	88	23	)	)	PUNCT
iajs-2801	88	24	,	,	PUNCT
iajs-2801	88	25	𝜇ω	𝜇ω	ADP
iajs-2801	88	26	−(𝛼)}and	−(𝛼)}and	NOUN
iajs-2801	88	27	𝜆ω	𝜆ω	X
iajs-2801	88	28	+	+	ADJ
iajs-2801	88	29	(	(	PUNCT
iajs-2801	88	30	𝛽	𝛽	NOUN
iajs-2801	88	31	)	)	PUNCT
iajs-2801	88	32	≥	≥	NOUN
iajs-2801	88	33	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	88	34	{	{	PUNCT
iajs-2801	88	35	𝜆ω	𝜆ω	X
iajs-2801	88	36	+	+	ADJ
iajs-2801	88	37	(	(	PUNCT
iajs-2801	88	38	𝛼	𝛼	NOUN
iajs-2801	88	39	∗	∗	NOUN
iajs-2801	88	40	𝛽)ˑ	𝛽)ˑ	NOUN
iajs-2801	88	41	,	,	PUNCT
iajs-2801	88	42	𝜆ω	𝜆ω	X
iajs-2801	88	43	+	+	ADJ
iajs-2801	88	44	(	(	PUNCT
iajs-2801	88	45	𝛼	𝛼	NOUN
iajs-2801	88	46	)	)	PUNCT
iajs-2801	88	47	}	}	PUNCT
iajs-2801	88	48	,	,	PUNCT
iajs-2801	88	49	𝜆ω	𝜆ω	PRON
iajs-2801	88	50	−(𝛽	−(𝛽	NOUN
iajs-2801	88	51	)	)	PUNCT
iajs-2801	88	52	≤	≤	NUM
iajs-2801	88	53	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-2801	88	54	{	{	PUNCT
iajs-2801	88	55	𝜆ω	𝜆ω	ADP
iajs-2801	88	56	−(𝛼	−(𝛼	NOUN
iajs-2801	88	57	∗	∗	NOUN
iajs-2801	88	58	𝛽)ˑ	𝛽)ˑ	NOUN
iajs-2801	88	59	,	,	PUNCT
iajs-2801	88	60	𝜆ω	𝜆ω	ADP
iajs-2801	88	61	−(𝛼	−(𝛼	NOUN
iajs-2801	88	62	)	)	PUNCT
iajs-2801	88	63	}	}	PUNCT
iajs-2801	88	64	,	,	PUNCT
iajs-2801	88	65	(	(	PUNCT
iajs-2801	88	66	bc3)𝜇ω	bc3)𝜇ω	ADP
iajs-2801	88	67	+	+	PROPN
iajs-2801	88	68	(	(	PUNCT
iajs-2801	88	69	𝛼	𝛼	PROPN
iajs-2801	88	70	∘	∘	PROPN
iajs-2801	88	71	𝛽	𝛽	NOUN
iajs-2801	88	72	)	)	PUNCT
iajs-2801	88	73	≥	≥	PROPN
iajs-2801	88	74	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	88	75	{	{	PUNCT
iajs-2801	88	76	𝜇ω	𝜇ω	X
iajs-2801	88	77	+	+	NOUN
iajs-2801	88	78	(	(	PUNCT
iajs-2801	88	79	𝛼)ˑ	𝛼)ˑ	ADJ
iajs-2801	88	80	,	,	PUNCT
iajs-2801	88	81	𝜇ω	𝜇ω	ADP
iajs-2801	88	82	+	+	PROPN
iajs-2801	88	83	(	(	PUNCT
iajs-2801	88	84	𝛽	𝛽	NOUN
iajs-2801	88	85	)	)	PUNCT
iajs-2801	88	86	}	}	PUNCT
iajs-2801	88	87	,	,	PUNCT
iajs-2801	88	88	𝜇ω	𝜇ω	NOUN
iajs-2801	88	89	−(𝛼	−(𝛼	NOUN
iajs-2801	88	90	∘	∘	NOUN
iajs-2801	88	91	𝛽	𝛽	NOUN
iajs-2801	88	92	)	)	PUNCT
iajs-2801	88	93	≤	≤	NOUN
iajs-2801	88	94	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	88	95	{	{	PUNCT
iajs-2801	88	96	�	�	PROPN
iajs-2801	88	97	̃	̃	PROPN
iajs-2801	88	98	�	�	NOUN
iajs-2801	88	99	ω	ω	NUM
iajs-2801	88	100	−(𝛼)ˑ	−(𝛼)ˑ	PROPN
iajs-2801	88	101	,	,	PUNCT
iajs-2801	88	102	𝜇ω	𝜇ω	NOUN
iajs-2801	88	103	−(𝛽	−(𝛽	NOUN
iajs-2801	88	104	)	)	PUNCT
iajs-2801	88	105	}	}	PUNCT
iajs-2801	88	106	and	and	CCONJ
iajs-2801	88	107	𝜆ω	𝜆ω	X
iajs-2801	89	1	+	+	ADJ
iajs-2801	89	2	(	(	PUNCT
iajs-2801	89	3	𝛼	𝛼	PROPN
iajs-2801	89	4	∘	∘	PROPN
iajs-2801	89	5	𝛽	𝛽	NOUN
iajs-2801	89	6	)	)	PUNCT
iajs-2801	89	7	≥	≥	NOUN
iajs-2801	89	8	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	89	9	{	{	PUNCT
iajs-2801	89	10	𝜆ω	𝜆ω	X
iajs-2801	89	11	+	+	ADJ
iajs-2801	89	12	(	(	PUNCT
iajs-2801	89	13	𝛼)ˑ	𝛼)ˑ	ADJ
iajs-2801	89	14	,	,	PUNCT
iajs-2801	89	15	𝜆ω	𝜆ω	X
iajs-2801	89	16	+	+	ADJ
iajs-2801	89	17	(	(	PUNCT
iajs-2801	89	18	𝛽	𝛽	NOUN
iajs-2801	89	19	)	)	PUNCT
iajs-2801	89	20	}	}	PUNCT
iajs-2801	89	21	,	,	PUNCT
iajs-2801	89	22	𝜆ω	𝜆ω	ADP
iajs-2801	89	23	−(𝛼	−(𝛼	NOUN
iajs-2801	89	24	∘	∘	NOUN
iajs-2801	89	25	𝛽	𝛽	NOUN
iajs-2801	89	26	)	)	PUNCT
iajs-2801	89	27	≤	≤	NUM
iajs-2801	89	28	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	89	29	{	{	PUNCT
iajs-2801	89	30	𝜆ω	𝜆ω	NOUN
iajs-2801	89	31	−(𝛼)ˑ	−(𝛼)ˑ	PROPN
iajs-2801	89	32	,	,	PUNCT
iajs-2801	89	33	𝜆ω	𝜆ω	DET
iajs-2801	89	34	−(𝛽	−(𝛽	NOUN
iajs-2801	89	35	)	)	PUNCT
iajs-2801	89	36	}	}	PUNCT
iajs-2801	89	37	.	.	PUNCT
iajs-2801	90	1	example	example	NOUN
iajs-2801	91	1	2.14[11	2.14[11	NUM
iajs-2801	91	2	]	]	X
iajs-2801	91	3	.	.	PUNCT
iajs-2801	92	1	if	if	SCONJ
iajs-2801	92	2	ℵ	ℵ	NOUN
iajs-2801	92	3	=	=	SYM
iajs-2801	92	4	{	{	PUNCT
iajs-2801	92	5	0,1,2	0,1,2	NOUN
iajs-2801	92	6	}	}	PUNCT
iajs-2801	92	7	is	be	AUX
iajs-2801	92	8	ˑa	ˑa	ADV
iajs-2801	92	9	set	set	VERB
iajs-2801	92	10	and	and	CCONJ
iajs-2801	92	11	two	two	NUM
iajs-2801	92	12	binary	binary	ADJ
iajs-2801	92	13	operations	operation	NOUN
iajs-2801	92	14	∗	∗	NOUN
iajs-2801	92	15	and	and	CCONJ
iajs-2801	92	16	∘	∘	NOUN
iajs-2801	92	17	are	be	AUX
iajs-2801	92	18	defined	define	VERB
iajs-2801	92	19	by	by	ADP
iajs-2801	92	20	the	the	DET
iajs-2801	92	21	following	following	NOUN
iajs-2801	92	22	.	.	PUNCT
iajs-2801	93	1	then(ℵ,∗,∘	then(ℵ,∗,∘	NOUN
iajs-2801	93	2	,	,	PUNCT
iajs-2801	93	3	0	0	NUM
iajs-2801	93	4	)	)	PUNCT
iajs-2801	93	5	ˑis	ˑis	VERB
iajs-2801	93	6	a	a	DET
iajs-2801	93	7	ku	ku	PROPN
iajs-2801	93	8	-	-	PUNCT
iajs-2801	93	9	semigroup	semigroup	PROPN
iajs-2801	93	10	.	.	PUNCT
iajs-2801	94	1	defineω	defineω	PROPN
iajs-2801	94	2	=	=	PUNCT
iajs-2801	94	3	〈	〈	PROPN
iajs-2801	94	4	𝑁	𝑁	PROPN
iajs-2801	94	5	,	,	PUNCT
iajs-2801	94	6	𝐾	𝐾	PROPN
iajs-2801	94	7	〉	〉	NOUN
iajs-2801	94	8	as	as	SCONJ
iajs-2801	94	9	follows	follow	VERB
iajs-2801	94	10	𝑁(𝛼	𝑁(𝛼	PRON
iajs-2801	94	11	)	)	PUNCT
iajs-2801	94	12	=	=	PRON
iajs-2801	94	13	{	{	PUNCT
iajs-2801	94	14	{	{	PUNCT
iajs-2801	95	1	[	[	X
iajs-2801	95	2	−0.3	−0.3	PROPN
iajs-2801	95	3	,	,	PUNCT
iajs-2801	95	4	−0.1	−0.1	PROPN
iajs-2801	95	5	]	]	X
iajs-2801	95	6	,	,	PUNCT
iajs-2801	95	7	[	[	X
iajs-2801	95	8	0.1,0.8	0.1,0.8	PROPN
iajs-2801	95	9	]	]	PUNCT
iajs-2801	95	10	}	}	PUNCT
iajs-2801	95	11	𝑖𝑓	𝑖𝑓	ADP
iajs-2801	95	12	𝛼	𝛼	NOUN
iajs-2801	95	13	=	=	NOUN
iajs-2801	95	14	0	0	PUNCT
iajs-2801	95	15	{	{	PUNCT
iajs-2801	96	1	[	[	X
iajs-2801	96	2	−0.7	−0.7	PROPN
iajs-2801	96	3	,	,	PUNCT
iajs-2801	96	4	−0.3	−0.3	PROPN
iajs-2801	96	5	]	]	PUNCT
iajs-2801	96	6	,	,	PUNCT
iajs-2801	96	7	[	[	X
iajs-2801	96	8	0.4,0.6	0.4,0.6	X
iajs-2801	96	9	]	]	PUNCT
iajs-2801	96	10	}	}	PUNCT
iajs-2801	96	11	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	NOUN
iajs-2801	96	12	,	,	PUNCT
iajs-2801	96	13	𝜆ω	𝜆ω	X
iajs-2801	96	14	+	+	ADJ
iajs-2801	96	15	(	(	PUNCT
iajs-2801	96	16	𝛼	𝛼	NOUN
iajs-2801	96	17	)	)	PUNCT
iajs-2801	96	18	=	=	SYM
iajs-2801	96	19	{	{	PUNCT
iajs-2801	97	1	0.9	0.9	NUM
iajs-2801	97	2	𝑖𝑓	𝑖𝑓	NUM
iajs-2801	97	3	𝛼	𝛼	NOUN
iajs-2801	97	4	=	=	NOUN
iajs-2801	97	5	0	0	NUM
iajs-2801	97	6	0.4	0.4	NUM
iajs-2801	97	7	𝑖𝑓	𝑖𝑓	NOUN
iajs-2801	97	8	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	PROPN
iajs-2801	97	9	𝜆ω	𝜆ω	ADP
iajs-2801	97	10	−(𝛼	−(𝛼	NOUN
iajs-2801	97	11	)	)	PUNCT
iajs-2801	98	1	=	=	PRON
iajs-2801	98	2	{	{	PUNCT
iajs-2801	98	3	−0.8	−0.8	PROPN
iajs-2801	98	4	𝑖𝑓	𝑖𝑓	NUM
iajs-2801	98	5	𝛼	𝛼	NOUN
iajs-2801	98	6	=	=	SYM
iajs-2801	98	7	0	0	NUM
iajs-2801	98	8	−0.3	−0.3	PROPN
iajs-2801	98	9	𝑖𝑓	𝑖𝑓	ADP
iajs-2801	98	10	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	PROPN
iajs-2801	98	11	we	we	PRON
iajs-2801	98	12	can	can	AUX
iajs-2801	98	13	easily	easily	ADV
iajs-2801	98	14	prove	prove	VERB
iajs-2801	98	15	thatω	thatω	NOUN
iajs-2801	98	16	=	=	PUNCT
iajs-2801	98	17	〈	〈	PROPN
iajs-2801	98	18	𝑁	𝑁	PROPN
iajs-2801	98	19	,	,	PUNCT
iajs-2801	98	20	𝐾〉is	𝐾〉is	PROPN
iajs-2801	98	21	a	a	DET
iajs-2801	98	22	cubic	cubic	ADJ
iajs-2801	98	23	bipolarideal	bipolarideal	NOUN
iajs-2801	98	24	ofℵˑ.	ofℵˑ.	PROPN
iajs-2801	98	25	definition	definition	NOUN
iajs-2801	98	26	2.15[11	2.15[11	NUM
iajs-2801	98	27	]	]	X
iajs-2801	98	28	.	.	PUNCT
iajs-2801	99	1	a	a	DET
iajs-2801	99	2	cubicbipolar	cubicbipolar	NOUN
iajs-2801	99	3	set	set	VERB
iajs-2801	99	4	ω	ω	PROPN
iajs-2801	99	5	=	=	PUNCT
iajs-2801	99	6	〈	〈	PROPN
iajs-2801	99	7	𝑁	𝑁	PROPN
iajs-2801	99	8	,	,	PUNCT
iajs-2801	99	9	𝐾〉in	𝐾〉in	NOUN
iajs-2801	99	10	ℵis	ℵis	NOUN
iajs-2801	99	11	called	call	VERB
iajs-2801	99	12	a	a	DET
iajs-2801	99	13	cubic	cubic	ADJ
iajs-2801	99	14	bipolark	bipolark	NOUN
iajs-2801	99	15	-	-	PUNCT
iajs-2801	99	16	ideal	ideal	NOUN
iajs-2801	99	17	of	of	ADP
iajs-2801	99	18	ℵ	ℵ	ADJ
iajs-2801	99	19	if	if	SCONJ
iajs-2801	99	20	,	,	PUNCT
iajs-2801	99	21	∀𝛼	∀𝛼	PRON
iajs-2801	99	22	,	,	PUNCT
iajs-2801	99	23	𝛽	𝛽	PROPN
iajs-2801	99	24	,	,	PUNCT
iajs-2801	99	25	δ	δ	PROPN
iajs-2801	99	26	∈	∈	PROPN
iajs-2801	99	27	ℵ	ℵ	X
iajs-2801	99	28	(	(	PUNCT
iajs-2801	99	29	a	a	NOUN
iajs-2801	99	30	)	)	PUNCT
iajs-2801	99	31	𝜇ω	𝜇ω	NOUN
iajs-2801	99	32	+	+	NOUN
iajs-2801	99	33	(	(	PUNCT
iajs-2801	99	34	0	0	NUM
iajs-2801	99	35	)	)	PUNCT
iajs-2801	99	36	≥	≥	NOUN
iajs-2801	99	37	𝜇ω	𝜇ω	ADP
iajs-2801	99	38	+	+	NOUN
iajs-2801	99	39	(	(	PUNCT
iajs-2801	99	40	𝛼	𝛼	NOUN
iajs-2801	99	41	)	)	PUNCT
iajs-2801	99	42	,	,	PUNCT
iajs-2801	99	43	𝜆ω	𝜆ω	X
iajs-2801	99	44	+	+	ADJ
iajs-2801	99	45	(	(	PUNCT
iajs-2801	99	46	0	0	NUM
iajs-2801	99	47	)	)	PUNCT
iajs-2801	99	48	≥	≥	NOUN
iajs-2801	99	49	𝜆ω	𝜆ω	X
iajs-2801	99	50	+	+	ADJ
iajs-2801	99	51	(	(	PUNCT
iajs-2801	99	52	𝛼	𝛼	NOUN
iajs-2801	99	53	)	)	PUNCT
iajs-2801	99	54	and	and	CCONJ
iajs-2801	99	55	𝜇ω	𝜇ω	ADP
iajs-2801	99	56	−(0	−(0	NOUN
iajs-2801	99	57	)	)	PUNCT
iajs-2801	99	58	≤	≤	NOUN
iajs-2801	99	59	𝜇ω	𝜇ω	ADP
iajs-2801	99	60	−(𝛼	−(𝛼	NOUN
iajs-2801	99	61	)	)	PUNCT
iajs-2801	99	62	,	,	PUNCT
iajs-2801	99	63	𝜆ω	𝜆ω	ADP
iajs-2801	99	64	−(0	−(0	NOUN
iajs-2801	99	65	)	)	PUNCT
iajs-2801	99	66	≤	≤	NOUN
iajs-2801	99	67	𝜆ω	𝜆ω	ADP
iajs-2801	99	68	−(𝛼	−(𝛼	NOUN
iajs-2801	99	69	)	)	PUNCT
iajs-2801	99	70	.	.	PUNCT
iajs-2801	100	1	(	(	PUNCT
iajs-2801	100	2	b	b	X
iajs-2801	100	3	)	)	PUNCT
iajs-2801	100	4	𝜇ω	𝜇ω	NOUN
iajs-2801	101	1	+	+	PROPN
iajs-2801	101	2	(	(	PUNCT
iajs-2801	101	3	𝛼	𝛼	X
iajs-2801	101	4	∗	∗	X
iajs-2801	101	5	δ	δ	PROPN
iajs-2801	101	6	)	)	PUNCT
iajs-2801	101	7	≥	≥	VERB
iajs-2801	101	8	𝑟𝑚𝑖𝑛{𝜇ω	𝑟𝑚𝑖𝑛{𝜇ω	NUM
iajs-2801	101	9	+	+	PROPN
iajs-2801	101	10	(	(	PUNCT
iajs-2801	101	11	(	(	PUNCT
iajs-2801	101	12	𝛼	𝛼	NOUN
iajs-2801	101	13	∗	∗	NOUN
iajs-2801	101	14	(	(	PUNCT
iajs-2801	101	15	𝛽	𝛽	PROPN
iajs-2801	101	16	∗	∗	X
iajs-2801	101	17	δ	δ	PROPN
iajs-2801	101	18	)	)	PUNCT
iajs-2801	101	19	)	)	PUNCT
iajs-2801	101	20	,	,	PUNCT
iajs-2801	101	21	𝜇ω	𝜇ω	ADP
iajs-2801	101	22	+	+	ADJ
iajs-2801	101	23	(	(	PUNCT
iajs-2801	101	24	𝛽	𝛽	NOUN
iajs-2801	101	25	)	)	PUNCT
iajs-2801	101	26	}	}	PUNCT
iajs-2801	101	27	,	,	PUNCT
iajs-2801	101	28	𝜇ω	𝜇ω	NOUN
iajs-2801	101	29	−(𝛼	−(𝛼	NOUN
iajs-2801	101	30	∗	∗	X
iajs-2801	101	31	δ	δ	PROPN
iajs-2801	101	32	)	)	PUNCT
iajs-2801	101	33	≤	≤	NOUN
iajs-2801	101	34	𝑟𝑚𝑎𝑥{𝜇ω	𝑟𝑚𝑎𝑥{𝜇ω	NUM
iajs-2801	101	35	−((𝛼	−((𝛼	PROPN
iajs-2801	101	36	∗	∗	NOUN
iajs-2801	101	37	(	(	PUNCT
iajs-2801	101	38	𝛽	𝛽	PROPN
iajs-2801	101	39	∗	∗	X
iajs-2801	101	40	δ	δ	PROPN
iajs-2801	101	41	)	)	PUNCT
iajs-2801	101	42	)	)	PUNCT
iajs-2801	101	43	,	,	PUNCT
iajs-2801	101	44	𝜇ω	𝜇ω	ADP
iajs-2801	101	45	−(𝛽)}and	−(𝛽)}and	NOUN
iajs-2801	101	46	𝜆ω	𝜆ω	X
iajs-2801	102	1	+	+	ADJ
iajs-2801	102	2	(	(	PUNCT
iajs-2801	102	3	𝛼	𝛼	X
iajs-2801	102	4	∗	∗	X
iajs-2801	102	5	δ	δ	PROPN
iajs-2801	102	6	)	)	PUNCT
iajs-2801	102	7	≥	≥	PROPN
iajs-2801	102	8	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	102	9	{	{	PUNCT
iajs-2801	102	10	𝜆ω	𝜆ω	X
iajs-2801	102	11	+	+	ADJ
iajs-2801	102	12	(	(	PUNCT
iajs-2801	102	13	(	(	PUNCT
iajs-2801	102	14	𝛼	𝛼	NOUN
iajs-2801	102	15	∗	∗	NOUN
iajs-2801	102	16	(	(	PUNCT
iajs-2801	102	17	𝛽	𝛽	NOUN
iajs-2801	102	18	∗	∗	NOUN
iajs-2801	102	19	δ))ˑ	δ))ˑ	NOUN
iajs-2801	102	20	,	,	PUNCT
iajs-2801	102	21	𝜆ω	𝜆ω	ADP
iajs-2801	102	22	+	+	ADJ
iajs-2801	102	23	(	(	PUNCT
iajs-2801	102	24	𝛽	𝛽	NOUN
iajs-2801	102	25	)	)	PUNCT
iajs-2801	102	26	}	}	PUNCT
iajs-2801	102	27	,	,	PUNCT
iajs-2801	102	28	𝜆ω	𝜆ω	ADP
iajs-2801	102	29	−(𝛼	−(𝛼	NOUN
iajs-2801	102	30	∗	∗	X
iajs-2801	102	31	δ	δ	PROPN
iajs-2801	102	32	)	)	PUNCT
iajs-2801	102	33	≤	≤	NUM
iajs-2801	102	34	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-2801	102	35	{	{	PUNCT
iajs-2801	102	36	𝜆ω	𝜆ω	X
iajs-2801	102	37	−((𝛼	−((𝛼	PROPN
iajs-2801	102	38	∗	∗	NOUN
iajs-2801	102	39	(	(	PUNCT
iajs-2801	102	40	𝛽	𝛽	NOUN
iajs-2801	102	41	∗	∗	NOUN
iajs-2801	102	42	δ))ˑ	δ))ˑ	NOUN
iajs-2801	102	43	,	,	PUNCT
iajs-2801	102	44	𝜆ω	𝜆ω	DET
iajs-2801	102	45	−(𝛽	−(𝛽	NOUN
iajs-2801	102	46	)	)	PUNCT
iajs-2801	102	47	}	}	PUNCT
iajs-2801	102	48	,	,	PUNCT
iajs-2801	102	49	(	(	PUNCT
iajs-2801	102	50	c)𝜇ω	c)𝜇ω	PROPN
iajs-2801	102	51	+	+	PROPN
iajs-2801	102	52	(	(	PUNCT
iajs-2801	102	53	𝛼	𝛼	PROPN
iajs-2801	102	54	∘	∘	PROPN
iajs-2801	102	55	𝛽	𝛽	NOUN
iajs-2801	102	56	)	)	PUNCT
iajs-2801	102	57	≥	≥	PROPN
iajs-2801	102	58	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	102	59	{	{	PUNCT
iajs-2801	102	60	𝜇ω	𝜇ω	X
iajs-2801	102	61	+	+	NOUN
iajs-2801	102	62	(	(	PUNCT
iajs-2801	102	63	𝛼)ˑ	𝛼)ˑ	ADJ
iajs-2801	102	64	,	,	PUNCT
iajs-2801	102	65	𝜇ω	𝜇ω	ADP
iajs-2801	102	66	+	+	PROPN
iajs-2801	102	67	(	(	PUNCT
iajs-2801	102	68	𝛽	𝛽	NOUN
iajs-2801	102	69	)	)	PUNCT
iajs-2801	102	70	}	}	PUNCT
iajs-2801	102	71	,	,	PUNCT
iajs-2801	102	72	𝜇ω	𝜇ω	NOUN
iajs-2801	102	73	−(𝛼	−(𝛼	NOUN
iajs-2801	102	74	∘	∘	NOUN
iajs-2801	102	75	𝛽	𝛽	NOUN
iajs-2801	102	76	)	)	PUNCT
iajs-2801	102	77	≤	≤	NOUN
iajs-2801	102	78	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	102	79	{	{	PUNCT
iajs-2801	102	80	�	�	PROPN
iajs-2801	102	81	̃	̃	PROPN
iajs-2801	102	82	�	�	NOUN
iajs-2801	102	83	ω	ω	NUM
iajs-2801	102	84	−(𝛼)ˑ	−(𝛼)ˑ	PROPN
iajs-2801	102	85	,	,	PUNCT
iajs-2801	102	86	𝜇ω	𝜇ω	NOUN
iajs-2801	102	87	−(𝛽	−(𝛽	NOUN
iajs-2801	102	88	)	)	PUNCT
iajs-2801	102	89	}	}	PUNCT
iajs-2801	102	90	𝜆ω	𝜆ω	PUNCT
iajs-2801	103	1	+	+	ADJ
iajs-2801	103	2	(	(	PUNCT
iajs-2801	103	3	𝛼	𝛼	PROPN
iajs-2801	103	4	∘	∘	PROPN
iajs-2801	103	5	𝛽	𝛽	NOUN
iajs-2801	103	6	)	)	PUNCT
iajs-2801	103	7	≥	≥	NOUN
iajs-2801	103	8	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	103	9	{	{	PUNCT
iajs-2801	103	10	𝜆ω	𝜆ω	X
iajs-2801	103	11	+	+	ADJ
iajs-2801	103	12	(	(	PUNCT
iajs-2801	103	13	𝛼)ˑ	𝛼)ˑ	ADJ
iajs-2801	103	14	,	,	PUNCT
iajs-2801	103	15	𝜆ω	𝜆ω	X
iajs-2801	103	16	+	+	ADJ
iajs-2801	103	17	(	(	PUNCT
iajs-2801	103	18	𝛽	𝛽	NOUN
iajs-2801	103	19	)	)	PUNCT
iajs-2801	103	20	}	}	PUNCT
iajs-2801	103	21	,	,	PUNCT
iajs-2801	103	22	𝜆ω	𝜆ω	ADP
iajs-2801	103	23	−(𝛼	−(𝛼	NOUN
iajs-2801	103	24	∘	∘	NOUN
iajs-2801	103	25	𝛽	𝛽	NOUN
iajs-2801	103	26	)	)	PUNCT
iajs-2801	103	27	≤	≤	NUM
iajs-2801	103	28	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	103	29	{	{	PUNCT
iajs-2801	103	30	𝜆ω	𝜆ω	NOUN
iajs-2801	103	31	−(𝛼)ˑ	−(𝛼)ˑ	PROPN
iajs-2801	103	32	,	,	PUNCT
iajs-2801	103	33	𝜆ω	𝜆ω	DET
iajs-2801	103	34	−(𝛽	−(𝛽	NOUN
iajs-2801	103	35	)	)	PUNCT
iajs-2801	103	36	}	}	PUNCT
iajs-2801	103	37	.	.	PUNCT
iajs-2801	104	1	3	3	X
iajs-2801	104	2	.	.	X
iajs-2801	104	3	a	a	DET
iajs-2801	104	4	cubic	cubic	ADJ
iajs-2801	104	5	bipolark	bipolark	NOUN
iajs-2801	104	6	-	-	PUNCT
iajs-2801	104	7	ideal	ideal	NOUN
iajs-2801	104	8	underhomomorphism	underhomomorphism	NOUN
iajs-2801	104	9	we	we	PRON
iajs-2801	104	10	study	study	VERB
iajs-2801	104	11	some	some	DET
iajs-2801	104	12	definitions	definition	NOUN
iajs-2801	104	13	of	of	ADP
iajs-2801	104	14	homomorphism	homomorphism	NOUN
iajs-2801	104	15	;	;	PUNCT
iajs-2801	104	16	the	the	DET
iajs-2801	104	17	product	product	NOUN
iajs-2801	104	18	of	of	ADP
iajs-2801	104	19	cubic	cubic	ADJ
iajs-2801	104	20	bipolar	bipolar	ADJ
iajs-2801	104	21	k	k	NOUN
iajs-2801	104	22	-	-	NOUN
iajs-2801	104	23	ideals	ideal	NOUN
iajs-2801	104	24	and	and	CCONJ
iajs-2801	104	25	a	a	DET
iajs-2801	104	26	cubic	cubic	ADJ
iajs-2801	104	27	bipolar	bipolar	ADJ
iajs-2801	104	28	ideal	ideal	NOUN
iajs-2801	104	29	.	.	PUNCT
iajs-2801	105	1	also	also	ADV
iajs-2801	105	2	some	some	DET
iajs-2801	105	3	theorems	theorem	NOUN
iajs-2801	105	4	are	be	AUX
iajs-2801	105	5	discussed	discuss	VERB
iajs-2801	105	6	.	.	PUNCT
iajs-2801	106	1	definition	definition	NOUN
iajs-2801	106	2	3.1	3.1	NUM
iajs-2801	106	3	.	.	PUNCT
iajs-2801	107	1	for	for	ADP
iajs-2801	107	2	any	any	DET
iajs-2801	107	3	𝛼	𝛼	PROPN
iajs-2801	107	4	∈	∈	NOUN
iajs-2801	107	5	ℵ.	ℵ.	NOUN
iajs-2801	108	1	we	we	PRON
iajs-2801	108	2	define	define	VERB
iajs-2801	108	3	a	a	DET
iajs-2801	108	4	new	new	ADJ
iajs-2801	108	5	cubicbipolar	cubicbipolar	NOUN
iajs-2801	108	6	fuzzy	fuzzy	NOUN
iajs-2801	108	7	set	set	VERB
iajs-2801	108	8	ω𝑓	ω𝑓	PROPN
iajs-2801	108	9	=	=	SYM
iajs-2801	108	10	(	(	PUNCT
iajs-2801	108	11	𝛼	𝛼	PROPN
iajs-2801	108	12	,	,	PUNCT
iajs-2801	108	13	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	108	14	+	+	PROPN
iajs-2801	108	15	,	,	PUNCT
iajs-2801	108	16	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	108	17	−	−	PROPN
iajs-2801	108	18	,	,	PUNCT
iajs-2801	108	19	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	108	20	−	−	NOUN
iajs-2801	108	21	,	,	PUNCT
iajs-2801	108	22	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	109	1	+	+	ADJ
iajs-2801	109	2	)	)	PUNCT
iajs-2801	109	3	in	in	ADP
iajs-2801	109	4	ℵ	ℵ	NOUN
iajs-2801	109	5	by	by	ADP
iajs-2801	109	6	𝜇𝑓	𝜇𝑓	NOUN
iajs-2801	109	7	−(𝛼	−(𝛼	NOUN
iajs-2801	109	8	)	)	PUNCT
iajs-2801	109	9	=	=	SYM
iajs-2801	109	10	𝜇−(𝑓(𝛼	𝜇−(𝑓(𝛼	PROPN
iajs-2801	109	11	)	)	PUNCT
iajs-2801	109	12	)	)	PUNCT
iajs-2801	110	1	and𝜇𝑓	and𝜇𝑓	PROPN
iajs-2801	110	2	+	+	PROPN
iajs-2801	110	3	(	(	PUNCT
iajs-2801	110	4	𝛼	𝛼	NOUN
iajs-2801	110	5	)	)	PUNCT
iajs-2801	110	6	=	=	SYM
iajs-2801	110	7	𝜇+(𝑓(𝛼)),𝜆𝑓	𝜇+(𝑓(𝛼)),𝜆𝑓	NOUN
iajs-2801	110	8	−(𝛼	−(𝛼	NOUN
iajs-2801	110	9	)	)	PUNCT
iajs-2801	110	10	=	=	SYM
iajs-2801	110	11	𝜆−(𝑓(𝛼	𝜆−(𝑓(𝛼	PROPN
iajs-2801	110	12	)	)	PUNCT
iajs-2801	110	13	)	)	PUNCT
iajs-2801	111	1	and𝜆𝑓	and𝜆𝑓	ADP
iajs-2801	111	2	+	+	NOUN
iajs-2801	111	3	(	(	PUNCT
iajs-2801	111	4	𝛼	𝛼	NOUN
iajs-2801	111	5	)	)	PUNCT
iajs-2801	111	6	=	=	SYM
iajs-2801	112	1	𝜆+(𝑓(𝛼)),where𝑓	𝜆+(𝑓(𝛼)),where𝑓	NOUN
iajs-2801	112	2	:	:	PUNCT
iajs-2801	112	3	ℵ	ℵ	X
iajs-2801	112	4	→	→	SYM
iajs-2801	112	5	ℵ′	ℵ′	PRON
iajs-2801	112	6	is	be	AUX
iajs-2801	112	7	a	a	DET
iajs-2801	112	8	ku	ku	PROPN
iajs-2801	112	9	-	-	PUNCT
iajs-2801	112	10	semigroup	semigroup	NOUN
iajs-2801	112	11	homomorphism	homomorphism	NOUN
iajs-2801	112	12	.	.	PUNCT
iajs-2801	113	1	for	for	ADP
iajs-2801	113	2	short	short	ADJ
iajs-2801	113	3	ω𝑓	ω𝑓	PROPN
iajs-2801	113	4	=	=	SYM
iajs-2801	113	5	(	(	PUNCT
iajs-2801	113	6	𝛼	𝛼	PROPN
iajs-2801	113	7	,	,	PUNCT
iajs-2801	113	8	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	113	9	+	+	PROPN
iajs-2801	113	10	,	,	PUNCT
iajs-2801	113	11	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	113	12	−	−	PROPN
iajs-2801	113	13	,	,	PUNCT
iajs-2801	113	14	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	113	15	−	−	NOUN
iajs-2801	113	16	,	,	PUNCT
iajs-2801	113	17	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	114	1	+	+	NOUN
iajs-2801	114	2	)	)	PUNCT
iajs-2801	114	3	is	be	AUX
iajs-2801	114	4	written	write	VERB
iajs-2801	114	5	ω𝑓	ω𝑓	PROPN
iajs-2801	114	6	and	and	CCONJ
iajs-2801	114	7	a	a	DET
iajs-2801	114	8	cubic	cubic	ADJ
iajs-2801	114	9	bipolar	bipolar	NOUN
iajs-2801	114	10	is	be	AUX
iajs-2801	114	11	acb	acb	NOUN
iajs-2801	114	12	.	.	PUNCT
iajs-2801	114	13	example3.2	example3.2	PROPN
iajs-2801	114	14	.	.	PUNCT
iajs-2801	115	1	in	in	ADP
iajs-2801	115	2	example2.14	example2.14	NOUN
iajs-2801	115	3	,	,	PUNCT
iajs-2801	115	4	we	we	PRON
iajs-2801	115	5	have	have	VERB
iajs-2801	115	6	ℵ′	ℵ′	ADV
iajs-2801	115	7	=	=	SYM
iajs-2801	115	8	{	{	PUNCT
iajs-2801	115	9	0′	0′	NUM
iajs-2801	115	10	,	,	PUNCT
iajs-2801	115	11	𝑎	𝑎	NOUN
iajs-2801	115	12	,	,	PUNCT
iajs-2801	115	13	𝑏	𝑏	NOUN
iajs-2801	115	14	}	}	PUNCT
iajs-2801	115	15	is	be	AUX
iajs-2801	115	16	a	a	DET
iajs-2801	115	17	set	set	NOUN
iajs-2801	115	18	and	and	CCONJ
iajs-2801	115	19	𝑓	𝑓	PRON
iajs-2801	115	20	:	:	PUNCT
iajs-2801	115	21	ℵ	ℵ	X
iajs-2801	115	22	→	→	SYM
iajs-2801	115	23	ℵ′	ℵ′	X
iajs-2801	115	24	is	be	AUX
iajs-2801	115	25	mapping	map	VERB
iajs-2801	115	26	such	such	ADJ
iajs-2801	115	27	that	that	SCONJ
iajs-2801	115	28	𝑓(𝜒	𝑓(𝜒	NOUN
iajs-2801	115	29	)	)	PUNCT
iajs-2801	115	30	=	=	SYM
iajs-2801	115	31	𝜒′	𝜒′	NOUN
iajs-2801	115	32	with	with	ADP
iajs-2801	115	33	two	two	NUM
iajs-2801	115	34	tables	table	NOUN
iajs-2801	115	35	∗	∗	NOUN
iajs-2801	115	36	0	0	NUM
iajs-2801	116	1	1	1	NUM
iajs-2801	116	2	2	2	NUM
iajs-2801	116	3	0	0	NUM
iajs-2801	116	4	0	0	NUM
iajs-2801	116	5	1	1	NUM
iajs-2801	116	6	2	2	NUM
iajs-2801	116	7	1	1	NUM
iajs-2801	116	8	0	0	NUM
iajs-2801	116	9	0	0	NUM
iajs-2801	116	10	1	1	NUM
iajs-2801	116	11	2	2	NUM
iajs-2801	116	12	0	0	NUM
iajs-2801	116	13	1	1	NUM
iajs-2801	116	14	0	0	NUM
iajs-2801	116	15	∘	∘	NUM
iajs-2801	116	16	0	0	NUM
iajs-2801	116	17	1	1	NUM
iajs-2801	116	18	2	2	NUM
iajs-2801	116	19	0	0	NUM
iajs-2801	116	20	0	0	NUM
iajs-2801	116	21	0	0	NUM
iajs-2801	116	22	0	0	NUM
iajs-2801	116	23	1	1	NUM
iajs-2801	116	24	0	0	NUM
iajs-2801	116	25	1	1	NUM
iajs-2801	116	26	0	0	NUM
iajs-2801	116	27	2	2	NUM
iajs-2801	116	28	0	0	NUM
iajs-2801	116	29	0	0	NUM
iajs-2801	116	30	2	2	NUM
iajs-2801	116	31	∗	∗	NOUN
iajs-2801	116	32	0′	0′	NUM
iajs-2801	117	1	a	a	DET
iajs-2801	117	2	b	b	PROPN
iajs-2801	117	3	0′	0′	NUM
iajs-2801	117	4	0′	0′	PROPN
iajs-2801	118	1	a	a	DET
iajs-2801	118	2	b	b	NOUN
iajs-2801	118	3	a	a	PRON
iajs-2801	118	4	0′	0′	NUM
iajs-2801	118	5	0′	0′	NUM
iajs-2801	119	1	b	b	PROPN
iajs-2801	119	2	b	b	PROPN
iajs-2801	119	3	0′	0′	PROPN
iajs-2801	119	4	b	b	PROPN
iajs-2801	119	5	0′	0′	PROPN
iajs-2801	120	1	∘	∘	PROPN
iajs-2801	120	2	0′	0′	PROPN
iajs-2801	121	1	a	a	DET
iajs-2801	121	2	b	b	PROPN
iajs-2801	121	3	0′	0′	PROPN
iajs-2801	121	4	0′	0′	NUM
iajs-2801	121	5	0′	0′	NUM
iajs-2801	121	6	0′	0′	PROPN
iajs-2801	122	1	a	a	DET
iajs-2801	122	2	0′	0′	NOUN
iajs-2801	122	3	a	a	DET
iajs-2801	122	4	0′	0′	PROPN
iajs-2801	122	5	b	b	PROPN
iajs-2801	122	6	0′	0′	PROPN
iajs-2801	122	7	0′	0′	PROPN
iajs-2801	123	1	a	a	DET
iajs-2801	123	2	ibn	ibn	PROPN
iajs-2801	123	3	al	al	PROPN
iajs-2801	123	4	-	-	PUNCT
iajs-2801	123	5	haitham	haitham	PROPN
iajs-2801	123	6	jour	jour	X
iajs-2801	123	7	.	.	PROPN
iajs-2801	123	8	for	for	ADP
iajs-2801	123	9	pure	pure	ADJ
iajs-2801	123	10	&	&	CCONJ
iajs-2801	123	11	appl	appl	PROPN
iajs-2801	123	12	.	.	PUNCT
iajs-2801	124	1	sci	sci	PROPN
iajs-2801	124	2	.	.	PUNCT
iajs-2801	125	1	35(1)2022	35(1)2022	NUM
iajs-2801	125	2	77	77	NUM
iajs-2801	126	1	then	then	ADV
iajs-2801	126	2	𝑓	𝑓	X
iajs-2801	126	3	:	:	PUNCT
iajs-2801	126	4	ℵ	ℵ	X
iajs-2801	126	5	→	→	SYM
iajs-2801	126	6	ℵ′	ℵ′	PRON
iajs-2801	126	7	is	be	AUX
iajs-2801	126	8	a	a	DET
iajs-2801	126	9	ku	ku	PROPN
iajs-2801	126	10	-	-	PUNCT
iajs-2801	126	11	semigroup	semigroup	NOUN
iajs-2801	126	12	homomorphism	homomorphism	NOUN
iajs-2801	126	13	and	and	CCONJ
iajs-2801	126	14	𝑁(𝜒′	𝑁(𝜒′	NOUN
iajs-2801	126	15	)	)	PUNCT
iajs-2801	126	16	=	=	PRON
iajs-2801	126	17	{	{	PUNCT
iajs-2801	126	18	{	{	PUNCT
iajs-2801	126	19	[	[	X
iajs-2801	126	20	−0.2	−0.2	PROPN
iajs-2801	126	21	,	,	PUNCT
iajs-2801	126	22	−0.1	−0.1	PROPN
iajs-2801	126	23	]	]	X
iajs-2801	126	24	,	,	PUNCT
iajs-2801	127	1	[	[	X
iajs-2801	127	2	0.2,0.9	0.2,0.9	X
iajs-2801	127	3	]	]	PUNCT
iajs-2801	127	4	}	}	PUNCT
iajs-2801	127	5	𝑖𝑓	𝑖𝑓	ADP
iajs-2801	127	6	𝜒	𝜒	X
iajs-2801	127	7	=	=	SYM
iajs-2801	127	8	0	0	PUNCT
iajs-2801	127	9	{	{	PUNCT
iajs-2801	127	10	[	[	X
iajs-2801	127	11	−0.8	−0.8	ADJ
iajs-2801	127	12	,	,	PUNCT
iajs-2801	127	13	−0.2	−0.2	PROPN
iajs-2801	127	14	]	]	PUNCT
iajs-2801	127	15	,	,	PUNCT
iajs-2801	127	16	[	[	X
iajs-2801	127	17	0.3,0.5	0.3,0.5	NUM
iajs-2801	127	18	]	]	PUNCT
iajs-2801	127	19	}	}	PUNCT
iajs-2801	127	20	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	NOUN
iajs-2801	127	21	,	,	PUNCT
iajs-2801	127	22	𝜆ω	𝜆ω	X
iajs-2801	127	23	+	+	ADJ
iajs-2801	127	24	(	(	PUNCT
iajs-2801	127	25	𝑥	𝑥	NOUN
iajs-2801	127	26	)	)	PUNCT
iajs-2801	127	27	=	=	NOUN
iajs-2801	127	28	{	{	PUNCT
iajs-2801	127	29	0.6	0.6	NUM
iajs-2801	127	30	𝑖𝑓	𝑖𝑓	NUM
iajs-2801	127	31	𝜒	𝜒	X
iajs-2801	127	32	=	=	SYM
iajs-2801	127	33	0	0	NUM
iajs-2801	127	34	0.2	0.2	NUM
iajs-2801	127	35	𝑖𝑓	𝑖𝑓	NOUN
iajs-2801	127	36	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	PROPN
iajs-2801	127	37	𝜆ω	𝜆ω	ADP
iajs-2801	127	38	−(𝑥	−(𝑥	NOUN
iajs-2801	127	39	)	)	PUNCT
iajs-2801	127	40	=	=	PRON
iajs-2801	128	1	{	{	PUNCT
iajs-2801	128	2	−0.9	−0.9	PROPN
iajs-2801	128	3	𝑖𝑓	𝑖𝑓	X
iajs-2801	128	4	𝜒	𝜒	X
iajs-2801	128	5	=	=	SYM
iajs-2801	128	6	0	0	NUM
iajs-2801	128	7	−0.4	−0.4	NUM
iajs-2801	128	8	𝑖𝑓	𝑖𝑓	ADP
iajs-2801	128	9	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	NOUN
iajs-2801	128	10	we	we	PRON
iajs-2801	128	11	have	have	VERB
iajs-2801	128	12	:	:	PUNCT
iajs-2801	128	13	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	128	14	−(0	−(0	NOUN
iajs-2801	128	15	)	)	PUNCT
iajs-2801	128	16	=	=	SYM
iajs-2801	128	17	𝜇−(𝑓(0	𝜇−(𝑓(0	PROPN
iajs-2801	128	18	)	)	PUNCT
iajs-2801	128	19	)	)	PUNCT
iajs-2801	129	1	=	=	SYM
iajs-2801	129	2	𝜇−(0′	𝜇−(0′	PROPN
iajs-2801	129	3	)	)	PUNCT
iajs-2801	129	4	=	=	PUNCT
iajs-2801	130	1	[	[	X
iajs-2801	130	2	−0.2	−0.2	PROPN
iajs-2801	130	3	,	,	PUNCT
iajs-2801	130	4	−0.1	−0.1	PROPN
iajs-2801	130	5	]	]	PUNCT
iajs-2801	130	6	and	and	CCONJ
iajs-2801	130	7	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	130	8	−(1	−(1	ADJ
iajs-2801	130	9	)	)	PUNCT
iajs-2801	130	10	=	=	SYM
iajs-2801	130	11	𝜇−(𝑓(1	𝜇−(𝑓(1	NOUN
iajs-2801	130	12	)	)	PUNCT
iajs-2801	130	13	)	)	PUNCT
iajs-2801	131	1	=	=	SYM
iajs-2801	131	2	𝜇−(𝑎	𝜇−(𝑎	PROPN
iajs-2801	131	3	)	)	PUNCT
iajs-2801	131	4	=	=	PUNCT
iajs-2801	132	1	[	[	X
iajs-2801	132	2	−0.8	−0.8	PROPN
iajs-2801	132	3	,	,	PUNCT
iajs-2801	132	4	−0.2	−0.2	PROPN
iajs-2801	132	5	]	]	PUNCT
iajs-2801	132	6	and	and	CCONJ
iajs-2801	132	7	so	so	ADV
iajs-2801	132	8	on	on	ADV
iajs-2801	132	9	.	.	PUNCT
iajs-2801	133	1	theorem	theorem	VERB
iajs-2801	133	2	3.3	3.3	NUM
iajs-2801	133	3	.	.	PUNCT
iajs-2801	134	1	let𝑓	let𝑓	NOUN
iajs-2801	134	2	:	:	PUNCT
iajs-2801	134	3	ℵ	ℵ	PROPN
iajs-2801	134	4	→	→	SYM
iajs-2801	134	5	ℵ′	ℵ′	PUNCT
iajs-2801	134	6	be	be	AUX
iajs-2801	134	7	a	a	DET
iajs-2801	134	8	ku	ku	PROPN
iajs-2801	134	9	-	-	PUNCT
iajs-2801	134	10	semigroup	semigroup	NOUN
iajs-2801	134	11	homomorphism	homomorphism	NOUN
iajs-2801	134	12	and	and	CCONJ
iajs-2801	134	13	onto	onto	ADP
iajs-2801	134	14	mapping	mapping	NOUN
iajs-2801	134	15	.	.	PUNCT
iajs-2801	135	1	then	then	ADV
iajs-2801	135	2	ω𝑓is	ω𝑓is	PROPN
iajs-2801	135	3	acb	acb	PROPN
iajs-2801	135	4	k	k	NOUN
iajs-2801	135	5	-	-	NOUN
iajs-2801	135	6	ideal	ideal	NOUN
iajs-2801	135	7	of	of	ADP
iajs-2801	135	8	ℵ′if	ℵ′if	PRON
iajs-2801	135	9	and	and	CCONJ
iajs-2801	135	10	only	only	ADV
iajs-2801	135	11	if	if	SCONJ
iajs-2801	135	12	ω𝑓is	ω𝑓is	PROPN
iajs-2801	135	13	acb	acb	PROPN
iajs-2801	135	14	k	k	NOUN
iajs-2801	135	15	-	-	NOUN
iajs-2801	135	16	ideal	ideal	NOUN
iajs-2801	135	17	of	of	ADP
iajs-2801	135	18	ℵ.	ℵ.	PROPN
iajs-2801	135	19	proof	proof	NOUN
iajs-2801	135	20	.	.	PUNCT
iajs-2801	136	1	for	for	ADP
iajs-2801	136	2	any𝛼	any𝛼	NOUN
iajs-2801	136	3	′	′	NUM
iajs-2801	136	4	∈	∈	PROPN
iajs-2801	136	5	ℵ′	ℵ′	PUNCT
iajs-2801	136	6	there	there	ADV
iajs-2801	136	7	exists𝛼	exists𝛼	NOUN
iajs-2801	136	8	∈	∈	PROPN
iajs-2801	136	9	ℵ	ℵ	ADP
iajs-2801	136	10	such	such	ADJ
iajs-2801	136	11	that𝑓(𝛼	that𝑓(𝛼	NUM
iajs-2801	136	12	)	)	PUNCT
iajs-2801	136	13	=	=	SYM
iajs-2801	136	14	𝛼	𝛼	NOUN
iajs-2801	136	15	′	′	NOUN
iajs-2801	136	16	,	,	PUNCT
iajs-2801	136	17	we	we	PRON
iajs-2801	136	18	have	have	VERB
iajs-2801	136	19	𝜇𝑓	𝜇𝑓	NOUN
iajs-2801	136	20	+	+	ADJ
iajs-2801	136	21	(	(	PUNCT
iajs-2801	136	22	0	0	NUM
iajs-2801	136	23	)	)	PUNCT
iajs-2801	136	24	=	=	SYM
iajs-2801	136	25	𝜇+(𝑓(0	𝜇+(𝑓(0	PROPN
iajs-2801	136	26	)	)	PUNCT
iajs-2801	136	27	)	)	PUNCT
iajs-2801	137	1	=	=	SYM
iajs-2801	137	2	𝜇+(0′	𝜇+(0′	PROPN
iajs-2801	137	3	)	)	PUNCT
iajs-2801	137	4	≥	≥	NUM
iajs-2801	137	5	𝜇+(𝛼	𝜇+(𝛼	NUM
iajs-2801	137	6	′	′	NUM
iajs-2801	137	7	)	)	PUNCT
iajs-2801	137	8	=	=	SYM
iajs-2801	137	9	𝜇+(𝑓(𝛼	𝜇+(𝑓(𝛼	PROPN
iajs-2801	137	10	)	)	PUNCT
iajs-2801	137	11	)	)	PUNCT
iajs-2801	138	1	=	=	PUNCT
iajs-2801	138	2	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	139	1	+	+	ADJ
iajs-2801	139	2	(	(	PUNCT
iajs-2801	139	3	𝛼	𝛼	NOUN
iajs-2801	139	4	)	)	PUNCT
iajs-2801	139	5	and𝜇𝑓	and𝜇𝑓	ADJ
iajs-2801	139	6	−(0	−(0	NOUN
iajs-2801	139	7	)	)	PUNCT
iajs-2801	139	8	=	=	SYM
iajs-2801	139	9	𝜇−(𝑓(0	𝜇−(𝑓(0	PROPN
iajs-2801	139	10	)	)	PUNCT
iajs-2801	139	11	)	)	PUNCT
iajs-2801	140	1	=	=	SYM
iajs-2801	140	2	𝜇−(0′	𝜇−(0′	PROPN
iajs-2801	140	3	)	)	PUNCT
iajs-2801	140	4	≤	≤	NOUN
iajs-2801	140	5	𝜇−(𝛼	𝜇−(𝛼	ADV
iajs-2801	140	6	′	′	NOUN
iajs-2801	140	7	)	)	PUNCT
iajs-2801	140	8	=	=	SYM
iajs-2801	140	9	𝜇−(𝑓(𝛼	𝜇−(𝑓(𝛼	PROPN
iajs-2801	140	10	)	)	PUNCT
iajs-2801	140	11	)	)	PUNCT
iajs-2801	141	1	=	=	SYM
iajs-2801	141	2	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	141	3	−(𝛼	−(𝛼	NOUN
iajs-2801	141	4	)	)	PUNCT
iajs-2801	141	5	.	.	PUNCT
iajs-2801	142	1	also	also	ADV
iajs-2801	142	2	,	,	PUNCT
iajs-2801	142	3	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	143	1	+	+	ADJ
iajs-2801	143	2	(	(	PUNCT
iajs-2801	143	3	0	0	NUM
iajs-2801	143	4	)	)	PUNCT
iajs-2801	143	5	=	=	SYM
iajs-2801	143	6	𝜆+(𝑓(0	𝜆+(𝑓(0	PROPN
iajs-2801	143	7	)	)	PUNCT
iajs-2801	143	8	)	)	PUNCT
iajs-2801	144	1	=	=	PUNCT
iajs-2801	144	2	𝜆+(0′	𝜆+(0′	PROPN
iajs-2801	144	3	)	)	PUNCT
iajs-2801	144	4	≥	≥	NOUN
iajs-2801	144	5	𝜆+(𝛼	𝜆+(𝛼	NOUN
iajs-2801	144	6	)	)	PUNCT
iajs-2801	144	7	=	=	SYM
iajs-2801	144	8	𝜆+(𝑓(𝛼	𝜆+(𝑓(𝛼	PROPN
iajs-2801	144	9	)	)	PUNCT
iajs-2801	144	10	)	)	PUNCT
iajs-2801	145	1	=	=	PUNCT
iajs-2801	145	2	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	146	1	+	+	ADJ
iajs-2801	146	2	(	(	PUNCT
iajs-2801	146	3	𝛼	𝛼	NOUN
iajs-2801	146	4	)	)	PUNCT
iajs-2801	146	5	and𝜆𝑓	and𝜆𝑓	NOUN
iajs-2801	146	6	−(0	−(0	NOUN
iajs-2801	146	7	)	)	PUNCT
iajs-2801	146	8	=	=	SYM
iajs-2801	146	9	𝜆−(𝑓(0	𝜆−(𝑓(0	PROPN
iajs-2801	146	10	)	)	PUNCT
iajs-2801	146	11	)	)	PUNCT
iajs-2801	147	1	=	=	SYM
iajs-2801	147	2	𝜆−(0′	𝜆−(0′	PROPN
iajs-2801	147	3	)	)	PUNCT
iajs-2801	147	4	≤	≤	PROPN
iajs-2801	147	5	𝜆−(𝛼	𝜆−(𝛼	VERB
iajs-2801	147	6	′	′	NUM
iajs-2801	147	7	)	)	PUNCT
iajs-2801	147	8	=	=	SYM
iajs-2801	147	9	𝜆−(𝑓(𝛼	𝜆−(𝑓(𝛼	PROPN
iajs-2801	147	10	)	)	PUNCT
iajs-2801	147	11	)	)	PUNCT
iajs-2801	148	1	=	=	PRON
iajs-2801	148	2	𝜆𝑓	𝜆𝑓	PRON
iajs-2801	148	3	−(𝛼	−(𝛼	NOUN
iajs-2801	148	4	)	)	PUNCT
iajs-2801	148	5	.	.	PUNCT
iajs-2801	149	1	let	let	VERB
iajs-2801	149	2	𝛼	𝛼	VERB
iajs-2801	149	3	,	,	PUNCT
iajs-2801	149	4	δ	δ	PROPN
iajs-2801	149	5	∈	∈	PROPN
iajs-2801	149	6	ℵ,𝛾	ℵ,𝛾	PROPN
iajs-2801	149	7	′	′	X
iajs-2801	149	8	∈	∈	PROPN
iajs-2801	149	9	ℵ′	ℵ′	PUNCT
iajs-2801	149	10	then	then	ADV
iajs-2801	149	11	there	there	PRON
iajs-2801	149	12	exists	exist	VERB
iajs-2801	149	13	𝛽	𝛽	PROPN
iajs-2801	149	14	∈	∈	PROPN
iajs-2801	149	15	ℵ	ℵ	ADP
iajs-2801	149	16	such	such	ADJ
iajs-2801	149	17	that	that	DET
iajs-2801	149	18	𝑓(𝛽	𝑓(𝛽	NOUN
iajs-2801	149	19	)	)	PUNCT
iajs-2801	149	20	=	=	NOUN
iajs-2801	149	21	𝛽′.	𝛽′.	NOUN
iajs-2801	149	22	we	we	PRON
iajs-2801	149	23	have	have	VERB
iajs-2801	149	24	𝜇𝑓	𝜇𝑓	NOUN
iajs-2801	150	1	+	+	NOUN
iajs-2801	150	2	(	(	PUNCT
iajs-2801	150	3	𝛼	𝛼	X
iajs-2801	150	4	∗	∗	X
iajs-2801	150	5	δ	δ	PROPN
iajs-2801	150	6	)	)	PUNCT
iajs-2801	150	7	=	=	SYM
iajs-2801	150	8	𝜇+(𝑓(𝛼	𝜇+(𝑓(𝛼	PROPN
iajs-2801	150	9	∗	∗	PROPN
iajs-2801	150	10	δ	δ	PROPN
iajs-2801	150	11	)	)	PUNCT
iajs-2801	150	12	)	)	PUNCT
iajs-2801	151	1	=	=	SYM
iajs-2801	151	2	𝜇+(𝑓(𝛼	𝜇+(𝑓(𝛼	PROPN
iajs-2801	151	3	)	)	PUNCT
iajs-2801	151	4	∗	∗	NOUN
iajs-2801	151	5	𝑓(δ	𝑓(δ	PROPN
iajs-2801	151	6	)	)	PUNCT
iajs-2801	151	7	)	)	PUNCT
iajs-2801	151	8	≥	≥	PROPN
iajs-2801	151	9	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	151	10	{	{	PUNCT
iajs-2801	151	11	𝜇+	𝜇+	PROPN
iajs-2801	151	12	(	(	PUNCT
iajs-2801	151	13	𝑓(𝛼	𝑓(𝛼	PROPN
iajs-2801	151	14	)	)	PUNCT
iajs-2801	151	15	∗	∗	NOUN
iajs-2801	151	16	(	(	PUNCT
iajs-2801	151	17	𝛽′	𝛽′	X
iajs-2801	151	18	∗	∗	NOUN
iajs-2801	151	19	𝑓(δ	𝑓(δ	NOUN
iajs-2801	151	20	)	)	PUNCT
iajs-2801	151	21	)	)	PUNCT
iajs-2801	151	22	,	,	PUNCT
iajs-2801	151	23	𝜇+(𝛽	𝜇+(𝛽	NOUN
iajs-2801	151	24	)	)	PUNCT
iajs-2801	151	25	}	}	PUNCT
iajs-2801	151	26	=	=	SYM
iajs-2801	151	27	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	151	28	{	{	PUNCT
iajs-2801	151	29	�	�	PROPN
iajs-2801	151	30	̃	̃	PROPN
iajs-2801	151	31	�	�	PROPN
iajs-2801	151	32	+(𝑓(𝛼	+(𝑓(𝛼	NUM
iajs-2801	151	33	)	)	PUNCT
iajs-2801	151	34	∗	∗	NOUN
iajs-2801	151	35	(	(	PUNCT
iajs-2801	151	36	𝑓(𝛽	𝑓(𝛽	NOUN
iajs-2801	151	37	)	)	PUNCT
iajs-2801	151	38	∗	∗	NOUN
iajs-2801	151	39	𝑓(δ	𝑓(δ	NOUN
iajs-2801	151	40	)	)	PUNCT
iajs-2801	151	41	)	)	PUNCT
iajs-2801	151	42	}	}	PUNCT
iajs-2801	151	43	,	,	PUNCT
iajs-2801	151	44	𝜇+(𝑓(𝛽	𝜇+(𝑓(𝛽	PROPN
iajs-2801	151	45	)	)	PUNCT
iajs-2801	151	46	}	}	PUNCT
iajs-2801	151	47	=	=	SYM
iajs-2801	151	48	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	151	49	{	{	PUNCT
iajs-2801	151	50	�	�	PROPN
iajs-2801	151	51	̃	̃	NOUN
iajs-2801	151	52	�	�	PROPN
iajs-2801	151	53	𝑓	𝑓	PROPN
iajs-2801	151	54	+	+	PROPN
iajs-2801	151	55	(	(	PUNCT
iajs-2801	151	56	𝛼	𝛼	NOUN
iajs-2801	151	57	∗	∗	NOUN
iajs-2801	151	58	(	(	PUNCT
iajs-2801	151	59	𝛽	𝛽	PROPN
iajs-2801	151	60	∗	∗	X
iajs-2801	151	61	δ	δ	PROPN
iajs-2801	151	62	)	)	PUNCT
iajs-2801	151	63	)	)	PUNCT
iajs-2801	151	64	,	,	PUNCT
iajs-2801	151	65	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	151	66	+	+	ADJ
iajs-2801	151	67	(	(	PUNCT
iajs-2801	151	68	𝛽	𝛽	NOUN
iajs-2801	151	69	)	)	PUNCT
iajs-2801	151	70	}	}	PUNCT
iajs-2801	151	71	.	.	PUNCT
iajs-2801	152	1	and	and	CCONJ
iajs-2801	152	2	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	152	3	−(𝛼	−(𝛼	PROPN
iajs-2801	152	4	∗	∗	PROPN
iajs-2801	152	5	δ	δ	PROPN
iajs-2801	152	6	)	)	PUNCT
iajs-2801	152	7	=	=	PUNCT
iajs-2801	152	8	𝜇−(𝑓(𝛼	𝜇−(𝑓(𝛼	PROPN
iajs-2801	152	9	∗	∗	PROPN
iajs-2801	152	10	δ	δ	PROPN
iajs-2801	152	11	)	)	PUNCT
iajs-2801	152	12	)	)	PUNCT
iajs-2801	153	1	=	=	PUNCT
iajs-2801	153	2	𝜇−(𝑓(𝛼	𝜇−(𝑓(𝛼	PROPN
iajs-2801	153	3	)	)	PUNCT
iajs-2801	153	4	∗	∗	NOUN
iajs-2801	153	5	𝑓(δ	𝑓(δ	PROPN
iajs-2801	153	6	)	)	PUNCT
iajs-2801	153	7	)	)	PUNCT
iajs-2801	153	8	≤	≤	NUM
iajs-2801	153	9	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	153	10	{	{	PUNCT
iajs-2801	153	11	𝜇−	𝜇−	PROPN
iajs-2801	153	12	(	(	PUNCT
iajs-2801	153	13	𝑓(𝛼	𝑓(𝛼	PROPN
iajs-2801	153	14	)	)	PUNCT
iajs-2801	153	15	∗	∗	NOUN
iajs-2801	153	16	(	(	PUNCT
iajs-2801	153	17	𝛽′	𝛽′	X
iajs-2801	153	18	∗	∗	NOUN
iajs-2801	153	19	𝑓(δ	𝑓(δ	NOUN
iajs-2801	153	20	)	)	PUNCT
iajs-2801	153	21	)	)	PUNCT
iajs-2801	153	22	,	,	PUNCT
iajs-2801	153	23	𝜇−(𝛽′	𝜇−(𝛽′	PROPN
iajs-2801	153	24	)	)	PUNCT
iajs-2801	153	25	}	}	PUNCT
iajs-2801	153	26	=	=	PUNCT
iajs-2801	153	27	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	153	28	{	{	PUNCT
iajs-2801	153	29	𝜇−(𝑓(𝛼	𝜇−(𝑓(𝛼	PROPN
iajs-2801	153	30	)	)	PUNCT
iajs-2801	153	31	∗	∗	NOUN
iajs-2801	153	32	(	(	PUNCT
iajs-2801	153	33	𝑓(𝛽	𝑓(𝛽	NOUN
iajs-2801	153	34	)	)	PUNCT
iajs-2801	153	35	∗	∗	NOUN
iajs-2801	153	36	𝑓(δ	𝑓(δ	NOUN
iajs-2801	153	37	)	)	PUNCT
iajs-2801	153	38	)	)	PUNCT
iajs-2801	153	39	}	}	PUNCT
iajs-2801	153	40	,	,	PUNCT
iajs-2801	153	41	𝜇−(𝑓(𝛽	𝜇−(𝑓(𝛽	NOUN
iajs-2801	153	42	)	)	PUNCT
iajs-2801	153	43	}	}	PUNCT
iajs-2801	153	44	=	=	PUNCT
iajs-2801	153	45	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	153	46	{	{	PUNCT
iajs-2801	153	47	𝜇𝑓	𝜇𝑓	NOUN
iajs-2801	153	48	−(𝛼	−(𝛼	PROPN
iajs-2801	153	49	∗	∗	NOUN
iajs-2801	153	50	(	(	PUNCT
iajs-2801	153	51	𝛽	𝛽	PROPN
iajs-2801	153	52	∗	∗	X
iajs-2801	153	53	δ	δ	PROPN
iajs-2801	153	54	)	)	PUNCT
iajs-2801	153	55	)	)	PUNCT
iajs-2801	153	56	,	,	PUNCT
iajs-2801	153	57	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	153	58	−(𝛽	−(𝛽	NOUN
iajs-2801	153	59	)	)	PUNCT
iajs-2801	153	60	}	}	PUNCT
iajs-2801	153	61	.	.	PUNCT
iajs-2801	154	1	also	also	ADV
iajs-2801	154	2	,	,	PUNCT
iajs-2801	154	3	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	155	1	+	+	ADJ
iajs-2801	155	2	(	(	PUNCT
iajs-2801	155	3	𝛼	𝛼	X
iajs-2801	155	4	∗	∗	X
iajs-2801	155	5	δ	δ	PROPN
iajs-2801	155	6	)	)	PUNCT
iajs-2801	155	7	=	=	SYM
iajs-2801	155	8	𝜆+(𝑓(𝛼	𝜆+(𝑓(𝛼	PROPN
iajs-2801	155	9	∗	∗	PROPN
iajs-2801	155	10	δ	δ	PROPN
iajs-2801	155	11	)	)	PUNCT
iajs-2801	155	12	)	)	PUNCT
iajs-2801	156	1	=	=	PUNCT
iajs-2801	156	2	𝜆+(𝑓(𝛼	𝜆+(𝑓(𝛼	PROPN
iajs-2801	156	3	)	)	PUNCT
iajs-2801	156	4	∗	∗	NOUN
iajs-2801	156	5	𝑓(δ	𝑓(δ	PROPN
iajs-2801	156	6	)	)	PUNCT
iajs-2801	156	7	)	)	PUNCT
iajs-2801	157	1	≥	≥	PROPN
iajs-2801	157	2	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	157	3	{	{	PUNCT
iajs-2801	157	4	𝜆+	𝜆+	PUNCT
iajs-2801	157	5	(	(	PUNCT
iajs-2801	157	6	𝑓(𝛼	𝑓(𝛼	PROPN
iajs-2801	157	7	)	)	PUNCT
iajs-2801	157	8	∗	∗	NOUN
iajs-2801	157	9	(	(	PUNCT
iajs-2801	157	10	𝛽′	𝛽′	X
iajs-2801	157	11	∗	∗	NOUN
iajs-2801	157	12	𝑓(δ	𝑓(δ	NOUN
iajs-2801	157	13	)	)	PUNCT
iajs-2801	157	14	)	)	PUNCT
iajs-2801	157	15	,	,	PUNCT
iajs-2801	158	1	𝜆+(𝛽′	𝜆+(𝛽′	X
iajs-2801	158	2	)	)	PUNCT
iajs-2801	158	3	}	}	PUNCT
iajs-2801	158	4	=	=	SYM
iajs-2801	158	5	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	158	6	{	{	PUNCT
iajs-2801	158	7	𝜆+(𝑓(𝛼	𝜆+(𝑓(𝛼	PROPN
iajs-2801	158	8	)	)	PUNCT
iajs-2801	158	9	∗	∗	NOUN
iajs-2801	158	10	(	(	PUNCT
iajs-2801	158	11	𝑓(𝛽	𝑓(𝛽	NOUN
iajs-2801	158	12	)	)	PUNCT
iajs-2801	158	13	∗	∗	NOUN
iajs-2801	158	14	𝑓(δ	𝑓(δ	NOUN
iajs-2801	158	15	)	)	PUNCT
iajs-2801	158	16	)	)	PUNCT
iajs-2801	158	17	}	}	PUNCT
iajs-2801	158	18	,	,	PUNCT
iajs-2801	158	19	𝜆+(𝑓(𝛽	𝜆+(𝑓(𝛽	PROPN
iajs-2801	158	20	)	)	PUNCT
iajs-2801	158	21	}	}	PUNCT
iajs-2801	158	22	=	=	SYM
iajs-2801	158	23	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	158	24	{	{	PUNCT
iajs-2801	158	25	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	159	1	+	+	ADJ
iajs-2801	159	2	(	(	PUNCT
iajs-2801	159	3	𝛼	𝛼	NOUN
iajs-2801	159	4	∗	∗	NOUN
iajs-2801	159	5	(	(	PUNCT
iajs-2801	159	6	𝛽	𝛽	PROPN
iajs-2801	159	7	∗	∗	X
iajs-2801	159	8	δ	δ	PROPN
iajs-2801	159	9	)	)	PUNCT
iajs-2801	159	10	)	)	PUNCT
iajs-2801	159	11	,	,	PUNCT
iajs-2801	159	12	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	160	1	+	+	ADJ
iajs-2801	160	2	(	(	PUNCT
iajs-2801	160	3	𝛽	𝛽	NOUN
iajs-2801	160	4	)	)	PUNCT
iajs-2801	160	5	}	}	PUNCT
iajs-2801	160	6	.	.	PUNCT
iajs-2801	161	1	and	and	CCONJ
iajs-2801	161	2	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	161	3	−(𝛼	−(𝛼	NOUN
iajs-2801	161	4	∗	∗	X
iajs-2801	161	5	δ	δ	PROPN
iajs-2801	161	6	)	)	PUNCT
iajs-2801	161	7	=	=	PUNCT
iajs-2801	162	1	𝜆−(𝑓(𝛼	𝜆−(𝑓(𝛼	PROPN
iajs-2801	162	2	∗	∗	X
iajs-2801	162	3	δ	δ	PROPN
iajs-2801	162	4	)	)	PUNCT
iajs-2801	162	5	)	)	PUNCT
iajs-2801	163	1	=	=	PUNCT
iajs-2801	163	2	𝜆−(𝑓(𝛼	𝜆−(𝑓(𝛼	PROPN
iajs-2801	163	3	)	)	PUNCT
iajs-2801	163	4	∗	∗	NOUN
iajs-2801	163	5	𝑓(δ	𝑓(δ	PROPN
iajs-2801	163	6	)	)	PUNCT
iajs-2801	163	7	)	)	PUNCT
iajs-2801	163	8	≤	≤	NUM
iajs-2801	163	9	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	163	10	{	{	PUNCT
iajs-2801	163	11	𝜆−	𝜆−	X
iajs-2801	163	12	(	(	PUNCT
iajs-2801	163	13	𝑓(𝛼	𝑓(𝛼	PROPN
iajs-2801	163	14	)	)	PUNCT
iajs-2801	163	15	∗	∗	NOUN
iajs-2801	163	16	(	(	PUNCT
iajs-2801	163	17	𝛽′	𝛽′	X
iajs-2801	163	18	∗	∗	NOUN
iajs-2801	163	19	𝑓(δ	𝑓(δ	NOUN
iajs-2801	163	20	)	)	PUNCT
iajs-2801	163	21	)	)	PUNCT
iajs-2801	163	22	,	,	PUNCT
iajs-2801	163	23	𝜆−(𝛽′	𝜆−(𝛽′	PROPN
iajs-2801	163	24	)	)	PUNCT
iajs-2801	163	25	}	}	PUNCT
iajs-2801	163	26	=	=	PUNCT
iajs-2801	163	27	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	163	28	{	{	PUNCT
iajs-2801	163	29	𝜆−(𝑓(𝛼	𝜆−(𝑓(𝛼	NOUN
iajs-2801	163	30	)	)	PUNCT
iajs-2801	163	31	∗	∗	NOUN
iajs-2801	163	32	(	(	PUNCT
iajs-2801	163	33	𝑓(𝛽	𝑓(𝛽	NOUN
iajs-2801	163	34	)	)	PUNCT
iajs-2801	163	35	∗	∗	NOUN
iajs-2801	163	36	𝑓(δ	𝑓(δ	NOUN
iajs-2801	163	37	)	)	PUNCT
iajs-2801	163	38	)	)	PUNCT
iajs-2801	163	39	}	}	PUNCT
iajs-2801	163	40	,	,	PUNCT
iajs-2801	163	41	𝜆−(𝑓(𝛽	𝜆−(𝑓(𝛽	NOUN
iajs-2801	163	42	)	)	PUNCT
iajs-2801	163	43	}	}	PUNCT
iajs-2801	163	44	=	=	PUNCT
iajs-2801	163	45	𝑚𝑎𝑥	𝑚𝑎𝑥	X
iajs-2801	163	46	{	{	PUNCT
iajs-2801	163	47	𝜆𝑓	𝜆𝑓	NOUN
iajs-2801	163	48	−(𝛼	−(𝛼	NOUN
iajs-2801	163	49	∗	∗	NOUN
iajs-2801	163	50	(	(	PUNCT
iajs-2801	163	51	𝛽	𝛽	PROPN
iajs-2801	163	52	∗	∗	X
iajs-2801	163	53	δ	δ	PROPN
iajs-2801	163	54	)	)	PUNCT
iajs-2801	163	55	)	)	PUNCT
iajs-2801	163	56	,	,	PUNCT
iajs-2801	163	57	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	163	58	−(𝛽	−(𝛽	NOUN
iajs-2801	163	59	)	)	PUNCT
iajs-2801	163	60	}	}	PUNCT
iajs-2801	163	61	.	.	PUNCT
iajs-2801	164	1	and	and	CCONJ
iajs-2801	164	2	the	the	DET
iajs-2801	164	3	condition	condition	NOUN
iajs-2801	164	4	(	(	PUNCT
iajs-2801	164	5	c	c	X
iajs-2801	164	6	)	)	PUNCT
iajs-2801	164	7	is	be	AUX
iajs-2801	164	8	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	164	9	+	+	PROPN
iajs-2801	164	10	(	(	PUNCT
iajs-2801	164	11	𝛼	𝛼	PROPN
iajs-2801	164	12	∘	∘	PROPN
iajs-2801	164	13	𝛽	𝛽	NOUN
iajs-2801	164	14	)	)	PUNCT
iajs-2801	164	15	=	=	PUNCT
iajs-2801	165	1	𝜇+(𝑓(𝛼	𝜇+(𝑓(𝛼	PROPN
iajs-2801	165	2	∘	∘	PROPN
iajs-2801	165	3	𝛽	𝛽	NOUN
iajs-2801	165	4	)	)	PUNCT
iajs-2801	165	5	)	)	PUNCT
iajs-2801	166	1	=	=	SYM
iajs-2801	166	2	𝜇+(𝑓(𝛼	𝜇+(𝑓(𝛼	PROPN
iajs-2801	166	3	)	)	PUNCT
iajs-2801	166	4	∘	∘	NOUN
iajs-2801	166	5	𝑓(𝛽	𝑓(𝛽	NOUN
iajs-2801	166	6	)	)	PUNCT
iajs-2801	166	7	)	)	PUNCT
iajs-2801	166	8	≥	≥	PROPN
iajs-2801	166	9	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	PROPN
iajs-2801	166	10	{	{	PUNCT
iajs-2801	166	11	𝜇+(𝑓(𝛼	𝜇+(𝑓(𝛼	PROPN
iajs-2801	166	12	)	)	PUNCT
iajs-2801	166	13	,	,	PUNCT
iajs-2801	166	14	𝜇+(𝑓(𝛽	𝜇+(𝑓(𝛽	PROPN
iajs-2801	166	15	)	)	PUNCT
iajs-2801	166	16	}	}	PUNCT
iajs-2801	166	17	=	=	PUNCT
iajs-2801	167	1	𝑟𝑚𝑖𝑛{𝜇𝑓	𝑟𝑚𝑖𝑛{𝜇𝑓	NUM
iajs-2801	167	2	+	+	ADJ
iajs-2801	167	3	(	(	PUNCT
iajs-2801	167	4	𝛼	𝛼	NOUN
iajs-2801	167	5	)	)	PUNCT
iajs-2801	167	6	,	,	PUNCT
iajs-2801	167	7	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	167	8	+	+	ADJ
iajs-2801	167	9	(	(	PUNCT
iajs-2801	167	10	𝛽	𝛽	NOUN
iajs-2801	167	11	)	)	PUNCT
iajs-2801	167	12	}	}	PUNCT
iajs-2801	167	13	and	and	CCONJ
iajs-2801	167	14	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	167	15	−(𝛼	−(𝛼	NOUN
iajs-2801	167	16	∘	∘	NOUN
iajs-2801	167	17	𝛽	𝛽	NOUN
iajs-2801	167	18	)	)	PUNCT
iajs-2801	167	19	=	=	PUNCT
iajs-2801	168	1	𝜇−(𝑓(𝛼	𝜇−(𝑓(𝛼	PROPN
iajs-2801	168	2	∘	∘	PROPN
iajs-2801	168	3	𝛽	𝛽	NOUN
iajs-2801	168	4	)	)	PUNCT
iajs-2801	168	5	)	)	PUNCT
iajs-2801	169	1	=	=	SYM
iajs-2801	169	2	𝜇−(𝑓(𝛼	𝜇−(𝑓(𝛼	PROPN
iajs-2801	169	3	)	)	PUNCT
iajs-2801	169	4	∘	∘	NOUN
iajs-2801	169	5	𝑓(𝛽	𝑓(𝛽	NOUN
iajs-2801	169	6	)	)	PUNCT
iajs-2801	169	7	)	)	PUNCT
iajs-2801	169	8	≤	≤	NUM
iajs-2801	169	9	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	169	10	{	{	PUNCT
iajs-2801	169	11	𝜇−(𝑓(𝛼	𝜇−(𝑓(𝛼	PROPN
iajs-2801	169	12	)	)	PUNCT
iajs-2801	169	13	,	,	PUNCT
iajs-2801	169	14	𝜇−(𝑓(𝛽	𝜇−(𝑓(𝛽	NOUN
iajs-2801	169	15	)	)	PUNCT
iajs-2801	169	16	}	}	PUNCT
iajs-2801	169	17	=	=	SYM
iajs-2801	169	18	𝑟𝑚𝑎𝑥{𝜇𝑓	𝑟𝑚𝑎𝑥{𝜇𝑓	NUM
iajs-2801	169	19	−(𝛼	−(𝛼	NOUN
iajs-2801	169	20	)	)	PUNCT
iajs-2801	169	21	,	,	PUNCT
iajs-2801	169	22	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	169	23	−(𝛽	−(𝛽	NOUN
iajs-2801	169	24	)	)	PUNCT
iajs-2801	169	25	}	}	PUNCT
iajs-2801	169	26	also	also	ADV
iajs-2801	169	27	,	,	PUNCT
iajs-2801	169	28	𝜆𝑓	𝜆𝑓	X
iajs-2801	170	1	+	+	ADJ
iajs-2801	170	2	(	(	PUNCT
iajs-2801	170	3	𝛼	𝛼	PROPN
iajs-2801	170	4	∘	∘	PROPN
iajs-2801	170	5	𝛽	𝛽	NOUN
iajs-2801	170	6	)	)	PUNCT
iajs-2801	170	7	=	=	PUNCT
iajs-2801	170	8	𝜆+(𝑓(𝛼	𝜆+(𝑓(𝛼	PROPN
iajs-2801	170	9	∘	∘	PROPN
iajs-2801	170	10	𝛽	𝛽	NOUN
iajs-2801	170	11	)	)	PUNCT
iajs-2801	170	12	)	)	PUNCT
iajs-2801	171	1	=	=	PUNCT
iajs-2801	171	2	𝜆+(𝑓(𝛼	𝜆+(𝑓(𝛼	PROPN
iajs-2801	171	3	)	)	PUNCT
iajs-2801	171	4	∘	∘	NOUN
iajs-2801	171	5	𝑓(𝛽	𝑓(𝛽	NOUN
iajs-2801	171	6	)	)	PUNCT
iajs-2801	171	7	)	)	PUNCT
iajs-2801	171	8	≥	≥	PROPN
iajs-2801	171	9	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
iajs-2801	171	10	{	{	PUNCT
iajs-2801	171	11	𝜆+(𝑓(𝛼	𝜆+(𝑓(𝛼	PROPN
iajs-2801	171	12	)	)	PUNCT
iajs-2801	171	13	,	,	PUNCT
iajs-2801	171	14	𝜆+(𝑓(𝛽	𝜆+(𝑓(𝛽	PROPN
iajs-2801	171	15	)	)	PUNCT
iajs-2801	171	16	}	}	PUNCT
iajs-2801	171	17	=	=	PUNCT
iajs-2801	171	18	𝑚𝑖𝑛{𝜆𝑓	𝑚𝑖𝑛{𝜆𝑓	PUNCT
iajs-2801	171	19	+	+	ADJ
iajs-2801	171	20	(	(	PUNCT
iajs-2801	171	21	𝛼	𝛼	NOUN
iajs-2801	171	22	)	)	PUNCT
iajs-2801	171	23	,	,	PUNCT
iajs-2801	171	24	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	172	1	+	+	ADJ
iajs-2801	172	2	(	(	PUNCT
iajs-2801	172	3	𝛽	𝛽	NOUN
iajs-2801	172	4	)	)	PUNCT
iajs-2801	172	5	}	}	PUNCT
iajs-2801	172	6	ibn	ibn	PROPN
iajs-2801	172	7	al	al	PROPN
iajs-2801	172	8	-	-	PUNCT
iajs-2801	172	9	haitham	haitham	PROPN
iajs-2801	172	10	jour	jour	X
iajs-2801	172	11	.	.	PROPN
iajs-2801	172	12	for	for	ADP
iajs-2801	172	13	pure	pure	ADJ
iajs-2801	172	14	&	&	CCONJ
iajs-2801	172	15	appl	appl	PROPN
iajs-2801	172	16	.	.	PUNCT
iajs-2801	173	1	sci	sci	PROPN
iajs-2801	173	2	.	.	PUNCT
iajs-2801	174	1	35(1)2022	35(1)2022	NUM
iajs-2801	174	2	78	78	NUM
iajs-2801	174	3	and	and	CCONJ
iajs-2801	174	4	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	174	5	−(𝛼	−(𝛼	NOUN
iajs-2801	174	6	∘	∘	NOUN
iajs-2801	174	7	𝛽	𝛽	NOUN
iajs-2801	174	8	)	)	PUNCT
iajs-2801	174	9	=	=	PUNCT
iajs-2801	175	1	𝜆−(𝑓(𝛼	𝜆−(𝑓(𝛼	VERB
iajs-2801	175	2	∘	∘	NUM
iajs-2801	175	3	𝛽	𝛽	NOUN
iajs-2801	175	4	)	)	PUNCT
iajs-2801	175	5	)	)	PUNCT
iajs-2801	176	1	=	=	PUNCT
iajs-2801	176	2	𝜆−(𝑓(𝛼	𝜆−(𝑓(𝛼	PROPN
iajs-2801	176	3	)	)	PUNCT
iajs-2801	176	4	∘	∘	NOUN
iajs-2801	176	5	𝑓(𝛽	𝑓(𝛽	NOUN
iajs-2801	176	6	)	)	PUNCT
iajs-2801	176	7	)	)	PUNCT
iajs-2801	177	1	≤	≤	NUM
iajs-2801	177	2	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	177	3	{	{	PUNCT
iajs-2801	177	4	𝜆−(𝑓(𝛼	𝜆−(𝑓(𝛼	PROPN
iajs-2801	177	5	)	)	PUNCT
iajs-2801	177	6	,	,	PUNCT
iajs-2801	177	7	𝜆−(𝑓(𝛽	𝜆−(𝑓(𝛽	NOUN
iajs-2801	177	8	)	)	PUNCT
iajs-2801	177	9	}	}	PUNCT
iajs-2801	177	10	=	=	SYM
iajs-2801	177	11	𝑚𝑎𝑥{𝜆𝑓	𝑚𝑎𝑥{𝜆𝑓	PUNCT
iajs-2801	177	12	−(𝛼	−(𝛼	NOUN
iajs-2801	177	13	)	)	PUNCT
iajs-2801	177	14	,	,	PUNCT
iajs-2801	177	15	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	177	16	−(𝛽	−(𝛽	NOUN
iajs-2801	177	17	)	)	PUNCT
iajs-2801	177	18	}	}	PUNCT
iajs-2801	177	19	conversely	conversely	ADV
iajs-2801	177	20	,	,	PUNCT
iajs-2801	177	21	since	since	SCONJ
iajs-2801	177	22	𝑓	𝑓	PRON
iajs-2801	177	23	:	:	PUNCT
iajs-2801	177	24	ℵ	ℵ	X
iajs-2801	177	25	→	→	SYM
iajs-2801	177	26	ℵ′	ℵ′	PRON
iajs-2801	177	27	is	be	AUX
iajs-2801	177	28	an	an	PRON
iajs-2801	177	29	onto	onto	ADP
iajs-2801	177	30	mapping	mapping	NOUN
iajs-2801	177	31	,	,	PUNCT
iajs-2801	177	32	then	then	ADV
iajs-2801	177	33	for	for	ADP
iajs-2801	177	34	any	any	DET
iajs-2801	177	35	𝛼	𝛼	PROPN
iajs-2801	177	36	,	,	PUNCT
iajs-2801	177	37	𝛽	𝛽	PROPN
iajs-2801	177	38	,	,	PUNCT
iajs-2801	177	39	δ	δ	PROPN
iajs-2801	177	40	∈	∈	PROPN
iajs-2801	177	41	ℵ′.	ℵ′.	SCONJ
iajs-2801	177	42	it	it	PRON
iajs-2801	177	43	follows	follow	VERB
iajs-2801	177	44	that	that	SCONJ
iajs-2801	177	45	,	,	PUNCT
iajs-2801	177	46	there	there	PRON
iajs-2801	177	47	exists	exist	VERB
iajs-2801	177	48	𝒂	𝒂	PRON
iajs-2801	177	49	,	,	PUNCT
iajs-2801	177	50	𝒃	𝒃	NOUN
iajs-2801	177	51	,	,	PUNCT
iajs-2801	177	52	𝒄	𝒄	PROPN
iajs-2801	177	53	∈	∈	PROPN
iajs-2801	177	54	ℵsuch	ℵsuch	ADJ
iajs-2801	177	55	that	that	SCONJ
iajs-2801	177	56	𝑓(𝒂	𝑓(𝒂	PROPN
iajs-2801	177	57	)	)	PUNCT
iajs-2801	177	58	=	=	SYM
iajs-2801	177	59	𝛼	𝛼	X
iajs-2801	177	60	,	,	PUNCT
iajs-2801	177	61	𝑓(𝒃	𝑓(𝒃	PROPN
iajs-2801	177	62	)	)	PUNCT
iajs-2801	177	63	=	=	SYM
iajs-2801	177	64	𝛽	𝛽	NOUN
iajs-2801	177	65	and	and	CCONJ
iajs-2801	177	66	𝑓(𝒄	𝑓(𝒄	NUM
iajs-2801	177	67	)	)	PUNCT
iajs-2801	178	1	=	=	SYM
iajs-2801	178	2	δ	δ	PROPN
iajs-2801	178	3	.	.	PUNCT
iajs-2801	179	1	we	we	PRON
iajs-2801	179	2	have	have	VERB
iajs-2801	179	3	𝜇𝑓	𝜇𝑓	NOUN
iajs-2801	179	4	+	+	NOUN
iajs-2801	179	5	(	(	PUNCT
iajs-2801	179	6	𝛼	𝛼	X
iajs-2801	179	7	∗	∗	X
iajs-2801	179	8	δ	δ	PROPN
iajs-2801	179	9	)	)	PUNCT
iajs-2801	179	10	=	=	SYM
iajs-2801	179	11	𝜇+(𝑓(𝒂	𝜇+(𝑓(𝒂	NOUN
iajs-2801	179	12	)	)	PUNCT
iajs-2801	179	13	∗	∗	NOUN
iajs-2801	179	14	𝑓(𝒄	𝑓(𝒄	NUM
iajs-2801	179	15	)	)	PUNCT
iajs-2801	179	16	)	)	PUNCT
iajs-2801	179	17	)	)	PUNCT
iajs-2801	180	1	=	=	PRON
iajs-2801	180	2	𝜇+(𝑓(𝒂	𝜇+(𝑓(𝒂	PROPN
iajs-2801	180	3	∗	∗	NOUN
iajs-2801	180	4	𝒄	𝒄	NOUN
iajs-2801	180	5	)	)	PUNCT
iajs-2801	180	6	)	)	PUNCT
iajs-2801	181	1	=	=	PUNCT
iajs-2801	181	2	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	182	1	+	+	NOUN
iajs-2801	182	2	(	(	PUNCT
iajs-2801	182	3	𝒂	𝒂	NOUN
iajs-2801	182	4	∗	∗	NOUN
iajs-2801	182	5	𝒄	𝒄	NOUN
iajs-2801	182	6	)	)	PUNCT
iajs-2801	182	7	≥	≥	PROPN
iajs-2801	182	8	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	182	9	{	{	PUNCT
iajs-2801	182	10	�	�	PROPN
iajs-2801	182	11	̃	̃	NOUN
iajs-2801	182	12	�	�	PROPN
iajs-2801	182	13	𝑓	𝑓	PROPN
iajs-2801	182	14	+	+	ADJ
iajs-2801	182	15	(	(	PUNCT
iajs-2801	182	16	𝒂	𝒂	NOUN
iajs-2801	182	17	∗	∗	NOUN
iajs-2801	182	18	(	(	PUNCT
iajs-2801	182	19	𝒃	𝒃	NOUN
iajs-2801	182	20	∗	∗	NOUN
iajs-2801	182	21	𝒄	𝒄	NOUN
iajs-2801	182	22	)	)	PUNCT
iajs-2801	182	23	)	)	PUNCT
iajs-2801	182	24	,	,	PUNCT
iajs-2801	182	25	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	182	26	+	+	ADJ
iajs-2801	182	27	(	(	PUNCT
iajs-2801	182	28	𝒃	𝒃	NOUN
iajs-2801	182	29	)	)	PUNCT
iajs-2801	182	30	}	}	PUNCT
iajs-2801	182	31	=	=	SYM
iajs-2801	182	32	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	182	33	{	{	PUNCT
iajs-2801	182	34	𝜇+(𝑓(𝒂	𝜇+(𝑓(𝒂	PROPN
iajs-2801	182	35	)	)	PUNCT
iajs-2801	182	36	∗	∗	NOUN
iajs-2801	182	37	(	(	PUNCT
iajs-2801	182	38	𝑓(𝒃	𝑓(𝒃	PROPN
iajs-2801	182	39	)	)	PUNCT
iajs-2801	182	40	∗	∗	NOUN
iajs-2801	182	41	𝑓(𝒄	𝑓(𝒄	NUM
iajs-2801	182	42	)	)	PUNCT
iajs-2801	182	43	)	)	PUNCT
iajs-2801	182	44	}	}	PUNCT
iajs-2801	182	45	,	,	PUNCT
iajs-2801	182	46	𝜇+(𝑓(𝒃	𝜇+(𝑓(𝒃	PROPN
iajs-2801	182	47	)	)	PUNCT
iajs-2801	182	48	}	}	PUNCT
iajs-2801	182	49	=	=	SYM
iajs-2801	182	50	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	182	51	{	{	PUNCT
iajs-2801	182	52	𝜇+(𝛼	𝜇+(𝛼	X
iajs-2801	182	53	∗	∗	NOUN
iajs-2801	182	54	(	(	PUNCT
iajs-2801	182	55	𝛽	𝛽	NOUN
iajs-2801	182	56	∗	∗	X
iajs-2801	182	57	δ	δ	PROPN
iajs-2801	182	58	)	)	PUNCT
iajs-2801	182	59	)	)	PUNCT
iajs-2801	182	60	,	,	PUNCT
iajs-2801	182	61	𝜇+(𝛽	𝜇+(𝛽	NOUN
iajs-2801	182	62	)	)	PUNCT
iajs-2801	182	63	}	}	PUNCT
iajs-2801	182	64	.	.	PUNCT
iajs-2801	183	1	and	and	CCONJ
iajs-2801	183	2	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	183	3	−(𝛼	−(𝛼	PROPN
iajs-2801	183	4	∗	∗	PROPN
iajs-2801	183	5	δ	δ	PROPN
iajs-2801	183	6	)	)	PUNCT
iajs-2801	183	7	=	=	SYM
iajs-2801	183	8	𝜇−(𝑓(𝒂	𝜇−(𝑓(𝒂	NOUN
iajs-2801	183	9	)	)	PUNCT
iajs-2801	183	10	∗	∗	NOUN
iajs-2801	183	11	𝑓(𝒄	𝑓(𝒄	NUM
iajs-2801	183	12	)	)	PUNCT
iajs-2801	183	13	)	)	PUNCT
iajs-2801	183	14	)	)	PUNCT
iajs-2801	184	1	=	=	PUNCT
iajs-2801	184	2	𝜇−(𝑓(𝒂	𝜇−(𝑓(𝒂	NOUN
iajs-2801	184	3	∗	∗	NOUN
iajs-2801	184	4	𝒄	𝒄	NOUN
iajs-2801	184	5	)	)	PUNCT
iajs-2801	184	6	)	)	PUNCT
iajs-2801	185	1	=	=	SYM
iajs-2801	185	2	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	185	3	−(𝒂	−(𝒂	NOUN
iajs-2801	185	4	∗	∗	X
iajs-2801	185	5	𝒄	𝒄	NOUN
iajs-2801	185	6	)	)	PUNCT
iajs-2801	185	7	≤	≤	NOUN
iajs-2801	186	1	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	186	2	{	{	PUNCT
iajs-2801	186	3	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	186	4	−(𝒂	−(𝒂	PROPN
iajs-2801	186	5	∗	∗	NOUN
iajs-2801	186	6	(	(	PUNCT
iajs-2801	186	7	𝒃	𝒃	NOUN
iajs-2801	186	8	∗	∗	NOUN
iajs-2801	186	9	𝒄	𝒄	NOUN
iajs-2801	186	10	)	)	PUNCT
iajs-2801	186	11	)	)	PUNCT
iajs-2801	186	12	,	,	PUNCT
iajs-2801	186	13	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	186	14	−(𝒃	−(𝒃	NOUN
iajs-2801	186	15	)	)	PUNCT
iajs-2801	186	16	}	}	PUNCT
iajs-2801	187	1	=	=	PUNCT
iajs-2801	187	2	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	187	3	{	{	PUNCT
iajs-2801	187	4	�	�	PROPN
iajs-2801	187	5	̃	̃	NOUN
iajs-2801	187	6	�	�	NOUN
iajs-2801	187	7	−(𝑓(𝒂	−(𝑓(𝒂	NOUN
iajs-2801	187	8	)	)	PUNCT
iajs-2801	187	9	∗	∗	NOUN
iajs-2801	187	10	(	(	PUNCT
iajs-2801	187	11	𝑓(𝒃	𝑓(𝒃	PROPN
iajs-2801	187	12	)	)	PUNCT
iajs-2801	187	13	∗	∗	NOUN
iajs-2801	187	14	𝑓(𝒄	𝑓(𝒄	NUM
iajs-2801	187	15	)	)	PUNCT
iajs-2801	187	16	)	)	PUNCT
iajs-2801	187	17	}	}	PUNCT
iajs-2801	187	18	,	,	PUNCT
iajs-2801	187	19	𝜇−(𝑓(𝒃	𝜇−(𝑓(𝒃	PROPN
iajs-2801	187	20	)	)	PUNCT
iajs-2801	187	21	}	}	PUNCT
iajs-2801	187	22	=	=	PUNCT
iajs-2801	187	23	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	187	24	{	{	PUNCT
iajs-2801	187	25	�	�	PROPN
iajs-2801	187	26	̃	̃	PROPN
iajs-2801	187	27	�	�	PROPN
iajs-2801	187	28	−(𝛼	−(𝛼	NOUN
iajs-2801	187	29	∗	∗	NOUN
iajs-2801	187	30	(	(	PUNCT
iajs-2801	187	31	𝛽	𝛽	PROPN
iajs-2801	187	32	∗	∗	X
iajs-2801	187	33	δ	δ	PROPN
iajs-2801	187	34	)	)	PUNCT
iajs-2801	187	35	)	)	PUNCT
iajs-2801	187	36	,	,	PUNCT
iajs-2801	187	37	𝜇−(𝛽	𝜇−(𝛽	PROPN
iajs-2801	187	38	)	)	PUNCT
iajs-2801	187	39	}	}	PUNCT
iajs-2801	187	40	.	.	PUNCT
iajs-2801	188	1	also	also	ADV
iajs-2801	188	2	,	,	PUNCT
iajs-2801	188	3	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	189	1	+	+	ADJ
iajs-2801	189	2	(	(	PUNCT
iajs-2801	189	3	𝛼	𝛼	X
iajs-2801	189	4	∗	∗	X
iajs-2801	189	5	δ	δ	PROPN
iajs-2801	189	6	)	)	PUNCT
iajs-2801	189	7	=	=	SYM
iajs-2801	189	8	𝜆+(𝑓(𝒂	𝜆+(𝑓(𝒂	PROPN
iajs-2801	189	9	)	)	PUNCT
iajs-2801	189	10	∗	∗	NOUN
iajs-2801	189	11	𝑓(𝒄	𝑓(𝒄	NUM
iajs-2801	189	12	)	)	PUNCT
iajs-2801	189	13	)	)	PUNCT
iajs-2801	189	14	)	)	PUNCT
iajs-2801	190	1	=	=	PUNCT
iajs-2801	190	2	𝜆+(𝑓(𝒂	𝜆+(𝑓(𝒂	NOUN
iajs-2801	190	3	∗	∗	NOUN
iajs-2801	190	4	𝒄	𝒄	NOUN
iajs-2801	190	5	)	)	PUNCT
iajs-2801	190	6	)	)	PUNCT
iajs-2801	191	1	=	=	PUNCT
iajs-2801	191	2	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	192	1	+	+	NOUN
iajs-2801	192	2	(	(	PUNCT
iajs-2801	192	3	𝒂	𝒂	NOUN
iajs-2801	192	4	∗	∗	NOUN
iajs-2801	192	5	𝒄	𝒄	NOUN
iajs-2801	192	6	)	)	PUNCT
iajs-2801	192	7	≥	≥	PROPN
iajs-2801	192	8	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	192	9	{	{	PUNCT
iajs-2801	192	10	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	192	11	+	+	ADJ
iajs-2801	192	12	(	(	PUNCT
iajs-2801	192	13	𝒂	𝒂	X
iajs-2801	192	14	∗	∗	NOUN
iajs-2801	192	15	(	(	PUNCT
iajs-2801	192	16	𝒃	𝒃	NOUN
iajs-2801	192	17	∗	∗	NOUN
iajs-2801	192	18	𝒄	𝒄	NOUN
iajs-2801	192	19	)	)	PUNCT
iajs-2801	192	20	)	)	PUNCT
iajs-2801	192	21	,	,	PUNCT
iajs-2801	192	22	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	193	1	+	+	ADJ
iajs-2801	193	2	(	(	PUNCT
iajs-2801	193	3	𝒃	𝒃	NOUN
iajs-2801	193	4	)	)	PUNCT
iajs-2801	193	5	}	}	PUNCT
iajs-2801	193	6	=	=	SYM
iajs-2801	193	7	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	193	8	{	{	PUNCT
iajs-2801	193	9	𝜆+(𝑓(𝒂	𝜆+(𝑓(𝒂	PROPN
iajs-2801	193	10	)	)	PUNCT
iajs-2801	193	11	∗	∗	NOUN
iajs-2801	193	12	(	(	PUNCT
iajs-2801	193	13	𝑓(𝒃	𝑓(𝒃	PROPN
iajs-2801	193	14	)	)	PUNCT
iajs-2801	193	15	∗	∗	NOUN
iajs-2801	193	16	𝑓(𝒄	𝑓(𝒄	NUM
iajs-2801	193	17	)	)	PUNCT
iajs-2801	193	18	)	)	PUNCT
iajs-2801	193	19	}	}	PUNCT
iajs-2801	193	20	,	,	PUNCT
iajs-2801	193	21	𝜆+(𝑓(𝒃	𝜆+(𝑓(𝒃	PROPN
iajs-2801	193	22	)	)	PUNCT
iajs-2801	193	23	}	}	PUNCT
iajs-2801	193	24	=	=	SYM
iajs-2801	193	25	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	193	26	{	{	PUNCT
iajs-2801	193	27	𝜆+(𝛼	𝜆+(𝛼	NOUN
iajs-2801	193	28	∗	∗	NOUN
iajs-2801	193	29	(	(	PUNCT
iajs-2801	193	30	𝛽	𝛽	PROPN
iajs-2801	193	31	∗	∗	X
iajs-2801	193	32	δ	δ	PROPN
iajs-2801	193	33	)	)	PUNCT
iajs-2801	193	34	)	)	PUNCT
iajs-2801	193	35	,	,	PUNCT
iajs-2801	193	36	𝜆+(𝛽	𝜆+(𝛽	NUM
iajs-2801	193	37	)	)	PUNCT
iajs-2801	193	38	}	}	PUNCT
iajs-2801	193	39	.	.	PUNCT
iajs-2801	194	1	and	and	CCONJ
iajs-2801	194	2	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	194	3	−(𝛼	−(𝛼	NOUN
iajs-2801	194	4	∗	∗	X
iajs-2801	194	5	δ	δ	PROPN
iajs-2801	194	6	)	)	PUNCT
iajs-2801	194	7	=	=	SYM
iajs-2801	194	8	𝜆−(𝑓(𝒂	𝜆−(𝑓(𝒂	NOUN
iajs-2801	194	9	)	)	PUNCT
iajs-2801	194	10	∗	∗	NOUN
iajs-2801	194	11	𝑓(𝒄	𝑓(𝒄	NUM
iajs-2801	194	12	)	)	PUNCT
iajs-2801	194	13	)	)	PUNCT
iajs-2801	194	14	)	)	PUNCT
iajs-2801	195	1	=	=	PUNCT
iajs-2801	195	2	𝜆−(𝑓(𝒂	𝜆−(𝑓(𝒂	NOUN
iajs-2801	195	3	∗	∗	NOUN
iajs-2801	195	4	𝒄	𝒄	NOUN
iajs-2801	195	5	)	)	PUNCT
iajs-2801	195	6	)	)	PUNCT
iajs-2801	196	1	=	=	PRON
iajs-2801	196	2	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	196	3	−(𝒂	−(𝒂	NOUN
iajs-2801	196	4	∗	∗	X
iajs-2801	196	5	𝒄	𝒄	NOUN
iajs-2801	196	6	)	)	PUNCT
iajs-2801	196	7	≤	≤	NUM
iajs-2801	196	8	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	196	9	{	{	PUNCT
iajs-2801	196	10	𝜆𝑓	𝜆𝑓	NOUN
iajs-2801	196	11	−(𝒂	−(𝒂	PROPN
iajs-2801	196	12	∗	∗	NOUN
iajs-2801	196	13	(	(	PUNCT
iajs-2801	196	14	𝒃	𝒃	NOUN
iajs-2801	196	15	∗	∗	NOUN
iajs-2801	196	16	𝒄	𝒄	NOUN
iajs-2801	196	17	)	)	PUNCT
iajs-2801	196	18	)	)	PUNCT
iajs-2801	196	19	,	,	PUNCT
iajs-2801	196	20	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	196	21	−(𝒃	−(𝒃	NOUN
iajs-2801	196	22	)	)	PUNCT
iajs-2801	196	23	}	}	PUNCT
iajs-2801	196	24	=	=	PUNCT
iajs-2801	196	25	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	196	26	{	{	PUNCT
iajs-2801	196	27	𝜆−(𝑓(𝒂	𝜆−(𝑓(𝒂	NOUN
iajs-2801	196	28	)	)	PUNCT
iajs-2801	196	29	∗	∗	NOUN
iajs-2801	196	30	(	(	PUNCT
iajs-2801	196	31	𝑓(𝒃	𝑓(𝒃	PROPN
iajs-2801	196	32	)	)	PUNCT
iajs-2801	196	33	∗	∗	NOUN
iajs-2801	196	34	𝑓(𝒄	𝑓(𝒄	NUM
iajs-2801	196	35	)	)	PUNCT
iajs-2801	196	36	)	)	PUNCT
iajs-2801	196	37	}	}	PUNCT
iajs-2801	196	38	,	,	PUNCT
iajs-2801	196	39	𝜆−(𝑓(𝒃	𝜆−(𝑓(𝒃	PROPN
iajs-2801	196	40	)	)	PUNCT
iajs-2801	196	41	}	}	PUNCT
iajs-2801	197	1	=	=	PUNCT
iajs-2801	197	2	𝑚𝑎𝑥	𝑚𝑎𝑥	X
iajs-2801	197	3	{	{	PUNCT
iajs-2801	197	4	𝜆−(𝛼	𝜆−(𝛼	NOUN
iajs-2801	197	5	∗	∗	NOUN
iajs-2801	197	6	(	(	PUNCT
iajs-2801	197	7	𝛽	𝛽	NOUN
iajs-2801	197	8	∗	∗	X
iajs-2801	197	9	δ	δ	PROPN
iajs-2801	197	10	)	)	PUNCT
iajs-2801	197	11	)	)	PUNCT
iajs-2801	197	12	,	,	PUNCT
iajs-2801	197	13	𝜆−(𝛽	𝜆−(𝛽	PROPN
iajs-2801	197	14	)	)	PUNCT
iajs-2801	197	15	}	}	PUNCT
iajs-2801	197	16	.	.	PUNCT
iajs-2801	198	1	and	and	CCONJ
iajs-2801	198	2	the	the	DET
iajs-2801	198	3	condition	condition	NOUN
iajs-2801	198	4	(	(	PUNCT
iajs-2801	198	5	c	c	X
iajs-2801	198	6	)	)	PUNCT
iajs-2801	198	7	is	be	AUX
iajs-2801	198	8	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	198	9	+	+	PROPN
iajs-2801	198	10	(	(	PUNCT
iajs-2801	198	11	𝛼	𝛼	PROPN
iajs-2801	198	12	∘	∘	PROPN
iajs-2801	198	13	𝛽	𝛽	NOUN
iajs-2801	198	14	)	)	PUNCT
iajs-2801	198	15	=	=	SYM
iajs-2801	198	16	𝜇+(𝑓(𝒂	𝜇+(𝑓(𝒂	NOUN
iajs-2801	198	17	)	)	PUNCT
iajs-2801	198	18	∘	∘	NOUN
iajs-2801	198	19	𝑓(𝒃	𝑓(𝒃	PROPN
iajs-2801	198	20	)	)	PUNCT
iajs-2801	198	21	)	)	PUNCT
iajs-2801	198	22	)	)	PUNCT
iajs-2801	199	1	≥	≥	PROPN
iajs-2801	199	2	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	199	3	{	{	PUNCT
iajs-2801	199	4	𝜇+(𝑓(𝒂	𝜇+(𝑓(𝒂	PROPN
iajs-2801	199	5	)	)	PUNCT
iajs-2801	199	6	)	)	PUNCT
iajs-2801	199	7	,	,	PUNCT
iajs-2801	199	8	𝜇+(𝑓(𝒃	𝜇+(𝑓(𝒃	PROPN
iajs-2801	199	9	)	)	PUNCT
iajs-2801	199	10	}	}	PUNCT
iajs-2801	200	1	=	=	PUNCT
iajs-2801	200	2	𝑟𝑚𝑖𝑛{𝜇𝑓	𝑟𝑚𝑖𝑛{𝜇𝑓	NUM
iajs-2801	200	3	+	+	ADJ
iajs-2801	200	4	(	(	PUNCT
iajs-2801	200	5	𝛼	𝛼	NOUN
iajs-2801	200	6	)	)	PUNCT
iajs-2801	200	7	,	,	PUNCT
iajs-2801	200	8	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	200	9	+	+	ADJ
iajs-2801	200	10	(	(	PUNCT
iajs-2801	200	11	𝛽	𝛽	NOUN
iajs-2801	200	12	)	)	PUNCT
iajs-2801	200	13	}	}	PUNCT
iajs-2801	200	14	and	and	CCONJ
iajs-2801	200	15	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	200	16	−(𝛼	−(𝛼	NOUN
iajs-2801	200	17	∘	∘	NOUN
iajs-2801	200	18	𝛽	𝛽	NOUN
iajs-2801	200	19	)	)	PUNCT
iajs-2801	200	20	=	=	SYM
iajs-2801	200	21	𝜇−(𝑓(𝒂	𝜇−(𝑓(𝒂	NOUN
iajs-2801	200	22	)	)	PUNCT
iajs-2801	200	23	∘	∘	NOUN
iajs-2801	200	24	𝑓(𝒃	𝑓(𝒃	NOUN
iajs-2801	200	25	)	)	PUNCT
iajs-2801	200	26	)	)	PUNCT
iajs-2801	200	27	)	)	PUNCT
iajs-2801	201	1	≤	≤	NUM
iajs-2801	201	2	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	VERB
iajs-2801	201	3	{	{	PUNCT
iajs-2801	201	4	𝜇−(𝑓(𝒂	𝜇−(𝑓(𝒂	NOUN
iajs-2801	201	5	)	)	PUNCT
iajs-2801	201	6	,	,	PUNCT
iajs-2801	201	7	𝜇−(𝑓(𝒃	𝜇−(𝑓(𝒃	PROPN
iajs-2801	201	8	)	)	PUNCT
iajs-2801	201	9	}	}	PUNCT
iajs-2801	201	10	=	=	SYM
iajs-2801	201	11	𝑟𝑚𝑎𝑥{𝜇𝑓	𝑟𝑚𝑎𝑥{𝜇𝑓	NUM
iajs-2801	201	12	−(𝛼	−(𝛼	NOUN
iajs-2801	201	13	)	)	PUNCT
iajs-2801	201	14	,	,	PUNCT
iajs-2801	201	15	𝜇𝑓	𝜇𝑓	PROPN
iajs-2801	201	16	−(𝛽	−(𝛽	NOUN
iajs-2801	201	17	)	)	PUNCT
iajs-2801	201	18	}	}	PUNCT
iajs-2801	201	19	also	also	ADV
iajs-2801	201	20	,	,	PUNCT
iajs-2801	201	21	𝜆𝑓	𝜆𝑓	X
iajs-2801	202	1	+	+	ADJ
iajs-2801	202	2	(	(	PUNCT
iajs-2801	202	3	𝛼	𝛼	PROPN
iajs-2801	202	4	∘	∘	PROPN
iajs-2801	202	5	𝛽	𝛽	NOUN
iajs-2801	202	6	)	)	PUNCT
iajs-2801	202	7	=	=	SYM
iajs-2801	202	8	𝜆+(𝑓(𝒂	𝜆+(𝑓(𝒂	PROPN
iajs-2801	202	9	)	)	PUNCT
iajs-2801	202	10	∘	∘	NOUN
iajs-2801	202	11	𝑓(𝒃	𝑓(𝒃	PROPN
iajs-2801	202	12	)	)	PUNCT
iajs-2801	202	13	)	)	PUNCT
iajs-2801	202	14	)	)	PUNCT
iajs-2801	203	1	≥	≥	PROPN
iajs-2801	203	2	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	203	3	{	{	PUNCT
iajs-2801	203	4	𝜆+(𝑓(𝒂	𝜆+(𝑓(𝒂	PROPN
iajs-2801	203	5	)	)	PUNCT
iajs-2801	203	6	,	,	PUNCT
iajs-2801	203	7	𝜆+(𝑓(𝒃	𝜆+(𝑓(𝒃	PROPN
iajs-2801	203	8	)	)	PUNCT
iajs-2801	203	9	}	}	PUNCT
iajs-2801	204	1	=	=	PUNCT
iajs-2801	204	2	𝑚𝑖𝑛{𝜆𝑓	𝑚𝑖𝑛{𝜆𝑓	PUNCT
iajs-2801	204	3	+	+	ADJ
iajs-2801	204	4	(	(	PUNCT
iajs-2801	204	5	𝛼	𝛼	NOUN
iajs-2801	204	6	)	)	PUNCT
iajs-2801	204	7	,	,	PUNCT
iajs-2801	204	8	𝜆𝑓	𝜆𝑓	VERB
iajs-2801	205	1	+	+	ADJ
iajs-2801	205	2	(	(	PUNCT
iajs-2801	205	3	𝛽	𝛽	NOUN
iajs-2801	205	4	)	)	PUNCT
iajs-2801	205	5	}	}	PUNCT
iajs-2801	205	6	and	and	CCONJ
iajs-2801	205	7	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	205	8	−(𝛼	−(𝛼	NOUN
iajs-2801	205	9	∘	∘	NOUN
iajs-2801	205	10	𝛽	𝛽	NOUN
iajs-2801	205	11	)	)	PUNCT
iajs-2801	205	12	=	=	SYM
iajs-2801	205	13	𝜆−(𝑓(𝒂	𝜆−(𝑓(𝒂	NOUN
iajs-2801	205	14	)	)	PUNCT
iajs-2801	205	15	∘	∘	NOUN
iajs-2801	205	16	𝑓(𝒃	𝑓(𝒃	NOUN
iajs-2801	205	17	)	)	PUNCT
iajs-2801	205	18	)	)	PUNCT
iajs-2801	205	19	)	)	PUNCT
iajs-2801	205	20	≤	≤	NUM
iajs-2801	205	21	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	205	22	{	{	PUNCT
iajs-2801	205	23	𝜆−(𝑓(𝒂	𝜆−(𝑓(𝒂	NOUN
iajs-2801	205	24	)	)	PUNCT
iajs-2801	205	25	,	,	PUNCT
iajs-2801	205	26	𝜆−(𝑓(𝒃	𝜆−(𝑓(𝒃	PROPN
iajs-2801	205	27	)	)	PUNCT
iajs-2801	205	28	}	}	PUNCT
iajs-2801	205	29	=	=	SYM
iajs-2801	205	30	𝑚𝑎𝑥{𝜆𝑓	𝑚𝑎𝑥{𝜆𝑓	PUNCT
iajs-2801	205	31	−(𝛼	−(𝛼	NOUN
iajs-2801	205	32	)	)	PUNCT
iajs-2801	205	33	,	,	PUNCT
iajs-2801	205	34	𝜆𝑓	𝜆𝑓	ADP
iajs-2801	205	35	−(𝛽	−(𝛽	NOUN
iajs-2801	205	36	)	)	PUNCT
iajs-2801	205	37	}	}	PUNCT
iajs-2801	205	38	therefore	therefore	ADV
iajs-2801	205	39	ω𝑓is	ω𝑓is	PROPN
iajs-2801	205	40	acb	acb	PROPN
iajs-2801	205	41	k	k	NOUN
iajs-2801	205	42	-	-	NOUN
iajs-2801	205	43	ideal	ideal	NOUN
iajs-2801	205	44	of	of	ADP
iajs-2801	205	45	ℵ′.	ℵ′.	NOUN
iajs-2801	205	46	in	in	ADP
iajs-2801	205	47	the	the	DET
iajs-2801	205	48	following	following	NOUN
iajs-2801	205	49	,	,	PUNCT
iajs-2801	205	50	we	we	PRON
iajs-2801	205	51	introduce	introduce	VERB
iajs-2801	205	52	the	the	DET
iajs-2801	205	53	product	product	NOUN
iajs-2801	205	54	of	of	ADP
iajs-2801	205	55	the	the	DET
iajs-2801	205	56	cubic	cubic	ADJ
iajs-2801	205	57	bipolar	bipolar	ADJ
iajs-2801	205	58	k	k	NOUN
iajs-2801	205	59	-	-	NOUN
iajs-2801	205	60	ideals	ideal	NOUN
iajs-2801	205	61	and	and	CCONJ
iajs-2801	205	62	a	a	DET
iajs-2801	205	63	cubic	cubic	ADJ
iajs-2801	205	64	bipolar	bipolar	ADJ
iajs-2801	205	65	ideal	ideal	NOUN
iajs-2801	205	66	as	as	SCONJ
iajs-2801	205	67	follows	follow	VERB
iajs-2801	205	68	.	.	PUNCT
iajs-2801	206	1	definition	definition	NOUN
iajs-2801	206	2	3.4	3.4	NUM
iajs-2801	206	3	.	.	PUNCT
iajs-2801	207	1	let	let	VERB
iajs-2801	207	2	ω𝑓1	ω𝑓1	NOUN
iajs-2801	207	3	and	and	CCONJ
iajs-2801	207	4	ω𝑓2	ω𝑓2	NUM
iajs-2801	207	5	be	be	AUX
iajs-2801	207	6	two	two	NUM
iajs-2801	207	7	cb	cb	NOUN
iajs-2801	207	8	fuzzy	fuzzy	ADJ
iajs-2801	207	9	sets	set	NOUN
iajs-2801	207	10	of	of	ADP
iajs-2801	207	11	ℵ.	ℵ.	NOUN
iajs-2801	208	1	the	the	DET
iajs-2801	208	2	product	product	NOUN
iajs-2801	208	3	ω𝑓1	ω𝑓1	NOUN
iajs-2801	208	4	×	×	NOUN
iajs-2801	208	5	ω𝑓2	ω𝑓2	PROPN
iajs-2801	209	1	=	=	SYM
iajs-2801	209	2	(	(	PUNCT
iajs-2801	209	3	(	(	PUNCT
iajs-2801	209	4	𝛼	𝛼	NOUN
iajs-2801	209	5	,	,	PUNCT
iajs-2801	209	6	𝛽	𝛽	NOUN
iajs-2801	209	7	)	)	PUNCT
iajs-2801	209	8	,	,	PUNCT
iajs-2801	209	9	;	;	PUNCT
iajs-2801	209	10	𝜇1	𝜇1	PROPN
iajs-2801	209	11	−	−	PROPN
iajs-2801	209	12	×	×	PROPN
iajs-2801	209	13	𝜇2	𝜇2	PROPN
iajs-2801	209	14	−	−	PROPN
iajs-2801	209	15	,	,	PUNCT
iajs-2801	209	16	;	;	PUNCT
iajs-2801	209	17	𝜇1	𝜇1	PROPN
iajs-2801	209	18	+	+	PROPN
iajs-2801	209	19	;	;	PUNCT
iajs-2801	209	20	×	×	NOUN
iajs-2801	209	21	;	;	PUNCT
iajs-2801	209	22	𝜇2	𝜇2	PROPN
iajs-2801	209	23	+	+	PROPN
iajs-2801	209	24	,	,	PUNCT
iajs-2801	209	25	;	;	PUNCT
iajs-2801	209	26	𝜆1	𝜆1	PROPN
iajs-2801	209	27	−;×	−;×	PROPN
iajs-2801	209	28	;	;	PUNCT
iajs-2801	209	29	𝜆2	𝜆2	PROPN
iajs-2801	209	30	−	−	PROPN
iajs-2801	209	31	,	,	PUNCT
iajs-2801	209	32	;	;	PUNCT
iajs-2801	209	33	𝜆1	𝜆1	VERB
iajs-2801	209	34	+	+	NOUN
iajs-2801	209	35	;	;	PUNCT
iajs-2801	209	36	×	×	NOUN
iajs-2801	209	37	;	;	PUNCT
iajs-2801	209	38	𝜆2	𝜆2	PROPN
iajs-2801	209	39	+	+	PROPN
iajs-2801	209	40	)	)	PUNCT
iajs-2801	209	41	is	be	AUX
iajs-2801	209	42	defined	define	VERB
iajs-2801	209	43	by	by	ADP
iajs-2801	209	44	the	the	DET
iajs-2801	209	45	following	following	NOUN
iajs-2801	209	46	:	:	PUNCT
iajs-2801	209	47	(	(	PUNCT
iajs-2801	209	48	𝜇1	𝜇1	ADJ
iajs-2801	209	49	−	−	PROPN
iajs-2801	209	50	×	×	PROPN
iajs-2801	209	51	𝜇2	𝜇2	PROPN
iajs-2801	209	52	−)(𝛼	−)(𝛼	PROPN
iajs-2801	209	53	,	,	PUNCT
iajs-2801	209	54	𝛽	𝛽	NOUN
iajs-2801	209	55	)	)	PUNCT
iajs-2801	209	56	=	=	VERB
iajs-2801	210	1	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	210	2	{	{	PUNCT
iajs-2801	210	3	;	;	PUNCT
iajs-2801	210	4	𝜇1	𝜇1	ADJ
iajs-2801	210	5	−(𝛼	−(𝛼	NOUN
iajs-2801	210	6	)	)	PUNCT
iajs-2801	210	7	,	,	PUNCT
iajs-2801	210	8	;	;	PUNCT
iajs-2801	210	9	𝜇2	𝜇2	PROPN
iajs-2801	210	10	−(𝛽	−(𝛽	NOUN
iajs-2801	210	11	)	)	PUNCT
iajs-2801	210	12	}	}	PUNCT
iajs-2801	210	13	,	,	PUNCT
iajs-2801	210	14	(	(	PUNCT
iajs-2801	210	15	𝜇1	𝜇1	PROPN
iajs-2801	210	16	+	+	PROPN
iajs-2801	210	17	;	;	PUNCT
iajs-2801	210	18	×	×	NOUN
iajs-2801	210	19	;	;	PUNCT
iajs-2801	210	20	𝜇2	𝜇2	PROPN
iajs-2801	210	21	+	+	PROPN
iajs-2801	210	22	)	)	PUNCT
iajs-2801	210	23	(	(	PUNCT
iajs-2801	210	24	𝛼	𝛼	X
iajs-2801	210	25	,	,	PUNCT
iajs-2801	210	26	𝛽	𝛽	NOUN
iajs-2801	210	27	)	)	PUNCT
iajs-2801	210	28	=	=	SYM
iajs-2801	210	29	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	210	30	{	{	PUNCT
iajs-2801	210	31	𝜇1	𝜇1	PROPN
iajs-2801	210	32	+	+	PROPN
iajs-2801	210	33	(	(	PUNCT
iajs-2801	210	34	𝛼	𝛼	NOUN
iajs-2801	210	35	)	)	PUNCT
iajs-2801	210	36	,	,	PUNCT
iajs-2801	210	37	𝜇2	𝜇2	PROPN
iajs-2801	210	38	+	+	PROPN
iajs-2801	210	39	(	(	PUNCT
iajs-2801	210	40	𝛽	𝛽	NOUN
iajs-2801	210	41	)	)	PUNCT
iajs-2801	210	42	}	}	PUNCT
iajs-2801	210	43	and	and	CCONJ
iajs-2801	210	44	(;	(;	PUNCT
iajs-2801	210	45	𝜆1	𝜆1	PROPN
iajs-2801	210	46	−;×	−;×	PROPN
iajs-2801	210	47	;	;	PUNCT
iajs-2801	210	48	𝜆2	𝜆2	PROPN
iajs-2801	210	49	−)(𝛼	−)(𝛼	PROPN
iajs-2801	210	50	,	,	PUNCT
iajs-2801	210	51	𝛽	𝛽	NOUN
iajs-2801	210	52	)	)	PUNCT
iajs-2801	210	53	=	=	PUNCT
iajs-2801	210	54	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-2801	210	55	{	{	PUNCT
iajs-2801	210	56	;	;	PUNCT
iajs-2801	210	57	𝜆1	𝜆1	VERB
iajs-2801	210	58	−(𝛼	−(𝛼	NOUN
iajs-2801	210	59	)	)	PUNCT
iajs-2801	210	60	,	,	PUNCT
iajs-2801	210	61	;	;	PUNCT
iajs-2801	210	62	𝜆2	𝜆2	NOUN
iajs-2801	210	63	−(𝛽	−(𝛽	NOUN
iajs-2801	210	64	)	)	PUNCT
iajs-2801	210	65	}	}	PUNCT
iajs-2801	210	66	,	,	PUNCT
iajs-2801	210	67	(;	(;	X
iajs-2801	210	68	𝜆1	𝜆1	X
iajs-2801	211	1	+	+	ADP
iajs-2801	211	2	;	;	PUNCT
iajs-2801	211	3	×	×	NOUN
iajs-2801	211	4	;	;	PUNCT
iajs-2801	211	5	𝜆2	𝜆2	PROPN
iajs-2801	211	6	+	+	PROPN
iajs-2801	211	7	)	)	PUNCT
iajs-2801	211	8	(	(	PUNCT
iajs-2801	211	9	𝛼	𝛼	X
iajs-2801	211	10	,	,	PUNCT
iajs-2801	211	11	𝛽	𝛽	NOUN
iajs-2801	211	12	)	)	PUNCT
iajs-2801	211	13	=	=	SYM
iajs-2801	211	14	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	211	15	{	{	PUNCT
iajs-2801	211	16	;	;	PUNCT
iajs-2801	211	17	𝜆1	𝜆1	VERB
iajs-2801	211	18	+	+	NOUN
iajs-2801	211	19	(	(	PUNCT
iajs-2801	211	20	𝛼	𝛼	NOUN
iajs-2801	211	21	)	)	PUNCT
iajs-2801	211	22	,	,	PUNCT
iajs-2801	211	23	;	;	PUNCT
iajs-2801	212	1	𝜆2	𝜆2	PROPN
iajs-2801	212	2	+	+	PROPN
iajs-2801	212	3	(	(	PUNCT
iajs-2801	212	4	𝛽)}where	𝛽)}where	ADV
iajs-2801	212	5	;	;	PUNCT
iajs-2801	212	6	𝜇1	𝜇1	PROPN
iajs-2801	212	7	−	−	PROPN
iajs-2801	212	8	×	×	NOUN
iajs-2801	212	9	;	;	PUNCT
iajs-2801	212	10	𝜇2	𝜇2	VERB
iajs-2801	212	11	−	−	PROPN
iajs-2801	212	12	:	:	PUNCT
iajs-2801	212	13	ℵ	ℵ	DET
iajs-2801	212	14	×	×	NOUN
iajs-2801	212	15	ℵ	ℵ	NOUN
iajs-2801	212	16	→	→	SYM
iajs-2801	212	17	[	[	X
iajs-2801	212	18	−1,0	−1,0	NOUN
iajs-2801	212	19	]	]	X
iajs-2801	212	20	,	,	PUNCT
iajs-2801	212	21	𝜇1	𝜇1	NOUN
iajs-2801	212	22	+	+	CCONJ
iajs-2801	212	23	×	×	PROPN
iajs-2801	212	24	𝜇2	𝜇2	NOUN
iajs-2801	212	25	+	+	NOUN
iajs-2801	212	26	:	:	PUNCT
iajs-2801	212	27	ℵ	ℵ	ADJ
iajs-2801	212	28	×	×	NOUN
iajs-2801	212	29	ℵ	ℵ	X
iajs-2801	212	30	→	→	SYM
iajs-2801	212	31	[	[	X
iajs-2801	212	32	0,1	0,1	NUM
iajs-2801	212	33	]	]	PUNCT
iajs-2801	212	34	and	and	CCONJ
iajs-2801	212	35	𝜆1	𝜆1	VERB
iajs-2801	212	36	−	−	PROPN
iajs-2801	212	37	×	×	PROPN
iajs-2801	212	38	𝜆2	𝜆2	NOUN
iajs-2801	212	39	−	−	NOUN
iajs-2801	212	40	:	:	PUNCT
iajs-2801	212	41	ℵ	ℵ	DET
iajs-2801	212	42	×	×	NOUN
iajs-2801	212	43	ℵ	ℵ	NOUN
iajs-2801	212	44	→	→	SYM
iajs-2801	212	45	[	[	X
iajs-2801	212	46	−1,0	−1,0	NOUN
iajs-2801	212	47	]	]	PUNCT
iajs-2801	212	48	,	,	PUNCT
iajs-2801	212	49	𝜆1	𝜆1	NOUN
iajs-2801	212	50	+	+	CCONJ
iajs-2801	212	51	×	×	PROPN
iajs-2801	212	52	𝜆2	𝜆2	NOUN
iajs-2801	213	1	+	+	NOUN
iajs-2801	213	2	:	:	PUNCT
iajs-2801	213	3	ℵ	ℵ	ADJ
iajs-2801	213	4	×	×	NOUN
iajs-2801	213	5	ℵ	ℵ	X
iajs-2801	213	6	→	→	SYM
iajs-2801	213	7	[	[	X
iajs-2801	213	8	0,1	0,1	NUM
iajs-2801	213	9	]	]	PUNCT
iajs-2801	213	10	,	,	PUNCT
iajs-2801	213	11	for	for	ADP
iajs-2801	213	12	all	all	DET
iajs-2801	213	13	𝛼	𝛼	PROPN
iajs-2801	213	14	,	,	PUNCT
iajs-2801	213	15	𝛽	𝛽	PROPN
iajs-2801	213	16	∈	∈	PRON
iajs-2801	213	17	ℵ.	ℵ.	PROPN
iajs-2801	214	1	ibn	ibn	PROPN
iajs-2801	214	2	al	al	PROPN
iajs-2801	214	3	-	-	PUNCT
iajs-2801	214	4	haitham	haitham	PROPN
iajs-2801	214	5	jour	jour	X
iajs-2801	214	6	.	.	PROPN
iajs-2801	214	7	for	for	ADP
iajs-2801	214	8	pure	pure	ADJ
iajs-2801	214	9	&	&	CCONJ
iajs-2801	214	10	appl	appl	PROPN
iajs-2801	214	11	.	.	PUNCT
iajs-2801	215	1	sci	sci	PROPN
iajs-2801	215	2	.	.	PUNCT
iajs-2801	216	1	35(1)2022	35(1)2022	NUM
iajs-2801	216	2	79	79	NUM
iajs-2801	216	3	theorem	theorem	VERB
iajs-2801	216	4	3.5	3.5	NUM
iajs-2801	216	5	.	.	PUNCT
iajs-2801	217	1	let	let	VERB
iajs-2801	217	2	ω𝑓1	ω𝑓1	NOUN
iajs-2801	217	3	and	and	CCONJ
iajs-2801	217	4	ω𝑓2	ω𝑓2	NUM
iajs-2801	217	5	be	be	AUX
iajs-2801	217	6	two	two	NUM
iajs-2801	217	7	cb	cb	PROPN
iajs-2801	217	8	k	k	X
iajs-2801	217	9	-	-	NOUN
iajs-2801	217	10	ideals	ideal	NOUN
iajs-2801	217	11	of	of	ADP
iajs-2801	217	12	ℵ	ℵ	NOUN
iajs-2801	217	13	,	,	PUNCT
iajs-2801	217	14	then	then	ADV
iajs-2801	218	1	ω𝑓1	ω𝑓1	NOUN
iajs-2801	218	2	×	×	PROPN
iajs-2801	218	3	ω𝑓2	ω𝑓2	NUM
iajs-2801	218	4	is	be	AUX
iajs-2801	218	5	acb	acb	PROPN
iajs-2801	218	6	k	k	NOUN
iajs-2801	218	7	-	-	NOUN
iajs-2801	218	8	ideal	ideal	NOUN
iajs-2801	218	9	of	of	ADP
iajs-2801	218	10	ℵ	ℵ	DET
iajs-2801	218	11	×	×	NOUN
iajs-2801	218	12	ℵ.	ℵ.	NOUN
iajs-2801	218	13	proof	proof	NOUN
iajs-2801	218	14	.	.	PUNCT
iajs-2801	219	1	let	let	VERB
iajs-2801	219	2	(	(	PUNCT
iajs-2801	219	3	𝛼	𝛼	NOUN
iajs-2801	219	4	,	,	PUNCT
iajs-2801	219	5	𝛽	𝛽	NOUN
iajs-2801	219	6	)	)	PUNCT
iajs-2801	219	7	∈	∈	PROPN
iajs-2801	219	8	ℵ	ℵ	ADP
iajs-2801	219	9	×	×	NOUN
iajs-2801	219	10	ℵ	ℵ	NOUN
iajs-2801	219	11	,	,	PUNCT
iajs-2801	219	12	we	we	PRON
iajs-2801	219	13	have	have	VERB
iajs-2801	219	14	(	(	PUNCT
iajs-2801	219	15	𝜇1	𝜇1	NOUN
iajs-2801	219	16	+	+	CCONJ
iajs-2801	219	17	×	×	PROPN
iajs-2801	219	18	𝜇2	𝜇2	NOUN
iajs-2801	219	19	+	+	PROPN
iajs-2801	219	20	)	)	PUNCT
iajs-2801	219	21	(	(	PUNCT
iajs-2801	219	22	0	0	NUM
iajs-2801	219	23	,	,	PUNCT
iajs-2801	219	24	0	0	NUM
iajs-2801	219	25	)	)	PUNCT
iajs-2801	219	26	=	=	SYM
iajs-2801	220	1	𝑟𝑚𝑖𝑛{	𝑟𝑚𝑖𝑛{	PROPN
iajs-2801	220	2	�	�	PROPN
iajs-2801	220	3	̃	̃	PROPN
iajs-2801	220	4	�	�	NOUN
iajs-2801	220	5	1	1	NUM
iajs-2801	220	6	+	+	ADJ
iajs-2801	220	7	(	(	PUNCT
iajs-2801	220	8	0	0	NUM
iajs-2801	220	9	)	)	PUNCT
iajs-2801	221	1	,	,	PUNCT
iajs-2801	221	2	𝜇2	𝜇2	PROPN
iajs-2801	221	3	+	+	PROPN
iajs-2801	221	4	(	(	PUNCT
iajs-2801	221	5	0	0	NUM
iajs-2801	221	6	)	)	PUNCT
iajs-2801	221	7	}	}	PUNCT
iajs-2801	221	8	≥	≥	X
iajs-2801	221	9	𝑟𝑚𝑖𝑛{𝜇1	𝑟𝑚𝑖𝑛{𝜇1	X
iajs-2801	222	1	+	+	ADJ
iajs-2801	222	2	(	(	PUNCT
iajs-2801	222	3	𝛼	𝛼	NOUN
iajs-2801	222	4	)	)	PUNCT
iajs-2801	222	5	,	,	PUNCT
iajs-2801	222	6	𝜇2	𝜇2	PROPN
iajs-2801	222	7	+	+	PROPN
iajs-2801	222	8	(	(	PUNCT
iajs-2801	222	9	𝛽	𝛽	NOUN
iajs-2801	222	10	)	)	PUNCT
iajs-2801	222	11	}	}	PUNCT
iajs-2801	222	12	=	=	SYM
iajs-2801	222	13	(	(	PUNCT
iajs-2801	222	14	𝜇1	𝜇1	NOUN
iajs-2801	222	15	+	+	CCONJ
iajs-2801	222	16	×	×	PROPN
iajs-2801	222	17	𝜇2	𝜇2	NOUN
iajs-2801	222	18	+	+	PROPN
iajs-2801	222	19	)	)	PUNCT
iajs-2801	222	20	(	(	PUNCT
iajs-2801	222	21	𝛼	𝛼	PROPN
iajs-2801	222	22	,	,	PUNCT
iajs-2801	222	23	𝛽	𝛽	NOUN
iajs-2801	222	24	)	)	PUNCT
iajs-2801	222	25	and	and	CCONJ
iajs-2801	222	26	(	(	PUNCT
iajs-2801	222	27	𝜇1	𝜇1	PROPN
iajs-2801	222	28	−	−	PROPN
iajs-2801	222	29	×	×	PROPN
iajs-2801	222	30	𝜇2	𝜇2	NOUN
iajs-2801	222	31	−	−	PROPN
iajs-2801	222	32	)	)	PUNCT
iajs-2801	222	33	(	(	PUNCT
iajs-2801	222	34	0	0	NUM
iajs-2801	222	35	,	,	PUNCT
iajs-2801	222	36	0	0	NUM
iajs-2801	222	37	)	)	PUNCT
iajs-2801	222	38	=	=	SYM
iajs-2801	222	39	𝑟𝑚𝑎𝑥{𝜇1	𝑟𝑚𝑎𝑥{𝜇1	PROPN
iajs-2801	222	40	−(0	−(0	NOUN
iajs-2801	222	41	)	)	PUNCT
iajs-2801	222	42	,	,	PUNCT
iajs-2801	222	43	𝜇2	𝜇2	PROPN
iajs-2801	222	44	−(0	−(0	NOUN
iajs-2801	222	45	)	)	PUNCT
iajs-2801	222	46	}	}	PUNCT
iajs-2801	222	47	≤	≤	PROPN
iajs-2801	222	48	𝑟𝑚𝑎𝑥{𝜇1	𝑟𝑚𝑎𝑥{𝜇1	NUM
iajs-2801	222	49	−(𝛼	−(𝛼	NOUN
iajs-2801	222	50	)	)	PUNCT
iajs-2801	222	51	,	,	PUNCT
iajs-2801	222	52	𝜇2	𝜇2	PROPN
iajs-2801	222	53	−(𝛽	−(𝛽	NOUN
iajs-2801	222	54	)	)	PUNCT
iajs-2801	222	55	}	}	PUNCT
iajs-2801	222	56	=	=	SYM
iajs-2801	222	57	(	(	PUNCT
iajs-2801	222	58	𝜇1	𝜇1	NOUN
iajs-2801	222	59	−	−	PROPN
iajs-2801	222	60	×	×	PROPN
iajs-2801	222	61	𝜇2	𝜇2	PROPN
iajs-2801	222	62	−)(𝛼	−)(𝛼	PROPN
iajs-2801	222	63	,	,	PUNCT
iajs-2801	222	64	𝛽	𝛽	NOUN
iajs-2801	222	65	)	)	PUNCT
iajs-2801	222	66	.	.	PUNCT
iajs-2801	223	1	let	let	VERB
iajs-2801	223	2	(	(	PUNCT
iajs-2801	223	3	𝛼1	𝛼1	NOUN
iajs-2801	223	4	,	,	PUNCT
iajs-2801	223	5	𝛼2	𝛼2	PROPN
iajs-2801	223	6	)	)	PUNCT
iajs-2801	223	7	,	,	PUNCT
iajs-2801	223	8	(	(	PUNCT
iajs-2801	223	9	𝛽1	𝛽1	NOUN
iajs-2801	223	10	,	,	PUNCT
iajs-2801	223	11	𝛽2	𝛽2	PROPN
iajs-2801	223	12	)	)	PUNCT
iajs-2801	223	13	and	and	CCONJ
iajs-2801	223	14	(	(	PUNCT
iajs-2801	223	15	δ1	δ1	NOUN
iajs-2801	223	16	,	,	PUNCT
iajs-2801	223	17	δ2	δ2	ADJ
iajs-2801	223	18	)	)	PUNCT
iajs-2801	223	19	∈	∈	PROPN
iajs-2801	223	20	ℵ	ℵ	ADP
iajs-2801	223	21	×	×	NOUN
iajs-2801	223	22	ℵ	ℵ	NOUN
iajs-2801	223	23	,	,	PUNCT
iajs-2801	223	24	then	then	ADV
iajs-2801	223	25	(	(	PUNCT
iajs-2801	223	26	�	�	PROPN
iajs-2801	223	27	̃	̃	NOUN
iajs-2801	223	28	�	�	NOUN
iajs-2801	223	29	1	1	NUM
iajs-2801	223	30	+	+	SYM
iajs-2801	223	31	×	×	PROPN
iajs-2801	223	32	𝜇2	𝜇2	NOUN
iajs-2801	223	33	+	+	PROPN
iajs-2801	223	34	)	)	PUNCT
iajs-2801	223	35	(	(	PUNCT
iajs-2801	223	36	𝛼1	𝛼1	NOUN
iajs-2801	223	37	∗	∗	NOUN
iajs-2801	223	38	δ1	δ1	NOUN
iajs-2801	223	39	,	,	PUNCT
iajs-2801	223	40	𝛼2	𝛼2	PROPN
iajs-2801	223	41	∗	∗	NOUN
iajs-2801	223	42	δ2	δ2	VERB
iajs-2801	223	43	)	)	PUNCT
iajs-2801	224	1	=	=	SYM
iajs-2801	224	2	𝑟𝑚𝑖𝑛{𝜇1	𝑟𝑚𝑖𝑛{𝜇1	X
iajs-2801	224	3	+	+	ADJ
iajs-2801	224	4	(	(	PUNCT
iajs-2801	224	5	𝛼1	𝛼1	NOUN
iajs-2801	224	6	∗	∗	NOUN
iajs-2801	224	7	𝜏1	𝜏1	NOUN
iajs-2801	224	8	)	)	PUNCT
iajs-2801	224	9	,	,	PUNCT
iajs-2801	224	10	𝜇2	𝜇2	PROPN
iajs-2801	224	11	+	+	PROPN
iajs-2801	224	12	(	(	PUNCT
iajs-2801	224	13	𝛼2	𝛼2	PROPN
iajs-2801	224	14	∗	∗	NOUN
iajs-2801	224	15	δ2	δ2	VERB
iajs-2801	224	16	)	)	PUNCT
iajs-2801	224	17	}	}	PUNCT
iajs-2801	224	18	≥	≥	PROPN
iajs-2801	224	19	𝑟𝑚𝑖𝑛{𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛{𝑟𝑚𝑖𝑛	PROPN
iajs-2801	224	20	{	{	PUNCT
iajs-2801	224	21	𝜇1	𝜇1	PROPN
iajs-2801	224	22	+	+	PROPN
iajs-2801	224	23	(	(	PUNCT
iajs-2801	224	24	𝛼1	𝛼1	NOUN
iajs-2801	224	25	∗	∗	NOUN
iajs-2801	224	26	(	(	PUNCT
iajs-2801	224	27	𝛽1	𝛽1	NOUN
iajs-2801	224	28	∗	∗	NOUN
iajs-2801	224	29	δ1	δ1	NOUN
iajs-2801	224	30	)	)	PUNCT
iajs-2801	224	31	)	)	PUNCT
iajs-2801	224	32	,	,	PUNCT
iajs-2801	224	33	𝜇1	𝜇1	PROPN
iajs-2801	224	34	+	+	PROPN
iajs-2801	224	35	(	(	PUNCT
iajs-2801	224	36	𝛽1	𝛽1	NOUN
iajs-2801	224	37	)	)	PUNCT
iajs-2801	224	38	}	}	PUNCT
iajs-2801	224	39	,	,	PUNCT
iajs-2801	224	40	𝑟𝑚𝑖𝑛{𝜇2	𝑟𝑚𝑖𝑛{𝜇2	X
iajs-2801	224	41	+	+	PROPN
iajs-2801	224	42	(	(	PUNCT
iajs-2801	224	43	𝛼2	𝛼2	PROPN
iajs-2801	224	44	∗	∗	NOUN
iajs-2801	224	45	(	(	PUNCT
iajs-2801	224	46	𝛽2	𝛽2	PROPN
iajs-2801	224	47	∗	∗	NOUN
iajs-2801	224	48	δ2	δ2	VERB
iajs-2801	224	49	)	)	PUNCT
iajs-2801	224	50	)	)	PUNCT
iajs-2801	224	51	,	,	PUNCT
iajs-2801	224	52	𝜇2	𝜇2	PROPN
iajs-2801	224	53	+	+	PROPN
iajs-2801	224	54	(	(	PUNCT
iajs-2801	224	55	𝛽2	𝛽2	NOUN
iajs-2801	224	56	)	)	PUNCT
iajs-2801	224	57	}	}	PUNCT
iajs-2801	224	58	}	}	PUNCT
iajs-2801	224	59	=	=	SYM
iajs-2801	224	60	𝑟𝑚𝑖𝑛{𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛{𝑟𝑚𝑖𝑛	PROPN
iajs-2801	224	61	{	{	PUNCT
iajs-2801	224	62	𝜇1	𝜇1	PROPN
iajs-2801	224	63	+	+	PROPN
iajs-2801	224	64	(	(	PUNCT
iajs-2801	224	65	𝛼1	𝛼1	NOUN
iajs-2801	224	66	∗	∗	NOUN
iajs-2801	224	67	(	(	PUNCT
iajs-2801	224	68	𝛽1	𝛽1	NOUN
iajs-2801	224	69	∗	∗	NOUN
iajs-2801	224	70	δ1	δ1	NOUN
iajs-2801	224	71	)	)	PUNCT
iajs-2801	224	72	)	)	PUNCT
iajs-2801	224	73	,	,	PUNCT
iajs-2801	224	74	𝜇2	𝜇2	PROPN
iajs-2801	224	75	+	+	PROPN
iajs-2801	224	76	(	(	PUNCT
iajs-2801	224	77	𝛼2	𝛼2	PROPN
iajs-2801	224	78	∗	∗	NOUN
iajs-2801	224	79	(	(	PUNCT
iajs-2801	224	80	𝛽2	𝛽2	PROPN
iajs-2801	224	81	∗	∗	NOUN
iajs-2801	224	82	δ2	δ2	VERB
iajs-2801	224	83	)	)	PUNCT
iajs-2801	224	84	}	}	PUNCT
iajs-2801	224	85	,	,	PUNCT
iajs-2801	224	86	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	224	87	{	{	PUNCT
iajs-2801	224	88	𝜇1	𝜇1	PROPN
iajs-2801	224	89	+	+	PROPN
iajs-2801	224	90	(	(	PUNCT
iajs-2801	224	91	𝛽1	𝛽1	NOUN
iajs-2801	224	92	)	)	PUNCT
iajs-2801	224	93	,	,	PUNCT
iajs-2801	224	94	𝜇2	𝜇2	PROPN
iajs-2801	224	95	+	+	PROPN
iajs-2801	224	96	(	(	PUNCT
iajs-2801	224	97	𝛽2	𝛽2	NOUN
iajs-2801	224	98	)	)	PUNCT
iajs-2801	224	99	}	}	PUNCT
iajs-2801	224	100	=	=	SYM
iajs-2801	224	101	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	224	102	{	{	PUNCT
iajs-2801	224	103	𝑟𝑚𝑖𝑛(	𝑟𝑚𝑖𝑛(	PROPN
iajs-2801	224	104	�	�	PROPN
iajs-2801	224	105	̃	̃	PROPN
iajs-2801	224	106	�	�	NOUN
iajs-2801	224	107	1	1	NUM
iajs-2801	224	108	+	+	SYM
iajs-2801	224	109	×	×	PROPN
iajs-2801	224	110	𝜇2	𝜇2	NOUN
iajs-2801	224	111	+	+	PROPN
iajs-2801	224	112	)	)	PUNCT
iajs-2801	224	113	{	{	PUNCT
iajs-2801	224	114	(	(	PUNCT
iajs-2801	224	115	𝛼1	𝛼1	NOUN
iajs-2801	224	116	∗	∗	NOUN
iajs-2801	224	117	(	(	PUNCT
iajs-2801	224	118	𝛽1	𝛽1	NOUN
iajs-2801	224	119	∗	∗	NOUN
iajs-2801	224	120	δ1	δ1	NOUN
iajs-2801	224	121	)	)	PUNCT
iajs-2801	224	122	)	)	PUNCT
iajs-2801	224	123	,	,	PUNCT
iajs-2801	224	124	(	(	PUNCT
iajs-2801	224	125	𝛼2	𝛼2	PROPN
iajs-2801	224	126	∗	∗	NOUN
iajs-2801	224	127	(	(	PUNCT
iajs-2801	224	128	𝛽2	𝛽2	PROPN
iajs-2801	224	129	∗	∗	NOUN
iajs-2801	224	130	δ2	δ2	VERB
iajs-2801	224	131	)	)	PUNCT
iajs-2801	224	132	)	)	PUNCT
iajs-2801	224	133	}	}	PUNCT
iajs-2801	224	134	,	,	PUNCT
iajs-2801	224	135	{	{	PUNCT
iajs-2801	224	136	(	(	PUNCT
iajs-2801	224	137	𝜇1	𝜇1	NOUN
iajs-2801	224	138	+	+	CCONJ
iajs-2801	224	139	×	×	PROPN
iajs-2801	224	140	𝜇2	𝜇2	NOUN
iajs-2801	224	141	+	+	PROPN
iajs-2801	224	142	)	)	PUNCT
iajs-2801	224	143	(	(	PUNCT
iajs-2801	224	144	𝛽1	𝛽1	NOUN
iajs-2801	224	145	,	,	PUNCT
iajs-2801	224	146	𝛽2	𝛽2	NOUN
iajs-2801	224	147	)	)	PUNCT
iajs-2801	224	148	}	}	PUNCT
iajs-2801	224	149	}	}	PUNCT
iajs-2801	224	150	and	and	CCONJ
iajs-2801	224	151	(	(	PUNCT
iajs-2801	224	152	�	�	PROPN
iajs-2801	224	153	̃	̃	NOUN
iajs-2801	224	154	�	�	NOUN
iajs-2801	224	155	1	1	NUM
iajs-2801	224	156	−	−	NOUN
iajs-2801	224	157	×	×	NOUN
iajs-2801	224	158	𝜇2	𝜇2	NOUN
iajs-2801	224	159	−)(𝛼1	−)(𝛼1	PROPN
iajs-2801	224	160	∗	∗	NOUN
iajs-2801	224	161	δ1	δ1	NOUN
iajs-2801	224	162	,	,	PUNCT
iajs-2801	224	163	𝛼2	𝛼2	PROPN
iajs-2801	224	164	∗	∗	NOUN
iajs-2801	224	165	δ2	δ2	VERB
iajs-2801	224	166	)	)	PUNCT
iajs-2801	224	167	=	=	SYM
iajs-2801	224	168	𝑟𝑚𝑎𝑥{𝜇1	𝑟𝑚𝑎𝑥{𝜇1	PROPN
iajs-2801	224	169	−(𝛼1	−(𝛼1	NUM
iajs-2801	224	170	∗	∗	NOUN
iajs-2801	224	171	δ1	δ1	NOUN
iajs-2801	224	172	)	)	PUNCT
iajs-2801	224	173	,	,	PUNCT
iajs-2801	224	174	𝜇2	𝜇2	VERB
iajs-2801	224	175	−(𝛼2	−(𝛼2	PRON
iajs-2801	224	176	∗	∗	X
iajs-2801	224	177	δ2	δ2	VERB
iajs-2801	224	178	)	)	PUNCT
iajs-2801	224	179	}	}	PUNCT
iajs-2801	224	180	≤	≤	NUM
iajs-2801	224	181	𝑟𝑚𝑎𝑥{𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥{𝑟𝑚𝑎𝑥	NUM
iajs-2801	224	182	{	{	PUNCT
iajs-2801	224	183	𝜇1	𝜇1	NOUN
iajs-2801	224	184	−(𝛼1	−(𝛼1	PROPN
iajs-2801	224	185	∗	∗	NOUN
iajs-2801	224	186	(	(	PUNCT
iajs-2801	224	187	𝛽1	𝛽1	NOUN
iajs-2801	224	188	∗	∗	NOUN
iajs-2801	224	189	δ1	δ1	NOUN
iajs-2801	224	190	)	)	PUNCT
iajs-2801	224	191	)	)	PUNCT
iajs-2801	224	192	,	,	PUNCT
iajs-2801	224	193	𝜇1	𝜇1	PROPN
iajs-2801	224	194	−(𝛽1	−(𝛽1	NUM
iajs-2801	224	195	)	)	PUNCT
iajs-2801	224	196	}	}	PUNCT
iajs-2801	224	197	,	,	PUNCT
iajs-2801	224	198	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	PROPN
iajs-2801	224	199	{	{	PUNCT
iajs-2801	224	200	𝜇2	𝜇2	PROPN
iajs-2801	224	201	−(𝛼2	−(𝛼2	PRON
iajs-2801	224	202	∗	∗	NOUN
iajs-2801	224	203	(	(	PUNCT
iajs-2801	224	204	𝛽2	𝛽2	PROPN
iajs-2801	224	205	∗	∗	NOUN
iajs-2801	224	206	δ2	δ2	VERB
iajs-2801	224	207	)	)	PUNCT
iajs-2801	224	208	,	,	PUNCT
iajs-2801	224	209	𝜇2	𝜇2	PROPN
iajs-2801	224	210	−(𝛽2	−(𝛽2	NOUN
iajs-2801	224	211	)	)	PUNCT
iajs-2801	224	212	}	}	PUNCT
iajs-2801	224	213	=	=	SYM
iajs-2801	224	214	𝑟𝑚𝑎𝑥{𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥{𝑟𝑚𝑎𝑥	NUM
iajs-2801	224	215	{	{	PUNCT
iajs-2801	224	216	�	�	PROPN
iajs-2801	224	217	̃	̃	NOUN
iajs-2801	224	218	�	�	NOUN
iajs-2801	224	219	1	1	NUM
iajs-2801	224	220	−(𝛼1	−(𝛼1	NUM
iajs-2801	224	221	∗	∗	NOUN
iajs-2801	224	222	(	(	PUNCT
iajs-2801	224	223	𝛽1	𝛽1	NOUN
iajs-2801	224	224	∗	∗	NOUN
iajs-2801	224	225	δ1	δ1	NOUN
iajs-2801	224	226	)	)	PUNCT
iajs-2801	224	227	)	)	PUNCT
iajs-2801	224	228	,	,	PUNCT
iajs-2801	224	229	𝜇2	𝜇2	VERB
iajs-2801	224	230	−(𝛼2	−(𝛼2	PRON
iajs-2801	224	231	∗	∗	NOUN
iajs-2801	224	232	(	(	PUNCT
iajs-2801	224	233	𝛽2	𝛽2	PROPN
iajs-2801	224	234	∗	∗	NOUN
iajs-2801	224	235	δ2	δ2	VERB
iajs-2801	224	236	)	)	PUNCT
iajs-2801	224	237	}	}	PUNCT
iajs-2801	224	238	,	,	PUNCT
iajs-2801	224	239	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	PROPN
iajs-2801	224	240	{	{	PUNCT
iajs-2801	224	241	𝜇1	𝜇1	NOUN
iajs-2801	224	242	−(𝛽1	−(𝛽1	NUM
iajs-2801	224	243	)	)	PUNCT
iajs-2801	224	244	,	,	PUNCT
iajs-2801	224	245	𝜇2	𝜇2	PROPN
iajs-2801	224	246	−(𝛽2	−(𝛽2	NOUN
iajs-2801	224	247	)	)	PUNCT
iajs-2801	224	248	}	}	PUNCT
iajs-2801	224	249	=	=	PUNCT
iajs-2801	224	250	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	224	251	{	{	PUNCT
iajs-2801	224	252	(	(	PUNCT
iajs-2801	224	253	�	�	PROPN
iajs-2801	224	254	̃	̃	NOUN
iajs-2801	224	255	�	�	NOUN
iajs-2801	224	256	1	1	NUM
iajs-2801	224	257	−	−	NOUN
iajs-2801	224	258	×	×	NOUN
iajs-2801	224	259	𝜇2	𝜇2	NOUN
iajs-2801	224	260	−	−	PROPN
iajs-2801	224	261	)	)	PUNCT
iajs-2801	224	262	{	{	PUNCT
iajs-2801	224	263	(	(	PUNCT
iajs-2801	224	264	𝛼1	𝛼1	NOUN
iajs-2801	224	265	∗	∗	NOUN
iajs-2801	224	266	(	(	PUNCT
iajs-2801	224	267	𝛽1	𝛽1	NOUN
iajs-2801	224	268	∗	∗	NOUN
iajs-2801	224	269	δ1	δ1	NOUN
iajs-2801	224	270	)	)	PUNCT
iajs-2801	224	271	)	)	PUNCT
iajs-2801	224	272	,	,	PUNCT
iajs-2801	224	273	(	(	PUNCT
iajs-2801	224	274	𝛼2	𝛼2	PROPN
iajs-2801	224	275	∗	∗	NOUN
iajs-2801	224	276	(	(	PUNCT
iajs-2801	224	277	𝛽2	𝛽2	PROPN
iajs-2801	224	278	∗	∗	NOUN
iajs-2801	224	279	δ2	δ2	VERB
iajs-2801	224	280	)	)	PUNCT
iajs-2801	224	281	)	)	PUNCT
iajs-2801	224	282	}	}	PUNCT
iajs-2801	224	283	,	,	PUNCT
iajs-2801	224	284	{	{	PUNCT
iajs-2801	224	285	(	(	PUNCT
iajs-2801	224	286	𝜇1	𝜇1	ADJ
iajs-2801	224	287	−	−	PROPN
iajs-2801	224	288	×	×	PROPN
iajs-2801	224	289	𝜇2	𝜇2	PROPN
iajs-2801	224	290	−)(𝛽1	−)(𝛽1	PROPN
iajs-2801	224	291	,	,	PUNCT
iajs-2801	224	292	𝛽2	𝛽2	NOUN
iajs-2801	224	293	)	)	PUNCT
iajs-2801	224	294	}	}	PUNCT
iajs-2801	224	295	}	}	PUNCT
iajs-2801	224	296	.	.	PUNCT
iajs-2801	225	1	also	also	ADV
iajs-2801	225	2	,	,	PUNCT
iajs-2801	225	3	(	(	PUNCT
iajs-2801	225	4	𝜆1	𝜆1	VERB
iajs-2801	225	5	+	+	CCONJ
iajs-2801	225	6	×	×	PROPN
iajs-2801	225	7	𝜆2	𝜆2	NOUN
iajs-2801	225	8	+	+	PROPN
iajs-2801	225	9	)	)	PUNCT
iajs-2801	225	10	(	(	PUNCT
iajs-2801	225	11	𝛼1	𝛼1	NOUN
iajs-2801	225	12	∗	∗	NOUN
iajs-2801	225	13	δ1	δ1	NOUN
iajs-2801	225	14	,	,	PUNCT
iajs-2801	225	15	𝛼2	𝛼2	PROPN
iajs-2801	225	16	∗	∗	NOUN
iajs-2801	225	17	δ2	δ2	VERB
iajs-2801	225	18	)	)	PUNCT
iajs-2801	225	19	=	=	PUNCT
iajs-2801	226	1	𝑚𝑖𝑛{𝜆1	𝑚𝑖𝑛{𝜆1	PUNCT
iajs-2801	226	2	+	+	NUM
iajs-2801	226	3	(	(	PUNCT
iajs-2801	226	4	𝛼1	𝛼1	NOUN
iajs-2801	226	5	∗	∗	NOUN
iajs-2801	226	6	δ1	δ1	NOUN
iajs-2801	226	7	)	)	PUNCT
iajs-2801	226	8	,	,	PUNCT
iajs-2801	226	9	𝜆2	𝜆2	PROPN
iajs-2801	226	10	+	+	PROPN
iajs-2801	226	11	(	(	PUNCT
iajs-2801	226	12	𝛼2	𝛼2	PROPN
iajs-2801	226	13	∗	∗	NOUN
iajs-2801	226	14	δ2	δ2	VERB
iajs-2801	226	15	)	)	PUNCT
iajs-2801	226	16	}	}	PUNCT
iajs-2801	226	17	≥	≥	PROPN
iajs-2801	226	18	𝑚𝑖𝑛{𝑚𝑖𝑛	𝑚𝑖𝑛{𝑚𝑖𝑛	NOUN
iajs-2801	226	19	{	{	PUNCT
iajs-2801	226	20	𝜆1	𝜆1	VERB
iajs-2801	227	1	+	+	PROPN
iajs-2801	227	2	(	(	PUNCT
iajs-2801	227	3	𝛼1	𝛼1	NOUN
iajs-2801	227	4	∗	∗	NOUN
iajs-2801	227	5	(	(	PUNCT
iajs-2801	227	6	𝛽1	𝛽1	NOUN
iajs-2801	227	7	∗	∗	NOUN
iajs-2801	227	8	δ1	δ1	NOUN
iajs-2801	227	9	)	)	PUNCT
iajs-2801	227	10	)	)	PUNCT
iajs-2801	227	11	,	,	PUNCT
iajs-2801	228	1	𝜆1	𝜆1	VERB
iajs-2801	228	2	+	+	PROPN
iajs-2801	228	3	(	(	PUNCT
iajs-2801	228	4	𝛽1	𝛽1	NOUN
iajs-2801	228	5	)	)	PUNCT
iajs-2801	228	6	}	}	PUNCT
iajs-2801	228	7	,	,	PUNCT
iajs-2801	228	8	𝑚𝑖𝑛{𝜆2	𝑚𝑖𝑛{𝜆2	NOUN
iajs-2801	228	9	+	+	X
iajs-2801	228	10	(	(	PUNCT
iajs-2801	228	11	𝛼2	𝛼2	PROPN
iajs-2801	228	12	∗	∗	NOUN
iajs-2801	228	13	(	(	PUNCT
iajs-2801	228	14	𝛽2	𝛽2	PROPN
iajs-2801	228	15	∗	∗	NOUN
iajs-2801	228	16	δ2	δ2	VERB
iajs-2801	228	17	)	)	PUNCT
iajs-2801	228	18	)	)	PUNCT
iajs-2801	228	19	,	,	PUNCT
iajs-2801	228	20	𝜆2	𝜆2	PROPN
iajs-2801	228	21	+	+	PROPN
iajs-2801	228	22	(	(	PUNCT
iajs-2801	228	23	𝛽2	𝛽2	NOUN
iajs-2801	228	24	)	)	PUNCT
iajs-2801	228	25	}	}	PUNCT
iajs-2801	228	26	}	}	PUNCT
iajs-2801	228	27	=	=	SYM
iajs-2801	228	28	𝑚𝑖𝑛{𝑚𝑖𝑛	𝑚𝑖𝑛{𝑚𝑖𝑛	NOUN
iajs-2801	228	29	{	{	PUNCT
iajs-2801	228	30	𝜆1	𝜆1	VERB
iajs-2801	228	31	+	+	PROPN
iajs-2801	228	32	(	(	PUNCT
iajs-2801	228	33	𝛼1	𝛼1	NOUN
iajs-2801	228	34	∗	∗	NOUN
iajs-2801	228	35	(	(	PUNCT
iajs-2801	228	36	𝛽1	𝛽1	NOUN
iajs-2801	228	37	∗	∗	NOUN
iajs-2801	228	38	δ1	δ1	NOUN
iajs-2801	228	39	)	)	PUNCT
iajs-2801	228	40	)	)	PUNCT
iajs-2801	228	41	,	,	PUNCT
iajs-2801	228	42	𝜆2	𝜆2	PROPN
iajs-2801	228	43	+	+	PROPN
iajs-2801	228	44	(	(	PUNCT
iajs-2801	228	45	𝛼2	𝛼2	PROPN
iajs-2801	228	46	∗	∗	NOUN
iajs-2801	228	47	(	(	PUNCT
iajs-2801	228	48	𝛽2	𝛽2	PROPN
iajs-2801	228	49	∗	∗	NOUN
iajs-2801	228	50	δ2	δ2	VERB
iajs-2801	228	51	)	)	PUNCT
iajs-2801	228	52	}	}	PUNCT
iajs-2801	228	53	,	,	PUNCT
iajs-2801	228	54	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	228	55	{	{	PUNCT
iajs-2801	228	56	𝜆1	𝜆1	VERB
iajs-2801	228	57	+	+	PROPN
iajs-2801	228	58	(	(	PUNCT
iajs-2801	228	59	𝛽1	𝛽1	NOUN
iajs-2801	228	60	)	)	PUNCT
iajs-2801	228	61	,	,	PUNCT
iajs-2801	228	62	𝜆2	𝜆2	PROPN
iajs-2801	228	63	+	+	PROPN
iajs-2801	228	64	(	(	PUNCT
iajs-2801	228	65	𝛽2	𝛽2	NOUN
iajs-2801	228	66	)	)	PUNCT
iajs-2801	228	67	}	}	PUNCT
iajs-2801	228	68	=	=	SYM
iajs-2801	228	69	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	228	70	{	{	PUNCT
iajs-2801	228	71	𝑚𝑖𝑛(𝜆1	𝑚𝑖𝑛(𝜆1	NOUN
iajs-2801	229	1	+	+	CCONJ
iajs-2801	229	2	×	×	PROPN
iajs-2801	229	3	𝜆2	𝜆2	NOUN
iajs-2801	229	4	+	+	NOUN
iajs-2801	229	5	)	)	PUNCT
iajs-2801	229	6	{	{	PUNCT
iajs-2801	229	7	(	(	PUNCT
iajs-2801	229	8	𝛼1	𝛼1	NOUN
iajs-2801	229	9	∗	∗	NOUN
iajs-2801	229	10	(	(	PUNCT
iajs-2801	229	11	𝛽1	𝛽1	NOUN
iajs-2801	229	12	∗	∗	NOUN
iajs-2801	229	13	δ1	δ1	NOUN
iajs-2801	229	14	)	)	PUNCT
iajs-2801	229	15	)	)	PUNCT
iajs-2801	229	16	,	,	PUNCT
iajs-2801	229	17	(	(	PUNCT
iajs-2801	229	18	𝛼2	𝛼2	PROPN
iajs-2801	229	19	∗	∗	NOUN
iajs-2801	229	20	(	(	PUNCT
iajs-2801	229	21	𝛽2	𝛽2	PROPN
iajs-2801	229	22	∗	∗	NOUN
iajs-2801	229	23	δ2	δ2	VERB
iajs-2801	229	24	)	)	PUNCT
iajs-2801	229	25	)	)	PUNCT
iajs-2801	229	26	}	}	PUNCT
iajs-2801	229	27	,	,	PUNCT
iajs-2801	229	28	{	{	PUNCT
iajs-2801	229	29	(;	(;	PUNCT
iajs-2801	229	30	𝜆1	𝜆1	NOUN
iajs-2801	229	31	+	+	CCONJ
iajs-2801	229	32	×	×	NOUN
iajs-2801	229	33	;	;	PUNCT
iajs-2801	229	34	𝜆2	𝜆2	PROPN
iajs-2801	229	35	+	+	PROPN
iajs-2801	229	36	)	)	PUNCT
iajs-2801	229	37	(	(	PUNCT
iajs-2801	229	38	𝛽1	𝛽1	NOUN
iajs-2801	229	39	,	,	PUNCT
iajs-2801	229	40	𝛽2	𝛽2	NOUN
iajs-2801	229	41	)	)	PUNCT
iajs-2801	229	42	}	}	PUNCT
iajs-2801	229	43	}	}	PUNCT
iajs-2801	229	44	and	and	CCONJ
iajs-2801	229	45	(;	(;	PUNCT
iajs-2801	229	46	𝜆1	𝜆1	NOUN
iajs-2801	229	47	−	−	ADP
iajs-2801	229	48	×	×	NOUN
iajs-2801	229	49	;	;	PUNCT
iajs-2801	229	50	𝜆2	𝜆2	PROPN
iajs-2801	229	51	−)(𝛼1	−)(𝛼1	PROPN
iajs-2801	229	52	∗	∗	NOUN
iajs-2801	229	53	δ1	δ1	NOUN
iajs-2801	229	54	,	,	PUNCT
iajs-2801	229	55	𝛼2	𝛼2	PROPN
iajs-2801	229	56	∗	∗	NOUN
iajs-2801	229	57	δ2	δ2	VERB
iajs-2801	229	58	)	)	PUNCT
iajs-2801	229	59	=	=	SYM
iajs-2801	229	60	𝑚𝑎𝑥{𝜆1	𝑚𝑎𝑥{𝜆1	NOUN
iajs-2801	229	61	−(𝛼1	−(𝛼1	ADP
iajs-2801	229	62	∗	∗	NOUN
iajs-2801	229	63	δ1	δ1	NOUN
iajs-2801	229	64	)	)	PUNCT
iajs-2801	229	65	,	,	PUNCT
iajs-2801	229	66	𝜆2	𝜆2	PROPN
iajs-2801	229	67	−(𝛼2	−(𝛼2	NOUN
iajs-2801	229	68	∗	∗	X
iajs-2801	229	69	δ2	δ2	VERB
iajs-2801	229	70	)	)	PUNCT
iajs-2801	229	71	}	}	PUNCT
iajs-2801	229	72	≤	≤	NUM
iajs-2801	229	73	𝑚𝑎𝑥{𝑚𝑎𝑥	𝑚𝑎𝑥{𝑚𝑎𝑥	X
iajs-2801	229	74	{	{	PUNCT
iajs-2801	229	75	𝜆1	𝜆1	VERB
iajs-2801	229	76	−(𝛼1	−(𝛼1	PRON
iajs-2801	229	77	∗	∗	NOUN
iajs-2801	229	78	(	(	PUNCT
iajs-2801	229	79	𝛽1	𝛽1	NOUN
iajs-2801	229	80	∗	∗	NOUN
iajs-2801	229	81	δ1	δ1	NOUN
iajs-2801	229	82	)	)	PUNCT
iajs-2801	229	83	)	)	PUNCT
iajs-2801	229	84	,	,	PUNCT
iajs-2801	229	85	𝜆1	𝜆1	PROPN
iajs-2801	229	86	−(𝛽1	−(𝛽1	PUNCT
iajs-2801	229	87	)	)	PUNCT
iajs-2801	229	88	}	}	PUNCT
iajs-2801	229	89	,	,	PUNCT
iajs-2801	229	90	𝑚𝑎𝑥	𝑚𝑎𝑥	X
iajs-2801	229	91	{	{	PUNCT
iajs-2801	229	92	𝜆2	𝜆2	NOUN
iajs-2801	229	93	−(𝛼2	−(𝛼2	PRON
iajs-2801	229	94	∗	∗	NOUN
iajs-2801	229	95	(	(	PUNCT
iajs-2801	229	96	𝛽2	𝛽2	PROPN
iajs-2801	229	97	∗	∗	NOUN
iajs-2801	229	98	δ2	δ2	VERB
iajs-2801	229	99	)	)	PUNCT
iajs-2801	229	100	,	,	PUNCT
iajs-2801	229	101	𝜆2	𝜆2	PROPN
iajs-2801	229	102	−(𝛽2	−(𝛽2	NUM
iajs-2801	229	103	)	)	PUNCT
iajs-2801	229	104	}	}	PUNCT
iajs-2801	229	105	=	=	SYM
iajs-2801	229	106	𝑚𝑎𝑥{𝑚𝑎𝑥	𝑚𝑎𝑥{𝑚𝑎𝑥	NOUN
iajs-2801	229	107	{	{	PUNCT
iajs-2801	229	108	𝜆1	𝜆1	VERB
iajs-2801	229	109	−(𝛼1	−(𝛼1	PRON
iajs-2801	229	110	∗	∗	NOUN
iajs-2801	229	111	(	(	PUNCT
iajs-2801	229	112	𝛽1	𝛽1	NOUN
iajs-2801	229	113	∗	∗	NOUN
iajs-2801	229	114	δ1	δ1	NOUN
iajs-2801	229	115	)	)	PUNCT
iajs-2801	229	116	)	)	PUNCT
iajs-2801	229	117	,	,	PUNCT
iajs-2801	229	118	𝜆2	𝜆2	NOUN
iajs-2801	229	119	−(𝛼2	−(𝛼2	PRON
iajs-2801	229	120	∗	∗	NOUN
iajs-2801	229	121	(	(	PUNCT
iajs-2801	229	122	𝛽2	𝛽2	PROPN
iajs-2801	229	123	∗	∗	NOUN
iajs-2801	229	124	δ2	δ2	VERB
iajs-2801	229	125	)	)	PUNCT
iajs-2801	229	126	}	}	PUNCT
iajs-2801	229	127	,	,	PUNCT
iajs-2801	229	128	𝑚𝑎𝑥	𝑚𝑎𝑥	X
iajs-2801	229	129	{	{	PUNCT
iajs-2801	229	130	𝜆1	𝜆1	NOUN
iajs-2801	229	131	−(𝛽1	−(𝛽1	NUM
iajs-2801	229	132	)	)	PUNCT
iajs-2801	229	133	,	,	PUNCT
iajs-2801	229	134	𝜆2	𝜆2	PROPN
iajs-2801	229	135	−(𝛽2	−(𝛽2	NUM
iajs-2801	229	136	)	)	PUNCT
iajs-2801	229	137	}	}	PUNCT
iajs-2801	229	138	=	=	PUNCT
iajs-2801	229	139	𝑚𝑎𝑥	𝑚𝑎𝑥	X
iajs-2801	229	140	{	{	PUNCT
iajs-2801	229	141	(	(	PUNCT
iajs-2801	229	142	𝜆1	𝜆1	VERB
iajs-2801	229	143	−	−	PROPN
iajs-2801	229	144	×	×	PROPN
iajs-2801	229	145	𝜆2	𝜆2	NOUN
iajs-2801	229	146	−	−	NOUN
iajs-2801	229	147	)	)	PUNCT
iajs-2801	229	148	{	{	PUNCT
iajs-2801	229	149	(	(	PUNCT
iajs-2801	229	150	𝛼1	𝛼1	NOUN
iajs-2801	229	151	∗	∗	NOUN
iajs-2801	229	152	(	(	PUNCT
iajs-2801	229	153	𝛽1	𝛽1	NOUN
iajs-2801	229	154	∗	∗	NOUN
iajs-2801	229	155	δ1	δ1	NOUN
iajs-2801	229	156	)	)	PUNCT
iajs-2801	229	157	)	)	PUNCT
iajs-2801	229	158	,	,	PUNCT
iajs-2801	229	159	(	(	PUNCT
iajs-2801	229	160	𝛼2	𝛼2	PROPN
iajs-2801	229	161	∗	∗	NOUN
iajs-2801	229	162	(	(	PUNCT
iajs-2801	229	163	𝛽2	𝛽2	PROPN
iajs-2801	229	164	∗	∗	NOUN
iajs-2801	229	165	δ2	δ2	VERB
iajs-2801	229	166	)	)	PUNCT
iajs-2801	229	167	)	)	PUNCT
iajs-2801	229	168	}	}	PUNCT
iajs-2801	229	169	,	,	PUNCT
iajs-2801	229	170	{	{	PUNCT
iajs-2801	229	171	(	(	PUNCT
iajs-2801	229	172	𝜆1	𝜆1	VERB
iajs-2801	229	173	−	−	PROPN
iajs-2801	229	174	×	×	PROPN
iajs-2801	229	175	𝜆2	𝜆2	PROPN
iajs-2801	229	176	−)(𝛽1	−)(𝛽1	PROPN
iajs-2801	229	177	,	,	PUNCT
iajs-2801	229	178	𝛽2	𝛽2	NOUN
iajs-2801	229	179	)	)	PUNCT
iajs-2801	229	180	}	}	PUNCT
iajs-2801	229	181	}	}	PUNCT
iajs-2801	229	182	.	.	PUNCT
iajs-2801	230	1	and	and	CCONJ
iajs-2801	230	2	(	(	PUNCT
iajs-2801	230	3	𝜇1	𝜇1	PROPN
iajs-2801	230	4	+	+	CCONJ
iajs-2801	230	5	×	×	PROPN
iajs-2801	230	6	𝜇2	𝜇2	NOUN
iajs-2801	230	7	+	+	PROPN
iajs-2801	230	8	)	)	PUNCT
iajs-2801	230	9	(	(	PUNCT
iajs-2801	230	10	𝛼1	𝛼1	NOUN
iajs-2801	230	11	𝛽1	𝛽1	NOUN
iajs-2801	230	12	,	,	PUNCT
iajs-2801	230	13	𝛼2	𝛼2	PROPN
iajs-2801	230	14	𝛽2	𝛽2	PROPN
iajs-2801	230	15	)	)	PUNCT
iajs-2801	230	16	=	=	SYM
iajs-2801	230	17	𝑟𝑚𝑖𝑛{	𝑟𝑚𝑖𝑛{	PROPN
iajs-2801	230	18	�	�	PROPN
iajs-2801	230	19	̃	̃	PROPN
iajs-2801	230	20	�	�	NOUN
iajs-2801	230	21	1	1	NUM
iajs-2801	230	22	+	+	NOUN
iajs-2801	230	23	(	(	PUNCT
iajs-2801	230	24	𝛼1	𝛼1	NOUN
iajs-2801	230	25	𝛽1	𝛽1	NOUN
iajs-2801	230	26	)	)	PUNCT
iajs-2801	230	27	,	,	PUNCT
iajs-2801	230	28	𝜇2	𝜇2	PROPN
iajs-2801	230	29	+	+	PROPN
iajs-2801	230	30	(	(	PUNCT
iajs-2801	230	31	𝛼2	𝛼2	PROPN
iajs-2801	230	32	𝛽2	𝛽2	PROPN
iajs-2801	230	33	)	)	PUNCT
iajs-2801	230	34	}	}	PUNCT
iajs-2801	230	35	≥	≥	PROPN
iajs-2801	230	36	𝑟𝑚𝑖𝑛{𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛{𝑟𝑚𝑖𝑛	PROPN
iajs-2801	230	37	{	{	PUNCT
iajs-2801	230	38	𝜇1	𝜇1	PROPN
iajs-2801	230	39	+	+	PROPN
iajs-2801	230	40	(	(	PUNCT
iajs-2801	230	41	𝛼1	𝛼1	NOUN
iajs-2801	230	42	)	)	PUNCT
iajs-2801	230	43	,	,	PUNCT
iajs-2801	230	44	𝜇1	𝜇1	PROPN
iajs-2801	230	45	+	+	PROPN
iajs-2801	230	46	(	(	PUNCT
iajs-2801	230	47	𝛽1	𝛽1	NOUN
iajs-2801	230	48	)	)	PUNCT
iajs-2801	230	49	}	}	PUNCT
iajs-2801	230	50	,	,	PUNCT
iajs-2801	230	51	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	230	52	{	{	PUNCT
iajs-2801	230	53	𝜇2	𝜇2	PROPN
iajs-2801	230	54	+	+	PROPN
iajs-2801	230	55	(	(	PUNCT
iajs-2801	230	56	𝛼2	𝛼2	PROPN
iajs-2801	230	57	)	)	PUNCT
iajs-2801	230	58	,	,	PUNCT
iajs-2801	230	59	𝜇2	𝜇2	PROPN
iajs-2801	230	60	+	+	PROPN
iajs-2801	230	61	(	(	PUNCT
iajs-2801	230	62	𝛽2	𝛽2	NOUN
iajs-2801	230	63	)	)	PUNCT
iajs-2801	230	64	}	}	PUNCT
iajs-2801	230	65	=	=	SYM
iajs-2801	230	66	𝑟𝑚𝑖𝑛{𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛{𝑟𝑚𝑖𝑛	PROPN
iajs-2801	230	67	{	{	PUNCT
iajs-2801	230	68	𝜇1	𝜇1	PROPN
iajs-2801	230	69	+	+	PROPN
iajs-2801	230	70	(	(	PUNCT
iajs-2801	230	71	𝛼1	𝛼1	NOUN
iajs-2801	230	72	)	)	PUNCT
iajs-2801	230	73	,	,	PUNCT
iajs-2801	230	74	𝜇2	𝜇2	PROPN
iajs-2801	230	75	+	+	PROPN
iajs-2801	230	76	(	(	PUNCT
iajs-2801	230	77	𝛼2	𝛼2	PROPN
iajs-2801	230	78	)	)	PUNCT
iajs-2801	230	79	}	}	PUNCT
iajs-2801	230	80	,	,	PUNCT
iajs-2801	230	81	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	230	82	{	{	PUNCT
iajs-2801	230	83	𝜇1	𝜇1	PROPN
iajs-2801	230	84	+	+	PROPN
iajs-2801	230	85	(	(	PUNCT
iajs-2801	230	86	𝛽1	𝛽1	NOUN
iajs-2801	230	87	)	)	PUNCT
iajs-2801	230	88	,	,	PUNCT
iajs-2801	230	89	𝜇2	𝜇2	PROPN
iajs-2801	230	90	+	+	PROPN
iajs-2801	230	91	(	(	PUNCT
iajs-2801	230	92	𝛽2	𝛽2	NOUN
iajs-2801	230	93	)	)	PUNCT
iajs-2801	230	94	}	}	PUNCT
iajs-2801	230	95	=	=	SYM
iajs-2801	230	96	𝑟𝑚𝑖𝑛{{(	𝑟𝑚𝑖𝑛{{(	NUM
iajs-2801	230	97	�	�	PROPN
iajs-2801	230	98	̃	̃	NOUN
iajs-2801	230	99	�	�	NOUN
iajs-2801	230	100	1	1	NUM
iajs-2801	230	101	+	+	SYM
iajs-2801	230	102	×	×	PROPN
iajs-2801	230	103	𝜇2	𝜇2	NOUN
iajs-2801	230	104	+	+	PROPN
iajs-2801	230	105	)	)	PUNCT
iajs-2801	230	106	(	(	PUNCT
iajs-2801	230	107	𝛼1	𝛼1	NOUN
iajs-2801	230	108	,	,	PUNCT
iajs-2801	230	109	𝛼2	𝛼2	PROPN
iajs-2801	230	110	)	)	PUNCT
iajs-2801	230	111	}	}	PUNCT
iajs-2801	230	112	,	,	PUNCT
iajs-2801	230	113	{	{	PUNCT
iajs-2801	230	114	(	(	PUNCT
iajs-2801	230	115	�	�	PROPN
iajs-2801	230	116	̃	̃	NOUN
iajs-2801	230	117	�	�	NOUN
iajs-2801	230	118	1	1	NUM
iajs-2801	230	119	+	+	SYM
iajs-2801	230	120	×	×	PROPN
iajs-2801	230	121	𝜇2	𝜇2	NOUN
iajs-2801	230	122	+	+	PROPN
iajs-2801	230	123	)	)	PUNCT
iajs-2801	230	124	(	(	PUNCT
iajs-2801	230	125	𝛽1	𝛽1	NOUN
iajs-2801	230	126	,	,	PUNCT
iajs-2801	230	127	𝛽2	𝛽2	NOUN
iajs-2801	230	128	)	)	PUNCT
iajs-2801	230	129	}	}	PUNCT
iajs-2801	230	130	}	}	PUNCT
iajs-2801	230	131	and	and	CCONJ
iajs-2801	230	132	(	(	PUNCT
iajs-2801	230	133	𝜇1	𝜇1	PROPN
iajs-2801	230	134	−	−	PROPN
iajs-2801	230	135	×	×	PROPN
iajs-2801	230	136	𝜇2	𝜇2	NOUN
iajs-2801	230	137	−)(𝛼1	−)(𝛼1	PROPN
iajs-2801	230	138	𝛽1	𝛽1	PROPN
iajs-2801	230	139	,	,	PUNCT
iajs-2801	230	140	𝛼2	𝛼2	PROPN
iajs-2801	230	141	𝛽2	𝛽2	NOUN
iajs-2801	230	142	)	)	PUNCT
iajs-2801	230	143	=	=	PUNCT
iajs-2801	230	144	𝑟𝑚𝑎𝑥{	𝑟𝑚𝑎𝑥{	NOUN
iajs-2801	230	145	�	�	PROPN
iajs-2801	230	146	̃	̃	PROPN
iajs-2801	230	147	�	�	NOUN
iajs-2801	230	148	1	1	NUM
iajs-2801	230	149	−(𝛼1	−(𝛼1	NUM
iajs-2801	230	150	𝛽1	𝛽1	NOUN
iajs-2801	230	151	)	)	PUNCT
iajs-2801	230	152	,	,	PUNCT
iajs-2801	230	153	𝜇2	𝜇2	VERB
iajs-2801	230	154	−(𝛼2	−(𝛼2	PRON
iajs-2801	230	155	𝛽2	𝛽2	NOUN
iajs-2801	230	156	)	)	PUNCT
iajs-2801	230	157	}	}	PUNCT
iajs-2801	230	158	≤	≤	NOUN
iajs-2801	230	159	𝑟𝑚𝑎𝑥{𝑟𝑚𝑎𝑥{𝜇1	𝑟𝑚𝑎𝑥{𝑟𝑚𝑎𝑥{𝜇1	VERB
iajs-2801	230	160	−(𝛼1	−(𝛼1	NUM
iajs-2801	230	161	)	)	PUNCT
iajs-2801	230	162	,	,	PUNCT
iajs-2801	230	163	𝜇1	𝜇1	PROPN
iajs-2801	230	164	−(𝛽1	−(𝛽1	NUM
iajs-2801	230	165	)	)	PUNCT
iajs-2801	230	166	}	}	PUNCT
iajs-2801	230	167	,	,	PUNCT
iajs-2801	230	168	𝑟𝑚𝑎𝑥{𝜇2	𝑟𝑚𝑎𝑥{𝜇2	X
iajs-2801	230	169	−(𝛼2	−(𝛼2	NOUN
iajs-2801	230	170	)	)	PUNCT
iajs-2801	230	171	,	,	PUNCT
iajs-2801	230	172	𝜇2	𝜇2	PROPN
iajs-2801	230	173	−(𝛽2	−(𝛽2	NOUN
iajs-2801	230	174	)	)	PUNCT
iajs-2801	230	175	}	}	PUNCT
iajs-2801	231	1	=	=	SYM
iajs-2801	231	2	𝑟𝑚𝑎𝑥{𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥{𝑟𝑚𝑎𝑥	NUM
iajs-2801	231	3	{	{	PUNCT
iajs-2801	231	4	𝜇1	𝜇1	NOUN
iajs-2801	231	5	−(𝛼1	−(𝛼1	PROPN
iajs-2801	231	6	)	)	PUNCT
iajs-2801	231	7	,	,	PUNCT
iajs-2801	231	8	𝜇2	𝜇2	VERB
iajs-2801	231	9	−(𝛼2	−(𝛼2	NOUN
iajs-2801	231	10	)	)	PUNCT
iajs-2801	231	11	}	}	PUNCT
iajs-2801	231	12	,	,	PUNCT
iajs-2801	231	13	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	PROPN
iajs-2801	231	14	{	{	PUNCT
iajs-2801	231	15	𝜇1	𝜇1	NOUN
iajs-2801	231	16	−(𝛽1	−(𝛽1	NUM
iajs-2801	231	17	)	)	PUNCT
iajs-2801	231	18	,	,	PUNCT
iajs-2801	231	19	𝜇2	𝜇2	PROPN
iajs-2801	231	20	−(𝛽2	−(𝛽2	NOUN
iajs-2801	231	21	)	)	PUNCT
iajs-2801	231	22	}	}	PUNCT
iajs-2801	231	23	=	=	SYM
iajs-2801	231	24	𝑟𝑚𝑎𝑥{{(	𝑟𝑚𝑎𝑥{{(	NUM
iajs-2801	231	25	�	�	PROPN
iajs-2801	231	26	̃	̃	NOUN
iajs-2801	231	27	�	�	NOUN
iajs-2801	231	28	1	1	NUM
iajs-2801	231	29	−	−	NOUN
iajs-2801	231	30	×	×	PROPN
iajs-2801	231	31	𝜇2	𝜇2	PROPN
iajs-2801	231	32	−)(𝛼1	−)(𝛼1	PROPN
iajs-2801	231	33	,	,	PUNCT
iajs-2801	231	34	𝛼2	𝛼2	PROPN
iajs-2801	231	35	)	)	PUNCT
iajs-2801	231	36	}	}	PUNCT
iajs-2801	231	37	,	,	PUNCT
iajs-2801	231	38	{	{	PUNCT
iajs-2801	231	39	(	(	PUNCT
iajs-2801	231	40	�	�	PROPN
iajs-2801	231	41	̃	̃	NOUN
iajs-2801	231	42	�	�	NOUN
iajs-2801	231	43	1	1	NUM
iajs-2801	231	44	−	−	NOUN
iajs-2801	231	45	×	×	PROPN
iajs-2801	231	46	𝜇2	𝜇2	PROPN
iajs-2801	231	47	−)(𝛽1	−)(𝛽1	PROPN
iajs-2801	231	48	,	,	PUNCT
iajs-2801	231	49	𝛽2	𝛽2	NOUN
iajs-2801	231	50	)	)	PUNCT
iajs-2801	231	51	}	}	PUNCT
iajs-2801	231	52	}	}	PUNCT
iajs-2801	231	53	.	.	PUNCT
iajs-2801	232	1	also	also	ADV
iajs-2801	232	2	,	,	PUNCT
iajs-2801	232	3	(	(	PUNCT
iajs-2801	232	4	𝜆1	𝜆1	VERB
iajs-2801	232	5	+	+	CCONJ
iajs-2801	232	6	×	×	PROPN
iajs-2801	232	7	𝜆2	𝜆2	NOUN
iajs-2801	232	8	+	+	PROPN
iajs-2801	232	9	)	)	PUNCT
iajs-2801	232	10	(	(	PUNCT
iajs-2801	232	11	𝛼1	𝛼1	NOUN
iajs-2801	232	12	𝛽1	𝛽1	NOUN
iajs-2801	232	13	,	,	PUNCT
iajs-2801	232	14	𝛼2	𝛼2	PROPN
iajs-2801	232	15	𝛽2	𝛽2	NOUN
iajs-2801	232	16	)	)	PUNCT
iajs-2801	232	17	=	=	PUNCT
iajs-2801	232	18	𝑚𝑖𝑛{𝜆1	𝑚𝑖𝑛{𝜆1	PUNCT
iajs-2801	232	19	+	+	NUM
iajs-2801	232	20	(	(	PUNCT
iajs-2801	232	21	𝛼1	𝛼1	NOUN
iajs-2801	232	22	𝛽1	𝛽1	NOUN
iajs-2801	232	23	)	)	PUNCT
iajs-2801	232	24	,	,	PUNCT
iajs-2801	232	25	𝜆2	𝜆2	PROPN
iajs-2801	232	26	+	+	PROPN
iajs-2801	232	27	(	(	PUNCT
iajs-2801	232	28	𝛼2	𝛼2	PROPN
iajs-2801	232	29	𝛽2	𝛽2	PROPN
iajs-2801	232	30	)	)	PUNCT
iajs-2801	232	31	}	}	PUNCT
iajs-2801	232	32	≥	≥	PROPN
iajs-2801	232	33	𝑚𝑖𝑛{𝑚𝑖𝑛	𝑚𝑖𝑛{𝑚𝑖𝑛	NOUN
iajs-2801	232	34	{	{	PUNCT
iajs-2801	232	35	𝜆1	𝜆1	VERB
iajs-2801	232	36	+	+	PROPN
iajs-2801	232	37	(	(	PUNCT
iajs-2801	232	38	𝛼1	𝛼1	NOUN
iajs-2801	232	39	)	)	PUNCT
iajs-2801	232	40	,	,	PUNCT
iajs-2801	232	41	𝜆1	𝜆1	VERB
iajs-2801	232	42	+	+	PROPN
iajs-2801	232	43	(	(	PUNCT
iajs-2801	232	44	𝛽1	𝛽1	NOUN
iajs-2801	232	45	)	)	PUNCT
iajs-2801	232	46	}	}	PUNCT
iajs-2801	232	47	,	,	PUNCT
iajs-2801	232	48	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	232	49	{	{	PUNCT
iajs-2801	232	50	𝜆2	𝜆2	PROPN
iajs-2801	232	51	+	+	PROPN
iajs-2801	232	52	(	(	PUNCT
iajs-2801	232	53	𝛼2	𝛼2	PROPN
iajs-2801	232	54	)	)	PUNCT
iajs-2801	232	55	,	,	PUNCT
iajs-2801	232	56	𝜆2	𝜆2	PROPN
iajs-2801	232	57	+	+	PROPN
iajs-2801	232	58	(	(	PUNCT
iajs-2801	232	59	𝛽2	𝛽2	NOUN
iajs-2801	232	60	)	)	PUNCT
iajs-2801	232	61	}	}	PUNCT
iajs-2801	232	62	=	=	PUNCT
iajs-2801	233	1			NUM
iajs-2801	233	2			PROPN
iajs-2801	233	3			PROPN
iajs-2801	233	4			PROPN
iajs-2801	233	5			PROPN
iajs-2801	233	6			PROPN
iajs-2801	233	7			PROPN
iajs-2801	233	8			PROPN
iajs-2801	233	9			PROPN
iajs-2801	233	10			PROPN
iajs-2801	233	11			PROPN
iajs-2801	233	12			PROPN
iajs-2801	233	13	ibn	ibn	PROPN
iajs-2801	233	14	al	al	PROPN
iajs-2801	233	15	-	-	PUNCT
iajs-2801	233	16	haitham	haitham	PROPN
iajs-2801	233	17	jour	jour	X
iajs-2801	233	18	.	.	PROPN
iajs-2801	233	19	for	for	ADP
iajs-2801	233	20	pure	pure	ADJ
iajs-2801	233	21	&	&	CCONJ
iajs-2801	233	22	appl	appl	PROPN
iajs-2801	233	23	.	.	PUNCT
iajs-2801	234	1	sci	sci	PROPN
iajs-2801	234	2	.	.	PUNCT
iajs-2801	235	1	35(1)2022	35(1)2022	NUM
iajs-2801	235	2	80	80	NUM
iajs-2801	235	3	𝑚𝑖𝑛{𝑚𝑖𝑛	𝑚𝑖𝑛{𝑚𝑖𝑛	NOUN
iajs-2801	235	4	{	{	PUNCT
iajs-2801	235	5	𝜆1	𝜆1	VERB
iajs-2801	235	6	+	+	PROPN
iajs-2801	235	7	(	(	PUNCT
iajs-2801	235	8	𝛼1	𝛼1	NOUN
iajs-2801	235	9	)	)	PUNCT
iajs-2801	235	10	,	,	PUNCT
iajs-2801	235	11	𝜆2	𝜆2	PROPN
iajs-2801	235	12	+	+	PROPN
iajs-2801	235	13	(	(	PUNCT
iajs-2801	235	14	𝛼2	𝛼2	PROPN
iajs-2801	235	15	)	)	PUNCT
iajs-2801	235	16	}	}	PUNCT
iajs-2801	235	17	,	,	PUNCT
iajs-2801	235	18	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	235	19	{	{	PUNCT
iajs-2801	235	20	𝜆1	𝜆1	VERB
iajs-2801	235	21	+	+	PROPN
iajs-2801	235	22	(	(	PUNCT
iajs-2801	235	23	𝛽1	𝛽1	NOUN
iajs-2801	235	24	)	)	PUNCT
iajs-2801	235	25	,	,	PUNCT
iajs-2801	235	26	𝜆2	𝜆2	PROPN
iajs-2801	235	27	+	+	PROPN
iajs-2801	235	28	(	(	PUNCT
iajs-2801	235	29	𝛽2	𝛽2	NOUN
iajs-2801	235	30	)	)	PUNCT
iajs-2801	235	31	}	}	PUNCT
iajs-2801	235	32	=	=	SYM
iajs-2801	235	33	𝑚𝑖𝑛{{(𝜆1	𝑚𝑖𝑛{{(𝜆1	X
iajs-2801	235	34	+	+	NUM
iajs-2801	235	35	×	×	NOUN
iajs-2801	235	36	𝜆2	𝜆2	NOUN
iajs-2801	235	37	+	+	PROPN
iajs-2801	235	38	)	)	PUNCT
iajs-2801	235	39	(	(	PUNCT
iajs-2801	235	40	𝛼1	𝛼1	NOUN
iajs-2801	235	41	,	,	PUNCT
iajs-2801	235	42	𝛼2	𝛼2	PROPN
iajs-2801	235	43	)	)	PUNCT
iajs-2801	235	44	}	}	PUNCT
iajs-2801	235	45	,	,	PUNCT
iajs-2801	235	46	{	{	PUNCT
iajs-2801	235	47	(	(	PUNCT
iajs-2801	235	48	𝜆1	𝜆1	VERB
iajs-2801	235	49	+	+	CCONJ
iajs-2801	235	50	×	×	PROPN
iajs-2801	235	51	𝜆2	𝜆2	NOUN
iajs-2801	235	52	+	+	PROPN
iajs-2801	235	53	)	)	PUNCT
iajs-2801	235	54	(	(	PUNCT
iajs-2801	235	55	𝛽1	𝛽1	NOUN
iajs-2801	235	56	,	,	PUNCT
iajs-2801	235	57	𝛽2	𝛽2	NOUN
iajs-2801	235	58	)	)	PUNCT
iajs-2801	235	59	}	}	PUNCT
iajs-2801	235	60	}	}	PUNCT
iajs-2801	235	61	and	and	CCONJ
iajs-2801	235	62	(	(	PUNCT
iajs-2801	235	63	𝜆1	𝜆1	VERB
iajs-2801	235	64	−	−	PROPN
iajs-2801	235	65	×	×	NOUN
iajs-2801	235	66	𝜆2	𝜆2	NOUN
iajs-2801	235	67	−)(𝛼1	−)(𝛼1	PROPN
iajs-2801	235	68	𝛽1	𝛽1	PROPN
iajs-2801	235	69	,	,	PUNCT
iajs-2801	235	70	𝛼2	𝛼2	PROPN
iajs-2801	235	71	𝛽2	𝛽2	NOUN
iajs-2801	235	72	)	)	PUNCT
iajs-2801	235	73	=	=	SYM
iajs-2801	235	74	𝑚𝑎𝑥{𝜆1	𝑚𝑎𝑥{𝜆1	VERB
iajs-2801	235	75	−(𝛼1	−(𝛼1	SYM
iajs-2801	235	76	𝛽1	𝛽1	NOUN
iajs-2801	235	77	)	)	PUNCT
iajs-2801	235	78	,	,	PUNCT
iajs-2801	235	79	𝜆2	𝜆2	PROPN
iajs-2801	235	80	−(𝛼2	−(𝛼2	DET
iajs-2801	235	81	𝛽2	𝛽2	PROPN
iajs-2801	235	82	)	)	PUNCT
iajs-2801	235	83	}	}	PUNCT
iajs-2801	235	84	≤	≤	NUM
iajs-2801	235	85	𝑚𝑎𝑥{𝑚𝑎𝑥{𝜆1	𝑚𝑎𝑥{𝑚𝑎𝑥{𝜆1	PROPN
iajs-2801	235	86	−(𝛼1	−(𝛼1	NOUN
iajs-2801	235	87	)	)	PUNCT
iajs-2801	235	88	,	,	PUNCT
iajs-2801	235	89	𝜆1	𝜆1	PROPN
iajs-2801	235	90	−(𝛽1	−(𝛽1	PRON
iajs-2801	235	91	)	)	PUNCT
iajs-2801	235	92	}	}	PUNCT
iajs-2801	235	93	,	,	PUNCT
iajs-2801	235	94	𝑚𝑎𝑥{𝜆2	𝑚𝑎𝑥{𝜆2	NOUN
iajs-2801	235	95	−(𝛼2	−(𝛼2	NOUN
iajs-2801	235	96	)	)	PUNCT
iajs-2801	235	97	,	,	PUNCT
iajs-2801	235	98	𝜆2	𝜆2	PROPN
iajs-2801	235	99	−(𝛽2	−(𝛽2	NUM
iajs-2801	235	100	)	)	PUNCT
iajs-2801	235	101	}	}	PUNCT
iajs-2801	235	102	=	=	SYM
iajs-2801	235	103	𝑚𝑎𝑥{𝑚𝑎𝑥	𝑚𝑎𝑥{𝑚𝑎𝑥	NOUN
iajs-2801	235	104	{	{	PUNCT
iajs-2801	235	105	𝜆1	𝜆1	VERB
iajs-2801	235	106	−(𝛼1	−(𝛼1	PROPN
iajs-2801	235	107	)	)	PUNCT
iajs-2801	235	108	,	,	PUNCT
iajs-2801	235	109	𝜆2	𝜆2	PROPN
iajs-2801	235	110	−(𝛼2	−(𝛼2	NUM
iajs-2801	235	111	)	)	PUNCT
iajs-2801	235	112	}	}	PUNCT
iajs-2801	235	113	,	,	PUNCT
iajs-2801	235	114	𝑚𝑎𝑥	𝑚𝑎𝑥	X
iajs-2801	235	115	{	{	PUNCT
iajs-2801	235	116	𝜆1	𝜆1	NOUN
iajs-2801	235	117	−(𝛽1	−(𝛽1	NUM
iajs-2801	235	118	)	)	PUNCT
iajs-2801	235	119	,	,	PUNCT
iajs-2801	235	120	𝜆2	𝜆2	PROPN
iajs-2801	235	121	−(𝛽2	−(𝛽2	NUM
iajs-2801	235	122	)	)	PUNCT
iajs-2801	235	123	}	}	PUNCT
iajs-2801	235	124	=	=	PUNCT
iajs-2801	235	125	𝑚𝑎𝑥{{(𝜆1	𝑚𝑎𝑥{{(𝜆1	ADJ
iajs-2801	235	126	−	−	NUM
iajs-2801	235	127	×	×	NOUN
iajs-2801	235	128	𝜆2	𝜆2	PROPN
iajs-2801	235	129	−)(𝛼1	−)(𝛼1	PROPN
iajs-2801	235	130	,	,	PUNCT
iajs-2801	235	131	𝛼2	𝛼2	PROPN
iajs-2801	235	132	)	)	PUNCT
iajs-2801	235	133	}	}	PUNCT
iajs-2801	235	134	,	,	PUNCT
iajs-2801	235	135	{	{	PUNCT
iajs-2801	235	136	(	(	PUNCT
iajs-2801	235	137	𝜆1	𝜆1	VERB
iajs-2801	235	138	−	−	PROPN
iajs-2801	235	139	×	×	PROPN
iajs-2801	235	140	𝜆2	𝜆2	PROPN
iajs-2801	235	141	−)(𝛽1	−)(𝛽1	PROPN
iajs-2801	235	142	,	,	PUNCT
iajs-2801	235	143	𝛽2	𝛽2	NOUN
iajs-2801	235	144	)	)	PUNCT
iajs-2801	235	145	}	}	PUNCT
iajs-2801	235	146	}	}	PUNCT
iajs-2801	235	147	.	.	PUNCT
iajs-2801	236	1	then	then	ADV
iajs-2801	236	2	ω𝑓1	ω𝑓1	INTJ
iajs-2801	236	3	×	×	PROPN
iajs-2801	236	4	ω𝑓2	ω𝑓2	NUM
iajs-2801	236	5	is	be	AUX
iajs-2801	236	6	acb	acb	PROPN
iajs-2801	236	7	k	k	NOUN
iajs-2801	236	8	-	-	NOUN
iajs-2801	236	9	ideal	ideal	NOUN
iajs-2801	236	10	of	of	ADP
iajs-2801	236	11	ℵ	ℵ	DET
iajs-2801	236	12	×	×	PROPN
iajs-2801	236	13	ℵ.	ℵ.	NOUN
iajs-2801	236	14	theorem	theorem	VERB
iajs-2801	236	15	3.6.let	3.6.let	NUM
iajs-2801	236	16	ω𝑓1	ω𝑓1	NOUN
iajs-2801	236	17	and	and	CCONJ
iajs-2801	236	18	ω𝑓2	ω𝑓2	NUM
iajs-2801	236	19	be	be	AUX
iajs-2801	236	20	two	two	NUM
iajs-2801	236	21	cb	cb	PROPN
iajs-2801	236	22	ideal	ideal	NOUN
iajs-2801	236	23	of	of	ADP
iajs-2801	236	24	ku	ku	PROPN
iajs-2801	236	25	-	-	PUNCT
iajs-2801	236	26	semigroupℵ	semigroupℵ	PROPN
iajs-2801	236	27	,	,	PUNCT
iajs-2801	236	28	such	such	ADJ
iajs-2801	236	29	that	that	PRON
iajs-2801	236	30	ω𝑓1	ω𝑓1	NOUN
iajs-2801	236	31	×	×	NOUN
iajs-2801	236	32	ω𝑓2	ω𝑓2	NUM
iajs-2801	236	33	is	be	AUX
iajs-2801	236	34	acb	acb	PROPN
iajs-2801	236	35	ideal	ideal	NOUN
iajs-2801	236	36	of	of	ADP
iajs-2801	236	37	ℵ	ℵ	DET
iajs-2801	236	38	×	×	NOUN
iajs-2801	236	39	ℵ.	ℵ.	NOUN
iajs-2801	237	1	we	we	PRON
iajs-2801	237	2	have	have	VERB
iajs-2801	237	3	(	(	PUNCT
iajs-2801	237	4	i	i	NOUN
iajs-2801	237	5	)	)	PUNCT
iajs-2801	237	6	either𝜇1	either𝜇1	X
iajs-2801	238	1	+	+	ADJ
iajs-2801	238	2	(	(	PUNCT
iajs-2801	238	3	0	0	NUM
iajs-2801	238	4	)	)	PUNCT
iajs-2801	238	5	≥	≥	NOUN
iajs-2801	238	6	𝜇1	𝜇1	NOUN
iajs-2801	238	7	+	+	PROPN
iajs-2801	238	8	(	(	PUNCT
iajs-2801	238	9	𝛼),𝜇1	𝛼),𝜇1	NUM
iajs-2801	238	10	−(0	−(0	NOUN
iajs-2801	238	11	)	)	PUNCT
iajs-2801	238	12	≤	≤	NOUN
iajs-2801	238	13	𝜇1	𝜇1	ADJ
iajs-2801	238	14	−(𝛼)or𝜇2	−(𝛼)or𝜇2	ADJ
iajs-2801	238	15	+	+	ADJ
iajs-2801	238	16	(	(	PUNCT
iajs-2801	238	17	0	0	NUM
iajs-2801	238	18	)	)	PUNCT
iajs-2801	238	19	≥	≥	NOUN
iajs-2801	238	20	𝜇2	𝜇2	VERB
iajs-2801	238	21	+	+	PROPN
iajs-2801	238	22	(	(	PUNCT
iajs-2801	238	23	𝛽),𝜇2	𝛽),𝜇2	X
iajs-2801	238	24	−(0	−(0	NOUN
iajs-2801	238	25	)	)	PUNCT
iajs-2801	238	26	≤	≤	NOUN
iajs-2801	238	27	𝜇2	𝜇2	PROPN
iajs-2801	238	28	−(𝛽	−(𝛽	NOUN
iajs-2801	238	29	)	)	PUNCT
iajs-2801	238	30	,	,	PUNCT
iajs-2801	238	31	also	also	ADV
iajs-2801	238	32	,	,	PUNCT
iajs-2801	238	33	𝜆1	𝜆1	VERB
iajs-2801	238	34	+	+	NOUN
iajs-2801	238	35	(	(	PUNCT
iajs-2801	238	36	0	0	NUM
iajs-2801	238	37	)	)	PUNCT
iajs-2801	238	38	≥	≥	NOUN
iajs-2801	238	39	𝜆1	𝜆1	VERB
iajs-2801	239	1	+	+	ADV
iajs-2801	239	2	(	(	PUNCT
iajs-2801	239	3	𝛼),𝜆1	𝛼),𝜆1	X
iajs-2801	239	4	−(0	−(0	NOUN
iajs-2801	239	5	)	)	PUNCT
iajs-2801	239	6	≤	≤	NOUN
iajs-2801	239	7	𝜆1	𝜆1	NOUN
iajs-2801	239	8	−(𝛼	−(𝛼	NOUN
iajs-2801	239	9	)	)	PUNCT
iajs-2801	239	10	or𝜆2	or𝜆2	VERB
iajs-2801	240	1	+	+	ADJ
iajs-2801	240	2	(	(	PUNCT
iajs-2801	240	3	0	0	NUM
iajs-2801	240	4	)	)	PUNCT
iajs-2801	240	5	≥	≥	NOUN
iajs-2801	240	6	𝜆2	𝜆2	NOUN
iajs-2801	241	1	+	+	NOUN
iajs-2801	241	2	(	(	PUNCT
iajs-2801	241	3	𝛽),𝜆2	𝛽),𝜆2	NOUN
iajs-2801	241	4	−(0	−(0	NOUN
iajs-2801	241	5	)	)	PUNCT
iajs-2801	241	6	≤	≤	NUM
iajs-2801	241	7	𝜆2	𝜆2	PROPN
iajs-2801	241	8	−(𝛽	−(𝛽	NOUN
iajs-2801	241	9	)	)	PUNCT
iajs-2801	241	10	for	for	ADP
iajs-2801	241	11	all	all	DET
iajs-2801	241	12	𝛼	𝛼	NOUN
iajs-2801	241	13	,	,	PUNCT
iajs-2801	241	14	𝛽	𝛽	PROPN
iajs-2801	241	15	∈	∈	ADV
iajs-2801	241	16	ℵ.	ℵ.	NOUN
iajs-2801	241	17	(	(	PUNCT
iajs-2801	241	18	ii	ii	NOUN
iajs-2801	241	19	)	)	PUNCT
iajs-2801	241	20	if	if	SCONJ
iajs-2801	241	21	𝜇1	𝜇1	PROPN
iajs-2801	241	22	+	+	PROPN
iajs-2801	241	23	(	(	PUNCT
iajs-2801	241	24	0	0	NUM
iajs-2801	241	25	)	)	PUNCT
iajs-2801	241	26	≥	≥	NOUN
iajs-2801	241	27	𝜇1	𝜇1	NOUN
iajs-2801	241	28	+	+	PROPN
iajs-2801	241	29	(	(	PUNCT
iajs-2801	241	30	𝛼	𝛼	NOUN
iajs-2801	241	31	)	)	PUNCT
iajs-2801	241	32	,	,	PUNCT
iajs-2801	241	33	𝜇1	𝜇1	PROPN
iajs-2801	241	34	−(0	−(0	NOUN
iajs-2801	241	35	)	)	PUNCT
iajs-2801	241	36	≤	≤	PROPN
iajs-2801	241	37	𝜇1	𝜇1	PROPN
iajs-2801	241	38	−(𝛼	−(𝛼	NOUN
iajs-2801	241	39	)	)	PUNCT
iajs-2801	241	40	and	and	CCONJ
iajs-2801	241	41	𝜆1	𝜆1	VERB
iajs-2801	241	42	+	+	NOUN
iajs-2801	241	43	(	(	PUNCT
iajs-2801	241	44	0	0	NUM
iajs-2801	241	45	)	)	PUNCT
iajs-2801	241	46	≥	≥	NOUN
iajs-2801	241	47	𝜆1	𝜆1	VERB
iajs-2801	242	1	+	+	ADV
iajs-2801	243	1	(	(	PUNCT
iajs-2801	243	2	𝛼),𝜆1	𝛼),𝜆1	X
iajs-2801	243	3	−(0	−(0	NOUN
iajs-2801	243	4	)	)	PUNCT
iajs-2801	243	5	≤	≤	NOUN
iajs-2801	243	6	𝜆1	𝜆1	NOUN
iajs-2801	243	7	−(𝛼)for	−(𝛼)for	ADP
iajs-2801	243	8	all	all	DET
iajs-2801	243	9	𝛼	𝛼	PROPN
iajs-2801	243	10	∈	∈	NOUN
iajs-2801	243	11	ℵ.	ℵ.	NOUN
iajs-2801	244	1	then	then	ADV
iajs-2801	244	2	either𝜇2	either𝜇2	X
iajs-2801	244	3	+	+	ADJ
iajs-2801	244	4	(	(	PUNCT
iajs-2801	244	5	0	0	NUM
iajs-2801	244	6	)	)	PUNCT
iajs-2801	244	7	≥	≥	NOUN
iajs-2801	244	8	𝜇1	𝜇1	NOUN
iajs-2801	244	9	+	+	PROPN
iajs-2801	244	10	(	(	PUNCT
iajs-2801	244	11	𝛼),𝜇2	𝛼),𝜇2	NUM
iajs-2801	244	12	−(0	−(0	NOUN
iajs-2801	244	13	)	)	PUNCT
iajs-2801	244	14	≤	≤	PROPN
iajs-2801	244	15	𝜇1	𝜇1	PROPN
iajs-2801	244	16	−(𝛼	−(𝛼	PROPN
iajs-2801	244	17	)	)	PUNCT
iajs-2801	244	18	and	and	CCONJ
iajs-2801	244	19	𝜆2	𝜆2	PROPN
iajs-2801	244	20	+	+	PROPN
iajs-2801	244	21	(	(	PUNCT
iajs-2801	244	22	0	0	NUM
iajs-2801	244	23	)	)	PUNCT
iajs-2801	244	24	≥	≥	NOUN
iajs-2801	244	25	𝜆1	𝜆1	VERB
iajs-2801	245	1	+	+	PROPN
iajs-2801	245	2	(	(	PUNCT
iajs-2801	245	3	𝛼),𝜆2	𝛼),𝜆2	NOUN
iajs-2801	245	4	−(0	−(0	NOUN
iajs-2801	245	5	)	)	PUNCT
iajs-2801	245	6	≤	≤	NOUN
iajs-2801	245	7	𝜆1	𝜆1	NOUN
iajs-2801	245	8	−(𝛼)or	−(𝛼)or	NOUN
iajs-2801	245	9	𝜇2	𝜇2	PROPN
iajs-2801	245	10	+	+	PROPN
iajs-2801	245	11	(	(	PUNCT
iajs-2801	245	12	0	0	NUM
iajs-2801	245	13	)	)	PUNCT
iajs-2801	245	14	≥	≥	NOUN
iajs-2801	246	1	𝜇2	𝜇2	VERB
iajs-2801	246	2	+	+	PROPN
iajs-2801	246	3	(	(	PUNCT
iajs-2801	246	4	𝛽),𝜇2	𝛽),𝜇2	X
iajs-2801	246	5	−(0	−(0	NOUN
iajs-2801	246	6	)	)	PUNCT
iajs-2801	246	7	≤	≤	NOUN
iajs-2801	246	8	𝜇2	𝜇2	PROPN
iajs-2801	247	1	−(𝛽)and	−(𝛽)and	PROPN
iajs-2801	247	2	𝜆2	𝜆2	PROPN
iajs-2801	248	1	+	+	PROPN
iajs-2801	248	2	(	(	PUNCT
iajs-2801	248	3	0	0	NUM
iajs-2801	248	4	)	)	PUNCT
iajs-2801	248	5	≥	≥	NOUN
iajs-2801	248	6	𝜆2	𝜆2	NOUN
iajs-2801	249	1	+	+	NOUN
iajs-2801	249	2	(	(	PUNCT
iajs-2801	249	3	𝛽),𝜆2	𝛽),𝜆2	NOUN
iajs-2801	249	4	−(0	−(0	NOUN
iajs-2801	249	5	)	)	PUNCT
iajs-2801	249	6	≤	≤	NUM
iajs-2801	249	7	𝜆2	𝜆2	NOUN
iajs-2801	249	8	−(𝛽)for	−(𝛽)for	ADP
iajs-2801	249	9	all𝛼	all𝛼	NOUN
iajs-2801	249	10	,	,	PUNCT
iajs-2801	249	11	𝛽	𝛽	NOUN
iajs-2801	249	12	∈	∈	ADV
iajs-2801	249	13	ℵ.	ℵ.	NOUN
iajs-2801	250	1	(	(	PUNCT
iajs-2801	250	2	iii	iii	X
iajs-2801	250	3	)	)	PUNCT
iajs-2801	250	4	if𝜇2	if𝜇2	VERB
iajs-2801	251	1	+	+	ADJ
iajs-2801	251	2	(	(	PUNCT
iajs-2801	251	3	0	0	NUM
iajs-2801	251	4	)	)	PUNCT
iajs-2801	251	5	≥	≥	NOUN
iajs-2801	251	6	𝜇2	𝜇2	VERB
iajs-2801	251	7	+	+	PROPN
iajs-2801	251	8	(	(	PUNCT
iajs-2801	251	9	𝛼	𝛼	NOUN
iajs-2801	251	10	)	)	PUNCT
iajs-2801	251	11	,	,	PUNCT
iajs-2801	251	12	𝜇2	𝜇2	PROPN
iajs-2801	251	13	−(0	−(0	NOUN
iajs-2801	251	14	)	)	PUNCT
iajs-2801	251	15	≤	≤	PROPN
iajs-2801	251	16	𝜇2	𝜇2	PROPN
iajs-2801	251	17	−(𝛼	−(𝛼	NOUN
iajs-2801	251	18	)	)	PUNCT
iajs-2801	251	19	,	,	PUNCT
iajs-2801	251	20	and	and	CCONJ
iajs-2801	251	21	λ2	λ2	NOUN
iajs-2801	251	22	+	+	PROPN
iajs-2801	251	23	(	(	PUNCT
iajs-2801	251	24	0	0	NUM
iajs-2801	251	25	)	)	PUNCT
iajs-2801	251	26	≥	≥	NOUN
iajs-2801	252	1	λ2	λ2	NOUN
iajs-2801	252	2	+	+	NOUN
iajs-2801	252	3	(	(	PUNCT
iajs-2801	252	4	α),λ2	α),λ2	X
iajs-2801	252	5	(	(	PUNCT
iajs-2801	252	6	0	0	NUM
iajs-2801	252	7	)	)	PUNCT
iajs-2801	252	8	≤	≤	NUM
iajs-2801	252	9	λ2	λ2	NOUN
iajs-2801	252	10	(	(	PUNCT
iajs-2801	252	11	α),for	α),for	ADP
iajs-2801	252	12	all	all	DET
iajs-2801	252	13	α	α	DET
iajs-2801	252	14	∈	∈	PROPN
iajs-2801	252	15	ℵ	ℵ	NOUN
iajs-2801	252	16	,	,	PUNCT
iajs-2801	252	17	then	then	ADV
iajs-2801	252	18	either	either	CCONJ
iajs-2801	252	19	𝜇1	𝜇1	PROPN
iajs-2801	252	20	+	+	PROPN
iajs-2801	252	21	(	(	PUNCT
iajs-2801	252	22	0	0	NUM
iajs-2801	252	23	)	)	PUNCT
iajs-2801	252	24	≥	≥	NOUN
iajs-2801	252	25	𝜇1	𝜇1	NOUN
iajs-2801	252	26	+	+	PROPN
iajs-2801	252	27	(	(	PUNCT
iajs-2801	252	28	𝛼),𝜇1	𝛼),𝜇1	NUM
iajs-2801	252	29	−(0	−(0	NOUN
iajs-2801	252	30	)	)	PUNCT
iajs-2801	252	31	≤	≤	NOUN
iajs-2801	252	32	𝜇1	𝜇1	ADJ
iajs-2801	252	33	−(𝛼	−(𝛼	NOUN
iajs-2801	252	34	)	)	PUNCT
iajs-2801	252	35	,	,	PUNCT
iajs-2801	252	36	and𝜆1	and𝜆1	PUNCT
iajs-2801	253	1	+	+	ADJ
iajs-2801	253	2	(	(	PUNCT
iajs-2801	253	3	0	0	NUM
iajs-2801	253	4	)	)	PUNCT
iajs-2801	253	5	≥	≥	NOUN
iajs-2801	253	6	𝜆1	𝜆1	VERB
iajs-2801	253	7	+	+	ADV
iajs-2801	253	8	(	(	PUNCT
iajs-2801	253	9	𝛼),𝜆1	𝛼),𝜆1	X
iajs-2801	253	10	−(0	−(0	NOUN
iajs-2801	253	11	)	)	PUNCT
iajs-2801	253	12	≤	≤	NOUN
iajs-2801	253	13	𝜆1	𝜆1	NOUN
iajs-2801	253	14	−(𝛼)or𝜇1	−(𝛼)or𝜇1	VERB
iajs-2801	253	15	+	+	ADJ
iajs-2801	253	16	(	(	PUNCT
iajs-2801	253	17	0	0	NUM
iajs-2801	253	18	)	)	PUNCT
iajs-2801	253	19	≥	≥	NOUN
iajs-2801	254	1	𝜇2	𝜇2	VERB
iajs-2801	254	2	+	+	PROPN
iajs-2801	254	3	(	(	PUNCT
iajs-2801	254	4	𝛼	𝛼	NOUN
iajs-2801	254	5	)	)	PUNCT
iajs-2801	254	6	,	,	PUNCT
iajs-2801	254	7	𝜇1	𝜇1	PROPN
iajs-2801	254	8	−(0	−(0	NOUN
iajs-2801	254	9	)	)	PUNCT
iajs-2801	254	10	≤	≤	PROPN
iajs-2801	254	11	𝜇2	𝜇2	PROPN
iajs-2801	254	12	−(𝛼	−(𝛼	NOUN
iajs-2801	254	13	)	)	PUNCT
iajs-2801	254	14	and	and	CCONJ
iajs-2801	254	15	𝜆1	𝜆1	VERB
iajs-2801	254	16	+	+	NOUN
iajs-2801	254	17	(	(	PUNCT
iajs-2801	254	18	0	0	NUM
iajs-2801	254	19	)	)	PUNCT
iajs-2801	254	20	≥	≥	NOUN
iajs-2801	254	21	𝜆2	𝜆2	NOUN
iajs-2801	255	1	+	+	PROPN
iajs-2801	255	2	(	(	PUNCT
iajs-2801	255	3	𝛼),𝜆1	𝛼),𝜆1	X
iajs-2801	255	4	−(0	−(0	NOUN
iajs-2801	255	5	)	)	PUNCT
iajs-2801	255	6	≤	≤	NUM
iajs-2801	255	7	𝜆2	𝜆2	NOUN
iajs-2801	255	8	−(𝛼)for	−(𝛼)for	ADP
iajs-2801	255	9	all𝛼	all𝛼	PROPN
iajs-2801	255	10	∈	∈	PROPN
iajs-2801	255	11	ℵ.	ℵ.	NOUN
iajs-2801	255	12	proof	proof	NOUN
iajs-2801	255	13	.	.	PUNCT
iajs-2801	256	1	(	(	PUNCT
iajs-2801	256	2	i)suppose	i)suppose	X
iajs-2801	256	3	that	that	DET
iajs-2801	256	4	𝜇1	𝜇1	PROPN
iajs-2801	256	5	+	+	PROPN
iajs-2801	256	6	(	(	PUNCT
iajs-2801	256	7	0	0	NUM
iajs-2801	256	8	)	)	PUNCT
iajs-2801	256	9	≥	≥	NOUN
iajs-2801	256	10	𝜇1	𝜇1	NOUN
iajs-2801	256	11	+	+	PROPN
iajs-2801	256	12	(	(	PUNCT
iajs-2801	256	13	𝛼),𝜇1	𝛼),𝜇1	NUM
iajs-2801	256	14	−(0	−(0	NOUN
iajs-2801	256	15	)	)	PUNCT
iajs-2801	256	16	≤	≤	PROPN
iajs-2801	256	17	𝜇1	𝜇1	PROPN
iajs-2801	256	18	−(𝛼	−(𝛼	PROPN
iajs-2801	256	19	)	)	PUNCT
iajs-2801	256	20	and	and	CCONJ
iajs-2801	256	21	𝜇2	𝜇2	VERB
iajs-2801	256	22	+	+	PROPN
iajs-2801	256	23	(	(	PUNCT
iajs-2801	256	24	0	0	NUM
iajs-2801	256	25	)	)	PUNCT
iajs-2801	256	26	≥	≥	NOUN
iajs-2801	256	27	𝜇2	𝜇2	VERB
iajs-2801	256	28	+	+	PROPN
iajs-2801	256	29	(	(	PUNCT
iajs-2801	256	30	𝑦),𝜇2	𝑦),𝜇2	VERB
iajs-2801	256	31	−(0	−(0	NOUN
iajs-2801	256	32	)	)	PUNCT
iajs-2801	256	33	≤	≤	NOUN
iajs-2801	256	34	𝜇2	𝜇2	PROPN
iajs-2801	256	35	−(𝛽	−(𝛽	NOUN
iajs-2801	256	36	)	)	PUNCT
iajs-2801	256	37	,	,	PUNCT
iajs-2801	256	38	also	also	ADV
iajs-2801	256	39	,	,	PUNCT
iajs-2801	256	40	𝜆1	𝜆1	VERB
iajs-2801	256	41	+	+	NOUN
iajs-2801	256	42	(	(	PUNCT
iajs-2801	256	43	0	0	NUM
iajs-2801	256	44	)	)	PUNCT
iajs-2801	256	45	≥	≥	NOUN
iajs-2801	256	46	𝜆1	𝜆1	VERB
iajs-2801	257	1	+	+	ADV
iajs-2801	257	2	(	(	PUNCT
iajs-2801	257	3	𝛼),𝜆1	𝛼),𝜆1	X
iajs-2801	257	4	−(0	−(0	NOUN
iajs-2801	257	5	)	)	PUNCT
iajs-2801	257	6	≤	≤	NOUN
iajs-2801	257	7	𝜆1	𝜆1	NOUN
iajs-2801	257	8	−(𝛼	−(𝛼	NOUN
iajs-2801	257	9	)	)	PUNCT
iajs-2801	257	10	and𝜆2	and𝜆2	PUNCT
iajs-2801	258	1	+	+	ADJ
iajs-2801	258	2	(	(	PUNCT
iajs-2801	258	3	0	0	NUM
iajs-2801	258	4	)	)	PUNCT
iajs-2801	258	5	≥	≥	NOUN
iajs-2801	258	6	𝜆2	𝜆2	NOUN
iajs-2801	259	1	+	+	NOUN
iajs-2801	259	2	(	(	PUNCT
iajs-2801	259	3	𝛽),𝜆2	𝛽),𝜆2	NOUN
iajs-2801	259	4	−(0	−(0	NOUN
iajs-2801	259	5	)	)	PUNCT
iajs-2801	259	6	≤	≤	NUM
iajs-2801	259	7	𝜆2	𝜆2	PROPN
iajs-2801	259	8	−(𝛽	−(𝛽	NOUN
iajs-2801	259	9	)	)	PUNCT
iajs-2801	259	10	,	,	PUNCT
iajs-2801	259	11	for	for	ADP
iajs-2801	259	12	some	some	DET
iajs-2801	259	13	𝛼	𝛼	NOUN
iajs-2801	259	14	,	,	PUNCT
iajs-2801	259	15	𝛽	𝛽	NOUN
iajs-2801	259	16	∈	∈	NOUN
iajs-2801	259	17	ℵ.then	ℵ.then	NOUN
iajs-2801	259	18	(	(	PUNCT
iajs-2801	259	19	𝜇1	𝜇1	NOUN
iajs-2801	259	20	+	+	CCONJ
iajs-2801	259	21	×	×	PROPN
iajs-2801	259	22	𝜇2	𝜇2	NOUN
iajs-2801	259	23	+	+	PROPN
iajs-2801	259	24	)	)	PUNCT
iajs-2801	259	25	(	(	PUNCT
iajs-2801	259	26	𝛼	𝛼	X
iajs-2801	259	27	,	,	PUNCT
iajs-2801	259	28	𝛽	𝛽	NOUN
iajs-2801	259	29	)	)	PUNCT
iajs-2801	259	30	=	=	SYM
iajs-2801	259	31	𝑟𝑚𝑖𝑛{	𝑟𝑚𝑖𝑛{	PROPN
iajs-2801	259	32	�	�	PROPN
iajs-2801	259	33	̃	̃	PROPN
iajs-2801	259	34	�	�	NOUN
iajs-2801	259	35	1	1	NUM
iajs-2801	259	36	+	+	ADJ
iajs-2801	259	37	(	(	PUNCT
iajs-2801	259	38	𝛼	𝛼	NOUN
iajs-2801	259	39	)	)	PUNCT
iajs-2801	259	40	,	,	PUNCT
iajs-2801	259	41	𝜇2	𝜇2	PROPN
iajs-2801	259	42	+	+	PROPN
iajs-2801	259	43	(	(	PUNCT
iajs-2801	259	44	𝛽	𝛽	NOUN
iajs-2801	259	45	)	)	PUNCT
iajs-2801	259	46	}	}	PUNCT
iajs-2801	259	47	≥	≥	X
iajs-2801	259	48	𝑟𝑚𝑖𝑛{𝜇1	𝑟𝑚𝑖𝑛{𝜇1	X
iajs-2801	259	49	+	+	ADJ
iajs-2801	259	50	(	(	PUNCT
iajs-2801	259	51	0	0	NUM
iajs-2801	259	52	)	)	PUNCT
iajs-2801	259	53	,	,	PUNCT
iajs-2801	259	54	𝜇2	𝜇2	PROPN
iajs-2801	259	55	+	+	PROPN
iajs-2801	259	56	(	(	PUNCT
iajs-2801	259	57	0	0	NUM
iajs-2801	259	58	)	)	PUNCT
iajs-2801	259	59	}	}	PUNCT
iajs-2801	259	60	=	=	SYM
iajs-2801	259	61	(	(	PUNCT
iajs-2801	259	62	�	�	PROPN
iajs-2801	259	63	̃	̃	NOUN
iajs-2801	259	64	�	�	NOUN
iajs-2801	259	65	1	1	NUM
iajs-2801	259	66	+	+	SYM
iajs-2801	259	67	×	×	PROPN
iajs-2801	259	68	𝜇2	𝜇2	NOUN
iajs-2801	259	69	+	+	PROPN
iajs-2801	259	70	)	)	PUNCT
iajs-2801	259	71	(	(	PUNCT
iajs-2801	259	72	0,0	0,0	NOUN
iajs-2801	259	73	)	)	PUNCT
iajs-2801	259	74	and	and	CCONJ
iajs-2801	259	75	(	(	PUNCT
iajs-2801	259	76	𝜇1	𝜇1	PROPN
iajs-2801	259	77	−	−	PROPN
iajs-2801	259	78	×	×	PROPN
iajs-2801	259	79	𝜇2	𝜇2	PROPN
iajs-2801	259	80	−)(𝛼	−)(𝛼	PROPN
iajs-2801	259	81	,	,	PUNCT
iajs-2801	259	82	𝛽	𝛽	NOUN
iajs-2801	259	83	)	)	PUNCT
iajs-2801	259	84	=	=	SYM
iajs-2801	259	85	𝑟𝑚𝑎𝑥{𝜇1	𝑟𝑚𝑎𝑥{𝜇1	PROPN
iajs-2801	259	86	−(𝛼	−(𝛼	NOUN
iajs-2801	259	87	)	)	PUNCT
iajs-2801	259	88	,	,	PUNCT
iajs-2801	259	89	𝜇2	𝜇2	PROPN
iajs-2801	259	90	−(𝛽	−(𝛽	NOUN
iajs-2801	259	91	)	)	PUNCT
iajs-2801	259	92	}	}	PUNCT
iajs-2801	259	93	≤	≤	NUM
iajs-2801	259	94	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
iajs-2801	259	95	{	{	PUNCT
iajs-2801	259	96	;	;	PUNCT
iajs-2801	259	97	𝜇1	𝜇1	PROPN
iajs-2801	259	98	−(0	−(0	NOUN
iajs-2801	259	99	)	)	PUNCT
iajs-2801	259	100	,	,	PUNCT
iajs-2801	259	101	;	;	PUNCT
iajs-2801	259	102	𝜇2	𝜇2	PROPN
iajs-2801	259	103	−(0	−(0	NOUN
iajs-2801	259	104	)	)	PUNCT
iajs-2801	259	105	}	}	PUNCT
iajs-2801	259	106	=	=	SYM
iajs-2801	259	107	(	(	PUNCT
iajs-2801	259	108	𝜇1	𝜇1	NOUN
iajs-2801	259	109	−	−	PROPN
iajs-2801	259	110	×	×	NOUN
iajs-2801	259	111	;	;	PUNCT
iajs-2801	259	112	𝜇2	𝜇2	PROPN
iajs-2801	259	113	−	−	PROPN
iajs-2801	259	114	)	)	PUNCT
iajs-2801	259	115	(;	(;	X
iajs-2801	259	116	0	0	NUM
iajs-2801	259	117	,	,	PUNCT
iajs-2801	259	118	;	;	PUNCT
iajs-2801	259	119	0	0	X
iajs-2801	259	120	)	)	PUNCT
iajs-2801	259	121	also	also	ADV
iajs-2801	259	122	,	,	PUNCT
iajs-2801	259	123	(;	(;	X
iajs-2801	259	124	𝜆1	𝜆1	NOUN
iajs-2801	259	125	+	+	CCONJ
iajs-2801	259	126	×	×	NOUN
iajs-2801	259	127	;	;	PUNCT
iajs-2801	259	128	𝜆2	𝜆2	PROPN
iajs-2801	259	129	+	+	PROPN
iajs-2801	259	130	)	)	PUNCT
iajs-2801	259	131	(	(	PUNCT
iajs-2801	259	132	𝛼	𝛼	X
iajs-2801	259	133	,	,	PUNCT
iajs-2801	259	134	𝛽	𝛽	NOUN
iajs-2801	259	135	)	)	PUNCT
iajs-2801	259	136	=	=	PUNCT
iajs-2801	260	1	𝑚𝑖𝑛{𝜆1	𝑚𝑖𝑛{𝜆1	X
iajs-2801	260	2	+	+	ADJ
iajs-2801	260	3	(	(	PUNCT
iajs-2801	260	4	𝛼	𝛼	NOUN
iajs-2801	260	5	)	)	PUNCT
iajs-2801	260	6	,	,	PUNCT
iajs-2801	260	7	𝜆2	𝜆2	PROPN
iajs-2801	260	8	+	+	PROPN
iajs-2801	260	9	(	(	PUNCT
iajs-2801	260	10	𝛽	𝛽	NOUN
iajs-2801	260	11	)	)	PUNCT
iajs-2801	260	12	}	}	PUNCT
iajs-2801	260	13	≥	≥	PROPN
iajs-2801	260	14	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	260	15	{	{	PUNCT
iajs-2801	260	16	;	;	PUNCT
iajs-2801	260	17	𝜆1	𝜆1	VERB
iajs-2801	260	18	+	+	NOUN
iajs-2801	260	19	(	(	PUNCT
iajs-2801	260	20	0	0	NUM
iajs-2801	260	21	)	)	PUNCT
iajs-2801	260	22	,	,	PUNCT
iajs-2801	260	23	;	;	PUNCT
iajs-2801	260	24	𝜆2	𝜆2	PROPN
iajs-2801	260	25	+	+	PROPN
iajs-2801	260	26	(	(	PUNCT
iajs-2801	260	27	0	0	NUM
iajs-2801	260	28	)	)	PUNCT
iajs-2801	260	29	}	}	PUNCT
iajs-2801	260	30	=	=	PUNCT
iajs-2801	260	31	(;	(;	PUNCT
iajs-2801	260	32	𝜆1	𝜆1	NOUN
iajs-2801	260	33	+	+	CCONJ
iajs-2801	260	34	×	×	NOUN
iajs-2801	260	35	;	;	PUNCT
iajs-2801	260	36	𝜆2	𝜆2	PROPN
iajs-2801	260	37	+	+	PROPN
iajs-2801	260	38	)	)	PUNCT
iajs-2801	260	39	(	(	PUNCT
iajs-2801	260	40	0,0	0,0	NOUN
iajs-2801	260	41	)	)	PUNCT
iajs-2801	260	42	and	and	CCONJ
iajs-2801	260	43	(	(	PUNCT
iajs-2801	260	44	𝜆1	𝜆1	VERB
iajs-2801	260	45	−	−	PROPN
iajs-2801	260	46	×	×	PROPN
iajs-2801	260	47	𝜆2	𝜆2	PROPN
iajs-2801	260	48	−)(𝛼	−)(𝛼	NOUN
iajs-2801	260	49	,	,	PUNCT
iajs-2801	260	50	𝛽	𝛽	NOUN
iajs-2801	260	51	)	)	PUNCT
iajs-2801	260	52	=	=	SYM
iajs-2801	260	53	𝑚𝑎𝑥{𝜆1	𝑚𝑎𝑥{𝜆1	NOUN
iajs-2801	260	54	−(𝛼	−(𝛼	NOUN
iajs-2801	260	55	)	)	PUNCT
iajs-2801	260	56	,	,	PUNCT
iajs-2801	260	57	𝜆2	𝜆2	PROPN
iajs-2801	260	58	−(𝛽	−(𝛽	NOUN
iajs-2801	260	59	)	)	PUNCT
iajs-2801	260	60	}	}	PUNCT
iajs-2801	260	61	≤	≤	NOUN
iajs-2801	260	62	𝑚𝑎𝑥{𝜆1	𝑚𝑎𝑥{𝜆1	NOUN
iajs-2801	260	63	−(0	−(0	NOUN
iajs-2801	260	64	)	)	PUNCT
iajs-2801	260	65	,	,	PUNCT
iajs-2801	260	66	𝜆2	𝜆2	NOUN
iajs-2801	260	67	−(0	−(0	NOUN
iajs-2801	260	68	)	)	PUNCT
iajs-2801	260	69	}	}	PUNCT
iajs-2801	260	70	=	=	SYM
iajs-2801	260	71	(	(	PUNCT
iajs-2801	260	72	𝜆1	𝜆1	VERB
iajs-2801	260	73	−	−	PROPN
iajs-2801	260	74	×	×	PROPN
iajs-2801	260	75	𝜆2	𝜆2	NOUN
iajs-2801	260	76	−)(0,0	−)(0,0	NOUN
iajs-2801	260	77	)	)	PUNCT
iajs-2801	260	78	,	,	PUNCT
iajs-2801	260	79	for	for	ADP
iajs-2801	260	80	all	all	DET
iajs-2801	260	81	𝛼	𝛼	NOUN
iajs-2801	260	82	,	,	PUNCT
iajs-2801	260	83	𝛽	𝛽	PROPN
iajs-2801	260	84	∈	∈	PRON
iajs-2801	260	85	ℵ.	ℵ.	NOUN
iajs-2801	261	1	this	this	PRON
iajs-2801	261	2	is	be	AUX
iajs-2801	261	3	a	a	DET
iajs-2801	261	4	contradiction	contradiction	NOUN
iajs-2801	261	5	.	.	PUNCT
iajs-2801	262	1	therefore	therefore	ADV
iajs-2801	262	2	,	,	PUNCT
iajs-2801	262	3	either𝜇1	either𝜇1	X
iajs-2801	263	1	+	+	ADJ
iajs-2801	263	2	(	(	PUNCT
iajs-2801	263	3	0	0	NUM
iajs-2801	263	4	)	)	PUNCT
iajs-2801	263	5	≥	≥	NOUN
iajs-2801	263	6	𝜇1	𝜇1	NOUN
iajs-2801	263	7	+	+	PROPN
iajs-2801	263	8	(	(	PUNCT
iajs-2801	263	9	𝛼),𝜇1	𝛼),𝜇1	NUM
iajs-2801	263	10	−(0	−(0	NOUN
iajs-2801	263	11	)	)	PUNCT
iajs-2801	263	12	≤	≤	PROPN
iajs-2801	263	13	𝜇1	𝜇1	PROPN
iajs-2801	263	14	−(𝛼	−(𝛼	PROPN
iajs-2801	263	15	)	)	PUNCT
iajs-2801	264	1	or𝜇2	or𝜇2	PROPN
iajs-2801	264	2	+	+	ADJ
iajs-2801	264	3	(	(	PUNCT
iajs-2801	264	4	0	0	NUM
iajs-2801	264	5	)	)	PUNCT
iajs-2801	264	6	≥	≥	NOUN
iajs-2801	264	7	𝜇2	𝜇2	VERB
iajs-2801	264	8	+	+	PROPN
iajs-2801	264	9	(	(	PUNCT
iajs-2801	264	10	𝛽),𝜇2	𝛽),𝜇2	X
iajs-2801	264	11	−(0	−(0	NOUN
iajs-2801	264	12	)	)	PUNCT
iajs-2801	264	13	≤	≤	NOUN
iajs-2801	264	14	𝜇2	𝜇2	PROPN
iajs-2801	264	15	−(𝛽	−(𝛽	NOUN
iajs-2801	264	16	)	)	PUNCT
iajs-2801	264	17	,	,	PUNCT
iajs-2801	264	18	also	also	ADV
iajs-2801	264	19	,	,	PUNCT
iajs-2801	264	20	𝜆1	𝜆1	VERB
iajs-2801	264	21	+	+	NOUN
iajs-2801	264	22	(	(	PUNCT
iajs-2801	264	23	0	0	NUM
iajs-2801	264	24	)	)	PUNCT
iajs-2801	264	25	≥	≥	NOUN
iajs-2801	264	26	𝜆1	𝜆1	VERB
iajs-2801	265	1	+	+	ADV
iajs-2801	265	2	(	(	PUNCT
iajs-2801	265	3	𝛼),𝜆1	𝛼),𝜆1	X
iajs-2801	265	4	−(0	−(0	NOUN
iajs-2801	265	5	)	)	PUNCT
iajs-2801	265	6	≤	≤	NOUN
iajs-2801	265	7	𝜆1	𝜆1	NOUN
iajs-2801	265	8	−(𝛼	−(𝛼	NOUN
iajs-2801	265	9	)	)	PUNCT
iajs-2801	265	10	or𝜆2	or𝜆2	VERB
iajs-2801	266	1	+	+	ADJ
iajs-2801	266	2	(	(	PUNCT
iajs-2801	266	3	0	0	NUM
iajs-2801	266	4	)	)	PUNCT
iajs-2801	266	5	≥	≥	NOUN
iajs-2801	266	6	𝜆2	𝜆2	NOUN
iajs-2801	267	1	+	+	NOUN
iajs-2801	267	2	(	(	PUNCT
iajs-2801	267	3	𝛽),𝜆2	𝛽),𝜆2	NOUN
iajs-2801	267	4	−(0	−(0	NOUN
iajs-2801	267	5	)	)	PUNCT
iajs-2801	267	6	≤	≤	NUM
iajs-2801	267	7	𝜆2	𝜆2	PROPN
iajs-2801	267	8	−(𝛽	−(𝛽	NOUN
iajs-2801	267	9	)	)	PUNCT
iajs-2801	267	10	for	for	ADP
iajs-2801	267	11	all	all	DET
iajs-2801	267	12	𝛼	𝛼	NOUN
iajs-2801	267	13	,	,	PUNCT
iajs-2801	267	14	𝛽	𝛽	PROPN
iajs-2801	267	15	∈	∈	ADV
iajs-2801	267	16	ℵ.	ℵ.	NOUN
iajs-2801	268	1	(	(	PUNCT
iajs-2801	268	2	ii)suppose	ii)suppose	VERB
iajs-2801	268	3	that	that	PRON
iajs-2801	268	4	;	;	PUNCT
iajs-2801	268	5	𝜇2	𝜇2	VERB
iajs-2801	268	6	+	+	PROPN
iajs-2801	268	7	(	(	PUNCT
iajs-2801	268	8	0	0	NUM
iajs-2801	268	9	)	)	PUNCT
iajs-2801	268	10	≤	≤	NOUN
iajs-2801	268	11	;	;	PUNCT
iajs-2801	268	12	𝜇1	𝜇1	PROPN
iajs-2801	268	13	+	+	PROPN
iajs-2801	268	14	(	(	PUNCT
iajs-2801	268	15	𝛼	𝛼	NOUN
iajs-2801	268	16	)	)	PUNCT
iajs-2801	268	17	,	,	PUNCT
iajs-2801	268	18	;	;	PUNCT
iajs-2801	268	19	𝜇2	𝜇2	PROPN
iajs-2801	268	20	−(0	−(0	NOUN
iajs-2801	268	21	)	)	PUNCT
iajs-2801	268	22	≥	≥	NUM
iajs-2801	268	23	;	;	PUNCT
iajs-2801	268	24	𝜇1	𝜇1	NOUN
iajs-2801	268	25	−(𝛼	−(𝛼	NOUN
iajs-2801	268	26	)	)	PUNCT
iajs-2801	268	27	and	and	CCONJ
iajs-2801	268	28	𝜇2	𝜇2	VERB
iajs-2801	268	29	+	+	PROPN
iajs-2801	268	30	(	(	PUNCT
iajs-2801	268	31	0	0	NUM
iajs-2801	268	32	)	)	PUNCT
iajs-2801	268	33	≤	≤	PUNCT
iajs-2801	268	34	𝜇2	𝜇2	PROPN
iajs-2801	269	1	+	+	PROPN
iajs-2801	269	2	(	(	PUNCT
iajs-2801	269	3	𝛽),𝜇2	𝛽),𝜇2	X
iajs-2801	269	4	−(0	−(0	NOUN
iajs-2801	269	5	)	)	PUNCT
iajs-2801	269	6	≥	≥	NOUN
iajs-2801	269	7	𝜇2	𝜇2	PROPN
iajs-2801	269	8	−(𝛽	−(𝛽	NOUN
iajs-2801	269	9	)	)	PUNCT
iajs-2801	270	1	also	also	ADV
iajs-2801	270	2	,	,	PUNCT
iajs-2801	270	3	;	;	PUNCT
iajs-2801	270	4	𝜆2	𝜆2	PROPN
iajs-2801	270	5	+	+	PROPN
iajs-2801	270	6	(	(	PUNCT
iajs-2801	270	7	0	0	NUM
iajs-2801	270	8	)	)	PUNCT
iajs-2801	270	9	;	;	PUNCT
iajs-2801	270	10	≤	≤	NUM
iajs-2801	270	11	;	;	PUNCT
iajs-2801	270	12	;	;	PUNCT
iajs-2801	270	13	𝜆1	𝜆1	VERB
iajs-2801	270	14	+	+	PROPN
iajs-2801	270	15	(	(	PUNCT
iajs-2801	270	16	𝛼	𝛼	NOUN
iajs-2801	270	17	)	)	PUNCT
iajs-2801	271	1	;	;	PUNCT
iajs-2801	271	2	,	,	PUNCT
iajs-2801	271	3	;	;	PUNCT
iajs-2801	271	4	𝜆2	𝜆2	NOUN
iajs-2801	271	5	−(0	−(0	NOUN
iajs-2801	271	6	)	)	PUNCT
iajs-2801	271	7	;	;	PUNCT
iajs-2801	271	8	≥	≥	NUM
iajs-2801	271	9	;	;	PUNCT
iajs-2801	271	10	𝜆1	𝜆1	NOUN
iajs-2801	271	11	−(𝛼	−(𝛼	NOUN
iajs-2801	271	12	)	)	PUNCT
iajs-2801	272	1	and	and	CCONJ
iajs-2801	272	2	;	;	PUNCT
iajs-2801	272	3	𝜆2	𝜆2	PROPN
iajs-2801	272	4	+	+	PROPN
iajs-2801	272	5	(	(	PUNCT
iajs-2801	272	6	0	0	NUM
iajs-2801	272	7	)	)	PUNCT
iajs-2801	272	8	≤	≤	NUM
iajs-2801	272	9	;	;	PUNCT
iajs-2801	272	10	𝜆2	𝜆2	PROPN
iajs-2801	272	11	+	+	PROPN
iajs-2801	272	12	(	(	PUNCT
iajs-2801	272	13	𝛽	𝛽	NOUN
iajs-2801	272	14	)	)	PUNCT
iajs-2801	272	15	;	;	PUNCT
iajs-2801	272	16	,	,	PUNCT
iajs-2801	272	17	;	;	PUNCT
iajs-2801	272	18	𝜆2	𝜆2	NOUN
iajs-2801	272	19	−(0	−(0	NOUN
iajs-2801	272	20	)	)	PUNCT
iajs-2801	272	21	;	;	PUNCT
iajs-2801	272	22	≥	≥	NUM
iajs-2801	272	23	;	;	PUNCT
iajs-2801	272	24	;	;	PUNCT
iajs-2801	272	25	𝜆2	𝜆2	NOUN
iajs-2801	272	26	−(𝛽	−(𝛽	NOUN
iajs-2801	272	27	)	)	PUNCT
iajs-2801	272	28	,	,	PUNCT
iajs-2801	272	29	for	for	ADP
iajs-2801	272	30	all𝛼	all𝛼	NOUN
iajs-2801	272	31	,	,	PUNCT
iajs-2801	272	32	𝛽	𝛽	NOUN
iajs-2801	272	33	∈	∈	PROPN
iajs-2801	272	34	ℵ.	ℵ.	PROPN
iajs-2801	273	1	then	then	ADV
iajs-2801	273	2	(	(	PUNCT
iajs-2801	273	3	𝜇1	𝜇1	NOUN
iajs-2801	273	4	+	+	CCONJ
iajs-2801	273	5	×	×	PROPN
iajs-2801	273	6	𝜇2	𝜇2	NOUN
iajs-2801	273	7	+	+	PROPN
iajs-2801	273	8	)	)	PUNCT
iajs-2801	273	9	(	(	PUNCT
iajs-2801	273	10	0,0	0,0	NUM
iajs-2801	273	11	)	)	PUNCT
iajs-2801	273	12	=	=	SYM
iajs-2801	273	13	𝑟𝑚𝑖𝑛{𝜇1	𝑟𝑚𝑖𝑛{𝜇1	X
iajs-2801	273	14	+	+	ADJ
iajs-2801	273	15	(	(	PUNCT
iajs-2801	273	16	0	0	NUM
iajs-2801	273	17	)	)	PUNCT
iajs-2801	273	18	,	,	PUNCT
iajs-2801	273	19	𝜇2	𝜇2	PROPN
iajs-2801	273	20	+	+	PROPN
iajs-2801	273	21	(	(	PUNCT
iajs-2801	273	22	0	0	NUM
iajs-2801	273	23	)	)	PUNCT
iajs-2801	273	24	}	}	PUNCT
iajs-2801	273	25	=	=	SYM
iajs-2801	273	26	𝜇2	𝜇2	NOUN
iajs-2801	273	27	+	+	NOUN
iajs-2801	273	28	(	(	PUNCT
iajs-2801	273	29	0	0	NUM
iajs-2801	273	30	)	)	PUNCT
iajs-2801	273	31	and	and	CCONJ
iajs-2801	273	32	(	(	PUNCT
iajs-2801	273	33	𝜇1	𝜇1	PROPN
iajs-2801	273	34	+	+	CCONJ
iajs-2801	273	35	×	×	PROPN
iajs-2801	273	36	𝜇2	𝜇2	NOUN
iajs-2801	273	37	+	+	PROPN
iajs-2801	273	38	)	)	PUNCT
iajs-2801	273	39	(	(	PUNCT
iajs-2801	273	40	𝛼	𝛼	X
iajs-2801	273	41	,	,	PUNCT
iajs-2801	273	42	𝛽	𝛽	NOUN
iajs-2801	273	43	)	)	PUNCT
iajs-2801	273	44	=	=	SYM
iajs-2801	274	1	𝑟𝑚𝑖𝑛{	𝑟𝑚𝑖𝑛{	PROPN
iajs-2801	274	2	�	�	PROPN
iajs-2801	274	3	̃	̃	PROPN
iajs-2801	274	4	�	�	NOUN
iajs-2801	274	5	1	1	NUM
iajs-2801	274	6	+	+	ADJ
iajs-2801	274	7	(	(	PUNCT
iajs-2801	274	8	𝛼	𝛼	NOUN
iajs-2801	274	9	)	)	PUNCT
iajs-2801	274	10	,	,	PUNCT
iajs-2801	274	11	𝜇2	𝜇2	PROPN
iajs-2801	274	12	+	+	PROPN
iajs-2801	274	13	(	(	PUNCT
iajs-2801	274	14	𝛽	𝛽	NOUN
iajs-2801	274	15	)	)	PUNCT
iajs-2801	274	16	}	}	PUNCT
iajs-2801	274	17	≥	≥	X
iajs-2801	274	18	{	{	PUNCT
iajs-2801	274	19	𝜇2	𝜇2	VERB
iajs-2801	274	20	+	+	PROPN
iajs-2801	274	21	(	(	PUNCT
iajs-2801	274	22	0	0	NUM
iajs-2801	274	23	)	)	PUNCT
iajs-2801	274	24	,	,	PUNCT
iajs-2801	274	25	𝜇2	𝜇2	PROPN
iajs-2801	274	26	+	+	PROPN
iajs-2801	274	27	(	(	PUNCT
iajs-2801	274	28	0	0	NUM
iajs-2801	274	29	)	)	PUNCT
iajs-2801	274	30	}	}	PUNCT
iajs-2801	274	31	=	=	SYM
iajs-2801	274	32	𝜇2	𝜇2	NOUN
iajs-2801	274	33	+	+	NOUN
iajs-2801	274	34	(	(	PUNCT
iajs-2801	274	35	0	0	NUM
iajs-2801	274	36	)	)	PUNCT
iajs-2801	275	1	=	=	SYM
iajs-2801	275	2	(	(	PUNCT
iajs-2801	275	3	�	�	PROPN
iajs-2801	275	4	̃	̃	NOUN
iajs-2801	275	5	�	�	NOUN
iajs-2801	275	6	1	1	NUM
iajs-2801	275	7	+	+	SYM
iajs-2801	275	8	×	×	PROPN
iajs-2801	275	9	𝜇2	𝜇2	NOUN
iajs-2801	275	10	+	+	PROPN
iajs-2801	275	11	)	)	PUNCT
iajs-2801	275	12	(	(	PUNCT
iajs-2801	275	13	0,0	0,0	NOUN
iajs-2801	275	14	)	)	PUNCT
iajs-2801	275	15	and	and	CCONJ
iajs-2801	275	16	(	(	PUNCT
iajs-2801	275	17	𝜇1	𝜇1	PROPN
iajs-2801	275	18	−	−	PROPN
iajs-2801	275	19	×	×	PROPN
iajs-2801	275	20	𝜇2	𝜇2	NOUN
iajs-2801	275	21	−)(0,0	−)(0,0	NOUN
iajs-2801	275	22	)	)	PUNCT
iajs-2801	275	23	=	=	SYM
iajs-2801	275	24	𝑟𝑚𝑎𝑥{𝜇1	𝑟𝑚𝑎𝑥{𝜇1	PROPN
iajs-2801	275	25	−(0	−(0	NOUN
iajs-2801	275	26	)	)	PUNCT
iajs-2801	275	27	,	,	PUNCT
iajs-2801	275	28	𝜇2	𝜇2	PROPN
iajs-2801	275	29	−(0	−(0	NOUN
iajs-2801	275	30	)	)	PUNCT
iajs-2801	275	31	}	}	PUNCT
iajs-2801	275	32	=	=	SYM
iajs-2801	275	33	𝜇2	𝜇2	PROPN
iajs-2801	275	34	−(0	−(0	NOUN
iajs-2801	275	35	)	)	PUNCT
iajs-2801	275	36	.	.	PUNCT
iajs-2801	276	1	(	(	PUNCT
iajs-2801	276	2	𝜇1	𝜇1	ADJ
iajs-2801	276	3	−	−	PROPN
iajs-2801	276	4	×	×	PROPN
iajs-2801	276	5	𝜇2	𝜇2	PROPN
iajs-2801	276	6	−)(𝛼	−)(𝛼	PROPN
iajs-2801	276	7	,	,	PUNCT
iajs-2801	276	8	𝛽	𝛽	NOUN
iajs-2801	276	9	)	)	PUNCT
iajs-2801	276	10	=	=	SYM
iajs-2801	276	11	𝑟𝑚𝑎𝑥{	𝑟𝑚𝑎𝑥{	NOUN
iajs-2801	276	12	�	�	PROPN
iajs-2801	276	13	̃	̃	PROPN
iajs-2801	276	14	�	�	PROPN
iajs-2801	276	15	1	1	NUM
iajs-2801	276	16	−(𝛼	−(𝛼	NOUN
iajs-2801	276	17	)	)	PUNCT
iajs-2801	276	18	,	,	PUNCT
iajs-2801	276	19	𝜇2	𝜇2	PROPN
iajs-2801	276	20	−(𝛽	−(𝛽	NOUN
iajs-2801	276	21	)	)	PUNCT
iajs-2801	276	22	}	}	PUNCT
iajs-2801	276	23	≤	≤	NUM
iajs-2801	276	24	𝑟𝑚𝑎𝑥{𝜇2	𝑟𝑚𝑎𝑥{𝜇2	NOUN
iajs-2801	276	25	−(0	−(0	NOUN
iajs-2801	276	26	)	)	PUNCT
iajs-2801	276	27	,	,	PUNCT
iajs-2801	276	28	𝜇2	𝜇2	PROPN
iajs-2801	276	29	−(0	−(0	NOUN
iajs-2801	276	30	)	)	PUNCT
iajs-2801	276	31	}	}	PUNCT
iajs-2801	276	32	=	=	SYM
iajs-2801	276	33	𝜇2	𝜇2	NOUN
iajs-2801	276	34	−(0	−(0	NOUN
iajs-2801	276	35	)	)	PUNCT
iajs-2801	276	36	=	=	SYM
iajs-2801	276	37	(	(	PUNCT
iajs-2801	276	38	𝜇1	𝜇1	NOUN
iajs-2801	276	39	−	−	PROPN
iajs-2801	276	40	×	×	PROPN
iajs-2801	276	41	𝜇2	𝜇2	NOUN
iajs-2801	277	1	−)(0,0)aaa	−)(0,0)aaa	NOUN
iajs-2801	278	1			X
iajs-2801	278	2			PROPN
iajs-2801	278	3			PROPN
iajs-2801	278	4			PROPN
iajs-2801	278	5	ibn	ibn	PROPN
iajs-2801	278	6	al	al	PROPN
iajs-2801	278	7	-	-	PUNCT
iajs-2801	278	8	haitham	haitham	PROPN
iajs-2801	278	9	jour	jour	X
iajs-2801	278	10	.	.	PROPN
iajs-2801	279	1	for	for	ADP
iajs-2801	279	2	pure	pure	ADJ
iajs-2801	279	3	&	&	CCONJ
iajs-2801	279	4	appl	appl	PROPN
iajs-2801	279	5	.	.	PUNCT
iajs-2801	280	1	sci	sci	PROPN
iajs-2801	280	2	.	.	PUNCT
iajs-2801	281	1	35(1)2022	35(1)2022	NUM
iajs-2801	281	2	81	81	NUM
iajs-2801	281	3	also	also	ADV
iajs-2801	281	4	,	,	PUNCT
iajs-2801	281	5	(;	(;	X
iajs-2801	281	6	𝜆1	𝜆1	NOUN
iajs-2801	281	7	+	+	CCONJ
iajs-2801	281	8	×	×	NOUN
iajs-2801	281	9	;	;	PUNCT
iajs-2801	281	10	𝜆2	𝜆2	PROPN
iajs-2801	281	11	+	+	PROPN
iajs-2801	281	12	;	;	PUNCT
iajs-2801	281	13	)	)	PUNCT
iajs-2801	281	14	(	(	PUNCT
iajs-2801	281	15	0,0	0,0	NUM
iajs-2801	281	16	)	)	PUNCT
iajs-2801	281	17	=	=	SYM
iajs-2801	281	18	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	281	19	{	{	PUNCT
iajs-2801	281	20	;	;	PUNCT
iajs-2801	281	21	𝜆1	𝜆1	VERB
iajs-2801	281	22	+	+	NOUN
iajs-2801	281	23	(	(	PUNCT
iajs-2801	281	24	0	0	NUM
iajs-2801	281	25	)	)	PUNCT
iajs-2801	281	26	;	;	PUNCT
iajs-2801	281	27	,	,	PUNCT
iajs-2801	281	28	;	;	PUNCT
iajs-2801	281	29	𝜆2	𝜆2	PROPN
iajs-2801	281	30	+	+	PROPN
iajs-2801	281	31	(	(	PUNCT
iajs-2801	281	32	0	0	NUM
iajs-2801	281	33	)	)	PUNCT
iajs-2801	281	34	;	;	PUNCT
iajs-2801	281	35	}	}	PUNCT
iajs-2801	281	36	=	=	PRON
iajs-2801	281	37	;	;	PUNCT
iajs-2801	281	38	𝜆2	𝜆2	PROPN
iajs-2801	281	39	+	+	PROPN
iajs-2801	281	40	(	(	PUNCT
iajs-2801	281	41	0	0	NUM
iajs-2801	281	42	)	)	PUNCT
iajs-2801	281	43	;	;	PUNCT
iajs-2801	281	44	and	and	CCONJ
iajs-2801	281	45	;	;	PUNCT
iajs-2801	281	46	;	;	PUNCT
iajs-2801	281	47	(;	(;	X
iajs-2801	281	48	𝜆1	𝜆1	NOUN
iajs-2801	282	1	+	+	ADP
iajs-2801	282	2	;	;	PUNCT
iajs-2801	282	3	×	×	NOUN
iajs-2801	282	4	;	;	PUNCT
iajs-2801	282	5	𝜆2	𝜆2	PROPN
iajs-2801	282	6	+	+	PROPN
iajs-2801	282	7	;	;	PUNCT
iajs-2801	282	8	)	)	PUNCT
iajs-2801	282	9	(	(	PUNCT
iajs-2801	282	10	𝛼	𝛼	X
iajs-2801	282	11	,	,	PUNCT
iajs-2801	282	12	𝛽	𝛽	NOUN
iajs-2801	282	13	)	)	PUNCT
iajs-2801	282	14	=	=	SYM
iajs-2801	282	15	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	282	16	{	{	PUNCT
iajs-2801	282	17	;	;	PUNCT
iajs-2801	282	18	𝜆1	𝜆1	VERB
iajs-2801	282	19	+	+	NOUN
iajs-2801	282	20	(	(	PUNCT
iajs-2801	282	21	𝛼	𝛼	NOUN
iajs-2801	282	22	)	)	PUNCT
iajs-2801	282	23	;	;	PUNCT
iajs-2801	282	24	,	,	PUNCT
iajs-2801	282	25	;	;	PUNCT
iajs-2801	283	1	𝜆2	𝜆2	PROPN
iajs-2801	283	2	+	+	PROPN
iajs-2801	283	3	(	(	PUNCT
iajs-2801	283	4	𝛽	𝛽	NOUN
iajs-2801	283	5	)	)	PUNCT
iajs-2801	283	6	;	;	PUNCT
iajs-2801	283	7	}	}	PUNCT
iajs-2801	283	8	≥	≥	X
iajs-2801	283	9	{	{	PUNCT
iajs-2801	283	10	;	;	PUNCT
iajs-2801	283	11	𝜆2	𝜆2	PROPN
iajs-2801	283	12	+	+	PROPN
iajs-2801	283	13	(	(	PUNCT
iajs-2801	283	14	0	0	NUM
iajs-2801	283	15	)	)	PUNCT
iajs-2801	283	16	;	;	PUNCT
iajs-2801	283	17	,	,	PUNCT
iajs-2801	283	18	;	;	PUNCT
iajs-2801	283	19	𝜆2	𝜆2	PROPN
iajs-2801	283	20	+	+	PROPN
iajs-2801	283	21	(	(	PUNCT
iajs-2801	283	22	0	0	NUM
iajs-2801	283	23	)	)	PUNCT
iajs-2801	283	24	;	;	PUNCT
iajs-2801	283	25	}	}	PUNCT
iajs-2801	283	26	=	=	PRON
iajs-2801	283	27	;	;	PUNCT
iajs-2801	283	28	𝜆2	𝜆2	PROPN
iajs-2801	283	29	+	+	PROPN
iajs-2801	283	30	(	(	PUNCT
iajs-2801	283	31	0	0	NUM
iajs-2801	283	32	)	)	PUNCT
iajs-2801	283	33	;	;	PUNCT
iajs-2801	283	34	=	=	SYM
iajs-2801	283	35	;	;	PUNCT
iajs-2801	283	36	(;	(;	PUNCT
iajs-2801	283	37	𝜆1	𝜆1	NOUN
iajs-2801	283	38	+	+	CCONJ
iajs-2801	283	39	×	×	NOUN
iajs-2801	283	40	;	;	PUNCT
iajs-2801	283	41	𝜆2	𝜆2	PROPN
iajs-2801	283	42	+	+	PROPN
iajs-2801	283	43	)	)	PUNCT
iajs-2801	283	44	(	(	PUNCT
iajs-2801	283	45	0,0	0,0	NOUN
iajs-2801	283	46	)	)	PUNCT
iajs-2801	283	47	.	.	PUNCT
iajs-2801	284	1	and	and	CCONJ
iajs-2801	284	2	(;	(;	PUNCT
iajs-2801	284	3	𝜆1	𝜆1	NOUN
iajs-2801	284	4	−	−	ADP
iajs-2801	284	5	×	×	NOUN
iajs-2801	284	6	;	;	PUNCT
iajs-2801	284	7	𝜆2	𝜆2	NOUN
iajs-2801	284	8	−	−	PROPN
iajs-2801	284	9	;	;	PUNCT
iajs-2801	284	10	)	)	PUNCT
iajs-2801	284	11	(	(	PUNCT
iajs-2801	284	12	0,0	0,0	NOUN
iajs-2801	284	13	)	)	PUNCT
iajs-2801	284	14	=	=	SYM
iajs-2801	284	15	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-2801	284	16	{	{	PUNCT
iajs-2801	284	17	;	;	PUNCT
iajs-2801	284	18	𝜆1	𝜆1	VERB
iajs-2801	284	19	−(0	−(0	NOUN
iajs-2801	284	20	)	)	PUNCT
iajs-2801	284	21	,	,	PUNCT
iajs-2801	284	22	;	;	PUNCT
iajs-2801	284	23	𝜆2	𝜆2	NOUN
iajs-2801	284	24	−(0	−(0	NOUN
iajs-2801	284	25	)	)	PUNCT
iajs-2801	284	26	}	}	PUNCT
iajs-2801	285	1	=	=	SYM
iajs-2801	285	2	;	;	PUNCT
iajs-2801	285	3	𝜆2	𝜆2	NOUN
iajs-2801	285	4	−(0	−(0	NOUN
iajs-2801	285	5	)	)	PUNCT
iajs-2801	285	6	.	.	PUNCT
iajs-2801	286	1	(;	(;	CCONJ
iajs-2801	286	2	𝜆1	𝜆1	NOUN
iajs-2801	286	3	−	−	ADP
iajs-2801	286	4	×	×	NOUN
iajs-2801	286	5	;	;	PUNCT
iajs-2801	286	6	𝜆2	𝜆2	NOUN
iajs-2801	286	7	−	−	PROPN
iajs-2801	286	8	;	;	PUNCT
iajs-2801	286	9	)	)	PUNCT
iajs-2801	286	10	(	(	PUNCT
iajs-2801	286	11	𝛼	𝛼	X
iajs-2801	286	12	,	,	PUNCT
iajs-2801	286	13	𝛽	𝛽	NOUN
iajs-2801	286	14	)	)	PUNCT
iajs-2801	286	15	=	=	SYM
iajs-2801	286	16	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-2801	286	17	{	{	PUNCT
iajs-2801	286	18	;	;	PUNCT
iajs-2801	286	19	𝜆1	𝜆1	VERB
iajs-2801	286	20	−(𝛼	−(𝛼	NOUN
iajs-2801	286	21	)	)	PUNCT
iajs-2801	286	22	,	,	PUNCT
iajs-2801	286	23	;	;	PUNCT
iajs-2801	286	24	𝜆2	𝜆2	NOUN
iajs-2801	286	25	−(𝛽	−(𝛽	NOUN
iajs-2801	286	26	)	)	PUNCT
iajs-2801	286	27	}	}	PUNCT
iajs-2801	286	28	≤	≤	NUM
iajs-2801	286	29	𝑚𝑎𝑥	𝑚𝑎𝑥	NUM
iajs-2801	286	30	{	{	PUNCT
iajs-2801	286	31	;	;	PUNCT
iajs-2801	286	32	𝜆2	𝜆2	NOUN
iajs-2801	286	33	−(0	−(0	NOUN
iajs-2801	286	34	)	)	PUNCT
iajs-2801	286	35	,	,	PUNCT
iajs-2801	286	36	;	;	PUNCT
iajs-2801	286	37	𝜆2	𝜆2	NOUN
iajs-2801	286	38	−(0	−(0	NOUN
iajs-2801	286	39	)	)	PUNCT
iajs-2801	286	40	}	}	PUNCT
iajs-2801	287	1	=	=	SYM
iajs-2801	287	2	;	;	PUNCT
iajs-2801	287	3	𝜆2	𝜆2	NOUN
iajs-2801	287	4	−(0	−(0	NOUN
iajs-2801	287	5	)	)	PUNCT
iajs-2801	287	6	=	=	PUNCT
iajs-2801	288	1	(;	(;	PUNCT
iajs-2801	288	2	𝜆1	𝜆1	NOUN
iajs-2801	288	3	−	−	ADP
iajs-2801	288	4	×	×	NOUN
iajs-2801	288	5	;	;	PUNCT
iajs-2801	288	6	𝜆2	𝜆2	PROPN
iajs-2801	288	7	−	−	PROPN
iajs-2801	288	8	)	)	PUNCT
iajs-2801	288	9	;	;	PUNCT
iajs-2801	288	10	(	(	PUNCT
iajs-2801	288	11	0,0	0,0	NOUN
iajs-2801	288	12	)	)	PUNCT
iajs-2801	288	13	.	.	PUNCT
iajs-2801	289	1	this	this	PRON
iajs-2801	289	2	is	be	AUX
iajs-2801	289	3	a	a	DET
iajs-2801	289	4	contradiction	contradiction	NOUN
iajs-2801	289	5	.	.	PUNCT
iajs-2801	290	1	therefore	therefore	ADV
iajs-2801	290	2	,	,	PUNCT
iajs-2801	290	3	either	either	CCONJ
iajs-2801	290	4	𝜇2	𝜇2	PROPN
iajs-2801	290	5	+	+	PROPN
iajs-2801	290	6	(	(	PUNCT
iajs-2801	290	7	0	0	NUM
iajs-2801	290	8	)	)	PUNCT
iajs-2801	290	9	≥	≥	NOUN
iajs-2801	290	10	𝜇1	𝜇1	NOUN
iajs-2801	290	11	+	+	PROPN
iajs-2801	290	12	(	(	PUNCT
iajs-2801	290	13	𝜒),𝜇2	𝜒),𝜇2	X
iajs-2801	290	14	−(0	−(0	NOUN
iajs-2801	290	15	)	)	PUNCT
iajs-2801	290	16	≤	≤	PROPN
iajs-2801	290	17	𝜇1	𝜇1	PROPN
iajs-2801	290	18	−(𝛼	−(𝛼	PROPN
iajs-2801	290	19	)	)	PUNCT
iajs-2801	290	20	and	and	CCONJ
iajs-2801	290	21	𝜆2	𝜆2	PROPN
iajs-2801	291	1	+	+	PROPN
iajs-2801	291	2	(	(	PUNCT
iajs-2801	291	3	0	0	NUM
iajs-2801	291	4	)	)	PUNCT
iajs-2801	291	5	≥	≥	NOUN
iajs-2801	291	6	𝜆1	𝜆1	VERB
iajs-2801	292	1	+	+	PROPN
iajs-2801	292	2	(	(	PUNCT
iajs-2801	292	3	𝛼),𝜆2	𝛼),𝜆2	NOUN
iajs-2801	292	4	−(0	−(0	NOUN
iajs-2801	292	5	)	)	PUNCT
iajs-2801	292	6	≤	≤	NOUN
iajs-2801	292	7	𝜆1	𝜆1	NOUN
iajs-2801	292	8	−(𝑥)or	−(𝑥)or	PROPN
iajs-2801	292	9	𝜇2	𝜇2	PROPN
iajs-2801	292	10	+	+	PROPN
iajs-2801	292	11	(	(	PUNCT
iajs-2801	292	12	0	0	NUM
iajs-2801	292	13	)	)	PUNCT
iajs-2801	292	14	≥	≥	NOUN
iajs-2801	293	1	𝜇2	𝜇2	VERB
iajs-2801	293	2	+	+	PROPN
iajs-2801	293	3	(	(	PUNCT
iajs-2801	293	4	𝛽),𝜇2	𝛽),𝜇2	X
iajs-2801	293	5	−(0	−(0	NOUN
iajs-2801	293	6	)	)	PUNCT
iajs-2801	293	7	≤	≤	NOUN
iajs-2801	293	8	𝜇2	𝜇2	PROPN
iajs-2801	294	1	−(𝛽)and	−(𝛽)and	PROPN
iajs-2801	294	2	𝜆2	𝜆2	PROPN
iajs-2801	295	1	+	+	PROPN
iajs-2801	295	2	(	(	PUNCT
iajs-2801	295	3	0	0	NUM
iajs-2801	295	4	)	)	PUNCT
iajs-2801	295	5	≥	≥	NOUN
iajs-2801	295	6	𝜆2	𝜆2	NOUN
iajs-2801	296	1	+	+	NOUN
iajs-2801	296	2	(	(	PUNCT
iajs-2801	296	3	𝛽),𝜆2	𝛽),𝜆2	NOUN
iajs-2801	296	4	−(0	−(0	NOUN
iajs-2801	296	5	)	)	PUNCT
iajs-2801	296	6	≤	≤	NUM
iajs-2801	296	7	𝜆2	𝜆2	PROPN
iajs-2801	296	8	−(𝛽	−(𝛽	NOUN
iajs-2801	296	9	)	)	PUNCT
iajs-2801	296	10	.	.	PUNCT
iajs-2801	297	1	(	(	PUNCT
iajs-2801	297	2	iii)the	iii)the	DET
iajs-2801	297	3	proof	proof	NOUN
iajs-2801	297	4	is	be	AUX
iajs-2801	297	5	similar	similar	ADJ
iajs-2801	297	6	to	to	ADP
iajs-2801	297	7	(	(	PUNCT
iajs-2801	297	8	ii	ii	NOUN
iajs-2801	297	9	)	)	PUNCT
iajs-2801	297	10	.	.	PUNCT
iajs-2801	298	1	the	the	DET
iajs-2801	298	2	partial	partial	ADJ
iajs-2801	298	3	converse	converse	NOUN
iajs-2801	298	4	of	of	ADP
iajs-2801	298	5	theorem	theorem	NOUN
iajs-2801	298	6	(	(	PUNCT
iajs-2801	298	7	3.5	3.5	NUM
iajs-2801	298	8	)	)	PUNCT
iajs-2801	298	9	is	be	AUX
iajs-2801	298	10	the	the	DET
iajs-2801	298	11	following	following	NOUN
iajs-2801	298	12	.	.	PUNCT
iajs-2801	299	1	theorem3.7	theorem3.7	NOUN
iajs-2801	299	2	.	.	PUNCT
iajs-2801	300	1	in	in	ADP
iajs-2801	300	2	a	a	DET
iajs-2801	300	3	ku	ku	NOUN
iajs-2801	300	4	-	-	PUNCT
iajs-2801	300	5	semigroupℵ.	semigroupℵ.	NOUN
iajs-2801	300	6	if	if	SCONJ
iajs-2801	300	7	ω𝑓1	ω𝑓1	NOUN
iajs-2801	300	8	×	×	PROPN
iajs-2801	300	9	ω𝑓2	ω𝑓2	NUM
iajs-2801	300	10	is	be	AUX
iajs-2801	300	11	acb	acb	PROPN
iajs-2801	300	12	ideal	ideal	NOUN
iajs-2801	300	13	of	of	ADP
iajs-2801	300	14	ℵ	ℵ	DET
iajs-2801	300	15	×	×	NOUN
iajs-2801	300	16	ℵ	ℵ	NOUN
iajs-2801	300	17	,	,	PUNCT
iajs-2801	300	18	then	then	ADV
iajs-2801	300	19	ωf1	ωf1	NOUN
iajs-2801	300	20	or	or	CCONJ
iajs-2801	300	21	ωf2	ωf2	NOUN
iajs-2801	300	22	is	be	AUX
iajs-2801	300	23	acb	acb	NOUN
iajs-2801	300	24	ideal	ideal	NOUN
iajs-2801	300	25	of	of	ADP
iajs-2801	300	26	ℵ.	ℵ.	PROPN
iajs-2801	300	27	proof	proof	NOUN
iajs-2801	300	28	.	.	PUNCT
iajs-2801	301	1	by	by	ADP
iajs-2801	301	2	use	use	VERB
iajs-2801	301	3	the	the	DET
iajs-2801	301	4	theorem	theorem	NOUN
iajs-2801	301	5	(	(	PUNCT
iajs-2801	301	6	3.5	3.5	NUM
iajs-2801	301	7	)	)	PUNCT
iajs-2801	301	8	(	(	PUNCT
iajs-2801	301	9	i	i	NOUN
iajs-2801	301	10	)	)	PUNCT
iajs-2801	301	11	,	,	PUNCT
iajs-2801	301	12	without	without	ADP
iajs-2801	301	13	loss	loss	NOUN
iajs-2801	301	14	of	of	ADP
iajs-2801	301	15	generality	generality	NOUN
iajs-2801	301	16	we	we	PRON
iajs-2801	301	17	suppose	suppose	VERB
iajs-2801	301	18	that	that	SCONJ
iajs-2801	301	19	𝜇2	𝜇2	PROPN
iajs-2801	301	20	+	+	PROPN
iajs-2801	301	21	(	(	PUNCT
iajs-2801	301	22	0	0	NUM
iajs-2801	301	23	)	)	PUNCT
iajs-2801	301	24	≥	≥	NOUN
iajs-2801	301	25	𝜇2	𝜇2	VERB
iajs-2801	301	26	+	+	PROPN
iajs-2801	301	27	(	(	PUNCT
iajs-2801	301	28	𝛼	𝛼	NOUN
iajs-2801	301	29	)	)	PUNCT
iajs-2801	301	30	,	,	PUNCT
iajs-2801	301	31	𝜇2	𝜇2	PROPN
iajs-2801	301	32	−(0	−(0	NOUN
iajs-2801	301	33	)	)	PUNCT
iajs-2801	301	34	≤	≤	PROPN
iajs-2801	301	35	𝜇2	𝜇2	PROPN
iajs-2801	301	36	−(𝛼	−(𝛼	NOUN
iajs-2801	301	37	)	)	PUNCT
iajs-2801	301	38	,	,	PUNCT
iajs-2801	301	39	and	and	CCONJ
iajs-2801	301	40	λ2	λ2	NOUN
iajs-2801	301	41	+	+	PROPN
iajs-2801	301	42	(	(	PUNCT
iajs-2801	301	43	0	0	NUM
iajs-2801	301	44	)	)	PUNCT
iajs-2801	301	45	≥	≥	NOUN
iajs-2801	301	46	λ2	λ2	NOUN
iajs-2801	302	1	+	+	NOUN
iajs-2801	302	2	(	(	PUNCT
iajs-2801	302	3	α),λ2	α),λ2	X
iajs-2801	302	4	(	(	PUNCT
iajs-2801	302	5	0	0	NUM
iajs-2801	302	6	)	)	PUNCT
iajs-2801	302	7	≤	≤	NUM
iajs-2801	302	8	λ2	λ2	NOUN
iajs-2801	302	9	(	(	PUNCT
iajs-2801	302	10	α),for	α),for	ADP
iajs-2801	302	11	allα	allα	PROPN
iajs-2801	302	12	∈	∈	PROPN
iajs-2801	302	13	ℵ.	ℵ.	PROPN
iajs-2801	303	1	it	it	PRON
iajs-2801	303	2	follows	follow	VERB
iajs-2801	303	3	from	from	ADP
iajs-2801	303	4	theorem	theorem	ADJ
iajs-2801	303	5	(	(	PUNCT
iajs-2801	303	6	4.6)(iii	4.6)(iii	NUM
iajs-2801	303	7	)	)	PUNCT
iajs-2801	304	1	that	that	PRON
iajs-2801	304	2	either	either	CCONJ
iajs-2801	304	3	then	then	ADV
iajs-2801	304	4	either	either	CCONJ
iajs-2801	304	5	𝜇1	𝜇1	PROPN
iajs-2801	304	6	+	+	PROPN
iajs-2801	304	7	(	(	PUNCT
iajs-2801	304	8	0	0	NUM
iajs-2801	304	9	)	)	PUNCT
iajs-2801	304	10	≥	≥	NOUN
iajs-2801	304	11	𝜇1	𝜇1	NOUN
iajs-2801	304	12	+	+	PROPN
iajs-2801	304	13	(	(	PUNCT
iajs-2801	304	14	𝛼),𝜇1	𝛼),𝜇1	NUM
iajs-2801	304	15	−(0	−(0	NOUN
iajs-2801	304	16	)	)	PUNCT
iajs-2801	304	17	≤	≤	NOUN
iajs-2801	304	18	𝜇1	𝜇1	ADJ
iajs-2801	304	19	−(𝛼	−(𝛼	NOUN
iajs-2801	304	20	)	)	PUNCT
iajs-2801	304	21	,	,	PUNCT
iajs-2801	305	1	and𝜆1	and𝜆1	PUNCT
iajs-2801	306	1	+	+	ADJ
iajs-2801	306	2	(	(	PUNCT
iajs-2801	306	3	0	0	NUM
iajs-2801	306	4	)	)	PUNCT
iajs-2801	306	5	≥	≥	NOUN
iajs-2801	306	6	𝜆1	𝜆1	VERB
iajs-2801	307	1	+	+	ADP
iajs-2801	307	2	𝛼,𝜆1	𝛼,𝜆1	PROPN
iajs-2801	307	3	−(0	−(0	NOUN
iajs-2801	307	4	)	)	PUNCT
iajs-2801	307	5	≤	≤	NOUN
iajs-2801	307	6	𝜆1	𝜆1	NOUN
iajs-2801	307	7	−(𝛼	−(𝛼	NOUN
iajs-2801	307	8	)	)	PUNCT
iajs-2801	307	9	or	or	CCONJ
iajs-2801	307	10	𝜇1	𝜇1	NOUN
iajs-2801	307	11	+	+	PROPN
iajs-2801	307	12	(	(	PUNCT
iajs-2801	307	13	0	0	NUM
iajs-2801	307	14	)	)	PUNCT
iajs-2801	308	1	≥	≥	NOUN
iajs-2801	308	2	𝜇2	𝜇2	VERB
iajs-2801	308	3	+	+	PROPN
iajs-2801	308	4	(	(	PUNCT
iajs-2801	308	5	𝛼	𝛼	NOUN
iajs-2801	308	6	)	)	PUNCT
iajs-2801	308	7	,	,	PUNCT
iajs-2801	308	8	;	;	PUNCT
iajs-2801	308	9	�	�	PROPN
iajs-2801	308	10	̃	̃	NOUN
iajs-2801	308	11	�	�	PROPN
iajs-2801	308	12	1	1	NUM
iajs-2801	308	13	−(0	−(0	NOUN
iajs-2801	308	14	)	)	PUNCT
iajs-2801	308	15	;	;	PUNCT
iajs-2801	308	16	≤	≤	NUM
iajs-2801	308	17	;	;	PUNCT
iajs-2801	308	18	�	�	PROPN
iajs-2801	308	19	̃	̃	PROPN
iajs-2801	308	20	�	�	PROPN
iajs-2801	308	21	2	2	NUM
iajs-2801	308	22	−(𝛼	−(𝛼	NOUN
iajs-2801	308	23	)	)	PUNCT
iajs-2801	308	24	;	;	PUNCT
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iajs-2801	308	28	+	+	PROPN
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iajs-2801	308	30	0	0	NUM
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iajs-2801	308	32	;	;	PUNCT
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iajs-2801	308	34	;	;	PUNCT
iajs-2801	308	35	𝜆2	𝜆2	PROPN
iajs-2801	308	36	+	+	PROPN
iajs-2801	308	37	(	(	PUNCT
iajs-2801	308	38	𝛼	𝛼	NOUN
iajs-2801	308	39	)	)	PUNCT
iajs-2801	308	40	,	,	PUNCT
iajs-2801	308	41	;	;	PUNCT
iajs-2801	308	42	𝜆1	𝜆1	VERB
iajs-2801	308	43	−(0	−(0	NOUN
iajs-2801	308	44	)	)	PUNCT
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iajs-2801	308	47	;	;	PUNCT
iajs-2801	308	48	𝜆2	𝜆2	NOUN
iajs-2801	308	49	−(𝛼	−(𝛼	NOUN
iajs-2801	308	50	)	)	PUNCT
iajs-2801	308	51	.	.	PUNCT
iajs-2801	309	1	,	,	PUNCT
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iajs-2801	309	4	α	α	NOUN
iajs-2801	309	5	∈	∈	PROPN
iajs-2801	309	6	ℵ.	ℵ.	NOUN
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iajs-2801	309	8	(;	(;	PUNCT
iajs-2801	309	9	�	�	PROPN
iajs-2801	309	10	̃	̃	NOUN
iajs-2801	309	11	�	�	NOUN
iajs-2801	309	12	1	1	NUM
iajs-2801	309	13	+	+	NUM
iajs-2801	309	14	×	×	NOUN
iajs-2801	309	15	;	;	PUNCT
iajs-2801	309	16	�	�	PROPN
iajs-2801	309	17	̃	̃	PROPN
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iajs-2801	309	19	2	2	NUM
iajs-2801	309	20	+	+	CCONJ
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iajs-2801	309	22	(	(	PUNCT
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iajs-2801	309	24	,	,	PUNCT
iajs-2801	309	25	𝛼	𝛼	NOUN
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iajs-2801	309	27	=	=	SYM
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iajs-2801	309	30	;	;	PUNCT
iajs-2801	309	31	�	�	PROPN
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iajs-2801	309	34	1	1	NUM
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iajs-2801	309	37	0	0	NUM
iajs-2801	309	38	)	)	PUNCT
iajs-2801	309	39	,	,	PUNCT
iajs-2801	309	40	;	;	PUNCT
iajs-2801	309	41	�	�	PROPN
iajs-2801	309	42	̃	̃	NOUN
iajs-2801	309	43	�	�	NOUN
iajs-2801	309	44	2	2	NUM
iajs-2801	309	45	+	+	NOUN
iajs-2801	309	46	(	(	PUNCT
iajs-2801	309	47	𝛼	𝛼	NOUN
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iajs-2801	309	49	}	}	PUNCT
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iajs-2801	309	52	�	�	PROPN
iajs-2801	309	53	̃	̃	NOUN
iajs-2801	309	54	�	�	NOUN
iajs-2801	309	55	2	2	NUM
iajs-2801	309	56	+	+	NOUN
iajs-2801	309	57	(	(	PUNCT
iajs-2801	309	58	𝛼	𝛼	NOUN
iajs-2801	309	59	)	)	PUNCT
iajs-2801	309	60	…	…	PUNCT
iajs-2801	309	61	.	.	PUNCT
iajs-2801	309	62	.	.	PUNCT
iajs-2801	310	1	(	(	PUNCT
iajs-2801	310	2	1	1	X
iajs-2801	310	3	)	)	PUNCT
iajs-2801	310	4	(;	(;	PUNCT
iajs-2801	310	5	�	�	PROPN
iajs-2801	310	6	̃	̃	NOUN
iajs-2801	310	7	�	�	NOUN
iajs-2801	310	8	1	1	NUM
iajs-2801	310	9	−	−	NOUN
iajs-2801	310	10	×	×	NOUN
iajs-2801	310	11	;	;	PUNCT
iajs-2801	310	12	�	�	PROPN
iajs-2801	310	13	̃	̃	PROPN
iajs-2801	310	14	�	�	PROPN
iajs-2801	310	15	2	2	NUM
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iajs-2801	310	18	(	(	PUNCT
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iajs-2801	310	21	𝛼	𝛼	NOUN
iajs-2801	310	22	)	)	PUNCT
iajs-2801	310	23	=	=	SYM
iajs-2801	310	24	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
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iajs-2801	310	30	1	1	NUM
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iajs-2801	310	33	,	,	PUNCT
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iajs-2801	310	35	�	�	PROPN
iajs-2801	310	36	̃	̃	PROPN
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iajs-2801	310	38	2	2	NUM
iajs-2801	310	39	−(𝛼	−(𝛼	NOUN
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iajs-2801	311	3	�	�	PROPN
iajs-2801	311	4	̃	̃	PROPN
iajs-2801	311	5	�	�	PROPN
iajs-2801	311	6	2	2	NUM
iajs-2801	311	7	−(𝛼	−(𝛼	NOUN
iajs-2801	311	8	)	)	PUNCT
iajs-2801	311	9	…	…	PUNCT
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iajs-2801	311	11	(	(	PUNCT
iajs-2801	311	12	2	2	NUM
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iajs-2801	311	14	also	also	ADV
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iajs-2801	311	17	𝜆1	𝜆1	VERB
iajs-2801	311	18	+	+	CCONJ
iajs-2801	311	19	×	×	PROPN
iajs-2801	311	20	𝜆2	𝜆2	NOUN
iajs-2801	311	21	+	+	PROPN
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iajs-2801	311	28	=	=	PUNCT
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iajs-2801	312	3	(	(	PUNCT
iajs-2801	312	4	0	0	NUM
iajs-2801	312	5	)	)	PUNCT
iajs-2801	312	6	,	,	PUNCT
iajs-2801	312	7	𝜆2	𝜆2	PROPN
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iajs-2801	312	9	(	(	PUNCT
iajs-2801	312	10	𝛼	𝛼	NOUN
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iajs-2801	312	12	}	}	PUNCT
iajs-2801	312	13	=	=	PUNCT
iajs-2801	312	14	𝜆2	𝜆2	PROPN
iajs-2801	312	15	+	+	PROPN
iajs-2801	312	16	(	(	PUNCT
iajs-2801	312	17	𝛼	𝛼	NOUN
iajs-2801	312	18	)	)	PUNCT
iajs-2801	312	19	…	…	PUNCT
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iajs-2801	312	21	(	(	PUNCT
iajs-2801	312	22	3	3	NUM
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iajs-2801	312	24	(	(	PUNCT
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iajs-2801	312	26	−	−	PROPN
iajs-2801	312	27	×	×	PROPN
iajs-2801	312	28	𝜆2	𝜆2	PROPN
iajs-2801	312	29	−)(0	−)(0	NOUN
iajs-2801	312	30	,	,	PUNCT
iajs-2801	312	31	𝛼	𝛼	NOUN
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iajs-2801	312	33	=	=	SYM
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iajs-2801	312	37	,	,	PUNCT
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iajs-2801	312	39	−(𝛼	−(𝛼	NOUN
iajs-2801	312	40	)	)	PUNCT
iajs-2801	312	41	}	}	PUNCT
iajs-2801	312	42	=	=	SYM
iajs-2801	312	43	𝜆2	𝜆2	NOUN
iajs-2801	312	44	−(𝛼	−(𝛼	NOUN
iajs-2801	312	45	)	)	PUNCT
iajs-2801	312	46	…	…	PUNCT
iajs-2801	312	47	.	.	PUNCT
iajs-2801	312	48	.	.	PUNCT
iajs-2801	313	1	(	(	PUNCT
iajs-2801	313	2	4	4	X
iajs-2801	313	3	)	)	PUNCT
iajs-2801	313	4	since	since	SCONJ
iajs-2801	313	5	ω𝑓1	ω𝑓1	NOUN
iajs-2801	313	6	×	×	PROPN
iajs-2801	314	1	ω𝑓2	ω𝑓2	NUM
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iajs-2801	314	3	acb	acb	PROPN
iajs-2801	314	4	ideal	ideal	NOUN
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iajs-2801	314	6			PROPN
iajs-2801	314	7	,	,	PUNCT
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iajs-2801	314	9	;	;	PUNCT
iajs-2801	314	10	(;	(;	X
iajs-2801	314	11	�	�	PROPN
iajs-2801	314	12	̃	̃	NOUN
iajs-2801	314	13	�	�	NOUN
iajs-2801	314	14	1	1	NUM
iajs-2801	314	15	+	+	NUM
iajs-2801	314	16	×	×	NOUN
iajs-2801	314	17	;	;	PUNCT
iajs-2801	314	18	�	�	PROPN
iajs-2801	314	19	̃	̃	PROPN
iajs-2801	314	20	�	�	NOUN
iajs-2801	314	21	2	2	NUM
iajs-2801	314	22	+	+	NUM
iajs-2801	314	23	)	)	PUNCT
iajs-2801	314	24	(	(	PUNCT
iajs-2801	314	25	𝛽	𝛽	NOUN
iajs-2801	314	26	1	1	NUM
iajs-2801	314	27	,	,	PUNCT
iajs-2801	314	28	𝛽	𝛽	NOUN
iajs-2801	314	29	2	2	NUM
iajs-2801	314	30	)	)	PUNCT
iajs-2801	314	31	;	;	PUNCT
iajs-2801	314	32	≥	≥	NUM
iajs-2801	314	33	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	314	34	{	{	PUNCT
iajs-2801	314	35	(;	(;	X
iajs-2801	314	36	�	�	PROPN
iajs-2801	314	37	̃	̃	NOUN
iajs-2801	314	38	�	�	NOUN
iajs-2801	314	39	1	1	NUM
iajs-2801	314	40	+	+	NUM
iajs-2801	314	41	×	×	NOUN
iajs-2801	314	42	;	;	PUNCT
iajs-2801	314	43	�	�	PROPN
iajs-2801	314	44	̃	̃	PROPN
iajs-2801	314	45	�	�	NOUN
iajs-2801	314	46	2	2	NUM
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iajs-2801	314	48	)	)	PUNCT
iajs-2801	314	49	(	(	PUNCT
iajs-2801	314	50	(	(	PUNCT
iajs-2801	314	51	𝛼1	𝛼1	NOUN
iajs-2801	314	52	,	,	PUNCT
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iajs-2801	314	55	∗	∗	NOUN
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iajs-2801	314	57	𝛽	𝛽	NOUN
iajs-2801	314	58	1	1	NUM
iajs-2801	314	59	,	,	PUNCT
iajs-2801	314	60	𝛽	𝛽	NOUN
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iajs-2801	314	62	)	)	PUNCT
iajs-2801	314	63	)	)	PUNCT
iajs-2801	314	64	,	,	PUNCT
iajs-2801	314	65	(	(	PUNCT
iajs-2801	314	66	�	�	PROPN
iajs-2801	314	67	̃	̃	NOUN
iajs-2801	314	68	�	�	NOUN
iajs-2801	314	69	1	1	NUM
iajs-2801	314	70	+	+	NUM
iajs-2801	314	71	×	×	PROPN
iajs-2801	314	72	�	�	PROPN
iajs-2801	314	73	̃	̃	PROPN
iajs-2801	314	74	�	�	NOUN
iajs-2801	314	75	2	2	NUM
iajs-2801	314	76	+	+	NOUN
iajs-2801	314	77	)	)	PUNCT
iajs-2801	314	78	(	(	PUNCT
iajs-2801	314	79	𝛼1	𝛼1	NOUN
iajs-2801	314	80	,	,	PUNCT
iajs-2801	314	81	𝛼2	𝛼2	ADJ
iajs-2801	314	82	)	)	PUNCT
iajs-2801	314	83	}	}	PUNCT
iajs-2801	314	84	=	=	SYM
iajs-2801	314	85	𝑟𝑚𝑖𝑛{(	𝑟𝑚𝑖𝑛{(	X
iajs-2801	314	86	�	�	PROPN
iajs-2801	314	87	̃	̃	PROPN
iajs-2801	314	88	�	�	NOUN
iajs-2801	314	89	1	1	NUM
iajs-2801	314	90	+	+	NUM
iajs-2801	314	91	×	×	PROPN
iajs-2801	314	92	�	�	PROPN
iajs-2801	314	93	̃	̃	PROPN
iajs-2801	314	94	�	�	NOUN
iajs-2801	314	95	2	2	NUM
iajs-2801	314	96	+	+	CCONJ
iajs-2801	314	97	)	)	PUNCT
iajs-2801	314	98	(	(	PUNCT
iajs-2801	314	99	𝛼1	𝛼1	NOUN
iajs-2801	314	100	∗	∗	NOUN
iajs-2801	314	101	𝛽	𝛽	NOUN
iajs-2801	314	102	1	1	NUM
iajs-2801	314	103	,	,	PUNCT
iajs-2801	314	104	𝛼2	𝛼2	PROPN
iajs-2801	314	105	∗	∗	NOUN
iajs-2801	314	106	𝛽	𝛽	NOUN
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iajs-2801	314	109	,	,	PUNCT
iajs-2801	314	110	(	(	PUNCT
iajs-2801	314	111	�	�	PROPN
iajs-2801	314	112	̃	̃	NOUN
iajs-2801	314	113	�	�	NOUN
iajs-2801	314	114	1	1	NUM
iajs-2801	314	115	+	+	NUM
iajs-2801	314	116	×	×	PROPN
iajs-2801	314	117	�	�	PROPN
iajs-2801	314	118	̃	̃	PROPN
iajs-2801	314	119	�	�	NOUN
iajs-2801	314	120	2	2	NUM
iajs-2801	314	121	+	+	CCONJ
iajs-2801	314	122	)	)	PUNCT
iajs-2801	314	123	(	(	PUNCT
iajs-2801	314	124	𝛼1	𝛼1	NOUN
iajs-2801	314	125	,	,	PUNCT
iajs-2801	314	126	𝛼2	𝛼2	ADJ
iajs-2801	314	127	)	)	PUNCT
iajs-2801	314	128	}	}	PUNCT
iajs-2801	314	129	put𝛼1	put𝛼1	NOUN
iajs-2801	315	1	=	=	SYM
iajs-2801	315	2	𝛽1	𝛽1	NOUN
iajs-2801	315	3	=	=	SYM
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iajs-2801	315	7	we	we	PRON
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iajs-2801	315	10	�	�	PROPN
iajs-2801	315	11	̃	̃	NOUN
iajs-2801	315	12	�	�	NOUN
iajs-2801	315	13	1	1	NUM
iajs-2801	315	14	+	+	NUM
iajs-2801	315	15	×	×	PROPN
iajs-2801	315	16	�	�	PROPN
iajs-2801	315	17	̃	̃	PROPN
iajs-2801	315	18	�	�	NOUN
iajs-2801	315	19	2	2	NUM
iajs-2801	315	20	+	+	CCONJ
iajs-2801	315	21	)	)	PUNCT
iajs-2801	315	22	(	(	PUNCT
iajs-2801	315	23	0	0	NUM
iajs-2801	315	24	,	,	PUNCT
iajs-2801	315	25	𝛽	𝛽	PROPN
iajs-2801	315	26	2	2	NUM
iajs-2801	315	27	)	)	PUNCT
iajs-2801	315	28	≥	≥	NOUN
iajs-2801	315	29	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	315	30	{	{	PUNCT
iajs-2801	315	31	(;	(;	X
iajs-2801	315	32	�	�	PROPN
iajs-2801	315	33	̃	̃	NOUN
iajs-2801	315	34	�	�	NOUN
iajs-2801	315	35	1	1	NUM
iajs-2801	315	36	+	+	NUM
iajs-2801	315	37	×	×	NOUN
iajs-2801	315	38	;	;	PUNCT
iajs-2801	315	39	�	�	PROPN
iajs-2801	315	40	̃	̃	PROPN
iajs-2801	315	41	�	�	NOUN
iajs-2801	315	42	2	2	NUM
iajs-2801	315	43	+	+	NOUN
iajs-2801	315	44	)	)	PUNCT
iajs-2801	315	45	(	(	PUNCT
iajs-2801	315	46	(	(	PUNCT
iajs-2801	315	47	0	0	NUM
iajs-2801	315	48	,	,	PUNCT
iajs-2801	315	49	𝛼2	𝛼2	ADJ
iajs-2801	315	50	)	)	PUNCT
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iajs-2801	315	53	0	0	NUM
iajs-2801	315	54	,	,	PUNCT
iajs-2801	315	55	𝛽	𝛽	NOUN
iajs-2801	315	56	2	2	NUM
iajs-2801	315	57	)	)	PUNCT
iajs-2801	315	58	)	)	PUNCT
iajs-2801	315	59	,	,	PUNCT
iajs-2801	315	60	(;	(;	X
iajs-2801	315	61	�	�	PROPN
iajs-2801	315	62	̃	̃	NOUN
iajs-2801	315	63	�	�	NOUN
iajs-2801	315	64	1	1	NUM
iajs-2801	315	65	+	+	NUM
iajs-2801	315	66	×	×	NOUN
iajs-2801	315	67	;	;	PUNCT
iajs-2801	315	68	�	�	PROPN
iajs-2801	315	69	̃	̃	PROPN
iajs-2801	315	70	�	�	NOUN
iajs-2801	315	71	2	2	NUM
iajs-2801	315	72	+	+	NOUN
iajs-2801	315	73	)	)	PUNCT
iajs-2801	315	74	(	(	PUNCT
iajs-2801	315	75	0	0	NUM
iajs-2801	315	76	,	,	PUNCT
iajs-2801	315	77	𝛼2	𝛼2	ADJ
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iajs-2801	315	79	}	}	PUNCT
iajs-2801	315	80	=	=	SYM
iajs-2801	315	81	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	315	82	{	{	PUNCT
iajs-2801	315	83	(;	(;	X
iajs-2801	315	84	�	�	PROPN
iajs-2801	315	85	̃	̃	NOUN
iajs-2801	315	86	�	�	NOUN
iajs-2801	315	87	1	1	NUM
iajs-2801	315	88	+	+	NUM
iajs-2801	315	89	×	×	NOUN
iajs-2801	315	90	;	;	PUNCT
iajs-2801	315	91	�	�	PROPN
iajs-2801	315	92	̃	̃	PROPN
iajs-2801	315	93	�	�	NOUN
iajs-2801	315	94	2	2	NUM
iajs-2801	315	95	+	+	CCONJ
iajs-2801	315	96	)	)	PUNCT
iajs-2801	315	97	(	(	PUNCT
iajs-2801	315	98	0	0	NUM
iajs-2801	315	99	,	,	PUNCT
iajs-2801	315	100	𝛼2	𝛼2	PROPN
iajs-2801	315	101	∗	∗	NOUN
iajs-2801	315	102	𝛽	𝛽	NOUN
iajs-2801	315	103	2	2	NUM
iajs-2801	315	104	)	)	PUNCT
iajs-2801	315	105	,	,	PUNCT
iajs-2801	315	106	(;	(;	X
iajs-2801	315	107	�	�	PROPN
iajs-2801	315	108	̃	̃	NOUN
iajs-2801	315	109	�	�	NOUN
iajs-2801	315	110	1	1	NUM
iajs-2801	315	111	+	+	NUM
iajs-2801	315	112	×	×	NOUN
iajs-2801	315	113	;	;	PUNCT
iajs-2801	315	114	�	�	PROPN
iajs-2801	315	115	̃	̃	PROPN
iajs-2801	315	116	�	�	NOUN
iajs-2801	315	117	2	2	NUM
iajs-2801	315	118	+	+	CCONJ
iajs-2801	315	119	)	)	PUNCT
iajs-2801	315	120	(	(	PUNCT
iajs-2801	315	121	0	0	NUM
iajs-2801	315	122	,	,	PUNCT
iajs-2801	315	123	𝛼2	𝛼2	ADJ
iajs-2801	315	124	)	)	PUNCT
iajs-2801	315	125	}	}	PUNCT
iajs-2801	315	126	and	and	CCONJ
iajs-2801	315	127	by	by	ADP
iajs-2801	315	128	equation	equation	NOUN
iajs-2801	315	129	(	(	PUNCT
iajs-2801	315	130	1	1	NUM
iajs-2801	315	131	)	)	PUNCT
iajs-2801	315	132	,	,	PUNCT
iajs-2801	315	133	then	then	ADV
iajs-2801	315	134	𝜇2	𝜇2	VERB
iajs-2801	315	135	+	+	PROPN
iajs-2801	315	136	(	(	PUNCT
iajs-2801	315	137	𝛽2	𝛽2	PROPN
iajs-2801	315	138	)	)	PUNCT
iajs-2801	315	139	≥	≥	NOUN
iajs-2801	315	140	𝑟𝑚𝑖𝑛{	𝑟𝑚𝑖𝑛{	PROPN
iajs-2801	315	141	�	�	PROPN
iajs-2801	315	142	̃	̃	PROPN
iajs-2801	315	143	�	�	NOUN
iajs-2801	315	144	2	2	NUM
iajs-2801	315	145	+	+	ADJ
iajs-2801	315	146	(	(	PUNCT
iajs-2801	315	147	𝛼2	𝛼2	PROPN
iajs-2801	315	148	∗	∗	NOUN
iajs-2801	315	149	𝛽2	𝛽2	NOUN
iajs-2801	315	150	)	)	PUNCT
iajs-2801	315	151	,	,	PUNCT
iajs-2801	315	152	𝜇2	𝜇2	PROPN
iajs-2801	315	153	+	+	PROPN
iajs-2801	315	154	(	(	PUNCT
iajs-2801	315	155	𝛼2	𝛼2	PROPN
iajs-2801	315	156	)	)	PUNCT
iajs-2801	315	157	}	}	PUNCT
iajs-2801	315	158	.	.	PUNCT
iajs-2801	316	1	and	and	CCONJ
iajs-2801	316	2	(	(	PUNCT
iajs-2801	316	3	�	�	PROPN
iajs-2801	316	4	̃	̃	NOUN
iajs-2801	316	5	�	�	NOUN
iajs-2801	316	6	1	1	NUM
iajs-2801	316	7	−	−	PROPN
iajs-2801	316	8	×	×	PROPN
iajs-2801	316	9	�	�	PROPN
iajs-2801	316	10	̃	̃	PROPN
iajs-2801	316	11	�	�	PROPN
iajs-2801	316	12	2	2	NUM
iajs-2801	316	13	−	−	NOUN
iajs-2801	316	14	)	)	PUNCT
iajs-2801	316	15	(	(	PUNCT
iajs-2801	316	16	𝛽	𝛽	NOUN
iajs-2801	316	17	1	1	NUM
iajs-2801	316	18	,	,	PUNCT
iajs-2801	316	19	𝛽	𝛽	PROPN
iajs-2801	316	20	2	2	NUM
iajs-2801	316	21	)	)	PUNCT
iajs-2801	316	22	≤	≤	NOUN
iajs-2801	316	23	𝑟𝑚𝑎𝑥{(	𝑟𝑚𝑎𝑥{(	PUNCT
iajs-2801	316	24	�	�	PROPN
iajs-2801	316	25	̃	̃	PROPN
iajs-2801	316	26	�	�	NOUN
iajs-2801	316	27	1	1	NUM
iajs-2801	316	28	−	−	PROPN
iajs-2801	316	29	×	×	PROPN
iajs-2801	316	30	�	�	PROPN
iajs-2801	316	31	̃	̃	PROPN
iajs-2801	316	32	�	�	PROPN
iajs-2801	316	33	2	2	NUM
iajs-2801	316	34	−)((𝛼1	−)((𝛼1	PROPN
iajs-2801	316	35	,	,	PUNCT
iajs-2801	316	36	𝛼2	𝛼2	ADJ
iajs-2801	316	37	)	)	PUNCT
iajs-2801	316	38	∗	∗	NOUN
iajs-2801	316	39	(	(	PUNCT
iajs-2801	316	40	𝛽	𝛽	NOUN
iajs-2801	316	41	1	1	NUM
iajs-2801	316	42	,	,	PUNCT
iajs-2801	316	43	𝛽	𝛽	NOUN
iajs-2801	316	44	2	2	NUM
iajs-2801	316	45	)	)	PUNCT
iajs-2801	316	46	)	)	PUNCT
iajs-2801	316	47	,	,	PUNCT
iajs-2801	316	48	(	(	PUNCT
iajs-2801	316	49	�	�	PROPN
iajs-2801	316	50	̃	̃	NOUN
iajs-2801	316	51	�	�	NOUN
iajs-2801	316	52	1	1	NUM
iajs-2801	316	53	−	−	PROPN
iajs-2801	316	54	×	×	PROPN
iajs-2801	316	55	�	�	PROPN
iajs-2801	316	56	̃	̃	PROPN
iajs-2801	316	57	�	�	PROPN
iajs-2801	316	58	2	2	NUM
iajs-2801	316	59	−)(𝛼1	−)(𝛼1	PROPN
iajs-2801	316	60	,	,	PUNCT
iajs-2801	316	61	𝛼2	𝛼2	ADJ
iajs-2801	316	62	)	)	PUNCT
iajs-2801	316	63	}	}	PUNCT
iajs-2801	316	64	=	=	SYM
iajs-2801	316	65	𝑟𝑚𝑎𝑥{(	𝑟𝑚𝑎𝑥{(	NUM
iajs-2801	316	66	�	�	PROPN
iajs-2801	316	67	̃	̃	NOUN
iajs-2801	316	68	�	�	NOUN
iajs-2801	316	69	1	1	NUM
iajs-2801	316	70	−	−	PROPN
iajs-2801	316	71	×	×	PROPN
iajs-2801	316	72	�	�	PROPN
iajs-2801	316	73	̃	̃	PROPN
iajs-2801	316	74	�	�	PROPN
iajs-2801	316	75	2	2	NUM
iajs-2801	316	76	−	−	NOUN
iajs-2801	316	77	)	)	PUNCT
iajs-2801	316	78	(	(	PUNCT
iajs-2801	316	79	𝛼1	𝛼1	NOUN
iajs-2801	316	80	∗	∗	NOUN
iajs-2801	316	81	𝛽	𝛽	NOUN
iajs-2801	316	82	1	1	NUM
iajs-2801	316	83	,	,	PUNCT
iajs-2801	316	84	𝛼2	𝛼2	PROPN
iajs-2801	316	85	∗	∗	NOUN
iajs-2801	316	86	𝛽	𝛽	NOUN
iajs-2801	316	87	2	2	NUM
iajs-2801	316	88	)	)	PUNCT
iajs-2801	316	89	,	,	PUNCT
iajs-2801	316	90	(	(	PUNCT
iajs-2801	316	91	�	�	PROPN
iajs-2801	316	92	̃	̃	NOUN
iajs-2801	316	93	�	�	NOUN
iajs-2801	316	94	1	1	NUM
iajs-2801	316	95	−	−	PROPN
iajs-2801	316	96	×	×	PROPN
iajs-2801	316	97	�	�	PROPN
iajs-2801	316	98	̃	̃	PROPN
iajs-2801	316	99	�	�	PROPN
iajs-2801	316	100	2	2	NUM
iajs-2801	316	101	−	−	NOUN
iajs-2801	316	102	)	)	PUNCT
iajs-2801	316	103	(	(	PUNCT
iajs-2801	316	104	𝛼1	𝛼1	NOUN
iajs-2801	316	105	,	,	PUNCT
iajs-2801	316	106	𝛼2	𝛼2	PROPN
iajs-2801	316	107	)	)	PUNCT
iajs-2801	316	108	}	}	PUNCT
iajs-2801	316	109	put	put	VERB
iajs-2801	316	110	𝛼1	𝛼1	NOUN
iajs-2801	316	111	=	=	SYM
iajs-2801	316	112	𝛽1	𝛽1	NOUN
iajs-2801	316	113	=	=	SYM
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iajs-2801	316	117	we	we	PRON
iajs-2801	316	118	have	have	VERB
iajs-2801	316	119	(	(	PUNCT
iajs-2801	316	120	�	�	PROPN
iajs-2801	316	121	̃	̃	NOUN
iajs-2801	316	122	�	�	NOUN
iajs-2801	316	123	1	1	NUM
iajs-2801	316	124	−	−	PROPN
iajs-2801	316	125	×	×	PROPN
iajs-2801	316	126	�	�	PROPN
iajs-2801	316	127	̃	̃	PROPN
iajs-2801	316	128	�	�	PROPN
iajs-2801	316	129	2	2	NUM
iajs-2801	316	130	−	−	NOUN
iajs-2801	316	131	)	)	PUNCT
iajs-2801	316	132	(	(	PUNCT
iajs-2801	316	133	0	0	NUM
iajs-2801	316	134	,	,	PUNCT
iajs-2801	316	135	𝛽	𝛽	NOUN
iajs-2801	316	136	2	2	NUM
iajs-2801	316	137	)	)	PUNCT
iajs-2801	316	138	≤	≤	NUM
iajs-2801	316	139	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	PROPN
iajs-2801	316	140	{	{	PUNCT
iajs-2801	316	141	(;	(;	X
iajs-2801	316	142	�	�	PROPN
iajs-2801	316	143	̃	̃	NOUN
iajs-2801	316	144	�	�	NOUN
iajs-2801	316	145	1	1	NUM
iajs-2801	316	146	−	−	NOUN
iajs-2801	316	147	×	×	NOUN
iajs-2801	316	148	;	;	PUNCT
iajs-2801	316	149	�	�	PROPN
iajs-2801	316	150	̃	̃	PROPN
iajs-2801	316	151	�	�	NOUN
iajs-2801	316	152	2	2	NUM
iajs-2801	316	153	−	−	NUM
iajs-2801	316	154	;	;	PUNCT
iajs-2801	316	155	)	)	PUNCT
iajs-2801	316	156	(	(	PUNCT
iajs-2801	316	157	(	(	PUNCT
iajs-2801	316	158	0	0	NUM
iajs-2801	316	159	,	,	PUNCT
iajs-2801	316	160	𝛼2	𝛼2	ADJ
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iajs-2801	316	162	∗	∗	NOUN
iajs-2801	316	163	(	(	PUNCT
iajs-2801	316	164	0	0	NUM
iajs-2801	316	165	,	,	PUNCT
iajs-2801	316	166	𝛽	𝛽	NOUN
iajs-2801	316	167	2	2	NUM
iajs-2801	316	168	)	)	PUNCT
iajs-2801	316	169	)	)	PUNCT
iajs-2801	316	170	,	,	PUNCT
iajs-2801	316	171	(;	(;	X
iajs-2801	316	172	�	�	PROPN
iajs-2801	316	173	̃	̃	NOUN
iajs-2801	316	174	�	�	NOUN
iajs-2801	316	175	1	1	NUM
iajs-2801	317	1	−	−	NOUN
iajs-2801	317	2	×	×	NOUN
iajs-2801	317	3	;	;	PUNCT
iajs-2801	317	4	�	�	PROPN
iajs-2801	317	5	̃	̃	PROPN
iajs-2801	317	6	�	�	NOUN
iajs-2801	317	7	2	2	NUM
iajs-2801	317	8	−	−	NUM
iajs-2801	317	9	;	;	PUNCT
iajs-2801	317	10	)	)	PUNCT
iajs-2801	317	11	(	(	PUNCT
iajs-2801	317	12	0	0	NUM
iajs-2801	317	13	,	,	PUNCT
iajs-2801	317	14	𝛼2	𝛼2	ADJ
iajs-2801	317	15	)	)	PUNCT
iajs-2801	317	16	}	}	PUNCT
iajs-2801	317	17	=	=	PUNCT
iajs-2801	317	18	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	PROPN
iajs-2801	317	19	{	{	PUNCT
iajs-2801	317	20	(;	(;	X
iajs-2801	317	21	�	�	PROPN
iajs-2801	317	22	̃	̃	NOUN
iajs-2801	317	23	�	�	NOUN
iajs-2801	317	24	1	1	NUM
iajs-2801	317	25	−	−	NOUN
iajs-2801	317	26	×	×	NOUN
iajs-2801	317	27	;	;	PUNCT
iajs-2801	317	28	�	�	PROPN
iajs-2801	317	29	̃	̃	PROPN
iajs-2801	317	30	�	�	NOUN
iajs-2801	317	31	2	2	NUM
iajs-2801	317	32	−	−	NUM
iajs-2801	317	33	;	;	PUNCT
iajs-2801	317	34	)	)	PUNCT
iajs-2801	317	35	(	(	PUNCT
iajs-2801	317	36	0	0	NUM
iajs-2801	317	37	,	,	PUNCT
iajs-2801	317	38	𝛼2	𝛼2	PROPN
iajs-2801	317	39	∗	∗	NOUN
iajs-2801	317	40	𝛽	𝛽	NOUN
iajs-2801	317	41	2	2	NUM
iajs-2801	317	42	)	)	PUNCT
iajs-2801	317	43	,	,	PUNCT
iajs-2801	317	44	(;	(;	X
iajs-2801	317	45	�	�	PROPN
iajs-2801	317	46	̃	̃	NOUN
iajs-2801	317	47	�	�	NOUN
iajs-2801	317	48	1	1	NUM
iajs-2801	317	49	−	−	NOUN
iajs-2801	317	50	×	×	NOUN
iajs-2801	317	51	;	;	PUNCT
iajs-2801	317	52	�	�	PROPN
iajs-2801	317	53	̃	̃	PROPN
iajs-2801	317	54	�	�	NOUN
iajs-2801	317	55	2	2	NUM
iajs-2801	317	56	−	−	NUM
iajs-2801	317	57	;	;	PUNCT
iajs-2801	317	58	)	)	PUNCT
iajs-2801	317	59	(	(	PUNCT
iajs-2801	317	60	0	0	NUM
iajs-2801	317	61	,	,	PUNCT
iajs-2801	317	62	𝛼2	𝛼2	ADJ
iajs-2801	317	63	)	)	PUNCT
iajs-2801	317	64	}	}	PUNCT
iajs-2801	317	65	ibn	ibn	PROPN
iajs-2801	317	66	al	al	PROPN
iajs-2801	317	67	-	-	PUNCT
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iajs-2801	320	1	35(1)2022	35(1)2022	NUM
iajs-2801	320	2	82	82	NUM
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iajs-2801	320	6	equation	equation	NOUN
iajs-2801	320	7	(	(	PUNCT
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iajs-2801	320	9	)	)	PUNCT
iajs-2801	320	10	,	,	PUNCT
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iajs-2801	320	12	have	have	AUX
iajs-2801	320	13	𝜇2	𝜇2	VERB
iajs-2801	320	14	−(𝛽2	−(𝛽2	NOUN
iajs-2801	320	15	)	)	PUNCT
iajs-2801	320	16	≤	≤	NUM
iajs-2801	320	17	𝑟𝑚𝑎𝑥{	𝑟𝑚𝑎𝑥{	NOUN
iajs-2801	320	18	�	�	NOUN
iajs-2801	320	19	̃	̃	NOUN
iajs-2801	320	20	�	�	NOUN
iajs-2801	320	21	2	2	NUM
iajs-2801	320	22	−(𝛼2	−(𝛼2	NOUN
iajs-2801	320	23	∗	∗	NOUN
iajs-2801	320	24	𝛽2	𝛽2	NOUN
iajs-2801	320	25	)	)	PUNCT
iajs-2801	320	26	,	,	PUNCT
iajs-2801	320	27	𝜇2	𝜇2	VERB
iajs-2801	320	28	−(𝛼2	−(𝛼2	NOUN
iajs-2801	320	29	)	)	PUNCT
iajs-2801	320	30	}	}	PUNCT
iajs-2801	320	31	.	.	PUNCT
iajs-2801	321	1	also	also	ADV
iajs-2801	321	2	,	,	PUNCT
iajs-2801	321	3	;	;	PUNCT
iajs-2801	321	4	(;	(;	X
iajs-2801	321	5	𝜆1	𝜆1	NOUN
iajs-2801	321	6	+	+	CCONJ
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iajs-2801	321	11	;	;	PUNCT
iajs-2801	321	12	)	)	PUNCT
iajs-2801	321	13	(	(	PUNCT
iajs-2801	321	14	𝛽1	𝛽1	NOUN
iajs-2801	321	15	,	,	PUNCT
iajs-2801	321	16	𝛽2	𝛽2	PROPN
iajs-2801	321	17	)	)	PUNCT
iajs-2801	321	18	≥	≥	NOUN
iajs-2801	321	19	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	321	20	{	{	PUNCT
iajs-2801	321	21	;	;	PUNCT
iajs-2801	321	22	(;	(;	X
iajs-2801	321	23	𝜆1	𝜆1	NOUN
iajs-2801	321	24	+	+	CCONJ
iajs-2801	321	25	×	×	NOUN
iajs-2801	321	26	;	;	PUNCT
iajs-2801	321	27	𝜆2	𝜆2	PROPN
iajs-2801	321	28	+	+	PROPN
iajs-2801	321	29	;	;	PUNCT
iajs-2801	321	30	)	)	PUNCT
iajs-2801	321	31	(	(	PUNCT
iajs-2801	321	32	(	(	PUNCT
iajs-2801	321	33	𝛼1	𝛼1	NOUN
iajs-2801	321	34	,	,	PUNCT
iajs-2801	321	35	𝛼2	𝛼2	ADJ
iajs-2801	321	36	)	)	PUNCT
iajs-2801	321	37	∗	∗	NOUN
iajs-2801	321	38	(	(	PUNCT
iajs-2801	321	39	𝛽1	𝛽1	NOUN
iajs-2801	321	40	,	,	PUNCT
iajs-2801	321	41	𝛽2	𝛽2	NOUN
iajs-2801	321	42	)	)	PUNCT
iajs-2801	321	43	)	)	PUNCT
iajs-2801	321	44	,	,	PUNCT
iajs-2801	321	45	(;	(;	PUNCT
iajs-2801	321	46	𝜆1	𝜆1	NOUN
iajs-2801	321	47	+	+	CCONJ
iajs-2801	321	48	×	×	NOUN
iajs-2801	321	49	;	;	PUNCT
iajs-2801	321	50	𝜆2	𝜆2	PROPN
iajs-2801	321	51	+	+	PROPN
iajs-2801	321	52	)	)	PUNCT
iajs-2801	321	53	(	(	PUNCT
iajs-2801	321	54	𝛼1	𝛼1	NOUN
iajs-2801	321	55	,	,	PUNCT
iajs-2801	321	56	𝛼2	𝛼2	ADJ
iajs-2801	321	57	)	)	PUNCT
iajs-2801	321	58	}	}	PUNCT
iajs-2801	321	59	=	=	SYM
iajs-2801	321	60	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	321	61	{	{	PUNCT
iajs-2801	321	62	(;	(;	ADJ
iajs-2801	321	63	𝜆1	𝜆1	NOUN
iajs-2801	321	64	+	+	CCONJ
iajs-2801	321	65	×	×	NOUN
iajs-2801	321	66	;	;	PUNCT
iajs-2801	321	67	𝜆2	𝜆2	PROPN
iajs-2801	321	68	+	+	PROPN
iajs-2801	321	69	)	)	PUNCT
iajs-2801	321	70	(	(	PUNCT
iajs-2801	321	71	𝛼1	𝛼1	NOUN
iajs-2801	321	72	∗	∗	NOUN
iajs-2801	321	73	𝛽1	𝛽1	NOUN
iajs-2801	321	74	,	,	PUNCT
iajs-2801	321	75	𝛼2	𝛼2	NOUN
iajs-2801	321	76	∗	∗	NOUN
iajs-2801	321	77	𝛽2	𝛽2	NOUN
iajs-2801	321	78	)	)	PUNCT
iajs-2801	321	79	,	,	PUNCT
iajs-2801	321	80	(;	(;	PUNCT
iajs-2801	321	81	𝜆1	𝜆1	NOUN
iajs-2801	321	82	+	+	CCONJ
iajs-2801	321	83	×	×	NOUN
iajs-2801	321	84	;	;	PUNCT
iajs-2801	321	85	𝜆2	𝜆2	PROPN
iajs-2801	321	86	+	+	PROPN
iajs-2801	321	87	)	)	PUNCT
iajs-2801	321	88	(	(	PUNCT
iajs-2801	321	89	𝛼1	𝛼1	NOUN
iajs-2801	321	90	,	,	PUNCT
iajs-2801	321	91	𝛼2	𝛼2	PROPN
iajs-2801	321	92	)	)	PUNCT
iajs-2801	321	93	}	}	PUNCT
iajs-2801	321	94	put	put	VERB
iajs-2801	321	95	𝛼1	𝛼1	NOUN
iajs-2801	321	96	=	=	SYM
iajs-2801	321	97	𝛽1	𝛽1	NOUN
iajs-2801	321	98	=	=	SYM
iajs-2801	321	99	0	0	NUM
iajs-2801	321	100	,	,	PUNCT
iajs-2801	321	101	then	then	ADV
iajs-2801	321	102	we	we	PRON
iajs-2801	321	103	have	have	AUX
iajs-2801	321	104	(:	(:	NOUN
iajs-2801	321	105	𝜆1	𝜆1	NOUN
iajs-2801	321	106	+	+	CCONJ
iajs-2801	321	107	×	×	NOUN
iajs-2801	321	108	:	:	PUNCT
iajs-2801	321	109	𝜆2	𝜆2	PROPN
iajs-2801	321	110	+	+	PROPN
iajs-2801	321	111	;	;	PUNCT
iajs-2801	321	112	)	)	PUNCT
iajs-2801	321	113	(	(	PUNCT
iajs-2801	321	114	0	0	NUM
iajs-2801	321	115	,	,	PUNCT
iajs-2801	321	116	𝛽	𝛽	PROPN
iajs-2801	321	117	2	2	NUM
iajs-2801	321	118	)	)	PUNCT
iajs-2801	321	119	≥	≥	NOUN
iajs-2801	321	120	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	321	121	{	{	PUNCT
iajs-2801	321	122	(:	(:	NOUN
iajs-2801	321	123	𝜆1	𝜆1	NOUN
iajs-2801	321	124	+	+	CCONJ
iajs-2801	321	125	×	×	NOUN
iajs-2801	321	126	:	:	PUNCT
iajs-2801	321	127	𝜆2	𝜆2	PROPN
iajs-2801	322	1	+	+	PROPN
iajs-2801	322	2	;)	;)	PUNCT
iajs-2801	322	3	(	(	PUNCT
iajs-2801	322	4	(	(	PUNCT
iajs-2801	322	5	0	0	NUM
iajs-2801	322	6	,	,	PUNCT
iajs-2801	322	7	𝛼2	𝛼2	ADJ
iajs-2801	322	8	)	)	PUNCT
iajs-2801	322	9	∗	∗	NOUN
iajs-2801	322	10	(	(	PUNCT
iajs-2801	322	11	0	0	NUM
iajs-2801	322	12	,	,	PUNCT
iajs-2801	322	13	𝛽	𝛽	NOUN
iajs-2801	322	14	2	2	NUM
iajs-2801	322	15	)	)	PUNCT
iajs-2801	322	16	)	)	PUNCT
iajs-2801	322	17	,	,	PUNCT
iajs-2801	322	18	(:	(:	VERB
iajs-2801	322	19	𝜆1	𝜆1	NOUN
iajs-2801	322	20	+	+	CCONJ
iajs-2801	322	21	×	×	NOUN
iajs-2801	322	22	:	:	PUNCT
iajs-2801	322	23	𝜆2	𝜆2	PROPN
iajs-2801	322	24	+	+	PROPN
iajs-2801	322	25	;	;	PUNCT
iajs-2801	322	26	)	)	PUNCT
iajs-2801	322	27	(	(	PUNCT
iajs-2801	322	28	0	0	NUM
iajs-2801	322	29	,	,	PUNCT
iajs-2801	322	30	𝛼2	𝛼2	ADJ
iajs-2801	322	31	)	)	PUNCT
iajs-2801	322	32	}	}	PUNCT
iajs-2801	322	33	=	=	SYM
iajs-2801	322	34	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	322	35	{	{	PUNCT
iajs-2801	322	36	(:	(:	NOUN
iajs-2801	322	37	𝜆1	𝜆1	NOUN
iajs-2801	322	38	+	+	CCONJ
iajs-2801	322	39	×	×	NOUN
iajs-2801	322	40	:	:	PUNCT
iajs-2801	322	41	𝜆2	𝜆2	PROPN
iajs-2801	322	42	+	+	PROPN
iajs-2801	322	43	)	)	PUNCT
iajs-2801	322	44	(	(	PUNCT
iajs-2801	322	45	0	0	NUM
iajs-2801	322	46	,	,	PUNCT
iajs-2801	322	47	𝛼2	𝛼2	PROPN
iajs-2801	322	48	∗	∗	NOUN
iajs-2801	322	49	𝛽	𝛽	NOUN
iajs-2801	322	50	2	2	NUM
iajs-2801	322	51	)	)	PUNCT
iajs-2801	322	52	,	,	PUNCT
iajs-2801	322	53	(:	(:	VERB
iajs-2801	322	54	𝜆1	𝜆1	NOUN
iajs-2801	322	55	+	+	CCONJ
iajs-2801	322	56	×	×	NOUN
iajs-2801	322	57	:	:	PUNCT
iajs-2801	322	58	𝜆2	𝜆2	PROPN
iajs-2801	322	59	+	+	PROPN
iajs-2801	322	60	;	;	PUNCT
iajs-2801	322	61	)	)	PUNCT
iajs-2801	322	62	(	(	PUNCT
iajs-2801	322	63	0	0	NUM
iajs-2801	322	64	,	,	PUNCT
iajs-2801	322	65	𝛼2	𝛼2	ADJ
iajs-2801	322	66	)	)	PUNCT
iajs-2801	322	67	}	}	PUNCT
iajs-2801	322	68	and	and	CCONJ
iajs-2801	322	69	by	by	ADP
iajs-2801	322	70	using	use	VERB
iajs-2801	322	71	equation	equation	NOUN
iajs-2801	322	72	(	(	PUNCT
iajs-2801	322	73	3	3	NUM
iajs-2801	322	74	)	)	PUNCT
iajs-2801	322	75	,	,	PUNCT
iajs-2801	322	76	we	we	PRON
iajs-2801	322	77	have	have	VERB
iajs-2801	322	78	𝜆2	𝜆2	PROPN
iajs-2801	322	79	+	+	NOUN
iajs-2801	322	80	(	(	PUNCT
iajs-2801	322	81	𝛽2	𝛽2	PROPN
iajs-2801	322	82	)	)	PUNCT
iajs-2801	322	83	≥	≥	NOUN
iajs-2801	322	84	𝑚𝑖𝑛{𝜆2	𝑚𝑖𝑛{𝜆2	X
iajs-2801	322	85	+	+	PROPN
iajs-2801	322	86	(	(	PUNCT
iajs-2801	322	87	𝛼2	𝛼2	PROPN
iajs-2801	322	88	∗	∗	NOUN
iajs-2801	322	89	𝛽2	𝛽2	NOUN
iajs-2801	322	90	)	)	PUNCT
iajs-2801	322	91	,	,	PUNCT
iajs-2801	322	92	𝜆2	𝜆2	PROPN
iajs-2801	322	93	+	+	PROPN
iajs-2801	322	94	(	(	PUNCT
iajs-2801	322	95	𝛼2	𝛼2	PROPN
iajs-2801	322	96	)	)	PUNCT
iajs-2801	322	97	}	}	PUNCT
iajs-2801	322	98	.	.	PUNCT
iajs-2801	323	1	and	and	CCONJ
iajs-2801	323	2	(;	(;	PUNCT
iajs-2801	323	3	𝜆1	𝜆1	NOUN
iajs-2801	323	4	−	−	ADP
iajs-2801	323	5	×	×	NOUN
iajs-2801	323	6	;	;	PUNCT
iajs-2801	323	7	𝜆2	𝜆2	NOUN
iajs-2801	323	8	−)(𝛽	−)(𝛽	NOUN
iajs-2801	323	9	1	1	NUM
iajs-2801	323	10	,	,	PUNCT
iajs-2801	323	11	𝛽	𝛽	NOUN
iajs-2801	323	12	2	2	NUM
iajs-2801	323	13	)	)	PUNCT
iajs-2801	323	14	≤	≤	NUM
iajs-2801	323	15	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	323	16	{	{	PUNCT
iajs-2801	323	17	(;	(;	ADJ
iajs-2801	323	18	𝜆1	𝜆1	NOUN
iajs-2801	324	1	−	−	PROPN
iajs-2801	324	2	×	×	NOUN
iajs-2801	324	3	;	;	PUNCT
iajs-2801	324	4	𝜆2	𝜆2	PROPN
iajs-2801	324	5	−)((𝛼1	−)((𝛼1	PROPN
iajs-2801	324	6	,	,	PUNCT
iajs-2801	324	7	𝛼2	𝛼2	PROPN
iajs-2801	324	8	)	)	PUNCT
iajs-2801	324	9	∗	∗	NOUN
iajs-2801	324	10	(	(	PUNCT
iajs-2801	324	11	𝛽	𝛽	NOUN
iajs-2801	324	12	1	1	NUM
iajs-2801	324	13	,	,	PUNCT
iajs-2801	324	14	𝛽	𝛽	NOUN
iajs-2801	324	15	2	2	NUM
iajs-2801	324	16	)	)	PUNCT
iajs-2801	324	17	)	)	PUNCT
iajs-2801	325	1	,	,	PUNCT
iajs-2801	325	2	(;	(;	PUNCT
iajs-2801	325	3	𝜆1	𝜆1	NOUN
iajs-2801	325	4	−	−	ADP
iajs-2801	325	5	×	×	NOUN
iajs-2801	325	6	;	;	PUNCT
iajs-2801	325	7	𝜆2	𝜆2	PROPN
iajs-2801	325	8	−)(𝛼1	−)(𝛼1	PROPN
iajs-2801	325	9	,	,	PUNCT
iajs-2801	325	10	𝛼2	𝛼2	ADJ
iajs-2801	325	11	)	)	PUNCT
iajs-2801	325	12	}	}	PUNCT
iajs-2801	325	13	=	=	SYM
iajs-2801	325	14	𝑚𝑎𝑥	𝑚𝑎𝑥	X
iajs-2801	325	15	{	{	PUNCT
iajs-2801	325	16	(;	(;	ADJ
iajs-2801	325	17	𝜆1	𝜆1	NOUN
iajs-2801	325	18	−	−	PROPN
iajs-2801	325	19	×	×	NOUN
iajs-2801	325	20	;	;	PUNCT
iajs-2801	325	21	𝜆2	𝜆2	PROPN
iajs-2801	325	22	−)(𝛼1	−)(𝛼1	PROPN
iajs-2801	325	23	∗	∗	NOUN
iajs-2801	325	24	𝛽	𝛽	NOUN
iajs-2801	325	25	1	1	NUM
iajs-2801	325	26	,	,	PUNCT
iajs-2801	325	27	𝛼2	𝛼2	PROPN
iajs-2801	325	28	∗	∗	NOUN
iajs-2801	325	29	𝛽	𝛽	NOUN
iajs-2801	325	30	2	2	NUM
iajs-2801	325	31	)	)	PUNCT
iajs-2801	325	32	,	,	PUNCT
iajs-2801	325	33	(;	(;	PUNCT
iajs-2801	325	34	𝜆1	𝜆1	NOUN
iajs-2801	325	35	−	−	ADP
iajs-2801	325	36	×	×	NOUN
iajs-2801	325	37	;	;	PUNCT
iajs-2801	325	38	𝜆2	𝜆2	PROPN
iajs-2801	325	39	−)(𝛼1	−)(𝛼1	PROPN
iajs-2801	325	40	,	,	PUNCT
iajs-2801	325	41	𝛼2	𝛼2	PROPN
iajs-2801	325	42	)	)	PUNCT
iajs-2801	325	43	}	}	PUNCT
iajs-2801	325	44	put𝛼1	put𝛼1	NOUN
iajs-2801	326	1	=	=	SYM
iajs-2801	326	2	𝛽1	𝛽1	NOUN
iajs-2801	326	3	=	=	SYM
iajs-2801	326	4	0	0	NUM
iajs-2801	326	5	,	,	PUNCT
iajs-2801	326	6	then	then	ADV
iajs-2801	326	7	we	we	PRON
iajs-2801	326	8	have	have	VERB
iajs-2801	326	9	(;	(;	PUNCT
iajs-2801	326	10	𝜆1	𝜆1	VERB
iajs-2801	327	1	−	−	PROPN
iajs-2801	327	2	×	×	NOUN
iajs-2801	327	3	;	;	PUNCT
iajs-2801	327	4	𝜆2	𝜆2	PROPN
iajs-2801	327	5	−)(0	−)(0	NOUN
iajs-2801	327	6	,	,	PUNCT
iajs-2801	327	7	𝛽	𝛽	PROPN
iajs-2801	327	8	2	2	NUM
iajs-2801	327	9	)	)	PUNCT
iajs-2801	327	10	≤	≤	NUM
iajs-2801	327	11	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	327	12	{	{	PUNCT
iajs-2801	327	13	(;	(;	ADJ
iajs-2801	327	14	𝜆1	𝜆1	NOUN
iajs-2801	327	15	−	−	PROPN
iajs-2801	327	16	×	×	NOUN
iajs-2801	327	17	;	;	PUNCT
iajs-2801	327	18	𝜆2	𝜆2	NOUN
iajs-2801	327	19	−	−	PROPN
iajs-2801	327	20	;	;	PUNCT
iajs-2801	327	21	)	)	PUNCT
iajs-2801	327	22	(	(	PUNCT
iajs-2801	327	23	(	(	PUNCT
iajs-2801	327	24	0	0	NUM
iajs-2801	327	25	,	,	PUNCT
iajs-2801	327	26	𝛼2	𝛼2	ADJ
iajs-2801	327	27	)	)	PUNCT
iajs-2801	327	28	∗	∗	NOUN
iajs-2801	327	29	(	(	PUNCT
iajs-2801	327	30	0	0	NUM
iajs-2801	327	31	,	,	PUNCT
iajs-2801	327	32	𝛽	𝛽	NOUN
iajs-2801	327	33	2	2	NUM
iajs-2801	327	34	)	)	PUNCT
iajs-2801	327	35	)	)	PUNCT
iajs-2801	327	36	,	,	PUNCT
iajs-2801	327	37	(;	(;	PUNCT
iajs-2801	328	1	𝜆1	𝜆1	NOUN
iajs-2801	328	2	−	−	ADP
iajs-2801	328	3	×	×	NOUN
iajs-2801	328	4	;	;	PUNCT
iajs-2801	328	5	𝜆2	𝜆2	NOUN
iajs-2801	328	6	−	−	PROPN
iajs-2801	328	7	;	;	PUNCT
iajs-2801	328	8	)	)	PUNCT
iajs-2801	328	9	(	(	PUNCT
iajs-2801	328	10	0	0	NUM
iajs-2801	328	11	,	,	PUNCT
iajs-2801	328	12	𝛼2	𝛼2	ADJ
iajs-2801	328	13	)	)	PUNCT
iajs-2801	328	14	}	}	PUNCT
iajs-2801	329	1	=	=	SYM
iajs-2801	329	2	𝑚𝑎𝑥	𝑚𝑎𝑥	X
iajs-2801	329	3	{	{	PUNCT
iajs-2801	329	4	(;	(;	ADJ
iajs-2801	329	5	𝜆1	𝜆1	NOUN
iajs-2801	329	6	−	−	PROPN
iajs-2801	329	7	×	×	NOUN
iajs-2801	329	8	;	;	PUNCT
iajs-2801	329	9	𝜆2	𝜆2	NOUN
iajs-2801	329	10	−	−	PROPN
iajs-2801	329	11	;	;	PUNCT
iajs-2801	329	12	)	)	PUNCT
iajs-2801	329	13	(	(	PUNCT
iajs-2801	329	14	0	0	NUM
iajs-2801	329	15	,	,	PUNCT
iajs-2801	329	16	𝛼2	𝛼2	PROPN
iajs-2801	329	17	∗	∗	NOUN
iajs-2801	329	18	𝛽	𝛽	NOUN
iajs-2801	329	19	2	2	NUM
iajs-2801	329	20	)	)	PUNCT
iajs-2801	329	21	,	,	PUNCT
iajs-2801	329	22	(;	(;	PUNCT
iajs-2801	329	23	𝜆1	𝜆1	NOUN
iajs-2801	329	24	−	−	ADP
iajs-2801	329	25	×	×	NOUN
iajs-2801	329	26	;	;	PUNCT
iajs-2801	329	27	𝜆2	𝜆2	NOUN
iajs-2801	329	28	−	−	PROPN
iajs-2801	329	29	;	;	PUNCT
iajs-2801	329	30	)	)	PUNCT
iajs-2801	329	31	(	(	PUNCT
iajs-2801	329	32	0	0	NUM
iajs-2801	329	33	,	,	PUNCT
iajs-2801	329	34	𝛼2)}and	𝛼2)}and	NOUN
iajs-2801	329	35	by	by	ADP
iajs-2801	329	36	using	use	VERB
iajs-2801	329	37	equation	equation	NOUN
iajs-2801	329	38	(	(	PUNCT
iajs-2801	329	39	4	4	NUM
iajs-2801	329	40	)	)	PUNCT
iajs-2801	329	41	,	,	PUNCT
iajs-2801	329	42	we	we	PRON
iajs-2801	329	43	have	have	VERB
iajs-2801	329	44	𝜆2	𝜆2	NOUN
iajs-2801	329	45	−(𝛽2	−(𝛽2	NOUN
iajs-2801	329	46	)	)	PUNCT
iajs-2801	329	47	≤	≤	NOUN
iajs-2801	329	48	𝑚𝑎𝑥{𝜆2	𝑚𝑎𝑥{𝜆2	X
iajs-2801	329	49	−(𝛼2	−(𝛼2	X
iajs-2801	329	50	∗	∗	NOUN
iajs-2801	329	51	𝛽2	𝛽2	NOUN
iajs-2801	329	52	)	)	PUNCT
iajs-2801	329	53	,	,	PUNCT
iajs-2801	329	54	𝜆2	𝜆2	PROPN
iajs-2801	329	55	−(𝛼2	−(𝛼2	NUM
iajs-2801	329	56	)	)	PUNCT
iajs-2801	329	57	}	}	PUNCT
iajs-2801	329	58	.	.	PUNCT
iajs-2801	330	1	and	and	CCONJ
iajs-2801	330	2	the	the	DET
iajs-2801	330	3	condition	condition	NOUN
iajs-2801	330	4	(	(	PUNCT
iajs-2801	330	5	bc3	bc3	PROPN
iajs-2801	330	6	)	)	PUNCT
iajs-2801	330	7	is	be	AUX
iajs-2801	330	8	(	(	PUNCT
iajs-2801	330	9	�	�	PROPN
iajs-2801	330	10	̃	̃	NOUN
iajs-2801	330	11	�	�	NOUN
iajs-2801	330	12	1	1	NUM
iajs-2801	330	13	+	+	NUM
iajs-2801	330	14	×	×	PROPN
iajs-2801	330	15	�	�	PROPN
iajs-2801	330	16	̃	̃	PROPN
iajs-2801	330	17	�	�	NOUN
iajs-2801	330	18	2	2	NUM
iajs-2801	330	19	+	+	CCONJ
iajs-2801	330	20	)	)	PUNCT
iajs-2801	330	21	(	(	PUNCT
iajs-2801	330	22	(	(	PUNCT
iajs-2801	330	23	𝛼1	𝛼1	NOUN
iajs-2801	330	24	,	,	PUNCT
iajs-2801	330	25	𝛼2	𝛼2	ADJ
iajs-2801	330	26	)	)	PUNCT
iajs-2801	330	27	∘	∘	NOUN
iajs-2801	330	28	(	(	PUNCT
iajs-2801	330	29	𝛽	𝛽	NOUN
iajs-2801	330	30	1	1	NUM
iajs-2801	330	31	,	,	PUNCT
iajs-2801	330	32	𝛽	𝛽	PROPN
iajs-2801	330	33	2	2	NUM
iajs-2801	330	34	)	)	PUNCT
iajs-2801	330	35	≥	≥	NOUN
iajs-2801	330	36	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	330	37	{	{	PUNCT
iajs-2801	330	38	(;	(;	X
iajs-2801	330	39	�	�	PROPN
iajs-2801	330	40	̃	̃	NOUN
iajs-2801	330	41	�	�	NOUN
iajs-2801	330	42	1	1	NUM
iajs-2801	330	43	+	+	NUM
iajs-2801	330	44	×	×	NOUN
iajs-2801	330	45	;	;	PUNCT
iajs-2801	330	46	�	�	PROPN
iajs-2801	330	47	̃	̃	PROPN
iajs-2801	330	48	�	�	NOUN
iajs-2801	330	49	2	2	NUM
iajs-2801	330	50	+	+	CCONJ
iajs-2801	330	51	)	)	PUNCT
iajs-2801	330	52	(	(	PUNCT
iajs-2801	330	53	𝛼1	𝛼1	NOUN
iajs-2801	330	54	,	,	PUNCT
iajs-2801	330	55	𝛼2	𝛼2	PROPN
iajs-2801	330	56	)	)	PUNCT
iajs-2801	330	57	,	,	PUNCT
iajs-2801	330	58	(;	(;	X
iajs-2801	330	59	�	�	PROPN
iajs-2801	330	60	̃	̃	NOUN
iajs-2801	330	61	�	�	NOUN
iajs-2801	330	62	1	1	NUM
iajs-2801	330	63	+	+	NUM
iajs-2801	330	64	×	×	NOUN
iajs-2801	330	65	;	;	PUNCT
iajs-2801	330	66	�	�	PROPN
iajs-2801	330	67	̃	̃	PROPN
iajs-2801	330	68	�	�	NOUN
iajs-2801	330	69	2	2	NUM
iajs-2801	330	70	+	+	NUM
iajs-2801	330	71	)	)	PUNCT
iajs-2801	330	72	(	(	PUNCT
iajs-2801	330	73	𝛽	𝛽	NOUN
iajs-2801	330	74	1	1	NUM
iajs-2801	330	75	,	,	PUNCT
iajs-2801	330	76	𝛽	𝛽	NOUN
iajs-2801	330	77	2	2	NUM
iajs-2801	330	78	)	)	PUNCT
iajs-2801	330	79	}	}	PUNCT
iajs-2801	330	80	(;	(;	PUNCT
iajs-2801	330	81	�	�	PROPN
iajs-2801	330	82	̃	̃	NOUN
iajs-2801	330	83	�	�	NOUN
iajs-2801	330	84	1	1	NUM
iajs-2801	330	85	+	+	CCONJ
iajs-2801	330	86	×	×	NOUN
iajs-2801	330	87	;	;	PUNCT
iajs-2801	330	88	�	�	PROPN
iajs-2801	330	89	̃	̃	PROPN
iajs-2801	330	90	�	�	NOUN
iajs-2801	330	91	2	2	NUM
iajs-2801	330	92	+	+	CCONJ
iajs-2801	330	93	)	)	PUNCT
iajs-2801	330	94	(	(	PUNCT
iajs-2801	330	95	𝛼1	𝛼1	NOUN
iajs-2801	330	96	∘	∘	NOUN
iajs-2801	330	97	𝛽	𝛽	NOUN
iajs-2801	330	98	1	1	NUM
iajs-2801	330	99	,	,	PUNCT
iajs-2801	330	100	𝛼2	𝛼2	VERB
iajs-2801	330	101	∘	∘	NOUN
iajs-2801	330	102	𝛽	𝛽	ADP
iajs-2801	330	103	2	2	NUM
iajs-2801	330	104	)	)	PUNCT
iajs-2801	330	105	≥	≥	NOUN
iajs-2801	330	106	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	330	107	{	{	PUNCT
iajs-2801	330	108	(;	(;	X
iajs-2801	330	109	�	�	PROPN
iajs-2801	330	110	̃	̃	NOUN
iajs-2801	330	111	�	�	NOUN
iajs-2801	330	112	1	1	NUM
iajs-2801	330	113	+	+	NUM
iajs-2801	330	114	×	×	NOUN
iajs-2801	330	115	;	;	PUNCT
iajs-2801	330	116	�	�	PROPN
iajs-2801	330	117	̃	̃	PROPN
iajs-2801	330	118	�	�	NOUN
iajs-2801	330	119	2	2	NUM
iajs-2801	330	120	+	+	CCONJ
iajs-2801	330	121	)	)	PUNCT
iajs-2801	330	122	(	(	PUNCT
iajs-2801	330	123	𝛼1	𝛼1	NOUN
iajs-2801	330	124	,	,	PUNCT
iajs-2801	330	125	𝛼2	𝛼2	PROPN
iajs-2801	330	126	)	)	PUNCT
iajs-2801	330	127	,	,	PUNCT
iajs-2801	330	128	(;	(;	X
iajs-2801	330	129	�	�	PROPN
iajs-2801	330	130	̃	̃	NOUN
iajs-2801	330	131	�	�	NOUN
iajs-2801	330	132	1	1	NUM
iajs-2801	330	133	+	+	NUM
iajs-2801	330	134	×	×	NOUN
iajs-2801	330	135	;	;	PUNCT
iajs-2801	330	136	�	�	PROPN
iajs-2801	330	137	̃	̃	PROPN
iajs-2801	330	138	�	�	NOUN
iajs-2801	330	139	2	2	NUM
iajs-2801	330	140	+	+	NUM
iajs-2801	330	141	)	)	PUNCT
iajs-2801	330	142	(	(	PUNCT
iajs-2801	330	143	𝛽	𝛽	NOUN
iajs-2801	330	144	1	1	NUM
iajs-2801	330	145	,	,	PUNCT
iajs-2801	330	146	𝛽	𝛽	NOUN
iajs-2801	330	147	2	2	NUM
iajs-2801	330	148	)	)	PUNCT
iajs-2801	330	149	}	}	PUNCT
iajs-2801	330	150	put	put	VERB
iajs-2801	330	151	𝛼1	𝛼1	NOUN
iajs-2801	330	152	=	=	SYM
iajs-2801	330	153	𝛽1	𝛽1	NOUN
iajs-2801	330	154	=	=	SYM
iajs-2801	330	155	0	0	NUM
iajs-2801	330	156	,	,	PUNCT
iajs-2801	330	157	then	then	ADV
iajs-2801	330	158	we	we	PRON
iajs-2801	330	159	have	have	VERB
iajs-2801	330	160	(;	(;	NOUN
iajs-2801	330	161	�	�	PROPN
iajs-2801	330	162	̃	̃	NOUN
iajs-2801	330	163	�	�	NOUN
iajs-2801	330	164	1	1	NUM
iajs-2801	330	165	+	+	NUM
iajs-2801	330	166	×	×	NOUN
iajs-2801	330	167	;	;	PUNCT
iajs-2801	330	168	�	�	PROPN
iajs-2801	330	169	̃	̃	PROPN
iajs-2801	330	170	�	�	NOUN
iajs-2801	330	171	2	2	NUM
iajs-2801	330	172	+	+	NOUN
iajs-2801	330	173	;	;	PUNCT
iajs-2801	330	174	)	)	PUNCT
iajs-2801	330	175	(	(	PUNCT
iajs-2801	330	176	0	0	NUM
iajs-2801	330	177	,	,	PUNCT
iajs-2801	330	178	𝛼2	𝛼2	VERB
iajs-2801	330	179	∘	∘	NOUN
iajs-2801	330	180	𝛽	𝛽	ADP
iajs-2801	330	181	2	2	NUM
iajs-2801	330	182	)	)	PUNCT
iajs-2801	330	183	≥	≥	NOUN
iajs-2801	330	184	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
iajs-2801	330	185	{	{	PUNCT
iajs-2801	330	186	(;	(;	X
iajs-2801	330	187	�	�	PROPN
iajs-2801	330	188	̃	̃	NOUN
iajs-2801	330	189	�	�	NOUN
iajs-2801	330	190	1	1	NUM
iajs-2801	330	191	+	+	NUM
iajs-2801	330	192	×	×	NOUN
iajs-2801	330	193	;	;	PUNCT
iajs-2801	330	194	�	�	PROPN
iajs-2801	330	195	̃	̃	PROPN
iajs-2801	330	196	�	�	NOUN
iajs-2801	330	197	2	2	NUM
iajs-2801	330	198	+	+	NOUN
iajs-2801	330	199	;	;	PUNCT
iajs-2801	330	200	)	)	PUNCT
iajs-2801	330	201	(	(	PUNCT
iajs-2801	330	202	0	0	NUM
iajs-2801	330	203	,	,	PUNCT
iajs-2801	330	204	𝑥2	𝑥2	NOUN
iajs-2801	330	205	)	)	PUNCT
iajs-2801	330	206	,	,	PUNCT
iajs-2801	330	207	(;	(;	X
iajs-2801	330	208	�	�	PROPN
iajs-2801	330	209	̃	̃	NOUN
iajs-2801	330	210	�	�	NOUN
iajs-2801	330	211	1	1	NUM
iajs-2801	330	212	+	+	NUM
iajs-2801	330	213	×	×	NOUN
iajs-2801	330	214	;	;	PUNCT
iajs-2801	330	215	�	�	PROPN
iajs-2801	330	216	̃	̃	PROPN
iajs-2801	330	217	�	�	NOUN
iajs-2801	330	218	2	2	NUM
iajs-2801	330	219	+	+	NOUN
iajs-2801	330	220	;	;	PUNCT
iajs-2801	330	221	)	)	PUNCT
iajs-2801	330	222	(	(	PUNCT
iajs-2801	330	223	0	0	NUM
iajs-2801	330	224	,	,	PUNCT
iajs-2801	330	225	𝛽	𝛽	NOUN
iajs-2801	330	226	2	2	NUM
iajs-2801	330	227	)	)	PUNCT
iajs-2801	330	228	}	}	PUNCT
iajs-2801	330	229	and	and	CCONJ
iajs-2801	330	230	by	by	ADP
iajs-2801	330	231	using	use	VERB
iajs-2801	330	232	equation	equation	NOUN
iajs-2801	330	233	(	(	PUNCT
iajs-2801	330	234	1	1	NUM
iajs-2801	330	235	)	)	PUNCT
iajs-2801	330	236	,	,	PUNCT
iajs-2801	330	237	we	we	PRON
iajs-2801	330	238	have	have	AUX
iajs-2801	330	239	𝜇2	𝜇2	VERB
iajs-2801	330	240	+	+	PROPN
iajs-2801	330	241	(	(	PUNCT
iajs-2801	330	242	𝛼2	𝛼2	PROPN
iajs-2801	330	243	∘	∘	ADJ
iajs-2801	330	244	𝛽2	𝛽2	NOUN
iajs-2801	330	245	)	)	PUNCT
iajs-2801	330	246	≥	≥	NOUN
iajs-2801	330	247	𝑟𝑚𝑖𝑛{	𝑟𝑚𝑖𝑛{	PROPN
iajs-2801	330	248	�	�	PROPN
iajs-2801	330	249	̃	̃	PROPN
iajs-2801	330	250	�	�	NOUN
iajs-2801	330	251	2	2	NUM
iajs-2801	330	252	+	+	ADJ
iajs-2801	330	253	(	(	PUNCT
iajs-2801	330	254	𝛼2	𝛼2	PROPN
iajs-2801	330	255	)	)	PUNCT
iajs-2801	330	256	,	,	PUNCT
iajs-2801	330	257	𝜇2	𝜇2	PROPN
iajs-2801	330	258	+	+	PROPN
iajs-2801	330	259	(	(	PUNCT
iajs-2801	330	260	𝛽2	𝛽2	NOUN
iajs-2801	330	261	)	)	PUNCT
iajs-2801	330	262	}	}	PUNCT
iajs-2801	330	263	and	and	CCONJ
iajs-2801	330	264	(	(	PUNCT
iajs-2801	330	265	�	�	PROPN
iajs-2801	330	266	̃	̃	NOUN
iajs-2801	330	267	�	�	NOUN
iajs-2801	330	268	1	1	NUM
iajs-2801	330	269	−	−	PROPN
iajs-2801	330	270	×	×	PROPN
iajs-2801	330	271	�	�	PROPN
iajs-2801	330	272	̃	̃	PROPN
iajs-2801	330	273	�	�	PROPN
iajs-2801	330	274	2	2	NUM
iajs-2801	330	275	−	−	NOUN
iajs-2801	330	276	)	)	PUNCT
iajs-2801	330	277	(	(	PUNCT
iajs-2801	330	278	(	(	PUNCT
iajs-2801	330	279	𝛼1	𝛼1	NOUN
iajs-2801	330	280	,	,	PUNCT
iajs-2801	330	281	𝛼2	𝛼2	ADJ
iajs-2801	330	282	)	)	PUNCT
iajs-2801	330	283	∘	∘	NOUN
iajs-2801	330	284	(	(	PUNCT
iajs-2801	330	285	𝛽	𝛽	NOUN
iajs-2801	330	286	1	1	NUM
iajs-2801	330	287	,	,	PUNCT
iajs-2801	330	288	𝛽	𝛽	PROPN
iajs-2801	330	289	2	2	NUM
iajs-2801	330	290	)	)	PUNCT
iajs-2801	330	291	≤	≤	NUM
iajs-2801	330	292	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	PROPN
iajs-2801	330	293	{	{	PUNCT
iajs-2801	330	294	(;	(;	X
iajs-2801	330	295	�	�	PROPN
iajs-2801	330	296	̃	̃	NOUN
iajs-2801	330	297	�	�	NOUN
iajs-2801	330	298	1	1	NUM
iajs-2801	330	299	−	−	NOUN
iajs-2801	330	300	×	×	NOUN
iajs-2801	330	301	;	;	PUNCT
iajs-2801	330	302	�	�	PROPN
iajs-2801	330	303	̃	̃	PROPN
iajs-2801	330	304	�	�	PROPN
iajs-2801	330	305	2	2	NUM
iajs-2801	330	306	−	−	NOUN
iajs-2801	330	307	)	)	PUNCT
iajs-2801	330	308	(	(	PUNCT
iajs-2801	330	309	𝛼1	𝛼1	NOUN
iajs-2801	330	310	,	,	PUNCT
iajs-2801	330	311	𝛼2	𝛼2	PROPN
iajs-2801	330	312	)	)	PUNCT
iajs-2801	330	313	,	,	PUNCT
iajs-2801	330	314	(;	(;	X
iajs-2801	330	315	�	�	PROPN
iajs-2801	330	316	̃	̃	NOUN
iajs-2801	330	317	�	�	NOUN
iajs-2801	330	318	1	1	NUM
iajs-2801	331	1	−	−	NOUN
iajs-2801	331	2	×	×	NOUN
iajs-2801	331	3	;	;	PUNCT
iajs-2801	331	4	�	�	PROPN
iajs-2801	331	5	̃	̃	PROPN
iajs-2801	331	6	�	�	PROPN
iajs-2801	331	7	2	2	NUM
iajs-2801	331	8	−	−	NOUN
iajs-2801	331	9	)	)	PUNCT
iajs-2801	331	10	(	(	PUNCT
iajs-2801	331	11	𝛽	𝛽	NOUN
iajs-2801	331	12	1	1	NUM
iajs-2801	331	13	,	,	PUNCT
iajs-2801	331	14	𝛽	𝛽	NOUN
iajs-2801	331	15	2	2	NUM
iajs-2801	331	16	)	)	PUNCT
iajs-2801	331	17	}	}	PUNCT
iajs-2801	331	18	(;	(;	PUNCT
iajs-2801	331	19	�	�	PROPN
iajs-2801	331	20	̃	̃	NOUN
iajs-2801	331	21	�	�	NOUN
iajs-2801	331	22	1	1	NUM
iajs-2801	331	23	−	−	NOUN
iajs-2801	331	24	×	×	NOUN
iajs-2801	331	25	;	;	PUNCT
iajs-2801	331	26	�	�	PROPN
iajs-2801	331	27	̃	̃	PROPN
iajs-2801	331	28	�	�	NOUN
iajs-2801	331	29	2	2	NUM
iajs-2801	331	30	−	−	NUM
iajs-2801	331	31	;	;	PUNCT
iajs-2801	331	32	)	)	PUNCT
iajs-2801	331	33	(	(	PUNCT
iajs-2801	331	34	𝛼1	𝛼1	NOUN
iajs-2801	331	35	∘	∘	NOUN
iajs-2801	331	36	𝛽	𝛽	NOUN
iajs-2801	331	37	1	1	NUM
iajs-2801	331	38	,	,	PUNCT
iajs-2801	331	39	𝛼2	𝛼2	VERB
iajs-2801	331	40	∘	∘	NOUN
iajs-2801	331	41	𝛽	𝛽	ADP
iajs-2801	331	42	2	2	NUM
iajs-2801	331	43	)	)	PUNCT
iajs-2801	331	44	≤	≤	NUM
iajs-2801	331	45	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	PROPN
iajs-2801	331	46	{	{	PUNCT
iajs-2801	331	47	(;	(;	X
iajs-2801	331	48	�	�	PROPN
iajs-2801	331	49	̃	̃	NOUN
iajs-2801	331	50	�	�	NOUN
iajs-2801	331	51	1	1	NUM
iajs-2801	331	52	−	−	NOUN
iajs-2801	331	53	×	×	NOUN
iajs-2801	331	54	;	;	PUNCT
iajs-2801	331	55	�	�	PROPN
iajs-2801	331	56	̃	̃	PROPN
iajs-2801	331	57	�	�	PROPN
iajs-2801	331	58	2	2	NUM
iajs-2801	331	59	−	−	NOUN
iajs-2801	331	60	)	)	PUNCT
iajs-2801	331	61	(	(	PUNCT
iajs-2801	331	62	𝛼1	𝛼1	NOUN
iajs-2801	331	63	,	,	PUNCT
iajs-2801	331	64	𝛼2	𝛼2	PROPN
iajs-2801	331	65	)	)	PUNCT
iajs-2801	331	66	;	;	PUNCT
iajs-2801	331	67	,	,	PUNCT
iajs-2801	331	68	(;	(;	X
iajs-2801	331	69	�	�	PROPN
iajs-2801	331	70	̃	̃	NOUN
iajs-2801	331	71	�	�	NOUN
iajs-2801	331	72	1	1	NUM
iajs-2801	331	73	−	−	NOUN
iajs-2801	331	74	×	×	NOUN
iajs-2801	331	75	;	;	PUNCT
iajs-2801	331	76	�	�	PROPN
iajs-2801	331	77	̃	̃	PROPN
iajs-2801	331	78	�	�	PROPN
iajs-2801	331	79	2	2	NUM
iajs-2801	331	80	−	−	NOUN
iajs-2801	331	81	)	)	PUNCT
iajs-2801	331	82	(;	(;	PUNCT
iajs-2801	331	83	𝛽	𝛽	NOUN
iajs-2801	331	84	1	1	NUM
iajs-2801	331	85	,	,	PUNCT
iajs-2801	331	86	𝛽	𝛽	PROPN
iajs-2801	331	87	2	2	NUM
iajs-2801	331	88	;	;	PUNCT
iajs-2801	331	89	)	)	PUNCT
iajs-2801	331	90	}	}	PUNCT
iajs-2801	331	91	put	put	VERB
iajs-2801	331	92	𝛼1	𝛼1	NOUN
iajs-2801	331	93	=	=	SYM
iajs-2801	331	94	𝛽1	𝛽1	NOUN
iajs-2801	331	95	=	=	SYM
iajs-2801	331	96	0	0	NUM
iajs-2801	331	97	,	,	PUNCT
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iajs-2801	331	99	we	we	PRON
iajs-2801	331	100	have	have	VERB
iajs-2801	331	101	(;	(;	NOUN
iajs-2801	331	102	�	�	PROPN
iajs-2801	331	103	̃	̃	NOUN
iajs-2801	331	104	�	�	NOUN
iajs-2801	331	105	1	1	NUM
iajs-2801	331	106	−	−	NOUN
iajs-2801	331	107	×	×	NOUN
iajs-2801	331	108	;	;	PUNCT
iajs-2801	331	109	�	�	PROPN
iajs-2801	331	110	̃	̃	PROPN
iajs-2801	331	111	�	�	NOUN
iajs-2801	331	112	2	2	NUM
iajs-2801	331	113	−	−	NUM
iajs-2801	331	114	;	;	PUNCT
iajs-2801	331	115	)	)	PUNCT
iajs-2801	331	116	(	(	PUNCT
iajs-2801	331	117	0	0	NUM
iajs-2801	331	118	,	,	PUNCT
iajs-2801	331	119	;	;	PUNCT
iajs-2801	331	120	𝛼2	𝛼2	VERB
iajs-2801	331	121	∘	∘	PROPN
iajs-2801	331	122	𝛽	𝛽	ADP
iajs-2801	331	123	2	2	NUM
iajs-2801	331	124	)	)	PUNCT
iajs-2801	331	125	≤	≤	NUM
iajs-2801	331	126	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	PROPN
iajs-2801	331	127	{	{	PUNCT
iajs-2801	331	128	(;	(;	X
iajs-2801	331	129	�	�	PROPN
iajs-2801	331	130	̃	̃	NOUN
iajs-2801	331	131	�	�	PROPN
iajs-2801	331	132	1	1	NUM
iajs-2801	331	133	−;×	−;×	NOUN
iajs-2801	331	134	;	;	PUNCT
iajs-2801	331	135	�	�	PROPN
iajs-2801	331	136	̃	̃	PROPN
iajs-2801	331	137	�	�	NOUN
iajs-2801	331	138	2	2	NUM
iajs-2801	331	139	−	−	NUM
iajs-2801	331	140	;	;	PUNCT
iajs-2801	331	141	)	)	PUNCT
iajs-2801	331	142	(	(	PUNCT
iajs-2801	331	143	0	0	NUM
iajs-2801	331	144	,	,	PUNCT
iajs-2801	331	145	𝛼2	𝛼2	PROPN
iajs-2801	331	146	)	)	PUNCT
iajs-2801	331	147	,	,	PUNCT
iajs-2801	331	148	(;	(;	X
iajs-2801	331	149	�	�	PROPN
iajs-2801	331	150	̃	̃	NOUN
iajs-2801	331	151	�	�	NOUN
iajs-2801	331	152	1	1	NUM
iajs-2801	331	153	−	−	NOUN
iajs-2801	331	154	×	×	NOUN
iajs-2801	331	155	;	;	PUNCT
iajs-2801	331	156	�	�	PROPN
iajs-2801	331	157	̃	̃	PROPN
iajs-2801	331	158	�	�	NOUN
iajs-2801	331	159	2	2	NUM
iajs-2801	331	160	−	−	NUM
iajs-2801	331	161	;	;	PUNCT
iajs-2801	331	162	)	)	PUNCT
iajs-2801	331	163	(	(	PUNCT
iajs-2801	331	164	0	0	NUM
iajs-2801	331	165	,	,	PUNCT
iajs-2801	331	166	𝛽	𝛽	NOUN
iajs-2801	331	167	2	2	NUM
iajs-2801	331	168	)	)	PUNCT
iajs-2801	331	169	}	}	PUNCT
iajs-2801	331	170	and	and	CCONJ
iajs-2801	331	171	by	by	ADP
iajs-2801	331	172	using	use	VERB
iajs-2801	331	173	equation	equation	NOUN
iajs-2801	331	174	(	(	PUNCT
iajs-2801	331	175	2	2	NUM
iajs-2801	331	176	)	)	PUNCT
iajs-2801	331	177	,	,	PUNCT
iajs-2801	331	178	we	we	PRON
iajs-2801	331	179	have	have	AUX
iajs-2801	331	180	𝜇2	𝜇2	VERB
iajs-2801	331	181	−(𝛼2	−(𝛼2	PRON
iajs-2801	331	182	∘	∘	PROPN
iajs-2801	331	183	𝛽2	𝛽2	NOUN
iajs-2801	331	184	)	)	PUNCT
iajs-2801	331	185	≤	≤	NUM
iajs-2801	331	186	𝑟𝑚𝑎𝑥{	𝑟𝑚𝑎𝑥{	NOUN
iajs-2801	331	187	�	�	NOUN
iajs-2801	331	188	̃	̃	PROPN
iajs-2801	331	189	�	�	PROPN
iajs-2801	331	190	2	2	NUM
iajs-2801	331	191	−(𝛼2	−(𝛼2	NOUN
iajs-2801	331	192	)	)	PUNCT
iajs-2801	331	193	,	,	PUNCT
iajs-2801	331	194	𝜇2	𝜇2	PROPN
iajs-2801	331	195	−(𝛽2	−(𝛽2	NOUN
iajs-2801	331	196	)	)	PUNCT
iajs-2801	331	197	}	}	PUNCT
iajs-2801	332	1	also	also	ADV
iajs-2801	332	2	,	,	PUNCT
iajs-2801	332	3	we	we	PRON
iajs-2801	332	4	have	have	AUX
iajs-2801	332	5	(	(	PUNCT
iajs-2801	332	6	𝜆1	𝜆1	VERB
iajs-2801	332	7	+	+	CCONJ
iajs-2801	332	8	×	×	PROPN
iajs-2801	332	9	𝜆2	𝜆2	NOUN
iajs-2801	332	10	+	+	PROPN
iajs-2801	332	11	)	)	PUNCT
iajs-2801	332	12	(	(	PUNCT
iajs-2801	332	13	(	(	PUNCT
iajs-2801	332	14	𝛼1	𝛼1	NOUN
iajs-2801	332	15	,	,	PUNCT
iajs-2801	332	16	𝛼2	𝛼2	ADJ
iajs-2801	332	17	)	)	PUNCT
iajs-2801	332	18	∘	∘	NOUN
iajs-2801	332	19	(	(	PUNCT
iajs-2801	332	20	𝛽	𝛽	NOUN
iajs-2801	332	21	1	1	NUM
iajs-2801	332	22	,	,	PUNCT
iajs-2801	332	23	𝛽	𝛽	PROPN
iajs-2801	332	24	2	2	NUM
iajs-2801	332	25	)	)	PUNCT
iajs-2801	332	26	≥	≥	NOUN
iajs-2801	332	27	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	332	28	{	{	PUNCT
iajs-2801	332	29	(;	(;	PUNCT
iajs-2801	332	30	𝜆1	𝜆1	NOUN
iajs-2801	332	31	+	+	CCONJ
iajs-2801	332	32	×	×	NOUN
iajs-2801	332	33	;	;	PUNCT
iajs-2801	332	34	𝜆2	𝜆2	PROPN
iajs-2801	332	35	+	+	PROPN
iajs-2801	332	36	)	)	PUNCT
iajs-2801	332	37	(	(	PUNCT
iajs-2801	332	38	𝛼1	𝛼1	NOUN
iajs-2801	332	39	,	,	PUNCT
iajs-2801	332	40	𝛼2	𝛼2	PROPN
iajs-2801	332	41	)	)	PUNCT
iajs-2801	332	42	,	,	PUNCT
iajs-2801	332	43	(;	(;	PUNCT
iajs-2801	332	44	𝜆1	𝜆1	NOUN
iajs-2801	332	45	+	+	CCONJ
iajs-2801	332	46	×	×	NOUN
iajs-2801	332	47	;	;	PUNCT
iajs-2801	332	48	𝜆2	𝜆2	PROPN
iajs-2801	332	49	+	+	PROPN
iajs-2801	332	50	)	)	PUNCT
iajs-2801	332	51	(	(	PUNCT
iajs-2801	332	52	𝛽	𝛽	NOUN
iajs-2801	332	53	1	1	NUM
iajs-2801	332	54	,	,	PUNCT
iajs-2801	332	55	𝛽	𝛽	NOUN
iajs-2801	332	56	2	2	NUM
iajs-2801	332	57	)	)	PUNCT
iajs-2801	332	58	}	}	PUNCT
iajs-2801	332	59	(;	(;	PUNCT
iajs-2801	332	60	𝜆1	𝜆1	NOUN
iajs-2801	332	61	+	+	CCONJ
iajs-2801	332	62	×	×	NOUN
iajs-2801	332	63	;	;	PUNCT
iajs-2801	332	64	𝜆2	𝜆2	PROPN
iajs-2801	332	65	+	+	PROPN
iajs-2801	332	66	)	)	PUNCT
iajs-2801	332	67	(	(	PUNCT
iajs-2801	332	68	𝛼1	𝛼1	NOUN
iajs-2801	332	69	∘	∘	NOUN
iajs-2801	332	70	𝛽	𝛽	NOUN
iajs-2801	332	71	1	1	NUM
iajs-2801	332	72	,	,	PUNCT
iajs-2801	332	73	𝛼2	𝛼2	VERB
iajs-2801	332	74	∘	∘	NOUN
iajs-2801	332	75	𝛽	𝛽	ADP
iajs-2801	332	76	2	2	NUM
iajs-2801	332	77	)	)	PUNCT
iajs-2801	332	78	≥	≥	NOUN
iajs-2801	332	79	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	332	80	{	{	PUNCT
iajs-2801	332	81	(;	(;	PUNCT
iajs-2801	332	82	𝜆1	𝜆1	NOUN
iajs-2801	332	83	+	+	CCONJ
iajs-2801	332	84	×	×	NOUN
iajs-2801	332	85	;	;	PUNCT
iajs-2801	332	86	𝜆2	𝜆2	PROPN
iajs-2801	332	87	+	+	PROPN
iajs-2801	332	88	)	)	PUNCT
iajs-2801	332	89	(	(	PUNCT
iajs-2801	332	90	𝛼1	𝛼1	NOUN
iajs-2801	332	91	,	,	PUNCT
iajs-2801	332	92	𝛼2	𝛼2	PROPN
iajs-2801	332	93	)	)	PUNCT
iajs-2801	332	94	,	,	PUNCT
iajs-2801	332	95	(;	(;	PUNCT
iajs-2801	332	96	𝜆1	𝜆1	NOUN
iajs-2801	332	97	+	+	CCONJ
iajs-2801	332	98	×	×	NOUN
iajs-2801	332	99	;	;	PUNCT
iajs-2801	332	100	𝜆2	𝜆2	PROPN
iajs-2801	332	101	+	+	PROPN
iajs-2801	332	102	)	)	PUNCT
iajs-2801	332	103	(	(	PUNCT
iajs-2801	332	104	𝛽	𝛽	NOUN
iajs-2801	332	105	1	1	NUM
iajs-2801	332	106	,	,	PUNCT
iajs-2801	332	107	𝛽	𝛽	NOUN
iajs-2801	332	108	2	2	NUM
iajs-2801	332	109	)	)	PUNCT
iajs-2801	332	110	}	}	PUNCT
iajs-2801	332	111	put	put	VERB
iajs-2801	332	112	𝛼1	𝛼1	NOUN
iajs-2801	332	113	=	=	SYM
iajs-2801	332	114	𝛽1	𝛽1	NOUN
iajs-2801	332	115	=	=	SYM
iajs-2801	332	116	0	0	NUM
iajs-2801	332	117	,	,	PUNCT
iajs-2801	332	118	then	then	ADV
iajs-2801	332	119	we	we	PRON
iajs-2801	332	120	have	have	VERB
iajs-2801	332	121	(;	(;	PUNCT
iajs-2801	332	122	𝜆1	𝜆1	VERB
iajs-2801	332	123	+	+	CCONJ
iajs-2801	332	124	×	×	NOUN
iajs-2801	332	125	;	;	PUNCT
iajs-2801	332	126	𝜆2	𝜆2	PROPN
iajs-2801	333	1	+	+	PROPN
iajs-2801	333	2	)	)	PUNCT
iajs-2801	333	3	(	(	PUNCT
iajs-2801	333	4	0	0	NUM
iajs-2801	333	5	,	,	PUNCT
iajs-2801	333	6	𝛼2	𝛼2	VERB
iajs-2801	333	7	∘	∘	NOUN
iajs-2801	333	8	𝛽	𝛽	ADP
iajs-2801	333	9	2	2	NUM
iajs-2801	333	10	)	)	PUNCT
iajs-2801	333	11	≥	≥	NOUN
iajs-2801	333	12	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2801	333	13	{	{	PUNCT
iajs-2801	333	14	(;	(;	PUNCT
iajs-2801	333	15	𝜆1	𝜆1	NOUN
iajs-2801	333	16	+	+	CCONJ
iajs-2801	333	17	×	×	NOUN
iajs-2801	333	18	;	;	PUNCT
iajs-2801	333	19	𝜆2	𝜆2	PROPN
iajs-2801	334	1	+	+	PROPN
iajs-2801	334	2	)	)	PUNCT
iajs-2801	334	3	(	(	PUNCT
iajs-2801	334	4	0	0	NUM
iajs-2801	334	5	,	,	PUNCT
iajs-2801	334	6	𝛼2	𝛼2	PROPN
iajs-2801	334	7	)	)	PUNCT
iajs-2801	334	8	,	,	PUNCT
iajs-2801	334	9	(;	(;	PUNCT
iajs-2801	335	1	𝜆1	𝜆1	NOUN
iajs-2801	335	2	+	+	CCONJ
iajs-2801	335	3	×	×	NOUN
iajs-2801	335	4	;	;	PUNCT
iajs-2801	335	5	𝜆2	𝜆2	PROPN
iajs-2801	335	6	+	+	PROPN
iajs-2801	335	7	)	)	PUNCT
iajs-2801	335	8	(	(	PUNCT
iajs-2801	335	9	0	0	NUM
iajs-2801	335	10	,	,	PUNCT
iajs-2801	335	11	𝛽	𝛽	NOUN
iajs-2801	335	12	2	2	NUM
iajs-2801	335	13	)	)	PUNCT
iajs-2801	335	14	}	}	PUNCT
iajs-2801	335	15	and	and	CCONJ
iajs-2801	335	16	by	by	ADP
iajs-2801	335	17	using	use	VERB
iajs-2801	335	18	equation	equation	NOUN
iajs-2801	335	19	(	(	PUNCT
iajs-2801	335	20	3	3	NUM
iajs-2801	335	21	)	)	PUNCT
iajs-2801	335	22	,	,	PUNCT
iajs-2801	335	23	we	we	PRON
iajs-2801	335	24	have	have	VERB
iajs-2801	335	25	𝜆2	𝜆2	PROPN
iajs-2801	336	1	+	+	PROPN
iajs-2801	336	2	(	(	PUNCT
iajs-2801	336	3	𝛼2	𝛼2	PROPN
iajs-2801	336	4	∘	∘	ADJ
iajs-2801	336	5	𝛽2	𝛽2	NOUN
iajs-2801	336	6	)	)	PUNCT
iajs-2801	336	7	≥	≥	NOUN
iajs-2801	336	8	𝑚𝑖𝑛{𝜆2	𝑚𝑖𝑛{𝜆2	PUNCT
iajs-2801	336	9	+	+	PROPN
iajs-2801	336	10	(	(	PUNCT
iajs-2801	336	11	𝛼2	𝛼2	PROPN
iajs-2801	336	12	)	)	PUNCT
iajs-2801	336	13	,	,	PUNCT
iajs-2801	336	14	𝜆2	𝜆2	PROPN
iajs-2801	336	15	+	+	PROPN
iajs-2801	336	16	(	(	PUNCT
iajs-2801	336	17	𝛽2	𝛽2	NOUN
iajs-2801	336	18	)	)	PUNCT
iajs-2801	336	19	}	}	PUNCT
iajs-2801	336	20	and	and	CCONJ
iajs-2801	336	21	(	(	PUNCT
iajs-2801	336	22	𝜆1	𝜆1	VERB
iajs-2801	336	23	−	−	PROPN
iajs-2801	336	24	×	×	PROPN
iajs-2801	336	25	𝜆2	𝜆2	PROPN
iajs-2801	336	26	−)((𝛼1	−)((𝛼1	PROPN
iajs-2801	336	27	,	,	PUNCT
iajs-2801	336	28	𝛼2	𝛼2	ADJ
iajs-2801	336	29	)	)	PUNCT
iajs-2801	336	30	∘	∘	NOUN
iajs-2801	336	31	(	(	PUNCT
iajs-2801	336	32	𝛽	𝛽	NOUN
iajs-2801	336	33	1	1	NUM
iajs-2801	336	34	,	,	PUNCT
iajs-2801	336	35	𝛽	𝛽	PROPN
iajs-2801	336	36	2	2	NUM
iajs-2801	336	37	)	)	PUNCT
iajs-2801	336	38	≤	≤	NUM
iajs-2801	336	39	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	336	40	{	{	PUNCT
iajs-2801	336	41	(;	(;	ADJ
iajs-2801	336	42	𝜆1	𝜆1	NOUN
iajs-2801	337	1	−	−	PROPN
iajs-2801	337	2	×	×	NOUN
iajs-2801	337	3	;	;	PUNCT
iajs-2801	337	4	𝜆2	𝜆2	NOUN
iajs-2801	337	5	−	−	PROPN
iajs-2801	337	6	;	;	PUNCT
iajs-2801	337	7	)	)	PUNCT
iajs-2801	337	8	(	(	PUNCT
iajs-2801	337	9	𝛼1	𝛼1	NOUN
iajs-2801	337	10	,	,	PUNCT
iajs-2801	337	11	𝛼2	𝛼2	PROPN
iajs-2801	337	12	)	)	PUNCT
iajs-2801	337	13	,	,	PUNCT
iajs-2801	337	14	(;	(;	PUNCT
iajs-2801	337	15	𝜆1	𝜆1	NOUN
iajs-2801	337	16	−	−	ADP
iajs-2801	337	17	×	×	NOUN
iajs-2801	337	18	;	;	PUNCT
iajs-2801	337	19	𝜆2	𝜆2	PROPN
iajs-2801	337	20	−	−	PROPN
iajs-2801	337	21	)	)	PUNCT
iajs-2801	337	22	(;	(;	PUNCT
iajs-2801	337	23	𝛽	𝛽	NOUN
iajs-2801	337	24	1	1	NUM
iajs-2801	337	25	,	,	PUNCT
iajs-2801	337	26	𝛽	𝛽	PROPN
iajs-2801	337	27	2	2	NUM
iajs-2801	337	28	;	;	PUNCT
iajs-2801	337	29	)	)	PUNCT
iajs-2801	337	30	}	}	PUNCT
iajs-2801	337	31	(;	(;	PUNCT
iajs-2801	337	32	𝜆1	𝜆1	NOUN
iajs-2801	337	33	−	−	ADP
iajs-2801	337	34	×	×	NOUN
iajs-2801	337	35	;	;	PUNCT
iajs-2801	337	36	𝜆2	𝜆2	NOUN
iajs-2801	337	37	−	−	PROPN
iajs-2801	337	38	;	;	PUNCT
iajs-2801	337	39	)	)	PUNCT
iajs-2801	337	40	(	(	PUNCT
iajs-2801	337	41	𝛼1	𝛼1	NOUN
iajs-2801	337	42	∘	∘	NOUN
iajs-2801	337	43	𝛽	𝛽	NOUN
iajs-2801	337	44	1	1	NUM
iajs-2801	337	45	,	,	PUNCT
iajs-2801	337	46	𝛼2	𝛼2	VERB
iajs-2801	337	47	∘	∘	NOUN
iajs-2801	337	48	𝛽	𝛽	ADP
iajs-2801	337	49	2	2	NUM
iajs-2801	337	50	)	)	PUNCT
iajs-2801	337	51	≤	≤	NUM
iajs-2801	337	52	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	337	53	{	{	PUNCT
iajs-2801	337	54	(;	(;	ADJ
iajs-2801	337	55	𝜆1	𝜆1	NOUN
iajs-2801	338	1	−	−	PROPN
iajs-2801	338	2	×	×	NOUN
iajs-2801	338	3	;	;	PUNCT
iajs-2801	338	4	𝜆2	𝜆2	NOUN
iajs-2801	338	5	−	−	PROPN
iajs-2801	338	6	;	;	PUNCT
iajs-2801	338	7	)	)	PUNCT
iajs-2801	338	8	(	(	PUNCT
iajs-2801	338	9	𝛼1	𝛼1	NOUN
iajs-2801	338	10	,	,	PUNCT
iajs-2801	338	11	𝛼2	𝛼2	PROPN
iajs-2801	338	12	)	)	PUNCT
iajs-2801	338	13	,	,	PUNCT
iajs-2801	338	14	(;	(;	PUNCT
iajs-2801	338	15	𝜆1	𝜆1	NOUN
iajs-2801	338	16	−	−	ADP
iajs-2801	338	17	×	×	NOUN
iajs-2801	338	18	;	;	PUNCT
iajs-2801	338	19	𝜆2	𝜆2	NOUN
iajs-2801	338	20	−	−	PROPN
iajs-2801	338	21	;	;	PUNCT
iajs-2801	338	22	)	)	PUNCT
iajs-2801	338	23	(	(	PUNCT
iajs-2801	338	24	𝛽	𝛽	NOUN
iajs-2801	338	25	1	1	NUM
iajs-2801	338	26	,	,	PUNCT
iajs-2801	338	27	𝛽	𝛽	NOUN
iajs-2801	338	28	2	2	NUM
iajs-2801	338	29	)	)	PUNCT
iajs-2801	338	30	}	}	PUNCT
iajs-2801	338	31	put	put	VERB
iajs-2801	338	32	𝛼1	𝛼1	NOUN
iajs-2801	338	33	=	=	SYM
iajs-2801	338	34	𝛽1	𝛽1	NOUN
iajs-2801	338	35	=	=	SYM
iajs-2801	338	36	0	0	NUM
iajs-2801	338	37	,	,	PUNCT
iajs-2801	338	38	then	then	ADV
iajs-2801	338	39	we	we	PRON
iajs-2801	338	40	have	have	VERB
iajs-2801	338	41	(;	(;	PUNCT
iajs-2801	339	1	𝜆1	𝜆1	VERB
iajs-2801	339	2	−	−	PROPN
iajs-2801	339	3	×	×	NOUN
iajs-2801	339	4	;	;	PUNCT
iajs-2801	339	5	𝜆2	𝜆2	PROPN
iajs-2801	339	6	−)(0	−)(0	NOUN
iajs-2801	339	7	,	,	PUNCT
iajs-2801	339	8	𝛼2	𝛼2	VERB
iajs-2801	339	9	∘	∘	NOUN
iajs-2801	339	10	𝛽	𝛽	ADP
iajs-2801	339	11	2	2	NUM
iajs-2801	339	12	)	)	PUNCT
iajs-2801	339	13	≤	≤	NUM
iajs-2801	339	14	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
iajs-2801	339	15	{	{	PUNCT
iajs-2801	339	16	(;	(;	ADJ
iajs-2801	339	17	𝜆1	𝜆1	NOUN
iajs-2801	340	1	−	−	PROPN
iajs-2801	340	2	×	×	NOUN
iajs-2801	340	3	;	;	PUNCT
iajs-2801	340	4	𝜆2	𝜆2	NOUN
iajs-2801	340	5	−	−	PROPN
iajs-2801	340	6	;	;	PUNCT
iajs-2801	340	7	)	)	PUNCT
iajs-2801	340	8	(	(	PUNCT
iajs-2801	340	9	0	0	NUM
iajs-2801	340	10	,	,	PUNCT
iajs-2801	340	11	𝛼2	𝛼2	PROPN
iajs-2801	340	12	)	)	PUNCT
iajs-2801	340	13	,	,	PUNCT
iajs-2801	340	14	(;	(;	PUNCT
iajs-2801	341	1	𝜆1	𝜆1	NOUN
iajs-2801	341	2	−	−	ADP
iajs-2801	341	3	×	×	NOUN
iajs-2801	341	4	;	;	PUNCT
iajs-2801	341	5	𝜆2	𝜆2	NOUN
iajs-2801	341	6	−	−	PROPN
iajs-2801	341	7	;	;	PUNCT
iajs-2801	341	8	)	)	PUNCT
iajs-2801	341	9	(	(	PUNCT
iajs-2801	341	10	0	0	NUM
iajs-2801	341	11	,	,	PUNCT
iajs-2801	341	12	𝛽	𝛽	NOUN
iajs-2801	341	13	2	2	NUM
iajs-2801	341	14	)	)	PUNCT
iajs-2801	341	15	}	}	PUNCT
iajs-2801	341	16	and	and	CCONJ
iajs-2801	341	17	by	by	ADP
iajs-2801	341	18	using	use	VERB
iajs-2801	341	19	equation	equation	NOUN
iajs-2801	341	20	(	(	PUNCT
iajs-2801	341	21	4	4	NUM
iajs-2801	341	22	)	)	PUNCT
iajs-2801	341	23	,	,	PUNCT
iajs-2801	341	24	we	we	PRON
iajs-2801	341	25	have	have	VERB
iajs-2801	341	26	𝜆2	𝜆2	NOUN
iajs-2801	341	27	−(𝛼2	−(𝛼2	PRON
iajs-2801	341	28	∘	∘	PROPN
iajs-2801	341	29	𝛽2	𝛽2	PROPN
iajs-2801	341	30	)	)	PUNCT
iajs-2801	341	31	≤	≤	NOUN
iajs-2801	341	32	𝑚𝑎𝑥{𝜆2	𝑚𝑎𝑥{𝜆2	X
iajs-2801	341	33	−(𝛼2	−(𝛼2	NOUN
iajs-2801	341	34	)	)	PUNCT
iajs-2801	341	35	,	,	PUNCT
iajs-2801	341	36	𝜆2	𝜆2	PROPN
iajs-2801	341	37	−(𝛽2	−(𝛽2	NUM
iajs-2801	341	38	)	)	PUNCT
iajs-2801	341	39	}	}	PUNCT
iajs-2801	341	40	ibn	ibn	PROPN
iajs-2801	341	41	al	al	PROPN
iajs-2801	341	42	-	-	PUNCT
iajs-2801	341	43	haitham	haitham	PROPN
iajs-2801	341	44	jour	jour	X
iajs-2801	341	45	.	.	PROPN
iajs-2801	341	46	for	for	ADP
iajs-2801	341	47	pure	pure	ADJ
iajs-2801	341	48	&	&	CCONJ
iajs-2801	341	49	appl	appl	PROPN
iajs-2801	341	50	.	.	PUNCT
iajs-2801	342	1	sci	sci	PROPN
iajs-2801	342	2	.	.	PUNCT
iajs-2801	343	1	35(1)2022	35(1)2022	NUM
iajs-2801	343	2	83	83	NUM
iajs-2801	343	3	then	then	ADV
iajs-2801	343	4	,	,	PUNCT
iajs-2801	343	5	it	it	PRON
iajs-2801	343	6	follows	follow	VERB
iajs-2801	343	7	that	that	SCONJ
iajs-2801	343	8	ωf2	ωf2	NOUN
iajs-2801	343	9	is	be	AUX
iajs-2801	343	10	acb	acb	NOUN
iajs-2801	343	11	ideal	ideal	NOUN
iajs-2801	343	12	of	of	ADP
iajs-2801	343	13	ℵ.	ℵ.	PROPN
iajs-2801	343	14	this	this	PRON
iajs-2801	343	15	completes	complete	VERB
iajs-2801	343	16	the	the	DET
iajs-2801	343	17	proof	proof	NOUN
iajs-2801	343	18	.	.	PUNCT
iajs-2801	344	1	references	reference	NOUN
iajs-2801	344	2	1	1	NUM
iajs-2801	344	3	.	.	PUNCT
iajs-2801	344	4	prabpayak	prabpayak	NOUN
iajs-2801	344	5	,	,	PUNCT
iajs-2801	344	6	c.	c.	PROPN
iajs-2801	344	7	;	;	PUNCT
iajs-2801	344	8	leerawat	leerawat	NOUN
iajs-2801	344	9	.	.	PUNCT
iajs-2801	345	1	u.	u.	VERB
iajs-2801	345	2	on	on	ADP
iajs-2801	345	3	ideals	ideal	NOUN
iajs-2801	345	4	and	and	CCONJ
iajs-2801	345	5	congruence	congruence	NOUN
iajs-2801	345	6	in	in	ADP
iajs-2801	345	7	ku	ku	PROPN
iajs-2801	345	8	-	-	PUNCT
iajs-2801	345	9	algebras	algebras	PROPN
iajs-2801	345	10	.	.	PUNCT
iajs-2801	346	1	scientia	scientia	PROPN
iajs-2801	346	2	magna	magna	PROPN
iajs-2801	346	3	.	.	PUNCT
iajs-2801	346	4	2009	2009	NUM
iajs-2801	346	5	,	,	PUNCT
iajs-2801	346	6	5	5	NUM
iajs-2801	346	7	,	,	PUNCT
iajs-2801	346	8	1	1	NUM
iajs-2801	346	9	,	,	PUNCT
iajs-2801	346	10	54	54	NUM
iajs-2801	346	11	-	-	SYM
iajs-2801	346	12	57	57	NUM
iajs-2801	346	13	.	.	X
iajs-2801	347	1	2	2	NUM
iajs-2801	347	2	.	.	X
iajs-2801	347	3	prabpayak	prabpayak	NOUN
iajs-2801	347	4	,	,	PUNCT
iajs-2801	347	5	c.	c.	PROPN
iajs-2801	347	6	;	;	PUNCT
iajs-2801	347	7	leerawat	leerawat	NOUN
iajs-2801	347	8	,	,	PUNCT
iajs-2801	347	9	u.	u.	PROPN
iajs-2801	347	10	on	on	ADP
iajs-2801	347	11	isomorphisms	isomorphism	NOUN
iajs-2801	347	12	of	of	ADP
iajs-2801	347	13	ku	ku	PROPN
iajs-2801	347	14	-	-	PUNCT
iajs-2801	347	15	algebras	algebras	PROPN
iajs-2801	347	16	.	.	PUNCT
iajs-2801	348	1	scientia	scientia	PROPN
iajs-2801	348	2	magna	magna	PROPN
iajs-2801	348	3	(	(	PUNCT
iajs-2801	348	4	international	international	ADJ
iajs-2801	348	5	book	book	NOUN
iajs-2801	348	6	series	series	PROPN
iajs-2801	348	7	)	)	PUNCT
iajs-2801	348	8	.	.	PUNCT
iajs-2801	349	1	2009	2009	NUM
iajs-2801	349	2	.	.	PUNCT
iajs-2801	350	1	5	5	NUM
iajs-2801	350	2	,	,	PUNCT
iajs-2801	350	3	3	3	NUM
iajs-2801	350	4	,	,	PUNCT
iajs-2801	350	5	25	25	NUM
iajs-2801	350	6	-	-	SYM
iajs-2801	350	7	31	31	NUM
iajs-2801	350	8	.	.	PUNCT
iajs-2801	351	1	3	3	X
iajs-2801	351	2	.	.	X
iajs-2801	351	3	mostafa	mostafa	PROPN
iajs-2801	351	4	,	,	PUNCT
iajs-2801	351	5	s.m	s.m	PROPN
iajs-2801	351	6	.	.	PROPN
iajs-2801	351	7	;	;	PUNCT
iajs-2801	351	8	abd	abd	PROPN
iajs-2801	351	9	-	-	PUNCT
iajs-2801	351	10	elnaby	elnaby	PROPN
iajs-2801	351	11	,	,	PUNCT
iajs-2801	351	12	m.a	m.a	PROPN
iajs-2801	351	13	.	.	PROPN
iajs-2801	351	14	;	;	PUNCT
iajs-2801	352	1	yousef	yousef	PROPN
iajs-2801	352	2	,	,	PUNCT
iajs-2801	352	3	m.m.m	m.m.m	INTJ
iajs-2801	352	4	.	.	PUNCT
iajs-2801	352	5	fuzzy	fuzzy	ADJ
iajs-2801	352	6	ideals	ideal	NOUN
iajs-2801	352	7	of	of	ADP
iajs-2801	352	8	ku	ku	PROPN
iajs-2801	352	9	-	-	PUNCT
iajs-2801	352	10	algebras	algebras	PROPN
iajs-2801	352	11	.	.	PUNCT
iajs-2801	353	1	int	int	NOUN
iajs-2801	353	2	.	.	PUNCT
iajs-2801	354	1	math	math	PROPN
iajs-2801	354	2	,	,	PUNCT
iajs-2801	354	3	forum	forum	PROPN
iajs-2801	354	4	.	.	PROPN
iajs-2801	355	1	2011	2011	NUM
iajs-2801	355	2	.	.	PUNCT
iajs-2801	356	1	6	6	NUM
iajs-2801	356	2	,	,	PUNCT
iajs-2801	356	3	63	63	NUM
iajs-2801	356	4	,	,	PUNCT
iajs-2801	356	5	3139	3139	NUM
iajs-2801	356	6	-	-	SYM
iajs-2801	356	7	3149	3149	NUM
iajs-2801	356	8	.	.	PUNCT
iajs-2801	357	1	4	4	X
iajs-2801	357	2	.	.	X
iajs-2801	357	3	mostafa	mostafa	PROPN
iajs-2801	357	4	,	,	PUNCT
iajs-2801	357	5	s.m	s.m	PROPN
iajs-2801	357	6	.	.	PROPN
iajs-2801	357	7	;	;	PUNCT
iajs-2801	357	8	abd	abd	PROPN
iajs-2801	357	9	-	-	PUNCT
iajs-2801	357	10	elnaby	elnaby	PROPN
iajs-2801	357	11	,	,	PUNCT
iajs-2801	357	12	m.a	m.a	PROPN
iajs-2801	357	13	.	.	PROPN
iajs-2801	357	14	;	;	PUNCT
iajs-2801	357	15	elgendy	elgendy	ADJ
iajs-2801	357	16	,	,	PUNCT
iajs-2801	357	17	o.	o.	PROPN
iajs-2801	357	18	r.	r.	PROPN
iajs-2801	357	19	interval	interval	PROPN
iajs-2801	357	20	-	-	PUNCT
iajs-2801	357	21	valued	value	VERB
iajs-2801	357	22	fuzzy	fuzzy	ADJ
iajs-2801	357	23	ku	ku	NOUN
iajs-2801	357	24	-	-	PUNCT
iajs-2801	357	25	ideals	ideal	NOUN
iajs-2801	357	26	in	in	ADP
iajs-2801	357	27	ku	ku	PROPN
iajs-2801	357	28	-	-	PUNCT
iajs-2801	357	29	algebras	algebras	PROPN
iajs-2801	357	30	.	.	PUNCT
iajs-2801	358	1	int	int	NOUN
iajs-2801	358	2	.	.	PUNCT
iajs-2801	359	1	math	math	PROPN
iajs-2801	359	2	,	,	PUNCT
iajs-2801	359	3	forum	forum	PROPN
iajs-2801	359	4	.	.	PROPN
iajs-2801	360	1	2011	2011	NUM
iajs-2801	360	2	.	.	PUNCT
iajs-2801	361	1	6	6	NUM
iajs-2801	361	2	,	,	PUNCT
iajs-2801	361	3	64	64	NUM
iajs-2801	361	4	,	,	PUNCT
iajs-2801	361	5	3151	3151	NUM
iajs-2801	361	6	-	-	SYM
iajs-2801	361	7	3159	3159	NUM
iajs-2801	361	8	.	.	PUNCT
iajs-2801	362	1	5	5	X
iajs-2801	362	2	.	.	X
iajs-2801	362	3	kareem	kareem	PROPN
iajs-2801	362	4	,	,	PUNCT
iajs-2801	362	5	f.f	f.f	PROPN
iajs-2801	362	6	.	.	PROPN
iajs-2801	362	7	;	;	PUNCT
iajs-2801	362	8	hasan	hasan	PROPN
iajs-2801	362	9	,	,	PUNCT
iajs-2801	362	10	e.r	e.r	PROPN
iajs-2801	362	11	.	.	PROPN
iajs-2801	362	12	on	on	ADP
iajs-2801	362	13	ku	ku	PROPN
iajs-2801	362	14	-	-	PUNCT
iajs-2801	362	15	semigroups	semigroup	NOUN
iajs-2801	362	16	.	.	PUNCT
iajs-2801	363	1	international	international	ADJ
iajs-2801	363	2	journal	journal	PROPN
iajs-2801	363	3	of	of	ADP
iajs-2801	363	4	science	science	NOUN
iajs-2801	363	5	and	and	CCONJ
iajs-2801	363	6	nature	nature	NOUN
iajs-2801	363	7	.	.	PUNCT
iajs-2801	364	1	2018	2018	NUM
iajs-2801	364	2	.	.	X
iajs-2801	365	1	1	1	NUM
iajs-2801	365	2	,	,	PUNCT
iajs-2801	365	3	9	9	NUM
iajs-2801	365	4	,	,	PUNCT
iajs-2801	365	5	79	79	NUM
iajs-2801	365	6	-	-	SYM
iajs-2801	365	7	84	84	NUM
iajs-2801	365	8	.	.	PUNCT
iajs-2801	366	1	6	6	NUM
iajs-2801	366	2	.	.	X
iajs-2801	367	1	hasan	hasan	PROPN
iajs-2801	367	2	,	,	PUNCT
iajs-2801	367	3	e.	e.	PROPN
iajs-2801	367	4	r.	r.	PROPN
iajs-2801	367	5	;	;	PUNCT
iajs-2801	367	6	kareem	kareem	PROPN
iajs-2801	367	7	,	,	PUNCT
iajs-2801	367	8	f.f	f.f	PROPN
iajs-2801	367	9	.	.	PROPN
iajs-2801	367	10	fuzzy	fuzzy	PROPN
iajs-2801	367	11	ku	ku	PROPN
iajs-2801	367	12	-	-	PUNCT
iajs-2801	367	13	semi	semi	NOUN
iajs-2801	367	14	-	-	NOUN
iajs-2801	367	15	groups	group	NOUN
iajs-2801	367	16	and	and	CCONJ
iajs-2801	367	17	investigate	investigate	VERB
iajs-2801	367	18	some	some	DET
iajs-2801	367	19	basic	basic	ADJ
iajs-2801	367	20	properties	property	NOUN
iajs-2801	367	21	,	,	PUNCT
iajs-2801	367	22	journal	journal	NOUN
iajs-2801	367	23	of	of	ADP
iajs-2801	367	24	engineering	engineering	NOUN
iajs-2801	367	25	and	and	CCONJ
iajs-2801	367	26	applied	apply	VERB
iajs-2801	367	27	science	science	NOUN
iajs-2801	367	28	.	.	PUNCT
iajs-2801	368	1	2018	2018	NUM
iajs-2801	368	2	.	.	PUNCT
iajs-2801	369	1	13	13	NUM
iajs-2801	369	2	,	,	PUNCT
iajs-2801	369	3	18	18	NUM
iajs-2801	369	4	,	,	PUNCT
iajs-2801	369	5	7739	7739	NUM
iajs-2801	369	6	-	-	SYM
iajs-2801	369	7	7744	7744	NUM
iajs-2801	369	8	.	.	PUNCT
iajs-2801	370	1	7	7	X
iajs-2801	370	2	.	.	X
iajs-2801	370	3	kareem	kareem	PROPN
iajs-2801	370	4	,	,	PUNCT
iajs-2801	370	5	f.f	f.f	PROPN
iajs-2801	370	6	.	.	PROPN
iajs-2801	370	7	;	;	PUNCT
iajs-2801	370	8	talib	talib	PROPN
iajs-2801	370	9	,	,	PUNCT
iajs-2801	370	10	s.a	s.a	PROPN
iajs-2801	370	11	.	.	PROPN
iajs-2801	370	12	interval	interval	NOUN
iajs-2801	370	13	value	value	NOUN
iajs-2801	370	14	fuzzy	fuzzy	ADJ
iajs-2801	370	15	k	k	NOUN
iajs-2801	370	16	-	-	NOUN
iajs-2801	370	17	ideal	ideal	NOUN
iajs-2801	370	18	of	of	ADP
iajs-2801	370	19	a	a	DET
iajs-2801	370	20	ku	ku	PROPN
iajs-2801	370	21	-	-	PUNCT
iajs-2801	370	22	semigroup	semigroup	PROPN
iajs-2801	370	23	,	,	PUNCT
iajs-2801	370	24	ibn	ibn	PROPN
iajs-2801	370	25	alhaitham	alhaitham	NOUN
iajs-2801	370	26	jour	jour	NOUN
iajs-2801	370	27	for	for	ADP
iajs-2801	370	28	pure	pure	ADJ
iajs-2801	370	29	&	&	CCONJ
iajs-2801	370	30	appl	appl	PROPN
iajs-2801	370	31	.	.	PUNCT
iajs-2801	371	1	sci	sci	PROPN
iajs-2801	371	2	.	.	PUNCT
iajs-2801	371	3	2020	2020	NUM
iajs-2801	371	4	.	.	PUNCT
iajs-2801	372	1	33	33	NUM
iajs-2801	372	2	,	,	PUNCT
iajs-2801	372	3	2	2	NUM
iajs-2801	372	4	,	,	PUNCT
iajs-2801	372	5	95	95	NUM
iajs-2801	372	6	-	-	SYM
iajs-2801	372	7	106	106	NUM
iajs-2801	372	8	.	.	PUNCT
iajs-2801	373	1	8	8	NUM
iajs-2801	373	2	.	.	X
iajs-2801	374	1	jun	jun	PROPN
iajs-2801	374	2	,	,	PUNCT
iajs-2801	374	3	y.	y.	PROPN
iajs-2801	374	4	b.	b.	PROPN
iajs-2801	374	5	;	;	PUNCT
iajs-2801	374	6	kim	kim	PROPN
iajs-2801	374	7	,	,	PUNCT
iajs-2801	374	8	c.	c.	PROPN
iajs-2801	374	9	s.	s.	PROPN
iajs-2801	374	10	;	;	PUNCT
iajs-2801	374	11	kang	kang	PROPN
iajs-2801	374	12	,	,	PUNCT
iajs-2801	374	13	m.	m.	PROPN
iajs-2801	374	14	s.	s.	PROPN
iajs-2801	374	15	cubic	cubic	PROPN
iajs-2801	374	16	subalgebras	subalgebras	PROPN
iajs-2801	374	17	and	and	CCONJ
iajs-2801	374	18	ideals	ideal	NOUN
iajs-2801	374	19	of	of	ADP
iajs-2801	374	20	bck	bck	PROPN
iajs-2801	374	21	/bci	/bci	NOUN
iajs-2801	374	22	-	-	PUNCT
iajs-2801	374	23	algebras	algebras	PROPN
iajs-2801	374	24	.	.	PUNCT
iajs-2801	375	1	far	far	PROPN
iajs-2801	375	2	east	east	PROPN
iajs-2801	375	3	journal	journal	PROPN
iajs-2801	375	4	of	of	ADP
iajs-2801	375	5	mathematical	mathematical	ADJ
iajs-2801	375	6	sciences	science	NOUN
iajs-2801	375	7	,	,	PUNCT
iajs-2801	375	8	2010	2010	NUM
iajs-2801	375	9	.	.	PUNCT
iajs-2801	376	1	2	2	NUM
iajs-2801	376	2	,	,	PUNCT
iajs-2801	376	3	44	44	NUM
iajs-2801	376	4	,	,	PUNCT
iajs-2801	376	5	239–250	239–250	NUM
iajs-2801	376	6	.	.	PUNCT
iajs-2801	377	1	9	9	NUM
iajs-2801	377	2	.	.	X
iajs-2801	377	3	jun	jun	PROPN
iajs-2801	377	4	,	,	PUNCT
iajs-2801	377	5	y.	y.	PROPN
iajs-2801	377	6	b.	b.	PROPN
iajs-2801	377	7	;	;	PUNCT
iajs-2801	377	8	kim	kim	PROPN
iajs-2801	377	9	c.	c.	PROPN
iajs-2801	377	10	s.	s.	PROPN
iajs-2801	377	11	;	;	PUNCT
iajs-2801	377	12	yang	yang	PROPN
iajs-2801	377	13	,	,	PUNCT
iajs-2801	377	14	k.o	k.o	PROPN
iajs-2801	377	15	.	.	PROPN
iajs-2801	377	16	cubic	cubic	ADJ
iajs-2801	377	17	sets	set	NOUN
iajs-2801	377	18	,	,	PUNCT
iajs-2801	377	19	annals	annal	NOUN
iajs-2801	377	20	of	of	ADP
iajs-2801	377	21	fuzzy	fuzzy	ADJ
iajs-2801	377	22	mathematics	mathematic	NOUN
iajs-2801	377	23	and	and	CCONJ
iajs-2801	377	24	informatics	informatic	NOUN
iajs-2801	377	25	.	.	PUNCT
iajs-2801	377	26	2012	2012	NUM
iajs-2801	377	27	.	.	PUNCT
iajs-2801	378	1	1	1	NUM
iajs-2801	378	2	,	,	PUNCT
iajs-2801	378	3	4	4	NUM
iajs-2801	378	4	,	,	PUNCT
iajs-2801	378	5	83–98	83–98	NUM
iajs-2801	378	6	.	.	PUNCT
iajs-2801	379	1	10	10	NUM
iajs-2801	379	2	.	.	X
iajs-2801	380	1	yaqoob	yaqoob	NOUN
iajs-2801	380	2	,	,	PUNCT
iajs-2801	380	3	n.	n.	PROPN
iajs-2801	380	4	;	;	PUNCT
iajs-2801	380	5	mostafa	mostafa	PROPN
iajs-2801	380	6	,	,	PUNCT
iajs-2801	380	7	s.	s.	PROPN
iajs-2801	380	8	m.	m.	PROPN
iajs-2801	380	9	;	;	PUNCT
iajs-2801	380	10	ansari	ansari	ADJ
iajs-2801	380	11	,	,	PUNCT
iajs-2801	380	12	m.	m.	NOUN
iajs-2801	380	13	a.	a.	NOUN
iajs-2801	380	14	on	on	ADP
iajs-2801	380	15	cubic	cubic	PROPN
iajs-2801	380	16	ku	ku	PROPN
iajs-2801	380	17	-	-	PUNCT
iajs-2801	380	18	ideals	ideal	NOUN
iajs-2801	380	19	of	of	ADP
iajs-2801	380	20	kualgebras	kualgebra	NOUN
iajs-2801	380	21	.	.	PUNCT
iajs-2801	381	1	international	international	ADJ
iajs-2801	381	2	scholarly	scholarly	ADJ
iajs-2801	381	3	research	research	NOUN
iajs-2801	381	4	notices	notice	NOUN
iajs-2801	381	5	,	,	PUNCT
iajs-2801	381	6	2013	2013	NUM
iajs-2801	381	7	.	.	PUNCT
iajs-2801	382	1	11	11	NUM
iajs-2801	382	2	.	.	PUNCT
iajs-2801	382	3	kareem	kareem	PROPN
iajs-2801	382	4	f.	f.	PROPN
iajs-2801	382	5	f.	f.	PROPN
iajs-2801	382	6	;	;	PUNCT
iajs-2801	382	7	awad	awad	PROPN
iajs-2801	382	8	,	,	PUNCT
iajs-2801	382	9	w.	w.	PROPN
iajs-2801	382	10	k.	k.	PROPN
iajs-2801	382	11	cubic	cubic	PROPN
iajs-2801	382	12	bipolar	bipolar	ADJ
iajs-2801	382	13	ideals	ideal	NOUN
iajs-2801	382	14	of	of	ADP
iajs-2801	382	15	a	a	DET
iajs-2801	382	16	semigroup	semigroup	NOUN
iajs-2801	382	17	in	in	ADP
iajs-2801	382	18	ku	ku	PROPN
iajs-2801	382	19	-	-	PUNCT
iajs-2801	382	20	algebra	algebra	PROPN
iajs-2801	382	21	,	,	PUNCT
iajs-2801	382	22	accepted	accept	VERB
iajs-2801	382	23	for	for	ADP
iajs-2801	382	24	aip	aip	PROPN
iajs-2801	382	25	conference	conference	NOUN
iajs-2801	382	26	ser	ser	NOUN
iajs-2801	382	27	.	.	PROPN
iajs-2801	382	28	2021	2021	NUM
iajs-2801	382	29	.	.	PUNCT