id	sid	tid	token	lemma	pos
ejpam-6538	1	1	european	european	PROPN
ejpam-6538	1	2	journal	journal	PROPN
ejpam-6538	1	3	of	of	ADP
ejpam-6538	1	4	pure	pure	ADJ
ejpam-6538	1	5	and	and	CCONJ
ejpam-6538	1	6	applied	applied	ADJ
ejpam-6538	1	7	mathematics	mathematic	NOUN
ejpam-6538	1	8	2025	2025	NUM
ejpam-6538	1	9	,	,	PUNCT
ejpam-6538	1	10	vol	vol	NOUN
ejpam-6538	1	11	.	.	PROPN
ejpam-6538	1	12	18	18	NUM
ejpam-6538	1	13	,	,	PUNCT
ejpam-6538	1	14	issue	issue	NOUN
ejpam-6538	1	15	3	3	NUM
ejpam-6538	1	16	,	,	PUNCT
ejpam-6538	1	17	article	article	NOUN
ejpam-6538	1	18	number	number	NOUN
ejpam-6538	1	19	6538	6538	NUM
ejpam-6538	1	20	issn	issn	PROPN
ejpam-6538	1	21	1307	1307	NUM
ejpam-6538	1	22	-	-	SYM
ejpam-6538	1	23	5543	5543	NUM
ejpam-6538	1	24	–	–	PUNCT
ejpam-6538	1	25	ejpam.com	ejpam.com	X
ejpam-6538	1	26	published	publish	VERB
ejpam-6538	1	27	by	by	ADP
ejpam-6538	1	28	new	new	PROPN
ejpam-6538	1	29	york	york	PROPN
ejpam-6538	1	30	business	business	PROPN
ejpam-6538	1	31	global	global	PROPN
ejpam-6538	1	32	an	an	DET
ejpam-6538	1	33	mpp	mpp	NOUN
ejpam-6538	1	34	monounary	monounary	PROPN
ejpam-6538	1	35	algebra	algebra	PROPN
ejpam-6538	1	36	induced	induce	VERB
ejpam-6538	1	37	by	by	ADP
ejpam-6538	1	38	an	an	DET
ejpam-6538	1	39	endomorphism	endomorphism	NOUN
ejpam-6538	1	40	of	of	ADP
ejpam-6538	1	41	the	the	DET
ejpam-6538	1	42	direct	direct	ADJ
ejpam-6538	1	43	product	product	NOUN
ejpam-6538	1	44	of	of	ADP
ejpam-6538	1	45	two	two	NUM
ejpam-6538	1	46	chains	chain	NOUN
ejpam-6538	1	47	aveya	aveya	PROPN
ejpam-6538	1	48	charoenpol1	charoenpol1	PROPN
ejpam-6538	1	49	,	,	PUNCT
ejpam-6538	1	50	udom	udom	PROPN
ejpam-6538	1	51	chotwattakawanit2,∗	chotwattakawanit2,∗	ADJ
ejpam-6538	1	52	1	1	NUM
ejpam-6538	1	53	division	division	NOUN
ejpam-6538	1	54	of	of	ADP
ejpam-6538	1	55	mathematics	mathematic	NOUN
ejpam-6538	1	56	,	,	PUNCT
ejpam-6538	1	57	faculty	faculty	NOUN
ejpam-6538	1	58	of	of	ADP
ejpam-6538	1	59	engineering	engineering	NOUN
ejpam-6538	1	60	,	,	PUNCT
ejpam-6538	1	61	rajamangala	rajamangala	PROPN
ejpam-6538	1	62	university	university	PROPN
ejpam-6538	1	63	of	of	ADP
ejpam-6538	1	64	technology	technology	PROPN
ejpam-6538	1	65	isan	isan	PROPN
ejpam-6538	1	66	khonkaen	khonkaen	PROPN
ejpam-6538	1	67	campus	campus	PROPN
ejpam-6538	1	68	,	,	PUNCT
ejpam-6538	1	69	khon	khon	PROPN
ejpam-6538	1	70	kaen	kaen	PROPN
ejpam-6538	1	71	40000	40000	NUM
ejpam-6538	1	72	,	,	PUNCT
ejpam-6538	1	73	thailand	thailand	PROPN
ejpam-6538	1	74	.	.	PROPN
ejpam-6538	2	1	2	2	NUM
ejpam-6538	2	2	department	department	NOUN
ejpam-6538	2	3	of	of	ADP
ejpam-6538	2	4	mathematics	mathematic	NOUN
ejpam-6538	2	5	,	,	PUNCT
ejpam-6538	2	6	faculty	faculty	NOUN
ejpam-6538	2	7	of	of	ADP
ejpam-6538	2	8	science	science	NOUN
ejpam-6538	2	9	,	,	PUNCT
ejpam-6538	2	10	khon	khon	PROPN
ejpam-6538	2	11	kaen	kaen	PROPN
ejpam-6538	2	12	university	university	PROPN
ejpam-6538	2	13	,	,	PUNCT
ejpam-6538	2	14	khon	khon	PROPN
ejpam-6538	2	15	kaen	kaen	PROPN
ejpam-6538	2	16	40002	40002	NUM
ejpam-6538	2	17	,	,	PUNCT
ejpam-6538	2	18	thailand	thailand	PROPN
ejpam-6538	2	19	.	.	PUNCT
ejpam-6538	3	1	abstract	abstract	PROPN
ejpam-6538	3	2	.	.	PUNCT
ejpam-6538	4	1	a	a	DET
ejpam-6538	4	2	finite	finite	ADJ
ejpam-6538	4	3	modular	modular	ADJ
ejpam-6538	4	4	lattice	lattice	NOUN
ejpam-6538	4	5	a	a	PRON
ejpam-6538	4	6	is	be	AUX
ejpam-6538	4	7	said	say	VERB
ejpam-6538	4	8	to	to	PART
ejpam-6538	4	9	be	be	AUX
ejpam-6538	4	10	mpp	mpp	NOUN
ejpam-6538	4	11	if	if	SCONJ
ejpam-6538	4	12	there	there	PRON
ejpam-6538	4	13	is	be	VERB
ejpam-6538	4	14	an	an	DET
ejpam-6538	4	15	endomorphism	endomorphism	NOUN
ejpam-6538	4	16	,	,	PUNCT
ejpam-6538	4	17	called	call	VERB
ejpam-6538	4	18	an	an	DET
ejpam-6538	4	19	mpp	mpp	NOUN
ejpam-6538	4	20	endomorphism	endomorphism	NOUN
ejpam-6538	4	21	,	,	PUNCT
ejpam-6538	4	22	whose	whose	DET
ejpam-6538	4	23	the	the	DET
ejpam-6538	4	24	pre	pre	NOUN
ejpam-6538	4	25	-	-	NOUN
ejpam-6538	4	26	period	period	NOUN
ejpam-6538	4	27	is	be	AUX
ejpam-6538	4	28	equal	equal	ADJ
ejpam-6538	4	29	to	to	ADP
ejpam-6538	4	30	the	the	DET
ejpam-6538	4	31	length	length	NOUN
ejpam-6538	4	32	ofa	ofa	PROPN
ejpam-6538	4	33	.	.	PUNCT
ejpam-6538	5	1	a	a	DET
ejpam-6538	5	2	monounary	monounary	ADJ
ejpam-6538	5	3	algebra	algebra	NOUN
ejpam-6538	5	4	(	(	PUNCT
ejpam-6538	5	5	a	a	DET
ejpam-6538	5	6	,	,	PUNCT
ejpam-6538	5	7	f	f	X
ejpam-6538	5	8	)	)	PUNCT
ejpam-6538	5	9	is	be	AUX
ejpam-6538	5	10	said	say	VERB
ejpam-6538	5	11	to	to	PART
ejpam-6538	5	12	be	be	AUX
ejpam-6538	5	13	mpp	mpp	NOUN
ejpam-6538	5	14	if	if	SCONJ
ejpam-6538	5	15	f	f	PROPN
ejpam-6538	5	16	is	be	AUX
ejpam-6538	5	17	an	an	DET
ejpam-6538	5	18	mpp	mpp	NOUN
ejpam-6538	5	19	endomorphism	endomorphism	NOUN
ejpam-6538	5	20	of	of	ADP
ejpam-6538	5	21	a	a	DET
ejpam-6538	5	22	lattice	lattice	NOUN
ejpam-6538	5	23	a	a	PRON
ejpam-6538	5	24	,	,	PUNCT
ejpam-6538	5	25	called	call	VERB
ejpam-6538	5	26	an	an	DET
ejpam-6538	5	27	mpp	mpp	NOUN
ejpam-6538	5	28	corresponding	correspond	VERB
ejpam-6538	5	29	lattice	lattice	PROPN
ejpam-6538	5	30	to	to	ADP
ejpam-6538	5	31	(	(	PUNCT
ejpam-6538	5	32	a	a	PRON
ejpam-6538	5	33	,	,	PUNCT
ejpam-6538	5	34	f	f	NOUN
ejpam-6538	5	35	)	)	PUNCT
ejpam-6538	5	36	.	.	PUNCT
ejpam-6538	6	1	in	in	ADP
ejpam-6538	6	2	this	this	DET
ejpam-6538	6	3	work	work	NOUN
ejpam-6538	6	4	,	,	PUNCT
ejpam-6538	6	5	we	we	PRON
ejpam-6538	6	6	show	show	VERB
ejpam-6538	6	7	all	all	DET
ejpam-6538	6	8	mpp	mpp	NOUN
ejpam-6538	6	9	monounary	monounary	PROPN
ejpam-6538	6	10	algebras	algebras	PROPN
ejpam-6538	6	11	induced	induce	VERB
ejpam-6538	6	12	by	by	ADP
ejpam-6538	6	13	endomorphisms	endomorphism	NOUN
ejpam-6538	6	14	of	of	ADP
ejpam-6538	6	15	the	the	DET
ejpam-6538	6	16	direct	direct	ADJ
ejpam-6538	6	17	products	product	NOUN
ejpam-6538	6	18	of	of	ADP
ejpam-6538	6	19	two	two	NUM
ejpam-6538	6	20	chains	chain	NOUN
ejpam-6538	6	21	.	.	PUNCT
ejpam-6538	7	1	2020	2020	NUM
ejpam-6538	7	2	mathematics	mathematic	NOUN
ejpam-6538	7	3	subject	subject	NOUN
ejpam-6538	7	4	classifications	classification	NOUN
ejpam-6538	7	5	:	:	PUNCT
ejpam-6538	7	6	06c05	06c05	NUM
ejpam-6538	7	7	,	,	PUNCT
ejpam-6538	7	8	08a60	08a60	NUM
ejpam-6538	7	9	,	,	PUNCT
ejpam-6538	7	10	08a35	08a35	VERB
ejpam-6538	7	11	key	key	ADJ
ejpam-6538	7	12	words	word	NOUN
ejpam-6538	7	13	and	and	CCONJ
ejpam-6538	7	14	phrases	phrase	NOUN
ejpam-6538	7	15	:	:	PUNCT
ejpam-6538	7	16	pre	pre	ADJ
ejpam-6538	7	17	-	-	NOUN
ejpam-6538	7	18	period	period	NOUN
ejpam-6538	7	19	,	,	PUNCT
ejpam-6538	7	20	monounary	monounary	ADJ
ejpam-6538	7	21	algebra	algebra	NOUN
ejpam-6538	7	22	,	,	PUNCT
ejpam-6538	7	23	chain	chain	NOUN
ejpam-6538	7	24	,	,	PUNCT
ejpam-6538	7	25	endomorphism	endomorphism	X
ejpam-6538	7	26	1	1	NUM
ejpam-6538	7	27	.	.	PUNCT
ejpam-6538	7	28	introduction	introduction	NOUN
ejpam-6538	7	29	one	one	NUM
ejpam-6538	7	30	of	of	ADP
ejpam-6538	7	31	universal	universal	ADJ
ejpam-6538	7	32	algebras	algebra	NOUN
ejpam-6538	7	33	which	which	PRON
ejpam-6538	7	34	play	play	VERB
ejpam-6538	7	35	important	important	ADJ
ejpam-6538	7	36	roles	role	NOUN
ejpam-6538	7	37	to	to	PART
ejpam-6538	7	38	simplify	simplify	VERB
ejpam-6538	7	39	many	many	ADJ
ejpam-6538	7	40	problems	problem	NOUN
ejpam-6538	7	41	in	in	ADP
ejpam-6538	7	42	computer	computer	NOUN
ejpam-6538	7	43	science	science	NOUN
ejpam-6538	7	44	is	be	AUX
ejpam-6538	7	45	a	a	DET
ejpam-6538	7	46	monounary	monounary	ADJ
ejpam-6538	7	47	algebra	algebra	NOUN
ejpam-6538	7	48	.	.	PUNCT
ejpam-6538	8	1	it	it	PRON
ejpam-6538	8	2	is	be	AUX
ejpam-6538	8	3	often	often	ADV
ejpam-6538	8	4	considered	consider	VERB
ejpam-6538	8	5	as	as	ADP
ejpam-6538	8	6	a	a	DET
ejpam-6538	8	7	special	special	ADJ
ejpam-6538	8	8	type	type	NOUN
ejpam-6538	8	9	of	of	ADP
ejpam-6538	8	10	automata	automata	NOUN
ejpam-6538	8	11	(	(	PUNCT
ejpam-6538	8	12	see	see	VERB
ejpam-6538	8	13	e.g.	e.g.	ADV
ejpam-6538	8	14	in	in	ADP
ejpam-6538	8	15	[	[	X
ejpam-6538	8	16	1	1	NUM
ejpam-6538	8	17	,	,	PUNCT
ejpam-6538	8	18	2	2	NUM
ejpam-6538	8	19	]	]	NUM
ejpam-6538	8	20	)	)	PUNCT
ejpam-6538	8	21	.	.	PUNCT
ejpam-6538	9	1	the	the	DET
ejpam-6538	9	2	advantage	advantage	NOUN
ejpam-6538	9	3	of	of	ADP
ejpam-6538	9	4	monounary	monounary	ADJ
ejpam-6538	9	5	algebras	algebras	PROPN
ejpam-6538	9	6	is	be	AUX
ejpam-6538	9	7	their	their	PRON
ejpam-6538	9	8	easy	easy	ADJ
ejpam-6538	9	9	visualization	visualization	NOUN
ejpam-6538	9	10	;	;	PUNCT
ejpam-6538	9	11	especially	especially	ADV
ejpam-6538	9	12	,	,	PUNCT
ejpam-6538	9	13	they	they	PRON
ejpam-6538	9	14	can	can	AUX
ejpam-6538	9	15	be	be	AUX
ejpam-6538	9	16	represented	represent	VERB
ejpam-6538	9	17	as	as	ADP
ejpam-6538	9	18	planar	planar	ADJ
ejpam-6538	9	19	directed	direct	VERB
ejpam-6538	9	20	graphs	graph	NOUN
ejpam-6538	9	21	.	.	PUNCT
ejpam-6538	10	1	the	the	DET
ejpam-6538	10	2	important	important	ADJ
ejpam-6538	10	3	theories	theory	NOUN
ejpam-6538	10	4	of	of	ADP
ejpam-6538	10	5	unary	unary	ADJ
ejpam-6538	10	6	and	and	CCONJ
ejpam-6538	10	7	monounary	monounary	ADJ
ejpam-6538	10	8	algebras	algebra	NOUN
ejpam-6538	10	9	are	be	AUX
ejpam-6538	10	10	shown	show	VERB
ejpam-6538	10	11	in	in	ADP
ejpam-6538	10	12	many	many	ADJ
ejpam-6538	10	13	monographs	monograph	NOUN
ejpam-6538	10	14	;	;	PUNCT
ejpam-6538	10	15	for	for	ADP
ejpam-6538	10	16	instance	instance	NOUN
ejpam-6538	10	17	,	,	PUNCT
ejpam-6538	10	18	[	[	X
ejpam-6538	10	19	3	3	NUM
ejpam-6538	10	20	]	]	PUNCT
ejpam-6538	10	21	.	.	PUNCT
ejpam-6538	11	1	moreover	moreover	ADV
ejpam-6538	11	2	,	,	PUNCT
ejpam-6538	11	3	monounary	monounary	ADJ
ejpam-6538	11	4	algebras	algebra	NOUN
ejpam-6538	11	5	have	have	AUX
ejpam-6538	11	6	closed	close	VERB
ejpam-6538	11	7	relationships	relationship	NOUN
ejpam-6538	11	8	with	with	ADP
ejpam-6538	11	9	all	all	DET
ejpam-6538	11	10	algebras	algebra	NOUN
ejpam-6538	11	11	via	via	ADP
ejpam-6538	11	12	their	their	PRON
ejpam-6538	11	13	endomorphisms	endomorphism	NOUN
ejpam-6538	11	14	.	.	PUNCT
ejpam-6538	12	1	a	a	DET
ejpam-6538	12	2	monounary	monounary	ADJ
ejpam-6538	12	3	algebra	algebra	NOUN
ejpam-6538	12	4	is	be	AUX
ejpam-6538	12	5	a	a	DET
ejpam-6538	12	6	set	set	NOUN
ejpam-6538	12	7	a	a	DET
ejpam-6538	12	8	equipped	equip	VERB
ejpam-6538	12	9	with	with	ADP
ejpam-6538	12	10	a	a	DET
ejpam-6538	12	11	unary	unary	ADJ
ejpam-6538	12	12	operation	operation	NOUN
ejpam-6538	12	13	f	f	NOUN
ejpam-6538	12	14	:	:	PUNCT
ejpam-6538	12	15	a	a	DET
ejpam-6538	12	16	→	→	X
ejpam-6538	12	17	a	a	NOUN
ejpam-6538	12	18	and	and	CCONJ
ejpam-6538	12	19	it	it	PRON
ejpam-6538	12	20	is	be	AUX
ejpam-6538	12	21	denoted	denote	VERB
ejpam-6538	12	22	by	by	ADP
ejpam-6538	12	23	a	a	PRON
ejpam-6538	12	24	=	=	X
ejpam-6538	12	25	(	(	PUNCT
ejpam-6538	12	26	a	a	PRON
ejpam-6538	12	27	,	,	PUNCT
ejpam-6538	12	28	f	f	NOUN
ejpam-6538	12	29	)	)	PUNCT
ejpam-6538	12	30	.	.	PUNCT
ejpam-6538	13	1	denote	denote	PROPN
ejpam-6538	13	2	f0	f0	PROPN
ejpam-6538	13	3	is	be	AUX
ejpam-6538	13	4	the	the	DET
ejpam-6538	13	5	identity	identity	NOUN
ejpam-6538	13	6	map	map	NOUN
ejpam-6538	13	7	on	on	ADP
ejpam-6538	13	8	a	a	PRON
ejpam-6538	13	9	and	and	CCONJ
ejpam-6538	13	10	fn	fn	NOUN
ejpam-6538	13	11	=	=	SYM
ejpam-6538	13	12	f	f	PROPN
ejpam-6538	13	13	◦	◦	VERB
ejpam-6538	13	14	fn−1	fn−1	ADJ
ejpam-6538	13	15	for	for	ADP
ejpam-6538	13	16	all	all	PRON
ejpam-6538	13	17	n	n	DET
ejpam-6538	13	18	∈	∈	PROPN
ejpam-6538	13	19	n.	n.	NOUN
ejpam-6538	13	20	a	a	DET
ejpam-6538	13	21	monounary	monounary	ADJ
ejpam-6538	13	22	algebra	algebra	NOUN
ejpam-6538	13	23	a	a	PRON
ejpam-6538	13	24	is	be	AUX
ejpam-6538	13	25	said	say	VERB
ejpam-6538	13	26	to	to	PART
ejpam-6538	13	27	be	be	AUX
ejpam-6538	13	28	connected	connect	VERB
ejpam-6538	13	29	if	if	SCONJ
ejpam-6538	13	30	for	for	ADP
ejpam-6538	13	31	each	each	DET
ejpam-6538	13	32	a	a	NOUN
ejpam-6538	13	33	,	,	PUNCT
ejpam-6538	13	34	b	b	X
ejpam-6538	13	35	∈	∈	PROPN
ejpam-6538	13	36	a	a	PRON
ejpam-6538	13	37	,	,	PUNCT
ejpam-6538	13	38	there	there	PRON
ejpam-6538	13	39	exist	exist	VERB
ejpam-6538	13	40	nonnegative	nonnegative	ADJ
ejpam-6538	13	41	integers	integer	NOUN
ejpam-6538	13	42	n	n	CCONJ
ejpam-6538	13	43	,	,	PUNCT
ejpam-6538	13	44	m	m	VERB
ejpam-6538	13	45	such	such	ADJ
ejpam-6538	13	46	that	that	SCONJ
ejpam-6538	13	47	fn(a	fn(a	PUNCT
ejpam-6538	13	48	)	)	PUNCT
ejpam-6538	13	49	=	=	SYM
ejpam-6538	13	50	fm(b	fm(b	NOUN
ejpam-6538	13	51	)	)	PUNCT
ejpam-6538	13	52	.	.	PUNCT
ejpam-6538	14	1	an	an	DET
ejpam-6538	14	2	element	element	NOUN
ejpam-6538	14	3	a	a	DET
ejpam-6538	14	4	∈	∈	NOUN
ejpam-6538	14	5	a	a	PRON
ejpam-6538	14	6	is	be	AUX
ejpam-6538	14	7	called	call	VERB
ejpam-6538	14	8	a	a	DET
ejpam-6538	14	9	cyclic	cyclic	NOUN
ejpam-6538	14	10	if	if	SCONJ
ejpam-6538	14	11	fn(a	fn(a	NOUN
ejpam-6538	14	12	)	)	PUNCT
ejpam-6538	14	13	=	=	SYM
ejpam-6538	14	14	a	a	PRON
ejpam-6538	14	15	for	for	ADP
ejpam-6538	14	16	some	some	DET
ejpam-6538	14	17	n	n	PRON
ejpam-6538	14	18	∈	∈	PROPN
ejpam-6538	14	19	n.	n.	NOUN
ejpam-6538	14	20	the	the	DET
ejpam-6538	14	21	height	height	NOUN
ejpam-6538	14	22	of	of	ADP
ejpam-6538	14	23	an	an	DET
ejpam-6538	14	24	element	element	NOUN
ejpam-6538	14	25	x	x	SYM
ejpam-6538	14	26	∈	∈	PROPN
ejpam-6538	14	27	a	a	PRON
ejpam-6538	14	28	,	,	PUNCT
ejpam-6538	14	29	denoted	denote	VERB
ejpam-6538	14	30	by	by	ADP
ejpam-6538	14	31	ht(x	ht(x	NOUN
ejpam-6538	14	32	)	)	PUNCT
ejpam-6538	14	33	,	,	PUNCT
ejpam-6538	14	34	is	be	AUX
ejpam-6538	14	35	the	the	DET
ejpam-6538	14	36	least	least	ADJ
ejpam-6538	14	37	non	non	ADJ
ejpam-6538	14	38	-	-	ADJ
ejpam-6538	14	39	negative	negative	ADJ
ejpam-6538	14	40	integer	integer	NOUN
ejpam-6538	14	41	i	i	PRON
ejpam-6538	14	42	such	such	ADJ
ejpam-6538	14	43	that	that	SCONJ
ejpam-6538	14	44	f	f	PROPN
ejpam-6538	14	45	i(x	i(x	PROPN
ejpam-6538	14	46	)	)	PUNCT
ejpam-6538	14	47	is	be	AUX
ejpam-6538	14	48	a	a	DET
ejpam-6538	14	49	cyclic	cyclic	ADJ
ejpam-6538	14	50	element	element	NOUN
ejpam-6538	14	51	.	.	PUNCT
ejpam-6538	15	1	the	the	DET
ejpam-6538	15	2	height	height	NOUN
ejpam-6538	15	3	of	of	ADP
ejpam-6538	15	4	the	the	DET
ejpam-6538	15	5	finite	finite	ADJ
ejpam-6538	15	6	monounary	monounary	PROPN
ejpam-6538	15	7	algebra	algebra	PROPN
ejpam-6538	15	8	a	a	PRON
ejpam-6538	15	9	is	be	AUX
ejpam-6538	15	10	defined	define	VERB
ejpam-6538	15	11	by	by	ADP
ejpam-6538	15	12	ht(a	ht(a	NOUN
ejpam-6538	15	13	)	)	PUNCT
ejpam-6538	15	14	:	:	PUNCT
ejpam-6538	15	15	=	=	SYM
ejpam-6538	15	16	max	max	X
ejpam-6538	15	17	{	{	PUNCT
ejpam-6538	15	18	ht(x	ht(x	PRON
ejpam-6538	15	19	)	)	PUNCT
ejpam-6538	16	1	|	|	ADV
ejpam-6538	16	2	x	x	SYM
ejpam-6538	16	3	∈	∈	PROPN
ejpam-6538	16	4	a	a	X
ejpam-6538	16	5	}	}	PUNCT
ejpam-6538	16	6	.	.	PUNCT
ejpam-6538	17	1	∗corresponding	∗corresponde	VERB
ejpam-6538	17	2	author	author	NOUN
ejpam-6538	17	3	.	.	PUNCT
ejpam-6538	18	1	doi	doi	NOUN
ejpam-6538	18	2	:	:	PUNCT
ejpam-6538	18	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6538	https://doi.org/10.29020/nybg.ejpam.v18i3.6538	ADJ
ejpam-6538	18	4	email	email	NOUN
ejpam-6538	18	5	addresses	address	NOUN
ejpam-6538	18	6	:	:	PUNCT
ejpam-6538	18	7	aveya.ch@rmuti.ac.th	aveya.ch@rmuti.ac.th	PROPN
ejpam-6538	18	8	(	(	PUNCT
ejpam-6538	18	9	a.	a.	NOUN
ejpam-6538	18	10	charoenpol	charoenpol	PROPN
ejpam-6538	18	11	)	)	PUNCT
ejpam-6538	18	12	,	,	PUNCT
ejpam-6538	18	13	udomch@kku.ac.th	udomch@kku.ac.th	NOUN
ejpam-6538	18	14	(	(	PUNCT
ejpam-6538	18	15	u.	u.	PROPN
ejpam-6538	18	16	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	18	17	)	)	PUNCT
ejpam-6538	18	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6538	19	1	1	1	NUM
ejpam-6538	19	2	copyright	copyright	NOUN
ejpam-6538	19	3	:	:	PUNCT
ejpam-6538	19	4	©	©	PROPN
ejpam-6538	19	5	2025	2025	NUM
ejpam-6538	19	6	the	the	DET
ejpam-6538	19	7	author(s	author(s	NOUN
ejpam-6538	19	8	)	)	PUNCT
ejpam-6538	19	9	.	.	PUNCT
ejpam-6538	20	1	(	(	PUNCT
ejpam-6538	20	2	cc	cc	NOUN
ejpam-6538	20	3	by	by	ADP
ejpam-6538	20	4	-	-	PUNCT
ejpam-6538	20	5	nc	nc	PROPN
ejpam-6538	20	6	4.0	4.0	NUM
ejpam-6538	20	7	)	)	PUNCT
ejpam-6538	20	8	a.	a.	NOUN
ejpam-6538	20	9	charoenpol	charoenpol	NOUN
ejpam-6538	20	10	,	,	PUNCT
ejpam-6538	20	11	u.	u.	PROPN
ejpam-6538	20	12	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	20	13	/	/	SYM
ejpam-6538	20	14	eur	eur	PROPN
ejpam-6538	20	15	.	.	PUNCT
ejpam-6538	21	1	j.	j.	PROPN
ejpam-6538	21	2	pure	pure	PROPN
ejpam-6538	21	3	appl	appl	PROPN
ejpam-6538	21	4	.	.	PROPN
ejpam-6538	21	5	math	math	PROPN
ejpam-6538	21	6	,	,	PUNCT
ejpam-6538	21	7	18	18	NUM
ejpam-6538	21	8	(	(	PUNCT
ejpam-6538	21	9	3	3	NUM
ejpam-6538	21	10	)	)	PUNCT
ejpam-6538	21	11	(	(	PUNCT
ejpam-6538	21	12	2025	2025	NUM
ejpam-6538	21	13	)	)	PUNCT
ejpam-6538	21	14	,	,	PUNCT
ejpam-6538	21	15	6538	6538	NUM
ejpam-6538	21	16	2	2	NUM
ejpam-6538	21	17	of	of	ADP
ejpam-6538	21	18	13	13	NUM
ejpam-6538	21	19	in	in	ADP
ejpam-6538	21	20	other	other	ADJ
ejpam-6538	21	21	words	word	NOUN
ejpam-6538	21	22	,	,	PUNCT
ejpam-6538	21	23	ht(a	ht(a	NOUN
ejpam-6538	21	24	)	)	PUNCT
ejpam-6538	21	25	is	be	AUX
ejpam-6538	21	26	the	the	DET
ejpam-6538	21	27	least	least	ADJ
ejpam-6538	21	28	non	non	ADJ
ejpam-6538	21	29	-	-	ADJ
ejpam-6538	21	30	negative	negative	ADJ
ejpam-6538	21	31	integer	integer	NOUN
ejpam-6538	21	32	λ(f	λ(f	NOUN
ejpam-6538	21	33	)	)	PUNCT
ejpam-6538	21	34	satisfying	satisfy	VERB
ejpam-6538	21	35	fλ(f)(a	fλ(f)(a	NOUN
ejpam-6538	21	36	)	)	PUNCT
ejpam-6538	22	1	=	=	SYM
ejpam-6538	22	2	fλ(f)+1(a	fλ(f)+1(a	PROPN
ejpam-6538	22	3	)	)	PUNCT
ejpam-6538	22	4	and	and	CCONJ
ejpam-6538	22	5	it	it	PRON
ejpam-6538	22	6	is	be	AUX
ejpam-6538	22	7	known	know	VERB
ejpam-6538	22	8	as	as	ADP
ejpam-6538	22	9	the	the	DET
ejpam-6538	22	10	pre	pre	NOUN
ejpam-6538	22	11	-	-	NOUN
ejpam-6538	22	12	period	period	NOUN
ejpam-6538	22	13	of	of	ADP
ejpam-6538	22	14	f	f	PROPN
ejpam-6538	22	15	(	(	PUNCT
ejpam-6538	22	16	see	see	VERB
ejpam-6538	22	17	[	[	X
ejpam-6538	22	18	4	4	NUM
ejpam-6538	22	19	]	]	NUM
ejpam-6538	22	20	)	)	PUNCT
ejpam-6538	22	21	.	.	PUNCT
ejpam-6538	23	1	for	for	ADP
ejpam-6538	23	2	any	any	DET
ejpam-6538	23	3	algebra	algebra	NOUN
ejpam-6538	23	4	a	a	X
ejpam-6538	23	5	,	,	PUNCT
ejpam-6538	23	6	we	we	PRON
ejpam-6538	23	7	can	can	AUX
ejpam-6538	23	8	study	study	VERB
ejpam-6538	23	9	the	the	DET
ejpam-6538	23	10	monounary	monounary	ADJ
ejpam-6538	23	11	algebra	algebra	PROPN
ejpam-6538	23	12	(	(	PUNCT
ejpam-6538	23	13	a	a	DET
ejpam-6538	23	14	,	,	PUNCT
ejpam-6538	23	15	f	f	NOUN
ejpam-6538	23	16	)	)	PUNCT
ejpam-6538	23	17	induced	induce	VERB
ejpam-6538	23	18	by	by	ADP
ejpam-6538	23	19	an	an	DET
ejpam-6538	23	20	endomorphism	endomorphism	PROPN
ejpam-6538	23	21	f	f	PROPN
ejpam-6538	23	22	of	of	ADP
ejpam-6538	23	23	a.	a.	PROPN
ejpam-6538	23	24	besides	besides	PROPN
ejpam-6538	23	25	,	,	PUNCT
ejpam-6538	23	26	an	an	DET
ejpam-6538	23	27	endomorphism	endomorphism	NOUN
ejpam-6538	23	28	is	be	AUX
ejpam-6538	23	29	studied	study	VERB
ejpam-6538	23	30	in	in	ADP
ejpam-6538	23	31	any	any	DET
ejpam-6538	23	32	category	category	NOUN
ejpam-6538	23	33	and	and	CCONJ
ejpam-6538	23	34	it	it	PRON
ejpam-6538	23	35	is	be	AUX
ejpam-6538	23	36	relevant	relevant	ADJ
ejpam-6538	23	37	to	to	PART
ejpam-6538	23	38	solve	solve	VERB
ejpam-6538	23	39	many	many	ADJ
ejpam-6538	23	40	problems	problem	NOUN
ejpam-6538	23	41	in	in	ADP
ejpam-6538	23	42	algebraic	algebraic	ADJ
ejpam-6538	23	43	structures	structure	NOUN
ejpam-6538	23	44	,	,	PUNCT
ejpam-6538	23	45	relational	relational	ADJ
ejpam-6538	23	46	structures	structure	NOUN
ejpam-6538	23	47	and	and	CCONJ
ejpam-6538	23	48	graphs	graph	NOUN
ejpam-6538	23	49	;	;	PUNCT
ejpam-6538	23	50	reader	reader	NOUN
ejpam-6538	23	51	may	may	AUX
ejpam-6538	23	52	look	look	VERB
ejpam-6538	23	53	in	in	ADP
ejpam-6538	23	54	[	[	X
ejpam-6538	23	55	5–9	5–9	NOUN
ejpam-6538	23	56	]	]	X
ejpam-6538	23	57	.	.	PUNCT
ejpam-6538	24	1	if	if	SCONJ
ejpam-6538	24	2	a	a	PRON
ejpam-6538	24	3	is	be	AUX
ejpam-6538	24	4	finite	finite	ADJ
ejpam-6538	24	5	,	,	PUNCT
ejpam-6538	24	6	one	one	PRON
ejpam-6538	24	7	can	can	AUX
ejpam-6538	24	8	see	see	VERB
ejpam-6538	24	9	that	that	PRON
ejpam-6538	24	10	|a|	|a|	NOUN
ejpam-6538	24	11	−	−	PROPN
ejpam-6538	24	12	1	1	NUM
ejpam-6538	24	13	is	be	AUX
ejpam-6538	24	14	an	an	DET
ejpam-6538	24	15	upper	upper	ADJ
ejpam-6538	24	16	bound	bound	NOUN
ejpam-6538	24	17	of	of	ADP
ejpam-6538	24	18	λ(f	λ(f	PROPN
ejpam-6538	24	19	)	)	PUNCT
ejpam-6538	24	20	;	;	PUNCT
ejpam-6538	24	21	so	so	CCONJ
ejpam-6538	24	22	,	,	PUNCT
ejpam-6538	24	23	it	it	PRON
ejpam-6538	24	24	is	be	AUX
ejpam-6538	24	25	interesting	interesting	ADJ
ejpam-6538	24	26	to	to	PART
ejpam-6538	24	27	study	study	VERB
ejpam-6538	24	28	the	the	DET
ejpam-6538	24	29	least	least	ADV
ejpam-6538	24	30	upper	upper	ADJ
ejpam-6538	24	31	bound	bind	VERB
ejpam-6538	24	32	as	as	ADP
ejpam-6538	24	33	follows	follow	VERB
ejpam-6538	24	34	.	.	PUNCT
ejpam-6538	25	1	the	the	DET
ejpam-6538	25	2	pre	pre	NOUN
ejpam-6538	25	3	-	-	NOUN
ejpam-6538	25	4	period	period	NOUN
ejpam-6538	25	5	of	of	ADP
ejpam-6538	25	6	algebra	algebra	NOUN
ejpam-6538	25	7	a	a	PRON
ejpam-6538	25	8	is	be	AUX
ejpam-6538	25	9	λ(a	λ(a	NOUN
ejpam-6538	25	10	)	)	PUNCT
ejpam-6538	26	1	=	=	SYM
ejpam-6538	26	2	sup	sup	NOUN
ejpam-6538	26	3	{	{	PUNCT
ejpam-6538	26	4	λ(f	λ(f	PROPN
ejpam-6538	26	5	)	)	PUNCT
ejpam-6538	27	1	|	|	ADV
ejpam-6538	27	2	f	f	PROPN
ejpam-6538	27	3	is	be	AUX
ejpam-6538	27	4	an	an	DET
ejpam-6538	27	5	endomorphism	endomorphism	NOUN
ejpam-6538	27	6	of	of	ADP
ejpam-6538	27	7	a	a	PRON
ejpam-6538	27	8	}	}	PUNCT
ejpam-6538	27	9	.	.	PUNCT
ejpam-6538	28	1	in	in	ADP
ejpam-6538	28	2	[	[	X
ejpam-6538	28	3	10	10	NUM
ejpam-6538	28	4	,	,	PUNCT
ejpam-6538	28	5	11	11	NUM
ejpam-6538	28	6	]	]	PUNCT
ejpam-6538	28	7	,	,	PUNCT
ejpam-6538	28	8	the	the	DET
ejpam-6538	28	9	authors	author	NOUN
ejpam-6538	28	10	focused	focus	VERB
ejpam-6538	28	11	on	on	ADP
ejpam-6538	28	12	a	a	DET
ejpam-6538	28	13	finite	finite	ADJ
ejpam-6538	28	14	lattice	lattice	NOUN
ejpam-6538	28	15	and	and	CCONJ
ejpam-6538	28	16	showed	show	VERB
ejpam-6538	28	17	that	that	SCONJ
ejpam-6538	28	18	for	for	ADP
ejpam-6538	28	19	a	a	DET
ejpam-6538	28	20	finite	finite	ADJ
ejpam-6538	28	21	modular	modular	PROPN
ejpam-6538	28	22	lattice	lattice	PROPN
ejpam-6538	28	23	l	l	PROPN
ejpam-6538	28	24	,	,	PUNCT
ejpam-6538	28	25	its	its	PRON
ejpam-6538	28	26	pre	pre	NOUN
ejpam-6538	28	27	-	-	NOUN
ejpam-6538	28	28	period	period	NOUN
ejpam-6538	28	29	is	be	AUX
ejpam-6538	28	30	less	less	ADJ
ejpam-6538	28	31	than	than	ADP
ejpam-6538	28	32	or	or	CCONJ
ejpam-6538	28	33	equal	equal	ADJ
ejpam-6538	28	34	to	to	ADP
ejpam-6538	28	35	the	the	DET
ejpam-6538	28	36	length	length	NOUN
ejpam-6538	28	37	of	of	ADP
ejpam-6538	28	38	l	l	NOUN
ejpam-6538	28	39	where	where	SCONJ
ejpam-6538	28	40	the	the	DET
ejpam-6538	28	41	length	length	NOUN
ejpam-6538	28	42	ℓ(l	ℓ(l	NOUN
ejpam-6538	28	43	)	)	PUNCT
ejpam-6538	28	44	of	of	ADP
ejpam-6538	28	45	l	l	NOUN
ejpam-6538	28	46	is	be	AUX
ejpam-6538	28	47	defined	define	VERB
ejpam-6538	28	48	by	by	ADP
ejpam-6538	28	49	|c|	|c|	PROPN
ejpam-6538	28	50	−	−	PROPN
ejpam-6538	28	51	1	1	NUM
ejpam-6538	28	52	for	for	ADP
ejpam-6538	28	53	the	the	DET
ejpam-6538	28	54	longest	long	ADJ
ejpam-6538	28	55	chain	chain	NOUN
ejpam-6538	28	56	c	c	NOUN
ejpam-6538	28	57	in	in	ADP
ejpam-6538	28	58	l.	l.	PROPN
ejpam-6538	28	59	a	a	DET
ejpam-6538	28	60	finite	finite	ADJ
ejpam-6538	28	61	modular	modular	ADJ
ejpam-6538	28	62	lattice	lattice	NOUN
ejpam-6538	28	63	a	a	PRON
ejpam-6538	28	64	is	be	AUX
ejpam-6538	28	65	said	say	VERB
ejpam-6538	28	66	to	to	PART
ejpam-6538	28	67	be	be	AUX
ejpam-6538	28	68	mpp	mpp	NOUN
ejpam-6538	28	69	if	if	SCONJ
ejpam-6538	28	70	there	there	PRON
ejpam-6538	28	71	is	be	VERB
ejpam-6538	28	72	an	an	DET
ejpam-6538	28	73	endomorphism	endomorphism	PROPN
ejpam-6538	28	74	f	f	PROPN
ejpam-6538	28	75	(	(	PUNCT
ejpam-6538	28	76	called	call	VERB
ejpam-6538	28	77	an	an	DET
ejpam-6538	28	78	mpp	mpp	NOUN
ejpam-6538	28	79	endomorphism	endomorphism	NOUN
ejpam-6538	28	80	)	)	PUNCT
ejpam-6538	28	81	whose	whose	DET
ejpam-6538	28	82	λ(f	λ(f	NOUN
ejpam-6538	28	83	)	)	PUNCT
ejpam-6538	28	84	=	=	SYM
ejpam-6538	28	85	ℓ(a	ℓ(a	PROPN
ejpam-6538	28	86	)	)	PUNCT
ejpam-6538	28	87	.	.	PUNCT
ejpam-6538	29	1	a	a	DET
ejpam-6538	29	2	monounary	monounary	ADJ
ejpam-6538	29	3	algebra	algebra	NOUN
ejpam-6538	29	4	(	(	PUNCT
ejpam-6538	29	5	a	a	DET
ejpam-6538	29	6	,	,	PUNCT
ejpam-6538	29	7	f	f	X
ejpam-6538	29	8	)	)	PUNCT
ejpam-6538	29	9	is	be	AUX
ejpam-6538	29	10	said	say	VERB
ejpam-6538	29	11	to	to	PART
ejpam-6538	29	12	be	be	AUX
ejpam-6538	29	13	mpp	mpp	NOUN
ejpam-6538	29	14	if	if	SCONJ
ejpam-6538	29	15	there	there	PRON
ejpam-6538	29	16	is	be	VERB
ejpam-6538	29	17	an	an	DET
ejpam-6538	29	18	mpp	mpp	NOUN
ejpam-6538	29	19	endomorphism	endomorphism	PROPN
ejpam-6538	29	20	g	g	PROPN
ejpam-6538	29	21	of	of	ADP
ejpam-6538	29	22	a	a	DET
ejpam-6538	29	23	lattice	lattice	NOUN
ejpam-6538	29	24	b	b	PROPN
ejpam-6538	29	25	such	such	ADJ
ejpam-6538	29	26	that	that	PRON
ejpam-6538	29	27	(	(	PUNCT
ejpam-6538	29	28	a	a	PRON
ejpam-6538	29	29	,	,	PUNCT
ejpam-6538	29	30	f	f	X
ejpam-6538	29	31	)	)	PUNCT
ejpam-6538	29	32	is	be	AUX
ejpam-6538	29	33	isomorphic	isomorphic	ADJ
ejpam-6538	29	34	to	to	ADP
ejpam-6538	29	35	(	(	PUNCT
ejpam-6538	29	36	b	b	X
ejpam-6538	29	37	,	,	PUNCT
ejpam-6538	29	38	g	g	NOUN
ejpam-6538	29	39	)	)	PUNCT
ejpam-6538	29	40	.	.	PUNCT
ejpam-6538	30	1	such	such	DET
ejpam-6538	30	2	the	the	DET
ejpam-6538	30	3	lattice	lattice	PROPN
ejpam-6538	30	4	b	b	PROPN
ejpam-6538	30	5	is	be	AUX
ejpam-6538	30	6	called	call	VERB
ejpam-6538	30	7	an	an	DET
ejpam-6538	30	8	mpp	mpp	NOUN
ejpam-6538	30	9	corresponding	correspond	VERB
ejpam-6538	30	10	lattice	lattice	PROPN
ejpam-6538	30	11	to	to	ADP
ejpam-6538	30	12	(	(	PUNCT
ejpam-6538	30	13	a	a	PRON
ejpam-6538	30	14	,	,	PUNCT
ejpam-6538	30	15	f	f	NOUN
ejpam-6538	30	16	)	)	PUNCT
ejpam-6538	30	17	.	.	PUNCT
ejpam-6538	31	1	in	in	ADP
ejpam-6538	31	2	the	the	DET
ejpam-6538	31	3	present	present	ADJ
ejpam-6538	31	4	work	work	NOUN
ejpam-6538	31	5	,	,	PUNCT
ejpam-6538	31	6	we	we	PRON
ejpam-6538	31	7	will	will	AUX
ejpam-6538	31	8	show	show	VERB
ejpam-6538	31	9	that	that	SCONJ
ejpam-6538	31	10	all	all	DET
ejpam-6538	31	11	monounary	monounary	ADJ
ejpam-6538	31	12	algebras	algebra	NOUN
ejpam-6538	31	13	induced	induce	VERB
ejpam-6538	31	14	by	by	ADP
ejpam-6538	31	15	an	an	DET
ejpam-6538	31	16	mpp	mpp	NOUN
ejpam-6538	31	17	endomorphism	endomorphism	NOUN
ejpam-6538	31	18	of	of	ADP
ejpam-6538	31	19	the	the	DET
ejpam-6538	31	20	direct	direct	ADJ
ejpam-6538	31	21	products	product	NOUN
ejpam-6538	31	22	of	of	ADP
ejpam-6538	31	23	two	two	NUM
ejpam-6538	31	24	chains	chain	NOUN
ejpam-6538	31	25	(	(	PUNCT
ejpam-6538	31	26	studied	study	VERB
ejpam-6538	31	27	in	in	ADP
ejpam-6538	31	28	[	[	X
ejpam-6538	31	29	10	10	NUM
ejpam-6538	31	30	]	]	PUNCT
ejpam-6538	31	31	)	)	PUNCT
ejpam-6538	31	32	are	be	AUX
ejpam-6538	31	33	isomorphic	isomorphic	ADJ
ejpam-6538	31	34	to	to	ADP
ejpam-6538	31	35	the	the	DET
ejpam-6538	31	36	monounary	monounary	ADJ
ejpam-6538	31	37	algebras	algebra	NOUN
ejpam-6538	31	38	(	(	PUNCT
ejpam-6538	31	39	an	an	DET
ejpam-6538	31	40	,	,	PUNCT
ejpam-6538	31	41	fn	fn	NOUN
ejpam-6538	31	42	)	)	PUNCT
ejpam-6538	31	43	and	and	CCONJ
ejpam-6538	31	44	(	(	PUNCT
ejpam-6538	31	45	bn	bn	X
ejpam-6538	31	46	,	,	PUNCT
ejpam-6538	31	47	gn	gn	PROPN
ejpam-6538	31	48	)	)	PUNCT
ejpam-6538	31	49	shown	show	VERB
ejpam-6538	31	50	in	in	ADP
ejpam-6538	31	51	the	the	DET
ejpam-6538	31	52	figures	figure	NOUN
ejpam-6538	31	53	1	1	NUM
ejpam-6538	31	54	,	,	PUNCT
ejpam-6538	31	55	2	2	NUM
ejpam-6538	31	56	and	and	CCONJ
ejpam-6538	31	57	3	3	NUM
ejpam-6538	31	58	.	.	PUNCT
ejpam-6538	31	59	?	?	PUNCT
ejpam-6538	31	60	?	?	PUNCT
ejpam-6538	31	61	?	?	PUNCT
ejpam-6538	31	62	?	?	PUNCT
ejpam-6538	31	63	?	?	PUNCT
ejpam-6538	31	64	?	?	PUNCT
ejpam-6538	31	65	?	?	PUNCT
ejpam-6538	31	66	?	?	PUNCT
ejpam-6538	31	67	?	?	PUNCT
ejpam-6538	31	68	?	?	PUNCT
ejpam-6538	31	69	?	?	PUNCT
ejpam-6538	31	70	?	?	PUNCT
ejpam-6538	31	71	?	?	PUNCT
ejpam-6538	31	72	?	?	PUNCT
ejpam-6538	31	73	?	?	PUNCT
ejpam-6538	31	74	?	?	PUNCT
ejpam-6538	31	75	?	?	PUNCT
ejpam-6538	31	76	?	?	PUNCT
ejpam-6538	31	77	?	?	PUNCT
ejpam-6538	31	78	?	?	PUNCT
ejpam-6538	32	1	�	�	PROPN
ejpam-6538	32	2	�	�	PROPN
ejpam-6538	32	3	�	�	PROPN
ejpam-6538	32	4	�	�	PROPN
ejpam-6538	32	5	�	�	PROPN
ejpam-6538	32	6	�	�	PROPN
ejpam-6538	32	7	�	�	PROPN
ejpam-6538	32	8	�	�	PROPN
ejpam-6538	32	9	�	�	PROPN
ejpam-6538	32	10	�	�	PROPN
ejpam-6538	32	11	�	�	PROPN
ejpam-6538	32	12	�	�	PROPN
ejpam-6538	32	13	�	�	PROPN
ejpam-6538	32	14	�	�	PROPN
ejpam-6538	32	15	�	�	PROPN
ejpam-6538	32	16	�	�	PROPN
ejpam-6538	32	17	�	�	PROPN
ejpam-6538	32	18	�	�	PROPN
ejpam-6538	32	19	�	�	PROPN
ejpam-6538	32	20	�	�	PROPN
ejpam-6538	32	21	�	�	PROPN
ejpam-6538	32	22	�	�	PROPN
ejpam-6538	32	23	�	�	PROPN
ejpam-6538	32	24	�	�	PROPN
ejpam-6538	32	25	r	r	NOUN
ejpam-6538	32	26	r	r	NOUN
ejpam-6538	32	27	r	r	NOUN
ejpam-6538	32	28	r	r	NOUN
ejpam-6538	32	29	r	r	NOUN
ejpam-6538	32	30	r	r	NOUN
ejpam-6538	32	31	r	r	NOUN
ejpam-6538	32	32	r	r	NOUN
ejpam-6538	32	33	r	r	NOUN
ejpam-6538	32	34	r	r	NOUN
ejpam-6538	32	35	r	r	NOUN
ejpam-6538	32	36	r	r	NOUN
ejpam-6538	32	37	r	r	NOUN
ejpam-6538	32	38	r	r	NOUN
ejpam-6538	32	39	r	r	NOUN
ejpam-6538	32	40	r	r	NOUN
ejpam-6538	32	41	r	r	NOUN
ejpam-6538	32	42	r	r	NOUN
ejpam-6538	32	43	r	r	NOUN
ejpam-6538	32	44	r	r	NOUN
ejpam-6538	32	45	r	r	NOUN
ejpam-6538	32	46	rp	rp	NOUN
ejpam-6538	32	47	p	p	NOUN
ejpam-6538	33	1	p	p	X
ejpam-6538	33	2	p	p	PROPN
ejpam-6538	33	3	p	p	PROPN
ejpam-6538	33	4	p	p	PROPN
ejpam-6538	33	5	p	p	X
ejpam-6538	33	6	p	p	PROPN
ejpam-6538	33	7	pppp	pppp	PROPN
ejpam-6538	33	8	ppp	ppp	PROPN
ejpam-6538	33	9	ppp	ppp	PROPN
ejpam-6538	33	10	⟲	⟲	PROPN
ejpam-6538	34	1	a1,n	a1,n	PROPN
ejpam-6538	34	2	a1,n−1	a1,n−1	ADJ
ejpam-6538	34	3	a1,5	a1,5	PROPN
ejpam-6538	34	4	a1,4	a1,4	ADV
ejpam-6538	34	5	a1,3	a1,3	DET
ejpam-6538	34	6	a1,2	a1,2	PROPN
ejpam-6538	34	7	a1,1	a1,1	NOUN
ejpam-6538	34	8	a1,0	a1,0	PROPN
ejpam-6538	34	9	a2,n	a2,n	ADV
ejpam-6538	34	10	a2,n−1	a2,n−1	PROPN
ejpam-6538	34	11	a2,5	a2,5	PROPN
ejpam-6538	34	12	a2,4	a2,4	PROPN
ejpam-6538	34	13	a2,3	a2,3	PROPN
ejpam-6538	34	14	a2,2	a2,2	PROPN
ejpam-6538	34	15	a3,n	a3,n	PROPN
ejpam-6538	34	16	a3,n−1	a3,n−1	PROPN
ejpam-6538	34	17	a3,5	a3,5	PROPN
ejpam-6538	34	18	a3,4	a3,4	ADJ
ejpam-6538	34	19	an	an	DET
ejpam-6538	34	20	2	2	NUM
ejpam-6538	34	21	,	,	PUNCT
ejpam-6538	34	22	n	n	CCONJ
ejpam-6538	34	23	an	an	DET
ejpam-6538	34	24	2	2	NUM
ejpam-6538	34	25	,	,	PUNCT
ejpam-6538	34	26	n−1	n−1	PROPN
ejpam-6538	34	27	an	an	DET
ejpam-6538	34	28	2	2	NUM
ejpam-6538	34	29	,	,	PUNCT
ejpam-6538	34	30	n−2	n−2	PROPN
ejpam-6538	34	31	an	an	DET
ejpam-6538	34	32	2	2	NUM
ejpam-6538	34	33	+1,n	+1,n	NOUN
ejpam-6538	34	34	figure	figure	NOUN
ejpam-6538	34	35	1	1	NUM
ejpam-6538	34	36	:	:	PUNCT
ejpam-6538	34	37	the	the	DET
ejpam-6538	34	38	graph	graph	NOUN
ejpam-6538	34	39	of	of	ADP
ejpam-6538	34	40	(	(	PUNCT
ejpam-6538	34	41	an	an	DET
ejpam-6538	34	42	,	,	PUNCT
ejpam-6538	34	43	fn	fn	NOUN
ejpam-6538	34	44	)	)	PUNCT
ejpam-6538	34	45	where	where	SCONJ
ejpam-6538	34	46	n	n	PRON
ejpam-6538	34	47	is	be	AUX
ejpam-6538	34	48	an	an	DET
ejpam-6538	34	49	even	even	ADV
ejpam-6538	34	50	natural	natural	ADJ
ejpam-6538	34	51	number	number	NOUN
ejpam-6538	34	52	.	.	PUNCT
ejpam-6538	35	1	2	2	NUM
ejpam-6538	35	2	.	.	NUM
ejpam-6538	35	3	basic	basic	ADJ
ejpam-6538	35	4	concepts	concept	NOUN
ejpam-6538	35	5	we	we	PRON
ejpam-6538	35	6	denote	denote	VERB
ejpam-6538	35	7	the	the	DET
ejpam-6538	35	8	top	top	NOUN
ejpam-6538	35	9	and	and	CCONJ
ejpam-6538	35	10	bottom	bottom	NOUN
ejpam-6538	35	11	of	of	ADP
ejpam-6538	35	12	a	a	DET
ejpam-6538	35	13	lattice	lattice	NOUN
ejpam-6538	35	14	a	a	PRON
ejpam-6538	35	15	by	by	ADP
ejpam-6538	35	16	1a	1a	NOUN
ejpam-6538	35	17	and	and	CCONJ
ejpam-6538	35	18	0a	0a	PROPN
ejpam-6538	35	19	(	(	PUNCT
ejpam-6538	35	20	shortly	shortly	ADV
ejpam-6538	35	21	,	,	PUNCT
ejpam-6538	35	22	1	1	NUM
ejpam-6538	35	23	and	and	CCONJ
ejpam-6538	35	24	0	0	NUM
ejpam-6538	35	25	)	)	PUNCT
ejpam-6538	35	26	,	,	PUNCT
ejpam-6538	35	27	respectively	respectively	ADV
ejpam-6538	35	28	.	.	PUNCT
ejpam-6538	36	1	a	a	DET
ejpam-6538	36	2	unary	unary	ADJ
ejpam-6538	36	3	operation	operation	NOUN
ejpam-6538	36	4	f	f	PROPN
ejpam-6538	36	5	on	on	ADP
ejpam-6538	36	6	a	a	DET
ejpam-6538	36	7	lattice	lattice	NOUN
ejpam-6538	36	8	a	a	DET
ejpam-6538	36	9	=	=	SYM
ejpam-6538	36	10	(	(	PUNCT
ejpam-6538	36	11	a;∨,∧	a;∨,∧	PROPN
ejpam-6538	36	12	)	)	PUNCT
ejpam-6538	36	13	is	be	AUX
ejpam-6538	36	14	said	say	VERB
ejpam-6538	36	15	to	to	PART
ejpam-6538	36	16	be	be	AUX
ejpam-6538	36	17	an	an	DET
ejpam-6538	36	18	endomorphism	endomorphism	NOUN
ejpam-6538	36	19	of	of	ADP
ejpam-6538	36	20	a.	a.	NOUN
ejpam-6538	36	21	charoenpol	charoenpol	NOUN
ejpam-6538	36	22	,	,	PUNCT
ejpam-6538	36	23	u.	u.	PROPN
ejpam-6538	36	24	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	36	25	/	/	SYM
ejpam-6538	36	26	eur	eur	PROPN
ejpam-6538	36	27	.	.	PUNCT
ejpam-6538	37	1	j.	j.	PROPN
ejpam-6538	37	2	pure	pure	PROPN
ejpam-6538	37	3	appl	appl	PROPN
ejpam-6538	37	4	.	.	PROPN
ejpam-6538	37	5	math	math	PROPN
ejpam-6538	37	6	,	,	PUNCT
ejpam-6538	37	7	18	18	NUM
ejpam-6538	37	8	(	(	PUNCT
ejpam-6538	37	9	3	3	NUM
ejpam-6538	37	10	)	)	PUNCT
ejpam-6538	37	11	(	(	PUNCT
ejpam-6538	37	12	2025	2025	NUM
ejpam-6538	37	13	)	)	PUNCT
ejpam-6538	37	14	,	,	PUNCT
ejpam-6538	37	15	6538	6538	NUM
ejpam-6538	37	16	3	3	NUM
ejpam-6538	37	17	of	of	ADP
ejpam-6538	37	18	13	13	NUM
ejpam-6538	37	19	?	?	PUNCT
ejpam-6538	37	20	?	?	PUNCT
ejpam-6538	37	21	?	?	PUNCT
ejpam-6538	37	22	?	?	PUNCT
ejpam-6538	37	23	?	?	PUNCT
ejpam-6538	37	24	?	?	PUNCT
ejpam-6538	37	25	?	?	PUNCT
ejpam-6538	37	26	?	?	PUNCT
ejpam-6538	37	27	?	?	PUNCT
ejpam-6538	37	28	?	?	PUNCT
ejpam-6538	37	29	?	?	PUNCT
ejpam-6538	37	30	?	?	PUNCT
ejpam-6538	37	31	?	?	PUNCT
ejpam-6538	37	32	?	?	PUNCT
ejpam-6538	37	33	?	?	PUNCT
ejpam-6538	37	34	?	?	PUNCT
ejpam-6538	37	35	?	?	PUNCT
ejpam-6538	37	36	?	?	PUNCT
ejpam-6538	37	37	?	?	PUNCT
ejpam-6538	37	38	?	?	PUNCT
ejpam-6538	37	39	?	?	PUNCT
ejpam-6538	37	40	?	?	PUNCT
ejpam-6538	37	41	?	?	PUNCT
ejpam-6538	37	42	?	?	PUNCT
ejpam-6538	37	43	?	?	PUNCT
ejpam-6538	38	1	�	�	PROPN
ejpam-6538	38	2	�	�	PROPN
ejpam-6538	38	3	�	�	PROPN
ejpam-6538	38	4	�	�	PROPN
ejpam-6538	38	5	�	�	PROPN
ejpam-6538	38	6	�	�	PROPN
ejpam-6538	38	7	�	�	PROPN
ejpam-6538	38	8	�	�	PROPN
ejpam-6538	38	9	�	�	PROPN
ejpam-6538	38	10	�	�	PROPN
ejpam-6538	38	11	�	�	PROPN
ejpam-6538	38	12	�	�	PROPN
ejpam-6538	38	13	�	�	PROPN
ejpam-6538	38	14	�	�	PROPN
ejpam-6538	38	15	�	�	PROPN
ejpam-6538	38	16	�	�	PROPN
ejpam-6538	38	17	�	�	PROPN
ejpam-6538	38	18	�	�	PROPN
ejpam-6538	38	19	�	�	PROPN
ejpam-6538	38	20	�	�	PROPN
ejpam-6538	38	21	�	�	PROPN
ejpam-6538	38	22	�	�	PROPN
ejpam-6538	38	23	�	�	PROPN
ejpam-6538	38	24	�	�	PROPN
ejpam-6538	38	25	r	r	NOUN
ejpam-6538	38	26	r	r	NOUN
ejpam-6538	38	27	r	r	NOUN
ejpam-6538	38	28	r	r	NOUN
ejpam-6538	38	29	r	r	NOUN
ejpam-6538	38	30	r	r	NOUN
ejpam-6538	38	31	r	r	NOUN
ejpam-6538	38	32	r	r	NOUN
ejpam-6538	38	33	r	r	NOUN
ejpam-6538	38	34	r	r	NOUN
ejpam-6538	38	35	r	r	NOUN
ejpam-6538	38	36	r	r	NOUN
ejpam-6538	38	37	r	r	NOUN
ejpam-6538	38	38	r	r	NOUN
ejpam-6538	38	39	r	r	NOUN
ejpam-6538	38	40	r	r	NOUN
ejpam-6538	38	41	r	r	NOUN
ejpam-6538	38	42	r	r	NOUN
ejpam-6538	38	43	r	r	NOUN
ejpam-6538	38	44	r	r	NOUN
ejpam-6538	38	45	r	r	NOUN
ejpam-6538	38	46	r	r	NOUN
ejpam-6538	38	47	r	r	NOUN
ejpam-6538	38	48	r	r	NOUN
ejpam-6538	38	49	r	r	NOUN
ejpam-6538	38	50	r	r	NOUN
ejpam-6538	38	51	rp	rp	NOUN
ejpam-6538	38	52	p	p	NOUN
ejpam-6538	38	53	p	p	X
ejpam-6538	38	54	p	p	PROPN
ejpam-6538	38	55	p	p	PROPN
ejpam-6538	38	56	p	p	PROPN
ejpam-6538	38	57	p	p	PROPN
ejpam-6538	38	58	p	p	PROPN
ejpam-6538	38	59	p	p	PROPN
ejpam-6538	38	60	p	p	X
ejpam-6538	38	61	p	p	PROPN
ejpam-6538	38	62	pppp	pppp	PROPN
ejpam-6538	38	63	ppp	ppp	PROPN
ejpam-6538	38	64	ppp	ppp	PROPN
ejpam-6538	38	65	⟲	⟲	PROPN
ejpam-6538	39	1	a1,n	a1,n	PROPN
ejpam-6538	39	2	a1,n−1	a1,n−1	ADJ
ejpam-6538	39	3	a1,n−2	a1,n−2	ADJ
ejpam-6538	39	4	a1,5	a1,5	PROPN
ejpam-6538	39	5	a1,4	a1,4	ADV
ejpam-6538	39	6	a1,3	a1,3	DET
ejpam-6538	39	7	a1,2	a1,2	PROPN
ejpam-6538	39	8	a1,1	a1,1	NOUN
ejpam-6538	39	9	a1,0	a1,0	PROPN
ejpam-6538	39	10	a2,n	a2,n	PROPN
ejpam-6538	39	11	a2,n−1	a2,n−1	PROPN
ejpam-6538	39	12	a2,n−2	a2,n−2	NOUN
ejpam-6538	39	13	a2,5	a2,5	PROPN
ejpam-6538	40	1	a2,4	a2,4	PROPN
ejpam-6538	40	2	a2,3	a2,3	PROPN
ejpam-6538	40	3	a2,2	a2,2	PROPN
ejpam-6538	40	4	a3,n	a3,n	PROPN
ejpam-6538	40	5	a3,n−1	a3,n−1	ADJ
ejpam-6538	40	6	a3,n−2	a3,n−2	NOUN
ejpam-6538	40	7	a3,5	a3,5	ADP
ejpam-6538	40	8	a3,4	a3,4	ADJ
ejpam-6538	40	9	an−1	an−1	ADJ
ejpam-6538	40	10	2	2	NUM
ejpam-6538	40	11	,	,	PUNCT
ejpam-6538	40	12	n	n	CCONJ
ejpam-6538	40	13	an−1	an−1	ADJ
ejpam-6538	40	14	2	2	NUM
ejpam-6538	40	15	,	,	PUNCT
ejpam-6538	40	16	n−1	n−1	PROPN
ejpam-6538	40	17	an−1	an−1	ADJ
ejpam-6538	40	18	2	2	NUM
ejpam-6538	40	19	,	,	PUNCT
ejpam-6538	40	20	n−2	n−2	PROPN
ejpam-6538	40	21	an−1	an−1	ADJ
ejpam-6538	40	22	2	2	NUM
ejpam-6538	40	23	,	,	PUNCT
ejpam-6538	40	24	n−3	n−3	PROPN
ejpam-6538	40	25	an+1	an+1	NOUN
ejpam-6538	40	26	2	2	NUM
ejpam-6538	40	27	,	,	PUNCT
ejpam-6538	40	28	n	n	X
ejpam-6538	40	29	an+1	an+1	NOUN
ejpam-6538	40	30	2	2	NUM
ejpam-6538	40	31	,	,	PUNCT
ejpam-6538	40	32	n−1	n−1	PROPN
ejpam-6538	40	33	figure	figure	NOUN
ejpam-6538	40	34	2	2	NUM
ejpam-6538	40	35	:	:	PUNCT
ejpam-6538	40	36	the	the	DET
ejpam-6538	40	37	graph	graph	NOUN
ejpam-6538	40	38	of	of	ADP
ejpam-6538	40	39	(	(	PUNCT
ejpam-6538	40	40	an	an	DET
ejpam-6538	40	41	,	,	PUNCT
ejpam-6538	40	42	fn	fn	NOUN
ejpam-6538	40	43	)	)	PUNCT
ejpam-6538	40	44	where	where	SCONJ
ejpam-6538	40	45	n	n	PRON
ejpam-6538	40	46	is	be	AUX
ejpam-6538	40	47	an	an	DET
ejpam-6538	40	48	odd	odd	ADJ
ejpam-6538	40	49	natural	natural	ADJ
ejpam-6538	40	50	number	number	NOUN
ejpam-6538	40	51	.	.	PUNCT
ejpam-6538	41	1	a	a	DET
ejpam-6538	41	2	if	if	SCONJ
ejpam-6538	41	3	f(a	f(a	PROPN
ejpam-6538	41	4	∨	∨	NUM
ejpam-6538	41	5	b	b	NOUN
ejpam-6538	41	6	)	)	PUNCT
ejpam-6538	41	7	=	=	SYM
ejpam-6538	41	8	f(a	f(a	PROPN
ejpam-6538	41	9	)	)	PUNCT
ejpam-6538	41	10	∨	∨	NUM
ejpam-6538	41	11	f(b	f(b	PROPN
ejpam-6538	41	12	)	)	PUNCT
ejpam-6538	41	13	and	and	CCONJ
ejpam-6538	41	14	f(a	f(a	PROPN
ejpam-6538	41	15	∧	∧	PROPN
ejpam-6538	41	16	b	b	PROPN
ejpam-6538	41	17	)	)	PUNCT
ejpam-6538	41	18	=	=	SYM
ejpam-6538	41	19	f(a	f(a	NOUN
ejpam-6538	41	20	)	)	PUNCT
ejpam-6538	41	21	∧	∧	NOUN
ejpam-6538	41	22	f(b	f(b	PROPN
ejpam-6538	41	23	)	)	PUNCT
ejpam-6538	41	24	for	for	ADP
ejpam-6538	41	25	all	all	DET
ejpam-6538	41	26	a	a	DET
ejpam-6538	41	27	,	,	PUNCT
ejpam-6538	41	28	b	b	X
ejpam-6538	41	29	∈	∈	PROPN
ejpam-6538	41	30	a.	a.	NOUN
ejpam-6538	41	31	the	the	DET
ejpam-6538	41	32	results	result	NOUN
ejpam-6538	41	33	in	in	ADP
ejpam-6538	41	34	[	[	X
ejpam-6538	41	35	11	11	NUM
ejpam-6538	41	36	,	,	PUNCT
ejpam-6538	41	37	corollary	corollary	ADJ
ejpam-6538	41	38	6	6	NUM
ejpam-6538	41	39	]	]	PUNCT
ejpam-6538	41	40	imply	imply	VERB
ejpam-6538	41	41	the	the	DET
ejpam-6538	41	42	following	follow	VERB
ejpam-6538	41	43	theorem	theorem	PROPN
ejpam-6538	41	44	.	.	PUNCT
ejpam-6538	41	45	theorem	theorem	NOUN
ejpam-6538	41	46	1	1	NUM
ejpam-6538	41	47	.	.	PUNCT
ejpam-6538	42	1	[	[	X
ejpam-6538	42	2	11	11	NUM
ejpam-6538	42	3	]	]	PUNCT
ejpam-6538	42	4	let	let	VERB
ejpam-6538	42	5	a	a	PRON
ejpam-6538	42	6	be	be	AUX
ejpam-6538	42	7	a	a	DET
ejpam-6538	42	8	finite	finite	ADJ
ejpam-6538	42	9	modular	modular	ADJ
ejpam-6538	42	10	lattice	lattice	NOUN
ejpam-6538	42	11	and	and	CCONJ
ejpam-6538	42	12	f	f	PROPN
ejpam-6538	42	13	be	be	AUX
ejpam-6538	42	14	an	an	DET
ejpam-6538	42	15	endomorphism	endomorphism	NOUN
ejpam-6538	42	16	of	of	ADP
ejpam-6538	42	17	a.	a.	NOUN
ejpam-6538	42	18	then	then	ADV
ejpam-6538	42	19	f	f	PROPN
ejpam-6538	42	20	is	be	AUX
ejpam-6538	42	21	mpp	mpp	NOUN
ejpam-6538	42	22	if	if	SCONJ
ejpam-6538	43	1	and	and	CCONJ
ejpam-6538	43	2	only	only	ADV
ejpam-6538	43	3	if	if	SCONJ
ejpam-6538	43	4	f	f	PROPN
ejpam-6538	43	5	satisfies	satisfy	VERB
ejpam-6538	43	6	either	either	CCONJ
ejpam-6538	43	7	0	0	NUM
ejpam-6538	43	8	=	=	SYM
ejpam-6538	43	9	fλ(f)(1	fλ(f)(1	NOUN
ejpam-6538	43	10	)	)	PUNCT
ejpam-6538	43	11	≺	≺	NOUN
ejpam-6538	43	12	fλ(f)−1(1	fλ(f)−1(1	ADJ
ejpam-6538	43	13	)	)	PUNCT
ejpam-6538	43	14	≺	≺	NOUN
ejpam-6538	43	15	.	.	PUNCT
ejpam-6538	43	16	.	.	PUNCT
ejpam-6538	44	1	.	.	PUNCT
ejpam-6538	45	1	≺	≺	NOUN
ejpam-6538	45	2	f(1	f(1	NOUN
ejpam-6538	45	3	)	)	PUNCT
ejpam-6538	45	4	≺	≺	NOUN
ejpam-6538	45	5	1	1	NUM
ejpam-6538	45	6	(	(	PUNCT
ejpam-6538	45	7	1	1	NUM
ejpam-6538	45	8	)	)	PUNCT
ejpam-6538	45	9	or	or	CCONJ
ejpam-6538	45	10	0	0	NUM
ejpam-6538	45	11	≺	≺	NOUN
ejpam-6538	45	12	f(0	f(0	NOUN
ejpam-6538	45	13	)	)	PUNCT
ejpam-6538	45	14	≺	≺	NOUN
ejpam-6538	45	15	.	.	PUNCT
ejpam-6538	45	16	.	.	PUNCT
ejpam-6538	45	17	.	.	PUNCT
ejpam-6538	46	1	≺	≺	NOUN
ejpam-6538	46	2	fλ(f)−1(0	fλ(f)−1(0	NOUN
ejpam-6538	46	3	)	)	PUNCT
ejpam-6538	46	4	≺	≺	NOUN
ejpam-6538	46	5	fλ(f)(0	fλ(f)(0	NOUN
ejpam-6538	46	6	)	)	PUNCT
ejpam-6538	46	7	=	=	SYM
ejpam-6538	47	1	1	1	X
ejpam-6538	47	2	.	.	PUNCT
ejpam-6538	47	3	(	(	PUNCT
ejpam-6538	47	4	2	2	NUM
ejpam-6538	47	5	)	)	PUNCT
ejpam-6538	47	6	corollary	corollary	ADJ
ejpam-6538	47	7	1	1	NUM
ejpam-6538	47	8	.	.	PUNCT
ejpam-6538	48	1	let	let	VERB
ejpam-6538	48	2	f	f	PRON
ejpam-6538	48	3	be	be	AUX
ejpam-6538	48	4	an	an	DET
ejpam-6538	48	5	mpp	mpp	NOUN
ejpam-6538	48	6	endomorphism	endomorphism	NOUN
ejpam-6538	48	7	of	of	ADP
ejpam-6538	48	8	a	a	DET
ejpam-6538	48	9	finite	finite	ADJ
ejpam-6538	48	10	modular	modular	PROPN
ejpam-6538	48	11	lattice	lattice	PROPN
ejpam-6538	48	12	a.	a.	NOUN
ejpam-6538	48	13	(	(	PUNCT
ejpam-6538	48	14	i	i	NOUN
ejpam-6538	48	15	)	)	PUNCT
ejpam-6538	48	16	if	if	SCONJ
ejpam-6538	48	17	f	f	PROPN
ejpam-6538	48	18	satisfies	satisfy	VERB
ejpam-6538	48	19	the	the	DET
ejpam-6538	48	20	condition	condition	NOUN
ejpam-6538	48	21	(	(	PUNCT
ejpam-6538	48	22	1	1	NUM
ejpam-6538	48	23	)	)	PUNCT
ejpam-6538	48	24	,	,	PUNCT
ejpam-6538	48	25	then	then	ADV
ejpam-6538	48	26	f(0	f(0	NOUN
ejpam-6538	48	27	)	)	PUNCT
ejpam-6538	48	28	=	=	SYM
ejpam-6538	48	29	0	0	NUM
ejpam-6538	48	30	,	,	PUNCT
ejpam-6538	48	31	ht(x	ht(x	NUM
ejpam-6538	48	32	)	)	PUNCT
ejpam-6538	49	1	=	=	SYM
ejpam-6538	49	2	min	min	NOUN
ejpam-6538	49	3	{	{	PUNCT
ejpam-6538	49	4	n	n	CCONJ
ejpam-6538	49	5	∈	∈	PROPN
ejpam-6538	49	6	n	n	NOUN
ejpam-6538	49	7	∪	∪	X
ejpam-6538	49	8	{	{	PUNCT
ejpam-6538	49	9	0	0	NUM
ejpam-6538	49	10	}	}	PUNCT
ejpam-6538	49	11	|	|	ADV
ejpam-6538	49	12	fn(x	fn(x	NOUN
ejpam-6538	49	13	)	)	PUNCT
ejpam-6538	49	14	=	=	SYM
ejpam-6538	49	15	0	0	X
ejpam-6538	49	16	}	}	PUNCT
ejpam-6538	49	17	for	for	ADP
ejpam-6538	49	18	all	all	DET
ejpam-6538	49	19	x	x	SYM
ejpam-6538	49	20	∈	∈	PROPN
ejpam-6538	49	21	a	a	PRON
ejpam-6538	49	22	and	and	CCONJ
ejpam-6538	49	23	ht(1	ht(1	PRON
ejpam-6538	49	24	)	)	PUNCT
ejpam-6538	49	25	=	=	SYM
ejpam-6538	49	26	ℓ(a	ℓ(a	PROPN
ejpam-6538	49	27	)	)	PUNCT
ejpam-6538	49	28	.	.	PUNCT
ejpam-6538	50	1	(	(	PUNCT
ejpam-6538	50	2	ii	ii	NOUN
ejpam-6538	50	3	)	)	PUNCT
ejpam-6538	50	4	if	if	SCONJ
ejpam-6538	50	5	f	f	PROPN
ejpam-6538	50	6	satisfies	satisfy	VERB
ejpam-6538	50	7	the	the	DET
ejpam-6538	50	8	condition	condition	NOUN
ejpam-6538	50	9	(	(	PUNCT
ejpam-6538	50	10	2	2	NUM
ejpam-6538	50	11	)	)	PUNCT
ejpam-6538	50	12	,	,	PUNCT
ejpam-6538	50	13	then	then	ADV
ejpam-6538	50	14	f(1	f(1	PROPN
ejpam-6538	50	15	)	)	PUNCT
ejpam-6538	50	16	=	=	SYM
ejpam-6538	50	17	1	1	NUM
ejpam-6538	50	18	,	,	PUNCT
ejpam-6538	50	19	ht(x	ht(x	PRON
ejpam-6538	50	20	)	)	PUNCT
ejpam-6538	51	1	=	=	SYM
ejpam-6538	51	2	min	min	NOUN
ejpam-6538	51	3	{	{	PUNCT
ejpam-6538	51	4	n	n	CCONJ
ejpam-6538	51	5	∈	∈	PROPN
ejpam-6538	51	6	n	n	NOUN
ejpam-6538	51	7	∪	∪	X
ejpam-6538	51	8	{	{	PUNCT
ejpam-6538	51	9	0	0	NUM
ejpam-6538	51	10	}	}	PUNCT
ejpam-6538	51	11	|	|	ADV
ejpam-6538	51	12	fn(x	fn(x	NOUN
ejpam-6538	51	13	)	)	PUNCT
ejpam-6538	51	14	=	=	SYM
ejpam-6538	51	15	1	1	X
ejpam-6538	51	16	}	}	PUNCT
ejpam-6538	51	17	for	for	ADP
ejpam-6538	51	18	all	all	DET
ejpam-6538	51	19	x	x	SYM
ejpam-6538	51	20	∈	∈	PROPN
ejpam-6538	51	21	a	a	PRON
ejpam-6538	51	22	and	and	CCONJ
ejpam-6538	51	23	ht(0	ht(0	NOUN
ejpam-6538	51	24	)	)	PUNCT
ejpam-6538	51	25	=	=	SYM
ejpam-6538	51	26	ℓ(a	ℓ(a	PROPN
ejpam-6538	51	27	)	)	PUNCT
ejpam-6538	51	28	.	.	PUNCT
ejpam-6538	52	1	we	we	PRON
ejpam-6538	52	2	denote	denote	VERB
ejpam-6538	52	3	the	the	DET
ejpam-6538	52	4	m	m	NOUN
ejpam-6538	52	5	-	-	ADJ
ejpam-6538	52	6	element	element	ADJ
ejpam-6538	52	7	chain	chain	NOUN
ejpam-6538	52	8	by	by	ADP
ejpam-6538	52	9	cm	cm	NOUN
ejpam-6538	52	10	=	=	SYM
ejpam-6538	52	11	{	{	PUNCT
ejpam-6538	52	12	1̄	1̄	NUM
ejpam-6538	52	13	≺	≺	NOUN
ejpam-6538	52	14	2̄	2̄	NOUN
ejpam-6538	52	15	≺	≺	NOUN
ejpam-6538	52	16	.	.	PUNCT
ejpam-6538	52	17	.	.	PUNCT
ejpam-6538	52	18	.	.	PUNCT
ejpam-6538	53	1	≺	≺	NOUN
ejpam-6538	53	2	m	m	VERB
ejpam-6538	53	3	}	}	PUNCT
ejpam-6538	53	4	for	for	ADP
ejpam-6538	53	5	m	m	PROPN
ejpam-6538	53	6	∈	∈	PROPN
ejpam-6538	53	7	n.	n.	NOUN
ejpam-6538	53	8	for	for	ADP
ejpam-6538	53	9	convenient	convenient	ADJ
ejpam-6538	53	10	,	,	PUNCT
ejpam-6538	53	11	let	let	VERB
ejpam-6538	53	12	a	a	PRON
ejpam-6538	53	13	=	=	SYM
ejpam-6538	53	14	1	1	NUM
ejpam-6538	53	15	and	and	CCONJ
ejpam-6538	53	16	b	b	X
ejpam-6538	53	17	=	=	NOUN
ejpam-6538	53	18	m	m	VERB
ejpam-6538	53	19	in	in	ADP
ejpam-6538	53	20	cm	cm	NOUN
ejpam-6538	53	21	for	for	ADP
ejpam-6538	53	22	all	all	DET
ejpam-6538	53	23	a	a	DET
ejpam-6538	53	24	≤	≤	NUM
ejpam-6538	53	25	1	1	NUM
ejpam-6538	53	26	and	and	CCONJ
ejpam-6538	53	27	b	b	NOUN
ejpam-6538	53	28	≥	≥	NOUN
ejpam-6538	53	29	m.	m.	NOUN
ejpam-6538	53	30	a.	a.	NOUN
ejpam-6538	53	31	charoenpol	charoenpol	PROPN
ejpam-6538	53	32	,	,	PUNCT
ejpam-6538	53	33	u.	u.	PROPN
ejpam-6538	53	34	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	53	35	/	/	SYM
ejpam-6538	53	36	eur	eur	PROPN
ejpam-6538	53	37	.	.	PUNCT
ejpam-6538	54	1	j.	j.	PROPN
ejpam-6538	54	2	pure	pure	PROPN
ejpam-6538	54	3	appl	appl	PROPN
ejpam-6538	54	4	.	.	PROPN
ejpam-6538	54	5	math	math	PROPN
ejpam-6538	54	6	,	,	PUNCT
ejpam-6538	54	7	18	18	NUM
ejpam-6538	54	8	(	(	PUNCT
ejpam-6538	54	9	3	3	NUM
ejpam-6538	54	10	)	)	PUNCT
ejpam-6538	54	11	(	(	PUNCT
ejpam-6538	54	12	2025	2025	NUM
ejpam-6538	54	13	)	)	PUNCT
ejpam-6538	54	14	,	,	PUNCT
ejpam-6538	54	15	6538	6538	NUM
ejpam-6538	54	16	4	4	NUM
ejpam-6538	54	17	of	of	ADP
ejpam-6538	54	18	13	13	NUM
ejpam-6538	54	19	?	?	PUNCT
ejpam-6538	54	20	?	?	PUNCT
ejpam-6538	54	21	?	?	PUNCT
ejpam-6538	55	1	�	�	PROPN
ejpam-6538	55	2	�	�	PROPN
ejpam-6538	55	3	�	�	PROPN
ejpam-6538	55	4	�	�	PROPN
ejpam-6538	55	5	?	?	PUNCT
ejpam-6538	56	1	�	�	PROPN
ejpam-6538	56	2	�	�	PROPN
ejpam-6538	56	3	r	r	NOUN
ejpam-6538	56	4	r	r	NOUN
ejpam-6538	56	5	r	r	NOUN
ejpam-6538	56	6	r	r	NOUN
ejpam-6538	56	7	r	r	NOUN
ejpam-6538	56	8	r	r	NOUN
ejpam-6538	56	9	r	r	NOUN
ejpam-6538	56	10	r	r	NOUN
ejpam-6538	56	11	r	r	NOUN
ejpam-6538	56	12	ppp	ppp	NOUN
ejpam-6538	56	13	⟲	⟲	PROPN
ejpam-6538	56	14	b2,1	b2,1	PROPN
ejpam-6538	56	15	b1,1	b1,1	PROPN
ejpam-6538	56	16	b1,2	b1,2	PROPN
ejpam-6538	56	17	b1,3	b1,3	PROPN
ejpam-6538	56	18	b1,n−1	b1,n−1	ADJ
ejpam-6538	56	19	b1,n	b1,n	PROPN
ejpam-6538	56	20	b2,2	b2,2	NOUN
ejpam-6538	56	21	b2,3	b2,3	PROPN
ejpam-6538	56	22	b2,n	b2,n	PROPN
ejpam-6538	56	23	figure	figure	NOUN
ejpam-6538	56	24	3	3	NUM
ejpam-6538	56	25	:	:	PUNCT
ejpam-6538	56	26	the	the	DET
ejpam-6538	56	27	graph	graph	NOUN
ejpam-6538	56	28	of	of	ADP
ejpam-6538	56	29	(	(	PUNCT
ejpam-6538	56	30	bn	bn	PROPN
ejpam-6538	56	31	,	,	PUNCT
ejpam-6538	56	32	gn	gn	PROPN
ejpam-6538	56	33	)	)	PUNCT
ejpam-6538	56	34	for	for	ADP
ejpam-6538	56	35	n	n	PRON
ejpam-6538	56	36	≥	≥	NUM
ejpam-6538	56	37	2	2	NUM
ejpam-6538	56	38	.	.	PUNCT
ejpam-6538	56	39	theorem	theorem	NOUN
ejpam-6538	56	40	2	2	NUM
ejpam-6538	56	41	.	.	PUNCT
ejpam-6538	57	1	[	[	X
ejpam-6538	57	2	10	10	NUM
ejpam-6538	57	3	]	]	PUNCT
ejpam-6538	57	4	for	for	ADP
ejpam-6538	57	5	each	each	DET
ejpam-6538	57	6	m	m	PROPN
ejpam-6538	57	7	∈	∈	PROPN
ejpam-6538	57	8	n	n	CCONJ
ejpam-6538	57	9	,	,	PUNCT
ejpam-6538	57	10	the	the	DET
ejpam-6538	57	11	unary	unary	ADJ
ejpam-6538	57	12	operation	operation	NOUN
ejpam-6538	57	13	φm×2	φm×2	PROPN
ejpam-6538	57	14	on	on	ADP
ejpam-6538	57	15	cm	cm	PROPN
ejpam-6538	57	16	×	×	PROPN
ejpam-6538	57	17	c2	c2	PROPN
ejpam-6538	57	18	defined	define	VERB
ejpam-6538	57	19	by	by	ADP
ejpam-6538	57	20	φm×2(i	φm×2(i	NOUN
ejpam-6538	57	21	,	,	PUNCT
ejpam-6538	57	22	j	j	NOUN
ejpam-6538	57	23	)	)	PUNCT
ejpam-6538	57	24	=	=	PRON
ejpam-6538	57	25	{	{	PUNCT
ejpam-6538	57	26	(	(	PUNCT
ejpam-6538	57	27	i−	i−	PROPN
ejpam-6538	57	28	1	1	NUM
ejpam-6538	57	29	,	,	PUNCT
ejpam-6538	57	30	2	2	NUM
ejpam-6538	57	31	)	)	PUNCT
ejpam-6538	57	32	if	if	SCONJ
ejpam-6538	57	33	i	i	PRON
ejpam-6538	57	34	>	>	X
ejpam-6538	57	35	1	1	NUM
ejpam-6538	57	36	,	,	PUNCT
ejpam-6538	57	37	(	(	PUNCT
ejpam-6538	57	38	1	1	NUM
ejpam-6538	57	39	,	,	PUNCT
ejpam-6538	57	40	1	1	NUM
ejpam-6538	57	41	)	)	PUNCT
ejpam-6538	57	42	if	if	SCONJ
ejpam-6538	57	43	i	i	PRON
ejpam-6538	57	44	=	=	NOUN
ejpam-6538	57	45	1	1	X
ejpam-6538	57	46	.	.	PUNCT
ejpam-6538	57	47	is	be	AUX
ejpam-6538	57	48	an	an	DET
ejpam-6538	57	49	mpp	mpp	NOUN
ejpam-6538	57	50	endomorphism	endomorphism	NOUN
ejpam-6538	57	51	of	of	ADP
ejpam-6538	57	52	cm	cm	PROPN
ejpam-6538	57	53	×c2	×c2	ADV
ejpam-6538	57	54	fixing	fix	VERB
ejpam-6538	57	55	the	the	DET
ejpam-6538	57	56	bottom	bottom	NOUN
ejpam-6538	57	57	.	.	PUNCT
ejpam-6538	58	1	by	by	ADP
ejpam-6538	58	2	theorem	theorem	NOUN
ejpam-6538	58	3	1	1	NUM
ejpam-6538	58	4	,	,	PUNCT
ejpam-6538	58	5	the	the	DET
ejpam-6538	58	6	operations	operation	NOUN
ejpam-6538	58	7	(	(	PUNCT
ejpam-6538	58	8	seen	see	VERB
ejpam-6538	58	9	in	in	ADP
ejpam-6538	58	10	[	[	X
ejpam-6538	58	11	10	10	NUM
ejpam-6538	58	12	]	]	PUNCT
ejpam-6538	58	13	)	)	PUNCT
ejpam-6538	58	14	in	in	ADP
ejpam-6538	58	15	the	the	DET
ejpam-6538	58	16	following	following	ADJ
ejpam-6538	58	17	theorem	theorem	NOUN
ejpam-6538	58	18	are	be	AUX
ejpam-6538	58	19	mpp	mpp	NOUN
ejpam-6538	58	20	endomorphisms	endomorphism	NOUN
ejpam-6538	58	21	.	.	PUNCT
ejpam-6538	59	1	theorem	theorem	VERB
ejpam-6538	59	2	3	3	NUM
ejpam-6538	59	3	.	.	X
ejpam-6538	59	4	for	for	ADP
ejpam-6538	59	5	each	each	DET
ejpam-6538	59	6	m	m	PROPN
ejpam-6538	59	7	∈	∈	PROPN
ejpam-6538	59	8	n	n	CCONJ
ejpam-6538	59	9	,	,	PUNCT
ejpam-6538	59	10	the	the	DET
ejpam-6538	59	11	operations	operation	NOUN
ejpam-6538	59	12	ζ(m	ζ(m	ADJ
ejpam-6538	59	13	,	,	PUNCT
ejpam-6538	59	14	m−1	m−1	PROPN
ejpam-6538	59	15	)	)	PUNCT
ejpam-6538	59	16	:	:	PUNCT
ejpam-6538	60	1	c	c	NOUN
ejpam-6538	60	2	2	2	NUM
ejpam-6538	60	3	m	m	PROPN
ejpam-6538	60	4	→	→	SYM
ejpam-6538	60	5	c2	c2	PROPN
ejpam-6538	60	6	m	m	PROPN
ejpam-6538	60	7	and	and	CCONJ
ejpam-6538	60	8	ζ(m−1,m	ζ(m−1,m	PROPN
ejpam-6538	60	9	)	)	PUNCT
ejpam-6538	60	10	:	:	PUNCT
ejpam-6538	61	1	c	c	NOUN
ejpam-6538	61	2	2	2	NUM
ejpam-6538	61	3	m	m	NOUN
ejpam-6538	61	4	→	→	SYM
ejpam-6538	61	5	c2	c2	PROPN
ejpam-6538	61	6	m	m	AUX
ejpam-6538	61	7	defined	define	VERB
ejpam-6538	61	8	by	by	ADP
ejpam-6538	61	9	ζ(m	ζ(m	ADJ
ejpam-6538	61	10	,	,	PUNCT
ejpam-6538	61	11	m−1)(i	m−1)(i	PROPN
ejpam-6538	61	12	,	,	PUNCT
ejpam-6538	61	13	j	j	NOUN
ejpam-6538	61	14	)	)	PUNCT
ejpam-6538	61	15	=	=	PUNCT
ejpam-6538	61	16	(	(	PUNCT
ejpam-6538	61	17	j	j	PROPN
ejpam-6538	61	18	,	,	PUNCT
ejpam-6538	61	19	i−	i−	PROPN
ejpam-6538	61	20	1	1	NUM
ejpam-6538	61	21	)	)	PUNCT
ejpam-6538	61	22	and	and	CCONJ
ejpam-6538	61	23	ζ(m−1,m)(i	ζ(m−1,m)(i	PROPN
ejpam-6538	61	24	,	,	PUNCT
ejpam-6538	61	25	j	j	PROPN
ejpam-6538	61	26	)	)	PUNCT
ejpam-6538	62	1	=	=	PUNCT
ejpam-6538	63	1	(	(	PUNCT
ejpam-6538	63	2	j	j	PROPN
ejpam-6538	63	3	−	−	PROPN
ejpam-6538	63	4	1	1	NUM
ejpam-6538	63	5	,	,	PUNCT
ejpam-6538	63	6	i	i	PRON
ejpam-6538	63	7	)	)	PUNCT
ejpam-6538	63	8	are	be	AUX
ejpam-6538	63	9	mpp	mpp	NOUN
ejpam-6538	63	10	endomorphisms	endomorphism	NOUN
ejpam-6538	63	11	of	of	ADP
ejpam-6538	63	12	c2	c2	PROPN
ejpam-6538	63	13	m	m	AUX
ejpam-6538	63	14	fixing	fix	VERB
ejpam-6538	63	15	the	the	DET
ejpam-6538	63	16	bottom	bottom	NOUN
ejpam-6538	63	17	.	.	PUNCT
ejpam-6538	64	1	lemma	lemma	PROPN
ejpam-6538	64	2	1	1	NUM
ejpam-6538	64	3	.	.	PUNCT
ejpam-6538	65	1	[	[	X
ejpam-6538	65	2	10	10	NUM
ejpam-6538	65	3	]	]	PUNCT
ejpam-6538	65	4	for	for	ADP
ejpam-6538	65	5	each	each	DET
ejpam-6538	65	6	m	m	NOUN
ejpam-6538	65	7	,	,	PUNCT
ejpam-6538	65	8	n	n	PRON
ejpam-6538	65	9	≥	≥	NOUN
ejpam-6538	65	10	3	3	NUM
ejpam-6538	65	11	,	,	PUNCT
ejpam-6538	65	12	if	if	SCONJ
ejpam-6538	65	13	f	f	PROPN
ejpam-6538	65	14	is	be	AUX
ejpam-6538	65	15	an	an	DET
ejpam-6538	65	16	mpp	mpp	NOUN
ejpam-6538	65	17	endomorphism	endomorphism	NOUN
ejpam-6538	65	18	of	of	ADP
ejpam-6538	65	19	cm	cm	PROPN
ejpam-6538	65	20	×cn	×cn	PROPN
ejpam-6538	65	21	fixing	fix	VERB
ejpam-6538	65	22	the	the	DET
ejpam-6538	65	23	bottom	bottom	NOUN
ejpam-6538	65	24	,	,	PUNCT
ejpam-6538	65	25	then	then	ADV
ejpam-6538	65	26	either	either	CCONJ
ejpam-6538	65	27	(	(	PUNCT
ejpam-6538	65	28	i	i	NOUN
ejpam-6538	65	29	)	)	PUNCT
ejpam-6538	65	30	f2k(m	f2k(m	PROPN
ejpam-6538	65	31	,	,	PUNCT
ejpam-6538	65	32	n	n	CCONJ
ejpam-6538	65	33	)	)	PUNCT
ejpam-6538	65	34	=	=	SYM
ejpam-6538	65	35	(	(	PUNCT
ejpam-6538	65	36	m−	m−	PROPN
ejpam-6538	65	37	k	k	PROPN
ejpam-6538	65	38	,	,	PUNCT
ejpam-6538	65	39	n−	n−	PROPN
ejpam-6538	65	40	k	k	NOUN
ejpam-6538	65	41	)	)	PUNCT
ejpam-6538	65	42	and	and	CCONJ
ejpam-6538	65	43	f2k+1(m	f2k+1(m	PROPN
ejpam-6538	65	44	,	,	PUNCT
ejpam-6538	65	45	n	n	CCONJ
ejpam-6538	65	46	)	)	PUNCT
ejpam-6538	65	47	=	=	SYM
ejpam-6538	65	48	(	(	PUNCT
ejpam-6538	65	49	m−	m−	PROPN
ejpam-6538	65	50	k	k	PROPN
ejpam-6538	65	51	,	,	PUNCT
ejpam-6538	65	52	n−	n−	PROPN
ejpam-6538	65	53	(	(	PUNCT
ejpam-6538	65	54	k	k	PROPN
ejpam-6538	65	55	+	+	PROPN
ejpam-6538	65	56	1	1	NUM
ejpam-6538	65	57	)	)	PUNCT
ejpam-6538	65	58	)	)	PUNCT
ejpam-6538	65	59	for	for	ADP
ejpam-6538	65	60	all	all	PRON
ejpam-6538	65	61	0	0	NUM
ejpam-6538	65	62	≤	≤	NUM
ejpam-6538	65	63	k	k	PROPN
ejpam-6538	65	64	≤	≤	NUM
ejpam-6538	65	65	min	min	NOUN
ejpam-6538	65	66	{	{	PUNCT
ejpam-6538	65	67	m−	m−	PROPN
ejpam-6538	65	68	1	1	NUM
ejpam-6538	65	69	,	,	PUNCT
ejpam-6538	65	70	n−	n−	NOUN
ejpam-6538	65	71	2	2	NUM
ejpam-6538	65	72	}	}	PUNCT
ejpam-6538	65	73	,	,	PUNCT
ejpam-6538	65	74	or	or	CCONJ
ejpam-6538	65	75	(	(	PUNCT
ejpam-6538	65	76	ii	ii	NOUN
ejpam-6538	65	77	)	)	PUNCT
ejpam-6538	65	78	f2k(m	f2k(m	PROPN
ejpam-6538	65	79	,	,	PUNCT
ejpam-6538	65	80	n	n	CCONJ
ejpam-6538	65	81	)	)	PUNCT
ejpam-6538	65	82	=	=	SYM
ejpam-6538	65	83	(	(	PUNCT
ejpam-6538	65	84	m−	m−	PROPN
ejpam-6538	65	85	k	k	PROPN
ejpam-6538	65	86	,	,	PUNCT
ejpam-6538	65	87	n−	n−	PROPN
ejpam-6538	65	88	k	k	NOUN
ejpam-6538	65	89	)	)	PUNCT
ejpam-6538	65	90	and	and	CCONJ
ejpam-6538	65	91	f2k+1(m	f2k+1(m	PROPN
ejpam-6538	65	92	,	,	PUNCT
ejpam-6538	65	93	n	n	CCONJ
ejpam-6538	65	94	)	)	PUNCT
ejpam-6538	65	95	=	=	SYM
ejpam-6538	65	96	(	(	PUNCT
ejpam-6538	65	97	m−	m−	PROPN
ejpam-6538	65	98	(	(	PUNCT
ejpam-6538	65	99	k	k	PROPN
ejpam-6538	65	100	+	+	PROPN
ejpam-6538	65	101	1	1	NUM
ejpam-6538	65	102	)	)	PUNCT
ejpam-6538	65	103	,	,	PUNCT
ejpam-6538	65	104	n−	n−	PROPN
ejpam-6538	65	105	k	k	NOUN
ejpam-6538	65	106	)	)	PUNCT
ejpam-6538	65	107	for	for	ADP
ejpam-6538	65	108	all	all	PRON
ejpam-6538	65	109	0	0	NUM
ejpam-6538	65	110	≤	≤	NUM
ejpam-6538	65	111	k	k	PROPN
ejpam-6538	65	112	≤	≤	NUM
ejpam-6538	65	113	min	min	NOUN
ejpam-6538	65	114	{	{	PUNCT
ejpam-6538	65	115	m−	m−	PROPN
ejpam-6538	65	116	2	2	NUM
ejpam-6538	65	117	,	,	PUNCT
ejpam-6538	65	118	n−	n−	NOUN
ejpam-6538	65	119	1	1	NUM
ejpam-6538	65	120	}	}	PUNCT
ejpam-6538	65	121	.	.	PUNCT
ejpam-6538	66	1	theorem	theorem	ADJ
ejpam-6538	66	2	4	4	NUM
ejpam-6538	66	3	.	.	PUNCT
ejpam-6538	67	1	[	[	X
ejpam-6538	67	2	10	10	NUM
ejpam-6538	67	3	]	]	X
ejpam-6538	67	4	let	let	VERB
ejpam-6538	67	5	m	m	PRON
ejpam-6538	67	6	,	,	PUNCT
ejpam-6538	67	7	n	n	PROPN
ejpam-6538	67	8	∈	∈	PROPN
ejpam-6538	67	9	n.	n.	NOUN
ejpam-6538	67	10	then	then	ADV
ejpam-6538	67	11	cm	cm	PROPN
ejpam-6538	67	12	×cn	×cn	PROPN
ejpam-6538	67	13	is	be	AUX
ejpam-6538	67	14	mpp	mpp	NOUN
ejpam-6538	67	15	if	if	SCONJ
ejpam-6538	68	1	and	and	CCONJ
ejpam-6538	68	2	only	only	ADV
ejpam-6538	68	3	if	if	SCONJ
ejpam-6538	68	4	either	either	DET
ejpam-6538	68	5	m	m	VERB
ejpam-6538	68	6	≤	≤	ADJ
ejpam-6538	68	7	2	2	NUM
ejpam-6538	68	8	,	,	PUNCT
ejpam-6538	68	9	n	n	DET
ejpam-6538	68	10	≤	≤	ADV
ejpam-6538	68	11	2	2	NUM
ejpam-6538	68	12	or	or	CCONJ
ejpam-6538	68	13	|m−	|m−	ADJ
ejpam-6538	68	14	n|	n|	PROPN
ejpam-6538	68	15	≤	≤	PROPN
ejpam-6538	68	16	1	1	NUM
ejpam-6538	68	17	.	.	PUNCT
ejpam-6538	68	18	a.	a.	NOUN
ejpam-6538	68	19	charoenpol	charoenpol	PROPN
ejpam-6538	68	20	,	,	PUNCT
ejpam-6538	68	21	u.	u.	PROPN
ejpam-6538	68	22	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	68	23	/	/	SYM
ejpam-6538	68	24	eur	eur	PROPN
ejpam-6538	68	25	.	.	PUNCT
ejpam-6538	69	1	j.	j.	PROPN
ejpam-6538	69	2	pure	pure	PROPN
ejpam-6538	69	3	appl	appl	PROPN
ejpam-6538	69	4	.	.	PROPN
ejpam-6538	69	5	math	math	PROPN
ejpam-6538	69	6	,	,	PUNCT
ejpam-6538	69	7	18	18	NUM
ejpam-6538	69	8	(	(	PUNCT
ejpam-6538	69	9	3	3	NUM
ejpam-6538	69	10	)	)	PUNCT
ejpam-6538	69	11	(	(	PUNCT
ejpam-6538	69	12	2025	2025	NUM
ejpam-6538	69	13	)	)	PUNCT
ejpam-6538	69	14	,	,	PUNCT
ejpam-6538	69	15	6538	6538	NUM
ejpam-6538	69	16	5	5	NUM
ejpam-6538	69	17	of	of	ADP
ejpam-6538	69	18	13	13	NUM
ejpam-6538	69	19	3	3	NUM
ejpam-6538	69	20	.	.	PUNCT
ejpam-6538	70	1	all	all	DET
ejpam-6538	70	2	mpp	mpp	NOUN
ejpam-6538	70	3	endomorphisms	endomorphism	NOUN
ejpam-6538	70	4	of	of	ADP
ejpam-6538	70	5	product	product	NOUN
ejpam-6538	70	6	of	of	ADP
ejpam-6538	70	7	two	two	NUM
ejpam-6538	70	8	chains	chain	NOUN
ejpam-6538	70	9	it	it	PRON
ejpam-6538	70	10	is	be	AUX
ejpam-6538	70	11	well	well	ADV
ejpam-6538	70	12	-	-	PUNCT
ejpam-6538	70	13	known	know	VERB
ejpam-6538	70	14	that	that	SCONJ
ejpam-6538	70	15	if	if	SCONJ
ejpam-6538	70	16	an	an	DET
ejpam-6538	70	17	algebra	algebra	NOUN
ejpam-6538	70	18	a	a	PRON
ejpam-6538	70	19	is	be	AUX
ejpam-6538	70	20	isomorphic	isomorphic	ADJ
ejpam-6538	70	21	to	to	ADP
ejpam-6538	70	22	an	an	DET
ejpam-6538	70	23	algebra	algebra	NOUN
ejpam-6538	70	24	b	b	PROPN
ejpam-6538	70	25	under	under	ADP
ejpam-6538	70	26	ϕ	ϕ	NOUN
ejpam-6538	70	27	,	,	PUNCT
ejpam-6538	70	28	the	the	DET
ejpam-6538	70	29	monoid	monoid	PROPN
ejpam-6538	70	30	end(a	end(a	PROPN
ejpam-6538	70	31	)	)	PUNCT
ejpam-6538	70	32	of	of	ADP
ejpam-6538	70	33	all	all	DET
ejpam-6538	70	34	endomorphisms	endomorphism	NOUN
ejpam-6538	70	35	of	of	ADP
ejpam-6538	70	36	a	a	PRON
ejpam-6538	70	37	is	be	AUX
ejpam-6538	70	38	isomorphic	isomorphic	ADJ
ejpam-6538	70	39	to	to	ADP
ejpam-6538	70	40	end(b	end(b	PRON
ejpam-6538	70	41	)	)	PUNCT
ejpam-6538	70	42	under	under	ADP
ejpam-6538	70	43	the	the	DET
ejpam-6538	70	44	isomorphism	isomorphism	NOUN
ejpam-6538	70	45	φ	φ	NOUN
ejpam-6538	70	46	defined	define	VERB
ejpam-6538	70	47	by	by	ADP
ejpam-6538	70	48	φ(f	φ(f	PROPN
ejpam-6538	70	49	)	)	PUNCT
ejpam-6538	71	1	=	=	PUNCT
ejpam-6538	72	1	ϕ	ϕ	PROPN
ejpam-6538	72	2	◦	◦	NOUN
ejpam-6538	72	3	f	f	NOUN
ejpam-6538	72	4	◦	◦	NOUN
ejpam-6538	72	5	ϕ−1	ϕ−1	PROPN
ejpam-6538	72	6	for	for	ADP
ejpam-6538	72	7	all	all	DET
ejpam-6538	72	8	f	f	PROPN
ejpam-6538	72	9	∈	∈	PROPN
ejpam-6538	72	10	end(a	end(a	PROPN
ejpam-6538	72	11	)	)	PUNCT
ejpam-6538	72	12	.	.	PUNCT
ejpam-6538	73	1	observe	observe	VERB
ejpam-6538	73	2	that	that	SCONJ
ejpam-6538	73	3	the	the	DET
ejpam-6538	73	4	pre	pre	NOUN
ejpam-6538	73	5	-	-	NOUN
ejpam-6538	73	6	period	period	NOUN
ejpam-6538	73	7	is	be	AUX
ejpam-6538	73	8	invariant	invariant	ADJ
ejpam-6538	73	9	under	under	ADP
ejpam-6538	73	10	φ	φ	PROPN
ejpam-6538	73	11	.	.	PUNCT
ejpam-6538	74	1	proposition	proposition	NOUN
ejpam-6538	74	2	1	1	NUM
ejpam-6538	74	3	.	.	PUNCT
ejpam-6538	75	1	let	let	VERB
ejpam-6538	75	2	ϕ	ϕ	NOUN
ejpam-6538	75	3	:	:	PUNCT
ejpam-6538	75	4	a	a	DET
ejpam-6538	75	5	→	→	SYM
ejpam-6538	75	6	b	b	X
ejpam-6538	75	7	be	be	AUX
ejpam-6538	75	8	an	an	DET
ejpam-6538	75	9	isomorphism	isomorphism	NOUN
ejpam-6538	75	10	between	between	ADP
ejpam-6538	75	11	finite	finite	PROPN
ejpam-6538	75	12	algebras	algebras	PROPN
ejpam-6538	75	13	a	a	PRON
ejpam-6538	75	14	and	and	CCONJ
ejpam-6538	75	15	b	b	NOUN
ejpam-6538	75	16	and	and	CCONJ
ejpam-6538	75	17	f	f	PROPN
ejpam-6538	75	18	∈	∈	PROPN
ejpam-6538	75	19	end(a	end(a	PROPN
ejpam-6538	75	20	)	)	PUNCT
ejpam-6538	75	21	.	.	PUNCT
ejpam-6538	76	1	then	then	ADV
ejpam-6538	76	2	(	(	PUNCT
ejpam-6538	76	3	i	i	NOUN
ejpam-6538	76	4	)	)	PUNCT
ejpam-6538	76	5	ϕ	ϕ	PROPN
ejpam-6538	76	6	◦	◦	NOUN
ejpam-6538	76	7	f	f	NOUN
ejpam-6538	76	8	◦	◦	NOUN
ejpam-6538	76	9	ϕ−1	ϕ−1	PUNCT
ejpam-6538	76	10	∈	∈	PROPN
ejpam-6538	76	11	end(b	end(b	PROPN
ejpam-6538	76	12	)	)	PUNCT
ejpam-6538	76	13	,	,	PUNCT
ejpam-6538	76	14	(	(	PUNCT
ejpam-6538	76	15	ii	ii	NOUN
ejpam-6538	76	16	)	)	PUNCT
ejpam-6538	76	17	λ(f	λ(f	NOUN
ejpam-6538	76	18	)	)	PUNCT
ejpam-6538	76	19	=	=	PUNCT
ejpam-6538	77	1	λ(ϕ	λ(ϕ	PROPN
ejpam-6538	77	2	◦	◦	NOUN
ejpam-6538	77	3	f	f	NOUN
ejpam-6538	77	4	◦	◦	NOUN
ejpam-6538	77	5	ϕ−1	ϕ−1	NUM
ejpam-6538	77	6	)	)	PUNCT
ejpam-6538	77	7	,	,	PUNCT
ejpam-6538	77	8	and	and	CCONJ
ejpam-6538	78	1	(	(	PUNCT
ejpam-6538	78	2	iii	iii	X
ejpam-6538	78	3	)	)	PUNCT
ejpam-6538	78	4	ϕ	ϕ	NOUN
ejpam-6538	78	5	is	be	AUX
ejpam-6538	78	6	an	an	DET
ejpam-6538	78	7	isomorphism	isomorphism	NOUN
ejpam-6538	78	8	from	from	ADP
ejpam-6538	78	9	(	(	PUNCT
ejpam-6538	78	10	a	a	PRON
ejpam-6538	78	11	,	,	PUNCT
ejpam-6538	78	12	f	f	NOUN
ejpam-6538	78	13	)	)	PUNCT
ejpam-6538	78	14	to	to	PART
ejpam-6538	78	15	(	(	PUNCT
ejpam-6538	78	16	b,ϕ	b,ϕ	PROPN
ejpam-6538	78	17	◦	◦	NOUN
ejpam-6538	78	18	f	f	NOUN
ejpam-6538	78	19	◦	◦	NOUN
ejpam-6538	78	20	ϕ−1	ϕ−1	PROPN
ejpam-6538	78	21	)	)	PUNCT
ejpam-6538	78	22	.	.	PUNCT
ejpam-6538	79	1	proof	proof	NOUN
ejpam-6538	79	2	.	.	PUNCT
ejpam-6538	80	1	let	let	VERB
ejpam-6538	80	2	g	g	NOUN
ejpam-6538	80	3	=	=	PUNCT
ejpam-6538	80	4	ϕ	ϕ	PROPN
ejpam-6538	80	5	◦	◦	NOUN
ejpam-6538	80	6	f	f	NOUN
ejpam-6538	80	7	◦	◦	NOUN
ejpam-6538	80	8	ϕ−1	ϕ−1	NUM
ejpam-6538	80	9	.	.	PUNCT
ejpam-6538	81	1	since	since	SCONJ
ejpam-6538	81	2	ϕ	ϕ	PROPN
ejpam-6538	81	3	,	,	PUNCT
ejpam-6538	81	4	f	f	PROPN
ejpam-6538	81	5	and	and	CCONJ
ejpam-6538	81	6	ϕ−1	ϕ−1	PROPN
ejpam-6538	81	7	are	be	AUX
ejpam-6538	81	8	homomorphisms	homomorphism	NOUN
ejpam-6538	81	9	,	,	PUNCT
ejpam-6538	81	10	so	so	ADV
ejpam-6538	81	11	is	be	AUX
ejpam-6538	81	12	g.	g.	PROPN
ejpam-6538	81	13	hence	hence	ADV
ejpam-6538	81	14	,	,	PUNCT
ejpam-6538	81	15	ϕ	ϕ	PROPN
ejpam-6538	81	16	◦	◦	NOUN
ejpam-6538	81	17	f	f	NOUN
ejpam-6538	81	18	◦	◦	NOUN
ejpam-6538	81	19	ϕ−1	ϕ−1	PUNCT
ejpam-6538	81	20	∈	∈	PROPN
ejpam-6538	81	21	end(b	end(b	PROPN
ejpam-6538	81	22	)	)	PUNCT
ejpam-6538	81	23	.	.	PUNCT
ejpam-6538	82	1	moreover	moreover	ADV
ejpam-6538	82	2	,	,	PUNCT
ejpam-6538	82	3	gλ(f)(b	gλ(f)(b	ADJ
ejpam-6538	82	4	)	)	PUNCT
ejpam-6538	83	1	=	=	SYM
ejpam-6538	83	2	ϕ	ϕ	PROPN
ejpam-6538	83	3	◦	◦	NOUN
ejpam-6538	83	4	fλ(f	fλ(f	NOUN
ejpam-6538	83	5	)	)	PUNCT
ejpam-6538	83	6	◦	◦	NOUN
ejpam-6538	83	7	ϕ−1(b	ϕ−1(b	PROPN
ejpam-6538	83	8	)	)	PUNCT
ejpam-6538	84	1	=	=	PUNCT
ejpam-6538	84	2	ϕ	ϕ	PROPN
ejpam-6538	84	3	◦	◦	NOUN
ejpam-6538	84	4	fλ(f)(a	fλ(f)(a	PROPN
ejpam-6538	84	5	)	)	PUNCT
ejpam-6538	85	1	=	=	PUNCT
ejpam-6538	85	2	ϕ	ϕ	PROPN
ejpam-6538	85	3	◦	◦	NOUN
ejpam-6538	85	4	fλ(f)+1(a	fλ(f)+1(a	PROPN
ejpam-6538	85	5	)	)	PUNCT
ejpam-6538	86	1	=	=	PUNCT
ejpam-6538	86	2	ϕ	ϕ	PROPN
ejpam-6538	86	3	◦	◦	NOUN
ejpam-6538	86	4	fλ(f)+1	fλ(f)+1	NOUN
ejpam-6538	86	5	◦	◦	NOUN
ejpam-6538	86	6	ϕ−1(b	ϕ−1(b	PROPN
ejpam-6538	86	7	)	)	PUNCT
ejpam-6538	86	8	=	=	SYM
ejpam-6538	86	9	gλ(f)+1(b	gλ(f)+1(b	NOUN
ejpam-6538	86	10	)	)	PUNCT
ejpam-6538	86	11	.	.	PUNCT
ejpam-6538	87	1	so	so	ADV
ejpam-6538	87	2	,	,	PUNCT
ejpam-6538	87	3	λ(g	λ(g	PROPN
ejpam-6538	87	4	)	)	PUNCT
ejpam-6538	87	5	≤	≤	NOUN
ejpam-6538	87	6	λ(f	λ(f	NOUN
ejpam-6538	87	7	)	)	PUNCT
ejpam-6538	87	8	.	.	PUNCT
ejpam-6538	88	1	similarly	similarly	ADV
ejpam-6538	88	2	,	,	PUNCT
ejpam-6538	88	3	λ(g	λ(g	PROPN
ejpam-6538	88	4	)	)	PUNCT
ejpam-6538	88	5	≥	≥	NOUN
ejpam-6538	88	6	λ(f	λ(f	NOUN
ejpam-6538	88	7	)	)	PUNCT
ejpam-6538	88	8	.	.	PUNCT
ejpam-6538	89	1	thus	thus	ADV
ejpam-6538	89	2	λ(g	λ(g	NOUN
ejpam-6538	89	3	)	)	PUNCT
ejpam-6538	89	4	=	=	SYM
ejpam-6538	90	1	λ(f	λ(f	NOUN
ejpam-6538	90	2	)	)	PUNCT
ejpam-6538	90	3	.	.	PUNCT
ejpam-6538	91	1	since	since	SCONJ
ejpam-6538	91	2	ϕ	ϕ	PROPN
ejpam-6538	91	3	◦	◦	NOUN
ejpam-6538	91	4	f	f	X
ejpam-6538	91	5	=	=	SYM
ejpam-6538	91	6	ϕ	ϕ	PROPN
ejpam-6538	91	7	◦	◦	NOUN
ejpam-6538	91	8	f	f	NOUN
ejpam-6538	91	9	◦	◦	NOUN
ejpam-6538	91	10	ϕ−1	ϕ−1	ADP
ejpam-6538	91	11	◦	◦	NOUN
ejpam-6538	91	12	ϕ	ϕ	NOUN
ejpam-6538	91	13	=	=	PUNCT
ejpam-6538	91	14	g	g	PROPN
ejpam-6538	91	15	◦	◦	NOUN
ejpam-6538	91	16	◦	◦	NOUN
ejpam-6538	91	17	ϕ	ϕ	NOUN
ejpam-6538	91	18	,	,	PUNCT
ejpam-6538	91	19	ϕ	ϕ	PROPN
ejpam-6538	91	20	is	be	AUX
ejpam-6538	91	21	an	an	DET
ejpam-6538	91	22	isomorphism	isomorphism	NOUN
ejpam-6538	91	23	from	from	ADP
ejpam-6538	91	24	(	(	PUNCT
ejpam-6538	91	25	a	a	PRON
ejpam-6538	91	26	,	,	PUNCT
ejpam-6538	91	27	f	f	NOUN
ejpam-6538	91	28	)	)	PUNCT
ejpam-6538	91	29	to	to	PART
ejpam-6538	91	30	(	(	PUNCT
ejpam-6538	91	31	b,ϕ	b,ϕ	PROPN
ejpam-6538	91	32	◦	◦	NOUN
ejpam-6538	91	33	f	f	NOUN
ejpam-6538	91	34	◦	◦	NOUN
ejpam-6538	91	35	ϕ−1	ϕ−1	PROPN
ejpam-6538	91	36	)	)	PUNCT
ejpam-6538	91	37	.	.	PUNCT
ejpam-6538	92	1	remark	remark	NOUN
ejpam-6538	92	2	1	1	NUM
ejpam-6538	92	3	.	.	PUNCT
ejpam-6538	93	1	let	let	VERB
ejpam-6538	93	2	m	m	PRON
ejpam-6538	93	3	,	,	PUNCT
ejpam-6538	93	4	n	n	PROPN
ejpam-6538	93	5	∈	∈	PROPN
ejpam-6538	93	6	n.	n.	NOUN
ejpam-6538	93	7	then	then	ADV
ejpam-6538	93	8	(	(	PUNCT
ejpam-6538	93	9	i	i	NOUN
ejpam-6538	93	10	)	)	PUNCT
ejpam-6538	93	11	ϕ	ϕ	NOUN
ejpam-6538	93	12	:	:	PUNCT
ejpam-6538	93	13	cm	cm	NOUN
ejpam-6538	93	14	×cn	×cn	PROPN
ejpam-6538	93	15	→	→	SYM
ejpam-6538	93	16	(	(	PUNCT
ejpam-6538	93	17	cm	cm	PROPN
ejpam-6538	93	18	×cn	×cn	PROPN
ejpam-6538	93	19	)	)	PUNCT
ejpam-6538	93	20	∂	∂	NUM
ejpam-6538	93	21	defined	define	VERB
ejpam-6538	93	22	by	by	ADP
ejpam-6538	93	23	ϕ(i	ϕ(i	PROPN
ejpam-6538	93	24	,	,	PUNCT
ejpam-6538	93	25	j	j	PROPN
ejpam-6538	93	26	)	)	PUNCT
ejpam-6538	94	1	=	=	PUNCT
ejpam-6538	94	2	(	(	PUNCT
ejpam-6538	94	3	m−	m−	PROPN
ejpam-6538	94	4	i+	i+	NUM
ejpam-6538	94	5	1	1	NUM
ejpam-6538	94	6	,	,	PUNCT
ejpam-6538	94	7	n−	n−	NOUN
ejpam-6538	94	8	j	j	NOUN
ejpam-6538	94	9	+	+	CCONJ
ejpam-6538	94	10	1	1	X
ejpam-6538	94	11	)	)	PUNCT
ejpam-6538	94	12	is	be	AUX
ejpam-6538	94	13	an	an	DET
ejpam-6538	94	14	isomorphism	isomorphism	NOUN
ejpam-6538	94	15	where	where	SCONJ
ejpam-6538	94	16	(	(	PUNCT
ejpam-6538	94	17	cm	cm	PROPN
ejpam-6538	94	18	×cn	×cn	PROPN
ejpam-6538	94	19	)	)	PUNCT
ejpam-6538	94	20	∂	∂	NUM
ejpam-6538	94	21	is	be	AUX
ejpam-6538	94	22	the	the	DET
ejpam-6538	94	23	dual	dual	ADJ
ejpam-6538	94	24	of	of	ADP
ejpam-6538	94	25	cm	cm	PROPN
ejpam-6538	94	26	×cn	×cn	PROPN
ejpam-6538	94	27	.	.	PUNCT
ejpam-6538	95	1	(	(	PUNCT
ejpam-6538	95	2	ii	ii	NOUN
ejpam-6538	95	3	)	)	PUNCT
ejpam-6538	95	4	ψ	ψ	X
ejpam-6538	95	5	:	:	PUNCT
ejpam-6538	95	6	cm	cm	PROPN
ejpam-6538	95	7	×cn	×cn	PROPN
ejpam-6538	95	8	→	→	PUNCT
ejpam-6538	95	9	cn	cn	PROPN
ejpam-6538	95	10	×cm	×cm	PROPN
ejpam-6538	95	11	defined	define	VERB
ejpam-6538	95	12	by	by	ADP
ejpam-6538	95	13	ψ(x	ψ(x	PROPN
ejpam-6538	95	14	,	,	PUNCT
ejpam-6538	95	15	y	y	NOUN
ejpam-6538	95	16	)	)	PUNCT
ejpam-6538	95	17	=	=	SYM
ejpam-6538	95	18	(	(	PUNCT
ejpam-6538	95	19	y	y	PROPN
ejpam-6538	95	20	,	,	PUNCT
ejpam-6538	95	21	x	x	X
ejpam-6538	95	22	)	)	PUNCT
ejpam-6538	95	23	is	be	AUX
ejpam-6538	95	24	an	an	DET
ejpam-6538	95	25	isomorphism	isomorphism	NOUN
ejpam-6538	95	26	.	.	PUNCT
ejpam-6538	96	1	a.	a.	NOUN
ejpam-6538	96	2	charoenpol	charoenpol	PROPN
ejpam-6538	96	3	,	,	PUNCT
ejpam-6538	96	4	u.	u.	PROPN
ejpam-6538	96	5	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	96	6	/	/	SYM
ejpam-6538	96	7	eur	eur	PROPN
ejpam-6538	96	8	.	.	PUNCT
ejpam-6538	97	1	j.	j.	PROPN
ejpam-6538	97	2	pure	pure	PROPN
ejpam-6538	97	3	appl	appl	PROPN
ejpam-6538	97	4	.	.	PROPN
ejpam-6538	97	5	math	math	PROPN
ejpam-6538	97	6	,	,	PUNCT
ejpam-6538	97	7	18	18	NUM
ejpam-6538	97	8	(	(	PUNCT
ejpam-6538	97	9	3	3	NUM
ejpam-6538	97	10	)	)	PUNCT
ejpam-6538	97	11	(	(	PUNCT
ejpam-6538	97	12	2025	2025	NUM
ejpam-6538	97	13	)	)	PUNCT
ejpam-6538	97	14	,	,	PUNCT
ejpam-6538	97	15	6538	6538	NUM
ejpam-6538	97	16	6	6	NUM
ejpam-6538	97	17	of	of	ADP
ejpam-6538	97	18	13	13	NUM
ejpam-6538	97	19	for	for	ADP
ejpam-6538	97	20	each	each	DET
ejpam-6538	97	21	f	f	PROPN
ejpam-6538	97	22	∈	∈	PROPN
ejpam-6538	97	23	end(cm	end(cm	PROPN
ejpam-6538	97	24	×cn	×cn	PROPN
ejpam-6538	97	25	)	)	PUNCT
ejpam-6538	98	1	,	,	PUNCT
ejpam-6538	98	2	we	we	PRON
ejpam-6538	98	3	denote	denote	VERB
ejpam-6538	98	4	f∂	f∂	NOUN
ejpam-6538	98	5	:	:	PUNCT
ejpam-6538	98	6	=	=	PUNCT
ejpam-6538	98	7	ϕ	ϕ	PROPN
ejpam-6538	98	8	◦	◦	NOUN
ejpam-6538	98	9	f	f	NOUN
ejpam-6538	98	10	◦	◦	NOUN
ejpam-6538	98	11	ϕ−1	ϕ−1	PROPN
ejpam-6538	98	12	and	and	CCONJ
ejpam-6538	98	13	f	f	NUM
ejpam-6538	98	14	⌣	⌣	NUM
ejpam-6538	98	15	:	:	PUNCT
ejpam-6538	99	1	=	=	PUNCT
ejpam-6538	99	2	ψ	ψ	X
ejpam-6538	99	3	◦	◦	NOUN
ejpam-6538	99	4	f	f	SYM
ejpam-6538	99	5	◦	◦	PROPN
ejpam-6538	99	6	ψ−1	ψ−1	PROPN
ejpam-6538	99	7	.	.	PUNCT
ejpam-6538	100	1	one	one	PRON
ejpam-6538	100	2	can	can	AUX
ejpam-6538	100	3	see	see	VERB
ejpam-6538	100	4	that	that	PRON
ejpam-6538	100	5	for	for	ADP
ejpam-6538	100	6	each	each	DET
ejpam-6538	100	7	f	f	PROPN
ejpam-6538	100	8	∈	∈	PROPN
ejpam-6538	100	9	end(cm	end(cm	NUM
ejpam-6538	100	10	×	×	PROPN
ejpam-6538	100	11	cn	cn	PROPN
ejpam-6538	100	12	)	)	PUNCT
ejpam-6538	100	13	,	,	PUNCT
ejpam-6538	100	14	f	f	PROPN
ejpam-6538	100	15	⌣	⌣	PROPN
ejpam-6538	100	16	∈	∈	PROPN
ejpam-6538	100	17	end(cn	end(cn	NOUN
ejpam-6538	100	18	×	×	NOUN
ejpam-6538	100	19	cm	cm	NOUN
ejpam-6538	100	20	)	)	PUNCT
ejpam-6538	100	21	and	and	CCONJ
ejpam-6538	100	22	f	f	PROPN
ejpam-6538	100	23	fixes	fix	VERB
ejpam-6538	100	24	the	the	DET
ejpam-6538	100	25	bottom	bottom	NOUN
ejpam-6538	100	26	if	if	SCONJ
ejpam-6538	100	27	and	and	CCONJ
ejpam-6538	100	28	only	only	ADV
ejpam-6538	100	29	if	if	SCONJ
ejpam-6538	100	30	f∂	f∂	NOUN
ejpam-6538	100	31	fixes	fix	NOUN
ejpam-6538	100	32	the	the	DET
ejpam-6538	100	33	top	top	NOUN
ejpam-6538	100	34	.	.	PUNCT
ejpam-6538	101	1	by	by	ADP
ejpam-6538	101	2	theorem	theorem	NOUN
ejpam-6538	101	3	4	4	NUM
ejpam-6538	101	4	and	and	CCONJ
ejpam-6538	101	5	proposition	proposition	NOUN
ejpam-6538	101	6	1	1	NUM
ejpam-6538	101	7	,	,	PUNCT
ejpam-6538	101	8	we	we	PRON
ejpam-6538	101	9	will	will	AUX
ejpam-6538	101	10	focus	focus	VERB
ejpam-6538	101	11	on	on	ADP
ejpam-6538	101	12	mpp	mpp	NOUN
ejpam-6538	101	13	endomorphisms	endomorphism	NOUN
ejpam-6538	101	14	of	of	ADP
ejpam-6538	101	15	cm	cm	PROPN
ejpam-6538	101	16	×c2	×c2	PROPN
ejpam-6538	101	17	,	,	PUNCT
ejpam-6538	101	18	cm	cm	PROPN
ejpam-6538	101	19	×cm	×cm	PROPN
ejpam-6538	101	20	and	and	CCONJ
ejpam-6538	101	21	cm	cm	NOUN
ejpam-6538	101	22	×cm−1	×cm−1	NOUN
ejpam-6538	101	23	fixing	fix	VERB
ejpam-6538	101	24	the	the	DET
ejpam-6538	101	25	bottom	bottom	NOUN
ejpam-6538	101	26	for	for	ADP
ejpam-6538	101	27	m	m	PROPN
ejpam-6538	101	28	∈	∈	PROPN
ejpam-6538	101	29	n	n	PRON
ejpam-6538	101	30	\	\	NOUN
ejpam-6538	101	31	{	{	PUNCT
ejpam-6538	101	32	1	1	NUM
ejpam-6538	101	33	}	}	PUNCT
ejpam-6538	101	34	.	.	PUNCT
ejpam-6538	102	1	lemma	lemma	PROPN
ejpam-6538	102	2	2	2	X
ejpam-6538	102	3	.	.	PUNCT
ejpam-6538	103	1	let	let	VERB
ejpam-6538	103	2	m	m	PRON
ejpam-6538	103	3	≥	≥	VERB
ejpam-6538	103	4	3	3	NUM
ejpam-6538	103	5	and	and	CCONJ
ejpam-6538	103	6	f	f	PROPN
ejpam-6538	103	7	be	be	AUX
ejpam-6538	103	8	an	an	DET
ejpam-6538	103	9	mpp	mpp	NOUN
ejpam-6538	103	10	endomorphism	endomorphism	NOUN
ejpam-6538	103	11	of	of	ADP
ejpam-6538	103	12	cm	cm	PROPN
ejpam-6538	103	13	×c2	×c2	ADV
ejpam-6538	103	14	fixing	fix	VERB
ejpam-6538	103	15	the	the	DET
ejpam-6538	103	16	bottom	bottom	NOUN
ejpam-6538	103	17	.	.	PUNCT
ejpam-6538	104	1	then	then	ADV
ejpam-6538	104	2	(	(	PUNCT
ejpam-6538	104	3	i	i	NOUN
ejpam-6538	104	4	)	)	PUNCT
ejpam-6538	104	5	f(m	f(m	PROPN
ejpam-6538	104	6	,	,	PUNCT
ejpam-6538	104	7	2̄	2̄	NUM
ejpam-6538	104	8	)	)	PUNCT
ejpam-6538	104	9	=	=	PUNCT
ejpam-6538	104	10	(	(	PUNCT
ejpam-6538	104	11	m−	m−	PROPN
ejpam-6538	104	12	1	1	NUM
ejpam-6538	104	13	,	,	PUNCT
ejpam-6538	104	14	2̄	2̄	NOUN
ejpam-6538	104	15	)	)	PUNCT
ejpam-6538	104	16	;	;	PUNCT
ejpam-6538	104	17	(	(	PUNCT
ejpam-6538	104	18	ii	ii	NOUN
ejpam-6538	104	19	)	)	PUNCT
ejpam-6538	104	20	if	if	SCONJ
ejpam-6538	104	21	f(m−	f(m−	NOUN
ejpam-6538	104	22	1	1	NUM
ejpam-6538	104	23	,	,	PUNCT
ejpam-6538	104	24	2̄	2̄	NUM
ejpam-6538	104	25	)	)	PUNCT
ejpam-6538	104	26	=	=	PUNCT
ejpam-6538	104	27	(	(	PUNCT
ejpam-6538	104	28	m−	m−	PROPN
ejpam-6538	104	29	1	1	NUM
ejpam-6538	104	30	,	,	PUNCT
ejpam-6538	104	31	1̄	1̄	NUM
ejpam-6538	104	32	)	)	PUNCT
ejpam-6538	104	33	,	,	PUNCT
ejpam-6538	104	34	then	then	ADV
ejpam-6538	104	35	m	m	VERB
ejpam-6538	104	36	=	=	NOUN
ejpam-6538	104	37	3	3	NUM
ejpam-6538	104	38	;	;	PUNCT
ejpam-6538	104	39	(	(	PUNCT
ejpam-6538	104	40	iii	iii	X
ejpam-6538	104	41	)	)	PUNCT
ejpam-6538	104	42	if	if	SCONJ
ejpam-6538	104	43	there	there	PRON
ejpam-6538	104	44	is	be	VERB
ejpam-6538	104	45	t	t	PROPN
ejpam-6538	104	46	<	<	X
ejpam-6538	104	47	m	m	NOUN
ejpam-6538	104	48	−	−	NOUN
ejpam-6538	104	49	1	1	NUM
ejpam-6538	104	50	such	such	ADJ
ejpam-6538	104	51	that	that	DET
ejpam-6538	104	52	f(i	f(i	PROPN
ejpam-6538	104	53	,	,	PUNCT
ejpam-6538	104	54	2̄	2̄	NUM
ejpam-6538	104	55	)	)	PUNCT
ejpam-6538	104	56	=	=	PUNCT
ejpam-6538	104	57	(	(	PUNCT
ejpam-6538	104	58	i−	i−	PROPN
ejpam-6538	104	59	1	1	NUM
ejpam-6538	104	60	,	,	PUNCT
ejpam-6538	104	61	2̄	2̄	NOUN
ejpam-6538	104	62	)	)	PUNCT
ejpam-6538	104	63	for	for	ADP
ejpam-6538	104	64	all	all	PRON
ejpam-6538	104	65	i	i	PRON
ejpam-6538	104	66	>	>	X
ejpam-6538	104	67	t	t	PROPN
ejpam-6538	104	68	and	and	CCONJ
ejpam-6538	104	69	f(t	f(t	NOUN
ejpam-6538	104	70	,	,	PUNCT
ejpam-6538	104	71	2̄	2̄	NUM
ejpam-6538	104	72	)	)	PUNCT
ejpam-6538	104	73	=	=	PUNCT
ejpam-6538	104	74	(	(	PUNCT
ejpam-6538	104	75	t	t	PROPN
ejpam-6538	104	76	,	,	PUNCT
ejpam-6538	104	77	1̄	1̄	NUM
ejpam-6538	104	78	)	)	PUNCT
ejpam-6538	104	79	,	,	PUNCT
ejpam-6538	104	80	then	then	ADV
ejpam-6538	104	81	t	t	PROPN
ejpam-6538	104	82	=	=	SYM
ejpam-6538	104	83	1	1	NUM
ejpam-6538	104	84	and	and	CCONJ
ejpam-6538	104	85	f(j	f(j	NOUN
ejpam-6538	104	86	,	,	PUNCT
ejpam-6538	104	87	1̄	1̄	NUM
ejpam-6538	104	88	)	)	PUNCT
ejpam-6538	104	89	=	=	PUNCT
ejpam-6538	104	90	(	(	PUNCT
ejpam-6538	104	91	j	j	PROPN
ejpam-6538	104	92	−	−	PROPN
ejpam-6538	104	93	1	1	NUM
ejpam-6538	104	94	,	,	PUNCT
ejpam-6538	104	95	2̄	2̄	NOUN
ejpam-6538	104	96	)	)	PUNCT
ejpam-6538	104	97	for	for	ADP
ejpam-6538	104	98	all	all	DET
ejpam-6538	104	99	j	j	PROPN
ejpam-6538	104	100	>	>	X
ejpam-6538	104	101	t.	t.	PROPN
ejpam-6538	104	102	proof	proof	NOUN
ejpam-6538	104	103	.	.	PUNCT
ejpam-6538	105	1	(	(	PUNCT
ejpam-6538	105	2	i	i	NOUN
ejpam-6538	105	3	)	)	PUNCT
ejpam-6538	105	4	assume	assume	VERB
ejpam-6538	105	5	that	that	SCONJ
ejpam-6538	105	6	f(m	f(m	PROPN
ejpam-6538	105	7	,	,	PUNCT
ejpam-6538	105	8	2̄	2̄	NUM
ejpam-6538	105	9	)	)	PUNCT
ejpam-6538	105	10	=	=	PUNCT
ejpam-6538	105	11	(	(	PUNCT
ejpam-6538	105	12	m	m	PROPN
ejpam-6538	105	13	,	,	PUNCT
ejpam-6538	105	14	1̄	1̄	NUM
ejpam-6538	105	15	)	)	PUNCT
ejpam-6538	105	16	.	.	PUNCT
ejpam-6538	106	1	then	then	ADV
ejpam-6538	106	2	f(m	f(m	PROPN
ejpam-6538	106	3	,	,	PUNCT
ejpam-6538	106	4	1̄	1̄	NUM
ejpam-6538	106	5	)	)	PUNCT
ejpam-6538	106	6	=	=	PUNCT
ejpam-6538	106	7	(	(	PUNCT
ejpam-6538	106	8	m−	m−	PROPN
ejpam-6538	106	9	1	1	NUM
ejpam-6538	106	10	,	,	PUNCT
ejpam-6538	106	11	1̄	1̄	NUM
ejpam-6538	106	12	)	)	PUNCT
ejpam-6538	106	13	.	.	PUNCT
ejpam-6538	107	1	since	since	SCONJ
ejpam-6538	107	2	f(1̄	f(1̄	PROPN
ejpam-6538	107	3	,	,	PUNCT
ejpam-6538	107	4	2̄	2̄	NOUN
ejpam-6538	107	5	)	)	PUNCT
ejpam-6538	107	6	≤	≤	NOUN
ejpam-6538	107	7	f(m	f(m	PROPN
ejpam-6538	107	8	,	,	PUNCT
ejpam-6538	107	9	2̄	2̄	NUM
ejpam-6538	107	10	)	)	PUNCT
ejpam-6538	107	11	=	=	PUNCT
ejpam-6538	107	12	(	(	PUNCT
ejpam-6538	107	13	m	m	PROPN
ejpam-6538	107	14	,	,	PUNCT
ejpam-6538	107	15	1̄	1̄	NUM
ejpam-6538	107	16	)	)	PUNCT
ejpam-6538	107	17	,	,	PUNCT
ejpam-6538	107	18	we	we	PRON
ejpam-6538	107	19	get	get	VERB
ejpam-6538	107	20	f(1̄	f(1̄	PROPN
ejpam-6538	107	21	,	,	PUNCT
ejpam-6538	107	22	2̄	2̄	NUM
ejpam-6538	107	23	)	)	PUNCT
ejpam-6538	107	24	=	=	PUNCT
ejpam-6538	108	1	(	(	PUNCT
ejpam-6538	108	2	k	k	X
ejpam-6538	108	3	,	,	PUNCT
ejpam-6538	108	4	1̄	1̄	NUM
ejpam-6538	108	5	)	)	PUNCT
ejpam-6538	108	6	for	for	ADP
ejpam-6538	108	7	some	some	PRON
ejpam-6538	108	8	1	1	NUM
ejpam-6538	108	9	≤	≤	NUM
ejpam-6538	108	10	k	k	PROPN
ejpam-6538	108	11	≤	≤	PROPN
ejpam-6538	108	12	m.	m.	NOUN
ejpam-6538	108	13	since	since	SCONJ
ejpam-6538	108	14	(	(	PUNCT
ejpam-6538	108	15	1̄	1̄	NUM
ejpam-6538	108	16	,	,	PUNCT
ejpam-6538	108	17	1̄	1̄	NUM
ejpam-6538	108	18	)	)	PUNCT
ejpam-6538	108	19	=	=	SYM
ejpam-6538	108	20	f(1̄	f(1̄	PROPN
ejpam-6538	108	21	,	,	PUNCT
ejpam-6538	108	22	1̄	1̄	NUM
ejpam-6538	108	23	)	)	PUNCT
ejpam-6538	109	1	=	=	SYM
ejpam-6538	109	2	f(1̄	f(1̄	PROPN
ejpam-6538	109	3	,	,	PUNCT
ejpam-6538	109	4	2̄	2̄	NOUN
ejpam-6538	109	5	)	)	PUNCT
ejpam-6538	109	6	∧	∧	PROPN
ejpam-6538	109	7	f(m	f(m	PROPN
ejpam-6538	109	8	,	,	PUNCT
ejpam-6538	109	9	1̄	1̄	NUM
ejpam-6538	109	10	)	)	PUNCT
ejpam-6538	109	11	=	=	SYM
ejpam-6538	109	12	(	(	PUNCT
ejpam-6538	109	13	k	k	X
ejpam-6538	109	14	,	,	PUNCT
ejpam-6538	109	15	1̄	1̄	NUM
ejpam-6538	109	16	)	)	PUNCT
ejpam-6538	109	17	∧	∧	PROPN
ejpam-6538	109	18	(	(	PUNCT
ejpam-6538	109	19	m−	m−	PROPN
ejpam-6538	109	20	1	1	NUM
ejpam-6538	109	21	,	,	PUNCT
ejpam-6538	109	22	1̄	1̄	NUM
ejpam-6538	109	23	)	)	PUNCT
ejpam-6538	109	24	,	,	PUNCT
ejpam-6538	109	25	we	we	PRON
ejpam-6538	109	26	get	get	VERB
ejpam-6538	109	27	k	k	NOUN
ejpam-6538	109	28	=	=	SYM
ejpam-6538	109	29	1	1	X
ejpam-6538	109	30	.	.	PUNCT
ejpam-6538	110	1	so	so	ADV
ejpam-6538	110	2	,	,	PUNCT
ejpam-6538	110	3	(	(	PUNCT
ejpam-6538	110	4	m	m	NOUN
ejpam-6538	110	5	,	,	PUNCT
ejpam-6538	110	6	1̄	1̄	NUM
ejpam-6538	110	7	)	)	PUNCT
ejpam-6538	110	8	=	=	PUNCT
ejpam-6538	110	9	f(m	f(m	PROPN
ejpam-6538	110	10	,	,	PUNCT
ejpam-6538	110	11	2̄	2̄	NUM
ejpam-6538	110	12	)	)	PUNCT
ejpam-6538	110	13	=	=	SYM
ejpam-6538	111	1	f(1̄	f(1̄	PROPN
ejpam-6538	111	2	,	,	PUNCT
ejpam-6538	111	3	2̄	2̄	NUM
ejpam-6538	111	4	)	)	PUNCT
ejpam-6538	111	5	∨	∨	NUM
ejpam-6538	111	6	f(m	f(m	PROPN
ejpam-6538	111	7	,	,	PUNCT
ejpam-6538	111	8	1̄	1̄	NUM
ejpam-6538	111	9	)	)	PUNCT
ejpam-6538	111	10	=	=	SYM
ejpam-6538	111	11	(	(	PUNCT
ejpam-6538	111	12	1̄	1̄	NUM
ejpam-6538	111	13	,	,	PUNCT
ejpam-6538	111	14	1̄	1̄	NUM
ejpam-6538	111	15	)	)	PUNCT
ejpam-6538	111	16	∨	∨	NOUN
ejpam-6538	111	17	(	(	PUNCT
ejpam-6538	111	18	m−	m−	PROPN
ejpam-6538	111	19	1	1	NUM
ejpam-6538	111	20	,	,	PUNCT
ejpam-6538	111	21	1̄	1̄	NUM
ejpam-6538	111	22	)	)	PUNCT
ejpam-6538	111	23	=	=	PUNCT
ejpam-6538	111	24	(	(	PUNCT
ejpam-6538	111	25	m−	m−	PROPN
ejpam-6538	111	26	1	1	NUM
ejpam-6538	111	27	,	,	PUNCT
ejpam-6538	111	28	1̄	1̄	NUM
ejpam-6538	111	29	)	)	PUNCT
ejpam-6538	111	30	,	,	PUNCT
ejpam-6538	111	31	a	a	DET
ejpam-6538	111	32	contradiction	contradiction	NOUN
ejpam-6538	111	33	.	.	PUNCT
ejpam-6538	112	1	by	by	ADP
ejpam-6538	112	2	theorem	theorem	NOUN
ejpam-6538	112	3	1	1	NUM
ejpam-6538	112	4	,	,	PUNCT
ejpam-6538	112	5	f(m	f(m	PROPN
ejpam-6538	112	6	,	,	PUNCT
ejpam-6538	112	7	2̄	2̄	NUM
ejpam-6538	112	8	)	)	PUNCT
ejpam-6538	112	9	=	=	PUNCT
ejpam-6538	112	10	(	(	PUNCT
ejpam-6538	112	11	m−	m−	PROPN
ejpam-6538	112	12	1	1	NUM
ejpam-6538	112	13	,	,	PUNCT
ejpam-6538	112	14	2̄	2̄	NOUN
ejpam-6538	112	15	)	)	PUNCT
ejpam-6538	112	16	.	.	PUNCT
ejpam-6538	113	1	(	(	PUNCT
ejpam-6538	113	2	ii	ii	NOUN
ejpam-6538	113	3	)	)	PUNCT
ejpam-6538	113	4	suppose	suppose	VERB
ejpam-6538	113	5	that	that	SCONJ
ejpam-6538	113	6	f(m−	f(m−	PROPN
ejpam-6538	113	7	1	1	NUM
ejpam-6538	113	8	,	,	PUNCT
ejpam-6538	113	9	2̄	2̄	NUM
ejpam-6538	113	10	)	)	PUNCT
ejpam-6538	113	11	=	=	PUNCT
ejpam-6538	113	12	(	(	PUNCT
ejpam-6538	113	13	m−	m−	PROPN
ejpam-6538	113	14	1	1	NUM
ejpam-6538	113	15	,	,	PUNCT
ejpam-6538	113	16	1̄	1̄	NUM
ejpam-6538	113	17	)	)	PUNCT
ejpam-6538	113	18	.	.	PUNCT
ejpam-6538	114	1	by	by	ADP
ejpam-6538	114	2	theorem	theorem	NOUN
ejpam-6538	114	3	1	1	NUM
ejpam-6538	114	4	,	,	PUNCT
ejpam-6538	114	5	f(m−	f(m−	NOUN
ejpam-6538	114	6	1	1	NUM
ejpam-6538	114	7	,	,	PUNCT
ejpam-6538	114	8	1̄	1̄	NUM
ejpam-6538	114	9	)	)	PUNCT
ejpam-6538	114	10	=	=	PUNCT
ejpam-6538	115	1	(	(	PUNCT
ejpam-6538	115	2	m−	m−	PROPN
ejpam-6538	115	3	2	2	NUM
ejpam-6538	115	4	,	,	PUNCT
ejpam-6538	115	5	1̄	1̄	NUM
ejpam-6538	115	6	)	)	PUNCT
ejpam-6538	115	7	.	.	PUNCT
ejpam-6538	116	1	since	since	SCONJ
ejpam-6538	116	2	f(m−	f(m−	NOUN
ejpam-6538	116	3	2	2	NUM
ejpam-6538	116	4	,	,	PUNCT
ejpam-6538	116	5	2̄	2̄	NOUN
ejpam-6538	116	6	)	)	PUNCT
ejpam-6538	116	7	≤	≤	NUM
ejpam-6538	116	8	f(m−	f(m−	PRON
ejpam-6538	116	9	1	1	NUM
ejpam-6538	116	10	,	,	PUNCT
ejpam-6538	116	11	2̄	2̄	NUM
ejpam-6538	116	12	)	)	PUNCT
ejpam-6538	116	13	=	=	PUNCT
ejpam-6538	117	1	(	(	PUNCT
ejpam-6538	117	2	m−	m−	PROPN
ejpam-6538	117	3	1	1	NUM
ejpam-6538	117	4	,	,	PUNCT
ejpam-6538	117	5	1̄	1̄	NUM
ejpam-6538	117	6	)	)	PUNCT
ejpam-6538	117	7	,	,	PUNCT
ejpam-6538	117	8	we	we	PRON
ejpam-6538	117	9	get	get	VERB
ejpam-6538	117	10	f(m−	f(m−	PRON
ejpam-6538	117	11	2	2	NUM
ejpam-6538	117	12	,	,	PUNCT
ejpam-6538	117	13	2̄	2̄	NUM
ejpam-6538	117	14	)	)	PUNCT
ejpam-6538	117	15	=	=	PUNCT
ejpam-6538	118	1	(	(	PUNCT
ejpam-6538	118	2	k	k	X
ejpam-6538	118	3	,	,	PUNCT
ejpam-6538	118	4	1̄	1̄	NUM
ejpam-6538	118	5	)	)	PUNCT
ejpam-6538	118	6	for	for	ADP
ejpam-6538	118	7	some	some	DET
ejpam-6538	118	8	1	1	NUM
ejpam-6538	118	9	≤	≤	NUM
ejpam-6538	118	10	k	k	NOUN
ejpam-6538	118	11	≤	≤	PROPN
ejpam-6538	118	12	m−	m−	PROPN
ejpam-6538	118	13	1	1	NUM
ejpam-6538	118	14	.	.	PUNCT
ejpam-6538	119	1	since	since	SCONJ
ejpam-6538	119	2	(	(	PUNCT
ejpam-6538	119	3	m−	m−	PROPN
ejpam-6538	119	4	1	1	NUM
ejpam-6538	119	5	,	,	PUNCT
ejpam-6538	119	6	1̄	1̄	NUM
ejpam-6538	119	7	)	)	PUNCT
ejpam-6538	119	8	=	=	NOUN
ejpam-6538	119	9	f(m−	f(m−	NOUN
ejpam-6538	119	10	1	1	NUM
ejpam-6538	119	11	,	,	PUNCT
ejpam-6538	119	12	2̄	2̄	NUM
ejpam-6538	119	13	)	)	PUNCT
ejpam-6538	119	14	=	=	NOUN
ejpam-6538	119	15	f(m−	f(m−	NOUN
ejpam-6538	119	16	1	1	NUM
ejpam-6538	119	17	,	,	PUNCT
ejpam-6538	119	18	1̄	1̄	NUM
ejpam-6538	119	19	)	)	PUNCT
ejpam-6538	119	20	∨	∨	NUM
ejpam-6538	119	21	f(m−	f(m−	NOUN
ejpam-6538	119	22	2	2	NUM
ejpam-6538	119	23	,	,	PUNCT
ejpam-6538	119	24	2̄	2̄	NUM
ejpam-6538	119	25	)	)	PUNCT
ejpam-6538	119	26	=	=	PUNCT
ejpam-6538	119	27	(	(	PUNCT
ejpam-6538	119	28	m−	m−	PROPN
ejpam-6538	119	29	2	2	NUM
ejpam-6538	119	30	,	,	PUNCT
ejpam-6538	119	31	1̄	1̄	NUM
ejpam-6538	119	32	)	)	PUNCT
ejpam-6538	119	33	∨	∨	NOUN
ejpam-6538	119	34	(	(	PUNCT
ejpam-6538	119	35	k	k	NOUN
ejpam-6538	119	36	,	,	PUNCT
ejpam-6538	119	37	1̄	1̄	NUM
ejpam-6538	119	38	)	)	PUNCT
ejpam-6538	119	39	,	,	PUNCT
ejpam-6538	119	40	we	we	PRON
ejpam-6538	119	41	get	get	VERB
ejpam-6538	119	42	k	k	PROPN
ejpam-6538	119	43	=	=	PUNCT
ejpam-6538	119	44	m−	m−	PROPN
ejpam-6538	119	45	1	1	NUM
ejpam-6538	119	46	.	.	PUNCT
ejpam-6538	120	1	since	since	SCONJ
ejpam-6538	120	2	f(m−	f(m−	NOUN
ejpam-6538	120	3	2	2	NUM
ejpam-6538	120	4	,	,	PUNCT
ejpam-6538	120	5	1̄	1̄	NUM
ejpam-6538	120	6	)	)	PUNCT
ejpam-6538	120	7	=	=	NOUN
ejpam-6538	120	8	f(m−	f(m−	NOUN
ejpam-6538	120	9	1	1	NUM
ejpam-6538	120	10	,	,	PUNCT
ejpam-6538	120	11	1̄	1̄	NUM
ejpam-6538	120	12	)	)	PUNCT
ejpam-6538	120	13	∧	∧	NOUN
ejpam-6538	120	14	f(m−	f(m−	NOUN
ejpam-6538	120	15	2	2	NUM
ejpam-6538	120	16	,	,	PUNCT
ejpam-6538	120	17	2̄	2̄	NUM
ejpam-6538	120	18	)	)	PUNCT
ejpam-6538	120	19	=	=	PUNCT
ejpam-6538	121	1	(	(	PUNCT
ejpam-6538	121	2	m−	m−	PROPN
ejpam-6538	121	3	2	2	NUM
ejpam-6538	121	4	,	,	PUNCT
ejpam-6538	121	5	1̄	1̄	NUM
ejpam-6538	121	6	)	)	PUNCT
ejpam-6538	121	7	∧	∧	PROPN
ejpam-6538	121	8	(	(	PUNCT
ejpam-6538	121	9	m−	m−	PROPN
ejpam-6538	121	10	1	1	NUM
ejpam-6538	121	11	,	,	PUNCT
ejpam-6538	121	12	1̄	1̄	NUM
ejpam-6538	121	13	)	)	PUNCT
ejpam-6538	121	14	=	=	PUNCT
ejpam-6538	121	15	(	(	PUNCT
ejpam-6538	121	16	m−	m−	PROPN
ejpam-6538	121	17	2	2	NUM
ejpam-6538	121	18	,	,	PUNCT
ejpam-6538	121	19	1̄	1̄	NUM
ejpam-6538	121	20	)	)	PUNCT
ejpam-6538	121	21	and	and	CCONJ
ejpam-6538	121	22	(	(	PUNCT
ejpam-6538	121	23	1	1	NUM
ejpam-6538	121	24	,	,	PUNCT
ejpam-6538	121	25	1̄	1̄	NUM
ejpam-6538	121	26	)	)	PUNCT
ejpam-6538	121	27	is	be	AUX
ejpam-6538	121	28	the	the	DET
ejpam-6538	121	29	unique	unique	ADJ
ejpam-6538	121	30	fixed	fix	VERB
ejpam-6538	121	31	point	point	NOUN
ejpam-6538	121	32	,	,	PUNCT
ejpam-6538	121	33	m−	m−	PROPN
ejpam-6538	121	34	2	2	NUM
ejpam-6538	121	35	=	=	SYM
ejpam-6538	121	36	1	1	NUM
ejpam-6538	121	37	;	;	PUNCT
ejpam-6538	121	38	that	that	PRON
ejpam-6538	121	39	is	be	AUX
ejpam-6538	121	40	,	,	PUNCT
ejpam-6538	121	41	m	m	VERB
ejpam-6538	121	42	=	=	NOUN
ejpam-6538	121	43	3	3	X
ejpam-6538	121	44	.	.	PUNCT
ejpam-6538	121	45	(	(	PUNCT
ejpam-6538	121	46	iii	iii	NOUN
ejpam-6538	121	47	)	)	PUNCT
ejpam-6538	121	48	suppose	suppose	VERB
ejpam-6538	121	49	that	that	SCONJ
ejpam-6538	121	50	there	there	PRON
ejpam-6538	121	51	is	be	VERB
ejpam-6538	121	52	t	t	PROPN
ejpam-6538	121	53	<	<	X
ejpam-6538	121	54	m	m	NOUN
ejpam-6538	121	55	−	−	NOUN
ejpam-6538	121	56	1	1	NUM
ejpam-6538	121	57	such	such	ADJ
ejpam-6538	121	58	that	that	DET
ejpam-6538	121	59	f(i	f(i	PROPN
ejpam-6538	121	60	,	,	PUNCT
ejpam-6538	121	61	2̄	2̄	NUM
ejpam-6538	121	62	)	)	PUNCT
ejpam-6538	121	63	=	=	PUNCT
ejpam-6538	122	1	(	(	PUNCT
ejpam-6538	122	2	i−	i−	PROPN
ejpam-6538	122	3	1	1	NUM
ejpam-6538	122	4	,	,	PUNCT
ejpam-6538	122	5	2̄	2̄	NOUN
ejpam-6538	122	6	)	)	PUNCT
ejpam-6538	122	7	for	for	ADP
ejpam-6538	122	8	all	all	PRON
ejpam-6538	122	9	i	i	PRON
ejpam-6538	122	10	>	>	X
ejpam-6538	122	11	t	t	PROPN
ejpam-6538	122	12	and	and	CCONJ
ejpam-6538	122	13	f(t	f(t	NOUN
ejpam-6538	122	14	,	,	PUNCT
ejpam-6538	122	15	2̄	2̄	NUM
ejpam-6538	122	16	)	)	PUNCT
ejpam-6538	122	17	=	=	PUNCT
ejpam-6538	122	18	(	(	PUNCT
ejpam-6538	122	19	t	t	PROPN
ejpam-6538	122	20	,	,	PUNCT
ejpam-6538	122	21	1̄	1̄	NUM
ejpam-6538	122	22	)	)	PUNCT
ejpam-6538	122	23	and	and	CCONJ
ejpam-6538	122	24	let	let	VERB
ejpam-6538	122	25	j	j	PROPN
ejpam-6538	122	26	>	>	X
ejpam-6538	122	27	t.	t.	PROPN
ejpam-6538	123	1	then	then	ADV
ejpam-6538	123	2	(	(	PUNCT
ejpam-6538	123	3	j	j	PROPN
ejpam-6538	123	4	−	−	PROPN
ejpam-6538	123	5	1	1	NUM
ejpam-6538	123	6	,	,	PUNCT
ejpam-6538	123	7	2̄	2̄	NUM
ejpam-6538	123	8	)	)	PUNCT
ejpam-6538	123	9	=	=	PUNCT
ejpam-6538	123	10	f(j	f(j	NOUN
ejpam-6538	123	11	,	,	PUNCT
ejpam-6538	123	12	2̄	2̄	NUM
ejpam-6538	123	13	)	)	PUNCT
ejpam-6538	123	14	=	=	PUNCT
ejpam-6538	123	15	f(t	f(t	NOUN
ejpam-6538	123	16	,	,	PUNCT
ejpam-6538	123	17	2̄	2̄	NUM
ejpam-6538	123	18	)	)	PUNCT
ejpam-6538	123	19	∨	∨	NOUN
ejpam-6538	123	20	f(j	f(j	NOUN
ejpam-6538	123	21	,	,	PUNCT
ejpam-6538	123	22	1̄	1̄	NUM
ejpam-6538	123	23	)	)	PUNCT
ejpam-6538	123	24	=	=	SYM
ejpam-6538	123	25	(	(	PUNCT
ejpam-6538	123	26	t	t	PROPN
ejpam-6538	123	27	,	,	PUNCT
ejpam-6538	123	28	1̄	1̄	NUM
ejpam-6538	123	29	)	)	PUNCT
ejpam-6538	123	30	∨	∨	NOUN
ejpam-6538	123	31	f(j	f(j	NOUN
ejpam-6538	123	32	,	,	PUNCT
ejpam-6538	123	33	1̄	1̄	NUM
ejpam-6538	123	34	)	)	PUNCT
ejpam-6538	123	35	.	.	PUNCT
ejpam-6538	124	1	a.	a.	NOUN
ejpam-6538	124	2	charoenpol	charoenpol	PROPN
ejpam-6538	124	3	,	,	PUNCT
ejpam-6538	124	4	u.	u.	PROPN
ejpam-6538	124	5	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	124	6	/	/	SYM
ejpam-6538	124	7	eur	eur	PROPN
ejpam-6538	124	8	.	.	PUNCT
ejpam-6538	125	1	j.	j.	PROPN
ejpam-6538	125	2	pure	pure	PROPN
ejpam-6538	125	3	appl	appl	PROPN
ejpam-6538	125	4	.	.	PROPN
ejpam-6538	125	5	math	math	PROPN
ejpam-6538	125	6	,	,	PUNCT
ejpam-6538	125	7	18	18	NUM
ejpam-6538	125	8	(	(	PUNCT
ejpam-6538	125	9	3	3	NUM
ejpam-6538	125	10	)	)	PUNCT
ejpam-6538	125	11	(	(	PUNCT
ejpam-6538	125	12	2025	2025	NUM
ejpam-6538	125	13	)	)	PUNCT
ejpam-6538	125	14	,	,	PUNCT
ejpam-6538	125	15	6538	6538	NUM
ejpam-6538	125	16	7	7	NUM
ejpam-6538	125	17	of	of	ADP
ejpam-6538	125	18	13	13	NUM
ejpam-6538	125	19	for	for	ADP
ejpam-6538	125	20	j	j	PROPN
ejpam-6538	125	21	>	>	X
ejpam-6538	125	22	t	t	PROPN
ejpam-6538	126	1	+	+	CCONJ
ejpam-6538	126	2	1	1	NUM
ejpam-6538	126	3	,	,	PUNCT
ejpam-6538	126	4	we	we	PRON
ejpam-6538	126	5	have	have	VERB
ejpam-6538	126	6	j	j	NOUN
ejpam-6538	126	7	−	−	ADP
ejpam-6538	126	8	1	1	NUM
ejpam-6538	126	9	>	>	SYM
ejpam-6538	126	10	t	t	NOUN
ejpam-6538	126	11	which	which	PRON
ejpam-6538	126	12	implies	imply	VERB
ejpam-6538	126	13	by	by	ADP
ejpam-6538	126	14	the	the	DET
ejpam-6538	126	15	property	property	NOUN
ejpam-6538	126	16	of	of	ADP
ejpam-6538	126	17	chain	chain	NOUN
ejpam-6538	126	18	that	that	SCONJ
ejpam-6538	126	19	f(j	f(j	NOUN
ejpam-6538	126	20	,	,	PUNCT
ejpam-6538	126	21	1̄	1̄	NUM
ejpam-6538	126	22	)	)	PUNCT
ejpam-6538	126	23	=	=	PUNCT
ejpam-6538	127	1	(	(	PUNCT
ejpam-6538	127	2	j	j	PROPN
ejpam-6538	127	3	−	−	PROPN
ejpam-6538	127	4	1	1	NUM
ejpam-6538	127	5	,	,	PUNCT
ejpam-6538	127	6	2̄	2̄	NOUN
ejpam-6538	127	7	)	)	PUNCT
ejpam-6538	127	8	and	and	CCONJ
ejpam-6538	127	9	f(t+	f(t+	NUM
ejpam-6538	127	10	1	1	NUM
ejpam-6538	127	11	,	,	PUNCT
ejpam-6538	127	12	1̄	1̄	NUM
ejpam-6538	127	13	)	)	PUNCT
ejpam-6538	127	14	=	=	PUNCT
ejpam-6538	128	1	f(t+	f(t+	NOUN
ejpam-6538	128	2	2	2	NUM
ejpam-6538	128	3	,	,	PUNCT
ejpam-6538	128	4	1̄	1̄	NUM
ejpam-6538	128	5	)	)	PUNCT
ejpam-6538	128	6	∧	∧	NOUN
ejpam-6538	128	7	f(t+	f(t+	NOUN
ejpam-6538	128	8	1	1	NUM
ejpam-6538	128	9	,	,	PUNCT
ejpam-6538	128	10	2̄	2̄	NUM
ejpam-6538	128	11	)	)	PUNCT
ejpam-6538	128	12	=	=	SYM
ejpam-6538	128	13	(	(	PUNCT
ejpam-6538	128	14	t+	t+	NOUN
ejpam-6538	128	15	1	1	NUM
ejpam-6538	128	16	,	,	PUNCT
ejpam-6538	128	17	2̄	2̄	NOUN
ejpam-6538	128	18	)	)	PUNCT
ejpam-6538	128	19	∧	∧	PROPN
ejpam-6538	128	20	(	(	PUNCT
ejpam-6538	128	21	t	t	PROPN
ejpam-6538	128	22	,	,	PUNCT
ejpam-6538	128	23	2̄	2̄	NOUN
ejpam-6538	128	24	)	)	PUNCT
ejpam-6538	128	25	=	=	PUNCT
ejpam-6538	128	26	(	(	PUNCT
ejpam-6538	128	27	t	t	PROPN
ejpam-6538	128	28	,	,	PUNCT
ejpam-6538	128	29	2̄	2̄	NOUN
ejpam-6538	128	30	)	)	PUNCT
ejpam-6538	128	31	.	.	PUNCT
ejpam-6538	129	1	hence	hence	ADV
ejpam-6538	129	2	,	,	PUNCT
ejpam-6538	129	3	f(t	f(t	PROPN
ejpam-6538	129	4	,	,	PUNCT
ejpam-6538	129	5	1̄	1̄	NUM
ejpam-6538	129	6	)	)	PUNCT
ejpam-6538	129	7	=	=	PUNCT
ejpam-6538	129	8	f(t	f(t	NOUN
ejpam-6538	129	9	,	,	PUNCT
ejpam-6538	129	10	2̄	2̄	NOUN
ejpam-6538	129	11	)	)	PUNCT
ejpam-6538	129	12	∧	∧	NOUN
ejpam-6538	129	13	f(t+	f(t+	NOUN
ejpam-6538	129	14	1	1	NUM
ejpam-6538	129	15	,	,	PUNCT
ejpam-6538	129	16	1̄	1̄	NUM
ejpam-6538	129	17	)	)	PUNCT
ejpam-6538	129	18	=	=	SYM
ejpam-6538	129	19	(	(	PUNCT
ejpam-6538	129	20	t	t	PROPN
ejpam-6538	129	21	,	,	PUNCT
ejpam-6538	129	22	1̄	1̄	NUM
ejpam-6538	129	23	)	)	PUNCT
ejpam-6538	129	24	∧	∧	PROPN
ejpam-6538	129	25	(	(	PUNCT
ejpam-6538	129	26	t	t	PROPN
ejpam-6538	129	27	,	,	PUNCT
ejpam-6538	129	28	2̄	2̄	NOUN
ejpam-6538	129	29	)	)	PUNCT
ejpam-6538	129	30	=	=	PUNCT
ejpam-6538	129	31	(	(	PUNCT
ejpam-6538	129	32	t	t	PROPN
ejpam-6538	129	33	,	,	PUNCT
ejpam-6538	129	34	1̄	1̄	NUM
ejpam-6538	129	35	)	)	PUNCT
ejpam-6538	129	36	.	.	PUNCT
ejpam-6538	130	1	since	since	SCONJ
ejpam-6538	130	2	(	(	PUNCT
ejpam-6538	130	3	1	1	NUM
ejpam-6538	130	4	,	,	PUNCT
ejpam-6538	130	5	1̄	1̄	NUM
ejpam-6538	130	6	)	)	PUNCT
ejpam-6538	130	7	is	be	AUX
ejpam-6538	130	8	the	the	DET
ejpam-6538	130	9	unique	unique	ADJ
ejpam-6538	130	10	fixed	fix	VERB
ejpam-6538	130	11	point	point	NOUN
ejpam-6538	130	12	,	,	PUNCT
ejpam-6538	130	13	t	t	NOUN
ejpam-6538	130	14	=	=	SYM
ejpam-6538	130	15	1	1	X
ejpam-6538	130	16	.	.	PUNCT
ejpam-6538	130	17	theorem	theorem	NOUN
ejpam-6538	130	18	5	5	NUM
ejpam-6538	130	19	.	.	PUNCT
ejpam-6538	131	1	let	let	VERB
ejpam-6538	131	2	m	m	PRON
ejpam-6538	131	3	∈	∈	VERB
ejpam-6538	131	4	n	n	X
ejpam-6538	131	5	with	with	ADP
ejpam-6538	131	6	m	m	PROPN
ejpam-6538	131	7	≥	≥	NOUN
ejpam-6538	131	8	2	2	NUM
ejpam-6538	131	9	.	.	PUNCT
ejpam-6538	132	1	(	(	PUNCT
ejpam-6538	132	2	i	i	NOUN
ejpam-6538	132	3	)	)	PUNCT
ejpam-6538	132	4	for	for	ADP
ejpam-6538	132	5	m	m	PROPN
ejpam-6538	132	6	≤	≤	NOUN
ejpam-6538	132	7	3	3	NUM
ejpam-6538	132	8	,	,	PUNCT
ejpam-6538	132	9	ζ(m	ζ(m	ADJ
ejpam-6538	132	10	,	,	PUNCT
ejpam-6538	132	11	m−1	m−1	PROPN
ejpam-6538	132	12	)	)	PUNCT
ejpam-6538	133	1	⇂	⇂	ADP
ejpam-6538	133	2	cm×c2	cm×c2	PROPN
ejpam-6538	133	3	and	and	CCONJ
ejpam-6538	133	4	φm×2	φm×2	PROPN
ejpam-6538	133	5	are	be	AUX
ejpam-6538	133	6	all	all	PRON
ejpam-6538	133	7	mpp	mpp	NOUN
ejpam-6538	133	8	endomorphisms	endomorphism	NOUN
ejpam-6538	133	9	of	of	ADP
ejpam-6538	133	10	cm	cm	PROPN
ejpam-6538	133	11	×	×	PROPN
ejpam-6538	133	12	c2	c2	PROPN
ejpam-6538	133	13	fixing	fix	VERB
ejpam-6538	133	14	the	the	DET
ejpam-6538	133	15	bottom	bottom	NOUN
ejpam-6538	133	16	.	.	PUNCT
ejpam-6538	134	1	(	(	PUNCT
ejpam-6538	134	2	ii	ii	NOUN
ejpam-6538	134	3	)	)	PUNCT
ejpam-6538	134	4	for	for	ADP
ejpam-6538	134	5	m	m	PROPN
ejpam-6538	134	6	>	>	X
ejpam-6538	134	7	3	3	NUM
ejpam-6538	134	8	,	,	PUNCT
ejpam-6538	134	9	φm×2	φm×2	PROPN
ejpam-6538	134	10	is	be	AUX
ejpam-6538	134	11	the	the	DET
ejpam-6538	134	12	unique	unique	ADJ
ejpam-6538	134	13	mpp	mpp	NOUN
ejpam-6538	134	14	endomorphism	endomorphism	NOUN
ejpam-6538	134	15	of	of	ADP
ejpam-6538	134	16	cm	cm	PROPN
ejpam-6538	134	17	×c2	×c2	ADV
ejpam-6538	134	18	fixing	fix	VERB
ejpam-6538	134	19	the	the	DET
ejpam-6538	134	20	bottom	bottom	NOUN
ejpam-6538	134	21	.	.	PUNCT
ejpam-6538	135	1	(	(	PUNCT
ejpam-6538	135	2	iii	iii	NOUN
ejpam-6538	135	3	)	)	PUNCT
ejpam-6538	135	4	for	for	ADP
ejpam-6538	135	5	m	m	PROPN
ejpam-6538	135	6	≥	≥	NOUN
ejpam-6538	135	7	3	3	NUM
ejpam-6538	135	8	,	,	PUNCT
ejpam-6538	135	9	ζ(m	ζ(m	ADJ
ejpam-6538	135	10	,	,	PUNCT
ejpam-6538	135	11	m−1	m−1	PROPN
ejpam-6538	135	12	)	)	PUNCT
ejpam-6538	135	13	and	and	CCONJ
ejpam-6538	135	14	ζ(m−1,m	ζ(m−1,m	PROPN
ejpam-6538	135	15	)	)	PUNCT
ejpam-6538	135	16	are	be	AUX
ejpam-6538	135	17	all	all	PRON
ejpam-6538	135	18	mpp	mpp	NOUN
ejpam-6538	135	19	endomorphisms	endomorphism	NOUN
ejpam-6538	135	20	of	of	ADP
ejpam-6538	135	21	cm	cm	PROPN
ejpam-6538	135	22	×cm	×cm	PROPN
ejpam-6538	135	23	fixing	fix	VERB
ejpam-6538	135	24	the	the	DET
ejpam-6538	135	25	bottom	bottom	NOUN
ejpam-6538	135	26	.	.	PUNCT
ejpam-6538	136	1	(	(	PUNCT
ejpam-6538	136	2	iv	iv	X
ejpam-6538	136	3	)	)	PUNCT
ejpam-6538	136	4	for	for	ADP
ejpam-6538	136	5	m	m	PROPN
ejpam-6538	136	6	>	>	X
ejpam-6538	136	7	3	3	NUM
ejpam-6538	136	8	,	,	PUNCT
ejpam-6538	136	9	ζ(m	ζ(m	ADJ
ejpam-6538	136	10	,	,	PUNCT
ejpam-6538	136	11	m−1	m−1	PROPN
ejpam-6538	136	12	)	)	PUNCT
ejpam-6538	137	1	⇂	⇂	ADP
ejpam-6538	137	2	cm×cm−1	cm×cm−1	PROPN
ejpam-6538	137	3	is	be	AUX
ejpam-6538	137	4	the	the	DET
ejpam-6538	137	5	unique	unique	ADJ
ejpam-6538	137	6	mpp	mpp	NOUN
ejpam-6538	137	7	endomorphism	endomorphism	NOUN
ejpam-6538	137	8	of	of	ADP
ejpam-6538	137	9	cm	cm	PROPN
ejpam-6538	137	10	×	×	PROPN
ejpam-6538	137	11	cm−1	cm−1	NOUN
ejpam-6538	137	12	fixing	fix	VERB
ejpam-6538	137	13	the	the	DET
ejpam-6538	137	14	bottom	bottom	NOUN
ejpam-6538	137	15	.	.	PUNCT
ejpam-6538	138	1	proof	proof	NOUN
ejpam-6538	138	2	.	.	PUNCT
ejpam-6538	139	1	(	(	PUNCT
ejpam-6538	139	2	i	i	NOUN
ejpam-6538	139	3	)	)	PUNCT
ejpam-6538	139	4	let	let	VERB
ejpam-6538	139	5	f	f	PRON
ejpam-6538	139	6	be	be	AUX
ejpam-6538	139	7	an	an	DET
ejpam-6538	139	8	mpp	mpp	NOUN
ejpam-6538	139	9	endomorphism	endomorphism	NOUN
ejpam-6538	139	10	of	of	ADP
ejpam-6538	139	11	c2	c2	PROPN
ejpam-6538	139	12	×	×	PROPN
ejpam-6538	139	13	c2	c2	PROPN
ejpam-6538	139	14	fixing	fix	VERB
ejpam-6538	139	15	the	the	DET
ejpam-6538	139	16	bottom	bottom	NOUN
ejpam-6538	139	17	.	.	PUNCT
ejpam-6538	140	1	then	then	ADV
ejpam-6538	140	2	f(2̄	f(2̄	PROPN
ejpam-6538	140	3	,	,	PUNCT
ejpam-6538	140	4	2̄	2̄	NUM
ejpam-6538	140	5	)	)	PUNCT
ejpam-6538	140	6	=	=	PUNCT
ejpam-6538	140	7	(	(	PUNCT
ejpam-6538	140	8	2̄	2̄	NOUN
ejpam-6538	140	9	,	,	PUNCT
ejpam-6538	140	10	1̄	1̄	NUM
ejpam-6538	140	11	)	)	PUNCT
ejpam-6538	140	12	or	or	CCONJ
ejpam-6538	140	13	f(2̄	f(2̄	PROPN
ejpam-6538	140	14	,	,	PUNCT
ejpam-6538	140	15	2̄	2̄	NOUN
ejpam-6538	140	16	)	)	PUNCT
ejpam-6538	140	17	=	=	PUNCT
ejpam-6538	140	18	(	(	PUNCT
ejpam-6538	140	19	1̄	1̄	NUM
ejpam-6538	140	20	,	,	PUNCT
ejpam-6538	140	21	2̄	2̄	NOUN
ejpam-6538	140	22	)	)	PUNCT
ejpam-6538	140	23	.	.	PUNCT
ejpam-6538	141	1	case	case	NOUN
ejpam-6538	141	2	f(2̄	f(2̄	PROPN
ejpam-6538	141	3	,	,	PUNCT
ejpam-6538	141	4	2̄	2̄	NUM
ejpam-6538	141	5	)	)	PUNCT
ejpam-6538	141	6	=	=	PUNCT
ejpam-6538	141	7	(	(	PUNCT
ejpam-6538	141	8	2̄	2̄	NOUN
ejpam-6538	141	9	,	,	PUNCT
ejpam-6538	141	10	1̄	1̄	NUM
ejpam-6538	141	11	)	)	PUNCT
ejpam-6538	141	12	.	.	PUNCT
ejpam-6538	142	1	then	then	ADV
ejpam-6538	142	2	f(2̄	f(2̄	PROPN
ejpam-6538	142	3	,	,	PUNCT
ejpam-6538	142	4	1̄	1̄	NUM
ejpam-6538	142	5	)	)	PUNCT
ejpam-6538	142	6	=	=	SYM
ejpam-6538	142	7	(	(	PUNCT
ejpam-6538	142	8	1̄	1̄	NUM
ejpam-6538	142	9	,	,	PUNCT
ejpam-6538	142	10	1̄	1̄	NUM
ejpam-6538	142	11	)	)	PUNCT
ejpam-6538	142	12	.	.	PUNCT
ejpam-6538	143	1	since	since	SCONJ
ejpam-6538	143	2	(	(	PUNCT
ejpam-6538	143	3	2̄	2̄	NOUN
ejpam-6538	143	4	,	,	PUNCT
ejpam-6538	143	5	1̄	1̄	NUM
ejpam-6538	143	6	)	)	PUNCT
ejpam-6538	143	7	=	=	SYM
ejpam-6538	143	8	f(2̄	f(2̄	PROPN
ejpam-6538	143	9	,	,	PUNCT
ejpam-6538	143	10	2̄	2̄	NOUN
ejpam-6538	143	11	)	)	PUNCT
ejpam-6538	143	12	=	=	SYM
ejpam-6538	143	13	f(2̄	f(2̄	PROPN
ejpam-6538	143	14	,	,	PUNCT
ejpam-6538	143	15	1̄	1̄	NUM
ejpam-6538	143	16	)	)	PUNCT
ejpam-6538	143	17	∨	∨	NUM
ejpam-6538	143	18	f(1̄	f(1̄	PROPN
ejpam-6538	143	19	,	,	PUNCT
ejpam-6538	143	20	2̄	2̄	NUM
ejpam-6538	143	21	)	)	PUNCT
ejpam-6538	143	22	=	=	PUNCT
ejpam-6538	143	23	(	(	PUNCT
ejpam-6538	143	24	1̄	1̄	NUM
ejpam-6538	143	25	,	,	PUNCT
ejpam-6538	143	26	1̄	1̄	NUM
ejpam-6538	143	27	)	)	PUNCT
ejpam-6538	143	28	∨	∨	NUM
ejpam-6538	143	29	f(1̄	f(1̄	PROPN
ejpam-6538	143	30	,	,	PUNCT
ejpam-6538	143	31	2̄	2̄	NOUN
ejpam-6538	143	32	)	)	PUNCT
ejpam-6538	143	33	,	,	PUNCT
ejpam-6538	143	34	f(1̄	f(1̄	PROPN
ejpam-6538	143	35	,	,	PUNCT
ejpam-6538	143	36	2̄	2̄	NUM
ejpam-6538	143	37	)	)	PUNCT
ejpam-6538	143	38	=	=	PUNCT
ejpam-6538	143	39	(	(	PUNCT
ejpam-6538	143	40	2̄	2̄	NOUN
ejpam-6538	143	41	,	,	PUNCT
ejpam-6538	143	42	1̄	1̄	NUM
ejpam-6538	143	43	)	)	PUNCT
ejpam-6538	143	44	which	which	PRON
ejpam-6538	143	45	implies	imply	VERB
ejpam-6538	143	46	that	that	SCONJ
ejpam-6538	143	47	f	f	PROPN
ejpam-6538	143	48	=	=	SYM
ejpam-6538	143	49	ζ(2,1	ζ(2,1	PROPN
ejpam-6538	143	50	)	)	PUNCT
ejpam-6538	143	51	.	.	PUNCT
ejpam-6538	144	1	case	case	NOUN
ejpam-6538	144	2	f(2̄	f(2̄	PROPN
ejpam-6538	144	3	,	,	PUNCT
ejpam-6538	144	4	2̄	2̄	NUM
ejpam-6538	144	5	)	)	PUNCT
ejpam-6538	144	6	=	=	PUNCT
ejpam-6538	144	7	(	(	PUNCT
ejpam-6538	144	8	1̄	1̄	NUM
ejpam-6538	144	9	,	,	PUNCT
ejpam-6538	144	10	2̄	2̄	NOUN
ejpam-6538	144	11	)	)	PUNCT
ejpam-6538	144	12	.	.	PUNCT
ejpam-6538	145	1	similarly	similarly	ADV
ejpam-6538	145	2	,	,	PUNCT
ejpam-6538	145	3	f	f	PROPN
ejpam-6538	145	4	=	=	SYM
ejpam-6538	145	5	ζ(1,2)(=	ζ(1,2)(=	NUM
ejpam-6538	145	6	φ2×2	φ2×2	NOUN
ejpam-6538	145	7	)	)	PUNCT
ejpam-6538	145	8	.	.	PUNCT
ejpam-6538	146	1	in	in	ADP
ejpam-6538	146	2	any	any	DET
ejpam-6538	146	3	cases	case	NOUN
ejpam-6538	146	4	,	,	PUNCT
ejpam-6538	146	5	we	we	PRON
ejpam-6538	146	6	are	be	AUX
ejpam-6538	146	7	done	do	VERB
ejpam-6538	146	8	for	for	ADP
ejpam-6538	146	9	m	m	PROPN
ejpam-6538	146	10	=	=	SYM
ejpam-6538	146	11	2	2	X
ejpam-6538	146	12	.	.	PUNCT
ejpam-6538	147	1	let	let	VERB
ejpam-6538	147	2	f	f	PRON
ejpam-6538	147	3	be	be	AUX
ejpam-6538	147	4	an	an	DET
ejpam-6538	147	5	mpp	mpp	NOUN
ejpam-6538	147	6	endomorphism	endomorphism	NOUN
ejpam-6538	147	7	of	of	ADP
ejpam-6538	147	8	c3	c3	PROPN
ejpam-6538	147	9	×	×	PROPN
ejpam-6538	147	10	c2	c2	PROPN
ejpam-6538	147	11	fixing	fix	VERB
ejpam-6538	147	12	the	the	DET
ejpam-6538	147	13	bottom	bottom	NOUN
ejpam-6538	147	14	.	.	PUNCT
ejpam-6538	148	1	by	by	ADP
ejpam-6538	148	2	lemma	lemma	PROPN
ejpam-6538	148	3	2	2	PROPN
ejpam-6538	148	4	(	(	PUNCT
ejpam-6538	148	5	i	i	NOUN
ejpam-6538	148	6	)	)	PUNCT
ejpam-6538	148	7	,	,	PUNCT
ejpam-6538	148	8	f(3	f(3	PROPN
ejpam-6538	148	9	,	,	PUNCT
ejpam-6538	148	10	2̄	2̄	NOUN
ejpam-6538	148	11	)	)	PUNCT
ejpam-6538	148	12	=	=	PUNCT
ejpam-6538	148	13	(	(	PUNCT
ejpam-6538	148	14	2	2	NUM
ejpam-6538	148	15	,	,	PUNCT
ejpam-6538	148	16	2̄	2̄	NOUN
ejpam-6538	148	17	)	)	PUNCT
ejpam-6538	148	18	;	;	PUNCT
ejpam-6538	148	19	and	and	CCONJ
ejpam-6538	148	20	so	so	ADV
ejpam-6538	148	21	,	,	PUNCT
ejpam-6538	148	22	f(3	f(3	PROPN
ejpam-6538	148	23	,	,	PUNCT
ejpam-6538	148	24	1̄	1̄	NUM
ejpam-6538	148	25	)	)	PUNCT
ejpam-6538	148	26	≤	≤	NOUN
ejpam-6538	148	27	(	(	PUNCT
ejpam-6538	148	28	2	2	NUM
ejpam-6538	148	29	,	,	PUNCT
ejpam-6538	148	30	2̄	2̄	NOUN
ejpam-6538	148	31	)	)	PUNCT
ejpam-6538	148	32	.	.	PUNCT
ejpam-6538	149	1	thus	thus	ADV
ejpam-6538	149	2	f	f	X
ejpam-6538	149	3	⇂	⇂	NOUN
ejpam-6538	149	4	c2×c2	c2×c2	PROPN
ejpam-6538	149	5	is	be	AUX
ejpam-6538	149	6	an	an	DET
ejpam-6538	149	7	mpp	mpp	NOUN
ejpam-6538	149	8	endomorphism	endomorphism	NOUN
ejpam-6538	149	9	of	of	ADP
ejpam-6538	149	10	c2	c2	PROPN
ejpam-6538	149	11	×c2	×c2	ADV
ejpam-6538	149	12	fixing	fix	VERB
ejpam-6538	149	13	the	the	DET
ejpam-6538	149	14	bottom	bottom	NOUN
ejpam-6538	149	15	.	.	PUNCT
ejpam-6538	150	1	case	case	NOUN
ejpam-6538	150	2	f	f	PROPN
ejpam-6538	151	1	⇂	⇂	NOUN
ejpam-6538	151	2	c2×c2=	c2×c2=	NOUN
ejpam-6538	151	3	ζ(2,1	ζ(2,1	NUM
ejpam-6538	151	4	)	)	PUNCT
ejpam-6538	151	5	.	.	PUNCT
ejpam-6538	152	1	thus	thus	ADV
ejpam-6538	152	2	f(2̄	f(2̄	PROPN
ejpam-6538	152	3	,	,	PUNCT
ejpam-6538	152	4	2̄	2̄	NUM
ejpam-6538	152	5	)	)	PUNCT
ejpam-6538	152	6	=	=	PUNCT
ejpam-6538	152	7	(	(	PUNCT
ejpam-6538	152	8	2̄	2̄	NOUN
ejpam-6538	152	9	,	,	PUNCT
ejpam-6538	152	10	1̄	1̄	NUM
ejpam-6538	152	11	)	)	PUNCT
ejpam-6538	152	12	and	and	CCONJ
ejpam-6538	152	13	f(2̄	f(2̄	PROPN
ejpam-6538	152	14	,	,	PUNCT
ejpam-6538	152	15	1̄	1̄	NUM
ejpam-6538	152	16	)	)	PUNCT
ejpam-6538	152	17	=	=	SYM
ejpam-6538	152	18	(	(	PUNCT
ejpam-6538	152	19	1̄	1̄	NUM
ejpam-6538	152	20	,	,	PUNCT
ejpam-6538	152	21	1̄	1̄	NUM
ejpam-6538	152	22	)	)	PUNCT
ejpam-6538	152	23	.	.	PUNCT
ejpam-6538	153	1	since	since	SCONJ
ejpam-6538	153	2	(	(	PUNCT
ejpam-6538	153	3	1̄	1̄	NUM
ejpam-6538	153	4	,	,	PUNCT
ejpam-6538	153	5	1̄	1̄	NUM
ejpam-6538	153	6	)	)	PUNCT
ejpam-6538	153	7	=	=	SYM
ejpam-6538	153	8	f(2̄	f(2̄	PROPN
ejpam-6538	153	9	,	,	PUNCT
ejpam-6538	153	10	1̄	1̄	NUM
ejpam-6538	153	11	)	)	PUNCT
ejpam-6538	153	12	=	=	SYM
ejpam-6538	153	13	f(2̄	f(2̄	PROPN
ejpam-6538	153	14	,	,	PUNCT
ejpam-6538	153	15	2̄	2̄	NOUN
ejpam-6538	153	16	)	)	PUNCT
ejpam-6538	153	17	∧	∧	PROPN
ejpam-6538	153	18	f(3	f(3	PROPN
ejpam-6538	153	19	,	,	PUNCT
ejpam-6538	153	20	1̄	1̄	NUM
ejpam-6538	153	21	)	)	PUNCT
ejpam-6538	153	22	=	=	PUNCT
ejpam-6538	153	23	(	(	PUNCT
ejpam-6538	153	24	2̄	2̄	NOUN
ejpam-6538	153	25	,	,	PUNCT
ejpam-6538	153	26	1̄	1̄	NUM
ejpam-6538	153	27	)	)	PUNCT
ejpam-6538	153	28	∧	∧	PROPN
ejpam-6538	153	29	f(3	f(3	PROPN
ejpam-6538	153	30	,	,	PUNCT
ejpam-6538	153	31	1̄	1̄	NUM
ejpam-6538	153	32	)	)	PUNCT
ejpam-6538	153	33	and	and	CCONJ
ejpam-6538	153	34	(	(	PUNCT
ejpam-6538	153	35	2̄	2̄	NOUN
ejpam-6538	153	36	,	,	PUNCT
ejpam-6538	153	37	2̄	2̄	NUM
ejpam-6538	153	38	)	)	PUNCT
ejpam-6538	153	39	=	=	SYM
ejpam-6538	153	40	f(3	f(3	PROPN
ejpam-6538	153	41	,	,	PUNCT
ejpam-6538	153	42	2̄	2̄	NOUN
ejpam-6538	153	43	)	)	PUNCT
ejpam-6538	153	44	=	=	SYM
ejpam-6538	153	45	f(2̄	f(2̄	PROPN
ejpam-6538	153	46	,	,	PUNCT
ejpam-6538	153	47	2̄	2̄	NOUN
ejpam-6538	153	48	)	)	PUNCT
ejpam-6538	153	49	∨	∨	NUM
ejpam-6538	153	50	f(3	f(3	PROPN
ejpam-6538	153	51	,	,	PUNCT
ejpam-6538	153	52	1̄	1̄	NUM
ejpam-6538	153	53	)	)	PUNCT
ejpam-6538	153	54	=	=	PUNCT
ejpam-6538	153	55	(	(	PUNCT
ejpam-6538	153	56	2̄	2̄	NOUN
ejpam-6538	153	57	,	,	PUNCT
ejpam-6538	153	58	1̄	1̄	NUM
ejpam-6538	153	59	)	)	PUNCT
ejpam-6538	153	60	∨	∨	NUM
ejpam-6538	153	61	f(3	f(3	PROPN
ejpam-6538	153	62	,	,	PUNCT
ejpam-6538	153	63	1̄	1̄	NUM
ejpam-6538	153	64	)	)	PUNCT
ejpam-6538	153	65	,	,	PUNCT
ejpam-6538	153	66	we	we	PRON
ejpam-6538	153	67	get	get	VERB
ejpam-6538	153	68	f(3	f(3	PROPN
ejpam-6538	153	69	,	,	PUNCT
ejpam-6538	153	70	1̄	1̄	NUM
ejpam-6538	153	71	)	)	PUNCT
ejpam-6538	153	72	=	=	PUNCT
ejpam-6538	153	73	(	(	PUNCT
ejpam-6538	153	74	1̄	1̄	NUM
ejpam-6538	153	75	,	,	PUNCT
ejpam-6538	153	76	2̄	2̄	NOUN
ejpam-6538	153	77	)	)	PUNCT
ejpam-6538	153	78	.	.	PUNCT
ejpam-6538	154	1	so	so	ADV
ejpam-6538	154	2	,	,	PUNCT
ejpam-6538	154	3	f	f	PROPN
ejpam-6538	154	4	=	=	SYM
ejpam-6538	154	5	ζ(3,2	ζ(3,2	PROPN
ejpam-6538	154	6	)	)	PUNCT
ejpam-6538	154	7	⇂	⇂	ADP
ejpam-6538	154	8	c3×c2	c3×c2	PROPN
ejpam-6538	154	9	.	.	PUNCT
ejpam-6538	155	1	case	case	NOUN
ejpam-6538	155	2	f	f	X
ejpam-6538	156	1	⇂	⇂	NOUN
ejpam-6538	156	2	c2×c2=	c2×c2=	NOUN
ejpam-6538	156	3	ζ(1,2	ζ(1,2	PROPN
ejpam-6538	156	4	)	)	PUNCT
ejpam-6538	156	5	.	.	PUNCT
ejpam-6538	157	1	thus	thus	ADV
ejpam-6538	157	2	f(2̄	f(2̄	PROPN
ejpam-6538	157	3	,	,	PUNCT
ejpam-6538	157	4	2̄	2̄	NUM
ejpam-6538	157	5	)	)	PUNCT
ejpam-6538	157	6	=	=	PUNCT
ejpam-6538	157	7	(	(	PUNCT
ejpam-6538	157	8	1̄	1̄	NUM
ejpam-6538	157	9	,	,	PUNCT
ejpam-6538	157	10	2̄	2̄	NUM
ejpam-6538	157	11	)	)	PUNCT
ejpam-6538	157	12	and	and	CCONJ
ejpam-6538	157	13	f(2̄	f(2̄	PROPN
ejpam-6538	157	14	,	,	PUNCT
ejpam-6538	157	15	1̄	1̄	NUM
ejpam-6538	157	16	)	)	PUNCT
ejpam-6538	157	17	=	=	SYM
ejpam-6538	157	18	(	(	PUNCT
ejpam-6538	157	19	1̄	1̄	NUM
ejpam-6538	157	20	,	,	PUNCT
ejpam-6538	157	21	2̄	2̄	NOUN
ejpam-6538	157	22	)	)	PUNCT
ejpam-6538	157	23	.	.	PUNCT
ejpam-6538	158	1	since	since	SCONJ
ejpam-6538	158	2	(	(	PUNCT
ejpam-6538	158	3	1̄	1̄	NUM
ejpam-6538	158	4	,	,	PUNCT
ejpam-6538	158	5	2̄	2̄	NUM
ejpam-6538	158	6	)	)	PUNCT
ejpam-6538	158	7	=	=	SYM
ejpam-6538	158	8	f(2̄	f(2̄	PROPN
ejpam-6538	158	9	,	,	PUNCT
ejpam-6538	158	10	1̄	1̄	NUM
ejpam-6538	158	11	)	)	PUNCT
ejpam-6538	158	12	=	=	SYM
ejpam-6538	158	13	f(2̄	f(2̄	PROPN
ejpam-6538	158	14	,	,	PUNCT
ejpam-6538	158	15	2̄	2̄	NOUN
ejpam-6538	158	16	)	)	PUNCT
ejpam-6538	158	17	∧	∧	PROPN
ejpam-6538	158	18	f(3	f(3	PROPN
ejpam-6538	158	19	,	,	PUNCT
ejpam-6538	158	20	1̄	1̄	NUM
ejpam-6538	158	21	)	)	PUNCT
ejpam-6538	158	22	=	=	PUNCT
ejpam-6538	158	23	(	(	PUNCT
ejpam-6538	158	24	1̄	1̄	NUM
ejpam-6538	158	25	,	,	PUNCT
ejpam-6538	158	26	2̄	2̄	NOUN
ejpam-6538	158	27	)	)	PUNCT
ejpam-6538	158	28	∧	∧	PROPN
ejpam-6538	158	29	f(3	f(3	PROPN
ejpam-6538	158	30	,	,	PUNCT
ejpam-6538	158	31	1̄	1̄	NUM
ejpam-6538	158	32	)	)	PUNCT
ejpam-6538	158	33	and	and	CCONJ
ejpam-6538	158	34	(	(	PUNCT
ejpam-6538	158	35	2̄	2̄	NOUN
ejpam-6538	158	36	,	,	PUNCT
ejpam-6538	158	37	2̄	2̄	NUM
ejpam-6538	158	38	)	)	PUNCT
ejpam-6538	158	39	=	=	SYM
ejpam-6538	158	40	f(3	f(3	PROPN
ejpam-6538	158	41	,	,	PUNCT
ejpam-6538	158	42	2̄	2̄	NOUN
ejpam-6538	158	43	)	)	PUNCT
ejpam-6538	158	44	=	=	SYM
ejpam-6538	158	45	f(2̄	f(2̄	PROPN
ejpam-6538	158	46	,	,	PUNCT
ejpam-6538	158	47	2̄	2̄	NOUN
ejpam-6538	158	48	)	)	PUNCT
ejpam-6538	158	49	∨	∨	NUM
ejpam-6538	158	50	f(3	f(3	PROPN
ejpam-6538	158	51	,	,	PUNCT
ejpam-6538	158	52	1̄	1̄	NUM
ejpam-6538	158	53	)	)	PUNCT
ejpam-6538	158	54	=	=	PUNCT
ejpam-6538	158	55	(	(	PUNCT
ejpam-6538	158	56	1̄	1̄	NUM
ejpam-6538	158	57	,	,	PUNCT
ejpam-6538	158	58	2̄	2̄	NOUN
ejpam-6538	158	59	)	)	PUNCT
ejpam-6538	158	60	∨	∨	NUM
ejpam-6538	158	61	f(3	f(3	PROPN
ejpam-6538	158	62	,	,	PUNCT
ejpam-6538	158	63	1̄	1̄	NUM
ejpam-6538	158	64	)	)	PUNCT
ejpam-6538	158	65	,	,	PUNCT
ejpam-6538	158	66	a.	a.	NOUN
ejpam-6538	158	67	charoenpol	charoenpol	NOUN
ejpam-6538	158	68	,	,	PUNCT
ejpam-6538	158	69	u.	u.	PROPN
ejpam-6538	158	70	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	158	71	/	/	SYM
ejpam-6538	158	72	eur	eur	PROPN
ejpam-6538	158	73	.	.	PUNCT
ejpam-6538	159	1	j.	j.	PROPN
ejpam-6538	159	2	pure	pure	PROPN
ejpam-6538	159	3	appl	appl	PROPN
ejpam-6538	159	4	.	.	PROPN
ejpam-6538	159	5	math	math	PROPN
ejpam-6538	159	6	,	,	PUNCT
ejpam-6538	159	7	18	18	NUM
ejpam-6538	159	8	(	(	PUNCT
ejpam-6538	159	9	3	3	NUM
ejpam-6538	159	10	)	)	PUNCT
ejpam-6538	159	11	(	(	PUNCT
ejpam-6538	159	12	2025	2025	NUM
ejpam-6538	159	13	)	)	PUNCT
ejpam-6538	159	14	,	,	PUNCT
ejpam-6538	159	15	6538	6538	NUM
ejpam-6538	159	16	8	8	NUM
ejpam-6538	159	17	of	of	ADP
ejpam-6538	159	18	13	13	NUM
ejpam-6538	159	19	we	we	PRON
ejpam-6538	159	20	get	get	VERB
ejpam-6538	159	21	f(3	f(3	PROPN
ejpam-6538	159	22	,	,	PUNCT
ejpam-6538	159	23	1̄	1̄	NUM
ejpam-6538	159	24	)	)	PUNCT
ejpam-6538	159	25	=	=	PUNCT
ejpam-6538	159	26	(	(	PUNCT
ejpam-6538	159	27	2̄	2̄	NOUN
ejpam-6538	159	28	,	,	PUNCT
ejpam-6538	159	29	2̄	2̄	NOUN
ejpam-6538	159	30	)	)	PUNCT
ejpam-6538	159	31	.	.	PUNCT
ejpam-6538	160	1	so	so	ADV
ejpam-6538	160	2	,	,	PUNCT
ejpam-6538	160	3	f	f	PROPN
ejpam-6538	160	4	=	=	PUNCT
ejpam-6538	160	5	φ3×2	φ3×2	PROPN
ejpam-6538	160	6	.	.	PUNCT
ejpam-6538	161	1	(	(	PUNCT
ejpam-6538	161	2	ii	ii	X
ejpam-6538	161	3	)	)	PUNCT
ejpam-6538	161	4	the	the	DET
ejpam-6538	161	5	proof	proof	NOUN
ejpam-6538	161	6	follows	follow	VERB
ejpam-6538	161	7	directly	directly	ADV
ejpam-6538	161	8	from	from	ADP
ejpam-6538	161	9	lemma	lemma	PROPN
ejpam-6538	161	10	2	2	NUM
ejpam-6538	161	11	(	(	PUNCT
ejpam-6538	161	12	ii	ii	NOUN
ejpam-6538	161	13	)	)	PUNCT
ejpam-6538	161	14	and	and	CCONJ
ejpam-6538	161	15	(	(	PUNCT
ejpam-6538	161	16	iii	iii	NOUN
ejpam-6538	161	17	)	)	PUNCT
ejpam-6538	161	18	.	.	PUNCT
ejpam-6538	162	1	(	(	PUNCT
ejpam-6538	162	2	iii	iii	X
ejpam-6538	162	3	)	)	PUNCT
ejpam-6538	162	4	we	we	PRON
ejpam-6538	162	5	will	will	AUX
ejpam-6538	162	6	prove	prove	VERB
ejpam-6538	162	7	by	by	ADP
ejpam-6538	162	8	the	the	DET
ejpam-6538	162	9	induction	induction	NOUN
ejpam-6538	162	10	under	under	ADP
ejpam-6538	162	11	the	the	DET
ejpam-6538	162	12	cardinality	cardinality	NOUN
ejpam-6538	162	13	of	of	ADP
ejpam-6538	162	14	the	the	DET
ejpam-6538	162	15	chain	chain	NOUN
ejpam-6538	162	16	.	.	PUNCT
ejpam-6538	163	1	by	by	ADP
ejpam-6538	163	2	(	(	PUNCT
ejpam-6538	163	3	i	i	NOUN
ejpam-6538	163	4	)	)	PUNCT
ejpam-6538	163	5	,	,	PUNCT
ejpam-6538	163	6	this	this	DET
ejpam-6538	163	7	statement	statement	NOUN
ejpam-6538	163	8	is	be	AUX
ejpam-6538	163	9	true	true	ADJ
ejpam-6538	163	10	for	for	ADP
ejpam-6538	163	11	m	m	PROPN
ejpam-6538	163	12	=	=	SYM
ejpam-6538	163	13	2	2	X
ejpam-6538	163	14	.	.	PUNCT
ejpam-6538	164	1	let	let	VERB
ejpam-6538	164	2	m	m	PRON
ejpam-6538	164	3	≥	≥	VERB
ejpam-6538	164	4	3	3	NUM
ejpam-6538	164	5	and	and	CCONJ
ejpam-6538	164	6	f	f	PROPN
ejpam-6538	164	7	be	be	AUX
ejpam-6538	164	8	an	an	DET
ejpam-6538	164	9	mpp	mpp	NOUN
ejpam-6538	164	10	endomorphism	endomorphism	NOUN
ejpam-6538	164	11	of	of	ADP
ejpam-6538	164	12	cm	cm	PROPN
ejpam-6538	164	13	×cm	×cm	PROPN
ejpam-6538	164	14	fixing	fix	VERB
ejpam-6538	164	15	the	the	DET
ejpam-6538	164	16	bottom	bottom	NOUN
ejpam-6538	164	17	.	.	PUNCT
ejpam-6538	165	1	by	by	ADP
ejpam-6538	165	2	lemma	lemma	PROPN
ejpam-6538	165	3	1	1	NUM
ejpam-6538	165	4	,	,	PUNCT
ejpam-6538	165	5	we	we	PRON
ejpam-6538	165	6	may	may	AUX
ejpam-6538	165	7	assume	assume	VERB
ejpam-6538	165	8	that	that	SCONJ
ejpam-6538	165	9	f2k(m	f2k(m	PROPN
ejpam-6538	165	10	,	,	PUNCT
ejpam-6538	165	11	m	m	NOUN
ejpam-6538	165	12	)	)	PUNCT
ejpam-6538	165	13	=	=	SYM
ejpam-6538	166	1	(	(	PUNCT
ejpam-6538	166	2	m−	m−	PROPN
ejpam-6538	166	3	k	k	PROPN
ejpam-6538	166	4	,	,	PUNCT
ejpam-6538	166	5	m−	m−	PROPN
ejpam-6538	166	6	k	k	NOUN
ejpam-6538	166	7	)	)	PUNCT
ejpam-6538	166	8	and	and	CCONJ
ejpam-6538	166	9	f2k+1(m	f2k+1(m	PROPN
ejpam-6538	166	10	,	,	PUNCT
ejpam-6538	166	11	m	m	NOUN
ejpam-6538	166	12	)	)	PUNCT
ejpam-6538	166	13	=	=	SYM
ejpam-6538	166	14	(	(	PUNCT
ejpam-6538	166	15	m−	m−	PROPN
ejpam-6538	166	16	k	k	PROPN
ejpam-6538	166	17	,	,	PUNCT
ejpam-6538	166	18	m−	m−	PROPN
ejpam-6538	166	19	(	(	PUNCT
ejpam-6538	166	20	k	k	PROPN
ejpam-6538	166	21	+	+	PROPN
ejpam-6538	166	22	1))	1))	NUM
ejpam-6538	166	23	.......	.......	PUNCT
ejpam-6538	166	24	(∗	(∗	NOUN
ejpam-6538	166	25	)	)	PUNCT
ejpam-6538	166	26	for	for	ADP
ejpam-6538	166	27	all	all	PRON
ejpam-6538	166	28	0	0	NUM
ejpam-6538	166	29	≤	≤	NUM
ejpam-6538	166	30	k	k	NOUN
ejpam-6538	166	31	≤	≤	PROPN
ejpam-6538	166	32	m−	m−	PROPN
ejpam-6538	166	33	2	2	NUM
ejpam-6538	166	34	.	.	PUNCT
ejpam-6538	166	35	then	then	ADV
ejpam-6538	166	36	for	for	ADP
ejpam-6538	166	37	each	each	DET
ejpam-6538	166	38	0	0	NUM
ejpam-6538	166	39	≤	≤	NUM
ejpam-6538	166	40	k	k	NOUN
ejpam-6538	166	41	≤	≤	ADJ
ejpam-6538	166	42	m−	m−	PROPN
ejpam-6538	166	43	2	2	NUM
ejpam-6538	166	44	and	and	CCONJ
ejpam-6538	166	45	1	1	NUM
ejpam-6538	166	46	≤	≤	NUM
ejpam-6538	166	47	i	i	PRON
ejpam-6538	166	48	≤	≤	ADJ
ejpam-6538	166	49	m−	m−	PROPN
ejpam-6538	166	50	k	k	NOUN
ejpam-6538	166	51	,	,	PUNCT
ejpam-6538	166	52	(	(	PUNCT
ejpam-6538	166	53	m−	m−	PROPN
ejpam-6538	166	54	k	k	PROPN
ejpam-6538	166	55	,	,	PUNCT
ejpam-6538	166	56	m−	m−	PROPN
ejpam-6538	166	57	(	(	PUNCT
ejpam-6538	166	58	k	k	PROPN
ejpam-6538	166	59	+	+	PROPN
ejpam-6538	166	60	1	1	NUM
ejpam-6538	166	61	)	)	PUNCT
ejpam-6538	166	62	)	)	PUNCT
ejpam-6538	167	1	=	=	PRON
ejpam-6538	167	2	f(m−	f(m−	PRON
ejpam-6538	168	1	k	k	NOUN
ejpam-6538	168	2	,	,	PUNCT
ejpam-6538	168	3	m−	m−	PROPN
ejpam-6538	168	4	k	k	NOUN
ejpam-6538	168	5	)	)	PUNCT
ejpam-6538	168	6	=	=	PRON
ejpam-6538	168	7	f(m−	f(m−	NUM
ejpam-6538	168	8	k	k	NOUN
ejpam-6538	168	9	,	,	PUNCT
ejpam-6538	168	10	m−	m−	PROPN
ejpam-6538	168	11	(	(	PUNCT
ejpam-6538	168	12	k	k	PROPN
ejpam-6538	168	13	+	+	PROPN
ejpam-6538	168	14	1	1	NUM
ejpam-6538	168	15	)	)	PUNCT
ejpam-6538	168	16	)	)	PUNCT
ejpam-6538	168	17	∨	∨	NUM
ejpam-6538	168	18	f(i	f(i	PROPN
ejpam-6538	168	19	,	,	PUNCT
ejpam-6538	168	20	m−	m−	PROPN
ejpam-6538	168	21	k	k	NOUN
ejpam-6538	168	22	)	)	PUNCT
ejpam-6538	168	23	=	=	SYM
ejpam-6538	168	24	(	(	PUNCT
ejpam-6538	168	25	m−	m−	PROPN
ejpam-6538	168	26	(	(	PUNCT
ejpam-6538	168	27	k	k	PROPN
ejpam-6538	168	28	+	+	PROPN
ejpam-6538	168	29	1),m−	1),m−	PROPN
ejpam-6538	168	30	(	(	PUNCT
ejpam-6538	168	31	k	k	NOUN
ejpam-6538	168	32	+	+	PROPN
ejpam-6538	168	33	1	1	NUM
ejpam-6538	168	34	)	)	PUNCT
ejpam-6538	168	35	)	)	PUNCT
ejpam-6538	168	36	∨	∨	NUM
ejpam-6538	168	37	f(i	f(i	PROPN
ejpam-6538	168	38	,	,	PUNCT
ejpam-6538	168	39	m−	m−	PROPN
ejpam-6538	168	40	k	k	PROPN
ejpam-6538	168	41	)	)	PUNCT
ejpam-6538	168	42	which	which	PRON
ejpam-6538	168	43	implies	imply	VERB
ejpam-6538	168	44	that	that	SCONJ
ejpam-6538	168	45	f(i	f(i	PROPN
ejpam-6538	168	46	,	,	PUNCT
ejpam-6538	168	47	m−	m−	PROPN
ejpam-6538	168	48	k	k	NOUN
ejpam-6538	168	49	)	)	PUNCT
ejpam-6538	168	50	=	=	SYM
ejpam-6538	168	51	(	(	PUNCT
ejpam-6538	168	52	m−	m−	PROPN
ejpam-6538	168	53	k	k	PROPN
ejpam-6538	168	54	,	,	PUNCT
ejpam-6538	168	55	j	j	PROPN
ejpam-6538	168	56	)	)	PUNCT
ejpam-6538	168	57	for	for	ADP
ejpam-6538	168	58	some	some	PRON
ejpam-6538	168	59	1	1	NUM
ejpam-6538	168	60	≤	≤	NUM
ejpam-6538	168	61	j	j	PROPN
ejpam-6538	168	62	≤	≤	PROPN
ejpam-6538	168	63	m−	m−	PROPN
ejpam-6538	168	64	(	(	PUNCT
ejpam-6538	168	65	k	k	PROPN
ejpam-6538	168	66	+	+	PROPN
ejpam-6538	168	67	1	1	NUM
ejpam-6538	168	68	)	)	PUNCT
ejpam-6538	168	69	(	(	PUNCT
ejpam-6538	168	70	3	3	NUM
ejpam-6538	168	71	)	)	PUNCT
ejpam-6538	168	72	and	and	CCONJ
ejpam-6538	168	73	f(i	f(i	NUM
ejpam-6538	168	74	,	,	PUNCT
ejpam-6538	168	75	m−	m−	PROPN
ejpam-6538	168	76	(	(	PUNCT
ejpam-6538	168	77	k	k	PROPN
ejpam-6538	168	78	+	+	PROPN
ejpam-6538	168	79	1	1	NUM
ejpam-6538	168	80	)	)	PUNCT
ejpam-6538	168	81	)	)	PUNCT
ejpam-6538	169	1	=	=	PRON
ejpam-6538	169	2	f(m−	f(m−	PRON
ejpam-6538	170	1	k	k	NOUN
ejpam-6538	170	2	,	,	PUNCT
ejpam-6538	170	3	m−	m−	PROPN
ejpam-6538	170	4	(	(	PUNCT
ejpam-6538	170	5	k	k	PROPN
ejpam-6538	170	6	+	+	PROPN
ejpam-6538	170	7	1	1	NUM
ejpam-6538	170	8	)	)	PUNCT
ejpam-6538	170	9	)	)	PUNCT
ejpam-6538	171	1	∧	∧	PROPN
ejpam-6538	171	2	f(i	f(i	PROPN
ejpam-6538	171	3	,	,	PUNCT
ejpam-6538	171	4	m−	m−	PROPN
ejpam-6538	171	5	k	k	NOUN
ejpam-6538	171	6	)	)	PUNCT
ejpam-6538	171	7	=	=	SYM
ejpam-6538	171	8	(	(	PUNCT
ejpam-6538	171	9	m−	m−	PROPN
ejpam-6538	171	10	(	(	PUNCT
ejpam-6538	171	11	k	k	PROPN
ejpam-6538	171	12	+	+	PROPN
ejpam-6538	171	13	1),m−	1),m−	PROPN
ejpam-6538	171	14	(	(	PUNCT
ejpam-6538	171	15	k	k	NOUN
ejpam-6538	171	16	+	+	PROPN
ejpam-6538	171	17	1	1	NUM
ejpam-6538	171	18	)	)	PUNCT
ejpam-6538	171	19	)	)	PUNCT
ejpam-6538	172	1	∧	∧	PROPN
ejpam-6538	172	2	(	(	PUNCT
ejpam-6538	172	3	m−	m−	PROPN
ejpam-6538	172	4	k	k	PROPN
ejpam-6538	172	5	,	,	PUNCT
ejpam-6538	172	6	j	j	PROPN
ejpam-6538	172	7	)	)	PUNCT
ejpam-6538	172	8	=	=	SYM
ejpam-6538	172	9	(	(	PUNCT
ejpam-6538	172	10	m−	m−	PROPN
ejpam-6538	172	11	(	(	PUNCT
ejpam-6538	172	12	k	k	PROPN
ejpam-6538	172	13	+	+	PROPN
ejpam-6538	172	14	1	1	NUM
ejpam-6538	172	15	)	)	PUNCT
ejpam-6538	172	16	,	,	PUNCT
ejpam-6538	172	17	j	j	PROPN
ejpam-6538	172	18	)	)	PUNCT
ejpam-6538	172	19	;	;	PUNCT
ejpam-6538	172	20	and	and	CCONJ
ejpam-6538	172	21	for	for	ADP
ejpam-6538	172	22	i	i	PRON
ejpam-6538	172	23	=	=	SYM
ejpam-6538	172	24	m−	m−	PROPN
ejpam-6538	172	25	(	(	PUNCT
ejpam-6538	172	26	k	k	PROPN
ejpam-6538	172	27	+	+	PROPN
ejpam-6538	172	28	1	1	NUM
ejpam-6538	172	29	)	)	PUNCT
ejpam-6538	172	30	,	,	PUNCT
ejpam-6538	172	31	we	we	PRON
ejpam-6538	172	32	get	get	VERB
ejpam-6538	172	33	by	by	ADP
ejpam-6538	172	34	(	(	PUNCT
ejpam-6538	172	35	∗	∗	NOUN
ejpam-6538	172	36	)	)	PUNCT
ejpam-6538	172	37	that	that	PRON
ejpam-6538	172	38	j	j	PROPN
ejpam-6538	173	1	=	=	PRON
ejpam-6538	173	2	m−	m−	PROPN
ejpam-6538	173	3	(	(	PUNCT
ejpam-6538	173	4	k	k	PROPN
ejpam-6538	173	5	+	+	PROPN
ejpam-6538	173	6	2	2	NUM
ejpam-6538	173	7	)	)	PUNCT
ejpam-6538	173	8	.	.	PUNCT
ejpam-6538	174	1	thus	thus	ADV
ejpam-6538	174	2	f(m−	f(m−	NOUN
ejpam-6538	174	3	(	(	PUNCT
ejpam-6538	174	4	k	k	PROPN
ejpam-6538	174	5	+	+	PROPN
ejpam-6538	174	6	1),m−	1),m−	PROPN
ejpam-6538	174	7	k	k	NOUN
ejpam-6538	174	8	)	)	PUNCT
ejpam-6538	174	9	=	=	SYM
ejpam-6538	174	10	(	(	PUNCT
ejpam-6538	174	11	m−	m−	PROPN
ejpam-6538	174	12	k	k	PROPN
ejpam-6538	174	13	,	,	PUNCT
ejpam-6538	174	14	m−	m−	PROPN
ejpam-6538	174	15	(	(	PUNCT
ejpam-6538	174	16	k	k	PROPN
ejpam-6538	174	17	+	+	PROPN
ejpam-6538	174	18	2	2	NUM
ejpam-6538	174	19	)	)	PUNCT
ejpam-6538	174	20	)	)	PUNCT
ejpam-6538	174	21	.	.	PUNCT
ejpam-6538	175	1	(	(	PUNCT
ejpam-6538	175	2	4	4	X
ejpam-6538	175	3	)	)	PUNCT
ejpam-6538	175	4	besides	besides	SCONJ
ejpam-6538	175	5	,	,	PUNCT
ejpam-6538	175	6	(	(	PUNCT
ejpam-6538	175	7	m−	m−	PROPN
ejpam-6538	175	8	k	k	PROPN
ejpam-6538	175	9	,	,	PUNCT
ejpam-6538	175	10	m−	m−	PROPN
ejpam-6538	175	11	(	(	PUNCT
ejpam-6538	175	12	k	k	PROPN
ejpam-6538	175	13	+	+	PROPN
ejpam-6538	175	14	1	1	NUM
ejpam-6538	175	15	)	)	PUNCT
ejpam-6538	175	16	)	)	PUNCT
ejpam-6538	176	1	=	=	PRON
ejpam-6538	176	2	f(m−	f(m−	PRON
ejpam-6538	177	1	k	k	NOUN
ejpam-6538	177	2	,	,	PUNCT
ejpam-6538	177	3	m−	m−	PROPN
ejpam-6538	177	4	k	k	NOUN
ejpam-6538	177	5	)	)	PUNCT
ejpam-6538	177	6	=	=	PRON
ejpam-6538	177	7	f(m−	f(m−	NUM
ejpam-6538	178	1	k	k	NOUN
ejpam-6538	178	2	,	,	PUNCT
ejpam-6538	178	3	i	i	NOUN
ejpam-6538	178	4	)	)	PUNCT
ejpam-6538	178	5	∨	∨	NUM
ejpam-6538	178	6	f(m−	f(m−	NOUN
ejpam-6538	178	7	(	(	PUNCT
ejpam-6538	178	8	k	k	PROPN
ejpam-6538	178	9	+	+	PROPN
ejpam-6538	178	10	1),m−	1),m−	PROPN
ejpam-6538	178	11	k	k	NOUN
ejpam-6538	178	12	)	)	PUNCT
ejpam-6538	178	13	=	=	NOUN
ejpam-6538	178	14	f(m−	f(m−	NUM
ejpam-6538	179	1	k	k	NOUN
ejpam-6538	179	2	,	,	PUNCT
ejpam-6538	179	3	i	i	NOUN
ejpam-6538	179	4	)	)	PUNCT
ejpam-6538	179	5	∨	∨	PROPN
ejpam-6538	179	6	(	(	PUNCT
ejpam-6538	179	7	m−	m−	PROPN
ejpam-6538	179	8	k	k	PROPN
ejpam-6538	179	9	,	,	PUNCT
ejpam-6538	179	10	m−	m−	PROPN
ejpam-6538	179	11	(	(	PUNCT
ejpam-6538	179	12	k	k	PROPN
ejpam-6538	179	13	+	+	PROPN
ejpam-6538	179	14	2	2	NUM
ejpam-6538	179	15	)	)	PUNCT
ejpam-6538	179	16	)	)	PUNCT
ejpam-6538	179	17	implies	imply	VERB
ejpam-6538	179	18	f(m−	f(m−	PROPN
ejpam-6538	179	19	k	k	PROPN
ejpam-6538	179	20	,	,	PUNCT
ejpam-6538	179	21	i	i	NOUN
ejpam-6538	179	22	)	)	PUNCT
ejpam-6538	179	23	=	=	SYM
ejpam-6538	179	24	(	(	PUNCT
ejpam-6538	179	25	j	j	PROPN
ejpam-6538	179	26	,	,	PUNCT
ejpam-6538	179	27	m−	m−	PROPN
ejpam-6538	179	28	(	(	PUNCT
ejpam-6538	179	29	k	k	PROPN
ejpam-6538	179	30	+	+	PROPN
ejpam-6538	179	31	1	1	NUM
ejpam-6538	179	32	)	)	PUNCT
ejpam-6538	179	33	)	)	PUNCT
ejpam-6538	179	34	for	for	ADP
ejpam-6538	179	35	some	some	DET
ejpam-6538	179	36	1	1	NUM
ejpam-6538	179	37	≤	≤	NUM
ejpam-6538	179	38	j	j	PROPN
ejpam-6538	179	39	≤	≤	PROPN
ejpam-6538	179	40	m−	m−	PROPN
ejpam-6538	179	41	k.	k.	PROPN
ejpam-6538	180	1	(	(	PUNCT
ejpam-6538	180	2	5	5	NUM
ejpam-6538	180	3	)	)	PUNCT
ejpam-6538	180	4	by	by	ADP
ejpam-6538	180	5	equations	equation	NOUN
ejpam-6538	180	6	(	(	PUNCT
ejpam-6538	180	7	3	3	NUM
ejpam-6538	180	8	)	)	PUNCT
ejpam-6538	180	9	and	and	CCONJ
ejpam-6538	180	10	(	(	PUNCT
ejpam-6538	180	11	5	5	NUM
ejpam-6538	180	12	)	)	PUNCT
ejpam-6538	180	13	(	(	PUNCT
ejpam-6538	180	14	k	k	NOUN
ejpam-6538	180	15	=	=	SYM
ejpam-6538	180	16	1	1	NUM
ejpam-6538	180	17	)	)	PUNCT
ejpam-6538	180	18	,	,	PUNCT
ejpam-6538	180	19	cm−1	cm−1	NOUN
ejpam-6538	180	20	×	×	PROPN
ejpam-6538	180	21	cm−1	cm−1	NOUN
ejpam-6538	180	22	is	be	AUX
ejpam-6538	180	23	closed	close	VERB
ejpam-6538	180	24	under	under	ADP
ejpam-6538	180	25	f	f	PROPN
ejpam-6538	180	26	.	.	PUNCT
ejpam-6538	181	1	by	by	ADP
ejpam-6538	181	2	the	the	DET
ejpam-6538	181	3	induction	induction	NOUN
ejpam-6538	181	4	hypothesis	hypothesis	NOUN
ejpam-6538	181	5	,	,	PUNCT
ejpam-6538	181	6	f	f	PROPN
ejpam-6538	181	7	⇂	⇂	PROPN
ejpam-6538	181	8	cm−1×cm−1	cm−1×cm−1	PROPN
ejpam-6538	181	9	is	be	AUX
ejpam-6538	181	10	either	either	PRON
ejpam-6538	181	11	ζ(m−1,m−2	ζ(m−1,m−2	NOUN
ejpam-6538	181	12	)	)	PUNCT
ejpam-6538	181	13	or	or	CCONJ
ejpam-6538	181	14	ζ(m−2,m−1	ζ(m−2,m−1	NOUN
ejpam-6538	181	15	)	)	PUNCT
ejpam-6538	181	16	.	.	PUNCT
ejpam-6538	182	1	by	by	ADP
ejpam-6538	182	2	the	the	DET
ejpam-6538	182	3	condition	condition	NOUN
ejpam-6538	182	4	(	(	PUNCT
ejpam-6538	182	5	∗	∗	NOUN
ejpam-6538	182	6	)	)	PUNCT
ejpam-6538	182	7	,	,	PUNCT
ejpam-6538	182	8	f	f	PROPN
ejpam-6538	182	9	⇂	⇂	NOUN
ejpam-6538	182	10	cm−1×cm−1=	cm−1×cm−1=	ADJ
ejpam-6538	182	11	ζ(m−1,m−2	ζ(m−1,m−2	NOUN
ejpam-6538	182	12	)	)	PUNCT
ejpam-6538	182	13	;	;	PUNCT
ejpam-6538	182	14	that	that	PRON
ejpam-6538	182	15	is	be	AUX
ejpam-6538	182	16	,	,	PUNCT
ejpam-6538	182	17	f(r	f(r	X
ejpam-6538	182	18	,	,	PUNCT
ejpam-6538	182	19	s	s	X
ejpam-6538	182	20	)	)	PUNCT
ejpam-6538	182	21	=	=	SYM
ejpam-6538	182	22	(	(	PUNCT
ejpam-6538	182	23	s	s	X
ejpam-6538	182	24	,	,	PUNCT
ejpam-6538	182	25	r	r	NOUN
ejpam-6538	182	26	−	−	NOUN
ejpam-6538	182	27	1	1	NUM
ejpam-6538	182	28	)	)	PUNCT
ejpam-6538	182	29	for	for	ADP
ejpam-6538	182	30	all	all	DET
ejpam-6538	182	31	1	1	NUM
ejpam-6538	182	32	≤	≤	NOUN
ejpam-6538	182	33	r	r	NOUN
ejpam-6538	182	34	,	,	PUNCT
ejpam-6538	182	35	s	s	PART
ejpam-6538	182	36	≤	≤	NOUN
ejpam-6538	182	37	m	m	VERB
ejpam-6538	182	38	−	−	PROPN
ejpam-6538	182	39	1	1	NUM
ejpam-6538	182	40	.	.	PUNCT
ejpam-6538	183	1	for	for	ADP
ejpam-6538	183	2	each	each	DET
ejpam-6538	183	3	1	1	NUM
ejpam-6538	183	4	≤	≤	NUM
ejpam-6538	183	5	i	i	PRON
ejpam-6538	183	6	≤	≤	ADJ
ejpam-6538	183	7	m−	m−	PROPN
ejpam-6538	183	8	1	1	NUM
ejpam-6538	183	9	,	,	PUNCT
ejpam-6538	183	10	(	(	PUNCT
ejpam-6538	183	11	m−	m−	PROPN
ejpam-6538	183	12	1	1	NUM
ejpam-6538	183	13	,	,	PUNCT
ejpam-6538	183	14	i−	i−	PROPN
ejpam-6538	183	15	1	1	NUM
ejpam-6538	183	16	)	)	PUNCT
ejpam-6538	183	17	=	=	SYM
ejpam-6538	183	18	f(i	f(i	PROPN
ejpam-6538	183	19	,	,	PUNCT
ejpam-6538	183	20	m−	m−	PROPN
ejpam-6538	183	21	1	1	NUM
ejpam-6538	183	22	)	)	PUNCT
ejpam-6538	183	23	=	=	SYM
ejpam-6538	183	24	f(i	f(i	PROPN
ejpam-6538	183	25	,	,	PUNCT
ejpam-6538	183	26	m	m	NOUN
ejpam-6538	183	27	)	)	PUNCT
ejpam-6538	183	28	∧	∧	NOUN
ejpam-6538	183	29	f(m−	f(m−	NOUN
ejpam-6538	183	30	1,m−	1,m−	NUM
ejpam-6538	183	31	1	1	NUM
ejpam-6538	183	32	)	)	PUNCT
ejpam-6538	183	33	=	=	SYM
ejpam-6538	183	34	f(i	f(i	PROPN
ejpam-6538	183	35	,	,	PUNCT
ejpam-6538	183	36	m	m	NOUN
ejpam-6538	183	37	)	)	PUNCT
ejpam-6538	183	38	∧	∧	PROPN
ejpam-6538	183	39	(	(	PUNCT
ejpam-6538	183	40	m−	m−	PROPN
ejpam-6538	183	41	1,m−	1,m−	NUM
ejpam-6538	183	42	2	2	NUM
ejpam-6538	183	43	)	)	PUNCT
ejpam-6538	183	44	implies	imply	VERB
ejpam-6538	183	45	by	by	ADP
ejpam-6538	183	46	the	the	DET
ejpam-6538	183	47	equation	equation	NOUN
ejpam-6538	183	48	(	(	PUNCT
ejpam-6538	183	49	3	3	NUM
ejpam-6538	183	50	)	)	PUNCT
ejpam-6538	183	51	that	that	SCONJ
ejpam-6538	183	52	f(i	f(i	PROPN
ejpam-6538	183	53	,	,	PUNCT
ejpam-6538	183	54	m	m	NOUN
ejpam-6538	183	55	)	)	PUNCT
ejpam-6538	183	56	=	=	SYM
ejpam-6538	183	57	(	(	PUNCT
ejpam-6538	183	58	m	m	PROPN
ejpam-6538	183	59	,	,	PUNCT
ejpam-6538	183	60	i−	i−	PROPN
ejpam-6538	183	61	1	1	NUM
ejpam-6538	183	62	)	)	PUNCT
ejpam-6538	183	63	.	.	PUNCT
ejpam-6538	184	1	for	for	ADP
ejpam-6538	184	2	each	each	DET
ejpam-6538	184	3	1	1	NUM
ejpam-6538	184	4	≤	≤	NUM
ejpam-6538	185	1	i	i	PRON
ejpam-6538	185	2	≤	≤	ADJ
ejpam-6538	185	3	m−	m−	PROPN
ejpam-6538	185	4	1	1	NUM
ejpam-6538	185	5	,	,	PUNCT
ejpam-6538	185	6	a.	a.	NOUN
ejpam-6538	185	7	charoenpol	charoenpol	NOUN
ejpam-6538	185	8	,	,	PUNCT
ejpam-6538	185	9	u.	u.	PROPN
ejpam-6538	185	10	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	185	11	/	/	SYM
ejpam-6538	185	12	eur	eur	PROPN
ejpam-6538	185	13	.	.	PUNCT
ejpam-6538	186	1	j.	j.	PROPN
ejpam-6538	186	2	pure	pure	PROPN
ejpam-6538	186	3	appl	appl	PROPN
ejpam-6538	186	4	.	.	PROPN
ejpam-6538	186	5	math	math	PROPN
ejpam-6538	186	6	,	,	PUNCT
ejpam-6538	186	7	18	18	NUM
ejpam-6538	186	8	(	(	PUNCT
ejpam-6538	186	9	3	3	NUM
ejpam-6538	186	10	)	)	PUNCT
ejpam-6538	186	11	(	(	PUNCT
ejpam-6538	186	12	2025	2025	NUM
ejpam-6538	186	13	)	)	PUNCT
ejpam-6538	186	14	,	,	PUNCT
ejpam-6538	186	15	6538	6538	NUM
ejpam-6538	186	16	9	9	NUM
ejpam-6538	186	17	of	of	ADP
ejpam-6538	186	18	13	13	NUM
ejpam-6538	186	19	(	(	PUNCT
ejpam-6538	186	20	i	i	PROPN
ejpam-6538	186	21	,	,	PUNCT
ejpam-6538	186	22	m−	m−	PROPN
ejpam-6538	186	23	2	2	NUM
ejpam-6538	186	24	)	)	PUNCT
ejpam-6538	186	25	=	=	PRON
ejpam-6538	186	26	f(m−	f(m−	NOUN
ejpam-6538	186	27	1	1	NUM
ejpam-6538	186	28	,	,	PUNCT
ejpam-6538	186	29	i	i	NOUN
ejpam-6538	186	30	)	)	PUNCT
ejpam-6538	186	31	=	=	SYM
ejpam-6538	187	1	f(m	f(m	PROPN
ejpam-6538	187	2	,	,	PUNCT
ejpam-6538	187	3	i	i	NOUN
ejpam-6538	187	4	)	)	PUNCT
ejpam-6538	187	5	∧	∧	PROPN
ejpam-6538	187	6	f(m−	f(m−	NOUN
ejpam-6538	187	7	1,m−	1,m−	NUM
ejpam-6538	187	8	1	1	NUM
ejpam-6538	187	9	)	)	PUNCT
ejpam-6538	187	10	=	=	PUNCT
ejpam-6538	188	1	f(m	f(m	PROPN
ejpam-6538	188	2	,	,	PUNCT
ejpam-6538	188	3	i	i	NOUN
ejpam-6538	188	4	)	)	PUNCT
ejpam-6538	188	5	∧	∧	PROPN
ejpam-6538	188	6	(	(	PUNCT
ejpam-6538	188	7	m−	m−	PROPN
ejpam-6538	188	8	1,m−	1,m−	NUM
ejpam-6538	188	9	2	2	NUM
ejpam-6538	188	10	)	)	PUNCT
ejpam-6538	188	11	implies	imply	VERB
ejpam-6538	188	12	by	by	ADP
ejpam-6538	188	13	the	the	DET
ejpam-6538	188	14	equation	equation	NOUN
ejpam-6538	188	15	(	(	PUNCT
ejpam-6538	188	16	5	5	NUM
ejpam-6538	188	17	)	)	PUNCT
ejpam-6538	188	18	that	that	SCONJ
ejpam-6538	188	19	f(m	f(m	PROPN
ejpam-6538	188	20	,	,	PUNCT
ejpam-6538	188	21	i	i	NOUN
ejpam-6538	188	22	)	)	PUNCT
ejpam-6538	188	23	=	=	SYM
ejpam-6538	189	1	(	(	PUNCT
ejpam-6538	189	2	i	i	PROPN
ejpam-6538	189	3	,	,	PUNCT
ejpam-6538	189	4	m−	m−	PROPN
ejpam-6538	189	5	1	1	NUM
ejpam-6538	189	6	)	)	PUNCT
ejpam-6538	189	7	.	.	PUNCT
ejpam-6538	190	1	hence	hence	ADV
ejpam-6538	190	2	,	,	PUNCT
ejpam-6538	190	3	f	f	PROPN
ejpam-6538	190	4	=	=	SYM
ejpam-6538	190	5	ζ(m	ζ(m	ADJ
ejpam-6538	190	6	,	,	PUNCT
ejpam-6538	190	7	m−1	m−1	PROPN
ejpam-6538	190	8	)	)	PUNCT
ejpam-6538	190	9	.	.	PUNCT
ejpam-6538	191	1	(	(	PUNCT
ejpam-6538	191	2	iv	iv	X
ejpam-6538	191	3	)	)	PUNCT
ejpam-6538	191	4	let	let	VERB
ejpam-6538	191	5	m	m	PRON
ejpam-6538	191	6	>	>	X
ejpam-6538	191	7	3	3	NUM
ejpam-6538	191	8	and	and	CCONJ
ejpam-6538	191	9	f	f	PROPN
ejpam-6538	191	10	be	be	AUX
ejpam-6538	191	11	an	an	DET
ejpam-6538	191	12	mpp	mpp	NOUN
ejpam-6538	191	13	endomorphism	endomorphism	NOUN
ejpam-6538	191	14	of	of	ADP
ejpam-6538	191	15	cm	cm	PROPN
ejpam-6538	191	16	×	×	PROPN
ejpam-6538	191	17	cm−1	cm−1	NOUN
ejpam-6538	191	18	fixing	fix	VERB
ejpam-6538	191	19	the	the	DET
ejpam-6538	191	20	bottom	bottom	NOUN
ejpam-6538	191	21	.	.	PUNCT
ejpam-6538	192	1	suppose	suppose	VERB
ejpam-6538	192	2	that	that	SCONJ
ejpam-6538	192	3	f(m	f(m	PROPN
ejpam-6538	192	4	,	,	PUNCT
ejpam-6538	192	5	m−	m−	PROPN
ejpam-6538	192	6	1	1	NUM
ejpam-6538	192	7	)	)	PUNCT
ejpam-6538	192	8	=	=	SYM
ejpam-6538	192	9	(	(	PUNCT
ejpam-6538	192	10	m	m	PROPN
ejpam-6538	192	11	,	,	PUNCT
ejpam-6538	192	12	m−	m−	PROPN
ejpam-6538	192	13	2	2	NUM
ejpam-6538	192	14	)	)	PUNCT
ejpam-6538	192	15	.	.	PUNCT
ejpam-6538	193	1	by	by	ADP
ejpam-6538	193	2	lemma	lemma	PROPN
ejpam-6538	193	3	1	1	NUM
ejpam-6538	193	4	,	,	PUNCT
ejpam-6538	193	5	f2(m−3)(m	f2(m−3)(m	NOUN
ejpam-6538	193	6	,	,	PUNCT
ejpam-6538	193	7	m−	m−	PROPN
ejpam-6538	193	8	1	1	NUM
ejpam-6538	193	9	)	)	PUNCT
ejpam-6538	193	10	=	=	NOUN
ejpam-6538	193	11	(	(	PUNCT
ejpam-6538	193	12	3	3	NUM
ejpam-6538	193	13	,	,	PUNCT
ejpam-6538	193	14	2	2	NUM
ejpam-6538	193	15	)	)	PUNCT
ejpam-6538	193	16	and	and	CCONJ
ejpam-6538	193	17	f2(m−3)+1(m	f2(m−3)+1(m	PROPN
ejpam-6538	193	18	,	,	PUNCT
ejpam-6538	193	19	m−	m−	PROPN
ejpam-6538	193	20	1	1	NUM
ejpam-6538	193	21	)	)	PUNCT
ejpam-6538	193	22	=	=	NOUN
ejpam-6538	193	23	(	(	PUNCT
ejpam-6538	193	24	3	3	NUM
ejpam-6538	193	25	,	,	PUNCT
ejpam-6538	193	26	1	1	NUM
ejpam-6538	193	27	)	)	PUNCT
ejpam-6538	193	28	.	.	PUNCT
ejpam-6538	194	1	again	again	ADV
ejpam-6538	194	2	by	by	ADP
ejpam-6538	194	3	theorem	theorem	NOUN
ejpam-6538	194	4	1	1	NUM
ejpam-6538	194	5	,	,	PUNCT
ejpam-6538	194	6	f2(m−2)(m	f2(m−2)(m	NOUN
ejpam-6538	194	7	,	,	PUNCT
ejpam-6538	194	8	m−	m−	PROPN
ejpam-6538	194	9	1	1	NUM
ejpam-6538	194	10	)	)	PUNCT
ejpam-6538	195	1	=	=	NOUN
ejpam-6538	195	2	(	(	PUNCT
ejpam-6538	195	3	2	2	NUM
ejpam-6538	195	4	,	,	PUNCT
ejpam-6538	195	5	1	1	NUM
ejpam-6538	195	6	)	)	PUNCT
ejpam-6538	195	7	and	and	CCONJ
ejpam-6538	195	8	f2(m−3)+1(m	f2(m−3)+1(m	PROPN
ejpam-6538	195	9	,	,	PUNCT
ejpam-6538	195	10	m−	m−	PROPN
ejpam-6538	195	11	1	1	NUM
ejpam-6538	195	12	)	)	PUNCT
ejpam-6538	195	13	=	=	NOUN
ejpam-6538	195	14	(	(	PUNCT
ejpam-6538	195	15	1	1	NUM
ejpam-6538	195	16	,	,	PUNCT
ejpam-6538	195	17	1	1	NUM
ejpam-6538	195	18	)	)	PUNCT
ejpam-6538	195	19	.	.	PUNCT
ejpam-6538	196	1	since	since	SCONJ
ejpam-6538	196	2	(	(	PUNCT
ejpam-6538	196	3	3	3	NUM
ejpam-6538	196	4	,	,	PUNCT
ejpam-6538	196	5	1	1	NUM
ejpam-6538	196	6	)	)	PUNCT
ejpam-6538	196	7	=	=	SYM
ejpam-6538	196	8	f(3	f(3	PROPN
ejpam-6538	196	9	,	,	PUNCT
ejpam-6538	196	10	2	2	NUM
ejpam-6538	196	11	)	)	PUNCT
ejpam-6538	196	12	=	=	SYM
ejpam-6538	196	13	f(3	f(3	PROPN
ejpam-6538	196	14	,	,	PUNCT
ejpam-6538	196	15	1	1	NUM
ejpam-6538	196	16	)	)	PUNCT
ejpam-6538	196	17	∨	∨	NOUN
ejpam-6538	196	18	f(2	f(2	PROPN
ejpam-6538	196	19	,	,	PUNCT
ejpam-6538	196	20	2	2	X
ejpam-6538	196	21	)	)	PUNCT
ejpam-6538	196	22	=	=	NOUN
ejpam-6538	196	23	(	(	PUNCT
ejpam-6538	196	24	2	2	NUM
ejpam-6538	196	25	,	,	PUNCT
ejpam-6538	196	26	1	1	NUM
ejpam-6538	196	27	)	)	PUNCT
ejpam-6538	196	28	∨	∨	NOUN
ejpam-6538	196	29	f(2	f(2	PROPN
ejpam-6538	196	30	,	,	PUNCT
ejpam-6538	196	31	2	2	NUM
ejpam-6538	196	32	)	)	PUNCT
ejpam-6538	196	33	,	,	PUNCT
ejpam-6538	196	34	we	we	PRON
ejpam-6538	196	35	get	get	VERB
ejpam-6538	196	36	f(2	f(2	PROPN
ejpam-6538	196	37	,	,	PUNCT
ejpam-6538	196	38	2	2	X
ejpam-6538	196	39	)	)	PUNCT
ejpam-6538	196	40	=	=	NOUN
ejpam-6538	196	41	(	(	PUNCT
ejpam-6538	196	42	3	3	NUM
ejpam-6538	196	43	,	,	PUNCT
ejpam-6538	196	44	1	1	NUM
ejpam-6538	196	45	)	)	PUNCT
ejpam-6538	196	46	.	.	PUNCT
ejpam-6538	197	1	since	since	SCONJ
ejpam-6538	197	2	(	(	PUNCT
ejpam-6538	197	3	1	1	NUM
ejpam-6538	197	4	,	,	PUNCT
ejpam-6538	197	5	1	1	NUM
ejpam-6538	197	6	)	)	PUNCT
ejpam-6538	197	7	=	=	SYM
ejpam-6538	197	8	f(2	f(2	PROPN
ejpam-6538	197	9	,	,	PUNCT
ejpam-6538	197	10	1	1	X
ejpam-6538	197	11	)	)	PUNCT
ejpam-6538	197	12	=	=	SYM
ejpam-6538	197	13	f(3	f(3	PROPN
ejpam-6538	197	14	,	,	PUNCT
ejpam-6538	197	15	1	1	X
ejpam-6538	197	16	)	)	PUNCT
ejpam-6538	197	17	∧	∧	PROPN
ejpam-6538	197	18	f(2	f(2	PROPN
ejpam-6538	197	19	,	,	PUNCT
ejpam-6538	197	20	2	2	X
ejpam-6538	197	21	)	)	PUNCT
ejpam-6538	197	22	=	=	NOUN
ejpam-6538	197	23	(	(	PUNCT
ejpam-6538	197	24	2	2	NUM
ejpam-6538	197	25	,	,	PUNCT
ejpam-6538	197	26	1	1	X
ejpam-6538	197	27	)	)	PUNCT
ejpam-6538	197	28	∧	∧	NOUN
ejpam-6538	197	29	(	(	PUNCT
ejpam-6538	197	30	3	3	NUM
ejpam-6538	197	31	,	,	PUNCT
ejpam-6538	197	32	1	1	NUM
ejpam-6538	197	33	)	)	PUNCT
ejpam-6538	197	34	=	=	NOUN
ejpam-6538	197	35	(	(	PUNCT
ejpam-6538	197	36	2	2	NUM
ejpam-6538	197	37	,	,	PUNCT
ejpam-6538	197	38	1	1	NUM
ejpam-6538	197	39	)	)	PUNCT
ejpam-6538	197	40	,	,	PUNCT
ejpam-6538	197	41	we	we	PRON
ejpam-6538	197	42	get	get	VERB
ejpam-6538	197	43	2	2	NUM
ejpam-6538	197	44	=	=	SYM
ejpam-6538	197	45	1	1	NUM
ejpam-6538	197	46	,	,	PUNCT
ejpam-6538	197	47	a	a	DET
ejpam-6538	197	48	contradiction	contradiction	NOUN
ejpam-6538	197	49	.	.	PUNCT
ejpam-6538	198	1	by	by	ADP
ejpam-6538	198	2	theorem	theorem	NOUN
ejpam-6538	198	3	1	1	NUM
ejpam-6538	198	4	,	,	PUNCT
ejpam-6538	198	5	f(m	f(m	PROPN
ejpam-6538	198	6	,	,	PUNCT
ejpam-6538	198	7	m−	m−	PROPN
ejpam-6538	198	8	1	1	NUM
ejpam-6538	198	9	)	)	PUNCT
ejpam-6538	198	10	=	=	PUNCT
ejpam-6538	199	1	(	(	PUNCT
ejpam-6538	199	2	m−	m−	PROPN
ejpam-6538	199	3	1,m−	1,m−	NUM
ejpam-6538	199	4	1	1	NUM
ejpam-6538	199	5	)	)	PUNCT
ejpam-6538	199	6	.	.	PUNCT
ejpam-6538	200	1	by	by	ADP
ejpam-6538	200	2	lemma	lemma	PROPN
ejpam-6538	200	3	1	1	NUM
ejpam-6538	200	4	,	,	PUNCT
ejpam-6538	200	5	f2k(m	f2k(m	PROPN
ejpam-6538	200	6	,	,	PUNCT
ejpam-6538	200	7	m−	m−	PROPN
ejpam-6538	200	8	1	1	NUM
ejpam-6538	200	9	)	)	PUNCT
ejpam-6538	200	10	=	=	SYM
ejpam-6538	201	1	(	(	PUNCT
ejpam-6538	201	2	m−	m−	PROPN
ejpam-6538	201	3	k	k	PROPN
ejpam-6538	201	4	,	,	PUNCT
ejpam-6538	201	5	m−	m−	PROPN
ejpam-6538	201	6	1−	1−	NUM
ejpam-6538	201	7	k	k	NOUN
ejpam-6538	201	8	)	)	PUNCT
ejpam-6538	201	9	and	and	CCONJ
ejpam-6538	201	10	f2k+1(m	f2k+1(m	PROPN
ejpam-6538	201	11	,	,	PUNCT
ejpam-6538	201	12	m−	m−	PROPN
ejpam-6538	201	13	1	1	NUM
ejpam-6538	201	14	)	)	PUNCT
ejpam-6538	201	15	=	=	SYM
ejpam-6538	201	16	(	(	PUNCT
ejpam-6538	201	17	m−	m−	PROPN
ejpam-6538	201	18	(	(	PUNCT
ejpam-6538	201	19	k	k	PROPN
ejpam-6538	201	20	+	+	PROPN
ejpam-6538	201	21	1),m−	1),m−	PROPN
ejpam-6538	201	22	1−	1−	NUM
ejpam-6538	201	23	k	k	NOUN
ejpam-6538	201	24	)	)	PUNCT
ejpam-6538	201	25	for	for	ADP
ejpam-6538	201	26	all	all	PRON
ejpam-6538	201	27	0	0	NUM
ejpam-6538	201	28	≤	≤	NUM
ejpam-6538	201	29	k	k	NOUN
ejpam-6538	201	30	≤	≤	ADV
ejpam-6538	201	31	m−2	m−2	PROPN
ejpam-6538	201	32	.	.	PUNCT
ejpam-6538	202	1	by	by	ADP
ejpam-6538	202	2	the	the	DET
ejpam-6538	202	3	same	same	ADJ
ejpam-6538	202	4	arguments	argument	NOUN
ejpam-6538	202	5	of	of	ADP
ejpam-6538	202	6	proving	prove	VERB
ejpam-6538	202	7	(	(	PUNCT
ejpam-6538	202	8	iii	iii	NOUN
ejpam-6538	202	9	)	)	PUNCT
ejpam-6538	202	10	,	,	PUNCT
ejpam-6538	202	11	we	we	PRON
ejpam-6538	202	12	get	get	VERB
ejpam-6538	202	13	f	f	NOUN
ejpam-6538	202	14	=	=	PUNCT
ejpam-6538	202	15	ζ(m	ζ(m	ADJ
ejpam-6538	202	16	,	,	PUNCT
ejpam-6538	202	17	m−1	m−1	PROPN
ejpam-6538	202	18	)	)	PUNCT
ejpam-6538	203	1	⇂	⇂	ADP
ejpam-6538	203	2	cm×cm−1	cm×cm−1	PROPN
ejpam-6538	203	3	.	.	PUNCT
ejpam-6538	203	4	example	example	NOUN
ejpam-6538	204	1	1	1	NUM
ejpam-6538	204	2	.	.	X
ejpam-6538	205	1	all	all	DET
ejpam-6538	205	2	mpp	mpp	NOUN
ejpam-6538	205	3	endomorphisms	endomorphism	NOUN
ejpam-6538	205	4	(	(	PUNCT
ejpam-6538	205	5	fixing	fix	VERB
ejpam-6538	205	6	the	the	DET
ejpam-6538	205	7	bottom	bottom	NOUN
ejpam-6538	205	8	)	)	PUNCT
ejpam-6538	205	9	of	of	ADP
ejpam-6538	205	10	c2×c2	c2×c2	PROPN
ejpam-6538	205	11	,	,	PUNCT
ejpam-6538	205	12	c3×c2	c3×c2	PROPN
ejpam-6538	205	13	,	,	PUNCT
ejpam-6538	205	14	c3×c3	c3×c3	PROPN
ejpam-6538	205	15	and	and	CCONJ
ejpam-6538	205	16	c4	c4	NOUN
ejpam-6538	205	17	×c3	×c3	NOUN
ejpam-6538	205	18	are	be	AUX
ejpam-6538	205	19	shown	show	VERB
ejpam-6538	205	20	in	in	ADP
ejpam-6538	205	21	the	the	DET
ejpam-6538	205	22	figure	figure	NOUN
ejpam-6538	205	23	4	4	NUM
ejpam-6538	205	24	,	,	PUNCT
ejpam-6538	205	25	5	5	NUM
ejpam-6538	205	26	,	,	PUNCT
ejpam-6538	205	27	6	6	NUM
ejpam-6538	205	28	and	and	CCONJ
ejpam-6538	205	29	7	7	NUM
ejpam-6538	205	30	,	,	PUNCT
ejpam-6538	205	31	respectively	respectively	ADV
ejpam-6538	205	32	.	.	PUNCT
ejpam-6538	206	1	�	�	PROPN
ejpam-6538	206	2	�	�	PROPN
ejpam-6538	206	3	�	�	PROPN
ejpam-6538	206	4	�	�	PROPN
ejpam-6538	206	5	�	�	PROPN
ejpam-6538	206	6	�	�	PROPN
ejpam-6538	206	7	�	�	PROPN
ejpam-6538	206	8	�	�	PROPN
ejpam-6538	206	9	?	?	PUNCT
ejpam-6538	206	10	r	r	NOUN
ejpam-6538	206	11	rr	rr	NOUN
ejpam-6538	206	12	r	r	PROPN
ejpam-6538	206	13	�	�	PROPN
ejpam-6538	206	14	�	�	PROPN
ejpam-6538	206	15	�	�	PROPN
ejpam-6538	206	16	�	�	PROPN
ejpam-6538	206	17	�	�	PROPN
ejpam-6538	206	18	�	�	PROPN
ejpam-6538	206	19	�	�	PROPN
ejpam-6538	206	20	�	�	PROPN
ejpam-6538	206	21	�	�	PROPN
ejpam-6538	206	22	?	?	PUNCT
ejpam-6538	206	23	r	r	NOUN
ejpam-6538	206	24	rr	rr	NOUN
ejpam-6538	206	25	r	r	NOUN
ejpam-6538	206	26	⟲⟲	⟲⟲	NOUN
ejpam-6538	206	27	figure	figure	NOUN
ejpam-6538	206	28	4	4	NUM
ejpam-6538	206	29	:	:	PUNCT
ejpam-6538	206	30	the	the	DET
ejpam-6538	206	31	mpp	mpp	NOUN
ejpam-6538	206	32	endomorphisms	endomorphism	NOUN
ejpam-6538	206	33	of	of	ADP
ejpam-6538	206	34	c2	c2	PROPN
ejpam-6538	206	35	×c2	×c2	PROPN
ejpam-6538	206	36	.	.	PUNCT
ejpam-6538	207	1	�	�	PROPN
ejpam-6538	207	2	�	�	PROPN
ejpam-6538	207	3	�	�	PROPN
ejpam-6538	207	4	�	�	PROPN
ejpam-6538	207	5	�	�	PROPN
ejpam-6538	207	6	�	�	PROPN
ejpam-6538	207	7	�	�	PROPN
ejpam-6538	207	8	�	�	PROPN
ejpam-6538	207	9	�	�	PROPN
ejpam-6538	207	10	�	�	PROPN
ejpam-6538	207	11	�	�	PROPN
ejpam-6538	207	12	�	�	PROPN
ejpam-6538	207	13	�	�	PROPN
ejpam-6538	207	14	�	�	PROPN
ejpam-6538	207	15	�	�	PROPN
ejpam-6538	207	16	�	�	PROPN
ejpam-6538	207	17	�	�	PROPN
ejpam-6538	207	18	�	�	PROPN
ejpam-6538	207	19	�	�	PROPN
ejpam-6538	207	20	?	?	PUNCT
ejpam-6538	208	1	r	r	NOUN
ejpam-6538	208	2	rr	rr	NOUN
ejpam-6538	208	3	r	r	NOUN
ejpam-6538	208	4	r	r	NOUN
ejpam-6538	208	5	r	r	NOUN
ejpam-6538	208	6	�	�	PROPN
ejpam-6538	208	7	�	�	PROPN
ejpam-6538	208	8	�	�	PROPN
ejpam-6538	208	9	�	�	PROPN
ejpam-6538	208	10	�	�	PROPN
ejpam-6538	208	11	�	�	PROPN
ejpam-6538	208	12	�	�	PROPN
ejpam-6538	208	13	�	�	PROPN
ejpam-6538	208	14	�	�	PROPN
ejpam-6538	208	15	�	�	PROPN
ejpam-6538	208	16	�	�	PROPN
ejpam-6538	208	17	�	�	PROPN
ejpam-6538	208	18	�	�	PROPN
ejpam-6538	208	19	?	?	PUNCT
ejpam-6538	209	1	�	�	PROPN
ejpam-6538	209	2	�	�	PROPN
ejpam-6538	209	3	�	�	PROPN
ejpam-6538	209	4	r	r	NOUN
ejpam-6538	209	5	rr	rr	NOUN
ejpam-6538	209	6	r	r	NOUN
ejpam-6538	209	7	r	r	NOUN
ejpam-6538	209	8	r	r	NOUN
ejpam-6538	209	9	⟲⟲	⟲⟲	X
ejpam-6538	209	10	figure	figure	NOUN
ejpam-6538	209	11	5	5	NUM
ejpam-6538	209	12	:	:	PUNCT
ejpam-6538	209	13	the	the	DET
ejpam-6538	209	14	mpp	mpp	NOUN
ejpam-6538	209	15	endomorphisms	endomorphism	NOUN
ejpam-6538	209	16	of	of	ADP
ejpam-6538	209	17	c3	c3	PROPN
ejpam-6538	209	18	×c2	×c2	PROPN
ejpam-6538	209	19	.	.	PUNCT
ejpam-6538	210	1	corollary	corollary	ADJ
ejpam-6538	210	2	2	2	NUM
ejpam-6538	210	3	.	.	PUNCT
ejpam-6538	211	1	let	let	VERB
ejpam-6538	211	2	m	m	PRON
ejpam-6538	211	3	∈	∈	VERB
ejpam-6538	211	4	n	n	X
ejpam-6538	211	5	with	with	ADP
ejpam-6538	211	6	m	m	PROPN
ejpam-6538	211	7	≥	≥	NOUN
ejpam-6538	211	8	2	2	NUM
ejpam-6538	211	9	.	.	PUNCT
ejpam-6538	212	1	(	(	PUNCT
ejpam-6538	212	2	i	i	NOUN
ejpam-6538	212	3	)	)	PUNCT
ejpam-6538	212	4	for	for	ADP
ejpam-6538	212	5	m	m	PROPN
ejpam-6538	212	6	≤	≤	NOUN
ejpam-6538	212	7	3	3	NUM
ejpam-6538	212	8	,	,	PUNCT
ejpam-6538	212	9	ζ(m	ζ(m	ADJ
ejpam-6538	212	10	,	,	PUNCT
ejpam-6538	212	11	m−1	m−1	PROPN
ejpam-6538	212	12	)	)	PUNCT
ejpam-6538	213	1	⇂	⇂	ADP
ejpam-6538	213	2	cm×c2	cm×c2	PROPN
ejpam-6538	213	3	,	,	PUNCT
ejpam-6538	213	4	φm×2	φm×2	PROPN
ejpam-6538	213	5	,	,	PUNCT
ejpam-6538	213	6	ζ(m	ζ(m	ADJ
ejpam-6538	213	7	,	,	PUNCT
ejpam-6538	213	8	m−1	m−1	PROPN
ejpam-6538	213	9	)	)	PUNCT
ejpam-6538	214	1	⇂	⇂	NOUN
ejpam-6538	214	2	∂	∂	NOUN
ejpam-6538	214	3	cm×c2	cm×c2	NOUN
ejpam-6538	214	4	and	and	CCONJ
ejpam-6538	214	5	φ∂	φ∂	ADJ
ejpam-6538	214	6	m×2	m×2	PROPN
ejpam-6538	214	7	are	be	AUX
ejpam-6538	214	8	all	all	PRON
ejpam-6538	214	9	mpp	mpp	NOUN
ejpam-6538	214	10	endomorphisms	endomorphism	NOUN
ejpam-6538	214	11	of	of	ADP
ejpam-6538	214	12	cm	cm	NOUN
ejpam-6538	214	13	×c2	×c2	PROPN
ejpam-6538	214	14	.	.	PUNCT
ejpam-6538	215	1	(	(	PUNCT
ejpam-6538	215	2	ii	ii	NOUN
ejpam-6538	215	3	)	)	PUNCT
ejpam-6538	215	4	for	for	ADP
ejpam-6538	215	5	m	m	PROPN
ejpam-6538	215	6	>	>	X
ejpam-6538	215	7	3	3	NUM
ejpam-6538	215	8	,	,	PUNCT
ejpam-6538	215	9	φm×2	φm×2	NUM
ejpam-6538	215	10	and	and	CCONJ
ejpam-6538	215	11	φ∂	φ∂	ADJ
ejpam-6538	215	12	m×2	m×2	PROPN
ejpam-6538	215	13	are	be	AUX
ejpam-6538	215	14	all	all	PRON
ejpam-6538	215	15	mpp	mpp	NOUN
ejpam-6538	215	16	endomorphisms	endomorphism	NOUN
ejpam-6538	215	17	of	of	ADP
ejpam-6538	215	18	cm	cm	NOUN
ejpam-6538	215	19	×c2	×c2	PROPN
ejpam-6538	215	20	.	.	PUNCT
ejpam-6538	216	1	(	(	PUNCT
ejpam-6538	216	2	iii	iii	NOUN
ejpam-6538	216	3	)	)	PUNCT
ejpam-6538	216	4	for	for	ADP
ejpam-6538	216	5	m	m	PROPN
ejpam-6538	216	6	≥	≥	NOUN
ejpam-6538	216	7	3	3	NUM
ejpam-6538	216	8	,	,	PUNCT
ejpam-6538	216	9	ζ(m	ζ(m	ADJ
ejpam-6538	216	10	,	,	PUNCT
ejpam-6538	216	11	m−1	m−1	PROPN
ejpam-6538	216	12	)	)	PUNCT
ejpam-6538	216	13	,	,	PUNCT
ejpam-6538	216	14	ζ(m−1,m	ζ(m−1,m	PROPN
ejpam-6538	216	15	)	)	PUNCT
ejpam-6538	216	16	,	,	PUNCT
ejpam-6538	216	17	ζ	ζ	NOUN
ejpam-6538	216	18	∂	∂	ADJ
ejpam-6538	216	19	(	(	PUNCT
ejpam-6538	216	20	m	m	PROPN
ejpam-6538	216	21	,	,	PUNCT
ejpam-6538	216	22	m−1	m−1	PROPN
ejpam-6538	216	23	)	)	PUNCT
ejpam-6538	216	24	and	and	CCONJ
ejpam-6538	216	25	ζ	ζ	NOUN
ejpam-6538	216	26	∂	∂	NOUN
ejpam-6538	216	27	(	(	PUNCT
ejpam-6538	216	28	m−1,m	m−1,m	PROPN
ejpam-6538	216	29	)	)	PUNCT
ejpam-6538	216	30	are	be	AUX
ejpam-6538	216	31	all	all	PRON
ejpam-6538	216	32	mpp	mpp	NOUN
ejpam-6538	216	33	endomorphisms	endomorphism	NOUN
ejpam-6538	216	34	of	of	ADP
ejpam-6538	216	35	cm	cm	PROPN
ejpam-6538	216	36	×cm	×cm	PROPN
ejpam-6538	216	37	.	.	PUNCT
ejpam-6538	217	1	a.	a.	NOUN
ejpam-6538	217	2	charoenpol	charoenpol	PROPN
ejpam-6538	217	3	,	,	PUNCT
ejpam-6538	217	4	u.	u.	PROPN
ejpam-6538	217	5	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	217	6	/	/	SYM
ejpam-6538	217	7	eur	eur	PROPN
ejpam-6538	217	8	.	.	PUNCT
ejpam-6538	218	1	j.	j.	PROPN
ejpam-6538	218	2	pure	pure	PROPN
ejpam-6538	218	3	appl	appl	PROPN
ejpam-6538	218	4	.	.	PROPN
ejpam-6538	218	5	math	math	PROPN
ejpam-6538	218	6	,	,	PUNCT
ejpam-6538	218	7	18	18	NUM
ejpam-6538	218	8	(	(	PUNCT
ejpam-6538	218	9	3	3	NUM
ejpam-6538	218	10	)	)	PUNCT
ejpam-6538	218	11	(	(	PUNCT
ejpam-6538	218	12	2025	2025	NUM
ejpam-6538	218	13	)	)	PUNCT
ejpam-6538	218	14	,	,	PUNCT
ejpam-6538	218	15	6538	6538	NUM
ejpam-6538	218	16	10	10	NUM
ejpam-6538	218	17	of	of	ADP
ejpam-6538	218	18	13	13	NUM
ejpam-6538	218	19	�	�	PROPN
ejpam-6538	218	20	�	�	PROPN
ejpam-6538	218	21	�	�	PROPN
ejpam-6538	218	22	�	�	PROPN
ejpam-6538	218	23	�	�	PROPN
ejpam-6538	218	24	�	�	PROPN
ejpam-6538	218	25	�	�	PROPN
ejpam-6538	218	26	�	�	PROPN
ejpam-6538	218	27	�	�	PROPN
ejpam-6538	218	28	�	�	PROPN
ejpam-6538	218	29	�	�	PROPN
ejpam-6538	218	30	�	�	PROPN
ejpam-6538	218	31	�	�	PROPN
ejpam-6538	218	32	�	�	PROPN
ejpam-6538	218	33	�	�	PROPN
ejpam-6538	218	34	�	�	PROPN
ejpam-6538	218	35	�	�	PROPN
ejpam-6538	218	36	�	�	PROPN
ejpam-6538	218	37	�	�	PROPN
ejpam-6538	218	38	@	@	ADP
ejpam-6538	218	39	@r	@r	PROPN
ejpam-6538	218	40	�	�	PROPN
ejpam-6538	218	41	�	�	PROPN
ejpam-6538	218	42	�	�	PROPN
ejpam-6538	218	43	�	�	PROPN
ejpam-6538	218	44	�	�	PROPN
ejpam-6538	218	45	?	?	PUNCT
ejpam-6538	218	46	?	?	PUNCT
ejpam-6538	219	1	r	r	NOUN
ejpam-6538	219	2	rr	rr	NOUN
ejpam-6538	220	1	r	r	NOUN
ejpam-6538	220	2	r	r	NOUN
ejpam-6538	220	3	r	r	NOUN
ejpam-6538	220	4	r	r	NOUN
ejpam-6538	220	5	r	r	NOUN
ejpam-6538	220	6	r	r	NOUN
ejpam-6538	220	7	⟲	⟲	ADJ
ejpam-6538	220	8	�	�	PROPN
ejpam-6538	220	9	�	�	PROPN
ejpam-6538	220	10	�	�	PROPN
ejpam-6538	220	11	�	�	PROPN
ejpam-6538	220	12	�	�	PROPN
ejpam-6538	220	13	�	�	PROPN
ejpam-6538	220	14	�	�	PROPN
ejpam-6538	220	15	�	�	PROPN
ejpam-6538	220	16	�	�	PROPN
ejpam-6538	220	17	�	�	PROPN
ejpam-6538	220	18	�	�	PROPN
ejpam-6538	220	19	�	�	PROPN
ejpam-6538	220	20	�	�	PROPN
ejpam-6538	220	21	�	�	PROPN
ejpam-6538	220	22	�	�	PROPN
ejpam-6538	220	23	�	�	PROPN
ejpam-6538	220	24	�	�	PROPN
ejpam-6538	220	25	�	�	PROPN
ejpam-6538	220	26	?	?	PUNCT
ejpam-6538	220	27	�	�	PROPN
ejpam-6538	220	28	�	�	PROPN
ejpam-6538	220	29	�	�	PROPN
ejpam-6538	220	30	�	�	PROPN
ejpam-6538	220	31	�	�	PROPN
ejpam-6538	220	32	�	�	PROPN
ejpam-6538	220	33	?	?	PUNCT
ejpam-6538	220	34	�	�	PROPN
ejpam-6538	220	35	�	�	PROPN
ejpam-6538	220	36	r	r	NOUN
ejpam-6538	220	37	rr	rr	NOUN
ejpam-6538	220	38	r	r	NOUN
ejpam-6538	220	39	r	r	NOUN
ejpam-6538	220	40	r	r	NOUN
ejpam-6538	220	41	r	r	NOUN
ejpam-6538	220	42	r	r	NOUN
ejpam-6538	220	43	r	r	NOUN
ejpam-6538	220	44	⟲	⟲	PUNCT
ejpam-6538	220	45	?	?	PUNCT
ejpam-6538	221	1	figure	figure	NOUN
ejpam-6538	221	2	6	6	NUM
ejpam-6538	221	3	:	:	PUNCT
ejpam-6538	221	4	the	the	DET
ejpam-6538	221	5	mpp	mpp	NOUN
ejpam-6538	221	6	endomorphisms	endomorphism	NOUN
ejpam-6538	221	7	of	of	ADP
ejpam-6538	221	8	c3	c3	PROPN
ejpam-6538	221	9	×c3	×c3	PROPN
ejpam-6538	221	10	.	.	PUNCT
ejpam-6538	222	1	�	�	PROPN
ejpam-6538	222	2	�	�	PROPN
ejpam-6538	222	3	�	�	PROPN
ejpam-6538	222	4	�	�	PROPN
ejpam-6538	222	5	�	�	PROPN
ejpam-6538	222	6	�	�	PROPN
ejpam-6538	222	7	�	�	PROPN
ejpam-6538	222	8	�	�	PROPN
ejpam-6538	222	9	�	�	PROPN
ejpam-6538	222	10	�	�	PROPN
ejpam-6538	222	11	�	�	PROPN
ejpam-6538	222	12	�	�	PROPN
ejpam-6538	222	13	�	�	PROPN
ejpam-6538	222	14	�	�	PROPN
ejpam-6538	222	15	�	�	PROPN
ejpam-6538	222	16	�	�	PROPN
ejpam-6538	222	17	�	�	PROPN
ejpam-6538	222	18	�	�	PROPN
ejpam-6538	222	19	�	�	PROPN
ejpam-6538	222	20	�	�	PROPN
ejpam-6538	222	21	�	�	PROPN
ejpam-6538	222	22	�	�	PROPN
ejpam-6538	222	23	�	�	PROPN
ejpam-6538	222	24	�	�	PROPN
ejpam-6538	222	25	�	�	PROPN
ejpam-6538	222	26	�	�	PROPN
ejpam-6538	222	27	�	�	PROPN
ejpam-6538	222	28	�	�	PROPN
ejpam-6538	222	29	�	�	PROPN
ejpam-6538	222	30	�	�	PROPN
ejpam-6538	222	31	�	�	PROPN
ejpam-6538	222	32	�	�	PROPN
ejpam-6538	222	33	?	?	PUNCT
ejpam-6538	222	34	?	?	PUNCT
ejpam-6538	223	1	@	@	PUNCT
ejpam-6538	224	1	@r	@r	PROPN
ejpam-6538	224	2	�	�	PROPN
ejpam-6538	224	3	�	�	PROPN
ejpam-6538	224	4	�	�	PROPN
ejpam-6538	224	5	�	�	PROPN
ejpam-6538	224	6	�	�	PROPN
ejpam-6538	224	7	�	�	PROPN
ejpam-6538	224	8	�	�	PROPN
ejpam-6538	224	9	�	�	PROPN
ejpam-6538	224	10	�	�	PROPN
ejpam-6538	224	11	�	�	PROPN
ejpam-6538	224	12	�	�	PROPN
ejpam-6538	224	13	�	�	PROPN
ejpam-6538	224	14	�	�	PROPN
ejpam-6538	224	15	)	)	PUNCT
ejpam-6538	225	1	-r	-r	VERB
ejpam-6538	225	2	r	r	NOUN
ejpam-6538	225	3	r	r	NOUN
ejpam-6538	225	4	r	r	NOUN
ejpam-6538	225	5	r	r	NOUN
ejpam-6538	225	6	r	r	NOUN
ejpam-6538	225	7	r	r	NOUN
ejpam-6538	225	8	r	r	NOUN
ejpam-6538	225	9	r	r	NOUN
ejpam-6538	225	10	r	r	NOUN
ejpam-6538	225	11	r	r	NOUN
ejpam-6538	225	12	r	r	NOUN
ejpam-6538	225	13	⟲	⟲	NOUN
ejpam-6538	225	14	figure	figure	NOUN
ejpam-6538	225	15	7	7	NUM
ejpam-6538	225	16	:	:	PUNCT
ejpam-6538	225	17	the	the	DET
ejpam-6538	225	18	mpp	mpp	NOUN
ejpam-6538	225	19	endomorphism	endomorphism	X
ejpam-6538	225	20	of	of	ADP
ejpam-6538	225	21	c4	c4	NOUN
ejpam-6538	225	22	×c3	×c3	PROPN
ejpam-6538	225	23	.	.	PUNCT
ejpam-6538	226	1	(	(	PUNCT
ejpam-6538	226	2	iv	iv	X
ejpam-6538	226	3	)	)	PUNCT
ejpam-6538	226	4	for	for	ADP
ejpam-6538	226	5	m	m	PROPN
ejpam-6538	226	6	>	>	X
ejpam-6538	226	7	3	3	NUM
ejpam-6538	226	8	,	,	PUNCT
ejpam-6538	226	9	ζ(m	ζ(m	ADJ
ejpam-6538	226	10	,	,	PUNCT
ejpam-6538	226	11	m−1	m−1	PROPN
ejpam-6538	226	12	)	)	PUNCT
ejpam-6538	227	1	⇂	⇂	ADP
ejpam-6538	227	2	cm×cm−1	cm×cm−1	PROPN
ejpam-6538	227	3	and	and	CCONJ
ejpam-6538	227	4	ζ(m	ζ(m	ADJ
ejpam-6538	227	5	,	,	PUNCT
ejpam-6538	227	6	m−1	m−1	PROPN
ejpam-6538	227	7	)	)	PUNCT
ejpam-6538	228	1	⇂	⇂	NOUN
ejpam-6538	228	2	∂	∂	ADJ
ejpam-6538	228	3	cm×cm−1	cm×cm−1	NOUN
ejpam-6538	228	4	are	be	AUX
ejpam-6538	228	5	all	all	PRON
ejpam-6538	228	6	mpp	mpp	NOUN
ejpam-6538	228	7	endomorphisms	endomorphism	NOUN
ejpam-6538	228	8	of	of	ADP
ejpam-6538	228	9	cm	cm	PROPN
ejpam-6538	228	10	×cm−1	×cm−1	PROPN
ejpam-6538	228	11	.	.	PUNCT
ejpam-6538	229	1	for	for	ADP
ejpam-6538	229	2	each	each	DET
ejpam-6538	229	3	n	n	PRON
ejpam-6538	229	4	∈	∈	PROPN
ejpam-6538	229	5	n	n	CCONJ
ejpam-6538	229	6	,	,	PUNCT
ejpam-6538	229	7	we	we	PRON
ejpam-6538	229	8	define	define	VERB
ejpam-6538	229	9	monounary	monounary	ADJ
ejpam-6538	229	10	algebras	algebra	NOUN
ejpam-6538	229	11	(	(	PUNCT
ejpam-6538	229	12	an	an	DET
ejpam-6538	229	13	,	,	PUNCT
ejpam-6538	229	14	fn	fn	NOUN
ejpam-6538	229	15	)	)	PUNCT
ejpam-6538	229	16	and	and	CCONJ
ejpam-6538	229	17	(	(	PUNCT
ejpam-6538	229	18	bn	bn	PROPN
ejpam-6538	229	19	,	,	PUNCT
ejpam-6538	229	20	gn	gn	PROPN
ejpam-6538	229	21	)	)	PUNCT
ejpam-6538	229	22	by	by	ADP
ejpam-6538	229	23	an	an	DET
ejpam-6538	229	24	=	=	X
ejpam-6538	229	25	{	{	PUNCT
ejpam-6538	229	26	ac	ac	PROPN
ejpam-6538	229	27	,	,	PUNCT
ejpam-6538	229	28	h	h	NOUN
ejpam-6538	230	1	|	|	ADV
ejpam-6538	230	2	2c−	2c−	NUM
ejpam-6538	230	3	2	2	NUM
ejpam-6538	230	4	≤	≤	NUM
ejpam-6538	230	5	h	h	NOUN
ejpam-6538	230	6	≤	≤	NOUN
ejpam-6538	230	7	n	n	CCONJ
ejpam-6538	230	8	for	for	ADP
ejpam-6538	230	9	some	some	DET
ejpam-6538	230	10	c	c	NOUN
ejpam-6538	230	11	∈	∈	PROPN
ejpam-6538	230	12	n	n	NOUN
ejpam-6538	230	13	and	and	CCONJ
ejpam-6538	230	14	h	h	NOUN
ejpam-6538	230	15	∈	∈	PROPN
ejpam-6538	230	16	n0	n0	PROPN
ejpam-6538	230	17	}	}	PUNCT
ejpam-6538	230	18	,	,	PUNCT
ejpam-6538	230	19	bn	bn	NOUN
ejpam-6538	230	20	=	=	SYM
ejpam-6538	230	21	{	{	PUNCT
ejpam-6538	230	22	bc	bc	PROPN
ejpam-6538	230	23	,	,	PUNCT
ejpam-6538	230	24	h	h	NOUN
ejpam-6538	231	1	|	|	NOUN
ejpam-6538	231	2	c	c	PROPN
ejpam-6538	231	3	∈	∈	PROPN
ejpam-6538	231	4	{	{	PUNCT
ejpam-6538	231	5	1	1	NUM
ejpam-6538	231	6	,	,	PUNCT
ejpam-6538	231	7	2	2	NUM
ejpam-6538	231	8	}	}	PUNCT
ejpam-6538	231	9	and	and	CCONJ
ejpam-6538	231	10	h	h	NOUN
ejpam-6538	231	11	∈	∈	PROPN
ejpam-6538	231	12	{	{	PUNCT
ejpam-6538	231	13	1	1	NUM
ejpam-6538	231	14	,	,	PUNCT
ejpam-6538	231	15	.	.	PUNCT
ejpam-6538	231	16	.	.	PUNCT
ejpam-6538	231	17	.	.	PUNCT
ejpam-6538	231	18	,	,	PUNCT
ejpam-6538	231	19	n	n	CCONJ
ejpam-6538	231	20	}	}	PUNCT
ejpam-6538	231	21	}	}	PUNCT
ejpam-6538	231	22	,	,	PUNCT
ejpam-6538	231	23	fn(ac	fn(ac	PROPN
ejpam-6538	231	24	,	,	PUNCT
ejpam-6538	231	25	h	h	NOUN
ejpam-6538	231	26	)	)	PUNCT
ejpam-6538	231	27	=	=	PUNCT
ejpam-6538	232	1			PRON
ejpam-6538	232	2	ac	ac	VERB
ejpam-6538	232	3	,	,	PUNCT
ejpam-6538	232	4	h−1	h−1	PROPN
ejpam-6538	232	5	if	if	SCONJ
ejpam-6538	232	6	2c−	2c−	PROPN
ejpam-6538	232	7	2	2	NUM
ejpam-6538	232	8	<	<	X
ejpam-6538	232	9	h	h	NOUN
ejpam-6538	232	10	,	,	PUNCT
ejpam-6538	232	11	ac−1,h−1	ac−1,h−1	VERB
ejpam-6538	232	12	if	if	SCONJ
ejpam-6538	232	13	2c−	2c−	PROPN
ejpam-6538	232	14	2	2	NUM
ejpam-6538	232	15	=	=	SYM
ejpam-6538	232	16	h	h	NOUN
ejpam-6538	232	17	,	,	PUNCT
ejpam-6538	232	18	a1,0	a1,0	PROPN
ejpam-6538	232	19	if	if	SCONJ
ejpam-6538	232	20	c	c	NOUN
ejpam-6538	232	21	=	=	SYM
ejpam-6538	232	22	1	1	NUM
ejpam-6538	232	23	and	and	CCONJ
ejpam-6538	232	24	h	h	NOUN
ejpam-6538	232	25	=	=	SYM
ejpam-6538	232	26	0	0	NUM
ejpam-6538	232	27	,	,	PUNCT
ejpam-6538	232	28	and	and	CCONJ
ejpam-6538	232	29	gn(bc	gn(bc	ADJ
ejpam-6538	232	30	,	,	PUNCT
ejpam-6538	232	31	h	h	NOUN
ejpam-6538	232	32	)	)	PUNCT
ejpam-6538	232	33	=	=	SYM
ejpam-6538	233	1			PROPN
ejpam-6538	233	2	bc	bc	VERB
ejpam-6538	233	3	,	,	PUNCT
ejpam-6538	233	4	h−1	h−1	PROPN
ejpam-6538	233	5	if	if	SCONJ
ejpam-6538	233	6	c	c	NOUN
ejpam-6538	233	7	=	=	SYM
ejpam-6538	233	8	1	1	NUM
ejpam-6538	233	9	and	and	CCONJ
ejpam-6538	233	10	h	h	NOUN
ejpam-6538	233	11	̸=	̸=	PROPN
ejpam-6538	233	12	1	1	NUM
ejpam-6538	233	13	,	,	PUNCT
ejpam-6538	233	14	bc−1,h−1	bc−1,h−1	NOUN
ejpam-6538	233	15	if	if	SCONJ
ejpam-6538	233	16	c	c	NOUN
ejpam-6538	233	17	=	=	SYM
ejpam-6538	233	18	2	2	NUM
ejpam-6538	233	19	and	and	CCONJ
ejpam-6538	233	20	h	h	NOUN
ejpam-6538	233	21	̸=	̸=	PROPN
ejpam-6538	233	22	1	1	NUM
ejpam-6538	233	23	,	,	PUNCT
ejpam-6538	233	24	b2,1	b2,1	ADJ
ejpam-6538	233	25	if	if	SCONJ
ejpam-6538	233	26	h	h	NOUN
ejpam-6538	233	27	=	=	NOUN
ejpam-6538	233	28	1	1	X
ejpam-6538	233	29	.	.	X
ejpam-6538	233	30	one	one	PRON
ejpam-6538	233	31	can	can	AUX
ejpam-6538	233	32	observe	observe	VERB
ejpam-6538	233	33	that	that	SCONJ
ejpam-6538	233	34	a.	a.	NOUN
ejpam-6538	233	35	charoenpol	charoenpol	NOUN
ejpam-6538	233	36	,	,	PUNCT
ejpam-6538	233	37	u.	u.	PROPN
ejpam-6538	233	38	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	233	39	/	/	SYM
ejpam-6538	233	40	eur	eur	PROPN
ejpam-6538	233	41	.	.	PUNCT
ejpam-6538	234	1	j.	j.	PROPN
ejpam-6538	234	2	pure	pure	PROPN
ejpam-6538	234	3	appl	appl	PROPN
ejpam-6538	234	4	.	.	PROPN
ejpam-6538	234	5	math	math	PROPN
ejpam-6538	234	6	,	,	PUNCT
ejpam-6538	234	7	18	18	NUM
ejpam-6538	234	8	(	(	PUNCT
ejpam-6538	234	9	3	3	NUM
ejpam-6538	234	10	)	)	PUNCT
ejpam-6538	234	11	(	(	PUNCT
ejpam-6538	234	12	2025	2025	NUM
ejpam-6538	234	13	)	)	PUNCT
ejpam-6538	234	14	,	,	PUNCT
ejpam-6538	234	15	6538	6538	NUM
ejpam-6538	234	16	11	11	NUM
ejpam-6538	234	17	of	of	ADP
ejpam-6538	234	18	13	13	NUM
ejpam-6538	234	19	f−1	f−1	PROPN
ejpam-6538	234	20	n	n	PROPN
ejpam-6538	234	21	(	(	PUNCT
ejpam-6538	234	22	{	{	PUNCT
ejpam-6538	234	23	ac	ac	PROPN
ejpam-6538	234	24	,	,	PUNCT
ejpam-6538	234	25	h	h	NOUN
ejpam-6538	234	26	}	}	PUNCT
ejpam-6538	234	27	)	)	PUNCT
ejpam-6538	235	1	=	=	PUNCT
ejpam-6538	235	2			NOUN
ejpam-6538	235	3	∅	∅	NOUN
ejpam-6538	235	4	if	if	SCONJ
ejpam-6538	235	5	h	h	NOUN
ejpam-6538	235	6	=	=	SYM
ejpam-6538	235	7	n	n	CCONJ
ejpam-6538	235	8	,	,	PUNCT
ejpam-6538	235	9	{	{	PUNCT
ejpam-6538	235	10	ac	ac	PROPN
ejpam-6538	235	11	,	,	PUNCT
ejpam-6538	235	12	h+1	h+1	VERB
ejpam-6538	235	13	}	}	PUNCT
ejpam-6538	235	14	if	if	SCONJ
ejpam-6538	235	15	2c−	2c−	PROPN
ejpam-6538	235	16	1	1	NUM
ejpam-6538	235	17	<	<	X
ejpam-6538	235	18	h	h	NOUN
ejpam-6538	235	19	<	<	X
ejpam-6538	235	20	n	n	CCONJ
ejpam-6538	235	21	,	,	PUNCT
ejpam-6538	235	22	{	{	PUNCT
ejpam-6538	235	23	ac	ac	PROPN
ejpam-6538	235	24	,	,	PUNCT
ejpam-6538	235	25	h+1	h+1	PRON
ejpam-6538	235	26	,	,	PUNCT
ejpam-6538	235	27	ac+1,h+1	ac+1,h+1	X
ejpam-6538	235	28	}	}	PUNCT
ejpam-6538	235	29	if	if	SCONJ
ejpam-6538	235	30	2c−	2c−	PROPN
ejpam-6538	235	31	1	1	NUM
ejpam-6538	235	32	=	=	SYM
ejpam-6538	235	33	h	h	NOUN
ejpam-6538	235	34	,	,	PUNCT
ejpam-6538	235	35	{	{	PUNCT
ejpam-6538	235	36	a1,0	a1,0	ADJ
ejpam-6538	235	37	,	,	PUNCT
ejpam-6538	235	38	a1,1	a1,1	NOUN
ejpam-6538	235	39	}	}	PUNCT
ejpam-6538	235	40	if	if	SCONJ
ejpam-6538	235	41	h	h	NOUN
ejpam-6538	235	42	=	=	NOUN
ejpam-6538	235	43	0	0	NUM
ejpam-6538	235	44	for	for	ADP
ejpam-6538	235	45	all	all	DET
ejpam-6538	235	46	ac	ac	PROPN
ejpam-6538	235	47	,	,	PUNCT
ejpam-6538	235	48	h	h	NOUN
ejpam-6538	235	49	∈	∈	PROPN
ejpam-6538	235	50	an	an	PRON
ejpam-6538	235	51	and	and	CCONJ
ejpam-6538	235	52	g−1	g−1	PROPN
ejpam-6538	235	53	n	n	PROPN
ejpam-6538	235	54	(	(	PUNCT
ejpam-6538	235	55	{	{	PUNCT
ejpam-6538	235	56	bc	bc	PROPN
ejpam-6538	235	57	,	,	PUNCT
ejpam-6538	235	58	h	h	NOUN
ejpam-6538	235	59	}	}	PUNCT
ejpam-6538	235	60	)	)	PUNCT
ejpam-6538	236	1	=	=	SYM
ejpam-6538	236	2			PRON
ejpam-6538	236	3	∅	∅	VERB
ejpam-6538	236	4	if	if	SCONJ
ejpam-6538	236	5	either	either	PRON
ejpam-6538	236	6	h	h	NOUN
ejpam-6538	236	7	=	=	PUNCT
ejpam-6538	236	8	n	n	PROPN
ejpam-6538	236	9	or	or	CCONJ
ejpam-6538	236	10	c	c	NOUN
ejpam-6538	236	11	=	=	SYM
ejpam-6538	236	12	2	2	NUM
ejpam-6538	236	13	and	and	CCONJ
ejpam-6538	236	14	h	h	NOUN
ejpam-6538	236	15	̸=	̸=	PROPN
ejpam-6538	236	16	1	1	NUM
ejpam-6538	236	17	,	,	PUNCT
ejpam-6538	236	18	{	{	PUNCT
ejpam-6538	236	19	b1,1	b1,1	PROPN
ejpam-6538	236	20	,	,	PUNCT
ejpam-6538	236	21	b2,1	b2,1	NUM
ejpam-6538	236	22	}	}	PUNCT
ejpam-6538	236	23	if	if	SCONJ
ejpam-6538	236	24	c	c	NOUN
ejpam-6538	236	25	=	=	SYM
ejpam-6538	236	26	2	2	NUM
ejpam-6538	236	27	and	and	CCONJ
ejpam-6538	236	28	h	h	NOUN
ejpam-6538	236	29	=	=	NOUN
ejpam-6538	236	30	1	1	NUM
ejpam-6538	236	31	,	,	PUNCT
ejpam-6538	236	32	{	{	PUNCT
ejpam-6538	236	33	bc	bc	PROPN
ejpam-6538	236	34	,	,	PUNCT
ejpam-6538	236	35	h+1	h+1	PRON
ejpam-6538	236	36	,	,	PUNCT
ejpam-6538	236	37	ac+1,h+1	ac+1,h+1	X
ejpam-6538	236	38	}	}	PUNCT
ejpam-6538	236	39	if	if	SCONJ
ejpam-6538	236	40	c	c	NOUN
ejpam-6538	236	41	=	=	SYM
ejpam-6538	236	42	1	1	NUM
ejpam-6538	236	43	and	and	CCONJ
ejpam-6538	236	44	h	h	NOUN
ejpam-6538	236	45	̸=	̸=	PROPN
ejpam-6538	236	46	n	n	PROPN
ejpam-6538	236	47	for	for	ADP
ejpam-6538	236	48	all	all	DET
ejpam-6538	236	49	bc	bc	PROPN
ejpam-6538	236	50	,	,	PUNCT
ejpam-6538	236	51	h	h	NOUN
ejpam-6538	236	52	∈	∈	PROPN
ejpam-6538	236	53	bn	bn	PROPN
ejpam-6538	236	54	.	.	PUNCT
ejpam-6538	237	1	for	for	ADP
ejpam-6538	237	2	each	each	DET
ejpam-6538	237	3	n	n	PRON
ejpam-6538	237	4	∈	∈	PROPN
ejpam-6538	237	5	n	n	CCONJ
ejpam-6538	237	6	,	,	PUNCT
ejpam-6538	237	7	let	let	VERB
ejpam-6538	237	8	ζn	ζn	PRON
ejpam-6538	237	9	=	=	PUNCT
ejpam-6538	237	10	ζ(m+1,m	ζ(m+1,m	PROPN
ejpam-6538	237	11	)	)	PUNCT
ejpam-6538	237	12	if	if	SCONJ
ejpam-6538	237	13	n	n	NOUN
ejpam-6538	237	14	=	=	SYM
ejpam-6538	237	15	2	2	NUM
ejpam-6538	237	16	m	m	PRON
ejpam-6538	237	17	and	and	CCONJ
ejpam-6538	237	18	let	let	VERB
ejpam-6538	237	19	ζn	ζn	PRON
ejpam-6538	237	20	=	=	SYM
ejpam-6538	237	21	ζ(m+1,m	ζ(m+1,m	PROPN
ejpam-6538	237	22	)	)	PUNCT
ejpam-6538	238	1	⇂	⇂	NOUN
ejpam-6538	238	2	cm+1×cm	cm+1×cm	VERB
ejpam-6538	238	3	if	if	SCONJ
ejpam-6538	238	4	n	n	NOUN
ejpam-6538	238	5	=	=	SYM
ejpam-6538	238	6	2m−	2m−	PROPN
ejpam-6538	238	7	1	1	NUM
ejpam-6538	238	8	.	.	PUNCT
ejpam-6538	238	9	theorem	theorem	VERB
ejpam-6538	238	10	6	6	NUM
ejpam-6538	238	11	.	.	PUNCT
ejpam-6538	239	1	all	all	DET
ejpam-6538	239	2	monounary	monounary	ADJ
ejpam-6538	239	3	algebras	algebra	NOUN
ejpam-6538	239	4	induced	induce	VERB
ejpam-6538	239	5	by	by	ADP
ejpam-6538	239	6	an	an	DET
ejpam-6538	239	7	mpp	mpp	NOUN
ejpam-6538	239	8	endomorphism	endomorphism	NOUN
ejpam-6538	239	9	of	of	ADP
ejpam-6538	239	10	the	the	DET
ejpam-6538	239	11	direct	direct	NOUN
ejpam-6538	239	12	of	of	ADP
ejpam-6538	239	13	two	two	NUM
ejpam-6538	239	14	chains	chain	NOUN
ejpam-6538	239	15	are	be	AUX
ejpam-6538	239	16	isomorphic	isomorphic	ADJ
ejpam-6538	239	17	to	to	ADP
ejpam-6538	239	18	either	either	CCONJ
ejpam-6538	239	19	(	(	PUNCT
ejpam-6538	239	20	an	an	DET
ejpam-6538	239	21	,	,	PUNCT
ejpam-6538	239	22	fn	fn	NOUN
ejpam-6538	239	23	)	)	PUNCT
ejpam-6538	239	24	or	or	CCONJ
ejpam-6538	239	25	(	(	PUNCT
ejpam-6538	239	26	bn	bn	PROPN
ejpam-6538	239	27	,	,	PUNCT
ejpam-6538	239	28	gn	gn	PROPN
ejpam-6538	239	29	)	)	PUNCT
ejpam-6538	239	30	for	for	ADP
ejpam-6538	239	31	some	some	DET
ejpam-6538	239	32	n	n	PRON
ejpam-6538	239	33	∈	∈	NOUN
ejpam-6538	239	34	n.	n.	NOUN
ejpam-6538	239	35	proof	proof	NOUN
ejpam-6538	239	36	.	.	PUNCT
ejpam-6538	240	1	by	by	ADP
ejpam-6538	240	2	theorem	theorem	NOUN
ejpam-6538	240	3	4	4	NUM
ejpam-6538	240	4	,	,	PUNCT
ejpam-6538	240	5	5	5	NUM
ejpam-6538	240	6	,	,	PUNCT
ejpam-6538	240	7	and	and	CCONJ
ejpam-6538	240	8	proposition	proposition	NOUN
ejpam-6538	240	9	1	1	NUM
ejpam-6538	240	10	,	,	PUNCT
ejpam-6538	240	11	it	it	PRON
ejpam-6538	240	12	suffices	suffice	VERB
ejpam-6538	240	13	to	to	PART
ejpam-6538	240	14	show	show	VERB
ejpam-6538	240	15	that	that	SCONJ
ejpam-6538	240	16	(	(	PUNCT
ejpam-6538	240	17	an	an	DET
ejpam-6538	240	18	,	,	PUNCT
ejpam-6538	240	19	fn	fn	NOUN
ejpam-6538	240	20	)	)	PUNCT
ejpam-6538	240	21	is	be	AUX
ejpam-6538	240	22	isomorphic	isomorphic	ADJ
ejpam-6538	240	23	to	to	ADP
ejpam-6538	240	24	(	(	PUNCT
ejpam-6538	240	25	c⌈n+2	c⌈n+2	PROPN
ejpam-6538	240	26	2	2	NUM
ejpam-6538	240	27	⌉	⌉	X
ejpam-6538	240	28	×	×	PROPN
ejpam-6538	240	29	c⌈n+1	c⌈n+1	PROPN
ejpam-6538	240	30	2	2	NUM
ejpam-6538	240	31	⌉	⌉	NOUN
ejpam-6538	240	32	,	,	PUNCT
ejpam-6538	240	33	ζn	ζn	NOUN
ejpam-6538	240	34	)	)	PUNCT
ejpam-6538	240	35	and	and	CCONJ
ejpam-6538	240	36	(	(	PUNCT
ejpam-6538	240	37	bn	bn	X
ejpam-6538	240	38	,	,	PUNCT
ejpam-6538	240	39	gn	gn	PROPN
ejpam-6538	240	40	)	)	PUNCT
ejpam-6538	240	41	is	be	AUX
ejpam-6538	240	42	isomorphic	isomorphic	ADJ
ejpam-6538	240	43	to	to	PART
ejpam-6538	240	44	(	(	PUNCT
ejpam-6538	240	45	cn	cn	PROPN
ejpam-6538	240	46	×	×	PROPN
ejpam-6538	240	47	c2	c2	PROPN
ejpam-6538	240	48	,	,	PUNCT
ejpam-6538	240	49	φn×2	φn×2	PROPN
ejpam-6538	240	50	)	)	PUNCT
ejpam-6538	240	51	for	for	ADP
ejpam-6538	240	52	all	all	PRON
ejpam-6538	240	53	n	n	DET
ejpam-6538	240	54	∈	∈	PROPN
ejpam-6538	240	55	n.	n.	NOUN
ejpam-6538	240	56	let	let	VERB
ejpam-6538	240	57	n	n	PRON
ejpam-6538	240	58	∈	∈	PROPN
ejpam-6538	240	59	n.	n.	NOUN
ejpam-6538	240	60	firstly	firstly	ADV
ejpam-6538	240	61	,	,	PUNCT
ejpam-6538	240	62	we	we	PRON
ejpam-6538	240	63	will	will	AUX
ejpam-6538	240	64	show	show	VERB
ejpam-6538	240	65	that	that	SCONJ
ejpam-6538	240	66	ϕn	ϕn	INTJ
ejpam-6538	240	67	:	:	PUNCT
ejpam-6538	240	68	an	an	DET
ejpam-6538	240	69	→	→	SYM
ejpam-6538	240	70	c⌈n+2	c⌈n+2	PROPN
ejpam-6538	240	71	2	2	NUM
ejpam-6538	240	72	⌉	⌉	X
ejpam-6538	240	73	×	×	PROPN
ejpam-6538	240	74	c⌈n+1	c⌈n+1	NOUN
ejpam-6538	240	75	2	2	NUM
ejpam-6538	240	76	⌉	⌉	VERB
ejpam-6538	240	77	defined	define	VERB
ejpam-6538	240	78	by	by	ADP
ejpam-6538	240	79	ϕn(ac	ϕn(ac	PROPN
ejpam-6538	240	80	,	,	PUNCT
ejpam-6538	240	81	h	h	NOUN
ejpam-6538	240	82	)	)	PUNCT
ejpam-6538	240	83	=	=	SYM
ejpam-6538	241	1			PROPN
ejpam-6538	241	2	(	(	PUNCT
ejpam-6538	241	3	h2	h2	NOUN
ejpam-6538	241	4	+	+	CCONJ
ejpam-6538	241	5	2−	2−	NUM
ejpam-6538	241	6	c	c	NOUN
ejpam-6538	241	7	,	,	PUNCT
ejpam-6538	241	8	h2	h2	NOUN
ejpam-6538	241	9	+	+	CCONJ
ejpam-6538	241	10	1	1	X
ejpam-6538	241	11	)	)	PUNCT
ejpam-6538	241	12	if	if	SCONJ
ejpam-6538	241	13	h	h	NOUN
ejpam-6538	241	14	∈	∈	PROPN
ejpam-6538	241	15	e	e	PROPN
ejpam-6538	241	16	,	,	PUNCT
ejpam-6538	241	17	(	(	PUNCT
ejpam-6538	241	18	h+3	h+3	NOUN
ejpam-6538	241	19	2	2	NUM
ejpam-6538	241	20	,	,	PUNCT
ejpam-6538	241	21	h+3	h+3	PROPN
ejpam-6538	241	22	2	2	NUM
ejpam-6538	241	23	−	−	NOUN
ejpam-6538	241	24	c	c	NOUN
ejpam-6538	241	25	)	)	PUNCT
ejpam-6538	241	26	if	if	SCONJ
ejpam-6538	241	27	h	h	NOUN
ejpam-6538	241	28	∈	∈	PROPN
ejpam-6538	241	29	o	o	NOUN
ejpam-6538	241	30	is	be	AUX
ejpam-6538	241	31	an	an	DET
ejpam-6538	241	32	isomorphism	isomorphism	NOUN
ejpam-6538	241	33	.	.	PUNCT
ejpam-6538	242	1	let	let	VERB
ejpam-6538	242	2	ac	ac	VERB
ejpam-6538	242	3	,	,	PUNCT
ejpam-6538	242	4	h	h	NOUN
ejpam-6538	242	5	∈	∈	PROPN
ejpam-6538	243	1	an	an	DET
ejpam-6538	243	2	.	.	PUNCT
ejpam-6538	243	3	case	case	NOUN
ejpam-6538	243	4	1	1	NUM
ejpam-6538	243	5	:	:	PUNCT
ejpam-6538	243	6	h	h	PROPN
ejpam-6538	243	7	∈	∈	PROPN
ejpam-6538	244	1	e.	e.	PROPN
ejpam-6538	245	1	if	if	SCONJ
ejpam-6538	245	2	ac	ac	PROPN
ejpam-6538	245	3	,	,	PUNCT
ejpam-6538	245	4	h	h	NOUN
ejpam-6538	245	5	=	=	SYM
ejpam-6538	245	6	a1,0	a1,0	PROPN
ejpam-6538	245	7	,	,	PUNCT
ejpam-6538	245	8	then	then	ADV
ejpam-6538	245	9	ϕn(fn(a1,0	ϕn(fn(a1,0	PROPN
ejpam-6538	245	10	)	)	PUNCT
ejpam-6538	245	11	)	)	PUNCT
ejpam-6538	246	1	=	=	PUNCT
ejpam-6538	246	2	ϕn(a1,0	ϕn(a1,0	ADJ
ejpam-6538	246	3	)	)	PUNCT
ejpam-6538	246	4	=	=	SYM
ejpam-6538	246	5	(	(	PUNCT
ejpam-6538	246	6	1	1	NUM
ejpam-6538	246	7	,	,	PUNCT
ejpam-6538	246	8	1	1	NUM
ejpam-6538	246	9	)	)	PUNCT
ejpam-6538	246	10	=	=	SYM
ejpam-6538	246	11	ζn(1	ζn(1	NOUN
ejpam-6538	246	12	,	,	PUNCT
ejpam-6538	246	13	1	1	NUM
ejpam-6538	246	14	)	)	PUNCT
ejpam-6538	246	15	=	=	SYM
ejpam-6538	246	16	ζn(ϕn(a1,0	ζn(ϕn(a1,0	PROPN
ejpam-6538	246	17	)	)	PUNCT
ejpam-6538	246	18	)	)	PUNCT
ejpam-6538	246	19	.	.	PUNCT
ejpam-6538	247	1	if	if	SCONJ
ejpam-6538	247	2	2c−	2c−	PROPN
ejpam-6538	247	3	2	2	NUM
ejpam-6538	247	4	<	<	X
ejpam-6538	247	5	h	h	NOUN
ejpam-6538	247	6	,	,	PUNCT
ejpam-6538	247	7	then	then	ADV
ejpam-6538	247	8	h	h	NOUN
ejpam-6538	247	9	2	2	NUM
ejpam-6538	247	10	+	+	NUM
ejpam-6538	247	11	2−	2−	NUM
ejpam-6538	247	12	c	c	NOUN
ejpam-6538	247	13	>	>	X
ejpam-6538	247	14	1	1	NUM
ejpam-6538	247	15	and	and	CCONJ
ejpam-6538	247	16	ϕn(fn(ac	ϕn(fn(ac	PROPN
ejpam-6538	247	17	,	,	PUNCT
ejpam-6538	247	18	h	h	NOUN
ejpam-6538	247	19	)	)	PUNCT
ejpam-6538	247	20	)	)	PUNCT
ejpam-6538	248	1	=	=	SYM
ejpam-6538	248	2	ϕn(ac	ϕn(ac	NOUN
ejpam-6538	248	3	,	,	PUNCT
ejpam-6538	248	4	h−1	h−1	PROPN
ejpam-6538	248	5	)	)	PUNCT
ejpam-6538	248	6	=	=	SYM
ejpam-6538	248	7	(	(	PUNCT
ejpam-6538	248	8	h+	h+	X
ejpam-6538	248	9	2	2	NUM
ejpam-6538	248	10	2	2	NUM
ejpam-6538	248	11	,	,	PUNCT
ejpam-6538	248	12	h+	h+	X
ejpam-6538	248	13	2	2	NUM
ejpam-6538	248	14	2	2	NUM
ejpam-6538	248	15	−	−	NOUN
ejpam-6538	248	16	c	c	NOUN
ejpam-6538	248	17	)	)	PUNCT
ejpam-6538	248	18	=	=	SYM
ejpam-6538	249	1	ζn	ζn	PROPN
ejpam-6538	249	2	(	(	PUNCT
ejpam-6538	249	3	h	h	NOUN
ejpam-6538	249	4	2	2	NUM
ejpam-6538	249	5	+	+	NUM
ejpam-6538	249	6	2−	2−	NUM
ejpam-6538	249	7	c	c	NOUN
ejpam-6538	249	8	,	,	PUNCT
ejpam-6538	249	9	h	h	NOUN
ejpam-6538	249	10	2	2	NUM
ejpam-6538	249	11	+	+	CCONJ
ejpam-6538	249	12	1	1	NUM
ejpam-6538	249	13	)	)	PUNCT
ejpam-6538	249	14	=	=	SYM
ejpam-6538	249	15	ζn(ϕn(ac	ζn(ϕn(ac	PROPN
ejpam-6538	249	16	,	,	PUNCT
ejpam-6538	249	17	h	h	NOUN
ejpam-6538	249	18	)	)	PUNCT
ejpam-6538	249	19	)	)	PUNCT
ejpam-6538	249	20	.	.	PUNCT
ejpam-6538	250	1	if	if	SCONJ
ejpam-6538	250	2	2c−	2c−	PROPN
ejpam-6538	250	3	2	2	NUM
ejpam-6538	250	4	=	=	SYM
ejpam-6538	250	5	h	h	NOUN
ejpam-6538	250	6	,	,	PUNCT
ejpam-6538	250	7	then	then	ADV
ejpam-6538	250	8	ϕn(fn(ac	ϕn(fn(ac	X
ejpam-6538	250	9	,	,	PUNCT
ejpam-6538	250	10	h	h	NOUN
ejpam-6538	250	11	)	)	PUNCT
ejpam-6538	250	12	)	)	PUNCT
ejpam-6538	251	1	=	=	SYM
ejpam-6538	251	2	ϕn(ac−1,h−1	ϕn(ac−1,h−1	NOUN
ejpam-6538	251	3	)	)	PUNCT
ejpam-6538	251	4	=	=	PUNCT
ejpam-6538	251	5	(	(	PUNCT
ejpam-6538	251	6	h+	h+	X
ejpam-6538	251	7	2	2	NUM
ejpam-6538	251	8	2	2	NUM
ejpam-6538	251	9	,	,	PUNCT
ejpam-6538	251	10	h+	h+	X
ejpam-6538	251	11	2	2	NUM
ejpam-6538	251	12	2	2	NUM
ejpam-6538	251	13	−	−	NOUN
ejpam-6538	251	14	c+	c+	NOUN
ejpam-6538	251	15	1	1	NUM
ejpam-6538	251	16	)	)	PUNCT
ejpam-6538	251	17	=	=	SYM
ejpam-6538	251	18	(	(	PUNCT
ejpam-6538	251	19	c	c	X
ejpam-6538	251	20	,	,	PUNCT
ejpam-6538	251	21	1	1	NUM
ejpam-6538	251	22	)	)	PUNCT
ejpam-6538	251	23	=	=	SYM
ejpam-6538	251	24	ζn(1	ζn(1	NOUN
ejpam-6538	251	25	,	,	PUNCT
ejpam-6538	251	26	c	c	NOUN
ejpam-6538	251	27	)	)	PUNCT
ejpam-6538	251	28	=	=	SYM
ejpam-6538	252	1	ζn	ζn	PROPN
ejpam-6538	252	2	(	(	PUNCT
ejpam-6538	252	3	h	h	NOUN
ejpam-6538	252	4	2	2	NUM
ejpam-6538	252	5	+	+	NUM
ejpam-6538	252	6	2−	2−	NUM
ejpam-6538	252	7	c	c	NOUN
ejpam-6538	252	8	,	,	PUNCT
ejpam-6538	252	9	h	h	NOUN
ejpam-6538	252	10	2	2	NUM
ejpam-6538	252	11	+	+	CCONJ
ejpam-6538	252	12	1	1	NUM
ejpam-6538	252	13	)	)	PUNCT
ejpam-6538	252	14	=	=	SYM
ejpam-6538	252	15	ζn(ϕn(ac	ζn(ϕn(ac	PROPN
ejpam-6538	252	16	,	,	PUNCT
ejpam-6538	252	17	h	h	NOUN
ejpam-6538	252	18	)	)	PUNCT
ejpam-6538	252	19	)	)	PUNCT
ejpam-6538	252	20	.	.	PUNCT
ejpam-6538	253	1	a.	a.	NOUN
ejpam-6538	253	2	charoenpol	charoenpol	PROPN
ejpam-6538	253	3	,	,	PUNCT
ejpam-6538	253	4	u.	u.	PROPN
ejpam-6538	253	5	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	253	6	/	/	SYM
ejpam-6538	253	7	eur	eur	PROPN
ejpam-6538	253	8	.	.	PUNCT
ejpam-6538	254	1	j.	j.	PROPN
ejpam-6538	254	2	pure	pure	PROPN
ejpam-6538	254	3	appl	appl	PROPN
ejpam-6538	254	4	.	.	PROPN
ejpam-6538	254	5	math	math	PROPN
ejpam-6538	254	6	,	,	PUNCT
ejpam-6538	254	7	18	18	NUM
ejpam-6538	254	8	(	(	PUNCT
ejpam-6538	254	9	3	3	NUM
ejpam-6538	254	10	)	)	PUNCT
ejpam-6538	254	11	(	(	PUNCT
ejpam-6538	254	12	2025	2025	NUM
ejpam-6538	254	13	)	)	PUNCT
ejpam-6538	254	14	,	,	PUNCT
ejpam-6538	254	15	6538	6538	NUM
ejpam-6538	254	16	12	12	NUM
ejpam-6538	254	17	of	of	ADP
ejpam-6538	254	18	13	13	NUM
ejpam-6538	254	19	case	case	NOUN
ejpam-6538	254	20	2	2	NUM
ejpam-6538	254	21	:	:	PUNCT
ejpam-6538	254	22	h	h	PROPN
ejpam-6538	254	23	∈	∈	PROPN
ejpam-6538	255	1	o.	o.	NOUN
ejpam-6538	255	2	then	then	ADV
ejpam-6538	255	3	2c−	2c−	NUM
ejpam-6538	255	4	2	2	NUM
ejpam-6538	255	5	<	<	X
ejpam-6538	255	6	h	h	NOUN
ejpam-6538	255	7	and	and	CCONJ
ejpam-6538	255	8	h	h	NOUN
ejpam-6538	255	9	̸=	̸=	PROPN
ejpam-6538	255	10	0	0	NUM
ejpam-6538	255	11	.	.	PUNCT
ejpam-6538	256	1	hence	hence	ADV
ejpam-6538	256	2	,	,	PUNCT
ejpam-6538	256	3	h+3	h+3	PROPN
ejpam-6538	256	4	2	2	NUM
ejpam-6538	256	5	>	>	SYM
ejpam-6538	256	6	c+	c+	VERB
ejpam-6538	256	7	1	1	NUM
ejpam-6538	256	8	2	2	NUM
ejpam-6538	256	9	>	>	SYM
ejpam-6538	256	10	1	1	NUM
ejpam-6538	256	11	and	and	CCONJ
ejpam-6538	256	12	ϕn(fn(ac	ϕn(fn(ac	PROPN
ejpam-6538	256	13	,	,	PUNCT
ejpam-6538	256	14	h	h	NOUN
ejpam-6538	256	15	)	)	PUNCT
ejpam-6538	256	16	)	)	PUNCT
ejpam-6538	257	1	=	=	SYM
ejpam-6538	257	2	ϕn(ac	ϕn(ac	NOUN
ejpam-6538	257	3	,	,	PUNCT
ejpam-6538	257	4	h−1	h−1	PROPN
ejpam-6538	257	5	)	)	PUNCT
ejpam-6538	257	6	=	=	PRON
ejpam-6538	257	7	(	(	PUNCT
ejpam-6538	257	8	h−	h−	NOUN
ejpam-6538	257	9	1	1	NUM
ejpam-6538	257	10	2	2	NUM
ejpam-6538	257	11	+	+	CCONJ
ejpam-6538	257	12	2−	2−	NUM
ejpam-6538	257	13	c	c	NOUN
ejpam-6538	257	14	,	,	PUNCT
ejpam-6538	257	15	h−	h−	PROPN
ejpam-6538	257	16	1	1	NUM
ejpam-6538	257	17	2	2	NUM
ejpam-6538	257	18	+	+	NUM
ejpam-6538	257	19	1	1	NUM
ejpam-6538	257	20	)	)	PUNCT
ejpam-6538	257	21	=	=	SYM
ejpam-6538	257	22	ζn	ζn	PROPN
ejpam-6538	257	23	(	(	PUNCT
ejpam-6538	257	24	h+	h+	PROPN
ejpam-6538	257	25	3	3	NUM
ejpam-6538	257	26	2	2	NUM
ejpam-6538	257	27	,	,	PUNCT
ejpam-6538	257	28	h+	h+	X
ejpam-6538	257	29	3	3	NUM
ejpam-6538	257	30	2	2	NUM
ejpam-6538	257	31	−	−	PROPN
ejpam-6538	257	32	c	c	NOUN
ejpam-6538	257	33	)	)	PUNCT
ejpam-6538	257	34	=	=	SYM
ejpam-6538	257	35	ζn(ϕn(ac	ζn(ϕn(ac	PROPN
ejpam-6538	257	36	,	,	PUNCT
ejpam-6538	257	37	h	h	NOUN
ejpam-6538	257	38	)	)	PUNCT
ejpam-6538	257	39	)	)	PUNCT
ejpam-6538	257	40	.	.	PUNCT
ejpam-6538	258	1	finally	finally	ADV
ejpam-6538	258	2	,	,	PUNCT
ejpam-6538	258	3	we	we	PRON
ejpam-6538	258	4	will	will	AUX
ejpam-6538	258	5	show	show	VERB
ejpam-6538	258	6	that	that	SCONJ
ejpam-6538	258	7	ψn	ψn	X
ejpam-6538	258	8	:	:	PUNCT
ejpam-6538	258	9	bn	bn	X
ejpam-6538	258	10	→	→	SYM
ejpam-6538	258	11	cn	cn	PROPN
ejpam-6538	258	12	×	×	PROPN
ejpam-6538	258	13	c2	c2	PROPN
ejpam-6538	258	14	defined	define	VERB
ejpam-6538	258	15	by	by	ADP
ejpam-6538	258	16	ψn(bc	ψn(bc	PROPN
ejpam-6538	258	17	,	,	PUNCT
ejpam-6538	258	18	h	h	NOUN
ejpam-6538	258	19	)	)	PUNCT
ejpam-6538	258	20	=	=	PRON
ejpam-6538	258	21	{	{	PUNCT
ejpam-6538	258	22	(	(	PUNCT
ejpam-6538	258	23	h	h	NOUN
ejpam-6538	258	24	,	,	PUNCT
ejpam-6538	258	25	2	2	X
ejpam-6538	258	26	)	)	PUNCT
ejpam-6538	258	27	if	if	SCONJ
ejpam-6538	258	28	c	c	NOUN
ejpam-6538	258	29	=	=	SYM
ejpam-6538	258	30	1	1	NUM
ejpam-6538	258	31	,	,	PUNCT
ejpam-6538	258	32	(	(	PUNCT
ejpam-6538	258	33	h	h	NOUN
ejpam-6538	258	34	,	,	PUNCT
ejpam-6538	258	35	1	1	X
ejpam-6538	258	36	)	)	PUNCT
ejpam-6538	258	37	if	if	SCONJ
ejpam-6538	258	38	c	c	NOUN
ejpam-6538	258	39	=	=	SYM
ejpam-6538	258	40	2	2	NUM
ejpam-6538	258	41	is	be	AUX
ejpam-6538	258	42	an	an	DET
ejpam-6538	258	43	isomorphism	isomorphism	NOUN
ejpam-6538	258	44	.	.	PUNCT
ejpam-6538	259	1	let	let	VERB
ejpam-6538	259	2	bc	bc	PROPN
ejpam-6538	259	3	,	,	PUNCT
ejpam-6538	259	4	h	h	NOUN
ejpam-6538	259	5	∈	∈	PROPN
ejpam-6538	260	1	bn	bn	PROPN
ejpam-6538	260	2	.	.	PUNCT
ejpam-6538	260	3	then	then	ADV
ejpam-6538	260	4	ψn(bc,1	ψn(bc,1	NOUN
ejpam-6538	260	5	)	)	PUNCT
ejpam-6538	260	6	∈	∈	PROPN
ejpam-6538	260	7	{	{	PUNCT
ejpam-6538	260	8	(	(	PUNCT
ejpam-6538	260	9	1	1	NUM
ejpam-6538	260	10	,	,	PUNCT
ejpam-6538	260	11	1	1	NUM
ejpam-6538	260	12	)	)	PUNCT
ejpam-6538	260	13	,	,	PUNCT
ejpam-6538	260	14	(	(	PUNCT
ejpam-6538	260	15	1	1	NUM
ejpam-6538	260	16	,	,	PUNCT
ejpam-6538	260	17	2	2	NUM
ejpam-6538	260	18	)	)	PUNCT
ejpam-6538	260	19	}	}	PUNCT
ejpam-6538	260	20	which	which	PRON
ejpam-6538	260	21	implies	imply	VERB
ejpam-6538	260	22	that	that	PRON
ejpam-6538	260	23	ψn(gn(bc,1	ψn(gn(bc,1	NOUN
ejpam-6538	260	24	)	)	PUNCT
ejpam-6538	260	25	)	)	PUNCT
ejpam-6538	261	1	=	=	SYM
ejpam-6538	261	2	ψn(b2,1	ψn(b2,1	NOUN
ejpam-6538	261	3	)	)	PUNCT
ejpam-6538	261	4	=	=	PUNCT
ejpam-6538	261	5	(	(	PUNCT
ejpam-6538	261	6	1	1	NUM
ejpam-6538	261	7	,	,	PUNCT
ejpam-6538	261	8	1	1	NUM
ejpam-6538	261	9	)	)	PUNCT
ejpam-6538	261	10	=	=	PUNCT
ejpam-6538	261	11	φn×2(ψn(bc,1	φn×2(ψn(bc,1	NUM
ejpam-6538	261	12	)	)	PUNCT
ejpam-6538	261	13	)	)	PUNCT
ejpam-6538	261	14	and	and	CCONJ
ejpam-6538	261	15	for	for	ADP
ejpam-6538	261	16	h	h	PROPN
ejpam-6538	261	17	≥	≥	NOUN
ejpam-6538	261	18	2	2	NUM
ejpam-6538	261	19	ψn(gn(b1,h	ψn(gn(b1,h	NOUN
ejpam-6538	261	20	)	)	PUNCT
ejpam-6538	261	21	)	)	PUNCT
ejpam-6538	262	1	=	=	PUNCT
ejpam-6538	262	2	ψn(b1,h−1	ψn(b1,h−1	X
ejpam-6538	262	3	)	)	PUNCT
ejpam-6538	262	4	=	=	PUNCT
ejpam-6538	263	1	(	(	PUNCT
ejpam-6538	263	2	h−	h−	PROPN
ejpam-6538	263	3	1	1	NUM
ejpam-6538	263	4	,	,	PUNCT
ejpam-6538	263	5	2	2	NUM
ejpam-6538	263	6	)	)	PUNCT
ejpam-6538	263	7	=	=	NOUN
ejpam-6538	263	8	φn×2(h	φn×2(h	NOUN
ejpam-6538	263	9	,	,	PUNCT
ejpam-6538	263	10	2	2	NUM
ejpam-6538	263	11	)	)	PUNCT
ejpam-6538	263	12	=	=	PUNCT
ejpam-6538	263	13	φn×2(ψn(b1,h	φn×2(ψn(b1,h	NOUN
ejpam-6538	263	14	)	)	PUNCT
ejpam-6538	263	15	)	)	PUNCT
ejpam-6538	263	16	and	and	CCONJ
ejpam-6538	263	17	ψn(gn(b2,h	ψn(gn(b2,h	NOUN
ejpam-6538	263	18	)	)	PUNCT
ejpam-6538	263	19	)	)	PUNCT
ejpam-6538	264	1	=	=	PUNCT
ejpam-6538	264	2	ψn(b1,h−1	ψn(b1,h−1	X
ejpam-6538	264	3	)	)	PUNCT
ejpam-6538	264	4	=	=	PUNCT
ejpam-6538	265	1	(	(	PUNCT
ejpam-6538	265	2	h−	h−	PROPN
ejpam-6538	265	3	1	1	NUM
ejpam-6538	265	4	,	,	PUNCT
ejpam-6538	265	5	2	2	NUM
ejpam-6538	265	6	)	)	PUNCT
ejpam-6538	265	7	=	=	NOUN
ejpam-6538	265	8	φn×2(h	φn×2(h	NOUN
ejpam-6538	265	9	,	,	PUNCT
ejpam-6538	265	10	1	1	NUM
ejpam-6538	265	11	)	)	PUNCT
ejpam-6538	265	12	=	=	SYM
ejpam-6538	265	13	φn×2(ψn(b2,h	φn×2(ψn(b2,h	NOUN
ejpam-6538	265	14	)	)	PUNCT
ejpam-6538	265	15	)	)	PUNCT
ejpam-6538	265	16	.	.	PUNCT
ejpam-6538	266	1	acknowledgements	acknowledgement	NOUN
ejpam-6538	266	2	this	this	DET
ejpam-6538	266	3	work	work	NOUN
ejpam-6538	266	4	was	be	AUX
ejpam-6538	266	5	financially	financially	ADV
ejpam-6538	266	6	supported	support	VERB
ejpam-6538	266	7	by	by	ADP
ejpam-6538	266	8	academic	academic	ADJ
ejpam-6538	266	9	affairs	affairs	PROPN
ejpam-6538	266	10	promotion	promotion	PROPN
ejpam-6538	266	11	fund	fund	PROPN
ejpam-6538	266	12	,	,	PUNCT
ejpam-6538	266	13	faculty	faculty	NOUN
ejpam-6538	266	14	of	of	ADP
ejpam-6538	266	15	science	science	NOUN
ejpam-6538	266	16	,	,	PUNCT
ejpam-6538	266	17	khon	khon	PROPN
ejpam-6538	266	18	kaen	kaen	PROPN
ejpam-6538	266	19	university	university	PROPN
ejpam-6538	266	20	,	,	PUNCT
ejpam-6538	266	21	fiscal	fiscal	ADJ
ejpam-6538	266	22	year	year	NOUN
ejpam-6538	266	23	2023(raapf	2023(raapf	NUM
ejpam-6538	266	24	)	)	PUNCT
ejpam-6538	266	25	.	.	PUNCT
ejpam-6538	267	1	references	reference	NOUN
ejpam-6538	268	1	[	[	X
ejpam-6538	268	2	1	1	NUM
ejpam-6538	268	3	]	]	PUNCT
ejpam-6538	268	4	miroslav	miroslav	ADJ
ejpam-6538	268	5	ciric	ciric	ADJ
ejpam-6538	268	6	and	and	CCONJ
ejpam-6538	268	7	stojan	stojan	ADJ
ejpam-6538	268	8	bogdanovic	bogdanovic	PROPN
ejpam-6538	268	9	.	.	PUNCT
ejpam-6538	269	1	lattices	lattice	NOUN
ejpam-6538	269	2	of	of	ADP
ejpam-6538	269	3	subautomata	subautomata	ADJ
ejpam-6538	269	4	and	and	CCONJ
ejpam-6538	269	5	direct	direct	ADJ
ejpam-6538	269	6	sum	sum	NOUN
ejpam-6538	269	7	decompositions	decomposition	NOUN
ejpam-6538	269	8	of	of	ADP
ejpam-6538	269	9	automata	automata	NOUN
ejpam-6538	269	10	.	.	PUNCT
ejpam-6538	270	1	in	in	ADP
ejpam-6538	270	2	algebra	algebra	PROPN
ejpam-6538	270	3	colloquium	colloquium	NOUN
ejpam-6538	270	4	,	,	PUNCT
ejpam-6538	270	5	volume	volume	NOUN
ejpam-6538	270	6	6	6	NUM
ejpam-6538	270	7	,	,	PUNCT
ejpam-6538	270	8	pages	page	NOUN
ejpam-6538	270	9	71–88	71–88	NUM
ejpam-6538	270	10	,	,	PUNCT
ejpam-6538	270	11	1999	1999	NUM
ejpam-6538	270	12	.	.	PUNCT
ejpam-6538	271	1	[	[	X
ejpam-6538	271	2	2	2	NUM
ejpam-6538	271	3	]	]	PUNCT
ejpam-6538	271	4	klaus	klaus	NOUN
ejpam-6538	271	5	denecke	denecke	NOUN
ejpam-6538	271	6	and	and	CCONJ
ejpam-6538	271	7	shelly	shelly	PROPN
ejpam-6538	271	8	l	l	PROPN
ejpam-6538	271	9	wismath	wismath	PROPN
ejpam-6538	271	10	.	.	PUNCT
ejpam-6538	272	1	universal	universal	ADJ
ejpam-6538	272	2	algebra	algebra	NOUN
ejpam-6538	272	3	and	and	CCONJ
ejpam-6538	272	4	applications	application	NOUN
ejpam-6538	272	5	in	in	ADP
ejpam-6538	272	6	theoretical	theoretical	ADJ
ejpam-6538	272	7	computer	computer	NOUN
ejpam-6538	272	8	science	science	NOUN
ejpam-6538	272	9	.	.	PUNCT
ejpam-6538	273	1	chapman	chapman	NOUN
ejpam-6538	273	2	and	and	CCONJ
ejpam-6538	273	3	hall	hall	PROPN
ejpam-6538	273	4	/	/	SYM
ejpam-6538	273	5	crc	crc	NOUN
ejpam-6538	273	6	,	,	PUNCT
ejpam-6538	273	7	2018	2018	NUM
ejpam-6538	273	8	.	.	PUNCT
ejpam-6538	274	1	[	[	X
ejpam-6538	274	2	3	3	X
ejpam-6538	274	3	]	]	PUNCT
ejpam-6538	274	4	bjarni	bjarni	PROPN
ejpam-6538	274	5	jónsson	jónsson	PROPN
ejpam-6538	274	6	.	.	PUNCT
ejpam-6538	274	7	topics	topic	NOUN
ejpam-6538	274	8	in	in	ADP
ejpam-6538	274	9	universal	universal	ADJ
ejpam-6538	274	10	algebra	algebra	NOUN
ejpam-6538	274	11	,	,	PUNCT
ejpam-6538	274	12	volume	volume	NOUN
ejpam-6538	274	13	250	250	NUM
ejpam-6538	274	14	.	.	PUNCT
ejpam-6538	274	15	springer	springer	NOUN
ejpam-6538	274	16	,	,	PUNCT
ejpam-6538	274	17	2006	2006	NUM
ejpam-6538	274	18	.	.	PUNCT
ejpam-6538	275	1	[	[	X
ejpam-6538	275	2	4	4	X
ejpam-6538	275	3	]	]	X
ejpam-6538	275	4	david	david	PROPN
ejpam-6538	275	5	zupnik	zupnik	PROPN
ejpam-6538	275	6	.	.	PUNCT
ejpam-6538	275	7	cayley	cayley	ADJ
ejpam-6538	275	8	functions	function	NOUN
ejpam-6538	275	9	.	.	PUNCT
ejpam-6538	276	1	in	in	ADP
ejpam-6538	276	2	semigroup	semigroup	PROPN
ejpam-6538	276	3	forum	forum	PROPN
ejpam-6538	276	4	,	,	PUNCT
ejpam-6538	276	5	volume	volume	NOUN
ejpam-6538	276	6	3	3	NUM
ejpam-6538	276	7	,	,	PUNCT
ejpam-6538	276	8	pages	page	NOUN
ejpam-6538	276	9	349–358	349–358	NUM
ejpam-6538	276	10	.	.	PUNCT
ejpam-6538	276	11	springer	springer	NOUN
ejpam-6538	276	12	,	,	PUNCT
ejpam-6538	276	13	1971	1971	NUM
ejpam-6538	276	14	.	.	PUNCT
ejpam-6538	277	1	[	[	X
ejpam-6538	277	2	5	5	NUM
ejpam-6538	277	3	]	]	X
ejpam-6538	277	4	jie	jie	PROPN
ejpam-6538	277	5	fang	fang	PROPN
ejpam-6538	277	6	and	and	CCONJ
ejpam-6538	277	7	zhong	zhong	PROPN
ejpam-6538	277	8	-	-	PUNCT
ejpam-6538	277	9	ju	ju	PROPN
ejpam-6538	277	10	sun	sun	PROPN
ejpam-6538	277	11	.	.	PUNCT
ejpam-6538	277	12	semilattices	semilattice	NOUN
ejpam-6538	277	13	with	with	ADP
ejpam-6538	277	14	the	the	DET
ejpam-6538	277	15	strong	strong	ADJ
ejpam-6538	277	16	endomorphism	endomorphism	PROPN
ejpam-6538	277	17	kernel	kernel	PROPN
ejpam-6538	277	18	property	property	PROPN
ejpam-6538	277	19	.	.	PUNCT
ejpam-6538	278	1	algebra	algebra	PROPN
ejpam-6538	278	2	universalis	universali	VERB
ejpam-6538	278	3	,	,	PUNCT
ejpam-6538	278	4	70(4):393–401	70(4):393–401	PROPN
ejpam-6538	278	5	,	,	PUNCT
ejpam-6538	278	6	2013	2013	NUM
ejpam-6538	278	7	.	.	PUNCT
ejpam-6538	279	1	[	[	X
ejpam-6538	279	2	6	6	NUM
ejpam-6538	279	3	]	]	PUNCT
ejpam-6538	279	4	jaroslav	jaroslav	ADJ
ejpam-6538	279	5	guričan	guričan	PROPN
ejpam-6538	279	6	and	and	CCONJ
ejpam-6538	279	7	miroslav	miroslav	ADJ
ejpam-6538	279	8	ploščica	ploščica	PROPN
ejpam-6538	279	9	.	.	PUNCT
ejpam-6538	280	1	the	the	DET
ejpam-6538	280	2	strong	strong	ADJ
ejpam-6538	280	3	endomorphism	endomorphism	PROPN
ejpam-6538	280	4	kernel	kernel	PROPN
ejpam-6538	280	5	property	property	NOUN
ejpam-6538	280	6	for	for	ADP
ejpam-6538	280	7	modular	modular	ADJ
ejpam-6538	280	8	p	p	NOUN
ejpam-6538	280	9	-	-	PUNCT
ejpam-6538	280	10	algebras	algebra	NOUN
ejpam-6538	280	11	and	and	CCONJ
ejpam-6538	280	12	for	for	ADP
ejpam-6538	280	13	distributive	distributive	ADJ
ejpam-6538	280	14	lattices	lattice	NOUN
ejpam-6538	280	15	.	.	PUNCT
ejpam-6538	281	1	algebra	algebra	NOUN
ejpam-6538	281	2	universalis	universali	VERB
ejpam-6538	281	3	,	,	PUNCT
ejpam-6538	281	4	75(2):243	75(2):243	NUM
ejpam-6538	281	5	–	–	PUNCT
ejpam-6538	281	6	255	255	NUM
ejpam-6538	281	7	,	,	PUNCT
ejpam-6538	281	8	2016	2016	NUM
ejpam-6538	281	9	.	.	PUNCT
ejpam-6538	282	1	[	[	X
ejpam-6538	282	2	7	7	X
ejpam-6538	282	3	]	]	SYM
ejpam-6538	282	4	emı́lia	emı́lia	NUM
ejpam-6538	282	5	halušková.	halušková.	ADV
ejpam-6538	282	6	some	some	DET
ejpam-6538	282	7	monounary	monounary	ADJ
ejpam-6538	282	8	algebras	algebra	NOUN
ejpam-6538	282	9	with	with	ADP
ejpam-6538	282	10	ekp	ekp	NOUN
ejpam-6538	282	11	.	.	PUNCT
ejpam-6538	283	1	mathematica	mathematica	PROPN
ejpam-6538	283	2	bohemica	bohemica	PROPN
ejpam-6538	283	3	,	,	PUNCT
ejpam-6538	283	4	145(4):401–414	145(4):401–414	NUM
ejpam-6538	283	5	,	,	PUNCT
ejpam-6538	283	6	2020	2020	NUM
ejpam-6538	283	7	.	.	PUNCT
ejpam-6538	284	1	a.	a.	NOUN
ejpam-6538	284	2	charoenpol	charoenpol	PROPN
ejpam-6538	284	3	,	,	PUNCT
ejpam-6538	284	4	u.	u.	PROPN
ejpam-6538	284	5	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	284	6	/	/	SYM
ejpam-6538	284	7	eur	eur	PROPN
ejpam-6538	284	8	.	.	PUNCT
ejpam-6538	285	1	j.	j.	PROPN
ejpam-6538	285	2	pure	pure	PROPN
ejpam-6538	285	3	appl	appl	PROPN
ejpam-6538	285	4	.	.	PROPN
ejpam-6538	285	5	math	math	PROPN
ejpam-6538	285	6	,	,	PUNCT
ejpam-6538	285	7	18	18	NUM
ejpam-6538	285	8	(	(	PUNCT
ejpam-6538	285	9	3	3	NUM
ejpam-6538	285	10	)	)	PUNCT
ejpam-6538	285	11	(	(	PUNCT
ejpam-6538	285	12	2025	2025	NUM
ejpam-6538	285	13	)	)	PUNCT
ejpam-6538	285	14	,	,	PUNCT
ejpam-6538	285	15	6538	6538	NUM
ejpam-6538	285	16	13	13	NUM
ejpam-6538	285	17	of	of	ADP
ejpam-6538	285	18	13	13	NUM
ejpam-6538	286	1	[	[	SYM
ejpam-6538	286	2	8	8	NUM
ejpam-6538	286	3	]	]	PUNCT
ejpam-6538	286	4	bv	bv	PROPN
ejpam-6538	286	5	popov	popov	PROPN
ejpam-6538	286	6	and	and	CCONJ
ejpam-6538	286	7	ov	ov	PROPN
ejpam-6538	286	8	kovaleva	kovaleva	PROPN
ejpam-6538	286	9	.	.	PUNCT
ejpam-6538	287	1	on	on	ADP
ejpam-6538	287	2	a	a	DET
ejpam-6538	287	3	characterization	characterization	NOUN
ejpam-6538	287	4	of	of	ADP
ejpam-6538	287	5	monounary	monounary	ADJ
ejpam-6538	287	6	algebras	algebra	NOUN
ejpam-6538	287	7	by	by	ADP
ejpam-6538	287	8	their	their	PRON
ejpam-6538	287	9	endomorphism	endomorphism	NOUN
ejpam-6538	287	10	semigroups	semigroup	NOUN
ejpam-6538	287	11	.	.	PUNCT
ejpam-6538	288	1	in	in	ADP
ejpam-6538	288	2	semigroup	semigroup	PROPN
ejpam-6538	288	3	forum	forum	PROPN
ejpam-6538	288	4	,	,	PUNCT
ejpam-6538	288	5	volume	volume	NOUN
ejpam-6538	288	6	73	73	NUM
ejpam-6538	288	7	,	,	PUNCT
ejpam-6538	288	8	pages	page	VERB
ejpam-6538	288	9	444–456	444–456	NUM
ejpam-6538	288	10	.	.	PUNCT
ejpam-6538	288	11	springer	springer	NOUN
ejpam-6538	288	12	,	,	PUNCT
ejpam-6538	288	13	2006	2006	NUM
ejpam-6538	288	14	.	.	PUNCT
ejpam-6538	289	1	[	[	X
ejpam-6538	289	2	9	9	NUM
ejpam-6538	289	3	]	]	SYM
ejpam-6538	289	4	yeni	yeni	PROPN
ejpam-6538	289	5	susanti	susanti	X
ejpam-6538	289	6	and	and	CCONJ
ejpam-6538	289	7	joerg	joerg	PROPN
ejpam-6538	289	8	koppitz	koppitz	PROPN
ejpam-6538	289	9	.	.	PUNCT
ejpam-6538	290	1	on	on	ADP
ejpam-6538	290	2	endomorphisms	endomorphism	NOUN
ejpam-6538	290	3	of	of	ADP
ejpam-6538	290	4	power	power	NOUN
ejpam-6538	290	5	-	-	PUNCT
ejpam-6538	290	6	semigroups	semigroup	NOUN
ejpam-6538	290	7	.	.	PUNCT
ejpam-6538	291	1	asianeuropean	asianeuropean	PROPN
ejpam-6538	291	2	journal	journal	PROPN
ejpam-6538	291	3	of	of	ADP
ejpam-6538	291	4	mathematics	mathematic	NOUN
ejpam-6538	291	5	,	,	PUNCT
ejpam-6538	291	6	10(03):1750058	10(03):1750058	NUM
ejpam-6538	291	7	,	,	PUNCT
ejpam-6538	291	8	2017	2017	NUM
ejpam-6538	291	9	.	.	PUNCT
ejpam-6538	292	1	[	[	X
ejpam-6538	292	2	10	10	NUM
ejpam-6538	292	3	]	]	X
ejpam-6538	292	4	aveya	aveya	PROPN
ejpam-6538	292	5	charoenpol	charoenpol	NOUN
ejpam-6538	292	6	and	and	CCONJ
ejpam-6538	292	7	udom	udom	PROPN
ejpam-6538	292	8	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	292	9	.	.	PUNCT
ejpam-6538	293	1	the	the	DET
ejpam-6538	293	2	maximum	maximum	ADJ
ejpam-6538	293	3	pre	pre	ADJ
ejpam-6538	293	4	-	-	ADJ
ejpam-6538	293	5	period	period	ADJ
ejpam-6538	293	6	property	property	NOUN
ejpam-6538	293	7	of	of	ADP
ejpam-6538	293	8	the	the	DET
ejpam-6538	293	9	direct	direct	ADJ
ejpam-6538	293	10	product	product	NOUN
ejpam-6538	293	11	of	of	ADP
ejpam-6538	293	12	chains	chain	NOUN
ejpam-6538	293	13	.	.	PUNCT
ejpam-6538	294	1	asian	asian	ADJ
ejpam-6538	294	2	-	-	PUNCT
ejpam-6538	294	3	european	european	ADJ
ejpam-6538	294	4	journal	journal	NOUN
ejpam-6538	294	5	of	of	ADP
ejpam-6538	294	6	mathematics	mathematic	NOUN
ejpam-6538	294	7	,	,	PUNCT
ejpam-6538	294	8	16(09):2350155	16(09):2350155	NUM
ejpam-6538	294	9	,	,	PUNCT
ejpam-6538	294	10	2023	2023	NUM
ejpam-6538	294	11	.	.	PUNCT
ejpam-6538	295	1	[	[	X
ejpam-6538	295	2	11	11	NUM
ejpam-6538	295	3	]	]	PUNCT
ejpam-6538	295	4	aveya	aveya	PROPN
ejpam-6538	295	5	charoenpol	charoenpol	NOUN
ejpam-6538	295	6	and	and	CCONJ
ejpam-6538	295	7	udom	udom	PROPN
ejpam-6538	295	8	chotwattakawanit	chotwattakawanit	PROPN
ejpam-6538	295	9	.	.	PUNCT
ejpam-6538	296	1	the	the	DET
ejpam-6538	296	2	pre	pre	NOUN
ejpam-6538	296	3	-	-	NOUN
ejpam-6538	296	4	period	period	NOUN
ejpam-6538	296	5	of	of	ADP
ejpam-6538	296	6	the	the	DET
ejpam-6538	296	7	glued	glue	VERB
ejpam-6538	296	8	sum	sum	NOUN
ejpam-6538	296	9	of	of	ADP
ejpam-6538	296	10	finite	finite	ADJ
ejpam-6538	296	11	modular	modular	ADJ
ejpam-6538	296	12	lattices	lattice	NOUN
ejpam-6538	296	13	.	.	PUNCT
ejpam-6538	297	1	discussiones	discussione	NOUN
ejpam-6538	297	2	mathematicae	mathematicae	VERB
ejpam-6538	297	3	:	:	PUNCT
ejpam-6538	297	4	general	general	ADJ
ejpam-6538	297	5	algebra	algebra	PROPN
ejpam-6538	297	6	&	&	CCONJ
ejpam-6538	297	7	applications	application	NOUN
ejpam-6538	297	8	,	,	PUNCT
ejpam-6538	297	9	43(2):223–231	43(2):223–231	PROPN
ejpam-6538	297	10	,	,	PUNCT
ejpam-6538	297	11	2023	2023	NUM
ejpam-6538	297	12	.	.	PUNCT