id	sid	tid	token	lemma	pos
ejpam-3912	1	1	european	european	PROPN
ejpam-3912	1	2	journal	journal	PROPN
ejpam-3912	1	3	of	of	ADP
ejpam-3912	1	4	pure	pure	ADJ
ejpam-3912	1	5	and	and	CCONJ
ejpam-3912	1	6	applied	apply	VERB
ejpam-3912	1	7	mathematics	mathematic	NOUN
ejpam-3912	1	8	vol	vol	NOUN
ejpam-3912	1	9	.	.	PUNCT
ejpam-3912	2	1	14	14	NUM
ejpam-3912	2	2	,	,	PUNCT
ejpam-3912	2	3	no	no	INTJ
ejpam-3912	2	4	.	.	NOUN
ejpam-3912	2	5	1	1	NUM
ejpam-3912	2	6	,	,	PUNCT
ejpam-3912	2	7	2021	2021	NUM
ejpam-3912	2	8	,	,	PUNCT
ejpam-3912	2	9	278	278	NUM
ejpam-3912	2	10	-	-	SYM
ejpam-3912	2	11	300	300	NUM
ejpam-3912	2	12	issn	issn	PROPN
ejpam-3912	2	13	1307	1307	NUM
ejpam-3912	2	14	-	-	SYM
ejpam-3912	2	15	5543	5543	NUM
ejpam-3912	2	16	–	–	PUNCT
ejpam-3912	2	17	ejpam.com	ejpam.com	X
ejpam-3912	2	18	published	publish	VERB
ejpam-3912	2	19	by	by	ADP
ejpam-3912	2	20	new	new	PROPN
ejpam-3912	2	21	york	york	PROPN
ejpam-3912	2	22	business	business	PROPN
ejpam-3912	2	23	global	global	ADJ
ejpam-3912	2	24	properties	property	NOUN
ejpam-3912	2	25	of	of	ADP
ejpam-3912	2	26	nilpotent	nilpotent	ADJ
ejpam-3912	2	27	evolution	evolution	NOUN
ejpam-3912	2	28	algebras	algebra	NOUN
ejpam-3912	2	29	with	with	ADP
ejpam-3912	2	30	no	no	DET
ejpam-3912	2	31	maximal	maximal	ADJ
ejpam-3912	2	32	nilindex	nilindex	NOUN
ejpam-3912	2	33	ahmad	ahmad	NOUN
ejpam-3912	2	34	alarafeen1	alarafeen1	PROPN
ejpam-3912	2	35	,	,	PUNCT
ejpam-3912	2	36	izzat	izzat	PROPN
ejpam-3912	2	37	qaralleh2,∗	qaralleh2,∗	PROPN
ejpam-3912	2	38	,	,	PUNCT
ejpam-3912	2	39	azhana	azhana	PROPN
ejpam-3912	2	40	ahmad1	ahmad1	NOUN
ejpam-3912	2	41	1	1	NUM
ejpam-3912	2	42	school	school	NOUN
ejpam-3912	2	43	of	of	ADP
ejpam-3912	2	44	mathematical	mathematical	ADJ
ejpam-3912	2	45	sciences	science	NOUN
ejpam-3912	2	46	,	,	PUNCT
ejpam-3912	2	47	universiti	universiti	PROPN
ejpam-3912	2	48	sains	sain	VERB
ejpam-3912	2	49	malaysia	malaysia	PROPN
ejpam-3912	2	50	11800	11800	NUM
ejpam-3912	2	51	usm	usm	PROPN
ejpam-3912	2	52	,	,	PUNCT
ejpam-3912	2	53	penang	penang	PROPN
ejpam-3912	2	54	,	,	PUNCT
ejpam-3912	2	55	malaysia	malaysia	PROPN
ejpam-3912	2	56	2	2	NUM
ejpam-3912	2	57	department	department	NOUN
ejpam-3912	2	58	of	of	ADP
ejpam-3912	2	59	mathematics	mathematic	NOUN
ejpam-3912	2	60	,	,	PUNCT
ejpam-3912	2	61	faculty	faculty	NOUN
ejpam-3912	2	62	of	of	ADP
ejpam-3912	2	63	science	science	NOUN
ejpam-3912	2	64	,	,	PUNCT
ejpam-3912	2	65	tafila	tafila	NOUN
ejpam-3912	2	66	technical	technical	ADJ
ejpam-3912	2	67	university	university	NOUN
ejpam-3912	2	68	,	,	PUNCT
ejpam-3912	2	69	tafila	tafila	NOUN
ejpam-3912	2	70	,	,	PUNCT
ejpam-3912	2	71	jordan	jordan	PROPN
ejpam-3912	2	72	abstract	abstract	PROPN
ejpam-3912	2	73	.	.	PUNCT
ejpam-3912	3	1	as	as	ADP
ejpam-3912	3	2	a	a	DET
ejpam-3912	3	3	system	system	NOUN
ejpam-3912	3	4	of	of	ADP
ejpam-3912	3	5	abstract	abstract	ADJ
ejpam-3912	3	6	algebra	algebra	NOUN
ejpam-3912	3	7	,	,	PUNCT
ejpam-3912	3	8	evolution	evolution	NOUN
ejpam-3912	3	9	algebras	algebra	NOUN
ejpam-3912	3	10	are	be	AUX
ejpam-3912	3	11	commutative	commutative	ADJ
ejpam-3912	3	12	and	and	CCONJ
ejpam-3912	3	13	non	non	ADJ
ejpam-3912	3	14	-	-	ADJ
ejpam-3912	3	15	associative	associative	ADJ
ejpam-3912	3	16	algebras	algebra	NOUN
ejpam-3912	3	17	.	.	PUNCT
ejpam-3912	4	1	there	there	PRON
ejpam-3912	4	2	is	be	VERB
ejpam-3912	4	3	no	no	DET
ejpam-3912	4	4	deep	deep	ADJ
ejpam-3912	4	5	structure	structure	NOUN
ejpam-3912	4	6	theorem	theorem	VERB
ejpam-3912	4	7	for	for	ADP
ejpam-3912	4	8	general	general	ADJ
ejpam-3912	4	9	non	non	ADJ
ejpam-3912	4	10	-	-	ADJ
ejpam-3912	4	11	associative	associative	ADJ
ejpam-3912	4	12	algebras	algebra	NOUN
ejpam-3912	4	13	.	.	PUNCT
ejpam-3912	5	1	however	however	ADV
ejpam-3912	5	2	,	,	PUNCT
ejpam-3912	5	3	there	there	PRON
ejpam-3912	5	4	are	be	VERB
ejpam-3912	5	5	deep	deep	ADJ
ejpam-3912	5	6	structure	structure	NOUN
ejpam-3912	5	7	theorem	theorem	NOUN
ejpam-3912	5	8	and	and	CCONJ
ejpam-3912	5	9	classification	classification	NOUN
ejpam-3912	5	10	theorem	theorem	NOUN
ejpam-3912	5	11	for	for	ADP
ejpam-3912	5	12	evolution	evolution	NOUN
ejpam-3912	5	13	algebras	algebra	NOUN
ejpam-3912	5	14	because	because	SCONJ
ejpam-3912	5	15	it	it	PRON
ejpam-3912	5	16	has	have	AUX
ejpam-3912	5	17	been	be	AUX
ejpam-3912	5	18	introduced	introduce	VERB
ejpam-3912	5	19	concepts	concept	NOUN
ejpam-3912	5	20	of	of	ADP
ejpam-3912	5	21	dynamical	dynamical	ADJ
ejpam-3912	5	22	systems	system	NOUN
ejpam-3912	5	23	to	to	ADP
ejpam-3912	5	24	evolution	evolution	NOUN
ejpam-3912	5	25	algebras	algebra	NOUN
ejpam-3912	5	26	.	.	PUNCT
ejpam-3912	6	1	recently	recently	ADV
ejpam-3912	6	2	,	,	PUNCT
ejpam-3912	6	3	in	in	ADP
ejpam-3912	6	4	[	[	X
ejpam-3912	6	5	25	25	NUM
ejpam-3912	6	6	]	]	PUNCT
ejpam-3912	6	7	,	,	PUNCT
ejpam-3912	6	8	it	it	PRON
ejpam-3912	6	9	has	have	AUX
ejpam-3912	6	10	been	be	AUX
ejpam-3912	6	11	studied	study	VERB
ejpam-3912	6	12	some	some	DET
ejpam-3912	6	13	properties	property	NOUN
ejpam-3912	6	14	of	of	ADP
ejpam-3912	6	15	nilpotent	nilpotent	ADJ
ejpam-3912	6	16	evolution	evolution	NOUN
ejpam-3912	6	17	algebra	algebra	NOUN
ejpam-3912	6	18	with	with	ADP
ejpam-3912	6	19	maximal	maximal	ADJ
ejpam-3912	6	20	index	index	NOUN
ejpam-3912	6	21	(	(	PUNCT
ejpam-3912	6	22	dim	dim	ADJ
ejpam-3912	6	23	e2	e2	NOUN
ejpam-3912	6	24	=	=	SYM
ejpam-3912	6	25	dim	dim	NOUN
ejpam-3912	6	26	e−	e−	PROPN
ejpam-3912	6	27	1	1	NUM
ejpam-3912	6	28	)	)	PUNCT
ejpam-3912	6	29	.	.	PUNCT
ejpam-3912	7	1	this	this	DET
ejpam-3912	7	2	paper	paper	NOUN
ejpam-3912	7	3	is	be	AUX
ejpam-3912	7	4	devoted	devote	VERB
ejpam-3912	7	5	to	to	ADP
ejpam-3912	7	6	studying	study	VERB
ejpam-3912	7	7	nilpotent	nilpotent	ADJ
ejpam-3912	7	8	finite	finite	ADJ
ejpam-3912	7	9	-	-	ADJ
ejpam-3912	7	10	dimensional	dimensional	ADJ
ejpam-3912	7	11	evolution	evolution	NOUN
ejpam-3912	7	12	algebras	algebras	PROPN
ejpam-3912	7	13	e	e	NOUN
ejpam-3912	7	14	with	with	ADP
ejpam-3912	7	15	dim	dim	ADJ
ejpam-3912	7	16	e2	e2	NOUN
ejpam-3912	7	17	=	=	SYM
ejpam-3912	7	18	dim	dim	ADJ
ejpam-3912	7	19	e	e	NOUN
ejpam-3912	7	20	−	−	PROPN
ejpam-3912	7	21	2	2	X
ejpam-3912	7	22	.	.	PUNCT
ejpam-3912	8	1	we	we	PRON
ejpam-3912	8	2	describe	describe	VERB
ejpam-3912	8	3	lie	lie	NOUN
ejpam-3912	8	4	algebras	algebra	NOUN
ejpam-3912	8	5	related	relate	VERB
ejpam-3912	8	6	to	to	ADP
ejpam-3912	8	7	the	the	DET
ejpam-3912	8	8	evolution	evolution	NOUN
ejpam-3912	8	9	of	of	ADP
ejpam-3912	8	10	algebras	algebras	PROPN
ejpam-3912	8	11	.	.	PUNCT
ejpam-3912	9	1	moreover	moreover	ADV
ejpam-3912	9	2	,	,	PUNCT
ejpam-3912	9	3	this	this	DET
ejpam-3912	9	4	result	result	NOUN
ejpam-3912	9	5	allowed	allow	VERB
ejpam-3912	9	6	us	we	PRON
ejpam-3912	9	7	to	to	PART
ejpam-3912	9	8	characterize	characterize	VERB
ejpam-3912	9	9	all	all	DET
ejpam-3912	9	10	local	local	ADJ
ejpam-3912	9	11	and	and	CCONJ
ejpam-3912	9	12	2	2	NUM
ejpam-3912	9	13	-	-	PUNCT
ejpam-3912	9	14	local	local	ADJ
ejpam-3912	9	15	derivations	derivation	NOUN
ejpam-3912	9	16	of	of	ADP
ejpam-3912	9	17	the	the	DET
ejpam-3912	9	18	considered	consider	VERB
ejpam-3912	9	19	evolution	evolution	NOUN
ejpam-3912	9	20	algebras	algebra	VERB
ejpam-3912	9	21	.	.	PUNCT
ejpam-3912	10	1	all	all	DET
ejpam-3912	10	2	automorphisms	automorphism	NOUN
ejpam-3912	10	3	and	and	CCONJ
ejpam-3912	10	4	local	local	ADJ
ejpam-3912	10	5	automorphisms	automorphism	NOUN
ejpam-3912	10	6	of	of	ADP
ejpam-3912	10	7	the	the	DET
ejpam-3912	10	8	nilpotent	nilpotent	ADJ
ejpam-3912	10	9	evolution	evolution	NOUN
ejpam-3912	10	10	algebras	algebra	NOUN
ejpam-3912	10	11	are	be	AUX
ejpam-3912	10	12	found	find	VERB
ejpam-3912	10	13	.	.	PUNCT
ejpam-3912	11	1	2020	2020	NUM
ejpam-3912	11	2	mathematics	mathematic	NOUN
ejpam-3912	11	3	subject	subject	NOUN
ejpam-3912	11	4	classifications	classification	NOUN
ejpam-3912	11	5	:	:	PUNCT
ejpam-3912	11	6	6s10	6s10	NUM
ejpam-3912	11	7	,	,	PUNCT
ejpam-3912	11	8	82b26	82b26	NUM
ejpam-3912	11	9	,	,	PUNCT
ejpam-3912	11	10	12j12	12j12	NUM
ejpam-3912	11	11	,	,	PUNCT
ejpam-3912	11	12	39a70	39a70	NUM
ejpam-3912	11	13	,	,	PUNCT
ejpam-3912	11	14	47h10	47h10	NUM
ejpam-3912	11	15	,	,	PUNCT
ejpam-3912	11	16	60k35	60k35	NUM
ejpam-3912	11	17	key	key	ADJ
ejpam-3912	11	18	words	word	NOUN
ejpam-3912	11	19	and	and	CCONJ
ejpam-3912	11	20	phrases	phrase	NOUN
ejpam-3912	11	21	:	:	PUNCT
ejpam-3912	11	22	evolution	evolution	NOUN
ejpam-3912	11	23	algebra	algebra	NOUN
ejpam-3912	11	24	,	,	PUNCT
ejpam-3912	11	25	derivation	derivation	NOUN
ejpam-3912	11	26	,	,	PUNCT
ejpam-3912	11	27	local	local	ADJ
ejpam-3912	11	28	derivation	derivation	NOUN
ejpam-3912	11	29	,	,	PUNCT
ejpam-3912	11	30	automorphism	automorphism	NOUN
ejpam-3912	11	31	,	,	PUNCT
ejpam-3912	11	32	local	local	ADJ
ejpam-3912	11	33	automorphism	automorphism	NOUN
ejpam-3912	11	34	1	1	NUM
ejpam-3912	11	35	.	.	PUNCT
ejpam-3912	11	36	introduction	introduction	NOUN
ejpam-3912	11	37	the	the	DET
ejpam-3912	11	38	departure	departure	NOUN
ejpam-3912	11	39	point	point	NOUN
ejpam-3912	11	40	of	of	ADP
ejpam-3912	11	41	a	a	DET
ejpam-3912	11	42	new	new	ADJ
ejpam-3912	11	43	type	type	NOUN
ejpam-3912	11	44	of	of	ADP
ejpam-3912	11	45	evolution	evolution	NOUN
ejpam-3912	11	46	algebra	algebra	NOUN
ejpam-3912	11	47	has	have	AUX
ejpam-3912	11	48	been	be	AUX
ejpam-3912	11	49	introduced	introduce	VERB
ejpam-3912	11	50	by	by	ADP
ejpam-3912	11	51	[	[	X
ejpam-3912	11	52	34	34	NUM
ejpam-3912	11	53	]	]	PUNCT
ejpam-3912	11	54	.	.	PUNCT
ejpam-3912	12	1	this	this	DET
ejpam-3912	12	2	algebra	algebra	NOUN
ejpam-3912	12	3	is	be	AUX
ejpam-3912	12	4	motivated	motivate	VERB
ejpam-3912	12	5	by	by	ADP
ejpam-3912	12	6	some	some	DET
ejpam-3912	12	7	evolution	evolution	NOUN
ejpam-3912	12	8	laws	law	NOUN
ejpam-3912	12	9	of	of	ADP
ejpam-3912	12	10	genetics	genetic	NOUN
ejpam-3912	12	11	.	.	PUNCT
ejpam-3912	13	1	the	the	DET
ejpam-3912	13	2	study	study	NOUN
ejpam-3912	13	3	of	of	ADP
ejpam-3912	13	4	evolution	evolution	NOUN
ejpam-3912	13	5	algebras	algebras	PROPN
ejpam-3912	13	6	serves	serve	VERB
ejpam-3912	13	7	as	as	ADP
ejpam-3912	13	8	a	a	DET
ejpam-3912	13	9	foundation	foundation	NOUN
ejpam-3912	13	10	of	of	ADP
ejpam-3912	13	11	a	a	DET
ejpam-3912	13	12	new	new	ADJ
ejpam-3912	13	13	research	research	NOUN
ejpam-3912	13	14	area	area	NOUN
ejpam-3912	13	15	in	in	ADP
ejpam-3912	13	16	algebra	algebra	NOUN
ejpam-3912	13	17	and	and	CCONJ
ejpam-3912	13	18	the	the	DET
ejpam-3912	13	19	theory	theory	NOUN
ejpam-3912	13	20	of	of	ADP
ejpam-3912	13	21	dynamic	dynamic	ADJ
ejpam-3912	13	22	systems	system	NOUN
ejpam-3912	13	23	.	.	PUNCT
ejpam-3912	14	1	many	many	ADJ
ejpam-3912	14	2	related	related	ADJ
ejpam-3912	14	3	open	open	ADJ
ejpam-3912	14	4	problems	problem	NOUN
ejpam-3912	14	5	have	have	VERB
ejpam-3912	14	6	to	to	PART
ejpam-3912	14	7	be	be	AUX
ejpam-3912	14	8	addressed	address	VERB
ejpam-3912	14	9	to	to	PART
ejpam-3912	14	10	develop	develop	VERB
ejpam-3912	14	11	research	research	NOUN
ejpam-3912	14	12	in	in	ADP
ejpam-3912	14	13	this	this	DET
ejpam-3912	14	14	area	area	NOUN
ejpam-3912	14	15	(	(	PUNCT
ejpam-3912	14	16	for	for	ADP
ejpam-3912	14	17	further	further	ADJ
ejpam-3912	14	18	details	detail	NOUN
ejpam-3912	14	19	,	,	PUNCT
ejpam-3912	14	20	we	we	PRON
ejpam-3912	14	21	refer	refer	VERB
ejpam-3912	14	22	to	to	ADP
ejpam-3912	14	23	[	[	X
ejpam-3912	14	24	33	33	NUM
ejpam-3912	14	25	]	]	PUNCT
ejpam-3912	14	26	)	)	PUNCT
ejpam-3912	14	27	.	.	PUNCT
ejpam-3912	15	1	we	we	PRON
ejpam-3912	15	2	note	note	VERB
ejpam-3912	15	3	that	that	SCONJ
ejpam-3912	15	4	evolution	evolution	NOUN
ejpam-3912	15	5	algebras	algebra	NOUN
ejpam-3912	15	6	are	be	AUX
ejpam-3912	15	7	not	not	PART
ejpam-3912	15	8	defined	define	VERB
ejpam-3912	15	9	by	by	ADP
ejpam-3912	15	10	identities	identity	NOUN
ejpam-3912	15	11	,	,	PUNCT
ejpam-3912	15	12	and	and	CCONJ
ejpam-3912	15	13	therefore	therefore	ADV
ejpam-3912	15	14	they	they	PRON
ejpam-3912	15	15	do	do	AUX
ejpam-3912	15	16	not	not	PART
ejpam-3912	15	17	form	form	VERB
ejpam-3912	15	18	a	a	DET
ejpam-3912	15	19	type	type	NOUN
ejpam-3912	15	20	of	of	ADP
ejpam-3912	15	21	non	non	ADJ
ejpam-3912	15	22	-	-	ADJ
ejpam-3912	15	23	associative	associative	ADJ
ejpam-3912	15	24	algebras	algebra	NOUN
ejpam-3912	15	25	,	,	PUNCT
ejpam-3912	15	26	such	such	ADJ
ejpam-3912	15	27	as	as	ADP
ejpam-3912	15	28	lie	lie	NOUN
ejpam-3912	15	29	,	,	PUNCT
ejpam-3912	15	30	jordan	jordan	PROPN
ejpam-3912	15	31	,	,	PUNCT
ejpam-3912	15	32	or	or	CCONJ
ejpam-3912	15	33	alternative	alternative	ADJ
ejpam-3912	15	34	algebras	algebra	NOUN
ejpam-3912	15	35	.	.	PUNCT
ejpam-3912	16	1	thus	thus	ADV
ejpam-3912	16	2	,	,	PUNCT
ejpam-3912	16	3	to	to	PART
ejpam-3912	16	4	investigate	investigate	VERB
ejpam-3912	16	5	such	such	ADJ
ejpam-3912	16	6	algebras	algebra	NOUN
ejpam-3912	16	7	,	,	PUNCT
ejpam-3912	16	8	a	a	DET
ejpam-3912	16	9	different	different	ADJ
ejpam-3912	16	10	approach	approach	NOUN
ejpam-3912	16	11	has	have	VERB
ejpam-3912	16	12	to	to	PART
ejpam-3912	16	13	be	be	AUX
ejpam-3912	16	14	used	use	VERB
ejpam-3912	16	15	(	(	PUNCT
ejpam-3912	16	16	see	see	VERB
ejpam-3912	16	17	[	[	X
ejpam-3912	16	18	7	7	NUM
ejpam-3912	16	19	,	,	PUNCT
ejpam-3912	16	20	9	9	NUM
ejpam-3912	16	21	,	,	PUNCT
ejpam-3912	16	22	12	12	NUM
ejpam-3912	16	23	]	]	PUNCT
ejpam-3912	16	24	)	)	PUNCT
ejpam-3912	16	25	.	.	PUNCT
ejpam-3912	17	1	in	in	ADP
ejpam-3912	17	2	[	[	X
ejpam-3912	17	3	12	12	NUM
ejpam-3912	17	4	]	]	PUNCT
ejpam-3912	17	5	,	,	PUNCT
ejpam-3912	17	6	the	the	DET
ejpam-3912	17	7	relationships	relationship	NOUN
ejpam-3912	17	8	among	among	ADP
ejpam-3912	17	9	nil	nil	ADJ
ejpam-3912	17	10	,	,	PUNCT
ejpam-3912	17	11	right	right	ADJ
ejpam-3912	17	12	nilpotent	nilpotent	ADJ
ejpam-3912	17	13	evolution	evolution	PROPN
ejpam-3912	17	14	algebras	algebra	NOUN
ejpam-3912	17	15	,	,	PUNCT
ejpam-3912	17	16	which	which	PRON
ejpam-3912	17	17	are	be	AUX
ejpam-3912	17	18	defined	define	VERB
ejpam-3912	17	19	by	by	ADP
ejpam-3912	17	20	an	an	DET
ejpam-3912	17	21	upper	upper	ADJ
ejpam-3912	17	22	triangular	triangular	NOUN
ejpam-3912	17	23	matrix	matrix	NOUN
ejpam-3912	17	24	of	of	ADP
ejpam-3912	17	25	structural	structural	ADJ
ejpam-3912	17	26	constants	constant	NOUN
ejpam-3912	17	27	,	,	PUNCT
ejpam-3912	17	28	have	have	AUX
ejpam-3912	17	29	been	be	AUX
ejpam-3912	17	30	found	find	VERB
ejpam-3912	17	31	.	.	PUNCT
ejpam-3912	18	1	a	a	DET
ejpam-3912	18	2	further	further	ADJ
ejpam-3912	18	3	∗corresponding	∗corresponde	VERB
ejpam-3912	18	4	author	author	NOUN
ejpam-3912	18	5	.	.	PUNCT
ejpam-3912	19	1	doi	doi	NOUN
ejpam-3912	19	2	:	:	PUNCT
ejpam-3912	19	3	https://doi.org/10.29020/nybg.ejpam.v14i1.3912	https://doi.org/10.29020/nybg.ejpam.v14i1.3912	ADJ
ejpam-3912	19	4	email	email	NOUN
ejpam-3912	19	5	addresses	address	VERB
ejpam-3912	19	6	:	:	PUNCT
ejpam-3912	19	7	ahmadalarfeen@gmail.com	ahmadalarfeen@gmail.com	X
ejpam-3912	19	8	(	(	PUNCT
ejpam-3912	19	9	a.	a.	PROPN
ejpam-3912	19	10	alarafeen	alarafeen	PROPN
ejpam-3912	19	11	)	)	PUNCT
ejpam-3912	19	12	,	,	PUNCT
ejpam-3912	19	13	izzat	izzat	PROPN
ejpam-3912	19	14	math@yahoo.com	math@yahoo.com	PROPN
ejpam-3912	19	15	(	(	PUNCT
ejpam-3912	19	16	i.	i.	PROPN
ejpam-3912	19	17	qaralleh	qaralleh	PROPN
ejpam-3912	19	18	)	)	PUNCT
ejpam-3912	19	19	,	,	PUNCT
ejpam-3912	19	20	azhana@usm.my	azhana@usm.my	X
ejpam-3912	19	21	(	(	PUNCT
ejpam-3912	19	22	a.	a.	PROPN
ejpam-3912	19	23	ahmad	ahmad	PROPN
ejpam-3912	19	24	)	)	PUNCT
ejpam-3912	19	25	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3912	20	1	278	278	NUM
ejpam-3912	20	2	c	c	AUX
ejpam-3912	20	3	©	©	PROPN
ejpam-3912	20	4	2021	2021	NUM
ejpam-3912	20	5	ejpam	ejpam	VERB
ejpam-3912	20	6	all	all	DET
ejpam-3912	20	7	rights	right	NOUN
ejpam-3912	20	8	reserved	reserve	VERB
ejpam-3912	20	9	.	.	PUNCT
ejpam-3912	21	1	a.	a.	PROPN
ejpam-3912	21	2	alarafeen	alarafeen	PROPN
ejpam-3912	21	3	,	,	PUNCT
ejpam-3912	21	4	i.	i.	PROPN
ejpam-3912	21	5	qaralleh	qaralleh	PROPN
ejpam-3912	21	6	,	,	PUNCT
ejpam-3912	21	7	a.	a.	PROPN
ejpam-3912	21	8	ahmad	ahmad	PROPN
ejpam-3912	21	9	/	/	SYM
ejpam-3912	21	10	eur	eur	PROPN
ejpam-3912	21	11	.	.	PUNCT
ejpam-3912	22	1	j.	j.	PROPN
ejpam-3912	22	2	pure	pure	PROPN
ejpam-3912	22	3	appl	appl	PROPN
ejpam-3912	22	4	.	.	PROPN
ejpam-3912	22	5	math	math	PROPN
ejpam-3912	22	6	,	,	PUNCT
ejpam-3912	22	7	14	14	NUM
ejpam-3912	22	8	(	(	PUNCT
ejpam-3912	22	9	1	1	NUM
ejpam-3912	22	10	)	)	PUNCT
ejpam-3912	22	11	(	(	PUNCT
ejpam-3912	22	12	2021	2021	NUM
ejpam-3912	22	13	)	)	PUNCT
ejpam-3912	22	14	,	,	PUNCT
ejpam-3912	22	15	278	278	NUM
ejpam-3912	22	16	-	-	SYM
ejpam-3912	22	17	300	300	NUM
ejpam-3912	22	18	279	279	NUM
ejpam-3912	22	19	problem	problem	NOUN
ejpam-3912	22	20	which	which	PRON
ejpam-3912	22	21	has	have	AUX
ejpam-3912	22	22	been	be	AUX
ejpam-3912	22	23	addressed	address	VERB
ejpam-3912	22	24	in	in	ADP
ejpam-3912	22	25	[	[	X
ejpam-3912	22	26	10	10	NUM
ejpam-3912	22	27	,	,	PUNCT
ejpam-3912	22	28	15	15	NUM
ejpam-3912	22	29	,	,	PUNCT
ejpam-3912	22	30	18	18	NUM
ejpam-3912	22	31	,	,	PUNCT
ejpam-3912	22	32	19	19	NUM
ejpam-3912	22	33	,	,	PUNCT
ejpam-3912	22	34	27	27	NUM
ejpam-3912	22	35	]	]	PUNCT
ejpam-3912	22	36	is	be	AUX
ejpam-3912	22	37	the	the	DET
ejpam-3912	22	38	classification	classification	NOUN
ejpam-3912	22	39	of	of	ADP
ejpam-3912	22	40	lowdimensional	lowdimensional	ADJ
ejpam-3912	22	41	evolution	evolution	NOUN
ejpam-3912	22	42	algebras	algebra	NOUN
ejpam-3912	22	43	.	.	PUNCT
ejpam-3912	23	1	nevertheless	nevertheless	ADV
ejpam-3912	23	2	,	,	PUNCT
ejpam-3912	23	3	a	a	DET
ejpam-3912	23	4	full	full	ADJ
ejpam-3912	23	5	classification	classification	NOUN
ejpam-3912	23	6	of	of	ADP
ejpam-3912	23	7	nilpotent	nilpotent	ADJ
ejpam-3912	23	8	evolution	evolution	NOUN
ejpam-3912	23	9	algebras	algebras	PROPN
ejpam-3912	23	10	is	be	AUX
ejpam-3912	23	11	a	a	DET
ejpam-3912	23	12	tricky	tricky	ADJ
ejpam-3912	23	13	task	task	NOUN
ejpam-3912	23	14	.	.	PUNCT
ejpam-3912	24	1	[	[	X
ejpam-3912	24	2	20	20	NUM
ejpam-3912	24	3	]	]	PUNCT
ejpam-3912	24	4	have	have	AUX
ejpam-3912	24	5	investigated	investigate	VERB
ejpam-3912	24	6	certain	certain	ADJ
ejpam-3912	24	7	properties	property	NOUN
ejpam-3912	24	8	of	of	ADP
ejpam-3912	24	9	nilpotent	nilpotent	ADJ
ejpam-3912	24	10	evolution	evolution	NOUN
ejpam-3912	24	11	algebras	algebra	NOUN
ejpam-3912	24	12	with	with	ADP
ejpam-3912	24	13	maximal	maximal	ADJ
ejpam-3912	24	14	nilindex	nilindex	NOUN
ejpam-3912	24	15	.	.	PUNCT
ejpam-3912	25	1	in	in	ADP
ejpam-3912	25	2	the	the	DET
ejpam-3912	25	3	current	current	ADJ
ejpam-3912	25	4	study	study	NOUN
ejpam-3912	25	5	,	,	PUNCT
ejpam-3912	25	6	we	we	PRON
ejpam-3912	25	7	analyze	analyze	VERB
ejpam-3912	25	8	some	some	DET
ejpam-3912	25	9	propensities	propensity	NOUN
ejpam-3912	25	10	of	of	ADP
ejpam-3912	25	11	nilpotent	nilpotent	ADJ
ejpam-3912	25	12	evolution	evolution	NOUN
ejpam-3912	25	13	algebras	algebra	NOUN
ejpam-3912	25	14	whose	whose	DET
ejpam-3912	25	15	index	index	NOUN
ejpam-3912	25	16	of	of	ADP
ejpam-3912	25	17	nilpotency	nilpotency	NOUN
ejpam-3912	25	18	is	be	AUX
ejpam-3912	25	19	2n−2	2n−2	NUM
ejpam-3912	25	20	+	+	NUM
ejpam-3912	25	21	1	1	NUM
ejpam-3912	25	22	.	.	PUNCT
ejpam-3912	26	1	the	the	DET
ejpam-3912	26	2	derivation	derivation	NOUN
ejpam-3912	26	3	of	of	ADP
ejpam-3912	26	4	non	non	ADJ
ejpam-3912	26	5	-	-	ADJ
ejpam-3912	26	6	associative	associative	ADJ
ejpam-3912	26	7	algebra	algebra	NOUN
ejpam-3912	26	8	forms	form	VERB
ejpam-3912	26	9	the	the	DET
ejpam-3912	26	10	lie	lie	NOUN
ejpam-3912	26	11	algebra	algebra	NOUN
ejpam-3912	26	12	,	,	PUNCT
ejpam-3912	26	13	which	which	PRON
ejpam-3912	26	14	is	be	AUX
ejpam-3912	26	15	considered	consider	VERB
ejpam-3912	26	16	as	as	ADP
ejpam-3912	26	17	one	one	NUM
ejpam-3912	26	18	of	of	ADP
ejpam-3912	26	19	the	the	DET
ejpam-3912	26	20	important	important	ADJ
ejpam-3912	26	21	tools	tool	NOUN
ejpam-3912	26	22	for	for	ADP
ejpam-3912	26	23	studying	study	VERB
ejpam-3912	26	24	its	its	PRON
ejpam-3912	26	25	structure	structure	NOUN
ejpam-3912	26	26	.	.	PUNCT
ejpam-3912	27	1	extensive	extensive	ADJ
ejpam-3912	27	2	work	work	NOUN
ejpam-3912	27	3	has	have	AUX
ejpam-3912	27	4	been	be	AUX
ejpam-3912	27	5	conducted	conduct	VERB
ejpam-3912	27	6	on	on	ADP
ejpam-3912	27	7	the	the	DET
ejpam-3912	27	8	subject	subject	NOUN
ejpam-3912	27	9	of	of	ADP
ejpam-3912	27	10	derivations	derivation	NOUN
ejpam-3912	27	11	of	of	ADP
ejpam-3912	27	12	genetic	genetic	ADJ
ejpam-3912	27	13	algebras	algebra	NOUN
ejpam-3912	27	14	(	(	PUNCT
ejpam-3912	27	15	[	[	X
ejpam-3912	27	16	13	13	NUM
ejpam-3912	27	17	]	]	PUNCT
ejpam-3912	27	18	,	,	PUNCT
ejpam-3912	27	19	[	[	X
ejpam-3912	27	20	17	17	NUM
ejpam-3912	27	21	]	]	PUNCT
ejpam-3912	27	22	,	,	PUNCT
ejpam-3912	27	23	[	[	X
ejpam-3912	27	24	20	20	NUM
ejpam-3912	27	25	]	]	PUNCT
ejpam-3912	27	26	,	,	PUNCT
ejpam-3912	27	27	[	[	X
ejpam-3912	27	28	28],[16],[1	28],[16],[1	NUM
ejpam-3912	27	29	]	]	PUNCT
ejpam-3912	27	30	)	)	PUNCT
ejpam-3912	27	31	.	.	PUNCT
ejpam-3912	28	1	since	since	SCONJ
ejpam-3912	28	2	the	the	DET
ejpam-3912	28	3	multiplication	multiplication	NOUN
ejpam-3912	28	4	is	be	AUX
ejpam-3912	28	5	trivial	trivial	ADJ
ejpam-3912	28	6	then	then	ADV
ejpam-3912	28	7	set	set	VERB
ejpam-3912	28	8	of	of	ADP
ejpam-3912	28	9	all	all	PRON
ejpam-3912	28	10	until	until	SCONJ
ejpam-3912	28	11	is	be	AUX
ejpam-3912	28	12	invertible	invertible	ADJ
ejpam-3912	28	13	in	in	ADP
ejpam-3912	28	14	fact	fact	NOUN
ejpam-3912	28	15	,	,	PUNCT
ejpam-3912	28	16	[	[	X
ejpam-3912	28	17	7	7	NUM
ejpam-3912	28	18	,	,	PUNCT
ejpam-3912	28	19	14	14	NUM
ejpam-3912	28	20	]	]	PUNCT
ejpam-3912	28	21	have	have	AUX
ejpam-3912	28	22	investigated	investigate	VERB
ejpam-3912	28	23	several	several	ADJ
ejpam-3912	28	24	properties	property	NOUN
ejpam-3912	28	25	of	of	ADP
ejpam-3912	28	26	derivations	derivation	NOUN
ejpam-3912	28	27	of	of	ADP
ejpam-3912	28	28	n	n	CCONJ
ejpam-3912	28	29	-	-	PUNCT
ejpam-3912	28	30	dimensional	dimensional	ADJ
ejpam-3912	28	31	complex	complex	ADJ
ejpam-3912	28	32	evolution	evolution	NOUN
ejpam-3912	28	33	algebras	algebra	NOUN
ejpam-3912	28	34	,	,	PUNCT
ejpam-3912	28	35	depending	depend	VERB
ejpam-3912	28	36	on	on	ADP
ejpam-3912	28	37	the	the	DET
ejpam-3912	28	38	rank	rank	NOUN
ejpam-3912	28	39	of	of	ADP
ejpam-3912	28	40	the	the	DET
ejpam-3912	28	41	appropriate	appropriate	ADJ
ejpam-3912	28	42	matrices	matrix	NOUN
ejpam-3912	28	43	.	.	PUNCT
ejpam-3912	29	1	recently	recently	ADV
ejpam-3912	29	2	,	,	PUNCT
ejpam-3912	29	3	many	many	ADJ
ejpam-3912	29	4	paper	paper	NOUN
ejpam-3912	29	5	have	have	AUX
ejpam-3912	29	6	been	be	AUX
ejpam-3912	29	7	devoted	devote	VERB
ejpam-3912	29	8	to	to	PART
ejpam-3912	29	9	study	study	VERB
ejpam-3912	29	10	the	the	DET
ejpam-3912	29	11	derivation	derivation	NOUN
ejpam-3912	29	12	of	of	ADP
ejpam-3912	29	13	evolution	evolution	NOUN
ejpam-3912	29	14	algebras	algebra	NOUN
ejpam-3912	29	15	see	see	VERB
ejpam-3912	29	16	for	for	ADP
ejpam-3912	29	17	instance	instance	NOUN
ejpam-3912	29	18	[	[	X
ejpam-3912	29	19	2	2	NUM
ejpam-3912	29	20	,	,	PUNCT
ejpam-3912	29	21	26	26	NUM
ejpam-3912	29	22	,	,	PUNCT
ejpam-3912	29	23	30	30	NUM
ejpam-3912	29	24	,	,	PUNCT
ejpam-3912	29	25	31	31	NUM
ejpam-3912	29	26	]	]	PUNCT
ejpam-3912	29	27	.	.	PUNCT
ejpam-3912	30	1	other	other	ADJ
ejpam-3912	30	2	properties	property	NOUN
ejpam-3912	30	3	of	of	ADP
ejpam-3912	30	4	evolution	evolution	NOUN
ejpam-3912	30	5	algebra	algebra	PROPN
ejpam-3912	30	6	have	have	AUX
ejpam-3912	30	7	been	be	AUX
ejpam-3912	30	8	investigated	investigate	VERB
ejpam-3912	30	9	in	in	ADP
ejpam-3912	30	10	[	[	X
ejpam-3912	30	11	5	5	NUM
ejpam-3912	30	12	,	,	PUNCT
ejpam-3912	30	13	6	6	NUM
ejpam-3912	30	14	,	,	PUNCT
ejpam-3912	30	15	8	8	NUM
ejpam-3912	30	16	,	,	PUNCT
ejpam-3912	30	17	9	9	NUM
ejpam-3912	30	18	,	,	PUNCT
ejpam-3912	30	19	11	11	NUM
ejpam-3912	30	20	,	,	PUNCT
ejpam-3912	30	21	23	23	NUM
ejpam-3912	30	22	,	,	PUNCT
ejpam-3912	30	23	29	29	NUM
ejpam-3912	30	24	]	]	PUNCT
ejpam-3912	30	25	.	.	PUNCT
ejpam-3912	31	1	in	in	ADP
ejpam-3912	31	2	[	[	X
ejpam-3912	31	3	25	25	NUM
ejpam-3912	31	4	]	]	PUNCT
ejpam-3912	31	5	,	,	PUNCT
ejpam-3912	31	6	it	it	PRON
ejpam-3912	31	7	has	have	AUX
ejpam-3912	31	8	been	be	AUX
ejpam-3912	31	9	study	study	VERB
ejpam-3912	31	10	the	the	DET
ejpam-3912	31	11	properties	property	NOUN
ejpam-3912	31	12	of	of	ADP
ejpam-3912	31	13	the	the	DET
ejpam-3912	31	14	nilpotent	nilpotent	ADJ
ejpam-3912	31	15	finite	finite	ADJ
ejpam-3912	31	16	-	-	ADJ
ejpam-3912	31	17	dimensional	dimensional	ADJ
ejpam-3912	31	18	evolution	evolution	NOUN
ejpam-3912	31	19	algebras	algebra	NOUN
ejpam-3912	31	20	with	with	ADP
ejpam-3912	31	21	maximal	maximal	ADJ
ejpam-3912	31	22	nil	nil	NOUN
ejpam-3912	31	23	index	index	NOUN
ejpam-3912	31	24	such	such	ADJ
ejpam-3912	31	25	as	as	ADP
ejpam-3912	31	26	derivation	derivation	NOUN
ejpam-3912	31	27	,	,	PUNCT
ejpam-3912	31	28	local	local	ADJ
ejpam-3912	31	29	derivation	derivation	NOUN
ejpam-3912	31	30	,	,	PUNCT
ejpam-3912	31	31	automorphism	automorphism	NOUN
ejpam-3912	31	32	,	,	PUNCT
ejpam-3912	31	33	and	and	CCONJ
ejpam-3912	31	34	local	local	ADJ
ejpam-3912	31	35	automorphism	automorphism	NOUN
ejpam-3912	31	36	.	.	PUNCT
ejpam-3912	32	1	in	in	ADP
ejpam-3912	32	2	the	the	DET
ejpam-3912	32	3	present	present	ADJ
ejpam-3912	32	4	study	study	NOUN
ejpam-3912	32	5	,	,	PUNCT
ejpam-3912	32	6	we	we	PRON
ejpam-3912	32	7	explicitly	explicitly	ADV
ejpam-3912	32	8	describe	describe	VERB
ejpam-3912	32	9	the	the	DET
ejpam-3912	32	10	space	space	NOUN
ejpam-3912	32	11	of	of	ADP
ejpam-3912	32	12	derivations	derivation	NOUN
ejpam-3912	32	13	of	of	ADP
ejpam-3912	32	14	evolution	evolution	NOUN
ejpam-3912	32	15	algebras	algebra	NOUN
ejpam-3912	32	16	with	with	ADP
ejpam-3912	32	17	nilindex	nilindex	NOUN
ejpam-3912	32	18	2(n−2	2(n−2	NOUN
ejpam-3912	32	19	)	)	PUNCT
ejpam-3912	32	20	+	+	NUM
ejpam-3912	32	21	1	1	NUM
ejpam-3912	32	22	,	,	PUNCT
ejpam-3912	32	23	which	which	PRON
ejpam-3912	32	24	allows	allow	VERB
ejpam-3912	32	25	us	we	PRON
ejpam-3912	32	26	to	to	PART
ejpam-3912	32	27	study	study	VERB
ejpam-3912	32	28	further	further	ADJ
ejpam-3912	32	29	properties	property	NOUN
ejpam-3912	32	30	of	of	ADP
ejpam-3912	32	31	the	the	DET
ejpam-3912	32	32	evolution	evolution	NOUN
ejpam-3912	32	33	algebras.moreover	algebras.moreover	ADP
ejpam-3912	32	34	,	,	PUNCT
ejpam-3912	32	35	we	we	PRON
ejpam-3912	32	36	describe	describe	VERB
ejpam-3912	32	37	all	all	DET
ejpam-3912	32	38	local	local	ADJ
ejpam-3912	32	39	and	and	CCONJ
ejpam-3912	32	40	2	2	NUM
ejpam-3912	32	41	-	-	PUNCT
ejpam-3912	32	42	local	local	ADJ
ejpam-3912	32	43	derivations	derivation	NOUN
ejpam-3912	32	44	of	of	ADP
ejpam-3912	32	45	the	the	DET
ejpam-3912	32	46	considered	consider	VERB
ejpam-3912	32	47	algebra.we	algebra.we	X
ejpam-3912	32	48	stress	stress	VERB
ejpam-3912	32	49	that	that	SCONJ
ejpam-3912	32	50	the	the	DET
ejpam-3912	32	51	notions	notion	NOUN
ejpam-3912	32	52	of	of	ADP
ejpam-3912	32	53	local	local	ADJ
ejpam-3912	32	54	automorphism	automorphism	NOUN
ejpam-3912	32	55	and	and	CCONJ
ejpam-3912	32	56	local	local	ADJ
ejpam-3912	32	57	derivation	derivation	NOUN
ejpam-3912	32	58	were	be	AUX
ejpam-3912	32	59	introduced	introduce	VERB
ejpam-3912	32	60	and	and	CCONJ
ejpam-3912	32	61	investigated	investigate	VERB
ejpam-3912	32	62	independently	independently	ADV
ejpam-3912	32	63	by	by	ADP
ejpam-3912	32	64	kadison	kadison	PROPN
ejpam-3912	33	1	[	[	X
ejpam-3912	33	2	22	22	NUM
ejpam-3912	33	3	]	]	PUNCT
ejpam-3912	33	4	and	and	CCONJ
ejpam-3912	33	5	larson	larson	PROPN
ejpam-3912	33	6	and	and	CCONJ
ejpam-3912	33	7	sourour	sourour	VERB
ejpam-3912	34	1	[	[	X
ejpam-3912	34	2	24	24	NUM
ejpam-3912	34	3	]	]	PUNCT
ejpam-3912	34	4	.	.	PUNCT
ejpam-3912	35	1	subsequently	subsequently	ADV
ejpam-3912	35	2	,	,	PUNCT
ejpam-3912	35	3	p.	p.	NOUN
ejpam-3912	35	4	šemrl	šemrl	PUNCT
ejpam-3912	36	1	[	[	X
ejpam-3912	36	2	32	32	NUM
ejpam-3912	36	3	]	]	PUNCT
ejpam-3912	36	4	introduced	introduce	VERB
ejpam-3912	36	5	the	the	DET
ejpam-3912	36	6	concepts	concept	NOUN
ejpam-3912	36	7	of	of	ADP
ejpam-3912	36	8	2	2	NUM
ejpam-3912	36	9	-	-	PUNCT
ejpam-3912	36	10	local	local	ADJ
ejpam-3912	36	11	automorphisms	automorphism	NOUN
ejpam-3912	36	12	and	and	CCONJ
ejpam-3912	36	13	2	2	NUM
ejpam-3912	36	14	-	-	PUNCT
ejpam-3912	36	15	local	local	ADJ
ejpam-3912	36	16	derivations	derivation	NOUN
ejpam-3912	36	17	.	.	PUNCT
ejpam-3912	37	1	the	the	DET
ejpam-3912	37	2	preceding	precede	VERB
ejpam-3912	37	3	studies	study	NOUN
ejpam-3912	37	4	have	have	AUX
ejpam-3912	37	5	led	lead	VERB
ejpam-3912	37	6	to	to	ADP
ejpam-3912	37	7	a	a	DET
ejpam-3912	37	8	series	series	NOUN
ejpam-3912	37	9	of	of	ADP
ejpam-3912	37	10	works	work	NOUN
ejpam-3912	37	11	devoted	devote	VERB
ejpam-3912	37	12	to	to	ADP
ejpam-3912	37	13	description	description	NOUN
ejpam-3912	37	14	of	of	ADP
ejpam-3912	37	15	mappings	mapping	NOUN
ejpam-3912	37	16	which	which	PRON
ejpam-3912	37	17	are	be	AUX
ejpam-3912	37	18	close	close	ADJ
ejpam-3912	37	19	to	to	ADP
ejpam-3912	37	20	automorphisms	automorphism	NOUN
ejpam-3912	37	21	and	and	CCONJ
ejpam-3912	37	22	derivations	derivation	NOUN
ejpam-3912	37	23	of	of	ADP
ejpam-3912	37	24	c∗-algebras	c∗-algebra	NOUN
ejpam-3912	37	25	and	and	CCONJ
ejpam-3912	37	26	operator	operator	NOUN
ejpam-3912	37	27	algebras	algebra	NOUN
ejpam-3912	37	28	.	.	PUNCT
ejpam-3912	38	1	for	for	ADP
ejpam-3912	38	2	details	detail	NOUN
ejpam-3912	38	3	and	and	CCONJ
ejpam-3912	38	4	the	the	DET
ejpam-3912	38	5	survey	survey	NOUN
ejpam-3912	38	6	,	,	PUNCT
ejpam-3912	38	7	we	we	PRON
ejpam-3912	38	8	refer	refer	VERB
ejpam-3912	38	9	to	to	ADP
ejpam-3912	38	10	the	the	DET
ejpam-3912	38	11	work	work	NOUN
ejpam-3912	38	12	of	of	ADP
ejpam-3912	38	13	[	[	X
ejpam-3912	38	14	3	3	NUM
ejpam-3912	38	15	,	,	PUNCT
ejpam-3912	38	16	4	4	NUM
ejpam-3912	38	17	]	]	PUNCT
ejpam-3912	38	18	.	.	PUNCT
ejpam-3912	39	1	the	the	DET
ejpam-3912	39	2	paper	paper	NOUN
ejpam-3912	39	3	is	be	AUX
ejpam-3912	39	4	organized	organize	VERB
ejpam-3912	39	5	as	as	SCONJ
ejpam-3912	39	6	follows	follow	VERB
ejpam-3912	39	7	.	.	PUNCT
ejpam-3912	40	1	section	section	NOUN
ejpam-3912	40	2	2	2	NUM
ejpam-3912	40	3	provides	provide	VERB
ejpam-3912	40	4	preliminary	preliminary	ADJ
ejpam-3912	40	5	information	information	NOUN
ejpam-3912	40	6	about	about	ADP
ejpam-3912	40	7	evolution	evolution	NOUN
ejpam-3912	40	8	algebras	algebra	NOUN
ejpam-3912	40	9	.	.	PUNCT
ejpam-3912	41	1	derivations	derivation	NOUN
ejpam-3912	41	2	of	of	ADP
ejpam-3912	41	3	non	non	ADJ
ejpam-3912	41	4	-	-	ADJ
ejpam-3912	41	5	associative	associative	ADJ
ejpam-3912	41	6	algebras	algebra	NOUN
ejpam-3912	41	7	form	form	VERB
ejpam-3912	41	8	the	the	DET
ejpam-3912	41	9	lie	lie	NOUN
ejpam-3912	41	10	algebra	algebra	NOUN
ejpam-3912	41	11	;	;	PUNCT
ejpam-3912	41	12	thus	thus	ADV
ejpam-3912	41	13	,	,	PUNCT
ejpam-3912	41	14	so	so	ADV
ejpam-3912	41	15	,	,	PUNCT
ejpam-3912	41	16	in	in	ADP
ejpam-3912	41	17	section	section	NOUN
ejpam-3912	41	18	3	3	NUM
ejpam-3912	41	19	we	we	PRON
ejpam-3912	41	20	describe	describe	VERB
ejpam-3912	41	21	the	the	DET
ejpam-3912	41	22	lie	lie	NOUN
ejpam-3912	41	23	algebra	algebra	NOUN
ejpam-3912	41	24	associated	associate	VERB
ejpam-3912	41	25	with	with	ADP
ejpam-3912	41	26	evolution	evolution	NOUN
ejpam-3912	41	27	algebras	algebra	NOUN
ejpam-3912	41	28	whose	whose	DET
ejpam-3912	41	29	nilindex	nilindex	NOUN
ejpam-3912	41	30	is	be	AUX
ejpam-3912	41	31	2(n−2)+1	2(n−2)+1	NOUN
ejpam-3912	41	32	.	.	PUNCT
ejpam-3912	42	1	furthermore	furthermore	ADV
ejpam-3912	42	2	,	,	PUNCT
ejpam-3912	42	3	based	base	VERB
ejpam-3912	42	4	on	on	ADP
ejpam-3912	42	5	results	result	NOUN
ejpam-3912	42	6	in	in	ADP
ejpam-3912	42	7	section	section	NOUN
ejpam-3912	42	8	3	3	NUM
ejpam-3912	42	9	,	,	PUNCT
ejpam-3912	42	10	section	section	NOUN
ejpam-3912	42	11	4	4	NUM
ejpam-3912	42	12	describes	describe	VERB
ejpam-3912	42	13	local	local	ADJ
ejpam-3912	42	14	and	and	CCONJ
ejpam-3912	42	15	2	2	NUM
ejpam-3912	42	16	-	-	PUNCT
ejpam-3912	42	17	local	local	ADJ
ejpam-3912	42	18	derivations	derivation	NOUN
ejpam-3912	42	19	of	of	ADP
ejpam-3912	42	20	the	the	DET
ejpam-3912	42	21	considered	consider	VERB
ejpam-3912	42	22	evolution	evolution	NOUN
ejpam-3912	42	23	algebras	algebra	VERB
ejpam-3912	42	24	.	.	PUNCT
ejpam-3912	43	1	in	in	ADP
ejpam-3912	43	2	section	section	NOUN
ejpam-3912	43	3	5	5	NUM
ejpam-3912	43	4	,	,	PUNCT
ejpam-3912	43	5	we	we	PRON
ejpam-3912	43	6	find	find	VERB
ejpam-3912	43	7	all	all	DET
ejpam-3912	43	8	automorphisms	automorphism	NOUN
ejpam-3912	43	9	and	and	CCONJ
ejpam-3912	43	10	local	local	ADJ
ejpam-3912	43	11	automorphisms	automorphism	NOUN
ejpam-3912	43	12	of	of	ADP
ejpam-3912	43	13	the	the	DET
ejpam-3912	43	14	nilpotent	nilpotent	ADJ
ejpam-3912	43	15	evolution	evolution	NOUN
ejpam-3912	43	16	algebras	algebras	PROPN
ejpam-3912	43	17	with	with	ADP
ejpam-3912	43	18	nilindex	nilindex	NOUN
ejpam-3912	43	19	2(n−2	2(n−2	NOUN
ejpam-3912	43	20	)	)	PUNCT
ejpam-3912	44	1	+	+	CCONJ
ejpam-3912	44	2	1	1	NUM
ejpam-3912	44	3	.	.	X
ejpam-3912	45	1	2	2	X
ejpam-3912	45	2	.	.	X
ejpam-3912	45	3	evolution	evolution	NOUN
ejpam-3912	45	4	algebras	algebras	PROPN
ejpam-3912	45	5	recall	recall	VERB
ejpam-3912	45	6	the	the	DET
ejpam-3912	45	7	definition	definition	NOUN
ejpam-3912	45	8	of	of	ADP
ejpam-3912	45	9	evolution	evolution	NOUN
ejpam-3912	45	10	algebras	algebras	X
ejpam-3912	45	11	.	.	PUNCT
ejpam-3912	46	1	let	let	VERB
ejpam-3912	46	2	e	e	PRON
ejpam-3912	46	3	be	be	AUX
ejpam-3912	46	4	a	a	DET
ejpam-3912	46	5	vector	vector	NOUN
ejpam-3912	46	6	space	space	NOUN
ejpam-3912	46	7	over	over	ADP
ejpam-3912	46	8	a	a	DET
ejpam-3912	46	9	field	field	NOUN
ejpam-3912	46	10	k.	k.	NOUN
ejpam-3912	46	11	in	in	ADP
ejpam-3912	46	12	the	the	DET
ejpam-3912	46	13	follows	follow	NOUN
ejpam-3912	46	14	,	,	PUNCT
ejpam-3912	46	15	we	we	PRON
ejpam-3912	46	16	always	always	ADV
ejpam-3912	46	17	assume	assume	VERB
ejpam-3912	46	18	that	that	SCONJ
ejpam-3912	46	19	k	k	PROPN
ejpam-3912	46	20	has	have	VERB
ejpam-3912	46	21	characteristic	characteristic	ADJ
ejpam-3912	46	22	zero	zero	NUM
ejpam-3912	46	23	.	.	PUNCT
ejpam-3912	47	1	the	the	DET
ejpam-3912	47	2	vector	vector	NOUN
ejpam-3912	47	3	space	space	NOUN
ejpam-3912	47	4	e	e	NOUN
ejpam-3912	47	5	is	be	AUX
ejpam-3912	47	6	called	call	VERB
ejpam-3912	47	7	evolution	evolution	NOUN
ejpam-3912	47	8	algebra	algebra	PROPN
ejpam-3912	47	9	w.r.t	w.r.t	VERB
ejpam-3912	47	10	.	.	PUNCT
ejpam-3912	48	1	natural	natural	ADJ
ejpam-3912	48	2	basis	basis	NOUN
ejpam-3912	48	3	{	{	PUNCT
ejpam-3912	48	4	e1	e1	PROPN
ejpam-3912	48	5	,	,	PUNCT
ejpam-3912	48	6	e2	e2	PROPN
ejpam-3912	48	7	,	,	PUNCT
ejpam-3912	48	8	...	...	PUNCT
ejpam-3912	48	9	}	}	PUNCT
ejpam-3912	48	10	if	if	SCONJ
ejpam-3912	48	11	a	a	DET
ejpam-3912	48	12	multiplication	multiplication	NOUN
ejpam-3912	48	13	rule	rule	NOUN
ejpam-3912	48	14	·	·	PUNCT
ejpam-3912	48	15	on	on	ADP
ejpam-3912	48	16	e	e	NOUN
ejpam-3912	48	17	satisfies	satisfie	NOUN
ejpam-3912	48	18	ei	ei	X
ejpam-3912	48	19	·	·	PUNCT
ejpam-3912	48	20	ej	ej	X
ejpam-3912	49	1	=	=	PUNCT
ejpam-3912	49	2	0	0	PROPN
ejpam-3912	49	3	,	,	PUNCT
ejpam-3912	49	4	i	i	PROPN
ejpam-3912	49	5	6=	6=	PROPN
ejpam-3912	49	6	j	j	PROPN
ejpam-3912	49	7	,	,	PUNCT
ejpam-3912	49	8	ei	ei	X
ejpam-3912	49	9	·	·	PUNCT
ejpam-3912	49	10	ei	ei	X
ejpam-3912	49	11	=	=	PUNCT
ejpam-3912	49	12	∑	∑	PROPN
ejpam-3912	49	13	k	k	PROPN
ejpam-3912	49	14	aikek	aikek	PROPN
ejpam-3912	49	15	,	,	PUNCT
ejpam-3912	49	16	i	i	PRON
ejpam-3912	49	17	≥	≥	VERB
ejpam-3912	49	18	1	1	NUM
ejpam-3912	49	19	.	.	PUNCT
ejpam-3912	50	1	from	from	ADP
ejpam-3912	50	2	the	the	DET
ejpam-3912	50	3	preceding	precede	VERB
ejpam-3912	50	4	definition	definition	NOUN
ejpam-3912	50	5	,	,	PUNCT
ejpam-3912	50	6	it	it	PRON
ejpam-3912	50	7	follows	follow	VERB
ejpam-3912	50	8	that	that	SCONJ
ejpam-3912	50	9	evolution	evolution	NOUN
ejpam-3912	50	10	algebras	algebra	NOUN
ejpam-3912	50	11	are	be	AUX
ejpam-3912	50	12	commutative	commutative	ADJ
ejpam-3912	50	13	(	(	PUNCT
ejpam-3912	50	14	therefore	therefore	ADV
ejpam-3912	50	15	,	,	PUNCT
ejpam-3912	50	16	flexible	flexible	ADJ
ejpam-3912	50	17	)	)	PUNCT
ejpam-3912	50	18	.	.	PUNCT
ejpam-3912	51	1	a.	a.	PROPN
ejpam-3912	51	2	alarafeen	alarafeen	PROPN
ejpam-3912	51	3	,	,	PUNCT
ejpam-3912	51	4	i.	i.	PROPN
ejpam-3912	51	5	qaralleh	qaralleh	PROPN
ejpam-3912	51	6	,	,	PUNCT
ejpam-3912	51	7	a.	a.	PROPN
ejpam-3912	51	8	ahmad	ahmad	PROPN
ejpam-3912	51	9	/	/	SYM
ejpam-3912	51	10	eur	eur	PROPN
ejpam-3912	51	11	.	.	PUNCT
ejpam-3912	52	1	j.	j.	PROPN
ejpam-3912	52	2	pure	pure	PROPN
ejpam-3912	52	3	appl	appl	PROPN
ejpam-3912	52	4	.	.	PROPN
ejpam-3912	52	5	math	math	PROPN
ejpam-3912	52	6	,	,	PUNCT
ejpam-3912	52	7	14	14	NUM
ejpam-3912	52	8	(	(	PUNCT
ejpam-3912	52	9	1	1	NUM
ejpam-3912	52	10	)	)	PUNCT
ejpam-3912	52	11	(	(	PUNCT
ejpam-3912	52	12	2021	2021	NUM
ejpam-3912	52	13	)	)	PUNCT
ejpam-3912	52	14	,	,	PUNCT
ejpam-3912	52	15	278	278	NUM
ejpam-3912	52	16	-	-	SYM
ejpam-3912	52	17	300	300	NUM
ejpam-3912	52	18	280	280	NUM
ejpam-3912	52	19	we	we	PRON
ejpam-3912	52	20	denote	denote	VERB
ejpam-3912	52	21	by	by	ADP
ejpam-3912	52	22	a	a	DET
ejpam-3912	52	23	=	=	X
ejpam-3912	52	24	(	(	PUNCT
ejpam-3912	52	25	aij	aij	PROPN
ejpam-3912	52	26	)	)	PUNCT
ejpam-3912	52	27	n	n	PROPN
ejpam-3912	53	1	i	i	PRON
ejpam-3912	53	2	,	,	PUNCT
ejpam-3912	53	3	j=1	j=1	NOUN
ejpam-3912	53	4	the	the	DET
ejpam-3912	53	5	matrix	matrix	NOUN
ejpam-3912	53	6	of	of	ADP
ejpam-3912	53	7	the	the	DET
ejpam-3912	53	8	structural	structural	ADJ
ejpam-3912	53	9	constants	constant	NOUN
ejpam-3912	53	10	of	of	ADP
ejpam-3912	53	11	the	the	DET
ejpam-3912	53	12	finitedimensional	finitedimensional	ADJ
ejpam-3912	53	13	evolution	evolution	NOUN
ejpam-3912	53	14	algebra	algebra	PROPN
ejpam-3912	53	15	e.	e.	PROPN
ejpam-3912	53	16	obviously	obviously	ADV
ejpam-3912	53	17	,	,	PUNCT
ejpam-3912	53	18	ranka	ranka	PROPN
ejpam-3912	53	19	=	=	SYM
ejpam-3912	53	20	dim(e	dim(e	PROPN
ejpam-3912	53	21	·	·	PUNCT
ejpam-3912	53	22	e	e	X
ejpam-3912	53	23	)	)	PUNCT
ejpam-3912	53	24	.	.	PUNCT
ejpam-3912	54	1	thus	thus	ADV
ejpam-3912	54	2	,	,	PUNCT
ejpam-3912	54	3	for	for	ADP
ejpam-3912	54	4	finitedimensional	finitedimensional	ADJ
ejpam-3912	54	5	evolution	evolution	NOUN
ejpam-3912	54	6	algebra	algebra	NOUN
ejpam-3912	54	7	,	,	PUNCT
ejpam-3912	54	8	the	the	DET
ejpam-3912	54	9	rank	rank	NOUN
ejpam-3912	54	10	of	of	ADP
ejpam-3912	54	11	the	the	DET
ejpam-3912	54	12	matrix	matrix	NOUN
ejpam-3912	54	13	does	do	AUX
ejpam-3912	54	14	not	not	PART
ejpam-3912	54	15	depend	depend	VERB
ejpam-3912	54	16	on	on	ADP
ejpam-3912	54	17	choice	choice	NOUN
ejpam-3912	54	18	of	of	ADP
ejpam-3912	54	19	natural	natural	ADJ
ejpam-3912	54	20	basis	basis	NOUN
ejpam-3912	54	21	.	.	PUNCT
ejpam-3912	55	1	in	in	ADP
ejpam-3912	55	2	the	the	DET
ejpam-3912	55	3	following	following	NOUN
ejpam-3912	55	4	,	,	PUNCT
ejpam-3912	55	5	for	for	ADP
ejpam-3912	55	6	convenience	convenience	NOUN
ejpam-3912	55	7	,	,	PUNCT
ejpam-3912	55	8	we	we	PRON
ejpam-3912	55	9	write	write	VERB
ejpam-3912	55	10	uv	uv	INTJ
ejpam-3912	55	11	instead	instead	ADV
ejpam-3912	55	12	u	u	NOUN
ejpam-3912	55	13	·	·	PROPN
ejpam-3912	55	14	v	v	NOUN
ejpam-3912	55	15	for	for	ADP
ejpam-3912	55	16	any	any	DET
ejpam-3912	55	17	u	u	NOUN
ejpam-3912	55	18	,	,	PUNCT
ejpam-3912	55	19	v	v	NOUN
ejpam-3912	55	20	∈	∈	NOUN
ejpam-3912	55	21	e	e	NOUN
ejpam-3912	56	1	and	and	CCONJ
ejpam-3912	56	2	we	we	PRON
ejpam-3912	56	3	write	write	VERB
ejpam-3912	56	4	e2	e2	PROPN
ejpam-3912	56	5	instead	instead	ADV
ejpam-3912	56	6	of	of	ADP
ejpam-3912	56	7	e	e	PROPN
ejpam-3912	56	8	·	·	PROPN
ejpam-3912	56	9	e.	e.	PROPN
ejpam-3912	56	10	a	a	DET
ejpam-3912	56	11	linear	linear	PROPN
ejpam-3912	56	12	map	map	NOUN
ejpam-3912	56	13	ψ	ψ	X
ejpam-3912	56	14	:	:	PUNCT
ejpam-3912	56	15	e1	e1	PROPN
ejpam-3912	56	16	→	→	SYM
ejpam-3912	56	17	e2	e2	PROPN
ejpam-3912	56	18	is	be	AUX
ejpam-3912	56	19	called	call	VERB
ejpam-3912	56	20	a	a	DET
ejpam-3912	56	21	homomorphism	homomorphism	NOUN
ejpam-3912	56	22	of	of	ADP
ejpam-3912	56	23	evolution	evolution	NOUN
ejpam-3912	56	24	algebras	algebra	VERB
ejpam-3912	56	25	if	if	SCONJ
ejpam-3912	56	26	ψ(uv	ψ(uv	NUM
ejpam-3912	56	27	)	)	PUNCT
ejpam-3912	56	28	=	=	SYM
ejpam-3912	56	29	ψ(u)ψ(v	ψ(u)ψ(v	NOUN
ejpam-3912	56	30	)	)	PUNCT
ejpam-3912	56	31	for	for	ADP
ejpam-3912	56	32	any	any	DET
ejpam-3912	56	33	u	u	NOUN
ejpam-3912	56	34	,	,	PUNCT
ejpam-3912	56	35	v	v	PROPN
ejpam-3912	56	36	∈	∈	PROPN
ejpam-3912	56	37	e1	e1	NOUN
ejpam-3912	56	38	.	.	PUNCT
ejpam-3912	57	1	moreover	moreover	ADV
ejpam-3912	57	2	,	,	PUNCT
ejpam-3912	57	3	if	if	SCONJ
ejpam-3912	57	4	ψ	ψ	NOUN
ejpam-3912	57	5	is	be	AUX
ejpam-3912	57	6	bijective	bijective	ADJ
ejpam-3912	57	7	,	,	PUNCT
ejpam-3912	57	8	then	then	ADV
ejpam-3912	57	9	it	it	PRON
ejpam-3912	57	10	is	be	AUX
ejpam-3912	57	11	called	call	VERB
ejpam-3912	57	12	an	an	DET
ejpam-3912	57	13	isomorphism	isomorphism	NOUN
ejpam-3912	57	14	.	.	PUNCT
ejpam-3912	58	1	in	in	ADP
ejpam-3912	58	2	this	this	DET
ejpam-3912	58	3	case	case	NOUN
ejpam-3912	58	4	,	,	PUNCT
ejpam-3912	58	5	the	the	DET
ejpam-3912	58	6	last	last	ADJ
ejpam-3912	58	7	relation	relation	NOUN
ejpam-3912	58	8	is	be	AUX
ejpam-3912	58	9	denoted	denote	VERB
ejpam-3912	58	10	by	by	ADP
ejpam-3912	58	11	e1	e1	NOUN
ejpam-3912	58	12	∼=	∼=	PROPN
ejpam-3912	58	13	e2	e2	NOUN
ejpam-3912	58	14	.	.	PUNCT
ejpam-3912	59	1	for	for	ADP
ejpam-3912	59	2	an	an	DET
ejpam-3912	59	3	evolution	evolution	NOUN
ejpam-3912	59	4	algebra	algebra	NOUN
ejpam-3912	59	5	e	e	NOUN
ejpam-3912	59	6	,	,	PUNCT
ejpam-3912	59	7	we	we	PRON
ejpam-3912	59	8	introduce	introduce	VERB
ejpam-3912	59	9	the	the	DET
ejpam-3912	59	10	following	follow	VERB
ejpam-3912	59	11	sequence	sequence	NOUN
ejpam-3912	59	12	,	,	PUNCT
ejpam-3912	59	13	k	k	PROPN
ejpam-3912	59	14	≥	≥	NUM
ejpam-3912	59	15	1	1	NUM
ejpam-3912	59	16	ek	ek	NOUN
ejpam-3912	59	17	=	=	SYM
ejpam-3912	59	18	k−1∑	k−1∑	PROPN
ejpam-3912	59	19	i=1	i=1	PROPN
ejpam-3912	59	20	eiek−i	eiek−i	PROPN
ejpam-3912	59	21	.	.	PUNCT
ejpam-3912	60	1	(	(	PUNCT
ejpam-3912	60	2	1	1	X
ejpam-3912	60	3	)	)	PUNCT
ejpam-3912	60	4	as	as	SCONJ
ejpam-3912	60	5	e	e	NOUN
ejpam-3912	60	6	is	be	AUX
ejpam-3912	60	7	commutative	commutative	ADJ
ejpam-3912	60	8	algebra	algebra	NOUN
ejpam-3912	60	9	,	,	PUNCT
ejpam-3912	60	10	we	we	PRON
ejpam-3912	60	11	obtain	obtain	VERB
ejpam-3912	60	12	ek	ek	NOUN
ejpam-3912	60	13	=	=	NOUN
ejpam-3912	60	14	bk/2c∑	bk/2c∑	NOUN
ejpam-3912	60	15	i=1	i=1	PROPN
ejpam-3912	60	16	eiek−i	eiek−i	PROPN
ejpam-3912	60	17	,	,	PUNCT
ejpam-3912	60	18	where	where	SCONJ
ejpam-3912	60	19	bxc	bxc	NOUN
ejpam-3912	60	20	denotes	denote	VERB
ejpam-3912	60	21	the	the	DET
ejpam-3912	60	22	integer	integer	NOUN
ejpam-3912	60	23	part	part	NOUN
ejpam-3912	60	24	of	of	ADP
ejpam-3912	60	25	x.	x.	NOUN
ejpam-3912	60	26	definition	definition	NOUN
ejpam-3912	60	27	1	1	NUM
ejpam-3912	60	28	.	.	PUNCT
ejpam-3912	61	1	an	an	DET
ejpam-3912	61	2	evolution	evolution	NOUN
ejpam-3912	61	3	algebra	algebra	NOUN
ejpam-3912	61	4	e	e	NOUN
ejpam-3912	61	5	is	be	AUX
ejpam-3912	61	6	called	call	VERB
ejpam-3912	61	7	nilpotent	nilpotent	ADJ
ejpam-3912	61	8	if	if	SCONJ
ejpam-3912	61	9	some	some	PRON
ejpam-3912	61	10	m	m	VERB
ejpam-3912	61	11	∈	∈	NOUN
ejpam-3912	61	12	n	n	PRON
ejpam-3912	61	13	such	such	ADJ
ejpam-3912	61	14	that	that	SCONJ
ejpam-3912	61	15	em	em	PRON
ejpam-3912	61	16	=	=	NOUN
ejpam-3912	61	17	0	0	PROPN
ejpam-3912	61	18	.	.	PUNCT
ejpam-3912	62	1	the	the	DET
ejpam-3912	62	2	smallest	small	ADJ
ejpam-3912	62	3	m	m	VERB
ejpam-3912	62	4	such	such	ADJ
ejpam-3912	62	5	that	that	SCONJ
ejpam-3912	62	6	em	em	PRON
ejpam-3912	62	7	=	=	SYM
ejpam-3912	62	8	0	0	NUM
ejpam-3912	62	9	is	be	AUX
ejpam-3912	62	10	called	call	VERB
ejpam-3912	62	11	the	the	DET
ejpam-3912	62	12	index	index	NOUN
ejpam-3912	62	13	of	of	ADP
ejpam-3912	62	14	nilpotency	nilpotency	NOUN
ejpam-3912	62	15	.	.	PUNCT
ejpam-3912	63	1	theorem	theorem	NOUN
ejpam-3912	63	2	1	1	NUM
ejpam-3912	63	3	.	.	PUNCT
ejpam-3912	64	1	[	[	X
ejpam-3912	64	2	12	12	NUM
ejpam-3912	64	3	]	]	PUNCT
ejpam-3912	64	4	an	an	DET
ejpam-3912	64	5	n	n	ADV
ejpam-3912	64	6	-	-	PUNCT
ejpam-3912	64	7	dimensional	dimensional	ADJ
ejpam-3912	64	8	evolution	evolution	NOUN
ejpam-3912	64	9	algebra	algebra	NOUN
ejpam-3912	64	10	e	e	NOUN
ejpam-3912	64	11	is	be	AUX
ejpam-3912	64	12	nilpotent	nilpotent	ADJ
ejpam-3912	64	13	iff	iff	PROPN
ejpam-3912	64	14	it	it	PRON
ejpam-3912	64	15	admits	admit	VERB
ejpam-3912	64	16	a	a	DET
ejpam-3912	64	17	natural	natural	ADJ
ejpam-3912	64	18	basis	basis	NOUN
ejpam-3912	64	19	such	such	ADJ
ejpam-3912	64	20	that	that	SCONJ
ejpam-3912	64	21	the	the	DET
ejpam-3912	64	22	matrix	matrix	NOUN
ejpam-3912	64	23	of	of	ADP
ejpam-3912	64	24	the	the	DET
ejpam-3912	64	25	structural	structural	ADJ
ejpam-3912	64	26	constants	constant	NOUN
ejpam-3912	64	27	corresponding	correspond	VERB
ejpam-3912	64	28	to	to	ADP
ejpam-3912	64	29	e	e	NOUN
ejpam-3912	64	30	on	on	ADP
ejpam-3912	64	31	this	this	DET
ejpam-3912	64	32	basis	basis	NOUN
ejpam-3912	64	33	is	be	AUX
ejpam-3912	64	34	represented	represent	VERB
ejpam-3912	64	35	in	in	ADP
ejpam-3912	64	36	the	the	DET
ejpam-3912	64	37	form	form	NOUN
ejpam-3912	64	38	ã	ã	PROPN
ejpam-3912	64	39	=	=	SYM
ejpam-3912	64	40			ADJ
ejpam-3912	64	41	0	0	NUM
ejpam-3912	64	42	ã12	ã12	X
ejpam-3912	64	43	ã13	ã13	NOUN
ejpam-3912	64	44	...	...	PUNCT
ejpam-3912	65	1	ã1n	ã1n	PROPN
ejpam-3912	65	2	0	0	NUM
ejpam-3912	65	3	0	0	NUM
ejpam-3912	66	1	ã23	ã23	CCONJ
ejpam-3912	66	2	...	...	PUNCT
ejpam-3912	67	1	ã2n	ã2n	CCONJ
ejpam-3912	67	2	...	...	PUNCT
ejpam-3912	67	3	...	...	PUNCT
ejpam-3912	67	4	...	...	PUNCT
ejpam-3912	67	5	.	.	PUNCT
ejpam-3912	67	6	.	.	PUNCT
ejpam-3912	67	7	.	.	PUNCT
ejpam-3912	68	1	...	...	PUNCT
ejpam-3912	69	1	0	0	NUM
ejpam-3912	69	2	0	0	NUM
ejpam-3912	69	3	0	0	NUM
ejpam-3912	69	4	...	...	PUNCT
ejpam-3912	69	5	ãn−1,n	ãn−1,n	NOUN
ejpam-3912	69	6	0	0	NUM
ejpam-3912	69	7	0	0	NUM
ejpam-3912	69	8	0	0	NUM
ejpam-3912	69	9	...	...	PUNCT
ejpam-3912	69	10	0	0	NUM
ejpam-3912	70	1			NOUN
ejpam-3912	70	2	.	.	PUNCT
ejpam-3912	71	1	due	due	ADJ
ejpam-3912	71	2	to	to	ADP
ejpam-3912	71	3	theorem	theorem	NOUN
ejpam-3912	71	4	1	1	NUM
ejpam-3912	71	5	,	,	PUNCT
ejpam-3912	71	6	any	any	DET
ejpam-3912	71	7	nilpotent	nilpotent	ADJ
ejpam-3912	71	8	evolution	evolution	NOUN
ejpam-3912	71	9	algebra	algebra	NOUN
ejpam-3912	71	10	e	e	NOUN
ejpam-3912	71	11	with	with	ADP
ejpam-3912	71	12	dim(e2	dim(e2	PROPN
ejpam-3912	71	13	)	)	PUNCT
ejpam-3912	71	14	=	=	SYM
ejpam-3912	72	1	n	n	CCONJ
ejpam-3912	72	2	−	−	PROPN
ejpam-3912	72	3	2	2	NUM
ejpam-3912	72	4	has	have	VERB
ejpam-3912	72	5	the	the	DET
ejpam-3912	72	6	following	follow	VERB
ejpam-3912	72	7	form	form	NOUN
ejpam-3912	72	8	:	:	PUNCT
ejpam-3912	72	9	e2	e2	PROPN
ejpam-3912	72	10	i	i	PRON
ejpam-3912	72	11	=	=	PUNCT
ejpam-3912	72	12			PROPN
ejpam-3912	72	13	n∑	n∑	PROPN
ejpam-3912	72	14	j	j	PROPN
ejpam-3912	72	15	=	=	NOUN
ejpam-3912	72	16	i+1	i+1	ADV
ejpam-3912	72	17	aijej	aijej	NOUN
ejpam-3912	72	18	,	,	PUNCT
ejpam-3912	72	19	i	i	PRON
ejpam-3912	72	20	≤	≤	VERB
ejpam-3912	72	21	n−	n−	NOUN
ejpam-3912	72	22	2	2	NUM
ejpam-3912	72	23	;	;	PUNCT
ejpam-3912	72	24	0	0	NUM
ejpam-3912	72	25	,	,	PUNCT
ejpam-3912	72	26	i	i	PRON
ejpam-3912	72	27	∈	∈	PROPN
ejpam-3912	72	28	{	{	PUNCT
ejpam-3912	72	29	n−	n−	NOUN
ejpam-3912	72	30	1	1	NUM
ejpam-3912	72	31	,	,	PUNCT
ejpam-3912	72	32	n	n	CCONJ
ejpam-3912	72	33	}	}	PUNCT
ejpam-3912	72	34	.	.	PUNCT
ejpam-3912	73	1	(	(	PUNCT
ejpam-3912	73	2	2	2	X
ejpam-3912	73	3	)	)	PUNCT
ejpam-3912	73	4	where	where	SCONJ
ejpam-3912	73	5	aij	aij	PROPN
ejpam-3912	73	6	∈	∈	PROPN
ejpam-3912	73	7	k	k	PROPN
ejpam-3912	73	8	and	and	CCONJ
ejpam-3912	73	9	ai	ai	VERB
ejpam-3912	73	10	,	,	PUNCT
ejpam-3912	73	11	i+1	i+1	ADJ
ejpam-3912	73	12	6=	6=	ADP
ejpam-3912	73	13	0	0	NUM
ejpam-3912	73	14	for	for	ADP
ejpam-3912	73	15	any	any	DET
ejpam-3912	73	16	i	i	PRON
ejpam-3912	73	17	<	<	X
ejpam-3912	73	18	n−	n−	NOUN
ejpam-3912	73	19	1	1	NUM
ejpam-3912	73	20	.	.	PUNCT
ejpam-3912	73	21	theorem	theorem	NOUN
ejpam-3912	73	22	2	2	NUM
ejpam-3912	73	23	.	.	PUNCT
ejpam-3912	74	1	[	[	X
ejpam-3912	74	2	11	11	NUM
ejpam-3912	74	3	]	]	PUNCT
ejpam-3912	74	4	let	let	VERB
ejpam-3912	74	5	e	e	PRON
ejpam-3912	74	6	be	be	AUX
ejpam-3912	74	7	a	a	DET
ejpam-3912	74	8	nilpotent	nilpotent	ADJ
ejpam-3912	74	9	evolution	evolution	NOUN
ejpam-3912	74	10	algebra	algebra	NOUN
ejpam-3912	74	11	.	.	PUNCT
ejpam-3912	75	1	then	then	ADV
ejpam-3912	75	2	,	,	PUNCT
ejpam-3912	75	3	e	e	NOUN
ejpam-3912	75	4	has	have	VERB
ejpam-3912	75	5	maximal	maximal	ADJ
ejpam-3912	75	6	index	index	NOUN
ejpam-3912	75	7	of	of	ADP
ejpam-3912	75	8	nilpotency	nilpotency	NOUN
ejpam-3912	75	9	2(n−2	2(n−2	PROPN
ejpam-3912	75	10	)	)	PUNCT
ejpam-3912	76	1	+	+	CCONJ
ejpam-3912	76	2	1	1	NUM
ejpam-3912	76	3	if	if	SCONJ
ejpam-3912	76	4	and	and	CCONJ
ejpam-3912	76	5	only	only	ADV
ejpam-3912	76	6	if	if	SCONJ
ejpam-3912	76	7	the	the	DET
ejpam-3912	76	8	multiplication	multiplication	NOUN
ejpam-3912	76	9	table	table	NOUN
ejpam-3912	76	10	of	of	ADP
ejpam-3912	76	11	e	e	PROPN
ejpam-3912	76	12	is	be	AUX
ejpam-3912	76	13	given	give	VERB
ejpam-3912	76	14	by	by	ADP
ejpam-3912	76	15	(	(	PUNCT
ejpam-3912	76	16	2	2	NUM
ejpam-3912	76	17	)	)	PUNCT
ejpam-3912	76	18	.	.	PUNCT
ejpam-3912	77	1	a.	a.	PROPN
ejpam-3912	77	2	alarafeen	alarafeen	PROPN
ejpam-3912	77	3	,	,	PUNCT
ejpam-3912	77	4	i.	i.	PROPN
ejpam-3912	77	5	qaralleh	qaralleh	PROPN
ejpam-3912	77	6	,	,	PUNCT
ejpam-3912	77	7	a.	a.	PROPN
ejpam-3912	77	8	ahmad	ahmad	PROPN
ejpam-3912	77	9	/	/	SYM
ejpam-3912	77	10	eur	eur	PROPN
ejpam-3912	77	11	.	.	PUNCT
ejpam-3912	78	1	j.	j.	PROPN
ejpam-3912	78	2	pure	pure	PROPN
ejpam-3912	78	3	appl	appl	PROPN
ejpam-3912	78	4	.	.	PROPN
ejpam-3912	78	5	math	math	PROPN
ejpam-3912	78	6	,	,	PUNCT
ejpam-3912	78	7	14	14	NUM
ejpam-3912	78	8	(	(	PUNCT
ejpam-3912	78	9	1	1	NUM
ejpam-3912	78	10	)	)	PUNCT
ejpam-3912	78	11	(	(	PUNCT
ejpam-3912	78	12	2021	2021	NUM
ejpam-3912	78	13	)	)	PUNCT
ejpam-3912	78	14	,	,	PUNCT
ejpam-3912	78	15	278	278	NUM
ejpam-3912	78	16	-	-	SYM
ejpam-3912	78	17	300	300	NUM
ejpam-3912	78	18	281	281	NUM
ejpam-3912	78	19	in	in	ADP
ejpam-3912	78	20	the	the	DET
ejpam-3912	78	21	following	following	NOUN
ejpam-3912	78	22	,	,	PUNCT
ejpam-3912	78	23	we	we	PRON
ejpam-3912	78	24	will	will	AUX
ejpam-3912	78	25	work	work	VERB
ejpam-3912	78	26	with	with	ADP
ejpam-3912	78	27	nilpotent	nilpotent	ADJ
ejpam-3912	78	28	evolution	evolution	NOUN
ejpam-3912	78	29	algebras	algebra	NOUN
ejpam-3912	78	30	with	with	ADP
ejpam-3912	78	31	2(n−2	2(n−2	NUM
ejpam-3912	78	32	)	)	PUNCT
ejpam-3912	78	33	+	+	SYM
ejpam-3912	78	34	1	1	NUM
ejpam-3912	78	35	index	index	NOUN
ejpam-3912	78	36	of	of	ADP
ejpam-3912	78	37	nilpotency	nilpotency	NOUN
ejpam-3912	78	38	.	.	PUNCT
ejpam-3912	79	1	due	due	ADP
ejpam-3912	79	2	to	to	ADP
ejpam-3912	79	3	the	the	DET
ejpam-3912	79	4	last	last	ADJ
ejpam-3912	79	5	theorem	theorem	NOUN
ejpam-3912	79	6	,	,	PUNCT
ejpam-3912	79	7	we	we	PRON
ejpam-3912	79	8	only	only	ADV
ejpam-3912	79	9	consider	consider	VERB
ejpam-3912	79	10	evolution	evolution	NOUN
ejpam-3912	79	11	algebras	algebra	NOUN
ejpam-3912	79	12	with	with	ADP
ejpam-3912	79	13	the	the	DET
ejpam-3912	79	14	multiplication	multiplication	NOUN
ejpam-3912	79	15	table	table	NOUN
ejpam-3912	79	16	given	give	VERB
ejpam-3912	79	17	by	by	ADP
ejpam-3912	79	18	(	(	PUNCT
ejpam-3912	79	19	2	2	NUM
ejpam-3912	79	20	)	)	PUNCT
ejpam-3912	79	21	.	.	PUNCT
ejpam-3912	80	1	lemma	lemma	PROPN
ejpam-3912	80	2	1	1	X
ejpam-3912	80	3	.	.	PUNCT
ejpam-3912	81	1	let	let	VERB
ejpam-3912	82	1	e1	e1	PROPN
ejpam-3912	82	2	,	,	PUNCT
ejpam-3912	82	3	e2	e2	PROPN
ejpam-3912	82	4	be	be	VERB
ejpam-3912	82	5	two	two	NUM
ejpam-3912	82	6	isomorphic	isomorphic	ADJ
ejpam-3912	82	7	evolution	evolution	NOUN
ejpam-3912	82	8	algebras	algebra	NOUN
ejpam-3912	82	9	.	.	PUNCT
ejpam-3912	83	1	then	then	ADV
ejpam-3912	83	2	,	,	PUNCT
ejpam-3912	83	3	der(e1	der(e1	PROPN
ejpam-3912	83	4	)	)	PUNCT
ejpam-3912	83	5	∼=	∼=	PROPN
ejpam-3912	83	6	der(e2	der(e2	NOUN
ejpam-3912	83	7	)	)	PUNCT
ejpam-3912	83	8	.	.	PUNCT
ejpam-3912	84	1	lemma	lemma	PROPN
ejpam-3912	84	2	2	2	X
ejpam-3912	84	3	.	.	PUNCT
ejpam-3912	85	1	let	let	VERB
ejpam-3912	85	2	e	e	NOUN
ejpam-3912	85	3	and	and	CCONJ
ejpam-3912	85	4	e′	e′	VERB
ejpam-3912	85	5	be	be	AUX
ejpam-3912	85	6	evolution	evolution	NOUN
ejpam-3912	85	7	algebras	algebra	NOUN
ejpam-3912	85	8	with	with	ADP
ejpam-3912	85	9	basis	basis	NOUN
ejpam-3912	85	10	{	{	PUNCT
ejpam-3912	85	11	ei}ni=1	ei}ni=1	PROPN
ejpam-3912	85	12	and	and	CCONJ
ejpam-3912	85	13	{	{	PUNCT
ejpam-3912	85	14	fi}ni=1	fi}ni=1	ADV
ejpam-3912	85	15	respectively	respectively	ADV
ejpam-3912	85	16	,	,	PUNCT
ejpam-3912	85	17	defined	define	VERB
ejpam-3912	85	18	by	by	ADP
ejpam-3912	85	19	e2	e2	PROPN
ejpam-3912	86	1	i	i	PRON
ejpam-3912	86	2	=	=	PUNCT
ejpam-3912	86	3	{	{	PUNCT
ejpam-3912	86	4	ai	ai	PROPN
ejpam-3912	86	5	,	,	PUNCT
ejpam-3912	86	6	i+1ei+1	i+1ei+1	NOUN
ejpam-3912	86	7	+	+	CCONJ
ejpam-3912	86	8	ain−1en−1	ain−1en−1	ADJ
ejpam-3912	86	9	+	+	CCONJ
ejpam-3912	86	10	ainen	ainen	NOUN
ejpam-3912	86	11	,	,	PUNCT
ejpam-3912	87	1	i	i	PRON
ejpam-3912	87	2	<	<	X
ejpam-3912	87	3	n−	n−	NOUN
ejpam-3912	87	4	1	1	NUM
ejpam-3912	87	5	;	;	PUNCT
ejpam-3912	87	6	0	0	NUM
ejpam-3912	87	7	,	,	PUNCT
ejpam-3912	87	8	i	i	PRON
ejpam-3912	87	9	∈	∈	PROPN
ejpam-3912	87	10	{	{	PUNCT
ejpam-3912	87	11	n−	n−	NOUN
ejpam-3912	87	12	1	1	NUM
ejpam-3912	87	13	,	,	PUNCT
ejpam-3912	87	14	n	n	CCONJ
ejpam-3912	87	15	}	}	PUNCT
ejpam-3912	87	16	.	.	PUNCT
ejpam-3912	88	1	f2	f2	PROPN
ejpam-3912	89	1	i	i	PRON
ejpam-3912	89	2	=	=	X
ejpam-3912	89	3	{	{	PUNCT
ejpam-3912	89	4	fi+1	fi+1	NOUN
ejpam-3912	89	5	,	,	PUNCT
ejpam-3912	89	6	i	i	PRON
ejpam-3912	89	7	<	<	X
ejpam-3912	89	8	n−	n−	NOUN
ejpam-3912	89	9	1	1	NUM
ejpam-3912	89	10	;	;	PUNCT
ejpam-3912	89	11	0	0	NUM
ejpam-3912	89	12	,	,	PUNCT
ejpam-3912	89	13	i	i	PRON
ejpam-3912	89	14	∈	∈	PROPN
ejpam-3912	89	15	{	{	PUNCT
ejpam-3912	89	16	n−	n−	NOUN
ejpam-3912	89	17	1	1	NUM
ejpam-3912	89	18	,	,	PUNCT
ejpam-3912	89	19	n	n	CCONJ
ejpam-3912	89	20	}	}	PUNCT
ejpam-3912	89	21	.	.	PUNCT
ejpam-3912	90	1	if	if	SCONJ
ejpam-3912	90	2	ai	ai	VERB
ejpam-3912	90	3	,	,	PUNCT
ejpam-3912	90	4	i+1	i+1	NUM
ejpam-3912	90	5	6=	6=	ADP
ejpam-3912	90	6	0	0	NUM
ejpam-3912	90	7	for	for	ADP
ejpam-3912	90	8	every	every	DET
ejpam-3912	90	9	i	i	PRON
ejpam-3912	90	10	<	<	X
ejpam-3912	90	11	n−	n−	NOUN
ejpam-3912	90	12	1	1	NUM
ejpam-3912	90	13	,	,	PUNCT
ejpam-3912	90	14	then	then	ADV
ejpam-3912	90	15	e	e	X
ejpam-3912	90	16	∼=	∼=	ADV
ejpam-3912	90	17	e′.	e′.	ADJ
ejpam-3912	90	18	proof	proof	NOUN
ejpam-3912	90	19	.	.	PUNCT
ejpam-3912	91	1	let	let	VERB
ejpam-3912	91	2	ai	ai	VERB
ejpam-3912	91	3	,	,	PUNCT
ejpam-3912	91	4	i+1	i+1	ADJ
ejpam-3912	91	5	6=	6=	ADP
ejpam-3912	91	6	0	0	NUM
ejpam-3912	91	7	for	for	ADP
ejpam-3912	91	8	every	every	DET
ejpam-3912	91	9	i	i	PRON
ejpam-3912	91	10	<	<	X
ejpam-3912	91	11	n−	n−	NOUN
ejpam-3912	91	12	1	1	NUM
ejpam-3912	91	13	.	.	PUNCT
ejpam-3912	92	1	if	if	SCONJ
ejpam-3912	92	2	n	n	NOUN
ejpam-3912	92	3	=	=	SYM
ejpam-3912	92	4	3	3	NUM
ejpam-3912	92	5	after	after	ADP
ejpam-3912	92	6	changing	change	VERB
ejpam-3912	92	7	the	the	DET
ejpam-3912	92	8	basis	basis	NOUN
ejpam-3912	92	9	e1	e1	NOUN
ejpam-3912	92	10	,	,	PUNCT
ejpam-3912	92	11	e2	e2	PROPN
ejpam-3912	92	12	,	,	PUNCT
ejpam-3912	92	13	e3	e3	NOUN
ejpam-3912	92	14	to	to	ADP
ejpam-3912	92	15	f1	f1	NOUN
ejpam-3912	92	16	=	=	SYM
ejpam-3912	92	17	e1	e1	PROPN
ejpam-3912	92	18	,	,	PUNCT
ejpam-3912	92	19	f2	f2	PROPN
ejpam-3912	92	20	=	=	PROPN
ejpam-3912	92	21	e2	e2	PROPN
ejpam-3912	92	22	1	1	NUM
ejpam-3912	92	23	,	,	PUNCT
ejpam-3912	92	24	and	and	CCONJ
ejpam-3912	92	25	f3	f3	PROPN
ejpam-3912	92	26	=	=	SYM
ejpam-3912	92	27	e3	e3	NOUN
ejpam-3912	92	28	,	,	PUNCT
ejpam-3912	92	29	we	we	PRON
ejpam-3912	92	30	immediately	immediately	ADV
ejpam-3912	92	31	get	get	VERB
ejpam-3912	92	32	e′.	e′.	NOUN
ejpam-3912	92	33	so	so	ADV
ejpam-3912	92	34	.	.	PUNCT
ejpam-3912	93	1	let	let	VERB
ejpam-3912	93	2	us	we	PRON
ejpam-3912	93	3	suppose	suppose	VERB
ejpam-3912	93	4	n	n	PRON
ejpam-3912	93	5	≥	≥	NUM
ejpam-3912	93	6	4	4	NUM
ejpam-3912	93	7	.	.	PUNCT
ejpam-3912	94	1	then	then	ADV
ejpam-3912	94	2	,	,	PUNCT
ejpam-3912	94	3	the	the	DET
ejpam-3912	94	4	linear	linear	PROPN
ejpam-3912	94	5	mapping	mapping	NOUN
ejpam-3912	94	6	ϕ	ϕ	NOUN
ejpam-3912	94	7	:	:	PUNCT
ejpam-3912	94	8	e→	e→	PROPN
ejpam-3912	94	9	e′	e′	PROPN
ejpam-3912	94	10	defined	define	VERB
ejpam-3912	94	11	by	by	ADP
ejpam-3912	94	12	ϕ	ϕ	NOUN
ejpam-3912	94	13	:	:	PUNCT
ejpam-3912	94	14			PROPN
ejpam-3912	94	15	f1	f1	NOUN
ejpam-3912	94	16	=	=	PUNCT
ejpam-3912	94	17	e1	e1	PROPN
ejpam-3912	94	18	f2	f2	PROPN
ejpam-3912	94	19	=	=	SYM
ejpam-3912	94	20	e2	e2	PROPN
ejpam-3912	94	21	1	1	NUM
ejpam-3912	94	22	fi+1	fi+1	NOUN
ejpam-3912	94	23	=	=	SYM
ejpam-3912	94	24	i−1∏	i−1∏	PROPN
ejpam-3912	94	25	k=1	k=1	NOUN
ejpam-3912	94	26	a2i−k	a2i−k	PROPN
ejpam-3912	94	27	k	k	PROPN
ejpam-3912	94	28	,	,	PUNCT
ejpam-3912	94	29	k+1e	k+1e	PROPN
ejpam-3912	94	30	2	2	NUM
ejpam-3912	94	31	i	i	NOUN
ejpam-3912	94	32	,	,	PUNCT
ejpam-3912	94	33	2	2	NUM
ejpam-3912	94	34	≤	≤	NUM
ejpam-3912	95	1	i	i	PRON
ejpam-3912	95	2	<	<	X
ejpam-3912	95	3	n−	n−	PROPN
ejpam-3912	95	4	1	1	NUM
ejpam-3912	95	5	fn	fn	NOUN
ejpam-3912	95	6	=	=	SYM
ejpam-3912	95	7	en	en	X
ejpam-3912	95	8	(	(	PUNCT
ejpam-3912	95	9	3	3	NUM
ejpam-3912	95	10	)	)	PUNCT
ejpam-3912	95	11	is	be	AUX
ejpam-3912	95	12	an	an	DET
ejpam-3912	95	13	isomorphism	isomorphism	NOUN
ejpam-3912	95	14	from	from	ADP
ejpam-3912	95	15	e	e	PRON
ejpam-3912	95	16	to	to	ADP
ejpam-3912	95	17	e′.	e′.	PROPN
ejpam-3912	95	18	3	3	NUM
ejpam-3912	95	19	.	.	PUNCT
ejpam-3912	95	20	derivations	derivation	NOUN
ejpam-3912	95	21	in	in	ADP
ejpam-3912	95	22	this	this	DET
ejpam-3912	95	23	section	section	NOUN
ejpam-3912	95	24	,	,	PUNCT
ejpam-3912	95	25	we	we	PRON
ejpam-3912	95	26	consider	consider	VERB
ejpam-3912	95	27	derivations	derivation	NOUN
ejpam-3912	95	28	of	of	ADP
ejpam-3912	95	29	nilpotent	nilpotent	ADJ
ejpam-3912	95	30	evolution	evolution	NOUN
ejpam-3912	95	31	algebras	algebra	NOUN
ejpam-3912	95	32	with	with	ADP
ejpam-3912	95	33	2n−2	2n−2	PROPN
ejpam-3912	95	34	+	+	SYM
ejpam-3912	95	35	1	1	NUM
ejpam-3912	95	36	index	index	NOUN
ejpam-3912	95	37	of	of	ADP
ejpam-3912	95	38	nilpotency	nilpotency	NOUN
ejpam-3912	95	39	.	.	PUNCT
ejpam-3912	96	1	recall	recall	VERB
ejpam-3912	96	2	that	that	DET
ejpam-3912	96	3	derivation	derivation	NOUN
ejpam-3912	96	4	of	of	ADP
ejpam-3912	96	5	an	an	DET
ejpam-3912	96	6	evolution	evolution	NOUN
ejpam-3912	96	7	algebra	algebra	NOUN
ejpam-3912	96	8	e	e	NOUN
ejpam-3912	96	9	is	be	AUX
ejpam-3912	96	10	a	a	DET
ejpam-3912	96	11	linear	linear	ADJ
ejpam-3912	96	12	mapping	mapping	NOUN
ejpam-3912	97	1	d	d	NOUN
ejpam-3912	97	2	:	:	PUNCT
ejpam-3912	97	3	e	e	X
ejpam-3912	97	4	→	→	PUNCT
ejpam-3912	97	5	e	e	X
ejpam-3912	97	6	such	such	ADJ
ejpam-3912	97	7	that	that	DET
ejpam-3912	97	8	d(uv	d(uv	NOUN
ejpam-3912	97	9	)	)	PUNCT
ejpam-3912	97	10	=	=	SYM
ejpam-3912	98	1	d(u)v	d(u)v	PROPN
ejpam-3912	99	1	+	+	CCONJ
ejpam-3912	99	2	ud(v	ud(v	NUM
ejpam-3912	99	3	)	)	PUNCT
ejpam-3912	99	4	for	for	ADP
ejpam-3912	99	5	all	all	DET
ejpam-3912	99	6	u	u	NOUN
ejpam-3912	99	7	,	,	PUNCT
ejpam-3912	99	8	v	v	PROPN
ejpam-3912	99	9	∈	∈	PROPN
ejpam-3912	99	10	e.	e.	NOUN
ejpam-3912	99	11	we	we	PRON
ejpam-3912	99	12	note	note	VERB
ejpam-3912	99	13	that	that	SCONJ
ejpam-3912	99	14	for	for	ADP
ejpam-3912	99	15	any	any	DET
ejpam-3912	99	16	algebra	algebra	NOUN
ejpam-3912	99	17	,	,	PUNCT
ejpam-3912	99	18	the	the	DET
ejpam-3912	99	19	space	space	NOUN
ejpam-3912	99	20	der(e	der(e	PROPN
ejpam-3912	99	21	)	)	PUNCT
ejpam-3912	99	22	of	of	ADP
ejpam-3912	99	23	all	all	DET
ejpam-3912	99	24	derivations	derivation	NOUN
ejpam-3912	99	25	is	be	AUX
ejpam-3912	99	26	a	a	DET
ejpam-3912	99	27	lie	lie	NOUN
ejpam-3912	99	28	algebra	algebra	NOUN
ejpam-3912	99	29	w.r.t	w.r.t	VERB
ejpam-3912	99	30	.	.	PUNCT
ejpam-3912	100	1	the	the	DET
ejpam-3912	100	2	commutator	commutator	NOUN
ejpam-3912	100	3	multiplication	multiplication	NOUN
ejpam-3912	100	4	:	:	PUNCT
ejpam-3912	100	5	[	[	X
ejpam-3912	100	6	d1	d1	NOUN
ejpam-3912	100	7	,	,	PUNCT
ejpam-3912	100	8	d2	d2	PROPN
ejpam-3912	100	9	]	]	PUNCT
ejpam-3912	100	10	=	=	PUNCT
ejpam-3912	100	11	d1d2	d1d2	PUNCT
ejpam-3912	100	12	−	−	NOUN
ejpam-3912	100	13	d2d1	d2d1	NOUN
ejpam-3912	100	14	,	,	PUNCT
ejpam-3912	100	15	∀d1	∀d1	ADJ
ejpam-3912	100	16	,	,	PUNCT
ejpam-3912	100	17	d2	d2	PROPN
ejpam-3912	100	18	∈	∈	PROPN
ejpam-3912	100	19	der(e	der(e	PROPN
ejpam-3912	100	20	)	)	PUNCT
ejpam-3912	100	21	.	.	PUNCT
ejpam-3912	101	1	for	for	ADP
ejpam-3912	101	2	a	a	DET
ejpam-3912	101	3	given	give	VERB
ejpam-3912	101	4	structural	structural	ADJ
ejpam-3912	101	5	matrixa	matrixa	NOUN
ejpam-3912	101	6	=	=	SYM
ejpam-3912	101	7	(	(	PUNCT
ejpam-3912	101	8	aij	aij	PROPN
ejpam-3912	101	9	)	)	PUNCT
ejpam-3912	101	10	n	n	PROPN
ejpam-3912	101	11	i	i	PRON
ejpam-3912	101	12	,	,	PUNCT
ejpam-3912	101	13	j≥1	j≥1	ADV
ejpam-3912	101	14	of	of	ADP
ejpam-3912	101	15	nilpotent	nilpotent	ADJ
ejpam-3912	101	16	evolution	evolution	NOUN
ejpam-3912	101	17	algebra	algebra	PROPN
ejpam-3912	101	18	e	e	NOUN
ejpam-3912	101	19	with	with	ADP
ejpam-3912	101	20	dim(e2	dim(e2	PROPN
ejpam-3912	101	21	)	)	PUNCT
ejpam-3912	101	22	=	=	NUM
ejpam-3912	101	23	n−	n−	NOUN
ejpam-3912	101	24	2	2	NUM
ejpam-3912	101	25	,	,	PUNCT
ejpam-3912	101	26	we	we	PRON
ejpam-3912	101	27	denote	denote	VERB
ejpam-3912	101	28	ia	ia	PROPN
ejpam-3912	101	29	=	=	PUNCT
ejpam-3912	101	30	{	{	PUNCT
ejpam-3912	101	31	(	(	PUNCT
ejpam-3912	101	32	i	i	PROPN
ejpam-3912	101	33	,	,	PUNCT
ejpam-3912	101	34	j	j	PROPN
ejpam-3912	101	35	)	)	PUNCT
ejpam-3912	101	36	:	:	PUNCT
ejpam-3912	101	37	i+	i+	NUM
ejpam-3912	101	38	1	1	NUM
ejpam-3912	101	39	<	<	X
ejpam-3912	101	40	j	j	X
ejpam-3912	101	41	<	<	X
ejpam-3912	101	42	n−	n−	PROPN
ejpam-3912	101	43	1	1	NUM
ejpam-3912	101	44	,	,	PUNCT
ejpam-3912	101	45	aij	aij	PROPN
ejpam-3912	101	46	6=	6=	PROPN
ejpam-3912	101	47	0	0	NUM
ejpam-3912	101	48	}	}	PUNCT
ejpam-3912	101	49	.	.	PUNCT
ejpam-3912	102	1	(	(	PUNCT
ejpam-3912	102	2	4	4	X
ejpam-3912	102	3	)	)	PUNCT
ejpam-3912	102	4	theorem	theorem	NOUN
ejpam-3912	102	5	3	3	X
ejpam-3912	102	6	.	.	PUNCT
ejpam-3912	103	1	let	let	VERB
ejpam-3912	103	2	e	e	PRON
ejpam-3912	103	3	be	be	AUX
ejpam-3912	103	4	an	an	DET
ejpam-3912	103	5	evolution	evolution	NOUN
ejpam-3912	103	6	algebra	algebra	NOUN
ejpam-3912	103	7	with	with	ADP
ejpam-3912	103	8	structural	structural	ADJ
ejpam-3912	103	9	matrix	matrix	NOUN
ejpam-3912	103	10	a	a	PRON
ejpam-3912	103	11	=	=	X
ejpam-3912	103	12	(	(	PUNCT
ejpam-3912	103	13	aij	aij	PROPN
ejpam-3912	103	14	)	)	PUNCT
ejpam-3912	104	1	n	n	PROPN
ejpam-3912	104	2	i	i	PRON
ejpam-3912	104	3	,	,	PUNCT
ejpam-3912	104	4	j≥1	j≥1	ADV
ejpam-3912	104	5	in	in	ADP
ejpam-3912	104	6	a	a	DET
ejpam-3912	104	7	natural	natural	ADJ
ejpam-3912	104	8	basis	basis	NOUN
ejpam-3912	104	9	{	{	PUNCT
ejpam-3912	104	10	ei}ni=1	ei}ni=1	NOUN
ejpam-3912	104	11	.	.	PUNCT
ejpam-3912	105	1	if	if	SCONJ
ejpam-3912	105	2	e	e	PROPN
ejpam-3912	105	3	is	be	AUX
ejpam-3912	105	4	a	a	DET
ejpam-3912	105	5	nilpotent	nilpotent	NOUN
ejpam-3912	105	6	with	with	ADP
ejpam-3912	105	7	ranka	ranka	PROPN
ejpam-3912	105	8	=	=	PROPN
ejpam-3912	105	9	n−2	n−2	PROPN
ejpam-3912	105	10	,	,	PUNCT
ejpam-3912	105	11	then	then	ADV
ejpam-3912	105	12	the	the	DET
ejpam-3912	105	13	following	follow	VERB
ejpam-3912	105	14	statements	statement	NOUN
ejpam-3912	105	15	hold	hold	VERB
ejpam-3912	105	16	a.	a.	PROPN
ejpam-3912	105	17	alarafeen	alarafeen	PROPN
ejpam-3912	105	18	,	,	PUNCT
ejpam-3912	105	19	i.	i.	PROPN
ejpam-3912	105	20	qaralleh	qaralleh	PROPN
ejpam-3912	105	21	,	,	PUNCT
ejpam-3912	105	22	a.	a.	PROPN
ejpam-3912	105	23	ahmad	ahmad	PROPN
ejpam-3912	105	24	/	/	SYM
ejpam-3912	105	25	eur	eur	PROPN
ejpam-3912	105	26	.	.	PUNCT
ejpam-3912	106	1	j.	j.	PROPN
ejpam-3912	106	2	pure	pure	PROPN
ejpam-3912	106	3	appl	appl	PROPN
ejpam-3912	106	4	.	.	PROPN
ejpam-3912	106	5	math	math	PROPN
ejpam-3912	106	6	,	,	PUNCT
ejpam-3912	106	7	14	14	NUM
ejpam-3912	106	8	(	(	PUNCT
ejpam-3912	106	9	1	1	NUM
ejpam-3912	106	10	)	)	PUNCT
ejpam-3912	106	11	(	(	PUNCT
ejpam-3912	106	12	2021	2021	NUM
ejpam-3912	106	13	)	)	PUNCT
ejpam-3912	106	14	,	,	PUNCT
ejpam-3912	106	15	278	278	NUM
ejpam-3912	106	16	-	-	SYM
ejpam-3912	106	17	300	300	NUM
ejpam-3912	106	18	282	282	NUM
ejpam-3912	106	19	(	(	PUNCT
ejpam-3912	106	20	i	i	NOUN
ejpam-3912	106	21	)	)	PUNCT
ejpam-3912	106	22	if	if	SCONJ
ejpam-3912	106	23	ia	ia	PROPN
ejpam-3912	106	24	6=	6=	PUNCT
ejpam-3912	106	25	∅	∅	NOUN
ejpam-3912	106	26	,	,	PUNCT
ejpam-3912	106	27	then	then	ADV
ejpam-3912	106	28	der(e	der(e	PROPN
ejpam-3912	106	29	)	)	PUNCT
ejpam-3912	106	30	=	=	PRON
ejpam-3912	106	31			X
ejpam-3912	106	32			NOUN
ejpam-3912	106	33	0	0	NUM
ejpam-3912	106	34	0	0	NUM
ejpam-3912	106	35	.	.	PUNCT
ejpam-3912	106	36	.	.	PUNCT
ejpam-3912	106	37	.	.	PUNCT
ejpam-3912	107	1	d1n−1	d1n−1	PROPN
ejpam-3912	107	2	d1n	d1n	PROPN
ejpam-3912	107	3	0	0	NUM
ejpam-3912	107	4	0	0	NUM
ejpam-3912	107	5	.	.	PUNCT
ejpam-3912	107	6	.	.	PUNCT
ejpam-3912	107	7	.	.	PUNCT
ejpam-3912	108	1	d2n−1	d2n−1	PROPN
ejpam-3912	108	2	d2n	d2n	PROPN
ejpam-3912	108	3	...	...	PUNCT
ejpam-3912	108	4	...	...	PUNCT
ejpam-3912	108	5	.	.	PUNCT
ejpam-3912	108	6	.	.	PUNCT
ejpam-3912	108	7	.	.	PUNCT
ejpam-3912	109	1	...	...	PUNCT
ejpam-3912	110	1	...	...	PUNCT
ejpam-3912	111	1	0	0	NUM
ejpam-3912	111	2	0	0	NUM
ejpam-3912	111	3	.	.	PUNCT
ejpam-3912	111	4	.	.	PUNCT
ejpam-3912	111	5	.	.	PUNCT
ejpam-3912	112	1	dn−1n−1	dn−1n−1	PROPN
ejpam-3912	112	2	dn−1n	dn−1n	PROPN
ejpam-3912	112	3	0	0	NUM
ejpam-3912	112	4	0	0	NUM
ejpam-3912	112	5	.	.	PUNCT
ejpam-3912	112	6	.	.	PUNCT
ejpam-3912	112	7	.	.	PUNCT
ejpam-3912	113	1	dnn−1	dnn−1	PROPN
ejpam-3912	113	2	dnn	dnn	PROPN
ejpam-3912	113	3			NOUN
ejpam-3912	113	4			NOUN
ejpam-3912	113	5	where	where	SCONJ
ejpam-3912	113	6	dn−1,n−1	dn−1,n−1	ADJ
ejpam-3912	113	7	=	=	SYM
ejpam-3912	113	8	−an−2,ndn	−an−2,ndn	ADJ
ejpam-3912	113	9	,	,	PUNCT
ejpam-3912	113	10	n−1	n−1	PROPN
ejpam-3912	113	11	;	;	PUNCT
ejpam-3912	113	12	dn−1,n	dn−1,n	X
ejpam-3912	113	13	=	=	SYM
ejpam-3912	113	14	−an−2,ndnn	−an−2,ndnn	NOUN
ejpam-3912	113	15	;	;	PUNCT
ejpam-3912	113	16	dim	dim	ADJ
ejpam-3912	113	17	=	=	SYM
ejpam-3912	113	18	−	−	PROPN
ejpam-3912	113	19	n−i∑	n−i∑	PROPN
ejpam-3912	113	20	k=1	k=1	PROPN
ejpam-3912	113	21	ai−1,k+idk+i	ai−1,k+idk+i	PROPN
ejpam-3912	113	22	,	,	PUNCT
ejpam-3912	113	23	m	m	PROPN
ejpam-3912	113	24	,	,	PUNCT
ejpam-3912	113	25	m	m	VERB
ejpam-3912	113	26	∈	∈	NOUN
ejpam-3912	113	27	{	{	PUNCT
ejpam-3912	113	28	n−	n−	NOUN
ejpam-3912	113	29	1	1	NUM
ejpam-3912	113	30	,	,	PUNCT
ejpam-3912	113	31	n	n	CCONJ
ejpam-3912	113	32	}	}	PUNCT
ejpam-3912	113	33	(	(	PUNCT
ejpam-3912	113	34	ii	ii	NOUN
ejpam-3912	113	35	)	)	PUNCT
ejpam-3912	114	1	if	if	SCONJ
ejpam-3912	114	2	ia	ia	NOUN
ejpam-3912	114	3	=	=	SYM
ejpam-3912	114	4	∅	∅	NOUN
ejpam-3912	114	5	,	,	PUNCT
ejpam-3912	114	6	then	then	ADV
ejpam-3912	114	7	der(e	der(e	PROPN
ejpam-3912	114	8	)	)	PUNCT
ejpam-3912	114	9	=	=	SYM
ejpam-3912	114	10			NUM
ejpam-3912	114	11			NOUN
ejpam-3912	114	12	α	α	NOUN
ejpam-3912	114	13	0	0	PUNCT
ejpam-3912	114	14	.	.	PUNCT
ejpam-3912	114	15	.	.	PUNCT
ejpam-3912	114	16	.	.	PUNCT
ejpam-3912	115	1	β	β	X
ejpam-3912	115	2	γ	γ	X
ejpam-3912	115	3	0	0	NUM
ejpam-3912	115	4	2α	2α	NOUN
ejpam-3912	115	5	.	.	PUNCT
ejpam-3912	115	6	.	.	PUNCT
ejpam-3912	115	7	.	.	PUNCT
ejpam-3912	116	1	d2,n−1	d2,n−1	ADJ
ejpam-3912	116	2	d2n	d2n	NOUN
ejpam-3912	116	3	...	...	PUNCT
ejpam-3912	116	4	...	...	PUNCT
ejpam-3912	116	5	.	.	PUNCT
ejpam-3912	116	6	.	.	PUNCT
ejpam-3912	116	7	.	.	PUNCT
ejpam-3912	117	1	...	...	PUNCT
ejpam-3912	118	1	...	...	PUNCT
ejpam-3912	119	1	0	0	NUM
ejpam-3912	119	2	0	0	NUM
ejpam-3912	119	3	.	.	PUNCT
ejpam-3912	119	4	.	.	PUNCT
ejpam-3912	119	5	.	.	PUNCT
ejpam-3912	120	1	dn−2,n−1	dn−2,n−1	PROPN
ejpam-3912	120	2	dn−2,n	dn−2,n	PROPN
ejpam-3912	120	3	0	0	NUM
ejpam-3912	120	4	0	0	NUM
ejpam-3912	120	5	.	.	PUNCT
ejpam-3912	120	6	.	.	PUNCT
ejpam-3912	120	7	.	.	PUNCT
ejpam-3912	121	1	dn−1,n−1	dn−1,n−1	ADJ
ejpam-3912	121	2	dn−1,n	dn−1,n	NOUN
ejpam-3912	121	3	0	0	NUM
ejpam-3912	121	4	0	0	NUM
ejpam-3912	121	5	.	.	PUNCT
ejpam-3912	121	6	.	.	PUNCT
ejpam-3912	121	7	.	.	PUNCT
ejpam-3912	122	1	s	s	PROPN
ejpam-3912	122	2	t	t	NOUN
ejpam-3912	122	3			PROPN
ejpam-3912	122	4	:	:	PUNCT
ejpam-3912	123	1	α	α	X
ejpam-3912	123	2	,	,	PUNCT
ejpam-3912	123	3	β	β	X
ejpam-3912	123	4	,	,	PUNCT
ejpam-3912	123	5	γ	γ	PROPN
ejpam-3912	123	6	,	,	PUNCT
ejpam-3912	123	7	s	s	PROPN
ejpam-3912	123	8	,	,	PUNCT
ejpam-3912	123	9	t	t	PROPN
ejpam-3912	123	10	∈	∈	PROPN
ejpam-3912	123	11	k	k	PROPN
ejpam-3912	123	12			VERB
ejpam-3912	123	13	where	where	SCONJ
ejpam-3912	123	14	dn−1,n−1	dn−1,n−1	ADJ
ejpam-3912	123	15	=	=	SYM
ejpam-3912	123	16	2n−2α−	2n−2α−	NUM
ejpam-3912	123	17	an−2,ns	an−2,ns	ADJ
ejpam-3912	123	18	dn−1,n	dn−1,n	NOUN
ejpam-3912	123	19	=	=	PUNCT
ejpam-3912	123	20	(	(	PUNCT
ejpam-3912	123	21	2n−2	2n−2	NUM
ejpam-3912	123	22	−	−	PROPN
ejpam-3912	123	23	t)an−2,n	t)an−2,n	X
ejpam-3912	123	24	di	di	NOUN
ejpam-3912	123	25	,	,	PUNCT
ejpam-3912	123	26	n−1	n−1	PROPN
ejpam-3912	123	27	=	=	SYM
ejpam-3912	123	28	(	(	PUNCT
ejpam-3912	123	29	2i−1	2i−1	NUM
ejpam-3912	123	30	−	−	PROPN
ejpam-3912	123	31	2n−2)αai−1,n−1	2n−2)αai−1,n−1	PROPN
ejpam-3912	123	32	+	+	CCONJ
ejpam-3912	123	33	(	(	PUNCT
ejpam-3912	123	34	ai−1,n−1an−2,n	ai−1,n−1an−2,n	ADV
ejpam-3912	123	35	−	−	PROPN
ejpam-3912	123	36	ai−1,n)s	ai−1,n)s	PROPN
ejpam-3912	123	37	di	di	PROPN
ejpam-3912	123	38	,	,	PUNCT
ejpam-3912	123	39	n	n	NOUN
ejpam-3912	123	40	=	=	SYM
ejpam-3912	123	41	ai−1,n−1dn−1,n	ai−1,n−1dn−1,n	NOUN
ejpam-3912	123	42	+	+	CCONJ
ejpam-3912	123	43	an−2,n(2i−1α−	an−2,n(2i−1α−	PROPN
ejpam-3912	123	44	t	t	PROPN
ejpam-3912	123	45	)	)	PUNCT
ejpam-3912	123	46	,	,	PUNCT
ejpam-3912	123	47	2	2	NUM
ejpam-3912	123	48	≤	≤	NUM
ejpam-3912	124	1	i	i	PRON
ejpam-3912	124	2	<	<	X
ejpam-3912	124	3	n−	n−	NOUN
ejpam-3912	124	4	1	1	NUM
ejpam-3912	124	5	.	.	PUNCT
ejpam-3912	125	1	proof	proof	NOUN
ejpam-3912	125	2	.	.	PUNCT
ejpam-3912	126	1	the	the	DET
ejpam-3912	126	2	(	(	PUNCT
ejpam-3912	126	3	i	i	NOUN
ejpam-3912	126	4	)	)	PUNCT
ejpam-3912	126	5	and	and	CCONJ
ejpam-3912	126	6	(	(	PUNCT
ejpam-3912	126	7	ii	ii	NOUN
ejpam-3912	126	8	)	)	PUNCT
ejpam-3912	126	9	are	be	AUX
ejpam-3912	126	10	easy	easy	ADJ
ejpam-3912	126	11	to	to	PART
ejpam-3912	126	12	check	check	VERB
ejpam-3912	126	13	for	for	ADP
ejpam-3912	126	14	n	n	NOUN
ejpam-3912	126	15	=	=	SYM
ejpam-3912	126	16	3	3	NUM
ejpam-3912	126	17	,	,	PUNCT
ejpam-3912	126	18	4	4	NUM
ejpam-3912	126	19	.	.	PUNCT
ejpam-3912	127	1	thus	thus	ADV
ejpam-3912	127	2	,	,	PUNCT
ejpam-3912	127	3	we	we	PRON
ejpam-3912	127	4	consider	consider	VERB
ejpam-3912	127	5	only	only	ADV
ejpam-3912	127	6	the	the	DET
ejpam-3912	127	7	case	case	NOUN
ejpam-3912	127	8	n	n	X
ejpam-3912	127	9	>	>	X
ejpam-3912	127	10	4	4	X
ejpam-3912	127	11	.	.	PUNCT
ejpam-3912	128	1	let	let	VERB
ejpam-3912	128	2	d	d	PRON
ejpam-3912	128	3	be	be	AUX
ejpam-3912	128	4	a	a	DET
ejpam-3912	128	5	derivation	derivation	NOUN
ejpam-3912	128	6	.	.	PUNCT
ejpam-3912	129	1	we	we	PRON
ejpam-3912	129	2	represent	represent	VERB
ejpam-3912	129	3	d	d	PROPN
ejpam-3912	129	4	in	in	ADP
ejpam-3912	129	5	a	a	DET
ejpam-3912	129	6	matrix	matrix	NOUN
ejpam-3912	129	7	form	form	NOUN
ejpam-3912	129	8	based	base	VERB
ejpam-3912	129	9	on	on	ADP
ejpam-3912	129	10	{	{	PUNCT
ejpam-3912	129	11	ei}ni=1	ei}ni=1	PROPN
ejpam-3912	129	12	as	as	SCONJ
ejpam-3912	129	13	follows	follow	VERB
ejpam-3912	129	14	:	:	PUNCT
ejpam-3912	129	15	d(ei	d(ei	X
ejpam-3912	129	16	)	)	PUNCT
ejpam-3912	129	17	=	=	SYM
ejpam-3912	130	1	∑n	∑n	NUM
ejpam-3912	130	2	j=1	j=1	PROPN
ejpam-3912	130	3	dijej	dijej	NOUN
ejpam-3912	130	4	.	.	PUNCT
ejpam-3912	131	1	then	then	ADV
ejpam-3912	131	2	,	,	PUNCT
ejpam-3912	131	3	we	we	PRON
ejpam-3912	131	4	have	have	VERB
ejpam-3912	131	5	djie	djie	NOUN
ejpam-3912	131	6	2	2	NUM
ejpam-3912	131	7	i	i	NOUN
ejpam-3912	131	8	+	+	CCONJ
ejpam-3912	131	9	dije	dije	X
ejpam-3912	131	10	2	2	NUM
ejpam-3912	131	11	j	j	NOUN
ejpam-3912	131	12	=	=	NOUN
ejpam-3912	131	13	0	0	PROPN
ejpam-3912	131	14	for	for	ADP
ejpam-3912	131	15	all	all	DET
ejpam-3912	131	16	1	1	NUM
ejpam-3912	131	17	≤	≤	NUM
ejpam-3912	132	1	i	i	PRON
ejpam-3912	132	2	<	<	X
ejpam-3912	132	3	j	j	PROPN
ejpam-3912	132	4	≤	≤	X
ejpam-3912	132	5	n.	n.	NOUN
ejpam-3912	132	6	as	as	ADP
ejpam-3912	132	7	e2	e2	PROPN
ejpam-3912	132	8	i	i	PRON
ejpam-3912	132	9	and	and	CCONJ
ejpam-3912	132	10	e2	e2	PROPN
ejpam-3912	132	11	j	j	PROPN
ejpam-3912	132	12	are	be	AUX
ejpam-3912	132	13	linearly	linearly	ADV
ejpam-3912	132	14	independent	independent	ADJ
ejpam-3912	132	15	,	,	PUNCT
ejpam-3912	132	16	then	then	ADV
ejpam-3912	132	17	dij	dij	VERB
ejpam-3912	132	18	=	=	SYM
ejpam-3912	132	19	dji	dji	PROPN
ejpam-3912	132	20	=	=	PUNCT
ejpam-3912	132	21	0	0	NUM
ejpam-3912	132	22	for	for	ADP
ejpam-3912	132	23	any	any	DET
ejpam-3912	132	24	1	1	NUM
ejpam-3912	132	25	≤	≤	NUM
ejpam-3912	133	1	i	i	PRON
ejpam-3912	133	2	<	<	X
ejpam-3912	133	3	j	j	X
ejpam-3912	133	4	<	<	X
ejpam-3912	133	5	n	n	CCONJ
ejpam-3912	133	6	−	−	PROPN
ejpam-3912	133	7	1	1	NUM
ejpam-3912	133	8	.	.	PUNCT
ejpam-3912	134	1	if	if	SCONJ
ejpam-3912	134	2	we	we	PRON
ejpam-3912	134	3	take	take	VERB
ejpam-3912	134	4	m	m	NOUN
ejpam-3912	134	5	∈	∈	NOUN
ejpam-3912	134	6	{	{	PUNCT
ejpam-3912	134	7	n	n	CCONJ
ejpam-3912	134	8	−	−	PROPN
ejpam-3912	134	9	1	1	NUM
ejpam-3912	134	10	,	,	PUNCT
ejpam-3912	134	11	n	n	CCONJ
ejpam-3912	134	12	}	}	PUNCT
ejpam-3912	134	13	,	,	PUNCT
ejpam-3912	134	14	then	then	ADV
ejpam-3912	134	15	considering	consider	VERB
ejpam-3912	134	16	that	that	SCONJ
ejpam-3912	134	17	e2	e2	PROPN
ejpam-3912	134	18	n−1	n−1	PROPN
ejpam-3912	134	19	=	=	PROPN
ejpam-3912	134	20	e2	e2	PROPN
ejpam-3912	134	21	n	n	PROPN
ejpam-3912	134	22	=	=	SYM
ejpam-3912	134	23	0	0	NUM
ejpam-3912	134	24	from	from	ADP
ejpam-3912	134	25	dmie	dmie	PROPN
ejpam-3912	134	26	2	2	NUM
ejpam-3912	134	27	i	i	NOUN
ejpam-3912	134	28	+	+	CCONJ
ejpam-3912	134	29	dime2	dime2	VERB
ejpam-3912	134	30	m	m	VERB
ejpam-3912	134	31	=	=	SYM
ejpam-3912	134	32	0	0	NUM
ejpam-3912	134	33	one	one	NUM
ejpam-3912	134	34	has	have	VERB
ejpam-3912	134	35	dmi	dmi	PROPN
ejpam-3912	134	36	=	=	SYM
ejpam-3912	134	37	0	0	PROPN
ejpam-3912	134	38	for	for	ADP
ejpam-3912	134	39	any	any	DET
ejpam-3912	134	40	i	i	PRON
ejpam-3912	134	41	<	<	X
ejpam-3912	134	42	m.	m.	NOUN
ejpam-3912	134	43	thus	thus	ADV
ejpam-3912	134	44	,	,	PUNCT
ejpam-3912	134	45	we	we	PRON
ejpam-3912	134	46	have	have	AUX
ejpam-3912	134	47	shown	show	VERB
ejpam-3912	134	48	the	the	DET
ejpam-3912	134	49	following	following	NOUN
ejpam-3912	134	50	:	:	PUNCT
ejpam-3912	134	51	dij	dij	PROPN
ejpam-3912	134	52	=	=	SYM
ejpam-3912	134	53	0	0	PROPN
ejpam-3912	134	54	,	,	PUNCT
ejpam-3912	134	55	if	if	SCONJ
ejpam-3912	134	56	i	i	PRON
ejpam-3912	134	57	6=	6=	PROPN
ejpam-3912	134	58	j	j	PROPN
ejpam-3912	134	59	,	,	PUNCT
ejpam-3912	134	60	i	i	PROPN
ejpam-3912	134	61	≤	≤	PROPN
ejpam-3912	134	62	n	n	CCONJ
ejpam-3912	134	63	,	,	PUNCT
ejpam-3912	134	64	j	j	PROPN
ejpam-3912	134	65	<	<	X
ejpam-3912	134	66	n−	n−	PROPN
ejpam-3912	134	67	1	1	NUM
ejpam-3912	134	68	.	.	PUNCT
ejpam-3912	135	1	(	(	PUNCT
ejpam-3912	135	2	5	5	X
ejpam-3912	135	3	)	)	PUNCT
ejpam-3912	135	4	a.	a.	NOUN
ejpam-3912	135	5	alarafeen	alarafeen	PROPN
ejpam-3912	135	6	,	,	PUNCT
ejpam-3912	135	7	i.	i.	PROPN
ejpam-3912	135	8	qaralleh	qaralleh	PROPN
ejpam-3912	135	9	,	,	PUNCT
ejpam-3912	135	10	a.	a.	PROPN
ejpam-3912	135	11	ahmad	ahmad	PROPN
ejpam-3912	135	12	/	/	SYM
ejpam-3912	135	13	eur	eur	PROPN
ejpam-3912	135	14	.	.	PUNCT
ejpam-3912	136	1	j.	j.	PROPN
ejpam-3912	136	2	pure	pure	PROPN
ejpam-3912	136	3	appl	appl	PROPN
ejpam-3912	136	4	.	.	PROPN
ejpam-3912	136	5	math	math	PROPN
ejpam-3912	136	6	,	,	PUNCT
ejpam-3912	136	7	14	14	NUM
ejpam-3912	136	8	(	(	PUNCT
ejpam-3912	136	9	1	1	NUM
ejpam-3912	136	10	)	)	PUNCT
ejpam-3912	136	11	(	(	PUNCT
ejpam-3912	136	12	2021	2021	NUM
ejpam-3912	136	13	)	)	PUNCT
ejpam-3912	136	14	,	,	PUNCT
ejpam-3912	136	15	278	278	NUM
ejpam-3912	136	16	-	-	SYM
ejpam-3912	136	17	300	300	NUM
ejpam-3912	136	18	283	283	NUM
ejpam-3912	136	19	on	on	ADP
ejpam-3912	136	20	the	the	DET
ejpam-3912	136	21	other	other	ADJ
ejpam-3912	136	22	hand	hand	NOUN
ejpam-3912	136	23	,	,	PUNCT
ejpam-3912	136	24	we	we	PRON
ejpam-3912	136	25	have	have	AUX
ejpam-3912	136	26	d(e2	d(e2	PROPN
ejpam-3912	136	27	i	i	NOUN
ejpam-3912	136	28	)	)	PUNCT
ejpam-3912	137	1	=	=	PUNCT
ejpam-3912	137	2	2diie	2diie	NUM
ejpam-3912	137	3	2	2	NUM
ejpam-3912	137	4	i	i	PRON
ejpam-3912	137	5	for	for	ADP
ejpam-3912	137	6	any	any	DET
ejpam-3912	137	7	i	i	PROPN
ejpam-3912	137	8	≤	≤	PROPN
ejpam-3912	137	9	n.	n.	NOUN
ejpam-3912	137	10	then	then	ADV
ejpam-3912	137	11	,	,	PUNCT
ejpam-3912	137	12	for	for	ADP
ejpam-3912	137	13	i	i	PRON
ejpam-3912	137	14	=	=	SYM
ejpam-3912	137	15	n	n	CCONJ
ejpam-3912	137	16	−	−	PROPN
ejpam-3912	137	17	2	2	NUM
ejpam-3912	137	18	using	use	VERB
ejpam-3912	137	19	(	(	PUNCT
ejpam-3912	137	20	2	2	NUM
ejpam-3912	137	21	)	)	PUNCT
ejpam-3912	137	22	,	,	PUNCT
ejpam-3912	137	23	we	we	PRON
ejpam-3912	137	24	obtain	obtain	VERB
ejpam-3912	137	25	d(en−1	d(en−1	PROPN
ejpam-3912	137	26	+	+	CCONJ
ejpam-3912	137	27	an−2,nen	an−2,nen	NOUN
ejpam-3912	137	28	)	)	PUNCT
ejpam-3912	137	29	=	=	SYM
ejpam-3912	138	1	2dn−2,n−2e	2dn−2,n−2e	NUM
ejpam-3912	138	2	2	2	NUM
ejpam-3912	138	3	n−2	n−2	PROPN
ejpam-3912	138	4	.	.	PUNCT
ejpam-3912	139	1	then	then	ADV
ejpam-3912	139	2	,	,	PUNCT
ejpam-3912	139	3	we	we	PRON
ejpam-3912	139	4	have	have	VERB
ejpam-3912	139	5	the	the	DET
ejpam-3912	139	6	following	follow	VERB
ejpam-3912	139	7	system	system	NOUN
ejpam-3912	139	8	:	:	PUNCT
ejpam-3912	139	9	dn−1,n−1	dn−1,n−1	ADJ
ejpam-3912	139	10	+	+	CCONJ
ejpam-3912	139	11	an−2,ndn	an−2,ndn	ADJ
ejpam-3912	139	12	,	,	PUNCT
ejpam-3912	139	13	n−1	n−1	PROPN
ejpam-3912	139	14	=	=	SYM
ejpam-3912	139	15	2dn−2,n−2	2dn−2,n−2	NUM
ejpam-3912	139	16	dn−1,n	dn−1,n	NOUN
ejpam-3912	139	17	+	+	CCONJ
ejpam-3912	139	18	an−2,ndn	an−2,ndn	ADJ
ejpam-3912	139	19	,	,	PUNCT
ejpam-3912	139	20	n	n	NOUN
ejpam-3912	139	21	=	=	SYM
ejpam-3912	139	22	2an−2,ndn−2,n−2	2an−2,ndn−2,n−2	PROPN
ejpam-3912	139	23	.	.	PUNCT
ejpam-3912	140	1	(	(	PUNCT
ejpam-3912	140	2	6	6	NUM
ejpam-3912	140	3	)	)	PUNCT
ejpam-3912	140	4	furthermore	furthermore	ADV
ejpam-3912	140	5	,	,	PUNCT
ejpam-3912	140	6	we	we	PRON
ejpam-3912	140	7	assume	assume	VERB
ejpam-3912	140	8	that	that	SCONJ
ejpam-3912	141	1	i	i	PRON
ejpam-3912	141	2	<	<	X
ejpam-3912	141	3	n−	n−	NOUN
ejpam-3912	141	4	2	2	NUM
ejpam-3912	141	5	.	.	PUNCT
ejpam-3912	142	1	then	then	ADV
ejpam-3912	142	2	,	,	PUNCT
ejpam-3912	142	3	one	one	PRON
ejpam-3912	142	4	finds	find	VERB
ejpam-3912	142	5	d(e2	d(e2	PROPN
ejpam-3912	142	6	i	i	PRON
ejpam-3912	142	7	)	)	PUNCT
ejpam-3912	143	1	=	=	PUNCT
ejpam-3912	144	1	d	d	X
ejpam-3912	144	2			PROPN
ejpam-3912	144	3	n∑	n∑	PROPN
ejpam-3912	144	4	j	j	PROPN
ejpam-3912	144	5	=	=	NOUN
ejpam-3912	144	6	i+1	i+1	PART
ejpam-3912	144	7	aijej	aijej	NOUN
ejpam-3912	144	8			PROPN
ejpam-3912	144	9	=	=	SYM
ejpam-3912	144	10	n∑	n∑	PROPN
ejpam-3912	144	11	j	j	PROPN
ejpam-3912	145	1	=	=	NOUN
ejpam-3912	145	2	i+1	i+1	NOUN
ejpam-3912	145	3	aijd(ej	aijd(ej	PROPN
ejpam-3912	145	4	)	)	PUNCT
ejpam-3912	145	5	=	=	SYM
ejpam-3912	145	6	n−2∑	n−2∑	NUM
ejpam-3912	145	7	j	j	X
ejpam-3912	145	8	=	=	NOUN
ejpam-3912	145	9	i+1	i+1	NOUN
ejpam-3912	145	10	aijdjjej	aijdjjej	NOUN
ejpam-3912	146	1	+	+	CCONJ
ejpam-3912	146	2	n∑	n∑	PROPN
ejpam-3912	146	3	j	j	PROPN
ejpam-3912	147	1	=	=	NOUN
ejpam-3912	147	2	i+1	i+1	NOUN
ejpam-3912	147	3	aijdj	aijdj	PROPN
ejpam-3912	147	4	,	,	PUNCT
ejpam-3912	147	5	n−1en−1	n−1en−1	NOUN
ejpam-3912	147	6	+	+	X
ejpam-3912	147	7	n∑	n∑	PROPN
ejpam-3912	147	8	j	j	X
ejpam-3912	147	9	=	=	NOUN
ejpam-3912	147	10	i+1	i+1	NOUN
ejpam-3912	147	11	aijdjnen	aijdjnen	NOUN
ejpam-3912	147	12	.	.	PUNCT
ejpam-3912	148	1	(	(	PUNCT
ejpam-3912	148	2	7	7	X
ejpam-3912	148	3	)	)	PUNCT
ejpam-3912	148	4	on	on	ADP
ejpam-3912	148	5	the	the	DET
ejpam-3912	148	6	other	other	ADJ
ejpam-3912	148	7	hand	hand	NOUN
ejpam-3912	148	8	,	,	PUNCT
ejpam-3912	148	9	from	from	ADP
ejpam-3912	148	10	d(e2	d(e2	PROPN
ejpam-3912	148	11	i	i	PROPN
ejpam-3912	148	12	)	)	PUNCT
ejpam-3912	149	1	=	=	PUNCT
ejpam-3912	149	2	2diie	2diie	NUM
ejpam-3912	149	3	2	2	NUM
ejpam-3912	149	4	i	i	NOUN
ejpam-3912	149	5	=	=	PROPN
ejpam-3912	150	1	2dii	2dii	NUM
ejpam-3912	150	2	n∑	n∑	PROPN
ejpam-3912	150	3	j	j	PROPN
ejpam-3912	151	1	=	=	NOUN
ejpam-3912	151	2	i+1	i+1	NOUN
ejpam-3912	151	3	aijej	aijej	NOUN
ejpam-3912	151	4	with	with	ADP
ejpam-3912	151	5	(	(	PUNCT
ejpam-3912	151	6	7	7	NUM
ejpam-3912	151	7	)	)	PUNCT
ejpam-3912	151	8	,	,	PUNCT
ejpam-3912	151	9	one	one	PRON
ejpam-3912	151	10	finds	find	VERB
ejpam-3912	151	11	2dii	2dii	NUM
ejpam-3912	151	12	=	=	SYM
ejpam-3912	151	13	di+1,i+1	di+1,i+1	NOUN
ejpam-3912	151	14	,	,	PUNCT
ejpam-3912	151	15	1	1	NUM
ejpam-3912	151	16	≤	≤	NUM
ejpam-3912	152	1	i	i	PRON
ejpam-3912	152	2	<	<	X
ejpam-3912	152	3	n−	n−	NOUN
ejpam-3912	152	4	2	2	NUM
ejpam-3912	152	5	(	(	PUNCT
ejpam-3912	152	6	8)	8)	NUM
ejpam-3912	152	7	aijdjj	aijdjj	NOUN
ejpam-3912	152	8	=	=	SYM
ejpam-3912	152	9	2aijdii	2aijdii	NUM
ejpam-3912	152	10	,	,	PUNCT
ejpam-3912	152	11	i+	i+	NUM
ejpam-3912	152	12	2	2	NUM
ejpam-3912	152	13	≤	≤	NUM
ejpam-3912	152	14	j	j	PROPN
ejpam-3912	152	15	≤	≤	PROPN
ejpam-3912	152	16	n−	n−	PROPN
ejpam-3912	152	17	2	2	NUM
ejpam-3912	152	18	(	(	PUNCT
ejpam-3912	152	19	9	9	NUM
ejpam-3912	152	20	)	)	PUNCT
ejpam-3912	152	21	n∑	n∑	NOUN
ejpam-3912	152	22	j	j	PROPN
ejpam-3912	153	1	=	=	NOUN
ejpam-3912	153	2	i+1	i+1	NOUN
ejpam-3912	153	3	aijdj	aijdj	ADJ
ejpam-3912	153	4	,	,	PUNCT
ejpam-3912	153	5	n−1	n−1	PROPN
ejpam-3912	153	6	=	=	SYM
ejpam-3912	153	7	2diiai	2diiai	PROPN
ejpam-3912	153	8	,	,	PUNCT
ejpam-3912	153	9	n−1	n−1	PROPN
ejpam-3912	153	10	,	,	PUNCT
ejpam-3912	153	11	1	1	NUM
ejpam-3912	153	12	≤	≤	NUM
ejpam-3912	154	1	i	i	PRON
ejpam-3912	154	2	<	<	X
ejpam-3912	154	3	n−	n−	NOUN
ejpam-3912	154	4	2	2	NUM
ejpam-3912	154	5	(	(	PUNCT
ejpam-3912	154	6	10	10	NUM
ejpam-3912	154	7	)	)	PUNCT
ejpam-3912	154	8	n∑	n∑	NOUN
ejpam-3912	154	9	j	j	X
ejpam-3912	155	1	=	=	NOUN
ejpam-3912	155	2	i+1	i+1	NOUN
ejpam-3912	155	3	aijdjn	aijdjn	NOUN
ejpam-3912	155	4	=	=	SYM
ejpam-3912	155	5	2diiain	2diiain	NUM
ejpam-3912	155	6	,	,	PUNCT
ejpam-3912	155	7	1	1	NUM
ejpam-3912	155	8	≤	≤	NUM
ejpam-3912	156	1	i	i	PRON
ejpam-3912	156	2	<	<	X
ejpam-3912	156	3	n−	n−	NOUN
ejpam-3912	156	4	2	2	NUM
ejpam-3912	156	5	.	.	PUNCT
ejpam-3912	157	1	(	(	PUNCT
ejpam-3912	157	2	11	11	NUM
ejpam-3912	157	3	)	)	PUNCT
ejpam-3912	157	4	from	from	ADP
ejpam-3912	157	5	(	(	PUNCT
ejpam-3912	157	6	8),(9	8),(9	NOUN
ejpam-3912	157	7	)	)	PUNCT
ejpam-3912	157	8	,	,	PUNCT
ejpam-3912	157	9	we	we	PRON
ejpam-3912	157	10	can	can	AUX
ejpam-3912	157	11	easily	easily	ADV
ejpam-3912	157	12	derive	derive	VERB
ejpam-3912	157	13	djj	djj	NOUN
ejpam-3912	157	14	=	=	SYM
ejpam-3912	157	15	2j−1d11	2j−1d11	NUM
ejpam-3912	157	16	,	,	PUNCT
ejpam-3912	157	17	2	2	NUM
ejpam-3912	157	18	≤	≤	NUM
ejpam-3912	157	19	j	j	PROPN
ejpam-3912	157	20	≤	≤	PROPN
ejpam-3912	157	21	n−	n−	PROPN
ejpam-3912	157	22	2	2	NUM
ejpam-3912	157	23	(	(	PUNCT
ejpam-3912	157	24	12	12	NUM
ejpam-3912	157	25	)	)	PUNCT
ejpam-3912	157	26	aijd11	aijd11	NOUN
ejpam-3912	157	27	=	=	SYM
ejpam-3912	157	28	0	0	NUM
ejpam-3912	157	29	,	,	PUNCT
ejpam-3912	157	30	i+	i+	NUM
ejpam-3912	157	31	2	2	NUM
ejpam-3912	157	32	≤	≤	NUM
ejpam-3912	157	33	j	j	PROPN
ejpam-3912	157	34	≤	≤	PROPN
ejpam-3912	157	35	n−	n−	PROPN
ejpam-3912	157	36	1	1	NUM
ejpam-3912	157	37	.	.	PUNCT
ejpam-3912	158	1	(	(	PUNCT
ejpam-3912	158	2	13	13	NUM
ejpam-3912	158	3	)	)	PUNCT
ejpam-3912	158	4	now	now	ADV
ejpam-3912	158	5	,	,	PUNCT
ejpam-3912	158	6	we	we	PRON
ejpam-3912	158	7	consider	consider	VERB
ejpam-3912	158	8	(	(	PUNCT
ejpam-3912	158	9	10	10	NUM
ejpam-3912	158	10	)	)	PUNCT
ejpam-3912	158	11	,	,	PUNCT
ejpam-3912	158	12	(	(	PUNCT
ejpam-3912	158	13	11	11	NUM
ejpam-3912	158	14	)	)	PUNCT
ejpam-3912	158	15	.	.	PUNCT
ejpam-3912	159	1	di+1,n−1	di+1,n−1	PROPN
ejpam-3912	159	2	=	=	SYM
ejpam-3912	159	3	2ai	2ai	PROPN
ejpam-3912	159	4	,	,	PUNCT
ejpam-3912	159	5	n−1dii	n−1dii	NOUN
ejpam-3912	159	6	−	−	PROPN
ejpam-3912	159	7	n−i∑	n−i∑	CCONJ
ejpam-3912	159	8	k=1	k=1	PROPN
ejpam-3912	159	9	ai−1,k+idk+i	ai−1,k+idk+i	PROPN
ejpam-3912	159	10	,	,	PUNCT
ejpam-3912	159	11	n−1	n−1	PROPN
ejpam-3912	159	12	di+1,n	di+1,n	NOUN
ejpam-3912	159	13	=	=	SYM
ejpam-3912	159	14	2ai	2ai	ADJ
ejpam-3912	159	15	,	,	PUNCT
ejpam-3912	159	16	ndii	ndii	VERB
ejpam-3912	159	17	−	−	PROPN
ejpam-3912	159	18	n−i∑	n−i∑	CCONJ
ejpam-3912	159	19	k=1	k=1	PROPN
ejpam-3912	159	20	ai−1,k+idk+i	ai−1,k+idk+i	PROPN
ejpam-3912	159	21	,	,	PUNCT
ejpam-3912	159	22	n.	n.	PROPN
ejpam-3912	159	23	(	(	PUNCT
ejpam-3912	159	24	14	14	NUM
ejpam-3912	159	25	)	)	PUNCT
ejpam-3912	159	26	a.	a.	NOUN
ejpam-3912	159	27	alarafeen	alarafeen	PROPN
ejpam-3912	159	28	,	,	PUNCT
ejpam-3912	159	29	i.	i.	PROPN
ejpam-3912	159	30	qaralleh	qaralleh	PROPN
ejpam-3912	159	31	,	,	PUNCT
ejpam-3912	159	32	a.	a.	PROPN
ejpam-3912	159	33	ahmad	ahmad	PROPN
ejpam-3912	159	34	/	/	SYM
ejpam-3912	159	35	eur	eur	PROPN
ejpam-3912	159	36	.	.	PUNCT
ejpam-3912	160	1	j.	j.	PROPN
ejpam-3912	160	2	pure	pure	PROPN
ejpam-3912	160	3	appl	appl	PROPN
ejpam-3912	160	4	.	.	PROPN
ejpam-3912	160	5	math	math	PROPN
ejpam-3912	160	6	,	,	PUNCT
ejpam-3912	160	7	14	14	NUM
ejpam-3912	160	8	(	(	PUNCT
ejpam-3912	160	9	1	1	NUM
ejpam-3912	160	10	)	)	PUNCT
ejpam-3912	160	11	(	(	PUNCT
ejpam-3912	160	12	2021	2021	NUM
ejpam-3912	160	13	)	)	PUNCT
ejpam-3912	160	14	,	,	PUNCT
ejpam-3912	160	15	278	278	NUM
ejpam-3912	160	16	-	-	SYM
ejpam-3912	160	17	300	300	NUM
ejpam-3912	160	18	284	284	NUM
ejpam-3912	160	19	thus	thus	ADV
ejpam-3912	160	20	,	,	PUNCT
ejpam-3912	160	21	from	from	ADP
ejpam-3912	160	22	(	(	PUNCT
ejpam-3912	160	23	5),(6),(12),(13	5),(6),(12),(13	ADJ
ejpam-3912	160	24	)	)	PUNCT
ejpam-3912	160	25	and	and	CCONJ
ejpam-3912	160	26	(	(	PUNCT
ejpam-3912	160	27	14	14	NUM
ejpam-3912	160	28	)	)	PUNCT
ejpam-3912	161	1	,	,	PUNCT
ejpam-3912	161	2	we	we	PRON
ejpam-3912	161	3	conclude	conclude	VERB
ejpam-3912	161	4	that	that	SCONJ
ejpam-3912	161	5	d	d	NOUN
ejpam-3912	161	6	is	be	AUX
ejpam-3912	161	7	a	a	DET
ejpam-3912	161	8	derivation	derivation	NOUN
ejpam-3912	161	9	of	of	ADP
ejpam-3912	161	10	evolution	evolution	NOUN
ejpam-3912	161	11	algebra	algebra	NOUN
ejpam-3912	161	12	given	give	VERB
ejpam-3912	161	13	by	by	ADP
ejpam-3912	161	14	(	(	PUNCT
ejpam-3912	161	15	2	2	X
ejpam-3912	161	16	)	)	PUNCT
ejpam-3912	161	17	if	if	SCONJ
ejpam-3912	161	18	and	and	CCONJ
ejpam-3912	161	19	only	only	ADV
ejpam-3912	161	20	if	if	SCONJ
ejpam-3912	161	21	dij	dij	ADJ
ejpam-3912	161	22	=	=	SYM
ejpam-3912	161	23	dn−1,i	dn−1,i	NOUN
ejpam-3912	161	24	=	=	SYM
ejpam-3912	161	25	dni	dni	PROPN
ejpam-3912	161	26	=	=	SYM
ejpam-3912	161	27	0	0	PROPN
ejpam-3912	161	28	,	,	PUNCT
ejpam-3912	161	29	1	1	NUM
ejpam-3912	161	30	≤	≤	NUM
ejpam-3912	161	31	i	i	PRON
ejpam-3912	161	32	6=	6=	PROPN
ejpam-3912	162	1	j	j	PROPN
ejpam-3912	162	2	≤	≤	PROPN
ejpam-3912	162	3	n−	n−	PROPN
ejpam-3912	162	4	2	2	NUM
ejpam-3912	162	5	(	(	PUNCT
ejpam-3912	162	6	15	15	NUM
ejpam-3912	162	7	)	)	PUNCT
ejpam-3912	162	8	djj	djj	NOUN
ejpam-3912	163	1	=	=	SYM
ejpam-3912	163	2	2j−1d11	2j−1d11	NUM
ejpam-3912	163	3	,	,	PUNCT
ejpam-3912	163	4	2	2	NUM
ejpam-3912	163	5	≤	≤	NUM
ejpam-3912	163	6	j	j	PROPN
ejpam-3912	163	7	≤	≤	PROPN
ejpam-3912	163	8	n−	n−	PROPN
ejpam-3912	163	9	2	2	NUM
ejpam-3912	163	10	(	(	PUNCT
ejpam-3912	163	11	16	16	NUM
ejpam-3912	163	12	)	)	PUNCT
ejpam-3912	163	13	aijd11	aijd11	NOUN
ejpam-3912	163	14	=	=	SYM
ejpam-3912	163	15	0	0	NUM
ejpam-3912	163	16	,	,	PUNCT
ejpam-3912	163	17	i+	i+	NUM
ejpam-3912	163	18	2	2	NUM
ejpam-3912	163	19	≤	≤	NUM
ejpam-3912	163	20	j	j	PROPN
ejpam-3912	163	21	≤	≤	PROPN
ejpam-3912	163	22	n−	n−	PROPN
ejpam-3912	163	23	2	2	NUM
ejpam-3912	163	24	(	(	PUNCT
ejpam-3912	163	25	17	17	NUM
ejpam-3912	163	26	)	)	PUNCT
ejpam-3912	163	27	di+1,n−1	di+1,n−1	NOUN
ejpam-3912	163	28	=	=	SYM
ejpam-3912	163	29	2ai	2ai	PROPN
ejpam-3912	163	30	,	,	PUNCT
ejpam-3912	163	31	n−1dii	n−1dii	NOUN
ejpam-3912	163	32	−	−	PROPN
ejpam-3912	163	33	n−i∑	n−i∑	CCONJ
ejpam-3912	163	34	k=1	k=1	PROPN
ejpam-3912	163	35	ai−1,k+idk+i	ai−1,k+idk+i	PROPN
ejpam-3912	163	36	,	,	PUNCT
ejpam-3912	163	37	n−1	n−1	PROPN
ejpam-3912	163	38	(	(	PUNCT
ejpam-3912	163	39	18	18	NUM
ejpam-3912	163	40	)	)	PUNCT
ejpam-3912	163	41	di+1,n	di+1,n	NOUN
ejpam-3912	163	42	=	=	SYM
ejpam-3912	163	43	2ai	2ai	ADJ
ejpam-3912	163	44	,	,	PUNCT
ejpam-3912	163	45	ndii	ndii	VERB
ejpam-3912	163	46	−	−	PROPN
ejpam-3912	163	47	n−i∑	n−i∑	CCONJ
ejpam-3912	163	48	k=1	k=1	PROPN
ejpam-3912	163	49	ai−1,k+idk+i	ai−1,k+idk+i	PROPN
ejpam-3912	163	50	,	,	PUNCT
ejpam-3912	163	51	n.	n.	PROPN
ejpam-3912	163	52	(	(	PUNCT
ejpam-3912	163	53	19	19	NUM
ejpam-3912	163	54	)	)	PUNCT
ejpam-3912	163	55	case	case	NOUN
ejpam-3912	163	56	ia	ia	PROPN
ejpam-3912	163	57	6=	6=	X
ejpam-3912	163	58	∅.	∅.	NOUN
ejpam-3912	163	59	in	in	ADP
ejpam-3912	163	60	this	this	DET
ejpam-3912	163	61	case	case	NOUN
ejpam-3912	163	62	,	,	PUNCT
ejpam-3912	163	63	we	we	PRON
ejpam-3912	163	64	have	have	VERB
ejpam-3912	163	65	ai0j0	ai0j0	NOUN
ejpam-3912	163	66	6=	6=	ADP
ejpam-3912	163	67	0	0	NUM
ejpam-3912	163	68	for	for	ADP
ejpam-3912	163	69	a	a	DET
ejpam-3912	163	70	pair	pair	NOUN
ejpam-3912	163	71	(	(	PUNCT
ejpam-3912	163	72	i0	i0	PROPN
ejpam-3912	163	73	,	,	PUNCT
ejpam-3912	163	74	j0	j0	PROPN
ejpam-3912	163	75	)	)	PUNCT
ejpam-3912	163	76	that	that	PRON
ejpam-3912	163	77	satisfies	satisfy	VERB
ejpam-3912	163	78	i0	i0	PROPN
ejpam-3912	163	79	+	+	CCONJ
ejpam-3912	163	80	2	2	NUM
ejpam-3912	163	81	≤	≤	NUM
ejpam-3912	163	82	j0	j0	PROPN
ejpam-3912	163	83	<	<	X
ejpam-3912	163	84	n−1	n−1	PROPN
ejpam-3912	163	85	.	.	PUNCT
ejpam-3912	164	1	then	then	ADV
ejpam-3912	164	2	,	,	PUNCT
ejpam-3912	164	3	from	from	ADP
ejpam-3912	164	4	(	(	PUNCT
ejpam-3912	164	5	17	17	NUM
ejpam-3912	164	6	)	)	PUNCT
ejpam-3912	164	7	,	,	PUNCT
ejpam-3912	164	8	one	one	PRON
ejpam-3912	164	9	finds	find	VERB
ejpam-3912	164	10	d11	d11	PROPN
ejpam-3912	164	11	=	=	SYM
ejpam-3912	164	12	0	0	X
ejpam-3912	164	13	.	.	X
ejpam-3912	164	14	plugging	plug	VERB
ejpam-3912	164	15	this	this	DET
ejpam-3912	164	16	fact	fact	NOUN
ejpam-3912	164	17	into	into	ADP
ejpam-3912	164	18	(	(	PUNCT
ejpam-3912	164	19	16),(18	16),(18	NUM
ejpam-3912	164	20	)	)	PUNCT
ejpam-3912	164	21	,	,	PUNCT
ejpam-3912	164	22	and	and	CCONJ
ejpam-3912	164	23	(	(	PUNCT
ejpam-3912	164	24	19	19	NUM
ejpam-3912	164	25	)	)	PUNCT
ejpam-3912	164	26	,	,	PUNCT
ejpam-3912	164	27	we	we	PRON
ejpam-3912	164	28	obtain	obtain	VERB
ejpam-3912	164	29	der(e	der(e	NOUN
ejpam-3912	164	30	)	)	PUNCT
ejpam-3912	165	1	=	=	PRON
ejpam-3912	165	2			X
ejpam-3912	165	3			NOUN
ejpam-3912	165	4	0	0	NUM
ejpam-3912	165	5	0	0	NUM
ejpam-3912	165	6	.	.	PUNCT
ejpam-3912	165	7	.	.	PUNCT
ejpam-3912	165	8	.	.	PUNCT
ejpam-3912	166	1	d1n−1	d1n−1	PROPN
ejpam-3912	166	2	d1n	d1n	PROPN
ejpam-3912	166	3	0	0	NUM
ejpam-3912	166	4	0	0	NUM
ejpam-3912	166	5	.	.	PUNCT
ejpam-3912	166	6	.	.	PUNCT
ejpam-3912	166	7	.	.	PUNCT
ejpam-3912	167	1	d2n−1	d2n−1	PROPN
ejpam-3912	167	2	d2n	d2n	PROPN
ejpam-3912	167	3	...	...	PUNCT
ejpam-3912	167	4	...	...	PUNCT
ejpam-3912	167	5	.	.	PUNCT
ejpam-3912	167	6	.	.	PUNCT
ejpam-3912	167	7	.	.	PUNCT
ejpam-3912	168	1	...	...	PUNCT
ejpam-3912	169	1	...	...	PUNCT
ejpam-3912	170	1	0	0	NUM
ejpam-3912	170	2	0	0	NUM
ejpam-3912	170	3	.	.	PUNCT
ejpam-3912	170	4	.	.	PUNCT
ejpam-3912	170	5	.	.	PUNCT
ejpam-3912	171	1	dn−1n−1	dn−1n−1	PROPN
ejpam-3912	171	2	dn−1n	dn−1n	PROPN
ejpam-3912	171	3	0	0	NUM
ejpam-3912	171	4	0	0	NUM
ejpam-3912	171	5	.	.	PUNCT
ejpam-3912	171	6	.	.	PUNCT
ejpam-3912	171	7	.	.	PUNCT
ejpam-3912	172	1	dnn−1	dnn−1	PROPN
ejpam-3912	172	2	dnn	dnn	PROPN
ejpam-3912	172	3			NOUN
ejpam-3912	172	4			NOUN
ejpam-3912	172	5	where	where	SCONJ
ejpam-3912	172	6	dn−1,n−1	dn−1,n−1	ADJ
ejpam-3912	172	7	=	=	SYM
ejpam-3912	172	8	−an−2,ndn	−an−2,ndn	ADJ
ejpam-3912	172	9	,	,	PUNCT
ejpam-3912	172	10	n−1	n−1	PROPN
ejpam-3912	172	11	;	;	PUNCT
ejpam-3912	172	12	dn−1,n	dn−1,n	X
ejpam-3912	172	13	=	=	SYM
ejpam-3912	172	14	−an−2,ndnn	−an−2,ndnn	NOUN
ejpam-3912	172	15	;	;	PUNCT
ejpam-3912	172	16	dim	dim	ADJ
ejpam-3912	172	17	=	=	SYM
ejpam-3912	172	18	−	−	PROPN
ejpam-3912	172	19	n−i∑	n−i∑	PROPN
ejpam-3912	172	20	k=1	k=1	PROPN
ejpam-3912	172	21	ai−1,k+idk+i	ai−1,k+idk+i	PROPN
ejpam-3912	172	22	,	,	PUNCT
ejpam-3912	172	23	m	m	PROPN
ejpam-3912	172	24	,	,	PUNCT
ejpam-3912	172	25	m	m	VERB
ejpam-3912	172	26	∈	∈	NOUN
ejpam-3912	172	27	{	{	PUNCT
ejpam-3912	172	28	n−	n−	NOUN
ejpam-3912	172	29	1	1	NUM
ejpam-3912	172	30	,	,	PUNCT
ejpam-3912	172	31	n	n	CCONJ
ejpam-3912	172	32	}	}	PUNCT
ejpam-3912	172	33	.	.	PUNCT
ejpam-3912	173	1	case	case	NOUN
ejpam-3912	173	2	ia	ia	NOUN
ejpam-3912	173	3	=	=	PUNCT
ejpam-3912	173	4	∅.	∅.	NOUN
ejpam-3912	173	5	in	in	ADP
ejpam-3912	173	6	this	this	DET
ejpam-3912	173	7	case	case	NOUN
ejpam-3912	173	8	,	,	PUNCT
ejpam-3912	173	9	(	(	PUNCT
ejpam-3912	173	10	17	17	NUM
ejpam-3912	173	11	)	)	PUNCT
ejpam-3912	173	12	is	be	AUX
ejpam-3912	173	13	true	true	ADJ
ejpam-3912	173	14	for	for	ADP
ejpam-3912	173	15	any	any	DET
ejpam-3912	173	16	d11	d11	PROPN
ejpam-3912	173	17	∈	∈	PROPN
ejpam-3912	173	18	k.	k.	PROPN
ejpam-3912	174	1	thus	thus	ADV
ejpam-3912	174	2	,	,	PUNCT
ejpam-3912	174	3	from	from	ADP
ejpam-3912	174	4	(	(	PUNCT
ejpam-3912	174	5	15),(16	15),(16	NUM
ejpam-3912	174	6	)	)	PUNCT
ejpam-3912	174	7	,	,	PUNCT
ejpam-3912	174	8	(	(	PUNCT
ejpam-3912	174	9	18	18	NUM
ejpam-3912	174	10	)	)	PUNCT
ejpam-3912	174	11	,	,	PUNCT
ejpam-3912	174	12	and	and	CCONJ
ejpam-3912	174	13	(	(	PUNCT
ejpam-3912	174	14	19	19	NUM
ejpam-3912	174	15	)	)	PUNCT
ejpam-3912	174	16	,	,	PUNCT
ejpam-3912	174	17	we	we	PRON
ejpam-3912	174	18	conclude	conclude	VERB
ejpam-3912	174	19	that	that	SCONJ
ejpam-3912	174	20	der(e	der(e	PROPN
ejpam-3912	174	21	)	)	PUNCT
ejpam-3912	175	1	=	=	SYM
ejpam-3912	175	2			NUM
ejpam-3912	176	1			NOUN
ejpam-3912	177	1	α	α	NOUN
ejpam-3912	177	2	0	0	PUNCT
ejpam-3912	177	3	.	.	PUNCT
ejpam-3912	177	4	.	.	PUNCT
ejpam-3912	177	5	.	.	PUNCT
ejpam-3912	178	1	β	β	X
ejpam-3912	178	2	γ	γ	X
ejpam-3912	178	3	0	0	NUM
ejpam-3912	178	4	2α	2α	NOUN
ejpam-3912	178	5	.	.	PUNCT
ejpam-3912	178	6	.	.	PUNCT
ejpam-3912	178	7	.	.	PUNCT
ejpam-3912	179	1	d2,n−1	d2,n−1	ADJ
ejpam-3912	179	2	d2n	d2n	NOUN
ejpam-3912	179	3	...	...	PUNCT
ejpam-3912	179	4	...	...	PUNCT
ejpam-3912	179	5	.	.	PUNCT
ejpam-3912	179	6	.	.	PUNCT
ejpam-3912	179	7	.	.	PUNCT
ejpam-3912	180	1	...	...	PUNCT
ejpam-3912	181	1	...	...	PUNCT
ejpam-3912	182	1	0	0	NUM
ejpam-3912	182	2	0	0	NUM
ejpam-3912	182	3	.	.	PUNCT
ejpam-3912	182	4	.	.	PUNCT
ejpam-3912	182	5	.	.	PUNCT
ejpam-3912	183	1	dn−2,n−1	dn−2,n−1	PROPN
ejpam-3912	183	2	dn−2,n	dn−2,n	PROPN
ejpam-3912	183	3	0	0	NUM
ejpam-3912	183	4	0	0	NUM
ejpam-3912	183	5	.	.	PUNCT
ejpam-3912	183	6	.	.	PUNCT
ejpam-3912	183	7	.	.	PUNCT
ejpam-3912	184	1	dn−1,n−1	dn−1,n−1	ADJ
ejpam-3912	184	2	dn−1,n	dn−1,n	NOUN
ejpam-3912	184	3	0	0	NUM
ejpam-3912	184	4	0	0	NUM
ejpam-3912	184	5	.	.	PUNCT
ejpam-3912	184	6	.	.	PUNCT
ejpam-3912	184	7	.	.	PUNCT
ejpam-3912	185	1	s	s	PROPN
ejpam-3912	185	2	t	t	NOUN
ejpam-3912	185	3			PROPN
ejpam-3912	185	4	:	:	PUNCT
ejpam-3912	186	1	α	α	X
ejpam-3912	186	2	,	,	PUNCT
ejpam-3912	186	3	β	β	X
ejpam-3912	186	4	,	,	PUNCT
ejpam-3912	186	5	s	s	PROPN
ejpam-3912	186	6	,	,	PUNCT
ejpam-3912	186	7	t	t	PROPN
ejpam-3912	186	8	∈	∈	PROPN
ejpam-3912	186	9	k	k	PROPN
ejpam-3912	186	10			VERB
ejpam-3912	186	11	where	where	SCONJ
ejpam-3912	186	12	dn−1,n−1	dn−1,n−1	ADJ
ejpam-3912	186	13	=	=	SYM
ejpam-3912	186	14	2n−2α−	2n−2α−	NUM
ejpam-3912	186	15	an−2,ns	an−2,ns	PROPN
ejpam-3912	186	16	a.	a.	NOUN
ejpam-3912	186	17	alarafeen	alarafeen	PROPN
ejpam-3912	186	18	,	,	PUNCT
ejpam-3912	186	19	i.	i.	PROPN
ejpam-3912	186	20	qaralleh	qaralleh	PROPN
ejpam-3912	186	21	,	,	PUNCT
ejpam-3912	186	22	a.	a.	PROPN
ejpam-3912	186	23	ahmad	ahmad	PROPN
ejpam-3912	186	24	/	/	SYM
ejpam-3912	186	25	eur	eur	PROPN
ejpam-3912	186	26	.	.	PUNCT
ejpam-3912	187	1	j.	j.	PROPN
ejpam-3912	187	2	pure	pure	PROPN
ejpam-3912	187	3	appl	appl	PROPN
ejpam-3912	187	4	.	.	PROPN
ejpam-3912	187	5	math	math	PROPN
ejpam-3912	187	6	,	,	PUNCT
ejpam-3912	187	7	14	14	NUM
ejpam-3912	187	8	(	(	PUNCT
ejpam-3912	187	9	1	1	NUM
ejpam-3912	187	10	)	)	PUNCT
ejpam-3912	187	11	(	(	PUNCT
ejpam-3912	187	12	2021	2021	NUM
ejpam-3912	187	13	)	)	PUNCT
ejpam-3912	187	14	,	,	PUNCT
ejpam-3912	187	15	278	278	NUM
ejpam-3912	187	16	-	-	SYM
ejpam-3912	187	17	300	300	NUM
ejpam-3912	187	18	285	285	NUM
ejpam-3912	187	19	dn−1,n	dn−1,n	NOUN
ejpam-3912	187	20	=	=	PUNCT
ejpam-3912	187	21	(	(	PUNCT
ejpam-3912	187	22	2n−2	2n−2	NUM
ejpam-3912	187	23	−	−	PROPN
ejpam-3912	187	24	t)an−2,n	t)an−2,n	X
ejpam-3912	187	25	di	di	NOUN
ejpam-3912	187	26	,	,	PUNCT
ejpam-3912	187	27	n−1	n−1	PROPN
ejpam-3912	187	28	=	=	SYM
ejpam-3912	187	29	(	(	PUNCT
ejpam-3912	187	30	2i−1	2i−1	NUM
ejpam-3912	187	31	−	−	PROPN
ejpam-3912	187	32	2n−2)αai−1,n−1	2n−2)αai−1,n−1	PROPN
ejpam-3912	187	33	+	+	CCONJ
ejpam-3912	187	34	(	(	PUNCT
ejpam-3912	187	35	ai−1,n−1an−2,n	ai−1,n−1an−2,n	ADV
ejpam-3912	187	36	−	−	PROPN
ejpam-3912	187	37	ai−1,n)s	ai−1,n)s	PROPN
ejpam-3912	187	38	di	di	PROPN
ejpam-3912	187	39	,	,	PUNCT
ejpam-3912	187	40	n	n	NOUN
ejpam-3912	187	41	=	=	SYM
ejpam-3912	187	42	ai−1,n−1dn−1,n	ai−1,n−1dn−1,n	NOUN
ejpam-3912	187	43	+	+	CCONJ
ejpam-3912	187	44	an−2,n(2i−1α−	an−2,n(2i−1α−	PROPN
ejpam-3912	187	45	t	t	PROPN
ejpam-3912	187	46	)	)	PUNCT
ejpam-3912	187	47	,	,	PUNCT
ejpam-3912	187	48	2	2	NUM
ejpam-3912	187	49	≤	≤	NUM
ejpam-3912	188	1	i	i	PRON
ejpam-3912	188	2	<	<	X
ejpam-3912	188	3	n−	n−	NOUN
ejpam-3912	188	4	1	1	NUM
ejpam-3912	188	5	.	.	PUNCT
ejpam-3912	189	1	the	the	DET
ejpam-3912	189	2	proof	proof	NOUN
ejpam-3912	189	3	is	be	AUX
ejpam-3912	189	4	complete	complete	ADJ
ejpam-3912	189	5	.	.	PUNCT
ejpam-3912	190	1	remark	remark	PROPN
ejpam-3912	190	2	1	1	NUM
ejpam-3912	190	3	.	.	PUNCT
ejpam-3912	191	1	i.	i.	PROPN
ejpam-3912	191	2	in	in	ADP
ejpam-3912	191	3	[	[	X
ejpam-3912	191	4	25	25	NUM
ejpam-3912	191	5	]	]	PUNCT
ejpam-3912	191	6	,	,	PUNCT
ejpam-3912	191	7	it	it	PRON
ejpam-3912	191	8	has	have	AUX
ejpam-3912	191	9	been	be	AUX
ejpam-3912	191	10	considered	consider	VERB
ejpam-3912	191	11	the	the	DET
ejpam-3912	191	12	nilpotent	nilpotent	ADJ
ejpam-3912	191	13	evolution	evolution	NOUN
ejpam-3912	191	14	algebras	algebra	VERB
ejpam-3912	191	15	with	with	ADP
ejpam-3912	191	16	maximal	maximal	ADJ
ejpam-3912	191	17	nil	nil	NOUN
ejpam-3912	191	18	index	index	NOUN
ejpam-3912	191	19	and	and	CCONJ
ejpam-3912	191	20	they	they	PRON
ejpam-3912	191	21	found	find	VERB
ejpam-3912	191	22	1	1	NUM
ejpam-3912	191	23	≤	≤	NUM
ejpam-3912	191	24	dimder(e	dimder(e	PROPN
ejpam-3912	191	25	)	)	PUNCT
ejpam-3912	191	26	≤	≤	NUM
ejpam-3912	191	27	2	2	NUM
ejpam-3912	191	28	.	.	X
ejpam-3912	191	29	ii	ii	PROPN
ejpam-3912	191	30	.	.	PROPN
ejpam-3912	192	1	from	from	ADP
ejpam-3912	192	2	the	the	DET
ejpam-3912	192	3	proved	prove	VERB
ejpam-3912	192	4	theorem	theorem	NOUN
ejpam-3912	192	5	,	,	PUNCT
ejpam-3912	192	6	we	we	PRON
ejpam-3912	192	7	infer	infer	VERB
ejpam-3912	192	8	that	that	SCONJ
ejpam-3912	192	9	1	1	NUM
ejpam-3912	192	10	≤	≤	NUM
ejpam-3912	192	11	dimder(e	dimder(e	NOUN
ejpam-3912	192	12	)	)	PUNCT
ejpam-3912	192	13	≤	≤	NOUN
ejpam-3912	192	14	5	5	NUM
ejpam-3912	192	15	.	.	PUNCT
ejpam-3912	193	1	this	this	DET
ejpam-3912	193	2	type	type	NOUN
ejpam-3912	193	3	of	of	ADP
ejpam-3912	193	4	result	result	NOUN
ejpam-3912	193	5	can	can	AUX
ejpam-3912	193	6	be	be	AUX
ejpam-3912	193	7	proved	prove	VERB
ejpam-3912	193	8	using	use	VERB
ejpam-3912	193	9	the	the	DET
ejpam-3912	193	10	work	work	NOUN
ejpam-3912	193	11	of	of	ADP
ejpam-3912	193	12	jacobson	jacobson	PROPN
ejpam-3912	194	1	[	[	X
ejpam-3912	194	2	21	21	NUM
ejpam-3912	194	3	]	]	PUNCT
ejpam-3912	194	4	.	.	PUNCT
ejpam-3912	195	1	however	however	ADV
ejpam-3912	195	2	,	,	PUNCT
ejpam-3912	195	3	the	the	DET
ejpam-3912	195	4	advantage	advantage	NOUN
ejpam-3912	195	5	of	of	ADP
ejpam-3912	195	6	theorem	theorem	ADJ
ejpam-3912	195	7	3	3	NUM
ejpam-3912	195	8	is	be	AUX
ejpam-3912	195	9	that	that	SCONJ
ejpam-3912	195	10	it	it	PRON
ejpam-3912	195	11	fully	fully	ADV
ejpam-3912	195	12	describes	describe	VERB
ejpam-3912	195	13	the	the	DET
ejpam-3912	195	14	structure	structure	NOUN
ejpam-3912	195	15	of	of	ADP
ejpam-3912	195	16	the	the	DET
ejpam-3912	195	17	derivations	derivation	NOUN
ejpam-3912	195	18	on	on	ADP
ejpam-3912	195	19	a	a	DET
ejpam-3912	195	20	natural	natural	ADJ
ejpam-3912	195	21	basis	basis	NOUN
ejpam-3912	195	22	.	.	PUNCT
ejpam-3912	196	1	corollary	corollary	ADJ
ejpam-3912	196	2	1	1	NUM
ejpam-3912	196	3	.	.	PUNCT
ejpam-3912	197	1	lie	lie	PROPN
ejpam-3912	197	2	algebras	algebras	PROPN
ejpam-3912	197	3	e	e	PROPN
ejpam-3912	197	4	=	=	PUNCT
ejpam-3912	197	5			PROPN
ejpam-3912	197	6			PROPN
ejpam-3912	197	7	α	α	PROPN
ejpam-3912	197	8	0	0	NUM
ejpam-3912	197	9	...	...	PUNCT
ejpam-3912	198	1	β	β	X
ejpam-3912	198	2	γ	γ	X
ejpam-3912	198	3	0	0	NUM
ejpam-3912	198	4	2α	2α	NOUN
ejpam-3912	198	5	...	...	PUNCT
ejpam-3912	199	1	0	0	NUM
ejpam-3912	199	2	0	0	NUM
ejpam-3912	199	3	...	...	PUNCT
ejpam-3912	199	4	...	...	PUNCT
ejpam-3912	199	5	.	.	PUNCT
ejpam-3912	199	6	.	.	PUNCT
ejpam-3912	199	7	.	.	PUNCT
ejpam-3912	200	1	...	...	PUNCT
ejpam-3912	201	1	...	...	PUNCT
ejpam-3912	202	1	0	0	NUM
ejpam-3912	202	2	0	0	NUM
ejpam-3912	202	3	...	...	PUNCT
ejpam-3912	203	1	2n−2α	2n−2α	NUM
ejpam-3912	203	2	0	0	NUM
ejpam-3912	203	3	0	0	NUM
ejpam-3912	203	4	0	0	NUM
ejpam-3912	203	5	...	...	PUNCT
ejpam-3912	204	1	s	s	PART
ejpam-3912	204	2	t	t	NOUN
ejpam-3912	205	1			NOUN
ejpam-3912	205	2	:	:	PUNCT
ejpam-3912	205	3	α	α	X
ejpam-3912	205	4	,	,	PUNCT
ejpam-3912	205	5	β	β	X
ejpam-3912	205	6	,	,	PUNCT
ejpam-3912	205	7	γ	γ	PROPN
ejpam-3912	205	8	,	,	PUNCT
ejpam-3912	205	9	s	s	PROPN
ejpam-3912	205	10	,	,	PUNCT
ejpam-3912	205	11	t	t	PROPN
ejpam-3912	205	12	∈	∈	PROPN
ejpam-3912	205	13	k	k	PROPN
ejpam-3912	205	14			NOUN
ejpam-3912	205	15	and	and	CCONJ
ejpam-3912	205	16	e′	e′	NOUN
ejpam-3912	205	17	=	=	SYM
ejpam-3912	205	18			PROPN
ejpam-3912	205	19			PROPN
ejpam-3912	205	20	α	α	PROPN
ejpam-3912	205	21	0	0	NUM
ejpam-3912	205	22	...	...	PUNCT
ejpam-3912	205	23	β	β	X
ejpam-3912	205	24	γ	γ	X
ejpam-3912	205	25	0	0	NUM
ejpam-3912	205	26	2α	2α	NUM
ejpam-3912	205	27	...	...	PUNCT
ejpam-3912	206	1	d2,n−1	d2,n−1	ADJ
ejpam-3912	206	2	d2n	d2n	NOUN
ejpam-3912	206	3	...	...	PUNCT
ejpam-3912	206	4	...	...	PUNCT
ejpam-3912	206	5	.	.	PUNCT
ejpam-3912	206	6	.	.	PUNCT
ejpam-3912	206	7	.	.	PUNCT
ejpam-3912	207	1	...	...	PUNCT
ejpam-3912	208	1	...	...	PUNCT
ejpam-3912	209	1	0	0	NUM
ejpam-3912	209	2	0	0	NUM
ejpam-3912	209	3	...	...	PUNCT
ejpam-3912	209	4	dn−1,n−1	dn−1,n−1	ADJ
ejpam-3912	209	5	dn−1,n	dn−1,n	ADJ
ejpam-3912	209	6	0	0	NUM
ejpam-3912	209	7	0	0	NUM
ejpam-3912	209	8	...	...	PUNCT
ejpam-3912	209	9	s	s	PART
ejpam-3912	209	10	t	t	NOUN
ejpam-3912	210	1			NOUN
ejpam-3912	210	2	:	:	PUNCT
ejpam-3912	210	3	α	α	X
ejpam-3912	210	4	,	,	PUNCT
ejpam-3912	210	5	β	β	X
ejpam-3912	210	6	,	,	PUNCT
ejpam-3912	210	7	γ	γ	PROPN
ejpam-3912	210	8	,	,	PUNCT
ejpam-3912	210	9	s	s	PROPN
ejpam-3912	210	10	,	,	PUNCT
ejpam-3912	210	11	t	t	PROPN
ejpam-3912	210	12	∈	∈	PROPN
ejpam-3912	210	13	k	k	NOUN
ejpam-3912	210	14			NOUN
ejpam-3912	210	15	are	be	AUX
ejpam-3912	210	16	isomorphic	isomorphic	ADJ
ejpam-3912	210	17	for	for	ADP
ejpam-3912	210	18	any	any	DET
ejpam-3912	210	19	di	di	NOUN
ejpam-3912	210	20	,	,	PUNCT
ejpam-3912	210	21	n−1	n−1	PROPN
ejpam-3912	210	22	,	,	PUNCT
ejpam-3912	210	23	di	di	NOUN
ejpam-3912	210	24	,	,	PUNCT
ejpam-3912	210	25	n	n	PROPN
ejpam-3912	210	26	∈	∈	PROPN
ejpam-3912	211	1	k	k	NOUN
ejpam-3912	211	2	,	,	PUNCT
ejpam-3912	211	3	i	i	PRON
ejpam-3912	211	4	=	=	NOUN
ejpam-3912	211	5	2	2	NUM
ejpam-3912	211	6	,	,	PUNCT
ejpam-3912	211	7	n−	n−	NOUN
ejpam-3912	211	8	1	1	NUM
ejpam-3912	211	9	.	.	PUNCT
ejpam-3912	211	10	remark	remark	NOUN
ejpam-3912	211	11	2	2	NUM
ejpam-3912	211	12	.	.	PUNCT
ejpam-3912	212	1	we	we	PRON
ejpam-3912	212	2	stress	stress	VERB
ejpam-3912	212	3	that	that	SCONJ
ejpam-3912	212	4	isomorphisms	isomorphism	NOUN
ejpam-3912	212	5	of	of	ADP
ejpam-3912	212	6	lie	lie	NOUN
ejpam-3912	212	7	algebras	algebra	NOUN
ejpam-3912	212	8	do	do	AUX
ejpam-3912	212	9	not	not	PART
ejpam-3912	212	10	imply	imply	VERB
ejpam-3912	212	11	isomorphism	isomorphism	NOUN
ejpam-3912	212	12	of	of	ADP
ejpam-3912	212	13	the	the	DET
ejpam-3912	212	14	corresponding	corresponding	ADJ
ejpam-3912	212	15	evolution	evolution	NOUN
ejpam-3912	212	16	algebras	algebra	NOUN
ejpam-3912	212	17	(	(	PUNCT
ejpam-3912	212	18	see	see	VERB
ejpam-3912	212	19	lemma	lemma	PROPN
ejpam-3912	212	20	1	1	NUM
ejpam-3912	212	21	)	)	PUNCT
ejpam-3912	212	22	.	.	PUNCT
ejpam-3912	213	1	4	4	X
ejpam-3912	213	2	.	.	X
ejpam-3912	213	3	local	local	ADJ
ejpam-3912	213	4	and	and	CCONJ
ejpam-3912	213	5	2	2	NUM
ejpam-3912	213	6	-	-	PUNCT
ejpam-3912	213	7	local	local	ADJ
ejpam-3912	213	8	derivations	derivation	NOUN
ejpam-3912	213	9	for	for	ADP
ejpam-3912	213	10	evolution	evolution	NOUN
ejpam-3912	213	11	algebras	algebra	VERB
ejpam-3912	213	12	the	the	DET
ejpam-3912	213	13	results	result	NOUN
ejpam-3912	213	14	of	of	ADP
ejpam-3912	213	15	section	section	NOUN
ejpam-3912	213	16	3	3	NUM
ejpam-3912	213	17	allow	allow	VERB
ejpam-3912	213	18	us	we	PRON
ejpam-3912	213	19	to	to	PART
ejpam-3912	213	20	describe	describe	VERB
ejpam-3912	213	21	local	local	ADJ
ejpam-3912	213	22	and	and	CCONJ
ejpam-3912	213	23	2	2	NUM
ejpam-3912	213	24	-	-	PUNCT
ejpam-3912	213	25	local	local	ADJ
ejpam-3912	213	26	derivations	derivation	NOUN
ejpam-3912	213	27	of	of	ADP
ejpam-3912	213	28	nilpotent	nilpotent	ADJ
ejpam-3912	213	29	evolution	evolution	NOUN
ejpam-3912	213	30	algebra	algebra	PROPN
ejpam-3912	213	31	.	.	PUNCT
ejpam-3912	214	1	in	in	ADP
ejpam-3912	214	2	this	this	DET
ejpam-3912	214	3	section	section	NOUN
ejpam-3912	214	4	,	,	PUNCT
ejpam-3912	214	5	we	we	PRON
ejpam-3912	214	6	want	want	VERB
ejpam-3912	214	7	to	to	PART
ejpam-3912	214	8	fully	fully	ADV
ejpam-3912	214	9	describe	describe	VERB
ejpam-3912	214	10	local	local	ADJ
ejpam-3912	214	11	and	and	CCONJ
ejpam-3912	214	12	2	2	NUM
ejpam-3912	214	13	-	-	PUNCT
ejpam-3912	214	14	local	local	ADJ
ejpam-3912	214	15	derivations	derivation	NOUN
ejpam-3912	214	16	of	of	ADP
ejpam-3912	214	17	nilpotent	nilpotent	ADJ
ejpam-3912	214	18	evolution	evolution	NOUN
ejpam-3912	214	19	algebras	algebra	NOUN
ejpam-3912	214	20	with	with	ADP
ejpam-3912	214	21	2n−2	2n−2	PROPN
ejpam-3912	214	22	+	+	SYM
ejpam-3912	214	23	1	1	NUM
ejpam-3912	214	24	index	index	NOUN
ejpam-3912	214	25	of	of	ADP
ejpam-3912	214	26	nilpotency	nilpotency	NOUN
ejpam-3912	214	27	.	.	PUNCT
ejpam-3912	215	1	recall	recall	VERB
ejpam-3912	215	2	that	that	SCONJ
ejpam-3912	215	3	a	a	DET
ejpam-3912	215	4	linear	linear	ADJ
ejpam-3912	215	5	mapping	mapping	NOUN
ejpam-3912	215	6	∆	∆	PROPN
ejpam-3912	215	7	on	on	ADP
ejpam-3912	215	8	e	e	PROPN
ejpam-3912	215	9	is	be	AUX
ejpam-3912	215	10	called	call	VERB
ejpam-3912	215	11	local	local	ADJ
ejpam-3912	215	12	derivation	derivation	NOUN
ejpam-3912	215	13	if	if	SCONJ
ejpam-3912	215	14	for	for	ADP
ejpam-3912	215	15	every	every	DET
ejpam-3912	215	16	u	u	PROPN
ejpam-3912	215	17	∈	∈	PROPN
ejpam-3912	215	18	e	e	NOUN
ejpam-3912	215	19	,	,	PUNCT
ejpam-3912	215	20	a	a	DET
ejpam-3912	215	21	derivation	derivation	NOUN
ejpam-3912	215	22	du	du	NOUN
ejpam-3912	215	23	exists	exist	VERB
ejpam-3912	215	24	such	such	ADJ
ejpam-3912	215	25	that	that	DET
ejpam-3912	215	26	∆(u	∆(u	NOUN
ejpam-3912	215	27	)	)	PUNCT
ejpam-3912	215	28	=	=	SYM
ejpam-3912	215	29	du(u	du(u	NOUN
ejpam-3912	215	30	)	)	PUNCT
ejpam-3912	215	31	.	.	PUNCT
ejpam-3912	216	1	a	a	DET
ejpam-3912	216	2	mapping	mapping	NOUN
ejpam-3912	216	3	(	(	PUNCT
ejpam-3912	216	4	not	not	PART
ejpam-3912	216	5	necessary	necessary	ADJ
ejpam-3912	216	6	linear	linear	NOUN
ejpam-3912	216	7	)	)	PUNCT
ejpam-3912	216	8	d	d	NOUN
ejpam-3912	216	9	:	:	PUNCT
ejpam-3912	216	10	e→	e→	NOUN
ejpam-3912	216	11	e	e	PROPN
ejpam-3912	216	12	is	be	AUX
ejpam-3912	216	13	called	call	VERB
ejpam-3912	216	14	2	2	NUM
ejpam-3912	216	15	-	-	PUNCT
ejpam-3912	216	16	local	local	ADJ
ejpam-3912	216	17	derivation	derivation	NOUN
ejpam-3912	216	18	of	of	ADP
ejpam-3912	216	19	algebra	algebra	NOUN
ejpam-3912	216	20	e	e	NOUN
ejpam-3912	216	21	if	if	SCONJ
ejpam-3912	216	22	for	for	ADP
ejpam-3912	216	23	every	every	DET
ejpam-3912	216	24	u	u	NOUN
ejpam-3912	216	25	,	,	PUNCT
ejpam-3912	216	26	v	v	NOUN
ejpam-3912	216	27	∈	∈	NOUN
ejpam-3912	216	28	e	e	NOUN
ejpam-3912	216	29	there	there	PRON
ejpam-3912	216	30	exists	exist	VERB
ejpam-3912	216	31	a	a	DET
ejpam-3912	216	32	derivation	derivation	NOUN
ejpam-3912	216	33	du	du	NOUN
ejpam-3912	216	34	,	,	PUNCT
ejpam-3912	216	35	v	v	NOUN
ejpam-3912	216	36	of	of	ADP
ejpam-3912	216	37	e	e	NOUN
ejpam-3912	216	38	such	such	ADJ
ejpam-3912	216	39	that	that	SCONJ
ejpam-3912	216	40	d(u	d(u	PROPN
ejpam-3912	216	41	)	)	PUNCT
ejpam-3912	216	42	=	=	SYM
ejpam-3912	216	43	du	du	X
ejpam-3912	216	44	,	,	PUNCT
ejpam-3912	216	45	v(u	v(u	NOUN
ejpam-3912	216	46	)	)	PUNCT
ejpam-3912	216	47	and	and	CCONJ
ejpam-3912	216	48	d(v	d(v	ADJ
ejpam-3912	216	49	)	)	PUNCT
ejpam-3912	216	50	=	=	SYM
ejpam-3912	216	51	du	du	X
ejpam-3912	216	52	,	,	PUNCT
ejpam-3912	216	53	v(v	v(v	PROPN
ejpam-3912	216	54	)	)	PUNCT
ejpam-3912	216	55	.	.	PUNCT
ejpam-3912	217	1	therefore	therefore	ADV
ejpam-3912	217	2	,	,	PUNCT
ejpam-3912	217	3	it	it	PRON
ejpam-3912	217	4	is	be	AUX
ejpam-3912	217	5	natural	natural	ADJ
ejpam-3912	217	6	to	to	PART
ejpam-3912	217	7	find	find	VERB
ejpam-3912	217	8	all	all	DET
ejpam-3912	217	9	local	local	ADJ
ejpam-3912	217	10	derivations	derivation	NOUN
ejpam-3912	217	11	of	of	ADP
ejpam-3912	217	12	e.	e.	PROPN
ejpam-3912	217	13	a.	a.	PROPN
ejpam-3912	217	14	alarafeen	alarafeen	PROPN
ejpam-3912	217	15	,	,	PUNCT
ejpam-3912	217	16	i.	i.	PROPN
ejpam-3912	217	17	qaralleh	qaralleh	PROPN
ejpam-3912	217	18	,	,	PUNCT
ejpam-3912	217	19	a.	a.	PROPN
ejpam-3912	217	20	ahmad	ahmad	PROPN
ejpam-3912	217	21	/	/	SYM
ejpam-3912	217	22	eur	eur	PROPN
ejpam-3912	217	23	.	.	PUNCT
ejpam-3912	218	1	j.	j.	PROPN
ejpam-3912	218	2	pure	pure	PROPN
ejpam-3912	218	3	appl	appl	PROPN
ejpam-3912	218	4	.	.	PROPN
ejpam-3912	218	5	math	math	PROPN
ejpam-3912	218	6	,	,	PUNCT
ejpam-3912	218	7	14	14	NUM
ejpam-3912	218	8	(	(	PUNCT
ejpam-3912	218	9	1	1	NUM
ejpam-3912	218	10	)	)	PUNCT
ejpam-3912	218	11	(	(	PUNCT
ejpam-3912	218	12	2021	2021	NUM
ejpam-3912	218	13	)	)	PUNCT
ejpam-3912	218	14	,	,	PUNCT
ejpam-3912	218	15	278	278	NUM
ejpam-3912	218	16	-	-	SYM
ejpam-3912	218	17	300	300	NUM
ejpam-3912	218	18	286	286	NUM
ejpam-3912	218	19	theorem	theorem	NOUN
ejpam-3912	218	20	4	4	NUM
ejpam-3912	218	21	.	.	PUNCT
ejpam-3912	219	1	let	let	VERB
ejpam-3912	219	2	e	e	PRON
ejpam-3912	219	3	be	be	AUX
ejpam-3912	219	4	an	an	DET
ejpam-3912	219	5	n	n	ADV
ejpam-3912	219	6	-	-	PUNCT
ejpam-3912	219	7	dimensional	dimensional	ADJ
ejpam-3912	219	8	nilpotent	nilpotent	ADJ
ejpam-3912	219	9	evolution	evolution	NOUN
ejpam-3912	219	10	algebra	algebra	NOUN
ejpam-3912	219	11	with	with	ADP
ejpam-3912	219	12	2(n−2	2(n−2	NOUN
ejpam-3912	219	13	)	)	PUNCT
ejpam-3912	219	14	+	+	SYM
ejpam-3912	219	15	1	1	NUM
ejpam-3912	219	16	index	index	NOUN
ejpam-3912	219	17	of	of	ADP
ejpam-3912	219	18	nilpotency	nilpotency	NOUN
ejpam-3912	219	19	.	.	PUNCT
ejpam-3912	220	1	then	then	ADV
ejpam-3912	220	2	,	,	PUNCT
ejpam-3912	220	3	the	the	DET
ejpam-3912	220	4	following	follow	VERB
ejpam-3912	220	5	statements	statement	NOUN
ejpam-3912	220	6	hold	hold	VERB
ejpam-3912	220	7	:	:	PUNCT
ejpam-3912	220	8	(	(	PUNCT
ejpam-3912	220	9	i	i	NOUN
ejpam-3912	220	10	)	)	PUNCT
ejpam-3912	220	11	if	if	SCONJ
ejpam-3912	220	12	n	n	NUM
ejpam-3912	220	13	=	=	SYM
ejpam-3912	220	14	3	3	NUM
ejpam-3912	220	15	,	,	PUNCT
ejpam-3912	220	16	then	then	ADV
ejpam-3912	220	17	the	the	DET
ejpam-3912	220	18	space	space	NOUN
ejpam-3912	220	19	of	of	ADP
ejpam-3912	220	20	all	all	DET
ejpam-3912	220	21	local	local	ADJ
ejpam-3912	220	22	derivations	derivation	NOUN
ejpam-3912	220	23	has	have	VERB
ejpam-3912	220	24	the	the	DET
ejpam-3912	220	25	following	follow	VERB
ejpam-3912	220	26	form:	form:	VERB
ejpam-3912	220	27			PROPN
ejpam-3912	220	28	α	α	PROPN
ejpam-3912	220	29	β	β	NOUN
ejpam-3912	220	30	γ	γ	X
ejpam-3912	220	31	0	0	NUM
ejpam-3912	220	32	δ	δ	PROPN
ejpam-3912	220	33	0	0	NUM
ejpam-3912	220	34	0	0	NUM
ejpam-3912	220	35	s	s	NOUN
ejpam-3912	220	36	t	t	NOUN
ejpam-3912	220	37			PROPN
ejpam-3912	220	38	:	:	PUNCT
ejpam-3912	220	39	α	α	X
ejpam-3912	220	40	,	,	PUNCT
ejpam-3912	220	41	β	β	X
ejpam-3912	220	42	,	,	PUNCT
ejpam-3912	220	43	γ	γ	PROPN
ejpam-3912	220	44	,	,	PUNCT
ejpam-3912	220	45	δ	δ	PROPN
ejpam-3912	220	46	,	,	PUNCT
ejpam-3912	220	47	s	s	PROPN
ejpam-3912	220	48	,	,	PUNCT
ejpam-3912	220	49	t	t	PROPN
ejpam-3912	220	50	∈	∈	PROPN
ejpam-3912	220	51	k	k	PROPN
ejpam-3912	220	52			PROPN
ejpam-3912	220	53	.	.	PUNCT
ejpam-3912	221	1	(	(	PUNCT
ejpam-3912	221	2	20	20	NUM
ejpam-3912	221	3	)	)	PUNCT
ejpam-3912	221	4	(	(	PUNCT
ejpam-3912	221	5	ii	ii	NOUN
ejpam-3912	221	6	)	)	PUNCT
ejpam-3912	221	7	if	if	SCONJ
ejpam-3912	221	8	n	n	PROPN
ejpam-3912	221	9	>	>	X
ejpam-3912	221	10	3	3	NUM
ejpam-3912	221	11	,	,	PUNCT
ejpam-3912	221	12	then	then	ADV
ejpam-3912	221	13	every	every	DET
ejpam-3912	221	14	local	local	ADJ
ejpam-3912	221	15	derivation	derivation	NOUN
ejpam-3912	221	16	of	of	ADP
ejpam-3912	221	17	e	e	PROPN
ejpam-3912	221	18	is	be	AUX
ejpam-3912	221	19	a	a	DET
ejpam-3912	221	20	derivation	derivation	NOUN
ejpam-3912	221	21	.	.	PUNCT
ejpam-3912	222	1	proof	proof	NOUN
ejpam-3912	222	2	.	.	PUNCT
ejpam-3912	223	1	(	(	PUNCT
ejpam-3912	223	2	i	i	NOUN
ejpam-3912	223	3	)	)	PUNCT
ejpam-3912	223	4	let	let	VERB
ejpam-3912	223	5	n	n	NOUN
ejpam-3912	223	6	=	=	SYM
ejpam-3912	223	7	3	3	X
ejpam-3912	223	8	.	.	NOUN
ejpam-3912	223	9	due	due	ADP
ejpam-3912	223	10	to	to	ADP
ejpam-3912	223	11	lemma	lemma	PROPN
ejpam-3912	223	12	2	2	NUM
ejpam-3912	223	13	,	,	PUNCT
ejpam-3912	223	14	we	we	PRON
ejpam-3912	223	15	may	may	AUX
ejpam-3912	223	16	assume	assume	VERB
ejpam-3912	223	17	that	that	SCONJ
ejpam-3912	223	18	an	an	DET
ejpam-3912	223	19	evolution	evolution	NOUN
ejpam-3912	223	20	algebra	algebra	NOUN
ejpam-3912	223	21	e	e	NOUN
ejpam-3912	223	22	is	be	AUX
ejpam-3912	223	23	given	give	VERB
ejpam-3912	223	24	by	by	ADP
ejpam-3912	223	25	e2	e2	PROPN
ejpam-3912	223	26	1	1	NUM
ejpam-3912	223	27	=	=	SYM
ejpam-3912	223	28	e2	e2	PROPN
ejpam-3912	223	29	and	and	CCONJ
ejpam-3912	223	30	e2	e2	PROPN
ejpam-3912	223	31	2	2	NUM
ejpam-3912	223	32	=	=	SYM
ejpam-3912	223	33	e2	e2	NOUN
ejpam-3912	223	34	3	3	NUM
ejpam-3912	223	35	=	=	SYM
ejpam-3912	223	36	0	0	X
ejpam-3912	223	37	.	.	PUNCT
ejpam-3912	224	1	take	take	VERB
ejpam-3912	224	2	an	an	DET
ejpam-3912	224	3	arbitrary	arbitrary	ADJ
ejpam-3912	224	4	linear	linear	NOUN
ejpam-3912	224	5	map	map	NOUN
ejpam-3912	224	6	∆	∆	PROPN
ejpam-3912	224	7	on	on	ADP
ejpam-3912	224	8	e	e	NOUN
ejpam-3912	224	9	,	,	PUNCT
ejpam-3912	224	10	i.e.	i.e.	X
ejpam-3912	224	11	,	,	PUNCT
ejpam-3912	224	12	∆(u	∆(u	ADJ
ejpam-3912	224	13	)	)	PUNCT
ejpam-3912	224	14	=	=	SYM
ejpam-3912	224	15	(	(	PUNCT
ejpam-3912	224	16	∆11u1+∆21u2+∆31u3)e1+(∆12u1+∆22u2+∆32u3)e2+(∆13u1+∆23u2+∆33u3)e3	∆11u1+∆21u2+∆31u3)e1+(∆12u1+∆22u2+∆32u3)e2+(∆13u1+∆23u2+∆33u3)e3	PROPN
ejpam-3912	224	17	,	,	PUNCT
ejpam-3912	224	18	∀u	∀u	NOUN
ejpam-3912	224	19	=	=	SYM
ejpam-3912	225	1	u1e1	u1e1	NOUN
ejpam-3912	225	2	+	+	CCONJ
ejpam-3912	225	3	u2e2	u2e2	PROPN
ejpam-3912	226	1	+	+	NUM
ejpam-3912	226	2	u3e3	u3e3	NOUN
ejpam-3912	226	3	.	.	PUNCT
ejpam-3912	227	1	if	if	SCONJ
ejpam-3912	227	2	∆	∆	PROPN
ejpam-3912	227	3	is	be	AUX
ejpam-3912	227	4	a	a	DET
ejpam-3912	227	5	local	local	ADJ
ejpam-3912	227	6	derivation	derivation	NOUN
ejpam-3912	227	7	,	,	PUNCT
ejpam-3912	227	8	then	then	ADV
ejpam-3912	227	9	for	for	ADP
ejpam-3912	227	10	any	any	DET
ejpam-3912	227	11	u	u	NOUN
ejpam-3912	227	12	,	,	PUNCT
ejpam-3912	227	13	there	there	PRON
ejpam-3912	227	14	exist	exist	VERB
ejpam-3912	227	15	αu	αu	PROPN
ejpam-3912	227	16	,	,	PUNCT
ejpam-3912	227	17	βu	βu	PROPN
ejpam-3912	227	18	,	,	PUNCT
ejpam-3912	227	19	su	su	PROPN
ejpam-3912	227	20	,	,	PUNCT
ejpam-3912	227	21	and	and	CCONJ
ejpam-3912	227	22	tu	tu	PROPN
ejpam-3912	227	23	such	such	ADJ
ejpam-3912	227	24	that	that	DET
ejpam-3912	227	25	∆11u1	∆11u1	NOUN
ejpam-3912	227	26	+	+	CCONJ
ejpam-3912	227	27	∆21u2	∆21u2	NOUN
ejpam-3912	227	28	+	+	CCONJ
ejpam-3912	227	29	∆31u3	∆31u3	NOUN
ejpam-3912	227	30	=	=	SYM
ejpam-3912	227	31	αuu1	αuu1	VERB
ejpam-3912	227	32	∆12u1	∆12u1	NOUN
ejpam-3912	227	33	+	+	CCONJ
ejpam-3912	227	34	∆22u2	∆22u2	PROPN
ejpam-3912	227	35	+	+	CCONJ
ejpam-3912	227	36	∆32u3	∆32u3	NOUN
ejpam-3912	227	37	=	=	SYM
ejpam-3912	227	38	βuu1	βuu1	NOUN
ejpam-3912	227	39	+	+	CCONJ
ejpam-3912	227	40	2αuu2	2αuu2	NUM
ejpam-3912	227	41	+	+	CCONJ
ejpam-3912	227	42	suu3	suu3	PROPN
ejpam-3912	227	43	∆13u1	∆13u1	ADJ
ejpam-3912	227	44	+	+	CCONJ
ejpam-3912	227	45	∆23u2	∆23u2	PROPN
ejpam-3912	227	46	+	+	CCONJ
ejpam-3912	227	47	∆33u3	∆33u3	NOUN
ejpam-3912	227	48	=	=	SYM
ejpam-3912	227	49	γuu1	γuu1	PROPN
ejpam-3912	227	50	+	+	CCONJ
ejpam-3912	227	51	tuu3	tuu3	PROPN
ejpam-3912	227	52	;	;	PUNCT
ejpam-3912	227	53	from	from	ADP
ejpam-3912	227	54	the	the	DET
ejpam-3912	227	55	first	first	ADJ
ejpam-3912	227	56	equation	equation	NOUN
ejpam-3912	227	57	,	,	PUNCT
ejpam-3912	227	58	we	we	PRON
ejpam-3912	227	59	get	get	VERB
ejpam-3912	227	60	∆21	∆21	NOUN
ejpam-3912	227	61	=	=	PUNCT
ejpam-3912	227	62	∆31	∆31	NOUN
ejpam-3912	227	63	=	=	PUNCT
ejpam-3912	228	1	0	0	X
ejpam-3912	228	2	.	.	PUNCT
ejpam-3912	229	1	if	if	SCONJ
ejpam-3912	229	2	we	we	PRON
ejpam-3912	229	3	take	take	VERB
ejpam-3912	229	4	u	u	PRON
ejpam-3912	229	5	such	such	ADJ
ejpam-3912	229	6	that	that	DET
ejpam-3912	229	7	u1	u1	NOUN
ejpam-3912	229	8	=	=	SYM
ejpam-3912	229	9	u3	u3	NOUN
ejpam-3912	229	10	=	=	SYM
ejpam-3912	229	11	0	0	NUM
ejpam-3912	229	12	,	,	PUNCT
ejpam-3912	229	13	then	then	ADV
ejpam-3912	229	14	from	from	ADP
ejpam-3912	229	15	the	the	DET
ejpam-3912	229	16	second	second	ADJ
ejpam-3912	229	17	equation	equation	NOUN
ejpam-3912	229	18	,	,	PUNCT
ejpam-3912	229	19	we	we	PRON
ejpam-3912	229	20	immediately	immediately	ADV
ejpam-3912	229	21	find	find	VERB
ejpam-3912	229	22	∆22	∆22	PRON
ejpam-3912	229	23	∈	∈	PROPN
ejpam-3912	229	24	{	{	PUNCT
ejpam-3912	229	25	0	0	NUM
ejpam-3912	229	26	,	,	PUNCT
ejpam-3912	229	27	2∆11	2∆11	NOUN
ejpam-3912	229	28	}	}	PUNCT
ejpam-3912	229	29	.	.	PUNCT
ejpam-3912	230	1	we	we	PRON
ejpam-3912	230	2	find	find	VERB
ejpam-3912	230	3	that	that	SCONJ
ejpam-3912	230	4	∆	∆	PROPN
ejpam-3912	230	5	is	be	AUX
ejpam-3912	230	6	a	a	DET
ejpam-3912	230	7	derivation	derivation	NOUN
ejpam-3912	230	8	of	of	ADP
ejpam-3912	230	9	e	e	NOUN
ejpam-3912	230	10	if	if	SCONJ
ejpam-3912	230	11	∆22	∆22	PROPN
ejpam-3912	230	12	=	=	SYM
ejpam-3912	230	13	2∆11	2∆11	PROPN
ejpam-3912	230	14	.	.	PUNCT
ejpam-3912	230	15	suppose	suppose	VERB
ejpam-3912	230	16	∆22	∆22	PROPN
ejpam-3912	230	17	=	=	SYM
ejpam-3912	230	18	0	0	PUNCT
ejpam-3912	230	19	and	and	CCONJ
ejpam-3912	230	20	∆11	∆11	X
ejpam-3912	230	21	6=	6=	ADP
ejpam-3912	230	22	0	0	NUM
ejpam-3912	230	23	.	.	PUNCT
ejpam-3912	231	1	then	then	ADV
ejpam-3912	231	2	,	,	PUNCT
ejpam-3912	231	3	for	for	ADP
ejpam-3912	231	4	every	every	DET
ejpam-3912	231	5	u	u	NOUN
ejpam-3912	231	6	,	,	PUNCT
ejpam-3912	231	7	we	we	PRON
ejpam-3912	231	8	can	can	AUX
ejpam-3912	231	9	find	find	VERB
ejpam-3912	231	10	that	that	SCONJ
ejpam-3912	231	11	derivation	derivation	NOUN
ejpam-3912	231	12	du	du	NOUN
ejpam-3912	231	13	satisfies	satisfie	NOUN
ejpam-3912	231	14	∆(u	∆(u	NOUN
ejpam-3912	231	15	)	)	PUNCT
ejpam-3912	231	16	=	=	SYM
ejpam-3912	231	17	du(u	du(u	NOUN
ejpam-3912	231	18	)	)	PUNCT
ejpam-3912	231	19	as	as	SCONJ
ejpam-3912	231	20	follows	follow	VERB
ejpam-3912	231	21	:	:	PUNCT
ejpam-3912	231	22	du	du	PROPN
ejpam-3912	231	23	=	=	SYM
ejpam-3912	231	24			X
ejpam-3912	232	1			PROPN
ejpam-3912	232	2	∆11	∆11	X
ejpam-3912	232	3	∆12	∆12	NOUN
ejpam-3912	232	4	−	−	PROPN
ejpam-3912	232	5	2∆11u2	2∆11u2	NUM
ejpam-3912	232	6	u1	u1	NOUN
ejpam-3912	232	7	∆13	∆13	PROPN
ejpam-3912	232	8	0	0	NUM
ejpam-3912	232	9	2∆11	2∆11	NUM
ejpam-3912	232	10	0	0	NUM
ejpam-3912	232	11	0	0	NUM
ejpam-3912	232	12	∆32	∆32	NOUN
ejpam-3912	232	13	∆33	∆33	DET
ejpam-3912	232	14			PROPN
ejpam-3912	232	15	,	,	PUNCT
ejpam-3912	232	16	if	if	SCONJ
ejpam-3912	232	17	u1	u1	NOUN
ejpam-3912	232	18	,	,	PUNCT
ejpam-3912	232	19	u3	u3	NOUN
ejpam-3912	232	20	6=	6=	ADP
ejpam-3912	232	21	0,	0,	ADP
ejpam-3912	232	22	0	0	SYM
ejpam-3912	232	23	0	0	NUM
ejpam-3912	232	24	0	0	NUM
ejpam-3912	232	25	0	0	NUM
ejpam-3912	232	26	0	0	NUM
ejpam-3912	232	27	0	0	NUM
ejpam-3912	232	28	0	0	NUM
ejpam-3912	232	29	0	0	NUM
ejpam-3912	232	30	0	0	NUM
ejpam-3912	233	1			PROPN
ejpam-3912	233	2	,	,	PUNCT
ejpam-3912	233	3	if	if	SCONJ
ejpam-3912	233	4	u1	u1	NOUN
ejpam-3912	233	5	=	=	SYM
ejpam-3912	233	6	u3	u3	NOUN
ejpam-3912	233	7	=	=	SYM
ejpam-3912	233	8	0	0	PROPN
ejpam-3912	233	9	.	.	PUNCT
ejpam-3912	234	1	this	this	DET
ejpam-3912	234	2	result	result	NOUN
ejpam-3912	234	3	means	mean	VERB
ejpam-3912	234	4	that	that	SCONJ
ejpam-3912	234	5	a	a	DET
ejpam-3912	234	6	linear	linear	ADJ
ejpam-3912	234	7	mapping	mapping	NOUN
ejpam-3912	234	8	defined	define	VERB
ejpam-3912	234	9	by	by	ADP
ejpam-3912	234	10	∆	∆	PROPN
ejpam-3912	234	11	=	=	PUNCT
ejpam-3912	235	1			PROPN
ejpam-3912	235	2	α	α	X
ejpam-3912	235	3	β	β	X
ejpam-3912	235	4	γ	γ	X
ejpam-3912	235	5	0	0	PROPN
ejpam-3912	235	6	0	0	NUM
ejpam-3912	235	7	0	0	NUM
ejpam-3912	235	8	0	0	NUM
ejpam-3912	235	9	s	s	NOUN
ejpam-3912	235	10	t	t	NOUN
ejpam-3912	235	11			PROPN
ejpam-3912	235	12	:	:	PUNCT
ejpam-3912	236	1	α	α	X
ejpam-3912	236	2	,	,	PUNCT
ejpam-3912	236	3	β	β	X
ejpam-3912	236	4	,	,	PUNCT
ejpam-3912	236	5	γ	γ	PROPN
ejpam-3912	236	6	,	,	PUNCT
ejpam-3912	236	7	s	s	PROPN
ejpam-3912	236	8	,	,	PUNCT
ejpam-3912	236	9	t	t	PROPN
ejpam-3912	236	10	∈	∈	PROPN
ejpam-3912	236	11	k	k	X
ejpam-3912	236	12	(	(	PUNCT
ejpam-3912	236	13	21	21	NUM
ejpam-3912	236	14	)	)	PUNCT
ejpam-3912	236	15	is	be	AUX
ejpam-3912	236	16	a	a	DET
ejpam-3912	236	17	local	local	ADJ
ejpam-3912	236	18	derivation	derivation	NOUN
ejpam-3912	236	19	of	of	ADP
ejpam-3912	236	20	e.	e.	PROPN
ejpam-3912	236	21	finally	finally	ADV
ejpam-3912	236	22	,	,	PUNCT
ejpam-3912	236	23	as	as	SCONJ
ejpam-3912	236	24	every	every	DET
ejpam-3912	236	25	derivation	derivation	NOUN
ejpam-3912	236	26	of	of	ADP
ejpam-3912	236	27	algebra	algebra	NOUN
ejpam-3912	236	28	e	e	NOUN
ejpam-3912	236	29	is	be	AUX
ejpam-3912	236	30	local	local	ADJ
ejpam-3912	236	31	derivation	derivation	NOUN
ejpam-3912	236	32	and	and	CCONJ
ejpam-3912	236	33	due	due	ADP
ejpam-3912	236	34	to	to	PART
ejpam-3912	236	35	(	(	PUNCT
ejpam-3912	236	36	21	21	NUM
ejpam-3912	236	37	)	)	PUNCT
ejpam-3912	236	38	,	,	PUNCT
ejpam-3912	236	39	one	one	NUM
ejpam-3912	236	40	obtains	obtain	VERB
ejpam-3912	236	41	(	(	PUNCT
ejpam-3912	236	42	20	20	NUM
ejpam-3912	236	43	)	)	PUNCT
ejpam-3912	236	44	.	.	PUNCT
ejpam-3912	237	1	a.	a.	PROPN
ejpam-3912	237	2	alarafeen	alarafeen	PROPN
ejpam-3912	237	3	,	,	PUNCT
ejpam-3912	237	4	i.	i.	PROPN
ejpam-3912	237	5	qaralleh	qaralleh	PROPN
ejpam-3912	237	6	,	,	PUNCT
ejpam-3912	237	7	a.	a.	PROPN
ejpam-3912	237	8	ahmad	ahmad	PROPN
ejpam-3912	237	9	/	/	SYM
ejpam-3912	237	10	eur	eur	PROPN
ejpam-3912	237	11	.	.	PUNCT
ejpam-3912	238	1	j.	j.	PROPN
ejpam-3912	238	2	pure	pure	PROPN
ejpam-3912	238	3	appl	appl	PROPN
ejpam-3912	238	4	.	.	PROPN
ejpam-3912	238	5	math	math	PROPN
ejpam-3912	238	6	,	,	PUNCT
ejpam-3912	238	7	14	14	NUM
ejpam-3912	238	8	(	(	PUNCT
ejpam-3912	238	9	1	1	NUM
ejpam-3912	238	10	)	)	PUNCT
ejpam-3912	238	11	(	(	PUNCT
ejpam-3912	238	12	2021	2021	NUM
ejpam-3912	238	13	)	)	PUNCT
ejpam-3912	238	14	,	,	PUNCT
ejpam-3912	238	15	278	278	NUM
ejpam-3912	238	16	-	-	SYM
ejpam-3912	238	17	300	300	NUM
ejpam-3912	238	18	287	287	NUM
ejpam-3912	238	19	(	(	PUNCT
ejpam-3912	238	20	ii	ii	NOUN
ejpam-3912	238	21	)	)	PUNCT
ejpam-3912	238	22	let	let	VERB
ejpam-3912	238	23	∆	∆	PROPN
ejpam-3912	238	24	be	be	AUX
ejpam-3912	238	25	a	a	DET
ejpam-3912	238	26	non	non	ADJ
ejpam-3912	238	27	-	-	ADJ
ejpam-3912	238	28	zero	zero	ADJ
ejpam-3912	238	29	local	local	ADJ
ejpam-3912	238	30	derivation	derivation	NOUN
ejpam-3912	238	31	given	give	VERB
ejpam-3912	238	32	by	by	ADP
ejpam-3912	238	33	matrix	matrix	NOUN
ejpam-3912	238	34	(	(	PUNCT
ejpam-3912	238	35	∆ij	∆ij	NOUN
ejpam-3912	238	36	)	)	PUNCT
ejpam-3912	239	1	n	n	PROPN
ejpam-3912	239	2	i	i	PRON
ejpam-3912	239	3	,	,	PUNCT
ejpam-3912	239	4	j≥1	j≥1	PROPN
ejpam-3912	239	5	.	.	PUNCT
ejpam-3912	240	1	assume	assume	VERB
ejpam-3912	240	2	that	that	SCONJ
ejpam-3912	240	3	ia	ia	PROPN
ejpam-3912	240	4	6=	6=	ADP
ejpam-3912	240	5	∅.	∅.	ADP
ejpam-3912	240	6	then	then	ADV
ejpam-3912	240	7	,	,	PUNCT
ejpam-3912	240	8	due	due	ADP
ejpam-3912	240	9	to	to	ADP
ejpam-3912	240	10	∆(ei	∆(ei	NUM
ejpam-3912	240	11	)	)	PUNCT
ejpam-3912	240	12	=	=	SYM
ejpam-3912	240	13	dei(ei	dei(ei	NOUN
ejpam-3912	240	14	)	)	PUNCT
ejpam-3912	240	15	,	,	PUNCT
ejpam-3912	240	16	for	for	ADP
ejpam-3912	240	17	any	any	DET
ejpam-3912	240	18	i	i	PROPN
ejpam-3912	240	19	≤	≤	PROPN
ejpam-3912	240	20	n	n	CCONJ
ejpam-3912	240	21	,	,	PUNCT
ejpam-3912	240	22	we	we	PRON
ejpam-3912	240	23	immediately	immediately	ADV
ejpam-3912	240	24	obtain	obtain	VERB
ejpam-3912	240	25	∆1,n−1	∆1,n−1	NOUN
ejpam-3912	240	26	=	=	SYM
ejpam-3912	241	1	d	d	PROPN
ejpam-3912	241	2	(	(	PUNCT
ejpam-3912	241	3	e1	e1	PROPN
ejpam-3912	241	4	)	)	PUNCT
ejpam-3912	241	5	1,n−1	1,n−1	NUM
ejpam-3912	241	6	,	,	PUNCT
ejpam-3912	241	7	∆1n	∆1n	NOUN
ejpam-3912	241	8	=	=	SYM
ejpam-3912	242	1	d	d	X
ejpam-3912	242	2	(	(	PUNCT
ejpam-3912	242	3	e1	e1	PROPN
ejpam-3912	242	4	)	)	PUNCT
ejpam-3912	242	5	1,n	1,n	NUM
ejpam-3912	242	6	;	;	PUNCT
ejpam-3912	242	7	(	(	PUNCT
ejpam-3912	242	8	22	22	NUM
ejpam-3912	242	9	)	)	PUNCT
ejpam-3912	242	10	∆im	∆im	VERB
ejpam-3912	243	1	=	=	SYM
ejpam-3912	243	2	d	d	X
ejpam-3912	243	3	(	(	PUNCT
ejpam-3912	243	4	ei	ei	NOUN
ejpam-3912	243	5	)	)	PUNCT
ejpam-3912	243	6	i	i	PRON
ejpam-3912	243	7	m	m	VERB
ejpam-3912	243	8	,	,	PUNCT
ejpam-3912	243	9	m	m	VERB
ejpam-3912	243	10	∈	∈	NOUN
ejpam-3912	243	11	{	{	PUNCT
ejpam-3912	243	12	n−	n−	NOUN
ejpam-3912	243	13	1	1	NUM
ejpam-3912	243	14	,	,	PUNCT
ejpam-3912	243	15	n	n	CCONJ
ejpam-3912	243	16	}	}	PUNCT
ejpam-3912	243	17	,	,	PUNCT
ejpam-3912	243	18	2	2	NUM
ejpam-3912	243	19	≤	≤	NUM
ejpam-3912	244	1	i	i	PRON
ejpam-3912	244	2	<	<	X
ejpam-3912	244	3	n−	n−	NOUN
ejpam-3912	244	4	1	1	NUM
ejpam-3912	244	5	;	;	PUNCT
ejpam-3912	244	6	(	(	PUNCT
ejpam-3912	244	7	23	23	X
ejpam-3912	244	8	)	)	PUNCT
ejpam-3912	244	9	∆n−1,n−1	∆n−1,n−1	NOUN
ejpam-3912	244	10	=	=	SYM
ejpam-3912	245	1	d	d	PROPN
ejpam-3912	245	2	(	(	PUNCT
ejpam-3912	245	3	en−1	en−1	PROPN
ejpam-3912	245	4	)	)	PUNCT
ejpam-3912	245	5	n−1,n−1	n−1,n−1	PROPN
ejpam-3912	245	6	,	,	PUNCT
ejpam-3912	245	7	∆n−1,n	∆n−1,n	X
ejpam-3912	245	8	=	=	SYM
ejpam-3912	245	9	d	d	PROPN
ejpam-3912	245	10	(	(	PUNCT
ejpam-3912	245	11	en−1	en−1	PROPN
ejpam-3912	245	12	)	)	PUNCT
ejpam-3912	245	13	n−1,n	n−1,n	PROPN
ejpam-3912	245	14	;	;	PUNCT
ejpam-3912	245	15	(	(	PUNCT
ejpam-3912	245	16	24	24	NUM
ejpam-3912	245	17	)	)	PUNCT
ejpam-3912	245	18	∆n	∆n	PROPN
ejpam-3912	245	19	,	,	PUNCT
ejpam-3912	245	20	n−1	n−1	PROPN
ejpam-3912	245	21	=	=	SYM
ejpam-3912	245	22	d(en	d(en	PROPN
ejpam-3912	245	23	)	)	PUNCT
ejpam-3912	245	24	n	n	CCONJ
ejpam-3912	245	25	,	,	PUNCT
ejpam-3912	245	26	n−1	n−1	PROPN
ejpam-3912	245	27	,	,	PUNCT
ejpam-3912	245	28	∆n	∆n	PROPN
ejpam-3912	245	29	,	,	PUNCT
ejpam-3912	245	30	n	n	NOUN
ejpam-3912	245	31	=	=	SYM
ejpam-3912	245	32	d(en	d(en	NOUN
ejpam-3912	245	33	)	)	PUNCT
ejpam-3912	245	34	nn	nn	PROPN
ejpam-3912	245	35	;	;	PUNCT
ejpam-3912	245	36	(	(	PUNCT
ejpam-3912	245	37	25	25	NUM
ejpam-3912	245	38	)	)	PUNCT
ejpam-3912	245	39	∆ij	∆ij	NOUN
ejpam-3912	245	40	=	=	SYM
ejpam-3912	245	41	0	0	NUM
ejpam-3912	245	42	,	,	PUNCT
ejpam-3912	245	43	otherwise	otherwise	ADV
ejpam-3912	245	44	.	.	PUNCT
ejpam-3912	246	1	(	(	PUNCT
ejpam-3912	246	2	26	26	NUM
ejpam-3912	246	3	)	)	PUNCT
ejpam-3912	246	4	taking	take	VERB
ejpam-3912	246	5	u	u	NOUN
ejpam-3912	246	6	=	=	PROPN
ejpam-3912	246	7	∑n−2	∑n−2	PROPN
ejpam-3912	246	8	k=2	k=2	PROPN
ejpam-3912	246	9	ek	ek	PROPN
ejpam-3912	246	10	.	.	PUNCT
ejpam-3912	247	1	we	we	PRON
ejpam-3912	247	2	obtain	obtain	VERB
ejpam-3912	247	3	∆im	∆im	NOUN
ejpam-3912	247	4	=	=	SYM
ejpam-3912	247	5	−	−	ADP
ejpam-3912	247	6	∑n−i	∑n−i	ADP
ejpam-3912	247	7	k=1	k=1	PROPN
ejpam-3912	247	8	ai−1,k+i∆k+i	ai−1,k+i∆k+i	NOUN
ejpam-3912	247	9	,	,	PUNCT
ejpam-3912	247	10	m.	m.	NOUN
ejpam-3912	247	11	we	we	PRON
ejpam-3912	247	12	consider	consider	VERB
ejpam-3912	247	13	that	that	PRON
ejpam-3912	247	14	,	,	PUNCT
ejpam-3912	247	15	v	v	NOUN
ejpam-3912	247	16	=	=	SYM
ejpam-3912	247	17	en−1	en−1	PROPN
ejpam-3912	247	18	+	+	CCONJ
ejpam-3912	247	19	an−2,nen	an−2,nen	PROPN
ejpam-3912	247	20	,	,	PUNCT
ejpam-3912	247	21	and	and	CCONJ
ejpam-3912	247	22	then	then	ADV
ejpam-3912	247	23	a	a	DET
ejpam-3912	247	24	derivation	derivation	NOUN
ejpam-3912	247	25	dv	dv	PROPN
ejpam-3912	247	26	exists	exist	VERB
ejpam-3912	247	27	such	such	ADJ
ejpam-3912	247	28	that	that	SCONJ
ejpam-3912	247	29	∆(v	∆(v	NOUN
ejpam-3912	247	30	)	)	PUNCT
ejpam-3912	247	31	=	=	PUNCT
ejpam-3912	247	32	dv(v	dv(v	PROPN
ejpam-3912	247	33	)	)	PUNCT
ejpam-3912	247	34	.	.	PUNCT
ejpam-3912	248	1	thus	thus	ADV
ejpam-3912	248	2	,	,	PUNCT
ejpam-3912	248	3	(	(	PUNCT
ejpam-3912	248	4	−an−2,nd	−an−2,nd	X
ejpam-3912	248	5	(	(	PUNCT
ejpam-3912	248	6	en−1	en−1	PROPN
ejpam-3912	248	7	)	)	PUNCT
ejpam-3912	248	8	n	n	CCONJ
ejpam-3912	248	9	,	,	PUNCT
ejpam-3912	248	10	n−1	n−1	PROPN
ejpam-3912	248	11	+	+	CCONJ
ejpam-3912	248	12	an−2,nd	an−2,nd	PROPN
ejpam-3912	248	13	(	(	PUNCT
ejpam-3912	248	14	en	en	NOUN
ejpam-3912	248	15	)	)	PUNCT
ejpam-3912	248	16	n	n	CCONJ
ejpam-3912	248	17	,	,	PUNCT
ejpam-3912	248	18	n−1)en−1	n−1)en−1	PROPN
ejpam-3912	248	19	+	+	CCONJ
ejpam-3912	248	20	(	(	PUNCT
ejpam-3912	248	21	−an−2,nd	−an−2,nd	PUNCT
ejpam-3912	248	22	(	(	PUNCT
ejpam-3912	248	23	en−1	en−1	PROPN
ejpam-3912	248	24	)	)	PUNCT
ejpam-3912	248	25	n	n	CCONJ
ejpam-3912	248	26	,	,	PUNCT
ejpam-3912	248	27	n	n	X
ejpam-3912	248	28	+	+	CCONJ
ejpam-3912	248	29	an−2,nd	an−2,nd	PROPN
ejpam-3912	248	30	(	(	PUNCT
ejpam-3912	248	31	en	en	X
ejpam-3912	248	32	)	)	PUNCT
ejpam-3912	248	33	nn	nn	NOUN
ejpam-3912	248	34	)	)	PUNCT
ejpam-3912	248	35	en	en	X
ejpam-3912	248	36	=	=	PUNCT
ejpam-3912	248	37	(	(	PUNCT
ejpam-3912	248	38	−an−2,nd	−an−2,nd	X
ejpam-3912	248	39	(	(	PUNCT
ejpam-3912	248	40	u	u	NOUN
ejpam-3912	248	41	)	)	PUNCT
ejpam-3912	248	42	n	n	CCONJ
ejpam-3912	248	43	,	,	PUNCT
ejpam-3912	248	44	n−1	n−1	PROPN
ejpam-3912	248	45	+	+	CCONJ
ejpam-3912	248	46	an−2,nd	an−2,nd	PROPN
ejpam-3912	248	47	(	(	PUNCT
ejpam-3912	248	48	u	u	NOUN
ejpam-3912	248	49	)	)	PUNCT
ejpam-3912	248	50	n	n	CCONJ
ejpam-3912	248	51	,	,	PUNCT
ejpam-3912	248	52	n−1)en−1	n−1)en−1	PROPN
ejpam-3912	248	53	+	+	CCONJ
ejpam-3912	248	54	(	(	PUNCT
ejpam-3912	248	55	−an−2,nd	−an−2,nd	PUNCT
ejpam-3912	248	56	(	(	PUNCT
ejpam-3912	248	57	u	u	NOUN
ejpam-3912	248	58	)	)	PUNCT
ejpam-3912	248	59	n	n	CCONJ
ejpam-3912	248	60	,	,	PUNCT
ejpam-3912	248	61	n	n	PROPN
ejpam-3912	248	62	+	+	CCONJ
ejpam-3912	248	63	an−2,nd	an−2,nd	PROPN
ejpam-3912	248	64	(	(	PUNCT
ejpam-3912	248	65	u	u	NOUN
ejpam-3912	248	66	)	)	PUNCT
ejpam-3912	248	67	nn	nn	PROPN
ejpam-3912	248	68	)	)	PUNCT
ejpam-3912	248	69	en	en	X
ejpam-3912	248	70	.	.	PUNCT
ejpam-3912	249	1	this	this	DET
ejpam-3912	249	2	result	result	NOUN
ejpam-3912	249	3	implies	imply	VERB
ejpam-3912	249	4	d	d	PROPN
ejpam-3912	249	5	(	(	PUNCT
ejpam-3912	249	6	en−1	en−1	PROPN
ejpam-3912	249	7	)	)	PUNCT
ejpam-3912	249	8	n	n	CCONJ
ejpam-3912	249	9	,	,	PUNCT
ejpam-3912	249	10	n−1	n−1	PROPN
ejpam-3912	249	11	=	=	SYM
ejpam-3912	249	12	d	d	PROPN
ejpam-3912	249	13	(	(	PUNCT
ejpam-3912	249	14	en	en	X
ejpam-3912	249	15	)	)	PUNCT
ejpam-3912	249	16	n	n	CCONJ
ejpam-3912	249	17	,	,	PUNCT
ejpam-3912	249	18	n−1	n−1	PROPN
ejpam-3912	249	19	,	,	PUNCT
ejpam-3912	249	20	d	d	X
ejpam-3912	249	21	(	(	PUNCT
ejpam-3912	249	22	en−1	en−1	PROPN
ejpam-3912	249	23	)	)	PUNCT
ejpam-3912	249	24	n	n	CCONJ
ejpam-3912	249	25	,	,	PUNCT
ejpam-3912	249	26	n	n	NOUN
ejpam-3912	249	27	=	=	SYM
ejpam-3912	249	28	d	d	PROPN
ejpam-3912	249	29	(	(	PUNCT
ejpam-3912	249	30	en	en	X
ejpam-3912	249	31	)	)	PUNCT
ejpam-3912	249	32	nn	nn	PROPN
ejpam-3912	249	33	.	.	PUNCT
ejpam-3912	250	1	therefore	therefore	ADV
ejpam-3912	250	2	,	,	PUNCT
ejpam-3912	250	3	one	one	PRON
ejpam-3912	250	4	has	have	VERB
ejpam-3912	250	5	∆n−1,n−1	∆n−1,n−1	NOUN
ejpam-3912	250	6	=	=	PUNCT
ejpam-3912	250	7	−an−1,n∆n	−an−1,n∆n	NOUN
ejpam-3912	250	8	,	,	PUNCT
ejpam-3912	250	9	n−1	n−1	PROPN
ejpam-3912	250	10	.	.	PROPN
ejpam-3912	250	11	suppose	suppose	VERB
ejpam-3912	250	12	that	that	SCONJ
ejpam-3912	250	13	ia	ia	PROPN
ejpam-3912	250	14	=	=	PUNCT
ejpam-3912	250	15	∅.we	∅.we	NOUN
ejpam-3912	250	16	establish	establish	VERB
ejpam-3912	250	17	that	that	SCONJ
ejpam-3912	250	18	∆	∆	PROPN
ejpam-3912	250	19	∈	∈	PROPN
ejpam-3912	250	20	der(e	der(e	PROPN
ejpam-3912	250	21	)	)	PUNCT
ejpam-3912	250	22	for	for	ADP
ejpam-3912	250	23	any	any	DET
ejpam-3912	250	24	local	local	ADJ
ejpam-3912	250	25	derivation	derivation	NOUN
ejpam-3912	250	26	∆.	∆.	NOUN
ejpam-3912	250	27	due	due	ADP
ejpam-3912	250	28	to	to	ADP
ejpam-3912	250	29	lemmas	lemmas	PROPN
ejpam-3912	250	30	2	2	NUM
ejpam-3912	250	31	and	and	CCONJ
ejpam-3912	250	32	1	1	NUM
ejpam-3912	250	33	,	,	PUNCT
ejpam-3912	250	34	to	to	PART
ejpam-3912	250	35	show	show	VERB
ejpam-3912	250	36	every	every	DET
ejpam-3912	250	37	local	local	ADJ
ejpam-3912	250	38	derivation	derivation	NOUN
ejpam-3912	250	39	can	can	AUX
ejpam-3912	250	40	be	be	AUX
ejpam-3912	250	41	a	a	DET
ejpam-3912	250	42	derivation	derivation	NOUN
ejpam-3912	250	43	we	we	PRON
ejpam-3912	250	44	need	need	VERB
ejpam-3912	250	45	to	to	PART
ejpam-3912	250	46	check	check	VERB
ejpam-3912	250	47	only	only	ADV
ejpam-3912	250	48	for	for	ADP
ejpam-3912	250	49	evolution	evolution	NOUN
ejpam-3912	250	50	algebra	algebra	NOUN
ejpam-3912	250	51	e′	e′	PROPN
ejpam-3912	250	52	(	(	PUNCT
ejpam-3912	250	53	see	see	VERB
ejpam-3912	250	54	lemma	lemma	PROPN
ejpam-3912	250	55	2	2	NUM
ejpam-3912	250	56	)	)	PUNCT
ejpam-3912	250	57	.	.	PUNCT
ejpam-3912	251	1	as	as	ADP
ejpam-3912	251	2	∆(ei	∆(ei	NOUN
ejpam-3912	251	3	)	)	PUNCT
ejpam-3912	251	4	=	=	SYM
ejpam-3912	251	5	dei(ei	dei(ei	NOUN
ejpam-3912	251	6	)	)	PUNCT
ejpam-3912	251	7	,	,	PUNCT
ejpam-3912	251	8	for	for	ADP
ejpam-3912	251	9	any	any	DET
ejpam-3912	251	10	i	i	PROPN
ejpam-3912	251	11	≤	≤	PROPN
ejpam-3912	251	12	n	n	CCONJ
ejpam-3912	251	13	,	,	PUNCT
ejpam-3912	251	14	we	we	PRON
ejpam-3912	251	15	can	can	AUX
ejpam-3912	251	16	easily	easily	ADV
ejpam-3912	251	17	find	find	VERB
ejpam-3912	251	18	∆ii	∆ii	NOUN
ejpam-3912	252	1	=	=	PUNCT
ejpam-3912	253	1	d	d	PROPN
ejpam-3912	253	2	(	(	PUNCT
ejpam-3912	253	3	ei	ei	NOUN
ejpam-3912	253	4	)	)	PUNCT
ejpam-3912	253	5	ii	ii	PROPN
ejpam-3912	253	6	,	,	PUNCT
ejpam-3912	253	7	i	i	PRON
ejpam-3912	253	8	≤	≤	VERB
ejpam-3912	253	9	n−	n−	PROPN
ejpam-3912	253	10	1	1	NUM
ejpam-3912	253	11	∆1,n−1	∆1,n−1	VERB
ejpam-3912	253	12	=	=	SYM
ejpam-3912	253	13	d	d	PROPN
ejpam-3912	253	14	(	(	PUNCT
ejpam-3912	253	15	e1	e1	PROPN
ejpam-3912	253	16	)	)	PUNCT
ejpam-3912	253	17	1,n−1	1,n−1	NUM
ejpam-3912	253	18	∆1n	∆1n	NOUN
ejpam-3912	254	1	=	=	SYM
ejpam-3912	254	2	d	d	X
ejpam-3912	254	3	(	(	PUNCT
ejpam-3912	254	4	e1	e1	PROPN
ejpam-3912	254	5	)	)	PUNCT
ejpam-3912	254	6	1n	1n	PROPN
ejpam-3912	254	7	∆n	∆n	PROPN
ejpam-3912	254	8	,	,	PUNCT
ejpam-3912	254	9	n−1	n−1	PROPN
ejpam-3912	254	10	=	=	SYM
ejpam-3912	254	11	d	d	PROPN
ejpam-3912	254	12	(	(	PUNCT
ejpam-3912	254	13	en	en	X
ejpam-3912	254	14	)	)	PUNCT
ejpam-3912	254	15	n	n	CCONJ
ejpam-3912	254	16	,	,	PUNCT
ejpam-3912	254	17	n−1	n−1	PROPN
ejpam-3912	254	18	∆n	∆n	PROPN
ejpam-3912	254	19	,	,	PUNCT
ejpam-3912	254	20	n	n	NOUN
ejpam-3912	254	21	=	=	SYM
ejpam-3912	254	22	d	d	PROPN
ejpam-3912	254	23	(	(	PUNCT
ejpam-3912	254	24	en	en	X
ejpam-3912	254	25	)	)	PUNCT
ejpam-3912	254	26	n	n	CCONJ
ejpam-3912	254	27	,	,	PUNCT
ejpam-3912	254	28	n	n	PRON
ejpam-3912	254	29	∆ij	∆ij	NOUN
ejpam-3912	254	30	=	=	SYM
ejpam-3912	254	31	0	0	NUM
ejpam-3912	254	32	,	,	PUNCT
ejpam-3912	254	33	otherwise	otherwise	ADV
ejpam-3912	254	34	.	.	PUNCT
ejpam-3912	255	1	(	(	PUNCT
ejpam-3912	255	2	27	27	NUM
ejpam-3912	255	3	)	)	PUNCT
ejpam-3912	255	4	taking	take	VERB
ejpam-3912	255	5	u	u	NOUN
ejpam-3912	255	6	=	=	NOUN
ejpam-3912	255	7	∑n−2	∑n−2	PROPN
ejpam-3912	255	8	k=1	k=1	X
ejpam-3912	256	1	ek	ek	PROPN
ejpam-3912	256	2	,	,	PUNCT
ejpam-3912	256	3	we	we	PRON
ejpam-3912	256	4	obtain	obtain	VERB
ejpam-3912	256	5	∆ii	∆ii	X
ejpam-3912	257	1	=	=	SYM
ejpam-3912	258	1	2i−1∆11	2i−1∆11	NUM
ejpam-3912	258	2	,	,	PUNCT
ejpam-3912	258	3	i	i	PRON
ejpam-3912	258	4	<	<	X
ejpam-3912	258	5	n−	n−	NOUN
ejpam-3912	258	6	1	1	NUM
ejpam-3912	258	7	.	.	PUNCT
ejpam-3912	259	1	(	(	PUNCT
ejpam-3912	259	2	28	28	NUM
ejpam-3912	259	3	)	)	PUNCT
ejpam-3912	259	4	consider	consider	VERB
ejpam-3912	259	5	v	v	NOUN
ejpam-3912	259	6	=	=	SYM
ejpam-3912	259	7	e2	e2	PROPN
ejpam-3912	259	8	+	+	CCONJ
ejpam-3912	259	9	en−1	en−1	PROPN
ejpam-3912	259	10	.	.	PUNCT
ejpam-3912	260	1	then	then	ADV
ejpam-3912	260	2	,	,	PUNCT
ejpam-3912	260	3	a	a	DET
ejpam-3912	260	4	derivation	derivation	NOUN
ejpam-3912	260	5	dv	dv	PROPN
ejpam-3912	260	6	exists	exist	VERB
ejpam-3912	260	7	such	such	ADJ
ejpam-3912	260	8	that	that	SCONJ
ejpam-3912	260	9	∆(v	∆(v	NOUN
ejpam-3912	260	10	)	)	PUNCT
ejpam-3912	260	11	=	=	PUNCT
ejpam-3912	260	12	dv(v	dv(v	PROPN
ejpam-3912	260	13	)	)	PUNCT
ejpam-3912	260	14	.	.	PUNCT
ejpam-3912	261	1	due	due	ADP
ejpam-3912	261	2	to	to	ADP
ejpam-3912	261	3	the	the	DET
ejpam-3912	261	4	assumption	assumption	NOUN
ejpam-3912	261	5	(	(	PUNCT
ejpam-3912	261	6	ii	ii	NOUN
ejpam-3912	261	7	)	)	PUNCT
ejpam-3912	261	8	of	of	ADP
ejpam-3912	261	9	theorem	theorem	NOUN
ejpam-3912	261	10	3	3	NUM
ejpam-3912	261	11	,	,	PUNCT
ejpam-3912	261	12	we	we	PRON
ejpam-3912	261	13	have	have	VERB
ejpam-3912	261	14	∆22e2	∆22e2	NOUN
ejpam-3912	261	15	+	+	NUM
ejpam-3912	261	16	∆n−1,n−1en	∆n−1,n−1en	ADJ
ejpam-3912	261	17	=	=	SYM
ejpam-3912	261	18	2d	2d	X
ejpam-3912	261	19	(	(	PUNCT
ejpam-3912	261	20	v	v	NOUN
ejpam-3912	261	21	)	)	PUNCT
ejpam-3912	261	22	11	11	NUM
ejpam-3912	261	23	e2	e2	NOUN
ejpam-3912	261	24	+	+	CCONJ
ejpam-3912	261	25	2n−2d	2n−2d	NUM
ejpam-3912	261	26	(	(	PUNCT
ejpam-3912	261	27	v	v	NOUN
ejpam-3912	261	28	)	)	PUNCT
ejpam-3912	261	29	11	11	NUM
ejpam-3912	261	30	en	en	X
ejpam-3912	261	31	.	.	PUNCT
ejpam-3912	262	1	this	this	DET
ejpam-3912	262	2	result	result	NOUN
ejpam-3912	262	3	implies	imply	VERB
ejpam-3912	262	4	2d	2d	NUM
ejpam-3912	262	5	(	(	PUNCT
ejpam-3912	262	6	v	v	NOUN
ejpam-3912	262	7	)	)	PUNCT
ejpam-3912	262	8	11	11	NUM
ejpam-3912	262	9	=	=	SYM
ejpam-3912	262	10	∆22	∆22	PRON
ejpam-3912	262	11	2n−2d	2n−2d	NUM
ejpam-3912	262	12	(	(	PUNCT
ejpam-3912	262	13	v	v	NOUN
ejpam-3912	262	14	)	)	PUNCT
ejpam-3912	262	15	11	11	NUM
ejpam-3912	262	16	=	=	SYM
ejpam-3912	262	17	∆n−1,n−1	∆n−1,n−1	PROPN
ejpam-3912	262	18	.	.	PUNCT
ejpam-3912	262	19	a.	a.	PROPN
ejpam-3912	262	20	alarafeen	alarafeen	PROPN
ejpam-3912	262	21	,	,	PUNCT
ejpam-3912	262	22	i.	i.	PROPN
ejpam-3912	262	23	qaralleh	qaralleh	PROPN
ejpam-3912	262	24	,	,	PUNCT
ejpam-3912	262	25	a.	a.	PROPN
ejpam-3912	262	26	ahmad	ahmad	PROPN
ejpam-3912	262	27	/	/	SYM
ejpam-3912	262	28	eur	eur	PROPN
ejpam-3912	262	29	.	.	PUNCT
ejpam-3912	263	1	j.	j.	PROPN
ejpam-3912	263	2	pure	pure	PROPN
ejpam-3912	263	3	appl	appl	PROPN
ejpam-3912	263	4	.	.	PROPN
ejpam-3912	263	5	math	math	PROPN
ejpam-3912	263	6	,	,	PUNCT
ejpam-3912	263	7	14	14	NUM
ejpam-3912	263	8	(	(	PUNCT
ejpam-3912	263	9	1	1	NUM
ejpam-3912	263	10	)	)	PUNCT
ejpam-3912	263	11	(	(	PUNCT
ejpam-3912	263	12	2021	2021	NUM
ejpam-3912	263	13	)	)	PUNCT
ejpam-3912	263	14	,	,	PUNCT
ejpam-3912	263	15	278	278	NUM
ejpam-3912	263	16	-	-	SYM
ejpam-3912	263	17	300	300	NUM
ejpam-3912	263	18	288	288	NUM
ejpam-3912	263	19	adding	add	VERB
ejpam-3912	263	20	the	the	DET
ejpam-3912	263	21	preceding	precede	VERB
ejpam-3912	263	22	equations	equation	NOUN
ejpam-3912	263	23	into	into	ADP
ejpam-3912	263	24	(	(	PUNCT
ejpam-3912	263	25	28	28	NUM
ejpam-3912	263	26	)	)	PUNCT
ejpam-3912	263	27	,	,	PUNCT
ejpam-3912	263	28	we	we	PRON
ejpam-3912	263	29	obtain	obtain	VERB
ejpam-3912	263	30	∆ii	∆ii	X
ejpam-3912	264	1	=	=	SYM
ejpam-3912	265	1	2i−1∆11	2i−1∆11	X
ejpam-3912	265	2	.	.	PUNCT
ejpam-3912	265	3	then	then	ADV
ejpam-3912	265	4	,	,	PUNCT
ejpam-3912	265	5	using	use	VERB
ejpam-3912	265	6	(	(	PUNCT
ejpam-3912	265	7	27	27	NUM
ejpam-3912	265	8	)	)	PUNCT
ejpam-3912	265	9	,	,	PUNCT
ejpam-3912	265	10	one	one	PRON
ejpam-3912	265	11	finds	find	VERB
ejpam-3912	265	12	∆ii	∆ii	X
ejpam-3912	266	1	=	=	SYM
ejpam-3912	266	2	d	d	PROPN
ejpam-3912	266	3	(	(	PUNCT
ejpam-3912	266	4	e1	e1	PROPN
ejpam-3912	266	5	)	)	PUNCT
ejpam-3912	266	6	ii	ii	NOUN
ejpam-3912	266	7	,	,	PUNCT
ejpam-3912	266	8	i	i	PRON
ejpam-3912	266	9	≤	≤	VERB
ejpam-3912	266	10	n−	n−	PROPN
ejpam-3912	266	11	1	1	NUM
ejpam-3912	266	12	∆1,n−1	∆1,n−1	VERB
ejpam-3912	267	1	=	=	SYM
ejpam-3912	267	2	d	d	PROPN
ejpam-3912	267	3	(	(	PUNCT
ejpam-3912	267	4	e1	e1	PROPN
ejpam-3912	267	5	)	)	PUNCT
ejpam-3912	267	6	1,n−1	1,n−1	NUM
ejpam-3912	267	7	∆1n	∆1n	NOUN
ejpam-3912	268	1	=	=	SYM
ejpam-3912	268	2	d	d	X
ejpam-3912	268	3	(	(	PUNCT
ejpam-3912	268	4	e1	e1	PROPN
ejpam-3912	268	5	)	)	PUNCT
ejpam-3912	268	6	1n	1n	PROPN
ejpam-3912	268	7	∆n	∆n	PROPN
ejpam-3912	268	8	,	,	PUNCT
ejpam-3912	268	9	n−1	n−1	PROPN
ejpam-3912	268	10	=	=	SYM
ejpam-3912	268	11	d	d	PROPN
ejpam-3912	268	12	(	(	PUNCT
ejpam-3912	268	13	en	en	X
ejpam-3912	268	14	)	)	PUNCT
ejpam-3912	268	15	n	n	CCONJ
ejpam-3912	268	16	,	,	PUNCT
ejpam-3912	268	17	n−1	n−1	PROPN
ejpam-3912	268	18	∆n	∆n	PROPN
ejpam-3912	268	19	,	,	PUNCT
ejpam-3912	268	20	n	n	NOUN
ejpam-3912	268	21	=	=	SYM
ejpam-3912	268	22	d	d	PROPN
ejpam-3912	268	23	(	(	PUNCT
ejpam-3912	268	24	en	en	X
ejpam-3912	268	25	)	)	PUNCT
ejpam-3912	268	26	n	n	CCONJ
ejpam-3912	268	27	,	,	PUNCT
ejpam-3912	268	28	n	n	PRON
ejpam-3912	268	29	∆ij	∆ij	NOUN
ejpam-3912	268	30	=	=	SYM
ejpam-3912	268	31	0	0	NUM
ejpam-3912	268	32	,	,	PUNCT
ejpam-3912	268	33	otherwise	otherwise	ADV
ejpam-3912	268	34	.	.	PUNCT
ejpam-3912	269	1	thus	thus	ADV
ejpam-3912	269	2	,	,	PUNCT
ejpam-3912	269	3	due	due	ADP
ejpam-3912	269	4	to	to	ADP
ejpam-3912	269	5	theorem	theorem	NOUN
ejpam-3912	269	6	3	3	NUM
ejpam-3912	269	7	,	,	PUNCT
ejpam-3912	269	8	we	we	PRON
ejpam-3912	269	9	conclude	conclude	VERB
ejpam-3912	269	10	that	that	SCONJ
ejpam-3912	269	11	∆	∆	PROPN
ejpam-3912	269	12	is	be	AUX
ejpam-3912	269	13	a	a	DET
ejpam-3912	269	14	derivation	derivation	NOUN
ejpam-3912	269	15	.	.	PUNCT
ejpam-3912	270	1	the	the	DET
ejpam-3912	270	2	proof	proof	NOUN
ejpam-3912	270	3	is	be	AUX
ejpam-3912	270	4	complete	complete	ADJ
ejpam-3912	270	5	.	.	PUNCT
ejpam-3912	271	1	remark	remark	NOUN
ejpam-3912	271	2	3	3	NUM
ejpam-3912	271	3	.	.	PUNCT
ejpam-3912	272	1	in	in	ADP
ejpam-3912	272	2	[	[	X
ejpam-3912	272	3	25	25	NUM
ejpam-3912	272	4	]	]	PUNCT
ejpam-3912	272	5	,	,	PUNCT
ejpam-3912	272	6	it	it	PRON
ejpam-3912	272	7	was	be	AUX
ejpam-3912	272	8	proven	prove	VERB
ejpam-3912	272	9	that	that	SCONJ
ejpam-3912	272	10	if	if	SCONJ
ejpam-3912	272	11	n	n	PROPN
ejpam-3912	272	12	>	>	X
ejpam-3912	272	13	2	2	NUM
ejpam-3912	272	14	then	then	ADV
ejpam-3912	272	15	all	all	DET
ejpam-3912	272	16	local	local	ADJ
ejpam-3912	272	17	derivation	derivation	NOUN
ejpam-3912	272	18	is	be	AUX
ejpam-3912	272	19	derivation	derivation	NOUN
ejpam-3912	272	20	,	,	PUNCT
ejpam-3912	272	21	in	in	ADP
ejpam-3912	272	22	the	the	DET
ejpam-3912	272	23	above	above	ADJ
ejpam-3912	272	24	theorem	theorem	NOUN
ejpam-3912	272	25	we	we	PRON
ejpam-3912	272	26	find	find	VERB
ejpam-3912	272	27	the	the	DET
ejpam-3912	272	28	if	if	SCONJ
ejpam-3912	272	29	n	n	PROPN
ejpam-3912	272	30	>	>	X
ejpam-3912	272	31	3	3	NUM
ejpam-3912	272	32	then	then	ADV
ejpam-3912	272	33	all	all	DET
ejpam-3912	272	34	local	local	ADJ
ejpam-3912	272	35	derivation	derivation	NOUN
ejpam-3912	272	36	is	be	AUX
ejpam-3912	272	37	derivation	derivation	NOUN
ejpam-3912	272	38	.	.	PUNCT
ejpam-3912	273	1	theorem	theorem	ADJ
ejpam-3912	273	2	5	5	NUM
ejpam-3912	273	3	.	.	PUNCT
ejpam-3912	274	1	every	every	DET
ejpam-3912	274	2	2	2	NUM
ejpam-3912	274	3	-	-	PUNCT
ejpam-3912	274	4	local	local	ADJ
ejpam-3912	274	5	derivation	derivation	NOUN
ejpam-3912	274	6	of	of	ADP
ejpam-3912	274	7	nilpotent	nilpotent	ADJ
ejpam-3912	274	8	evolution	evolution	NOUN
ejpam-3912	274	9	algebras	algebra	NOUN
ejpam-3912	274	10	with	with	ADP
ejpam-3912	274	11	2n−2	2n−2	PROPN
ejpam-3912	274	12	+	+	SYM
ejpam-3912	274	13	1	1	NUM
ejpam-3912	274	14	index	index	NOUN
ejpam-3912	274	15	of	of	ADP
ejpam-3912	274	16	nilpotency	nilpotency	NOUN
ejpam-3912	274	17	is	be	AUX
ejpam-3912	274	18	a	a	DET
ejpam-3912	274	19	derivation	derivation	NOUN
ejpam-3912	274	20	.	.	PUNCT
ejpam-3912	275	1	proof	proof	NOUN
ejpam-3912	275	2	.	.	PUNCT
ejpam-3912	276	1	let	let	VERB
ejpam-3912	276	2	d	d	PRON
ejpam-3912	276	3	be	be	AUX
ejpam-3912	276	4	a	a	DET
ejpam-3912	276	5	non	non	ADJ
ejpam-3912	276	6	-	-	ADJ
ejpam-3912	276	7	zero	zero	NUM
ejpam-3912	276	8	2	2	NUM
ejpam-3912	276	9	-	-	PUNCT
ejpam-3912	276	10	local	local	ADJ
ejpam-3912	276	11	derivation	derivation	NOUN
ejpam-3912	276	12	of	of	ADP
ejpam-3912	276	13	e.	e.	PROPN
ejpam-3912	276	14	denote	denote	PROPN
ejpam-3912	276	15	γ1	γ1	PROPN
ejpam-3912	276	16	=	=	SYM
ejpam-3912	276	17	{	{	PUNCT
ejpam-3912	276	18	u	u	X
ejpam-3912	276	19	∈	∈	PROPN
ejpam-3912	276	20	e	e	NOUN
ejpam-3912	276	21	:	:	PUNCT
ejpam-3912	276	22	u1	u1	PROPN
ejpam-3912	276	23	6=	6=	PRON
ejpam-3912	276	24	0	0	NUM
ejpam-3912	276	25	}	}	PUNCT
ejpam-3912	276	26	,	,	PUNCT
ejpam-3912	276	27	γ2	γ2	NOUN
ejpam-3912	276	28	=	=	SYM
ejpam-3912	276	29	{	{	PUNCT
ejpam-3912	276	30	u	u	NOUN
ejpam-3912	276	31	∈	∈	PROPN
ejpam-3912	276	32	e	e	NOUN
ejpam-3912	276	33	:	:	PUNCT
ejpam-3912	276	34	un	un	PROPN
ejpam-3912	276	35	6=	6=	PROPN
ejpam-3912	276	36	0	0	NUM
ejpam-3912	276	37	}	}	PUNCT
ejpam-3912	276	38	.	.	PUNCT
ejpam-3912	277	1	case	case	NOUN
ejpam-3912	277	2	ia	ia	NOUN
ejpam-3912	277	3	=	=	PUNCT
ejpam-3912	277	4	∅.	∅.	NOUN
ejpam-3912	277	5	by	by	ADP
ejpam-3912	277	6	definition	definition	NOUN
ejpam-3912	277	7	,	,	PUNCT
ejpam-3912	277	8	functionals	functional	VERB
ejpam-3912	277	9	αu	αu	NOUN
ejpam-3912	277	10	,	,	PUNCT
ejpam-3912	277	11	v	v	NOUN
ejpam-3912	277	12	,	,	PUNCT
ejpam-3912	277	13	βu	βu	NOUN
ejpam-3912	277	14	,	,	PUNCT
ejpam-3912	277	15	v	v	NOUN
ejpam-3912	277	16	,	,	PUNCT
ejpam-3912	277	17	γu	γu	NOUN
ejpam-3912	277	18	,	,	PUNCT
ejpam-3912	277	19	v	v	PROPN
ejpam-3912	277	20	,	,	PUNCT
ejpam-3912	277	21	su	su	PROPN
ejpam-3912	277	22	,	,	PUNCT
ejpam-3912	277	23	v	v	PROPN
ejpam-3912	277	24	and	and	CCONJ
ejpam-3912	277	25	tu	tu	PROPN
ejpam-3912	277	26	,	,	PUNCT
ejpam-3912	277	27	v	v	PRON
ejpam-3912	277	28	exist	exist	VERB
ejpam-3912	277	29	such	such	ADJ
ejpam-3912	277	30	that	that	SCONJ
ejpam-3912	277	31	d(u	d(u	PROPN
ejpam-3912	277	32	)	)	PUNCT
ejpam-3912	277	33	=	=	PUNCT
ejpam-3912	278	1	n−2∑	n−2∑	PROPN
ejpam-3912	279	1	k=1	k=1	PROPN
ejpam-3912	279	2	2k−1αu	2k−1αu	NUM
ejpam-3912	279	3	,	,	PUNCT
ejpam-3912	279	4	vukek+	vukek+	PRON
ejpam-3912	279	5	(	(	PUNCT
ejpam-3912	279	6	βu	βu	NOUN
ejpam-3912	279	7	,	,	PUNCT
ejpam-3912	279	8	vu1	vu1	X
ejpam-3912	279	9	+	+	CCONJ
ejpam-3912	279	10	(	(	PUNCT
ejpam-3912	279	11	kn−1αu	kn−1αu	NUM
ejpam-3912	279	12	,	,	PUNCT
ejpam-3912	279	13	v	v	ADP
ejpam-3912	279	14	−mn−1su	−mn−1su	NOUN
ejpam-3912	279	15	,	,	PUNCT
ejpam-3912	279	16	v)un−1	v)un−1	PROPN
ejpam-3912	279	17	+	+	PROPN
ejpam-3912	279	18	su	su	PROPN
ejpam-3912	279	19	,	,	PUNCT
ejpam-3912	279	20	vun	vun	PROPN
ejpam-3912	279	21	+	+	CCONJ
ejpam-3912	279	22	n−2∑	n−2∑	NUM
ejpam-3912	279	23	i=2	i=2	PROPN
ejpam-3912	279	24	(	(	PUNCT
ejpam-3912	279	25	kiαu	kiαu	PROPN
ejpam-3912	279	26	,	,	PUNCT
ejpam-3912	279	27	v	v	ADP
ejpam-3912	279	28	+	+	NOUN
ejpam-3912	279	29	misu	misu	NOUN
ejpam-3912	279	30	,	,	PUNCT
ejpam-3912	279	31	v)ui	v)ui	PROPN
ejpam-3912	279	32	)	)	PUNCT
ejpam-3912	279	33	en−1	en−1	PROPN
ejpam-3912	279	34	+	+	CCONJ
ejpam-3912	279	35	(	(	PUNCT
ejpam-3912	279	36	γu	γu	PROPN
ejpam-3912	279	37	,	,	PUNCT
ejpam-3912	279	38	vu1	vu1	X
ejpam-3912	279	39	+	+	CCONJ
ejpam-3912	279	40	(	(	PUNCT
ejpam-3912	279	41	ln−1αu	ln−1αu	NOUN
ejpam-3912	279	42	,	,	PUNCT
ejpam-3912	279	43	v	v	ADP
ejpam-3912	279	44	−nn−1tu	−nn−1tu	ADJ
ejpam-3912	279	45	,	,	PUNCT
ejpam-3912	279	46	v)un−1	v)un−1	PROPN
ejpam-3912	279	47	+	+	PROPN
ejpam-3912	279	48	tu	tu	PROPN
ejpam-3912	279	49	,	,	PUNCT
ejpam-3912	279	50	vun	vun	PROPN
ejpam-3912	279	51	+	+	CCONJ
ejpam-3912	279	52	n−2∑	n−2∑	NUM
ejpam-3912	279	53	i=2	i=2	PROPN
ejpam-3912	279	54	(	(	PUNCT
ejpam-3912	279	55	liαu	liαu	PROPN
ejpam-3912	279	56	,	,	PUNCT
ejpam-3912	279	57	v	v	ADP
ejpam-3912	279	58	+	+	NOUN
ejpam-3912	279	59	nitu	nitu	ADJ
ejpam-3912	279	60	,	,	PUNCT
ejpam-3912	279	61	v)ui	v)ui	PROPN
ejpam-3912	279	62	)	)	PUNCT
ejpam-3912	279	63	en	en	X
ejpam-3912	279	64	d(v	d(v	PROPN
ejpam-3912	279	65	)	)	PUNCT
ejpam-3912	279	66	=	=	PUNCT
ejpam-3912	280	1	n−2∑	n−2∑	PROPN
ejpam-3912	281	1	k=1	k=1	PROPN
ejpam-3912	281	2	2k−1αu	2k−1αu	NUM
ejpam-3912	281	3	,	,	PUNCT
ejpam-3912	281	4	vvkek+	vvkek+	X
ejpam-3912	281	5	(	(	PUNCT
ejpam-3912	281	6	βu	βu	NOUN
ejpam-3912	281	7	,	,	PUNCT
ejpam-3912	281	8	vv1	vv1	NOUN
ejpam-3912	281	9	+	+	CCONJ
ejpam-3912	281	10	(	(	PUNCT
ejpam-3912	281	11	kn−1αu	kn−1αu	NUM
ejpam-3912	281	12	,	,	PUNCT
ejpam-3912	281	13	v	v	ADP
ejpam-3912	281	14	−mn−1su	−mn−1su	NOUN
ejpam-3912	281	15	,	,	PUNCT
ejpam-3912	281	16	v	v	NOUN
ejpam-3912	281	17	)	)	PUNCT
ejpam-3912	281	18	vn−1	vn−1	PROPN
ejpam-3912	281	19	+	+	NUM
ejpam-3912	281	20	su	su	PROPN
ejpam-3912	281	21	,	,	PUNCT
ejpam-3912	281	22	vvn	vvn	PROPN
ejpam-3912	281	23	+	+	CCONJ
ejpam-3912	281	24	n−2∑	n−2∑	NUM
ejpam-3912	281	25	i=2	i=2	PROPN
ejpam-3912	281	26	(	(	PUNCT
ejpam-3912	281	27	kiαu	kiαu	PROPN
ejpam-3912	281	28	,	,	PUNCT
ejpam-3912	281	29	v	v	ADP
ejpam-3912	281	30	+	+	NOUN
ejpam-3912	281	31	misu	misu	NOUN
ejpam-3912	281	32	,	,	PUNCT
ejpam-3912	281	33	v	v	NOUN
ejpam-3912	281	34	)	)	PUNCT
ejpam-3912	281	35	vi	vi	NOUN
ejpam-3912	281	36	)	)	PUNCT
ejpam-3912	282	1	en−1	en−1	PROPN
ejpam-3912	282	2	+	+	CCONJ
ejpam-3912	282	3	(	(	PUNCT
ejpam-3912	282	4	γu	γu	PROPN
ejpam-3912	282	5	,	,	PUNCT
ejpam-3912	282	6	vv1	vv1	NOUN
ejpam-3912	282	7	+	+	CCONJ
ejpam-3912	282	8	(	(	PUNCT
ejpam-3912	282	9	ln−1αu	ln−1αu	NOUN
ejpam-3912	282	10	,	,	PUNCT
ejpam-3912	282	11	v	v	ADP
ejpam-3912	282	12	−nn−1tu	−nn−1tu	ADJ
ejpam-3912	282	13	,	,	PUNCT
ejpam-3912	282	14	v	v	NOUN
ejpam-3912	282	15	)	)	PUNCT
ejpam-3912	282	16	vn−1	vn−1	PROPN
ejpam-3912	282	17	+	+	CCONJ
ejpam-3912	282	18	tu	tu	PROPN
ejpam-3912	282	19	,	,	PUNCT
ejpam-3912	282	20	vvn	vvn	PROPN
ejpam-3912	282	21	+	+	CCONJ
ejpam-3912	282	22	n−2∑	n−2∑	NUM
ejpam-3912	282	23	i=2	i=2	PROPN
ejpam-3912	282	24	(	(	PUNCT
ejpam-3912	282	25	liαu	liαu	PROPN
ejpam-3912	282	26	,	,	PUNCT
ejpam-3912	282	27	v	v	ADP
ejpam-3912	282	28	+	+	SYM
ejpam-3912	282	29	nitu	nitu	ADJ
ejpam-3912	282	30	,	,	PUNCT
ejpam-3912	282	31	v	v	NOUN
ejpam-3912	282	32	)	)	PUNCT
ejpam-3912	282	33	vi	vi	NOUN
ejpam-3912	282	34	)	)	PUNCT
ejpam-3912	282	35	en	en	X
ejpam-3912	282	36	(	(	PUNCT
ejpam-3912	282	37	29	29	NUM
ejpam-3912	282	38	)	)	PUNCT
ejpam-3912	282	39	where	where	SCONJ
ejpam-3912	282	40	u	u	NOUN
ejpam-3912	282	41	=	=	PUNCT
ejpam-3912	282	42	∑n	∑n	PROPN
ejpam-3912	282	43	k=1	k=1	PROPN
ejpam-3912	282	44	ukek	ukek	NOUN
ejpam-3912	282	45	and	and	CCONJ
ejpam-3912	282	46	v	v	NOUN
ejpam-3912	282	47	=	=	SYM
ejpam-3912	282	48	∑n	∑n	NOUN
ejpam-3912	282	49	k=1	k=1	X
ejpam-3912	282	50	vkek	vkek	PROPN
ejpam-3912	282	51	.	.	PUNCT
ejpam-3912	283	1	take	take	VERB
ejpam-3912	283	2	an	an	DET
ejpam-3912	283	3	arbitrary	arbitrary	ADJ
ejpam-3912	283	4	non	non	ADJ
ejpam-3912	283	5	-	-	ADJ
ejpam-3912	283	6	zero	zero	NUM
ejpam-3912	283	7	u	u	NOUN
ejpam-3912	283	8	∈	∈	PROPN
ejpam-3912	283	9	e.	e.	PROPN
ejpam-3912	283	10	then	then	ADV
ejpam-3912	283	11	,	,	PUNCT
ejpam-3912	283	12	for	for	ADP
ejpam-3912	283	13	a.	a.	PROPN
ejpam-3912	283	14	alarafeen	alarafeen	PROPN
ejpam-3912	283	15	,	,	PUNCT
ejpam-3912	283	16	i.	i.	PROPN
ejpam-3912	283	17	qaralleh	qaralleh	PROPN
ejpam-3912	283	18	,	,	PUNCT
ejpam-3912	283	19	a.	a.	PROPN
ejpam-3912	283	20	ahmad	ahmad	PROPN
ejpam-3912	283	21	/	/	SYM
ejpam-3912	283	22	eur	eur	PROPN
ejpam-3912	283	23	.	.	PUNCT
ejpam-3912	284	1	j.	j.	PROPN
ejpam-3912	284	2	pure	pure	PROPN
ejpam-3912	284	3	appl	appl	PROPN
ejpam-3912	284	4	.	.	PROPN
ejpam-3912	284	5	math	math	PROPN
ejpam-3912	284	6	,	,	PUNCT
ejpam-3912	284	7	14	14	NUM
ejpam-3912	284	8	(	(	PUNCT
ejpam-3912	284	9	1	1	NUM
ejpam-3912	284	10	)	)	PUNCT
ejpam-3912	284	11	(	(	PUNCT
ejpam-3912	284	12	2021	2021	NUM
ejpam-3912	284	13	)	)	PUNCT
ejpam-3912	284	14	,	,	PUNCT
ejpam-3912	284	15	278	278	NUM
ejpam-3912	284	16	-	-	SYM
ejpam-3912	284	17	300	300	NUM
ejpam-3912	284	18	289	289	NUM
ejpam-3912	284	19	any	any	DET
ejpam-3912	284	20	v	v	NOUN
ejpam-3912	284	21	,	,	PUNCT
ejpam-3912	284	22	v′	v′	NOUN
ejpam-3912	284	23	∈	∈	PROPN
ejpam-3912	284	24	e	e	NOUN
ejpam-3912	284	25	from	from	ADP
ejpam-3912	284	26	the	the	DET
ejpam-3912	284	27	preceding	precede	VERB
ejpam-3912	284	28	equations	equation	NOUN
ejpam-3912	285	1	,	,	PUNCT
ejpam-3912	285	2	we	we	PRON
ejpam-3912	285	3	find	find	VERB
ejpam-3912	285	4	n−2∑	n−2∑	NUM
ejpam-3912	285	5	k=1	k=1	PROPN
ejpam-3912	285	6	2k−1αu	2k−1αu	PROPN
ejpam-3912	285	7	,	,	PUNCT
ejpam-3912	285	8	vukek+	vukek+	PRON
ejpam-3912	285	9	(	(	PUNCT
ejpam-3912	285	10	βu	βu	NOUN
ejpam-3912	285	11	,	,	PUNCT
ejpam-3912	285	12	vu1	vu1	X
ejpam-3912	285	13	+	+	CCONJ
ejpam-3912	285	14	(	(	PUNCT
ejpam-3912	285	15	kn−1αu	kn−1αu	NUM
ejpam-3912	285	16	,	,	PUNCT
ejpam-3912	285	17	v	v	ADP
ejpam-3912	285	18	−mn−1su	−mn−1su	NOUN
ejpam-3912	285	19	,	,	PUNCT
ejpam-3912	285	20	v)un−1	v)un−1	PROPN
ejpam-3912	285	21	+	+	PROPN
ejpam-3912	285	22	su	su	PROPN
ejpam-3912	285	23	,	,	PUNCT
ejpam-3912	285	24	vun	vun	PROPN
ejpam-3912	285	25	+	+	CCONJ
ejpam-3912	285	26	n−2∑	n−2∑	NUM
ejpam-3912	285	27	i=2	i=2	PROPN
ejpam-3912	285	28	(	(	PUNCT
ejpam-3912	285	29	kiαu	kiαu	PROPN
ejpam-3912	285	30	,	,	PUNCT
ejpam-3912	285	31	v	v	ADP
ejpam-3912	285	32	+	+	NOUN
ejpam-3912	285	33	misu	misu	NOUN
ejpam-3912	285	34	,	,	PUNCT
ejpam-3912	285	35	v)ui	v)ui	PROPN
ejpam-3912	285	36	)	)	PUNCT
ejpam-3912	285	37	en−1	en−1	PROPN
ejpam-3912	285	38	+	+	CCONJ
ejpam-3912	285	39	(	(	PUNCT
ejpam-3912	285	40	γu	γu	PROPN
ejpam-3912	285	41	,	,	PUNCT
ejpam-3912	285	42	vu1	vu1	X
ejpam-3912	285	43	+	+	CCONJ
ejpam-3912	285	44	(	(	PUNCT
ejpam-3912	285	45	ln−1αu	ln−1αu	NOUN
ejpam-3912	285	46	,	,	PUNCT
ejpam-3912	285	47	v	v	ADP
ejpam-3912	285	48	−nn−1tu	−nn−1tu	ADJ
ejpam-3912	285	49	,	,	PUNCT
ejpam-3912	285	50	v)un−1	v)un−1	PROPN
ejpam-3912	285	51	+	+	PROPN
ejpam-3912	285	52	tu	tu	PROPN
ejpam-3912	285	53	,	,	PUNCT
ejpam-3912	285	54	vun	vun	PROPN
ejpam-3912	285	55	+	+	CCONJ
ejpam-3912	285	56	n−2∑	n−2∑	NUM
ejpam-3912	285	57	i=2	i=2	PROPN
ejpam-3912	285	58	(	(	PUNCT
ejpam-3912	285	59	liαu	liαu	PROPN
ejpam-3912	285	60	,	,	PUNCT
ejpam-3912	285	61	v	v	ADP
ejpam-3912	285	62	+	+	NOUN
ejpam-3912	285	63	nitu	nitu	ADJ
ejpam-3912	285	64	,	,	PUNCT
ejpam-3912	285	65	v)ui	v)ui	PROPN
ejpam-3912	285	66	)	)	PUNCT
ejpam-3912	285	67	en	en	X
ejpam-3912	285	68	=	=	SYM
ejpam-3912	285	69	n−2∑	n−2∑	PROPN
ejpam-3912	285	70	k=1	k=1	PROPN
ejpam-3912	285	71	2k−1αu	2k−1αu	NUM
ejpam-3912	285	72	,	,	PUNCT
ejpam-3912	285	73	v′ukek+	v′ukek+	PROPN
ejpam-3912	285	74	(	(	PUNCT
ejpam-3912	285	75	βu	βu	NOUN
ejpam-3912	285	76	,	,	PUNCT
ejpam-3912	285	77	v′u1	v′u1	NOUN
ejpam-3912	285	78	+	+	CCONJ
ejpam-3912	285	79	(	(	PUNCT
ejpam-3912	285	80	kn−1αu	kn−1αu	NUM
ejpam-3912	285	81	,	,	PUNCT
ejpam-3912	285	82	v′	v′	NOUN
ejpam-3912	285	83	−mn−1su	−mn−1su	PROPN
ejpam-3912	285	84	,	,	PUNCT
ejpam-3912	285	85	v′	v′	NOUN
ejpam-3912	285	86	)	)	PUNCT
ejpam-3912	286	1	un−1	un−1	PROPN
ejpam-3912	286	2	+	+	NUM
ejpam-3912	286	3	su	su	PROPN
ejpam-3912	286	4	,	,	PUNCT
ejpam-3912	286	5	v′un	v′un	NOUN
ejpam-3912	286	6	+	+	CCONJ
ejpam-3912	286	7	n−2∑	n−2∑	NUM
ejpam-3912	286	8	i=2	i=2	PROPN
ejpam-3912	286	9	(	(	PUNCT
ejpam-3912	286	10	kiαu	kiαu	PROPN
ejpam-3912	286	11	,	,	PUNCT
ejpam-3912	286	12	v′	v′	NOUN
ejpam-3912	287	1	+	+	NOUN
ejpam-3912	287	2	misu	misu	NOUN
ejpam-3912	287	3	,	,	PUNCT
ejpam-3912	287	4	v′	v′	NUM
ejpam-3912	287	5	)	)	PUNCT
ejpam-3912	287	6	ui	ui	PROPN
ejpam-3912	287	7	)	)	PUNCT
ejpam-3912	288	1	en−1	en−1	PROPN
ejpam-3912	288	2	+	+	CCONJ
ejpam-3912	288	3	(	(	PUNCT
ejpam-3912	288	4	γu	γu	PROPN
ejpam-3912	288	5	,	,	PUNCT
ejpam-3912	288	6	v′u1	v′u1	NOUN
ejpam-3912	288	7	+	+	CCONJ
ejpam-3912	288	8	(	(	PUNCT
ejpam-3912	288	9	ln−1αu	ln−1αu	PROPN
ejpam-3912	288	10	,	,	PUNCT
ejpam-3912	288	11	v′	v′	X
ejpam-3912	288	12	−nn−1tu	−nn−1tu	ADJ
ejpam-3912	288	13	,	,	PUNCT
ejpam-3912	288	14	v′	v′	NOUN
ejpam-3912	288	15	)	)	PUNCT
ejpam-3912	289	1	un−1	un−1	PROPN
ejpam-3912	289	2	+	+	CCONJ
ejpam-3912	289	3	tu	tu	PROPN
ejpam-3912	289	4	,	,	PUNCT
ejpam-3912	289	5	v′un	v′un	NOUN
ejpam-3912	289	6	+	+	CCONJ
ejpam-3912	289	7	n−2∑	n−2∑	NUM
ejpam-3912	289	8	i=2	i=2	PROPN
ejpam-3912	289	9	(	(	PUNCT
ejpam-3912	289	10	liαu	liαu	PROPN
ejpam-3912	289	11	,	,	PUNCT
ejpam-3912	289	12	v′	v′	X
ejpam-3912	289	13	+	+	SYM
ejpam-3912	289	14	nitu	nitu	ADJ
ejpam-3912	289	15	,	,	PUNCT
ejpam-3912	289	16	v′	v′	NOUN
ejpam-3912	289	17	)	)	PUNCT
ejpam-3912	289	18	ui	ui	PROPN
ejpam-3912	289	19	)	)	PUNCT
ejpam-3912	289	20	en	en	ADP
ejpam-3912	289	21	,	,	PUNCT
ejpam-3912	289	22	(	(	PUNCT
ejpam-3912	289	23	30	30	NUM
ejpam-3912	289	24	)	)	PUNCT
ejpam-3912	289	25	which	which	PRON
ejpam-3912	289	26	is	be	AUX
ejpam-3912	289	27	equivalent	equivalent	ADJ
ejpam-3912	289	28	to	to	ADP
ejpam-3912	289	29	αu	αu	NOUN
ejpam-3912	289	30	,	,	PUNCT
ejpam-3912	289	31	vuk	vuk	NOUN
ejpam-3912	289	32	=	=	SYM
ejpam-3912	289	33	αu	αu	PROPN
ejpam-3912	289	34	,	,	PUNCT
ejpam-3912	289	35	v′uk	v′uk	PROPN
ejpam-3912	289	36	,	,	PUNCT
ejpam-3912	289	37	k	k	PROPN
ejpam-3912	290	1	=	=	SYM
ejpam-3912	290	2	1	1	NUM
ejpam-3912	290	3	,	,	PUNCT
ejpam-3912	290	4	n−	n−	NOUN
ejpam-3912	290	5	2	2	NUM
ejpam-3912	290	6	(	(	PUNCT
ejpam-3912	290	7	βu	βu	SYM
ejpam-3912	290	8	,	,	PUNCT
ejpam-3912	290	9	vu1	vu1	X
ejpam-3912	290	10	+	+	CCONJ
ejpam-3912	290	11	(	(	PUNCT
ejpam-3912	290	12	kn−1αu	kn−1αu	NUM
ejpam-3912	290	13	,	,	PUNCT
ejpam-3912	290	14	v	v	ADP
ejpam-3912	290	15	−mn−1su	−mn−1su	NOUN
ejpam-3912	290	16	,	,	PUNCT
ejpam-3912	290	17	v)un−1	v)un−1	PROPN
ejpam-3912	290	18	+	+	PROPN
ejpam-3912	290	19	su	su	PROPN
ejpam-3912	290	20	,	,	PUNCT
ejpam-3912	290	21	vun	vun	PROPN
ejpam-3912	290	22	+	+	CCONJ
ejpam-3912	290	23	n−2∑	n−2∑	NUM
ejpam-3912	290	24	i=2	i=2	PROPN
ejpam-3912	290	25	(	(	PUNCT
ejpam-3912	290	26	kiαu	kiαu	PROPN
ejpam-3912	290	27	,	,	PUNCT
ejpam-3912	290	28	v	v	ADP
ejpam-3912	290	29	+	+	NOUN
ejpam-3912	290	30	misu	misu	NOUN
ejpam-3912	290	31	,	,	PUNCT
ejpam-3912	290	32	v)ui	v)ui	PROPN
ejpam-3912	290	33	)	)	PUNCT
ejpam-3912	290	34	=(	=(	NOUN
ejpam-3912	290	35	βu	βu	PROPN
ejpam-3912	290	36	,	,	PUNCT
ejpam-3912	290	37	v′u1	v′u1	NOUN
ejpam-3912	290	38	+	+	CCONJ
ejpam-3912	290	39	(	(	PUNCT
ejpam-3912	290	40	kn−1αu	kn−1αu	NUM
ejpam-3912	290	41	,	,	PUNCT
ejpam-3912	290	42	v′	v′	NOUN
ejpam-3912	290	43	−mn−1su	−mn−1su	PROPN
ejpam-3912	290	44	,	,	PUNCT
ejpam-3912	290	45	v′	v′	NOUN
ejpam-3912	290	46	)	)	PUNCT
ejpam-3912	291	1	un−1	un−1	PROPN
ejpam-3912	291	2	+	+	NUM
ejpam-3912	291	3	su	su	PROPN
ejpam-3912	291	4	,	,	PUNCT
ejpam-3912	291	5	v′un	v′un	NOUN
ejpam-3912	291	6	+	+	CCONJ
ejpam-3912	291	7	n−2∑	n−2∑	NUM
ejpam-3912	291	8	i=2	i=2	PROPN
ejpam-3912	291	9	(	(	PUNCT
ejpam-3912	291	10	kiαu	kiαu	PROPN
ejpam-3912	291	11	,	,	PUNCT
ejpam-3912	291	12	v′	v′	NOUN
ejpam-3912	292	1	+	+	NOUN
ejpam-3912	292	2	misu	misu	NOUN
ejpam-3912	292	3	,	,	PUNCT
ejpam-3912	292	4	v′	v′	NUM
ejpam-3912	292	5	)	)	PUNCT
ejpam-3912	292	6	ui	ui	PROPN
ejpam-3912	292	7	)	)	PUNCT
ejpam-3912	293	1	(	(	PUNCT
ejpam-3912	293	2	γu	γu	INTJ
ejpam-3912	293	3	,	,	PUNCT
ejpam-3912	293	4	vu1	vu1	X
ejpam-3912	293	5	+	+	CCONJ
ejpam-3912	293	6	(	(	PUNCT
ejpam-3912	293	7	ln−1αu	ln−1αu	NOUN
ejpam-3912	293	8	,	,	PUNCT
ejpam-3912	293	9	v	v	ADP
ejpam-3912	293	10	−nn−1tu	−nn−1tu	ADJ
ejpam-3912	293	11	,	,	PUNCT
ejpam-3912	293	12	v)un−1	v)un−1	PROPN
ejpam-3912	293	13	+	+	PROPN
ejpam-3912	293	14	tu	tu	PROPN
ejpam-3912	293	15	,	,	PUNCT
ejpam-3912	293	16	vun	vun	PROPN
ejpam-3912	293	17	+	+	CCONJ
ejpam-3912	293	18	n−2∑	n−2∑	NUM
ejpam-3912	293	19	i=2	i=2	PROPN
ejpam-3912	293	20	(	(	PUNCT
ejpam-3912	293	21	liαu	liαu	PROPN
ejpam-3912	293	22	,	,	PUNCT
ejpam-3912	293	23	v	v	ADP
ejpam-3912	293	24	+	+	NOUN
ejpam-3912	293	25	nitu	nitu	ADJ
ejpam-3912	293	26	,	,	PUNCT
ejpam-3912	293	27	v)ui	v)ui	PROPN
ejpam-3912	293	28	)	)	PUNCT
ejpam-3912	293	29	=(	=(	PROPN
ejpam-3912	293	30	γu	γu	PROPN
ejpam-3912	293	31	,	,	PUNCT
ejpam-3912	293	32	v′u1	v′u1	NOUN
ejpam-3912	293	33	+	+	CCONJ
ejpam-3912	293	34	(	(	PUNCT
ejpam-3912	293	35	ln−1αu	ln−1αu	PROPN
ejpam-3912	293	36	,	,	PUNCT
ejpam-3912	293	37	v′	v′	X
ejpam-3912	293	38	−nn−1tu	−nn−1tu	ADJ
ejpam-3912	293	39	,	,	PUNCT
ejpam-3912	293	40	v′	v′	NOUN
ejpam-3912	293	41	)	)	PUNCT
ejpam-3912	294	1	un−1	un−1	PROPN
ejpam-3912	294	2	+	+	CCONJ
ejpam-3912	294	3	tu	tu	PROPN
ejpam-3912	294	4	,	,	PUNCT
ejpam-3912	294	5	v′un	v′un	NOUN
ejpam-3912	294	6	+	+	CCONJ
ejpam-3912	294	7	n−2∑	n−2∑	NUM
ejpam-3912	294	8	i=2	i=2	PROPN
ejpam-3912	294	9	(	(	PUNCT
ejpam-3912	294	10	liαu	liαu	PROPN
ejpam-3912	294	11	,	,	PUNCT
ejpam-3912	294	12	v′	v′	X
ejpam-3912	294	13	+	+	SYM
ejpam-3912	294	14	nitu	nitu	ADJ
ejpam-3912	294	15	,	,	PUNCT
ejpam-3912	294	16	v′	v′	NOUN
ejpam-3912	294	17	)	)	PUNCT
ejpam-3912	294	18	ui	ui	PROPN
ejpam-3912	294	19	)	)	PUNCT
ejpam-3912	294	20	.	.	PUNCT
ejpam-3912	295	1	as	as	ADP
ejpam-3912	295	2	,	,	PUNCT
ejpam-3912	295	3	u	u	PROPN
ejpam-3912	295	4	6=	6=	PROPN
ejpam-3912	295	5	0	0	NUM
ejpam-3912	295	6	,	,	PUNCT
ejpam-3912	295	7	we	we	PRON
ejpam-3912	295	8	obtain	obtain	VERB
ejpam-3912	295	9	αu	αu	NOUN
ejpam-3912	295	10	,	,	PUNCT
ejpam-3912	295	11	v	v	NOUN
ejpam-3912	295	12	=	=	SYM
ejpam-3912	295	13	αu	αu	NOUN
ejpam-3912	295	14	,	,	PUNCT
ejpam-3912	295	15	v′	v′	NOUN
ejpam-3912	295	16	for	for	ADP
ejpam-3912	295	17	any	any	DET
ejpam-3912	295	18	v	v	NOUN
ejpam-3912	295	19	,	,	PUNCT
ejpam-3912	295	20	v′	v′	PROPN
ejpam-3912	295	21	∈	∈	PROPN
ejpam-3912	295	22	e.	e.	PROPN
ejpam-3912	296	1	this	this	DET
ejpam-3912	296	2	result	result	NOUN
ejpam-3912	296	3	means	mean	VERB
ejpam-3912	296	4	that	that	SCONJ
ejpam-3912	296	5	αu	αu	NOUN
ejpam-3912	296	6	,	,	PUNCT
ejpam-3912	296	7	v	v	NOUN
ejpam-3912	296	8	=	=	NOUN
ejpam-3912	296	9	:	:	PUNCT
ejpam-3912	296	10	αu	αu	NOUN
ejpam-3912	296	11	.	.	PROPN
ejpam-3912	296	12	(	(	PUNCT
ejpam-3912	296	13	31	31	NUM
ejpam-3912	296	14	)	)	PUNCT
ejpam-3912	296	15	moreover	moreover	ADV
ejpam-3912	296	16	,	,	PUNCT
ejpam-3912	296	17	if	if	SCONJ
ejpam-3912	296	18	u	u	PROPN
ejpam-3912	296	19	∈	∈	PROPN
ejpam-3912	296	20	γ	γ	X
ejpam-3912	296	21	,	,	PUNCT
ejpam-3912	296	22	then	then	ADV
ejpam-3912	296	23	one	one	NUM
ejpam-3912	296	24	finds	find	VERB
ejpam-3912	296	25	βu	βu	ADP
ejpam-3912	296	26	,	,	PUNCT
ejpam-3912	296	27	v	v	NOUN
ejpam-3912	296	28	=	=	NOUN
ejpam-3912	296	29	:	:	PUNCT
ejpam-3912	296	30	βu	βu	NOUN
ejpam-3912	296	31	,	,	PUNCT
ejpam-3912	296	32	γu	γu	PROPN
ejpam-3912	296	33	,	,	PUNCT
ejpam-3912	296	34	v	v	NOUN
ejpam-3912	296	35	=	=	PRON
ejpam-3912	296	36	:	:	PUNCT
ejpam-3912	296	37	γu	γu	PROPN
ejpam-3912	296	38	.	.	PUNCT
ejpam-3912	297	1	(	(	PUNCT
ejpam-3912	297	2	32	32	NUM
ejpam-3912	297	3	)	)	PUNCT
ejpam-3912	297	4	now	now	ADV
ejpam-3912	297	5	,	,	PUNCT
ejpam-3912	297	6	if	if	SCONJ
ejpam-3912	297	7	u	u	PROPN
ejpam-3912	297	8	∈	∈	PROPN
ejpam-3912	297	9	γ2	γ2	NOUN
ejpam-3912	297	10	,	,	PUNCT
ejpam-3912	297	11	then	then	ADV
ejpam-3912	297	12	one	one	NUM
ejpam-3912	297	13	finds	find	VERB
ejpam-3912	297	14	su	su	PROPN
ejpam-3912	297	15	,	,	PUNCT
ejpam-3912	297	16	v	v	NOUN
ejpam-3912	297	17	=	=	NOUN
ejpam-3912	297	18	:	:	PUNCT
ejpam-3912	297	19	su	su	PROPN
ejpam-3912	297	20	,	,	PUNCT
ejpam-3912	297	21	tu	tu	PROPN
ejpam-3912	297	22	,	,	PUNCT
ejpam-3912	297	23	v	v	NOUN
ejpam-3912	297	24	=	=	NOUN
ejpam-3912	297	25	:	:	PUNCT
ejpam-3912	297	26	tu	tu	PROPN
ejpam-3912	297	27	.	.	PUNCT
ejpam-3912	298	1	(	(	PUNCT
ejpam-3912	298	2	33	33	NUM
ejpam-3912	298	3	)	)	PUNCT
ejpam-3912	298	4	a.	a.	NOUN
ejpam-3912	298	5	alarafeen	alarafeen	PROPN
ejpam-3912	298	6	,	,	PUNCT
ejpam-3912	298	7	i.	i.	PROPN
ejpam-3912	298	8	qaralleh	qaralleh	PROPN
ejpam-3912	298	9	,	,	PUNCT
ejpam-3912	298	10	a.	a.	PROPN
ejpam-3912	298	11	ahmad	ahmad	PROPN
ejpam-3912	298	12	/	/	SYM
ejpam-3912	298	13	eur	eur	PROPN
ejpam-3912	298	14	.	.	PUNCT
ejpam-3912	299	1	j.	j.	PROPN
ejpam-3912	299	2	pure	pure	PROPN
ejpam-3912	299	3	appl	appl	PROPN
ejpam-3912	299	4	.	.	PROPN
ejpam-3912	299	5	math	math	PROPN
ejpam-3912	299	6	,	,	PUNCT
ejpam-3912	299	7	14	14	NUM
ejpam-3912	299	8	(	(	PUNCT
ejpam-3912	299	9	1	1	NUM
ejpam-3912	299	10	)	)	PUNCT
ejpam-3912	299	11	(	(	PUNCT
ejpam-3912	299	12	2021	2021	NUM
ejpam-3912	299	13	)	)	PUNCT
ejpam-3912	299	14	,	,	PUNCT
ejpam-3912	299	15	278	278	NUM
ejpam-3912	299	16	-	-	SYM
ejpam-3912	299	17	300	300	NUM
ejpam-3912	299	18	290	290	NUM
ejpam-3912	299	19	taking	taking	NOUN
ejpam-3912	299	20	(	(	PUNCT
ejpam-3912	299	21	31),(32),(33	31),(32),(33	NOUN
ejpam-3912	299	22	)	)	PUNCT
ejpam-3912	299	23	into	into	ADP
ejpam-3912	299	24	(	(	PUNCT
ejpam-3912	299	25	36	36	NUM
ejpam-3912	299	26	)	)	PUNCT
ejpam-3912	300	1	,	,	PUNCT
ejpam-3912	300	2	we	we	PRON
ejpam-3912	300	3	conclude	conclude	VERB
ejpam-3912	300	4	that	that	SCONJ
ejpam-3912	300	5	mapping	mapping	NOUN
ejpam-3912	300	6	d	d	NOUN
ejpam-3912	300	7	can	can	AUX
ejpam-3912	300	8	be	be	AUX
ejpam-3912	300	9	defined	define	VERB
ejpam-3912	300	10	as	as	ADP
ejpam-3912	300	11	d(u	d(u	PROPN
ejpam-3912	300	12	)	)	PUNCT
ejpam-3912	300	13	=	=	PUNCT
ejpam-3912	300	14			NUM
ejpam-3912	300	15	n−2∑	n−2∑	PROPN
ejpam-3912	300	16	k=1	k=1	X
ejpam-3912	300	17	2k−1αuukek+	2k−1αuukek+	PROPN
ejpam-3912	300	18	(	(	PUNCT
ejpam-3912	300	19	βuu1	βuu1	PROPN
ejpam-3912	300	20	+	+	CCONJ
ejpam-3912	300	21	(	(	PUNCT
ejpam-3912	300	22	kn−1αu	kn−1αu	NUM
ejpam-3912	300	23	−mn−1su)un−1	−mn−1su)un−1	X
ejpam-3912	300	24	+	+	CCONJ
ejpam-3912	300	25	suun	suun	PROPN
ejpam-3912	300	26	+	+	CCONJ
ejpam-3912	300	27	n−2∑	n−2∑	NUM
ejpam-3912	300	28	i=2	i=2	PROPN
ejpam-3912	300	29	(	(	PUNCT
ejpam-3912	300	30	kiαu	kiαu	NOUN
ejpam-3912	300	31	+	+	NOUN
ejpam-3912	300	32	misu)ui	misu)ui	NOUN
ejpam-3912	300	33	)	)	PUNCT
ejpam-3912	301	1	en−1	en−1	PROPN
ejpam-3912	301	2	+	+	CCONJ
ejpam-3912	301	3	(	(	PUNCT
ejpam-3912	301	4	γuu1	γuu1	PROPN
ejpam-3912	301	5	+	+	CCONJ
ejpam-3912	301	6	(	(	PUNCT
ejpam-3912	301	7	ln−1αu	ln−1αu	DET
ejpam-3912	301	8	−nn−1tu)un−1	−nn−1tu)un−1	ADJ
ejpam-3912	301	9	+	+	NUM
ejpam-3912	301	10	tuun	tuun	ADJ
ejpam-3912	301	11	+	+	CCONJ
ejpam-3912	301	12	n−2∑	n−2∑	NUM
ejpam-3912	301	13	i=2	i=2	PROPN
ejpam-3912	301	14	(	(	PUNCT
ejpam-3912	301	15	liαu	liαu	NOUN
ejpam-3912	301	16	+	+	NOUN
ejpam-3912	301	17	nitu)ui	nitu)ui	NOUN
ejpam-3912	301	18	)	)	PUNCT
ejpam-3912	301	19	en	en	ADP
ejpam-3912	301	20	if	if	SCONJ
ejpam-3912	301	21	u	u	PROPN
ejpam-3912	301	22	∈	∈	PROPN
ejpam-3912	301	23	γ1	γ1	NOUN
ejpam-3912	301	24	∪	∪	ADP
ejpam-3912	301	25	γ2	γ2	PROPN
ejpam-3912	301	26	n−2∑	n−2∑	NUM
ejpam-3912	301	27	k=2	k=2	PROPN
ejpam-3912	301	28	2k−1αuukek	2k−1αuukek	NUM
ejpam-3912	301	29	+	+	CCONJ
ejpam-3912	301	30	(	(	PUNCT
ejpam-3912	301	31	(	(	PUNCT
ejpam-3912	301	32	kn−1αu	kn−1αu	X
ejpam-3912	301	33	−mn−1su)un−1	−mn−1su)un−1	NUM
ejpam-3912	301	34	+	+	CCONJ
ejpam-3912	301	35	n−2∑	n−2∑	NUM
ejpam-3912	301	36	i=2	i=2	PROPN
ejpam-3912	301	37	(	(	PUNCT
ejpam-3912	301	38	kiαu	kiαu	NOUN
ejpam-3912	301	39	+	+	NOUN
ejpam-3912	301	40	misu)ui	misu)ui	NOUN
ejpam-3912	301	41	)	)	PUNCT
ejpam-3912	302	1	en−1	en−1	PROPN
ejpam-3912	302	2	+	+	CCONJ
ejpam-3912	302	3	(	(	PUNCT
ejpam-3912	302	4	(	(	PUNCT
ejpam-3912	302	5	ln−1αu	ln−1αu	PRON
ejpam-3912	302	6	−nn−1tu)un−1	−nn−1tu)un−1	ADJ
ejpam-3912	302	7	+	+	NUM
ejpam-3912	302	8	n−2∑	n−2∑	NUM
ejpam-3912	302	9	i=2	i=2	PROPN
ejpam-3912	302	10	(	(	PUNCT
ejpam-3912	302	11	liαu	liαu	NOUN
ejpam-3912	302	12	+	+	NOUN
ejpam-3912	302	13	nitu)ui	nitu)ui	NOUN
ejpam-3912	302	14	)	)	PUNCT
ejpam-3912	302	15	en	en	ADP
ejpam-3912	302	16	if	if	SCONJ
ejpam-3912	302	17	u	u	PROPN
ejpam-3912	302	18	6∈	6∈	PROPN
ejpam-3912	302	19	γ1	γ1	PROPN
ejpam-3912	302	20	∪	∪	ADP
ejpam-3912	302	21	γ2	γ2	PROPN
ejpam-3912	302	22	.	.	PUNCT
ejpam-3912	303	1	(	(	PUNCT
ejpam-3912	303	2	34	34	NUM
ejpam-3912	303	3	)	)	PUNCT
ejpam-3912	303	4	then	then	ADV
ejpam-3912	303	5	,	,	PUNCT
ejpam-3912	303	6	for	for	ADP
ejpam-3912	303	7	any	any	DET
ejpam-3912	303	8	u′,v′	u′,v′	PROPN
ejpam-3912	303	9	∈	∈	PROPN
ejpam-3912	303	10	e	e	NOUN
ejpam-3912	303	11	,	,	PUNCT
ejpam-3912	303	12	we	we	PRON
ejpam-3912	303	13	can	can	AUX
ejpam-3912	303	14	find	find	VERB
ejpam-3912	303	15	derivation	derivation	NOUN
ejpam-3912	303	16	d	d	NOUN
ejpam-3912	303	17	given	give	VERB
ejpam-3912	303	18	by	by	ADP
ejpam-3912	303	19	dij	dij	PROPN
ejpam-3912	303	20	=	=	SYM
ejpam-3912	303	21			NUM
ejpam-3912	303	22	2i−1α	2i−1α	NUM
ejpam-3912	303	23	,	,	PUNCT
ejpam-3912	303	24	if	if	SCONJ
ejpam-3912	303	25	1	1	NUM
ejpam-3912	303	26	≤	≤	NOUN
ejpam-3912	304	1	i	i	PRON
ejpam-3912	304	2	=	=	SYM
ejpam-3912	304	3	j	j	X
ejpam-3912	304	4	<	<	X
ejpam-3912	304	5	n−	n−	PROPN
ejpam-3912	304	6	1	1	NUM
ejpam-3912	304	7	β	β	NOUN
ejpam-3912	304	8	,	,	PUNCT
ejpam-3912	304	9	if	if	SCONJ
ejpam-3912	304	10	i	i	PRON
ejpam-3912	304	11	=	=	NOUN
ejpam-3912	304	12	1	1	NUM
ejpam-3912	304	13	,	,	PUNCT
ejpam-3912	304	14	j	j	NOUN
ejpam-3912	304	15	=	=	PUNCT
ejpam-3912	304	16	n−	n−	PROPN
ejpam-3912	304	17	1	1	NUM
ejpam-3912	304	18	γ	γ	NOUN
ejpam-3912	304	19	,	,	PUNCT
ejpam-3912	304	20	if	if	SCONJ
ejpam-3912	304	21	i	i	PRON
ejpam-3912	304	22	=	=	NOUN
ejpam-3912	304	23	1	1	NUM
ejpam-3912	304	24	,	,	PUNCT
ejpam-3912	304	25	j	j	PROPN
ejpam-3912	304	26	=	=	PUNCT
ejpam-3912	304	27	n	n	PROPN
ejpam-3912	304	28	s	s	PROPN
ejpam-3912	304	29	,	,	PUNCT
ejpam-3912	304	30	ifi	ifi	PROPN
ejpam-3912	304	31	=	=	SYM
ejpam-3912	304	32	n	n	PROPN
ejpam-3912	304	33	,	,	PUNCT
ejpam-3912	304	34	j	j	PROPN
ejpam-3912	304	35	=	=	PUNCT
ejpam-3912	304	36	n−	n−	PROPN
ejpam-3912	304	37	1	1	NUM
ejpam-3912	304	38	t	t	PROPN
ejpam-3912	304	39	,	,	PUNCT
ejpam-3912	304	40	ifi	ifi	PROPN
ejpam-3912	304	41	=	=	SYM
ejpam-3912	304	42	n	n	PROPN
ejpam-3912	304	43	,	,	PUNCT
ejpam-3912	304	44	j	j	PROPN
ejpam-3912	304	45	=	=	PROPN
ejpam-3912	304	46	n	n	PRON
ejpam-3912	304	47	kn−1α−mn−1s	kn−1α−mn−1	NOUN
ejpam-3912	304	48	,	,	PUNCT
ejpam-3912	304	49	if	if	SCONJ
ejpam-3912	304	50	i	i	PRON
ejpam-3912	304	51	=	=	VERB
ejpam-3912	304	52	n−	n−	NOUN
ejpam-3912	304	53	1	1	NUM
ejpam-3912	304	54	,	,	PUNCT
ejpam-3912	304	55	j	j	NOUN
ejpam-3912	304	56	=	=	PUNCT
ejpam-3912	304	57	n−	n−	PROPN
ejpam-3912	304	58	1	1	NUM
ejpam-3912	304	59	ln−1α−nn−1	ln−1α−nn−1	PROPN
ejpam-3912	304	60	t	t	NOUN
ejpam-3912	304	61	,	,	PUNCT
ejpam-3912	304	62	if	if	SCONJ
ejpam-3912	304	63	i	i	PRON
ejpam-3912	304	64	=	=	VERB
ejpam-3912	304	65	n−	n−	NOUN
ejpam-3912	304	66	1	1	NUM
ejpam-3912	304	67	,	,	PUNCT
ejpam-3912	304	68	j	j	PROPN
ejpam-3912	304	69	=	=	SYM
ejpam-3912	304	70	n	n	PRON
ejpam-3912	304	71	kiα+nis	kiα+nis	NOUN
ejpam-3912	304	72	,	,	PUNCT
ejpam-3912	304	73	if	if	SCONJ
ejpam-3912	304	74	2	2	NUM
ejpam-3912	304	75	≤	≤	NUM
ejpam-3912	304	76	i	i	NOUN
ejpam-3912	304	77	≤	≤	ADJ
ejpam-3912	304	78	n−	n−	PROPN
ejpam-3912	304	79	2	2	NUM
ejpam-3912	304	80	,	,	PUNCT
ejpam-3912	304	81	j	j	NOUN
ejpam-3912	304	82	=	=	PUNCT
ejpam-3912	304	83	n−	n−	PROPN
ejpam-3912	304	84	1	1	NUM
ejpam-3912	304	85	liα+nit	liα+nit	ADJ
ejpam-3912	304	86	,	,	PUNCT
ejpam-3912	304	87	if	if	SCONJ
ejpam-3912	304	88	2	2	NUM
ejpam-3912	304	89	≤	≤	NUM
ejpam-3912	304	90	i	i	NOUN
ejpam-3912	304	91	≤	≤	ADJ
ejpam-3912	304	92	n−	n−	PROPN
ejpam-3912	304	93	2	2	NUM
ejpam-3912	304	94	,	,	PUNCT
ejpam-3912	304	95	j	j	PROPN
ejpam-3912	304	96	=	=	PUNCT
ejpam-3912	304	97	n	n	PROPN
ejpam-3912	304	98	0	0	NUM
ejpam-3912	304	99	,	,	PUNCT
ejpam-3912	304	100	otherwise	otherwise	ADV
ejpam-3912	304	101	such	such	ADJ
ejpam-3912	304	102	that	that	SCONJ
ejpam-3912	304	103	d(u′	d(u′	NOUN
ejpam-3912	304	104	)	)	PUNCT
ejpam-3912	304	105	=	=	SYM
ejpam-3912	304	106	d(u′	d(u′	PROPN
ejpam-3912	304	107	)	)	PUNCT
ejpam-3912	304	108	,	,	PUNCT
ejpam-3912	304	109	d(v′	d(v′	PROPN
ejpam-3912	304	110	)	)	PUNCT
ejpam-3912	304	111	=	=	SYM
ejpam-3912	304	112	d(v′	d(v′	PROPN
ejpam-3912	304	113	)	)	PUNCT
ejpam-3912	304	114	.	.	PUNCT
ejpam-3912	305	1	then	then	ADV
ejpam-3912	305	2	,	,	PUNCT
ejpam-3912	305	3	from	from	ADP
ejpam-3912	305	4	(	(	PUNCT
ejpam-3912	305	5	34	34	NUM
ejpam-3912	305	6	)	)	PUNCT
ejpam-3912	305	7	one	one	NOUN
ejpam-3912	305	8	obtains	obtain	VERB
ejpam-3912	305	9	αu′	αu′	NOUN
ejpam-3912	305	10	=	=	SYM
ejpam-3912	305	11	αv′	αv′	NOUN
ejpam-3912	306	1	=	=	PUNCT
ejpam-3912	306	2	α	α	NOUN
ejpam-3912	306	3	for	for	ADP
ejpam-3912	306	4	any	any	DET
ejpam-3912	306	5	u′,v′	u′,v′	PROPN
ejpam-3912	306	6	∈	∈	PROPN
ejpam-3912	306	7	e.	e.	PROPN
ejpam-3912	306	8	(	(	PUNCT
ejpam-3912	306	9	35	35	NUM
ejpam-3912	306	10	)	)	PUNCT
ejpam-3912	306	11	this	this	DET
ejpam-3912	306	12	result	result	NOUN
ejpam-3912	306	13	means	mean	VERB
ejpam-3912	306	14	that	that	SCONJ
ejpam-3912	306	15	functional	functional	ADJ
ejpam-3912	306	16	αu	αu	NOUN
ejpam-3912	306	17	is	be	AUX
ejpam-3912	306	18	a	a	DET
ejpam-3912	306	19	constant	constant	ADJ
ejpam-3912	306	20	.	.	PUNCT
ejpam-3912	307	1	to	to	PART
ejpam-3912	307	2	complete	complete	VERB
ejpam-3912	307	3	the	the	DET
ejpam-3912	307	4	proof	proof	NOUN
ejpam-3912	307	5	,	,	PUNCT
ejpam-3912	307	6	we	we	PRON
ejpam-3912	307	7	show	show	VERB
ejpam-3912	307	8	βu	βu	ADP
ejpam-3912	307	9	,	,	PUNCT
ejpam-3912	307	10	γu	γu	PROPN
ejpam-3912	307	11	,	,	PUNCT
ejpam-3912	307	12	su	su	PROPN
ejpam-3912	307	13	,	,	PUNCT
ejpam-3912	307	14	and	and	CCONJ
ejpam-3912	307	15	tu	tu	PROPN
ejpam-3912	307	16	are	be	AUX
ejpam-3912	307	17	constants	constant	NOUN
ejpam-3912	307	18	for	for	ADP
ejpam-3912	307	19	any	any	DET
ejpam-3912	307	20	u	u	PROPN
ejpam-3912	307	21	∈	∈	PROPN
ejpam-3912	307	22	e.	e.	NOUN
ejpam-3912	307	23	we	we	PRON
ejpam-3912	307	24	consider	consider	VERB
ejpam-3912	307	25	non	non	ADJ
ejpam-3912	307	26	-	-	ADJ
ejpam-3912	307	27	zero	zero	NUM
ejpam-3912	307	28	points	point	NOUN
ejpam-3912	307	29	u	u	NOUN
ejpam-3912	307	30	,	,	PUNCT
ejpam-3912	307	31	v	v	NOUN
ejpam-3912	307	32	∈	∈	PROPN
ejpam-3912	307	33	γ1∪γ2	γ1∪γ2	NOUN
ejpam-3912	307	34	.	.	PUNCT
ejpam-3912	308	1	using	use	VERB
ejpam-3912	308	2	the	the	DET
ejpam-3912	308	3	first	first	ADJ
ejpam-3912	308	4	equality	equality	NOUN
ejpam-3912	308	5	of	of	ADP
ejpam-3912	308	6	(	(	PUNCT
ejpam-3912	308	7	34	34	NUM
ejpam-3912	308	8	)	)	PUNCT
ejpam-3912	308	9	and	and	CCONJ
ejpam-3912	308	10	noting	note	VERB
ejpam-3912	308	11	(	(	PUNCT
ejpam-3912	308	12	35	35	NUM
ejpam-3912	308	13	)	)	PUNCT
ejpam-3912	308	14	by	by	ADP
ejpam-3912	308	15	definition	definition	NOUN
ejpam-3912	308	16	of	of	ADP
ejpam-3912	308	17	2	2	NUM
ejpam-3912	308	18	-	-	PUNCT
ejpam-3912	308	19	local	local	ADJ
ejpam-3912	308	20	derivation	derivation	NOUN
ejpam-3912	308	21	,	,	PUNCT
ejpam-3912	308	22	we	we	PRON
ejpam-3912	308	23	obtains	obtain	VERB
ejpam-3912	308	24	βu	βu	PUNCT
ejpam-3912	308	25	=	=	PUNCT
ejpam-3912	308	26	βv	βv	PROPN
ejpam-3912	308	27	,	,	PUNCT
ejpam-3912	308	28	γu	γu	NOUN
ejpam-3912	308	29	=	=	SYM
ejpam-3912	308	30	γv	γv	PROPN
ejpam-3912	308	31	,	,	PUNCT
ejpam-3912	308	32	su	su	PROPN
ejpam-3912	308	33	=	=	PUNCT
ejpam-3912	308	34	sv	sv	PROPN
ejpam-3912	308	35	,	,	PUNCT
ejpam-3912	308	36	and	and	CCONJ
ejpam-3912	308	37	tu	tu	PROPN
ejpam-3912	308	38	=	=	NOUN
ejpam-3912	308	39	tv	tv	PROPN
ejpam-3912	308	40	.	.	PUNCT
ejpam-3912	309	1	this	this	DET
ejpam-3912	309	2	result	result	NOUN
ejpam-3912	309	3	means	mean	VERB
ejpam-3912	309	4	that	that	SCONJ
ejpam-3912	309	5	βu	βu	ADP
ejpam-3912	309	6	,	,	PUNCT
ejpam-3912	309	7	γu	γu	PROPN
ejpam-3912	309	8	,	,	PUNCT
ejpam-3912	309	9	su	su	PROPN
ejpam-3912	310	1	and	and	CCONJ
ejpam-3912	310	2	tu	tu	PROPN
ejpam-3912	310	3	do	do	AUX
ejpam-3912	310	4	not	not	PART
ejpam-3912	310	5	depend	depend	VERB
ejpam-3912	310	6	on	on	ADP
ejpam-3912	310	7	u	u	NOUN
ejpam-3912	310	8	,	,	PUNCT
ejpam-3912	310	9	i.e.	i.e.	X
ejpam-3912	310	10	,	,	PUNCT
ejpam-3912	310	11	βu	βu	PUNCT
ejpam-3912	310	12	=	=	SYM
ejpam-3912	310	13	β	β	X
ejpam-3912	310	14	,	,	PUNCT
ejpam-3912	310	15	γu	γu	NOUN
ejpam-3912	310	16	=	=	SYM
ejpam-3912	310	17	γ	γ	X
ejpam-3912	310	18	,	,	PUNCT
ejpam-3912	310	19	su	su	PROPN
ejpam-3912	310	20	=	=	SYM
ejpam-3912	310	21	s	s	PROPN
ejpam-3912	310	22	and	and	CCONJ
ejpam-3912	311	1	tu	tu	PROPN
ejpam-3912	311	2	=	=	PROPN
ejpam-3912	311	3	t	t	PROPN
ejpam-3912	311	4	for	for	ADP
ejpam-3912	311	5	any	any	DET
ejpam-3912	311	6	u	u	PROPN
ejpam-3912	311	7	∈	∈	PROPN
ejpam-3912	311	8	γ1	γ1	NOUN
ejpam-3912	311	9	∪γ2	∪γ2	NOUN
ejpam-3912	311	10	.	.	PUNCT
ejpam-3912	312	1	placing	place	VERB
ejpam-3912	312	2	this	this	DET
ejpam-3912	312	3	result	result	NOUN
ejpam-3912	312	4	and	and	CCONJ
ejpam-3912	312	5	(	(	PUNCT
ejpam-3912	312	6	35	35	NUM
ejpam-3912	312	7	)	)	PUNCT
ejpam-3912	312	8	into	into	ADP
ejpam-3912	312	9	(	(	PUNCT
ejpam-3912	312	10	34	34	NUM
ejpam-3912	312	11	)	)	PUNCT
ejpam-3912	312	12	yields	yield	NOUN
ejpam-3912	312	13	d	d	NOUN
ejpam-3912	312	14	,	,	PUNCT
ejpam-3912	312	15	which	which	PRON
ejpam-3912	312	16	has	have	VERB
ejpam-3912	312	17	the	the	DET
ejpam-3912	312	18	following	follow	VERB
ejpam-3912	312	19	form	form	NOUN
ejpam-3912	312	20	:	:	PUNCT
ejpam-3912	312	21	a.	a.	PROPN
ejpam-3912	312	22	alarafeen	alarafeen	PROPN
ejpam-3912	312	23	,	,	PUNCT
ejpam-3912	312	24	i.	i.	PROPN
ejpam-3912	312	25	qaralleh	qaralleh	PROPN
ejpam-3912	312	26	,	,	PUNCT
ejpam-3912	312	27	a.	a.	PROPN
ejpam-3912	312	28	ahmad	ahmad	PROPN
ejpam-3912	312	29	/	/	SYM
ejpam-3912	312	30	eur	eur	PROPN
ejpam-3912	312	31	.	.	PUNCT
ejpam-3912	313	1	j.	j.	PROPN
ejpam-3912	313	2	pure	pure	PROPN
ejpam-3912	313	3	appl	appl	PROPN
ejpam-3912	313	4	.	.	PROPN
ejpam-3912	313	5	math	math	PROPN
ejpam-3912	313	6	,	,	PUNCT
ejpam-3912	313	7	14	14	NUM
ejpam-3912	313	8	(	(	PUNCT
ejpam-3912	313	9	1	1	NUM
ejpam-3912	313	10	)	)	PUNCT
ejpam-3912	313	11	(	(	PUNCT
ejpam-3912	313	12	2021	2021	NUM
ejpam-3912	313	13	)	)	PUNCT
ejpam-3912	313	14	,	,	PUNCT
ejpam-3912	313	15	278	278	NUM
ejpam-3912	313	16	-	-	SYM
ejpam-3912	313	17	300	300	NUM
ejpam-3912	313	18	291	291	NUM
ejpam-3912	313	19	d(u	d(u	NOUN
ejpam-3912	313	20	)	)	PUNCT
ejpam-3912	313	21	=	=	PUNCT
ejpam-3912	314	1	n−2∑	n−2∑	PROPN
ejpam-3912	314	2	k=1	k=1	PRON
ejpam-3912	314	3	2k−1αukek+	2k−1αukek+	NUM
ejpam-3912	314	4	(	(	PUNCT
ejpam-3912	314	5	βu1	βu1	NOUN
ejpam-3912	314	6	+	+	CCONJ
ejpam-3912	314	7	(	(	PUNCT
ejpam-3912	314	8	kn−1α−mn−1s)un−1	kn−1α−mn−1s)un−1	PROPN
ejpam-3912	314	9	+	+	CCONJ
ejpam-3912	314	10	sun	sun	NOUN
ejpam-3912	314	11	+	+	CCONJ
ejpam-3912	314	12	n−2∑	n−2∑	NUM
ejpam-3912	314	13	i=2	i=2	PROPN
ejpam-3912	314	14	(	(	PUNCT
ejpam-3912	314	15	kiα+mis)ui	kiα+mis)ui	PROPN
ejpam-3912	314	16	)	)	PUNCT
ejpam-3912	314	17	en−1	en−1	PROPN
ejpam-3912	314	18	+	+	CCONJ
ejpam-3912	314	19	(	(	PUNCT
ejpam-3912	314	20	γu1	γu1	VERB
ejpam-3912	314	21	+	+	CCONJ
ejpam-3912	314	22	(	(	PUNCT
ejpam-3912	314	23	ln−1α−nn−1t)un−1	ln−1α−nn−1t)un−1	PROPN
ejpam-3912	314	24	+	+	NUM
ejpam-3912	314	25	tun	tun	X
ejpam-3912	314	26	+	+	CCONJ
ejpam-3912	314	27	n−2∑	n−2∑	NUM
ejpam-3912	314	28	i=2	i=2	PROPN
ejpam-3912	314	29	(	(	PUNCT
ejpam-3912	314	30	liα+nit)ui	liα+nit)ui	NOUN
ejpam-3912	314	31	)	)	PUNCT
ejpam-3912	314	32	en	en	ADP
ejpam-3912	314	33	.	.	PUNCT
ejpam-3912	315	1	(	(	PUNCT
ejpam-3912	315	2	36	36	NUM
ejpam-3912	315	3	)	)	PUNCT
ejpam-3912	315	4	due	due	ADP
ejpam-3912	315	5	to	to	ADP
ejpam-3912	315	6	theorem	theorem	VERB
ejpam-3912	315	7	3	3	NUM
ejpam-3912	315	8	(	(	PUNCT
ejpam-3912	315	9	ii	ii	NOUN
ejpam-3912	315	10	)	)	PUNCT
ejpam-3912	315	11	,	,	PUNCT
ejpam-3912	315	12	d	d	X
ejpam-3912	315	13	is	be	AUX
ejpam-3912	315	14	a	a	DET
ejpam-3912	315	15	derivation	derivation	NOUN
ejpam-3912	315	16	.	.	PUNCT
ejpam-3912	316	1	case	case	NOUN
ejpam-3912	316	2	ia	ia	PROPN
ejpam-3912	316	3	6=	6=	ADP
ejpam-3912	316	4	∅.	∅.	ADP
ejpam-3912	316	5	by	by	ADP
ejpam-3912	316	6	definition	definition	NOUN
ejpam-3912	316	7	,	,	PUNCT
ejpam-3912	316	8	there	there	PRON
ejpam-3912	316	9	exist	exist	VERB
ejpam-3912	316	10	functionals	functional	NOUN
ejpam-3912	316	11	βu	βu	ADP
ejpam-3912	316	12	,	,	PUNCT
ejpam-3912	316	13	v	v	NOUN
ejpam-3912	316	14	,	,	PUNCT
ejpam-3912	316	15	γu	γu	NOUN
ejpam-3912	316	16	,	,	PUNCT
ejpam-3912	316	17	v	v	PROPN
ejpam-3912	316	18	,	,	PUNCT
ejpam-3912	316	19	su	su	PROPN
ejpam-3912	316	20	,	,	PUNCT
ejpam-3912	316	21	v	v	PROPN
ejpam-3912	316	22	and	and	CCONJ
ejpam-3912	316	23	tu	tu	PROPN
ejpam-3912	316	24	,	,	PUNCT
ejpam-3912	316	25	v	v	ADP
ejpam-3912	316	26	such	such	ADJ
ejpam-3912	316	27	that	that	SCONJ
ejpam-3912	316	28	d(u	d(u	PROPN
ejpam-3912	316	29	)	)	PUNCT
ejpam-3912	317	1	=	=	PRON
ejpam-3912	317	2	(	(	PUNCT
ejpam-3912	317	3	βu	βu	ADP
ejpam-3912	317	4	,	,	PUNCT
ejpam-3912	317	5	vu1	vu1	X
ejpam-3912	317	6	+	+	CCONJ
ejpam-3912	317	7	su	su	PROPN
ejpam-3912	317	8	,	,	PUNCT
ejpam-3912	317	9	vun	vun	PROPN
ejpam-3912	317	10	+	+	PROPN
ejpam-3912	317	11	su	su	PROPN
ejpam-3912	317	12	,	,	PUNCT
ejpam-3912	317	13	v	v	ADP
ejpam-3912	317	14	n−2∑	n−2∑	PROPN
ejpam-3912	317	15	i=2	i=2	PROPN
ejpam-3912	317	16	diui	diui	PROPN
ejpam-3912	317	17	)	)	PUNCT
ejpam-3912	317	18	en−1	en−1	PROPN
ejpam-3912	317	19	+	+	CCONJ
ejpam-3912	317	20	(	(	PUNCT
ejpam-3912	317	21	γu	γu	PROPN
ejpam-3912	317	22	,	,	PUNCT
ejpam-3912	317	23	vu1	vu1	X
ejpam-3912	317	24	+	+	CCONJ
ejpam-3912	317	25	tu	tu	PROPN
ejpam-3912	317	26	,	,	PUNCT
ejpam-3912	317	27	vun	vun	PROPN
ejpam-3912	317	28	+	+	PROPN
ejpam-3912	317	29	tu	tu	PROPN
ejpam-3912	317	30	,	,	PUNCT
ejpam-3912	317	31	v	v	ADP
ejpam-3912	317	32	n−2∑	n−2∑	PROPN
ejpam-3912	317	33	i=2	i=2	PROPN
ejpam-3912	317	34	diui	diui	PROPN
ejpam-3912	317	35	)	)	PUNCT
ejpam-3912	317	36	en	en	X
ejpam-3912	317	37	d(v	d(v	PROPN
ejpam-3912	317	38	)	)	PUNCT
ejpam-3912	317	39	=	=	PRON
ejpam-3912	317	40	(	(	PUNCT
ejpam-3912	317	41	βu	βu	ADP
ejpam-3912	317	42	,	,	PUNCT
ejpam-3912	317	43	vv1	vv1	NOUN
ejpam-3912	317	44	+	+	CCONJ
ejpam-3912	317	45	su	su	PROPN
ejpam-3912	317	46	,	,	PUNCT
ejpam-3912	317	47	vvn	vvn	PROPN
ejpam-3912	317	48	+	+	CCONJ
ejpam-3912	317	49	su	su	PROPN
ejpam-3912	317	50	,	,	PUNCT
ejpam-3912	317	51	v	v	ADP
ejpam-3912	317	52	n−2∑	n−2∑	NUM
ejpam-3912	317	53	i=2	i=2	PROPN
ejpam-3912	317	54	divi	divi	PROPN
ejpam-3912	317	55	)	)	PUNCT
ejpam-3912	318	1	en−1	en−1	PROPN
ejpam-3912	318	2	+	+	CCONJ
ejpam-3912	318	3	(	(	PUNCT
ejpam-3912	318	4	γu	γu	PROPN
ejpam-3912	318	5	,	,	PUNCT
ejpam-3912	318	6	vv1	vv1	NOUN
ejpam-3912	318	7	+	+	CCONJ
ejpam-3912	318	8	tu	tu	PROPN
ejpam-3912	318	9	,	,	PUNCT
ejpam-3912	318	10	vvn	vvn	PROPN
ejpam-3912	318	11	+	+	CCONJ
ejpam-3912	318	12	tu	tu	PROPN
ejpam-3912	318	13	,	,	PUNCT
ejpam-3912	318	14	v	v	ADP
ejpam-3912	318	15	n−2∑	n−2∑	PROPN
ejpam-3912	318	16	i=2	i=2	PROPN
ejpam-3912	318	17	divi	divi	PROPN
ejpam-3912	318	18	)	)	PUNCT
ejpam-3912	318	19	en	en	X
ejpam-3912	318	20	(	(	PUNCT
ejpam-3912	318	21	37	37	NUM
ejpam-3912	318	22	)	)	PUNCT
ejpam-3912	318	23	where	where	SCONJ
ejpam-3912	318	24	u	u	NOUN
ejpam-3912	318	25	=	=	PUNCT
ejpam-3912	318	26	∑n	∑n	PROPN
ejpam-3912	318	27	k=1	k=1	PROPN
ejpam-3912	318	28	ukek	ukek	NOUN
ejpam-3912	318	29	and	and	CCONJ
ejpam-3912	318	30	v	v	NOUN
ejpam-3912	318	31	=	=	SYM
ejpam-3912	318	32	∑n	∑n	NOUN
ejpam-3912	318	33	k=1	k=1	X
ejpam-3912	318	34	vkek	vkek	PROPN
ejpam-3912	318	35	.	.	PUNCT
ejpam-3912	319	1	take	take	VERB
ejpam-3912	319	2	arbitrary	arbitrary	ADJ
ejpam-3912	319	3	u	u	NOUN
ejpam-3912	319	4	∈	∈	PROPN
ejpam-3912	319	5	γ1	γ1	NOUN
ejpam-3912	319	6	∪	∪	ADP
ejpam-3912	319	7	γ2	γ2	PROPN
ejpam-3912	319	8	.	.	PUNCT
ejpam-3912	320	1	then	then	ADV
ejpam-3912	320	2	from	from	ADP
ejpam-3912	320	3	the	the	DET
ejpam-3912	320	4	first	first	ADJ
ejpam-3912	320	5	equation	equation	NOUN
ejpam-3912	320	6	of	of	ADP
ejpam-3912	320	7	(	(	PUNCT
ejpam-3912	320	8	37	37	NUM
ejpam-3912	320	9	)	)	PUNCT
ejpam-3912	320	10	we	we	PRON
ejpam-3912	320	11	obtain	obtain	VERB
ejpam-3912	320	12	βu	βu	ADP
ejpam-3912	320	13	,	,	PUNCT
ejpam-3912	320	14	v	v	NOUN
ejpam-3912	320	15	=	=	SYM
ejpam-3912	320	16	βu	βu	NOUN
ejpam-3912	320	17	,	,	PUNCT
ejpam-3912	320	18	v′	v′	PROPN
ejpam-3912	320	19	,	,	PUNCT
ejpam-3912	320	20	su	su	PROPN
ejpam-3912	320	21	,	,	PUNCT
ejpam-3912	320	22	v	v	NOUN
ejpam-3912	320	23	=	=	SYM
ejpam-3912	320	24	su	su	PROPN
ejpam-3912	320	25	,	,	PUNCT
ejpam-3912	320	26	v′	v′	PROPN
ejpam-3912	320	27	,	,	PUNCT
ejpam-3912	320	28	tu	tu	PROPN
ejpam-3912	320	29	,	,	PUNCT
ejpam-3912	320	30	v	v	NOUN
ejpam-3912	320	31	=	=	SYM
ejpam-3912	320	32	tu	tu	PROPN
ejpam-3912	320	33	,	,	PUNCT
ejpam-3912	320	34	v′	v′	NOUN
ejpam-3912	320	35	for	for	ADP
ejpam-3912	320	36	any	any	DET
ejpam-3912	320	37	v	v	NOUN
ejpam-3912	320	38	,	,	PUNCT
ejpam-3912	320	39	v′	v′	PROPN
ejpam-3912	320	40	∈	∈	PROPN
ejpam-3912	320	41	e.	e.	PROPN
ejpam-3912	321	1	this	this	DET
ejpam-3912	321	2	result	result	NOUN
ejpam-3912	321	3	means	mean	VERB
ejpam-3912	321	4	that	that	SCONJ
ejpam-3912	321	5	βu	βu	ADP
ejpam-3912	321	6	,	,	PUNCT
ejpam-3912	321	7	v	v	PROPN
ejpam-3912	321	8	,	,	PUNCT
ejpam-3912	321	9	tu	tu	PROPN
ejpam-3912	321	10	,	,	PUNCT
ejpam-3912	321	11	v	v	NOUN
ejpam-3912	321	12	,	,	PUNCT
ejpam-3912	321	13	and	and	CCONJ
ejpam-3912	321	14	tu	tu	PROPN
ejpam-3912	321	15	,	,	PUNCT
ejpam-3912	321	16	v	v	X
ejpam-3912	321	17	do	do	AUX
ejpam-3912	321	18	not	not	PART
ejpam-3912	321	19	depend	depend	VERB
ejpam-3912	321	20	on	on	ADP
ejpam-3912	321	21	v	v	NOUN
ejpam-3912	321	22	,	,	PUNCT
ejpam-3912	321	23	i.e.	i.e.	X
ejpam-3912	321	24	,	,	PUNCT
ejpam-3912	321	25	βu	βu	NOUN
ejpam-3912	321	26	,	,	PUNCT
ejpam-3912	321	27	v	v	NOUN
ejpam-3912	321	28	=	=	SYM
ejpam-3912	321	29	βu	βu	PROPN
ejpam-3912	321	30	,	,	PUNCT
ejpam-3912	321	31	su	su	PROPN
ejpam-3912	321	32	,	,	PUNCT
ejpam-3912	321	33	v	v	NOUN
ejpam-3912	321	34	=	=	SYM
ejpam-3912	321	35	su	su	PROPN
ejpam-3912	321	36	,	,	PUNCT
ejpam-3912	321	37	tu	tu	PROPN
ejpam-3912	321	38	,	,	PUNCT
ejpam-3912	321	39	v	v	NOUN
ejpam-3912	321	40	=	=	SYM
ejpam-3912	321	41	tu	tu	PROPN
ejpam-3912	321	42	,	,	PUNCT
ejpam-3912	321	43	∀u	∀u	NOUN
ejpam-3912	321	44	∈	∈	PROPN
ejpam-3912	321	45	γ1	γ1	NOUN
ejpam-3912	321	46	∪	∪	ADP
ejpam-3912	321	47	γ2	γ2	PROPN
ejpam-3912	321	48	.	.	PUNCT
ejpam-3912	322	1	on	on	ADP
ejpam-3912	322	2	the	the	DET
ejpam-3912	322	3	other	other	ADJ
ejpam-3912	322	4	hand	hand	NOUN
ejpam-3912	322	5	,	,	PUNCT
ejpam-3912	322	6	from	from	ADP
ejpam-3912	322	7	the	the	DET
ejpam-3912	322	8	second	second	ADJ
ejpam-3912	322	9	equation	equation	NOUN
ejpam-3912	322	10	of	of	ADP
ejpam-3912	322	11	(	(	PUNCT
ejpam-3912	322	12	37	37	NUM
ejpam-3912	322	13	)	)	PUNCT
ejpam-3912	322	14	we	we	PRON
ejpam-3912	322	15	obtains	obtain	VERB
ejpam-3912	322	16	βu	βu	NOUN
ejpam-3912	322	17	,	,	PUNCT
ejpam-3912	322	18	v	v	NOUN
ejpam-3912	322	19	=	=	SYM
ejpam-3912	322	20	βv	βv	PROPN
ejpam-3912	322	21	,	,	PUNCT
ejpam-3912	322	22	su	su	PROPN
ejpam-3912	322	23	,	,	PUNCT
ejpam-3912	322	24	v	v	NOUN
ejpam-3912	322	25	=	=	SYM
ejpam-3912	322	26	sv	sv	PROPN
ejpam-3912	322	27	and	and	CCONJ
ejpam-3912	322	28	tu	tu	PROPN
ejpam-3912	322	29	,	,	PUNCT
ejpam-3912	322	30	v	v	NOUN
ejpam-3912	322	31	=	=	SYM
ejpam-3912	322	32	tv	tv	NOUN
ejpam-3912	322	33	for	for	ADP
ejpam-3912	322	34	any	any	DET
ejpam-3912	322	35	v	v	PROPN
ejpam-3912	322	36	∈	∈	PROPN
ejpam-3912	322	37	γ1	γ1	NOUN
ejpam-3912	322	38	∪	∪	ADP
ejpam-3912	322	39	γ2	γ2	PROPN
ejpam-3912	322	40	.	.	PUNCT
ejpam-3912	323	1	these	these	DET
ejpam-3912	323	2	facts	fact	NOUN
ejpam-3912	323	3	yield	yield	VERB
ejpam-3912	323	4	that	that	PRON
ejpam-3912	323	5	βu	βu	PUNCT
ejpam-3912	324	1	=	=	NOUN
ejpam-3912	324	2	:	:	PUNCT
ejpam-3912	324	3	β	β	X
ejpam-3912	324	4	,	,	PUNCT
ejpam-3912	324	5	su	su	PROPN
ejpam-3912	325	1	=	=	NOUN
ejpam-3912	325	2	:	:	PUNCT
ejpam-3912	325	3	s	s	X
ejpam-3912	325	4	and	and	CCONJ
ejpam-3912	325	5	tu	tu	PROPN
ejpam-3912	326	1	=	=	NOUN
ejpam-3912	326	2	:	:	PUNCT
ejpam-3912	326	3	t	t	NOUN
ejpam-3912	326	4	for	for	ADP
ejpam-3912	326	5	any	any	DET
ejpam-3912	326	6	u	u	NOUN
ejpam-3912	326	7	,	,	PUNCT
ejpam-3912	326	8	v	v	PROPN
ejpam-3912	326	9	∈	∈	PROPN
ejpam-3912	326	10	e.	e.	PROPN
ejpam-3912	326	11	consequently	consequently	ADV
ejpam-3912	326	12	,	,	PUNCT
ejpam-3912	326	13	we	we	PRON
ejpam-3912	326	14	have	have	VERB
ejpam-3912	326	15	d(u	d(u	PROPN
ejpam-3912	326	16	)	)	PUNCT
ejpam-3912	326	17	=	=	PRON
ejpam-3912	326	18	(	(	PUNCT
ejpam-3912	326	19	βu1	βu1	NOUN
ejpam-3912	326	20	+	+	CCONJ
ejpam-3912	326	21	sun	sun	NOUN
ejpam-3912	326	22	+	+	CCONJ
ejpam-3912	326	23	s	s	NOUN
ejpam-3912	326	24	n−2∑	n−2∑	NUM
ejpam-3912	326	25	i=2	i=2	PROPN
ejpam-3912	326	26	diui	diui	PROPN
ejpam-3912	326	27	)	)	PUNCT
ejpam-3912	326	28	en−1	en−1	PROPN
ejpam-3912	326	29	+	+	CCONJ
ejpam-3912	326	30	(	(	PUNCT
ejpam-3912	326	31	γu1	γu1	VERB
ejpam-3912	326	32	+	+	CCONJ
ejpam-3912	326	33	tun	tun	NOUN
ejpam-3912	326	34	+	+	CCONJ
ejpam-3912	326	35	t	t	PROPN
ejpam-3912	326	36	n−2∑	n−2∑	NUM
ejpam-3912	326	37	i=2	i=2	PROPN
ejpam-3912	326	38	diui	diui	PROPN
ejpam-3912	326	39	)	)	PUNCT
ejpam-3912	326	40	en	en	ADP
ejpam-3912	326	41	.	.	PROPN
ejpam-3912	326	42	due	due	ADP
ejpam-3912	326	43	to	to	ADP
ejpam-3912	326	44	theorem	theorem	VERB
ejpam-3912	326	45	3	3	NUM
ejpam-3912	326	46	(	(	PUNCT
ejpam-3912	326	47	i	i	NOUN
ejpam-3912	326	48	)	)	PUNCT
ejpam-3912	326	49	,	,	PUNCT
ejpam-3912	326	50	we	we	PRON
ejpam-3912	326	51	obtain	obtain	VERB
ejpam-3912	326	52	d	d	PROPN
ejpam-3912	326	53	∈	∈	PROPN
ejpam-3912	326	54	der(e	der(e	PROPN
ejpam-3912	326	55	)	)	PUNCT
ejpam-3912	326	56	.	.	PUNCT
ejpam-3912	327	1	5	5	X
ejpam-3912	327	2	.	.	X
ejpam-3912	327	3	automorphisms	automorphisms	PROPN
ejpam-3912	327	4	and	and	CCONJ
ejpam-3912	327	5	local	local	ADJ
ejpam-3912	327	6	automorphisms	automorphism	NOUN
ejpam-3912	327	7	recall	recall	VERB
ejpam-3912	327	8	that	that	SCONJ
ejpam-3912	327	9	by	by	ADP
ejpam-3912	327	10	an	an	DET
ejpam-3912	327	11	automorphism	automorphism	NOUN
ejpam-3912	327	12	of	of	ADP
ejpam-3912	327	13	an	an	DET
ejpam-3912	327	14	evolution	evolution	NOUN
ejpam-3912	327	15	algebra	algebra	NOUN
ejpam-3912	327	16	e	e	NOUN
ejpam-3912	327	17	,	,	PUNCT
ejpam-3912	327	18	we	we	PRON
ejpam-3912	327	19	mean	mean	VERB
ejpam-3912	327	20	an	an	DET
ejpam-3912	327	21	isomorphism	isomorphism	NOUN
ejpam-3912	327	22	of	of	ADP
ejpam-3912	327	23	e	e	NOUN
ejpam-3912	327	24	into	into	ADP
ejpam-3912	327	25	itself	itself	PRON
ejpam-3912	327	26	.	.	PUNCT
ejpam-3912	328	1	the	the	DET
ejpam-3912	328	2	set	set	NOUN
ejpam-3912	328	3	of	of	ADP
ejpam-3912	328	4	all	all	DET
ejpam-3912	328	5	automorphisms	automorphisms	PROPN
ejpam-3912	328	6	is	be	AUX
ejpam-3912	328	7	denoted	denote	VERB
ejpam-3912	328	8	by	by	ADP
ejpam-3912	328	9	aut(e	aut(e	PROPN
ejpam-3912	328	10	)	)	PUNCT
ejpam-3912	328	11	.	.	PUNCT
ejpam-3912	329	1	it	it	PRON
ejpam-3912	329	2	is	be	AUX
ejpam-3912	329	3	known	know	VERB
ejpam-3912	329	4	that	that	SCONJ
ejpam-3912	329	5	aut(e	aut(e	PROPN
ejpam-3912	329	6	)	)	PUNCT
ejpam-3912	329	7	is	be	AUX
ejpam-3912	329	8	a	a	DET
ejpam-3912	329	9	group	group	NOUN
ejpam-3912	329	10	.	.	PUNCT
ejpam-3912	330	1	in	in	ADP
ejpam-3912	330	2	this	this	DET
ejpam-3912	330	3	section	section	NOUN
ejpam-3912	330	4	,	,	PUNCT
ejpam-3912	330	5	to	to	PART
ejpam-3912	330	6	describe	describe	VERB
ejpam-3912	330	7	aut(e	aut(e	PROPN
ejpam-3912	330	8	)	)	PUNCT
ejpam-3912	330	9	of	of	ADP
ejpam-3912	330	10	nilpotent	nilpotent	ADJ
ejpam-3912	330	11	evolution	evolution	NOUN
ejpam-3912	330	12	algebras	algebra	NOUN
ejpam-3912	330	13	with	with	ADP
ejpam-3912	330	14	maximal	maximal	ADJ
ejpam-3912	330	15	index	index	NOUN
ejpam-3912	330	16	of	of	ADP
ejpam-3912	330	17	nilpotency	nilpotency	NOUN
ejpam-3912	330	18	.	.	PUNCT
ejpam-3912	331	1	if	if	SCONJ
ejpam-3912	331	2	ia	ia	PROPN
ejpam-3912	331	3	6=	6=	PUNCT
ejpam-3912	331	4	∅	∅	NOUN
ejpam-3912	331	5	,	,	PUNCT
ejpam-3912	331	6	then	then	ADV
ejpam-3912	331	7	by	by	ADP
ejpam-3912	331	8	η	η	PROPN
ejpam-3912	331	9	we	we	PRON
ejpam-3912	331	10	denote	denote	VERB
ejpam-3912	331	11	the	the	DET
ejpam-3912	331	12	largest	large	ADJ
ejpam-3912	331	13	common	common	ADJ
ejpam-3912	331	14	divisor	divisor	NOUN
ejpam-3912	331	15	of	of	ADP
ejpam-3912	331	16	all	all	DET
ejpam-3912	331	17	numbers	number	NOUN
ejpam-3912	331	18	2j−1	2j−1	NUM
ejpam-3912	331	19	−	−	NOUN
ejpam-3912	331	20	2i	2i	NUM
ejpam-3912	331	21	where	where	SCONJ
ejpam-3912	331	22	(	(	PUNCT
ejpam-3912	331	23	i	i	PROPN
ejpam-3912	331	24	,	,	PUNCT
ejpam-3912	331	25	j	j	PROPN
ejpam-3912	331	26	)	)	PUNCT
ejpam-3912	331	27	∈	∈	PROPN
ejpam-3912	331	28	ia	ia	PROPN
ejpam-3912	331	29	,	,	PUNCT
ejpam-3912	331	30	i.e.	i.e.	X
ejpam-3912	331	31	,	,	PUNCT
ejpam-3912	331	32	η	η	PROPN
ejpam-3912	331	33	=	=	SYM
ejpam-3912	331	34	lcd(i	lcd(i	PROPN
ejpam-3912	331	35	,	,	PUNCT
ejpam-3912	331	36	j)∈ia(2j−1	j)∈ia(2j−1	PROPN
ejpam-3912	331	37	−	−	PROPN
ejpam-3912	331	38	2i	2i	NUM
ejpam-3912	331	39	)	)	PUNCT
ejpam-3912	331	40	.	.	PUNCT
ejpam-3912	332	1	(	(	PUNCT
ejpam-3912	332	2	38	38	NUM
ejpam-3912	332	3	)	)	PUNCT
ejpam-3912	332	4	theorem	theorem	VERB
ejpam-3912	332	5	6	6	NUM
ejpam-3912	332	6	.	.	PUNCT
ejpam-3912	333	1	let	let	VERB
ejpam-3912	333	2	e	e	PRON
ejpam-3912	333	3	be	be	AUX
ejpam-3912	333	4	an	an	DET
ejpam-3912	333	5	n	n	ADV
ejpam-3912	333	6	-	-	PUNCT
ejpam-3912	333	7	dimensional	dimensional	ADJ
ejpam-3912	333	8	nilpotent	nilpotent	ADJ
ejpam-3912	333	9	evolution	evolution	NOUN
ejpam-3912	333	10	algebra	algebra	NOUN
ejpam-3912	333	11	with	with	ADP
ejpam-3912	333	12	2n−2	2n−2	PROPN
ejpam-3912	333	13	+	+	SYM
ejpam-3912	333	14	1	1	NUM
ejpam-3912	333	15	index	index	NOUN
ejpam-3912	333	16	of	of	ADP
ejpam-3912	333	17	nilpotency	nilpotency	NOUN
ejpam-3912	333	18	and	and	CCONJ
ejpam-3912	333	19	a	a	DET
ejpam-3912	333	20	=	=	X
ejpam-3912	333	21	(	(	PUNCT
ejpam-3912	333	22	aij	aij	PROPN
ejpam-3912	333	23	)	)	PUNCT
ejpam-3912	333	24	n	n	PROPN
ejpam-3912	333	25	i	i	PRON
ejpam-3912	333	26	,	,	PUNCT
ejpam-3912	333	27	j=1	j=1	PROPN
ejpam-3912	333	28	be	be	VERB
ejpam-3912	333	29	its	its	PRON
ejpam-3912	333	30	structural	structural	ADJ
ejpam-3912	333	31	matrix	matrix	NOUN
ejpam-3912	333	32	in	in	ADP
ejpam-3912	333	33	a	a	DET
ejpam-3912	333	34	natural	natural	ADJ
ejpam-3912	333	35	basis	basis	NOUN
ejpam-3912	333	36	{	{	PUNCT
ejpam-3912	333	37	ei}ni=1	ei}ni=1	PROPN
ejpam-3912	333	38	.	.	PUNCT
ejpam-3912	334	1	then	then	ADV
ejpam-3912	334	2	,	,	PUNCT
ejpam-3912	334	3	the	the	DET
ejpam-3912	334	4	following	follow	VERB
ejpam-3912	334	5	statements	statement	NOUN
ejpam-3912	334	6	hold	hold	VERB
ejpam-3912	334	7	:	:	PUNCT
ejpam-3912	334	8	a.	a.	PROPN
ejpam-3912	334	9	alarafeen	alarafeen	PROPN
ejpam-3912	334	10	,	,	PUNCT
ejpam-3912	334	11	i.	i.	PROPN
ejpam-3912	334	12	qaralleh	qaralleh	PROPN
ejpam-3912	334	13	,	,	PUNCT
ejpam-3912	334	14	a.	a.	PROPN
ejpam-3912	334	15	ahmad	ahmad	PROPN
ejpam-3912	334	16	/	/	SYM
ejpam-3912	334	17	eur	eur	PROPN
ejpam-3912	334	18	.	.	PUNCT
ejpam-3912	335	1	j.	j.	PROPN
ejpam-3912	335	2	pure	pure	PROPN
ejpam-3912	335	3	appl	appl	PROPN
ejpam-3912	335	4	.	.	PROPN
ejpam-3912	335	5	math	math	PROPN
ejpam-3912	335	6	,	,	PUNCT
ejpam-3912	335	7	14	14	NUM
ejpam-3912	335	8	(	(	PUNCT
ejpam-3912	335	9	1	1	NUM
ejpam-3912	335	10	)	)	PUNCT
ejpam-3912	335	11	(	(	PUNCT
ejpam-3912	335	12	2021	2021	NUM
ejpam-3912	335	13	)	)	PUNCT
ejpam-3912	335	14	,	,	PUNCT
ejpam-3912	335	15	278	278	NUM
ejpam-3912	335	16	-	-	SYM
ejpam-3912	335	17	300	300	NUM
ejpam-3912	335	18	292	292	NUM
ejpam-3912	335	19	(	(	PUNCT
ejpam-3912	335	20	i	i	NOUN
ejpam-3912	335	21	)	)	PUNCT
ejpam-3912	335	22	if	if	SCONJ
ejpam-3912	335	23	ia	ia	PROPN
ejpam-3912	335	24	6=	6=	PUNCT
ejpam-3912	335	25	∅	∅	NOUN
ejpam-3912	335	26	then	then	ADV
ejpam-3912	335	27	aut(e	aut(e	PROPN
ejpam-3912	335	28	)	)	PUNCT
ejpam-3912	335	29	=	=	SYM
ejpam-3912	336	1			NUM
ejpam-3912	337	1			NOUN
ejpam-3912	337	2	α	α	NOUN
ejpam-3912	337	3	0	0	PUNCT
ejpam-3912	337	4	.	.	PUNCT
ejpam-3912	337	5	.	.	PUNCT
ejpam-3912	338	1	.	.	PUNCT
ejpam-3912	338	2	0	0	PUNCT
ejpam-3912	339	1	β	β	X
ejpam-3912	339	2	γ	γ	X
ejpam-3912	339	3	0	0	PROPN
ejpam-3912	339	4	α2	α2	PROPN
ejpam-3912	339	5	.	.	PUNCT
ejpam-3912	339	6	.	.	PUNCT
ejpam-3912	340	1	.	.	PUNCT
ejpam-3912	340	2	0	0	PUNCT
ejpam-3912	341	1	ϕ2,n−1	ϕ2,n−1	ADJ
ejpam-3912	341	2	ϕ2,n	ϕ2,n	PROPN
ejpam-3912	341	3	...	...	PUNCT
ejpam-3912	341	4	...	...	PUNCT
ejpam-3912	341	5	.	.	PUNCT
ejpam-3912	341	6	.	.	PUNCT
ejpam-3912	341	7	.	.	PUNCT
ejpam-3912	342	1	...	...	PUNCT
ejpam-3912	343	1	...	...	PUNCT
ejpam-3912	344	1	0	0	NUM
ejpam-3912	344	2	0	0	NUM
ejpam-3912	344	3	.	.	PUNCT
ejpam-3912	344	4	.	.	PUNCT
ejpam-3912	344	5	.	.	PUNCT
ejpam-3912	345	1	α2n−2	α2n−2	PROPN
ejpam-3912	345	2	ϕn−2,n−1	ϕn−2,n−1	VERB
ejpam-3912	346	1	ϕn−2,n	ϕn−2,n	ADV
ejpam-3912	346	2	0	0	NUM
ejpam-3912	346	3	0	0	NUM
ejpam-3912	346	4	.	.	PUNCT
ejpam-3912	346	5	.	.	PUNCT
ejpam-3912	347	1	.	.	PUNCT
ejpam-3912	347	2	0	0	NUM
ejpam-3912	348	1	ϕn−1,n−1	ϕn−1,n−1	PROPN
ejpam-3912	348	2	ϕn−1,n	ϕn−1,n	PROPN
ejpam-3912	348	3	0	0	NUM
ejpam-3912	348	4	0	0	NUM
ejpam-3912	348	5	.	.	PUNCT
ejpam-3912	348	6	.	.	PUNCT
ejpam-3912	349	1	.	.	PUNCT
ejpam-3912	350	1	0	0	NUM
ejpam-3912	350	2	s	s	X
ejpam-3912	350	3	t	t	NOUN
ejpam-3912	350	4			PROPN
ejpam-3912	350	5	:	:	PUNCT
ejpam-3912	350	6	α	α	X
ejpam-3912	350	7	,	,	PUNCT
ejpam-3912	350	8	β	β	X
ejpam-3912	350	9	,	,	PUNCT
ejpam-3912	350	10	γ	γ	PROPN
ejpam-3912	350	11	,	,	PUNCT
ejpam-3912	350	12	s	s	PROPN
ejpam-3912	350	13	,	,	PUNCT
ejpam-3912	350	14	t	t	PROPN
ejpam-3912	350	15	∈	∈	PROPN
ejpam-3912	350	16	k	k	PROPN
ejpam-3912	350	17	,	,	PUNCT
ejpam-3912	350	18	αη	αη	PROPN
ejpam-3912	350	19	=	=	SYM
ejpam-3912	350	20	1	1	NUM
ejpam-3912	350	21			NOUN
ejpam-3912	350	22	where	where	SCONJ
ejpam-3912	350	23	η	η	PROPN
ejpam-3912	350	24	is	be	AUX
ejpam-3912	350	25	defined	define	VERB
ejpam-3912	350	26	as	as	ADP
ejpam-3912	350	27	(	(	PUNCT
ejpam-3912	350	28	38	38	NUM
ejpam-3912	350	29	)	)	PUNCT
ejpam-3912	350	30	,	,	PUNCT
ejpam-3912	350	31	and	and	CCONJ
ejpam-3912	350	32	ϕin−1	ϕin−1	PROPN
ejpam-3912	350	33	,	,	PUNCT
ejpam-3912	350	34	ϕin	ϕin	PROPN
ejpam-3912	350	35	is	be	AUX
ejpam-3912	350	36	given	give	VERB
ejpam-3912	350	37	by	by	ADP
ejpam-3912	350	38	the	the	DET
ejpam-3912	350	39	following	follow	VERB
ejpam-3912	350	40	recurrence	recurrence	NOUN
ejpam-3912	350	41	formula	formula	NOUN
ejpam-3912	350	42	.	.	PUNCT
ejpam-3912	351	1	ϕn−1,n−1	ϕn−1,n−1	PROPN
ejpam-3912	351	2	=	=	PUNCT
ejpam-3912	351	3	α2n−2	α2n−2	PROPN
ejpam-3912	351	4	−	−	PROPN
ejpam-3912	351	5	an−2,ns	an−2,ns	PROPN
ejpam-3912	351	6	,	,	PUNCT
ejpam-3912	351	7	ϕn−1,n	ϕn−1,n	VERB
ejpam-3912	351	8	=	=	SYM
ejpam-3912	351	9	an−2,n	an−2,n	ADJ
ejpam-3912	351	10	(	(	PUNCT
ejpam-3912	351	11	α2n−2	α2n−2	PROPN
ejpam-3912	351	12	−	−	PROPN
ejpam-3912	351	13	t	t	PROPN
ejpam-3912	351	14	)	)	PUNCT
ejpam-3912	351	15	,	,	PUNCT
ejpam-3912	351	16	ϕi	ϕi	ADP
ejpam-3912	351	17	,	,	PUNCT
ejpam-3912	351	18	n−1	n−1	PROPN
ejpam-3912	351	19	=	=	SYM
ejpam-3912	351	20	ai−1,n−1α	ai−1,n−1α	NOUN
ejpam-3912	351	21	2i−1	2i−1	NUM
ejpam-3912	351	22	−	−	PROPN
ejpam-3912	351	23	n−i∑	n−i∑	PRON
ejpam-3912	351	24	j	j	NOUN
ejpam-3912	351	25	=	=	PROPN
ejpam-3912	351	26	i+1	i+1	NOUN
ejpam-3912	351	27	ai−1,jϕj	ai−1,jϕj	ADJ
ejpam-3912	351	28	,	,	PUNCT
ejpam-3912	351	29	n−1	n−1	PROPN
ejpam-3912	351	30	,	,	PUNCT
ejpam-3912	351	31	1	1	NUM
ejpam-3912	351	32	<	<	X
ejpam-3912	351	33	i	i	PRON
ejpam-3912	351	34	<	<	X
ejpam-3912	351	35	n−	n−	NOUN
ejpam-3912	351	36	1	1	NUM
ejpam-3912	351	37	,	,	PUNCT
ejpam-3912	351	38	ϕi	ϕi	ADP
ejpam-3912	351	39	,	,	PUNCT
ejpam-3912	351	40	n	n	NOUN
ejpam-3912	351	41	=	=	PUNCT
ejpam-3912	351	42	ai−1,nα	ai−1,nα	PROPN
ejpam-3912	351	43	2i−1	2i−1	NUM
ejpam-3912	351	44	−	−	PROPN
ejpam-3912	351	45	n−i∑	n−i∑	PRON
ejpam-3912	351	46	j	j	NOUN
ejpam-3912	351	47	=	=	PROPN
ejpam-3912	351	48	i+1	i+1	NOUN
ejpam-3912	351	49	ai−1,jϕj	ai−1,jϕj	ADJ
ejpam-3912	351	50	,	,	PUNCT
ejpam-3912	351	51	n	n	CCONJ
ejpam-3912	351	52	,	,	PUNCT
ejpam-3912	351	53	1	1	NUM
ejpam-3912	351	54	<	<	X
ejpam-3912	351	55	i	i	PRON
ejpam-3912	351	56	<	<	X
ejpam-3912	351	57	n−	n−	NOUN
ejpam-3912	351	58	1	1	NUM
ejpam-3912	351	59	.	.	PUNCT
ejpam-3912	351	60	(	(	PUNCT
ejpam-3912	351	61	ii	ii	NOUN
ejpam-3912	351	62	)	)	PUNCT
ejpam-3912	351	63	if	if	SCONJ
ejpam-3912	351	64	ia	ia	NOUN
ejpam-3912	351	65	=	=	SYM
ejpam-3912	351	66	∅	∅	NOUN
ejpam-3912	351	67	then	then	ADV
ejpam-3912	351	68	aut(e	aut(e	PROPN
ejpam-3912	351	69	)	)	PUNCT
ejpam-3912	351	70	=	=	SYM
ejpam-3912	351	71			NUM
ejpam-3912	351	72			NOUN
ejpam-3912	351	73	α	α	NOUN
ejpam-3912	351	74	0	0	PUNCT
ejpam-3912	351	75	.	.	PUNCT
ejpam-3912	351	76	.	.	PUNCT
ejpam-3912	352	1	.	.	PUNCT
ejpam-3912	352	2	0	0	PUNCT
ejpam-3912	353	1	β	β	X
ejpam-3912	353	2	γ	γ	X
ejpam-3912	353	3	0	0	PROPN
ejpam-3912	353	4	α2	α2	PROPN
ejpam-3912	353	5	.	.	PUNCT
ejpam-3912	353	6	.	.	PUNCT
ejpam-3912	354	1	.	.	PUNCT
ejpam-3912	354	2	0	0	PUNCT
ejpam-3912	355	1	ϕ2,n−1	ϕ2,n−1	ADJ
ejpam-3912	355	2	ϕ2,n	ϕ2,n	PROPN
ejpam-3912	355	3	...	...	PUNCT
ejpam-3912	355	4	...	...	PUNCT
ejpam-3912	355	5	.	.	PUNCT
ejpam-3912	355	6	.	.	PUNCT
ejpam-3912	355	7	.	.	PUNCT
ejpam-3912	356	1	...	...	PUNCT
ejpam-3912	357	1	...	...	PUNCT
ejpam-3912	358	1	0	0	NUM
ejpam-3912	358	2	0	0	NUM
ejpam-3912	358	3	.	.	PUNCT
ejpam-3912	358	4	.	.	PUNCT
ejpam-3912	358	5	.	.	PUNCT
ejpam-3912	359	1	α2n−2	α2n−2	PROPN
ejpam-3912	359	2	ϕn−2,n−1	ϕn−2,n−1	VERB
ejpam-3912	360	1	ϕn−2,n	ϕn−2,n	ADV
ejpam-3912	360	2	0	0	NUM
ejpam-3912	360	3	0	0	NUM
ejpam-3912	360	4	.	.	PUNCT
ejpam-3912	360	5	.	.	PUNCT
ejpam-3912	361	1	.	.	PUNCT
ejpam-3912	361	2	0	0	NUM
ejpam-3912	362	1	ϕn−1,n−1	ϕn−1,n−1	PROPN
ejpam-3912	362	2	ϕn−1,n	ϕn−1,n	PROPN
ejpam-3912	362	3	0	0	NUM
ejpam-3912	362	4	0	0	NUM
ejpam-3912	362	5	.	.	PUNCT
ejpam-3912	362	6	.	.	PUNCT
ejpam-3912	363	1	.	.	PUNCT
ejpam-3912	364	1	0	0	NUM
ejpam-3912	364	2	s	s	X
ejpam-3912	364	3	t	t	NOUN
ejpam-3912	364	4			PROPN
ejpam-3912	364	5	:	:	PUNCT
ejpam-3912	364	6	α	α	X
ejpam-3912	364	7	,	,	PUNCT
ejpam-3912	364	8	β	β	X
ejpam-3912	364	9	,	,	PUNCT
ejpam-3912	364	10	γ	γ	PROPN
ejpam-3912	364	11	,	,	PUNCT
ejpam-3912	364	12	s	s	PROPN
ejpam-3912	364	13	,	,	PUNCT
ejpam-3912	364	14	t	t	PROPN
ejpam-3912	364	15	∈	∈	PROPN
ejpam-3912	364	16	k	k	PROPN
ejpam-3912	364	17	,	,	PUNCT
ejpam-3912	364	18	α	α	PROPN
ejpam-3912	364	19	6=	6=	ADP
ejpam-3912	364	20	0	0	NUM
ejpam-3912	364	21			NOUN
ejpam-3912	364	22	where	where	SCONJ
ejpam-3912	364	23	ϕin−1	ϕin−1	PROPN
ejpam-3912	364	24	,	,	PUNCT
ejpam-3912	364	25	ϕin	ϕin	PROPN
ejpam-3912	364	26	is	be	AUX
ejpam-3912	364	27	given	give	VERB
ejpam-3912	364	28	by	by	ADP
ejpam-3912	364	29	the	the	DET
ejpam-3912	364	30	following	follow	VERB
ejpam-3912	364	31	recurrence	recurrence	NOUN
ejpam-3912	364	32	formula	formula	NOUN
ejpam-3912	364	33	:	:	PUNCT
ejpam-3912	364	34	ϕn−1,n−1	ϕn−1,n−1	PROPN
ejpam-3912	364	35	=	=	SYM
ejpam-3912	364	36	α2n−2	α2n−2	PROPN
ejpam-3912	364	37	−	−	PROPN
ejpam-3912	364	38	an−2,ns	an−2,ns	PROPN
ejpam-3912	364	39	,	,	PUNCT
ejpam-3912	364	40	ϕn−1,n	ϕn−1,n	VERB
ejpam-3912	364	41	=	=	SYM
ejpam-3912	364	42	an−2,n	an−2,n	ADJ
ejpam-3912	364	43	(	(	PUNCT
ejpam-3912	364	44	α2n−2	α2n−2	PROPN
ejpam-3912	364	45	−	−	PROPN
ejpam-3912	364	46	t	t	PROPN
ejpam-3912	364	47	)	)	PUNCT
ejpam-3912	364	48	,	,	PUNCT
ejpam-3912	364	49	ϕi	ϕi	ADP
ejpam-3912	364	50	,	,	PUNCT
ejpam-3912	364	51	n−1	n−1	PROPN
ejpam-3912	364	52	=	=	SYM
ejpam-3912	364	53	ai−1,n−1	ai−1,n−1	PROPN
ejpam-3912	364	54	(	(	PUNCT
ejpam-3912	364	55	α2i−1	α2i−1	PROPN
ejpam-3912	364	56	−	−	PROPN
ejpam-3912	364	57	ϕn−1,n−1	ϕn−1,n−1	PROPN
ejpam-3912	364	58	)	)	PUNCT
ejpam-3912	364	59	−	−	ADP
ejpam-3912	364	60	ai−1,ns	ai−1,ns	NOUN
ejpam-3912	364	61	,	,	PUNCT
ejpam-3912	364	62	1	1	NUM
ejpam-3912	364	63	<	<	X
ejpam-3912	364	64	i	i	PRON
ejpam-3912	364	65	<	<	X
ejpam-3912	364	66	n−	n−	NOUN
ejpam-3912	364	67	1	1	NUM
ejpam-3912	364	68	,	,	PUNCT
ejpam-3912	364	69	ϕi	ϕi	ADP
ejpam-3912	364	70	,	,	PUNCT
ejpam-3912	364	71	n	n	NOUN
ejpam-3912	364	72	=	=	PUNCT
ejpam-3912	364	73	ai−1,n	ai−1,n	NOUN
ejpam-3912	364	74	(	(	PUNCT
ejpam-3912	364	75	α2i−1	α2i−1	PROPN
ejpam-3912	364	76	−	−	PROPN
ejpam-3912	364	77	t	t	PROPN
ejpam-3912	364	78	)	)	PUNCT
ejpam-3912	365	1	−	−	PROPN
ejpam-3912	365	2	ai−1,n−1ϕn−1,n	ai−1,n−1ϕn−1,n	ADJ
ejpam-3912	365	3	,	,	PUNCT
ejpam-3912	365	4	1	1	NUM
ejpam-3912	365	5	<	<	X
ejpam-3912	365	6	i	i	PRON
ejpam-3912	365	7	<	<	X
ejpam-3912	365	8	n−	n−	NOUN
ejpam-3912	365	9	1	1	NUM
ejpam-3912	365	10	.	.	PUNCT
ejpam-3912	366	1	proof	proof	NOUN
ejpam-3912	366	2	.	.	PUNCT
ejpam-3912	367	1	let	let	VERB
ejpam-3912	367	2	ϕ	ϕ	NOUN
ejpam-3912	367	3	be	be	AUX
ejpam-3912	367	4	a	a	DET
ejpam-3912	367	5	linear	linear	ADJ
ejpam-3912	367	6	mapping	mapping	NOUN
ejpam-3912	367	7	on	on	ADP
ejpam-3912	367	8	e.	e.	PROPN
ejpam-3912	367	9	now	now	ADV
ejpam-3912	367	10	,	,	PUNCT
ejpam-3912	367	11	we	we	PRON
ejpam-3912	367	12	represent	represent	VERB
ejpam-3912	367	13	ϕ	ϕ	NOUN
ejpam-3912	367	14	on	on	ADP
ejpam-3912	367	15	the	the	DET
ejpam-3912	367	16	basis	basis	NOUN
ejpam-3912	367	17	elements	element	NOUN
ejpam-3912	367	18	as	as	SCONJ
ejpam-3912	367	19	follows	follow	VERB
ejpam-3912	367	20	:	:	PUNCT
ejpam-3912	367	21	ϕ(ei	ϕ(ei	X
ejpam-3912	367	22	)	)	PUNCT
ejpam-3912	368	1	=	=	SYM
ejpam-3912	368	2	n∑	n∑	NOUN
ejpam-3912	368	3	j=1	j=1	PROPN
ejpam-3912	368	4	ϕijej	ϕijej	PROPN
ejpam-3912	368	5	,	,	PUNCT
ejpam-3912	368	6	1	1	NUM
ejpam-3912	368	7	≤	≤	NUM
ejpam-3912	368	8	i	i	PRON
ejpam-3912	368	9	≤	≤	NUM
ejpam-3912	368	10	n.	n.	NOUN
ejpam-3912	368	11	we	we	PRON
ejpam-3912	368	12	want	want	VERB
ejpam-3912	368	13	to	to	PART
ejpam-3912	368	14	describe	describe	VERB
ejpam-3912	368	15	matrix	matrix	NOUN
ejpam-3912	368	16	(	(	PUNCT
ejpam-3912	368	17	ϕij	ϕij	NOUN
ejpam-3912	368	18	)	)	PUNCT
ejpam-3912	369	1	n	n	PROPN
ejpam-3912	370	1	i	i	PRON
ejpam-3912	370	2	,	,	PUNCT
ejpam-3912	370	3	j=1	j=1	PROPN
ejpam-3912	370	4	when	when	SCONJ
ejpam-3912	370	5	ϕ	ϕ	NOUN
ejpam-3912	370	6	is	be	AUX
ejpam-3912	370	7	an	an	DET
ejpam-3912	370	8	automorphism	automorphism	NOUN
ejpam-3912	370	9	of	of	ADP
ejpam-3912	370	10	e.	e.	PROPN
ejpam-3912	370	11	suppose	suppose	VERB
ejpam-3912	370	12	that	that	SCONJ
ejpam-3912	370	13	ϕ	ϕ	NOUN
ejpam-3912	370	14	is	be	AUX
ejpam-3912	370	15	an	an	DET
ejpam-3912	370	16	automorphism	automorphism	NOUN
ejpam-3912	370	17	.	.	PUNCT
ejpam-3912	371	1	then	then	ADV
ejpam-3912	371	2	,	,	PUNCT
ejpam-3912	371	3	we	we	PRON
ejpam-3912	371	4	have	have	VERB
ejpam-3912	371	5	ϕ(ei)ϕ(ej	ϕ(ei)ϕ(ej	PUNCT
ejpam-3912	371	6	)	)	PUNCT
ejpam-3912	372	1	=	=	SYM
ejpam-3912	372	2	0	0	NUM
ejpam-3912	372	3	,	,	PUNCT
ejpam-3912	372	4	i	i	PROPN
ejpam-3912	372	5	6=	6=	PROPN
ejpam-3912	373	1	j	j	PROPN
ejpam-3912	373	2	ϕ(e2	ϕ(e2	NOUN
ejpam-3912	373	3	i	i	NOUN
ejpam-3912	373	4	)	)	PUNCT
ejpam-3912	374	1	=	=	PUNCT
ejpam-3912	375	1	[	[	X
ejpam-3912	375	2	ϕ(ei	ϕ(ei	NOUN
ejpam-3912	375	3	)	)	PUNCT
ejpam-3912	375	4	]	]	PUNCT
ejpam-3912	375	5	2	2	NUM
ejpam-3912	375	6	,	,	PUNCT
ejpam-3912	375	7	1	1	NUM
ejpam-3912	375	8	≤	≤	NUM
ejpam-3912	375	9	i	i	NOUN
ejpam-3912	375	10	≤	≤	PROPN
ejpam-3912	375	11	n	n	PRON
ejpam-3912	375	12	a.	a.	NOUN
ejpam-3912	375	13	alarafeen	alarafeen	PROPN
ejpam-3912	375	14	,	,	PUNCT
ejpam-3912	375	15	i.	i.	PROPN
ejpam-3912	375	16	qaralleh	qaralleh	PROPN
ejpam-3912	375	17	,	,	PUNCT
ejpam-3912	375	18	a.	a.	PROPN
ejpam-3912	375	19	ahmad	ahmad	PROPN
ejpam-3912	375	20	/	/	SYM
ejpam-3912	375	21	eur	eur	PROPN
ejpam-3912	375	22	.	.	PUNCT
ejpam-3912	376	1	j.	j.	PROPN
ejpam-3912	376	2	pure	pure	PROPN
ejpam-3912	376	3	appl	appl	PROPN
ejpam-3912	376	4	.	.	PROPN
ejpam-3912	376	5	math	math	PROPN
ejpam-3912	376	6	,	,	PUNCT
ejpam-3912	376	7	14	14	NUM
ejpam-3912	376	8	(	(	PUNCT
ejpam-3912	376	9	1	1	NUM
ejpam-3912	376	10	)	)	PUNCT
ejpam-3912	376	11	(	(	PUNCT
ejpam-3912	376	12	2021	2021	NUM
ejpam-3912	376	13	)	)	PUNCT
ejpam-3912	376	14	,	,	PUNCT
ejpam-3912	376	15	278	278	NUM
ejpam-3912	376	16	-	-	SYM
ejpam-3912	376	17	300	300	NUM
ejpam-3912	376	18	293	293	NUM
ejpam-3912	376	19	which	which	PRON
ejpam-3912	376	20	is	be	AUX
ejpam-3912	376	21	equivalent	equivalent	ADJ
ejpam-3912	376	22	to	to	ADP
ejpam-3912	376	23	the	the	DET
ejpam-3912	376	24	followings	following	NOUN
ejpam-3912	376	25	:	:	PUNCT
ejpam-3912	376	26	n−1∑	n−1∑	NUM
ejpam-3912	376	27	k=1	k=1	PUNCT
ejpam-3912	377	1	ϕikϕjke	ϕikϕjke	PROPN
ejpam-3912	377	2	2	2	NUM
ejpam-3912	378	1	k	k	NOUN
ejpam-3912	378	2	=	=	SYM
ejpam-3912	378	3	0	0	PROPN
ejpam-3912	378	4	,	,	PUNCT
ejpam-3912	378	5	i	i	PROPN
ejpam-3912	378	6	6=	6=	PROPN
ejpam-3912	378	7	j	j	PROPN
ejpam-3912	378	8	(	(	PUNCT
ejpam-3912	378	9	39	39	NUM
ejpam-3912	378	10	)	)	PUNCT
ejpam-3912	378	11	n∑	n∑	NOUN
ejpam-3912	378	12	j	j	X
ejpam-3912	379	1	=	=	NOUN
ejpam-3912	379	2	i+1	i+1	NOUN
ejpam-3912	379	3	aij	aij	PROPN
ejpam-3912	379	4	n∑	n∑	PROPN
ejpam-3912	379	5	k=1	k=1	PROPN
ejpam-3912	379	6	ϕjkek	ϕjkek	NOUN
ejpam-3912	379	7	=	=	PUNCT
ejpam-3912	379	8	n−1∑	n−1∑	NOUN
ejpam-3912	379	9	k=1	k=1	INTJ
ejpam-3912	380	1	ϕ2	ϕ2	ADV
ejpam-3912	380	2	ike	ike	PROPN
ejpam-3912	380	3	2	2	NUM
ejpam-3912	380	4	k	k	NOUN
ejpam-3912	380	5	,	,	PUNCT
ejpam-3912	380	6	i	i	PRON
ejpam-3912	380	7	≤	≤	VERB
ejpam-3912	380	8	n−	n−	NOUN
ejpam-3912	380	9	2	2	NUM
ejpam-3912	380	10	(	(	PUNCT
ejpam-3912	380	11	40	40	NUM
ejpam-3912	380	12	)	)	PUNCT
ejpam-3912	380	13	an−1,n	an−1,n	PROPN
ejpam-3912	380	14	(	(	PUNCT
ejpam-3912	380	15	n∑	n∑	NOUN
ejpam-3912	380	16	k=1	k=1	PROPN
ejpam-3912	380	17	ϕnkek	ϕnkek	PROPN
ejpam-3912	380	18	)	)	PUNCT
ejpam-3912	380	19	=	=	SYM
ejpam-3912	381	1	n−1∑	n−1∑	NOUN
ejpam-3912	381	2	k=1	k=1	VERB
ejpam-3912	382	1	ϕ2	ϕ2	ADV
ejpam-3912	382	2	n−1,ke	n−1,ke	ADV
ejpam-3912	382	3	2	2	NUM
ejpam-3912	382	4	k	k	NOUN
ejpam-3912	382	5	,	,	PUNCT
ejpam-3912	382	6	(	(	PUNCT
ejpam-3912	382	7	41	41	NUM
ejpam-3912	382	8	)	)	PUNCT
ejpam-3912	382	9	n−1∑	n−1∑	NOUN
ejpam-3912	382	10	k=1	k=1	PUNCT
ejpam-3912	383	1	ϕ2	ϕ2	ADV
ejpam-3912	383	2	nke	nke	PROPN
ejpam-3912	383	3	2	2	NUM
ejpam-3912	383	4	k	k	NOUN
ejpam-3912	383	5	=	=	SYM
ejpam-3912	383	6	0	0	PROPN
ejpam-3912	383	7	.	.	PUNCT
ejpam-3912	384	1	(	(	PUNCT
ejpam-3912	384	2	42	42	NUM
ejpam-3912	384	3	)	)	PUNCT
ejpam-3912	384	4	the	the	DET
ejpam-3912	384	5	linear	linear	ADJ
ejpam-3912	384	6	independence	independence	NOUN
ejpam-3912	384	7	of	of	ADP
ejpam-3912	384	8	{	{	PUNCT
ejpam-3912	384	9	e2	e2	PROPN
ejpam-3912	384	10	1	1	NUM
ejpam-3912	384	11	,	,	PUNCT
ejpam-3912	384	12	e	e	NOUN
ejpam-3912	384	13	2	2	NUM
ejpam-3912	384	14	2	2	NUM
ejpam-3912	384	15	,	,	PUNCT
ejpam-3912	384	16	·	·	PUNCT
ejpam-3912	384	17	·	·	PUNCT
ejpam-3912	384	18	·	·	PUNCT
ejpam-3912	384	19	,	,	PUNCT
ejpam-3912	384	20	e2	e2	PROPN
ejpam-3912	384	21	n−2	n−2	PROPN
ejpam-3912	384	22	}	}	PUNCT
ejpam-3912	384	23	together	together	ADV
ejpam-3912	384	24	with	with	ADP
ejpam-3912	384	25	(	(	PUNCT
ejpam-3912	384	26	39),(42	39),(42	NUM
ejpam-3912	384	27	)	)	PUNCT
ejpam-3912	384	28	implies	imply	VERB
ejpam-3912	384	29	ϕikϕjk	ϕikϕjk	NOUN
ejpam-3912	384	30	=	=	SYM
ejpam-3912	384	31	0	0	NUM
ejpam-3912	384	32	,	,	PUNCT
ejpam-3912	384	33	i	i	PROPN
ejpam-3912	384	34	6=	6=	PROPN
ejpam-3912	384	35	j	j	PROPN
ejpam-3912	384	36	,	,	PUNCT
ejpam-3912	384	37	k	k	PROPN
ejpam-3912	384	38	≤	≤	PROPN
ejpam-3912	384	39	n−	n−	NOUN
ejpam-3912	384	40	2	2	NUM
ejpam-3912	384	41	(	(	PUNCT
ejpam-3912	384	42	43	43	NUM
ejpam-3912	384	43	)	)	PUNCT
ejpam-3912	384	44	ϕn−1,k	ϕn−1,k	PROPN
ejpam-3912	384	45	=	=	SYM
ejpam-3912	384	46	ϕnk	ϕnk	PROPN
ejpam-3912	385	1	=	=	SYM
ejpam-3912	385	2	0	0	PROPN
ejpam-3912	385	3	,	,	PUNCT
ejpam-3912	385	4	k	k	PROPN
ejpam-3912	385	5	≤	≤	PROPN
ejpam-3912	385	6	n−	n−	PROPN
ejpam-3912	385	7	2	2	NUM
ejpam-3912	385	8	.	.	PUNCT
ejpam-3912	386	1	(	(	PUNCT
ejpam-3912	386	2	44	44	NUM
ejpam-3912	386	3	)	)	PUNCT
ejpam-3912	386	4	we	we	PRON
ejpam-3912	386	5	find	find	VERB
ejpam-3912	386	6	that	that	SCONJ
ejpam-3912	386	7	ϕn−2,n−2	ϕn−2,n−2	PROPN
ejpam-3912	386	8	6=	6=	ADP
ejpam-3912	386	9	0	0	NUM
ejpam-3912	386	10	.	.	X
ejpam-3912	387	1	plugging	plug	VERB
ejpam-3912	387	2	(	(	PUNCT
ejpam-3912	387	3	44	44	NUM
ejpam-3912	387	4	)	)	PUNCT
ejpam-3912	387	5	into	into	ADP
ejpam-3912	387	6	(	(	PUNCT
ejpam-3912	387	7	41	41	NUM
ejpam-3912	387	8	)	)	PUNCT
ejpam-3912	387	9	,	,	PUNCT
ejpam-3912	387	10	we	we	PRON
ejpam-3912	387	11	find	find	VERB
ejpam-3912	387	12	ϕn−2,n−2	ϕn−2,n−2	NOUN
ejpam-3912	387	13	=	=	PUNCT
ejpam-3912	387	14	ϕ2	ϕ2	ADV
ejpam-3912	387	15	n−3,n−3	n−3,n−3	X
ejpam-3912	387	16	ϕn−3,k	ϕn−3,k	ADV
ejpam-3912	387	17	=	=	SYM
ejpam-3912	387	18	0	0	NUM
ejpam-3912	387	19	,	,	PUNCT
ejpam-3912	387	20	k	k	PROPN
ejpam-3912	387	21	≤	≤	PROPN
ejpam-3912	387	22	n−	n−	PROPN
ejpam-3912	387	23	3	3	NUM
ejpam-3912	387	24	(	(	PUNCT
ejpam-3912	387	25	45	45	NUM
ejpam-3912	387	26	)	)	PUNCT
ejpam-3912	387	27	inserting	insert	VERB
ejpam-3912	387	28	e2	e2	PROPN
ejpam-3912	387	29	l	l	NOUN
ejpam-3912	387	30	=	=	PUNCT
ejpam-3912	388	1	∑n	∑n	PROPN
ejpam-3912	388	2	j	j	PROPN
ejpam-3912	388	3	=	=	PROPN
ejpam-3912	388	4	l+1	l+1	PROPN
ejpam-3912	388	5	aljej	aljej	NOUN
ejpam-3912	388	6	,	,	PUNCT
ejpam-3912	388	7	l	l	NOUN
ejpam-3912	388	8	≤	≤	X
ejpam-3912	388	9	n−	n−	NOUN
ejpam-3912	388	10	2	2	NUM
ejpam-3912	388	11	into	into	ADP
ejpam-3912	388	12	(	(	PUNCT
ejpam-3912	388	13	40	40	NUM
ejpam-3912	388	14	)	)	PUNCT
ejpam-3912	388	15	,	,	PUNCT
ejpam-3912	388	16	we	we	PRON
ejpam-3912	388	17	obtain	obtain	VERB
ejpam-3912	388	18	n∑	n∑	PROPN
ejpam-3912	388	19	j	j	PROPN
ejpam-3912	389	1	=	=	NOUN
ejpam-3912	389	2	i+1	i+1	NOUN
ejpam-3912	389	3	aijϕjl	aijϕjl	NOUN
ejpam-3912	389	4	=	=	PUNCT
ejpam-3912	389	5	l−1∑	l−1∑	PROPN
ejpam-3912	389	6	j=1	j=1	PROPN
ejpam-3912	389	7	ajlϕ	ajlϕ	ADJ
ejpam-3912	389	8	2	2	NUM
ejpam-3912	389	9	ij	ij	NOUN
ejpam-3912	389	10	,	,	PUNCT
ejpam-3912	389	11	i	i	PRON
ejpam-3912	389	12	≤	≤	VERB
ejpam-3912	389	13	n−	n−	NOUN
ejpam-3912	389	14	2	2	NUM
ejpam-3912	389	15	,	,	PUNCT
ejpam-3912	389	16	l	l	X
ejpam-3912	389	17	≥	≥	NUM
ejpam-3912	389	18	2	2	NUM
ejpam-3912	389	19	(	(	PUNCT
ejpam-3912	389	20	46	46	NUM
ejpam-3912	389	21	)	)	PUNCT
ejpam-3912	389	22	n∑	n∑	NOUN
ejpam-3912	389	23	j	j	X
ejpam-3912	389	24	=	=	NOUN
ejpam-3912	389	25	i+1	i+1	PART
ejpam-3912	389	26	aijϕj1	aijϕj1	VERB
ejpam-3912	390	1	=	=	SYM
ejpam-3912	390	2	0	0	NUM
ejpam-3912	390	3	,	,	PUNCT
ejpam-3912	390	4	i	i	PRON
ejpam-3912	390	5	≤	≤	VERB
ejpam-3912	390	6	n−	n−	NOUN
ejpam-3912	390	7	2	2	NUM
ejpam-3912	390	8	(	(	PUNCT
ejpam-3912	390	9	47	47	NUM
ejpam-3912	390	10	)	)	PUNCT
ejpam-3912	390	11	we	we	PRON
ejpam-3912	390	12	claim	claim	VERB
ejpam-3912	390	13	:	:	PUNCT
ejpam-3912	390	14	ϕil	ϕil	ADP
ejpam-3912	390	15	=	=	SYM
ejpam-3912	390	16	0	0	PROPN
ejpam-3912	390	17	,	,	PUNCT
ejpam-3912	390	18	l	l	NOUN
ejpam-3912	391	1	+	+	NOUN
ejpam-3912	391	2	1	1	X
ejpam-3912	391	3	≤	≤	NUM
ejpam-3912	392	1	i	i	PRON
ejpam-3912	392	2	ϕj+1,j+1	ϕj+1,j+1	NOUN
ejpam-3912	393	1	=	=	PUNCT
ejpam-3912	394	1	ϕ2	ϕ2	ADV
ejpam-3912	394	2	jj	jj	PROPN
ejpam-3912	394	3	,	,	PUNCT
ejpam-3912	394	4	j	j	PROPN
ejpam-3912	394	5	≤	≤	PROPN
ejpam-3912	394	6	n−	n−	PROPN
ejpam-3912	394	7	2	2	NUM
ejpam-3912	394	8	.	.	PUNCT
ejpam-3912	395	1	(	(	PUNCT
ejpam-3912	395	2	48	48	NUM
ejpam-3912	395	3	)	)	PUNCT
ejpam-3912	395	4	let	let	VERB
ejpam-3912	395	5	us	we	PRON
ejpam-3912	395	6	prove	prove	VERB
ejpam-3912	395	7	the	the	DET
ejpam-3912	395	8	last	last	ADJ
ejpam-3912	395	9	relations	relation	NOUN
ejpam-3912	395	10	by	by	ADP
ejpam-3912	395	11	induction	induction	NOUN
ejpam-3912	395	12	.	.	PUNCT
ejpam-3912	396	1	due	due	ADP
ejpam-3912	396	2	to	to	ADP
ejpam-3912	396	3	(	(	PUNCT
ejpam-3912	396	4	44),(45	44),(45	NOUN
ejpam-3912	396	5	)	)	PUNCT
ejpam-3912	396	6	,	,	PUNCT
ejpam-3912	396	7	the	the	DET
ejpam-3912	396	8	first	first	ADJ
ejpam-3912	396	9	step	step	NOUN
ejpam-3912	396	10	is	be	AUX
ejpam-3912	396	11	satisfied	satisfied	ADJ
ejpam-3912	396	12	.	.	PUNCT
ejpam-3912	397	1	we	we	PRON
ejpam-3912	397	2	take	take	VERB
ejpam-3912	397	3	an	an	DET
ejpam-3912	397	4	arbitrary	arbitrary	ADJ
ejpam-3912	397	5	i0	i0	PROPN
ejpam-3912	397	6	>	>	X
ejpam-3912	397	7	1	1	NUM
ejpam-3912	397	8	,	,	PUNCT
ejpam-3912	397	9	and	and	CCONJ
ejpam-3912	397	10	assume	assume	VERB
ejpam-3912	397	11	that	that	SCONJ
ejpam-3912	397	12	for	for	ADP
ejpam-3912	397	13	any	any	DET
ejpam-3912	397	14	i	i	PROPN
ejpam-3912	397	15	>	>	X
ejpam-3912	397	16	i0	i0	PROPN
ejpam-3912	397	17	,	,	PUNCT
ejpam-3912	397	18	assertion	assertion	NOUN
ejpam-3912	397	19	(	(	PUNCT
ejpam-3912	397	20	48	48	NUM
ejpam-3912	397	21	)	)	PUNCT
ejpam-3912	397	22	holds	hold	VERB
ejpam-3912	397	23	.	.	PUNCT
ejpam-3912	398	1	we	we	PRON
ejpam-3912	398	2	must	must	AUX
ejpam-3912	398	3	prove	prove	VERB
ejpam-3912	398	4	that	that	SCONJ
ejpam-3912	398	5	ϕi0l	ϕi0l	PROPN
ejpam-3912	398	6	=	=	PRON
ejpam-3912	398	7	0	0	NUM
ejpam-3912	398	8	for	for	ADP
ejpam-3912	398	9	any	any	DET
ejpam-3912	398	10	l	l	NOUN
ejpam-3912	398	11	≤	≤	NOUN
ejpam-3912	398	12	i0	i0	PROPN
ejpam-3912	398	13	−	−	PROPN
ejpam-3912	398	14	1	1	NUM
ejpam-3912	398	15	and	and	CCONJ
ejpam-3912	398	16	ϕi0i0	ϕi0i0	NOUN
ejpam-3912	398	17	=	=	PROPN
ejpam-3912	398	18	ϕ2	ϕ2	PROPN
ejpam-3912	398	19	i0−1,i0−1	i0−1,i0−1	PROPN
ejpam-3912	398	20	.	.	PUNCT
ejpam-3912	399	1	rewriting	rewrite	VERB
ejpam-3912	399	2	(	(	PUNCT
ejpam-3912	399	3	46	46	NUM
ejpam-3912	399	4	)	)	PUNCT
ejpam-3912	399	5	for	for	ADP
ejpam-3912	399	6	i	i	PRON
ejpam-3912	399	7	=	=	SYM
ejpam-3912	399	8	i0	i0	PROPN
ejpam-3912	399	9	>	>	X
ejpam-3912	399	10	1	1	NUM
ejpam-3912	399	11	,	,	PUNCT
ejpam-3912	399	12	we	we	PRON
ejpam-3912	399	13	find	find	VERB
ejpam-3912	399	14	n∑	n∑	PROPN
ejpam-3912	399	15	j	j	PROPN
ejpam-3912	399	16	=	=	PROPN
ejpam-3912	399	17	i0	i0	PROPN
ejpam-3912	399	18	+	+	PROPN
ejpam-3912	399	19	1	1	NUM
ejpam-3912	399	20	ai0jϕjl	ai0jϕjl	PUNCT
ejpam-3912	399	21	=	=	SYM
ejpam-3912	400	1	l−1∑	l−1∑	NOUN
ejpam-3912	400	2	j=1	j=1	PROPN
ejpam-3912	400	3	ajlϕ	ajlϕ	ADJ
ejpam-3912	400	4	2	2	NUM
ejpam-3912	400	5	i0j	i0j	NOUN
ejpam-3912	400	6	,	,	PUNCT
ejpam-3912	400	7	l	l	PROPN
ejpam-3912	400	8	≥	≥	NUM
ejpam-3912	400	9	2	2	NUM
ejpam-3912	400	10	(	(	PUNCT
ejpam-3912	400	11	49	49	NUM
ejpam-3912	400	12	)	)	PUNCT
ejpam-3912	400	13	a.	a.	NOUN
ejpam-3912	400	14	alarafeen	alarafeen	PROPN
ejpam-3912	400	15	,	,	PUNCT
ejpam-3912	400	16	i.	i.	PROPN
ejpam-3912	400	17	qaralleh	qaralleh	PROPN
ejpam-3912	400	18	,	,	PUNCT
ejpam-3912	400	19	a.	a.	PROPN
ejpam-3912	400	20	ahmad	ahmad	PROPN
ejpam-3912	400	21	/	/	SYM
ejpam-3912	400	22	eur	eur	PROPN
ejpam-3912	400	23	.	.	PUNCT
ejpam-3912	401	1	j.	j.	PROPN
ejpam-3912	401	2	pure	pure	PROPN
ejpam-3912	401	3	appl	appl	PROPN
ejpam-3912	401	4	.	.	PROPN
ejpam-3912	401	5	math	math	PROPN
ejpam-3912	401	6	,	,	PUNCT
ejpam-3912	401	7	14	14	NUM
ejpam-3912	401	8	(	(	PUNCT
ejpam-3912	401	9	1	1	NUM
ejpam-3912	401	10	)	)	PUNCT
ejpam-3912	401	11	(	(	PUNCT
ejpam-3912	401	12	2021	2021	NUM
ejpam-3912	401	13	)	)	PUNCT
ejpam-3912	401	14	,	,	PUNCT
ejpam-3912	401	15	278	278	NUM
ejpam-3912	401	16	-	-	SYM
ejpam-3912	401	17	300	300	NUM
ejpam-3912	401	18	294	294	NUM
ejpam-3912	401	19	if	if	SCONJ
ejpam-3912	401	20	j	j	PROPN
ejpam-3912	401	21	>	>	X
ejpam-3912	401	22	i0	i0	PROPN
ejpam-3912	401	23	,	,	PUNCT
ejpam-3912	401	24	then	then	ADV
ejpam-3912	401	25	due	due	ADP
ejpam-3912	401	26	to	to	ADP
ejpam-3912	401	27	the	the	DET
ejpam-3912	401	28	assumption	assumption	NOUN
ejpam-3912	401	29	,	,	PUNCT
ejpam-3912	401	30	we	we	PRON
ejpam-3912	401	31	have	have	VERB
ejpam-3912	401	32	ϕjl	ϕjl	NOUN
ejpam-3912	401	33	=	=	NOUN
ejpam-3912	401	34	0	0	NUM
ejpam-3912	401	35	for	for	ADP
ejpam-3912	401	36	any	any	DET
ejpam-3912	401	37	l	l	NOUN
ejpam-3912	401	38	≤	≤	ADV
ejpam-3912	401	39	i0	i0	PROPN
ejpam-3912	401	40	.	.	PUNCT
ejpam-3912	402	1	as	as	ADP
ejpam-3912	402	2	,	,	PUNCT
ejpam-3912	402	3	for	for	ADP
ejpam-3912	402	4	any	any	DET
ejpam-3912	402	5	l	l	NOUN
ejpam-3912	402	6	≤	≤	NOUN
ejpam-3912	402	7	i0	i0	PROPN
ejpam-3912	402	8	the	the	DET
ejpam-3912	402	9	left	left	ADJ
ejpam-3912	402	10	side	side	NOUN
ejpam-3912	402	11	of	of	ADP
ejpam-3912	402	12	(	(	PUNCT
ejpam-3912	402	13	49	49	NUM
ejpam-3912	402	14	)	)	PUNCT
ejpam-3912	402	15	is	be	AUX
ejpam-3912	402	16	equals	equal	VERB
ejpam-3912	402	17	to	to	ADP
ejpam-3912	402	18	zero	zero	NUM
ejpam-3912	402	19	.	.	PUNCT
ejpam-3912	403	1	thus	thus	ADV
ejpam-3912	403	2	,	,	PUNCT
ejpam-3912	403	3	l−1∑	l−1∑	ADJ
ejpam-3912	403	4	j=1	j=1	NOUN
ejpam-3912	403	5	ϕ2	ϕ2	ADV
ejpam-3912	403	6	i0jajl	i0jajl	X
ejpam-3912	403	7	=	=	SYM
ejpam-3912	403	8	0	0	NUM
ejpam-3912	403	9	,	,	PUNCT
ejpam-3912	403	10	2	2	NUM
ejpam-3912	403	11	≤	≤	NUM
ejpam-3912	403	12	l	l	NOUN
ejpam-3912	403	13	≤	≤	ADJ
ejpam-3912	403	14	i0	i0	PROPN
ejpam-3912	403	15	.	.	PUNCT
ejpam-3912	404	1	(	(	PUNCT
ejpam-3912	404	2	50	50	NUM
ejpam-3912	404	3	)	)	PUNCT
ejpam-3912	404	4	if	if	SCONJ
ejpam-3912	404	5	l	l	NOUN
ejpam-3912	404	6	=	=	SYM
ejpam-3912	404	7	2	2	NUM
ejpam-3912	404	8	then	then	ADV
ejpam-3912	404	9	from	from	ADP
ejpam-3912	404	10	(	(	PUNCT
ejpam-3912	404	11	50	50	NUM
ejpam-3912	404	12	)	)	PUNCT
ejpam-3912	404	13	we	we	PRON
ejpam-3912	404	14	obtain	obtain	VERB
ejpam-3912	404	15	ϕi01	ϕi01	PROPN
ejpam-3912	404	16	=	=	SYM
ejpam-3912	404	17	0	0	PROPN
ejpam-3912	404	18	.	.	PUNCT
ejpam-3912	404	19	suppose	suppose	VERB
ejpam-3912	404	20	that	that	SCONJ
ejpam-3912	404	21	ϕi0,l	ϕi0,l	PROPN
ejpam-3912	404	22	=	=	NOUN
ejpam-3912	404	23	0	0	NUM
ejpam-3912	404	24	for	for	ADP
ejpam-3912	404	25	every	every	DET
ejpam-3912	404	26	l	l	NOUN
ejpam-3912	404	27	<	<	X
ejpam-3912	404	28	l0	l0	NOUN
ejpam-3912	404	29	≤	≤	PUNCT
ejpam-3912	404	30	i0	i0	PROPN
ejpam-3912	404	31	.	.	PUNCT
ejpam-3912	405	1	then	then	ADV
ejpam-3912	405	2	this	this	DET
ejpam-3912	405	3	fact	fact	NOUN
ejpam-3912	405	4	together	together	ADV
ejpam-3912	405	5	with	with	ADP
ejpam-3912	405	6	(	(	PUNCT
ejpam-3912	405	7	50	50	NUM
ejpam-3912	405	8	)	)	PUNCT
ejpam-3912	405	9	for	for	ADP
ejpam-3912	405	10	l	l	NOUN
ejpam-3912	405	11	=	=	SYM
ejpam-3912	405	12	l0	l0	PROPN
ejpam-3912	405	13	implies	imply	VERB
ejpam-3912	405	14	ϕi0,l0	ϕi0,l0	PROPN
ejpam-3912	405	15	=	=	SYM
ejpam-3912	405	16	0	0	X
ejpam-3912	405	17	.	.	PUNCT
ejpam-3912	406	1	thus	thus	ADV
ejpam-3912	406	2	,	,	PUNCT
ejpam-3912	406	3	we	we	PRON
ejpam-3912	406	4	have	have	AUX
ejpam-3912	406	5	shown	show	VERB
ejpam-3912	406	6	that	that	SCONJ
ejpam-3912	406	7	ϕi0,l	ϕi0,l	NOUN
ejpam-3912	406	8	=	=	NOUN
ejpam-3912	406	9	0	0	NUM
ejpam-3912	406	10	for	for	ADP
ejpam-3912	406	11	every	every	DET
ejpam-3912	406	12	l	l	NOUN
ejpam-3912	406	13	≤	≤	ADV
ejpam-3912	406	14	i0	i0	PROPN
ejpam-3912	406	15	.	.	PUNCT
ejpam-3912	407	1	from	from	ADP
ejpam-3912	407	2	the	the	DET
ejpam-3912	407	3	arbitrary	arbitrary	ADJ
ejpam-3912	407	4	-	-	PUNCT
ejpam-3912	407	5	ness	ness	NOUN
ejpam-3912	407	6	of	of	ADP
ejpam-3912	407	7	i0	i0	PROPN
ejpam-3912	407	8	>	>	X
ejpam-3912	407	9	1	1	NUM
ejpam-3912	407	10	,	,	PUNCT
ejpam-3912	407	11	we	we	PRON
ejpam-3912	407	12	conclude	conclude	VERB
ejpam-3912	407	13	that	that	SCONJ
ejpam-3912	407	14	ϕil	ϕil	ADP
ejpam-3912	408	1	=	=	SYM
ejpam-3912	408	2	0	0	PROPN
ejpam-3912	408	3	,	,	PUNCT
ejpam-3912	408	4	l	l	NOUN
ejpam-3912	409	1	+	+	CCONJ
ejpam-3912	409	2	1	1	NUM
ejpam-3912	409	3	<	<	X
ejpam-3912	409	4	i.	i.	NOUN
ejpam-3912	409	5	(	(	PUNCT
ejpam-3912	409	6	51	51	NUM
ejpam-3912	409	7	)	)	PUNCT
ejpam-3912	409	8	on	on	ADP
ejpam-3912	409	9	the	the	DET
ejpam-3912	409	10	other	other	ADJ
ejpam-3912	409	11	hand	hand	NOUN
ejpam-3912	409	12	,	,	PUNCT
ejpam-3912	409	13	rewriting	rewrite	VERB
ejpam-3912	409	14	(	(	PUNCT
ejpam-3912	409	15	46	46	NUM
ejpam-3912	409	16	)	)	PUNCT
ejpam-3912	409	17	for	for	ADP
ejpam-3912	409	18	l	l	NOUN
ejpam-3912	409	19	=	=	PUNCT
ejpam-3912	409	20	i+	i+	PUNCT
ejpam-3912	409	21	1	1	NUM
ejpam-3912	409	22	and	and	CCONJ
ejpam-3912	409	23	keeping	keep	VERB
ejpam-3912	409	24	in	in	ADP
ejpam-3912	409	25	mind	mind	NOUN
ejpam-3912	409	26	(	(	PUNCT
ejpam-3912	409	27	51	51	NUM
ejpam-3912	409	28	)	)	PUNCT
ejpam-3912	409	29	,	,	PUNCT
ejpam-3912	409	30	we	we	PRON
ejpam-3912	409	31	obtain	obtain	VERB
ejpam-3912	409	32	ϕi+1,i+1	ϕi+1,i+1	NOUN
ejpam-3912	410	1	=	=	SYM
ejpam-3912	411	1	ϕ2	ϕ2	PROPN
ejpam-3912	411	2	ii	ii	PROPN
ejpam-3912	411	3	,	,	PUNCT
ejpam-3912	411	4	i	i	PRON
ejpam-3912	411	5	≤	≤	VERB
ejpam-3912	411	6	n−	n−	NOUN
ejpam-3912	411	7	2	2	NUM
ejpam-3912	411	8	.	.	PUNCT
ejpam-3912	412	1	the	the	DET
ejpam-3912	412	2	last	last	ADJ
ejpam-3912	412	3	equality	equality	NOUN
ejpam-3912	412	4	yields	yield	VERB
ejpam-3912	412	5	ϕi+1,i+1	ϕi+1,i+1	NOUN
ejpam-3912	413	1	=	=	SYM
ejpam-3912	413	2	ϕ2	ϕ2	ADV
ejpam-3912	413	3	ii	ii	PROPN
ejpam-3912	413	4	for	for	ADP
ejpam-3912	413	5	every	every	DET
ejpam-3912	413	6	i	i	PROPN
ejpam-3912	413	7	≤	≤	ADJ
ejpam-3912	413	8	n−	n−	NOUN
ejpam-3912	413	9	2	2	NUM
ejpam-3912	413	10	.	.	PUNCT
ejpam-3912	414	1	this	this	PRON
ejpam-3912	414	2	together	together	ADV
ejpam-3912	414	3	with	with	ADP
ejpam-3912	414	4	(	(	PUNCT
ejpam-3912	414	5	45	45	NUM
ejpam-3912	414	6	)	)	PUNCT
ejpam-3912	414	7	implies	imply	VERB
ejpam-3912	414	8	ϕii	ϕii	NOUN
ejpam-3912	415	1	=	=	SYM
ejpam-3912	415	2	ϕ2i−1	ϕ2i−1	PROPN
ejpam-3912	415	3	11	11	NUM
ejpam-3912	415	4	6=	6=	NUM
ejpam-3912	415	5	0	0	NUM
ejpam-3912	415	6	,	,	PUNCT
ejpam-3912	415	7	i	i	PRON
ejpam-3912	415	8	≤	≤	VERB
ejpam-3912	415	9	n−	n−	NOUN
ejpam-3912	415	10	2	2	NUM
ejpam-3912	415	11	.	.	PUNCT
ejpam-3912	415	12	(	(	PUNCT
ejpam-3912	415	13	52	52	NUM
ejpam-3912	415	14	)	)	PUNCT
ejpam-3912	415	15	thus	thus	ADV
ejpam-3912	415	16	,	,	PUNCT
ejpam-3912	415	17	from	from	ADP
ejpam-3912	415	18	(	(	PUNCT
ejpam-3912	415	19	51	51	NUM
ejpam-3912	415	20	)	)	PUNCT
ejpam-3912	415	21	and	and	CCONJ
ejpam-3912	415	22	(	(	PUNCT
ejpam-3912	415	23	52	52	NUM
ejpam-3912	415	24	)	)	PUNCT
ejpam-3912	415	25	,	,	PUNCT
ejpam-3912	415	26	it	it	PRON
ejpam-3912	415	27	follows	follow	VERB
ejpam-3912	415	28	(	(	PUNCT
ejpam-3912	415	29	48	48	NUM
ejpam-3912	415	30	)	)	PUNCT
ejpam-3912	415	31	.	.	PUNCT
ejpam-3912	416	1	plugging	plug	VERB
ejpam-3912	416	2	(	(	PUNCT
ejpam-3912	416	3	51	51	NUM
ejpam-3912	416	4	)	)	PUNCT
ejpam-3912	416	5	into	into	ADP
ejpam-3912	416	6	(	(	PUNCT
ejpam-3912	416	7	43	43	NUM
ejpam-3912	416	8	)	)	PUNCT
ejpam-3912	416	9	,	,	PUNCT
ejpam-3912	416	10	we	we	PRON
ejpam-3912	416	11	obtain	obtain	VERB
ejpam-3912	416	12	ϕij	ϕij	NOUN
ejpam-3912	416	13	=	=	SYM
ejpam-3912	416	14	0	0	NUM
ejpam-3912	416	15	,	,	PUNCT
ejpam-3912	416	16	i	i	PRON
ejpam-3912	416	17	<	<	X
ejpam-3912	416	18	j	j	X
ejpam-3912	416	19	<	<	X
ejpam-3912	416	20	n−	n−	PROPN
ejpam-3912	416	21	1	1	NUM
ejpam-3912	416	22	.	.	PUNCT
ejpam-3912	417	1	(	(	PUNCT
ejpam-3912	417	2	53	53	NUM
ejpam-3912	417	3	)	)	PUNCT
ejpam-3912	417	4	let	let	VERB
ejpam-3912	417	5	us	we	PRON
ejpam-3912	417	6	consider	consider	VERB
ejpam-3912	417	7	(	(	PUNCT
ejpam-3912	417	8	46	46	NUM
ejpam-3912	417	9	)	)	PUNCT
ejpam-3912	417	10	for	for	ADP
ejpam-3912	417	11	l	l	NOUN
ejpam-3912	417	12	>	>	X
ejpam-3912	417	13	i+	i+	PROPN
ejpam-3912	418	1	1	1	X
ejpam-3912	418	2	.	.	PUNCT
ejpam-3912	419	1	then	then	ADV
ejpam-3912	419	2	,	,	PUNCT
ejpam-3912	419	3	for	for	ADP
ejpam-3912	419	4	every	every	DET
ejpam-3912	419	5	i	i	NOUN
ejpam-3912	419	6	≤	≤	ADJ
ejpam-3912	419	7	n−	n−	NOUN
ejpam-3912	419	8	2	2	NUM
ejpam-3912	419	9	,	,	PUNCT
ejpam-3912	419	10	we	we	PRON
ejpam-3912	419	11	obtain	obtain	VERB
ejpam-3912	419	12	ailϕll	ailϕll	NOUN
ejpam-3912	419	13	=	=	SYM
ejpam-3912	419	14	ailϕ	ailϕ	PROPN
ejpam-3912	419	15	2	2	NUM
ejpam-3912	419	16	ii	ii	NOUN
ejpam-3912	419	17	,	,	PUNCT
ejpam-3912	419	18	i+	i+	ADV
ejpam-3912	419	19	1	1	NUM
ejpam-3912	419	20	<	<	X
ejpam-3912	419	21	l	l	X
ejpam-3912	419	22	<	<	X
ejpam-3912	419	23	n−	n−	NOUN
ejpam-3912	419	24	1	1	NUM
ejpam-3912	419	25	(	(	PUNCT
ejpam-3912	419	26	54	54	NUM
ejpam-3912	419	27	)	)	PUNCT
ejpam-3912	419	28	n∑	n∑	NOUN
ejpam-3912	420	1	j	j	X
ejpam-3912	421	1	=	=	NOUN
ejpam-3912	421	2	i+1	i+1	NOUN
ejpam-3912	421	3	aijϕj	aijϕj	ADJ
ejpam-3912	421	4	,	,	PUNCT
ejpam-3912	421	5	n−1	n−1	PROPN
ejpam-3912	421	6	=	=	SYM
ejpam-3912	421	7	ai	ai	PROPN
ejpam-3912	421	8	,	,	PUNCT
ejpam-3912	421	9	n−1ϕ	n−1ϕ	NOUN
ejpam-3912	421	10	2	2	NUM
ejpam-3912	421	11	ii	ii	NOUN
ejpam-3912	421	12	,	,	PUNCT
ejpam-3912	421	13	l	l	NOUN
ejpam-3912	421	14	=	=	PUNCT
ejpam-3912	421	15	n−	n−	NOUN
ejpam-3912	421	16	1	1	NUM
ejpam-3912	421	17	.	.	PUNCT
ejpam-3912	422	1	(	(	PUNCT
ejpam-3912	422	2	55	55	NUM
ejpam-3912	422	3	)	)	PUNCT
ejpam-3912	422	4	n∑	n∑	NOUN
ejpam-3912	422	5	j	j	X
ejpam-3912	423	1	=	=	NOUN
ejpam-3912	423	2	i+1	i+1	NOUN
ejpam-3912	423	3	aijϕjn	aijϕjn	NOUN
ejpam-3912	423	4	=	=	SYM
ejpam-3912	423	5	ainϕ	ainϕ	ADJ
ejpam-3912	423	6	2	2	NUM
ejpam-3912	423	7	ii	ii	NOUN
ejpam-3912	423	8	,	,	PUNCT
ejpam-3912	423	9	l	l	PROPN
ejpam-3912	423	10	=	=	PUNCT
ejpam-3912	423	11	n.	n.	NOUN
ejpam-3912	423	12	(	(	PUNCT
ejpam-3912	423	13	56	56	NUM
ejpam-3912	423	14	)	)	PUNCT
ejpam-3912	423	15	from	from	ADP
ejpam-3912	423	16	(	(	PUNCT
ejpam-3912	423	17	56	56	NUM
ejpam-3912	423	18	)	)	PUNCT
ejpam-3912	423	19	with	with	ADP
ejpam-3912	423	20	(	(	PUNCT
ejpam-3912	423	21	52	52	NUM
ejpam-3912	423	22	)	)	PUNCT
ejpam-3912	423	23	we	we	PRON
ejpam-3912	423	24	obtain	obtain	VERB
ejpam-3912	423	25	a	a	DET
ejpam-3912	423	26	recurrence	recurrence	NOUN
ejpam-3912	423	27	formula	formula	NOUN
ejpam-3912	423	28	for	for	ADP
ejpam-3912	423	29	ϕin−1	ϕin−1	PROPN
ejpam-3912	423	30	,	,	PUNCT
ejpam-3912	423	31	ϕin	ϕin	PROPN
ejpam-3912	423	32	as	as	SCONJ
ejpam-3912	423	33	follows	follow	VERB
ejpam-3912	423	34	:	:	PUNCT
ejpam-3912	423	35	ϕn−1,n−1	ϕn−1,n−1	PROPN
ejpam-3912	423	36	=	=	SYM
ejpam-3912	423	37	α2n−2	α2n−2	PROPN
ejpam-3912	423	38	−	−	PROPN
ejpam-3912	423	39	an−2,ns	an−2,ns	PROPN
ejpam-3912	423	40	,	,	PUNCT
ejpam-3912	423	41	ϕn−1,n	ϕn−1,n	VERB
ejpam-3912	423	42	=	=	SYM
ejpam-3912	423	43	an−2,n	an−2,n	ADJ
ejpam-3912	423	44	(	(	PUNCT
ejpam-3912	423	45	α2n−2	α2n−2	PROPN
ejpam-3912	423	46	−	−	PROPN
ejpam-3912	423	47	t	t	PROPN
ejpam-3912	423	48	)	)	PUNCT
ejpam-3912	423	49	,	,	PUNCT
ejpam-3912	423	50	ϕi	ϕi	ADP
ejpam-3912	423	51	,	,	PUNCT
ejpam-3912	423	52	n−1	n−1	PROPN
ejpam-3912	423	53	=	=	SYM
ejpam-3912	423	54	ai−1,n−1α	ai−1,n−1α	NOUN
ejpam-3912	423	55	2i−1	2i−1	NUM
ejpam-3912	423	56	−	−	PROPN
ejpam-3912	423	57	n−i∑	n−i∑	PRON
ejpam-3912	423	58	j	j	NOUN
ejpam-3912	423	59	=	=	PROPN
ejpam-3912	423	60	i+1	i+1	NOUN
ejpam-3912	423	61	ai−1,jϕj	ai−1,jϕj	ADJ
ejpam-3912	423	62	,	,	PUNCT
ejpam-3912	423	63	n−1	n−1	PROPN
ejpam-3912	423	64	,	,	PUNCT
ejpam-3912	423	65	1	1	NUM
ejpam-3912	423	66	<	<	X
ejpam-3912	423	67	i	i	PRON
ejpam-3912	423	68	<	<	X
ejpam-3912	423	69	n−	n−	NOUN
ejpam-3912	423	70	1	1	NUM
ejpam-3912	423	71	,	,	PUNCT
ejpam-3912	423	72	ϕi	ϕi	ADP
ejpam-3912	423	73	,	,	PUNCT
ejpam-3912	423	74	n	n	NOUN
ejpam-3912	423	75	=	=	PUNCT
ejpam-3912	423	76	ai−1,nα	ai−1,nα	PROPN
ejpam-3912	424	1	2i−1	2i−1	NUM
ejpam-3912	424	2	−	−	PROPN
ejpam-3912	424	3	n−i∑	n−i∑	PRON
ejpam-3912	424	4	j	j	NOUN
ejpam-3912	424	5	=	=	PROPN
ejpam-3912	424	6	i+1	i+1	NOUN
ejpam-3912	424	7	ai−1,jϕj	ai−1,jϕj	ADJ
ejpam-3912	424	8	,	,	PUNCT
ejpam-3912	424	9	n	n	CCONJ
ejpam-3912	424	10	,	,	PUNCT
ejpam-3912	424	11	1	1	NUM
ejpam-3912	424	12	<	<	X
ejpam-3912	424	13	i	i	PRON
ejpam-3912	424	14	<	<	X
ejpam-3912	424	15	n−	n−	NOUN
ejpam-3912	424	16	1	1	NUM
ejpam-3912	424	17	.	.	PUNCT
ejpam-3912	425	1	(	(	PUNCT
ejpam-3912	425	2	57	57	NUM
ejpam-3912	425	3	)	)	PUNCT
ejpam-3912	425	4	a.	a.	NOUN
ejpam-3912	425	5	alarafeen	alarafeen	PROPN
ejpam-3912	425	6	,	,	PUNCT
ejpam-3912	425	7	i.	i.	PROPN
ejpam-3912	425	8	qaralleh	qaralleh	PROPN
ejpam-3912	425	9	,	,	PUNCT
ejpam-3912	425	10	a.	a.	PROPN
ejpam-3912	425	11	ahmad	ahmad	PROPN
ejpam-3912	425	12	/	/	SYM
ejpam-3912	425	13	eur	eur	PROPN
ejpam-3912	425	14	.	.	PUNCT
ejpam-3912	426	1	j.	j.	PROPN
ejpam-3912	426	2	pure	pure	PROPN
ejpam-3912	426	3	appl	appl	PROPN
ejpam-3912	426	4	.	.	PROPN
ejpam-3912	426	5	math	math	PROPN
ejpam-3912	426	6	,	,	PUNCT
ejpam-3912	426	7	14	14	NUM
ejpam-3912	426	8	(	(	PUNCT
ejpam-3912	426	9	1	1	NUM
ejpam-3912	426	10	)	)	PUNCT
ejpam-3912	426	11	(	(	PUNCT
ejpam-3912	426	12	2021	2021	NUM
ejpam-3912	426	13	)	)	PUNCT
ejpam-3912	426	14	,	,	PUNCT
ejpam-3912	426	15	278	278	NUM
ejpam-3912	426	16	-	-	SYM
ejpam-3912	426	17	300	300	NUM
ejpam-3912	426	18	295	295	NUM
ejpam-3912	426	19	hence	hence	ADV
ejpam-3912	426	20	,	,	PUNCT
ejpam-3912	426	21	we	we	PRON
ejpam-3912	426	22	infer	infer	VERB
ejpam-3912	426	23	that	that	SCONJ
ejpam-3912	426	24	ϕ	ϕ	NOUN
ejpam-3912	426	25	is	be	AUX
ejpam-3912	426	26	an	an	DET
ejpam-3912	426	27	automorphism	automorphism	NOUN
ejpam-3912	426	28	of	of	ADP
ejpam-3912	426	29	evolution	evolution	NOUN
ejpam-3912	426	30	algebra	algebra	NOUN
ejpam-3912	426	31	(	(	PUNCT
ejpam-3912	426	32	2	2	NUM
ejpam-3912	426	33	)	)	PUNCT
ejpam-3912	427	1	if	if	SCONJ
ejpam-3912	428	1	and	and	CCONJ
ejpam-3912	428	2	only	only	ADV
ejpam-3912	428	3	if	if	SCONJ
ejpam-3912	428	4	the	the	DET
ejpam-3912	428	5	followings	following	NOUN
ejpam-3912	428	6	holds	hold	VERB
ejpam-3912	428	7	:	:	PUNCT
ejpam-3912	428	8	ϕij	ϕij	NOUN
ejpam-3912	428	9	=	=	SYM
ejpam-3912	428	10	0	0	NUM
ejpam-3912	428	11	,	,	PUNCT
ejpam-3912	428	12	i	i	PROPN
ejpam-3912	428	13	6=	6=	PROPN
ejpam-3912	428	14	j	j	PROPN
ejpam-3912	428	15	,	,	PUNCT
ejpam-3912	428	16	j	j	PROPN
ejpam-3912	428	17	<	<	X
ejpam-3912	428	18	n−	n−	PROPN
ejpam-3912	428	19	1	1	NUM
ejpam-3912	428	20	ϕii	ϕii	VERB
ejpam-3912	429	1	=	=	SYM
ejpam-3912	429	2	ϕ2i−1	ϕ2i−1	PROPN
ejpam-3912	429	3	11	11	NUM
ejpam-3912	429	4	,	,	PUNCT
ejpam-3912	429	5	i	i	PRON
ejpam-3912	429	6	≤	≤	VERB
ejpam-3912	429	7	n−	n−	NOUN
ejpam-3912	429	8	2	2	NUM
ejpam-3912	429	9	ailϕll	ailϕll	NOUN
ejpam-3912	429	10	=	=	PRON
ejpam-3912	429	11	ailϕ	ailϕ	PROPN
ejpam-3912	429	12	2	2	NUM
ejpam-3912	429	13	ii	ii	NOUN
ejpam-3912	429	14	,	,	PUNCT
ejpam-3912	429	15	i+	i+	ADV
ejpam-3912	429	16	1	1	NUM
ejpam-3912	429	17	<	<	X
ejpam-3912	429	18	l	l	X
ejpam-3912	429	19	<	<	X
ejpam-3912	429	20	n−	n−	NOUN
ejpam-3912	429	21	1	1	NUM
ejpam-3912	429	22	ϕn−1,n−1	ϕn−1,n−1	NOUN
ejpam-3912	429	23	=	=	SYM
ejpam-3912	429	24	α2n−2	α2n−2	PROPN
ejpam-3912	429	25	−	−	PROPN
ejpam-3912	429	26	an−2,ns	an−2,ns	PROPN
ejpam-3912	429	27	,	,	PUNCT
ejpam-3912	429	28	ϕn−1,n	ϕn−1,n	VERB
ejpam-3912	429	29	=	=	SYM
ejpam-3912	429	30	an−2,n	an−2,n	ADJ
ejpam-3912	429	31	(	(	PUNCT
ejpam-3912	429	32	α2n−2	α2n−2	PROPN
ejpam-3912	429	33	−	−	PROPN
ejpam-3912	429	34	t	t	PROPN
ejpam-3912	429	35	)	)	PUNCT
ejpam-3912	429	36	,	,	PUNCT
ejpam-3912	429	37	ϕi	ϕi	ADP
ejpam-3912	429	38	,	,	PUNCT
ejpam-3912	429	39	n−1	n−1	PROPN
ejpam-3912	429	40	=	=	SYM
ejpam-3912	429	41	ai−1,n−1α	ai−1,n−1α	NOUN
ejpam-3912	429	42	2i−1	2i−1	NUM
ejpam-3912	429	43	−	−	PROPN
ejpam-3912	429	44	n−i∑	n−i∑	PRON
ejpam-3912	429	45	j	j	NOUN
ejpam-3912	429	46	=	=	PROPN
ejpam-3912	429	47	i+1	i+1	NOUN
ejpam-3912	429	48	ai−1,jϕj	ai−1,jϕj	ADJ
ejpam-3912	429	49	,	,	PUNCT
ejpam-3912	429	50	n−1	n−1	PROPN
ejpam-3912	429	51	,	,	PUNCT
ejpam-3912	429	52	1	1	NUM
ejpam-3912	429	53	<	<	X
ejpam-3912	429	54	i	i	PRON
ejpam-3912	429	55	<	<	X
ejpam-3912	429	56	n−	n−	NOUN
ejpam-3912	429	57	1	1	NUM
ejpam-3912	429	58	,	,	PUNCT
ejpam-3912	429	59	ϕi	ϕi	ADP
ejpam-3912	429	60	,	,	PUNCT
ejpam-3912	429	61	n	n	NOUN
ejpam-3912	429	62	=	=	PUNCT
ejpam-3912	429	63	ai−1,nα	ai−1,nα	PROPN
ejpam-3912	430	1	2i−1	2i−1	NUM
ejpam-3912	430	2	−	−	PROPN
ejpam-3912	430	3	n−i∑	n−i∑	PRON
ejpam-3912	430	4	j	j	NOUN
ejpam-3912	430	5	=	=	PROPN
ejpam-3912	430	6	i+1	i+1	NOUN
ejpam-3912	430	7	ai−1,jϕj	ai−1,jϕj	ADJ
ejpam-3912	430	8	,	,	PUNCT
ejpam-3912	430	9	n	n	CCONJ
ejpam-3912	430	10	,	,	PUNCT
ejpam-3912	430	11	1	1	NUM
ejpam-3912	430	12	<	<	X
ejpam-3912	430	13	i	i	PRON
ejpam-3912	430	14	<	<	X
ejpam-3912	430	15	n−	n−	NOUN
ejpam-3912	430	16	1	1	NUM
ejpam-3912	430	17	.	.	PUNCT
ejpam-3912	431	1	(	(	PUNCT
ejpam-3912	431	2	58	58	NUM
ejpam-3912	431	3	)	)	PUNCT
ejpam-3912	431	4	now	now	ADV
ejpam-3912	431	5	let	let	VERB
ejpam-3912	431	6	us	we	PRON
ejpam-3912	431	7	consider	consider	VERB
ejpam-3912	431	8	two	two	NUM
ejpam-3912	431	9	cases	case	NOUN
ejpam-3912	431	10	w.r.t.ia	w.r.t.ia	PROPN
ejpam-3912	431	11	.	.	PUNCT
ejpam-3912	432	1	case	case	NOUN
ejpam-3912	432	2	ia	ia	PROPN
ejpam-3912	432	3	6=	6=	X
ejpam-3912	432	4	∅.	∅.	VERB
ejpam-3912	432	5	for	for	ADP
ejpam-3912	432	6	the	the	DET
ejpam-3912	432	7	sake	sake	NOUN
ejpam-3912	432	8	of	of	ADP
ejpam-3912	432	9	convenience	convenience	NOUN
ejpam-3912	432	10	,	,	PUNCT
ejpam-3912	432	11	we	we	PRON
ejpam-3912	432	12	denote	denote	VERB
ejpam-3912	432	13	ϕ11	ϕ11	PROPN
ejpam-3912	432	14	=	=	SYM
ejpam-3912	432	15	α	α	PROPN
ejpam-3912	432	16	6=	6=	ADP
ejpam-3912	432	17	0	0	NUM
ejpam-3912	432	18	.	.	PUNCT
ejpam-3912	433	1	then	then	ADV
ejpam-3912	433	2	,	,	PUNCT
ejpam-3912	433	3	from	from	ADP
ejpam-3912	433	4	(	(	PUNCT
ejpam-3912	433	5	58	58	X
ejpam-3912	433	6	)	)	PUNCT
ejpam-3912	433	7	one	one	NOUN
ejpam-3912	433	8	obtains	obtain	VERB
ejpam-3912	433	9	ϕij	ϕij	NOUN
ejpam-3912	434	1	=	=	SYM
ejpam-3912	434	2	ϕji	ϕji	ADJ
ejpam-3912	434	3	=	=	SYM
ejpam-3912	434	4	0	0	PROPN
ejpam-3912	434	5	,	,	PUNCT
ejpam-3912	434	6	i	i	PROPN
ejpam-3912	434	7	6=	6=	PROPN
ejpam-3912	434	8	j	j	PROPN
ejpam-3912	434	9	,	,	PUNCT
ejpam-3912	434	10	j	j	PROPN
ejpam-3912	434	11	<	<	X
ejpam-3912	434	12	n−	n−	PROPN
ejpam-3912	434	13	1	1	NUM
ejpam-3912	434	14	ϕii	ϕii	NOUN
ejpam-3912	435	1	=	=	SYM
ejpam-3912	435	2	α2i−1	α2i−1	PROPN
ejpam-3912	435	3	,	,	PUNCT
ejpam-3912	436	1	i	i	PRON
ejpam-3912	436	2	≤	≤	ADJ
ejpam-3912	436	3	n−	n−	NOUN
ejpam-3912	436	4	2	2	NUM
ejpam-3912	436	5	α2l−1−2i	α2l−1−2i	NOUN
ejpam-3912	436	6	=	=	SYM
ejpam-3912	436	7	1	1	NUM
ejpam-3912	436	8	,	,	PUNCT
ejpam-3912	436	9	(	(	PUNCT
ejpam-3912	436	10	i	i	NOUN
ejpam-3912	436	11	,	,	PUNCT
ejpam-3912	436	12	l	l	NOUN
ejpam-3912	436	13	)	)	PUNCT
ejpam-3912	436	14	∈	∈	PROPN
ejpam-3912	436	15	ia	ia	PROPN
ejpam-3912	436	16	ϕ1,n−1	ϕ1,n−1	ADJ
ejpam-3912	436	17	=	=	SYM
ejpam-3912	436	18	γ	γ	X
ejpam-3912	436	19	,	,	PUNCT
ejpam-3912	436	20	ϕ1n	ϕ1n	PUNCT
ejpam-3912	436	21	=	=	SYM
ejpam-3912	436	22	β	β	X
ejpam-3912	436	23	,	,	PUNCT
ejpam-3912	436	24	ϕn	ϕn	INTJ
ejpam-3912	436	25	,	,	PUNCT
ejpam-3912	436	26	n−1	n−1	PROPN
ejpam-3912	436	27	=	=	SYM
ejpam-3912	436	28	s	s	PROPN
ejpam-3912	436	29	,	,	PUNCT
ejpam-3912	436	30	ϕn	ϕn	INTJ
ejpam-3912	436	31	,	,	PUNCT
ejpam-3912	436	32	n	n	PROPN
ejpam-3912	436	33	=	=	SYM
ejpam-3912	436	34	t	t	NOUN
ejpam-3912	436	35	ϕn−1,n−1	ϕn−1,n−1	PROPN
ejpam-3912	437	1	=	=	SYM
ejpam-3912	437	2	α2n−2	α2n−2	PROPN
ejpam-3912	437	3	−	−	PROPN
ejpam-3912	437	4	an−2,ns	an−2,ns	PROPN
ejpam-3912	437	5	,	,	PUNCT
ejpam-3912	437	6	ϕn−1,n	ϕn−1,n	VERB
ejpam-3912	437	7	=	=	SYM
ejpam-3912	437	8	an−2,n	an−2,n	ADJ
ejpam-3912	437	9	(	(	PUNCT
ejpam-3912	437	10	α2n−2	α2n−2	PROPN
ejpam-3912	437	11	−	−	PROPN
ejpam-3912	437	12	t	t	PROPN
ejpam-3912	437	13	)	)	PUNCT
ejpam-3912	437	14	,	,	PUNCT
ejpam-3912	437	15	ϕi	ϕi	ADP
ejpam-3912	437	16	,	,	PUNCT
ejpam-3912	437	17	n−1	n−1	PROPN
ejpam-3912	437	18	=	=	SYM
ejpam-3912	437	19	ai−1,n−1α	ai−1,n−1α	NOUN
ejpam-3912	437	20	2i−1	2i−1	NUM
ejpam-3912	437	21	−	−	PROPN
ejpam-3912	437	22	n−i∑	n−i∑	PRON
ejpam-3912	437	23	j	j	NOUN
ejpam-3912	437	24	=	=	PROPN
ejpam-3912	437	25	i+1	i+1	NOUN
ejpam-3912	437	26	ai−1,jϕj	ai−1,jϕj	ADJ
ejpam-3912	437	27	,	,	PUNCT
ejpam-3912	437	28	n−1	n−1	PROPN
ejpam-3912	437	29	,	,	PUNCT
ejpam-3912	437	30	1	1	NUM
ejpam-3912	437	31	<	<	X
ejpam-3912	437	32	i	i	PRON
ejpam-3912	437	33	<	<	X
ejpam-3912	437	34	n−	n−	NOUN
ejpam-3912	437	35	1	1	NUM
ejpam-3912	437	36	,	,	PUNCT
ejpam-3912	437	37	ϕi	ϕi	ADP
ejpam-3912	437	38	,	,	PUNCT
ejpam-3912	437	39	n	n	NOUN
ejpam-3912	437	40	=	=	PUNCT
ejpam-3912	437	41	ai−1,nα	ai−1,nα	PROPN
ejpam-3912	437	42	2i−1	2i−1	NUM
ejpam-3912	437	43	−	−	PROPN
ejpam-3912	437	44	n−i∑	n−i∑	PRON
ejpam-3912	437	45	j	j	NOUN
ejpam-3912	437	46	=	=	PROPN
ejpam-3912	437	47	i+1	i+1	NOUN
ejpam-3912	437	48	ai−1,jϕj	ai−1,jϕj	ADJ
ejpam-3912	437	49	,	,	PUNCT
ejpam-3912	437	50	n	n	CCONJ
ejpam-3912	437	51	,	,	PUNCT
ejpam-3912	437	52	1	1	NUM
ejpam-3912	437	53	<	<	X
ejpam-3912	437	54	i	i	PRON
ejpam-3912	437	55	<	<	X
ejpam-3912	437	56	n−	n−	PROPN
ejpam-3912	437	57	1	1	NUM
ejpam-3912	437	58	.	.	PUNCT
ejpam-3912	438	1	where	where	SCONJ
ejpam-3912	438	2	α	α	NOUN
ejpam-3912	438	3	,	,	PUNCT
ejpam-3912	438	4	β	β	X
ejpam-3912	438	5	,	,	PUNCT
ejpam-3912	438	6	γ	γ	PROPN
ejpam-3912	438	7	,	,	PUNCT
ejpam-3912	438	8	s	s	PROPN
ejpam-3912	438	9	,	,	PUNCT
ejpam-3912	438	10	t	t	PROPN
ejpam-3912	438	11	∈	∈	PROPN
ejpam-3912	438	12	k	k	PROPN
ejpam-3912	438	13	,	,	PUNCT
ejpam-3912	438	14	and	and	CCONJ
ejpam-3912	438	15	αη	αη	X
ejpam-3912	438	16	=	=	SYM
ejpam-3912	438	17	1	1	NUM
ejpam-3912	438	18	,	,	PUNCT
ejpam-3912	438	19	which	which	PRON
ejpam-3912	438	20	implies	imply	VERB
ejpam-3912	438	21	the	the	DET
ejpam-3912	438	22	assertion	assertion	NOUN
ejpam-3912	438	23	.	.	PUNCT
ejpam-3912	439	1	case	case	NOUN
ejpam-3912	439	2	ia	ia	NOUN
ejpam-3912	439	3	=	=	PUNCT
ejpam-3912	439	4	∅.	∅.	NOUN
ejpam-3912	439	5	for	for	ADP
ejpam-3912	439	6	the	the	DET
ejpam-3912	439	7	automorphism	automorphism	NOUN
ejpam-3912	439	8	ϕ	ϕ	NOUN
ejpam-3912	439	9	,	,	PUNCT
ejpam-3912	439	10	we	we	PRON
ejpam-3912	439	11	have	have	VERB
ejpam-3912	439	12	ϕij	ϕij	NOUN
ejpam-3912	440	1	=	=	SYM
ejpam-3912	440	2	ϕji	ϕji	ADJ
ejpam-3912	440	3	=	=	SYM
ejpam-3912	440	4	0	0	PROPN
ejpam-3912	440	5	,	,	PUNCT
ejpam-3912	440	6	i	i	PROPN
ejpam-3912	440	7	6=	6=	PROPN
ejpam-3912	440	8	j	j	PROPN
ejpam-3912	440	9	,	,	PUNCT
ejpam-3912	440	10	j	j	PROPN
ejpam-3912	440	11	<	<	X
ejpam-3912	440	12	n−	n−	PROPN
ejpam-3912	440	13	1	1	NUM
ejpam-3912	440	14	ϕii	ϕii	NOUN
ejpam-3912	441	1	=	=	SYM
ejpam-3912	441	2	α2i−1	α2i−1	PROPN
ejpam-3912	441	3	,	,	PUNCT
ejpam-3912	441	4	1	1	NUM
ejpam-3912	441	5	≤	≤	NUM
ejpam-3912	441	6	i	i	PRON
ejpam-3912	441	7	≤	≤	ADJ
ejpam-3912	441	8	n−	n−	PROPN
ejpam-3912	441	9	2	2	NUM
ejpam-3912	441	10	ϕ1,n−1	ϕ1,n−1	ADJ
ejpam-3912	441	11	=	=	SYM
ejpam-3912	441	12	γ	γ	X
ejpam-3912	441	13	,	,	PUNCT
ejpam-3912	441	14	ϕ1n	ϕ1n	PUNCT
ejpam-3912	441	15	=	=	SYM
ejpam-3912	441	16	β	β	X
ejpam-3912	441	17	,	,	PUNCT
ejpam-3912	441	18	ϕn	ϕn	INTJ
ejpam-3912	441	19	,	,	PUNCT
ejpam-3912	441	20	n−1	n−1	PROPN
ejpam-3912	441	21	=	=	SYM
ejpam-3912	441	22	s	s	PROPN
ejpam-3912	441	23	,	,	PUNCT
ejpam-3912	441	24	ϕn	ϕn	INTJ
ejpam-3912	441	25	,	,	PUNCT
ejpam-3912	441	26	n	n	PROPN
ejpam-3912	441	27	=	=	SYM
ejpam-3912	441	28	t	t	NOUN
ejpam-3912	441	29	ϕn−1,n−1	ϕn−1,n−1	PROPN
ejpam-3912	442	1	=	=	SYM
ejpam-3912	442	2	α2n−2	α2n−2	PROPN
ejpam-3912	442	3	−	−	PROPN
ejpam-3912	442	4	an−2,ns	an−2,ns	PROPN
ejpam-3912	442	5	,	,	PUNCT
ejpam-3912	442	6	ϕn−1,n	ϕn−1,n	VERB
ejpam-3912	442	7	=	=	SYM
ejpam-3912	442	8	an−2,n	an−2,n	ADJ
ejpam-3912	442	9	(	(	PUNCT
ejpam-3912	442	10	α2n−2	α2n−2	PROPN
ejpam-3912	442	11	−	−	PROPN
ejpam-3912	442	12	t	t	PROPN
ejpam-3912	442	13	)	)	PUNCT
ejpam-3912	442	14	,	,	PUNCT
ejpam-3912	442	15	ϕi	ϕi	ADP
ejpam-3912	442	16	,	,	PUNCT
ejpam-3912	442	17	n−1	n−1	PROPN
ejpam-3912	442	18	=	=	SYM
ejpam-3912	442	19	ai−1,n−1	ai−1,n−1	PROPN
ejpam-3912	442	20	(	(	PUNCT
ejpam-3912	442	21	α2i−1	α2i−1	PROPN
ejpam-3912	442	22	−	−	PROPN
ejpam-3912	442	23	ϕn−1,n−1	ϕn−1,n−1	PROPN
ejpam-3912	442	24	)	)	PUNCT
ejpam-3912	442	25	−	−	ADP
ejpam-3912	442	26	ai−1,ns	ai−1,ns	NOUN
ejpam-3912	442	27	,	,	PUNCT
ejpam-3912	442	28	1	1	NUM
ejpam-3912	442	29	<	<	X
ejpam-3912	442	30	i	i	PRON
ejpam-3912	442	31	<	<	X
ejpam-3912	442	32	n−	n−	NOUN
ejpam-3912	442	33	1	1	NUM
ejpam-3912	442	34	,	,	PUNCT
ejpam-3912	442	35	ϕi	ϕi	ADP
ejpam-3912	442	36	,	,	PUNCT
ejpam-3912	442	37	n	n	NOUN
ejpam-3912	442	38	=	=	PUNCT
ejpam-3912	442	39	ai−1,n	ai−1,n	NOUN
ejpam-3912	442	40	(	(	PUNCT
ejpam-3912	442	41	α2i−1	α2i−1	PROPN
ejpam-3912	442	42	−	−	PROPN
ejpam-3912	442	43	t	t	PROPN
ejpam-3912	442	44	)	)	PUNCT
ejpam-3912	443	1	−	−	PROPN
ejpam-3912	443	2	ai−1,n−1ϕn−1,n	ai−1,n−1ϕn−1,n	ADJ
ejpam-3912	443	3	,	,	PUNCT
ejpam-3912	443	4	1	1	NUM
ejpam-3912	443	5	<	<	X
ejpam-3912	443	6	i	i	PRON
ejpam-3912	443	7	<	<	X
ejpam-3912	443	8	n−	n−	NOUN
ejpam-3912	443	9	1	1	NUM
ejpam-3912	443	10	.	.	PUNCT
ejpam-3912	443	11	a.	a.	PROPN
ejpam-3912	443	12	alarafeen	alarafeen	PROPN
ejpam-3912	443	13	,	,	PUNCT
ejpam-3912	443	14	i.	i.	PROPN
ejpam-3912	443	15	qaralleh	qaralleh	PROPN
ejpam-3912	443	16	,	,	PUNCT
ejpam-3912	443	17	a.	a.	PROPN
ejpam-3912	443	18	ahmad	ahmad	PROPN
ejpam-3912	443	19	/	/	SYM
ejpam-3912	443	20	eur	eur	PROPN
ejpam-3912	443	21	.	.	PUNCT
ejpam-3912	444	1	j.	j.	PROPN
ejpam-3912	444	2	pure	pure	PROPN
ejpam-3912	444	3	appl	appl	PROPN
ejpam-3912	444	4	.	.	PROPN
ejpam-3912	444	5	math	math	PROPN
ejpam-3912	444	6	,	,	PUNCT
ejpam-3912	444	7	14	14	NUM
ejpam-3912	444	8	(	(	PUNCT
ejpam-3912	444	9	1	1	NUM
ejpam-3912	444	10	)	)	PUNCT
ejpam-3912	444	11	(	(	PUNCT
ejpam-3912	444	12	2021	2021	NUM
ejpam-3912	444	13	)	)	PUNCT
ejpam-3912	444	14	,	,	PUNCT
ejpam-3912	444	15	278	278	NUM
ejpam-3912	444	16	-	-	SYM
ejpam-3912	444	17	300	300	NUM
ejpam-3912	444	18	296	296	NUM
ejpam-3912	444	19	where	where	SCONJ
ejpam-3912	444	20	α	α	X
ejpam-3912	444	21	,	,	PUNCT
ejpam-3912	444	22	β	β	X
ejpam-3912	444	23	,	,	PUNCT
ejpam-3912	444	24	γ	γ	PROPN
ejpam-3912	444	25	,	,	PUNCT
ejpam-3912	444	26	s	s	PROPN
ejpam-3912	444	27	,	,	PUNCT
ejpam-3912	444	28	t	t	PROPN
ejpam-3912	444	29	∈	∈	PROPN
ejpam-3912	444	30	k	k	PROPN
ejpam-3912	444	31	,	,	PUNCT
ejpam-3912	444	32	which	which	PRON
ejpam-3912	444	33	implies	imply	VERB
ejpam-3912	444	34	the	the	DET
ejpam-3912	444	35	assertion	assertion	NOUN
ejpam-3912	444	36	.	.	PUNCT
ejpam-3912	445	1	the	the	DET
ejpam-3912	445	2	proof	proof	NOUN
ejpam-3912	445	3	is	be	AUX
ejpam-3912	445	4	complete	complete	ADJ
ejpam-3912	445	5	.	.	PUNCT
ejpam-3912	446	1	5.1	5.1	NUM
ejpam-3912	446	2	.	.	PUNCT
ejpam-3912	447	1	local	local	ADJ
ejpam-3912	447	2	automorphisms	automorphism	NOUN
ejpam-3912	447	3	of	of	ADP
ejpam-3912	447	4	evolution	evolution	NOUN
ejpam-3912	447	5	algebras	algebra	NOUN
ejpam-3912	447	6	in	in	ADP
ejpam-3912	447	7	the	the	DET
ejpam-3912	447	8	previous	previous	ADJ
ejpam-3912	447	9	section	section	NOUN
ejpam-3912	447	10	,	,	PUNCT
ejpam-3912	447	11	we	we	PRON
ejpam-3912	447	12	have	have	AUX
ejpam-3912	447	13	been	be	AUX
ejpam-3912	447	14	able	able	ADJ
ejpam-3912	447	15	to	to	PART
ejpam-3912	447	16	find	find	VERB
ejpam-3912	447	17	the	the	DET
ejpam-3912	447	18	set	set	NOUN
ejpam-3912	447	19	of	of	ADP
ejpam-3912	447	20	all	all	DET
ejpam-3912	447	21	automorphisms	automorphism	NOUN
ejpam-3912	447	22	of	of	ADP
ejpam-3912	447	23	evolution	evolution	NOUN
ejpam-3912	447	24	algebra	algebra	NOUN
ejpam-3912	447	25	(	(	PUNCT
ejpam-3912	447	26	2	2	NUM
ejpam-3912	447	27	)	)	PUNCT
ejpam-3912	447	28	.	.	PUNCT
ejpam-3912	448	1	now	now	ADV
ejpam-3912	448	2	,	,	PUNCT
ejpam-3912	448	3	we	we	PRON
ejpam-3912	448	4	show	show	VERB
ejpam-3912	448	5	that	that	SCONJ
ejpam-3912	448	6	every	every	DET
ejpam-3912	448	7	local	local	ADJ
ejpam-3912	448	8	automorphism	automorphism	NOUN
ejpam-3912	448	9	is	be	AUX
ejpam-3912	448	10	an	an	DET
ejpam-3912	448	11	automorphism	automorphism	NOUN
ejpam-3912	448	12	if	if	SCONJ
ejpam-3912	448	13	evolution	evolution	NOUN
ejpam-3912	448	14	algebra	algebra	NOUN
ejpam-3912	448	15	is	be	AUX
ejpam-3912	448	16	defined	define	VERB
ejpam-3912	448	17	by	by	ADP
ejpam-3912	448	18	(	(	PUNCT
ejpam-3912	448	19	2	2	NUM
ejpam-3912	448	20	)	)	PUNCT
ejpam-3912	448	21	with	with	ADP
ejpam-3912	448	22	n	n	PROPN
ejpam-3912	448	23	>	>	SYM
ejpam-3912	448	24	3	3	X
ejpam-3912	448	25	.	.	X
ejpam-3912	448	26	recall	recall	VERB
ejpam-3912	448	27	that	that	SCONJ
ejpam-3912	448	28	a	a	DET
ejpam-3912	448	29	linear	linear	ADJ
ejpam-3912	448	30	mapping	mapping	NOUN
ejpam-3912	448	31	ψ	ψ	NOUN
ejpam-3912	448	32	from	from	ADP
ejpam-3912	448	33	e	e	NOUN
ejpam-3912	448	34	to	to	ADP
ejpam-3912	448	35	e	e	PROPN
ejpam-3912	448	36	is	be	AUX
ejpam-3912	448	37	called	call	VERB
ejpam-3912	448	38	local	local	ADJ
ejpam-3912	448	39	automorphism	automorphism	NOUN
ejpam-3912	448	40	if	if	SCONJ
ejpam-3912	448	41	for	for	ADP
ejpam-3912	448	42	every	every	DET
ejpam-3912	448	43	u	u	NOUN
ejpam-3912	448	44	∈	∈	PROPN
ejpam-3912	448	45	e	e	NOUN
ejpam-3912	448	46	there	there	PRON
ejpam-3912	448	47	exists	exist	VERB
ejpam-3912	448	48	an	an	DET
ejpam-3912	448	49	automorphism	automorphism	NOUN
ejpam-3912	448	50	ϕu	ϕu	ADP
ejpam-3912	448	51	∈	∈	PROPN
ejpam-3912	448	52	aut(e	aut(e	PROPN
ejpam-3912	448	53	)	)	PUNCT
ejpam-3912	448	54	such	such	ADJ
ejpam-3912	448	55	that	that	SCONJ
ejpam-3912	448	56	ψ(u	ψ(u	PROPN
ejpam-3912	448	57	)	)	PUNCT
ejpam-3912	448	58	=	=	PUNCT
ejpam-3912	448	59	ϕu(u	ϕu(u	NUM
ejpam-3912	448	60	)	)	PUNCT
ejpam-3912	448	61	.	.	PUNCT
ejpam-3912	449	1	theorem	theorem	ADJ
ejpam-3912	449	2	7	7	NUM
ejpam-3912	449	3	.	.	PUNCT
ejpam-3912	450	1	let	let	VERB
ejpam-3912	450	2	e	e	PRON
ejpam-3912	450	3	be	be	AUX
ejpam-3912	450	4	an	an	DET
ejpam-3912	450	5	n	n	ADV
ejpam-3912	450	6	-	-	PUNCT
ejpam-3912	450	7	dimensional	dimensional	ADJ
ejpam-3912	450	8	nilpotent	nilpotent	ADJ
ejpam-3912	450	9	evolution	evolution	NOUN
ejpam-3912	450	10	algebra	algebra	NOUN
ejpam-3912	450	11	with	with	ADP
ejpam-3912	450	12	2n−2	2n−2	PROPN
ejpam-3912	450	13	+	+	SYM
ejpam-3912	450	14	1	1	NUM
ejpam-3912	450	15	index	index	NOUN
ejpam-3912	450	16	of	of	ADP
ejpam-3912	450	17	nilpotency	nilpotency	NOUN
ejpam-3912	450	18	.	.	PUNCT
ejpam-3912	451	1	then	then	ADV
ejpam-3912	451	2	,	,	PUNCT
ejpam-3912	451	3	the	the	DET
ejpam-3912	451	4	following	follow	VERB
ejpam-3912	451	5	statements	statement	NOUN
ejpam-3912	451	6	hold	hold	VERB
ejpam-3912	451	7	:	:	PUNCT
ejpam-3912	451	8	(	(	PUNCT
ejpam-3912	451	9	i	i	NOUN
ejpam-3912	451	10	)	)	PUNCT
ejpam-3912	451	11	if	if	SCONJ
ejpam-3912	451	12	n	n	NUM
ejpam-3912	451	13	=	=	SYM
ejpam-3912	451	14	3	3	NUM
ejpam-3912	451	15	,	,	PUNCT
ejpam-3912	451	16	then	then	ADV
ejpam-3912	451	17	the	the	DET
ejpam-3912	451	18	set	set	NOUN
ejpam-3912	451	19	of	of	ADP
ejpam-3912	451	20	all	all	DET
ejpam-3912	451	21	local	local	ADJ
ejpam-3912	451	22	automorphisms	automorphism	NOUN
ejpam-3912	451	23	has	have	VERB
ejpam-3912	451	24	the	the	DET
ejpam-3912	451	25	following	follow	VERB
ejpam-3912	451	26	form:	form:	VERB
ejpam-3912	451	27			PROPN
ejpam-3912	451	28	α	α	PROPN
ejpam-3912	451	29	β	β	X
ejpam-3912	451	30	γ	γ	X
ejpam-3912	451	31	0	0	NUM
ejpam-3912	451	32	l2	l2	NOUN
ejpam-3912	451	33	0	0	NUM
ejpam-3912	451	34	0	0	NUM
ejpam-3912	452	1	s	s	NOUN
ejpam-3912	452	2	t	t	NOUN
ejpam-3912	452	3			PROPN
ejpam-3912	452	4	:	:	PUNCT
ejpam-3912	452	5	α	α	X
ejpam-3912	452	6	,	,	PUNCT
ejpam-3912	452	7	β	β	X
ejpam-3912	452	8	,	,	PUNCT
ejpam-3912	452	9	γ	γ	X
ejpam-3912	452	10	,	,	PUNCT
ejpam-3912	452	11	l	l	PROPN
ejpam-3912	452	12	,	,	PUNCT
ejpam-3912	452	13	s	s	X
ejpam-3912	452	14	,	,	PUNCT
ejpam-3912	452	15	t	t	PROPN
ejpam-3912	452	16	∈	∈	PROPN
ejpam-3912	453	1	k	k	PROPN
ejpam-3912	453	2	,	,	PUNCT
ejpam-3912	453	3	αl	αl	ADP
ejpam-3912	453	4	6=	6=	PRON
ejpam-3912	453	5	0	0	PUNCT
ejpam-3912	454	1			NOUN
ejpam-3912	454	2	.	.	PUNCT
ejpam-3912	455	1	(	(	PUNCT
ejpam-3912	455	2	59	59	NUM
ejpam-3912	455	3	)	)	PUNCT
ejpam-3912	455	4	(	(	PUNCT
ejpam-3912	455	5	ii	ii	NOUN
ejpam-3912	455	6	)	)	PUNCT
ejpam-3912	455	7	if	if	SCONJ
ejpam-3912	455	8	n	n	PROPN
ejpam-3912	455	9	>	>	X
ejpam-3912	455	10	3	3	NUM
ejpam-3912	455	11	,	,	PUNCT
ejpam-3912	455	12	then	then	ADV
ejpam-3912	455	13	every	every	DET
ejpam-3912	455	14	local	local	ADJ
ejpam-3912	455	15	automorphism	automorphism	NOUN
ejpam-3912	455	16	of	of	ADP
ejpam-3912	455	17	e	e	PROPN
ejpam-3912	455	18	is	be	AUX
ejpam-3912	455	19	an	an	DET
ejpam-3912	455	20	automorphism	automorphism	NOUN
ejpam-3912	455	21	.	.	PUNCT
ejpam-3912	456	1	proof	proof	NOUN
ejpam-3912	456	2	.	.	PUNCT
ejpam-3912	457	1	(	(	PUNCT
ejpam-3912	457	2	i	i	NOUN
ejpam-3912	457	3	)	)	PUNCT
ejpam-3912	457	4	let	let	VERB
ejpam-3912	457	5	n	n	NOUN
ejpam-3912	457	6	=	=	SYM
ejpam-3912	457	7	3	3	X
ejpam-3912	457	8	.	.	NOUN
ejpam-3912	457	9	due	due	ADP
ejpam-3912	457	10	to	to	ADP
ejpam-3912	457	11	lemma	lemma	PROPN
ejpam-3912	457	12	2	2	NUM
ejpam-3912	457	13	,	,	PUNCT
ejpam-3912	457	14	we	we	PRON
ejpam-3912	457	15	may	may	AUX
ejpam-3912	457	16	assume	assume	VERB
ejpam-3912	457	17	that	that	SCONJ
ejpam-3912	457	18	an	an	DET
ejpam-3912	457	19	evolution	evolution	NOUN
ejpam-3912	457	20	algebra	algebra	NOUN
ejpam-3912	457	21	e	e	NOUN
ejpam-3912	457	22	is	be	AUX
ejpam-3912	457	23	given	give	VERB
ejpam-3912	457	24	by	by	ADP
ejpam-3912	457	25	e2	e2	PROPN
ejpam-3912	457	26	1	1	NUM
ejpam-3912	457	27	=	=	SYM
ejpam-3912	457	28	e2	e2	PROPN
ejpam-3912	457	29	and	and	CCONJ
ejpam-3912	457	30	e2	e2	PROPN
ejpam-3912	457	31	2	2	NUM
ejpam-3912	457	32	=	=	SYM
ejpam-3912	457	33	e2	e2	NOUN
ejpam-3912	457	34	3	3	NUM
ejpam-3912	457	35	=	=	SYM
ejpam-3912	457	36	0	0	X
ejpam-3912	457	37	.	.	PUNCT
ejpam-3912	458	1	take	take	VERB
ejpam-3912	458	2	an	an	DET
ejpam-3912	458	3	arbitrary	arbitrary	ADJ
ejpam-3912	458	4	linear	linear	NOUN
ejpam-3912	458	5	map	map	NOUN
ejpam-3912	458	6	ψ	ψ	X
ejpam-3912	458	7	on	on	ADP
ejpam-3912	458	8	e	e	NOUN
ejpam-3912	458	9	,	,	PUNCT
ejpam-3912	458	10	i.e.	i.e.	X
ejpam-3912	458	11	,	,	PUNCT
ejpam-3912	458	12	ψ(u	ψ(u	PROPN
ejpam-3912	458	13	)	)	PUNCT
ejpam-3912	458	14	=	=	PUNCT
ejpam-3912	459	1	(	(	PUNCT
ejpam-3912	459	2	ψ11u1	ψ11u1	X
ejpam-3912	460	1	+	+	CCONJ
ejpam-3912	460	2	ψ21u2	ψ21u2	X
ejpam-3912	460	3	+	+	CCONJ
ejpam-3912	460	4	ψ31u3)e1	ψ31u3)e1	PRON
ejpam-3912	460	5	+	+	CCONJ
ejpam-3912	460	6	(	(	PUNCT
ejpam-3912	460	7	ψ12u1	ψ12u1	NOUN
ejpam-3912	460	8	+	+	CCONJ
ejpam-3912	460	9	ψ22u2	ψ22u2	NOUN
ejpam-3912	460	10	+	+	CCONJ
ejpam-3912	460	11	ψ32u3)e2	ψ32u3)e2	ADJ
ejpam-3912	460	12	+	+	CCONJ
ejpam-3912	460	13	(	(	PUNCT
ejpam-3912	460	14	ψ13u1	ψ13u1	PRON
ejpam-3912	460	15	+	+	NUM
ejpam-3912	460	16	ψ23u2	ψ23u2	VERB
ejpam-3912	460	17	+	+	CCONJ
ejpam-3912	460	18	ψ33u3)e3	ψ33u3)e3	NOUN
ejpam-3912	460	19	∀u	∀u	NOUN
ejpam-3912	460	20	=	=	SYM
ejpam-3912	460	21	u1e1	u1e1	NOUN
ejpam-3912	460	22	+	+	CCONJ
ejpam-3912	460	23	u2e2	u2e2	PROPN
ejpam-3912	461	1	+	+	NUM
ejpam-3912	461	2	u3e3	u3e3	NOUN
ejpam-3912	461	3	.	.	PUNCT
ejpam-3912	462	1	if	if	SCONJ
ejpam-3912	462	2	ψ	ψ	NOUN
ejpam-3912	462	3	is	be	AUX
ejpam-3912	462	4	a	a	DET
ejpam-3912	462	5	local	local	ADJ
ejpam-3912	462	6	automorphism	automorphism	NOUN
ejpam-3912	462	7	,	,	PUNCT
ejpam-3912	462	8	then	then	ADV
ejpam-3912	462	9	for	for	ADP
ejpam-3912	462	10	any	any	DET
ejpam-3912	462	11	u	u	NOUN
ejpam-3912	462	12	,	,	PUNCT
ejpam-3912	462	13	there	there	PRON
ejpam-3912	462	14	exist	exist	VERB
ejpam-3912	462	15	αu	αu	PROPN
ejpam-3912	462	16	,	,	PUNCT
ejpam-3912	462	17	βu	βu	NOUN
ejpam-3912	462	18	,	,	PUNCT
ejpam-3912	462	19	γu	γu	PROPN
ejpam-3912	462	20	,	,	PUNCT
ejpam-3912	462	21	su	su	PROPN
ejpam-3912	462	22	and	and	CCONJ
ejpam-3912	462	23	tu	tu	PROPN
ejpam-3912	462	24	,	,	PUNCT
ejpam-3912	462	25	such	such	ADJ
ejpam-3912	462	26	that	that	PRON
ejpam-3912	462	27	ψ11u1	ψ11u1	NOUN
ejpam-3912	463	1	+	+	CCONJ
ejpam-3912	463	2	ψ21u2	ψ21u2	X
ejpam-3912	463	3	+	+	NUM
ejpam-3912	463	4	ψ31u3	ψ31u3	NOUN
ejpam-3912	463	5	=	=	SYM
ejpam-3912	463	6	αuu1	αuu1	PROPN
ejpam-3912	463	7	ψ12u1	ψ12u1	NOUN
ejpam-3912	464	1	+	+	CCONJ
ejpam-3912	464	2	ψ22u2	ψ22u2	NOUN
ejpam-3912	464	3	+	+	CCONJ
ejpam-3912	464	4	ψ32u3	ψ32u3	NOUN
ejpam-3912	464	5	=	=	X
ejpam-3912	464	6	βuu1	βuu1	PROPN
ejpam-3912	464	7	+	+	CCONJ
ejpam-3912	464	8	α2	α2	ADJ
ejpam-3912	464	9	uu2	uu2	ADJ
ejpam-3912	464	10	+	+	CCONJ
ejpam-3912	464	11	suu3	suu3	PROPN
ejpam-3912	464	12	ψ13u1	ψ13u1	PROPN
ejpam-3912	464	13	+	+	NUM
ejpam-3912	464	14	ψ23u2	ψ23u2	PROPN
ejpam-3912	464	15	+	+	CCONJ
ejpam-3912	464	16	ψ33u3	ψ33u3	NOUN
ejpam-3912	464	17	=	=	SYM
ejpam-3912	464	18	γuu1	γuu1	PROPN
ejpam-3912	464	19	+	+	CCONJ
ejpam-3912	464	20	tuu3	tuu3	PROPN
ejpam-3912	464	21	.	.	PUNCT
ejpam-3912	465	1	from	from	ADP
ejpam-3912	465	2	the	the	DET
ejpam-3912	465	3	first	first	ADJ
ejpam-3912	465	4	equation	equation	NOUN
ejpam-3912	465	5	,	,	PUNCT
ejpam-3912	465	6	we	we	PRON
ejpam-3912	465	7	obtain	obtain	VERB
ejpam-3912	465	8	ψ21	ψ21	VERB
ejpam-3912	465	9	=	=	SYM
ejpam-3912	465	10	ψ31	ψ31	NOUN
ejpam-3912	465	11	=	=	SYM
ejpam-3912	465	12	0	0	NUM
ejpam-3912	465	13	,	,	PUNCT
ejpam-3912	465	14	and	and	CCONJ
ejpam-3912	465	15	from	from	ADP
ejpam-3912	465	16	the	the	DET
ejpam-3912	465	17	third	third	ADJ
ejpam-3912	465	18	equation	equation	NOUN
ejpam-3912	465	19	,	,	PUNCT
ejpam-3912	465	20	we	we	PRON
ejpam-3912	465	21	have	have	VERB
ejpam-3912	465	22	ψ23	ψ23	NOUN
ejpam-3912	465	23	=	=	NOUN
ejpam-3912	465	24	0	0	PROPN
ejpam-3912	465	25	.	.	PUNCT
ejpam-3912	466	1	if	if	SCONJ
ejpam-3912	466	2	we	we	PRON
ejpam-3912	466	3	take	take	VERB
ejpam-3912	466	4	u	u	PRON
ejpam-3912	466	5	such	such	ADJ
ejpam-3912	466	6	that	that	DET
ejpam-3912	466	7	u1	u1	NOUN
ejpam-3912	466	8	=	=	SYM
ejpam-3912	466	9	u3	u3	NOUN
ejpam-3912	466	10	=	=	SYM
ejpam-3912	466	11	0	0	NUM
ejpam-3912	466	12	,	,	PUNCT
ejpam-3912	466	13	then	then	ADV
ejpam-3912	466	14	from	from	ADP
ejpam-3912	466	15	the	the	DET
ejpam-3912	466	16	second	second	ADJ
ejpam-3912	466	17	equation	equation	NOUN
ejpam-3912	466	18	,	,	PUNCT
ejpam-3912	466	19	we	we	PRON
ejpam-3912	466	20	immediately	immediately	ADV
ejpam-3912	466	21	find	find	VERB
ejpam-3912	466	22	ψ22	ψ22	NOUN
ejpam-3912	466	23	=	=	SYM
ejpam-3912	466	24	α2	α2	NOUN
ejpam-3912	466	25	u.	u.	VERB
ejpam-3912	466	26	it	it	PRON
ejpam-3912	466	27	yields	yield	VERB
ejpam-3912	466	28	that	that	SCONJ
ejpam-3912	466	29	if	if	SCONJ
ejpam-3912	466	30	ψ	ψ	NOUN
ejpam-3912	466	31	is	be	AUX
ejpam-3912	466	32	a	a	DET
ejpam-3912	466	33	local	local	ADJ
ejpam-3912	466	34	automorphism	automorphism	NOUN
ejpam-3912	466	35	,	,	PUNCT
ejpam-3912	466	36	it	it	PRON
ejpam-3912	466	37	has	have	VERB
ejpam-3912	466	38	the	the	DET
ejpam-3912	466	39	following	follow	VERB
ejpam-3912	466	40	form	form	NOUN
ejpam-3912	466	41	:	:	PUNCT
ejpam-3912	466	42			PUNCT
ejpam-3912	466	43			PROPN
ejpam-3912	466	44	α	α	X
ejpam-3912	466	45	β	β	X
ejpam-3912	466	46	γ	γ	X
ejpam-3912	466	47	0	0	NUM
ejpam-3912	466	48	l2	l2	NOUN
ejpam-3912	466	49	0	0	NUM
ejpam-3912	466	50	0	0	NUM
ejpam-3912	466	51	s	s	NOUN
ejpam-3912	466	52	t	t	NOUN
ejpam-3912	466	53			PROPN
ejpam-3912	466	54	:	:	PUNCT
ejpam-3912	466	55	α	α	X
ejpam-3912	466	56	,	,	PUNCT
ejpam-3912	466	57	β	β	X
ejpam-3912	466	58	,	,	PUNCT
ejpam-3912	466	59	γ	γ	X
ejpam-3912	466	60	,	,	PUNCT
ejpam-3912	466	61	l	l	PROPN
ejpam-3912	466	62	,	,	PUNCT
ejpam-3912	466	63	s	s	X
ejpam-3912	466	64	,	,	PUNCT
ejpam-3912	467	1	t	t	PROPN
ejpam-3912	467	2	∈	∈	PROPN
ejpam-3912	467	3	k	k	PROPN
ejpam-3912	467	4	,	,	PUNCT
ejpam-3912	467	5	αl	αl	ADP
ejpam-3912	467	6	6=	6=	PRON
ejpam-3912	467	7	0	0	PUNCT
ejpam-3912	468	1			NOUN
ejpam-3912	468	2	(	(	PUNCT
ejpam-3912	468	3	60	60	NUM
ejpam-3912	468	4	)	)	PUNCT
ejpam-3912	468	5	a.	a.	NOUN
ejpam-3912	468	6	alarafeen	alarafeen	PROPN
ejpam-3912	468	7	,	,	PUNCT
ejpam-3912	468	8	i.	i.	PROPN
ejpam-3912	468	9	qaralleh	qaralleh	PROPN
ejpam-3912	468	10	,	,	PUNCT
ejpam-3912	468	11	a.	a.	PROPN
ejpam-3912	468	12	ahmad	ahmad	PROPN
ejpam-3912	468	13	/	/	SYM
ejpam-3912	468	14	eur	eur	PROPN
ejpam-3912	468	15	.	.	PUNCT
ejpam-3912	469	1	j.	j.	PROPN
ejpam-3912	469	2	pure	pure	PROPN
ejpam-3912	469	3	appl	appl	PROPN
ejpam-3912	469	4	.	.	PROPN
ejpam-3912	469	5	math	math	PROPN
ejpam-3912	469	6	,	,	PUNCT
ejpam-3912	469	7	14	14	NUM
ejpam-3912	469	8	(	(	PUNCT
ejpam-3912	469	9	1	1	NUM
ejpam-3912	469	10	)	)	PUNCT
ejpam-3912	469	11	(	(	PUNCT
ejpam-3912	469	12	2021	2021	NUM
ejpam-3912	469	13	)	)	PUNCT
ejpam-3912	469	14	,	,	PUNCT
ejpam-3912	469	15	278	278	NUM
ejpam-3912	469	16	-	-	SYM
ejpam-3912	469	17	300	300	NUM
ejpam-3912	469	18	297	297	NUM
ejpam-3912	469	19	we	we	PRON
ejpam-3912	469	20	show	show	VERB
ejpam-3912	469	21	that	that	SCONJ
ejpam-3912	469	22	(	(	PUNCT
ejpam-3912	469	23	60	60	NUM
ejpam-3912	469	24	)	)	PUNCT
ejpam-3912	469	25	is	be	AUX
ejpam-3912	469	26	indeed	indeed	ADV
ejpam-3912	469	27	a	a	DET
ejpam-3912	469	28	local	local	ADJ
ejpam-3912	469	29	automorphism	automorphism	NOUN
ejpam-3912	469	30	of	of	ADP
ejpam-3912	469	31	(	(	PUNCT
ejpam-3912	469	32	2	2	NUM
ejpam-3912	469	33	)	)	PUNCT
ejpam-3912	469	34	.	.	PUNCT
ejpam-3912	470	1	in	in	ADP
ejpam-3912	470	2	fact	fact	NOUN
ejpam-3912	470	3	,	,	PUNCT
ejpam-3912	470	4	for	for	ADP
ejpam-3912	470	5	any	any	DET
ejpam-3912	470	6	u	u	PROPN
ejpam-3912	470	7	∈	∈	PROPN
ejpam-3912	470	8	e	e	NOUN
ejpam-3912	470	9	,	,	PUNCT
ejpam-3912	470	10	we	we	PRON
ejpam-3912	470	11	may	may	AUX
ejpam-3912	470	12	take	take	VERB
ejpam-3912	470	13	an	an	DET
ejpam-3912	470	14	automorphism	automorphism	NOUN
ejpam-3912	470	15	ϕu	ϕu	NOUN
ejpam-3912	470	16	of	of	ADP
ejpam-3912	470	17	(	(	PUNCT
ejpam-3912	470	18	2	2	NUM
ejpam-3912	470	19	)	)	PUNCT
ejpam-3912	470	20	as	as	SCONJ
ejpam-3912	470	21	follows	follow	VERB
ejpam-3912	470	22	:	:	PUNCT
ejpam-3912	470	23	ϕu	ϕu	PROPN
ejpam-3912	470	24	=	=	PUNCT
ejpam-3912	470	25			PROPN
ejpam-3912	470	26			VERB
ejpam-3912	470	27	α	α	X
ejpam-3912	470	28	β	β	X
ejpam-3912	471	1	+	+	CCONJ
ejpam-3912	471	2	(	(	PUNCT
ejpam-3912	471	3	l2−α2)u2	l2−α2)u2	NOUN
ejpam-3912	471	4	u1	u1	VERB
ejpam-3912	471	5	γ	γ	X
ejpam-3912	471	6	0	0	X
ejpam-3912	471	7	α2	α2	PROPN
ejpam-3912	471	8	0	0	NUM
ejpam-3912	471	9	0	0	NUM
ejpam-3912	472	1	s	s	PART
ejpam-3912	472	2	t	t	NOUN
ejpam-3912	472	3			NOUN
ejpam-3912	472	4	,	,	PUNCT
ejpam-3912	472	5	if	if	SCONJ
ejpam-3912	472	6	u1u3	u1u3	NOUN
ejpam-3912	472	7	6=	6=	X
ejpam-3912	472	8	0	0	SYM
ejpam-3912	473	1			PROPN
ejpam-3912	473	2	l	l	NOUN
ejpam-3912	473	3	0	0	NUM
ejpam-3912	473	4	0	0	SYM
ejpam-3912	473	5	0	0	NUM
ejpam-3912	473	6	l2	l2	NOUN
ejpam-3912	473	7	0	0	NUM
ejpam-3912	473	8	0	0	NUM
ejpam-3912	473	9	0	0	NUM
ejpam-3912	473	10	0	0	NUM
ejpam-3912	474	1			PROPN
ejpam-3912	474	2	,	,	PUNCT
ejpam-3912	474	3	if	if	SCONJ
ejpam-3912	474	4	u1	u1	NOUN
ejpam-3912	474	5	=	=	SYM
ejpam-3912	474	6	u3	u3	NOUN
ejpam-3912	474	7	=	=	NOUN
ejpam-3912	474	8	0	0	NUM
ejpam-3912	474	9	from	from	ADP
ejpam-3912	474	10	this	this	PRON
ejpam-3912	474	11	,	,	PUNCT
ejpam-3912	474	12	one	one	PRON
ejpam-3912	474	13	can	can	AUX
ejpam-3912	474	14	check	check	VERB
ejpam-3912	474	15	that	that	PRON
ejpam-3912	474	16	ψ(u	ψ(u	PROPN
ejpam-3912	474	17	)	)	PUNCT
ejpam-3912	474	18	=	=	PUNCT
ejpam-3912	474	19	ϕu(u	ϕu(u	NUM
ejpam-3912	474	20	)	)	PUNCT
ejpam-3912	474	21	.	.	PUNCT
ejpam-3912	475	1	(	(	PUNCT
ejpam-3912	475	2	ii	ii	NOUN
ejpam-3912	475	3	)	)	PUNCT
ejpam-3912	475	4	let	let	VERB
ejpam-3912	475	5	n	n	INTJ
ejpam-3912	475	6	>	>	X
ejpam-3912	475	7	3	3	X
ejpam-3912	475	8	.	.	PUNCT
ejpam-3912	476	1	let	let	VERB
ejpam-3912	476	2	ψ	ψ	PART
ejpam-3912	476	3	be	be	AUX
ejpam-3912	476	4	a	a	DET
ejpam-3912	476	5	local	local	ADJ
ejpam-3912	476	6	automorphism	automorphism	NOUN
ejpam-3912	476	7	for	for	ADP
ejpam-3912	476	8	(	(	PUNCT
ejpam-3912	476	9	2	2	NUM
ejpam-3912	476	10	)	)	PUNCT
ejpam-3912	476	11	.	.	PUNCT
ejpam-3912	477	1	by	by	ADP
ejpam-3912	477	2	definition	definition	NOUN
ejpam-3912	477	3	of	of	ADP
ejpam-3912	477	4	local	local	ADJ
ejpam-3912	477	5	automorphism	automorphism	NOUN
ejpam-3912	477	6	,	,	PUNCT
ejpam-3912	477	7	for	for	SCONJ
ejpam-3912	477	8	every	every	DET
ejpam-3912	477	9	u	u	NOUN
ejpam-3912	477	10	∈	∈	PROPN
ejpam-3912	477	11	e	e	NOUN
ejpam-3912	477	12	we	we	PRON
ejpam-3912	477	13	have	have	VERB
ejpam-3912	477	14	ψ(u	ψ(u	PROPN
ejpam-3912	477	15	)	)	PUNCT
ejpam-3912	477	16	=	=	PUNCT
ejpam-3912	477	17	ϕu(u	ϕu(u	NUM
ejpam-3912	477	18	)	)	PUNCT
ejpam-3912	477	19	,	,	PUNCT
ejpam-3912	477	20	where	where	SCONJ
ejpam-3912	477	21	ϕu	ϕu	PROPN
ejpam-3912	477	22	is	be	AUX
ejpam-3912	477	23	an	an	DET
ejpam-3912	477	24	automorphism	automorphism	NOUN
ejpam-3912	477	25	.	.	PUNCT
ejpam-3912	478	1	then	then	ADV
ejpam-3912	478	2	,	,	PUNCT
ejpam-3912	478	3	theorem	theorem	VERB
ejpam-3912	478	4	6	6	NUM
ejpam-3912	478	5	implies	implie	NOUN
ejpam-3912	478	6	ψij	ψij	VERB
ejpam-3912	478	7	=	=	SYM
ejpam-3912	478	8	0	0	NUM
ejpam-3912	478	9	for	for	ADP
ejpam-3912	478	10	every	every	DET
ejpam-3912	478	11	i	i	PROPN
ejpam-3912	478	12	6=	6=	PROPN
ejpam-3912	478	13	j	j	PROPN
ejpam-3912	478	14	,	,	PUNCT
ejpam-3912	478	15	j	j	PROPN
ejpam-3912	478	16	<	<	X
ejpam-3912	478	17	n	n	CCONJ
ejpam-3912	478	18	−	−	PROPN
ejpam-3912	478	19	1	1	NUM
ejpam-3912	478	20	.	.	PUNCT
ejpam-3912	479	1	on	on	ADP
ejpam-3912	479	2	the	the	DET
ejpam-3912	479	3	other	other	ADJ
ejpam-3912	479	4	hand	hand	NOUN
ejpam-3912	479	5	,	,	PUNCT
ejpam-3912	479	6	taking	take	VERB
ejpam-3912	479	7	u	u	NOUN
ejpam-3912	479	8	=	=	SYM
ejpam-3912	479	9	ei	ei	PROPN
ejpam-3912	479	10	,	,	PUNCT
ejpam-3912	479	11	i	i	PROPN
ejpam-3912	479	12	≤	≤	NOUN
ejpam-3912	479	13	n	n	CCONJ
ejpam-3912	479	14	,	,	PUNCT
ejpam-3912	479	15	we	we	PRON
ejpam-3912	479	16	conclude	conclude	VERB
ejpam-3912	479	17	that	that	SCONJ
ejpam-3912	479	18	the	the	DET
ejpam-3912	479	19	local	local	ADJ
ejpam-3912	479	20	automorphism	automorphism	NOUN
ejpam-3912	479	21	ψ	ψ	NOUN
ejpam-3912	479	22	has	have	VERB
ejpam-3912	479	23	the	the	DET
ejpam-3912	479	24	following	follow	VERB
ejpam-3912	479	25	form	form	NOUN
ejpam-3912	479	26	:	:	PUNCT
ejpam-3912	479	27	ψ	ψ	NOUN
ejpam-3912	479	28	=	=	SYM
ejpam-3912	479	29			VERB
ejpam-3912	479	30	αe1	αe1	PROPN
ejpam-3912	479	31	0	0	NUM
ejpam-3912	479	32	0	0	NUM
ejpam-3912	479	33	...	...	SYM
ejpam-3912	479	34	0	0	NUM
ejpam-3912	480	1	βe1	βe1	NOUN
ejpam-3912	480	2	γe1	γe1	NOUN
ejpam-3912	480	3	0	0	PUNCT
ejpam-3912	480	4	α2	α2	PROPN
ejpam-3912	480	5	e2	e2	PROPN
ejpam-3912	480	6	0	0	NUM
ejpam-3912	480	7	...	...	PUNCT
ejpam-3912	480	8	0	0	NUM
ejpam-3912	481	1	ϕ	ϕ	X
ejpam-3912	481	2	(	(	PUNCT
ejpam-3912	481	3	e2	e2	PROPN
ejpam-3912	481	4	)	)	PUNCT
ejpam-3912	481	5	2,n−1	2,n−1	PROPN
ejpam-3912	481	6	ϕ	ϕ	X
ejpam-3912	481	7	(	(	PUNCT
ejpam-3912	481	8	e2	e2	PROPN
ejpam-3912	481	9	)	)	PUNCT
ejpam-3912	481	10	2n	2n	NUM
ejpam-3912	481	11	...	...	PUNCT
ejpam-3912	481	12	...	...	PUNCT
ejpam-3912	481	13	...	...	PUNCT
ejpam-3912	481	14	.	.	PUNCT
ejpam-3912	481	15	.	.	PUNCT
ejpam-3912	481	16	.	.	PUNCT
ejpam-3912	481	17	...	...	PUNCT
ejpam-3912	482	1	...	...	PUNCT
ejpam-3912	483	1	0	0	NUM
ejpam-3912	483	2	0	0	NUM
ejpam-3912	483	3	0	0	NUM
ejpam-3912	483	4	...	...	PUNCT
ejpam-3912	484	1	α2n−2	α2n−2	PROPN
ejpam-3912	484	2	en−2	en−2	PROPN
ejpam-3912	484	3	ϕ	ϕ	PROPN
ejpam-3912	484	4	(	(	PUNCT
ejpam-3912	484	5	en−2	en−2	PROPN
ejpam-3912	484	6	)	)	PUNCT
ejpam-3912	484	7	n−2,n−1	n−2,n−1	PROPN
ejpam-3912	484	8	ϕ	ϕ	X
ejpam-3912	484	9	(	(	PUNCT
ejpam-3912	484	10	en−2	en−2	PROPN
ejpam-3912	484	11	)	)	PUNCT
ejpam-3912	484	12	n−2,n	n−2,n	NOUN
ejpam-3912	484	13	0	0	NUM
ejpam-3912	484	14	0	0	NUM
ejpam-3912	484	15	0	0	NUM
ejpam-3912	484	16	...	...	PUNCT
ejpam-3912	484	17	0	0	NUM
ejpam-3912	485	1	ϕ	ϕ	X
ejpam-3912	485	2	(	(	PUNCT
ejpam-3912	485	3	en−1	en−1	PROPN
ejpam-3912	485	4	)	)	PUNCT
ejpam-3912	485	5	n−1,n−1	n−1,n−1	PROPN
ejpam-3912	486	1	ϕ	ϕ	X
ejpam-3912	487	1	(	(	PUNCT
ejpam-3912	487	2	en−1	en−1	PROPN
ejpam-3912	487	3	)	)	PUNCT
ejpam-3912	487	4	n−1,n	n−1,n	PROPN
ejpam-3912	487	5	0	0	NUM
ejpam-3912	487	6	0	0	NUM
ejpam-3912	487	7	0	0	NUM
ejpam-3912	487	8	...	...	SYM
ejpam-3912	487	9	0	0	NUM
ejpam-3912	487	10	sen	sen	PROPN
ejpam-3912	487	11	ten	ten	PROPN
ejpam-3912	487	12			NOUN
ejpam-3912	487	13	now	now	ADV
ejpam-3912	487	14	,	,	PUNCT
ejpam-3912	487	15	we	we	PRON
ejpam-3912	487	16	take	take	VERB
ejpam-3912	487	17	arbitrary	arbitrary	ADJ
ejpam-3912	487	18	v	v	NOUN
ejpam-3912	487	19	=	=	SYM
ejpam-3912	487	20	∑n	∑n	PROPN
ejpam-3912	487	21	i=1	i=1	PROPN
ejpam-3912	487	22	viei	viei	PROPN
ejpam-3912	487	23	.	.	PUNCT
ejpam-3912	488	1	then	then	ADV
ejpam-3912	488	2	,	,	PUNCT
ejpam-3912	488	3	from	from	ADP
ejpam-3912	488	4	ψ(v	ψ(v	PROPN
ejpam-3912	488	5	)	)	PUNCT
ejpam-3912	488	6	=	=	PUNCT
ejpam-3912	488	7	ϕv(v	ϕv(v	NUM
ejpam-3912	488	8	)	)	PUNCT
ejpam-3912	488	9	,	,	PUNCT
ejpam-3912	488	10	we	we	PRON
ejpam-3912	488	11	obtain	obtain	VERB
ejpam-3912	488	12	α2i−1	α2i−1	PROPN
ejpam-3912	488	13	ei	ei	NOUN
ejpam-3912	488	14	vi	vi	PROPN
ejpam-3912	488	15	=	=	SYM
ejpam-3912	488	16	α2i−1	α2i−1	PROPN
ejpam-3912	488	17	v	v	NUM
ejpam-3912	488	18	vi	vi	PROPN
ejpam-3912	488	19	,	,	PUNCT
ejpam-3912	488	20	i	i	PRON
ejpam-3912	488	21	<	<	X
ejpam-3912	488	22	n−	n−	NOUN
ejpam-3912	488	23	1	1	NUM
ejpam-3912	488	24	(	(	PUNCT
ejpam-3912	488	25	61	61	NUM
ejpam-3912	488	26	)	)	PUNCT
ejpam-3912	488	27	βe1v1	βe1v1	PUNCT
ejpam-3912	488	28	+	+	NUM
ejpam-3912	488	29	senvn	senvn	NOUN
ejpam-3912	488	30	+	+	CCONJ
ejpam-3912	489	1	n−1∑	n−1∑	PROPN
ejpam-3912	489	2	k=2	k=2	PROPN
ejpam-3912	489	3	ϕ	ϕ	X
ejpam-3912	489	4	(	(	PUNCT
ejpam-3912	489	5	ek	ek	PROPN
ejpam-3912	489	6	)	)	PUNCT
ejpam-3912	489	7	k	k	NOUN
ejpam-3912	489	8	,	,	PUNCT
ejpam-3912	489	9	n−1vk	n−1vk	NOUN
ejpam-3912	489	10	=	=	VERB
ejpam-3912	489	11	βvv1	βvv1	PROPN
ejpam-3912	490	1	+	+	CCONJ
ejpam-3912	490	2	svvn	svvn	VERB
ejpam-3912	490	3	+	+	CCONJ
ejpam-3912	490	4	n−1∑	n−1∑	PROPN
ejpam-3912	490	5	k=2	k=2	PROPN
ejpam-3912	490	6	ϕ	ϕ	X
ejpam-3912	490	7	(	(	PUNCT
ejpam-3912	490	8	v	v	NOUN
ejpam-3912	490	9	)	)	PUNCT
ejpam-3912	490	10	k	k	NOUN
ejpam-3912	490	11	,	,	PUNCT
ejpam-3912	490	12	n−1vk	n−1vk	PROPN
ejpam-3912	490	13	(	(	PUNCT
ejpam-3912	490	14	62	62	NUM
ejpam-3912	490	15	)	)	PUNCT
ejpam-3912	490	16	γe1v1	γe1v1	PROPN
ejpam-3912	491	1	+	+	CCONJ
ejpam-3912	491	2	tenvn	tenvn	NOUN
ejpam-3912	491	3	+	+	CCONJ
ejpam-3912	491	4	n−1∑	n−1∑	PROPN
ejpam-3912	491	5	k=2	k=2	PROPN
ejpam-3912	491	6	ϕ	ϕ	X
ejpam-3912	491	7	(	(	PUNCT
ejpam-3912	491	8	ek	ek	PROPN
ejpam-3912	491	9	)	)	PUNCT
ejpam-3912	491	10	k	k	NOUN
ejpam-3912	491	11	,	,	PUNCT
ejpam-3912	491	12	n	n	PROPN
ejpam-3912	491	13	vk	vk	NOUN
ejpam-3912	491	14	=	=	PUNCT
ejpam-3912	491	15	βvv1	βvv1	NOUN
ejpam-3912	492	1	+	+	CCONJ
ejpam-3912	492	2	tvvn	tvvn	ADJ
ejpam-3912	492	3	+	+	CCONJ
ejpam-3912	492	4	n−1∑	n−1∑	PROPN
ejpam-3912	492	5	k=2	k=2	PROPN
ejpam-3912	492	6	ϕ	ϕ	X
ejpam-3912	492	7	(	(	PUNCT
ejpam-3912	492	8	v	v	NOUN
ejpam-3912	492	9	)	)	PUNCT
ejpam-3912	492	10	k	k	NOUN
ejpam-3912	492	11	,	,	PUNCT
ejpam-3912	492	12	nvk	nvk	NOUN
ejpam-3912	492	13	.	.	PUNCT
ejpam-3912	493	1	(	(	PUNCT
ejpam-3912	493	2	63	63	NUM
ejpam-3912	493	3	)	)	PUNCT
ejpam-3912	493	4	from	from	ADP
ejpam-3912	493	5	(	(	PUNCT
ejpam-3912	493	6	61	61	NUM
ejpam-3912	493	7	)	)	PUNCT
ejpam-3912	493	8	we	we	PRON
ejpam-3912	493	9	find	find	VERB
ejpam-3912	493	10	α2i−1	α2i−1	PROPN
ejpam-3912	493	11	ei	ei	NOUN
ejpam-3912	493	12	=	=	SYM
ejpam-3912	493	13	α2i−1	α2i−1	PROPN
ejpam-3912	493	14	e1	e1	PROPN
ejpam-3912	493	15	,	,	PUNCT
ejpam-3912	494	1	i	i	PRON
ejpam-3912	494	2	<	<	X
ejpam-3912	494	3	n−	n−	NOUN
ejpam-3912	494	4	1	1	NUM
ejpam-3912	494	5	(	(	PUNCT
ejpam-3912	494	6	64	64	NUM
ejpam-3912	494	7	)	)	PUNCT
ejpam-3912	494	8	consequently	consequently	ADV
ejpam-3912	494	9	,	,	PUNCT
ejpam-3912	494	10	ϕ	ϕ	PROPN
ejpam-3912	494	11	(	(	PUNCT
ejpam-3912	494	12	ek	ek	NOUN
ejpam-3912	494	13	)	)	PUNCT
ejpam-3912	494	14	k	k	PROPN
ejpam-3912	494	15	,	,	PUNCT
ejpam-3912	494	16	n−1	n−1	PROPN
ejpam-3912	494	17	=	=	SYM
ejpam-3912	494	18	ϕ	ϕ	PROPN
ejpam-3912	494	19	(	(	PUNCT
ejpam-3912	494	20	e1	e1	PROPN
ejpam-3912	494	21	)	)	PUNCT
ejpam-3912	494	22	k	k	NOUN
ejpam-3912	494	23	,	,	PUNCT
ejpam-3912	494	24	n−1	n−1	PROPN
ejpam-3912	494	25	and	and	CCONJ
ejpam-3912	494	26	ϕ	ϕ	PROPN
ejpam-3912	494	27	(	(	PUNCT
ejpam-3912	494	28	ek	ek	NOUN
ejpam-3912	494	29	)	)	PUNCT
ejpam-3912	494	30	kn	kn	PROPN
ejpam-3912	494	31	=	=	PUNCT
ejpam-3912	494	32	ϕ	ϕ	PROPN
ejpam-3912	494	33	(	(	PUNCT
ejpam-3912	494	34	e1	e1	PROPN
ejpam-3912	494	35	)	)	PUNCT
ejpam-3912	494	36	kn	kn	PROPN
ejpam-3912	494	37	for	for	ADP
ejpam-3912	494	38	any	any	DET
ejpam-3912	494	39	k	k	PROPN
ejpam-3912	494	40	<	<	X
ejpam-3912	494	41	n.	n.	PROPN
ejpam-3912	494	42	based	base	VERB
ejpam-3912	494	43	on	on	ADP
ejpam-3912	494	44	this	this	DET
ejpam-3912	494	45	fact	fact	NOUN
ejpam-3912	494	46	,	,	PUNCT
ejpam-3912	494	47	the	the	DET
ejpam-3912	494	48	following	follow	VERB
ejpam-3912	494	49	is	be	AUX
ejpam-3912	494	50	obtained	obtain	VERB
ejpam-3912	494	51	from	from	ADP
ejpam-3912	494	52	(	(	PUNCT
ejpam-3912	494	53	62	62	NUM
ejpam-3912	494	54	)	)	PUNCT
ejpam-3912	494	55	and	and	CCONJ
ejpam-3912	494	56	(	(	PUNCT
ejpam-3912	494	57	63	63	NUM
ejpam-3912	494	58	)	)	PUNCT
ejpam-3912	494	59	,	,	PUNCT
ejpam-3912	495	1	γe1v1	γe1v1	PROPN
ejpam-3912	495	2	+	+	NUM
ejpam-3912	495	3	senvn	senvn	NOUN
ejpam-3912	495	4	=	=	SYM
ejpam-3912	495	5	γvv1	γvv1	NOUN
ejpam-3912	495	6	+	+	CCONJ
ejpam-3912	495	7	svvn	svvn	ADV
ejpam-3912	495	8	,	,	PUNCT
ejpam-3912	495	9	βe1v1	βe1v1	PUNCT
ejpam-3912	495	10	+	+	NUM
ejpam-3912	495	11	tenvn	tenvn	NOUN
ejpam-3912	495	12	=	=	SYM
ejpam-3912	495	13	βvv1	βvv1	NOUN
ejpam-3912	495	14	+	+	CCONJ
ejpam-3912	495	15	svvn	svvn	ADV
ejpam-3912	495	16	.	.	PUNCT
ejpam-3912	496	1	(	(	PUNCT
ejpam-3912	496	2	65	65	NUM
ejpam-3912	496	3	)	)	PUNCT
ejpam-3912	496	4	finally	finally	ADV
ejpam-3912	496	5	,	,	PUNCT
ejpam-3912	496	6	taking	take	VERB
ejpam-3912	496	7	v′	v′	NOUN
ejpam-3912	496	8	=	=	SYM
ejpam-3912	496	9	e2	e2	PROPN
ejpam-3912	496	10	+	+	CCONJ
ejpam-3912	496	11	en	en	X
ejpam-3912	496	12	,	,	PUNCT
ejpam-3912	496	13	we	we	PRON
ejpam-3912	496	14	obtain	obtain	VERB
ejpam-3912	496	15	γe1	γe1	NOUN
ejpam-3912	496	16	=	=	SYM
ejpam-3912	496	17	γv	γv	PROPN
ejpam-3912	496	18	,	,	PUNCT
ejpam-3912	496	19	βe1	βe1	NOUN
ejpam-3912	496	20	=	=	SYM
ejpam-3912	496	21	βv	βv	PROPN
ejpam-3912	496	22	,	,	PUNCT
ejpam-3912	496	23	sen	sen	PROPN
ejpam-3912	496	24	=	=	PUNCT
ejpam-3912	496	25	sv	sv	PROPN
ejpam-3912	496	26	,	,	PUNCT
ejpam-3912	496	27	and	and	CCONJ
ejpam-3912	496	28	ten	ten	NUM
ejpam-3912	496	29	=	=	NOUN
ejpam-3912	496	30	tv	tv	NOUN
ejpam-3912	496	31	,	,	PUNCT
ejpam-3912	496	32	for	for	ADP
ejpam-3912	496	33	any	any	DET
ejpam-3912	496	34	v	v	PROPN
ejpam-3912	496	35	∈	∈	PROPN
ejpam-3912	496	36	e.	e.	PROPN
ejpam-3912	496	37	references	reference	NOUN
ejpam-3912	496	38	298	298	NUM
ejpam-3912	496	39	thus	thus	ADV
ejpam-3912	496	40	,	,	PUNCT
ejpam-3912	496	41	we	we	PRON
ejpam-3912	496	42	conclude	conclude	VERB
ejpam-3912	496	43	that	that	SCONJ
ejpam-3912	496	44	local	local	ADJ
ejpam-3912	496	45	automorphism	automorphism	NOUN
ejpam-3912	496	46	ψ	ψ	X
ejpam-3912	496	47	=	=	SYM
ejpam-3912	496	48	(	(	PUNCT
ejpam-3912	496	49	ϕij	ϕij	NOUN
ejpam-3912	496	50	)	)	PUNCT
ejpam-3912	496	51	has	have	VERB
ejpam-3912	496	52	the	the	DET
ejpam-3912	496	53	following	follow	VERB
ejpam-3912	496	54	form	form	NOUN
ejpam-3912	496	55	:	:	PUNCT
ejpam-3912	496	56	ϕij	ϕij	NOUN
ejpam-3912	496	57	=	=	SYM
ejpam-3912	496	58			PROPN
ejpam-3912	496	59	α2i−1	α2i−1	PROPN
ejpam-3912	496	60	e1	e1	NOUN
ejpam-3912	496	61	,	,	PUNCT
ejpam-3912	497	1	i	i	PRON
ejpam-3912	497	2	=	=	PUNCT
ejpam-3912	497	3	j	j	X
ejpam-3912	497	4	>	>	PUNCT
ejpam-3912	497	5	n−	n−	NOUN
ejpam-3912	497	6	1	1	NUM
ejpam-3912	497	7	γe1	γe1	NOUN
ejpam-3912	497	8	,	,	PUNCT
ejpam-3912	497	9	i	i	PRON
ejpam-3912	497	10	=	=	NOUN
ejpam-3912	497	11	1	1	NUM
ejpam-3912	497	12	,	,	PUNCT
ejpam-3912	497	13	j	j	NOUN
ejpam-3912	498	1	=	=	PUNCT
ejpam-3912	498	2	n−	n−	PROPN
ejpam-3912	498	3	1	1	NUM
ejpam-3912	498	4	βe1	βe1	NOUN
ejpam-3912	498	5	,	,	PUNCT
ejpam-3912	498	6	i	i	PRON
ejpam-3912	498	7	=	=	NOUN
ejpam-3912	498	8	1	1	NUM
ejpam-3912	498	9	,	,	PUNCT
ejpam-3912	498	10	j	j	PROPN
ejpam-3912	499	1	=	=	PUNCT
ejpam-3912	499	2	n	n	PROPN
ejpam-3912	499	3	ϕ	ϕ	PROPN
ejpam-3912	499	4	(	(	PUNCT
ejpam-3912	499	5	e1	e1	PROPN
ejpam-3912	499	6	)	)	PUNCT
ejpam-3912	499	7	i	i	PROPN
ejpam-3912	499	8	,	,	PUNCT
ejpam-3912	499	9	n−1	n−1	PROPN
ejpam-3912	499	10	,	,	PUNCT
ejpam-3912	499	11	i	i	PRON
ejpam-3912	499	12	>	>	X
ejpam-3912	499	13	1	1	NUM
ejpam-3912	499	14	,	,	PUNCT
ejpam-3912	499	15	j	j	NOUN
ejpam-3912	499	16	=	=	PUNCT
ejpam-3912	499	17	n−	n−	PROPN
ejpam-3912	499	18	1	1	NUM
ejpam-3912	499	19	ϕ	ϕ	X
ejpam-3912	499	20	(	(	PUNCT
ejpam-3912	499	21	e1	e1	PROPN
ejpam-3912	499	22	)	)	PUNCT
ejpam-3912	499	23	in	in	ADP
ejpam-3912	499	24	,	,	PUNCT
ejpam-3912	499	25	i	i	PRON
ejpam-3912	499	26	>	>	X
ejpam-3912	499	27	1	1	NUM
ejpam-3912	499	28	,	,	PUNCT
ejpam-3912	499	29	j	j	PROPN
ejpam-3912	499	30	=	=	PUNCT
ejpam-3912	499	31	n	n	PROPN
ejpam-3912	499	32	se1	se1	NOUN
ejpam-3912	499	33	,	,	PUNCT
ejpam-3912	499	34	i	i	PRON
ejpam-3912	499	35	=	=	SYM
ejpam-3912	499	36	n	n	CCONJ
ejpam-3912	499	37	,	,	PUNCT
ejpam-3912	499	38	j	j	PROPN
ejpam-3912	499	39	=	=	PUNCT
ejpam-3912	499	40	n−	n−	NOUN
ejpam-3912	499	41	1	1	NUM
ejpam-3912	499	42	te1	te1	NOUN
ejpam-3912	499	43	,	,	PUNCT
ejpam-3912	499	44	i	i	PRON
ejpam-3912	499	45	=	=	SYM
ejpam-3912	499	46	n	n	CCONJ
ejpam-3912	499	47	,	,	PUNCT
ejpam-3912	499	48	j	j	PROPN
ejpam-3912	499	49	=	=	SYM
ejpam-3912	499	50	n	n	PROPN
ejpam-3912	499	51	0	0	NUM
ejpam-3912	499	52	,	,	PUNCT
ejpam-3912	499	53	otherwise	otherwise	ADV
ejpam-3912	499	54	.	.	PUNCT
ejpam-3912	500	1	thus	thus	ADV
ejpam-3912	500	2	,	,	PUNCT
ejpam-3912	500	3	theorem	theorem	VERB
ejpam-3912	500	4	6	6	NUM
ejpam-3912	500	5	implies	imply	VERB
ejpam-3912	500	6	that	that	SCONJ
ejpam-3912	500	7	the	the	DET
ejpam-3912	500	8	local	local	ADJ
ejpam-3912	500	9	automorphism	automorphism	NOUN
ejpam-3912	500	10	ψ	ψ	NOUN
ejpam-3912	500	11	is	be	AUX
ejpam-3912	500	12	an	an	DET
ejpam-3912	500	13	automorphism	automorphism	NOUN
ejpam-3912	500	14	.	.	PUNCT
ejpam-3912	501	1	the	the	DET
ejpam-3912	501	2	proof	proof	NOUN
ejpam-3912	501	3	is	be	AUX
ejpam-3912	501	4	complete	complete	ADJ
ejpam-3912	501	5	.	.	PUNCT
ejpam-3912	502	1	remark	remark	PROPN
ejpam-3912	502	2	4	4	NUM
ejpam-3912	502	3	.	.	PUNCT
ejpam-3912	503	1	in	in	ADP
ejpam-3912	503	2	[	[	X
ejpam-3912	503	3	25	25	NUM
ejpam-3912	503	4	]	]	PUNCT
ejpam-3912	503	5	,	,	PUNCT
ejpam-3912	503	6	it	it	PRON
ejpam-3912	503	7	was	be	AUX
ejpam-3912	503	8	proven	prove	VERB
ejpam-3912	503	9	that	that	SCONJ
ejpam-3912	503	10	if	if	SCONJ
ejpam-3912	503	11	n	n	PROPN
ejpam-3912	503	12	>	>	X
ejpam-3912	503	13	2	2	NUM
ejpam-3912	503	14	then	then	ADV
ejpam-3912	503	15	all	all	DET
ejpam-3912	503	16	local	local	ADJ
ejpam-3912	503	17	automorphism	automorphism	NOUN
ejpam-3912	503	18	is	be	AUX
ejpam-3912	503	19	automorphism	automorphism	NOUN
ejpam-3912	503	20	,	,	PUNCT
ejpam-3912	503	21	in	in	ADP
ejpam-3912	503	22	the	the	DET
ejpam-3912	503	23	above	above	ADJ
ejpam-3912	503	24	theorem	theorem	NOUN
ejpam-3912	503	25	we	we	PRON
ejpam-3912	503	26	find	find	VERB
ejpam-3912	503	27	that	that	SCONJ
ejpam-3912	503	28	if	if	SCONJ
ejpam-3912	503	29	n	n	PROPN
ejpam-3912	503	30	>	>	X
ejpam-3912	503	31	3	3	NUM
ejpam-3912	503	32	then	then	ADV
ejpam-3912	503	33	all	all	DET
ejpam-3912	503	34	local	local	ADJ
ejpam-3912	503	35	automorphism	automorphism	NOUN
ejpam-3912	503	36	is	be	AUX
ejpam-3912	503	37	automorphism	automorphism	NOUN
ejpam-3912	503	38	.	.	PUNCT
ejpam-3912	504	1	references	reference	NOUN
ejpam-3912	504	2	[	[	X
ejpam-3912	504	3	1	1	X
ejpam-3912	504	4	]	]	X
ejpam-3912	504	5	ahmad	ahmad	PROPN
ejpam-3912	504	6	alarafeen	alarafeen	PROPN
ejpam-3912	504	7	,	,	PUNCT
ejpam-3912	504	8	izzat	izzat	PROPN
ejpam-3912	504	9	qaralleh	qaralleh	NOUN
ejpam-3912	504	10	,	,	PUNCT
ejpam-3912	504	11	and	and	CCONJ
ejpam-3912	504	12	azhana	azhana	PROPN
ejpam-3912	504	13	ahmad	ahmad	PROPN
ejpam-3912	504	14	.	.	PUNCT
ejpam-3912	505	1	derivation	derivation	NOUN
ejpam-3912	505	2	of	of	ADP
ejpam-3912	505	3	five	five	NUM
ejpam-3912	505	4	-	-	PUNCT
ejpam-3912	505	5	dimensional	dimensional	ADJ
ejpam-3912	505	6	lotka	lotka	ADJ
ejpam-3912	505	7	-	-	PUNCT
ejpam-3912	505	8	voltera	voltera	NOUN
ejpam-3912	505	9	algebra	algebra	NOUN
ejpam-3912	505	10	.	.	PUNCT
ejpam-3912	506	1	arxiv	arxiv	PROPN
ejpam-3912	506	2	preprint	preprint	VERB
ejpam-3912	506	3	arxiv:1912.08594	arxiv:1912.08594	PROPN
ejpam-3912	506	4	,	,	PUNCT
ejpam-3912	506	5	2019	2019	NUM
ejpam-3912	506	6	.	.	PUNCT
ejpam-3912	507	1	[	[	X
ejpam-3912	507	2	2	2	X
ejpam-3912	507	3	]	]	PUNCT
ejpam-3912	507	4	abdelwahab	abdelwahab	NOUN
ejpam-3912	507	5	alsarayreh	alsarayreh	NOUN
ejpam-3912	507	6	,	,	PUNCT
ejpam-3912	507	7	izzat	izzat	PROPN
ejpam-3912	507	8	qaralleh	qaralleh	NOUN
ejpam-3912	507	9	,	,	PUNCT
ejpam-3912	507	10	and	and	CCONJ
ejpam-3912	507	11	muhammad	muhammad	PROPN
ejpam-3912	507	12	zaini	zaini	PROPN
ejpam-3912	507	13	ahmad	ahmad	PROPN
ejpam-3912	507	14	.	.	PUNCT
ejpam-3912	508	1	derivation	derivation	NOUN
ejpam-3912	508	2	of	of	ADP
ejpam-3912	508	3	three	three	NUM
ejpam-3912	508	4	-	-	PUNCT
ejpam-3912	508	5	dimensional	dimensional	ADJ
ejpam-3912	508	6	evolution	evolution	NOUN
ejpam-3912	508	7	algebra	algebra	NOUN
ejpam-3912	508	8	.	.	PUNCT
ejpam-3912	509	1	jp	jp	PROPN
ejpam-3912	509	2	j.	j.	PROPN
ejpam-3912	509	3	algebra	algebra	PROPN
ejpam-3912	509	4	number	number	NOUN
ejpam-3912	509	5	theory	theory	NOUN
ejpam-3912	509	6	appl	appl	NOUN
ejpam-3912	509	7	,	,	PUNCT
ejpam-3912	509	8	39:4	39:4	NUM
ejpam-3912	509	9	,	,	PUNCT
ejpam-3912	509	10	2017	2017	NUM
ejpam-3912	509	11	.	.	PUNCT
ejpam-3912	510	1	[	[	X
ejpam-3912	510	2	3	3	X
ejpam-3912	510	3	]	]	X
ejpam-3912	510	4	shavkat	shavkat	PROPN
ejpam-3912	510	5	ayupov	ayupov	PROPN
ejpam-3912	510	6	,	,	PUNCT
ejpam-3912	510	7	abror	abror	NOUN
ejpam-3912	510	8	khudoyberdiyev	khudoyberdiyev	PROPN
ejpam-3912	510	9	,	,	PUNCT
ejpam-3912	510	10	and	and	CCONJ
ejpam-3912	510	11	bakhtiyor	bakhtiyor	PROPN
ejpam-3912	510	12	yusupov	yusupov	NOUN
ejpam-3912	510	13	.	.	PUNCT
ejpam-3912	511	1	local	local	ADJ
ejpam-3912	511	2	and	and	CCONJ
ejpam-3912	511	3	2local	2local	ADJ
ejpam-3912	511	4	derivations	derivation	NOUN
ejpam-3912	511	5	of	of	ADP
ejpam-3912	511	6	solvable	solvable	ADJ
ejpam-3912	511	7	leibniz	leibniz	PROPN
ejpam-3912	511	8	algebras	algebras	PROPN
ejpam-3912	511	9	.	.	PUNCT
ejpam-3912	512	1	international	international	ADJ
ejpam-3912	512	2	journal	journal	PROPN
ejpam-3912	512	3	of	of	ADP
ejpam-3912	512	4	algebra	algebra	NOUN
ejpam-3912	512	5	and	and	CCONJ
ejpam-3912	512	6	computation	computation	NOUN
ejpam-3912	512	7	,	,	PUNCT
ejpam-3912	512	8	2020	2020	NUM
ejpam-3912	512	9	.	.	PUNCT
ejpam-3912	513	1	[	[	X
ejpam-3912	513	2	4	4	NUM
ejpam-3912	513	3	]	]	X
ejpam-3912	513	4	shavkat	shavkat	PROPN
ejpam-3912	513	5	ayupov	ayupov	PROPN
ejpam-3912	513	6	,	,	PUNCT
ejpam-3912	513	7	karimbergen	karimbergen	PROPN
ejpam-3912	513	8	kudaybergenov	kudaybergenov	PROPN
ejpam-3912	513	9	,	,	PUNCT
ejpam-3912	513	10	and	and	CCONJ
ejpam-3912	513	11	antonio	antonio	PROPN
ejpam-3912	513	12	m	m	PROPN
ejpam-3912	513	13	peralta	peralta	PROPN
ejpam-3912	513	14	.	.	PUNCT
ejpam-3912	514	1	a	a	DET
ejpam-3912	514	2	survey	survey	NOUN
ejpam-3912	514	3	on	on	ADP
ejpam-3912	514	4	local	local	ADJ
ejpam-3912	514	5	and	and	CCONJ
ejpam-3912	514	6	2	2	NUM
ejpam-3912	514	7	-	-	PUNCT
ejpam-3912	514	8	local	local	ADJ
ejpam-3912	514	9	derivations	derivation	NOUN
ejpam-3912	514	10	on	on	ADP
ejpam-3912	514	11	c∗-and	c∗-and	PROPN
ejpam-3912	514	12	von	von	PROPN
ejpam-3912	514	13	neumann	neumann	PROPN
ejpam-3912	514	14	algebras	algebras	PROPN
ejpam-3912	514	15	.	.	PUNCT
ejpam-3912	515	1	topics	topic	NOUN
ejpam-3912	515	2	in	in	ADP
ejpam-3912	515	3	functional	functional	ADJ
ejpam-3912	515	4	analysis	analysis	NOUN
ejpam-3912	515	5	and	and	CCONJ
ejpam-3912	515	6	algebra	algebra	NOUN
ejpam-3912	515	7	,	,	PUNCT
ejpam-3912	515	8	contemporary	contemporary	ADJ
ejpam-3912	515	9	mathematics	mathematic	NOUN
ejpam-3912	515	10	,	,	PUNCT
ejpam-3912	515	11	672:73–126	672:73–126	NOUN
ejpam-3912	515	12	,	,	PUNCT
ejpam-3912	515	13	2016	2016	NUM
ejpam-3912	515	14	.	.	PUNCT
ejpam-3912	516	1	[	[	X
ejpam-3912	516	2	5	5	NUM
ejpam-3912	516	3	]	]	PUNCT
ejpam-3912	516	4	julio	julio	PROPN
ejpam-3912	516	5	becerra	becerra	PROPN
ejpam-3912	516	6	,	,	PUNCT
ejpam-3912	516	7	maŕıa	maŕıa	ADV
ejpam-3912	516	8	beltrán	beltrán	NOUN
ejpam-3912	516	9	,	,	PUNCT
ejpam-3912	516	10	and	and	CCONJ
ejpam-3912	516	11	m	m	PROPN
ejpam-3912	516	12	velasco	velasco	PROPN
ejpam-3912	516	13	.	.	PUNCT
ejpam-3912	517	1	pulse	pulse	NOUN
ejpam-3912	517	2	processes	process	NOUN
ejpam-3912	517	3	in	in	ADP
ejpam-3912	517	4	networks	network	NOUN
ejpam-3912	517	5	and	and	CCONJ
ejpam-3912	517	6	evolution	evolution	NOUN
ejpam-3912	517	7	algebras	algebra	NOUN
ejpam-3912	517	8	.	.	PUNCT
ejpam-3912	518	1	mathematics	mathematic	NOUN
ejpam-3912	518	2	,	,	PUNCT
ejpam-3912	518	3	8(3):387	8(3):387	NUM
ejpam-3912	518	4	,	,	PUNCT
ejpam-3912	518	5	2020	2020	NUM
ejpam-3912	518	6	.	.	PUNCT
ejpam-3912	519	1	[	[	X
ejpam-3912	519	2	6	6	NUM
ejpam-3912	519	3	]	]	PUNCT
ejpam-3912	519	4	paula	paula	PROPN
ejpam-3912	519	5	cadavid	cadavid	PROPN
ejpam-3912	519	6	,	,	PUNCT
ejpam-3912	519	7	mary	mary	PROPN
ejpam-3912	519	8	luz	luz	PROPN
ejpam-3912	519	9	rodiño	rodiño	PROPN
ejpam-3912	519	10	montoya	montoya	PROPN
ejpam-3912	519	11	,	,	PUNCT
ejpam-3912	519	12	and	and	CCONJ
ejpam-3912	519	13	pablo	pablo	PROPN
ejpam-3912	519	14	m	m	PROPN
ejpam-3912	519	15	rodriguez	rodriguez	PROPN
ejpam-3912	519	16	.	.	PUNCT
ejpam-3912	520	1	the	the	DET
ejpam-3912	520	2	connection	connection	NOUN
ejpam-3912	520	3	between	between	ADP
ejpam-3912	520	4	evolution	evolution	NOUN
ejpam-3912	520	5	algebras	algebra	NOUN
ejpam-3912	520	6	,	,	PUNCT
ejpam-3912	520	7	random	random	ADJ
ejpam-3912	520	8	walks	walk	NOUN
ejpam-3912	520	9	and	and	CCONJ
ejpam-3912	520	10	graphs	graph	NOUN
ejpam-3912	520	11	.	.	PUNCT
ejpam-3912	521	1	journal	journal	NOUN
ejpam-3912	521	2	of	of	ADP
ejpam-3912	521	3	algebra	algebra	PROPN
ejpam-3912	521	4	and	and	CCONJ
ejpam-3912	521	5	its	its	PRON
ejpam-3912	521	6	applications	application	NOUN
ejpam-3912	521	7	,	,	PUNCT
ejpam-3912	521	8	19(02):2050023	19(02):2050023	NUM
ejpam-3912	521	9	,	,	PUNCT
ejpam-3912	521	10	2020	2020	NUM
ejpam-3912	521	11	.	.	PUNCT
ejpam-3912	522	1	[	[	X
ejpam-3912	522	2	7	7	X
ejpam-3912	522	3	]	]	X
ejpam-3912	522	4	lm	lm	NOUN
ejpam-3912	522	5	camacho	camacho	PROPN
ejpam-3912	522	6	,	,	PUNCT
ejpam-3912	522	7	jr	jr	PROPN
ejpam-3912	522	8	gómez	gómez	PROPN
ejpam-3912	522	9	,	,	PUNCT
ejpam-3912	522	10	ba	ba	PROPN
ejpam-3912	522	11	omirov	omirov	ADJ
ejpam-3912	522	12	,	,	PUNCT
ejpam-3912	522	13	and	and	CCONJ
ejpam-3912	522	14	rm	rm	PROPN
ejpam-3912	522	15	turdibaev	turdibaev	PROPN
ejpam-3912	522	16	.	.	PUNCT
ejpam-3912	523	1	the	the	DET
ejpam-3912	523	2	derivations	derivation	NOUN
ejpam-3912	523	3	of	of	ADP
ejpam-3912	523	4	some	some	DET
ejpam-3912	523	5	evolution	evolution	NOUN
ejpam-3912	523	6	algebras	algebra	NOUN
ejpam-3912	523	7	.	.	PUNCT
ejpam-3912	524	1	linear	linear	PROPN
ejpam-3912	524	2	and	and	CCONJ
ejpam-3912	524	3	multilinear	multilinear	PROPN
ejpam-3912	524	4	algebra	algebra	PROPN
ejpam-3912	524	5	,	,	PUNCT
ejpam-3912	524	6	61(3):309–322	61(3):309–322	PROPN
ejpam-3912	524	7	,	,	PUNCT
ejpam-3912	524	8	2013	2013	NUM
ejpam-3912	524	9	.	.	PUNCT
ejpam-3912	525	1	references	reference	NOUN
ejpam-3912	525	2	299	299	NUM
ejpam-3912	526	1	[	[	X
ejpam-3912	526	2	8	8	NUM
ejpam-3912	526	3	]	]	PUNCT
ejpam-3912	526	4	lm	lm	NOUN
ejpam-3912	526	5	camacho	camacho	PROPN
ejpam-3912	526	6	,	,	PUNCT
ejpam-3912	526	7	a	a	DET
ejpam-3912	526	8	kh	kh	PROPN
ejpam-3912	526	9	khudoyberdiyev	khudoyberdiyev	PROPN
ejpam-3912	526	10	,	,	PUNCT
ejpam-3912	526	11	and	and	CCONJ
ejpam-3912	526	12	ba	ba	PROPN
ejpam-3912	526	13	omirov	omirov	ADJ
ejpam-3912	526	14	.	.	PUNCT
ejpam-3912	527	1	on	on	ADP
ejpam-3912	527	2	the	the	DET
ejpam-3912	527	3	property	property	NOUN
ejpam-3912	527	4	of	of	ADP
ejpam-3912	527	5	subalgebras	subalgebra	NOUN
ejpam-3912	527	6	of	of	ADP
ejpam-3912	527	7	evolution	evolution	NOUN
ejpam-3912	527	8	algebras	algebras	PROPN
ejpam-3912	527	9	.	.	PUNCT
ejpam-3912	527	10	algebras	algebras	PROPN
ejpam-3912	527	11	and	and	CCONJ
ejpam-3912	527	12	representation	representation	NOUN
ejpam-3912	527	13	theory	theory	NOUN
ejpam-3912	527	14	,	,	PUNCT
ejpam-3912	527	15	22(2):281–296	22(2):281–296	NOUN
ejpam-3912	527	16	,	,	PUNCT
ejpam-3912	527	17	2019	2019	NUM
ejpam-3912	527	18	.	.	PUNCT
ejpam-3912	528	1	[	[	X
ejpam-3912	528	2	9	9	NUM
ejpam-3912	528	3	]	]	PUNCT
ejpam-3912	528	4	luisa	luisa	NOUN
ejpam-3912	528	5	maŕıa	maŕıa	ADP
ejpam-3912	528	6	camacho	camacho	PROPN
ejpam-3912	528	7	santana	santana	PROPN
ejpam-3912	528	8	,	,	PUNCT
ejpam-3912	528	9	josé	josé	ADJ
ejpam-3912	528	10	ramón	ramón	NOUN
ejpam-3912	528	11	gómez	gómez	NOUN
ejpam-3912	528	12	mart́ın	mart́ın	AUX
ejpam-3912	528	13	,	,	PUNCT
ejpam-3912	528	14	bakhrom	bakhrom	VERB
ejpam-3912	528	15	a	a	DET
ejpam-3912	528	16	omirov	omirov	ADJ
ejpam-3912	528	17	,	,	PUNCT
ejpam-3912	528	18	and	and	CCONJ
ejpam-3912	528	19	rm	rm	PROPN
ejpam-3912	528	20	turdibaev	turdibaev	PROPN
ejpam-3912	528	21	.	.	PUNCT
ejpam-3912	529	1	some	some	DET
ejpam-3912	529	2	properties	property	NOUN
ejpam-3912	529	3	of	of	ADP
ejpam-3912	529	4	evolution	evolution	NOUN
ejpam-3912	529	5	algebras	algebra	NOUN
ejpam-3912	529	6	.	.	PUNCT
ejpam-3912	529	7	bulletin	bulletin	NOUN
ejpam-3912	529	8	of	of	ADP
ejpam-3912	529	9	the	the	DET
ejpam-3912	529	10	korean	korean	PROPN
ejpam-3912	529	11	mathematical	mathematical	ADJ
ejpam-3912	529	12	society	society	NOUN
ejpam-3912	529	13	,	,	PUNCT
ejpam-3912	529	14	50	50	NUM
ejpam-3912	529	15	(	(	PUNCT
ejpam-3912	529	16	5	5	NUM
ejpam-3912	529	17	)	)	PUNCT
ejpam-3912	529	18	,	,	PUNCT
ejpam-3912	529	19	1481	1481	NUM
ejpam-3912	529	20	-	-	SYM
ejpam-3912	529	21	1494	1494	NUM
ejpam-3912	529	22	.	.	PUNCT
ejpam-3912	529	23	,	,	PUNCT
ejpam-3912	529	24	2013	2013	NUM
ejpam-3912	529	25	.	.	PUNCT
ejpam-3912	530	1	[	[	X
ejpam-3912	530	2	10	10	NUM
ejpam-3912	530	3	]	]	X
ejpam-3912	530	4	yolanda	yolanda	PROPN
ejpam-3912	530	5	cabrera	cabrera	PROPN
ejpam-3912	530	6	casado	casado	PROPN
ejpam-3912	530	7	,	,	PUNCT
ejpam-3912	530	8	mercedes	mercedes	PROPN
ejpam-3912	530	9	siles	siles	PROPN
ejpam-3912	530	10	molina	molina	PROPN
ejpam-3912	530	11	,	,	PUNCT
ejpam-3912	530	12	and	and	CCONJ
ejpam-3912	530	13	m	m	PROPN
ejpam-3912	530	14	victoria	victoria	PROPN
ejpam-3912	530	15	velasco	velasco	PROPN
ejpam-3912	530	16	.	.	PUNCT
ejpam-3912	531	1	classification	classification	NOUN
ejpam-3912	531	2	of	of	ADP
ejpam-3912	531	3	three	three	NUM
ejpam-3912	531	4	-	-	PUNCT
ejpam-3912	531	5	dimensional	dimensional	ADJ
ejpam-3912	531	6	evolution	evolution	NOUN
ejpam-3912	531	7	algebras	algebra	NOUN
ejpam-3912	531	8	.	.	PUNCT
ejpam-3912	532	1	linear	linear	PROPN
ejpam-3912	532	2	algebra	algebra	PROPN
ejpam-3912	532	3	and	and	CCONJ
ejpam-3912	532	4	its	its	PRON
ejpam-3912	532	5	applications	application	NOUN
ejpam-3912	532	6	,	,	PUNCT
ejpam-3912	532	7	524:68–108	524:68–108	NUM
ejpam-3912	532	8	,	,	PUNCT
ejpam-3912	532	9	2017	2017	NUM
ejpam-3912	532	10	.	.	PUNCT
ejpam-3912	533	1	[	[	X
ejpam-3912	533	2	11	11	NUM
ejpam-3912	533	3	]	]	X
ejpam-3912	533	4	jm	jm	PROPN
ejpam-3912	533	5	casas	casas	PROPN
ejpam-3912	533	6	,	,	PUNCT
ejpam-3912	533	7	m	m	PROPN
ejpam-3912	533	8	ladra	ladra	PROPN
ejpam-3912	533	9	,	,	PUNCT
ejpam-3912	533	10	ba	ba	PROPN
ejpam-3912	533	11	omirov	omirov	ADJ
ejpam-3912	533	12	,	,	PUNCT
ejpam-3912	533	13	and	and	CCONJ
ejpam-3912	533	14	ua	ua	PROPN
ejpam-3912	533	15	rozikov	rozikov	NOUN
ejpam-3912	533	16	.	.	PUNCT
ejpam-3912	534	1	index	index	NOUN
ejpam-3912	534	2	and	and	CCONJ
ejpam-3912	534	3	dibaricity	dibaricity	NOUN
ejpam-3912	534	4	of	of	ADP
ejpam-3912	534	5	evolution	evolution	NOUN
ejpam-3912	534	6	algebras	algebra	NOUN
ejpam-3912	534	7	.	.	PUNCT
ejpam-3912	535	1	linear	linear	PROPN
ejpam-3912	535	2	algebra	algebra	PROPN
ejpam-3912	535	3	and	and	CCONJ
ejpam-3912	535	4	its	its	PRON
ejpam-3912	535	5	applications	application	NOUN
ejpam-3912	535	6	,	,	PUNCT
ejpam-3912	535	7	439(1):90–105	439(1):90–105	PROPN
ejpam-3912	535	8	,	,	PUNCT
ejpam-3912	535	9	2013	2013	NUM
ejpam-3912	535	10	.	.	PUNCT
ejpam-3912	536	1	[	[	X
ejpam-3912	536	2	12	12	NUM
ejpam-3912	536	3	]	]	X
ejpam-3912	536	4	josé	josé	PROPN
ejpam-3912	536	5	m	m	PROPN
ejpam-3912	536	6	casas	casas	PROPN
ejpam-3912	536	7	,	,	PUNCT
ejpam-3912	536	8	manuel	manuel	PROPN
ejpam-3912	536	9	ladra	ladra	PROPN
ejpam-3912	536	10	,	,	PUNCT
ejpam-3912	536	11	bakhrom	bakhrom	VERB
ejpam-3912	536	12	a	a	DET
ejpam-3912	536	13	omirov	omirov	ADJ
ejpam-3912	536	14	,	,	PUNCT
ejpam-3912	536	15	and	and	CCONJ
ejpam-3912	536	16	utkir	utkir	VERB
ejpam-3912	536	17	a	a	DET
ejpam-3912	536	18	rozikov	rozikov	NOUN
ejpam-3912	536	19	.	.	PUNCT
ejpam-3912	537	1	on	on	ADP
ejpam-3912	537	2	evolution	evolution	NOUN
ejpam-3912	537	3	algebras	algebra	NOUN
ejpam-3912	537	4	.	.	PUNCT
ejpam-3912	538	1	in	in	ADP
ejpam-3912	538	2	algebra	algebra	PROPN
ejpam-3912	538	3	colloquium	colloquium	NOUN
ejpam-3912	538	4	,	,	PUNCT
ejpam-3912	538	5	volume	volume	NOUN
ejpam-3912	538	6	21	21	NUM
ejpam-3912	538	7	,	,	PUNCT
ejpam-3912	538	8	pages	page	NOUN
ejpam-3912	538	9	331–342	331–342	NUM
ejpam-3912	538	10	.	.	PUNCT
ejpam-3912	539	1	world	world	NOUN
ejpam-3912	539	2	scientific	scientific	PROPN
ejpam-3912	539	3	,	,	PUNCT
ejpam-3912	539	4	2014	2014	NUM
ejpam-3912	539	5	.	.	PUNCT
ejpam-3912	540	1	[	[	X
ejpam-3912	540	2	13	13	NUM
ejpam-3912	540	3	]	]	SYM
ejpam-3912	540	4	r	r	NOUN
ejpam-3912	540	5	costa	costa	PROPN
ejpam-3912	540	6	.	.	PUNCT
ejpam-3912	541	1	on	on	ADP
ejpam-3912	541	2	the	the	DET
ejpam-3912	541	3	derivation	derivation	NOUN
ejpam-3912	541	4	algebra	algebra	NOUN
ejpam-3912	541	5	of	of	ADP
ejpam-3912	541	6	zygotic	zygotic	ADJ
ejpam-3912	541	7	algebras	algebra	NOUN
ejpam-3912	541	8	for	for	ADP
ejpam-3912	541	9	polyploidy	polyploidy	ADJ
ejpam-3912	541	10	with	with	ADP
ejpam-3912	541	11	multiple	multiple	ADJ
ejpam-3912	541	12	alleles	allele	NOUN
ejpam-3912	541	13	.	.	PUNCT
ejpam-3912	542	1	boletim	boletim	PROPN
ejpam-3912	542	2	da	da	PROPN
ejpam-3912	542	3	sociedade	sociedade	PROPN
ejpam-3912	542	4	brasileira	brasileira	PROPN
ejpam-3912	542	5	de	de	PROPN
ejpam-3912	542	6	matemática	matemática	PROPN
ejpam-3912	542	7	-	-	PUNCT
ejpam-3912	542	8	bulletin	bulletin	ADJ
ejpam-3912	542	9	/	/	SYM
ejpam-3912	542	10	brazilian	brazilian	ADJ
ejpam-3912	542	11	mathematical	mathematical	ADJ
ejpam-3912	542	12	society	society	NOUN
ejpam-3912	542	13	,	,	PUNCT
ejpam-3912	542	14	14(1):63–80	14(1):63–80	NUM
ejpam-3912	542	15	,	,	PUNCT
ejpam-3912	542	16	1983	1983	NUM
ejpam-3912	542	17	.	.	PUNCT
ejpam-3912	543	1	[	[	X
ejpam-3912	543	2	14	14	NUM
ejpam-3912	543	3	]	]	X
ejpam-3912	543	4	hamza	hamza	PROPN
ejpam-3912	543	5	abd	abd	PROPN
ejpam-3912	543	6	el	el	PROPN
ejpam-3912	543	7	-	-	PUNCT
ejpam-3912	543	8	qader	qader	NOUN
ejpam-3912	543	9	,	,	PUNCT
ejpam-3912	543	10	ahmad	ahmad	PROPN
ejpam-3912	543	11	termimi	termimi	PROPN
ejpam-3912	543	12	ab	ab	PROPN
ejpam-3912	543	13	ghani	ghani	PROPN
ejpam-3912	543	14	,	,	PUNCT
ejpam-3912	543	15	and	and	CCONJ
ejpam-3912	543	16	izzat	izzat	PROPN
ejpam-3912	543	17	qaralleh	qaralleh	NOUN
ejpam-3912	543	18	.	.	PUNCT
ejpam-3912	544	1	on	on	ADP
ejpam-3912	544	2	evolution	evolution	NOUN
ejpam-3912	544	3	algebras	algebra	NOUN
ejpam-3912	544	4	and	and	CCONJ
ejpam-3912	544	5	their	their	PRON
ejpam-3912	544	6	derivations	derivation	NOUN
ejpam-3912	544	7	.	.	PUNCT
ejpam-3912	545	1	journal	journal	PROPN
ejpam-3912	545	2	of	of	ADP
ejpam-3912	545	3	mathematics	mathematics	PROPN
ejpam-3912	545	4	and	and	CCONJ
ejpam-3912	545	5	computer	computer	NOUN
ejpam-3912	545	6	scinces	scince	NOUN
ejpam-3912	545	7	,	,	PUNCT
ejpam-3912	545	8	21(3):213–230	21(3):213–230	NUM
ejpam-3912	545	9	,	,	PUNCT
ejpam-3912	545	10	2020	2020	NUM
ejpam-3912	545	11	.	.	PUNCT
ejpam-3912	546	1	[	[	X
ejpam-3912	546	2	15	15	NUM
ejpam-3912	546	3	]	]	X
ejpam-3912	546	4	alberto	alberto	NOUN
ejpam-3912	546	5	elduque	elduque	ADJ
ejpam-3912	546	6	and	and	CCONJ
ejpam-3912	546	7	alicia	alicia	PROPN
ejpam-3912	546	8	labra	labra	PROPN
ejpam-3912	546	9	.	.	PUNCT
ejpam-3912	547	1	on	on	ADP
ejpam-3912	547	2	nilpotent	nilpotent	ADJ
ejpam-3912	547	3	evolution	evolution	NOUN
ejpam-3912	547	4	algebras	algebra	NOUN
ejpam-3912	547	5	.	.	PUNCT
ejpam-3912	548	1	linear	linear	PROPN
ejpam-3912	548	2	algebra	algebra	PROPN
ejpam-3912	548	3	and	and	CCONJ
ejpam-3912	548	4	its	its	PRON
ejpam-3912	548	5	applications	application	NOUN
ejpam-3912	548	6	,	,	PUNCT
ejpam-3912	548	7	505:11–31	505:11–31	PROPN
ejpam-3912	548	8	,	,	PUNCT
ejpam-3912	548	9	2016	2016	NUM
ejpam-3912	548	10	.	.	PUNCT
ejpam-3912	549	1	[	[	X
ejpam-3912	549	2	16	16	NUM
ejpam-3912	549	3	]	]	X
ejpam-3912	549	4	rasul	rasul	PROPN
ejpam-3912	549	5	ganikhodzhaev	ganikhodzhaev	PROPN
ejpam-3912	549	6	,	,	PUNCT
ejpam-3912	549	7	farrukh	farrukh	PROPN
ejpam-3912	549	8	mukhamedov	mukhamedov	PROPN
ejpam-3912	549	9	,	,	PUNCT
ejpam-3912	549	10	abror	abror	NOUN
ejpam-3912	549	11	pirnapasov	pirnapasov	NOUN
ejpam-3912	549	12	,	,	PUNCT
ejpam-3912	549	13	and	and	CCONJ
ejpam-3912	549	14	izzat	izzat	PROPN
ejpam-3912	549	15	qaralleh	qaralleh	NOUN
ejpam-3912	549	16	.	.	PUNCT
ejpam-3912	550	1	genetic	genetic	ADJ
ejpam-3912	550	2	volterra	volterra	PROPN
ejpam-3912	550	3	algebras	algebra	NOUN
ejpam-3912	550	4	and	and	CCONJ
ejpam-3912	550	5	their	their	PRON
ejpam-3912	550	6	derivations	derivation	NOUN
ejpam-3912	550	7	.	.	PUNCT
ejpam-3912	551	1	communications	communication	NOUN
ejpam-3912	551	2	in	in	ADP
ejpam-3912	551	3	algebra	algebra	NOUN
ejpam-3912	551	4	,	,	PUNCT
ejpam-3912	551	5	46(3):1353–1366	46(3):1353–1366	NUM
ejpam-3912	551	6	,	,	PUNCT
ejpam-3912	551	7	2018	2018	NUM
ejpam-3912	551	8	.	.	PUNCT
ejpam-3912	552	1	[	[	X
ejpam-3912	552	2	17	17	NUM
ejpam-3912	552	3	]	]	X
ejpam-3912	552	4	harry	harry	PROPN
ejpam-3912	552	5	gonshor	gonshor	NOUN
ejpam-3912	552	6	.	.	PUNCT
ejpam-3912	553	1	derivations	derivation	NOUN
ejpam-3912	553	2	in	in	ADP
ejpam-3912	553	3	genetic	genetic	ADJ
ejpam-3912	553	4	algebras	algebra	NOUN
ejpam-3912	553	5	.	.	PUNCT
ejpam-3912	554	1	communications	communication	NOUN
ejpam-3912	554	2	in	in	ADP
ejpam-3912	554	3	algebra	algebra	NOUN
ejpam-3912	554	4	,	,	PUNCT
ejpam-3912	554	5	16(8):1525–1542	16(8):1525–1542	NUM
ejpam-3912	554	6	,	,	PUNCT
ejpam-3912	554	7	1988	1988	NUM
ejpam-3912	554	8	.	.	PUNCT
ejpam-3912	555	1	[	[	X
ejpam-3912	555	2	18	18	NUM
ejpam-3912	555	3	]	]	PUNCT
ejpam-3912	555	4	as	as	ADP
ejpam-3912	555	5	hegazi	hegazi	ADV
ejpam-3912	555	6	and	and	CCONJ
ejpam-3912	555	7	hani	hani	PROPN
ejpam-3912	555	8	abdelwahab	abdelwahab	PROPN
ejpam-3912	555	9	.	.	PUNCT
ejpam-3912	556	1	five	five	NUM
ejpam-3912	556	2	-	-	PUNCT
ejpam-3912	556	3	dimensional	dimensional	ADJ
ejpam-3912	556	4	nilpotent	nilpotent	ADJ
ejpam-3912	556	5	evolution	evolution	NOUN
ejpam-3912	556	6	algebras	algebras	PROPN
ejpam-3912	556	7	.	.	PUNCT
ejpam-3912	557	1	arxiv	arxiv	PROPN
ejpam-3912	557	2	preprint	preprint	PROPN
ejpam-3912	557	3	arxiv:1508.07442	arxiv:1508.07442	NOUN
ejpam-3912	557	4	,	,	PUNCT
ejpam-3912	557	5	2015	2015	NUM
ejpam-3912	557	6	.	.	PUNCT
ejpam-3912	558	1	[	[	X
ejpam-3912	558	2	19	19	NUM
ejpam-3912	558	3	]	]	PUNCT
ejpam-3912	558	4	as	as	ADP
ejpam-3912	558	5	hegazi	hegazi	ADV
ejpam-3912	558	6	and	and	CCONJ
ejpam-3912	558	7	hani	hani	PROPN
ejpam-3912	558	8	abdelwahab	abdelwahab	PROPN
ejpam-3912	558	9	.	.	PUNCT
ejpam-3912	559	1	nilpotent	nilpotent	ADJ
ejpam-3912	559	2	evolution	evolution	NOUN
ejpam-3912	559	3	algebras	algebras	PROPN
ejpam-3912	559	4	over	over	ADP
ejpam-3912	559	5	arbitrary	arbitrary	ADJ
ejpam-3912	559	6	fields	field	NOUN
ejpam-3912	559	7	.	.	PUNCT
ejpam-3912	560	1	linear	linear	ADJ
ejpam-3912	560	2	algebra	algebra	NOUN
ejpam-3912	560	3	and	and	CCONJ
ejpam-3912	560	4	its	its	PRON
ejpam-3912	560	5	applications	application	NOUN
ejpam-3912	560	6	,	,	PUNCT
ejpam-3912	560	7	486:345–360	486:345–360	NUM
ejpam-3912	560	8	,	,	PUNCT
ejpam-3912	560	9	2015	2015	NUM
ejpam-3912	560	10	.	.	PUNCT
ejpam-3912	561	1	[	[	X
ejpam-3912	561	2	20	20	NUM
ejpam-3912	561	3	]	]	X
ejpam-3912	561	4	p	p	X
ejpam-3912	561	5	holgate	holgate	PROPN
ejpam-3912	561	6	.	.	PUNCT
ejpam-3912	562	1	the	the	DET
ejpam-3912	562	2	interpretation	interpretation	NOUN
ejpam-3912	562	3	of	of	ADP
ejpam-3912	562	4	derivations	derivation	NOUN
ejpam-3912	562	5	in	in	ADP
ejpam-3912	562	6	genetic	genetic	ADJ
ejpam-3912	562	7	algebras	algebra	NOUN
ejpam-3912	562	8	.	.	PUNCT
ejpam-3912	563	1	linear	linear	PROPN
ejpam-3912	563	2	algebra	algebra	PROPN
ejpam-3912	563	3	and	and	CCONJ
ejpam-3912	563	4	its	its	PRON
ejpam-3912	563	5	applications	application	NOUN
ejpam-3912	563	6	,	,	PUNCT
ejpam-3912	563	7	85:75–79	85:75–79	NUM
ejpam-3912	563	8	,	,	PUNCT
ejpam-3912	563	9	1987	1987	NUM
ejpam-3912	563	10	.	.	PUNCT
ejpam-3912	564	1	[	[	X
ejpam-3912	564	2	21	21	NUM
ejpam-3912	564	3	]	]	X
ejpam-3912	564	4	nathan	nathan	PROPN
ejpam-3912	564	5	jacobson	jacobson	PROPN
ejpam-3912	564	6	.	.	PUNCT
ejpam-3912	565	1	a	a	DET
ejpam-3912	565	2	note	note	NOUN
ejpam-3912	565	3	on	on	ADP
ejpam-3912	565	4	automorphisms	automorphism	NOUN
ejpam-3912	565	5	and	and	CCONJ
ejpam-3912	565	6	derivations	derivation	NOUN
ejpam-3912	565	7	of	of	ADP
ejpam-3912	565	8	lie	lie	NOUN
ejpam-3912	565	9	algebras	algebra	NOUN
ejpam-3912	565	10	.	.	PUNCT
ejpam-3912	566	1	in	in	ADP
ejpam-3912	566	2	nathan	nathan	PROPN
ejpam-3912	566	3	jacobson	jacobson	PROPN
ejpam-3912	566	4	collected	collect	VERB
ejpam-3912	566	5	mathematical	mathematical	ADJ
ejpam-3912	566	6	papers	paper	NOUN
ejpam-3912	566	7	,	,	PUNCT
ejpam-3912	566	8	pages	page	NOUN
ejpam-3912	566	9	251–253	251–253	NUM
ejpam-3912	566	10	.	.	PUNCT
ejpam-3912	566	11	springer	springer	NOUN
ejpam-3912	566	12	,	,	PUNCT
ejpam-3912	566	13	1989	1989	NUM
ejpam-3912	566	14	.	.	PUNCT
ejpam-3912	567	1	references	reference	NOUN
ejpam-3912	567	2	300	300	NUM
ejpam-3912	567	3	[	[	X
ejpam-3912	567	4	22	22	NUM
ejpam-3912	567	5	]	]	PUNCT
ejpam-3912	567	6	richard	richard	PROPN
ejpam-3912	567	7	v	v	PROPN
ejpam-3912	567	8	kadison	kadison	PROPN
ejpam-3912	567	9	.	.	PUNCT
ejpam-3912	568	1	local	local	ADJ
ejpam-3912	568	2	derivations	derivation	NOUN
ejpam-3912	568	3	.	.	PUNCT
ejpam-3912	569	1	journal	journal	PROPN
ejpam-3912	569	2	of	of	ADP
ejpam-3912	569	3	algebra	algebra	PROPN
ejpam-3912	569	4	,	,	PUNCT
ejpam-3912	569	5	130(2):494–509	130(2):494–509	NUM
ejpam-3912	569	6	,	,	PUNCT
ejpam-3912	569	7	1990	1990	NUM
ejpam-3912	569	8	.	.	PUNCT
ejpam-3912	570	1	[	[	X
ejpam-3912	570	2	23	23	NUM
ejpam-3912	570	3	]	]	PUNCT
ejpam-3912	570	4	a	a	DET
ejpam-3912	570	5	kh	kh	PROPN
ejpam-3912	570	6	khudoyberdiyev	khudoyberdiyev	PROPN
ejpam-3912	570	7	,	,	PUNCT
ejpam-3912	570	8	bakhrom	bakhrom	VERB
ejpam-3912	570	9	a	a	DET
ejpam-3912	570	10	omirov	omirov	ADJ
ejpam-3912	570	11	,	,	PUNCT
ejpam-3912	570	12	and	and	CCONJ
ejpam-3912	570	13	izzat	izzat	PROPN
ejpam-3912	570	14	qaralleh	qaralleh	NOUN
ejpam-3912	570	15	.	.	PUNCT
ejpam-3912	571	1	few	few	ADJ
ejpam-3912	571	2	remarks	remark	NOUN
ejpam-3912	571	3	on	on	ADP
ejpam-3912	571	4	evolution	evolution	NOUN
ejpam-3912	571	5	algebras	algebras	PROPN
ejpam-3912	571	6	.	.	PUNCT
ejpam-3912	571	7	journal	journal	PROPN
ejpam-3912	571	8	of	of	ADP
ejpam-3912	571	9	algebra	algebra	PROPN
ejpam-3912	571	10	and	and	CCONJ
ejpam-3912	571	11	its	its	PRON
ejpam-3912	571	12	applications	application	NOUN
ejpam-3912	571	13	,	,	PUNCT
ejpam-3912	571	14	14(04):1550053	14(04):1550053	NUM
ejpam-3912	571	15	,	,	PUNCT
ejpam-3912	571	16	2015	2015	NUM
ejpam-3912	571	17	.	.	PUNCT
ejpam-3912	572	1	[	[	X
ejpam-3912	572	2	24	24	NUM
ejpam-3912	572	3	]	]	X
ejpam-3912	572	4	d.	d.	PROPN
ejpam-3912	572	5	r.	r.	PROPN
ejpam-3912	572	6	larson	larson	PROPN
ejpam-3912	572	7	and	and	CCONJ
ejpam-3912	572	8	a.	a.	PROPN
ejpam-3912	572	9	r.	r.	PROPN
ejpam-3912	572	10	sourour	sourour	PROPN
ejpam-3912	572	11	.	.	PUNCT
ejpam-3912	573	1	local	local	ADJ
ejpam-3912	573	2	derivations	derivation	NOUN
ejpam-3912	573	3	and	and	CCONJ
ejpam-3912	573	4	local	local	ADJ
ejpam-3912	573	5	automorphisms	automorphism	NOUN
ejpam-3912	573	6	of	of	ADP
ejpam-3912	573	7	b(x	b(x	NOUN
ejpam-3912	573	8	)	)	PUNCT
ejpam-3912	573	9	.	.	PUNCT
ejpam-3912	574	1	in	in	ADP
ejpam-3912	574	2	proc	proc	PROPN
ejpam-3912	574	3	.	.	PUNCT
ejpam-3912	575	1	sympos	sympos	PROPN
ejpam-3912	575	2	.	.	PUNCT
ejpam-3912	576	1	pure	pure	ADJ
ejpam-3912	576	2	math	math	NOUN
ejpam-3912	576	3	.	.	PUNCT
ejpam-3912	577	1	51	51	NUM
ejpam-3912	577	2	,	,	PUNCT
ejpam-3912	577	3	pages	page	NOUN
ejpam-3912	577	4	187–194	187–194	NUM
ejpam-3912	577	5	.	.	PUNCT
ejpam-3912	578	1	american	american	PROPN
ejpam-3912	578	2	mathematical	mathematical	PROPN
ejpam-3912	578	3	society	society	NOUN
ejpam-3912	578	4	,	,	PUNCT
ejpam-3912	578	5	1990	1990	NUM
ejpam-3912	578	6	.	.	PUNCT
ejpam-3912	579	1	[	[	X
ejpam-3912	579	2	25	25	NUM
ejpam-3912	579	3	]	]	X
ejpam-3912	579	4	farrukh	farrukh	PROPN
ejpam-3912	579	5	mukhamedov	mukhamedov	PROPN
ejpam-3912	579	6	,	,	PUNCT
ejpam-3912	579	7	otabek	otabek	PROPN
ejpam-3912	579	8	khakimov	khakimov	PROPN
ejpam-3912	579	9	,	,	PUNCT
ejpam-3912	579	10	bakhrom	bakhrom	NOUN
ejpam-3912	579	11	omirov	omirov	ADJ
ejpam-3912	579	12	,	,	PUNCT
ejpam-3912	579	13	and	and	CCONJ
ejpam-3912	579	14	izzat	izzat	PROPN
ejpam-3912	579	15	qaralleh	qaralleh	NOUN
ejpam-3912	579	16	.	.	PUNCT
ejpam-3912	580	1	derivations	derivation	NOUN
ejpam-3912	580	2	and	and	CCONJ
ejpam-3912	580	3	automorphisms	automorphism	NOUN
ejpam-3912	580	4	of	of	ADP
ejpam-3912	580	5	nilpotent	nilpotent	ADJ
ejpam-3912	580	6	evolution	evolution	NOUN
ejpam-3912	580	7	algebras	algebra	NOUN
ejpam-3912	580	8	with	with	ADP
ejpam-3912	580	9	maximal	maximal	ADJ
ejpam-3912	580	10	nilindex	nilindex	NOUN
ejpam-3912	580	11	.	.	PUNCT
ejpam-3912	581	1	journal	journal	PROPN
ejpam-3912	581	2	of	of	ADP
ejpam-3912	581	3	algebra	algebra	PROPN
ejpam-3912	581	4	and	and	CCONJ
ejpam-3912	581	5	its	its	PRON
ejpam-3912	581	6	applications	application	NOUN
ejpam-3912	581	7	,	,	PUNCT
ejpam-3912	581	8	18(12):1950233	18(12):1950233	NUM
ejpam-3912	581	9	,	,	PUNCT
ejpam-3912	581	10	2019	2019	NUM
ejpam-3912	581	11	.	.	PUNCT
ejpam-3912	582	1	[	[	X
ejpam-3912	582	2	26	26	NUM
ejpam-3912	582	3	]	]	X
ejpam-3912	582	4	farrukh	farrukh	PROPN
ejpam-3912	582	5	mukhamedov	mukhamedov	PROPN
ejpam-3912	582	6	,	,	PUNCT
ejpam-3912	582	7	otabek	otabek	PROPN
ejpam-3912	582	8	khakimov	khakimov	PROPN
ejpam-3912	582	9	,	,	PUNCT
ejpam-3912	582	10	and	and	CCONJ
ejpam-3912	582	11	izzat	izzat	PROPN
ejpam-3912	582	12	qaralleh	qaralleh	NOUN
ejpam-3912	582	13	.	.	PUNCT
ejpam-3912	583	1	classification	classification	NOUN
ejpam-3912	583	2	of	of	ADP
ejpam-3912	583	3	nilpotent	nilpotent	ADJ
ejpam-3912	583	4	evolution	evolution	NOUN
ejpam-3912	583	5	algebras	algebra	NOUN
ejpam-3912	583	6	and	and	CCONJ
ejpam-3912	583	7	extensions	extension	NOUN
ejpam-3912	583	8	of	of	ADP
ejpam-3912	583	9	their	their	PRON
ejpam-3912	583	10	derivations	derivation	NOUN
ejpam-3912	583	11	.	.	PUNCT
ejpam-3912	584	1	communications	communication	NOUN
ejpam-3912	584	2	in	in	ADP
ejpam-3912	584	3	algebra	algebra	NOUN
ejpam-3912	584	4	,	,	PUNCT
ejpam-3912	584	5	pages	page	NOUN
ejpam-3912	584	6	1–15	1–15	NUM
ejpam-3912	584	7	,	,	PUNCT
ejpam-3912	584	8	2020	2020	NUM
ejpam-3912	584	9	.	.	PUNCT
ejpam-3912	585	1	[	[	X
ejpam-3912	585	2	27	27	NUM
ejpam-3912	585	3	]	]	X
ejpam-3912	585	4	farrukh	farrukh	PROPN
ejpam-3912	585	5	mukhamedov	mukhamedov	PROPN
ejpam-3912	585	6	,	,	PUNCT
ejpam-3912	585	7	bakhrom	bakhrom	NOUN
ejpam-3912	585	8	omirov	omirov	ADJ
ejpam-3912	585	9	,	,	PUNCT
ejpam-3912	585	10	and	and	CCONJ
ejpam-3912	585	11	izzat	izzat	PROPN
ejpam-3912	585	12	qaralleh	qaralleh	NOUN
ejpam-3912	585	13	.	.	PUNCT
ejpam-3912	586	1	description	description	NOUN
ejpam-3912	586	2	of	of	ADP
ejpam-3912	586	3	three	three	NUM
ejpam-3912	586	4	dimensional	dimensional	ADJ
ejpam-3912	586	5	solvable	solvable	ADJ
ejpam-3912	586	6	evaluation	evaluation	NOUN
ejpam-3912	586	7	algebras	algebra	NOUN
ejpam-3912	586	8	.	.	PUNCT
ejpam-3912	587	1	in	in	ADP
ejpam-3912	587	2	international	international	ADJ
ejpam-3912	587	3	conference	conference	NOUN
ejpam-3912	587	4	on	on	ADP
ejpam-3912	587	5	mathematical	mathematical	ADJ
ejpam-3912	587	6	sciences	science	NOUN
ejpam-3912	587	7	and	and	CCONJ
ejpam-3912	587	8	statistics	statistic	NOUN
ejpam-3912	587	9	2013	2013	NUM
ejpam-3912	587	10	,	,	PUNCT
ejpam-3912	587	11	pages	page	NOUN
ejpam-3912	587	12	165–174	165–174	NUM
ejpam-3912	587	13	.	.	PUNCT
ejpam-3912	587	14	springer	springer	NOUN
ejpam-3912	587	15	,	,	PUNCT
ejpam-3912	587	16	2014	2014	NUM
ejpam-3912	587	17	.	.	PUNCT
ejpam-3912	588	1	[	[	X
ejpam-3912	588	2	28	28	NUM
ejpam-3912	588	3	]	]	X
ejpam-3912	588	4	farrukh	farrukh	PROPN
ejpam-3912	588	5	mukhamedov	mukhamedov	PROPN
ejpam-3912	588	6	and	and	CCONJ
ejpam-3912	588	7	izzat	izzat	PROPN
ejpam-3912	588	8	qaralleh	qaralleh	NOUN
ejpam-3912	588	9	.	.	PUNCT
ejpam-3912	589	1	on	on	ADP
ejpam-3912	589	2	derivations	derivation	NOUN
ejpam-3912	589	3	of	of	ADP
ejpam-3912	589	4	genetic	genetic	ADJ
ejpam-3912	589	5	algebras	algebra	NOUN
ejpam-3912	589	6	.	.	PUNCT
ejpam-3912	590	1	in	in	ADP
ejpam-3912	590	2	journal	journal	PROPN
ejpam-3912	590	3	of	of	ADP
ejpam-3912	590	4	physics	physics	PROPN
ejpam-3912	590	5	:	:	PUNCT
ejpam-3912	590	6	conference	conference	NOUN
ejpam-3912	590	7	series	series	NOUN
ejpam-3912	590	8	,	,	PUNCT
ejpam-3912	590	9	volume	volume	NOUN
ejpam-3912	590	10	553	553	NUM
ejpam-3912	590	11	,	,	PUNCT
ejpam-3912	590	12	2014	2014	NUM
ejpam-3912	590	13	.	.	PUNCT
ejpam-3912	591	1	[	[	X
ejpam-3912	591	2	29	29	NUM
ejpam-3912	591	3	]	]	X
ejpam-3912	591	4	farrukh	farrukh	PROPN
ejpam-3912	591	5	mukhamedov	mukhamedov	PROPN
ejpam-3912	591	6	,	,	PUNCT
ejpam-3912	591	7	izzat	izzat	PROPN
ejpam-3912	591	8	qaralleh	qaralleh	NOUN
ejpam-3912	591	9	,	,	PUNCT
ejpam-3912	591	10	and	and	CCONJ
ejpam-3912	591	11	abror	abror	NOUN
ejpam-3912	591	12	pirnapasov	pirnapasov	NOUN
ejpam-3912	591	13	.	.	PUNCT
ejpam-3912	592	1	on	on	ADP
ejpam-3912	592	2	genetic	genetic	ADJ
ejpam-3912	592	3	and	and	CCONJ
ejpam-3912	592	4	evolution	evolution	NOUN
ejpam-3912	592	5	algebras	algebra	NOUN
ejpam-3912	592	6	in	in	ADP
ejpam-3912	592	7	dimension	dimension	NOUN
ejpam-3912	592	8	three	three	NUM
ejpam-3912	592	9	.	.	PUNCT
ejpam-3912	593	1	international	international	ADJ
ejpam-3912	593	2	journal	journal	NOUN
ejpam-3912	593	3	of	of	ADP
ejpam-3912	593	4	algebra	algebra	PROPN
ejpam-3912	593	5	,	,	PUNCT
ejpam-3912	593	6	10(7):327–334	10(7):327–334	PROPN
ejpam-3912	593	7	,	,	PUNCT
ejpam-3912	593	8	2016	2016	NUM
ejpam-3912	593	9	.	.	PUNCT
ejpam-3912	594	1	[	[	X
ejpam-3912	594	2	30	30	NUM
ejpam-3912	594	3	]	]	X
ejpam-3912	594	4	izzat	izzat	PROPN
ejpam-3912	594	5	qaralleh	qaralleh	NOUN
ejpam-3912	594	6	.	.	PUNCT
ejpam-3912	595	1	a	a	DET
ejpam-3912	595	2	description	description	NOUN
ejpam-3912	595	3	of	of	ADP
ejpam-3912	595	4	derivations	derivation	NOUN
ejpam-3912	595	5	of	of	ADP
ejpam-3912	595	6	a	a	DET
ejpam-3912	595	7	class	class	NOUN
ejpam-3912	595	8	of	of	ADP
ejpam-3912	595	9	nilpotent	nilpotent	ADJ
ejpam-3912	595	10	evolution	evolution	NOUN
ejpam-3912	595	11	algebras	algebra	NOUN
ejpam-3912	595	12	.	.	PUNCT
ejpam-3912	595	13	14(2):295–304	14(2):295–304	NUM
ejpam-3912	595	14	,	,	PUNCT
ejpam-3912	595	15	2020	2020	NUM
ejpam-3912	595	16	.	.	PUNCT
ejpam-3912	596	1	[	[	X
ejpam-3912	596	2	31	31	NUM
ejpam-3912	596	3	]	]	X
ejpam-3912	596	4	izzat	izzat	PROPN
ejpam-3912	596	5	qaralleh	qaralleh	PROPN
ejpam-3912	596	6	and	and	CCONJ
ejpam-3912	596	7	farrukh	farrukh	PROPN
ejpam-3912	596	8	mukhamedov	mukhamedov	PROPN
ejpam-3912	596	9	.	.	PUNCT
ejpam-3912	597	1	volterra	volterra	PROPN
ejpam-3912	597	2	evolution	evolution	PROPN
ejpam-3912	597	3	algebras	algebra	NOUN
ejpam-3912	597	4	and	and	CCONJ
ejpam-3912	597	5	their	their	PRON
ejpam-3912	597	6	graphs	graph	NOUN
ejpam-3912	597	7	.	.	PUNCT
ejpam-3912	598	1	linear	linear	ADJ
ejpam-3912	598	2	and	and	CCONJ
ejpam-3912	598	3	multilinear	multilinear	PROPN
ejpam-3912	598	4	algebra	algebra	PROPN
ejpam-3912	598	5	,	,	PUNCT
ejpam-3912	598	6	pages	page	NOUN
ejpam-3912	598	7	1–17	1–17	PROPN
ejpam-3912	598	8	,	,	PUNCT
ejpam-3912	598	9	2019	2019	NUM
ejpam-3912	598	10	.	.	PUNCT
ejpam-3912	599	1	[	[	X
ejpam-3912	599	2	32	32	NUM
ejpam-3912	599	3	]	]	X
ejpam-3912	599	4	peter	peter	PROPN
ejpam-3912	599	5	šemrl	šemrl	PROPN
ejpam-3912	599	6	.	.	PUNCT
ejpam-3912	600	1	local	local	ADJ
ejpam-3912	600	2	automorphisms	automorphism	NOUN
ejpam-3912	600	3	and	and	CCONJ
ejpam-3912	600	4	derivations	derivation	NOUN
ejpam-3912	600	5	on	on	ADP
ejpam-3912	600	6	b(h	b(h	NOUN
ejpam-3912	600	7	)	)	PUNCT
ejpam-3912	600	8	.	.	PUNCT
ejpam-3912	601	1	proceedings	proceeding	NOUN
ejpam-3912	601	2	of	of	ADP
ejpam-3912	601	3	the	the	DET
ejpam-3912	601	4	american	american	PROPN
ejpam-3912	601	5	mathematical	mathematical	PROPN
ejpam-3912	601	6	society	society	NOUN
ejpam-3912	601	7	,	,	PUNCT
ejpam-3912	601	8	125(9):2677–2680	125(9):2677–2680	NUM
ejpam-3912	601	9	,	,	PUNCT
ejpam-3912	601	10	1997	1997	NUM
ejpam-3912	601	11	.	.	PUNCT
ejpam-3912	602	1	[	[	X
ejpam-3912	602	2	33	33	NUM
ejpam-3912	602	3	]	]	X
ejpam-3912	602	4	jianjun	jianjun	PROPN
ejpam-3912	602	5	paul	paul	PROPN
ejpam-3912	602	6	tian	tian	PROPN
ejpam-3912	602	7	.	.	PUNCT
ejpam-3912	603	1	evolution	evolution	PROPN
ejpam-3912	603	2	algebras	algebra	NOUN
ejpam-3912	603	3	and	and	CCONJ
ejpam-3912	603	4	their	their	PRON
ejpam-3912	603	5	applications	application	NOUN
ejpam-3912	603	6	.	.	PUNCT
ejpam-3912	604	1	springer	springer	NOUN
ejpam-3912	604	2	,	,	PUNCT
ejpam-3912	604	3	2007	2007	NUM
ejpam-3912	604	4	.	.	PUNCT
ejpam-3912	605	1	[	[	X
ejpam-3912	605	2	34	34	NUM
ejpam-3912	605	3	]	]	X
ejpam-3912	605	4	jianjun	jianjun	PROPN
ejpam-3912	605	5	-	-	PUNCT
ejpam-3912	605	6	paul	paul	PROPN
ejpam-3912	605	7	tian	tian	PROPN
ejpam-3912	605	8	and	and	CCONJ
ejpam-3912	605	9	piotr	piotr	PROPN
ejpam-3912	605	10	vojtĕchovskỳ.	vojtĕchovskỳ.	NUM
ejpam-3912	605	11	mathematical	mathematical	ADJ
ejpam-3912	605	12	concepts	concept	NOUN
ejpam-3912	605	13	of	of	ADP
ejpam-3912	605	14	evolution	evolution	NOUN
ejpam-3912	605	15	algebras	algebra	NOUN
ejpam-3912	605	16	in	in	ADP
ejpam-3912	605	17	non	non	ADJ
ejpam-3912	605	18	-	-	ADJ
ejpam-3912	605	19	mendelian	mendelian	ADJ
ejpam-3912	605	20	genetics	genetic	NOUN
ejpam-3912	605	21	.	.	PUNCT
ejpam-3912	606	1	quasigroups	quasigroup	NOUN
ejpam-3912	606	2	and	and	CCONJ
ejpam-3912	606	3	related	related	ADJ
ejpam-3912	606	4	systems	system	NOUN
ejpam-3912	606	5	,	,	PUNCT
ejpam-3912	606	6	14(1):111–122	14(1):111–122	NUM
ejpam-3912	606	7	,	,	PUNCT
ejpam-3912	606	8	2006	2006	NUM
ejpam-3912	606	9	.	.	PUNCT