id	sid	tid	token	lemma	pos
ejpam-5626	1	1	european	european	PROPN
ejpam-5626	1	2	journal	journal	PROPN
ejpam-5626	1	3	of	of	ADP
ejpam-5626	1	4	pure	pure	ADJ
ejpam-5626	1	5	and	and	CCONJ
ejpam-5626	1	6	applied	applied	ADJ
ejpam-5626	1	7	mathematics	mathematic	NOUN
ejpam-5626	1	8	2025	2025	NUM
ejpam-5626	1	9	,	,	PUNCT
ejpam-5626	1	10	vol	vol	NOUN
ejpam-5626	1	11	.	.	PROPN
ejpam-5626	1	12	18	18	NUM
ejpam-5626	1	13	,	,	PUNCT
ejpam-5626	1	14	issue	issue	NOUN
ejpam-5626	1	15	1	1	NUM
ejpam-5626	1	16	,	,	PUNCT
ejpam-5626	1	17	article	article	NOUN
ejpam-5626	1	18	number	number	NOUN
ejpam-5626	1	19	5626	5626	NUM
ejpam-5626	1	20	issn	issn	PROPN
ejpam-5626	1	21	1307	1307	NUM
ejpam-5626	1	22	-	-	SYM
ejpam-5626	1	23	5543	5543	NUM
ejpam-5626	1	24	–	–	PUNCT
ejpam-5626	1	25	ejpam.com	ejpam.com	X
ejpam-5626	1	26	published	publish	VERB
ejpam-5626	1	27	by	by	ADP
ejpam-5626	1	28	new	new	PROPN
ejpam-5626	1	29	york	york	PROPN
ejpam-5626	1	30	business	business	PROPN
ejpam-5626	1	31	global	global	PROPN
ejpam-5626	1	32	a	a	DET
ejpam-5626	1	33	note	note	NOUN
ejpam-5626	1	34	on	on	ADP
ejpam-5626	1	35	nonlinear	nonlinear	ADJ
ejpam-5626	1	36	mixed	mixed	ADJ
ejpam-5626	1	37	(	(	PUNCT
ejpam-5626	1	38	bi	bi	NOUN
ejpam-5626	1	39	-	-	NOUN
ejpam-5626	1	40	skew	skew	ADJ
ejpam-5626	1	41	,	,	PUNCT
ejpam-5626	1	42	skew	skew	ADJ
ejpam-5626	1	43	lie	lie	NOUN
ejpam-5626	1	44	)	)	PUNCT
ejpam-5626	1	45	triple	triple	ADJ
ejpam-5626	1	46	derivations	derivation	NOUN
ejpam-5626	1	47	on	on	ADP
ejpam-5626	1	48	∗-algebras	∗-algebras	PROPN
ejpam-5626	1	49	m.	m.	PROPN
ejpam-5626	1	50	arif	arif	PROPN
ejpam-5626	1	51	raza1	raza1	PROPN
ejpam-5626	1	52	,	,	PUNCT
ejpam-5626	1	53	junaid	junaid	VERB
ejpam-5626	1	54	nisar2,∗	nisar2,∗	PROPN
ejpam-5626	1	55	,	,	PUNCT
ejpam-5626	1	56	nadeem	nadeem	PROPN
ejpam-5626	1	57	ur	ur	INTJ
ejpam-5626	1	58	rehman3	rehman3	PROPN
ejpam-5626	1	59	,	,	PUNCT
ejpam-5626	1	60	vahid	vahid	PROPN
ejpam-5626	1	61	darvish4	darvish4	PROPN
ejpam-5626	1	62	1	1	NUM
ejpam-5626	1	63	department	department	NOUN
ejpam-5626	1	64	of	of	ADP
ejpam-5626	1	65	mathematics	mathematic	NOUN
ejpam-5626	1	66	,	,	PUNCT
ejpam-5626	1	67	faculty	faculty	NOUN
ejpam-5626	1	68	of	of	ADP
ejpam-5626	1	69	science	science	PROPN
ejpam-5626	1	70	&	&	CCONJ
ejpam-5626	1	71	arts	art	NOUN
ejpam-5626	1	72	-	-	PUNCT
ejpam-5626	1	73	rabigh	rabigh	VERB
ejpam-5626	1	74	,	,	PUNCT
ejpam-5626	1	75	king	king	NOUN
ejpam-5626	1	76	abdulaziz	abdulaziz	PROPN
ejpam-5626	1	77	university	university	PROPN
ejpam-5626	1	78	,	,	PUNCT
ejpam-5626	1	79	ksa	ksa	PROPN
ejpam-5626	1	80	2	2	NUM
ejpam-5626	1	81	department	department	NOUN
ejpam-5626	1	82	of	of	ADP
ejpam-5626	1	83	applied	apply	VERB
ejpam-5626	1	84	sciences	science	NOUN
ejpam-5626	1	85	,	,	PUNCT
ejpam-5626	1	86	symbiosis	symbiosis	NOUN
ejpam-5626	1	87	institute	institute	PROPN
ejpam-5626	1	88	of	of	ADP
ejpam-5626	1	89	technology	technology	PROPN
ejpam-5626	1	90	,	,	PUNCT
ejpam-5626	1	91	symbiosis	symbiosis	NOUN
ejpam-5626	1	92	international	international	ADJ
ejpam-5626	1	93	(	(	PUNCT
ejpam-5626	1	94	deemed	deem	VERB
ejpam-5626	1	95	)	)	PUNCT
ejpam-5626	1	96	university	university	NOUN
ejpam-5626	1	97	,	,	PUNCT
ejpam-5626	1	98	lavale	lavale	NOUN
ejpam-5626	1	99	,	,	PUNCT
ejpam-5626	1	100	pune	pune	NOUN
ejpam-5626	1	101	,	,	PUNCT
ejpam-5626	1	102	india	india	PROPN
ejpam-5626	1	103	3	3	NUM
ejpam-5626	1	104	department	department	NOUN
ejpam-5626	1	105	of	of	ADP
ejpam-5626	1	106	mathematics	mathematics	PROPN
ejpam-5626	1	107	,	,	PUNCT
ejpam-5626	1	108	aligarh	aligarh	PROPN
ejpam-5626	1	109	muslim	muslim	PROPN
ejpam-5626	1	110	university	university	PROPN
ejpam-5626	1	111	,	,	PUNCT
ejpam-5626	1	112	aligarh-202002	aligarh-202002	NOUN
ejpam-5626	1	113	india	india	PROPN
ejpam-5626	1	114	4	4	NUM
ejpam-5626	1	115	school	school	NOUN
ejpam-5626	1	116	of	of	ADP
ejpam-5626	1	117	mathematics	mathematic	NOUN
ejpam-5626	1	118	and	and	CCONJ
ejpam-5626	1	119	statistics	statistic	NOUN
ejpam-5626	1	120	,	,	PUNCT
ejpam-5626	1	121	nanjing	nanjing	PROPN
ejpam-5626	1	122	university	university	PROPN
ejpam-5626	1	123	of	of	ADP
ejpam-5626	1	124	information	information	NOUN
ejpam-5626	1	125	science	science	NOUN
ejpam-5626	1	126	and	and	CCONJ
ejpam-5626	1	127	technology	technology	NOUN
ejpam-5626	1	128	,	,	PUNCT
ejpam-5626	1	129	nanjing	nanjing	PROPN
ejpam-5626	1	130	210044	210044	NUM
ejpam-5626	1	131	,	,	PUNCT
ejpam-5626	1	132	china	china	PROPN
ejpam-5626	1	133	abstract	abstract	NOUN
ejpam-5626	1	134	.	.	PUNCT
ejpam-5626	2	1	let	let	VERB
ejpam-5626	2	2	a	a	PRON
ejpam-5626	2	3	be	be	AUX
ejpam-5626	2	4	a	a	DET
ejpam-5626	2	5	unital	unital	ADJ
ejpam-5626	2	6	∗-algebra	∗-algebra	NOUN
ejpam-5626	2	7	containing	contain	VERB
ejpam-5626	2	8	non	non	ADJ
ejpam-5626	2	9	-	-	ADJ
ejpam-5626	2	10	trivial	trivial	ADJ
ejpam-5626	2	11	projection	projection	NOUN
ejpam-5626	2	12	.	.	PUNCT
ejpam-5626	3	1	we	we	PRON
ejpam-5626	3	2	prove	prove	VERB
ejpam-5626	3	3	that	that	SCONJ
ejpam-5626	3	4	if	if	SCONJ
ejpam-5626	3	5	a	a	DET
ejpam-5626	3	6	map	map	NOUN
ejpam-5626	3	7	λ	λ	X
ejpam-5626	3	8	:	:	PUNCT
ejpam-5626	3	9	a	a	PRON
ejpam-5626	3	10	→	→	X
ejpam-5626	3	11	a	a	DET
ejpam-5626	3	12	such	such	ADJ
ejpam-5626	3	13	that	that	SCONJ
ejpam-5626	3	14	λ([[l	λ([[l	ADJ
ejpam-5626	3	15	,	,	PUNCT
ejpam-5626	3	16	m]•,n]∗	m]•,n]∗	NOUN
ejpam-5626	3	17	)	)	PUNCT
ejpam-5626	3	18	=	=	NOUN
ejpam-5626	4	1	[	[	X
ejpam-5626	4	2	[	[	X
ejpam-5626	4	3	λ(l),m]•,n]∗	λ(l),m]•,n]∗	X
ejpam-5626	4	4	+	+	X
ejpam-5626	4	5	[	[	X
ejpam-5626	4	6	[	[	X
ejpam-5626	4	7	l	l	NOUN
ejpam-5626	4	8	,	,	PUNCT
ejpam-5626	4	9	λ(m)]•,n]∗	λ(m)]•,n]∗	NOUN
ejpam-5626	5	1	+	+	X
ejpam-5626	6	1	[	[	X
ejpam-5626	6	2	[	[	X
ejpam-5626	6	3	l	l	NOUN
ejpam-5626	6	4	,	,	PUNCT
ejpam-5626	6	5	m]•,λ(n)]∗	m]•,λ(n)]∗	VERB
ejpam-5626	6	6	for	for	ADP
ejpam-5626	6	7	all	all	DET
ejpam-5626	6	8	l	l	NOUN
ejpam-5626	6	9	,	,	PUNCT
ejpam-5626	6	10	m	m	PROPN
ejpam-5626	6	11	,	,	PUNCT
ejpam-5626	6	12	n	n	PROPN
ejpam-5626	6	13	∈	∈	PROPN
ejpam-5626	6	14	a	a	PRON
ejpam-5626	6	15	,	,	PUNCT
ejpam-5626	6	16	then	then	ADV
ejpam-5626	6	17	λ	λ	PROPN
ejpam-5626	6	18	is	be	AUX
ejpam-5626	6	19	additive	additive	ADJ
ejpam-5626	6	20	.	.	PUNCT
ejpam-5626	7	1	moreover	moreover	ADV
ejpam-5626	7	2	,	,	PUNCT
ejpam-5626	7	3	if	if	SCONJ
ejpam-5626	7	4	λ(i	λ(i	PROPN
ejpam-5626	7	5	)	)	PUNCT
ejpam-5626	7	6	is	be	AUX
ejpam-5626	7	7	self	self	NOUN
ejpam-5626	7	8	-	-	PUNCT
ejpam-5626	7	9	adjoint	adjoint	NOUN
ejpam-5626	7	10	,	,	PUNCT
ejpam-5626	7	11	then	then	ADV
ejpam-5626	7	12	λ	λ	PROPN
ejpam-5626	7	13	is	be	AUX
ejpam-5626	7	14	a	a	DET
ejpam-5626	7	15	∗-derivation	∗-derivation	NOUN
ejpam-5626	7	16	.	.	PUNCT
ejpam-5626	8	1	additionally	additionally	ADV
ejpam-5626	8	2	,	,	PUNCT
ejpam-5626	8	3	as	as	ADP
ejpam-5626	8	4	an	an	DET
ejpam-5626	8	5	application	application	NOUN
ejpam-5626	8	6	,	,	PUNCT
ejpam-5626	8	7	we	we	PRON
ejpam-5626	8	8	can	can	AUX
ejpam-5626	8	9	also	also	ADV
ejpam-5626	8	10	apply	apply	VERB
ejpam-5626	8	11	our	our	PRON
ejpam-5626	8	12	results	result	NOUN
ejpam-5626	8	13	on	on	ADP
ejpam-5626	8	14	factor	factor	NOUN
ejpam-5626	8	15	von	von	PROPN
ejpam-5626	8	16	neumann	neumann	PROPN
ejpam-5626	8	17	algebras	algebras	PROPN
ejpam-5626	8	18	,	,	PUNCT
ejpam-5626	8	19	standard	standard	ADJ
ejpam-5626	8	20	operator	operator	NOUN
ejpam-5626	8	21	algebras	algebra	NOUN
ejpam-5626	8	22	and	and	CCONJ
ejpam-5626	8	23	prime	prime	ADJ
ejpam-5626	8	24	∗-algebras	∗-algebra	NOUN
ejpam-5626	8	25	.	.	PUNCT
ejpam-5626	9	1	2020	2020	NUM
ejpam-5626	9	2	mathematics	mathematics	PROPN
ejpam-5626	9	3	subject	subject	NOUN
ejpam-5626	9	4	classifications	classification	NOUN
ejpam-5626	9	5	:	:	PUNCT
ejpam-5626	9	6	16w10	16w10	NUM
ejpam-5626	9	7	,	,	PUNCT
ejpam-5626	9	8	47b47	47b47	NOUN
ejpam-5626	9	9	,	,	PUNCT
ejpam-5626	9	10	46k15	46k15	NUM
ejpam-5626	9	11	.	.	PUNCT
ejpam-5626	10	1	key	key	ADJ
ejpam-5626	10	2	words	word	NOUN
ejpam-5626	10	3	and	and	CCONJ
ejpam-5626	10	4	phrases	phrase	NOUN
ejpam-5626	10	5	:	:	PUNCT
ejpam-5626	10	6	mixed	mixed	ADJ
ejpam-5626	10	7	bi	bi	NOUN
ejpam-5626	10	8	-	-	ADJ
ejpam-5626	10	9	skew	skew	NOUN
ejpam-5626	10	10	lie	lie	VERB
ejpam-5626	10	11	triple	triple	ADJ
ejpam-5626	10	12	derivation	derivation	NOUN
ejpam-5626	10	13	,	,	PUNCT
ejpam-5626	10	14	∗-derivation	∗-derivation	NOUN
ejpam-5626	10	15	,	,	PUNCT
ejpam-5626	10	16	∗algebra	∗algebra	NOUN
ejpam-5626	10	17	1	1	NUM
ejpam-5626	10	18	.	.	X
ejpam-5626	11	1	introduction	introduction	NOUN
ejpam-5626	11	2	let	let	VERB
ejpam-5626	11	3	a	a	PRON
ejpam-5626	11	4	be	be	AUX
ejpam-5626	11	5	an	an	DET
ejpam-5626	11	6	∗-algebra	∗-algebra	NOUN
ejpam-5626	11	7	over	over	ADP
ejpam-5626	11	8	the	the	DET
ejpam-5626	11	9	complex	complex	ADJ
ejpam-5626	11	10	field	field	NOUN
ejpam-5626	11	11	c.	c.	NOUN
ejpam-5626	11	12	for	for	ADP
ejpam-5626	11	13	l	l	NOUN
ejpam-5626	11	14	,	,	PUNCT
ejpam-5626	11	15	m	m	PROPN
ejpam-5626	11	16	∈	∈	PROPN
ejpam-5626	11	17	a	a	PRON
ejpam-5626	11	18	,	,	PUNCT
ejpam-5626	11	19	we	we	PRON
ejpam-5626	11	20	call	call	VERB
ejpam-5626	11	21	[	[	X
ejpam-5626	11	22	l	l	NOUN
ejpam-5626	11	23	,	,	PUNCT
ejpam-5626	11	24	m]∗	m]∗	NOUN
ejpam-5626	11	25	=	=	SYM
ejpam-5626	11	26	lm	lm	NUM
ejpam-5626	11	27	−	−	PROPN
ejpam-5626	11	28	ml∗	ml∗	VERB
ejpam-5626	11	29	the	the	DET
ejpam-5626	11	30	skew	skew	ADJ
ejpam-5626	11	31	lie	lie	NOUN
ejpam-5626	11	32	product	product	NOUN
ejpam-5626	11	33	and	and	CCONJ
ejpam-5626	11	34	[	[	X
ejpam-5626	11	35	l	l	NOUN
ejpam-5626	11	36	,	,	PUNCT
ejpam-5626	11	37	m]•	m]•	X
ejpam-5626	11	38	=	=	PUNCT
ejpam-5626	11	39	lm∗	lm∗	X
ejpam-5626	11	40	−	−	PROPN
ejpam-5626	11	41	ml∗	ml∗	PRON
ejpam-5626	11	42	denotes	denote	VERB
ejpam-5626	11	43	the	the	DET
ejpam-5626	11	44	bi	bi	PROPN
ejpam-5626	11	45	-	-	ADJ
ejpam-5626	11	46	skew	skew	ADJ
ejpam-5626	11	47	lie	lie	NOUN
ejpam-5626	11	48	product	product	NOUN
ejpam-5626	11	49	.	.	PUNCT
ejpam-5626	12	1	the	the	DET
ejpam-5626	12	2	skew	skew	ADJ
ejpam-5626	12	3	lie	lie	NOUN
ejpam-5626	12	4	product	product	NOUN
ejpam-5626	12	5	,	,	PUNCT
ejpam-5626	12	6	jordan	jordan	PROPN
ejpam-5626	12	7	product	product	NOUN
ejpam-5626	12	8	,	,	PUNCT
ejpam-5626	12	9	and	and	CCONJ
ejpam-5626	12	10	bi	bi	ADJ
ejpam-5626	12	11	-	-	ADJ
ejpam-5626	12	12	skew	skew	ADJ
ejpam-5626	12	13	lie	lie	NOUN
ejpam-5626	12	14	product	product	NOUN
ejpam-5626	12	15	have	have	AUX
ejpam-5626	12	16	become	become	VERB
ejpam-5626	12	17	increasingly	increasingly	ADV
ejpam-5626	12	18	relevant	relevant	ADJ
ejpam-5626	12	19	in	in	ADP
ejpam-5626	12	20	various	various	ADJ
ejpam-5626	12	21	research	research	NOUN
ejpam-5626	12	22	fields	field	NOUN
ejpam-5626	12	23	,	,	PUNCT
ejpam-5626	12	24	and	and	CCONJ
ejpam-5626	12	25	numerous	numerous	ADJ
ejpam-5626	12	26	authors	author	NOUN
ejpam-5626	12	27	have	have	AUX
ejpam-5626	12	28	shown	show	VERB
ejpam-5626	12	29	a	a	DET
ejpam-5626	12	30	keen	keen	ADJ
ejpam-5626	12	31	interest	interest	NOUN
ejpam-5626	12	32	in	in	ADP
ejpam-5626	12	33	their	their	PRON
ejpam-5626	12	34	exploration	exploration	NOUN
ejpam-5626	12	35	.	.	PUNCT
ejpam-5626	13	1	this	this	PRON
ejpam-5626	13	2	is	be	AUX
ejpam-5626	13	3	evident	evident	ADJ
ejpam-5626	13	4	from	from	ADP
ejpam-5626	13	5	the	the	DET
ejpam-5626	13	6	numerous	numerous	ADJ
ejpam-5626	13	7	studies	study	NOUN
ejpam-5626	13	8	by	by	ADP
ejpam-5626	13	9	authors	author	NOUN
ejpam-5626	13	10	(	(	PUNCT
ejpam-5626	13	11	see	see	VERB
ejpam-5626	13	12	[	[	X
ejpam-5626	13	13	1	1	NUM
ejpam-5626	13	14	,	,	PUNCT
ejpam-5626	13	15	2	2	NUM
ejpam-5626	13	16	,	,	PUNCT
ejpam-5626	13	17	4–7	4–7	NOUN
ejpam-5626	13	18	,	,	PUNCT
ejpam-5626	13	19	9	9	NUM
ejpam-5626	13	20	,	,	PUNCT
ejpam-5626	13	21	10	10	NUM
ejpam-5626	13	22	,	,	PUNCT
ejpam-5626	13	23	13	13	NUM
ejpam-5626	13	24	]	]	NUM
ejpam-5626	13	25	)	)	PUNCT
ejpam-5626	13	26	.	.	PUNCT
ejpam-5626	14	1	recall	recall	VERB
ejpam-5626	14	2	that	that	SCONJ
ejpam-5626	14	3	an	an	DET
ejpam-5626	14	4	additive	additive	ADJ
ejpam-5626	14	5	map	map	NOUN
ejpam-5626	14	6	λ	λ	X
ejpam-5626	14	7	:	:	PUNCT
ejpam-5626	14	8	a	a	PRON
ejpam-5626	14	9	→	→	X
ejpam-5626	14	10	a	a	PRON
ejpam-5626	14	11	is	be	AUX
ejpam-5626	14	12	called	call	VERB
ejpam-5626	14	13	an	an	DET
ejpam-5626	14	14	additive	additive	ADJ
ejpam-5626	14	15	derivation	derivation	NOUN
ejpam-5626	14	16	if	if	SCONJ
ejpam-5626	14	17	λ(lm	λ(lm	NUM
ejpam-5626	14	18	)	)	PUNCT
ejpam-5626	14	19	=	=	SYM
ejpam-5626	15	1	λ(l)m+lλ(m	λ(l)m+lλ(m	NOUN
ejpam-5626	15	2	)	)	PUNCT
ejpam-5626	15	3	for	for	ADP
ejpam-5626	15	4	all	all	DET
ejpam-5626	15	5	l	l	NOUN
ejpam-5626	15	6	,	,	PUNCT
ejpam-5626	15	7	m	m	VERB
ejpam-5626	15	8	∈	∈	NOUN
ejpam-5626	15	9	a.	a.	NOUN
ejpam-5626	15	10	if	if	SCONJ
ejpam-5626	15	11	λ(l∗	λ(l∗	NOUN
ejpam-5626	15	12	)	)	PUNCT
ejpam-5626	15	13	=	=	SYM
ejpam-5626	15	14	λ(l)∗	λ(l)∗	NOUN
ejpam-5626	15	15	for	for	ADP
ejpam-5626	15	16	all	all	DET
ejpam-5626	15	17	l	l	NOUN
ejpam-5626	15	18	∈	∈	PROPN
ejpam-5626	15	19	a	a	PRON
ejpam-5626	15	20	,	,	PUNCT
ejpam-5626	15	21	then	then	ADV
ejpam-5626	15	22	λ	λ	PROPN
ejpam-5626	15	23	is	be	AUX
ejpam-5626	15	24	an	an	DET
ejpam-5626	15	25	additive	additive	ADJ
ejpam-5626	15	26	∗-derivation	∗-derivation	NOUN
ejpam-5626	15	27	.	.	PUNCT
ejpam-5626	16	1	let	let	VERB
ejpam-5626	16	2	λ	λ	X
ejpam-5626	16	3	:	:	PUNCT
ejpam-5626	16	4	a	a	PRON
ejpam-5626	16	5	→	→	X
ejpam-5626	16	6	a	a	DET
ejpam-5626	16	7	be	be	AUX
ejpam-5626	16	8	a	a	DET
ejpam-5626	16	9	map	map	NOUN
ejpam-5626	16	10	(	(	PUNCT
ejpam-5626	16	11	without	without	ADP
ejpam-5626	16	12	the	the	DET
ejpam-5626	16	13	additivity	additivity	NOUN
ejpam-5626	16	14	assumption	assumption	NOUN
ejpam-5626	16	15	)	)	PUNCT
ejpam-5626	16	16	.	.	PUNCT
ejpam-5626	17	1	we	we	PRON
ejpam-5626	17	2	say	say	VERB
ejpam-5626	17	3	λ	λ	NOUN
ejpam-5626	17	4	is	be	AUX
ejpam-5626	17	5	a	a	DET
ejpam-5626	17	6	nonlinear	nonlinear	ADJ
ejpam-5626	17	7	skew	skew	ADJ
ejpam-5626	17	8	lie	lie	NOUN
ejpam-5626	17	9	derivation	derivation	NOUN
ejpam-5626	17	10	or	or	CCONJ
ejpam-5626	17	11	nonlinear	nonlinear	ADJ
ejpam-5626	17	12	skew	skew	NOUN
ejpam-5626	17	13	lie	lie	VERB
ejpam-5626	17	14	triple	triple	ADJ
ejpam-5626	17	15	derivation	derivation	NOUN
ejpam-5626	17	16	if	if	SCONJ
ejpam-5626	17	17	λ([l	λ([l	PROPN
ejpam-5626	17	18	,	,	PUNCT
ejpam-5626	17	19	m]∗	m]∗	NOUN
ejpam-5626	17	20	)	)	PUNCT
ejpam-5626	17	21	=	=	PUNCT
ejpam-5626	18	1	[	[	X
ejpam-5626	18	2	λ(l),m]∗	λ(l),m]∗	X
ejpam-5626	18	3	+	+	X
ejpam-5626	19	1	[	[	X
ejpam-5626	19	2	l	l	NOUN
ejpam-5626	19	3	,	,	PUNCT
ejpam-5626	19	4	λ(m)]∗	λ(m)]∗	NOUN
ejpam-5626	19	5	∗corresponding	∗corresponde	VERB
ejpam-5626	19	6	author	author	NOUN
ejpam-5626	19	7	.	.	PUNCT
ejpam-5626	20	1	doi	doi	NOUN
ejpam-5626	20	2	:	:	PUNCT
ejpam-5626	20	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5626	https://doi.org/10.29020/nybg.ejpam.v18i1.5626	ADJ
ejpam-5626	20	4	email	email	NOUN
ejpam-5626	20	5	addresses	address	VERB
ejpam-5626	20	6	:	:	PUNCT
ejpam-5626	20	7	arifraza03@gmail.com	arifraza03@gmail.com	X
ejpam-5626	20	8	(	(	PUNCT
ejpam-5626	20	9	m.	m.	NOUN
ejpam-5626	20	10	raza	raza	PROPN
ejpam-5626	20	11	)	)	PUNCT
ejpam-5626	20	12	,	,	PUNCT
ejpam-5626	20	13	junaidnisar73@gmail.com	junaidnisar73@gmail.com	X
ejpam-5626	20	14	(	(	PUNCT
ejpam-5626	20	15	j.	j.	PROPN
ejpam-5626	20	16	nisar	nisar	PROPN
ejpam-5626	20	17	)	)	PUNCT
ejpam-5626	20	18	,	,	PUNCT
ejpam-5626	20	19	nu.rehman.mm@amu.ac.in	nu.rehman.mm@amu.ac.in	PROPN
ejpam-5626	20	20	(	(	PUNCT
ejpam-5626	20	21	n.	n.	PROPN
ejpam-5626	20	22	rehman	rehman	PROPN
ejpam-5626	20	23	)	)	PUNCT
ejpam-5626	20	24	,	,	PUNCT
ejpam-5626	20	25	vdarvish@nuist.edu.cn	vdarvish@nuist.edu.cn	NOUN
ejpam-5626	20	26	(	(	PUNCT
ejpam-5626	20	27	v.	v.	X
ejpam-5626	20	28	darvish	darvish	PROPN
ejpam-5626	20	29	)	)	PUNCT
ejpam-5626	20	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5626	20	31	1	1	NUM
ejpam-5626	20	32	copyright	copyright	NOUN
ejpam-5626	20	33	:	:	PUNCT
ejpam-5626	21	1	©	©	PROPN
ejpam-5626	21	2	2025	2025	NUM
ejpam-5626	21	3	the	the	DET
ejpam-5626	21	4	author(s	author(s	NOUN
ejpam-5626	21	5	)	)	PUNCT
ejpam-5626	21	6	.	.	PUNCT
ejpam-5626	22	1	(	(	PUNCT
ejpam-5626	22	2	cc	cc	NOUN
ejpam-5626	22	3	by	by	ADP
ejpam-5626	22	4	-	-	PUNCT
ejpam-5626	22	5	nc	nc	PROPN
ejpam-5626	22	6	4.0	4.0	NUM
ejpam-5626	22	7	)	)	PUNCT
ejpam-5626	22	8	m.	m.	NOUN
ejpam-5626	22	9	a.	a.	PROPN
ejpam-5626	22	10	raza	raza	PROPN
ejpam-5626	22	11	et	et	PROPN
ejpam-5626	22	12	al	al	PROPN
ejpam-5626	22	13	.	.	PUNCT
ejpam-5626	22	14	/	/	SYM
ejpam-5626	22	15	eur	eur	PROPN
ejpam-5626	22	16	.	.	PUNCT
ejpam-5626	23	1	j.	j.	PROPN
ejpam-5626	23	2	pure	pure	PROPN
ejpam-5626	23	3	appl	appl	PROPN
ejpam-5626	23	4	.	.	PROPN
ejpam-5626	23	5	math	math	PROPN
ejpam-5626	23	6	,	,	PUNCT
ejpam-5626	23	7	18	18	NUM
ejpam-5626	23	8	(	(	PUNCT
ejpam-5626	23	9	1	1	NUM
ejpam-5626	23	10	)	)	PUNCT
ejpam-5626	23	11	(	(	PUNCT
ejpam-5626	23	12	2025	2025	NUM
ejpam-5626	23	13	)	)	PUNCT
ejpam-5626	23	14	,	,	PUNCT
ejpam-5626	23	15	5626	5626	NUM
ejpam-5626	23	16	2	2	NUM
ejpam-5626	23	17	of	of	ADP
ejpam-5626	23	18	10	10	NUM
ejpam-5626	23	19	or	or	CCONJ
ejpam-5626	23	20	λ([[l	λ([[l	NUM
ejpam-5626	23	21	,	,	PUNCT
ejpam-5626	23	22	m]∗,n]∗	m]∗,n]∗	NOUN
ejpam-5626	23	23	)	)	PUNCT
ejpam-5626	23	24	=	=	NOUN
ejpam-5626	24	1	[	[	X
ejpam-5626	24	2	[	[	X
ejpam-5626	24	3	λ(l),m]∗,n]∗	λ(l),m]∗,n]∗	X
ejpam-5626	24	4	+	+	X
ejpam-5626	24	5	[	[	X
ejpam-5626	24	6	[	[	X
ejpam-5626	24	7	l	l	NOUN
ejpam-5626	24	8	,	,	PUNCT
ejpam-5626	24	9	λ(m)]∗,n]∗	λ(m)]∗,n]∗	ADV
ejpam-5626	24	10	+	+	X
ejpam-5626	25	1	[	[	X
ejpam-5626	25	2	[	[	X
ejpam-5626	25	3	l	l	X
ejpam-5626	25	4	,	,	PUNCT
ejpam-5626	25	5	m]∗,λ(n)]∗	m]∗,λ(n)]∗	VERB
ejpam-5626	25	6	for	for	ADP
ejpam-5626	25	7	all	all	DET
ejpam-5626	25	8	l	l	NOUN
ejpam-5626	25	9	,	,	PUNCT
ejpam-5626	25	10	m	m	PROPN
ejpam-5626	25	11	,	,	PUNCT
ejpam-5626	25	12	n	n	PROPN
ejpam-5626	25	13	∈	∈	NOUN
ejpam-5626	25	14	a.	a.	NOUN
ejpam-5626	25	15	similarly	similarly	ADV
ejpam-5626	25	16	,	,	PUNCT
ejpam-5626	25	17	a	a	DET
ejpam-5626	25	18	map	map	NOUN
ejpam-5626	25	19	λ	λ	X
ejpam-5626	25	20	:	:	PUNCT
ejpam-5626	25	21	a	a	PRON
ejpam-5626	25	22	→	→	X
ejpam-5626	25	23	a	a	PRON
ejpam-5626	25	24	is	be	AUX
ejpam-5626	25	25	said	say	VERB
ejpam-5626	25	26	to	to	PART
ejpam-5626	25	27	be	be	AUX
ejpam-5626	25	28	a	a	DET
ejpam-5626	25	29	nonlinear	nonlinear	ADJ
ejpam-5626	25	30	bi	bi	ADJ
ejpam-5626	25	31	-	-	ADJ
ejpam-5626	25	32	skew	skew	ADJ
ejpam-5626	25	33	lie	lie	NOUN
ejpam-5626	25	34	derivation	derivation	NOUN
ejpam-5626	25	35	or	or	CCONJ
ejpam-5626	25	36	nonlinear	nonlinear	ADJ
ejpam-5626	25	37	bi	bi	ADJ
ejpam-5626	25	38	-	-	ADJ
ejpam-5626	25	39	skew	skew	NOUN
ejpam-5626	25	40	lie	lie	VERB
ejpam-5626	25	41	triple	triple	ADJ
ejpam-5626	25	42	derivation	derivation	NOUN
ejpam-5626	25	43	if	if	SCONJ
ejpam-5626	25	44	λ([l	λ([l	PROPN
ejpam-5626	25	45	,	,	PUNCT
ejpam-5626	25	46	m]•	m]•	PROPN
ejpam-5626	25	47	)	)	PUNCT
ejpam-5626	25	48	=	=	NOUN
ejpam-5626	26	1	[	[	X
ejpam-5626	26	2	λ(l),m]•	λ(l),m]•	X
ejpam-5626	26	3	+	+	X
ejpam-5626	27	1	[	[	X
ejpam-5626	27	2	l	l	X
ejpam-5626	27	3	,	,	PUNCT
ejpam-5626	27	4	λ(m)]•	λ(m)]•	NOUN
ejpam-5626	27	5	or	or	CCONJ
ejpam-5626	27	6	λ([[l	λ([[l	NUM
ejpam-5626	27	7	,	,	PUNCT
ejpam-5626	27	8	m]•,n]•	m]•,n]•	NOUN
ejpam-5626	27	9	)	)	PUNCT
ejpam-5626	27	10	=	=	PUNCT
ejpam-5626	28	1	[	[	X
ejpam-5626	28	2	[	[	X
ejpam-5626	28	3	λ(l),m]•,n]•	λ(l),m]•,n]•	X
ejpam-5626	28	4	+	+	PUNCT
ejpam-5626	28	5	[	[	X
ejpam-5626	28	6	[	[	X
ejpam-5626	28	7	l	l	NOUN
ejpam-5626	28	8	,	,	PUNCT
ejpam-5626	28	9	λ(m)]•,n]∗	λ(m)]•,n]∗	NOUN
ejpam-5626	29	1	+	+	X
ejpam-5626	30	1	[	[	X
ejpam-5626	30	2	[	[	X
ejpam-5626	30	3	l	l	NOUN
ejpam-5626	30	4	,	,	PUNCT
ejpam-5626	30	5	m]•,λ(n)]•	m]•,λ(n)]•	X
ejpam-5626	30	6	for	for	ADP
ejpam-5626	30	7	all	all	DET
ejpam-5626	30	8	l	l	NOUN
ejpam-5626	30	9	,	,	PUNCT
ejpam-5626	30	10	m	m	PROPN
ejpam-5626	30	11	,	,	PUNCT
ejpam-5626	30	12	n	n	PROPN
ejpam-5626	30	13	∈	∈	NOUN
ejpam-5626	30	14	a.	a.	NOUN
ejpam-5626	30	15	in	in	ADP
ejpam-5626	30	16	2021	2021	NUM
ejpam-5626	30	17	,	,	PUNCT
ejpam-5626	30	18	a.	a.	PROPN
ejpam-5626	30	19	khan	khan	PROPN
ejpam-5626	31	1	[	[	X
ejpam-5626	31	2	3	3	X
ejpam-5626	31	3	]	]	PUNCT
ejpam-5626	31	4	established	establish	VERB
ejpam-5626	31	5	a	a	DET
ejpam-5626	31	6	proof	proof	NOUN
ejpam-5626	31	7	demonstrating	demonstrate	VERB
ejpam-5626	31	8	that	that	SCONJ
ejpam-5626	31	9	any	any	DET
ejpam-5626	31	10	multiplicative	multiplicative	ADJ
ejpam-5626	31	11	or	or	CCONJ
ejpam-5626	31	12	nonadditive	nonadditive	ADJ
ejpam-5626	31	13	bi	bi	ADJ
ejpam-5626	31	14	-	-	ADJ
ejpam-5626	31	15	skew	skew	ADJ
ejpam-5626	31	16	lie	lie	VERB
ejpam-5626	31	17	triple	triple	ADJ
ejpam-5626	31	18	derivation	derivation	NOUN
ejpam-5626	31	19	acting	act	VERB
ejpam-5626	31	20	on	on	ADP
ejpam-5626	31	21	a	a	DET
ejpam-5626	31	22	factor	factor	NOUN
ejpam-5626	31	23	von	von	PROPN
ejpam-5626	31	24	neumann	neumann	PROPN
ejpam-5626	31	25	algebra	algebra	PROPN
ejpam-5626	31	26	can	can	AUX
ejpam-5626	31	27	be	be	AUX
ejpam-5626	31	28	characterized	characterize	VERB
ejpam-5626	31	29	as	as	ADP
ejpam-5626	31	30	an	an	DET
ejpam-5626	31	31	additive	additive	ADJ
ejpam-5626	31	32	∗-derivation	∗-derivation	NOUN
ejpam-5626	31	33	.	.	PUNCT
ejpam-5626	32	1	numerous	numerous	ADJ
ejpam-5626	32	2	authors	author	NOUN
ejpam-5626	32	3	have	have	AUX
ejpam-5626	32	4	recently	recently	ADV
ejpam-5626	32	5	explored	explore	VERB
ejpam-5626	32	6	the	the	DET
ejpam-5626	32	7	derivations	derivation	NOUN
ejpam-5626	32	8	and	and	CCONJ
ejpam-5626	32	9	isomorphisms	isomorphism	NOUN
ejpam-5626	32	10	corresponding	correspond	VERB
ejpam-5626	32	11	to	to	ADP
ejpam-5626	32	12	the	the	DET
ejpam-5626	32	13	novel	novel	ADJ
ejpam-5626	32	14	products	product	NOUN
ejpam-5626	32	15	created	create	VERB
ejpam-5626	32	16	by	by	ADP
ejpam-5626	32	17	combining	combine	VERB
ejpam-5626	32	18	lie	lie	NOUN
ejpam-5626	32	19	and	and	CCONJ
ejpam-5626	32	20	skew	skew	ADJ
ejpam-5626	32	21	lie	lie	NOUN
ejpam-5626	32	22	products	product	NOUN
ejpam-5626	32	23	,	,	PUNCT
ejpam-5626	32	24	skew	skew	ADJ
ejpam-5626	32	25	lie	lie	NOUN
ejpam-5626	32	26	and	and	CCONJ
ejpam-5626	32	27	skew	skew	VERB
ejpam-5626	32	28	jordan	jordan	PROPN
ejpam-5626	32	29	product	product	PROPN
ejpam-5626	32	30	see	see	VERB
ejpam-5626	32	31	[	[	X
ejpam-5626	32	32	8	8	NUM
ejpam-5626	32	33	,	,	PUNCT
ejpam-5626	32	34	11	11	NUM
ejpam-5626	32	35	,	,	PUNCT
ejpam-5626	32	36	12	12	NUM
ejpam-5626	32	37	]	]	PUNCT
ejpam-5626	32	38	.	.	PUNCT
ejpam-5626	33	1	as	as	ADP
ejpam-5626	33	2	an	an	DET
ejpam-5626	33	3	illustration	illustration	NOUN
ejpam-5626	33	4	,	,	PUNCT
ejpam-5626	33	5	li	li	PROPN
ejpam-5626	33	6	and	and	CCONJ
ejpam-5626	33	7	zhang	zhang	PROPN
ejpam-5626	33	8	[	[	X
ejpam-5626	33	9	8	8	NUM
ejpam-5626	33	10	]	]	PUNCT
ejpam-5626	33	11	delved	delve	VERB
ejpam-5626	33	12	into	into	ADP
ejpam-5626	33	13	an	an	DET
ejpam-5626	33	14	investigation	investigation	NOUN
ejpam-5626	33	15	focused	focus	VERB
ejpam-5626	33	16	on	on	ADP
ejpam-5626	33	17	understanding	understand	VERB
ejpam-5626	33	18	the	the	DET
ejpam-5626	33	19	arrangement	arrangement	NOUN
ejpam-5626	33	20	and	and	CCONJ
ejpam-5626	33	21	properties	property	NOUN
ejpam-5626	33	22	of	of	ADP
ejpam-5626	33	23	the	the	DET
ejpam-5626	33	24	nonlinear	nonlinear	ADJ
ejpam-5626	33	25	mixed	mix	VERB
ejpam-5626	33	26	jordan	jordan	PROPN
ejpam-5626	33	27	triple	triple	ADJ
ejpam-5626	33	28	∗-derivation	∗-derivation	NOUN
ejpam-5626	33	29	within	within	ADP
ejpam-5626	33	30	the	the	DET
ejpam-5626	33	31	domain	domain	NOUN
ejpam-5626	33	32	of	of	ADP
ejpam-5626	33	33	∗-algebras	∗-algebra	NOUN
ejpam-5626	33	34	.	.	PUNCT
ejpam-5626	34	1	in	in	ADP
ejpam-5626	34	2	2023	2023	NUM
ejpam-5626	34	3	,	,	PUNCT
ejpam-5626	34	4	rehman	rehman	PROPN
ejpam-5626	34	5	et	et	PROPN
ejpam-5626	34	6	.	.	PUNCT
ejpam-5626	35	1	al	al	PROPN
ejpam-5626	35	2	.	.	PUNCT
ejpam-5626	36	1	[	[	X
ejpam-5626	36	2	12	12	NUM
ejpam-5626	36	3	]	]	X
ejpam-5626	36	4	mixed	mix	VERB
ejpam-5626	36	5	the	the	DET
ejpam-5626	36	6	concept	concept	NOUN
ejpam-5626	36	7	of	of	ADP
ejpam-5626	36	8	jordan	jordan	PROPN
ejpam-5626	36	9	and	and	CCONJ
ejpam-5626	36	10	jordan	jordan	PROPN
ejpam-5626	36	11	∗-product	∗-product	PROPN
ejpam-5626	36	12	and	and	CCONJ
ejpam-5626	36	13	gives	give	VERB
ejpam-5626	36	14	the	the	DET
ejpam-5626	36	15	complete	complete	ADJ
ejpam-5626	36	16	characterization	characterization	NOUN
ejpam-5626	36	17	of	of	ADP
ejpam-5626	36	18	nonlinear	nonlinear	ADJ
ejpam-5626	36	19	mixed	mixed	ADJ
ejpam-5626	36	20	jordan	jordan	PROPN
ejpam-5626	36	21	∗-triple	∗-triple	PROPN
ejpam-5626	36	22	derivation	derivation	NOUN
ejpam-5626	36	23	on	on	ADP
ejpam-5626	36	24	∗-algebras	∗-algebra	NOUN
ejpam-5626	36	25	.	.	PUNCT
ejpam-5626	37	1	inspired	inspire	VERB
ejpam-5626	37	2	by	by	ADP
ejpam-5626	37	3	the	the	DET
ejpam-5626	37	4	above	above	ADJ
ejpam-5626	37	5	results	result	NOUN
ejpam-5626	37	6	,	,	PUNCT
ejpam-5626	37	7	in	in	ADP
ejpam-5626	37	8	the	the	DET
ejpam-5626	37	9	present	present	ADJ
ejpam-5626	37	10	paper	paper	NOUN
ejpam-5626	37	11	,	,	PUNCT
ejpam-5626	37	12	we	we	PRON
ejpam-5626	37	13	combined	combine	VERB
ejpam-5626	37	14	skew	skew	ADJ
ejpam-5626	37	15	lie	lie	NOUN
ejpam-5626	37	16	product	product	NOUN
ejpam-5626	37	17	and	and	CCONJ
ejpam-5626	37	18	bi	bi	NOUN
ejpam-5626	37	19	-	-	ADJ
ejpam-5626	37	20	skew	skew	ADJ
ejpam-5626	37	21	lie	lie	NOUN
ejpam-5626	37	22	product	product	NOUN
ejpam-5626	37	23	and	and	CCONJ
ejpam-5626	37	24	defined	define	VERB
ejpam-5626	37	25	nonlinear	nonlinear	ADJ
ejpam-5626	37	26	mixed	mixed	ADJ
ejpam-5626	37	27	bi	bi	NOUN
ejpam-5626	37	28	-	-	ADJ
ejpam-5626	37	29	skew	skew	NOUN
ejpam-5626	37	30	lie	lie	VERB
ejpam-5626	37	31	triple	triple	ADJ
ejpam-5626	37	32	derivations	derivation	NOUN
ejpam-5626	37	33	on	on	ADP
ejpam-5626	37	34	∗-algebras	∗-algebra	NOUN
ejpam-5626	37	35	.	.	PUNCT
ejpam-5626	38	1	a	a	DET
ejpam-5626	38	2	map	map	NOUN
ejpam-5626	38	3	λ	λ	NOUN
ejpam-5626	38	4	:	:	PUNCT
ejpam-5626	38	5	a	a	PRON
ejpam-5626	38	6	→	→	X
ejpam-5626	38	7	a	a	PRON
ejpam-5626	38	8	is	be	AUX
ejpam-5626	38	9	called	call	VERB
ejpam-5626	38	10	nonlinear	nonlinear	ADJ
ejpam-5626	38	11	mixed	mixed	ADJ
ejpam-5626	38	12	bi	bi	NOUN
ejpam-5626	38	13	-	-	ADJ
ejpam-5626	38	14	skew	skew	NOUN
ejpam-5626	38	15	lie	lie	VERB
ejpam-5626	38	16	triple	triple	ADJ
ejpam-5626	38	17	derivations	derivation	NOUN
ejpam-5626	38	18	if	if	SCONJ
ejpam-5626	38	19	λ([[l	λ([[l	NUM
ejpam-5626	38	20	,	,	PUNCT
ejpam-5626	38	21	m]•,n]∗	m]•,n]∗	NOUN
ejpam-5626	38	22	)	)	PUNCT
ejpam-5626	38	23	=	=	NOUN
ejpam-5626	39	1	[	[	X
ejpam-5626	39	2	[	[	X
ejpam-5626	39	3	λ(l),m]•,n]∗	λ(l),m]•,n]∗	X
ejpam-5626	39	4	+	+	X
ejpam-5626	39	5	[	[	X
ejpam-5626	39	6	[	[	X
ejpam-5626	39	7	l	l	NOUN
ejpam-5626	39	8	,	,	PUNCT
ejpam-5626	39	9	λ(m)]•,n]∗	λ(m)]•,n]∗	NOUN
ejpam-5626	40	1	+	+	X
ejpam-5626	41	1	[	[	X
ejpam-5626	41	2	[	[	X
ejpam-5626	41	3	l	l	NOUN
ejpam-5626	41	4	,	,	PUNCT
ejpam-5626	41	5	m]•,λ(n)]∗	m]•,λ(n)]∗	VERB
ejpam-5626	41	6	for	for	ADP
ejpam-5626	41	7	all	all	DET
ejpam-5626	41	8	l	l	NOUN
ejpam-5626	41	9	,	,	PUNCT
ejpam-5626	41	10	m	m	PROPN
ejpam-5626	41	11	,	,	PUNCT
ejpam-5626	41	12	n	n	PRON
ejpam-5626	41	13	∈	∈	NOUN
ejpam-5626	41	14	a.our	a.our	PRON
ejpam-5626	41	15	proof	proof	NOUN
ejpam-5626	41	16	establishes	establish	VERB
ejpam-5626	41	17	that	that	SCONJ
ejpam-5626	41	18	when	when	SCONJ
ejpam-5626	41	19	λ	λ	PROPN
ejpam-5626	41	20	represents	represent	VERB
ejpam-5626	41	21	a	a	DET
ejpam-5626	41	22	nonlinear	nonlinear	ADJ
ejpam-5626	41	23	mixed	mixed	ADJ
ejpam-5626	41	24	bi	bi	NOUN
ejpam-5626	41	25	-	-	ADJ
ejpam-5626	41	26	skew	skew	NOUN
ejpam-5626	41	27	lie	lie	VERB
ejpam-5626	41	28	triple	triple	ADJ
ejpam-5626	41	29	derivation	derivation	NOUN
ejpam-5626	41	30	acting	act	VERB
ejpam-5626	41	31	on	on	ADP
ejpam-5626	41	32	∗-algebras	∗-algebra	NOUN
ejpam-5626	41	33	,	,	PUNCT
ejpam-5626	41	34	it	it	PRON
ejpam-5626	41	35	necessarily	necessarily	ADV
ejpam-5626	41	36	possesses	possess	VERB
ejpam-5626	41	37	additivity	additivity	NOUN
ejpam-5626	41	38	.	.	PUNCT
ejpam-5626	42	1	furthermore	furthermore	ADV
ejpam-5626	42	2	,	,	PUNCT
ejpam-5626	42	3	if	if	SCONJ
ejpam-5626	42	4	the	the	DET
ejpam-5626	42	5	image	image	NOUN
ejpam-5626	42	6	of	of	ADP
ejpam-5626	42	7	λ	λ	PROPN
ejpam-5626	42	8	under	under	ADP
ejpam-5626	42	9	the	the	DET
ejpam-5626	42	10	transformation	transformation	NOUN
ejpam-5626	42	11	of	of	ADP
ejpam-5626	42	12	the	the	DET
ejpam-5626	42	13	identity	identity	NOUN
ejpam-5626	42	14	element	element	NOUN
ejpam-5626	42	15	(	(	PUNCT
ejpam-5626	42	16	λ(i	λ(i	NOUN
ejpam-5626	42	17	)	)	PUNCT
ejpam-5626	42	18	)	)	PUNCT
ejpam-5626	42	19	is	be	AUX
ejpam-5626	42	20	self	self	NOUN
ejpam-5626	42	21	-	-	PUNCT
ejpam-5626	42	22	adjoint	adjoint	NOUN
ejpam-5626	42	23	,	,	PUNCT
ejpam-5626	42	24	then	then	ADV
ejpam-5626	42	25	λ	λ	PROPN
ejpam-5626	42	26	can	can	AUX
ejpam-5626	42	27	be	be	AUX
ejpam-5626	42	28	identified	identify	VERB
ejpam-5626	42	29	as	as	ADP
ejpam-5626	42	30	an	an	DET
ejpam-5626	42	31	∗-derivation	∗-derivation	NOUN
ejpam-5626	42	32	.	.	PUNCT
ejpam-5626	43	1	in	in	ADP
ejpam-5626	43	2	simpler	simple	ADJ
ejpam-5626	43	3	terms	term	NOUN
ejpam-5626	43	4	,	,	PUNCT
ejpam-5626	43	5	the	the	DET
ejpam-5626	43	6	study	study	NOUN
ejpam-5626	43	7	demonstrates	demonstrate	VERB
ejpam-5626	43	8	that	that	SCONJ
ejpam-5626	43	9	specific	specific	ADJ
ejpam-5626	43	10	properties	property	NOUN
ejpam-5626	43	11	,	,	PUNCT
ejpam-5626	43	12	such	such	ADJ
ejpam-5626	43	13	as	as	ADP
ejpam-5626	43	14	additivity	additivity	NOUN
ejpam-5626	43	15	and	and	CCONJ
ejpam-5626	43	16	self	self	NOUN
ejpam-5626	43	17	-	-	PUNCT
ejpam-5626	43	18	adjointness	adjointness	NOUN
ejpam-5626	43	19	,	,	PUNCT
ejpam-5626	43	20	can	can	AUX
ejpam-5626	43	21	be	be	AUX
ejpam-5626	43	22	attributed	attribute	VERB
ejpam-5626	43	23	to	to	ADP
ejpam-5626	43	24	the	the	DET
ejpam-5626	43	25	nature	nature	NOUN
ejpam-5626	43	26	of	of	ADP
ejpam-5626	43	27	nonlinear	nonlinear	ADJ
ejpam-5626	43	28	mixed	mixed	ADJ
ejpam-5626	43	29	bi	bi	NOUN
ejpam-5626	43	30	-	-	ADJ
ejpam-5626	43	31	skew	skew	NOUN
ejpam-5626	43	32	lie	lie	VERB
ejpam-5626	43	33	triple	triple	ADJ
ejpam-5626	43	34	derivations	derivation	NOUN
ejpam-5626	43	35	on	on	ADP
ejpam-5626	43	36	∗-algebras	∗-algebra	NOUN
ejpam-5626	43	37	.	.	PUNCT
ejpam-5626	44	1	2	2	X
ejpam-5626	44	2	.	.	X
ejpam-5626	44	3	main	main	ADJ
ejpam-5626	44	4	result	result	NOUN
ejpam-5626	44	5	our	our	PRON
ejpam-5626	44	6	first	first	ADJ
ejpam-5626	44	7	theorem	theorem	NOUN
ejpam-5626	44	8	is	be	AUX
ejpam-5626	44	9	as	as	SCONJ
ejpam-5626	44	10	follows	follow	VERB
ejpam-5626	44	11	:	:	PUNCT
ejpam-5626	44	12	theorem	theorem	NOUN
ejpam-5626	44	13	2.1	2.1	NUM
ejpam-5626	44	14	.	.	PUNCT
ejpam-5626	45	1	let	let	VERB
ejpam-5626	45	2	a	a	PRON
ejpam-5626	45	3	be	be	AUX
ejpam-5626	45	4	a	a	DET
ejpam-5626	45	5	unital	unital	ADJ
ejpam-5626	45	6	∗-algebra	∗-algebra	NOUN
ejpam-5626	45	7	with	with	ADP
ejpam-5626	45	8	unity	unity	NOUN
ejpam-5626	45	9	i	i	NOUN
ejpam-5626	45	10	containing	contain	VERB
ejpam-5626	45	11	a	a	DET
ejpam-5626	45	12	non	non	ADJ
ejpam-5626	45	13	-	-	ADJ
ejpam-5626	45	14	trivial	trivial	ADJ
ejpam-5626	45	15	projection	projection	NOUN
ejpam-5626	45	16	p	p	NOUN
ejpam-5626	45	17	satisfies	satisfy	VERB
ejpam-5626	45	18	xap	xap	X
ejpam-5626	46	1	=	=	SYM
ejpam-5626	46	2	0	0	PUNCT
ejpam-5626	47	1	=	=	NOUN
ejpam-5626	47	2	⇒	⇒	NOUN
ejpam-5626	47	3	x	x	PUNCT
ejpam-5626	47	4	=	=	SYM
ejpam-5626	47	5	0	0	NUM
ejpam-5626	47	6	(	(	PUNCT
ejpam-5626	47	7	▲	▲	PUNCT
ejpam-5626	47	8	)	)	PUNCT
ejpam-5626	47	9	and	and	CCONJ
ejpam-5626	47	10	xa(i−	xa(i−	PUNCT
ejpam-5626	48	1	p	p	X
ejpam-5626	48	2	)	)	PUNCT
ejpam-5626	48	3	=	=	SYM
ejpam-5626	48	4	0	0	PUNCT
ejpam-5626	49	1	=	=	NOUN
ejpam-5626	49	2	⇒	⇒	NOUN
ejpam-5626	49	3	x	x	PUNCT
ejpam-5626	50	1	=	=	SYM
ejpam-5626	50	2	0	0	PROPN
ejpam-5626	50	3	.	.	PUNCT
ejpam-5626	51	1	(	(	PUNCT
ejpam-5626	51	2	▼	▼	NOUN
ejpam-5626	51	3	)	)	PUNCT
ejpam-5626	51	4	m.	m.	NOUN
ejpam-5626	51	5	a.	a.	PROPN
ejpam-5626	51	6	raza	raza	PROPN
ejpam-5626	51	7	et	et	PROPN
ejpam-5626	51	8	al	al	PROPN
ejpam-5626	51	9	.	.	PUNCT
ejpam-5626	51	10	/	/	SYM
ejpam-5626	51	11	eur	eur	PROPN
ejpam-5626	51	12	.	.	PUNCT
ejpam-5626	52	1	j.	j.	PROPN
ejpam-5626	52	2	pure	pure	PROPN
ejpam-5626	52	3	appl	appl	PROPN
ejpam-5626	52	4	.	.	PROPN
ejpam-5626	52	5	math	math	PROPN
ejpam-5626	52	6	,	,	PUNCT
ejpam-5626	52	7	18	18	NUM
ejpam-5626	52	8	(	(	PUNCT
ejpam-5626	52	9	1	1	NUM
ejpam-5626	52	10	)	)	PUNCT
ejpam-5626	52	11	(	(	PUNCT
ejpam-5626	52	12	2025	2025	NUM
ejpam-5626	52	13	)	)	PUNCT
ejpam-5626	52	14	,	,	PUNCT
ejpam-5626	52	15	5626	5626	NUM
ejpam-5626	52	16	3	3	NUM
ejpam-5626	52	17	of	of	ADP
ejpam-5626	52	18	10	10	NUM
ejpam-5626	52	19	define	define	VERB
ejpam-5626	52	20	a	a	DET
ejpam-5626	52	21	map	map	NOUN
ejpam-5626	53	1	λ	λ	X
ejpam-5626	53	2	:	:	PUNCT
ejpam-5626	53	3	a	a	PRON
ejpam-5626	53	4	→	→	X
ejpam-5626	53	5	a	a	DET
ejpam-5626	53	6	such	such	ADJ
ejpam-5626	53	7	that	that	SCONJ
ejpam-5626	53	8	λ([[l	λ([[l	ADJ
ejpam-5626	53	9	,	,	PUNCT
ejpam-5626	53	10	m]•,n]∗	m]•,n]∗	NOUN
ejpam-5626	53	11	)	)	PUNCT
ejpam-5626	53	12	=	=	NOUN
ejpam-5626	54	1	[	[	X
ejpam-5626	54	2	[	[	X
ejpam-5626	54	3	λ(l),m]•,n]∗	λ(l),m]•,n]∗	X
ejpam-5626	54	4	+	+	X
ejpam-5626	54	5	[	[	X
ejpam-5626	54	6	[	[	X
ejpam-5626	54	7	l	l	NOUN
ejpam-5626	54	8	,	,	PUNCT
ejpam-5626	54	9	λ(m)]•,n]∗	λ(m)]•,n]∗	NOUN
ejpam-5626	55	1	+	+	X
ejpam-5626	56	1	[	[	X
ejpam-5626	56	2	[	[	X
ejpam-5626	56	3	l	l	NOUN
ejpam-5626	56	4	,	,	PUNCT
ejpam-5626	56	5	m]•,λ(n)]∗	m]•,λ(n)]∗	AUX
ejpam-5626	56	6	then	then	ADV
ejpam-5626	56	7	λ	λ	PROPN
ejpam-5626	56	8	is	be	AUX
ejpam-5626	56	9	an	an	DET
ejpam-5626	56	10	additive	additive	NOUN
ejpam-5626	56	11	.	.	PUNCT
ejpam-5626	57	1	proof	proof	NOUN
ejpam-5626	57	2	.	.	PUNCT
ejpam-5626	58	1	let	let	VERB
ejpam-5626	58	2	p	p	NOUN
ejpam-5626	58	3	=	=	NOUN
ejpam-5626	58	4	p1	p1	NOUN
ejpam-5626	58	5	be	be	VERB
ejpam-5626	58	6	a	a	DET
ejpam-5626	58	7	non	non	ADJ
ejpam-5626	58	8	-	-	ADJ
ejpam-5626	58	9	trivial	trivial	ADJ
ejpam-5626	58	10	projection	projection	NOUN
ejpam-5626	58	11	in	in	ADP
ejpam-5626	58	12	a	a	PRON
ejpam-5626	58	13	and	and	CCONJ
ejpam-5626	58	14	p2	p2	PROPN
ejpam-5626	59	1	=	=	SYM
ejpam-5626	60	1	i	i	PRON
ejpam-5626	60	2	−	−	PROPN
ejpam-5626	60	3	p1	p1	PROPN
ejpam-5626	60	4	,	,	PUNCT
ejpam-5626	60	5	where	where	SCONJ
ejpam-5626	60	6	i	i	PRON
ejpam-5626	60	7	is	be	AUX
ejpam-5626	60	8	the	the	DET
ejpam-5626	60	9	unity	unity	NOUN
ejpam-5626	60	10	of	of	ADP
ejpam-5626	60	11	this	this	DET
ejpam-5626	60	12	algebra	algebra	NOUN
ejpam-5626	60	13	.	.	PUNCT
ejpam-5626	61	1	then	then	ADV
ejpam-5626	61	2	by	by	ADP
ejpam-5626	61	3	peirce	peirce	NOUN
ejpam-5626	61	4	decomposition	decomposition	NOUN
ejpam-5626	61	5	of	of	ADP
ejpam-5626	61	6	a	a	PRON
ejpam-5626	61	7	,	,	PUNCT
ejpam-5626	61	8	we	we	PRON
ejpam-5626	61	9	have	have	VERB
ejpam-5626	61	10	a	a	DET
ejpam-5626	61	11	=	=	PUNCT
ejpam-5626	61	12	p1ap1⊕p1ap2⊕	p1ap1⊕p1ap2⊕	NOUN
ejpam-5626	61	13	p2ap1⊕p2ap2	p2ap1⊕p2ap2	VERB
ejpam-5626	61	14	and	and	CCONJ
ejpam-5626	61	15	,	,	PUNCT
ejpam-5626	61	16	denote	denote	VERB
ejpam-5626	61	17	a11	a11	PROPN
ejpam-5626	61	18	=	=	SYM
ejpam-5626	62	1	p1ap1,a12	p1ap1,a12	NOUN
ejpam-5626	62	2	=	=	SYM
ejpam-5626	62	3	p1ap2,a21	p1ap2,a21	NOUN
ejpam-5626	62	4	=	=	SYM
ejpam-5626	62	5	p2ap1	p2ap1	ADJ
ejpam-5626	62	6	and	and	CCONJ
ejpam-5626	62	7	a22	a22	PROPN
ejpam-5626	62	8	=	=	PUNCT
ejpam-5626	62	9	p2ap2	p2ap2	PROPN
ejpam-5626	62	10	.	.	PUNCT
ejpam-5626	63	1	note	note	VERB
ejpam-5626	63	2	that	that	SCONJ
ejpam-5626	63	3	any	any	DET
ejpam-5626	63	4	l	l	NOUN
ejpam-5626	63	5	∈	∈	NOUN
ejpam-5626	63	6	a	a	PRON
ejpam-5626	63	7	can	can	AUX
ejpam-5626	63	8	be	be	AUX
ejpam-5626	63	9	written	write	VERB
ejpam-5626	63	10	as	as	ADP
ejpam-5626	63	11	l	l	NOUN
ejpam-5626	63	12	=	=	SYM
ejpam-5626	63	13	l11	l11	PROPN
ejpam-5626	63	14	+	+	CCONJ
ejpam-5626	63	15	l12	l12	NOUN
ejpam-5626	63	16	+	+	CCONJ
ejpam-5626	63	17	l21	l21	NOUN
ejpam-5626	63	18	+	+	CCONJ
ejpam-5626	63	19	l22	l22	NOUN
ejpam-5626	63	20	,	,	PUNCT
ejpam-5626	63	21	where	where	SCONJ
ejpam-5626	63	22	lij	lij	PROPN
ejpam-5626	63	23	∈	∈	PROPN
ejpam-5626	63	24	aij	aij	PROPN
ejpam-5626	63	25	and	and	CCONJ
ejpam-5626	63	26	l∗	l∗	PROPN
ejpam-5626	63	27	ij	ij	NOUN
ejpam-5626	63	28	∈	∈	PROPN
ejpam-5626	63	29	aji	aji	PROPN
ejpam-5626	63	30	for	for	ADP
ejpam-5626	63	31	i	i	PROPN
ejpam-5626	63	32	,	,	PUNCT
ejpam-5626	63	33	j	j	PROPN
ejpam-5626	63	34	=	=	SYM
ejpam-5626	63	35	1	1	NUM
ejpam-5626	63	36	,	,	PUNCT
ejpam-5626	63	37	2	2	NUM
ejpam-5626	63	38	.	.	PUNCT
ejpam-5626	63	39	several	several	ADJ
ejpam-5626	63	40	lemmas	lemma	NOUN
ejpam-5626	63	41	are	be	AUX
ejpam-5626	63	42	used	use	VERB
ejpam-5626	63	43	to	to	PART
ejpam-5626	63	44	prove	prove	VERB
ejpam-5626	63	45	theorem	theorem	VERB
ejpam-5626	63	46	2.1	2.1	NUM
ejpam-5626	63	47	.	.	PUNCT
ejpam-5626	64	1	lemma	lemma	PROPN
ejpam-5626	64	2	2.1	2.1	NUM
ejpam-5626	64	3	.	.	PUNCT
ejpam-5626	65	1	λ(0	λ(0	NOUN
ejpam-5626	65	2	)	)	PUNCT
ejpam-5626	66	1	=	=	SYM
ejpam-5626	66	2	0	0	X
ejpam-5626	66	3	.	.	PUNCT
ejpam-5626	67	1	proof	proof	NOUN
ejpam-5626	67	2	.	.	PUNCT
ejpam-5626	68	1	it	it	PRON
ejpam-5626	68	2	is	be	AUX
ejpam-5626	68	3	trivial	trivial	ADJ
ejpam-5626	68	4	that	that	SCONJ
ejpam-5626	68	5	λ(0	λ(0	NOUN
ejpam-5626	68	6	)	)	PUNCT
ejpam-5626	69	1	=	=	SYM
ejpam-5626	69	2	λ([[0	λ([[0	NOUN
ejpam-5626	69	3	,	,	PUNCT
ejpam-5626	69	4	0]•	0]•	NUM
ejpam-5626	69	5	,	,	PUNCT
ejpam-5626	69	6	0]∗	0]∗	NUM
ejpam-5626	69	7	)	)	PUNCT
ejpam-5626	69	8	=	=	PUNCT
ejpam-5626	70	1	[	[	X
ejpam-5626	70	2	[	[	X
ejpam-5626	70	3	λ(0	λ(0	NOUN
ejpam-5626	70	4	)	)	PUNCT
ejpam-5626	70	5	,	,	PUNCT
ejpam-5626	70	6	0]•	0]•	NUM
ejpam-5626	70	7	,	,	PUNCT
ejpam-5626	70	8	0]∗	0]∗	NOUN
ejpam-5626	70	9	+	+	X
ejpam-5626	71	1	[	[	X
ejpam-5626	71	2	[	[	X
ejpam-5626	71	3	0,λ(0)]•	0,λ(0)]•	NUM
ejpam-5626	71	4	,	,	PUNCT
ejpam-5626	71	5	0]∗	0]∗	PRON
ejpam-5626	71	6	+	+	X
ejpam-5626	72	1	[	[	X
ejpam-5626	72	2	[	[	X
ejpam-5626	72	3	0	0	NUM
ejpam-5626	72	4	,	,	PUNCT
ejpam-5626	72	5	0]•,λ(0)]∗	0]•,λ(0)]∗	NOUN
ejpam-5626	72	6	=	=	SYM
ejpam-5626	72	7	0	0	X
ejpam-5626	72	8	.	.	PUNCT
ejpam-5626	73	1	lemma	lemma	PROPN
ejpam-5626	73	2	2.2	2.2	NUM
ejpam-5626	73	3	.	.	PUNCT
ejpam-5626	74	1	for	for	ADP
ejpam-5626	74	2	any	any	DET
ejpam-5626	74	3	lij	lij	PROPN
ejpam-5626	74	4	∈	∈	PROPN
ejpam-5626	74	5	aij	aij	PROPN
ejpam-5626	74	6	,	,	PUNCT
ejpam-5626	74	7	1	1	NUM
ejpam-5626	74	8	≤	≤	NUM
ejpam-5626	74	9	i	i	PRON
ejpam-5626	74	10	,	,	PUNCT
ejpam-5626	74	11	j	j	PROPN
ejpam-5626	74	12	≤	≤	PROPN
ejpam-5626	74	13	2	2	NUM
ejpam-5626	74	14	,	,	PUNCT
ejpam-5626	74	15	we	we	PRON
ejpam-5626	74	16	have	have	VERB
ejpam-5626	74	17	λ	λ	NOUN
ejpam-5626	74	18	(	(	PUNCT
ejpam-5626	74	19	2∑	2∑	NUM
ejpam-5626	74	20	i	i	NOUN
ejpam-5626	74	21	,	,	PUNCT
ejpam-5626	74	22	j=1	j=1	PROPN
ejpam-5626	74	23	lij	lij	PROPN
ejpam-5626	74	24	)	)	PUNCT
ejpam-5626	75	1	=	=	PUNCT
ejpam-5626	76	1	2∑	2∑	NUM
ejpam-5626	76	2	i	i	INTJ
ejpam-5626	76	3	,	,	PUNCT
ejpam-5626	76	4	j=1	j=1	PROPN
ejpam-5626	76	5	λ(lij	λ(lij	PROPN
ejpam-5626	76	6	)	)	PUNCT
ejpam-5626	76	7	.	.	PUNCT
ejpam-5626	77	1	proof	proof	NOUN
ejpam-5626	77	2	.	.	PUNCT
ejpam-5626	78	1	let	let	VERB
ejpam-5626	78	2	m	m	VERB
ejpam-5626	78	3	=	=	PRON
ejpam-5626	78	4	λ(l11	λ(l11	ADV
ejpam-5626	79	1	+	+	X
ejpam-5626	79	2	l12	l12	ADJ
ejpam-5626	79	3	+	+	CCONJ
ejpam-5626	79	4	l21	l21	NOUN
ejpam-5626	79	5	+	+	CCONJ
ejpam-5626	79	6	l22	l22	NOUN
ejpam-5626	79	7	)	)	PUNCT
ejpam-5626	79	8	−	−	NOUN
ejpam-5626	79	9	λ(l11	λ(l11	ADJ
ejpam-5626	79	10	)	)	PUNCT
ejpam-5626	79	11	−	−	NOUN
ejpam-5626	79	12	λ(l12	λ(l12	NOUN
ejpam-5626	79	13	)	)	PUNCT
ejpam-5626	80	1	−	−	NOUN
ejpam-5626	80	2	λ(l21	λ(l21	NOUN
ejpam-5626	80	3	)	)	PUNCT
ejpam-5626	81	1	−	−	NOUN
ejpam-5626	81	2	λ(l22	λ(l22	NOUN
ejpam-5626	81	3	)	)	PUNCT
ejpam-5626	81	4	.	.	PUNCT
ejpam-5626	82	1	in	in	ADP
ejpam-5626	82	2	order	order	NOUN
ejpam-5626	82	3	to	to	PART
ejpam-5626	82	4	prove	prove	VERB
ejpam-5626	82	5	that	that	PRON
ejpam-5626	82	6	λ(l11	λ(l11	VERB
ejpam-5626	82	7	+	+	X
ejpam-5626	82	8	l12	l12	ADJ
ejpam-5626	82	9	+	+	CCONJ
ejpam-5626	82	10	l21	l21	NOUN
ejpam-5626	82	11	+	+	CCONJ
ejpam-5626	82	12	l22	l22	NOUN
ejpam-5626	82	13	)	)	PUNCT
ejpam-5626	82	14	=	=	SYM
ejpam-5626	82	15	λ(l11	λ(l11	ADJ
ejpam-5626	82	16	)	)	PUNCT
ejpam-5626	83	1	+	+	CCONJ
ejpam-5626	83	2	λ(l12	λ(l12	NOUN
ejpam-5626	83	3	)	)	PUNCT
ejpam-5626	84	1	+	+	SYM
ejpam-5626	84	2	λ(l21	λ(l21	X
ejpam-5626	84	3	)	)	PUNCT
ejpam-5626	85	1	+	+	SYM
ejpam-5626	85	2	λ(l22	λ(l22	NOUN
ejpam-5626	85	3	)	)	PUNCT
ejpam-5626	85	4	,	,	PUNCT
ejpam-5626	85	5	we	we	PRON
ejpam-5626	85	6	show	show	VERB
ejpam-5626	85	7	m	m	VERB
ejpam-5626	85	8	=	=	NOUN
ejpam-5626	85	9	0	0	NUM
ejpam-5626	85	10	.	.	PUNCT
ejpam-5626	86	1	since	since	SCONJ
ejpam-5626	86	2	[	[	X
ejpam-5626	86	3	[	[	X
ejpam-5626	86	4	l12,p1]•,p1]∗	l12,p1]•,p1]∗	X
ejpam-5626	86	5	=	=	PUNCT
ejpam-5626	87	1	[	[	X
ejpam-5626	87	2	[	[	X
ejpam-5626	87	3	l21,p1]•,p1]∗	l21,p1]•,p1]∗	ADJ
ejpam-5626	87	4	=	=	PUNCT
ejpam-5626	88	1	[	[	X
ejpam-5626	88	2	[	[	X
ejpam-5626	88	3	l22,p1]•,p1]∗	l22,p1]•,p1]∗	X
ejpam-5626	88	4	=	=	SYM
ejpam-5626	88	5	0	0	X
ejpam-5626	88	6	.	.	PUNCT
ejpam-5626	89	1	it	it	PRON
ejpam-5626	89	2	follows	follow	VERB
ejpam-5626	89	3	from	from	ADP
ejpam-5626	89	4	lemma	lemma	PROPN
ejpam-5626	89	5	2.1	2.1	NUM
ejpam-5626	89	6	that	that	DET
ejpam-5626	89	7	λ([[l11	λ([[l11	PROPN
ejpam-5626	89	8	+	+	CCONJ
ejpam-5626	89	9	l12	l12	ADJ
ejpam-5626	89	10	+	+	CCONJ
ejpam-5626	89	11	l21	l21	NOUN
ejpam-5626	89	12	+	+	CCONJ
ejpam-5626	89	13	l22,p1]•,p1]∗	l22,p1]•,p1]∗	NOUN
ejpam-5626	89	14	)	)	PUNCT
ejpam-5626	89	15	=	=	SYM
ejpam-5626	90	1	λ([[l11,p1]•,p1]∗	λ([[l11,p1]•,p1]∗	X
ejpam-5626	90	2	)	)	PUNCT
ejpam-5626	90	3	+	+	CCONJ
ejpam-5626	90	4	λ([[l12,p1]•,p1]∗	λ([[l12,p1]•,p1]∗	PROPN
ejpam-5626	90	5	)	)	PUNCT
ejpam-5626	90	6	+	+	NOUN
ejpam-5626	90	7	λ([[l21,p1]•,p1]∗	λ([[l21,p1]•,p1]∗	X
ejpam-5626	90	8	)	)	PUNCT
ejpam-5626	90	9	+	+	CCONJ
ejpam-5626	90	10	λ([[l22,p1]•,p1]∗	λ([[l22,p1]•,p1]∗	NOUN
ejpam-5626	90	11	)	)	PUNCT
ejpam-5626	90	12	=	=	PUNCT
ejpam-5626	91	1	[	[	X
ejpam-5626	91	2	[	[	X
ejpam-5626	91	3	λ(l11	λ(l11	ADV
ejpam-5626	91	4	)	)	PUNCT
ejpam-5626	91	5	+	+	NUM
ejpam-5626	91	6	λ(l12	λ(l12	NOUN
ejpam-5626	91	7	)	)	PUNCT
ejpam-5626	91	8	+	+	SYM
ejpam-5626	91	9	λ(l21	λ(l21	X
ejpam-5626	91	10	)	)	PUNCT
ejpam-5626	91	11	+	+	CCONJ
ejpam-5626	92	1	λ(l22),p1]•,p1]∗	λ(l22),p1]•,p1]∗	X
ejpam-5626	92	2	+	+	PROPN
ejpam-5626	92	3	[	[	X
ejpam-5626	92	4	[	[	X
ejpam-5626	92	5	l11	l11	X
ejpam-5626	92	6	+	+	CCONJ
ejpam-5626	92	7	l12	l12	NOUN
ejpam-5626	92	8	+	+	CCONJ
ejpam-5626	92	9	l21	l21	NOUN
ejpam-5626	92	10	+	+	CCONJ
ejpam-5626	92	11	l22,λ(p1)]•,p1]∗	l22,λ(p1)]•,p1]∗	PUNCT
ejpam-5626	93	1	+	+	PUNCT
ejpam-5626	93	2	[	[	X
ejpam-5626	93	3	[	[	X
ejpam-5626	93	4	l11	l11	X
ejpam-5626	93	5	+	+	CCONJ
ejpam-5626	93	6	l12	l12	NOUN
ejpam-5626	93	7	+	+	CCONJ
ejpam-5626	93	8	l21	l21	NOUN
ejpam-5626	93	9	+	+	CCONJ
ejpam-5626	93	10	l22,p1]•,λ(p1)]∗	l22,p1]•,λ(p1)]∗	NOUN
ejpam-5626	93	11	and	and	CCONJ
ejpam-5626	93	12	λ([[l11	λ([[l11	PROPN
ejpam-5626	93	13	+	+	CCONJ
ejpam-5626	93	14	l12	l12	ADJ
ejpam-5626	93	15	+	+	CCONJ
ejpam-5626	93	16	l21	l21	NOUN
ejpam-5626	93	17	+	+	CCONJ
ejpam-5626	93	18	l22,p1]•,p1]∗	l22,p1]•,p1]∗	NOUN
ejpam-5626	93	19	)	)	PUNCT
ejpam-5626	94	1	=	=	PUNCT
ejpam-5626	95	1	[	[	X
ejpam-5626	95	2	[	[	X
ejpam-5626	95	3	λ(l11	λ(l11	X
ejpam-5626	95	4	+	+	X
ejpam-5626	95	5	l12	l12	ADJ
ejpam-5626	95	6	+	+	CCONJ
ejpam-5626	95	7	l21	l21	NOUN
ejpam-5626	95	8	+	+	CCONJ
ejpam-5626	95	9	l22),p1]•,p1]∗	l22),p1]•,p1]∗	PROPN
ejpam-5626	95	10	+	+	NOUN
ejpam-5626	96	1	[	[	X
ejpam-5626	96	2	[	[	X
ejpam-5626	96	3	l11	l11	X
ejpam-5626	96	4	+	+	CCONJ
ejpam-5626	96	5	l12	l12	NOUN
ejpam-5626	96	6	+	+	CCONJ
ejpam-5626	96	7	l21	l21	NOUN
ejpam-5626	96	8	+	+	CCONJ
ejpam-5626	96	9	l22,λ(p1)]•,p1]∗	l22,λ(p1)]•,p1]∗	PUNCT
ejpam-5626	97	1	+	+	PUNCT
ejpam-5626	97	2	[	[	X
ejpam-5626	97	3	[	[	X
ejpam-5626	97	4	l11	l11	X
ejpam-5626	97	5	+	+	CCONJ
ejpam-5626	97	6	l12	l12	NOUN
ejpam-5626	97	7	+	+	CCONJ
ejpam-5626	97	8	l21	l21	NOUN
ejpam-5626	97	9	+	+	CCONJ
ejpam-5626	97	10	l22,p1]•,λ(p1)]∗.	l22,p1]•,λ(p1)]∗.	VERB
ejpam-5626	97	11	from	from	ADP
ejpam-5626	97	12	the	the	DET
ejpam-5626	97	13	above	above	ADJ
ejpam-5626	97	14	equations	equation	NOUN
ejpam-5626	97	15	,	,	PUNCT
ejpam-5626	97	16	we	we	PRON
ejpam-5626	97	17	get	get	VERB
ejpam-5626	97	18	[	[	X
ejpam-5626	97	19	[	[	X
ejpam-5626	97	20	m	m	NOUN
ejpam-5626	97	21	,	,	PUNCT
ejpam-5626	97	22	p1]•,p1]∗	p1]•,p1]∗	PROPN
ejpam-5626	97	23	=	=	SYM
ejpam-5626	97	24	0	0	PROPN
ejpam-5626	97	25	.	.	PUNCT
ejpam-5626	98	1	this	this	PRON
ejpam-5626	98	2	implies	imply	VERB
ejpam-5626	98	3	that	that	SCONJ
ejpam-5626	98	4	mp1−p1	mp1−p1	PROPN
ejpam-5626	98	5	m	m	VERB
ejpam-5626	98	6	∗p1−	∗p1−	NOUN
ejpam-5626	98	7	p1	p1	PROPN
ejpam-5626	98	8	m	m	PROPN
ejpam-5626	98	9	∗	∗	NOUN
ejpam-5626	98	10	+	+	CCONJ
ejpam-5626	98	11	p1mp1	p1mp1	NOUN
ejpam-5626	98	12	=	=	SYM
ejpam-5626	98	13	0	0	NUM
ejpam-5626	98	14	.	.	PUNCT
ejpam-5626	99	1	by	by	ADP
ejpam-5626	99	2	multiplying	multiply	VERB
ejpam-5626	99	3	p2	p2	PROPN
ejpam-5626	99	4	from	from	ADP
ejpam-5626	99	5	left	left	ADJ
ejpam-5626	99	6	,	,	PUNCT
ejpam-5626	99	7	we	we	PRON
ejpam-5626	99	8	get	get	VERB
ejpam-5626	99	9	p2mp1	p2mp1	NOUN
ejpam-5626	99	10	=	=	NOUN
ejpam-5626	99	11	0	0	X
ejpam-5626	99	12	.	.	PUNCT
ejpam-5626	100	1	similarly	similarly	ADV
ejpam-5626	100	2	,	,	PUNCT
ejpam-5626	100	3	by	by	ADP
ejpam-5626	100	4	m.	m.	NOUN
ejpam-5626	100	5	a.	a.	PROPN
ejpam-5626	100	6	raza	raza	PROPN
ejpam-5626	100	7	et	et	PROPN
ejpam-5626	100	8	al	al	PROPN
ejpam-5626	100	9	.	.	PUNCT
ejpam-5626	100	10	/	/	SYM
ejpam-5626	100	11	eur	eur	PROPN
ejpam-5626	100	12	.	.	PUNCT
ejpam-5626	101	1	j.	j.	PROPN
ejpam-5626	101	2	pure	pure	PROPN
ejpam-5626	101	3	appl	appl	PROPN
ejpam-5626	101	4	.	.	PROPN
ejpam-5626	101	5	math	math	PROPN
ejpam-5626	101	6	,	,	PUNCT
ejpam-5626	101	7	18	18	NUM
ejpam-5626	101	8	(	(	PUNCT
ejpam-5626	101	9	1	1	NUM
ejpam-5626	101	10	)	)	PUNCT
ejpam-5626	101	11	(	(	PUNCT
ejpam-5626	101	12	2025	2025	NUM
ejpam-5626	101	13	)	)	PUNCT
ejpam-5626	101	14	,	,	PUNCT
ejpam-5626	101	15	5626	5626	NUM
ejpam-5626	101	16	4	4	NUM
ejpam-5626	101	17	of	of	ADP
ejpam-5626	101	18	10	10	NUM
ejpam-5626	101	19	applying	apply	VERB
ejpam-5626	101	20	p2	p2	PROPN
ejpam-5626	101	21	instead	instead	ADV
ejpam-5626	101	22	of	of	ADP
ejpam-5626	101	23	p1	p1	NOUN
ejpam-5626	101	24	,	,	PUNCT
ejpam-5626	101	25	we	we	PRON
ejpam-5626	101	26	get	get	VERB
ejpam-5626	101	27	p1mp2	p1mp2	ADJ
ejpam-5626	101	28	=	=	NOUN
ejpam-5626	101	29	0	0	X
ejpam-5626	101	30	.	.	PUNCT
ejpam-5626	102	1	also	also	ADV
ejpam-5626	102	2	,	,	PUNCT
ejpam-5626	102	3	for	for	ADP
ejpam-5626	102	4	any	any	DET
ejpam-5626	102	5	x12	x12	NUM
ejpam-5626	102	6	∈	∈	PROPN
ejpam-5626	102	7	a12	a12	NOUN
ejpam-5626	102	8	,	,	PUNCT
ejpam-5626	102	9	we	we	PRON
ejpam-5626	102	10	have	have	VERB
ejpam-5626	102	11	λ([[l11	λ([[l11	NOUN
ejpam-5626	102	12	+	+	CCONJ
ejpam-5626	102	13	l12	l12	ADJ
ejpam-5626	102	14	+	+	CCONJ
ejpam-5626	102	15	l21	l21	NOUN
ejpam-5626	102	16	+	+	CCONJ
ejpam-5626	102	17	l22,x12]•,p2]∗	l22,x12]•,p2]∗	PROPN
ejpam-5626	102	18	)	)	PUNCT
ejpam-5626	102	19	=	=	PUNCT
ejpam-5626	103	1	[	[	X
ejpam-5626	103	2	[	[	X
ejpam-5626	103	3	λ(l11	λ(l11	X
ejpam-5626	103	4	+	+	X
ejpam-5626	103	5	l12	l12	ADJ
ejpam-5626	103	6	+	+	CCONJ
ejpam-5626	103	7	l21	l21	NOUN
ejpam-5626	103	8	+	+	CCONJ
ejpam-5626	103	9	l22),x12]•,p2]∗	l22),x12]•,p2]∗	VERB
ejpam-5626	104	1	+	+	PROPN
ejpam-5626	104	2	[	[	X
ejpam-5626	104	3	[	[	X
ejpam-5626	104	4	l11	l11	X
ejpam-5626	104	5	+	+	CCONJ
ejpam-5626	104	6	l12	l12	NOUN
ejpam-5626	104	7	+	+	CCONJ
ejpam-5626	104	8	l21	l21	NOUN
ejpam-5626	104	9	+	+	CCONJ
ejpam-5626	104	10	l22,λ(x12)]•,p2]∗	l22,λ(x12)]•,p2]∗	NOUN
ejpam-5626	105	1	+	+	ADP
ejpam-5626	105	2	[	[	X
ejpam-5626	105	3	[	[	X
ejpam-5626	105	4	l11	l11	X
ejpam-5626	105	5	+	+	CCONJ
ejpam-5626	105	6	l12	l12	NOUN
ejpam-5626	105	7	+	+	CCONJ
ejpam-5626	105	8	l21	l21	NOUN
ejpam-5626	105	9	+	+	CCONJ
ejpam-5626	105	10	l22,x12]•,λ(p2)]∗.	l22,x12]•,λ(p2)]∗.	PROPN
ejpam-5626	105	11	from	from	ADP
ejpam-5626	105	12	lemma	lemma	PROPN
ejpam-5626	105	13	2.1	2.1	NUM
ejpam-5626	105	14	,	,	PUNCT
ejpam-5626	105	15	we	we	PRON
ejpam-5626	105	16	get	get	VERB
ejpam-5626	105	17	λ([[l11	λ([[l11	NOUN
ejpam-5626	105	18	+	+	CCONJ
ejpam-5626	105	19	l12	l12	ADJ
ejpam-5626	105	20	+	+	CCONJ
ejpam-5626	105	21	l21	l21	NOUN
ejpam-5626	105	22	+	+	CCONJ
ejpam-5626	105	23	l22,x12]•,p2]∗	l22,x12]•,p2]∗	NOUN
ejpam-5626	105	24	)	)	PUNCT
ejpam-5626	105	25	=	=	SYM
ejpam-5626	105	26	λ([[l11,x12]•,p2]∗	λ([[l11,x12]•,p2]∗	NOUN
ejpam-5626	105	27	)	)	PUNCT
ejpam-5626	106	1	+	+	SYM
ejpam-5626	106	2	λ([[l12,x12]•,p2]∗	λ([[l12,x12]•,p2]∗	NOUN
ejpam-5626	106	3	)	)	PUNCT
ejpam-5626	106	4	+	+	NOUN
ejpam-5626	106	5	λ([[l21,x12]•,p2]∗	λ([[l21,x12]•,p2]∗	NOUN
ejpam-5626	106	6	)	)	PUNCT
ejpam-5626	106	7	+	+	SYM
ejpam-5626	106	8	λ([[l22,x12]•,p2]∗	λ([[l22,x12]•,p2]∗	NOUN
ejpam-5626	106	9	)	)	PUNCT
ejpam-5626	106	10	=	=	PUNCT
ejpam-5626	107	1	[	[	X
ejpam-5626	107	2	[	[	X
ejpam-5626	107	3	λ(l11),x12]•,p2]∗	λ(l11),x12]•,p2]∗	X
ejpam-5626	107	4	+	+	X
ejpam-5626	107	5	[	[	X
ejpam-5626	107	6	[	[	X
ejpam-5626	107	7	l11,λ(x12)]•,p2]∗	l11,λ(x12)]•,p2]∗	X
ejpam-5626	107	8	+	+	NOUN
ejpam-5626	107	9	[	[	X
ejpam-5626	107	10	[	[	X
ejpam-5626	107	11	l11,x12]•,λ(p2)]∗	l11,x12]•,λ(p2)]∗	NOUN
ejpam-5626	107	12	+	+	X
ejpam-5626	108	1	[	[	X
ejpam-5626	108	2	[	[	X
ejpam-5626	108	3	λ(l12),x12]•,p2]∗	λ(l12),x12]•,p2]∗	X
ejpam-5626	108	4	+	+	NOUN
ejpam-5626	108	5	[	[	X
ejpam-5626	108	6	[	[	X
ejpam-5626	108	7	l12,λ(x12)]•,p2]∗	l12,λ(x12)]•,p2]∗	X
ejpam-5626	108	8	+	+	X
ejpam-5626	108	9	[	[	X
ejpam-5626	108	10	[	[	X
ejpam-5626	108	11	l12,x12]•,λ(p2)]∗	l12,x12]•,λ(p2)]∗	X
ejpam-5626	108	12	+	+	NOUN
ejpam-5626	108	13	[	[	X
ejpam-5626	108	14	[	[	X
ejpam-5626	108	15	λ(l21),x12]•,p2]∗	λ(l21),x12]•,p2]∗	X
ejpam-5626	108	16	+	+	NOUN
ejpam-5626	108	17	[	[	X
ejpam-5626	108	18	[	[	X
ejpam-5626	108	19	l21,λ(x12)]•,p2]∗	l21,λ(x12)]•,p2]∗	X
ejpam-5626	108	20	+	+	NOUN
ejpam-5626	108	21	[	[	X
ejpam-5626	108	22	[	[	X
ejpam-5626	108	23	l21,x12]•,λ(p2)]∗	l21,x12]•,λ(p2)]∗	X
ejpam-5626	108	24	+	+	X
ejpam-5626	109	1	[	[	X
ejpam-5626	109	2	[	[	X
ejpam-5626	109	3	λ(l22),x12]•,p2]∗	λ(l22),x12]•,p2]∗	X
ejpam-5626	109	4	+	+	NOUN
ejpam-5626	109	5	[	[	X
ejpam-5626	109	6	[	[	X
ejpam-5626	109	7	l22,λ(x12)]•,p2]∗	l22,λ(x12)]•,p2]∗	X
ejpam-5626	109	8	+	+	X
ejpam-5626	109	9	[	[	X
ejpam-5626	109	10	[	[	X
ejpam-5626	109	11	l22,x12]•,λ(p2)]∗.	l22,x12]•,λ(p2)]∗.	PROPN
ejpam-5626	109	12	from	from	ADP
ejpam-5626	109	13	the	the	DET
ejpam-5626	109	14	above	above	ADJ
ejpam-5626	109	15	two	two	NUM
ejpam-5626	109	16	equations	equation	NOUN
ejpam-5626	109	17	,	,	PUNCT
ejpam-5626	109	18	we	we	PRON
ejpam-5626	109	19	get	get	VERB
ejpam-5626	109	20	[	[	X
ejpam-5626	109	21	[	[	X
ejpam-5626	109	22	m	m	ADJ
ejpam-5626	109	23	,	,	PUNCT
ejpam-5626	109	24	x12]•,p2]∗	x12]•,p2]∗	NOUN
ejpam-5626	109	25	=	=	SYM
ejpam-5626	109	26	0	0	PROPN
ejpam-5626	109	27	.	.	PUNCT
ejpam-5626	110	1	that	that	PRON
ejpam-5626	110	2	means	mean	VERB
ejpam-5626	110	3	−x12	−x12	X
ejpam-5626	110	4	m	m	VERB
ejpam-5626	110	5	∗p2	∗p2	NOUN
ejpam-5626	110	6	+	+	NOUN
ejpam-5626	110	7	p2mx∗	p2mx∗	NOUN
ejpam-5626	110	8	12	12	NUM
ejpam-5626	110	9	=	=	SYM
ejpam-5626	110	10	0	0	NUM
ejpam-5626	110	11	.	.	PUNCT
ejpam-5626	111	1	by	by	ADP
ejpam-5626	111	2	multiplying	multiply	VERB
ejpam-5626	111	3	p1	p1	PROPN
ejpam-5626	111	4	from	from	ADP
ejpam-5626	111	5	left	left	ADJ
ejpam-5626	111	6	,	,	PUNCT
ejpam-5626	111	7	we	we	PRON
ejpam-5626	111	8	get	get	VERB
ejpam-5626	111	9	p2mx∗	p2mx∗	NOUN
ejpam-5626	111	10	12	12	NUM
ejpam-5626	111	11	=	=	SYM
ejpam-5626	111	12	0	0	NUM
ejpam-5626	111	13	.	.	PUNCT
ejpam-5626	112	1	thus	thus	ADV
ejpam-5626	112	2	,	,	PUNCT
ejpam-5626	112	3	p2mp2	p2mp2	PROPN
ejpam-5626	112	4	=	=	NOUN
ejpam-5626	112	5	0	0	NUM
ejpam-5626	112	6	by	by	ADP
ejpam-5626	112	7	using	use	VERB
ejpam-5626	112	8	(	(	PUNCT
ejpam-5626	112	9	▲	▲	PUNCT
ejpam-5626	112	10	)	)	PUNCT
ejpam-5626	112	11	and	and	CCONJ
ejpam-5626	112	12	(	(	PUNCT
ejpam-5626	112	13	▼	▼	NOUN
ejpam-5626	112	14	)	)	PUNCT
ejpam-5626	112	15	.	.	PUNCT
ejpam-5626	113	1	in	in	ADP
ejpam-5626	113	2	the	the	DET
ejpam-5626	113	3	similar	similar	ADJ
ejpam-5626	113	4	way	way	NOUN
ejpam-5626	113	5	,	,	PUNCT
ejpam-5626	113	6	we	we	PRON
ejpam-5626	113	7	can	can	AUX
ejpam-5626	113	8	show	show	VERB
ejpam-5626	113	9	that	that	DET
ejpam-5626	113	10	p1mp1	p1mp1	NOUN
ejpam-5626	113	11	=	=	NOUN
ejpam-5626	113	12	0	0	NUM
ejpam-5626	113	13	by	by	ADP
ejpam-5626	113	14	choosing	choose	VERB
ejpam-5626	113	15	x21	x21	PROPN
ejpam-5626	113	16	and	and	CCONJ
ejpam-5626	113	17	p1	p1	PROPN
ejpam-5626	113	18	instead	instead	ADV
ejpam-5626	113	19	of	of	ADP
ejpam-5626	113	20	x21	x21	NUM
ejpam-5626	113	21	and	and	CCONJ
ejpam-5626	113	22	p1	p1	NOUN
ejpam-5626	113	23	respectively	respectively	ADV
ejpam-5626	113	24	in	in	ADP
ejpam-5626	113	25	above	above	ADV
ejpam-5626	113	26	.	.	PUNCT
ejpam-5626	114	1	hence	hence	ADV
ejpam-5626	114	2	m	m	VERB
ejpam-5626	114	3	=	=	ADJ
ejpam-5626	114	4	0	0	X
ejpam-5626	114	5	.	.	PUNCT
ejpam-5626	115	1	it	it	PRON
ejpam-5626	115	2	follows	follow	VERB
ejpam-5626	115	3	that	that	SCONJ
ejpam-5626	115	4	λ	λ	PROPN
ejpam-5626	115	5	(	(	PUNCT
ejpam-5626	115	6	∑2	∑2	PROPN
ejpam-5626	115	7	i	i	PROPN
ejpam-5626	115	8	,	,	PUNCT
ejpam-5626	115	9	j=1lij	j=1lij	PROPN
ejpam-5626	115	10	)	)	PUNCT
ejpam-5626	116	1	=	=	SYM
ejpam-5626	116	2	∑2	∑2	NOUN
ejpam-5626	117	1	i	i	PRON
ejpam-5626	117	2	,	,	PUNCT
ejpam-5626	117	3	j=1	j=1	PROPN
ejpam-5626	117	4	λ(lij	λ(lij	PROPN
ejpam-5626	117	5	)	)	PUNCT
ejpam-5626	117	6	.	.	PUNCT
ejpam-5626	118	1	lemma	lemma	PROPN
ejpam-5626	118	2	2.3	2.3	NUM
ejpam-5626	118	3	.	.	PUNCT
ejpam-5626	119	1	for	for	ADP
ejpam-5626	119	2	each	each	DET
ejpam-5626	119	3	l12,m12	l12,m12	PROPN
ejpam-5626	119	4	∈	∈	PROPN
ejpam-5626	119	5	a12	a12	NOUN
ejpam-5626	119	6	and	and	CCONJ
ejpam-5626	119	7	l21,m21	l21,m21	NOUN
ejpam-5626	119	8	∈	∈	PROPN
ejpam-5626	119	9	a21	a21	NOUN
ejpam-5626	119	10	,	,	PUNCT
ejpam-5626	119	11	we	we	PRON
ejpam-5626	119	12	have	have	VERB
ejpam-5626	119	13	(	(	PUNCT
ejpam-5626	119	14	i	i	NOUN
ejpam-5626	119	15	)	)	PUNCT
ejpam-5626	119	16	λ(l12	λ(l12	NOUN
ejpam-5626	120	1	+	+	SYM
ejpam-5626	120	2	m12	m12	NOUN
ejpam-5626	120	3	)	)	PUNCT
ejpam-5626	120	4	=	=	SYM
ejpam-5626	120	5	λ(l12	λ(l12	NOUN
ejpam-5626	120	6	)	)	PUNCT
ejpam-5626	121	1	+	+	CCONJ
ejpam-5626	121	2	λ(m12	λ(m12	NUM
ejpam-5626	121	3	)	)	PUNCT
ejpam-5626	121	4	.	.	PUNCT
ejpam-5626	122	1	(	(	PUNCT
ejpam-5626	122	2	ii	ii	NOUN
ejpam-5626	122	3	)	)	PUNCT
ejpam-5626	122	4	λ(l21	λ(l21	NOUN
ejpam-5626	123	1	+	+	SYM
ejpam-5626	123	2	m21	m21	X
ejpam-5626	123	3	)	)	PUNCT
ejpam-5626	123	4	=	=	SYM
ejpam-5626	123	5	λ(l21	λ(l21	ADJ
ejpam-5626	123	6	)	)	PUNCT
ejpam-5626	123	7	+	+	NUM
ejpam-5626	123	8	λ(m21	λ(m21	NOUN
ejpam-5626	123	9	)	)	PUNCT
ejpam-5626	123	10	.	.	PUNCT
ejpam-5626	124	1	proof	proof	NOUN
ejpam-5626	124	2	.	.	PUNCT
ejpam-5626	125	1	(	(	PUNCT
ejpam-5626	125	2	1	1	X
ejpam-5626	125	3	)	)	PUNCT
ejpam-5626	125	4	let	let	VERB
ejpam-5626	125	5	t	t	NOUN
ejpam-5626	125	6	=	=	SYM
ejpam-5626	125	7	λ(l12	λ(l12	NOUN
ejpam-5626	125	8	+	+	NOUN
ejpam-5626	125	9	m12)−λ(l12)−λ(m12	m12)−λ(l12)−λ(m12	ADJ
ejpam-5626	125	10	)	)	PUNCT
ejpam-5626	125	11	.	.	PUNCT
ejpam-5626	126	1	it	it	PRON
ejpam-5626	126	2	follows	follow	VERB
ejpam-5626	126	3	from	from	ADP
ejpam-5626	126	4	lemma	lemma	PROPN
ejpam-5626	126	5	2.1	2.1	NUM
ejpam-5626	126	6	that	that	DET
ejpam-5626	126	7	λ([[l12	λ([[l12	NOUN
ejpam-5626	126	8	+	+	NOUN
ejpam-5626	126	9	m12,p1]•,p2]∗	m12,p1]•,p2]∗	NOUN
ejpam-5626	126	10	)	)	PUNCT
ejpam-5626	126	11	=	=	SYM
ejpam-5626	127	1	λ([[l12,p1]•,p2]∗	λ([[l12,p1]•,p2]∗	X
ejpam-5626	127	2	)	)	PUNCT
ejpam-5626	127	3	+	+	SYM
ejpam-5626	127	4	λ([[m12,p1]•,p2]∗	λ([[m12,p1]•,p2]∗	NOUN
ejpam-5626	127	5	)	)	PUNCT
ejpam-5626	127	6	=	=	PUNCT
ejpam-5626	128	1	[	[	X
ejpam-5626	128	2	[	[	X
ejpam-5626	128	3	λ(l12),p1]•,p2]∗	λ(l12),p1]•,p2]∗	X
ejpam-5626	128	4	+	+	NOUN
ejpam-5626	128	5	[	[	X
ejpam-5626	128	6	[	[	X
ejpam-5626	128	7	l12,λ(p1)]•,p2]∗	l12,λ(p1)]•,p2]∗	X
ejpam-5626	128	8	+	+	X
ejpam-5626	129	1	[	[	X
ejpam-5626	129	2	[	[	X
ejpam-5626	129	3	l12,p1]•,λ(p2)]∗	l12,p1]•,λ(p2)]∗	X
ejpam-5626	129	4	+	+	NOUN
ejpam-5626	129	5	[	[	X
ejpam-5626	129	6	[	[	X
ejpam-5626	129	7	λ(m12),p1]•,p2]∗	λ(m12),p1]•,p2]∗	X
ejpam-5626	129	8	+	+	X
ejpam-5626	129	9	[	[	X
ejpam-5626	129	10	[	[	X
ejpam-5626	129	11	m12,λ(p1)]•,p2]∗	m12,λ(p1)]•,p2]∗	X
ejpam-5626	129	12	+	+	X
ejpam-5626	130	1	[	[	X
ejpam-5626	130	2	[	[	X
ejpam-5626	130	3	m12,p1]•,λ(p2)]∗.	m12,p1]•,λ(p2)]∗.	PROPN
ejpam-5626	130	4	alternatively	alternatively	ADV
ejpam-5626	130	5	,	,	PUNCT
ejpam-5626	130	6	we	we	PRON
ejpam-5626	130	7	have	have	VERB
ejpam-5626	130	8	λ([[l12	λ([[l12	NOUN
ejpam-5626	130	9	+	+	NOUN
ejpam-5626	130	10	m12,p1]•,p2]∗	m12,p1]•,p2]∗	NOUN
ejpam-5626	130	11	)	)	PUNCT
ejpam-5626	130	12	=	=	NOUN
ejpam-5626	131	1	[	[	X
ejpam-5626	131	2	[	[	X
ejpam-5626	131	3	λ(l12	λ(l12	X
ejpam-5626	131	4	+	+	NOUN
ejpam-5626	131	5	m12),p1]•,p2]∗	m12),p1]•,p2]∗	NOUN
ejpam-5626	131	6	+	+	X
ejpam-5626	132	1	[	[	X
ejpam-5626	132	2	[	[	X
ejpam-5626	132	3	l12	l12	ADJ
ejpam-5626	132	4	+	+	NOUN
ejpam-5626	132	5	m12,λ(p1)]•,p2]∗	m12,λ(p1)]•,p2]∗	NOUN
ejpam-5626	132	6	+	+	NOUN
ejpam-5626	132	7	[	[	X
ejpam-5626	132	8	[	[	X
ejpam-5626	132	9	l12	l12	NOUN
ejpam-5626	132	10	+	+	X
ejpam-5626	132	11	m12,p1]•,λ(p2)]∗.	m12,p1]•,λ(p2)]∗.	NOUN
ejpam-5626	132	12	by	by	ADP
ejpam-5626	132	13	comparing	compare	VERB
ejpam-5626	132	14	the	the	DET
ejpam-5626	132	15	above	above	ADJ
ejpam-5626	132	16	two	two	NUM
ejpam-5626	132	17	expressions	expression	NOUN
ejpam-5626	132	18	,	,	PUNCT
ejpam-5626	132	19	we	we	PRON
ejpam-5626	132	20	get	get	VERB
ejpam-5626	132	21	[	[	X
ejpam-5626	132	22	[	[	X
ejpam-5626	132	23	t	t	NOUN
ejpam-5626	132	24	,	,	PUNCT
ejpam-5626	132	25	p1]•,p2]∗	p1]•,p2]∗	NOUN
ejpam-5626	132	26	=	=	SYM
ejpam-5626	132	27	0	0	X
ejpam-5626	132	28	.	.	PUNCT
ejpam-5626	133	1	this	this	PRON
ejpam-5626	133	2	implies	imply	VERB
ejpam-5626	133	3	that	that	SCONJ
ejpam-5626	133	4	p2tp1	p2tp1	NOUN
ejpam-5626	133	5	=	=	SYM
ejpam-5626	133	6	0	0	NUM
ejpam-5626	133	7	.	.	PUNCT
ejpam-5626	134	1	similarly	similarly	ADV
ejpam-5626	134	2	,	,	PUNCT
ejpam-5626	134	3	p1tp2	p1tp2	NOUN
ejpam-5626	134	4	=	=	NOUN
ejpam-5626	134	5	0	0	X
ejpam-5626	134	6	.	.	PUNCT
ejpam-5626	135	1	for	for	ADP
ejpam-5626	135	2	any	any	DET
ejpam-5626	135	3	x12	x12	NUM
ejpam-5626	135	4	∈	∈	PROPN
ejpam-5626	135	5	a12	a12	NOUN
ejpam-5626	135	6	,	,	PUNCT
ejpam-5626	135	7	we	we	PRON
ejpam-5626	135	8	have	have	VERB
ejpam-5626	135	9	λ([[x12,l12	λ([[x12,l12	PROPN
ejpam-5626	135	10	+	+	ADJ
ejpam-5626	135	11	m12]•,p2]∗	m12]•,p2]∗	ADJ
ejpam-5626	135	12	)	)	PUNCT
ejpam-5626	135	13	=	=	PUNCT
ejpam-5626	136	1	[	[	X
ejpam-5626	136	2	[	[	X
ejpam-5626	136	3	λ(x12),l12	λ(x12),l12	X
ejpam-5626	136	4	+	+	NUM
ejpam-5626	136	5	m12]•,p2]∗	m12]•,p2]∗	ADJ
ejpam-5626	137	1	+	+	X
ejpam-5626	138	1	[	[	X
ejpam-5626	138	2	[	[	X
ejpam-5626	138	3	x12,λ(l12	x12,λ(l12	X
ejpam-5626	138	4	+	+	NOUN
ejpam-5626	138	5	m12)]•,p2]∗	m12)]•,p2]∗	X
ejpam-5626	138	6	m.	m.	NOUN
ejpam-5626	138	7	a.	a.	NOUN
ejpam-5626	138	8	raza	raza	PROPN
ejpam-5626	138	9	et	et	PROPN
ejpam-5626	138	10	al	al	PROPN
ejpam-5626	138	11	.	.	PUNCT
ejpam-5626	138	12	/	/	SYM
ejpam-5626	138	13	eur	eur	PROPN
ejpam-5626	138	14	.	.	PUNCT
ejpam-5626	139	1	j.	j.	PROPN
ejpam-5626	139	2	pure	pure	PROPN
ejpam-5626	139	3	appl	appl	PROPN
ejpam-5626	139	4	.	.	PROPN
ejpam-5626	139	5	math	math	PROPN
ejpam-5626	139	6	,	,	PUNCT
ejpam-5626	139	7	18	18	NUM
ejpam-5626	139	8	(	(	PUNCT
ejpam-5626	139	9	1	1	NUM
ejpam-5626	139	10	)	)	PUNCT
ejpam-5626	139	11	(	(	PUNCT
ejpam-5626	139	12	2025	2025	NUM
ejpam-5626	139	13	)	)	PUNCT
ejpam-5626	139	14	,	,	PUNCT
ejpam-5626	139	15	5626	5626	NUM
ejpam-5626	139	16	5	5	NUM
ejpam-5626	139	17	of	of	ADP
ejpam-5626	139	18	10	10	NUM
ejpam-5626	140	1	+	+	NOUN
ejpam-5626	140	2	[	[	X
ejpam-5626	140	3	[	[	X
ejpam-5626	140	4	x12,l12	x12,l12	INTJ
ejpam-5626	140	5	+	+	ADJ
ejpam-5626	140	6	m12]•,λ(p2)]∗.	m12]•,λ(p2)]∗.	NOUN
ejpam-5626	140	7	since	since	SCONJ
ejpam-5626	140	8	[	[	X
ejpam-5626	140	9	[	[	X
ejpam-5626	140	10	x12,l12]•,p2]∗	x12,l12]•,p2]∗	X
ejpam-5626	140	11	=	=	SYM
ejpam-5626	140	12	0	0	PUNCT
ejpam-5626	140	13	and	and	CCONJ
ejpam-5626	140	14	using	use	VERB
ejpam-5626	140	15	lemma	lemma	PROPN
ejpam-5626	140	16	2.1	2.1	NUM
ejpam-5626	140	17	,	,	PUNCT
ejpam-5626	140	18	we	we	PRON
ejpam-5626	140	19	have	have	VERB
ejpam-5626	140	20	λ([[x12,l12	λ([[x12,l12	PROPN
ejpam-5626	141	1	+	+	ADJ
ejpam-5626	141	2	m12]•,p2]∗	m12]•,p2]∗	ADJ
ejpam-5626	141	3	)	)	PUNCT
ejpam-5626	141	4	=	=	SYM
ejpam-5626	141	5	λ([[x12,l12]•,p2]∗	λ([[x12,l12]•,p2]∗	PROPN
ejpam-5626	141	6	)	)	PUNCT
ejpam-5626	142	1	+	+	SYM
ejpam-5626	142	2	λ([[x12,m12]•,p2]∗	λ([[x12,m12]•,p2]∗	NOUN
ejpam-5626	142	3	)	)	PUNCT
ejpam-5626	142	4	=	=	PUNCT
ejpam-5626	143	1	[	[	X
ejpam-5626	143	2	[	[	X
ejpam-5626	143	3	λ(x12),l12]•,p2]∗	λ(x12),l12]•,p2]∗	X
ejpam-5626	143	4	+	+	NOUN
ejpam-5626	144	1	[	[	X
ejpam-5626	144	2	[	[	X
ejpam-5626	144	3	x12,λ(l12)]•,p2]∗	x12,λ(l12)]•,p2]∗	X
ejpam-5626	144	4	+	+	NOUN
ejpam-5626	144	5	[	[	X
ejpam-5626	144	6	[	[	X
ejpam-5626	144	7	x12,l12]•,λ(p2)]∗	x12,l12]•,λ(p2)]∗	X
ejpam-5626	144	8	+	+	X
ejpam-5626	145	1	[	[	X
ejpam-5626	145	2	[	[	X
ejpam-5626	145	3	λ(x12),m12]•,p2]∗	λ(x12),m12]•,p2]∗	X
ejpam-5626	145	4	+	+	NOUN
ejpam-5626	145	5	[	[	X
ejpam-5626	145	6	[	[	X
ejpam-5626	145	7	x12,λ(m12)]•,p2]∗	x12,λ(m12)]•,p2]∗	X
ejpam-5626	145	8	+	+	X
ejpam-5626	145	9	[	[	X
ejpam-5626	145	10	[	[	X
ejpam-5626	145	11	x12,m12]•,λ(p2)]∗.	x12,m12]•,λ(p2)]∗.	NUM
ejpam-5626	145	12	from	from	ADP
ejpam-5626	145	13	the	the	DET
ejpam-5626	145	14	last	last	ADJ
ejpam-5626	145	15	two	two	NUM
ejpam-5626	145	16	expressions	expression	NOUN
ejpam-5626	145	17	,	,	PUNCT
ejpam-5626	145	18	we	we	PRON
ejpam-5626	145	19	get	get	VERB
ejpam-5626	145	20	[	[	X
ejpam-5626	145	21	[	[	X
ejpam-5626	145	22	x12	x12	NUM
ejpam-5626	145	23	,	,	PUNCT
ejpam-5626	145	24	t	t	X
ejpam-5626	145	25	]	]	X
ejpam-5626	145	26	•,p2]∗	•,p2]∗	NOUN
ejpam-5626	145	27	=	=	NOUN
ejpam-5626	145	28	0	0	PROPN
ejpam-5626	145	29	.	.	PUNCT
ejpam-5626	146	1	that	that	PRON
ejpam-5626	146	2	means	mean	VERB
ejpam-5626	146	3	x12	x12	NUM
ejpam-5626	146	4	t	t	NOUN
ejpam-5626	146	5	∗p2	∗p2	NOUN
ejpam-5626	146	6	−	−	NOUN
ejpam-5626	146	7	p2mx∗	p2mx∗	NOUN
ejpam-5626	146	8	12	12	NUM
ejpam-5626	146	9	=	=	SYM
ejpam-5626	146	10	0	0	X
ejpam-5626	146	11	.	.	PUNCT
ejpam-5626	147	1	multiplying	multiply	VERB
ejpam-5626	147	2	left	leave	VERB
ejpam-5626	147	3	side	side	NOUN
ejpam-5626	147	4	by	by	ADP
ejpam-5626	147	5	p2	p2	PROPN
ejpam-5626	147	6	and	and	CCONJ
ejpam-5626	147	7	then	then	ADV
ejpam-5626	147	8	using	use	VERB
ejpam-5626	147	9	(	(	PUNCT
ejpam-5626	147	10	▲	▲	PUNCT
ejpam-5626	147	11	)	)	PUNCT
ejpam-5626	147	12	and	and	CCONJ
ejpam-5626	147	13	(	(	PUNCT
ejpam-5626	147	14	▼	▼	NOUN
ejpam-5626	147	15	)	)	PUNCT
ejpam-5626	147	16	,	,	PUNCT
ejpam-5626	147	17	we	we	PRON
ejpam-5626	147	18	get	get	VERB
ejpam-5626	147	19	p2tp2	p2tp2	NOUN
ejpam-5626	147	20	=	=	NOUN
ejpam-5626	147	21	0	0	X
ejpam-5626	147	22	.	.	PUNCT
ejpam-5626	148	1	similarly	similarly	ADV
ejpam-5626	148	2	,	,	PUNCT
ejpam-5626	148	3	p1tp1	p1tp1	NOUN
ejpam-5626	148	4	=	=	SYM
ejpam-5626	148	5	0	0	NUM
ejpam-5626	148	6	.	.	PUNCT
ejpam-5626	149	1	hence	hence	ADV
ejpam-5626	149	2	,	,	PUNCT
ejpam-5626	149	3	t	t	PROPN
ejpam-5626	149	4	=	=	SYM
ejpam-5626	149	5	0	0	PROPN
ejpam-5626	149	6	.	.	PUNCT
ejpam-5626	150	1	(	(	PUNCT
ejpam-5626	150	2	2	2	NUM
ejpam-5626	150	3	)	)	PUNCT
ejpam-5626	150	4	by	by	ADP
ejpam-5626	150	5	using	use	VERB
ejpam-5626	150	6	the	the	DET
ejpam-5626	150	7	similar	similar	ADJ
ejpam-5626	150	8	argument	argument	NOUN
ejpam-5626	150	9	as	as	ADP
ejpam-5626	150	10	in	in	ADP
ejpam-5626	150	11	(	(	PUNCT
ejpam-5626	150	12	1	1	NUM
ejpam-5626	150	13	)	)	PUNCT
ejpam-5626	150	14	,	,	PUNCT
ejpam-5626	150	15	we	we	PRON
ejpam-5626	150	16	get	get	VERB
ejpam-5626	150	17	the	the	DET
ejpam-5626	150	18	required	required	ADJ
ejpam-5626	150	19	conclusion	conclusion	NOUN
ejpam-5626	150	20	.	.	PUNCT
ejpam-5626	151	1	lemma	lemma	PROPN
ejpam-5626	151	2	2.4	2.4	NUM
ejpam-5626	151	3	.	.	PUNCT
ejpam-5626	152	1	for	for	ADP
ejpam-5626	152	2	each	each	DET
ejpam-5626	152	3	lii	lii	NOUN
ejpam-5626	152	4	,	,	PUNCT
ejpam-5626	152	5	mii	mii	PROPN
ejpam-5626	152	6	∈	∈	PROPN
ejpam-5626	152	7	aii	aii	NOUN
ejpam-5626	152	8	such	such	ADJ
ejpam-5626	152	9	that	that	SCONJ
ejpam-5626	152	10	1	1	NUM
ejpam-5626	152	11	≤	≤	NUM
ejpam-5626	153	1	i	i	X
ejpam-5626	153	2	≤	≤	ADV
ejpam-5626	153	3	2	2	NUM
ejpam-5626	153	4	,	,	PUNCT
ejpam-5626	153	5	we	we	PRON
ejpam-5626	153	6	have	have	VERB
ejpam-5626	153	7	λ(lii	λ(lii	PROPN
ejpam-5626	154	1	+	+	NOUN
ejpam-5626	154	2	mii	mii	NOUN
ejpam-5626	154	3	)	)	PUNCT
ejpam-5626	154	4	=	=	SYM
ejpam-5626	154	5	λ(lii	λ(lii	PROPN
ejpam-5626	154	6	)	)	PUNCT
ejpam-5626	154	7	+	+	NUM
ejpam-5626	154	8	λ(mii	λ(mii	NOUN
ejpam-5626	154	9	)	)	PUNCT
ejpam-5626	154	10	.	.	PUNCT
ejpam-5626	155	1	proof	proof	NOUN
ejpam-5626	155	2	.	.	PUNCT
ejpam-5626	156	1	let	let	VERB
ejpam-5626	156	2	t	t	NOUN
ejpam-5626	157	1	=	=	PUNCT
ejpam-5626	157	2	λ(lii	λ(lii	PROPN
ejpam-5626	158	1	+	+	PROPN
ejpam-5626	158	2	mii)−	mii)−	PROPN
ejpam-5626	158	3	λ(lii)−	λ(lii)−	PRON
ejpam-5626	158	4	λ(mii	λ(mii	NOUN
ejpam-5626	158	5	)	)	PUNCT
ejpam-5626	158	6	.	.	PUNCT
ejpam-5626	159	1	it	it	PRON
ejpam-5626	159	2	follows	follow	VERB
ejpam-5626	159	3	from	from	ADP
ejpam-5626	159	4	lemma	lemma	PROPN
ejpam-5626	159	5	2.1	2.1	NUM
ejpam-5626	159	6	and	and	CCONJ
ejpam-5626	159	7	i	i	PRON
ejpam-5626	159	8	̸=	̸=	PROPN
ejpam-5626	159	9	j	j	PROPN
ejpam-5626	160	1	that	that	PRON
ejpam-5626	160	2	λ([[pj	λ([[pj	ADV
ejpam-5626	160	3	,	,	PUNCT
ejpam-5626	160	4	lii	lii	VERB
ejpam-5626	160	5	+	+	ADV
ejpam-5626	160	6	mii]•,pi]∗	mii]•,pi]∗	ADJ
ejpam-5626	160	7	)	)	PUNCT
ejpam-5626	161	1	=	=	PUNCT
ejpam-5626	161	2	λ([[pj	λ([[pj	ADV
ejpam-5626	161	3	,	,	PUNCT
ejpam-5626	161	4	lii]•,pi]∗	lii]•,pi]∗	ADJ
ejpam-5626	161	5	)	)	PUNCT
ejpam-5626	162	1	+	+	CCONJ
ejpam-5626	162	2	λ([[pj	λ([[pj	ADV
ejpam-5626	162	3	,	,	PUNCT
ejpam-5626	162	4	mii]•,pi]∗	mii]•,pi]∗	ADJ
ejpam-5626	162	5	)	)	PUNCT
ejpam-5626	162	6	=	=	PUNCT
ejpam-5626	163	1	[	[	X
ejpam-5626	163	2	[	[	X
ejpam-5626	163	3	λ(pj),lii]•,pi]∗	λ(pj),lii]•,pi]∗	ADJ
ejpam-5626	163	4	+	+	X
ejpam-5626	163	5	[	[	X
ejpam-5626	163	6	[	[	X
ejpam-5626	163	7	pj	pj	X
ejpam-5626	163	8	,	,	PUNCT
ejpam-5626	163	9	λ(lii)]•,pi]∗	λ(lii)]•,pi]∗	VERB
ejpam-5626	163	10	+	+	X
ejpam-5626	164	1	[	[	X
ejpam-5626	164	2	[	[	X
ejpam-5626	164	3	pj	pj	X
ejpam-5626	164	4	,	,	PUNCT
ejpam-5626	164	5	lii]•,λ(pi)]∗	lii]•,λ(pi)]∗	PUNCT
ejpam-5626	165	1	+	+	PUNCT
ejpam-5626	166	1	[	[	X
ejpam-5626	166	2	[	[	X
ejpam-5626	166	3	λ(pj),mii]•,pi]∗	λ(pj),mii]•,pi]∗	ADJ
ejpam-5626	166	4	+	+	X
ejpam-5626	167	1	[	[	X
ejpam-5626	167	2	[	[	X
ejpam-5626	167	3	pj	pj	PROPN
ejpam-5626	167	4	,	,	PUNCT
ejpam-5626	167	5	λ(mii)]•,pi]∗	λ(mii)]•,pi]∗	VERB
ejpam-5626	167	6	+	+	X
ejpam-5626	168	1	[	[	X
ejpam-5626	168	2	[	[	X
ejpam-5626	168	3	pj	pj	X
ejpam-5626	168	4	,	,	PUNCT
ejpam-5626	168	5	mii]•,λ(pi)]∗	mii]•,λ(pi)]∗	PUNCT
ejpam-5626	168	6	and	and	CCONJ
ejpam-5626	168	7	λ([[pj	λ([[pj	ADV
ejpam-5626	168	8	,	,	PUNCT
ejpam-5626	168	9	lii	lii	PROPN
ejpam-5626	168	10	+	+	ADV
ejpam-5626	168	11	mii]•,pi]∗	mii]•,pi]∗	ADJ
ejpam-5626	168	12	)	)	PUNCT
ejpam-5626	168	13	=	=	PUNCT
ejpam-5626	169	1	[	[	X
ejpam-5626	169	2	[	[	X
ejpam-5626	169	3	λ(pj),lii	λ(pj),lii	VERB
ejpam-5626	169	4	+	+	ADV
ejpam-5626	169	5	mii]•,pi]∗	mii]•,pi]∗	ADJ
ejpam-5626	169	6	+	+	X
ejpam-5626	170	1	[	[	X
ejpam-5626	170	2	[	[	X
ejpam-5626	170	3	pj	pj	PROPN
ejpam-5626	170	4	,	,	PUNCT
ejpam-5626	170	5	λ(lii	λ(lii	PROPN
ejpam-5626	170	6	+	+	NOUN
ejpam-5626	170	7	mii)]•,pi]∗	mii)]•,pi]∗	ADJ
ejpam-5626	170	8	+	+	NOUN
ejpam-5626	170	9	[	[	X
ejpam-5626	170	10	[	[	X
ejpam-5626	170	11	pj	pj	X
ejpam-5626	170	12	,	,	PUNCT
ejpam-5626	170	13	lii	lii	VERB
ejpam-5626	170	14	+	+	CCONJ
ejpam-5626	170	15	mii]•,λ(pi)]∗.	mii]•,λ(pi)]∗.	NOUN
ejpam-5626	170	16	by	by	ADP
ejpam-5626	170	17	comparing	compare	VERB
ejpam-5626	170	18	the	the	DET
ejpam-5626	170	19	last	last	ADJ
ejpam-5626	170	20	two	two	NUM
ejpam-5626	170	21	expressions	expression	NOUN
ejpam-5626	170	22	,	,	PUNCT
ejpam-5626	170	23	we	we	PRON
ejpam-5626	170	24	get	get	VERB
ejpam-5626	170	25	[	[	X
ejpam-5626	170	26	[	[	X
ejpam-5626	170	27	pj	pj	PROPN
ejpam-5626	170	28	,	,	PUNCT
ejpam-5626	170	29	t	t	PROPN
ejpam-5626	170	30	]	]	PUNCT
ejpam-5626	170	31	•,pi]∗	•,pi]∗	PROPN
ejpam-5626	170	32	=	=	SYM
ejpam-5626	171	1	0	0	PROPN
ejpam-5626	171	2	.	.	PUNCT
ejpam-5626	172	1	this	this	PRON
ejpam-5626	172	2	gives	give	VERB
ejpam-5626	172	3	pitpj	pitpj	NOUN
ejpam-5626	172	4	=	=	PUNCT
ejpam-5626	172	5	0	0	NUM
ejpam-5626	172	6	with	with	ADP
ejpam-5626	172	7	i	i	PRON
ejpam-5626	172	8	̸=	̸=	PROPN
ejpam-5626	172	9	j.	j.	PROPN
ejpam-5626	172	10	also	also	ADV
ejpam-5626	172	11	,	,	PUNCT
ejpam-5626	172	12	for	for	ADP
ejpam-5626	172	13	any	any	DET
ejpam-5626	172	14	xij	xij	PROPN
ejpam-5626	172	15	∈	∈	PROPN
ejpam-5626	172	16	aij	aij	PROPN
ejpam-5626	172	17	,	,	PUNCT
ejpam-5626	172	18	we	we	PRON
ejpam-5626	172	19	have	have	VERB
ejpam-5626	172	20	λ([[xij	λ([[xij	PROPN
ejpam-5626	172	21	,	,	PUNCT
ejpam-5626	172	22	lii	lii	VERB
ejpam-5626	172	23	+	+	PROPN
ejpam-5626	172	24	mii]•,pi]∗	mii]•,pi]∗	ADJ
ejpam-5626	172	25	)	)	PUNCT
ejpam-5626	172	26	=	=	PUNCT
ejpam-5626	173	1	[	[	X
ejpam-5626	173	2	[	[	X
ejpam-5626	173	3	λ(xij),lii	λ(xij),lii	X
ejpam-5626	173	4	+	+	ADV
ejpam-5626	173	5	mii]•,pi]∗	mii]•,pi]∗	ADJ
ejpam-5626	173	6	+	+	X
ejpam-5626	174	1	[	[	X
ejpam-5626	174	2	[	[	X
ejpam-5626	174	3	xij	xij	NOUN
ejpam-5626	174	4	,	,	PUNCT
ejpam-5626	174	5	λ(lii	λ(lii	PROPN
ejpam-5626	174	6	+	+	NOUN
ejpam-5626	174	7	mii)]•,pi]∗	mii)]•,pi]∗	NOUN
ejpam-5626	174	8	)	)	PUNCT
ejpam-5626	175	1	+	+	PUNCT
ejpam-5626	175	2	[	[	X
ejpam-5626	175	3	[	[	X
ejpam-5626	175	4	xij	xij	X
ejpam-5626	175	5	,	,	PUNCT
ejpam-5626	175	6	lii	lii	VERB
ejpam-5626	175	7	+	+	ADV
ejpam-5626	175	8	mii]•,λ(pi)]∗.	mii]•,λ(pi)]∗.	NOUN
ejpam-5626	175	9	under	under	ADP
ejpam-5626	175	10	other	other	ADJ
ejpam-5626	175	11	conditions	condition	NOUN
ejpam-5626	175	12	,	,	PUNCT
ejpam-5626	175	13	[	[	X
ejpam-5626	175	14	[	[	X
ejpam-5626	175	15	xij	xij	NOUN
ejpam-5626	175	16	,	,	PUNCT
ejpam-5626	175	17	lii]•,pi]∗	lii]•,pi]∗	ADJ
ejpam-5626	175	18	=	=	PUNCT
ejpam-5626	175	19	0	0	PUNCT
ejpam-5626	175	20	and	and	CCONJ
ejpam-5626	175	21	using	use	VERB
ejpam-5626	175	22	lemma	lemma	PROPN
ejpam-5626	175	23	2.1	2.1	NUM
ejpam-5626	175	24	,	,	PUNCT
ejpam-5626	175	25	we	we	PRON
ejpam-5626	175	26	have	have	VERB
ejpam-5626	175	27	λ([[xij	λ([[xij	PROPN
ejpam-5626	175	28	,	,	PUNCT
ejpam-5626	175	29	lii	lii	VERB
ejpam-5626	175	30	+	+	PROPN
ejpam-5626	175	31	mii]•,pi]∗	mii]•,pi]∗	ADJ
ejpam-5626	175	32	)	)	PUNCT
ejpam-5626	176	1	=	=	SYM
ejpam-5626	176	2	λ([[xij	λ([[xij	PROPN
ejpam-5626	176	3	,	,	PUNCT
ejpam-5626	176	4	lii]•,pi]∗	lii]•,pi]∗	ADJ
ejpam-5626	176	5	)	)	PUNCT
ejpam-5626	177	1	+	+	CCONJ
ejpam-5626	177	2	λ([[xij	λ([[xij	PROPN
ejpam-5626	177	3	,	,	PUNCT
ejpam-5626	177	4	mii]•,pi]∗	mii]•,pi]∗	ADJ
ejpam-5626	177	5	)	)	PUNCT
ejpam-5626	177	6	=	=	PUNCT
ejpam-5626	178	1	[	[	X
ejpam-5626	178	2	[	[	X
ejpam-5626	178	3	λ(xij),lii]•,pi]∗	λ(xij),lii]•,pi]∗	X
ejpam-5626	178	4	+	+	X
ejpam-5626	179	1	[	[	X
ejpam-5626	179	2	[	[	X
ejpam-5626	179	3	xij	xij	X
ejpam-5626	179	4	,	,	PUNCT
ejpam-5626	179	5	λ(lii)]•,pi]∗	λ(lii)]•,pi]∗	VERB
ejpam-5626	179	6	+	+	X
ejpam-5626	180	1	[	[	X
ejpam-5626	180	2	[	[	X
ejpam-5626	180	3	xij	xij	NOUN
ejpam-5626	180	4	,	,	PUNCT
ejpam-5626	180	5	lii]•,λ(pi)]∗	lii]•,λ(pi)]∗	PUNCT
ejpam-5626	181	1	+	+	PUNCT
ejpam-5626	182	1	[	[	X
ejpam-5626	182	2	[	[	X
ejpam-5626	182	3	λ(xij),mii]•,pi]∗	λ(xij),mii]•,pi]∗	ADJ
ejpam-5626	182	4	+	+	X
ejpam-5626	183	1	[	[	X
ejpam-5626	183	2	[	[	X
ejpam-5626	183	3	xij	xij	X
ejpam-5626	183	4	,	,	PUNCT
ejpam-5626	183	5	λ(mii)]•,pi]∗	λ(mii)]•,pi]∗	VERB
ejpam-5626	183	6	+	+	X
ejpam-5626	184	1	[	[	X
ejpam-5626	184	2	[	[	X
ejpam-5626	184	3	xij	xij	NOUN
ejpam-5626	184	4	,	,	PUNCT
ejpam-5626	184	5	mii]•,λ(pi)]∗.	mii]•,λ(pi)]∗.	NOUN
ejpam-5626	184	6	from	from	ADP
ejpam-5626	184	7	the	the	DET
ejpam-5626	184	8	last	last	ADJ
ejpam-5626	184	9	two	two	NUM
ejpam-5626	184	10	expressions	expression	NOUN
ejpam-5626	184	11	,	,	PUNCT
ejpam-5626	184	12	we	we	PRON
ejpam-5626	184	13	get	get	VERB
ejpam-5626	184	14	[	[	X
ejpam-5626	184	15	[	[	X
ejpam-5626	184	16	xij	xij	X
ejpam-5626	184	17	,	,	PUNCT
ejpam-5626	184	18	t	t	PROPN
ejpam-5626	184	19	]	]	PUNCT
ejpam-5626	184	20	•,pi]∗	•,pi]∗	PROPN
ejpam-5626	184	21	=	=	SYM
ejpam-5626	184	22	0	0	PROPN
ejpam-5626	184	23	.	.	PUNCT
ejpam-5626	185	1	that	that	PRON
ejpam-5626	185	2	means	mean	VERB
ejpam-5626	185	3	xijt	xijt	PROPN
ejpam-5626	185	4	∗pi	∗pi	PUNCT
ejpam-5626	186	1	−	−	PROPN
ejpam-5626	187	1	tx∗	tx∗	PRON
ejpam-5626	187	2	ij	ij	INTJ
ejpam-5626	187	3	−	−	PROPN
ejpam-5626	187	4	pitx	pitx	ADP
ejpam-5626	187	5	∗	∗	X
ejpam-5626	187	6	ij	ij	NOUN
ejpam-5626	187	7	+	+	CCONJ
ejpam-5626	187	8	xijt	xijt	PROPN
ejpam-5626	187	9	∗	∗	NOUN
ejpam-5626	187	10	=	=	SYM
ejpam-5626	187	11	0	0	X
ejpam-5626	187	12	.	.	PUNCT
ejpam-5626	188	1	left	leave	VERB
ejpam-5626	188	2	multiplying	multiply	VERB
ejpam-5626	188	3	by	by	ADP
ejpam-5626	188	4	pj	pj	PROPN
ejpam-5626	188	5	both	both	DET
ejpam-5626	188	6	sides	side	NOUN
ejpam-5626	188	7	and	and	CCONJ
ejpam-5626	188	8	using	use	VERB
ejpam-5626	188	9	(	(	PUNCT
ejpam-5626	188	10	▲	▲	PUNCT
ejpam-5626	188	11	)	)	PUNCT
ejpam-5626	188	12	and	and	CCONJ
ejpam-5626	188	13	(	(	PUNCT
ejpam-5626	188	14	▼	▼	NOUN
ejpam-5626	188	15	)	)	PUNCT
ejpam-5626	188	16	,	,	PUNCT
ejpam-5626	188	17	we	we	PRON
ejpam-5626	188	18	find	find	VERB
ejpam-5626	188	19	pjtpj	pjtpj	NOUN
ejpam-5626	188	20	=	=	SYM
ejpam-5626	188	21	0	0	X
ejpam-5626	188	22	.	.	PUNCT
ejpam-5626	188	23	m.	m.	NOUN
ejpam-5626	188	24	a.	a.	PROPN
ejpam-5626	188	25	raza	raza	PROPN
ejpam-5626	188	26	et	et	PROPN
ejpam-5626	188	27	al	al	PROPN
ejpam-5626	188	28	.	.	PUNCT
ejpam-5626	188	29	/	/	SYM
ejpam-5626	188	30	eur	eur	PROPN
ejpam-5626	188	31	.	.	PUNCT
ejpam-5626	189	1	j.	j.	PROPN
ejpam-5626	189	2	pure	pure	PROPN
ejpam-5626	189	3	appl	appl	PROPN
ejpam-5626	189	4	.	.	PROPN
ejpam-5626	189	5	math	math	PROPN
ejpam-5626	189	6	,	,	PUNCT
ejpam-5626	189	7	18	18	NUM
ejpam-5626	189	8	(	(	PUNCT
ejpam-5626	189	9	1	1	NUM
ejpam-5626	189	10	)	)	PUNCT
ejpam-5626	189	11	(	(	PUNCT
ejpam-5626	189	12	2025	2025	NUM
ejpam-5626	189	13	)	)	PUNCT
ejpam-5626	189	14	,	,	PUNCT
ejpam-5626	189	15	5626	5626	NUM
ejpam-5626	189	16	6	6	NUM
ejpam-5626	189	17	of	of	ADP
ejpam-5626	189	18	10	10	NUM
ejpam-5626	189	19	lemma	lemma	PROPN
ejpam-5626	189	20	2.5	2.5	NUM
ejpam-5626	189	21	.	.	PUNCT
ejpam-5626	190	1	λ	λ	NOUN
ejpam-5626	190	2	is	be	AUX
ejpam-5626	190	3	an	an	DET
ejpam-5626	190	4	additive	additive	ADJ
ejpam-5626	190	5	map	map	NOUN
ejpam-5626	190	6	.	.	PUNCT
ejpam-5626	191	1	proof	proof	NOUN
ejpam-5626	191	2	.	.	PUNCT
ejpam-5626	192	1	for	for	ADP
ejpam-5626	192	2	any	any	DET
ejpam-5626	192	3	l	l	NOUN
ejpam-5626	192	4	,	,	PUNCT
ejpam-5626	192	5	m	m	VERB
ejpam-5626	192	6	∈	∈	PROPN
ejpam-5626	192	7	a	a	PRON
ejpam-5626	192	8	,	,	PUNCT
ejpam-5626	192	9	we	we	PRON
ejpam-5626	192	10	write	write	VERB
ejpam-5626	192	11	l	l	NOUN
ejpam-5626	192	12	=	=	SYM
ejpam-5626	192	13	l11	l11	PROPN
ejpam-5626	193	1	+	+	NOUN
ejpam-5626	193	2	l12	l12	ADJ
ejpam-5626	193	3	+	+	ADJ
ejpam-5626	193	4	l21	l21	NOUN
ejpam-5626	193	5	+	+	NOUN
ejpam-5626	193	6	l22	l22	NOUN
ejpam-5626	193	7	and	and	CCONJ
ejpam-5626	193	8	m	m	NOUN
ejpam-5626	193	9	=	=	NOUN
ejpam-5626	193	10	m11	m11	NOUN
ejpam-5626	193	11	+	+	NOUN
ejpam-5626	193	12	m12	m12	NOUN
ejpam-5626	193	13	+	+	CCONJ
ejpam-5626	193	14	m21	m21	PROPN
ejpam-5626	193	15	+	+	PROPN
ejpam-5626	193	16	m22	m22	PROPN
ejpam-5626	193	17	.	.	PUNCT
ejpam-5626	194	1	by	by	ADP
ejpam-5626	194	2	using	use	VERB
ejpam-5626	194	3	lemmas	lemmas	PROPN
ejpam-5626	194	4	2.2	2.2	NUM
ejpam-5626	194	5	2.4	2.4	NUM
ejpam-5626	194	6	,	,	PUNCT
ejpam-5626	194	7	we	we	PRON
ejpam-5626	194	8	get	get	VERB
ejpam-5626	194	9	λ(l+m	λ(l+m	PRON
ejpam-5626	194	10	)	)	PUNCT
ejpam-5626	194	11	=	=	PUNCT
ejpam-5626	195	1	λ(l11	λ(l11	AUX
ejpam-5626	195	2	+	+	X
ejpam-5626	195	3	l12	l12	ADJ
ejpam-5626	195	4	+	+	CCONJ
ejpam-5626	195	5	l21	l21	NOUN
ejpam-5626	195	6	+	+	CCONJ
ejpam-5626	195	7	l22	l22	NOUN
ejpam-5626	195	8	+	+	NOUN
ejpam-5626	195	9	m11	m11	NOUN
ejpam-5626	195	10	+	+	NOUN
ejpam-5626	195	11	m12	m12	NOUN
ejpam-5626	195	12	+	+	ADJ
ejpam-5626	195	13	m21	m21	PROPN
ejpam-5626	195	14	+	+	ADJ
ejpam-5626	195	15	m22	m22	PROPN
ejpam-5626	195	16	)	)	PUNCT
ejpam-5626	195	17	=	=	PUNCT
ejpam-5626	196	1	λ(l11	λ(l11	NOUN
ejpam-5626	196	2	+	+	NOUN
ejpam-5626	196	3	m11	m11	NOUN
ejpam-5626	196	4	)	)	PUNCT
ejpam-5626	197	1	+	+	NUM
ejpam-5626	197	2	λ(l12	λ(l12	NOUN
ejpam-5626	197	3	+	+	SYM
ejpam-5626	197	4	m12	m12	NOUN
ejpam-5626	197	5	)	)	PUNCT
ejpam-5626	197	6	+	+	NUM
ejpam-5626	197	7	λ(l21	λ(l21	X
ejpam-5626	198	1	+	+	NOUN
ejpam-5626	198	2	m21	m21	NOUN
ejpam-5626	198	3	)	)	PUNCT
ejpam-5626	198	4	+	+	NUM
ejpam-5626	198	5	λ(l22	λ(l22	NOUN
ejpam-5626	198	6	+	+	NOUN
ejpam-5626	198	7	m22	m22	NUM
ejpam-5626	198	8	)	)	PUNCT
ejpam-5626	198	9	=	=	PUNCT
ejpam-5626	198	10	λ(l11	λ(l11	ADJ
ejpam-5626	198	11	)	)	PUNCT
ejpam-5626	199	1	+	+	CCONJ
ejpam-5626	199	2	λ(m11	λ(m11	X
ejpam-5626	199	3	)	)	PUNCT
ejpam-5626	200	1	+	+	NUM
ejpam-5626	200	2	λ(l12	λ(l12	NOUN
ejpam-5626	200	3	)	)	PUNCT
ejpam-5626	201	1	+	+	CCONJ
ejpam-5626	201	2	λ(m12	λ(m12	NUM
ejpam-5626	201	3	)	)	PUNCT
ejpam-5626	202	1	+	+	X
ejpam-5626	202	2	λ(l21	λ(l21	X
ejpam-5626	202	3	)	)	PUNCT
ejpam-5626	203	1	+	+	NUM
ejpam-5626	203	2	λ(m21	λ(m21	NOUN
ejpam-5626	203	3	)	)	PUNCT
ejpam-5626	204	1	+	+	CCONJ
ejpam-5626	204	2	λ(l22	λ(l22	NOUN
ejpam-5626	204	3	)	)	PUNCT
ejpam-5626	204	4	+	+	CCONJ
ejpam-5626	204	5	λ(m22	λ(m22	X
ejpam-5626	204	6	)	)	PUNCT
ejpam-5626	205	1	=	=	PRON
ejpam-5626	205	2	λ(l11	λ(l11	AUX
ejpam-5626	205	3	+	+	X
ejpam-5626	205	4	l12	l12	ADJ
ejpam-5626	205	5	+	+	CCONJ
ejpam-5626	205	6	l21	l21	NOUN
ejpam-5626	205	7	+	+	CCONJ
ejpam-5626	205	8	l22	l22	NOUN
ejpam-5626	205	9	)	)	PUNCT
ejpam-5626	206	1	+	+	NUM
ejpam-5626	206	2	λ(m11	λ(m11	NOUN
ejpam-5626	206	3	+	+	ADJ
ejpam-5626	206	4	m12	m12	ADJ
ejpam-5626	206	5	+	+	ADJ
ejpam-5626	206	6	m21	m21	PROPN
ejpam-5626	206	7	+	+	ADJ
ejpam-5626	206	8	m22	m22	PROPN
ejpam-5626	206	9	)	)	PUNCT
ejpam-5626	206	10	=	=	SYM
ejpam-5626	206	11	λ(l	λ(l	PROPN
ejpam-5626	206	12	)	)	PUNCT
ejpam-5626	206	13	+	+	NUM
ejpam-5626	206	14	λ(m	λ(m	NOUN
ejpam-5626	206	15	)	)	PUNCT
ejpam-5626	206	16	.	.	PUNCT
ejpam-5626	207	1	hence	hence	ADV
ejpam-5626	207	2	,	,	PUNCT
ejpam-5626	207	3	λ	λ	PROPN
ejpam-5626	207	4	is	be	AUX
ejpam-5626	207	5	additive	additive	ADJ
ejpam-5626	207	6	.	.	PUNCT
ejpam-5626	208	1	this	this	PRON
ejpam-5626	208	2	completes	complete	VERB
ejpam-5626	208	3	the	the	DET
ejpam-5626	208	4	proof	proof	NOUN
ejpam-5626	208	5	of	of	ADP
ejpam-5626	208	6	theorem	theorem	ADJ
ejpam-5626	208	7	2.1	2.1	NUM
ejpam-5626	208	8	.	.	PUNCT
ejpam-5626	208	9	theorem	theorem	VERB
ejpam-5626	208	10	2.2	2.2	NUM
ejpam-5626	208	11	.	.	PUNCT
ejpam-5626	209	1	let	let	VERB
ejpam-5626	209	2	a	a	PRON
ejpam-5626	209	3	be	be	AUX
ejpam-5626	209	4	a	a	DET
ejpam-5626	209	5	unital	unital	ADJ
ejpam-5626	209	6	∗-algebra	∗-algebra	NOUN
ejpam-5626	209	7	with	with	ADP
ejpam-5626	209	8	unity	unity	NOUN
ejpam-5626	209	9	i	i	NOUN
ejpam-5626	209	10	containing	contain	VERB
ejpam-5626	209	11	a	a	DET
ejpam-5626	209	12	non	non	ADJ
ejpam-5626	209	13	-	-	ADJ
ejpam-5626	209	14	trivial	trivial	ADJ
ejpam-5626	209	15	projection	projection	NOUN
ejpam-5626	209	16	p	p	NOUN
ejpam-5626	209	17	satisfies	satisfie	NOUN
ejpam-5626	209	18	(	(	PUNCT
ejpam-5626	209	19	▲	▲	PUNCT
ejpam-5626	209	20	)	)	PUNCT
ejpam-5626	209	21	and	and	CCONJ
ejpam-5626	209	22	(	(	PUNCT
ejpam-5626	209	23	▼	▼	NOUN
ejpam-5626	209	24	)	)	PUNCT
ejpam-5626	209	25	.	.	PUNCT
ejpam-5626	210	1	let	let	VERB
ejpam-5626	211	1	the	the	DET
ejpam-5626	211	2	map	map	NOUN
ejpam-5626	211	3	λ	λ	INTJ
ejpam-5626	211	4	:	:	PUNCT
ejpam-5626	211	5	a	a	DET
ejpam-5626	211	6	→	→	X
ejpam-5626	211	7	a	a	DET
ejpam-5626	211	8	satisfy	satisfy	NOUN
ejpam-5626	211	9	the	the	DET
ejpam-5626	211	10	condition	condition	NOUN
ejpam-5626	211	11	λ([[l	λ([[l	ADJ
ejpam-5626	211	12	,	,	PUNCT
ejpam-5626	211	13	m]•,n]∗	m]•,n]∗	NOUN
ejpam-5626	211	14	)	)	PUNCT
ejpam-5626	211	15	=	=	NOUN
ejpam-5626	212	1	[	[	X
ejpam-5626	212	2	[	[	X
ejpam-5626	212	3	λ(l),m]•,n]∗	λ(l),m]•,n]∗	X
ejpam-5626	212	4	+	+	X
ejpam-5626	212	5	[	[	X
ejpam-5626	212	6	[	[	X
ejpam-5626	212	7	l	l	NOUN
ejpam-5626	212	8	,	,	PUNCT
ejpam-5626	212	9	λ(m)]•,n]∗	λ(m)]•,n]∗	NOUN
ejpam-5626	213	1	+	+	X
ejpam-5626	214	1	[	[	X
ejpam-5626	214	2	[	[	X
ejpam-5626	214	3	l	l	NOUN
ejpam-5626	214	4	,	,	PUNCT
ejpam-5626	214	5	m]•,λ(n)]∗	m]•,λ(n)]∗	VERB
ejpam-5626	214	6	for	for	ADP
ejpam-5626	214	7	l	l	PROPN
ejpam-5626	214	8	,	,	PUNCT
ejpam-5626	214	9	m	m	PROPN
ejpam-5626	214	10	,	,	PUNCT
ejpam-5626	214	11	n	n	PROPN
ejpam-5626	214	12	∈	∈	NOUN
ejpam-5626	214	13	a.	a.	NOUN
ejpam-5626	214	14	if	if	SCONJ
ejpam-5626	214	15	λ(i	λ(i	PROPN
ejpam-5626	214	16	)	)	PUNCT
ejpam-5626	214	17	is	be	AUX
ejpam-5626	214	18	self	self	NOUN
ejpam-5626	214	19	-	-	PUNCT
ejpam-5626	214	20	adjoint	adjoint	NOUN
ejpam-5626	214	21	,	,	PUNCT
ejpam-5626	214	22	then	then	ADV
ejpam-5626	214	23	λ	λ	PROPN
ejpam-5626	214	24	is	be	AUX
ejpam-5626	214	25	an	an	DET
ejpam-5626	214	26	∗-derivation	∗-derivation	NOUN
ejpam-5626	214	27	.	.	PUNCT
ejpam-5626	215	1	proof	proof	NOUN
ejpam-5626	215	2	of	of	ADP
ejpam-5626	215	3	theorem	theorem	ADJ
ejpam-5626	215	4	2.2	2.2	NUM
ejpam-5626	215	5	we	we	PRON
ejpam-5626	215	6	present	present	VERB
ejpam-5626	215	7	the	the	DET
ejpam-5626	215	8	proof	proof	NOUN
ejpam-5626	215	9	of	of	ADP
ejpam-5626	215	10	the	the	DET
ejpam-5626	215	11	above	above	ADJ
ejpam-5626	215	12	theorem	theorem	NOUN
ejpam-5626	215	13	with	with	ADP
ejpam-5626	215	14	several	several	ADJ
ejpam-5626	215	15	lemmas	lemma	NOUN
ejpam-5626	215	16	.	.	PUNCT
ejpam-5626	216	1	lemma	lemma	PROPN
ejpam-5626	216	2	2.6	2.6	NUM
ejpam-5626	216	3	.	.	PUNCT
ejpam-5626	217	1	we	we	PRON
ejpam-5626	217	2	show	show	VERB
ejpam-5626	217	3	that	that	SCONJ
ejpam-5626	217	4	if	if	SCONJ
ejpam-5626	217	5	λ(i	λ(i	PROPN
ejpam-5626	217	6	)	)	PUNCT
ejpam-5626	217	7	is	be	AUX
ejpam-5626	217	8	self	self	NOUN
ejpam-5626	217	9	-	-	PUNCT
ejpam-5626	217	10	adjoint	adjoint	NOUN
ejpam-5626	217	11	then	then	ADV
ejpam-5626	217	12	λ(ii	λ(ii	NOUN
ejpam-5626	217	13	)	)	PUNCT
ejpam-5626	217	14	=	=	SYM
ejpam-5626	217	15	λ(i	λ(i	PROPN
ejpam-5626	217	16	)	)	PUNCT
ejpam-5626	217	17	=	=	SYM
ejpam-5626	217	18	0	0	X
ejpam-5626	217	19	.	.	PUNCT
ejpam-5626	218	1	proof	proof	NOUN
ejpam-5626	218	2	.	.	PUNCT
ejpam-5626	219	1	we	we	PRON
ejpam-5626	219	2	know	know	VERB
ejpam-5626	219	3	that	that	SCONJ
ejpam-5626	219	4	λ([[ii	λ([[ii	PROPN
ejpam-5626	219	5	,	,	PUNCT
ejpam-5626	219	6	i]•	i]•	ADP
ejpam-5626	219	7	,	,	PUNCT
ejpam-5626	219	8	i]∗	i]∗	ADJ
ejpam-5626	219	9	)	)	PUNCT
ejpam-5626	219	10	=	=	PUNCT
ejpam-5626	220	1	[	[	X
ejpam-5626	220	2	[	[	X
ejpam-5626	220	3	λ(ii	λ(ii	NOUN
ejpam-5626	220	4	)	)	PUNCT
ejpam-5626	220	5	,	,	PUNCT
ejpam-5626	220	6	i]•	i]•	PROPN
ejpam-5626	220	7	,	,	PUNCT
ejpam-5626	220	8	i]∗	i]∗	PROPN
ejpam-5626	220	9	+	+	PUNCT
ejpam-5626	221	1	[	[	X
ejpam-5626	221	2	[	[	X
ejpam-5626	221	3	ii	ii	X
ejpam-5626	221	4	,	,	PUNCT
ejpam-5626	221	5	λ(i)]•	λ(i)]•	PROPN
ejpam-5626	221	6	,	,	PUNCT
ejpam-5626	221	7	i]∗	i]∗	VERB
ejpam-5626	221	8	+	+	PUNCT
ejpam-5626	222	1	[	[	X
ejpam-5626	222	2	[	[	X
ejpam-5626	222	3	ii	ii	X
ejpam-5626	222	4	,	,	PUNCT
ejpam-5626	222	5	i]•,λ(i)]∗	i]•,λ(i)]∗	VERB
ejpam-5626	222	6	=	=	SYM
ejpam-5626	222	7	2λ(ii)−	2λ(ii)−	NUM
ejpam-5626	222	8	2λ(ii)∗	2λ(ii)∗	NUM
ejpam-5626	222	9	+	+	CCONJ
ejpam-5626	222	10	2iλ(i)∗	2iλ(i)∗	NUM
ejpam-5626	222	11	+	+	CCONJ
ejpam-5626	222	12	2iλ(i	2iλ(i	NUM
ejpam-5626	222	13	)	)	PUNCT
ejpam-5626	223	1	+	+	NUM
ejpam-5626	223	2	4iλ(i	4iλ(i	NUM
ejpam-5626	223	3	)	)	PUNCT
ejpam-5626	223	4	.	.	PUNCT
ejpam-5626	224	1	also	also	ADV
ejpam-5626	224	2	,	,	PUNCT
ejpam-5626	224	3	from	from	ADP
ejpam-5626	224	4	the	the	DET
ejpam-5626	224	5	other	other	ADJ
ejpam-5626	224	6	side	side	NOUN
ejpam-5626	224	7	,	,	PUNCT
ejpam-5626	224	8	we	we	PRON
ejpam-5626	224	9	have	have	VERB
ejpam-5626	224	10	λ([[ii	λ([[ii	NOUN
ejpam-5626	224	11	,	,	PUNCT
ejpam-5626	224	12	i]•	i]•	ADP
ejpam-5626	224	13	,	,	PUNCT
ejpam-5626	224	14	i]∗	i]∗	PROPN
ejpam-5626	224	15	)	)	PUNCT
ejpam-5626	224	16	=	=	SYM
ejpam-5626	224	17	4λ(ii	4λ(ii	NUM
ejpam-5626	224	18	)	)	PUNCT
ejpam-5626	224	19	.	.	PUNCT
ejpam-5626	225	1	by	by	ADP
ejpam-5626	225	2	using	use	VERB
ejpam-5626	225	3	above	above	ADP
ejpam-5626	225	4	two	two	NUM
ejpam-5626	225	5	equations	equation	NOUN
ejpam-5626	225	6	,	,	PUNCT
ejpam-5626	225	7	we	we	PRON
ejpam-5626	225	8	get	get	VERB
ejpam-5626	225	9	2λ(ii)−	2λ(ii)−	NUM
ejpam-5626	225	10	2λ(ii)∗	2λ(ii)∗	NUM
ejpam-5626	225	11	+	+	CCONJ
ejpam-5626	225	12	2iλ(i)∗	2iλ(i)∗	NUM
ejpam-5626	225	13	+	+	CCONJ
ejpam-5626	225	14	2iλ(i	2iλ(i	NUM
ejpam-5626	225	15	)	)	PUNCT
ejpam-5626	226	1	+	+	NUM
ejpam-5626	226	2	4iλ(i)−	4iλ(i)−	PROPN
ejpam-5626	226	3	4λ(ii	4λ(ii	NUM
ejpam-5626	226	4	)	)	PUNCT
ejpam-5626	227	1	=	=	SYM
ejpam-5626	227	2	0	0	X
ejpam-5626	227	3	.	.	PUNCT
ejpam-5626	228	1	(	(	PUNCT
ejpam-5626	228	2	2.1	2.1	NUM
ejpam-5626	228	3	)	)	PUNCT
ejpam-5626	228	4	alternatively	alternatively	ADV
ejpam-5626	228	5	,	,	PUNCT
ejpam-5626	228	6	we	we	PRON
ejpam-5626	228	7	have	have	VERB
ejpam-5626	228	8	λ([[ii	λ([[ii	NOUN
ejpam-5626	228	9	,	,	PUNCT
ejpam-5626	228	10	i]•	i]•	ADJ
ejpam-5626	228	11	,	,	PUNCT
ejpam-5626	228	12	ii]∗	ii]∗	ADJ
ejpam-5626	228	13	)	)	PUNCT
ejpam-5626	228	14	=	=	SYM
ejpam-5626	228	15	−4λ(i	−4λ(i	NOUN
ejpam-5626	228	16	)	)	PUNCT
ejpam-5626	228	17	.	.	PUNCT
ejpam-5626	229	1	also	also	ADV
ejpam-5626	229	2	,	,	PUNCT
ejpam-5626	229	3	we	we	PRON
ejpam-5626	229	4	have	have	VERB
ejpam-5626	229	5	λ([[ii	λ([[ii	NOUN
ejpam-5626	229	6	,	,	PUNCT
ejpam-5626	229	7	i]•	i]•	ADJ
ejpam-5626	229	8	,	,	PUNCT
ejpam-5626	229	9	ii]∗	ii]∗	ADJ
ejpam-5626	229	10	)	)	PUNCT
ejpam-5626	229	11	=	=	PUNCT
ejpam-5626	230	1	2iλ(ii)−	2iλ(ii)−	NUM
ejpam-5626	230	2	2iλ(ii)∗	2iλ(ii)∗	NUM
ejpam-5626	230	3	−	−	NOUN
ejpam-5626	230	4	2λ(i)∗	2λ(i)∗	NUM
ejpam-5626	230	5	−	−	NOUN
ejpam-5626	230	6	2λ(i	2λ(i	NUM
ejpam-5626	230	7	)	)	PUNCT
ejpam-5626	231	1	+	+	NUM
ejpam-5626	231	2	4iλ(ii	4iλ(ii	NUM
ejpam-5626	231	3	)	)	PUNCT
ejpam-5626	231	4	.	.	PUNCT
ejpam-5626	232	1	m.	m.	NOUN
ejpam-5626	232	2	a.	a.	PROPN
ejpam-5626	232	3	raza	raza	PROPN
ejpam-5626	232	4	et	et	PROPN
ejpam-5626	232	5	al	al	PROPN
ejpam-5626	232	6	.	.	PUNCT
ejpam-5626	232	7	/	/	SYM
ejpam-5626	232	8	eur	eur	PROPN
ejpam-5626	232	9	.	.	PUNCT
ejpam-5626	233	1	j.	j.	PROPN
ejpam-5626	233	2	pure	pure	PROPN
ejpam-5626	233	3	appl	appl	PROPN
ejpam-5626	233	4	.	.	PROPN
ejpam-5626	233	5	math	math	PROPN
ejpam-5626	233	6	,	,	PUNCT
ejpam-5626	233	7	18	18	NUM
ejpam-5626	233	8	(	(	PUNCT
ejpam-5626	233	9	1	1	NUM
ejpam-5626	233	10	)	)	PUNCT
ejpam-5626	233	11	(	(	PUNCT
ejpam-5626	233	12	2025	2025	NUM
ejpam-5626	233	13	)	)	PUNCT
ejpam-5626	233	14	,	,	PUNCT
ejpam-5626	233	15	5626	5626	NUM
ejpam-5626	233	16	7	7	NUM
ejpam-5626	233	17	of	of	ADP
ejpam-5626	233	18	10	10	NUM
ejpam-5626	233	19	from	from	ADP
ejpam-5626	233	20	the	the	DET
ejpam-5626	233	21	last	last	ADJ
ejpam-5626	233	22	two	two	NUM
ejpam-5626	233	23	expressions	expression	NOUN
ejpam-5626	233	24	,	,	PUNCT
ejpam-5626	233	25	we	we	PRON
ejpam-5626	233	26	have	have	VERB
ejpam-5626	233	27	4λ(i	4λ(i	NUM
ejpam-5626	233	28	)	)	PUNCT
ejpam-5626	234	1	+	+	CCONJ
ejpam-5626	235	1	2iλ(ii)−	2iλ(ii)−	NUM
ejpam-5626	235	2	2iλ(ii)∗	2iλ(ii)∗	NUM
ejpam-5626	235	3	−	−	NOUN
ejpam-5626	235	4	2λ(i)∗	2λ(i)∗	NUM
ejpam-5626	235	5	−	−	NOUN
ejpam-5626	235	6	2λ(i	2λ(i	NUM
ejpam-5626	235	7	)	)	PUNCT
ejpam-5626	236	1	+	+	CCONJ
ejpam-5626	236	2	4iλ(ii	4iλ(ii	X
ejpam-5626	236	3	)	)	PUNCT
ejpam-5626	236	4	=	=	SYM
ejpam-5626	236	5	0	0	NUM
ejpam-5626	236	6	(	(	PUNCT
ejpam-5626	236	7	2.2	2.2	NUM
ejpam-5626	236	8	)	)	PUNCT
ejpam-5626	236	9	multiplying	multiplying	NOUN
ejpam-5626	236	10	(	(	PUNCT
ejpam-5626	236	11	2.2	2.2	NUM
ejpam-5626	236	12	)	)	PUNCT
ejpam-5626	236	13	by	by	ADP
ejpam-5626	236	14	i	i	PRON
ejpam-5626	236	15	,	,	PUNCT
ejpam-5626	236	16	we	we	PRON
ejpam-5626	236	17	get	get	VERB
ejpam-5626	236	18	4iλ(i)−	4iλ(i)−	NOUN
ejpam-5626	236	19	2λ(ii	2λ(ii	NUM
ejpam-5626	236	20	)	)	PUNCT
ejpam-5626	237	1	+	+	CCONJ
ejpam-5626	238	1	2λ(ii)∗	2λ(ii)∗	NUM
ejpam-5626	238	2	−	−	NOUN
ejpam-5626	238	3	2iλ(i)∗	2iλ(i)∗	NUM
ejpam-5626	239	1	−	−	PROPN
ejpam-5626	239	2	2iλ(i)−	2iλ(i)−	PROPN
ejpam-5626	239	3	4λ(ii	4λ(ii	NUM
ejpam-5626	239	4	)	)	PUNCT
ejpam-5626	240	1	=	=	SYM
ejpam-5626	240	2	0	0	NUM
ejpam-5626	240	3	(	(	PUNCT
ejpam-5626	240	4	2.3	2.3	NUM
ejpam-5626	240	5	)	)	PUNCT
ejpam-5626	240	6	adding	add	VERB
ejpam-5626	240	7	(	(	PUNCT
ejpam-5626	240	8	2.1	2.1	NUM
ejpam-5626	240	9	)	)	PUNCT
ejpam-5626	240	10	and	and	CCONJ
ejpam-5626	240	11	(	(	PUNCT
ejpam-5626	240	12	2.3	2.3	NUM
ejpam-5626	240	13	)	)	PUNCT
ejpam-5626	240	14	,	,	PUNCT
ejpam-5626	240	15	we	we	PRON
ejpam-5626	240	16	get	get	VERB
ejpam-5626	240	17	λ(ii	λ(ii	NOUN
ejpam-5626	240	18	)	)	PUNCT
ejpam-5626	240	19	=	=	SYM
ejpam-5626	240	20	iλ(i	iλ(i	NOUN
ejpam-5626	240	21	)	)	PUNCT
ejpam-5626	240	22	.	.	PUNCT
ejpam-5626	241	1	(	(	PUNCT
ejpam-5626	241	2	2.4	2.4	NUM
ejpam-5626	241	3	)	)	PUNCT
ejpam-5626	241	4	using	use	VERB
ejpam-5626	241	5	(	(	PUNCT
ejpam-5626	241	6	2.4	2.4	NUM
ejpam-5626	241	7	)	)	PUNCT
ejpam-5626	241	8	in	in	ADP
ejpam-5626	241	9	(	(	PUNCT
ejpam-5626	241	10	2.3	2.3	NUM
ejpam-5626	241	11	)	)	PUNCT
ejpam-5626	241	12	,	,	PUNCT
ejpam-5626	241	13	we	we	PRON
ejpam-5626	241	14	get	get	VERB
ejpam-5626	241	15	λ(i)∗	λ(i)∗	NOUN
ejpam-5626	241	16	=	=	PUNCT
ejpam-5626	241	17	−λ(i	−λ(i	NOUN
ejpam-5626	241	18	)	)	PUNCT
ejpam-5626	241	19	.	.	PUNCT
ejpam-5626	242	1	(	(	PUNCT
ejpam-5626	242	2	2.5	2.5	NUM
ejpam-5626	242	3	)	)	PUNCT
ejpam-5626	242	4	since	since	SCONJ
ejpam-5626	242	5	λ(i	λ(i	PROPN
ejpam-5626	242	6	)	)	PUNCT
ejpam-5626	242	7	is	be	AUX
ejpam-5626	242	8	self	self	NOUN
ejpam-5626	242	9	-	-	PUNCT
ejpam-5626	242	10	adjoint	adjoint	NOUN
ejpam-5626	242	11	,	,	PUNCT
ejpam-5626	242	12	then	then	ADV
ejpam-5626	242	13	λ(i	λ(i	VERB
ejpam-5626	242	14	)	)	PUNCT
ejpam-5626	242	15	=	=	SYM
ejpam-5626	243	1	λ(ii	λ(ii	NUM
ejpam-5626	243	2	)	)	PUNCT
ejpam-5626	243	3	=	=	SYM
ejpam-5626	243	4	0	0	X
ejpam-5626	243	5	.	.	PUNCT
ejpam-5626	244	1	lemma	lemma	PROPN
ejpam-5626	244	2	2.7	2.7	NUM
ejpam-5626	244	3	.	.	PUNCT
ejpam-5626	245	1	λ	λ	PROPN
ejpam-5626	245	2	preserves	preserve	VERB
ejpam-5626	245	3	star	star	NOUN
ejpam-5626	245	4	,	,	PUNCT
ejpam-5626	245	5	i.e.	i.e.	X
ejpam-5626	245	6	,	,	PUNCT
ejpam-5626	245	7	λ(l∗	λ(l∗	NOUN
ejpam-5626	245	8	)	)	PUNCT
ejpam-5626	245	9	=	=	SYM
ejpam-5626	245	10	λ(l)∗	λ(l)∗	NOUN
ejpam-5626	245	11	for	for	ADP
ejpam-5626	245	12	all	all	DET
ejpam-5626	245	13	l	l	NOUN
ejpam-5626	245	14	∈	∈	NOUN
ejpam-5626	245	15	a.	a.	NOUN
ejpam-5626	245	16	proof	proof	NOUN
ejpam-5626	245	17	.	.	PUNCT
ejpam-5626	246	1	from	from	ADP
ejpam-5626	246	2	lemma	lemma	PROPN
ejpam-5626	246	3	2.6	2.6	NUM
ejpam-5626	246	4	,	,	PUNCT
ejpam-5626	246	5	we	we	PRON
ejpam-5626	246	6	have	have	VERB
ejpam-5626	246	7	λ([[l	λ([[l	NUM
ejpam-5626	246	8	,	,	PUNCT
ejpam-5626	246	9	ii]•	ii]•	ADJ
ejpam-5626	246	10	,	,	PUNCT
ejpam-5626	246	11	ii]∗	ii]∗	PROPN
ejpam-5626	246	12	)	)	PUNCT
ejpam-5626	246	13	=	=	PUNCT
ejpam-5626	247	1	[	[	X
ejpam-5626	247	2	[	[	X
ejpam-5626	247	3	λ(l	λ(l	X
ejpam-5626	247	4	)	)	PUNCT
ejpam-5626	247	5	,	,	PUNCT
ejpam-5626	247	6	ii]•	ii]•	NOUN
ejpam-5626	247	7	,	,	PUNCT
ejpam-5626	247	8	ii]∗	ii]∗	VERB
ejpam-5626	247	9	=	=	PUNCT
ejpam-5626	248	1	[	[	X
ejpam-5626	248	2	[	[	X
ejpam-5626	248	3	−iλ(l)−	−iλ(l)−	PROPN
ejpam-5626	248	4	iλ(l)∗	iλ(l)∗	PROPN
ejpam-5626	248	5	,	,	PUNCT
ejpam-5626	248	6	ii]∗	ii]∗	VERB
ejpam-5626	248	7	=	=	PROPN
ejpam-5626	248	8	2λ(l	2λ(l	NUM
ejpam-5626	248	9	)	)	PUNCT
ejpam-5626	249	1	+	+	CCONJ
ejpam-5626	249	2	2λ(l)∗.	2λ(l)∗.	NUM
ejpam-5626	249	3	on	on	ADP
ejpam-5626	249	4	the	the	DET
ejpam-5626	249	5	other	other	ADJ
ejpam-5626	249	6	hand	hand	NOUN
ejpam-5626	249	7	,	,	PUNCT
ejpam-5626	249	8	we	we	PRON
ejpam-5626	249	9	have	have	VERB
ejpam-5626	249	10	λ([[l	λ([[l	NUM
ejpam-5626	249	11	,	,	PUNCT
ejpam-5626	249	12	ii]•	ii]•	ADJ
ejpam-5626	249	13	,	,	PUNCT
ejpam-5626	249	14	ii]∗	ii]∗	PROPN
ejpam-5626	249	15	)	)	PUNCT
ejpam-5626	249	16	=	=	SYM
ejpam-5626	249	17	2λ(l	2λ(l	NUM
ejpam-5626	249	18	)	)	PUNCT
ejpam-5626	250	1	+	+	NUM
ejpam-5626	250	2	2λ(l∗	2λ(l∗	NOUN
ejpam-5626	250	3	)	)	PUNCT
ejpam-5626	250	4	.	.	PUNCT
ejpam-5626	251	1	from	from	ADP
ejpam-5626	251	2	the	the	DET
ejpam-5626	251	3	last	last	ADJ
ejpam-5626	251	4	two	two	NUM
ejpam-5626	251	5	equations	equation	NOUN
ejpam-5626	251	6	,	,	PUNCT
ejpam-5626	251	7	we	we	PRON
ejpam-5626	251	8	get	get	VERB
ejpam-5626	251	9	λ(l∗	λ(l∗	NOUN
ejpam-5626	251	10	)	)	PUNCT
ejpam-5626	251	11	=	=	SYM
ejpam-5626	251	12	λ(l)∗.	λ(l)∗.	NOUN
ejpam-5626	251	13	lemma	lemma	PROPN
ejpam-5626	251	14	2.8	2.8	NUM
ejpam-5626	251	15	.	.	PUNCT
ejpam-5626	252	1	we	we	PRON
ejpam-5626	252	2	prove	prove	VERB
ejpam-5626	252	3	that	that	SCONJ
ejpam-5626	252	4	λ(il	λ(il	VERB
ejpam-5626	252	5	)	)	PUNCT
ejpam-5626	252	6	=	=	SYM
ejpam-5626	252	7	iλ(l	iλ(l	X
ejpam-5626	252	8	)	)	PUNCT
ejpam-5626	252	9	for	for	ADP
ejpam-5626	252	10	all	all	DET
ejpam-5626	252	11	l	l	NOUN
ejpam-5626	252	12	∈	∈	NOUN
ejpam-5626	252	13	a.	a.	NOUN
ejpam-5626	252	14	proof	proof	NOUN
ejpam-5626	252	15	.	.	PUNCT
ejpam-5626	253	1	it	it	PRON
ejpam-5626	253	2	follows	follow	VERB
ejpam-5626	253	3	from	from	ADP
ejpam-5626	253	4	lemma	lemma	PROPN
ejpam-5626	253	5	2.6	2.6	NUM
ejpam-5626	253	6	that	that	PRON
ejpam-5626	253	7	λ([[il	λ([[il	NOUN
ejpam-5626	253	8	,	,	PUNCT
ejpam-5626	253	9	i]•	i]•	ADP
ejpam-5626	253	10	,	,	PUNCT
ejpam-5626	253	11	i]∗	i]∗	ADJ
ejpam-5626	253	12	)	)	PUNCT
ejpam-5626	253	13	=	=	PUNCT
ejpam-5626	254	1	[	[	X
ejpam-5626	254	2	λ(il	λ(il	X
ejpam-5626	254	3	)	)	PUNCT
ejpam-5626	254	4	,	,	PUNCT
ejpam-5626	254	5	i]•	i]•	ADP
ejpam-5626	254	6	,	,	PUNCT
ejpam-5626	254	7	i]∗	i]∗	PROPN
ejpam-5626	254	8	=	=	SYM
ejpam-5626	254	9	2λ(il)−	2λ(il)−	PROPN
ejpam-5626	254	10	2λ(il)∗.	2λ(il)∗.	NUM
ejpam-5626	254	11	hence	hence	ADV
ejpam-5626	254	12	λ(2il+	λ(2il+	NUM
ejpam-5626	254	13	2il∗	2il∗	NUM
ejpam-5626	254	14	)	)	PUNCT
ejpam-5626	254	15	=	=	SYM
ejpam-5626	255	1	2λ(il)−	2λ(il)−	PROPN
ejpam-5626	255	2	2λ(il)∗.	2λ(il)∗.	NUM
ejpam-5626	255	3	(	(	PUNCT
ejpam-5626	255	4	2.6	2.6	NUM
ejpam-5626	255	5	)	)	PUNCT
ejpam-5626	255	6	from	from	ADP
ejpam-5626	255	7	the	the	DET
ejpam-5626	255	8	other	other	ADJ
ejpam-5626	255	9	side	side	NOUN
ejpam-5626	255	10	,	,	PUNCT
ejpam-5626	255	11	we	we	PRON
ejpam-5626	255	12	have	have	VERB
ejpam-5626	255	13	λ([[l	λ([[l	NUM
ejpam-5626	255	14	,	,	PUNCT
ejpam-5626	255	15	ii]•	ii]•	ADJ
ejpam-5626	255	16	,	,	PUNCT
ejpam-5626	255	17	i]∗	i]∗	PROPN
ejpam-5626	255	18	)	)	PUNCT
ejpam-5626	255	19	=	=	PUNCT
ejpam-5626	256	1	[	[	X
ejpam-5626	256	2	λ(l	λ(l	X
ejpam-5626	256	3	)	)	PUNCT
ejpam-5626	256	4	,	,	PUNCT
ejpam-5626	256	5	ii]•	ii]•	ADJ
ejpam-5626	256	6	,	,	PUNCT
ejpam-5626	256	7	i]∗	i]∗	PROPN
ejpam-5626	256	8	=	=	SYM
ejpam-5626	256	9	−2iλ(l)−	−2iλ(l)−	PROPN
ejpam-5626	256	10	2iλ(l)∗	2iλ(l)∗	PROPN
ejpam-5626	256	11	it	it	PRON
ejpam-5626	256	12	follows	follow	VERB
ejpam-5626	256	13	that	that	SCONJ
ejpam-5626	256	14	λ(−2il−	λ(−2il−	ADP
ejpam-5626	256	15	2il∗	2il∗	NUM
ejpam-5626	256	16	)	)	PUNCT
ejpam-5626	256	17	=	=	SYM
ejpam-5626	257	1	−2iλ(l)−	−2iλ(l)−	PROPN
ejpam-5626	257	2	2iλ(l)∗.	2iλ(l)∗.	NUM
ejpam-5626	257	3	(	(	PUNCT
ejpam-5626	257	4	2.7	2.7	NUM
ejpam-5626	257	5	)	)	PUNCT
ejpam-5626	257	6	m.	m.	NOUN
ejpam-5626	257	7	a.	a.	PROPN
ejpam-5626	257	8	raza	raza	PROPN
ejpam-5626	257	9	et	et	PROPN
ejpam-5626	257	10	al	al	PROPN
ejpam-5626	257	11	.	.	PUNCT
ejpam-5626	257	12	/	/	SYM
ejpam-5626	257	13	eur	eur	PROPN
ejpam-5626	257	14	.	.	PUNCT
ejpam-5626	258	1	j.	j.	PROPN
ejpam-5626	258	2	pure	pure	PROPN
ejpam-5626	258	3	appl	appl	PROPN
ejpam-5626	258	4	.	.	PROPN
ejpam-5626	258	5	math	math	PROPN
ejpam-5626	258	6	,	,	PUNCT
ejpam-5626	258	7	18	18	NUM
ejpam-5626	258	8	(	(	PUNCT
ejpam-5626	258	9	1	1	NUM
ejpam-5626	258	10	)	)	PUNCT
ejpam-5626	258	11	(	(	PUNCT
ejpam-5626	258	12	2025	2025	NUM
ejpam-5626	258	13	)	)	PUNCT
ejpam-5626	258	14	,	,	PUNCT
ejpam-5626	258	15	5626	5626	NUM
ejpam-5626	258	16	8	8	NUM
ejpam-5626	258	17	of	of	ADP
ejpam-5626	258	18	10	10	NUM
ejpam-5626	258	19	adding	add	VERB
ejpam-5626	258	20	(	(	PUNCT
ejpam-5626	258	21	2.6	2.6	NUM
ejpam-5626	258	22	)	)	PUNCT
ejpam-5626	258	23	and	and	CCONJ
ejpam-5626	258	24	(	(	PUNCT
ejpam-5626	258	25	2.7	2.7	NUM
ejpam-5626	258	26	)	)	PUNCT
ejpam-5626	259	1	,	,	PUNCT
ejpam-5626	259	2	we	we	PRON
ejpam-5626	259	3	get	get	VERB
ejpam-5626	259	4	λ(i(l+	λ(i(l+	NOUN
ejpam-5626	259	5	l∗	l∗	NOUN
ejpam-5626	259	6	)	)	PUNCT
ejpam-5626	259	7	)	)	PUNCT
ejpam-5626	260	1	=	=	PUNCT
ejpam-5626	260	2	iλ(l+	iλ(l+	NOUN
ejpam-5626	260	3	l∗	l∗	PROPN
ejpam-5626	260	4	)	)	PUNCT
ejpam-5626	260	5	.	.	PUNCT
ejpam-5626	261	1	(	(	PUNCT
ejpam-5626	261	2	2.8	2.8	NUM
ejpam-5626	261	3	)	)	PUNCT
ejpam-5626	261	4	since	since	SCONJ
ejpam-5626	261	5	(	(	PUNCT
ejpam-5626	261	6	2.8	2.8	NUM
ejpam-5626	261	7	)	)	PUNCT
ejpam-5626	261	8	is	be	AUX
ejpam-5626	261	9	true	true	ADJ
ejpam-5626	261	10	for	for	ADP
ejpam-5626	261	11	any	any	DET
ejpam-5626	261	12	self	self	NOUN
ejpam-5626	261	13	-	-	PUNCT
ejpam-5626	261	14	adjoint	adjoint	NOUN
ejpam-5626	261	15	then	then	ADV
ejpam-5626	261	16	for	for	ADP
ejpam-5626	261	17	any	any	DET
ejpam-5626	261	18	member	member	NOUN
ejpam-5626	261	19	of	of	ADP
ejpam-5626	261	20	l	l	PROPN
ejpam-5626	261	21	,	,	PUNCT
ejpam-5626	261	22	we	we	PRON
ejpam-5626	261	23	have	have	VERB
ejpam-5626	261	24	λ(il	λ(il	NOUN
ejpam-5626	261	25	)	)	PUNCT
ejpam-5626	261	26	=	=	SYM
ejpam-5626	261	27	iλ(l	iλ(l	PROPN
ejpam-5626	261	28	)	)	PUNCT
ejpam-5626	261	29	.	.	PUNCT
ejpam-5626	262	1	lemma	lemma	PROPN
ejpam-5626	262	2	2.9	2.9	NUM
ejpam-5626	262	3	.	.	PUNCT
ejpam-5626	263	1	we	we	PRON
ejpam-5626	263	2	show	show	VERB
ejpam-5626	263	3	that	that	SCONJ
ejpam-5626	263	4	λ	λ	NOUN
ejpam-5626	263	5	is	be	AUX
ejpam-5626	263	6	a	a	DET
ejpam-5626	263	7	derivation	derivation	NOUN
ejpam-5626	263	8	,	,	PUNCT
ejpam-5626	263	9	i.e	i.e	X
ejpam-5626	263	10	,	,	PUNCT
ejpam-5626	263	11	λ(lm	λ(lm	PROPN
ejpam-5626	263	12	)	)	PUNCT
ejpam-5626	263	13	=	=	SYM
ejpam-5626	263	14	λ(l)m+	λ(l)m+	NOUN
ejpam-5626	263	15	lλ(m	lλ(m	VERB
ejpam-5626	263	16	)	)	PUNCT
ejpam-5626	263	17	.	.	PUNCT
ejpam-5626	264	1	proof	proof	NOUN
ejpam-5626	264	2	.	.	PUNCT
ejpam-5626	265	1	it	it	PRON
ejpam-5626	265	2	is	be	AUX
ejpam-5626	265	3	easy	easy	ADJ
ejpam-5626	265	4	to	to	PART
ejpam-5626	265	5	check	check	VERB
ejpam-5626	265	6	that	that	SCONJ
ejpam-5626	265	7	λ([[l	λ([[l	ADJ
ejpam-5626	265	8	,	,	PUNCT
ejpam-5626	265	9	m]•	m]•	PROPN
ejpam-5626	265	10	,	,	PUNCT
ejpam-5626	265	11	i]∗	i]∗	PROPN
ejpam-5626	265	12	)	)	PUNCT
ejpam-5626	265	13	=	=	SYM
ejpam-5626	265	14	2λ(lm∗)−	2λ(lm∗)−	NUM
ejpam-5626	265	15	2λ(ml∗	2λ(ml∗	NOUN
ejpam-5626	265	16	)	)	PUNCT
ejpam-5626	265	17	.	.	PUNCT
ejpam-5626	266	1	also	also	ADV
ejpam-5626	266	2	,	,	PUNCT
ejpam-5626	266	3	it	it	PRON
ejpam-5626	266	4	follows	follow	VERB
ejpam-5626	266	5	from	from	ADP
ejpam-5626	266	6	lemma	lemma	PROPN
ejpam-5626	266	7	2.6	2.6	NUM
ejpam-5626	266	8	that	that	SCONJ
ejpam-5626	266	9	λ([[l	λ([[l	NUM
ejpam-5626	266	10	,	,	PUNCT
ejpam-5626	266	11	m]•	m]•	PROPN
ejpam-5626	266	12	,	,	PUNCT
ejpam-5626	266	13	i]∗	i]∗	PROPN
ejpam-5626	266	14	)	)	PUNCT
ejpam-5626	266	15	=	=	PUNCT
ejpam-5626	267	1	[	[	X
ejpam-5626	267	2	[	[	X
ejpam-5626	267	3	λ(l),m]•	λ(l),m]•	NOUN
ejpam-5626	267	4	,	,	PUNCT
ejpam-5626	267	5	i]∗	i]∗	ADJ
ejpam-5626	267	6	+	+	PUNCT
ejpam-5626	268	1	[	[	X
ejpam-5626	268	2	[	[	X
ejpam-5626	268	3	l	l	X
ejpam-5626	268	4	,	,	PUNCT
ejpam-5626	268	5	λ(m)]•	λ(m)]•	ADJ
ejpam-5626	268	6	,	,	PUNCT
ejpam-5626	268	7	i]∗	i]∗	PROPN
ejpam-5626	268	8	=	=	SYM
ejpam-5626	268	9	2λ(l)m∗	2λ(l)m∗	NUM
ejpam-5626	268	10	−	−	PROPN
ejpam-5626	269	1	2mλ(l)∗	2mλ(l)∗	PROPN
ejpam-5626	269	2	+	+	PROPN
ejpam-5626	270	1	2lλ(m)∗	2lλ(m)∗	PROPN
ejpam-5626	270	2	−	−	NOUN
ejpam-5626	270	3	2λ(m)l∗.	2λ(m)l∗.	NUM
ejpam-5626	270	4	by	by	ADP
ejpam-5626	270	5	comparing	compare	VERB
ejpam-5626	270	6	the	the	DET
ejpam-5626	270	7	last	last	ADJ
ejpam-5626	270	8	two	two	NUM
ejpam-5626	270	9	expressions	expression	NOUN
ejpam-5626	270	10	,	,	PUNCT
ejpam-5626	270	11	we	we	PRON
ejpam-5626	270	12	have	have	VERB
ejpam-5626	270	13	λ(lm∗)−	λ(lm∗)−	PRON
ejpam-5626	270	14	λ(ml∗	λ(ml∗	NOUN
ejpam-5626	270	15	)	)	PUNCT
ejpam-5626	271	1	=	=	SYM
ejpam-5626	271	2	λ(l)m∗	λ(l)m∗	PROPN
ejpam-5626	272	1	−mλ(l)∗	−mλ(l)∗	NOUN
ejpam-5626	272	2	+	+	CCONJ
ejpam-5626	272	3	lλ(m)∗	lλ(m)∗	PRON
ejpam-5626	272	4	−	−	X
ejpam-5626	272	5	λ(m)l∗	λ(m)l∗	PROPN
ejpam-5626	272	6	(	(	PUNCT
ejpam-5626	272	7	2.9	2.9	NUM
ejpam-5626	272	8	)	)	PUNCT
ejpam-5626	272	9	on	on	ADP
ejpam-5626	272	10	the	the	DET
ejpam-5626	272	11	other	other	ADJ
ejpam-5626	272	12	hand	hand	NOUN
ejpam-5626	272	13	,	,	PUNCT
ejpam-5626	272	14	we	we	PRON
ejpam-5626	272	15	have	have	VERB
ejpam-5626	272	16	λ([[il	λ([[il	NOUN
ejpam-5626	272	17	,	,	PUNCT
ejpam-5626	272	18	m]•	m]•	PROPN
ejpam-5626	272	19	,	,	PUNCT
ejpam-5626	272	20	ii]∗	ii]∗	ADJ
ejpam-5626	272	21	)	)	PUNCT
ejpam-5626	272	22	=	=	SYM
ejpam-5626	272	23	−λ(lm∗)−	−λ(lm∗)−	NOUN
ejpam-5626	272	24	λ(ml∗	λ(ml∗	NOUN
ejpam-5626	272	25	)	)	PUNCT
ejpam-5626	272	26	.	.	PUNCT
ejpam-5626	273	1	by	by	ADP
ejpam-5626	273	2	using	use	VERB
ejpam-5626	273	3	lemma	lemma	PROPN
ejpam-5626	273	4	2.6	2.6	NUM
ejpam-5626	273	5	and	and	CCONJ
ejpam-5626	273	6	lemma	lemma	PROPN
ejpam-5626	273	7	2.8	2.8	NUM
ejpam-5626	273	8	,	,	PUNCT
ejpam-5626	273	9	we	we	PRON
ejpam-5626	273	10	have	have	VERB
ejpam-5626	273	11	λ([[il	λ([[il	NOUN
ejpam-5626	273	12	,	,	PUNCT
ejpam-5626	273	13	m]•	m]•	PROPN
ejpam-5626	273	14	,	,	PUNCT
ejpam-5626	273	15	ii]∗	ii]∗	NUM
ejpam-5626	273	16	)	)	PUNCT
ejpam-5626	273	17	=	=	PUNCT
ejpam-5626	274	1	[	[	X
ejpam-5626	274	2	[	[	X
ejpam-5626	274	3	λ(il),m]•	λ(il),m]•	NOUN
ejpam-5626	274	4	,	,	PUNCT
ejpam-5626	274	5	ii]∗	ii]∗	VERB
ejpam-5626	274	6	+	+	PUNCT
ejpam-5626	275	1	[	[	X
ejpam-5626	275	2	[	[	X
ejpam-5626	275	3	il	il	PROPN
ejpam-5626	275	4	,	,	PUNCT
ejpam-5626	275	5	λ(m)]•	λ(m)]•	PROPN
ejpam-5626	275	6	,	,	PUNCT
ejpam-5626	275	7	ii]∗	ii]∗	VERB
ejpam-5626	275	8	=	=	SYM
ejpam-5626	275	9	iλ(il)m∗	iλ(il)m∗	PROPN
ejpam-5626	276	1	−	−	PROPN
ejpam-5626	277	1	imλ(il)∗	imλ(il)∗	NOUN
ejpam-5626	277	2	−	−	PROPN
ejpam-5626	278	1	lλ(m)∗	lλ(m)∗	INTJ
ejpam-5626	278	2	−	−	PROPN
ejpam-5626	279	1	λ(m)l∗	λ(m)l∗	PROPN
ejpam-5626	279	2	=	=	SYM
ejpam-5626	279	3	−λ(l)m∗	−λ(l)m∗	INTJ
ejpam-5626	279	4	−mλ(l)∗	−mλ(l)∗	INTJ
ejpam-5626	279	5	−	−	PROPN
ejpam-5626	280	1	lλ(m)∗	lλ(m)∗	INTJ
ejpam-5626	280	2	−	−	X
ejpam-5626	280	3	λ(m)l∗.	λ(m)l∗.	NUM
ejpam-5626	280	4	by	by	ADP
ejpam-5626	280	5	comparing	compare	VERB
ejpam-5626	280	6	the	the	DET
ejpam-5626	280	7	last	last	ADJ
ejpam-5626	280	8	two	two	NUM
ejpam-5626	280	9	expressions	expression	NOUN
ejpam-5626	280	10	,	,	PUNCT
ejpam-5626	280	11	we	we	PRON
ejpam-5626	280	12	have	have	VERB
ejpam-5626	280	13	λ(lm∗	λ(lm∗	PRON
ejpam-5626	280	14	)	)	PUNCT
ejpam-5626	281	1	+	+	CCONJ
ejpam-5626	281	2	λ(ml∗	λ(ml∗	X
ejpam-5626	281	3	)	)	PUNCT
ejpam-5626	282	1	=	=	PUNCT
ejpam-5626	283	1	λ(l)m∗	λ(l)m∗	PROPN
ejpam-5626	284	1	+	+	ADJ
ejpam-5626	284	2	mλ(l)∗	mλ(l)∗	NOUN
ejpam-5626	284	3	+	+	CCONJ
ejpam-5626	284	4	lλ(m)∗	lλ(m)∗	PROPN
ejpam-5626	284	5	+	+	NUM
ejpam-5626	284	6	λ(m)l∗	λ(m)l∗	PROPN
ejpam-5626	284	7	(	(	PUNCT
ejpam-5626	284	8	2.10	2.10	NUM
ejpam-5626	284	9	)	)	PUNCT
ejpam-5626	284	10	adding	add	VERB
ejpam-5626	284	11	(	(	PUNCT
ejpam-5626	284	12	2.9	2.9	NUM
ejpam-5626	284	13	)	)	PUNCT
ejpam-5626	284	14	and	and	CCONJ
ejpam-5626	284	15	(	(	PUNCT
ejpam-5626	284	16	2.10	2.10	NUM
ejpam-5626	284	17	)	)	PUNCT
ejpam-5626	284	18	,	,	PUNCT
ejpam-5626	284	19	we	we	PRON
ejpam-5626	284	20	get	get	VERB
ejpam-5626	284	21	λ(lm∗	λ(lm∗	PRON
ejpam-5626	284	22	)	)	PUNCT
ejpam-5626	285	1	=	=	PUNCT
ejpam-5626	286	1	λ(l)m∗	λ(l)m∗	PROPN
ejpam-5626	286	2	+	+	NUM
ejpam-5626	286	3	lλ(m∗	lλ(m∗	NOUN
ejpam-5626	286	4	)	)	PUNCT
ejpam-5626	286	5	.	.	PUNCT
ejpam-5626	287	1	(	(	PUNCT
ejpam-5626	287	2	2.11	2.11	NUM
ejpam-5626	287	3	)	)	PUNCT
ejpam-5626	287	4	replacing	replace	VERB
ejpam-5626	287	5	m∗	m∗	NOUN
ejpam-5626	287	6	by	by	ADP
ejpam-5626	287	7	m	m	PRON
ejpam-5626	287	8	,	,	PUNCT
ejpam-5626	287	9	we	we	PRON
ejpam-5626	287	10	get	get	VERB
ejpam-5626	287	11	λ(lm	λ(lm	NUM
ejpam-5626	287	12	)	)	PUNCT
ejpam-5626	287	13	=	=	SYM
ejpam-5626	288	1	λ(l)m+	λ(l)m+	NOUN
ejpam-5626	288	2	lλ(m	lλ(m	VERB
ejpam-5626	288	3	)	)	PUNCT
ejpam-5626	288	4	.	.	PUNCT
ejpam-5626	289	1	hence	hence	ADV
ejpam-5626	289	2	,	,	PUNCT
ejpam-5626	289	3	λ	λ	PROPN
ejpam-5626	289	4	is	be	AUX
ejpam-5626	289	5	a	a	DET
ejpam-5626	289	6	derivation	derivation	NOUN
ejpam-5626	289	7	.	.	PUNCT
ejpam-5626	290	1	this	this	PRON
ejpam-5626	290	2	completes	complete	VERB
ejpam-5626	290	3	the	the	DET
ejpam-5626	290	4	proof	proof	NOUN
ejpam-5626	290	5	of	of	ADP
ejpam-5626	290	6	theorem	theorem	ADJ
ejpam-5626	290	7	2.2	2.2	NUM
ejpam-5626	290	8	.	.	PUNCT
ejpam-5626	291	1	now	now	ADV
ejpam-5626	291	2	,	,	PUNCT
ejpam-5626	291	3	we	we	PRON
ejpam-5626	291	4	provide	provide	VERB
ejpam-5626	291	5	an	an	DET
ejpam-5626	291	6	example	example	NOUN
ejpam-5626	291	7	to	to	PART
ejpam-5626	291	8	demonstrate	demonstrate	VERB
ejpam-5626	291	9	the	the	DET
ejpam-5626	291	10	necessity	necessity	NOUN
ejpam-5626	291	11	of	of	ADP
ejpam-5626	291	12	the	the	DET
ejpam-5626	291	13	conditions	condition	NOUN
ejpam-5626	291	14	(	(	PUNCT
ejpam-5626	291	15	▲	▲	PUNCT
ejpam-5626	291	16	)	)	PUNCT
ejpam-5626	291	17	and	and	CCONJ
ejpam-5626	291	18	(	(	PUNCT
ejpam-5626	291	19	▼	▼	NOUN
ejpam-5626	291	20	)	)	PUNCT
ejpam-5626	291	21	in	in	ADP
ejpam-5626	291	22	theorem	theorem	ADJ
ejpam-5626	291	23	2.1	2.1	NUM
ejpam-5626	291	24	.	.	PUNCT
ejpam-5626	291	25	m.	m.	NOUN
ejpam-5626	291	26	a.	a.	PROPN
ejpam-5626	291	27	raza	raza	PROPN
ejpam-5626	291	28	et	et	PROPN
ejpam-5626	291	29	al	al	PROPN
ejpam-5626	291	30	.	.	PUNCT
ejpam-5626	291	31	/	/	SYM
ejpam-5626	291	32	eur	eur	PROPN
ejpam-5626	291	33	.	.	PUNCT
ejpam-5626	292	1	j.	j.	PROPN
ejpam-5626	292	2	pure	pure	PROPN
ejpam-5626	292	3	appl	appl	PROPN
ejpam-5626	292	4	.	.	PROPN
ejpam-5626	292	5	math	math	PROPN
ejpam-5626	292	6	,	,	PUNCT
ejpam-5626	292	7	18	18	NUM
ejpam-5626	292	8	(	(	PUNCT
ejpam-5626	292	9	1	1	NUM
ejpam-5626	292	10	)	)	PUNCT
ejpam-5626	292	11	(	(	PUNCT
ejpam-5626	292	12	2025	2025	NUM
ejpam-5626	292	13	)	)	PUNCT
ejpam-5626	292	14	,	,	PUNCT
ejpam-5626	292	15	5626	5626	NUM
ejpam-5626	292	16	9	9	NUM
ejpam-5626	292	17	of	of	ADP
ejpam-5626	292	18	10	10	NUM
ejpam-5626	292	19	example	example	NOUN
ejpam-5626	292	20	2.1	2.1	NUM
ejpam-5626	292	21	.	.	PUNCT
ejpam-5626	293	1	consider	consider	VERB
ejpam-5626	293	2	a	a	PRON
ejpam-5626	293	3	=	=	X
ejpam-5626	293	4	{	{	PUNCT
ejpam-5626	293	5	(	(	PUNCT
ejpam-5626	293	6	a	a	DET
ejpam-5626	293	7	0	0	NUM
ejpam-5626	293	8	c	c	NOUN
ejpam-5626	293	9	d	d	NOUN
ejpam-5626	293	10	)	)	PUNCT
ejpam-5626	293	11	}	}	PUNCT
ejpam-5626	293	12	,	,	PUNCT
ejpam-5626	294	1	the	the	DET
ejpam-5626	294	2	algebra	algebra	NOUN
ejpam-5626	294	3	of	of	ADP
ejpam-5626	294	4	all	all	DET
ejpam-5626	294	5	lower	low	ADJ
ejpam-5626	294	6	triangular	triangular	NOUN
ejpam-5626	294	7	matrix	matrix	NOUN
ejpam-5626	294	8	of	of	ADP
ejpam-5626	294	9	order	order	NOUN
ejpam-5626	294	10	2	2	NUM
ejpam-5626	294	11	over	over	ADP
ejpam-5626	294	12	the	the	DET
ejpam-5626	294	13	field	field	NOUN
ejpam-5626	294	14	of	of	ADP
ejpam-5626	294	15	complex	complex	ADJ
ejpam-5626	294	16	numbers	number	NOUN
ejpam-5626	294	17	c	c	NOUN
ejpam-5626	295	1	and	and	CCONJ
ejpam-5626	295	2	i	i	PRON
ejpam-5626	295	3	=	=	PUNCT
ejpam-5626	296	1	(	(	PUNCT
ejpam-5626	296	2	1	1	NUM
ejpam-5626	296	3	0	0	NUM
ejpam-5626	296	4	0	0	NUM
ejpam-5626	296	5	1	1	NUM
ejpam-5626	296	6	)	)	PUNCT
ejpam-5626	296	7	be	be	AUX
ejpam-5626	296	8	unity	unity	NOUN
ejpam-5626	296	9	of	of	ADP
ejpam-5626	296	10	a.	a.	NOUN
ejpam-5626	296	11	the	the	DET
ejpam-5626	296	12	map	map	NOUN
ejpam-5626	296	13	∗	∗	VERB
ejpam-5626	296	14	:	:	PUNCT
ejpam-5626	296	15	a	a	DET
ejpam-5626	296	16	→	→	X
ejpam-5626	296	17	a	a	DET
ejpam-5626	296	18	given	give	VERB
ejpam-5626	296	19	by	by	ADP
ejpam-5626	296	20	∗(l	∗(l	PROPN
ejpam-5626	296	21	)	)	PUNCT
ejpam-5626	297	1	=	=	SYM
ejpam-5626	297	2	lθ	lθ	NOUN
ejpam-5626	297	3	,	,	PUNCT
ejpam-5626	297	4	where	where	SCONJ
ejpam-5626	297	5	lθ	lθ	NOUN
ejpam-5626	297	6	denotes	denote	VERB
ejpam-5626	297	7	the	the	DET
ejpam-5626	297	8	conjugate	conjugate	ADJ
ejpam-5626	297	9	transpose	transpose	NOUN
ejpam-5626	297	10	of	of	ADP
ejpam-5626	297	11	matrix	matrix	NOUN
ejpam-5626	297	12	a	a	PRON
ejpam-5626	297	13	,	,	PUNCT
ejpam-5626	297	14	is	be	AUX
ejpam-5626	297	15	an	an	DET
ejpam-5626	297	16	involution	involution	NOUN
ejpam-5626	297	17	.	.	PUNCT
ejpam-5626	298	1	hence	hence	ADV
ejpam-5626	298	2	,	,	PUNCT
ejpam-5626	298	3	a	a	PRON
ejpam-5626	298	4	is	be	AUX
ejpam-5626	298	5	a	a	DET
ejpam-5626	298	6	unital	unital	ADJ
ejpam-5626	298	7	∗-algebra	∗-algebra	NOUN
ejpam-5626	298	8	with	with	ADP
ejpam-5626	298	9	unity	unity	NOUN
ejpam-5626	298	10	i.	i.	NOUN
ejpam-5626	298	11	now	now	ADV
ejpam-5626	298	12	,	,	PUNCT
ejpam-5626	298	13	define	define	VERB
ejpam-5626	298	14	a	a	DET
ejpam-5626	298	15	map	map	NOUN
ejpam-5626	298	16	π	π	NOUN
ejpam-5626	298	17	:	:	PUNCT
ejpam-5626	298	18	a	a	PRON
ejpam-5626	298	19	→	→	X
ejpam-5626	298	20	a	a	DET
ejpam-5626	298	21	such	such	ADJ
ejpam-5626	298	22	that	that	SCONJ
ejpam-5626	298	23	π	π	PROPN
ejpam-5626	298	24	(	(	PUNCT
ejpam-5626	298	25	a	a	DET
ejpam-5626	298	26	0	0	NUM
ejpam-5626	298	27	c	c	NOUN
ejpam-5626	298	28	d	d	NOUN
ejpam-5626	298	29	)	)	PUNCT
ejpam-5626	298	30	=	=	PUNCT
ejpam-5626	299	1	(	(	PUNCT
ejpam-5626	299	2	0	0	NUM
ejpam-5626	299	3	0	0	NUM
ejpam-5626	299	4	−ic	−ic	PROPN
ejpam-5626	299	5	0	0	NUM
ejpam-5626	299	6	)	)	PUNCT
ejpam-5626	299	7	.	.	PUNCT
ejpam-5626	300	1	note	note	VERB
ejpam-5626	300	2	that	that	SCONJ
ejpam-5626	300	3	π	π	PROPN
ejpam-5626	300	4	is	be	AUX
ejpam-5626	300	5	a	a	DET
ejpam-5626	300	6	derivation	derivation	NOUN
ejpam-5626	300	7	on	on	ADP
ejpam-5626	300	8	a.	a.	NOUN
ejpam-5626	301	1	so	so	ADV
ejpam-5626	301	2	,	,	PUNCT
ejpam-5626	301	3	it	it	PRON
ejpam-5626	301	4	also	also	ADV
ejpam-5626	301	5	satisfies	satisfy	VERB
ejpam-5626	301	6	λ([[l	λ([[l	NUM
ejpam-5626	301	7	,	,	PUNCT
ejpam-5626	301	8	m]•,n]∗	m]•,n]∗	NOUN
ejpam-5626	301	9	)	)	PUNCT
ejpam-5626	301	10	=	=	NOUN
ejpam-5626	302	1	[	[	X
ejpam-5626	302	2	[	[	X
ejpam-5626	302	3	λ(l),m]•,n]∗	λ(l),m]•,n]∗	X
ejpam-5626	302	4	+	+	X
ejpam-5626	302	5	[	[	X
ejpam-5626	302	6	[	[	X
ejpam-5626	302	7	l	l	NOUN
ejpam-5626	302	8	,	,	PUNCT
ejpam-5626	302	9	λ(m)]•,n]∗	λ(m)]•,n]∗	NOUN
ejpam-5626	303	1	+	+	X
ejpam-5626	304	1	[	[	X
ejpam-5626	304	2	[	[	X
ejpam-5626	304	3	l	l	NOUN
ejpam-5626	304	4	,	,	PUNCT
ejpam-5626	304	5	m]•,λ(n)]∗	m]•,λ(n)]∗	VERB
ejpam-5626	304	6	for	for	ADP
ejpam-5626	304	7	all	all	DET
ejpam-5626	304	8	l	l	NOUN
ejpam-5626	304	9	,	,	PUNCT
ejpam-5626	304	10	m	m	PROPN
ejpam-5626	304	11	,	,	PUNCT
ejpam-5626	304	12	n	n	PROPN
ejpam-5626	304	13	∈	∈	NOUN
ejpam-5626	304	14	a.	a.	NOUN
ejpam-5626	304	15	let	let	VERB
ejpam-5626	304	16	p	p	NOUN
ejpam-5626	304	17	=	=	X
ejpam-5626	304	18	(	(	PUNCT
ejpam-5626	304	19	0	0	NUM
ejpam-5626	304	20	0	0	NUM
ejpam-5626	304	21	0	0	NUM
ejpam-5626	304	22	1	1	NUM
ejpam-5626	304	23	)	)	PUNCT
ejpam-5626	304	24	is	be	AUX
ejpam-5626	304	25	a	a	DET
ejpam-5626	304	26	non	non	ADJ
ejpam-5626	304	27	-	-	ADJ
ejpam-5626	304	28	trivial	trivial	ADJ
ejpam-5626	304	29	projection	projection	NOUN
ejpam-5626	304	30	,	,	PUNCT
ejpam-5626	304	31	so	so	ADV
ejpam-5626	304	32	p	p	ADJ
ejpam-5626	304	33	2	2	NUM
ejpam-5626	304	34	=	=	SYM
ejpam-5626	304	35	p	p	NOUN
ejpam-5626	304	36	and	and	CCONJ
ejpam-5626	304	37	p	p	NOUN
ejpam-5626	304	38	∗	∗	NOUN
ejpam-5626	304	39	=	=	SYM
ejpam-5626	304	40	p	p	NOUN
ejpam-5626	304	41	.	.	PUNCT
ejpam-5626	305	1	for	for	ADP
ejpam-5626	305	2	w	w	NOUN
ejpam-5626	305	3	=	=	PUNCT
ejpam-5626	305	4	(	(	PUNCT
ejpam-5626	305	5	0	0	NUM
ejpam-5626	305	6	0	0	NUM
ejpam-5626	305	7	1	1	NUM
ejpam-5626	305	8	0	0	NUM
ejpam-5626	305	9	)	)	PUNCT
ejpam-5626	305	10	̸=	̸=	NOUN
ejpam-5626	305	11	0	0	NUM
ejpam-5626	305	12	∈	∈	PROPN
ejpam-5626	305	13	a	a	PRON
ejpam-5626	305	14	and	and	CCONJ
ejpam-5626	305	15	hence	hence	ADV
ejpam-5626	305	16	wap	wap	PROPN
ejpam-5626	305	17	=	=	SYM
ejpam-5626	305	18	(	(	PUNCT
ejpam-5626	305	19	0	0	NUM
ejpam-5626	305	20	)	)	PUNCT
ejpam-5626	306	1	but	but	CCONJ
ejpam-5626	306	2	0	0	NUM
ejpam-5626	306	3	̸=	̸=	PROPN
ejpam-5626	306	4	w	w	PROPN
ejpam-5626	306	5	∈	∈	PROPN
ejpam-5626	306	6	a.	a.	NOUN
ejpam-5626	306	7	however	however	ADV
ejpam-5626	306	8	,	,	PUNCT
ejpam-5626	306	9	π	π	PROPN
ejpam-5626	306	10	is	be	AUX
ejpam-5626	306	11	not	not	PART
ejpam-5626	306	12	an	an	DET
ejpam-5626	306	13	additive	additive	ADJ
ejpam-5626	306	14	∗-derivation	∗-derivation	NOUN
ejpam-5626	306	15	because	because	SCONJ
ejpam-5626	306	16	π(l∗	π(l∗	X
ejpam-5626	306	17	)	)	PUNCT
ejpam-5626	306	18	̸=	̸=	PROPN
ejpam-5626	306	19	(	(	PUNCT
ejpam-5626	306	20	π(l))∗	π(l))∗	VERB
ejpam-5626	306	21	for	for	ADP
ejpam-5626	306	22	some	some	DET
ejpam-5626	306	23	l	l	NOUN
ejpam-5626	306	24	∈	∈	PROPN
ejpam-5626	306	25	a.	a.	NOUN
ejpam-5626	306	26	3	3	X
ejpam-5626	306	27	.	.	PUNCT
ejpam-5626	306	28	corollaries	corollary	NOUN
ejpam-5626	306	29	as	as	ADP
ejpam-5626	306	30	a	a	DET
ejpam-5626	306	31	direct	direct	ADJ
ejpam-5626	306	32	consequence	consequence	NOUN
ejpam-5626	306	33	of	of	ADP
ejpam-5626	306	34	theorem	theorem	NOUN
ejpam-5626	306	35	2.1	2.1	NUM
ejpam-5626	306	36	,	,	PUNCT
ejpam-5626	306	37	we	we	PRON
ejpam-5626	306	38	have	have	VERB
ejpam-5626	306	39	the	the	DET
ejpam-5626	306	40	following	follow	VERB
ejpam-5626	306	41	corollaries	corollary	NOUN
ejpam-5626	306	42	:	:	PUNCT
ejpam-5626	306	43	corollary	corollary	ADJ
ejpam-5626	306	44	3.1	3.1	NUM
ejpam-5626	306	45	.	.	PUNCT
ejpam-5626	307	1	let	let	VERB
ejpam-5626	307	2	a	a	PRON
ejpam-5626	307	3	be	be	AUX
ejpam-5626	307	4	a	a	DET
ejpam-5626	307	5	standard	standard	ADJ
ejpam-5626	307	6	operator	operator	NOUN
ejpam-5626	307	7	algebra	algebra	NOUN
ejpam-5626	307	8	on	on	ADP
ejpam-5626	307	9	an	an	DET
ejpam-5626	307	10	infinite	infinite	ADJ
ejpam-5626	307	11	dimensional	dimensional	ADJ
ejpam-5626	307	12	complex	complex	ADJ
ejpam-5626	307	13	hilbert	hilbert	NOUN
ejpam-5626	307	14	space	space	NOUN
ejpam-5626	307	15	h	h	NOUN
ejpam-5626	307	16	containing	contain	VERB
ejpam-5626	307	17	identity	identity	NOUN
ejpam-5626	307	18	operator	operator	NOUN
ejpam-5626	307	19	i.	i.	NOUN
ejpam-5626	307	20	suppose	suppose	VERB
ejpam-5626	307	21	that	that	SCONJ
ejpam-5626	307	22	a	a	PRON
ejpam-5626	307	23	is	be	AUX
ejpam-5626	307	24	closed	close	VERB
ejpam-5626	307	25	under	under	ADP
ejpam-5626	307	26	adjoint	adjoint	NOUN
ejpam-5626	307	27	operation	operation	NOUN
ejpam-5626	307	28	.	.	PUNCT
ejpam-5626	308	1	define	define	VERB
ejpam-5626	308	2	λ	λ	X
ejpam-5626	308	3	:	:	PUNCT
ejpam-5626	308	4	a	a	PRON
ejpam-5626	308	5	→	→	X
ejpam-5626	308	6	a	a	DET
ejpam-5626	308	7	such	such	ADJ
ejpam-5626	308	8	that	that	SCONJ
ejpam-5626	308	9	λ([[l	λ([[l	ADJ
ejpam-5626	308	10	,	,	PUNCT
ejpam-5626	308	11	m]•,n]∗	m]•,n]∗	NOUN
ejpam-5626	308	12	)	)	PUNCT
ejpam-5626	308	13	=	=	NOUN
ejpam-5626	309	1	[	[	X
ejpam-5626	309	2	[	[	X
ejpam-5626	309	3	λ(l),m]•,n]∗	λ(l),m]•,n]∗	X
ejpam-5626	309	4	+	+	X
ejpam-5626	309	5	[	[	X
ejpam-5626	309	6	[	[	X
ejpam-5626	309	7	l	l	NOUN
ejpam-5626	309	8	,	,	PUNCT
ejpam-5626	309	9	λ(m)]•,n]∗	λ(m)]•,n]∗	NOUN
ejpam-5626	310	1	+	+	X
ejpam-5626	311	1	[	[	X
ejpam-5626	311	2	[	[	X
ejpam-5626	311	3	l	l	NOUN
ejpam-5626	311	4	,	,	PUNCT
ejpam-5626	311	5	m]•,λ(n)]∗	m]•,λ(n)]∗	VERB
ejpam-5626	311	6	for	for	ADP
ejpam-5626	311	7	all	all	DET
ejpam-5626	311	8	l	l	NOUN
ejpam-5626	311	9	,	,	PUNCT
ejpam-5626	311	10	m	m	PROPN
ejpam-5626	311	11	,	,	PUNCT
ejpam-5626	311	12	n	n	PROPN
ejpam-5626	311	13	∈	∈	PROPN
ejpam-5626	311	14	a	a	PRON
ejpam-5626	311	15	,	,	PUNCT
ejpam-5626	311	16	then	then	ADV
ejpam-5626	311	17	λ	λ	PROPN
ejpam-5626	311	18	is	be	AUX
ejpam-5626	311	19	an	an	DET
ejpam-5626	311	20	additive	additive	NOUN
ejpam-5626	311	21	.	.	PUNCT
ejpam-5626	312	1	if	if	SCONJ
ejpam-5626	312	2	λ(i	λ(i	PROPN
ejpam-5626	312	3	)	)	PUNCT
ejpam-5626	312	4	is	be	AUX
ejpam-5626	312	5	self	self	NOUN
ejpam-5626	312	6	-	-	PUNCT
ejpam-5626	312	7	adjoint	adjoint	NOUN
ejpam-5626	312	8	,	,	PUNCT
ejpam-5626	312	9	then	then	ADV
ejpam-5626	312	10	λ	λ	PROPN
ejpam-5626	312	11	is	be	AUX
ejpam-5626	312	12	an	an	DET
ejpam-5626	312	13	∗-derivation	∗-derivation	NOUN
ejpam-5626	312	14	.	.	PUNCT
ejpam-5626	313	1	corollary	corollary	ADJ
ejpam-5626	313	2	3.2	3.2	NUM
ejpam-5626	313	3	.	.	PUNCT
ejpam-5626	314	1	let	let	VERB
ejpam-5626	314	2	m	m	AUX
ejpam-5626	314	3	ba	ba	VERB
ejpam-5626	314	4	a	a	DET
ejpam-5626	314	5	factor	factor	NOUN
ejpam-5626	314	6	von	von	PROPN
ejpam-5626	314	7	neumann	neumann	PROPN
ejpam-5626	314	8	algebra	algebra	PROPN
ejpam-5626	314	9	with	with	ADP
ejpam-5626	314	10	dimm	dimm	NOUN
ejpam-5626	314	11	≥	≥	NOUN
ejpam-5626	314	12	2	2	NUM
ejpam-5626	314	13	.	.	PUNCT
ejpam-5626	315	1	define	define	VERB
ejpam-5626	315	2	λ	λ	PROPN
ejpam-5626	315	3	:	:	PUNCT
ejpam-5626	315	4	m	m	VERB
ejpam-5626	315	5	→	→	NOUN
ejpam-5626	315	6	m	m	VERB
ejpam-5626	315	7	such	such	ADJ
ejpam-5626	315	8	that	that	SCONJ
ejpam-5626	315	9	λ([[l	λ([[l	ADJ
ejpam-5626	315	10	,	,	PUNCT
ejpam-5626	315	11	m]•,n]∗	m]•,n]∗	NOUN
ejpam-5626	315	12	)	)	PUNCT
ejpam-5626	315	13	=	=	NOUN
ejpam-5626	316	1	[	[	X
ejpam-5626	316	2	[	[	X
ejpam-5626	316	3	λ(l),m]•,n]∗	λ(l),m]•,n]∗	X
ejpam-5626	316	4	+	+	X
ejpam-5626	316	5	[	[	X
ejpam-5626	316	6	[	[	X
ejpam-5626	316	7	l	l	NOUN
ejpam-5626	316	8	,	,	PUNCT
ejpam-5626	316	9	λ(m)]•,n]∗	λ(m)]•,n]∗	NOUN
ejpam-5626	317	1	+	+	X
ejpam-5626	318	1	[	[	X
ejpam-5626	318	2	[	[	X
ejpam-5626	318	3	l	l	NOUN
ejpam-5626	318	4	,	,	PUNCT
ejpam-5626	318	5	m]•,λ(n)]∗	m]•,λ(n)]∗	VERB
ejpam-5626	318	6	for	for	ADP
ejpam-5626	318	7	all	all	DET
ejpam-5626	318	8	l	l	NOUN
ejpam-5626	318	9	,	,	PUNCT
ejpam-5626	318	10	m	m	PROPN
ejpam-5626	318	11	,	,	PUNCT
ejpam-5626	318	12	n	n	PROPN
ejpam-5626	318	13	∈	∈	PROPN
ejpam-5626	318	14	a	a	PRON
ejpam-5626	318	15	,	,	PUNCT
ejpam-5626	318	16	then	then	ADV
ejpam-5626	318	17	λ	λ	PROPN
ejpam-5626	318	18	is	be	AUX
ejpam-5626	318	19	an	an	DET
ejpam-5626	318	20	additive	additive	NOUN
ejpam-5626	318	21	.	.	PUNCT
ejpam-5626	319	1	if	if	SCONJ
ejpam-5626	319	2	λ(i	λ(i	PROPN
ejpam-5626	319	3	)	)	PUNCT
ejpam-5626	319	4	is	be	AUX
ejpam-5626	319	5	self	self	NOUN
ejpam-5626	319	6	-	-	PUNCT
ejpam-5626	319	7	adjoint	adjoint	NOUN
ejpam-5626	319	8	,	,	PUNCT
ejpam-5626	319	9	then	then	ADV
ejpam-5626	319	10	λ	λ	PROPN
ejpam-5626	319	11	is	be	AUX
ejpam-5626	319	12	an	an	DET
ejpam-5626	319	13	∗-derivation	∗-derivation	NOUN
ejpam-5626	319	14	.	.	PUNCT
ejpam-5626	320	1	corollary	corollary	ADJ
ejpam-5626	320	2	3.3	3.3	NUM
ejpam-5626	320	3	.	.	PUNCT
ejpam-5626	321	1	let	let	VERB
ejpam-5626	321	2	a	a	PRON
ejpam-5626	321	3	be	be	AUX
ejpam-5626	321	4	a	a	DET
ejpam-5626	321	5	prime	prime	ADJ
ejpam-5626	321	6	∗-algebra	∗-algebra	NOUN
ejpam-5626	321	7	with	with	ADP
ejpam-5626	321	8	unit	unit	NOUN
ejpam-5626	321	9	i	i	PRON
ejpam-5626	321	10	containing	contain	VERB
ejpam-5626	321	11	non	non	ADJ
ejpam-5626	321	12	-	-	ADJ
ejpam-5626	321	13	trivial	trivial	ADJ
ejpam-5626	321	14	projection	projection	NOUN
ejpam-5626	321	15	p	p	NOUN
ejpam-5626	321	16	.	.	PUNCT
ejpam-5626	322	1	a	a	DET
ejpam-5626	322	2	map	map	NOUN
ejpam-5626	322	3	λ	λ	X
ejpam-5626	322	4	:	:	PUNCT
ejpam-5626	322	5	a	a	DET
ejpam-5626	322	6	→	→	X
ejpam-5626	322	7	a	a	DET
ejpam-5626	322	8	satisfies	satisfie	NOUN
ejpam-5626	322	9	λ([[l	λ([[l	NUM
ejpam-5626	322	10	,	,	PUNCT
ejpam-5626	322	11	m]•,n]∗	m]•,n]∗	NOUN
ejpam-5626	322	12	)	)	PUNCT
ejpam-5626	322	13	=	=	NOUN
ejpam-5626	323	1	[	[	X
ejpam-5626	323	2	[	[	X
ejpam-5626	323	3	λ(l),m]•,n]∗	λ(l),m]•,n]∗	X
ejpam-5626	323	4	+	+	X
ejpam-5626	323	5	[	[	X
ejpam-5626	323	6	[	[	X
ejpam-5626	323	7	l	l	NOUN
ejpam-5626	323	8	,	,	PUNCT
ejpam-5626	323	9	λ(m)]•,n]∗	λ(m)]•,n]∗	NOUN
ejpam-5626	324	1	+	+	X
ejpam-5626	325	1	[	[	X
ejpam-5626	325	2	[	[	X
ejpam-5626	325	3	l	l	NOUN
ejpam-5626	325	4	,	,	PUNCT
ejpam-5626	325	5	m]•,λ(n)]∗	m]•,λ(n)]∗	VERB
ejpam-5626	325	6	for	for	ADP
ejpam-5626	325	7	all	all	DET
ejpam-5626	325	8	l	l	NOUN
ejpam-5626	325	9	,	,	PUNCT
ejpam-5626	325	10	m	m	PROPN
ejpam-5626	325	11	,	,	PUNCT
ejpam-5626	325	12	n	n	PROPN
ejpam-5626	325	13	∈	∈	PROPN
ejpam-5626	325	14	a	a	PRON
ejpam-5626	325	15	,	,	PUNCT
ejpam-5626	325	16	then	then	ADV
ejpam-5626	325	17	λ	λ	PROPN
ejpam-5626	325	18	is	be	AUX
ejpam-5626	325	19	an	an	DET
ejpam-5626	325	20	additive	additive	NOUN
ejpam-5626	325	21	.	.	PUNCT
ejpam-5626	326	1	if	if	SCONJ
ejpam-5626	326	2	λ(i	λ(i	PROPN
ejpam-5626	326	3	)	)	PUNCT
ejpam-5626	326	4	is	be	AUX
ejpam-5626	326	5	self	self	NOUN
ejpam-5626	326	6	-	-	PUNCT
ejpam-5626	326	7	adjoint	adjoint	NOUN
ejpam-5626	326	8	,	,	PUNCT
ejpam-5626	326	9	then	then	ADV
ejpam-5626	326	10	λ	λ	PROPN
ejpam-5626	326	11	is	be	AUX
ejpam-5626	326	12	an	an	DET
ejpam-5626	326	13	∗-derivation	∗-derivation	NOUN
ejpam-5626	326	14	.	.	PUNCT
ejpam-5626	327	1	conflicts	conflict	NOUN
ejpam-5626	327	2	of	of	ADP
ejpam-5626	327	3	interest	interest	NOUN
ejpam-5626	327	4	:	:	PUNCT
ejpam-5626	327	5	the	the	DET
ejpam-5626	327	6	authors	author	NOUN
ejpam-5626	327	7	declare	declare	VERB
ejpam-5626	327	8	no	no	DET
ejpam-5626	327	9	conflict	conflict	NOUN
ejpam-5626	327	10	of	of	ADP
ejpam-5626	327	11	interest	interest	NOUN
ejpam-5626	327	12	.	.	PUNCT
ejpam-5626	328	1	m.	m.	NOUN
ejpam-5626	328	2	a.	a.	PROPN
ejpam-5626	328	3	raza	raza	PROPN
ejpam-5626	328	4	et	et	PROPN
ejpam-5626	328	5	al	al	PROPN
ejpam-5626	328	6	.	.	PUNCT
ejpam-5626	328	7	/	/	SYM
ejpam-5626	328	8	eur	eur	PROPN
ejpam-5626	328	9	.	.	PUNCT
ejpam-5626	329	1	j.	j.	PROPN
ejpam-5626	329	2	pure	pure	PROPN
ejpam-5626	329	3	appl	appl	PROPN
ejpam-5626	329	4	.	.	PROPN
ejpam-5626	329	5	math	math	PROPN
ejpam-5626	329	6	,	,	PUNCT
ejpam-5626	329	7	18	18	NUM
ejpam-5626	329	8	(	(	PUNCT
ejpam-5626	329	9	1	1	NUM
ejpam-5626	329	10	)	)	PUNCT
ejpam-5626	329	11	(	(	PUNCT
ejpam-5626	329	12	2025	2025	NUM
ejpam-5626	329	13	)	)	PUNCT
ejpam-5626	329	14	,	,	PUNCT
ejpam-5626	329	15	5626	5626	NUM
ejpam-5626	329	16	10	10	NUM
ejpam-5626	329	17	of	of	ADP
ejpam-5626	329	18	10	10	NUM
ejpam-5626	329	19	references	reference	NOUN
ejpam-5626	329	20	[	[	X
ejpam-5626	329	21	1	1	NUM
ejpam-5626	329	22	]	]	PUNCT
ejpam-5626	329	23	m.	m.	NOUN
ejpam-5626	329	24	ashraf	ashraf	PROPN
ejpam-5626	329	25	,	,	PUNCT
ejpam-5626	329	26	md	md	PROPN
ejpam-5626	329	27	.	.	PROPN
ejpam-5626	329	28	shamim	shamim	PROPN
ejpam-5626	329	29	akhter	akhter	PROPN
ejpam-5626	329	30	,	,	PUNCT
ejpam-5626	329	31	and	and	CCONJ
ejpam-5626	329	32	m.	m.	NOUN
ejpam-5626	329	33	ansari	ansari	PROPN
ejpam-5626	329	34	.	.	PUNCT
ejpam-5626	330	1	nonlinear	nonlinear	ADJ
ejpam-5626	330	2	bi	bi	ADJ
ejpam-5626	330	3	-	-	ADJ
ejpam-5626	330	4	skew	skew	ADJ
ejpam-5626	330	5	jordan	jordan	PROPN
ejpam-5626	330	6	-	-	PUNCT
ejpam-5626	330	7	type	type	NOUN
ejpam-5626	330	8	derivations	derivation	NOUN
ejpam-5626	330	9	on	on	ADP
ejpam-5626	330	10	factor	factor	NOUN
ejpam-5626	330	11	von	von	PROPN
ejpam-5626	330	12	neumann	neumann	PROPN
ejpam-5626	330	13	algebras	algebras	PROPN
ejpam-5626	330	14	.	.	PUNCT
ejpam-5626	331	1	filomat	filomat	PROPN
ejpam-5626	331	2	,	,	PUNCT
ejpam-5626	331	3	37(17):5591–5599	37(17):5591–5599	NUM
ejpam-5626	331	4	,	,	PUNCT
ejpam-5626	331	5	2023	2023	NUM
ejpam-5626	331	6	.	.	PUNCT
ejpam-5626	332	1	[	[	X
ejpam-5626	332	2	2	2	X
ejpam-5626	332	3	]	]	X
ejpam-5626	332	4	d.	d.	PROPN
ejpam-5626	332	5	huo	huo	PROPN
ejpam-5626	332	6	,	,	PUNCT
ejpam-5626	332	7	b.	b.	PROPN
ejpam-5626	332	8	zheng	zheng	PROPN
ejpam-5626	332	9	,	,	PUNCT
ejpam-5626	332	10	j.	j.	PROPN
ejpam-5626	332	11	xu	xu	PROPN
ejpam-5626	332	12	,	,	PUNCT
ejpam-5626	332	13	and	and	CCONJ
ejpam-5626	332	14	h.	h.	PROPN
ejpam-5626	332	15	liu	liu	PROPN
ejpam-5626	332	16	.	.	PUNCT
ejpam-5626	333	1	nonlinear	nonlinear	ADJ
ejpam-5626	333	2	mappings	mapping	NOUN
ejpam-5626	333	3	preserving	preserve	VERB
ejpam-5626	333	4	jordan	jordan	PROPN
ejpam-5626	333	5	multiple	multiple	ADJ
ejpam-5626	333	6	∗	∗	NOUN
ejpam-5626	333	7	–	–	PUNCT
ejpam-5626	333	8	product	product	NOUN
ejpam-5626	333	9	on	on	ADP
ejpam-5626	333	10	factor	factor	NOUN
ejpam-5626	333	11	von	von	PROPN
ejpam-5626	333	12	neumann	neumann	PROPN
ejpam-5626	333	13	algebras	algebras	PROPN
ejpam-5626	333	14	.	.	PUNCT
ejpam-5626	334	1	linear	linear	PROPN
ejpam-5626	334	2	and	and	CCONJ
ejpam-5626	334	3	multilinear	multilinear	PROPN
ejpam-5626	334	4	algebra	algebra	PROPN
ejpam-5626	334	5	,	,	PUNCT
ejpam-5626	334	6	63(5):1026–1036	63(5):1026–1036	PROPN
ejpam-5626	334	7	,	,	PUNCT
ejpam-5626	334	8	2015	2015	NUM
ejpam-5626	334	9	.	.	PUNCT
ejpam-5626	335	1	[	[	X
ejpam-5626	335	2	3	3	NUM
ejpam-5626	335	3	]	]	PUNCT
ejpam-5626	335	4	a.	a.	PROPN
ejpam-5626	335	5	khan	khan	PROPN
ejpam-5626	335	6	.	.	PUNCT
ejpam-5626	336	1	multiplicative	multiplicative	ADJ
ejpam-5626	336	2	biskew	biskew	NOUN
ejpam-5626	336	3	lie	lie	VERB
ejpam-5626	336	4	triple	triple	ADJ
ejpam-5626	336	5	derivations	derivation	NOUN
ejpam-5626	336	6	on	on	ADP
ejpam-5626	336	7	factor	factor	NOUN
ejpam-5626	336	8	von	von	PROPN
ejpam-5626	336	9	neumann	neumann	PROPN
ejpam-5626	336	10	algebras	algebras	PROPN
ejpam-5626	336	11	.	.	PUNCT
ejpam-5626	337	1	rocky	rocky	ADJ
ejpam-5626	337	2	mountain	mountain	PROPN
ejpam-5626	337	3	journal	journal	NOUN
ejpam-5626	337	4	of	of	ADP
ejpam-5626	337	5	mathematics	mathematic	NOUN
ejpam-5626	337	6	,	,	PUNCT
ejpam-5626	337	7	51(6):2103–2114	51(6):2103–2114	NUM
ejpam-5626	337	8	,	,	PUNCT
ejpam-5626	337	9	2021	2021	NUM
ejpam-5626	337	10	.	.	PUNCT
ejpam-5626	338	1	[	[	X
ejpam-5626	338	2	4	4	NUM
ejpam-5626	338	3	]	]	X
ejpam-5626	338	4	l.	l.	PROPN
ejpam-5626	338	5	kong	kong	PROPN
ejpam-5626	338	6	and	and	CCONJ
ejpam-5626	338	7	j.	j.	PROPN
ejpam-5626	338	8	zhang	zhang	PROPN
ejpam-5626	338	9	.	.	PUNCT
ejpam-5626	339	1	nonlinear	nonlinear	PROPN
ejpam-5626	339	2	skew	skew	ADJ
ejpam-5626	339	3	lie	lie	NOUN
ejpam-5626	339	4	derivations	derivation	NOUN
ejpam-5626	339	5	on	on	ADP
ejpam-5626	339	6	prime	prime	ADJ
ejpam-5626	339	7	∗-rings	∗-ring	NOUN
ejpam-5626	339	8	.	.	PUNCT
ejpam-5626	340	1	indian	indian	ADJ
ejpam-5626	340	2	journal	journal	PROPN
ejpam-5626	340	3	of	of	ADP
ejpam-5626	340	4	pure	pure	ADJ
ejpam-5626	340	5	and	and	CCONJ
ejpam-5626	340	6	applied	applied	ADJ
ejpam-5626	340	7	mathematics	mathematic	NOUN
ejpam-5626	340	8	,	,	PUNCT
ejpam-5626	340	9	54(2):475–484	54(2):475–484	PROPN
ejpam-5626	340	10	,	,	PUNCT
ejpam-5626	340	11	2023	2023	NUM
ejpam-5626	340	12	.	.	PUNCT
ejpam-5626	341	1	[	[	X
ejpam-5626	341	2	5	5	NUM
ejpam-5626	341	3	]	]	PUNCT
ejpam-5626	341	4	c.	c.	PROPN
ejpam-5626	341	5	li	li	PROPN
ejpam-5626	341	6	,	,	PUNCT
ejpam-5626	341	7	q.	q.	PROPN
ejpam-5626	341	8	chen	chen	PROPN
ejpam-5626	341	9	,	,	PUNCT
ejpam-5626	341	10	and	and	CCONJ
ejpam-5626	341	11	t.	t.	PROPN
ejpam-5626	341	12	wang	wang	PROPN
ejpam-5626	341	13	.	.	PUNCT
ejpam-5626	342	1	nonlinear	nonlinear	ADJ
ejpam-5626	342	2	maps	map	NOUN
ejpam-5626	342	3	preserving	preserve	VERB
ejpam-5626	342	4	the	the	DET
ejpam-5626	342	5	jordan	jordan	PROPN
ejpam-5626	342	6	triple	triple	ADJ
ejpam-5626	342	7	∗-product	∗-product	NUM
ejpam-5626	342	8	on	on	ADP
ejpam-5626	342	9	factor	factor	NOUN
ejpam-5626	342	10	von	von	PROPN
ejpam-5626	342	11	neumann	neumann	PROPN
ejpam-5626	342	12	algebras	algebras	PROPN
ejpam-5626	342	13	.	.	PUNCT
ejpam-5626	343	1	chin	chin	PROPN
ejpam-5626	343	2	.	.	PUNCT
ejpam-5626	344	1	ann	ann	PROPN
ejpam-5626	344	2	.	.	PUNCT
ejpam-5626	344	3	math	math	PROPN
ejpam-5626	344	4	.	.	PUNCT
ejpam-5626	345	1	ser	ser	PROPN
ejpam-5626	345	2	.	.	PUNCT
ejpam-5626	346	1	b	b	NUM
ejpam-5626	346	2	,	,	PUNCT
ejpam-5626	346	3	39(4):633–642	39(4):633–642	PROPN
ejpam-5626	346	4	,	,	PUNCT
ejpam-5626	346	5	2018	2018	NUM
ejpam-5626	346	6	.	.	PUNCT
ejpam-5626	347	1	[	[	X
ejpam-5626	347	2	6	6	NUM
ejpam-5626	347	3	]	]	X
ejpam-5626	347	4	c.	c.	PROPN
ejpam-5626	347	5	li	li	PROPN
ejpam-5626	347	6	,	,	PUNCT
ejpam-5626	347	7	q.	q.	PROPN
ejpam-5626	347	8	chen	chen	PROPN
ejpam-5626	347	9	,	,	PUNCT
ejpam-5626	347	10	and	and	CCONJ
ejpam-5626	347	11	t.	t.	PROPN
ejpam-5626	347	12	wang	wang	PROPN
ejpam-5626	347	13	.	.	PUNCT
ejpam-5626	348	1	nonlinear	nonlinear	ADJ
ejpam-5626	348	2	maps	map	NOUN
ejpam-5626	348	3	preserving	preserve	VERB
ejpam-5626	348	4	the	the	DET
ejpam-5626	348	5	jordan	jordan	PROPN
ejpam-5626	348	6	triple∗product	triple∗product	PROPN
ejpam-5626	348	7	on	on	ADP
ejpam-5626	348	8	factor	factor	NOUN
ejpam-5626	348	9	von	von	PROPN
ejpam-5626	348	10	neumann	neumann	PROPN
ejpam-5626	348	11	algebras	algebras	PROPN
ejpam-5626	348	12	.	.	PUNCT
ejpam-5626	349	1	chinese	chinese	ADJ
ejpam-5626	349	2	annals	annal	NOUN
ejpam-5626	349	3	of	of	ADP
ejpam-5626	349	4	mathematics	mathematic	NOUN
ejpam-5626	349	5	,	,	PUNCT
ejpam-5626	349	6	series	series	NOUN
ejpam-5626	349	7	b	b	PROPN
ejpam-5626	349	8	,	,	PUNCT
ejpam-5626	349	9	39(4):633–642	39(4):633–642	PROPN
ejpam-5626	349	10	,	,	PUNCT
ejpam-5626	349	11	2018	2018	NUM
ejpam-5626	349	12	.	.	PUNCT
ejpam-5626	350	1	[	[	X
ejpam-5626	350	2	7	7	X
ejpam-5626	350	3	]	]	X
ejpam-5626	350	4	c.	c.	PROPN
ejpam-5626	350	5	li	li	PROPN
ejpam-5626	350	6	and	and	CCONJ
ejpam-5626	350	7	f.	f.	PROPN
ejpam-5626	350	8	lu	lu	PROPN
ejpam-5626	350	9	.	.	PUNCT
ejpam-5626	351	1	nonlinear	nonlinear	ADJ
ejpam-5626	351	2	maps	map	NOUN
ejpam-5626	351	3	preserving	preserve	VERB
ejpam-5626	351	4	the	the	DET
ejpam-5626	351	5	jordan	jordan	PROPN
ejpam-5626	351	6	triple	triple	ADV
ejpam-5626	351	7	1∗-product	1∗-product	PROPN
ejpam-5626	351	8	on	on	ADP
ejpam-5626	351	9	von	von	PROPN
ejpam-5626	351	10	neumann	neumann	PROPN
ejpam-5626	351	11	algebras	algebras	PROPN
ejpam-5626	351	12	.	.	PUNCT
ejpam-5626	352	1	complex	complex	ADJ
ejpam-5626	352	2	analysis	analysis	NOUN
ejpam-5626	352	3	and	and	CCONJ
ejpam-5626	352	4	operator	operator	NOUN
ejpam-5626	352	5	theory	theory	NOUN
ejpam-5626	352	6	,	,	PUNCT
ejpam-5626	352	7	11:109–117	11:109–117	PROPN
ejpam-5626	352	8	,	,	PUNCT
ejpam-5626	352	9	2017	2017	NUM
ejpam-5626	352	10	.	.	PUNCT
ejpam-5626	353	1	[	[	X
ejpam-5626	353	2	8	8	NUM
ejpam-5626	353	3	]	]	X
ejpam-5626	353	4	c.	c.	PROPN
ejpam-5626	353	5	li	li	PROPN
ejpam-5626	353	6	and	and	CCONJ
ejpam-5626	353	7	d.	d.	PROPN
ejpam-5626	353	8	zhang	zhang	PROPN
ejpam-5626	353	9	.	.	PUNCT
ejpam-5626	354	1	nonlinear	nonlinear	PROPN
ejpam-5626	354	2	mixed	mixed	PROPN
ejpam-5626	354	3	jordan	jordan	PROPN
ejpam-5626	354	4	triple	triple	ADJ
ejpam-5626	354	5	-	-	PUNCT
ejpam-5626	354	6	derivations	derivation	NOUN
ejpam-5626	354	7	on	on	ADP
ejpam-5626	354	8	-	-	PUNCT
ejpam-5626	354	9	algebras	algebras	X
ejpam-5626	354	10	.	.	PUNCT
ejpam-5626	355	1	siberian	siberian	PROPN
ejpam-5626	355	2	mathematical	mathematical	ADJ
ejpam-5626	355	3	journal	journal	NOUN
ejpam-5626	355	4	,	,	PUNCT
ejpam-5626	355	5	63(4):735–742	63(4):735–742	NUM
ejpam-5626	355	6	,	,	PUNCT
ejpam-5626	355	7	2022	2022	NUM
ejpam-5626	355	8	.	.	PUNCT
ejpam-5626	356	1	[	[	X
ejpam-5626	356	2	9	9	NUM
ejpam-5626	356	3	]	]	X
ejpam-5626	356	4	c.	c.	PROPN
ejpam-5626	356	5	li	li	PROPN
ejpam-5626	356	6	,	,	PUNCT
ejpam-5626	356	7	f.	f.	PROPN
ejpam-5626	356	8	zhao	zhao	PROPN
ejpam-5626	356	9	,	,	PUNCT
ejpam-5626	356	10	and	and	CCONJ
ejpam-5626	356	11	q.	q.	PROPN
ejpam-5626	356	12	chen	chen	PROPN
ejpam-5626	356	13	.	.	PUNCT
ejpam-5626	357	1	nonlinear	nonlinear	PROPN
ejpam-5626	357	2	skew	skew	NOUN
ejpam-5626	357	3	lie	lie	VERB
ejpam-5626	357	4	triple	triple	ADJ
ejpam-5626	357	5	derivations	derivation	NOUN
ejpam-5626	357	6	between	between	ADP
ejpam-5626	357	7	factors	factor	NOUN
ejpam-5626	357	8	.	.	PUNCT
ejpam-5626	358	1	acta	acta	PROPN
ejpam-5626	358	2	mathematica	mathematica	PROPN
ejpam-5626	358	3	sinica	sinica	PROPN
ejpam-5626	358	4	,	,	PUNCT
ejpam-5626	358	5	english	english	ADJ
ejpam-5626	358	6	series	series	NOUN
ejpam-5626	358	7	,	,	PUNCT
ejpam-5626	358	8	32(7):821–830	32(7):821–830	PROPN
ejpam-5626	358	9	,	,	PUNCT
ejpam-5626	358	10	2016	2016	NUM
ejpam-5626	358	11	.	.	PUNCT
ejpam-5626	359	1	[	[	X
ejpam-5626	359	2	10	10	NUM
ejpam-5626	359	3	]	]	X
ejpam-5626	359	4	c.	c.	PROPN
ejpam-5626	359	5	li	li	PROPN
ejpam-5626	359	6	,	,	PUNCT
ejpam-5626	359	7	y.	y.	PROPN
ejpam-5626	359	8	zhao	zhao	PROPN
ejpam-5626	359	9	,	,	PUNCT
ejpam-5626	359	10	and	and	CCONJ
ejpam-5626	359	11	f.	f.	PROPN
ejpam-5626	359	12	zhao	zhao	PROPN
ejpam-5626	359	13	.	.	PUNCT
ejpam-5626	360	1	nonlinear*-jordan	nonlinear*-jordan	ADJ
ejpam-5626	360	2	-	-	PUNCT
ejpam-5626	360	3	type	type	NOUN
ejpam-5626	360	4	derivations	derivation	NOUN
ejpam-5626	360	5	on	on	ADP
ejpam-5626	360	6	∗-algebras	∗-algebra	NOUN
ejpam-5626	360	7	.	.	PUNCT
ejpam-5626	361	1	rocky	rocky	ADJ
ejpam-5626	361	2	mountain	mountain	PROPN
ejpam-5626	361	3	journal	journal	NOUN
ejpam-5626	361	4	of	of	ADP
ejpam-5626	361	5	mathematics	mathematic	NOUN
ejpam-5626	361	6	,	,	PUNCT
ejpam-5626	361	7	51(2):601–612	51(2):601–612	PROPN
ejpam-5626	361	8	,	,	PUNCT
ejpam-5626	361	9	2021	2021	NUM
ejpam-5626	361	10	.	.	PUNCT
ejpam-5626	362	1	[	[	X
ejpam-5626	362	2	11	11	NUM
ejpam-5626	362	3	]	]	X
ejpam-5626	362	4	y.	y.	PROPN
ejpam-5626	362	5	liang	liang	PROPN
ejpam-5626	362	6	and	and	CCONJ
ejpam-5626	362	7	j.	j.	PROPN
ejpam-5626	362	8	zhang	zhang	PROPN
ejpam-5626	362	9	.	.	PUNCT
ejpam-5626	363	1	nonlinear	nonlinear	PROPN
ejpam-5626	363	2	mixed	mix	VERB
ejpam-5626	363	3	lie	lie	NOUN
ejpam-5626	363	4	triple	triple	ADJ
ejpam-5626	363	5	derivations	derivation	NOUN
ejpam-5626	363	6	on	on	ADP
ejpam-5626	363	7	factor	factor	NOUN
ejpam-5626	363	8	von	von	PROPN
ejpam-5626	363	9	neumann	neumann	PROPN
ejpam-5626	363	10	algebras	algebras	PROPN
ejpam-5626	363	11	.	.	PUNCT
ejpam-5626	364	1	acta	acta	PROPN
ejpam-5626	364	2	math	math	PROPN
ejpam-5626	364	3	sci	sci	PROPN
ejpam-5626	364	4	chinese	chinese	PROPN
ejpam-5626	364	5	series	series	PROPN
ejpam-5626	364	6	,	,	PUNCT
ejpam-5626	364	7	62:1–13	62:1–13	NUM
ejpam-5626	364	8	,	,	PUNCT
ejpam-5626	364	9	2019	2019	NUM
ejpam-5626	364	10	.	.	PUNCT
ejpam-5626	365	1	[	[	X
ejpam-5626	365	2	12	12	NUM
ejpam-5626	365	3	]	]	X
ejpam-5626	365	4	n.	n.	PROPN
ejpam-5626	365	5	rehman	rehman	PROPN
ejpam-5626	365	6	,	,	PUNCT
ejpam-5626	365	7	j.	j.	PROPN
ejpam-5626	365	8	nisar	nisar	PROPN
ejpam-5626	365	9	,	,	PUNCT
ejpam-5626	365	10	and	and	CCONJ
ejpam-5626	365	11	m.	m.	PROPN
ejpam-5626	365	12	nazim	nazim	PROPN
ejpam-5626	365	13	.	.	PUNCT
ejpam-5626	366	1	a	a	DET
ejpam-5626	366	2	note	note	NOUN
ejpam-5626	366	3	on	on	ADP
ejpam-5626	366	4	nonlinear	nonlinear	ADJ
ejpam-5626	366	5	mixed	mix	VERB
ejpam-5626	366	6	jordan	jordan	PROPN
ejpam-5626	366	7	triple	triple	ADJ
ejpam-5626	366	8	derivation	derivation	NOUN
ejpam-5626	366	9	on∗-algebras	on∗-algebra	NOUN
ejpam-5626	366	10	.	.	PUNCT
ejpam-5626	367	1	communications	communication	NOUN
ejpam-5626	367	2	in	in	ADP
ejpam-5626	367	3	algebra	algebra	NOUN
ejpam-5626	367	4	,	,	PUNCT
ejpam-5626	367	5	51(4):1334–1343	51(4):1334–1343	PROPN
ejpam-5626	367	6	,	,	PUNCT
ejpam-5626	367	7	2023	2023	NUM
ejpam-5626	367	8	.	.	PUNCT
ejpam-5626	368	1	[	[	X
ejpam-5626	368	2	13	13	NUM
ejpam-5626	368	3	]	]	PUNCT
ejpam-5626	368	4	f.	f.	PROPN
ejpam-5626	368	5	zhang	zhang	PROPN
ejpam-5626	368	6	.	.	PUNCT
ejpam-5626	369	1	nonlinear	nonlinear	PROPN
ejpam-5626	369	2	η	η	PROPN
ejpam-5626	369	3	-	-	PROPN
ejpam-5626	369	4	jordan	jordan	PROPN
ejpam-5626	369	5	triple	triple	ADJ
ejpam-5626	369	6	∗-derivation	∗-derivation	NOUN
ejpam-5626	369	7	on	on	ADP
ejpam-5626	369	8	prime	prime	ADJ
ejpam-5626	369	9	∗-algebras	∗-algebra	NOUN
ejpam-5626	369	10	.	.	PUNCT
ejpam-5626	370	1	rocky	rocky	ADJ
ejpam-5626	370	2	mountain	mountain	PROPN
ejpam-5626	370	3	j.	j.	PROPN
ejpam-5626	370	4	math	math	PROPN
ejpam-5626	370	5	,	,	PUNCT
ejpam-5626	370	6	52:323–333	52:323–333	PROPN
ejpam-5626	370	7	,	,	PUNCT
ejpam-5626	370	8	2022	2022	NUM
ejpam-5626	370	9	.	.	PUNCT