id	sid	tid	token	lemma	pos
ejpam-6607	1	1	european	european	PROPN
ejpam-6607	1	2	journal	journal	PROPN
ejpam-6607	1	3	of	of	ADP
ejpam-6607	1	4	pure	pure	ADJ
ejpam-6607	1	5	and	and	CCONJ
ejpam-6607	1	6	applied	applied	ADJ
ejpam-6607	1	7	mathematics	mathematic	NOUN
ejpam-6607	1	8	2025	2025	NUM
ejpam-6607	1	9	,	,	PUNCT
ejpam-6607	1	10	vol	vol	NOUN
ejpam-6607	1	11	.	.	PROPN
ejpam-6607	1	12	18	18	NUM
ejpam-6607	1	13	,	,	PUNCT
ejpam-6607	1	14	issue	issue	NOUN
ejpam-6607	1	15	3	3	NUM
ejpam-6607	1	16	,	,	PUNCT
ejpam-6607	1	17	article	article	NOUN
ejpam-6607	1	18	number	number	NOUN
ejpam-6607	1	19	6607	6607	NUM
ejpam-6607	1	20	issn	issn	PROPN
ejpam-6607	1	21	1307	1307	NUM
ejpam-6607	1	22	-	-	SYM
ejpam-6607	1	23	5543	5543	NUM
ejpam-6607	1	24	–	–	PUNCT
ejpam-6607	1	25	ejpam.com	ejpam.com	X
ejpam-6607	1	26	published	publish	VERB
ejpam-6607	1	27	by	by	ADP
ejpam-6607	1	28	new	new	PROPN
ejpam-6607	1	29	york	york	PROPN
ejpam-6607	1	30	business	business	PROPN
ejpam-6607	1	31	global	global	ADJ
ejpam-6607	1	32	harnessing	harness	VERB
ejpam-6607	1	33	quantum	quantum	ADJ
ejpam-6607	1	34	superposition	superposition	NOUN
ejpam-6607	1	35	in	in	ADP
ejpam-6607	1	36	soft	soft	ADJ
ejpam-6607	1	37	set	set	NOUN
ejpam-6607	1	38	theory	theory	NOUN
ejpam-6607	1	39	:	:	PUNCT
ejpam-6607	1	40	introducing	introduce	VERB
ejpam-6607	1	41	quantum	quantum	ADJ
ejpam-6607	1	42	hypersoft	hypersoft	NOUN
ejpam-6607	1	43	and	and	CCONJ
ejpam-6607	1	44	superhypersoft	superhypersoft	PROPN
ejpam-6607	1	45	sets	set	VERB
ejpam-6607	1	46	takaaki	takaaki	NOUN
ejpam-6607	1	47	fujita1,∗	fujita1,∗	PROPN
ejpam-6607	1	48	,	,	PUNCT
ejpam-6607	1	49	florentin	florentin	NOUN
ejpam-6607	1	50	smarandache2	smarandache2	PROPN
ejpam-6607	1	51	1	1	NUM
ejpam-6607	1	52	independent	independent	ADJ
ejpam-6607	1	53	researcher	researcher	NOUN
ejpam-6607	1	54	,	,	PUNCT
ejpam-6607	1	55	shinjuku	shinjuku	PROPN
ejpam-6607	1	56	,	,	PUNCT
ejpam-6607	1	57	shinjuku	shinjuku	PROPN
ejpam-6607	1	58	-	-	PUNCT
ejpam-6607	1	59	ku	ku	PROPN
ejpam-6607	1	60	,	,	PUNCT
ejpam-6607	1	61	tokyo	tokyo	PROPN
ejpam-6607	1	62	,	,	PUNCT
ejpam-6607	1	63	japan	japan	PROPN
ejpam-6607	1	64	2	2	NUM
ejpam-6607	1	65	university	university	NOUN
ejpam-6607	1	66	of	of	ADP
ejpam-6607	1	67	new	new	PROPN
ejpam-6607	1	68	mexico	mexico	PROPN
ejpam-6607	1	69	,	,	PUNCT
ejpam-6607	1	70	gallup	gallup	PROPN
ejpam-6607	1	71	campus	campus	PROPN
ejpam-6607	1	72	,	,	PUNCT
ejpam-6607	1	73	nm	nm	PROPN
ejpam-6607	1	74	87301	87301	NUM
ejpam-6607	1	75	,	,	PUNCT
ejpam-6607	1	76	usa	usa	PROPN
ejpam-6607	1	77	abstract	abstract	PROPN
ejpam-6607	1	78	.	.	PUNCT
ejpam-6607	2	1	this	this	DET
ejpam-6607	2	2	paper	paper	NOUN
ejpam-6607	2	3	presents	present	VERB
ejpam-6607	2	4	two	two	NUM
ejpam-6607	2	5	novel	novel	ADJ
ejpam-6607	2	6	extensions	extension	NOUN
ejpam-6607	2	7	of	of	ADP
ejpam-6607	2	8	the	the	DET
ejpam-6607	2	9	quantum	quantum	ADJ
ejpam-6607	2	10	soft	soft	ADJ
ejpam-6607	2	11	set	set	NOUN
ejpam-6607	2	12	framework	framework	NOUN
ejpam-6607	2	13	by	by	ADP
ejpam-6607	2	14	integrating	integrate	VERB
ejpam-6607	2	15	the	the	DET
ejpam-6607	2	16	hierarchical	hierarchical	ADJ
ejpam-6607	2	17	structures	structure	NOUN
ejpam-6607	2	18	of	of	ADP
ejpam-6607	2	19	hypersoft	hypersoft	NOUN
ejpam-6607	2	20	and	and	CCONJ
ejpam-6607	2	21	superhypersoft	superhypersoft	PROPN
ejpam-6607	2	22	sets	set	VERB
ejpam-6607	2	23	with	with	ADP
ejpam-6607	2	24	quantum	quantum	ADJ
ejpam-6607	2	25	superposition	superposition	NOUN
ejpam-6607	2	26	principles	principle	NOUN
ejpam-6607	2	27	.	.	PUNCT
ejpam-6607	3	1	soft	soft	ADJ
ejpam-6607	3	2	sets	set	NOUN
ejpam-6607	3	3	offer	offer	VERB
ejpam-6607	3	4	a	a	DET
ejpam-6607	3	5	versatile	versatile	ADJ
ejpam-6607	3	6	approach	approach	NOUN
ejpam-6607	3	7	to	to	ADP
ejpam-6607	3	8	decision	decision	NOUN
ejpam-6607	3	9	making	making	NOUN
ejpam-6607	3	10	by	by	ADP
ejpam-6607	3	11	associating	associate	VERB
ejpam-6607	3	12	parameters	parameter	NOUN
ejpam-6607	3	13	with	with	ADP
ejpam-6607	3	14	subsets	subset	NOUN
ejpam-6607	3	15	of	of	ADP
ejpam-6607	3	16	a	a	DET
ejpam-6607	3	17	universal	universal	ADJ
ejpam-6607	3	18	set	set	NOUN
ejpam-6607	3	19	,	,	PUNCT
ejpam-6607	3	20	effectively	effectively	ADV
ejpam-6607	3	21	capturing	capture	VERB
ejpam-6607	3	22	uncertainty	uncertainty	NOUN
ejpam-6607	3	23	and	and	CCONJ
ejpam-6607	3	24	imprecision	imprecision	NOUN
ejpam-6607	3	25	[	[	X
ejpam-6607	3	26	1	1	NUM
ejpam-6607	3	27	,	,	PUNCT
ejpam-6607	3	28	2	2	NUM
ejpam-6607	3	29	]	]	PUNCT
ejpam-6607	3	30	.	.	PUNCT
ejpam-6607	4	1	hypersoft	hypersoft	PROPN
ejpam-6607	4	2	and	and	CCONJ
ejpam-6607	4	3	superhypersoft	superhypersoft	PROPN
ejpam-6607	4	4	sets	set	VERB
ejpam-6607	4	5	further	far	ADV
ejpam-6607	4	6	generalize	generalize	VERB
ejpam-6607	4	7	this	this	DET
ejpam-6607	4	8	paradigm	paradigm	NOUN
ejpam-6607	4	9	for	for	ADP
ejpam-6607	4	10	increasingly	increasingly	ADV
ejpam-6607	4	11	complex	complex	ADJ
ejpam-6607	4	12	scenarios	scenario	NOUN
ejpam-6607	4	13	.	.	PUNCT
ejpam-6607	5	1	a	a	DET
ejpam-6607	5	2	quantum	quantum	ADJ
ejpam-6607	5	3	soft	soft	ADJ
ejpam-6607	5	4	set	set	NOUN
ejpam-6607	5	5	maps	map	NOUN
ejpam-6607	5	6	each	each	DET
ejpam-6607	5	7	parameter	parameter	NOUN
ejpam-6607	5	8	to	to	ADP
ejpam-6607	5	9	a	a	DET
ejpam-6607	5	10	normalized	normalize	VERB
ejpam-6607	5	11	quantum	quantum	ADJ
ejpam-6607	5	12	state	state	NOUN
ejpam-6607	5	13	[	[	X
ejpam-6607	5	14	3	3	NUM
ejpam-6607	5	15	]	]	PUNCT
ejpam-6607	5	16	,	,	PUNCT
ejpam-6607	5	17	enabling	enable	VERB
ejpam-6607	5	18	probabilistic	probabilistic	ADJ
ejpam-6607	5	19	membership	membership	NOUN
ejpam-6607	5	20	via	via	ADP
ejpam-6607	5	21	amplitude	amplitude	NOUN
ejpam-6607	5	22	coefficients	coefficient	NOUN
ejpam-6607	5	23	.	.	PUNCT
ejpam-6607	6	1	we	we	PRON
ejpam-6607	6	2	rigorously	rigorously	ADV
ejpam-6607	6	3	define	define	VERB
ejpam-6607	6	4	the	the	DET
ejpam-6607	6	5	quantum	quantum	ADJ
ejpam-6607	6	6	hypersoft	hypersoft	NOUN
ejpam-6607	6	7	set	set	VERB
ejpam-6607	6	8	and	and	CCONJ
ejpam-6607	6	9	the	the	DET
ejpam-6607	6	10	quantum	quantum	PROPN
ejpam-6607	6	11	superhypersoft	superhypersoft	NOUN
ejpam-6607	6	12	set	set	VERB
ejpam-6607	6	13	,	,	PUNCT
ejpam-6607	6	14	laying	lay	VERB
ejpam-6607	6	15	a	a	DET
ejpam-6607	6	16	foundation	foundation	NOUN
ejpam-6607	6	17	for	for	ADP
ejpam-6607	6	18	future	future	ADJ
ejpam-6607	6	19	advances	advance	NOUN
ejpam-6607	6	20	in	in	ADP
ejpam-6607	6	21	quantum	quantum	NOUN
ejpam-6607	6	22	-	-	PUNCT
ejpam-6607	6	23	enhanced	enhance	VERB
ejpam-6607	6	24	decision	decision	NOUN
ejpam-6607	6	25	analysis	analysis	NOUN
ejpam-6607	6	26	,	,	PUNCT
ejpam-6607	6	27	topological	topological	ADJ
ejpam-6607	6	28	modeling	modeling	NOUN
ejpam-6607	6	29	,	,	PUNCT
ejpam-6607	6	30	and	and	CCONJ
ejpam-6607	6	31	algebraic	algebraic	ADJ
ejpam-6607	6	32	applications	application	NOUN
ejpam-6607	6	33	.	.	PUNCT
ejpam-6607	7	1	2020	2020	NUM
ejpam-6607	7	2	mathematics	mathematic	NOUN
ejpam-6607	7	3	subject	subject	NOUN
ejpam-6607	7	4	classifications	classification	NOUN
ejpam-6607	7	5	:	:	PUNCT
ejpam-6607	7	6	06d72	06d72	NUM
ejpam-6607	7	7	key	key	ADJ
ejpam-6607	7	8	words	word	NOUN
ejpam-6607	7	9	and	and	CCONJ
ejpam-6607	7	10	phrases	phrase	NOUN
ejpam-6607	7	11	:	:	PUNCT
ejpam-6607	7	12	superhypersoft	superhypersoft	PROPN
ejpam-6607	7	13	set	set	PROPN
ejpam-6607	7	14	,	,	PUNCT
ejpam-6607	7	15	soft	soft	ADJ
ejpam-6607	7	16	set	set	NOUN
ejpam-6607	7	17	,	,	PUNCT
ejpam-6607	7	18	hypersoft	hypersoft	NOUN
ejpam-6607	7	19	set	set	NOUN
ejpam-6607	7	20	,	,	PUNCT
ejpam-6607	7	21	quantum	quantum	ADJ
ejpam-6607	7	22	hypersoft	hypersoft	NOUN
ejpam-6607	7	23	set	set	NOUN
ejpam-6607	7	24	,	,	PUNCT
ejpam-6607	7	25	quantum	quantum	ADJ
ejpam-6607	7	26	soft	soft	ADJ
ejpam-6607	7	27	set	set	NOUN
ejpam-6607	7	28	,	,	PUNCT
ejpam-6607	7	29	quantum	quantum	PROPN
ejpam-6607	7	30	superhypersoft	superhypersoft	NOUN
ejpam-6607	7	31	set	set	VERB
ejpam-6607	7	32	1	1	NUM
ejpam-6607	7	33	.	.	PUNCT
ejpam-6607	7	34	introduction	introduction	NOUN
ejpam-6607	7	35	1.1	1.1	NUM
ejpam-6607	7	36	.	.	PUNCT
ejpam-6607	8	1	soft	soft	ADJ
ejpam-6607	8	2	sets	set	NOUN
ejpam-6607	8	3	and	and	CCONJ
ejpam-6607	8	4	their	their	PRON
ejpam-6607	8	5	extensions	extension	NOUN
ejpam-6607	8	6	the	the	DET
ejpam-6607	8	7	challenge	challenge	NOUN
ejpam-6607	8	8	of	of	ADP
ejpam-6607	8	9	modeling	model	VERB
ejpam-6607	8	10	uncertainty	uncertainty	NOUN
ejpam-6607	8	11	has	have	AUX
ejpam-6607	8	12	led	lead	VERB
ejpam-6607	8	13	to	to	ADP
ejpam-6607	8	14	a	a	DET
ejpam-6607	8	15	variety	variety	NOUN
ejpam-6607	8	16	of	of	ADP
ejpam-6607	8	17	mathematical	mathematical	ADJ
ejpam-6607	8	18	frameworks	framework	NOUN
ejpam-6607	8	19	,	,	PUNCT
ejpam-6607	8	20	including	include	VERB
ejpam-6607	8	21	fuzzy	fuzzy	ADJ
ejpam-6607	8	22	sets	set	NOUN
ejpam-6607	8	23	[	[	X
ejpam-6607	8	24	4	4	NUM
ejpam-6607	8	25	]	]	PUNCT
ejpam-6607	8	26	,	,	PUNCT
ejpam-6607	8	27	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6607	8	28	sets	set	VERB
ejpam-6607	8	29	[	[	X
ejpam-6607	8	30	5	5	NUM
ejpam-6607	8	31	,	,	PUNCT
ejpam-6607	8	32	6	6	NUM
ejpam-6607	8	33	]	]	PUNCT
ejpam-6607	8	34	,	,	PUNCT
ejpam-6607	8	35	super	super	ADJ
ejpam-6607	8	36	-	-	ADJ
ejpam-6607	8	37	hyperfuzzy	hyperfuzzy	ADJ
ejpam-6607	8	38	sets	set	NOUN
ejpam-6607	8	39	[	[	X
ejpam-6607	8	40	7	7	NUM
ejpam-6607	8	41	]	]	PUNCT
ejpam-6607	8	42	,	,	PUNCT
ejpam-6607	8	43	rough	rough	ADJ
ejpam-6607	8	44	sets	set	NOUN
ejpam-6607	8	45	[	[	X
ejpam-6607	8	46	8	8	NUM
ejpam-6607	8	47	]	]	PUNCT
ejpam-6607	8	48	,	,	PUNCT
ejpam-6607	8	49	hyperrough	hyperrough	NOUN
ejpam-6607	8	50	sets	set	VERB
ejpam-6607	8	51	[	[	X
ejpam-6607	8	52	9	9	NUM
ejpam-6607	8	53	]	]	PUNCT
ejpam-6607	8	54	,	,	PUNCT
ejpam-6607	8	55	intuitionistic	intuitionistic	ADJ
ejpam-6607	8	56	fuzzy	fuzzy	ADJ
ejpam-6607	8	57	sets	set	NOUN
ejpam-6607	8	58	[	[	X
ejpam-6607	8	59	10	10	NUM
ejpam-6607	8	60	,	,	PUNCT
ejpam-6607	8	61	11	11	NUM
ejpam-6607	8	62	]	]	PUNCT
ejpam-6607	8	63	,	,	PUNCT
ejpam-6607	8	64	picture	picture	NOUN
ejpam-6607	8	65	fuzzy	fuzzy	ADJ
ejpam-6607	8	66	sets	set	NOUN
ejpam-6607	8	67	[	[	X
ejpam-6607	8	68	12	12	NUM
ejpam-6607	8	69	]	]	PUNCT
ejpam-6607	8	70	,	,	PUNCT
ejpam-6607	8	71	bipolar	bipolar	ADJ
ejpam-6607	8	72	fuzzy	fuzzy	ADJ
ejpam-6607	8	73	sets	set	NOUN
ejpam-6607	8	74	[	[	X
ejpam-6607	8	75	13	13	NUM
ejpam-6607	8	76	,	,	PUNCT
ejpam-6607	8	77	14	14	NUM
ejpam-6607	8	78	]	]	PUNCT
ejpam-6607	8	79	,	,	PUNCT
ejpam-6607	8	80	hesitant	hesitant	ADJ
ejpam-6607	8	81	fuzzy	fuzzy	ADJ
ejpam-6607	8	82	sets	set	NOUN
ejpam-6607	8	83	[	[	X
ejpam-6607	8	84	15	15	NUM
ejpam-6607	8	85	,	,	PUNCT
ejpam-6607	8	86	16	16	NUM
ejpam-6607	8	87	]	]	PUNCT
ejpam-6607	8	88	,	,	PUNCT
ejpam-6607	8	89	neutrosophic	neutrosophic	ADJ
ejpam-6607	8	90	sets	set	NOUN
ejpam-6607	8	91	[	[	X
ejpam-6607	8	92	17	17	NUM
ejpam-6607	8	93	,	,	PUNCT
ejpam-6607	8	94	18	18	NUM
ejpam-6607	8	95	]	]	PUNCT
ejpam-6607	8	96	,	,	PUNCT
ejpam-6607	8	97	and	and	CCONJ
ejpam-6607	8	98	plithogenic	plithogenic	ADJ
ejpam-6607	8	99	sets	set	NOUN
ejpam-6607	8	100	[	[	X
ejpam-6607	8	101	19	19	NUM
ejpam-6607	8	102	,	,	PUNCT
ejpam-6607	8	103	20	20	NUM
ejpam-6607	8	104	]	]	PUNCT
ejpam-6607	8	105	.	.	PUNCT
ejpam-6607	9	1	among	among	ADP
ejpam-6607	9	2	these	these	DET
ejpam-6607	9	3	,	,	PUNCT
ejpam-6607	9	4	soft	soft	ADJ
ejpam-6607	9	5	sets	set	NOUN
ejpam-6607	9	6	[	[	X
ejpam-6607	9	7	1	1	NUM
ejpam-6607	9	8	,	,	PUNCT
ejpam-6607	9	9	2	2	NUM
ejpam-6607	9	10	]	]	PUNCT
ejpam-6607	9	11	are	be	AUX
ejpam-6607	9	12	notable	notable	ADJ
ejpam-6607	9	13	for	for	ADP
ejpam-6607	9	14	associating	associate	VERB
ejpam-6607	9	15	each	each	DET
ejpam-6607	9	16	parameter	parameter	NOUN
ejpam-6607	9	17	with	with	ADP
ejpam-6607	9	18	a	a	DET
ejpam-6607	9	19	subset	subset	NOUN
ejpam-6607	9	20	of	of	ADP
ejpam-6607	9	21	a	a	DET
ejpam-6607	9	22	universal	universal	ADJ
ejpam-6607	9	23	set	set	NOUN
ejpam-6607	9	24	,	,	PUNCT
ejpam-6607	9	25	thereby	thereby	ADV
ejpam-6607	9	26	offering	offer	VERB
ejpam-6607	9	27	a	a	DET
ejpam-6607	9	28	flexible	flexible	ADJ
ejpam-6607	9	29	tool	tool	NOUN
ejpam-6607	9	30	for	for	ADP
ejpam-6607	9	31	decision	decision	NOUN
ejpam-6607	9	32	-	-	PUNCT
ejpam-6607	9	33	making	making	NOUN
ejpam-6607	9	34	under	under	ADP
ejpam-6607	9	35	imprecision	imprecision	NOUN
ejpam-6607	9	36	.	.	PUNCT
ejpam-6607	10	1	building	build	VERB
ejpam-6607	10	2	on	on	ADP
ejpam-6607	10	3	this	this	DET
ejpam-6607	10	4	idea	idea	NOUN
ejpam-6607	10	5	,	,	PUNCT
ejpam-6607	10	6	researchers	researcher	NOUN
ejpam-6607	10	7	have	have	AUX
ejpam-6607	10	8	proposed	propose	VERB
ejpam-6607	10	9	numerous	numerous	ADJ
ejpam-6607	10	10	generalizations	generalization	NOUN
ejpam-6607	10	11	:	:	PUNCT
ejpam-6607	10	12	∗corresponding	∗corresponde	VERB
ejpam-6607	10	13	author	author	NOUN
ejpam-6607	10	14	.	.	PUNCT
ejpam-6607	11	1	doi	doi	NOUN
ejpam-6607	11	2	:	:	PUNCT
ejpam-6607	11	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6607	https://doi.org/10.29020/nybg.ejpam.v18i3.6607	ADJ
ejpam-6607	11	4	email	email	NOUN
ejpam-6607	11	5	addresses	address	NOUN
ejpam-6607	11	6	:	:	PUNCT
ejpam-6607	11	7	takaaki.fujita060@gmail.com	takaaki.fujita060@gmail.com	X
ejpam-6607	11	8	(	(	PUNCT
ejpam-6607	11	9	t.fujita	t.fujita	NUM
ejpam-6607	11	10	)	)	PUNCT
ejpam-6607	11	11	,	,	PUNCT
ejpam-6607	11	12	smarand@unm.edu	smarand@unm.edu	PROPN
ejpam-6607	11	13	(	(	PUNCT
ejpam-6607	11	14	f.	f.	PROPN
ejpam-6607	11	15	smarandache	smarandache	PROPN
ejpam-6607	11	16	)	)	PUNCT
ejpam-6607	11	17	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6607	11	18	1	1	NUM
ejpam-6607	11	19	copyright	copyright	NOUN
ejpam-6607	11	20	:	:	PUNCT
ejpam-6607	12	1	©	©	PROPN
ejpam-6607	12	2	2025	2025	NUM
ejpam-6607	12	3	the	the	DET
ejpam-6607	12	4	author(s	author(s	NOUN
ejpam-6607	12	5	)	)	PUNCT
ejpam-6607	12	6	.	.	PUNCT
ejpam-6607	13	1	(	(	PUNCT
ejpam-6607	13	2	cc	cc	NOUN
ejpam-6607	13	3	by	by	ADP
ejpam-6607	13	4	-	-	PUNCT
ejpam-6607	13	5	nc	nc	PROPN
ejpam-6607	13	6	4.0	4.0	NUM
ejpam-6607	13	7	)	)	PUNCT
ejpam-6607	13	8	t.	t.	PROPN
ejpam-6607	13	9	fujita	fujita	PROPN
ejpam-6607	13	10	,	,	PUNCT
ejpam-6607	13	11	f.smarandache	f.smarandache	NOUN
ejpam-6607	13	12	/	/	SYM
ejpam-6607	13	13	eur	eur	PROPN
ejpam-6607	13	14	.	.	PUNCT
ejpam-6607	14	1	j.	j.	PROPN
ejpam-6607	14	2	pure	pure	PROPN
ejpam-6607	14	3	appl	appl	PROPN
ejpam-6607	14	4	.	.	PROPN
ejpam-6607	14	5	math	math	PROPN
ejpam-6607	14	6	,	,	PUNCT
ejpam-6607	14	7	18	18	NUM
ejpam-6607	14	8	(	(	PUNCT
ejpam-6607	14	9	3	3	NUM
ejpam-6607	14	10	)	)	PUNCT
ejpam-6607	14	11	(	(	PUNCT
ejpam-6607	14	12	2025	2025	NUM
ejpam-6607	14	13	)	)	PUNCT
ejpam-6607	14	14	,	,	PUNCT
ejpam-6607	14	15	6607	6607	NUM
ejpam-6607	14	16	2	2	NUM
ejpam-6607	14	17	of	of	ADP
ejpam-6607	14	18	33	33	NUM
ejpam-6607	14	19	•	•	NOUN
ejpam-6607	14	20	hypersoft	hypersoft	NOUN
ejpam-6607	14	21	sets	set	VERB
ejpam-6607	14	22	[	[	X
ejpam-6607	14	23	21	21	NUM
ejpam-6607	14	24	,	,	PUNCT
ejpam-6607	14	25	22	22	NUM
ejpam-6607	14	26	]	]	PUNCT
ejpam-6607	14	27	and	and	CCONJ
ejpam-6607	14	28	superhypersoft	superhypersoft	PROPN
ejpam-6607	14	29	sets	set	VERB
ejpam-6607	14	30	[	[	X
ejpam-6607	14	31	23	23	NUM
ejpam-6607	14	32	]	]	PUNCT
ejpam-6607	14	33	,	,	PUNCT
ejpam-6607	14	34	which	which	PRON
ejpam-6607	14	35	add	add	VERB
ejpam-6607	14	36	layers	layer	NOUN
ejpam-6607	14	37	of	of	ADP
ejpam-6607	14	38	parameter	parameter	NOUN
ejpam-6607	14	39	interactions	interaction	NOUN
ejpam-6607	14	40	;	;	PUNCT
ejpam-6607	14	41	•	•	NUM
ejpam-6607	14	42	expert	expert	NOUN
ejpam-6607	14	43	soft	soft	ADJ
ejpam-6607	14	44	sets	set	NOUN
ejpam-6607	14	45	[	[	X
ejpam-6607	14	46	24	24	NUM
ejpam-6607	14	47	]	]	PUNCT
ejpam-6607	14	48	and	and	CCONJ
ejpam-6607	14	49	hypersoft	hypersoft	NOUN
ejpam-6607	14	50	expert	expert	NOUN
ejpam-6607	14	51	sets	set	VERB
ejpam-6607	14	52	[	[	X
ejpam-6607	14	53	25	25	NUM
ejpam-6607	14	54	,	,	PUNCT
ejpam-6607	14	55	26	26	NUM
ejpam-6607	14	56	]	]	PUNCT
ejpam-6607	14	57	,	,	PUNCT
ejpam-6607	14	58	integrating	integrate	VERB
ejpam-6607	14	59	expert	expert	ADJ
ejpam-6607	14	60	judgments	judgment	NOUN
ejpam-6607	14	61	;	;	PUNCT
ejpam-6607	14	62	•	•	NUM
ejpam-6607	14	63	fuzzy	fuzzy	ADJ
ejpam-6607	14	64	soft	soft	ADJ
ejpam-6607	14	65	sets	set	NOUN
ejpam-6607	14	66	[	[	X
ejpam-6607	14	67	27	27	NUM
ejpam-6607	14	68	]	]	PUNCT
ejpam-6607	14	69	and	and	CCONJ
ejpam-6607	14	70	indetermsoft	indetermsoft	PROPN
ejpam-6607	14	71	sets	set	VERB
ejpam-6607	14	72	[	[	X
ejpam-6607	14	73	28–30	28–30	NOUN
ejpam-6607	14	74	]	]	X
ejpam-6607	14	75	,	,	PUNCT
ejpam-6607	14	76	which	which	PRON
ejpam-6607	14	77	blend	blend	VERB
ejpam-6607	14	78	fuzzy	fuzzy	ADJ
ejpam-6607	14	79	membership	membership	NOUN
ejpam-6607	14	80	or	or	CCONJ
ejpam-6607	14	81	indeterminacy	indeterminacy	NOUN
ejpam-6607	14	82	with	with	ADP
ejpam-6607	14	83	soft	soft	ADJ
ejpam-6607	14	84	parameters	parameter	NOUN
ejpam-6607	14	85	;	;	PUNCT
ejpam-6607	14	86	•	•	NUM
ejpam-6607	14	87	treesoft	treesoft	NOUN
ejpam-6607	14	88	sets	set	NOUN
ejpam-6607	14	89	[	[	X
ejpam-6607	14	90	31	31	NUM
ejpam-6607	14	91	,	,	PUNCT
ejpam-6607	14	92	32	32	NUM
ejpam-6607	14	93	]	]	PUNCT
ejpam-6607	14	94	,	,	PUNCT
ejpam-6607	14	95	organizing	organize	VERB
ejpam-6607	14	96	parameters	parameter	NOUN
ejpam-6607	14	97	into	into	ADP
ejpam-6607	14	98	hierarchies	hierarchy	NOUN
ejpam-6607	14	99	,	,	PUNCT
ejpam-6607	14	100	and	and	CCONJ
ejpam-6607	14	101	forestsoft	forestsoft	NOUN
ejpam-6607	14	102	sets	set	NOUN
ejpam-6607	14	103	[	[	X
ejpam-6607	14	104	33	33	NUM
ejpam-6607	14	105	]	]	PUNCT
ejpam-6607	14	106	,	,	PUNCT
ejpam-6607	14	107	which	which	PRON
ejpam-6607	14	108	combine	combine	VERB
ejpam-6607	14	109	multiple	multiple	ADJ
ejpam-6607	14	110	trees	tree	NOUN
ejpam-6607	14	111	into	into	ADP
ejpam-6607	14	112	a	a	DET
ejpam-6607	14	113	cohesive	cohesive	ADJ
ejpam-6607	14	114	framework	framework	NOUN
ejpam-6607	14	115	.	.	PUNCT
ejpam-6607	15	1	soft	soft	ADJ
ejpam-6607	15	2	sets	set	NOUN
ejpam-6607	15	3	have	have	AUX
ejpam-6607	15	4	proven	prove	VERB
ejpam-6607	15	5	useful	useful	ADJ
ejpam-6607	15	6	across	across	ADP
ejpam-6607	15	7	decision	decision	NOUN
ejpam-6607	15	8	analysis	analysis	NOUN
ejpam-6607	15	9	[	[	X
ejpam-6607	15	10	34	34	NUM
ejpam-6607	15	11	]	]	PUNCT
ejpam-6607	15	12	,	,	PUNCT
ejpam-6607	15	13	topology	topology	NOUN
ejpam-6607	15	14	[	[	X
ejpam-6607	15	15	35	35	NUM
ejpam-6607	15	16	]	]	PUNCT
ejpam-6607	15	17	,	,	PUNCT
ejpam-6607	15	18	graph	graph	NOUN
ejpam-6607	15	19	theory	theory	NOUN
ejpam-6607	15	20	[	[	X
ejpam-6607	15	21	36	36	NUM
ejpam-6607	15	22	]	]	PUNCT
ejpam-6607	15	23	,	,	PUNCT
ejpam-6607	15	24	risk	risk	NOUN
ejpam-6607	15	25	assessment	assessment	NOUN
ejpam-6607	15	26	[	[	X
ejpam-6607	15	27	25	25	NUM
ejpam-6607	15	28	]	]	PUNCT
ejpam-6607	15	29	,	,	PUNCT
ejpam-6607	15	30	and	and	CCONJ
ejpam-6607	15	31	algebraic	algebraic	ADJ
ejpam-6607	15	32	structures	structure	NOUN
ejpam-6607	15	33	.	.	PUNCT
ejpam-6607	16	1	consequently	consequently	ADV
ejpam-6607	16	2	,	,	PUNCT
ejpam-6607	16	3	advancing	advance	VERB
ejpam-6607	16	4	soft	soft	ADJ
ejpam-6607	16	5	set	set	NOUN
ejpam-6607	16	6	theory	theory	NOUN
ejpam-6607	16	7	and	and	CCONJ
ejpam-6607	16	8	its	its	PRON
ejpam-6607	16	9	variants	variant	NOUN
ejpam-6607	16	10	remains	remain	VERB
ejpam-6607	16	11	an	an	DET
ejpam-6607	16	12	important	important	ADJ
ejpam-6607	16	13	endeavor	endeavor	NOUN
ejpam-6607	16	14	.	.	PUNCT
ejpam-6607	17	1	in	in	ADP
ejpam-6607	17	2	this	this	DET
ejpam-6607	17	3	paper	paper	NOUN
ejpam-6607	17	4	,	,	PUNCT
ejpam-6607	17	5	we	we	PRON
ejpam-6607	17	6	explore	explore	VERB
ejpam-6607	17	7	how	how	SCONJ
ejpam-6607	17	8	soft	soft	ADJ
ejpam-6607	17	9	sets	set	NOUN
ejpam-6607	17	10	,	,	PUNCT
ejpam-6607	17	11	hypersoft	hypersoft	NOUN
ejpam-6607	17	12	sets	set	NOUN
ejpam-6607	17	13	,	,	PUNCT
ejpam-6607	17	14	and	and	CCONJ
ejpam-6607	17	15	superhypersoft	superhypersoft	PROPN
ejpam-6607	17	16	sets	set	NOUN
ejpam-6607	17	17	can	can	AUX
ejpam-6607	17	18	be	be	AUX
ejpam-6607	17	19	treated	treat	VERB
ejpam-6607	17	20	within	within	ADP
ejpam-6607	17	21	the	the	DET
ejpam-6607	17	22	framework	framework	NOUN
ejpam-6607	17	23	of	of	ADP
ejpam-6607	17	24	quantum	quantum	NOUN
ejpam-6607	17	25	theory	theory	NOUN
ejpam-6607	17	26	.	.	PUNCT
ejpam-6607	18	1	as	as	SCONJ
ejpam-6607	18	2	summarized	summarize	VERB
ejpam-6607	18	3	in	in	ADP
ejpam-6607	18	4	table	table	NOUN
ejpam-6607	18	5	1	1	NUM
ejpam-6607	18	6	,	,	PUNCT
ejpam-6607	18	7	the	the	DET
ejpam-6607	18	8	three	three	NUM
ejpam-6607	18	9	frameworks	framework	NOUN
ejpam-6607	18	10	differ	differ	VERB
ejpam-6607	18	11	in	in	ADP
ejpam-6607	18	12	how	how	SCONJ
ejpam-6607	18	13	they	they	PRON
ejpam-6607	18	14	map	map	VERB
ejpam-6607	18	15	parameters	parameter	NOUN
ejpam-6607	18	16	or	or	CCONJ
ejpam-6607	18	17	attribute	attribute	NOUN
ejpam-6607	18	18	combinations	combination	NOUN
ejpam-6607	18	19	to	to	ADP
ejpam-6607	18	20	subsets	subset	NOUN
ejpam-6607	18	21	of	of	ADP
ejpam-6607	18	22	the	the	DET
ejpam-6607	18	23	universe	universe	NOUN
ejpam-6607	18	24	and	and	CCONJ
ejpam-6607	18	25	in	in	ADP
ejpam-6607	18	26	the	the	DET
ejpam-6607	18	27	depth	depth	NOUN
ejpam-6607	18	28	of	of	ADP
ejpam-6607	18	29	their	their	PRON
ejpam-6607	18	30	parameter	parameter	NOUN
ejpam-6607	18	31	interactions	interaction	NOUN
ejpam-6607	18	32	.	.	PUNCT
ejpam-6607	19	1	consequently	consequently	ADV
ejpam-6607	19	2	,	,	PUNCT
ejpam-6607	19	3	hypersoft	hypersoft	NOUN
ejpam-6607	19	4	sets	set	NOUN
ejpam-6607	19	5	and	and	CCONJ
ejpam-6607	19	6	superhypersoft	superhypersoft	NOUN
ejpam-6607	19	7	sets	set	NOUN
ejpam-6607	19	8	are	be	AUX
ejpam-6607	19	9	well	well	ADV
ejpam-6607	19	10	suited	suited	ADJ
ejpam-6607	19	11	for	for	ADP
ejpam-6607	19	12	modeling	model	VERB
ejpam-6607	19	13	real	real	ADJ
ejpam-6607	19	14	-	-	PUNCT
ejpam-6607	19	15	world	world	NOUN
ejpam-6607	19	16	phenomena	phenomenon	NOUN
ejpam-6607	19	17	characterized	characterize	VERB
ejpam-6607	19	18	by	by	ADP
ejpam-6607	19	19	multi	multi	ADJ
ejpam-6607	19	20	-	-	ADJ
ejpam-6607	19	21	layered	layered	ADJ
ejpam-6607	19	22	,	,	PUNCT
ejpam-6607	19	23	complex	complex	ADJ
ejpam-6607	19	24	uncertainty	uncertainty	NOUN
ejpam-6607	19	25	.	.	PUNCT
ejpam-6607	20	1	concept	concept	NOUN
ejpam-6607	20	2	mapping	map	VERB
ejpam-6607	20	3	key	key	ADJ
ejpam-6607	20	4	feature	feature	NOUN
ejpam-6607	20	5	soft	soft	ADJ
ejpam-6607	20	6	set	set	NOUN
ejpam-6607	21	1	f	f	NOUN
ejpam-6607	21	2	:	:	PUNCT
ejpam-6607	21	3	s	s	X
ejpam-6607	21	4	→	→	SYM
ejpam-6607	21	5	p(u	p(u	ADJ
ejpam-6607	21	6	)	)	PUNCT
ejpam-6607	21	7	associates	associate	NOUN
ejpam-6607	21	8	each	each	DET
ejpam-6607	21	9	parameter	parameter	NOUN
ejpam-6607	21	10	α	α	PROPN
ejpam-6607	21	11	∈	∈	PROPN
ejpam-6607	21	12	s	s	PART
ejpam-6607	21	13	with	with	ADP
ejpam-6607	21	14	a	a	DET
ejpam-6607	21	15	subset	subset	NOUN
ejpam-6607	21	16	f(α	f(α	NOUN
ejpam-6607	21	17	)	)	PUNCT
ejpam-6607	21	18	⊆	⊆	NUM
ejpam-6607	21	19	u	u	NOUN
ejpam-6607	21	20	[	[	X
ejpam-6607	21	21	1	1	NUM
ejpam-6607	21	22	]	]	PUNCT
ejpam-6607	21	23	.	.	PUNCT
ejpam-6607	22	1	hypersoft	hypersoft	PROPN
ejpam-6607	22	2	set	set	VERB
ejpam-6607	22	3	g	g	NOUN
ejpam-6607	22	4	:	:	PUNCT
ejpam-6607	22	5	a1	a1	PROPN
ejpam-6607	22	6	×	×	NOUN
ejpam-6607	22	7	·	·	PUNCT
ejpam-6607	22	8	·	·	PUNCT
ejpam-6607	22	9	·	·	PUNCT
ejpam-6607	22	10	×	×	NOUN
ejpam-6607	22	11	am	be	AUX
ejpam-6607	22	12	→	→	SYM
ejpam-6607	22	13	p(u	p(u	ADJ
ejpam-6607	22	14	)	)	PUNCT
ejpam-6607	22	15	maps	map	VERB
ejpam-6607	22	16	each	each	DET
ejpam-6607	22	17	m	m	NOUN
ejpam-6607	22	18	-	-	NOUN
ejpam-6607	22	19	tuple	tuple	NOUN
ejpam-6607	22	20	of	of	ADP
ejpam-6607	22	21	attribute	attribute	NOUN
ejpam-6607	22	22	values	value	NOUN
ejpam-6607	22	23	(	(	PUNCT
ejpam-6607	22	24	γ1	γ1	PROPN
ejpam-6607	22	25	,	,	PUNCT
ejpam-6607	22	26	.	.	PUNCT
ejpam-6607	22	27	.	.	PUNCT
ejpam-6607	22	28	.	.	PUNCT
ejpam-6607	23	1	,	,	PUNCT
ejpam-6607	23	2	γm	γm	X
ejpam-6607	23	3	)	)	PUNCT
ejpam-6607	23	4	to	to	ADP
ejpam-6607	23	5	a	a	DET
ejpam-6607	23	6	subset	subset	ADJ
ejpam-6607	23	7	g(γ	g(γ	NOUN
ejpam-6607	23	8	)	)	PUNCT
ejpam-6607	23	9	⊆	⊆	NUM
ejpam-6607	23	10	u	u	NOUN
ejpam-6607	23	11	,	,	PUNCT
ejpam-6607	23	12	enabling	enable	VERB
ejpam-6607	23	13	multi	multi	ADJ
ejpam-6607	23	14	-	-	NOUN
ejpam-6607	23	15	attribute	attribute	NOUN
ejpam-6607	23	16	combinations[21	combinations[21	NOUN
ejpam-6607	23	17	]	]	PUNCT
ejpam-6607	23	18	.	.	PUNCT
ejpam-6607	24	1	superhypersoft	superhypersoft	PROPN
ejpam-6607	24	2	set	set	VERB
ejpam-6607	24	3	f	f	PROPN
ejpam-6607	24	4	:	:	PUNCT
ejpam-6607	24	5	p(a1)×	p(a1)×	PROPN
ejpam-6607	24	6	·	·	PUNCT
ejpam-6607	24	7	·	·	PUNCT
ejpam-6607	24	8	·	·	PUNCT
ejpam-6607	25	1	×	×	NOUN
ejpam-6607	25	2	p(an)→	p(an)→	NOUN
ejpam-6607	25	3	p(u	p(u	NOUN
ejpam-6607	25	4	)	)	PUNCT
ejpam-6607	25	5	extends	extend	VERB
ejpam-6607	25	6	hypersoft	hypersoft	PROPN
ejpam-6607	25	7	by	by	ADP
ejpam-6607	25	8	using	use	VERB
ejpam-6607	25	9	powerset	powerset	NOUN
ejpam-6607	25	10	layers	layer	NOUN
ejpam-6607	25	11	of	of	ADP
ejpam-6607	25	12	each	each	DET
ejpam-6607	25	13	attribute	attribute	NOUN
ejpam-6607	25	14	domain	domain	NOUN
ejpam-6607	25	15	,	,	PUNCT
ejpam-6607	25	16	capturing	capture	VERB
ejpam-6607	25	17	interactions	interaction	NOUN
ejpam-6607	25	18	among	among	ADP
ejpam-6607	25	19	arbitrary	arbitrary	ADJ
ejpam-6607	25	20	subsets	subset	NOUN
ejpam-6607	25	21	of	of	ADP
ejpam-6607	25	22	values[37	values[37	ADP
ejpam-6607	25	23	]	]	PUNCT
ejpam-6607	25	24	.	.	PUNCT
ejpam-6607	26	1	table	table	NOUN
ejpam-6607	26	2	1	1	NUM
ejpam-6607	26	3	:	:	PUNCT
ejpam-6607	26	4	overview	overview	NOUN
ejpam-6607	26	5	of	of	ADP
ejpam-6607	26	6	soft	soft	ADJ
ejpam-6607	26	7	set	set	NOUN
ejpam-6607	26	8	,	,	PUNCT
ejpam-6607	26	9	hypersoft	hypersoft	NOUN
ejpam-6607	26	10	set	set	NOUN
ejpam-6607	26	11	,	,	PUNCT
ejpam-6607	26	12	and	and	CCONJ
ejpam-6607	26	13	superhypersoft	superhypersoft	PROPN
ejpam-6607	26	14	set	set	VERB
ejpam-6607	26	15	1.2	1.2	NUM
ejpam-6607	26	16	.	.	PUNCT
ejpam-6607	26	17	quantum	quantum	ADJ
ejpam-6607	26	18	theory	theory	NOUN
ejpam-6607	26	19	quantum	quantum	NOUN
ejpam-6607	26	20	theory	theory	NOUN
ejpam-6607	26	21	describes	describe	VERB
ejpam-6607	26	22	the	the	DET
ejpam-6607	26	23	behavior	behavior	NOUN
ejpam-6607	26	24	of	of	ADP
ejpam-6607	26	25	matter	matter	NOUN
ejpam-6607	26	26	and	and	CCONJ
ejpam-6607	26	27	energy	energy	NOUN
ejpam-6607	26	28	at	at	ADP
ejpam-6607	26	29	atomic	atomic	ADJ
ejpam-6607	26	30	scales	scale	NOUN
ejpam-6607	26	31	,	,	PUNCT
ejpam-6607	26	32	employing	employ	VERB
ejpam-6607	26	33	superposition	superposition	NOUN
ejpam-6607	26	34	,	,	PUNCT
ejpam-6607	26	35	wave	wave	NOUN
ejpam-6607	26	36	–	–	PUNCT
ejpam-6607	26	37	particle	particle	NOUN
ejpam-6607	26	38	duality	duality	NOUN
ejpam-6607	26	39	,	,	PUNCT
ejpam-6607	26	40	and	and	CCONJ
ejpam-6607	26	41	probabilistic	probabilistic	ADJ
ejpam-6607	26	42	measurement	measurement	NOUN
ejpam-6607	26	43	outcomes	outcome	NOUN
ejpam-6607	27	1	[	[	X
ejpam-6607	27	2	38	38	NUM
ejpam-6607	27	3	,	,	PUNCT
ejpam-6607	27	4	39	39	NUM
ejpam-6607	27	5	]	]	PUNCT
ejpam-6607	27	6	.	.	PUNCT
ejpam-6607	28	1	these	these	DET
ejpam-6607	28	2	principles	principle	NOUN
ejpam-6607	28	3	have	have	AUX
ejpam-6607	28	4	garnered	garner	VERB
ejpam-6607	28	5	significant	significant	ADJ
ejpam-6607	28	6	attention	attention	NOUN
ejpam-6607	28	7	in	in	ADP
ejpam-6607	28	8	recent	recent	ADJ
ejpam-6607	28	9	years	year	NOUN
ejpam-6607	28	10	,	,	PUNCT
ejpam-6607	28	11	particularly	particularly	ADV
ejpam-6607	28	12	in	in	ADP
ejpam-6607	28	13	contexts	context	NOUN
ejpam-6607	28	14	such	such	ADJ
ejpam-6607	28	15	as	as	ADP
ejpam-6607	28	16	quantum	quantum	NOUN
ejpam-6607	28	17	computing	computing	NOUN
ejpam-6607	28	18	[	[	X
ejpam-6607	28	19	40	40	NUM
ejpam-6607	28	20	,	,	PUNCT
ejpam-6607	28	21	41	41	NUM
ejpam-6607	28	22	]	]	PUNCT
ejpam-6607	28	23	.	.	PUNCT
ejpam-6607	29	1	as	as	SCONJ
ejpam-6607	29	2	noted	note	VERB
ejpam-6607	29	3	above	above	ADV
ejpam-6607	29	4	,	,	PUNCT
ejpam-6607	29	5	this	this	DET
ejpam-6607	29	6	paper	paper	NOUN
ejpam-6607	29	7	explores	explore	VERB
ejpam-6607	29	8	whether	whether	SCONJ
ejpam-6607	29	9	soft	soft	ADJ
ejpam-6607	29	10	sets	set	NOUN
ejpam-6607	29	11	,	,	PUNCT
ejpam-6607	29	12	hypersoft	hypersoft	NOUN
ejpam-6607	29	13	sets	set	NOUN
ejpam-6607	29	14	,	,	PUNCT
ejpam-6607	29	15	and	and	CCONJ
ejpam-6607	29	16	superhypersoft	superhypersoft	PROPN
ejpam-6607	29	17	sets	set	NOUN
ejpam-6607	29	18	can	can	AUX
ejpam-6607	29	19	be	be	AUX
ejpam-6607	29	20	extended	extend	VERB
ejpam-6607	29	21	within	within	ADP
ejpam-6607	29	22	the	the	DET
ejpam-6607	29	23	framework	framework	NOUN
ejpam-6607	29	24	of	of	ADP
ejpam-6607	29	25	quantum	quantum	NOUN
ejpam-6607	29	26	theory	theory	NOUN
ejpam-6607	29	27	.	.	PUNCT
ejpam-6607	30	1	in	in	ADP
ejpam-6607	30	2	the	the	DET
ejpam-6607	30	3	field	field	NOUN
ejpam-6607	30	4	of	of	ADP
ejpam-6607	30	5	soft	soft	ADJ
ejpam-6607	30	6	set	set	NOUN
ejpam-6607	30	7	theory	theory	NOUN
ejpam-6607	30	8	,	,	PUNCT
ejpam-6607	30	9	the	the	DET
ejpam-6607	30	10	quantum	quantum	NOUN
ejpam-6607	30	11	-	-	PUNCT
ejpam-6607	30	12	soft	soft	ADJ
ejpam-6607	30	13	set	set	NOUN
ejpam-6607	30	14	[	[	X
ejpam-6607	30	15	3	3	X
ejpam-6607	30	16	]	]	PUNCT
ejpam-6607	30	17	has	have	AUX
ejpam-6607	30	18	already	already	ADV
ejpam-6607	30	19	been	be	AUX
ejpam-6607	30	20	introduced	introduce	VERB
ejpam-6607	30	21	.	.	PUNCT
ejpam-6607	31	1	the	the	DET
ejpam-6607	31	2	quantum	quantum	NOUN
ejpam-6607	31	3	-	-	PUNCT
ejpam-6607	31	4	soft	soft	ADJ
ejpam-6607	31	5	t.	t.	PROPN
ejpam-6607	31	6	fujita	fujita	PROPN
ejpam-6607	31	7	,	,	PUNCT
ejpam-6607	31	8	f.smarandache	f.smarandache	NOUN
ejpam-6607	31	9	/	/	SYM
ejpam-6607	31	10	eur	eur	PROPN
ejpam-6607	31	11	.	.	PUNCT
ejpam-6607	32	1	j.	j.	PROPN
ejpam-6607	32	2	pure	pure	PROPN
ejpam-6607	32	3	appl	appl	PROPN
ejpam-6607	32	4	.	.	PROPN
ejpam-6607	32	5	math	math	PROPN
ejpam-6607	32	6	,	,	PUNCT
ejpam-6607	32	7	18	18	NUM
ejpam-6607	32	8	(	(	PUNCT
ejpam-6607	32	9	3	3	NUM
ejpam-6607	32	10	)	)	PUNCT
ejpam-6607	32	11	(	(	PUNCT
ejpam-6607	32	12	2025	2025	NUM
ejpam-6607	32	13	)	)	PUNCT
ejpam-6607	32	14	,	,	PUNCT
ejpam-6607	32	15	6607	6607	NUM
ejpam-6607	32	16	3	3	NUM
ejpam-6607	32	17	of	of	ADP
ejpam-6607	32	18	33	33	NUM
ejpam-6607	32	19	set	set	NOUN
ejpam-6607	32	20	enriches	enrich	VERB
ejpam-6607	32	21	the	the	DET
ejpam-6607	32	22	classical	classical	ADJ
ejpam-6607	32	23	soft	soft	ADJ
ejpam-6607	32	24	set	set	NOUN
ejpam-6607	32	25	by	by	ADP
ejpam-6607	32	26	mapping	map	VERB
ejpam-6607	32	27	each	each	DET
ejpam-6607	32	28	parameter	parameter	NOUN
ejpam-6607	32	29	to	to	ADP
ejpam-6607	32	30	a	a	DET
ejpam-6607	32	31	normalized	normalize	VERB
ejpam-6607	32	32	quantum	quantum	ADJ
ejpam-6607	32	33	superposition	superposition	NOUN
ejpam-6607	32	34	in	in	ADP
ejpam-6607	32	35	a	a	DET
ejpam-6607	32	36	hilbert	hilbert	NOUN
ejpam-6607	32	37	space	space	NOUN
ejpam-6607	32	38	,	,	PUNCT
ejpam-6607	32	39	thereby	thereby	ADV
ejpam-6607	32	40	encoding	encode	VERB
ejpam-6607	32	41	membership	membership	NOUN
ejpam-6607	32	42	via	via	ADP
ejpam-6607	32	43	amplitude	amplitude	NOUN
ejpam-6607	32	44	coefficients	coefficient	NOUN
ejpam-6607	32	45	and	and	CCONJ
ejpam-6607	32	46	measurement	measurement	NOUN
ejpam-6607	32	47	probabilities	probability	NOUN
ejpam-6607	32	48	.	.	PUNCT
ejpam-6607	33	1	a	a	DET
ejpam-6607	33	2	related	relate	VERB
ejpam-6607	33	3	framework	framework	NOUN
ejpam-6607	33	4	,	,	PUNCT
ejpam-6607	33	5	the	the	DET
ejpam-6607	33	6	quantum	quantum	ADJ
ejpam-6607	33	7	fuzzy	fuzzy	NOUN
ejpam-6607	33	8	set	set	NOUN
ejpam-6607	33	9	,	,	PUNCT
ejpam-6607	33	10	has	have	AUX
ejpam-6607	33	11	also	also	ADV
ejpam-6607	33	12	been	be	AUX
ejpam-6607	33	13	proposed	propose	VERB
ejpam-6607	33	14	(	(	PUNCT
ejpam-6607	33	15	cf	cf	NOUN
ejpam-6607	33	16	.	.	PUNCT
ejpam-6607	34	1	[	[	X
ejpam-6607	34	2	42–44	42–44	NUM
ejpam-6607	34	3	]	]	X
ejpam-6607	34	4	)	)	PUNCT
ejpam-6607	34	5	.	.	PUNCT
ejpam-6607	35	1	in	in	ADP
ejpam-6607	35	2	view	view	NOUN
ejpam-6607	35	3	of	of	ADP
ejpam-6607	35	4	these	these	DET
ejpam-6607	35	5	quantum	quantum	NOUN
ejpam-6607	35	6	-	-	PUNCT
ejpam-6607	35	7	enhanced	enhance	VERB
ejpam-6607	35	8	approaches	approach	NOUN
ejpam-6607	35	9	to	to	ADP
ejpam-6607	35	10	uncertainty	uncertainty	NOUN
ejpam-6607	35	11	modeling	modeling	NOUN
ejpam-6607	35	12	,	,	PUNCT
ejpam-6607	35	13	we	we	PRON
ejpam-6607	35	14	anticipate	anticipate	VERB
ejpam-6607	35	15	that	that	SCONJ
ejpam-6607	35	16	quantum	quantum	NOUN
ejpam-6607	35	17	-	-	PUNCT
ejpam-6607	35	18	soft	soft	ADJ
ejpam-6607	35	19	sets	set	NOUN
ejpam-6607	35	20	will	will	AUX
ejpam-6607	35	21	play	play	VERB
ejpam-6607	35	22	a	a	DET
ejpam-6607	35	23	central	central	ADJ
ejpam-6607	35	24	role	role	NOUN
ejpam-6607	35	25	in	in	ADP
ejpam-6607	35	26	future	future	ADJ
ejpam-6607	35	27	scientific	scientific	ADJ
ejpam-6607	35	28	and	and	CCONJ
ejpam-6607	35	29	technological	technological	ADJ
ejpam-6607	35	30	developments	development	NOUN
ejpam-6607	35	31	,	,	PUNCT
ejpam-6607	35	32	and	and	CCONJ
ejpam-6607	35	33	we	we	PRON
ejpam-6607	35	34	therefore	therefore	ADV
ejpam-6607	35	35	regard	regard	VERB
ejpam-6607	35	36	their	their	PRON
ejpam-6607	35	37	rigorous	rigorous	ADJ
ejpam-6607	35	38	study	study	NOUN
ejpam-6607	35	39	as	as	ADP
ejpam-6607	35	40	both	both	CCONJ
ejpam-6607	35	41	timely	timely	ADJ
ejpam-6607	35	42	and	and	CCONJ
ejpam-6607	35	43	essential	essential	ADJ
ejpam-6607	35	44	.	.	PUNCT
ejpam-6607	36	1	1.3	1.3	NUM
ejpam-6607	36	2	.	.	PUNCT
ejpam-6607	37	1	our	our	PRON
ejpam-6607	37	2	contributions	contribution	NOUN
ejpam-6607	37	3	research	research	NOUN
ejpam-6607	37	4	on	on	ADP
ejpam-6607	37	5	soft	soft	ADJ
ejpam-6607	37	6	sets	set	NOUN
ejpam-6607	37	7	and	and	CCONJ
ejpam-6607	37	8	quantum	quantum	NOUN
ejpam-6607	37	9	theory	theory	NOUN
ejpam-6607	37	10	is	be	AUX
ejpam-6607	37	11	of	of	ADP
ejpam-6607	37	12	considerable	considerable	ADJ
ejpam-6607	37	13	importance	importance	NOUN
ejpam-6607	37	14	both	both	CCONJ
ejpam-6607	37	15	in	in	ADP
ejpam-6607	37	16	foundational	foundational	ADJ
ejpam-6607	37	17	mathematics	mathematic	NOUN
ejpam-6607	37	18	and	and	CCONJ
ejpam-6607	37	19	physics	physics	NOUN
ejpam-6607	37	20	as	as	ADV
ejpam-6607	37	21	well	well	ADV
ejpam-6607	37	22	as	as	ADP
ejpam-6607	37	23	in	in	ADP
ejpam-6607	37	24	practical	practical	ADJ
ejpam-6607	37	25	applications	application	NOUN
ejpam-6607	37	26	.	.	PUNCT
ejpam-6607	38	1	extending	extend	VERB
ejpam-6607	38	2	soft	soft	ADJ
ejpam-6607	38	3	sets	set	NOUN
ejpam-6607	38	4	to	to	ADP
ejpam-6607	38	5	richer	rich	ADJ
ejpam-6607	38	6	frameworks	framework	NOUN
ejpam-6607	38	7	is	be	AUX
ejpam-6607	38	8	therefore	therefore	ADV
ejpam-6607	38	9	a	a	DET
ejpam-6607	38	10	valuable	valuable	ADJ
ejpam-6607	38	11	and	and	CCONJ
ejpam-6607	38	12	meaningful	meaningful	ADJ
ejpam-6607	38	13	pursuit	pursuit	NOUN
ejpam-6607	38	14	.	.	PUNCT
ejpam-6607	39	1	while	while	SCONJ
ejpam-6607	39	2	the	the	DET
ejpam-6607	39	3	quantum	quantum	NOUN
ejpam-6607	39	4	-	-	PUNCT
ejpam-6607	39	5	soft	soft	ADJ
ejpam-6607	39	6	set	set	NOUN
ejpam-6607	39	7	has	have	AUX
ejpam-6607	39	8	been	be	AUX
ejpam-6607	39	9	defined	define	VERB
ejpam-6607	39	10	,	,	PUNCT
ejpam-6607	39	11	its	its	PRON
ejpam-6607	39	12	integration	integration	NOUN
ejpam-6607	39	13	into	into	ADP
ejpam-6607	39	14	more	more	ADV
ejpam-6607	39	15	advanced	advanced	ADJ
ejpam-6607	39	16	soft	soft	ADJ
ejpam-6607	39	17	set	set	NOUN
ejpam-6607	39	18	models	model	NOUN
ejpam-6607	39	19	remains	remain	VERB
ejpam-6607	39	20	underexplored	underexplored	ADJ
ejpam-6607	39	21	.	.	PUNCT
ejpam-6607	40	1	in	in	ADP
ejpam-6607	40	2	this	this	DET
ejpam-6607	40	3	paper	paper	NOUN
ejpam-6607	40	4	,	,	PUNCT
ejpam-6607	40	5	we	we	PRON
ejpam-6607	40	6	introduce	introduce	VERB
ejpam-6607	40	7	and	and	CCONJ
ejpam-6607	40	8	formalize	formalize	VERB
ejpam-6607	40	9	the	the	DET
ejpam-6607	40	10	quantum	quantum	ADJ
ejpam-6607	40	11	hypersoft	hypersoft	NOUN
ejpam-6607	40	12	set	set	VERB
ejpam-6607	40	13	and	and	CCONJ
ejpam-6607	40	14	the	the	DET
ejpam-6607	40	15	quantum	quantum	PROPN
ejpam-6607	40	16	superhypersoft	superhypersoft	NOUN
ejpam-6607	40	17	set	set	VERB
ejpam-6607	40	18	,	,	PUNCT
ejpam-6607	40	19	deriving	derive	VERB
ejpam-6607	40	20	their	their	PRON
ejpam-6607	40	21	core	core	NOUN
ejpam-6607	40	22	properties	property	NOUN
ejpam-6607	40	23	and	and	CCONJ
ejpam-6607	40	24	structural	structural	ADJ
ejpam-6607	40	25	characteristics	characteristic	NOUN
ejpam-6607	40	26	.	.	PUNCT
ejpam-6607	41	1	by	by	ADP
ejpam-6607	41	2	merging	merge	VERB
ejpam-6607	41	3	the	the	DET
ejpam-6607	41	4	quantum	quantum	NOUN
ejpam-6607	41	5	-	-	PUNCT
ejpam-6607	41	6	soft	soft	ADJ
ejpam-6607	41	7	paradigm	paradigm	NOUN
ejpam-6607	41	8	with	with	ADP
ejpam-6607	41	9	hypersoft	hypersoft	PROPN
ejpam-6607	41	10	and	and	CCONJ
ejpam-6607	41	11	superhypersoft	superhypersoft	PROPN
ejpam-6607	41	12	structures	structure	NOUN
ejpam-6607	41	13	,	,	PUNCT
ejpam-6607	41	14	we	we	PRON
ejpam-6607	41	15	aim	aim	VERB
ejpam-6607	41	16	to	to	PART
ejpam-6607	41	17	stimulate	stimulate	VERB
ejpam-6607	41	18	new	new	ADJ
ejpam-6607	41	19	advances	advance	NOUN
ejpam-6607	41	20	in	in	ADP
ejpam-6607	41	21	set	set	NOUN
ejpam-6607	41	22	theory	theory	NOUN
ejpam-6607	41	23	,	,	PUNCT
ejpam-6607	41	24	decision	decision	NOUN
ejpam-6607	41	25	-	-	PUNCT
ejpam-6607	41	26	making	make	VERB
ejpam-6607	41	27	methodologies	methodology	NOUN
ejpam-6607	41	28	,	,	PUNCT
ejpam-6607	41	29	topological	topological	ADJ
ejpam-6607	41	30	analysis	analysis	NOUN
ejpam-6607	41	31	,	,	PUNCT
ejpam-6607	41	32	algebraic	algebraic	ADJ
ejpam-6607	41	33	modeling	modeling	NOUN
ejpam-6607	41	34	,	,	PUNCT
ejpam-6607	41	35	and	and	CCONJ
ejpam-6607	41	36	quantum	quantum	ADJ
ejpam-6607	41	37	applications	application	NOUN
ejpam-6607	41	38	.	.	PUNCT
ejpam-6607	42	1	as	as	SCONJ
ejpam-6607	42	2	summarized	summarize	VERB
ejpam-6607	42	3	in	in	ADP
ejpam-6607	42	4	table	table	NOUN
ejpam-6607	42	5	2	2	NUM
ejpam-6607	42	6	,	,	PUNCT
ejpam-6607	42	7	the	the	DET
ejpam-6607	42	8	three	three	NUM
ejpam-6607	42	9	quantum	quantum	NOUN
ejpam-6607	42	10	-	-	PUNCT
ejpam-6607	42	11	enhanced	enhance	VERB
ejpam-6607	42	12	soft	soft	ADJ
ejpam-6607	42	13	set	set	VERB
ejpam-6607	42	14	frameworks	framework	NOUN
ejpam-6607	42	15	differ	differ	VERB
ejpam-6607	42	16	in	in	ADP
ejpam-6607	42	17	how	how	SCONJ
ejpam-6607	42	18	they	they	PRON
ejpam-6607	42	19	map	map	VERB
ejpam-6607	42	20	parameters	parameter	NOUN
ejpam-6607	42	21	or	or	CCONJ
ejpam-6607	42	22	attribute	attribute	NOUN
ejpam-6607	42	23	combinations	combination	NOUN
ejpam-6607	42	24	to	to	ADP
ejpam-6607	42	25	quantum	quantum	ADJ
ejpam-6607	42	26	states	state	NOUN
ejpam-6607	42	27	and	and	CCONJ
ejpam-6607	42	28	in	in	ADP
ejpam-6607	42	29	the	the	DET
ejpam-6607	42	30	scope	scope	NOUN
ejpam-6607	42	31	of	of	ADP
ejpam-6607	42	32	their	their	PRON
ejpam-6607	42	33	attribute	attribute	NOUN
ejpam-6607	42	34	interactions	interaction	NOUN
ejpam-6607	42	35	.	.	PUNCT
ejpam-6607	43	1	concept	concept	NOUN
ejpam-6607	43	2	mapping	map	VERB
ejpam-6607	43	3	key	key	ADJ
ejpam-6607	43	4	feature	feature	NOUN
ejpam-6607	43	5	quantum	quantum	NOUN
ejpam-6607	43	6	-	-	PUNCT
ejpam-6607	43	7	soft	soft	ADJ
ejpam-6607	43	8	set	set	NOUN
ejpam-6607	43	9	f	f	NOUN
ejpam-6607	43	10	:	:	PUNCT
ejpam-6607	43	11	a→	a→	PROPN
ejpam-6607	43	12	h(u	h(u	PROPN
ejpam-6607	43	13	)	)	PUNCT
ejpam-6607	43	14	assigns	assign	VERB
ejpam-6607	43	15	each	each	DET
ejpam-6607	43	16	attribute	attribute	NOUN
ejpam-6607	43	17	a	a	DET
ejpam-6607	43	18	∈	∈	PROPN
ejpam-6607	44	1	a	a	DET
ejpam-6607	44	2	to	to	ADP
ejpam-6607	44	3	a	a	DET
ejpam-6607	44	4	normalized	normalize	VERB
ejpam-6607	44	5	quantum	quantum	ADJ
ejpam-6607	44	6	state	state	NOUN
ejpam-6607	44	7	|ψa⟩	|ψa⟩	PROPN
ejpam-6607	44	8	,	,	PUNCT
ejpam-6607	44	9	where	where	SCONJ
ejpam-6607	44	10	|αi	|αi	X
ejpam-6607	44	11	,	,	PUNCT
ejpam-6607	44	12	a|2	a|2	PROPN
ejpam-6607	44	13	gives	give	VERB
ejpam-6607	44	14	the	the	DET
ejpam-6607	44	15	membership	membership	NOUN
ejpam-6607	44	16	probability	probability	NOUN
ejpam-6607	44	17	of	of	ADP
ejpam-6607	44	18	ui[3	ui[3	PROPN
ejpam-6607	44	19	]	]	PUNCT
ejpam-6607	44	20	.	.	PUNCT
ejpam-6607	45	1	quantum	quantum	PROPN
ejpam-6607	45	2	-	-	PUNCT
ejpam-6607	45	3	hypersoft	hypersoft	NOUN
ejpam-6607	45	4	set	set	VERB
ejpam-6607	45	5	q	q	NOUN
ejpam-6607	45	6	:	:	PUNCT
ejpam-6607	45	7	a1	a1	PROPN
ejpam-6607	45	8	×	×	NOUN
ejpam-6607	45	9	·	·	PUNCT
ejpam-6607	45	10	·	·	PUNCT
ejpam-6607	45	11	·	·	PUNCT
ejpam-6607	45	12	×	×	NOUN
ejpam-6607	45	13	am	am	NOUN
ejpam-6607	45	14	→	→	SYM
ejpam-6607	45	15	h(u	h(u	PROPN
ejpam-6607	45	16	)	)	PUNCT
ejpam-6607	45	17	maps	map	VERB
ejpam-6607	45	18	each	each	DET
ejpam-6607	45	19	tuple	tuple	NOUN
ejpam-6607	45	20	of	of	ADP
ejpam-6607	45	21	values	value	NOUN
ejpam-6607	45	22	(	(	PUNCT
ejpam-6607	45	23	γ1	γ1	PROPN
ejpam-6607	45	24	,	,	PUNCT
ejpam-6607	45	25	.	.	PUNCT
ejpam-6607	45	26	.	.	PUNCT
ejpam-6607	46	1	.	.	PUNCT
ejpam-6607	47	1	,	,	PUNCT
ejpam-6607	47	2	γm	γm	X
ejpam-6607	47	3	)	)	PUNCT
ejpam-6607	47	4	to	to	ADP
ejpam-6607	47	5	a	a	DET
ejpam-6607	47	6	quantum	quantum	ADJ
ejpam-6607	47	7	superposition	superposition	NOUN
ejpam-6607	47	8	,	,	PUNCT
ejpam-6607	47	9	capturing	capture	VERB
ejpam-6607	47	10	joint	joint	ADJ
ejpam-6607	47	11	multi	multi	ADJ
ejpam-6607	47	12	-	-	ADJ
ejpam-6607	47	13	attribute	attribute	NOUN
ejpam-6607	47	14	influence	influence	NOUN
ejpam-6607	47	15	via	via	ADP
ejpam-6607	47	16	amplitude	amplitude	NOUN
ejpam-6607	47	17	interference	interference	NOUN
ejpam-6607	47	18	.	.	PUNCT
ejpam-6607	48	1	quantum	quantum	NOUN
ejpam-6607	48	2	-	-	PUNCT
ejpam-6607	48	3	superhypersoft	superhypersoft	NOUN
ejpam-6607	48	4	set	set	VERB
ejpam-6607	48	5	q	q	NOUN
ejpam-6607	48	6	:	:	PUNCT
ejpam-6607	48	7	p(a1	p(a1	NOUN
ejpam-6607	48	8	)	)	PUNCT
ejpam-6607	48	9	×	×	NOUN
ejpam-6607	48	10	·	·	PUNCT
ejpam-6607	48	11	·	·	PUNCT
ejpam-6607	48	12	·	·	PUNCT
ejpam-6607	48	13	×	×	NOUN
ejpam-6607	48	14	p(an	p(an	NOUN
ejpam-6607	48	15	)	)	PUNCT
ejpam-6607	48	16	→	→	SYM
ejpam-6607	48	17	h(u	h(u	PROPN
ejpam-6607	48	18	)	)	PUNCT
ejpam-6607	48	19	extends	extend	VERB
ejpam-6607	48	20	hypersoft	hypersoft	NOUN
ejpam-6607	48	21	by	by	ADP
ejpam-6607	48	22	mapping	map	VERB
ejpam-6607	48	23	each	each	DET
ejpam-6607	48	24	subset	subset	NOUN
ejpam-6607	48	25	-	-	PUNCT
ejpam-6607	48	26	tuple	tuple	NOUN
ejpam-6607	48	27	of	of	ADP
ejpam-6607	48	28	attribute	attribute	NOUN
ejpam-6607	48	29	values	value	NOUN
ejpam-6607	48	30	to	to	ADP
ejpam-6607	48	31	a	a	DET
ejpam-6607	48	32	quantum	quantum	ADJ
ejpam-6607	48	33	state	state	NOUN
ejpam-6607	48	34	,	,	PUNCT
ejpam-6607	48	35	modeling	model	VERB
ejpam-6607	48	36	interactions	interaction	NOUN
ejpam-6607	48	37	among	among	ADP
ejpam-6607	48	38	arbitrary	arbitrary	ADJ
ejpam-6607	48	39	subsets	subset	NOUN
ejpam-6607	48	40	of	of	ADP
ejpam-6607	48	41	values	value	NOUN
ejpam-6607	48	42	.	.	PUNCT
ejpam-6607	49	1	table	table	NOUN
ejpam-6607	49	2	2	2	NUM
ejpam-6607	49	3	:	:	PUNCT
ejpam-6607	49	4	overview	overview	NOUN
ejpam-6607	49	5	of	of	ADP
ejpam-6607	49	6	quantum	quantum	ADJ
ejpam-6607	49	7	soft	soft	ADJ
ejpam-6607	49	8	set	set	NOUN
ejpam-6607	49	9	,	,	PUNCT
ejpam-6607	49	10	quantum	quantum	ADJ
ejpam-6607	49	11	hypersoft	hypersoft	NOUN
ejpam-6607	49	12	set	set	NOUN
ejpam-6607	49	13	,	,	PUNCT
ejpam-6607	49	14	and	and	CCONJ
ejpam-6607	49	15	quantum	quantum	PROPN
ejpam-6607	49	16	superhypersoft	superhypersoft	NOUN
ejpam-6607	49	17	set	set	VERB
ejpam-6607	49	18	t.	t.	PROPN
ejpam-6607	49	19	fujita	fujita	PROPN
ejpam-6607	49	20	,	,	PUNCT
ejpam-6607	49	21	f.smarandache	f.smarandache	NOUN
ejpam-6607	49	22	/	/	SYM
ejpam-6607	49	23	eur	eur	PROPN
ejpam-6607	49	24	.	.	PUNCT
ejpam-6607	50	1	j.	j.	PROPN
ejpam-6607	50	2	pure	pure	PROPN
ejpam-6607	50	3	appl	appl	PROPN
ejpam-6607	50	4	.	.	PROPN
ejpam-6607	50	5	math	math	PROPN
ejpam-6607	50	6	,	,	PUNCT
ejpam-6607	50	7	18	18	NUM
ejpam-6607	50	8	(	(	PUNCT
ejpam-6607	50	9	3	3	NUM
ejpam-6607	50	10	)	)	PUNCT
ejpam-6607	50	11	(	(	PUNCT
ejpam-6607	50	12	2025	2025	NUM
ejpam-6607	50	13	)	)	PUNCT
ejpam-6607	50	14	,	,	PUNCT
ejpam-6607	50	15	6607	6607	NUM
ejpam-6607	50	16	4	4	NUM
ejpam-6607	50	17	of	of	ADP
ejpam-6607	50	18	33	33	NUM
ejpam-6607	50	19	1.4	1.4	NUM
ejpam-6607	50	20	.	.	PUNCT
ejpam-6607	51	1	structure	structure	NOUN
ejpam-6607	51	2	of	of	ADP
ejpam-6607	51	3	this	this	DET
ejpam-6607	51	4	paper	paper	NOUN
ejpam-6607	51	5	the	the	DET
ejpam-6607	51	6	remainder	remainder	NOUN
ejpam-6607	51	7	of	of	ADP
ejpam-6607	51	8	this	this	DET
ejpam-6607	51	9	paper	paper	NOUN
ejpam-6607	51	10	is	be	AUX
ejpam-6607	51	11	organized	organize	VERB
ejpam-6607	51	12	as	as	SCONJ
ejpam-6607	51	13	follows	follow	VERB
ejpam-6607	51	14	.	.	PUNCT
ejpam-6607	52	1	section	section	NOUN
ejpam-6607	52	2	2	2	NUM
ejpam-6607	52	3	reviews	review	NOUN
ejpam-6607	52	4	soft	soft	ADJ
ejpam-6607	52	5	sets	set	NOUN
ejpam-6607	52	6	,	,	PUNCT
ejpam-6607	52	7	hypersoft	hypersoft	NOUN
ejpam-6607	52	8	sets	set	NOUN
ejpam-6607	52	9	,	,	PUNCT
ejpam-6607	52	10	superhypersoft	superhypersoft	NOUN
ejpam-6607	52	11	sets	set	VERB
ejpam-6607	52	12	,	,	PUNCT
ejpam-6607	52	13	and	and	CCONJ
ejpam-6607	52	14	quantum	quantum	ADJ
ejpam-6607	52	15	soft	soft	ADJ
ejpam-6607	52	16	sets	set	NOUN
ejpam-6607	52	17	.	.	PUNCT
ejpam-6607	53	1	section	section	NOUN
ejpam-6607	53	2	3	3	NUM
ejpam-6607	53	3	introduces	introduce	NOUN
ejpam-6607	53	4	and	and	CCONJ
ejpam-6607	53	5	analyzes	analyze	VERB
ejpam-6607	53	6	quantum	quantum	NOUN
ejpam-6607	53	7	–	–	PUNCT
ejpam-6607	53	8	hypersoft	hypersoft	NOUN
ejpam-6607	53	9	sets	set	NOUN
ejpam-6607	53	10	and	and	CCONJ
ejpam-6607	53	11	quantum	quantum	NOUN
ejpam-6607	53	12	–	–	PUNCT
ejpam-6607	53	13	superhypersoft	superhypersoft	NOUN
ejpam-6607	53	14	sets	set	VERB
ejpam-6607	53	15	.	.	PUNCT
ejpam-6607	54	1	section	section	NOUN
ejpam-6607	54	2	4	4	NUM
ejpam-6607	54	3	briefly	briefly	NOUN
ejpam-6607	54	4	examines	examine	VERB
ejpam-6607	54	5	the	the	DET
ejpam-6607	54	6	construction	construction	NOUN
ejpam-6607	54	7	algorithms	algorithm	NOUN
ejpam-6607	54	8	.	.	PUNCT
ejpam-6607	55	1	section	section	NOUN
ejpam-6607	55	2	5	5	NUM
ejpam-6607	55	3	concludes	conclude	VERB
ejpam-6607	55	4	the	the	DET
ejpam-6607	55	5	paper	paper	NOUN
ejpam-6607	55	6	and	and	CCONJ
ejpam-6607	55	7	discusses	discuss	VERB
ejpam-6607	55	8	directions	direction	NOUN
ejpam-6607	55	9	for	for	ADP
ejpam-6607	55	10	future	future	ADJ
ejpam-6607	55	11	work	work	NOUN
ejpam-6607	55	12	.	.	PUNCT
ejpam-6607	56	1	2	2	X
ejpam-6607	56	2	.	.	X
ejpam-6607	56	3	preliminaries	preliminary	NOUN
ejpam-6607	56	4	in	in	ADP
ejpam-6607	56	5	this	this	DET
ejpam-6607	56	6	section	section	NOUN
ejpam-6607	56	7	,	,	PUNCT
ejpam-6607	56	8	we	we	PRON
ejpam-6607	56	9	present	present	VERB
ejpam-6607	56	10	the	the	DET
ejpam-6607	56	11	foundational	foundational	ADJ
ejpam-6607	56	12	concepts	concept	NOUN
ejpam-6607	56	13	of	of	ADP
ejpam-6607	56	14	soft	soft	ADJ
ejpam-6607	56	15	sets	set	NOUN
ejpam-6607	56	16	,	,	PUNCT
ejpam-6607	56	17	hypersoft	hypersoft	NOUN
ejpam-6607	56	18	sets	set	NOUN
ejpam-6607	56	19	,	,	PUNCT
ejpam-6607	56	20	and	and	CCONJ
ejpam-6607	56	21	superhypersoft	superhypersoft	NOUN
ejpam-6607	56	22	sets	set	VERB
ejpam-6607	56	23	.	.	PUNCT
ejpam-6607	57	1	we	we	PRON
ejpam-6607	57	2	also	also	ADV
ejpam-6607	57	3	provide	provide	VERB
ejpam-6607	57	4	a	a	DET
ejpam-6607	57	5	concise	concise	ADJ
ejpam-6607	57	6	explanation	explanation	NOUN
ejpam-6607	57	7	of	of	ADP
ejpam-6607	57	8	the	the	DET
ejpam-6607	57	9	definition	definition	NOUN
ejpam-6607	57	10	of	of	ADP
ejpam-6607	57	11	quantum	quantum	ADJ
ejpam-6607	57	12	soft	soft	ADJ
ejpam-6607	57	13	sets	set	NOUN
ejpam-6607	57	14	.	.	PUNCT
ejpam-6607	58	1	2.1	2.1	NUM
ejpam-6607	58	2	.	.	PUNCT
ejpam-6607	58	3	notation	notation	NOUN
ejpam-6607	58	4	throughout	throughout	ADP
ejpam-6607	58	5	this	this	DET
ejpam-6607	58	6	paper	paper	NOUN
ejpam-6607	58	7	,	,	PUNCT
ejpam-6607	58	8	all	all	DET
ejpam-6607	58	9	sets	set	NOUN
ejpam-6607	58	10	are	be	AUX
ejpam-6607	58	11	assumed	assume	VERB
ejpam-6607	58	12	to	to	PART
ejpam-6607	58	13	be	be	AUX
ejpam-6607	58	14	finite	finite	VERB
ejpam-6607	58	15	.	.	PUNCT
ejpam-6607	59	1	the	the	DET
ejpam-6607	59	2	empty	empty	ADJ
ejpam-6607	59	3	set	set	NOUN
ejpam-6607	59	4	is	be	AUX
ejpam-6607	59	5	considered	consider	VERB
ejpam-6607	59	6	to	to	PART
ejpam-6607	59	7	be	be	AUX
ejpam-6607	59	8	a	a	DET
ejpam-6607	59	9	subset	subset	NOUN
ejpam-6607	59	10	of	of	ADP
ejpam-6607	59	11	any	any	DET
ejpam-6607	59	12	set	set	NOUN
ejpam-6607	59	13	.	.	PUNCT
ejpam-6607	60	1	for	for	ADP
ejpam-6607	60	2	the	the	DET
ejpam-6607	60	3	basic	basic	ADJ
ejpam-6607	60	4	operations	operation	NOUN
ejpam-6607	60	5	related	relate	VERB
ejpam-6607	60	6	to	to	ADP
ejpam-6607	60	7	each	each	DET
ejpam-6607	60	8	concept	concept	NOUN
ejpam-6607	60	9	,	,	PUNCT
ejpam-6607	60	10	the	the	DET
ejpam-6607	60	11	reader	reader	NOUN
ejpam-6607	60	12	is	be	AUX
ejpam-6607	60	13	referred	refer	VERB
ejpam-6607	60	14	to	to	ADP
ejpam-6607	60	15	the	the	DET
ejpam-6607	60	16	corresponding	corresponding	ADJ
ejpam-6607	60	17	references	reference	NOUN
ejpam-6607	60	18	.	.	PUNCT
ejpam-6607	61	1	in	in	ADP
ejpam-6607	61	2	this	this	DET
ejpam-6607	61	3	paper	paper	NOUN
ejpam-6607	61	4	,	,	PUNCT
ejpam-6607	61	5	we	we	PRON
ejpam-6607	61	6	use	use	VERB
ejpam-6607	61	7	the	the	DET
ejpam-6607	61	8	following	follow	VERB
ejpam-6607	61	9	notation	notation	NOUN
ejpam-6607	61	10	.	.	PUNCT
ejpam-6607	62	1	•	•	NUM
ejpam-6607	62	2	u	u	NOUN
ejpam-6607	62	3	=	=	NOUN
ejpam-6607	62	4	{	{	PUNCT
ejpam-6607	62	5	u1	u1	NOUN
ejpam-6607	62	6	,	,	PUNCT
ejpam-6607	62	7	.	.	PUNCT
ejpam-6607	62	8	.	.	PUNCT
ejpam-6607	62	9	.	.	PUNCT
ejpam-6607	63	1	,	,	PUNCT
ejpam-6607	63	2	un	un	PROPN
ejpam-6607	63	3	}	}	PUNCT
ejpam-6607	63	4	:	:	PUNCT
ejpam-6607	64	1	a	a	DET
ejpam-6607	64	2	finite	finite	ADJ
ejpam-6607	64	3	universe	universe	NOUN
ejpam-6607	64	4	•	•	ADP
ejpam-6607	64	5	p(u	p(u	ADJ
ejpam-6607	64	6	):	):	PUNCT
ejpam-6607	64	7	the	the	DET
ejpam-6607	64	8	power	power	NOUN
ejpam-6607	64	9	set	set	NOUN
ejpam-6607	64	10	of	of	ADP
ejpam-6607	64	11	u	u	NOUN
ejpam-6607	64	12	•	•	ADP
ejpam-6607	64	13	h(u	h(u	PROPN
ejpam-6607	64	14	):	):	PUNCT
ejpam-6607	64	15	the	the	DET
ejpam-6607	64	16	n	n	CCONJ
ejpam-6607	64	17	-	-	PUNCT
ejpam-6607	64	18	dimensional	dimensional	ADJ
ejpam-6607	64	19	complex	complex	ADJ
ejpam-6607	64	20	hilbert	hilbert	NOUN
ejpam-6607	64	21	space	space	NOUN
ejpam-6607	64	22	with	with	ADP
ejpam-6607	64	23	orthonormal	orthonormal	ADJ
ejpam-6607	64	24	basis	basis	NOUN
ejpam-6607	64	25	{	{	PUNCT
ejpam-6607	64	26	|ui⟩}ni=1	|ui⟩}ni=1	NUM
ejpam-6607	64	27	•	•	NOUN
ejpam-6607	64	28	c	c	X
ejpam-6607	64	29	:	:	PUNCT
ejpam-6607	64	30	the	the	DET
ejpam-6607	64	31	cartesian	cartesian	ADJ
ejpam-6607	64	32	product	product	NOUN
ejpam-6607	64	33	of	of	ADP
ejpam-6607	64	34	the	the	DET
ejpam-6607	64	35	attribute	attribute	NOUN
ejpam-6607	64	36	domains	domain	NOUN
ejpam-6607	64	37	(	(	PUNCT
ejpam-6607	64	38	or	or	CCONJ
ejpam-6607	64	39	of	of	ADP
ejpam-6607	64	40	their	their	PRON
ejpam-6607	64	41	power	power	NOUN
ejpam-6607	64	42	sets	set	NOUN
ejpam-6607	64	43	)	)	PUNCT
ejpam-6607	64	44	•	•	NOUN
ejpam-6607	64	45	general	general	ADJ
ejpam-6607	64	46	quantum	quantum	ADJ
ejpam-6607	64	47	state	state	NOUN
ejpam-6607	64	48	:	:	PUNCT
ejpam-6607	64	49	|ψ⟩	|ψ⟩	PROPN
ejpam-6607	64	50	=	=	PUNCT
ejpam-6607	65	1	n∑	n∑	PROPN
ejpam-6607	65	2	i=1	i=1	PROPN
ejpam-6607	65	3	αi	αi	ADV
ejpam-6607	65	4	|ui⟩	|ui⟩	X
ejpam-6607	65	5	,	,	PUNCT
ejpam-6607	65	6	n∑	n∑	PROPN
ejpam-6607	65	7	i=1	i=1	PROPN
ejpam-6607	66	1	∣∣αi	∣∣αi	PROPN
ejpam-6607	66	2	∣∣2	∣∣2	PROPN
ejpam-6607	66	3	=	=	SYM
ejpam-6607	66	4	1	1	NUM
ejpam-6607	66	5	•	•	NUM
ejpam-6607	66	6	measurement	measurement	NOUN
ejpam-6607	66	7	probability	probability	NOUN
ejpam-6607	66	8	:	:	PUNCT
ejpam-6607	66	9	p	p	X
ejpam-6607	66	10	(	(	PUNCT
ejpam-6607	66	11	ui	ui	PROPN
ejpam-6607	66	12	|	|	ADV
ejpam-6607	66	13	γ	γ	NOUN
ejpam-6607	66	14	)	)	PUNCT
ejpam-6607	67	1	=	=	SYM
ejpam-6607	67	2	∣∣αi	∣∣αi	NOUN
ejpam-6607	67	3	,	,	PUNCT
ejpam-6607	67	4	γ	γ	PROPN
ejpam-6607	67	5	∣∣2	∣∣2	PROPN
ejpam-6607	67	6	2.2	2.2	NUM
ejpam-6607	67	7	.	.	PUNCT
ejpam-6607	68	1	soft	soft	ADJ
ejpam-6607	68	2	sets	set	NOUN
ejpam-6607	68	3	let	let	VERB
ejpam-6607	68	4	u	u	PRON
ejpam-6607	68	5	=	=	NOUN
ejpam-6607	68	6	{	{	PUNCT
ejpam-6607	68	7	u1	u1	NOUN
ejpam-6607	68	8	,	,	PUNCT
ejpam-6607	68	9	.	.	PUNCT
ejpam-6607	68	10	.	.	PUNCT
ejpam-6607	69	1	.	.	PUNCT
ejpam-6607	70	1	,	,	PUNCT
ejpam-6607	70	2	un	un	AUX
ejpam-6607	70	3	}	}	PUNCT
ejpam-6607	70	4	be	be	AUX
ejpam-6607	70	5	a	a	DET
ejpam-6607	70	6	finite	finite	ADJ
ejpam-6607	70	7	universe	universe	NOUN
ejpam-6607	70	8	and	and	CCONJ
ejpam-6607	70	9	let	let	VERB
ejpam-6607	70	10	a	a	PRON
ejpam-6607	70	11	be	be	AUX
ejpam-6607	70	12	a	a	DET
ejpam-6607	70	13	finite	finite	ADJ
ejpam-6607	70	14	set	set	NOUN
ejpam-6607	70	15	of	of	ADP
ejpam-6607	70	16	parameters	parameter	NOUN
ejpam-6607	70	17	.	.	PUNCT
ejpam-6607	71	1	we	we	PRON
ejpam-6607	71	2	denote	denote	VERB
ejpam-6607	71	3	by	by	ADP
ejpam-6607	71	4	p(u	p(u	PROPN
ejpam-6607	71	5	)	)	PUNCT
ejpam-6607	71	6	the	the	DET
ejpam-6607	71	7	power	power	NOUN
ejpam-6607	71	8	set	set	NOUN
ejpam-6607	71	9	of	of	ADP
ejpam-6607	71	10	u	u	PROPN
ejpam-6607	71	11	.	.	PUNCT
ejpam-6607	72	1	given	give	VERB
ejpam-6607	72	2	a	a	DET
ejpam-6607	72	3	subset	subset	NOUN
ejpam-6607	72	4	s	s	VERB
ejpam-6607	72	5	⊆	⊆	NUM
ejpam-6607	72	6	a	a	PRON
ejpam-6607	72	7	of	of	ADP
ejpam-6607	72	8	chosen	choose	VERB
ejpam-6607	72	9	parameters	parameter	NOUN
ejpam-6607	72	10	,	,	PUNCT
ejpam-6607	72	11	a	a	DET
ejpam-6607	72	12	soft	soft	ADJ
ejpam-6607	72	13	set	set	NOUN
ejpam-6607	72	14	over	over	ADP
ejpam-6607	72	15	u	u	NOUN
ejpam-6607	72	16	(	(	PUNCT
ejpam-6607	72	17	with	with	ADP
ejpam-6607	72	18	respect	respect	NOUN
ejpam-6607	72	19	to	to	ADP
ejpam-6607	72	20	s	s	NOUN
ejpam-6607	72	21	)	)	PUNCT
ejpam-6607	72	22	is	be	AUX
ejpam-6607	72	23	defined	define	VERB
ejpam-6607	72	24	as	as	ADP
ejpam-6607	72	25	follows	follow	VERB
ejpam-6607	72	26	.	.	PUNCT
ejpam-6607	73	1	definition	definition	NOUN
ejpam-6607	73	2	1	1	NUM
ejpam-6607	73	3	(	(	PUNCT
ejpam-6607	73	4	soft	soft	ADJ
ejpam-6607	73	5	set	set	NOUN
ejpam-6607	73	6	[	[	X
ejpam-6607	73	7	2	2	NUM
ejpam-6607	73	8	]	]	NUM
ejpam-6607	73	9	)	)	PUNCT
ejpam-6607	73	10	.	.	PUNCT
ejpam-6607	74	1	a	a	DET
ejpam-6607	74	2	soft	soft	ADJ
ejpam-6607	74	3	set	set	NOUN
ejpam-6607	74	4	over	over	ADP
ejpam-6607	74	5	u	u	NOUN
ejpam-6607	74	6	parameterized	parameterized	ADJ
ejpam-6607	74	7	by	by	ADP
ejpam-6607	74	8	s	s	PROPN
ejpam-6607	74	9	is	be	AUX
ejpam-6607	74	10	a	a	DET
ejpam-6607	74	11	pair	pair	NOUN
ejpam-6607	74	12	(	(	PUNCT
ejpam-6607	74	13	f	f	PROPN
ejpam-6607	74	14	,	,	PUNCT
ejpam-6607	74	15	s	s	PROPN
ejpam-6607	74	16	)	)	PUNCT
ejpam-6607	74	17	where	where	SCONJ
ejpam-6607	74	18	f	f	X
ejpam-6607	74	19	:	:	PUNCT
ejpam-6607	74	20	s	s	VERB
ejpam-6607	74	21	−→	−→	NOUN
ejpam-6607	74	22	p(u	p(u	NOUN
ejpam-6607	74	23	)	)	PUNCT
ejpam-6607	74	24	t.	t.	PROPN
ejpam-6607	74	25	fujita	fujita	PROPN
ejpam-6607	74	26	,	,	PUNCT
ejpam-6607	74	27	f.smarandache	f.smarandache	NOUN
ejpam-6607	74	28	/	/	SYM
ejpam-6607	74	29	eur	eur	PROPN
ejpam-6607	74	30	.	.	PUNCT
ejpam-6607	75	1	j.	j.	PROPN
ejpam-6607	75	2	pure	pure	PROPN
ejpam-6607	75	3	appl	appl	PROPN
ejpam-6607	75	4	.	.	PROPN
ejpam-6607	75	5	math	math	PROPN
ejpam-6607	75	6	,	,	PUNCT
ejpam-6607	75	7	18	18	NUM
ejpam-6607	75	8	(	(	PUNCT
ejpam-6607	75	9	3	3	NUM
ejpam-6607	75	10	)	)	PUNCT
ejpam-6607	75	11	(	(	PUNCT
ejpam-6607	75	12	2025	2025	NUM
ejpam-6607	75	13	)	)	PUNCT
ejpam-6607	75	14	,	,	PUNCT
ejpam-6607	75	15	6607	6607	NUM
ejpam-6607	75	16	5	5	NUM
ejpam-6607	75	17	of	of	ADP
ejpam-6607	75	18	33	33	NUM
ejpam-6607	75	19	is	be	AUX
ejpam-6607	75	20	a	a	DET
ejpam-6607	75	21	function	function	NOUN
ejpam-6607	75	22	assigning	assign	VERB
ejpam-6607	75	23	to	to	ADP
ejpam-6607	75	24	each	each	DET
ejpam-6607	75	25	parameter	parameter	NOUN
ejpam-6607	75	26	α	α	PROPN
ejpam-6607	75	27	∈	∈	PROPN
ejpam-6607	75	28	s	s	VERB
ejpam-6607	75	29	a	a	DET
ejpam-6607	75	30	subset	subset	NOUN
ejpam-6607	75	31	f(α	f(α	NOUN
ejpam-6607	75	32	)	)	PUNCT
ejpam-6607	75	33	⊆	⊆	NUM
ejpam-6607	75	34	u	u	NOUN
ejpam-6607	75	35	.	.	PUNCT
ejpam-6607	76	1	equivalently	equivalently	ADV
ejpam-6607	76	2	,	,	PUNCT
ejpam-6607	76	3	(	(	PUNCT
ejpam-6607	76	4	f	f	X
ejpam-6607	76	5	,	,	PUNCT
ejpam-6607	76	6	s	s	X
ejpam-6607	76	7	)	)	PUNCT
ejpam-6607	76	8	=	=	SYM
ejpam-6607	76	9	{	{	PUNCT
ejpam-6607	76	10	(	(	PUNCT
ejpam-6607	76	11	α	α	NOUN
ejpam-6607	76	12	,	,	PUNCT
ejpam-6607	76	13	f(α	f(α	NOUN
ejpam-6607	76	14	)	)	PUNCT
ejpam-6607	76	15	)	)	PUNCT
ejpam-6607	76	16	∣∣	∣∣	VERB
ejpam-6607	76	17	α	α	PROPN
ejpam-6607	76	18	∈	∈	PROPN
ejpam-6607	76	19	s	s	PROPN
ejpam-6607	76	20	,	,	PUNCT
ejpam-6607	76	21	f(α	f(α	NOUN
ejpam-6607	76	22	)	)	PUNCT
ejpam-6607	76	23	⊆	⊆	NUM
ejpam-6607	76	24	u	u	NOUN
ejpam-6607	76	25	}	}	PUNCT
ejpam-6607	76	26	.	.	PUNCT
ejpam-6607	77	1	example	example	NOUN
ejpam-6607	77	2	1	1	NUM
ejpam-6607	77	3	(	(	PUNCT
ejpam-6607	77	4	restaurant	restaurant	NOUN
ejpam-6607	77	5	selection	selection	NOUN
ejpam-6607	77	6	)	)	PUNCT
ejpam-6607	77	7	.	.	PUNCT
ejpam-6607	78	1	let	let	VERB
ejpam-6607	78	2	u	u	PRON
ejpam-6607	78	3	=	=	X
ejpam-6607	78	4	{	{	PUNCT
ejpam-6607	78	5	r1	r1	PROPN
ejpam-6607	78	6	,	,	PUNCT
ejpam-6607	78	7	r2	r2	PROPN
ejpam-6607	78	8	,	,	PUNCT
ejpam-6607	78	9	r3	r3	PROPN
ejpam-6607	78	10	,	,	PUNCT
ejpam-6607	78	11	r4	r4	NOUN
ejpam-6607	78	12	,	,	PUNCT
ejpam-6607	78	13	r5	r5	PROPN
ejpam-6607	78	14	}	}	PUNCT
ejpam-6607	78	15	be	be	VERB
ejpam-6607	78	16	a	a	DET
ejpam-6607	78	17	set	set	NOUN
ejpam-6607	78	18	of	of	ADP
ejpam-6607	78	19	restaurants	restaurant	NOUN
ejpam-6607	78	20	in	in	ADP
ejpam-6607	78	21	a	a	DET
ejpam-6607	78	22	city	city	NOUN
ejpam-6607	78	23	,	,	PUNCT
ejpam-6607	78	24	and	and	CCONJ
ejpam-6607	78	25	let	let	VERB
ejpam-6607	78	26	a	a	DET
ejpam-6607	78	27	=	=	X
ejpam-6607	78	28	{	{	PUNCT
ejpam-6607	78	29	italian	italian	ADJ
ejpam-6607	78	30	,	,	PUNCT
ejpam-6607	78	31	japanese	japanese	ADJ
ejpam-6607	78	32	,	,	PUNCT
ejpam-6607	78	33	cheap	cheap	ADJ
ejpam-6607	78	34	,	,	PUNCT
ejpam-6607	78	35	finedining	finedining	NOUN
ejpam-6607	78	36	,	,	PUNCT
ejpam-6607	78	37	familyfriendly	familyfriendly	ADV
ejpam-6607	78	38	}	}	PUNCT
ejpam-6607	78	39	be	be	AUX
ejpam-6607	78	40	the	the	DET
ejpam-6607	78	41	full	full	ADJ
ejpam-6607	78	42	parameter	parameter	NOUN
ejpam-6607	78	43	set	set	NOUN
ejpam-6607	78	44	.	.	PUNCT
ejpam-6607	79	1	suppose	suppose	VERB
ejpam-6607	79	2	a	a	DET
ejpam-6607	79	3	user	user	NOUN
ejpam-6607	79	4	selects	select	NOUN
ejpam-6607	79	5	s	s	PART
ejpam-6607	79	6	=	=	PUNCT
ejpam-6607	79	7	{	{	PUNCT
ejpam-6607	79	8	italian	italian	ADJ
ejpam-6607	79	9	,	,	PUNCT
ejpam-6607	79	10	cheap	cheap	ADJ
ejpam-6607	79	11	,	,	PUNCT
ejpam-6607	79	12	familyfriendly	familyfriendly	ADV
ejpam-6607	79	13	}	}	PUNCT
ejpam-6607	79	14	.	.	PUNCT
ejpam-6607	80	1	define	define	VERB
ejpam-6607	80	2	the	the	DET
ejpam-6607	80	3	soft	soft	ADJ
ejpam-6607	80	4	set	set	NOUN
ejpam-6607	80	5	(	(	PUNCT
ejpam-6607	80	6	f	f	X
ejpam-6607	80	7	,	,	PUNCT
ejpam-6607	80	8	s	s	PROPN
ejpam-6607	80	9	)	)	PUNCT
ejpam-6607	80	10	by	by	ADP
ejpam-6607	80	11	f(italian	f(italian	ADJ
ejpam-6607	80	12	)	)	PUNCT
ejpam-6607	80	13	=	=	PRON
ejpam-6607	80	14	{	{	PUNCT
ejpam-6607	80	15	r1	r1	PROPN
ejpam-6607	80	16	,	,	PUNCT
ejpam-6607	80	17	r3	r3	PROPN
ejpam-6607	80	18	,	,	PUNCT
ejpam-6607	80	19	r5	r5	PROPN
ejpam-6607	80	20	}	}	PUNCT
ejpam-6607	80	21	,	,	PUNCT
ejpam-6607	80	22	f(cheap	f(cheap	NOUN
ejpam-6607	80	23	)	)	PUNCT
ejpam-6607	81	1	=	=	PRON
ejpam-6607	81	2	{	{	PUNCT
ejpam-6607	81	3	r2	r2	PROPN
ejpam-6607	81	4	,	,	PUNCT
ejpam-6607	81	5	r3	r3	PROPN
ejpam-6607	81	6	,	,	PUNCT
ejpam-6607	81	7	r4	r4	NOUN
ejpam-6607	81	8	}	}	PUNCT
ejpam-6607	81	9	,	,	PUNCT
ejpam-6607	81	10	f(familyfriendly	f(familyfriendly	ADV
ejpam-6607	81	11	)	)	PUNCT
ejpam-6607	81	12	=	=	SYM
ejpam-6607	81	13	{	{	PUNCT
ejpam-6607	81	14	r1	r1	PROPN
ejpam-6607	81	15	,	,	PUNCT
ejpam-6607	81	16	r4	r4	NOUN
ejpam-6607	81	17	,	,	PUNCT
ejpam-6607	81	18	r5	r5	PROPN
ejpam-6607	81	19	}	}	PUNCT
ejpam-6607	81	20	.	.	PUNCT
ejpam-6607	82	1	then	then	ADV
ejpam-6607	82	2	:	:	PUNCT
ejpam-6607	82	3	•	•	NUM
ejpam-6607	82	4	f(italian	f(italian	NOUN
ejpam-6607	82	5	)	)	PUNCT
ejpam-6607	82	6	=	=	PRON
ejpam-6607	82	7	{	{	PUNCT
ejpam-6607	82	8	r1	r1	PROPN
ejpam-6607	82	9	,	,	PUNCT
ejpam-6607	82	10	r3	r3	PROPN
ejpam-6607	82	11	,	,	PUNCT
ejpam-6607	82	12	r5	r5	PROPN
ejpam-6607	82	13	}	}	PUNCT
ejpam-6607	82	14	is	be	AUX
ejpam-6607	82	15	the	the	DET
ejpam-6607	82	16	set	set	NOUN
ejpam-6607	82	17	of	of	ADP
ejpam-6607	82	18	italian	italian	ADJ
ejpam-6607	82	19	restaurants	restaurant	NOUN
ejpam-6607	82	20	.	.	PUNCT
ejpam-6607	83	1	•	•	NUM
ejpam-6607	83	2	f(cheap	f(cheap	NOUN
ejpam-6607	83	3	)	)	PUNCT
ejpam-6607	84	1	=	=	PRON
ejpam-6607	84	2	{	{	PUNCT
ejpam-6607	84	3	r2	r2	PROPN
ejpam-6607	84	4	,	,	PUNCT
ejpam-6607	84	5	r3	r3	PROPN
ejpam-6607	84	6	,	,	PUNCT
ejpam-6607	84	7	r4	r4	PROPN
ejpam-6607	84	8	}	}	PUNCT
ejpam-6607	84	9	is	be	AUX
ejpam-6607	84	10	the	the	DET
ejpam-6607	84	11	set	set	NOUN
ejpam-6607	84	12	of	of	ADP
ejpam-6607	84	13	low	low	ADJ
ejpam-6607	84	14	-	-	PUNCT
ejpam-6607	84	15	cost	cost	NOUN
ejpam-6607	84	16	restaurants	restaurant	NOUN
ejpam-6607	84	17	.	.	PUNCT
ejpam-6607	85	1	•	•	NUM
ejpam-6607	85	2	f(familyfriendly	f(familyfriendly	ADV
ejpam-6607	85	3	)	)	PUNCT
ejpam-6607	85	4	=	=	PRON
ejpam-6607	85	5	{	{	PUNCT
ejpam-6607	85	6	r1	r1	PROPN
ejpam-6607	85	7	,	,	PUNCT
ejpam-6607	85	8	r4	r4	NOUN
ejpam-6607	85	9	,	,	PUNCT
ejpam-6607	85	10	r5	r5	PROPN
ejpam-6607	85	11	}	}	PUNCT
ejpam-6607	85	12	is	be	AUX
ejpam-6607	85	13	the	the	DET
ejpam-6607	85	14	set	set	NOUN
ejpam-6607	85	15	of	of	ADP
ejpam-6607	85	16	family	family	NOUN
ejpam-6607	85	17	-	-	PUNCT
ejpam-6607	85	18	friendly	friendly	ADJ
ejpam-6607	85	19	restaurants	restaurant	NOUN
ejpam-6607	85	20	.	.	PUNCT
ejpam-6607	86	1	for	for	ADP
ejpam-6607	86	2	instance	instance	NOUN
ejpam-6607	86	3	,	,	PUNCT
ejpam-6607	86	4	f(italian	f(italian	ADJ
ejpam-6607	86	5	)	)	PUNCT
ejpam-6607	86	6	∩	∩	ADJ
ejpam-6607	86	7	f(cheap	f(cheap	NOUN
ejpam-6607	86	8	)	)	PUNCT
ejpam-6607	86	9	=	=	PRON
ejpam-6607	86	10	{	{	PUNCT
ejpam-6607	86	11	r3	r3	PROPN
ejpam-6607	86	12	}	}	PUNCT
ejpam-6607	86	13	identifies	identify	VERB
ejpam-6607	86	14	r3	r3	PROPN
ejpam-6607	86	15	as	as	ADP
ejpam-6607	86	16	the	the	DET
ejpam-6607	86	17	unique	unique	ADJ
ejpam-6607	86	18	restaurant	restaurant	NOUN
ejpam-6607	86	19	that	that	PRON
ejpam-6607	86	20	is	be	AUX
ejpam-6607	86	21	both	both	PRON
ejpam-6607	86	22	italian	italian	ADJ
ejpam-6607	86	23	and	and	CCONJ
ejpam-6607	86	24	inexpensive	inexpensive	ADJ
ejpam-6607	86	25	,	,	PUNCT
ejpam-6607	86	26	while	while	SCONJ
ejpam-6607	86	27	f(italian	f(italian	ADJ
ejpam-6607	86	28	)	)	PUNCT
ejpam-6607	86	29	∩	∩	NOUN
ejpam-6607	86	30	f(familyfriendly	f(familyfriendly	ADV
ejpam-6607	86	31	)	)	PUNCT
ejpam-6607	86	32	=	=	SYM
ejpam-6607	86	33	{	{	PUNCT
ejpam-6607	86	34	r1	r1	PROPN
ejpam-6607	86	35	,	,	PUNCT
ejpam-6607	86	36	r5	r5	PROPN
ejpam-6607	86	37	}	}	PUNCT
ejpam-6607	86	38	identifies	identify	VERB
ejpam-6607	86	39	the	the	DET
ejpam-6607	86	40	italian	italian	ADJ
ejpam-6607	86	41	restaurants	restaurant	NOUN
ejpam-6607	86	42	suitable	suitable	ADJ
ejpam-6607	86	43	for	for	ADP
ejpam-6607	86	44	families	family	NOUN
ejpam-6607	86	45	.	.	PUNCT
ejpam-6607	87	1	the	the	DET
ejpam-6607	87	2	soft	soft	ADJ
ejpam-6607	87	3	set	set	NOUN
ejpam-6607	87	4	formalism	formalism	NOUN
ejpam-6607	87	5	thus	thus	ADV
ejpam-6607	87	6	enables	enable	VERB
ejpam-6607	87	7	flexible	flexible	ADJ
ejpam-6607	87	8	,	,	PUNCT
ejpam-6607	87	9	parameter	parameter	NOUN
ejpam-6607	87	10	-	-	PUNCT
ejpam-6607	87	11	driven	drive	VERB
ejpam-6607	87	12	filtering	filtering	NOUN
ejpam-6607	87	13	of	of	ADP
ejpam-6607	87	14	u	u	NOUN
ejpam-6607	87	15	under	under	ADP
ejpam-6607	87	16	uncertainty	uncertainty	NOUN
ejpam-6607	87	17	.	.	PUNCT
ejpam-6607	88	1	2.3	2.3	NUM
ejpam-6607	88	2	.	.	PUNCT
ejpam-6607	89	1	hypersoft	hypersoft	NOUN
ejpam-6607	89	2	sets	set	NOUN
ejpam-6607	89	3	let	let	VERB
ejpam-6607	89	4	u	u	PRON
ejpam-6607	89	5	=	=	NOUN
ejpam-6607	89	6	{	{	PUNCT
ejpam-6607	89	7	u1	u1	NOUN
ejpam-6607	89	8	,	,	PUNCT
ejpam-6607	89	9	.	.	PUNCT
ejpam-6607	89	10	.	.	PUNCT
ejpam-6607	90	1	.	.	PUNCT
ejpam-6607	91	1	,	,	PUNCT
ejpam-6607	91	2	un	un	AUX
ejpam-6607	91	3	}	}	PUNCT
ejpam-6607	91	4	be	be	AUX
ejpam-6607	91	5	a	a	DET
ejpam-6607	91	6	finite	finite	ADJ
ejpam-6607	91	7	universe	universe	NOUN
ejpam-6607	91	8	and	and	CCONJ
ejpam-6607	91	9	let	let	VERB
ejpam-6607	91	10	p(u	p(u	NOUN
ejpam-6607	91	11	)	)	PUNCT
ejpam-6607	91	12	denote	denote	VERB
ejpam-6607	91	13	its	its	PRON
ejpam-6607	91	14	power	power	NOUN
ejpam-6607	91	15	set	set	NOUN
ejpam-6607	91	16	.	.	PUNCT
ejpam-6607	92	1	for	for	ADP
ejpam-6607	92	2	a	a	DET
ejpam-6607	92	3	positive	positive	ADJ
ejpam-6607	92	4	integer	integer	NOUN
ejpam-6607	92	5	m	m	NOUN
ejpam-6607	92	6	,	,	PUNCT
ejpam-6607	92	7	let	let	VERB
ejpam-6607	92	8	a1,a2	a1,a2	PROPN
ejpam-6607	92	9	,	,	PUNCT
ejpam-6607	92	10	.	.	PUNCT
ejpam-6607	92	11	.	.	PUNCT
ejpam-6607	93	1	.	.	PUNCT
ejpam-6607	94	1	,	,	PUNCT
ejpam-6607	94	2	am	be	AUX
ejpam-6607	94	3	be	be	AUX
ejpam-6607	94	4	m	m	PROPN
ejpam-6607	94	5	disjoint	disjoint	NOUN
ejpam-6607	94	6	attribute	attribute	NOUN
ejpam-6607	94	7	domains	domain	NOUN
ejpam-6607	94	8	.	.	PUNCT
ejpam-6607	95	1	we	we	PRON
ejpam-6607	95	2	form	form	VERB
ejpam-6607	95	3	their	their	PRON
ejpam-6607	95	4	cartesian	cartesian	ADJ
ejpam-6607	95	5	product	product	NOUN
ejpam-6607	95	6	c	c	NOUN
ejpam-6607	95	7	=	=	NOUN
ejpam-6607	95	8	a1	a1	PROPN
ejpam-6607	95	9	×a2	×a2	PROPN
ejpam-6607	95	10	×	×	PROPN
ejpam-6607	95	11	·	·	PUNCT
ejpam-6607	95	12	·	·	PUNCT
ejpam-6607	95	13	·	·	PUNCT
ejpam-6607	96	1	×	×	NOUN
ejpam-6607	96	2	am	be	AUX
ejpam-6607	96	3	,	,	PUNCT
ejpam-6607	96	4	so	so	SCONJ
ejpam-6607	96	5	that	that	SCONJ
ejpam-6607	96	6	each	each	DET
ejpam-6607	96	7	γ	γ	PROPN
ejpam-6607	96	8	∈	∈	PROPN
ejpam-6607	96	9	c	c	NOUN
ejpam-6607	96	10	is	be	AUX
ejpam-6607	96	11	an	an	DET
ejpam-6607	96	12	m	m	NOUN
ejpam-6607	96	13	-	-	PUNCT
ejpam-6607	96	14	tuple	tuple	ADJ
ejpam-6607	96	15	γ	γ	X
ejpam-6607	96	16	=	=	SYM
ejpam-6607	96	17	(	(	PUNCT
ejpam-6607	96	18	γ1	γ1	PROPN
ejpam-6607	96	19	,	,	PUNCT
ejpam-6607	96	20	γ2	γ2	PROPN
ejpam-6607	96	21	,	,	PUNCT
ejpam-6607	96	22	.	.	PUNCT
ejpam-6607	96	23	.	.	PUNCT
ejpam-6607	96	24	.	.	PUNCT
ejpam-6607	97	1	,	,	PUNCT
ejpam-6607	97	2	γm	γm	ADJ
ejpam-6607	97	3	)	)	PUNCT
ejpam-6607	97	4	,	,	PUNCT
ejpam-6607	97	5	γi	γi	X
ejpam-6607	97	6	∈	∈	PRON
ejpam-6607	97	7	ai	ai	VERB
ejpam-6607	97	8	.	.	PUNCT
ejpam-6607	98	1	a	a	DET
ejpam-6607	98	2	hypersoft	hypersoft	NOUN
ejpam-6607	98	3	set	set	VERB
ejpam-6607	98	4	over	over	ADP
ejpam-6607	98	5	u	u	NOUN
ejpam-6607	98	6	is	be	AUX
ejpam-6607	98	7	then	then	ADV
ejpam-6607	98	8	defined	define	VERB
ejpam-6607	98	9	as	as	SCONJ
ejpam-6607	98	10	follows	follow	VERB
ejpam-6607	98	11	.	.	PUNCT
ejpam-6607	99	1	t.	t.	PROPN
ejpam-6607	99	2	fujita	fujita	PROPN
ejpam-6607	99	3	,	,	PUNCT
ejpam-6607	99	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	99	5	/	/	SYM
ejpam-6607	99	6	eur	eur	PROPN
ejpam-6607	99	7	.	.	PUNCT
ejpam-6607	100	1	j.	j.	PROPN
ejpam-6607	100	2	pure	pure	PROPN
ejpam-6607	100	3	appl	appl	PROPN
ejpam-6607	100	4	.	.	PROPN
ejpam-6607	100	5	math	math	PROPN
ejpam-6607	100	6	,	,	PUNCT
ejpam-6607	100	7	18	18	NUM
ejpam-6607	100	8	(	(	PUNCT
ejpam-6607	100	9	3	3	NUM
ejpam-6607	100	10	)	)	PUNCT
ejpam-6607	100	11	(	(	PUNCT
ejpam-6607	100	12	2025	2025	NUM
ejpam-6607	100	13	)	)	PUNCT
ejpam-6607	100	14	,	,	PUNCT
ejpam-6607	100	15	6607	6607	NUM
ejpam-6607	100	16	6	6	NUM
ejpam-6607	100	17	of	of	ADP
ejpam-6607	100	18	33	33	NUM
ejpam-6607	100	19	definition	definition	NOUN
ejpam-6607	100	20	2	2	NUM
ejpam-6607	100	21	(	(	PUNCT
ejpam-6607	100	22	hypersoft	hypersoft	NOUN
ejpam-6607	100	23	set	set	VERB
ejpam-6607	100	24	[	[	X
ejpam-6607	100	25	21	21	NUM
ejpam-6607	100	26	]	]	PUNCT
ejpam-6607	100	27	)	)	PUNCT
ejpam-6607	100	28	.	.	PUNCT
ejpam-6607	101	1	a	a	DET
ejpam-6607	101	2	hypersoft	hypersoft	NOUN
ejpam-6607	101	3	set	set	VERB
ejpam-6607	101	4	over	over	ADP
ejpam-6607	101	5	u	u	NOUN
ejpam-6607	101	6	with	with	ADP
ejpam-6607	101	7	respect	respect	NOUN
ejpam-6607	101	8	to	to	ADP
ejpam-6607	101	9	the	the	DET
ejpam-6607	101	10	attribute	attribute	NOUN
ejpam-6607	101	11	product	product	NOUN
ejpam-6607	101	12	c	c	NOUN
ejpam-6607	101	13	is	be	AUX
ejpam-6607	101	14	a	a	DET
ejpam-6607	101	15	pair	pair	NOUN
ejpam-6607	101	16	(	(	PUNCT
ejpam-6607	101	17	g	g	NOUN
ejpam-6607	101	18	,	,	PUNCT
ejpam-6607	101	19	c	c	NOUN
ejpam-6607	101	20	)	)	PUNCT
ejpam-6607	101	21	where	where	SCONJ
ejpam-6607	101	22	g	g	NOUN
ejpam-6607	101	23	:	:	PUNCT
ejpam-6607	101	24	c	c	X
ejpam-6607	101	25	−→	−→	NOUN
ejpam-6607	101	26	p(u	p(u	NOUN
ejpam-6607	101	27	)	)	PUNCT
ejpam-6607	101	28	is	be	AUX
ejpam-6607	101	29	a	a	DET
ejpam-6607	101	30	function	function	NOUN
ejpam-6607	101	31	assigning	assign	VERB
ejpam-6607	101	32	to	to	ADP
ejpam-6607	101	33	each	each	DET
ejpam-6607	101	34	γ	γ	X
ejpam-6607	101	35	∈	∈	PROPN
ejpam-6607	101	36	c	c	PROPN
ejpam-6607	101	37	a	a	DET
ejpam-6607	101	38	subset	subset	ADJ
ejpam-6607	101	39	g(γ	g(γ	PROPN
ejpam-6607	101	40	)	)	PUNCT
ejpam-6607	101	41	⊆	⊆	NUM
ejpam-6607	101	42	u	u	NOUN
ejpam-6607	101	43	.	.	PUNCT
ejpam-6607	102	1	equivalently	equivalently	ADV
ejpam-6607	102	2	,	,	PUNCT
ejpam-6607	102	3	(	(	PUNCT
ejpam-6607	102	4	g	g	NOUN
ejpam-6607	102	5	,	,	PUNCT
ejpam-6607	102	6	c	c	NOUN
ejpam-6607	102	7	)	)	PUNCT
ejpam-6607	102	8	=	=	SYM
ejpam-6607	102	9	{	{	PUNCT
ejpam-6607	102	10	(	(	PUNCT
ejpam-6607	102	11	γ	γ	X
ejpam-6607	102	12	,	,	PUNCT
ejpam-6607	102	13	g(γ	g(γ	PROPN
ejpam-6607	102	14	)	)	PUNCT
ejpam-6607	102	15	)	)	PUNCT
ejpam-6607	103	1	|	|	ADV
ejpam-6607	103	2	γ	γ	X
ejpam-6607	103	3	∈	∈	PROPN
ejpam-6607	103	4	c	c	X
ejpam-6607	103	5	,	,	PUNCT
ejpam-6607	103	6	g(γ	g(γ	PROPN
ejpam-6607	103	7	)	)	PUNCT
ejpam-6607	103	8	⊆	⊆	NUM
ejpam-6607	103	9	u	u	NOUN
ejpam-6607	103	10	}	}	PUNCT
ejpam-6607	103	11	.	.	PUNCT
ejpam-6607	104	1	example	example	NOUN
ejpam-6607	104	2	2	2	NUM
ejpam-6607	104	3	(	(	PUNCT
ejpam-6607	104	4	laptop	laptop	NOUN
ejpam-6607	104	5	purchase	purchase	NOUN
ejpam-6607	104	6	)	)	PUNCT
ejpam-6607	104	7	.	.	PUNCT
ejpam-6607	105	1	let	let	VERB
ejpam-6607	105	2	u	u	PRON
ejpam-6607	105	3	=	=	X
ejpam-6607	105	4	{	{	PUNCT
ejpam-6607	105	5	xps13	xps13	NOUN
ejpam-6607	105	6	,	,	PUNCT
ejpam-6607	105	7	envy13	envy13	ADV
ejpam-6607	105	8	,	,	PUNCT
ejpam-6607	105	9	macbookair	macbookair	NOUN
ejpam-6607	105	10	,	,	PUNCT
ejpam-6607	105	11	zenbook	zenbook	PROPN
ejpam-6607	105	12	,	,	PUNCT
ejpam-6607	105	13	thinkpad	thinkpad	PROPN
ejpam-6607	105	14	}	}	PUNCT
ejpam-6607	105	15	be	be	AUX
ejpam-6607	105	16	a	a	DET
ejpam-6607	105	17	set	set	NOUN
ejpam-6607	105	18	of	of	ADP
ejpam-6607	105	19	laptop	laptop	NOUN
ejpam-6607	105	20	models	model	NOUN
ejpam-6607	105	21	.	.	PUNCT
ejpam-6607	106	1	consider	consider	VERB
ejpam-6607	106	2	three	three	NUM
ejpam-6607	106	3	attribute	attribute	NOUN
ejpam-6607	106	4	domains	domain	NOUN
ejpam-6607	106	5	:	:	PUNCT
ejpam-6607	106	6	a1	a1	NOUN
ejpam-6607	106	7	=	=	SYM
ejpam-6607	106	8	{	{	PUNCT
ejpam-6607	106	9	dell	dell	NOUN
ejpam-6607	106	10	,	,	PUNCT
ejpam-6607	106	11	hp	hp	NOUN
ejpam-6607	106	12	,	,	PUNCT
ejpam-6607	106	13	apple	apple	NOUN
ejpam-6607	106	14	}	}	PUNCT
ejpam-6607	106	15	,	,	PUNCT
ejpam-6607	106	16	a2	a2	PROPN
ejpam-6607	106	17	=	=	PUNCT
ejpam-6607	106	18	{	{	PUNCT
ejpam-6607	106	19	under1k	under1k	NOUN
ejpam-6607	106	20	,	,	PUNCT
ejpam-6607	106	21	1k–2k	1k–2k	NOUN
ejpam-6607	106	22	,	,	PUNCT
ejpam-6607	106	23	over2k	over2k	ADJ
ejpam-6607	106	24	}	}	PUNCT
ejpam-6607	106	25	,	,	PUNCT
ejpam-6607	106	26	a3	a3	NOUN
ejpam-6607	106	27	=	=	SYM
ejpam-6607	106	28	{	{	PUNCT
ejpam-6607	106	29	ssd	ssd	PROPN
ejpam-6607	106	30	,	,	PUNCT
ejpam-6607	106	31	hdd	hdd	NOUN
ejpam-6607	106	32	}	}	PUNCT
ejpam-6607	106	33	.	.	PUNCT
ejpam-6607	107	1	form	form	NOUN
ejpam-6607	107	2	c	c	NOUN
ejpam-6607	107	3	=	=	SYM
ejpam-6607	107	4	a1	a1	PROPN
ejpam-6607	107	5	×a2	×a2	PROPN
ejpam-6607	107	6	×a3	×a3	PROPN
ejpam-6607	107	7	,	,	PUNCT
ejpam-6607	107	8	so	so	SCONJ
ejpam-6607	107	9	each	each	DET
ejpam-6607	107	10	γ	γ	X
ejpam-6607	107	11	=	=	SYM
ejpam-6607	107	12	(	(	PUNCT
ejpam-6607	107	13	γ1	γ1	PROPN
ejpam-6607	107	14	,	,	PUNCT
ejpam-6607	107	15	γ2	γ2	PROPN
ejpam-6607	107	16	,	,	PUNCT
ejpam-6607	107	17	γ3	γ3	NOUN
ejpam-6607	107	18	)	)	PUNCT
ejpam-6607	107	19	specifies	specify	VERB
ejpam-6607	107	20	a	a	DET
ejpam-6607	107	21	brand	brand	NOUN
ejpam-6607	107	22	,	,	PUNCT
ejpam-6607	107	23	price	price	NOUN
ejpam-6607	107	24	-	-	PUNCT
ejpam-6607	107	25	range	range	NOUN
ejpam-6607	107	26	,	,	PUNCT
ejpam-6607	107	27	and	and	CCONJ
ejpam-6607	107	28	storage	storage	NOUN
ejpam-6607	107	29	type	type	NOUN
ejpam-6607	107	30	.	.	PUNCT
ejpam-6607	108	1	define	define	VERB
ejpam-6607	108	2	the	the	DET
ejpam-6607	108	3	hypersoft	hypersoft	NOUN
ejpam-6607	108	4	set	set	NOUN
ejpam-6607	108	5	(	(	PUNCT
ejpam-6607	108	6	g	g	NOUN
ejpam-6607	108	7	,	,	PUNCT
ejpam-6607	108	8	c	c	NOUN
ejpam-6607	108	9	)	)	PUNCT
ejpam-6607	108	10	by	by	ADP
ejpam-6607	108	11	:	:	PUNCT
ejpam-6607	108	12	g	g	PROPN
ejpam-6607	108	13	(	(	PUNCT
ejpam-6607	108	14	(	(	PUNCT
ejpam-6607	108	15	dell	dell	NOUN
ejpam-6607	108	16	,	,	PUNCT
ejpam-6607	108	17	1k−2k	1k−2k	NUM
ejpam-6607	108	18	,	,	PUNCT
ejpam-6607	108	19	ssd	ssd	NOUN
ejpam-6607	108	20	)	)	PUNCT
ejpam-6607	108	21	)	)	PUNCT
ejpam-6607	109	1	=	=	PRON
ejpam-6607	109	2	{	{	PUNCT
ejpam-6607	109	3	xps13	xps13	NOUN
ejpam-6607	109	4	,	,	PUNCT
ejpam-6607	109	5	envy13	envy13	ADV
ejpam-6607	109	6	}	}	PUNCT
ejpam-6607	109	7	,	,	PUNCT
ejpam-6607	109	8	g	g	PROPN
ejpam-6607	109	9	(	(	PUNCT
ejpam-6607	109	10	(	(	PUNCT
ejpam-6607	109	11	apple	apple	NOUN
ejpam-6607	109	12	,	,	PUNCT
ejpam-6607	109	13	over2k	over2k	ADJ
ejpam-6607	109	14	,	,	PUNCT
ejpam-6607	109	15	ssd	ssd	NOUN
ejpam-6607	109	16	)	)	PUNCT
ejpam-6607	109	17	)	)	PUNCT
ejpam-6607	110	1	=	=	PRON
ejpam-6607	111	1	{	{	PUNCT
ejpam-6607	111	2	macbookair	macbookair	NOUN
ejpam-6607	111	3	}	}	PUNCT
ejpam-6607	111	4	,	,	PUNCT
ejpam-6607	111	5	g	g	PROPN
ejpam-6607	111	6	(	(	PUNCT
ejpam-6607	111	7	(	(	PUNCT
ejpam-6607	111	8	hp	hp	NOUN
ejpam-6607	111	9	,	,	PUNCT
ejpam-6607	111	10	under1k	under1k	ADJ
ejpam-6607	111	11	,	,	PUNCT
ejpam-6607	111	12	hdd	hdd	NOUN
ejpam-6607	111	13	)	)	PUNCT
ejpam-6607	111	14	)	)	PUNCT
ejpam-6607	112	1	=	=	PRON
ejpam-6607	112	2	{	{	PUNCT
ejpam-6607	112	3	envy13	envy13	ADV
ejpam-6607	112	4	}	}	PUNCT
ejpam-6607	112	5	,	,	PUNCT
ejpam-6607	112	6	g	g	PROPN
ejpam-6607	112	7	(	(	PUNCT
ejpam-6607	112	8	(	(	PUNCT
ejpam-6607	112	9	apple	apple	NOUN
ejpam-6607	112	10	,	,	PUNCT
ejpam-6607	112	11	1k−2k	1k−2k	NUM
ejpam-6607	112	12	,	,	PUNCT
ejpam-6607	112	13	hdd	hdd	NOUN
ejpam-6607	112	14	)	)	PUNCT
ejpam-6607	112	15	)	)	PUNCT
ejpam-6607	112	16	=	=	PRON
ejpam-6607	112	17	{	{	PUNCT
ejpam-6607	112	18	macbookair	macbookair	NOUN
ejpam-6607	112	19	,	,	PUNCT
ejpam-6607	112	20	zenbook	zenbook	PROPN
ejpam-6607	112	21	}	}	PUNCT
ejpam-6607	112	22	,	,	PUNCT
ejpam-6607	112	23	g	g	PROPN
ejpam-6607	112	24	(	(	PUNCT
ejpam-6607	112	25	(	(	PUNCT
ejpam-6607	112	26	dell	dell	NOUN
ejpam-6607	112	27	,	,	PUNCT
ejpam-6607	112	28	under1k	under1k	NOUN
ejpam-6607	112	29	,	,	PUNCT
ejpam-6607	112	30	ssd	ssd	NOUN
ejpam-6607	112	31	)	)	PUNCT
ejpam-6607	112	32	)	)	PUNCT
ejpam-6607	112	33	=	=	PRON
ejpam-6607	112	34	{	{	PUNCT
ejpam-6607	112	35	zenbook	zenbook	NOUN
ejpam-6607	112	36	}	}	PUNCT
ejpam-6607	112	37	,	,	PUNCT
ejpam-6607	112	38	g	g	PROPN
ejpam-6607	112	39	(	(	PUNCT
ejpam-6607	112	40	(	(	PUNCT
ejpam-6607	112	41	hp	hp	ADJ
ejpam-6607	112	42	,	,	PUNCT
ejpam-6607	112	43	over2k	over2k	ADJ
ejpam-6607	112	44	,	,	PUNCT
ejpam-6607	112	45	ssd	ssd	NOUN
ejpam-6607	112	46	)	)	PUNCT
ejpam-6607	112	47	)	)	PUNCT
ejpam-6607	112	48	=	=	PRON
ejpam-6607	112	49	{	{	PUNCT
ejpam-6607	112	50	thinkpad	thinkpad	NOUN
ejpam-6607	112	51	}	}	PUNCT
ejpam-6607	112	52	.	.	PUNCT
ejpam-6607	113	1	for	for	ADP
ejpam-6607	113	2	example	example	NOUN
ejpam-6607	113	3	,	,	PUNCT
ejpam-6607	113	4	g((dell	g((dell	PROPN
ejpam-6607	113	5	,	,	PUNCT
ejpam-6607	113	6	1k–2k	1k–2k	NOUN
ejpam-6607	113	7	,	,	PUNCT
ejpam-6607	113	8	ssd	ssd	NOUN
ejpam-6607	113	9	)	)	PUNCT
ejpam-6607	113	10	)	)	PUNCT
ejpam-6607	114	1	=	=	PRON
ejpam-6607	114	2	{	{	PUNCT
ejpam-6607	114	3	xps13	xps13	NOUN
ejpam-6607	114	4	,	,	PUNCT
ejpam-6607	114	5	envy13	envy13	ADV
ejpam-6607	114	6	}	}	PUNCT
ejpam-6607	114	7	lists	list	VERB
ejpam-6607	114	8	all	all	DET
ejpam-6607	114	9	dell	dell	NOUN
ejpam-6607	114	10	laptops	laptop	NOUN
ejpam-6607	114	11	in	in	ADP
ejpam-6607	114	12	the	the	DET
ejpam-6607	114	13	$	$	SYM
ejpam-6607	114	14	1k–$2k	1k–$2k	NUM
ejpam-6607	114	15	range	range	NOUN
ejpam-6607	114	16	with	with	ADP
ejpam-6607	114	17	ssd	ssd	NOUN
ejpam-6607	114	18	storage	storage	NOUN
ejpam-6607	114	19	.	.	PUNCT
ejpam-6607	115	1	this	this	DET
ejpam-6607	115	2	hypersoft	hypersoft	PROPN
ejpam-6607	115	3	set	set	NOUN
ejpam-6607	115	4	enables	enable	VERB
ejpam-6607	115	5	a	a	DET
ejpam-6607	115	6	buyer	buyer	NOUN
ejpam-6607	115	7	to	to	PART
ejpam-6607	115	8	filter	filter	NOUN
ejpam-6607	115	9	models	model	NOUN
ejpam-6607	115	10	by	by	ADP
ejpam-6607	115	11	any	any	DET
ejpam-6607	115	12	combination	combination	NOUN
ejpam-6607	115	13	of	of	ADP
ejpam-6607	115	14	brand	brand	NOUN
ejpam-6607	115	15	,	,	PUNCT
ejpam-6607	115	16	price	price	NOUN
ejpam-6607	115	17	,	,	PUNCT
ejpam-6607	115	18	and	and	CCONJ
ejpam-6607	115	19	storage	storage	NOUN
ejpam-6607	115	20	type	type	NOUN
ejpam-6607	115	21	,	,	PUNCT
ejpam-6607	115	22	even	even	ADV
ejpam-6607	115	23	when	when	SCONJ
ejpam-6607	115	24	some	some	DET
ejpam-6607	115	25	models	model	NOUN
ejpam-6607	115	26	lack	lack	VERB
ejpam-6607	115	27	complete	complete	ADJ
ejpam-6607	115	28	attribute	attribute	NOUN
ejpam-6607	115	29	information	information	NOUN
ejpam-6607	115	30	.	.	PUNCT
ejpam-6607	116	1	2.4	2.4	NUM
ejpam-6607	116	2	.	.	X
ejpam-6607	117	1	superhypersoft	superhypersoft	PROPN
ejpam-6607	117	2	sets	set	VERB
ejpam-6607	117	3	let	let	VERB
ejpam-6607	117	4	u	u	PRON
ejpam-6607	117	5	=	=	NOUN
ejpam-6607	117	6	{	{	PUNCT
ejpam-6607	117	7	u1	u1	NOUN
ejpam-6607	117	8	,	,	PUNCT
ejpam-6607	117	9	.	.	PUNCT
ejpam-6607	117	10	.	.	PUNCT
ejpam-6607	118	1	.	.	PUNCT
ejpam-6607	119	1	,	,	PUNCT
ejpam-6607	119	2	un	un	AUX
ejpam-6607	119	3	}	}	PUNCT
ejpam-6607	119	4	be	be	AUX
ejpam-6607	119	5	a	a	DET
ejpam-6607	119	6	finite	finite	ADJ
ejpam-6607	119	7	universe	universe	NOUN
ejpam-6607	119	8	and	and	CCONJ
ejpam-6607	119	9	let	let	VERB
ejpam-6607	119	10	p(u	p(u	NOUN
ejpam-6607	119	11	)	)	PUNCT
ejpam-6607	119	12	denote	denote	VERB
ejpam-6607	119	13	its	its	PRON
ejpam-6607	119	14	power	power	NOUN
ejpam-6607	119	15	set	set	NOUN
ejpam-6607	119	16	.	.	PUNCT
ejpam-6607	120	1	let	let	VERB
ejpam-6607	120	2	m	m	PRON
ejpam-6607	120	3	be	be	AUX
ejpam-6607	120	4	a	a	DET
ejpam-6607	120	5	positive	positive	ADJ
ejpam-6607	120	6	integer	integer	NOUN
ejpam-6607	120	7	,	,	PUNCT
ejpam-6607	120	8	and	and	CCONJ
ejpam-6607	120	9	let	let	VERB
ejpam-6607	120	10	a1	a1	NOUN
ejpam-6607	120	11	,	,	PUNCT
ejpam-6607	120	12	a2	a2	PROPN
ejpam-6607	120	13	,	,	PUNCT
ejpam-6607	120	14	.	.	PUNCT
ejpam-6607	120	15	.	.	PUNCT
ejpam-6607	121	1	.	.	PUNCT
ejpam-6607	122	1	,	,	PUNCT
ejpam-6607	122	2	am	be	AUX
ejpam-6607	122	3	be	be	AUX
ejpam-6607	122	4	m	m	PROPN
ejpam-6607	122	5	pairwise	pairwise	NOUN
ejpam-6607	122	6	disjoint	disjoint	NOUN
ejpam-6607	122	7	finite	finite	PROPN
ejpam-6607	122	8	attribute	attribute	NOUN
ejpam-6607	122	9	value	value	NOUN
ejpam-6607	122	10	–	–	PUNCT
ejpam-6607	122	11	sets	set	NOUN
ejpam-6607	122	12	:	:	PUNCT
ejpam-6607	122	13	ai	ai	VERB
ejpam-6607	122	14	∩aj	∩aj	NOUN
ejpam-6607	122	15	=	=	NOUN
ejpam-6607	122	16	∅	∅	NOUN
ejpam-6607	122	17	(	(	PUNCT
ejpam-6607	122	18	i	i	PRON
ejpam-6607	122	19	̸=	̸=	PROPN
ejpam-6607	122	20	j	j	PROPN
ejpam-6607	122	21	)	)	PUNCT
ejpam-6607	122	22	.	.	PUNCT
ejpam-6607	123	1	t.	t.	PROPN
ejpam-6607	123	2	fujita	fujita	PROPN
ejpam-6607	123	3	,	,	PUNCT
ejpam-6607	123	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	123	5	/	/	SYM
ejpam-6607	123	6	eur	eur	PROPN
ejpam-6607	123	7	.	.	PUNCT
ejpam-6607	124	1	j.	j.	PROPN
ejpam-6607	124	2	pure	pure	PROPN
ejpam-6607	124	3	appl	appl	PROPN
ejpam-6607	124	4	.	.	PROPN
ejpam-6607	124	5	math	math	PROPN
ejpam-6607	124	6	,	,	PUNCT
ejpam-6607	124	7	18	18	NUM
ejpam-6607	124	8	(	(	PUNCT
ejpam-6607	124	9	3	3	NUM
ejpam-6607	124	10	)	)	PUNCT
ejpam-6607	124	11	(	(	PUNCT
ejpam-6607	124	12	2025	2025	NUM
ejpam-6607	124	13	)	)	PUNCT
ejpam-6607	124	14	,	,	PUNCT
ejpam-6607	124	15	6607	6607	NUM
ejpam-6607	124	16	7	7	NUM
ejpam-6607	124	17	of	of	ADP
ejpam-6607	124	18	33	33	NUM
ejpam-6607	124	19	for	for	ADP
ejpam-6607	124	20	each	each	DET
ejpam-6607	124	21	i	i	PROPN
ejpam-6607	124	22	,	,	PUNCT
ejpam-6607	124	23	write	write	VERB
ejpam-6607	124	24	p(ai	p(ai	NOUN
ejpam-6607	124	25	)	)	PUNCT
ejpam-6607	124	26	for	for	ADP
ejpam-6607	124	27	the	the	DET
ejpam-6607	124	28	power	power	NOUN
ejpam-6607	124	29	set	set	NOUN
ejpam-6607	124	30	of	of	ADP
ejpam-6607	124	31	ai	ai	NOUN
ejpam-6607	124	32	,	,	PUNCT
ejpam-6607	124	33	and	and	CCONJ
ejpam-6607	124	34	form	form	VERB
ejpam-6607	124	35	the	the	DET
ejpam-6607	124	36	cartesian	cartesian	ADJ
ejpam-6607	124	37	product	product	NOUN
ejpam-6607	124	38	c	c	NOUN
ejpam-6607	124	39	=	=	PUNCT
ejpam-6607	124	40	p(a1)×	p(a1)×	PROPN
ejpam-6607	124	41	p(a2)×	p(a2)×	NOUN
ejpam-6607	124	42	·	·	PUNCT
ejpam-6607	124	43	·	·	PUNCT
ejpam-6607	124	44	·	·	PUNCT
ejpam-6607	125	1	×	×	PROPN
ejpam-6607	125	2	p(am	p(am	NOUN
ejpam-6607	125	3	)	)	PUNCT
ejpam-6607	125	4	.	.	PUNCT
ejpam-6607	126	1	each	each	DET
ejpam-6607	126	2	element	element	NOUN
ejpam-6607	126	3	γ	γ	PROPN
ejpam-6607	126	4	∈	∈	PROPN
ejpam-6607	126	5	c	c	NOUN
ejpam-6607	126	6	is	be	AUX
ejpam-6607	126	7	an	an	DET
ejpam-6607	126	8	m	m	NOUN
ejpam-6607	126	9	-	-	PUNCT
ejpam-6607	126	10	tuple	tuple	ADJ
ejpam-6607	126	11	γ	γ	X
ejpam-6607	126	12	=	=	SYM
ejpam-6607	126	13	(	(	PUNCT
ejpam-6607	126	14	α1	α1	PROPN
ejpam-6607	126	15	,	,	PUNCT
ejpam-6607	126	16	α2	α2	ADJ
ejpam-6607	126	17	,	,	PUNCT
ejpam-6607	126	18	.	.	PUNCT
ejpam-6607	126	19	.	.	PUNCT
ejpam-6607	127	1	.	.	PUNCT
ejpam-6607	128	1	,	,	PUNCT
ejpam-6607	128	2	αm	αm	INTJ
ejpam-6607	128	3	)	)	PUNCT
ejpam-6607	128	4	,	,	PUNCT
ejpam-6607	128	5	αi	αi	VERB
ejpam-6607	128	6	⊆	⊆	NUM
ejpam-6607	128	7	ai	ai	NOUN
ejpam-6607	128	8	.	.	PUNCT
ejpam-6607	129	1	a	a	DET
ejpam-6607	129	2	superhypersoft	superhypersoft	NOUN
ejpam-6607	129	3	set	set	VERB
ejpam-6607	129	4	over	over	ADP
ejpam-6607	129	5	u	u	NOUN
ejpam-6607	129	6	is	be	AUX
ejpam-6607	129	7	defined	define	VERB
ejpam-6607	129	8	as	as	ADP
ejpam-6607	129	9	follows	follow	VERB
ejpam-6607	129	10	.	.	PUNCT
ejpam-6607	130	1	definition	definition	NOUN
ejpam-6607	130	2	3	3	NUM
ejpam-6607	130	3	(	(	PUNCT
ejpam-6607	130	4	superhypersoft	superhypersoft	NOUN
ejpam-6607	130	5	set	set	VERB
ejpam-6607	130	6	[	[	X
ejpam-6607	130	7	23	23	NUM
ejpam-6607	130	8	]	]	PUNCT
ejpam-6607	130	9	)	)	PUNCT
ejpam-6607	130	10	.	.	PUNCT
ejpam-6607	131	1	a	a	DET
ejpam-6607	131	2	superhypersoft	superhypersoft	NOUN
ejpam-6607	131	3	set	set	VERB
ejpam-6607	131	4	over	over	ADP
ejpam-6607	131	5	the	the	DET
ejpam-6607	131	6	universe	universe	ADJ
ejpam-6607	131	7	u	u	NOUN
ejpam-6607	131	8	with	with	ADP
ejpam-6607	131	9	respect	respect	NOUN
ejpam-6607	131	10	to	to	ADP
ejpam-6607	131	11	the	the	DET
ejpam-6607	131	12	attribute	attribute	NOUN
ejpam-6607	131	13	–	–	PUNCT
ejpam-6607	131	14	power	power	NOUN
ejpam-6607	131	15	product	product	NOUN
ejpam-6607	131	16	c	c	NOUN
ejpam-6607	131	17	is	be	AUX
ejpam-6607	131	18	a	a	DET
ejpam-6607	131	19	pair	pair	NOUN
ejpam-6607	131	20	(	(	PUNCT
ejpam-6607	131	21	f	f	X
ejpam-6607	131	22	,	,	PUNCT
ejpam-6607	131	23	c	c	NOUN
ejpam-6607	131	24	)	)	PUNCT
ejpam-6607	131	25	where	where	SCONJ
ejpam-6607	131	26	f	f	NOUN
ejpam-6607	131	27	:	:	PUNCT
ejpam-6607	131	28	c	c	X
ejpam-6607	131	29	−→	−→	NOUN
ejpam-6607	131	30	p(u	p(u	NOUN
ejpam-6607	131	31	)	)	PUNCT
ejpam-6607	131	32	assigns	assign	NOUN
ejpam-6607	131	33	to	to	ADP
ejpam-6607	131	34	each	each	DET
ejpam-6607	131	35	γ	γ	X
ejpam-6607	131	36	∈	∈	PROPN
ejpam-6607	131	37	c	c	PROPN
ejpam-6607	131	38	a	a	DET
ejpam-6607	131	39	subset	subset	NOUN
ejpam-6607	131	40	f	f	X
ejpam-6607	131	41	(	(	PUNCT
ejpam-6607	131	42	γ	γ	PROPN
ejpam-6607	131	43	)	)	PUNCT
ejpam-6607	131	44	⊆	⊆	NUM
ejpam-6607	131	45	u	u	NOUN
ejpam-6607	131	46	.	.	PUNCT
ejpam-6607	132	1	equivalently	equivalently	ADV
ejpam-6607	132	2	,	,	PUNCT
ejpam-6607	132	3	(	(	PUNCT
ejpam-6607	132	4	f	f	X
ejpam-6607	132	5	,	,	PUNCT
ejpam-6607	132	6	c	c	NOUN
ejpam-6607	132	7	)	)	PUNCT
ejpam-6607	132	8	=	=	SYM
ejpam-6607	132	9	{	{	PUNCT
ejpam-6607	132	10	(	(	PUNCT
ejpam-6607	132	11	γ	γ	PROPN
ejpam-6607	132	12	,	,	PUNCT
ejpam-6607	132	13	f	f	PROPN
ejpam-6607	132	14	(	(	PUNCT
ejpam-6607	132	15	γ	γ	PROPN
ejpam-6607	132	16	)	)	PUNCT
ejpam-6607	132	17	)	)	PUNCT
ejpam-6607	133	1	|	|	ADV
ejpam-6607	133	2	γ	γ	X
ejpam-6607	133	3	∈	∈	PROPN
ejpam-6607	133	4	c	c	PROPN
ejpam-6607	133	5	,	,	PUNCT
ejpam-6607	133	6	f	f	PROPN
ejpam-6607	133	7	(	(	PUNCT
ejpam-6607	133	8	γ	γ	PROPN
ejpam-6607	133	9	)	)	PUNCT
ejpam-6607	133	10	⊆	⊆	NUM
ejpam-6607	133	11	u	u	NOUN
ejpam-6607	133	12	}	}	PUNCT
ejpam-6607	133	13	.	.	PUNCT
ejpam-6607	134	1	example	example	NOUN
ejpam-6607	134	2	3	3	NUM
ejpam-6607	134	3	(	(	PUNCT
ejpam-6607	134	4	laptop	laptop	NOUN
ejpam-6607	134	5	selection	selection	NOUN
ejpam-6607	134	6	)	)	PUNCT
ejpam-6607	134	7	.	.	PUNCT
ejpam-6607	135	1	let	let	VERB
ejpam-6607	135	2	u	u	PRON
ejpam-6607	135	3	=	=	X
ejpam-6607	135	4	{	{	PUNCT
ejpam-6607	135	5	xps13	xps13	NOUN
ejpam-6607	135	6	,	,	PUNCT
ejpam-6607	135	7	envy13	envy13	ADV
ejpam-6607	135	8	,	,	PUNCT
ejpam-6607	135	9	macbookair	macbookair	NOUN
ejpam-6607	135	10	,	,	PUNCT
ejpam-6607	135	11	macbookpro	macbookpro	ADJ
ejpam-6607	135	12	}	}	PUNCT
ejpam-6607	135	13	.	.	PUNCT
ejpam-6607	136	1	consider	consider	VERB
ejpam-6607	136	2	three	three	NUM
ejpam-6607	136	3	attribute	attribute	NOUN
ejpam-6607	136	4	value	value	NOUN
ejpam-6607	136	5	–	–	PUNCT
ejpam-6607	136	6	sets	set	NOUN
ejpam-6607	136	7	:	:	PUNCT
ejpam-6607	136	8	a1	a1	NOUN
ejpam-6607	136	9	=	=	SYM
ejpam-6607	136	10	{	{	PUNCT
ejpam-6607	136	11	dell	dell	NOUN
ejpam-6607	136	12	,	,	PUNCT
ejpam-6607	136	13	hp	hp	NOUN
ejpam-6607	136	14	,	,	PUNCT
ejpam-6607	136	15	apple	apple	NOUN
ejpam-6607	136	16	}	}	PUNCT
ejpam-6607	136	17	,	,	PUNCT
ejpam-6607	136	18	a2	a2	PROPN
ejpam-6607	136	19	=	=	SYM
ejpam-6607	136	20	{	{	PUNCT
ejpam-6607	136	21	i5	i5	ADJ
ejpam-6607	136	22	,	,	PUNCT
ejpam-6607	136	23	i7	i7	NOUN
ejpam-6607	136	24	,	,	PUNCT
ejpam-6607	136	25	i9	i9	NOUN
ejpam-6607	136	26	}	}	PUNCT
ejpam-6607	136	27	,	,	PUNCT
ejpam-6607	136	28	a3	a3	NOUN
ejpam-6607	136	29	=	=	SYM
ejpam-6607	136	30	{	{	PUNCT
ejpam-6607	136	31	budget	budget	NOUN
ejpam-6607	136	32	,	,	PUNCT
ejpam-6607	136	33	midrange	midrange	NOUN
ejpam-6607	136	34	,	,	PUNCT
ejpam-6607	136	35	premium	premium	NOUN
ejpam-6607	136	36	}	}	PUNCT
ejpam-6607	136	37	,	,	PUNCT
ejpam-6607	136	38	which	which	PRON
ejpam-6607	136	39	are	be	AUX
ejpam-6607	136	40	pairwise	pairwise	PROPN
ejpam-6607	136	41	disjoint	disjoint	NOUN
ejpam-6607	136	42	.	.	PUNCT
ejpam-6607	137	1	form	form	NOUN
ejpam-6607	137	2	c	c	NOUN
ejpam-6607	137	3	=	=	PUNCT
ejpam-6607	137	4	p(a1)×	p(a1)×	PROPN
ejpam-6607	137	5	p(a2)×	p(a2)×	NOUN
ejpam-6607	137	6	p(a3	p(a3	NOUN
ejpam-6607	137	7	)	)	PUNCT
ejpam-6607	137	8	.	.	PUNCT
ejpam-6607	138	1	define	define	VERB
ejpam-6607	138	2	the	the	DET
ejpam-6607	138	3	superhypersoft	superhypersoft	NOUN
ejpam-6607	138	4	set	set	NOUN
ejpam-6607	138	5	(	(	PUNCT
ejpam-6607	138	6	f	f	X
ejpam-6607	138	7	,	,	PUNCT
ejpam-6607	138	8	c	c	NOUN
ejpam-6607	138	9	)	)	PUNCT
ejpam-6607	138	10	by	by	ADP
ejpam-6607	138	11	,	,	PUNCT
ejpam-6607	138	12	for	for	ADP
ejpam-6607	138	13	example	example	NOUN
ejpam-6607	138	14	,	,	PUNCT
ejpam-6607	138	15	f	f	PROPN
ejpam-6607	138	16	(	(	PUNCT
ejpam-6607	138	17	{	{	PUNCT
ejpam-6607	138	18	dell	dell	NOUN
ejpam-6607	138	19	,	,	PUNCT
ejpam-6607	138	20	hp	hp	PROPN
ejpam-6607	138	21	}	}	PUNCT
ejpam-6607	138	22	,	,	PUNCT
ejpam-6607	138	23	{	{	PUNCT
ejpam-6607	138	24	i7	i7	NOUN
ejpam-6607	138	25	}	}	PUNCT
ejpam-6607	138	26	,	,	PUNCT
ejpam-6607	138	27	{	{	PUNCT
ejpam-6607	138	28	midrange	midrange	NOUN
ejpam-6607	138	29	}	}	PUNCT
ejpam-6607	138	30	)	)	PUNCT
ejpam-6607	139	1	=	=	SYM
ejpam-6607	139	2	{	{	PUNCT
ejpam-6607	139	3	xps13	xps13	NOUN
ejpam-6607	139	4	,	,	PUNCT
ejpam-6607	139	5	envy13	envy13	ADV
ejpam-6607	139	6	}	}	PUNCT
ejpam-6607	139	7	,	,	PUNCT
ejpam-6607	139	8	f	f	PROPN
ejpam-6607	139	9	(	(	PUNCT
ejpam-6607	139	10	{	{	PUNCT
ejpam-6607	139	11	apple	apple	NOUN
ejpam-6607	139	12	}	}	PUNCT
ejpam-6607	139	13	,	,	PUNCT
ejpam-6607	139	14	{	{	PUNCT
ejpam-6607	139	15	i5	i5	ADJ
ejpam-6607	139	16	,	,	PUNCT
ejpam-6607	139	17	i7	i7	NOUN
ejpam-6607	139	18	}	}	PUNCT
ejpam-6607	139	19	,	,	PUNCT
ejpam-6607	139	20	{	{	PUNCT
ejpam-6607	139	21	premium	premium	NOUN
ejpam-6607	139	22	}	}	PUNCT
ejpam-6607	139	23	)	)	PUNCT
ejpam-6607	139	24	=	=	PRON
ejpam-6607	139	25	{	{	PUNCT
ejpam-6607	139	26	macbookair	macbookair	NOUN
ejpam-6607	139	27	,	,	PUNCT
ejpam-6607	139	28	macbookpro	macbookpro	ADJ
ejpam-6607	139	29	}	}	PUNCT
ejpam-6607	139	30	.	.	PUNCT
ejpam-6607	140	1	here	here	ADV
ejpam-6607	140	2	:	:	PUNCT
ejpam-6607	140	3	•	•	NUM
ejpam-6607	140	4	γ1	γ1	NOUN
ejpam-6607	140	5	=	=	SYM
ejpam-6607	140	6	(	(	PUNCT
ejpam-6607	140	7	{	{	PUNCT
ejpam-6607	140	8	dell	dell	NOUN
ejpam-6607	140	9	,	,	PUNCT
ejpam-6607	140	10	hp	hp	PROPN
ejpam-6607	140	11	}	}	PUNCT
ejpam-6607	140	12	,	,	PUNCT
ejpam-6607	140	13	{	{	PUNCT
ejpam-6607	140	14	i7	i7	NOUN
ejpam-6607	140	15	}	}	PUNCT
ejpam-6607	140	16	,	,	PUNCT
ejpam-6607	140	17	{	{	PUNCT
ejpam-6607	140	18	midrange	midrange	NOUN
ejpam-6607	140	19	}	}	PUNCT
ejpam-6607	140	20	)	)	PUNCT
ejpam-6607	140	21	yields	yield	VERB
ejpam-6607	140	22	f	f	PROPN
ejpam-6607	140	23	(	(	PUNCT
ejpam-6607	140	24	γ1	γ1	PROPN
ejpam-6607	140	25	)	)	PUNCT
ejpam-6607	140	26	=	=	PUNCT
ejpam-6607	140	27	{	{	PUNCT
ejpam-6607	140	28	xps13,envy13	xps13,envy13	NUM
ejpam-6607	140	29	}	}	PUNCT
ejpam-6607	140	30	,	,	PUNCT
ejpam-6607	140	31	the	the	DET
ejpam-6607	140	32	midrange	midrange	ADJ
ejpam-6607	140	33	i7	i7	NOUN
ejpam-6607	140	34	models	model	NOUN
ejpam-6607	140	35	from	from	ADP
ejpam-6607	140	36	dell	dell	NOUN
ejpam-6607	140	37	and	and	CCONJ
ejpam-6607	140	38	hp	hp	PROPN
ejpam-6607	140	39	.	.	PROPN
ejpam-6607	140	40	•	•	NOUN
ejpam-6607	140	41	γ2	γ2	PROPN
ejpam-6607	140	42	=	=	SYM
ejpam-6607	140	43	(	(	PUNCT
ejpam-6607	140	44	{	{	PUNCT
ejpam-6607	140	45	apple	apple	NOUN
ejpam-6607	140	46	}	}	PUNCT
ejpam-6607	140	47	,	,	PUNCT
ejpam-6607	140	48	{	{	PUNCT
ejpam-6607	140	49	i5	i5	ADJ
ejpam-6607	140	50	,	,	PUNCT
ejpam-6607	140	51	i7	i7	NOUN
ejpam-6607	140	52	}	}	PUNCT
ejpam-6607	140	53	,	,	PUNCT
ejpam-6607	140	54	{	{	PUNCT
ejpam-6607	140	55	premium	premium	NOUN
ejpam-6607	140	56	}	}	PUNCT
ejpam-6607	140	57	)	)	PUNCT
ejpam-6607	140	58	yields	yield	VERB
ejpam-6607	140	59	f	f	PROPN
ejpam-6607	140	60	(	(	PUNCT
ejpam-6607	140	61	γ2	γ2	PROPN
ejpam-6607	140	62	)	)	PUNCT
ejpam-6607	140	63	=	=	SYM
ejpam-6607	140	64	{	{	PUNCT
ejpam-6607	140	65	macbookair	macbookair	NOUN
ejpam-6607	140	66	,	,	PUNCT
ejpam-6607	140	67	macbookpro	macbookpro	ADJ
ejpam-6607	140	68	}	}	PUNCT
ejpam-6607	140	69	,	,	PUNCT
ejpam-6607	140	70	the	the	DET
ejpam-6607	140	71	premium	premium	NOUN
ejpam-6607	140	72	apple	apple	NOUN
ejpam-6607	140	73	models	model	NOUN
ejpam-6607	140	74	.	.	PUNCT
ejpam-6607	141	1	example	example	NOUN
ejpam-6607	141	2	4	4	NUM
ejpam-6607	141	3	(	(	PUNCT
ejpam-6607	141	4	candidate	candidate	NOUN
ejpam-6607	141	5	recruitment	recruitment	NOUN
ejpam-6607	141	6	)	)	PUNCT
ejpam-6607	141	7	.	.	PUNCT
ejpam-6607	142	1	let	let	VERB
ejpam-6607	142	2	u	u	PRON
ejpam-6607	142	3	=	=	PUNCT
ejpam-6607	142	4	{	{	PUNCT
ejpam-6607	142	5	alice	alice	PROPN
ejpam-6607	142	6	,	,	PUNCT
ejpam-6607	142	7	bob	bob	PROPN
ejpam-6607	142	8	,	,	PUNCT
ejpam-6607	142	9	carol	carol	NOUN
ejpam-6607	142	10	}	}	PUNCT
ejpam-6607	142	11	t.	t.	PROPN
ejpam-6607	142	12	fujita	fujita	PROPN
ejpam-6607	142	13	,	,	PUNCT
ejpam-6607	142	14	f.smarandache	f.smarandache	NOUN
ejpam-6607	142	15	/	/	SYM
ejpam-6607	142	16	eur	eur	PROPN
ejpam-6607	142	17	.	.	PUNCT
ejpam-6607	143	1	j.	j.	PROPN
ejpam-6607	143	2	pure	pure	PROPN
ejpam-6607	143	3	appl	appl	PROPN
ejpam-6607	143	4	.	.	PROPN
ejpam-6607	143	5	math	math	PROPN
ejpam-6607	143	6	,	,	PUNCT
ejpam-6607	143	7	18	18	NUM
ejpam-6607	143	8	(	(	PUNCT
ejpam-6607	143	9	3	3	NUM
ejpam-6607	143	10	)	)	PUNCT
ejpam-6607	143	11	(	(	PUNCT
ejpam-6607	143	12	2025	2025	NUM
ejpam-6607	143	13	)	)	PUNCT
ejpam-6607	143	14	,	,	PUNCT
ejpam-6607	143	15	6607	6607	NUM
ejpam-6607	143	16	8	8	NUM
ejpam-6607	143	17	of	of	ADP
ejpam-6607	143	18	33	33	NUM
ejpam-6607	143	19	be	be	AUX
ejpam-6607	143	20	a	a	DET
ejpam-6607	143	21	set	set	NOUN
ejpam-6607	143	22	of	of	ADP
ejpam-6607	143	23	applicants	applicant	NOUN
ejpam-6607	143	24	.	.	PUNCT
ejpam-6607	144	1	consider	consider	VERB
ejpam-6607	144	2	three	three	NUM
ejpam-6607	144	3	attributes	attribute	NOUN
ejpam-6607	144	4	:	:	PUNCT
ejpam-6607	144	5	a1	a1	NOUN
ejpam-6607	144	6	=	=	SYM
ejpam-6607	144	7	{	{	PUNCT
ejpam-6607	144	8	developer	developer	NOUN
ejpam-6607	144	9	,	,	PUNCT
ejpam-6607	144	10	manager	manager	NOUN
ejpam-6607	144	11	}	}	PUNCT
ejpam-6607	144	12	,	,	PUNCT
ejpam-6607	144	13	a2	a2	PROPN
ejpam-6607	144	14	=	=	PUNCT
ejpam-6607	144	15	{	{	PUNCT
ejpam-6607	144	16	java	java	PROPN
ejpam-6607	144	17	,	,	PUNCT
ejpam-6607	144	18	python	python	PROPN
ejpam-6607	144	19	}	}	PUNCT
ejpam-6607	144	20	,	,	PUNCT
ejpam-6607	144	21	a3	a3	NOUN
ejpam-6607	144	22	=	=	SYM
ejpam-6607	144	23	{	{	PUNCT
ejpam-6607	144	24	remote	remote	ADJ
ejpam-6607	144	25	,	,	PUNCT
ejpam-6607	144	26	onsite	onsite	ADJ
ejpam-6607	144	27	}	}	PUNCT
ejpam-6607	144	28	,	,	PUNCT
ejpam-6607	144	29	with	with	ADP
ejpam-6607	144	30	c	c	PROPN
ejpam-6607	144	31	=	=	SYM
ejpam-6607	144	32	p(a1)×	p(a1)×	PROPN
ejpam-6607	144	33	p(a2)×	p(a2)×	NOUN
ejpam-6607	144	34	p(a3	p(a3	NOUN
ejpam-6607	144	35	)	)	PUNCT
ejpam-6607	144	36	.	.	PUNCT
ejpam-6607	145	1	define	define	VERB
ejpam-6607	145	2	f	f	PROPN
ejpam-6607	145	3	(	(	PUNCT
ejpam-6607	145	4	{	{	PUNCT
ejpam-6607	145	5	developer	developer	NOUN
ejpam-6607	145	6	}	}	PUNCT
ejpam-6607	145	7	,	,	PUNCT
ejpam-6607	145	8	{	{	PUNCT
ejpam-6607	145	9	python	python	NOUN
ejpam-6607	145	10	}	}	PUNCT
ejpam-6607	145	11	,	,	PUNCT
ejpam-6607	145	12	{	{	PUNCT
ejpam-6607	145	13	remote	remote	ADJ
ejpam-6607	145	14	,	,	PUNCT
ejpam-6607	145	15	onsite	onsite	ADJ
ejpam-6607	145	16	}	}	PUNCT
ejpam-6607	145	17	)	)	PUNCT
ejpam-6607	146	1	=	=	PRON
ejpam-6607	146	2	{	{	PUNCT
ejpam-6607	146	3	alice	alice	PROPN
ejpam-6607	146	4	,	,	PUNCT
ejpam-6607	146	5	bob	bob	PROPN
ejpam-6607	146	6	}	}	PUNCT
ejpam-6607	146	7	,	,	PUNCT
ejpam-6607	146	8	f	f	PROPN
ejpam-6607	146	9	(	(	PUNCT
ejpam-6607	146	10	{	{	PUNCT
ejpam-6607	146	11	developer	developer	NOUN
ejpam-6607	146	12	,	,	PUNCT
ejpam-6607	146	13	manager	manager	NOUN
ejpam-6607	146	14	}	}	PUNCT
ejpam-6607	146	15	,	,	PUNCT
ejpam-6607	146	16	{	{	PUNCT
ejpam-6607	146	17	java	java	NOUN
ejpam-6607	146	18	}	}	PUNCT
ejpam-6607	146	19	,	,	PUNCT
ejpam-6607	146	20	{	{	PUNCT
ejpam-6607	146	21	onsite	onsite	ADJ
ejpam-6607	146	22	}	}	PUNCT
ejpam-6607	146	23	)	)	PUNCT
ejpam-6607	146	24	=	=	SYM
ejpam-6607	146	25	{	{	PUNCT
ejpam-6607	146	26	bob	bob	PROPN
ejpam-6607	146	27	,	,	PUNCT
ejpam-6607	146	28	carol	carol	NOUN
ejpam-6607	146	29	}	}	PUNCT
ejpam-6607	146	30	.	.	PUNCT
ejpam-6607	147	1	thus	thus	ADV
ejpam-6607	147	2	:	:	PUNCT
ejpam-6607	147	3	•	•	NOUN
ejpam-6607	147	4	for	for	ADP
ejpam-6607	147	5	γ1	γ1	NOUN
ejpam-6607	147	6	=	=	SYM
ejpam-6607	147	7	(	(	PUNCT
ejpam-6607	147	8	{	{	PUNCT
ejpam-6607	147	9	developer	developer	NOUN
ejpam-6607	147	10	}	}	PUNCT
ejpam-6607	147	11	,	,	PUNCT
ejpam-6607	147	12	{	{	PUNCT
ejpam-6607	147	13	python	python	NOUN
ejpam-6607	147	14	}	}	PUNCT
ejpam-6607	147	15	,	,	PUNCT
ejpam-6607	147	16	{	{	PUNCT
ejpam-6607	147	17	remote	remote	ADJ
ejpam-6607	147	18	,	,	PUNCT
ejpam-6607	147	19	onsite	onsite	ADJ
ejpam-6607	147	20	}	}	PUNCT
ejpam-6607	147	21	)	)	PUNCT
ejpam-6607	147	22	,	,	PUNCT
ejpam-6607	147	23	f	f	PROPN
ejpam-6607	147	24	(	(	PUNCT
ejpam-6607	147	25	γ1	γ1	PROPN
ejpam-6607	147	26	)	)	PUNCT
ejpam-6607	147	27	=	=	PRON
ejpam-6607	147	28	{	{	PUNCT
ejpam-6607	147	29	alice	alice	PROPN
ejpam-6607	147	30	,	,	PUNCT
ejpam-6607	147	31	bob	bob	PROPN
ejpam-6607	147	32	}	}	PUNCT
ejpam-6607	147	33	.	.	PUNCT
ejpam-6607	148	1	•	•	NOUN
ejpam-6607	148	2	for	for	ADP
ejpam-6607	148	3	γ2	γ2	NOUN
ejpam-6607	148	4	=	=	SYM
ejpam-6607	148	5	(	(	PUNCT
ejpam-6607	148	6	{	{	PUNCT
ejpam-6607	148	7	developer	developer	NOUN
ejpam-6607	148	8	,	,	PUNCT
ejpam-6607	148	9	manager	manager	NOUN
ejpam-6607	148	10	}	}	PUNCT
ejpam-6607	148	11	,	,	PUNCT
ejpam-6607	148	12	{	{	PUNCT
ejpam-6607	148	13	java	java	NOUN
ejpam-6607	148	14	}	}	PUNCT
ejpam-6607	148	15	,	,	PUNCT
ejpam-6607	148	16	{	{	PUNCT
ejpam-6607	148	17	onsite	onsite	ADV
ejpam-6607	148	18	}	}	PUNCT
ejpam-6607	148	19	)	)	PUNCT
ejpam-6607	148	20	,	,	PUNCT
ejpam-6607	148	21	f	f	PROPN
ejpam-6607	148	22	(	(	PUNCT
ejpam-6607	148	23	γ2	γ2	PROPN
ejpam-6607	148	24	)	)	PUNCT
ejpam-6607	148	25	=	=	PRON
ejpam-6607	148	26	{	{	PUNCT
ejpam-6607	148	27	bob	bob	PROPN
ejpam-6607	148	28	,	,	PUNCT
ejpam-6607	148	29	carol	carol	NOUN
ejpam-6607	148	30	}	}	PUNCT
ejpam-6607	148	31	.	.	PUNCT
ejpam-6607	149	1	2.5	2.5	NUM
ejpam-6607	149	2	.	.	PUNCT
ejpam-6607	150	1	quantum	quantum	NOUN
ejpam-6607	150	2	-	-	PUNCT
ejpam-6607	150	3	soft	soft	ADJ
ejpam-6607	150	4	sets	set	NOUN
ejpam-6607	150	5	a	a	DET
ejpam-6607	150	6	complex	complex	ADJ
ejpam-6607	150	7	hilbert	hilbert	NOUN
ejpam-6607	150	8	space	space	NOUN
ejpam-6607	150	9	is	be	AUX
ejpam-6607	150	10	a	a	DET
ejpam-6607	150	11	complete	complete	ADJ
ejpam-6607	150	12	inner	inner	ADJ
ejpam-6607	150	13	-	-	PUNCT
ejpam-6607	150	14	product	product	NOUN
ejpam-6607	150	15	space	space	NOUN
ejpam-6607	150	16	over	over	ADP
ejpam-6607	150	17	c.	c.	PROPN
ejpam-6607	150	18	in	in	ADP
ejpam-6607	150	19	the	the	DET
ejpam-6607	150	20	finitedimensional	finitedimensional	ADJ
ejpam-6607	150	21	setting	setting	NOUN
ejpam-6607	150	22	,	,	PUNCT
ejpam-6607	150	23	let	let	VERB
ejpam-6607	150	24	u	u	PRON
ejpam-6607	150	25	=	=	NOUN
ejpam-6607	150	26	{	{	PUNCT
ejpam-6607	150	27	u1	u1	NOUN
ejpam-6607	150	28	,	,	PUNCT
ejpam-6607	150	29	u2	u2	NOUN
ejpam-6607	150	30	,	,	PUNCT
ejpam-6607	150	31	.	.	PUNCT
ejpam-6607	150	32	.	.	PUNCT
ejpam-6607	151	1	.	.	PUNCT
ejpam-6607	152	1	,	,	PUNCT
ejpam-6607	152	2	un	un	AUX
ejpam-6607	152	3	}	}	PUNCT
ejpam-6607	152	4	be	be	AUX
ejpam-6607	152	5	a	a	DET
ejpam-6607	152	6	finite	finite	ADJ
ejpam-6607	152	7	universe	universe	NOUN
ejpam-6607	152	8	,	,	PUNCT
ejpam-6607	152	9	and	and	CCONJ
ejpam-6607	152	10	denote	denote	VERB
ejpam-6607	152	11	by	by	ADP
ejpam-6607	152	12	h(u	h(u	PROPN
ejpam-6607	152	13	)	)	PUNCT
ejpam-6607	152	14	the	the	DET
ejpam-6607	152	15	n	n	ADV
ejpam-6607	152	16	-	-	PUNCT
ejpam-6607	152	17	dimensional	dimensional	ADJ
ejpam-6607	152	18	complex	complex	ADJ
ejpam-6607	152	19	hilbert	hilbert	NOUN
ejpam-6607	152	20	space	space	NOUN
ejpam-6607	152	21	with	with	ADP
ejpam-6607	152	22	orthonormal	orthonormal	ADJ
ejpam-6607	152	23	basis	basis	NOUN
ejpam-6607	152	24	{	{	PUNCT
ejpam-6607	152	25	|ui⟩}ni=1	|ui⟩}ni=1	NOUN
ejpam-6607	152	26	.	.	PUNCT
ejpam-6607	153	1	definition	definition	NOUN
ejpam-6607	153	2	4	4	NUM
ejpam-6607	153	3	(	(	PUNCT
ejpam-6607	153	4	quantum	quantum	NOUN
ejpam-6607	153	5	-	-	PUNCT
ejpam-6607	153	6	soft	soft	ADJ
ejpam-6607	153	7	set	set	NOUN
ejpam-6607	153	8	[	[	X
ejpam-6607	153	9	3	3	NUM
ejpam-6607	153	10	]	]	NUM
ejpam-6607	153	11	)	)	PUNCT
ejpam-6607	153	12	.	.	PUNCT
ejpam-6607	154	1	let	let	VERB
ejpam-6607	154	2	a	a	DET
ejpam-6607	154	3	=	=	PUNCT
ejpam-6607	154	4	{	{	PUNCT
ejpam-6607	154	5	a1	a1	PROPN
ejpam-6607	154	6	,	,	PUNCT
ejpam-6607	154	7	a2	a2	PROPN
ejpam-6607	154	8	,	,	PUNCT
ejpam-6607	154	9	.	.	PUNCT
ejpam-6607	154	10	.	.	PUNCT
ejpam-6607	155	1	.	.	PUNCT
ejpam-6607	156	1	,	,	PUNCT
ejpam-6607	156	2	am	be	AUX
ejpam-6607	156	3	}	}	PUNCT
ejpam-6607	156	4	be	be	AUX
ejpam-6607	156	5	a	a	DET
ejpam-6607	156	6	finite	finite	ADJ
ejpam-6607	156	7	set	set	NOUN
ejpam-6607	156	8	of	of	ADP
ejpam-6607	156	9	parameters	parameter	NOUN
ejpam-6607	156	10	.	.	PUNCT
ejpam-6607	157	1	a	a	DET
ejpam-6607	157	2	quantum	quantum	NOUN
ejpam-6607	157	3	-	-	PUNCT
ejpam-6607	157	4	soft	soft	ADJ
ejpam-6607	157	5	set	set	NOUN
ejpam-6607	157	6	over	over	ADP
ejpam-6607	157	7	(	(	PUNCT
ejpam-6607	157	8	u	u	NOUN
ejpam-6607	157	9	,	,	PUNCT
ejpam-6607	157	10	a	a	PRON
ejpam-6607	157	11	)	)	PUNCT
ejpam-6607	157	12	is	be	AUX
ejpam-6607	157	13	a	a	DET
ejpam-6607	157	14	mapping	mapping	NOUN
ejpam-6607	157	15	f	f	NOUN
ejpam-6607	157	16	:	:	PUNCT
ejpam-6607	157	17	a	a	DET
ejpam-6607	157	18	−→	−→	NOUN
ejpam-6607	157	19	h(u	h(u	PROPN
ejpam-6607	157	20	)	)	PUNCT
ejpam-6607	157	21	,	,	PUNCT
ejpam-6607	157	22	aj	aj	PROPN
ejpam-6607	157	23	7→	7→	PROPN
ejpam-6607	157	24	|ψaj	|ψaj	VERB
ejpam-6607	157	25	⟩	⟩	NOUN
ejpam-6607	157	26	=	=	SYM
ejpam-6607	157	27	n∑	n∑	PROPN
ejpam-6607	157	28	i=1	i=1	PROPN
ejpam-6607	158	1	αi	αi	PROPN
ejpam-6607	158	2	,	,	PUNCT
ejpam-6607	158	3	j	j	PROPN
ejpam-6607	158	4	|ui⟩	|ui⟩	NUM
ejpam-6607	158	5	,	,	PUNCT
ejpam-6607	158	6	subject	subject	ADJ
ejpam-6607	158	7	to	to	ADP
ejpam-6607	158	8	the	the	DET
ejpam-6607	158	9	normalization	normalization	NOUN
ejpam-6607	158	10	condition	condition	NOUN
ejpam-6607	158	11	n∑	n∑	PROPN
ejpam-6607	158	12	i=1	i=1	PROPN
ejpam-6607	159	1	∣∣αi	∣∣αi	PROPN
ejpam-6607	159	2	,	,	PUNCT
ejpam-6607	159	3	j	j	PROPN
ejpam-6607	159	4	∣∣2	∣∣2	PROPN
ejpam-6607	159	5	=	=	SYM
ejpam-6607	159	6	1	1	NUM
ejpam-6607	159	7	,	,	PUNCT
ejpam-6607	159	8	j	j	PROPN
ejpam-6607	159	9	=	=	SYM
ejpam-6607	159	10	1	1	NUM
ejpam-6607	159	11	,	,	PUNCT
ejpam-6607	159	12	2	2	NUM
ejpam-6607	159	13	,	,	PUNCT
ejpam-6607	159	14	.	.	PUNCT
ejpam-6607	159	15	.	.	PUNCT
ejpam-6607	160	1	.	.	PUNCT
ejpam-6607	161	1	,	,	PUNCT
ejpam-6607	161	2	m.	m.	NOUN
ejpam-6607	161	3	measuring	measure	VERB
ejpam-6607	161	4	the	the	DET
ejpam-6607	161	5	state	state	NOUN
ejpam-6607	161	6	|ψaj	|ψaj	NOUN
ejpam-6607	161	7	⟩	⟩	NOUN
ejpam-6607	161	8	in	in	ADP
ejpam-6607	161	9	the	the	DET
ejpam-6607	161	10	computational	computational	ADJ
ejpam-6607	161	11	basis	basis	NOUN
ejpam-6607	161	12	{	{	PUNCT
ejpam-6607	161	13	|ui⟩	|ui⟩	PROPN
ejpam-6607	161	14	}	}	PUNCT
ejpam-6607	161	15	yields	yield	NOUN
ejpam-6607	161	16	outcome	outcome	VERB
ejpam-6607	161	17	|ui⟩	|ui⟩	NOUN
ejpam-6607	161	18	with	with	ADP
ejpam-6607	161	19	probability	probability	NOUN
ejpam-6607	161	20	p	p	X
ejpam-6607	161	21	(	(	PUNCT
ejpam-6607	161	22	ui	ui	NOUN
ejpam-6607	161	23	|	|	ADV
ejpam-6607	161	24	aj	aj	ADV
ejpam-6607	161	25	)	)	PUNCT
ejpam-6607	162	1	=	=	PUNCT
ejpam-6607	162	2	∣∣αi	∣∣αi	PROPN
ejpam-6607	162	3	,	,	PUNCT
ejpam-6607	162	4	j	j	PROPN
ejpam-6607	162	5	∣∣2	∣∣2	PROPN
ejpam-6607	162	6	.	.	PROPN
ejpam-6607	162	7	example	example	NOUN
ejpam-6607	162	8	5	5	NUM
ejpam-6607	162	9	(	(	PUNCT
ejpam-6607	162	10	investment	investment	NOUN
ejpam-6607	162	11	portfolio	portfolio	NOUN
ejpam-6607	162	12	selection	selection	NOUN
ejpam-6607	162	13	)	)	PUNCT
ejpam-6607	162	14	.	.	PUNCT
ejpam-6607	163	1	let	let	VERB
ejpam-6607	163	2	u	u	PRON
ejpam-6607	163	3	=	=	X
ejpam-6607	163	4	{	{	PUNCT
ejpam-6607	163	5	tech	tech	NOUN
ejpam-6607	163	6	,	,	PUNCT
ejpam-6607	163	7	pharma	pharma	NOUN
ejpam-6607	163	8	,	,	PUNCT
ejpam-6607	163	9	energy	energy	NOUN
ejpam-6607	163	10	}	}	PUNCT
ejpam-6607	163	11	,	,	PUNCT
ejpam-6607	163	12	a	a	DET
ejpam-6607	163	13	=	=	NOUN
ejpam-6607	163	14	{	{	PUNCT
ejpam-6607	163	15	growth	growth	NOUN
ejpam-6607	163	16	,	,	PUNCT
ejpam-6607	163	17	stability	stability	NOUN
ejpam-6607	163	18	}	}	PUNCT
ejpam-6607	163	19	.	.	PUNCT
ejpam-6607	164	1	identify	identify	VERB
ejpam-6607	164	2	h(u	h(u	PROPN
ejpam-6607	164	3	)	)	PUNCT
ejpam-6607	164	4	with	with	ADP
ejpam-6607	164	5	c3	c3	PROPN
ejpam-6607	164	6	via	via	ADP
ejpam-6607	164	7	the	the	DET
ejpam-6607	164	8	basis	basis	NOUN
ejpam-6607	164	9	{	{	PUNCT
ejpam-6607	164	10	|tech⟩	|tech⟩	ADV
ejpam-6607	164	11	,	,	PUNCT
ejpam-6607	164	12	|pharma⟩	|pharma⟩	NOUN
ejpam-6607	164	13	,	,	PUNCT
ejpam-6607	164	14	|energy⟩	|energy⟩	NOUN
ejpam-6607	164	15	}	}	PUNCT
ejpam-6607	164	16	.	.	PUNCT
ejpam-6607	165	1	define	define	VERB
ejpam-6607	165	2	the	the	DET
ejpam-6607	165	3	mapping	mapping	NOUN
ejpam-6607	165	4	f	f	NOUN
ejpam-6607	165	5	:	:	PUNCT
ejpam-6607	165	6	a→	a→	PROPN
ejpam-6607	165	7	h(u	h(u	PROPN
ejpam-6607	165	8	)	)	PUNCT
ejpam-6607	165	9	by	by	ADP
ejpam-6607	165	10	|ψgrowth⟩	|ψgrowth⟩	PROPN
ejpam-6607	165	11	=	=	PUNCT
ejpam-6607	165	12	√	√	NUM
ejpam-6607	165	13	0.60	0.60	NUM
ejpam-6607	165	14	|tech⟩+	|tech⟩+	NOUN
ejpam-6607	165	15	√	√	NOUN
ejpam-6607	165	16	0.30	0.30	NUM
ejpam-6607	165	17	|pharma⟩+	|pharma⟩+	ADJ
ejpam-6607	165	18	√	√	NUM
ejpam-6607	165	19	0.10	0.10	NUM
ejpam-6607	165	20	|energy⟩	|energy⟩	NOUN
ejpam-6607	165	21	,	,	PUNCT
ejpam-6607	165	22	t.	t.	PROPN
ejpam-6607	165	23	fujita	fujita	PROPN
ejpam-6607	165	24	,	,	PUNCT
ejpam-6607	165	25	f.smarandache	f.smarandache	NOUN
ejpam-6607	165	26	/	/	SYM
ejpam-6607	165	27	eur	eur	PROPN
ejpam-6607	165	28	.	.	PUNCT
ejpam-6607	166	1	j.	j.	PROPN
ejpam-6607	166	2	pure	pure	PROPN
ejpam-6607	166	3	appl	appl	PROPN
ejpam-6607	166	4	.	.	PROPN
ejpam-6607	166	5	math	math	PROPN
ejpam-6607	166	6	,	,	PUNCT
ejpam-6607	166	7	18	18	NUM
ejpam-6607	166	8	(	(	PUNCT
ejpam-6607	166	9	3	3	NUM
ejpam-6607	166	10	)	)	PUNCT
ejpam-6607	166	11	(	(	PUNCT
ejpam-6607	166	12	2025	2025	NUM
ejpam-6607	166	13	)	)	PUNCT
ejpam-6607	166	14	,	,	PUNCT
ejpam-6607	166	15	6607	6607	NUM
ejpam-6607	166	16	9	9	NUM
ejpam-6607	166	17	of	of	ADP
ejpam-6607	166	18	33	33	NUM
ejpam-6607	166	19	|ψstability⟩	|ψstability⟩	NOUN
ejpam-6607	166	20	=	=	PUNCT
ejpam-6607	166	21	√	√	NUM
ejpam-6607	166	22	0.20	0.20	NUM
ejpam-6607	166	23	|tech⟩+	|tech⟩+	NOUN
ejpam-6607	166	24	√	√	NOUN
ejpam-6607	166	25	0.50	0.50	NUM
ejpam-6607	166	26	|pharma⟩+	|pharma⟩+	NOUN
ejpam-6607	166	27	√	√	NUM
ejpam-6607	166	28	0.30	0.30	NUM
ejpam-6607	166	29	|energy⟩	|energy⟩	NOUN
ejpam-6607	166	30	.	.	PUNCT
ejpam-6607	167	1	each	each	DET
ejpam-6607	167	2	state	state	NOUN
ejpam-6607	167	3	is	be	AUX
ejpam-6607	167	4	manifestly	manifestly	ADV
ejpam-6607	167	5	normalized	normalize	VERB
ejpam-6607	167	6	(	(	PUNCT
ejpam-6607	167	7	e.g.	e.g.	ADV
ejpam-6607	167	8	0.60	0.60	NUM
ejpam-6607	167	9	+	+	NUM
ejpam-6607	167	10	0.30	0.30	NUM
ejpam-6607	167	11	+	+	CCONJ
ejpam-6607	167	12	0.10	0.10	NUM
ejpam-6607	167	13	=	=	SYM
ejpam-6607	167	14	1	1	NUM
ejpam-6607	167	15	)	)	PUNCT
ejpam-6607	167	16	.	.	PUNCT
ejpam-6607	168	1	measuring	measure	VERB
ejpam-6607	168	2	in	in	ADP
ejpam-6607	168	3	the	the	DET
ejpam-6607	168	4	basis	basis	NOUN
ejpam-6607	168	5	{	{	PUNCT
ejpam-6607	168	6	|tech⟩	|tech⟩	ADV
ejpam-6607	168	7	,	,	PUNCT
ejpam-6607	168	8	|pharma⟩	|pharma⟩	NOUN
ejpam-6607	168	9	,	,	PUNCT
ejpam-6607	168	10	|energy⟩	|energy⟩	NOUN
ejpam-6607	168	11	}	}	PUNCT
ejpam-6607	168	12	yields	yield	NOUN
ejpam-6607	168	13	p	p	NOUN
ejpam-6607	168	14	(	(	PUNCT
ejpam-6607	168	15	tech	tech	NOUN
ejpam-6607	168	16	|	|	NOUN
ejpam-6607	168	17	growth	growth	NOUN
ejpam-6607	168	18	)	)	PUNCT
ejpam-6607	168	19	=	=	SYM
ejpam-6607	169	1	0.60	0.60	NUM
ejpam-6607	169	2	,	,	PUNCT
ejpam-6607	169	3	p	p	X
ejpam-6607	169	4	(	(	PUNCT
ejpam-6607	169	5	pharma	pharma	NOUN
ejpam-6607	169	6	|	|	ADV
ejpam-6607	169	7	growth	growth	NOUN
ejpam-6607	169	8	)	)	PUNCT
ejpam-6607	170	1	=	=	SYM
ejpam-6607	170	2	0.30	0.30	NUM
ejpam-6607	170	3	,	,	PUNCT
ejpam-6607	170	4	p	p	X
ejpam-6607	170	5	(	(	PUNCT
ejpam-6607	170	6	energy	energy	NOUN
ejpam-6607	170	7	|	|	NOUN
ejpam-6607	170	8	growth	growth	NOUN
ejpam-6607	170	9	)	)	PUNCT
ejpam-6607	171	1	=	=	SYM
ejpam-6607	171	2	0.10	0.10	NUM
ejpam-6607	171	3	,	,	PUNCT
ejpam-6607	171	4	p	p	X
ejpam-6607	171	5	(	(	PUNCT
ejpam-6607	171	6	tech	tech	NOUN
ejpam-6607	171	7	|	|	NOUN
ejpam-6607	171	8	stability	stability	NOUN
ejpam-6607	171	9	)	)	PUNCT
ejpam-6607	172	1	=	=	SYM
ejpam-6607	172	2	0.20	0.20	NUM
ejpam-6607	172	3	,	,	PUNCT
ejpam-6607	172	4	p	p	X
ejpam-6607	172	5	(	(	PUNCT
ejpam-6607	172	6	pharma	pharma	PROPN
ejpam-6607	172	7	|	|	ADV
ejpam-6607	172	8	stability	stability	NOUN
ejpam-6607	172	9	)	)	PUNCT
ejpam-6607	173	1	=	=	SYM
ejpam-6607	173	2	0.50	0.50	NUM
ejpam-6607	173	3	,	,	PUNCT
ejpam-6607	173	4	p	p	X
ejpam-6607	173	5	(	(	PUNCT
ejpam-6607	173	6	energy	energy	NOUN
ejpam-6607	173	7	|	|	NOUN
ejpam-6607	173	8	stability	stability	NOUN
ejpam-6607	173	9	)	)	PUNCT
ejpam-6607	173	10	=	=	SYM
ejpam-6607	174	1	0.30	0.30	NUM
ejpam-6607	174	2	.	.	PUNCT
ejpam-6607	175	1	this	this	PRON
ejpam-6607	175	2	illustrates	illustrate	VERB
ejpam-6607	175	3	how	how	SCONJ
ejpam-6607	175	4	a	a	DET
ejpam-6607	175	5	classical	classical	ADJ
ejpam-6607	175	6	soft	soft	ADJ
ejpam-6607	175	7	-	-	PUNCT
ejpam-6607	175	8	set	set	NOUN
ejpam-6607	175	9	membership	membership	NOUN
ejpam-6607	175	10	(	(	PUNCT
ejpam-6607	175	11	uniform	uniform	NOUN
ejpam-6607	175	12	or	or	CCONJ
ejpam-6607	175	13	weighted	weight	VERB
ejpam-6607	175	14	)	)	PUNCT
ejpam-6607	175	15	can	can	AUX
ejpam-6607	175	16	be	be	AUX
ejpam-6607	175	17	embedded	embed	VERB
ejpam-6607	175	18	into	into	ADP
ejpam-6607	175	19	a	a	DET
ejpam-6607	175	20	quantum	quantum	ADJ
ejpam-6607	175	21	state	state	NOUN
ejpam-6607	175	22	by	by	ADP
ejpam-6607	175	23	choosing	choose	VERB
ejpam-6607	175	24	amplitudes	amplitude	NOUN
ejpam-6607	175	25	whose	whose	DET
ejpam-6607	175	26	squared	square	VERB
ejpam-6607	175	27	moduli	modulus	NOUN
ejpam-6607	175	28	reproduce	reproduce	VERB
ejpam-6607	175	29	the	the	DET
ejpam-6607	175	30	desired	desire	VERB
ejpam-6607	175	31	probabilities	probability	NOUN
ejpam-6607	175	32	.	.	PUNCT
ejpam-6607	176	1	we	we	PRON
ejpam-6607	176	2	present	present	VERB
ejpam-6607	176	3	below	below	ADP
ejpam-6607	176	4	several	several	ADJ
ejpam-6607	176	5	mathematical	mathematical	ADJ
ejpam-6607	176	6	theorems	theorem	NOUN
ejpam-6607	176	7	related	relate	VERB
ejpam-6607	176	8	to	to	ADP
ejpam-6607	176	9	quantum	quantum	ADJ
ejpam-6607	176	10	soft	soft	ADJ
ejpam-6607	176	11	sets	set	NOUN
ejpam-6607	176	12	.	.	PUNCT
ejpam-6607	177	1	theorem	theorem	ADJ
ejpam-6607	177	2	1	1	NUM
ejpam-6607	177	3	(	(	PUNCT
ejpam-6607	177	4	soft	soft	ADJ
ejpam-6607	177	5	set	set	NOUN
ejpam-6607	177	6	embedding	embed	VERB
ejpam-6607	177	7	)	)	PUNCT
ejpam-6607	177	8	.	.	PUNCT
ejpam-6607	178	1	let	let	VERB
ejpam-6607	178	2	(	(	PUNCT
ejpam-6607	178	3	f	f	X
ejpam-6607	178	4	,	,	PUNCT
ejpam-6607	178	5	s	s	AUX
ejpam-6607	178	6	)	)	PUNCT
ejpam-6607	178	7	be	be	AUX
ejpam-6607	178	8	a	a	DET
ejpam-6607	178	9	classical	classical	ADJ
ejpam-6607	178	10	soft	soft	ADJ
ejpam-6607	178	11	set	set	NOUN
ejpam-6607	178	12	over	over	ADP
ejpam-6607	178	13	the	the	DET
ejpam-6607	178	14	finite	finite	ADJ
ejpam-6607	178	15	universe	universe	NOUN
ejpam-6607	178	16	u	u	NOUN
ejpam-6607	178	17	=	=	PUNCT
ejpam-6607	178	18	{	{	PUNCT
ejpam-6607	178	19	u1	u1	NOUN
ejpam-6607	178	20	,	,	PUNCT
ejpam-6607	178	21	.	.	PUNCT
ejpam-6607	178	22	.	.	PUNCT
ejpam-6607	178	23	.	.	PUNCT
ejpam-6607	179	1	,	,	PUNCT
ejpam-6607	179	2	un	un	PROPN
ejpam-6607	179	3	}	}	PUNCT
ejpam-6607	179	4	with	with	ADP
ejpam-6607	179	5	parameter	parameter	NOUN
ejpam-6607	179	6	set	set	NOUN
ejpam-6607	179	7	s	s	PART
ejpam-6607	179	8	=	=	NOUN
ejpam-6607	179	9	{	{	PUNCT
ejpam-6607	179	10	a1	a1	NOUN
ejpam-6607	179	11	,	,	PUNCT
ejpam-6607	179	12	.	.	PUNCT
ejpam-6607	179	13	.	.	PUNCT
ejpam-6607	180	1	.	.	PUNCT
ejpam-6607	181	1	,	,	PUNCT
ejpam-6607	181	2	am	be	AUX
ejpam-6607	181	3	}	}	PUNCT
ejpam-6607	181	4	and	and	CCONJ
ejpam-6607	181	5	f	f	X
ejpam-6607	181	6	:	:	PUNCT
ejpam-6607	181	7	s	s	VERB
ejpam-6607	181	8	−→	−→	NOUN
ejpam-6607	181	9	p(u	p(u	NOUN
ejpam-6607	181	10	)	)	PUNCT
ejpam-6607	181	11	,	,	PUNCT
ejpam-6607	181	12	aj	aj	PROPN
ejpam-6607	181	13	7→	7→	PROPN
ejpam-6607	181	14	f(aj	f(aj	PROPN
ejpam-6607	181	15	)	)	PUNCT
ejpam-6607	181	16	⊆	⊆	NUM
ejpam-6607	181	17	u.	u.	NOUN
ejpam-6607	181	18	define	define	VERB
ejpam-6607	181	19	a	a	DET
ejpam-6607	181	20	map	map	NOUN
ejpam-6607	181	21	fq	fq	NOUN
ejpam-6607	181	22	:	:	PUNCT
ejpam-6607	181	23	s	s	AUX
ejpam-6607	181	24	−→	−→	ADJ
ejpam-6607	181	25	h(u	h(u	PROPN
ejpam-6607	181	26	)	)	PUNCT
ejpam-6607	181	27	by	by	ADP
ejpam-6607	181	28	assigning	assign	VERB
ejpam-6607	181	29	to	to	ADP
ejpam-6607	181	30	each	each	DET
ejpam-6607	181	31	aj	aj	PROPN
ejpam-6607	181	32	∈	∈	PROPN
ejpam-6607	181	33	s	s	VERB
ejpam-6607	181	34	the	the	DET
ejpam-6607	181	35	quantum	quantum	ADJ
ejpam-6607	181	36	state	state	NOUN
ejpam-6607	181	37	|ψj⟩	|ψj⟩	ADP
ejpam-6607	181	38	=	=	SYM
ejpam-6607	181	39	n∑	n∑	PROPN
ejpam-6607	181	40	i=1	i=1	PROPN
ejpam-6607	181	41	αij	αij	NOUN
ejpam-6607	181	42	|ui⟩	|ui⟩	PROPN
ejpam-6607	181	43	,	,	PUNCT
ejpam-6607	181	44	where	where	SCONJ
ejpam-6607	181	45	αij	αij	NOUN
ejpam-6607	181	46	=	=	PUNCT
ejpam-6607	181	47			PROPN
ejpam-6607	181	48	1√∣∣f(aj	1√∣∣f(aj	NUM
ejpam-6607	181	49	)	)	PUNCT
ejpam-6607	181	50	∣∣	∣∣	VERB
ejpam-6607	181	51	if	if	SCONJ
ejpam-6607	181	52	ui	ui	PROPN
ejpam-6607	181	53	∈	∈	PROPN
ejpam-6607	181	54	f(aj	f(aj	PROPN
ejpam-6607	181	55	)	)	PUNCT
ejpam-6607	181	56	,	,	PUNCT
ejpam-6607	181	57	0	0	NUM
ejpam-6607	181	58	otherwise	otherwise	ADV
ejpam-6607	181	59	.	.	PUNCT
ejpam-6607	182	1	then	then	ADV
ejpam-6607	182	2	fq	fq	PROPN
ejpam-6607	182	3	is	be	AUX
ejpam-6607	182	4	a	a	DET
ejpam-6607	182	5	valid	valid	ADJ
ejpam-6607	182	6	quantum	quantum	NOUN
ejpam-6607	182	7	-	-	PUNCT
ejpam-6607	182	8	soft	soft	ADJ
ejpam-6607	182	9	set	set	NOUN
ejpam-6607	182	10	over	over	ADP
ejpam-6607	182	11	(	(	PUNCT
ejpam-6607	182	12	u	u	NOUN
ejpam-6607	182	13	,	,	PUNCT
ejpam-6607	182	14	s	s	PART
ejpam-6607	182	15	)	)	PUNCT
ejpam-6607	182	16	.	.	PUNCT
ejpam-6607	183	1	moreover	moreover	ADV
ejpam-6607	183	2	,	,	PUNCT
ejpam-6607	183	3	measuring	measure	VERB
ejpam-6607	183	4	|ψj⟩	|ψj⟩	ADP
ejpam-6607	183	5	yields	yield	NOUN
ejpam-6607	183	6	exactly	exactly	ADV
ejpam-6607	183	7	the	the	DET
ejpam-6607	183	8	classical	classical	ADJ
ejpam-6607	183	9	soft	soft	ADJ
ejpam-6607	183	10	set	set	NOUN
ejpam-6607	183	11	membership	membership	NOUN
ejpam-6607	183	12	:	:	PUNCT
ejpam-6607	183	13	p	p	X
ejpam-6607	183	14	(	(	PUNCT
ejpam-6607	183	15	ui	ui	PROPN
ejpam-6607	183	16	|	|	ADV
ejpam-6607	183	17	aj	aj	PROPN
ejpam-6607	183	18	)	)	PUNCT
ejpam-6607	183	19	=	=	SYM
ejpam-6607	183	20	∣∣αij	∣∣αij	X
ejpam-6607	183	21	∣∣2	∣∣2	NUM
ejpam-6607	183	22	=	=	SYM
ejpam-6607	183	23			PUNCT
ejpam-6607	183	24	1∣∣f(aj	1∣∣f(aj	NUM
ejpam-6607	183	25	)	)	PUNCT
ejpam-6607	183	26	∣∣	∣∣	NUM
ejpam-6607	183	27	,	,	PUNCT
ejpam-6607	183	28	ui	ui	PROPN
ejpam-6607	183	29	∈	∈	PROPN
ejpam-6607	183	30	f(aj	f(aj	PROPN
ejpam-6607	183	31	)	)	PUNCT
ejpam-6607	183	32	,	,	PUNCT
ejpam-6607	183	33	0	0	NUM
ejpam-6607	183	34	,	,	PUNCT
ejpam-6607	183	35	ui	ui	NOUN
ejpam-6607	183	36	/∈	/∈	PUNCT
ejpam-6607	183	37	f(aj	f(aj	PROPN
ejpam-6607	183	38	)	)	PUNCT
ejpam-6607	183	39	.	.	PUNCT
ejpam-6607	184	1	proof	proof	NOUN
ejpam-6607	184	2	.	.	PUNCT
ejpam-6607	185	1	fix	fix	VERB
ejpam-6607	185	2	aj	aj	PROPN
ejpam-6607	185	3	∈	∈	PROPN
ejpam-6607	185	4	s.	s.	PROPN
ejpam-6607	185	5	by	by	ADP
ejpam-6607	185	6	construction	construction	NOUN
ejpam-6607	185	7	,	,	PUNCT
ejpam-6607	185	8	αij	αij	NOUN
ejpam-6607	185	9	̸=	̸=	PROPN
ejpam-6607	185	10	0	0	NUM
ejpam-6607	185	11	precisely	precisely	ADV
ejpam-6607	185	12	when	when	SCONJ
ejpam-6607	185	13	ui	ui	PROPN
ejpam-6607	185	14	∈	∈	PROPN
ejpam-6607	185	15	f(aj	f(aj	PROPN
ejpam-6607	185	16	)	)	PUNCT
ejpam-6607	185	17	,	,	PUNCT
ejpam-6607	185	18	and	and	CCONJ
ejpam-6607	185	19	there	there	PRON
ejpam-6607	185	20	are∣∣f(aj	are∣∣f(aj	NOUN
ejpam-6607	185	21	)	)	PUNCT
ejpam-6607	186	1	∣∣	∣∣	VERB
ejpam-6607	186	2	such	such	ADJ
ejpam-6607	186	3	indices	index	NOUN
ejpam-6607	186	4	.	.	PUNCT
ejpam-6607	187	1	hence	hence	ADV
ejpam-6607	187	2	n∑	n∑	NOUN
ejpam-6607	187	3	i=1	i=1	PROPN
ejpam-6607	187	4	∣∣αij	∣∣αij	PROPN
ejpam-6607	187	5	∣∣2	∣∣2	PROPN
ejpam-6607	187	6	=	=	SYM
ejpam-6607	187	7	∣∣f(aj	∣∣f(aj	NOUN
ejpam-6607	187	8	)	)	PUNCT
ejpam-6607	187	9	∣∣×	∣∣×	PROPN
ejpam-6607	187	10	1∣∣f(aj	1∣∣f(aj	NUM
ejpam-6607	187	11	)	)	PUNCT
ejpam-6607	187	12	∣∣	∣∣	X
ejpam-6607	188	1	=	=	SYM
ejpam-6607	188	2	1	1	NUM
ejpam-6607	188	3	,	,	PUNCT
ejpam-6607	188	4	so	so	ADV
ejpam-6607	188	5	|ψj⟩	|ψj⟩	PROPN
ejpam-6607	188	6	is	be	AUX
ejpam-6607	188	7	normalized	normalize	VERB
ejpam-6607	188	8	.	.	PUNCT
ejpam-6607	189	1	upon	upon	SCONJ
ejpam-6607	189	2	measurement	measurement	NOUN
ejpam-6607	189	3	in	in	ADP
ejpam-6607	189	4	the	the	DET
ejpam-6607	189	5	basis	basis	NOUN
ejpam-6607	189	6	{	{	PUNCT
ejpam-6607	189	7	|ui⟩	|ui⟩	X
ejpam-6607	189	8	}	}	PUNCT
ejpam-6607	189	9	,	,	PUNCT
ejpam-6607	189	10	the	the	DET
ejpam-6607	189	11	born	bear	VERB
ejpam-6607	189	12	rule	rule	NOUN
ejpam-6607	189	13	gives	give	VERB
ejpam-6607	189	14	p	p	NOUN
ejpam-6607	189	15	(	(	PUNCT
ejpam-6607	189	16	ui	ui	NOUN
ejpam-6607	189	17	|	|	ADV
ejpam-6607	189	18	aj	aj	PROPN
ejpam-6607	189	19	)	)	PUNCT
ejpam-6607	189	20	=	=	SYM
ejpam-6607	189	21	∣∣αij	∣∣αij	X
ejpam-6607	189	22	∣∣2	∣∣2	NUM
ejpam-6607	189	23	=	=	SYM
ejpam-6607	189	24			PUNCT
ejpam-6607	189	25	1∣∣f(aj	1∣∣f(aj	NUM
ejpam-6607	189	26	)	)	PUNCT
ejpam-6607	189	27	∣∣	∣∣	NUM
ejpam-6607	189	28	,	,	PUNCT
ejpam-6607	189	29	if	if	SCONJ
ejpam-6607	189	30	ui	ui	PROPN
ejpam-6607	189	31	∈	∈	PROPN
ejpam-6607	189	32	f(aj	f(aj	PROPN
ejpam-6607	189	33	)	)	PUNCT
ejpam-6607	189	34	,	,	PUNCT
ejpam-6607	189	35	0	0	NUM
ejpam-6607	189	36	,	,	PUNCT
ejpam-6607	189	37	otherwise	otherwise	ADV
ejpam-6607	189	38	,	,	PUNCT
ejpam-6607	189	39	which	which	PRON
ejpam-6607	189	40	matches	match	VERB
ejpam-6607	189	41	exactly	exactly	ADV
ejpam-6607	189	42	the	the	DET
ejpam-6607	189	43	uniform	uniform	ADJ
ejpam-6607	189	44	membership	membership	NOUN
ejpam-6607	189	45	values	value	NOUN
ejpam-6607	189	46	of	of	ADP
ejpam-6607	189	47	the	the	DET
ejpam-6607	189	48	classical	classical	ADJ
ejpam-6607	189	49	soft	soft	ADJ
ejpam-6607	189	50	set	set	NOUN
ejpam-6607	189	51	f	f	NOUN
ejpam-6607	189	52	.	.	PUNCT
ejpam-6607	190	1	therefore	therefore	ADV
ejpam-6607	190	2	,	,	PUNCT
ejpam-6607	190	3	fq	fq	PROPN
ejpam-6607	190	4	is	be	AUX
ejpam-6607	190	5	a	a	DET
ejpam-6607	190	6	quantum	quantum	NOUN
ejpam-6607	190	7	-	-	PUNCT
ejpam-6607	190	8	soft	soft	ADJ
ejpam-6607	190	9	set	set	NOUN
ejpam-6607	190	10	whose	whose	DET
ejpam-6607	190	11	measurement	measurement	NOUN
ejpam-6607	190	12	reproduces	reproduce	VERB
ejpam-6607	190	13	(	(	PUNCT
ejpam-6607	190	14	f	f	PROPN
ejpam-6607	190	15	,	,	PUNCT
ejpam-6607	190	16	s	s	PROPN
ejpam-6607	190	17	)	)	PUNCT
ejpam-6607	190	18	.	.	PUNCT
ejpam-6607	191	1	t.	t.	PROPN
ejpam-6607	191	2	fujita	fujita	PROPN
ejpam-6607	191	3	,	,	PUNCT
ejpam-6607	191	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	191	5	/	/	SYM
ejpam-6607	191	6	eur	eur	PROPN
ejpam-6607	191	7	.	.	PUNCT
ejpam-6607	192	1	j.	j.	PROPN
ejpam-6607	192	2	pure	pure	PROPN
ejpam-6607	192	3	appl	appl	PROPN
ejpam-6607	192	4	.	.	PROPN
ejpam-6607	192	5	math	math	PROPN
ejpam-6607	192	6	,	,	PUNCT
ejpam-6607	192	7	18	18	NUM
ejpam-6607	192	8	(	(	PUNCT
ejpam-6607	192	9	3	3	NUM
ejpam-6607	192	10	)	)	PUNCT
ejpam-6607	192	11	(	(	PUNCT
ejpam-6607	192	12	2025	2025	NUM
ejpam-6607	192	13	)	)	PUNCT
ejpam-6607	192	14	,	,	PUNCT
ejpam-6607	192	15	6607	6607	NUM
ejpam-6607	192	16	10	10	NUM
ejpam-6607	192	17	of	of	ADP
ejpam-6607	192	18	33	33	NUM
ejpam-6607	192	19	theorem	theorem	ADJ
ejpam-6607	192	20	2	2	NUM
ejpam-6607	192	21	(	(	PUNCT
ejpam-6607	192	22	unitary	unitary	ADJ
ejpam-6607	192	23	invariance	invariance	NOUN
ejpam-6607	192	24	)	)	PUNCT
ejpam-6607	192	25	.	.	PUNCT
ejpam-6607	193	1	let	let	VERB
ejpam-6607	193	2	f	f	NOUN
ejpam-6607	193	3	:	:	PUNCT
ejpam-6607	193	4	a	a	PRON
ejpam-6607	193	5	→	→	SYM
ejpam-6607	193	6	h(u	h(u	PROPN
ejpam-6607	193	7	)	)	PUNCT
ejpam-6607	193	8	be	be	VERB
ejpam-6607	193	9	any	any	DET
ejpam-6607	193	10	quantum	quantum	NOUN
ejpam-6607	193	11	-	-	PUNCT
ejpam-6607	193	12	soft	soft	ADJ
ejpam-6607	193	13	set	set	NOUN
ejpam-6607	193	14	over	over	ADP
ejpam-6607	193	15	(	(	PUNCT
ejpam-6607	193	16	u	u	NOUN
ejpam-6607	193	17	,	,	PUNCT
ejpam-6607	193	18	a	a	PRON
ejpam-6607	193	19	)	)	PUNCT
ejpam-6607	193	20	.	.	PUNCT
ejpam-6607	194	1	for	for	ADP
ejpam-6607	194	2	each	each	DET
ejpam-6607	194	3	a	a	DET
ejpam-6607	194	4	∈	∈	PROPN
ejpam-6607	194	5	a	a	NOUN
ejpam-6607	194	6	,	,	PUNCT
ejpam-6607	194	7	let	let	VERB
ejpam-6607	194	8	ua	ua	PRON
ejpam-6607	194	9	be	be	AUX
ejpam-6607	194	10	a	a	DET
ejpam-6607	194	11	unitary	unitary	ADJ
ejpam-6607	194	12	operator	operator	NOUN
ejpam-6607	194	13	on	on	ADP
ejpam-6607	194	14	h(u	h(u	PROPN
ejpam-6607	194	15	)	)	PUNCT
ejpam-6607	194	16	.	.	PUNCT
ejpam-6607	195	1	define	define	VERB
ejpam-6607	195	2	a	a	DET
ejpam-6607	195	3	new	new	ADJ
ejpam-6607	195	4	map	map	NOUN
ejpam-6607	195	5	f	f	NOUN
ejpam-6607	196	1	′	′	NUM
ejpam-6607	196	2	:	:	PUNCT
ejpam-6607	196	3	a	a	DET
ejpam-6607	196	4	−→	−→	NOUN
ejpam-6607	196	5	h(u	h(u	PROPN
ejpam-6607	196	6	)	)	PUNCT
ejpam-6607	196	7	,	,	PUNCT
ejpam-6607	196	8	a	a	DET
ejpam-6607	196	9	7→	7→	NUM
ejpam-6607	196	10	|ψ′	|ψ′	NOUN
ejpam-6607	196	11	a⟩	a⟩	PRON
ejpam-6607	196	12	=	=	PUNCT
ejpam-6607	196	13	ua	ua	PROPN
ejpam-6607	196	14	|ψa⟩	|ψa⟩	INTJ
ejpam-6607	196	15	,	,	PUNCT
ejpam-6607	196	16	where	where	SCONJ
ejpam-6607	196	17	|ψa⟩	|ψa⟩	ADP
ejpam-6607	196	18	=	=	SYM
ejpam-6607	196	19	f	f	PROPN
ejpam-6607	196	20	(	(	PUNCT
ejpam-6607	196	21	a	a	NOUN
ejpam-6607	196	22	)	)	PUNCT
ejpam-6607	196	23	.	.	PUNCT
ejpam-6607	197	1	then	then	ADV
ejpam-6607	197	2	f	f	PROPN
ejpam-6607	197	3	′	′	NOUN
ejpam-6607	197	4	is	be	AUX
ejpam-6607	197	5	also	also	ADV
ejpam-6607	197	6	a	a	DET
ejpam-6607	197	7	quantum	quantum	NOUN
ejpam-6607	197	8	-	-	PUNCT
ejpam-6607	197	9	soft	soft	ADJ
ejpam-6607	197	10	set	set	NOUN
ejpam-6607	197	11	over	over	ADP
ejpam-6607	197	12	(	(	PUNCT
ejpam-6607	197	13	u	u	NOUN
ejpam-6607	197	14	,	,	PUNCT
ejpam-6607	197	15	a	a	PRON
ejpam-6607	197	16	)	)	PUNCT
ejpam-6607	197	17	.	.	PUNCT
ejpam-6607	198	1	proof	proof	NOUN
ejpam-6607	198	2	.	.	PUNCT
ejpam-6607	199	1	fix	fix	VERB
ejpam-6607	199	2	a	a	DET
ejpam-6607	199	3	∈	∈	NOUN
ejpam-6607	199	4	a.	a.	NOUN
ejpam-6607	199	5	since	since	SCONJ
ejpam-6607	199	6	ua	ua	PROPN
ejpam-6607	199	7	is	be	AUX
ejpam-6607	199	8	unitary	unitary	ADJ
ejpam-6607	199	9	,	,	PUNCT
ejpam-6607	199	10	it	it	PRON
ejpam-6607	199	11	preserves	preserve	VERB
ejpam-6607	199	12	inner	inner	ADJ
ejpam-6607	199	13	products	product	NOUN
ejpam-6607	199	14	and	and	CCONJ
ejpam-6607	199	15	norms	norm	NOUN
ejpam-6607	199	16	.	.	PUNCT
ejpam-6607	200	1	in	in	ADP
ejpam-6607	200	2	particular	particular	ADJ
ejpam-6607	200	3	,	,	PUNCT
ejpam-6607	200	4	〈	〈	PROPN
ejpam-6607	200	5	ψa	ψa	ADV
ejpam-6607	200	6	|	|	ADV
ejpam-6607	200	7	ψa	ψa	VERB
ejpam-6607	200	8	〉	〉	NOUN
ejpam-6607	200	9	=	=	SYM
ejpam-6607	200	10	1	1	NUM
ejpam-6607	200	11	=	=	NOUN
ejpam-6607	200	12	⇒	⇒	X
ejpam-6607	200	13	〈	〈	PROPN
ejpam-6607	200	14	ψ′	ψ′	PROPN
ejpam-6607	200	15	a	a	DET
ejpam-6607	200	16	|	|	NOUN
ejpam-6607	200	17	ψ′	ψ′	PUNCT
ejpam-6607	200	18	a	a	DET
ejpam-6607	200	19	〉	〉	NOUN
ejpam-6607	200	20	=	=	SYM
ejpam-6607	200	21	〈	〈	PROPN
ejpam-6607	200	22	uaψa	uaψa	NOUN
ejpam-6607	200	23	|	|	ADV
ejpam-6607	200	24	uaψa	uaψa	ADJ
ejpam-6607	200	25	〉	〉	NOUN
ejpam-6607	200	26	=	=	PUNCT
ejpam-6607	200	27	〈	〈	PROPN
ejpam-6607	200	28	ψa	ψa	NOUN
ejpam-6607	200	29	|	|	ADV
ejpam-6607	200	30	u	u	PROPN
ejpam-6607	200	31	†	†	PROPN
ejpam-6607	200	32	aua	aua	PROPN
ejpam-6607	200	33	|	|	ADV
ejpam-6607	200	34	ψa	ψa	VERB
ejpam-6607	200	35	〉	〉	NOUN
ejpam-6607	200	36	=	=	PUNCT
ejpam-6607	200	37	〈	〈	PROPN
ejpam-6607	200	38	ψa	ψa	NOUN
ejpam-6607	200	39	|	|	ADV
ejpam-6607	200	40	ψa	ψa	X
ejpam-6607	200	41	〉	〉	NOUN
ejpam-6607	200	42	=	=	SYM
ejpam-6607	200	43	1	1	X
ejpam-6607	200	44	.	.	X
ejpam-6607	200	45	hence	hence	ADV
ejpam-6607	200	46	each	each	DET
ejpam-6607	200	47	|ψ′	|ψ′	NOUN
ejpam-6607	200	48	a⟩	a⟩	VERB
ejpam-6607	200	49	is	be	AUX
ejpam-6607	200	50	normalized	normalize	VERB
ejpam-6607	200	51	and	and	CCONJ
ejpam-6607	200	52	f	f	PROPN
ejpam-6607	200	53	′	′	NUM
ejpam-6607	200	54	satisfies	satisfy	VERB
ejpam-6607	200	55	the	the	DET
ejpam-6607	200	56	definition	definition	NOUN
ejpam-6607	200	57	of	of	ADP
ejpam-6607	200	58	a	a	DET
ejpam-6607	200	59	quantum	quantum	NOUN
ejpam-6607	200	60	-	-	PUNCT
ejpam-6607	200	61	soft	soft	ADJ
ejpam-6607	200	62	set	set	NOUN
ejpam-6607	200	63	.	.	PUNCT
ejpam-6607	201	1	theorem	theorem	VERB
ejpam-6607	201	2	3	3	NUM
ejpam-6607	201	3	(	(	PUNCT
ejpam-6607	201	4	crisp	crisp	ADJ
ejpam-6607	201	5	state	state	NOUN
ejpam-6607	201	6	characterization	characterization	NOUN
ejpam-6607	201	7	)	)	PUNCT
ejpam-6607	201	8	.	.	PUNCT
ejpam-6607	202	1	let	let	VERB
ejpam-6607	202	2	f	f	NOUN
ejpam-6607	202	3	:	:	PUNCT
ejpam-6607	202	4	a	a	PRON
ejpam-6607	202	5	→	→	SYM
ejpam-6607	202	6	h(u	h(u	PROPN
ejpam-6607	202	7	)	)	PUNCT
ejpam-6607	202	8	be	be	AUX
ejpam-6607	202	9	a	a	DET
ejpam-6607	202	10	quantum	quantum	NOUN
ejpam-6607	202	11	-	-	PUNCT
ejpam-6607	202	12	soft	soft	ADJ
ejpam-6607	202	13	set	set	NOUN
ejpam-6607	202	14	.	.	PUNCT
ejpam-6607	203	1	then	then	ADV
ejpam-6607	203	2	f	f	PROPN
ejpam-6607	203	3	induces	induce	VERB
ejpam-6607	203	4	a	a	DET
ejpam-6607	203	5	classical	classical	ADJ
ejpam-6607	203	6	(	(	PUNCT
ejpam-6607	203	7	crisp	crisp	ADJ
ejpam-6607	203	8	)	)	PUNCT
ejpam-6607	203	9	soft	soft	ADJ
ejpam-6607	203	10	set	set	NOUN
ejpam-6607	203	11	if	if	SCONJ
ejpam-6607	203	12	and	and	CCONJ
ejpam-6607	203	13	only	only	ADV
ejpam-6607	203	14	if	if	SCONJ
ejpam-6607	203	15	,	,	PUNCT
ejpam-6607	203	16	for	for	ADP
ejpam-6607	203	17	every	every	DET
ejpam-6607	203	18	a	a	DET
ejpam-6607	203	19	∈	∈	PROPN
ejpam-6607	203	20	a	a	PRON
ejpam-6607	203	21	,	,	PUNCT
ejpam-6607	203	22	the	the	DET
ejpam-6607	203	23	quantum	quantum	ADJ
ejpam-6607	203	24	state	state	NOUN
ejpam-6607	203	25	|ψa⟩	|ψa⟩	ADP
ejpam-6607	203	26	has	have	VERB
ejpam-6607	203	27	exactly	exactly	ADV
ejpam-6607	203	28	one	one	NUM
ejpam-6607	203	29	nonzero	nonzero	NOUN
ejpam-6607	203	30	amplitude	amplitude	NOUN
ejpam-6607	203	31	(	(	PUNCT
ejpam-6607	203	32	up	up	ADP
ejpam-6607	203	33	to	to	ADP
ejpam-6607	203	34	a	a	DET
ejpam-6607	203	35	global	global	ADJ
ejpam-6607	203	36	phase	phase	NOUN
ejpam-6607	203	37	)	)	PUNCT
ejpam-6607	203	38	.	.	PUNCT
ejpam-6607	204	1	equivalently	equivalently	ADV
ejpam-6607	204	2	,	,	PUNCT
ejpam-6607	204	3	there	there	PRON
ejpam-6607	204	4	exists	exist	VERB
ejpam-6607	204	5	an	an	DET
ejpam-6607	204	6	index	index	NOUN
ejpam-6607	204	7	ia	ia	NOUN
ejpam-6607	204	8	such	such	ADJ
ejpam-6607	204	9	that∣∣αia	that∣∣αia	NOUN
ejpam-6607	204	10	,	,	PUNCT
ejpam-6607	204	11	a	a	DET
ejpam-6607	204	12	∣∣	∣∣	NUM
ejpam-6607	204	13	=	=	SYM
ejpam-6607	204	14	1	1	NUM
ejpam-6607	204	15	,	,	PUNCT
ejpam-6607	204	16	and	and	CCONJ
ejpam-6607	204	17	αi	αi	NOUN
ejpam-6607	204	18	,	,	PUNCT
ejpam-6607	204	19	a	a	DET
ejpam-6607	204	20	=	=	SYM
ejpam-6607	204	21	0	0	NUM
ejpam-6607	204	22	(	(	PUNCT
ejpam-6607	204	23	∀	∀	X
ejpam-6607	204	24	i	i	PRON
ejpam-6607	204	25	̸=	̸=	PROPN
ejpam-6607	204	26	ia	ia	PROPN
ejpam-6607	204	27	)	)	PUNCT
ejpam-6607	204	28	.	.	PUNCT
ejpam-6607	205	1	in	in	ADP
ejpam-6607	205	2	that	that	DET
ejpam-6607	205	3	case	case	NOUN
ejpam-6607	205	4	,	,	PUNCT
ejpam-6607	205	5	measuring	measure	VERB
ejpam-6607	205	6	|ψa⟩	|ψa⟩	ADP
ejpam-6607	205	7	yields	yield	NOUN
ejpam-6607	205	8	the	the	DET
ejpam-6607	205	9	deterministic	deterministic	ADJ
ejpam-6607	205	10	outcome	outcome	NOUN
ejpam-6607	205	11	|uia⟩	|uia⟩	PRON
ejpam-6607	205	12	,	,	PUNCT
ejpam-6607	205	13	reproducing	reproduce	VERB
ejpam-6607	205	14	the	the	DET
ejpam-6607	205	15	classical	classical	ADJ
ejpam-6607	205	16	soft	soft	ADJ
ejpam-6607	205	17	set	set	NOUN
ejpam-6607	205	18	assignment	assignment	NOUN
ejpam-6607	205	19	f(a	f(a	NOUN
ejpam-6607	205	20	)	)	PUNCT
ejpam-6607	206	1	=	=	PRON
ejpam-6607	206	2	{	{	PUNCT
ejpam-6607	206	3	uia	uia	PROPN
ejpam-6607	206	4	}	}	PUNCT
ejpam-6607	206	5	.	.	PUNCT
ejpam-6607	207	1	proof	proof	NOUN
ejpam-6607	207	2	.	.	PUNCT
ejpam-6607	208	1	⇒	⇒	PROPN
ejpam-6607	208	2	suppose	suppose	VERB
ejpam-6607	208	3	f	f	PROPN
ejpam-6607	208	4	induces	induce	VERB
ejpam-6607	208	5	a	a	DET
ejpam-6607	208	6	crisp	crisp	ADJ
ejpam-6607	208	7	soft	soft	ADJ
ejpam-6607	208	8	set	set	NOUN
ejpam-6607	208	9	(	(	PUNCT
ejpam-6607	208	10	f	f	PROPN
ejpam-6607	208	11	,	,	PUNCT
ejpam-6607	208	12	a	a	PRON
ejpam-6607	208	13	)	)	PUNCT
ejpam-6607	208	14	.	.	PUNCT
ejpam-6607	209	1	by	by	ADP
ejpam-6607	209	2	definition	definition	NOUN
ejpam-6607	209	3	,	,	PUNCT
ejpam-6607	209	4	for	for	ADP
ejpam-6607	209	5	each	each	DET
ejpam-6607	209	6	a	a	DET
ejpam-6607	209	7	∈	∈	PROPN
ejpam-6607	209	8	a	a	PRON
ejpam-6607	209	9	,	,	PUNCT
ejpam-6607	209	10	measuring	measure	VERB
ejpam-6607	209	11	|ψa⟩	|ψa⟩	ADP
ejpam-6607	209	12	must	must	AUX
ejpam-6607	209	13	collapse	collapse	VERB
ejpam-6607	209	14	deterministically	deterministically	ADV
ejpam-6607	209	15	to	to	ADP
ejpam-6607	209	16	a	a	DET
ejpam-6607	209	17	single	single	ADJ
ejpam-6607	209	18	element	element	NOUN
ejpam-6607	209	19	uia	uia	NOUN
ejpam-6607	209	20	.	.	PUNCT
ejpam-6607	210	1	the	the	DET
ejpam-6607	210	2	born	bear	VERB
ejpam-6607	210	3	rule	rule	NOUN
ejpam-6607	210	4	then	then	ADV
ejpam-6607	210	5	implies	imply	VERB
ejpam-6607	210	6	∣∣αia	∣∣αia	PROPN
ejpam-6607	210	7	,	,	PUNCT
ejpam-6607	210	8	a	a	DET
ejpam-6607	210	9	∣∣2	∣∣2	PROPN
ejpam-6607	210	10	=	=	SYM
ejpam-6607	210	11	1	1	NUM
ejpam-6607	210	12	and	and	CCONJ
ejpam-6607	210	13	∣∣αi	∣∣αi	NOUN
ejpam-6607	210	14	,	,	PUNCT
ejpam-6607	210	15	a	a	DET
ejpam-6607	210	16	∣∣2	∣∣2	PROPN
ejpam-6607	210	17	=	=	SYM
ejpam-6607	210	18	0	0	NUM
ejpam-6607	210	19	for	for	ADP
ejpam-6607	210	20	i	i	PROPN
ejpam-6607	210	21	̸=	̸=	PROPN
ejpam-6607	210	22	ia	ia	PROPN
ejpam-6607	210	23	.	.	PUNCT
ejpam-6607	211	1	thus	thus	ADV
ejpam-6607	211	2	αia	αia	PRON
ejpam-6607	211	3	,	,	PUNCT
ejpam-6607	211	4	a	a	DET
ejpam-6607	211	5	=	=	SYM
ejpam-6607	211	6	eiθ	eiθ	PROPN
ejpam-6607	211	7	(	(	PUNCT
ejpam-6607	211	8	global	global	ADJ
ejpam-6607	211	9	phase	phase	NOUN
ejpam-6607	211	10	)	)	PUNCT
ejpam-6607	211	11	and	and	CCONJ
ejpam-6607	211	12	αi	αi	NOUN
ejpam-6607	211	13	,	,	PUNCT
ejpam-6607	211	14	a	a	PRON
ejpam-6607	211	15	=	=	SYM
ejpam-6607	211	16	0	0	NUM
ejpam-6607	211	17	otherwise	otherwise	ADV
ejpam-6607	211	18	.	.	PUNCT
ejpam-6607	212	1	⇐	⇐	ADV
ejpam-6607	212	2	conversely	conversely	ADV
ejpam-6607	212	3	,	,	PUNCT
ejpam-6607	212	4	if	if	SCONJ
ejpam-6607	212	5	for	for	ADP
ejpam-6607	212	6	each	each	DET
ejpam-6607	212	7	a	a	DET
ejpam-6607	212	8	∈	∈	PROPN
ejpam-6607	212	9	a	a	PRON
ejpam-6607	212	10	there	there	PRON
ejpam-6607	212	11	is	be	VERB
ejpam-6607	212	12	a	a	DET
ejpam-6607	212	13	unique	unique	ADJ
ejpam-6607	212	14	index	index	NOUN
ejpam-6607	212	15	ia	ia	NOUN
ejpam-6607	212	16	with	with	ADP
ejpam-6607	212	17	∣∣αia	∣∣αia	PROPN
ejpam-6607	212	18	,	,	PUNCT
ejpam-6607	212	19	a	a	DET
ejpam-6607	212	20	∣∣	∣∣	NUM
ejpam-6607	212	21	=	=	SYM
ejpam-6607	212	22	1	1	NUM
ejpam-6607	212	23	and	and	CCONJ
ejpam-6607	212	24	αi	αi	NOUN
ejpam-6607	212	25	,	,	PUNCT
ejpam-6607	212	26	a	a	DET
ejpam-6607	212	27	=	=	SYM
ejpam-6607	212	28	0	0	NUM
ejpam-6607	212	29	for	for	ADP
ejpam-6607	212	30	i	i	PROPN
ejpam-6607	212	31	̸=	̸=	PROPN
ejpam-6607	212	32	ia	ia	PROPN
ejpam-6607	212	33	,	,	PUNCT
ejpam-6607	212	34	then	then	ADV
ejpam-6607	212	35	n∑	n∑	PROPN
ejpam-6607	212	36	i=1	i=1	PROPN
ejpam-6607	212	37	∣∣αi	∣∣αi	PROPN
ejpam-6607	212	38	,	,	PUNCT
ejpam-6607	212	39	a	a	DET
ejpam-6607	212	40	∣∣2	∣∣2	PROPN
ejpam-6607	212	41	=	=	SYM
ejpam-6607	212	42	12	12	NUM
ejpam-6607	212	43	=	=	SYM
ejpam-6607	212	44	1	1	NUM
ejpam-6607	212	45	,	,	PUNCT
ejpam-6607	212	46	and	and	CCONJ
ejpam-6607	212	47	measurement	measurement	NOUN
ejpam-6607	212	48	of	of	ADP
ejpam-6607	212	49	|ψa⟩	|ψa⟩	ADP
ejpam-6607	212	50	yields	yield	NOUN
ejpam-6607	212	51	p	p	X
ejpam-6607	212	52	(	(	PUNCT
ejpam-6607	212	53	ui	ui	NOUN
ejpam-6607	212	54	|	|	ADV
ejpam-6607	212	55	a	a	X
ejpam-6607	212	56	)	)	PUNCT
ejpam-6607	213	1	=	=	SYM
ejpam-6607	213	2	∣∣αi	∣∣αi	NOUN
ejpam-6607	213	3	,	,	PUNCT
ejpam-6607	213	4	a	a	DET
ejpam-6607	213	5	∣∣2	∣∣2	PROPN
ejpam-6607	213	6	=	=	SYM
ejpam-6607	213	7	{	{	PUNCT
ejpam-6607	213	8	1	1	NUM
ejpam-6607	213	9	,	,	PUNCT
ejpam-6607	213	10	i	i	PRON
ejpam-6607	213	11	=	=	SYM
ejpam-6607	213	12	ia	ia	PROPN
ejpam-6607	213	13	,	,	PUNCT
ejpam-6607	213	14	0	0	NUM
ejpam-6607	213	15	,	,	PUNCT
ejpam-6607	213	16	i	i	PRON
ejpam-6607	213	17	̸=	̸=	PROPN
ejpam-6607	213	18	ia	ia	PROPN
ejpam-6607	213	19	,	,	PUNCT
ejpam-6607	213	20	deterministically	deterministically	ADV
ejpam-6607	213	21	collapsing	collapse	VERB
ejpam-6607	213	22	to	to	ADP
ejpam-6607	213	23	|uia⟩.	|uia⟩.	NOUN
ejpam-6607	213	24	defining	define	VERB
ejpam-6607	213	25	f(a	f(a	NOUN
ejpam-6607	213	26	)	)	PUNCT
ejpam-6607	214	1	=	=	PRON
ejpam-6607	214	2	{	{	PUNCT
ejpam-6607	214	3	uia	uia	PROPN
ejpam-6607	214	4	}	}	PUNCT
ejpam-6607	214	5	recovers	recover	VERB
ejpam-6607	214	6	a	a	DET
ejpam-6607	214	7	classical	classical	ADJ
ejpam-6607	214	8	soft	soft	ADJ
ejpam-6607	214	9	set	set	NOUN
ejpam-6607	214	10	.	.	PUNCT
ejpam-6607	215	1	t.	t.	PROPN
ejpam-6607	215	2	fujita	fujita	PROPN
ejpam-6607	215	3	,	,	PUNCT
ejpam-6607	215	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	215	5	/	/	SYM
ejpam-6607	215	6	eur	eur	PROPN
ejpam-6607	215	7	.	.	PUNCT
ejpam-6607	216	1	j.	j.	PROPN
ejpam-6607	216	2	pure	pure	PROPN
ejpam-6607	216	3	appl	appl	PROPN
ejpam-6607	216	4	.	.	PROPN
ejpam-6607	216	5	math	math	PROPN
ejpam-6607	216	6	,	,	PUNCT
ejpam-6607	216	7	18	18	NUM
ejpam-6607	216	8	(	(	PUNCT
ejpam-6607	216	9	3	3	NUM
ejpam-6607	216	10	)	)	PUNCT
ejpam-6607	216	11	(	(	PUNCT
ejpam-6607	216	12	2025	2025	NUM
ejpam-6607	216	13	)	)	PUNCT
ejpam-6607	216	14	,	,	PUNCT
ejpam-6607	216	15	6607	6607	NUM
ejpam-6607	216	16	11	11	NUM
ejpam-6607	216	17	of	of	ADP
ejpam-6607	216	18	33	33	NUM
ejpam-6607	216	19	theorem	theorem	ADJ
ejpam-6607	216	20	4	4	NUM
ejpam-6607	216	21	(	(	PUNCT
ejpam-6607	216	22	normalization	normalization	NOUN
ejpam-6607	216	23	implies	imply	VERB
ejpam-6607	216	24	probability	probability	NOUN
ejpam-6607	216	25	distribution	distribution	NOUN
ejpam-6607	216	26	)	)	PUNCT
ejpam-6607	216	27	.	.	PUNCT
ejpam-6607	217	1	let	let	VERB
ejpam-6607	217	2	f	f	NOUN
ejpam-6607	217	3	:	:	PUNCT
ejpam-6607	217	4	a	a	PRON
ejpam-6607	217	5	→	→	SYM
ejpam-6607	217	6	h(u	h(u	PROPN
ejpam-6607	217	7	)	)	PUNCT
ejpam-6607	217	8	be	be	AUX
ejpam-6607	217	9	a	a	DET
ejpam-6607	217	10	quantum	quantum	NOUN
ejpam-6607	217	11	-	-	PUNCT
ejpam-6607	217	12	soft	soft	ADJ
ejpam-6607	217	13	set	set	NOUN
ejpam-6607	217	14	with	with	ADP
ejpam-6607	217	15	|ψa⟩	|ψa⟩	ADP
ejpam-6607	217	16	=	=	PROPN
ejpam-6607	217	17	n∑	n∑	PROPN
ejpam-6607	217	18	i=1	i=1	PROPN
ejpam-6607	218	1	αi	αi	PROPN
ejpam-6607	218	2	,	,	PUNCT
ejpam-6607	218	3	a	a	DET
ejpam-6607	218	4	|ui⟩	|ui⟩	PROPN
ejpam-6607	218	5	,	,	PUNCT
ejpam-6607	218	6	n∑	n∑	PROPN
ejpam-6607	218	7	i=1	i=1	PROPN
ejpam-6607	218	8	∣∣αi	∣∣αi	PROPN
ejpam-6607	218	9	,	,	PUNCT
ejpam-6607	218	10	a	a	DET
ejpam-6607	218	11	∣∣2	∣∣2	PROPN
ejpam-6607	218	12	=	=	SYM
ejpam-6607	218	13	1	1	NUM
ejpam-6607	218	14	.	.	PUNCT
ejpam-6607	219	1	then	then	ADV
ejpam-6607	219	2	for	for	ADP
ejpam-6607	219	3	each	each	PRON
ejpam-6607	219	4	a	a	DET
ejpam-6607	219	5	∈	∈	PROPN
ejpam-6607	219	6	a	a	PRON
ejpam-6607	219	7	,	,	PUNCT
ejpam-6607	219	8	the	the	DET
ejpam-6607	219	9	collection	collection	NOUN
ejpam-6607	219	10	{	{	PUNCT
ejpam-6607	219	11	|αi	|αi	X
ejpam-6607	219	12	,	,	PUNCT
ejpam-6607	219	13	a|2	a|2	PROPN
ejpam-6607	219	14	|	|	ADV
ejpam-6607	219	15	i	i	NOUN
ejpam-6607	219	16	=	=	NOUN
ejpam-6607	219	17	1	1	NUM
ejpam-6607	219	18	,	,	PUNCT
ejpam-6607	219	19	.	.	PUNCT
ejpam-6607	219	20	.	.	PUNCT
ejpam-6607	219	21	.	.	PUNCT
ejpam-6607	220	1	,	,	PUNCT
ejpam-6607	220	2	n	n	CCONJ
ejpam-6607	220	3	}	}	PUNCT
ejpam-6607	220	4	forms	form	VERB
ejpam-6607	220	5	a	a	DET
ejpam-6607	220	6	probability	probability	NOUN
ejpam-6607	220	7	distribution	distribution	NOUN
ejpam-6607	220	8	on	on	ADP
ejpam-6607	220	9	u	u	PROPN
ejpam-6607	220	10	.	.	PUNCT
ejpam-6607	221	1	in	in	ADP
ejpam-6607	221	2	particular	particular	ADJ
ejpam-6607	221	3	,	,	PUNCT
ejpam-6607	221	4	0	0	NUM
ejpam-6607	221	5	≤	≤	NUM
ejpam-6607	221	6	|αi	|αi	NUM
ejpam-6607	221	7	,	,	PUNCT
ejpam-6607	221	8	a|2	a|2	PROPN
ejpam-6607	221	9	≤	≤	PROPN
ejpam-6607	221	10	1	1	NUM
ejpam-6607	221	11	,	,	PUNCT
ejpam-6607	221	12	n∑	n∑	NOUN
ejpam-6607	221	13	i=1	i=1	PROPN
ejpam-6607	222	1	|αi	|αi	X
ejpam-6607	222	2	,	,	PUNCT
ejpam-6607	222	3	a|2	a|2	PROPN
ejpam-6607	222	4	=	=	SYM
ejpam-6607	222	5	1	1	X
ejpam-6607	222	6	.	.	PUNCT
ejpam-6607	223	1	proof	proof	NOUN
ejpam-6607	223	2	.	.	PUNCT
ejpam-6607	224	1	since	since	SCONJ
ejpam-6607	224	2	αi	αi	NOUN
ejpam-6607	224	3	,	,	PUNCT
ejpam-6607	224	4	a	a	DET
ejpam-6607	224	5	∈	∈	PROPN
ejpam-6607	224	6	c	c	NOUN
ejpam-6607	224	7	,	,	PUNCT
ejpam-6607	224	8	each	each	DET
ejpam-6607	224	9	∣∣αi	∣∣αi	NOUN
ejpam-6607	224	10	,	,	PUNCT
ejpam-6607	224	11	a	a	DET
ejpam-6607	224	12	∣∣2	∣∣2	PROPN
ejpam-6607	224	13	is	be	AUX
ejpam-6607	224	14	a	a	DET
ejpam-6607	224	15	real	real	ADJ
ejpam-6607	224	16	number	number	NOUN
ejpam-6607	224	17	satisfying	satisfy	VERB
ejpam-6607	224	18	0	0	NUM
ejpam-6607	224	19	≤	≤	NUM
ejpam-6607	224	20	∣∣αi	∣∣αi	NOUN
ejpam-6607	224	21	,	,	PUNCT
ejpam-6607	224	22	a	a	DET
ejpam-6607	224	23	∣∣2	∣∣2	PROPN
ejpam-6607	224	24	≤	≤	NUM
ejpam-6607	224	25	1	1	NUM
ejpam-6607	224	26	.	.	PUNCT
ejpam-6607	225	1	the	the	DET
ejpam-6607	225	2	normalization	normalization	NOUN
ejpam-6607	225	3	condition	condition	NOUN
ejpam-6607	225	4	∑n	∑n	PROPN
ejpam-6607	225	5	i=1	i=1	PRON
ejpam-6607	225	6	∣∣αi	∣∣αi	PROPN
ejpam-6607	225	7	,	,	PUNCT
ejpam-6607	225	8	a	a	DET
ejpam-6607	225	9	∣∣2	∣∣2	PROPN
ejpam-6607	225	10	=	=	SYM
ejpam-6607	225	11	1	1	NUM
ejpam-6607	225	12	then	then	ADV
ejpam-6607	225	13	implies	imply	VERB
ejpam-6607	225	14	{	{	PUNCT
ejpam-6607	225	15	|αi	|αi	NUM
ejpam-6607	225	16	,	,	PUNCT
ejpam-6607	225	17	a|2	a|2	PROPN
ejpam-6607	225	18	}	}	PUNCT
ejpam-6607	225	19	is	be	AUX
ejpam-6607	225	20	a	a	DET
ejpam-6607	225	21	discrete	discrete	ADJ
ejpam-6607	225	22	probability	probability	NOUN
ejpam-6607	225	23	distribution	distribution	NOUN
ejpam-6607	225	24	indexed	index	VERB
ejpam-6607	225	25	by	by	ADP
ejpam-6607	225	26	i	i	PROPN
ejpam-6607	225	27	=	=	NOUN
ejpam-6607	225	28	1	1	NUM
ejpam-6607	225	29	,	,	PUNCT
ejpam-6607	225	30	.	.	PUNCT
ejpam-6607	225	31	.	.	PUNCT
ejpam-6607	226	1	.	.	PUNCT
ejpam-6607	227	1	,	,	PUNCT
ejpam-6607	227	2	n.	n.	PROPN
ejpam-6607	227	3	hence	hence	ADV
ejpam-6607	227	4	the	the	DET
ejpam-6607	227	5	measurement	measurement	NOUN
ejpam-6607	227	6	outcomes	outcome	NOUN
ejpam-6607	227	7	|ui⟩	|ui⟩	NOUN
ejpam-6607	227	8	occur	occur	VERB
ejpam-6607	227	9	with	with	ADP
ejpam-6607	227	10	probability	probability	NOUN
ejpam-6607	227	11	|αi	|αi	X
ejpam-6607	227	12	,	,	PUNCT
ejpam-6607	227	13	a|2	a|2	PROPN
ejpam-6607	227	14	.	.	PROPN
ejpam-6607	227	15	3	3	NUM
ejpam-6607	227	16	.	.	X
ejpam-6607	227	17	result	result	NOUN
ejpam-6607	227	18	:	:	PUNCT
ejpam-6607	227	19	quantum	quantum	NOUN
ejpam-6607	227	20	-	-	PUNCT
ejpam-6607	227	21	hypersoft	hypersoft	NOUN
ejpam-6607	227	22	set	set	NOUN
ejpam-6607	227	23	and	and	CCONJ
ejpam-6607	227	24	quantum	quantum	NOUN
ejpam-6607	227	25	-	-	PUNCT
ejpam-6607	227	26	superhypersoft	superhypersoft	NOUN
ejpam-6607	227	27	set	set	NOUN
ejpam-6607	227	28	in	in	ADP
ejpam-6607	227	29	this	this	DET
ejpam-6607	227	30	section	section	NOUN
ejpam-6607	227	31	,	,	PUNCT
ejpam-6607	227	32	we	we	PRON
ejpam-6607	227	33	present	present	VERB
ejpam-6607	227	34	the	the	DET
ejpam-6607	227	35	main	main	ADJ
ejpam-6607	227	36	results	result	NOUN
ejpam-6607	227	37	of	of	ADP
ejpam-6607	227	38	this	this	DET
ejpam-6607	227	39	paper	paper	NOUN
ejpam-6607	227	40	by	by	ADP
ejpam-6607	227	41	providing	provide	VERB
ejpam-6607	227	42	the	the	DET
ejpam-6607	227	43	definitions	definition	NOUN
ejpam-6607	227	44	,	,	PUNCT
ejpam-6607	227	45	concrete	concrete	ADJ
ejpam-6607	227	46	examples	example	NOUN
ejpam-6607	227	47	,	,	PUNCT
ejpam-6607	227	48	and	and	CCONJ
ejpam-6607	227	49	mathematical	mathematical	ADJ
ejpam-6607	227	50	theorems	theorem	NOUN
ejpam-6607	227	51	of	of	ADP
ejpam-6607	227	52	the	the	DET
ejpam-6607	227	53	quantum	quantum	NOUN
ejpam-6607	227	54	-	-	PUNCT
ejpam-6607	227	55	hypersoft	hypersoft	NOUN
ejpam-6607	227	56	set	set	NOUN
ejpam-6607	227	57	and	and	CCONJ
ejpam-6607	227	58	the	the	DET
ejpam-6607	227	59	quantum	quantum	NOUN
ejpam-6607	227	60	-	-	PUNCT
ejpam-6607	227	61	superhypersoft	superhypersoft	NOUN
ejpam-6607	227	62	set	set	NOUN
ejpam-6607	227	63	.	.	PUNCT
ejpam-6607	228	1	3.1	3.1	NUM
ejpam-6607	228	2	.	.	PUNCT
ejpam-6607	228	3	quantum	quantum	NOUN
ejpam-6607	228	4	-	-	PUNCT
ejpam-6607	228	5	hypersoft	hypersoft	NOUN
ejpam-6607	228	6	sets	set	VERB
ejpam-6607	228	7	quantum	quantum	NOUN
ejpam-6607	228	8	-	-	PUNCT
ejpam-6607	228	9	hypersoft	hypersoft	NOUN
ejpam-6607	228	10	set	set	NOUN
ejpam-6607	228	11	assigns	assign	NOUN
ejpam-6607	228	12	each	each	DET
ejpam-6607	228	13	attribute	attribute	NOUN
ejpam-6607	228	14	tuple	tuple	NOUN
ejpam-6607	228	15	to	to	ADP
ejpam-6607	228	16	a	a	DET
ejpam-6607	228	17	normalized	normalize	VERB
ejpam-6607	228	18	quantum	quantum	ADJ
ejpam-6607	228	19	superposition	superposition	NOUN
ejpam-6607	228	20	over	over	ADP
ejpam-6607	228	21	universe	universe	NOUN
ejpam-6607	228	22	.	.	PUNCT
ejpam-6607	229	1	the	the	DET
ejpam-6607	229	2	definition	definition	NOUN
ejpam-6607	229	3	is	be	AUX
ejpam-6607	229	4	stated	state	VERB
ejpam-6607	229	5	as	as	SCONJ
ejpam-6607	229	6	follows	follow	VERB
ejpam-6607	229	7	.	.	PUNCT
ejpam-6607	230	1	definition	definition	NOUN
ejpam-6607	230	2	5	5	NUM
ejpam-6607	230	3	(	(	PUNCT
ejpam-6607	230	4	quantum	quantum	NOUN
ejpam-6607	230	5	-	-	PUNCT
ejpam-6607	230	6	hypersoft	hypersoft	NOUN
ejpam-6607	230	7	set	set	NOUN
ejpam-6607	230	8	)	)	PUNCT
ejpam-6607	230	9	.	.	PUNCT
ejpam-6607	231	1	let	let	VERB
ejpam-6607	231	2	u	u	PRON
ejpam-6607	231	3	=	=	NOUN
ejpam-6607	231	4	{	{	PUNCT
ejpam-6607	231	5	u1	u1	NOUN
ejpam-6607	231	6	,	,	PUNCT
ejpam-6607	231	7	u2	u2	NOUN
ejpam-6607	231	8	,	,	PUNCT
ejpam-6607	231	9	.	.	PUNCT
ejpam-6607	231	10	.	.	PUNCT
ejpam-6607	232	1	.	.	PUNCT
ejpam-6607	233	1	,	,	PUNCT
ejpam-6607	233	2	un	un	AUX
ejpam-6607	233	3	}	}	PUNCT
ejpam-6607	233	4	be	be	AUX
ejpam-6607	233	5	a	a	DET
ejpam-6607	233	6	finite	finite	ADJ
ejpam-6607	233	7	universe	universe	NOUN
ejpam-6607	233	8	and	and	CCONJ
ejpam-6607	233	9	let	let	VERB
ejpam-6607	233	10	a1	a1	NOUN
ejpam-6607	233	11	,	,	PUNCT
ejpam-6607	233	12	.	.	PUNCT
ejpam-6607	233	13	.	.	PUNCT
ejpam-6607	234	1	.	.	PUNCT
ejpam-6607	235	1	,	,	PUNCT
ejpam-6607	235	2	am	be	AUX
ejpam-6607	235	3	be	be	AUX
ejpam-6607	235	4	m	m	NOUN
ejpam-6607	235	5	distinct	distinct	ADJ
ejpam-6607	235	6	attribute	attribute	NOUN
ejpam-6607	235	7	domains	domain	NOUN
ejpam-6607	235	8	.	.	PUNCT
ejpam-6607	236	1	form	form	VERB
ejpam-6607	236	2	the	the	DET
ejpam-6607	236	3	cartesian	cartesian	ADJ
ejpam-6607	236	4	product	product	NOUN
ejpam-6607	236	5	c	c	NOUN
ejpam-6607	236	6	=	=	NOUN
ejpam-6607	236	7	a1	a1	NOUN
ejpam-6607	236	8	×	×	NOUN
ejpam-6607	236	9	·	·	PUNCT
ejpam-6607	236	10	·	·	PUNCT
ejpam-6607	236	11	·	·	PUNCT
ejpam-6607	237	1	×	×	NOUN
ejpam-6607	237	2	am	be	AUX
ejpam-6607	237	3	,	,	PUNCT
ejpam-6607	237	4	so	so	SCONJ
ejpam-6607	237	5	that	that	SCONJ
ejpam-6607	237	6	each	each	DET
ejpam-6607	237	7	γ	γ	X
ejpam-6607	237	8	=	=	SYM
ejpam-6607	237	9	(	(	PUNCT
ejpam-6607	237	10	γ1	γ1	PROPN
ejpam-6607	237	11	,	,	PUNCT
ejpam-6607	237	12	.	.	PUNCT
ejpam-6607	237	13	.	.	PUNCT
ejpam-6607	237	14	.	.	PUNCT
ejpam-6607	237	15	,	,	PUNCT
ejpam-6607	237	16	γm	γm	X
ejpam-6607	237	17	)	)	PUNCT
ejpam-6607	237	18	∈	∈	PROPN
ejpam-6607	237	19	c	c	NOUN
ejpam-6607	237	20	is	be	AUX
ejpam-6607	237	21	an	an	DET
ejpam-6607	237	22	m	m	NOUN
ejpam-6607	237	23	-	-	NOUN
ejpam-6607	237	24	tuple	tuple	NOUN
ejpam-6607	237	25	with	with	ADP
ejpam-6607	237	26	γi	γi	X
ejpam-6607	237	27	∈	∈	NOUN
ejpam-6607	237	28	ai	ai	VERB
ejpam-6607	237	29	.	.	PUNCT
ejpam-6607	238	1	let	let	VERB
ejpam-6607	238	2	h(u	h(u	PROPN
ejpam-6607	238	3	)	)	PUNCT
ejpam-6607	238	4	be	be	AUX
ejpam-6607	238	5	the	the	DET
ejpam-6607	238	6	complex	complex	ADJ
ejpam-6607	238	7	hilbert	hilbert	NOUN
ejpam-6607	238	8	space	space	NOUN
ejpam-6607	238	9	with	with	ADP
ejpam-6607	238	10	orthonormal	orthonormal	ADJ
ejpam-6607	238	11	basis	basis	NOUN
ejpam-6607	238	12	{	{	PUNCT
ejpam-6607	238	13	|ui⟩}ni=1	|ui⟩}ni=1	NOUN
ejpam-6607	238	14	.	.	PUNCT
ejpam-6607	239	1	a	a	DET
ejpam-6607	239	2	quantum	quantum	NOUN
ejpam-6607	239	3	-	-	PUNCT
ejpam-6607	239	4	hypersoft	hypersoft	NOUN
ejpam-6607	239	5	set	set	VERB
ejpam-6607	239	6	over	over	ADP
ejpam-6607	239	7	(	(	PUNCT
ejpam-6607	239	8	u	u	NOUN
ejpam-6607	239	9	,	,	PUNCT
ejpam-6607	239	10	c	c	NOUN
ejpam-6607	239	11	)	)	PUNCT
ejpam-6607	239	12	is	be	AUX
ejpam-6607	239	13	a	a	DET
ejpam-6607	239	14	map	map	NOUN
ejpam-6607	239	15	q	q	NOUN
ejpam-6607	239	16	:	:	PUNCT
ejpam-6607	239	17	c	c	AUX
ejpam-6607	239	18	−→	−→	NOUN
ejpam-6607	239	19	h(u	h(u	PROPN
ejpam-6607	239	20	)	)	PUNCT
ejpam-6607	239	21	,	,	PUNCT
ejpam-6607	239	22	γ	γ	PROPN
ejpam-6607	239	23	7→	7→	PROPN
ejpam-6607	239	24	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	239	25	=	=	SYM
ejpam-6607	239	26	n∑	n∑	PROPN
ejpam-6607	239	27	i=1	i=1	PROPN
ejpam-6607	240	1	αi	αi	PROPN
ejpam-6607	240	2	,	,	PUNCT
ejpam-6607	240	3	γ	γ	X
ejpam-6607	240	4	|ui⟩	|ui⟩	NOUN
ejpam-6607	240	5	,	,	PUNCT
ejpam-6607	240	6	subject	subject	ADJ
ejpam-6607	240	7	to	to	ADP
ejpam-6607	240	8	the	the	DET
ejpam-6607	240	9	normalization	normalization	NOUN
ejpam-6607	240	10	condition	condition	NOUN
ejpam-6607	240	11	n∑	n∑	PROPN
ejpam-6607	240	12	i=1	i=1	PROPN
ejpam-6607	241	1	∣∣αi	∣∣αi	PROPN
ejpam-6607	241	2	,	,	PUNCT
ejpam-6607	241	3	γ	γ	PROPN
ejpam-6607	241	4	∣∣2	∣∣2	PROPN
ejpam-6607	241	5	=	=	SYM
ejpam-6607	241	6	1	1	NUM
ejpam-6607	241	7	for	for	ADP
ejpam-6607	241	8	each	each	DET
ejpam-6607	241	9	γ	γ	PROPN
ejpam-6607	241	10	∈	∈	PROPN
ejpam-6607	241	11	c.	c.	PROPN
ejpam-6607	241	12	t.	t.	PROPN
ejpam-6607	241	13	fujita	fujita	PROPN
ejpam-6607	241	14	,	,	PUNCT
ejpam-6607	241	15	f.smarandache	f.smarandache	NOUN
ejpam-6607	241	16	/	/	SYM
ejpam-6607	241	17	eur	eur	PROPN
ejpam-6607	241	18	.	.	PUNCT
ejpam-6607	242	1	j.	j.	PROPN
ejpam-6607	242	2	pure	pure	PROPN
ejpam-6607	242	3	appl	appl	PROPN
ejpam-6607	242	4	.	.	PROPN
ejpam-6607	242	5	math	math	PROPN
ejpam-6607	242	6	,	,	PUNCT
ejpam-6607	242	7	18	18	NUM
ejpam-6607	242	8	(	(	PUNCT
ejpam-6607	242	9	3	3	NUM
ejpam-6607	242	10	)	)	PUNCT
ejpam-6607	242	11	(	(	PUNCT
ejpam-6607	242	12	2025	2025	NUM
ejpam-6607	242	13	)	)	PUNCT
ejpam-6607	242	14	,	,	PUNCT
ejpam-6607	242	15	6607	6607	NUM
ejpam-6607	242	16	12	12	NUM
ejpam-6607	242	17	of	of	ADP
ejpam-6607	242	18	33	33	NUM
ejpam-6607	242	19	here	here	ADV
ejpam-6607	242	20	αi	αi	NOUN
ejpam-6607	242	21	,	,	PUNCT
ejpam-6607	242	22	γ	γ	PROPN
ejpam-6607	242	23	∈	∈	PROPN
ejpam-6607	242	24	c	c	NOUN
ejpam-6607	242	25	is	be	AUX
ejpam-6607	242	26	the	the	DET
ejpam-6607	242	27	amplitude	amplitude	NOUN
ejpam-6607	242	28	of	of	ADP
ejpam-6607	242	29	element	element	NOUN
ejpam-6607	242	30	ui	ui	PROPN
ejpam-6607	242	31	under	under	ADP
ejpam-6607	242	32	the	the	DET
ejpam-6607	242	33	combined	combine	VERB
ejpam-6607	242	34	attribute	attribute	NOUN
ejpam-6607	242	35	γ	γ	PROPN
ejpam-6607	242	36	.	.	PUNCT
ejpam-6607	242	37	measuring	measure	VERB
ejpam-6607	242	38	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	242	39	in	in	ADP
ejpam-6607	242	40	the	the	DET
ejpam-6607	242	41	computational	computational	ADJ
ejpam-6607	242	42	basis	basis	NOUN
ejpam-6607	242	43	yields	yield	NOUN
ejpam-6607	242	44	p	p	X
ejpam-6607	242	45	(	(	PUNCT
ejpam-6607	242	46	ui	ui	PROPN
ejpam-6607	242	47	|	|	ADV
ejpam-6607	242	48	γ	γ	NOUN
ejpam-6607	242	49	)	)	PUNCT
ejpam-6607	242	50	=	=	SYM
ejpam-6607	242	51	∣∣αi	∣∣αi	PROPN
ejpam-6607	242	52	,	,	PUNCT
ejpam-6607	242	53	γ	γ	PROPN
ejpam-6607	242	54	∣∣2	∣∣2	PROPN
ejpam-6607	242	55	,	,	PUNCT
ejpam-6607	242	56	so	so	SCONJ
ejpam-6607	242	57	that	that	SCONJ
ejpam-6607	242	58	the	the	DET
ejpam-6607	242	59	post	post	ADJ
ejpam-6607	242	60	-	-	ADJ
ejpam-6607	242	61	measurement	measurement	ADJ
ejpam-6607	242	62	membership	membership	NOUN
ejpam-6607	242	63	degrees	degree	NOUN
ejpam-6607	242	64	µγ(ui	µγ(ui	PROPN
ejpam-6607	242	65	)	)	PUNCT
ejpam-6607	243	1	=	=	SYM
ejpam-6607	244	1	p	p	X
ejpam-6607	244	2	(	(	PUNCT
ejpam-6607	244	3	ui	ui	PROPN
ejpam-6607	244	4	|	|	ADV
ejpam-6607	244	5	γ	γ	NOUN
ejpam-6607	244	6	)	)	PUNCT
ejpam-6607	244	7	form	form	VERB
ejpam-6607	244	8	a	a	DET
ejpam-6607	244	9	probability	probability	NOUN
ejpam-6607	244	10	distribution	distribution	NOUN
ejpam-6607	244	11	on	on	ADP
ejpam-6607	244	12	u	u	PROPN
ejpam-6607	244	13	.	.	PUNCT
ejpam-6607	245	1	example	example	NOUN
ejpam-6607	245	2	6	6	NUM
ejpam-6607	245	3	(	(	PUNCT
ejpam-6607	245	4	quantum	quantum	NOUN
ejpam-6607	245	5	-	-	PUNCT
ejpam-6607	245	6	hypersoft	hypersoft	NOUN
ejpam-6607	245	7	set	set	NOUN
ejpam-6607	245	8	for	for	ADP
ejpam-6607	245	9	medical	medical	ADJ
ejpam-6607	245	10	diagnosis	diagnosis	NOUN
ejpam-6607	245	11	)	)	PUNCT
ejpam-6607	245	12	.	.	PUNCT
ejpam-6607	246	1	let	let	VERB
ejpam-6607	246	2	u	u	PRON
ejpam-6607	246	3	=	=	X
ejpam-6607	246	4	{	{	PUNCT
ejpam-6607	246	5	flu	flu	PROPN
ejpam-6607	246	6	,	,	PUNCT
ejpam-6607	246	7	covid-19	covid-19	PROPN
ejpam-6607	246	8	,	,	PUNCT
ejpam-6607	246	9	commoncold	commoncold	NOUN
ejpam-6607	246	10	}	}	PUNCT
ejpam-6607	246	11	be	be	AUX
ejpam-6607	246	12	the	the	DET
ejpam-6607	246	13	set	set	NOUN
ejpam-6607	246	14	of	of	ADP
ejpam-6607	246	15	possible	possible	ADJ
ejpam-6607	246	16	diagnoses	diagnosis	NOUN
ejpam-6607	246	17	.	.	PUNCT
ejpam-6607	247	1	consider	consider	VERB
ejpam-6607	247	2	three	three	NUM
ejpam-6607	247	3	symptom	symptom	NOUN
ejpam-6607	247	4	-	-	PUNCT
ejpam-6607	247	5	attribute	attribute	NOUN
ejpam-6607	247	6	domains	domain	NOUN
ejpam-6607	247	7	:	:	PUNCT
ejpam-6607	247	8	a1	a1	NOUN
ejpam-6607	247	9	=	=	PUNCT
ejpam-6607	247	10	{	{	PUNCT
ejpam-6607	247	11	highfever	highfever	ADV
ejpam-6607	247	12	,	,	PUNCT
ejpam-6607	247	13	lowfever	lowfever	NOUN
ejpam-6607	247	14	}	}	PUNCT
ejpam-6607	247	15	,	,	PUNCT
ejpam-6607	247	16	a2	a2	PROPN
ejpam-6607	247	17	=	=	PUNCT
ejpam-6607	247	18	{	{	PUNCT
ejpam-6607	247	19	drycough	drycough	PROPN
ejpam-6607	247	20	,	,	PUNCT
ejpam-6607	247	21	wetcough	wetcough	PROPN
ejpam-6607	247	22	}	}	PUNCT
ejpam-6607	247	23	,	,	PUNCT
ejpam-6607	247	24	a3	a3	NOUN
ejpam-6607	247	25	=	=	SYM
ejpam-6607	247	26	{	{	PUNCT
ejpam-6607	247	27	fatigue	fatigue	NOUN
ejpam-6607	247	28	,	,	PUNCT
ejpam-6607	247	29	nofatigue	nofatigue	PROPN
ejpam-6607	247	30	}	}	PUNCT
ejpam-6607	247	31	.	.	PUNCT
ejpam-6607	248	1	form	form	VERB
ejpam-6607	248	2	the	the	DET
ejpam-6607	248	3	cartesian	cartesian	ADJ
ejpam-6607	248	4	product	product	NOUN
ejpam-6607	248	5	c	c	NOUN
ejpam-6607	248	6	=	=	SYM
ejpam-6607	248	7	a1	a1	PROPN
ejpam-6607	248	8	×a2	×a2	PROPN
ejpam-6607	248	9	×a3	×a3	PROPN
ejpam-6607	248	10	,	,	PUNCT
ejpam-6607	248	11	so	so	SCONJ
ejpam-6607	248	12	that	that	SCONJ
ejpam-6607	248	13	each	each	DET
ejpam-6607	248	14	γ	γ	X
ejpam-6607	248	15	=	=	SYM
ejpam-6607	248	16	(	(	PUNCT
ejpam-6607	248	17	γ1	γ1	PROPN
ejpam-6607	248	18	,	,	PUNCT
ejpam-6607	248	19	γ2	γ2	PROPN
ejpam-6607	248	20	,	,	PUNCT
ejpam-6607	248	21	γ3	γ3	NOUN
ejpam-6607	248	22	)	)	PUNCT
ejpam-6607	248	23	is	be	AUX
ejpam-6607	248	24	a	a	DET
ejpam-6607	248	25	symptom	symptom	NOUN
ejpam-6607	248	26	-	-	PUNCT
ejpam-6607	248	27	combination	combination	NOUN
ejpam-6607	248	28	.	.	PUNCT
ejpam-6607	249	1	let	let	VERB
ejpam-6607	249	2	h(u	h(u	PROPN
ejpam-6607	249	3	)	)	PUNCT
ejpam-6607	249	4	be	be	AUX
ejpam-6607	249	5	the	the	DET
ejpam-6607	249	6	complex	complex	ADJ
ejpam-6607	249	7	hilbert	hilbert	NOUN
ejpam-6607	249	8	space	space	NOUN
ejpam-6607	249	9	with	with	ADP
ejpam-6607	249	10	orthonormal	orthonormal	ADJ
ejpam-6607	249	11	basis	basis	NOUN
ejpam-6607	249	12	{	{	PUNCT
ejpam-6607	249	13	|flu⟩	|flu⟩	X
ejpam-6607	249	14	,	,	PUNCT
ejpam-6607	249	15	|covid-19⟩	|covid-19⟩	PROPN
ejpam-6607	249	16	,	,	PUNCT
ejpam-6607	249	17	|commoncold⟩	|commoncold⟩	PROPN
ejpam-6607	249	18	}	}	PUNCT
ejpam-6607	249	19	.	.	PUNCT
ejpam-6607	250	1	case	case	NOUN
ejpam-6607	250	2	1	1	NUM
ejpam-6607	250	3	:	:	PUNCT
ejpam-6607	250	4	γ1	γ1	PROPN
ejpam-6607	250	5	=	=	SYM
ejpam-6607	250	6	(	(	PUNCT
ejpam-6607	250	7	highfever	highfever	ADV
ejpam-6607	250	8	,	,	PUNCT
ejpam-6607	250	9	drycough	drycough	ADV
ejpam-6607	250	10	,	,	PUNCT
ejpam-6607	250	11	fatigue	fatigue	NOUN
ejpam-6607	250	12	)	)	PUNCT
ejpam-6607	250	13	.	.	PUNCT
ejpam-6607	251	1	define	define	VERB
ejpam-6607	251	2	the	the	DET
ejpam-6607	251	3	quantum	quantum	ADJ
ejpam-6607	251	4	state	state	NOUN
ejpam-6607	251	5	|ψγ1⟩	|ψγ1⟩	NOUN
ejpam-6607	251	6	=	=	PUNCT
ejpam-6607	251	7	√	√	NUM
ejpam-6607	251	8	0.65	0.65	NUM
ejpam-6607	251	9	|covid-19⟩+	|covid-19⟩+	NOUN
ejpam-6607	251	10	√	√	NOUN
ejpam-6607	251	11	0.25	0.25	NUM
ejpam-6607	251	12	|flu⟩+	|flu⟩+	NOUN
ejpam-6607	251	13	√	√	ADP
ejpam-6607	251	14	0.10	0.10	NUM
ejpam-6607	251	15	|commoncold⟩	|commoncold⟩	NOUN
ejpam-6607	251	16	.	.	PUNCT
ejpam-6607	252	1	normalization	normalization	NOUN
ejpam-6607	252	2	check	check	NOUN
ejpam-6607	252	3	:	:	PUNCT
ejpam-6607	252	4	0.65	0.65	NUM
ejpam-6607	253	1	+	+	NUM
ejpam-6607	253	2	0.25	0.25	NUM
ejpam-6607	254	1	+	+	CCONJ
ejpam-6607	254	2	0.10	0.10	NUM
ejpam-6607	254	3	=	=	SYM
ejpam-6607	254	4	1.00	1.00	NUM
ejpam-6607	254	5	.	.	PUNCT
ejpam-6607	255	1	measurement	measurement	NOUN
ejpam-6607	255	2	probabilities	probability	NOUN
ejpam-6607	255	3	:	:	PUNCT
ejpam-6607	255	4	p	p	X
ejpam-6607	255	5	(	(	PUNCT
ejpam-6607	255	6	covid-19	covid-19	PROPN
ejpam-6607	255	7	|	|	NOUN
ejpam-6607	255	8	γ1	γ1	PROPN
ejpam-6607	255	9	)	)	PUNCT
ejpam-6607	256	1	=	=	SYM
ejpam-6607	256	2	0.65	0.65	NUM
ejpam-6607	256	3	,	,	PUNCT
ejpam-6607	256	4	p	p	X
ejpam-6607	256	5	(	(	PUNCT
ejpam-6607	256	6	flu	flu	NOUN
ejpam-6607	256	7	|	|	NOUN
ejpam-6607	256	8	γ1	γ1	PROPN
ejpam-6607	256	9	)	)	PUNCT
ejpam-6607	257	1	=	=	PUNCT
ejpam-6607	257	2	0.25	0.25	NUM
ejpam-6607	257	3	,	,	PUNCT
ejpam-6607	257	4	p	p	X
ejpam-6607	257	5	(	(	PUNCT
ejpam-6607	257	6	commoncold	commoncold	NOUN
ejpam-6607	257	7	|	|	NOUN
ejpam-6607	257	8	γ1	γ1	NOUN
ejpam-6607	257	9	)	)	PUNCT
ejpam-6607	258	1	=	=	PUNCT
ejpam-6607	258	2	0.10	0.10	NUM
ejpam-6607	258	3	.	.	PUNCT
ejpam-6607	258	4	case	case	NOUN
ejpam-6607	258	5	2	2	NUM
ejpam-6607	258	6	:	:	PUNCT
ejpam-6607	258	7	γ2	γ2	NOUN
ejpam-6607	258	8	=	=	SYM
ejpam-6607	258	9	(	(	PUNCT
ejpam-6607	258	10	lowfever	lowfever	PROPN
ejpam-6607	258	11	,	,	PUNCT
ejpam-6607	258	12	wetcough	wetcough	PROPN
ejpam-6607	258	13	,	,	PUNCT
ejpam-6607	258	14	nofatigue	nofatigue	NOUN
ejpam-6607	258	15	)	)	PUNCT
ejpam-6607	258	16	.	.	PUNCT
ejpam-6607	259	1	define	define	VERB
ejpam-6607	259	2	|ψγ2⟩	|ψγ2⟩	NOUN
ejpam-6607	259	3	=	=	PUNCT
ejpam-6607	259	4	√	√	NUM
ejpam-6607	259	5	0.15	0.15	NUM
ejpam-6607	259	6	|covid-19⟩+	|covid-19⟩+	NOUN
ejpam-6607	259	7	√	√	NOUN
ejpam-6607	259	8	0.30	0.30	NUM
ejpam-6607	259	9	|flu⟩+	|flu⟩+	PUNCT
ejpam-6607	259	10	√	√	ADP
ejpam-6607	259	11	0.55	0.55	NUM
ejpam-6607	259	12	|commoncold⟩	|commoncold⟩	NOUN
ejpam-6607	259	13	,	,	PUNCT
ejpam-6607	259	14	with	with	ADP
ejpam-6607	259	15	0.15	0.15	NUM
ejpam-6607	259	16	+	+	CCONJ
ejpam-6607	259	17	0.30	0.30	NUM
ejpam-6607	260	1	+	+	NUM
ejpam-6607	260	2	0.55	0.55	NUM
ejpam-6607	260	3	=	=	SYM
ejpam-6607	260	4	1.00	1.00	NUM
ejpam-6607	260	5	.	.	PUNCT
ejpam-6607	261	1	thus	thus	ADV
ejpam-6607	261	2	p	p	X
ejpam-6607	261	3	(	(	PUNCT
ejpam-6607	261	4	covid-19	covid-19	PROPN
ejpam-6607	261	5	|	|	ADV
ejpam-6607	261	6	γ2	γ2	NOUN
ejpam-6607	261	7	)	)	PUNCT
ejpam-6607	261	8	=	=	PUNCT
ejpam-6607	262	1	0.15	0.15	NUM
ejpam-6607	262	2	,	,	PUNCT
ejpam-6607	262	3	p	p	X
ejpam-6607	262	4	(	(	PUNCT
ejpam-6607	262	5	flu	flu	NOUN
ejpam-6607	262	6	|	|	ADV
ejpam-6607	262	7	γ2	γ2	PROPN
ejpam-6607	262	8	)	)	PUNCT
ejpam-6607	263	1	=	=	SYM
ejpam-6607	263	2	0.30	0.30	NUM
ejpam-6607	263	3	,	,	PUNCT
ejpam-6607	263	4	p	p	X
ejpam-6607	263	5	(	(	PUNCT
ejpam-6607	263	6	commoncold	commoncold	NOUN
ejpam-6607	263	7	|	|	ADV
ejpam-6607	263	8	γ2	γ2	ADJ
ejpam-6607	263	9	)	)	PUNCT
ejpam-6607	263	10	=	=	PUNCT
ejpam-6607	264	1	0.55	0.55	NUM
ejpam-6607	264	2	.	.	PUNCT
ejpam-6607	265	1	interpretation	interpretation	NOUN
ejpam-6607	265	2	.	.	PUNCT
ejpam-6607	266	1	•	•	NUM
ejpam-6607	266	2	for	for	ADP
ejpam-6607	266	3	γ1	γ1	NOUN
ejpam-6607	266	4	,	,	PUNCT
ejpam-6607	266	5	the	the	DET
ejpam-6607	266	6	“	"	PUNCT
ejpam-6607	266	7	highfever	highfever	ADV
ejpam-6607	266	8	+	+	NUM
ejpam-6607	266	9	drycough	drycough	ADJ
ejpam-6607	266	10	+	+	CCONJ
ejpam-6607	266	11	fatigue	fatigue	NOUN
ejpam-6607	266	12	”	"	PUNCT
ejpam-6607	266	13	combination	combination	NOUN
ejpam-6607	266	14	strongly	strongly	ADV
ejpam-6607	266	15	suggests	suggest	VERB
ejpam-6607	266	16	covid19	covid19	NOUN
ejpam-6607	266	17	(	(	PUNCT
ejpam-6607	266	18	65	65	NUM
ejpam-6607	266	19	%	%	NOUN
ejpam-6607	266	20	)	)	PUNCT
ejpam-6607	266	21	,	,	PUNCT
ejpam-6607	266	22	moderately	moderately	ADV
ejpam-6607	266	23	suggests	suggest	VERB
ejpam-6607	266	24	flu	flu	NOUN
ejpam-6607	266	25	(	(	PUNCT
ejpam-6607	266	26	25	25	NUM
ejpam-6607	266	27	%	%	NOUN
ejpam-6607	266	28	)	)	PUNCT
ejpam-6607	266	29	,	,	PUNCT
ejpam-6607	266	30	and	and	CCONJ
ejpam-6607	266	31	rarely	rarely	ADV
ejpam-6607	266	32	common	common	ADJ
ejpam-6607	266	33	cold	cold	ADJ
ejpam-6607	266	34	(	(	PUNCT
ejpam-6607	266	35	10	10	NUM
ejpam-6607	266	36	%	%	NOUN
ejpam-6607	266	37	)	)	PUNCT
ejpam-6607	266	38	.	.	PUNCT
ejpam-6607	267	1	t.	t.	PROPN
ejpam-6607	267	2	fujita	fujita	PROPN
ejpam-6607	267	3	,	,	PUNCT
ejpam-6607	267	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	267	5	/	/	SYM
ejpam-6607	267	6	eur	eur	PROPN
ejpam-6607	267	7	.	.	PUNCT
ejpam-6607	268	1	j.	j.	PROPN
ejpam-6607	268	2	pure	pure	PROPN
ejpam-6607	268	3	appl	appl	PROPN
ejpam-6607	268	4	.	.	PROPN
ejpam-6607	268	5	math	math	PROPN
ejpam-6607	268	6	,	,	PUNCT
ejpam-6607	268	7	18	18	NUM
ejpam-6607	268	8	(	(	PUNCT
ejpam-6607	268	9	3	3	NUM
ejpam-6607	268	10	)	)	PUNCT
ejpam-6607	268	11	(	(	PUNCT
ejpam-6607	268	12	2025	2025	NUM
ejpam-6607	268	13	)	)	PUNCT
ejpam-6607	268	14	,	,	PUNCT
ejpam-6607	268	15	6607	6607	NUM
ejpam-6607	268	16	13	13	NUM
ejpam-6607	268	17	of	of	ADP
ejpam-6607	268	18	33	33	NUM
ejpam-6607	268	19	•	•	NOUN
ejpam-6607	268	20	for	for	ADP
ejpam-6607	268	21	γ2	γ2	NOUN
ejpam-6607	268	22	,	,	PUNCT
ejpam-6607	268	23	the	the	DET
ejpam-6607	268	24	“	"	PUNCT
ejpam-6607	268	25	lowfever	lowfever	NOUN
ejpam-6607	268	26	+	+	CCONJ
ejpam-6607	268	27	wetcough	wetcough	NOUN
ejpam-6607	268	28	+	+	CCONJ
ejpam-6607	268	29	nofatigue	nofatigue	NOUN
ejpam-6607	268	30	”	"	PUNCT
ejpam-6607	268	31	combination	combination	NOUN
ejpam-6607	268	32	most	most	ADV
ejpam-6607	268	33	likely	likely	ADJ
ejpam-6607	268	34	corresponds	correspond	VERB
ejpam-6607	268	35	to	to	ADP
ejpam-6607	268	36	common	common	ADJ
ejpam-6607	268	37	cold	cold	NOUN
ejpam-6607	268	38	(	(	PUNCT
ejpam-6607	268	39	55	55	NUM
ejpam-6607	268	40	%	%	NOUN
ejpam-6607	268	41	)	)	PUNCT
ejpam-6607	268	42	,	,	PUNCT
ejpam-6607	268	43	with	with	ADP
ejpam-6607	268	44	lower	low	ADJ
ejpam-6607	268	45	likelihoods	likelihood	NOUN
ejpam-6607	268	46	for	for	ADP
ejpam-6607	268	47	flu	flu	NOUN
ejpam-6607	268	48	(	(	PUNCT
ejpam-6607	268	49	30	30	NUM
ejpam-6607	268	50	%	%	NOUN
ejpam-6607	268	51	)	)	PUNCT
ejpam-6607	268	52	and	and	CCONJ
ejpam-6607	268	53	covid-19	covid-19	PROPN
ejpam-6607	268	54	(	(	PUNCT
ejpam-6607	268	55	15	15	NUM
ejpam-6607	268	56	%	%	NOUN
ejpam-6607	268	57	)	)	PUNCT
ejpam-6607	268	58	.	.	PUNCT
ejpam-6607	269	1	this	this	DET
ejpam-6607	269	2	quantum	quantum	NOUN
ejpam-6607	269	3	-	-	PUNCT
ejpam-6607	269	4	hypersoft	hypersoft	NOUN
ejpam-6607	269	5	set	set	VERB
ejpam-6607	269	6	q	q	NOUN
ejpam-6607	269	7	:	:	PUNCT
ejpam-6607	269	8	c	c	PROPN
ejpam-6607	269	9	→	→	SYM
ejpam-6607	269	10	h(u	h(u	PROPN
ejpam-6607	269	11	)	)	PUNCT
ejpam-6607	269	12	thus	thus	ADV
ejpam-6607	269	13	models	model	VERB
ejpam-6607	269	14	uncertain	uncertain	ADJ
ejpam-6607	269	15	diagnoses	diagnosis	NOUN
ejpam-6607	269	16	by	by	ADP
ejpam-6607	269	17	encoding	encode	VERB
ejpam-6607	269	18	symptom	symptom	NOUN
ejpam-6607	269	19	combinations	combination	NOUN
ejpam-6607	269	20	as	as	ADP
ejpam-6607	269	21	quantum	quantum	NOUN
ejpam-6607	269	22	-	-	PUNCT
ejpam-6607	269	23	like	like	ADJ
ejpam-6607	269	24	superpositions	superposition	NOUN
ejpam-6607	269	25	,	,	PUNCT
ejpam-6607	269	26	whose	whose	DET
ejpam-6607	269	27	measurement	measurement	NOUN
ejpam-6607	269	28	probabilities	probability	NOUN
ejpam-6607	269	29	yield	yield	VERB
ejpam-6607	269	30	a	a	DET
ejpam-6607	269	31	soft	soft	ADJ
ejpam-6607	269	32	membership	membership	NOUN
ejpam-6607	269	33	degree	degree	NOUN
ejpam-6607	269	34	of	of	ADP
ejpam-6607	269	35	each	each	DET
ejpam-6607	269	36	disease	disease	NOUN
ejpam-6607	269	37	given	give	VERB
ejpam-6607	269	38	the	the	DET
ejpam-6607	269	39	observed	observed	ADJ
ejpam-6607	269	40	symptoms	symptom	NOUN
ejpam-6607	269	41	.	.	PUNCT
ejpam-6607	270	1	example	example	NOUN
ejpam-6607	270	2	7	7	NUM
ejpam-6607	270	3	(	(	PUNCT
ejpam-6607	270	4	quantum	quantum	NOUN
ejpam-6607	270	5	-	-	PUNCT
ejpam-6607	270	6	hypersoft	hypersoft	NOUN
ejpam-6607	270	7	set	set	NOUN
ejpam-6607	270	8	for	for	ADP
ejpam-6607	270	9	credit	credit	NOUN
ejpam-6607	270	10	risk	risk	NOUN
ejpam-6607	270	11	assessment	assessment	NOUN
ejpam-6607	270	12	)	)	PUNCT
ejpam-6607	270	13	.	.	PUNCT
ejpam-6607	271	1	let	let	VERB
ejpam-6607	271	2	u	u	PRON
ejpam-6607	271	3	=	=	PUNCT
ejpam-6607	271	4	{	{	PUNCT
ejpam-6607	271	5	approve	approve	PROPN
ejpam-6607	271	6	,	,	PUNCT
ejpam-6607	271	7	review	review	NOUN
ejpam-6607	271	8	,	,	PUNCT
ejpam-6607	271	9	deny	deny	AUX
ejpam-6607	271	10	}	}	PUNCT
ejpam-6607	271	11	be	be	VERB
ejpam-6607	271	12	the	the	DET
ejpam-6607	271	13	set	set	NOUN
ejpam-6607	271	14	of	of	ADP
ejpam-6607	271	15	possible	possible	ADJ
ejpam-6607	271	16	credit	credit	NOUN
ejpam-6607	271	17	decisions	decision	NOUN
ejpam-6607	271	18	.	.	PUNCT
ejpam-6607	272	1	consider	consider	VERB
ejpam-6607	272	2	three	three	NUM
ejpam-6607	272	3	financial	financial	ADJ
ejpam-6607	272	4	-	-	PUNCT
ejpam-6607	272	5	attribute	attribute	NOUN
ejpam-6607	272	6	domains	domain	NOUN
ejpam-6607	272	7	:	:	PUNCT
ejpam-6607	272	8	a1	a1	NOUN
ejpam-6607	272	9	=	=	SYM
ejpam-6607	272	10	{	{	PUNCT
ejpam-6607	272	11	highincome	highincome	INTJ
ejpam-6607	272	12	,	,	PUNCT
ejpam-6607	272	13	lowincome	lowincome	NOUN
ejpam-6607	272	14	}	}	PUNCT
ejpam-6607	272	15	,	,	PUNCT
ejpam-6607	272	16	a2	a2	PROPN
ejpam-6607	272	17	=	=	PUNCT
ejpam-6607	272	18	{	{	PUNCT
ejpam-6607	272	19	goodhistory	goodhistory	ADJ
ejpam-6607	272	20	,	,	PUNCT
ejpam-6607	272	21	poorhistory	poorhistory	NOUN
ejpam-6607	272	22	}	}	PUNCT
ejpam-6607	272	23	,	,	PUNCT
ejpam-6607	272	24	a3	a3	NOUN
ejpam-6607	272	25	=	=	SYM
ejpam-6607	272	26	{	{	PUNCT
ejpam-6607	272	27	lowdti	lowdti	ADJ
ejpam-6607	272	28	,	,	PUNCT
ejpam-6607	272	29	highdti	highdti	NOUN
ejpam-6607	272	30	}	}	PUNCT
ejpam-6607	272	31	,	,	PUNCT
ejpam-6607	272	32	where	where	SCONJ
ejpam-6607	272	33	dti	dti	PROPN
ejpam-6607	272	34	=	=	PROPN
ejpam-6607	272	35	debt	debt	NOUN
ejpam-6607	272	36	-	-	PUNCT
ejpam-6607	272	37	to	to	ADP
ejpam-6607	272	38	-	-	PUNCT
ejpam-6607	272	39	income	income	NOUN
ejpam-6607	272	40	ratio	ratio	NOUN
ejpam-6607	272	41	.	.	PUNCT
ejpam-6607	273	1	form	form	NOUN
ejpam-6607	273	2	c	c	NOUN
ejpam-6607	273	3	=	=	SYM
ejpam-6607	273	4	a1	a1	PROPN
ejpam-6607	273	5	×a2	×a2	PROPN
ejpam-6607	273	6	×a3	×a3	PROPN
ejpam-6607	273	7	.	.	PUNCT
ejpam-6607	274	1	let	let	VERB
ejpam-6607	274	2	h(u	h(u	PROPN
ejpam-6607	274	3	)	)	PUNCT
ejpam-6607	274	4	be	be	AUX
ejpam-6607	274	5	the	the	DET
ejpam-6607	274	6	complex	complex	ADJ
ejpam-6607	274	7	hilbert	hilbert	NOUN
ejpam-6607	274	8	space	space	NOUN
ejpam-6607	274	9	with	with	ADP
ejpam-6607	274	10	orthonormal	orthonormal	ADJ
ejpam-6607	274	11	basis	basis	NOUN
ejpam-6607	274	12	{	{	PUNCT
ejpam-6607	274	13	|approve⟩	|approve⟩	NOUN
ejpam-6607	274	14	,	,	PUNCT
ejpam-6607	274	15	|review⟩	|review⟩	NOUN
ejpam-6607	274	16	,	,	PUNCT
ejpam-6607	274	17	|deny⟩	|deny⟩	PROPN
ejpam-6607	274	18	}	}	PUNCT
ejpam-6607	274	19	.	.	PUNCT
ejpam-6607	275	1	case	case	NOUN
ejpam-6607	275	2	1	1	NUM
ejpam-6607	275	3	:	:	PUNCT
ejpam-6607	275	4	γ1	γ1	PROPN
ejpam-6607	275	5	=	=	SYM
ejpam-6607	275	6	(	(	PUNCT
ejpam-6607	275	7	highincome	highincome	ADJ
ejpam-6607	275	8	,	,	PUNCT
ejpam-6607	275	9	goodhistory	goodhistory	ADJ
ejpam-6607	275	10	,	,	PUNCT
ejpam-6607	275	11	lowdti	lowdti	ADJ
ejpam-6607	275	12	)	)	PUNCT
ejpam-6607	275	13	.	.	PUNCT
ejpam-6607	276	1	define	define	VERB
ejpam-6607	276	2	|ψγ1⟩	|ψγ1⟩	NOUN
ejpam-6607	276	3	=	=	PUNCT
ejpam-6607	276	4	√	√	PROPN
ejpam-6607	276	5	0.80	0.80	NUM
ejpam-6607	276	6	|approve⟩+	|approve⟩+	NOUN
ejpam-6607	276	7	√	√	ADP
ejpam-6607	276	8	0.15	0.15	NUM
ejpam-6607	276	9	|review⟩+	|review⟩+	ADP
ejpam-6607	276	10	√	√	NUM
ejpam-6607	276	11	0.05	0.05	NUM
ejpam-6607	276	12	|deny⟩	|deny⟩	NOUN
ejpam-6607	276	13	,	,	PUNCT
ejpam-6607	276	14	so	so	SCONJ
ejpam-6607	276	15	that	that	SCONJ
ejpam-6607	276	16	p	p	X
ejpam-6607	276	17	(	(	PUNCT
ejpam-6607	276	18	approve	approve	VERB
ejpam-6607	276	19	|	|	ADV
ejpam-6607	276	20	γ1	γ1	NOUN
ejpam-6607	276	21	)	)	PUNCT
ejpam-6607	276	22	=	=	PUNCT
ejpam-6607	276	23	0.80	0.80	NUM
ejpam-6607	276	24	,	,	PUNCT
ejpam-6607	276	25	p	p	X
ejpam-6607	276	26	(	(	PUNCT
ejpam-6607	276	27	review	review	NOUN
ejpam-6607	276	28	|	|	NOUN
ejpam-6607	276	29	γ1	γ1	NOUN
ejpam-6607	276	30	)	)	PUNCT
ejpam-6607	276	31	=	=	PUNCT
ejpam-6607	277	1	0.15	0.15	NUM
ejpam-6607	277	2	,	,	PUNCT
ejpam-6607	277	3	p	p	X
ejpam-6607	277	4	(	(	PUNCT
ejpam-6607	277	5	deny	deny	VERB
ejpam-6607	277	6	|	|	NOUN
ejpam-6607	277	7	γ1	γ1	NOUN
ejpam-6607	277	8	)	)	PUNCT
ejpam-6607	277	9	=	=	PUNCT
ejpam-6607	277	10	0.05	0.05	NUM
ejpam-6607	277	11	.	.	PUNCT
ejpam-6607	277	12	case	case	NOUN
ejpam-6607	277	13	2	2	NUM
ejpam-6607	277	14	:	:	PUNCT
ejpam-6607	277	15	γ2	γ2	NOUN
ejpam-6607	277	16	=	=	SYM
ejpam-6607	277	17	(	(	PUNCT
ejpam-6607	277	18	lowincome	lowincome	PROPN
ejpam-6607	277	19	,	,	PUNCT
ejpam-6607	277	20	poorhistory	poorhistory	NOUN
ejpam-6607	277	21	,	,	PUNCT
ejpam-6607	277	22	highdti	highdti	NOUN
ejpam-6607	277	23	)	)	PUNCT
ejpam-6607	277	24	.	.	PUNCT
ejpam-6607	278	1	define	define	VERB
ejpam-6607	278	2	|ψγ2⟩	|ψγ2⟩	NOUN
ejpam-6607	278	3	=	=	PUNCT
ejpam-6607	278	4	√	√	ADP
ejpam-6607	278	5	0.10	0.10	NUM
ejpam-6607	278	6	|approve⟩+	|approve⟩+	NOUN
ejpam-6607	278	7	√	√	ADP
ejpam-6607	278	8	0.20	0.20	NUM
ejpam-6607	278	9	|review⟩+	|review⟩+	ADP
ejpam-6607	278	10	√	√	PROPN
ejpam-6607	278	11	0.70	0.70	NUM
ejpam-6607	278	12	|deny⟩	|deny⟩	NOUN
ejpam-6607	278	13	,	,	PUNCT
ejpam-6607	278	14	with	with	ADP
ejpam-6607	278	15	p	p	NOUN
ejpam-6607	278	16	(	(	PUNCT
ejpam-6607	278	17	approve	approve	VERB
ejpam-6607	278	18	|	|	ADV
ejpam-6607	278	19	γ2	γ2	ADJ
ejpam-6607	278	20	)	)	PUNCT
ejpam-6607	279	1	=	=	SYM
ejpam-6607	279	2	0.10	0.10	NUM
ejpam-6607	279	3	,	,	PUNCT
ejpam-6607	279	4	p	p	X
ejpam-6607	279	5	(	(	PUNCT
ejpam-6607	279	6	review	review	NOUN
ejpam-6607	279	7	|	|	ADV
ejpam-6607	279	8	γ2	γ2	ADJ
ejpam-6607	279	9	)	)	PUNCT
ejpam-6607	280	1	=	=	SYM
ejpam-6607	280	2	0.20	0.20	NUM
ejpam-6607	280	3	,	,	PUNCT
ejpam-6607	280	4	p	p	X
ejpam-6607	280	5	(	(	PUNCT
ejpam-6607	280	6	deny	deny	VERB
ejpam-6607	280	7	|	|	ADV
ejpam-6607	280	8	γ2	γ2	NOUN
ejpam-6607	280	9	)	)	PUNCT
ejpam-6607	280	10	=	=	PUNCT
ejpam-6607	281	1	0.70	0.70	NUM
ejpam-6607	281	2	.	.	PUNCT
ejpam-6607	282	1	interpretation	interpretation	NOUN
ejpam-6607	282	2	.	.	PUNCT
ejpam-6607	283	1	•	•	NUM
ejpam-6607	283	2	under	under	ADP
ejpam-6607	283	3	γ1	γ1	NOUN
ejpam-6607	283	4	,	,	PUNCT
ejpam-6607	283	5	strong	strong	ADJ
ejpam-6607	283	6	profile	profile	NOUN
ejpam-6607	283	7	yields	yield	VERB
ejpam-6607	283	8	an	an	DET
ejpam-6607	283	9	80	80	NUM
ejpam-6607	283	10	•	•	NOUN
ejpam-6607	283	11	under	under	ADP
ejpam-6607	283	12	γ2	γ2	ADJ
ejpam-6607	283	13	,	,	PUNCT
ejpam-6607	283	14	weak	weak	ADJ
ejpam-6607	283	15	profile	profile	NOUN
ejpam-6607	283	16	yields	yield	VERB
ejpam-6607	283	17	a	a	DET
ejpam-6607	283	18	70	70	NUM
ejpam-6607	283	19	t.	t.	PROPN
ejpam-6607	283	20	fujita	fujita	PROPN
ejpam-6607	283	21	,	,	PUNCT
ejpam-6607	283	22	f.smarandache	f.smarandache	NOUN
ejpam-6607	283	23	/	/	SYM
ejpam-6607	283	24	eur	eur	PROPN
ejpam-6607	283	25	.	.	PUNCT
ejpam-6607	284	1	j.	j.	PROPN
ejpam-6607	284	2	pure	pure	PROPN
ejpam-6607	284	3	appl	appl	PROPN
ejpam-6607	284	4	.	.	PROPN
ejpam-6607	284	5	math	math	PROPN
ejpam-6607	284	6	,	,	PUNCT
ejpam-6607	284	7	18	18	NUM
ejpam-6607	284	8	(	(	PUNCT
ejpam-6607	284	9	3	3	NUM
ejpam-6607	284	10	)	)	PUNCT
ejpam-6607	284	11	(	(	PUNCT
ejpam-6607	284	12	2025	2025	NUM
ejpam-6607	284	13	)	)	PUNCT
ejpam-6607	284	14	,	,	PUNCT
ejpam-6607	284	15	6607	6607	NUM
ejpam-6607	284	16	14	14	NUM
ejpam-6607	284	17	of	of	ADP
ejpam-6607	284	18	33	33	NUM
ejpam-6607	284	19	example	example	NOUN
ejpam-6607	284	20	8	8	NUM
ejpam-6607	284	21	(	(	PUNCT
ejpam-6607	284	22	quantum	quantum	NOUN
ejpam-6607	284	23	-	-	PUNCT
ejpam-6607	284	24	hypersoft	hypersoft	NOUN
ejpam-6607	284	25	set	set	NOUN
ejpam-6607	284	26	for	for	ADP
ejpam-6607	284	27	traffic	traffic	NOUN
ejpam-6607	284	28	incident	incident	NOUN
ejpam-6607	284	29	prediction	prediction	NOUN
ejpam-6607	284	30	)	)	PUNCT
ejpam-6607	284	31	.	.	PUNCT
ejpam-6607	285	1	let	let	VERB
ejpam-6607	285	2	u	u	PRON
ejpam-6607	285	3	=	=	NOUN
ejpam-6607	285	4	{	{	PUNCT
ejpam-6607	285	5	noincident	noincident	NOUN
ejpam-6607	285	6	,	,	PUNCT
ejpam-6607	285	7	minorincident	minorincident	NOUN
ejpam-6607	285	8	,	,	PUNCT
ejpam-6607	285	9	majorincident	majorincident	NOUN
ejpam-6607	285	10	}	}	PUNCT
ejpam-6607	285	11	be	be	VERB
ejpam-6607	285	12	the	the	DET
ejpam-6607	285	13	set	set	NOUN
ejpam-6607	285	14	of	of	ADP
ejpam-6607	285	15	traffic	traffic	NOUN
ejpam-6607	285	16	-	-	PUNCT
ejpam-6607	285	17	incident	incident	NOUN
ejpam-6607	285	18	outcomes	outcome	NOUN
ejpam-6607	285	19	.	.	PUNCT
ejpam-6607	286	1	consider	consider	VERB
ejpam-6607	286	2	three	three	NUM
ejpam-6607	286	3	sensor	sensor	NOUN
ejpam-6607	286	4	-	-	PUNCT
ejpam-6607	286	5	attribute	attribute	NOUN
ejpam-6607	286	6	domains	domain	NOUN
ejpam-6607	286	7	:	:	PUNCT
ejpam-6607	286	8	a1	a1	NOUN
ejpam-6607	286	9	=	=	SYM
ejpam-6607	286	10	{	{	PUNCT
ejpam-6607	286	11	heavyflow	heavyflow	NOUN
ejpam-6607	286	12	,	,	PUNCT
ejpam-6607	286	13	lightflow	lightflow	NOUN
ejpam-6607	286	14	}	}	PUNCT
ejpam-6607	286	15	,	,	PUNCT
ejpam-6607	286	16	a2	a2	PROPN
ejpam-6607	286	17	=	=	PUNCT
ejpam-6607	286	18	{	{	PUNCT
ejpam-6607	286	19	adverseweather	adverseweather	ADJ
ejpam-6607	286	20	,	,	PUNCT
ejpam-6607	286	21	clearweather	clearweather	NOUN
ejpam-6607	286	22	}	}	PUNCT
ejpam-6607	286	23	,	,	PUNCT
ejpam-6607	286	24	a3	a3	NOUN
ejpam-6607	286	25	=	=	SYM
ejpam-6607	286	26	{	{	PUNCT
ejpam-6607	286	27	daytime	daytime	NOUN
ejpam-6607	286	28	,	,	PUNCT
ejpam-6607	286	29	nighttime	nighttime	NOUN
ejpam-6607	286	30	}	}	PUNCT
ejpam-6607	286	31	.	.	PUNCT
ejpam-6607	287	1	form	form	NOUN
ejpam-6607	287	2	c	c	NOUN
ejpam-6607	287	3	=	=	SYM
ejpam-6607	287	4	a1	a1	PROPN
ejpam-6607	287	5	×a2	×a2	PROPN
ejpam-6607	287	6	×a3	×a3	PROPN
ejpam-6607	287	7	,	,	PUNCT
ejpam-6607	287	8	and	and	CCONJ
ejpam-6607	287	9	let	let	VERB
ejpam-6607	287	10	h(u	h(u	PROPN
ejpam-6607	287	11	)	)	PUNCT
ejpam-6607	287	12	have	have	VERB
ejpam-6607	287	13	basis	basis	NOUN
ejpam-6607	287	14	{	{	PUNCT
ejpam-6607	287	15	|noincident⟩	|noincident⟩	NOUN
ejpam-6607	287	16	,	,	PUNCT
ejpam-6607	287	17	|minorincident⟩	|minorincident⟩	ADJ
ejpam-6607	287	18	,	,	PUNCT
ejpam-6607	287	19	|majorincident⟩	|majorincident⟩	ADJ
ejpam-6607	287	20	}	}	PUNCT
ejpam-6607	287	21	.	.	PUNCT
ejpam-6607	288	1	case	case	NOUN
ejpam-6607	288	2	1	1	NUM
ejpam-6607	288	3	:	:	PUNCT
ejpam-6607	288	4	γ1	γ1	PROPN
ejpam-6607	288	5	=	=	SYM
ejpam-6607	288	6	(	(	PUNCT
ejpam-6607	288	7	heavyflow	heavyflow	PROPN
ejpam-6607	288	8	,	,	PUNCT
ejpam-6607	288	9	adverseweather	adverseweather	ADJ
ejpam-6607	288	10	,	,	PUNCT
ejpam-6607	288	11	nighttime	nighttime	NOUN
ejpam-6607	288	12	)	)	PUNCT
ejpam-6607	288	13	.	.	PUNCT
ejpam-6607	289	1	define	define	VERB
ejpam-6607	289	2	|ψγ1⟩	|ψγ1⟩	NOUN
ejpam-6607	289	3	=	=	PUNCT
ejpam-6607	289	4	√	√	NUM
ejpam-6607	289	5	0.20	0.20	NUM
ejpam-6607	289	6	|noincident⟩+	|noincident⟩+	NOUN
ejpam-6607	289	7	√	√	PROPN
ejpam-6607	289	8	0.50	0.50	NUM
ejpam-6607	289	9	|minorincident⟩+	|minorincident⟩+	NOUN
ejpam-6607	289	10	√	√	NUM
ejpam-6607	289	11	0.30	0.30	NUM
ejpam-6607	289	12	|majorincident⟩	|majorincident⟩	NOUN
ejpam-6607	289	13	,	,	PUNCT
ejpam-6607	289	14	so	so	SCONJ
ejpam-6607	289	15	that	that	SCONJ
ejpam-6607	289	16	p	p	X
ejpam-6607	289	17	(	(	PUNCT
ejpam-6607	289	18	noincident	noincident	NOUN
ejpam-6607	289	19	|	|	NOUN
ejpam-6607	289	20	γ1	γ1	NOUN
ejpam-6607	289	21	)	)	PUNCT
ejpam-6607	289	22	=	=	SYM
ejpam-6607	289	23	0.20	0.20	NUM
ejpam-6607	289	24	,	,	PUNCT
ejpam-6607	289	25	p	p	X
ejpam-6607	289	26	(	(	PUNCT
ejpam-6607	289	27	minorincident	minorincident	NOUN
ejpam-6607	289	28	|	|	NOUN
ejpam-6607	289	29	γ1	γ1	NOUN
ejpam-6607	289	30	)	)	PUNCT
ejpam-6607	289	31	=	=	SYM
ejpam-6607	289	32	0.50	0.50	NUM
ejpam-6607	289	33	,	,	PUNCT
ejpam-6607	289	34	p	p	X
ejpam-6607	289	35	(	(	PUNCT
ejpam-6607	289	36	majorincident	majorincident	NOUN
ejpam-6607	289	37	|	|	NOUN
ejpam-6607	289	38	γ1	γ1	NOUN
ejpam-6607	289	39	)	)	PUNCT
ejpam-6607	289	40	=	=	SYM
ejpam-6607	289	41	0.30	0.30	NUM
ejpam-6607	289	42	.	.	PUNCT
ejpam-6607	290	1	case	case	NOUN
ejpam-6607	290	2	2	2	NUM
ejpam-6607	290	3	:	:	PUNCT
ejpam-6607	290	4	γ2	γ2	NOUN
ejpam-6607	290	5	=	=	SYM
ejpam-6607	290	6	(	(	PUNCT
ejpam-6607	290	7	lightflow	lightflow	PROPN
ejpam-6607	290	8	,	,	PUNCT
ejpam-6607	290	9	clearweather	clearweather	NOUN
ejpam-6607	290	10	,	,	PUNCT
ejpam-6607	290	11	daytime	daytime	NOUN
ejpam-6607	290	12	)	)	PUNCT
ejpam-6607	290	13	.	.	PUNCT
ejpam-6607	291	1	define	define	VERB
ejpam-6607	291	2	|ψγ2⟩	|ψγ2⟩	NOUN
ejpam-6607	291	3	=	=	SYM
ejpam-6607	291	4	√	√	NUM
ejpam-6607	291	5	0.75	0.75	NUM
ejpam-6607	291	6	|noincident⟩+	|noincident⟩+	NOUN
ejpam-6607	291	7	√	√	NUM
ejpam-6607	291	8	0.20	0.20	NUM
ejpam-6607	291	9	|minorincident⟩+	|minorincident⟩+	NOUN
ejpam-6607	291	10	√	√	NUM
ejpam-6607	291	11	0.05	0.05	NUM
ejpam-6607	291	12	|majorincident⟩	|majorincident⟩	NOUN
ejpam-6607	291	13	,	,	PUNCT
ejpam-6607	291	14	yielding	yield	VERB
ejpam-6607	291	15	p	p	X
ejpam-6607	291	16	(	(	PUNCT
ejpam-6607	291	17	noincident	noincident	NOUN
ejpam-6607	291	18	|	|	ADV
ejpam-6607	291	19	γ2	γ2	NOUN
ejpam-6607	291	20	)	)	PUNCT
ejpam-6607	291	21	=	=	SYM
ejpam-6607	291	22	0.75	0.75	NUM
ejpam-6607	291	23	,	,	PUNCT
ejpam-6607	291	24	p	p	X
ejpam-6607	291	25	(	(	PUNCT
ejpam-6607	291	26	minorincident	minorincident	NOUN
ejpam-6607	291	27	|	|	ADV
ejpam-6607	291	28	γ2	γ2	NOUN
ejpam-6607	291	29	)	)	PUNCT
ejpam-6607	291	30	=	=	SYM
ejpam-6607	291	31	0.20	0.20	NUM
ejpam-6607	291	32	,	,	PUNCT
ejpam-6607	291	33	p	p	X
ejpam-6607	291	34	(	(	PUNCT
ejpam-6607	291	35	majorincident	majorincident	NOUN
ejpam-6607	291	36	|	|	ADV
ejpam-6607	291	37	γ2	γ2	NOUN
ejpam-6607	291	38	)	)	PUNCT
ejpam-6607	291	39	=	=	PUNCT
ejpam-6607	291	40	0.05	0.05	NUM
ejpam-6607	291	41	.	.	PUNCT
ejpam-6607	292	1	interpretation	interpretation	NOUN
ejpam-6607	292	2	.	.	PUNCT
ejpam-6607	293	1	•	•	NUM
ejpam-6607	293	2	under	under	ADP
ejpam-6607	293	3	γ1	γ1	NOUN
ejpam-6607	293	4	,	,	PUNCT
ejpam-6607	293	5	high	high	ADJ
ejpam-6607	293	6	risk	risk	NOUN
ejpam-6607	293	7	conditions	condition	NOUN
ejpam-6607	293	8	yield	yield	VERB
ejpam-6607	293	9	a	a	DET
ejpam-6607	293	10	30	30	NUM
ejpam-6607	293	11	%	%	NOUN
ejpam-6607	293	12	chance	chance	NOUN
ejpam-6607	293	13	of	of	ADP
ejpam-6607	293	14	a	a	DET
ejpam-6607	293	15	major	major	ADJ
ejpam-6607	293	16	incident	incident	NOUN
ejpam-6607	293	17	.	.	PUNCT
ejpam-6607	294	1	•	•	NUM
ejpam-6607	294	2	under	under	ADP
ejpam-6607	294	3	γ2	γ2	ADJ
ejpam-6607	294	4	,	,	PUNCT
ejpam-6607	294	5	benign	benign	ADJ
ejpam-6607	294	6	conditions	condition	NOUN
ejpam-6607	294	7	yield	yield	VERB
ejpam-6607	294	8	a	a	DET
ejpam-6607	294	9	75	75	NUM
ejpam-6607	294	10	%	%	NOUN
ejpam-6607	294	11	chance	chance	NOUN
ejpam-6607	294	12	of	of	ADP
ejpam-6607	294	13	no	no	DET
ejpam-6607	294	14	incident	incident	NOUN
ejpam-6607	294	15	.	.	PUNCT
ejpam-6607	295	1	theorem	theorem	NOUN
ejpam-6607	295	2	5	5	NUM
ejpam-6607	295	3	.	.	PUNCT
ejpam-6607	296	1	every	every	DET
ejpam-6607	296	2	hypersoft	hypersoft	NOUN
ejpam-6607	296	3	set	set	VERB
ejpam-6607	296	4	and	and	CCONJ
ejpam-6607	296	5	every	every	DET
ejpam-6607	296	6	quantum	quantum	NOUN
ejpam-6607	296	7	-	-	PUNCT
ejpam-6607	296	8	soft	soft	ADJ
ejpam-6607	296	9	set	set	NOUN
ejpam-6607	296	10	arises	arise	VERB
ejpam-6607	296	11	as	as	ADP
ejpam-6607	296	12	a	a	DET
ejpam-6607	296	13	special	special	ADJ
ejpam-6607	296	14	case	case	NOUN
ejpam-6607	296	15	of	of	ADP
ejpam-6607	296	16	a	a	DET
ejpam-6607	296	17	quantum	quantum	NOUN
ejpam-6607	296	18	-	-	PUNCT
ejpam-6607	296	19	hypersoft	hypersoft	NOUN
ejpam-6607	296	20	set	set	NOUN
ejpam-6607	296	21	.	.	PUNCT
ejpam-6607	297	1	proof	proof	NOUN
ejpam-6607	297	2	.	.	PUNCT
ejpam-6607	298	1	(	(	PUNCT
ejpam-6607	298	2	i	i	NOUN
ejpam-6607	298	3	)	)	PUNCT
ejpam-6607	298	4	reduction	reduction	NOUN
ejpam-6607	298	5	to	to	ADP
ejpam-6607	298	6	hypersoft	hypersoft	PROPN
ejpam-6607	298	7	set	set	PROPN
ejpam-6607	298	8	.	.	PUNCT
ejpam-6607	299	1	let	let	AUX
ejpam-6607	299	2	(	(	PUNCT
ejpam-6607	299	3	g	g	NOUN
ejpam-6607	299	4	,	,	PUNCT
ejpam-6607	299	5	c	c	AUX
ejpam-6607	299	6	)	)	PUNCT
ejpam-6607	299	7	be	be	AUX
ejpam-6607	299	8	a	a	DET
ejpam-6607	299	9	classical	classical	ADJ
ejpam-6607	299	10	hypersoft	hypersoft	NOUN
ejpam-6607	299	11	set	set	VERB
ejpam-6607	299	12	over	over	ADP
ejpam-6607	299	13	u	u	NOUN
ejpam-6607	299	14	,	,	PUNCT
ejpam-6607	299	15	so	so	ADV
ejpam-6607	299	16	g	g	NOUN
ejpam-6607	299	17	:	:	PUNCT
ejpam-6607	299	18	c	c	X
ejpam-6607	299	19	→	→	SYM
ejpam-6607	299	20	p(u	p(u	ADJ
ejpam-6607	299	21	)	)	PUNCT
ejpam-6607	299	22	with	with	ADP
ejpam-6607	299	23	g(γ	g(γ	PROPN
ejpam-6607	299	24	)	)	PUNCT
ejpam-6607	299	25	⊆	⊆	NUM
ejpam-6607	299	26	u	u	NOUN
ejpam-6607	299	27	for	for	ADP
ejpam-6607	299	28	each	each	DET
ejpam-6607	299	29	γ	γ	NOUN
ejpam-6607	299	30	[	[	X
ejpam-6607	299	31	21	21	NUM
ejpam-6607	299	32	]	]	PUNCT
ejpam-6607	299	33	.	.	PUNCT
ejpam-6607	300	1	define	define	VERB
ejpam-6607	300	2	amplitudes	amplitude	NOUN
ejpam-6607	300	3	αi	αi	ADP
ejpam-6607	300	4	,	,	PUNCT
ejpam-6607	300	5	γ	γ	X
ejpam-6607	300	6	=	=	SYM
ejpam-6607	300	7			PROPN
ejpam-6607	300	8	1√	1√	PROPN
ejpam-6607	300	9	|g(γ)|	|g(γ)|	PROPN
ejpam-6607	300	10	if	if	SCONJ
ejpam-6607	300	11	ui	ui	PROPN
ejpam-6607	300	12	∈	∈	PROPN
ejpam-6607	300	13	g(γ	g(γ	PROPN
ejpam-6607	300	14	)	)	PUNCT
ejpam-6607	300	15	,	,	PUNCT
ejpam-6607	300	16	0	0	NUM
ejpam-6607	300	17	otherwise	otherwise	ADV
ejpam-6607	300	18	.	.	PUNCT
ejpam-6607	301	1	t.	t.	PROPN
ejpam-6607	301	2	fujita	fujita	PROPN
ejpam-6607	301	3	,	,	PUNCT
ejpam-6607	301	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	301	5	/	/	SYM
ejpam-6607	301	6	eur	eur	PROPN
ejpam-6607	301	7	.	.	PUNCT
ejpam-6607	302	1	j.	j.	PROPN
ejpam-6607	302	2	pure	pure	PROPN
ejpam-6607	302	3	appl	appl	PROPN
ejpam-6607	302	4	.	.	PROPN
ejpam-6607	302	5	math	math	PROPN
ejpam-6607	302	6	,	,	PUNCT
ejpam-6607	302	7	18	18	NUM
ejpam-6607	302	8	(	(	PUNCT
ejpam-6607	302	9	3	3	NUM
ejpam-6607	302	10	)	)	PUNCT
ejpam-6607	302	11	(	(	PUNCT
ejpam-6607	302	12	2025	2025	NUM
ejpam-6607	302	13	)	)	PUNCT
ejpam-6607	302	14	,	,	PUNCT
ejpam-6607	302	15	6607	6607	NUM
ejpam-6607	302	16	15	15	NUM
ejpam-6607	302	17	of	of	ADP
ejpam-6607	302	18	33	33	NUM
ejpam-6607	302	19	then	then	ADV
ejpam-6607	302	20	∑	∑	ADV
ejpam-6607	302	21	i	i	PRON
ejpam-6607	302	22	|αi	|αi	NUM
ejpam-6607	302	23	,	,	PUNCT
ejpam-6607	302	24	γ	γ	X
ejpam-6607	302	25	|2	|2	X
ejpam-6607	302	26	=	=	SYM
ejpam-6607	302	27	|g(γ)|	|g(γ)|	PROPN
ejpam-6607	302	28	·	·	SYM
ejpam-6607	302	29	1	1	NUM
ejpam-6607	302	30	|g(γ)|	|g(γ)|	PROPN
ejpam-6607	302	31	=	=	SYM
ejpam-6607	302	32	1	1	NUM
ejpam-6607	302	33	,	,	PUNCT
ejpam-6607	302	34	so	so	ADV
ejpam-6607	302	35	q(γ	q(γ	PROPN
ejpam-6607	302	36	)	)	PUNCT
ejpam-6607	303	1	=	=	PRON
ejpam-6607	303	2	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	303	3	is	be	AUX
ejpam-6607	303	4	a	a	DET
ejpam-6607	303	5	valid	valid	ADJ
ejpam-6607	303	6	quantum	quantum	NOUN
ejpam-6607	303	7	-	-	PUNCT
ejpam-6607	303	8	hypersoft	hypersoft	NOUN
ejpam-6607	303	9	state	state	NOUN
ejpam-6607	303	10	.	.	PUNCT
ejpam-6607	304	1	moreover	moreover	ADV
ejpam-6607	304	2	,	,	PUNCT
ejpam-6607	304	3	the	the	DET
ejpam-6607	304	4	measurement	measurement	NOUN
ejpam-6607	304	5	probabilities	probability	NOUN
ejpam-6607	304	6	satisfy	satisfy	VERB
ejpam-6607	304	7	p	p	PROPN
ejpam-6607	304	8	(	(	PUNCT
ejpam-6607	304	9	ui	ui	PROPN
ejpam-6607	304	10	|	|	ADV
ejpam-6607	304	11	γ	γ	PROPN
ejpam-6607	304	12	)	)	PUNCT
ejpam-6607	304	13	=	=	SYM
ejpam-6607	304	14	|αi	|αi	X
ejpam-6607	304	15	,	,	PUNCT
ejpam-6607	304	16	γ	γ	X
ejpam-6607	304	17	|2	|2	NUM
ejpam-6607	304	18	=	=	SYM
ejpam-6607	304	19			PUNCT
ejpam-6607	304	20	1	1	NUM
ejpam-6607	304	21	|g(γ)|	|g(γ)|	PROPN
ejpam-6607	304	22	,	,	PUNCT
ejpam-6607	304	23	ui	ui	PROPN
ejpam-6607	304	24	∈	∈	PROPN
ejpam-6607	304	25	g(γ	g(γ	PROPN
ejpam-6607	304	26	)	)	PUNCT
ejpam-6607	304	27	,	,	PUNCT
ejpam-6607	304	28	0	0	NUM
ejpam-6607	304	29	,	,	PUNCT
ejpam-6607	304	30	else	else	ADV
ejpam-6607	304	31	,	,	PUNCT
ejpam-6607	304	32	recovering	recover	VERB
ejpam-6607	304	33	exactly	exactly	ADV
ejpam-6607	304	34	the	the	DET
ejpam-6607	304	35	classical	classical	ADJ
ejpam-6607	304	36	hypersoft	hypersoft	NOUN
ejpam-6607	304	37	membership	membership	NOUN
ejpam-6607	304	38	ui	ui	PROPN
ejpam-6607	304	39	∈	∈	PROPN
ejpam-6607	304	40	g(γ	g(γ	PROPN
ejpam-6607	304	41	)	)	PUNCT
ejpam-6607	304	42	.	.	PUNCT
ejpam-6607	305	1	(	(	PUNCT
ejpam-6607	305	2	ii	ii	NOUN
ejpam-6607	305	3	)	)	PUNCT
ejpam-6607	305	4	reduction	reduction	NOUN
ejpam-6607	305	5	to	to	ADP
ejpam-6607	305	6	quantum	quantum	NOUN
ejpam-6607	305	7	-	-	PUNCT
ejpam-6607	305	8	soft	soft	ADJ
ejpam-6607	305	9	set	set	NOUN
ejpam-6607	305	10	.	.	PUNCT
ejpam-6607	306	1	if	if	SCONJ
ejpam-6607	306	2	m	m	VERB
ejpam-6607	306	3	=	=	NOUN
ejpam-6607	306	4	1	1	NUM
ejpam-6607	306	5	,	,	PUNCT
ejpam-6607	306	6	then	then	ADV
ejpam-6607	306	7	c	c	NOUN
ejpam-6607	306	8	=	=	NOUN
ejpam-6607	306	9	a1	a1	NOUN
ejpam-6607	306	10	is	be	AUX
ejpam-6607	306	11	a	a	DET
ejpam-6607	306	12	single	single	ADJ
ejpam-6607	306	13	attribute	attribute	NOUN
ejpam-6607	306	14	domain	domain	NOUN
ejpam-6607	306	15	and	and	CCONJ
ejpam-6607	306	16	the	the	DET
ejpam-6607	306	17	map	map	NOUN
ejpam-6607	306	18	q	q	NOUN
ejpam-6607	306	19	:	:	PUNCT
ejpam-6607	306	20	a1	a1	PROPN
ejpam-6607	306	21	→	→	SYM
ejpam-6607	306	22	h(u	h(u	PROPN
ejpam-6607	306	23	)	)	PUNCT
ejpam-6607	306	24	,	,	PUNCT
ejpam-6607	306	25	a	a	DET
ejpam-6607	306	26	7→	7→	NUM
ejpam-6607	306	27	|ψa⟩	|ψa⟩	ADP
ejpam-6607	306	28	=	=	PROPN
ejpam-6607	306	29	n∑	n∑	PROPN
ejpam-6607	306	30	i=1	i=1	PROPN
ejpam-6607	306	31	αi	αi	PROPN
ejpam-6607	306	32	,	,	PUNCT
ejpam-6607	306	33	a	a	DET
ejpam-6607	306	34	|ui⟩	|ui⟩	NOUN
ejpam-6607	306	35	,	,	PUNCT
ejpam-6607	306	36	matches	match	VERB
ejpam-6607	306	37	precisely	precisely	ADV
ejpam-6607	306	38	the	the	DET
ejpam-6607	306	39	definition	definition	NOUN
ejpam-6607	306	40	of	of	ADP
ejpam-6607	306	41	a	a	DET
ejpam-6607	306	42	quantum	quantum	NOUN
ejpam-6607	306	43	-	-	PUNCT
ejpam-6607	306	44	soft	soft	ADJ
ejpam-6607	306	45	set	set	NOUN
ejpam-6607	306	46	,	,	PUNCT
ejpam-6607	306	47	in	in	ADP
ejpam-6607	306	48	which	which	PRON
ejpam-6607	306	49	each	each	DET
ejpam-6607	306	50	attribute	attribute	NOUN
ejpam-6607	306	51	a	a	PRON
ejpam-6607	306	52	is	be	AUX
ejpam-6607	306	53	assigned	assign	VERB
ejpam-6607	306	54	a	a	DET
ejpam-6607	306	55	normalized	normalize	VERB
ejpam-6607	306	56	superposition	superposition	NOUN
ejpam-6607	306	57	|ψa⟩	|ψa⟩	ADP
ejpam-6607	306	58	over	over	ADP
ejpam-6607	306	59	u	u	NOUN
ejpam-6607	306	60	[	[	X
ejpam-6607	306	61	3	3	NUM
ejpam-6607	306	62	]	]	PUNCT
ejpam-6607	306	63	.	.	PUNCT
ejpam-6607	307	1	thus	thus	ADV
ejpam-6607	307	2	both	both	CCONJ
ejpam-6607	307	3	classical	classical	ADJ
ejpam-6607	307	4	hypersoft	hypersoft	NOUN
ejpam-6607	307	5	and	and	CCONJ
ejpam-6607	307	6	quantum	quantum	NOUN
ejpam-6607	307	7	-	-	PUNCT
ejpam-6607	307	8	soft	soft	ADJ
ejpam-6607	307	9	sets	set	NOUN
ejpam-6607	307	10	embed	embe	VERB
ejpam-6607	307	11	naturally	naturally	ADV
ejpam-6607	307	12	in	in	ADP
ejpam-6607	307	13	the	the	DET
ejpam-6607	307	14	quantumhypersoft	quantumhypersoft	NOUN
ejpam-6607	307	15	framework	framework	NOUN
ejpam-6607	307	16	.	.	PUNCT
ejpam-6607	308	1	theorem	theorem	VERB
ejpam-6607	308	2	6	6	NUM
ejpam-6607	308	3	(	(	PUNCT
ejpam-6607	308	4	unitary	unitary	ADJ
ejpam-6607	308	5	invariance	invariance	NOUN
ejpam-6607	308	6	)	)	PUNCT
ejpam-6607	308	7	.	.	PUNCT
ejpam-6607	309	1	let	let	VERB
ejpam-6607	309	2	q	q	PRON
ejpam-6607	309	3	be	be	AUX
ejpam-6607	309	4	a	a	DET
ejpam-6607	309	5	quantum	quantum	NOUN
ejpam-6607	309	6	-	-	PUNCT
ejpam-6607	309	7	hypersoft	hypersoft	NOUN
ejpam-6607	309	8	set	set	VERB
ejpam-6607	309	9	over	over	ADP
ejpam-6607	309	10	(	(	PUNCT
ejpam-6607	309	11	u	u	NOUN
ejpam-6607	309	12	,	,	PUNCT
ejpam-6607	309	13	c	c	NOUN
ejpam-6607	309	14	)	)	PUNCT
ejpam-6607	309	15	.	.	PUNCT
ejpam-6607	310	1	for	for	ADP
ejpam-6607	310	2	each	each	DET
ejpam-6607	310	3	γ	γ	X
ejpam-6607	310	4	∈	∈	PROPN
ejpam-6607	310	5	c	c	NOUN
ejpam-6607	310	6	,	,	PUNCT
ejpam-6607	310	7	let	let	VERB
ejpam-6607	310	8	uγ	uγ	ADP
ejpam-6607	310	9	be	be	AUX
ejpam-6607	310	10	a	a	DET
ejpam-6607	310	11	unitary	unitary	ADJ
ejpam-6607	310	12	operator	operator	NOUN
ejpam-6607	310	13	on	on	ADP
ejpam-6607	310	14	h(u	h(u	PROPN
ejpam-6607	310	15	)	)	PUNCT
ejpam-6607	310	16	,	,	PUNCT
ejpam-6607	310	17	and	and	CCONJ
ejpam-6607	310	18	define	define	VERB
ejpam-6607	310	19	q′(γ	q′(γ	NUM
ejpam-6607	310	20	)	)	PUNCT
ejpam-6607	310	21	=	=	PUNCT
ejpam-6607	311	1	uγ	uγ	ADP
ejpam-6607	311	2	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	311	3	.	.	PUNCT
ejpam-6607	312	1	then	then	ADV
ejpam-6607	312	2	q′	q′	NOUN
ejpam-6607	312	3	is	be	AUX
ejpam-6607	312	4	also	also	ADV
ejpam-6607	312	5	a	a	DET
ejpam-6607	312	6	quantum	quantum	NOUN
ejpam-6607	312	7	-	-	PUNCT
ejpam-6607	312	8	hypersoft	hypersoft	NOUN
ejpam-6607	312	9	set	set	VERB
ejpam-6607	312	10	over	over	ADP
ejpam-6607	312	11	(	(	PUNCT
ejpam-6607	312	12	u	u	NOUN
ejpam-6607	312	13	,	,	PUNCT
ejpam-6607	312	14	c	c	NOUN
ejpam-6607	312	15	)	)	PUNCT
ejpam-6607	312	16	.	.	PUNCT
ejpam-6607	313	1	proof	proof	NOUN
ejpam-6607	313	2	.	.	PUNCT
ejpam-6607	314	1	since	since	SCONJ
ejpam-6607	314	2	each	each	DET
ejpam-6607	314	3	uγ	uγ	NOUN
ejpam-6607	314	4	is	be	AUX
ejpam-6607	314	5	unitary	unitary	ADJ
ejpam-6607	314	6	,	,	PUNCT
ejpam-6607	314	7	it	it	PRON
ejpam-6607	314	8	preserves	preserve	VERB
ejpam-6607	314	9	inner	inner	ADJ
ejpam-6607	314	10	products	product	NOUN
ejpam-6607	314	11	and	and	CCONJ
ejpam-6607	314	12	norms	norm	NOUN
ejpam-6607	314	13	.	.	PUNCT
ejpam-6607	315	1	in	in	ADP
ejpam-6607	315	2	particular	particular	ADJ
ejpam-6607	315	3	,	,	PUNCT
ejpam-6607	315	4	〈	〈	PROPN
ejpam-6607	315	5	ψγ	ψγ	X
ejpam-6607	315	6	|	|	ADV
ejpam-6607	315	7	ψγ	ψγ	NOUN
ejpam-6607	315	8	〉	〉	NOUN
ejpam-6607	315	9	=	=	SYM
ejpam-6607	315	10	1	1	NUM
ejpam-6607	315	11	=	=	NOUN
ejpam-6607	315	12	⇒	⇒	X
ejpam-6607	315	13	〈	〈	NOUN
ejpam-6607	315	14	uγψγ	uγψγ	NOUN
ejpam-6607	315	15	|	|	ADV
ejpam-6607	315	16	uγψγ	uγψγ	ADJ
ejpam-6607	315	17	〉	〉	NOUN
ejpam-6607	315	18	=	=	SYM
ejpam-6607	315	19	〈	〈	PROPN
ejpam-6607	315	20	ψγ	ψγ	X
ejpam-6607	315	21	|	|	ADV
ejpam-6607	315	22	u	u	PROPN
ejpam-6607	315	23	†	†	PROPN
ejpam-6607	315	24	γuγ	γuγ	PROPN
ejpam-6607	315	25	|	|	ADV
ejpam-6607	315	26	ψγ	ψγ	SYM
ejpam-6607	315	27	〉	〉	NOUN
ejpam-6607	315	28	=	=	PUNCT
ejpam-6607	315	29	〈	〈	PROPN
ejpam-6607	315	30	ψγ	ψγ	X
ejpam-6607	315	31	|	|	ADV
ejpam-6607	315	32	ψγ	ψγ	NOUN
ejpam-6607	315	33	〉	〉	NOUN
ejpam-6607	315	34	=	=	SYM
ejpam-6607	315	35	1	1	NUM
ejpam-6607	315	36	.	.	PUNCT
ejpam-6607	315	37	thus	thus	ADV
ejpam-6607	315	38	q′(γ	q′(γ	NUM
ejpam-6607	315	39	)	)	PUNCT
ejpam-6607	316	1	=	=	VERB
ejpam-6607	316	2	uγ	uγ	ADP
ejpam-6607	316	3	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	316	4	remains	remain	VERB
ejpam-6607	316	5	normalized	normalize	VERB
ejpam-6607	316	6	for	for	ADP
ejpam-6607	316	7	every	every	DET
ejpam-6607	316	8	γ	γ	NOUN
ejpam-6607	316	9	,	,	PUNCT
ejpam-6607	316	10	so	so	ADV
ejpam-6607	316	11	q′	q′	NOUN
ejpam-6607	316	12	satisfies	satisfy	VERB
ejpam-6607	316	13	the	the	DET
ejpam-6607	316	14	definition	definition	NOUN
ejpam-6607	316	15	of	of	ADP
ejpam-6607	316	16	a	a	DET
ejpam-6607	316	17	quantum	quantum	NOUN
ejpam-6607	316	18	-	-	PUNCT
ejpam-6607	316	19	hypersoft	hypersoft	NOUN
ejpam-6607	316	20	set	set	NOUN
ejpam-6607	316	21	.	.	PUNCT
ejpam-6607	317	1	theorem	theorem	VERB
ejpam-6607	317	2	7	7	NUM
ejpam-6607	317	3	(	(	PUNCT
ejpam-6607	317	4	crisp	crisp	ADJ
ejpam-6607	317	5	hypersoft	hypersoft	NOUN
ejpam-6607	317	6	embedding	embed	VERB
ejpam-6607	317	7	)	)	PUNCT
ejpam-6607	317	8	.	.	PUNCT
ejpam-6607	318	1	a	a	DET
ejpam-6607	318	2	quantum	quantum	NOUN
ejpam-6607	318	3	-	-	PUNCT
ejpam-6607	318	4	hypersoft	hypersoft	NOUN
ejpam-6607	318	5	set	set	VERB
ejpam-6607	318	6	q	q	NOUN
ejpam-6607	318	7	induces	induce	VERB
ejpam-6607	318	8	a	a	DET
ejpam-6607	318	9	crisp	crisp	ADJ
ejpam-6607	318	10	hypersoft	hypersoft	NOUN
ejpam-6607	318	11	set	set	VERB
ejpam-6607	318	12	if	if	SCONJ
ejpam-6607	318	13	and	and	CCONJ
ejpam-6607	318	14	only	only	ADV
ejpam-6607	318	15	if	if	SCONJ
ejpam-6607	318	16	for	for	ADP
ejpam-6607	318	17	each	each	DET
ejpam-6607	318	18	γ	γ	X
ejpam-6607	318	19	∈	∈	PROPN
ejpam-6607	318	20	c	c	NOUN
ejpam-6607	318	21	there	there	PRON
ejpam-6607	318	22	exists	exist	VERB
ejpam-6607	318	23	a	a	DET
ejpam-6607	318	24	unique	unique	ADJ
ejpam-6607	318	25	index	index	NOUN
ejpam-6607	318	26	iγ	iγ	ADP
ejpam-6607	318	27	such	such	ADJ
ejpam-6607	318	28	that	that	DET
ejpam-6607	318	29	|αiγ	|αiγ	NOUN
ejpam-6607	318	30	,	,	PUNCT
ejpam-6607	318	31	γ	γ	X
ejpam-6607	318	32	|	|	NOUN
ejpam-6607	318	33	=	=	SYM
ejpam-6607	318	34	1	1	NUM
ejpam-6607	318	35	and	and	CCONJ
ejpam-6607	318	36	αi	αi	NOUN
ejpam-6607	318	37	,	,	PUNCT
ejpam-6607	318	38	γ	γ	X
ejpam-6607	318	39	=	=	SYM
ejpam-6607	318	40	0	0	NUM
ejpam-6607	318	41	(	(	PUNCT
ejpam-6607	318	42	∀	∀	X
ejpam-6607	319	1	i	i	PRON
ejpam-6607	319	2	̸=	̸=	PROPN
ejpam-6607	319	3	iγ	iγ	NOUN
ejpam-6607	319	4	)	)	PUNCT
ejpam-6607	319	5	.	.	PUNCT
ejpam-6607	320	1	in	in	ADP
ejpam-6607	320	2	that	that	DET
ejpam-6607	320	3	case	case	NOUN
ejpam-6607	320	4	,	,	PUNCT
ejpam-6607	320	5	measurement	measurement	NOUN
ejpam-6607	320	6	of	of	ADP
ejpam-6607	320	7	|ψγ⟩	|ψγ⟩	ADJ
ejpam-6607	320	8	yields	yield	VERB
ejpam-6607	320	9	µγ(uiγ	µγ(uiγ	PROPN
ejpam-6607	320	10	)	)	PUNCT
ejpam-6607	321	1	=	=	SYM
ejpam-6607	321	2	1	1	NUM
ejpam-6607	321	3	and	and	CCONJ
ejpam-6607	321	4	µγ(ui	µγ(ui	PROPN
ejpam-6607	321	5	)	)	PUNCT
ejpam-6607	322	1	=	=	SYM
ejpam-6607	322	2	0	0	PUNCT
ejpam-6607	323	1	for	for	ADP
ejpam-6607	323	2	i	i	PRON
ejpam-6607	323	3	̸=	̸=	PROPN
ejpam-6607	323	4	iγ	iγ	NOUN
ejpam-6607	323	5	,	,	PUNCT
ejpam-6607	323	6	corresponding	correspond	VERB
ejpam-6607	323	7	exactly	exactly	ADV
ejpam-6607	323	8	to	to	ADP
ejpam-6607	323	9	the	the	DET
ejpam-6607	323	10	classical	classical	ADJ
ejpam-6607	323	11	hypersoft	hypersoft	NOUN
ejpam-6607	323	12	assignment	assignment	NOUN
ejpam-6607	323	13	g(γ	g(γ	PROPN
ejpam-6607	323	14	)	)	PUNCT
ejpam-6607	323	15	=	=	PRON
ejpam-6607	323	16	{	{	PUNCT
ejpam-6607	323	17	uiγ	uiγ	PROPN
ejpam-6607	323	18	}	}	PUNCT
ejpam-6607	323	19	.	.	PUNCT
ejpam-6607	324	1	proof	proof	NOUN
ejpam-6607	324	2	.	.	PUNCT
ejpam-6607	325	1	(	(	PUNCT
ejpam-6607	325	2	⇒	⇒	PROPN
ejpam-6607	325	3	)	)	PUNCT
ejpam-6607	325	4	if	if	SCONJ
ejpam-6607	325	5	q	q	NOUN
ejpam-6607	325	6	is	be	AUX
ejpam-6607	325	7	such	such	ADJ
ejpam-6607	325	8	that	that	SCONJ
ejpam-6607	325	9	each	each	DET
ejpam-6607	325	10	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	325	11	collapses	collapse	VERB
ejpam-6607	325	12	deterministically	deterministically	ADV
ejpam-6607	325	13	to	to	ADP
ejpam-6607	325	14	a	a	DET
ejpam-6607	325	15	single	single	ADJ
ejpam-6607	325	16	element	element	NOUN
ejpam-6607	325	17	uiγ	uiγ	NOUN
ejpam-6607	325	18	,	,	PUNCT
ejpam-6607	325	19	then	then	ADV
ejpam-6607	325	20	the	the	DET
ejpam-6607	325	21	born	bear	VERB
ejpam-6607	325	22	rule	rule	NOUN
ejpam-6607	325	23	implies	imply	VERB
ejpam-6607	325	24	|αiγ	|αiγ	NOUN
ejpam-6607	325	25	,	,	PUNCT
ejpam-6607	325	26	γ	γ	X
ejpam-6607	325	27	|2	|2	X
ejpam-6607	325	28	=	=	SYM
ejpam-6607	325	29	1	1	NUM
ejpam-6607	325	30	and	and	CCONJ
ejpam-6607	325	31	|αi	|αi	NOUN
ejpam-6607	325	32	,	,	PUNCT
ejpam-6607	325	33	γ	γ	X
ejpam-6607	325	34	|2	|2	X
ejpam-6607	325	35	=	=	SYM
ejpam-6607	325	36	0	0	NUM
ejpam-6607	325	37	for	for	SCONJ
ejpam-6607	325	38	i	i	PRON
ejpam-6607	325	39	̸=	̸=	PROPN
ejpam-6607	325	40	iγ	iγ	NOUN
ejpam-6607	325	41	.	.	PUNCT
ejpam-6607	326	1	hence	hence	ADV
ejpam-6607	326	2	αiγ	αiγ	PROPN
ejpam-6607	326	3	,	,	PUNCT
ejpam-6607	326	4	γ	γ	PROPN
ejpam-6607	326	5	=	=	SYM
ejpam-6607	326	6	±1	±1	VERB
ejpam-6607	326	7	(	(	PUNCT
ejpam-6607	326	8	up	up	ADP
ejpam-6607	326	9	to	to	ADP
ejpam-6607	326	10	a	a	DET
ejpam-6607	326	11	global	global	ADJ
ejpam-6607	326	12	phase	phase	NOUN
ejpam-6607	326	13	)	)	PUNCT
ejpam-6607	326	14	and	and	CCONJ
ejpam-6607	326	15	all	all	DET
ejpam-6607	326	16	other	other	ADJ
ejpam-6607	326	17	amplitudes	amplitude	NOUN
ejpam-6607	326	18	vanish	vanish	VERB
ejpam-6607	326	19	.	.	PUNCT
ejpam-6607	327	1	t.	t.	PROPN
ejpam-6607	327	2	fujita	fujita	PROPN
ejpam-6607	327	3	,	,	PUNCT
ejpam-6607	327	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	327	5	/	/	SYM
ejpam-6607	327	6	eur	eur	PROPN
ejpam-6607	327	7	.	.	PUNCT
ejpam-6607	328	1	j.	j.	PROPN
ejpam-6607	328	2	pure	pure	PROPN
ejpam-6607	328	3	appl	appl	PROPN
ejpam-6607	328	4	.	.	PROPN
ejpam-6607	328	5	math	math	PROPN
ejpam-6607	328	6	,	,	PUNCT
ejpam-6607	328	7	18	18	NUM
ejpam-6607	328	8	(	(	PUNCT
ejpam-6607	328	9	3	3	NUM
ejpam-6607	328	10	)	)	PUNCT
ejpam-6607	328	11	(	(	PUNCT
ejpam-6607	328	12	2025	2025	NUM
ejpam-6607	328	13	)	)	PUNCT
ejpam-6607	328	14	,	,	PUNCT
ejpam-6607	328	15	6607	6607	NUM
ejpam-6607	328	16	16	16	NUM
ejpam-6607	328	17	of	of	ADP
ejpam-6607	328	18	33	33	NUM
ejpam-6607	328	19	(	(	PUNCT
ejpam-6607	328	20	⇐	⇐	NOUN
ejpam-6607	328	21	)	)	PUNCT
ejpam-6607	328	22	conversely	conversely	ADV
ejpam-6607	328	23	,	,	PUNCT
ejpam-6607	328	24	if	if	SCONJ
ejpam-6607	328	25	the	the	DET
ejpam-6607	328	26	amplitude	amplitude	NOUN
ejpam-6607	328	27	condition	condition	NOUN
ejpam-6607	328	28	holds	hold	VERB
ejpam-6607	328	29	,	,	PUNCT
ejpam-6607	328	30	then	then	ADV
ejpam-6607	328	31	∑	∑	ADP
ejpam-6607	328	32	i	i	PRON
ejpam-6607	328	33	|αi	|αi	NUM
ejpam-6607	328	34	,	,	PUNCT
ejpam-6607	328	35	γ	γ	X
ejpam-6607	328	36	|2	|2	X
ejpam-6607	328	37	=	=	SYM
ejpam-6607	328	38	12	12	NUM
ejpam-6607	328	39	=	=	SYM
ejpam-6607	328	40	1	1	NUM
ejpam-6607	328	41	and	and	CCONJ
ejpam-6607	328	42	measurement	measurement	NOUN
ejpam-6607	328	43	yields	yield	NOUN
ejpam-6607	328	44	p	p	X
ejpam-6607	328	45	(	(	PUNCT
ejpam-6607	328	46	ui	ui	PROPN
ejpam-6607	328	47	|	|	ADV
ejpam-6607	328	48	γ	γ	NOUN
ejpam-6607	328	49	)	)	PUNCT
ejpam-6607	328	50	=	=	NOUN
ejpam-6607	328	51	{	{	PUNCT
ejpam-6607	328	52	1	1	NUM
ejpam-6607	328	53	,	,	PUNCT
ejpam-6607	328	54	i	i	PRON
ejpam-6607	328	55	=	=	PUNCT
ejpam-6607	328	56	iγ	iγ	PROPN
ejpam-6607	328	57	,	,	PUNCT
ejpam-6607	328	58	0	0	NUM
ejpam-6607	328	59	,	,	PUNCT
ejpam-6607	328	60	i	i	PRON
ejpam-6607	328	61	̸=	̸=	PROPN
ejpam-6607	328	62	iγ	iγ	VERB
ejpam-6607	328	63	,	,	PUNCT
ejpam-6607	328	64	so	so	CCONJ
ejpam-6607	328	65	the	the	DET
ejpam-6607	328	66	post	post	ADJ
ejpam-6607	328	67	-	-	ADJ
ejpam-6607	328	68	measurement	measurement	ADJ
ejpam-6607	328	69	membership	membership	NOUN
ejpam-6607	328	70	is	be	AUX
ejpam-6607	328	71	crisp	crisp	ADJ
ejpam-6607	328	72	,	,	PUNCT
ejpam-6607	328	73	g(γ	g(γ	PROPN
ejpam-6607	328	74	)	)	PUNCT
ejpam-6607	329	1	=	=	PRON
ejpam-6607	329	2	{	{	PUNCT
ejpam-6607	329	3	uiγ	uiγ	PROPN
ejpam-6607	329	4	}	}	PUNCT
ejpam-6607	329	5	.	.	PUNCT
ejpam-6607	330	1	theorem	theorem	ADJ
ejpam-6607	330	2	8	8	NUM
ejpam-6607	330	3	(	(	PUNCT
ejpam-6607	330	4	maximum	maximum	ADJ
ejpam-6607	330	5	entropy	entropy	NOUN
ejpam-6607	330	6	in	in	ADP
ejpam-6607	330	7	uniform	uniform	ADJ
ejpam-6607	330	8	superposition	superposition	NOUN
ejpam-6607	330	9	)	)	PUNCT
ejpam-6607	330	10	.	.	PUNCT
ejpam-6607	331	1	define	define	VERB
ejpam-6607	331	2	the	the	DET
ejpam-6607	331	3	shannon	shannon	PROPN
ejpam-6607	331	4	entropy	entropy	PROPN
ejpam-6607	331	5	of	of	ADP
ejpam-6607	331	6	the	the	DET
ejpam-6607	331	7	measurement	measurement	NOUN
ejpam-6607	331	8	distribution	distribution	NOUN
ejpam-6607	331	9	at	at	ADP
ejpam-6607	331	10	γ	γ	X
ejpam-6607	331	11	by	by	ADP
ejpam-6607	331	12	h(γ	h(γ	NOUN
ejpam-6607	331	13	)	)	PUNCT
ejpam-6607	331	14	=	=	SYM
ejpam-6607	332	1	−	−	PROPN
ejpam-6607	332	2	n∑	n∑	INTJ
ejpam-6607	332	3	i=1	i=1	PROPN
ejpam-6607	333	1	p	p	X
ejpam-6607	333	2	(	(	PUNCT
ejpam-6607	333	3	ui	ui	PROPN
ejpam-6607	333	4	|	|	ADV
ejpam-6607	333	5	γ	γ	PROPN
ejpam-6607	333	6	)	)	PUNCT
ejpam-6607	333	7	logp	logp	NOUN
ejpam-6607	333	8	(	(	PUNCT
ejpam-6607	333	9	ui	ui	NOUN
ejpam-6607	333	10	|	|	ADV
ejpam-6607	333	11	γ	γ	PROPN
ejpam-6607	333	12	)	)	PUNCT
ejpam-6607	333	13	=	=	PUNCT
ejpam-6607	334	1	−	−	PROPN
ejpam-6607	334	2	n∑	n∑	NOUN
ejpam-6607	334	3	i=1	i=1	PROPN
ejpam-6607	334	4	∣∣αi	∣∣αi	PROPN
ejpam-6607	334	5	,	,	PUNCT
ejpam-6607	334	6	γ	γ	PROPN
ejpam-6607	334	7	∣∣2	∣∣2	PROPN
ejpam-6607	334	8	log	log	NOUN
ejpam-6607	334	9	∣∣αi	∣∣αi	NOUN
ejpam-6607	334	10	,	,	PUNCT
ejpam-6607	334	11	γ	γ	PROPN
ejpam-6607	334	12	∣∣2	∣∣2	PROPN
ejpam-6607	334	13	.	.	PUNCT
ejpam-6607	335	1	then	then	ADV
ejpam-6607	335	2	h(γ	h(γ	PROPN
ejpam-6607	335	3	)	)	PUNCT
ejpam-6607	335	4	is	be	AUX
ejpam-6607	335	5	maximized	maximize	VERB
ejpam-6607	335	6	if	if	SCONJ
ejpam-6607	335	7	and	and	CCONJ
ejpam-6607	335	8	only	only	ADV
ejpam-6607	335	9	if	if	SCONJ
ejpam-6607	335	10	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	335	11	is	be	AUX
ejpam-6607	335	12	the	the	DET
ejpam-6607	335	13	uniform	uniform	ADJ
ejpam-6607	335	14	superposition	superposition	PROPN
ejpam-6607	335	15	1√	1√	PROPN
ejpam-6607	335	16	n	n	ADP
ejpam-6607	335	17	∑n	∑n	PROPN
ejpam-6607	335	18	i=1	i=1	PROPN
ejpam-6607	335	19	|ui⟩	|ui⟩	PROPN
ejpam-6607	335	20	,	,	PUNCT
ejpam-6607	335	21	in	in	ADP
ejpam-6607	335	22	which	which	DET
ejpam-6607	335	23	case	case	NOUN
ejpam-6607	335	24	h(γ	h(γ	PROPN
ejpam-6607	335	25	)	)	PUNCT
ejpam-6607	335	26	=	=	PUNCT
ejpam-6607	335	27	logn	logn	NOUN
ejpam-6607	335	28	.	.	PUNCT
ejpam-6607	336	1	proof	proof	NOUN
ejpam-6607	336	2	.	.	PUNCT
ejpam-6607	337	1	by	by	ADP
ejpam-6607	337	2	the	the	DET
ejpam-6607	337	3	concavity	concavity	NOUN
ejpam-6607	337	4	of	of	ADP
ejpam-6607	337	5	the	the	DET
ejpam-6607	337	6	shannon	shannon	PROPN
ejpam-6607	337	7	entropy	entropy	PROPN
ejpam-6607	337	8	on	on	ADP
ejpam-6607	337	9	probability	probability	NOUN
ejpam-6607	337	10	distributions	distribution	NOUN
ejpam-6607	337	11	,	,	PUNCT
ejpam-6607	337	12	the	the	DET
ejpam-6607	337	13	maximum	maximum	NOUN
ejpam-6607	337	14	occurs	occur	VERB
ejpam-6607	337	15	at	at	ADP
ejpam-6607	337	16	the	the	DET
ejpam-6607	337	17	uniform	uniform	ADJ
ejpam-6607	337	18	distribution	distribution	NOUN
ejpam-6607	337	19	p	p	NOUN
ejpam-6607	337	20	(	(	PUNCT
ejpam-6607	337	21	ui	ui	PROPN
ejpam-6607	337	22	|	|	ADV
ejpam-6607	337	23	γ	γ	NOUN
ejpam-6607	337	24	)	)	PUNCT
ejpam-6607	337	25	=	=	SYM
ejpam-6607	337	26	1	1	NUM
ejpam-6607	337	27	/	/	SYM
ejpam-6607	337	28	n	n	NOUN
ejpam-6607	337	29	for	for	ADP
ejpam-6607	337	30	all	all	DET
ejpam-6607	337	31	i.	i.	NOUN
ejpam-6607	337	32	the	the	PRON
ejpam-6607	337	33	only	only	ADV
ejpam-6607	337	34	normalized	normalize	VERB
ejpam-6607	337	35	pure	pure	ADJ
ejpam-6607	337	36	state	state	NOUN
ejpam-6607	337	37	yielding	yield	VERB
ejpam-6607	337	38	this	this	DET
ejpam-6607	337	39	distribution	distribution	NOUN
ejpam-6607	337	40	is	be	AUX
ejpam-6607	337	41	|ψγ⟩	|ψγ⟩	ADJ
ejpam-6607	337	42	=	=	SYM
ejpam-6607	337	43	1√	1√	PROPN
ejpam-6607	337	44	n	n	X
ejpam-6607	337	45	∑	∑	ADP
ejpam-6607	337	46	i	i	PRON
ejpam-6607	337	47	|ui⟩.	|ui⟩.	VERB
ejpam-6607	337	48	hence	hence	ADV
ejpam-6607	337	49	h(γ	h(γ	PROPN
ejpam-6607	337	50	)	)	PUNCT
ejpam-6607	337	51	≤	≤	NUM
ejpam-6607	338	1	−n	−n	ADV
ejpam-6607	338	2	(	(	PUNCT
ejpam-6607	338	3	1	1	NUM
ejpam-6607	338	4	/	/	SYM
ejpam-6607	338	5	n	n	CCONJ
ejpam-6607	338	6	)	)	PUNCT
ejpam-6607	338	7	log(1	log(1	NOUN
ejpam-6607	338	8	/	/	SYM
ejpam-6607	338	9	n	n	CCONJ
ejpam-6607	338	10	)	)	PUNCT
ejpam-6607	338	11	=	=	PRON
ejpam-6607	338	12	log	log	NOUN
ejpam-6607	338	13	n	n	CCONJ
ejpam-6607	338	14	,	,	PUNCT
ejpam-6607	338	15	with	with	ADP
ejpam-6607	338	16	equality	equality	NOUN
ejpam-6607	338	17	if	if	SCONJ
ejpam-6607	338	18	and	and	CCONJ
ejpam-6607	338	19	only	only	ADV
ejpam-6607	338	20	if	if	SCONJ
ejpam-6607	338	21	αi	αi	NOUN
ejpam-6607	338	22	,	,	PUNCT
ejpam-6607	338	23	γ	γ	X
ejpam-6607	338	24	=	=	SYM
ejpam-6607	338	25	1/	1/	NUM
ejpam-6607	338	26	√	√	PROPN
ejpam-6607	338	27	n	n	CCONJ
ejpam-6607	338	28	up	up	ADP
ejpam-6607	338	29	to	to	ADP
ejpam-6607	338	30	phases	phase	NOUN
ejpam-6607	338	31	.	.	PUNCT
ejpam-6607	339	1	3.2	3.2	NUM
ejpam-6607	339	2	.	.	PUNCT
ejpam-6607	339	3	quantum	quantum	NOUN
ejpam-6607	339	4	-	-	PUNCT
ejpam-6607	339	5	superhypersoft	superhypersoft	NOUN
ejpam-6607	339	6	sets	set	VERB
ejpam-6607	339	7	quantum	quantum	NOUN
ejpam-6607	339	8	-	-	PUNCT
ejpam-6607	339	9	superhypersoft	superhypersoft	NOUN
ejpam-6607	339	10	set	set	NOUN
ejpam-6607	339	11	maps	map	VERB
ejpam-6607	339	12	each	each	DET
ejpam-6607	339	13	power	power	NOUN
ejpam-6607	339	14	-	-	PUNCT
ejpam-6607	339	15	set	set	VERB
ejpam-6607	339	16	combination	combination	NOUN
ejpam-6607	339	17	of	of	ADP
ejpam-6607	339	18	multi	multi	ADJ
ejpam-6607	339	19	-	-	ADJ
ejpam-6607	339	20	valued	value	VERB
ejpam-6607	339	21	attributes	attribute	NOUN
ejpam-6607	339	22	to	to	PART
ejpam-6607	339	23	normalized	normalize	VERB
ejpam-6607	339	24	quantum	quantum	ADJ
ejpam-6607	339	25	states	state	NOUN
ejpam-6607	339	26	.	.	PUNCT
ejpam-6607	340	1	the	the	DET
ejpam-6607	340	2	definition	definition	NOUN
ejpam-6607	340	3	is	be	AUX
ejpam-6607	340	4	stated	state	VERB
ejpam-6607	340	5	as	as	SCONJ
ejpam-6607	340	6	follows	follow	VERB
ejpam-6607	340	7	.	.	PUNCT
ejpam-6607	341	1	definition	definition	NOUN
ejpam-6607	341	2	6	6	NUM
ejpam-6607	341	3	(	(	PUNCT
ejpam-6607	341	4	quantum	quantum	NOUN
ejpam-6607	341	5	–	–	PUNCT
ejpam-6607	341	6	superhypersoft	superhypersoft	NOUN
ejpam-6607	341	7	set	set	NOUN
ejpam-6607	341	8	)	)	PUNCT
ejpam-6607	341	9	.	.	PUNCT
ejpam-6607	342	1	let	let	VERB
ejpam-6607	342	2	u	u	PRON
ejpam-6607	342	3	=	=	NOUN
ejpam-6607	342	4	{	{	PUNCT
ejpam-6607	342	5	u1	u1	NOUN
ejpam-6607	342	6	,	,	PUNCT
ejpam-6607	342	7	u2	u2	NOUN
ejpam-6607	342	8	,	,	PUNCT
ejpam-6607	342	9	.	.	PUNCT
ejpam-6607	342	10	.	.	PUNCT
ejpam-6607	343	1	.	.	PUNCT
ejpam-6607	344	1	,	,	PUNCT
ejpam-6607	344	2	un	un	AUX
ejpam-6607	344	3	}	}	PUNCT
ejpam-6607	344	4	be	be	AUX
ejpam-6607	344	5	a	a	DET
ejpam-6607	344	6	finite	finite	ADJ
ejpam-6607	344	7	universe	universe	NOUN
ejpam-6607	344	8	and	and	CCONJ
ejpam-6607	344	9	let	let	VERB
ejpam-6607	344	10	a1	a1	NOUN
ejpam-6607	344	11	,	,	PUNCT
ejpam-6607	344	12	a2	a2	PROPN
ejpam-6607	344	13	,	,	PUNCT
ejpam-6607	344	14	.	.	PUNCT
ejpam-6607	344	15	.	.	PUNCT
ejpam-6607	345	1	.	.	PUNCT
ejpam-6607	346	1	,	,	PUNCT
ejpam-6607	346	2	am	be	AUX
ejpam-6607	346	3	be	be	AUX
ejpam-6607	346	4	m	m	VERB
ejpam-6607	346	5	distinct	distinct	ADJ
ejpam-6607	346	6	attributes	attribute	NOUN
ejpam-6607	346	7	with	with	ADP
ejpam-6607	346	8	corresponding	correspond	VERB
ejpam-6607	346	9	finite	finite	NOUN
ejpam-6607	346	10	,	,	PUNCT
ejpam-6607	346	11	pairwise	pairwise	NOUN
ejpam-6607	346	12	disjoint	disjoint	NOUN
ejpam-6607	346	13	value	value	NOUN
ejpam-6607	346	14	-	-	PUNCT
ejpam-6607	346	15	sets	set	NOUN
ejpam-6607	346	16	a1	a1	NOUN
ejpam-6607	346	17	,	,	PUNCT
ejpam-6607	346	18	a2	a2	PROPN
ejpam-6607	346	19	,	,	PUNCT
ejpam-6607	346	20	.	.	PUNCT
ejpam-6607	346	21	.	.	PUNCT
ejpam-6607	347	1	.	.	PUNCT
ejpam-6607	348	1	,	,	PUNCT
ejpam-6607	348	2	am	be	AUX
ejpam-6607	348	3	:	:	PUNCT
ejpam-6607	348	4	ai	ai	VERB
ejpam-6607	348	5	∩aj	∩aj	NOUN
ejpam-6607	348	6	=	=	NOUN
ejpam-6607	348	7	∅	∅	NOUN
ejpam-6607	348	8	(	(	PUNCT
ejpam-6607	348	9	i	i	PRON
ejpam-6607	348	10	̸=	̸=	PROPN
ejpam-6607	348	11	j	j	PROPN
ejpam-6607	348	12	)	)	PUNCT
ejpam-6607	348	13	.	.	PUNCT
ejpam-6607	349	1	form	form	VERB
ejpam-6607	349	2	the	the	DET
ejpam-6607	349	3	cartesian	cartesian	ADJ
ejpam-6607	349	4	product	product	NOUN
ejpam-6607	349	5	of	of	ADP
ejpam-6607	349	6	power	power	NOUN
ejpam-6607	349	7	-	-	PUNCT
ejpam-6607	349	8	sets	set	NOUN
ejpam-6607	349	9	c	c	NOUN
ejpam-6607	349	10	=	=	SYM
ejpam-6607	349	11	p(a1)×	p(a1)×	NOUN
ejpam-6607	349	12	p(a2)×	p(a2)×	NOUN
ejpam-6607	349	13	·	·	PUNCT
ejpam-6607	349	14	·	·	PUNCT
ejpam-6607	349	15	·	·	PUNCT
ejpam-6607	350	1	×	×	PROPN
ejpam-6607	350	2	p(am	p(am	NOUN
ejpam-6607	350	3	)	)	PUNCT
ejpam-6607	350	4	,	,	PUNCT
ejpam-6607	350	5	so	so	SCONJ
ejpam-6607	350	6	each	each	DET
ejpam-6607	350	7	γ	γ	X
ejpam-6607	350	8	=	=	SYM
ejpam-6607	350	9	(	(	PUNCT
ejpam-6607	350	10	α1	α1	PROPN
ejpam-6607	350	11	,	,	PUNCT
ejpam-6607	350	12	α2	α2	ADJ
ejpam-6607	350	13	,	,	PUNCT
ejpam-6607	350	14	.	.	PUNCT
ejpam-6607	350	15	.	.	PUNCT
ejpam-6607	350	16	.	.	PUNCT
ejpam-6607	351	1	,	,	PUNCT
ejpam-6607	351	2	αm	αm	X
ejpam-6607	351	3	)	)	PUNCT
ejpam-6607	351	4	∈	∈	PROPN
ejpam-6607	351	5	c	c	NOUN
ejpam-6607	351	6	with	with	ADP
ejpam-6607	351	7	αi	αi	NOUN
ejpam-6607	351	8	⊆	⊆	NUM
ejpam-6607	351	9	ai	ai	NOUN
ejpam-6607	351	10	.	.	PUNCT
ejpam-6607	352	1	let	let	VERB
ejpam-6607	352	2	h(u	h(u	PROPN
ejpam-6607	352	3	)	)	PUNCT
ejpam-6607	352	4	be	be	AUX
ejpam-6607	352	5	the	the	DET
ejpam-6607	352	6	complex	complex	ADJ
ejpam-6607	352	7	hilbert	hilbert	NOUN
ejpam-6607	352	8	space	space	NOUN
ejpam-6607	352	9	with	with	ADP
ejpam-6607	352	10	orthonormal	orthonormal	ADJ
ejpam-6607	352	11	basis	basis	NOUN
ejpam-6607	352	12	{	{	PUNCT
ejpam-6607	352	13	|ui⟩}ni=1	|ui⟩}ni=1	NOUN
ejpam-6607	352	14	.	.	PUNCT
ejpam-6607	353	1	a	a	DET
ejpam-6607	353	2	quantum	quantum	NOUN
ejpam-6607	353	3	–	–	PUNCT
ejpam-6607	353	4	superhypersoft	superhypersoft	NOUN
ejpam-6607	353	5	set	set	VERB
ejpam-6607	353	6	over	over	ADP
ejpam-6607	353	7	(	(	PUNCT
ejpam-6607	353	8	u	u	NOUN
ejpam-6607	353	9	,	,	PUNCT
ejpam-6607	353	10	c	c	NOUN
ejpam-6607	353	11	)	)	PUNCT
ejpam-6607	353	12	is	be	AUX
ejpam-6607	353	13	a	a	DET
ejpam-6607	353	14	map	map	NOUN
ejpam-6607	353	15	q	q	NOUN
ejpam-6607	353	16	:	:	PUNCT
ejpam-6607	353	17	c	c	AUX
ejpam-6607	353	18	−→	−→	NOUN
ejpam-6607	353	19	h(u	h(u	PROPN
ejpam-6607	353	20	)	)	PUNCT
ejpam-6607	353	21	,	,	PUNCT
ejpam-6607	353	22	γ	γ	PROPN
ejpam-6607	353	23	7→	7→	PROPN
ejpam-6607	353	24	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	353	25	=	=	SYM
ejpam-6607	353	26	n∑	n∑	PROPN
ejpam-6607	353	27	i=1	i=1	PROPN
ejpam-6607	354	1	αi	αi	PROPN
ejpam-6607	354	2	,	,	PUNCT
ejpam-6607	354	3	γ	γ	X
ejpam-6607	354	4	|ui⟩	|ui⟩	X
ejpam-6607	354	5	,	,	PUNCT
ejpam-6607	354	6	t.	t.	PROPN
ejpam-6607	354	7	fujita	fujita	PROPN
ejpam-6607	354	8	,	,	PUNCT
ejpam-6607	354	9	f.smarandache	f.smarandache	NOUN
ejpam-6607	354	10	/	/	SYM
ejpam-6607	354	11	eur	eur	PROPN
ejpam-6607	354	12	.	.	PUNCT
ejpam-6607	355	1	j.	j.	PROPN
ejpam-6607	355	2	pure	pure	PROPN
ejpam-6607	355	3	appl	appl	PROPN
ejpam-6607	355	4	.	.	PROPN
ejpam-6607	355	5	math	math	PROPN
ejpam-6607	355	6	,	,	PUNCT
ejpam-6607	355	7	18	18	NUM
ejpam-6607	355	8	(	(	PUNCT
ejpam-6607	355	9	3	3	NUM
ejpam-6607	355	10	)	)	PUNCT
ejpam-6607	355	11	(	(	PUNCT
ejpam-6607	355	12	2025	2025	NUM
ejpam-6607	355	13	)	)	PUNCT
ejpam-6607	355	14	,	,	PUNCT
ejpam-6607	355	15	6607	6607	NUM
ejpam-6607	355	16	17	17	NUM
ejpam-6607	355	17	of	of	ADP
ejpam-6607	355	18	33	33	NUM
ejpam-6607	355	19	subject	subject	NOUN
ejpam-6607	355	20	to	to	ADP
ejpam-6607	355	21	the	the	DET
ejpam-6607	355	22	normalization	normalization	NOUN
ejpam-6607	355	23	condition	condition	NOUN
ejpam-6607	355	24	n∑	n∑	PROPN
ejpam-6607	355	25	i=1	i=1	PROPN
ejpam-6607	355	26	∣∣αi	∣∣αi	PROPN
ejpam-6607	355	27	,	,	PUNCT
ejpam-6607	355	28	γ	γ	PROPN
ejpam-6607	355	29	∣∣2	∣∣2	PROPN
ejpam-6607	355	30	=	=	SYM
ejpam-6607	355	31	1	1	NUM
ejpam-6607	355	32	for	for	ADP
ejpam-6607	355	33	each	each	DET
ejpam-6607	355	34	γ	γ	PROPN
ejpam-6607	355	35	∈	∈	PROPN
ejpam-6607	355	36	c.	c.	PROPN
ejpam-6607	355	37	here	here	ADV
ejpam-6607	355	38	αi	αi	VERB
ejpam-6607	355	39	,	,	PUNCT
ejpam-6607	355	40	γ	γ	PROPN
ejpam-6607	355	41	∈	∈	PROPN
ejpam-6607	355	42	c	c	NOUN
ejpam-6607	355	43	is	be	AUX
ejpam-6607	355	44	the	the	DET
ejpam-6607	355	45	amplitude	amplitude	NOUN
ejpam-6607	355	46	of	of	ADP
ejpam-6607	355	47	element	element	NOUN
ejpam-6607	355	48	ui	ui	PROPN
ejpam-6607	355	49	under	under	ADP
ejpam-6607	355	50	the	the	DET
ejpam-6607	355	51	combined	combine	VERB
ejpam-6607	355	52	(	(	PUNCT
ejpam-6607	355	53	possibly	possibly	ADV
ejpam-6607	355	54	multi	multi	ADJ
ejpam-6607	355	55	-	-	ADJ
ejpam-6607	355	56	valued	value	VERB
ejpam-6607	355	57	)	)	PUNCT
ejpam-6607	355	58	attribute	attribute	NOUN
ejpam-6607	355	59	γ	γ	PROPN
ejpam-6607	355	60	.	.	PROPN
ejpam-6607	355	61	measuring	measure	VERB
ejpam-6607	355	62	|ψγ⟩	|ψγ⟩	ADJ
ejpam-6607	355	63	yields	yield	VERB
ejpam-6607	355	64	the	the	DET
ejpam-6607	355	65	probability	probability	NOUN
ejpam-6607	355	66	distribution	distribution	NOUN
ejpam-6607	355	67	µγ(ui	µγ(ui	PROPN
ejpam-6607	355	68	)	)	PUNCT
ejpam-6607	356	1	=	=	SYM
ejpam-6607	356	2	|αi	|αi	X
ejpam-6607	356	3	,	,	PUNCT
ejpam-6607	356	4	γ	γ	X
ejpam-6607	356	5	|2	|2	NUM
ejpam-6607	356	6	on	on	ADP
ejpam-6607	356	7	u	u	PROPN
ejpam-6607	356	8	.	.	PUNCT
ejpam-6607	356	9	example	example	NOUN
ejpam-6607	356	10	9	9	NUM
ejpam-6607	356	11	(	(	PUNCT
ejpam-6607	356	12	quantum	quantum	NOUN
ejpam-6607	356	13	–	–	PUNCT
ejpam-6607	356	14	superhypersoft	superhypersoft	NOUN
ejpam-6607	356	15	set	set	VERB
ejpam-6607	356	16	for	for	ADP
ejpam-6607	356	17	smartphone	smartphone	NOUN
ejpam-6607	356	18	recommendation	recommendation	NOUN
ejpam-6607	356	19	)	)	PUNCT
ejpam-6607	356	20	.	.	PUNCT
ejpam-6607	357	1	let	let	VERB
ejpam-6607	357	2	u	u	PRON
ejpam-6607	357	3	=	=	NOUN
ejpam-6607	357	4	{	{	PUNCT
ejpam-6607	357	5	phonex	phonex	NOUN
ejpam-6607	357	6	,	,	PUNCT
ejpam-6607	357	7	phoney	phoney	NOUN
ejpam-6607	357	8	,	,	PUNCT
ejpam-6607	357	9	phonez	phonez	PROPN
ejpam-6607	357	10	}	}	PUNCT
ejpam-6607	357	11	be	be	VERB
ejpam-6607	357	12	three	three	NUM
ejpam-6607	357	13	candidate	candidate	NOUN
ejpam-6607	357	14	smartphones	smartphone	NOUN
ejpam-6607	357	15	.	.	PUNCT
ejpam-6607	358	1	consider	consider	VERB
ejpam-6607	358	2	three	three	NUM
ejpam-6607	358	3	attribute	attribute	NOUN
ejpam-6607	358	4	domains	domain	NOUN
ejpam-6607	358	5	with	with	ADP
ejpam-6607	358	6	disjoint	disjoint	NOUN
ejpam-6607	358	7	value	value	NOUN
ejpam-6607	358	8	-	-	PUNCT
ejpam-6607	358	9	sets	set	NOUN
ejpam-6607	358	10	:	:	PUNCT
ejpam-6607	358	11	a1	a1	NOUN
ejpam-6607	358	12	=	=	SYM
ejpam-6607	358	13	{	{	PUNCT
ejpam-6607	358	14	apple	apple	PROPN
ejpam-6607	358	15	,	,	PUNCT
ejpam-6607	358	16	samsung	samsung	PROPN
ejpam-6607	358	17	,	,	PUNCT
ejpam-6607	358	18	google	google	PROPN
ejpam-6607	358	19	}	}	PUNCT
ejpam-6607	358	20	,	,	PUNCT
ejpam-6607	358	21	a2	a2	PROPN
ejpam-6607	358	22	=	=	PUNCT
ejpam-6607	358	23	{	{	PUNCT
ejpam-6607	358	24	ios	ios	PROPN
ejpam-6607	358	25	,	,	PUNCT
ejpam-6607	358	26	android	android	NOUN
ejpam-6607	358	27	}	}	PUNCT
ejpam-6607	358	28	,	,	PUNCT
ejpam-6607	358	29	a3	a3	NOUN
ejpam-6607	358	30	=	=	SYM
ejpam-6607	358	31	{	{	PUNCT
ejpam-6607	358	32	4	4	NUM
ejpam-6607	358	33	g	g	NOUN
ejpam-6607	358	34	,	,	PUNCT
ejpam-6607	358	35	5	5	NUM
ejpam-6607	358	36	g	g	NOUN
ejpam-6607	358	37	}	}	PUNCT
ejpam-6607	358	38	.	.	PUNCT
ejpam-6607	359	1	form	form	VERB
ejpam-6607	359	2	the	the	DET
ejpam-6607	359	3	cartesian	cartesian	ADJ
ejpam-6607	359	4	product	product	NOUN
ejpam-6607	359	5	of	of	ADP
ejpam-6607	359	6	power	power	NOUN
ejpam-6607	359	7	-	-	PUNCT
ejpam-6607	359	8	sets	set	NOUN
ejpam-6607	359	9	c	c	NOUN
ejpam-6607	359	10	=	=	SYM
ejpam-6607	359	11	p(a1)×	p(a1)×	PROPN
ejpam-6607	359	12	p(a2)×	p(a2)×	NOUN
ejpam-6607	359	13	p(a3	p(a3	NOUN
ejpam-6607	359	14	)	)	PUNCT
ejpam-6607	359	15	,	,	PUNCT
ejpam-6607	359	16	so	so	ADV
ejpam-6607	359	17	each	each	DET
ejpam-6607	359	18	element	element	NOUN
ejpam-6607	359	19	γ	γ	X
ejpam-6607	359	20	=	=	SYM
ejpam-6607	359	21	(	(	PUNCT
ejpam-6607	359	22	α1	α1	PROPN
ejpam-6607	359	23	,	,	PUNCT
ejpam-6607	359	24	α2	α2	ADJ
ejpam-6607	359	25	,	,	PUNCT
ejpam-6607	359	26	α3	α3	PROPN
ejpam-6607	359	27	)	)	PUNCT
ejpam-6607	359	28	consists	consist	VERB
ejpam-6607	359	29	of	of	ADP
ejpam-6607	359	30	α1	α1	PROPN
ejpam-6607	359	31	⊆	⊆	NUM
ejpam-6607	359	32	a1	a1	NOUN
ejpam-6607	359	33	,	,	PUNCT
ejpam-6607	359	34	α2	α2	PROPN
ejpam-6607	359	35	⊆	⊆	NUM
ejpam-6607	359	36	a2	a2	PROPN
ejpam-6607	359	37	,	,	PUNCT
ejpam-6607	359	38	α3	α3	NOUN
ejpam-6607	359	39	⊆	⊆	NUM
ejpam-6607	359	40	a3	a3	NOUN
ejpam-6607	359	41	.	.	PUNCT
ejpam-6607	360	1	let	let	VERB
ejpam-6607	360	2	h(u	h(u	PROPN
ejpam-6607	360	3	)	)	PUNCT
ejpam-6607	360	4	be	be	AUX
ejpam-6607	360	5	the	the	DET
ejpam-6607	360	6	complex	complex	ADJ
ejpam-6607	360	7	hilbert	hilbert	NOUN
ejpam-6607	360	8	space	space	NOUN
ejpam-6607	360	9	with	with	ADP
ejpam-6607	360	10	orthonormal	orthonormal	ADJ
ejpam-6607	360	11	basis	basis	NOUN
ejpam-6607	360	12	{	{	PUNCT
ejpam-6607	360	13	|phonex⟩	|phonex⟩	NOUN
ejpam-6607	360	14	,	,	PUNCT
ejpam-6607	360	15	|phoney⟩	|phoney⟩	PROPN
ejpam-6607	360	16	,	,	PUNCT
ejpam-6607	360	17	|phonez⟩	|phonez⟩	PROPN
ejpam-6607	360	18	}	}	PUNCT
ejpam-6607	360	19	.	.	PUNCT
ejpam-6607	361	1	case	case	NOUN
ejpam-6607	361	2	1	1	NUM
ejpam-6607	361	3	:	:	PUNCT
ejpam-6607	361	4	premium	premium	NOUN
ejpam-6607	361	5	apple	apple	NOUN
ejpam-6607	361	6	5	5	NUM
ejpam-6607	361	7	g	g	NOUN
ejpam-6607	361	8	user	user	NOUN
ejpam-6607	361	9	γ1	γ1	NOUN
ejpam-6607	361	10	=	=	SYM
ejpam-6607	361	11	(	(	PUNCT
ejpam-6607	361	12	{	{	PUNCT
ejpam-6607	361	13	apple	apple	NOUN
ejpam-6607	361	14	}	}	PUNCT
ejpam-6607	361	15	,	,	PUNCT
ejpam-6607	361	16	{	{	PUNCT
ejpam-6607	361	17	ios	ios	PROPN
ejpam-6607	361	18	}	}	PUNCT
ejpam-6607	361	19	,	,	PUNCT
ejpam-6607	361	20	{	{	PUNCT
ejpam-6607	361	21	5	5	NUM
ejpam-6607	361	22	g	g	NOUN
ejpam-6607	361	23	}	}	PUNCT
ejpam-6607	361	24	)	)	PUNCT
ejpam-6607	361	25	.	.	PUNCT
ejpam-6607	362	1	define	define	VERB
ejpam-6607	362	2	the	the	DET
ejpam-6607	362	3	quantum	quantum	ADJ
ejpam-6607	362	4	state	state	NOUN
ejpam-6607	362	5	|ψγ1⟩	|ψγ1⟩	NOUN
ejpam-6607	362	6	=	=	PUNCT
ejpam-6607	362	7	√	√	PROPN
ejpam-6607	362	8	0.70	0.70	NUM
ejpam-6607	362	9	|phonex⟩+	|phonex⟩+	VERB
ejpam-6607	362	10	√	√	NUM
ejpam-6607	362	11	0.20	0.20	NUM
ejpam-6607	362	12	|phoney⟩+	|phoney⟩+	NOUN
ejpam-6607	362	13	√	√	ADP
ejpam-6607	362	14	0.10	0.10	NUM
ejpam-6607	362	15	|phonez⟩	|phonez⟩	PROPN
ejpam-6607	362	16	.	.	PUNCT
ejpam-6607	363	1	check	check	VERB
ejpam-6607	363	2	normalization	normalization	NOUN
ejpam-6607	363	3	:	:	PUNCT
ejpam-6607	363	4	0.70	0.70	NUM
ejpam-6607	363	5	+	+	NOUN
ejpam-6607	363	6	0.20	0.20	NUM
ejpam-6607	363	7	+	+	CCONJ
ejpam-6607	363	8	0.10	0.10	NUM
ejpam-6607	363	9	=	=	SYM
ejpam-6607	363	10	1.00	1.00	NUM
ejpam-6607	363	11	.	.	PUNCT
ejpam-6607	364	1	measurement	measurement	NOUN
ejpam-6607	364	2	probabilities	probability	NOUN
ejpam-6607	364	3	:	:	PUNCT
ejpam-6607	364	4	p	p	X
ejpam-6607	364	5	(	(	PUNCT
ejpam-6607	364	6	phonex	phonex	ADV
ejpam-6607	364	7	|	|	ADV
ejpam-6607	364	8	γ1	γ1	NOUN
ejpam-6607	364	9	)	)	PUNCT
ejpam-6607	364	10	=	=	PUNCT
ejpam-6607	364	11	0.70	0.70	NUM
ejpam-6607	364	12	,	,	PUNCT
ejpam-6607	364	13	p	p	X
ejpam-6607	364	14	(	(	PUNCT
ejpam-6607	364	15	phoney	phoney	ADJ
ejpam-6607	364	16	|	|	NOUN
ejpam-6607	364	17	γ1	γ1	NOUN
ejpam-6607	364	18	)	)	PUNCT
ejpam-6607	364	19	=	=	SYM
ejpam-6607	364	20	0.20	0.20	NUM
ejpam-6607	364	21	,	,	PUNCT
ejpam-6607	364	22	p	p	X
ejpam-6607	364	23	(	(	PUNCT
ejpam-6607	364	24	phonez	phonez	PROPN
ejpam-6607	364	25	|	|	NOUN
ejpam-6607	364	26	γ1	γ1	NOUN
ejpam-6607	364	27	)	)	PUNCT
ejpam-6607	364	28	=	=	SYM
ejpam-6607	364	29	0.10	0.10	NUM
ejpam-6607	364	30	.	.	PUNCT
ejpam-6607	365	1	case	case	NOUN
ejpam-6607	365	2	2	2	NUM
ejpam-6607	365	3	:	:	PUNCT
ejpam-6607	365	4	cross	cross	ADJ
ejpam-6607	365	5	-	-	ADJ
ejpam-6607	365	6	platform	platform	ADJ
ejpam-6607	365	7	budget	budget	NOUN
ejpam-6607	365	8	4	4	NUM
ejpam-6607	365	9	g	g	NOUN
ejpam-6607	365	10	user	user	NOUN
ejpam-6607	365	11	γ2	γ2	NOUN
ejpam-6607	365	12	=	=	SYM
ejpam-6607	365	13	(	(	PUNCT
ejpam-6607	365	14	{	{	PUNCT
ejpam-6607	365	15	samsung	samsung	PROPN
ejpam-6607	365	16	,	,	PUNCT
ejpam-6607	365	17	google	google	PROPN
ejpam-6607	365	18	}	}	PUNCT
ejpam-6607	365	19	,	,	PUNCT
ejpam-6607	365	20	{	{	PUNCT
ejpam-6607	365	21	android	android	PROPN
ejpam-6607	365	22	}	}	PUNCT
ejpam-6607	365	23	,	,	PUNCT
ejpam-6607	365	24	{	{	PUNCT
ejpam-6607	365	25	4	4	NUM
ejpam-6607	365	26	g	g	NOUN
ejpam-6607	365	27	}	}	PUNCT
ejpam-6607	365	28	)	)	PUNCT
ejpam-6607	365	29	.	.	PUNCT
ejpam-6607	366	1	define	define	VERB
ejpam-6607	366	2	|ψγ2⟩	|ψγ2⟩	NOUN
ejpam-6607	366	3	=	=	PUNCT
ejpam-6607	366	4	√	√	PROPN
ejpam-6607	366	5	0.15	0.15	NUM
ejpam-6607	366	6	|phonex⟩+	|phonex⟩+	VERB
ejpam-6607	366	7	√	√	ADV
ejpam-6607	366	8	0.55	0.55	NUM
ejpam-6607	366	9	|phoney⟩+	|phoney⟩+	NOUN
ejpam-6607	366	10	√	√	NUM
ejpam-6607	366	11	0.30	0.30	NUM
ejpam-6607	366	12	|phonez⟩	|phonez⟩	PROPN
ejpam-6607	366	13	,	,	PUNCT
ejpam-6607	366	14	and	and	CCONJ
ejpam-6607	366	15	verify	verify	VERB
ejpam-6607	366	16	0.15	0.15	NUM
ejpam-6607	367	1	+	+	CCONJ
ejpam-6607	367	2	0.55	0.55	NUM
ejpam-6607	367	3	+	+	CCONJ
ejpam-6607	367	4	0.30	0.30	NUM
ejpam-6607	367	5	=	=	SYM
ejpam-6607	367	6	1.00	1.00	NUM
ejpam-6607	367	7	.	.	PUNCT
ejpam-6607	368	1	thus	thus	ADV
ejpam-6607	368	2	p	p	X
ejpam-6607	368	3	(	(	PUNCT
ejpam-6607	368	4	phonex	phonex	ADV
ejpam-6607	368	5	|	|	ADV
ejpam-6607	368	6	γ2	γ2	ADJ
ejpam-6607	368	7	)	)	PUNCT
ejpam-6607	368	8	=	=	PUNCT
ejpam-6607	369	1	0.15	0.15	NUM
ejpam-6607	369	2	,	,	PUNCT
ejpam-6607	369	3	p	p	X
ejpam-6607	369	4	(	(	PUNCT
ejpam-6607	369	5	phoney	phoney	NOUN
ejpam-6607	369	6	|	|	ADV
ejpam-6607	369	7	γ2	γ2	ADJ
ejpam-6607	369	8	)	)	PUNCT
ejpam-6607	369	9	=	=	PUNCT
ejpam-6607	370	1	0.55	0.55	NUM
ejpam-6607	370	2	,	,	PUNCT
ejpam-6607	370	3	p	p	X
ejpam-6607	370	4	(	(	PUNCT
ejpam-6607	370	5	phonez	phonez	PROPN
ejpam-6607	370	6	|	|	ADV
ejpam-6607	370	7	γ2	γ2	NOUN
ejpam-6607	370	8	)	)	PUNCT
ejpam-6607	370	9	=	=	SYM
ejpam-6607	371	1	0.30	0.30	NUM
ejpam-6607	371	2	.	.	PUNCT
ejpam-6607	372	1	interpretation	interpretation	NOUN
ejpam-6607	372	2	.	.	PUNCT
ejpam-6607	373	1	t.	t.	PROPN
ejpam-6607	373	2	fujita	fujita	PROPN
ejpam-6607	373	3	,	,	PUNCT
ejpam-6607	373	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	373	5	/	/	SYM
ejpam-6607	373	6	eur	eur	PROPN
ejpam-6607	373	7	.	.	PUNCT
ejpam-6607	374	1	j.	j.	PROPN
ejpam-6607	374	2	pure	pure	PROPN
ejpam-6607	374	3	appl	appl	PROPN
ejpam-6607	374	4	.	.	PROPN
ejpam-6607	374	5	math	math	PROPN
ejpam-6607	374	6	,	,	PUNCT
ejpam-6607	374	7	18	18	NUM
ejpam-6607	374	8	(	(	PUNCT
ejpam-6607	374	9	3	3	NUM
ejpam-6607	374	10	)	)	PUNCT
ejpam-6607	374	11	(	(	PUNCT
ejpam-6607	374	12	2025	2025	NUM
ejpam-6607	374	13	)	)	PUNCT
ejpam-6607	374	14	,	,	PUNCT
ejpam-6607	374	15	6607	6607	NUM
ejpam-6607	374	16	18	18	NUM
ejpam-6607	374	17	of	of	ADP
ejpam-6607	374	18	33	33	NUM
ejpam-6607	374	19	•	•	NOUN
ejpam-6607	374	20	under	under	ADP
ejpam-6607	374	21	γ1	γ1	PROPN
ejpam-6607	374	22	(	(	PUNCT
ejpam-6607	374	23	apple	apple	NOUN
ejpam-6607	374	24	,	,	PUNCT
ejpam-6607	374	25	ios	ios	PROPN
ejpam-6607	374	26	,	,	PUNCT
ejpam-6607	374	27	5	5	NUM
ejpam-6607	374	28	g	g	NOUN
ejpam-6607	374	29	)	)	PUNCT
ejpam-6607	374	30	,	,	PUNCT
ejpam-6607	374	31	phonex	phonex	PROPN
ejpam-6607	374	32	is	be	AUX
ejpam-6607	374	33	strongly	strongly	ADV
ejpam-6607	374	34	preferred	prefer	VERB
ejpam-6607	374	35	(	(	PUNCT
ejpam-6607	374	36	70	70	NUM
ejpam-6607	374	37	%	%	NOUN
ejpam-6607	374	38	)	)	PUNCT
ejpam-6607	374	39	,	,	PUNCT
ejpam-6607	374	40	phoney	phoney	NOUN
ejpam-6607	374	41	moderately	moderately	ADV
ejpam-6607	374	42	(	(	PUNCT
ejpam-6607	374	43	20	20	NUM
ejpam-6607	374	44	%	%	NOUN
ejpam-6607	374	45	)	)	PUNCT
ejpam-6607	374	46	,	,	PUNCT
ejpam-6607	374	47	and	and	CCONJ
ejpam-6607	374	48	phonez	phonez	NOUN
ejpam-6607	374	49	rarely	rarely	ADV
ejpam-6607	374	50	(	(	PUNCT
ejpam-6607	374	51	10	10	NUM
ejpam-6607	374	52	%	%	NOUN
ejpam-6607	374	53	)	)	PUNCT
ejpam-6607	374	54	.	.	PUNCT
ejpam-6607	375	1	•	•	NOUN
ejpam-6607	375	2	under	under	ADP
ejpam-6607	375	3	γ2	γ2	PROPN
ejpam-6607	375	4	(	(	PUNCT
ejpam-6607	375	5	samsung	samsung	PROPN
ejpam-6607	375	6	or	or	CCONJ
ejpam-6607	375	7	google	google	PROPN
ejpam-6607	375	8	,	,	PUNCT
ejpam-6607	375	9	android	android	PROPN
ejpam-6607	375	10	,	,	PUNCT
ejpam-6607	375	11	4	4	NUM
ejpam-6607	375	12	g	g	NOUN
ejpam-6607	375	13	)	)	PUNCT
ejpam-6607	375	14	,	,	PUNCT
ejpam-6607	375	15	phoney	phoney	NOUN
ejpam-6607	375	16	is	be	AUX
ejpam-6607	375	17	most	most	ADV
ejpam-6607	375	18	likely	likely	ADJ
ejpam-6607	375	19	(	(	PUNCT
ejpam-6607	375	20	55	55	NUM
ejpam-6607	375	21	%	%	NOUN
ejpam-6607	375	22	)	)	PUNCT
ejpam-6607	375	23	,	,	PUNCT
ejpam-6607	375	24	phonez	phonez	NOUN
ejpam-6607	375	25	next	next	ADV
ejpam-6607	375	26	(	(	PUNCT
ejpam-6607	375	27	30	30	NUM
ejpam-6607	375	28	%	%	NOUN
ejpam-6607	375	29	)	)	PUNCT
ejpam-6607	375	30	,	,	PUNCT
ejpam-6607	375	31	and	and	CCONJ
ejpam-6607	375	32	phonex	phonex	ADV
ejpam-6607	375	33	least	least	ADJ
ejpam-6607	375	34	(	(	PUNCT
ejpam-6607	375	35	15	15	NUM
ejpam-6607	375	36	%	%	NOUN
ejpam-6607	375	37	)	)	PUNCT
ejpam-6607	375	38	.	.	PUNCT
ejpam-6607	376	1	this	this	DET
ejpam-6607	376	2	quantum	quantum	NOUN
ejpam-6607	376	3	–	–	PUNCT
ejpam-6607	376	4	superhypersoft	superhypersoft	NOUN
ejpam-6607	376	5	set	set	VERB
ejpam-6607	376	6	q	q	NOUN
ejpam-6607	376	7	:	:	PUNCT
ejpam-6607	376	8	c	c	PROPN
ejpam-6607	376	9	→	→	SYM
ejpam-6607	376	10	h(u	h(u	PROPN
ejpam-6607	376	11	)	)	PUNCT
ejpam-6607	376	12	encodes	encode	NOUN
ejpam-6607	376	13	complex	complex	ADJ
ejpam-6607	376	14	,	,	PUNCT
ejpam-6607	376	15	overlapping	overlap	VERB
ejpam-6607	376	16	user	user	NOUN
ejpam-6607	376	17	preferences	preference	NOUN
ejpam-6607	376	18	(	(	PUNCT
ejpam-6607	376	19	multi	multi	ADJ
ejpam-6607	376	20	-	-	ADJ
ejpam-6607	376	21	brand	brand	ADJ
ejpam-6607	376	22	,	,	PUNCT
ejpam-6607	376	23	multi	multi	NOUN
ejpam-6607	376	24	-	-	NOUN
ejpam-6607	376	25	network	network	NOUN
ejpam-6607	376	26	)	)	PUNCT
ejpam-6607	376	27	as	as	ADP
ejpam-6607	376	28	quantum	quantum	NOUN
ejpam-6607	376	29	superpositions	superposition	NOUN
ejpam-6607	376	30	.	.	PUNCT
ejpam-6607	377	1	measurement	measurement	NOUN
ejpam-6607	377	2	yields	yield	VERB
ejpam-6607	377	3	a	a	DET
ejpam-6607	377	4	soft	soft	ADJ
ejpam-6607	377	5	ranking	ranking	NOUN
ejpam-6607	377	6	of	of	ADP
ejpam-6607	377	7	the	the	DET
ejpam-6607	377	8	three	three	NUM
ejpam-6607	377	9	phones	phone	NOUN
ejpam-6607	377	10	for	for	ADP
ejpam-6607	377	11	each	each	DET
ejpam-6607	377	12	preference	preference	NOUN
ejpam-6607	377	13	combination	combination	NOUN
ejpam-6607	377	14	.	.	PUNCT
ejpam-6607	378	1	example	example	NOUN
ejpam-6607	378	2	10	10	NUM
ejpam-6607	378	3	(	(	PUNCT
ejpam-6607	378	4	quantum	quantum	PROPN
ejpam-6607	378	5	–	–	PUNCT
ejpam-6607	378	6	superhypersoft	superhypersoft	NOUN
ejpam-6607	378	7	set	set	VERB
ejpam-6607	378	8	for	for	ADP
ejpam-6607	378	9	movie	movie	NOUN
ejpam-6607	378	10	recommendation	recommendation	NOUN
ejpam-6607	378	11	)	)	PUNCT
ejpam-6607	378	12	.	.	PUNCT
ejpam-6607	379	1	let	let	VERB
ejpam-6607	379	2	u	u	PRON
ejpam-6607	379	3	=	=	NOUN
ejpam-6607	379	4	{	{	PUNCT
ejpam-6607	379	5	moviea	moviea	ADJ
ejpam-6607	379	6	,	,	PUNCT
ejpam-6607	379	7	movieb	movieb	NOUN
ejpam-6607	379	8	,	,	PUNCT
ejpam-6607	379	9	moviec	moviec	PROPN
ejpam-6607	379	10	}	}	PUNCT
ejpam-6607	379	11	be	be	VERB
ejpam-6607	379	12	three	three	NUM
ejpam-6607	379	13	candidate	candidate	NOUN
ejpam-6607	379	14	films	film	NOUN
ejpam-6607	379	15	.	.	PUNCT
ejpam-6607	380	1	consider	consider	VERB
ejpam-6607	380	2	three	three	NUM
ejpam-6607	380	3	attribute	attribute	NOUN
ejpam-6607	380	4	domains	domain	NOUN
ejpam-6607	380	5	:	:	PUNCT
ejpam-6607	380	6	a1	a1	NOUN
ejpam-6607	380	7	=	=	SYM
ejpam-6607	380	8	{	{	PUNCT
ejpam-6607	380	9	action	action	NOUN
ejpam-6607	380	10	,	,	PUNCT
ejpam-6607	380	11	drama	drama	NOUN
ejpam-6607	380	12	}	}	PUNCT
ejpam-6607	380	13	,	,	PUNCT
ejpam-6607	380	14	a2	a2	PROPN
ejpam-6607	380	15	=	=	PUNCT
ejpam-6607	380	16	{	{	PUNCT
ejpam-6607	380	17	light	light	ADJ
ejpam-6607	380	18	,	,	PUNCT
ejpam-6607	380	19	dark	dark	ADJ
ejpam-6607	380	20	}	}	PUNCT
ejpam-6607	380	21	,	,	PUNCT
ejpam-6607	380	22	a3	a3	NOUN
ejpam-6607	380	23	=	=	SYM
ejpam-6607	380	24	{	{	PUNCT
ejpam-6607	380	25	theater	theater	NOUN
ejpam-6607	380	26	,	,	PUNCT
ejpam-6607	380	27	streaming	streaming	NOUN
ejpam-6607	380	28	}	}	PUNCT
ejpam-6607	380	29	.	.	PUNCT
ejpam-6607	381	1	form	form	VERB
ejpam-6607	381	2	the	the	DET
ejpam-6607	381	3	cartesian	cartesian	ADJ
ejpam-6607	381	4	product	product	NOUN
ejpam-6607	381	5	of	of	ADP
ejpam-6607	381	6	power	power	NOUN
ejpam-6607	381	7	-	-	PUNCT
ejpam-6607	381	8	sets	set	NOUN
ejpam-6607	381	9	c	c	NOUN
ejpam-6607	381	10	=	=	SYM
ejpam-6607	381	11	p(a1)×	p(a1)×	PROPN
ejpam-6607	381	12	p(a2)×	p(a2)×	NOUN
ejpam-6607	381	13	p(a3	p(a3	NOUN
ejpam-6607	381	14	)	)	PUNCT
ejpam-6607	381	15	,	,	PUNCT
ejpam-6607	381	16	so	so	SCONJ
ejpam-6607	381	17	each	each	DET
ejpam-6607	381	18	γ	γ	X
ejpam-6607	381	19	=	=	SYM
ejpam-6607	381	20	(	(	PUNCT
ejpam-6607	381	21	α1	α1	PROPN
ejpam-6607	381	22	,	,	PUNCT
ejpam-6607	381	23	α2	α2	ADJ
ejpam-6607	381	24	,	,	PUNCT
ejpam-6607	381	25	α3	α3	PROPN
ejpam-6607	381	26	)	)	PUNCT
ejpam-6607	381	27	with	with	ADP
ejpam-6607	381	28	αi	αi	NOUN
ejpam-6607	381	29	⊆	⊆	NUM
ejpam-6607	381	30	ai	ai	NOUN
ejpam-6607	381	31	.	.	PUNCT
ejpam-6607	382	1	let	let	VERB
ejpam-6607	382	2	h(u	h(u	PROPN
ejpam-6607	382	3	)	)	PUNCT
ejpam-6607	382	4	be	be	AUX
ejpam-6607	382	5	the	the	DET
ejpam-6607	382	6	hilbert	hilbert	NOUN
ejpam-6607	382	7	space	space	NOUN
ejpam-6607	382	8	with	with	ADP
ejpam-6607	382	9	basis	basis	NOUN
ejpam-6607	382	10	{	{	PUNCT
ejpam-6607	382	11	|moviea⟩	|moviea⟩	PROPN
ejpam-6607	382	12	,	,	PUNCT
ejpam-6607	382	13	|movieb⟩	|movieb⟩	NOUN
ejpam-6607	382	14	,	,	PUNCT
ejpam-6607	382	15	|moviec⟩	|moviec⟩	NOUN
ejpam-6607	382	16	}	}	PUNCT
ejpam-6607	382	17	.	.	PUNCT
ejpam-6607	383	1	case	case	NOUN
ejpam-6607	383	2	1	1	NUM
ejpam-6607	383	3	:	:	PUNCT
ejpam-6607	383	4	action	action	NOUN
ejpam-6607	383	5	-	-	PUNCT
ejpam-6607	383	6	light	light	NOUN
ejpam-6607	383	7	-	-	PUNCT
ejpam-6607	383	8	streaming	streaming	NOUN
ejpam-6607	383	9	γ1	γ1	NOUN
ejpam-6607	383	10	=	=	SYM
ejpam-6607	383	11	(	(	PUNCT
ejpam-6607	383	12	{	{	PUNCT
ejpam-6607	383	13	action	action	NOUN
ejpam-6607	383	14	}	}	PUNCT
ejpam-6607	383	15	,	,	PUNCT
ejpam-6607	383	16	{	{	PUNCT
ejpam-6607	383	17	light	light	NOUN
ejpam-6607	383	18	}	}	PUNCT
ejpam-6607	383	19	,	,	PUNCT
ejpam-6607	383	20	{	{	PUNCT
ejpam-6607	383	21	streaming	streaming	NOUN
ejpam-6607	383	22	}	}	PUNCT
ejpam-6607	383	23	)	)	PUNCT
ejpam-6607	383	24	.	.	PUNCT
ejpam-6607	384	1	define	define	VERB
ejpam-6607	384	2	|ψγ1⟩	|ψγ1⟩	NOUN
ejpam-6607	384	3	=	=	PUNCT
ejpam-6607	384	4	√	√	PROPN
ejpam-6607	384	5	0.80	0.80	NUM
ejpam-6607	384	6	|moviea⟩+	|moviea⟩+	NOUN
ejpam-6607	384	7	√	√	PROPN
ejpam-6607	384	8	0.15	0.15	NUM
ejpam-6607	384	9	|movieb⟩+	|movieb⟩+	ADJ
ejpam-6607	384	10	√	√	NUM
ejpam-6607	384	11	0.05	0.05	NUM
ejpam-6607	384	12	|moviec⟩	|moviec⟩	NOUN
ejpam-6607	384	13	.	.	PUNCT
ejpam-6607	385	1	check	check	VERB
ejpam-6607	385	2	normalization	normalization	NOUN
ejpam-6607	385	3	:	:	PUNCT
ejpam-6607	385	4	0.80	0.80	NUM
ejpam-6607	385	5	+	+	CCONJ
ejpam-6607	385	6	0.15	0.15	NUM
ejpam-6607	385	7	+	+	NOUN
ejpam-6607	385	8	0.05	0.05	NUM
ejpam-6607	385	9	=	=	SYM
ejpam-6607	385	10	1.00	1.00	NUM
ejpam-6607	385	11	.	.	PUNCT
ejpam-6607	386	1	thus	thus	ADV
ejpam-6607	386	2	p	p	X
ejpam-6607	386	3	(	(	PUNCT
ejpam-6607	386	4	moviea	moviea	ADJ
ejpam-6607	386	5	|	|	NOUN
ejpam-6607	386	6	γ1	γ1	NOUN
ejpam-6607	386	7	)	)	PUNCT
ejpam-6607	386	8	=	=	PUNCT
ejpam-6607	386	9	0.80	0.80	NUM
ejpam-6607	386	10	,	,	PUNCT
ejpam-6607	386	11	p	p	X
ejpam-6607	386	12	(	(	PUNCT
ejpam-6607	386	13	movieb	movieb	PROPN
ejpam-6607	386	14	|	|	NOUN
ejpam-6607	386	15	γ1	γ1	NOUN
ejpam-6607	386	16	)	)	PUNCT
ejpam-6607	386	17	=	=	PUNCT
ejpam-6607	387	1	0.15	0.15	NUM
ejpam-6607	387	2	,	,	PUNCT
ejpam-6607	387	3	p	p	X
ejpam-6607	387	4	(	(	PUNCT
ejpam-6607	387	5	moviec	moviec	NOUN
ejpam-6607	387	6	|	|	NOUN
ejpam-6607	387	7	γ1	γ1	NOUN
ejpam-6607	387	8	)	)	PUNCT
ejpam-6607	387	9	=	=	PUNCT
ejpam-6607	387	10	0.05	0.05	NUM
ejpam-6607	387	11	.	.	PUNCT
ejpam-6607	388	1	case	case	NOUN
ejpam-6607	388	2	2	2	NUM
ejpam-6607	388	3	:	:	PUNCT
ejpam-6607	388	4	drama	drama	NOUN
ejpam-6607	388	5	-	-	PUNCT
ejpam-6607	388	6	dark	dark	ADJ
ejpam-6607	388	7	-	-	PUNCT
ejpam-6607	388	8	theater	theater	NOUN
ejpam-6607	388	9	γ2	γ2	NOUN
ejpam-6607	388	10	=	=	SYM
ejpam-6607	388	11	(	(	PUNCT
ejpam-6607	388	12	{	{	PUNCT
ejpam-6607	388	13	drama	drama	NOUN
ejpam-6607	388	14	}	}	PUNCT
ejpam-6607	388	15	,	,	PUNCT
ejpam-6607	388	16	{	{	PUNCT
ejpam-6607	388	17	dark	dark	ADJ
ejpam-6607	388	18	}	}	PUNCT
ejpam-6607	388	19	,	,	PUNCT
ejpam-6607	388	20	{	{	PUNCT
ejpam-6607	388	21	theater	theater	NOUN
ejpam-6607	388	22	}	}	PUNCT
ejpam-6607	388	23	)	)	PUNCT
ejpam-6607	388	24	.	.	PUNCT
ejpam-6607	389	1	t.	t.	PROPN
ejpam-6607	389	2	fujita	fujita	PROPN
ejpam-6607	389	3	,	,	PUNCT
ejpam-6607	389	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	389	5	/	/	SYM
ejpam-6607	389	6	eur	eur	PROPN
ejpam-6607	389	7	.	.	PUNCT
ejpam-6607	390	1	j.	j.	PROPN
ejpam-6607	390	2	pure	pure	PROPN
ejpam-6607	390	3	appl	appl	PROPN
ejpam-6607	390	4	.	.	PROPN
ejpam-6607	390	5	math	math	PROPN
ejpam-6607	390	6	,	,	PUNCT
ejpam-6607	390	7	18	18	NUM
ejpam-6607	390	8	(	(	PUNCT
ejpam-6607	390	9	3	3	NUM
ejpam-6607	390	10	)	)	PUNCT
ejpam-6607	390	11	(	(	PUNCT
ejpam-6607	390	12	2025	2025	NUM
ejpam-6607	390	13	)	)	PUNCT
ejpam-6607	390	14	,	,	PUNCT
ejpam-6607	390	15	6607	6607	NUM
ejpam-6607	390	16	19	19	NUM
ejpam-6607	390	17	of	of	ADP
ejpam-6607	390	18	33	33	NUM
ejpam-6607	390	19	define	define	VERB
ejpam-6607	390	20	|ψγ2⟩	|ψγ2⟩	NOUN
ejpam-6607	390	21	=	=	SYM
ejpam-6607	390	22	√	√	ADP
ejpam-6607	390	23	0.10	0.10	NUM
ejpam-6607	390	24	|moviea⟩+	|moviea⟩+	NOUN
ejpam-6607	390	25	√	√	ADP
ejpam-6607	390	26	0.70	0.70	NUM
ejpam-6607	390	27	|movieb⟩+	|movieb⟩+	ADJ
ejpam-6607	390	28	√	√	ADP
ejpam-6607	390	29	0.20	0.20	NUM
ejpam-6607	390	30	|moviec⟩	|moviec⟩	NOUN
ejpam-6607	390	31	,	,	PUNCT
ejpam-6607	390	32	with	with	ADP
ejpam-6607	390	33	0.10	0.10	NUM
ejpam-6607	390	34	+	+	CCONJ
ejpam-6607	390	35	0.70	0.70	NUM
ejpam-6607	390	36	+	+	NOUN
ejpam-6607	390	37	0.20	0.20	NUM
ejpam-6607	390	38	=	=	SYM
ejpam-6607	390	39	1.00	1.00	NUM
ejpam-6607	390	40	.	.	PUNCT
ejpam-6607	391	1	hence	hence	ADV
ejpam-6607	391	2	p	p	X
ejpam-6607	391	3	(	(	PUNCT
ejpam-6607	391	4	moviea	moviea	ADJ
ejpam-6607	391	5	|	|	NOUN
ejpam-6607	391	6	γ2	γ2	NOUN
ejpam-6607	391	7	)	)	PUNCT
ejpam-6607	391	8	=	=	SYM
ejpam-6607	391	9	0.10	0.10	NUM
ejpam-6607	391	10	,	,	PUNCT
ejpam-6607	391	11	p	p	X
ejpam-6607	391	12	(	(	PUNCT
ejpam-6607	391	13	movieb	movieb	PROPN
ejpam-6607	391	14	|	|	ADV
ejpam-6607	391	15	γ2	γ2	NOUN
ejpam-6607	391	16	)	)	PUNCT
ejpam-6607	391	17	=	=	SYM
ejpam-6607	392	1	0.70	0.70	NUM
ejpam-6607	392	2	,	,	PUNCT
ejpam-6607	392	3	p	p	X
ejpam-6607	392	4	(	(	PUNCT
ejpam-6607	392	5	moviec	moviec	NOUN
ejpam-6607	392	6	|	|	ADV
ejpam-6607	392	7	γ2	γ2	ADJ
ejpam-6607	392	8	)	)	PUNCT
ejpam-6607	392	9	=	=	SYM
ejpam-6607	392	10	0.20	0.20	NUM
ejpam-6607	392	11	.	.	PUNCT
ejpam-6607	393	1	this	this	DET
ejpam-6607	393	2	example	example	NOUN
ejpam-6607	393	3	shows	show	VERB
ejpam-6607	393	4	how	how	SCONJ
ejpam-6607	393	5	a	a	DET
ejpam-6607	393	6	quantum	quantum	NOUN
ejpam-6607	393	7	–	–	PUNCT
ejpam-6607	393	8	superhypersoft	superhypersoft	NOUN
ejpam-6607	393	9	set	set	NOUN
ejpam-6607	393	10	models	model	NOUN
ejpam-6607	393	11	complex	complex	ADJ
ejpam-6607	393	12	viewer	viewer	NOUN
ejpam-6607	393	13	preferences	preference	NOUN
ejpam-6607	393	14	—	—	PUNCT
ejpam-6607	393	15	genre	genre	NOUN
ejpam-6607	393	16	,	,	PUNCT
ejpam-6607	393	17	mood	mood	NOUN
ejpam-6607	393	18	,	,	PUNCT
ejpam-6607	393	19	and	and	CCONJ
ejpam-6607	393	20	platform	platform	NOUN
ejpam-6607	393	21	—	—	PUNCT
ejpam-6607	393	22	as	as	ADP
ejpam-6607	393	23	quantum	quantum	NOUN
ejpam-6607	393	24	superpositions	superposition	NOUN
ejpam-6607	393	25	,	,	PUNCT
ejpam-6607	393	26	yielding	yield	VERB
ejpam-6607	393	27	soft	soft	ADJ
ejpam-6607	393	28	rankings	ranking	NOUN
ejpam-6607	393	29	of	of	ADP
ejpam-6607	393	30	films	film	NOUN
ejpam-6607	393	31	for	for	ADP
ejpam-6607	393	32	each	each	DET
ejpam-6607	393	33	preference	preference	NOUN
ejpam-6607	393	34	combination	combination	NOUN
ejpam-6607	393	35	.	.	PUNCT
ejpam-6607	394	1	example	example	NOUN
ejpam-6607	394	2	11	11	NUM
ejpam-6607	394	3	(	(	PUNCT
ejpam-6607	394	4	quantum	quantum	NOUN
ejpam-6607	394	5	–	–	PUNCT
ejpam-6607	394	6	superhypersoft	superhypersoft	NOUN
ejpam-6607	394	7	set	set	VERB
ejpam-6607	394	8	for	for	ADP
ejpam-6607	394	9	supplier	supplier	NOUN
ejpam-6607	394	10	selection	selection	NOUN
ejpam-6607	394	11	)	)	PUNCT
ejpam-6607	394	12	.	.	PUNCT
ejpam-6607	395	1	let	let	VERB
ejpam-6607	395	2	u	u	PRON
ejpam-6607	395	3	=	=	X
ejpam-6607	395	4	{	{	PUNCT
ejpam-6607	395	5	s1	s1	NOUN
ejpam-6607	395	6	,	,	PUNCT
ejpam-6607	395	7	s2	s2	PROPN
ejpam-6607	395	8	,	,	PUNCT
ejpam-6607	395	9	s3	s3	PROPN
ejpam-6607	395	10	}	}	PUNCT
ejpam-6607	395	11	be	be	VERB
ejpam-6607	395	12	three	three	NUM
ejpam-6607	395	13	potential	potential	ADJ
ejpam-6607	395	14	suppliers	supplier	NOUN
ejpam-6607	395	15	.	.	PUNCT
ejpam-6607	396	1	consider	consider	VERB
ejpam-6607	396	2	three	three	NUM
ejpam-6607	396	3	attribute	attribute	NOUN
ejpam-6607	396	4	domains	domain	NOUN
ejpam-6607	396	5	:	:	PUNCT
ejpam-6607	396	6	a1	a1	NOUN
ejpam-6607	396	7	=	=	SYM
ejpam-6607	396	8	{	{	PUNCT
ejpam-6607	396	9	local	local	ADJ
ejpam-6607	396	10	,	,	PUNCT
ejpam-6607	396	11	overseas	overseas	ADJ
ejpam-6607	396	12	}	}	PUNCT
ejpam-6607	396	13	,	,	PUNCT
ejpam-6607	396	14	a2	a2	PROPN
ejpam-6607	396	15	=	=	PUNCT
ejpam-6607	396	16	{	{	PUNCT
ejpam-6607	396	17	lowcost	lowcost	NOUN
ejpam-6607	396	18	,	,	PUNCT
ejpam-6607	396	19	highcost	highcost	NOUN
ejpam-6607	396	20	}	}	PUNCT
ejpam-6607	396	21	,	,	PUNCT
ejpam-6607	396	22	a3	a3	NOUN
ejpam-6607	396	23	=	=	SYM
ejpam-6607	396	24	{	{	PUNCT
ejpam-6607	396	25	shortlead	shortlead	NOUN
ejpam-6607	396	26	,	,	PUNCT
ejpam-6607	396	27	longlead	longlead	NOUN
ejpam-6607	396	28	}	}	PUNCT
ejpam-6607	396	29	.	.	PUNCT
ejpam-6607	397	1	form	form	NOUN
ejpam-6607	397	2	c	c	NOUN
ejpam-6607	397	3	=	=	SYM
ejpam-6607	397	4	p(a1)×	p(a1)×	PROPN
ejpam-6607	397	5	p(a2)×	p(a2)×	NOUN
ejpam-6607	397	6	p(a3	p(a3	NOUN
ejpam-6607	397	7	)	)	PUNCT
ejpam-6607	397	8	,	,	PUNCT
ejpam-6607	397	9	and	and	CCONJ
ejpam-6607	397	10	let	let	VERB
ejpam-6607	397	11	the	the	DET
ejpam-6607	397	12	basis	basis	NOUN
ejpam-6607	397	13	be	be	AUX
ejpam-6607	397	14	{	{	PUNCT
ejpam-6607	397	15	|s1⟩	|s1⟩	NOUN
ejpam-6607	397	16	,	,	PUNCT
ejpam-6607	397	17	|s2⟩	|s2⟩	PRON
ejpam-6607	397	18	,	,	PUNCT
ejpam-6607	397	19	|s3⟩	|s3⟩	PROPN
ejpam-6607	397	20	}	}	PUNCT
ejpam-6607	397	21	.	.	PUNCT
ejpam-6607	398	1	case	case	NOUN
ejpam-6607	398	2	1	1	NUM
ejpam-6607	398	3	:	:	PUNCT
ejpam-6607	398	4	local	local	ADJ
ejpam-6607	398	5	,	,	PUNCT
ejpam-6607	398	6	lowcost	lowcost	PROPN
ejpam-6607	398	7	,	,	PUNCT
ejpam-6607	398	8	shortlead	shortlead	NOUN
ejpam-6607	398	9	γ1	γ1	NOUN
ejpam-6607	398	10	=	=	SYM
ejpam-6607	398	11	(	(	PUNCT
ejpam-6607	398	12	{	{	PUNCT
ejpam-6607	398	13	local	local	ADJ
ejpam-6607	398	14	}	}	PUNCT
ejpam-6607	398	15	,	,	PUNCT
ejpam-6607	398	16	{	{	PUNCT
ejpam-6607	398	17	lowcost	lowcost	ADV
ejpam-6607	398	18	}	}	PUNCT
ejpam-6607	398	19	,	,	PUNCT
ejpam-6607	398	20	{	{	PUNCT
ejpam-6607	398	21	shortlead	shortlead	NOUN
ejpam-6607	398	22	}	}	PUNCT
ejpam-6607	398	23	)	)	PUNCT
ejpam-6607	398	24	.	.	PUNCT
ejpam-6607	399	1	set	set	VERB
ejpam-6607	399	2	|ψγ1⟩	|ψγ1⟩	NOUN
ejpam-6607	399	3	=	=	PUNCT
ejpam-6607	399	4	√	√	NUM
ejpam-6607	399	5	0.60	0.60	NUM
ejpam-6607	399	6	|s1⟩+	|s1⟩+	NOUN
ejpam-6607	399	7	√	√	PROPN
ejpam-6607	399	8	0.30	0.30	NUM
ejpam-6607	399	9	|s2⟩+	|s2⟩+	NOUN
ejpam-6607	399	10	√	√	ADP
ejpam-6607	399	11	0.10	0.10	NUM
ejpam-6607	399	12	|s3⟩	|s3⟩	NOUN
ejpam-6607	399	13	,	,	PUNCT
ejpam-6607	399	14	so	so	ADV
ejpam-6607	399	15	p	p	X
ejpam-6607	399	16	(	(	PUNCT
ejpam-6607	399	17	s1	s1	PROPN
ejpam-6607	399	18	|	|	NOUN
ejpam-6607	399	19	γ1	γ1	PROPN
ejpam-6607	399	20	)	)	PUNCT
ejpam-6607	399	21	=	=	SYM
ejpam-6607	400	1	0.60	0.60	NUM
ejpam-6607	400	2	,	,	PUNCT
ejpam-6607	400	3	p	p	X
ejpam-6607	400	4	(	(	PUNCT
ejpam-6607	400	5	s2	s2	PROPN
ejpam-6607	400	6	|	|	ADV
ejpam-6607	400	7	γ1	γ1	NOUN
ejpam-6607	400	8	)	)	PUNCT
ejpam-6607	400	9	=	=	SYM
ejpam-6607	400	10	0.30	0.30	NUM
ejpam-6607	400	11	,	,	PUNCT
ejpam-6607	400	12	p	p	X
ejpam-6607	400	13	(	(	PUNCT
ejpam-6607	400	14	s3	s3	PROPN
ejpam-6607	400	15	|	|	NOUN
ejpam-6607	400	16	γ1	γ1	NOUN
ejpam-6607	400	17	)	)	PUNCT
ejpam-6607	400	18	=	=	SYM
ejpam-6607	400	19	0.10	0.10	NUM
ejpam-6607	400	20	.	.	PUNCT
ejpam-6607	400	21	case	case	NOUN
ejpam-6607	400	22	2	2	NUM
ejpam-6607	400	23	:	:	PUNCT
ejpam-6607	400	24	overseas	overseas	ADJ
ejpam-6607	400	25	,	,	PUNCT
ejpam-6607	400	26	highcost	highcost	NOUN
ejpam-6607	400	27	,	,	PUNCT
ejpam-6607	400	28	longlead	longlead	NOUN
ejpam-6607	400	29	γ2	γ2	NOUN
ejpam-6607	400	30	=	=	SYM
ejpam-6607	400	31	(	(	PUNCT
ejpam-6607	400	32	{	{	PUNCT
ejpam-6607	400	33	overseas	overseas	ADV
ejpam-6607	400	34	}	}	PUNCT
ejpam-6607	400	35	,	,	PUNCT
ejpam-6607	400	36	{	{	PUNCT
ejpam-6607	400	37	highcost	highcost	NOUN
ejpam-6607	400	38	}	}	PUNCT
ejpam-6607	400	39	,	,	PUNCT
ejpam-6607	400	40	{	{	PUNCT
ejpam-6607	400	41	longlead	longlead	NOUN
ejpam-6607	400	42	}	}	PUNCT
ejpam-6607	400	43	)	)	PUNCT
ejpam-6607	400	44	.	.	PUNCT
ejpam-6607	401	1	set	set	VERB
ejpam-6607	401	2	|ψγ2⟩	|ψγ2⟩	NOUN
ejpam-6607	401	3	=	=	SYM
ejpam-6607	401	4	√	√	NUM
ejpam-6607	401	5	0.05	0.05	NUM
ejpam-6607	401	6	|s1⟩+	|s1⟩+	NOUN
ejpam-6607	401	7	√	√	NUM
ejpam-6607	401	8	0.25	0.25	NUM
ejpam-6607	401	9	|s2⟩+	|s2⟩+	NOUN
ejpam-6607	401	10	√	√	ADP
ejpam-6607	401	11	0.70	0.70	NUM
ejpam-6607	401	12	|s3⟩	|s3⟩	NOUN
ejpam-6607	401	13	,	,	PUNCT
ejpam-6607	401	14	yielding	yield	VERB
ejpam-6607	401	15	p	p	X
ejpam-6607	401	16	(	(	PUNCT
ejpam-6607	401	17	s1	s1	PROPN
ejpam-6607	401	18	|	|	ADV
ejpam-6607	401	19	γ2	γ2	NOUN
ejpam-6607	401	20	)	)	PUNCT
ejpam-6607	402	1	=	=	SYM
ejpam-6607	402	2	0.05	0.05	NUM
ejpam-6607	402	3	,	,	PUNCT
ejpam-6607	402	4	p	p	X
ejpam-6607	402	5	(	(	PUNCT
ejpam-6607	402	6	s2	s2	PROPN
ejpam-6607	402	7	|	|	ADV
ejpam-6607	402	8	γ2	γ2	NOUN
ejpam-6607	402	9	)	)	PUNCT
ejpam-6607	402	10	=	=	SYM
ejpam-6607	403	1	0.25	0.25	NUM
ejpam-6607	403	2	,	,	PUNCT
ejpam-6607	403	3	p	p	X
ejpam-6607	403	4	(	(	PUNCT
ejpam-6607	403	5	s3	s3	PROPN
ejpam-6607	403	6	|	|	ADV
ejpam-6607	403	7	γ2	γ2	NOUN
ejpam-6607	403	8	)	)	PUNCT
ejpam-6607	403	9	=	=	PUNCT
ejpam-6607	404	1	0.70	0.70	NUM
ejpam-6607	404	2	.	.	PUNCT
ejpam-6607	405	1	this	this	PRON
ejpam-6607	405	2	shows	show	VERB
ejpam-6607	405	3	how	how	SCONJ
ejpam-6607	405	4	a	a	DET
ejpam-6607	405	5	quantum	quantum	NOUN
ejpam-6607	405	6	–	–	PUNCT
ejpam-6607	405	7	superhypersoft	superhypersoft	NOUN
ejpam-6607	405	8	set	set	NOUN
ejpam-6607	405	9	can	can	AUX
ejpam-6607	405	10	encode	encode	VERB
ejpam-6607	405	11	multi	multi	ADJ
ejpam-6607	405	12	-	-	ADJ
ejpam-6607	405	13	criteria	criteria	ADJ
ejpam-6607	405	14	supplier	supplier	NOUN
ejpam-6607	405	15	characteristics	characteristic	NOUN
ejpam-6607	405	16	as	as	ADP
ejpam-6607	405	17	quantum	quantum	NOUN
ejpam-6607	405	18	-	-	PUNCT
ejpam-6607	405	19	like	like	ADJ
ejpam-6607	405	20	states	state	NOUN
ejpam-6607	405	21	,	,	PUNCT
ejpam-6607	405	22	with	with	ADP
ejpam-6607	405	23	measurement	measurement	NOUN
ejpam-6607	405	24	probabilities	probability	NOUN
ejpam-6607	405	25	giving	give	VERB
ejpam-6607	405	26	soft	soft	ADJ
ejpam-6607	405	27	selection	selection	NOUN
ejpam-6607	405	28	weights	weight	NOUN
ejpam-6607	405	29	.	.	PUNCT
ejpam-6607	406	1	t.	t.	PROPN
ejpam-6607	406	2	fujita	fujita	PROPN
ejpam-6607	406	3	,	,	PUNCT
ejpam-6607	406	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	406	5	/	/	SYM
ejpam-6607	406	6	eur	eur	PROPN
ejpam-6607	406	7	.	.	PUNCT
ejpam-6607	407	1	j.	j.	PROPN
ejpam-6607	407	2	pure	pure	PROPN
ejpam-6607	407	3	appl	appl	PROPN
ejpam-6607	407	4	.	.	PROPN
ejpam-6607	407	5	math	math	PROPN
ejpam-6607	407	6	,	,	PUNCT
ejpam-6607	407	7	18	18	NUM
ejpam-6607	407	8	(	(	PUNCT
ejpam-6607	407	9	3	3	NUM
ejpam-6607	407	10	)	)	PUNCT
ejpam-6607	407	11	(	(	PUNCT
ejpam-6607	407	12	2025	2025	NUM
ejpam-6607	407	13	)	)	PUNCT
ejpam-6607	407	14	,	,	PUNCT
ejpam-6607	407	15	6607	6607	NUM
ejpam-6607	407	16	20	20	NUM
ejpam-6607	407	17	of	of	ADP
ejpam-6607	407	18	33	33	NUM
ejpam-6607	407	19	example	example	NOUN
ejpam-6607	407	20	12	12	NUM
ejpam-6607	407	21	(	(	PUNCT
ejpam-6607	407	22	quantum	quantum	NOUN
ejpam-6607	407	23	–	–	PUNCT
ejpam-6607	407	24	superhypersoft	superhypersoft	NOUN
ejpam-6607	407	25	set	set	VERB
ejpam-6607	407	26	for	for	ADP
ejpam-6607	407	27	algorithm	algorithm	NOUN
ejpam-6607	407	28	selection	selection	NOUN
ejpam-6607	407	29	on	on	ADP
ejpam-6607	407	30	quantum	quantum	ADJ
ejpam-6607	407	31	hardware	hardware	NOUN
ejpam-6607	407	32	)	)	PUNCT
ejpam-6607	407	33	.	.	PUNCT
ejpam-6607	408	1	let	let	VERB
ejpam-6607	408	2	u	u	PRON
ejpam-6607	408	3	=	=	PUNCT
ejpam-6607	408	4	{	{	PUNCT
ejpam-6607	408	5	grover	grover	NOUN
ejpam-6607	408	6	,	,	PUNCT
ejpam-6607	408	7	qaoa	qaoa	PROPN
ejpam-6607	408	8	,	,	PUNCT
ejpam-6607	408	9	vqe	vqe	PROPN
ejpam-6607	408	10	}	}	PUNCT
ejpam-6607	408	11	be	be	VERB
ejpam-6607	408	12	the	the	DET
ejpam-6607	408	13	set	set	NOUN
ejpam-6607	408	14	of	of	ADP
ejpam-6607	408	15	candidate	candidate	NOUN
ejpam-6607	408	16	quantum	quantum	ADJ
ejpam-6607	408	17	algorithms	algorithm	NOUN
ejpam-6607	408	18	.	.	PUNCT
ejpam-6607	409	1	consider	consider	VERB
ejpam-6607	409	2	three	three	NUM
ejpam-6607	409	3	attribute	attribute	NOUN
ejpam-6607	409	4	domains	domain	NOUN
ejpam-6607	409	5	with	with	ADP
ejpam-6607	409	6	disjoint	disjoint	NOUN
ejpam-6607	409	7	value	value	NOUN
ejpam-6607	409	8	-	-	PUNCT
ejpam-6607	409	9	sets	set	NOUN
ejpam-6607	409	10	:	:	PUNCT
ejpam-6607	409	11	a1	a1	NOUN
ejpam-6607	409	12	=	=	SYM
ejpam-6607	409	13	{	{	PUNCT
ejpam-6607	409	14	ibm	ibm	PROPN
ejpam-6607	409	15	,	,	PUNCT
ejpam-6607	409	16	rigetti	rigetti	NOUN
ejpam-6607	409	17	,	,	PUNCT
ejpam-6607	409	18	ionq	ionq	PROPN
ejpam-6607	409	19	}	}	PUNCT
ejpam-6607	409	20	,	,	PUNCT
ejpam-6607	409	21	a2	a2	PROPN
ejpam-6607	409	22	=	=	PUNCT
ejpam-6607	409	23	{	{	PUNCT
ejpam-6607	409	24	superconducting	superconducting	NOUN
ejpam-6607	409	25	,	,	PUNCT
ejpam-6607	409	26	trappedion	trappedion	NOUN
ejpam-6607	409	27	}	}	PUNCT
ejpam-6607	409	28	,	,	PUNCT
ejpam-6607	409	29	a3	a3	NOUN
ejpam-6607	409	30	=	=	SYM
ejpam-6607	409	31	{	{	PUNCT
ejpam-6607	409	32	alltoall	alltoall	NOUN
ejpam-6607	409	33	,	,	PUNCT
ejpam-6607	409	34	linear	linear	ADJ
ejpam-6607	409	35	}	}	PUNCT
ejpam-6607	409	36	.	.	PUNCT
ejpam-6607	410	1	form	form	VERB
ejpam-6607	410	2	the	the	DET
ejpam-6607	410	3	cartesian	cartesian	ADJ
ejpam-6607	410	4	product	product	NOUN
ejpam-6607	410	5	of	of	ADP
ejpam-6607	410	6	power	power	NOUN
ejpam-6607	410	7	-	-	PUNCT
ejpam-6607	410	8	sets	set	NOUN
ejpam-6607	410	9	c	c	NOUN
ejpam-6607	410	10	=	=	SYM
ejpam-6607	410	11	p(a1)×	p(a1)×	PROPN
ejpam-6607	410	12	p(a2)×	p(a2)×	NOUN
ejpam-6607	410	13	p(a3	p(a3	NOUN
ejpam-6607	410	14	)	)	PUNCT
ejpam-6607	410	15	,	,	PUNCT
ejpam-6607	410	16	so	so	SCONJ
ejpam-6607	410	17	each	each	DET
ejpam-6607	410	18	γ	γ	X
ejpam-6607	410	19	=	=	SYM
ejpam-6607	410	20	(	(	PUNCT
ejpam-6607	410	21	α1	α1	PROPN
ejpam-6607	410	22	,	,	PUNCT
ejpam-6607	410	23	α2	α2	ADJ
ejpam-6607	410	24	,	,	PUNCT
ejpam-6607	410	25	α3	α3	PROPN
ejpam-6607	410	26	)	)	PUNCT
ejpam-6607	410	27	with	with	ADP
ejpam-6607	410	28	αi	αi	NOUN
ejpam-6607	410	29	⊆	⊆	NUM
ejpam-6607	410	30	ai	ai	NOUN
ejpam-6607	410	31	.	.	PUNCT
ejpam-6607	411	1	let	let	VERB
ejpam-6607	411	2	h(u	h(u	PROPN
ejpam-6607	411	3	)	)	PUNCT
ejpam-6607	411	4	be	be	AUX
ejpam-6607	411	5	the	the	DET
ejpam-6607	411	6	3	3	NUM
ejpam-6607	411	7	-	-	PUNCT
ejpam-6607	411	8	dimensional	dimensional	ADJ
ejpam-6607	411	9	complex	complex	ADJ
ejpam-6607	411	10	hilbert	hilbert	NOUN
ejpam-6607	411	11	space	space	NOUN
ejpam-6607	411	12	with	with	ADP
ejpam-6607	411	13	orthonormal	orthonormal	ADJ
ejpam-6607	411	14	basis	basis	NOUN
ejpam-6607	411	15	{	{	PUNCT
ejpam-6607	411	16	|grover⟩	|grover⟩	NOUN
ejpam-6607	411	17	,	,	PUNCT
ejpam-6607	411	18	|qaoa⟩	|qaoa⟩	NOUN
ejpam-6607	411	19	,	,	PUNCT
ejpam-6607	411	20	|vqe⟩	|vqe⟩	ADP
ejpam-6607	411	21	}	}	PUNCT
ejpam-6607	411	22	.	.	PUNCT
ejpam-6607	412	1	case	case	NOUN
ejpam-6607	412	2	1	1	NUM
ejpam-6607	412	3	:	:	PUNCT
ejpam-6607	412	4	hybrid	hybrid	ADJ
ejpam-6607	412	5	superconducting	superconducting	NOUN
ejpam-6607	412	6	,	,	PUNCT
ejpam-6607	412	7	all	all	PRON
ejpam-6607	412	8	-	-	PUNCT
ejpam-6607	412	9	to	to	ADP
ejpam-6607	412	10	-	-	PUNCT
ejpam-6607	412	11	all	all	PRON
ejpam-6607	412	12	on	on	ADP
ejpam-6607	412	13	ibm	ibm	PROPN
ejpam-6607	412	14	or	or	CCONJ
ejpam-6607	412	15	rigetti	rigetti	PROPN
ejpam-6607	412	16	γ1	γ1	NOUN
ejpam-6607	412	17	=	=	SYM
ejpam-6607	412	18	(	(	PUNCT
ejpam-6607	412	19	{	{	PUNCT
ejpam-6607	412	20	ibm	ibm	PROPN
ejpam-6607	412	21	,	,	PUNCT
ejpam-6607	412	22	rigetti	rigetti	NOUN
ejpam-6607	412	23	}	}	PUNCT
ejpam-6607	412	24	,	,	PUNCT
ejpam-6607	412	25	{	{	PUNCT
ejpam-6607	412	26	superconducting	superconducte	VERB
ejpam-6607	412	27	}	}	PUNCT
ejpam-6607	412	28	,	,	PUNCT
ejpam-6607	412	29	{	{	PUNCT
ejpam-6607	412	30	alltoall	alltoall	NOUN
ejpam-6607	412	31	}	}	PUNCT
ejpam-6607	412	32	)	)	PUNCT
ejpam-6607	412	33	.	.	PUNCT
ejpam-6607	413	1	define	define	VERB
ejpam-6607	413	2	the	the	DET
ejpam-6607	413	3	quantum	quantum	ADJ
ejpam-6607	413	4	state	state	NOUN
ejpam-6607	413	5	|ψγ1⟩	|ψγ1⟩	NOUN
ejpam-6607	413	6	=	=	PUNCT
ejpam-6607	413	7	√	√	NUM
ejpam-6607	413	8	0.50	0.50	NUM
ejpam-6607	413	9	|qaoa⟩+	|qaoa⟩+	ADP
ejpam-6607	413	10	√	√	NUM
ejpam-6607	413	11	0.30	0.30	NUM
ejpam-6607	413	12	|grover⟩+	|grover⟩+	NOUN
ejpam-6607	413	13	√	√	ADP
ejpam-6607	413	14	0.20	0.20	NUM
ejpam-6607	413	15	|vqe⟩	|vqe⟩	PUNCT
ejpam-6607	413	16	,	,	PUNCT
ejpam-6607	413	17	which	which	PRON
ejpam-6607	413	18	satisfies	satisfy	VERB
ejpam-6607	413	19	0.50	0.50	NUM
ejpam-6607	413	20	+	+	CCONJ
ejpam-6607	413	21	0.30	0.30	NUM
ejpam-6607	414	1	+	+	NUM
ejpam-6607	414	2	0.20	0.20	NUM
ejpam-6607	414	3	=	=	SYM
ejpam-6607	414	4	1	1	NUM
ejpam-6607	414	5	.	.	X
ejpam-6607	414	6	measuring	measure	VERB
ejpam-6607	414	7	in	in	ADP
ejpam-6607	414	8	the	the	DET
ejpam-6607	414	9	basis	basis	NOUN
ejpam-6607	414	10	{	{	PUNCT
ejpam-6607	414	11	|grover⟩	|grover⟩	NOUN
ejpam-6607	414	12	,	,	PUNCT
ejpam-6607	414	13	|qaoa⟩	|qaoa⟩	NOUN
ejpam-6607	414	14	,	,	PUNCT
ejpam-6607	414	15	|vqe⟩	|vqe⟩	ADP
ejpam-6607	414	16	}	}	PUNCT
ejpam-6607	414	17	yields	yield	NOUN
ejpam-6607	414	18	p	p	NOUN
ejpam-6607	414	19	(	(	PUNCT
ejpam-6607	414	20	qaoa	qaoa	PROPN
ejpam-6607	414	21	|	|	ADV
ejpam-6607	414	22	γ1	γ1	VERB
ejpam-6607	414	23	)	)	PUNCT
ejpam-6607	414	24	=	=	SYM
ejpam-6607	414	25	0.50	0.50	NUM
ejpam-6607	414	26	,	,	PUNCT
ejpam-6607	414	27	p	p	X
ejpam-6607	414	28	(	(	PUNCT
ejpam-6607	414	29	grover	grover	NOUN
ejpam-6607	414	30	|	|	NOUN
ejpam-6607	414	31	γ1	γ1	PROPN
ejpam-6607	414	32	)	)	PUNCT
ejpam-6607	414	33	=	=	SYM
ejpam-6607	414	34	0.30	0.30	NUM
ejpam-6607	414	35	,	,	PUNCT
ejpam-6607	414	36	p	p	X
ejpam-6607	414	37	(	(	PUNCT
ejpam-6607	414	38	vqe	vqe	NOUN
ejpam-6607	414	39	|	|	NOUN
ejpam-6607	414	40	γ1	γ1	NOUN
ejpam-6607	414	41	)	)	PUNCT
ejpam-6607	414	42	=	=	SYM
ejpam-6607	414	43	0.20	0.20	NUM
ejpam-6607	414	44	.	.	PUNCT
ejpam-6607	414	45	case	case	NOUN
ejpam-6607	414	46	2	2	NUM
ejpam-6607	414	47	:	:	PUNCT
ejpam-6607	414	48	ion	ion	NOUN
ejpam-6607	414	49	-	-	PUNCT
ejpam-6607	414	50	trapped	trap	VERB
ejpam-6607	414	51	,	,	PUNCT
ejpam-6607	414	52	linear	linear	ADJ
ejpam-6607	414	53	connectivity	connectivity	NOUN
ejpam-6607	414	54	on	on	ADP
ejpam-6607	414	55	ionq	ionq	ADJ
ejpam-6607	414	56	γ2	γ2	NOUN
ejpam-6607	414	57	=	=	SYM
ejpam-6607	414	58	(	(	PUNCT
ejpam-6607	414	59	{	{	PUNCT
ejpam-6607	414	60	ionq	ionq	PROPN
ejpam-6607	414	61	}	}	PUNCT
ejpam-6607	414	62	,	,	PUNCT
ejpam-6607	414	63	{	{	PUNCT
ejpam-6607	414	64	trappedion	trappedion	NOUN
ejpam-6607	414	65	}	}	PUNCT
ejpam-6607	414	66	,	,	PUNCT
ejpam-6607	414	67	{	{	PUNCT
ejpam-6607	414	68	linear	linear	NOUN
ejpam-6607	414	69	}	}	PUNCT
ejpam-6607	414	70	)	)	PUNCT
ejpam-6607	414	71	.	.	PUNCT
ejpam-6607	415	1	define	define	VERB
ejpam-6607	415	2	|ψγ2⟩	|ψγ2⟩	NOUN
ejpam-6607	415	3	=	=	SYM
ejpam-6607	415	4	√	√	ADP
ejpam-6607	415	5	0.10	0.10	NUM
ejpam-6607	415	6	|qaoa⟩+	|qaoa⟩+	ADP
ejpam-6607	415	7	√	√	NUM
ejpam-6607	415	8	0.20	0.20	NUM
ejpam-6607	415	9	|grover⟩+	|grover⟩+	NOUN
ejpam-6607	415	10	√	√	ADP
ejpam-6607	415	11	0.70	0.70	NUM
ejpam-6607	415	12	|vqe⟩	|vqe⟩	PUNCT
ejpam-6607	415	13	,	,	PUNCT
ejpam-6607	415	14	with	with	ADP
ejpam-6607	415	15	0.10	0.10	NUM
ejpam-6607	415	16	+	+	NOUN
ejpam-6607	415	17	0.20	0.20	NUM
ejpam-6607	415	18	+	+	CCONJ
ejpam-6607	415	19	0.70	0.70	NUM
ejpam-6607	415	20	=	=	SYM
ejpam-6607	415	21	1	1	NUM
ejpam-6607	415	22	.	.	PUNCT
ejpam-6607	416	1	thus	thus	ADV
ejpam-6607	416	2	p	p	X
ejpam-6607	416	3	(	(	PUNCT
ejpam-6607	416	4	vqe	vqe	NOUN
ejpam-6607	416	5	|	|	ADV
ejpam-6607	416	6	γ2	γ2	NOUN
ejpam-6607	416	7	)	)	PUNCT
ejpam-6607	416	8	=	=	SYM
ejpam-6607	417	1	0.70	0.70	NUM
ejpam-6607	417	2	,	,	PUNCT
ejpam-6607	417	3	p	p	X
ejpam-6607	417	4	(	(	PUNCT
ejpam-6607	417	5	grover	grover	NOUN
ejpam-6607	417	6	|	|	ADV
ejpam-6607	417	7	γ2	γ2	NOUN
ejpam-6607	417	8	)	)	PUNCT
ejpam-6607	417	9	=	=	SYM
ejpam-6607	417	10	0.20	0.20	NUM
ejpam-6607	417	11	,	,	PUNCT
ejpam-6607	417	12	p	p	X
ejpam-6607	417	13	(	(	PUNCT
ejpam-6607	417	14	qaoa	qaoa	PROPN
ejpam-6607	417	15	|	|	ADV
ejpam-6607	417	16	γ2	γ2	ADJ
ejpam-6607	417	17	)	)	PUNCT
ejpam-6607	417	18	=	=	SYM
ejpam-6607	417	19	0.10	0.10	NUM
ejpam-6607	417	20	.	.	PUNCT
ejpam-6607	418	1	interpretation	interpretation	NOUN
ejpam-6607	418	2	.	.	PUNCT
ejpam-6607	419	1	•	•	NUM
ejpam-6607	419	2	under	under	ADP
ejpam-6607	419	3	γ1	γ1	NOUN
ejpam-6607	419	4	,	,	PUNCT
ejpam-6607	419	5	hybrid	hybrid	ADJ
ejpam-6607	419	6	superconducting	superconducte	VERB
ejpam-6607	419	7	hardware	hardware	NOUN
ejpam-6607	419	8	with	with	ADP
ejpam-6607	419	9	full	full	ADJ
ejpam-6607	419	10	connectivity	connectivity	NOUN
ejpam-6607	419	11	favors	favor	NOUN
ejpam-6607	419	12	qaoa	qaoa	X
ejpam-6607	419	13	(	(	PUNCT
ejpam-6607	419	14	50	50	NUM
ejpam-6607	419	15	%	%	NOUN
ejpam-6607	419	16	)	)	PUNCT
ejpam-6607	419	17	,	,	PUNCT
ejpam-6607	419	18	then	then	ADV
ejpam-6607	419	19	grover	grover	NOUN
ejpam-6607	419	20	(	(	PUNCT
ejpam-6607	419	21	30	30	NUM
ejpam-6607	419	22	%	%	NOUN
ejpam-6607	419	23	)	)	PUNCT
ejpam-6607	419	24	,	,	PUNCT
ejpam-6607	419	25	then	then	ADV
ejpam-6607	419	26	vqe	vqe	NOUN
ejpam-6607	419	27	(	(	PUNCT
ejpam-6607	419	28	20	20	NUM
ejpam-6607	419	29	%	%	NOUN
ejpam-6607	419	30	)	)	PUNCT
ejpam-6607	419	31	.	.	PUNCT
ejpam-6607	420	1	t.	t.	PROPN
ejpam-6607	420	2	fujita	fujita	PROPN
ejpam-6607	420	3	,	,	PUNCT
ejpam-6607	420	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	420	5	/	/	SYM
ejpam-6607	420	6	eur	eur	PROPN
ejpam-6607	420	7	.	.	PUNCT
ejpam-6607	421	1	j.	j.	PROPN
ejpam-6607	421	2	pure	pure	PROPN
ejpam-6607	421	3	appl	appl	PROPN
ejpam-6607	421	4	.	.	PROPN
ejpam-6607	421	5	math	math	PROPN
ejpam-6607	421	6	,	,	PUNCT
ejpam-6607	421	7	18	18	NUM
ejpam-6607	421	8	(	(	PUNCT
ejpam-6607	421	9	3	3	NUM
ejpam-6607	421	10	)	)	PUNCT
ejpam-6607	421	11	(	(	PUNCT
ejpam-6607	421	12	2025	2025	NUM
ejpam-6607	421	13	)	)	PUNCT
ejpam-6607	421	14	,	,	PUNCT
ejpam-6607	421	15	6607	6607	NUM
ejpam-6607	421	16	21	21	NUM
ejpam-6607	421	17	of	of	ADP
ejpam-6607	421	18	33	33	NUM
ejpam-6607	421	19	•	•	NOUN
ejpam-6607	421	20	under	under	ADP
ejpam-6607	421	21	γ2	γ2	ADJ
ejpam-6607	421	22	,	,	PUNCT
ejpam-6607	421	23	trapped	trap	VERB
ejpam-6607	421	24	-	-	PUNCT
ejpam-6607	421	25	ion	ion	NOUN
ejpam-6607	421	26	hardware	hardware	NOUN
ejpam-6607	421	27	with	with	ADP
ejpam-6607	421	28	linear	linear	ADJ
ejpam-6607	421	29	connectivity	connectivity	NOUN
ejpam-6607	421	30	strongly	strongly	ADV
ejpam-6607	421	31	favors	favor	VERB
ejpam-6607	421	32	vqe	vqe	NOUN
ejpam-6607	421	33	(	(	PUNCT
ejpam-6607	421	34	70	70	NUM
ejpam-6607	421	35	%	%	NOUN
ejpam-6607	421	36	)	)	PUNCT
ejpam-6607	421	37	for	for	ADP
ejpam-6607	421	38	chemistry	chemistry	NOUN
ejpam-6607	421	39	simulations	simulation	NOUN
ejpam-6607	421	40	,	,	PUNCT
ejpam-6607	421	41	with	with	ADP
ejpam-6607	421	42	lower	low	ADJ
ejpam-6607	421	43	probabilities	probability	NOUN
ejpam-6607	421	44	for	for	ADP
ejpam-6607	421	45	grover	grover	NOUN
ejpam-6607	421	46	(	(	PUNCT
ejpam-6607	421	47	20	20	NUM
ejpam-6607	421	48	%	%	NOUN
ejpam-6607	421	49	)	)	PUNCT
ejpam-6607	421	50	and	and	CCONJ
ejpam-6607	421	51	qaoa	qaoa	PROPN
ejpam-6607	421	52	(	(	PUNCT
ejpam-6607	421	53	10	10	NUM
ejpam-6607	421	54	%	%	NOUN
ejpam-6607	421	55	)	)	PUNCT
ejpam-6607	421	56	.	.	PUNCT
ejpam-6607	422	1	example	example	NOUN
ejpam-6607	422	2	13	13	NUM
ejpam-6607	422	3	(	(	PUNCT
ejpam-6607	422	4	quantum	quantum	PROPN
ejpam-6607	422	5	–	–	PUNCT
ejpam-6607	422	6	superhypersoft	superhypersoft	NOUN
ejpam-6607	422	7	set	set	VERB
ejpam-6607	422	8	for	for	ADP
ejpam-6607	422	9	dynamic	dynamic	ADJ
ejpam-6607	422	10	circuit	circuit	NOUN
ejpam-6607	422	11	compilation	compilation	NOUN
ejpam-6607	422	12	)	)	PUNCT
ejpam-6607	422	13	.	.	PUNCT
ejpam-6607	423	1	let	let	VERB
ejpam-6607	423	2	u	u	PRON
ejpam-6607	423	3	=	=	NOUN
ejpam-6607	423	4	{	{	PUNCT
ejpam-6607	423	5	optimizedepth	optimizedepth	NOUN
ejpam-6607	423	6	,	,	PUNCT
ejpam-6607	423	7	minimizeerror	minimizeerror	NOUN
ejpam-6607	423	8	,	,	PUNCT
ejpam-6607	423	9	balance	balance	NOUN
ejpam-6607	423	10	}	}	PUNCT
ejpam-6607	423	11	be	be	AUX
ejpam-6607	423	12	compiler	compiler	NOUN
ejpam-6607	423	13	optimization	optimization	NOUN
ejpam-6607	423	14	strategies	strategy	NOUN
ejpam-6607	423	15	.	.	PUNCT
ejpam-6607	424	1	consider	consider	VERB
ejpam-6607	424	2	three	three	NUM
ejpam-6607	424	3	attribute	attribute	NOUN
ejpam-6607	424	4	domains	domain	NOUN
ejpam-6607	424	5	:	:	PUNCT
ejpam-6607	424	6	a1	a1	NOUN
ejpam-6607	424	7	=	=	SYM
ejpam-6607	424	8	{	{	PUNCT
ejpam-6607	424	9	highgateerror	highgateerror	NOUN
ejpam-6607	424	10	,	,	PUNCT
ejpam-6607	424	11	lowgateerror	lowgateerror	NOUN
ejpam-6607	424	12	}	}	PUNCT
ejpam-6607	424	13	,	,	PUNCT
ejpam-6607	424	14	a2	a2	PROPN
ejpam-6607	424	15	=	=	PUNCT
ejpam-6607	424	16	{	{	PUNCT
ejpam-6607	424	17	shortqubitlifetime	shortqubitlifetime	NOUN
ejpam-6607	424	18	,	,	PUNCT
ejpam-6607	424	19	longqubitlifetime	longqubitlifetime	PROPN
ejpam-6607	424	20	}	}	PUNCT
ejpam-6607	424	21	,	,	PUNCT
ejpam-6607	424	22	a3	a3	NOUN
ejpam-6607	424	23	=	=	SYM
ejpam-6607	424	24	{	{	PUNCT
ejpam-6607	424	25	noisyinterconnect	noisyinterconnect	ADJ
ejpam-6607	424	26	,	,	PUNCT
ejpam-6607	424	27	reliableinterconnect	reliableinterconnect	ADJ
ejpam-6607	424	28	}	}	PUNCT
ejpam-6607	424	29	.	.	PUNCT
ejpam-6607	425	1	form	form	NOUN
ejpam-6607	425	2	c	c	NOUN
ejpam-6607	425	3	=	=	SYM
ejpam-6607	425	4	p(a1)×	p(a1)×	PROPN
ejpam-6607	425	5	p(a2)×	p(a2)×	NOUN
ejpam-6607	425	6	p(a3	p(a3	NOUN
ejpam-6607	425	7	)	)	PUNCT
ejpam-6607	425	8	,	,	PUNCT
ejpam-6607	425	9	and	and	CCONJ
ejpam-6607	425	10	let	let	VERB
ejpam-6607	425	11	h(u	h(u	PROPN
ejpam-6607	425	12	)	)	PUNCT
ejpam-6607	425	13	have	have	VERB
ejpam-6607	425	14	orthonormal	orthonormal	ADJ
ejpam-6607	425	15	basis	basis	NOUN
ejpam-6607	425	16	{	{	PUNCT
ejpam-6607	425	17	|optimizedepth⟩	|optimizedepth⟩	NOUN
ejpam-6607	425	18	,	,	PUNCT
ejpam-6607	425	19	|minimizeerror⟩	|minimizeerror⟩	NOUN
ejpam-6607	425	20	,	,	PUNCT
ejpam-6607	425	21	|balance⟩	|balance⟩	NUM
ejpam-6607	425	22	}	}	PUNCT
ejpam-6607	425	23	.	.	PUNCT
ejpam-6607	426	1	case	case	NOUN
ejpam-6607	426	2	1	1	NUM
ejpam-6607	426	3	:	:	PUNCT
ejpam-6607	426	4	high	high	ADJ
ejpam-6607	426	5	error	error	NOUN
ejpam-6607	426	6	,	,	PUNCT
ejpam-6607	426	7	short	short	ADJ
ejpam-6607	426	8	lifetime	lifetime	NOUN
ejpam-6607	426	9	,	,	PUNCT
ejpam-6607	426	10	noisy	noisy	ADJ
ejpam-6607	426	11	links	link	NOUN
ejpam-6607	426	12	γ3	γ3	NOUN
ejpam-6607	426	13	=	=	SYM
ejpam-6607	426	14	(	(	PUNCT
ejpam-6607	426	15	{	{	PUNCT
ejpam-6607	426	16	highgateerror	highgateerror	NOUN
ejpam-6607	426	17	}	}	PUNCT
ejpam-6607	426	18	,	,	PUNCT
ejpam-6607	426	19	{	{	PUNCT
ejpam-6607	426	20	shortqubitlifetime	shortqubitlifetime	NOUN
ejpam-6607	426	21	}	}	PUNCT
ejpam-6607	426	22	,	,	PUNCT
ejpam-6607	426	23	{	{	PUNCT
ejpam-6607	426	24	noisyinterconnect	noisyinterconnect	ADJ
ejpam-6607	426	25	}	}	PUNCT
ejpam-6607	426	26	)	)	PUNCT
ejpam-6607	426	27	.	.	PUNCT
ejpam-6607	427	1	set	set	VERB
ejpam-6607	427	2	|ψγ3⟩	|ψγ3⟩	NOUN
ejpam-6607	427	3	=	=	NUM
ejpam-6607	427	4	√	√	ADP
ejpam-6607	427	5	0.10	0.10	NUM
ejpam-6607	427	6	|optimizedepth⟩+	|optimizedepth⟩+	NOUN
ejpam-6607	427	7	√	√	ADP
ejpam-6607	427	8	0.70	0.70	NUM
ejpam-6607	427	9	|minimizeerror⟩+	|minimizeerror⟩+	NOUN
ejpam-6607	427	10	√	√	ADP
ejpam-6607	427	11	0.20	0.20	NUM
ejpam-6607	427	12	|balance⟩	|balance⟩	NOUN
ejpam-6607	427	13	,	,	PUNCT
ejpam-6607	427	14	so	so	ADV
ejpam-6607	427	15	p	p	X
ejpam-6607	427	16	(	(	PUNCT
ejpam-6607	427	17	minimizeerror	minimizeerror	NOUN
ejpam-6607	427	18	|	|	NOUN
ejpam-6607	427	19	γ3	γ3	NOUN
ejpam-6607	427	20	)	)	PUNCT
ejpam-6607	428	1	=	=	PUNCT
ejpam-6607	429	1	0.70	0.70	NUM
ejpam-6607	429	2	,	,	PUNCT
ejpam-6607	429	3	p	p	X
ejpam-6607	429	4	(	(	PUNCT
ejpam-6607	429	5	balance	balance	NOUN
ejpam-6607	429	6	|	|	NOUN
ejpam-6607	429	7	γ3	γ3	NOUN
ejpam-6607	429	8	)	)	PUNCT
ejpam-6607	430	1	=	=	SYM
ejpam-6607	430	2	0.20	0.20	NUM
ejpam-6607	430	3	,	,	PUNCT
ejpam-6607	430	4	p	p	X
ejpam-6607	430	5	(	(	PUNCT
ejpam-6607	430	6	optimizedepth	optimizedepth	INTJ
ejpam-6607	430	7	|	|	NOUN
ejpam-6607	430	8	γ3	γ3	NOUN
ejpam-6607	430	9	)	)	PUNCT
ejpam-6607	430	10	=	=	PUNCT
ejpam-6607	431	1	0.10	0.10	NUM
ejpam-6607	431	2	.	.	PUNCT
ejpam-6607	431	3	case	case	NOUN
ejpam-6607	431	4	2	2	NUM
ejpam-6607	431	5	:	:	PUNCT
ejpam-6607	431	6	low	low	ADJ
ejpam-6607	431	7	error	error	NOUN
ejpam-6607	431	8	,	,	PUNCT
ejpam-6607	431	9	long	long	ADJ
ejpam-6607	431	10	lifetime	lifetime	NOUN
ejpam-6607	431	11	,	,	PUNCT
ejpam-6607	431	12	reliable	reliable	ADJ
ejpam-6607	431	13	links	link	NOUN
ejpam-6607	431	14	γ4	γ4	NOUN
ejpam-6607	431	15	=	=	SYM
ejpam-6607	431	16	(	(	PUNCT
ejpam-6607	431	17	{	{	PUNCT
ejpam-6607	431	18	lowgateerror	lowgateerror	NOUN
ejpam-6607	431	19	}	}	PUNCT
ejpam-6607	431	20	,	,	PUNCT
ejpam-6607	431	21	{	{	PUNCT
ejpam-6607	431	22	longqubitlifetime	longqubitlifetime	NOUN
ejpam-6607	431	23	}	}	PUNCT
ejpam-6607	431	24	,	,	PUNCT
ejpam-6607	431	25	{	{	PUNCT
ejpam-6607	431	26	reliableinterconnect	reliableinterconnect	ADJ
ejpam-6607	431	27	}	}	PUNCT
ejpam-6607	431	28	)	)	PUNCT
ejpam-6607	431	29	.	.	PUNCT
ejpam-6607	432	1	set	set	VERB
ejpam-6607	432	2	|ψγ4⟩	|ψγ4⟩	NOUN
ejpam-6607	432	3	=	=	SYM
ejpam-6607	432	4	√	√	NUM
ejpam-6607	432	5	0.40	0.40	NUM
ejpam-6607	432	6	|optimizedepth⟩+	|optimizedepth⟩+	NOUN
ejpam-6607	432	7	√	√	ADP
ejpam-6607	432	8	0.30	0.30	NUM
ejpam-6607	432	9	|balance⟩+	|balance⟩+	NOUN
ejpam-6607	432	10	√	√	NUM
ejpam-6607	432	11	0.30	0.30	NUM
ejpam-6607	432	12	|minimizeerror⟩	|minimizeerror⟩	NOUN
ejpam-6607	432	13	,	,	PUNCT
ejpam-6607	432	14	giving	give	VERB
ejpam-6607	432	15	p	p	X
ejpam-6607	432	16	(	(	PUNCT
ejpam-6607	432	17	optimizedepth	optimizedepth	INTJ
ejpam-6607	432	18	|	|	CCONJ
ejpam-6607	432	19	γ4	γ4	NOUN
ejpam-6607	432	20	)	)	PUNCT
ejpam-6607	432	21	=	=	SYM
ejpam-6607	432	22	0.40	0.40	NUM
ejpam-6607	432	23	,	,	PUNCT
ejpam-6607	432	24	p	p	X
ejpam-6607	432	25	(	(	PUNCT
ejpam-6607	432	26	balance	balance	NOUN
ejpam-6607	432	27	|	|	NOUN
ejpam-6607	432	28	γ4	γ4	NOUN
ejpam-6607	432	29	)	)	PUNCT
ejpam-6607	432	30	=	=	SYM
ejpam-6607	432	31	0.30	0.30	NUM
ejpam-6607	432	32	,	,	PUNCT
ejpam-6607	432	33	p	p	X
ejpam-6607	432	34	(	(	PUNCT
ejpam-6607	432	35	minimizeerror	minimizeerror	NOUN
ejpam-6607	432	36	|	|	NOUN
ejpam-6607	432	37	γ4	γ4	NOUN
ejpam-6607	432	38	)	)	PUNCT
ejpam-6607	432	39	=	=	SYM
ejpam-6607	432	40	0.30	0.30	NUM
ejpam-6607	432	41	.	.	PUNCT
ejpam-6607	433	1	interpretation	interpretation	NOUN
ejpam-6607	433	2	.	.	PUNCT
ejpam-6607	434	1	•	•	NOUN
ejpam-6607	434	2	under	under	ADP
ejpam-6607	434	3	γ3	γ3	NOUN
ejpam-6607	434	4	,	,	PUNCT
ejpam-6607	434	5	high	high	ADJ
ejpam-6607	434	6	-	-	PUNCT
ejpam-6607	434	7	noise	noise	NOUN
ejpam-6607	434	8	,	,	PUNCT
ejpam-6607	434	9	short	short	ADJ
ejpam-6607	434	10	-	-	PUNCT
ejpam-6607	434	11	lived	live	VERB
ejpam-6607	434	12	hardware	hardware	NOUN
ejpam-6607	434	13	drives	drive	VERB
ejpam-6607	434	14	error	error	NOUN
ejpam-6607	434	15	-	-	PUNCT
ejpam-6607	434	16	minimization	minimization	NOUN
ejpam-6607	434	17	(	(	PUNCT
ejpam-6607	434	18	70	70	NUM
ejpam-6607	434	19	%	%	NOUN
ejpam-6607	434	20	)	)	PUNCT
ejpam-6607	434	21	over	over	ADP
ejpam-6607	434	22	depth	depth	NOUN
ejpam-6607	434	23	optimization	optimization	NOUN
ejpam-6607	434	24	(	(	PUNCT
ejpam-6607	434	25	10	10	NUM
ejpam-6607	434	26	%	%	NOUN
ejpam-6607	434	27	)	)	PUNCT
ejpam-6607	434	28	or	or	CCONJ
ejpam-6607	434	29	balanced	balanced	ADJ
ejpam-6607	434	30	trade	trade	NOUN
ejpam-6607	434	31	-	-	PUNCT
ejpam-6607	434	32	offs	off	NOUN
ejpam-6607	434	33	(	(	PUNCT
ejpam-6607	434	34	20	20	NUM
ejpam-6607	434	35	%	%	NOUN
ejpam-6607	434	36	)	)	PUNCT
ejpam-6607	434	37	.	.	PUNCT
ejpam-6607	435	1	t.	t.	PROPN
ejpam-6607	435	2	fujita	fujita	PROPN
ejpam-6607	435	3	,	,	PUNCT
ejpam-6607	435	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	435	5	/	/	SYM
ejpam-6607	435	6	eur	eur	PROPN
ejpam-6607	435	7	.	.	PUNCT
ejpam-6607	436	1	j.	j.	PROPN
ejpam-6607	436	2	pure	pure	PROPN
ejpam-6607	436	3	appl	appl	PROPN
ejpam-6607	436	4	.	.	PROPN
ejpam-6607	436	5	math	math	PROPN
ejpam-6607	436	6	,	,	PUNCT
ejpam-6607	436	7	18	18	NUM
ejpam-6607	436	8	(	(	PUNCT
ejpam-6607	436	9	3	3	NUM
ejpam-6607	436	10	)	)	PUNCT
ejpam-6607	436	11	(	(	PUNCT
ejpam-6607	436	12	2025	2025	NUM
ejpam-6607	436	13	)	)	PUNCT
ejpam-6607	436	14	,	,	PUNCT
ejpam-6607	436	15	6607	6607	NUM
ejpam-6607	436	16	22	22	NUM
ejpam-6607	436	17	of	of	ADP
ejpam-6607	436	18	33	33	NUM
ejpam-6607	436	19	•	•	NOUN
ejpam-6607	436	20	under	under	ADP
ejpam-6607	436	21	γ4	γ4	NOUN
ejpam-6607	436	22	,	,	PUNCT
ejpam-6607	436	23	reliable	reliable	ADJ
ejpam-6607	436	24	hardware	hardware	NOUN
ejpam-6607	436	25	allows	allow	VERB
ejpam-6607	436	26	deeper	deep	ADJ
ejpam-6607	436	27	circuits	circuit	NOUN
ejpam-6607	436	28	(	(	PUNCT
ejpam-6607	436	29	40	40	NUM
ejpam-6607	436	30	%	%	NOUN
ejpam-6607	436	31	)	)	PUNCT
ejpam-6607	436	32	with	with	ADP
ejpam-6607	436	33	balanced	balanced	ADJ
ejpam-6607	436	34	(	(	PUNCT
ejpam-6607	436	35	30	30	NUM
ejpam-6607	436	36	%	%	NOUN
ejpam-6607	436	37	)	)	PUNCT
ejpam-6607	436	38	or	or	CCONJ
ejpam-6607	436	39	error	error	NOUN
ejpam-6607	436	40	-	-	PUNCT
ejpam-6607	436	41	focused	focus	VERB
ejpam-6607	436	42	(	(	PUNCT
ejpam-6607	436	43	30	30	NUM
ejpam-6607	436	44	%	%	NOUN
ejpam-6607	436	45	)	)	PUNCT
ejpam-6607	436	46	strategies	strategy	NOUN
ejpam-6607	436	47	.	.	PUNCT
ejpam-6607	437	1	theorem	theorem	ADJ
ejpam-6607	437	2	9	9	NUM
ejpam-6607	437	3	(	(	PUNCT
ejpam-6607	437	4	generalization	generalization	NOUN
ejpam-6607	437	5	of	of	ADP
ejpam-6607	437	6	superhypersoft	superhypersoft	PROPN
ejpam-6607	437	7	sets	set	NOUN
ejpam-6607	437	8	)	)	PUNCT
ejpam-6607	437	9	.	.	PUNCT
ejpam-6607	438	1	let	let	VERB
ejpam-6607	438	2	(	(	PUNCT
ejpam-6607	438	3	f	f	X
ejpam-6607	438	4	,	,	PUNCT
ejpam-6607	438	5	c	c	AUX
ejpam-6607	438	6	)	)	PUNCT
ejpam-6607	438	7	be	be	AUX
ejpam-6607	438	8	a	a	DET
ejpam-6607	438	9	classical	classical	ADJ
ejpam-6607	438	10	superhypersoft	superhypersoft	NOUN
ejpam-6607	438	11	set	set	VERB
ejpam-6607	438	12	f	f	PROPN
ejpam-6607	438	13	:	:	PUNCT
ejpam-6607	438	14	c	c	X
ejpam-6607	438	15	→	→	SYM
ejpam-6607	438	16	p(u	p(u	ADJ
ejpam-6607	438	17	)	)	PUNCT
ejpam-6607	438	18	.	.	PUNCT
ejpam-6607	439	1	define	define	VERB
ejpam-6607	439	2	amplitudes	amplitude	NOUN
ejpam-6607	439	3	αi	αi	NOUN
ejpam-6607	439	4	,	,	PUNCT
ejpam-6607	439	5	γ	γ	X
ejpam-6607	439	6	=	=	SYM
ejpam-6607	439	7			PROPN
ejpam-6607	439	8	1√∣∣f	1√∣∣f	NOUN
ejpam-6607	439	9	(	(	PUNCT
ejpam-6607	439	10	γ	γ	X
ejpam-6607	439	11	)	)	PUNCT
ejpam-6607	439	12	∣∣	∣∣	X
ejpam-6607	439	13	if	if	SCONJ
ejpam-6607	439	14	ui	ui	PROPN
ejpam-6607	439	15	∈	∈	PROPN
ejpam-6607	439	16	f	f	X
ejpam-6607	439	17	(	(	PUNCT
ejpam-6607	439	18	γ	γ	PROPN
ejpam-6607	439	19	)	)	PUNCT
ejpam-6607	439	20	,	,	PUNCT
ejpam-6607	439	21	0	0	NUM
ejpam-6607	440	1	otherwise	otherwise	ADV
ejpam-6607	440	2	.	.	PUNCT
ejpam-6607	441	1	then	then	ADV
ejpam-6607	441	2	the	the	DET
ejpam-6607	441	3	map	map	NOUN
ejpam-6607	441	4	q	q	X
ejpam-6607	441	5	:	:	PUNCT
ejpam-6607	441	6	c	c	PROPN
ejpam-6607	441	7	→	→	SYM
ejpam-6607	441	8	h(u	h(u	PROPN
ejpam-6607	441	9	)	)	PUNCT
ejpam-6607	441	10	with	with	ADP
ejpam-6607	441	11	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	441	12	=	=	PUNCT
ejpam-6607	441	13	∑	∑	PROPN
ejpam-6607	441	14	i	i	PRON
ejpam-6607	441	15	αi	αi	VERB
ejpam-6607	441	16	,	,	PUNCT
ejpam-6607	441	17	γ	γ	X
ejpam-6607	441	18	|ui⟩	|ui⟩	PROPN
ejpam-6607	441	19	is	be	AUX
ejpam-6607	441	20	a	a	DET
ejpam-6607	441	21	quantum	quantum	NOUN
ejpam-6607	441	22	–	–	PUNCT
ejpam-6607	441	23	superhypersoft	superhypersoft	NOUN
ejpam-6607	441	24	set	set	VERB
ejpam-6607	441	25	whose	whose	DET
ejpam-6607	441	26	measurement	measurement	NOUN
ejpam-6607	441	27	-	-	PUNCT
ejpam-6607	441	28	based	base	VERB
ejpam-6607	441	29	membership	membership	NOUN
ejpam-6607	441	30	µγ(ui	µγ(ui	PROPN
ejpam-6607	441	31	)	)	PUNCT
ejpam-6607	442	1	=	=	SYM
ejpam-6607	442	2	|αi	|αi	X
ejpam-6607	442	3	,	,	PUNCT
ejpam-6607	442	4	γ	γ	PROPN
ejpam-6607	442	5	|2	|2	NOUN
ejpam-6607	442	6	recovers	recover	NOUN
ejpam-6607	442	7	exactly	exactly	ADV
ejpam-6607	442	8	the	the	DET
ejpam-6607	442	9	classical	classical	ADJ
ejpam-6607	442	10	assignment	assignment	NOUN
ejpam-6607	442	11	ui	ui	PROPN
ejpam-6607	442	12	∈	∈	PROPN
ejpam-6607	442	13	f	f	PROPN
ejpam-6607	442	14	(	(	PUNCT
ejpam-6607	442	15	γ	γ	PROPN
ejpam-6607	442	16	)	)	PUNCT
ejpam-6607	442	17	.	.	PUNCT
ejpam-6607	443	1	proof	proof	NOUN
ejpam-6607	443	2	.	.	PUNCT
ejpam-6607	444	1	for	for	ADP
ejpam-6607	444	2	each	each	DET
ejpam-6607	444	3	γ	γ	NOUN
ejpam-6607	444	4	,	,	PUNCT
ejpam-6607	444	5	since	since	SCONJ
ejpam-6607	444	6	αi	αi	NOUN
ejpam-6607	444	7	,	,	PUNCT
ejpam-6607	444	8	γ	γ	PROPN
ejpam-6607	444	9	̸=	̸=	PROPN
ejpam-6607	444	10	0	0	PUNCT
ejpam-6607	444	11	exactly	exactly	ADV
ejpam-6607	444	12	when	when	SCONJ
ejpam-6607	444	13	ui	ui	PROPN
ejpam-6607	444	14	∈	∈	PROPN
ejpam-6607	444	15	f	f	X
ejpam-6607	444	16	(	(	PUNCT
ejpam-6607	444	17	γ	γ	PROPN
ejpam-6607	444	18	)	)	PUNCT
ejpam-6607	444	19	and	and	CCONJ
ejpam-6607	444	20	there	there	PRON
ejpam-6607	444	21	are	be	VERB
ejpam-6607	444	22	|f	|f	PROPN
ejpam-6607	444	23	(	(	PUNCT
ejpam-6607	444	24	γ)|	γ)|	ADP
ejpam-6607	444	25	such	such	ADJ
ejpam-6607	444	26	i	i	PROPN
ejpam-6607	444	27	,	,	PUNCT
ejpam-6607	444	28	we	we	PRON
ejpam-6607	444	29	have	have	VERB
ejpam-6607	444	30	n∑	n∑	PROPN
ejpam-6607	444	31	i=1	i=1	PROPN
ejpam-6607	445	1	∣∣αi	∣∣αi	PROPN
ejpam-6607	445	2	,	,	PUNCT
ejpam-6607	445	3	γ	γ	PROPN
ejpam-6607	445	4	∣∣2	∣∣2	PROPN
ejpam-6607	445	5	=	=	SYM
ejpam-6607	445	6	|f	|f	PROPN
ejpam-6607	446	1	(	(	PUNCT
ejpam-6607	446	2	γ)|	γ)|	NOUN
ejpam-6607	446	3	×	×	NOUN
ejpam-6607	446	4	1	1	NUM
ejpam-6607	446	5	|f	|f	PROPN
ejpam-6607	446	6	(	(	PUNCT
ejpam-6607	446	7	γ)|	γ)|	NOUN
ejpam-6607	446	8	=	=	NOUN
ejpam-6607	446	9	1	1	X
ejpam-6607	446	10	.	.	PUNCT
ejpam-6607	447	1	hence	hence	ADV
ejpam-6607	447	2	q	q	X
ejpam-6607	447	3	is	be	AUX
ejpam-6607	447	4	normalized	normalize	VERB
ejpam-6607	447	5	.	.	PUNCT
ejpam-6607	448	1	moreover	moreover	ADV
ejpam-6607	448	2	µγ(ui	µγ(ui	PROPN
ejpam-6607	448	3	)	)	PUNCT
ejpam-6607	449	1	=	=	SYM
ejpam-6607	449	2	|αi	|αi	X
ejpam-6607	449	3	,	,	PUNCT
ejpam-6607	449	4	γ	γ	X
ejpam-6607	449	5	|2	|2	X
ejpam-6607	449	6	=	=	NOUN
ejpam-6607	449	7	{	{	PUNCT
ejpam-6607	449	8	1	1	NUM
ejpam-6607	449	9	|f	|f	PRON
ejpam-6607	449	10	(	(	PUNCT
ejpam-6607	449	11	γ)|	γ)|	NOUN
ejpam-6607	449	12	,	,	PUNCT
ejpam-6607	449	13	ui	ui	PROPN
ejpam-6607	449	14	∈	∈	PROPN
ejpam-6607	449	15	f	f	X
ejpam-6607	449	16	(	(	PUNCT
ejpam-6607	449	17	γ	γ	PROPN
ejpam-6607	449	18	)	)	PUNCT
ejpam-6607	449	19	,	,	PUNCT
ejpam-6607	449	20	0	0	NUM
ejpam-6607	449	21	,	,	PUNCT
ejpam-6607	449	22	ui	ui	NOUN
ejpam-6607	449	23	/∈	/∈	PUNCT
ejpam-6607	450	1	f	f	PROPN
ejpam-6607	450	2	(	(	PUNCT
ejpam-6607	450	3	γ	γ	PROPN
ejpam-6607	450	4	)	)	PUNCT
ejpam-6607	450	5	,	,	PUNCT
ejpam-6607	450	6	so	so	ADV
ejpam-6607	450	7	measuring	measure	VERB
ejpam-6607	450	8	|ψγ⟩	|ψγ⟩	PROPN
ejpam-6607	450	9	yields	yield	VERB
ejpam-6607	450	10	a	a	DET
ejpam-6607	450	11	uniform	uniform	ADJ
ejpam-6607	450	12	distribution	distribution	NOUN
ejpam-6607	450	13	on	on	ADP
ejpam-6607	450	14	the	the	DET
ejpam-6607	450	15	classical	classical	ADJ
ejpam-6607	450	16	set	set	NOUN
ejpam-6607	450	17	f	f	PROPN
ejpam-6607	450	18	(	(	PUNCT
ejpam-6607	450	19	γ	γ	PROPN
ejpam-6607	450	20	)	)	PUNCT
ejpam-6607	450	21	,	,	PUNCT
ejpam-6607	450	22	thereby	thereby	ADV
ejpam-6607	450	23	embedding	embed	VERB
ejpam-6607	450	24	the	the	DET
ejpam-6607	450	25	superhypersoft	superhypersoft	NOUN
ejpam-6607	450	26	set	set	VERB
ejpam-6607	450	27	into	into	ADP
ejpam-6607	450	28	the	the	DET
ejpam-6607	450	29	quantum	quantum	NOUN
ejpam-6607	450	30	framework	framework	NOUN
ejpam-6607	450	31	.	.	PUNCT
ejpam-6607	451	1	theorem	theorem	VERB
ejpam-6607	451	2	10	10	NUM
ejpam-6607	451	3	(	(	PUNCT
ejpam-6607	451	4	generalization	generalization	NOUN
ejpam-6607	451	5	of	of	ADP
ejpam-6607	451	6	quantum	quantum	NOUN
ejpam-6607	451	7	-	-	PUNCT
ejpam-6607	451	8	soft	soft	ADJ
ejpam-6607	451	9	sets	set	NOUN
ejpam-6607	451	10	)	)	PUNCT
ejpam-6607	451	11	.	.	PUNCT
ejpam-6607	452	1	let	let	VERB
ejpam-6607	452	2	q	q	PRON
ejpam-6607	452	3	be	be	AUX
ejpam-6607	452	4	a	a	DET
ejpam-6607	452	5	quantum	quantum	NOUN
ejpam-6607	452	6	–	–	PUNCT
ejpam-6607	452	7	superhypersoft	superhypersoft	NOUN
ejpam-6607	452	8	set	set	VERB
ejpam-6607	452	9	over	over	ADP
ejpam-6607	452	10	(	(	PUNCT
ejpam-6607	452	11	u	u	NOUN
ejpam-6607	452	12	,	,	PUNCT
ejpam-6607	452	13	c	c	NOUN
ejpam-6607	452	14	)	)	PUNCT
ejpam-6607	452	15	with	with	ADP
ejpam-6607	452	16	m	m	PROPN
ejpam-6607	452	17	=	=	SYM
ejpam-6607	452	18	1	1	NUM
ejpam-6607	452	19	and	and	CCONJ
ejpam-6607	452	20	a1	a1	NOUN
ejpam-6607	452	21	=	=	NOUN
ejpam-6607	452	22	a.	a.	NOUN
ejpam-6607	452	23	then	then	ADV
ejpam-6607	452	24	restricting	restrict	VERB
ejpam-6607	452	25	the	the	DET
ejpam-6607	452	26	domain	domain	NOUN
ejpam-6607	452	27	to	to	ADP
ejpam-6607	452	28	{	{	PUNCT
ejpam-6607	452	29	{	{	PUNCT
ejpam-6607	452	30	a	a	NOUN
ejpam-6607	452	31	}	}	PUNCT
ejpam-6607	452	32	|	|	ADV
ejpam-6607	452	33	a	a	DET
ejpam-6607	452	34	∈	∈	PROPN
ejpam-6607	452	35	a	a	DET
ejpam-6607	452	36	}	}	PUNCT
ejpam-6607	452	37	⊆	⊆	NUM
ejpam-6607	452	38	p(a	p(a	NOUN
ejpam-6607	452	39	)	)	PUNCT
ejpam-6607	452	40	gives	give	VERB
ejpam-6607	452	41	a	a	DET
ejpam-6607	452	42	map	map	NOUN
ejpam-6607	452	43	q′	q′	NOUN
ejpam-6607	452	44	:	:	PUNCT
ejpam-6607	452	45	a	a	DET
ejpam-6607	452	46	−→	−→	NOUN
ejpam-6607	452	47	h(u	h(u	PROPN
ejpam-6607	452	48	)	)	PUNCT
ejpam-6607	452	49	,	,	PUNCT
ejpam-6607	452	50	a	a	DET
ejpam-6607	452	51	7→	7→	NUM
ejpam-6607	452	52	|ψ{a}⟩	|ψ{a}⟩	NOUN
ejpam-6607	452	53	,	,	PUNCT
ejpam-6607	452	54	which	which	PRON
ejpam-6607	452	55	is	be	AUX
ejpam-6607	452	56	precisely	precisely	ADV
ejpam-6607	452	57	a	a	DET
ejpam-6607	452	58	quantum	quantum	NOUN
ejpam-6607	452	59	-	-	PUNCT
ejpam-6607	452	60	soft	soft	ADJ
ejpam-6607	452	61	set	set	NOUN
ejpam-6607	452	62	over	over	ADP
ejpam-6607	452	63	a.	a.	NOUN
ejpam-6607	452	64	proof	proof	NOUN
ejpam-6607	452	65	.	.	PUNCT
ejpam-6607	453	1	when	when	SCONJ
ejpam-6607	453	2	m	m	VERB
ejpam-6607	453	3	=	=	SYM
ejpam-6607	453	4	1	1	NUM
ejpam-6607	453	5	,	,	PUNCT
ejpam-6607	453	6	c	c	NOUN
ejpam-6607	453	7	=	=	SYM
ejpam-6607	453	8	p(a	p(a	PROPN
ejpam-6607	453	9	)	)	PUNCT
ejpam-6607	453	10	.	.	PUNCT
ejpam-6607	454	1	each	each	DET
ejpam-6607	454	2	singleton	singleton	PROPN
ejpam-6607	454	3	{	{	PUNCT
ejpam-6607	454	4	a	a	PROPN
ejpam-6607	454	5	}	}	PUNCT
ejpam-6607	454	6	⊆	⊆	NUM
ejpam-6607	454	7	a	a	DET
ejpam-6607	454	8	defines	define	NOUN
ejpam-6607	454	9	a	a	DET
ejpam-6607	454	10	quantum	quantum	ADJ
ejpam-6607	454	11	state	state	NOUN
ejpam-6607	454	12	|ψ{a}⟩	|ψ{a}⟩	NOUN
ejpam-6607	454	13	with	with	ADP
ejpam-6607	454	14	∑	∑	PUNCT
ejpam-6607	454	15	i	i	PRON
ejpam-6607	454	16	|αi,{a}|2	|αi,{a}|2	ADJ
ejpam-6607	454	17	=	=	NOUN
ejpam-6607	454	18	1	1	X
ejpam-6607	454	19	.	.	X
ejpam-6607	454	20	identifying	identify	VERB
ejpam-6607	454	21	the	the	DET
ejpam-6607	454	22	label	label	NOUN
ejpam-6607	454	23	{	{	PUNCT
ejpam-6607	454	24	a	a	PROPN
ejpam-6607	454	25	}	}	PUNCT
ejpam-6607	454	26	↔	↔	PROPN
ejpam-6607	454	27	a	a	PRON
ejpam-6607	454	28	and	and	CCONJ
ejpam-6607	454	29	renaming	rename	VERB
ejpam-6607	454	30	|ψa⟩	|ψa⟩	ADP
ejpam-6607	454	31	=	=	PUNCT
ejpam-6607	454	32	|ψ{a}⟩	|ψ{a}⟩	NOUN
ejpam-6607	454	33	recovers	recover	VERB
ejpam-6607	454	34	the	the	DET
ejpam-6607	454	35	quantum	quantum	NOUN
ejpam-6607	454	36	-	-	PUNCT
ejpam-6607	454	37	soft	soft	ADJ
ejpam-6607	454	38	set	set	NOUN
ejpam-6607	454	39	definition	definition	NOUN
ejpam-6607	454	40	.	.	PUNCT
ejpam-6607	455	1	theorem	theorem	ADJ
ejpam-6607	455	2	11	11	NUM
ejpam-6607	455	3	(	(	PUNCT
ejpam-6607	455	4	generalization	generalization	NOUN
ejpam-6607	455	5	of	of	ADP
ejpam-6607	455	6	quantum	quantum	NOUN
ejpam-6607	455	7	–	–	PUNCT
ejpam-6607	455	8	hypersoft	hypersoft	NOUN
ejpam-6607	455	9	sets	set	NOUN
ejpam-6607	455	10	)	)	PUNCT
ejpam-6607	455	11	.	.	PUNCT
ejpam-6607	456	1	let	let	VERB
ejpam-6607	456	2	q	q	PRON
ejpam-6607	456	3	be	be	AUX
ejpam-6607	456	4	a	a	DET
ejpam-6607	456	5	quantum	quantum	NOUN
ejpam-6607	456	6	–	–	PUNCT
ejpam-6607	456	7	superhypersoft	superhypersoft	NOUN
ejpam-6607	456	8	set	set	VERB
ejpam-6607	456	9	over	over	ADP
ejpam-6607	456	10	(	(	PUNCT
ejpam-6607	456	11	u	u	NOUN
ejpam-6607	456	12	,	,	PUNCT
ejpam-6607	456	13	c	c	NOUN
ejpam-6607	456	14	)	)	PUNCT
ejpam-6607	456	15	.	.	PUNCT
ejpam-6607	457	1	restrict	restrict	VERB
ejpam-6607	457	2	the	the	DET
ejpam-6607	457	3	domain	domain	NOUN
ejpam-6607	457	4	to	to	ADP
ejpam-6607	457	5	{	{	PUNCT
ejpam-6607	457	6	(	(	PUNCT
ejpam-6607	457	7	{	{	PUNCT
ejpam-6607	457	8	a1	a1	NOUN
ejpam-6607	457	9	}	}	PUNCT
ejpam-6607	457	10	,	,	PUNCT
ejpam-6607	457	11	{	{	PUNCT
ejpam-6607	457	12	a2	a2	NOUN
ejpam-6607	457	13	}	}	PUNCT
ejpam-6607	457	14	,	,	PUNCT
ejpam-6607	457	15	.	.	PUNCT
ejpam-6607	457	16	.	.	PUNCT
ejpam-6607	458	1	.	.	PUNCT
ejpam-6607	459	1	,	,	PUNCT
ejpam-6607	459	2	{	{	PUNCT
ejpam-6607	459	3	am	be	AUX
ejpam-6607	459	4	}	}	PUNCT
ejpam-6607	459	5	)	)	PUNCT
ejpam-6607	460	1	|	|	ADV
ejpam-6607	460	2	ai	ai	VERB
ejpam-6607	460	3	∈	∈	PROPN
ejpam-6607	460	4	ai	ai	VERB
ejpam-6607	460	5	}	}	PUNCT
ejpam-6607	460	6	⊆	⊆	NUM
ejpam-6607	460	7	c.	c.	NOUN
ejpam-6607	460	8	then	then	ADV
ejpam-6607	460	9	the	the	DET
ejpam-6607	460	10	induced	induced	ADJ
ejpam-6607	460	11	map	map	NOUN
ejpam-6607	460	12	q′′	q′′	VERB
ejpam-6607	460	13	:	:	PUNCT
ejpam-6607	460	14	a1	a1	VERB
ejpam-6607	460	15	×	×	NOUN
ejpam-6607	460	16	·	·	PUNCT
ejpam-6607	460	17	·	·	PUNCT
ejpam-6607	460	18	·	·	PUNCT
ejpam-6607	461	1	×am	×am	ADP
ejpam-6607	461	2	−→	−→	NOUN
ejpam-6607	461	3	h(u	h(u	PROPN
ejpam-6607	461	4	)	)	PUNCT
ejpam-6607	461	5	,	,	PUNCT
ejpam-6607	461	6	(	(	PUNCT
ejpam-6607	461	7	a1	a1	NOUN
ejpam-6607	461	8	,	,	PUNCT
ejpam-6607	461	9	.	.	PUNCT
ejpam-6607	461	10	.	.	PUNCT
ejpam-6607	462	1	.	.	PUNCT
ejpam-6607	463	1	,	,	PUNCT
ejpam-6607	463	2	am	be	AUX
ejpam-6607	463	3	)	)	PUNCT
ejpam-6607	463	4	7→	7→	NUM
ejpam-6607	463	5	|ψ({a1},	|ψ({a1},	NOUN
ejpam-6607	463	6	...	...	PUNCT
ejpam-6607	463	7	,{am})⟩	,{am})⟩	PROPN
ejpam-6607	463	8	is	be	AUX
ejpam-6607	463	9	exactly	exactly	ADV
ejpam-6607	463	10	a	a	DET
ejpam-6607	463	11	quantum	quantum	NOUN
ejpam-6607	463	12	–	–	PUNCT
ejpam-6607	463	13	hypersoft	hypersoft	NOUN
ejpam-6607	463	14	set	set	VERB
ejpam-6607	463	15	over	over	ADP
ejpam-6607	463	16	a1	a1	NOUN
ejpam-6607	463	17	,	,	PUNCT
ejpam-6607	463	18	.	.	PUNCT
ejpam-6607	463	19	.	.	PUNCT
ejpam-6607	464	1	.	.	PUNCT
ejpam-6607	465	1	,	,	PUNCT
ejpam-6607	465	2	am	be	AUX
ejpam-6607	465	3	.	.	PUNCT
ejpam-6607	466	1	t.	t.	PROPN
ejpam-6607	466	2	fujita	fujita	PROPN
ejpam-6607	466	3	,	,	PUNCT
ejpam-6607	466	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	466	5	/	/	SYM
ejpam-6607	466	6	eur	eur	PROPN
ejpam-6607	466	7	.	.	PUNCT
ejpam-6607	467	1	j.	j.	PROPN
ejpam-6607	467	2	pure	pure	PROPN
ejpam-6607	467	3	appl	appl	PROPN
ejpam-6607	467	4	.	.	PROPN
ejpam-6607	467	5	math	math	PROPN
ejpam-6607	467	6	,	,	PUNCT
ejpam-6607	467	7	18	18	NUM
ejpam-6607	467	8	(	(	PUNCT
ejpam-6607	467	9	3	3	NUM
ejpam-6607	467	10	)	)	PUNCT
ejpam-6607	467	11	(	(	PUNCT
ejpam-6607	467	12	2025	2025	NUM
ejpam-6607	467	13	)	)	PUNCT
ejpam-6607	467	14	,	,	PUNCT
ejpam-6607	467	15	6607	6607	NUM
ejpam-6607	467	16	23	23	NUM
ejpam-6607	467	17	of	of	ADP
ejpam-6607	467	18	33	33	NUM
ejpam-6607	467	19	proof	proof	NOUN
ejpam-6607	467	20	.	.	PUNCT
ejpam-6607	468	1	each	each	DET
ejpam-6607	468	2	tuple	tuple	NOUN
ejpam-6607	468	3	of	of	ADP
ejpam-6607	468	4	singletons	singleton	NOUN
ejpam-6607	468	5	(	(	PUNCT
ejpam-6607	468	6	{	{	PUNCT
ejpam-6607	468	7	a1	a1	NOUN
ejpam-6607	468	8	}	}	PUNCT
ejpam-6607	468	9	,	,	PUNCT
ejpam-6607	468	10	.	.	PUNCT
ejpam-6607	468	11	.	.	PUNCT
ejpam-6607	468	12	.	.	PUNCT
ejpam-6607	469	1	,	,	PUNCT
ejpam-6607	469	2	{	{	PUNCT
ejpam-6607	469	3	am	be	AUX
ejpam-6607	469	4	}	}	PUNCT
ejpam-6607	469	5	)	)	PUNCT
ejpam-6607	469	6	is	be	AUX
ejpam-6607	469	7	an	an	DET
ejpam-6607	469	8	element	element	NOUN
ejpam-6607	469	9	of	of	ADP
ejpam-6607	469	10	p(a1)×	p(a1)×	PROPN
ejpam-6607	469	11	·	·	PUNCT
ejpam-6607	469	12	·	·	PUNCT
ejpam-6607	469	13	·	·	PUNCT
ejpam-6607	469	14	×p(am	×p(am	NOUN
ejpam-6607	469	15	)	)	PUNCT
ejpam-6607	469	16	,	,	PUNCT
ejpam-6607	469	17	and	and	CCONJ
ejpam-6607	469	18	the	the	DET
ejpam-6607	469	19	associated	associated	ADJ
ejpam-6607	469	20	state	state	NOUN
ejpam-6607	469	21	|ψ({a1},	|ψ({a1},	PROPN
ejpam-6607	469	22	...	...	PUNCT
ejpam-6607	469	23	,{am})⟩	,{am})⟩	PROPN
ejpam-6607	469	24	is	be	AUX
ejpam-6607	469	25	normalized	normalize	VERB
ejpam-6607	469	26	by	by	ADP
ejpam-6607	469	27	assumption	assumption	NOUN
ejpam-6607	469	28	.	.	PUNCT
ejpam-6607	470	1	renaming	rename	VERB
ejpam-6607	470	2	indices	index	NOUN
ejpam-6607	470	3	to	to	PART
ejpam-6607	470	4	absorb	absorb	VERB
ejpam-6607	470	5	the	the	DET
ejpam-6607	470	6	singleton	singleton	NOUN
ejpam-6607	470	7	braces	brace	VERB
ejpam-6607	470	8	yields	yield	VERB
ejpam-6607	470	9	a	a	DET
ejpam-6607	470	10	map	map	NOUN
ejpam-6607	470	11	on	on	ADP
ejpam-6607	470	12	a1	a1	PROPN
ejpam-6607	470	13	×	×	PROPN
ejpam-6607	470	14	·	·	PUNCT
ejpam-6607	470	15	·	·	PUNCT
ejpam-6607	470	16	·	·	PUNCT
ejpam-6607	471	1	×	×	NOUN
ejpam-6607	471	2	am	be	AUX
ejpam-6607	471	3	exactly	exactly	ADV
ejpam-6607	471	4	in	in	ADP
ejpam-6607	471	5	the	the	DET
ejpam-6607	471	6	form	form	NOUN
ejpam-6607	471	7	of	of	ADP
ejpam-6607	471	8	the	the	DET
ejpam-6607	471	9	quantum	quantum	NOUN
ejpam-6607	471	10	–	–	PUNCT
ejpam-6607	471	11	hypersoft	hypersoft	NOUN
ejpam-6607	471	12	set	set	VERB
ejpam-6607	471	13	definition	definition	NOUN
ejpam-6607	471	14	.	.	PUNCT
ejpam-6607	472	1	theorem	theorem	NOUN
ejpam-6607	472	2	12	12	NUM
ejpam-6607	472	3	(	(	PUNCT
ejpam-6607	472	4	unitary	unitary	ADJ
ejpam-6607	472	5	invariance	invariance	NOUN
ejpam-6607	472	6	)	)	PUNCT
ejpam-6607	472	7	.	.	PUNCT
ejpam-6607	473	1	let	let	VERB
ejpam-6607	473	2	q	q	PRON
ejpam-6607	473	3	be	be	AUX
ejpam-6607	473	4	a	a	DET
ejpam-6607	473	5	quantum	quantum	NOUN
ejpam-6607	473	6	–	–	PUNCT
ejpam-6607	473	7	superhypersoft	superhypersoft	NOUN
ejpam-6607	473	8	set	set	VERB
ejpam-6607	473	9	over	over	ADP
ejpam-6607	473	10	(	(	PUNCT
ejpam-6607	473	11	u	u	NOUN
ejpam-6607	473	12	,	,	PUNCT
ejpam-6607	473	13	c	c	NOUN
ejpam-6607	473	14	)	)	PUNCT
ejpam-6607	473	15	.	.	PUNCT
ejpam-6607	474	1	for	for	ADP
ejpam-6607	474	2	each	each	DET
ejpam-6607	474	3	γ	γ	X
ejpam-6607	474	4	∈	∈	PROPN
ejpam-6607	474	5	c	c	NOUN
ejpam-6607	474	6	,	,	PUNCT
ejpam-6607	474	7	let	let	VERB
ejpam-6607	474	8	uγ	uγ	ADP
ejpam-6607	474	9	be	be	AUX
ejpam-6607	474	10	a	a	DET
ejpam-6607	474	11	unitary	unitary	ADJ
ejpam-6607	474	12	operator	operator	NOUN
ejpam-6607	474	13	on	on	ADP
ejpam-6607	474	14	h(u	h(u	PROPN
ejpam-6607	474	15	)	)	PUNCT
ejpam-6607	474	16	,	,	PUNCT
ejpam-6607	474	17	and	and	CCONJ
ejpam-6607	474	18	define	define	VERB
ejpam-6607	474	19	q′(γ	q′(γ	NUM
ejpam-6607	474	20	)	)	PUNCT
ejpam-6607	474	21	=	=	PUNCT
ejpam-6607	475	1	uγ	uγ	ADP
ejpam-6607	475	2	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	475	3	.	.	PUNCT
ejpam-6607	476	1	then	then	ADV
ejpam-6607	476	2	q′	q′	NOUN
ejpam-6607	476	3	is	be	AUX
ejpam-6607	476	4	also	also	ADV
ejpam-6607	476	5	a	a	DET
ejpam-6607	476	6	quantum	quantum	NOUN
ejpam-6607	476	7	–	–	PUNCT
ejpam-6607	476	8	superhypersoft	superhypersoft	NOUN
ejpam-6607	476	9	set	set	VERB
ejpam-6607	476	10	over	over	ADP
ejpam-6607	476	11	(	(	PUNCT
ejpam-6607	476	12	u	u	NOUN
ejpam-6607	476	13	,	,	PUNCT
ejpam-6607	476	14	c	c	NOUN
ejpam-6607	476	15	)	)	PUNCT
ejpam-6607	476	16	.	.	PUNCT
ejpam-6607	477	1	proof	proof	NOUN
ejpam-6607	477	2	.	.	PUNCT
ejpam-6607	478	1	since	since	SCONJ
ejpam-6607	478	2	each	each	DET
ejpam-6607	478	3	uγ	uγ	NOUN
ejpam-6607	478	4	is	be	AUX
ejpam-6607	478	5	unitary	unitary	ADJ
ejpam-6607	478	6	,	,	PUNCT
ejpam-6607	478	7	it	it	PRON
ejpam-6607	478	8	preserves	preserve	VERB
ejpam-6607	478	9	inner	inner	ADJ
ejpam-6607	478	10	products	product	NOUN
ejpam-6607	478	11	and	and	CCONJ
ejpam-6607	478	12	norms	norm	NOUN
ejpam-6607	478	13	.	.	PUNCT
ejpam-6607	479	1	in	in	ADP
ejpam-6607	479	2	particular	particular	ADJ
ejpam-6607	479	3	,	,	PUNCT
ejpam-6607	479	4	〈	〈	PROPN
ejpam-6607	479	5	ψγ	ψγ	X
ejpam-6607	479	6	|	|	ADV
ejpam-6607	479	7	ψγ	ψγ	NOUN
ejpam-6607	479	8	〉	〉	NOUN
ejpam-6607	479	9	=	=	SYM
ejpam-6607	479	10	1	1	NUM
ejpam-6607	479	11	=	=	NOUN
ejpam-6607	479	12	⇒	⇒	X
ejpam-6607	479	13	〈	〈	NOUN
ejpam-6607	479	14	uγψγ	uγψγ	NOUN
ejpam-6607	479	15	|	|	ADV
ejpam-6607	479	16	uγψγ	uγψγ	ADJ
ejpam-6607	479	17	〉	〉	NOUN
ejpam-6607	479	18	=	=	SYM
ejpam-6607	479	19	〈	〈	PROPN
ejpam-6607	479	20	ψγ	ψγ	X
ejpam-6607	479	21	|	|	ADV
ejpam-6607	479	22	u	u	PROPN
ejpam-6607	479	23	†	†	PROPN
ejpam-6607	479	24	γuγ	γuγ	PROPN
ejpam-6607	479	25	|	|	ADV
ejpam-6607	479	26	ψγ	ψγ	SYM
ejpam-6607	479	27	〉	〉	NOUN
ejpam-6607	479	28	=	=	PUNCT
ejpam-6607	479	29	〈	〈	PROPN
ejpam-6607	479	30	ψγ	ψγ	X
ejpam-6607	479	31	|	|	ADV
ejpam-6607	479	32	ψγ	ψγ	NOUN
ejpam-6607	479	33	〉	〉	NOUN
ejpam-6607	479	34	=	=	SYM
ejpam-6607	479	35	1	1	NUM
ejpam-6607	479	36	.	.	PUNCT
ejpam-6607	479	37	thus	thus	ADV
ejpam-6607	479	38	each	each	DET
ejpam-6607	479	39	state	state	NOUN
ejpam-6607	479	40	|ψ′	|ψ′	PROPN
ejpam-6607	479	41	γ⟩	γ⟩	PUNCT
ejpam-6607	480	1	=	=	PUNCT
ejpam-6607	480	2	uγ	uγ	ADP
ejpam-6607	480	3	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	480	4	remains	remain	VERB
ejpam-6607	480	5	normalized	normalize	VERB
ejpam-6607	480	6	,	,	PUNCT
ejpam-6607	480	7	so	so	ADV
ejpam-6607	480	8	q′	q′	NOUN
ejpam-6607	480	9	satisfies	satisfy	VERB
ejpam-6607	480	10	the	the	DET
ejpam-6607	480	11	definition	definition	NOUN
ejpam-6607	480	12	of	of	ADP
ejpam-6607	480	13	a	a	DET
ejpam-6607	480	14	quantum	quantum	NOUN
ejpam-6607	480	15	–	–	PUNCT
ejpam-6607	480	16	superhypersoft	superhypersoft	NOUN
ejpam-6607	480	17	set	set	NOUN
ejpam-6607	480	18	.	.	PUNCT
ejpam-6607	481	1	theorem	theorem	VERB
ejpam-6607	481	2	13	13	NUM
ejpam-6607	481	3	(	(	PUNCT
ejpam-6607	481	4	crisp	crisp	ADJ
ejpam-6607	481	5	embedding	embedding	NOUN
ejpam-6607	481	6	)	)	PUNCT
ejpam-6607	481	7	.	.	PUNCT
ejpam-6607	482	1	a	a	DET
ejpam-6607	482	2	quantum	quantum	NOUN
ejpam-6607	482	3	–	–	PUNCT
ejpam-6607	482	4	superhypersoft	superhypersoft	NOUN
ejpam-6607	482	5	set	set	VERB
ejpam-6607	482	6	q	q	NOUN
ejpam-6607	482	7	induces	induce	VERB
ejpam-6607	482	8	a	a	DET
ejpam-6607	482	9	crisp	crisp	ADJ
ejpam-6607	482	10	superhypersoft	superhypersoft	NOUN
ejpam-6607	482	11	set	set	VERB
ejpam-6607	482	12	if	if	SCONJ
ejpam-6607	482	13	and	and	CCONJ
ejpam-6607	482	14	only	only	ADV
ejpam-6607	482	15	if	if	SCONJ
ejpam-6607	482	16	for	for	ADP
ejpam-6607	482	17	each	each	DET
ejpam-6607	482	18	γ	γ	X
ejpam-6607	482	19	∈	∈	PROPN
ejpam-6607	482	20	c	c	NOUN
ejpam-6607	482	21	there	there	PRON
ejpam-6607	482	22	is	be	VERB
ejpam-6607	482	23	a	a	DET
ejpam-6607	482	24	unique	unique	ADJ
ejpam-6607	482	25	index	index	NOUN
ejpam-6607	482	26	iγ	iγ	ADP
ejpam-6607	482	27	such	such	ADJ
ejpam-6607	482	28	that	that	DET
ejpam-6607	482	29	|αiγ	|αiγ	NOUN
ejpam-6607	482	30	,	,	PUNCT
ejpam-6607	482	31	γ	γ	X
ejpam-6607	482	32	|	|	NOUN
ejpam-6607	482	33	=	=	SYM
ejpam-6607	482	34	1	1	NUM
ejpam-6607	482	35	and	and	CCONJ
ejpam-6607	482	36	αi	αi	NOUN
ejpam-6607	482	37	,	,	PUNCT
ejpam-6607	482	38	γ	γ	X
ejpam-6607	482	39	=	=	SYM
ejpam-6607	482	40	0	0	NUM
ejpam-6607	482	41	(	(	PUNCT
ejpam-6607	482	42	∀	∀	X
ejpam-6607	483	1	i	i	PRON
ejpam-6607	483	2	̸=	̸=	PROPN
ejpam-6607	483	3	iγ	iγ	NOUN
ejpam-6607	483	4	)	)	PUNCT
ejpam-6607	483	5	.	.	PUNCT
ejpam-6607	484	1	in	in	ADP
ejpam-6607	484	2	that	that	DET
ejpam-6607	484	3	case	case	NOUN
ejpam-6607	484	4	,	,	PUNCT
ejpam-6607	484	5	measurement	measurement	NOUN
ejpam-6607	484	6	of	of	ADP
ejpam-6607	484	7	|ψγ⟩	|ψγ⟩	ADJ
ejpam-6607	484	8	yields	yield	VERB
ejpam-6607	484	9	µγ(uiγ	µγ(uiγ	PROPN
ejpam-6607	484	10	)	)	PUNCT
ejpam-6607	485	1	=	=	SYM
ejpam-6607	485	2	1	1	NUM
ejpam-6607	485	3	and	and	CCONJ
ejpam-6607	485	4	µγ(ui	µγ(ui	PROPN
ejpam-6607	485	5	)	)	PUNCT
ejpam-6607	486	1	=	=	SYM
ejpam-6607	486	2	0	0	PUNCT
ejpam-6607	487	1	for	for	ADP
ejpam-6607	487	2	i	i	PRON
ejpam-6607	487	3	̸=	̸=	PROPN
ejpam-6607	487	4	iγ	iγ	NOUN
ejpam-6607	487	5	,	,	PUNCT
ejpam-6607	487	6	corresponding	correspond	VERB
ejpam-6607	487	7	exactly	exactly	ADV
ejpam-6607	487	8	to	to	ADP
ejpam-6607	487	9	the	the	DET
ejpam-6607	487	10	classical	classical	ADJ
ejpam-6607	487	11	superhypersoft	superhypersoft	PROPN
ejpam-6607	487	12	assignment	assignment	NOUN
ejpam-6607	487	13	f	f	PROPN
ejpam-6607	487	14	(	(	PUNCT
ejpam-6607	487	15	γ	γ	PROPN
ejpam-6607	487	16	)	)	PUNCT
ejpam-6607	487	17	=	=	SYM
ejpam-6607	487	18	{	{	PUNCT
ejpam-6607	487	19	uiγ	uiγ	PROPN
ejpam-6607	487	20	}	}	PUNCT
ejpam-6607	487	21	.	.	PUNCT
ejpam-6607	488	1	proof	proof	NOUN
ejpam-6607	488	2	.	.	PUNCT
ejpam-6607	489	1	(	(	PUNCT
ejpam-6607	489	2	⇒	⇒	PROPN
ejpam-6607	489	3	)	)	PUNCT
ejpam-6607	489	4	if	if	SCONJ
ejpam-6607	489	5	q	q	PROPN
ejpam-6607	489	6	collapses	collapse	VERB
ejpam-6607	489	7	deterministically	deterministically	ADV
ejpam-6607	489	8	to	to	ADP
ejpam-6607	489	9	a	a	DET
ejpam-6607	489	10	single	single	ADJ
ejpam-6607	489	11	element	element	NOUN
ejpam-6607	489	12	uiγ	uiγ	NOUN
ejpam-6607	489	13	,	,	PUNCT
ejpam-6607	489	14	then	then	ADV
ejpam-6607	489	15	the	the	DET
ejpam-6607	489	16	born	bear	VERB
ejpam-6607	489	17	rule	rule	NOUN
ejpam-6607	489	18	implies	imply	VERB
ejpam-6607	489	19	|αiγ	|αiγ	NOUN
ejpam-6607	489	20	,	,	PUNCT
ejpam-6607	489	21	γ	γ	X
ejpam-6607	489	22	|2	|2	X
ejpam-6607	489	23	=	=	SYM
ejpam-6607	489	24	1	1	NUM
ejpam-6607	489	25	and	and	CCONJ
ejpam-6607	489	26	|αi	|αi	NOUN
ejpam-6607	489	27	,	,	PUNCT
ejpam-6607	489	28	γ	γ	X
ejpam-6607	489	29	|2	|2	X
ejpam-6607	489	30	=	=	SYM
ejpam-6607	489	31	0	0	NUM
ejpam-6607	489	32	for	for	SCONJ
ejpam-6607	489	33	i	i	PRON
ejpam-6607	489	34	̸=	̸=	PROPN
ejpam-6607	489	35	iγ	iγ	NOUN
ejpam-6607	489	36	.	.	PUNCT
ejpam-6607	490	1	thus	thus	ADV
ejpam-6607	490	2	αiγ	αiγ	PROPN
ejpam-6607	490	3	,	,	PUNCT
ejpam-6607	490	4	γ	γ	X
ejpam-6607	490	5	=	=	SYM
ejpam-6607	490	6	eiθ	eiθ	PROPN
ejpam-6607	490	7	(	(	PUNCT
ejpam-6607	490	8	global	global	ADJ
ejpam-6607	490	9	phase	phase	NOUN
ejpam-6607	490	10	)	)	PUNCT
ejpam-6607	490	11	and	and	CCONJ
ejpam-6607	490	12	other	other	ADJ
ejpam-6607	490	13	amplitudes	amplitude	NOUN
ejpam-6607	490	14	vanish	vanish	VERB
ejpam-6607	490	15	.	.	PUNCT
ejpam-6607	491	1	(	(	PUNCT
ejpam-6607	491	2	⇐	⇐	NOUN
ejpam-6607	491	3	)	)	PUNCT
ejpam-6607	491	4	conversely	conversely	ADV
ejpam-6607	491	5	,	,	PUNCT
ejpam-6607	491	6	if	if	SCONJ
ejpam-6607	491	7	the	the	DET
ejpam-6607	491	8	amplitude	amplitude	NOUN
ejpam-6607	491	9	condition	condition	NOUN
ejpam-6607	491	10	holds	hold	VERB
ejpam-6607	491	11	,	,	PUNCT
ejpam-6607	491	12	then	then	ADV
ejpam-6607	491	13	∑	∑	ADP
ejpam-6607	491	14	i	i	PRON
ejpam-6607	491	15	|αi	|αi	NUM
ejpam-6607	491	16	,	,	PUNCT
ejpam-6607	491	17	γ	γ	X
ejpam-6607	491	18	|2	|2	X
ejpam-6607	491	19	=	=	SYM
ejpam-6607	491	20	1	1	NUM
ejpam-6607	491	21	and	and	CCONJ
ejpam-6607	491	22	measurement	measurement	NOUN
ejpam-6607	491	23	yields	yield	NOUN
ejpam-6607	491	24	p	p	X
ejpam-6607	491	25	(	(	PUNCT
ejpam-6607	491	26	ui	ui	PROPN
ejpam-6607	491	27	|	|	ADV
ejpam-6607	491	28	γ	γ	NOUN
ejpam-6607	491	29	)	)	PUNCT
ejpam-6607	491	30	=	=	NOUN
ejpam-6607	491	31	{	{	PUNCT
ejpam-6607	491	32	1	1	NUM
ejpam-6607	491	33	,	,	PUNCT
ejpam-6607	492	1	i	i	PRON
ejpam-6607	492	2	=	=	PUNCT
ejpam-6607	492	3	iγ	iγ	PROPN
ejpam-6607	492	4	,	,	PUNCT
ejpam-6607	492	5	0	0	NUM
ejpam-6607	492	6	,	,	PUNCT
ejpam-6607	492	7	i	i	PRON
ejpam-6607	492	8	̸=	̸=	PROPN
ejpam-6607	492	9	iγ	iγ	VERB
ejpam-6607	492	10	,	,	PUNCT
ejpam-6607	492	11	so	so	CCONJ
ejpam-6607	492	12	the	the	DET
ejpam-6607	492	13	post	post	ADJ
ejpam-6607	492	14	-	-	ADJ
ejpam-6607	492	15	measurement	measurement	ADJ
ejpam-6607	492	16	membership	membership	NOUN
ejpam-6607	492	17	is	be	AUX
ejpam-6607	492	18	crisp	crisp	ADJ
ejpam-6607	492	19	,	,	PUNCT
ejpam-6607	492	20	f	f	PROPN
ejpam-6607	492	21	(	(	PUNCT
ejpam-6607	492	22	γ	γ	PROPN
ejpam-6607	492	23	)	)	PUNCT
ejpam-6607	492	24	=	=	SYM
ejpam-6607	492	25	{	{	PUNCT
ejpam-6607	492	26	uiγ	uiγ	PROPN
ejpam-6607	492	27	}	}	PUNCT
ejpam-6607	492	28	.	.	PUNCT
ejpam-6607	493	1	theorem	theorem	NOUN
ejpam-6607	493	2	14	14	NUM
ejpam-6607	493	3	(	(	PUNCT
ejpam-6607	493	4	entropy	entropy	NOUN
ejpam-6607	493	5	bounds	bound	NOUN
ejpam-6607	493	6	)	)	PUNCT
ejpam-6607	493	7	.	.	PUNCT
ejpam-6607	494	1	define	define	VERB
ejpam-6607	494	2	the	the	DET
ejpam-6607	494	3	shannon	shannon	PROPN
ejpam-6607	494	4	entropy	entropy	PROPN
ejpam-6607	494	5	of	of	ADP
ejpam-6607	494	6	the	the	DET
ejpam-6607	494	7	measurement	measurement	NOUN
ejpam-6607	494	8	distribution	distribution	NOUN
ejpam-6607	494	9	at	at	ADP
ejpam-6607	494	10	γ	γ	X
ejpam-6607	494	11	by	by	ADP
ejpam-6607	494	12	h(γ	h(γ	NOUN
ejpam-6607	494	13	)	)	PUNCT
ejpam-6607	494	14	=	=	SYM
ejpam-6607	495	1	−	−	PROPN
ejpam-6607	495	2	n∑	n∑	NOUN
ejpam-6607	495	3	i=1	i=1	PROPN
ejpam-6607	495	4	∣∣αi	∣∣αi	PROPN
ejpam-6607	495	5	,	,	PUNCT
ejpam-6607	495	6	γ	γ	PROPN
ejpam-6607	495	7	∣∣2	∣∣2	PROPN
ejpam-6607	495	8	log	log	NOUN
ejpam-6607	495	9	∣∣αi	∣∣αi	NOUN
ejpam-6607	495	10	,	,	PUNCT
ejpam-6607	495	11	γ	γ	PROPN
ejpam-6607	495	12	∣∣2	∣∣2	PROPN
ejpam-6607	495	13	.	.	PUNCT
ejpam-6607	496	1	then	then	ADV
ejpam-6607	496	2	0	0	NUM
ejpam-6607	496	3	≤	≤	NUM
ejpam-6607	496	4	h(γ	h(γ	NOUN
ejpam-6607	496	5	)	)	PUNCT
ejpam-6607	496	6	≤	≤	NUM
ejpam-6607	496	7	log	log	NOUN
ejpam-6607	496	8	n	n	CCONJ
ejpam-6607	496	9	,	,	PUNCT
ejpam-6607	496	10	with	with	ADP
ejpam-6607	496	11	h(γ	h(γ	NOUN
ejpam-6607	496	12	)	)	PUNCT
ejpam-6607	496	13	=	=	SYM
ejpam-6607	496	14	0	0	PUNCT
ejpam-6607	497	1	if	if	SCONJ
ejpam-6607	497	2	and	and	CCONJ
ejpam-6607	497	3	only	only	ADV
ejpam-6607	497	4	if	if	SCONJ
ejpam-6607	497	5	q	q	NOUN
ejpam-6607	497	6	is	be	AUX
ejpam-6607	497	7	crisp	crisp	ADJ
ejpam-6607	497	8	at	at	ADP
ejpam-6607	497	9	γ	γ	X
ejpam-6607	497	10	,	,	PUNCT
ejpam-6607	497	11	and	and	CCONJ
ejpam-6607	497	12	h(γ	h(γ	NOUN
ejpam-6607	497	13	)	)	PUNCT
ejpam-6607	497	14	=	=	PRON
ejpam-6607	497	15	log	log	VERB
ejpam-6607	497	16	n	n	CCONJ
ejpam-6607	497	17	if	if	SCONJ
ejpam-6607	497	18	and	and	CCONJ
ejpam-6607	497	19	only	only	ADV
ejpam-6607	497	20	if	if	SCONJ
ejpam-6607	497	21	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	497	22	=	=	SYM
ejpam-6607	497	23	1√	1√	PROPN
ejpam-6607	497	24	n	n	CCONJ
ejpam-6607	497	25	∑n	∑n	PROPN
ejpam-6607	497	26	i=1	i=1	PROPN
ejpam-6607	497	27	|ui⟩.	|ui⟩.	PROPN
ejpam-6607	497	28	t.	t.	PROPN
ejpam-6607	497	29	fujita	fujita	PROPN
ejpam-6607	497	30	,	,	PUNCT
ejpam-6607	497	31	f.smarandache	f.smarandache	NOUN
ejpam-6607	497	32	/	/	SYM
ejpam-6607	497	33	eur	eur	PROPN
ejpam-6607	497	34	.	.	PUNCT
ejpam-6607	498	1	j.	j.	PROPN
ejpam-6607	498	2	pure	pure	PROPN
ejpam-6607	498	3	appl	appl	PROPN
ejpam-6607	498	4	.	.	PROPN
ejpam-6607	498	5	math	math	PROPN
ejpam-6607	498	6	,	,	PUNCT
ejpam-6607	498	7	18	18	NUM
ejpam-6607	498	8	(	(	PUNCT
ejpam-6607	498	9	3	3	NUM
ejpam-6607	498	10	)	)	PUNCT
ejpam-6607	498	11	(	(	PUNCT
ejpam-6607	498	12	2025	2025	NUM
ejpam-6607	498	13	)	)	PUNCT
ejpam-6607	498	14	,	,	PUNCT
ejpam-6607	498	15	6607	6607	NUM
ejpam-6607	498	16	24	24	NUM
ejpam-6607	498	17	of	of	ADP
ejpam-6607	498	18	33	33	NUM
ejpam-6607	498	19	proof	proof	NOUN
ejpam-6607	498	20	.	.	PUNCT
ejpam-6607	499	1	by	by	ADP
ejpam-6607	499	2	definition	definition	NOUN
ejpam-6607	499	3	,	,	PUNCT
ejpam-6607	499	4	shannon	shannon	PROPN
ejpam-6607	499	5	entropy	entropy	PROPN
ejpam-6607	499	6	on	on	ADP
ejpam-6607	499	7	a	a	DET
ejpam-6607	499	8	probability	probability	NOUN
ejpam-6607	499	9	distribution	distribution	NOUN
ejpam-6607	499	10	is	be	AUX
ejpam-6607	499	11	nonnegative	nonnegative	ADJ
ejpam-6607	499	12	,	,	PUNCT
ejpam-6607	499	13	so	so	SCONJ
ejpam-6607	499	14	h(γ	h(γ	PROPN
ejpam-6607	499	15	)	)	PUNCT
ejpam-6607	499	16	≥	≥	NOUN
ejpam-6607	499	17	0	0	NUM
ejpam-6607	499	18	,	,	PUNCT
ejpam-6607	499	19	with	with	ADP
ejpam-6607	499	20	equality	equality	NOUN
ejpam-6607	499	21	exactly	exactly	ADV
ejpam-6607	499	22	when	when	SCONJ
ejpam-6607	499	23	one	one	NUM
ejpam-6607	499	24	outcome	outcome	NOUN
ejpam-6607	499	25	has	have	VERB
ejpam-6607	499	26	probability	probability	NOUN
ejpam-6607	499	27	1	1	NUM
ejpam-6607	499	28	(	(	PUNCT
ejpam-6607	499	29	crisp	crisp	ADJ
ejpam-6607	499	30	case	case	NOUN
ejpam-6607	499	31	)	)	PUNCT
ejpam-6607	499	32	.	.	PUNCT
ejpam-6607	500	1	concavity	concavity	NOUN
ejpam-6607	500	2	of	of	ADP
ejpam-6607	500	3	entropy	entropy	NOUN
ejpam-6607	500	4	on	on	ADP
ejpam-6607	500	5	the	the	DET
ejpam-6607	500	6	simplex	simplex	NOUN
ejpam-6607	500	7	implies	imply	VERB
ejpam-6607	500	8	the	the	DET
ejpam-6607	500	9	maximum	maximum	NOUN
ejpam-6607	500	10	occurs	occur	VERB
ejpam-6607	500	11	at	at	ADP
ejpam-6607	500	12	the	the	DET
ejpam-6607	500	13	uniform	uniform	NOUN
ejpam-6607	500	14	distribution∣∣αi	distribution∣∣αi	NOUN
ejpam-6607	500	15	,	,	PUNCT
ejpam-6607	500	16	γ	γ	PROPN
ejpam-6607	500	17	∣∣2	∣∣2	PROPN
ejpam-6607	500	18	=	=	SYM
ejpam-6607	500	19	1	1	NUM
ejpam-6607	500	20	/	/	SYM
ejpam-6607	500	21	n	n	CCONJ
ejpam-6607	500	22	,	,	PUNCT
ejpam-6607	500	23	yielding	yield	VERB
ejpam-6607	500	24	h(γ	h(γ	PROPN
ejpam-6607	500	25	)	)	PUNCT
ejpam-6607	500	26	≤	≤	NUM
ejpam-6607	501	1	−n	−n	ADV
ejpam-6607	501	2	(	(	PUNCT
ejpam-6607	501	3	1	1	NUM
ejpam-6607	501	4	/	/	SYM
ejpam-6607	501	5	n	n	CCONJ
ejpam-6607	501	6	)	)	PUNCT
ejpam-6607	501	7	log(1	log(1	NOUN
ejpam-6607	501	8	/	/	SYM
ejpam-6607	501	9	n	n	CCONJ
ejpam-6607	501	10	)	)	PUNCT
ejpam-6607	501	11	=	=	PRON
ejpam-6607	501	12	log	log	NOUN
ejpam-6607	501	13	n	n	CCONJ
ejpam-6607	501	14	,	,	PUNCT
ejpam-6607	501	15	with	with	ADP
ejpam-6607	501	16	equality	equality	NOUN
ejpam-6607	501	17	if	if	SCONJ
ejpam-6607	501	18	and	and	CCONJ
ejpam-6607	501	19	only	only	ADV
ejpam-6607	501	20	if	if	SCONJ
ejpam-6607	501	21	αi	αi	NOUN
ejpam-6607	501	22	,	,	PUNCT
ejpam-6607	501	23	γ	γ	X
ejpam-6607	501	24	=	=	SYM
ejpam-6607	501	25	1/	1/	NUM
ejpam-6607	501	26	√	√	PROPN
ejpam-6607	501	27	n	n	CCONJ
ejpam-6607	501	28	up	up	ADP
ejpam-6607	501	29	to	to	PART
ejpam-6607	501	30	phase	phase	VERB
ejpam-6607	501	31	for	for	ADP
ejpam-6607	501	32	all	all	DET
ejpam-6607	501	33	i.	i.	NOUN
ejpam-6607	501	34	theorem	theorem	NOUN
ejpam-6607	501	35	15	15	NUM
ejpam-6607	501	36	(	(	PUNCT
ejpam-6607	501	37	orthogonality	orthogonality	NOUN
ejpam-6607	501	38	of	of	ADP
ejpam-6607	501	39	disjoint	disjoint	ADJ
ejpam-6607	501	40	crisp	crisp	ADJ
ejpam-6607	501	41	states	state	NOUN
ejpam-6607	501	42	)	)	PUNCT
ejpam-6607	501	43	.	.	PUNCT
ejpam-6607	502	1	let	let	VERB
ejpam-6607	502	2	q	q	PRON
ejpam-6607	502	3	be	be	AUX
ejpam-6607	502	4	the	the	DET
ejpam-6607	502	5	crisp	crisp	ADJ
ejpam-6607	502	6	embedding	embedding	NOUN
ejpam-6607	502	7	of	of	ADP
ejpam-6607	502	8	a	a	DET
ejpam-6607	502	9	superhypersoft	superhypersoft	NOUN
ejpam-6607	502	10	set	set	VERB
ejpam-6607	502	11	f	f	PROPN
ejpam-6607	502	12	,	,	PUNCT
ejpam-6607	502	13	as	as	ADP
ejpam-6607	502	14	in	in	ADP
ejpam-6607	502	15	theorem	theorem	NOUN
ejpam-6607	502	16	2	2	NUM
ejpam-6607	502	17	.	.	PUNCT
ejpam-6607	503	1	then	then	ADV
ejpam-6607	503	2	for	for	ADP
ejpam-6607	503	3	any	any	DET
ejpam-6607	503	4	γ	γ	NOUN
ejpam-6607	503	5	,	,	PUNCT
ejpam-6607	503	6	γ′	γ′	X
ejpam-6607	503	7	∈	∈	PROPN
ejpam-6607	503	8	c	c	NOUN
ejpam-6607	503	9	,	,	PUNCT
ejpam-6607	503	10	f	f	PROPN
ejpam-6607	503	11	(	(	PUNCT
ejpam-6607	503	12	γ	γ	NOUN
ejpam-6607	503	13	)	)	PUNCT
ejpam-6607	503	14	∩	∩	ADJ
ejpam-6607	503	15	f	f	X
ejpam-6607	503	16	(	(	PUNCT
ejpam-6607	503	17	γ′	γ′	PROPN
ejpam-6607	503	18	)	)	PUNCT
ejpam-6607	503	19	=	=	NOUN
ejpam-6607	503	20	∅	∅	NOUN
ejpam-6607	503	21	=	=	NOUN
ejpam-6607	503	22	⇒	⇒	X
ejpam-6607	503	23	〈	〈	PROPN
ejpam-6607	504	1	ψγ	ψγ	PART
ejpam-6607	504	2	|	|	ADV
ejpam-6607	504	3	ψγ′	ψγ′	VERB
ejpam-6607	504	4	〉	〉	NOUN
ejpam-6607	504	5	=	=	SYM
ejpam-6607	504	6	0	0	X
ejpam-6607	504	7	.	.	PUNCT
ejpam-6607	504	8	proof	proof	NOUN
ejpam-6607	504	9	.	.	PUNCT
ejpam-6607	505	1	by	by	ADP
ejpam-6607	505	2	construction	construction	NOUN
ejpam-6607	505	3	,	,	PUNCT
ejpam-6607	505	4	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	505	5	=	=	PUNCT
ejpam-6607	505	6	∑	∑	NOUN
ejpam-6607	505	7	ui∈f	ui∈f	X
ejpam-6607	505	8	(	(	PUNCT
ejpam-6607	505	9	γ	γ	NOUN
ejpam-6607	505	10	)	)	PUNCT
ejpam-6607	505	11	1√	1√	PROPN
ejpam-6607	505	12	|f	|f	PROPN
ejpam-6607	505	13	(	(	PUNCT
ejpam-6607	505	14	γ)|	γ)|	NOUN
ejpam-6607	505	15	|ui⟩	|ui⟩	X
ejpam-6607	505	16	and	and	CCONJ
ejpam-6607	505	17	similarly	similarly	ADV
ejpam-6607	505	18	for	for	ADP
ejpam-6607	505	19	|ψγ′⟩.	|ψγ′⟩.	NOUN
ejpam-6607	505	20	hence	hence	ADV
ejpam-6607	505	21	〈	〈	PROPN
ejpam-6607	506	1	ψγ	ψγ	NUM
ejpam-6607	506	2	|	|	ADV
ejpam-6607	506	3	ψγ′	ψγ′	VERB
ejpam-6607	506	4	〉	〉	NOUN
ejpam-6607	506	5	=	=	PUNCT
ejpam-6607	506	6	n∑	n∑	PROPN
ejpam-6607	506	7	i=1	i=1	PROPN
ejpam-6607	506	8	αi	αi	PROPN
ejpam-6607	506	9	,	,	PUNCT
ejpam-6607	506	10	γ	γ	X
ejpam-6607	506	11	αi	αi	PROPN
ejpam-6607	506	12	,	,	PUNCT
ejpam-6607	506	13	γ′√	γ′√	PRON
ejpam-6607	506	14	|f	|f	PRON
ejpam-6607	506	15	(	(	PUNCT
ejpam-6607	506	16	γ)|	γ)|	NOUN
ejpam-6607	506	17	|f	|f	PROPN
ejpam-6607	506	18	(	(	PUNCT
ejpam-6607	506	19	γ′)|	γ′)|	NOUN
ejpam-6607	506	20	=	=	PUNCT
ejpam-6607	506	21	∑	∑	PUNCT
ejpam-6607	506	22	ui∈f	ui∈f	INTJ
ejpam-6607	506	23	(	(	PUNCT
ejpam-6607	506	24	γ)∩f	γ)∩f	PROPN
ejpam-6607	506	25	(	(	PUNCT
ejpam-6607	506	26	γ′	γ′	PROPN
ejpam-6607	506	27	)	)	PUNCT
ejpam-6607	506	28	1√	1√	PROPN
ejpam-6607	506	29	|f	|f	PROPN
ejpam-6607	507	1	(	(	PUNCT
ejpam-6607	507	2	γ)|	γ)|	NOUN
ejpam-6607	507	3	|f	|f	PROPN
ejpam-6607	507	4	(	(	PUNCT
ejpam-6607	507	5	γ′)|	γ′)|	INTJ
ejpam-6607	507	6	.	.	PUNCT
ejpam-6607	508	1	if	if	SCONJ
ejpam-6607	508	2	f	f	PROPN
ejpam-6607	508	3	(	(	PUNCT
ejpam-6607	508	4	γ	γ	NOUN
ejpam-6607	508	5	)	)	PUNCT
ejpam-6607	508	6	∩	∩	ADJ
ejpam-6607	508	7	f	f	X
ejpam-6607	508	8	(	(	PUNCT
ejpam-6607	508	9	γ′	γ′	PROPN
ejpam-6607	508	10	)	)	PUNCT
ejpam-6607	508	11	=	=	SYM
ejpam-6607	508	12	∅	∅	NOUN
ejpam-6607	508	13	,	,	PUNCT
ejpam-6607	508	14	this	this	DET
ejpam-6607	508	15	sum	sum	NOUN
ejpam-6607	508	16	is	be	AUX
ejpam-6607	508	17	zero	zero	NUM
ejpam-6607	508	18	.	.	PUNCT
ejpam-6607	509	1	theorem	theorem	VERB
ejpam-6607	509	2	16	16	NUM
ejpam-6607	509	3	(	(	PUNCT
ejpam-6607	509	4	fidelity	fidelity	PROPN
ejpam-6607	509	5	equals	equal	VERB
ejpam-6607	509	6	classical	classical	ADJ
ejpam-6607	509	7	overlap	overlap	NOUN
ejpam-6607	509	8	for	for	ADP
ejpam-6607	509	9	crisp	crisp	ADJ
ejpam-6607	509	10	states	state	NOUN
ejpam-6607	509	11	)	)	PUNCT
ejpam-6607	509	12	.	.	PUNCT
ejpam-6607	510	1	under	under	ADP
ejpam-6607	510	2	the	the	DET
ejpam-6607	510	3	same	same	ADJ
ejpam-6607	510	4	crisp	crisp	ADJ
ejpam-6607	510	5	embedding	embedding	NOUN
ejpam-6607	510	6	,	,	PUNCT
ejpam-6607	510	7	∣∣⟨ψγ	∣∣⟨ψγ	PROPN
ejpam-6607	510	8	|	|	ADV
ejpam-6607	510	9	ψγ′⟩	ψγ′⟩	NOUN
ejpam-6607	510	10	∣∣2	∣∣2	PROPN
ejpam-6607	510	11	=	=	SYM
ejpam-6607	510	12	∣∣f	∣∣f	PROPN
ejpam-6607	510	13	(	(	PUNCT
ejpam-6607	510	14	γ	γ	NOUN
ejpam-6607	510	15	)	)	PUNCT
ejpam-6607	510	16	∩	∩	ADJ
ejpam-6607	510	17	f	f	X
ejpam-6607	510	18	(	(	PUNCT
ejpam-6607	510	19	γ′	γ′	PROPN
ejpam-6607	510	20	)	)	PUNCT
ejpam-6607	510	21	∣∣2	∣∣2	PROPN
ejpam-6607	510	22	|f	|f	PROPN
ejpam-6607	510	23	(	(	PUNCT
ejpam-6607	510	24	γ)|	γ)|	NOUN
ejpam-6607	510	25	|f	|f	PROPN
ejpam-6607	510	26	(	(	PUNCT
ejpam-6607	510	27	γ′)|	γ′)|	X
ejpam-6607	510	28	.	.	PUNCT
ejpam-6607	511	1	proof	proof	NOUN
ejpam-6607	511	2	.	.	PUNCT
ejpam-6607	512	1	from	from	ADP
ejpam-6607	512	2	the	the	DET
ejpam-6607	512	3	proof	proof	NOUN
ejpam-6607	512	4	above	above	ADP
ejpam-6607	512	5	,	,	PUNCT
ejpam-6607	512	6	⟨ψγ	⟨ψγ	PROPN
ejpam-6607	512	7	|ψγ′⟩	|ψγ′⟩	PROPN
ejpam-6607	512	8	=	=	SYM
ejpam-6607	512	9	|f	|f	PROPN
ejpam-6607	512	10	(	(	PUNCT
ejpam-6607	512	11	γ)∩f	γ)∩f	PROPN
ejpam-6607	512	12	(	(	PUNCT
ejpam-6607	512	13	γ′)|√	γ′)|√	PROPN
ejpam-6607	512	14	|f	|f	PROPN
ejpam-6607	512	15	(	(	PUNCT
ejpam-6607	512	16	γ)|	γ)|	NOUN
ejpam-6607	512	17	|f	|f	PROPN
ejpam-6607	512	18	(	(	PUNCT
ejpam-6607	512	19	γ′)|	γ′)|	X
ejpam-6607	512	20	.	.	PUNCT
ejpam-6607	513	1	squaring	square	VERB
ejpam-6607	513	2	the	the	DET
ejpam-6607	513	3	modulus	modulus	ADJ
ejpam-6607	513	4	yields	yield	NOUN
ejpam-6607	513	5	the	the	DET
ejpam-6607	513	6	stated	state	VERB
ejpam-6607	513	7	formula	formula	NOUN
ejpam-6607	513	8	.	.	PUNCT
ejpam-6607	514	1	theorem	theorem	VERB
ejpam-6607	514	2	17	17	NUM
ejpam-6607	514	3	(	(	PUNCT
ejpam-6607	514	4	total	total	ADJ
ejpam-6607	514	5	variation	variation	NOUN
ejpam-6607	514	6	distance	distance	NOUN
ejpam-6607	514	7	bound	bind	VERB
ejpam-6607	514	8	)	)	PUNCT
ejpam-6607	514	9	.	.	PUNCT
ejpam-6607	515	1	for	for	ADP
ejpam-6607	515	2	any	any	DET
ejpam-6607	515	3	two	two	NUM
ejpam-6607	515	4	quantum	quantum	NOUN
ejpam-6607	515	5	states	state	NOUN
ejpam-6607	515	6	|ψγ⟩	|ψγ⟩	ADV
ejpam-6607	515	7	,	,	PUNCT
ejpam-6607	515	8	|ψγ′⟩	|ψγ′⟩	VERB
ejpam-6607	515	9	in	in	ADP
ejpam-6607	515	10	a	a	DET
ejpam-6607	515	11	quantum	quantum	NOUN
ejpam-6607	515	12	–	–	PUNCT
ejpam-6607	515	13	superhypersoft	superhypersoft	NOUN
ejpam-6607	515	14	set	set	NOUN
ejpam-6607	515	15	,	,	PUNCT
ejpam-6607	515	16	let	let	VERB
ejpam-6607	515	17	{	{	PUNCT
ejpam-6607	515	18	p	p	X
ejpam-6607	515	19	(	(	PUNCT
ejpam-6607	515	20	ui	ui	PROPN
ejpam-6607	515	21	|	|	ADV
ejpam-6607	515	22	γ	γ	NOUN
ejpam-6607	515	23	)	)	PUNCT
ejpam-6607	515	24	}	}	PUNCT
ejpam-6607	515	25	and	and	CCONJ
ejpam-6607	515	26	{	{	PUNCT
ejpam-6607	515	27	p	p	X
ejpam-6607	515	28	(	(	PUNCT
ejpam-6607	515	29	ui	ui	NOUN
ejpam-6607	515	30	|	|	ADV
ejpam-6607	515	31	γ′	γ′	NOUN
ejpam-6607	515	32	)	)	PUNCT
ejpam-6607	515	33	}	}	PUNCT
ejpam-6607	515	34	be	be	AUX
ejpam-6607	515	35	their	their	PRON
ejpam-6607	515	36	measurement	measurement	NOUN
ejpam-6607	515	37	distributions	distribution	NOUN
ejpam-6607	515	38	.	.	PUNCT
ejpam-6607	516	1	then	then	ADV
ejpam-6607	516	2	the	the	DET
ejpam-6607	516	3	total	total	ADJ
ejpam-6607	516	4	variation	variation	NOUN
ejpam-6607	516	5	distance	distance	NOUN
ejpam-6607	516	6	tv	tv	NOUN
ejpam-6607	516	7	satisfies	satisfy	VERB
ejpam-6607	516	8	tv	tv	NOUN
ejpam-6607	516	9	(	(	PUNCT
ejpam-6607	516	10	p	p	X
ejpam-6607	516	11	(	(	PUNCT
ejpam-6607	516	12	·	·	PUNCT
ejpam-6607	516	13	|γ	|γ	NOUN
ejpam-6607	516	14	)	)	PUNCT
ejpam-6607	516	15	,	,	PUNCT
ejpam-6607	516	16	p	p	X
ejpam-6607	516	17	(	(	PUNCT
ejpam-6607	516	18	·	·	PUNCT
ejpam-6607	516	19	|γ′	|γ′	PROPN
ejpam-6607	516	20	)	)	PUNCT
ejpam-6607	516	21	)	)	PUNCT
ejpam-6607	516	22	≤	≤	NOUN
ejpam-6607	517	1	√	√	NUM
ejpam-6607	517	2	1−	1−	NUM
ejpam-6607	518	1	∣∣⟨ψγ	∣∣⟨ψγ	PROPN
ejpam-6607	518	2	|	|	ADV
ejpam-6607	518	3	ψγ′⟩	ψγ′⟩	PUNCT
ejpam-6607	518	4	∣∣2	∣∣2	PROPN
ejpam-6607	518	5	.	.	PUNCT
ejpam-6607	519	1	proof	proof	NOUN
ejpam-6607	519	2	.	.	PUNCT
ejpam-6607	520	1	it	it	PRON
ejpam-6607	520	2	is	be	AUX
ejpam-6607	520	3	known	know	VERB
ejpam-6607	520	4	that	that	SCONJ
ejpam-6607	520	5	for	for	ADP
ejpam-6607	520	6	pure	pure	ADJ
ejpam-6607	520	7	states	state	NOUN
ejpam-6607	520	8	the	the	DET
ejpam-6607	520	9	fidelity	fidelity	PROPN
ejpam-6607	520	10	f	f	PROPN
ejpam-6607	520	11	=	=	SYM
ejpam-6607	520	12	|⟨ψγ	|⟨ψγ	PROPN
ejpam-6607	520	13	|ψγ′⟩|2	|ψγ′⟩|2	PROPN
ejpam-6607	520	14	and	and	CCONJ
ejpam-6607	520	15	the	the	DET
ejpam-6607	520	16	classical	classical	ADJ
ejpam-6607	520	17	total	total	ADJ
ejpam-6607	520	18	variation	variation	NOUN
ejpam-6607	520	19	distance	distance	NOUN
ejpam-6607	520	20	satisfy	satisfy	NOUN
ejpam-6607	520	21	tv(p	tv(p	NUM
ejpam-6607	520	22	,	,	PUNCT
ejpam-6607	520	23	p	p	NOUN
ejpam-6607	520	24	′	′	NOUN
ejpam-6607	520	25	)	)	PUNCT
ejpam-6607	520	26	≤	≤	NOUN
ejpam-6607	521	1	√	√	ADP
ejpam-6607	521	2	1−	1−	NUM
ejpam-6607	521	3	f	f	NOUN
ejpam-6607	521	4	.	.	PUNCT
ejpam-6607	522	1	applying	apply	VERB
ejpam-6607	522	2	this	this	PRON
ejpam-6607	522	3	to	to	ADP
ejpam-6607	522	4	the	the	DET
ejpam-6607	522	5	two	two	NUM
ejpam-6607	522	6	measurement	measurement	NOUN
ejpam-6607	522	7	distributions	distribution	NOUN
ejpam-6607	522	8	yields	yield	VERB
ejpam-6607	522	9	the	the	DET
ejpam-6607	522	10	bound	bind	VERB
ejpam-6607	522	11	.	.	PUNCT
ejpam-6607	523	1	t.	t.	PROPN
ejpam-6607	523	2	fujita	fujita	PROPN
ejpam-6607	523	3	,	,	PUNCT
ejpam-6607	523	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	523	5	/	/	SYM
ejpam-6607	523	6	eur	eur	PROPN
ejpam-6607	523	7	.	.	PUNCT
ejpam-6607	524	1	j.	j.	PROPN
ejpam-6607	524	2	pure	pure	PROPN
ejpam-6607	524	3	appl	appl	PROPN
ejpam-6607	524	4	.	.	PROPN
ejpam-6607	524	5	math	math	PROPN
ejpam-6607	524	6	,	,	PUNCT
ejpam-6607	524	7	18	18	NUM
ejpam-6607	524	8	(	(	PUNCT
ejpam-6607	524	9	3	3	NUM
ejpam-6607	524	10	)	)	PUNCT
ejpam-6607	524	11	(	(	PUNCT
ejpam-6607	524	12	2025	2025	NUM
ejpam-6607	524	13	)	)	PUNCT
ejpam-6607	524	14	,	,	PUNCT
ejpam-6607	524	15	6607	6607	NUM
ejpam-6607	524	16	25	25	NUM
ejpam-6607	524	17	of	of	ADP
ejpam-6607	524	18	33	33	NUM
ejpam-6607	524	19	theorem	theorem	ADJ
ejpam-6607	524	20	18	18	NUM
ejpam-6607	524	21	(	(	PUNCT
ejpam-6607	524	22	projector	projector	NOUN
ejpam-6607	524	23	-	-	PUNCT
ejpam-6607	524	24	induced	induce	VERB
ejpam-6607	524	25	sub	sub	NOUN
ejpam-6607	524	26	-	-	ADJ
ejpam-6607	524	27	set	set	ADJ
ejpam-6607	524	28	)	)	PUNCT
ejpam-6607	524	29	.	.	PUNCT
ejpam-6607	525	1	let	let	VERB
ejpam-6607	525	2	q	q	PRON
ejpam-6607	525	3	be	be	AUX
ejpam-6607	525	4	a	a	DET
ejpam-6607	525	5	quantum	quantum	NOUN
ejpam-6607	525	6	–	–	PUNCT
ejpam-6607	525	7	superhypersoft	superhypersoft	NOUN
ejpam-6607	525	8	set	set	VERB
ejpam-6607	525	9	and	and	CCONJ
ejpam-6607	525	10	let	let	VERB
ejpam-6607	525	11	π	π	NOUN
ejpam-6607	525	12	be	be	AUX
ejpam-6607	525	13	any	any	DET
ejpam-6607	525	14	projector	projector	NOUN
ejpam-6607	525	15	on	on	ADP
ejpam-6607	525	16	h(u	h(u	PROPN
ejpam-6607	525	17	)	)	PUNCT
ejpam-6607	525	18	that	that	PRON
ejpam-6607	525	19	is	be	AUX
ejpam-6607	525	20	diagonal	diagonal	ADJ
ejpam-6607	525	21	in	in	ADP
ejpam-6607	525	22	the	the	DET
ejpam-6607	525	23	{	{	PUNCT
ejpam-6607	525	24	|ui⟩	|ui⟩	NOUN
ejpam-6607	525	25	}	}	PUNCT
ejpam-6607	525	26	basis	basis	NOUN
ejpam-6607	525	27	.	.	PUNCT
ejpam-6607	526	1	define	define	VERB
ejpam-6607	526	2	|φγ⟩	|φγ⟩	NOUN
ejpam-6607	526	3	=	=	NOUN
ejpam-6607	526	4	π	π	X
ejpam-6607	526	5	|ψγ⟩∥∥π	|ψγ⟩∥∥π	PROPN
ejpam-6607	526	6	|ψγ⟩	|ψγ⟩	ADV
ejpam-6607	526	7	∥∥	∥∥	X
ejpam-6607	526	8	,	,	PUNCT
ejpam-6607	526	9	whenever	whenever	SCONJ
ejpam-6607	526	10	π	π	PROPN
ejpam-6607	526	11	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	526	12	̸=	̸=	PROPN
ejpam-6607	526	13	0	0	NUM
ejpam-6607	526	14	.	.	PUNCT
ejpam-6607	527	1	then	then	ADV
ejpam-6607	527	2	the	the	DET
ejpam-6607	527	3	map	map	NOUN
ejpam-6607	527	4	γ	γ	PROPN
ejpam-6607	527	5	7→	7→	PROPN
ejpam-6607	527	6	|φγ⟩	|φγ⟩	NOUN
ejpam-6607	527	7	is	be	AUX
ejpam-6607	527	8	itself	itself	PRON
ejpam-6607	527	9	a	a	DET
ejpam-6607	527	10	quantum	quantum	NOUN
ejpam-6607	527	11	–	–	PUNCT
ejpam-6607	527	12	superhypersoft	superhypersoft	NOUN
ejpam-6607	527	13	set	set	NOUN
ejpam-6607	527	14	(	(	PUNCT
ejpam-6607	527	15	over	over	ADP
ejpam-6607	527	16	the	the	DET
ejpam-6607	527	17	restricted	restricted	ADJ
ejpam-6607	527	18	universe	universe	NOUN
ejpam-6607	527	19	corresponding	correspond	VERB
ejpam-6607	527	20	to	to	ADP
ejpam-6607	527	21	π	π	PROPN
ejpam-6607	527	22	)	)	PUNCT
ejpam-6607	527	23	.	.	PUNCT
ejpam-6607	528	1	proof	proof	NOUN
ejpam-6607	528	2	.	.	PUNCT
ejpam-6607	529	1	because	because	SCONJ
ejpam-6607	529	2	π	π	PROPN
ejpam-6607	529	3	is	be	AUX
ejpam-6607	529	4	diagonal	diagonal	ADJ
ejpam-6607	529	5	in	in	ADP
ejpam-6607	529	6	the	the	DET
ejpam-6607	529	7	measurement	measurement	NOUN
ejpam-6607	529	8	basis	basis	NOUN
ejpam-6607	529	9	,	,	PUNCT
ejpam-6607	529	10	it	it	PRON
ejpam-6607	529	11	acts	act	VERB
ejpam-6607	529	12	by	by	ADP
ejpam-6607	529	13	zeroing	zero	VERB
ejpam-6607	529	14	some	some	DET
ejpam-6607	529	15	amplitudes	amplitude	NOUN
ejpam-6607	529	16	and	and	CCONJ
ejpam-6607	529	17	leaving	leave	VERB
ejpam-6607	529	18	others	other	NOUN
ejpam-6607	529	19	unchanged	unchanged	ADJ
ejpam-6607	529	20	.	.	PUNCT
ejpam-6607	530	1	thus	thus	ADV
ejpam-6607	530	2	∥π	∥π	NOUN
ejpam-6607	530	3	|ψγ⟩	|ψγ⟩	ADJ
ejpam-6607	530	4	∥	∥	PUNCT
ejpam-6607	530	5	≤	≤	NUM
ejpam-6607	530	6	1	1	NUM
ejpam-6607	530	7	,	,	PUNCT
ejpam-6607	530	8	and	and	CCONJ
ejpam-6607	530	9	normalizing	normalize	VERB
ejpam-6607	530	10	restores	restore	VERB
ejpam-6607	530	11	unit	unit	NOUN
ejpam-6607	530	12	norm	norm	NOUN
ejpam-6607	530	13	:	:	PUNCT
ejpam-6607	530	14	〈	〈	PROPN
ejpam-6607	530	15	φγ	φγ	PUNCT
ejpam-6607	530	16	|	|	ADV
ejpam-6607	530	17	φγ	φγ	ADP
ejpam-6607	530	18	〉	〉	NOUN
ejpam-6607	530	19	=	=	SYM
ejpam-6607	530	20	⟨ψγ	⟨ψγ	PROPN
ejpam-6607	530	21	|π†π|ψγ⟩	|π†π|ψγ⟩	NOUN
ejpam-6607	530	22	⟨ψγ	⟨ψγ	PROPN
ejpam-6607	530	23	|π†π|ψγ⟩	|π†π|ψγ⟩	NOUN
ejpam-6607	530	24	=	=	SYM
ejpam-6607	531	1	1	1	X
ejpam-6607	531	2	.	.	PUNCT
ejpam-6607	531	3	hence	hence	ADV
ejpam-6607	531	4	|φγ⟩	|φγ⟩	PROPN
ejpam-6607	531	5	is	be	AUX
ejpam-6607	531	6	a	a	DET
ejpam-6607	531	7	valid	valid	ADJ
ejpam-6607	531	8	quantum	quantum	ADJ
ejpam-6607	531	9	state	state	NOUN
ejpam-6607	531	10	for	for	ADP
ejpam-6607	531	11	each	each	DET
ejpam-6607	531	12	γ	γ	PROPN
ejpam-6607	531	13	.	.	PROPN
ejpam-6607	531	14	3.3	3.3	NUM
ejpam-6607	531	15	.	.	PUNCT
ejpam-6607	532	1	algorithm	algorithm	NOUN
ejpam-6607	532	2	for	for	ADP
ejpam-6607	532	3	constructing	construct	VERB
ejpam-6607	532	4	quantum	quantum	NOUN
ejpam-6607	532	5	-	-	PUNCT
ejpam-6607	532	6	hypersoft	hypersoft	NOUN
ejpam-6607	532	7	set	set	VERB
ejpam-6607	532	8	and	and	CCONJ
ejpam-6607	532	9	quantumsuperhypersoft	quantumsuperhypersoft	ADV
ejpam-6607	532	10	set	set	VERB
ejpam-6607	532	11	with	with	ADP
ejpam-6607	532	12	a	a	DET
ejpam-6607	532	13	view	view	NOUN
ejpam-6607	532	14	toward	toward	ADP
ejpam-6607	532	15	future	future	ADJ
ejpam-6607	532	16	computational	computational	ADJ
ejpam-6607	532	17	experiments	experiment	NOUN
ejpam-6607	532	18	,	,	PUNCT
ejpam-6607	532	19	we	we	PRON
ejpam-6607	532	20	further	far	ADV
ejpam-6607	532	21	examine	examine	VERB
ejpam-6607	532	22	the	the	DET
ejpam-6607	532	23	construction	construction	NOUN
ejpam-6607	532	24	algorithms	algorithm	NOUN
ejpam-6607	532	25	for	for	ADP
ejpam-6607	532	26	both	both	CCONJ
ejpam-6607	532	27	the	the	DET
ejpam-6607	532	28	quantum	quantum	NOUN
ejpam-6607	532	29	-	-	PUNCT
ejpam-6607	532	30	hypersoft	hypersoft	NOUN
ejpam-6607	532	31	set	set	NOUN
ejpam-6607	532	32	and	and	CCONJ
ejpam-6607	532	33	the	the	DET
ejpam-6607	532	34	quantum	quantum	NOUN
ejpam-6607	532	35	-	-	PUNCT
ejpam-6607	532	36	superhypersoft	superhypersoft	NOUN
ejpam-6607	532	37	set	set	NOUN
ejpam-6607	532	38	.	.	PUNCT
ejpam-6607	533	1	algorithm	algorithm	PROPN
ejpam-6607	533	2	1	1	NUM
ejpam-6607	533	3	(	(	PUNCT
ejpam-6607	533	4	ht	ht	PROPN
ejpam-6607	533	5	)	)	PUNCT
ejpam-6607	533	6	.	.	PUNCT
ejpam-6607	534	1	construct	construct	VERB
ejpam-6607	534	2	quantum	quantum	NOUN
ejpam-6607	534	3	-	-	PUNCT
ejpam-6607	534	4	hypersoft	hypersoft	NOUN
ejpam-6607	534	5	set	set	VERB
ejpam-6607	534	6	classical	classical	ADJ
ejpam-6607	534	7	hypersoft	hypersoft	NOUN
ejpam-6607	534	8	set	set	VERB
ejpam-6607	534	9	g	g	NOUN
ejpam-6607	534	10	:	:	PUNCT
ejpam-6607	534	11	c	c	NOUN
ejpam-6607	534	12	→	→	SYM
ejpam-6607	534	13	p(u	p(u	ADJ
ejpam-6607	534	14	)	)	PUNCT
ejpam-6607	534	15	,	,	PUNCT
ejpam-6607	534	16	universe	universe	NOUN
ejpam-6607	534	17	u	u	NOUN
ejpam-6607	534	18	=	=	SYM
ejpam-6607	534	19	{	{	PUNCT
ejpam-6607	534	20	u1	u1	NOUN
ejpam-6607	534	21	,	,	PUNCT
ejpam-6607	534	22	.	.	PUNCT
ejpam-6607	534	23	.	.	PUNCT
ejpam-6607	535	1	.	.	PUNCT
ejpam-6607	536	1	,	,	PUNCT
ejpam-6607	536	2	un	un	PROPN
ejpam-6607	536	3	}	}	PUNCT
ejpam-6607	536	4	.	.	PUNCT
ejpam-6607	537	1	quantum	quantum	PROPN
ejpam-6607	537	2	-	-	PUNCT
ejpam-6607	537	3	hypersoft	hypersoft	NOUN
ejpam-6607	537	4	set	set	VERB
ejpam-6607	537	5	q	q	NOUN
ejpam-6607	537	6	:	:	PUNCT
ejpam-6607	537	7	c	c	PROPN
ejpam-6607	537	8	→	→	SYM
ejpam-6607	537	9	h(u	h(u	PROPN
ejpam-6607	537	10	)	)	PUNCT
ejpam-6607	537	11	.	.	PUNCT
ejpam-6607	538	1	γ	γ	PROPN
ejpam-6607	538	2	∈	∈	PROPN
ejpam-6607	538	3	c	c	PROPN
ejpam-6607	538	4	s	s	PART
ejpam-6607	538	5	←	←	PROPN
ejpam-6607	538	6	g(γ	g(γ	PROPN
ejpam-6607	538	7	)	)	PUNCT
ejpam-6607	539	1	k	k	PROPN
ejpam-6607	539	2	←	←	PROPN
ejpam-6607	539	3	|s|	|s|	PROPN
ejpam-6607	539	4	i	i	PROPN
ejpam-6607	539	5	←	←	PROPN
ejpam-6607	539	6	1	1	NUM
ejpam-6607	539	7	n	n	NUM
ejpam-6607	539	8	ui	ui	NOUN
ejpam-6607	539	9	∈	∈	PROPN
ejpam-6607	539	10	s	s	VERB
ejpam-6607	539	11	αi	αi	NOUN
ejpam-6607	539	12	,	,	PUNCT
ejpam-6607	539	13	γ	γ	PROPN
ejpam-6607	539	14	←	←	PROPN
ejpam-6607	539	15	1/	1/	NUM
ejpam-6607	539	16	√	√	PROPN
ejpam-6607	539	17	k	k	PROPN
ejpam-6607	539	18	αi	αi	PROPN
ejpam-6607	539	19	,	,	PUNCT
ejpam-6607	539	20	γ	γ	PROPN
ejpam-6607	539	21	←	←	PROPN
ejpam-6607	539	22	0	0	NUM
ejpam-6607	540	1	|ψγ⟩	|ψγ⟩	PROPN
ejpam-6607	540	2	←	←	PROPN
ejpam-6607	541	1	n∑	n∑	PROPN
ejpam-6607	541	2	i=1	i=1	PROPN
ejpam-6607	541	3	αi	αi	PROPN
ejpam-6607	541	4	,	,	PUNCT
ejpam-6607	541	5	γ	γ	X
ejpam-6607	541	6	|ui⟩	|ui⟩	PROPN
ejpam-6607	541	7	q(γ)←	q(γ)←	PROPN
ejpam-6607	541	8	|ψγ⟩	|ψγ⟩	PROPN
ejpam-6607	541	9	q	q	PROPN
ejpam-6607	541	10	example	example	NOUN
ejpam-6607	541	11	14	14	NUM
ejpam-6607	541	12	(	(	PUNCT
ejpam-6607	541	13	quantum	quantum	NOUN
ejpam-6607	541	14	-	-	PUNCT
ejpam-6607	541	15	hypersoft	hypersoft	NOUN
ejpam-6607	541	16	set	set	NOUN
ejpam-6607	541	17	for	for	ADP
ejpam-6607	541	18	quantum	quantum	ADJ
ejpam-6607	541	19	algorithm	algorithm	NOUN
ejpam-6607	541	20	selection	selection	NOUN
ejpam-6607	541	21	)	)	PUNCT
ejpam-6607	541	22	.	.	PUNCT
ejpam-6607	542	1	consider	consider	VERB
ejpam-6607	542	2	the	the	DET
ejpam-6607	542	3	problem	problem	NOUN
ejpam-6607	542	4	of	of	ADP
ejpam-6607	542	5	choosing	choose	VERB
ejpam-6607	542	6	among	among	ADP
ejpam-6607	542	7	three	three	NUM
ejpam-6607	542	8	quantum	quantum	ADJ
ejpam-6607	542	9	algorithms	algorithm	NOUN
ejpam-6607	542	10	u	u	NOUN
ejpam-6607	542	11	=	=	PUNCT
ejpam-6607	542	12	{	{	PUNCT
ejpam-6607	542	13	grover	grover	NOUN
ejpam-6607	542	14	,	,	PUNCT
ejpam-6607	542	15	qaoa	qaoa	PROPN
ejpam-6607	542	16	,	,	PUNCT
ejpam-6607	542	17	vqe	vqe	PROPN
ejpam-6607	542	18	}	}	PUNCT
ejpam-6607	542	19	based	base	VERB
ejpam-6607	542	20	on	on	ADP
ejpam-6607	542	21	hardware	hardware	NOUN
ejpam-6607	542	22	and	and	CCONJ
ejpam-6607	542	23	noise	noise	NOUN
ejpam-6607	542	24	characteristics	characteristic	NOUN
ejpam-6607	542	25	.	.	PUNCT
ejpam-6607	543	1	define	define	VERB
ejpam-6607	543	2	three	three	NUM
ejpam-6607	543	3	attribute	attribute	NOUN
ejpam-6607	543	4	domains	domain	NOUN
ejpam-6607	543	5	:	:	PUNCT
ejpam-6607	543	6	a1	a1	NOUN
ejpam-6607	543	7	=	=	SYM
ejpam-6607	543	8	{	{	PUNCT
ejpam-6607	543	9	ibm	ibm	PROPN
ejpam-6607	543	10	,	,	PUNCT
ejpam-6607	543	11	ionq	ionq	PROPN
ejpam-6607	543	12	}	}	PUNCT
ejpam-6607	543	13	,	,	PUNCT
ejpam-6607	543	14	a2	a2	PROPN
ejpam-6607	543	15	=	=	PUNCT
ejpam-6607	543	16	{	{	PUNCT
ejpam-6607	543	17	alltoall	alltoall	NOUN
ejpam-6607	543	18	,	,	PUNCT
ejpam-6607	543	19	linear	linear	ADJ
ejpam-6607	543	20	}	}	PUNCT
ejpam-6607	543	21	,	,	PUNCT
ejpam-6607	543	22	a3	a3	NOUN
ejpam-6607	543	23	=	=	SYM
ejpam-6607	543	24	{	{	PUNCT
ejpam-6607	543	25	lownoise	lownoise	ADJ
ejpam-6607	543	26	,	,	PUNCT
ejpam-6607	543	27	highnoise	highnoise	PROPN
ejpam-6607	543	28	}	}	PUNCT
ejpam-6607	543	29	.	.	PUNCT
ejpam-6607	544	1	form	form	VERB
ejpam-6607	544	2	the	the	DET
ejpam-6607	544	3	cartesian	cartesian	ADJ
ejpam-6607	544	4	product	product	NOUN
ejpam-6607	544	5	c	c	NOUN
ejpam-6607	544	6	=	=	PUNCT
ejpam-6607	544	7	a1×a2×a3	a1×a2×a3	PROPN
ejpam-6607	544	8	.	.	PUNCT
ejpam-6607	545	1	let	let	VERB
ejpam-6607	545	2	g	g	NOUN
ejpam-6607	545	3	:	:	PUNCT
ejpam-6607	545	4	c	c	X
ejpam-6607	545	5	→	→	SYM
ejpam-6607	545	6	p(u	p(u	CCONJ
ejpam-6607	545	7	)	)	PUNCT
ejpam-6607	545	8	be	be	VERB
ejpam-6607	545	9	the	the	DET
ejpam-6607	545	10	classical	classical	ADJ
ejpam-6607	545	11	hypersoft	hypersoft	NOUN
ejpam-6607	545	12	set	set	NOUN
ejpam-6607	545	13	defined	define	VERB
ejpam-6607	545	14	by	by	ADP
ejpam-6607	545	15	:	:	PUNCT
ejpam-6607	545	16	g	g	PROPN
ejpam-6607	545	17	(	(	PUNCT
ejpam-6607	545	18	(	(	PUNCT
ejpam-6607	545	19	ibm	ibm	PROPN
ejpam-6607	545	20	,	,	PUNCT
ejpam-6607	545	21	alltoall	alltoall	NOUN
ejpam-6607	545	22	,	,	PUNCT
ejpam-6607	545	23	lownoise	lownoise	ADJ
ejpam-6607	545	24	)	)	PUNCT
ejpam-6607	545	25	)	)	PUNCT
ejpam-6607	546	1	=	=	PRON
ejpam-6607	546	2	{	{	PUNCT
ejpam-6607	546	3	qaoa	qaoa	PROPN
ejpam-6607	546	4	,	,	PUNCT
ejpam-6607	546	5	vqe	vqe	PROPN
ejpam-6607	546	6	}	}	PUNCT
ejpam-6607	546	7	,	,	PUNCT
ejpam-6607	546	8	g	g	PROPN
ejpam-6607	546	9	(	(	PUNCT
ejpam-6607	546	10	(	(	PUNCT
ejpam-6607	546	11	ibm	ibm	PROPN
ejpam-6607	546	12	,	,	PUNCT
ejpam-6607	546	13	linear	linear	ADJ
ejpam-6607	546	14	,	,	PUNCT
ejpam-6607	546	15	highnoise	highnoise	NOUN
ejpam-6607	546	16	)	)	PUNCT
ejpam-6607	546	17	)	)	PUNCT
ejpam-6607	547	1	=	=	PRON
ejpam-6607	547	2	{	{	PUNCT
ejpam-6607	547	3	vqe	vqe	PROPN
ejpam-6607	547	4	}	}	PUNCT
ejpam-6607	547	5	,	,	PUNCT
ejpam-6607	547	6	g	g	PROPN
ejpam-6607	547	7	(	(	PUNCT
ejpam-6607	547	8	(	(	PUNCT
ejpam-6607	547	9	ionq	ionq	ADJ
ejpam-6607	547	10	,	,	PUNCT
ejpam-6607	547	11	alltoall	alltoall	ADV
ejpam-6607	547	12	,	,	PUNCT
ejpam-6607	547	13	highnoise	highnoise	NOUN
ejpam-6607	547	14	)	)	PUNCT
ejpam-6607	547	15	)	)	PUNCT
ejpam-6607	548	1	=	=	PRON
ejpam-6607	548	2	{	{	PUNCT
ejpam-6607	548	3	grover	grover	NOUN
ejpam-6607	548	4	,	,	PUNCT
ejpam-6607	548	5	vqe	vqe	PROPN
ejpam-6607	548	6	}	}	PUNCT
ejpam-6607	548	7	,	,	PUNCT
ejpam-6607	548	8	g	g	PROPN
ejpam-6607	548	9	(	(	PUNCT
ejpam-6607	548	10	(	(	PUNCT
ejpam-6607	548	11	ionq	ionq	ADJ
ejpam-6607	548	12	,	,	PUNCT
ejpam-6607	548	13	linear	linear	ADJ
ejpam-6607	548	14	,	,	PUNCT
ejpam-6607	548	15	lownoise	lownoise	ADJ
ejpam-6607	548	16	)	)	PUNCT
ejpam-6607	548	17	)	)	PUNCT
ejpam-6607	549	1	=	=	PRON
ejpam-6607	549	2	{	{	PUNCT
ejpam-6607	549	3	qaoa	qaoa	PROPN
ejpam-6607	549	4	}	}	PUNCT
ejpam-6607	549	5	.	.	PUNCT
ejpam-6607	550	1	t.	t.	PROPN
ejpam-6607	550	2	fujita	fujita	PROPN
ejpam-6607	550	3	,	,	PUNCT
ejpam-6607	550	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	550	5	/	/	SYM
ejpam-6607	550	6	eur	eur	PROPN
ejpam-6607	550	7	.	.	PUNCT
ejpam-6607	551	1	j.	j.	PROPN
ejpam-6607	551	2	pure	pure	PROPN
ejpam-6607	551	3	appl	appl	PROPN
ejpam-6607	551	4	.	.	PROPN
ejpam-6607	551	5	math	math	PROPN
ejpam-6607	551	6	,	,	PUNCT
ejpam-6607	551	7	18	18	NUM
ejpam-6607	551	8	(	(	PUNCT
ejpam-6607	551	9	3	3	NUM
ejpam-6607	551	10	)	)	PUNCT
ejpam-6607	551	11	(	(	PUNCT
ejpam-6607	551	12	2025	2025	NUM
ejpam-6607	551	13	)	)	PUNCT
ejpam-6607	551	14	,	,	PUNCT
ejpam-6607	551	15	6607	6607	NUM
ejpam-6607	551	16	26	26	NUM
ejpam-6607	551	17	of	of	ADP
ejpam-6607	551	18	33	33	NUM
ejpam-6607	551	19	applying	apply	VERB
ejpam-6607	551	20	algorithm	algorithm	NOUN
ejpam-6607	551	21	1	1	NUM
ejpam-6607	551	22	to	to	ADP
ejpam-6607	551	23	g	g	PROPN
ejpam-6607	551	24	yields	yield	NOUN
ejpam-6607	551	25	the	the	DET
ejpam-6607	551	26	quantum	quantum	NOUN
ejpam-6607	551	27	-	-	PUNCT
ejpam-6607	551	28	hypersoft	hypersoft	NOUN
ejpam-6607	551	29	set	set	VERB
ejpam-6607	551	30	q	q	NOUN
ejpam-6607	551	31	:	:	PUNCT
ejpam-6607	551	32	c	c	PROPN
ejpam-6607	551	33	→	→	SYM
ejpam-6607	551	34	h(u	h(u	PROPN
ejpam-6607	551	35	)	)	PUNCT
ejpam-6607	551	36	.	.	PUNCT
ejpam-6607	552	1	for	for	ADP
ejpam-6607	552	2	example	example	NOUN
ejpam-6607	552	3	:	:	PUNCT
ejpam-6607	552	4	|ψ(ibm	|ψ(ibm	NUM
ejpam-6607	552	5	,	,	PUNCT
ejpam-6607	552	6	alltoall	alltoall	ADV
ejpam-6607	552	7	,	,	PUNCT
ejpam-6607	552	8	lownoise)⟩	lownoise)⟩	NOUN
ejpam-6607	552	9	=	=	SYM
ejpam-6607	552	10	1√	1√	PROPN
ejpam-6607	552	11	2	2	NUM
ejpam-6607	552	12	|qaoa⟩+	|qaoa⟩+	ADP
ejpam-6607	552	13	1√	1√	PROPN
ejpam-6607	552	14	2	2	NUM
ejpam-6607	552	15	|vqe⟩	|vqe⟩	PROPN
ejpam-6607	552	16	,	,	PUNCT
ejpam-6607	552	17	|ψ(ibm	|ψ(ibm	NUM
ejpam-6607	552	18	,	,	PUNCT
ejpam-6607	552	19	linear	linear	NOUN
ejpam-6607	552	20	,	,	PUNCT
ejpam-6607	552	21	highnoise)⟩	highnoise)⟩	NOUN
ejpam-6607	552	22	=	=	SYM
ejpam-6607	552	23	1	1	NUM
ejpam-6607	552	24	·	·	PUNCT
ejpam-6607	552	25	|vqe⟩	|vqe⟩	NUM
ejpam-6607	552	26	,	,	PUNCT
ejpam-6607	552	27	|ψ(ionq	|ψ(ionq	PROPN
ejpam-6607	552	28	,	,	PUNCT
ejpam-6607	552	29	alltoall	alltoall	ADV
ejpam-6607	552	30	,	,	PUNCT
ejpam-6607	552	31	highnoise)⟩	highnoise)⟩	NOUN
ejpam-6607	552	32	=	=	SYM
ejpam-6607	552	33	1√	1√	PROPN
ejpam-6607	552	34	2	2	NUM
ejpam-6607	552	35	|grover⟩+	|grover⟩+	NOUN
ejpam-6607	552	36	1√	1√	PROPN
ejpam-6607	552	37	2	2	NUM
ejpam-6607	552	38	|vqe⟩	|vqe⟩	PROPN
ejpam-6607	552	39	,	,	PUNCT
ejpam-6607	552	40	|ψ(ionq	|ψ(ionq	PROPN
ejpam-6607	552	41	,	,	PUNCT
ejpam-6607	552	42	linear	linear	NOUN
ejpam-6607	552	43	,	,	PUNCT
ejpam-6607	552	44	lownoise)⟩	lownoise)⟩	NOUN
ejpam-6607	552	45	=	=	SYM
ejpam-6607	552	46	1	1	NUM
ejpam-6607	552	47	·	·	PUNCT
ejpam-6607	552	48	|qaoa⟩	|qaoa⟩	PROPN
ejpam-6607	552	49	.	.	PUNCT
ejpam-6607	553	1	each	each	DET
ejpam-6607	553	2	state	state	NOUN
ejpam-6607	553	3	is	be	AUX
ejpam-6607	553	4	normalized	normalize	VERB
ejpam-6607	553	5	,	,	PUNCT
ejpam-6607	553	6	and	and	CCONJ
ejpam-6607	553	7	measuring	measure	VERB
ejpam-6607	553	8	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	553	9	in	in	ADP
ejpam-6607	553	10	the	the	DET
ejpam-6607	553	11	basis	basis	NOUN
ejpam-6607	553	12	{	{	PUNCT
ejpam-6607	553	13	|grover⟩	|grover⟩	NOUN
ejpam-6607	553	14	,	,	PUNCT
ejpam-6607	553	15	|qaoa⟩	|qaoa⟩	NOUN
ejpam-6607	553	16	,	,	PUNCT
ejpam-6607	553	17	|vqe⟩	|vqe⟩	ADP
ejpam-6607	553	18	}	}	PUNCT
ejpam-6607	553	19	yields	yield	NOUN
ejpam-6607	553	20	the	the	DET
ejpam-6607	553	21	recommended	recommend	VERB
ejpam-6607	553	22	algorithm	algorithm	NOUN
ejpam-6607	553	23	with	with	ADP
ejpam-6607	553	24	the	the	DET
ejpam-6607	553	25	appropriate	appropriate	ADJ
ejpam-6607	553	26	probabilities	probability	NOUN
ejpam-6607	553	27	.	.	PUNCT
ejpam-6607	554	1	algorithm	algorithm	NOUN
ejpam-6607	554	2	2	2	NUM
ejpam-6607	554	3	(	(	PUNCT
ejpam-6607	554	4	ht	ht	PROPN
ejpam-6607	554	5	)	)	PUNCT
ejpam-6607	554	6	.	.	PUNCT
ejpam-6607	555	1	construct	construct	VERB
ejpam-6607	555	2	quantum	quantum	NOUN
ejpam-6607	555	3	-	-	PUNCT
ejpam-6607	555	4	superhypersoft	superhypersoft	NOUN
ejpam-6607	555	5	set	set	VERB
ejpam-6607	555	6	classical	classical	ADJ
ejpam-6607	555	7	superhypersoft	superhypersoft	NOUN
ejpam-6607	555	8	set	set	VERB
ejpam-6607	555	9	f	f	PROPN
ejpam-6607	555	10	:	:	PUNCT
ejpam-6607	555	11	c	c	X
ejpam-6607	555	12	→	→	SYM
ejpam-6607	555	13	p(u	p(u	ADJ
ejpam-6607	555	14	)	)	PUNCT
ejpam-6607	555	15	,	,	PUNCT
ejpam-6607	555	16	universe	universe	NOUN
ejpam-6607	555	17	u	u	NOUN
ejpam-6607	555	18	=	=	SYM
ejpam-6607	555	19	{	{	PUNCT
ejpam-6607	555	20	u1	u1	NOUN
ejpam-6607	555	21	,	,	PUNCT
ejpam-6607	555	22	.	.	PUNCT
ejpam-6607	555	23	.	.	PUNCT
ejpam-6607	556	1	.	.	PUNCT
ejpam-6607	557	1	,	,	PUNCT
ejpam-6607	557	2	un	un	PROPN
ejpam-6607	557	3	}	}	PUNCT
ejpam-6607	557	4	.	.	PUNCT
ejpam-6607	558	1	quantum	quantum	PROPN
ejpam-6607	558	2	-	-	PUNCT
ejpam-6607	558	3	superhypersoft	superhypersoft	NOUN
ejpam-6607	558	4	set	set	VERB
ejpam-6607	558	5	q	q	NOUN
ejpam-6607	558	6	:	:	PUNCT
ejpam-6607	558	7	c	c	PROPN
ejpam-6607	558	8	→	→	SYM
ejpam-6607	558	9	h(u	h(u	PROPN
ejpam-6607	558	10	)	)	PUNCT
ejpam-6607	558	11	.	.	PUNCT
ejpam-6607	559	1	γ	γ	PROPN
ejpam-6607	559	2	∈	∈	PROPN
ejpam-6607	559	3	c	c	PROPN
ejpam-6607	559	4	s	s	PROPN
ejpam-6607	559	5	←	←	PROPN
ejpam-6607	559	6	f	f	PROPN
ejpam-6607	559	7	(	(	PUNCT
ejpam-6607	559	8	γ	γ	PROPN
ejpam-6607	559	9	)	)	PUNCT
ejpam-6607	559	10	k	k	PROPN
ejpam-6607	559	11	←	←	PROPN
ejpam-6607	559	12	|s|	|s|	PROPN
ejpam-6607	559	13	i←	i←	PROPN
ejpam-6607	559	14	1	1	NUM
ejpam-6607	559	15	n	n	DET
ejpam-6607	559	16	ui	ui	NOUN
ejpam-6607	559	17	∈	∈	PROPN
ejpam-6607	559	18	s	s	VERB
ejpam-6607	559	19	αi	αi	NOUN
ejpam-6607	559	20	,	,	PUNCT
ejpam-6607	559	21	γ	γ	PROPN
ejpam-6607	559	22	←	←	PROPN
ejpam-6607	559	23	1/	1/	NUM
ejpam-6607	559	24	√	√	PROPN
ejpam-6607	559	25	k	k	PROPN
ejpam-6607	559	26	αi	αi	PROPN
ejpam-6607	559	27	,	,	PUNCT
ejpam-6607	559	28	γ	γ	PROPN
ejpam-6607	559	29	←	←	PROPN
ejpam-6607	559	30	0	0	NUM
ejpam-6607	559	31	|ψγ⟩	|ψγ⟩	PROPN
ejpam-6607	559	32	←	←	PROPN
ejpam-6607	559	33	n∑	n∑	PROPN
ejpam-6607	559	34	i=1	i=1	PROPN
ejpam-6607	559	35	αi	αi	PROPN
ejpam-6607	559	36	,	,	PUNCT
ejpam-6607	559	37	γ	γ	X
ejpam-6607	559	38	|ui⟩	|ui⟩	PROPN
ejpam-6607	559	39	q(γ)←	q(γ)←	PROPN
ejpam-6607	559	40	|ψγ⟩	|ψγ⟩	PROPN
ejpam-6607	559	41	q	q	PROPN
ejpam-6607	559	42	example	example	NOUN
ejpam-6607	559	43	15	15	NUM
ejpam-6607	559	44	(	(	PUNCT
ejpam-6607	559	45	quantum	quantum	NOUN
ejpam-6607	559	46	–	–	PUNCT
ejpam-6607	559	47	superhypersoft	superhypersoft	NOUN
ejpam-6607	559	48	set	set	VERB
ejpam-6607	559	49	for	for	ADP
ejpam-6607	559	50	quantum	quantum	ADJ
ejpam-6607	559	51	algorithm	algorithm	NOUN
ejpam-6607	559	52	deployment	deployment	NOUN
ejpam-6607	559	53	)	)	PUNCT
ejpam-6607	559	54	.	.	PUNCT
ejpam-6607	560	1	consider	consider	VERB
ejpam-6607	560	2	a	a	DET
ejpam-6607	560	3	pool	pool	NOUN
ejpam-6607	560	4	of	of	ADP
ejpam-6607	560	5	quantum	quantum	ADJ
ejpam-6607	560	6	algorithms	algorithm	NOUN
ejpam-6607	560	7	u	u	NOUN
ejpam-6607	560	8	=	=	PUNCT
ejpam-6607	560	9	{	{	PUNCT
ejpam-6607	560	10	grover	grover	NOUN
ejpam-6607	560	11	,	,	PUNCT
ejpam-6607	560	12	qaoa	qaoa	PROPN
ejpam-6607	560	13	,	,	PUNCT
ejpam-6607	560	14	vqe	vqe	PROPN
ejpam-6607	560	15	}	}	PUNCT
ejpam-6607	560	16	.	.	PUNCT
ejpam-6607	561	1	suppose	suppose	VERB
ejpam-6607	561	2	we	we	PRON
ejpam-6607	561	3	have	have	VERB
ejpam-6607	561	4	three	three	NUM
ejpam-6607	561	5	attribute	attribute	NOUN
ejpam-6607	561	6	domains	domain	NOUN
ejpam-6607	561	7	with	with	ADP
ejpam-6607	561	8	disjoint	disjoint	NOUN
ejpam-6607	561	9	value	value	NOUN
ejpam-6607	561	10	-	-	PUNCT
ejpam-6607	561	11	sets	set	NOUN
ejpam-6607	561	12	:	:	PUNCT
ejpam-6607	561	13	a1	a1	NOUN
ejpam-6607	561	14	=	=	SYM
ejpam-6607	561	15	{	{	PUNCT
ejpam-6607	561	16	ibm	ibm	PROPN
ejpam-6607	561	17	,	,	PUNCT
ejpam-6607	561	18	ionq	ionq	PROPN
ejpam-6607	561	19	,	,	PUNCT
ejpam-6607	561	20	rigetti	rigetti	NOUN
ejpam-6607	561	21	}	}	PUNCT
ejpam-6607	561	22	,	,	PUNCT
ejpam-6607	561	23	a2	a2	PROPN
ejpam-6607	561	24	=	=	PUNCT
ejpam-6607	561	25	{	{	PUNCT
ejpam-6607	561	26	alltoall	alltoall	NOUN
ejpam-6607	561	27	,	,	PUNCT
ejpam-6607	561	28	linear	linear	ADJ
ejpam-6607	561	29	}	}	PUNCT
ejpam-6607	561	30	,	,	PUNCT
ejpam-6607	561	31	a3	a3	NOUN
ejpam-6607	561	32	=	=	SYM
ejpam-6607	561	33	{	{	PUNCT
ejpam-6607	561	34	lownoise	lownoise	ADJ
ejpam-6607	561	35	,	,	PUNCT
ejpam-6607	561	36	highnoise	highnoise	PROPN
ejpam-6607	561	37	}	}	PUNCT
ejpam-6607	561	38	.	.	PUNCT
ejpam-6607	562	1	form	form	VERB
ejpam-6607	562	2	the	the	DET
ejpam-6607	562	3	cartesian	cartesian	ADJ
ejpam-6607	562	4	product	product	NOUN
ejpam-6607	562	5	of	of	ADP
ejpam-6607	562	6	power	power	NOUN
ejpam-6607	562	7	-	-	PUNCT
ejpam-6607	562	8	sets	set	NOUN
ejpam-6607	562	9	:	:	PUNCT
ejpam-6607	562	10	c	c	NOUN
ejpam-6607	562	11	=	=	SYM
ejpam-6607	562	12	p(a1)×	p(a1)×	PROPN
ejpam-6607	562	13	p(a2)×	p(a2)×	NOUN
ejpam-6607	562	14	p(a3	p(a3	NOUN
ejpam-6607	562	15	)	)	PUNCT
ejpam-6607	562	16	.	.	PUNCT
ejpam-6607	563	1	define	define	VERB
ejpam-6607	563	2	the	the	DET
ejpam-6607	563	3	classical	classical	ADJ
ejpam-6607	563	4	superhypersoft	superhypersoft	NOUN
ejpam-6607	563	5	set	set	VERB
ejpam-6607	563	6	f	f	PROPN
ejpam-6607	563	7	:	:	PUNCT
ejpam-6607	563	8	c	c	X
ejpam-6607	563	9	→	→	SYM
ejpam-6607	563	10	p(u	p(u	ADJ
ejpam-6607	563	11	)	)	PUNCT
ejpam-6607	563	12	by	by	ADP
ejpam-6607	563	13	:	:	PUNCT
ejpam-6607	563	14	f	f	X
ejpam-6607	563	15	(	(	PUNCT
ejpam-6607	563	16	{	{	PUNCT
ejpam-6607	563	17	ibm	ibm	PROPN
ejpam-6607	563	18	,	,	PUNCT
ejpam-6607	563	19	rigetti	rigetti	NOUN
ejpam-6607	563	20	}	}	PUNCT
ejpam-6607	563	21	,	,	PUNCT
ejpam-6607	563	22	{	{	PUNCT
ejpam-6607	563	23	alltoall	alltoall	ADV
ejpam-6607	563	24	,	,	PUNCT
ejpam-6607	563	25	linear	linear	PROPN
ejpam-6607	563	26	}	}	PUNCT
ejpam-6607	563	27	,	,	PUNCT
ejpam-6607	563	28	{	{	PUNCT
ejpam-6607	563	29	lownoise	lownoise	ADJ
ejpam-6607	563	30	}	}	PUNCT
ejpam-6607	563	31	)	)	PUNCT
ejpam-6607	564	1	=	=	PRON
ejpam-6607	564	2	{	{	PUNCT
ejpam-6607	564	3	qaoa	qaoa	PROPN
ejpam-6607	564	4	,	,	PUNCT
ejpam-6607	564	5	vqe	vqe	PROPN
ejpam-6607	564	6	}	}	PUNCT
ejpam-6607	564	7	,	,	PUNCT
ejpam-6607	564	8	f	f	PROPN
ejpam-6607	564	9	(	(	PUNCT
ejpam-6607	564	10	{	{	PUNCT
ejpam-6607	564	11	ionq	ionq	PROPN
ejpam-6607	564	12	}	}	PUNCT
ejpam-6607	564	13	,	,	PUNCT
ejpam-6607	564	14	{	{	PUNCT
ejpam-6607	564	15	alltoall	alltoall	NOUN
ejpam-6607	564	16	}	}	PUNCT
ejpam-6607	564	17	,	,	PUNCT
ejpam-6607	564	18	{	{	PUNCT
ejpam-6607	564	19	highnoise	highnoise	NOUN
ejpam-6607	564	20	}	}	PUNCT
ejpam-6607	564	21	)	)	PUNCT
ejpam-6607	565	1	=	=	PRON
ejpam-6607	565	2	{	{	PUNCT
ejpam-6607	565	3	grover	grover	NOUN
ejpam-6607	565	4	,	,	PUNCT
ejpam-6607	565	5	vqe	vqe	PROPN
ejpam-6607	565	6	}	}	PUNCT
ejpam-6607	565	7	,	,	PUNCT
ejpam-6607	565	8	f	f	PROPN
ejpam-6607	565	9	(	(	PUNCT
ejpam-6607	565	10	{	{	PUNCT
ejpam-6607	565	11	ibm	ibm	PROPN
ejpam-6607	565	12	,	,	PUNCT
ejpam-6607	565	13	ionq	ionq	PROPN
ejpam-6607	565	14	}	}	PUNCT
ejpam-6607	565	15	,	,	PUNCT
ejpam-6607	565	16	{	{	PUNCT
ejpam-6607	565	17	linear	linear	NOUN
ejpam-6607	565	18	}	}	PUNCT
ejpam-6607	565	19	,	,	PUNCT
ejpam-6607	565	20	{	{	PUNCT
ejpam-6607	565	21	lownoise	lownoise	ADJ
ejpam-6607	565	22	,	,	PUNCT
ejpam-6607	565	23	highnoise	highnoise	NOUN
ejpam-6607	565	24	}	}	PUNCT
ejpam-6607	565	25	)	)	PUNCT
ejpam-6607	565	26	=	=	PRON
ejpam-6607	565	27	{	{	PUNCT
ejpam-6607	565	28	grover	grover	NOUN
ejpam-6607	565	29	,	,	PUNCT
ejpam-6607	565	30	qaoa	qaoa	PROPN
ejpam-6607	565	31	}	}	PUNCT
ejpam-6607	565	32	.	.	PUNCT
ejpam-6607	566	1	applying	apply	VERB
ejpam-6607	566	2	algorithm	algorithm	NOUN
ejpam-6607	566	3	2	2	NUM
ejpam-6607	566	4	to	to	ADP
ejpam-6607	566	5	f	f	PROPN
ejpam-6607	566	6	yields	yield	VERB
ejpam-6607	566	7	the	the	DET
ejpam-6607	566	8	quantum	quantum	PROPN
ejpam-6607	566	9	–	–	PUNCT
ejpam-6607	566	10	superhypersoft	superhypersoft	NOUN
ejpam-6607	566	11	set	set	VERB
ejpam-6607	566	12	q	q	NOUN
ejpam-6607	566	13	:	:	PUNCT
ejpam-6607	566	14	c	c	PROPN
ejpam-6607	566	15	→	→	SYM
ejpam-6607	566	16	h(u	h(u	PROPN
ejpam-6607	566	17	)	)	PUNCT
ejpam-6607	566	18	.	.	PUNCT
ejpam-6607	567	1	for	for	ADP
ejpam-6607	567	2	example	example	NOUN
ejpam-6607	567	3	:	:	PUNCT
ejpam-6607	567	4	|ψ{ibm	|ψ{ibm	NOUN
ejpam-6607	567	5	,	,	PUNCT
ejpam-6607	567	6	rigetti},{alltoall	rigetti},{alltoall	NOUN
ejpam-6607	567	7	,	,	PUNCT
ejpam-6607	567	8	linear},{lownoise}⟩	linear},{lownoise}⟩	ADP
ejpam-6607	567	9	=	=	SYM
ejpam-6607	567	10	1√	1√	NUM
ejpam-6607	567	11	2	2	NUM
ejpam-6607	567	12	|qaoa⟩+	|qaoa⟩+	ADP
ejpam-6607	567	13	1√	1√	PROPN
ejpam-6607	567	14	2	2	NUM
ejpam-6607	567	15	|vqe⟩	|vqe⟩	PROPN
ejpam-6607	567	16	,	,	PUNCT
ejpam-6607	567	17	|ψ{ionq},{alltoall},{highnoise}⟩	|ψ{ionq},{alltoall},{highnoise}⟩	PROPN
ejpam-6607	567	18	=	=	SYM
ejpam-6607	567	19	1√	1√	NUM
ejpam-6607	567	20	2	2	NUM
ejpam-6607	567	21	|grover⟩+	|grover⟩+	NOUN
ejpam-6607	567	22	1√	1√	PROPN
ejpam-6607	567	23	2	2	NUM
ejpam-6607	567	24	|vqe⟩	|vqe⟩	PROPN
ejpam-6607	567	25	,	,	PUNCT
ejpam-6607	567	26	t.	t.	PROPN
ejpam-6607	567	27	fujita	fujita	PROPN
ejpam-6607	567	28	,	,	PUNCT
ejpam-6607	567	29	f.smarandache	f.smarandache	NOUN
ejpam-6607	567	30	/	/	SYM
ejpam-6607	567	31	eur	eur	PROPN
ejpam-6607	567	32	.	.	PUNCT
ejpam-6607	568	1	j.	j.	PROPN
ejpam-6607	568	2	pure	pure	PROPN
ejpam-6607	568	3	appl	appl	PROPN
ejpam-6607	568	4	.	.	PROPN
ejpam-6607	568	5	math	math	PROPN
ejpam-6607	568	6	,	,	PUNCT
ejpam-6607	568	7	18	18	NUM
ejpam-6607	568	8	(	(	PUNCT
ejpam-6607	568	9	3	3	NUM
ejpam-6607	568	10	)	)	PUNCT
ejpam-6607	568	11	(	(	PUNCT
ejpam-6607	568	12	2025	2025	NUM
ejpam-6607	568	13	)	)	PUNCT
ejpam-6607	568	14	,	,	PUNCT
ejpam-6607	568	15	6607	6607	NUM
ejpam-6607	568	16	27	27	NUM
ejpam-6607	568	17	of	of	ADP
ejpam-6607	568	18	33	33	NUM
ejpam-6607	568	19	|ψ{ibm	|ψ{ibm	PROPN
ejpam-6607	568	20	,	,	PUNCT
ejpam-6607	568	21	ionq},{linear},{lownoise	ionq},{linear},{lownoise	PRON
ejpam-6607	568	22	,	,	PUNCT
ejpam-6607	568	23	highnoise}⟩	highnoise}⟩	PROPN
ejpam-6607	568	24	=	=	SYM
ejpam-6607	568	25	1√	1√	NUM
ejpam-6607	568	26	2	2	NUM
ejpam-6607	568	27	|grover⟩+	|grover⟩+	NOUN
ejpam-6607	568	28	1√	1√	PROPN
ejpam-6607	568	29	2	2	NUM
ejpam-6607	568	30	|qaoa⟩	|qaoa⟩	NOUN
ejpam-6607	568	31	.	.	PUNCT
ejpam-6607	569	1	each	each	DET
ejpam-6607	569	2	state	state	NOUN
ejpam-6607	569	3	is	be	AUX
ejpam-6607	569	4	manifestly	manifestly	ADV
ejpam-6607	569	5	normalized	normalize	VERB
ejpam-6607	569	6	.	.	PUNCT
ejpam-6607	570	1	measuring	measure	VERB
ejpam-6607	570	2	any	any	DET
ejpam-6607	570	3	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	570	4	in	in	ADP
ejpam-6607	570	5	the	the	DET
ejpam-6607	570	6	computational	computational	ADJ
ejpam-6607	570	7	basis	basis	NOUN
ejpam-6607	570	8	{	{	PUNCT
ejpam-6607	570	9	|grover⟩	|grover⟩	NOUN
ejpam-6607	570	10	,	,	PUNCT
ejpam-6607	570	11	|qaoa⟩	|qaoa⟩	NOUN
ejpam-6607	570	12	,	,	PUNCT
ejpam-6607	570	13	|vqe⟩	|vqe⟩	ADP
ejpam-6607	570	14	}	}	PUNCT
ejpam-6607	570	15	yields	yield	VERB
ejpam-6607	570	16	a	a	DET
ejpam-6607	570	17	soft	soft	ADJ
ejpam-6607	570	18	ranking	ranking	NOUN
ejpam-6607	570	19	of	of	ADP
ejpam-6607	570	20	algorithms	algorithm	NOUN
ejpam-6607	570	21	adapted	adapt	VERB
ejpam-6607	570	22	to	to	ADP
ejpam-6607	570	23	multiple	multiple	ADJ
ejpam-6607	570	24	-	-	PUNCT
ejpam-6607	570	25	vendor	vendor	NOUN
ejpam-6607	570	26	,	,	PUNCT
ejpam-6607	570	27	connectivity	connectivity	NOUN
ejpam-6607	570	28	,	,	PUNCT
ejpam-6607	570	29	and	and	CCONJ
ejpam-6607	570	30	noise	noise	NOUN
ejpam-6607	570	31	-	-	PUNCT
ejpam-6607	570	32	level	level	NOUN
ejpam-6607	570	33	preferences	preference	NOUN
ejpam-6607	570	34	.	.	PUNCT
ejpam-6607	571	1	theorem	theorem	ADJ
ejpam-6607	571	2	19	19	NUM
ejpam-6607	571	3	(	(	PUNCT
ejpam-6607	571	4	correctness	correctness	NOUN
ejpam-6607	571	5	of	of	ADP
ejpam-6607	571	6	construct	construct	VERB
ejpam-6607	571	7	quantum	quantum	NOUN
ejpam-6607	571	8	-	-	PUNCT
ejpam-6607	571	9	hypersoft	hypersoft	NOUN
ejpam-6607	571	10	set	set	NOUN
ejpam-6607	571	11	)	)	PUNCT
ejpam-6607	571	12	.	.	PUNCT
ejpam-6607	572	1	let	let	VERB
ejpam-6607	572	2	g	g	NOUN
ejpam-6607	572	3	:	:	PUNCT
ejpam-6607	572	4	c	c	X
ejpam-6607	572	5	→	→	SYM
ejpam-6607	572	6	p(u	p(u	ADJ
ejpam-6607	572	7	)	)	PUNCT
ejpam-6607	572	8	be	be	VERB
ejpam-6607	572	9	any	any	DET
ejpam-6607	572	10	classical	classical	ADJ
ejpam-6607	572	11	hypersoft	hypersoft	NOUN
ejpam-6607	572	12	set	set	VERB
ejpam-6607	572	13	over	over	ADP
ejpam-6607	572	14	the	the	DET
ejpam-6607	572	15	finite	finite	ADJ
ejpam-6607	572	16	universe	universe	NOUN
ejpam-6607	572	17	u	u	NOUN
ejpam-6607	572	18	=	=	PUNCT
ejpam-6607	572	19	{	{	PUNCT
ejpam-6607	572	20	u1	u1	NOUN
ejpam-6607	572	21	,	,	PUNCT
ejpam-6607	572	22	.	.	PUNCT
ejpam-6607	572	23	.	.	PUNCT
ejpam-6607	573	1	.	.	PUNCT
ejpam-6607	574	1	,	,	PUNCT
ejpam-6607	574	2	un	un	PROPN
ejpam-6607	574	3	}	}	PUNCT
ejpam-6607	574	4	.	.	PUNCT
ejpam-6607	575	1	algorithm	algorithm	NOUN
ejpam-6607	575	2	1	1	NUM
ejpam-6607	575	3	produces	produce	VERB
ejpam-6607	575	4	a	a	DET
ejpam-6607	575	5	map	map	NOUN
ejpam-6607	575	6	q	q	NOUN
ejpam-6607	575	7	:	:	PUNCT
ejpam-6607	575	8	c	c	AUX
ejpam-6607	575	9	−→	−→	NOUN
ejpam-6607	575	10	h(u	h(u	PROPN
ejpam-6607	575	11	)	)	PUNCT
ejpam-6607	575	12	,	,	PUNCT
ejpam-6607	575	13	γ	γ	PROPN
ejpam-6607	575	14	7→	7→	NUM
ejpam-6607	575	15	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	575	16	such	such	ADJ
ejpam-6607	575	17	that	that	SCONJ
ejpam-6607	575	18	each	each	DET
ejpam-6607	575	19	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	575	20	is	be	AUX
ejpam-6607	575	21	a	a	DET
ejpam-6607	575	22	unit	unit	NOUN
ejpam-6607	575	23	vector	vector	NOUN
ejpam-6607	575	24	in	in	ADP
ejpam-6607	575	25	the	the	DET
ejpam-6607	575	26	hilbert	hilbert	NOUN
ejpam-6607	575	27	space	space	NOUN
ejpam-6607	575	28	h(u	h(u	PROPN
ejpam-6607	575	29	)	)	PUNCT
ejpam-6607	575	30	.	.	PUNCT
ejpam-6607	576	1	hence	hence	ADV
ejpam-6607	576	2	q	q	X
ejpam-6607	576	3	is	be	AUX
ejpam-6607	576	4	a	a	DET
ejpam-6607	576	5	valid	valid	ADJ
ejpam-6607	576	6	quantumhypersoft	quantumhypersoft	NOUN
ejpam-6607	576	7	set	set	NOUN
ejpam-6607	576	8	.	.	PUNCT
ejpam-6607	577	1	proof	proof	NOUN
ejpam-6607	577	2	.	.	PUNCT
ejpam-6607	578	1	fix	fix	VERB
ejpam-6607	578	2	an	an	DET
ejpam-6607	578	3	arbitrary	arbitrary	ADJ
ejpam-6607	578	4	γ	γ	X
ejpam-6607	578	5	∈	∈	PROPN
ejpam-6607	578	6	c	c	NOUN
ejpam-6607	578	7	and	and	CCONJ
ejpam-6607	578	8	let	let	VERB
ejpam-6607	578	9	s	s	PRON
ejpam-6607	578	10	=	=	VERB
ejpam-6607	578	11	g(γ	g(γ	PROPN
ejpam-6607	578	12	)	)	PUNCT
ejpam-6607	578	13	⊆	⊆	NUM
ejpam-6607	578	14	u	u	NOUN
ejpam-6607	578	15	with	with	ADP
ejpam-6607	578	16	|s|	|s|	PROPN
ejpam-6607	578	17	=	=	SYM
ejpam-6607	578	18	k.	k.	PROPN
ejpam-6607	578	19	in	in	ADP
ejpam-6607	578	20	the	the	DET
ejpam-6607	578	21	inner	inner	ADJ
ejpam-6607	578	22	loop	loop	NOUN
ejpam-6607	578	23	,	,	PUNCT
ejpam-6607	578	24	the	the	DET
ejpam-6607	578	25	algorithm	algorithm	NOUN
ejpam-6607	578	26	sets	set	VERB
ejpam-6607	578	27	αi	αi	NOUN
ejpam-6607	578	28	,	,	PUNCT
ejpam-6607	578	29	γ	γ	X
ejpam-6607	578	30	=	=	X
ejpam-6607	578	31	{	{	PUNCT
ejpam-6607	578	32	1/	1/	NUM
ejpam-6607	578	33	√	√	NUM
ejpam-6607	578	34	k	k	NOUN
ejpam-6607	578	35	,	,	PUNCT
ejpam-6607	578	36	if	if	SCONJ
ejpam-6607	578	37	ui	ui	PROPN
ejpam-6607	578	38	∈	∈	PROPN
ejpam-6607	578	39	s	s	PROPN
ejpam-6607	578	40	,	,	PUNCT
ejpam-6607	578	41	0	0	NUM
ejpam-6607	578	42	,	,	PUNCT
ejpam-6607	578	43	otherwise	otherwise	ADV
ejpam-6607	578	44	.	.	PUNCT
ejpam-6607	579	1	thus	thus	ADV
ejpam-6607	579	2	n∑	n∑	PROPN
ejpam-6607	579	3	i=1	i=1	PROPN
ejpam-6607	579	4	∣∣αi	∣∣αi	PROPN
ejpam-6607	579	5	,	,	PUNCT
ejpam-6607	579	6	γ	γ	PROPN
ejpam-6607	579	7	∣∣2	∣∣2	PROPN
ejpam-6607	579	8	=	=	SYM
ejpam-6607	579	9	∑	∑	PROPN
ejpam-6607	579	10	ui∈s	ui∈s	ADP
ejpam-6607	579	11	1	1	NUM
ejpam-6607	579	12	k	k	NOUN
ejpam-6607	579	13	=	=	SYM
ejpam-6607	580	1	k	k	PROPN
ejpam-6607	580	2	k	k	PROPN
ejpam-6607	580	3	=	=	PUNCT
ejpam-6607	580	4	1	1	X
ejpam-6607	580	5	.	.	PUNCT
ejpam-6607	580	6	by	by	ADP
ejpam-6607	580	7	construction	construction	NOUN
ejpam-6607	580	8	,	,	PUNCT
ejpam-6607	580	9	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	580	10	=	=	PUNCT
ejpam-6607	580	11	∑n	∑n	PROPN
ejpam-6607	580	12	i=1	i=1	PROPN
ejpam-6607	580	13	αi	αi	PROPN
ejpam-6607	580	14	,	,	PUNCT
ejpam-6607	580	15	γ	γ	PROPN
ejpam-6607	580	16	|ui⟩	|ui⟩	NOUN
ejpam-6607	580	17	is	be	AUX
ejpam-6607	580	18	normalized	normalize	VERB
ejpam-6607	580	19	.	.	PUNCT
ejpam-6607	581	1	since	since	SCONJ
ejpam-6607	581	2	this	this	PRON
ejpam-6607	581	3	holds	hold	VERB
ejpam-6607	581	4	for	for	ADP
ejpam-6607	581	5	every	every	DET
ejpam-6607	581	6	γ	γ	NOUN
ejpam-6607	581	7	,	,	PUNCT
ejpam-6607	581	8	the	the	DET
ejpam-6607	581	9	output	output	NOUN
ejpam-6607	581	10	map	map	NOUN
ejpam-6607	581	11	q	q	NOUN
ejpam-6607	581	12	satisfies	satisfy	VERB
ejpam-6607	581	13	the	the	DET
ejpam-6607	581	14	definition	definition	NOUN
ejpam-6607	581	15	of	of	ADP
ejpam-6607	581	16	a	a	DET
ejpam-6607	581	17	quantum	quantum	NOUN
ejpam-6607	581	18	-	-	PUNCT
ejpam-6607	581	19	hypersoft	hypersoft	NOUN
ejpam-6607	581	20	set	set	NOUN
ejpam-6607	581	21	.	.	PUNCT
ejpam-6607	582	1	theorem	theorem	VERB
ejpam-6607	582	2	20	20	NUM
ejpam-6607	582	3	(	(	PUNCT
ejpam-6607	582	4	correctness	correctness	NOUN
ejpam-6607	582	5	of	of	ADP
ejpam-6607	582	6	construct	construct	VERB
ejpam-6607	582	7	quantum	quantum	NOUN
ejpam-6607	582	8	-	-	PUNCT
ejpam-6607	582	9	superhypersoft	superhypersoft	NOUN
ejpam-6607	582	10	set	set	NOUN
ejpam-6607	582	11	)	)	PUNCT
ejpam-6607	582	12	.	.	PUNCT
ejpam-6607	583	1	let	let	VERB
ejpam-6607	583	2	f	f	NOUN
ejpam-6607	583	3	:	:	PUNCT
ejpam-6607	583	4	c	c	X
ejpam-6607	583	5	→	→	SYM
ejpam-6607	583	6	p(u	p(u	CCONJ
ejpam-6607	583	7	)	)	PUNCT
ejpam-6607	583	8	be	be	VERB
ejpam-6607	583	9	any	any	DET
ejpam-6607	583	10	classical	classical	ADJ
ejpam-6607	583	11	superhypersoft	superhypersoft	NOUN
ejpam-6607	583	12	set	set	VERB
ejpam-6607	583	13	over	over	ADP
ejpam-6607	583	14	u	u	NOUN
ejpam-6607	583	15	=	=	NOUN
ejpam-6607	583	16	{	{	PUNCT
ejpam-6607	583	17	u1	u1	NOUN
ejpam-6607	583	18	,	,	PUNCT
ejpam-6607	583	19	.	.	PUNCT
ejpam-6607	583	20	.	.	PUNCT
ejpam-6607	584	1	.	.	PUNCT
ejpam-6607	585	1	,	,	PUNCT
ejpam-6607	585	2	un	un	PROPN
ejpam-6607	585	3	}	}	PUNCT
ejpam-6607	585	4	.	.	PUNCT
ejpam-6607	586	1	algorithm	algorithm	NOUN
ejpam-6607	586	2	2	2	NUM
ejpam-6607	586	3	produces	produce	VERB
ejpam-6607	586	4	a	a	DET
ejpam-6607	586	5	map	map	NOUN
ejpam-6607	586	6	q	q	NOUN
ejpam-6607	586	7	:	:	PUNCT
ejpam-6607	586	8	c	c	AUX
ejpam-6607	586	9	−→	−→	NOUN
ejpam-6607	586	10	h(u	h(u	PROPN
ejpam-6607	586	11	)	)	PUNCT
ejpam-6607	586	12	,	,	PUNCT
ejpam-6607	586	13	γ	γ	PROPN
ejpam-6607	586	14	7→	7→	NUM
ejpam-6607	586	15	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	586	16	with	with	ADP
ejpam-6607	586	17	each	each	DET
ejpam-6607	586	18	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	586	19	normalized	normalize	VERB
ejpam-6607	586	20	,	,	PUNCT
ejpam-6607	586	21	so	so	ADV
ejpam-6607	586	22	q	q	X
ejpam-6607	586	23	is	be	AUX
ejpam-6607	586	24	a	a	DET
ejpam-6607	586	25	valid	valid	ADJ
ejpam-6607	586	26	quantum	quantum	NOUN
ejpam-6607	586	27	–	–	PUNCT
ejpam-6607	586	28	superhypersoft	superhypersoft	NOUN
ejpam-6607	586	29	set	set	NOUN
ejpam-6607	586	30	.	.	PUNCT
ejpam-6607	587	1	proof	proof	NOUN
ejpam-6607	587	2	.	.	PUNCT
ejpam-6607	588	1	identical	identical	ADJ
ejpam-6607	588	2	to	to	ADP
ejpam-6607	588	3	the	the	DET
ejpam-6607	588	4	proof	proof	NOUN
ejpam-6607	588	5	of	of	ADP
ejpam-6607	588	6	theorem	theorem	ADJ
ejpam-6607	588	7	19	19	NUM
ejpam-6607	588	8	,	,	PUNCT
ejpam-6607	588	9	replacing	replace	VERB
ejpam-6607	588	10	s	s	PART
ejpam-6607	588	11	=	=	ADJ
ejpam-6607	588	12	g(γ	g(γ	PROPN
ejpam-6607	588	13	)	)	PUNCT
ejpam-6607	588	14	by	by	ADP
ejpam-6607	588	15	s	s	NOUN
ejpam-6607	588	16	=	=	SYM
ejpam-6607	588	17	f	f	PROPN
ejpam-6607	588	18	(	(	PUNCT
ejpam-6607	588	19	γ	γ	PROPN
ejpam-6607	588	20	)	)	PUNCT
ejpam-6607	588	21	.	.	PUNCT
ejpam-6607	589	1	the	the	DET
ejpam-6607	589	2	same	same	ADJ
ejpam-6607	589	3	calculation	calculation	NOUN
ejpam-6607	589	4	shows	show	VERB
ejpam-6607	589	5	∑	∑	PROPN
ejpam-6607	589	6	i	i	PRON
ejpam-6607	589	7	|αi	|αi	NUM
ejpam-6607	589	8	,	,	PUNCT
ejpam-6607	589	9	γ	γ	X
ejpam-6607	589	10	|2	|2	X
ejpam-6607	589	11	=	=	SYM
ejpam-6607	589	12	1	1	NUM
ejpam-6607	589	13	and	and	CCONJ
ejpam-6607	589	14	hence	hence	ADV
ejpam-6607	589	15	each	each	DET
ejpam-6607	589	16	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	589	17	is	be	AUX
ejpam-6607	589	18	unit	unit	NOUN
ejpam-6607	589	19	-	-	PUNCT
ejpam-6607	589	20	norm	norm	NOUN
ejpam-6607	589	21	.	.	PUNCT
ejpam-6607	590	1	theorem	theorem	ADJ
ejpam-6607	590	2	21	21	NUM
ejpam-6607	590	3	(	(	PUNCT
ejpam-6607	590	4	time	time	NOUN
ejpam-6607	590	5	and	and	CCONJ
ejpam-6607	590	6	space	space	NOUN
ejpam-6607	590	7	complexity	complexity	NOUN
ejpam-6607	590	8	)	)	PUNCT
ejpam-6607	590	9	.	.	PUNCT
ejpam-6607	591	1	assume	assume	VERB
ejpam-6607	591	2	membership	membership	NOUN
ejpam-6607	591	3	in	in	ADP
ejpam-6607	591	4	each	each	DET
ejpam-6607	591	5	s	s	PART
ejpam-6607	591	6	=	=	SYM
ejpam-6607	591	7	g(γ	g(γ	PROPN
ejpam-6607	591	8	)	)	PUNCT
ejpam-6607	591	9	or	or	CCONJ
ejpam-6607	591	10	s	s	NOUN
ejpam-6607	591	11	=	=	SYM
ejpam-6607	591	12	f	f	PROPN
ejpam-6607	591	13	(	(	PUNCT
ejpam-6607	591	14	γ	γ	X
ejpam-6607	591	15	)	)	PUNCT
ejpam-6607	591	16	can	can	AUX
ejpam-6607	591	17	be	be	AUX
ejpam-6607	591	18	tested	test	VERB
ejpam-6607	591	19	in	in	ADP
ejpam-6607	591	20	o(1	o(1	NOUN
ejpam-6607	591	21	)	)	PUNCT
ejpam-6607	591	22	time	time	NOUN
ejpam-6607	591	23	(	(	PUNCT
ejpam-6607	591	24	e.g.	e.g.	ADV
ejpam-6607	591	25	using	use	VERB
ejpam-6607	591	26	a	a	DET
ejpam-6607	591	27	hash	hash	NOUN
ejpam-6607	591	28	set	set	NOUN
ejpam-6607	591	29	)	)	PUNCT
ejpam-6607	591	30	.	.	PUNCT
ejpam-6607	592	1	then	then	ADV
ejpam-6607	592	2	both	both	PRON
ejpam-6607	592	3	algorithm	algorithm	NOUN
ejpam-6607	592	4	1	1	NUM
ejpam-6607	592	5	and	and	CCONJ
ejpam-6607	592	6	algorithm	algorithm	PROPN
ejpam-6607	592	7	2	2	NUM
ejpam-6607	592	8	run	run	NOUN
ejpam-6607	592	9	in	in	ADP
ejpam-6607	592	10	o(|c|	o(|c|	PROPN
ejpam-6607	592	11	·	·	PUNCT
ejpam-6607	592	12	n	n	CCONJ
ejpam-6607	592	13	)	)	PUNCT
ejpam-6607	592	14	time	time	NOUN
ejpam-6607	592	15	and	and	CCONJ
ejpam-6607	592	16	use	use	VERB
ejpam-6607	592	17	o(n	o(n	PROPN
ejpam-6607	592	18	·	·	PUNCT
ejpam-6607	592	19	|c|	|c|	PROPN
ejpam-6607	592	20	)	)	PUNCT
ejpam-6607	592	21	space	space	NOUN
ejpam-6607	592	22	.	.	PUNCT
ejpam-6607	593	1	proof	proof	NOUN
ejpam-6607	593	2	.	.	PUNCT
ejpam-6607	594	1	let	let	VERB
ejpam-6607	594	2	|c|	|c|	PROPN
ejpam-6607	594	3	be	be	AUX
ejpam-6607	594	4	the	the	DET
ejpam-6607	594	5	number	number	NOUN
ejpam-6607	594	6	of	of	ADP
ejpam-6607	594	7	attribute	attribute	NOUN
ejpam-6607	594	8	combinations	combination	NOUN
ejpam-6607	594	9	and	and	CCONJ
ejpam-6607	594	10	n	n	CCONJ
ejpam-6607	594	11	=	=	PUNCT
ejpam-6607	594	12	|u	|u	ADJ
ejpam-6607	594	13	|	|	NOUN
ejpam-6607	594	14	.	.	PUNCT
ejpam-6607	595	1	for	for	ADP
ejpam-6607	595	2	each	each	DET
ejpam-6607	595	3	γ	γ	NOUN
ejpam-6607	595	4	,	,	PUNCT
ejpam-6607	595	5	the	the	DET
ejpam-6607	595	6	algorithm	algorithm	NOUN
ejpam-6607	595	7	:	:	PUNCT
ejpam-6607	595	8	(	(	PUNCT
ejpam-6607	595	9	i	i	NOUN
ejpam-6607	595	10	)	)	PUNCT
ejpam-6607	595	11	retrieves	retrieve	VERB
ejpam-6607	595	12	s	s	PROPN
ejpam-6607	595	13	⊆	⊆	NUM
ejpam-6607	595	14	u	u	NOUN
ejpam-6607	595	15	in	in	ADP
ejpam-6607	595	16	o(1	o(1	NOUN
ejpam-6607	595	17	)	)	PUNCT
ejpam-6607	595	18	.	.	PUNCT
ejpam-6607	596	1	(	(	PUNCT
ejpam-6607	596	2	ii	ii	NOUN
ejpam-6607	596	3	)	)	PUNCT
ejpam-6607	596	4	computes	compute	VERB
ejpam-6607	596	5	k	k	NOUN
ejpam-6607	596	6	=	=	PUNCT
ejpam-6607	596	7	|s|	|s|	PROPN
ejpam-6607	596	8	in	in	ADP
ejpam-6607	596	9	o(1	o(1	NOUN
ejpam-6607	596	10	)	)	PUNCT
ejpam-6607	596	11	.	.	PUNCT
ejpam-6607	597	1	t.	t.	PROPN
ejpam-6607	597	2	fujita	fujita	PROPN
ejpam-6607	597	3	,	,	PUNCT
ejpam-6607	597	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	597	5	/	/	SYM
ejpam-6607	597	6	eur	eur	PROPN
ejpam-6607	597	7	.	.	PUNCT
ejpam-6607	598	1	j.	j.	PROPN
ejpam-6607	598	2	pure	pure	PROPN
ejpam-6607	598	3	appl	appl	PROPN
ejpam-6607	598	4	.	.	PROPN
ejpam-6607	598	5	math	math	PROPN
ejpam-6607	598	6	,	,	PUNCT
ejpam-6607	598	7	18	18	NUM
ejpam-6607	598	8	(	(	PUNCT
ejpam-6607	598	9	3	3	NUM
ejpam-6607	598	10	)	)	PUNCT
ejpam-6607	598	11	(	(	PUNCT
ejpam-6607	598	12	2025	2025	NUM
ejpam-6607	598	13	)	)	PUNCT
ejpam-6607	598	14	,	,	PUNCT
ejpam-6607	598	15	6607	6607	NUM
ejpam-6607	598	16	28	28	NUM
ejpam-6607	598	17	of	of	ADP
ejpam-6607	598	18	33	33	NUM
ejpam-6607	598	19	(	(	PUNCT
ejpam-6607	598	20	iii	iii	NOUN
ejpam-6607	598	21	)	)	PUNCT
ejpam-6607	598	22	executes	execute	VERB
ejpam-6607	598	23	an	an	DET
ejpam-6607	598	24	n	n	CCONJ
ejpam-6607	598	25	-	-	PUNCT
ejpam-6607	598	26	iteration	iteration	NOUN
ejpam-6607	598	27	loop	loop	NOUN
ejpam-6607	598	28	where	where	SCONJ
ejpam-6607	598	29	each	each	DET
ejpam-6607	598	30	membership	membership	NOUN
ejpam-6607	598	31	test	test	VERB
ejpam-6607	598	32	ui	ui	PROPN
ejpam-6607	599	1	∈	∈	PROPN
ejpam-6607	599	2	s	s	PART
ejpam-6607	599	3	takes	take	NOUN
ejpam-6607	599	4	o(1	o(1	NOUN
ejpam-6607	599	5	)	)	PUNCT
ejpam-6607	599	6	.	.	PUNCT
ejpam-6607	600	1	thus	thus	ADV
ejpam-6607	600	2	the	the	DET
ejpam-6607	600	3	inner	inner	ADJ
ejpam-6607	600	4	loop	loop	NOUN
ejpam-6607	600	5	is	be	AUX
ejpam-6607	600	6	o(n	o(n	NUM
ejpam-6607	600	7	)	)	PUNCT
ejpam-6607	600	8	.	.	PUNCT
ejpam-6607	601	1	(	(	PUNCT
ejpam-6607	601	2	iv	iv	X
ejpam-6607	601	3	)	)	PUNCT
ejpam-6607	601	4	forms	form	VERB
ejpam-6607	601	5	the	the	DET
ejpam-6607	601	6	vector	vector	NOUN
ejpam-6607	601	7	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	601	8	or	or	CCONJ
ejpam-6607	601	9	|ψγ⟩	|ψγ⟩	NOUN
ejpam-6607	601	10	in	in	ADP
ejpam-6607	601	11	o(n	o(n	NOUN
ejpam-6607	601	12	)	)	PUNCT
ejpam-6607	601	13	by	by	ADP
ejpam-6607	601	14	summing	sum	VERB
ejpam-6607	601	15	n	n	PRON
ejpam-6607	601	16	amplitudes	amplitude	NOUN
ejpam-6607	601	17	.	.	PUNCT
ejpam-6607	602	1	steps	step	NOUN
ejpam-6607	602	2	3–4	3–4	NUM
ejpam-6607	602	3	dominate	dominate	VERB
ejpam-6607	602	4	,	,	PUNCT
ejpam-6607	602	5	yielding	yield	VERB
ejpam-6607	602	6	o(n	o(n	NOUN
ejpam-6607	602	7	)	)	PUNCT
ejpam-6607	602	8	per	per	ADP
ejpam-6607	602	9	γ	γ	X
ejpam-6607	602	10	.	.	PROPN
ejpam-6607	602	11	over	over	ADP
ejpam-6607	602	12	all	all	DET
ejpam-6607	602	13	γ	γ	PROPN
ejpam-6607	602	14	∈	∈	PROPN
ejpam-6607	602	15	c	c	NOUN
ejpam-6607	603	1	,	,	PUNCT
ejpam-6607	603	2	the	the	DET
ejpam-6607	603	3	total	total	ADJ
ejpam-6607	603	4	time	time	NOUN
ejpam-6607	603	5	is	be	AUX
ejpam-6607	603	6	o	o	NOUN
ejpam-6607	603	7	(	(	PUNCT
ejpam-6607	603	8	|c|	|c|	PROPN
ejpam-6607	603	9	×	×	PROPN
ejpam-6607	603	10	n	n	CCONJ
ejpam-6607	603	11	)	)	PUNCT
ejpam-6607	603	12	.	.	PUNCT
ejpam-6607	604	1	space	space	NOUN
ejpam-6607	604	2	usage	usage	NOUN
ejpam-6607	604	3	arises	arise	VERB
ejpam-6607	604	4	from	from	ADP
ejpam-6607	604	5	storing	store	VERB
ejpam-6607	604	6	one	one	NUM
ejpam-6607	604	7	length	length	NOUN
ejpam-6607	604	8	-	-	PUNCT
ejpam-6607	604	9	n	n	CCONJ
ejpam-6607	604	10	complex	complex	ADJ
ejpam-6607	604	11	vector	vector	NOUN
ejpam-6607	604	12	per	per	ADP
ejpam-6607	604	13	γ	γ	PROPN
ejpam-6607	604	14	,	,	PUNCT
ejpam-6607	604	15	for	for	ADP
ejpam-6607	604	16	total	total	ADJ
ejpam-6607	604	17	o	o	NOUN
ejpam-6607	604	18	(	(	PUNCT
ejpam-6607	604	19	n	n	X
ejpam-6607	604	20	·	·	PUNCT
ejpam-6607	604	21	|c|	|c|	PROPN
ejpam-6607	604	22	)	)	PUNCT
ejpam-6607	604	23	complex	complex	ADJ
ejpam-6607	604	24	numbers	number	NOUN
ejpam-6607	604	25	.	.	PUNCT
ejpam-6607	605	1	this	this	PRON
ejpam-6607	605	2	completes	complete	VERB
ejpam-6607	605	3	the	the	DET
ejpam-6607	605	4	complexity	complexity	NOUN
ejpam-6607	605	5	analysis	analysis	NOUN
ejpam-6607	605	6	.	.	PUNCT
ejpam-6607	606	1	4	4	X
ejpam-6607	606	2	.	.	X
ejpam-6607	606	3	conclusion	conclusion	NOUN
ejpam-6607	606	4	and	and	CCONJ
ejpam-6607	606	5	future	future	NOUN
ejpam-6607	606	6	works	work	VERB
ejpam-6607	606	7	4.1	4.1	NUM
ejpam-6607	606	8	.	.	PUNCT
ejpam-6607	607	1	conclusion	conclusion	NOUN
ejpam-6607	607	2	in	in	ADP
ejpam-6607	607	3	this	this	DET
ejpam-6607	607	4	paper	paper	NOUN
ejpam-6607	607	5	,	,	PUNCT
ejpam-6607	607	6	we	we	PRON
ejpam-6607	607	7	introduced	introduce	VERB
ejpam-6607	607	8	and	and	CCONJ
ejpam-6607	607	9	rigorously	rigorously	ADV
ejpam-6607	607	10	formalized	formalize	VERB
ejpam-6607	607	11	the	the	DET
ejpam-6607	607	12	concepts	concept	NOUN
ejpam-6607	607	13	of	of	ADP
ejpam-6607	607	14	the	the	DET
ejpam-6607	607	15	quantum	quantum	ADJ
ejpam-6607	607	16	hypersoft	hypersoft	NOUN
ejpam-6607	607	17	set	set	VERB
ejpam-6607	607	18	and	and	CCONJ
ejpam-6607	607	19	the	the	DET
ejpam-6607	607	20	quantum	quantum	PROPN
ejpam-6607	607	21	superhypersoft	superhypersoft	NOUN
ejpam-6607	607	22	set	set	NOUN
ejpam-6607	607	23	,	,	PUNCT
ejpam-6607	607	24	thereby	thereby	ADV
ejpam-6607	607	25	extending	extend	VERB
ejpam-6607	607	26	the	the	DET
ejpam-6607	607	27	existing	exist	VERB
ejpam-6607	607	28	theory	theory	NOUN
ejpam-6607	607	29	of	of	ADP
ejpam-6607	607	30	quantum	quantum	ADJ
ejpam-6607	607	31	soft	soft	ADJ
ejpam-6607	607	32	sets	set	NOUN
ejpam-6607	607	33	.	.	PUNCT
ejpam-6607	608	1	we	we	PRON
ejpam-6607	608	2	also	also	ADV
ejpam-6607	608	3	provided	provide	VERB
ejpam-6607	608	4	initial	initial	ADJ
ejpam-6607	608	5	algorithmic	algorithmic	ADJ
ejpam-6607	608	6	formulations	formulation	NOUN
ejpam-6607	608	7	for	for	ADP
ejpam-6607	608	8	their	their	PRON
ejpam-6607	608	9	construction	construction	NOUN
ejpam-6607	608	10	.	.	PUNCT
ejpam-6607	609	1	these	these	DET
ejpam-6607	609	2	newly	newly	ADV
ejpam-6607	609	3	proposed	propose	VERB
ejpam-6607	609	4	structures	structure	NOUN
ejpam-6607	609	5	offer	offer	VERB
ejpam-6607	609	6	a	a	DET
ejpam-6607	609	7	promising	promising	ADJ
ejpam-6607	609	8	foundation	foundation	NOUN
ejpam-6607	609	9	for	for	ADP
ejpam-6607	609	10	representing	represent	VERB
ejpam-6607	609	11	and	and	CCONJ
ejpam-6607	609	12	reasoning	reasoning	NOUN
ejpam-6607	609	13	about	about	ADP
ejpam-6607	609	14	complex	complex	ADJ
ejpam-6607	609	15	uncertainty	uncertainty	NOUN
ejpam-6607	609	16	in	in	ADP
ejpam-6607	609	17	both	both	DET
ejpam-6607	609	18	quantum	quantum	ADJ
ejpam-6607	609	19	theory	theory	NOUN
ejpam-6607	609	20	and	and	CCONJ
ejpam-6607	609	21	soft	soft	ADJ
ejpam-6607	609	22	computing	computing	NOUN
ejpam-6607	609	23	.	.	PUNCT
ejpam-6607	610	1	however	however	ADV
ejpam-6607	610	2	,	,	PUNCT
ejpam-6607	610	3	since	since	SCONJ
ejpam-6607	610	4	this	this	DET
ejpam-6607	610	5	work	work	NOUN
ejpam-6607	610	6	is	be	AUX
ejpam-6607	610	7	purely	purely	ADV
ejpam-6607	610	8	theoretical	theoretical	ADJ
ejpam-6607	610	9	,	,	PUNCT
ejpam-6607	610	10	further	further	ADJ
ejpam-6607	610	11	validation	validation	NOUN
ejpam-6607	610	12	through	through	ADP
ejpam-6607	610	13	computational	computational	ADJ
ejpam-6607	610	14	experiments	experiment	NOUN
ejpam-6607	610	15	and	and	CCONJ
ejpam-6607	610	16	practical	practical	ADJ
ejpam-6607	610	17	implementations	implementation	NOUN
ejpam-6607	610	18	is	be	AUX
ejpam-6607	610	19	required	require	VERB
ejpam-6607	610	20	in	in	ADP
ejpam-6607	610	21	future	future	ADJ
ejpam-6607	610	22	research	research	NOUN
ejpam-6607	610	23	.	.	PUNCT
ejpam-6607	611	1	4.2	4.2	NUM
ejpam-6607	611	2	.	.	PUNCT
ejpam-6607	612	1	future	future	ADJ
ejpam-6607	612	2	works	work	NOUN
ejpam-6607	612	3	in	in	ADP
ejpam-6607	612	4	future	future	ADJ
ejpam-6607	612	5	work	work	NOUN
ejpam-6607	612	6	,	,	PUNCT
ejpam-6607	612	7	we	we	PRON
ejpam-6607	612	8	plan	plan	VERB
ejpam-6607	612	9	to	to	PART
ejpam-6607	612	10	extend	extend	VERB
ejpam-6607	612	11	these	these	DET
ejpam-6607	612	12	quantum	quantum	NOUN
ejpam-6607	612	13	-	-	PUNCT
ejpam-6607	612	14	set	set	NOUN
ejpam-6607	612	15	-	-	PUNCT
ejpam-6607	612	16	based	base	VERB
ejpam-6607	612	17	models	model	NOUN
ejpam-6607	612	18	to	to	ADP
ejpam-6607	612	19	more	more	ADJ
ejpam-6607	612	20	general	general	ADJ
ejpam-6607	612	21	structures	structure	NOUN
ejpam-6607	612	22	such	such	ADJ
ejpam-6607	612	23	as	as	ADP
ejpam-6607	612	24	graphs	graph	NOUN
ejpam-6607	612	25	[	[	X
ejpam-6607	612	26	45	45	NUM
ejpam-6607	612	27	]	]	PUNCT
ejpam-6607	612	28	,	,	PUNCT
ejpam-6607	612	29	hypergraphs	hypergraph	NOUN
ejpam-6607	613	1	[	[	X
ejpam-6607	613	2	46	46	NUM
ejpam-6607	613	3	,	,	PUNCT
ejpam-6607	613	4	47	47	NUM
ejpam-6607	613	5	]	]	PUNCT
ejpam-6607	613	6	,	,	PUNCT
ejpam-6607	613	7	bidirected	bidirecte	VERB
ejpam-6607	613	8	graphs	graph	NOUN
ejpam-6607	613	9	[	[	X
ejpam-6607	613	10	48	48	NUM
ejpam-6607	613	11	,	,	PUNCT
ejpam-6607	613	12	49	49	NUM
ejpam-6607	613	13	]	]	PUNCT
ejpam-6607	613	14	,	,	PUNCT
ejpam-6607	613	15	and	and	CCONJ
ejpam-6607	613	16	superhypergraphs	superhypergraph	VERB
ejpam-6607	613	17	[	[	X
ejpam-6607	613	18	50	50	NUM
ejpam-6607	613	19	,	,	PUNCT
ejpam-6607	613	20	51	51	NUM
ejpam-6607	613	21	]	]	PUNCT
ejpam-6607	613	22	.	.	PUNCT
ejpam-6607	614	1	moreover	moreover	ADV
ejpam-6607	614	2	,	,	PUNCT
ejpam-6607	614	3	we	we	PRON
ejpam-6607	614	4	aim	aim	VERB
ejpam-6607	614	5	to	to	PART
ejpam-6607	614	6	incorporate	incorporate	VERB
ejpam-6607	614	7	advanced	advanced	ADJ
ejpam-6607	614	8	soft	soft	ADJ
ejpam-6607	614	9	computing	computing	NOUN
ejpam-6607	614	10	paradigms	paradigm	NOUN
ejpam-6607	614	11	such	such	ADJ
ejpam-6607	614	12	as	as	ADP
ejpam-6607	614	13	the	the	DET
ejpam-6607	614	14	soft	soft	ADJ
ejpam-6607	614	15	expert	expert	NOUN
ejpam-6607	614	16	set	set	VERB
ejpam-6607	614	17	[	[	X
ejpam-6607	614	18	52	52	NUM
ejpam-6607	614	19	,	,	PUNCT
ejpam-6607	614	20	53	53	NUM
ejpam-6607	614	21	]	]	PUNCT
ejpam-6607	614	22	,	,	PUNCT
ejpam-6607	614	23	indetermsoft	indetermsoft	ADV
ejpam-6607	614	24	sets[54	sets[54	NOUN
ejpam-6607	614	25	,	,	PUNCT
ejpam-6607	614	26	55	55	NUM
ejpam-6607	614	27	]	]	PUNCT
ejpam-6607	614	28	,	,	PUNCT
ejpam-6607	614	29	indetermhypersoft	indetermhypersoft	ADJ
ejpam-6607	614	30	sets[55	sets[55	PROPN
ejpam-6607	614	31	,	,	PUNCT
ejpam-6607	614	32	56	56	NUM
ejpam-6607	614	33	]	]	PUNCT
ejpam-6607	614	34	,	,	PUNCT
ejpam-6607	614	35	fuzzy	fuzzy	ADJ
ejpam-6607	614	36	soft	soft	ADJ
ejpam-6607	614	37	sets[57	sets[57	NOUN
ejpam-6607	614	38	]	]	PUNCT
ejpam-6607	614	39	,	,	PUNCT
ejpam-6607	614	40	and	and	CCONJ
ejpam-6607	614	41	indetermsuperhypersoft	indetermsuperhypersoft	PROPN
ejpam-6607	614	42	sets[33	sets[33	PROPN
ejpam-6607	614	43	]	]	PUNCT
ejpam-6607	614	44	.	.	PUNCT
ejpam-6607	615	1	potential	potential	ADJ
ejpam-6607	615	2	extensions	extension	NOUN
ejpam-6607	615	3	based	base	VERB
ejpam-6607	615	4	on	on	ADP
ejpam-6607	615	5	fuzzy	fuzzy	ADJ
ejpam-6607	615	6	sets[4	sets[4	PROPN
ejpam-6607	615	7	,	,	PUNCT
ejpam-6607	615	8	58	58	NUM
ejpam-6607	615	9	]	]	PUNCT
ejpam-6607	615	10	,	,	PUNCT
ejpam-6607	615	11	hyperrough	hyperrough	PROPN
ejpam-6607	615	12	sets[59	sets[59	PROPN
ejpam-6607	615	13	,	,	PUNCT
ejpam-6607	615	14	60	60	NUM
ejpam-6607	615	15	]	]	PUNCT
ejpam-6607	615	16	,	,	PUNCT
ejpam-6607	615	17	intuitionistic	intuitionistic	ADJ
ejpam-6607	615	18	fuzzy	fuzzy	ADJ
ejpam-6607	615	19	sets[61	sets[61	NOUN
ejpam-6607	615	20	,	,	PUNCT
ejpam-6607	615	21	62	62	NUM
ejpam-6607	615	22	]	]	PUNCT
ejpam-6607	615	23	,	,	PUNCT
ejpam-6607	615	24	neutrosophic	neutrosophic	ADJ
ejpam-6607	615	25	sets[18	sets[18	NOUN
ejpam-6607	615	26	,	,	PUNCT
ejpam-6607	615	27	63	63	NUM
ejpam-6607	615	28	]	]	PUNCT
ejpam-6607	615	29	,	,	PUNCT
ejpam-6607	615	30	and	and	CCONJ
ejpam-6607	615	31	plithogenic	plithogenic	ADJ
ejpam-6607	615	32	sets[20	sets[20	NOUN
ejpam-6607	615	33	,	,	PUNCT
ejpam-6607	615	34	64	64	NUM
ejpam-6607	615	35	]	]	PUNCT
ejpam-6607	615	36	also	also	ADV
ejpam-6607	615	37	offer	offer	VERB
ejpam-6607	615	38	rich	rich	ADJ
ejpam-6607	615	39	avenues	avenue	NOUN
ejpam-6607	615	40	for	for	ADP
ejpam-6607	615	41	further	further	ADJ
ejpam-6607	615	42	development	development	NOUN
ejpam-6607	615	43	.	.	PUNCT
ejpam-6607	616	1	we	we	PRON
ejpam-6607	616	2	hope	hope	VERB
ejpam-6607	616	3	that	that	SCONJ
ejpam-6607	616	4	future	future	ADJ
ejpam-6607	616	5	research	research	NOUN
ejpam-6607	616	6	will	will	AUX
ejpam-6607	616	7	pursue	pursue	VERB
ejpam-6607	616	8	computational	computational	ADJ
ejpam-6607	616	9	implementations	implementation	NOUN
ejpam-6607	616	10	and	and	CCONJ
ejpam-6607	616	11	practical	practical	ADJ
ejpam-6607	616	12	applications	application	NOUN
ejpam-6607	616	13	of	of	ADP
ejpam-6607	616	14	these	these	DET
ejpam-6607	616	15	models	model	NOUN
ejpam-6607	616	16	in	in	ADP
ejpam-6607	616	17	real	real	ADJ
ejpam-6607	616	18	-	-	PUNCT
ejpam-6607	616	19	world	world	NOUN
ejpam-6607	616	20	decision	decision	NOUN
ejpam-6607	616	21	-	-	PUNCT
ejpam-6607	616	22	making	making	NOUN
ejpam-6607	616	23	and	and	CCONJ
ejpam-6607	616	24	uncertainty	uncertainty	NOUN
ejpam-6607	616	25	reasoning	reason	VERB
ejpam-6607	616	26	scenarios	scenario	NOUN
ejpam-6607	616	27	.	.	PUNCT
ejpam-6607	617	1	acknowledgements	acknowledgement	NOUN
ejpam-6607	617	2	we	we	PRON
ejpam-6607	617	3	wish	wish	VERB
ejpam-6607	617	4	to	to	PART
ejpam-6607	617	5	thank	thank	VERB
ejpam-6607	617	6	everyone	everyone	PRON
ejpam-6607	617	7	whose	whose	DET
ejpam-6607	617	8	guidance	guidance	NOUN
ejpam-6607	617	9	,	,	PUNCT
ejpam-6607	617	10	ideas	idea	NOUN
ejpam-6607	617	11	,	,	PUNCT
ejpam-6607	617	12	and	and	CCONJ
ejpam-6607	617	13	assistance	assistance	NOUN
ejpam-6607	617	14	contributed	contribute	VERB
ejpam-6607	617	15	to	to	ADP
ejpam-6607	617	16	this	this	DET
ejpam-6607	617	17	research	research	NOUN
ejpam-6607	617	18	.	.	PUNCT
ejpam-6607	618	1	our	our	PRON
ejpam-6607	618	2	appreciation	appreciation	NOUN
ejpam-6607	618	3	goes	go	VERB
ejpam-6607	618	4	to	to	ADP
ejpam-6607	618	5	the	the	DET
ejpam-6607	618	6	readers	reader	NOUN
ejpam-6607	618	7	for	for	ADP
ejpam-6607	618	8	their	their	PRON
ejpam-6607	618	9	interest	interest	NOUN
ejpam-6607	618	10	and	and	CCONJ
ejpam-6607	618	11	to	to	ADP
ejpam-6607	618	12	the	the	DET
ejpam-6607	618	13	scholars	scholar	NOUN
ejpam-6607	618	14	whose	whose	DET
ejpam-6607	618	15	publications	publication	NOUN
ejpam-6607	618	16	provided	provide	VERB
ejpam-6607	618	17	the	the	DET
ejpam-6607	618	18	groundwork	groundwork	NOUN
ejpam-6607	618	19	for	for	ADP
ejpam-6607	618	20	this	this	DET
ejpam-6607	618	21	study	study	NOUN
ejpam-6607	618	22	.	.	PUNCT
ejpam-6607	619	1	we	we	PRON
ejpam-6607	619	2	are	be	AUX
ejpam-6607	619	3	also	also	ADV
ejpam-6607	619	4	indebted	indebted	ADJ
ejpam-6607	619	5	to	to	ADP
ejpam-6607	619	6	the	the	DET
ejpam-6607	619	7	t.	t.	PROPN
ejpam-6607	619	8	fujita	fujita	PROPN
ejpam-6607	619	9	,	,	PUNCT
ejpam-6607	619	10	f.smarandache	f.smarandache	NOUN
ejpam-6607	619	11	/	/	SYM
ejpam-6607	619	12	eur	eur	PROPN
ejpam-6607	619	13	.	.	PUNCT
ejpam-6607	620	1	j.	j.	PROPN
ejpam-6607	620	2	pure	pure	PROPN
ejpam-6607	620	3	appl	appl	PROPN
ejpam-6607	620	4	.	.	PROPN
ejpam-6607	620	5	math	math	PROPN
ejpam-6607	620	6	,	,	PUNCT
ejpam-6607	620	7	18	18	NUM
ejpam-6607	620	8	(	(	PUNCT
ejpam-6607	620	9	3	3	NUM
ejpam-6607	620	10	)	)	PUNCT
ejpam-6607	620	11	(	(	PUNCT
ejpam-6607	620	12	2025	2025	NUM
ejpam-6607	620	13	)	)	PUNCT
ejpam-6607	620	14	,	,	PUNCT
ejpam-6607	620	15	6607	6607	NUM
ejpam-6607	620	16	29	29	NUM
ejpam-6607	620	17	of	of	ADP
ejpam-6607	620	18	33	33	NUM
ejpam-6607	620	19	individuals	individual	NOUN
ejpam-6607	620	20	and	and	CCONJ
ejpam-6607	620	21	institutions	institution	NOUN
ejpam-6607	620	22	that	that	PRON
ejpam-6607	620	23	supplied	supply	VERB
ejpam-6607	620	24	the	the	DET
ejpam-6607	620	25	resources	resource	NOUN
ejpam-6607	620	26	and	and	CCONJ
ejpam-6607	620	27	infrastructure	infrastructure	NOUN
ejpam-6607	620	28	necessary	necessary	ADJ
ejpam-6607	620	29	for	for	ADP
ejpam-6607	620	30	completing	complete	VERB
ejpam-6607	620	31	and	and	CCONJ
ejpam-6607	620	32	disseminating	disseminate	VERB
ejpam-6607	620	33	this	this	DET
ejpam-6607	620	34	paper	paper	NOUN
ejpam-6607	620	35	.	.	PUNCT
ejpam-6607	621	1	lastly	lastly	ADV
ejpam-6607	621	2	,	,	PUNCT
ejpam-6607	621	3	we	we	PRON
ejpam-6607	621	4	extend	extend	VERB
ejpam-6607	621	5	our	our	PRON
ejpam-6607	621	6	gratitude	gratitude	NOUN
ejpam-6607	621	7	to	to	ADP
ejpam-6607	621	8	all	all	PRON
ejpam-6607	621	9	who	who	PRON
ejpam-6607	621	10	offered	offer	VERB
ejpam-6607	621	11	their	their	PRON
ejpam-6607	621	12	support	support	NOUN
ejpam-6607	621	13	in	in	ADP
ejpam-6607	621	14	various	various	ADJ
ejpam-6607	621	15	capacities	capacity	NOUN
ejpam-6607	621	16	.	.	PUNCT
ejpam-6607	622	1	data	datum	NOUN
ejpam-6607	622	2	availability	availability	NOUN
ejpam-6607	622	3	this	this	DET
ejpam-6607	622	4	paper	paper	NOUN
ejpam-6607	622	5	is	be	AUX
ejpam-6607	622	6	purely	purely	ADV
ejpam-6607	622	7	theoretical	theoretical	ADJ
ejpam-6607	622	8	and	and	CCONJ
ejpam-6607	622	9	does	do	AUX
ejpam-6607	622	10	not	not	PART
ejpam-6607	622	11	involve	involve	VERB
ejpam-6607	622	12	any	any	DET
ejpam-6607	622	13	empirical	empirical	ADJ
ejpam-6607	622	14	data	datum	NOUN
ejpam-6607	622	15	.	.	PUNCT
ejpam-6607	623	1	we	we	PRON
ejpam-6607	623	2	welcome	welcome	VERB
ejpam-6607	623	3	future	future	ADJ
ejpam-6607	623	4	empirical	empirical	ADJ
ejpam-6607	623	5	studies	study	NOUN
ejpam-6607	623	6	that	that	PRON
ejpam-6607	623	7	build	build	VERB
ejpam-6607	623	8	upon	upon	SCONJ
ejpam-6607	623	9	and	and	CCONJ
ejpam-6607	623	10	test	test	VERB
ejpam-6607	623	11	the	the	DET
ejpam-6607	623	12	concepts	concept	NOUN
ejpam-6607	623	13	presented	present	VERB
ejpam-6607	623	14	here	here	ADV
ejpam-6607	623	15	.	.	PUNCT
ejpam-6607	624	1	ethical	ethical	ADJ
ejpam-6607	624	2	approval	approval	NOUN
ejpam-6607	624	3	as	as	SCONJ
ejpam-6607	624	4	this	this	DET
ejpam-6607	624	5	work	work	NOUN
ejpam-6607	624	6	is	be	AUX
ejpam-6607	624	7	entirely	entirely	ADV
ejpam-6607	624	8	conceptual	conceptual	ADJ
ejpam-6607	624	9	and	and	CCONJ
ejpam-6607	624	10	involves	involve	VERB
ejpam-6607	624	11	no	no	DET
ejpam-6607	624	12	human	human	ADJ
ejpam-6607	624	13	or	or	CCONJ
ejpam-6607	624	14	animal	animal	NOUN
ejpam-6607	624	15	subjects	subject	NOUN
ejpam-6607	624	16	,	,	PUNCT
ejpam-6607	624	17	ethical	ethical	ADJ
ejpam-6607	624	18	approval	approval	NOUN
ejpam-6607	624	19	was	be	AUX
ejpam-6607	624	20	not	not	PART
ejpam-6607	624	21	required	require	VERB
ejpam-6607	624	22	.	.	PUNCT
ejpam-6607	625	1	conflicts	conflict	NOUN
ejpam-6607	625	2	of	of	ADP
ejpam-6607	625	3	interest	interest	NOUN
ejpam-6607	625	4	the	the	DET
ejpam-6607	625	5	authors	author	NOUN
ejpam-6607	625	6	declare	declare	VERB
ejpam-6607	625	7	no	no	DET
ejpam-6607	625	8	conflicts	conflict	NOUN
ejpam-6607	625	9	of	of	ADP
ejpam-6607	625	10	interest	interest	NOUN
ejpam-6607	625	11	in	in	ADP
ejpam-6607	625	12	connection	connection	NOUN
ejpam-6607	625	13	with	with	ADP
ejpam-6607	625	14	this	this	DET
ejpam-6607	625	15	study	study	NOUN
ejpam-6607	625	16	or	or	CCONJ
ejpam-6607	625	17	its	its	PRON
ejpam-6607	625	18	publication	publication	NOUN
ejpam-6607	625	19	.	.	PUNCT
ejpam-6607	626	1	author	author	NOUN
ejpam-6607	626	2	contributions	contribution	NOUN
ejpam-6607	626	3	conceptualization	conceptualization	NOUN
ejpam-6607	626	4	,	,	PUNCT
ejpam-6607	626	5	takaaki	takaaki	NOUN
ejpam-6607	626	6	fujita	fujita	NOUN
ejpam-6607	626	7	and	and	CCONJ
ejpam-6607	626	8	florentin	florentin	PROPN
ejpam-6607	626	9	smarandache	smarandache	NOUN
ejpam-6607	626	10	;	;	PUNCT
ejpam-6607	626	11	investigation	investigation	NOUN
ejpam-6607	626	12	,	,	PUNCT
ejpam-6607	626	13	takaaki	takaaki	NOUN
ejpam-6607	626	14	fujita	fujita	PROPN
ejpam-6607	626	15	;	;	PUNCT
ejpam-6607	626	16	methodology	methodology	NOUN
ejpam-6607	626	17	,	,	PUNCT
ejpam-6607	626	18	takaaki	takaaki	NOUN
ejpam-6607	626	19	fujita	fujita	PROPN
ejpam-6607	626	20	;	;	PUNCT
ejpam-6607	626	21	writing	write	VERB
ejpam-6607	626	22	–	–	PUNCT
ejpam-6607	626	23	original	original	ADJ
ejpam-6607	626	24	draft	draft	NOUN
ejpam-6607	626	25	,	,	PUNCT
ejpam-6607	626	26	takaaki	takaaki	NOUN
ejpam-6607	626	27	fujita	fujita	NOUN
ejpam-6607	626	28	;	;	PUNCT
ejpam-6607	626	29	writing	write	VERB
ejpam-6607	626	30	–	–	PUNCT
ejpam-6607	626	31	review	review	NOUN
ejpam-6607	626	32	&	&	CCONJ
ejpam-6607	626	33	editing	editing	NOUN
ejpam-6607	626	34	,	,	PUNCT
ejpam-6607	626	35	takaaki	takaaki	NOUN
ejpam-6607	626	36	fujita	fujita	NOUN
ejpam-6607	626	37	and	and	CCONJ
ejpam-6607	626	38	florentin	florentin	PROPN
ejpam-6607	626	39	smarandache	smarandache	PROPN
ejpam-6607	626	40	.	.	PUNCT
ejpam-6607	627	1	disclaimer	disclaimer	NOUN
ejpam-6607	627	2	(	(	PUNCT
ejpam-6607	627	3	limitations	limitation	NOUN
ejpam-6607	627	4	and	and	CCONJ
ejpam-6607	627	5	claims	claim	NOUN
ejpam-6607	627	6	)	)	PUNCT
ejpam-6607	628	1	the	the	DET
ejpam-6607	628	2	theoretical	theoretical	ADJ
ejpam-6607	628	3	concepts	concept	NOUN
ejpam-6607	628	4	presented	present	VERB
ejpam-6607	628	5	in	in	ADP
ejpam-6607	628	6	this	this	DET
ejpam-6607	628	7	paper	paper	NOUN
ejpam-6607	628	8	have	have	AUX
ejpam-6607	628	9	not	not	PART
ejpam-6607	628	10	yet	yet	ADV
ejpam-6607	628	11	been	be	AUX
ejpam-6607	628	12	subject	subject	ADJ
ejpam-6607	628	13	to	to	ADP
ejpam-6607	628	14	practical	practical	ADJ
ejpam-6607	628	15	implementation	implementation	NOUN
ejpam-6607	628	16	or	or	CCONJ
ejpam-6607	628	17	empirical	empirical	ADJ
ejpam-6607	628	18	validation	validation	NOUN
ejpam-6607	628	19	.	.	PUNCT
ejpam-6607	629	1	future	future	ADJ
ejpam-6607	629	2	researchers	researcher	NOUN
ejpam-6607	629	3	are	be	AUX
ejpam-6607	629	4	invited	invite	VERB
ejpam-6607	629	5	to	to	PART
ejpam-6607	629	6	explore	explore	VERB
ejpam-6607	629	7	these	these	DET
ejpam-6607	629	8	ideas	idea	NOUN
ejpam-6607	629	9	in	in	ADP
ejpam-6607	629	10	applied	applied	ADJ
ejpam-6607	629	11	or	or	CCONJ
ejpam-6607	629	12	experimental	experimental	ADJ
ejpam-6607	629	13	settings	setting	NOUN
ejpam-6607	629	14	.	.	PUNCT
ejpam-6607	630	1	although	although	SCONJ
ejpam-6607	630	2	every	every	DET
ejpam-6607	630	3	effort	effort	NOUN
ejpam-6607	630	4	has	have	AUX
ejpam-6607	630	5	been	be	AUX
ejpam-6607	630	6	made	make	VERB
ejpam-6607	630	7	to	to	PART
ejpam-6607	630	8	ensure	ensure	VERB
ejpam-6607	630	9	the	the	DET
ejpam-6607	630	10	accuracy	accuracy	NOUN
ejpam-6607	630	11	of	of	ADP
ejpam-6607	630	12	the	the	DET
ejpam-6607	630	13	content	content	NOUN
ejpam-6607	630	14	and	and	CCONJ
ejpam-6607	630	15	the	the	DET
ejpam-6607	630	16	proper	proper	ADJ
ejpam-6607	630	17	citation	citation	NOUN
ejpam-6607	630	18	of	of	ADP
ejpam-6607	630	19	sources	source	NOUN
ejpam-6607	630	20	,	,	PUNCT
ejpam-6607	630	21	unintentional	unintentional	ADJ
ejpam-6607	630	22	errors	error	NOUN
ejpam-6607	630	23	or	or	CCONJ
ejpam-6607	630	24	omissions	omission	NOUN
ejpam-6607	630	25	may	may	AUX
ejpam-6607	630	26	persist	persist	VERB
ejpam-6607	630	27	.	.	PUNCT
ejpam-6607	631	1	readers	reader	NOUN
ejpam-6607	631	2	should	should	AUX
ejpam-6607	631	3	independently	independently	ADV
ejpam-6607	631	4	verify	verify	VERB
ejpam-6607	631	5	any	any	DET
ejpam-6607	631	6	referenced	referenced	ADJ
ejpam-6607	631	7	materials	material	NOUN
ejpam-6607	631	8	.	.	PUNCT
ejpam-6607	632	1	to	to	ADP
ejpam-6607	632	2	the	the	DET
ejpam-6607	632	3	best	good	ADJ
ejpam-6607	632	4	of	of	ADP
ejpam-6607	632	5	the	the	DET
ejpam-6607	632	6	authors	author	NOUN
ejpam-6607	632	7	’	’	PART
ejpam-6607	632	8	knowledge	knowledge	NOUN
ejpam-6607	632	9	,	,	PUNCT
ejpam-6607	632	10	all	all	DET
ejpam-6607	632	11	mathematical	mathematical	ADJ
ejpam-6607	632	12	statements	statement	NOUN
ejpam-6607	632	13	and	and	CCONJ
ejpam-6607	632	14	proofs	proof	NOUN
ejpam-6607	632	15	contained	contain	VERB
ejpam-6607	632	16	herein	herein	NOUN
ejpam-6607	632	17	are	be	AUX
ejpam-6607	632	18	correct	correct	ADJ
ejpam-6607	632	19	and	and	CCONJ
ejpam-6607	632	20	have	have	AUX
ejpam-6607	632	21	been	be	AUX
ejpam-6607	632	22	thoroughly	thoroughly	ADV
ejpam-6607	632	23	vetted	vet	VERB
ejpam-6607	632	24	.	.	PUNCT
ejpam-6607	633	1	should	should	AUX
ejpam-6607	633	2	you	you	PRON
ejpam-6607	633	3	identify	identify	VERB
ejpam-6607	633	4	any	any	DET
ejpam-6607	633	5	potential	potential	ADJ
ejpam-6607	633	6	errors	error	NOUN
ejpam-6607	633	7	or	or	CCONJ
ejpam-6607	633	8	ambiguities	ambiguity	NOUN
ejpam-6607	633	9	,	,	PUNCT
ejpam-6607	633	10	please	please	INTJ
ejpam-6607	633	11	feel	feel	VERB
ejpam-6607	633	12	free	free	ADJ
ejpam-6607	633	13	to	to	PART
ejpam-6607	633	14	contact	contact	VERB
ejpam-6607	633	15	the	the	DET
ejpam-6607	633	16	authors	author	NOUN
ejpam-6607	633	17	for	for	ADP
ejpam-6607	633	18	clarification	clarification	NOUN
ejpam-6607	633	19	.	.	PUNCT
ejpam-6607	634	1	the	the	DET
ejpam-6607	634	2	results	result	NOUN
ejpam-6607	634	3	presented	present	VERB
ejpam-6607	634	4	are	be	AUX
ejpam-6607	634	5	valid	valid	ADJ
ejpam-6607	634	6	only	only	ADV
ejpam-6607	634	7	under	under	ADP
ejpam-6607	634	8	the	the	DET
ejpam-6607	634	9	specific	specific	ADJ
ejpam-6607	634	10	assumptions	assumption	NOUN
ejpam-6607	634	11	and	and	CCONJ
ejpam-6607	634	12	conditions	condition	NOUN
ejpam-6607	634	13	detailed	detail	VERB
ejpam-6607	634	14	in	in	ADP
ejpam-6607	634	15	the	the	DET
ejpam-6607	634	16	manuscript	manuscript	NOUN
ejpam-6607	634	17	.	.	PUNCT
ejpam-6607	635	1	extending	extend	VERB
ejpam-6607	635	2	these	these	DET
ejpam-6607	635	3	findings	finding	NOUN
ejpam-6607	635	4	to	to	ADP
ejpam-6607	635	5	broader	broad	ADJ
ejpam-6607	635	6	mathematical	mathematical	ADJ
ejpam-6607	635	7	structures	structure	NOUN
ejpam-6607	635	8	may	may	AUX
ejpam-6607	635	9	require	require	VERB
ejpam-6607	635	10	additional	additional	ADJ
ejpam-6607	635	11	research	research	NOUN
ejpam-6607	635	12	.	.	PUNCT
ejpam-6607	636	1	the	the	DET
ejpam-6607	636	2	opinions	opinion	NOUN
ejpam-6607	636	3	and	and	CCONJ
ejpam-6607	636	4	conclusions	conclusion	NOUN
ejpam-6607	636	5	expressed	express	VERB
ejpam-6607	636	6	in	in	ADP
ejpam-6607	636	7	this	this	DET
ejpam-6607	636	8	work	work	NOUN
ejpam-6607	636	9	are	be	AUX
ejpam-6607	636	10	those	those	PRON
ejpam-6607	636	11	of	of	ADP
ejpam-6607	636	12	the	the	DET
ejpam-6607	636	13	authors	author	NOUN
ejpam-6607	636	14	alone	alone	ADJ
ejpam-6607	636	15	and	and	CCONJ
ejpam-6607	636	16	do	do	AUX
ejpam-6607	636	17	not	not	PART
ejpam-6607	636	18	necessarily	necessarily	ADV
ejpam-6607	636	19	reflect	reflect	VERB
ejpam-6607	636	20	the	the	DET
ejpam-6607	636	21	official	official	ADJ
ejpam-6607	636	22	positions	position	NOUN
ejpam-6607	636	23	of	of	ADP
ejpam-6607	636	24	their	their	PRON
ejpam-6607	636	25	affiliated	affiliated	ADJ
ejpam-6607	636	26	institutions	institution	NOUN
ejpam-6607	636	27	.	.	PUNCT
ejpam-6607	637	1	t.	t.	PROPN
ejpam-6607	637	2	fujita	fujita	PROPN
ejpam-6607	637	3	,	,	PUNCT
ejpam-6607	637	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	637	5	/	/	SYM
ejpam-6607	637	6	eur	eur	PROPN
ejpam-6607	637	7	.	.	PUNCT
ejpam-6607	638	1	j.	j.	PROPN
ejpam-6607	638	2	pure	pure	PROPN
ejpam-6607	638	3	appl	appl	PROPN
ejpam-6607	638	4	.	.	PROPN
ejpam-6607	638	5	math	math	PROPN
ejpam-6607	638	6	,	,	PUNCT
ejpam-6607	638	7	18	18	NUM
ejpam-6607	638	8	(	(	PUNCT
ejpam-6607	638	9	3	3	NUM
ejpam-6607	638	10	)	)	PUNCT
ejpam-6607	638	11	(	(	PUNCT
ejpam-6607	638	12	2025	2025	NUM
ejpam-6607	638	13	)	)	PUNCT
ejpam-6607	638	14	,	,	PUNCT
ejpam-6607	638	15	6607	6607	NUM
ejpam-6607	638	16	30	30	NUM
ejpam-6607	638	17	of	of	ADP
ejpam-6607	638	18	33	33	NUM
ejpam-6607	638	19	references	reference	NOUN
ejpam-6607	638	20	[	[	X
ejpam-6607	638	21	1	1	NUM
ejpam-6607	638	22	]	]	PUNCT
ejpam-6607	638	23	pradip	pradip	NOUN
ejpam-6607	638	24	kumar	kumar	PROPN
ejpam-6607	638	25	maji	maji	PROPN
ejpam-6607	638	26	,	,	PUNCT
ejpam-6607	638	27	ranjit	ranjit	PROPN
ejpam-6607	638	28	biswas	biswas	PROPN
ejpam-6607	638	29	,	,	PUNCT
ejpam-6607	638	30	and	and	CCONJ
ejpam-6607	638	31	a	a	DET
ejpam-6607	638	32	ranjan	ranjan	PROPN
ejpam-6607	638	33	roy	roy	PROPN
ejpam-6607	638	34	.	.	PROPN
ejpam-6607	638	35	soft	soft	ADJ
ejpam-6607	638	36	set	set	NOUN
ejpam-6607	638	37	theory	theory	NOUN
ejpam-6607	638	38	.	.	PUNCT
ejpam-6607	639	1	computers	computer	NOUN
ejpam-6607	639	2	&	&	CCONJ
ejpam-6607	639	3	mathematics	mathematics	PROPN
ejpam-6607	639	4	with	with	ADP
ejpam-6607	639	5	applications	application	NOUN
ejpam-6607	639	6	,	,	PUNCT
ejpam-6607	639	7	45(4	45(4	NOUN
ejpam-6607	639	8	-	-	PUNCT
ejpam-6607	639	9	5):555–562	5):555–562	NUM
ejpam-6607	639	10	,	,	PUNCT
ejpam-6607	639	11	2003	2003	NUM
ejpam-6607	639	12	.	.	PUNCT
ejpam-6607	640	1	[	[	X
ejpam-6607	640	2	2	2	NUM
ejpam-6607	640	3	]	]	X
ejpam-6607	640	4	dmitriy	dmitriy	PROPN
ejpam-6607	640	5	molodtsov	molodtsov	PROPN
ejpam-6607	640	6	.	.	PUNCT
ejpam-6607	641	1	soft	soft	ADJ
ejpam-6607	641	2	set	set	NOUN
ejpam-6607	641	3	theory	theory	NOUN
ejpam-6607	641	4	-	-	PUNCT
ejpam-6607	641	5	first	first	ADJ
ejpam-6607	641	6	results	result	NOUN
ejpam-6607	641	7	.	.	PUNCT
ejpam-6607	642	1	computers	computer	NOUN
ejpam-6607	642	2	&	&	CCONJ
ejpam-6607	642	3	mathematics	mathematics	PROPN
ejpam-6607	642	4	with	with	ADP
ejpam-6607	642	5	applications	application	NOUN
ejpam-6607	642	6	,	,	PUNCT
ejpam-6607	642	7	37(4	37(4	PROPN
ejpam-6607	642	8	-	-	PUNCT
ejpam-6607	642	9	5):19–31	5):19–31	NUM
ejpam-6607	642	10	,	,	PUNCT
ejpam-6607	642	11	1999	1999	NUM
ejpam-6607	642	12	.	.	PUNCT
ejpam-6607	643	1	[	[	X
ejpam-6607	643	2	3	3	X
ejpam-6607	643	3	]	]	X
ejpam-6607	643	4	sheng’en	sheng’en	PROPN
ejpam-6607	643	5	li	li	X
ejpam-6607	643	6	.	.	PROPN
ejpam-6607	643	7	quantumsoft	quantumsoft	PROPN
ejpam-6607	643	8	set	set	PROPN
ejpam-6607	643	9	:	:	PUNCT
ejpam-6607	643	10	a	a	DET
ejpam-6607	643	11	quantum	quantum	NOUN
ejpam-6607	643	12	-	-	PUNCT
ejpam-6607	643	13	inspired	inspire	VERB
ejpam-6607	643	14	extension	extension	NOUN
ejpam-6607	643	15	of	of	ADP
ejpam-6607	643	16	soft	soft	ADJ
ejpam-6607	643	17	sets	set	NOUN
ejpam-6607	643	18	for	for	ADP
ejpam-6607	643	19	evaluating	evaluate	VERB
ejpam-6607	643	20	multimedia	multimedia	NOUN
ejpam-6607	643	21	teaching	teaching	NOUN
ejpam-6607	643	22	effectiveness	effectiveness	NOUN
ejpam-6607	643	23	in	in	ADP
ejpam-6607	643	24	college	college	PROPN
ejpam-6607	643	25	english	english	PROPN
ejpam-6607	643	26	.	.	PUNCT
ejpam-6607	644	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	644	2	sets	set	NOUN
ejpam-6607	644	3	and	and	CCONJ
ejpam-6607	644	4	systems	system	NOUN
ejpam-6607	644	5	,	,	PUNCT
ejpam-6607	644	6	85:951–959	85:951–959	NOUN
ejpam-6607	644	7	,	,	PUNCT
ejpam-6607	644	8	2025	2025	NUM
ejpam-6607	644	9	.	.	PUNCT
ejpam-6607	645	1	[	[	X
ejpam-6607	645	2	4	4	NUM
ejpam-6607	645	3	]	]	PUNCT
ejpam-6607	645	4	lotfi	lotfi	X
ejpam-6607	645	5	a	a	DET
ejpam-6607	645	6	zadeh	zadeh	PROPN
ejpam-6607	645	7	.	.	PUNCT
ejpam-6607	645	8	fuzzy	fuzzy	ADJ
ejpam-6607	645	9	sets	set	NOUN
ejpam-6607	645	10	.	.	PUNCT
ejpam-6607	646	1	information	information	NOUN
ejpam-6607	646	2	and	and	CCONJ
ejpam-6607	646	3	control	control	NOUN
ejpam-6607	646	4	,	,	PUNCT
ejpam-6607	646	5	8(3):338–353	8(3):338–353	NUM
ejpam-6607	646	6	,	,	PUNCT
ejpam-6607	646	7	1965	1965	NUM
ejpam-6607	646	8	.	.	PUNCT
ejpam-6607	647	1	[	[	X
ejpam-6607	647	2	5	5	NUM
ejpam-6607	647	3	]	]	PUNCT
ejpam-6607	647	4	young	young	ADJ
ejpam-6607	647	5	bae	bae	PROPN
ejpam-6607	647	6	jun	jun	PROPN
ejpam-6607	647	7	,	,	PUNCT
ejpam-6607	647	8	kul	kul	PROPN
ejpam-6607	647	9	hur	hur	PROPN
ejpam-6607	647	10	,	,	PUNCT
ejpam-6607	647	11	and	and	CCONJ
ejpam-6607	647	12	kyoung	kyoung	PROPN
ejpam-6607	647	13	ja	ja	PROPN
ejpam-6607	647	14	lee	lee	PROPN
ejpam-6607	647	15	.	.	PROPN
ejpam-6607	647	16	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6607	647	17	subalgebras	subalgebras	PROPN
ejpam-6607	647	18	of	of	ADP
ejpam-6607	647	19	bck	bck	PROPN
ejpam-6607	647	20	/	/	SYM
ejpam-6607	647	21	bcialgebras	bcialgebra	NOUN
ejpam-6607	647	22	.	.	PUNCT
ejpam-6607	648	1	annals	annal	NOUN
ejpam-6607	648	2	of	of	ADP
ejpam-6607	648	3	fuzzy	fuzzy	ADJ
ejpam-6607	648	4	mathematics	mathematic	NOUN
ejpam-6607	648	5	and	and	CCONJ
ejpam-6607	648	6	informatics	informatic	NOUN
ejpam-6607	648	7	,	,	PUNCT
ejpam-6607	648	8	2017	2017	NUM
ejpam-6607	648	9	.	.	PUNCT
ejpam-6607	649	1	[	[	X
ejpam-6607	649	2	6	6	NUM
ejpam-6607	649	3	]	]	PUNCT
ejpam-6607	649	4	jayanta	jayanta	PROPN
ejpam-6607	649	5	ghosh	ghosh	PROPN
ejpam-6607	649	6	and	and	CCONJ
ejpam-6607	649	7	tapas	tapas	PROPN
ejpam-6607	649	8	kumar	kumar	PROPN
ejpam-6607	649	9	samanta	samanta	PROPN
ejpam-6607	649	10	.	.	PUNCT
ejpam-6607	649	11	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6607	649	12	sets	set	NOUN
ejpam-6607	649	13	and	and	CCONJ
ejpam-6607	649	14	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6607	649	15	group	group	NOUN
ejpam-6607	649	16	.	.	PUNCT
ejpam-6607	650	1	int	int	NOUN
ejpam-6607	650	2	.	.	PUNCT
ejpam-6607	651	1	j.	j.	PROPN
ejpam-6607	651	2	adv	adv	PROPN
ejpam-6607	651	3	.	.	PUNCT
ejpam-6607	652	1	sci	sci	PROPN
ejpam-6607	652	2	.	.	PROPN
ejpam-6607	652	3	technol	technol	PROPN
ejpam-6607	652	4	,	,	PUNCT
ejpam-6607	652	5	41:27–37	41:27–37	PROPN
ejpam-6607	652	6	,	,	PUNCT
ejpam-6607	652	7	2012	2012	NUM
ejpam-6607	652	8	.	.	PUNCT
ejpam-6607	653	1	[	[	X
ejpam-6607	653	2	7	7	X
ejpam-6607	653	3	]	]	X
ejpam-6607	653	4	florentin	florentin	PROPN
ejpam-6607	653	5	smarandache	smarandache	NOUN
ejpam-6607	653	6	.	.	PUNCT
ejpam-6607	654	1	hyperuncertain	hyperuncertain	PROPN
ejpam-6607	654	2	,	,	PUNCT
ejpam-6607	654	3	superuncertain	superuncertain	VERB
ejpam-6607	654	4	,	,	PUNCT
ejpam-6607	654	5	and	and	CCONJ
ejpam-6607	654	6	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6607	654	7	sets	set	NOUN
ejpam-6607	654	8	/	/	SYM
ejpam-6607	654	9	logics	logic	NOUN
ejpam-6607	654	10	/	/	SYM
ejpam-6607	654	11	probabilities	probability	NOUN
ejpam-6607	654	12	/	/	SYM
ejpam-6607	654	13	statistics	statistic	NOUN
ejpam-6607	654	14	.	.	PUNCT
ejpam-6607	655	1	infinite	infinite	ADJ
ejpam-6607	655	2	study	study	NOUN
ejpam-6607	655	3	,	,	PUNCT
ejpam-6607	655	4	2017	2017	NUM
ejpam-6607	655	5	.	.	PUNCT
ejpam-6607	656	1	[	[	X
ejpam-6607	656	2	8	8	NUM
ejpam-6607	656	3	]	]	PUNCT
ejpam-6607	656	4	zdzis	zdzis	NOUN
ejpam-6607	656	5	law	law	NOUN
ejpam-6607	656	6	pawlak	pawlak	NOUN
ejpam-6607	656	7	.	.	PUNCT
ejpam-6607	657	1	rough	rough	ADJ
ejpam-6607	657	2	sets	set	NOUN
ejpam-6607	657	3	.	.	PUNCT
ejpam-6607	658	1	international	international	ADJ
ejpam-6607	658	2	journal	journal	PROPN
ejpam-6607	658	3	of	of	ADP
ejpam-6607	658	4	computer	computer	PROPN
ejpam-6607	658	5	&	&	CCONJ
ejpam-6607	658	6	information	information	NOUN
ejpam-6607	658	7	sciences	sciences	PROPN
ejpam-6607	658	8	,	,	PUNCT
ejpam-6607	658	9	11:341–356	11:341–356	NUM
ejpam-6607	658	10	,	,	PUNCT
ejpam-6607	658	11	1982	1982	NUM
ejpam-6607	658	12	.	.	PUNCT
ejpam-6607	659	1	[	[	X
ejpam-6607	659	2	9	9	NUM
ejpam-6607	659	3	]	]	PUNCT
ejpam-6607	659	4	takaaki	takaaki	NOUN
ejpam-6607	659	5	fujita	fujita	NOUN
ejpam-6607	659	6	and	and	CCONJ
ejpam-6607	659	7	florentin	florentin	PROPN
ejpam-6607	659	8	smarandache	smarandache	PROPN
ejpam-6607	659	9	.	.	PUNCT
ejpam-6607	660	1	a	a	DET
ejpam-6607	660	2	concise	concise	ADJ
ejpam-6607	660	3	introduction	introduction	NOUN
ejpam-6607	660	4	to	to	ADP
ejpam-6607	660	5	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6607	660	6	,	,	PUNCT
ejpam-6607	660	7	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6607	660	8	,	,	PUNCT
ejpam-6607	660	9	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6607	660	10	,	,	PUNCT
ejpam-6607	660	11	hypersoft	hypersoft	NOUN
ejpam-6607	660	12	,	,	PUNCT
ejpam-6607	660	13	and	and	CCONJ
ejpam-6607	660	14	hyperrough	hyperrough	NOUN
ejpam-6607	660	15	sets	set	VERB
ejpam-6607	660	16	with	with	ADP
ejpam-6607	660	17	practical	practical	ADJ
ejpam-6607	660	18	examples	example	NOUN
ejpam-6607	660	19	.	.	PUNCT
ejpam-6607	661	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	661	2	sets	set	NOUN
ejpam-6607	661	3	and	and	CCONJ
ejpam-6607	661	4	systems	system	NOUN
ejpam-6607	661	5	,	,	PUNCT
ejpam-6607	661	6	80:609–631	80:609–631	NUM
ejpam-6607	661	7	,	,	PUNCT
ejpam-6607	661	8	2025	2025	NUM
ejpam-6607	661	9	.	.	PUNCT
ejpam-6607	662	1	[	[	X
ejpam-6607	662	2	10	10	NUM
ejpam-6607	662	3	]	]	X
ejpam-6607	662	4	krassimir	krassimir	NOUN
ejpam-6607	662	5	atanassov	atanassov	NOUN
ejpam-6607	662	6	and	and	CCONJ
ejpam-6607	662	7	george	george	PROPN
ejpam-6607	662	8	gargov	gargov	PROPN
ejpam-6607	662	9	.	.	PUNCT
ejpam-6607	663	1	elements	element	NOUN
ejpam-6607	663	2	of	of	ADP
ejpam-6607	663	3	intuitionistic	intuitionistic	ADJ
ejpam-6607	663	4	fuzzy	fuzzy	ADJ
ejpam-6607	663	5	logic	logic	NOUN
ejpam-6607	663	6	.	.	PUNCT
ejpam-6607	664	1	part	part	NOUN
ejpam-6607	664	2	i.	i.	PROPN
ejpam-6607	664	3	fuzzy	fuzzy	PROPN
ejpam-6607	664	4	sets	set	NOUN
ejpam-6607	664	5	and	and	CCONJ
ejpam-6607	664	6	systems	system	NOUN
ejpam-6607	664	7	,	,	PUNCT
ejpam-6607	664	8	95(1):39–52	95(1):39–52	NUM
ejpam-6607	664	9	,	,	PUNCT
ejpam-6607	664	10	1998	1998	NUM
ejpam-6607	664	11	.	.	PUNCT
ejpam-6607	665	1	[	[	X
ejpam-6607	665	2	11	11	NUM
ejpam-6607	665	3	]	]	X
ejpam-6607	665	4	muhammad	muhammad	PROPN
ejpam-6607	665	5	akram	akram	PROPN
ejpam-6607	665	6	,	,	PUNCT
ejpam-6607	665	7	bijan	bijan	PROPN
ejpam-6607	665	8	davvaz	davvaz	NOUN
ejpam-6607	665	9	,	,	PUNCT
ejpam-6607	665	10	and	and	CCONJ
ejpam-6607	665	11	feng	feng	PROPN
ejpam-6607	665	12	feng	feng	PROPN
ejpam-6607	665	13	.	.	PUNCT
ejpam-6607	666	1	intuitionistic	intuitionistic	ADJ
ejpam-6607	666	2	fuzzy	fuzzy	ADJ
ejpam-6607	666	3	soft	soft	ADJ
ejpam-6607	666	4	k	k	NOUN
ejpam-6607	666	5	-	-	PUNCT
ejpam-6607	666	6	algebras	algebra	NOUN
ejpam-6607	666	7	.	.	PUNCT
ejpam-6607	667	1	mathematics	mathematic	NOUN
ejpam-6607	667	2	in	in	ADP
ejpam-6607	667	3	computer	computer	NOUN
ejpam-6607	667	4	science	science	NOUN
ejpam-6607	667	5	,	,	PUNCT
ejpam-6607	667	6	7:353–365	7:353–365	PROPN
ejpam-6607	667	7	,	,	PUNCT
ejpam-6607	667	8	2013	2013	NUM
ejpam-6607	667	9	.	.	PUNCT
ejpam-6607	668	1	[	[	X
ejpam-6607	668	2	12	12	NUM
ejpam-6607	668	3	]	]	X
ejpam-6607	668	4	bui	bui	PROPN
ejpam-6607	668	5	cong	cong	NOUN
ejpam-6607	668	6	cuong	cuong	PROPN
ejpam-6607	668	7	and	and	CCONJ
ejpam-6607	668	8	vladik	vladik	PROPN
ejpam-6607	668	9	kreinovich	kreinovich	PROPN
ejpam-6607	668	10	.	.	PUNCT
ejpam-6607	669	1	picture	picture	NOUN
ejpam-6607	669	2	fuzzy	fuzzy	ADJ
ejpam-6607	669	3	sets	set	NOUN
ejpam-6607	669	4	-	-	PUNCT
ejpam-6607	669	5	a	a	DET
ejpam-6607	669	6	new	new	ADJ
ejpam-6607	669	7	concept	concept	NOUN
ejpam-6607	669	8	for	for	ADP
ejpam-6607	669	9	computational	computational	ADJ
ejpam-6607	669	10	intelligence	intelligence	NOUN
ejpam-6607	669	11	problems	problem	NOUN
ejpam-6607	669	12	.	.	PUNCT
ejpam-6607	670	1	in	in	ADP
ejpam-6607	670	2	2013	2013	NUM
ejpam-6607	670	3	third	third	ADJ
ejpam-6607	670	4	world	world	NOUN
ejpam-6607	670	5	congress	congress	PROPN
ejpam-6607	670	6	on	on	ADP
ejpam-6607	670	7	information	information	NOUN
ejpam-6607	670	8	and	and	CCONJ
ejpam-6607	670	9	communication	communication	NOUN
ejpam-6607	670	10	technologies	technology	NOUN
ejpam-6607	670	11	(	(	PUNCT
ejpam-6607	670	12	wict	wict	NOUN
ejpam-6607	670	13	2013	2013	NUM
ejpam-6607	670	14	)	)	PUNCT
ejpam-6607	670	15	,	,	PUNCT
ejpam-6607	670	16	pages	page	NOUN
ejpam-6607	670	17	1–6	1–6	NUM
ejpam-6607	670	18	.	.	PUNCT
ejpam-6607	670	19	ieee	ieee	PROPN
ejpam-6607	670	20	,	,	PUNCT
ejpam-6607	670	21	2013	2013	NUM
ejpam-6607	670	22	.	.	PUNCT
ejpam-6607	671	1	[	[	X
ejpam-6607	671	2	13	13	NUM
ejpam-6607	671	3	]	]	X
ejpam-6607	671	4	wen	wen	PROPN
ejpam-6607	671	5	-	-	PUNCT
ejpam-6607	671	6	ran	run	VERB
ejpam-6607	671	7	zhang	zhang	PROPN
ejpam-6607	671	8	.	.	PUNCT
ejpam-6607	672	1	bipolar	bipolar	ADJ
ejpam-6607	672	2	fuzzy	fuzzy	ADJ
ejpam-6607	672	3	sets	set	NOUN
ejpam-6607	672	4	.	.	PUNCT
ejpam-6607	673	1	1997	1997	NUM
ejpam-6607	673	2	.	.	PUNCT
ejpam-6607	674	1	[	[	X
ejpam-6607	674	2	14	14	NUM
ejpam-6607	674	3	]	]	X
ejpam-6607	674	4	wen	wen	PROPN
ejpam-6607	674	5	-	-	PUNCT
ejpam-6607	674	6	ran	run	VERB
ejpam-6607	674	7	zhang	zhang	PROPN
ejpam-6607	674	8	.	.	PUNCT
ejpam-6607	675	1	bipolar	bipolar	ADJ
ejpam-6607	675	2	fuzzy	fuzzy	ADJ
ejpam-6607	675	3	sets	set	NOUN
ejpam-6607	675	4	and	and	CCONJ
ejpam-6607	675	5	relations	relation	NOUN
ejpam-6607	675	6	:	:	PUNCT
ejpam-6607	675	7	a	a	DET
ejpam-6607	675	8	computational	computational	ADJ
ejpam-6607	675	9	framework	framework	NOUN
ejpam-6607	675	10	for	for	ADP
ejpam-6607	675	11	cognitive	cognitive	ADJ
ejpam-6607	675	12	modeling	modeling	NOUN
ejpam-6607	675	13	and	and	CCONJ
ejpam-6607	675	14	multiagent	multiagent	ADJ
ejpam-6607	675	15	decision	decision	NOUN
ejpam-6607	675	16	analysis	analysis	NOUN
ejpam-6607	675	17	.	.	PUNCT
ejpam-6607	676	1	nafips	nafip	NOUN
ejpam-6607	676	2	/	/	SYM
ejpam-6607	676	3	ifis	ifis	PROPN
ejpam-6607	676	4	/	/	SYM
ejpam-6607	676	5	nasa	nasa	PROPN
ejpam-6607	676	6	’	'	PUNCT
ejpam-6607	676	7	94	94	NUM
ejpam-6607	676	8	.	.	PUNCT
ejpam-6607	677	1	proceedings	proceeding	NOUN
ejpam-6607	677	2	of	of	ADP
ejpam-6607	677	3	the	the	DET
ejpam-6607	677	4	first	first	ADJ
ejpam-6607	677	5	international	international	ADJ
ejpam-6607	677	6	joint	joint	ADJ
ejpam-6607	677	7	conference	conference	NOUN
ejpam-6607	677	8	of	of	ADP
ejpam-6607	677	9	the	the	DET
ejpam-6607	677	10	north	north	ADJ
ejpam-6607	677	11	american	american	ADJ
ejpam-6607	677	12	fuzzy	fuzzy	ADJ
ejpam-6607	677	13	information	information	NOUN
ejpam-6607	677	14	processing	processing	NOUN
ejpam-6607	677	15	society	society	NOUN
ejpam-6607	677	16	biannual	biannual	ADJ
ejpam-6607	677	17	conference	conference	NOUN
ejpam-6607	677	18	.	.	PUNCT
ejpam-6607	678	1	the	the	DET
ejpam-6607	678	2	industrial	industrial	ADJ
ejpam-6607	678	3	fuzzy	fuzzy	ADJ
ejpam-6607	678	4	control	control	NOUN
ejpam-6607	678	5	and	and	CCONJ
ejpam-6607	678	6	intellige	intellige	NOUN
ejpam-6607	678	7	,	,	PUNCT
ejpam-6607	678	8	pages	page	NOUN
ejpam-6607	678	9	305–309	305–309	NUM
ejpam-6607	678	10	,	,	PUNCT
ejpam-6607	678	11	1994	1994	NUM
ejpam-6607	678	12	.	.	PUNCT
ejpam-6607	679	1	[	[	X
ejpam-6607	679	2	15	15	NUM
ejpam-6607	679	3	]	]	X
ejpam-6607	679	4	vicenç	vicenç	PROPN
ejpam-6607	679	5	torra	torra	VERB
ejpam-6607	679	6	and	and	CCONJ
ejpam-6607	679	7	yasuo	yasuo	NOUN
ejpam-6607	679	8	narukawa	narukawa	NOUN
ejpam-6607	679	9	.	.	PUNCT
ejpam-6607	680	1	on	on	ADP
ejpam-6607	680	2	hesitant	hesitant	ADJ
ejpam-6607	680	3	fuzzy	fuzzy	ADJ
ejpam-6607	680	4	sets	set	NOUN
ejpam-6607	680	5	and	and	CCONJ
ejpam-6607	680	6	decision	decision	NOUN
ejpam-6607	680	7	.	.	PUNCT
ejpam-6607	681	1	in	in	ADP
ejpam-6607	681	2	2009	2009	NUM
ejpam-6607	681	3	ieee	ieee	NOUN
ejpam-6607	681	4	international	international	ADJ
ejpam-6607	681	5	conference	conference	NOUN
ejpam-6607	681	6	on	on	ADP
ejpam-6607	681	7	fuzzy	fuzzy	ADJ
ejpam-6607	681	8	systems	system	NOUN
ejpam-6607	681	9	,	,	PUNCT
ejpam-6607	681	10	pages	page	NOUN
ejpam-6607	681	11	1378–1382	1378–1382	NUM
ejpam-6607	681	12	.	.	PUNCT
ejpam-6607	682	1	ieee	ieee	PROPN
ejpam-6607	682	2	,	,	PUNCT
ejpam-6607	682	3	2009	2009	NUM
ejpam-6607	682	4	.	.	PUNCT
ejpam-6607	683	1	[	[	X
ejpam-6607	683	2	16	16	NUM
ejpam-6607	683	3	]	]	X
ejpam-6607	683	4	zeshui	zeshui	PROPN
ejpam-6607	684	1	xu	xu	PROPN
ejpam-6607	684	2	.	.	PUNCT
ejpam-6607	685	1	hesitant	hesitant	ADJ
ejpam-6607	685	2	fuzzy	fuzzy	ADJ
ejpam-6607	685	3	sets	set	NOUN
ejpam-6607	685	4	theory	theory	NOUN
ejpam-6607	685	5	,	,	PUNCT
ejpam-6607	685	6	volume	volume	NOUN
ejpam-6607	685	7	314	314	NUM
ejpam-6607	685	8	.	.	PUNCT
ejpam-6607	685	9	springer	springer	NOUN
ejpam-6607	685	10	,	,	PUNCT
ejpam-6607	685	11	2014	2014	NUM
ejpam-6607	685	12	.	.	PUNCT
ejpam-6607	686	1	[	[	X
ejpam-6607	686	2	17	17	NUM
ejpam-6607	686	3	]	]	PUNCT
ejpam-6607	686	4	florentin	florentin	PROPN
ejpam-6607	686	5	smarandache	smarandache	NOUN
ejpam-6607	686	6	.	.	PUNCT
ejpam-6607	687	1	neutrosophy	neutrosophy	NOUN
ejpam-6607	687	2	:	:	PUNCT
ejpam-6607	687	3	neutrosophic	neutrosophic	ADJ
ejpam-6607	687	4	probability	probability	NOUN
ejpam-6607	687	5	,	,	PUNCT
ejpam-6607	687	6	set	set	NOUN
ejpam-6607	687	7	,	,	PUNCT
ejpam-6607	687	8	and	and	CCONJ
ejpam-6607	687	9	logic	logic	NOUN
ejpam-6607	687	10	:	:	PUNCT
ejpam-6607	687	11	analytic	analytic	ADJ
ejpam-6607	687	12	synthesis	synthesis	NOUN
ejpam-6607	687	13	&	&	CCONJ
ejpam-6607	687	14	synthetic	synthetic	ADJ
ejpam-6607	687	15	analysis	analysis	NOUN
ejpam-6607	687	16	.	.	PUNCT
ejpam-6607	688	1	1998	1998	NUM
ejpam-6607	688	2	.	.	PUNCT
ejpam-6607	689	1	[	[	X
ejpam-6607	689	2	18	18	NUM
ejpam-6607	689	3	]	]	PUNCT
ejpam-6607	689	4	said	say	VERB
ejpam-6607	689	5	broumi	broumi	PROPN
ejpam-6607	689	6	,	,	PUNCT
ejpam-6607	689	7	mohamed	mohamed	PROPN
ejpam-6607	689	8	talea	talea	PROPN
ejpam-6607	689	9	,	,	PUNCT
ejpam-6607	689	10	assia	assia	PROPN
ejpam-6607	689	11	bakali	bakali	VERB
ejpam-6607	689	12	,	,	PUNCT
ejpam-6607	689	13	and	and	CCONJ
ejpam-6607	689	14	florentin	florentin	PROPN
ejpam-6607	689	15	smarandache	smarandache	NOUN
ejpam-6607	689	16	.	.	PUNCT
ejpam-6607	690	1	single	single	ADJ
ejpam-6607	690	2	valued	value	VERB
ejpam-6607	690	3	neutrosophic	neutrosophic	ADJ
ejpam-6607	690	4	graphs	graph	NOUN
ejpam-6607	690	5	.	.	PUNCT
ejpam-6607	691	1	journal	journal	NOUN
ejpam-6607	691	2	of	of	ADP
ejpam-6607	691	3	new	new	ADJ
ejpam-6607	691	4	theory	theory	NOUN
ejpam-6607	691	5	,	,	PUNCT
ejpam-6607	691	6	(	(	PUNCT
ejpam-6607	691	7	10):86–101	10):86–101	PROPN
ejpam-6607	691	8	,	,	PUNCT
ejpam-6607	691	9	2016	2016	NUM
ejpam-6607	691	10	.	.	PUNCT
ejpam-6607	692	1	[	[	X
ejpam-6607	692	2	19	19	NUM
ejpam-6607	692	3	]	]	PUNCT
ejpam-6607	692	4	florentin	florentin	PROPN
ejpam-6607	692	5	smarandache	smarandache	PROPN
ejpam-6607	692	6	.	.	PUNCT
ejpam-6607	693	1	plithogeny	plithogeny	PROPN
ejpam-6607	693	2	,	,	PUNCT
ejpam-6607	693	3	plithogenic	plithogenic	ADJ
ejpam-6607	693	4	set	set	NOUN
ejpam-6607	693	5	,	,	PUNCT
ejpam-6607	693	6	logic	logic	NOUN
ejpam-6607	693	7	,	,	PUNCT
ejpam-6607	693	8	probability	probability	NOUN
ejpam-6607	693	9	,	,	PUNCT
ejpam-6607	693	10	and	and	CCONJ
ejpam-6607	693	11	statistics	statistic	NOUN
ejpam-6607	693	12	.	.	PUNCT
ejpam-6607	694	1	infinite	infinite	ADJ
ejpam-6607	694	2	study	study	NOUN
ejpam-6607	694	3	,	,	PUNCT
ejpam-6607	694	4	2017	2017	NUM
ejpam-6607	694	5	.	.	PUNCT
ejpam-6607	695	1	t.	t.	PROPN
ejpam-6607	695	2	fujita	fujita	PROPN
ejpam-6607	695	3	,	,	PUNCT
ejpam-6607	695	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	695	5	/	/	SYM
ejpam-6607	695	6	eur	eur	PROPN
ejpam-6607	695	7	.	.	PUNCT
ejpam-6607	696	1	j.	j.	PROPN
ejpam-6607	696	2	pure	pure	PROPN
ejpam-6607	696	3	appl	appl	PROPN
ejpam-6607	696	4	.	.	PROPN
ejpam-6607	696	5	math	math	PROPN
ejpam-6607	696	6	,	,	PUNCT
ejpam-6607	696	7	18	18	NUM
ejpam-6607	696	8	(	(	PUNCT
ejpam-6607	696	9	3	3	NUM
ejpam-6607	696	10	)	)	PUNCT
ejpam-6607	696	11	(	(	PUNCT
ejpam-6607	696	12	2025	2025	NUM
ejpam-6607	696	13	)	)	PUNCT
ejpam-6607	696	14	,	,	PUNCT
ejpam-6607	696	15	6607	6607	NUM
ejpam-6607	696	16	31	31	NUM
ejpam-6607	696	17	of	of	ADP
ejpam-6607	696	18	33	33	NUM
ejpam-6607	696	19	[	[	SYM
ejpam-6607	696	20	20	20	NUM
ejpam-6607	696	21	]	]	PUNCT
ejpam-6607	696	22	nivetha	nivetha	PROPN
ejpam-6607	696	23	martin	martin	PROPN
ejpam-6607	696	24	.	.	PUNCT
ejpam-6607	697	1	plithogenic	plithogenic	PROPN
ejpam-6607	697	2	swara	swara	NOUN
ejpam-6607	697	3	-	-	PUNCT
ejpam-6607	697	4	topsis	topsis	NOUN
ejpam-6607	697	5	decision	decision	NOUN
ejpam-6607	697	6	making	make	VERB
ejpam-6607	697	7	on	on	ADP
ejpam-6607	697	8	food	food	NOUN
ejpam-6607	697	9	processing	processing	NOUN
ejpam-6607	697	10	methods	method	NOUN
ejpam-6607	697	11	with	with	ADP
ejpam-6607	697	12	different	different	ADJ
ejpam-6607	697	13	normalization	normalization	NOUN
ejpam-6607	697	14	techniques	technique	NOUN
ejpam-6607	697	15	.	.	PUNCT
ejpam-6607	698	1	advances	advance	NOUN
ejpam-6607	698	2	in	in	ADP
ejpam-6607	698	3	decision	decision	NOUN
ejpam-6607	698	4	making	making	NOUN
ejpam-6607	698	5	,	,	PUNCT
ejpam-6607	698	6	69	69	NUM
ejpam-6607	698	7	,	,	PUNCT
ejpam-6607	698	8	2022	2022	NUM
ejpam-6607	698	9	.	.	PUNCT
ejpam-6607	699	1	[	[	X
ejpam-6607	699	2	21	21	NUM
ejpam-6607	699	3	]	]	PUNCT
ejpam-6607	699	4	florentin	florentin	PROPN
ejpam-6607	699	5	smarandache	smarandache	NOUN
ejpam-6607	699	6	.	.	PUNCT
ejpam-6607	700	1	extension	extension	NOUN
ejpam-6607	700	2	of	of	ADP
ejpam-6607	700	3	soft	soft	ADJ
ejpam-6607	700	4	set	set	NOUN
ejpam-6607	700	5	to	to	ADP
ejpam-6607	700	6	hypersoft	hypersoft	PROPN
ejpam-6607	700	7	set	set	PROPN
ejpam-6607	700	8	,	,	PUNCT
ejpam-6607	700	9	and	and	CCONJ
ejpam-6607	700	10	then	then	ADV
ejpam-6607	700	11	to	to	ADP
ejpam-6607	700	12	plithogenic	plithogenic	ADJ
ejpam-6607	700	13	hypersoft	hypersoft	PROPN
ejpam-6607	700	14	set	set	PROPN
ejpam-6607	700	15	.	.	PUNCT
ejpam-6607	701	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	701	2	sets	set	NOUN
ejpam-6607	701	3	and	and	CCONJ
ejpam-6607	701	4	systems	system	NOUN
ejpam-6607	701	5	,	,	PUNCT
ejpam-6607	701	6	22(1):168–170	22(1):168–170	PROPN
ejpam-6607	701	7	,	,	PUNCT
ejpam-6607	701	8	2018	2018	NUM
ejpam-6607	701	9	.	.	PUNCT
ejpam-6607	702	1	[	[	X
ejpam-6607	702	2	22	22	NUM
ejpam-6607	702	3	]	]	PUNCT
ejpam-6607	702	4	sagvan	sagvan	NOUN
ejpam-6607	702	5	y	y	PROPN
ejpam-6607	702	6	musa	musa	PROPN
ejpam-6607	702	7	and	and	CCONJ
ejpam-6607	702	8	baravan	baravan	NOUN
ejpam-6607	702	9	a	a	DET
ejpam-6607	702	10	asaad	asaad	NOUN
ejpam-6607	702	11	.	.	PUNCT
ejpam-6607	703	1	mappings	mapping	NOUN
ejpam-6607	703	2	on	on	ADP
ejpam-6607	703	3	bipolar	bipolar	ADJ
ejpam-6607	703	4	hypersoft	hypersoft	NOUN
ejpam-6607	703	5	classes	class	NOUN
ejpam-6607	703	6	.	.	PUNCT
ejpam-6607	704	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	704	2	sets	set	NOUN
ejpam-6607	704	3	and	and	CCONJ
ejpam-6607	704	4	systems	system	NOUN
ejpam-6607	704	5	,	,	PUNCT
ejpam-6607	704	6	53(1):36	53(1):36	NOUN
ejpam-6607	704	7	,	,	PUNCT
ejpam-6607	704	8	2023	2023	NUM
ejpam-6607	704	9	.	.	PUNCT
ejpam-6607	705	1	[	[	X
ejpam-6607	705	2	23	23	NUM
ejpam-6607	705	3	]	]	PUNCT
ejpam-6607	705	4	florentin	florentin	PROPN
ejpam-6607	705	5	smarandache	smarandache	PROPN
ejpam-6607	705	6	.	.	PUNCT
ejpam-6607	706	1	foundation	foundation	NOUN
ejpam-6607	706	2	of	of	ADP
ejpam-6607	706	3	the	the	DET
ejpam-6607	706	4	superhypersoft	superhypersoft	PROPN
ejpam-6607	706	5	set	set	VERB
ejpam-6607	706	6	and	and	CCONJ
ejpam-6607	706	7	the	the	DET
ejpam-6607	706	8	fuzzy	fuzzy	ADJ
ejpam-6607	706	9	extension	extension	NOUN
ejpam-6607	706	10	superhypersoft	superhypersoft	PROPN
ejpam-6607	706	11	set	set	VERB
ejpam-6607	706	12	:	:	PUNCT
ejpam-6607	706	13	a	a	DET
ejpam-6607	706	14	new	new	ADJ
ejpam-6607	706	15	vision	vision	NOUN
ejpam-6607	706	16	.	.	PUNCT
ejpam-6607	707	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	707	2	systems	system	NOUN
ejpam-6607	707	3	with	with	ADP
ejpam-6607	707	4	applications	application	NOUN
ejpam-6607	707	5	,	,	PUNCT
ejpam-6607	707	6	11:48–51	11:48–51	NUM
ejpam-6607	707	7	,	,	PUNCT
ejpam-6607	707	8	2023	2023	NUM
ejpam-6607	707	9	.	.	PUNCT
ejpam-6607	708	1	[	[	X
ejpam-6607	708	2	24	24	NUM
ejpam-6607	708	3	]	]	PUNCT
ejpam-6607	708	4	vakkas	vakkas	NOUN
ejpam-6607	708	5	ulucay	ulucay	NOUN
ejpam-6607	708	6	,	,	PUNCT
ejpam-6607	708	7	memet	memet	ADJ
ejpam-6607	708	8	sahin	sahin	NOUN
ejpam-6607	708	9	,	,	PUNCT
ejpam-6607	708	10	and	and	CCONJ
ejpam-6607	708	11	nasruddin	nasruddin	VERB
ejpam-6607	708	12	hassan	hassan	PROPN
ejpam-6607	708	13	.	.	PUNCT
ejpam-6607	709	1	generalized	generalize	VERB
ejpam-6607	709	2	neutrosophic	neutrosophic	ADJ
ejpam-6607	709	3	soft	soft	ADJ
ejpam-6607	709	4	expert	expert	NOUN
ejpam-6607	709	5	set	set	VERB
ejpam-6607	709	6	for	for	ADP
ejpam-6607	709	7	multiple	multiple	ADJ
ejpam-6607	709	8	-	-	PUNCT
ejpam-6607	709	9	criteria	criterion	NOUN
ejpam-6607	709	10	decision	decision	NOUN
ejpam-6607	709	11	-	-	PUNCT
ejpam-6607	709	12	making	making	NOUN
ejpam-6607	709	13	.	.	PUNCT
ejpam-6607	710	1	symmetry	symmetry	NOUN
ejpam-6607	710	2	,	,	PUNCT
ejpam-6607	710	3	10:437	10:437	NUM
ejpam-6607	710	4	,	,	PUNCT
ejpam-6607	710	5	2018	2018	NUM
ejpam-6607	710	6	.	.	PUNCT
ejpam-6607	711	1	[	[	X
ejpam-6607	711	2	25	25	NUM
ejpam-6607	711	3	]	]	X
ejpam-6607	711	4	mohammed	mohammed	PROPN
ejpam-6607	711	5	abdullah	abdullah	PROPN
ejpam-6607	711	6	al	al	PROPN
ejpam-6607	711	7	-	-	PUNCT
ejpam-6607	711	8	hagery	hagery	PROPN
ejpam-6607	711	9	,	,	PUNCT
ejpam-6607	711	10	abdalla	abdalla	PROPN
ejpam-6607	712	1	i	i	PROPN
ejpam-6607	712	2	abdalla	abdalla	PROPN
ejpam-6607	712	3	musa	musa	PROPN
ejpam-6607	712	4	,	,	PUNCT
ejpam-6607	712	5	et	et	PROPN
ejpam-6607	712	6	al	al	PROPN
ejpam-6607	712	7	.	.	PROPN
ejpam-6607	712	8	automated	automate	VERB
ejpam-6607	712	9	credit	credit	NOUN
ejpam-6607	712	10	card	card	NOUN
ejpam-6607	712	11	risk	risk	NOUN
ejpam-6607	712	12	assessment	assessment	NOUN
ejpam-6607	712	13	using	use	VERB
ejpam-6607	712	14	fuzzy	fuzzy	ADJ
ejpam-6607	712	15	parameterized	parameterized	ADJ
ejpam-6607	712	16	neutrosophic	neutrosophic	ADJ
ejpam-6607	712	17	hypersoft	hypersoft	PROPN
ejpam-6607	712	18	expert	expert	NOUN
ejpam-6607	712	19	set	set	VERB
ejpam-6607	712	20	.	.	PUNCT
ejpam-6607	713	1	international	international	ADJ
ejpam-6607	713	2	journal	journal	PROPN
ejpam-6607	713	3	of	of	ADP
ejpam-6607	713	4	neutrosophic	neutrosophic	ADJ
ejpam-6607	713	5	science	science	NOUN
ejpam-6607	713	6	,	,	PUNCT
ejpam-6607	713	7	(	(	PUNCT
ejpam-6607	713	8	1):93–103	1):93–103	NUM
ejpam-6607	713	9	,	,	PUNCT
ejpam-6607	713	10	2025	2025	NUM
ejpam-6607	713	11	.	.	PUNCT
ejpam-6607	714	1	[	[	X
ejpam-6607	714	2	26	26	NUM
ejpam-6607	714	3	]	]	X
ejpam-6607	714	4	muhammad	muhammad	PROPN
ejpam-6607	714	5	ihsan	ihsan	PROPN
ejpam-6607	714	6	,	,	PUNCT
ejpam-6607	714	7	atiqe	atiqe	ADP
ejpam-6607	714	8	ur	ur	PROPN
ejpam-6607	714	9	rahman	rahman	PROPN
ejpam-6607	714	10	,	,	PUNCT
ejpam-6607	714	11	and	and	CCONJ
ejpam-6607	714	12	muhammad	muhammad	PROPN
ejpam-6607	714	13	haris	haris	PROPN
ejpam-6607	714	14	saeed	saeed	PROPN
ejpam-6607	714	15	.	.	PUNCT
ejpam-6607	715	1	single	single	ADJ
ejpam-6607	715	2	valued	value	VERB
ejpam-6607	715	3	neutrosophic	neutrosophic	ADJ
ejpam-6607	715	4	hypersoft	hypersoft	NOUN
ejpam-6607	715	5	expert	expert	NOUN
ejpam-6607	715	6	set	set	VERB
ejpam-6607	715	7	with	with	ADP
ejpam-6607	715	8	application	application	NOUN
ejpam-6607	715	9	in	in	ADP
ejpam-6607	715	10	decision	decision	NOUN
ejpam-6607	715	11	making	making	NOUN
ejpam-6607	715	12	.	.	PUNCT
ejpam-6607	715	13	2021	2021	NUM
ejpam-6607	715	14	.	.	PUNCT
ejpam-6607	716	1	[	[	X
ejpam-6607	716	2	27	27	NUM
ejpam-6607	716	3	]	]	PUNCT
ejpam-6607	716	4	t.	t.	PROPN
ejpam-6607	716	5	r.	r.	PROPN
ejpam-6607	716	6	sooraj	sooraj	PROPN
ejpam-6607	716	7	,	,	PUNCT
ejpam-6607	716	8	r.	r.	PROPN
ejpam-6607	716	9	k.	k.	PROPN
ejpam-6607	716	10	mohanty	mohanty	PROPN
ejpam-6607	716	11	,	,	PUNCT
ejpam-6607	716	12	and	and	CCONJ
ejpam-6607	717	1	b.	b.	PROPN
ejpam-6607	717	2	k.	k.	PROPN
ejpam-6607	717	3	tripathy	tripathy	PROPN
ejpam-6607	717	4	.	.	PUNCT
ejpam-6607	718	1	fuzzy	fuzzy	ADJ
ejpam-6607	718	2	soft	soft	ADJ
ejpam-6607	718	3	set	set	NOUN
ejpam-6607	718	4	theory	theory	NOUN
ejpam-6607	718	5	and	and	CCONJ
ejpam-6607	718	6	its	its	PRON
ejpam-6607	718	7	application	application	NOUN
ejpam-6607	718	8	in	in	ADP
ejpam-6607	718	9	group	group	NOUN
ejpam-6607	718	10	decision	decision	NOUN
ejpam-6607	718	11	making	making	NOUN
ejpam-6607	718	12	.	.	PUNCT
ejpam-6607	719	1	2016	2016	NUM
ejpam-6607	719	2	.	.	PUNCT
ejpam-6607	720	1	[	[	X
ejpam-6607	720	2	28	28	NUM
ejpam-6607	720	3	]	]	X
ejpam-6607	720	4	takaaki	takaaki	NOUN
ejpam-6607	720	5	fujita	fujita	PROPN
ejpam-6607	720	6	.	.	PUNCT
ejpam-6607	721	1	triple	triple	ADV
ejpam-6607	721	2	-	-	PUNCT
ejpam-6607	721	3	valued	value	VERB
ejpam-6607	721	4	neutrosophic	neutrosophic	ADJ
ejpam-6607	721	5	set	set	NOUN
ejpam-6607	721	6	,	,	PUNCT
ejpam-6607	721	7	quadruple	quadruple	ADV
ejpam-6607	721	8	-	-	PUNCT
ejpam-6607	721	9	valued	value	VERB
ejpam-6607	721	10	neutrosophic	neutrosophic	ADJ
ejpam-6607	721	11	set	set	NOUN
ejpam-6607	721	12	,	,	PUNCT
ejpam-6607	721	13	quintuple	quintuple	ADV
ejpam-6607	721	14	-	-	PUNCT
ejpam-6607	721	15	valued	value	VERB
ejpam-6607	721	16	neutrosophic	neutrosophic	ADJ
ejpam-6607	721	17	set	set	NOUN
ejpam-6607	721	18	,	,	PUNCT
ejpam-6607	721	19	and	and	CCONJ
ejpam-6607	721	20	double	double	ADV
ejpam-6607	721	21	-	-	PUNCT
ejpam-6607	721	22	valued	value	VERB
ejpam-6607	721	23	indetermsoft	indetermsoft	ADV
ejpam-6607	721	24	set	set	PROPN
ejpam-6607	721	25	.	.	PUNCT
ejpam-6607	722	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	722	2	systems	system	NOUN
ejpam-6607	722	3	with	with	ADP
ejpam-6607	722	4	applications	application	NOUN
ejpam-6607	722	5	,	,	PUNCT
ejpam-6607	722	6	25(5):3	25(5):3	PROPN
ejpam-6607	722	7	,	,	PUNCT
ejpam-6607	722	8	2025	2025	NUM
ejpam-6607	722	9	.	.	PUNCT
ejpam-6607	723	1	[	[	X
ejpam-6607	723	2	29	29	NUM
ejpam-6607	723	3	]	]	X
ejpam-6607	723	4	tao	tao	PROPN
ejpam-6607	723	5	shen	shen	PROPN
ejpam-6607	723	6	and	and	CCONJ
ejpam-6607	723	7	chunmei	chunmei	PROPN
ejpam-6607	723	8	mao	mao	PROPN
ejpam-6607	723	9	.	.	PUNCT
ejpam-6607	724	1	indetermsoft	indetermsoft	PROPN
ejpam-6607	724	2	set	set	VERB
ejpam-6607	724	3	for	for	ADP
ejpam-6607	724	4	digital	digital	ADJ
ejpam-6607	724	5	marketing	marketing	NOUN
ejpam-6607	724	6	effectiveness	effectiveness	NOUN
ejpam-6607	724	7	evaluation	evaluation	NOUN
ejpam-6607	724	8	driven	drive	VERB
ejpam-6607	724	9	by	by	ADP
ejpam-6607	724	10	big	big	ADJ
ejpam-6607	724	11	data	datum	NOUN
ejpam-6607	724	12	based	base	VERB
ejpam-6607	724	13	on	on	ADP
ejpam-6607	724	14	consumer	consumer	NOUN
ejpam-6607	724	15	behavior	behavior	NOUN
ejpam-6607	724	16	.	.	PUNCT
ejpam-6607	725	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	725	2	sets	set	NOUN
ejpam-6607	725	3	and	and	CCONJ
ejpam-6607	725	4	systems	system	NOUN
ejpam-6607	725	5	,	,	PUNCT
ejpam-6607	725	6	82:352–369	82:352–369	PROPN
ejpam-6607	725	7	,	,	PUNCT
ejpam-6607	725	8	2025	2025	NUM
ejpam-6607	725	9	.	.	PUNCT
ejpam-6607	726	1	[	[	X
ejpam-6607	726	2	30	30	NUM
ejpam-6607	726	3	]	]	X
ejpam-6607	726	4	li	li	PROPN
ejpam-6607	726	5	li	li	PROPN
ejpam-6607	726	6	.	.	PROPN
ejpam-6607	726	7	indetermsoft	indetermsoft	PROPN
ejpam-6607	726	8	set	set	VERB
ejpam-6607	726	9	for	for	ADP
ejpam-6607	726	10	talent	talent	NOUN
ejpam-6607	726	11	training	training	NOUN
ejpam-6607	726	12	quality	quality	NOUN
ejpam-6607	726	13	assessment	assessment	NOUN
ejpam-6607	726	14	in	in	ADP
ejpam-6607	726	15	university	university	NOUN
ejpam-6607	726	16	engineering	engineering	NOUN
ejpam-6607	726	17	management	management	NOUN
ejpam-6607	726	18	under	under	ADP
ejpam-6607	726	19	the	the	DET
ejpam-6607	726	20	background	background	NOUN
ejpam-6607	726	21	of	of	ADP
ejpam-6607	726	22	”	"	PUNCT
ejpam-6607	726	23	dual	dual	ADJ
ejpam-6607	726	24	carbon	carbon	NOUN
ejpam-6607	726	25	”	"	PUNCT
ejpam-6607	726	26	.	.	PUNCT
ejpam-6607	727	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	727	2	sets	set	NOUN
ejpam-6607	727	3	and	and	CCONJ
ejpam-6607	727	4	systems	system	NOUN
ejpam-6607	727	5	,	,	PUNCT
ejpam-6607	727	6	83:148–158	83:148–158	NUM
ejpam-6607	727	7	,	,	PUNCT
ejpam-6607	727	8	2025	2025	NUM
ejpam-6607	727	9	.	.	PUNCT
ejpam-6607	728	1	[	[	X
ejpam-6607	728	2	31	31	NUM
ejpam-6607	728	3	]	]	PUNCT
ejpam-6607	728	4	florentin	florentin	PROPN
ejpam-6607	728	5	smarandache	smarandache	PROPN
ejpam-6607	728	6	.	.	PUNCT
ejpam-6607	729	1	treesoft	treesoft	PROPN
ejpam-6607	729	2	set	set	PROPN
ejpam-6607	729	3	vs.	vs.	ADP
ejpam-6607	729	4	hypersoft	hypersoft	NOUN
ejpam-6607	729	5	set	set	VERB
ejpam-6607	729	6	and	and	CCONJ
ejpam-6607	729	7	fuzzy	fuzzy	ADJ
ejpam-6607	729	8	-	-	PUNCT
ejpam-6607	729	9	extensions	extension	NOUN
ejpam-6607	729	10	of	of	ADP
ejpam-6607	729	11	treesoft	treesoft	NOUN
ejpam-6607	729	12	sets	set	NOUN
ejpam-6607	729	13	.	.	PUNCT
ejpam-6607	730	1	hypersoft	hypersoft	NOUN
ejpam-6607	730	2	set	set	VERB
ejpam-6607	730	3	methods	method	NOUN
ejpam-6607	730	4	in	in	ADP
ejpam-6607	730	5	engineering	engineering	NOUN
ejpam-6607	730	6	,	,	PUNCT
ejpam-6607	730	7	2024	2024	NUM
ejpam-6607	730	8	.	.	PUNCT
ejpam-6607	731	1	[	[	X
ejpam-6607	731	2	32	32	NUM
ejpam-6607	731	3	]	]	X
ejpam-6607	731	4	m	m	VERB
ejpam-6607	731	5	myvizhi	myvizhi	PROPN
ejpam-6607	731	6	,	,	PUNCT
ejpam-6607	731	7	ahmed	ahme	VERB
ejpam-6607	731	8	a	a	DET
ejpam-6607	731	9	metwaly	metwaly	NOUN
ejpam-6607	731	10	,	,	PUNCT
ejpam-6607	731	11	and	and	CCONJ
ejpam-6607	731	12	ahmed	ahmed	PROPN
ejpam-6607	731	13	m	m	PROPN
ejpam-6607	731	14	ali	ali	PROPN
ejpam-6607	731	15	.	.	PROPN
ejpam-6607	731	16	treesoft	treesoft	PROPN
ejpam-6607	731	17	approach	approach	NOUN
ejpam-6607	731	18	for	for	ADP
ejpam-6607	731	19	refining	refine	VERB
ejpam-6607	731	20	air	air	NOUN
ejpam-6607	731	21	pollution	pollution	NOUN
ejpam-6607	731	22	analysis	analysis	NOUN
ejpam-6607	731	23	:	:	PUNCT
ejpam-6607	731	24	a	a	DET
ejpam-6607	731	25	case	case	NOUN
ejpam-6607	731	26	study	study	NOUN
ejpam-6607	731	27	.	.	PUNCT
ejpam-6607	732	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	732	2	sets	set	NOUN
ejpam-6607	732	3	and	and	CCONJ
ejpam-6607	732	4	systems	system	NOUN
ejpam-6607	732	5	,	,	PUNCT
ejpam-6607	732	6	68(1):17	68(1):17	NOUN
ejpam-6607	732	7	,	,	PUNCT
ejpam-6607	732	8	2024	2024	NUM
ejpam-6607	732	9	.	.	PUNCT
ejpam-6607	733	1	[	[	X
ejpam-6607	733	2	33	33	NUM
ejpam-6607	733	3	]	]	PUNCT
ejpam-6607	733	4	takaaki	takaaki	NOUN
ejpam-6607	733	5	fujita	fujita	NOUN
ejpam-6607	733	6	and	and	CCONJ
ejpam-6607	733	7	florentin	florentin	PROPN
ejpam-6607	733	8	smarandache	smarandache	PROPN
ejpam-6607	733	9	.	.	PUNCT
ejpam-6607	734	1	an	an	DET
ejpam-6607	734	2	introduction	introduction	NOUN
ejpam-6607	734	3	to	to	ADP
ejpam-6607	734	4	advanced	advanced	ADJ
ejpam-6607	734	5	soft	soft	ADJ
ejpam-6607	734	6	set	set	ADJ
ejpam-6607	734	7	variants	variant	NOUN
ejpam-6607	734	8	:	:	PUNCT
ejpam-6607	734	9	superhypersoft	superhypersoft	PROPN
ejpam-6607	734	10	sets	set	VERB
ejpam-6607	734	11	,	,	PUNCT
ejpam-6607	734	12	indetermsuperhypersoft	indetermsuperhypersoft	NOUN
ejpam-6607	734	13	sets	set	NOUN
ejpam-6607	734	14	,	,	PUNCT
ejpam-6607	734	15	indetermtreesoft	indetermtreesoft	ADJ
ejpam-6607	734	16	sets	set	NOUN
ejpam-6607	734	17	,	,	PUNCT
ejpam-6607	734	18	bihypersoft	bihypersoft	NOUN
ejpam-6607	734	19	sets	set	NOUN
ejpam-6607	734	20	,	,	PUNCT
ejpam-6607	734	21	graphicsoft	graphicsoft	PROPN
ejpam-6607	734	22	sets	set	NOUN
ejpam-6607	734	23	,	,	PUNCT
ejpam-6607	734	24	and	and	CCONJ
ejpam-6607	734	25	beyond	beyond	ADP
ejpam-6607	734	26	.	.	PUNCT
ejpam-6607	734	27	neutrosophic	neutrosophic	ADJ
ejpam-6607	734	28	sets	set	NOUN
ejpam-6607	734	29	and	and	CCONJ
ejpam-6607	734	30	systems	system	NOUN
ejpam-6607	734	31	,	,	PUNCT
ejpam-6607	734	32	82:817	82:817	NUM
ejpam-6607	734	33	–	–	PUNCT
ejpam-6607	734	34	843	843	NUM
ejpam-6607	734	35	,	,	PUNCT
ejpam-6607	734	36	2025	2025	NUM
ejpam-6607	734	37	.	.	PUNCT
ejpam-6607	735	1	[	[	X
ejpam-6607	735	2	34	34	NUM
ejpam-6607	735	3	]	]	X
ejpam-6607	735	4	r.	r.	PROPN
ejpam-6607	735	5	hema	hema	PROPN
ejpam-6607	735	6	,	,	PUNCT
ejpam-6607	735	7	r.	r.	PROPN
ejpam-6607	735	8	sudharani	sudharani	PROPN
ejpam-6607	735	9	,	,	PUNCT
ejpam-6607	735	10	and	and	CCONJ
ejpam-6607	735	11	m.	m.	PROPN
ejpam-6607	735	12	kavitha	kavitha	PROPN
ejpam-6607	735	13	.	.	PUNCT
ejpam-6607	736	1	a	a	DET
ejpam-6607	736	2	novel	novel	ADJ
ejpam-6607	736	3	approach	approach	NOUN
ejpam-6607	736	4	on	on	ADP
ejpam-6607	736	5	plithogenic	plithogenic	ADJ
ejpam-6607	736	6	interval	interval	NOUN
ejpam-6607	736	7	valued	value	VERB
ejpam-6607	736	8	neutrosophic	neutrosophic	ADJ
ejpam-6607	736	9	hypersoft	hypersoft	NOUN
ejpam-6607	736	10	sets	set	NOUN
ejpam-6607	736	11	and	and	CCONJ
ejpam-6607	736	12	its	its	PRON
ejpam-6607	736	13	application	application	NOUN
ejpam-6607	736	14	in	in	ADP
ejpam-6607	736	15	decision	decision	NOUN
ejpam-6607	736	16	making	making	NOUN
ejpam-6607	736	17	.	.	PUNCT
ejpam-6607	737	1	indian	indian	ADJ
ejpam-6607	737	2	journal	journal	PROPN
ejpam-6607	737	3	of	of	ADP
ejpam-6607	737	4	science	science	NOUN
ejpam-6607	737	5	and	and	CCONJ
ejpam-6607	737	6	technology	technology	NOUN
ejpam-6607	737	7	,	,	PUNCT
ejpam-6607	737	8	2023	2023	NUM
ejpam-6607	737	9	.	.	PUNCT
ejpam-6607	738	1	[	[	X
ejpam-6607	738	2	35	35	NUM
ejpam-6607	738	3	]	]	X
ejpam-6607	738	4	sagvan	sagvan	NOUN
ejpam-6607	738	5	y	y	PROPN
ejpam-6607	738	6	musa	musa	PROPN
ejpam-6607	738	7	and	and	CCONJ
ejpam-6607	738	8	baravan	baravan	NOUN
ejpam-6607	738	9	a	a	DET
ejpam-6607	738	10	asaad	asaad	NOUN
ejpam-6607	738	11	.	.	PUNCT
ejpam-6607	739	1	a	a	DET
ejpam-6607	739	2	progressive	progressive	ADJ
ejpam-6607	739	3	approach	approach	NOUN
ejpam-6607	739	4	to	to	ADP
ejpam-6607	739	5	multi	multi	ADJ
ejpam-6607	739	6	-	-	ADJ
ejpam-6607	739	7	criteria	criterion	NOUN
ejpam-6607	739	8	group	group	NOUN
ejpam-6607	739	9	decision	decision	NOUN
ejpam-6607	739	10	-	-	PUNCT
ejpam-6607	739	11	making	making	NOUN
ejpam-6607	739	12	:	:	PUNCT
ejpam-6607	739	13	n	n	CCONJ
ejpam-6607	739	14	-	-	PUNCT
ejpam-6607	739	15	bipolar	bipolar	ADJ
ejpam-6607	739	16	hypersoft	hypersoft	NOUN
ejpam-6607	739	17	topology	topology	NOUN
ejpam-6607	739	18	perspective	perspective	NOUN
ejpam-6607	739	19	.	.	PUNCT
ejpam-6607	740	1	plos	plos	PROPN
ejpam-6607	740	2	one	one	NUM
ejpam-6607	740	3	,	,	PUNCT
ejpam-6607	740	4	19(5):e0304016	19(5):e0304016	NUM
ejpam-6607	740	5	,	,	PUNCT
ejpam-6607	740	6	2024	2024	NUM
ejpam-6607	740	7	.	.	PUNCT
ejpam-6607	741	1	[	[	X
ejpam-6607	741	2	36	36	NUM
ejpam-6607	741	3	]	]	X
ejpam-6607	741	4	muhammad	muhammad	PROPN
ejpam-6607	741	5	saeed	saeed	PROPN
ejpam-6607	741	6	,	,	PUNCT
ejpam-6607	741	7	muhammad	muhammad	PROPN
ejpam-6607	741	8	khubab	khubab	PROPN
ejpam-6607	741	9	siddique	siddique	PROPN
ejpam-6607	741	10	,	,	PUNCT
ejpam-6607	741	11	muhammad	muhammad	PROPN
ejpam-6607	741	12	ahsan	ahsan	PROPN
ejpam-6607	741	13	,	,	PUNCT
ejpam-6607	741	14	muhammad	muhammad	PROPN
ejpam-6607	741	15	rayees	rayees	PROPN
ejpam-6607	741	16	ahmad	ahmad	PROPN
ejpam-6607	741	17	,	,	PUNCT
ejpam-6607	741	18	and	and	CCONJ
ejpam-6607	741	19	atiqe	atiqe	ADP
ejpam-6607	741	20	ur	ur	PROPN
ejpam-6607	741	21	rahman	rahman	PROPN
ejpam-6607	741	22	.	.	PUNCT
ejpam-6607	742	1	a	a	DET
ejpam-6607	742	2	novel	novel	ADJ
ejpam-6607	742	3	approach	approach	NOUN
ejpam-6607	742	4	to	to	ADP
ejpam-6607	742	5	the	the	DET
ejpam-6607	742	6	rudiments	rudiment	NOUN
ejpam-6607	742	7	of	of	ADP
ejpam-6607	742	8	t.	t.	PROPN
ejpam-6607	742	9	fujita	fujita	PROPN
ejpam-6607	742	10	,	,	PUNCT
ejpam-6607	742	11	f.smarandache	f.smarandache	NOUN
ejpam-6607	742	12	/	/	SYM
ejpam-6607	742	13	eur	eur	PROPN
ejpam-6607	742	14	.	.	PUNCT
ejpam-6607	743	1	j.	j.	PROPN
ejpam-6607	743	2	pure	pure	PROPN
ejpam-6607	743	3	appl	appl	PROPN
ejpam-6607	743	4	.	.	PROPN
ejpam-6607	743	5	math	math	PROPN
ejpam-6607	743	6	,	,	PUNCT
ejpam-6607	743	7	18	18	NUM
ejpam-6607	743	8	(	(	PUNCT
ejpam-6607	743	9	3	3	NUM
ejpam-6607	743	10	)	)	PUNCT
ejpam-6607	743	11	(	(	PUNCT
ejpam-6607	743	12	2025	2025	NUM
ejpam-6607	743	13	)	)	PUNCT
ejpam-6607	743	14	,	,	PUNCT
ejpam-6607	743	15	6607	6607	NUM
ejpam-6607	743	16	32	32	NUM
ejpam-6607	743	17	of	of	ADP
ejpam-6607	743	18	33	33	NUM
ejpam-6607	743	19	hypersoft	hypersoft	NOUN
ejpam-6607	743	20	graphs	graph	NOUN
ejpam-6607	743	21	.	.	PUNCT
ejpam-6607	744	1	theory	theory	NOUN
ejpam-6607	744	2	and	and	CCONJ
ejpam-6607	744	3	application	application	NOUN
ejpam-6607	744	4	of	of	ADP
ejpam-6607	744	5	hypersoft	hypersoft	PROPN
ejpam-6607	744	6	set	set	NOUN
ejpam-6607	744	7	,	,	PUNCT
ejpam-6607	744	8	pons	pon	NOUN
ejpam-6607	744	9	publication	publication	NOUN
ejpam-6607	744	10	house	house	PROPN
ejpam-6607	744	11	,	,	PUNCT
ejpam-6607	744	12	brussel	brussel	PROPN
ejpam-6607	744	13	,	,	PUNCT
ejpam-6607	744	14	pages	page	NOUN
ejpam-6607	744	15	203–214	203–214	NUM
ejpam-6607	744	16	,	,	PUNCT
ejpam-6607	744	17	2021	2021	NUM
ejpam-6607	744	18	.	.	PUNCT
ejpam-6607	745	1	[	[	X
ejpam-6607	745	2	37	37	NUM
ejpam-6607	745	3	]	]	X
ejpam-6607	745	4	mona	mona	PROPN
ejpam-6607	745	5	mohamed	mohamed	PROPN
ejpam-6607	745	6	,	,	PUNCT
ejpam-6607	745	7	ahmed	ahmed	PROPN
ejpam-6607	745	8	m	m	PROPN
ejpam-6607	745	9	abdelmouty	abdelmouty	PROPN
ejpam-6607	745	10	,	,	PUNCT
ejpam-6607	745	11	khalid	khalid	PROPN
ejpam-6607	745	12	mohamed	mohamed	PROPN
ejpam-6607	745	13	,	,	PUNCT
ejpam-6607	745	14	and	and	CCONJ
ejpam-6607	745	15	florentin	florentin	PROPN
ejpam-6607	745	16	smarandache	smarandache	PROPN
ejpam-6607	745	17	.	.	PUNCT
ejpam-6607	745	18	superhypersoft	superhypersoft	NOUN
ejpam-6607	745	19	-	-	PUNCT
ejpam-6607	745	20	driven	drive	VERB
ejpam-6607	745	21	evaluation	evaluation	NOUN
ejpam-6607	745	22	of	of	ADP
ejpam-6607	745	23	smart	smart	ADJ
ejpam-6607	745	24	transportation	transportation	NOUN
ejpam-6607	745	25	in	in	ADP
ejpam-6607	745	26	centroidousmoosra	centroidousmoosra	NOUN
ejpam-6607	745	27	:	:	PUNCT
ejpam-6607	745	28	real	real	ADJ
ejpam-6607	745	29	-	-	PUNCT
ejpam-6607	745	30	world	world	NOUN
ejpam-6607	745	31	insights	insight	NOUN
ejpam-6607	745	32	for	for	ADP
ejpam-6607	745	33	the	the	DET
ejpam-6607	745	34	uav	uav	PROPN
ejpam-6607	745	35	era	era	NOUN
ejpam-6607	745	36	.	.	PUNCT
ejpam-6607	746	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	746	2	sets	set	NOUN
ejpam-6607	746	3	and	and	CCONJ
ejpam-6607	746	4	systems	system	NOUN
ejpam-6607	746	5	,	,	PUNCT
ejpam-6607	746	6	78:149	78:149	NUM
ejpam-6607	746	7	–	–	PUNCT
ejpam-6607	746	8	163	163	NUM
ejpam-6607	746	9	,	,	PUNCT
ejpam-6607	746	10	2025	2025	NUM
ejpam-6607	746	11	.	.	PUNCT
ejpam-6607	747	1	[	[	X
ejpam-6607	747	2	38	38	NUM
ejpam-6607	747	3	]	]	PUNCT
ejpam-6607	747	4	john	john	PROPN
ejpam-6607	747	5	archibald	archibald	PROPN
ejpam-6607	747	6	wheeler	wheeler	PROPN
ejpam-6607	747	7	and	and	CCONJ
ejpam-6607	747	8	wojciech	wojciech	PROPN
ejpam-6607	747	9	hubert	hubert	PROPN
ejpam-6607	747	10	zurek	zurek	PROPN
ejpam-6607	747	11	.	.	PUNCT
ejpam-6607	747	12	quantum	quantum	PROPN
ejpam-6607	747	13	theory	theory	NOUN
ejpam-6607	747	14	and	and	CCONJ
ejpam-6607	747	15	measurement	measurement	NOUN
ejpam-6607	747	16	.	.	PUNCT
ejpam-6607	748	1	princeton	princeton	PROPN
ejpam-6607	748	2	university	university	PROPN
ejpam-6607	748	3	press	press	NOUN
ejpam-6607	748	4	,	,	PUNCT
ejpam-6607	748	5	2014	2014	NUM
ejpam-6607	748	6	.	.	PUNCT
ejpam-6607	749	1	[	[	X
ejpam-6607	749	2	39	39	NUM
ejpam-6607	749	3	]	]	PUNCT
ejpam-6607	749	4	paul	paul	PROPN
ejpam-6607	749	5	busch	busch	PROPN
ejpam-6607	749	6	,	,	PUNCT
ejpam-6607	749	7	pekka	pekka	PROPN
ejpam-6607	749	8	j	j	PROPN
ejpam-6607	749	9	lahti	lahti	PROPN
ejpam-6607	749	10	,	,	PUNCT
ejpam-6607	749	11	and	and	CCONJ
ejpam-6607	749	12	peter	peter	PROPN
ejpam-6607	749	13	mittelstaedt	mittelstaedt	NOUN
ejpam-6607	749	14	.	.	PUNCT
ejpam-6607	750	1	the	the	DET
ejpam-6607	750	2	quantum	quantum	PROPN
ejpam-6607	750	3	theory	theory	NOUN
ejpam-6607	750	4	of	of	ADP
ejpam-6607	750	5	measurement	measurement	NOUN
ejpam-6607	750	6	.	.	PUNCT
ejpam-6607	751	1	springer	springer	NOUN
ejpam-6607	751	2	,	,	PUNCT
ejpam-6607	751	3	1996	1996	NUM
ejpam-6607	751	4	.	.	PUNCT
ejpam-6607	752	1	[	[	X
ejpam-6607	752	2	40	40	NUM
ejpam-6607	752	3	]	]	PUNCT
ejpam-6607	752	4	jozef	jozef	PROPN
ejpam-6607	752	5	gruska	gruska	PROPN
ejpam-6607	752	6	et	et	PROPN
ejpam-6607	752	7	al	al	PROPN
ejpam-6607	752	8	.	.	PUNCT
ejpam-6607	752	9	quantum	quantum	PROPN
ejpam-6607	752	10	computing	computing	NOUN
ejpam-6607	752	11	,	,	PUNCT
ejpam-6607	752	12	volume	volume	NOUN
ejpam-6607	752	13	2005	2005	NUM
ejpam-6607	752	14	.	.	PUNCT
ejpam-6607	753	1	mcgraw	mcgraw	PROPN
ejpam-6607	753	2	-	-	PUNCT
ejpam-6607	753	3	hill	hill	PROPN
ejpam-6607	753	4	london	london	PROPN
ejpam-6607	753	5	,	,	PUNCT
ejpam-6607	753	6	1999	1999	NUM
ejpam-6607	753	7	.	.	PUNCT
ejpam-6607	754	1	[	[	X
ejpam-6607	754	2	41	41	NUM
ejpam-6607	754	3	]	]	X
ejpam-6607	754	4	andrew	andrew	PROPN
ejpam-6607	754	5	steane	steane	PROPN
ejpam-6607	754	6	.	.	PUNCT
ejpam-6607	755	1	quantum	quantum	PROPN
ejpam-6607	755	2	computing	computing	NOUN
ejpam-6607	755	3	.	.	PUNCT
ejpam-6607	756	1	reports	report	NOUN
ejpam-6607	756	2	on	on	ADP
ejpam-6607	756	3	progress	progress	NOUN
ejpam-6607	756	4	in	in	ADP
ejpam-6607	756	5	physics	physics	NOUN
ejpam-6607	756	6	,	,	PUNCT
ejpam-6607	756	7	61(2):117	61(2):117	NUM
ejpam-6607	756	8	,	,	PUNCT
ejpam-6607	756	9	1998	1998	NUM
ejpam-6607	756	10	.	.	PUNCT
ejpam-6607	757	1	[	[	X
ejpam-6607	757	2	42	42	NUM
ejpam-6607	757	3	]	]	PUNCT
ejpam-6607	757	4	renata	renata	NOUN
ejpam-6607	757	5	reiser	reiser	NOUN
ejpam-6607	757	6	,	,	PUNCT
ejpam-6607	757	7	alexandre	alexandre	PROPN
ejpam-6607	757	8	lemke	lemke	PROPN
ejpam-6607	757	9	,	,	PUNCT
ejpam-6607	757	10	anderson	anderson	PROPN
ejpam-6607	757	11	avila	avila	PROPN
ejpam-6607	757	12	,	,	PUNCT
ejpam-6607	757	13	júlia	júlia	PROPN
ejpam-6607	757	14	vieira	vieira	PROPN
ejpam-6607	757	15	,	,	PUNCT
ejpam-6607	757	16	mauŕıcio	mauŕıcio	NOUN
ejpam-6607	757	17	pilla	pilla	NOUN
ejpam-6607	757	18	,	,	PUNCT
ejpam-6607	757	19	and	and	CCONJ
ejpam-6607	757	20	andré	andré	ADJ
ejpam-6607	757	21	du	du	PROPN
ejpam-6607	757	22	bois	bois	PROPN
ejpam-6607	757	23	.	.	PUNCT
ejpam-6607	757	24	interpretations	interpretation	NOUN
ejpam-6607	757	25	on	on	ADP
ejpam-6607	757	26	quantum	quantum	ADJ
ejpam-6607	757	27	fuzzy	fuzzy	ADJ
ejpam-6607	757	28	computing	computing	NOUN
ejpam-6607	757	29	:	:	PUNCT
ejpam-6607	757	30	intuitionistic	intuitionistic	ADJ
ejpam-6607	757	31	fuzzy	fuzzy	ADJ
ejpam-6607	757	32	operations×	operations×	ADJ
ejpam-6607	757	33	quantum	quantum	NOUN
ejpam-6607	757	34	operators	operator	NOUN
ejpam-6607	757	35	.	.	PUNCT
ejpam-6607	758	1	electronic	electronic	ADJ
ejpam-6607	758	2	notes	note	NOUN
ejpam-6607	758	3	in	in	ADP
ejpam-6607	758	4	theoretical	theoretical	ADJ
ejpam-6607	758	5	computer	computer	NOUN
ejpam-6607	758	6	science	science	NOUN
ejpam-6607	758	7	,	,	PUNCT
ejpam-6607	758	8	324:135–150	324:135–150	NUM
ejpam-6607	758	9	,	,	PUNCT
ejpam-6607	758	10	2016	2016	NUM
ejpam-6607	758	11	.	.	PUNCT
ejpam-6607	759	1	[	[	X
ejpam-6607	759	2	43	43	NUM
ejpam-6607	759	3	]	]	X
ejpam-6607	759	4	nguyen	nguyen	PROPN
ejpam-6607	759	5	van	van	PROPN
ejpam-6607	759	6	han	han	PROPN
ejpam-6607	759	7	and	and	CCONJ
ejpam-6607	759	8	phan	phan	PROPN
ejpam-6607	759	9	cong	cong	PROPN
ejpam-6607	759	10	vinh	vinh	PROPN
ejpam-6607	759	11	.	.	PUNCT
ejpam-6607	760	1	modeling	model	VERB
ejpam-6607	760	2	with	with	ADP
ejpam-6607	760	3	words	word	NOUN
ejpam-6607	760	4	:	:	PUNCT
ejpam-6607	760	5	steps	step	NOUN
ejpam-6607	760	6	towards	towards	ADP
ejpam-6607	760	7	a	a	DET
ejpam-6607	760	8	fuzzy	fuzzy	ADJ
ejpam-6607	760	9	quantum	quantum	ADJ
ejpam-6607	760	10	logic	logic	NOUN
ejpam-6607	760	11	.	.	PUNCT
ejpam-6607	761	1	in	in	ADP
ejpam-6607	761	2	international	international	ADJ
ejpam-6607	761	3	conference	conference	NOUN
ejpam-6607	761	4	on	on	ADP
ejpam-6607	761	5	nature	nature	NOUN
ejpam-6607	761	6	of	of	ADP
ejpam-6607	761	7	computation	computation	NOUN
ejpam-6607	761	8	and	and	CCONJ
ejpam-6607	761	9	communication	communication	NOUN
ejpam-6607	761	10	,	,	PUNCT
ejpam-6607	761	11	pages	page	NOUN
ejpam-6607	761	12	3–8	3–8	NUM
ejpam-6607	761	13	.	.	PUNCT
ejpam-6607	761	14	springer	springer	NOUN
ejpam-6607	761	15	,	,	PUNCT
ejpam-6607	761	16	2022	2022	NUM
ejpam-6607	761	17	.	.	PUNCT
ejpam-6607	762	1	[	[	X
ejpam-6607	762	2	44	44	NUM
ejpam-6607	762	3	]	]	PUNCT
ejpam-6607	762	4	raymond	raymond	PROPN
ejpam-6607	762	5	muscat	muscat	PROPN
ejpam-6607	762	6	.	.	PUNCT
ejpam-6607	763	1	data	data	NOUN
ejpam-6607	763	2	-	-	PUNCT
ejpam-6607	763	3	driven	drive	VERB
ejpam-6607	763	4	modelling	modelling	NOUN
ejpam-6607	763	5	and	and	CCONJ
ejpam-6607	763	6	prediction	prediction	NOUN
ejpam-6607	763	7	of	of	ADP
ejpam-6607	763	8	alloy	alloy	NOUN
ejpam-6607	763	9	steel	steel	NOUN
ejpam-6607	763	10	properties	property	NOUN
ejpam-6607	763	11	using	use	VERB
ejpam-6607	763	12	fuzzy	fuzzy	ADJ
ejpam-6607	763	13	systems	system	NOUN
ejpam-6607	763	14	with	with	ADP
ejpam-6607	763	15	special	special	ADJ
ejpam-6607	763	16	emphasis	emphasis	NOUN
ejpam-6607	763	17	on	on	ADP
ejpam-6607	763	18	type-2	type-2	NUM
ejpam-6607	763	19	and	and	CCONJ
ejpam-6607	763	20	quantum	quantum	ADJ
ejpam-6607	763	21	fuzzy	fuzzy	ADJ
ejpam-6607	763	22	sets	set	NOUN
ejpam-6607	763	23	.	.	PUNCT
ejpam-6607	764	1	phd	phd	NOUN
ejpam-6607	764	2	thesis	thesis	PROPN
ejpam-6607	764	3	,	,	PUNCT
ejpam-6607	764	4	university	university	PROPN
ejpam-6607	764	5	of	of	ADP
ejpam-6607	764	6	sheffield	sheffield	PROPN
ejpam-6607	764	7	,	,	PUNCT
ejpam-6607	764	8	2020	2020	NUM
ejpam-6607	764	9	.	.	PUNCT
ejpam-6607	765	1	[	[	X
ejpam-6607	765	2	45	45	NUM
ejpam-6607	765	3	]	]	PUNCT
ejpam-6607	765	4	reinhard	reinhard	NOUN
ejpam-6607	765	5	diestel	diestel	PROPN
ejpam-6607	765	6	.	.	PUNCT
ejpam-6607	765	7	graph	graph	NOUN
ejpam-6607	765	8	theory	theory	NOUN
ejpam-6607	765	9	3rd	3rd	PROPN
ejpam-6607	765	10	ed	ed	NOUN
ejpam-6607	765	11	.	.	PUNCT
ejpam-6607	766	1	graduate	graduate	ADJ
ejpam-6607	766	2	texts	text	NOUN
ejpam-6607	766	3	in	in	ADP
ejpam-6607	766	4	mathematics	mathematic	NOUN
ejpam-6607	766	5	,	,	PUNCT
ejpam-6607	766	6	173(33):12	173(33):12	NUM
ejpam-6607	766	7	,	,	PUNCT
ejpam-6607	766	8	2005	2005	NUM
ejpam-6607	766	9	.	.	PUNCT
ejpam-6607	767	1	[	[	X
ejpam-6607	767	2	46	46	NUM
ejpam-6607	767	3	]	]	PUNCT
ejpam-6607	767	4	alain	alain	PROPN
ejpam-6607	767	5	bretto	bretto	PROPN
ejpam-6607	767	6	.	.	PUNCT
ejpam-6607	768	1	hypergraph	hypergraph	PROPN
ejpam-6607	768	2	theory	theory	NOUN
ejpam-6607	768	3	.	.	PUNCT
ejpam-6607	769	1	an	an	DET
ejpam-6607	769	2	introduction	introduction	NOUN
ejpam-6607	769	3	.	.	PUNCT
ejpam-6607	770	1	mathematical	mathematical	ADJ
ejpam-6607	770	2	engineering	engineering	NOUN
ejpam-6607	770	3	.	.	PUNCT
ejpam-6607	771	1	cham	cham	PROPN
ejpam-6607	771	2	:	:	PUNCT
ejpam-6607	771	3	springer	springer	NOUN
ejpam-6607	771	4	,	,	PUNCT
ejpam-6607	771	5	1	1	NUM
ejpam-6607	771	6	,	,	PUNCT
ejpam-6607	771	7	2013	2013	NUM
ejpam-6607	771	8	.	.	PUNCT
ejpam-6607	772	1	[	[	X
ejpam-6607	772	2	47	47	NUM
ejpam-6607	772	3	]	]	PUNCT
ejpam-6607	772	4	claude	claude	PROPN
ejpam-6607	772	5	berge	berge	PROPN
ejpam-6607	772	6	.	.	PUNCT
ejpam-6607	773	1	hypergraphs	hypergraph	NOUN
ejpam-6607	773	2	:	:	PUNCT
ejpam-6607	773	3	combinatorics	combinatoric	NOUN
ejpam-6607	773	4	of	of	ADP
ejpam-6607	773	5	finite	finite	PROPN
ejpam-6607	773	6	sets	set	NOUN
ejpam-6607	773	7	,	,	PUNCT
ejpam-6607	773	8	volume	volume	NOUN
ejpam-6607	773	9	45	45	NUM
ejpam-6607	773	10	.	.	PUNCT
ejpam-6607	774	1	elsevier	elsevier	NOUN
ejpam-6607	774	2	,	,	PUNCT
ejpam-6607	774	3	1984	1984	NUM
ejpam-6607	774	4	.	.	PUNCT
ejpam-6607	775	1	[	[	X
ejpam-6607	775	2	48	48	NUM
ejpam-6607	775	3	]	]	X
ejpam-6607	775	4	rui	rui	PROPN
ejpam-6607	775	5	xu	xu	PROPN
ejpam-6607	775	6	and	and	CCONJ
ejpam-6607	775	7	cun	cun	PROPN
ejpam-6607	775	8	-	-	PUNCT
ejpam-6607	775	9	quan	quan	PROPN
ejpam-6607	775	10	zhang	zhang	PROPN
ejpam-6607	775	11	.	.	PUNCT
ejpam-6607	776	1	on	on	ADP
ejpam-6607	776	2	flows	flow	NOUN
ejpam-6607	776	3	in	in	ADP
ejpam-6607	776	4	bidirected	bidirected	ADJ
ejpam-6607	776	5	graphs	graph	NOUN
ejpam-6607	776	6	.	.	PUNCT
ejpam-6607	777	1	discrete	discrete	ADJ
ejpam-6607	777	2	mathematics	mathematic	NOUN
ejpam-6607	777	3	,	,	PUNCT
ejpam-6607	777	4	299(1	299(1	NUM
ejpam-6607	777	5	-	-	SYM
ejpam-6607	777	6	3):335–343	3):335–343	NUM
ejpam-6607	777	7	,	,	PUNCT
ejpam-6607	777	8	2005	2005	NUM
ejpam-6607	777	9	.	.	PUNCT
ejpam-6607	778	1	[	[	X
ejpam-6607	778	2	49	49	NUM
ejpam-6607	778	3	]	]	X
ejpam-6607	778	4	ouahiba	ouahiba	PROPN
ejpam-6607	778	5	bessouf	bessouf	PROPN
ejpam-6607	778	6	,	,	PUNCT
ejpam-6607	778	7	abdelkader	abdelkader	PROPN
ejpam-6607	778	8	khelladi	khelladi	PROPN
ejpam-6607	778	9	,	,	PUNCT
ejpam-6607	778	10	and	and	CCONJ
ejpam-6607	778	11	thomas	thomas	PROPN
ejpam-6607	778	12	zaslavsky	zaslavsky	PROPN
ejpam-6607	778	13	.	.	PUNCT
ejpam-6607	779	1	transitive	transitive	ADJ
ejpam-6607	779	2	closure	closure	NOUN
ejpam-6607	779	3	and	and	CCONJ
ejpam-6607	779	4	transitive	transitive	ADJ
ejpam-6607	779	5	reduction	reduction	NOUN
ejpam-6607	779	6	in	in	ADP
ejpam-6607	779	7	bidirected	bidirected	ADJ
ejpam-6607	779	8	graphs	graph	NOUN
ejpam-6607	779	9	.	.	PUNCT
ejpam-6607	780	1	czechoslovak	czechoslovak	ADJ
ejpam-6607	780	2	mathematical	mathematical	PROPN
ejpam-6607	780	3	journal	journal	NOUN
ejpam-6607	780	4	,	,	PUNCT
ejpam-6607	780	5	69:295	69:295	NUM
ejpam-6607	780	6	–	–	PUNCT
ejpam-6607	780	7	315	315	NUM
ejpam-6607	780	8	,	,	PUNCT
ejpam-6607	780	9	2016	2016	NUM
ejpam-6607	780	10	.	.	PUNCT
ejpam-6607	781	1	[	[	X
ejpam-6607	781	2	50	50	NUM
ejpam-6607	781	3	]	]	PUNCT
ejpam-6607	781	4	florentin	florentin	PROPN
ejpam-6607	781	5	smarandache	smarandache	NOUN
ejpam-6607	781	6	.	.	PUNCT
ejpam-6607	782	1	extension	extension	NOUN
ejpam-6607	782	2	of	of	ADP
ejpam-6607	782	3	hypergraph	hypergraph	NOUN
ejpam-6607	782	4	to	to	ADP
ejpam-6607	782	5	n	n	CCONJ
ejpam-6607	782	6	-	-	PUNCT
ejpam-6607	782	7	superhypergraph	superhypergraph	NOUN
ejpam-6607	782	8	and	and	CCONJ
ejpam-6607	782	9	to	to	ADP
ejpam-6607	782	10	plithogenic	plithogenic	ADJ
ejpam-6607	782	11	n	n	CCONJ
ejpam-6607	782	12	-	-	PUNCT
ejpam-6607	782	13	superhypergraph	superhypergraph	NOUN
ejpam-6607	782	14	,	,	PUNCT
ejpam-6607	782	15	and	and	CCONJ
ejpam-6607	782	16	extension	extension	NOUN
ejpam-6607	782	17	of	of	ADP
ejpam-6607	782	18	hyperalgebra	hyperalgebra	NOUN
ejpam-6607	782	19	to	to	ADP
ejpam-6607	782	20	n	n	CCONJ
ejpam-6607	782	21	-	-	PUNCT
ejpam-6607	782	22	ary	ary	PROPN
ejpam-6607	782	23	(	(	PUNCT
ejpam-6607	782	24	classical	classical	ADJ
ejpam-6607	782	25	/	/	SYM
ejpam-6607	782	26	neutro-/anti-	neutro-/anti-	NOUN
ejpam-6607	782	27	)	)	PUNCT
ejpam-6607	782	28	hyperalgebra	hyperalgebra	NOUN
ejpam-6607	782	29	.	.	PUNCT
ejpam-6607	783	1	infinite	infinite	ADJ
ejpam-6607	783	2	study	study	NOUN
ejpam-6607	783	3	,	,	PUNCT
ejpam-6607	783	4	2020	2020	NUM
ejpam-6607	783	5	.	.	PUNCT
ejpam-6607	784	1	[	[	X
ejpam-6607	784	2	51	51	NUM
ejpam-6607	784	3	]	]	PUNCT
ejpam-6607	784	4	takaaki	takaaki	NOUN
ejpam-6607	784	5	fujita	fujita	NOUN
ejpam-6607	784	6	and	and	CCONJ
ejpam-6607	784	7	florentin	florentin	PROPN
ejpam-6607	784	8	smarandache	smarandache	PROPN
ejpam-6607	784	9	.	.	PUNCT
ejpam-6607	785	1	a	a	DET
ejpam-6607	785	2	concise	concise	ADJ
ejpam-6607	785	3	study	study	NOUN
ejpam-6607	785	4	of	of	ADP
ejpam-6607	785	5	some	some	DET
ejpam-6607	785	6	superhypergraph	superhypergraph	NOUN
ejpam-6607	785	7	classes	class	NOUN
ejpam-6607	785	8	.	.	PUNCT
ejpam-6607	786	1	neutrosophic	neutrosophic	ADJ
ejpam-6607	786	2	sets	set	NOUN
ejpam-6607	786	3	and	and	CCONJ
ejpam-6607	786	4	systems	system	NOUN
ejpam-6607	786	5	,	,	PUNCT
ejpam-6607	786	6	77:548–593	77:548–593	PROPN
ejpam-6607	786	7	,	,	PUNCT
ejpam-6607	786	8	2024	2024	NUM
ejpam-6607	786	9	.	.	PUNCT
ejpam-6607	787	1	[	[	X
ejpam-6607	787	2	52	52	NUM
ejpam-6607	787	3	]	]	X
ejpam-6607	787	4	yousef	yousef	PROPN
ejpam-6607	787	5	al	al	PROPN
ejpam-6607	787	6	-	-	PUNCT
ejpam-6607	787	7	qudah	qudah	PROPN
ejpam-6607	787	8	and	and	CCONJ
ejpam-6607	787	9	nasruddin	nasruddin	VERB
ejpam-6607	787	10	hassan	hassan	PROPN
ejpam-6607	787	11	.	.	PUNCT
ejpam-6607	788	1	bipolar	bipolar	ADJ
ejpam-6607	788	2	fuzzy	fuzzy	ADJ
ejpam-6607	788	3	soft	soft	ADJ
ejpam-6607	788	4	expert	expert	NOUN
ejpam-6607	788	5	set	set	VERB
ejpam-6607	788	6	and	and	CCONJ
ejpam-6607	788	7	its	its	PRON
ejpam-6607	788	8	application	application	NOUN
ejpam-6607	788	9	in	in	ADP
ejpam-6607	788	10	decision	decision	NOUN
ejpam-6607	788	11	making	making	NOUN
ejpam-6607	788	12	.	.	PUNCT
ejpam-6607	789	1	int	int	NOUN
ejpam-6607	789	2	.	.	PUNCT
ejpam-6607	790	1	j.	j.	PROPN
ejpam-6607	790	2	appl	appl	PROPN
ejpam-6607	790	3	.	.	PROPN
ejpam-6607	791	1	decis	decis	PROPN
ejpam-6607	791	2	.	.	PUNCT
ejpam-6607	792	1	sci	sci	PROPN
ejpam-6607	792	2	.	.	PROPN
ejpam-6607	792	3	,	,	PUNCT
ejpam-6607	792	4	10:175–191	10:175–191	NUM
ejpam-6607	792	5	,	,	PUNCT
ejpam-6607	792	6	2017	2017	NUM
ejpam-6607	792	7	.	.	PUNCT
ejpam-6607	793	1	[	[	X
ejpam-6607	793	2	53	53	NUM
ejpam-6607	793	3	]	]	PUNCT
ejpam-6607	793	4	muhammad	muhammad	PROPN
ejpam-6607	793	5	akram	akram	PROPN
ejpam-6607	793	6	,	,	PUNCT
ejpam-6607	793	7	ghous	ghous	PROPN
ejpam-6607	793	8	ali	ali	PROPN
ejpam-6607	793	9	,	,	PUNCT
ejpam-6607	793	10	xindong	xindong	PROPN
ejpam-6607	793	11	peng	peng	PROPN
ejpam-6607	793	12	,	,	PUNCT
ejpam-6607	793	13	and	and	CCONJ
ejpam-6607	793	14	muhammad	muhammad	PROPN
ejpam-6607	793	15	zain	zain	PROPN
ejpam-6607	793	16	ul	ul	PROPN
ejpam-6607	793	17	abidin	abidin	PROPN
ejpam-6607	793	18	.	.	PUNCT
ejpam-6607	793	19	hybrid	hybrid	ADJ
ejpam-6607	793	20	group	group	NOUN
ejpam-6607	793	21	decision	decision	NOUN
ejpam-6607	793	22	-	-	PUNCT
ejpam-6607	793	23	making	making	NOUN
ejpam-6607	793	24	technique	technique	NOUN
ejpam-6607	793	25	under	under	ADP
ejpam-6607	793	26	spherical	spherical	ADJ
ejpam-6607	793	27	fuzzy	fuzzy	ADJ
ejpam-6607	793	28	n	n	CCONJ
ejpam-6607	793	29	-	-	PUNCT
ejpam-6607	793	30	soft	soft	ADJ
ejpam-6607	793	31	expert	expert	NOUN
ejpam-6607	793	32	sets	set	NOUN
ejpam-6607	793	33	.	.	PUNCT
ejpam-6607	794	1	artificial	artificial	ADJ
ejpam-6607	794	2	intelligence	intelligence	NOUN
ejpam-6607	794	3	review	review	NOUN
ejpam-6607	794	4	,	,	PUNCT
ejpam-6607	794	5	55:4117	55:4117	NUM
ejpam-6607	794	6	–	–	PUNCT
ejpam-6607	794	7	4163	4163	NUM
ejpam-6607	794	8	,	,	PUNCT
ejpam-6607	794	9	2021	2021	NUM
ejpam-6607	794	10	.	.	PUNCT
ejpam-6607	795	1	t.	t.	PROPN
ejpam-6607	795	2	fujita	fujita	PROPN
ejpam-6607	795	3	,	,	PUNCT
ejpam-6607	795	4	f.smarandache	f.smarandache	NOUN
ejpam-6607	795	5	/	/	SYM
ejpam-6607	795	6	eur	eur	PROPN
ejpam-6607	795	7	.	.	PUNCT
ejpam-6607	796	1	j.	j.	PROPN
ejpam-6607	796	2	pure	pure	PROPN
ejpam-6607	796	3	appl	appl	PROPN
ejpam-6607	796	4	.	.	PROPN
ejpam-6607	796	5	math	math	PROPN
ejpam-6607	796	6	,	,	PUNCT
ejpam-6607	796	7	18	18	NUM
ejpam-6607	796	8	(	(	PUNCT
ejpam-6607	796	9	3	3	NUM
ejpam-6607	796	10	)	)	PUNCT
ejpam-6607	796	11	(	(	PUNCT
ejpam-6607	796	12	2025	2025	NUM
ejpam-6607	796	13	)	)	PUNCT
ejpam-6607	796	14	,	,	PUNCT
ejpam-6607	796	15	6607	6607	NUM
ejpam-6607	796	16	33	33	NUM
ejpam-6607	796	17	of	of	ADP
ejpam-6607	796	18	33	33	NUM
ejpam-6607	796	19	[	[	SYM
ejpam-6607	796	20	54	54	NUM
ejpam-6607	796	21	]	]	PUNCT
ejpam-6607	796	22	florentin	florentin	PROPN
ejpam-6607	796	23	smarandache	smarandache	PROPN
ejpam-6607	796	24	.	.	PUNCT
ejpam-6607	797	1	soft	soft	ADJ
ejpam-6607	797	2	set	set	VERB
ejpam-6607	797	3	product	product	NOUN
ejpam-6607	797	4	extended	extend	VERB
ejpam-6607	797	5	to	to	ADP
ejpam-6607	797	6	hypersoft	hypersoft	NOUN
ejpam-6607	797	7	set	set	VERB
ejpam-6607	797	8	and	and	CCONJ
ejpam-6607	797	9	indetermsoft	indetermsoft	ADV
ejpam-6607	797	10	set	set	VERB
ejpam-6607	797	11	cartesian	cartesian	ADJ
ejpam-6607	797	12	product	product	NOUN
ejpam-6607	797	13	extended	extend	VERB
ejpam-6607	797	14	to	to	ADP
ejpam-6607	797	15	indetermhypersoft	indetermhypersoft	ADV
ejpam-6607	797	16	set	set	VERB
ejpam-6607	797	17	.	.	PUNCT
ejpam-6607	798	1	journal	journal	NOUN
ejpam-6607	798	2	of	of	ADP
ejpam-6607	798	3	fuzzy	fuzzy	ADJ
ejpam-6607	798	4	extension	extension	NOUN
ejpam-6607	798	5	and	and	CCONJ
ejpam-6607	798	6	applications	application	NOUN
ejpam-6607	798	7	,	,	PUNCT
ejpam-6607	798	8	3(4):313–316	3(4):313–316	NUM
ejpam-6607	798	9	,	,	PUNCT
ejpam-6607	798	10	2022	2022	NUM
ejpam-6607	798	11	.	.	PUNCT
ejpam-6607	799	1	[	[	X
ejpam-6607	799	2	55	55	NUM
ejpam-6607	799	3	]	]	PUNCT
ejpam-6607	799	4	florentin	florentin	PROPN
ejpam-6607	799	5	smarandache	smarandache	PROPN
ejpam-6607	799	6	.	.	PUNCT
ejpam-6607	800	1	introduction	introduction	NOUN
ejpam-6607	800	2	to	to	ADP
ejpam-6607	800	3	superhyperalgebra	superhyperalgebra	NOUN
ejpam-6607	800	4	and	and	CCONJ
ejpam-6607	800	5	neutrosophic	neutrosophic	ADJ
ejpam-6607	800	6	superhyperalgebra	superhyperalgebra	NOUN
ejpam-6607	800	7	.	.	PUNCT
ejpam-6607	801	1	infinite	infinite	ADJ
ejpam-6607	801	2	study	study	NOUN
ejpam-6607	801	3	,	,	PUNCT
ejpam-6607	801	4	2022	2022	NUM
ejpam-6607	801	5	.	.	PUNCT
ejpam-6607	802	1	[	[	X
ejpam-6607	802	2	56	56	NUM
ejpam-6607	802	3	]	]	PUNCT
ejpam-6607	802	4	adebisi	adebisi	PROPN
ejpam-6607	802	5	sunday	sunday	PROPN
ejpam-6607	802	6	adesina	adesina	PROPN
ejpam-6607	802	7	.	.	PUNCT
ejpam-6607	803	1	further	further	ADJ
ejpam-6607	803	2	operations	operation	NOUN
ejpam-6607	803	3	(	(	PUNCT
ejpam-6607	803	4	complement	complement	NOUN
ejpam-6607	803	5	,	,	PUNCT
ejpam-6607	803	6	intersection	intersection	NOUN
ejpam-6607	803	7	,	,	PUNCT
ejpam-6607	803	8	union	union	NOUN
ejpam-6607	803	9	)	)	PUNCT
ejpam-6607	803	10	for	for	ADP
ejpam-6607	803	11	indetermsoft	indetermsoft	PROPN
ejpam-6607	803	12	set	set	NOUN
ejpam-6607	803	13	,	,	PUNCT
ejpam-6607	803	14	indetermhypersoft	indetermhypersoft	ADV
ejpam-6607	803	15	set	set	NOUN
ejpam-6607	803	16	,	,	PUNCT
ejpam-6607	803	17	and	and	CCONJ
ejpam-6607	803	18	treesoft	treesoft	NOUN
ejpam-6607	803	19	set	set	VERB
ejpam-6607	803	20	and	and	CCONJ
ejpam-6607	803	21	their	their	PRON
ejpam-6607	803	22	applications	application	NOUN
ejpam-6607	803	23	.	.	PUNCT
ejpam-6607	804	1	journal	journal	NOUN
ejpam-6607	804	2	of	of	ADP
ejpam-6607	804	3	basic	basic	ADJ
ejpam-6607	804	4	&	&	CCONJ
ejpam-6607	804	5	applied	applied	ADJ
ejpam-6607	804	6	sciences	science	NOUN
ejpam-6607	804	7	,	,	PUNCT
ejpam-6607	804	8	21:47–52	21:47–52	NUM
ejpam-6607	804	9	,	,	PUNCT
ejpam-6607	804	10	2025	2025	NUM
ejpam-6607	804	11	.	.	PUNCT
ejpam-6607	805	1	[	[	X
ejpam-6607	805	2	57	57	NUM
ejpam-6607	805	3	]	]	X
ejpam-6607	805	4	ajoy	ajoy	PROPN
ejpam-6607	805	5	kanti	kanti	PROPN
ejpam-6607	805	6	das	das	PROPN
ejpam-6607	805	7	.	.	PROPN
ejpam-6607	805	8	weighted	weight	VERB
ejpam-6607	805	9	fuzzy	fuzzy	ADJ
ejpam-6607	805	10	soft	soft	ADJ
ejpam-6607	805	11	multiset	multiset	NOUN
ejpam-6607	805	12	and	and	CCONJ
ejpam-6607	805	13	decision	decision	NOUN
ejpam-6607	805	14	-	-	PUNCT
ejpam-6607	805	15	making	making	NOUN
ejpam-6607	805	16	.	.	PUNCT
ejpam-6607	806	1	international	international	ADJ
ejpam-6607	806	2	journal	journal	PROPN
ejpam-6607	806	3	of	of	ADP
ejpam-6607	806	4	machine	machine	NOUN
ejpam-6607	806	5	learning	learning	NOUN
ejpam-6607	806	6	and	and	CCONJ
ejpam-6607	806	7	cybernetics	cybernetic	NOUN
ejpam-6607	806	8	,	,	PUNCT
ejpam-6607	806	9	9(5):787–794	9(5):787–794	NOUN
ejpam-6607	806	10	,	,	PUNCT
ejpam-6607	806	11	2018	2018	NUM
ejpam-6607	806	12	.	.	PUNCT
ejpam-6607	807	1	[	[	X
ejpam-6607	807	2	58	58	NUM
ejpam-6607	807	3	]	]	PUNCT
ejpam-6607	807	4	tm	tm	PROPN
ejpam-6607	807	5	nishad	nishad	PROPN
ejpam-6607	807	6	,	,	PUNCT
ejpam-6607	807	7	talal	talal	PROPN
ejpam-6607	807	8	ali	ali	PROPN
ejpam-6607	807	9	al	al	PROPN
ejpam-6607	807	10	-	-	PUNCT
ejpam-6607	807	11	hawary	hawary	PROPN
ejpam-6607	807	12	,	,	PUNCT
ejpam-6607	807	13	and	and	CCONJ
ejpam-6607	807	14	b	b	PROPN
ejpam-6607	807	15	mohamed	mohamed	PROPN
ejpam-6607	807	16	harif	harif	PROPN
ejpam-6607	807	17	.	.	PUNCT
ejpam-6607	808	1	general	general	ADJ
ejpam-6607	808	2	fuzzy	fuzzy	ADJ
ejpam-6607	808	3	graphs	graph	NOUN
ejpam-6607	808	4	.	.	PUNCT
ejpam-6607	809	1	ratio	ratio	PROPN
ejpam-6607	809	2	mathematica	mathematica	PROPN
ejpam-6607	809	3	,	,	PUNCT
ejpam-6607	809	4	47	47	NUM
ejpam-6607	809	5	,	,	PUNCT
ejpam-6607	809	6	2023	2023	NUM
ejpam-6607	809	7	.	.	PUNCT
ejpam-6607	810	1	[	[	X
ejpam-6607	810	2	59	59	NUM
ejpam-6607	810	3	]	]	PUNCT
ejpam-6607	810	4	takaaki	takaaki	NOUN
ejpam-6607	810	5	fujita	fujita	PROPN
ejpam-6607	810	6	.	.	PUNCT
ejpam-6607	811	1	short	short	ADJ
ejpam-6607	811	2	introduction	introduction	NOUN
ejpam-6607	811	3	to	to	ADP
ejpam-6607	811	4	rough	rough	ADJ
ejpam-6607	811	5	,	,	PUNCT
ejpam-6607	811	6	hyperrough	hyperrough	NOUN
ejpam-6607	811	7	,	,	PUNCT
ejpam-6607	811	8	superhyperrough	superhyperrough	ADJ
ejpam-6607	811	9	,	,	PUNCT
ejpam-6607	811	10	treerough	treerough	NOUN
ejpam-6607	811	11	,	,	PUNCT
ejpam-6607	811	12	and	and	CCONJ
ejpam-6607	811	13	multirough	multirough	NOUN
ejpam-6607	811	14	set	set	NOUN
ejpam-6607	811	15	.	.	PUNCT
ejpam-6607	812	1	advancing	advance	VERB
ejpam-6607	812	2	uncertain	uncertain	ADJ
ejpam-6607	812	3	combinatorics	combinatoric	NOUN
ejpam-6607	812	4	through	through	ADP
ejpam-6607	812	5	graphization	graphization	NOUN
ejpam-6607	812	6	,	,	PUNCT
ejpam-6607	812	7	hyperization	hyperization	NOUN
ejpam-6607	812	8	,	,	PUNCT
ejpam-6607	812	9	and	and	CCONJ
ejpam-6607	812	10	uncertainization	uncertainization	NOUN
ejpam-6607	812	11	:	:	PUNCT
ejpam-6607	812	12	fuzzy	fuzzy	ADJ
ejpam-6607	812	13	,	,	PUNCT
ejpam-6607	812	14	neutrosophic	neutrosophic	ADJ
ejpam-6607	812	15	,	,	PUNCT
ejpam-6607	812	16	soft	soft	ADJ
ejpam-6607	812	17	,	,	PUNCT
ejpam-6607	812	18	rough	rough	ADJ
ejpam-6607	812	19	,	,	PUNCT
ejpam-6607	812	20	and	and	CCONJ
ejpam-6607	812	21	beyond	beyond	ADP
ejpam-6607	812	22	:	:	PUNCT
ejpam-6607	812	23	fifth	fifth	ADJ
ejpam-6607	812	24	volume	volume	NOUN
ejpam-6607	812	25	:	:	PUNCT
ejpam-6607	812	26	various	various	ADJ
ejpam-6607	812	27	superhyperconcepts	superhyperconcept	NOUN
ejpam-6607	812	28	(	(	PUNCT
ejpam-6607	812	29	collected	collect	VERB
ejpam-6607	812	30	papers	paper	NOUN
ejpam-6607	812	31	)	)	PUNCT
ejpam-6607	812	32	,	,	PUNCT
ejpam-6607	812	33	page	page	NOUN
ejpam-6607	812	34	394	394	NUM
ejpam-6607	812	35	,	,	PUNCT
ejpam-6607	812	36	2025	2025	NUM
ejpam-6607	812	37	.	.	PUNCT
ejpam-6607	813	1	[	[	X
ejpam-6607	813	2	60	60	NUM
ejpam-6607	813	3	]	]	PUNCT
ejpam-6607	813	4	takaaki	takaaki	NOUN
ejpam-6607	813	5	fujita	fujita	PROPN
ejpam-6607	813	6	.	.	PUNCT
ejpam-6607	814	1	hyperrough	hyperrough	PROPN
ejpam-6607	814	2	cubic	cubic	PROPN
ejpam-6607	814	3	set	set	NOUN
ejpam-6607	814	4	and	and	CCONJ
ejpam-6607	814	5	superhyperrough	superhyperrough	ADP
ejpam-6607	814	6	cubic	cubic	ADJ
ejpam-6607	814	7	set	set	NOUN
ejpam-6607	814	8	.	.	PUNCT
ejpam-6607	815	1	prospects	prospect	NOUN
ejpam-6607	815	2	for	for	ADP
ejpam-6607	815	3	applied	applied	ADJ
ejpam-6607	815	4	mathematics	mathematic	NOUN
ejpam-6607	815	5	and	and	CCONJ
ejpam-6607	815	6	data	datum	NOUN
ejpam-6607	815	7	analysis	analysis	NOUN
ejpam-6607	815	8	,	,	PUNCT
ejpam-6607	815	9	4(1):28–35	4(1):28–35	NUM
ejpam-6607	815	10	,	,	PUNCT
ejpam-6607	815	11	2024	2024	NUM
ejpam-6607	815	12	.	.	PUNCT
ejpam-6607	816	1	[	[	X
ejpam-6607	816	2	61	61	NUM
ejpam-6607	816	3	]	]	PUNCT
ejpam-6607	816	4	krassimir	krassimir	PROPN
ejpam-6607	816	5	t	t	PROPN
ejpam-6607	816	6	atanassov	atanassov	NOUN
ejpam-6607	816	7	.	.	PUNCT
ejpam-6607	817	1	on	on	ADP
ejpam-6607	817	2	intuitionistic	intuitionistic	ADJ
ejpam-6607	817	3	fuzzy	fuzzy	ADJ
ejpam-6607	817	4	sets	set	NOUN
ejpam-6607	817	5	theory	theory	NOUN
ejpam-6607	817	6	,	,	PUNCT
ejpam-6607	817	7	volume	volume	NOUN
ejpam-6607	817	8	283	283	NUM
ejpam-6607	817	9	.	.	PUNCT
ejpam-6607	818	1	springer	springer	NOUN
ejpam-6607	818	2	,	,	PUNCT
ejpam-6607	818	3	2012	2012	NUM
ejpam-6607	818	4	.	.	PUNCT
ejpam-6607	819	1	[	[	X
ejpam-6607	819	2	62	62	NUM
ejpam-6607	819	3	]	]	PUNCT
ejpam-6607	819	4	ajoy	ajoy	PROPN
ejpam-6607	819	5	kanti	kanti	PROPN
ejpam-6607	819	6	das	das	PROPN
ejpam-6607	819	7	and	and	CCONJ
ejpam-6607	819	8	carlos	carlos	PROPN
ejpam-6607	819	9	granados	granados	PROPN
ejpam-6607	819	10	.	.	PUNCT
ejpam-6607	820	1	fp	fp	ADJ
ejpam-6607	820	2	-	-	PUNCT
ejpam-6607	820	3	intuitionistic	intuitionistic	ADJ
ejpam-6607	820	4	multi	multi	ADJ
ejpam-6607	820	5	fuzzy	fuzzy	ADJ
ejpam-6607	820	6	n	n	CCONJ
ejpam-6607	820	7	-	-	PUNCT
ejpam-6607	820	8	soft	soft	ADJ
ejpam-6607	820	9	set	set	NOUN
ejpam-6607	820	10	and	and	CCONJ
ejpam-6607	820	11	its	its	PRON
ejpam-6607	820	12	induced	induced	ADJ
ejpam-6607	820	13	fp	fp	ADJ
ejpam-6607	820	14	-	-	PUNCT
ejpam-6607	820	15	hesitant	hesitant	ADJ
ejpam-6607	820	16	n	n	CCONJ
ejpam-6607	820	17	soft	soft	ADJ
ejpam-6607	820	18	set	set	NOUN
ejpam-6607	820	19	in	in	ADP
ejpam-6607	820	20	decision	decision	NOUN
ejpam-6607	820	21	-	-	PUNCT
ejpam-6607	820	22	making	making	NOUN
ejpam-6607	820	23	.	.	PUNCT
ejpam-6607	821	1	decision	decision	NOUN
ejpam-6607	821	2	making	making	NOUN
ejpam-6607	821	3	:	:	PUNCT
ejpam-6607	821	4	applications	application	NOUN
ejpam-6607	821	5	in	in	ADP
ejpam-6607	821	6	management	management	NOUN
ejpam-6607	821	7	and	and	CCONJ
ejpam-6607	821	8	engineering	engineering	NOUN
ejpam-6607	821	9	,	,	PUNCT
ejpam-6607	821	10	2022	2022	NUM
ejpam-6607	821	11	.	.	PUNCT
ejpam-6607	822	1	[	[	X
ejpam-6607	822	2	63	63	NUM
ejpam-6607	822	3	]	]	PUNCT
ejpam-6607	822	4	said	say	VERB
ejpam-6607	822	5	broumi	broumi	PROPN
ejpam-6607	822	6	,	,	PUNCT
ejpam-6607	822	7	mohamed	mohamed	PROPN
ejpam-6607	822	8	talea	talea	PROPN
ejpam-6607	822	9	,	,	PUNCT
ejpam-6607	822	10	assia	assia	PROPN
ejpam-6607	822	11	bakali	bakali	VERB
ejpam-6607	822	12	,	,	PUNCT
ejpam-6607	822	13	and	and	CCONJ
ejpam-6607	822	14	florentin	florentin	PROPN
ejpam-6607	822	15	smarandache	smarandache	NOUN
ejpam-6607	822	16	.	.	PUNCT
ejpam-6607	823	1	interval	interval	NOUN
ejpam-6607	823	2	valued	value	VERB
ejpam-6607	823	3	neutrosophic	neutrosophic	ADJ
ejpam-6607	823	4	graphs	graph	NOUN
ejpam-6607	823	5	.	.	PUNCT
ejpam-6607	824	1	critical	critical	ADJ
ejpam-6607	824	2	review	review	NOUN
ejpam-6607	824	3	,	,	PUNCT
ejpam-6607	824	4	xii	xii	PROPN
ejpam-6607	824	5	,	,	PUNCT
ejpam-6607	824	6	2016:5–33	2016:5–33	NUM
ejpam-6607	824	7	,	,	PUNCT
ejpam-6607	824	8	2016	2016	NUM
ejpam-6607	824	9	.	.	PUNCT
ejpam-6607	825	1	[	[	X
ejpam-6607	825	2	64	64	NUM
ejpam-6607	825	3	]	]	PUNCT
ejpam-6607	825	4	florentin	florentin	NOUN
ejpam-6607	825	5	smarandache	smarandache	PROPN
ejpam-6607	825	6	.	.	PUNCT
ejpam-6607	825	7	plithogeny	plithogeny	PROPN
ejpam-6607	825	8	,	,	PUNCT
ejpam-6607	825	9	plithogenic	plithogenic	ADJ
ejpam-6607	825	10	set	set	NOUN
ejpam-6607	825	11	,	,	PUNCT
ejpam-6607	825	12	logic	logic	NOUN
ejpam-6607	825	13	,	,	PUNCT
ejpam-6607	825	14	probability	probability	NOUN
ejpam-6607	825	15	,	,	PUNCT
ejpam-6607	825	16	and	and	CCONJ
ejpam-6607	825	17	statistics	statistic	NOUN
ejpam-6607	825	18	.	.	PUNCT
ejpam-6607	826	1	arxiv	arxiv	PROPN
ejpam-6607	826	2	preprint	preprint	VERB
ejpam-6607	826	3	arxiv:1808.03948	arxiv:1808.03948	NOUN
ejpam-6607	826	4	,	,	PUNCT
ejpam-6607	826	5	2018	2018	NUM
ejpam-6607	826	6	.	.	PUNCT