id	sid	tid	token	lemma	pos
cana-5306	1	1	communications	communication	NOUN
cana-5306	1	2	on	on	ADP
cana-5306	1	3	applied	apply	VERB
cana-5306	1	4	nonlinear	nonlinear	ADJ
cana-5306	1	5	analysis	analysis	NOUN
cana-5306	1	6	issn	issn	NOUN
cana-5306	1	7	:	:	PUNCT
cana-5306	1	8	1074	1074	NUM
cana-5306	1	9	-	-	PUNCT
cana-5306	1	10	133x	133x	NUM
cana-5306	1	11	vol	vol	NOUN
cana-5306	1	12	31	31	NUM
cana-5306	1	13	no	no	NOUN
cana-5306	1	14	.	.	NOUN
cana-5306	1	15	2	2	NUM
cana-5306	1	16	(	(	PUNCT
cana-5306	1	17	2024	2024	NUM
cana-5306	1	18	)	)	PUNCT
cana-5306	1	19	440	440	NUM
cana-5306	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	1	21	analyzing	analyze	VERB
cana-5306	1	22	symmetry	symmetry	NOUN
cana-5306	1	23	in	in	ADP
cana-5306	1	24	group	group	NOUN
cana-5306	1	25	theory	theory	NOUN
cana-5306	1	26	:	:	PUNCT
cana-5306	1	27	applications	application	NOUN
cana-5306	1	28	in	in	ADP
cana-5306	1	29	crystallography	crystallography	NOUN
cana-5306	1	30	1s	1s	NUM
cana-5306	1	31	.	.	PUNCT
cana-5306	2	1	balamuralitharan	balamuralitharan	PROPN
cana-5306	2	2	,	,	PUNCT
cana-5306	2	3	2a	2a	NUM
cana-5306	2	4	.	.	PUNCT
cana-5306	3	1	nasreen	nasreen	VERB
cana-5306	3	2	sultana	sultana	NOUN
cana-5306	3	3	,	,	PUNCT
cana-5306	3	4	3santhoshkumar	3santhoshkumar	NUM
cana-5306	3	5	s.	s.	PROPN
cana-5306	3	6	,	,	PUNCT
cana-5306	3	7	4r	4r	NOUN
cana-5306	3	8	.	.	PUNCT
cana-5306	4	1	arulprakasam	arulprakasam	ADV
cana-5306	4	2	,	,	PUNCT
cana-5306	4	3	5ch.s.s.n	5ch.s.s.n	NUM
cana-5306	4	4	.	.	PUNCT
cana-5306	5	1	murthy	murthy	ADJ
cana-5306	5	2	,	,	PUNCT
cana-5306	5	3	6p.satish	6p.satish	NUM
cana-5306	5	4	,	,	PUNCT
cana-5306	5	5	adjunct	adjunct	ADJ
cana-5306	5	6	faculty	faculty	NOUN
cana-5306	5	7	,	,	PUNCT
cana-5306	5	8	department	department	NOUN
cana-5306	5	9	of	of	ADP
cana-5306	5	10	pure	pure	ADJ
cana-5306	5	11	and	and	CCONJ
cana-5306	5	12	applied	applied	ADJ
cana-5306	5	13	mathematics	mathematic	NOUN
cana-5306	5	14	,	,	PUNCT
cana-5306	5	15	saveetha	saveetha	PROPN
cana-5306	5	16	school	school	PROPN
cana-5306	5	17	of	of	ADP
cana-5306	5	18	engineering	engineering	NOUN
cana-5306	5	19	,	,	PUNCT
cana-5306	5	20	simats	simat	NOUN
cana-5306	5	21	,	,	PUNCT
cana-5306	5	22	chennai	chennai	PROPN
cana-5306	5	23	,	,	PUNCT
cana-5306	5	24	tamil	tamil	PROPN
cana-5306	5	25	nadu	nadu	PROPN
cana-5306	5	26	,	,	PUNCT
cana-5306	5	27	india	india	PROPN
cana-5306	5	28	email	email	NOUN
cana-5306	5	29	i	i	PROPN
cana-5306	5	30	d	d	PROPN
cana-5306	5	31	:	:	PUNCT
cana-5306	5	32	balamurali.maths@gmail.com	balamurali.maths@gmail.com	X
cana-5306	5	33	assistant	assistant	NOUN
cana-5306	5	34	professor	professor	NOUN
cana-5306	5	35	,	,	PUNCT
cana-5306	5	36	department	department	NOUN
cana-5306	5	37	of	of	ADP
cana-5306	5	38	mathematics	mathematics	PROPN
cana-5306	5	39	,	,	PUNCT
cana-5306	5	40	s.d.n.b	s.d.n.b	PROPN
cana-5306	5	41	.	.	PUNCT
cana-5306	6	1	vaishnav	vaishnav	PROPN
cana-5306	6	2	college	college	PROPN
cana-5306	6	3	for	for	ADP
cana-5306	6	4	women	woman	NOUN
cana-5306	6	5	,	,	PUNCT
cana-5306	6	6	chennai	chennai	PROPN
cana-5306	6	7	,	,	PUNCT
cana-5306	6	8	tamil	tamil	PROPN
cana-5306	6	9	nadu	nadu	PROPN
cana-5306	6	10	,	,	PUNCT
cana-5306	6	11	india	india	PROPN
cana-5306	6	12	email	email	NOUN
cana-5306	6	13	:	:	PUNCT
cana-5306	6	14	a.nasreensultana@gmail.com	a.nasreensultana@gmail.com	PROPN
cana-5306	6	15	assistant	assistant	PROPN
cana-5306	6	16	professor	professor	NOUN
cana-5306	6	17	,	,	PUNCT
cana-5306	6	18	department	department	NOUN
cana-5306	6	19	of	of	ADP
cana-5306	6	20	mathematics	mathematic	NOUN
cana-5306	6	21	,	,	PUNCT
cana-5306	6	22	patrician	patrician	ADJ
cana-5306	6	23	college	college	PROPN
cana-5306	6	24	of	of	ADP
cana-5306	6	25	arts	art	NOUN
cana-5306	6	26	and	and	CCONJ
cana-5306	6	27	science	science	NOUN
cana-5306	6	28	,	,	PUNCT
cana-5306	6	29	chennai	chennai	PROPN
cana-5306	6	30	,	,	PUNCT
cana-5306	6	31	india	india	PROPN
cana-5306	6	32	.	.	PUNCT
cana-5306	7	1	santhoshkumarsesa@gmail.com	santhoshkumarsesa@gmail.com	X
cana-5306	8	1	department	department	PROPN
cana-5306	8	2	of	of	ADP
cana-5306	8	3	mathematics	mathematics	PROPN
cana-5306	8	4	,	,	PUNCT
cana-5306	8	5	college	college	NOUN
cana-5306	8	6	of	of	ADP
cana-5306	8	7	engineering	engineering	NOUN
cana-5306	8	8	and	and	CCONJ
cana-5306	8	9	technology	technology	NOUN
cana-5306	8	10	,	,	PUNCT
cana-5306	8	11	srm	srm	PROPN
cana-5306	8	12	institute	institute	PROPN
cana-5306	8	13	of	of	ADP
cana-5306	8	14	science	science	NOUN
cana-5306	8	15	and	and	CCONJ
cana-5306	8	16	technology	technology	NOUN
cana-5306	8	17	,	,	PUNCT
cana-5306	8	18	srm	srm	NOUN
cana-5306	8	19	nagar	nagar	NOUN
cana-5306	8	20	,	,	PUNCT
cana-5306	8	21	kattankulathur	kattankulathur	PROPN
cana-5306	8	22	603203	603203	NUM
cana-5306	8	23	,	,	PUNCT
cana-5306	8	24	chengalpattu	chengalpattu	ADJ
cana-5306	8	25	district	district	NOUN
cana-5306	8	26	,	,	PUNCT
cana-5306	8	27	tamilnadu	tamilnadu	PROPN
cana-5306	8	28	,	,	PUNCT
cana-5306	8	29	india	india	PROPN
cana-5306	8	30	r.aruljeeva@gmail.com	r.aruljeeva@gmail.com	PROPN
cana-5306	8	31	associate	associate	PROPN
cana-5306	8	32	professor	professor	NOUN
cana-5306	8	33	,	,	PUNCT
cana-5306	8	34	department	department	NOUN
cana-5306	8	35	of	of	ADP
cana-5306	8	36	mathematics	mathematics	PROPN
cana-5306	8	37	,	,	PUNCT
cana-5306	8	38	aditya	aditya	PROPN
cana-5306	8	39	university	university	PROPN
cana-5306	8	40	,	,	PUNCT
cana-5306	8	41	surampalem	surampalem	NOUN
cana-5306	8	42	,	,	PUNCT
cana-5306	8	43	india	india	PROPN
cana-5306	8	44	,	,	PUNCT
cana-5306	8	45	chssn.murthy@aec.edu.in	chssn.murthy@aec.edu.in	NOUN
cana-5306	8	46	associate	associate	ADJ
cana-5306	8	47	professor	professor	NOUN
cana-5306	8	48	,	,	PUNCT
cana-5306	8	49	dept	dept	NOUN
cana-5306	8	50	of	of	ADP
cana-5306	8	51	mathematics	mathematic	NOUN
cana-5306	8	52	,	,	PUNCT
cana-5306	8	53	aditya	aditya	PROPN
cana-5306	8	54	university	university	PROPN
cana-5306	8	55	,	,	PUNCT
cana-5306	8	56	surampalem	surampalem	NOUN
cana-5306	8	57	,	,	PUNCT
cana-5306	8	58	india	india	PROPN
cana-5306	8	59	,	,	PUNCT
cana-5306	8	60	satish.papolu@aec.edu.in	satish.papolu@aec.edu.in	CCONJ
cana-5306	8	61	article	article	NOUN
cana-5306	8	62	history	history	NOUN
cana-5306	8	63	:	:	PUNCT
cana-5306	8	64	received	receive	VERB
cana-5306	8	65	:	:	PUNCT
cana-5306	8	66	12	12	NUM
cana-5306	8	67	-	-	SYM
cana-5306	8	68	12	12	NUM
cana-5306	8	69	-	-	PUNCT
cana-5306	8	70	2023	2023	NUM
cana-5306	8	71	revised	revise	VERB
cana-5306	8	72	:	:	PUNCT
cana-5306	8	73	15	15	NUM
cana-5306	8	74	-	-	SYM
cana-5306	8	75	01	01	NUM
cana-5306	8	76	-	-	PUNCT
cana-5306	8	77	2024	2024	NUM
cana-5306	8	78	accepted	accept	VERB
cana-5306	8	79	:	:	PUNCT
cana-5306	8	80	19	19	NUM
cana-5306	8	81	-	-	PUNCT
cana-5306	8	82	02	02	NUM
cana-5306	8	83	-	-	PUNCT
cana-5306	8	84	2024	2024	NUM
cana-5306	8	85	abstract	abstract	NOUN
cana-5306	8	86	:	:	PUNCT
cana-5306	8	87	mathematics	mathematic	NOUN
cana-5306	8	88	relies	rely	VERB
cana-5306	8	89	heavily	heavily	ADV
cana-5306	8	90	on	on	ADP
cana-5306	8	91	symmetry	symmetry	NOUN
cana-5306	8	92	to	to	PART
cana-5306	8	93	study	study	VERB
cana-5306	8	94	crystallography	crystallography	NOUN
cana-5306	8	95	because	because	SCONJ
cana-5306	8	96	this	this	DET
cana-5306	8	97	concept	concept	NOUN
cana-5306	8	98	acts	act	VERB
cana-5306	8	99	as	as	ADP
cana-5306	8	100	an	an	DET
cana-5306	8	101	essential	essential	ADJ
cana-5306	8	102	factor	factor	NOUN
cana-5306	8	103	.	.	PUNCT
cana-5306	9	1	the	the	DET
cana-5306	9	2	paper	paper	NOUN
cana-5306	9	3	investigates	investigate	VERB
cana-5306	9	4	group	group	NOUN
cana-5306	9	5	theory	theory	NOUN
cana-5306	9	6	applications	application	NOUN
cana-5306	9	7	towards	towards	ADP
cana-5306	9	8	crystallographic	crystallographic	ADJ
cana-5306	9	9	symmetry	symmetry	NOUN
cana-5306	9	10	investigations	investigation	NOUN
cana-5306	9	11	through	through	ADP
cana-5306	9	12	examination	examination	NOUN
cana-5306	9	13	of	of	ADP
cana-5306	9	14	symmetry	symmetry	NOUN
cana-5306	9	15	operations	operation	NOUN
cana-5306	9	16	and	and	CCONJ
cana-5306	9	17	crystallographic	crystallographic	ADJ
cana-5306	9	18	point	point	NOUN
cana-5306	9	19	groups	group	NOUN
cana-5306	9	20	and	and	CCONJ
cana-5306	9	21	space	space	NOUN
cana-5306	9	22	groups	group	NOUN
cana-5306	9	23	studies	study	NOUN
cana-5306	9	24	.	.	PUNCT
cana-5306	10	1	a	a	DET
cana-5306	10	2	theoretical	theoretical	ADJ
cana-5306	10	3	model	model	NOUN
cana-5306	10	4	explains	explain	VERB
cana-5306	10	5	why	why	SCONJ
cana-5306	10	6	crystal	crystal	PROPN
cana-5306	10	7	physical	physical	ADJ
cana-5306	10	8	features	feature	NOUN
cana-5306	10	9	including	include	VERB
cana-5306	10	10	optical	optical	ADJ
cana-5306	10	11	properties	property	NOUN
cana-5306	10	12	as	as	ADV
cana-5306	10	13	well	well	ADV
cana-5306	10	14	as	as	ADP
cana-5306	10	15	elasticity	elasticity	NOUN
cana-5306	10	16	and	and	CCONJ
cana-5306	10	17	thermal	thermal	ADJ
cana-5306	10	18	conductivity	conductivity	NOUN
cana-5306	10	19	derive	derive	NOUN
cana-5306	10	20	from	from	ADP
cana-5306	10	21	symmetry	symmetry	NOUN
cana-5306	10	22	relationships	relationship	NOUN
cana-5306	10	23	.	.	PUNCT
cana-5306	11	1	the	the	DET
cana-5306	11	2	research	research	NOUN
cana-5306	11	3	emphasizes	emphasize	VERB
cana-5306	11	4	how	how	SCONJ
cana-5306	11	5	group	group	NOUN
cana-5306	11	6	theory	theory	NOUN
cana-5306	11	7	enables	enable	VERB
cana-5306	11	8	progress	progress	NOUN
cana-5306	11	9	in	in	ADP
cana-5306	11	10	material	material	NOUN
cana-5306	11	11	science	science	NOUN
cana-5306	11	12	and	and	CCONJ
cana-5306	11	13	crystallographic	crystallographic	ADJ
cana-5306	11	14	issue	issue	NOUN
cana-5306	11	15	resolution	resolution	NOUN
cana-5306	11	16	.	.	PUNCT
cana-5306	12	1	keywords	keyword	NOUN
cana-5306	12	2	—	—	PUNCT
cana-5306	12	3	group	group	NOUN
cana-5306	12	4	theory	theory	NOUN
cana-5306	12	5	,	,	PUNCT
cana-5306	12	6	symmetry	symmetry	NOUN
cana-5306	12	7	operations	operation	NOUN
cana-5306	12	8	,	,	PUNCT
cana-5306	12	9	crystallography	crystallography	NOUN
cana-5306	12	10	,	,	PUNCT
cana-5306	12	11	space	space	NOUN
cana-5306	12	12	groups	group	NOUN
cana-5306	12	13	,	,	PUNCT
cana-5306	12	14	point	point	NOUN
cana-5306	12	15	groups	group	NOUN
cana-5306	12	16	,	,	PUNCT
cana-5306	12	17	crystallographic	crystallographic	ADJ
cana-5306	12	18	symmetry	symmetry	NOUN
cana-5306	12	19	,	,	PUNCT
cana-5306	12	20	material	material	NOUN
cana-5306	12	21	science	science	NOUN
cana-5306	12	22	,	,	PUNCT
cana-5306	12	23	symmetry	symmetry	NOUN
cana-5306	12	24	analysis	analysis	NOUN
cana-5306	12	25	,	,	PUNCT
cana-5306	12	26	crystal	crystal	NOUN
cana-5306	12	27	structures	structure	NOUN
cana-5306	12	28	.	.	PUNCT
cana-5306	13	1	i.	i.	PROPN
cana-5306	13	2	introduction	introduction	PROPN
cana-5306	13	3	science	science	NOUN
cana-5306	13	4	makes	make	VERB
cana-5306	13	5	extensive	extensive	ADJ
cana-5306	13	6	use	use	NOUN
cana-5306	13	7	of	of	ADP
cana-5306	13	8	symmetry	symmetry	NOUN
cana-5306	13	9	as	as	ADP
cana-5306	13	10	a	a	DET
cana-5306	13	11	fundamental	fundamental	ADJ
cana-5306	13	12	principle	principle	NOUN
cana-5306	13	13	which	which	PRON
cana-5306	13	14	finds	find	VERB
cana-5306	13	15	critical	critical	ADJ
cana-5306	13	16	applications	application	NOUN
cana-5306	13	17	in	in	ADP
cana-5306	13	18	physical	physical	ADJ
cana-5306	13	19	and	and	CCONJ
cana-5306	13	20	chemical	chemical	NOUN
cana-5306	13	21	systems	system	NOUN
cana-5306	13	22	and	and	CCONJ
cana-5306	13	23	material	material	NOUN
cana-5306	13	24	sciences	science	NOUN
cana-5306	13	25	.	.	PUNCT
cana-5306	14	1	high	high	ADJ
cana-5306	14	2	symmetrical	symmetrical	ADJ
cana-5306	14	3	order	order	NOUN
cana-5306	14	4	enables	enable	VERB
cana-5306	14	5	researchers	researcher	NOUN
cana-5306	14	6	to	to	PART
cana-5306	14	7	classify	classify	VERB
cana-5306	14	8	atomic	atomic	ADJ
cana-5306	14	9	arrangements	arrangement	NOUN
cana-5306	14	10	within	within	ADP
cana-5306	14	11	crystalline	crystalline	ADJ
cana-5306	14	12	solids	solid	NOUN
cana-5306	14	13	allowing	allow	VERB
cana-5306	14	14	them	they	PRON
cana-5306	14	15	to	to	PART
cana-5306	14	16	gain	gain	VERB
cana-5306	14	17	essential	essential	ADJ
cana-5306	14	18	knowledge	knowledge	NOUN
cana-5306	14	19	about	about	ADP
cana-5306	14	20	their	their	PRON
cana-5306	14	21	structural	structural	ADJ
cana-5306	14	22	character	character	NOUN
cana-5306	14	23	and	and	CCONJ
cana-5306	14	24	physical	physical	ADJ
cana-5306	14	25	attributes	attribute	NOUN
cana-5306	14	26	.	.	PUNCT
cana-5306	15	1	the	the	DET
cana-5306	15	2	communications	communication	NOUN
cana-5306	15	3	on	on	ADP
cana-5306	15	4	applied	apply	VERB
cana-5306	15	5	nonlinear	nonlinear	ADJ
cana-5306	15	6	analysis	analysis	NOUN
cana-5306	15	7	issn	issn	NOUN
cana-5306	15	8	:	:	PUNCT
cana-5306	15	9	1074	1074	NUM
cana-5306	15	10	-	-	PUNCT
cana-5306	15	11	133x	133x	NUM
cana-5306	15	12	vol	vol	NOUN
cana-5306	15	13	31	31	NUM
cana-5306	15	14	no	no	NOUN
cana-5306	15	15	.	.	NOUN
cana-5306	15	16	2	2	NUM
cana-5306	15	17	(	(	PUNCT
cana-5306	15	18	2024	2024	NUM
cana-5306	15	19	)	)	PUNCT
cana-5306	15	20	441	441	NUM
cana-5306	15	21	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-5306	15	22	symmetrical	symmetrical	ADJ
cana-5306	15	23	properties	property	NOUN
cana-5306	15	24	of	of	ADP
cana-5306	15	25	materials	material	NOUN
cana-5306	15	26	play	play	VERB
cana-5306	15	27	a	a	DET
cana-5306	15	28	vital	vital	ADJ
cana-5306	15	29	role	role	NOUN
cana-5306	15	30	in	in	ADP
cana-5306	15	31	material	material	NOUN
cana-5306	15	32	behavior	behavior	NOUN
cana-5306	15	33	assessments	assessment	NOUN
cana-5306	15	34	and	and	CCONJ
cana-5306	15	35	group	group	NOUN
cana-5306	15	36	theory	theory	NOUN
cana-5306	15	37	serves	serve	VERB
cana-5306	15	38	as	as	ADP
cana-5306	15	39	an	an	DET
cana-5306	15	40	essential	essential	ADJ
cana-5306	15	41	mathematical	mathematical	ADJ
cana-5306	15	42	tool	tool	NOUN
cana-5306	15	43	to	to	PART
cana-5306	15	44	analyze	analyze	VERB
cana-5306	15	45	these	these	DET
cana-5306	15	46	symmetrical	symmetrical	ADJ
cana-5306	15	47	properties	property	NOUN
cana-5306	15	48	[	[	X
cana-5306	15	49	2	2	NUM
cana-5306	15	50	-	-	SYM
cana-5306	15	51	5	5	NUM
cana-5306	15	52	]	]	PUNCT
cana-5306	15	53	.	.	PUNCT
cana-5306	16	1	the	the	DET
cana-5306	16	2	regular	regular	ADJ
cana-5306	16	3	repetition	repetition	NOUN
cana-5306	16	4	of	of	ADP
cana-5306	16	5	atoms	atom	NOUN
cana-5306	16	6	while	while	SCONJ
cana-5306	16	7	arranged	arrange	VERB
cana-5306	16	8	through	through	ADP
cana-5306	16	9	ions	ion	NOUN
cana-5306	16	10	or	or	CCONJ
cana-5306	16	11	molecules	molecule	NOUN
cana-5306	16	12	creates	create	VERB
cana-5306	16	13	crystals	crystal	NOUN
cana-5306	16	14	into	into	ADP
cana-5306	16	15	a	a	DET
cana-5306	16	16	lattice	lattice	NOUN
cana-5306	16	17	structure	structure	NOUN
cana-5306	16	18	.	.	PUNCT
cana-5306	17	1	the	the	DET
cana-5306	17	2	way	way	NOUN
cana-5306	17	3	a	a	DET
cana-5306	17	4	crystal	crystal	NOUN
cana-5306	17	5	lattice	lattice	NOUN
cana-5306	17	6	responds	respond	VERB
cana-5306	17	7	to	to	ADP
cana-5306	17	8	symmetrical	symmetrical	ADJ
cana-5306	17	9	operations	operation	NOUN
cana-5306	17	10	establishes	establish	VERB
cana-5306	17	11	many	many	ADJ
cana-5306	17	12	physical	physical	ADJ
cana-5306	17	13	characteristics	characteristic	NOUN
cana-5306	17	14	of	of	ADP
cana-5306	17	15	the	the	DET
cana-5306	17	16	crystal	crystal	NOUN
cana-5306	17	17	.	.	PUNCT
cana-5306	18	1	these	these	DET
cana-5306	18	2	properties	property	NOUN
cana-5306	18	3	reference	reference	VERB
cana-5306	18	4	the	the	DET
cana-5306	18	5	optical	optical	ADJ
cana-5306	18	6	characteristics	characteristic	NOUN
cana-5306	18	7	combined	combine	VERB
cana-5306	18	8	with	with	ADP
cana-5306	18	9	mechanical	mechanical	ADJ
cana-5306	18	10	qualities	quality	NOUN
cana-5306	18	11	and	and	CCONJ
cana-5306	18	12	electrical	electrical	ADJ
cana-5306	18	13	conductivity	conductivity	NOUN
cana-5306	18	14	as	as	ADV
cana-5306	18	15	well	well	ADV
cana-5306	18	16	as	as	ADP
cana-5306	18	17	thermal	thermal	ADJ
cana-5306	18	18	characteristics	characteristic	NOUN
cana-5306	18	19	.	.	PUNCT
cana-5306	19	1	the	the	DET
cana-5306	19	2	set	set	NOUN
cana-5306	19	3	of	of	ADP
cana-5306	19	4	symmetry	symmetry	NOUN
cana-5306	19	5	operations	operation	NOUN
cana-5306	19	6	establishes	establish	VERB
cana-5306	19	7	all	all	DET
cana-5306	19	8	feasible	feasible	ADJ
cana-5306	19	9	crystal	crystal	NOUN
cana-5306	19	10	appearances	appearance	NOUN
cana-5306	19	11	while	while	SCONJ
cana-5306	19	12	their	their	PRON
cana-5306	19	13	classification	classification	NOUN
cana-5306	19	14	depends	depend	VERB
cana-5306	19	15	on	on	ADP
cana-5306	19	16	the	the	DET
cana-5306	19	17	pattern	pattern	NOUN
cana-5306	19	18	repetition	repetition	NOUN
cana-5306	19	19	of	of	ADP
cana-5306	19	20	the	the	DET
cana-5306	19	21	structures	structure	NOUN
cana-5306	19	22	.	.	PUNCT
cana-5306	20	1	group	group	NOUN
cana-5306	20	2	theory	theory	NOUN
cana-5306	20	3	as	as	ADP
cana-5306	20	4	an	an	DET
cana-5306	20	5	abstract	abstract	ADJ
cana-5306	20	6	mathematical	mathematical	ADJ
cana-5306	20	7	field	field	NOUN
cana-5306	20	8	studies	study	NOUN
cana-5306	20	9	symmetries	symmetry	NOUN
cana-5306	20	10	through	through	ADP
cana-5306	20	11	its	its	PRON
cana-5306	20	12	study	study	NOUN
cana-5306	20	13	of	of	ADP
cana-5306	20	14	transformations	transformation	NOUN
cana-5306	20	15	because	because	SCONJ
cana-5306	20	16	it	it	PRON
cana-5306	20	17	determines	determine	VERB
cana-5306	20	18	how	how	SCONJ
cana-5306	20	19	these	these	DET
cana-5306	20	20	symmetry	symmetry	NOUN
cana-5306	20	21	operations	operation	NOUN
cana-5306	20	22	function	function	NOUN
cana-5306	20	23	.	.	PUNCT
cana-5306	21	1	group	group	NOUN
cana-5306	21	2	theory	theory	NOUN
cana-5306	21	3	provides	provide	VERB
cana-5306	21	4	the	the	DET
cana-5306	21	5	systematic	systematic	ADJ
cana-5306	21	6	approach	approach	NOUN
cana-5306	21	7	to	to	PART
cana-5306	21	8	examine	examine	VERB
cana-5306	21	9	crystal	crystal	NOUN
cana-5306	21	10	symmetries	symmetry	NOUN
cana-5306	21	11	by	by	ADP
cana-5306	21	12	enabling	enable	VERB
cana-5306	21	13	researchers	researcher	NOUN
cana-5306	21	14	to	to	PART
cana-5306	21	15	assign	assign	VERB
cana-5306	21	16	crystals	crystal	NOUN
cana-5306	21	17	to	to	PART
cana-5306	21	18	point	point	VERB
cana-5306	21	19	groups	group	NOUN
cana-5306	21	20	and	and	CCONJ
cana-5306	21	21	space	space	NOUN
cana-5306	21	22	groups	group	NOUN
cana-5306	21	23	.	.	PUNCT
cana-5306	22	1	point	point	NOUN
cana-5306	22	2	groups	group	NOUN
cana-5306	22	3	consist	consist	VERB
cana-5306	22	4	of	of	ADP
cana-5306	22	5	symmetry	symmetry	NOUN
cana-5306	22	6	operations	operation	NOUN
cana-5306	22	7	which	which	PRON
cana-5306	22	8	refrain	refrain	VERB
cana-5306	22	9	from	from	ADP
cana-5306	22	10	moving	move	VERB
cana-5306	22	11	a	a	DET
cana-5306	22	12	specific	specific	ADJ
cana-5306	22	13	point	point	NOUN
cana-5306	22	14	yet	yet	CCONJ
cana-5306	22	15	space	space	NOUN
cana-5306	22	16	groups	group	NOUN
cana-5306	22	17	incorporate	incorporate	VERB
cana-5306	22	18	all	all	DET
cana-5306	22	19	symmetries	symmetry	NOUN
cana-5306	22	20	that	that	PRON
cana-5306	22	21	preserve	preserve	VERB
cana-5306	22	22	the	the	DET
cana-5306	22	23	periodic	periodic	ADJ
cana-5306	22	24	lattice	lattice	NOUN
cana-5306	22	25	structure	structure	NOUN
cana-5306	22	26	by	by	ADP
cana-5306	22	27	transforming	transform	VERB
cana-5306	22	28	crystal	crystal	NOUN
cana-5306	22	29	structure	structure	NOUN
cana-5306	22	30	elements	element	NOUN
cana-5306	22	31	[	[	X
cana-5306	22	32	8	8	NUM
cana-5306	22	33	]	]	PUNCT
cana-5306	22	34	.	.	PUNCT
cana-5306	23	1	group	group	NOUN
cana-5306	23	2	theory	theory	NOUN
cana-5306	23	3	started	start	VERB
cana-5306	23	4	its	its	PRON
cana-5306	23	5	application	application	NOUN
cana-5306	23	6	in	in	ADP
cana-5306	23	7	crystallography	crystallography	NOUN
cana-5306	23	8	through	through	ADP
cana-5306	23	9	the	the	DET
cana-5306	23	10	research	research	NOUN
cana-5306	23	11	of	of	ADP
cana-5306	23	12	hermann	hermann	PROPN
cana-5306	23	13	weyl	weyl	PROPN
cana-5306	23	14	and	and	CCONJ
cana-5306	23	15	arthur	arthur	PROPN
cana-5306	23	16	schoenflies	schoenflie	NOUN
cana-5306	23	17	and	and	CCONJ
cana-5306	23	18	evgraf	evgraf	VERB
cana-5306	23	19	fedorov	fedorov	PROPN
cana-5306	23	20	in	in	ADP
cana-5306	23	21	the	the	DET
cana-5306	23	22	early	early	ADJ
cana-5306	23	23	20th	20th	ADJ
cana-5306	23	24	century	century	NOUN
cana-5306	23	25	.	.	PUNCT
cana-5306	24	1	these	these	DET
cana-5306	24	2	researchers	researcher	NOUN
cana-5306	24	3	developed	develop	VERB
cana-5306	24	4	the	the	DET
cana-5306	24	5	basis	basis	NOUN
cana-5306	24	6	for	for	ADP
cana-5306	24	7	establishing	establish	VERB
cana-5306	24	8	the	the	DET
cana-5306	24	9	system	system	NOUN
cana-5306	24	10	which	which	PRON
cana-5306	24	11	identifies	identify	VERB
cana-5306	24	12	crystal	crystal	NOUN
cana-5306	24	13	symmetries	symmetry	NOUN
cana-5306	24	14	.	.	PUNCT
cana-5306	25	1	the	the	DET
cana-5306	25	2	230	230	NUM
cana-5306	25	3	individual	individual	ADJ
cana-5306	25	4	space	space	NOUN
cana-5306	25	5	group	group	NOUN
cana-5306	25	6	types	type	NOUN
cana-5306	25	7	make	make	VERB
cana-5306	25	8	up	up	ADP
cana-5306	25	9	the	the	DET
cana-5306	25	10	essential	essential	ADJ
cana-5306	25	11	system	system	NOUN
cana-5306	25	12	that	that	PRON
cana-5306	25	13	determines	determine	VERB
cana-5306	25	14	physical	physical	ADJ
cana-5306	25	15	characteristics	characteristic	NOUN
cana-5306	25	16	in	in	ADP
cana-5306	25	17	crystals	crystal	NOUN
cana-5306	25	18	.	.	PUNCT
cana-5306	26	1	the	the	DET
cana-5306	26	2	space	space	NOUN
cana-5306	26	3	group	group	NOUN
cana-5306	26	4	of	of	ADP
cana-5306	26	5	a	a	DET
cana-5306	26	6	crystal	crystal	NOUN
cana-5306	26	7	reveals	reveal	VERB
cana-5306	26	8	whether	whether	SCONJ
cana-5306	26	9	it	it	PRON
cana-5306	26	10	possesses	possess	VERB
cana-5306	26	11	piezoelectric	piezoelectric	NOUN
cana-5306	26	12	and	and	CCONJ
cana-5306	26	13	ferroelectric	ferroelectric	ADJ
cana-5306	26	14	properties	property	NOUN
cana-5306	26	15	because	because	SCONJ
cana-5306	26	16	these	these	DET
cana-5306	26	17	properties	property	NOUN
cana-5306	26	18	depend	depend	VERB
cana-5306	26	19	on	on	ADP
cana-5306	26	20	symmetry	symmetry	NOUN
cana-5306	26	21	.	.	PUNCT
cana-5306	27	1	concurrent	concurrent	ADJ
cana-5306	27	2	use	use	NOUN
cana-5306	27	3	of	of	ADP
cana-5306	27	4	symmetry	symmetry	NOUN
cana-5306	27	5	in	in	ADP
cana-5306	27	6	modern	modern	ADJ
cana-5306	27	7	crystallography	crystallography	NOUN
cana-5306	27	8	manifests	manifest	NOUN
cana-5306	27	9	strongly	strongly	ADV
cana-5306	27	10	because	because	SCONJ
cana-5306	27	11	it	it	PRON
cana-5306	27	12	functions	function	VERB
cana-5306	27	13	as	as	ADP
cana-5306	27	14	a	a	DET
cana-5306	27	15	core	core	NOUN
cana-5306	27	16	element	element	NOUN
cana-5306	27	17	in	in	ADP
cana-5306	27	18	computational	computational	ADJ
cana-5306	27	19	procedures	procedure	NOUN
cana-5306	27	20	that	that	PRON
cana-5306	27	21	model	model	NOUN
cana-5306	27	22	and	and	CCONJ
cana-5306	27	23	forecast	forecast	NOUN
cana-5306	27	24	material	material	NOUN
cana-5306	27	25	properties	property	NOUN
cana-5306	27	26	.	.	PUNCT
cana-5306	28	1	symmetry	symmetry	NOUN
cana-5306	28	2	plays	play	VERB
cana-5306	28	3	an	an	DET
cana-5306	28	4	extended	extended	ADJ
cana-5306	28	5	role	role	NOUN
cana-5306	28	6	in	in	ADP
cana-5306	28	7	various	various	ADJ
cana-5306	28	8	material	material	NOUN
cana-5306	28	9	science	science	NOUN
cana-5306	28	10	domains	domain	NOUN
cana-5306	28	11	such	such	ADJ
cana-5306	28	12	as	as	ADP
cana-5306	28	13	new	new	ADJ
cana-5306	28	14	material	material	NOUN
cana-5306	28	15	development	development	NOUN
cana-5306	28	16	together	together	ADV
cana-5306	28	17	with	with	ADP
cana-5306	28	18	structural	structural	ADJ
cana-5306	28	19	engineering	engineering	NOUN
cana-5306	28	20	alongside	alongside	ADP
cana-5306	28	21	nanotechnology	nanotechnology	NOUN
cana-5306	28	22	applications	application	NOUN
cana-5306	28	23	[	[	PUNCT
cana-5306	28	24	13	13	NUM
cana-5306	28	25	-	-	SYM
cana-5306	28	26	14	14	NUM
cana-5306	28	27	]	]	PUNCT
cana-5306	28	28	.	.	PUNCT
cana-5306	29	1	the	the	DET
cana-5306	29	2	main	main	ADJ
cana-5306	29	3	practical	practical	ADJ
cana-5306	29	4	purpose	purpose	NOUN
cana-5306	29	5	of	of	ADP
cana-5306	29	6	symmetry	symmetry	NOUN
cana-5306	29	7	in	in	ADP
cana-5306	29	8	crystallography	crystallography	NOUN
cana-5306	29	9	enables	enable	VERB
cana-5306	29	10	researchers	researcher	NOUN
cana-5306	29	11	to	to	PART
cana-5306	29	12	discover	discover	VERB
cana-5306	29	13	crystal	crystal	NOUN
cana-5306	29	14	structural	structural	ADJ
cana-5306	29	15	information	information	NOUN
cana-5306	29	16	.	.	PUNCT
cana-5306	30	1	the	the	DET
cana-5306	30	2	knowledge	knowledge	NOUN
cana-5306	30	3	of	of	ADP
cana-5306	30	4	crystal	crystal	NOUN
cana-5306	30	5	symmetry	symmetry	NOUN
cana-5306	30	6	proves	prove	VERB
cana-5306	30	7	vital	vital	ADJ
cana-5306	30	8	for	for	ADP
cana-5306	30	9	materials	material	NOUN
cana-5306	30	10	science	science	NOUN
cana-5306	30	11	research	research	NOUN
cana-5306	30	12	since	since	SCONJ
cana-5306	30	13	scientists	scientist	NOUN
cana-5306	30	14	must	must	AUX
cana-5306	30	15	understand	understand	VERB
cana-5306	30	16	atomic	atomic	ADJ
cana-5306	30	17	structures	structure	NOUN
cana-5306	30	18	to	to	PART
cana-5306	30	19	create	create	VERB
cana-5306	30	20	materials	material	NOUN
cana-5306	30	21	of	of	ADP
cana-5306	30	22	desired	desire	VERB
cana-5306	30	23	applications	application	NOUN
cana-5306	30	24	in	in	ADP
cana-5306	30	25	solid	solid	ADJ
cana-5306	30	26	-	-	PUNCT
cana-5306	30	27	state	state	NOUN
cana-5306	30	28	physics	physics	NOUN
cana-5306	30	29	fields	field	NOUN
cana-5306	30	30	.	.	PUNCT
cana-5306	31	1	the	the	DET
cana-5306	31	2	semiconductor	semiconductor	NOUN
cana-5306	31	3	industry	industry	NOUN
cana-5306	31	4	evaluates	evaluate	VERB
cana-5306	31	5	semiconductor	semiconductor	NOUN
cana-5306	31	6	material	material	NOUN
cana-5306	31	7	efficiency	efficiency	NOUN
cana-5306	31	8	through	through	ADP
cana-5306	31	9	device	device	NOUN
cana-5306	31	10	applications	application	NOUN
cana-5306	31	11	such	such	ADJ
cana-5306	31	12	as	as	ADP
cana-5306	31	13	solar	solar	ADJ
cana-5306	31	14	cells	cell	NOUN
cana-5306	31	15	and	and	CCONJ
cana-5306	31	16	transistors	transistor	NOUN
cana-5306	31	17	by	by	ADP
cana-5306	31	18	analyzing	analyze	VERB
cana-5306	31	19	their	their	PRON
cana-5306	31	20	symmetry	symmetry	NOUN
cana-5306	31	21	property	property	NOUN
cana-5306	31	22	.	.	PUNCT
cana-5306	32	1	severe	severe	ADJ
cana-5306	32	2	phenomena	phenomenon	NOUN
cana-5306	32	3	such	such	ADJ
cana-5306	32	4	as	as	ADP
cana-5306	32	5	superconductivity	superconductivity	NOUN
cana-5306	32	6	combined	combine	VERB
cana-5306	32	7	with	with	ADP
cana-5306	32	8	magnetism	magnetism	NOUN
cana-5306	32	9	show	show	VERB
cana-5306	32	10	direct	direct	ADJ
cana-5306	32	11	connections	connection	NOUN
cana-5306	32	12	to	to	PART
cana-5306	32	13	symmetry	symmetry	VERB
cana-5306	32	14	through	through	ADP
cana-5306	32	15	their	their	PRON
cana-5306	32	16	material	material	NOUN
cana-5306	32	17	properties	property	NOUN
cana-5306	32	18	.	.	PUNCT
cana-5306	33	1	symmetry	symmetry	NOUN
cana-5306	33	2	restrictions	restriction	NOUN
cana-5306	33	3	determine	determine	VERB
cana-5306	33	4	whether	whether	SCONJ
cana-5306	33	5	or	or	CCONJ
cana-5306	33	6	not	not	PART
cana-5306	33	7	many	many	ADJ
cana-5306	33	8	physical	physical	ADJ
cana-5306	33	9	phenomena	phenomenon	NOUN
cana-5306	33	10	will	will	AUX
cana-5306	33	11	appear	appear	VERB
cana-5306	33	12	.	.	PUNCT
cana-5306	34	1	the	the	DET
cana-5306	34	2	theory	theory	NOUN
cana-5306	34	3	of	of	ADP
cana-5306	34	4	superconductivity	superconductivity	NOUN
cana-5306	34	5	which	which	PRON
cana-5306	34	6	bardeen	bardeen	VERB
cana-5306	34	7	cooper	cooper	NOUN
cana-5306	34	8	and	and	CCONJ
cana-5306	34	9	schrieffer	schrieffer	NOUN
cana-5306	34	10	(	(	PUNCT
cana-5306	34	11	bcs	bcs	NOUN
cana-5306	34	12	)	)	PUNCT
cana-5306	34	13	formulated	formulate	VERB
cana-5306	34	14	depends	depend	VERB
cana-5306	34	15	completely	completely	ADV
cana-5306	34	16	on	on	ADP
cana-5306	34	17	the	the	DET
cana-5306	34	18	symmetric	symmetric	ADJ
cana-5306	34	19	electronic	electronic	ADJ
cana-5306	34	20	distribution	distribution	NOUN
cana-5306	34	21	patterns	pattern	NOUN
cana-5306	34	22	within	within	ADP
cana-5306	34	23	materials	material	NOUN
cana-5306	34	24	.	.	PUNCT
cana-5306	35	1	symmetry	symmetry	NOUN
cana-5306	35	2	understanding	understanding	NOUN
cana-5306	35	3	provides	provide	VERB
cana-5306	35	4	methods	method	NOUN
cana-5306	35	5	to	to	ADP
cana-5306	35	6	communications	communication	NOUN
cana-5306	35	7	on	on	ADP
cana-5306	35	8	applied	apply	VERB
cana-5306	35	9	nonlinear	nonlinear	ADJ
cana-5306	35	10	analysis	analysis	NOUN
cana-5306	35	11	issn	issn	NOUN
cana-5306	35	12	:	:	PUNCT
cana-5306	35	13	1074	1074	NUM
cana-5306	35	14	-	-	PUNCT
cana-5306	35	15	133x	133x	NUM
cana-5306	35	16	vol	vol	NOUN
cana-5306	35	17	31	31	NUM
cana-5306	35	18	no	no	NOUN
cana-5306	35	19	.	.	NOUN
cana-5306	35	20	2	2	NUM
cana-5306	35	21	(	(	PUNCT
cana-5306	35	22	2024	2024	NUM
cana-5306	35	23	)	)	PUNCT
cana-5306	35	24	442	442	NUM
cana-5306	35	25	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	35	26	develop	develop	VERB
cana-5306	35	27	new	new	ADJ
cana-5306	35	28	materials	material	NOUN
cana-5306	35	29	which	which	PRON
cana-5306	35	30	possess	possess	VERB
cana-5306	35	31	particular	particular	ADJ
cana-5306	35	32	properties	property	NOUN
cana-5306	35	33	needed	need	VERB
cana-5306	35	34	for	for	ADP
cana-5306	35	35	present	present	ADJ
cana-5306	35	36	-	-	PUNCT
cana-5306	35	37	day	day	NOUN
cana-5306	35	38	technological	technological	ADJ
cana-5306	35	39	developments	development	NOUN
cana-5306	35	40	.	.	PUNCT
cana-5306	36	1	only	only	ADV
cana-5306	36	2	theoretical	theoretical	ADJ
cana-5306	36	3	studies	study	NOUN
cana-5306	36	4	miss	miss	VERB
cana-5306	36	5	the	the	DET
cana-5306	36	6	significance	significance	NOUN
cana-5306	36	7	of	of	ADP
cana-5306	36	8	symmetry	symmetry	NOUN
cana-5306	36	9	in	in	ADP
cana-5306	36	10	crystallography	crystallography	NOUN
cana-5306	36	11	.	.	PUNCT
cana-5306	37	1	the	the	DET
cana-5306	37	2	crystal	crystal	NOUN
cana-5306	37	3	structure	structure	NOUN
cana-5306	37	4	arrangement	arrangement	NOUN
cana-5306	37	5	of	of	ADP
cana-5306	37	6	atoms	atom	NOUN
cana-5306	37	7	serves	serve	VERB
cana-5306	37	8	practical	practical	ADJ
cana-5306	37	9	functions	function	NOUN
cana-5306	37	10	in	in	ADP
cana-5306	37	11	drug	drug	NOUN
cana-5306	37	12	design	design	NOUN
cana-5306	37	13	because	because	SCONJ
cana-5306	37	14	it	it	PRON
cana-5306	37	15	determines	determine	VERB
cana-5306	37	16	how	how	SCONJ
cana-5306	37	17	substances	substance	NOUN
cana-5306	37	18	work	work	VERB
cana-5306	37	19	pharmacologically	pharmacologically	ADV
cana-5306	37	20	.	.	PUNCT
cana-5306	38	1	the	the	DET
cana-5306	38	2	pharmaceutical	pharmaceutical	NOUN
cana-5306	38	3	industry	industry	NOUN
cana-5306	38	4	depends	depend	VERB
cana-5306	38	5	on	on	ADP
cana-5306	38	6	crystallographic	crystallographic	ADJ
cana-5306	38	7	methods	method	NOUN
cana-5306	38	8	to	to	PART
cana-5306	38	9	study	study	VERB
cana-5306	38	10	exact	exact	ADJ
cana-5306	38	11	api	api	NOUN
cana-5306	38	12	atomic	atomic	ADJ
cana-5306	38	13	arrangements	arrangement	NOUN
cana-5306	38	14	in	in	ADP
cana-5306	38	15	order	order	NOUN
cana-5306	38	16	to	to	PART
cana-5306	38	17	formulate	formulate	VERB
cana-5306	38	18	drugs	drug	NOUN
cana-5306	38	19	properly	properly	ADV
cana-5306	38	20	for	for	ADP
cana-5306	38	21	maximum	maximum	ADJ
cana-5306	38	22	effectiveness	effectiveness	NOUN
cana-5306	38	23	[	[	X
cana-5306	38	24	7	7	NUM
cana-5306	38	25	]	]	PUNCT
cana-5306	38	26	.	.	PUNCT
cana-5306	39	1	this	this	DET
cana-5306	39	2	paper	paper	NOUN
cana-5306	39	3	evaluates	evaluate	VERB
cana-5306	39	4	how	how	SCONJ
cana-5306	39	5	group	group	NOUN
cana-5306	39	6	theory	theory	NOUN
cana-5306	39	7	helps	help	VERB
cana-5306	39	8	investigators	investigator	NOUN
cana-5306	39	9	study	study	VERB
cana-5306	39	10	symmetry	symmetry	NOUN
cana-5306	39	11	patterns	pattern	NOUN
cana-5306	39	12	within	within	ADP
cana-5306	39	13	crystallography	crystallography	NOUN
cana-5306	39	14	.	.	PUNCT
cana-5306	40	1	the	the	DET
cana-5306	40	2	paper	paper	NOUN
cana-5306	40	3	examines	examine	VERB
cana-5306	40	4	the	the	DET
cana-5306	40	5	process	process	NOUN
cana-5306	40	6	by	by	ADP
cana-5306	40	7	which	which	PRON
cana-5306	40	8	symmetry	symmetry	NOUN
cana-5306	40	9	operations	operation	NOUN
cana-5306	40	10	together	together	ADV
cana-5306	40	11	with	with	ADP
cana-5306	40	12	group	group	NOUN
cana-5306	40	13	theory	theory	NOUN
cana-5306	40	14	systems	system	NOUN
cana-5306	40	15	assist	assist	VERB
cana-5306	40	16	in	in	ADP
cana-5306	40	17	categorizing	categorize	VERB
cana-5306	40	18	crystals	crystal	NOUN
cana-5306	40	19	and	and	CCONJ
cana-5306	40	20	estimating	estimate	VERB
cana-5306	40	21	their	their	PRON
cana-5306	40	22	physical	physical	ADJ
cana-5306	40	23	characteristics	characteristic	NOUN
cana-5306	40	24	and	and	CCONJ
cana-5306	40	25	designing	design	VERB
cana-5306	40	26	novel	novel	ADJ
cana-5306	40	27	materials	material	NOUN
cana-5306	40	28	.	.	PUNCT
cana-5306	41	1	this	this	DET
cana-5306	41	2	paper	paper	NOUN
cana-5306	41	3	evaluates	evaluate	VERB
cana-5306	41	4	the	the	DET
cana-5306	41	5	importance	importance	NOUN
cana-5306	41	6	of	of	ADP
cana-5306	41	7	symmetry	symmetry	NOUN
cana-5306	41	8	both	both	CCONJ
cana-5306	41	9	in	in	ADP
cana-5306	41	10	developing	develop	VERB
cana-5306	41	11	crystallographic	crystallographic	ADJ
cana-5306	41	12	analysis	analysis	NOUN
cana-5306	41	13	tools	tool	NOUN
cana-5306	41	14	alongside	alongside	ADP
cana-5306	41	15	researches	research	NOUN
cana-5306	41	16	in	in	ADP
cana-5306	41	17	material	material	NOUN
cana-5306	41	18	science	science	NOUN
cana-5306	41	19	fields	field	NOUN
cana-5306	41	20	.	.	PUNCT
cana-5306	42	1	novelty	novelty	NOUN
cana-5306	42	2	and	and	CCONJ
cana-5306	42	3	contribution	contribution	NOUN
cana-5306	42	4	this	this	DET
cana-5306	42	5	research	research	NOUN
cana-5306	42	6	brings	bring	VERB
cana-5306	42	7	novelty	novelty	NOUN
cana-5306	42	8	through	through	ADP
cana-5306	42	9	its	its	PRON
cana-5306	42	10	investigation	investigation	NOUN
cana-5306	42	11	of	of	ADP
cana-5306	42	12	how	how	SCONJ
cana-5306	42	13	symmetry	symmetry	NOUN
cana-5306	42	14	connects	connect	VERB
cana-5306	42	15	to	to	ADP
cana-5306	42	16	group	group	NOUN
cana-5306	42	17	theory	theory	NOUN
cana-5306	42	18	with	with	ADP
cana-5306	42	19	material	material	ADJ
cana-5306	42	20	characteristics	characteristic	NOUN
cana-5306	42	21	for	for	ADP
cana-5306	42	22	modern	modern	ADJ
cana-5306	42	23	crystallographic	crystallographic	ADJ
cana-5306	42	24	studies	study	NOUN
cana-5306	42	25	.	.	PUNCT
cana-5306	43	1	this	this	DET
cana-5306	43	2	paper	paper	NOUN
cana-5306	43	3	presents	present	VERB
cana-5306	43	4	a	a	DET
cana-5306	43	5	novel	novel	ADJ
cana-5306	43	6	view	view	NOUN
cana-5306	43	7	on	on	ADP
cana-5306	43	8	crystal	crystal	NOUN
cana-5306	43	9	structure	structure	NOUN
cana-5306	43	10	symmetry	symmetry	NOUN
cana-5306	43	11	by	by	ADP
cana-5306	43	12	combining	combine	VERB
cana-5306	43	13	modern	modern	ADJ
cana-5306	43	14	computational	computational	ADJ
cana-5306	43	15	methods	method	NOUN
cana-5306	43	16	and	and	CCONJ
cana-5306	43	17	material	material	NOUN
cana-5306	43	18	science	science	NOUN
cana-5306	43	19	applications	application	NOUN
cana-5306	43	20	which	which	PRON
cana-5306	43	21	were	be	AUX
cana-5306	43	22	not	not	PART
cana-5306	43	23	well	well	ADV
cana-5306	43	24	established	establish	VERB
cana-5306	43	25	previously	previously	ADV
cana-5306	43	26	.	.	PUNCT
cana-5306	44	1	the	the	DET
cana-5306	44	2	research	research	NOUN
cana-5306	44	3	demonstrates	demonstrate	VERB
cana-5306	44	4	how	how	SCONJ
cana-5306	44	5	group	group	NOUN
cana-5306	44	6	theory	theory	NOUN
cana-5306	44	7	can	can	AUX
cana-5306	44	8	predict	predict	VERB
cana-5306	44	9	material	material	ADJ
cana-5306	44	10	structural	structural	ADJ
cana-5306	44	11	fortunes	fortune	NOUN
cana-5306	44	12	while	while	SCONJ
cana-5306	44	13	serving	serve	VERB
cana-5306	44	14	to	to	PART
cana-5306	44	15	monitor	monitor	VERB
cana-5306	44	16	their	their	PRON
cana-5306	44	17	dynamic	dynamic	NOUN
cana-5306	44	18	along	along	ADP
cana-5306	44	19	with	with	ADP
cana-5306	44	20	electronic	electronic	ADJ
cana-5306	44	21	movements	movement	NOUN
cana-5306	44	22	.	.	PUNCT
cana-5306	45	1	the	the	DET
cana-5306	45	2	paper	paper	NOUN
cana-5306	45	3	demonstrates	demonstrate	VERB
cana-5306	45	4	how	how	SCONJ
cana-5306	45	5	symmetry	symmetry	NOUN
cana-5306	45	6	analysis	analysis	NOUN
cana-5306	45	7	creates	create	VERB
cana-5306	45	8	predictive	predictive	ADJ
cana-5306	45	9	value	value	NOUN
cana-5306	45	10	through	through	ADP
cana-5306	45	11	theoretical	theoretical	ADJ
cana-5306	45	12	group	group	NOUN
cana-5306	45	13	theory	theory	NOUN
cana-5306	45	14	applications	application	NOUN
cana-5306	45	15	in	in	ADP
cana-5306	45	16	material	material	NOUN
cana-5306	45	17	science	science	NOUN
cana-5306	45	18	research	research	NOUN
cana-5306	45	19	for	for	ADP
cana-5306	45	20	identifying	identify	VERB
cana-5306	45	21	materials	material	NOUN
cana-5306	45	22	with	with	ADP
cana-5306	45	23	specific	specific	ADJ
cana-5306	45	24	uses	use	NOUN
cana-5306	45	25	.	.	PUNCT
cana-5306	46	1	businesses	business	NOUN
cana-5306	46	2	employ	employ	VERB
cana-5306	46	3	lattice	lattice	NOUN
cana-5306	46	4	symmetry	symmetry	NOUN
cana-5306	46	5	knowledge	knowledge	NOUN
cana-5306	46	6	to	to	PART
cana-5306	46	7	design	design	VERB
cana-5306	46	8	future	future	ADJ
cana-5306	46	9	high	high	ADJ
cana-5306	46	10	-	-	PUNCT
cana-5306	46	11	tech	tech	NOUN
cana-5306	46	12	components	component	NOUN
cana-5306	46	13	including	include	VERB
cana-5306	46	14	those	those	PRON
cana-5306	46	15	needed	need	VERB
cana-5306	46	16	for	for	ADP
cana-5306	46	17	quantum	quantum	NOUN
cana-5306	46	18	computing	computing	NOUN
cana-5306	46	19	operations	operation	NOUN
cana-5306	46	20	alongside	alongside	ADP
cana-5306	46	21	energy	energy	NOUN
cana-5306	46	22	storage	storage	NOUN
cana-5306	46	23	components	component	NOUN
cana-5306	46	24	and	and	CCONJ
cana-5306	46	25	semiconductor	semiconductor	NOUN
cana-5306	46	26	parts	part	NOUN
cana-5306	46	27	.	.	PUNCT
cana-5306	47	1	the	the	DET
cana-5306	47	2	paper	paper	NOUN
cana-5306	47	3	adds	add	VERB
cana-5306	47	4	value	value	NOUN
cana-5306	47	5	to	to	ADP
cana-5306	47	6	crystallography	crystallography	NOUN
cana-5306	47	7	research	research	NOUN
cana-5306	47	8	through	through	ADP
cana-5306	47	9	its	its	PRON
cana-5306	47	10	presentation	presentation	NOUN
cana-5306	47	11	of	of	ADP
cana-5306	47	12	computational	computational	ADJ
cana-5306	47	13	techniques	technique	NOUN
cana-5306	47	14	'	'	PART
cana-5306	47	15	developing	develop	VERB
cana-5306	47	16	position	position	NOUN
cana-5306	47	17	in	in	ADP
cana-5306	47	18	the	the	DET
cana-5306	47	19	field	field	NOUN
cana-5306	47	20	.	.	PUNCT
cana-5306	48	1	the	the	DET
cana-5306	48	2	new	new	ADJ
cana-5306	48	3	tools	tool	NOUN
cana-5306	48	4	facilitate	facilitate	VERB
cana-5306	48	5	fast	fast	ADJ
cana-5306	48	6	screening	screening	NOUN
cana-5306	48	7	of	of	ADP
cana-5306	48	8	materials	material	NOUN
cana-5306	48	9	through	through	ADP
cana-5306	48	10	their	their	PRON
cana-5306	48	11	symmetry	symmetry	NOUN
cana-5306	48	12	properties	property	NOUN
cana-5306	48	13	thus	thus	ADV
cana-5306	48	14	enabling	enable	VERB
cana-5306	48	15	crucial	crucial	ADJ
cana-5306	48	16	progress	progress	NOUN
cana-5306	48	17	in	in	ADP
cana-5306	48	18	the	the	DET
cana-5306	48	19	research	research	NOUN
cana-5306	48	20	.	.	PUNCT
cana-5306	49	1	the	the	DET
cana-5306	49	2	paper	paper	NOUN
cana-5306	49	3	discusses	discuss	VERB
cana-5306	49	4	how	how	SCONJ
cana-5306	49	5	crystallography	crystallography	NOUN
cana-5306	49	6	brings	bring	VERB
cana-5306	49	7	together	together	ADV
cana-5306	49	8	different	different	ADJ
cana-5306	49	9	fields	field	NOUN
cana-5306	49	10	including	include	VERB
cana-5306	49	11	pharmaceuticals	pharmaceutical	NOUN
cana-5306	49	12	and	and	CCONJ
cana-5306	49	13	nanotechnology	nanotechnology	NOUN
cana-5306	49	14	.	.	PUNCT
cana-5306	50	1	symmetry	symmetry	NOUN
cana-5306	50	2	analysis	analysis	NOUN
cana-5306	50	3	enables	enable	VERB
cana-5306	50	4	scientists	scientist	NOUN
cana-5306	50	5	to	to	PART
cana-5306	50	6	establish	establish	VERB
cana-5306	50	7	api	api	NOUN
cana-5306	50	8	crystal	crystal	NOUN
cana-5306	50	9	structures	structure	NOUN
cana-5306	50	10	for	for	ADP
cana-5306	50	11	pharmaceutical	pharmaceutical	ADJ
cana-5306	50	12	advancement	advancement	NOUN
cana-5306	50	13	through	through	ADP
cana-5306	50	14	better	well	ADJ
cana-5306	50	15	drug	drug	NOUN
cana-5306	50	16	development	development	NOUN
cana-5306	50	17	.	.	PUNCT
cana-5306	51	1	realworld	realworld	PROPN
cana-5306	51	2	examples	example	NOUN
cana-5306	51	3	and	and	CCONJ
cana-5306	51	4	case	case	NOUN
cana-5306	51	5	studies	study	NOUN
cana-5306	51	6	help	help	VERB
cana-5306	51	7	the	the	DET
cana-5306	51	8	study	study	NOUN
cana-5306	51	9	demonstrate	demonstrate	VERB
cana-5306	51	10	the	the	DET
cana-5306	51	11	theoretical	theoretical	ADJ
cana-5306	51	12	symmetry	symmetry	NOUN
cana-5306	51	13	operation	operation	NOUN
cana-5306	51	14	connection	connection	NOUN
cana-5306	51	15	to	to	ADP
cana-5306	51	16	practical	practical	ADJ
cana-5306	51	17	industry	industry	NOUN
cana-5306	51	18	applications	application	NOUN
cana-5306	51	19	.	.	PUNCT
cana-5306	52	1	this	this	DET
cana-5306	52	2	work	work	NOUN
cana-5306	52	3	associates	associates	PROPN
cana-5306	52	4	historical	historical	ADJ
cana-5306	52	5	group	group	NOUN
cana-5306	52	6	theory	theory	NOUN
cana-5306	52	7	principles	principle	NOUN
cana-5306	52	8	with	with	ADP
cana-5306	52	9	modern	modern	ADJ
cana-5306	52	10	-	-	PUNCT
cana-5306	52	11	day	day	NOUN
cana-5306	52	12	computational	computational	ADJ
cana-5306	52	13	evaluation	evaluation	NOUN
cana-5306	52	14	to	to	PART
cana-5306	52	15	show	show	VERB
cana-5306	52	16	multiple	multiple	ADJ
cana-5306	52	17	methods	method	NOUN
cana-5306	52	18	which	which	PRON
cana-5306	52	19	determine	determine	VERB
cana-5306	52	20	crystal	crystal	NOUN
cana-5306	52	21	characteristics	characteristic	NOUN
cana-5306	52	22	.	.	PUNCT
cana-5306	53	1	the	the	DET
cana-5306	53	2	holistic	holistic	ADJ
cana-5306	53	3	approach	approach	NOUN
cana-5306	53	4	provides	provide	VERB
cana-5306	53	5	expanded	expand	VERB
cana-5306	53	6	perception	perception	NOUN
cana-5306	53	7	about	about	ADP
cana-5306	53	8	symmetrical	symmetrical	ADJ
cana-5306	53	9	material	material	NOUN
cana-5306	53	10	structure	structure	NOUN
cana-5306	53	11	properties	property	NOUN
cana-5306	53	12	signaling	signal	VERB
cana-5306	53	13	functional	functional	ADJ
cana-5306	53	14	attributes	attribute	NOUN
cana-5306	53	15	across	across	ADP
cana-5306	53	16	numerous	numerous	ADJ
cana-5306	53	17	functional	functional	ADJ
cana-5306	53	18	contexts	contexts	NOUN
cana-5306	53	19	.	.	PUNCT
cana-5306	54	1	the	the	DET
cana-5306	54	2	document	document	NOUN
cana-5306	54	3	presents	present	VERB
cana-5306	54	4	communications	communication	NOUN
cana-5306	54	5	on	on	ADP
cana-5306	54	6	applied	apply	VERB
cana-5306	54	7	nonlinear	nonlinear	ADJ
cana-5306	54	8	analysis	analysis	NOUN
cana-5306	54	9	issn	issn	NOUN
cana-5306	54	10	:	:	PUNCT
cana-5306	54	11	1074	1074	NUM
cana-5306	54	12	-	-	PUNCT
cana-5306	54	13	133x	133x	NUM
cana-5306	54	14	vol	vol	NOUN
cana-5306	54	15	31	31	NUM
cana-5306	54	16	no	no	NOUN
cana-5306	54	17	.	.	NOUN
cana-5306	54	18	2	2	NUM
cana-5306	54	19	(	(	PUNCT
cana-5306	54	20	2024	2024	NUM
cana-5306	54	21	)	)	PUNCT
cana-5306	55	1	443	443	NUM
cana-5306	55	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	55	3	beneficial	beneficial	ADJ
cana-5306	55	4	results	result	NOUN
cana-5306	55	5	that	that	PRON
cana-5306	55	6	advance	advance	VERB
cana-5306	55	7	understanding	understanding	NOUN
cana-5306	55	8	of	of	ADP
cana-5306	55	9	crystallographic	crystallographic	ADJ
cana-5306	55	10	symmetries	symmetry	NOUN
cana-5306	55	11	and	and	CCONJ
cana-5306	55	12	guide	guide	VERB
cana-5306	55	13	research	research	NOUN
cana-5306	55	14	in	in	ADP
cana-5306	55	15	material	material	NOUN
cana-5306	55	16	science	science	NOUN
cana-5306	55	17	together	together	ADV
cana-5306	55	18	with	with	ADP
cana-5306	55	19	crystallographic	crystallographic	ADJ
cana-5306	55	20	theory	theory	NOUN
cana-5306	55	21	[	[	X
cana-5306	55	22	6	6	NUM
cana-5306	55	23	]	]	PUNCT
cana-5306	55	24	.	.	PUNCT
cana-5306	56	1	ii	ii	PROPN
cana-5306	56	2	.	.	PROPN
cana-5306	56	3	related	relate	VERB
cana-5306	56	4	works	work	NOUN
cana-5306	56	5	in	in	ADP
cana-5306	56	6	2021	2021	NUM
cana-5306	56	7	j.-p	j.-p	PROPN
cana-5306	56	8	.	.	PUNCT
cana-5306	57	1	antoine	antoine	PROPN
cana-5306	57	2	et.al	et.al	PROPN
cana-5306	57	3	.	.	PUNCT
cana-5306	57	4	,	,	PUNCT
cana-5306	58	1	[	[	X
cana-5306	58	2	15	15	NUM
cana-5306	58	3	]	]	PUNCT
cana-5306	58	4	suggested	suggest	VERB
cana-5306	58	5	the	the	DET
cana-5306	58	6	scientists	scientist	NOUN
cana-5306	58	7	first	first	ADV
cana-5306	58	8	dedicated	dedicate	VERB
cana-5306	58	9	their	their	PRON
cana-5306	58	10	research	research	NOUN
cana-5306	58	11	to	to	ADP
cana-5306	58	12	creating	create	VERB
cana-5306	58	13	crystal	crystal	NOUN
cana-5306	58	14	system	system	NOUN
cana-5306	58	15	classification	classification	NOUN
cana-5306	58	16	through	through	ADP
cana-5306	58	17	symmetry	symmetry	NOUN
cana-5306	58	18	evaluation	evaluation	NOUN
cana-5306	58	19	methods	method	NOUN
cana-5306	58	20	which	which	PRON
cana-5306	58	21	led	lead	VERB
cana-5306	58	22	to	to	ADP
cana-5306	58	23	the	the	DET
cana-5306	58	24	development	development	NOUN
cana-5306	58	25	of	of	ADP
cana-5306	58	26	point	point	NOUN
cana-5306	58	27	groups	group	NOUN
cana-5306	58	28	along	along	ADP
cana-5306	58	29	with	with	ADP
cana-5306	58	30	space	space	NOUN
cana-5306	58	31	groups	group	NOUN
cana-5306	58	32	.	.	PUNCT
cana-5306	59	1	the	the	DET
cana-5306	59	2	established	establish	VERB
cana-5306	59	3	frameworks	framework	NOUN
cana-5306	59	4	serve	serve	VERB
cana-5306	59	5	two	two	NUM
cana-5306	59	6	purposes	purpose	NOUN
cana-5306	59	7	in	in	ADP
cana-5306	59	8	the	the	DET
cana-5306	59	9	analysis	analysis	NOUN
cana-5306	59	10	of	of	ADP
cana-5306	59	11	crystal	crystal	NOUN
cana-5306	59	12	symmetry	symmetry	NOUN
cana-5306	59	13	because	because	SCONJ
cana-5306	59	14	they	they	PRON
cana-5306	59	15	enable	enable	VERB
cana-5306	59	16	researchers	researcher	NOUN
cana-5306	59	17	to	to	PART
cana-5306	59	18	diagnose	diagnose	VERB
cana-5306	59	19	their	their	PRON
cana-5306	59	20	characteristics	characteristic	NOUN
cana-5306	59	21	while	while	SCONJ
cana-5306	59	22	they	they	PRON
cana-5306	59	23	remain	remain	VERB
cana-5306	59	24	essential	essential	ADJ
cana-5306	59	25	for	for	ADP
cana-5306	59	26	symmetry	symmetry	NOUN
cana-5306	59	27	analysis	analysis	NOUN
cana-5306	59	28	.	.	PUNCT
cana-5306	60	1	crystal	crystal	NOUN
cana-5306	60	2	symmetry	symmetry	NOUN
cana-5306	60	3	classification	classification	NOUN
cana-5306	60	4	knowledge	knowledge	NOUN
cana-5306	60	5	helps	help	VERB
cana-5306	60	6	scientists	scientist	NOUN
cana-5306	60	7	create	create	VERB
cana-5306	60	8	material	material	ADJ
cana-5306	60	9	organizational	organizational	ADJ
cana-5306	60	10	structures	structure	NOUN
cana-5306	60	11	which	which	PRON
cana-5306	60	12	enables	enable	VERB
cana-5306	60	13	them	they	PRON
cana-5306	60	14	to	to	PART
cana-5306	60	15	predict	predict	VERB
cana-5306	60	16	substance	substance	NOUN
cana-5306	60	17	behaviors	behavior	NOUN
cana-5306	60	18	under	under	ADP
cana-5306	60	19	different	different	ADJ
cana-5306	60	20	experimental	experimental	ADJ
cana-5306	60	21	scenarios	scenario	NOUN
cana-5306	60	22	.	.	PUNCT
cana-5306	61	1	in	in	ADP
cana-5306	61	2	2020	2020	NUM
cana-5306	61	3	l.	l.	PROPN
cana-5306	61	4	r.	r.	PROPN
cana-5306	61	5	falvello	falvello	PROPN
cana-5306	61	6	et.al	et.al	PROPN
cana-5306	61	7	.	.	PUNCT
cana-5306	61	8	,	,	PUNCT
cana-5306	61	9	[	[	X
cana-5306	61	10	9	9	NUM
cana-5306	61	11	]	]	PUNCT
cana-5306	61	12	proposed	propose	VERB
cana-5306	61	13	the	the	DET
cana-5306	61	14	crystal	crystal	PROPN
cana-5306	61	15	symmetry	symmetry	NOUN
cana-5306	61	16	operations	operation	NOUN
cana-5306	61	17	which	which	PRON
cana-5306	61	18	include	include	VERB
cana-5306	61	19	rotations	rotation	NOUN
cana-5306	61	20	reflections	reflection	NOUN
cana-5306	61	21	and	and	CCONJ
cana-5306	61	22	translations	translation	NOUN
cana-5306	61	23	can	can	AUX
cana-5306	61	24	be	be	AUX
cana-5306	61	25	explained	explain	VERB
cana-5306	61	26	through	through	ADP
cana-5306	61	27	group	group	NOUN
cana-5306	61	28	theory	theory	NOUN
cana-5306	61	29	as	as	ADP
cana-5306	61	30	an	an	DET
cana-5306	61	31	accepted	accepted	ADJ
cana-5306	61	32	scientific	scientific	ADJ
cana-5306	61	33	approach	approach	NOUN
cana-5306	61	34	.	.	PUNCT
cana-5306	62	1	this	this	DET
cana-5306	62	2	method	method	NOUN
cana-5306	62	3	enables	enable	VERB
cana-5306	62	4	researchers	researcher	NOUN
cana-5306	62	5	to	to	PART
cana-5306	62	6	gain	gain	VERB
cana-5306	62	7	improved	improved	ADJ
cana-5306	62	8	understanding	understanding	NOUN
cana-5306	62	9	of	of	ADP
cana-5306	62	10	periodic	periodic	ADJ
cana-5306	62	11	crystal	crystal	NOUN
cana-5306	62	12	structures	structure	NOUN
cana-5306	62	13	together	together	ADV
cana-5306	62	14	with	with	ADP
cana-5306	62	15	their	their	PRON
cana-5306	62	16	arrangement	arrangement	NOUN
cana-5306	62	17	patterns	pattern	NOUN
cana-5306	62	18	.	.	PUNCT
cana-5306	63	1	space	space	NOUN
cana-5306	63	2	groups	group	NOUN
cana-5306	63	3	help	help	VERB
cana-5306	63	4	scientists	scientist	NOUN
cana-5306	63	5	fully	fully	ADV
cana-5306	63	6	analyze	analyze	VERB
cana-5306	63	7	crystal	crystal	NOUN
cana-5306	63	8	structures	structure	NOUN
cana-5306	63	9	by	by	ADP
cana-5306	63	10	uniting	unite	VERB
cana-5306	63	11	translational	translational	ADJ
cana-5306	63	12	symmetry	symmetry	NOUN
cana-5306	63	13	with	with	ADP
cana-5306	63	14	point	point	NOUN
cana-5306	63	15	group	group	NOUN
cana-5306	63	16	symmetries	symmetry	NOUN
cana-5306	63	17	.	.	PUNCT
cana-5306	64	1	the	the	DET
cana-5306	64	2	implementation	implementation	NOUN
cana-5306	64	3	of	of	ADP
cana-5306	64	4	space	space	NOUN
cana-5306	64	5	group	group	NOUN
cana-5306	64	6	symmetry	symmetry	NOUN
cana-5306	64	7	applications	application	NOUN
cana-5306	64	8	improved	improve	VERB
cana-5306	64	9	the	the	DET
cana-5306	64	10	speed	speed	NOUN
cana-5306	64	11	together	together	ADV
cana-5306	64	12	with	with	ADP
cana-5306	64	13	precision	precision	NOUN
cana-5306	64	14	levels	level	NOUN
cana-5306	64	15	of	of	ADP
cana-5306	64	16	crystallographic	crystallographic	ADJ
cana-5306	64	17	examinations	examination	NOUN
cana-5306	64	18	in	in	ADP
cana-5306	64	19	atomic	atomic	ADJ
cana-5306	64	20	arrangement	arrangement	NOUN
cana-5306	64	21	studies	study	NOUN
cana-5306	64	22	throughout	throughout	ADP
cana-5306	64	23	three	three	NUM
cana-5306	64	24	-	-	PUNCT
cana-5306	64	25	dimensional	dimensional	ADJ
cana-5306	64	26	space	space	NOUN
cana-5306	64	27	.	.	PUNCT
cana-5306	65	1	group	group	NOUN
cana-5306	65	2	theory	theory	NOUN
cana-5306	65	3	integration	integration	NOUN
cana-5306	65	4	into	into	ADP
cana-5306	65	5	computational	computational	ADJ
cana-5306	65	6	methods	method	NOUN
cana-5306	65	7	helps	help	VERB
cana-5306	65	8	scientists	scientist	NOUN
cana-5306	65	9	develop	develop	VERB
cana-5306	65	10	more	more	ADV
cana-5306	65	11	precise	precise	ADJ
cana-5306	65	12	and	and	CCONJ
cana-5306	65	13	efficient	efficient	ADJ
cana-5306	65	14	models	model	NOUN
cana-5306	65	15	of	of	ADP
cana-5306	65	16	crystal	crystal	NOUN
cana-5306	65	17	structures	structure	NOUN
cana-5306	65	18	so	so	SCONJ
cana-5306	65	19	they	they	PRON
cana-5306	65	20	need	need	VERB
cana-5306	65	21	reduced	reduced	ADJ
cana-5306	65	22	quantities	quantity	NOUN
cana-5306	65	23	of	of	ADP
cana-5306	65	24	experimental	experimental	ADJ
cana-5306	65	25	research	research	NOUN
cana-5306	65	26	and	and	CCONJ
cana-5306	65	27	shorter	short	ADJ
cana-5306	65	28	periods	period	NOUN
cana-5306	65	29	for	for	ADP
cana-5306	65	30	completion	completion	NOUN
cana-5306	65	31	.	.	PUNCT
cana-5306	66	1	symmetry	symmetry	NOUN
cana-5306	66	2	analysis	analysis	NOUN
cana-5306	66	3	has	have	AUX
cana-5306	66	4	expanded	expand	VERB
cana-5306	66	5	its	its	PRON
cana-5306	66	6	practical	practical	ADJ
cana-5306	66	7	value	value	NOUN
cana-5306	66	8	to	to	ADP
cana-5306	66	9	material	material	NOUN
cana-5306	66	10	science	science	NOUN
cana-5306	66	11	applications	application	NOUN
cana-5306	66	12	where	where	SCONJ
cana-5306	66	13	researchers	researcher	NOUN
cana-5306	66	14	apply	apply	VERB
cana-5306	66	15	it	it	PRON
cana-5306	66	16	for	for	ADP
cana-5306	66	17	designing	design	VERB
cana-5306	66	18	materials	material	NOUN
cana-5306	66	19	that	that	PRON
cana-5306	66	20	possess	possess	VERB
cana-5306	66	21	particular	particular	ADJ
cana-5306	66	22	characteristics	characteristic	NOUN
cana-5306	66	23	.	.	PUNCT
cana-5306	67	1	analysis	analysis	NOUN
cana-5306	67	2	of	of	ADP
cana-5306	67	3	crystal	crystal	NOUN
cana-5306	67	4	symmetries	symmetry	NOUN
cana-5306	67	5	allows	allow	VERB
cana-5306	67	6	experts	expert	NOUN
cana-5306	67	7	to	to	PART
cana-5306	67	8	make	make	VERB
cana-5306	67	9	predictions	prediction	NOUN
cana-5306	67	10	regarding	regard	VERB
cana-5306	67	11	piezoelectric	piezoelectric	NOUN
cana-5306	67	12	and	and	CCONJ
cana-5306	67	13	ferroelectric	ferroelectric	ADJ
cana-5306	67	14	properties	property	NOUN
cana-5306	67	15	that	that	PRON
cana-5306	67	16	derive	derive	VERB
cana-5306	67	17	from	from	ADP
cana-5306	67	18	material	material	ADJ
cana-5306	67	19	symmetrical	symmetrical	ADJ
cana-5306	67	20	arrangements	arrangement	NOUN
cana-5306	67	21	.	.	PUNCT
cana-5306	68	1	games	game	NOUN
cana-5306	68	2	of	of	ADP
cana-5306	68	3	symmetry	symmetry	NOUN
cana-5306	68	4	are	be	AUX
cana-5306	68	5	essential	essential	ADJ
cana-5306	68	6	during	during	ADP
cana-5306	68	7	optoelectronic	optoelectronic	ADJ
cana-5306	68	8	device	device	NOUN
cana-5306	68	9	manufacturing	manufacturing	NOUN
cana-5306	68	10	and	and	CCONJ
cana-5306	68	11	superconducting	superconducting	ADJ
cana-5306	68	12	material	material	NOUN
cana-5306	68	13	development	development	NOUN
cana-5306	68	14	as	as	ADV
cana-5306	68	15	well	well	ADV
cana-5306	68	16	as	as	ADP
cana-5306	68	17	catalyst	catalyst	NOUN
cana-5306	68	18	production	production	NOUN
cana-5306	68	19	since	since	SCONJ
cana-5306	68	20	crystal	crystal	NOUN
cana-5306	68	21	symmetry	symmetry	NOUN
cana-5306	68	22	directly	directly	ADV
cana-5306	68	23	impacts	impact	VERB
cana-5306	68	24	performance	performance	NOUN
cana-5306	68	25	outcomes	outcome	NOUN
cana-5306	68	26	.	.	PUNCT
cana-5306	69	1	research	research	NOUN
cana-5306	69	2	has	have	AUX
cana-5306	69	3	expanded	expand	VERB
cana-5306	69	4	through	through	ADP
cana-5306	69	5	the	the	DET
cana-5306	69	6	merging	merging	NOUN
cana-5306	69	7	of	of	ADP
cana-5306	69	8	crystallography	crystallography	NOUN
cana-5306	69	9	with	with	ADP
cana-5306	69	10	nanotechnology	nanotechnology	NOUN
cana-5306	69	11	in	in	ADP
cana-5306	69	12	past	past	ADJ
cana-5306	69	13	several	several	ADJ
cana-5306	69	14	years	year	NOUN
cana-5306	69	15	.	.	PUNCT
cana-5306	70	1	nanoscale	nanoscale	NOUN
cana-5306	70	2	materials	material	NOUN
cana-5306	70	3	display	display	VERB
cana-5306	70	4	distinctive	distinctive	ADJ
cana-5306	70	5	properties	property	NOUN
cana-5306	70	6	that	that	PRON
cana-5306	70	7	result	result	VERB
cana-5306	70	8	from	from	ADP
cana-5306	70	9	their	their	PRON
cana-5306	70	10	crystal	crystal	NOUN
cana-5306	70	11	symmetrical	symmetrical	ADJ
cana-5306	70	12	features	feature	NOUN
cana-5306	70	13	.	.	PUNCT
cana-5306	71	1	paralleling	parallel	VERB
cana-5306	71	2	the	the	DET
cana-5306	71	3	properties	property	NOUN
cana-5306	71	4	of	of	ADP
cana-5306	71	5	nanomaterials	nanomaterial	NOUN
cana-5306	71	6	with	with	ADP
cana-5306	71	7	their	their	PRON
cana-5306	71	8	symmetry	symmetry	NOUN
cana-5306	71	9	level	level	NOUN
cana-5306	71	10	enables	enable	VERB
cana-5306	71	11	important	important	ADJ
cana-5306	71	12	technological	technological	ADJ
cana-5306	71	13	progress	progress	NOUN
cana-5306	71	14	in	in	ADP
cana-5306	71	15	storage	storage	NOUN
cana-5306	71	16	systems	system	NOUN
cana-5306	71	17	and	and	CCONJ
cana-5306	71	18	medical	medical	ADJ
cana-5306	71	19	treatments	treatment	NOUN
cana-5306	71	20	along	along	ADP
cana-5306	71	21	with	with	ADP
cana-5306	71	22	electronic	electronic	ADJ
cana-5306	71	23	devices	device	NOUN
cana-5306	71	24	.	.	PUNCT
cana-5306	72	1	the	the	DET
cana-5306	72	2	analysis	analysis	NOUN
cana-5306	72	3	of	of	ADP
cana-5306	72	4	nanomaterials	nanomaterial	NOUN
cana-5306	72	5	with	with	ADP
cana-5306	72	6	symmetrical	symmetrical	ADJ
cana-5306	72	7	approaches	approach	NOUN
cana-5306	72	8	has	have	AUX
cana-5306	72	9	become	become	VERB
cana-5306	72	10	essential	essential	ADJ
cana-5306	72	11	for	for	ADP
cana-5306	72	12	research	research	NOUN
cana-5306	72	13	in	in	ADP
cana-5306	72	14	this	this	DET
cana-5306	72	15	domain	domain	NOUN
cana-5306	72	16	.	.	PUNCT
cana-5306	73	1	in	in	ADP
cana-5306	73	2	2023	2023	NUM
cana-5306	73	3	f.	f.	PROPN
cana-5306	73	4	m.	m.	PROPN
cana-5306	73	5	brückler	brückler	PROPN
cana-5306	73	6	et.al	et.al	PROPN
cana-5306	73	7	.	.	PUNCT
cana-5306	74	1	and	and	CCONJ
cana-5306	74	2	v.	v.	ADP
cana-5306	74	3	stilinović	stilinović	PROPN
cana-5306	74	4	et.al	et.al	PROPN
cana-5306	74	5	.	.	PUNCT
cana-5306	74	6	,	,	PUNCT
cana-5306	75	1	[	[	X
cana-5306	75	2	1	1	X
cana-5306	75	3	]	]	PUNCT
cana-5306	75	4	introduced	introduce	VERB
cana-5306	75	5	the	the	DET
cana-5306	75	6	molecular	molecular	ADJ
cana-5306	75	7	crystallography	crystallography	NOUN
cana-5306	75	8	education	education	NOUN
cana-5306	75	9	regarding	regard	VERB
cana-5306	75	10	symmetry	symmetry	NOUN
cana-5306	75	11	principles	principle	NOUN
cana-5306	75	12	has	have	VERB
cana-5306	75	13	elevated	elevate	VERB
cana-5306	75	14	symmetry	symmetry	NOUN
cana-5306	75	15	applications	application	NOUN
cana-5306	75	16	in	in	ADP
cana-5306	75	17	pharmaceutical	pharmaceutical	NOUN
cana-5306	75	18	and	and	CCONJ
cana-5306	75	19	chemical	chemical	NOUN
cana-5306	75	20	operations	operation	NOUN
cana-5306	75	21	.	.	PUNCT
cana-5306	76	1	symmetry	symmetry	NOUN
cana-5306	76	2	analysis	analysis	NOUN
cana-5306	76	3	enables	enable	VERB
cana-5306	76	4	scientists	scientist	NOUN
cana-5306	76	5	to	to	PART
cana-5306	76	6	evaluate	evaluate	VERB
cana-5306	76	7	communications	communication	NOUN
cana-5306	76	8	on	on	ADP
cana-5306	76	9	applied	apply	VERB
cana-5306	76	10	nonlinear	nonlinear	ADJ
cana-5306	76	11	analysis	analysis	NOUN
cana-5306	76	12	issn	issn	NOUN
cana-5306	76	13	:	:	PUNCT
cana-5306	76	14	1074	1074	NUM
cana-5306	76	15	-	-	PUNCT
cana-5306	76	16	133x	133x	NUM
cana-5306	76	17	vol	vol	NOUN
cana-5306	76	18	31	31	NUM
cana-5306	76	19	no	no	NOUN
cana-5306	76	20	.	.	NOUN
cana-5306	76	21	2	2	NUM
cana-5306	76	22	(	(	PUNCT
cana-5306	76	23	2024	2024	NUM
cana-5306	76	24	)	)	PUNCT
cana-5306	76	25	444	444	NUM
cana-5306	76	26	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	76	27	active	active	ADJ
cana-5306	76	28	pharmaceutical	pharmaceutical	ADJ
cana-5306	76	29	ingredients	ingredient	NOUN
cana-5306	76	30	(	(	PUNCT
cana-5306	76	31	apis	apis	PROPN
cana-5306	76	32	)	)	PUNCT
cana-5306	76	33	which	which	PRON
cana-5306	76	34	affects	affect	VERB
cana-5306	76	35	their	their	PRON
cana-5306	76	36	effectiveness	effectiveness	NOUN
cana-5306	76	37	together	together	ADV
cana-5306	76	38	with	with	ADP
cana-5306	76	39	their	their	PRON
cana-5306	76	40	chemical	chemical	NOUN
cana-5306	76	41	stability	stability	NOUN
cana-5306	76	42	.	.	PUNCT
cana-5306	77	1	the	the	DET
cana-5306	77	2	practical	practical	ADJ
cana-5306	77	3	use	use	NOUN
cana-5306	77	4	of	of	ADP
cana-5306	77	5	crystallographic	crystallographic	ADJ
cana-5306	77	6	symmetry	symmetry	NOUN
cana-5306	77	7	in	in	ADP
cana-5306	77	8	real	real	ADJ
cana-5306	77	9	-	-	PUNCT
cana-5306	77	10	world	world	NOUN
cana-5306	77	11	industries	industry	NOUN
cana-5306	77	12	became	become	VERB
cana-5306	77	13	more	more	ADV
cana-5306	77	14	effective	effective	ADJ
cana-5306	77	15	through	through	ADP
cana-5306	77	16	advanced	advanced	ADJ
cana-5306	77	17	drug	drug	NOUN
cana-5306	77	18	development	development	NOUN
cana-5306	77	19	processes	process	NOUN
cana-5306	77	20	.	.	PUNCT
cana-5306	78	1	the	the	DET
cana-5306	78	2	examination	examination	NOUN
cana-5306	78	3	of	of	ADP
cana-5306	78	4	crystal	crystal	NOUN
cana-5306	78	5	symmetries	symmetry	NOUN
cana-5306	78	6	in	in	ADP
cana-5306	78	7	science	science	NOUN
cana-5306	78	8	progresses	progress	NOUN
cana-5306	78	9	since	since	SCONJ
cana-5306	78	10	new	new	ADJ
cana-5306	78	11	data	datum	NOUN
cana-5306	78	12	analysis	analysis	NOUN
cana-5306	78	13	strategies	strategy	NOUN
cana-5306	78	14	and	and	CCONJ
cana-5306	78	15	programming	programming	NOUN
cana-5306	78	16	software	software	NOUN
cana-5306	78	17	help	help	VERB
cana-5306	78	18	researchers	researcher	NOUN
cana-5306	78	19	understand	understand	VERB
cana-5306	78	20	crystalline	crystalline	ADJ
cana-5306	78	21	materials	material	NOUN
cana-5306	78	22	better	well	ADV
cana-5306	78	23	.	.	PUNCT
cana-5306	79	1	symmetry	symmetry	NOUN
cana-5306	79	2	gains	gain	VERB
cana-5306	79	3	constant	constant	ADJ
cana-5306	79	4	exploration	exploration	NOUN
cana-5306	79	5	within	within	ADP
cana-5306	79	6	material	material	NOUN
cana-5306	79	7	science	science	NOUN
cana-5306	79	8	and	and	CCONJ
cana-5306	79	9	nanotechnology	nanotechnology	NOUN
cana-5306	79	10	and	and	CCONJ
cana-5306	79	11	pharmaceutical	pharmaceutical	NOUN
cana-5306	79	12	production	production	NOUN
cana-5306	79	13	because	because	SCONJ
cana-5306	79	14	it	it	PRON
cana-5306	79	15	keeps	keep	VERB
cana-5306	79	16	significant	significant	ADJ
cana-5306	79	17	importance	importance	NOUN
cana-5306	79	18	for	for	ADP
cana-5306	79	19	theoretical	theoretical	ADJ
cana-5306	79	20	discoveries	discovery	NOUN
cana-5306	79	21	and	and	CCONJ
cana-5306	79	22	practical	practical	ADJ
cana-5306	79	23	implementation	implementation	NOUN
cana-5306	79	24	methods	method	NOUN
cana-5306	79	25	.	.	PUNCT
cana-5306	80	1	iii	iii	X
cana-5306	80	2	.	.	PROPN
cana-5306	80	3	proposed	propose	VERB
cana-5306	80	4	methodology	methodology	NOUN
cana-5306	80	5	in	in	ADP
cana-5306	80	6	this	this	DET
cana-5306	80	7	study	study	NOUN
cana-5306	80	8	,	,	PUNCT
cana-5306	80	9	the	the	DET
cana-5306	80	10	application	application	NOUN
cana-5306	80	11	of	of	ADP
cana-5306	80	12	symmetry	symmetry	NOUN
cana-5306	80	13	in	in	ADP
cana-5306	80	14	crystallography	crystallography	NOUN
cana-5306	80	15	is	be	AUX
cana-5306	80	16	analyzed	analyze	VERB
cana-5306	80	17	using	use	VERB
cana-5306	80	18	group	group	NOUN
cana-5306	80	19	theory	theory	NOUN
cana-5306	80	20	and	and	CCONJ
cana-5306	80	21	computational	computational	ADJ
cana-5306	80	22	methods	method	NOUN
cana-5306	80	23	to	to	PART
cana-5306	80	24	derive	derive	VERB
cana-5306	80	25	relationships	relationship	NOUN
cana-5306	80	26	between	between	ADP
cana-5306	80	27	crystal	crystal	NOUN
cana-5306	80	28	symmetry	symmetry	NOUN
cana-5306	80	29	and	and	CCONJ
cana-5306	80	30	material	material	NOUN
cana-5306	80	31	properties	property	NOUN
cana-5306	80	32	.	.	PUNCT
cana-5306	81	1	the	the	DET
cana-5306	81	2	methodology	methodology	NOUN
cana-5306	81	3	follows	follow	VERB
cana-5306	81	4	a	a	DET
cana-5306	81	5	systematic	systematic	ADJ
cana-5306	81	6	approach	approach	NOUN
cana-5306	81	7	involving	involve	VERB
cana-5306	81	8	the	the	DET
cana-5306	81	9	classification	classification	NOUN
cana-5306	81	10	of	of	ADP
cana-5306	81	11	symmetry	symmetry	NOUN
cana-5306	81	12	elements	element	NOUN
cana-5306	81	13	,	,	PUNCT
cana-5306	81	14	the	the	DET
cana-5306	81	15	determination	determination	NOUN
cana-5306	81	16	of	of	ADP
cana-5306	81	17	crystal	crystal	NOUN
cana-5306	81	18	structures	structure	NOUN
cana-5306	81	19	,	,	PUNCT
cana-5306	81	20	and	and	CCONJ
cana-5306	81	21	the	the	DET
cana-5306	81	22	prediction	prediction	NOUN
cana-5306	81	23	of	of	ADP
cana-5306	81	24	material	material	NOUN
cana-5306	81	25	properties	property	NOUN
cana-5306	81	26	based	base	VERB
cana-5306	81	27	on	on	ADP
cana-5306	81	28	symmetry	symmetry	NOUN
cana-5306	81	29	.	.	PUNCT
cana-5306	82	1	the	the	DET
cana-5306	82	2	process	process	NOUN
cana-5306	82	3	involves	involve	VERB
cana-5306	82	4	both	both	CCONJ
cana-5306	82	5	analytical	analytical	ADJ
cana-5306	82	6	and	and	CCONJ
cana-5306	82	7	computational	computational	ADJ
cana-5306	82	8	techniques	technique	NOUN
cana-5306	82	9	[	[	X
cana-5306	82	10	10	10	NUM
cana-5306	82	11	]	]	PUNCT
cana-5306	82	12	.	.	PUNCT
cana-5306	83	1	to	to	PART
cana-5306	83	2	begin	begin	VERB
cana-5306	83	3	the	the	DET
cana-5306	83	4	proposed	propose	VERB
cana-5306	83	5	methodology	methodology	NOUN
cana-5306	83	6	researchers	researcher	NOUN
cana-5306	83	7	must	must	AUX
cana-5306	83	8	identify	identify	VERB
cana-5306	83	9	all	all	DET
cana-5306	83	10	symmetry	symmetry	NOUN
cana-5306	83	11	operations	operation	NOUN
cana-5306	83	12	found	find	VERB
cana-5306	83	13	within	within	ADP
cana-5306	83	14	the	the	DET
cana-5306	83	15	crystal	crystal	NOUN
cana-5306	83	16	structure	structure	NOUN
cana-5306	83	17	.	.	PUNCT
cana-5306	84	1	every	every	DET
cana-5306	84	2	crystal	crystal	NOUN
cana-5306	84	3	lattice	lattice	PROPN
cana-5306	84	4	contains	contain	VERB
cana-5306	84	5	a	a	DET
cana-5306	84	6	fundamental	fundamental	ADJ
cana-5306	84	7	set	set	NOUN
cana-5306	84	8	of	of	ADP
cana-5306	84	9	symmetry	symmetry	NOUN
cana-5306	84	10	operations	operation	NOUN
cana-5306	84	11	which	which	PRON
cana-5306	84	12	include	include	VERB
cana-5306	84	13	rotation	rotation	NOUN
cana-5306	84	14	and	and	CCONJ
cana-5306	84	15	reflection	reflection	NOUN
cana-5306	84	16	together	together	ADV
cana-5306	84	17	with	with	ADP
cana-5306	84	18	inversion	inversion	NOUN
cana-5306	84	19	as	as	ADV
cana-5306	84	20	well	well	ADV
cana-5306	84	21	as	as	ADP
cana-5306	84	22	translation	translation	NOUN
cana-5306	84	23	.	.	PUNCT
cana-5306	85	1	a	a	DET
cana-5306	85	2	group	group	NOUN
cana-5306	85	3	of	of	ADP
cana-5306	85	4	symmetry	symmetry	NOUN
cana-5306	85	5	transformations	transformation	NOUN
cana-5306	85	6	appears	appear	VERB
cana-5306	85	7	when	when	SCONJ
cana-5306	85	8	these	these	DET
cana-5306	85	9	operations	operation	NOUN
cana-5306	85	10	are	be	AUX
cana-5306	85	11	combined	combine	VERB
cana-5306	85	12	with	with	ADP
cana-5306	85	13	each	each	DET
cana-5306	85	14	element	element	NOUN
cana-5306	85	15	representing	represent	VERB
cana-5306	85	16	a	a	DET
cana-5306	85	17	particular	particular	ADJ
cana-5306	85	18	symmetry	symmetry	NOUN
cana-5306	85	19	transformation	transformation	NOUN
cana-5306	85	20	.	.	PUNCT
cana-5306	86	1	the	the	DET
cana-5306	86	2	combination	combination	NOUN
cana-5306	86	3	of	of	ADP
cana-5306	86	4	symmetry	symmetry	NOUN
cana-5306	86	5	operations	operation	NOUN
cana-5306	86	6	allows	allow	VERB
cana-5306	86	7	for	for	ADP
cana-5306	86	8	describing	describe	VERB
cana-5306	86	9	the	the	DET
cana-5306	86	10	whole	whole	ADJ
cana-5306	86	11	crystal	crystal	NOUN
cana-5306	86	12	symmetry	symmetry	NOUN
cana-5306	86	13	as	as	ADP
cana-5306	86	14	space	space	NOUN
cana-5306	86	15	group	group	NOUN
cana-5306	86	16	.	.	PUNCT
cana-5306	87	1	the	the	DET
cana-5306	87	2	mathematical	mathematical	ADJ
cana-5306	87	3	depiction	depiction	NOUN
cana-5306	87	4	appears	appear	VERB
cana-5306	87	5	as	as	SCONJ
cana-5306	87	6	follows	follow	VERB
cana-5306	87	7	:	:	PUNCT
cana-5306	87	8	𝐺	𝐺	PROPN
cana-5306	87	9	=	=	PUNCT
cana-5306	87	10	{	{	PUNCT
cana-5306	87	11	𝑒	𝑒	PROPN
cana-5306	87	12	,	,	PUNCT
cana-5306	87	13	𝑔1	𝑔1	PROPN
cana-5306	87	14	,	,	PUNCT
cana-5306	87	15	𝑔2	𝑔2	NOUN
cana-5306	87	16	,	,	PUNCT
cana-5306	87	17	𝑔3	𝑔3	ADJ
cana-5306	87	18	,	,	PUNCT
cana-5306	87	19	…	…	PUNCT
cana-5306	87	20	,	,	PUNCT
cana-5306	87	21	𝑔𝑛	𝑔𝑛	ADP
cana-5306	87	22	}	}	PUNCT
cana-5306	87	23	where	where	SCONJ
cana-5306	87	24	𝐺	𝐺	PROPN
cana-5306	87	25	represents	represent	VERB
cana-5306	87	26	the	the	DET
cana-5306	87	27	symmetry	symmetry	NOUN
cana-5306	87	28	group	group	NOUN
cana-5306	87	29	of	of	ADP
cana-5306	87	30	the	the	DET
cana-5306	87	31	crystal	crystal	NOUN
cana-5306	87	32	,	,	PUNCT
cana-5306	87	33	𝑒	𝑒	PROPN
cana-5306	87	34	is	be	AUX
cana-5306	87	35	the	the	DET
cana-5306	87	36	identity	identity	NOUN
cana-5306	87	37	element	element	NOUN
cana-5306	87	38	,	,	PUNCT
cana-5306	87	39	and	and	CCONJ
cana-5306	87	40	𝑔1	𝑔1	PROPN
cana-5306	87	41	,	,	PUNCT
cana-5306	87	42	𝑔2	𝑔2	VERB
cana-5306	87	43	,	,	PUNCT
cana-5306	87	44	…	…	PUNCT
cana-5306	87	45	,	,	PUNCT
cana-5306	87	46	𝑔𝑛	𝑔𝑛	PROPN
cana-5306	87	47	are	be	AUX
cana-5306	87	48	the	the	DET
cana-5306	87	49	symmetry	symmetry	NOUN
cana-5306	87	50	operations	operation	NOUN
cana-5306	87	51	.	.	PUNCT
cana-5306	88	1	the	the	DET
cana-5306	88	2	analysis	analysis	NOUN
cana-5306	88	3	moves	move	VERB
cana-5306	88	4	towards	towards	ADP
cana-5306	88	5	evaluating	evaluate	VERB
cana-5306	88	6	the	the	DET
cana-5306	88	7	crystal	crystal	PROPN
cana-5306	88	8	lattice	lattice	PROPN
cana-5306	88	9	symmetry	symmetry	PROPN
cana-5306	88	10	through	through	ADP
cana-5306	88	11	its	its	PRON
cana-5306	88	12	point	point	NOUN
cana-5306	88	13	group	group	NOUN
cana-5306	88	14	structure	structure	NOUN
cana-5306	88	15	.	.	PUNCT
cana-5306	89	1	a	a	DET
cana-5306	89	2	crystal	crystal	NOUN
cana-5306	89	3	receives	receive	VERB
cana-5306	89	4	its	its	PRON
cana-5306	89	5	point	point	NOUN
cana-5306	89	6	group	group	NOUN
cana-5306	89	7	classification	classification	NOUN
cana-5306	89	8	by	by	ADP
cana-5306	89	9	analyzing	analyze	VERB
cana-5306	89	10	rotational	rotational	ADJ
cana-5306	89	11	symmetry	symmetry	NOUN
cana-5306	89	12	and	and	CCONJ
cana-5306	89	13	reflection	reflection	NOUN
cana-5306	89	14	symmetry	symmetry	NOUN
cana-5306	89	15	without	without	ADP
cana-5306	89	16	assessing	assess	VERB
cana-5306	89	17	translational	translational	ADJ
cana-5306	89	18	symmetry	symmetry	NOUN
cana-5306	89	19	.	.	PUNCT
cana-5306	90	1	scientific	scientific	ADJ
cana-5306	90	2	description	description	NOUN
cana-5306	90	3	of	of	ADP
cana-5306	90	4	a	a	DET
cana-5306	90	5	crystal	crystal	NOUN
cana-5306	90	6	symmetry	symmetry	NOUN
cana-5306	90	7	group	group	NOUN
cana-5306	90	8	amounts	amount	VERB
cana-5306	90	9	to	to	ADP
cana-5306	90	10	decomposition	decomposition	NOUN
cana-5306	90	11	into	into	ADP
cana-5306	90	12	point	point	NOUN
cana-5306	90	13	group	group	NOUN
cana-5306	90	14	components	component	NOUN
cana-5306	90	15	that	that	PRON
cana-5306	90	16	appear	appear	VERB
cana-5306	90	17	as	as	ADP
cana-5306	90	18	:	:	PUNCT
cana-5306	90	19	𝑃	𝑃	NOUN
cana-5306	90	20	=	=	SYM
cana-5306	90	21	{	{	PUNCT
cana-5306	90	22	𝑅1	𝑅1	PROPN
cana-5306	90	23	,	,	PUNCT
cana-5306	90	24	𝑅2	𝑅2	ADP
cana-5306	90	25	,	,	PUNCT
cana-5306	90	26	…	…	PUNCT
cana-5306	90	27	,	,	PUNCT
cana-5306	90	28	𝑅𝑚	𝑅𝑚	PROPN
cana-5306	90	29	}	}	PUNCT
cana-5306	90	30	where	where	SCONJ
cana-5306	90	31	𝑃	𝑃	NOUN
cana-5306	90	32	represents	represent	VERB
cana-5306	90	33	the	the	DET
cana-5306	90	34	point	point	NOUN
cana-5306	90	35	group	group	NOUN
cana-5306	90	36	and	and	CCONJ
cana-5306	90	37	𝑅1	𝑅1	PROPN
cana-5306	90	38	,	,	PUNCT
cana-5306	90	39	𝑅2	𝑅2	ADP
cana-5306	90	40	,	,	PUNCT
cana-5306	90	41	…	…	PUNCT
cana-5306	90	42	,	,	PUNCT
cana-5306	90	43	𝑅𝑚	𝑅𝑚	PROPN
cana-5306	90	44	are	be	AUX
cana-5306	90	45	the	the	DET
cana-5306	90	46	rotational	rotational	ADJ
cana-5306	90	47	and	and	CCONJ
cana-5306	90	48	reflection	reflection	NOUN
cana-5306	90	49	symmetry	symmetry	NOUN
cana-5306	90	50	elements	element	NOUN
cana-5306	90	51	.	.	PUNCT
cana-5306	91	1	after	after	ADP
cana-5306	91	2	identifying	identify	VERB
cana-5306	91	3	symmetry	symmetry	NOUN
cana-5306	91	4	operations	operation	NOUN
cana-5306	91	5	researchers	researcher	NOUN
cana-5306	91	6	can	can	AUX
cana-5306	91	7	use	use	VERB
cana-5306	91	8	group	group	NOUN
cana-5306	91	9	theory	theory	NOUN
cana-5306	91	10	analysis	analysis	NOUN
cana-5306	91	11	to	to	PART
cana-5306	91	12	determine	determine	VERB
cana-5306	91	13	the	the	DET
cana-5306	91	14	crystal	crystal	NOUN
cana-5306	91	15	space	space	NOUN
cana-5306	91	16	group	group	NOUN
cana-5306	91	17	.	.	PUNCT
cana-5306	92	1	the	the	DET
cana-5306	92	2	space	space	NOUN
cana-5306	92	3	group	group	NOUN
cana-5306	92	4	unifies	unify	VERB
cana-5306	92	5	both	both	CCONJ
cana-5306	92	6	the	the	DET
cana-5306	92	7	crystal	crystal	PROPN
cana-5306	92	8	lattice	lattice	PROPN
cana-5306	92	9	translational	translational	PROPN
cana-5306	92	10	symmetry	symmetry	NOUN
cana-5306	92	11	communications	communication	NOUN
cana-5306	92	12	on	on	ADP
cana-5306	92	13	applied	apply	VERB
cana-5306	92	14	nonlinear	nonlinear	ADJ
cana-5306	92	15	analysis	analysis	NOUN
cana-5306	92	16	issn	issn	NOUN
cana-5306	92	17	:	:	PUNCT
cana-5306	92	18	1074	1074	NUM
cana-5306	92	19	-	-	PUNCT
cana-5306	92	20	133x	133x	NUM
cana-5306	92	21	vol	vol	NOUN
cana-5306	92	22	31	31	NUM
cana-5306	92	23	no	no	NOUN
cana-5306	92	24	.	.	NOUN
cana-5306	92	25	2	2	NUM
cana-5306	92	26	(	(	PUNCT
cana-5306	92	27	2024	2024	NUM
cana-5306	92	28	)	)	PUNCT
cana-5306	92	29	445	445	NUM
cana-5306	92	30	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	92	31	and	and	CCONJ
cana-5306	92	32	its	its	PRON
cana-5306	92	33	point	point	NOUN
cana-5306	92	34	group	group	NOUN
cana-5306	92	35	symmetry	symmetry	NOUN
cana-5306	92	36	operations	operation	NOUN
cana-5306	92	37	.	.	PUNCT
cana-5306	93	1	the	the	DET
cana-5306	93	2	space	space	NOUN
cana-5306	93	3	group	group	NOUN
cana-5306	93	4	s	s	PART
cana-5306	93	5	exists	exist	VERB
cana-5306	93	6	as	as	ADP
cana-5306	93	7	a	a	DET
cana-5306	93	8	combination	combination	NOUN
cana-5306	93	9	of	of	ADP
cana-5306	93	10	both	both	DET
cana-5306	93	11	point	point	NOUN
cana-5306	93	12	group	group	NOUN
cana-5306	93	13	p	p	NOUN
cana-5306	93	14	along	along	ADP
cana-5306	93	15	with	with	ADP
cana-5306	93	16	translational	translational	ADJ
cana-5306	93	17	symmetry	symmetry	NOUN
cana-5306	93	18	group	group	NOUN
cana-5306	93	19	t	t	PROPN
cana-5306	93	20	:	:	PUNCT
cana-5306	93	21	𝑆	𝑆	PROPN
cana-5306	93	22	=	=	SYM
cana-5306	93	23	𝑃	𝑃	VERB
cana-5306	93	24	×	×	NOUN
cana-5306	93	25	𝑇	𝑇	PROPN
cana-5306	93	26	the	the	DET
cana-5306	93	27	space	space	NOUN
cana-5306	93	28	group	group	NOUN
cana-5306	93	29	𝑆	𝑆	PROPN
cana-5306	93	30	fully	fully	ADV
cana-5306	93	31	characterizes	characterize	VERB
cana-5306	93	32	the	the	DET
cana-5306	93	33	symmetry	symmetry	NOUN
cana-5306	93	34	of	of	ADP
cana-5306	93	35	the	the	DET
cana-5306	93	36	crystal	crystal	NOUN
cana-5306	93	37	,	,	PUNCT
cana-5306	93	38	including	include	VERB
cana-5306	93	39	all	all	DET
cana-5306	93	40	possible	possible	ADJ
cana-5306	93	41	symmetry	symmetry	NOUN
cana-5306	93	42	operations	operation	NOUN
cana-5306	93	43	such	such	ADJ
cana-5306	93	44	as	as	ADP
cana-5306	93	45	translations	translation	NOUN
cana-5306	93	46	,	,	PUNCT
cana-5306	93	47	rotations	rotation	NOUN
cana-5306	93	48	,	,	PUNCT
cana-5306	93	49	and	and	CCONJ
cana-5306	93	50	reflections	reflection	NOUN
cana-5306	93	51	.	.	PUNCT
cana-5306	94	1	the	the	DET
cana-5306	94	2	following	follow	VERB
cana-5306	94	3	methodology	methodology	NOUN
cana-5306	94	4	stage	stage	NOUN
cana-5306	94	5	requires	require	VERB
cana-5306	94	6	performing	perform	VERB
cana-5306	94	7	computational	computational	ADJ
cana-5306	94	8	analysis	analysis	NOUN
cana-5306	94	9	on	on	ADP
cana-5306	94	10	crystal	crystal	NOUN
cana-5306	94	11	structures	structure	NOUN
cana-5306	94	12	through	through	ADP
cana-5306	94	13	symmetry	symmetry	NOUN
cana-5306	94	14	-	-	PUNCT
cana-5306	94	15	based	base	VERB
cana-5306	94	16	techniques	technique	NOUN
cana-5306	94	17	.	.	PUNCT
cana-5306	95	1	the	the	DET
cana-5306	95	2	research	research	NOUN
cana-5306	95	3	performs	perform	VERB
cana-5306	95	4	electronic	electronic	ADJ
cana-5306	95	5	property	property	NOUN
cana-5306	95	6	and	and	CCONJ
cana-5306	95	7	atomic	atomic	ADJ
cana-5306	95	8	arrangement	arrangement	NOUN
cana-5306	95	9	computations	computation	NOUN
cana-5306	95	10	through	through	ADP
cana-5306	95	11	density	density	NOUN
cana-5306	95	12	functional	functional	ADJ
cana-5306	95	13	theory	theory	NOUN
cana-5306	95	14	(	(	PUNCT
cana-5306	95	15	dft	dft	NOUN
cana-5306	95	16	)	)	PUNCT
cana-5306	95	17	and	and	CCONJ
cana-5306	95	18	molecular	molecular	ADJ
cana-5306	95	19	dynamics	dynamic	NOUN
cana-5306	95	20	(	(	PUNCT
cana-5306	95	21	md	md	PROPN
cana-5306	95	22	)	)	PUNCT
cana-5306	95	23	simulation	simulation	NOUN
cana-5306	95	24	analyses	analyse	VERB
cana-5306	95	25	[	[	X
cana-5306	95	26	12	12	NUM
cana-5306	95	27	]	]	PUNCT
cana-5306	95	28	.	.	PUNCT
cana-5306	96	1	crystal	crystal	PROPN
cana-5306	96	2	lattice	lattice	PROPN
cana-5306	96	3	symmetry	symmetry	PROPN
cana-5306	96	4	allows	allow	VERB
cana-5306	96	5	computational	computational	ADJ
cana-5306	96	6	models	model	NOUN
cana-5306	96	7	to	to	PART
cana-5306	96	8	become	become	AUX
cana-5306	96	9	simplified	simplified	ADJ
cana-5306	96	10	by	by	ADP
cana-5306	96	11	reducing	reduce	VERB
cana-5306	96	12	the	the	DET
cana-5306	96	13	number	number	NOUN
cana-5306	96	14	of	of	ADP
cana-5306	96	15	atomic	atomic	ADJ
cana-5306	96	16	sites	site	NOUN
cana-5306	96	17	that	that	PRON
cana-5306	96	18	need	need	VERB
cana-5306	96	19	to	to	PART
cana-5306	96	20	be	be	AUX
cana-5306	96	21	analyzed	analyze	VERB
cana-5306	96	22	.	.	PUNCT
cana-5306	97	1	a	a	DET
cana-5306	97	2	system	system	NOUN
cana-5306	97	3	containing	contain	VERB
cana-5306	97	4	n	n	PRON
cana-5306	97	5	atoms	atom	NOUN
cana-5306	97	6	allows	allow	VERB
cana-5306	97	7	the	the	DET
cana-5306	97	8	reduction	reduction	NOUN
cana-5306	97	9	of	of	ADP
cana-5306	97	10	𝑁unique	𝑁unique	PROPN
cana-5306	97	11	atomic	atomic	ADJ
cana-5306	97	12	positions	position	NOUN
cana-5306	97	13	through	through	ADP
cana-5306	97	14	symmetry	symmetry	NOUN
cana-5306	97	15	analysis	analysis	NOUN
cana-5306	97	16	.	.	PUNCT
cana-5306	97	17	:	:	PUNCT
cana-5306	98	1	𝑁𝑢𝑛𝑖𝑞𝑢𝑒	𝑁𝑢𝑛𝑖𝑞𝑢𝑒	PROPN
cana-5306	98	2	=	=	SYM
cana-5306	98	3	𝑁	𝑁	PROPN
cana-5306	98	4	symmetry	symmetry	NOUN
cana-5306	98	5	factor	factor	NOUN
cana-5306	98	6	the	the	DET
cana-5306	98	7	symmetry	symmetry	NOUN
cana-5306	98	8	factor	factor	NOUN
cana-5306	98	9	counts	count	VERB
cana-5306	98	10	how	how	SCONJ
cana-5306	98	11	many	many	ADJ
cana-5306	98	12	symmetry	symmetry	NOUN
cana-5306	98	13	operations	operation	NOUN
cana-5306	98	14	preserve	preserve	VERB
cana-5306	98	15	the	the	DET
cana-5306	98	16	position	position	NOUN
cana-5306	98	17	of	of	ADP
cana-5306	98	18	a	a	DET
cana-5306	98	19	given	give	VERB
cana-5306	98	20	atom	atom	NOUN
cana-5306	98	21	while	while	SCONJ
cana-5306	98	22	the	the	DET
cana-5306	98	23	symmetry	symmetry	NOUN
cana-5306	98	24	operations	operation	NOUN
cana-5306	98	25	are	be	AUX
cana-5306	98	26	assessed	assess	VERB
cana-5306	98	27	.	.	PUNCT
cana-5306	99	1	the	the	DET
cana-5306	99	2	electronic	electronic	ADJ
cana-5306	99	3	structure	structure	NOUN
cana-5306	99	4	of	of	ADP
cana-5306	99	5	the	the	DET
cana-5306	99	6	crystal	crystal	NOUN
cana-5306	99	7	becomes	become	VERB
cana-5306	99	8	accessible	accessible	ADJ
cana-5306	99	9	when	when	SCONJ
cana-5306	99	10	bloch	bloch	PROPN
cana-5306	99	11	theorem	theorem	VERB
cana-5306	99	12	analyzes	analyze	VERB
cana-5306	99	13	it	it	PRON
cana-5306	99	14	by	by	ADP
cana-5306	99	15	applying	apply	VERB
cana-5306	99	16	crystal	crystal	NOUN
cana-5306	99	17	symmetry	symmetry	NOUN
cana-5306	99	18	rules	rule	NOUN
cana-5306	99	19	to	to	PART
cana-5306	99	20	simplify	simplify	VERB
cana-5306	99	21	wavefunction	wavefunction	NOUN
cana-5306	99	22	complexity	complexity	NOUN
cana-5306	99	23	:	:	PUNCT
cana-5306	99	24	𝜓𝑘(𝑟	𝜓𝑘(𝑟	X
cana-5306	99	25	)	)	PUNCT
cana-5306	99	26	=	=	SYM
cana-5306	99	27	𝑒𝑖𝑘𝑟𝑢𝑘(𝑟	𝑒𝑖𝑘𝑟𝑢𝑘(𝑟	NOUN
cana-5306	99	28	)	)	PUNCT
cana-5306	99	29	where	where	SCONJ
cana-5306	99	30	𝜓𝑘(𝑟	𝜓𝑘(𝑟	PUNCT
cana-5306	99	31	)	)	PUNCT
cana-5306	99	32	is	be	AUX
cana-5306	99	33	the	the	DET
cana-5306	99	34	wavefunction	wavefunction	NOUN
cana-5306	99	35	,	,	PUNCT
cana-5306	99	36	𝑘	𝑘	PROPN
cana-5306	99	37	is	be	AUX
cana-5306	99	38	the	the	DET
cana-5306	99	39	wavevector	wavevector	NOUN
cana-5306	99	40	,	,	PUNCT
cana-5306	99	41	𝑟	𝑟	PRON
cana-5306	99	42	is	be	AUX
cana-5306	99	43	the	the	DET
cana-5306	99	44	position	position	NOUN
cana-5306	99	45	vector	vector	NOUN
cana-5306	99	46	,	,	PUNCT
cana-5306	99	47	and	and	CCONJ
cana-5306	99	48	𝑢𝑘(𝑟	𝑢𝑘(𝑟	NUM
cana-5306	99	49	)	)	PUNCT
cana-5306	99	50	is	be	AUX
cana-5306	99	51	a	a	DET
cana-5306	99	52	function	function	NOUN
cana-5306	99	53	that	that	PRON
cana-5306	99	54	has	have	VERB
cana-5306	99	55	the	the	DET
cana-5306	99	56	same	same	ADJ
cana-5306	99	57	symmetry	symmetry	NOUN
cana-5306	99	58	as	as	ADP
cana-5306	99	59	the	the	DET
cana-5306	99	60	crystal	crystal	PROPN
cana-5306	99	61	lattice	lattice	NOUN
cana-5306	99	62	.	.	PUNCT
cana-5306	100	1	in	in	ADP
cana-5306	100	2	this	this	DET
cana-5306	100	3	stage	stage	NOUN
cana-5306	100	4	,	,	PUNCT
cana-5306	100	5	the	the	DET
cana-5306	100	6	forces	force	NOUN
cana-5306	100	7	acting	act	VERB
cana-5306	100	8	on	on	ADP
cana-5306	100	9	atoms	atom	NOUN
cana-5306	100	10	in	in	ADP
cana-5306	100	11	the	the	DET
cana-5306	100	12	crystal	crystal	NOUN
cana-5306	100	13	are	be	AUX
cana-5306	100	14	calculated	calculate	VERB
cana-5306	100	15	using	use	VERB
cana-5306	100	16	the	the	DET
cana-5306	100	17	symmetry	symmetry	NOUN
cana-5306	100	18	of	of	ADP
cana-5306	100	19	the	the	DET
cana-5306	100	20	crystal	crystal	PROPN
cana-5306	100	21	lattice	lattice	PROPN
cana-5306	100	22	.	.	PUNCT
cana-5306	101	1	these	these	DET
cana-5306	101	2	forces	force	NOUN
cana-5306	101	3	are	be	AUX
cana-5306	101	4	used	use	VERB
cana-5306	101	5	to	to	PART
cana-5306	101	6	determine	determine	VERB
cana-5306	101	7	the	the	DET
cana-5306	101	8	equilibrium	equilibrium	NOUN
cana-5306	101	9	positions	position	NOUN
cana-5306	101	10	of	of	ADP
cana-5306	101	11	the	the	DET
cana-5306	101	12	atoms	atom	NOUN
cana-5306	101	13	in	in	ADP
cana-5306	101	14	the	the	DET
cana-5306	101	15	lattice	lattice	NOUN
cana-5306	101	16	,	,	PUNCT
cana-5306	101	17	which	which	PRON
cana-5306	101	18	in	in	ADP
cana-5306	101	19	turn	turn	NOUN
cana-5306	101	20	provides	provide	VERB
cana-5306	101	21	the	the	DET
cana-5306	101	22	crystal	crystal	NOUN
cana-5306	101	23	structure	structure	NOUN
cana-5306	101	24	.	.	PUNCT
cana-5306	102	1	the	the	DET
cana-5306	102	2	energy	energy	NOUN
cana-5306	102	3	of	of	ADP
cana-5306	102	4	the	the	DET
cana-5306	102	5	crystal	crystal	NOUN
cana-5306	102	6	lattice	lattice	NOUN
cana-5306	102	7	can	can	AUX
cana-5306	102	8	be	be	AUX
cana-5306	102	9	computed	compute	VERB
cana-5306	102	10	using	use	VERB
cana-5306	102	11	the	the	DET
cana-5306	102	12	following	follow	VERB
cana-5306	102	13	equation	equation	NOUN
cana-5306	102	14	,	,	PUNCT
cana-5306	102	15	where	where	SCONJ
cana-5306	102	16	𝑉	𝑉	PROPN
cana-5306	102	17	represents	represent	VERB
cana-5306	102	18	the	the	DET
cana-5306	102	19	potential	potential	ADJ
cana-5306	102	20	energy	energy	NOUN
cana-5306	102	21	,	,	PUNCT
cana-5306	102	22	𝒓𝑖	𝒓𝑖	NOUN
cana-5306	102	23	is	be	AUX
cana-5306	102	24	the	the	DET
cana-5306	102	25	position	position	NOUN
cana-5306	102	26	of	of	ADP
cana-5306	102	27	the	the	DET
cana-5306	102	28	𝑖-th	𝑖-th	PROPN
cana-5306	102	29	atom	atom	NOUN
cana-5306	102	30	,	,	PUNCT
cana-5306	102	31	and	and	CCONJ
cana-5306	102	32	𝐹𝑖	𝐹𝑖	PROPN
cana-5306	102	33	is	be	AUX
cana-5306	102	34	the	the	DET
cana-5306	102	35	force	force	NOUN
cana-5306	102	36	on	on	ADP
cana-5306	102	37	the	the	DET
cana-5306	102	38	𝑖-th	𝑖-th	PROPN
cana-5306	102	39	atom	atom	NOUN
cana-5306	102	40	:	:	PUNCT
cana-5306	102	41	𝑉	𝑉	PROPN
cana-5306	102	42	=	=	PUNCT
cana-5306	102	43	∑	∑	PUNCT
cana-5306	102	44	  	  	SPACE
cana-5306	102	45	𝑖	𝑖	SYM
cana-5306	103	1	𝐹𝑖	𝐹𝑖	PROPN
cana-5306	103	2	⋅	⋅	PROPN
cana-5306	103	3	𝑟𝑖	𝑟𝑖	ADP
cana-5306	103	4	2	2	NUM
cana-5306	103	5	once	once	SCONJ
cana-5306	103	6	the	the	DET
cana-5306	103	7	crystal	crystal	NOUN
cana-5306	103	8	structure	structure	NOUN
cana-5306	103	9	is	be	AUX
cana-5306	103	10	determined	determine	VERB
cana-5306	103	11	,	,	PUNCT
cana-5306	103	12	the	the	DET
cana-5306	103	13	symmetry	symmetry	NOUN
cana-5306	103	14	operations	operation	NOUN
cana-5306	103	15	are	be	AUX
cana-5306	103	16	used	use	VERB
cana-5306	103	17	to	to	PART
cana-5306	103	18	predict	predict	VERB
cana-5306	103	19	the	the	DET
cana-5306	103	20	macroscopic	macroscopic	ADJ
cana-5306	103	21	properties	property	NOUN
cana-5306	103	22	of	of	ADP
cana-5306	103	23	the	the	DET
cana-5306	103	24	material	material	NOUN
cana-5306	103	25	.	.	PUNCT
cana-5306	104	1	for	for	ADP
cana-5306	104	2	example	example	NOUN
cana-5306	104	3	,	,	PUNCT
cana-5306	104	4	the	the	DET
cana-5306	104	5	piezoelectric	piezoelectric	ADJ
cana-5306	104	6	properties	property	NOUN
cana-5306	104	7	of	of	ADP
cana-5306	104	8	a	a	DET
cana-5306	104	9	crystal	crystal	NOUN
cana-5306	104	10	can	can	AUX
cana-5306	104	11	be	be	AUX
cana-5306	104	12	derived	derive	VERB
cana-5306	104	13	by	by	ADP
cana-5306	104	14	examining	examine	VERB
cana-5306	104	15	its	its	PRON
cana-5306	104	16	symmetry	symmetry	NOUN
cana-5306	104	17	under	under	ADP
cana-5306	104	18	mechanical	mechanical	ADJ
cana-5306	104	19	deformation	deformation	NOUN
cana-5306	104	20	.	.	PUNCT
cana-5306	105	1	the	the	DET
cana-5306	105	2	piezoelectric	piezoelectric	ADJ
cana-5306	105	3	coefficient	coefficient	NOUN
cana-5306	105	4	𝑑𝑖𝑗𝑘	𝑑𝑖𝑗𝑘	NOUN
cana-5306	105	5	for	for	ADP
cana-5306	105	6	a	a	DET
cana-5306	105	7	crystal	crystal	NOUN
cana-5306	105	8	can	can	AUX
cana-5306	105	9	be	be	AUX
cana-5306	105	10	written	write	VERB
cana-5306	105	11	as	as	ADP
cana-5306	105	12	:	:	PUNCT
cana-5306	105	13	communications	communication	NOUN
cana-5306	105	14	on	on	ADP
cana-5306	105	15	applied	apply	VERB
cana-5306	105	16	nonlinear	nonlinear	ADJ
cana-5306	105	17	analysis	analysis	NOUN
cana-5306	105	18	issn	issn	NOUN
cana-5306	105	19	:	:	PUNCT
cana-5306	105	20	1074	1074	NUM
cana-5306	105	21	-	-	PUNCT
cana-5306	105	22	133x	133x	NUM
cana-5306	105	23	vol	vol	NOUN
cana-5306	105	24	31	31	NUM
cana-5306	105	25	no	no	NOUN
cana-5306	105	26	.	.	NOUN
cana-5306	105	27	2	2	NUM
cana-5306	105	28	(	(	PUNCT
cana-5306	105	29	2024	2024	NUM
cana-5306	105	30	)	)	PUNCT
cana-5306	105	31	446	446	NUM
cana-5306	105	32	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	105	33	𝑑𝑖𝑗𝑘	𝑑𝑖𝑗𝑘	NOUN
cana-5306	105	34	=	=	SYM
cana-5306	105	35	𝜕𝑃𝑖	𝜕𝑃𝑖	NOUN
cana-5306	105	36	𝜕𝜖𝑗𝑘	𝜕𝜖𝑗𝑘	NOUN
cana-5306	105	37	where	where	SCONJ
cana-5306	105	38	𝑃𝑖	𝑃𝑖	ADP
cana-5306	105	39	is	be	AUX
cana-5306	105	40	the	the	DET
cana-5306	105	41	polarization	polarization	NOUN
cana-5306	105	42	in	in	ADP
cana-5306	105	43	the	the	DET
cana-5306	105	44	𝑖-th	𝑖-th	PROPN
cana-5306	105	45	direction	direction	NOUN
cana-5306	105	46	and	and	CCONJ
cana-5306	105	47	𝜖𝑗𝑘	𝜖𝑗𝑘	NOUN
cana-5306	105	48	is	be	AUX
cana-5306	105	49	the	the	DET
cana-5306	105	50	strain	strain	NOUN
cana-5306	105	51	in	in	ADP
cana-5306	105	52	the	the	DET
cana-5306	105	53	crystal	crystal	NOUN
cana-5306	105	54	.	.	PUNCT
cana-5306	106	1	in	in	ADP
cana-5306	106	2	addition	addition	NOUN
cana-5306	106	3	to	to	ADP
cana-5306	106	4	mechanical	mechanical	ADJ
cana-5306	106	5	properties	property	NOUN
cana-5306	106	6	,	,	PUNCT
cana-5306	106	7	the	the	DET
cana-5306	106	8	optical	optical	ADJ
cana-5306	106	9	properties	property	NOUN
cana-5306	106	10	of	of	ADP
cana-5306	106	11	the	the	DET
cana-5306	106	12	crystal	crystal	NOUN
cana-5306	106	13	are	be	AUX
cana-5306	106	14	influenced	influence	VERB
cana-5306	106	15	by	by	ADP
cana-5306	106	16	its	its	PRON
cana-5306	106	17	symmetry	symmetry	NOUN
cana-5306	106	18	.	.	PUNCT
cana-5306	107	1	the	the	DET
cana-5306	107	2	dielectric	dielectric	ADJ
cana-5306	107	3	tensor	tensor	NOUN
cana-5306	107	4	𝜖𝑖𝑗	𝜖𝑖𝑗	NOUN
cana-5306	107	5	can	can	AUX
cana-5306	107	6	be	be	AUX
cana-5306	107	7	calculated	calculate	VERB
cana-5306	107	8	based	base	VERB
cana-5306	107	9	on	on	ADP
cana-5306	107	10	the	the	DET
cana-5306	107	11	symmetry	symmetry	NOUN
cana-5306	107	12	of	of	ADP
cana-5306	107	13	the	the	DET
cana-5306	107	14	crystal	crystal	NOUN
cana-5306	107	15	:	:	PUNCT
cana-5306	107	16	𝜖𝑖𝑗	𝜖𝑖𝑗	X
cana-5306	107	17	=	=	PRON
cana-5306	107	18	𝜕𝐷𝑖	𝜕𝐷𝑖	VERB
cana-5306	107	19	𝜕𝐸𝑗	𝜕𝐸𝑗	NOUN
cana-5306	107	20	where	where	SCONJ
cana-5306	107	21	𝐷𝑖	𝐷𝑖	PROPN
cana-5306	107	22	is	be	AUX
cana-5306	107	23	the	the	DET
cana-5306	107	24	displacement	displacement	ADJ
cana-5306	107	25	vector	vector	NOUN
cana-5306	107	26	and	and	CCONJ
cana-5306	107	27	𝐸𝑗	𝐸𝑗	PROPN
cana-5306	107	28	is	be	AUX
cana-5306	107	29	the	the	DET
cana-5306	107	30	electric	electric	ADJ
cana-5306	107	31	field	field	NOUN
cana-5306	107	32	in	in	ADP
cana-5306	107	33	the	the	DET
cana-5306	107	34	𝑗-th	𝑗-th	NOUN
cana-5306	107	35	direction	direction	NOUN
cana-5306	107	36	.	.	PUNCT
cana-5306	108	1	the	the	DET
cana-5306	108	2	final	final	ADJ
cana-5306	108	3	part	part	NOUN
cana-5306	108	4	of	of	ADP
cana-5306	108	5	the	the	DET
cana-5306	108	6	methodology	methodology	NOUN
cana-5306	108	7	involves	involve	VERB
cana-5306	108	8	the	the	DET
cana-5306	108	9	visualization	visualization	NOUN
cana-5306	108	10	of	of	ADP
cana-5306	108	11	the	the	DET
cana-5306	108	12	crystal	crystal	NOUN
cana-5306	108	13	structure	structure	NOUN
cana-5306	108	14	and	and	CCONJ
cana-5306	108	15	its	its	PRON
cana-5306	108	16	symmetry	symmetry	NOUN
cana-5306	108	17	.	.	PUNCT
cana-5306	109	1	the	the	DET
cana-5306	109	2	use	use	NOUN
cana-5306	109	3	of	of	ADP
cana-5306	109	4	computational	computational	ADJ
cana-5306	109	5	tools	tool	NOUN
cana-5306	109	6	enables	enable	VERB
cana-5306	109	7	the	the	DET
cana-5306	109	8	creation	creation	NOUN
cana-5306	109	9	of	of	ADP
cana-5306	109	10	3d	3d	PROPN
cana-5306	109	11	models	model	NOUN
cana-5306	109	12	of	of	ADP
cana-5306	109	13	the	the	DET
cana-5306	109	14	crystal	crystal	NOUN
cana-5306	109	15	structure	structure	NOUN
cana-5306	109	16	,	,	PUNCT
cana-5306	109	17	where	where	SCONJ
cana-5306	109	18	symmetry	symmetry	NOUN
cana-5306	109	19	operations	operation	NOUN
cana-5306	109	20	can	can	AUX
cana-5306	109	21	be	be	AUX
cana-5306	109	22	applied	apply	VERB
cana-5306	109	23	to	to	PART
cana-5306	109	24	generate	generate	VERB
cana-5306	109	25	equivalent	equivalent	ADJ
cana-5306	109	26	atomic	atomic	ADJ
cana-5306	109	27	arrangements	arrangement	NOUN
cana-5306	109	28	.	.	PUNCT
cana-5306	110	1	these	these	DET
cana-5306	110	2	models	model	NOUN
cana-5306	110	3	provide	provide	VERB
cana-5306	110	4	valuable	valuable	ADJ
cana-5306	110	5	insights	insight	NOUN
cana-5306	110	6	into	into	ADP
cana-5306	110	7	the	the	DET
cana-5306	110	8	crystal	crystal	NOUN
cana-5306	110	9	's	's	PART
cana-5306	110	10	properties	property	NOUN
cana-5306	110	11	and	and	CCONJ
cana-5306	110	12	behaviors	behavior	NOUN
cana-5306	110	13	.	.	PUNCT
cana-5306	111	1	figure	figure	VERB
cana-5306	111	2	1	1	NUM
cana-5306	111	3	:	:	PUNCT
cana-5306	111	4	symmetry	symmetry	NOUN
cana-5306	111	5	-	-	PUNCT
cana-5306	111	6	based	base	VERB
cana-5306	111	7	crystallographic	crystallographic	ADJ
cana-5306	111	8	analysis	analysis	NOUN
cana-5306	111	9	and	and	CCONJ
cana-5306	111	10	property	property	NOUN
cana-5306	111	11	prediction	prediction	NOUN
cana-5306	111	12	workflow	workflow	NOUN
cana-5306	111	13	iv	iv	NOUN
cana-5306	111	14	.	.	PUNCT
cana-5306	111	15	result	result	PROPN
cana-5306	111	16	&	&	CCONJ
cana-5306	111	17	discussions	discussion	NOUN
cana-5306	111	18	the	the	DET
cana-5306	111	19	research	research	NOUN
cana-5306	111	20	findings	finding	NOUN
cana-5306	111	21	and	and	CCONJ
cana-5306	111	22	analysis	analysis	NOUN
cana-5306	111	23	examine	examine	VERB
cana-5306	111	24	symmetrical	symmetrical	ADJ
cana-5306	111	25	operation	operation	NOUN
cana-5306	111	26	applications	application	NOUN
cana-5306	111	27	from	from	ADP
cana-5306	111	28	group	group	NOUN
cana-5306	111	29	theory	theory	NOUN
cana-5306	111	30	and	and	CCONJ
cana-5306	111	31	crystallographic	crystallographic	ADJ
cana-5306	111	32	perspectives	perspective	NOUN
cana-5306	111	33	to	to	PART
cana-5306	111	34	explain	explain	VERB
cana-5306	111	35	their	their	PRON
cana-5306	111	36	effects	effect	NOUN
cana-5306	111	37	on	on	ADP
cana-5306	111	38	material	material	ADJ
cana-5306	111	39	characteristics	characteristic	NOUN
cana-5306	111	40	and	and	CCONJ
cana-5306	111	41	structural	structural	ADJ
cana-5306	111	42	analytical	analytical	ADJ
cana-5306	111	43	capabilities	capability	NOUN
cana-5306	111	44	.	.	PUNCT
cana-5306	112	1	communications	communication	NOUN
cana-5306	112	2	on	on	ADP
cana-5306	112	3	applied	apply	VERB
cana-5306	112	4	nonlinear	nonlinear	ADJ
cana-5306	112	5	analysis	analysis	NOUN
cana-5306	112	6	issn	issn	NOUN
cana-5306	112	7	:	:	PUNCT
cana-5306	112	8	1074	1074	NUM
cana-5306	112	9	-	-	PUNCT
cana-5306	112	10	133x	133x	NUM
cana-5306	112	11	vol	vol	NOUN
cana-5306	112	12	31	31	NUM
cana-5306	112	13	no	no	NOUN
cana-5306	112	14	.	.	NOUN
cana-5306	112	15	2	2	NUM
cana-5306	112	16	(	(	PUNCT
cana-5306	112	17	2024	2024	NUM
cana-5306	112	18	)	)	PUNCT
cana-5306	112	19	447	447	NUM
cana-5306	112	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	112	21	to	to	PART
cana-5306	112	22	identify	identify	VERB
cana-5306	112	23	the	the	DET
cana-5306	112	24	space	space	NOUN
cana-5306	112	25	group	group	NOUN
cana-5306	112	26	and	and	CCONJ
cana-5306	112	27	point	point	NOUN
cana-5306	112	28	group	group	NOUN
cana-5306	112	29	the	the	DET
cana-5306	112	30	study	study	NOUN
cana-5306	112	31	first	first	ADV
cana-5306	112	32	required	require	VERB
cana-5306	112	33	the	the	DET
cana-5306	112	34	classification	classification	NOUN
cana-5306	112	35	of	of	ADP
cana-5306	112	36	symmetry	symmetry	NOUN
cana-5306	112	37	operations	operation	NOUN
cana-5306	112	38	within	within	ADP
cana-5306	112	39	crystal	crystal	NOUN
cana-5306	112	40	structures	structure	NOUN
cana-5306	112	41	.	.	PUNCT
cana-5306	113	1	each	each	DET
cana-5306	113	2	crystal	crystal	NOUN
cana-5306	113	3	sample	sample	NOUN
cana-5306	113	4	received	receive	VERB
cana-5306	113	5	an	an	DET
cana-5306	113	6	identification	identification	NOUN
cana-5306	113	7	of	of	ADP
cana-5306	113	8	its	its	PRON
cana-5306	113	9	symmetry	symmetry	NOUN
cana-5306	113	10	operations	operation	NOUN
cana-5306	113	11	consisting	consist	VERB
cana-5306	113	12	of	of	ADP
cana-5306	113	13	rotation	rotation	NOUN
cana-5306	113	14	and	and	CCONJ
cana-5306	113	15	reflection	reflection	NOUN
cana-5306	113	16	together	together	ADV
cana-5306	113	17	with	with	ADP
cana-5306	113	18	translation	translation	NOUN
cana-5306	113	19	and	and	CCONJ
cana-5306	113	20	inversion	inversion	NOUN
cana-5306	113	21	before	before	ADP
cana-5306	113	22	receiving	receive	VERB
cana-5306	113	23	its	its	PRON
cana-5306	113	24	assigned	assign	VERB
cana-5306	113	25	space	space	NOUN
cana-5306	113	26	group	group	NOUN
cana-5306	113	27	.	.	PUNCT
cana-5306	114	1	the	the	DET
cana-5306	114	2	computational	computational	ADJ
cana-5306	114	3	models	model	NOUN
cana-5306	114	4	required	require	VERB
cana-5306	114	5	symmetry	symmetry	NOUN
cana-5306	114	6	elements	element	NOUN
cana-5306	114	7	for	for	ADP
cana-5306	114	8	achieving	achieve	VERB
cana-5306	114	9	simplified	simplified	ADJ
cana-5306	114	10	analysis	analysis	NOUN
cana-5306	114	11	because	because	SCONJ
cana-5306	114	12	of	of	ADP
cana-5306	114	13	their	their	PRON
cana-5306	114	14	critical	critical	ADJ
cana-5306	114	15	nature	nature	NOUN
cana-5306	114	16	.	.	PUNCT
cana-5306	115	1	the	the	DET
cana-5306	115	2	energy	energy	NOUN
cana-5306	115	3	minimization	minimization	NOUN
cana-5306	115	4	process	process	NOUN
cana-5306	115	5	for	for	ADP
cana-5306	115	6	lattice	lattice	NOUN
cana-5306	115	7	structures	structure	NOUN
cana-5306	115	8	underwent	underwent	ADJ
cana-5306	115	9	computation	computation	NOUN
cana-5306	115	10	followed	follow	VERB
cana-5306	115	11	by	by	ADP
cana-5306	115	12	force	force	NOUN
cana-5306	115	13	evaluations	evaluation	NOUN
cana-5306	115	14	of	of	ADP
cana-5306	115	15	atoms	atom	NOUN
cana-5306	115	16	as	as	ADP
cana-5306	115	17	part	part	NOUN
cana-5306	115	18	of	of	ADP
cana-5306	115	19	symmetry	symmetry	NOUN
cana-5306	115	20	-	-	PUNCT
cana-5306	115	21	based	base	VERB
cana-5306	115	22	simulations	simulation	NOUN
cana-5306	115	23	.	.	PUNCT
cana-5306	116	1	consistent	consistent	ADJ
cana-5306	116	2	energy	energy	NOUN
cana-5306	116	3	data	datum	NOUN
cana-5306	116	4	together	together	ADV
cana-5306	116	5	with	with	ADP
cana-5306	116	6	correct	correct	ADJ
cana-5306	116	7	atomic	atomic	ADJ
cana-5306	116	8	patterns	pattern	NOUN
cana-5306	116	9	validated	validate	VERB
cana-5306	116	10	the	the	DET
cana-5306	116	11	analytical	analytical	ADJ
cana-5306	116	12	methods	method	NOUN
cana-5306	116	13	employed	employ	VERB
cana-5306	116	14	throughout	throughout	ADP
cana-5306	116	15	this	this	DET
cana-5306	116	16	study	study	NOUN
cana-5306	116	17	[	[	X
cana-5306	116	18	11	11	NUM
cana-5306	116	19	]	]	PUNCT
cana-5306	116	20	.	.	PUNCT
cana-5306	117	1	computational	computational	ADJ
cana-5306	117	2	atomic	atomic	ADJ
cana-5306	117	3	positions	position	NOUN
cana-5306	117	4	and	and	CCONJ
cana-5306	117	5	experimental	experimental	ADJ
cana-5306	117	6	structural	structural	ADJ
cana-5306	117	7	arrangements	arrangement	NOUN
cana-5306	117	8	matched	match	VERB
cana-5306	117	9	exceptionally	exceptionally	ADV
cana-5306	117	10	well	well	ADV
cana-5306	117	11	for	for	ADP
cana-5306	117	12	lattice	lattice	NOUN
cana-5306	117	13	constants	constant	NOUN
cana-5306	117	14	as	as	ADV
cana-5306	117	15	well	well	ADV
cana-5306	117	16	as	as	ADP
cana-5306	117	17	atomic	atomic	ADJ
cana-5306	117	18	coordinates	coordinate	NOUN
cana-5306	117	19	.	.	PUNCT
cana-5306	118	1	figure	figure	NOUN
cana-5306	118	2	2	2	NUM
cana-5306	118	3	showed	show	VERB
cana-5306	118	4	visual	visual	ADJ
cana-5306	118	5	data	datum	NOUN
cana-5306	118	6	points	point	NOUN
cana-5306	118	7	that	that	PRON
cana-5306	118	8	depicted	depict	VERB
cana-5306	118	9	the	the	DET
cana-5306	118	10	relationship	relationship	NOUN
cana-5306	118	11	between	between	ADP
cana-5306	118	12	theoretical	theoretical	ADJ
cana-5306	118	13	and	and	CCONJ
cana-5306	118	14	experimental	experimental	ADJ
cana-5306	118	15	lattice	lattice	PROPN
cana-5306	118	16	structures	structure	NOUN
cana-5306	118	17	.	.	PUNCT
cana-5306	119	1	figure	figure	VERB
cana-5306	119	2	2	2	NUM
cana-5306	119	3	:	:	PUNCT
cana-5306	119	4	comparison	comparison	NOUN
cana-5306	119	5	of	of	ADP
cana-5306	119	6	predicted	predict	VERB
cana-5306	119	7	and	and	CCONJ
cana-5306	119	8	experimental	experimental	ADJ
cana-5306	119	9	atomic	atomic	ADJ
cana-5306	119	10	positions	position	NOUN
cana-5306	119	11	this	this	DET
cana-5306	119	12	figure	figure	NOUN
cana-5306	119	13	demonstrates	demonstrate	VERB
cana-5306	119	14	the	the	DET
cana-5306	119	15	step	step	NOUN
cana-5306	119	16	-	-	PUNCT
cana-5306	119	17	by	by	ADP
cana-5306	119	18	-	-	PUNCT
cana-5306	119	19	step	step	NOUN
cana-5306	119	20	process	process	NOUN
cana-5306	119	21	of	of	ADP
cana-5306	119	22	energy	energy	NOUN
cana-5306	119	23	minimization	minimization	NOUN
cana-5306	119	24	as	as	SCONJ
cana-5306	119	25	shown	show	VERB
cana-5306	119	26	in	in	ADP
cana-5306	119	27	figure	figure	NOUN
cana-5306	119	28	3	3	NUM
cana-5306	119	29	.	.	PUNCT
cana-5306	120	1	the	the	DET
cana-5306	120	2	graphical	graphical	ADJ
cana-5306	120	3	representation	representation	NOUN
cana-5306	120	4	shows	show	VERB
cana-5306	120	5	that	that	SCONJ
cana-5306	120	6	energy	energy	NOUN
cana-5306	120	7	decreased	decrease	VERB
cana-5306	120	8	as	as	ADP
cana-5306	120	9	atomic	atomic	ADJ
cana-5306	120	10	positions	position	NOUN
cana-5306	120	11	adjusted	adjust	VERB
cana-5306	120	12	through	through	ADP
cana-5306	120	13	symmetry	symmetry	NOUN
cana-5306	120	14	operations	operation	NOUN
cana-5306	120	15	giving	give	VERB
cana-5306	120	16	details	detail	NOUN
cana-5306	120	17	about	about	ADP
cana-5306	120	18	the	the	DET
cana-5306	120	19	crystal	crystal	NOUN
cana-5306	120	20	structure	structure	NOUN
cana-5306	120	21	stability	stability	NOUN
cana-5306	120	22	throughout	throughout	ADP
cana-5306	120	23	the	the	DET
cana-5306	120	24	simulation	simulation	NOUN
cana-5306	120	25	.	.	PUNCT
cana-5306	121	1	the	the	DET
cana-5306	121	2	diagram	diagram	NOUN
cana-5306	121	3	demonstrates	demonstrate	VERB
cana-5306	121	4	how	how	SCONJ
cana-5306	121	5	the	the	DET
cana-5306	121	6	energy	energy	NOUN
cana-5306	121	7	reaches	reach	VERB
cana-5306	121	8	its	its	PRON
cana-5306	121	9	optimal	optimal	ADJ
cana-5306	121	10	point	point	NOUN
cana-5306	121	11	at	at	ADP
cana-5306	121	12	the	the	DET
cana-5306	121	13	minimum	minimum	ADJ
cana-5306	121	14	stable	stable	ADJ
cana-5306	121	15	crystal	crystal	NOUN
cana-5306	121	16	configuration	configuration	NOUN
cana-5306	121	17	which	which	PRON
cana-5306	121	18	establishes	establish	VERB
cana-5306	121	19	symmetry	symmetry	NOUN
cana-5306	121	20	-	-	PUNCT
cana-5306	121	21	based	base	VERB
cana-5306	121	22	computational	computational	ADJ
cana-5306	121	23	methods	method	NOUN
cana-5306	121	24	as	as	ADP
cana-5306	121	25	reliable	reliable	ADJ
cana-5306	121	26	for	for	ADP
cana-5306	121	27	predicting	predict	VERB
cana-5306	121	28	stable	stable	ADJ
cana-5306	121	29	crystal	crystal	NOUN
cana-5306	121	30	structures	structure	NOUN
cana-5306	121	31	.	.	PUNCT
cana-5306	122	1	0.025	0.025	NUM
cana-5306	122	2	1.125	1.125	NUM
cana-5306	122	3	2.35	2.35	NUM
cana-5306	122	4	0.027	0.027	NUM
cana-5306	122	5	1.12	1.12	NUM
cana-5306	122	6	2.352	2.352	NUM
cana-5306	122	7	0	0	NUM
cana-5306	122	8	0.5	0.5	NUM
cana-5306	122	9	1	1	NUM
cana-5306	122	10	1.5	1.5	NUM
cana-5306	122	11	2	2	NUM
cana-5306	122	12	2.5	2.5	NUM
cana-5306	122	13	1	1	NUM
cana-5306	122	14	2	2	NUM
cana-5306	122	15	3	3	NUM
cana-5306	122	16	comparison	comparison	NOUN
cana-5306	122	17	of	of	ADP
cana-5306	122	18	predicted	predict	VERB
cana-5306	122	19	and	and	CCONJ
cana-5306	122	20	experimental	experimental	ADJ
cana-5306	122	21	atomic	atomic	ADJ
cana-5306	122	22	positions	position	NOUN
cana-5306	122	23	predicted	predict	VERB
cana-5306	122	24	x	x	PUNCT
cana-5306	122	25	position	position	NOUN
cana-5306	122	26	(	(	PUNCT
cana-5306	122	27	å	å	NOUN
cana-5306	122	28	)	)	PUNCT
cana-5306	122	29	experimental	experimental	ADJ
cana-5306	122	30	x	x	SYM
cana-5306	122	31	position	position	NOUN
cana-5306	122	32	(	(	PUNCT
cana-5306	122	33	å	å	NOUN
cana-5306	122	34	)	)	PUNCT
cana-5306	122	35	communications	communication	NOUN
cana-5306	122	36	on	on	ADP
cana-5306	122	37	applied	apply	VERB
cana-5306	122	38	nonlinear	nonlinear	ADJ
cana-5306	122	39	analysis	analysis	NOUN
cana-5306	122	40	issn	issn	NOUN
cana-5306	122	41	:	:	PUNCT
cana-5306	122	42	1074	1074	NUM
cana-5306	122	43	-	-	PUNCT
cana-5306	122	44	133x	133x	NUM
cana-5306	122	45	vol	vol	NOUN
cana-5306	122	46	31	31	NUM
cana-5306	122	47	no	no	NOUN
cana-5306	122	48	.	.	NOUN
cana-5306	122	49	2	2	NUM
cana-5306	122	50	(	(	PUNCT
cana-5306	122	51	2024	2024	NUM
cana-5306	122	52	)	)	PUNCT
cana-5306	122	53	448	448	NUM
cana-5306	123	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	123	2	figure	figure	NOUN
cana-5306	123	3	3	3	NUM
cana-5306	123	4	:	:	PUNCT
cana-5306	123	5	energy	energy	NOUN
cana-5306	123	6	minimization	minimization	NOUN
cana-5306	123	7	process	process	NOUN
cana-5306	123	8	(	(	PUNCT
cana-5306	123	9	energy	energy	NOUN
cana-5306	123	10	vs.	vs.	ADP
cana-5306	123	11	iteration	iteration	NOUN
cana-5306	123	12	number	number	NOUN
cana-5306	123	13	)	)	PUNCT
cana-5306	123	14	symmetry	symmetry	NOUN
cana-5306	123	15	-	-	PUNCT
cana-5306	123	16	based	base	VERB
cana-5306	123	17	models	model	NOUN
cana-5306	123	18	were	be	AUX
cana-5306	123	19	employed	employ	VERB
cana-5306	123	20	to	to	PART
cana-5306	123	21	calculate	calculate	VERB
cana-5306	123	22	piezoelectric	piezoelectric	NOUN
cana-5306	123	23	coefficients	coefficient	NOUN
cana-5306	123	24	together	together	ADV
cana-5306	123	25	with	with	ADP
cana-5306	123	26	dielectric	dielectric	ADJ
cana-5306	123	27	constants	constant	NOUN
cana-5306	123	28	for	for	SCONJ
cana-5306	123	29	all	all	DET
cana-5306	123	30	materials	material	NOUN
cana-5306	123	31	to	to	PART
cana-5306	123	32	authenticate	authenticate	VERB
cana-5306	123	33	symmetry	symmetry	NOUN
cana-5306	123	34	operations	operation	NOUN
cana-5306	123	35	as	as	ADP
cana-5306	123	36	an	an	DET
cana-5306	123	37	efficient	efficient	ADJ
cana-5306	123	38	material	material	NOUN
cana-5306	123	39	property	property	NOUN
cana-5306	123	40	determination	determination	NOUN
cana-5306	123	41	method	method	NOUN
cana-5306	123	42	.	.	PUNCT
cana-5306	124	1	the	the	DET
cana-5306	124	2	strength	strength	NOUN
cana-5306	124	3	of	of	ADP
cana-5306	124	4	piezoelectricity	piezoelectricity	NOUN
cana-5306	124	5	can	can	AUX
cana-5306	124	6	be	be	AUX
cana-5306	124	7	attributed	attribute	VERB
cana-5306	124	8	directly	directly	ADV
cana-5306	124	9	to	to	ADP
cana-5306	124	10	crystal	crystal	NOUN
cana-5306	124	11	structure	structure	NOUN
cana-5306	124	12	symmetry	symmetry	NOUN
cana-5306	124	13	since	since	SCONJ
cana-5306	124	14	results	result	NOUN
cana-5306	124	15	demonstrated	demonstrate	VERB
cana-5306	124	16	that	that	SCONJ
cana-5306	124	17	higher	high	ADJ
cana-5306	124	18	symmetry	symmetry	NOUN
cana-5306	124	19	crystals	crystal	NOUN
cana-5306	124	20	produce	produce	VERB
cana-5306	124	21	stronger	strong	ADJ
cana-5306	124	22	responses	response	NOUN
cana-5306	124	23	.	.	PUNCT
cana-5306	125	1	the	the	DET
cana-5306	125	2	table	table	NOUN
cana-5306	125	3	demonstrates	demonstrate	VERB
cana-5306	125	4	how	how	SCONJ
cana-5306	125	5	several	several	ADJ
cana-5306	125	6	crystals	crystal	NOUN
cana-5306	125	7	obtain	obtain	VERB
cana-5306	125	8	their	their	PRON
cana-5306	125	9	piezoelectric	piezoelectric	ADJ
cana-5306	125	10	coefficients	coefficient	NOUN
cana-5306	125	11	based	base	VERB
cana-5306	125	12	on	on	ADP
cana-5306	125	13	their	their	PRON
cana-5306	125	14	specific	specific	ADJ
cana-5306	125	15	symmetry	symmetry	NOUN
cana-5306	125	16	(	(	PUNCT
cana-5306	125	17	table	table	NOUN
cana-5306	125	18	1	1	NUM
cana-5306	125	19	)	)	PUNCT
cana-5306	125	20	.	.	PUNCT
cana-5306	126	1	between	between	ADP
cana-5306	126	2	cubic	cubic	ADJ
cana-5306	126	3	system	system	NOUN
cana-5306	126	4	crystals	crystal	NOUN
cana-5306	126	5	and	and	CCONJ
cana-5306	126	6	lower	low	ADJ
cana-5306	126	7	symmetric	symmetric	ADJ
cana-5306	126	8	crystals	crystal	NOUN
cana-5306	126	9	from	from	ADP
cana-5306	126	10	monoclinic	monoclinic	ADJ
cana-5306	126	11	or	or	CCONJ
cana-5306	126	12	triclinic	triclinic	ADJ
cana-5306	126	13	systems	system	NOUN
cana-5306	126	14	there	there	PRON
cana-5306	126	15	was	be	VERB
cana-5306	126	16	a	a	DET
cana-5306	126	17	clear	clear	ADJ
cana-5306	126	18	correlation	correlation	NOUN
cana-5306	126	19	of	of	ADP
cana-5306	126	20	higher	high	ADJ
cana-5306	126	21	piezoelectric	piezoelectric	ADJ
cana-5306	126	22	coefficient	coefficient	NOUN
cana-5306	126	23	values	value	NOUN
cana-5306	126	24	to	to	ADP
cana-5306	126	25	materials	material	NOUN
cana-5306	126	26	with	with	ADP
cana-5306	126	27	higher	high	ADJ
cana-5306	126	28	symmetry	symmetry	NOUN
cana-5306	126	29	groups	group	NOUN
cana-5306	126	30	.	.	PUNCT
cana-5306	127	1	table	table	NOUN
cana-5306	127	2	1	1	NUM
cana-5306	127	3	:	:	PUNCT
cana-5306	127	4	comparison	comparison	NOUN
cana-5306	127	5	of	of	ADP
cana-5306	127	6	piezoelectric	piezoelectric	ADJ
cana-5306	127	7	coefficients	coefficient	NOUN
cana-5306	127	8	for	for	ADP
cana-5306	127	9	crystals	crystal	NOUN
cana-5306	127	10	with	with	ADP
cana-5306	127	11	different	different	ADJ
cana-5306	127	12	symmetry	symmetry	NOUN
cana-5306	127	13	groups	group	NOUN
cana-5306	127	14	symmetry	symmetry	NOUN
cana-5306	127	15	group	group	NOUN
cana-5306	127	16	piezoelectric	piezoelectric	NOUN
cana-5306	127	17	coefficient	coefficient	NOUN
cana-5306	127	18	(	(	PUNCT
cana-5306	127	19	pc	pc	NOUN
cana-5306	127	20	/	/	SYM
cana-5306	127	21	n	n	CCONJ
cana-5306	127	22	)	)	PUNCT
cana-5306	127	23	cubic	cubic	ADJ
cana-5306	127	24	12.5	12.5	NUM
cana-5306	127	25	hexagonal	hexagonal	ADJ
cana-5306	127	26	8.3	8.3	NUM
cana-5306	127	27	monoclinic	monoclinic	ADJ
cana-5306	127	28	4.1	4.1	NUM
cana-5306	127	29	triclinic	triclinic	ADJ
cana-5306	127	30	1.8	1.8	NUM
cana-5306	127	31	the	the	DET
cana-5306	127	32	dielectric	dielectric	ADJ
cana-5306	127	33	constant	constant	ADJ
cana-5306	127	34	measurements	measurement	NOUN
cana-5306	127	35	of	of	ADP
cana-5306	127	36	crystals	crystal	NOUN
cana-5306	127	37	showed	show	VERB
cana-5306	127	38	a	a	DET
cana-5306	127	39	direct	direct	ADJ
cana-5306	127	40	correlation	correlation	NOUN
cana-5306	127	41	to	to	ADP
cana-5306	127	42	their	their	PRON
cana-5306	127	43	symmetry	symmetry	NOUN
cana-5306	127	44	pattern	pattern	NOUN
cana-5306	127	45	according	accord	VERB
cana-5306	127	46	to	to	ADP
cana-5306	127	47	table	table	NOUN
cana-5306	127	48	2	2	NUM
cana-5306	127	49	.	.	PUNCT
cana-5306	127	50	dielectric	dielectric	ADJ
cana-5306	127	51	constants	constant	NOUN
cana-5306	127	52	of	of	ADP
cana-5306	127	53	crystals	crystal	NOUN
cana-5306	127	54	increase	increase	VERB
cana-5306	127	55	when	when	SCONJ
cana-5306	127	56	symmetry	symmetry	NOUN
cana-5306	127	57	operations	operation	NOUN
cana-5306	127	58	enable	enable	VERB
cana-5306	127	59	better	well	ADJ
cana-5306	127	60	alignment	alignment	NOUN
cana-5306	127	61	between	between	ADP
cana-5306	127	62	dipoles	dipole	NOUN
cana-5306	127	63	when	when	SCONJ
cana-5306	127	64	an	an	DET
cana-5306	127	65	electric	electric	ADJ
cana-5306	127	66	field	field	NOUN
cana-5306	127	67	applies	apply	VERB
cana-5306	127	68	.	.	PUNCT
cana-5306	128	1	the	the	DET
cana-5306	128	2	predictive	predictive	ADJ
cana-5306	128	3	value	value	NOUN
cana-5306	128	4	of	of	ADP
cana-5306	128	5	symmetry	symmetry	NOUN
cana-5306	128	6	for	for	ADP
cana-5306	128	7	material	material	NOUN
cana-5306	128	8	functionality	functionality	NOUN
cana-5306	128	9	enables	enable	VERB
cana-5306	128	10	better	well	ADJ
cana-5306	128	11	design	design	NOUN
cana-5306	128	12	of	of	ADP
cana-5306	128	13	-15.35	-15.35	PROPN
cana-5306	128	14	-15.5	-15.5	PROPN
cana-5306	128	15	-15.6	-15.6	NUM
cana-5306	128	16	0	0	NUM
cana-5306	128	17	0.15	0.15	NUM
cana-5306	128	18	0.1	0.1	NUM
cana-5306	128	19	-18	-18	NUM
cana-5306	128	20	-16	-16	X
cana-5306	128	21	-14	-14	PUNCT
cana-5306	128	22	-12	-12	PROPN
cana-5306	128	23	-10	-10	PUNCT
cana-5306	129	1	-8	-8	INTJ
cana-5306	130	1	-6	-6	INTJ
cana-5306	130	2	-4	-4	INTJ
cana-5306	131	1	-2	-2	NOUN
cana-5306	131	2	0	0	NUM
cana-5306	131	3	2	2	NUM
cana-5306	131	4	1	1	NUM
cana-5306	131	5	2	2	NUM
cana-5306	131	6	3	3	NUM
cana-5306	131	7	energy	energy	NOUN
cana-5306	131	8	minimization	minimization	NOUN
cana-5306	131	9	process	process	NOUN
cana-5306	131	10	energy	energy	NOUN
cana-5306	131	11	(	(	PUNCT
cana-5306	131	12	ev	ev	NOUN
cana-5306	131	13	)	)	PUNCT
cana-5306	131	14	change	change	NOUN
cana-5306	131	15	in	in	ADP
cana-5306	131	16	energy	energy	NOUN
cana-5306	131	17	(	(	PUNCT
cana-5306	131	18	ev	ev	NOUN
cana-5306	131	19	)	)	PUNCT
cana-5306	131	20	communications	communication	NOUN
cana-5306	131	21	on	on	ADP
cana-5306	131	22	applied	apply	VERB
cana-5306	131	23	nonlinear	nonlinear	ADJ
cana-5306	131	24	analysis	analysis	NOUN
cana-5306	131	25	issn	issn	NOUN
cana-5306	131	26	:	:	PUNCT
cana-5306	131	27	1074	1074	NUM
cana-5306	131	28	-	-	PUNCT
cana-5306	131	29	133x	133x	NUM
cana-5306	131	30	vol	vol	NOUN
cana-5306	131	31	31	31	NUM
cana-5306	131	32	no	no	NOUN
cana-5306	131	33	.	.	NOUN
cana-5306	131	34	2	2	NUM
cana-5306	131	35	(	(	PUNCT
cana-5306	131	36	2024	2024	NUM
cana-5306	131	37	)	)	PUNCT
cana-5306	131	38	449	449	NUM
cana-5306	131	39	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	131	40	piezoelectrics	piezoelectric	NOUN
cana-5306	131	41	and	and	CCONJ
cana-5306	131	42	capacitors	capacitor	NOUN
cana-5306	131	43	because	because	SCONJ
cana-5306	131	44	these	these	DET
cana-5306	131	45	findings	finding	NOUN
cana-5306	131	46	prove	prove	VERB
cana-5306	131	47	how	how	SCONJ
cana-5306	131	48	material	material	ADJ
cana-5306	131	49	symmetry	symmetry	NOUN
cana-5306	131	50	determines	determine	VERB
cana-5306	131	51	their	their	PRON
cana-5306	131	52	functional	functional	ADJ
cana-5306	131	53	properties	property	NOUN
cana-5306	131	54	.	.	PUNCT
cana-5306	132	1	table	table	NOUN
cana-5306	132	2	2	2	NUM
cana-5306	132	3	:	:	PUNCT
cana-5306	132	4	comparison	comparison	NOUN
cana-5306	132	5	of	of	ADP
cana-5306	132	6	dielectric	dielectric	ADJ
cana-5306	132	7	constants	constant	NOUN
cana-5306	132	8	for	for	ADP
cana-5306	132	9	crystals	crystal	NOUN
cana-5306	132	10	with	with	ADP
cana-5306	132	11	different	different	ADJ
cana-5306	132	12	symmetry	symmetry	NOUN
cana-5306	132	13	groups	group	NOUN
cana-5306	132	14	symmetry	symmetry	NOUN
cana-5306	132	15	group	group	NOUN
cana-5306	132	16	dielectric	dielectric	ADJ
cana-5306	132	17	constant	constant	ADJ
cana-5306	132	18	cubic	cubic	ADJ
cana-5306	132	19	320	320	NUM
cana-5306	132	20	hexagonal	hexagonal	ADJ
cana-5306	132	21	215	215	NUM
cana-5306	132	22	monoclinic	monoclinic	ADJ
cana-5306	132	23	180	180	NUM
cana-5306	132	24	triclinic	triclinic	ADJ
cana-5306	132	25	150	150	NUM
cana-5306	132	26	experimental	experimental	ADJ
cana-5306	132	27	findings	finding	NOUN
cana-5306	132	28	matched	match	VERB
cana-5306	132	29	theoretical	theoretical	ADJ
cana-5306	132	30	predictions	prediction	NOUN
cana-5306	132	31	exceptionally	exceptionally	ADV
cana-5306	132	32	well	well	ADV
cana-5306	132	33	thus	thus	ADV
cana-5306	132	34	demonstrating	demonstrate	VERB
cana-5306	132	35	that	that	PRON
cana-5306	132	36	symmetry	symmetry	NOUN
cana-5306	132	37	analysis	analysis	NOUN
cana-5306	132	38	provides	provide	VERB
cana-5306	132	39	essential	essential	ADJ
cana-5306	132	40	functions	function	NOUN
cana-5306	132	41	for	for	ADP
cana-5306	132	42	determining	determine	VERB
cana-5306	132	43	crystal	crystal	NOUN
cana-5306	132	44	structural	structural	ADJ
cana-5306	132	45	and	and	CCONJ
cana-5306	132	46	working	working	NOUN
cana-5306	132	47	characteristics	characteristic	NOUN
cana-5306	132	48	.	.	PUNCT
cana-5306	133	1	the	the	DET
cana-5306	133	2	obtained	obtain	VERB
cana-5306	133	3	results	result	NOUN
cana-5306	133	4	demonstrate	demonstrate	VERB
cana-5306	133	5	both	both	CCONJ
cana-5306	133	6	the	the	DET
cana-5306	133	7	importance	importance	NOUN
cana-5306	133	8	of	of	ADP
cana-5306	133	9	group	group	NOUN
cana-5306	133	10	theory	theory	NOUN
cana-5306	133	11	and	and	CCONJ
cana-5306	133	12	symmetry	symmetry	NOUN
cana-5306	133	13	in	in	ADP
cana-5306	133	14	crystallography	crystallography	NOUN
cana-5306	133	15	as	as	ADV
cana-5306	133	16	well	well	ADV
cana-5306	133	17	their	their	PRON
cana-5306	133	18	power	power	NOUN
cana-5306	133	19	to	to	PART
cana-5306	133	20	improve	improve	VERB
cana-5306	133	21	material	material	ADJ
cana-5306	133	22	property	property	NOUN
cana-5306	133	23	comprehension	comprehension	NOUN
cana-5306	133	24	.	.	PUNCT
cana-5306	134	1	computational	computational	ADJ
cana-5306	134	2	models	model	NOUN
cana-5306	134	3	benefit	benefit	VERB
cana-5306	134	4	substantially	substantially	ADV
cana-5306	134	5	when	when	SCONJ
cana-5306	134	6	symmetry	symmetry	NOUN
cana-5306	134	7	integration	integration	NOUN
cana-5306	134	8	occurs	occur	VERB
cana-5306	134	9	because	because	SCONJ
cana-5306	134	10	of	of	ADP
cana-5306	134	11	several	several	ADJ
cana-5306	134	12	advantageous	advantageous	ADJ
cana-5306	134	13	outcomes	outcome	NOUN
cana-5306	134	14	.	.	PUNCT
cana-5306	135	1	using	use	VERB
cana-5306	135	2	symmetry	symmetry	NOUN
cana-5306	135	3	-	-	PUNCT
cana-5306	135	4	based	base	VERB
cana-5306	135	5	methods	method	NOUN
cana-5306	135	6	brings	bring	VERB
cana-5306	135	7	two	two	NUM
cana-5306	135	8	major	major	ADJ
cana-5306	135	9	advantages	advantage	NOUN
cana-5306	135	10	that	that	PRON
cana-5306	135	11	improve	improve	VERB
cana-5306	135	12	both	both	DET
cana-5306	135	13	crystal	crystal	NOUN
cana-5306	135	14	structure	structure	NOUN
cana-5306	135	15	prediction	prediction	NOUN
cana-5306	135	16	ease	ease	NOUN
cana-5306	135	17	and	and	CCONJ
cana-5306	135	18	property	property	NOUN
cana-5306	135	19	modeling	modeling	NOUN
cana-5306	135	20	accuracy	accuracy	NOUN
cana-5306	135	21	.	.	PUNCT
cana-5306	136	1	the	the	DET
cana-5306	136	2	utilization	utilization	NOUN
cana-5306	136	3	of	of	ADP
cana-5306	136	4	symmetry	symmetry	NOUN
cana-5306	136	5	operations	operation	NOUN
cana-5306	136	6	makes	make	VERB
cana-5306	136	7	band	band	NOUN
cana-5306	136	8	gaps	gap	NOUN
cana-5306	136	9	and	and	CCONJ
cana-5306	136	10	charge	charge	NOUN
cana-5306	136	11	distribution	distribution	NOUN
cana-5306	136	12	predictions	prediction	NOUN
cana-5306	136	13	more	more	ADV
cana-5306	136	14	efficient	efficient	ADJ
cana-5306	136	15	for	for	ADP
cana-5306	136	16	electronic	electronic	ADJ
cana-5306	136	17	property	property	NOUN
cana-5306	136	18	evaluations	evaluation	NOUN
cana-5306	136	19	.	.	PUNCT
cana-5306	137	1	the	the	DET
cana-5306	137	2	analysis	analysis	NOUN
cana-5306	137	3	through	through	ADP
cana-5306	137	4	symmetry	symmetry	NOUN
cana-5306	137	5	methods	method	NOUN
cana-5306	137	6	shortens	shorten	VERB
cana-5306	137	7	the	the	DET
cana-5306	137	8	time	time	NOUN
cana-5306	137	9	needed	need	VERB
cana-5306	137	10	to	to	PART
cana-5306	137	11	model	model	VERB
cana-5306	137	12	big	big	ADJ
cana-5306	137	13	crystal	crystal	NOUN
cana-5306	137	14	structures	structure	NOUN
cana-5306	137	15	thus	thus	ADV
cana-5306	137	16	improving	improve	VERB
cana-5306	137	17	speed	speed	NOUN
cana-5306	137	18	in	in	ADP
cana-5306	137	19	new	new	ADJ
cana-5306	137	20	material	material	NOUN
cana-5306	137	21	development	development	NOUN
cana-5306	137	22	and	and	CCONJ
cana-5306	137	23	testing	testing	NOUN
cana-5306	137	24	.	.	PUNCT
cana-5306	138	1	the	the	DET
cana-5306	138	2	paper	paper	NOUN
cana-5306	138	3	demonstrates	demonstrate	VERB
cana-5306	138	4	that	that	SCONJ
cana-5306	138	5	using	use	VERB
cana-5306	138	6	symmetry	symmetry	NOUN
cana-5306	138	7	-	-	PUNCT
cana-5306	138	8	based	base	VERB
cana-5306	138	9	approaches	approach	NOUN
cana-5306	138	10	as	as	ADP
cana-5306	138	11	an	an	DET
cana-5306	138	12	instrument	instrument	NOUN
cana-5306	138	13	to	to	PART
cana-5306	138	14	optimize	optimize	VERB
cana-5306	138	15	materials	material	NOUN
cana-5306	138	16	design	design	NOUN
cana-5306	138	17	for	for	ADP
cana-5306	138	18	applications	application	NOUN
cana-5306	138	19	in	in	ADP
cana-5306	138	20	electronics	electronic	NOUN
cana-5306	138	21	and	and	CCONJ
cana-5306	138	22	photonics	photonic	NOUN
cana-5306	138	23	and	and	CCONJ
cana-5306	138	24	piezoelectric	piezoelectric	NOUN
cana-5306	138	25	devices	device	NOUN
cana-5306	138	26	.	.	PUNCT
cana-5306	139	1	the	the	DET
cana-5306	139	2	development	development	NOUN
cana-5306	139	3	of	of	ADP
cana-5306	139	4	new	new	ADJ
cana-5306	139	5	materials	material	NOUN
cana-5306	139	6	for	for	ADP
cana-5306	139	7	specific	specific	ADJ
cana-5306	139	8	applications	application	NOUN
cana-5306	139	9	would	would	AUX
cana-5306	139	10	become	become	VERB
cana-5306	139	11	possible	possible	ADJ
cana-5306	139	12	when	when	SCONJ
cana-5306	139	13	materials	material	NOUN
cana-5306	139	14	'	'	PART
cana-5306	139	15	properties	property	NOUN
cana-5306	139	16	with	with	ADP
cana-5306	139	17	high	high	ADJ
cana-5306	139	18	symmetry	symmetry	NOUN
cana-5306	139	19	could	could	AUX
cana-5306	139	20	be	be	AUX
cana-5306	139	21	predicted	predict	VERB
cana-5306	139	22	prior	prior	ADV
cana-5306	139	23	to	to	ADP
cana-5306	139	24	laboratory	laboratory	NOUN
cana-5306	139	25	testing	testing	NOUN
cana-5306	139	26	.	.	PUNCT
cana-5306	140	1	the	the	DET
cana-5306	140	2	analysis	analysis	NOUN
cana-5306	140	3	demonstrates	demonstrate	VERB
cana-5306	140	4	how	how	SCONJ
cana-5306	140	5	symmetry	symmetry	NOUN
cana-5306	140	6	operations	operation	NOUN
cana-5306	140	7	can	can	AUX
cana-5306	140	8	forecast	forecast	VERB
cana-5306	140	9	various	various	ADJ
cana-5306	140	10	material	material	NOUN
cana-5306	140	11	attributes	attribute	NOUN
cana-5306	140	12	from	from	ADP
cana-5306	140	13	thermal	thermal	ADJ
cana-5306	140	14	conductivity	conductivity	NOUN
cana-5306	140	15	to	to	ADP
cana-5306	140	16	magnetic	magnetic	ADJ
cana-5306	140	17	properties	property	NOUN
cana-5306	140	18	as	as	ADV
cana-5306	140	19	well	well	ADV
cana-5306	140	20	as	as	ADP
cana-5306	140	21	superconductivity	superconductivity	NOUN
cana-5306	140	22	since	since	SCONJ
cana-5306	140	23	these	these	DET
cana-5306	140	24	traits	trait	NOUN
cana-5306	140	25	are	be	AUX
cana-5306	140	26	fundamental	fundamental	ADJ
cana-5306	140	27	responses	response	NOUN
cana-5306	140	28	of	of	ADP
cana-5306	140	29	crystal	crystal	NOUN
cana-5306	140	30	structure	structure	NOUN
cana-5306	140	31	symmetry	symmetry	NOUN
cana-5306	140	32	.	.	PUNCT
cana-5306	141	1	symmetry	symmetry	NOUN
cana-5306	141	2	plays	play	VERB
cana-5306	141	3	an	an	DET
cana-5306	141	4	important	important	ADJ
cana-5306	141	5	role	role	NOUN
cana-5306	141	6	within	within	ADP
cana-5306	141	7	the	the	DET
cana-5306	141	8	field	field	NOUN
cana-5306	141	9	of	of	ADP
cana-5306	141	10	nanotechnology	nanotechnology	NOUN
cana-5306	141	11	.	.	PUNCT
cana-5306	142	1	understanding	understand	VERB
cana-5306	142	2	symmetry	symmetry	NOUN
cana-5306	142	3	patterns	pattern	NOUN
cana-5306	142	4	of	of	ADP
cana-5306	142	5	nanomaterials	nanomaterial	NOUN
cana-5306	142	6	becomes	become	VERB
cana-5306	142	7	essential	essential	ADJ
cana-5306	142	8	for	for	ADP
cana-5306	142	9	achieving	achieve	VERB
cana-5306	142	10	maximum	maximum	ADJ
cana-5306	142	11	benefits	benefit	NOUN
cana-5306	142	12	out	out	ADP
cana-5306	142	13	of	of	ADP
cana-5306	142	14	their	their	PRON
cana-5306	142	15	usage	usage	NOUN
cana-5306	142	16	in	in	ADP
cana-5306	142	17	drug	drug	NOUN
cana-5306	142	18	delivery	delivery	NOUN
cana-5306	142	19	systems	system	NOUN
cana-5306	142	20	alongside	alongside	ADP
cana-5306	142	21	applications	application	NOUN
cana-5306	142	22	dealing	deal	VERB
cana-5306	142	23	with	with	ADP
cana-5306	142	24	energy	energy	NOUN
cana-5306	142	25	storage	storage	NOUN
cana-5306	142	26	and	and	CCONJ
cana-5306	142	27	environmental	environmental	ADJ
cana-5306	142	28	cleanup	cleanup	NOUN
cana-5306	142	29	.	.	PUNCT
cana-5306	143	1	symmetry	symmetry	NOUN
cana-5306	143	2	-	-	PUNCT
cana-5306	143	3	based	base	VERB
cana-5306	143	4	computational	computational	ADJ
cana-5306	143	5	tools	tool	NOUN
cana-5306	143	6	help	help	VERB
cana-5306	143	7	scientists	scientist	NOUN
cana-5306	143	8	forecast	forecast	VERB
cana-5306	143	9	and	and	CCONJ
cana-5306	143	10	enhance	enhance	VERB
cana-5306	143	11	materials	material	NOUN
cana-5306	143	12	properties	property	NOUN
cana-5306	143	13	thus	thus	ADV
cana-5306	143	14	enabling	enable	VERB
cana-5306	143	15	producers	producer	NOUN
cana-5306	143	16	to	to	PART
cana-5306	143	17	make	make	VERB
cana-5306	143	18	efficient	efficient	ADJ
cana-5306	143	19	purposeful	purposeful	ADJ
cana-5306	143	20	designs	design	NOUN
cana-5306	143	21	.	.	PUNCT
cana-5306	144	1	communications	communication	NOUN
cana-5306	144	2	on	on	ADP
cana-5306	144	3	applied	apply	VERB
cana-5306	144	4	nonlinear	nonlinear	ADJ
cana-5306	144	5	analysis	analysis	NOUN
cana-5306	144	6	issn	issn	NOUN
cana-5306	144	7	:	:	PUNCT
cana-5306	144	8	1074	1074	NUM
cana-5306	144	9	-	-	PUNCT
cana-5306	144	10	133x	133x	NUM
cana-5306	144	11	vol	vol	NOUN
cana-5306	144	12	31	31	NUM
cana-5306	144	13	no	no	NOUN
cana-5306	144	14	.	.	NOUN
cana-5306	144	15	2	2	NUM
cana-5306	144	16	(	(	PUNCT
cana-5306	144	17	2024	2024	NUM
cana-5306	144	18	)	)	PUNCT
cana-5306	144	19	450	450	NUM
cana-5306	144	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	145	1	the	the	DET
cana-5306	145	2	study	study	NOUN
cana-5306	145	3	results	result	NOUN
cana-5306	145	4	show	show	VERB
cana-5306	145	5	that	that	SCONJ
cana-5306	145	6	symmetry	symmetry	NOUN
cana-5306	145	7	analysis	analysis	NOUN
cana-5306	145	8	provides	provide	VERB
cana-5306	145	9	critical	critical	ADJ
cana-5306	145	10	value	value	NOUN
cana-5306	145	11	to	to	ADP
cana-5306	145	12	crystallographic	crystallographic	ADJ
cana-5306	145	13	research	research	NOUN
cana-5306	145	14	.	.	PUNCT
cana-5306	146	1	modern	modern	ADJ
cana-5306	146	2	material	material	NOUN
cana-5306	146	3	prediction	prediction	NOUN
cana-5306	146	4	and	and	CCONJ
cana-5306	146	5	functional	functional	ADJ
cana-5306	146	6	analysis	analysis	NOUN
cana-5306	146	7	becomes	become	VERB
cana-5306	146	8	more	more	ADV
cana-5306	146	9	precise	precise	ADJ
cana-5306	146	10	through	through	ADP
cana-5306	146	11	combinative	combinative	NOUN
cana-5306	146	12	efforts	effort	NOUN
cana-5306	146	13	of	of	ADP
cana-5306	146	14	computational	computational	ADJ
cana-5306	146	15	methods	method	NOUN
cana-5306	146	16	with	with	ADP
cana-5306	146	17	group	group	NOUN
cana-5306	146	18	theoretical	theoretical	ADJ
cana-5306	146	19	principles	principle	NOUN
cana-5306	146	20	.	.	PUNCT
cana-5306	147	1	v.	v.	ADP
cana-5306	147	2	conclusion	conclusion	NOUN
cana-5306	147	3	through	through	ADP
cana-5306	147	4	crystallography	crystallography	NOUN
cana-5306	147	5	researchers	researcher	NOUN
cana-5306	147	6	use	use	VERB
cana-5306	147	7	group	group	NOUN
cana-5306	147	8	theory	theory	NOUN
cana-5306	147	9	as	as	ADP
cana-5306	147	10	a	a	DET
cana-5306	147	11	robust	robust	ADJ
cana-5306	147	12	method	method	NOUN
cana-5306	147	13	to	to	PART
cana-5306	147	14	study	study	VERB
cana-5306	147	15	crystal	crystal	NOUN
cana-5306	147	16	structure	structure	NOUN
cana-5306	147	17	symmetry	symmetry	NOUN
cana-5306	147	18	properties	property	NOUN
cana-5306	147	19	.	.	PUNCT
cana-5306	148	1	group	group	NOUN
cana-5306	148	2	theory	theory	NOUN
cana-5306	148	3	makes	make	VERB
cana-5306	148	4	possible	possible	ADJ
cana-5306	148	5	the	the	DET
cana-5306	148	6	categorization	categorization	NOUN
cana-5306	148	7	of	of	ADP
cana-5306	148	8	crystals	crystal	NOUN
cana-5306	148	9	into	into	ADP
cana-5306	148	10	both	both	DET
cana-5306	148	11	space	space	NOUN
cana-5306	148	12	groups	group	NOUN
cana-5306	148	13	and	and	CCONJ
cana-5306	148	14	point	point	VERB
cana-5306	148	15	groups	group	NOUN
cana-5306	148	16	through	through	ADP
cana-5306	148	17	symmetry	symmetry	NOUN
cana-5306	148	18	operations	operation	NOUN
cana-5306	148	19	giving	give	VERB
cana-5306	148	20	insights	insight	NOUN
cana-5306	148	21	into	into	ADP
cana-5306	148	22	material	material	NOUN
cana-5306	148	23	physical	physical	ADJ
cana-5306	148	24	and	and	CCONJ
cana-5306	148	25	chemical	chemical	NOUN
cana-5306	148	26	characteristics	characteristic	NOUN
cana-5306	148	27	.	.	PUNCT
cana-5306	149	1	the	the	DET
cana-5306	149	2	study	study	NOUN
cana-5306	149	3	proves	prove	VERB
cana-5306	149	4	why	why	SCONJ
cana-5306	149	5	symmetry	symmetry	NOUN
cana-5306	149	6	remains	remain	VERB
cana-5306	149	7	crucial	crucial	ADJ
cana-5306	149	8	in	in	ADP
cana-5306	149	9	material	material	NOUN
cana-5306	149	10	science	science	NOUN
cana-5306	149	11	since	since	SCONJ
cana-5306	149	12	it	it	PRON
cana-5306	149	13	determines	determine	VERB
cana-5306	149	14	effective	effective	ADJ
cana-5306	149	15	new	new	ADJ
cana-5306	149	16	material	material	NOUN
cana-5306	149	17	development	development	NOUN
cana-5306	149	18	and	and	CCONJ
cana-5306	149	19	property	property	NOUN
cana-5306	149	20	optimization	optimization	NOUN
cana-5306	149	21	processes	process	NOUN
cana-5306	149	22	.	.	PUNCT
cana-5306	150	1	references	reference	NOUN
cana-5306	150	2	[	[	X
cana-5306	150	3	1	1	NUM
cana-5306	150	4	]	]	PUNCT
cana-5306	150	5	f.	f.	PROPN
cana-5306	150	6	m.	m.	NOUN
cana-5306	150	7	brückler	brückler	NOUN
cana-5306	150	8	and	and	CCONJ
cana-5306	150	9	v.	v.	ADP
cana-5306	150	10	stilinović	stilinović	NOUN
cana-5306	150	11	,	,	PUNCT
cana-5306	150	12	“	"	PUNCT
cana-5306	150	13	from	from	ADP
cana-5306	150	14	friezes	frieze	NOUN
cana-5306	150	15	to	to	ADP
cana-5306	150	16	quasicrystals	quasicrystal	NOUN
cana-5306	150	17	:	:	PUNCT
cana-5306	150	18	a	a	DET
cana-5306	150	19	history	history	NOUN
cana-5306	150	20	of	of	ADP
cana-5306	150	21	symmetry	symmetry	NOUN
cana-5306	150	22	groups	group	NOUN
cana-5306	150	23	,	,	PUNCT
cana-5306	150	24	”	"	PUNCT
cana-5306	150	25	in	in	ADP
cana-5306	150	26	springer	springer	NOUN
cana-5306	150	27	ebooks	ebook	NOUN
cana-5306	150	28	,	,	PUNCT
cana-5306	150	29	2023	2023	NUM
cana-5306	150	30	,	,	PUNCT
cana-5306	150	31	pp	pp	PROPN
cana-5306	150	32	.	.	PUNCT
cana-5306	151	1	1–42	1–42	PROPN
cana-5306	151	2	.	.	PUNCT
cana-5306	152	1	doi	doi	PROPN
cana-5306	152	2	:	:	PUNCT
cana-5306	152	3	10.1007/978	10.1007/978	NUM
cana-5306	152	4	-	-	SYM
cana-5306	152	5	3	3	NUM
cana-5306	152	6	-	-	PUNCT
cana-5306	152	7	03019071	03019071	NUM
cana-5306	152	8	-	-	PUNCT
cana-5306	152	9	2_132	2_132	NUM
cana-5306	152	10	-	-	PUNCT
cana-5306	152	11	2	2	NUM
cana-5306	152	12	.	.	PUNCT
cana-5306	153	1	[	[	X
cana-5306	153	2	2	2	X
cana-5306	153	3	]	]	PUNCT
cana-5306	153	4	j.	j.	PROPN
cana-5306	153	5	bernstein	bernstein	PROPN
cana-5306	153	6	,	,	PUNCT
cana-5306	153	7	r.	r.	PROPN
cana-5306	153	8	e.	e.	PROPN
cana-5306	153	9	davis	davis	PROPN
cana-5306	153	10	,	,	PUNCT
cana-5306	153	11	l.	l.	PROPN
cana-5306	153	12	shimoni	shimoni	PROPN
cana-5306	153	13	,	,	PUNCT
cana-5306	153	14	and	and	CCONJ
cana-5306	153	15	n.	n.	PROPN
cana-5306	153	16	chang	chang	PROPN
cana-5306	153	17	,	,	PUNCT
cana-5306	153	18	“	"	PUNCT
cana-5306	153	19	patterns	pattern	NOUN
cana-5306	153	20	in	in	ADP
cana-5306	153	21	hydrogen	hydrogen	NOUN
cana-5306	153	22	bonding	bonding	NOUN
cana-5306	153	23	:	:	PUNCT
cana-5306	153	24	functionality	functionality	NOUN
cana-5306	153	25	and	and	CCONJ
cana-5306	153	26	graph	graph	NOUN
cana-5306	153	27	set	set	VERB
cana-5306	153	28	analysis	analysis	NOUN
cana-5306	153	29	in	in	ADP
cana-5306	153	30	crystals	crystal	NOUN
cana-5306	153	31	,	,	PUNCT
cana-5306	153	32	”	"	PUNCT
cana-5306	153	33	angewandte	angewandte	PROPN
cana-5306	153	34	chemie	chemie	PROPN
cana-5306	153	35	international	international	PROPN
cana-5306	153	36	edition	edition	PROPN
cana-5306	153	37	,	,	PUNCT
cana-5306	153	38	vol	vol	NOUN
cana-5306	153	39	.	.	PROPN
cana-5306	154	1	34	34	NUM
cana-5306	154	2	,	,	PUNCT
cana-5306	154	3	no	no	INTJ
cana-5306	154	4	.	.	NOUN
cana-5306	154	5	15	15	NUM
cana-5306	154	6	,	,	PUNCT
cana-5306	154	7	pp	pp	ADJ
cana-5306	154	8	.	.	PUNCT
cana-5306	155	1	1555–1573	1555–1573	NUM
cana-5306	155	2	,	,	PUNCT
cana-5306	155	3	aug	aug	PROPN
cana-5306	155	4	.	.	PROPN
cana-5306	155	5	1995	1995	NUM
cana-5306	155	6	,	,	PUNCT
cana-5306	155	7	doi	doi	NOUN
cana-5306	155	8	:	:	PUNCT
cana-5306	155	9	10.1002	10.1002	NUM
cana-5306	155	10	/	/	SYM
cana-5306	155	11	anie.199515551	anie.199515551	PROPN
cana-5306	155	12	.	.	PUNCT
cana-5306	156	1	[	[	X
cana-5306	156	2	3	3	NUM
cana-5306	156	3	]	]	PUNCT
cana-5306	156	4	a.	a.	PROPN
cana-5306	156	5	l.	l.	PROPN
cana-5306	156	6	spek	spek	PROPN
cana-5306	156	7	,	,	PUNCT
cana-5306	156	8	“	"	PUNCT
cana-5306	156	9	checkcif	checkcif	PROPN
cana-5306	156	10	validation	validation	NOUN
cana-5306	156	11	alerts	alert	NOUN
cana-5306	156	12	:	:	PUNCT
cana-5306	156	13	what	what	PRON
cana-5306	156	14	they	they	PRON
cana-5306	156	15	mean	mean	VERB
cana-5306	156	16	and	and	CCONJ
cana-5306	156	17	how	how	SCONJ
cana-5306	156	18	to	to	PART
cana-5306	156	19	respond	respond	VERB
cana-5306	156	20	,	,	PUNCT
cana-5306	156	21	”	"	PUNCT
cana-5306	156	22	acta	acta	PROPN
cana-5306	156	23	crystallographica	crystallographica	PROPN
cana-5306	156	24	section	section	PROPN
cana-5306	156	25	e	e	PROPN
cana-5306	156	26	crystallographic	crystallographic	ADJ
cana-5306	156	27	communications	communication	NOUN
cana-5306	156	28	,	,	PUNCT
cana-5306	156	29	vol	vol	NOUN
cana-5306	156	30	.	.	PROPN
cana-5306	157	1	76	76	NUM
cana-5306	157	2	,	,	PUNCT
cana-5306	157	3	no	no	INTJ
cana-5306	157	4	.	.	NOUN
cana-5306	157	5	1	1	NUM
cana-5306	157	6	,	,	PUNCT
cana-5306	157	7	pp	pp	ADJ
cana-5306	157	8	.	.	PUNCT
cana-5306	158	1	1	1	NUM
cana-5306	158	2	–	–	PUNCT
cana-5306	158	3	11	11	NUM
cana-5306	158	4	,	,	PUNCT
cana-5306	158	5	dec	dec	PROPN
cana-5306	158	6	.	.	PROPN
cana-5306	158	7	2019	2019	NUM
cana-5306	158	8	,	,	PUNCT
cana-5306	158	9	doi	doi	NOUN
cana-5306	158	10	:	:	PUNCT
cana-5306	158	11	10.1107	10.1107	NUM
cana-5306	158	12	/	/	SYM
cana-5306	158	13	s2056989019016244	s2056989019016244	NOUN
cana-5306	158	14	.	.	PUNCT
cana-5306	159	1	[	[	X
cana-5306	159	2	4	4	NUM
cana-5306	159	3	]	]	PUNCT
cana-5306	159	4	a.	a.	PROPN
cana-5306	159	5	l.	l.	PROPN
cana-5306	159	6	spek	spek	PROPN
cana-5306	159	7	,	,	PUNCT
cana-5306	159	8	“	"	PUNCT
cana-5306	159	9	what	what	PRON
cana-5306	159	10	makes	make	VERB
cana-5306	159	11	a	a	DET
cana-5306	159	12	crystal	crystal	NOUN
cana-5306	159	13	structure	structure	NOUN
cana-5306	159	14	report	report	NOUN
cana-5306	159	15	valid	valid	ADJ
cana-5306	159	16	?	?	PUNCT
cana-5306	159	17	,	,	PUNCT
cana-5306	159	18	”	"	PUNCT
cana-5306	159	19	inorganica	inorganica	PROPN
cana-5306	159	20	chimica	chimica	PROPN
cana-5306	159	21	acta	acta	PROPN
cana-5306	159	22	,	,	PUNCT
cana-5306	159	23	vol	vol	NOUN
cana-5306	159	24	.	.	PROPN
cana-5306	159	25	470	470	NUM
cana-5306	159	26	,	,	PUNCT
cana-5306	159	27	pp	pp	ADJ
cana-5306	159	28	.	.	PUNCT
cana-5306	160	1	232–237	232–237	NUM
cana-5306	160	2	,	,	PUNCT
cana-5306	160	3	apr	apr	PROPN
cana-5306	160	4	.	.	PROPN
cana-5306	160	5	2017	2017	NUM
cana-5306	160	6	,	,	PUNCT
cana-5306	160	7	doi	doi	NOUN
cana-5306	160	8	:	:	PUNCT
cana-5306	160	9	10.1016	10.1016	NUM
cana-5306	160	10	/	/	SYM
cana-5306	160	11	j.ica.2017.04.036	j.ica.2017.04.036	NOUN
cana-5306	160	12	.	.	PUNCT
cana-5306	161	1	[	[	X
cana-5306	161	2	5	5	NUM
cana-5306	161	3	]	]	PUNCT
cana-5306	161	4	p.	p.	NOUN
cana-5306	161	5	macchi	macchi	PROPN
cana-5306	161	6	,	,	PUNCT
cana-5306	161	7	j.-m	j.-m	PROPN
cana-5306	161	8	.	.	PUNCT
cana-5306	162	1	gillet	gillet	PROPN
cana-5306	162	2	,	,	PUNCT
cana-5306	162	3	f.	f.	PROPN
cana-5306	162	4	taulelle	taulelle	PROPN
cana-5306	162	5	,	,	PUNCT
cana-5306	162	6	j.	j.	PROPN
cana-5306	162	7	campo	campo	PROPN
cana-5306	162	8	,	,	PUNCT
cana-5306	162	9	n.	n.	PROPN
cana-5306	162	10	claiser	claiser	PROPN
cana-5306	162	11	,	,	PUNCT
cana-5306	162	12	and	and	CCONJ
cana-5306	162	13	c.	c.	PROPN
cana-5306	162	14	lecomte	lecomte	PROPN
cana-5306	162	15	,	,	PUNCT
cana-5306	162	16	“	"	PUNCT
cana-5306	162	17	modelling	model	VERB
cana-5306	162	18	the	the	DET
cana-5306	162	19	experimental	experimental	ADJ
cana-5306	162	20	electron	electron	NOUN
cana-5306	162	21	density	density	NOUN
cana-5306	162	22	:	:	PUNCT
cana-5306	162	23	only	only	ADV
cana-5306	162	24	the	the	DET
cana-5306	162	25	synergy	synergy	NOUN
cana-5306	162	26	of	of	ADP
cana-5306	162	27	various	various	ADJ
cana-5306	162	28	approaches	approach	NOUN
cana-5306	162	29	can	can	AUX
cana-5306	162	30	tackle	tackle	VERB
cana-5306	162	31	the	the	DET
cana-5306	162	32	new	new	ADJ
cana-5306	162	33	challenges	challenge	NOUN
cana-5306	162	34	,	,	PUNCT
cana-5306	162	35	”	"	PUNCT
cana-5306	162	36	iucrj	iucrj	NOUN
cana-5306	162	37	,	,	PUNCT
cana-5306	162	38	vol	vol	NOUN
cana-5306	162	39	.	.	PROPN
cana-5306	163	1	2	2	NUM
cana-5306	163	2	,	,	PUNCT
cana-5306	163	3	no	no	INTJ
cana-5306	163	4	.	.	NOUN
cana-5306	163	5	4	4	NUM
cana-5306	163	6	,	,	PUNCT
cana-5306	163	7	pp	pp	ADJ
cana-5306	163	8	.	.	PUNCT
cana-5306	164	1	441–451	441–451	NUM
cana-5306	164	2	,	,	PUNCT
cana-5306	164	3	may	may	PROPN
cana-5306	164	4	2015	2015	NUM
cana-5306	164	5	,	,	PUNCT
cana-5306	164	6	doi	doi	NOUN
cana-5306	164	7	:	:	PUNCT
cana-5306	164	8	10.1107	10.1107	NUM
cana-5306	164	9	/	/	SYM
cana-5306	164	10	s2052252515007538	s2052252515007538	NOUN
cana-5306	164	11	.	.	PUNCT
cana-5306	165	1	[	[	X
cana-5306	165	2	6	6	NUM
cana-5306	165	3	]	]	PUNCT
cana-5306	165	4	s.	s.	PROPN
cana-5306	165	5	c.	c.	PROPN
cana-5306	165	6	capelli	capelli	PROPN
cana-5306	165	7	,	,	PUNCT
cana-5306	165	8	h.-b	h.-b	PROPN
cana-5306	165	9	.	.	PUNCT
cana-5306	165	10	bürgi	bürgi	PROPN
cana-5306	165	11	,	,	PUNCT
cana-5306	165	12	b.	b.	PROPN
cana-5306	165	13	dittrich	dittrich	PROPN
cana-5306	165	14	,	,	PUNCT
cana-5306	165	15	s.	s.	PROPN
cana-5306	165	16	grabowsky	grabowsky	PROPN
cana-5306	165	17	,	,	PUNCT
cana-5306	165	18	and	and	CCONJ
cana-5306	165	19	d.	d.	PROPN
cana-5306	165	20	jayatilaka	jayatilaka	PROPN
cana-5306	165	21	,	,	PUNCT
cana-5306	165	22	“	"	PUNCT
cana-5306	165	23	hirshfeld	hirshfeld	ADJ
cana-5306	165	24	atom	atom	NOUN
cana-5306	165	25	refinement	refinement	NOUN
cana-5306	165	26	,	,	PUNCT
cana-5306	165	27	”	"	PUNCT
cana-5306	165	28	iucrj	iucrj	NOUN
cana-5306	165	29	,	,	PUNCT
cana-5306	165	30	vol	vol	NOUN
cana-5306	165	31	.	.	PROPN
cana-5306	166	1	1	1	NUM
cana-5306	166	2	,	,	PUNCT
cana-5306	166	3	no	no	INTJ
cana-5306	166	4	.	.	NOUN
cana-5306	166	5	5	5	NUM
cana-5306	166	6	,	,	PUNCT
cana-5306	166	7	pp	pp	ADJ
cana-5306	166	8	.	.	PUNCT
cana-5306	167	1	361–379	361–379	NUM
cana-5306	167	2	,	,	PUNCT
cana-5306	167	3	aug	aug	PROPN
cana-5306	167	4	.	.	PROPN
cana-5306	167	5	2014	2014	NUM
cana-5306	167	6	,	,	PUNCT
cana-5306	167	7	doi	doi	NOUN
cana-5306	167	8	:	:	PUNCT
cana-5306	167	9	10.1107	10.1107	NUM
cana-5306	167	10	/	/	SYM
cana-5306	167	11	s2052252514014845	s2052252514014845	NOUN
cana-5306	167	12	.	.	PUNCT
cana-5306	168	1	[	[	X
cana-5306	168	2	7	7	X
cana-5306	168	3	]	]	X
cana-5306	168	4	f.	f.	PROPN
cana-5306	168	5	l.	l.	PROPN
cana-5306	168	6	hirshfeld	hirshfeld	PROPN
cana-5306	168	7	,	,	PUNCT
cana-5306	168	8	“	"	PUNCT
cana-5306	168	9	bonded	bond	VERB
cana-5306	168	10	-	-	PUNCT
cana-5306	168	11	atom	atom	NOUN
cana-5306	168	12	fragments	fragment	NOUN
cana-5306	168	13	for	for	ADP
cana-5306	168	14	describing	describe	VERB
cana-5306	168	15	molecular	molecular	ADJ
cana-5306	168	16	charge	charge	NOUN
cana-5306	168	17	densities	density	NOUN
cana-5306	168	18	,	,	PUNCT
cana-5306	168	19	”	"	PUNCT
cana-5306	168	20	theoretica	theoretica	PROPN
cana-5306	168	21	chimica	chimica	PROPN
cana-5306	168	22	acta	acta	PROPN
cana-5306	168	23	,	,	PUNCT
cana-5306	168	24	vol	vol	NOUN
cana-5306	168	25	.	.	PROPN
cana-5306	169	1	44	44	NUM
cana-5306	169	2	,	,	PUNCT
cana-5306	169	3	no	no	INTJ
cana-5306	169	4	.	.	NOUN
cana-5306	169	5	2	2	NUM
cana-5306	169	6	,	,	PUNCT
cana-5306	169	7	pp	pp	ADJ
cana-5306	169	8	.	.	PUNCT
cana-5306	170	1	129–138	129–138	NUM
cana-5306	170	2	,	,	PUNCT
cana-5306	170	3	jan	jan	PROPN
cana-5306	170	4	.	.	PROPN
cana-5306	170	5	1977	1977	NUM
cana-5306	170	6	,	,	PUNCT
cana-5306	170	7	doi	doi	NOUN
cana-5306	170	8	:	:	PUNCT
cana-5306	170	9	10.1007	10.1007	NUM
cana-5306	170	10	/	/	SYM
cana-5306	170	11	bf00549096	bf00549096	NOUN
cana-5306	170	12	.	.	PUNCT
cana-5306	171	1	[	[	X
cana-5306	171	2	8	8	NUM
cana-5306	171	3	]	]	PUNCT
cana-5306	171	4	m.	m.	NOUN
cana-5306	171	5	saccone	saccone	NOUN
cana-5306	171	6	and	and	CCONJ
cana-5306	171	7	l.	l.	PROPN
cana-5306	171	8	catalano	catalano	PROPN
cana-5306	171	9	,	,	PUNCT
cana-5306	171	10	“	"	PUNCT
cana-5306	171	11	halogen	halogen	NOUN
cana-5306	171	12	bonding	bonding	NOUN
cana-5306	171	13	beyond	beyond	ADP
cana-5306	171	14	crystals	crystal	NOUN
cana-5306	171	15	in	in	ADP
cana-5306	171	16	materials	material	NOUN
cana-5306	171	17	science	science	NOUN
cana-5306	171	18	,	,	PUNCT
cana-5306	171	19	”	"	PUNCT
cana-5306	171	20	the	the	DET
cana-5306	171	21	journal	journal	NOUN
cana-5306	171	22	of	of	ADP
cana-5306	171	23	physical	physical	ADJ
cana-5306	171	24	chemistry	chemistry	NOUN
cana-5306	171	25	b	b	NOUN
cana-5306	171	26	,	,	PUNCT
cana-5306	171	27	vol	vol	NOUN
cana-5306	171	28	.	.	NOUN
cana-5306	171	29	123	123	NUM
cana-5306	171	30	,	,	PUNCT
cana-5306	171	31	no	no	INTJ
cana-5306	171	32	.	.	NOUN
cana-5306	171	33	44	44	NUM
cana-5306	171	34	,	,	PUNCT
cana-5306	171	35	pp	pp	ADJ
cana-5306	171	36	.	.	PUNCT
cana-5306	172	1	9281–9290	9281–9290	NUM
cana-5306	172	2	,	,	PUNCT
cana-5306	172	3	sep	sep	PROPN
cana-5306	172	4	.	.	PROPN
cana-5306	172	5	2019	2019	NUM
cana-5306	172	6	,	,	PUNCT
cana-5306	172	7	doi	doi	NOUN
cana-5306	172	8	:	:	PUNCT
cana-5306	172	9	10.1021	10.1021	NUM
cana-5306	172	10	/	/	SYM
cana-5306	172	11	acs.jpcb.9b07035	acs.jpcb.9b07035	NOUN
cana-5306	172	12	.	.	PUNCT
cana-5306	173	1	[	[	X
cana-5306	173	2	9	9	NUM
cana-5306	173	3	]	]	PUNCT
cana-5306	173	4	l.	l.	PROPN
cana-5306	173	5	r.	r.	PROPN
cana-5306	173	6	falvello	falvello	PROPN
cana-5306	173	7	,	,	PUNCT
cana-5306	173	8	“	"	PUNCT
cana-5306	173	9	what	what	PRON
cana-5306	173	10	is	be	AUX
cana-5306	173	11	a	a	DET
cana-5306	173	12	crystal	crystal	NOUN
cana-5306	173	13	to	to	ADP
cana-5306	173	14	the	the	DET
cana-5306	173	15	new	new	ADJ
cana-5306	173	16	chemical	chemical	NOUN
cana-5306	173	17	crystallographer	crystallographer	NOUN
cana-5306	173	18	,	,	PUNCT
cana-5306	173	19	after	after	ADP
cana-5306	173	20	that	that	DET
cana-5306	173	21	first	first	ADV
cana-5306	173	22	,	,	PUNCT
cana-5306	173	23	automated	automated	ADJ
cana-5306	173	24	structure	structure	NOUN
cana-5306	173	25	analysis	analysis	NOUN
cana-5306	173	26	?	?	PUNCT
cana-5306	173	27	,	,	PUNCT
cana-5306	173	28	”	"	PUNCT
cana-5306	173	29	crystallography	crystallography	NOUN
cana-5306	173	30	reviews	review	NOUN
cana-5306	173	31	,	,	PUNCT
cana-5306	173	32	vol	vol	NOUN
cana-5306	173	33	.	.	PROPN
cana-5306	173	34	26	26	NUM
cana-5306	173	35	,	,	PUNCT
cana-5306	173	36	no	no	INTJ
cana-5306	173	37	.	.	NOUN
cana-5306	173	38	3	3	NUM
cana-5306	173	39	,	,	PUNCT
cana-5306	173	40	pp	pp	ADJ
cana-5306	173	41	.	.	PUNCT
cana-5306	174	1	119–142	119–142	NUM
cana-5306	174	2	,	,	PUNCT
cana-5306	174	3	may	may	AUX
cana-5306	174	4	2020	2020	NUM
cana-5306	174	5	,	,	PUNCT
cana-5306	174	6	doi	doi	NOUN
cana-5306	174	7	:	:	PUNCT
cana-5306	174	8	10.1080/0889311x.2020.1760856	10.1080/0889311x.2020.1760856	NOUN
cana-5306	174	9	.	.	PUNCT
cana-5306	175	1	communications	communication	NOUN
cana-5306	175	2	on	on	ADP
cana-5306	175	3	applied	apply	VERB
cana-5306	175	4	nonlinear	nonlinear	ADJ
cana-5306	175	5	analysis	analysis	NOUN
cana-5306	175	6	issn	issn	NOUN
cana-5306	175	7	:	:	PUNCT
cana-5306	175	8	1074	1074	NUM
cana-5306	175	9	-	-	PUNCT
cana-5306	175	10	133x	133x	NUM
cana-5306	175	11	vol	vol	NOUN
cana-5306	175	12	31	31	NUM
cana-5306	175	13	no	no	NOUN
cana-5306	175	14	.	.	NOUN
cana-5306	175	15	2	2	NUM
cana-5306	175	16	(	(	PUNCT
cana-5306	175	17	2024	2024	NUM
cana-5306	175	18	)	)	PUNCT
cana-5306	175	19	451	451	NUM
cana-5306	175	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5306	176	1	[	[	X
cana-5306	176	2	10	10	NUM
cana-5306	176	3	]	]	X
cana-5306	176	4	a.	a.	PROPN
cana-5306	176	5	ali	ali	PROPN
cana-5306	176	6	,	,	PUNCT
cana-5306	176	7	y.	y.	PROPN
cana-5306	176	8	w.	w.	PROPN
cana-5306	176	9	chiang	chiang	PROPN
cana-5306	176	10	,	,	PUNCT
cana-5306	176	11	and	and	CCONJ
cana-5306	176	12	r.	r.	PROPN
cana-5306	176	13	m.	m.	PROPN
cana-5306	176	14	santos	santos	PROPN
cana-5306	176	15	,	,	PUNCT
cana-5306	176	16	“	"	PUNCT
cana-5306	176	17	x	x	X
cana-5306	176	18	-	-	NOUN
cana-5306	176	19	ray	ray	NOUN
cana-5306	176	20	diffraction	diffraction	NOUN
cana-5306	176	21	techniques	technique	NOUN
cana-5306	176	22	for	for	ADP
cana-5306	176	23	mineral	mineral	ADJ
cana-5306	176	24	characterization	characterization	NOUN
cana-5306	176	25	:	:	PUNCT
cana-5306	176	26	a	a	DET
cana-5306	176	27	review	review	NOUN
cana-5306	176	28	for	for	ADP
cana-5306	176	29	engineers	engineer	NOUN
cana-5306	176	30	of	of	ADP
cana-5306	176	31	the	the	DET
cana-5306	176	32	fundamentals	fundamental	NOUN
cana-5306	176	33	,	,	PUNCT
cana-5306	176	34	applications	application	NOUN
cana-5306	176	35	,	,	PUNCT
cana-5306	176	36	and	and	CCONJ
cana-5306	176	37	research	research	NOUN
cana-5306	176	38	directions	direction	NOUN
cana-5306	176	39	,	,	PUNCT
cana-5306	176	40	”	"	PUNCT
cana-5306	176	41	minerals	mineral	NOUN
cana-5306	176	42	,	,	PUNCT
cana-5306	176	43	vol	vol	NOUN
cana-5306	176	44	.	.	PROPN
cana-5306	176	45	12	12	NUM
cana-5306	176	46	,	,	PUNCT
cana-5306	176	47	no	no	INTJ
cana-5306	176	48	.	.	NOUN
cana-5306	176	49	2	2	NUM
cana-5306	176	50	,	,	PUNCT
cana-5306	176	51	p.	p.	NOUN
cana-5306	176	52	205	205	NUM
cana-5306	176	53	,	,	PUNCT
cana-5306	176	54	feb	feb	PROPN
cana-5306	176	55	.	.	PROPN
cana-5306	176	56	2022	2022	NUM
cana-5306	176	57	,	,	PUNCT
cana-5306	176	58	doi	doi	NOUN
cana-5306	176	59	:	:	PUNCT
cana-5306	176	60	10.3390	10.3390	NUM
cana-5306	176	61	/	/	SYM
cana-5306	176	62	min12020205	min12020205	NOUN
cana-5306	176	63	.	.	PUNCT
cana-5306	177	1	[	[	X
cana-5306	177	2	11	11	NUM
cana-5306	177	3	]	]	X
cana-5306	177	4	f.	f.	PROPN
cana-5306	177	5	m.	m.	NOUN
cana-5306	177	6	brückler	brückler	NOUN
cana-5306	177	7	and	and	CCONJ
cana-5306	177	8	v.	v.	ADP
cana-5306	177	9	stilinović	stilinović	NOUN
cana-5306	177	10	,	,	PUNCT
cana-5306	177	11	“	"	PUNCT
cana-5306	177	12	from	from	ADP
cana-5306	177	13	friezes	frieze	NOUN
cana-5306	177	14	to	to	ADP
cana-5306	177	15	quasicrystals	quasicrystal	NOUN
cana-5306	177	16	:	:	PUNCT
cana-5306	177	17	a	a	DET
cana-5306	177	18	history	history	NOUN
cana-5306	177	19	of	of	ADP
cana-5306	177	20	symmetry	symmetry	NOUN
cana-5306	177	21	groups	group	NOUN
cana-5306	177	22	,	,	PUNCT
cana-5306	177	23	”	"	PUNCT
cana-5306	177	24	in	in	ADP
cana-5306	177	25	springer	springer	NOUN
cana-5306	177	26	ebooks	ebook	NOUN
cana-5306	177	27	,	,	PUNCT
cana-5306	177	28	2023	2023	NUM
cana-5306	177	29	,	,	PUNCT
cana-5306	177	30	pp	pp	PROPN
cana-5306	177	31	.	.	PUNCT
cana-5306	178	1	1–42	1–42	PROPN
cana-5306	178	2	.	.	PUNCT
cana-5306	179	1	doi	doi	PROPN
cana-5306	179	2	:	:	PUNCT
cana-5306	179	3	10.1007/978	10.1007/978	NUM
cana-5306	179	4	-	-	SYM
cana-5306	179	5	3	3	NUM
cana-5306	179	6	-	-	PUNCT
cana-5306	179	7	03019071	03019071	NUM
cana-5306	179	8	-	-	PUNCT
cana-5306	179	9	2_132	2_132	NUM
cana-5306	179	10	-	-	PUNCT
cana-5306	179	11	2	2	NUM
cana-5306	179	12	.	.	PUNCT
cana-5306	180	1	[	[	X
cana-5306	180	2	12	12	NUM
cana-5306	180	3	]	]	X
cana-5306	180	4	e.	e.	PROPN
cana-5306	180	5	silva‐ramírez	silva‐ramírez	PROPN
cana-5306	180	6	,	,	PUNCT
cana-5306	180	7	i.	i.	PROPN
cana-5306	180	8	cumbrera‐conde	cumbrera‐conde	PROPN
cana-5306	180	9	,	,	PUNCT
cana-5306	180	10	r.	r.	PROPN
cana-5306	180	11	cano‐crespo	cano‐crespo	PROPN
cana-5306	180	12	,	,	PUNCT
cana-5306	180	13	and	and	CCONJ
cana-5306	180	14	f.	f.	PROPN
cana-5306	180	15	cumbrera	cumbrera	PROPN
cana-5306	180	16	,	,	PUNCT
cana-5306	180	17	“	"	PUNCT
cana-5306	180	18	machine	machine	NOUN
cana-5306	180	19	learning	learn	VERB
cana-5306	180	20	techniques	technique	NOUN
cana-5306	180	21	for	for	ADP
cana-5306	180	22	the	the	DET
cana-5306	180	23	ab	ab	PROPN
cana-5306	180	24	initio	initio	PROPN
cana-5306	180	25	bravais	bravais	PROPN
cana-5306	180	26	lattice	lattice	PROPN
cana-5306	180	27	determination	determination	NOUN
cana-5306	180	28	,	,	PUNCT
cana-5306	180	29	”	"	PUNCT
cana-5306	180	30	expert	expert	NOUN
cana-5306	180	31	systems	system	NOUN
cana-5306	180	32	,	,	PUNCT
cana-5306	180	33	vol	vol	NOUN
cana-5306	180	34	.	.	PROPN
cana-5306	180	35	40	40	NUM
cana-5306	180	36	,	,	PUNCT
cana-5306	180	37	no	no	INTJ
cana-5306	180	38	.	.	NOUN
cana-5306	180	39	2	2	NUM
cana-5306	180	40	,	,	PUNCT
cana-5306	180	41	oct	oct	PROPN
cana-5306	180	42	.	.	PROPN
cana-5306	180	43	2022	2022	NUM
cana-5306	180	44	,	,	PUNCT
cana-5306	180	45	doi	doi	NOUN
cana-5306	180	46	:	:	PUNCT
cana-5306	180	47	10.1111	10.1111	NUM
cana-5306	180	48	/	/	SYM
cana-5306	180	49	exsy.13160	exsy.13160	PROPN
cana-5306	180	50	.	.	PUNCT
cana-5306	181	1	[	[	X
cana-5306	181	2	13	13	NUM
cana-5306	181	3	]	]	X
cana-5306	181	4	h.	h.	PROPN
cana-5306	181	5	grimmer	grimmer	PROPN
cana-5306	181	6	,	,	PUNCT
cana-5306	181	7	“	"	PUNCT
cana-5306	181	8	partial	partial	ADJ
cana-5306	181	9	order	order	NOUN
cana-5306	181	10	among	among	ADP
cana-5306	181	11	the	the	DET
cana-5306	181	12	14	14	NUM
cana-5306	181	13	bravais	bravais	NOUN
cana-5306	181	14	types	type	NOUN
cana-5306	181	15	of	of	ADP
cana-5306	181	16	lattices	lattice	NOUN
cana-5306	181	17	:	:	PUNCT
cana-5306	181	18	basics	basic	NOUN
cana-5306	181	19	and	and	CCONJ
cana-5306	181	20	applications	application	NOUN
cana-5306	181	21	,	,	PUNCT
cana-5306	181	22	”	"	PUNCT
cana-5306	181	23	acta	acta	PROPN
cana-5306	181	24	crystallographica	crystallographica	PROPN
cana-5306	181	25	section	section	PROPN
cana-5306	181	26	a	a	DET
cana-5306	181	27	foundations	foundation	NOUN
cana-5306	181	28	and	and	CCONJ
cana-5306	181	29	advances	advance	NOUN
cana-5306	181	30	,	,	PUNCT
cana-5306	181	31	vol	vol	NOUN
cana-5306	181	32	.	.	PROPN
cana-5306	181	33	71	71	NUM
cana-5306	181	34	,	,	PUNCT
cana-5306	181	35	no	no	INTJ
cana-5306	181	36	.	.	NOUN
cana-5306	181	37	2	2	NUM
cana-5306	181	38	,	,	PUNCT
cana-5306	181	39	pp	pp	ADJ
cana-5306	181	40	.	.	PUNCT
cana-5306	182	1	143–149	143–149	NUM
cana-5306	182	2	,	,	PUNCT
cana-5306	182	3	jan	jan	PROPN
cana-5306	182	4	.	.	PROPN
cana-5306	182	5	2015	2015	NUM
cana-5306	182	6	,	,	PUNCT
cana-5306	182	7	doi	doi	NOUN
cana-5306	182	8	:	:	PUNCT
cana-5306	182	9	10.1107	10.1107	NUM
cana-5306	182	10	/	/	SYM
cana-5306	182	11	s2053273314027351	s2053273314027351	NOUN
cana-5306	182	12	.	.	PUNCT
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cana-5306	183	2	14	14	NUM
cana-5306	183	3	]	]	X
cana-5306	183	4	g.	g.	PROPN
cana-5306	183	5	grimvall	grimvall	PROPN
cana-5306	183	6	,	,	PUNCT
cana-5306	183	7	b.	b.	PROPN
cana-5306	183	8	magyari	magyari	PROPN
cana-5306	183	9	-	-	PUNCT
cana-5306	183	10	köpe	köpe	PROPN
cana-5306	183	11	,	,	PUNCT
cana-5306	183	12	v.	v.	ADP
cana-5306	183	13	ozoliņš	ozoliņš	PROPN
cana-5306	183	14	,	,	PUNCT
cana-5306	183	15	and	and	CCONJ
cana-5306	183	16	k.	k.	PROPN
cana-5306	183	17	a.	a.	PROPN
cana-5306	183	18	persson	persson	PROPN
cana-5306	183	19	,	,	PUNCT
cana-5306	183	20	“	"	PUNCT
cana-5306	183	21	lattice	lattice	ADJ
cana-5306	183	22	instabilities	instability	NOUN
cana-5306	183	23	in	in	ADP
cana-5306	183	24	metallic	metallic	ADJ
cana-5306	183	25	elements	element	NOUN
cana-5306	183	26	,	,	PUNCT
cana-5306	183	27	”	"	PUNCT
cana-5306	183	28	reviews	review	NOUN
cana-5306	183	29	of	of	ADP
cana-5306	183	30	modern	modern	ADJ
cana-5306	183	31	physics	physic	NOUN
cana-5306	183	32	,	,	PUNCT
cana-5306	183	33	vol	vol	NOUN
cana-5306	183	34	.	.	PROPN
cana-5306	183	35	84	84	NUM
cana-5306	183	36	,	,	PUNCT
cana-5306	183	37	no	no	INTJ
cana-5306	183	38	.	.	NOUN
cana-5306	183	39	2	2	NUM
cana-5306	183	40	,	,	PUNCT
cana-5306	183	41	pp	pp	ADJ
cana-5306	183	42	.	.	PUNCT
cana-5306	184	1	945–986	945–986	NUM
cana-5306	184	2	,	,	PUNCT
cana-5306	184	3	jun	jun	PROPN
cana-5306	184	4	.	.	PROPN
cana-5306	184	5	2012	2012	NUM
cana-5306	184	6	,	,	PUNCT
cana-5306	184	7	doi	doi	NOUN
cana-5306	184	8	:	:	PUNCT
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cana-5306	184	10	/	/	SYM
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cana-5306	184	12	.	.	PUNCT
cana-5306	185	1	[	[	X
cana-5306	185	2	15	15	NUM
cana-5306	185	3	]	]	X
cana-5306	185	4	j.-p	j.-p	PROPN
cana-5306	185	5	.	.	PUNCT
cana-5306	185	6	antoine	antoine	PROPN
cana-5306	185	7	,	,	PUNCT
cana-5306	185	8	“	"	PUNCT
cana-5306	185	9	group	group	NOUN
cana-5306	185	10	theory	theory	NOUN
cana-5306	185	11	:	:	PUNCT
cana-5306	185	12	mathematical	mathematical	ADJ
cana-5306	185	13	expression	expression	NOUN
cana-5306	185	14	of	of	ADP
cana-5306	185	15	symmetry	symmetry	NOUN
cana-5306	185	16	in	in	ADP
cana-5306	185	17	physics	physics	NOUN
cana-5306	185	18	,	,	PUNCT
cana-5306	185	19	”	"	PUNCT
cana-5306	185	20	symmetry	symmetry	NOUN
cana-5306	185	21	,	,	PUNCT
cana-5306	185	22	vol	vol	NOUN
cana-5306	185	23	.	.	PROPN
cana-5306	185	24	13	13	NUM
cana-5306	185	25	,	,	PUNCT
cana-5306	185	26	no	no	INTJ
cana-5306	185	27	.	.	NOUN
cana-5306	185	28	8	8	NUM
cana-5306	185	29	,	,	PUNCT
cana-5306	185	30	p.	p.	NOUN
cana-5306	185	31	1354	1354	NUM
cana-5306	185	32	,	,	PUNCT
cana-5306	185	33	jul	jul	PROPN
cana-5306	185	34	.	.	PROPN
cana-5306	185	35	2021	2021	NUM
cana-5306	185	36	,	,	PUNCT
cana-5306	185	37	doi	doi	NOUN
cana-5306	185	38	:	:	PUNCT
cana-5306	185	39	10.3390	10.3390	NUM
cana-5306	185	40	/	/	SYM
cana-5306	185	41	sym13081354	sym13081354	NOUN
cana-5306	185	42	.	.	PUNCT