id	sid	tid	token	lemma	pos
ajtas-2922	1	1	american	american	PROPN
ajtas-2922	1	2	journal	journal	PROPN
ajtas-2922	1	3	of	of	ADP
ajtas-2922	1	4	technology	technology	NOUN
ajtas-2922	1	5	and	and	CCONJ
ajtas-2922	1	6	applied	apply	VERB
ajtas-2922	1	7	sciences	sciences	PROPN
ajtas-2922	1	8	issn	issn	X
ajtas-2922	1	9	(	(	PUNCT
ajtas-2922	1	10	e	e	NOUN
ajtas-2922	1	11	):	):	PUNCT
ajtas-2922	1	12	2832	2832	NUM
ajtas-2922	1	13	-	-	SYM
ajtas-2922	1	14	1766	1766	NUM
ajtas-2922	1	15	volume	volume	NOUN
ajtas-2922	1	16	36	36	NUM
ajtas-2922	1	17	,	,	PUNCT
ajtas-2922	1	18	may	may	AUX
ajtas-2922	1	19	2025	2025	NUM
ajtas-2922	1	20	p	p	NOUN
ajtas-2922	1	21	a	a	DET
ajtas-2922	1	22	g	g	NOUN
ajtas-2922	1	23	e	e	NOUN
ajtas-2922	1	24	|	|	ADV
ajtas-2922	1	25	13	13	NUM
ajtas-2922	1	26	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-2922	1	27	flexural	flexural	ADJ
ajtas-2922	1	28	vibrations	vibration	NOUN
ajtas-2922	1	29	of	of	ADP
ajtas-2922	1	30	a	a	DET
ajtas-2922	1	31	double	double	ADJ
ajtas-2922	1	32	-	-	PUNCT
ajtas-2922	1	33	layer	layer	NOUN
ajtas-2922	1	34	elastic	elastic	ADJ
ajtas-2922	1	35	plate	plate	NOUN
ajtas-2922	1	36	narzullaev	narzullaev	ADP
ajtas-2922	1	37	muhammad	muhammad	PROPN
ajtas-2922	1	38	azamat	azamat	PROPN
ajtas-2922	1	39	,	,	PUNCT
ajtas-2922	1	40	doctoral	doctoral	ADJ
ajtas-2922	1	41	student	student	NOUN
ajtas-2922	1	42	bukhara	bukhara	PROPN
ajtas-2922	1	43	state	state	PROPN
ajtas-2922	1	44	technical	technical	PROPN
ajtas-2922	1	45	university	university	PROPN
ajtas-2922	1	46	(	(	PUNCT
ajtas-2922	1	47	uzbekistan	uzbekistan	PROPN
ajtas-2922	1	48	)	)	PUNCT
ajtas-2922	2	1	a	a	DET
ajtas-2922	2	2	b	b	PROPN
ajtas-2922	2	3	s	s	ADP
ajtas-2922	2	4	t	t	PROPN
ajtas-2922	2	5	r	r	NOUN
ajtas-2922	2	6	a	a	DET
ajtas-2922	2	7	c	c	NOUN
ajtas-2922	2	8	t	t	NOUN
ajtas-2922	2	9	k	k	X
ajtas-2922	2	10	e	e	PROPN
ajtas-2922	2	11	y	y	PROPN
ajtas-2922	2	12	w	w	NOUN
ajtas-2922	2	13	o	o	NOUN
ajtas-2922	2	14	r	r	NOUN
ajtas-2922	2	15	d	d	NOUN
ajtas-2922	2	16	s	s	PRON
ajtas-2922	2	17	consider	consider	VERB
ajtas-2922	2	18	a	a	DET
ajtas-2922	2	19	plate	plate	NOUN
ajtas-2922	2	20	whose	whose	DET
ajtas-2922	2	21	neutral	neutral	ADJ
ajtas-2922	2	22	plane	plane	NOUN
ajtas-2922	2	23	coincides	coincide	VERB
ajtas-2922	2	24	with	with	ADP
ajtas-2922	2	25	the	the	DET
ajtas-2922	2	26	plane	plane	NOUN
ajtas-2922	2	27	x	x	NOUN
ajtas-2922	2	28	,	,	PUNCT
ajtas-2922	2	29	z	z	NOUN
ajtas-2922	2	30	,	,	PUNCT
ajtas-2922	2	31	and	and	CCONJ
ajtas-2922	2	32	the	the	DET
ajtas-2922	2	33	y	y	PROPN
ajtas-2922	2	34	coordinate	coordinate	NOUN
ajtas-2922	2	35	coincides	coincide	VERB
ajtas-2922	2	36	with	with	ADP
ajtas-2922	2	37	the	the	DET
ajtas-2922	2	38	direction	direction	NOUN
ajtas-2922	2	39	of	of	ADP
ajtas-2922	2	40	thickness	thickness	NOUN
ajtas-2922	2	41	.	.	PUNCT
ajtas-2922	3	1	analysis	analysis	NOUN
ajtas-2922	3	2	of	of	ADP
ajtas-2922	3	3	numerical	numerical	ADJ
ajtas-2922	3	4	,	,	PUNCT
ajtas-2922	3	5	material	material	ADJ
ajtas-2922	3	6	density	density	NOUN
ajtas-2922	3	7	,	,	PUNCT
ajtas-2922	3	8	problem	problem	NOUN
ajtas-2922	3	9	solving	solving	NOUN
ajtas-2922	3	10	,	,	PUNCT
ajtas-2922	3	11	harmonic	harmonic	ADJ
ajtas-2922	3	12	wave	wave	NOUN
ajtas-2922	3	13	,	,	PUNCT
ajtas-2922	3	14	wave	wave	NOUN
ajtas-2922	3	15	number	number	NOUN
ajtas-2922	3	16	,	,	PUNCT
ajtas-2922	3	17	deformation	deformation	NOUN
ajtas-2922	3	18	,	,	PUNCT
ajtas-2922	3	19	linear	linear	ADJ
ajtas-2922	3	20	elasticity	elasticity	NOUN
ajtas-2922	3	21	,	,	PUNCT
ajtas-2922	3	22	isotropic	isotropic	NOUN
ajtas-2922	3	23	material	material	NOUN
ajtas-2922	3	24	,	,	PUNCT
ajtas-2922	3	25	algebraic	algebraic	ADJ
ajtas-2922	3	26	equations	equation	NOUN
ajtas-2922	3	27	,	,	PUNCT
ajtas-2922	3	28	transcendental	transcendental	ADJ
ajtas-2922	3	29	equation	equation	NOUN
ajtas-2922	3	30	,	,	PUNCT
ajtas-2922	3	31	müller	müller	PROPN
ajtas-2922	3	32	's	's	PART
ajtas-2922	3	33	method	method	NOUN
ajtas-2922	3	34	,	,	PUNCT
ajtas-2922	3	35	newton	newton	PROPN
ajtas-2922	3	36	's	's	PART
ajtas-2922	3	37	method	method	NOUN
ajtas-2922	3	38	.	.	PUNCT
ajtas-2922	4	1	introduction	introduction	NOUN
ajtas-2922	4	2	consider	consider	VERB
ajtas-2922	4	3	a	a	DET
ajtas-2922	4	4	plate	plate	NOUN
ajtas-2922	4	5	whose	whose	DET
ajtas-2922	4	6	neutral	neutral	ADJ
ajtas-2922	4	7	plane	plane	NOUN
ajtas-2922	4	8	coincides	coincide	VERB
ajtas-2922	4	9	with	with	ADP
ajtas-2922	4	10	the	the	DET
ajtas-2922	4	11	plane	plane	NOUN
ajtas-2922	4	12	x	x	NOUN
ajtas-2922	4	13	,	,	PUNCT
ajtas-2922	4	14	z	z	NOUN
ajtas-2922	4	15	,	,	PUNCT
ajtas-2922	4	16	and	and	CCONJ
ajtas-2922	4	17	the	the	DET
ajtas-2922	4	18	y	y	PROPN
ajtas-2922	4	19	coordinate	coordinate	NOUN
ajtas-2922	4	20	coincides	coincide	VERB
ajtas-2922	4	21	with	with	ADP
ajtas-2922	4	22	the	the	DET
ajtas-2922	4	23	direction	direction	NOUN
ajtas-2922	4	24	of	of	ADP
ajtas-2922	4	25	thickness	thickness	NOUN
ajtas-2922	4	26	.	.	PUNCT
ajtas-2922	5	1	let	let	VERB
ajtas-2922	5	2	harmonic	harmonic	ADJ
ajtas-2922	5	3	bending	bend	VERB
ajtas-2922	5	4	waves	wave	NOUN
ajtas-2922	5	5	propagate	propagate	VERB
ajtas-2922	5	6	along	along	ADP
ajtas-2922	5	7	the	the	DET
ajtas-2922	5	8	plate	plate	NOUN
ajtas-2922	5	9	in	in	ADP
ajtas-2922	5	10	the	the	DET
ajtas-2922	5	11	direction	direction	NOUN
ajtas-2922	5	12	of	of	ADP
ajtas-2922	5	13	the	the	DET
ajtas-2922	5	14	z	z	NOUN
ajtas-2922	5	15	axis	axis	NOUN
ajtas-2922	5	16	.	.	PUNCT
ajtas-2922	6	1	the	the	DET
ajtas-2922	6	2	base	base	NOUN
ajtas-2922	6	3	material	material	NOUN
ajtas-2922	6	4	22	22	NUM
ajtas-2922	6	5	b	b	PROPN
ajtas-2922	6	6	y	y	PROPN
ajtas-2922	6	7	b	b	PROPN
ajtas-2922	6	8	−	−	NOUN
ajtas-2922	6	9	of	of	ADP
ajtas-2922	6	10	the	the	DET
ajtas-2922	6	11	plate	plate	NOUN
ajtas-2922	6	12	occupies	occupy	VERB
ajtas-2922	6	13	a	a	DET
ajtas-2922	6	14	sphere	sphere	NOUN
ajtas-2922	6	15	,	,	PUNCT
ajtas-2922	6	16	and	and	CCONJ
ajtas-2922	6	17	the	the	DET
ajtas-2922	6	18	coating	coating	NOUN
ajtas-2922	6	19	,	,	PUNCT
ajtas-2922	6	20	each	each	PRON
ajtas-2922	6	21	of	of	ADP
ajtas-2922	6	22	which	which	PRON
ajtas-2922	6	23	has	have	VERB
ajtas-2922	6	24	the	the	DET
ajtas-2922	6	25	same	same	ADJ
ajtas-2922	6	26	thickness	thickness	NOUN
ajtas-2922	6	27	b/2	b/2	NOUN
ajtas-2922	6	28	everywhere	everywhere	ADV
ajtas-2922	6	29	,	,	PUNCT
ajtas-2922	6	30	occupies	occupy	VERB
ajtas-2922	6	31	the	the	DET
ajtas-2922	6	32	sphere	sphere	NOUN
ajtas-2922	6	33	(	(	PUNCT
ajtas-2922	6	34	)	)	PUNCT
ajtas-2922	6	35	hbyhhybn	hbyhhybn	PROPN
ajtas-2922	7	1	+	+	PROPN
ajtas-2922	7	2	−+−	−+−	PROPN
ajtas-2922	7	3	2/;2/	2/;2/	NUM
ajtas-2922	7	4	.	.	PUNCT
ajtas-2922	8	1	let	let	VERB
ajtas-2922	8	2	g	g	NOUN
ajtas-2922	8	3	,	,	PUNCT
ajtas-2922	8	4			NOUN
ajtas-2922	8	5	and	and	CCONJ
ajtas-2922	8	6			NOUN
ajtas-2922	8	7	denote	denote	VERB
ajtas-2922	8	8	the	the	DET
ajtas-2922	8	9	modulus	modulus	NOUN
ajtas-2922	8	10	of	of	ADP
ajtas-2922	8	11	volumetric	volumetric	NOUN
ajtas-2922	8	12	compression	compression	NOUN
ajtas-2922	8	13	,	,	PUNCT
ajtas-2922	8	14	the	the	DET
ajtas-2922	8	15	modulus	modulus	NOUN
ajtas-2922	8	16	of	of	ADP
ajtas-2922	8	17	shear	shear	NOUN
ajtas-2922	8	18	,	,	PUNCT
ajtas-2922	8	19	and	and	CCONJ
ajtas-2922	8	20	the	the	DET
ajtas-2922	8	21	density	density	NOUN
ajtas-2922	8	22	of	of	ADP
ajtas-2922	8	23	the	the	DET
ajtas-2922	8	24	base	base	NOUN
ajtas-2922	8	25	layer	layer	NOUN
ajtas-2922	8	26	material	material	NOUN
ajtas-2922	8	27	,	,	PUNCT
ajtas-2922	8	28	respectively	respectively	ADV
ajtas-2922	8	29	.	.	PUNCT
ajtas-2922	9	1	in	in	ADP
ajtas-2922	9	2	this	this	DET
ajtas-2922	9	3	case	case	NOUN
ajtas-2922	9	4	,	,	PUNCT
ajtas-2922	9	5	the	the	DET
ajtas-2922	9	6	solution	solution	NOUN
ajtas-2922	9	7	of	of	ADP
ajtas-2922	9	8	the	the	DET
ajtas-2922	9	9	rayleigh	rayleigh	PROPN
ajtas-2922	9	10	-	-	PUNCT
ajtas-2922	9	11	lamb	lamb	PROPN
ajtas-2922	9	12	problem	problem	NOUN
ajtas-2922	9	13	for	for	ADP
ajtas-2922	9	14	the	the	DET
ajtas-2922	9	15	main	main	ADJ
ajtas-2922	9	16	layer	layer	NOUN
ajtas-2922	9	17	is	be	AUX
ajtas-2922	9	18	obtained	obtain	VERB
ajtas-2922	9	19	using	use	VERB
ajtas-2922	9	20	the	the	DET
ajtas-2922	9	21	variable	variable	ADJ
ajtas-2922	9	22	separation	separation	NOUN
ajtas-2922	9	23	method	method	NOUN
ajtas-2922	9	24	,	,	PUNCT
ajtas-2922	9	25	and	and	CCONJ
ajtas-2922	9	26	the	the	DET
ajtas-2922	9	27	displacements	displacement	NOUN
ajtas-2922	9	28	u	u	NOUN
ajtas-2922	9	29	,	,	PUNCT
ajtas-2922	9	30	v	v	NOUN
ajtas-2922	9	31	,	,	PUNCT
ajtas-2922	9	32	w	w	X
ajtas-2922	9	33	(	(	PUNCT
ajtas-2922	9	34	along	along	ADP
ajtas-2922	9	35	the	the	DET
ajtas-2922	9	36	x	x	NOUN
ajtas-2922	9	37	,	,	PUNCT
ajtas-2922	9	38	y	y	PROPN
ajtas-2922	9	39	,	,	PUNCT
ajtas-2922	9	40	and	and	CCONJ
ajtas-2922	9	41	z	z	NOUN
ajtas-2922	9	42	axes	axis	NOUN
ajtas-2922	9	43	,	,	PUNCT
ajtas-2922	9	44	respectively	respectively	ADV
ajtas-2922	9	45	)	)	PUNCT
ajtas-2922	9	46	in	in	ADP
ajtas-2922	9	47	the	the	DET
ajtas-2922	9	48	propagation	propagation	NOUN
ajtas-2922	9	49	of	of	ADP
ajtas-2922	9	50	a	a	DET
ajtas-2922	9	51	harmonic	harmonic	ADJ
ajtas-2922	9	52	wave	wave	NOUN
ajtas-2922	9	53	with	with	ADP
ajtas-2922	9	54	a	a	DET
ajtas-2922	9	55	frequency	frequency	NOUN
ajtas-2922	9	56	and	and	CCONJ
ajtas-2922	9	57	wave	wave	NOUN
ajtas-2922	9	58	number	number	NOUN
ajtas-2922	9	59	k	k	PROPN
ajtas-2922	9	60	are	be	AUX
ajtas-2922	9	61	of	of	ADP
ajtas-2922	9	62	the	the	DET
ajtas-2922	9	63	form	form	NOUN
ajtas-2922	9	64	:	:	PUNCT
ajtas-2922	9	65	(	(	PUNCT
ajtas-2922	9	66	)	)	PUNCT
ajtas-2922	9	67	(	(	PUNCT
ajtas-2922	9	68	)	)	PUNCT
ajtas-2922	9	69	kztiexshkcxchau	kztiexshkcxchau	VERB
ajtas-2922	9	70	−−==	−−==	PROPN
ajtas-2922	9	71			PRON
ajtas-2922	9	72	2121;0	2121;0	PROPN
ajtas-2922	9	73	,	,	PUNCT
ajtas-2922	9	74	(	(	PUNCT
ajtas-2922	9	75	)	)	PUNCT
ajtas-2922	9	76	(	(	PUNCT
ajtas-2922	9	77	)	)	PUNCT
ajtas-2922	9	78	kztieyshciychikaw	kztieyshciychikaw	PROPN
ajtas-2922	9	79	−+−=	−+−=	PUNCT
ajtas-2922	10	1			PUNCT
ajtas-2922	10	2	1	1	NUM
ajtas-2922	10	3	,	,	PUNCT
ajtas-2922	10	4	,	,	PUNCT
ajtas-2922	10	5	22	22	NUM
ajtas-2922	10	6	b	b	NOUN
ajtas-2922	10	7	y	y	PROPN
ajtas-2922	10	8	b	b	PROPN
ajtas-2922	10	9	−	−	NOUN
ajtas-2922	10	10	for	for	ADP
ajtas-2922	10	11	where	where	SCONJ
ajtas-2922	10	12	a1	a1	NOUN
ajtas-2922	10	13	and	and	CCONJ
ajtas-2922	10	14	s1	s1	NOUN
ajtas-2922	10	15	are	be	AUX
ajtas-2922	10	16	constants	constant	NOUN
ajtas-2922	10	17	,	,	PUNCT
ajtas-2922	10	18	and	and	CCONJ
ajtas-2922	10	19	the	the	DET
ajtas-2922	10	20	parameters	parameter	NOUN
ajtas-2922	10	21	are	be	AUX
ajtas-2922	10	22	defined	define	VERB
ajtas-2922	10	23	using	use	VERB
ajtas-2922	10	24	the	the	DET
ajtas-2922	10	25	following	follow	VERB
ajtas-2922	10	26			NOUN
ajtas-2922	10	27			NOUN
ajtas-2922	10	28	expressions	expression	NOUN
ajtas-2922	10	29	:	:	PUNCT
ajtas-2922	10	30	.	.	PUNCT
ajtas-2922	11	1	;	;	PUNCT
ajtas-2922	11	2	3	3	NUM
ajtas-2922	11	3	4	4	NUM
ajtas-2922	11	4	2	2	NUM
ajtas-2922	11	5	22	22	NUM
ajtas-2922	11	6	2	2	NUM
ajtas-2922	11	7	22	22	NUM
ajtas-2922	11	8			NOUN
ajtas-2922	11	9			NOUN
ajtas-2922	11	10			PROPN
ajtas-2922	11	11			PROPN
ajtas-2922	11	12			PROPN
ajtas-2922	11	13			X
ajtas-2922	11	14	−=	−=	X
ajtas-2922	11	15	+	+	PUNCT
ajtas-2922	11	16	−=	−=	NOUN
ajtas-2922	11	17	k	k	PROPN
ajtas-2922	11	18	g	g	PROPN
ajtas-2922	11	19	k	k	PROPN
ajtas-2922	11	20	(	(	PUNCT
ajtas-2922	11	21	1	1	X
ajtas-2922	11	22	)	)	PUNCT
ajtas-2922	11	23	american	american	ADJ
ajtas-2922	11	24	journal	journal	NOUN
ajtas-2922	11	25	of	of	ADP
ajtas-2922	11	26	technology	technology	NOUN
ajtas-2922	11	27	and	and	CCONJ
ajtas-2922	11	28	applied	apply	VERB
ajtas-2922	11	29	sciences	science	NOUN
ajtas-2922	11	30	36	36	NUM
ajtas-2922	11	31	,	,	PUNCT
ajtas-2922	11	32	may	may	AUX
ajtas-2922	11	33	2025	2025	NUM
ajtas-2922	11	34	p	p	NOUN
ajtas-2922	11	35	a	a	DET
ajtas-2922	11	36	g	g	NOUN
ajtas-2922	11	37	e	e	NOUN
ajtas-2922	11	38	|	|	ADV
ajtas-2922	11	39	14	14	NUM
ajtas-2922	11	40	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-2922	11	41	based	base	VERB
ajtas-2922	11	42	on	on	ADP
ajtas-2922	11	43	the	the	DET
ajtas-2922	11	44	relationship	relationship	NOUN
ajtas-2922	11	45	between	between	ADP
ajtas-2922	11	46	stresses	stress	NOUN
ajtas-2922	11	47	and	and	CCONJ
ajtas-2922	11	48	strains	strain	NOUN
ajtas-2922	11	49	of	of	ADP
ajtas-2922	11	50	the	the	DET
ajtas-2922	11	51	theory	theory	NOUN
ajtas-2922	11	52	of	of	ADP
ajtas-2922	11	53	linear	linear	PROPN
ajtas-2922	11	54	elasticity	elasticity	NOUN
ajtas-2922	11	55	for	for	ADP
ajtas-2922	11	56	a	a	DET
ajtas-2922	11	57	homogeneous	homogeneous	ADJ
ajtas-2922	11	58	isotropic	isotropic	NOUN
ajtas-2922	11	59	material	material	NOUN
ajtas-2922	11	60	figure	figure	NOUN
ajtas-2922	11	61	1	1	NUM
ajtas-2922	11	62	.	.	PUNCT
ajtas-2922	12	1	change	change	NOUN
ajtas-2922	12	2	in	in	ADP
ajtas-2922	12	3	frequency	frequency	NOUN
ajtas-2922	12	4	depending	depend	VERB
ajtas-2922	12	5	on	on	ADP
ajtas-2922	12	6	the	the	DET
ajtas-2922	12	7	ratio	ratio	NOUN
ajtas-2922	12	8	of	of	ADP
ajtas-2922	12	9	thicknesses	thickness	NOUN
ajtas-2922	12	10	of	of	ADP
ajtas-2922	12	11	real	real	ADJ
ajtas-2922	12	12	and	and	CCONJ
ajtas-2922	12	13	abstract	abstract	ADJ
ajtas-2922	12	14	parts	part	NOUN
ajtas-2922	12	15	(	(	PUNCT
ajtas-2922	12	16	)	)	PUNCT
ajtas-2922	12	17	(	(	PUNCT
ajtas-2922	12	18	)	)	PUNCT
ajtas-2922	12	19	;	;	PUNCT
ajtas-2922	12	20	3/2	3/2	NUM
ajtas-2922	12	21	22	22	NUM
ajtas-2922	12	22	1	1	NUM
ajtas-2922	12	23	yshkagxz	yshkagxz	PROPN
ajtas-2922	12	24			PROPN
ajtas-2922	12	25	−−=	−−=	INTJ
ajtas-2922	12	26	(	(	PUNCT
ajtas-2922	12	27	)	)	PUNCT
ajtas-2922	12	28	(	(	PUNCT
ajtas-2922	12	29	)	)	PUNCT
ajtas-2922	12	30			PROPN
ajtas-2922	12	31			NOUN
ajtas-2922	12	32	;	;	PUNCT
ajtas-2922	12	33	223/2	223/2	NUM
ajtas-2922	12	34	1	1	NUM
ajtas-2922	12	35	222	222	NUM
ajtas-2922	12	36	1	1	NUM
ajtas-2922	12	37	yshckyshkgayy	yshckyshkgayy	PRON
ajtas-2922	12	38			PUNCT
ajtas-2922	12	39	−+−−=	−+−−=	PROPN
ajtas-2922	12	40	0==	0==	NUM
ajtas-2922	13	1	xxxy	xxxy	PROPN
ajtas-2922	13	2			NOUN
ajtas-2922	13	3	;	;	PUNCT
ajtas-2922	13	4	(	(	PUNCT
ajtas-2922	13	5	)	)	PUNCT
ajtas-2922	13	6	;	;	PUNCT
ajtas-2922	13	7	2	2	NUM
ajtas-2922	13	8	22	22	NUM
ajtas-2922	13	9	11	11	NUM
ajtas-2922	13	10	ychkcichxyikayz	ychkcichxyikayz	PROPN
ajtas-2922	13	11			PROPN
ajtas-2922	13	12	+	+	PROPN
ajtas-2922	13	13	+	+	ADJ
ajtas-2922	13	14	−=	−=	PUNCT
ajtas-2922	13	15	(	(	PUNCT
ajtas-2922	13	16	)	)	PUNCT
ajtas-2922	13	17	(	(	PUNCT
ajtas-2922	13	18	)	)	PUNCT
ajtas-2922	13	19			PROPN
ajtas-2922	13	20			PROPN
ajtas-2922	13	21	.223/2	.223/2	PROPN
ajtas-2922	13	22	1	1	NUM
ajtas-2922	13	23	222	222	NUM
ajtas-2922	13	24	1	1	NUM
ajtas-2922	13	25	yshckyshkgayy	yshckyshkgayy	NOUN
ajtas-2922	13	26			PUNCT
ajtas-2922	14	1	+	+	ADJ
ajtas-2922	14	2	+	+	ADJ
ajtas-2922	14	3	−+=	−+=	ADJ
ajtas-2922	14	4	expressions	expression	NOUN
ajtas-2922	14	5	for	for	ADP
ajtas-2922	14	6	moving	move	VERB
ajtas-2922	14	7	points	point	NOUN
ajtas-2922	14	8	on	on	ADP
ajtas-2922	14	9	the	the	DET
ajtas-2922	14	10	top	top	ADJ
ajtas-2922	14	11	outer	outer	ADJ
ajtas-2922	14	12	layer	layer	NOUN
ajtas-2922	14	13	that	that	PRON
ajtas-2922	14	14	satisfy	satisfy	VERB
ajtas-2922	14	15	the	the	DET
ajtas-2922	14	16	equations	equation	NOUN
ajtas-2922	14	17	of	of	ADP
ajtas-2922	14	18	motion	motion	NOUN
ajtas-2922	14	19	are	be	AUX
ajtas-2922	14	20	generally	generally	ADV
ajtas-2922	14	21	as	as	SCONJ
ajtas-2922	14	22	follows	follow	VERB
ajtas-2922	14	23	:	:	PUNCT
ajtas-2922	14	24	u=0	u=0	ADP
ajtas-2922	14	25	;	;	PUNCT
ajtas-2922	14	26	(	(	PUNCT
ajtas-2922	14	27	)	)	PUNCT
ajtas-2922	14	28	(	(	PUNCT
ajtas-2922	14	29	)	)	PUNCT
ajtas-2922	14	30			NOUN
ajtas-2922	14	31			PROPN
ajtas-2922	14	32	(	(	PUNCT
ajtas-2922	14	33	)	)	PUNCT
ajtas-2922	14	34	(	(	PUNCT
ajtas-2922	14	35	)	)	PUNCT
ajtas-2922	14	36			NOUN
ajtas-2922	14	37	hyshmhychdkhychfhyshc	hyshmhychdkhychfhyshc	ADP
ajtas-2922	14	38	ccee	ccee	NOUN
ajtas-2922	14	39	−+−+−+−−=	−+−+−+−−=	NOUN
ajtas-2922	14	40			PROPN
ajtas-2922	14	41	1111	1111	NUM
ajtas-2922	14	42	(	(	PUNCT
ajtas-2922	14	43	)	)	PUNCT
ajtas-2922	14	44	(	(	PUNCT
ajtas-2922	14	45	)	)	PUNCT
ajtas-2922	14	46			NOUN
ajtas-2922	14	47			PROPN
ajtas-2922	14	48	(	(	PUNCT
ajtas-2922	14	49	)	)	PUNCT
ajtas-2922	14	50	(	(	PUNCT
ajtas-2922	14	51	)	)	PUNCT
ajtas-2922	14	52			ADJ
ajtas-2922	14	53	hychmhyshdihyshfhychikw	hychmhyshdihyshfhychikw	NOUN
ajtas-2922	14	54	cccee	cccee	NOUN
ajtas-2922	14	55	−+−−−+−=	−+−−−+−=	PROPN
ajtas-2922	14	56			PROPN
ajtas-2922	14	57	1111	1111	NUM
ajtas-2922	14	58	here	here	ADV
ajtas-2922	14	59	,	,	PUNCT
ajtas-2922	14	60	b1	b1	NOUN
ajtas-2922	14	61	,	,	PUNCT
ajtas-2922	14	62	d1	d1	NOUN
ajtas-2922	14	63	,	,	PUNCT
ajtas-2922	14	64	f1	f1	NOUN
ajtas-2922	14	65	,	,	PUNCT
ajtas-2922	14	66	m1	m1	PROPN
ajtas-2922	14	67	are	be	AUX
ajtas-2922	14	68	constants	constant	NOUN
ajtas-2922	14	69	,	,	PUNCT
ajtas-2922	14	70	с	с	PROPN
ajtas-2922	14	71	and	and	CCONJ
ajtas-2922	14	72	the	the	DET
ajtas-2922	14	73	с	с	PROPN
ajtas-2922	14	74	parameters	parameter	NOUN
ajtas-2922	14	75	are	be	AUX
ajtas-2922	14	76	defined	define	VERB
ajtas-2922	14	77	from	from	ADP
ajtas-2922	14	78	the	the	DET
ajtas-2922	14	79	following	follow	VERB
ajtas-2922	14	80	ratios	ratio	NOUN
ajtas-2922	14	81	,	,	PUNCT
ajtas-2922	14	82	which	which	PRON
ajtas-2922	14	83	are	be	AUX
ajtas-2922	14	84	similar	similar	ADJ
ajtas-2922	14	85	:	:	PUNCT
ajtas-2922	14	86	,	,	PUNCT
ajtas-2922	14	87	;	;	PUNCT
ajtas-2922	14	88	3	3	NUM
ajtas-2922	14	89	4	4	NUM
ajtas-2922	14	90	2	2	NUM
ajtas-2922	14	91	22	22	NUM
ajtas-2922	14	92	2	2	NUM
ajtas-2922	14	93	22	22	NUM
ajtas-2922	14	94	c	c	NOUN
ajtas-2922	14	95	c	c	PROPN
ajtas-2922	14	96	c	c	PROPN
ajtas-2922	14	97	ce	ce	PROPN
ajtas-2922	14	98	c	c	PROPN
ajtas-2922	14	99	с	с	PROPN
ajtas-2922	14	100	k	k	PROPN
ajtas-2922	14	101	g	g	PROPN
ajtas-2922	14	102	k	k	PROPN
ajtas-2922	14	103			NOUN
ajtas-2922	14	104			PROPN
ajtas-2922	14	105			PROPN
ajtas-2922	14	106			NOUN
ajtas-2922	14	107			NOUN
ajtas-2922	14	108			X
ajtas-2922	14	109	−=	−=	X
ajtas-2922	14	110	+	+	X
ajtas-2922	14	111	−=	−=	VERB
ajtas-2922	14	112	here	here	ADV
ajtas-2922	14	113	,	,	PUNCT
ajtas-2922	14	114	the	the	DET
ajtas-2922	14	115	c	c	PROPN
ajtas-2922	14	116	index	index	NOUN
ajtas-2922	14	117	refers	refer	VERB
ajtas-2922	14	118	to	to	ADP
ajtas-2922	14	119	the	the	DET
ajtas-2922	14	120	characteristics	characteristic	NOUN
ajtas-2922	14	121	of	of	ADP
ajtas-2922	14	122	the	the	DET
ajtas-2922	14	123	coating	coating	NOUN
ajtas-2922	14	124	material	material	NOUN
ajtas-2922	14	125	.	.	PUNCT
ajtas-2922	15	1	(	(	PUNCT
ajtas-2922	15	2	)	)	PUNCT
ajtas-2922	15	3	hybbh	hybbh	NOUN
ajtas-2922	15	4	−+−=−	−+−=−	NOUN
ajtas-2922	15	5	2/1	2/1	NUM
ajtas-2922	15	6	using	use	VERB
ajtas-2922	15	7	the	the	DET
ajtas-2922	15	8	antisymmetry	antisymmetry	NOUN
ajtas-2922	15	9	property	property	NOUN
ajtas-2922	15	10	of	of	ADP
ajtas-2922	15	11	a	a	DET
ajtas-2922	15	12	bending	bend	VERB
ajtas-2922	15	13	wave	wave	NOUN
ajtas-2922	15	14	for	for	ADP
ajtas-2922	15	15	a	a	DET
ajtas-2922	15	16	field	field	NOUN
ajtas-2922	15	17	,	,	PUNCT
ajtas-2922	15	18	it	it	PRON
ajtas-2922	15	19	is	be	AUX
ajtas-2922	15	20	possible	possible	ADJ
ajtas-2922	15	21	to	to	PART
ajtas-2922	15	22	measure	measure	VERB
ajtas-2922	15	23	the	the	DET
ajtas-2922	15	24	following	follow	VERB
ajtas-2922	15	25	families	family	NOUN
ajtas-2922	15	26	of	of	ADP
ajtas-2922	15	27	bonds	bond	NOUN
ajtas-2922	15	28	:	:	PUNCT
ajtas-2922	15	29	(	(	PUNCT
ajtas-2922	15	30	)	)	PUNCT
ajtas-2922	15	31	(	(	PUNCT
ajtas-2922	15	32	)	)	PUNCT
ajtas-2922	15	33	(	(	PUNCT
ajtas-2922	15	34	)	)	PUNCT
ajtas-2922	15	35	(	(	PUNCT
ajtas-2922	15	36	)	)	PUNCT
ajtas-2922	15	37	(	(	PUNCT
ajtas-2922	15	38	)	)	PUNCT
ajtas-2922	15	39	(	(	PUNCT
ajtas-2922	15	40	)	)	PUNCT
ajtas-2922	15	41	ywywyyyuyu	ywywyyyuyu	PROPN
ajtas-2922	15	42	−−=−=−=	−−=−=−=	PROPN
ajtas-2922	15	43	;	;	PUNCT
ajtas-2922	15	44	;	;	PUNCT
ajtas-2922	15	45			PROPN
ajtas-2922	15	46	(	(	PUNCT
ajtas-2922	15	47	2	2	NUM
ajtas-2922	15	48	)	)	PUNCT
ajtas-2922	15	49	american	american	ADJ
ajtas-2922	15	50	journal	journal	NOUN
ajtas-2922	15	51	of	of	ADP
ajtas-2922	15	52	technology	technology	NOUN
ajtas-2922	15	53	and	and	CCONJ
ajtas-2922	15	54	applied	apply	VERB
ajtas-2922	15	55	sciences	science	NOUN
ajtas-2922	15	56	36	36	NUM
ajtas-2922	15	57	,	,	PUNCT
ajtas-2922	15	58	may	may	AUX
ajtas-2922	15	59	2025	2025	NUM
ajtas-2922	15	60	p	p	NOUN
ajtas-2922	15	61	a	a	DET
ajtas-2922	15	62	g	g	NOUN
ajtas-2922	15	63	e	e	NOUN
ajtas-2922	15	64	|	|	ADV
ajtas-2922	15	65	15	15	NUM
ajtas-2922	15	66	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-2922	15	67	taking	take	VERB
ajtas-2922	15	68	into	into	ADP
ajtas-2922	15	69	account	account	NOUN
ajtas-2922	15	70	the	the	DET
ajtas-2922	15	71	properties	property	NOUN
ajtas-2922	15	72	of	of	ADP
ajtas-2922	15	73	solution	solution	NOUN
ajtas-2922	15	74	(	(	PUNCT
ajtas-2922	15	75	2	2	NUM
ajtas-2922	15	76	)	)	PUNCT
ajtas-2922	15	77	,	,	PUNCT
ajtas-2922	15	78	we	we	PRON
ajtas-2922	15	79	will	will	AUX
ajtas-2922	15	80	limit	limit	VERB
ajtas-2922	15	81	ourselves	ourselves	PRON
ajtas-2922	15	82	to	to	ADP
ajtas-2922	15	83	considering	consider	VERB
ajtas-2922	15	84	the	the	DET
ajtas-2922	15	85	region	region	NOUN
ajtas-2922	15	86	below	below	ADP
ajtas-2922	15	87	ну	ну	PROPN
ajtas-2922	15	88	0	0	PROPN
ajtas-2922	15	89	.	.	PUNCT
ajtas-2922	16	1	the	the	DET
ajtas-2922	16	2	following	follow	VERB
ajtas-2922	16	3	boundary	boundary	ADJ
ajtas-2922	16	4	conditions	condition	NOUN
ajtas-2922	16	5	must	must	AUX
ajtas-2922	16	6	be	be	AUX
ajtas-2922	16	7	met	meet	VERB
ajtas-2922	16	8	on	on	ADP
ajtas-2922	16	9	a	a	DET
ajtas-2922	16	10	free	free	ADJ
ajtas-2922	16	11	surface	surface	NOUN
ajtas-2922	16	12	y	y	PROPN
ajtas-2922	16	13	=	=	ADJ
ajtas-2922	16	14	h	h	NOUN
ajtas-2922	16	15	:	:	PUNCT
ajtas-2922	16	16	0===	0===	NOUN
ajtas-2922	16	17	yzyyxy	yzyyxy	NOUN
ajtas-2922	16	18			PROPN
ajtas-2922	16	19	in	in	ADP
ajtas-2922	16	20	addition	addition	NOUN
ajtas-2922	16	21	,	,	PUNCT
ajtas-2922	16	22	the	the	DET
ajtas-2922	16	23	condition	condition	NOUN
ajtas-2922	16	24	of	of	ADP
ajtas-2922	16	25	continuity	continuity	NOUN
ajtas-2922	16	26	of	of	ADP
ajtas-2922	16	27	displacements	displacement	NOUN
ajtas-2922	16	28	on	on	ADP
ajtas-2922	16	29	the	the	DET
ajtas-2922	16	30	contact	contact	NOUN
ajtas-2922	16	31	surface	surface	NOUN
ajtas-2922	16	32	is	be	AUX
ajtas-2922	16	33	y	y	PROPN
ajtas-2922	16	34	=	=	SYM
ajtas-2922	16	35	b	b	PROPN
ajtas-2922	16	36	(	(	PUNCT
ajtas-2922	16	37	)	)	PUNCT
ajtas-2922	16	38	(	(	PUNCT
ajtas-2922	16	39	)	)	PUNCT
ajtas-2922	16	40	(	(	PUNCT
ajtas-2922	16	41	)	)	PUNCT
ajtas-2922	16	42	(	(	PUNCT
ajtas-2922	16	43	)	)	PUNCT
ajtas-2922	16	44	(	(	PUNCT
ajtas-2922	16	45	)	)	PUNCT
ajtas-2922	16	46	(	(	PUNCT
ajtas-2922	16	47	)	)	PUNCT
ajtas-2922	17	1	+	+	NOUN
ajtas-2922	17	2	−+−+−	−+−+−	NOUN
ajtas-2922	17	3	=	=	NOUN
ajtas-2922	17	4	=	=	SYM
ajtas-2922	17	5	=	=	X
ajtas-2922	17	6	bwbwbbbubu	bwbwbbbubu	ADV
ajtas-2922	17	7	,	,	PUNCT
ajtas-2922	17	8	;	;	PUNCT
ajtas-2922	17	9			PROPN
ajtas-2922	17	10	(	(	PUNCT
ajtas-2922	17	11	3	3	NUM
ajtas-2922	17	12	)	)	PUNCT
ajtas-2922	17	13	and	and	CCONJ
ajtas-2922	17	14	the	the	DET
ajtas-2922	17	15	condition	condition	NOUN
ajtas-2922	17	16	of	of	ADP
ajtas-2922	17	17	equality	equality	NOUN
ajtas-2922	17	18	:	:	PUNCT
ajtas-2922	17	19	(	(	PUNCT
ajtas-2922	17	20	)	)	PUNCT
ajtas-2922	17	21	(	(	PUNCT
ajtas-2922	17	22	)	)	PUNCT
ajtas-2922	17	23	(	(	PUNCT
ajtas-2922	17	24	)	)	PUNCT
ajtas-2922	17	25	(	(	PUNCT
ajtas-2922	17	26	)	)	PUNCT
ajtas-2922	17	27	(	(	PUNCT
ajtas-2922	17	28	)	)	PUNCT
ajtas-2922	17	29	(	(	PUNCT
ajtas-2922	17	30	)	)	PUNCT
ajtas-2922	18	1	+	+	NOUN
ajtas-2922	18	2	−+−+−	−+−+−	NOUN
ajtas-2922	18	3	=	=	NOUN
ajtas-2922	18	4	=	=	SYM
ajtas-2922	18	5	=	=	NOUN
ajtas-2922	18	6	bbbbbb	bbbbbb	NOUN
ajtas-2922	18	7	yzyzxyyyyyxy	yzyzxyyyyyxy	NOUN
ajtas-2922	18	8			X
ajtas-2922	18	9	;	;	PUNCT
ajtas-2922	18	10	;	;	PUNCT
ajtas-2922	18	11	where	where	SCONJ
ajtas-2922	18	12	(	(	PUNCT
ajtas-2922	18	13	b	b	NOUN
ajtas-2922	18	14	=	=	NOUN
ajtas-2922	18	15	b/2	b/2	NOUN
ajtas-2922	18	16	)	)	PUNCT
ajtas-2922	18	17	must	must	AUX
ajtas-2922	18	18	be	be	AUX
ajtas-2922	18	19	satisfied	satisfied	ADJ
ajtas-2922	18	20	.	.	PUNCT
ajtas-2922	19	1	based	base	VERB
ajtas-2922	19	2	on	on	ADP
ajtas-2922	19	3	conditions	condition	NOUN
ajtas-2922	19	4	(	(	PUNCT
ajtas-2922	19	5	1	1	NUM
ajtas-2922	19	6	)	)	PUNCT
ajtas-2922	19	7	,	,	PUNCT
ajtas-2922	19	8	(	(	PUNCT
ajtas-2922	19	9	2	2	NUM
ajtas-2922	19	10	)	)	PUNCT
ajtas-2922	19	11	,	,	PUNCT
ajtas-2922	19	12	(	(	PUNCT
ajtas-2922	19	13	3	3	X
ajtas-2922	19	14	)	)	PUNCT
ajtas-2922	19	15	and	and	CCONJ
ajtas-2922	19	16	symmetry	symmetry	NOUN
ajtas-2922	19	17	conditions	condition	NOUN
ajtas-2922	19	18	,	,	PUNCT
ajtas-2922	19	19	we	we	PRON
ajtas-2922	19	20	construct	construct	VERB
ajtas-2922	19	21	a	a	DET
ajtas-2922	19	22	system	system	NOUN
ajtas-2922	19	23	of	of	ADP
ajtas-2922	19	24	six	six	NUM
ajtas-2922	19	25	homogeneous	homogeneous	ADJ
ajtas-2922	19	26	linear	linear	ADJ
ajtas-2922	19	27	algebraic	algebraic	ADJ
ajtas-2922	19	28	equations	equation	NOUN
ajtas-2922	19	29	with	with	ADP
ajtas-2922	19	30	respect	respect	NOUN
ajtas-2922	19	31	to	to	ADP
ajtas-2922	19	32	six	six	NUM
ajtas-2922	19	33	invariants	invariant	NOUN
ajtas-2922	19	34	(	(	PUNCT
ajtas-2922	19	35	a1	a1	NOUN
ajtas-2922	19	36	,	,	PUNCT
ajtas-2922	19	37	b1	b1	NOUN
ajtas-2922	19	38	,	,	PUNCT
ajtas-2922	19	39	c1	c1	NOUN
ajtas-2922	19	40	,	,	PUNCT
ajtas-2922	19	41	d1	d1	PROPN
ajtas-2922	19	42	,	,	PUNCT
ajtas-2922	19	43	f1	f1	NOUN
ajtas-2922	19	44	,	,	PUNCT
ajtas-2922	19	45	and	and	CCONJ
ajtas-2922	19	46	m1	m1	NOUN
ajtas-2922	19	47	)	)	PUNCT
ajtas-2922	19	48	.	.	PUNCT
ajtas-2922	20	1	the	the	DET
ajtas-2922	20	2	first	first	ADJ
ajtas-2922	20	3	of	of	ADP
ajtas-2922	20	4	these	these	DET
ajtas-2922	20	5	constants	constant	NOUN
ajtas-2922	20	6	determines	determine	VERB
ajtas-2922	20	7	the	the	DET
ajtas-2922	20	8	deformation	deformation	NOUN
ajtas-2922	20	9	state	state	NOUN
ajtas-2922	20	10	of	of	ADP
ajtas-2922	20	11	the	the	DET
ajtas-2922	20	12	base	base	NOUN
ajtas-2922	20	13	layer	layer	NOUN
ajtas-2922	20	14	,	,	PUNCT
ajtas-2922	20	15	the	the	DET
ajtas-2922	20	16	other	other	ADJ
ajtas-2922	20	17	four	four	NUM
ajtas-2922	20	18	determine	determine	NOUN
ajtas-2922	20	19	the	the	DET
ajtas-2922	20	20	deformation	deformation	NOUN
ajtas-2922	20	21	state	state	NOUN
ajtas-2922	20	22	of	of	ADP
ajtas-2922	20	23	the	the	DET
ajtas-2922	20	24	top	top	ADJ
ajtas-2922	20	25	layer	layer	NOUN
ajtas-2922	20	26	of	of	ADP
ajtas-2922	20	27	the	the	DET
ajtas-2922	20	28	coating	coating	NOUN
ajtas-2922	20	29	:	:	PUNCT
ajtas-2922	20	30			ADJ
ajtas-2922	20	31			NOUN
ajtas-2922	20	32			PROPN
ajtas-2922	20	33			PROPN
ajtas-2922	20	34	0	0	NOUN
ajtas-2922	20	35	=	=	NOUN
ajtas-2922	20	36	qс	qс	ADP
ajtas-2922	20	37	.	.	PUNCT
ajtas-2922	21	1	in	in	ADP
ajtas-2922	21	2	order	order	NOUN
ajtas-2922	21	3	for	for	SCONJ
ajtas-2922	21	4	a	a	DET
ajtas-2922	21	5	system	system	NOUN
ajtas-2922	21	6	of	of	ADP
ajtas-2922	21	7	equations	equation	NOUN
ajtas-2922	21	8	to	to	PART
ajtas-2922	21	9	have	have	VERB
ajtas-2922	21	10	non	non	ADJ
ajtas-2922	21	11	-	-	ADJ
ajtas-2922	21	12	trivial	trivial	ADJ
ajtas-2922	21	13	solutions	solution	NOUN
ajtas-2922	21	14	,	,	PUNCT
ajtas-2922	21	15	the	the	DET
ajtas-2922	21	16	determinant	determinant	NOUN
ajtas-2922	21	17	of	of	ADP
ajtas-2922	21	18	the	the	DET
ajtas-2922	21	19	matrix	matrix	NOUN
ajtas-2922	21	20	formed	form	VERB
ajtas-2922	21	21	from	from	ADP
ajtas-2922	21	22	the	the	DET
ajtas-2922	21	23	coefficients	coefficient	NOUN
ajtas-2922	21	24	of	of	ADP
ajtas-2922	21	25	the	the	DET
ajtas-2922	21	26	system	system	NOUN
ajtas-2922	21	27	must	must	AUX
ajtas-2922	21	28	be	be	AUX
ajtas-2922	21	29	equal	equal	ADJ
ajtas-2922	21	30	to	to	ADP
ajtas-2922	21	31	zero	zero	NUM
ajtas-2922	21	32	:	:	PUNCT
ajtas-2922	21	33	f(	f(	NOUN
ajtas-2922	21	34	)	)	PUNCT
ajtas-2922	21	35	=	=	NOUN
ajtas-2922	21	36			NOUN
ajtas-2922	21	37			NOUN
ajtas-2922	21	38	0	0	NUM
ajtas-2922	21	39	=	=	SYM
ajtas-2922	21	40	с	с	PROPN
ajtas-2922	21	41	(	(	PUNCT
ajtas-2922	21	42	4	4	NUM
ajtas-2922	21	43	)	)	PUNCT
ajtas-2922	21	44	in	in	ADP
ajtas-2922	21	45	here	here	ADV
ajtas-2922	21	46	(	(	PUNCT
ajtas-2922	21	47	)	)	PUNCT
ajtas-2922	21	48	(	(	PUNCT
ajtas-2922	21	49	)	)	PUNCT
ajtas-2922	21	50	(	(	PUNCT
ajtas-2922	21	51	)	)	PUNCT
ajtas-2922	21	52	;	;	PUNCT
ajtas-2922	21	53	;	;	PUNCT
ajtas-2922	21	54	;	;	PUNCT
ajtas-2922	21	55	;	;	PUNCT
ajtas-2922	21	56	;	;	PUNCT
ajtas-2922	21	57	1514	1514	NUM
ajtas-2922	21	58	131211	131211	NUM
ajtas-2922	21	59	hbkchchbchc	hbkchchbchc	NOUN
ajtas-2922	21	60	hbshckkchckсhс	hbshckkchckсhс	NOUN
ajtas-2922	21	61	ccc	ccc	PROPN
ajtas-2922	21	62	cc	cc	ADP
ajtas-2922	21	63	−=−=	−=−=	PROPN
ajtas-2922	21	64	−=−==	−=−==	PROPN
ajtas-2922	21	65			PROPN
ajtas-2922	21	66			X
ajtas-2922	21	67	(	(	PUNCT
ajtas-2922	21	68	)	)	PUNCT
ajtas-2922	21	69	hshcbkshchbkshc	hshcbkshchbkshc	PROPN
ajtas-2922	21	70			NOUN
ajtas-2922	21	71	=	=	SYM
ajtas-2922	21	72	−=−−=	−=−−=	NOUN
ajtas-2922	21	73	222116	222116	NUM
ajtas-2922	21	74	;	;	PUNCT
ajtas-2922	21	75	;	;	PUNCT
ajtas-2922	21	76	(	(	PUNCT
ajtas-2922	21	77	)	)	PUNCT
ajtas-2922	21	78	(	(	PUNCT
ajtas-2922	21	79	)	)	PUNCT
ajtas-2922	21	80	(	(	PUNCT
ajtas-2922	21	81	)	)	PUNCT
ajtas-2922	21	82	(	(	PUNCT
ajtas-2922	21	83	)	)	PUNCT
ajtas-2922	21	84	bshkcbshc	bshkcbshc	PROPN
ajtas-2922	21	85	hbshchbshc	hbshchbshc	PROPN
ajtas-2922	21	86	hbkchchbkchc	hbkchchbkchc	PROPN
ajtas-2922	21	87	ccc	ccc	PROPN
ajtas-2922	21	88	cc	cc	PROPN
ajtas-2922	21	89			PROPN
ajtas-2922	21	90			ADJ
ajtas-2922	21	91			ADP
ajtas-2922	21	92	2	2	NUM
ajtas-2922	21	93	;	;	PUNCT
ajtas-2922	21	94	;	;	PUNCT
ajtas-2922	21	95	;	;	PUNCT
ajtas-2922	21	96	;	;	PUNCT
ajtas-2922	21	97	;	;	PUNCT
ajtas-2922	21	98	32131	32131	NUM
ajtas-2922	21	99	2625	2625	NUM
ajtas-2922	21	100	2423	2423	NUM
ajtas-2922	21	101	−==	−==	ADJ
ajtas-2922	21	102	−=−=	−=−=	NUM
ajtas-2922	21	103	−−=−−=	−−=−−=	PROPN
ajtas-2922	21	104	(	(	PUNCT
ajtas-2922	21	105	)	)	PUNCT
ajtas-2922	21	106	(	(	PUNCT
ajtas-2922	21	107	)	)	PUNCT
ajtas-2922	21	108	(	(	PUNCT
ajtas-2922	21	109	)	)	PUNCT
ajtas-2922	21	110	(	(	PUNCT
ajtas-2922	21	111	)	)	PUNCT
ajtas-2922	21	112	;	;	PUNCT
ajtas-2922	21	113	;	;	PUNCT
ajtas-2922	21	114	2	2	NUM
ajtas-2922	21	115	;	;	PUNCT
ajtas-2922	21	116	2;2	2;2	NUM
ajtas-2922	21	117	;	;	PUNCT
ajtas-2922	21	118	;	;	PUNCT
ajtas-2922	21	119	34241	34241	NUM
ajtas-2922	21	120	3535	3535	NUM
ajtas-2922	21	121	234233	234233	NUM
ajtas-2922	21	122	hchchchkc	hchchchkc	NOUN
ajtas-2922	21	123	hbchkchbshkc	hbchkchbshkc	NOUN
ajtas-2922	21	124	hbchchbсhс	hbchchbсhс	PROPN
ajtas-2922	21	125	cccccc	cccccc	PROPN
ajtas-2922	21	126	cc	cc	PROPN
ajtas-2922	21	127			PROPN
ajtas-2922	21	128			X
ajtas-2922	21	129			X
ajtas-2922	21	130	=	=	PUNCT
ajtas-2922	21	131	−=	−=	PART
ajtas-2922	21	132	−=−=	−=−=	PROPN
ajtas-2922	21	133	−−=−−=	−−=−−=	NOUN
ajtas-2922	21	134	(	(	PUNCT
ajtas-2922	21	135	)	)	PUNCT
ajtas-2922	21	136	(	(	PUNCT
ajtas-2922	21	137	)	)	PUNCT
ajtas-2922	21	138	(	(	PUNCT
ajtas-2922	21	139	)	)	PUNCT
ajtas-2922	21	140	(	(	PUNCT
ajtas-2922	21	141	)	)	PUNCT
ajtas-2922	21	142	;	;	PUNCT
ajtas-2922	21	143	;	;	PUNCT
ajtas-2922	21	144	;	;	PUNCT
ajtas-2922	21	145	2;2	2;2	NUM
ajtas-2922	21	146	146145	146145	NUM
ajtas-2922	21	147	4443	4443	NUM
ajtas-2922	21	148	hbshchbchc	hbshchbchc	NOUN
ajtas-2922	21	149	hbchkchbshkc	hbchkchbshkc	NOUN
ajtas-2922	21	150	cccc	cccc	PROPN
ajtas-2922	21	151	cccccc	cccccc	PROPN
ajtas-2922	21	152	−=−=	−=−=	PROPN
ajtas-2922	21	153	−−=−−=	−−=−−=	PROPN
ajtas-2922	21	154			PROPN
ajtas-2922	21	155			PROPN
ajtas-2922	21	156	;	;	PUNCT
ajtas-2922	21	157	;	;	PUNCT
ajtas-2922	21	158	2;0	2;0	NUM
ajtas-2922	21	159	;	;	PUNCT
ajtas-2922	21	160	2;;0	2;;0	NUM
ajtas-2922	21	161	656466636261	656466636261	NUM
ajtas-2922	21	162	5635355545251	5635355545251	NUM
ajtas-2922	21	163	cccc	cccc	PROPN
ajtas-2922	21	164	cc	cc	PROPN
ajtas-2922	21	165	сkcсссс	сkcсссс	PROPN
ajtas-2922	21	166	kcccccc	kcccccc	PROPN
ajtas-2922	21	167			ADP
ajtas-2922	21	168			NOUN
ajtas-2922	21	169	=	=	SYM
ajtas-2922	21	170	−=====	−=====	NOUN
ajtas-2922	21	171	−=−=====	−=−=====	NOUN
ajtas-2922	21	172	in	in	ADP
ajtas-2922	21	173	here	here	ADV
ajtas-2922	21	174	american	american	PROPN
ajtas-2922	21	175	journal	journal	PROPN
ajtas-2922	21	176	of	of	ADP
ajtas-2922	21	177	technology	technology	NOUN
ajtas-2922	21	178	and	and	CCONJ
ajtas-2922	21	179	applied	apply	VERB
ajtas-2922	21	180	sciences	science	NOUN
ajtas-2922	21	181	36	36	NUM
ajtas-2922	21	182	,	,	PUNCT
ajtas-2922	21	183	may	may	AUX
ajtas-2922	21	184	2025	2025	NUM
ajtas-2922	21	185	p	p	NOUN
ajtas-2922	21	186	a	a	DET
ajtas-2922	21	187	g	g	NOUN
ajtas-2922	21	188	e	e	NOUN
ajtas-2922	22	1	|	|	ADV
ajtas-2922	22	2	16	16	NUM
ajtas-2922	22	3	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-2922	22	4	(	(	PUNCT
ajtas-2922	22	5	)	)	PUNCT
ajtas-2922	22	6	(	(	PUNCT
ajtas-2922	22	7	)	)	PUNCT
ajtas-2922	22	8	(	(	PUNCT
ajtas-2922	22	9	)	)	PUNCT
ajtas-2922	22	10	(	(	PUNCT
ajtas-2922	22	11	)	)	PUNCT
ajtas-2922	22	12	.;2	.;2	PUNCT
ajtas-2922	22	13	3	3	NUM
ajtas-2922	22	14	2	2	NUM
ajtas-2922	22	15	;	;	PUNCT
ajtas-2922	22	16	;	;	PUNCT
ajtas-2922	22	17	3	3	NUM
ajtas-2922	22	18	2	2	NUM
ajtas-2922	22	19	22	22	NUM
ajtas-2922	22	20	4	4	NUM
ajtas-2922	22	21	2222	2222	NUM
ajtas-2922	22	22	3	3	NUM
ajtas-2922	22	23	22	22	NUM
ajtas-2922	22	24	2	2	NUM
ajtas-2922	22	25	2222	2222	NUM
ajtas-2922	22	26	1	1	NUM
ajtas-2922	22	27	cccc	cccc	NOUN
ajtas-2922	22	28	kkkg	kkkg	NOUN
ajtas-2922	22	29	kkkg	kkkg	NOUN
ajtas-2922	22	30			PUNCT
ajtas-2922	22	31			NOUN
ajtas-2922	22	32	+	+	NOUN
ajtas-2922	22	33	=	=	ADJ
ajtas-2922	22	34	+	+	ADJ
ajtas-2922	22	35	−−=	−−=	NOUN
ajtas-2922	22	36	+	+	ADJ
ajtas-2922	22	37	=	=	ADJ
ajtas-2922	22	38	+	+	ADJ
ajtas-2922	22	39	−−=	−−=	PROPN
ajtas-2922	22	40	transcendental	transcendental	ADJ
ajtas-2922	22	41	equation	equation	NOUN
ajtas-2922	22	42	(	(	PUNCT
ajtas-2922	22	43	4	4	X
ajtas-2922	22	44	)	)	PUNCT
ajtas-2922	22	45	is	be	AUX
ajtas-2922	22	46	solved	solve	VERB
ajtas-2922	22	47	numerically	numerically	ADV
ajtas-2922	22	48	using	use	VERB
ajtas-2922	22	49	the	the	DET
ajtas-2922	22	50	müller	müller	PROPN
ajtas-2922	22	51	method	method	NOUN
ajtas-2922	22	52	.	.	PUNCT
ajtas-2922	23	1	three	three	NUM
ajtas-2922	23	2	methods	method	NOUN
ajtas-2922	23	3	can	can	AUX
ajtas-2922	23	4	be	be	AUX
ajtas-2922	23	5	used	use	VERB
ajtas-2922	23	6	to	to	PART
ajtas-2922	23	7	solve	solve	VERB
ajtas-2922	23	8	the	the	DET
ajtas-2922	23	9	frequency	frequency	ADJ
ajtas-2922	23	10	transcendental	transcendental	ADJ
ajtas-2922	23	11	equation	equation	NOUN
ajtas-2922	23	12	(	(	PUNCT
ajtas-2922	23	13	4	4	NUM
ajtas-2922	23	14	):	):	PUNCT
ajtas-2922	23	15	figure	figure	NOUN
ajtas-2922	23	16	2	2	NUM
ajtas-2922	23	17	.	.	PUNCT
ajtas-2922	23	18	frequency	frequency	NOUN
ajtas-2922	23	19	change	change	NOUN
ajtas-2922	23	20	depending	depend	VERB
ajtas-2922	23	21	on	on	ADP
ajtas-2922	23	22	the	the	DET
ajtas-2922	23	23	ratio	ratio	NOUN
ajtas-2922	23	24	of	of	ADP
ajtas-2922	23	25	thickness	thickness	NOUN
ajtas-2922	23	26	of	of	ADP
ajtas-2922	23	27	abstract	abstract	ADJ
ajtas-2922	23	28	parts	part	NOUN
ajtas-2922	23	29	a	a	NOUN
ajtas-2922	23	30	)	)	PUNCT
ajtas-2922	23	31	the	the	DET
ajtas-2922	23	32	solution	solution	NOUN
ajtas-2922	23	33	of	of	ADP
ajtas-2922	23	34	a	a	DET
ajtas-2922	23	35	system	system	NOUN
ajtas-2922	23	36	of	of	ADP
ajtas-2922	23	37	two	two	NUM
ajtas-2922	23	38	transcendental	transcendental	ADJ
ajtas-2922	23	39	equations	equation	NOUN
ajtas-2922	23	40	;	;	PUNCT
ajtas-2922	23	41	b	b	X
ajtas-2922	23	42	)	)	PUNCT
ajtas-2922	23	43	direct	direct	ADJ
ajtas-2922	23	44	complex	complex	ADJ
ajtas-2922	23	45	roots	root	NOUN
ajtas-2922	23	46	using	use	VERB
ajtas-2922	23	47	numerical	numerical	ADJ
ajtas-2922	23	48	methods	method	NOUN
ajtas-2922	23	49	(	(	PUNCT
ajtas-2922	23	50	müller	müller	PROPN
ajtas-2922	23	51	's	's	PART
ajtas-2922	23	52	method	method	NOUN
ajtas-2922	23	53	,	,	PUNCT
ajtas-2922	23	54	newton	newton	PROPN
ajtas-2922	23	55	's	's	PART
ajtas-2922	23	56	method	method	NOUN
ajtas-2922	23	57	and	and	CCONJ
ajtas-2922	23	58	other	other	ADJ
ajtas-2922	23	59	methods	method	NOUN
ajtas-2922	23	60	)	)	PUNCT
ajtas-2922	23	61	;	;	PUNCT
ajtas-2922	23	62	c	c	X
ajtas-2922	23	63	)	)	PUNCT
ajtas-2922	23	64	approximate	approximate	ADJ
ajtas-2922	23	65	solution	solution	NOUN
ajtas-2922	23	66	of	of	ADP
ajtas-2922	23	67	the	the	DET
ajtas-2922	23	68	frequency	frequency	NOUN
ajtas-2922	23	69	equation	equation	NOUN
ajtas-2922	23	70	by	by	ADP
ajtas-2922	23	71	the	the	DET
ajtas-2922	23	72	method	method	NOUN
ajtas-2922	23	73	of	of	ADP
ajtas-2922	23	74	small	small	ADJ
ajtas-2922	23	75	parameters	parameter	NOUN
ajtas-2922	23	76	.	.	PUNCT
ajtas-2922	24	1	if	if	SCONJ
ajtas-2922	24	2	f(	f(	PROPN
ajtas-2922	24	3	)	)	PUNCT
ajtas-2922	24	4	is	be	AUX
ajtas-2922	24	5	the	the	DET
ajtas-2922	24	6	value	value	NOUN
ajtas-2922	24	7	of	of	ADP
ajtas-2922	24	8	the	the	DET
ajtas-2922	24	9	determinant	determinant	NOUN
ajtas-2922	24	10	of	of	ADP
ajtas-2922	24	11	equation	equation	NOUN
ajtas-2922	24	12	(	(	PUNCT
ajtas-2922	24	13	4	4	NUM
ajtas-2922	24	14	)	)	PUNCT
ajtas-2922	24	15	,	,	PUNCT
ajtas-2922	24	16	then	then	ADV
ajtas-2922	24	17	equation	equation	NOUN
ajtas-2922	24	18	(	(	PUNCT
ajtas-2922	24	19	4	4	X
ajtas-2922	24	20	)	)	PUNCT
ajtas-2922	24	21	can	can	AUX
ajtas-2922	24	22	be	be	AUX
ajtas-2922	24	23	divided	divide	VERB
ajtas-2922	24	24	into	into	ADP
ajtas-2922	24	25	two	two	NUM
ajtas-2922	24	26	with	with	ADP
ajtas-2922	24	27	extreme	extreme	ADJ
ajtas-2922	24	28	caution	caution	NOUN
ajtas-2922	24	29	in	in	ADP
ajtas-2922	24	30	interpreting	interpret	VERB
ajtas-2922	24	31	the	the	DET
ajtas-2922	24	32	results	result	NOUN
ajtas-2922	24	33	.	.	PUNCT
ajtas-2922	25	1	figure	figure	VERB
ajtas-2922	25	2	3	3	NUM
ajtas-2922	25	3	.	.	PUNCT
ajtas-2922	25	4	change	change	NOUN
ajtas-2922	25	5	in	in	ADP
ajtas-2922	25	6	natural	natural	ADJ
ajtas-2922	25	7	frequency	frequency	NOUN
ajtas-2922	25	8	(	(	PUNCT
ajtas-2922	25	9	r	r	NOUN
ajtas-2922	25	10	)	)	PUNCT
ajtas-2922	25	11	and	and	CCONJ
ajtas-2922	25	12	attenuation	attenuation	NOUN
ajtas-2922	25	13	coefficient	coefficient	NOUN
ajtas-2922	25	14	as	as	ADP
ajtas-2922	25	15	a	a	DET
ajtas-2922	25	16	function	function	NOUN
ajtas-2922	25	17	of	of	ADP
ajtas-2922	25	18	wavelength	wavelength	NOUN
ajtas-2922	25	19	american	american	PROPN
ajtas-2922	25	20	journal	journal	PROPN
ajtas-2922	25	21	of	of	ADP
ajtas-2922	25	22	technology	technology	NOUN
ajtas-2922	25	23	and	and	CCONJ
ajtas-2922	25	24	applied	apply	VERB
ajtas-2922	25	25	sciences	science	NOUN
ajtas-2922	25	26	36	36	NUM
ajtas-2922	25	27	,	,	PUNCT
ajtas-2922	25	28	may	may	AUX
ajtas-2922	25	29	2025	2025	NUM
ajtas-2922	25	30	p	p	NOUN
ajtas-2922	25	31	a	a	DET
ajtas-2922	25	32	g	g	NOUN
ajtas-2922	25	33	e	e	NOUN
ajtas-2922	25	34	|	|	ADV
ajtas-2922	25	35	17	17	NUM
ajtas-2922	25	36	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-2922	25	37	the	the	DET
ajtas-2922	25	38	frequency	frequency	NOUN
ajtas-2922	25	39	equation	equation	NOUN
ajtas-2922	25	40	(	(	PUNCT
ajtas-2922	25	41	4	4	X
ajtas-2922	25	42	)	)	PUNCT
ajtas-2922	25	43	is	be	AUX
ajtas-2922	25	44	solved	solve	VERB
ajtas-2922	25	45	by	by	ADP
ajtas-2922	25	46	the	the	DET
ajtas-2922	25	47	müller	müller	PROPN
ajtas-2922	25	48	method	method	NOUN
ajtas-2922	25	49	.	.	PUNCT
ajtas-2922	26	1	in	in	ADP
ajtas-2922	26	2	all	all	DET
ajtas-2922	26	3	cases	case	NOUN
ajtas-2922	26	4	,	,	PUNCT
ajtas-2922	26	5	the	the	DET
ajtas-2922	26	6	poisson	poisson	NOUN
ajtas-2922	26	7	's	's	PART
ajtas-2922	26	8	ratio	ratio	NOUN
ajtas-2922	26	9	is	be	AUX
ajtas-2922	26	10	assumed	assume	VERB
ajtas-2922	26	11	to	to	PART
ajtas-2922	26	12	be	be	AUX
ajtas-2922	26	13	0.30	0.30	NUM
ajtas-2922	26	14	and	and	CCONJ
ajtas-2922	26	15	0.25	0.25	NUM
ajtas-2922	26	16	for	for	ADP
ajtas-2922	26	17	the	the	DET
ajtas-2922	26	18	middle	middle	ADJ
ajtas-2922	26	19	layer	layer	NOUN
ajtas-2922	26	20	and	and	CCONJ
ajtas-2922	26	21	the	the	DET
ajtas-2922	26	22	cover	cover	NOUN
ajtas-2922	26	23	layer	layer	NOUN
ajtas-2922	26	24	,	,	PUNCT
ajtas-2922	26	25	respectively	respectively	ADV
ajtas-2922	26	26	;	;	PUNCT
ajtas-2922	26	27	cpc	cpc	PROPN
ajtas-2922	26	28	=	=	SYM
ajtas-2922	26	29	5400	5400	NUM
ajtas-2922	26	30	m	m	PROPN
ajtas-2922	26	31	/	/	SYM
ajtas-2922	26	32	s	s	PROPN
ajtas-2922	26	33	;	;	PUNCT
ajtas-2922	26	34	sc	sc	PROPN
ajtas-2922	26	35	=	=	PROPN
ajtas-2922	26	36	3195	3195	NUM
ajtas-2922	26	37	m	m	PROPN
ajtas-2922	26	38	/	/	SYM
ajtas-2922	26	39	s	s	PROPN
ajtas-2922	26	40	;	;	PUNCT
ajtas-2922	26	41	clpk	clpk	NOUN
ajtas-2922	26	42	=	=	SYM
ajtas-2922	26	43	2300	2300	NUM
ajtas-2922	26	44	m	m	PROPN
ajtas-2922	26	45	/	/	SYM
ajtas-2922	26	46	s	s	PROPN
ajtas-2922	26	47	;	;	PUNCT
ajtas-2922	26	48	сspk	сspk	NOUN
ajtas-2922	26	49	=	=	SYM
ajtas-2922	26	50	2300	2300	NUM
ajtas-2922	26	51	m	m	PROPN
ajtas-2922	26	52	/	/	SYM
ajtas-2922	26	53	s	s	PROPN
ajtas-2922	26	54	;	;	PUNCT
ajtas-2922	26	55	h	h	X
ajtas-2922	26	56	/	/	SYM
ajtas-2922	26	57	b	b	NOUN
ajtas-2922	26	58	=	=	SYM
ajtas-2922	26	59	0.1	0.1	NUM
ajtas-2922	26	60	,	,	PUNCT
ajtas-2922	26	61	4452.0==	4452.0==	PUNCT
ajtas-2922	27	1	с	с	NOUN
ajtas-2922	27	2	рк	рк	VERB
ajtas-2922	27	3	ср	ср	X
ajtas-2922	27	4			ADP
ajtas-2922	27	5			ADP
ajtas-2922	27	6			X
ajtas-2922	27	7	(	(	PUNCT
ajtas-2922	27	8	ratio	ratio	NOUN
ajtas-2922	27	9	of	of	ADP
ajtas-2922	27	10	coating	coat	VERB
ajtas-2922	27	11	to	to	ADP
ajtas-2922	27	12	middle	middle	ADJ
ajtas-2922	27	13	layer	layer	NOUN
ajtas-2922	27	14	)	)	PUNCT
ajtas-2922	27	15	.	.	PUNCT
ajtas-2922	28	1	rheological	rheological	ADJ
ajtas-2922	28	2	properties	property	NOUN
ajtas-2922	28	3	of	of	ADP
ajtas-2922	28	4	the	the	DET
ajtas-2922	28	5	coating	coating	NOUN
ajtas-2922	28	6	0,048	0,048	NUM
ajtas-2922	28	7	;	;	PUNCT
ajtas-2922	28	8	0,05	0,05	NUM
ajtas-2922	28	9	;	;	PUNCT
ajtas-2922	29	1	0,1.a	0,1.a	PROPN
ajtas-2922	29	2	b	b	NOUN
ajtas-2922	29	3	a=	a=	NOUN
ajtas-2922	29	4	=	=	PUNCT
ajtas-2922	30	1	=	=	PUNCT
ajtas-2922	30	2	the	the	DET
ajtas-2922	30	3	values	value	NOUN
ajtas-2922	30	4	given	give	VERB
ajtas-2922	30	5	are	be	AUX
ajtas-2922	30	6	valid	valid	ADJ
ajtas-2922	30	7	for	for	ADP
ajtas-2922	30	8	the	the	DET
ajtas-2922	30	9	middle	middle	ADJ
ajtas-2922	30	10	layer	layer	NOUN
ajtas-2922	30	11	of	of	ADP
ajtas-2922	30	12	duralumin	duralumin	PROPN
ajtas-2922	30	13	and	and	CCONJ
ajtas-2922	30	14	for	for	ADP
ajtas-2922	30	15	the	the	DET
ajtas-2922	30	16	acrylic	acrylic	NOUN
ajtas-2922	30	17	coating	coating	NOUN
ajtas-2922	30	18	.	.	PUNCT
ajtas-2922	31	1	the	the	DET
ajtas-2922	31	2	change	change	NOUN
ajtas-2922	31	3	in	in	ADP
ajtas-2922	31	4	frequency	frequency	NOUN
ajtas-2922	31	5	depending	depend	VERB
ajtas-2922	31	6	on	on	ADP
ajtas-2922	31	7	the	the	DET
ajtas-2922	31	8	ratio	ratio	NOUN
ajtas-2922	31	9	of	of	ADP
ajtas-2922	31	10	the	the	DET
ajtas-2922	31	11	thickness	thickness	NOUN
ajtas-2922	31	12	of	of	ADP
ajtas-2922	31	13	the	the	DET
ajtas-2922	31	14	abstract	abstract	ADJ
ajtas-2922	31	15	parts	part	NOUN
ajtas-2922	31	16	is	be	AUX
ajtas-2922	31	17	shown	show	VERB
ajtas-2922	31	18	in	in	ADP
ajtas-2922	31	19	figure	figure	NOUN
ajtas-2922	31	20	2	2	NUM
ajtas-2922	31	21	.	.	PUNCT
ajtas-2922	32	1	the	the	DET
ajtas-2922	32	2	shells	shell	NOUN
ajtas-2922	32	3	are	be	AUX
ajtas-2922	32	4	not	not	PART
ajtas-2922	32	5	elastic	elastic	ADJ
ajtas-2922	32	6	and	and	CCONJ
ajtas-2922	32	7	diffusive	diffusive	ADJ
ajtas-2922	32	8	.	.	PUNCT
ajtas-2922	33	1	the	the	DET
ajtas-2922	33	2	filling	filling	NOUN
ajtas-2922	33	3	of	of	ADP
ajtas-2922	33	4	the	the	DET
ajtas-2922	33	5	cavity	cavity	NOUN
ajtas-2922	33	6	is	be	AUX
ajtas-2922	33	7	elastic	elastic	ADJ
ajtas-2922	33	8	.	.	PUNCT
ajtas-2922	34	1	in	in	ADP
ajtas-2922	34	2	other	other	ADJ
ajtas-2922	34	3	words	word	NOUN
ajtas-2922	34	4	,	,	PUNCT
ajtas-2922	34	5	the	the	DET
ajtas-2922	34	6	construction	construction	NOUN
ajtas-2922	34	7	is	be	AUX
ajtas-2922	34	8	dissipatively	dissipatively	ADV
ajtas-2922	34	9	heterogeneous	heterogeneous	ADJ
ajtas-2922	34	10	.	.	PUNCT
ajtas-2922	35	1	figure	figure	NOUN
ajtas-2922	35	2	4	4	NUM
ajtas-2922	35	3	.	.	PUNCT
ajtas-2922	36	1	change	change	NOUN
ajtas-2922	36	2	in	in	ADP
ajtas-2922	36	3	extinction	extinction	NOUN
ajtas-2922	36	4	coefficient	coefficient	NOUN
ajtas-2922	36	5	as	as	ADP
ajtas-2922	36	6	a	a	DET
ajtas-2922	36	7	function	function	NOUN
ajtas-2922	36	8	of	of	ADP
ajtas-2922	36	9	wavelength	wavelength	NOUN
ajtas-2922	36	10	the	the	DET
ajtas-2922	36	11	results	result	NOUN
ajtas-2922	36	12	are	be	AUX
ajtas-2922	36	13	presented	present	VERB
ajtas-2922	36	14	graphically	graphically	ADV
ajtas-2922	36	15	as	as	ADP
ajtas-2922	36	16	a	a	DET
ajtas-2922	36	17	real	real	ADJ
ajtas-2922	36	18	part	part	NOUN
ajtas-2922	36	19	of	of	ADP
ajtas-2922	36	20	the	the	DET
ajtas-2922	36	21	frequency	frequency	NOUN
ajtas-2922	36	22	and	and	CCONJ
ajtas-2922	36	23	the	the	DET
ajtas-2922	36	24	change	change	NOUN
ajtas-2922	36	25	in	in	ADP
ajtas-2922	36	26	the	the	DET
ajtas-2922	36	27	loss	loss	NOUN
ajtas-2922	36	28	coefficient	coefficient	NOUN
ajtas-2922	36	29	(	(	PUNCT
ajtas-2922	36	30	potter	potter	NOUN
ajtas-2922	36	31	's	's	PART
ajtas-2922	36	32	coefficient	coefficient	NOUN
ajtas-2922	36	33	)	)	PUNCT
ajtas-2922	36	34	relative	relative	ADJ
ajtas-2922	36	35	to	to	ADP
ajtas-2922	36	36	the	the	DET
ajtas-2922	36	37	dimensionless	dimensionless	NOUN
ajtas-2922	36	38	wave	wave	NOUN
ajtas-2922	36	39	number	number	NOUN
ajtas-2922	36	40	(	(	PUNCT
ajtas-2922	36	41	the	the	DET
ajtas-2922	36	42	ratio	ratio	NOUN
ajtas-2922	36	43	of	of	ADP
ajtas-2922	36	44	the	the	DET
ajtas-2922	36	45	halfthickness	halfthickness	NOUN
ajtas-2922	36	46	of	of	ADP
ajtas-2922	36	47	the	the	DET
ajtas-2922	36	48	layer	layer	NOUN
ajtas-2922	36	49	of	of	ADP
ajtas-2922	36	50	the	the	DET
ajtas-2922	36	51	medium	medium	NOUN
ajtas-2922	36	52	to	to	ADP
ajtas-2922	36	53	the	the	DET
ajtas-2922	36	54	wavelength	wavelength	NOUN
ajtas-2922	36	55	)	)	PUNCT
ajtas-2922	36	56	.	.	PUNCT
ajtas-2922	37	1	the	the	DET
ajtas-2922	37	2	absolute	absolute	ADJ
ajtas-2922	37	3	error	error	NOUN
ajtas-2922	37	4	of	of	ADP
ajtas-2922	37	5	the	the	DET
ajtas-2922	37	6	eigenvalues	eigenvalue	NOUN
ajtas-2922	37	7	in	in	ADP
ajtas-2922	37	8	the	the	DET
ajtas-2922	37	9	calculations	calculation	NOUN
ajtas-2922	37	10	was	be	AUX
ajtas-2922	37	11	about	about	ADP
ajtas-2922	37	12	the	the	DET
ajtas-2922	37	13	exact	exact	ADJ
ajtas-2922	37	14	equations	equation	NOUN
ajtas-2922	37	15	61014	61014	NUM
ajtas-2922	38	1	−	−	VERB
ajtas-2922	38	2	of	of	ADP
ajtas-2922	38	3	.	.	PUNCT
ajtas-2922	39	1	figure	figure	NOUN
ajtas-2922	39	2	3	3	NUM
ajtas-2922	39	3	shows	show	VERB
ajtas-2922	39	4	the	the	DET
ajtas-2922	39	5	change	change	NOUN
ajtas-2922	39	6	in	in	ADP
ajtas-2922	39	7	the	the	DET
ajtas-2922	39	8	real	real	ADJ
ajtas-2922	39	9	and	and	CCONJ
ajtas-2922	39	10	abstract	abstract	ADJ
ajtas-2922	39	11	parts	part	NOUN
ajtas-2922	39	12	of	of	ADP
ajtas-2922	39	13	the	the	DET
ajtas-2922	39	14	complex	complex	ADJ
ajtas-2922	39	15	frequency	frequency	NOUN
ajtas-2922	39	16	relative	relative	NOUN
ajtas-2922	39	17	to	to	ADP
ajtas-2922	39	18	the	the	DET
ajtas-2922	39	19	dimensionless	dimensionless	NOUN
ajtas-2922	39	20	wavelength	wavelength	NOUN
ajtas-2922	39	21	.	.	PUNCT
ajtas-2922	40	1	in	in	ADP
ajtas-2922	40	2	the	the	DET
ajtas-2922	40	3	case	case	NOUN
ajtas-2922	40	4	of	of	ADP
ajtas-2922	40	5	dissipative	dissipative	ADJ
ajtas-2922	40	6	inhomogeneous	inhomogeneous	ADJ
ajtas-2922	40	7	mechanical	mechanical	ADJ
ajtas-2922	40	8	systems	system	NOUN
ajtas-2922	40	9	,	,	PUNCT
ajtas-2922	40	10	a	a	DET
ajtas-2922	40	11	non	non	ADJ
ajtas-2922	40	12	-	-	ADJ
ajtas-2922	40	13	monotonic	monotonic	ADJ
ajtas-2922	40	14	dependence	dependence	NOUN
ajtas-2922	40	15	of	of	ADP
ajtas-2922	40	16	the	the	DET
ajtas-2922	40	17	attenuation	attenuation	NOUN
ajtas-2922	40	18	coefficient	coefficient	NOUN
ajtas-2922	40	19	on	on	ADP
ajtas-2922	40	20	the	the	DET
ajtas-2922	40	21	wavelength	wavelength	NOUN
ajtas-2922	40	22	was	be	AUX
ajtas-2922	40	23	found	find	VERB
ajtas-2922	40	24	.	.	PUNCT
ajtas-2922	41	1	here	here	ADV
ajtas-2922	41	2	,	,	PUNCT
ajtas-2922	41	3	the	the	DET
ajtas-2922	41	4	function	function	NOUN
ajtas-2922	41	5	of	of	ADP
ajtas-2922	41	6	the	the	DET
ajtas-2922	41	7	global	global	ADJ
ajtas-2922	41	8	attenuation	attenuation	NOUN
ajtas-2922	41	9	coefficient	coefficient	NOUN
ajtas-2922	41	10	is	be	AUX
ajtas-2922	41	11	performed	perform	VERB
ajtas-2922	41	12	by	by	ADP
ajtas-2922	41	13	the	the	DET
ajtas-2922	41	14	abstract	abstract	ADJ
ajtas-2922	41	15	parts	part	NOUN
ajtas-2922	41	16	of	of	ADP
ajtas-2922	41	17	the	the	DET
ajtas-2922	41	18	first	first	ADJ
ajtas-2922	41	19	and	and	CCONJ
ajtas-2922	41	20	second	second	ADJ
ajtas-2922	41	21	natural	natural	ADJ
ajtas-2922	41	22	frequencies	frequency	NOUN
ajtas-2922	41	23	.	.	PUNCT
ajtas-2922	42	1	when	when	SCONJ
ajtas-2922	42	2	these	these	DET
ajtas-2922	42	3	(	(	PUNCT
ajtas-2922	42	4	rk	rk	NOUN
ajtas-2922	42	5	)	)	PUNCT
ajtas-2922	42	6	frequencies	frequency	NOUN
ajtas-2922	42	7	converge	converge	VERB
ajtas-2922	42	8	,	,	PUNCT
ajtas-2922	42	9	the	the	DET
ajtas-2922	42	10	intersection	intersection	NOUN
ajtas-2922	42	11	of	of	ADP
ajtas-2922	42	12	the	the	DET
ajtas-2922	42	13	abstract	abstract	ADJ
ajtas-2922	42	14	parts	part	NOUN
ajtas-2922	42	15	of	of	ADP
ajtas-2922	42	16	the	the	DET
ajtas-2922	42	17	first	first	ADJ
ajtas-2922	42	18	and	and	CCONJ
ajtas-2922	42	19	second	second	ADJ
ajtas-2922	42	20	modes	mode	NOUN
ajtas-2922	42	21	of	of	ADP
ajtas-2922	42	22	natural	natural	ADJ
ajtas-2922	42	23	frequencies	frequency	NOUN
ajtas-2922	42	24	is	be	AUX
ajtas-2922	42	25	observed	observe	VERB
ajtas-2922	42	26	.	.	PUNCT
ajtas-2922	43	1	a	a	DET
ajtas-2922	43	2	similar	similar	ADJ
ajtas-2922	43	3	effect	effect	NOUN
ajtas-2922	43	4	was	be	AUX
ajtas-2922	43	5	observed	observe	VERB
ajtas-2922	43	6	in	in	ADP
ajtas-2922	43	7	the	the	DET
ajtas-2922	43	8	work	work	NOUN
ajtas-2922	43	9	of	of	ADP
ajtas-2922	43	10	yu.n	yu.n	PROPN
ajtas-2922	43	11	.	.	PUNCT
ajtas-2922	44	1	rabotnov	rabotnov	PROPN
ajtas-2922	44	2	.	.	PROPN
ajtas-2922	44	3	was	be	AUX
ajtas-2922	44	4	also	also	ADV
ajtas-2922	44	5	discovered	discover	VERB
ajtas-2922	44	6	when	when	SCONJ
ajtas-2922	44	7	using	use	VERB
ajtas-2922	44	8	a	a	DET
ajtas-2922	44	9	fractional	fractional	ADJ
ajtas-2922	44	10	-	-	PUNCT
ajtas-2922	44	11	exponential	exponential	ADJ
ajtas-2922	44	12	nucleus	nucleus	NOUN
ajtas-2922	44	13	graphs	graph	NOUN
ajtas-2922	44	14	of	of	ADP
ajtas-2922	44	15	dispersion	dispersion	NOUN
ajtas-2922	44	16	curves	curve	NOUN
ajtas-2922	44	17	,	,	PUNCT
ajtas-2922	44	18	k	k	NOUN
ajtas-2922	44	19	*	*	PUNCT
ajtas-2922	44	20	,	,	PUNCT
ajtas-2922	44	21	as	as	ADV
ajtas-2922	44	22	well	well	ADV
ajtas-2922	44	23	as	as	ADP
ajtas-2922	44	24	their	their	PRON
ajtas-2922	44	25	projections	projection	NOUN
ajtas-2922	44	26	on	on	ADP
ajtas-2922	44	27	the	the	DET
ajtas-2922	44	28	plane	plane	NOUN
ajtas-2922	44	29	(	(	PUNCT
ajtas-2922	44	30	ω	ω	PROPN
ajtas-2922	44	31	*	*	PROPN
ajtas-2922	44	32	,	,	PUNCT
ajtas-2922	44	33	k	k	NOUN
ajtas-2922	44	34	)	)	PUNCT
ajtas-2922	44	35	for	for	ADP
ajtas-2922	44	36	both	both	CCONJ
ajtas-2922	44	37	positive	positive	ADJ
ajtas-2922	44	38	and	and	CCONJ
ajtas-2922	44	39	negative	negative	ADJ
ajtas-2922	44	40	imaginary	imaginary	ADJ
ajtas-2922	44	41	parts	part	NOUN
ajtas-2922	44	42	of	of	ADP
ajtas-2922	44	43	k	k	PROPN
ajtas-2922	44	44	*	*	VERB
ajtas-2922	44	45	were	be	AUX
ajtas-2922	44	46	considered	consider	VERB
ajtas-2922	44	47	.	.	PUNCT
ajtas-2922	45	1	projections	projection	NOUN
ajtas-2922	45	2	of	of	ADP
ajtas-2922	45	3	k	k	X
ajtas-2922	45	4	*	*	VERB
ajtas-2922	45	5	on	on	ADP
ajtas-2922	45	6	the	the	DET
ajtas-2922	45	7	plane	plane	NOUN
ajtas-2922	45	8	(	(	PUNCT
ajtas-2922	45	9	ω	ω	PROPN
ajtas-2922	45	10	*	*	PROPN
ajtas-2922	45	11	,	,	PUNCT
ajtas-2922	45	12	α	α	NOUN
ajtas-2922	45	13	)	)	PUNCT
ajtas-2922	45	14	for	for	ADP
ajtas-2922	45	15	both	both	CCONJ
ajtas-2922	45	16	positive	positive	ADJ
ajtas-2922	45	17	american	american	ADJ
ajtas-2922	45	18	journal	journal	NOUN
ajtas-2922	45	19	of	of	ADP
ajtas-2922	45	20	technology	technology	NOUN
ajtas-2922	45	21	and	and	CCONJ
ajtas-2922	45	22	applied	apply	VERB
ajtas-2922	45	23	sciences	science	NOUN
ajtas-2922	45	24	36	36	NUM
ajtas-2922	45	25	,	,	PUNCT
ajtas-2922	45	26	may	may	AUX
ajtas-2922	45	27	2025	2025	NUM
ajtas-2922	45	28	p	p	NOUN
ajtas-2922	45	29	a	a	DET
ajtas-2922	45	30	g	g	NOUN
ajtas-2922	45	31	e	e	NOUN
ajtas-2922	45	32	|	|	NOUN
ajtas-2922	45	33	18	18	NUM
ajtas-2922	45	34	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-2922	45	35	and	and	CCONJ
ajtas-2922	45	36	negative	negative	ADJ
ajtas-2922	45	37	real	real	ADJ
ajtas-2922	45	38	parts	part	NOUN
ajtas-2922	45	39	of	of	ADP
ajtas-2922	45	40	k	k	NOUN
ajtas-2922	45	41	*	*	PUNCT
ajtas-2922	45	42	at	at	ADP
ajtas-2922	45	43	different	different	ADJ
ajtas-2922	45	44	values	value	NOUN
ajtas-2922	45	45	of	of	ADP
ajtas-2922	45	46	the	the	DET
ajtas-2922	45	47	parameters	parameter	NOUN
ajtas-2922	45	48	k	k	PROPN
ajtas-2922	45	49	were	be	AUX
ajtas-2922	45	50	consideredand	consideredand	ADV
ajtas-2922	45	51	β	β	NOUN
ajtas-2922	46	1	that	that	PRON
ajtas-2922	46	2	represent	represent	VERB
ajtas-2922	46	3	the	the	DET
ajtas-2922	46	4	hereditary	hereditary	ADJ
ajtas-2922	46	5	properties	property	NOUN
ajtas-2922	46	6	of	of	ADP
ajtas-2922	46	7	the	the	DET
ajtas-2922	46	8	material	material	NOUN
ajtas-2922	46	9	.	.	PUNCT
ajtas-2922	47	1	analysis	analysis	NOUN
ajtas-2922	47	2	of	of	ADP
ajtas-2922	47	3	numerical	numerical	ADJ
ajtas-2922	47	4	solutions	solution	NOUN
ajtas-2922	47	5	shows	show	VERB
ajtas-2922	47	6	that	that	SCONJ
ajtas-2922	47	7	the	the	DET
ajtas-2922	47	8	greater	great	ADJ
ajtas-2922	47	9	m	m	NOUN
ajtas-2922	47	10	or	or	CCONJ
ajtas-2922	47	11	the	the	PRON
ajtas-2922	47	12	lower	low	ADJ
ajtas-2922	47	13	the	the	DET
ajtas-2922	47	14	value	value	NOUN
ajtas-2922	47	15	of	of	ADP
ajtas-2922	47	16	β	β	X
ajtas-2922	47	17	,	,	PUNCT
ajtas-2922	47	18	the	the	PRON
ajtas-2922	47	19	earlier	early	ADJ
ajtas-2922	47	20	and	and	CCONJ
ajtas-2922	47	21	more	more	ADV
ajtas-2922	47	22	widely	widely	ADV
ajtas-2922	47	23	the	the	DET
ajtas-2922	47	24	variance	variance	NOUN
ajtas-2922	47	25	curves	curve	VERB
ajtas-2922	47	26	k	k	NOUN
ajtas-2922	47	27	*	*	PUNCT
ajtas-2922	47	28	with	with	SCONJ
ajtas-2922	47	29	the	the	DET
ajtas-2922	47	30	positive	positive	ADJ
ajtas-2922	47	31	and	and	CCONJ
ajtas-2922	47	32	negative	negative	ADJ
ajtas-2922	47	33	imaginary	imaginary	ADJ
ajtas-2922	47	34	parts	part	NOUN
ajtas-2922	47	35	begin	begin	VERB
ajtas-2922	47	36	to	to	PART
ajtas-2922	47	37	diverge	diverge	VERB
ajtas-2922	47	38	.	.	PUNCT
ajtas-2922	48	1	numerical	numerical	PROPN
ajtas-2922	48	2	calculations	calculation	NOUN
ajtas-2922	48	3	show	show	VERB
ajtas-2922	48	4	that	that	SCONJ
ajtas-2922	48	5	with	with	ADP
ajtas-2922	48	6	a	a	DET
ajtas-2922	48	7	decrease	decrease	NOUN
ajtas-2922	48	8	in	in	ADP
ajtas-2922	48	9	the	the	DET
ajtas-2922	48	10	value	value	NOUN
ajtas-2922	48	11	of	of	ADP
ajtas-2922	48	12	m	m	PRON
ajtas-2922	48	13	or	or	CCONJ
ajtas-2922	48	14	an	an	DET
ajtas-2922	48	15	increase	increase	NOUN
ajtas-2922	48	16	in	in	ADP
ajtas-2922	48	17	the	the	DET
ajtas-2922	48	18	value	value	NOUN
ajtas-2922	48	19	of	of	ADP
ajtas-2922	48	20	β	β	X
ajtas-2922	48	21	,	,	PUNCT
ajtas-2922	48	22	the	the	DET
ajtas-2922	48	23	dispersion	dispersion	NOUN
ajtas-2922	48	24	curves	curve	NOUN
ajtas-2922	48	25	tend	tend	VERB
ajtas-2922	48	26	to	to	PART
ajtas-2922	48	27	become	become	VERB
ajtas-2922	48	28	elastic	elastic	ADJ
ajtas-2922	48	29	.	.	PUNCT
ajtas-2922	49	1	in	in	ADP
ajtas-2922	49	2	addition	addition	NOUN
ajtas-2922	49	3	,	,	PUNCT
ajtas-2922	49	4	it	it	PRON
ajtas-2922	49	5	has	have	AUX
ajtas-2922	49	6	been	be	AUX
ajtas-2922	49	7	established	establish	VERB
ajtas-2922	49	8	that	that	SCONJ
ajtas-2922	49	9	the	the	DET
ajtas-2922	49	10	dispersion	dispersion	NOUN
ajtas-2922	49	11	curves	curve	NOUN
ajtas-2922	49	12	of	of	ADP
ajtas-2922	49	13	the	the	DET
ajtas-2922	49	14	hereditary	hereditary	ADJ
ajtas-2922	49	15	elastic	elastic	ADJ
ajtas-2922	49	16	spectrum	spectrum	NOUN
ajtas-2922	49	17	,	,	PUNCT
ajtas-2922	49	18	belonging	belong	VERB
ajtas-2922	49	19	to	to	ADP
ajtas-2922	49	20	the	the	DET
ajtas-2922	49	21	elastic	elastic	ADJ
ajtas-2922	49	22	spectrum	spectrum	NOUN
ajtas-2922	49	23	,	,	PUNCT
ajtas-2922	49	24	consist	consist	VERB
ajtas-2922	49	25	of	of	ADP
ajtas-2922	49	26	a	a	DET
ajtas-2922	49	27	complex	complex	ADJ
ajtas-2922	49	28	number	number	NOUN
ajtas-2922	49	29	k	k	NOUN
ajtas-2922	49	30	*	*	PUNCT
ajtas-2922	49	31	with	with	ADP
ajtas-2922	49	32	negative	negative	ADJ
ajtas-2922	49	33	imaginary	imaginary	ADJ
ajtas-2922	49	34	parts	part	NOUN
ajtas-2922	49	35	,	,	PUNCT
ajtas-2922	49	36	which	which	PRON
ajtas-2922	49	37	determines	determine	VERB
ajtas-2922	49	38	the	the	DET
ajtas-2922	49	39	attenuation	attenuation	NOUN
ajtas-2922	49	40	of	of	ADP
ajtas-2922	49	41	the	the	DET
ajtas-2922	49	42	solution	solution	NOUN
ajtas-2922	49	43	by	by	ADP
ajtas-2922	49	44	the	the	DET
ajtas-2922	49	45	coordinate	coordinate	NOUN
ajtas-2922	49	46	.	.	PUNCT
ajtas-2922	50	1	figure	figure	NOUN
ajtas-2922	50	2	5	5	NUM
ajtas-2922	50	3	.	.	PUNCT
ajtas-2922	51	1	change	change	NOUN
ajtas-2922	51	2	in	in	ADP
ajtas-2922	51	3	extinction	extinction	NOUN
ajtas-2922	51	4	coefficient	coefficient	NOUN
ajtas-2922	51	5	as	as	ADP
ajtas-2922	51	6	a	a	DET
ajtas-2922	51	7	function	function	NOUN
ajtas-2922	51	8	of	of	ADP
ajtas-2922	51	9	wavelength	wavelength	NOUN
ajtas-2922	51	10	figure	figure	NOUN
ajtas-2922	51	11	6	6	NUM
ajtas-2922	51	12	.	.	PUNCT
ajtas-2922	52	1	change	change	NOUN
ajtas-2922	52	2	in	in	ADP
ajtas-2922	52	3	attenuation	attenuation	NOUN
ajtas-2922	52	4	coefficient	coefficient	NOUN
ajtas-2922	52	5	and	and	CCONJ
ajtas-2922	52	6	actual	actual	ADJ
ajtas-2922	52	7	part	part	NOUN
ajtas-2922	52	8	of	of	ADP
ajtas-2922	52	9	frequency	frequency	NOUN
ajtas-2922	52	10	as	as	ADP
ajtas-2922	52	11	a	a	DET
ajtas-2922	52	12	function	function	NOUN
ajtas-2922	52	13	of	of	ADP
ajtas-2922	52	14	wavelength	wavelength	NOUN
ajtas-2922	52	15	american	american	PROPN
ajtas-2922	52	16	journal	journal	PROPN
ajtas-2922	52	17	of	of	ADP
ajtas-2922	52	18	technology	technology	NOUN
ajtas-2922	52	19	and	and	CCONJ
ajtas-2922	52	20	applied	apply	VERB
ajtas-2922	52	21	sciences	science	NOUN
ajtas-2922	52	22	36	36	NUM
ajtas-2922	52	23	,	,	PUNCT
ajtas-2922	52	24	may	may	AUX
ajtas-2922	52	25	2025	2025	NUM
ajtas-2922	52	26	p	p	NOUN
ajtas-2922	52	27	a	a	DET
ajtas-2922	52	28	g	g	NOUN
ajtas-2922	52	29	e	e	NOUN
ajtas-2922	52	30	|	|	ADV
ajtas-2922	52	31	19	19	NUM
ajtas-2922	52	32	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-2922	52	33	figures	figure	NOUN
ajtas-2922	52	34	5	5	NUM
ajtas-2922	52	35	and	and	CCONJ
ajtas-2922	52	36	4	4	NUM
ajtas-2922	52	37	show	show	VERB
ajtas-2922	52	38	the	the	DET
ajtas-2922	52	39	change	change	NOUN
ajtas-2922	52	40	in	in	ADP
ajtas-2922	52	41	the	the	DET
ajtas-2922	52	42	extinction	extinction	NOUN
ajtas-2922	52	43	coefficient	coefficient	NOUN
ajtas-2922	52	44	as	as	ADP
ajtas-2922	52	45	a	a	DET
ajtas-2922	52	46	function	function	NOUN
ajtas-2922	52	47	of	of	ADP
ajtas-2922	52	48	wavelength	wavelength	NOUN
ajtas-2922	52	49	.	.	PUNCT
ajtas-2922	53	1	this	this	PRON
ajtas-2922	53	2	is	be	AUX
ajtas-2922	53	3	also	also	ADV
ajtas-2922	53	4	obtained	obtain	VERB
ajtas-2922	53	5	for	for	ADP
ajtas-2922	53	6	a	a	DET
ajtas-2922	53	7	dissipative	dissipative	ADJ
ajtas-2922	53	8	inhomogeneous	inhomogeneous	ADJ
ajtas-2922	53	9	mechanical	mechanical	ADJ
ajtas-2922	53	10	system	system	NOUN
ajtas-2922	53	11	.	.	PUNCT
ajtas-2922	54	1	the	the	DET
ajtas-2922	54	2	change	change	NOUN
ajtas-2922	54	3	in	in	ADP
ajtas-2922	54	4	the	the	DET
ajtas-2922	54	5	attenuation	attenuation	NOUN
ajtas-2922	54	6	coefficient	coefficient	NOUN
ajtas-2922	54	7	and	and	CCONJ
ajtas-2922	54	8	the	the	DET
ajtas-2922	54	9	actual	actual	ADJ
ajtas-2922	54	10	part	part	NOUN
ajtas-2922	54	11	of	of	ADP
ajtas-2922	54	12	the	the	DET
ajtas-2922	54	13	frequency	frequency	NOUN
ajtas-2922	54	14	as	as	ADP
ajtas-2922	54	15	a	a	DET
ajtas-2922	54	16	function	function	NOUN
ajtas-2922	54	17	of	of	ADP
ajtas-2922	54	18	the	the	DET
ajtas-2922	54	19	wavelength	wavelength	NOUN
ajtas-2922	54	20	is	be	AUX
ajtas-2922	54	21	shown	show	VERB
ajtas-2922	54	22	in	in	ADP
ajtas-2922	54	23	figure	figure	NOUN
ajtas-2922	54	24	6	6	NUM
ajtas-2922	54	25	.	.	PUNCT
ajtas-2922	55	1	it	it	PRON
ajtas-2922	55	2	should	should	AUX
ajtas-2922	55	3	be	be	AUX
ajtas-2922	55	4	noted	note	VERB
ajtas-2922	55	5	that	that	SCONJ
ajtas-2922	55	6	the	the	DET
ajtas-2922	55	7	concepts	concept	NOUN
ajtas-2922	55	8	of	of	ADP
ajtas-2922	55	9	"	"	PUNCT
ajtas-2922	55	10	closing	closing	NOUN
ajtas-2922	55	11	frequency	frequency	NOUN
ajtas-2922	55	12	"	"	PUNCT
ajtas-2922	55	13	(	(	PUNCT
ajtas-2922	55	14	locking	locking	NOUN
ajtas-2922	55	15	frequency	frequency	NOUN
ajtas-2922	55	16	)	)	PUNCT
ajtas-2922	55	17	(	(	PUNCT
ajtas-2922	55	18	k	k	X
ajtas-2922	55	19	*	*	PUNCT
ajtas-2922	55	20	=	=	SYM
ajtas-2922	55	21	0	0	NUM
ajtas-2922	55	22	,	,	PUNCT
ajtas-2922	55	23	ω	ω	X
ajtas-2922	55	24	*	*	PUNCT
ajtas-2922	55	25	>	>	X
ajtas-2922	55	26	0	0	NUM
ajtas-2922	55	27	,	,	PUNCT
ajtas-2922	55	28	since	since	SCONJ
ajtas-2922	55	29	there	there	PRON
ajtas-2922	55	30	are	be	VERB
ajtas-2922	55	31	no	no	DET
ajtas-2922	55	32	roots	root	NOUN
ajtas-2922	55	33	of	of	ADP
ajtas-2922	55	34	the	the	DET
ajtas-2922	55	35	dispersion	dispersion	NOUN
ajtas-2922	55	36	equation	equation	NOUN
ajtas-2922	55	37	)	)	PUNCT
ajtas-2922	55	38	and	and	CCONJ
ajtas-2922	55	39	"	"	PUNCT
ajtas-2922	55	40	frequency	frequency	NOUN
ajtas-2922	55	41	minimum	minimum	NOUN
ajtas-2922	55	42	"	"	PUNCT
ajtas-2922	55	43	(	(	PUNCT
ajtas-2922	55	44	since	since	SCONJ
ajtas-2922	55	45	ω	ω	PROPN
ajtas-2922	55	46	*	*	VERB
ajtas-2922	55	47	monotonically	monotonically	ADV
ajtas-2922	55	48	increases	increase	VERB
ajtas-2922	55	49	as	as	SCONJ
ajtas-2922	55	50	you	you	PRON
ajtas-2922	55	51	move	move	VERB
ajtas-2922	55	52	along	along	ADP
ajtas-2922	55	53	the	the	DET
ajtas-2922	55	54	network	network	NOUN
ajtas-2922	55	55	)	)	PUNCT
ajtas-2922	55	56	lose	lose	VERB
ajtas-2922	55	57	their	their	PRON
ajtas-2922	55	58	meaning	meaning	NOUN
ajtas-2922	55	59	for	for	ADP
ajtas-2922	55	60	the	the	DET
ajtas-2922	55	61	genetic	genetic	ADJ
ajtas-2922	55	62	-	-	PUNCT
ajtas-2922	55	63	elastic	elastic	ADJ
ajtas-2922	55	64	spectrum	spectrum	NOUN
ajtas-2922	55	65	.	.	PUNCT
ajtas-2922	56	1	analysis	analysis	NOUN
ajtas-2922	56	2	of	of	ADP
ajtas-2922	56	3	the	the	DET
ajtas-2922	56	4	numerical	numerical	ADJ
ajtas-2922	56	5	results	result	NOUN
ajtas-2922	56	6	shows	show	VERB
ajtas-2922	56	7	that	that	SCONJ
ajtas-2922	56	8	elastic	elastic	ADJ
ajtas-2922	56	9	-	-	PUNCT
ajtas-2922	56	10	elastic	elastic	ADJ
ajtas-2922	56	11	spectral	spectral	ADJ
ajtas-2922	56	12	networks	network	NOUN
ajtas-2922	56	13	have	have	VERB
ajtas-2922	56	14	the	the	DET
ajtas-2922	56	15	greatest	great	ADJ
ajtas-2922	56	16	curvature	curvature	NOUN
ajtas-2922	56	17	around	around	ADP
ajtas-2922	56	18	the	the	DET
ajtas-2922	56	19	closing	close	VERB
ajtas-2922	56	20	frequencies	frequency	NOUN
ajtas-2922	56	21	and	and	CCONJ
ajtas-2922	56	22	frequency	frequency	NOUN
ajtas-2922	56	23	minima	minima	NOUN
ajtas-2922	56	24	in	in	ADP
ajtas-2922	56	25	the	the	DET
ajtas-2922	56	26	elastic	elastic	ADJ
ajtas-2922	56	27	spectral	spectral	ADJ
ajtas-2922	56	28	network	network	NOUN
ajtas-2922	56	29	.	.	PUNCT
ajtas-2922	57	1	an	an	DET
ajtas-2922	57	2	increase	increase	NOUN
ajtas-2922	57	3	in	in	ADP
ajtas-2922	57	4	m	m	PROPN
ajtas-2922	57	5	values	value	NOUN
ajtas-2922	57	6	,	,	PUNCT
ajtas-2922	57	7	as	as	ADV
ajtas-2922	57	8	well	well	ADV
ajtas-2922	57	9	as	as	ADP
ajtas-2922	57	10	a	a	DET
ajtas-2922	57	11	decrease	decrease	NOUN
ajtas-2922	57	12	in	in	ADP
ajtas-2922	57	13	β	β	PROPN
ajtas-2922	57	14	values	value	NOUN
ajtas-2922	57	15	,	,	PUNCT
ajtas-2922	57	16	leads	lead	VERB
ajtas-2922	57	17	to	to	ADP
ajtas-2922	57	18	smoothing	smooth	VERB
ajtas-2922	57	19	of	of	ADP
ajtas-2922	57	20	dispersion	dispersion	NOUN
ajtas-2922	57	21	curves	curve	NOUN
ajtas-2922	57	22	in	in	ADP
ajtas-2922	57	23	these	these	DET
ajtas-2922	57	24	regions	region	NOUN
ajtas-2922	57	25	.	.	PUNCT
ajtas-2922	58	1	thus	thus	ADV
ajtas-2922	58	2	,	,	PUNCT
ajtas-2922	58	3	for	for	ADP
ajtas-2922	58	4	the	the	DET
ajtas-2922	58	5	elastic	elastic	ADJ
ajtas-2922	58	6	spectrum	spectrum	NOUN
ajtas-2922	58	7	,	,	PUNCT
ajtas-2922	58	8	the	the	DET
ajtas-2922	58	9	elastic	elastic	ADJ
ajtas-2922	58	10	spectrum	spectrum	NOUN
ajtas-2922	58	11	is	be	AUX
ajtas-2922	58	12	approximately	approximately	ADV
ajtas-2922	58	13	the	the	DET
ajtas-2922	58	14	same	same	ADJ
ajtas-2922	58	15	as	as	ADP
ajtas-2922	58	16	for	for	ADP
ajtas-2922	58	17	the	the	DET
ajtas-2922	58	18	hereditary	hereditary	ADJ
ajtas-2922	58	19	elastic	elastic	ADJ
ajtas-2922	58	20	spectrum	spectrum	NOUN
ajtas-2922	58	21	,	,	PUNCT
ajtas-2922	58	22	m→0	m→0	PROPN
ajtas-2922	58	23	,	,	PUNCT
ajtas-2922	58	24	it	it	PRON
ajtas-2922	58	25	can	can	AUX
ajtas-2922	58	26	be	be	AUX
ajtas-2922	58	27	considered	consider	VERB
ajtas-2922	58	28	asymptotic	asymptotic	ADJ
ajtas-2922	58	29	at	at	ADP
ajtas-2922	58	30	β>>1	β>>1	ADJ
ajtas-2922	58	31	.	.	PUNCT
ajtas-2922	59	1	asymptotic	asymptotic	ADJ
ajtas-2922	59	2	roots	root	NOUN
ajtas-2922	59	3	for	for	ADP
ajtas-2922	59	4	the	the	DET
ajtas-2922	59	5	first	first	ADJ
ajtas-2922	59	6	mode	mode	NOUN
ajtas-2922	59	7	near	near	ADP
ajtas-2922	59	8	zero	zero	NUM
ajtas-2922	59	9	frequency	frequency	NOUN
ajtas-2922	59	10	are	be	AUX
ajtas-2922	59	11	obtained	obtain	VERB
ajtas-2922	59	12	.	.	PUNCT
ajtas-2922	60	1	for	for	ADP
ajtas-2922	60	2	the	the	DET
ajtas-2922	60	3	symmetrical	symmetrical	ADJ
ajtas-2922	60	4	dkx	dkx	ADJ
ajtas-2922	60	5	case	case	NOUN
ajtas-2922	60	6	for	for	ADP
ajtas-2922	60	7	the	the	DET
ajtas-2922	60	8	first	first	ADJ
ajtas-2922	60	9	mode	mode	NOUN
ajtas-2922	60	10	,	,	PUNCT
ajtas-2922	60	11	we	we	PRON
ajtas-2922	60	12	get	get	VERB
ajtas-2922	60	13	:	:	PUNCT
ajtas-2922	60	14	k1	k1	NOUN
ajtas-2922	60	15	=	=	NOUN
ajtas-2922	60	16	c12ω+c13ω3/2	c12ω+c13ω3/2	ADJ
ajtas-2922	60	17	+	+	NOUN
ajtas-2922	60	18	o(ω2	o(ω2	X
ajtas-2922	60	19	)	)	PUNCT
ajtas-2922	60	20	,	,	PUNCT
ajtas-2922	60	21	α1	α1	PROPN
ajtas-2922	60	22	=	=	SYM
ajtas-2922	60	23	d13ω3/2	d13ω3/2	PROPN
ajtas-2922	60	24	+	+	NOUN
ajtas-2922	60	25	o(ω2	o(ω2	X
ajtas-2922	60	26	)	)	PUNCT
ajtas-2922	60	27	where	where	SCONJ
ajtas-2922	60	28	c12	c12	PROPN
ajtas-2922	60	29	,	,	PUNCT
ajtas-2922	60	30	c13	c13	PROPN
ajtas-2922	60	31	,	,	PUNCT
ajtas-2922	60	32	d13	d13	PROPN
ajtas-2922	60	33	are	be	AUX
ajtas-2922	60	34	functions	function	NOUN
ajtas-2922	60	35	dependent	dependent	ADJ
ajtas-2922	60	36	on	on	ADP
ajtas-2922	60	37	ν	ν	PROPN
ajtas-2922	60	38	,	,	PUNCT
ajtas-2922	60	39	m	m	PRON
ajtas-2922	60	40	,	,	PUNCT
ajtas-2922	60	41	β	β	NOUN
ajtas-2922	60	42	.	.	PUNCT
ajtas-2922	61	1	it	it	PRON
ajtas-2922	61	2	was	be	AUX
ajtas-2922	61	3	shown	show	VERB
ajtas-2922	61	4	that	that	SCONJ
ajtas-2922	61	5	at	at	ADP
ajtas-2922	61	6	m	m	PROPN
ajtas-2922	61	7	=	=	NOUN
ajtas-2922	61	8	0	0	NUM
ajtas-2922	61	9	these	these	DET
ajtas-2922	61	10	asymptotics	asymptotic	NOUN
ajtas-2922	61	11	overlap	overlap	VERB
ajtas-2922	61	12	with	with	ADP
ajtas-2922	61	13	similar	similar	ADJ
ajtas-2922	61	14	asymptotics	asymptotic	NOUN
ajtas-2922	61	15	of	of	ADP
ajtas-2922	61	16	the	the	DET
ajtas-2922	61	17	elastic	elastic	ADJ
ajtas-2922	61	18	layer	layer	NOUN
ajtas-2922	61	19	.	.	PUNCT
ajtas-2922	62	1	numerical	numerical	PROPN
ajtas-2922	62	2	calculations	calculations	PROPN
ajtas-2922	62	3	show	show	VERB
ajtas-2922	62	4	that	that	SCONJ
ajtas-2922	62	5	numerical	numerical	ADJ
ajtas-2922	62	6	solutions	solution	NOUN
ajtas-2922	62	7	and	and	CCONJ
ajtas-2922	62	8	asymptotics	asymptotic	NOUN
ajtas-2922	62	9	overlap	overlap	VERB
ajtas-2922	62	10	in	in	ADP
ajtas-2922	62	11	the	the	DET
ajtas-2922	62	12	regions	region	NOUN
ajtas-2922	62	13	under	under	ADP
ajtas-2922	62	14	consideration	consideration	NOUN
ajtas-2922	62	15	.	.	PUNCT
ajtas-2922	63	1	the	the	DET
ajtas-2922	63	2	analysis	analysis	NOUN
ajtas-2922	63	3	of	of	ADP
ajtas-2922	63	4	dispersion	dispersion	NOUN
ajtas-2922	63	5	equations	equation	NOUN
ajtas-2922	63	6	and	and	CCONJ
ajtas-2922	63	7	their	their	PRON
ajtas-2922	63	8	numerical	numerical	ADJ
ajtas-2922	63	9	solutions	solution	NOUN
ajtas-2922	63	10	allows	allow	VERB
ajtas-2922	63	11	us	we	PRON
ajtas-2922	63	12	to	to	PART
ajtas-2922	63	13	draw	draw	VERB
ajtas-2922	63	14	the	the	DET
ajtas-2922	63	15	following	following	ADJ
ajtas-2922	63	16	conclusions	conclusion	NOUN
ajtas-2922	63	17	:	:	PUNCT
ajtas-2922	63	18	when	when	SCONJ
ajtas-2922	63	19	replacing	replace	VERB
ajtas-2922	63	20	k	k	X
ajtas-2922	63	21	~	~	PUNCT
ajtas-2922	63	22	with	with	SCONJ
ajtas-2922	63	23	k	k	PROPN
ajtas-2922	63	24	~	~	PUNCT
ajtas-2922	63	25	symmetry	symmetry	NOUN
ajtas-2922	63	26	of	of	ADP
ajtas-2922	63	27	dispersion	dispersion	NOUN
ajtas-2922	63	28	curves	curve	NOUN
ajtas-2922	63	29	is	be	AUX
ajtas-2922	63	30	observed	observe	VERB
ajtas-2922	63	31	;	;	PUNCT
ajtas-2922	63	32	the	the	PRON
ajtas-2922	63	33	higher	high	ADJ
ajtas-2922	63	34	the	the	DET
ajtas-2922	63	35	value	value	NOUN
ajtas-2922	63	36	of	of	ADP
ajtas-2922	63	37	m	m	PRON
ajtas-2922	63	38	or	or	CCONJ
ajtas-2922	63	39	the	the	PRON
ajtas-2922	63	40	lower	low	ADJ
ajtas-2922	63	41	the	the	DET
ajtas-2922	63	42	value	value	NOUN
ajtas-2922	63	43	of	of	ADP
ajtas-2922	63	44	β	β	X
ajtas-2922	63	45	,	,	PUNCT
ajtas-2922	63	46	the	the	DET
ajtas-2922	63	47	earlier	early	ADJ
ajtas-2922	63	48	and	and	CCONJ
ajtas-2922	63	49	faster	fast	ADV
ajtas-2922	63	50	the	the	DET
ajtas-2922	63	51	dispersion	dispersion	NOUN
ajtas-2922	63	52	curves	curve	VERB
ajtas-2922	63	53	with	with	ADP
ajtas-2922	63	54	the	the	DET
ajtas-2922	63	55	positive	positive	ADJ
ajtas-2922	63	56	and	and	CCONJ
ajtas-2922	63	57	negative	negative	ADJ
ajtas-2922	63	58	imaginary	imaginary	ADJ
ajtas-2922	63	59	parts	part	NOUN
ajtas-2922	63	60	diverge	diverge	VERB
ajtas-2922	63	61	;	;	PUNCT
ajtas-2922	63	62	-the	-the	X
ajtas-2922	63	63	higher	high	ADJ
ajtas-2922	63	64	the	the	DET
ajtas-2922	63	65	value	value	NOUN
ajtas-2922	63	66	of	of	ADP
ajtas-2922	63	67	m	m	PROPN
ajtas-2922	63	68	and	and	CCONJ
ajtas-2922	63	69	the	the	PRON
ajtas-2922	63	70	lower	low	ADJ
ajtas-2922	63	71	the	the	DET
ajtas-2922	63	72	value	value	NOUN
ajtas-2922	63	73	of	of	ADP
ajtas-2922	63	74	b	b	NOUN
ajtas-2922	63	75	,	,	PUNCT
ajtas-2922	63	76	the	the	PRON
ajtas-2922	63	77	faster	fast	ADV
ajtas-2922	63	78	the	the	DET
ajtas-2922	63	79	variance	variance	NOUN
ajtas-2922	63	80	curve	curve	NOUN
ajtas-2922	63	81	with	with	ADP
ajtas-2922	63	82	positive	positive	ADJ
ajtas-2922	63	83	and	and	CCONJ
ajtas-2922	63	84	negative	negative	ADJ
ajtas-2922	63	85	fractions	fraction	NOUN
ajtas-2922	63	86	;	;	PUNCT
ajtas-2922	63	87	dispersion	dispersion	NOUN
ajtas-2922	63	88	curves	curve	NOUN
ajtas-2922	63	89	of	of	ADP
ajtas-2922	63	90	the	the	DET
ajtas-2922	63	91	genetic	genetic	ADJ
ajtas-2922	63	92	-	-	PUNCT
ajtas-2922	63	93	elastic	elastic	ADJ
ajtas-2922	63	94	spectrum	spectrum	NOUN
ajtas-2922	63	95	,	,	PUNCT
ajtas-2922	63	96	corresponding	correspond	VERB
ajtas-2922	63	97	to	to	ADP
ajtas-2922	63	98	the	the	DET
ajtas-2922	63	99	real	real	ADJ
ajtas-2922	63	100	grid	grid	NOUN
ajtas-2922	63	101	of	of	ADP
ajtas-2922	63	102	the	the	DET
ajtas-2922	63	103	elastic	elastic	ADJ
ajtas-2922	63	104	spectrum	spectrum	NOUN
ajtas-2922	63	105	,	,	PUNCT
ajtas-2922	63	106	consist	consist	VERB
ajtas-2922	63	107	of	of	ADP
ajtas-2922	63	108	a	a	DET
ajtas-2922	63	109	complex	complex	ADJ
ajtas-2922	63	110	number	number	NOUN
ajtas-2922	63	111	,	,	PUNCT
ajtas-2922	63	112	the	the	DET
ajtas-2922	63	113	abstract	abstract	ADJ
ajtas-2922	63	114	part	part	NOUN
ajtas-2922	63	115	of	of	ADP
ajtas-2922	63	116	which	which	PRON
ajtas-2922	63	117	is	be	AUX
ajtas-2922	63	118	positive	positive	ADJ
ajtas-2922	63	119	,	,	PUNCT
ajtas-2922	63	120	and	and	CCONJ
ajtas-2922	63	121	this	this	DET
ajtas-2922	63	122	solution	solution	NOUN
ajtas-2922	63	123	determines	determine	VERB
ajtas-2922	63	124	the	the	DET
ajtas-2922	63	125	inversion	inversion	NOUN
ajtas-2922	63	126	to	to	ADP
ajtas-2922	63	127	zero	zero	NUM
ajtas-2922	63	128	of	of	ADP
ajtas-2922	63	129	the	the	DET
ajtas-2922	63	130	coordinate	coordinate	NOUN
ajtas-2922	63	131	;	;	PUNCT
ajtas-2922	63	132	the	the	DET
ajtas-2922	63	133	concept	concept	NOUN
ajtas-2922	63	134	of	of	ADP
ajtas-2922	63	135	a	a	DET
ajtas-2922	63	136	closing	closing	NOUN
ajtas-2922	63	137	frequency	frequency	NOUN
ajtas-2922	63	138	for	for	ADP
ajtas-2922	63	139	the	the	DET
ajtas-2922	63	140	hereditary	hereditary	ADJ
ajtas-2922	63	141	-	-	PUNCT
ajtas-2922	63	142	elastic	elastic	ADJ
ajtas-2922	63	143	spectrum	spectrum	NOUN
ajtas-2922	63	144	loses	lose	VERB
ajtas-2922	63	145	its	its	PRON
ajtas-2922	63	146	meaning	meaning	NOUN
ajtas-2922	63	147	,	,	PUNCT
ajtas-2922	63	148	since	since	SCONJ
ajtas-2922	63	149	y	y	PROPN
ajtas-2922	63	150	=	=	SYM
ajtas-2922	63	151	0	0	NUM
ajtas-2922	63	152	and	and	CCONJ
ajtas-2922	63	153	ω>0	ω>0	NUM
ajtas-2922	63	154	will	will	AUX
ajtas-2922	63	155	not	not	PART
ajtas-2922	63	156	be	be	AUX
ajtas-2922	63	157	the	the	DET
ajtas-2922	63	158	roots	root	NOUN
ajtas-2922	63	159	of	of	ADP
ajtas-2922	63	160	the	the	DET
ajtas-2922	63	161	dispersion	dispersion	NOUN
ajtas-2922	63	162	equation	equation	NOUN
ajtas-2922	63	163	;	;	PUNCT
ajtas-2922	63	164	-networks	-network	NOUN
ajtas-2922	63	165	of	of	ADP
ajtas-2922	63	166	the	the	DET
ajtas-2922	63	167	hereditarily	hereditarily	ADV
ajtas-2922	63	168	elastic	elastic	ADJ
ajtas-2922	63	169	spectrum	spectrum	NOUN
ajtas-2922	63	170	have	have	VERB
ajtas-2922	63	171	the	the	DET
ajtas-2922	63	172	greatest	great	ADJ
ajtas-2922	63	173	curvature	curvature	NOUN
ajtas-2922	63	174	near	near	ADP
ajtas-2922	63	175	the	the	DET
ajtas-2922	63	176	closing	closing	NOUN
ajtas-2922	63	177	frequency	frequency	NOUN
ajtas-2922	63	178	of	of	ADP
ajtas-2922	63	179	the	the	DET
ajtas-2922	63	180	elastic	elastic	ADJ
ajtas-2922	63	181	spectrum	spectrum	NOUN
ajtas-2922	63	182	.	.	PUNCT
ajtas-2922	64	1	an	an	DET
ajtas-2922	64	2	increase	increase	NOUN
ajtas-2922	64	3	in	in	ADP
ajtas-2922	64	4	the	the	DET
ajtas-2922	64	5	values	value	NOUN
ajtas-2922	64	6	of	of	ADP
ajtas-2922	64	7	m	m	PRON
ajtas-2922	64	8	,	,	PUNCT
ajtas-2922	64	9	as	as	ADV
ajtas-2922	64	10	well	well	ADV
ajtas-2922	64	11	as	as	ADP
ajtas-2922	64	12	a	a	DET
ajtas-2922	64	13	decrease	decrease	NOUN
ajtas-2922	64	14	in	in	ADP
ajtas-2922	64	15	the	the	DET
ajtas-2922	64	16	values	value	NOUN
ajtas-2922	64	17	of	of	ADP
ajtas-2922	64	18	β	β	NOUN
ajtas-2922	64	19	,	,	PUNCT
ajtas-2922	64	20	leads	lead	VERB
ajtas-2922	64	21	to	to	ADP
ajtas-2922	64	22	smoothing	smoothing	NOUN
ajtas-2922	64	23	of	of	ADP
ajtas-2922	64	24	the	the	DET
ajtas-2922	64	25	dispersion	dispersion	NOUN
ajtas-2922	64	26	curves	curve	VERB
ajtas-2922	64	27	in	in	ADP
ajtas-2922	64	28	these	these	DET
ajtas-2922	64	29	regions	region	NOUN
ajtas-2922	64	30	.	.	PUNCT
ajtas-2922	65	1	thus	thus	ADV
ajtas-2922	65	2	,	,	PUNCT
ajtas-2922	65	3	the	the	DET
ajtas-2922	65	4	elastic	elastic	ADJ
ajtas-2922	65	5	spectrum	spectrum	NOUN
ajtas-2922	65	6	can	can	AUX
ajtas-2922	65	7	be	be	AUX
ajtas-2922	65	8	considered	consider	VERB
ajtas-2922	65	9	asymptotic	asymptotic	ADJ
ajtas-2922	65	10	to	to	ADP
ajtas-2922	65	11	the	the	DET
ajtas-2922	65	12	hereditary	hereditary	ADJ
ajtas-2922	65	13	elastic	elastic	ADJ
ajtas-2922	65	14	spectrum	spectrum	NOUN
ajtas-2922	65	15	at	at	ADP
ajtas-2922	65	16	k	k	PROPN
ajtas-2922	65	17	→	→	X
ajtas-2922	65	18	0	0	PROPN
ajtas-2922	65	19	,	,	PUNCT
ajtas-2922	65	20	β	β	PROPN
ajtas-2922	65	21	≫	≫	PROPN
ajtas-2922	65	22	1	1	NUM
ajtas-2922	65	23	.	.	PUNCT
ajtas-2922	65	24	american	american	PROPN
ajtas-2922	65	25	journal	journal	PROPN
ajtas-2922	65	26	of	of	ADP
ajtas-2922	65	27	technology	technology	NOUN
ajtas-2922	65	28	and	and	CCONJ
ajtas-2922	65	29	applied	apply	VERB
ajtas-2922	65	30	sciences	science	NOUN
ajtas-2922	65	31	36	36	NUM
ajtas-2922	65	32	,	,	PUNCT
ajtas-2922	65	33	may	may	AUX
ajtas-2922	65	34	2025	2025	NUM
ajtas-2922	65	35	p	p	NOUN
ajtas-2922	65	36	a	a	DET
ajtas-2922	65	37	g	g	NOUN
ajtas-2922	65	38	e	e	NOUN
ajtas-2922	65	39	|	|	ADV
ajtas-2922	65	40	20	20	NUM
ajtas-2922	65	41	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-2922	65	42	references	reference	NOUN
ajtas-2922	65	43	1	1	NUM
ajtas-2922	65	44	.	.	PUNCT
ajtas-2922	65	45	cui	cui	PROPN
ajtas-2922	65	46	,	,	PUNCT
ajtas-2922	65	47	j.	j.	PROPN
ajtas-2922	65	48	;	;	PUNCT
ajtas-2922	65	49	ye	ye	PROPN
ajtas-2922	65	50	,	,	PUNCT
ajtas-2922	65	51	r.	r.	PROPN
ajtas-2922	65	52	;	;	PUNCT
ajtas-2922	65	53	zhao	zhao	X
ajtas-2922	65	54	,	,	PUNCT
ajtas-2922	65	55	n.	n.	PROPN
ajtas-2922	65	56	;	;	PUNCT
ajtas-2922	65	57	wu	wu	PROPN
ajtas-2922	65	58	,	,	PUNCT
ajtas-2922	65	59	j.	j.	PROPN
ajtas-2922	65	60	;	;	PUNCT
ajtas-2922	65	61	wang	wang	PROPN
ajtas-2922	65	62	,	,	PUNCT
ajtas-2922	65	63	m.	m.	NOUN
ajtas-2922	65	64	assessment	assessment	NOUN
ajtas-2922	65	65	on	on	ADP
ajtas-2922	65	66	energy	energy	NOUN
ajtas-2922	65	67	absorption	absorption	NOUN
ajtas-2922	65	68	of	of	ADP
ajtas-2922	65	69	double	double	ADJ
ajtas-2922	65	70	layered	layered	ADJ
ajtas-2922	65	71	and	and	CCONJ
ajtas-2922	65	72	sandwich	sandwich	NOUN
ajtas-2922	65	73	plates	plate	NOUN
ajtas-2922	65	74	under	under	ADP
ajtas-2922	65	75	ballistic	ballistic	ADJ
ajtas-2922	65	76	impact	impact	NOUN
ajtas-2922	65	77	.	.	PUNCT
ajtas-2922	66	1	thin‐walled	thin‐walle	VERB
ajtas-2922	66	2	struct	struct	NOUN
ajtas-2922	66	3	.	.	PUNCT
ajtas-2922	67	1	2018	2018	NUM
ajtas-2922	67	2	,	,	PUNCT
ajtas-2922	67	3	130	130	NUM
ajtas-2922	67	4	,	,	PUNCT
ajtas-2922	67	5	520–534	520–534	NUM
ajtas-2922	67	6	.	.	PUNCT
ajtas-2922	68	1	2	2	NUM
ajtas-2922	68	2	.	.	X
ajtas-2922	68	3	tian	tian	PROPN
ajtas-2922	68	4	,	,	PUNCT
ajtas-2922	68	5	a.	a.	NOUN
ajtas-2922	68	6	;	;	PUNCT
ajtas-2922	68	7	ye	ye	PROPN
ajtas-2922	68	8	,	,	PUNCT
ajtas-2922	68	9	r.	r.	PROPN
ajtas-2922	68	10	;	;	PUNCT
ajtas-2922	68	11	ren	ren	PROPN
ajtas-2922	68	12	,	,	PUNCT
ajtas-2922	68	13	p.	p.	PROPN
ajtas-2922	68	14	;	;	PUNCT
ajtas-2922	69	1	jiang	jiang	PROPN
ajtas-2922	69	2	,	,	PUNCT
ajtas-2922	69	3	p.	p.	PROPN
ajtas-2922	69	4	;	;	PUNCT
ajtas-2922	69	5	chen	chen	PROPN
ajtas-2922	69	6	,	,	PUNCT
ajtas-2922	69	7	z.	z.	PROPN
ajtas-2922	69	8	;	;	PUNCT
ajtas-2922	69	9	yin	yin	PROPN
ajtas-2922	69	10	,	,	PUNCT
ajtas-2922	69	11	x.	x.	PROPN
ajtas-2922	69	12	;	;	PUNCT
ajtas-2922	69	13	zhao	zhao	X
ajtas-2922	69	14	,	,	PUNCT
ajtas-2922	69	15	y.	y.	PROPN
ajtas-2922	69	16	new	new	ADJ
ajtas-2922	69	17	higher‐	higher‐	NOUN
ajtas-2922	69	18	order	order	NOUN
ajtas-2922	69	19	models	model	NOUN
ajtas-2922	69	20	for	for	ADP
ajtas-2922	69	21	sandwich	sandwich	NOUN
ajtas-2922	69	22	plates	plate	NOUN
ajtas-2922	69	23	with	with	ADP
ajtas-2922	69	24	a	a	DET
ajtas-2922	69	25	flexible	flexible	ADJ
ajtas-2922	69	26	core	core	NOUN
ajtas-2922	69	27	and	and	CCONJ
ajtas-2922	69	28	their	their	PRON
ajtas-2922	69	29	accuracy	accuracy	NOUN
ajtas-2922	69	30	assessment	assessment	NOUN
ajtas-2922	69	31	.	.	PUNCT
ajtas-2922	70	1	int	int	NOUN
ajtas-2922	70	2	.	.	PUNCT
ajtas-2922	71	1	j.	j.	PROPN
ajtas-2922	71	2	struct	struct	PROPN
ajtas-2922	71	3	.	.	PUNCT
ajtas-2922	72	1	stab	stab	PROPN
ajtas-2922	72	2	.	.	PUNCT
ajtas-2922	73	1	dyn	dyn	PROPN
ajtas-2922	73	2	.	.	PUNCT
ajtas-2922	74	1	2019	2019	NUM
ajtas-2922	74	2	,	,	PUNCT
ajtas-2922	74	3	19	19	NUM
ajtas-2922	74	4	,	,	PUNCT
ajtas-2922	74	5	1950024	1950024	NUM
ajtas-2922	74	6	.	.	PUNCT
ajtas-2922	75	1	3	3	X
ajtas-2922	75	2	.	.	X
ajtas-2922	75	3	zhao	zhao	PROPN
ajtas-2922	75	4	,	,	PUNCT
ajtas-2922	75	5	n.	n.	NOUN
ajtas-2922	75	6	;	;	PUNCT
ajtas-2922	75	7	ye	ye	PROPN
ajtas-2922	75	8	,	,	PUNCT
ajtas-2922	75	9	r.	r.	PROPN
ajtas-2922	75	10	;	;	PUNCT
ajtas-2922	75	11	tian	tian	PROPN
ajtas-2922	75	12	,	,	PUNCT
ajtas-2922	75	13	a.	a.	NOUN
ajtas-2922	75	14	;	;	PUNCT
ajtas-2922	75	15	cui	cui	PROPN
ajtas-2922	75	16	,	,	PUNCT
ajtas-2922	75	17	j.	j.	PROPN
ajtas-2922	75	18	;	;	PUNCT
ajtas-2922	75	19	ren	ren	PROPN
ajtas-2922	75	20	,	,	PUNCT
ajtas-2922	75	21	p.	p.	PROPN
ajtas-2922	75	22	;	;	PUNCT
ajtas-2922	75	23	wang	wang	PROPN
ajtas-2922	75	24	,	,	PUNCT
ajtas-2922	75	25	m.	m.	NOUN
ajtas-2922	75	26	experimental	experimental	ADJ
ajtas-2922	75	27	and	and	CCONJ
ajtas-2922	75	28	numerical	numerical	ADJ
ajtas-2922	75	29	investigation	investigation	NOUN
ajtas-2922	75	30	on	on	ADP
ajtas-2922	75	31	the	the	DET
ajtas-2922	75	32	anti‐	anti‐	NOUN
ajtas-2922	75	33	penetration	penetration	NOUN
ajtas-2922	75	34	performance	performance	NOUN
ajtas-2922	75	35	of	of	ADP
ajtas-2922	75	36	metallic	metallic	ADJ
ajtas-2922	75	37	sandwich	sandwich	NOUN
ajtas-2922	75	38	plates	plate	NOUN
ajtas-2922	75	39	for	for	ADP
ajtas-2922	75	40	marine	marine	ADJ
ajtas-2922	75	41	applications	application	NOUN
ajtas-2922	75	42	.	.	PUNCT
ajtas-2922	76	1	j.	j.	PROPN
ajtas-2922	76	2	sandw	sandw	PROPN
ajtas-2922	76	3	.	.	PUNCT
ajtas-2922	76	4	struct	struct	NOUN
ajtas-2922	76	5	.	.	PUNCT
ajtas-2922	77	1	mater	mater	NOUN
ajtas-2922	77	2	.	.	PUNCT
ajtas-2922	78	1	2019	2019	NUM
ajtas-2922	78	2	.	.	PUNCT
ajtas-2922	79	1	doi:10.1177/1099636219855335	doi:10.1177/1099636219855335	X
ajtas-2922	79	2	.	.	PUNCT
ajtas-2922	79	3	4	4	NUM
ajtas-2922	79	4	.	.	X
ajtas-2922	79	5	kirchhoff	kirchhoff	PROPN
ajtas-2922	79	6	,	,	PUNCT
ajtas-2922	79	7	v.g	v.g	PROPN
ajtas-2922	79	8	.	.	PROPN
ajtas-2922	79	9	uber	uber	PROPN
ajtas-2922	79	10	das	das	PROPN
ajtas-2922	79	11	gleichgewicht	gleichgewicht	PROPN
ajtas-2922	79	12	und	und	VERB
ajtas-2922	79	13	die	die	NOUN
ajtas-2922	79	14	bewegung	bewegung	NOUN
ajtas-2922	79	15	einer	einer	NOUN
ajtas-2922	79	16	elastischen	elastischen	X
ajtas-2922	79	17	scheibe	scheibe	NOUN
ajtas-2922	79	18	.	.	PUNCT
ajtas-2922	80	1	j.	j.	PROPN
ajtas-2922	80	2	fur	fur	PROPN
ajtas-2922	80	3	die	die	VERB
ajtas-2922	80	4	reine	reine	PROPN
ajtas-2922	80	5	und	und	PROPN
ajtas-2922	80	6	angew	angew	PROPN
ajtas-2922	80	7	.	.	PUNCT
ajtas-2922	81	1	math	math	NOUN
ajtas-2922	81	2	.	.	PUNCT
ajtas-2922	82	1	1850	1850	NUM
ajtas-2922	82	2	,	,	PUNCT
ajtas-2922	82	3	40	40	NUM
ajtas-2922	82	4	,	,	PUNCT
ajtas-2922	82	5	51–88	51–88	NUM
ajtas-2922	82	6	.	.	PUNCT
ajtas-2922	83	1	5	5	NUM
ajtas-2922	83	2	.	.	X
ajtas-2922	83	3	mohammadi	mohammadi	NOUN
ajtas-2922	83	4	,	,	PUNCT
ajtas-2922	83	5	m.	m.	NOUN
ajtas-2922	83	6	;	;	PUNCT
ajtas-2922	83	7	saidi	saidi	PROPN
ajtas-2922	83	8	,	,	PUNCT
ajtas-2922	83	9	a.r	a.r	PROPN
ajtas-2922	83	10	.	.	PROPN
ajtas-2922	83	11	;	;	PUNCT
ajtas-2922	84	1	jomehzadeh	jomehzadeh	PROPN
ajtas-2922	84	2	,	,	PUNCT
ajtas-2922	84	3	e.	e.	PROPN
ajtas-2922	84	4	levy	levy	PROPN
ajtas-2922	84	5	solution	solution	NOUN
ajtas-2922	84	6	for	for	ADP
ajtas-2922	84	7	buckling	buckle	VERB
ajtas-2922	84	8	analysis	analysis	NOUN
ajtas-2922	84	9	of	of	ADP
ajtas-2922	84	10	functionally	functionally	ADV
ajtas-2922	84	11	graded	grade	VERB
ajtas-2922	84	12	rectangular	rectangular	ADJ
ajtas-2922	84	13	plates	plate	NOUN
ajtas-2922	84	14	.	.	PUNCT
ajtas-2922	85	1	appl	appl	PROPN
ajtas-2922	85	2	.	.	PUNCT
ajtas-2922	86	1	compos	compos	PROPN
ajtas-2922	86	2	.	.	PUNCT
ajtas-2922	87	1	mater	mater	PROPN
ajtas-2922	87	2	.	.	PUNCT
ajtas-2922	88	1	2010	2010	NUM
ajtas-2922	88	2	,	,	PUNCT
ajtas-2922	88	3	17	17	NUM
ajtas-2922	88	4	,	,	PUNCT
ajtas-2922	88	5	81–93	81–93	NUM
ajtas-2922	88	6	.	.	PUNCT
ajtas-2922	89	1	6	6	NUM
ajtas-2922	89	2	.	.	X
ajtas-2922	89	3	mindlin	mindlin	PROPN
ajtas-2922	89	4	,	,	PUNCT
ajtas-2922	89	5	r.d	r.d	PROPN
ajtas-2922	89	6	.	.	PROPN
ajtas-2922	89	7	influence	influence	NOUN
ajtas-2922	89	8	of	of	ADP
ajtas-2922	89	9	rotatory	rotatory	ADJ
ajtas-2922	89	10	inertia	inertia	NOUN
ajtas-2922	89	11	and	and	CCONJ
ajtas-2922	89	12	shear	shear	NOUN
ajtas-2922	89	13	on	on	ADP
ajtas-2922	89	14	flexural	flexural	ADJ
ajtas-2922	89	15	motions	motion	NOUN
ajtas-2922	89	16	of	of	ADP
ajtas-2922	89	17	isotropic	isotropic	NOUN
ajtas-2922	89	18	,	,	PUNCT
ajtas-2922	89	19	elastic	elastic	ADJ
ajtas-2922	89	20	plates	plate	NOUN
ajtas-2922	89	21	.	.	PUNCT
ajtas-2922	90	1	j.	j.	PROPN
ajtas-2922	90	2	appl	appl	PROPN
ajtas-2922	90	3	.	.	PROPN
ajtas-2922	90	4	mech	mech	PROPN
ajtas-2922	90	5	.	.	PUNCT
ajtas-2922	91	1	1951	1951	NUM
ajtas-2922	91	2	,	,	PUNCT
ajtas-2922	91	3	18	18	NUM
ajtas-2922	91	4	,	,	PUNCT
ajtas-2922	91	5	31–38	31–38	NUM
ajtas-2922	91	6	.	.	NOUN
ajtas-2922	91	7	7	7	NUM
ajtas-2922	91	8	.	.	X
ajtas-2922	91	9	ardestani	ardestani	PROPN
ajtas-2922	91	10	,	,	PUNCT
ajtas-2922	91	11	m.m	m.m	PROPN
ajtas-2922	91	12	.	.	PROPN
ajtas-2922	91	13	;	;	PUNCT
ajtas-2922	91	14	soltani	soltani	PROPN
ajtas-2922	91	15	,	,	PUNCT
ajtas-2922	91	16	b.	b.	PROPN
ajtas-2922	91	17	;	;	PUNCT
ajtas-2922	91	18	shams	sham	NOUN
ajtas-2922	91	19	,	,	PUNCT
ajtas-2922	91	20	s.	s.	PROPN
ajtas-2922	91	21	analysis	analysis	NOUN
ajtas-2922	91	22	of	of	ADP
ajtas-2922	91	23	functionally	functionally	ADV
ajtas-2922	91	24	graded	grade	VERB
ajtas-2922	91	25	stiffened	stiffen	VERB
ajtas-2922	91	26	plates	plate	NOUN
ajtas-2922	91	27	based	base	VERB
ajtas-2922	91	28	on	on	ADP
ajtas-2922	91	29	fsdt	fsdt	NOUN
ajtas-2922	91	30	utilizing	utilize	VERB
ajtas-2922	91	31	reproducing	reproduce	VERB
ajtas-2922	91	32	kernel	kernel	PROPN
ajtas-2922	91	33	particle	particle	NOUN
ajtas-2922	91	34	method	method	NOUN
ajtas-2922	91	35	.	.	PUNCT
ajtas-2922	92	1	compos	compos	NOUN
ajtas-2922	92	2	.	.	PUNCT
ajtas-2922	93	1	struct	struct	NOUN
ajtas-2922	93	2	.	.	PUNCT
ajtas-2922	94	1	2014	2014	NUM
ajtas-2922	94	2	.	.	PUNCT