id	sid	tid	token	lemma	pos
american_scientific_journal-7074	1	1	1	1	NUM
american_scientific_journal-7074	1	2	american	american	ADJ
american_scientific_journal-7074	1	3	academic	academic	ADJ
american_scientific_journal-7074	1	4	scientific	scientific	ADJ
american_scientific_journal-7074	1	5	research	research	NOUN
american_scientific_journal-7074	1	6	journal	journal	NOUN
american_scientific_journal-7074	1	7	for	for	ADP
american_scientific_journal-7074	1	8	engineering	engineering	NOUN
american_scientific_journal-7074	1	9	,	,	PUNCT
american_scientific_journal-7074	1	10	technology	technology	NOUN
american_scientific_journal-7074	1	11	,	,	PUNCT
american_scientific_journal-7074	1	12	and	and	CCONJ
american_scientific_journal-7074	1	13	sciences	sciences	PROPN
american_scientific_journal-7074	1	14	issn	issn	PROPN
american_scientific_journal-7074	1	15	(	(	PUNCT
american_scientific_journal-7074	1	16	print	print	NOUN
american_scientific_journal-7074	1	17	)	)	PUNCT
american_scientific_journal-7074	1	18	2313	2313	NUM
american_scientific_journal-7074	1	19	-	-	SYM
american_scientific_journal-7074	1	20	4410	4410	NUM
american_scientific_journal-7074	1	21	,	,	PUNCT
american_scientific_journal-7074	1	22	issn	issn	PROPN
american_scientific_journal-7074	1	23	(	(	PUNCT
american_scientific_journal-7074	1	24	online	online	ADJ
american_scientific_journal-7074	1	25	)	)	PUNCT
american_scientific_journal-7074	1	26	2313	2313	NUM
american_scientific_journal-7074	1	27	-	-	SYM
american_scientific_journal-7074	1	28	4402	4402	NUM
american_scientific_journal-7074	1	29	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-7074	1	30	linear	linear	ADJ
american_scientific_journal-7074	1	31	strain	strain	NOUN
american_scientific_journal-7074	1	32	triangle	triangle	NOUN
american_scientific_journal-7074	1	33	mathematics	mathematic	NOUN
american_scientific_journal-7074	1	34	:	:	PUNCT
american_scientific_journal-7074	1	35	stiffness	stiffness	ADJ
american_scientific_journal-7074	1	36	,	,	PUNCT
american_scientific_journal-7074	1	37	stress	stress	NOUN
american_scientific_journal-7074	1	38	and	and	CCONJ
american_scientific_journal-7074	1	39	consistent	consistent	ADJ
american_scientific_journal-7074	1	40	load	load	NOUN
american_scientific_journal-7074	1	41	vector	vector	NOUN
american_scientific_journal-7074	1	42	mohamed	mohamed	PROPN
american_scientific_journal-7074	1	43	abdalla	abdalla	PROPN
american_scientific_journal-7074	1	44	almheriegh	almheriegh	PROPN
american_scientific_journal-7074	1	45	*	*	PUNCT
american_scientific_journal-7074	1	46	associate	associate	NOUN
american_scientific_journal-7074	1	47	professor	professor	NOUN
american_scientific_journal-7074	1	48	,	,	PUNCT
american_scientific_journal-7074	1	49	department	department	NOUN
american_scientific_journal-7074	1	50	of	of	ADP
american_scientific_journal-7074	1	51	civil	civil	ADJ
american_scientific_journal-7074	1	52	engineering	engineering	NOUN
american_scientific_journal-7074	1	53	,	,	PUNCT
american_scientific_journal-7074	1	54	faculty	faculty	NOUN
american_scientific_journal-7074	1	55	of	of	ADP
american_scientific_journal-7074	1	56	engineering	engineering	PROPN
american_scientific_journal-7074	1	57	tripoli	tripoli	PROPN
american_scientific_journal-7074	1	58	university	university	PROPN
american_scientific_journal-7074	1	59	,	,	PUNCT
american_scientific_journal-7074	1	60	p	p	PROPN
american_scientific_journal-7074	1	61	o	o	PROPN
american_scientific_journal-7074	1	62	box	box	NOUN
american_scientific_journal-7074	1	63	82677	82677	NUM
american_scientific_journal-7074	1	64	,	,	PUNCT
american_scientific_journal-7074	1	65	tripoli	tripoli	PROPN
american_scientific_journal-7074	1	66	,	,	PUNCT
american_scientific_journal-7074	1	67	libya	libya	PROPN
american_scientific_journal-7074	1	68	email	email	NOUN
american_scientific_journal-7074	1	69	:	:	PUNCT
american_scientific_journal-7074	1	70	malmherigh@gmail.com	malmherigh@gmail.com	X
american_scientific_journal-7074	2	1	abstract	abstract	PROPN
american_scientific_journal-7074	2	2	typically	typically	ADV
american_scientific_journal-7074	2	3	,	,	PUNCT
american_scientific_journal-7074	2	4	linear	linear	ADJ
american_scientific_journal-7074	2	5	strain	strain	NOUN
american_scientific_journal-7074	2	6	triangle	triangle	NOUN
american_scientific_journal-7074	2	7	lst	lst	VERB
american_scientific_journal-7074	2	8	is	be	AUX
american_scientific_journal-7074	2	9	widely	widely	ADV
american_scientific_journal-7074	2	10	used	use	VERB
american_scientific_journal-7074	2	11	for	for	ADP
american_scientific_journal-7074	2	12	elastic	elastic	ADJ
american_scientific_journal-7074	2	13	analysis	analysis	NOUN
american_scientific_journal-7074	2	14	not	not	PART
american_scientific_journal-7074	2	15	only	only	ADV
american_scientific_journal-7074	2	16	due	due	ADJ
american_scientific_journal-7074	2	17	to	to	ADP
american_scientific_journal-7074	2	18	its	its	PRON
american_scientific_journal-7074	2	19	ease	ease	NOUN
american_scientific_journal-7074	2	20	but	but	CCONJ
american_scientific_journal-7074	2	21	also	also	ADV
american_scientific_journal-7074	2	22	due	due	ADP
american_scientific_journal-7074	2	23	to	to	ADP
american_scientific_journal-7074	2	24	the	the	DET
american_scientific_journal-7074	2	25	good	good	ADJ
american_scientific_journal-7074	2	26	results	result	NOUN
american_scientific_journal-7074	2	27	it	it	PRON
american_scientific_journal-7074	2	28	can	can	AUX
american_scientific_journal-7074	2	29	lead	lead	VERB
american_scientific_journal-7074	2	30	to	to	ADP
american_scientific_journal-7074	2	31	over	over	ADP
american_scientific_journal-7074	2	32	the	the	DET
american_scientific_journal-7074	2	33	traditional	traditional	ADJ
american_scientific_journal-7074	2	34	constant	constant	ADJ
american_scientific_journal-7074	2	35	strain	strain	NOUN
american_scientific_journal-7074	2	36	triangle	triangle	NOUN
american_scientific_journal-7074	2	37	cst	cst	PROPN
american_scientific_journal-7074	2	38	.	.	PUNCT
american_scientific_journal-7074	3	1	in	in	ADP
american_scientific_journal-7074	3	2	plane	plane	NOUN
american_scientific_journal-7074	3	3	elastic	elastic	ADJ
american_scientific_journal-7074	3	4	analysis	analysis	NOUN
american_scientific_journal-7074	3	5	of	of	ADP
american_scientific_journal-7074	3	6	two	two	NUM
american_scientific_journal-7074	3	7	combined	combine	VERB
american_scientific_journal-7074	3	8	materials	material	NOUN
american_scientific_journal-7074	3	9	the	the	DET
american_scientific_journal-7074	3	10	lst	lst	NOUN
american_scientific_journal-7074	3	11	is	be	AUX
american_scientific_journal-7074	3	12	quite	quite	ADV
american_scientific_journal-7074	3	13	reliable	reliable	ADJ
american_scientific_journal-7074	3	14	and	and	CCONJ
american_scientific_journal-7074	3	15	trust	trust	VERB
american_scientific_journal-7074	3	16	worthy	worthy	ADJ
american_scientific_journal-7074	3	17	in	in	ADP
american_scientific_journal-7074	3	18	terms	term	NOUN
american_scientific_journal-7074	3	19	of	of	ADP
american_scientific_journal-7074	3	20	stress	stress	NOUN
american_scientific_journal-7074	3	21	results	result	NOUN
american_scientific_journal-7074	3	22	for	for	ADP
american_scientific_journal-7074	3	23	the	the	DET
american_scientific_journal-7074	3	24	same	same	ADJ
american_scientific_journal-7074	3	25	element	element	NOUN
american_scientific_journal-7074	3	26	size	size	NOUN
american_scientific_journal-7074	3	27	,	,	PUNCT
american_scientific_journal-7074	3	28	lst	lst	INTJ
american_scientific_journal-7074	3	29	is	be	AUX
american_scientific_journal-7074	3	30	very	very	ADV
american_scientific_journal-7074	3	31	useful	useful	ADJ
american_scientific_journal-7074	3	32	in	in	ADP
american_scientific_journal-7074	3	33	modelling	model	VERB
american_scientific_journal-7074	3	34	combined	combine	VERB
american_scientific_journal-7074	3	35	materials	material	NOUN
american_scientific_journal-7074	3	36	thus	thus	ADV
american_scientific_journal-7074	3	37	believed	believe	VERB
american_scientific_journal-7074	3	38	to	to	PART
american_scientific_journal-7074	3	39	be	be	AUX
american_scientific_journal-7074	3	40	efficient	efficient	ADJ
american_scientific_journal-7074	3	41	and	and	CCONJ
american_scientific_journal-7074	3	42	can	can	AUX
american_scientific_journal-7074	3	43	easily	easily	ADV
american_scientific_journal-7074	3	44	take	take	VERB
american_scientific_journal-7074	3	45	into	into	ADP
american_scientific_journal-7074	3	46	consideration	consideration	NOUN
american_scientific_journal-7074	3	47	,	,	PUNCT
american_scientific_journal-7074	3	48	self	self	NOUN
american_scientific_journal-7074	3	49	-	-	PUNCT
american_scientific_journal-7074	3	50	weight	weight	NOUN
american_scientific_journal-7074	3	51	of	of	ADP
american_scientific_journal-7074	3	52	used	use	VERB
american_scientific_journal-7074	3	53	materials	material	NOUN
american_scientific_journal-7074	3	54	,	,	PUNCT
american_scientific_journal-7074	3	55	strains	strain	NOUN
american_scientific_journal-7074	3	56	due	due	ADJ
american_scientific_journal-7074	3	57	to	to	ADP
american_scientific_journal-7074	3	58	causes	cause	VERB
american_scientific_journal-7074	3	59	other	other	ADJ
american_scientific_journal-7074	3	60	than	than	ADP
american_scientific_journal-7074	3	61	loading	loading	NOUN
american_scientific_journal-7074	3	62	;	;	PUNCT
american_scientific_journal-7074	3	63	such	such	ADJ
american_scientific_journal-7074	3	64	as	as	ADP
american_scientific_journal-7074	3	65	moisture	moisture	NOUN
american_scientific_journal-7074	3	66	,	,	PUNCT
american_scientific_journal-7074	3	67	temperature	temperature	NOUN
american_scientific_journal-7074	3	68	,	,	PUNCT
american_scientific_journal-7074	3	69	creep	creep	NOUN
american_scientific_journal-7074	3	70	and	and	CCONJ
american_scientific_journal-7074	3	71	shrinkage	shrinkage	NOUN
american_scientific_journal-7074	3	72	are	be	AUX
american_scientific_journal-7074	3	73	easily	easily	ADV
american_scientific_journal-7074	3	74	incorporated	incorporate	VERB
american_scientific_journal-7074	3	75	.	.	PUNCT
american_scientific_journal-7074	4	1	a	a	DET
american_scientific_journal-7074	4	2	mathematical	mathematical	ADJ
american_scientific_journal-7074	4	3	formulation	formulation	NOUN
american_scientific_journal-7074	4	4	of	of	ADP
american_scientific_journal-7074	4	5	stiffness	stiffness	ADJ
american_scientific_journal-7074	4	6	matrix	matrix	NOUN
american_scientific_journal-7074	4	7	,	,	PUNCT
american_scientific_journal-7074	4	8	stress	stress	NOUN
american_scientific_journal-7074	4	9	and	and	CCONJ
american_scientific_journal-7074	4	10	the	the	PRON
american_scientific_journal-7074	4	11	more	more	ADV
american_scientific_journal-7074	4	12	rarely	rarely	ADV
american_scientific_journal-7074	4	13	dealt	deal	VERB
american_scientific_journal-7074	4	14	with	with	ADP
american_scientific_journal-7074	4	15	consistent	consistent	ADJ
american_scientific_journal-7074	4	16	load	load	NOUN
american_scientific_journal-7074	4	17	vector	vector	NOUN
american_scientific_journal-7074	4	18	for	for	ADP
american_scientific_journal-7074	4	19	loads	load	NOUN
american_scientific_journal-7074	4	20	distributed	distribute	VERB
american_scientific_journal-7074	4	21	on	on	ADP
american_scientific_journal-7074	4	22	element	element	ADJ
american_scientific_journal-7074	4	23	edge	edge	NOUN
american_scientific_journal-7074	4	24	are	be	AUX
american_scientific_journal-7074	4	25	proved	prove	VERB
american_scientific_journal-7074	4	26	and	and	CCONJ
american_scientific_journal-7074	4	27	highlighted	highlight	VERB
american_scientific_journal-7074	4	28	for	for	ADP
american_scientific_journal-7074	4	29	young	young	ADJ
american_scientific_journal-7074	4	30	engineers	engineer	NOUN
american_scientific_journal-7074	4	31	who	who	PRON
american_scientific_journal-7074	4	32	mostly	mostly	ADV
american_scientific_journal-7074	4	33	dealing	deal	VERB
american_scientific_journal-7074	4	34	with	with	ADP
american_scientific_journal-7074	4	35	readily	readily	ADV
american_scientific_journal-7074	4	36	used	use	VERB
american_scientific_journal-7074	4	37	fe	fe	NOUN
american_scientific_journal-7074	4	38	codes	code	NOUN
american_scientific_journal-7074	4	39	,	,	PUNCT
american_scientific_journal-7074	4	40	the	the	DET
american_scientific_journal-7074	4	41	formula	formula	NOUN
american_scientific_journal-7074	4	42	proved	prove	VERB
american_scientific_journal-7074	4	43	for	for	ADP
american_scientific_journal-7074	4	44	lst	lst	NOUN
american_scientific_journal-7074	4	45	element	element	NOUN
american_scientific_journal-7074	4	46	load	load	NOUN
american_scientific_journal-7074	4	47	vector	vector	NOUN
american_scientific_journal-7074	4	48	is	be	AUX
american_scientific_journal-7074	4	49	further	far	ADV
american_scientific_journal-7074	4	50	extended	extend	VERB
american_scientific_journal-7074	4	51	and	and	CCONJ
american_scientific_journal-7074	4	52	thus	thus	ADV
american_scientific_journal-7074	4	53	a	a	DET
american_scientific_journal-7074	4	54	consisted	consist	VERB
american_scientific_journal-7074	4	55	load	load	NOUN
american_scientific_journal-7074	4	56	vector	vector	NOUN
american_scientific_journal-7074	4	57	for	for	ADP
american_scientific_journal-7074	4	58	conical	conical	ADJ
american_scientific_journal-7074	4	59	axe	axe	NOUN
american_scientific_journal-7074	4	60	-	-	PUNCT
american_scientific_journal-7074	4	61	symmetric	symmetric	ADJ
american_scientific_journal-7074	4	62	shell	shell	NOUN
american_scientific_journal-7074	4	63	element	element	NOUN
american_scientific_journal-7074	4	64	is	be	AUX
american_scientific_journal-7074	4	65	introduced	introduce	VERB
american_scientific_journal-7074	4	66	.	.	PUNCT
american_scientific_journal-7074	5	1	keywords	keyword	NOUN
american_scientific_journal-7074	5	2	:	:	PUNCT
american_scientific_journal-7074	5	3	consistent	consistent	ADJ
american_scientific_journal-7074	5	4	load	load	NOUN
american_scientific_journal-7074	5	5	vector	vector	NOUN
american_scientific_journal-7074	5	6	for	for	ADP
american_scientific_journal-7074	5	7	conical	conical	ADJ
american_scientific_journal-7074	5	8	axe	axe	NOUN
american_scientific_journal-7074	5	9	-	-	PUNCT
american_scientific_journal-7074	5	10	symmetric	symmetric	ADJ
american_scientific_journal-7074	5	11	shell	shell	NOUN
american_scientific_journal-7074	5	12	element	element	NOUN
american_scientific_journal-7074	5	13	or	or	CCONJ
american_scientific_journal-7074	5	14	pressure	pressure	NOUN
american_scientific_journal-7074	5	15	vessel	vessel	NOUN
american_scientific_journal-7074	5	16	element	element	NOUN
american_scientific_journal-7074	5	17	;	;	PUNCT
american_scientific_journal-7074	5	18	modeling	modeling	NOUN
american_scientific_journal-7074	5	19	of	of	ADP
american_scientific_journal-7074	5	20	multiple	multiple	ADJ
american_scientific_journal-7074	5	21	materials	material	NOUN
american_scientific_journal-7074	5	22	;	;	PUNCT
american_scientific_journal-7074	5	23	mathematics	mathematic	NOUN
american_scientific_journal-7074	5	24	of	of	ADP
american_scientific_journal-7074	5	25	finite	finite	PROPN
american_scientific_journal-7074	5	26	element	element	PROPN
american_scientific_journal-7074	5	27	lst	lst	PROPN
american_scientific_journal-7074	5	28	;	;	PUNCT
american_scientific_journal-7074	5	29	stiffness	stiffness	ADJ
american_scientific_journal-7074	5	30	matrix	matrix	NOUN
american_scientific_journal-7074	5	31	,	,	PUNCT
american_scientific_journal-7074	5	32	stress	stress	NOUN
american_scientific_journal-7074	5	33	and	and	CCONJ
american_scientific_journal-7074	5	34	,	,	PUNCT
american_scientific_journal-7074	5	35	consistent	consistent	ADJ
american_scientific_journal-7074	5	36	load	load	NOUN
american_scientific_journal-7074	5	37	vector	vector	NOUN
american_scientific_journal-7074	5	38	.	.	PUNCT
american_scientific_journal-7074	6	1	1	1	X
american_scientific_journal-7074	6	2	.	.	X
american_scientific_journal-7074	6	3	introduction	introduction	NOUN
american_scientific_journal-7074	6	4	the	the	DET
american_scientific_journal-7074	6	5	constant	constant	ADJ
american_scientific_journal-7074	6	6	strain	strain	NOUN
american_scientific_journal-7074	6	7	triangle	triangle	NOUN
american_scientific_journal-7074	6	8	cst	cst	PROPN
american_scientific_journal-7074	6	9	provides	provide	VERB
american_scientific_journal-7074	6	10	good	good	ADJ
american_scientific_journal-7074	6	11	introduction	introduction	NOUN
american_scientific_journal-7074	6	12	that	that	PRON
american_scientific_journal-7074	6	13	is	be	AUX
american_scientific_journal-7074	6	14	easily	easily	ADV
american_scientific_journal-7074	6	15	understood	understand	VERB
american_scientific_journal-7074	6	16	and	and	CCONJ
american_scientific_journal-7074	6	17	formulated	formulate	VERB
american_scientific_journal-7074	6	18	.	.	PUNCT
american_scientific_journal-7074	7	1	it	it	PRON
american_scientific_journal-7074	7	2	is	be	AUX
american_scientific_journal-7074	7	3	also	also	ADV
american_scientific_journal-7074	7	4	a	a	DET
american_scientific_journal-7074	7	5	useful	useful	ADJ
american_scientific_journal-7074	7	6	element	element	NOUN
american_scientific_journal-7074	7	7	for	for	ADP
american_scientific_journal-7074	7	8	practical	practical	ADJ
american_scientific_journal-7074	7	9	problems	problem	NOUN
american_scientific_journal-7074	7	10	,	,	PUNCT
american_scientific_journal-7074	7	11	but	but	CCONJ
american_scientific_journal-7074	7	12	does	do	AUX
american_scientific_journal-7074	7	13	require	require	VERB
american_scientific_journal-7074	7	14	that	that	SCONJ
american_scientific_journal-7074	7	15	rather	rather	ADV
american_scientific_journal-7074	7	16	small	small	ADJ
american_scientific_journal-7074	7	17	elements	element	NOUN
american_scientific_journal-7074	7	18	be	be	AUX
american_scientific_journal-7074	7	19	used	use	VERB
american_scientific_journal-7074	7	20	in	in	ADP
american_scientific_journal-7074	7	21	regions	region	NOUN
american_scientific_journal-7074	7	22	where	where	SCONJ
american_scientific_journal-7074	7	23	stress	stress	NOUN
american_scientific_journal-7074	7	24	varies	vary	VERB
american_scientific_journal-7074	7	25	abruptly	abruptly	ADV
american_scientific_journal-7074	7	26	.	.	PUNCT
american_scientific_journal-7074	8	1	this	this	PRON
american_scientific_journal-7074	8	2	means	mean	VERB
american_scientific_journal-7074	8	3	that	that	SCONJ
american_scientific_journal-7074	8	4	the	the	DET
american_scientific_journal-7074	8	5	number	number	NOUN
american_scientific_journal-7074	8	6	of	of	ADP
american_scientific_journal-7074	8	7	such	such	ADJ
american_scientific_journal-7074	8	8	elements	element	NOUN
american_scientific_journal-7074	8	9	tends	tend	VERB
american_scientific_journal-7074	8	10	to	to	PART
american_scientific_journal-7074	8	11	be	be	AUX
american_scientific_journal-7074	8	12	large	large	ADJ
american_scientific_journal-7074	8	13	when	when	SCONJ
american_scientific_journal-7074	8	14	reliable	reliable	ADJ
american_scientific_journal-7074	8	15	stress	stress	NOUN
american_scientific_journal-7074	8	16	values	value	NOUN
american_scientific_journal-7074	8	17	are	be	AUX
american_scientific_journal-7074	8	18	needed	need	VERB
american_scientific_journal-7074	8	19	.	.	PUNCT
american_scientific_journal-7074	9	1	by	by	ADP
american_scientific_journal-7074	9	2	using	use	VERB
american_scientific_journal-7074	9	3	more	more	ADV
american_scientific_journal-7074	9	4	advanced	advanced	ADJ
american_scientific_journal-7074	9	5	elements	element	NOUN
american_scientific_journal-7074	9	6	such	such	ADJ
american_scientific_journal-7074	9	7	as	as	ADP
american_scientific_journal-7074	9	8	lst	lst	NOUN
american_scientific_journal-7074	9	9	,	,	PUNCT
american_scientific_journal-7074	9	10	in	in	ADP
american_scientific_journal-7074	9	11	which	which	PRON
american_scientific_journal-7074	9	12	the	the	DET
american_scientific_journal-7074	9	13	stress	stress	NOUN
american_scientific_journal-7074	9	14	may	may	AUX
american_scientific_journal-7074	9	15	vary	vary	VERB
american_scientific_journal-7074	9	16	within	within	ADP
american_scientific_journal-7074	9	17	the	the	DET
american_scientific_journal-7074	9	18	element	element	NOUN
american_scientific_journal-7074	9	19	,	,	PUNCT
american_scientific_journal-7074	9	20	much	much	ADV
american_scientific_journal-7074	9	21	better	well	ADJ
american_scientific_journal-7074	9	22	results	result	NOUN
american_scientific_journal-7074	9	23	can	can	AUX
american_scientific_journal-7074	9	24	be	be	AUX
american_scientific_journal-7074	9	25	obtained	obtain	VERB
american_scientific_journal-7074	9	26	with	with	ADP
american_scientific_journal-7074	9	27	the	the	DET
american_scientific_journal-7074	9	28	same	same	ADJ
american_scientific_journal-7074	9	29	number	number	NOUN
american_scientific_journal-7074	9	30	of	of	ADP
american_scientific_journal-7074	9	31	elements	element	NOUN
american_scientific_journal-7074	9	32	.	.	PUNCT
american_scientific_journal-7074	10	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-7074	11	1	*	*	PUNCT
american_scientific_journal-7074	11	2	corresponding	correspond	VERB
american_scientific_journal-7074	11	3	author	author	NOUN
american_scientific_journal-7074	11	4	.	.	PUNCT
american_scientific_journal-7074	12	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-7074	12	2	american	american	PROPN
american_scientific_journal-7074	12	3	academic	academic	PROPN
american_scientific_journal-7074	12	4	scientific	scientific	ADJ
american_scientific_journal-7074	12	5	research	research	NOUN
american_scientific_journal-7074	12	6	journal	journal	NOUN
american_scientific_journal-7074	12	7	for	for	ADP
american_scientific_journal-7074	12	8	engineering	engineering	NOUN
american_scientific_journal-7074	12	9	,	,	PUNCT
american_scientific_journal-7074	12	10	technology	technology	NOUN
american_scientific_journal-7074	12	11	,	,	PUNCT
american_scientific_journal-7074	12	12	and	and	CCONJ
american_scientific_journal-7074	12	13	sciences	science	NOUN
american_scientific_journal-7074	12	14	(	(	PUNCT
american_scientific_journal-7074	12	15	asrjets	asrjet	NOUN
american_scientific_journal-7074	12	16	)	)	PUNCT
american_scientific_journal-7074	12	17	(	(	PUNCT
american_scientific_journal-7074	12	18	2021	2021	NUM
american_scientific_journal-7074	12	19	)	)	PUNCT
american_scientific_journal-7074	12	20	volume	volume	NOUN
american_scientific_journal-7074	12	21	83	83	NUM
american_scientific_journal-7074	12	22	,	,	PUNCT
american_scientific_journal-7074	12	23	no	no	DET
american_scientific_journal-7074	12	24	1	1	NUM
american_scientific_journal-7074	12	25	,	,	PUNCT
american_scientific_journal-7074	12	26	pp	pp	ADV
american_scientific_journal-7074	12	27	1	1	NUM
american_scientific_journal-7074	12	28	-	-	SYM
american_scientific_journal-7074	12	29	11	11	NUM
american_scientific_journal-7074	12	30	2	2	NUM
american_scientific_journal-7074	12	31	there	there	PRON
american_scientific_journal-7074	12	32	is	be	VERB
american_scientific_journal-7074	12	33	no	no	DET
american_scientific_journal-7074	12	34	limit	limit	NOUN
american_scientific_journal-7074	12	35	to	to	ADP
american_scientific_journal-7074	12	36	the	the	DET
american_scientific_journal-7074	12	37	degree	degree	NOUN
american_scientific_journal-7074	12	38	of	of	ADP
american_scientific_journal-7074	12	39	variation	variation	NOUN
american_scientific_journal-7074	12	40	in	in	ADP
american_scientific_journal-7074	12	41	stress	stress	NOUN
american_scientific_journal-7074	12	42	that	that	PRON
american_scientific_journal-7074	12	43	can	can	AUX
american_scientific_journal-7074	12	44	be	be	AUX
american_scientific_journal-7074	12	45	specified	specify	VERB
american_scientific_journal-7074	12	46	and	and	CCONJ
american_scientific_journal-7074	12	47	,	,	PUNCT
american_scientific_journal-7074	12	48	in	in	ADP
american_scientific_journal-7074	12	49	this	this	DET
american_scientific_journal-7074	12	50	paper	paper	NOUN
american_scientific_journal-7074	12	51	,	,	PUNCT
american_scientific_journal-7074	12	52	only	only	ADV
american_scientific_journal-7074	12	53	one	one	NUM
american_scientific_journal-7074	12	54	step	step	NOUN
american_scientific_journal-7074	12	55	in	in	ADP
american_scientific_journal-7074	12	56	this	this	DET
american_scientific_journal-7074	12	57	direction	direction	NOUN
american_scientific_journal-7074	12	58	will	will	AUX
american_scientific_journal-7074	12	59	be	be	AUX
american_scientific_journal-7074	12	60	taken	take	VERB
american_scientific_journal-7074	12	61	;	;	PUNCT
american_scientific_journal-7074	12	62	provision	provision	NOUN
american_scientific_journal-7074	12	63	will	will	AUX
american_scientific_journal-7074	12	64	be	be	AUX
american_scientific_journal-7074	12	65	made	make	VERB
american_scientific_journal-7074	12	66	for	for	SCONJ
american_scientific_journal-7074	12	67	the	the	DET
american_scientific_journal-7074	12	68	stress	stress	NOUN
american_scientific_journal-7074	12	69	to	to	PART
american_scientific_journal-7074	12	70	vary	vary	VERB
american_scientific_journal-7074	12	71	linearly	linearly	ADV
american_scientific_journal-7074	12	72	within	within	ADP
american_scientific_journal-7074	12	73	the	the	DET
american_scientific_journal-7074	12	74	element	element	NOUN
american_scientific_journal-7074	12	75	a	a	DET
american_scientific_journal-7074	12	76	mathematical	mathematical	ADJ
american_scientific_journal-7074	12	77	presentation	presentation	NOUN
american_scientific_journal-7074	12	78	of	of	ADP
american_scientific_journal-7074	12	79	stiffens	stiffen	NOUN
american_scientific_journal-7074	12	80	matrix	matrix	NOUN
american_scientific_journal-7074	12	81	,	,	PUNCT
american_scientific_journal-7074	12	82	stress	stress	NOUN
american_scientific_journal-7074	12	83	and	and	CCONJ
american_scientific_journal-7074	12	84	the	the	PRON
american_scientific_journal-7074	12	85	rarely	rarely	ADV
american_scientific_journal-7074	12	86	dealt	deal	VERB
american_scientific_journal-7074	12	87	with	with	ADP
american_scientific_journal-7074	12	88	consistent	consistent	ADJ
american_scientific_journal-7074	12	89	load	load	NOUN
american_scientific_journal-7074	12	90	vector	vector	NOUN
american_scientific_journal-7074	12	91	is	be	AUX
american_scientific_journal-7074	12	92	proved	prove	VERB
american_scientific_journal-7074	12	93	based	base	VERB
american_scientific_journal-7074	12	94	on	on	ADP
american_scientific_journal-7074	12	95	conservation	conservation	NOUN
american_scientific_journal-7074	12	96	of	of	ADP
american_scientific_journal-7074	12	97	energy	energy	NOUN
american_scientific_journal-7074	12	98	principle	principle	NOUN
american_scientific_journal-7074	12	99	the	the	DET
american_scientific_journal-7074	12	100	formula	formula	NOUN
american_scientific_journal-7074	12	101	is	be	AUX
american_scientific_journal-7074	12	102	readily	readily	ADV
american_scientific_journal-7074	12	103	extended	extend	VERB
american_scientific_journal-7074	12	104	to	to	ADP
american_scientific_journal-7074	12	105	axe	axe	NOUN
american_scientific_journal-7074	12	106	-	-	PUNCT
american_scientific_journal-7074	12	107	symmetric	symmetric	ADJ
american_scientific_journal-7074	12	108	or	or	CCONJ
american_scientific_journal-7074	12	109	pressure	pressure	NOUN
american_scientific_journal-7074	12	110	vessel	vessel	NOUN
american_scientific_journal-7074	12	111	element	element	NOUN
american_scientific_journal-7074	12	112	.	.	PUNCT
american_scientific_journal-7074	13	1	2	2	X
american_scientific_journal-7074	13	2	.	.	X
american_scientific_journal-7074	13	3	displacement	displacement	ADJ
american_scientific_journal-7074	13	4	functions	function	NOUN
american_scientific_journal-7074	13	5	later	later	ADV
american_scientific_journal-7074	13	6	it	it	PRON
american_scientific_journal-7074	13	7	will	will	AUX
american_scientific_journal-7074	13	8	be	be	AUX
american_scientific_journal-7074	13	9	shown	show	VERB
american_scientific_journal-7074	13	10	that	that	SCONJ
american_scientific_journal-7074	13	11	the	the	DET
american_scientific_journal-7074	13	12	strain	strain	NOUN
american_scientific_journal-7074	13	13	,	,	PUNCT
american_scientific_journal-7074	13	14	and	and	CCONJ
american_scientific_journal-7074	13	15	hence	hence	ADV
american_scientific_journal-7074	13	16	the	the	DET
american_scientific_journal-7074	13	17	stress	stress	NOUN
american_scientific_journal-7074	13	18	varies	vary	VERB
american_scientific_journal-7074	13	19	linearly	linearly	ADV
american_scientific_journal-7074	13	20	if	if	SCONJ
american_scientific_journal-7074	13	21	the	the	DET
american_scientific_journal-7074	13	22	displacement	displacement	NOUN
american_scientific_journal-7074	13	23	function	function	NOUN
american_scientific_journal-7074	13	24	is	be	AUX
american_scientific_journal-7074	13	25	of	of	ADP
american_scientific_journal-7074	13	26	the	the	DET
american_scientific_journal-7074	13	27	form	form	NOUN
american_scientific_journal-7074	14	1	u=	u=	NOUN
american_scientific_journal-7074	14	2	α1+α2x+	α1+α2x+	PUNCT
american_scientific_journal-7074	14	3	α3y+	α3y+	NOUN
american_scientific_journal-7074	14	4	α4x	α4x	PROPN
american_scientific_journal-7074	14	5	2	2	NUM
american_scientific_journal-7074	14	6	+	+	CCONJ
american_scientific_journal-7074	14	7	α5xy+	α5xy+	PROPN
american_scientific_journal-7074	14	8	α6y	α6y	SYM
american_scientific_journal-7074	14	9	2	2	NUM
american_scientific_journal-7074	14	10	v=	v=	NOUN
american_scientific_journal-7074	14	11	α7+α8x+	α7+α8x+	PUNCT
american_scientific_journal-7074	14	12	α9y+	α9y+	NOUN
american_scientific_journal-7074	14	13	α10x	α10x	NOUN
american_scientific_journal-7074	14	14	2	2	NUM
american_scientific_journal-7074	14	15	+	+	CCONJ
american_scientific_journal-7074	14	16	α11xy+	α11xy+	PROPN
american_scientific_journal-7074	14	17	α12y	α12y	ADP
american_scientific_journal-7074	14	18	2	2	NUM
american_scientific_journal-7074	14	19	or	or	CCONJ
american_scientific_journal-7074	14	20	,	,	PUNCT
american_scientific_journal-7074	14	21	u	u	NOUN
american_scientific_journal-7074	14	22	v	v	NOUN
american_scientific_journal-7074	14	23	=	=	NOUN
american_scientific_journal-7074	14	24	pα	pα	NOUN
american_scientific_journal-7074	14	25	1	1	NUM
american_scientific_journal-7074	14	26	and	and	CCONJ
american_scientific_journal-7074	14	27	1	1	NUM
american_scientific_journal-7074	14	28	x	x	SYM
american_scientific_journal-7074	14	29	y	y	NOUN
american_scientific_journal-7074	14	30	x	x	SYM
american_scientific_journal-7074	14	31	2	2	NUM
american_scientific_journal-7074	14	32	xy	xy	NOUN
american_scientific_journal-7074	14	33	y	y	PROPN
american_scientific_journal-7074	14	34	2	2	NUM
american_scientific_journal-7074	14	35	0	0	NUM
american_scientific_journal-7074	14	36	0	0	NUM
american_scientific_journal-7074	14	37	0	0	NUM
american_scientific_journal-7074	14	38	0	0	NUM
american_scientific_journal-7074	14	39	0	0	NUM
american_scientific_journal-7074	14	40	0	0	NUM
american_scientific_journal-7074	14	41	p=	p=	NOUN
american_scientific_journal-7074	14	42	0	0	NUM
american_scientific_journal-7074	14	43	0	0	NUM
american_scientific_journal-7074	14	44	0	0	NUM
american_scientific_journal-7074	14	45	0	0	NUM
american_scientific_journal-7074	14	46	0	0	NUM
american_scientific_journal-7074	14	47	0	0	NUM
american_scientific_journal-7074	14	48	1	1	NUM
american_scientific_journal-7074	14	49	x	x	SYM
american_scientific_journal-7074	14	50	y	y	NOUN
american_scientific_journal-7074	14	51	x	x	SYM
american_scientific_journal-7074	14	52	2	2	NUM
american_scientific_journal-7074	14	53	xy	xy	NOUN
american_scientific_journal-7074	14	54	y	y	PROPN
american_scientific_journal-7074	14	55	2	2	NUM
american_scientific_journal-7074	14	56	2	2	NUM
american_scientific_journal-7074	14	57	to	to	PART
american_scientific_journal-7074	14	58	determine	determine	VERB
american_scientific_journal-7074	14	59	the	the	DET
american_scientific_journal-7074	14	60	six	six	NUM
american_scientific_journal-7074	14	61	-	-	PUNCT
american_scientific_journal-7074	14	62	unknown	unknown	ADJ
american_scientific_journal-7074	14	63	coefficients	coefficient	NOUN
american_scientific_journal-7074	14	64	in	in	ADP
american_scientific_journal-7074	14	65	the	the	DET
american_scientific_journal-7074	14	66	function	function	NOUN
american_scientific_journal-7074	14	67	for	for	ADP
american_scientific_journal-7074	14	68	u	u	NOUN
american_scientific_journal-7074	14	69	we	we	PRON
american_scientific_journal-7074	14	70	must	must	AUX
american_scientific_journal-7074	14	71	know	know	VERB
american_scientific_journal-7074	14	72	six	six	NUM
american_scientific_journal-7074	14	73	horizontal	horizontal	ADJ
american_scientific_journal-7074	14	74	displacements	displacement	NOUN
american_scientific_journal-7074	14	75	at	at	ADP
american_scientific_journal-7074	14	76	six	six	NUM
american_scientific_journal-7074	14	77	specified	specified	ADJ
american_scientific_journal-7074	14	78	points	point	NOUN
american_scientific_journal-7074	14	79	.	.	PUNCT
american_scientific_journal-7074	15	1	the	the	DET
american_scientific_journal-7074	15	2	same	same	ADJ
american_scientific_journal-7074	15	3	is	be	AUX
american_scientific_journal-7074	15	4	true	true	ADJ
american_scientific_journal-7074	15	5	for	for	ADP
american_scientific_journal-7074	15	6	the	the	DET
american_scientific_journal-7074	15	7	unknowns	unknown	NOUN
american_scientific_journal-7074	15	8	in	in	ADP
american_scientific_journal-7074	15	9	the	the	DET
american_scientific_journal-7074	15	10	v	v	NOUN
american_scientific_journal-7074	15	11	function	function	NOUN
american_scientific_journal-7074	15	12	.	.	PUNCT
american_scientific_journal-7074	16	1	this	this	PRON
american_scientific_journal-7074	16	2	can	can	AUX
american_scientific_journal-7074	16	3	be	be	AUX
american_scientific_journal-7074	16	4	accomplished	accomplish	VERB
american_scientific_journal-7074	16	5	by	by	ADP
american_scientific_journal-7074	16	6	introducing	introduce	VERB
american_scientific_journal-7074	16	7	nodes	node	NOUN
american_scientific_journal-7074	16	8	at	at	ADP
american_scientific_journal-7074	16	9	the	the	DET
american_scientific_journal-7074	16	10	midpoints	midpoint	NOUN
american_scientific_journal-7074	16	11	of	of	ADP
american_scientific_journal-7074	16	12	the	the	DET
american_scientific_journal-7074	16	13	element	element	NOUN
american_scientific_journal-7074	16	14	sides	side	NOUN
american_scientific_journal-7074	16	15	as	as	SCONJ
american_scientific_journal-7074	16	16	shown	show	VERB
american_scientific_journal-7074	16	17	in	in	ADP
american_scientific_journal-7074	16	18	figures	figure	NOUN
american_scientific_journal-7074	16	19	(	(	PUNCT
american_scientific_journal-7074	16	20	a	a	DET
american_scientific_journal-7074	16	21	,	,	PUNCT
american_scientific_journal-7074	16	22	b	b	PROPN
american_scientific_journal-7074	16	23	and	and	CCONJ
american_scientific_journal-7074	16	24	c	c	X
american_scientific_journal-7074	16	25	)	)	PUNCT
american_scientific_journal-7074	16	26	it	it	PRON
american_scientific_journal-7074	16	27	will	will	AUX
american_scientific_journal-7074	16	28	be	be	AUX
american_scientific_journal-7074	16	29	noted	note	VERB
american_scientific_journal-7074	16	30	that	that	SCONJ
american_scientific_journal-7074	16	31	local	local	ADJ
american_scientific_journal-7074	16	32	axis	axis	NOUN
american_scientific_journal-7074	16	33	has	have	AUX
american_scientific_journal-7074	16	34	been	be	AUX
american_scientific_journal-7074	16	35	established	establish	VERB
american_scientific_journal-7074	16	36	with	with	ADP
american_scientific_journal-7074	16	37	origin	origin	NOUN
american_scientific_journal-7074	16	38	at	at	ADP
american_scientific_journal-7074	16	39	the	the	DET
american_scientific_journal-7074	16	40	centroid	centroid	NOUN
american_scientific_journal-7074	16	41	of	of	ADP
american_scientific_journal-7074	16	42	the	the	DET
american_scientific_journal-7074	16	43	element	element	NOUN
american_scientific_journal-7074	16	44	.	.	PUNCT
american_scientific_journal-7074	17	1	dealing	deal	VERB
american_scientific_journal-7074	17	2	with	with	ADP
american_scientific_journal-7074	17	3	these	these	DET
american_scientific_journal-7074	17	4	local	local	ADJ
american_scientific_journal-7074	17	5	axes	axis	NOUN
american_scientific_journal-7074	17	6	does	do	AUX
american_scientific_journal-7074	17	7	not	not	PART
american_scientific_journal-7074	17	8	alter	alter	VERB
american_scientific_journal-7074	17	9	the	the	DET
american_scientific_journal-7074	17	10	values	value	NOUN
american_scientific_journal-7074	17	11	in	in	ADP
american_scientific_journal-7074	17	12	the	the	DET
american_scientific_journal-7074	17	13	stiffness	stiffness	ADJ
american_scientific_journal-7074	17	14	matrix	matrix	NOUN
american_scientific_journal-7074	17	15	but	but	CCONJ
american_scientific_journal-7074	17	16	does	do	AUX
american_scientific_journal-7074	17	17	make	make	VERB
american_scientific_journal-7074	17	18	it	it	PRON
american_scientific_journal-7074	17	19	easier	easy	ADJ
american_scientific_journal-7074	17	20	to	to	PART
american_scientific_journal-7074	17	21	perform	perform	VERB
american_scientific_journal-7074	17	22	the	the	DET
american_scientific_journal-7074	17	23	integration	integration	NOUN
american_scientific_journal-7074	17	24	in	in	ADP
american_scientific_journal-7074	17	25	the	the	DET
american_scientific_journal-7074	17	26	stiffness	stiffness	ADJ
american_scientific_journal-7074	17	27	formula	formula	NOUN
american_scientific_journal-7074	17	28	k=	k=	X
american_scientific_journal-7074	18	1	[	[	PUNCT
american_scientific_journal-7074	18	2	a	a	X
american_scientific_journal-7074	18	3	-1	-1	X
american_scientific_journal-7074	18	4	]	]	PUNCT
american_scientific_journal-7074	19	1	t	t	PROPN
american_scientific_journal-7074	19	2	∫	∫	PROPN
american_scientific_journal-7074	20	1	b	b	PROPN
american_scientific_journal-7074	20	2	t	t	PROPN
american_scientific_journal-7074	20	3	db	db	PROPN
american_scientific_journal-7074	20	4	dv	dv	PROPN
american_scientific_journal-7074	20	5	a	a	X
american_scientific_journal-7074	20	6	-1	-1	ADP
american_scientific_journal-7074	20	7	the	the	DET
american_scientific_journal-7074	20	8	displacements	displacement	NOUN
american_scientific_journal-7074	20	9	at	at	ADP
american_scientific_journal-7074	20	10	node	node	NOUN
american_scientific_journal-7074	20	11	1	1	NUM
american_scientific_journal-7074	20	12	,	,	PUNCT
american_scientific_journal-7074	20	13	δ1	δ1	NOUN
american_scientific_journal-7074	20	14	and	and	CCONJ
american_scientific_journal-7074	20	15	δ7	δ7	NOUN
american_scientific_journal-7074	20	16	are	be	AUX
american_scientific_journal-7074	20	17	given	give	VERB
american_scientific_journal-7074	20	18	as	as	ADP
american_scientific_journal-7074	20	19	δ1	δ1	NOUN
american_scientific_journal-7074	20	20	δ7	δ7	NOUN
american_scientific_journal-7074	20	21	=	=	SYM
american_scientific_journal-7074	20	22	p	p	NOUN
american_scientific_journal-7074	20	23	x	x	X
american_scientific_journal-7074	20	24	=	=	SYM
american_scientific_journal-7074	20	25	x1	x1	PROPN
american_scientific_journal-7074	20	26	.	.	PUNCT
american_scientific_journal-7074	21	1	α	α	NOUN
american_scientific_journal-7074	22	1	3	3	NUM
american_scientific_journal-7074	22	2	y=	y=	NUM
american_scientific_journal-7074	22	3	y1	y1	NOUN
american_scientific_journal-7074	22	4	1	1	NUM
american_scientific_journal-7074	22	5	x1	x1	NUM
american_scientific_journal-7074	22	6	y1	y1	NOUN
american_scientific_journal-7074	22	7	x1	x1	PROPN
american_scientific_journal-7074	22	8	2	2	NUM
american_scientific_journal-7074	22	9	x1y1	x1y1	NUM
american_scientific_journal-7074	22	10	y1	y1	NOUN
american_scientific_journal-7074	22	11	2	2	NUM
american_scientific_journal-7074	22	12	0	0	NUM
american_scientific_journal-7074	22	13	0	0	NUM
american_scientific_journal-7074	22	14	0	0	NUM
american_scientific_journal-7074	22	15	0	0	NUM
american_scientific_journal-7074	22	16	0	0	NUM
american_scientific_journal-7074	22	17	0	0	NUM
american_scientific_journal-7074	23	1	=	=	SYM
american_scientific_journal-7074	23	2	0	0	NUM
american_scientific_journal-7074	23	3	0	0	NUM
american_scientific_journal-7074	23	4	0	0	NUM
american_scientific_journal-7074	23	5	0	0	NUM
american_scientific_journal-7074	23	6	0	0	NUM
american_scientific_journal-7074	23	7	0	0	NUM
american_scientific_journal-7074	23	8	1	1	NUM
american_scientific_journal-7074	23	9	x1	x1	NUM
american_scientific_journal-7074	23	10	y1	y1	NOUN
american_scientific_journal-7074	23	11	x1	x1	PROPN
american_scientific_journal-7074	23	12	2	2	NUM
american_scientific_journal-7074	23	13	x1y1	x1y1	NUM
american_scientific_journal-7074	23	14	y1	y1	NOUN
american_scientific_journal-7074	23	15	2	2	NUM
american_scientific_journal-7074	23	16	α	α	DET
american_scientific_journal-7074	23	17	similar	similar	ADJ
american_scientific_journal-7074	23	18	equations	equation	NOUN
american_scientific_journal-7074	23	19	can	can	AUX
american_scientific_journal-7074	23	20	be	be	AUX
american_scientific_journal-7074	23	21	written	write	VERB
american_scientific_journal-7074	23	22	for	for	ADP
american_scientific_journal-7074	23	23	δ	δ	PROPN
american_scientific_journal-7074	23	24	components	component	NOUN
american_scientific_journal-7074	23	25	at	at	ADP
american_scientific_journal-7074	23	26	all	all	DET
american_scientific_journal-7074	23	27	other	other	ADJ
american_scientific_journal-7074	23	28	nodes	node	NOUN
american_scientific_journal-7074	23	29	.	.	PUNCT
american_scientific_journal-7074	24	1	when	when	SCONJ
american_scientific_journal-7074	24	2	the	the	DET
american_scientific_journal-7074	24	3	δ	δ	PROPN
american_scientific_journal-7074	24	4	components	component	NOUN
american_scientific_journal-7074	24	5	are	be	AUX
american_scientific_journal-7074	24	6	put	put	VERB
american_scientific_journal-7074	24	7	into	into	ADP
american_scientific_journal-7074	24	8	numerical	numerical	ADJ
american_scientific_journal-7074	24	9	order	order	NOUN
american_scientific_journal-7074	24	10	these	these	DET
american_scientific_journal-7074	24	11	equations	equation	NOUN
american_scientific_journal-7074	24	12	become	become	VERB
american_scientific_journal-7074	24	13	ᾱ	ᾱ	X
american_scientific_journal-7074	24	14	0	0	NUM
american_scientific_journal-7074	24	15	american	american	ADJ
american_scientific_journal-7074	24	16	academic	academic	ADJ
american_scientific_journal-7074	24	17	scientific	scientific	ADJ
american_scientific_journal-7074	24	18	research	research	NOUN
american_scientific_journal-7074	24	19	journal	journal	NOUN
american_scientific_journal-7074	24	20	for	for	ADP
american_scientific_journal-7074	24	21	engineering	engineering	NOUN
american_scientific_journal-7074	24	22	,	,	PUNCT
american_scientific_journal-7074	24	23	technology	technology	NOUN
american_scientific_journal-7074	24	24	,	,	PUNCT
american_scientific_journal-7074	24	25	and	and	CCONJ
american_scientific_journal-7074	24	26	sciences	science	NOUN
american_scientific_journal-7074	24	27	(	(	PUNCT
american_scientific_journal-7074	24	28	asrjets	asrjet	NOUN
american_scientific_journal-7074	24	29	)	)	PUNCT
american_scientific_journal-7074	24	30	(	(	PUNCT
american_scientific_journal-7074	24	31	2021	2021	NUM
american_scientific_journal-7074	24	32	)	)	PUNCT
american_scientific_journal-7074	24	33	volume	volume	NOUN
american_scientific_journal-7074	24	34	83	83	NUM
american_scientific_journal-7074	24	35	,	,	PUNCT
american_scientific_journal-7074	24	36	no	no	DET
american_scientific_journal-7074	24	37	1	1	NUM
american_scientific_journal-7074	24	38	,	,	PUNCT
american_scientific_journal-7074	24	39	pp	pp	ADV
american_scientific_journal-7074	24	40	1	1	NUM
american_scientific_journal-7074	24	41	-	-	SYM
american_scientific_journal-7074	24	42	11	11	NUM
american_scientific_journal-7074	24	43	3	3	NUM
american_scientific_journal-7074	24	44	δ=	δ=	NOUN
american_scientific_journal-7074	24	45	0	0	NUM
american_scientific_journal-7074	24	46	ᾱ	ᾱ	SYM
american_scientific_journal-7074	24	47	α	α	NOUN
american_scientific_journal-7074	24	48	4	4	NUM
american_scientific_journal-7074	24	49	where	where	SCONJ
american_scientific_journal-7074	24	50	1	1	NUM
american_scientific_journal-7074	24	51	x1	x1	NOUN
american_scientific_journal-7074	24	52	y1	y1	NOUN
american_scientific_journal-7074	24	53	x1	x1	PROPN
american_scientific_journal-7074	24	54	2	2	NUM
american_scientific_journal-7074	24	55	x1y1	x1y1	NUM
american_scientific_journal-7074	24	56	y1	y1	NOUN
american_scientific_journal-7074	24	57	2	2	NUM
american_scientific_journal-7074	24	58	1	1	NUM
american_scientific_journal-7074	24	59	x2	x2	NOUN
american_scientific_journal-7074	25	1	y2	y2	NOUN
american_scientific_journal-7074	25	2	x2	x2	NOUN
american_scientific_journal-7074	26	1	2	2	X
american_scientific_journal-7074	26	2	x2y2	x2y2	NUM
american_scientific_journal-7074	27	1	y2	y2	NOUN
american_scientific_journal-7074	27	2	2	2	NUM
american_scientific_journal-7074	27	3	ᾱ	ᾱ	NOUN
american_scientific_journal-7074	27	4	=	=	SYM
american_scientific_journal-7074	27	5	1	1	NUM
american_scientific_journal-7074	27	6	x3	x3	NOUN
american_scientific_journal-7074	27	7	y3	y3	NOUN
american_scientific_journal-7074	27	8	x3	x3	ADJ
american_scientific_journal-7074	27	9	2	2	NUM
american_scientific_journal-7074	27	10	x3y3	x3y3	SYM
american_scientific_journal-7074	27	11	y3	y3	NOUN
american_scientific_journal-7074	27	12	2	2	NUM
american_scientific_journal-7074	27	13	5	5	NUM
american_scientific_journal-7074	27	14	1	1	NUM
american_scientific_journal-7074	27	15	x4	x4	PROPN
american_scientific_journal-7074	27	16	y4	y4	NOUN
american_scientific_journal-7074	27	17	x4	x4	PROPN
american_scientific_journal-7074	27	18	2	2	NUM
american_scientific_journal-7074	28	1	x4y4	x4y4	AUX
american_scientific_journal-7074	28	2	y4	y4	VERB
american_scientific_journal-7074	28	3	2	2	NUM
american_scientific_journal-7074	28	4	1	1	NUM
american_scientific_journal-7074	28	5	x5	x5	NOUN
american_scientific_journal-7074	28	6	y5	y5	NOUN
american_scientific_journal-7074	28	7	x5	x5	NOUN
american_scientific_journal-7074	28	8	2	2	NUM
american_scientific_journal-7074	28	9	x5y5	x5y5	SYM
american_scientific_journal-7074	28	10	y5	y5	NOUN
american_scientific_journal-7074	28	11	2	2	NUM
american_scientific_journal-7074	28	12	1	1	NUM
american_scientific_journal-7074	28	13	x6	x6	NOUN
american_scientific_journal-7074	28	14	y6	y6	ADJ
american_scientific_journal-7074	28	15	x6	x6	PROPN
american_scientific_journal-7074	28	16	2	2	NUM
american_scientific_journal-7074	28	17	x6y6	x6y6	NOUN
american_scientific_journal-7074	28	18	y6	y6	NOUN
american_scientific_journal-7074	28	19	2	2	NUM
american_scientific_journal-7074	28	20	then	then	ADV
american_scientific_journal-7074	28	21	equation	equation	NOUN
american_scientific_journal-7074	28	22	4	4	NUM
american_scientific_journal-7074	28	23	becomes	become	VERB
american_scientific_journal-7074	28	24	ᾱ	ᾱ	NOUN
american_scientific_journal-7074	28	25	0	0	NUM
american_scientific_journal-7074	28	26	δ=	δ=	NOUN
american_scientific_journal-7074	28	27	a	a	DET
american_scientific_journal-7074	28	28	α	α	NOUN
american_scientific_journal-7074	28	29	and	and	CCONJ
american_scientific_journal-7074	28	30	a	a	DET
american_scientific_journal-7074	28	31	=	=	NUM
american_scientific_journal-7074	28	32	6	6	NUM
american_scientific_journal-7074	28	33	0	0	NUM
american_scientific_journal-7074	28	34	ᾱ	ᾱ	NOUN
american_scientific_journal-7074	28	35	solving	solving	NOUN
american_scientific_journal-7074	28	36	for	for	ADP
american_scientific_journal-7074	28	37	α	α	NOUN
american_scientific_journal-7074	28	38	gives	give	VERB
american_scientific_journal-7074	28	39	α=	α=	NUM
american_scientific_journal-7074	28	40	a	a	DET
american_scientific_journal-7074	28	41	-1	-1	PUNCT
american_scientific_journal-7074	28	42	δ	δ	PROPN
american_scientific_journal-7074	28	43	7	7	NUM
american_scientific_journal-7074	28	44	a	a	PRON
american_scientific_journal-7074	28	45	is	be	AUX
american_scientific_journal-7074	28	46	a12x12	a12x12	ADJ
american_scientific_journal-7074	28	47	matrix	matrix	NOUN
american_scientific_journal-7074	28	48	and	and	CCONJ
american_scientific_journal-7074	28	49	could	could	AUX
american_scientific_journal-7074	28	50	be	be	AUX
american_scientific_journal-7074	28	51	inverted	invert	VERB
american_scientific_journal-7074	28	52	directly	directly	ADV
american_scientific_journal-7074	28	53	,	,	PUNCT
american_scientific_journal-7074	28	54	but	but	CCONJ
american_scientific_journal-7074	28	55	much	much	ADJ
american_scientific_journal-7074	28	56	time	time	NOUN
american_scientific_journal-7074	28	57	is	be	AUX
american_scientific_journal-7074	28	58	saved	save	VERB
american_scientific_journal-7074	28	59	by	by	ADP
american_scientific_journal-7074	28	60	inverting	invert	VERB
american_scientific_journal-7074	28	61	the	the	DET
american_scientific_journal-7074	28	62	submatrix	submatrix	NOUN
american_scientific_journal-7074	28	63	ᾱ	ᾱ	NOUN
american_scientific_journal-7074	28	64	and	and	CCONJ
american_scientific_journal-7074	28	65	then	then	ADV
american_scientific_journal-7074	28	66	incorporate	incorporate	VERB
american_scientific_journal-7074	28	67	in	in	ADP
american_scientific_journal-7074	28	68	a	a	PRON
american_scientific_journal-7074	28	69	-1	-1	PUNCT
american_scientific_journal-7074	28	70	the	the	DET
american_scientific_journal-7074	28	71	displacement	displacement	ADJ
american_scientific_journal-7074	28	72	function	function	NOUN
american_scientific_journal-7074	28	73	in	in	ADP
american_scientific_journal-7074	28	74	1	1	NUM
american_scientific_journal-7074	28	75	is	be	AUX
american_scientific_journal-7074	28	76	then	then	ADV
american_scientific_journal-7074	28	77	written	write	VERB
american_scientific_journal-7074	28	78	u	u	NOUN
american_scientific_journal-7074	29	1	=	=	NOUN
american_scientific_journal-7074	29	2	p	p	PROPN
american_scientific_journal-7074	29	3	a	a	PRON
american_scientific_journal-7074	29	4	-1	-1	INTJ
american_scientific_journal-7074	29	5	δ	δ	PROPN
american_scientific_journal-7074	29	6	8	8	NUM
american_scientific_journal-7074	29	7	v	v	ADP
american_scientific_journal-7074	29	8	now	now	ADV
american_scientific_journal-7074	29	9	compatibility	compatibility	NOUN
american_scientific_journal-7074	29	10	of	of	ADP
american_scientific_journal-7074	29	11	the	the	DET
american_scientific_journal-7074	29	12	displacements	displacement	NOUN
american_scientific_journal-7074	29	13	is	be	AUX
american_scientific_journal-7074	29	14	then	then	ADV
american_scientific_journal-7074	29	15	checked	check	VERB
american_scientific_journal-7074	29	16	at	at	ADP
american_scientific_journal-7074	29	17	points	point	NOUN
american_scientific_journal-7074	29	18	located	locate	VERB
american_scientific_journal-7074	29	19	on	on	ADP
american_scientific_journal-7074	29	20	the	the	DET
american_scientific_journal-7074	29	21	common	common	ADJ
american_scientific_journal-7074	29	22	boundary	boundary	NOUN
american_scientific_journal-7074	29	23	between	between	ADP
american_scientific_journal-7074	29	24	adjacent	adjacent	ADJ
american_scientific_journal-7074	29	25	elements	element	NOUN
american_scientific_journal-7074	29	26	.	.	PUNCT
american_scientific_journal-7074	30	1	that	that	PRON
american_scientific_journal-7074	30	2	is	is	ADV
american_scientific_journal-7074	30	3	,	,	PUNCT
american_scientific_journal-7074	30	4	we	we	PRON
american_scientific_journal-7074	30	5	will	will	AUX
american_scientific_journal-7074	30	6	determine	determine	VERB
american_scientific_journal-7074	30	7	if	if	SCONJ
american_scientific_journal-7074	30	8	pairs	pair	NOUN
american_scientific_journal-7074	30	9	of	of	ADP
american_scientific_journal-7074	30	10	points	point	NOUN
american_scientific_journal-7074	30	11	that	that	PRON
american_scientific_journal-7074	30	12	touched	touch	VERB
american_scientific_journal-7074	30	13	one	one	NUM
american_scientific_journal-7074	30	14	another	another	DET
american_scientific_journal-7074	30	15	across	across	ADP
american_scientific_journal-7074	30	16	a	a	DET
american_scientific_journal-7074	30	17	boundary	boundary	NOUN
american_scientific_journal-7074	30	18	before	before	ADP
american_scientific_journal-7074	30	19	displacement	displacement	NOUN
american_scientific_journal-7074	30	20	,	,	PUNCT
american_scientific_journal-7074	30	21	remain	remain	VERB
american_scientific_journal-7074	30	22	in	in	ADP
american_scientific_journal-7074	30	23	contact	contact	NOUN
american_scientific_journal-7074	30	24	after	after	ADP
american_scientific_journal-7074	30	25	displacement	displacement	NOUN
american_scientific_journal-7074	30	26	and	and	CCONJ
american_scientific_journal-7074	30	27	hence	hence	ADV
american_scientific_journal-7074	30	28	whether	whether	SCONJ
american_scientific_journal-7074	30	29	displacement	displacement	NOUN
american_scientific_journal-7074	30	30	causes	cause	VERB
american_scientific_journal-7074	30	31	gaps	gap	NOUN
american_scientific_journal-7074	30	32	to	to	PART
american_scientific_journal-7074	30	33	appear	appear	VERB
american_scientific_journal-7074	30	34	.	.	PUNCT
american_scientific_journal-7074	31	1	considering	consider	VERB
american_scientific_journal-7074	31	2	only	only	ADV
american_scientific_journal-7074	31	3	u	u	PRON
american_scientific_journal-7074	31	4	displacement	displacement	NOUN
american_scientific_journal-7074	31	5	,	,	PUNCT
american_scientific_journal-7074	31	6	the	the	DET
american_scientific_journal-7074	31	7	function	function	NOUN
american_scientific_journal-7074	31	8	in	in	ADP
american_scientific_journal-7074	31	9	general	general	ADJ
american_scientific_journal-7074	31	10	is	be	AUX
american_scientific_journal-7074	31	11	u=	u=	ADV
american_scientific_journal-7074	31	12	α1+α2x+	α1+α2x+	ADV
american_scientific_journal-7074	31	13	α3y+	α3y+	NOUN
american_scientific_journal-7074	31	14	α4x	α4x	PROPN
american_scientific_journal-7074	31	15	2	2	NUM
american_scientific_journal-7074	31	16	+	+	CCONJ
american_scientific_journal-7074	31	17	α5xy+	α5xy+	PROPN
american_scientific_journal-7074	31	18	α6y	α6y	SYM
american_scientific_journal-7074	31	19	2	2	NUM
american_scientific_journal-7074	31	20	american	american	ADJ
american_scientific_journal-7074	31	21	academic	academic	ADJ
american_scientific_journal-7074	31	22	scientific	scientific	ADJ
american_scientific_journal-7074	31	23	research	research	NOUN
american_scientific_journal-7074	31	24	journal	journal	NOUN
american_scientific_journal-7074	31	25	for	for	ADP
american_scientific_journal-7074	31	26	engineering	engineering	NOUN
american_scientific_journal-7074	31	27	,	,	PUNCT
american_scientific_journal-7074	31	28	technology	technology	NOUN
american_scientific_journal-7074	31	29	,	,	PUNCT
american_scientific_journal-7074	31	30	and	and	CCONJ
american_scientific_journal-7074	31	31	sciences	science	NOUN
american_scientific_journal-7074	31	32	(	(	PUNCT
american_scientific_journal-7074	31	33	asrjets	asrjet	NOUN
american_scientific_journal-7074	31	34	)	)	PUNCT
american_scientific_journal-7074	31	35	(	(	PUNCT
american_scientific_journal-7074	31	36	2021	2021	NUM
american_scientific_journal-7074	31	37	)	)	PUNCT
american_scientific_journal-7074	31	38	volume	volume	NOUN
american_scientific_journal-7074	31	39	83	83	NUM
american_scientific_journal-7074	31	40	,	,	PUNCT
american_scientific_journal-7074	31	41	no	no	DET
american_scientific_journal-7074	31	42	1	1	NUM
american_scientific_journal-7074	31	43	,	,	PUNCT
american_scientific_journal-7074	31	44	pp	pp	ADV
american_scientific_journal-7074	31	45	1	1	NUM
american_scientific_journal-7074	31	46	-	-	SYM
american_scientific_journal-7074	31	47	11	11	NUM
american_scientific_journal-7074	31	48	4	4	NUM
american_scientific_journal-7074	31	49	5	5	NUM
american_scientific_journal-7074	31	50	4	4	NUM
american_scientific_journal-7074	31	51	6	6	NUM
american_scientific_journal-7074	31	52	centroid	centroid	NOUN
american_scientific_journal-7074	31	53	3	3	NUM
american_scientific_journal-7074	31	54	1	1	NUM
american_scientific_journal-7074	31	55	2	2	NUM
american_scientific_journal-7074	31	56	alocal	alocal	ADJ
american_scientific_journal-7074	31	57	axis	axis	NOUN
american_scientific_journal-7074	31	58	and	and	CCONJ
american_scientific_journal-7074	31	59	local	local	ADJ
american_scientific_journal-7074	31	60	numbering	numbering	NOUN
american_scientific_journal-7074	31	61	system	system	NOUN
american_scientific_journal-7074	31	62	δ11	δ11	PROPN
american_scientific_journal-7074	31	63	δ5	δ5	NOUN
american_scientific_journal-7074	31	64	δ12	δ12	PROPN
american_scientific_journal-7074	31	65	δ10	δ10	PROPN
american_scientific_journal-7074	31	66	δ9	δ9	PROPN
american_scientific_journal-7074	31	67	δ6	δ6	PROPN
american_scientific_journal-7074	31	68	δ4	δ4	PROPN
american_scientific_journal-7074	31	69	δ7	δ7	PROPN
american_scientific_journal-7074	31	70	δ8	δ8	VERB
american_scientific_journal-7074	31	71	δ3	δ3	PROPN
american_scientific_journal-7074	31	72	δ2	δ2	VERB
american_scientific_journal-7074	31	73	δ1	δ1	PROPN
american_scientific_journal-7074	31	74	bnodal	bnodal	NOUN
american_scientific_journal-7074	31	75	displacement	displacement	NOUN
american_scientific_journal-7074	31	76	components	component	NOUN
american_scientific_journal-7074	31	77	f11	f11	PROPN
american_scientific_journal-7074	31	78	f5	f5	VERB
american_scientific_journal-7074	31	79	f10	f10	NOUN
american_scientific_journal-7074	31	80	f12	f12	NOUN
american_scientific_journal-7074	31	81	f4	f4	PROPN
american_scientific_journal-7074	31	82	f9	f9	PROPN
american_scientific_journal-7074	31	83	f6	f6	PROPN
american_scientific_journal-7074	31	84	f7	f7	PROPN
american_scientific_journal-7074	31	85	f8	f8	PROPN
american_scientific_journal-7074	31	86	f3	f3	PROPN
american_scientific_journal-7074	31	87	f2	f2	PROPN
american_scientific_journal-7074	31	88	f1	f1	PROPN
american_scientific_journal-7074	31	89	cforces	cforce	NOUN
american_scientific_journal-7074	31	90	acting	act	VERB
american_scientific_journal-7074	31	91	on	on	ADP
american_scientific_journal-7074	31	92	element	element	NOUN
american_scientific_journal-7074	31	93	however	however	ADV
american_scientific_journal-7074	31	94	,	,	PUNCT
american_scientific_journal-7074	31	95	we	we	PRON
american_scientific_journal-7074	31	96	are	be	AUX
american_scientific_journal-7074	31	97	interested	interested	ADJ
american_scientific_journal-7074	31	98	in	in	ADP
american_scientific_journal-7074	31	99	u	u	NOUN
american_scientific_journal-7074	31	100	only	only	ADV
american_scientific_journal-7074	31	101	at	at	ADP
american_scientific_journal-7074	31	102	points	point	NOUN
american_scientific_journal-7074	31	103	on	on	ADP
american_scientific_journal-7074	31	104	a	a	DET
american_scientific_journal-7074	31	105	particular	particular	ADJ
american_scientific_journal-7074	31	106	boundary	boundary	NOUN
american_scientific_journal-7074	31	107	.	.	PUNCT
american_scientific_journal-7074	32	1	let	let	VERB
american_scientific_journal-7074	32	2	the	the	DET
american_scientific_journal-7074	32	3	boundary	boundary	ADJ
american_scientific_journal-7074	32	4	be	be	AUX
american_scientific_journal-7074	32	5	parallel	parallel	ADJ
american_scientific_journal-7074	32	6	to	to	ADP
american_scientific_journal-7074	32	7	y	y	PROPN
american_scientific_journal-7074	32	8	axis	axis	NOUN
american_scientific_journal-7074	32	9	which	which	PRON
american_scientific_journal-7074	32	10	means	mean	VERB
american_scientific_journal-7074	32	11	that	that	SCONJ
american_scientific_journal-7074	32	12	all	all	DET
american_scientific_journal-7074	32	13	x	x	NUM
american_scientific_journal-7074	32	14	components	component	NOUN
american_scientific_journal-7074	32	15	are	be	AUX
american_scientific_journal-7074	32	16	constants	constant	NOUN
american_scientific_journal-7074	32	17	and	and	CCONJ
american_scientific_journal-7074	32	18	the	the	DET
american_scientific_journal-7074	32	19	u	u	NOUN
american_scientific_journal-7074	32	20	function	function	NOUN
american_scientific_journal-7074	32	21	takes	take	VERB
american_scientific_journal-7074	32	22	the	the	DET
american_scientific_journal-7074	32	23	parabolic	parabolic	ADJ
american_scientific_journal-7074	32	24	form	form	NOUN
american_scientific_journal-7074	32	25	ub	ub	VERB
american_scientific_journal-7074	32	26	=	=	NOUN
american_scientific_journal-7074	32	27	a	a	PRON
american_scientific_journal-7074	32	28	+	+	NOUN
american_scientific_journal-7074	32	29	by	by	ADP
american_scientific_journal-7074	32	30	+	+	PROPN
american_scientific_journal-7074	32	31	cy	cy	PROPN
american_scientific_journal-7074	32	32	2	2	NUM
american_scientific_journal-7074	32	33	,	,	PUNCT
american_scientific_journal-7074	32	34	on	on	ADP
american_scientific_journal-7074	32	35	this	this	DET
american_scientific_journal-7074	32	36	boundary	boundary	NOUN
american_scientific_journal-7074	32	37	there	there	PRON
american_scientific_journal-7074	32	38	are	be	VERB
american_scientific_journal-7074	32	39	3	3	NUM
american_scientific_journal-7074	32	40	nodes	node	NOUN
american_scientific_journal-7074	32	41	,	,	PUNCT
american_scientific_journal-7074	32	42	hence	hence	ADV
american_scientific_journal-7074	32	43	3	3	NUM
american_scientific_journal-7074	32	44	unknown	unknown	ADJ
american_scientific_journal-7074	32	45	values	value	NOUN
american_scientific_journal-7074	32	46	of	of	ADP
american_scientific_journal-7074	32	47	ub	ub	NOUN
american_scientific_journal-7074	32	48	are	be	AUX
american_scientific_journal-7074	32	49	the	the	DET
american_scientific_journal-7074	32	50	constants	constant	NOUN
american_scientific_journal-7074	32	51	a	a	DET
american_scientific_journal-7074	32	52	,	,	PUNCT
american_scientific_journal-7074	32	53	b	b	NOUN
american_scientific_journal-7074	32	54	and	and	CCONJ
american_scientific_journal-7074	32	55	c	c	NOUN
american_scientific_journal-7074	32	56	can	can	AUX
american_scientific_journal-7074	32	57	be	be	AUX
american_scientific_journal-7074	32	58	determined	determine	VERB
american_scientific_journal-7074	32	59	and	and	CCONJ
american_scientific_journal-7074	32	60	shape	shape	NOUN
american_scientific_journal-7074	32	61	of	of	ADP
american_scientific_journal-7074	32	62	the	the	DET
american_scientific_journal-7074	32	63	displaced	displace	VERB
american_scientific_journal-7074	32	64	edge	edge	NOUN
american_scientific_journal-7074	32	65	would	would	AUX
american_scientific_journal-7074	32	66	be	be	AUX
american_scientific_journal-7074	32	67	a	a	DET
american_scientific_journal-7074	32	68	uniquely	uniquely	ADV
american_scientific_journal-7074	32	69	determined	determined	ADJ
american_scientific_journal-7074	32	70	parabola	parabola	NOUN
american_scientific_journal-7074	32	71	.	.	PUNCT
american_scientific_journal-7074	33	1	if	if	SCONJ
american_scientific_journal-7074	33	2	we	we	PRON
american_scientific_journal-7074	33	3	now	now	ADV
american_scientific_journal-7074	33	4	consider	consider	VERB
american_scientific_journal-7074	33	5	the	the	DET
american_scientific_journal-7074	33	6	u	u	NOUN
american_scientific_journal-7074	33	7	displacements	displacement	NOUN
american_scientific_journal-7074	33	8	of	of	ADP
american_scientific_journal-7074	33	9	points	point	NOUN
american_scientific_journal-7074	33	10	just	just	ADV
american_scientific_journal-7074	33	11	across	across	ADP
american_scientific_journal-7074	33	12	the	the	DET
american_scientific_journal-7074	33	13	boundary	boundary	NOUN
american_scientific_journal-7074	33	14	,	,	PUNCT
american_scientific_journal-7074	33	15	they	they	PRON
american_scientific_journal-7074	33	16	too	too	ADV
american_scientific_journal-7074	33	17	vary	vary	VERB
american_scientific_journal-7074	33	18	parabolically	parabolically	ADV
american_scientific_journal-7074	33	19	and	and	CCONJ
american_scientific_journal-7074	33	20	are	be	AUX
american_scientific_journal-7074	33	21	uniquely	uniquely	ADV
american_scientific_journal-7074	33	22	determined	determine	VERB
american_scientific_journal-7074	33	23	by	by	ADP
american_scientific_journal-7074	33	24	the	the	DET
american_scientific_journal-7074	33	25	motion	motion	NOUN
american_scientific_journal-7074	33	26	of	of	ADP
american_scientific_journal-7074	33	27	three	three	NUM
american_scientific_journal-7074	33	28	nodes	node	NOUN
american_scientific_journal-7074	33	29	.	.	PUNCT
american_scientific_journal-7074	34	1	since	since	SCONJ
american_scientific_journal-7074	34	2	displacements	displacement	NOUN
american_scientific_journal-7074	34	3	are	be	AUX
american_scientific_journal-7074	34	4	common	common	ADJ
american_scientific_journal-7074	34	5	at	at	ADP
american_scientific_journal-7074	34	6	the	the	DET
american_scientific_journal-7074	34	7	three	three	NUM
american_scientific_journal-7074	34	8	nodal	nodal	NOUN
american_scientific_journal-7074	34	9	points	point	NOUN
american_scientific_journal-7074	34	10	,	,	PUNCT
american_scientific_journal-7074	34	11	the	the	DET
american_scientific_journal-7074	34	12	parabolic	parabolic	ADJ
american_scientific_journal-7074	34	13	displacements	displacement	NOUN
american_scientific_journal-7074	34	14	on	on	ADP
american_scientific_journal-7074	34	15	both	both	DET
american_scientific_journal-7074	34	16	sides	side	NOUN
american_scientific_journal-7074	34	17	of	of	ADP
american_scientific_journal-7074	34	18	the	the	DET
american_scientific_journal-7074	34	19	boundary	boundary	NOUN
american_scientific_journal-7074	34	20	are	be	AUX
american_scientific_journal-7074	34	21	identical	identical	ADJ
american_scientific_journal-7074	34	22	.	.	PUNCT
american_scientific_journal-7074	35	1	hence	hence	ADV
american_scientific_journal-7074	35	2	there	there	PRON
american_scientific_journal-7074	35	3	will	will	AUX
american_scientific_journal-7074	35	4	be	be	AUX
american_scientific_journal-7074	35	5	no	no	DET
american_scientific_journal-7074	35	6	tendency	tendency	NOUN
american_scientific_journal-7074	35	7	for	for	SCONJ
american_scientific_journal-7074	35	8	gaps	gap	NOUN
american_scientific_journal-7074	35	9	open	open	ADJ
american_scientific_journal-7074	35	10	or	or	CCONJ
american_scientific_journal-7074	35	11	for	for	ADP
american_scientific_journal-7074	35	12	overlap	overlap	NOUN
american_scientific_journal-7074	35	13	to	to	PART
american_scientific_journal-7074	35	14	occur	occur	VERB
american_scientific_journal-7074	35	15	.	.	PUNCT
american_scientific_journal-7074	36	1	similar	similar	ADJ
american_scientific_journal-7074	36	2	treatment	treatment	NOUN
american_scientific_journal-7074	36	3	of	of	ADP
american_scientific_journal-7074	36	4	vb	vb	NOUN
american_scientific_journal-7074	36	5	would	would	AUX
american_scientific_journal-7074	36	6	show	show	VERB
american_scientific_journal-7074	36	7	that	that	SCONJ
american_scientific_journal-7074	36	8	there	there	PRON
american_scientific_journal-7074	36	9	is	be	VERB
american_scientific_journal-7074	36	10	no	no	DET
american_scientific_journal-7074	36	11	slipping	slipping	NOUN
american_scientific_journal-7074	36	12	along	along	ADP
american_scientific_journal-7074	36	13	the	the	DET
american_scientific_journal-7074	36	14	interface	interface	NOUN
american_scientific_journal-7074	36	15	formed	form	VERB
american_scientific_journal-7074	36	16	by	by	ADP
american_scientific_journal-7074	36	17	the	the	DET
american_scientific_journal-7074	36	18	boundary	boundary	NOUN
american_scientific_journal-7074	36	19	.	.	PUNCT
american_scientific_journal-7074	37	1	for	for	ADP
american_scientific_journal-7074	37	2	an	an	DET
american_scientific_journal-7074	37	3	oblique	oblique	ADJ
american_scientific_journal-7074	37	4	boundary	boundary	NOUN
american_scientific_journal-7074	37	5	the	the	DET
american_scientific_journal-7074	37	6	manipulations	manipulation	NOUN
american_scientific_journal-7074	37	7	would	would	AUX
american_scientific_journal-7074	37	8	be	be	AUX
american_scientific_journal-7074	37	9	more	more	ADV
american_scientific_journal-7074	37	10	complex	complex	ADJ
american_scientific_journal-7074	37	11	but	but	CCONJ
american_scientific_journal-7074	37	12	the	the	DET
american_scientific_journal-7074	37	13	conclusions	conclusion	NOUN
american_scientific_journal-7074	37	14	identical	identical	ADJ
american_scientific_journal-7074	37	15	.	.	PUNCT
american_scientific_journal-7074	38	1	consequently	consequently	ADV
american_scientific_journal-7074	38	2	,	,	PUNCT
american_scientific_journal-7074	38	3	displacements	displacement	NOUN
american_scientific_journal-7074	38	4	are	be	AUX
american_scientific_journal-7074	38	5	compatible	compatible	ADJ
american_scientific_journal-7074	38	6	at	at	ADP
american_scientific_journal-7074	38	7	all	all	DET
american_scientific_journal-7074	38	8	element	element	ADJ
american_scientific_journal-7074	38	9	interfaces	interface	NOUN
american_scientific_journal-7074	38	10	.	.	PUNCT
american_scientific_journal-7074	39	1	american	american	ADJ
american_scientific_journal-7074	39	2	academic	academic	ADJ
american_scientific_journal-7074	39	3	scientific	scientific	ADJ
american_scientific_journal-7074	39	4	research	research	NOUN
american_scientific_journal-7074	39	5	journal	journal	NOUN
american_scientific_journal-7074	39	6	for	for	ADP
american_scientific_journal-7074	39	7	engineering	engineering	NOUN
american_scientific_journal-7074	39	8	,	,	PUNCT
american_scientific_journal-7074	39	9	technology	technology	NOUN
american_scientific_journal-7074	39	10	,	,	PUNCT
american_scientific_journal-7074	39	11	and	and	CCONJ
american_scientific_journal-7074	39	12	sciences	science	NOUN
american_scientific_journal-7074	39	13	(	(	PUNCT
american_scientific_journal-7074	39	14	asrjets	asrjet	NOUN
american_scientific_journal-7074	39	15	)	)	PUNCT
american_scientific_journal-7074	39	16	(	(	PUNCT
american_scientific_journal-7074	39	17	2021	2021	NUM
american_scientific_journal-7074	39	18	)	)	PUNCT
american_scientific_journal-7074	39	19	volume	volume	NOUN
american_scientific_journal-7074	39	20	83	83	NUM
american_scientific_journal-7074	39	21	,	,	PUNCT
american_scientific_journal-7074	39	22	no	no	DET
american_scientific_journal-7074	39	23	1	1	NUM
american_scientific_journal-7074	39	24	,	,	PUNCT
american_scientific_journal-7074	39	25	pp	pp	ADV
american_scientific_journal-7074	39	26	1	1	NUM
american_scientific_journal-7074	39	27	-	-	SYM
american_scientific_journal-7074	39	28	11	11	NUM
american_scientific_journal-7074	39	29	5	5	NUM
american_scientific_journal-7074	39	30	3	3	NUM
american_scientific_journal-7074	39	31	.	.	PUNCT
american_scientific_journal-7074	39	32	stiffness	stiffness	NOUN
american_scientific_journal-7074	39	33	of	of	ADP
american_scientific_journal-7074	39	34	the	the	DET
american_scientific_journal-7074	39	35	linear	linear	ADJ
american_scientific_journal-7074	39	36	strain	strain	NOUN
american_scientific_journal-7074	39	37	triangle	triangle	NOUN
american_scientific_journal-7074	39	38	in	in	ADP
american_scientific_journal-7074	39	39	the	the	DET
american_scientific_journal-7074	39	40	strain	strain	NOUN
american_scientific_journal-7074	39	41	formula	formula	NOUN
american_scientific_journal-7074	39	42	ɛ	ɛ	X
american_scientific_journal-7074	39	43	=	=	PUNCT
american_scientific_journal-7074	39	44	δ	δ	PROPN
american_scientific_journal-7074	39	45	p	p	NOUN
american_scientific_journal-7074	39	46	a	a	DET
american_scientific_journal-7074	39	47	-1	-1	INTJ
american_scientific_journal-7074	39	48	δ	δ	PROPN
american_scientific_journal-7074	39	49	in	in	ADP
american_scientific_journal-7074	39	50	which	which	PRON
american_scientific_journal-7074	39	51	the	the	DET
american_scientific_journal-7074	39	52	deferential	deferential	ADJ
american_scientific_journal-7074	39	53	operator	operator	NOUN
american_scientific_journal-7074	39	54	matrix	matrix	NOUN
american_scientific_journal-7074	40	1	𝜕	𝜕	PROPN
american_scientific_journal-7074	40	2	𝜕𝑥	𝜕𝑥	X
american_scientific_journal-7074	40	3	0	0	NUM
american_scientific_journal-7074	40	4	δ	δ	X
american_scientific_journal-7074	40	5	=	=	SYM
american_scientific_journal-7074	40	6	0	0	PUNCT
american_scientific_journal-7074	41	1	𝛿	𝛿	DET
american_scientific_journal-7074	41	2	𝛿𝑦	𝛿𝑦	PROPN
american_scientific_journal-7074	41	3	𝛿	𝛿	PROPN
american_scientific_journal-7074	41	4	𝛿𝑦	𝛿𝑦	PROPN
american_scientific_journal-7074	41	5	𝜕	𝜕	PROPN
american_scientific_journal-7074	41	6	𝜕𝑥	𝜕𝑥	X
american_scientific_journal-7074	41	7	the	the	DET
american_scientific_journal-7074	41	8	polynomial	polynomial	ADJ
american_scientific_journal-7074	41	9	matrix	matrix	NOUN
american_scientific_journal-7074	41	10	given	give	VERB
american_scientific_journal-7074	41	11	earlier	early	ADV
american_scientific_journal-7074	41	12	in	in	ADP
american_scientific_journal-7074	41	13	2	2	NUM
american_scientific_journal-7074	41	14	from	from	ADP
american_scientific_journal-7074	41	15	which	which	PRON
american_scientific_journal-7074	41	16	b	b	NOUN
american_scientific_journal-7074	41	17	=	=	SYM
american_scientific_journal-7074	41	18	δ	δ	PROPN
american_scientific_journal-7074	41	19	p	p	NOUN
american_scientific_journal-7074	41	20	becomes	become	VERB
american_scientific_journal-7074	41	21	b	b	NOUN
american_scientific_journal-7074	41	22	=	=	SYM
american_scientific_journal-7074	41	23	𝜕	𝜕	PROPN
american_scientific_journal-7074	41	24	𝜕𝑥	𝜕𝑥	X
american_scientific_journal-7074	41	25	0	0	NUM
american_scientific_journal-7074	41	26	0	0	NUM
american_scientific_journal-7074	41	27	𝛿	𝛿	DET
american_scientific_journal-7074	41	28	𝛿𝑦	𝛿𝑦	NOUN
american_scientific_journal-7074	41	29	𝛿	𝛿	PROPN
american_scientific_journal-7074	41	30	𝛿𝑦	𝛿𝑦	PROPN
american_scientific_journal-7074	41	31	𝜕	𝜕	PROPN
american_scientific_journal-7074	41	32	𝜕𝑥	𝜕𝑥	X
american_scientific_journal-7074	41	33	1	1	NUM
american_scientific_journal-7074	41	34	x	x	SYM
american_scientific_journal-7074	41	35	y	y	NOUN
american_scientific_journal-7074	41	36	x	x	SYM
american_scientific_journal-7074	41	37	2	2	NUM
american_scientific_journal-7074	41	38	xy	xy	NOUN
american_scientific_journal-7074	41	39	y	y	PROPN
american_scientific_journal-7074	41	40	2	2	NUM
american_scientific_journal-7074	41	41	0	0	NUM
american_scientific_journal-7074	41	42	0	0	NUM
american_scientific_journal-7074	41	43	0	0	NUM
american_scientific_journal-7074	41	44	0	0	NUM
american_scientific_journal-7074	41	45	0	0	NUM
american_scientific_journal-7074	41	46	0	0	NUM
american_scientific_journal-7074	41	47	0	0	NUM
american_scientific_journal-7074	41	48	0	0	NUM
american_scientific_journal-7074	41	49	0	0	NUM
american_scientific_journal-7074	41	50	0	0	NUM
american_scientific_journal-7074	41	51	0	0	NUM
american_scientific_journal-7074	41	52	0	0	NUM
american_scientific_journal-7074	41	53	1	1	NUM
american_scientific_journal-7074	41	54	x	x	SYM
american_scientific_journal-7074	41	55	y	y	NOUN
american_scientific_journal-7074	41	56	x	x	SYM
american_scientific_journal-7074	41	57	2	2	NUM
american_scientific_journal-7074	41	58	xy	xy	NOUN
american_scientific_journal-7074	41	59	y	y	PROPN
american_scientific_journal-7074	41	60	2	2	NUM
american_scientific_journal-7074	41	61	0	0	NUM
american_scientific_journal-7074	41	62	1	1	NUM
american_scientific_journal-7074	41	63	0	0	NUM
american_scientific_journal-7074	41	64	2x	2x	NUM
american_scientific_journal-7074	41	65	y	y	PROPN
american_scientific_journal-7074	41	66	0	0	NUM
american_scientific_journal-7074	41	67	0	0	NUM
american_scientific_journal-7074	41	68	0	0	NUM
american_scientific_journal-7074	41	69	0	0	NUM
american_scientific_journal-7074	41	70	0	0	NUM
american_scientific_journal-7074	41	71	0	0	NUM
american_scientific_journal-7074	41	72	0	0	NUM
american_scientific_journal-7074	42	1	=	=	SYM
american_scientific_journal-7074	42	2	0	0	NUM
american_scientific_journal-7074	42	3	0	0	NUM
american_scientific_journal-7074	42	4	0	0	NUM
american_scientific_journal-7074	42	5	0	0	NUM
american_scientific_journal-7074	42	6	0	0	NUM
american_scientific_journal-7074	42	7	0	0	NUM
american_scientific_journal-7074	42	8	0	0	NUM
american_scientific_journal-7074	42	9	0	0	NUM
american_scientific_journal-7074	42	10	1	1	NUM
american_scientific_journal-7074	42	11	0	0	NUM
american_scientific_journal-7074	42	12	x	x	SYM
american_scientific_journal-7074	42	13	2y	2y	NUM
american_scientific_journal-7074	43	1	9	9	NUM
american_scientific_journal-7074	43	2	0	0	NUM
american_scientific_journal-7074	43	3	0	0	NUM
american_scientific_journal-7074	43	4	1	1	NUM
american_scientific_journal-7074	43	5	0	0	NUM
american_scientific_journal-7074	43	6	x	x	SYM
american_scientific_journal-7074	43	7	2y	2y	NUM
american_scientific_journal-7074	43	8	0	0	NUM
american_scientific_journal-7074	43	9	1	1	NUM
american_scientific_journal-7074	43	10	0	0	NUM
american_scientific_journal-7074	43	11	2x	2x	NUM
american_scientific_journal-7074	43	12	y	y	NOUN
american_scientific_journal-7074	43	13	0	0	NUM
american_scientific_journal-7074	43	14	in	in	ADP
american_scientific_journal-7074	43	15	the	the	DET
american_scientific_journal-7074	43	16	strain	strain	NOUN
american_scientific_journal-7074	43	17	equation	equation	NOUN
american_scientific_journal-7074	43	18	ɛ	ɛ	NOUN
american_scientific_journal-7074	43	19	=	=	SYM
american_scientific_journal-7074	43	20	b	b	PROPN
american_scientific_journal-7074	43	21	a	a	DET
american_scientific_journal-7074	43	22	-1	-1	INTJ
american_scientific_journal-7074	43	23	δ	δ	NOUN
american_scientific_journal-7074	43	24	the	the	DET
american_scientific_journal-7074	43	25	only	only	ADJ
american_scientific_journal-7074	43	26	variables	variable	NOUN
american_scientific_journal-7074	43	27	occur	occur	VERB
american_scientific_journal-7074	43	28	in	in	ADP
american_scientific_journal-7074	43	29	matrix	matrix	NOUN
american_scientific_journal-7074	43	30	b	b	NOUN
american_scientific_journal-7074	43	31	and	and	CCONJ
american_scientific_journal-7074	43	32	hence	hence	ADV
american_scientific_journal-7074	43	33	are	be	AUX
american_scientific_journal-7074	43	34	seen	see	VERB
american_scientific_journal-7074	43	35	to	to	PART
american_scientific_journal-7074	43	36	have	have	VERB
american_scientific_journal-7074	43	37	unit	unit	NOUN
american_scientific_journal-7074	43	38	exponent	exponent	NOUN
american_scientific_journal-7074	43	39	,	,	PUNCT
american_scientific_journal-7074	43	40	consequently	consequently	ADV
american_scientific_journal-7074	43	41	strain	strain	VERB
american_scientific_journal-7074	43	42	varies	vary	VERB
american_scientific_journal-7074	43	43	linearly	linearly	ADV
american_scientific_journal-7074	43	44	within	within	ADP
american_scientific_journal-7074	43	45	the	the	DET
american_scientific_journal-7074	43	46	element	element	NOUN
american_scientific_journal-7074	43	47	.	.	PUNCT
american_scientific_journal-7074	44	1	with	with	ADP
american_scientific_journal-7074	44	2	matrix	matrix	NOUN
american_scientific_journal-7074	44	3	d	d	NOUN
american_scientific_journal-7074	44	4	given	give	VERB
american_scientific_journal-7074	44	5	by	by	ADP
american_scientific_journal-7074	44	6	1	1	NUM
american_scientific_journal-7074	44	7	𝒗	𝒗	PROPN
american_scientific_journal-7074	44	8	0	0	PUNCT
american_scientific_journal-7074	44	9	d	d	NOUN
american_scientific_journal-7074	44	10	=	=	SYM
american_scientific_journal-7074	44	11	𝐸	𝐸	PROPN
american_scientific_journal-7074	44	12	1−𝑣	1−𝑣	NUM
american_scientific_journal-7074	44	13	𝒗	𝒗	NOUN
american_scientific_journal-7074	44	14	1	1	NUM
american_scientific_journal-7074	44	15	0	0	NUM
american_scientific_journal-7074	44	16	american	american	ADJ
american_scientific_journal-7074	44	17	academic	academic	ADJ
american_scientific_journal-7074	44	18	scientific	scientific	ADJ
american_scientific_journal-7074	44	19	research	research	NOUN
american_scientific_journal-7074	44	20	journal	journal	NOUN
american_scientific_journal-7074	44	21	for	for	ADP
american_scientific_journal-7074	44	22	engineering	engineering	NOUN
american_scientific_journal-7074	44	23	,	,	PUNCT
american_scientific_journal-7074	44	24	technology	technology	NOUN
american_scientific_journal-7074	44	25	,	,	PUNCT
american_scientific_journal-7074	44	26	and	and	CCONJ
american_scientific_journal-7074	44	27	sciences	science	NOUN
american_scientific_journal-7074	44	28	(	(	PUNCT
american_scientific_journal-7074	44	29	asrjets	asrjet	NOUN
american_scientific_journal-7074	44	30	)	)	PUNCT
american_scientific_journal-7074	44	31	(	(	PUNCT
american_scientific_journal-7074	44	32	2021	2021	NUM
american_scientific_journal-7074	44	33	)	)	PUNCT
american_scientific_journal-7074	44	34	volume	volume	NOUN
american_scientific_journal-7074	44	35	83	83	NUM
american_scientific_journal-7074	44	36	,	,	PUNCT
american_scientific_journal-7074	44	37	no	no	DET
american_scientific_journal-7074	44	38	1	1	NUM
american_scientific_journal-7074	44	39	,	,	PUNCT
american_scientific_journal-7074	44	40	pp	pp	ADV
american_scientific_journal-7074	44	41	1	1	NUM
american_scientific_journal-7074	44	42	-	-	SYM
american_scientific_journal-7074	44	43	11	11	NUM
american_scientific_journal-7074	44	44	6	6	NUM
american_scientific_journal-7074	44	45	0	0	NUM
american_scientific_journal-7074	44	46	0	0	NUM
american_scientific_journal-7074	44	47	1−𝑣	1−𝑣	NUM
american_scientific_journal-7074	44	48	2	2	NUM
american_scientific_journal-7074	44	49	all	all	DET
american_scientific_journal-7074	44	50	matrices	matrix	NOUN
american_scientific_journal-7074	44	51	in	in	ADP
american_scientific_journal-7074	44	52	the	the	DET
american_scientific_journal-7074	44	53	stiffness	stiffness	ADJ
american_scientific_journal-7074	44	54	equation	equation	NOUN
american_scientific_journal-7074	44	55	k	k	PROPN
american_scientific_journal-7074	44	56	above	above	ADV
american_scientific_journal-7074	44	57	are	be	AUX
american_scientific_journal-7074	44	58	known	know	VERB
american_scientific_journal-7074	44	59	with	with	ADP
american_scientific_journal-7074	44	60	the	the	DET
american_scientific_journal-7074	44	61	incremental	incremental	ADJ
american_scientific_journal-7074	44	62	volume	volume	NOUN
american_scientific_journal-7074	44	63	dv	dv	PROPN
american_scientific_journal-7074	44	64	for	for	ADP
american_scientific_journal-7074	44	65	an	an	DET
american_scientific_journal-7074	44	66	element	element	NOUN
american_scientific_journal-7074	44	67	with	with	ADP
american_scientific_journal-7074	44	68	a	a	DET
american_scientific_journal-7074	44	69	uniform	uniform	ADJ
american_scientific_journal-7074	44	70	thickness	thickness	NOUN
american_scientific_journal-7074	44	71	,	,	PUNCT
american_scientific_journal-7074	44	72	t	t	PROPN
american_scientific_journal-7074	44	73	can	can	AUX
american_scientific_journal-7074	44	74	be	be	AUX
american_scientific_journal-7074	44	75	taken	take	VERB
american_scientific_journal-7074	44	76	as	as	ADP
american_scientific_journal-7074	44	77	dv	dv	PROPN
american_scientific_journal-7074	44	78	=	=	PROPN
american_scientific_journal-7074	44	79	t	t	X
american_scientific_journal-7074	44	80	da	da	PROPN
american_scientific_journal-7074	44	81	,	,	PUNCT
american_scientific_journal-7074	44	82	therefor	therefor	ADP
american_scientific_journal-7074	44	83	k=	k=	CCONJ
american_scientific_journal-7074	44	84	𝐴-1	𝐴-1	PROPN
american_scientific_journal-7074	44	85	t	t	PROPN
american_scientific_journal-7074	44	86	t	t	PROPN
american_scientific_journal-7074	44	87	ʃ	ʃ	PROPN
american_scientific_journal-7074	44	88	b	b	PROPN
american_scientific_journal-7074	44	89	t	t	PROPN
american_scientific_journal-7074	45	1	d	d	X
american_scientific_journal-7074	45	2	b	b	X
american_scientific_journal-7074	45	3	da	da	PROPN
american_scientific_journal-7074	45	4	a	a	DET
american_scientific_journal-7074	45	5	-1	-1	ADJ
american_scientific_journal-7074	45	6	10	10	NUM
american_scientific_journal-7074	45	7	matrix	matrix	NOUN
american_scientific_journal-7074	45	8	b	b	NOUN
american_scientific_journal-7074	45	9	contains	contain	VERB
american_scientific_journal-7074	45	10	x	x	PUNCT
american_scientific_journal-7074	45	11	and	and	CCONJ
american_scientific_journal-7074	45	12	y	y	PROPN
american_scientific_journal-7074	45	13	terms	term	NOUN
american_scientific_journal-7074	45	14	as	as	ADV
american_scientific_journal-7074	45	15	well	well	ADV
american_scientific_journal-7074	45	16	as	as	ADP
american_scientific_journal-7074	45	17	constants	constant	NOUN
american_scientific_journal-7074	45	18	therefore	therefore	ADV
american_scientific_journal-7074	45	19	when	when	SCONJ
american_scientific_journal-7074	45	20	product	product	NOUN
american_scientific_journal-7074	45	21	of	of	ADP
american_scientific_journal-7074	45	22	b	b	PROPN
american_scientific_journal-7074	45	23	t	t	PROPN
american_scientific_journal-7074	45	24	d	d	PROPN
american_scientific_journal-7074	45	25	b	b	PROPN
american_scientific_journal-7074	45	26	is	be	AUX
american_scientific_journal-7074	45	27	considered	consider	VERB
american_scientific_journal-7074	45	28	,	,	PUNCT
american_scientific_journal-7074	45	29	it	it	PRON
american_scientific_journal-7074	45	30	is	be	AUX
american_scientific_journal-7074	45	31	evident	evident	ADJ
american_scientific_journal-7074	45	32	that	that	SCONJ
american_scientific_journal-7074	45	33	we	we	PRON
american_scientific_journal-7074	45	34	must	must	AUX
american_scientific_journal-7074	45	35	integrate	integrate	VERB
american_scientific_journal-7074	45	36	terms	term	NOUN
american_scientific_journal-7074	45	37	containing	contain	VERB
american_scientific_journal-7074	45	38	constants	constant	NOUN
american_scientific_journal-7074	45	39	,	,	PUNCT
american_scientific_journal-7074	45	40	x	x	PRON
american_scientific_journal-7074	45	41	,	,	PUNCT
american_scientific_journal-7074	45	42	y	y	PROPN
american_scientific_journal-7074	45	43	x	x	SYM
american_scientific_journal-7074	45	44	2	2	NUM
american_scientific_journal-7074	45	45	,	,	PUNCT
american_scientific_journal-7074	45	46	xy	xy	PROPN
american_scientific_journal-7074	45	47	,	,	PUNCT
american_scientific_journal-7074	45	48	y	y	PROPN
american_scientific_journal-7074	45	49	2	2	NUM
american_scientific_journal-7074	45	50	.	.	PUNCT
american_scientific_journal-7074	46	1	these	these	DET
american_scientific_journal-7074	46	2	integrations	integration	NOUN
american_scientific_journal-7074	46	3	lead	lead	VERB
american_scientific_journal-7074	46	4	to	to	ADP
american_scientific_journal-7074	46	5	some	some	DET
american_scientific_journal-7074	46	6	intricate	intricate	ADJ
american_scientific_journal-7074	46	7	formulas	formula	NOUN
american_scientific_journal-7074	46	8	except	except	SCONJ
american_scientific_journal-7074	46	9	in	in	ADP
american_scientific_journal-7074	46	10	the	the	DET
american_scientific_journal-7074	46	11	case	case	NOUN
american_scientific_journal-7074	46	12	where	where	SCONJ
american_scientific_journal-7074	46	13	the	the	DET
american_scientific_journal-7074	46	14	origin	origin	NOUN
american_scientific_journal-7074	46	15	is	be	AUX
american_scientific_journal-7074	46	16	at	at	ADP
american_scientific_journal-7074	46	17	the	the	DET
american_scientific_journal-7074	46	18	centroid	centroid	NOUN
american_scientific_journal-7074	46	19	,	,	PUNCT
american_scientific_journal-7074	46	20	then	then	ADV
american_scientific_journal-7074	46	21	the	the	DET
american_scientific_journal-7074	46	22	solutions	solution	NOUN
american_scientific_journal-7074	46	23	are	be	AUX
american_scientific_journal-7074	46	24	quite	quite	ADV
american_scientific_journal-7074	46	25	simple	simple	ADJ
american_scientific_journal-7074	46	26	.	.	PUNCT
american_scientific_journal-7074	47	1	even	even	ADV
american_scientific_journal-7074	47	2	these	these	PRON
american_scientific_journal-7074	47	3	are	be	AUX
american_scientific_journal-7074	47	4	difficult	difficult	ADJ
american_scientific_journal-7074	47	5	to	to	PART
american_scientific_journal-7074	47	6	compute	compute	VERB
american_scientific_journal-7074	47	7	when	when	SCONJ
american_scientific_journal-7074	47	8	working	work	VERB
american_scientific_journal-7074	47	9	with	with	ADP
american_scientific_journal-7074	47	10	cartesian	cartesian	ADJ
american_scientific_journal-7074	47	11	coordinates	coordinate	NOUN
american_scientific_journal-7074	47	12	;	;	PUNCT
american_scientific_journal-7074	47	13	but	but	CCONJ
american_scientific_journal-7074	47	14	by	by	ADP
american_scientific_journal-7074	47	15	means	mean	NOUN
american_scientific_journal-7074	47	16	of	of	ADP
american_scientific_journal-7074	47	17	area	area	NOUN
american_scientific_journal-7074	47	18	coordinates	coordinate	NOUN
american_scientific_journal-7074	47	19	following	follow	VERB
american_scientific_journal-7074	47	20	[	[	X
american_scientific_journal-7074	47	21	1,2	1,2	NUM
american_scientific_journal-7074	47	22	]	]	PUNCT
american_scientific_journal-7074	47	23	,	,	PUNCT
american_scientific_journal-7074	47	24	through	through	SCONJ
american_scientific_journal-7074	47	25	[	[	PUNCT
american_scientific_journal-7074	47	26	7	7	NUM
american_scientific_journal-7074	47	27	]	]	X
american_scientific_journal-7074	47	28	formulas	formula	NOUN
american_scientific_journal-7074	47	29	can	can	AUX
american_scientific_journal-7074	47	30	be	be	AUX
american_scientific_journal-7074	47	31	derived	derive	VERB
american_scientific_journal-7074	47	32	.	.	PUNCT
american_scientific_journal-7074	48	1	with	with	ADP
american_scientific_journal-7074	48	2	the	the	DET
american_scientific_journal-7074	48	3	use	use	NOUN
american_scientific_journal-7074	48	4	of	of	ADP
american_scientific_journal-7074	48	5	these	these	DET
american_scientific_journal-7074	48	6	formulas	formula	NOUN
american_scientific_journal-7074	48	7	,	,	PUNCT
american_scientific_journal-7074	48	8	we	we	PRON
american_scientific_journal-7074	48	9	found	find	VERB
american_scientific_journal-7074	48	10	that	that	SCONJ
american_scientific_journal-7074	48	11	∫	∫	PROPN
american_scientific_journal-7074	48	12	b	b	PROPN
american_scientific_journal-7074	48	13	t	t	PROPN
american_scientific_journal-7074	48	14	d	d	X
american_scientific_journal-7074	48	15	b	b	X
american_scientific_journal-7074	48	16	da	da	ADJ
american_scientific_journal-7074	48	17	=	=	PUNCT
american_scientific_journal-7074	48	18	𝑎𝑟𝑒𝑎	𝑎𝑟𝑒𝑎	NOUN
american_scientific_journal-7074	49	1	𝑥	𝑥	PROPN
american_scientific_journal-7074	49	2	𝐸	𝐸	PROPN
american_scientific_journal-7074	49	3	1−v2	1−v2	NUM
american_scientific_journal-7074	49	4	x	x	SYM
american_scientific_journal-7074	49	5	0	0	NUM
american_scientific_journal-7074	49	6	0	0	NUM
american_scientific_journal-7074	49	7	0	0	NUM
american_scientific_journal-7074	49	8	0	0	NUM
american_scientific_journal-7074	49	9	0	0	NUM
american_scientific_journal-7074	49	10	0	0	NUM
american_scientific_journal-7074	49	11	0	0	NUM
american_scientific_journal-7074	49	12	0	0	NUM
american_scientific_journal-7074	49	13	0	0	NUM
american_scientific_journal-7074	49	14	0	0	NUM
american_scientific_journal-7074	49	15	0	0	NUM
american_scientific_journal-7074	49	16	0	0	NUM
american_scientific_journal-7074	49	17	0	0	NUM
american_scientific_journal-7074	49	18	1	1	NUM
american_scientific_journal-7074	49	19	0	0	NUM
american_scientific_journal-7074	49	20	0	0	NUM
american_scientific_journal-7074	49	21	0	0	NUM
american_scientific_journal-7074	49	22	0	0	NUM
american_scientific_journal-7074	49	23	0	0	NUM
american_scientific_journal-7074	49	24	0	0	NUM
american_scientific_journal-7074	49	25	𝒗	𝒗	PROPN
american_scientific_journal-7074	49	26	0	0	NUM
american_scientific_journal-7074	49	27	0	0	NUM
american_scientific_journal-7074	49	28	0	0	NUM
american_scientific_journal-7074	49	29	0	0	NUM
american_scientific_journal-7074	49	30	0	0	NUM
american_scientific_journal-7074	49	31	μ	μ	NOUN
american_scientific_journal-7074	49	32	0	0	NUM
american_scientific_journal-7074	49	33	0	0	NUM
american_scientific_journal-7074	49	34	0	0	NUM
american_scientific_journal-7074	49	35	0	0	NUM
american_scientific_journal-7074	49	36	μ	μ	NOUN
american_scientific_journal-7074	49	37	0	0	NUM
american_scientific_journal-7074	49	38	0	0	NUM
american_scientific_journal-7074	49	39	0	0	NUM
american_scientific_journal-7074	49	40	0	0	NUM
american_scientific_journal-7074	49	41	0	0	NUM
american_scientific_journal-7074	49	42	0	0	NUM
american_scientific_journal-7074	49	43	0	0	NUM
american_scientific_journal-7074	49	44	4ꭓꭓ	4ꭓꭓ	NOUN
american_scientific_journal-7074	49	45	2ꭕу	2ꭕу	ADJ
american_scientific_journal-7074	49	46	0	0	NUM
american_scientific_journal-7074	49	47	0	0	NUM
american_scientific_journal-7074	49	48	0	0	NUM
american_scientific_journal-7074	49	49	0	0	NUM
american_scientific_journal-7074	49	50	0	0	NUM
american_scientific_journal-7074	50	1	2𝒗ꭓꭕ	2𝒗ꭓꭕ	NUM
american_scientific_journal-7074	50	2	4𝒗ꭓу	4𝒗ꭓу	PROPN
american_scientific_journal-7074	50	3	0	0	NUM
american_scientific_journal-7074	50	4	0	0	NUM
american_scientific_journal-7074	50	5	0	0	NUM
american_scientific_journal-7074	51	1	2ꭕу	2ꭕу	NOUN
american_scientific_journal-7074	52	1	μꭓꭕ+уу	μꭓꭕ+уу	NUM
american_scientific_journal-7074	52	2	2ꭕу	2ꭕу	ADJ
american_scientific_journal-7074	52	3	0	0	NUM
american_scientific_journal-7074	52	4	0	0	NUM
american_scientific_journal-7074	52	5	0	0	NUM
american_scientific_journal-7074	52	6	2μꭓꭕ	2μꭓꭕ	NUM
american_scientific_journal-7074	52	7	(	(	PUNCT
american_scientific_journal-7074	52	8	μ+𝒗)ꭕу	μ+𝒗)ꭕу	PROPN
american_scientific_journal-7074	52	9	2	2	NUM
american_scientific_journal-7074	52	10	𝒗уу	𝒗уу	NOUN
american_scientific_journal-7074	52	11	0	0	NUM
american_scientific_journal-7074	52	12	0	0	NUM
american_scientific_journal-7074	52	13	0	0	NUM
american_scientific_journal-7074	52	14	0	0	NUM
american_scientific_journal-7074	52	15	2μꭕу	2μꭕу	NUM
american_scientific_journal-7074	53	1	4μуу	4μуу	NUM
american_scientific_journal-7074	53	2	0	0	NUM
american_scientific_journal-7074	53	3	0	0	NUM
american_scientific_journal-7074	53	4	0	0	NUM
american_scientific_journal-7074	54	1	4μꭕу	4μꭕу	NUM
american_scientific_journal-7074	54	2	2μуу	2μуу	VERB
american_scientific_journal-7074	54	3	0	0	NUM
american_scientific_journal-7074	54	4	0	0	NUM
american_scientific_journal-7074	54	5	0	0	NUM
american_scientific_journal-7074	54	6	0	0	NUM
american_scientific_journal-7074	54	7	0	0	NUM
american_scientific_journal-7074	54	8	0	0	NUM
american_scientific_journal-7074	54	9	0	0	NUM
american_scientific_journal-7074	54	10	0	0	NUM
american_scientific_journal-7074	54	11	0	0	NUM
american_scientific_journal-7074	54	12	0	0	NUM
american_scientific_journal-7074	54	13	0	0	NUM
american_scientific_journal-7074	54	14	0	0	NUM
american_scientific_journal-7074	54	15	0	0	NUM
american_scientific_journal-7074	54	16	0	0	NUM
american_scientific_journal-7074	54	17	0	0	NUM
american_scientific_journal-7074	55	1	μ	μ	NOUN
american_scientific_journal-7074	55	2	0	0	NUM
american_scientific_journal-7074	55	3	0	0	NUM
american_scientific_journal-7074	55	4	0	0	NUM
american_scientific_journal-7074	55	5	0	0	NUM
american_scientific_journal-7074	55	6	μ	μ	NOUN
american_scientific_journal-7074	55	7	0	0	NUM
american_scientific_journal-7074	55	8	0	0	NUM
american_scientific_journal-7074	55	9	0	0	NUM
american_scientific_journal-7074	55	10	0	0	NUM
american_scientific_journal-7074	55	11	11	11	NUM
american_scientific_journal-7074	55	12	0	0	NUM
american_scientific_journal-7074	55	13	𝒗	𝒗	PROPN
american_scientific_journal-7074	55	14	0	0	NUM
american_scientific_journal-7074	55	15	0	0	NUM
american_scientific_journal-7074	55	16	0	0	NUM
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american_scientific_journal-7074	55	20	1	1	NUM
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american_scientific_journal-7074	55	23	0	0	NUM
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american_scientific_journal-7074	55	26	0	0	NUM
american_scientific_journal-7074	55	27	0	0	NUM
american_scientific_journal-7074	56	1	2μꭓꭕ	2μꭓꭕ	NUM
american_scientific_journal-7074	56	2	4μꭕу	4μꭕу	NUM
american_scientific_journal-7074	56	3	0	0	NUM
american_scientific_journal-7074	56	4	0	0	NUM
american_scientific_journal-7074	56	5	0	0	NUM
american_scientific_journal-7074	57	1	4μꭓꭕ	4μꭓꭕ	NUM
american_scientific_journal-7074	57	2	2μꭕу	2μꭕу	NUM
american_scientific_journal-7074	57	3	0	0	NUM
american_scientific_journal-7074	57	4	0	0	NUM
american_scientific_journal-7074	57	5	0	0	NUM
american_scientific_journal-7074	57	6	0	0	NUM
american_scientific_journal-7074	58	1	2𝒗ꭓꭕ	2𝒗ꭓꭕ	PROPN
american_scientific_journal-7074	58	2	(	(	PUNCT
american_scientific_journal-7074	58	3	μ+𝒗)ꭕу	μ+𝒗)ꭕу	PROPN
american_scientific_journal-7074	58	4	2μуу	2μуу	ADJ
american_scientific_journal-7074	58	5	0	0	NUM
american_scientific_journal-7074	58	6	0	0	NUM
american_scientific_journal-7074	58	7	0	0	NUM
american_scientific_journal-7074	58	8	2μꭕу	2μꭕу	NUM
american_scientific_journal-7074	58	9	ꭓꭕ+μуу	ꭓꭕ+μуу	X
american_scientific_journal-7074	58	10	0	0	NUM
american_scientific_journal-7074	58	11	american	american	ADJ
american_scientific_journal-7074	58	12	academic	academic	ADJ
american_scientific_journal-7074	58	13	scientific	scientific	ADJ
american_scientific_journal-7074	58	14	research	research	NOUN
american_scientific_journal-7074	58	15	journal	journal	NOUN
american_scientific_journal-7074	58	16	for	for	ADP
american_scientific_journal-7074	58	17	engineering	engineering	NOUN
american_scientific_journal-7074	58	18	,	,	PUNCT
american_scientific_journal-7074	58	19	technology	technology	NOUN
american_scientific_journal-7074	58	20	,	,	PUNCT
american_scientific_journal-7074	58	21	and	and	CCONJ
american_scientific_journal-7074	58	22	sciences	science	NOUN
american_scientific_journal-7074	58	23	(	(	PUNCT
american_scientific_journal-7074	58	24	asrjets	asrjet	NOUN
american_scientific_journal-7074	58	25	)	)	PUNCT
american_scientific_journal-7074	58	26	(	(	PUNCT
american_scientific_journal-7074	58	27	2021	2021	NUM
american_scientific_journal-7074	58	28	)	)	PUNCT
american_scientific_journal-7074	58	29	volume	volume	NOUN
american_scientific_journal-7074	58	30	83	83	NUM
american_scientific_journal-7074	58	31	,	,	PUNCT
american_scientific_journal-7074	58	32	no	no	DET
american_scientific_journal-7074	58	33	1	1	NUM
american_scientific_journal-7074	58	34	,	,	PUNCT
american_scientific_journal-7074	58	35	pp	pp	ADV
american_scientific_journal-7074	58	36	1	1	NUM
american_scientific_journal-7074	58	37	-	-	SYM
american_scientific_journal-7074	58	38	11	11	NUM
american_scientific_journal-7074	58	39	7	7	NUM
american_scientific_journal-7074	58	40	0	0	NUM
american_scientific_journal-7074	58	41	0	0	NUM
american_scientific_journal-7074	58	42	0	0	NUM
american_scientific_journal-7074	58	43	4𝒗ꭓу	4𝒗ꭓу	PROPN
american_scientific_journal-7074	58	44	2𝒗уу	2𝒗уу	NUM
american_scientific_journal-7074	58	45	0	0	NUM
american_scientific_journal-7074	58	46	0	0	NUM
american_scientific_journal-7074	58	47	0	0	NUM
american_scientific_journal-7074	58	48	0	0	NUM
american_scientific_journal-7074	58	49	0	0	NUM
american_scientific_journal-7074	58	50	2ꭕу	2ꭕу	ADJ
american_scientific_journal-7074	58	51	4уу	4уу	NOUN
american_scientific_journal-7074	58	52	where	where	SCONJ
american_scientific_journal-7074	58	53	μ	μ	NOUN
american_scientific_journal-7074	58	54	=	=	SYM
american_scientific_journal-7074	58	55	(	(	PUNCT
american_scientific_journal-7074	58	56	1	1	NUM
american_scientific_journal-7074	58	57	–	–	PUNCT
american_scientific_journal-7074	58	58	𝒗	𝒗	NOUN
american_scientific_journal-7074	58	59	)	)	PUNCT
american_scientific_journal-7074	58	60	̸	̸	NUM
american_scientific_journal-7074	58	61	2	2	NUM
american_scientific_journal-7074	58	62	ꭓꭕ	ꭓꭕ	NOUN
american_scientific_journal-7074	58	63	=	=	SYM
american_scientific_journal-7074	58	64	1	1	NUM
american_scientific_journal-7074	58	65	̸	̸	NUM
american_scientific_journal-7074	58	66	12	12	NUM
american_scientific_journal-7074	58	67	(	(	PUNCT
american_scientific_journal-7074	58	68	ꭕ1	ꭕ1	ADJ
american_scientific_journal-7074	58	69	2	2	NUM
american_scientific_journal-7074	58	70	+	+	NUM
american_scientific_journal-7074	58	71	ꭕ3	ꭕ3	ADJ
american_scientific_journal-7074	58	72	2	2	NUM
american_scientific_journal-7074	58	73	+	+	NOUN
american_scientific_journal-7074	58	74	ꭕ5	ꭕ5	VERB
american_scientific_journal-7074	58	75	2	2	NUM
american_scientific_journal-7074	58	76	)	)	PUNCT
american_scientific_journal-7074	58	77	ꭕу	ꭕу	PROPN
american_scientific_journal-7074	58	78	=	=	SYM
american_scientific_journal-7074	58	79	1/	1/	NUM
american_scientific_journal-7074	58	80	12	12	NUM
american_scientific_journal-7074	58	81	(	(	PUNCT
american_scientific_journal-7074	58	82	ꭕ1у1	ꭕ1у1	PUNCT
american_scientific_journal-7074	58	83	+	+	CCONJ
american_scientific_journal-7074	58	84	ꭕ3у3	ꭕ3у3	SYM
american_scientific_journal-7074	58	85	+	+	NUM
american_scientific_journal-7074	58	86	ꭕ5у5	ꭕ5у5	NOUN
american_scientific_journal-7074	58	87	)	)	PUNCT
american_scientific_journal-7074	58	88	уу	уу	NOUN
american_scientific_journal-7074	58	89	=	=	SYM
american_scientific_journal-7074	58	90	1/	1/	NUM
american_scientific_journal-7074	58	91	12	12	NUM
american_scientific_journal-7074	59	1	(	(	PUNCT
american_scientific_journal-7074	59	2	у1	у1	PROPN
american_scientific_journal-7074	59	3	2	2	NUM
american_scientific_journal-7074	59	4	+	+	NUM
american_scientific_journal-7074	59	5	у3	у3	NOUN
american_scientific_journal-7074	59	6	2	2	NUM
american_scientific_journal-7074	59	7	+	+	CCONJ
american_scientific_journal-7074	59	8	у5	у5	ADJ
american_scientific_journal-7074	59	9	2	2	NUM
american_scientific_journal-7074	59	10	)	)	PUNCT
american_scientific_journal-7074	59	11	we	we	PRON
american_scientific_journal-7074	59	12	are	be	AUX
american_scientific_journal-7074	59	13	now	now	ADV
american_scientific_journal-7074	59	14	able	able	ADJ
american_scientific_journal-7074	59	15	to	to	PART
american_scientific_journal-7074	59	16	evaluate	evaluate	VERB
american_scientific_journal-7074	59	17	the	the	DET
american_scientific_journal-7074	59	18	stiffness	stiffness	ADJ
american_scientific_journal-7074	59	19	matrix	matrix	NOUN
american_scientific_journal-7074	59	20	for	for	ADP
american_scientific_journal-7074	59	21	any	any	DET
american_scientific_journal-7074	59	22	element	element	NOUN
american_scientific_journal-7074	59	23	using	use	VERB
american_scientific_journal-7074	59	24	the	the	DET
american_scientific_journal-7074	59	25	elastic	elastic	ADJ
american_scientific_journal-7074	59	26	constants	constant	NOUN
american_scientific_journal-7074	59	27	of	of	ADP
american_scientific_journal-7074	59	28	the	the	DET
american_scientific_journal-7074	59	29	material	material	NOUN
american_scientific_journal-7074	59	30	,	,	PUNCT
american_scientific_journal-7074	59	31	the	the	DET
american_scientific_journal-7074	59	32	element	element	ADJ
american_scientific_journal-7074	59	33	stiffness	stiffness	NOUN
american_scientific_journal-7074	59	34	and	and	CCONJ
american_scientific_journal-7074	59	35	the	the	DET
american_scientific_journal-7074	59	36	coordinates	coordinate	NOUN
american_scientific_journal-7074	59	37	of	of	ADP
american_scientific_journal-7074	59	38	the	the	DET
american_scientific_journal-7074	59	39	nodes	node	NOUN
american_scientific_journal-7074	59	40	based	base	VERB
american_scientific_journal-7074	59	41	on	on	ADP
american_scientific_journal-7074	59	42	axes	axis	NOUN
american_scientific_journal-7074	59	43	having	have	VERB
american_scientific_journal-7074	59	44	origin	origin	NOUN
american_scientific_journal-7074	59	45	at	at	ADP
american_scientific_journal-7074	59	46	the	the	DET
american_scientific_journal-7074	59	47	centroid	centroid	NOUN
american_scientific_journal-7074	59	48	of	of	ADP
american_scientific_journal-7074	59	49	the	the	DET
american_scientific_journal-7074	59	50	element	element	NOUN
american_scientific_journal-7074	59	51	.	.	PUNCT
american_scientific_journal-7074	60	1	with	with	ADP
american_scientific_journal-7074	60	2	a	a	DET
american_scientific_journal-7074	60	3	-1	-1	ADV
american_scientific_journal-7074	60	4	evaluated	evaluated	ADJ
american_scientific_journal-7074	60	5	,	,	PUNCT
american_scientific_journal-7074	60	6	stiffness	stiffness	ADJ
american_scientific_journal-7074	60	7	matrix	matrix	NOUN
american_scientific_journal-7074	60	8	is	be	AUX
american_scientific_journal-7074	60	9	done	do	VERB
american_scientific_journal-7074	60	10	using	use	VERB
american_scientific_journal-7074	60	11	equations	equation	NOUN
american_scientific_journal-7074	60	12	5	5	NUM
american_scientific_journal-7074	60	13	,	,	PUNCT
american_scientific_journal-7074	60	14	10	10	NUM
american_scientific_journal-7074	60	15	and11	and11	NOUN
american_scientific_journal-7074	60	16	.	.	PUNCT
american_scientific_journal-7074	61	1	4	4	X
american_scientific_journal-7074	61	2	.	.	X
american_scientific_journal-7074	61	3	stress	stress	ADJ
american_scientific_journal-7074	61	4	calculation	calculation	NOUN
american_scientific_journal-7074	61	5	in	in	ADP
american_scientific_journal-7074	61	6	lst	lst	NOUN
american_scientific_journal-7074	61	7	the	the	DET
american_scientific_journal-7074	61	8	stiffness	stiffness	NOUN
american_scientific_journal-7074	61	9	of	of	ADP
american_scientific_journal-7074	61	10	each	each	DET
american_scientific_journal-7074	61	11	element	element	NOUN
american_scientific_journal-7074	61	12	in	in	ADP
american_scientific_journal-7074	61	13	turn	turn	NOUN
american_scientific_journal-7074	61	14	is	be	AUX
american_scientific_journal-7074	61	15	accumulated	accumulate	VERB
american_scientific_journal-7074	61	16	to	to	PART
american_scientific_journal-7074	61	17	give	give	VERB
american_scientific_journal-7074	61	18	the	the	DET
american_scientific_journal-7074	61	19	stiffness	stiffness	ADJ
american_scientific_journal-7074	61	20	matrix	matrix	NOUN
american_scientific_journal-7074	61	21	for	for	ADP
american_scientific_journal-7074	61	22	the	the	DET
american_scientific_journal-7074	61	23	assembly	assembly	NOUN
american_scientific_journal-7074	61	24	of	of	ADP
american_scientific_journal-7074	61	25	elements	element	NOUN
american_scientific_journal-7074	61	26	.	.	PUNCT
american_scientific_journal-7074	62	1	loads	load	NOUN
american_scientific_journal-7074	62	2	and	and	CCONJ
american_scientific_journal-7074	62	3	constraints	constraint	NOUN
american_scientific_journal-7074	62	4	are	be	AUX
american_scientific_journal-7074	62	5	applied	apply	VERB
american_scientific_journal-7074	62	6	and	and	CCONJ
american_scientific_journal-7074	62	7	solution	solution	NOUN
american_scientific_journal-7074	62	8	is	be	AUX
american_scientific_journal-7074	62	9	run	run	VERB
american_scientific_journal-7074	62	10	to	to	PART
american_scientific_journal-7074	62	11	give	give	VERB
american_scientific_journal-7074	62	12	all	all	DET
american_scientific_journal-7074	62	13	displacements	displacement	NOUN
american_scientific_journal-7074	62	14	u	u	NOUN
american_scientific_journal-7074	62	15	,	,	PUNCT
american_scientific_journal-7074	62	16	taking	take	VERB
american_scientific_journal-7074	62	17	each	each	DET
american_scientific_journal-7074	62	18	element	element	NOUN
american_scientific_journal-7074	62	19	in	in	ADP
american_scientific_journal-7074	62	20	turn	turn	NOUN
american_scientific_journal-7074	62	21	the	the	DET
american_scientific_journal-7074	62	22	values	value	NOUN
american_scientific_journal-7074	62	23	in	in	ADP
american_scientific_journal-7074	62	24	δ	δ	PROPN
american_scientific_journal-7074	62	25	are	be	AUX
american_scientific_journal-7074	62	26	extracted	extract	VERB
american_scientific_journal-7074	62	27	from	from	ADP
american_scientific_journal-7074	62	28	u	u	NOUN
american_scientific_journal-7074	62	29	and	and	CCONJ
american_scientific_journal-7074	62	30	used	use	VERB
american_scientific_journal-7074	62	31	to	to	PART
american_scientific_journal-7074	62	32	calculate	calculate	VERB
american_scientific_journal-7074	62	33	stress	stress	NOUN
american_scientific_journal-7074	62	34	by	by	ADP
american_scientific_journal-7074	62	35	σ	σ	NOUN
american_scientific_journal-7074	62	36	=	=	PROPN
american_scientific_journal-7074	62	37	db	db	PROPN
american_scientific_journal-7074	62	38	a	a	DET
american_scientific_journal-7074	62	39	-1	-1	PUNCT
american_scientific_journal-7074	62	40	δ	δ	PROPN
american_scientific_journal-7074	62	41	12	12	NUM
american_scientific_journal-7074	62	42	it	it	PRON
american_scientific_journal-7074	62	43	is	be	AUX
american_scientific_journal-7074	62	44	evident	evident	ADJ
american_scientific_journal-7074	62	45	that	that	SCONJ
american_scientific_journal-7074	62	46	stress	stress	NOUN
american_scientific_journal-7074	62	47	is	be	AUX
american_scientific_journal-7074	62	48	linear	linear	ADJ
american_scientific_journal-7074	62	49	within	within	ADP
american_scientific_journal-7074	62	50	the	the	DET
american_scientific_journal-7074	62	51	element	element	NOUN
american_scientific_journal-7074	62	52	or	or	CCONJ
american_scientific_journal-7074	62	53	function	function	NOUN
american_scientific_journal-7074	62	54	of	of	ADP
american_scientific_journal-7074	62	55	x	x	PUNCT
american_scientific_journal-7074	62	56	and	and	CCONJ
american_scientific_journal-7074	62	57	y	y	PROPN
american_scientific_journal-7074	62	58	coordinated	coordinate	VERB
american_scientific_journal-7074	62	59	.	.	PUNCT
american_scientific_journal-7074	63	1	compared	compare	VERB
american_scientific_journal-7074	63	2	with	with	ADP
american_scientific_journal-7074	63	3	constant	constant	ADJ
american_scientific_journal-7074	63	4	strain	strain	NOUN
american_scientific_journal-7074	63	5	triangle	triangle	NOUN
american_scientific_journal-7074	63	6	cst	cst	PROPN
american_scientific_journal-7074	63	7	and	and	CCONJ
american_scientific_journal-7074	63	8	for	for	ADP
american_scientific_journal-7074	63	9	triangles	triangle	NOUN
american_scientific_journal-7074	63	10	meshed	mesh	VERB
american_scientific_journal-7074	63	11	with	with	ADP
american_scientific_journal-7074	63	12	same	same	ADJ
american_scientific_journal-7074	63	13	size	size	NOUN
american_scientific_journal-7074	63	14	,	,	PUNCT
american_scientific_journal-7074	63	15	when	when	SCONJ
american_scientific_journal-7074	63	16	compared	compare	VERB
american_scientific_journal-7074	63	17	with	with	ADP
american_scientific_journal-7074	63	18	known	known	ADJ
american_scientific_journal-7074	63	19	solution	solution	NOUN
american_scientific_journal-7074	63	20	the	the	DET
american_scientific_journal-7074	63	21	lst	lst	NOUN
american_scientific_journal-7074	63	22	shows	show	VERB
american_scientific_journal-7074	63	23	more	more	ADV
american_scientific_journal-7074	63	24	accurate	accurate	ADJ
american_scientific_journal-7074	63	25	values	value	NOUN
american_scientific_journal-7074	63	26	given	give	VERB
american_scientific_journal-7074	63	27	that	that	SCONJ
american_scientific_journal-7074	63	28	the	the	DET
american_scientific_journal-7074	63	29	analyst	analyst	NOUN
american_scientific_journal-7074	63	30	is	be	AUX
american_scientific_journal-7074	63	31	guarding	guard	VERB
american_scientific_journal-7074	63	32	against	against	ADP
american_scientific_journal-7074	63	33	errors	error	NOUN
american_scientific_journal-7074	63	34	[	[	X
american_scientific_journal-7074	63	35	3	3	NUM
american_scientific_journal-7074	63	36	]	]	PUNCT
american_scientific_journal-7074	63	37	and	and	CCONJ
american_scientific_journal-7074	63	38	[	[	X
american_scientific_journal-7074	63	39	4	4	NUM
american_scientific_journal-7074	63	40	]	]	PUNCT
american_scientific_journal-7074	63	41	.	.	PUNCT
american_scientific_journal-7074	64	1	5	5	X
american_scientific_journal-7074	64	2	.	.	X
american_scientific_journal-7074	64	3	consistent	consistent	ADJ
american_scientific_journal-7074	64	4	load	load	NOUN
american_scientific_journal-7074	64	5	vector	vector	NOUN
american_scientific_journal-7074	64	6	when	when	SCONJ
american_scientific_journal-7074	64	7	concentrated	concentrated	ADJ
american_scientific_journal-7074	64	8	loads	load	NOUN
american_scientific_journal-7074	64	9	occur	occur	VERB
american_scientific_journal-7074	64	10	,	,	PUNCT
american_scientific_journal-7074	64	11	they	they	PRON
american_scientific_journal-7074	64	12	are	be	AUX
american_scientific_journal-7074	64	13	handled	handle	VERB
american_scientific_journal-7074	64	14	simply	simply	ADV
american_scientific_journal-7074	64	15	by	by	ADP
american_scientific_journal-7074	64	16	placing	place	VERB
american_scientific_journal-7074	64	17	a	a	DET
american_scientific_journal-7074	64	18	node	node	NOUN
american_scientific_journal-7074	64	19	at	at	ADP
american_scientific_journal-7074	64	20	the	the	DET
american_scientific_journal-7074	64	21	point	point	NOUN
american_scientific_journal-7074	64	22	of	of	ADP
american_scientific_journal-7074	64	23	load	load	NOUN
american_scientific_journal-7074	64	24	application	application	NOUN
american_scientific_journal-7074	64	25	and	and	CCONJ
american_scientific_journal-7074	64	26	taking	take	VERB
american_scientific_journal-7074	64	27	the	the	DET
american_scientific_journal-7074	64	28	load	load	NOUN
american_scientific_journal-7074	64	29	components	component	NOUN
american_scientific_journal-7074	64	30	as	as	ADP
american_scientific_journal-7074	64	31	known	know	VERB
american_scientific_journal-7074	64	32	force	force	NOUN
american_scientific_journal-7074	64	33	components	component	NOUN
american_scientific_journal-7074	64	34	.	.	PUNCT
american_scientific_journal-7074	65	1	however	however	ADV
american_scientific_journal-7074	65	2	,	,	PUNCT
american_scientific_journal-7074	65	3	a	a	DET
american_scientific_journal-7074	65	4	distributed	distribute	VERB
american_scientific_journal-7074	65	5	traction	traction	NOUN
american_scientific_journal-7074	65	6	acting	act	VERB
american_scientific_journal-7074	65	7	on	on	ADP
american_scientific_journal-7074	65	8	an	an	DET
american_scientific_journal-7074	65	9	element	element	NOUN
american_scientific_journal-7074	65	10	boundary	boundary	NOUN
american_scientific_journal-7074	65	11	is	be	AUX
american_scientific_journal-7074	65	12	more	more	ADV
american_scientific_journal-7074	65	13	difficult	difficult	ADJ
american_scientific_journal-7074	65	14	to	to	PART
american_scientific_journal-7074	65	15	deal	deal	VERB
american_scientific_journal-7074	65	16	with	with	ADP
american_scientific_journal-7074	65	17	.	.	PUNCT
american_scientific_journal-7074	66	1	in	in	ADP
american_scientific_journal-7074	66	2	the	the	DET
american_scientific_journal-7074	66	3	lst	lst	NOUN
american_scientific_journal-7074	66	4	(	(	PUNCT
american_scientific_journal-7074	66	5	linear	linear	ADJ
american_scientific_journal-7074	66	6	strain	strain	NOUN
american_scientific_journal-7074	66	7	triangle	triangle	NOUN
american_scientific_journal-7074	66	8	)	)	PUNCT
american_scientific_journal-7074	66	9	,	,	PUNCT
american_scientific_journal-7074	66	10	a	a	DET
american_scientific_journal-7074	66	11	traction	traction	NOUN
american_scientific_journal-7074	66	12	on	on	ADP
american_scientific_journal-7074	66	13	an	an	DET
american_scientific_journal-7074	66	14	element	element	NOUN
american_scientific_journal-7074	66	15	edge	edge	NOUN
american_scientific_journal-7074	66	16	could	could	AUX
american_scientific_journal-7074	66	17	be	be	AUX
american_scientific_journal-7074	66	18	treated	treat	VERB
american_scientific_journal-7074	66	19	as	as	ADP
american_scientific_journal-7074	66	20	concentrated	concentrate	VERB
american_scientific_journal-7074	66	21	loads	load	NOUN
american_scientific_journal-7074	66	22	at	at	ADP
american_scientific_journal-7074	66	23	the	the	DET
american_scientific_journal-7074	66	24	end	end	NOUN
american_scientific_journal-7074	66	25	nodes	node	NOUN
american_scientific_journal-7074	66	26	by	by	ADP
american_scientific_journal-7074	66	27	making	make	VERB
american_scientific_journal-7074	66	28	the	the	DET
american_scientific_journal-7074	66	29	tow	tow	NOUN
american_scientific_journal-7074	66	30	systems	system	NOUN
american_scientific_journal-7074	66	31	statically	statically	ADV
american_scientific_journal-7074	66	32	equivalent	equivalent	ADJ
american_scientific_journal-7074	66	33	.	.	PUNCT
american_scientific_journal-7074	67	1	with	with	ADP
american_scientific_journal-7074	67	2	the	the	DET
american_scientific_journal-7074	67	3	lst	lst	NOUN
american_scientific_journal-7074	67	4	,	,	PUNCT
american_scientific_journal-7074	67	5	there	there	PRON
american_scientific_journal-7074	67	6	are	be	VERB
american_scientific_journal-7074	67	7	three	three	NUM
american_scientific_journal-7074	67	8	nodes	node	NOUN
american_scientific_journal-7074	67	9	on	on	ADP
american_scientific_journal-7074	67	10	any	any	DET
american_scientific_journal-7074	67	11	edge	edge	NOUN
american_scientific_journal-7074	67	12	and	and	CCONJ
american_scientific_journal-7074	67	13	the	the	DET
american_scientific_journal-7074	67	14	principle	principle	NOUN
american_scientific_journal-7074	67	15	of	of	ADP
american_scientific_journal-7074	67	16	static	static	ADJ
american_scientific_journal-7074	67	17	equivalence	equivalence	NOUN
american_scientific_journal-7074	67	18	is	be	AUX
american_scientific_journal-7074	67	19	not	not	PART
american_scientific_journal-7074	67	20	sufficient	sufficient	ADJ
american_scientific_journal-7074	67	21	to	to	PART
american_scientific_journal-7074	67	22	determine	determine	VERB
american_scientific_journal-7074	67	23	distribution	distribution	NOUN
american_scientific_journal-7074	67	24	uniquely	uniquely	ADV
american_scientific_journal-7074	67	25	.	.	PUNCT
american_scientific_journal-7074	68	1	the	the	DET
american_scientific_journal-7074	68	2	solution	solution	NOUN
american_scientific_journal-7074	68	3	to	to	ADP
american_scientific_journal-7074	68	4	this	this	DET
american_scientific_journal-7074	68	5	problem	problem	NOUN
american_scientific_journal-7074	68	6	will	will	AUX
american_scientific_journal-7074	68	7	be	be	AUX
american_scientific_journal-7074	68	8	found	find	VERB
american_scientific_journal-7074	68	9	by	by	ADP
american_scientific_journal-7074	68	10	resorting	resort	VERB
american_scientific_journal-7074	68	11	to	to	ADP
american_scientific_journal-7074	68	12	energy	energy	NOUN
american_scientific_journal-7074	68	13	principles	principle	NOUN
american_scientific_journal-7074	68	14	.	.	PUNCT
american_scientific_journal-7074	69	1	consider	consider	VERB
american_scientific_journal-7074	69	2	an	an	DET
american_scientific_journal-7074	69	3	element	element	NOUN
american_scientific_journal-7074	69	4	boundary	boundary	NOUN
american_scientific_journal-7074	69	5	such	such	ADJ
american_scientific_journal-7074	69	6	as	as	ADP
american_scientific_journal-7074	69	7	1	1	NUM
american_scientific_journal-7074	69	8	-	-	SYM
american_scientific_journal-7074	69	9	2	2	NUM
american_scientific_journal-7074	69	10	-	-	SYM
american_scientific_journal-7074	69	11	3	3	NUM
american_scientific_journal-7074	69	12	in	in	ADP
american_scientific_journal-7074	69	13	the	the	DET
american_scientific_journal-7074	69	14	shown	show	VERB
american_scientific_journal-7074	69	15	figure	figure	NOUN
american_scientific_journal-7074	69	16	,	,	PUNCT
american_scientific_journal-7074	69	17	if	if	SCONJ
american_scientific_journal-7074	69	18	a	a	DET
american_scientific_journal-7074	69	19	horizontal	horizontal	ADJ
american_scientific_journal-7074	69	20	displacement	displacement	NOUN
american_scientific_journal-7074	69	21	occurs	occur	VERB
american_scientific_journal-7074	69	22	,	,	PUNCT
american_scientific_journal-7074	69	23	the	the	DET
american_scientific_journal-7074	69	24	edge	edge	NOUN
american_scientific_journal-7074	69	25	displacement	displacement	NOUN
american_scientific_journal-7074	69	26	will	will	AUX
american_scientific_journal-7074	69	27	be	be	AUX
american_scientific_journal-7074	69	28	parabolic	parabolic	ADJ
american_scientific_journal-7074	69	29	in	in	ADP
american_scientific_journal-7074	69	30	form	form	NOUN
american_scientific_journal-7074	69	31	and	and	CCONJ
american_scientific_journal-7074	69	32	the	the	DET
american_scientific_journal-7074	69	33	new	new	ADJ
american_scientific_journal-7074	69	34	edge	edge	NOUN
american_scientific_journal-7074	69	35	location	location	NOUN
american_scientific_journal-7074	69	36	may	may	AUX
american_scientific_journal-7074	69	37	be	be	AUX
american_scientific_journal-7074	69	38	taken	take	VERB
american_scientific_journal-7074	69	39	as	as	ADP
american_scientific_journal-7074	69	40	1’-2’-3	1’-2’-3	NOUN
american_scientific_journal-7074	69	41	’	'	PUNCT
american_scientific_journal-7074	69	42	as	as	SCONJ
american_scientific_journal-7074	69	43	shown	show	VERB
american_scientific_journal-7074	69	44	by	by	ADP
american_scientific_journal-7074	69	45	the	the	DET
american_scientific_journal-7074	69	46	broken	broken	ADJ
american_scientific_journal-7074	69	47	lines	line	NOUN
american_scientific_journal-7074	69	48	.	.	PUNCT
american_scientific_journal-7074	70	1	american	american	ADJ
american_scientific_journal-7074	70	2	academic	academic	ADJ
american_scientific_journal-7074	70	3	scientific	scientific	ADJ
american_scientific_journal-7074	70	4	research	research	NOUN
american_scientific_journal-7074	70	5	journal	journal	NOUN
american_scientific_journal-7074	70	6	for	for	ADP
american_scientific_journal-7074	70	7	engineering	engineering	NOUN
american_scientific_journal-7074	70	8	,	,	PUNCT
american_scientific_journal-7074	70	9	technology	technology	NOUN
american_scientific_journal-7074	70	10	,	,	PUNCT
american_scientific_journal-7074	70	11	and	and	CCONJ
american_scientific_journal-7074	70	12	sciences	science	NOUN
american_scientific_journal-7074	70	13	(	(	PUNCT
american_scientific_journal-7074	70	14	asrjets	asrjet	NOUN
american_scientific_journal-7074	70	15	)	)	PUNCT
american_scientific_journal-7074	70	16	(	(	PUNCT
american_scientific_journal-7074	70	17	2021	2021	NUM
american_scientific_journal-7074	70	18	)	)	PUNCT
american_scientific_journal-7074	70	19	volume	volume	NOUN
american_scientific_journal-7074	70	20	83	83	NUM
american_scientific_journal-7074	70	21	,	,	PUNCT
american_scientific_journal-7074	70	22	no	no	DET
american_scientific_journal-7074	70	23	1	1	NUM
american_scientific_journal-7074	70	24	,	,	PUNCT
american_scientific_journal-7074	70	25	pp	pp	ADV
american_scientific_journal-7074	70	26	1	1	NUM
american_scientific_journal-7074	70	27	-	-	SYM
american_scientific_journal-7074	70	28	11	11	NUM
american_scientific_journal-7074	70	29	8	8	NUM
american_scientific_journal-7074	70	30	the	the	DET
american_scientific_journal-7074	70	31	edge	edge	NOUN
american_scientific_journal-7074	70	32	displacement	displacement	NOUN
american_scientific_journal-7074	70	33	is	be	AUX
american_scientific_journal-7074	70	34	given	give	VERB
american_scientific_journal-7074	70	35	by	by	ADP
american_scientific_journal-7074	70	36	a	a	DET
american_scientific_journal-7074	70	37	u=	u=	ADJ
american_scientific_journal-7074	70	38	ay	ay	NOUN
american_scientific_journal-7074	70	39	2	2	NUM
american_scientific_journal-7074	70	40	+	+	ADJ
american_scientific_journal-7074	70	41	by	by	ADP
american_scientific_journal-7074	70	42	+	+	NOUN
american_scientific_journal-7074	70	43	c	c	NOUN
american_scientific_journal-7074	70	44	=	=	PUNCT
american_scientific_journal-7074	71	1	[	[	X
american_scientific_journal-7074	71	2	y	y	PROPN
american_scientific_journal-7074	71	3	2	2	NUM
american_scientific_journal-7074	71	4	y	y	PROPN
american_scientific_journal-7074	71	5	1	1	NUM
american_scientific_journal-7074	71	6	]	]	SYM
american_scientific_journal-7074	71	7	b	b	X
american_scientific_journal-7074	71	8	c	c	NOUN
american_scientific_journal-7074	71	9	when	when	SCONJ
american_scientific_journal-7074	71	10	this	this	DET
american_scientific_journal-7074	71	11	displacement	displacement	NOUN
american_scientific_journal-7074	71	12	takes	take	VERB
american_scientific_journal-7074	71	13	place	place	NOUN
american_scientific_journal-7074	71	14	,	,	PUNCT
american_scientific_journal-7074	71	15	the	the	DET
american_scientific_journal-7074	71	16	edge	edge	NOUN
american_scientific_journal-7074	71	17	load	load	NOUN
american_scientific_journal-7074	71	18	,	,	PUNCT
american_scientific_journal-7074	71	19	p	p	X
american_scientific_journal-7074	71	20	,	,	PUNCT
american_scientific_journal-7074	71	21	does	do	AUX
american_scientific_journal-7074	71	22	work	work	VERB
american_scientific_journal-7074	71	23	on	on	ADP
american_scientific_journal-7074	71	24	the	the	DET
american_scientific_journal-7074	71	25	system	system	NOUN
american_scientific_journal-7074	71	26	.	.	PUNCT
american_scientific_journal-7074	72	1	over	over	ADP
american_scientific_journal-7074	72	2	an	an	DET
american_scientific_journal-7074	72	3	incremental	incremental	ADJ
american_scientific_journal-7074	72	4	length	length	NOUN
american_scientific_journal-7074	72	5	of	of	ADP
american_scientific_journal-7074	72	6	edge	edge	NOUN
american_scientific_journal-7074	72	7	dy	dy	NOUN
american_scientific_journal-7074	72	8	long	long	ADV
american_scientific_journal-7074	72	9	the	the	DET
american_scientific_journal-7074	72	10	work	work	NOUN
american_scientific_journal-7074	72	11	done	do	VERB
american_scientific_journal-7074	72	12	is	be	AUX
american_scientific_journal-7074	72	13	a	a	DET
american_scientific_journal-7074	72	14	y	y	PROPN
american_scientific_journal-7074	72	15	3	3	NUM
american_scientific_journal-7074	72	16	3	3	NUM
american_scientific_journal-7074	72	17	’	’	SYM
american_scientific_journal-7074	72	18	2	2	NUM
american_scientific_journal-7074	72	19	’	’	SYM
american_scientific_journal-7074	72	20	2	2	NUM
american_scientific_journal-7074	72	21	y	y	PROPN
american_scientific_journal-7074	72	22	l/	l/	NOUN
american_scientific_journal-7074	72	23	2	2	NUM
american_scientific_journal-7074	72	24	l/	l/	X
american_scientific_journal-7074	72	25	2	2	NUM
american_scientific_journal-7074	72	26	1	1	NUM
american_scientific_journal-7074	72	27	1	1	NUM
american_scientific_journal-7074	72	28	’	'	PUNCT
american_scientific_journal-7074	72	29	x	x	NOUN
american_scientific_journal-7074	72	30	p0	p0	NOUN
american_scientific_journal-7074	72	31	p	p	NOUN
american_scientific_journal-7074	72	32	=	=	NOUN
american_scientific_journal-7074	72	33	p0	p0	NOUN
american_scientific_journal-7074	72	34	+	+	CCONJ
american_scientific_journal-7074	72	35	sy	sy	CCONJ
american_scientific_journal-7074	72	36	u	u	NOUN
american_scientific_journal-7074	72	37	=	=	PROPN
american_scientific_journal-7074	72	38	ay	ay	PROPN
american_scientific_journal-7074	72	39	2	2	NUM
american_scientific_journal-7074	72	40	+	+	CCONJ
american_scientific_journal-7074	72	41	by	by	ADP
american_scientific_journal-7074	72	42	+	+	NOUN
american_scientific_journal-7074	72	43	c	c	PROPN
american_scientific_journal-7074	72	44	american	american	ADJ
american_scientific_journal-7074	72	45	academic	academic	PROPN
american_scientific_journal-7074	72	46	scientific	scientific	ADJ
american_scientific_journal-7074	72	47	research	research	NOUN
american_scientific_journal-7074	72	48	journal	journal	NOUN
american_scientific_journal-7074	72	49	for	for	ADP
american_scientific_journal-7074	72	50	engineering	engineering	NOUN
american_scientific_journal-7074	72	51	,	,	PUNCT
american_scientific_journal-7074	72	52	technology	technology	NOUN
american_scientific_journal-7074	72	53	,	,	PUNCT
american_scientific_journal-7074	72	54	and	and	CCONJ
american_scientific_journal-7074	72	55	sciences	science	NOUN
american_scientific_journal-7074	72	56	(	(	PUNCT
american_scientific_journal-7074	72	57	asrjets	asrjet	NOUN
american_scientific_journal-7074	72	58	)	)	PUNCT
american_scientific_journal-7074	72	59	(	(	PUNCT
american_scientific_journal-7074	72	60	2021	2021	NUM
american_scientific_journal-7074	72	61	)	)	PUNCT
american_scientific_journal-7074	72	62	volume	volume	NOUN
american_scientific_journal-7074	72	63	83	83	NUM
american_scientific_journal-7074	72	64	,	,	PUNCT
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american_scientific_journal-7074	72	66	1	1	NUM
american_scientific_journal-7074	72	67	,	,	PUNCT
american_scientific_journal-7074	72	68	pp	pp	ADV
american_scientific_journal-7074	72	69	1	1	NUM
american_scientific_journal-7074	72	70	-	-	SYM
american_scientific_journal-7074	72	71	11	11	NUM
american_scientific_journal-7074	72	72	9	9	NUM
american_scientific_journal-7074	72	73	dwp	dwp	NOUN
american_scientific_journal-7074	72	74	=	=	PUNCT
american_scientific_journal-7074	73	1	p	p	NOUN
american_scientific_journal-7074	73	2	u	u	NOUN
american_scientific_journal-7074	73	3	t	t	NOUN
american_scientific_journal-7074	73	4	dy	dy	NOUN
american_scientific_journal-7074	73	5	=	=	SYM
american_scientific_journal-7074	73	6	(	(	PUNCT
american_scientific_journal-7074	73	7	p0	p0	NOUN
american_scientific_journal-7074	73	8	+	+	CCONJ
american_scientific_journal-7074	73	9	sy	sy	NOUN
american_scientific_journal-7074	73	10	)	)	PUNCT
american_scientific_journal-7074	74	1	[	[	X
american_scientific_journal-7074	74	2	y	y	NOUN
american_scientific_journal-7074	74	3	2	2	NUM
american_scientific_journal-7074	74	4	y	y	PROPN
american_scientific_journal-7074	74	5	1	1	NUM
american_scientific_journal-7074	74	6	]	]	SYM
american_scientific_journal-7074	74	7	b	b	X
american_scientific_journal-7074	74	8	t	t	NOUN
american_scientific_journal-7074	74	9	dy	dy	X
american_scientific_journal-7074	74	10	c	c	PROPN
american_scientific_journal-7074	74	11	a	a	PRON
american_scientific_journal-7074	74	12	=	=	X
american_scientific_journal-7074	75	1	[	[	X
american_scientific_journal-7074	75	2	p0y	p0y	ADJ
american_scientific_journal-7074	75	3	2	2	NUM
american_scientific_journal-7074	75	4	+	+	CCONJ
american_scientific_journal-7074	75	5	sy	sy	PROPN
american_scientific_journal-7074	75	6	3	3	NUM
american_scientific_journal-7074	75	7	p0y	p0y	PROPN
american_scientific_journal-7074	75	8	+	+	PROPN
american_scientific_journal-7074	75	9	sy	sy	PROPN
american_scientific_journal-7074	75	10	2	2	NUM
american_scientific_journal-7074	75	11	p0+sy	p0+sy	NOUN
american_scientific_journal-7074	75	12	]	]	X
american_scientific_journal-7074	75	13	b	b	NOUN
american_scientific_journal-7074	75	14	t	t	NOUN
american_scientific_journal-7074	75	15	dy	dy	NOUN
american_scientific_journal-7074	75	16	c	c	PROPN
american_scientific_journal-7074	75	17	and	and	CCONJ
american_scientific_journal-7074	75	18	the	the	DET
american_scientific_journal-7074	75	19	work	work	NOUN
american_scientific_journal-7074	75	20	done	do	VERB
american_scientific_journal-7074	75	21	on	on	ADP
american_scientific_journal-7074	75	22	the	the	DET
american_scientific_journal-7074	75	23	whole	whole	ADJ
american_scientific_journal-7074	75	24	edge	edge	NOUN
american_scientific_journal-7074	75	25	is	be	AUX
american_scientific_journal-7074	75	26	a	a	DET
american_scientific_journal-7074	75	27	wp	wp	NOUN
american_scientific_journal-7074	75	28	=	=	SYM
american_scientific_journal-7074	75	29	∫	∫	PROPN
american_scientific_journal-7074	75	30	dwp	dwp	PROPN
american_scientific_journal-7074	75	31	=	=	SYM
american_scientific_journal-7074	75	32	t	t	PROPN
american_scientific_journal-7074	76	1	[	[	X
american_scientific_journal-7074	76	2	p0l	p0l	PROPN
american_scientific_journal-7074	76	3	3	3	NUM
american_scientific_journal-7074	76	4	/12	/12	PUNCT
american_scientific_journal-7074	76	5	sl	sl	VERB
american_scientific_journal-7074	76	6	3	3	NUM
american_scientific_journal-7074	76	7	/12	/12	PUNCT
american_scientific_journal-7074	76	8	p0l	p0l	PROPN
american_scientific_journal-7074	76	9	]	]	X
american_scientific_journal-7074	76	10	b	b	X
american_scientific_journal-7074	76	11	c	c	NOUN
american_scientific_journal-7074	76	12	consider	consider	VERB
american_scientific_journal-7074	76	13	now	now	ADV
american_scientific_journal-7074	76	14	a	a	DET
american_scientific_journal-7074	76	15	concentrated	concentrated	ADJ
american_scientific_journal-7074	76	16	load	load	NOUN
american_scientific_journal-7074	76	17	system	system	NOUN
american_scientific_journal-7074	76	18	,	,	PUNCT
american_scientific_journal-7074	76	19	p1	p1	NOUN
american_scientific_journal-7074	76	20	,	,	PUNCT
american_scientific_journal-7074	76	21	p2	p2	PROPN
american_scientific_journal-7074	76	22	and	and	CCONJ
american_scientific_journal-7074	76	23	p3	p3	NOUN
american_scientific_journal-7074	76	24	which	which	PRON
american_scientific_journal-7074	76	25	would	would	AUX
american_scientific_journal-7074	76	26	be	be	AUX
american_scientific_journal-7074	76	27	used	use	VERB
american_scientific_journal-7074	76	28	to	to	PART
american_scientific_journal-7074	76	29	replace	replace	VERB
american_scientific_journal-7074	76	30	the	the	DET
american_scientific_journal-7074	76	31	distributed	distribute	VERB
american_scientific_journal-7074	76	32	system	system	NOUN
american_scientific_journal-7074	76	33	.	.	PUNCT
american_scientific_journal-7074	77	1	these	these	DET
american_scientific_journal-7074	77	2	forces	force	NOUN
american_scientific_journal-7074	77	3	move	move	VERB
american_scientific_journal-7074	77	4	through	through	ADP
american_scientific_journal-7074	77	5	distances	distance	NOUN
american_scientific_journal-7074	77	6	u1	u1	PROPN
american_scientific_journal-7074	77	7	,	,	PUNCT
american_scientific_journal-7074	77	8	u2	u2	NOUN
american_scientific_journal-7074	77	9	and	and	CCONJ
american_scientific_journal-7074	77	10	u3	u3	NOUN
american_scientific_journal-7074	77	11	which	which	PRON
american_scientific_journal-7074	77	12	can	can	AUX
american_scientific_journal-7074	77	13	be	be	AUX
american_scientific_journal-7074	77	14	written	write	VERB
american_scientific_journal-7074	77	15	u1	u1	NOUN
american_scientific_journal-7074	77	16	u	u	PROPN
american_scientific_journal-7074	77	17	(	(	PUNCT
american_scientific_journal-7074	77	18	y=-l/2	y=-l/2	PROPN
american_scientific_journal-7074	77	19	)	)	PUNCT
american_scientific_journal-7074	77	20	(	(	PUNCT
american_scientific_journal-7074	77	21	-l/2	-l/2	PROPN
american_scientific_journal-7074	77	22	)	)	PUNCT
american_scientific_journal-7074	77	23	2	2	NUM
american_scientific_journal-7074	77	24	-l/2	-l/2	PROPN
american_scientific_journal-7074	77	25	1	1	NUM
american_scientific_journal-7074	77	26	a	a	DET
american_scientific_journal-7074	77	27	u2	u2	PROPN
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american_scientific_journal-7074	78	3	1	1	NUM
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american_scientific_journal-7074	78	17	1	1	NUM
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american_scientific_journal-7074	80	21	equivalent	equivalent	ADJ
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american_scientific_journal-7074	81	11	t	t	PROPN
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american_scientific_journal-7074	82	15	-	-	PUNCT
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american_scientific_journal-7074	89	14	amount	amount	NOUN
american_scientific_journal-7074	89	15	of	of	ADP
american_scientific_journal-7074	89	16	work	work	NOUN
american_scientific_journal-7074	89	17	during	during	ADP
american_scientific_journal-7074	89	18	a	a	DET
american_scientific_journal-7074	89	19	displacement	displacement	NOUN
american_scientific_journal-7074	89	20	.	.	PUNCT
american_scientific_journal-7074	90	1	the	the	DET
american_scientific_journal-7074	90	2	work	work	NOUN
american_scientific_journal-7074	90	3	equality	equality	NOUN
american_scientific_journal-7074	90	4	was	be	AUX
american_scientific_journal-7074	90	5	based	base	VERB
american_scientific_journal-7074	90	6	on	on	ADP
american_scientific_journal-7074	90	7	an	an	DET
american_scientific_journal-7074	90	8	edge	edge	NOUN
american_scientific_journal-7074	90	9	displacement	displacement	NOUN
american_scientific_journal-7074	90	10	function	function	NOUN
american_scientific_journal-7074	90	11	which	which	PRON
american_scientific_journal-7074	90	12	is	be	AUX
american_scientific_journal-7074	90	13	consistent	consistent	ADJ
american_scientific_journal-7074	90	14	with	with	ADP
american_scientific_journal-7074	90	15	the	the	DET
american_scientific_journal-7074	90	16	assumed	assumed	ADJ
american_scientific_journal-7074	90	17	displacement	displacement	ADJ
american_scientific_journal-7074	90	18	function	function	NOUN
american_scientific_journal-7074	90	19	for	for	ADP
american_scientific_journal-7074	90	20	all	all	DET
american_scientific_journal-7074	90	21	points	point	NOUN
american_scientific_journal-7074	90	22	in	in	ADP
american_scientific_journal-7074	90	23	the	the	DET
american_scientific_journal-7074	90	24	element	element	NOUN
american_scientific_journal-7074	90	25	,	,	PUNCT
american_scientific_journal-7074	90	26	hence	hence	ADV
american_scientific_journal-7074	90	27	,	,	PUNCT
american_scientific_journal-7074	90	28	the	the	DET
american_scientific_journal-7074	90	29	designation	designation	NOUN
american_scientific_journal-7074	90	30	“	"	PUNCT
american_scientific_journal-7074	90	31	consistent	consistent	ADJ
american_scientific_journal-7074	90	32	load	load	NOUN
american_scientific_journal-7074	90	33	vector	vector	NOUN
american_scientific_journal-7074	90	34	”	"	PUNCT
american_scientific_journal-7074	90	35	.	.	PUNCT
american_scientific_journal-7074	91	1	7	7	X
american_scientific_journal-7074	91	2	.	.	X
american_scientific_journal-7074	91	3	concluding	conclude	VERB
american_scientific_journal-7074	91	4	remarks	remark	VERB
american_scientific_journal-7074	91	5	a	a	DET
american_scientific_journal-7074	91	6	mathematical	mathematical	ADJ
american_scientific_journal-7074	91	7	formulation	formulation	NOUN
american_scientific_journal-7074	91	8	of	of	ADP
american_scientific_journal-7074	91	9	stiffness	stiffness	ADJ
american_scientific_journal-7074	91	10	matrix	matrix	NOUN
american_scientific_journal-7074	91	11	,	,	PUNCT
american_scientific_journal-7074	91	12	stress	stress	NOUN
american_scientific_journal-7074	91	13	and	and	CCONJ
american_scientific_journal-7074	91	14	a	a	DET
american_scientific_journal-7074	91	15	consistent	consistent	ADJ
american_scientific_journal-7074	91	16	load	load	NOUN
american_scientific_journal-7074	91	17	vector	vector	NOUN
american_scientific_journal-7074	91	18	is	be	AUX
american_scientific_journal-7074	91	19	proved	prove	VERB
american_scientific_journal-7074	91	20	for	for	ADP
american_scientific_journal-7074	91	21	the	the	DET
american_scientific_journal-7074	91	22	linear	linear	ADJ
american_scientific_journal-7074	91	23	strain	strain	NOUN
american_scientific_journal-7074	91	24	triangle	triangle	NOUN
american_scientific_journal-7074	91	25	element	element	NOUN
american_scientific_journal-7074	91	26	lst	lst	NOUN
american_scientific_journal-7074	91	27	simple	simple	ADJ
american_scientific_journal-7074	91	28	but	but	CCONJ
american_scientific_journal-7074	91	29	efficient	efficient	ADJ
american_scientific_journal-7074	91	30	in	in	ADP
american_scientific_journal-7074	91	31	modelling	model	VERB
american_scientific_journal-7074	91	32	multiple	multiple	ADJ
american_scientific_journal-7074	91	33	materials	material	NOUN
american_scientific_journal-7074	91	34	with	with	ADP
american_scientific_journal-7074	91	35	good	good	ADJ
american_scientific_journal-7074	91	36	results	result	NOUN
american_scientific_journal-7074	91	37	compared	compare	VERB
american_scientific_journal-7074	91	38	to	to	ADP
american_scientific_journal-7074	91	39	the	the	DET
american_scientific_journal-7074	91	40	simpler	simple	ADJ
american_scientific_journal-7074	91	41	cst	cst	PROPN
american_scientific_journal-7074	91	42	element	element	NOUN
american_scientific_journal-7074	91	43	and	and	CCONJ
american_scientific_journal-7074	91	44	more	more	ADV
american_scientific_journal-7074	91	45	difficult	difficult	ADJ
american_scientific_journal-7074	91	46	and	and	CCONJ
american_scientific_journal-7074	91	47	time	time	NOUN
american_scientific_journal-7074	91	48	-	-	PUNCT
american_scientific_journal-7074	91	49	consuming	consume	VERB
american_scientific_journal-7074	91	50	advanced	advanced	ADJ
american_scientific_journal-7074	91	51	elements	element	NOUN
american_scientific_journal-7074	91	52	.	.	PUNCT
american_scientific_journal-7074	92	1	the	the	DET
american_scientific_journal-7074	92	2	formula	formula	NOUN
american_scientific_journal-7074	92	3	extracted	extract	VERB
american_scientific_journal-7074	92	4	for	for	ADP
american_scientific_journal-7074	92	5	american	american	ADJ
american_scientific_journal-7074	92	6	academic	academic	ADJ
american_scientific_journal-7074	92	7	scientific	scientific	ADJ
american_scientific_journal-7074	92	8	research	research	NOUN
american_scientific_journal-7074	92	9	journal	journal	NOUN
american_scientific_journal-7074	92	10	for	for	ADP
american_scientific_journal-7074	92	11	engineering	engineering	NOUN
american_scientific_journal-7074	92	12	,	,	PUNCT
american_scientific_journal-7074	92	13	technology	technology	NOUN
american_scientific_journal-7074	92	14	,	,	PUNCT
american_scientific_journal-7074	92	15	and	and	CCONJ
american_scientific_journal-7074	92	16	sciences	science	NOUN
american_scientific_journal-7074	92	17	(	(	PUNCT
american_scientific_journal-7074	92	18	asrjets	asrjet	NOUN
american_scientific_journal-7074	92	19	)	)	PUNCT
american_scientific_journal-7074	92	20	(	(	PUNCT
american_scientific_journal-7074	92	21	2021	2021	NUM
american_scientific_journal-7074	92	22	)	)	PUNCT
american_scientific_journal-7074	92	23	volume	volume	NOUN
american_scientific_journal-7074	92	24	83	83	NUM
american_scientific_journal-7074	92	25	,	,	PUNCT
american_scientific_journal-7074	92	26	no	no	DET
american_scientific_journal-7074	92	27	1	1	NUM
american_scientific_journal-7074	92	28	,	,	PUNCT
american_scientific_journal-7074	92	29	pp	pp	ADV
american_scientific_journal-7074	92	30	1	1	NUM
american_scientific_journal-7074	92	31	-	-	SYM
american_scientific_journal-7074	92	32	11	11	NUM
american_scientific_journal-7074	92	33	11	11	NUM
american_scientific_journal-7074	92	34	consistent	consistent	ADJ
american_scientific_journal-7074	92	35	load	load	NOUN
american_scientific_journal-7074	92	36	vector	vector	NOUN
american_scientific_journal-7074	92	37	for	for	ADP
american_scientific_journal-7074	92	38	the	the	DET
american_scientific_journal-7074	92	39	lst	lst	NOUN
american_scientific_journal-7074	92	40	is	be	AUX
american_scientific_journal-7074	92	41	readily	readily	ADV
american_scientific_journal-7074	92	42	extended	extend	VERB
american_scientific_journal-7074	92	43	for	for	ADP
american_scientific_journal-7074	92	44	the	the	DET
american_scientific_journal-7074	92	45	conical	conical	ADJ
american_scientific_journal-7074	92	46	axe	axe	ADJ
american_scientific_journal-7074	92	47	-	-	PUNCT
american_scientific_journal-7074	92	48	symmetric	symmetric	ADJ
american_scientific_journal-7074	92	49	pressure	pressure	NOUN
american_scientific_journal-7074	92	50	vessel	vessel	NOUN
american_scientific_journal-7074	92	51	element	element	NOUN
american_scientific_journal-7074	92	52	for	for	ADP
american_scientific_journal-7074	92	53	convenience	convenience	NOUN
american_scientific_journal-7074	92	54	,	,	PUNCT
american_scientific_journal-7074	92	55	[	[	X
american_scientific_journal-7074	92	56	8	8	NUM
american_scientific_journal-7074	92	57	]	]	PUNCT
american_scientific_journal-7074	92	58	through	through	ADP
american_scientific_journal-7074	92	59	[	[	X
american_scientific_journal-7074	92	60	13	13	NUM
american_scientific_journal-7074	92	61	]	]	PUNCT
american_scientific_journal-7074	92	62	.	.	PUNCT
american_scientific_journal-7074	93	1	references	reference	NOUN
american_scientific_journal-7074	93	2	[	[	X
american_scientific_journal-7074	93	3	1	1	NUM
american_scientific_journal-7074	93	4	]	]	X
american_scientific_journal-7074	93	5	desai	desai	PROPN
american_scientific_journal-7074	93	6	,	,	PUNCT
american_scientific_journal-7074	93	7	c.	c.	PROPN
american_scientific_journal-7074	93	8	s.	s.	PROPN
american_scientific_journal-7074	93	9	,	,	PUNCT
american_scientific_journal-7074	93	10	and	and	CCONJ
american_scientific_journal-7074	93	11	j.	j.	PROPN
american_scientific_journal-7074	93	12	f.	f.	PROPN
american_scientific_journal-7074	93	13	adel	adel	PROPN
american_scientific_journal-7074	93	14	,	,	PUNCT
american_scientific_journal-7074	93	15	introduction	introduction	NOUN
american_scientific_journal-7074	93	16	to	to	ADP
american_scientific_journal-7074	93	17	the	the	DET
american_scientific_journal-7074	93	18	finite	finite	ADJ
american_scientific_journal-7074	93	19	element	element	NOUN
american_scientific_journal-7074	93	20	method	method	NOUN
american_scientific_journal-7074	93	21	,	,	PUNCT
american_scientific_journal-7074	93	22	(	(	PUNCT
american_scientific_journal-7074	93	23	new	new	PROPN
american_scientific_journal-7074	93	24	york	york	PROPN
american_scientific_journal-7074	93	25	:	:	PUNCT
american_scientific_journal-7074	93	26	van	van	PROPN
american_scientific_journal-7074	93	27	nostrand	nostrand	PROPN
american_scientific_journal-7074	93	28	reinhold	reinhold	PROPN
american_scientific_journal-7074	93	29	,	,	PUNCT
american_scientific_journal-7074	93	30	1972	1972	NUM
american_scientific_journal-7074	93	31	)	)	PUNCT
american_scientific_journal-7074	94	1	[	[	X
american_scientific_journal-7074	94	2	2	2	NUM
american_scientific_journal-7074	94	3	]	]	PUNCT
american_scientific_journal-7074	94	4	zeinkiewicz	zeinkiewicz	NOUN
american_scientific_journal-7074	94	5	.	.	PUNCT
american_scientific_journal-7074	95	1	o.	o.	PROPN
american_scientific_journal-7074	95	2	c.m	c.m	PROPN
american_scientific_journal-7074	95	3	,	,	PUNCT
american_scientific_journal-7074	95	4	the	the	DET
american_scientific_journal-7074	95	5	finite	finite	ADJ
american_scientific_journal-7074	95	6	element	element	NOUN
american_scientific_journal-7074	95	7	method	method	NOUN
american_scientific_journal-7074	95	8	in	in	ADP
american_scientific_journal-7074	95	9	engineering	engineering	NOUN
american_scientific_journal-7074	95	10	science	science	NOUN
american_scientific_journal-7074	95	11	,	,	PUNCT
american_scientific_journal-7074	95	12	second	second	ADJ
american_scientific_journal-7074	95	13	edition	edition	NOUN
american_scientific_journal-7074	95	14	(	(	PUNCT
american_scientific_journal-7074	95	15	new	new	PROPN
american_scientific_journal-7074	95	16	york	york	PROPN
american_scientific_journal-7074	95	17	:	:	PUNCT
american_scientific_journal-7074	95	18	mcgraw	mcgraw	PROPN
american_scientific_journal-7074	95	19	hill	hill	PROPN
american_scientific_journal-7074	95	20	,	,	PUNCT
american_scientific_journal-7074	95	21	1971	1971	NUM
american_scientific_journal-7074	95	22	)	)	PUNCT
american_scientific_journal-7074	96	1	[	[	X
american_scientific_journal-7074	96	2	3	3	X
american_scientific_journal-7074	96	3	]	]	X
american_scientific_journal-7074	96	4	william	william	PROPN
american_scientific_journal-7074	96	5	h.	h.	PROPN
american_scientific_journal-7074	96	6	bowes	bowes	PROPN
american_scientific_journal-7074	96	7	and	and	CCONJ
american_scientific_journal-7074	96	8	leslie	leslie	PROPN
american_scientific_journal-7074	96	9	t.	t.	PROPN
american_scientific_journal-7074	96	10	russel	russel	PROPN
american_scientific_journal-7074	96	11	,	,	PUNCT
american_scientific_journal-7074	96	12	stress	stress	VERB
american_scientific_journal-7074	96	13	analysis	analysis	NOUN
american_scientific_journal-7074	96	14	by	by	ADP
american_scientific_journal-7074	96	15	the	the	DET
american_scientific_journal-7074	96	16	finite	finite	PROPN
american_scientific_journal-7074	96	17	element	element	NOUN
american_scientific_journal-7074	96	18	method	method	NOUN
american_scientific_journal-7074	96	19	for	for	ADP
american_scientific_journal-7074	96	20	practicing	practice	VERB
american_scientific_journal-7074	96	21	engineers	engineer	NOUN
american_scientific_journal-7074	96	22	,	,	PUNCT
american_scientific_journal-7074	96	23	lixengton	lixengton	NOUN
american_scientific_journal-7074	96	24	books	book	NOUN
american_scientific_journal-7074	96	25	.	.	PUNCT
american_scientific_journal-7074	97	1	d.c	d.c	PROPN
american_scientific_journal-7074	97	2	.	.	PROPN
american_scientific_journal-7074	97	3	heath	heath	PROPN
american_scientific_journal-7074	97	4	and	and	CCONJ
american_scientific_journal-7074	97	5	company	company	PROPN
american_scientific_journal-7074	97	6	,	,	PUNCT
american_scientific_journal-7074	97	7	toronto	toronto	PROPN
american_scientific_journal-7074	97	8	,	,	PUNCT
american_scientific_journal-7074	97	9	1975	1975	NUM
american_scientific_journal-7074	98	1	[	[	X
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american_scientific_journal-7074	98	3	]	]	PUNCT
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american_scientific_journal-7074	98	5	almheriegh	almheriegh	PROPN
american_scientific_journal-7074	98	6	.	.	PUNCT
american_scientific_journal-7074	99	1	“	"	PUNCT
american_scientific_journal-7074	99	2	initial	initial	ADJ
american_scientific_journal-7074	99	3	strain	strain	NOUN
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american_scientific_journal-7074	99	6	of	of	ADP
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american_scientific_journal-7074	99	8	materials	material	NOUN
american_scientific_journal-7074	99	9	”	"	PUNCT
american_scientific_journal-7074	99	10	iosr	iosr	ADJ
american_scientific_journal-7074	99	11	journals	journal	NOUN
american_scientific_journal-7074	99	12	of	of	ADP
american_scientific_journal-7074	99	13	mechanical	mechanical	ADJ
american_scientific_journal-7074	99	14	and	and	CCONJ
american_scientific_journal-7074	99	15	civil	civil	ADJ
american_scientific_journal-7074	99	16	engineering	engineering	NOUN
american_scientific_journal-7074	99	17	,	,	PUNCT
american_scientific_journal-7074	99	18	iosr	iosr	ADJ
american_scientific_journal-7074	99	19	journals	journal	NOUN
american_scientific_journal-7074	99	20	,	,	PUNCT
american_scientific_journal-7074	99	21	international	international	ADJ
american_scientific_journal-7074	99	22	organization	organization	NOUN
american_scientific_journal-7074	99	23	of	of	ADP
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american_scientific_journal-7074	99	25	research	research	NOUN
american_scientific_journal-7074	99	26	,	,	PUNCT
american_scientific_journal-7074	99	27	.	.	PUNCT
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american_scientific_journal-7074	100	2	:	:	PUNCT
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american_scientific_journal-7074	100	5	:	:	PUNCT
american_scientific_journal-7074	100	6	1	1	NUM
american_scientific_journal-7074	100	7	,	,	PUNCT
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american_scientific_journal-7074	100	10	-	-	SYM
american_scientific_journal-7074	100	11	47	47	NUM
american_scientific_journal-7074	100	12	(	(	PUNCT
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american_scientific_journal-7074	100	14	-4	-4	NOUN
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american_scientific_journal-7074	100	17	-	-	PUNCT
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american_scientific_journal-7074	100	19	:	:	PUNCT
american_scientific_journal-7074	100	20	2278	2278	NUM
american_scientific_journal-7074	100	21	-	-	SYM
american_scientific_journal-7074	100	22	1684	1684	NUM
american_scientific_journal-7074	100	23	p	p	NOUN
american_scientific_journal-7074	100	24	-	-	PUNCT
american_scientific_journal-7074	100	25	issn	issn	NOUN
american_scientific_journal-7074	100	26	:	:	PUNCT
american_scientific_journal-7074	100	27	2320	2320	NUM
american_scientific_journal-7074	100	28	-	-	SYM
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american_scientific_journal-7074	100	30	.	.	PUNCT
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american_scientific_journal-7074	101	4	.	.	PUNCT
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american_scientific_journal-7074	102	2	.	.	PROPN
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american_scientific_journal-7074	102	4	and	and	CCONJ
american_scientific_journal-7074	102	5	l.r	l.r	PROPN
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american_scientific_journal-7074	102	8	,	,	PUNCT
american_scientific_journal-7074	102	9	the	the	DET
american_scientific_journal-7074	102	10	mathematical	mathematical	ADJ
american_scientific_journal-7074	102	11	theory	theory	NOUN
american_scientific_journal-7074	102	12	of	of	ADP
american_scientific_journal-7074	102	13	finite	finite	ADJ
american_scientific_journal-7074	102	14	element	element	NOUN
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american_scientific_journal-7074	102	16	,	,	PUNCT
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american_scientific_journal-7074	102	18	science	science	NOUN
american_scientific_journal-7074	102	19	+	+	CCONJ
american_scientific_journal-7074	102	20	buiness	buiness	PROPN
american_scientific_journal-7074	102	21	media	medium	NOUN
american_scientific_journal-7074	102	22	llc	llc	PROPN
american_scientific_journal-7074	102	23	.	.	PUNCT
american_scientific_journal-7074	103	1	3rd	3rd	ADJ
american_scientific_journal-7074	103	2	eds	eds	PROPN
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american_scientific_journal-7074	103	4	,	,	PUNCT
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american_scientific_journal-7074	103	6	.	.	PUNCT
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american_scientific_journal-7074	104	4	.	.	PUNCT
american_scientific_journal-7074	104	5	mcneal	mcneal	PROPN
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american_scientific_journal-7074	104	8	,	,	PUNCT
american_scientific_journal-7074	104	9	(	(	PUNCT
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american_scientific_journal-7074	104	12	a	a	DET
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american_scientific_journal-7074	104	17	,	,	PUNCT
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american_scientific_journal-7074	104	19	and	and	CCONJ
american_scientific_journal-7074	104	20	structures	structure	NOUN
american_scientific_journal-7074	104	21	,	,	PUNCT
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american_scientific_journal-7074	104	23	.	.	PROPN
american_scientific_journal-7074	104	24	8	8	NUM
american_scientific_journal-7074	104	25	,	,	PUNCT
american_scientific_journal-7074	104	26	pp	pp	ADJ
american_scientific_journal-7074	104	27	.	.	PUNCT
american_scientific_journal-7074	104	28	175	175	NUM
american_scientific_journal-7074	104	29	-	-	SYM
american_scientific_journal-7074	104	30	183	183	NUM
american_scientific_journal-7074	104	31	.	.	PUNCT
american_scientific_journal-7074	105	1	[	[	X
american_scientific_journal-7074	105	2	7	7	NUM
american_scientific_journal-7074	105	3	]	]	PUNCT
american_scientific_journal-7074	105	4	.	.	PUNCT
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american_scientific_journal-7074	106	2	r.	r.	PROPN
american_scientific_journal-7074	106	3	w.	w.	PROPN
american_scientific_journal-7074	106	4	and	and	CCONJ
american_scientific_journal-7074	106	5	tocher	tocher	ADJ
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american_scientific_journal-7074	106	8	,	,	PUNCT
american_scientific_journal-7074	106	9	(	(	PUNCT
american_scientific_journal-7074	106	10	1965	1965	NUM
american_scientific_journal-7074	106	11	)	)	PUNCT
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american_scientific_journal-7074	106	13	element	element	NOUN
american_scientific_journal-7074	106	14	stiffness	stiffness	NOUN
american_scientific_journal-7074	106	15	matrices	matrix	NOUN
american_scientific_journal-7074	106	16	for	for	ADP
american_scientific_journal-7074	106	17	analysis	analysis	NOUN
american_scientific_journal-7074	106	18	of	of	ADP
american_scientific_journal-7074	106	19	plate	plate	NOUN
american_scientific_journal-7074	106	20	bending	bending	NOUN
american_scientific_journal-7074	106	21	,	,	PUNCT
american_scientific_journal-7074	106	22	proc	proc	NOUN
american_scientific_journal-7074	106	23	.	.	PUNCT
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american_scientific_journal-7074	107	2	on	on	ADP
american_scientific_journal-7074	107	3	matrix	matrix	NOUN
american_scientific_journal-7074	107	4	methods	method	NOUN
american_scientific_journal-7074	107	5	in	in	ADP
american_scientific_journal-7074	107	6	structural	structural	ADJ
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american_scientific_journal-7074	107	8	,	,	PUNCT
american_scientific_journal-7074	107	9	wpafb	wpafb	NOUN
american_scientific_journal-7074	107	10	,	,	PUNCT
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american_scientific_journal-7074	107	12	,	,	PUNCT
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american_scientific_journal-7074	107	14	.	.	PUNCT
american_scientific_journal-7074	108	1	515	515	NUM
american_scientific_journal-7074	108	2	-	-	SYM
american_scientific_journal-7074	108	3	545	545	NUM
american_scientific_journal-7074	108	4	.	.	PUNCT
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american_scientific_journal-7074	109	2	8	8	NUM
american_scientific_journal-7074	109	3	]	]	PUNCT
american_scientific_journal-7074	109	4	.	.	PUNCT
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american_scientific_journal-7074	110	2	b.	b.	PROPN
american_scientific_journal-7074	110	3	e.	e.	PROPN
american_scientific_journal-7074	110	4	,	,	PUNCT
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american_scientific_journal-7074	110	6	d.	d.	PROPN
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american_scientific_journal-7074	110	8	,	,	PUNCT
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american_scientific_journal-7074	110	10	weikel	weikel	PROPN
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american_scientific_journal-7074	110	12	c.	c.	PROPN
american_scientific_journal-7074	110	13	,	,	PUNCT
american_scientific_journal-7074	110	14	(	(	PUNCT
american_scientific_journal-7074	110	15	1961	1961	NUM
american_scientific_journal-7074	110	16	)	)	PUNCT
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american_scientific_journal-7074	110	18	of	of	ADP
american_scientific_journal-7074	110	19	the	the	DET
american_scientific_journal-7074	110	20	stiffness	stiffness	ADJ
american_scientific_journal-7074	110	21	method	method	NOUN
american_scientific_journal-7074	110	22	to	to	ADP
american_scientific_journal-7074	110	23	the	the	DET
american_scientific_journal-7074	110	24	analysis	analysis	NOUN
american_scientific_journal-7074	110	25	of	of	ADP
american_scientific_journal-7074	110	26	shell	shell	ADJ
american_scientific_journal-7074	110	27	structures	structure	NOUN
american_scientific_journal-7074	110	28	,	,	PUNCT
american_scientific_journal-7074	110	29	procedures	procedure	NOUN
american_scientific_journal-7074	110	30	on	on	ADP
american_scientific_journal-7074	110	31	aviation	aviation	NOUN
american_scientific_journal-7074	110	32	conference	conference	NOUN
american_scientific_journal-7074	110	33	,	,	PUNCT
american_scientific_journal-7074	110	34	american	american	ADJ
american_scientific_journal-7074	110	35	society	society	NOUN
american_scientific_journal-7074	110	36	of	of	ADP
american_scientific_journal-7074	110	37	mechanical	mechanical	ADJ
american_scientific_journal-7074	110	38	engineers	engineer	NOUN
american_scientific_journal-7074	110	39	,	,	PUNCT
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american_scientific_journal-7074	110	42	,	,	PUNCT
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american_scientific_journal-7074	110	44	.	.	PUNCT
american_scientific_journal-7074	111	1	[	[	X
american_scientific_journal-7074	111	2	9	9	NUM
american_scientific_journal-7074	111	3	]	]	PUNCT
american_scientific_journal-7074	111	4	.	.	PUNCT
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american_scientific_journal-7074	111	6	,	,	PUNCT
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american_scientific_journal-7074	111	8	p.	p.	PROPN
american_scientific_journal-7074	111	9	,	,	PUNCT
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american_scientific_journal-7074	111	11	y.	y.	PROPN
american_scientific_journal-7074	111	12	k.	k.	PROPN
american_scientific_journal-7074	111	13	,	,	PUNCT
american_scientific_journal-7074	111	14	irons	irons	PROPN
american_scientific_journal-7074	111	15	b.	b.	PROPN
american_scientific_journal-7074	111	16	m.	m.	PROPN
american_scientific_journal-7074	111	17	and	and	CCONJ
american_scientific_journal-7074	111	18	zienkiewicz	zienkiewicz	NOUN
american_scientific_journal-7074	111	19	,	,	PUNCT
american_scientific_journal-7074	111	20	o.	o.	PROPN
american_scientific_journal-7074	111	21	c.	c.	PROPN
american_scientific_journal-7074	111	22	,	,	PUNCT
american_scientific_journal-7074	111	23	(	(	PUNCT
american_scientific_journal-7074	111	24	1966	1966	NUM
american_scientific_journal-7074	111	25	)	)	PUNCT
american_scientific_journal-7074	112	1	triangular	triangular	NOUN
american_scientific_journal-7074	112	2	elements	element	NOUN
american_scientific_journal-7074	112	3	in	in	ADP
american_scientific_journal-7074	112	4	plate	plate	NOUN
american_scientific_journal-7074	112	5	bending	bending	NOUN
american_scientific_journal-7074	112	6	,	,	PUNCT
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american_scientific_journal-7074	112	8	and	and	CCONJ
american_scientific_journal-7074	112	9	non	non	ADJ
american_scientific_journal-7074	112	10	–	–	PUNCT
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american_scientific_journal-7074	112	13	,	,	PUNCT
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american_scientific_journal-7074	112	15	.	.	PUNCT
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american_scientific_journal-7074	113	2	conference	conference	NOUN
american_scientific_journal-7074	113	3	on	on	ADP
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american_scientific_journal-7074	113	5	methods	method	NOUN
american_scientific_journal-7074	113	6	in	in	ADP
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american_scientific_journal-7074	113	9	,	,	PUNCT
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american_scientific_journal-7074	113	11	.	.	PUNCT
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american_scientific_journal-7074	114	2	-	-	SYM
american_scientific_journal-7074	114	3	576	576	NUM
american_scientific_journal-7074	114	4	,	,	PUNCT
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american_scientific_journal-7074	114	7	af	af	PROPN
american_scientific_journal-7074	114	8	base	base	PROPN
american_scientific_journal-7074	114	9	,	,	PUNCT
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american_scientific_journal-7074	114	11	.	.	PUNCT
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american_scientific_journal-7074	115	2	10	10	NUM
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american_scientific_journal-7074	115	4	cleveland	cleveland	PROPN
american_scientific_journal-7074	115	5	state	state	PROPN
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american_scientific_journal-7074	115	7	,	,	PUNCT
american_scientific_journal-7074	115	8	fe	fe	X
american_scientific_journal-7074	115	9	course	course	NOUN
american_scientific_journal-7074	115	10	https://academic.csuohio.edu/duffy_s/cve_512_8.pdf	https://academic.csuohio.edu/duffy_s/cve_512_8.pdf	X
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american_scientific_journal-7074	116	2	11	11	NUM
american_scientific_journal-7074	116	3	]	]	PUNCT
american_scientific_journal-7074	116	4	.	.	PUNCT
american_scientific_journal-7074	117	1	cowper	cowper	NOUN
american_scientific_journal-7074	117	2	,	,	PUNCT
american_scientific_journal-7074	117	3	g.r	g.r	PROPN
american_scientific_journal-7074	117	4	.	.	PUNCT
american_scientific_journal-7074	117	5	:	:	PUNCT
american_scientific_journal-7074	118	1	gaussian	gaussian	ADJ
american_scientific_journal-7074	118	2	quadrature	quadrature	NOUN
american_scientific_journal-7074	118	3	formulas	formula	NOUN
american_scientific_journal-7074	118	4	for	for	ADP
american_scientific_journal-7074	118	5	triangles	triangle	NOUN
american_scientific_journal-7074	118	6	.	.	PUNCT
american_scientific_journal-7074	119	1	int	int	NOUN
american_scientific_journal-7074	119	2	.	.	PUNCT
american_scientific_journal-7074	120	1	j.	j.	PROPN
american_scientific_journal-7074	120	2	numer	numer	PROPN
american_scientific_journal-7074	120	3	.	.	PUNCT
american_scientific_journal-7074	121	1	methods	methods	PROPN
american_scientific_journal-7074	121	2	eng	eng	PROPN
american_scientific_journal-7074	121	3	.	.	PROPN
american_scientific_journal-7074	122	1	7	7	NUM
american_scientific_journal-7074	122	2	,	,	PUNCT
american_scientific_journal-7074	122	3	405–408	405–408	NUM
american_scientific_journal-7074	122	4	(	(	PUNCT
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american_scientific_journal-7074	122	6	)	)	PUNCT
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american_scientific_journal-7074	123	2	12	12	NUM
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american_scientific_journal-7074	123	4	.	.	PUNCT
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american_scientific_journal-7074	124	2	,	,	PUNCT
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american_scientific_journal-7074	124	4	.	.	PROPN
american_scientific_journal-7074	124	5	:	:	PUNCT
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american_scientific_journal-7074	125	3	-	-	PUNCT
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american_scientific_journal-7074	125	13	analysis	analysis	NOUN
american_scientific_journal-7074	125	14	.	.	PUNCT
american_scientific_journal-7074	126	1	j.	j.	PROPN
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american_scientific_journal-7074	126	3	.	.	PROPN
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american_scientific_journal-7074	126	5	.	.	PUNCT
american_scientific_journal-7074	127	1	73	73	NUM
american_scientific_journal-7074	127	2	,	,	PUNCT
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american_scientific_journal-7074	127	4	(	(	PUNCT
american_scientific_journal-7074	127	5	2006	2006	NUM
american_scientific_journal-7074	127	6	)	)	PUNCT
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american_scientific_journal-7074	128	2	13	13	NUM
american_scientific_journal-7074	128	3	]	]	PUNCT
american_scientific_journal-7074	128	4	.	.	PUNCT
american_scientific_journal-7074	129	1	cook	cook	PROPN
american_scientific_journal-7074	129	2	,	,	PUNCT
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american_scientific_journal-7074	129	4	.	.	PROPN
american_scientific_journal-7074	129	5	:	:	PUNCT
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american_scientific_journal-7074	129	10	and	and	CCONJ
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american_scientific_journal-7074	129	14	.	.	PUNCT
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american_scientific_journal-7074	130	2	.	.	PUNCT
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american_scientific_journal-7074	130	4	.	.	PUNCT
american_scientific_journal-7074	131	1	22	22	NUM
american_scientific_journal-7074	131	2	,	,	PUNCT
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american_scientific_journal-7074	131	4	(	(	PUNCT
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american_scientific_journal-7074	131	6	)	)	PUNCT
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