id	sid	tid	token	lemma	pos
american_scientific_journal-5305	1	1	868	868	NUM
american_scientific_journal-5305	1	2	american	american	ADJ
american_scientific_journal-5305	1	3	scientific	scientific	ADJ
american_scientific_journal-5305	1	4	research	research	NOUN
american_scientific_journal-5305	1	5	journal	journal	NOUN
american_scientific_journal-5305	1	6	for	for	ADP
american_scientific_journal-5305	1	7	engineering	engineering	NOUN
american_scientific_journal-5305	1	8	,	,	PUNCT
american_scientific_journal-5305	1	9	technology	technology	NOUN
american_scientific_journal-5305	1	10	,	,	PUNCT
american_scientific_journal-5305	1	11	and	and	CCONJ
american_scientific_journal-5305	1	12	sciences	science	NOUN
american_scientific_journal-5305	1	13	(	(	PUNCT
american_scientific_journal-5305	1	14	asrjets	asrjet	NOUN
american_scientific_journal-5305	1	15	)	)	PUNCT
american_scientific_journal-5305	1	16	issn	issn	PROPN
american_scientific_journal-5305	1	17	(	(	PUNCT
american_scientific_journal-5305	1	18	print	print	NOUN
american_scientific_journal-5305	1	19	)	)	PUNCT
american_scientific_journal-5305	1	20	2313	2313	NUM
american_scientific_journal-5305	1	21	-	-	SYM
american_scientific_journal-5305	1	22	4410	4410	NUM
american_scientific_journal-5305	1	23	,	,	PUNCT
american_scientific_journal-5305	1	24	issn	issn	PROPN
american_scientific_journal-5305	1	25	(	(	PUNCT
american_scientific_journal-5305	1	26	online	online	ADJ
american_scientific_journal-5305	1	27	)	)	PUNCT
american_scientific_journal-5305	1	28	2313	2313	NUM
american_scientific_journal-5305	1	29	-	-	SYM
american_scientific_journal-5305	1	30	4402	4402	NUM
american_scientific_journal-5305	1	31	©	©	PROPN
american_scientific_journal-5305	1	32	global	global	ADJ
american_scientific_journal-5305	1	33	society	society	NOUN
american_scientific_journal-5305	1	34	of	of	ADP
american_scientific_journal-5305	1	35	scientific	scientific	ADJ
american_scientific_journal-5305	1	36	research	research	NOUN
american_scientific_journal-5305	1	37	and	and	CCONJ
american_scientific_journal-5305	1	38	researchers	researcher	NOUN
american_scientific_journal-5305	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PRON
american_scientific_journal-5305	1	40	invariant	invariant	ADJ
american_scientific_journal-5305	1	41	variational	variational	ADJ
american_scientific_journal-5305	1	42	problems	problem	NOUN
american_scientific_journal-5305	1	43	i.	i.	PROPN
american_scientific_journal-5305	1	44	h.	h.	PROPN
american_scientific_journal-5305	1	45	gamar	gamar	PROPN
american_scientific_journal-5305	1	46	a	a	PROPN
american_scientific_journal-5305	1	47	*	*	X
american_scientific_journal-5305	1	48	,	,	PUNCT
american_scientific_journal-5305	1	49	m.	m.	NOUN
american_scientific_journal-5305	1	50	a.	a.	PROPN
american_scientific_journal-5305	1	51	bashir	bashir	PROPN
american_scientific_journal-5305	1	52	b	b	PROPN
american_scientific_journal-5305	1	53	email	email	NOUN
american_scientific_journal-5305	1	54	:	:	PUNCT
american_scientific_journal-5305	1	55	idrishgamar@gmail.com	idrishgamar@gmail.com	X
american_scientific_journal-5305	2	1	abstract	abstract	ADJ
american_scientific_journal-5305	2	2	this	this	DET
american_scientific_journal-5305	2	3	research	research	NOUN
american_scientific_journal-5305	2	4	is	be	AUX
american_scientific_journal-5305	2	5	the	the	DET
american_scientific_journal-5305	2	6	study	study	NOUN
american_scientific_journal-5305	2	7	of	of	ADP
american_scientific_journal-5305	2	8	conservation	conservation	NOUN
american_scientific_journal-5305	2	9	laws	law	NOUN
american_scientific_journal-5305	2	10	using	use	VERB
american_scientific_journal-5305	2	11	lie	lie	NOUN
american_scientific_journal-5305	2	12	algebra	algebra	NOUN
american_scientific_journal-5305	2	13	of	of	ADP
american_scientific_journal-5305	2	14	the	the	DET
american_scientific_journal-5305	2	15	symmetry	symmetry	NOUN
american_scientific_journal-5305	2	16	lie	lie	NOUN
american_scientific_journal-5305	2	17	group	group	NOUN
american_scientific_journal-5305	2	18	.	.	PUNCT
american_scientific_journal-5305	3	1	in	in	ADP
american_scientific_journal-5305	3	2	particular	particular	ADJ
american_scientific_journal-5305	3	3	,	,	PUNCT
american_scientific_journal-5305	3	4	we	we	PRON
american_scientific_journal-5305	3	5	consider	consider	VERB
american_scientific_journal-5305	3	6	conservation	conservation	NOUN
american_scientific_journal-5305	3	7	laws	law	NOUN
american_scientific_journal-5305	3	8	for	for	ADP
american_scientific_journal-5305	3	9	invariant	invariant	ADJ
american_scientific_journal-5305	3	10	variational	variational	ADJ
american_scientific_journal-5305	3	11	problems	problem	NOUN
american_scientific_journal-5305	3	12	based	base	VERB
american_scientific_journal-5305	3	13	on	on	ADP
american_scientific_journal-5305	3	14	noether	noether	PROPN
american_scientific_journal-5305	3	15	theorem	theorem	PROPN
american_scientific_journal-5305	3	16	.	.	PUNCT
american_scientific_journal-5305	4	1	we	we	PRON
american_scientific_journal-5305	4	2	have	have	AUX
american_scientific_journal-5305	4	3	provided	provide	VERB
american_scientific_journal-5305	4	4	a	a	DET
american_scientific_journal-5305	4	5	formula	formula	NOUN
american_scientific_journal-5305	4	6	of	of	ADP
american_scientific_journal-5305	4	7	conservation	conservation	NOUN
american_scientific_journal-5305	4	8	laws	law	NOUN
american_scientific_journal-5305	4	9	in	in	ADP
american_scientific_journal-5305	4	10	terms	term	NOUN
american_scientific_journal-5305	4	11	of	of	ADP
american_scientific_journal-5305	4	12	the	the	DET
american_scientific_journal-5305	4	13	lie	lie	NOUN
american_scientific_journal-5305	4	14	algebra	algebra	PROPN
american_scientific_journal-5305	4	15	of	of	ADP
american_scientific_journal-5305	4	16	symmetry	symmetry	NOUN
american_scientific_journal-5305	4	17	lie	lie	NOUN
american_scientific_journal-5305	4	18	group	group	NOUN
american_scientific_journal-5305	4	19	.	.	PUNCT
american_scientific_journal-5305	5	1	keywords	keyword	NOUN
american_scientific_journal-5305	5	2	:	:	PUNCT
american_scientific_journal-5305	5	3	conservation	conservation	NOUN
american_scientific_journal-5305	5	4	laws	law	NOUN
american_scientific_journal-5305	5	5	;	;	PUNCT
american_scientific_journal-5305	5	6	lie	lie	NOUN
american_scientific_journal-5305	5	7	algebra	algebra	NOUN
american_scientific_journal-5305	5	8	;	;	PUNCT
american_scientific_journal-5305	5	9	noether	noether	PROPN
american_scientific_journal-5305	5	10	theorem	theorem	PROPN
american_scientific_journal-5305	5	11	;	;	PUNCT
american_scientific_journal-5305	5	12	invariant	invariant	ADJ
american_scientific_journal-5305	5	13	variational	variational	ADJ
american_scientific_journal-5305	5	14	problems	problem	NOUN
american_scientific_journal-5305	5	15	.	.	PUNCT
american_scientific_journal-5305	6	1	1	1	X
american_scientific_journal-5305	6	2	.	.	X
american_scientific_journal-5305	6	3	introduction	introduction	NOUN
american_scientific_journal-5305	6	4	lie	lie	NOUN
american_scientific_journal-5305	6	5	groups	group	NOUN
american_scientific_journal-5305	6	6	and	and	CCONJ
american_scientific_journal-5305	6	7	their	their	PRON
american_scientific_journal-5305	6	8	lie	lie	NOUN
american_scientific_journal-5305	6	9	algebras	algebra	NOUN
american_scientific_journal-5305	6	10	are	be	AUX
american_scientific_journal-5305	6	11	essential	essential	ADJ
american_scientific_journal-5305	6	12	tools	tool	NOUN
american_scientific_journal-5305	6	13	in	in	ADP
american_scientific_journal-5305	6	14	the	the	DET
american_scientific_journal-5305	6	15	study	study	NOUN
american_scientific_journal-5305	6	16	of	of	ADP
american_scientific_journal-5305	6	17	general	general	ADJ
american_scientific_journal-5305	6	18	mathematical	mathematical	ADJ
american_scientific_journal-5305	6	19	fields	field	NOUN
american_scientific_journal-5305	6	20	.	.	PUNCT
american_scientific_journal-5305	7	1	these	these	PRON
american_scientific_journal-5305	7	2	include	include	VERB
american_scientific_journal-5305	7	3	partial	partial	ADJ
american_scientific_journal-5305	7	4	differential	differential	ADJ
american_scientific_journal-5305	7	5	equations	equation	NOUN
american_scientific_journal-5305	7	6	,	,	PUNCT
american_scientific_journal-5305	7	7	physical	physical	ADJ
american_scientific_journal-5305	7	8	fields	field	NOUN
american_scientific_journal-5305	7	9	and	and	CCONJ
american_scientific_journal-5305	7	10	their	their	PRON
american_scientific_journal-5305	7	11	classification	classification	NOUN
american_scientific_journal-5305	7	12	,	,	PUNCT
american_scientific_journal-5305	7	13	homogenous	homogenous	ADJ
american_scientific_journal-5305	7	14	spaces	space	NOUN
american_scientific_journal-5305	7	15	,	,	PUNCT
american_scientific_journal-5305	7	16	symmetric	symmetric	ADJ
american_scientific_journal-5305	7	17	spaces	space	NOUN
american_scientific_journal-5305	7	18	and	and	CCONJ
american_scientific_journal-5305	7	19	differential	differential	ADJ
american_scientific_journal-5305	7	20	geometry	geometry	NOUN
american_scientific_journal-5305	7	21	in	in	ADP
american_scientific_journal-5305	7	22	general	general	ADJ
american_scientific_journal-5305	7	23	.	.	PUNCT
american_scientific_journal-5305	8	1	conservation	conservation	NOUN
american_scientific_journal-5305	8	2	laws	law	NOUN
american_scientific_journal-5305	8	3	and	and	CCONJ
american_scientific_journal-5305	8	4	symmetries	symmetry	NOUN
american_scientific_journal-5305	8	5	have	have	AUX
american_scientific_journal-5305	8	6	always	always	ADV
american_scientific_journal-5305	8	7	been	be	AUX
american_scientific_journal-5305	8	8	of	of	ADP
american_scientific_journal-5305	8	9	considerable	considerable	ADJ
american_scientific_journal-5305	8	10	interest	interest	NOUN
american_scientific_journal-5305	8	11	in	in	ADP
american_scientific_journal-5305	8	12	science	science	NOUN
american_scientific_journal-5305	8	13	.	.	PUNCT
american_scientific_journal-5305	9	1	they	they	PRON
american_scientific_journal-5305	9	2	are	be	AUX
american_scientific_journal-5305	9	3	important	important	ADJ
american_scientific_journal-5305	9	4	in	in	ADP
american_scientific_journal-5305	9	5	the	the	DET
american_scientific_journal-5305	9	6	formulation	formulation	NOUN
american_scientific_journal-5305	9	7	and	and	CCONJ
american_scientific_journal-5305	9	8	investigation	investigation	NOUN
american_scientific_journal-5305	9	9	of	of	ADP
american_scientific_journal-5305	9	10	many	many	ADJ
american_scientific_journal-5305	9	11	mathematical	mathematical	ADJ
american_scientific_journal-5305	9	12	models	model	NOUN
american_scientific_journal-5305	9	13	.	.	PUNCT
american_scientific_journal-5305	10	1	they	they	PRON
american_scientific_journal-5305	10	2	were	be	AUX
american_scientific_journal-5305	10	3	used	use	VERB
american_scientific_journal-5305	10	4	e.g.	e.g.	ADV
american_scientific_journal-5305	10	5	for	for	ADP
american_scientific_journal-5305	10	6	proving	prove	VERB
american_scientific_journal-5305	10	7	global	global	ADJ
american_scientific_journal-5305	10	8	existence	existence	NOUN
american_scientific_journal-5305	10	9	theorems	theorem	NOUN
american_scientific_journal-5305	11	1	[	[	X
american_scientific_journal-5305	11	2	1–3	1–3	X
american_scientific_journal-5305	11	3	]	]	X
american_scientific_journal-5305	11	4	in	in	ADP
american_scientific_journal-5305	11	5	problems	problem	NOUN
american_scientific_journal-5305	11	6	of	of	ADP
american_scientific_journal-5305	11	7	stability	stability	NOUN
american_scientific_journal-5305	12	1	[	[	X
american_scientific_journal-5305	12	2	4,5	4,5	X
american_scientific_journal-5305	12	3	]	]	PUNCT
american_scientific_journal-5305	12	4	in	in	ADP
american_scientific_journal-5305	12	5	elasticity	elasticity	NOUN
american_scientific_journal-5305	12	6	for	for	ADP
american_scientific_journal-5305	12	7	studying	study	VERB
american_scientific_journal-5305	12	8	cracks	crack	NOUN
american_scientific_journal-5305	12	9	and	and	CCONJ
american_scientific_journal-5305	12	10	dislocations	dislocation	NOUN
american_scientific_journal-5305	13	1	[	[	X
american_scientific_journal-5305	13	2	6,7	6,7	NUM
american_scientific_journal-5305	13	3	]	]	PUNCT
american_scientific_journal-5305	13	4	in	in	ADP
american_scientific_journal-5305	13	5	astrophysics	astrophysic	NOUN
american_scientific_journal-5305	13	6	[	[	X
american_scientific_journal-5305	13	7	8–10	8–10	NOUN
american_scientific_journal-5305	13	8	]	]	PUNCT
american_scientific_journal-5305	13	9	,	,	PUNCT
american_scientific_journal-5305	13	10	in	in	ADP
american_scientific_journal-5305	13	11	designing	design	VERB
american_scientific_journal-5305	13	12	new	new	ADJ
american_scientific_journal-5305	13	13	radio	radio	NOUN
american_scientific_journal-5305	13	14	antennas	antenna	NOUN
american_scientific_journal-5305	13	15	'	'	PART
american_scientific_journal-5305	14	1	[	[	X
american_scientific_journal-5305	14	2	11	11	NUM
american_scientific_journal-5305	14	3	]	]	PUNCT
american_scientific_journal-5305	14	4	and	and	CCONJ
american_scientific_journal-5305	14	5	so	so	ADV
american_scientific_journal-5305	14	6	on	on	ADV
american_scientific_journal-5305	14	7	.	.	PUNCT
american_scientific_journal-5305	15	1	in	in	ADP
american_scientific_journal-5305	15	2	this	this	DET
american_scientific_journal-5305	15	3	paper	paper	NOUN
american_scientific_journal-5305	15	4	we	we	PRON
american_scientific_journal-5305	15	5	consider	consider	VERB
american_scientific_journal-5305	15	6	the	the	DET
american_scientific_journal-5305	15	7	invariant	invariant	ADJ
american_scientific_journal-5305	15	8	variational	variational	ADJ
american_scientific_journal-5305	15	9	problems	problem	NOUN
american_scientific_journal-5305	15	10	which	which	PRON
american_scientific_journal-5305	15	11	are	be	AUX
american_scientific_journal-5305	15	12	invariant	invariant	ADJ
american_scientific_journal-5305	15	13	under	under	ADP
american_scientific_journal-5305	15	14	the	the	DET
american_scientific_journal-5305	15	15	continuous	continuous	ADJ
american_scientific_journal-5305	15	16	group	group	NOUN
american_scientific_journal-5305	15	17	according	accord	VERB
american_scientific_journal-5305	15	18	to	to	ADP
american_scientific_journal-5305	15	19	lie	lie	NOUN
american_scientific_journal-5305	15	20	theory	theory	NOUN
american_scientific_journal-5305	15	21	and	and	CCONJ
american_scientific_journal-5305	15	22	noether	noether	ADJ
american_scientific_journal-5305	15	23	theorem	theorem	NOUN
american_scientific_journal-5305	15	24	for	for	ADP
american_scientific_journal-5305	15	25	symmetry	symmetry	NOUN
american_scientific_journal-5305	15	26	lie	lie	NOUN
american_scientific_journal-5305	15	27	groups	group	NOUN
american_scientific_journal-5305	15	28	2	2	NUM
american_scientific_journal-5305	15	29	.	.	PUNCT
american_scientific_journal-5305	15	30	preliminary	preliminary	ADJ
american_scientific_journal-5305	15	31	2.1	2.1	NUM
american_scientific_journal-5305	15	32	.	.	PUNCT
american_scientific_journal-5305	16	1	lie	lie	NOUN
american_scientific_journal-5305	16	2	group	group	NOUN
american_scientific_journal-5305	16	3	g	g	PROPN
american_scientific_journal-5305	16	4	is	be	AUX
american_scientific_journal-5305	16	5	differentiable	differentiable	ADJ
american_scientific_journal-5305	16	6	manifold	manifold	ADJ
american_scientific_journal-5305	16	7	which	which	PRON
american_scientific_journal-5305	16	8	is	be	AUX
american_scientific_journal-5305	16	9	also	also	ADV
american_scientific_journal-5305	16	10	a	a	DET
american_scientific_journal-5305	16	11	group	group	NOUN
american_scientific_journal-5305	16	12	such	such	ADJ
american_scientific_journal-5305	16	13	that	that	SCONJ
american_scientific_journal-5305	16	14	the	the	DET
american_scientific_journal-5305	16	15	product	product	NOUN
american_scientific_journal-5305	16	16	and	and	CCONJ
american_scientific_journal-5305	16	17	inverse	inverse	NOUN
american_scientific_journal-5305	16	18	operations	operation	NOUN
american_scientific_journal-5305	16	19	are	be	AUX
american_scientific_journal-5305	16	20	differentiable	differentiable	ADJ
american_scientific_journal-5305	16	21	i.	i.	NOUN
american_scientific_journal-5305	16	22	m	m	PROPN
american_scientific_journal-5305	16	23	:	:	PUNCT
american_scientific_journal-5305	16	24	g	g	PROPN
american_scientific_journal-5305	16	25	g	g	PROPN
american_scientific_journal-5305	16	26	g	g	PROPN
american_scientific_journal-5305	16	27	,	,	PUNCT
american_scientific_journal-5305	16	28	m(x	m(x	PROPN
american_scientific_journal-5305	16	29	,	,	PUNCT
american_scientific_journal-5305	16	30	y	y	NOUN
american_scientific_journal-5305	16	31	)	)	PUNCT
american_scientific_journal-5305	16	32	=	=	PUNCT
american_scientific_journal-5305	17	1	x	x	PUNCT
american_scientific_journal-5305	17	2	y	y	PROPN
american_scientific_journal-5305	17	3	is	be	AUX
american_scientific_journal-5305	17	4	differentiable	differentiable	PROPN
american_scientific_journal-5305	17	5	ii	ii	NOUN
american_scientific_journal-5305	17	6	.	.	PUNCT
american_scientific_journal-5305	18	1	i	i	PRON
american_scientific_journal-5305	18	2	:	:	PUNCT
american_scientific_journal-5305	18	3	g	g	PROPN
american_scientific_journal-5305	18	4	g	g	PROPN
american_scientific_journal-5305	18	5	,	,	PUNCT
american_scientific_journal-5305	18	6	i(x	i(x	PROPN
american_scientific_journal-5305	18	7	)	)	PUNCT
american_scientific_journal-5305	18	8	=	=	VERB
american_scientific_journal-5305	18	9	is	be	AUX
american_scientific_journal-5305	18	10	differentiable	differentiable	ADJ
american_scientific_journal-5305	18	11	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-5305	18	12	*	*	PUNCT
american_scientific_journal-5305	18	13	corresponding	correspond	VERB
american_scientific_journal-5305	18	14	author	author	NOUN
american_scientific_journal-5305	18	15	american	american	PROPN
american_scientific_journal-5305	18	16	scientific	scientific	PROPN
american_scientific_journal-5305	18	17	research	research	PROPN
american_scientific_journal-5305	18	18	journal	journal	NOUN
american_scientific_journal-5305	18	19	for	for	ADP
american_scientific_journal-5305	18	20	engineering	engineering	NOUN
american_scientific_journal-5305	18	21	,	,	PUNCT
american_scientific_journal-5305	18	22	technology	technology	NOUN
american_scientific_journal-5305	18	23	,	,	PUNCT
american_scientific_journal-5305	18	24	and	and	CCONJ
american_scientific_journal-5305	18	25	sciences	science	NOUN
american_scientific_journal-5305	18	26	(	(	PUNCT
american_scientific_journal-5305	18	27	asrjets	asrjet	NOUN
american_scientific_journal-5305	18	28	)	)	PUNCT
american_scientific_journal-5305	18	29	(	(	PUNCT
american_scientific_journal-5305	18	30	2019	2019	NUM
american_scientific_journal-5305	18	31	)	)	PUNCT
american_scientific_journal-5305	18	32	volume	volume	NOUN
american_scientific_journal-5305	18	33	61	61	NUM
american_scientific_journal-5305	18	34	,	,	PUNCT
american_scientific_journal-5305	18	35	no	no	DET
american_scientific_journal-5305	18	36	1	1	NUM
american_scientific_journal-5305	18	37	,	,	PUNCT
american_scientific_journal-5305	18	38	pp	pp	ADV
american_scientific_journal-5305	18	39	268	268	NUM
american_scientific_journal-5305	18	40	-	-	SYM
american_scientific_journal-5305	18	41	279	279	NUM
american_scientific_journal-5305	18	42	869	869	NUM
american_scientific_journal-5305	18	43	(	(	PUNCT
american_scientific_journal-5305	18	44	a	a	DET
american_scientific_journal-5305	18	45	lie	lie	NOUN
american_scientific_journal-5305	18	46	group	group	NOUN
american_scientific_journal-5305	18	47	g	g	PROPN
american_scientific_journal-5305	18	48	is	be	AUX
american_scientific_journal-5305	18	49	an	an	DET
american_scientific_journal-5305	18	50	abstract	abstract	ADJ
american_scientific_journal-5305	18	51	group	group	NOUN
american_scientific_journal-5305	18	52	and	and	CCONJ
american_scientific_journal-5305	18	53	smooth	smooth	ADJ
american_scientific_journal-5305	18	54	n	n	CCONJ
american_scientific_journal-5305	18	55	-	-	PUNCT
american_scientific_journal-5305	18	56	dimensional	dimensional	ADJ
american_scientific_journal-5305	18	57	manifold	manifold	NOUN
american_scientific_journal-5305	18	58	so	so	SCONJ
american_scientific_journal-5305	18	59	that	that	SCONJ
american_scientific_journal-5305	18	60	multiplication	multiplication	NOUN
american_scientific_journal-5305	18	61	and	and	CCONJ
american_scientific_journal-5305	18	62	inverse	inverse	NOUN
american_scientific_journal-5305	18	63	are	be	AUX
american_scientific_journal-5305	18	64	smooth	smooth	ADJ
american_scientific_journal-5305	18	65	)	)	PUNCT
american_scientific_journal-5305	18	66	.	.	PUNCT
american_scientific_journal-5305	19	1	2.2	2.2	NUM
american_scientific_journal-5305	19	2	.	.	PUNCT
american_scientific_journal-5305	20	1	lie	lie	PROPN
american_scientific_journal-5305	20	2	algebra	algebra	NOUN
american_scientific_journal-5305	20	3	over	over	ADP
american_scientific_journal-5305	20	4	r	r	NOUN
american_scientific_journal-5305	20	5	or	or	CCONJ
american_scientific_journal-5305	20	6	c	c	NOUN
american_scientific_journal-5305	20	7	is	be	AUX
american_scientific_journal-5305	20	8	a	a	DET
american_scientific_journal-5305	20	9	vector	vector	NOUN
american_scientific_journal-5305	20	10	space	space	NOUN
american_scientific_journal-5305	20	11	r	r	NOUN
american_scientific_journal-5305	20	12	with	with	ADP
american_scientific_journal-5305	20	13	askew	askew	NOUN
american_scientific_journal-5305	20	14	-	-	PUNCT
american_scientific_journal-5305	20	15	symmetric	symmetric	ADJ
american_scientific_journal-5305	20	16	r	r	NOUN
american_scientific_journal-5305	20	17	-	-	PUNCT
american_scientific_journal-5305	20	18	bilinear	bilinear	ADJ
american_scientific_journal-5305	20	19	form	form	NOUN
american_scientific_journal-5305	20	20	(	(	PUNCT
american_scientific_journal-5305	20	21	lie	lie	NOUN
american_scientific_journal-5305	20	22	bracket	bracket	NOUN
american_scientific_journal-5305	20	23	)	)	PUNCT
american_scientific_journal-5305	21	1	[	[	X
american_scientific_journal-5305	21	2	,	,	X
american_scientific_journal-5305	21	3	]	]	X
american_scientific_journal-5305	21	4	v	v	NUM
american_scientific_journal-5305	21	5	which	which	PRON
american_scientific_journal-5305	21	6	satisfies	satisfy	VERB
american_scientific_journal-5305	21	7	jacobian	jacobian	ADJ
american_scientific_journal-5305	21	8	identity	identity	NOUN
american_scientific_journal-5305	21	9	.	.	PUNCT
american_scientific_journal-5305	22	1	we	we	PRON
american_scientific_journal-5305	22	2	relate	relate	VERB
american_scientific_journal-5305	22	3	the	the	DET
american_scientific_journal-5305	22	4	two	two	NUM
american_scientific_journal-5305	22	5	via	via	ADP
american_scientific_journal-5305	22	6	the	the	DET
american_scientific_journal-5305	22	7	so	so	ADV
american_scientific_journal-5305	22	8	called	call	VERB
american_scientific_journal-5305	22	9	left	left	ADJ
american_scientific_journal-5305	22	10	invariant	invariant	ADJ
american_scientific_journal-5305	22	11	vector	vector	NOUN
american_scientific_journal-5305	22	12	fields	field	NOUN
american_scientific_journal-5305	22	13	:	:	PUNCT
american_scientific_journal-5305	22	14	we	we	PRON
american_scientific_journal-5305	22	15	use	use	VERB
american_scientific_journal-5305	22	16	the	the	DET
american_scientific_journal-5305	22	17	standard	standard	ADJ
american_scientific_journal-5305	22	18	notation	notation	NOUN
american_scientific_journal-5305	22	19	we	we	PRON
american_scientific_journal-5305	22	20	define	define	VERB
american_scientific_journal-5305	22	21	a	a	DET
american_scientific_journal-5305	22	22	vector	vector	NOUN
american_scientific_journal-5305	22	23	field	field	NOUN
american_scientific_journal-5305	22	24	x	x	PUNCT
american_scientific_journal-5305	22	25	on	on	SCONJ
american_scientific_journal-5305	22	26	a	a	DET
american_scientific_journal-5305	22	27	lie	lie	NOUN
american_scientific_journal-5305	22	28	group	group	NOUN
american_scientific_journal-5305	22	29	g	g	PROPN
american_scientific_journal-5305	22	30	to	to	PART
american_scientific_journal-5305	22	31	be	be	AUX
american_scientific_journal-5305	22	32	left	leave	VERB
american_scientific_journal-5305	22	33	invariant	invariant	ADJ
american_scientific_journal-5305	22	34	if	if	SCONJ
american_scientific_journal-5305	22	35	d	d	PROPN
american_scientific_journal-5305	22	36	(	(	PUNCT
american_scientific_journal-5305	22	37	(	(	PUNCT
american_scientific_journal-5305	22	38	(	(	PUNCT
american_scientific_journal-5305	22	39	)	)	PUNCT
american_scientific_journal-5305	22	40	(	(	PUNCT
american_scientific_journal-5305	22	41	for	for	ADP
american_scientific_journal-5305	22	42	all	all	DET
american_scientific_journal-5305	22	43	g	g	NOUN
american_scientific_journal-5305	22	44	or	or	CCONJ
american_scientific_journal-5305	22	45	for	for	ADP
american_scientific_journal-5305	22	46	short	short	ADJ
american_scientific_journal-5305	22	47	(	(	PUNCT
american_scientific_journal-5305	22	48	(	(	PUNCT
american_scientific_journal-5305	22	49	geometrically	geometrically	ADV
american_scientific_journal-5305	22	50	the	the	DET
american_scientific_journal-5305	22	51	left	left	ADJ
american_scientific_journal-5305	22	52	invariant	invariant	ADJ
american_scientific_journal-5305	22	53	vector	vector	NOUN
american_scientific_journal-5305	22	54	field	field	NOUN
american_scientific_journal-5305	22	55	can	can	AUX
american_scientific_journal-5305	22	56	be	be	AUX
american_scientific_journal-5305	22	57	identified	identify	VERB
american_scientific_journal-5305	22	58	with	with	ADP
american_scientific_journal-5305	22	59	the	the	DET
american_scientific_journal-5305	22	60	tangent	tangent	ADJ
american_scientific_journal-5305	22	61	space	space	NOUN
american_scientific_journal-5305	22	62	to	to	ADP
american_scientific_journal-5305	22	63	g	g	PROPN
american_scientific_journal-5305	22	64	at	at	ADP
american_scientific_journal-5305	22	65	e.	e.	PROPN
american_scientific_journal-5305	22	66	these	these	PRON
american_scientific_journal-5305	22	67	are	be	AUX
american_scientific_journal-5305	22	68	the	the	DET
american_scientific_journal-5305	22	69	infinitesimal	infinitesimal	ADJ
american_scientific_journal-5305	22	70	generators	generator	NOUN
american_scientific_journal-5305	22	71	of	of	ADP
american_scientific_journal-5305	22	72	the	the	DET
american_scientific_journal-5305	22	73	group	group	NOUN
american_scientific_journal-5305	22	74	g.	g.	PROPN
american_scientific_journal-5305	22	75	2.3	2.3	NUM
american_scientific_journal-5305	22	76	.	.	PUNCT
american_scientific_journal-5305	23	1	concept	concept	NOUN
american_scientific_journal-5305	23	2	of	of	ADP
american_scientific_journal-5305	23	3	invariant	invariant	ADJ
american_scientific_journal-5305	23	4	variational	variational	ADJ
american_scientific_journal-5305	23	5	problems	problem	NOUN
american_scientific_journal-5305	23	6	in	in	ADP
american_scientific_journal-5305	23	7	mathematics	mathematics	PROPN
american_scientific_journal-5305	23	8	an	an	DET
american_scientific_journal-5305	23	9	invariant	invariant	ADJ
american_scientific_journal-5305	23	10	property	property	NOUN
american_scientific_journal-5305	23	11	,	,	PUNCT
american_scientific_journal-5305	23	12	hold	hold	VERB
american_scientific_journal-5305	23	13	by	by	ADP
american_scientific_journal-5305	23	14	a	a	DET
american_scientific_journal-5305	23	15	class	class	NOUN
american_scientific_journal-5305	23	16	of	of	ADP
american_scientific_journal-5305	23	17	mathematical	mathematical	ADJ
american_scientific_journal-5305	23	18	objects	object	NOUN
american_scientific_journal-5305	23	19	,	,	PUNCT
american_scientific_journal-5305	23	20	which	which	PRON
american_scientific_journal-5305	23	21	remain	remain	VERB
american_scientific_journal-5305	23	22	unchanged	unchanged	ADJ
american_scientific_journal-5305	23	23	when	when	SCONJ
american_scientific_journal-5305	23	24	transformations	transformation	NOUN
american_scientific_journal-5305	23	25	of	of	ADP
american_scientific_journal-5305	23	26	certain	certain	ADJ
american_scientific_journal-5305	23	27	type	type	NOUN
american_scientific_journal-5305	23	28	are	be	AUX
american_scientific_journal-5305	23	29	applied	apply	VERB
american_scientific_journal-5305	23	30	to	to	ADP
american_scientific_journal-5305	23	31	the	the	DET
american_scientific_journal-5305	23	32	objects	object	NOUN
american_scientific_journal-5305	23	33	.	.	PUNCT
american_scientific_journal-5305	24	1	consider	consider	VERB
american_scientific_journal-5305	24	2	the	the	DET
american_scientific_journal-5305	24	3	euler	euler	ADJ
american_scientific_journal-5305	24	4	-	-	PUNCT
american_scientific_journal-5305	24	5	lagrange	lagrange	NOUN
american_scientific_journal-5305	24	6	equations	equation	NOUN
american_scientific_journal-5305	24	7	:	:	PUNCT
american_scientific_journal-5305	24	8	(	(	PUNCT
american_scientific_journal-5305	24	9	)	)	PUNCT
american_scientific_journal-5305	24	10	(	(	PUNCT
american_scientific_journal-5305	24	11	2.1	2.1	NUM
american_scientific_journal-5305	24	12	)	)	PUNCT
american_scientific_journal-5305	24	13	they	they	PRON
american_scientific_journal-5305	24	14	give	give	VERB
american_scientific_journal-5305	24	15	a	a	DET
american_scientific_journal-5305	24	16	condition	condition	NOUN
american_scientific_journal-5305	24	17	for	for	ADP
american_scientific_journal-5305	24	18	q(t	q(t	NOUN
american_scientific_journal-5305	24	19	)	)	PUNCT
american_scientific_journal-5305	24	20	to	to	PART
american_scientific_journal-5305	24	21	provided	provide	VERB
american_scientific_journal-5305	24	22	extremum	extremum	ADJ
american_scientific_journal-5305	24	23	of	of	ADP
american_scientific_journal-5305	24	24	the	the	DET
american_scientific_journal-5305	24	25	integral	integral	ADJ
american_scientific_journal-5305	24	26	∫	∫	NOUN
american_scientific_journal-5305	24	27	(	(	PUNCT
american_scientific_journal-5305	24	28	(	(	PUNCT
american_scientific_journal-5305	24	29	a	a	DET
american_scientific_journal-5305	24	30	variation	variation	NOUN
american_scientific_journal-5305	24	31	of	of	ADP
american_scientific_journal-5305	24	32	integral	integral	ADJ
american_scientific_journal-5305	24	33	(	(	PUNCT
american_scientific_journal-5305	24	34	2.2	2.2	NUM
american_scientific_journal-5305	24	35	)	)	PUNCT
american_scientific_journal-5305	24	36	is	be	AUX
american_scientific_journal-5305	24	37	invariant	invariant	ADJ
american_scientific_journal-5305	24	38	under	under	ADP
american_scientific_journal-5305	24	39	the	the	DET
american_scientific_journal-5305	24	40	group	group	NOUN
american_scientific_journal-5305	24	41	g	g	PROPN
american_scientific_journal-5305	24	42	if	if	SCONJ
american_scientific_journal-5305	24	43	∫	∫	PROPN
american_scientific_journal-5305	24	44	(	(	PUNCT
american_scientific_journal-5305	24	45	̅	̅	NOUN
american_scientific_journal-5305	24	46	̅	̅	X
american_scientific_journal-5305	24	47	̅	̅	NOUN
american_scientific_journal-5305	24	48	(	(	PUNCT
american_scientific_journal-5305	24	49	̅	̅	NOUN
american_scientific_journal-5305	24	50	(	(	PUNCT
american_scientific_journal-5305	24	51	)	)	PUNCT
american_scientific_journal-5305	24	52	∫	∫	PROPN
american_scientific_journal-5305	25	1	(	(	PUNCT
american_scientific_journal-5305	25	2	(	(	PUNCT
american_scientific_journal-5305	25	3	(	(	PUNCT
american_scientific_journal-5305	25	4	(	(	PUNCT
american_scientific_journal-5305	25	5	̅	̅	NOUN
american_scientific_journal-5305	25	6	the	the	DET
american_scientific_journal-5305	25	7	invariance	invariance	NOUN
american_scientific_journal-5305	25	8	condition	condition	NOUN
american_scientific_journal-5305	25	9	is	be	AUX
american_scientific_journal-5305	25	10	given	give	VERB
american_scientific_journal-5305	25	11	by	by	ADP
american_scientific_journal-5305	25	12	following	follow	VERB
american_scientific_journal-5305	25	13	lemma	lemma	PROPN
american_scientific_journal-5305	25	14	lemma2.1	lemma2.1	PROPN
american_scientific_journal-5305	25	15	an	an	DET
american_scientific_journal-5305	25	16	integral	integral	ADJ
american_scientific_journal-5305	25	17	∫	∫	NOUN
american_scientific_journal-5305	25	18	(	(	PUNCT
american_scientific_journal-5305	25	19	(	(	PUNCT
american_scientific_journal-5305	25	20	(	(	PUNCT
american_scientific_journal-5305	25	21	)	)	PUNCT
american_scientific_journal-5305	25	22	(	(	PUNCT
american_scientific_journal-5305	25	23	is	be	AUX
american_scientific_journal-5305	25	24	invariant	invariant	ADJ
american_scientific_journal-5305	25	25	under	under	ADP
american_scientific_journal-5305	25	26	the	the	DET
american_scientific_journal-5305	25	27	group	group	NOUN
american_scientific_journal-5305	25	28	g	g	PROPN
american_scientific_journal-5305	25	29	if	if	SCONJ
american_scientific_journal-5305	26	1	and	and	CCONJ
american_scientific_journal-5305	26	2	only	only	ADV
american_scientific_journal-5305	26	3	if	if	SCONJ
american_scientific_journal-5305	26	4	american	american	ADJ
american_scientific_journal-5305	26	5	scientific	scientific	ADJ
american_scientific_journal-5305	26	6	research	research	NOUN
american_scientific_journal-5305	26	7	journal	journal	NOUN
american_scientific_journal-5305	26	8	for	for	ADP
american_scientific_journal-5305	26	9	engineering	engineering	NOUN
american_scientific_journal-5305	26	10	,	,	PUNCT
american_scientific_journal-5305	26	11	technology	technology	NOUN
american_scientific_journal-5305	26	12	,	,	PUNCT
american_scientific_journal-5305	26	13	and	and	CCONJ
american_scientific_journal-5305	26	14	sciences	science	NOUN
american_scientific_journal-5305	26	15	(	(	PUNCT
american_scientific_journal-5305	26	16	asrjets	asrjet	NOUN
american_scientific_journal-5305	26	17	)	)	PUNCT
american_scientific_journal-5305	26	18	(	(	PUNCT
american_scientific_journal-5305	26	19	2019	2019	NUM
american_scientific_journal-5305	26	20	)	)	PUNCT
american_scientific_journal-5305	26	21	volume	volume	NOUN
american_scientific_journal-5305	26	22	61	61	NUM
american_scientific_journal-5305	26	23	,	,	PUNCT
american_scientific_journal-5305	26	24	no	no	DET
american_scientific_journal-5305	26	25	1	1	NUM
american_scientific_journal-5305	26	26	,	,	PUNCT
american_scientific_journal-5305	26	27	pp	pp	ADV
american_scientific_journal-5305	26	28	268	268	NUM
american_scientific_journal-5305	26	29	-	-	SYM
american_scientific_journal-5305	26	30	279	279	NUM
american_scientific_journal-5305	26	31	872	872	NUM
american_scientific_journal-5305	26	32	(	(	PUNCT
american_scientific_journal-5305	26	33	(	(	PUNCT
american_scientific_journal-5305	26	34	(	(	PUNCT
american_scientific_journal-5305	26	35	here	here	ADV
american_scientific_journal-5305	26	36	x	x	PUNCT
american_scientific_journal-5305	26	37	is	be	AUX
american_scientific_journal-5305	26	38	infinitesimal	infinitesimal	ADJ
american_scientific_journal-5305	26	39	generator	generator	NOUN
american_scientific_journal-5305	26	40	of	of	ADP
american_scientific_journal-5305	26	41	the	the	DET
american_scientific_journal-5305	26	42	group	group	NOUN
american_scientific_journal-5305	26	43	g	g	PROPN
american_scientific_journal-5305	26	44	,	,	PUNCT
american_scientific_journal-5305	26	45	it	it	PRON
american_scientific_journal-5305	26	46	has	have	VERB
american_scientific_journal-5305	26	47	the	the	DET
american_scientific_journal-5305	26	48	form	form	NOUN
american_scientific_journal-5305	26	49	(	(	PUNCT
american_scientific_journal-5305	26	50	(	(	PUNCT
american_scientific_journal-5305	26	51	(	(	PUNCT
american_scientific_journal-5305	26	52	and	and	CCONJ
american_scientific_journal-5305	26	53	x	x	X
american_scientific_journal-5305	26	54	in	in	ADP
american_scientific_journal-5305	26	55	a	a	DET
american_scientific_journal-5305	26	56	prolonged	prolonged	ADJ
american_scientific_journal-5305	26	57	version	version	NOUN
american_scientific_journal-5305	26	58	of	of	ADP
american_scientific_journal-5305	26	59	the	the	DET
american_scientific_journal-5305	26	60	generator	generator	NOUN
american_scientific_journal-5305	26	61	(	(	PUNCT
american_scientific_journal-5305	26	62	2.6	2.6	NUM
american_scientific_journal-5305	26	63	)	)	PUNCT
american_scientific_journal-5305	26	64	is	be	AUX
american_scientific_journal-5305	26	65	(	(	PUNCT
american_scientific_journal-5305	26	66	where	where	SCONJ
american_scientific_journal-5305	26	67	(	(	PUNCT
american_scientific_journal-5305	26	68	)	)	PUNCT
american_scientific_journal-5305	26	69	(	(	PUNCT
american_scientific_journal-5305	26	70	)	)	PUNCT
american_scientific_journal-5305	26	71	.	.	PUNCT
american_scientific_journal-5305	27	1	2	2	X
american_scientific_journal-5305	27	2	.	.	X
american_scientific_journal-5305	27	3	variational	variational	ADJ
american_scientific_journal-5305	27	4	problems	problem	NOUN
american_scientific_journal-5305	27	5	in	in	ADP
american_scientific_journal-5305	27	6	order	order	NOUN
american_scientific_journal-5305	27	7	to	to	PART
american_scientific_journal-5305	27	8	derive	derive	VERB
american_scientific_journal-5305	27	9	the	the	DET
american_scientific_journal-5305	27	10	general	general	ADJ
american_scientific_journal-5305	27	11	solution	solution	NOUN
american_scientific_journal-5305	27	12	of	of	ADP
american_scientific_journal-5305	27	13	noether‟s	noether‟s	PROPN
american_scientific_journal-5305	27	14	variational	variational	ADJ
american_scientific_journal-5305	27	15	problem	problem	NOUN
american_scientific_journal-5305	27	16	,	,	PUNCT
american_scientific_journal-5305	27	17	we	we	PRON
american_scientific_journal-5305	27	18	begin	begin	VERB
american_scientific_journal-5305	27	19	by	by	ADP
american_scientific_journal-5305	27	20	considering	consider	VERB
american_scientific_journal-5305	27	21	the	the	DET
american_scientific_journal-5305	27	22	variation	variation	NOUN
american_scientific_journal-5305	27	23	in	in	ADP
american_scientific_journal-5305	27	24	the	the	DET
american_scientific_journal-5305	27	25	action	action	NOUN
american_scientific_journal-5305	27	26	arising	arise	VERB
american_scientific_journal-5305	27	27	from	from	ADP
american_scientific_journal-5305	27	28	a	a	DET
american_scientific_journal-5305	27	29	variation	variation	NOUN
american_scientific_journal-5305	27	30	of	of	ADP
american_scientific_journal-5305	27	31	the	the	DET
american_scientific_journal-5305	27	32	both	both	CCONJ
american_scientific_journal-5305	27	33	dependent	dependent	ADJ
american_scientific_journal-5305	27	34	and	and	CCONJ
american_scientific_journal-5305	27	35	the	the	DET
american_scientific_journal-5305	27	36	independent	independent	ADJ
american_scientific_journal-5305	27	37	variables	variable	NOUN
american_scientific_journal-5305	27	38	:	:	PUNCT
american_scientific_journal-5305	27	39	∫	∫	PROPN
american_scientific_journal-5305	27	40	{	{	PUNCT
american_scientific_journal-5305	27	41	(	(	PUNCT
american_scientific_journal-5305	27	42	̇	̇	PROPN
american_scientific_journal-5305	27	43	)	)	PUNCT
american_scientific_journal-5305	27	44	∫	∫	PROPN
american_scientific_journal-5305	27	45	(	(	PUNCT
american_scientific_journal-5305	27	46	̇	̇	PROPN
american_scientific_journal-5305	27	47	(	(	PUNCT
american_scientific_journal-5305	27	48	is	be	AUX
american_scientific_journal-5305	27	49	over	over	ADP
american_scientific_journal-5305	27	50	compact	compact	ADJ
american_scientific_journal-5305	27	51	space	space	NOUN
american_scientific_journal-5305	27	52	-	-	PUNCT
american_scientific_journal-5305	27	53	time	time	NOUN
american_scientific_journal-5305	27	54	regions	region	NOUN
american_scientific_journal-5305	27	55	r	r	NOUN
american_scientific_journal-5305	27	56	and	and	CCONJ
american_scientific_journal-5305	27	57	,	,	PUNCT
american_scientific_journal-5305	27	58	bounded	bound	VERB
american_scientific_journal-5305	27	59	by	by	ADP
american_scientific_journal-5305	27	60	initial	initial	ADJ
american_scientific_journal-5305	27	61	and	and	CCONJ
american_scientific_journal-5305	27	62	final	final	ADJ
american_scientific_journal-5305	27	63	space	space	NOUN
american_scientific_journal-5305	27	64	–	–	PUNCT
american_scientific_journal-5305	27	65	like	like	ADP
american_scientific_journal-5305	27	66	surfaces	surface	NOUN
american_scientific_journal-5305	27	67	,	,	PUNCT
american_scientific_journal-5305	27	68	the	the	DET
american_scientific_journal-5305	27	69	original	original	NOUN
american_scientific_journal-5305	27	70	of	of	ADP
american_scientific_journal-5305	27	71	integration	integration	NOUN
american_scientific_journal-5305	27	72	r	r	NOUN
american_scientific_journal-5305	27	73	being	be	AUX
american_scientific_journal-5305	27	74	mapped	map	VERB
american_scientific_journal-5305	27	75	to	to	ADP
american_scientific_journal-5305	27	76	the	the	DET
american_scientific_journal-5305	27	77	new	new	ADJ
american_scientific_journal-5305	27	78	region	region	NOUN
american_scientific_journal-5305	27	79	of	of	ADP
american_scientific_journal-5305	27	80	integration	integration	NOUN
american_scientific_journal-5305	27	81	by	by	ADP
american_scientific_journal-5305	27	82	the	the	DET
american_scientific_journal-5305	27	83	point	point	NOUN
american_scientific_journal-5305	27	84	transformations	transformation	NOUN
american_scientific_journal-5305	27	85	corresponding	correspond	VERB
american_scientific_journal-5305	27	86	to	to	ADP
american_scientific_journal-5305	27	87	(	(	PUNCT
american_scientific_journal-5305	27	88	(	(	PUNCT
american_scientific_journal-5305	27	89	(	(	PUNCT
american_scientific_journal-5305	27	90	we	we	PRON
american_scientific_journal-5305	27	91	perform	perform	VERB
american_scientific_journal-5305	27	92	a	a	DET
american_scientific_journal-5305	27	93	change	change	NOUN
american_scientific_journal-5305	27	94	of	of	ADP
american_scientific_journal-5305	27	95	variables	variable	NOUN
american_scientific_journal-5305	27	96	in	in	ADP
american_scientific_journal-5305	27	97	order	order	NOUN
american_scientific_journal-5305	27	98	to	to	PART
american_scientific_journal-5305	27	99	make	make	VERB
american_scientific_journal-5305	27	100	the	the	DET
american_scientific_journal-5305	27	101	regions	region	NOUN
american_scientific_journal-5305	27	102	of	of	ADP
american_scientific_journal-5305	27	103	integration	integration	NOUN
american_scientific_journal-5305	27	104	the	the	DET
american_scientific_journal-5305	27	105	same	same	ADJ
american_scientific_journal-5305	27	106	:	:	PUNCT
american_scientific_journal-5305	27	107	∫	∫	PROPN
american_scientific_journal-5305	27	108	(	(	PUNCT
american_scientific_journal-5305	27	109	̇	̇	PROPN
american_scientific_journal-5305	27	110	(	(	PUNCT
american_scientific_journal-5305	27	111	̇	̇	PROPN
american_scientific_journal-5305	27	112	(	(	PUNCT
american_scientific_journal-5305	27	113	-∫	-∫	NUM
american_scientific_journal-5305	27	114	(	(	PUNCT
american_scientific_journal-5305	27	115	̇	̇	PROPN
american_scientific_journal-5305	27	116	.	.	PUNCT
american_scientific_journal-5305	28	1	(	(	PUNCT
american_scientific_journal-5305	28	2	3.3	3.3	NUM
american_scientific_journal-5305	28	3	)	)	PUNCT
american_scientific_journal-5305	28	4	where	where	SCONJ
american_scientific_journal-5305	28	5	the	the	DET
american_scientific_journal-5305	28	6	transformation	transformation	NOUN
american_scientific_journal-5305	28	7	of	of	ADP
american_scientific_journal-5305	28	8	the	the	DET
american_scientific_journal-5305	28	9	volume	volume	NOUN
american_scientific_journal-5305	28	10	element	element	NOUN
american_scientific_journal-5305	28	11	proceeds	proceed	NOUN
american_scientific_journal-5305	28	12	via	via	ADP
american_scientific_journal-5305	28	13	the	the	DET
american_scientific_journal-5305	28	14	jacobian	jacobian	PROPN
american_scientific_journal-5305	28	15	⁄	⁄	PROPN
american_scientific_journal-5305	28	16	and	and	CCONJ
american_scientific_journal-5305	28	17	is	be	AUX
american_scientific_journal-5305	28	18	correct	correct	ADJ
american_scientific_journal-5305	28	19	to	to	ADP
american_scientific_journal-5305	28	20	first	first	ADJ
american_scientific_journal-5305	28	21	-	-	PUNCT
american_scientific_journal-5305	28	22	order	order	NOUN
american_scientific_journal-5305	28	23	.	.	PUNCT
american_scientific_journal-5305	29	1	hence	hence	ADV
american_scientific_journal-5305	29	2	,	,	PUNCT
american_scientific_journal-5305	29	3	to	to	ADP
american_scientific_journal-5305	29	4	first	first	ADJ
american_scientific_journal-5305	29	5	order	order	NOUN
american_scientific_journal-5305	29	6	∫	∫	PROPN
american_scientific_journal-5305	29	7	(	(	PUNCT
american_scientific_journal-5305	29	8	̇	̇	PROPN
american_scientific_journal-5305	29	9	(	(	PUNCT
american_scientific_journal-5305	29	10	̇	̇	PROPN
american_scientific_journal-5305	29	11	(	(	PUNCT
american_scientific_journal-5305	29	12	.	.	PUNCT
american_scientific_journal-5305	29	13	(	(	PUNCT
american_scientific_journal-5305	29	14	3.4	3.4	NUM
american_scientific_journal-5305	29	15	)	)	PUNCT
american_scientific_journal-5305	29	16	american	american	ADJ
american_scientific_journal-5305	29	17	scientific	scientific	ADJ
american_scientific_journal-5305	29	18	research	research	NOUN
american_scientific_journal-5305	29	19	journal	journal	NOUN
american_scientific_journal-5305	29	20	for	for	ADP
american_scientific_journal-5305	29	21	engineering	engineering	NOUN
american_scientific_journal-5305	29	22	,	,	PUNCT
american_scientific_journal-5305	29	23	technology	technology	NOUN
american_scientific_journal-5305	29	24	,	,	PUNCT
american_scientific_journal-5305	29	25	and	and	CCONJ
american_scientific_journal-5305	29	26	sciences	science	NOUN
american_scientific_journal-5305	29	27	(	(	PUNCT
american_scientific_journal-5305	29	28	asrjets	asrjet	NOUN
american_scientific_journal-5305	29	29	)	)	PUNCT
american_scientific_journal-5305	29	30	(	(	PUNCT
american_scientific_journal-5305	29	31	2019	2019	NUM
american_scientific_journal-5305	29	32	)	)	PUNCT
american_scientific_journal-5305	29	33	volume	volume	NOUN
american_scientific_journal-5305	29	34	61	61	NUM
american_scientific_journal-5305	29	35	,	,	PUNCT
american_scientific_journal-5305	29	36	no	no	DET
american_scientific_journal-5305	29	37	1	1	NUM
american_scientific_journal-5305	29	38	,	,	PUNCT
american_scientific_journal-5305	29	39	pp	pp	ADV
american_scientific_journal-5305	29	40	268	268	NUM
american_scientific_journal-5305	29	41	-	-	SYM
american_scientific_journal-5305	29	42	279	279	NUM
american_scientific_journal-5305	29	43	872	872	NUM
american_scientific_journal-5305	29	44	for	for	ADP
american_scientific_journal-5305	29	45	the	the	DET
american_scientific_journal-5305	29	46	first	first	ADJ
american_scientific_journal-5305	29	47	term	term	NOUN
american_scientific_journal-5305	29	48	,	,	PUNCT
american_scientific_journal-5305	29	49	we	we	PRON
american_scientific_journal-5305	29	50	use	use	VERB
american_scientific_journal-5305	29	51	taylor	taylor	NOUN
american_scientific_journal-5305	29	52	expansions	expansion	NOUN
american_scientific_journal-5305	29	53	for	for	ADP
american_scientific_journal-5305	29	54	in	in	ADP
american_scientific_journal-5305	29	55	each	each	PRON
american_scientific_journal-5305	29	56	of	of	ADP
american_scientific_journal-5305	29	57	the	the	DET
american_scientific_journal-5305	29	58	variables	variable	NOUN
american_scientific_journal-5305	29	59	on	on	ADP
american_scientific_journal-5305	29	60	which	which	PRON
american_scientific_journal-5305	29	61	depends	depend	VERB
american_scientific_journal-5305	29	62	,	,	PUNCT
american_scientific_journal-5305	29	63	and	and	CCONJ
american_scientific_journal-5305	29	64	again	again	ADV
american_scientific_journal-5305	29	65	impose	impose	VERB
american_scientific_journal-5305	29	66	the	the	DET
american_scientific_journal-5305	29	67	requirement	requirement	NOUN
american_scientific_journal-5305	29	68	that	that	SCONJ
american_scientific_journal-5305	29	69	we	we	PRON
american_scientific_journal-5305	29	70	are	be	AUX
american_scientific_journal-5305	29	71	considering	consider	VERB
american_scientific_journal-5305	29	72	first	first	ADJ
american_scientific_journal-5305	29	73	-	-	PUNCT
american_scientific_journal-5305	29	74	order	order	NOUN
american_scientific_journal-5305	29	75	variations	variation	NOUN
american_scientific_journal-5305	29	76	,	,	PUNCT
american_scientific_journal-5305	29	77	therefore	therefore	ADV
american_scientific_journal-5305	29	78	restricting	restrict	VERB
american_scientific_journal-5305	29	79	ourselves	ourselves	PRON
american_scientific_journal-5305	29	80	to	to	PART
american_scientific_journal-5305	29	81	firstorder	firstorder	VERB
american_scientific_journal-5305	29	82	taylor	taylor	PROPN
american_scientific_journal-5305	29	83	expansions	expansion	NOUN
american_scientific_journal-5305	29	84	.	.	PUNCT
american_scientific_journal-5305	30	1	thus	thus	ADV
american_scientific_journal-5305	30	2	:	:	PUNCT
american_scientific_journal-5305	30	3	∫∑	∫∑	NOUN
american_scientific_journal-5305	30	4	{	{	PUNCT
american_scientific_journal-5305	30	5	(	(	PUNCT
american_scientific_journal-5305	30	6	(	(	PUNCT
american_scientific_journal-5305	30	7	+	+	ADV
american_scientific_journal-5305	30	8	(	(	PUNCT
american_scientific_journal-5305	30	9	+	+	CCONJ
american_scientific_journal-5305	30	10	(	(	PUNCT
american_scientific_journal-5305	30	11	}	}	PUNCT
american_scientific_journal-5305	30	12	=	=	SYM
american_scientific_journal-5305	30	13	∫∑	∫∑	NOUN
american_scientific_journal-5305	30	14	{	{	PUNCT
american_scientific_journal-5305	30	15	(	(	PUNCT
american_scientific_journal-5305	30	16	(	(	PUNCT
american_scientific_journal-5305	30	17	+	+	X
american_scientific_journal-5305	30	18	(	(	PUNCT
american_scientific_journal-5305	30	19	}	}	PUNCT
american_scientific_journal-5305	30	20	.	.	PUNCT
american_scientific_journal-5305	31	1	(	(	PUNCT
american_scientific_journal-5305	31	2	3.5	3.5	NUM
american_scientific_journal-5305	31	3	)	)	PUNCT
american_scientific_journal-5305	31	4	then	then	ADV
american_scientific_journal-5305	31	5	,	,	PUNCT
american_scientific_journal-5305	31	6	since	since	SCONJ
american_scientific_journal-5305	31	7	=	=	PRON
american_scientific_journal-5305	31	8	(	(	PUNCT
american_scientific_journal-5305	31	9	(	(	PUNCT
american_scientific_journal-5305	31	10	(	(	PUNCT
american_scientific_journal-5305	31	11	(	(	PUNCT
american_scientific_journal-5305	31	12	(	(	PUNCT
american_scientific_journal-5305	31	13	is	be	AUX
american_scientific_journal-5305	31	14	(	(	PUNCT
american_scientific_journal-5305	31	15	(	(	PUNCT
american_scientific_journal-5305	31	16	(	(	PUNCT
american_scientific_journal-5305	31	17	we	we	PRON
american_scientific_journal-5305	31	18	get	get	VERB
american_scientific_journal-5305	31	19	:	:	PUNCT
american_scientific_journal-5305	31	20	∫∑	∫∑	NOUN
american_scientific_journal-5305	31	21	{	{	PUNCT
american_scientific_journal-5305	31	22	(	(	PUNCT
american_scientific_journal-5305	31	23	(	(	PUNCT
american_scientific_journal-5305	31	24	+	+	X
american_scientific_journal-5305	31	25	(	(	PUNCT
american_scientific_journal-5305	31	26	}	}	PUNCT
american_scientific_journal-5305	31	27	.	.	PUNCT
american_scientific_journal-5305	32	1	(	(	PUNCT
american_scientific_journal-5305	32	2	3.7	3.7	NUM
american_scientific_journal-5305	32	3	)	)	PUNCT
american_scientific_journal-5305	32	4	=	=	NOUN
american_scientific_journal-5305	32	5	∫∑	∫∑	X
american_scientific_journal-5305	32	6	{	{	PUNCT
american_scientific_journal-5305	32	7	(	(	PUNCT
american_scientific_journal-5305	32	8	(	(	PUNCT
american_scientific_journal-5305	32	9	)	)	PUNCT
american_scientific_journal-5305	32	10	)	)	PUNCT
american_scientific_journal-5305	32	11	(	(	PUNCT
american_scientific_journal-5305	32	12	(	(	PUNCT
american_scientific_journal-5305	32	13	)	)	PUNCT
american_scientific_journal-5305	32	14	+	+	CCONJ
american_scientific_journal-5305	32	15	(	(	PUNCT
american_scientific_journal-5305	32	16	}	}	PUNCT
american_scientific_journal-5305	32	17	=	=	NOUN
american_scientific_journal-5305	32	18	∫∑	∫∑	NOUN
american_scientific_journal-5305	32	19	{	{	PUNCT
american_scientific_journal-5305	32	20	(	(	PUNCT
american_scientific_journal-5305	32	21	(	(	PUNCT
american_scientific_journal-5305	32	22	(	(	PUNCT
american_scientific_journal-5305	32	23	(	(	PUNCT
american_scientific_journal-5305	32	24	)	)	PUNCT
american_scientific_journal-5305	32	25	thus	thus	ADV
american_scientific_journal-5305	32	26	,	,	PUNCT
american_scientific_journal-5305	32	27	the	the	DET
american_scientific_journal-5305	32	28	variation	variation	NOUN
american_scientific_journal-5305	32	29	in	in	ADP
american_scientific_journal-5305	32	30	the	the	DET
american_scientific_journal-5305	32	31	action	action	NOUN
american_scientific_journal-5305	32	32	consists	consist	VERB
american_scientific_journal-5305	32	33	of	of	ADP
american_scientific_journal-5305	32	34	an	an	DET
american_scientific_journal-5305	32	35	“	"	PUNCT
american_scientific_journal-5305	32	36	interior	interior	ADJ
american_scientific_journal-5305	32	37	”	"	PUNCT
american_scientific_journal-5305	32	38	term	term	NOUN
american_scientific_journal-5305	32	39	(	(	PUNCT
american_scientific_journal-5305	32	40	the	the	DET
american_scientific_journal-5305	32	41	first	first	ADJ
american_scientific_journal-5305	32	42	term	term	NOUN
american_scientific_journal-5305	32	43	)	)	PUNCT
american_scientific_journal-5305	32	44	and	and	CCONJ
american_scientific_journal-5305	32	45	a	a	DET
american_scientific_journal-5305	32	46	„	„	PUNCT
american_scientific_journal-5305	32	47	boundary‟	boundary‟	NOUN
american_scientific_journal-5305	32	48	term	term	NOUN
american_scientific_journal-5305	32	49	(	(	PUNCT
american_scientific_journal-5305	32	50	the	the	DET
american_scientific_journal-5305	32	51	second	second	ADJ
american_scientific_journal-5305	32	52	terms	term	NOUN
american_scientific_journal-5305	32	53	)	)	PUNCT
american_scientific_journal-5305	32	54	.	.	PUNCT
american_scientific_journal-5305	33	1	finally	finally	ADV
american_scientific_journal-5305	33	2	,	,	PUNCT
american_scientific_journal-5305	33	3	we	we	PRON
american_scientific_journal-5305	33	4	reach	reach	VERB
american_scientific_journal-5305	33	5	the	the	DET
american_scientific_journal-5305	33	6	following	follow	VERB
american_scientific_journal-5305	33	7	solution	solution	NOUN
american_scientific_journal-5305	33	8	of	of	ADP
american_scientific_journal-5305	33	9	noether‟s	noether‟s	PROPN
american_scientific_journal-5305	33	10	variational	variational	ADJ
american_scientific_journal-5305	33	11	problem	problem	NOUN
american_scientific_journal-5305	33	12	:	:	PUNCT
american_scientific_journal-5305	33	13	∑	∑	PUNCT
american_scientific_journal-5305	33	14	(	(	PUNCT
american_scientific_journal-5305	33	15	(	(	PUNCT
american_scientific_journal-5305	33	16	)	)	PUNCT
american_scientific_journal-5305	33	17	)	)	PUNCT
american_scientific_journal-5305	33	18	̇	̇	VERB
american_scientific_journal-5305	33	19	∑	∑	PROPN
american_scientific_journal-5305	33	20	(	(	PUNCT
american_scientific_journal-5305	33	21	(	(	PUNCT
american_scientific_journal-5305	33	22	)	)	PUNCT
american_scientific_journal-5305	33	23	)	)	PUNCT
american_scientific_journal-5305	33	24	(	(	PUNCT
american_scientific_journal-5305	33	25	3.8	3.8	NUM
american_scientific_journal-5305	33	26	)	)	PUNCT
american_scientific_journal-5305	33	27	here	here	ADV
american_scientific_journal-5305	33	28	we	we	PRON
american_scientific_journal-5305	33	29	have	have	AUX
american_scientific_journal-5305	33	30	used	use	VERB
american_scientific_journal-5305	33	31	the	the	DET
american_scientific_journal-5305	33	32	symbol	symbol	NOUN
american_scientific_journal-5305	33	33	„	„	PUNCT
american_scientific_journal-5305	33	34	̇‟to	̇‟to	X
american_scientific_journal-5305	33	35	indicate	indicate	VERB
american_scientific_journal-5305	33	36	that	that	SCONJ
american_scientific_journal-5305	33	37	this	this	DET
american_scientific_journal-5305	33	38	relation	relation	NOUN
american_scientific_journal-5305	33	39	has	have	AUX
american_scientific_journal-5305	33	40	been	be	AUX
american_scientific_journal-5305	33	41	derived	derive	VERB
american_scientific_journal-5305	33	42	without	without	ADP
american_scientific_journal-5305	33	43	using	use	VERB
american_scientific_journal-5305	33	44	any	any	DET
american_scientific_journal-5305	33	45	eulerlagrange	eulerlagrange	NOUN
american_scientific_journal-5305	33	46	equations	equation	NOUN
american_scientific_journal-5305	33	47	.	.	PUNCT
american_scientific_journal-5305	34	1	if	if	SCONJ
american_scientific_journal-5305	34	2	the	the	DET
american_scientific_journal-5305	34	3	euler	euler	PROPN
american_scientific_journal-5305	34	4	-	-	PUNCT
american_scientific_journal-5305	34	5	lagrange	lagrange	NOUN
american_scientific_journal-5305	34	6	equations	equation	NOUN
american_scientific_journal-5305	34	7	are	be	AUX
american_scientific_journal-5305	34	8	satisfied	satisfied	ADJ
american_scientific_journal-5305	34	9	by	by	ADP
american_scientific_journal-5305	34	10	all	all	DET
american_scientific_journal-5305	34	11	the	the	DET
american_scientific_journal-5305	34	12	dependent	dependent	ADJ
american_scientific_journal-5305	34	13	variables	variable	NOUN
american_scientific_journal-5305	34	14	involved	involve	VERB
american_scientific_journal-5305	34	15	in	in	ADP
american_scientific_journal-5305	34	16	the	the	DET
american_scientific_journal-5305	34	17	variation	variation	NOUN
american_scientific_journal-5305	34	18	,	,	PUNCT
american_scientific_journal-5305	34	19	then	then	ADV
american_scientific_journal-5305	34	20	(	(	PUNCT
american_scientific_journal-5305	34	21	3.8	3.8	NUM
american_scientific_journal-5305	34	22	)	)	PUNCT
american_scientific_journal-5305	34	23	becomes	become	VERB
american_scientific_journal-5305	34	24	:	:	PUNCT
american_scientific_journal-5305	34	25	∑	∑	PUNCT
american_scientific_journal-5305	34	26	(	(	PUNCT
american_scientific_journal-5305	34	27	(	(	PUNCT
american_scientific_journal-5305	34	28	)	)	PUNCT
american_scientific_journal-5305	34	29	)	)	PUNCT
american_scientific_journal-5305	35	1	(	(	PUNCT
american_scientific_journal-5305	35	2	american	american	PROPN
american_scientific_journal-5305	35	3	scientific	scientific	ADJ
american_scientific_journal-5305	35	4	research	research	NOUN
american_scientific_journal-5305	35	5	journal	journal	NOUN
american_scientific_journal-5305	35	6	for	for	ADP
american_scientific_journal-5305	35	7	engineering	engineering	NOUN
american_scientific_journal-5305	35	8	,	,	PUNCT
american_scientific_journal-5305	35	9	technology	technology	NOUN
american_scientific_journal-5305	35	10	,	,	PUNCT
american_scientific_journal-5305	35	11	and	and	CCONJ
american_scientific_journal-5305	35	12	sciences	science	NOUN
american_scientific_journal-5305	35	13	(	(	PUNCT
american_scientific_journal-5305	35	14	asrjets	asrjet	NOUN
american_scientific_journal-5305	35	15	)	)	PUNCT
american_scientific_journal-5305	35	16	(	(	PUNCT
american_scientific_journal-5305	35	17	2019	2019	NUM
american_scientific_journal-5305	35	18	)	)	PUNCT
american_scientific_journal-5305	35	19	volume	volume	NOUN
american_scientific_journal-5305	35	20	61	61	NUM
american_scientific_journal-5305	35	21	,	,	PUNCT
american_scientific_journal-5305	35	22	no	no	DET
american_scientific_journal-5305	35	23	1	1	NUM
american_scientific_journal-5305	35	24	,	,	PUNCT
american_scientific_journal-5305	35	25	pp	pp	ADV
american_scientific_journal-5305	35	26	268	268	NUM
american_scientific_journal-5305	35	27	-	-	SYM
american_scientific_journal-5305	35	28	279	279	NUM
american_scientific_journal-5305	35	29	878	878	NUM
american_scientific_journal-5305	35	30	the	the	DET
american_scientific_journal-5305	35	31	analogous	analogous	ADJ
american_scientific_journal-5305	35	32	expressions	expression	NOUN
american_scientific_journal-5305	35	33	for	for	ADP
american_scientific_journal-5305	35	34	lagrangians	lagrangians	PROPN
american_scientific_journal-5305	35	35	,	,	PUNCT
american_scientific_journal-5305	35	36	rather	rather	ADV
american_scientific_journal-5305	35	37	than	than	ADP
american_scientific_journal-5305	35	38	lagrangian	lagrangian	ADJ
american_scientific_journal-5305	35	39	densities	density	NOUN
american_scientific_journal-5305	35	40	,	,	PUNCT
american_scientific_journal-5305	35	41	are	be	AUX
american_scientific_journal-5305	35	42	:	:	PUNCT
american_scientific_journal-5305	35	43	∑	∑	PUNCT
american_scientific_journal-5305	35	44	(	(	PUNCT
american_scientific_journal-5305	35	45	̇	̇	PROPN
american_scientific_journal-5305	35	46	)	)	PUNCT
american_scientific_journal-5305	35	47	̇	̇	VERB
american_scientific_journal-5305	35	48	∑	∑	PROPN
american_scientific_journal-5305	35	49	(	(	PUNCT
american_scientific_journal-5305	35	50	̇	̇	PROPN
american_scientific_journal-5305	35	51	)	)	PUNCT
american_scientific_journal-5305	35	52	(	(	PUNCT
american_scientific_journal-5305	35	53	and	and	CCONJ
american_scientific_journal-5305	35	54	,	,	PUNCT
american_scientific_journal-5305	35	55	when	when	SCONJ
american_scientific_journal-5305	35	56	euler	euler	NOUN
american_scientific_journal-5305	35	57	-	-	PUNCT
american_scientific_journal-5305	35	58	lagrange	lagrange	NOUN
american_scientific_journal-5305	35	59	equations	equation	NOUN
american_scientific_journal-5305	35	60	satisfied	satisfy	VERB
american_scientific_journal-5305	35	61	by	by	ADP
american_scientific_journal-5305	35	62	all	all	DET
american_scientific_journal-5305	35	63	the	the	PRON
american_scientific_journal-5305	35	64	,	,	PUNCT
american_scientific_journal-5305	35	65	∑	∑	PROPN
american_scientific_journal-5305	35	66	(	(	PUNCT
american_scientific_journal-5305	35	67	̇	̇	PROPN
american_scientific_journal-5305	35	68	)	)	PUNCT
american_scientific_journal-5305	35	69	(	(	PUNCT
american_scientific_journal-5305	35	70	this	this	PRON
american_scientific_journal-5305	35	71	concludes	conclude	VERB
american_scientific_journal-5305	35	72	the	the	DET
american_scientific_journal-5305	35	73	derivation	derivation	NOUN
american_scientific_journal-5305	35	74	of	of	ADP
american_scientific_journal-5305	35	75	the	the	DET
american_scientific_journal-5305	35	76	general	general	ADJ
american_scientific_journal-5305	35	77	solution	solution	NOUN
american_scientific_journal-5305	35	78	to	to	ADP
american_scientific_journal-5305	35	79	noether‟s	noether‟s	PROPN
american_scientific_journal-5305	35	80	variational	variational	ADJ
american_scientific_journal-5305	35	81	problem	problem	NOUN
american_scientific_journal-5305	35	82	in	in	ADP
american_scientific_journal-5305	35	83	its	its	PRON
american_scientific_journal-5305	35	84	original	original	ADJ
american_scientific_journal-5305	35	85	form	form	NOUN
american_scientific_journal-5305	35	86	.	.	PUNCT
american_scientific_journal-5305	36	1	3.1	3.1	NUM
american_scientific_journal-5305	36	2	.	.	PUNCT
american_scientific_journal-5305	36	3	eulerlagrange	eulerlagrange	NOUN
american_scientific_journal-5305	36	4	equations	equation	NOUN
american_scientific_journal-5305	36	5	consider	consider	VERB
american_scientific_journal-5305	36	6	independent	independent	ADJ
american_scientific_journal-5305	36	7	variables	variable	NOUN
american_scientific_journal-5305	36	8	x	x	PUNCT
american_scientific_journal-5305	36	9	=	=	SYM
american_scientific_journal-5305	36	10	(	(	PUNCT
american_scientific_journal-5305	36	11	)	)	PUNCT
american_scientific_journal-5305	36	12	=	=	SYM
american_scientific_journal-5305	36	13	(	(	PUNCT
american_scientific_journal-5305	36	14	and	and	CCONJ
american_scientific_journal-5305	36	15	dependent	dependent	ADJ
american_scientific_journal-5305	36	16	differential	differential	NOUN
american_scientific_journal-5305	36	17	variables	variable	NOUN
american_scientific_journal-5305	36	18	u	u	NOUN
american_scientific_journal-5305	36	19	=	=	PUNCT
american_scientific_journal-5305	36	20	(	(	PUNCT
american_scientific_journal-5305	36	21	)	)	PUNCT
american_scientific_journal-5305	36	22	=	=	SYM
american_scientific_journal-5305	37	1	(	(	PUNCT
american_scientific_journal-5305	37	2	.	.	PUNCT
american_scientific_journal-5305	37	3	consider	consider	VERB
american_scientific_journal-5305	37	4	the	the	DET
american_scientific_journal-5305	37	5	variation	variation	NOUN
american_scientific_journal-5305	37	6	(	(	PUNCT
american_scientific_journal-5305	37	7	x	x	NOUN
american_scientific_journal-5305	37	8	,	,	PUNCT
american_scientific_journal-5305	37	9	u	u	NOUN
american_scientific_journal-5305	37	10	)	)	PUNCT
american_scientific_journal-5305	37	11	,	,	PUNCT
american_scientific_journal-5305	37	12	compute	compute	VERB
american_scientific_journal-5305	37	13	the	the	DET
american_scientific_journal-5305	37	14	variation	variation	NOUN
american_scientific_journal-5305	37	15	of	of	ADP
american_scientific_journal-5305	37	16	that	that	PRON
american_scientific_journal-5305	37	17	of	of	ADP
american_scientific_journal-5305	37	18	i	i	PRON
american_scientific_journal-5305	37	19	=	=	PUNCT
american_scientific_journal-5305	38	1	∫	∫	PROPN
american_scientific_journal-5305	38	2	∫	∫	PROPN
american_scientific_journal-5305	38	3	(	(	PUNCT
american_scientific_journal-5305	38	4	)	)	PUNCT
american_scientific_journal-5305	38	5	.	.	PUNCT
american_scientific_journal-5305	39	1	(	(	PUNCT
american_scientific_journal-5305	39	2	3.12	3.12	NUM
american_scientific_journal-5305	39	3	)	)	PUNCT
american_scientific_journal-5305	39	4	use	use	NOUN
american_scientific_journal-5305	39	5	integration	integration	NOUN
american_scientific_journal-5305	39	6	by	by	ADP
american_scientific_journal-5305	39	7	parts	part	NOUN
american_scientific_journal-5305	39	8	to	to	PART
american_scientific_journal-5305	39	9	obtain	obtain	VERB
american_scientific_journal-5305	39	10	the	the	DET
american_scientific_journal-5305	39	11	euler	euler	NOUN
american_scientific_journal-5305	39	12	-	-	PUNCT
american_scientific_journal-5305	39	13	lagrange	lagrange	NOUN
american_scientific_journal-5305	39	14	equation	equation	NOUN
american_scientific_journal-5305	39	15	.	.	PUNCT
american_scientific_journal-5305	40	1	in	in	ADP
american_scientific_journal-5305	40	2	the	the	DET
american_scientific_journal-5305	40	3	case	case	NOUN
american_scientific_journal-5305	40	4	x	x	X
american_scientific_journal-5305	40	5	=	=	SYM
american_scientific_journal-5305	40	6	t	t	PROPN
american_scientific_journal-5305	40	7	,	,	PUNCT
american_scientific_journal-5305	40	8	u	u	NOUN
american_scientific_journal-5305	40	9	=	=	NOUN
american_scientific_journal-5305	40	10	q	q	NOUN
american_scientific_journal-5305	41	1	=	=	PUNCT
american_scientific_journal-5305	41	2	(	(	PUNCT
american_scientific_journal-5305	41	3	we	we	PRON
american_scientific_journal-5305	41	4	have	have	AUX
american_scientific_journal-5305	41	5	define	define	VERB
american_scientific_journal-5305	41	6	the	the	DET
american_scientific_journal-5305	41	7	variational	variational	ADJ
american_scientific_journal-5305	41	8	derivative	derivative	NOUN
american_scientific_journal-5305	41	9	of	of	ADP
american_scientific_journal-5305	41	10	also	also	ADV
american_scientific_journal-5305	41	11	called	call	VERB
american_scientific_journal-5305	41	12	euler	euler	NOUN
american_scientific_journal-5305	41	13	-	-	PUNCT
american_scientific_journal-5305	41	14	lagrange	lagrange	NOUN
american_scientific_journal-5305	41	15	derivative	derivative	NOUN
american_scientific_journal-5305	41	16	or	or	CCONJ
american_scientific_journal-5305	41	17	euler	euler	NOUN
american_scientific_journal-5305	41	18	-	-	PUNCT
american_scientific_journal-5305	41	19	lagrange	lagrange	NOUN
american_scientific_journal-5305	41	20	differential	differential	NOUN
american_scientific_journal-5305	41	21	.	.	PUNCT
american_scientific_journal-5305	42	1	denoted	denote	VERB
american_scientific_journal-5305	42	2	it	it	PRON
american_scientific_journal-5305	42	3	by	by	ADP
american_scientific_journal-5305	42	4	or	or	CCONJ
american_scientific_journal-5305	42	5	e	e	NOUN
american_scientific_journal-5305	42	6	.	.	PUNCT
american_scientific_journal-5305	43	1	a	a	DET
american_scientific_journal-5305	43	2	necessary	necessary	ADJ
american_scientific_journal-5305	43	3	condition	condition	NOUN
american_scientific_journal-5305	43	4	for	for	ADP
american_scientific_journal-5305	43	5	a	a	DET
american_scientific_journal-5305	43	6	map	map	NOUN
american_scientific_journal-5305	43	7	(	(	PUNCT
american_scientific_journal-5305	43	8	with	with	ADP
american_scientific_journal-5305	43	9	fixed	fix	VERB
american_scientific_journal-5305	43	10	value	value	NOUN
american_scientific_journal-5305	43	11	on	on	ADP
american_scientific_journal-5305	43	12	the	the	DET
american_scientific_journal-5305	43	13	boundary	boundary	NOUN
american_scientific_journal-5305	43	14	of	of	ADP
american_scientific_journal-5305	43	15	the	the	DET
american_scientific_journal-5305	43	16	domain	domain	NOUN
american_scientific_journal-5305	43	17	of	of	ADP
american_scientific_journal-5305	43	18	integration	integration	NOUN
american_scientific_journal-5305	43	19	to	to	PART
american_scientific_journal-5305	43	20	minimize	minimize	VERB
american_scientific_journal-5305	43	21	the	the	DET
american_scientific_journal-5305	43	22	integral	integral	ADJ
american_scientific_journal-5305	43	23	(	(	PUNCT
american_scientific_journal-5305	43	24	3.12	3.12	NUM
american_scientific_journal-5305	43	25	)	)	PUNCT
american_scientific_journal-5305	43	26	is	be	AUX
american_scientific_journal-5305	43	27	the	the	DET
american_scientific_journal-5305	43	28	euler	euler	NOUN
american_scientific_journal-5305	43	29	-	-	PUNCT
american_scientific_journal-5305	43	30	lagrange	lagrange	NOUN
american_scientific_journal-5305	43	31	equation	equation	NOUN
american_scientific_journal-5305	43	32	e	e	NOUN
american_scientific_journal-5305	44	1	=	=	NOUN
american_scientific_journal-5305	44	2	0	0	NUM
american_scientific_journal-5305	44	3	lagrangian	lagrangian	NOUN
american_scientific_journal-5305	44	4	of	of	ADP
american_scientific_journal-5305	44	5	order1	order1	NOUN
american_scientific_journal-5305	44	6	(	(	PUNCT
american_scientific_journal-5305	44	7	e	e	NOUN
american_scientific_journal-5305	44	8	=	=	SYM
american_scientific_journal-5305	44	9	=	=	PUNCT
american_scientific_journal-5305	44	10	̇	̇	VERB
american_scientific_journal-5305	44	11	.	.	PUNCT
american_scientific_journal-5305	45	1	(	(	PUNCT
american_scientific_journal-5305	45	2	3.13	3.13	NUM
american_scientific_journal-5305	45	3	)	)	PUNCT
american_scientific_journal-5305	45	4	the	the	DET
american_scientific_journal-5305	45	5	euler	euler	NOUN
american_scientific_journal-5305	45	6	-	-	PUNCT
american_scientific_journal-5305	45	7	lagrange	lagrange	NOUN
american_scientific_journal-5305	45	8	equation	equation	NOUN
american_scientific_journal-5305	45	9	in	in	ADP
american_scientific_journal-5305	45	10	this	this	DET
american_scientific_journal-5305	45	11	case	case	NOUN
american_scientific_journal-5305	45	12	is	be	AUX
american_scientific_journal-5305	45	13	̇	̇	VERB
american_scientific_journal-5305	45	14	(	(	PUNCT
american_scientific_journal-5305	45	15	lagrangian	lagrangian	NOUN
american_scientific_journal-5305	45	16	of	of	ADP
american_scientific_journal-5305	45	17	order	order	NOUN
american_scientific_journal-5305	45	18	k	k	X
american_scientific_journal-5305	45	19	(	(	PUNCT
american_scientific_journal-5305	45	20	e	e	NOUN
american_scientific_journal-5305	45	21	̇	̇	VERB
american_scientific_journal-5305	45	22	̈	̈	PUNCT
american_scientific_journal-5305	45	23	(	(	PUNCT
american_scientific_journal-5305	45	24	̇	̇	PROPN
american_scientific_journal-5305	45	25	(	(	PUNCT
american_scientific_journal-5305	45	26	(	(	PUNCT
american_scientific_journal-5305	45	27	the	the	DET
american_scientific_journal-5305	45	28	eulerlagrange	eulerlagrange	NOUN
american_scientific_journal-5305	45	29	equation	equation	NOUN
american_scientific_journal-5305	45	30	in	in	ADP
american_scientific_journal-5305	45	31	this	this	DET
american_scientific_journal-5305	45	32	case	case	NOUN
american_scientific_journal-5305	45	33	is	be	AUX
american_scientific_journal-5305	45	34	american	american	ADJ
american_scientific_journal-5305	45	35	scientific	scientific	ADJ
american_scientific_journal-5305	45	36	research	research	NOUN
american_scientific_journal-5305	45	37	journal	journal	NOUN
american_scientific_journal-5305	45	38	for	for	ADP
american_scientific_journal-5305	45	39	engineering	engineering	NOUN
american_scientific_journal-5305	45	40	,	,	PUNCT
american_scientific_journal-5305	45	41	technology	technology	NOUN
american_scientific_journal-5305	45	42	,	,	PUNCT
american_scientific_journal-5305	45	43	and	and	CCONJ
american_scientific_journal-5305	45	44	sciences	science	NOUN
american_scientific_journal-5305	45	45	(	(	PUNCT
american_scientific_journal-5305	45	46	asrjets	asrjet	NOUN
american_scientific_journal-5305	45	47	)	)	PUNCT
american_scientific_journal-5305	45	48	(	(	PUNCT
american_scientific_journal-5305	45	49	2019	2019	NUM
american_scientific_journal-5305	45	50	)	)	PUNCT
american_scientific_journal-5305	45	51	volume	volume	NOUN
american_scientific_journal-5305	45	52	61	61	NUM
american_scientific_journal-5305	45	53	,	,	PUNCT
american_scientific_journal-5305	45	54	no	no	DET
american_scientific_journal-5305	45	55	1	1	NUM
american_scientific_journal-5305	45	56	,	,	PUNCT
american_scientific_journal-5305	45	57	pp	pp	ADV
american_scientific_journal-5305	45	58	268	268	NUM
american_scientific_journal-5305	45	59	-	-	SYM
american_scientific_journal-5305	45	60	279	279	NUM
american_scientific_journal-5305	45	61	872	872	NUM
american_scientific_journal-5305	45	62	̇	̇	VERB
american_scientific_journal-5305	45	63	̈	̈	PUNCT
american_scientific_journal-5305	45	64	(	(	PUNCT
american_scientific_journal-5305	45	65	̇	̇	PROPN
american_scientific_journal-5305	45	66	(	(	PUNCT
american_scientific_journal-5305	45	67	(	(	PUNCT
american_scientific_journal-5305	45	68	3.2	3.2	NUM
american_scientific_journal-5305	45	69	.	.	PUNCT
american_scientific_journal-5305	46	1	symmetry	symmetry	NOUN
american_scientific_journal-5305	46	2	transformations	transformation	NOUN
american_scientific_journal-5305	46	3	expressed	express	VERB
american_scientific_journal-5305	46	4	through	through	ADP
american_scientific_journal-5305	46	5	invariance	invariance	NOUN
american_scientific_journal-5305	46	6	of	of	ADP
american_scientific_journal-5305	46	7	the	the	DET
american_scientific_journal-5305	46	8	lagrangian	lagrangian	ADJ
american_scientific_journal-5305	46	9	we	we	PRON
american_scientific_journal-5305	46	10	consider	consider	VERB
american_scientific_journal-5305	46	11	a	a	DET
american_scientific_journal-5305	46	12	continuous	continuous	ADJ
american_scientific_journal-5305	46	13	set	set	NOUN
american_scientific_journal-5305	46	14	of	of	ADP
american_scientific_journal-5305	46	15	time	time	NOUN
american_scientific_journal-5305	46	16	independent	independent	ADJ
american_scientific_journal-5305	46	17	coordinate	coordinate	NOUN
american_scientific_journal-5305	46	18	transformations	transformation	NOUN
american_scientific_journal-5305	46	19	(	(	PUNCT
american_scientific_journal-5305	46	20	(	(	PUNCT
american_scientific_journal-5305	46	21	and	and	CCONJ
american_scientific_journal-5305	46	22	assume	assume	VERB
american_scientific_journal-5305	46	23	this	this	PRON
american_scientific_journal-5305	46	24	to	to	PART
american_scientific_journal-5305	46	25	be	be	AUX
american_scientific_journal-5305	46	26	symmetry	symmetry	NOUN
american_scientific_journal-5305	46	27	transformation	transformation	NOUN
american_scientific_journal-5305	46	28	in	in	ADP
american_scientific_journal-5305	46	29	the	the	DET
american_scientific_journal-5305	46	30	sense	sense	NOUN
american_scientific_journal-5305	46	31	that	that	SCONJ
american_scientific_journal-5305	46	32	it	it	PRON
american_scientific_journal-5305	46	33	leaves	leave	VERB
american_scientific_journal-5305	46	34	the	the	DET
american_scientific_journal-5305	46	35	lagrangian	lagrangian	ADJ
american_scientific_journal-5305	46	36	invariant	invariant	ADJ
american_scientific_journal-5305	46	37	(	(	PUNCT
american_scientific_journal-5305	46	38	or	or	CCONJ
american_scientific_journal-5305	46	39	unchanged	unchanged	ADJ
american_scientific_journal-5305	46	40	)	)	PUNCT
american_scientific_journal-5305	46	41	,	,	PUNCT
american_scientific_journal-5305	46	42	(	(	PUNCT
american_scientific_journal-5305	46	43	,	,	PUNCT
american_scientific_journal-5305	46	44	̇	̇	PROPN
american_scientific_journal-5305	46	45	=	=	SYM
american_scientific_journal-5305	46	46	(	(	PUNCT
american_scientific_journal-5305	46	47	q	q	X
american_scientific_journal-5305	46	48	,	,	PUNCT
american_scientific_journal-5305	46	49	̇	̇	VERB
american_scientific_journal-5305	46	50	.	.	PUNCT
american_scientific_journal-5305	47	1	(	(	PUNCT
american_scientific_journal-5305	47	2	3.18	3.18	NUM
american_scientific_journal-5305	47	3	)	)	PUNCT
american_scientific_journal-5305	47	4	this	this	PRON
american_scientific_journal-5305	47	5	means	mean	VERB
american_scientific_journal-5305	47	6	that	that	SCONJ
american_scientific_journal-5305	47	7	the	the	DET
american_scientific_journal-5305	47	8	coordinate	coordinate	NOUN
american_scientific_journal-5305	47	9	transformation	transformation	NOUN
american_scientific_journal-5305	47	10	gives	give	VERB
american_scientific_journal-5305	47	11	a	a	DET
american_scientific_journal-5305	47	12	lagrangian	lagrangian	NOUN
american_scientific_journal-5305	47	13	with	with	ADP
american_scientific_journal-5305	47	14	same	same	ADJ
american_scientific_journal-5305	47	15	functional	functional	ADJ
american_scientific_journal-5305	47	16	dependence	dependence	NOUN
american_scientific_journal-5305	47	17	of	of	ADP
american_scientific_journal-5305	47	18	the	the	DET
american_scientific_journal-5305	47	19	new	new	ADJ
american_scientific_journal-5305	47	20	and	and	CCONJ
american_scientific_journal-5305	47	21	old	old	ADJ
american_scientific_journal-5305	47	22	variables	variable	NOUN
american_scientific_journal-5305	47	23	.	.	PUNCT
american_scientific_journal-5305	48	1	since	since	SCONJ
american_scientific_journal-5305	48	2	the	the	DET
american_scientific_journal-5305	48	3	lagrangian	lagrangian	ADJ
american_scientific_journal-5305	48	4	determines	determine	VERB
american_scientific_journal-5305	48	5	the	the	DET
american_scientific_journal-5305	48	6	form	form	NOUN
american_scientific_journal-5305	48	7	of	of	ADP
american_scientific_journal-5305	48	8	the	the	DET
american_scientific_journal-5305	48	9	equations	equation	NOUN
american_scientific_journal-5305	48	10	of	of	ADP
american_scientific_journal-5305	48	11	motion	motion	NOUN
american_scientific_journal-5305	48	12	(	(	PUNCT
american_scientific_journal-5305	48	13	the	the	DET
american_scientific_journal-5305	48	14	lagrange	lagrange	PROPN
american_scientific_journal-5305	48	15	equation	equation	NOUN
american_scientific_journal-5305	48	16	)	)	PUNCT
american_scientific_journal-5305	48	17	,	,	PUNCT
american_scientific_journal-5305	48	18	it	it	PRON
american_scientific_journal-5305	48	19	follows	follow	VERB
american_scientific_journal-5305	48	20	that	that	SCONJ
american_scientific_journal-5305	48	21	a	a	DET
american_scientific_journal-5305	48	22	physical	physical	ADJ
american_scientific_journal-5305	48	23	time	time	NOUN
american_scientific_journal-5305	48	24	evolution	evolution	NOUN
american_scientific_journal-5305	48	25	is	be	AUX
american_scientific_journal-5305	48	26	described	describe	VERB
american_scientific_journal-5305	48	27	by	by	ADP
american_scientific_journal-5305	48	28	coordinates	coordinate	NOUN
american_scientific_journal-5305	48	29	q(t	q(t	PROPN
american_scientific_journal-5305	48	30	)	)	PUNCT
american_scientific_journal-5305	48	31	and	and	CCONJ
american_scientific_journal-5305	48	32	(	(	PUNCT
american_scientific_journal-5305	48	33	that	that	PRON
american_scientific_journal-5305	48	34	satisfy	satisfy	VERB
american_scientific_journal-5305	48	35	the	the	DET
american_scientific_journal-5305	48	36	same	same	ADJ
american_scientific_journal-5305	48	37	equations	equation	NOUN
american_scientific_journal-5305	48	38	of	of	ADP
american_scientific_journal-5305	48	39	motion	motion	NOUN
american_scientific_journal-5305	48	40	.	.	PUNCT
american_scientific_journal-5305	49	1	we	we	PRON
american_scientific_journal-5305	49	2	will	will	AUX
american_scientific_journal-5305	49	3	demonstrate	demonstrate	VERB
american_scientific_journal-5305	49	4	this	this	PRON
american_scientific_journal-5305	49	5	explicitly	explicitly	ADV
american_scientific_journal-5305	49	6	by	by	ADP
american_scientific_journal-5305	49	7	assuming	assume	VERB
american_scientific_journal-5305	49	8	that	that	SCONJ
american_scientific_journal-5305	49	9	if	if	SCONJ
american_scientific_journal-5305	49	10	q(t	q(t	PROPN
american_scientific_journal-5305	49	11	)	)	PUNCT
american_scientific_journal-5305	49	12	satisfy	satisfy	NOUN
american_scientific_journal-5305	49	13	lagrange‟s	lagrange‟s	ADJ
american_scientific_journal-5305	49	14	equation	equation	NOUN
american_scientific_journal-5305	49	15	,	,	PUNCT
american_scientific_journal-5305	49	16	then	then	ADV
american_scientific_journal-5305	49	17	invariance	invariance	NOUN
american_scientific_journal-5305	49	18	of	of	ADP
american_scientific_journal-5305	49	19	under	under	ADP
american_scientific_journal-5305	49	20	the	the	DET
american_scientific_journal-5305	49	21	coordinate	coordinate	NOUN
american_scientific_journal-5305	49	22	transformation	transformation	NOUN
american_scientific_journal-5305	49	23	q	q	PROPN
american_scientific_journal-5305	49	24	implies	imply	VERB
american_scientific_journal-5305	49	25	that	that	SCONJ
american_scientific_journal-5305	49	26	q‟(t	q‟(t	NOUN
american_scientific_journal-5305	49	27	)	)	PUNCT
american_scientific_journal-5305	49	28	satisfies	satisfy	VERB
american_scientific_journal-5305	49	29	the	the	DET
american_scientific_journal-5305	49	30	same	same	ADJ
american_scientific_journal-5305	49	31	lagrange‟s	lagrange‟s	ADJ
american_scientific_journal-5305	49	32	equations	equation	NOUN
american_scientific_journal-5305	49	33	.	.	PUNCT
american_scientific_journal-5305	50	1	we	we	PRON
american_scientific_journal-5305	50	2	consider	consider	VERB
american_scientific_journal-5305	50	3	the	the	DET
american_scientific_journal-5305	50	4	change	change	NOUN
american_scientific_journal-5305	50	5	of	of	ADP
american_scientific_journal-5305	50	6	the	the	DET
american_scientific_journal-5305	50	7	variables	variable	NOUN
american_scientific_journal-5305	50	8	in	in	ADP
american_scientific_journal-5305	50	9	the	the	DET
american_scientific_journal-5305	50	10	partial	partial	ADJ
american_scientific_journal-5305	50	11	derivatives	derivative	NOUN
american_scientific_journal-5305	50	12	of	of	ADP
american_scientific_journal-5305	50	13	the	the	DET
american_scientific_journal-5305	50	14	lagrangian	lagrangian	ADJ
american_scientific_journal-5305	50	15	∑	∑	PROPN
american_scientific_journal-5305	50	16	(	(	PUNCT
american_scientific_journal-5305	50	17	̇	̇	VERB
american_scientific_journal-5305	50	18	̇	̇	VERB
american_scientific_journal-5305	50	19	̇	̇	VERB
american_scientific_journal-5305	50	20	∑	∑	PUNCT
american_scientific_journal-5305	50	21	̇	̇	VERB
american_scientific_journal-5305	50	22	̇	̇	PROPN
american_scientific_journal-5305	50	23	̇	̇	PROPN
american_scientific_journal-5305	50	24	(	(	PUNCT
american_scientific_journal-5305	50	25	note	note	VERB
american_scientific_journal-5305	50	26	that	that	SCONJ
american_scientific_journal-5305	50	27	in	in	ADP
american_scientific_journal-5305	50	28	the	the	DET
american_scientific_journal-5305	50	29	last	last	ADJ
american_scientific_journal-5305	50	30	expression	expression	NOUN
american_scientific_journal-5305	50	31	there	there	PRON
american_scientific_journal-5305	50	32	is	be	VERB
american_scientific_journal-5305	50	33	no	no	DET
american_scientific_journal-5305	50	34	term	term	NOUN
american_scientific_journal-5305	50	35	proportional	proportional	ADJ
american_scientific_journal-5305	50	36	to	to	PART
american_scientific_journal-5305	50	37	̇	̇	VERB
american_scientific_journal-5305	50	38	⁄	⁄	PROPN
american_scientific_journal-5305	50	39	,	,	PUNCT
american_scientific_journal-5305	50	40	since	since	SCONJ
american_scientific_journal-5305	50	41	in	in	ADP
american_scientific_journal-5305	50	42	a	a	DET
american_scientific_journal-5305	50	43	coordinate	coordinate	NOUN
american_scientific_journal-5305	50	44	transformation	transformation	NOUN
american_scientific_journal-5305	50	45	the	the	DET
american_scientific_journal-5305	50	46	old	old	ADJ
american_scientific_journal-5305	50	47	coordinates	coordinate	NOUN
american_scientific_journal-5305	50	48	q	q	X
american_scientific_journal-5305	50	49	will	will	AUX
american_scientific_journal-5305	50	50	not	not	PART
american_scientific_journal-5305	50	51	depend	depend	VERB
american_scientific_journal-5305	50	52	on	on	ADP
american_scientific_journal-5305	50	53	the	the	DET
american_scientific_journal-5305	50	54	new	new	ADJ
american_scientific_journal-5305	50	55	velocities	velocity	NOUN
american_scientific_journal-5305	50	56	̇	̇	VERB
american_scientific_journal-5305	50	57	,	,	PUNCT
american_scientific_journal-5305	50	58	but	but	CCONJ
american_scientific_journal-5305	50	59	only	only	ADV
american_scientific_journal-5305	50	60	on	on	ADP
american_scientific_journal-5305	50	61	the	the	DET
american_scientific_journal-5305	50	62	new	new	ADJ
american_scientific_journal-5305	50	63	coordinates	coordinate	NOUN
american_scientific_journal-5305	50	64	.	.	PUNCT
american_scientific_journal-5305	51	1	the	the	DET
american_scientific_journal-5305	51	2	relation	relation	NOUN
american_scientific_journal-5305	51	3	between	between	ADP
american_scientific_journal-5305	51	4	the	the	DET
american_scientific_journal-5305	51	5	velocities	velocity	NOUN
american_scientific_journal-5305	51	6	is	be	AUX
american_scientific_journal-5305	51	7	̇	̇	VERB
american_scientific_journal-5305	51	8	∑	∑	PUNCT
american_scientific_journal-5305	51	9	̇	̇	PROPN
american_scientific_journal-5305	51	10	(	(	PUNCT
american_scientific_journal-5305	51	11	which	which	PRON
american_scientific_journal-5305	51	12	implies	imply	VERB
american_scientific_journal-5305	51	13	that	that	PRON
american_scientific_journal-5305	51	14	̇	̇	VERB
american_scientific_journal-5305	51	15	̇	̇	PROPN
american_scientific_journal-5305	51	16	(	(	PUNCT
american_scientific_journal-5305	51	17	this	this	PRON
american_scientific_journal-5305	51	18	allows	allow	VERB
american_scientific_journal-5305	51	19	a	a	DET
american_scientific_journal-5305	51	20	reformulation	reformulation	NOUN
american_scientific_journal-5305	51	21	of	of	ADP
american_scientific_journal-5305	51	22	the	the	DET
american_scientific_journal-5305	51	23	partial	partial	ADJ
american_scientific_journal-5305	51	24	derivative	derivative	NOUN
american_scientific_journal-5305	51	25	of	of	ADP
american_scientific_journal-5305	51	26	with	with	ADP
american_scientific_journal-5305	51	27	respect	respect	NOUN
american_scientific_journal-5305	51	28	to	to	ADP
american_scientific_journal-5305	51	29	velocities	velocity	NOUN
american_scientific_journal-5305	51	30	american	american	PROPN
american_scientific_journal-5305	51	31	scientific	scientific	ADJ
american_scientific_journal-5305	51	32	research	research	NOUN
american_scientific_journal-5305	51	33	journal	journal	NOUN
american_scientific_journal-5305	51	34	for	for	ADP
american_scientific_journal-5305	51	35	engineering	engineering	NOUN
american_scientific_journal-5305	51	36	,	,	PUNCT
american_scientific_journal-5305	51	37	technology	technology	NOUN
american_scientific_journal-5305	51	38	,	,	PUNCT
american_scientific_journal-5305	51	39	and	and	CCONJ
american_scientific_journal-5305	51	40	sciences	science	NOUN
american_scientific_journal-5305	51	41	(	(	PUNCT
american_scientific_journal-5305	51	42	asrjets	asrjet	NOUN
american_scientific_journal-5305	51	43	)	)	PUNCT
american_scientific_journal-5305	51	44	(	(	PUNCT
american_scientific_journal-5305	51	45	2019	2019	NUM
american_scientific_journal-5305	51	46	)	)	PUNCT
american_scientific_journal-5305	51	47	volume	volume	NOUN
american_scientific_journal-5305	51	48	61	61	NUM
american_scientific_journal-5305	51	49	,	,	PUNCT
american_scientific_journal-5305	51	50	no	no	DET
american_scientific_journal-5305	51	51	1	1	NUM
american_scientific_journal-5305	51	52	,	,	PUNCT
american_scientific_journal-5305	51	53	pp	pp	ADV
american_scientific_journal-5305	51	54	268	268	NUM
american_scientific_journal-5305	51	55	-	-	SYM
american_scientific_journal-5305	51	56	279	279	NUM
american_scientific_journal-5305	51	57	872	872	NUM
american_scientific_journal-5305	51	58	̇	̇	NOUN
american_scientific_journal-5305	51	59	∑	∑	PUNCT
american_scientific_journal-5305	51	60	̇	̇	PROPN
american_scientific_journal-5305	51	61	(	(	PUNCT
american_scientific_journal-5305	51	62	we	we	PRON
american_scientific_journal-5305	51	63	are	be	AUX
american_scientific_journal-5305	51	64	interested	interested	ADJ
american_scientific_journal-5305	51	65	in	in	ADP
american_scientific_journal-5305	51	66	the	the	DET
american_scientific_journal-5305	51	67	total	total	ADJ
american_scientific_journal-5305	51	68	time	time	NOUN
american_scientific_journal-5305	51	69	derivative	derivative	NOUN
american_scientific_journal-5305	51	70	(	(	PUNCT
american_scientific_journal-5305	51	71	̇	̇	PROPN
american_scientific_journal-5305	51	72	)	)	PUNCT
american_scientific_journal-5305	51	73	∑	∑	PROPN
american_scientific_journal-5305	51	74	(	(	PUNCT
american_scientific_journal-5305	51	75	̇	̇	PROPN
american_scientific_journal-5305	51	76	)	)	PUNCT
american_scientific_journal-5305	51	77	∑	∑	PUNCT
american_scientific_journal-5305	51	78	̇	̇	PROPN
american_scientific_journal-5305	51	79	(	(	PUNCT
american_scientific_journal-5305	51	80	)	)	PUNCT
american_scientific_journal-5305	51	81	(	(	PUNCT
american_scientific_journal-5305	51	82	where	where	SCONJ
american_scientific_journal-5305	51	83	the	the	DET
american_scientific_journal-5305	51	84	last	last	ADJ
american_scientific_journal-5305	51	85	term	term	NOUN
american_scientific_journal-5305	51	86	can	can	AUX
american_scientific_journal-5305	51	87	be	be	AUX
american_scientific_journal-5305	51	88	rewritten	rewrite	VERB
american_scientific_journal-5305	51	89	as	as	ADP
american_scientific_journal-5305	51	90	(	(	PUNCT
american_scientific_journal-5305	51	91	)	)	PUNCT
american_scientific_journal-5305	51	92	∑	∑	PUNCT
american_scientific_journal-5305	51	93	̇	̇	VERB
american_scientific_journal-5305	51	94	(	(	PUNCT
american_scientific_journal-5305	51	95	∑	∑	ADV
american_scientific_journal-5305	51	96	̇	̇	ADJ
american_scientific_journal-5305	51	97	)	)	PUNCT
american_scientific_journal-5305	51	98	̇	̇	PROPN
american_scientific_journal-5305	51	99	(	(	PUNCT
american_scientific_journal-5305	51	100	we	we	PRON
american_scientific_journal-5305	51	101	finally	finally	ADV
american_scientific_journal-5305	51	102	collect	collect	VERB
american_scientific_journal-5305	51	103	expressions	expression	NOUN
american_scientific_journal-5305	51	104	from	from	ADP
american_scientific_journal-5305	51	105	(	(	PUNCT
american_scientific_journal-5305	51	106	3.19	3.19	NUM
american_scientific_journal-5305	51	107	)	)	PUNCT
american_scientific_journal-5305	51	108	,	,	PUNCT
american_scientific_journal-5305	51	109	(	(	PUNCT
american_scientific_journal-5305	51	110	3.23	3.23	NUM
american_scientific_journal-5305	51	111	)	)	PUNCT
american_scientific_journal-5305	51	112	,	,	PUNCT
american_scientific_journal-5305	51	113	and	and	CCONJ
american_scientific_journal-5305	51	114	(	(	PUNCT
american_scientific_journal-5305	51	115	3.24	3.24	NUM
american_scientific_journal-5305	51	116	)	)	PUNCT
american_scientific_journal-5305	51	117	,	,	PUNCT
american_scientific_journal-5305	51	118	which	which	PRON
american_scientific_journal-5305	51	119	give	give	VERB
american_scientific_journal-5305	51	120	the	the	DET
american_scientific_journal-5305	51	121	following	follow	VERB
american_scientific_journal-5305	51	122	relation	relation	NOUN
american_scientific_journal-5305	51	123	(	(	PUNCT
american_scientific_journal-5305	51	124	̇	̇	PROPN
american_scientific_journal-5305	51	125	)	)	PUNCT
american_scientific_journal-5305	51	126	∑	∑	PROPN
american_scientific_journal-5305	51	127	(	(	PUNCT
american_scientific_journal-5305	51	128	(	(	PUNCT
american_scientific_journal-5305	51	129	̇	̇	NOUN
american_scientific_journal-5305	51	130	)	)	PUNCT
american_scientific_journal-5305	51	131	(	(	PUNCT
american_scientific_journal-5305	51	132	this	this	PRON
american_scientific_journal-5305	51	133	demonstrates	demonstrate	VERB
american_scientific_journal-5305	51	134	explicitly	explicitly	ADV
american_scientific_journal-5305	51	135	that	that	SCONJ
american_scientific_journal-5305	51	136	if	if	SCONJ
american_scientific_journal-5305	51	137	(	(	PUNCT
american_scientific_journal-5305	51	138	satisfies	satisfie	NOUN
american_scientific_journal-5305	51	139	lagrange‟s	lagrange‟s	PROPN
american_scientific_journal-5305	51	140	equations	equation	NOUN
american_scientific_journal-5305	51	141	,	,	PUNCT
american_scientific_journal-5305	51	142	and	and	CCONJ
american_scientific_journal-5305	51	143	thereby	thereby	ADV
american_scientific_journal-5305	51	144	the	the	DET
american_scientific_journal-5305	51	145	right	right	ADJ
american_scientific_journal-5305	51	146	hand	hand	NOUN
american_scientific_journal-5305	51	147	side	side	NOUN
american_scientific_journal-5305	51	148	of	of	ADP
american_scientific_journal-5305	51	149	(	(	PUNCT
american_scientific_journal-5305	51	150	3.25	3.25	NUM
american_scientific_journal-5305	51	151	)	)	PUNCT
american_scientific_journal-5305	51	152	vanishes	vanish	VERB
american_scientific_journal-5305	51	153	,	,	PUNCT
american_scientific_journal-5305	51	154	then	then	ADV
american_scientific_journal-5305	51	155	the	the	DET
american_scientific_journal-5305	51	156	transformed	transform	VERB
american_scientific_journal-5305	51	157	coordinates	coordinate	NOUN
american_scientific_journal-5305	51	158	(	(	PUNCT
american_scientific_journal-5305	51	159	t	t	NOUN
american_scientific_journal-5305	51	160	)	)	PUNCT
american_scientific_journal-5305	51	161	will	will	AUX
american_scientific_journal-5305	51	162	also	also	ADV
american_scientific_journal-5305	51	163	satisfy	satisfy	VERB
american_scientific_journal-5305	51	164	(	(	PUNCT
american_scientific_journal-5305	51	165	the	the	DET
american_scientific_journal-5305	51	166	same	same	ADJ
american_scientific_journal-5305	51	167	set	set	NOUN
american_scientific_journal-5305	51	168	of	of	ADP
american_scientific_journal-5305	51	169	)	)	PUNCT
american_scientific_journal-5305	51	170	lagrange	lagrange	NOUN
american_scientific_journal-5305	51	171	's	's	PART
american_scientific_journal-5305	51	172	equation	equation	NOUN
american_scientific_journal-5305	51	173	.	.	PUNCT
american_scientific_journal-5305	52	1	thus	thus	ADV
american_scientific_journal-5305	52	2	,	,	PUNCT
american_scientific_journal-5305	52	3	a	a	DET
american_scientific_journal-5305	52	4	coordinate	coordinate	NOUN
american_scientific_journal-5305	52	5	transformation	transformation	NOUN
american_scientific_journal-5305	52	6	that	that	PRON
american_scientific_journal-5305	52	7	is	be	AUX
american_scientific_journal-5305	52	8	a	a	DET
american_scientific_journal-5305	52	9	symmetry	symmetry	NOUN
american_scientific_journal-5305	52	10	transformation	transformation	NOUN
american_scientific_journal-5305	52	11	in	in	ADP
american_scientific_journal-5305	52	12	the	the	DET
american_scientific_journal-5305	52	13	sense	sense	NOUN
american_scientific_journal-5305	52	14	that	that	SCONJ
american_scientific_journal-5305	52	15	it	it	PRON
american_scientific_journal-5305	52	16	leaves	leave	VERB
american_scientific_journal-5305	52	17	the	the	DET
american_scientific_journal-5305	52	18	lagrangian	lagrangian	ADJ
american_scientific_journal-5305	52	19	invariant	invariant	NOUN
american_scientific_journal-5305	52	20	will	will	AUX
american_scientific_journal-5305	52	21	also	also	ADV
american_scientific_journal-5305	52	22	be	be	AUX
american_scientific_journal-5305	52	23	a	a	DET
american_scientific_journal-5305	52	24	symmetry	symmetry	NOUN
american_scientific_journal-5305	52	25	transformation	transformation	NOUN
american_scientific_journal-5305	52	26	in	in	ADP
american_scientific_journal-5305	52	27	the	the	DET
american_scientific_journal-5305	52	28	sense	sense	NOUN
american_scientific_journal-5305	52	29	that	that	SCONJ
american_scientific_journal-5305	52	30	it	it	PRON
american_scientific_journal-5305	52	31	maps	map	VERB
american_scientific_journal-5305	52	32	solutions	solution	NOUN
american_scientific_journal-5305	52	33	of	of	ADP
american_scientific_journal-5305	52	34	the	the	DET
american_scientific_journal-5305	52	35	equations	equation	NOUN
american_scientific_journal-5305	52	36	of	of	ADP
american_scientific_journal-5305	52	37	motion	motion	NOUN
american_scientific_journal-5305	52	38	into	into	ADP
american_scientific_journal-5305	52	39	new	new	ADJ
american_scientific_journal-5305	52	40	solutions	solution	NOUN
american_scientific_journal-5305	52	41	.	.	PUNCT
american_scientific_journal-5305	53	1	note	note	NOUN
american_scientific_journal-5305	53	2	,	,	PUNCT
american_scientific_journal-5305	53	3	however	however	ADV
american_scientific_journal-5305	53	4	,	,	PUNCT
american_scientific_journal-5305	53	5	that	that	SCONJ
american_scientific_journal-5305	53	6	the	the	DET
american_scientific_journal-5305	53	7	opposite	opposite	NOUN
american_scientific_journal-5305	53	8	may	may	AUX
american_scientific_journal-5305	53	9	not	not	PART
american_scientific_journal-5305	53	10	always	always	ADV
american_scientific_journal-5305	53	11	be	be	AUX
american_scientific_journal-5305	53	12	true	true	ADJ
american_scientific_journal-5305	53	13	.	.	PUNCT
american_scientific_journal-5305	54	1	there	there	PRON
american_scientific_journal-5305	54	2	may	may	AUX
american_scientific_journal-5305	54	3	be	be	AUX
american_scientific_journal-5305	54	4	coordinate	coordinate	ADJ
american_scientific_journal-5305	54	5	transformations	transformation	NOUN
american_scientific_journal-5305	54	6	that	that	PRON
american_scientific_journal-5305	54	7	maps	map	VERB
american_scientific_journal-5305	54	8	solutions	solution	NOUN
american_scientific_journal-5305	54	9	of	of	ADP
american_scientific_journal-5305	54	10	the	the	DET
american_scientific_journal-5305	54	11	equations	equation	NOUN
american_scientific_journal-5305	54	12	of	of	ADP
american_scientific_journal-5305	54	13	motion	motion	NOUN
american_scientific_journal-5305	54	14	into	into	ADP
american_scientific_journal-5305	54	15	new	new	ADJ
american_scientific_journal-5305	54	16	solution	solution	NOUN
american_scientific_journal-5305	54	17	without	without	ADP
american_scientific_journal-5305	54	18	leaving	leave	VERB
american_scientific_journal-5305	54	19	the	the	DET
american_scientific_journal-5305	54	20	lagrangian	lagrangian	ADJ
american_scientific_journal-5305	54	21	unchanged	unchanged	ADJ
american_scientific_journal-5305	54	22	.	.	PUNCT
american_scientific_journal-5305	55	1	3.3	3.3	NUM
american_scientific_journal-5305	55	2	.	.	PUNCT
american_scientific_journal-5305	56	1	a	a	DET
american_scientific_journal-5305	56	2	lie	lie	NOUN
american_scientific_journal-5305	56	3	group	group	NOUN
american_scientific_journal-5305	56	4	transformations	transformation	NOUN
american_scientific_journal-5305	56	5	and	and	CCONJ
american_scientific_journal-5305	56	6	noether	noether	PROPN
american_scientific_journal-5305	56	7	's	's	PART
american_scientific_journal-5305	56	8	theorem	theorem	NOUN
american_scientific_journal-5305	56	9	assume	assume	VERB
american_scientific_journal-5305	56	10	that	that	SCONJ
american_scientific_journal-5305	56	11	the	the	DET
american_scientific_journal-5305	56	12	euler	euler	PROPN
american_scientific_journal-5305	56	13	-	-	PUNCT
american_scientific_journal-5305	56	14	lagrange	lagrange	NOUN
american_scientific_journal-5305	56	15	equations	equation	NOUN
american_scientific_journal-5305	56	16	(	(	PUNCT
american_scientific_journal-5305	56	17	admit	admit	VERB
american_scientific_journal-5305	56	18	a	a	DET
american_scientific_journal-5305	56	19	one	one	NUM
american_scientific_journal-5305	56	20	-	-	PUNCT
american_scientific_journal-5305	56	21	parameter	parameter	NOUN
american_scientific_journal-5305	56	22	lie	lie	NOUN
american_scientific_journal-5305	56	23	transformation	transformation	NOUN
american_scientific_journal-5305	56	24	group	group	NOUN
american_scientific_journal-5305	56	25	g	g	PROPN
american_scientific_journal-5305	56	26	,	,	PUNCT
american_scientific_journal-5305	56	27	i.e.	i.e.	X
american_scientific_journal-5305	56	28	a	a	DET
american_scientific_journal-5305	56	29	local	local	ADJ
american_scientific_journal-5305	56	30	group	group	NOUN
american_scientific_journal-5305	56	31	of	of	ADP
american_scientific_journal-5305	56	32	transformations	transformation	NOUN
american_scientific_journal-5305	56	33	.	.	PUNCT
american_scientific_journal-5305	57	1	̅	̅	NOUN
american_scientific_journal-5305	57	2	(	(	PUNCT
american_scientific_journal-5305	57	3	̅	̅	X
american_scientific_journal-5305	57	4	(	(	PUNCT
american_scientific_journal-5305	57	5	(	(	PUNCT
american_scientific_journal-5305	57	6	where	where	SCONJ
american_scientific_journal-5305	57	7	(	(	PUNCT
american_scientific_journal-5305	57	8	(	(	PUNCT
american_scientific_journal-5305	57	9	and	and	CCONJ
american_scientific_journal-5305	57	10	(	(	PUNCT
american_scientific_journal-5305	57	11	(	(	PUNCT
american_scientific_journal-5305	57	12	american	american	ADJ
american_scientific_journal-5305	57	13	scientific	scientific	ADJ
american_scientific_journal-5305	57	14	research	research	NOUN
american_scientific_journal-5305	57	15	journal	journal	NOUN
american_scientific_journal-5305	57	16	for	for	ADP
american_scientific_journal-5305	57	17	engineering	engineering	NOUN
american_scientific_journal-5305	57	18	,	,	PUNCT
american_scientific_journal-5305	57	19	technology	technology	NOUN
american_scientific_journal-5305	57	20	,	,	PUNCT
american_scientific_journal-5305	57	21	and	and	CCONJ
american_scientific_journal-5305	57	22	sciences	science	NOUN
american_scientific_journal-5305	57	23	(	(	PUNCT
american_scientific_journal-5305	57	24	asrjets	asrjet	NOUN
american_scientific_journal-5305	57	25	)	)	PUNCT
american_scientific_journal-5305	57	26	(	(	PUNCT
american_scientific_journal-5305	57	27	2019	2019	NUM
american_scientific_journal-5305	57	28	)	)	PUNCT
american_scientific_journal-5305	57	29	volume	volume	NOUN
american_scientific_journal-5305	57	30	61	61	NUM
american_scientific_journal-5305	57	31	,	,	PUNCT
american_scientific_journal-5305	57	32	no	no	DET
american_scientific_journal-5305	57	33	1	1	NUM
american_scientific_journal-5305	57	34	,	,	PUNCT
american_scientific_journal-5305	57	35	pp	pp	ADV
american_scientific_journal-5305	57	36	268	268	NUM
american_scientific_journal-5305	57	37	-	-	SYM
american_scientific_journal-5305	57	38	279	279	NUM
american_scientific_journal-5305	57	39	872	872	NUM
american_scientific_journal-5305	57	40	the	the	DET
american_scientific_journal-5305	57	41	infinitesimal	infinitesimal	ADJ
american_scientific_journal-5305	57	42	generator	generator	NOUN
american_scientific_journal-5305	57	43	of	of	ADP
american_scientific_journal-5305	57	44	the	the	DET
american_scientific_journal-5305	57	45	group	group	NOUN
american_scientific_journal-5305	57	46	g	g	PROPN
american_scientific_journal-5305	57	47	has	have	VERB
american_scientific_journal-5305	57	48	the	the	DET
american_scientific_journal-5305	57	49	from	from	ADP
american_scientific_journal-5305	57	50	(	(	PUNCT
american_scientific_journal-5305	57	51	(	(	PUNCT
american_scientific_journal-5305	57	52	(	(	PUNCT
american_scientific_journal-5305	57	53	where	where	SCONJ
american_scientific_journal-5305	57	54	(	(	PUNCT
american_scientific_journal-5305	57	55	(	(	PUNCT
american_scientific_journal-5305	57	56	,	,	PUNCT
american_scientific_journal-5305	57	57	(	(	PUNCT
american_scientific_journal-5305	57	58	(	(	PUNCT
american_scientific_journal-5305	57	59	.	.	PUNCT
american_scientific_journal-5305	58	1	definition	definition	NOUN
american_scientific_journal-5305	58	2	:	:	PUNCT
american_scientific_journal-5305	58	3	a	a	DET
american_scientific_journal-5305	58	4	variational	variational	NOUN
american_scientific_journal-5305	58	5	of	of	ADP
american_scientific_journal-5305	58	6	integral	integral	ADJ
american_scientific_journal-5305	58	7	(	(	PUNCT
american_scientific_journal-5305	58	8	)	)	PUNCT
american_scientific_journal-5305	58	9	(	(	PUNCT
american_scientific_journal-5305	58	10	is	be	AUX
american_scientific_journal-5305	58	11	invariant	invariant	ADJ
american_scientific_journal-5305	58	12	under	under	ADP
american_scientific_journal-5305	58	13	the	the	DET
american_scientific_journal-5305	58	14	group	group	NOUN
american_scientific_journal-5305	58	15	g	g	PROPN
american_scientific_journal-5305	58	16	if	if	SCONJ
american_scientific_journal-5305	58	17	∫	∫	PROPN
american_scientific_journal-5305	58	18	(	(	PUNCT
american_scientific_journal-5305	58	19	̅	̅	NOUN
american_scientific_journal-5305	58	20	̅	̅	X
american_scientific_journal-5305	58	21	̅	̅	NOUN
american_scientific_journal-5305	58	22	(	(	PUNCT
american_scientific_journal-5305	58	23	̅	̅	NOUN
american_scientific_journal-5305	58	24	(	(	PUNCT
american_scientific_journal-5305	58	25	̅	̅	NOUN
american_scientific_journal-5305	58	26	∫	∫	PROPN
american_scientific_journal-5305	58	27	(	(	PUNCT
american_scientific_journal-5305	58	28	(	(	PUNCT
american_scientific_journal-5305	58	29	(	(	PUNCT
american_scientific_journal-5305	58	30	)	)	PUNCT
american_scientific_journal-5305	58	31	)	)	PUNCT
american_scientific_journal-5305	58	32	̅	̅	NOUN
american_scientific_journal-5305	58	33	(	(	PUNCT
american_scientific_journal-5305	58	34	the	the	DET
american_scientific_journal-5305	58	35	invariance	invariance	NOUN
american_scientific_journal-5305	58	36	condition	condition	NOUN
american_scientific_journal-5305	58	37	is	be	AUX
american_scientific_journal-5305	58	38	given	give	VERB
american_scientific_journal-5305	58	39	by	by	ADP
american_scientific_journal-5305	58	40	the	the	DET
american_scientific_journal-5305	58	41	following	follow	VERB
american_scientific_journal-5305	58	42	lemma	lemma	PROPN
american_scientific_journal-5305	58	43	.	.	PUNCT
american_scientific_journal-5305	59	1	lemma	lemma	PROPN
american_scientific_journal-5305	59	2	3.1	3.1	NUM
american_scientific_journal-5305	59	3	an	an	DET
american_scientific_journal-5305	59	4	integral	integral	ADJ
american_scientific_journal-5305	59	5	∫	∫	NOUN
american_scientific_journal-5305	59	6	(	(	PUNCT
american_scientific_journal-5305	59	7	(	(	PUNCT
american_scientific_journal-5305	59	8	(	(	PUNCT
american_scientific_journal-5305	59	9	(	(	PUNCT
american_scientific_journal-5305	59	10	is	be	AUX
american_scientific_journal-5305	59	11	invariant	invariant	ADJ
american_scientific_journal-5305	59	12	under	under	ADP
american_scientific_journal-5305	59	13	the	the	DET
american_scientific_journal-5305	59	14	group	group	NOUN
american_scientific_journal-5305	59	15	g	g	PROPN
american_scientific_journal-5305	60	1	if	if	SCONJ
american_scientific_journal-5305	61	1	and	and	CCONJ
american_scientific_journal-5305	61	2	only	only	ADV
american_scientific_journal-5305	61	3	if	if	SCONJ
american_scientific_journal-5305	61	4	(	(	PUNCT
american_scientific_journal-5305	61	5	(	(	PUNCT
american_scientific_journal-5305	61	6	(	(	PUNCT
american_scientific_journal-5305	61	7	here	here	ADV
american_scientific_journal-5305	61	8	x	x	PUNCT
american_scientific_journal-5305	61	9	is	be	AUX
american_scientific_journal-5305	61	10	a	a	DET
american_scientific_journal-5305	61	11	prolonged	prolonged	ADJ
american_scientific_journal-5305	61	12	version	version	NOUN
american_scientific_journal-5305	61	13	of	of	ADP
american_scientific_journal-5305	61	14	the	the	DET
american_scientific_journal-5305	61	15	generator	generator	NOUN
american_scientific_journal-5305	61	16	(	(	PUNCT
american_scientific_journal-5305	61	17	3.28	3.28	NUM
american_scientific_journal-5305	61	18	)	)	PUNCT
american_scientific_journal-5305	61	19	(	(	PUNCT
american_scientific_journal-5305	61	20	where	where	SCONJ
american_scientific_journal-5305	61	21	(	(	PUNCT
american_scientific_journal-5305	61	22	)	)	PUNCT
american_scientific_journal-5305	61	23	(	(	PUNCT
american_scientific_journal-5305	61	24	)	)	PUNCT
american_scientific_journal-5305	61	25	.	.	PUNCT
american_scientific_journal-5305	62	1	noether	noether	PROPN
american_scientific_journal-5305	62	2	proved	prove	VERB
american_scientific_journal-5305	62	3	her	she	PRON
american_scientific_journal-5305	62	4	theorem	theorem	NOUN
american_scientific_journal-5305	62	5	by	by	ADP
american_scientific_journal-5305	62	6	the	the	DET
american_scientific_journal-5305	62	7	application	application	NOUN
american_scientific_journal-5305	62	8	of	of	ADP
american_scientific_journal-5305	62	9	the	the	DET
american_scientific_journal-5305	62	10	variational	variational	ADJ
american_scientific_journal-5305	62	11	procedure	procedure	NOUN
american_scientific_journal-5305	62	12	to	to	ADP
american_scientific_journal-5305	62	13	the	the	DET
american_scientific_journal-5305	62	14	integral	integral	ADJ
american_scientific_journal-5305	62	15	of	of	ADP
american_scientific_journal-5305	62	16	action	action	NOUN
american_scientific_journal-5305	62	17	.	.	PUNCT
american_scientific_journal-5305	63	1	using	use	VERB
american_scientific_journal-5305	63	2	her	her	PRON
american_scientific_journal-5305	63	3	idea	idea	NOUN
american_scientific_journal-5305	63	4	hill	hill	NOUN
american_scientific_journal-5305	63	5	presented	present	VERB
american_scientific_journal-5305	63	6	the	the	DET
american_scientific_journal-5305	63	7	explicit	explicit	ADJ
american_scientific_journal-5305	63	8	form	form	NOUN
american_scientific_journal-5305	63	9	of	of	ADP
american_scientific_journal-5305	63	10	conserved	conserve	VERB
american_scientific_journal-5305	63	11	quantities	quantity	NOUN
american_scientific_journal-5305	63	12	in	in	ADP
american_scientific_journal-5305	63	13	the	the	DET
american_scientific_journal-5305	63	14	case	case	NOUN
american_scientific_journal-5305	63	15	of	of	ADP
american_scientific_journal-5305	63	16	the	the	DET
american_scientific_journal-5305	63	17	first	first	ADJ
american_scientific_journal-5305	63	18	-	-	PUNCT
american_scientific_journal-5305	63	19	order	order	NOUN
american_scientific_journal-5305	63	20	lagrangians	lagrangian	NOUN
american_scientific_journal-5305	63	21	(	(	PUNCT
american_scientific_journal-5305	63	22	x	x	X
american_scientific_journal-5305	63	23	,	,	PUNCT
american_scientific_journal-5305	63	24	u	u	NOUN
american_scientific_journal-5305	63	25	,	,	PUNCT
american_scientific_journal-5305	63	26	u(1	u(1	PROPN
american_scientific_journal-5305	63	27	)	)	PUNCT
american_scientific_journal-5305	63	28	)	)	PUNCT
american_scientific_journal-5305	63	29	.	.	PUNCT
american_scientific_journal-5305	64	1	we	we	PRON
american_scientific_journal-5305	64	2	have	have	AUX
american_scientific_journal-5305	64	3	used	use	VERB
american_scientific_journal-5305	64	4	the	the	DET
american_scientific_journal-5305	64	5	following	following	ADJ
american_scientific_journal-5305	64	6	generalized	generalized	ADJ
american_scientific_journal-5305	64	7	form	form	NOUN
american_scientific_journal-5305	64	8	of	of	ADP
american_scientific_journal-5305	64	9	noether	noether	PROPN
american_scientific_journal-5305	64	10	's	's	PART
american_scientific_journal-5305	64	11	theorem	theorem	ADJ
american_scientific_journal-5305	64	12	,	,	PUNCT
american_scientific_journal-5305	64	13	proved	prove	VERB
american_scientific_journal-5305	64	14	by	by	ADP
american_scientific_journal-5305	64	15	ibragimov	ibragimov	NOUN
american_scientific_journal-5305	64	16	on	on	ADP
american_scientific_journal-5305	64	17	the	the	DET
american_scientific_journal-5305	64	18	basis	basis	NOUN
american_scientific_journal-5305	64	19	of	of	ADP
american_scientific_journal-5305	64	20	the	the	DET
american_scientific_journal-5305	64	21	grouptheoretical	grouptheoretical	ADJ
american_scientific_journal-5305	64	22	approach	approach	NOUN
american_scientific_journal-5305	64	23	.	.	PUNCT
american_scientific_journal-5305	65	1	american	american	ADJ
american_scientific_journal-5305	65	2	scientific	scientific	ADJ
american_scientific_journal-5305	65	3	research	research	PROPN
american_scientific_journal-5305	65	4	journal	journal	NOUN
american_scientific_journal-5305	65	5	for	for	ADP
american_scientific_journal-5305	65	6	engineering	engineering	NOUN
american_scientific_journal-5305	65	7	,	,	PUNCT
american_scientific_journal-5305	65	8	technology	technology	NOUN
american_scientific_journal-5305	65	9	,	,	PUNCT
american_scientific_journal-5305	65	10	and	and	CCONJ
american_scientific_journal-5305	65	11	sciences	science	NOUN
american_scientific_journal-5305	65	12	(	(	PUNCT
american_scientific_journal-5305	65	13	asrjets	asrjet	NOUN
american_scientific_journal-5305	65	14	)	)	PUNCT
american_scientific_journal-5305	65	15	(	(	PUNCT
american_scientific_journal-5305	65	16	2019	2019	NUM
american_scientific_journal-5305	65	17	)	)	PUNCT
american_scientific_journal-5305	65	18	volume	volume	NOUN
american_scientific_journal-5305	65	19	61	61	NUM
american_scientific_journal-5305	65	20	,	,	PUNCT
american_scientific_journal-5305	65	21	no	no	DET
american_scientific_journal-5305	65	22	1	1	NUM
american_scientific_journal-5305	65	23	,	,	PUNCT
american_scientific_journal-5305	65	24	pp	pp	ADV
american_scientific_journal-5305	65	25	268	268	NUM
american_scientific_journal-5305	65	26	-	-	SYM
american_scientific_journal-5305	65	27	279	279	NUM
american_scientific_journal-5305	65	28	876	876	NUM
american_scientific_journal-5305	65	29	theorem	theorem	VERB
american_scientific_journal-5305	65	30	3.1	3.1	NUM
american_scientific_journal-5305	65	31	let	let	VERB
american_scientific_journal-5305	65	32	the	the	DET
american_scientific_journal-5305	65	33	variational	variational	ADJ
american_scientific_journal-5305	65	34	integral	integral	ADJ
american_scientific_journal-5305	65	35	(	(	PUNCT
american_scientific_journal-5305	65	36	3.31	3.31	NUM
american_scientific_journal-5305	65	37	)	)	PUNCT
american_scientific_journal-5305	65	38	be	be	AUX
american_scientific_journal-5305	65	39	invariant	invariant	ADJ
american_scientific_journal-5305	65	40	with	with	ADP
american_scientific_journal-5305	65	41	respect	respect	NOUN
american_scientific_journal-5305	65	42	to	to	ADP
american_scientific_journal-5305	65	43	a	a	DET
american_scientific_journal-5305	65	44	group	group	NOUN
american_scientific_journal-5305	65	45	g	g	NOUN
american_scientific_journal-5305	65	46	with	with	ADP
american_scientific_journal-5305	65	47	generator	generator	NOUN
american_scientific_journal-5305	65	48	(	(	PUNCT
american_scientific_journal-5305	65	49	3.28	3.28	NUM
american_scientific_journal-5305	65	50	)	)	PUNCT
american_scientific_journal-5305	65	51	,	,	PUNCT
american_scientific_journal-5305	65	52	then	then	ADV
american_scientific_journal-5305	65	53	a	a	DET
american_scientific_journal-5305	65	54	vector	vector	NOUN
american_scientific_journal-5305	65	55	c	c	NOUN
american_scientific_journal-5305	65	56	with	with	ADP
american_scientific_journal-5305	65	57	components	component	NOUN
american_scientific_journal-5305	65	58	(	(	PUNCT
american_scientific_journal-5305	65	59	(	(	PUNCT
american_scientific_journal-5305	65	60	is	be	AUX
american_scientific_journal-5305	65	61	conserved	conserve	VERB
american_scientific_journal-5305	65	62	vector	vector	NOUN
american_scientific_journal-5305	65	63	for	for	ADP
american_scientific_journal-5305	65	64	the	the	DET
american_scientific_journal-5305	65	65	eulerlagrange‟s	eulerlagrange‟s	NOUN
american_scientific_journal-5305	65	66	equations	equation	NOUN
american_scientific_journal-5305	65	67	(	(	PUNCT
american_scientific_journal-5305	65	68	3.26	3.26	NUM
american_scientific_journal-5305	65	69	)	)	PUNCT
american_scientific_journal-5305	65	70	i.e.	i.e.	X
american_scientific_journal-5305	65	71	(	(	PUNCT
american_scientific_journal-5305	65	72	(	(	PUNCT
american_scientific_journal-5305	65	73	(	(	PUNCT
american_scientific_journal-5305	65	74	here	here	ADV
american_scientific_journal-5305	65	75	are	be	AUX
american_scientific_journal-5305	65	76	ibragimov‟s	ibragimov‟s	ADV
american_scientific_journal-5305	65	77	operator‟s	operator‟s	ADJ
american_scientific_journal-5305	65	78	.	.	PUNCT
american_scientific_journal-5305	66	1	{	{	PUNCT
american_scientific_journal-5305	66	2	∑	∑	PROPN
american_scientific_journal-5305	66	3	(	(	PUNCT
american_scientific_journal-5305	66	4	}	}	PUNCT
american_scientific_journal-5305	66	5	∑	∑	PROPN
american_scientific_journal-5305	66	6	(	(	PUNCT
american_scientific_journal-5305	66	7	{	{	PUNCT
american_scientific_journal-5305	66	8	∑	∑	PROPN
american_scientific_journal-5305	66	9	(	(	PUNCT
american_scientific_journal-5305	66	10	}	}	PUNCT
american_scientific_journal-5305	66	11	(	(	PUNCT
american_scientific_journal-5305	66	12	where	where	SCONJ
american_scientific_journal-5305	66	13	proof	proof	NOUN
american_scientific_journal-5305	66	14	of	of	ADP
american_scientific_journal-5305	66	15	theorem	theorem	NOUN
american_scientific_journal-5305	66	16	3.1	3.1	NUM
american_scientific_journal-5305	66	17	.	.	PUNCT
american_scientific_journal-5305	67	1	if	if	SCONJ
american_scientific_journal-5305	67	2	the	the	DET
american_scientific_journal-5305	67	3	variational	variational	ADJ
american_scientific_journal-5305	67	4	integral	integral	ADJ
american_scientific_journal-5305	67	5	(	(	PUNCT
american_scientific_journal-5305	67	6	3.31	3.31	NUM
american_scientific_journal-5305	67	7	)	)	PUNCT
american_scientific_journal-5305	67	8	i.e.	i.e.	X
american_scientific_journal-5305	67	9	∫	∫	PROPN
american_scientific_journal-5305	67	10	(	(	PUNCT
american_scientific_journal-5305	67	11	(	(	PUNCT
american_scientific_journal-5305	67	12	(	(	PUNCT
american_scientific_journal-5305	67	13	is	be	AUX
american_scientific_journal-5305	67	14	invariant	invariant	ADJ
american_scientific_journal-5305	67	15	it	it	PRON
american_scientific_journal-5305	67	16	fulfill	fulfill	VERB
american_scientific_journal-5305	68	1	[	[	X
american_scientific_journal-5305	68	2	x	x	X
american_scientific_journal-5305	68	3	(	(	PUNCT
american_scientific_journal-5305	68	4	)	)	PUNCT
american_scientific_journal-5305	68	5	]	]	PUNCT
american_scientific_journal-5305	68	6	(	(	PUNCT
american_scientific_journal-5305	68	7	=	=	NOUN
american_scientific_journal-5305	68	8	0	0	NUM
american_scientific_journal-5305	68	9	according	accord	VERB
american_scientific_journal-5305	68	10	to	to	ADP
american_scientific_journal-5305	68	11	lemma	lemma	PROPN
american_scientific_journal-5305	68	12	(	(	PUNCT
american_scientific_journal-5305	68	13	2.1	2.1	NUM
american_scientific_journal-5305	68	14	)	)	PUNCT
american_scientific_journal-5305	68	15	.	.	PUNCT
american_scientific_journal-5305	69	1	by	by	ADP
american_scientific_journal-5305	69	2	rewriting	rewrite	VERB
american_scientific_journal-5305	69	3	the	the	DET
american_scientific_journal-5305	69	4	operator	operator	NOUN
american_scientific_journal-5305	69	5	(	(	PUNCT
american_scientific_journal-5305	69	6	2.4	2.4	NUM
american_scientific_journal-5305	69	7	)	)	PUNCT
american_scientific_journal-5305	69	8	according	accord	VERB
american_scientific_journal-5305	69	9	to	to	ADP
american_scientific_journal-5305	69	10	equation	equation	NOUN
american_scientific_journal-5305	69	11	x	x	PUNCT
american_scientific_journal-5305	69	12	=	=	PUNCT
american_scientific_journal-5305	69	13	+	+	PUNCT
american_scientific_journal-5305	69	14	+	+	CCONJ
american_scientific_journal-5305	69	15	(	(	PUNCT
american_scientific_journal-5305	69	16	)	)	PUNCT
american_scientific_journal-5305	69	17	.	.	PUNCT
american_scientific_journal-5305	70	1	(	(	PUNCT
american_scientific_journal-5305	70	2	3.37	3.37	NUM
american_scientific_journal-5305	70	3	)	)	PUNCT
american_scientific_journal-5305	70	4	straightforward	straightforward	ADJ
american_scientific_journal-5305	70	5	calculations	calculation	NOUN
american_scientific_journal-5305	70	6	yield	yield	VERB
american_scientific_journal-5305	70	7	x	x	X
american_scientific_journal-5305	70	8	(	(	PUNCT
american_scientific_journal-5305	70	9	(	(	PUNCT
american_scientific_journal-5305	70	10	(	(	PUNCT
american_scientific_journal-5305	70	11	(	(	PUNCT
american_scientific_journal-5305	70	12	(	(	PUNCT
american_scientific_journal-5305	70	13	=	=	SYM
american_scientific_journal-5305	70	14	(	(	PUNCT
american_scientific_journal-5305	70	15	(	(	PUNCT
american_scientific_journal-5305	70	16	(	(	PUNCT
american_scientific_journal-5305	70	17	(	(	PUNCT
american_scientific_journal-5305	70	18	=	=	SYM
american_scientific_journal-5305	70	19	(	(	PUNCT
american_scientific_journal-5305	70	20	(	(	PUNCT
american_scientific_journal-5305	70	21	)	)	PUNCT
american_scientific_journal-5305	70	22	(	(	PUNCT
american_scientific_journal-5305	70	23	)	)	PUNCT
american_scientific_journal-5305	70	24	=	=	SYM
american_scientific_journal-5305	70	25	(	(	PUNCT
american_scientific_journal-5305	70	26	)	)	PUNCT
american_scientific_journal-5305	70	27	(	(	PUNCT
american_scientific_journal-5305	70	28	3.38	3.38	NUM
american_scientific_journal-5305	70	29	)	)	PUNCT
american_scientific_journal-5305	70	30	american	american	ADJ
american_scientific_journal-5305	70	31	scientific	scientific	ADJ
american_scientific_journal-5305	70	32	research	research	NOUN
american_scientific_journal-5305	70	33	journal	journal	NOUN
american_scientific_journal-5305	70	34	for	for	ADP
american_scientific_journal-5305	70	35	engineering	engineering	NOUN
american_scientific_journal-5305	70	36	,	,	PUNCT
american_scientific_journal-5305	70	37	technology	technology	NOUN
american_scientific_journal-5305	70	38	,	,	PUNCT
american_scientific_journal-5305	70	39	and	and	CCONJ
american_scientific_journal-5305	70	40	sciences	science	NOUN
american_scientific_journal-5305	70	41	(	(	PUNCT
american_scientific_journal-5305	70	42	asrjets	asrjet	NOUN
american_scientific_journal-5305	70	43	)	)	PUNCT
american_scientific_journal-5305	70	44	(	(	PUNCT
american_scientific_journal-5305	70	45	2019	2019	NUM
american_scientific_journal-5305	70	46	)	)	PUNCT
american_scientific_journal-5305	70	47	volume	volume	NOUN
american_scientific_journal-5305	70	48	61	61	NUM
american_scientific_journal-5305	70	49	,	,	PUNCT
american_scientific_journal-5305	70	50	no	no	DET
american_scientific_journal-5305	70	51	1	1	NUM
american_scientific_journal-5305	70	52	,	,	PUNCT
american_scientific_journal-5305	70	53	pp	pp	ADV
american_scientific_journal-5305	70	54	268	268	NUM
american_scientific_journal-5305	70	55	-	-	SYM
american_scientific_journal-5305	70	56	279	279	NUM
american_scientific_journal-5305	70	57	877	877	NUM
american_scientific_journal-5305	70	58	we	we	PRON
american_scientific_journal-5305	70	59	know	know	VERB
american_scientific_journal-5305	70	60	that	that	SCONJ
american_scientific_journal-5305	70	61	for	for	ADP
american_scientific_journal-5305	70	62	the	the	DET
american_scientific_journal-5305	70	63	solutions	solution	NOUN
american_scientific_journal-5305	70	64	to	to	ADP
american_scientific_journal-5305	70	65	the	the	DET
american_scientific_journal-5305	70	66	euler	euler	NOUN
american_scientific_journal-5305	70	67	-	-	PUNCT
american_scientific_journal-5305	70	68	lagrange	lagrange	NOUN
american_scientific_journal-5305	70	69	equations	equation	NOUN
american_scientific_journal-5305	70	70	we	we	PRON
american_scientific_journal-5305	70	71	have	have	VERB
american_scientific_journal-5305	70	72	that	that	PRON
american_scientific_journal-5305	70	73	then	then	ADV
american_scientific_journal-5305	70	74	,	,	PUNCT
american_scientific_journal-5305	70	75	since	since	SCONJ
american_scientific_journal-5305	70	76	x	x	X
american_scientific_journal-5305	70	77	(	(	PUNCT
american_scientific_journal-5305	70	78	(	(	PUNCT
american_scientific_journal-5305	70	79	(	(	PUNCT
american_scientific_journal-5305	70	80	)	)	PUNCT
american_scientific_journal-5305	70	81	hence	hence	ADV
american_scientific_journal-5305	70	82	(	(	PUNCT
american_scientific_journal-5305	70	83	)	)	PUNCT
american_scientific_journal-5305	70	84	(	(	PUNCT
american_scientific_journal-5305	70	85	3.39	3.39	NUM
american_scientific_journal-5305	70	86	)	)	PUNCT
american_scientific_journal-5305	70	87	according	accord	VERB
american_scientific_journal-5305	70	88	to	to	ADP
american_scientific_journal-5305	70	89	(	(	PUNCT
american_scientific_journal-5305	70	90	or	or	CCONJ
american_scientific_journal-5305	70	91	(	(	PUNCT
american_scientific_journal-5305	70	92	(	(	PUNCT
american_scientific_journal-5305	70	93	it	it	PRON
american_scientific_journal-5305	70	94	follows	follow	VERB
american_scientific_journal-5305	70	95	that	that	SCONJ
american_scientific_journal-5305	70	96	vector	vector	NOUN
american_scientific_journal-5305	70	97	t=	t=	PRON
american_scientific_journal-5305	70	98	(	(	PUNCT
american_scientific_journal-5305	70	99	(	(	PUNCT
american_scientific_journal-5305	70	100	(	(	PUNCT
american_scientific_journal-5305	70	101	(	(	PUNCT
american_scientific_journal-5305	70	102	is	be	AUX
american_scientific_journal-5305	70	103	conserved	conserve	VERB
american_scientific_journal-5305	70	104	vector	vector	NOUN
american_scientific_journal-5305	70	105	for	for	ADP
american_scientific_journal-5305	70	106	#	#	NOUN
american_scientific_journal-5305	70	107	corollary	corollary	NOUN
american_scientific_journal-5305	70	108	:	:	PUNCT
american_scientific_journal-5305	70	109	if	if	SCONJ
american_scientific_journal-5305	70	110	for	for	ADP
american_scientific_journal-5305	70	111	some	some	DET
american_scientific_journal-5305	70	112	one	one	NUM
american_scientific_journal-5305	70	113	–	–	PUNCT
american_scientific_journal-5305	70	114	parameter	parameter	NOUN
american_scientific_journal-5305	70	115	transformation	transformation	NOUN
american_scientific_journal-5305	70	116	group	group	NOUN
american_scientific_journal-5305	70	117	the	the	DET
american_scientific_journal-5305	70	118	invariance	invariance	NOUN
american_scientific_journal-5305	70	119	condition	condition	NOUN
american_scientific_journal-5305	70	120	(	(	PUNCT
american_scientific_journal-5305	70	121	3.32	3.32	NUM
american_scientific_journal-5305	70	122	)	)	PUNCT
american_scientific_journal-5305	70	123	is	be	AUX
american_scientific_journal-5305	70	124	not	not	PART
american_scientific_journal-5305	70	125	satisfied	satisfied	ADJ
american_scientific_journal-5305	70	126	but	but	CCONJ
american_scientific_journal-5305	70	127	the	the	DET
american_scientific_journal-5305	70	128	“	"	PUNCT
american_scientific_journal-5305	70	129	divergence	divergence	ADJ
american_scientific_journal-5305	70	130	”	"	PUNCT
american_scientific_journal-5305	70	131	condition	condition	NOUN
american_scientific_journal-5305	70	132	.	.	PUNCT
american_scientific_journal-5305	71	1	(	(	PUNCT
american_scientific_journal-5305	71	2	(	(	PUNCT
american_scientific_journal-5305	71	3	(	(	PUNCT
american_scientific_journal-5305	71	4	(	(	PUNCT
american_scientific_journal-5305	71	5	holds	hold	NOUN
american_scientific_journal-5305	71	6	,	,	PUNCT
american_scientific_journal-5305	71	7	then	then	ADV
american_scientific_journal-5305	71	8	the	the	DET
american_scientific_journal-5305	71	9	components	component	NOUN
american_scientific_journal-5305	71	10	of	of	ADP
american_scientific_journal-5305	71	11	the	the	DET
american_scientific_journal-5305	71	12	corresponding	corresponding	ADJ
american_scientific_journal-5305	71	13	conserved	conserve	VERB
american_scientific_journal-5305	71	14	vector	vector	NOUN
american_scientific_journal-5305	71	15	,	,	PUNCT
american_scientific_journal-5305	71	16	have	have	VERB
american_scientific_journal-5305	71	17	the	the	DET
american_scientific_journal-5305	71	18	form	form	NOUN
american_scientific_journal-5305	71	19	.	.	PUNCT
american_scientific_journal-5305	72	1	(	(	PUNCT
american_scientific_journal-5305	72	2	(	(	PUNCT
american_scientific_journal-5305	72	3	example	example	NOUN
american_scientific_journal-5305	72	4	4.4	4.4	NUM
american_scientific_journal-5305	72	5	.	.	PUNCT
american_scientific_journal-5305	73	1	the	the	DET
american_scientific_journal-5305	73	2	motion	motion	NOUN
american_scientific_journal-5305	73	3	of	of	ADP
american_scientific_journal-5305	73	4	the	the	DET
american_scientific_journal-5305	73	5	free	free	ADJ
american_scientific_journal-5305	73	6	particle	particle	NOUN
american_scientific_journal-5305	73	7	in	in	ADP
american_scientific_journal-5305	73	8	special	special	ADJ
american_scientific_journal-5305	73	9	relativity	relativity	NOUN
american_scientific_journal-5305	73	10	is	be	AUX
american_scientific_journal-5305	73	11	described	describe	VERB
american_scientific_journal-5305	73	12	by	by	ADP
american_scientific_journal-5305	73	13	the	the	DET
american_scientific_journal-5305	73	14	relativistic	relativistic	ADJ
american_scientific_journal-5305	73	15	lagrangian	lagrangian	ADJ
american_scientific_journal-5305	73	16	√	√	PROPN
american_scientific_journal-5305	73	17	(	(	PUNCT
american_scientific_journal-5305	73	18	4.1	4.1	NUM
american_scientific_journal-5305	73	19	)	)	PUNCT
american_scientific_journal-5305	73	20	where	where	SCONJ
american_scientific_journal-5305	73	21	∑	∑	PUNCT
american_scientific_journal-5305	73	22	(	(	PUNCT
american_scientific_journal-5305	73	23	the	the	DET
american_scientific_journal-5305	73	24	space	space	NOUN
american_scientific_journal-5305	73	25	coordinates	coordinate	NOUN
american_scientific_journal-5305	73	26	of	of	ADP
american_scientific_journal-5305	73	27	the	the	DET
american_scientific_journal-5305	73	28	particle	particle	NOUN
american_scientific_journal-5305	73	29	is	be	AUX
american_scientific_journal-5305	73	30	(	(	PUNCT
american_scientific_journal-5305	73	31	and	and	CCONJ
american_scientific_journal-5305	73	32	the	the	DET
american_scientific_journal-5305	73	33	velocity	velocity	NOUN
american_scientific_journal-5305	73	34	is	be	AUX
american_scientific_journal-5305	73	35	(	(	PUNCT
american_scientific_journal-5305	73	36	such	such	ADJ
american_scientific_journal-5305	73	37	that	that	DET
american_scientific_journal-5305	73	38	v	v	NOUN
american_scientific_journal-5305	73	39	=	=	SYM
american_scientific_journal-5305	73	40	,	,	PUNCT
american_scientific_journal-5305	73	41	where	where	SCONJ
american_scientific_journal-5305	73	42	t	t	PROPN
american_scientific_journal-5305	73	43	is	be	AUX
american_scientific_journal-5305	73	44	time	time	NOUN
american_scientific_journal-5305	73	45	.	.	PUNCT
american_scientific_journal-5305	74	1	we	we	PRON
american_scientific_journal-5305	74	2	have	have	VERB
american_scientific_journal-5305	74	3	that	that	PRON
american_scientific_journal-5305	74	4	x	x	PRON
american_scientific_journal-5305	74	5	is	be	AUX
american_scientific_journal-5305	74	6	our	our	PRON
american_scientific_journal-5305	74	7	differential	differential	ADJ
american_scientific_journal-5305	74	8	variables	variable	NOUN
american_scientific_journal-5305	74	9	and	and	CCONJ
american_scientific_journal-5305	74	10	t	t	PROPN
american_scientific_journal-5305	74	11	is	be	AUX
american_scientific_journal-5305	74	12	our	our	PRON
american_scientific_journal-5305	74	13	only	only	ADJ
american_scientific_journal-5305	74	14	independent	independent	ADJ
american_scientific_journal-5305	74	15	variable	variable	NOUN
american_scientific_journal-5305	74	16	.	.	PUNCT
american_scientific_journal-5305	75	1	the	the	DET
american_scientific_journal-5305	75	2	generator	generator	NOUN
american_scientific_journal-5305	75	3	of	of	ADP
american_scientific_journal-5305	75	4	the	the	DET
american_scientific_journal-5305	75	5	lorentz	lorentz	PROPN
american_scientific_journal-5305	75	6	group	group	NOUN
american_scientific_journal-5305	75	7	(	(	PUNCT
american_scientific_journal-5305	75	8	classical	classical	ADJ
american_scientific_journal-5305	75	9	dynamic	dynamic	NOUN
american_scientific_journal-5305	75	10	)	)	PUNCT
american_scientific_journal-5305	75	11	is	be	AUX
american_scientific_journal-5305	75	12	given	give	VERB
american_scientific_journal-5305	75	13	by	by	ADP
american_scientific_journal-5305	75	14	,	,	PUNCT
american_scientific_journal-5305	75	15	,	,	PUNCT
american_scientific_journal-5305	75	16	.	.	PUNCT
american_scientific_journal-5305	76	1	(	(	PUNCT
american_scientific_journal-5305	76	2	4.2	4.2	NUM
american_scientific_journal-5305	76	3	)	)	PUNCT
american_scientific_journal-5305	76	4	by	by	ADP
american_scientific_journal-5305	76	5	applying	apply	VERB
american_scientific_journal-5305	76	6	noether‟s	noether‟s	NOUN
american_scientific_journal-5305	76	7	theorem	theorem	NOUN
american_scientific_journal-5305	76	8	to	to	ADP
american_scientific_journal-5305	76	9	each	each	PRON
american_scientific_journal-5305	76	10	of	of	ADP
american_scientific_journal-5305	76	11	these	these	DET
american_scientific_journal-5305	76	12	generators	generator	NOUN
american_scientific_journal-5305	76	13	with	with	ADP
american_scientific_journal-5305	76	14	the	the	DET
american_scientific_journal-5305	76	15	given	give	VERB
american_scientific_journal-5305	76	16	lagrangian	lagrangian	NOUN
american_scientific_journal-5305	76	17	we	we	PRON
american_scientific_journal-5305	76	18	wish	wish	VERB
american_scientific_journal-5305	76	19	to	to	PART
american_scientific_journal-5305	76	20	find	find	VERB
american_scientific_journal-5305	76	21	the	the	DET
american_scientific_journal-5305	76	22	corresponding	correspond	VERB
american_scientific_journal-5305	76	23	conservation	conservation	NOUN
american_scientific_journal-5305	76	24	law	law	NOUN
american_scientific_journal-5305	76	25	.	.	PUNCT
american_scientific_journal-5305	77	1	we	we	PRON
american_scientific_journal-5305	77	2	have	have	VERB
american_scientific_journal-5305	77	3	generators	generator	NOUN
american_scientific_journal-5305	77	4	of	of	ADP
american_scientific_journal-5305	77	5	the	the	DET
american_scientific_journal-5305	77	6	form	form	NOUN
american_scientific_journal-5305	77	7	(	(	PUNCT
american_scientific_journal-5305	77	8	(	(	PUNCT
american_scientific_journal-5305	77	9	,	,	PUNCT
american_scientific_journal-5305	77	10	(	(	PUNCT
american_scientific_journal-5305	77	11	4.3	4.3	NUM
american_scientific_journal-5305	77	12	)	)	PUNCT
american_scientific_journal-5305	77	13	american	american	ADJ
american_scientific_journal-5305	77	14	scientific	scientific	ADJ
american_scientific_journal-5305	77	15	research	research	NOUN
american_scientific_journal-5305	77	16	journal	journal	NOUN
american_scientific_journal-5305	77	17	for	for	ADP
american_scientific_journal-5305	77	18	engineering	engineering	NOUN
american_scientific_journal-5305	77	19	,	,	PUNCT
american_scientific_journal-5305	77	20	technology	technology	NOUN
american_scientific_journal-5305	77	21	,	,	PUNCT
american_scientific_journal-5305	77	22	and	and	CCONJ
american_scientific_journal-5305	77	23	sciences	science	NOUN
american_scientific_journal-5305	77	24	(	(	PUNCT
american_scientific_journal-5305	77	25	asrjets	asrjet	NOUN
american_scientific_journal-5305	77	26	)	)	PUNCT
american_scientific_journal-5305	77	27	(	(	PUNCT
american_scientific_journal-5305	77	28	2019	2019	NUM
american_scientific_journal-5305	77	29	)	)	PUNCT
american_scientific_journal-5305	77	30	volume	volume	NOUN
american_scientific_journal-5305	77	31	61	61	NUM
american_scientific_journal-5305	77	32	,	,	PUNCT
american_scientific_journal-5305	77	33	no	no	DET
american_scientific_journal-5305	77	34	1	1	NUM
american_scientific_journal-5305	77	35	,	,	PUNCT
american_scientific_journal-5305	77	36	pp	pp	ADV
american_scientific_journal-5305	77	37	268	268	NUM
american_scientific_journal-5305	77	38	-	-	SYM
american_scientific_journal-5305	77	39	279	279	NUM
american_scientific_journal-5305	77	40	878	878	NUM
american_scientific_journal-5305	77	41	we	we	PRON
american_scientific_journal-5305	77	42	will	will	AUX
american_scientific_journal-5305	77	43	get	get	VERB
american_scientific_journal-5305	77	44	a	a	DET
american_scientific_journal-5305	77	45	conserved	conserved	ADJ
american_scientific_journal-5305	77	46	quantity	quantity	NOUN
american_scientific_journal-5305	77	47	of	of	ADP
american_scientific_journal-5305	77	48	the	the	DET
american_scientific_journal-5305	77	49	form	form	NOUN
american_scientific_journal-5305	77	50	(	(	PUNCT
american_scientific_journal-5305	77	51	,	,	PUNCT
american_scientific_journal-5305	77	52	(	(	PUNCT
american_scientific_journal-5305	77	53	4.4	4.4	NUM
american_scientific_journal-5305	77	54	)	)	PUNCT
american_scientific_journal-5305	77	55	where	where	SCONJ
american_scientific_journal-5305	77	56	√	√	INTJ
american_scientific_journal-5305	77	57	(	(	PUNCT
american_scientific_journal-5305	77	58	for	for	SCONJ
american_scientific_journal-5305	77	59	we	we	PRON
american_scientific_journal-5305	77	60	have	have	VERB
american_scientific_journal-5305	77	61	equation	equation	NOUN
american_scientific_journal-5305	77	62	(	(	PUNCT
american_scientific_journal-5305	77	63	4.10	4.10	NUM
american_scientific_journal-5305	77	64	)	)	PUNCT
american_scientific_journal-5305	77	65	yields	yield	NOUN
american_scientific_journal-5305	77	66	(	(	PUNCT
american_scientific_journal-5305	77	67	putting	put	VERB
american_scientific_journal-5305	77	68	we	we	PRON
american_scientific_journal-5305	77	69	get	get	VERB
american_scientific_journal-5305	77	70	,	,	PUNCT
american_scientific_journal-5305	77	71	i.e.	i.e.	X
american_scientific_journal-5305	77	72	conservation	conservation	NOUN
american_scientific_journal-5305	77	73	of	of	ADP
american_scientific_journal-5305	77	74	energy	energy	NOUN
american_scientific_journal-5305	77	75	.	.	PUNCT
american_scientific_journal-5305	78	1	for	for	SCONJ
american_scientific_journal-5305	78	2	we	we	PRON
american_scientific_journal-5305	78	3	get	get	VERB
american_scientific_journal-5305	78	4	a	a	DET
american_scientific_journal-5305	78	5	conserved	conserved	ADJ
american_scientific_journal-5305	78	6	vector	vector	NOUN
american_scientific_journal-5305	78	7	(	(	PUNCT
american_scientific_journal-5305	78	8	.here	.here	ADV
american_scientific_journal-5305	78	9	we	we	PRON
american_scientific_journal-5305	78	10	have	have	AUX
american_scientific_journal-5305	78	11	while	while	NOUN
american_scientific_journal-5305	78	12	.	.	PUNCT
american_scientific_journal-5305	79	1	equation	equation	NOUN
american_scientific_journal-5305	79	2	(	(	PUNCT
american_scientific_journal-5305	79	3	4.10	4.10	NUM
american_scientific_journal-5305	79	4	)	)	PUNCT
american_scientific_journal-5305	79	5	yields	yield	NOUN
american_scientific_journal-5305	79	6	(	(	PUNCT
american_scientific_journal-5305	79	7	4.7	4.7	NUM
american_scientific_journal-5305	79	8	)	)	PUNCT
american_scientific_journal-5305	79	9	leading	lead	VERB
american_scientific_journal-5305	79	10	to	to	ADP
american_scientific_journal-5305	79	11	the	the	DET
american_scientific_journal-5305	79	12	conserved	conserved	ADJ
american_scientific_journal-5305	79	13	vector	vector	NOUN
american_scientific_journal-5305	79	14	,	,	PUNCT
american_scientific_journal-5305	79	15	i.e.	i.e.	X
american_scientific_journal-5305	79	16	conservation	conservation	NOUN
american_scientific_journal-5305	79	17	of	of	ADP
american_scientific_journal-5305	79	18	relativistic	relativistic	ADJ
american_scientific_journal-5305	79	19	momentum	momentum	NOUN
american_scientific_journal-5305	79	20	.	.	PUNCT
american_scientific_journal-5305	80	1	for	for	ADP
american_scientific_journal-5305	80	2	the	the	DET
american_scientific_journal-5305	80	3	generator	generator	NOUN
american_scientific_journal-5305	80	4	,	,	PUNCT
american_scientific_journal-5305	80	5	we	we	PRON
american_scientific_journal-5305	80	6	have	have	VERB
american_scientific_journal-5305	80	7	a	a	DET
american_scientific_journal-5305	80	8	rotational	rotational	ADJ
american_scientific_journal-5305	80	9	symmetry	symmetry	NOUN
american_scientific_journal-5305	80	10	.	.	PUNCT
american_scientific_journal-5305	81	1	with	with	ADP
american_scientific_journal-5305	81	2	and	and	CCONJ
american_scientific_journal-5305	81	3	.	.	PUNCT
american_scientific_journal-5305	82	1	equation	equation	NOUN
american_scientific_journal-5305	82	2	(	(	PUNCT
american_scientific_journal-5305	82	3	4.10	4.10	NUM
american_scientific_journal-5305	82	4	)	)	PUNCT
american_scientific_journal-5305	82	5	yields	yield	NOUN
american_scientific_journal-5305	82	6	(	(	PUNCT
american_scientific_journal-5305	82	7	(	(	PUNCT
american_scientific_journal-5305	82	8	(	(	PUNCT
american_scientific_journal-5305	82	9	.	.	PUNCT
american_scientific_journal-5305	82	10	(	(	PUNCT
american_scientific_journal-5305	82	11	4.8	4.8	NUM
american_scientific_journal-5305	82	12	)	)	PUNCT
american_scientific_journal-5305	82	13	we	we	PRON
american_scientific_journal-5305	82	14	get	get	VERB
american_scientific_journal-5305	82	15	the	the	DET
american_scientific_journal-5305	82	16	conserved	conserved	ADJ
american_scientific_journal-5305	82	17	vector	vector	NOUN
american_scientific_journal-5305	82	18	(	(	PUNCT
american_scientific_journal-5305	82	19	putting	put	VERB
american_scientific_journal-5305	82	20	we	we	PRON
american_scientific_journal-5305	82	21	get	get	VERB
american_scientific_journal-5305	82	22	the	the	DET
american_scientific_journal-5305	82	23	conserved	conserved	ADJ
american_scientific_journal-5305	82	24	vector	vector	NOUN
american_scientific_journal-5305	82	25	(	(	PUNCT
american_scientific_journal-5305	82	26	,	,	PUNCT
american_scientific_journal-5305	82	27	i.e.	i.e.	X
american_scientific_journal-5305	82	28	conservation	conservation	NOUN
american_scientific_journal-5305	82	29	of	of	ADP
american_scientific_journal-5305	82	30	angular	angular	ADJ
american_scientific_journal-5305	82	31	momentum	momentum	NOUN
american_scientific_journal-5305	82	32	.	.	PUNCT
american_scientific_journal-5305	83	1	for	for	ADP
american_scientific_journal-5305	83	2	the	the	DET
american_scientific_journal-5305	83	3	generator	generator	NOUN
american_scientific_journal-5305	83	4	,	,	PUNCT
american_scientific_journal-5305	83	5	we	we	PRON
american_scientific_journal-5305	83	6	get	get	VERB
american_scientific_journal-5305	83	7	a	a	DET
american_scientific_journal-5305	83	8	vector	vector	NOUN
american_scientific_journal-5305	83	9	(	(	PUNCT
american_scientific_journal-5305	83	10	for	for	ADP
american_scientific_journal-5305	83	11	the	the	DET
american_scientific_journal-5305	83	12	first	first	ADJ
american_scientific_journal-5305	83	13	component	component	NOUN
american_scientific_journal-5305	83	14	we	we	PRON
american_scientific_journal-5305	83	15	have	have	VERB
american_scientific_journal-5305	83	16	ξ	ξ	PROPN
american_scientific_journal-5305	83	17	american	american	ADJ
american_scientific_journal-5305	83	18	scientific	scientific	ADJ
american_scientific_journal-5305	83	19	research	research	NOUN
american_scientific_journal-5305	83	20	journal	journal	NOUN
american_scientific_journal-5305	83	21	for	for	ADP
american_scientific_journal-5305	83	22	engineering	engineering	NOUN
american_scientific_journal-5305	83	23	,	,	PUNCT
american_scientific_journal-5305	83	24	technology	technology	NOUN
american_scientific_journal-5305	83	25	,	,	PUNCT
american_scientific_journal-5305	83	26	and	and	CCONJ
american_scientific_journal-5305	83	27	sciences	science	NOUN
american_scientific_journal-5305	83	28	(	(	PUNCT
american_scientific_journal-5305	83	29	asrjets	asrjet	NOUN
american_scientific_journal-5305	83	30	)	)	PUNCT
american_scientific_journal-5305	83	31	(	(	PUNCT
american_scientific_journal-5305	83	32	2019	2019	NUM
american_scientific_journal-5305	83	33	)	)	PUNCT
american_scientific_journal-5305	83	34	volume	volume	NOUN
american_scientific_journal-5305	83	35	61	61	NUM
american_scientific_journal-5305	83	36	,	,	PUNCT
american_scientific_journal-5305	83	37	no	no	DET
american_scientific_journal-5305	83	38	1	1	NUM
american_scientific_journal-5305	83	39	,	,	PUNCT
american_scientific_journal-5305	83	40	pp	pp	ADV
american_scientific_journal-5305	83	41	268	268	NUM
american_scientific_journal-5305	83	42	-	-	SYM
american_scientific_journal-5305	83	43	279	279	NUM
american_scientific_journal-5305	83	44	879	879	NUM
american_scientific_journal-5305	83	45	=	=	NOUN
american_scientific_journal-5305	83	46	,	,	PUNCT
american_scientific_journal-5305	83	47	,	,	PUNCT
american_scientific_journal-5305	83	48	equation	equation	NOUN
american_scientific_journal-5305	83	49	(	(	PUNCT
american_scientific_journal-5305	83	50	4	4	NUM
american_scientific_journal-5305	83	51	.	.	NOUN
american_scientific_journal-5305	83	52	10	10	NUM
american_scientific_journal-5305	83	53	)	)	PUNCT
american_scientific_journal-5305	83	54	yields	yield	NOUN
american_scientific_journal-5305	83	55	(	(	PUNCT
american_scientific_journal-5305	83	56	(	(	PUNCT
american_scientific_journal-5305	83	57	(	(	PUNCT
american_scientific_journal-5305	83	58	[	[	PUNCT
american_scientific_journal-5305	83	59	]	]	X
american_scientific_journal-5305	83	60	(	(	PUNCT
american_scientific_journal-5305	83	61	(	(	PUNCT
american_scientific_journal-5305	83	62	a	a	DET
american_scientific_journal-5305	83	63	similar	similar	ADJ
american_scientific_journal-5305	83	64	procedure	procedure	NOUN
american_scientific_journal-5305	83	65	for	for	ADP
american_scientific_journal-5305	83	66	the	the	DET
american_scientific_journal-5305	83	67	remaining	remain	VERB
american_scientific_journal-5305	83	68	two	two	NUM
american_scientific_journal-5305	83	69	components	component	NOUN
american_scientific_journal-5305	83	70	and	and	CCONJ
american_scientific_journal-5305	83	71	putting	put	VERB
american_scientific_journal-5305	83	72	leads	lead	NOUN
american_scientific_journal-5305	83	73	to	to	ADP
american_scientific_journal-5305	83	74	the	the	DET
american_scientific_journal-5305	83	75	conserved	conserved	ADJ
american_scientific_journal-5305	83	76	vector	vector	NOUN
american_scientific_journal-5305	83	77	(	(	PUNCT
american_scientific_journal-5305	83	78	i.e.	i.e.	X
american_scientific_journal-5305	83	79	conservation	conservation	NOUN
american_scientific_journal-5305	83	80	of	of	ADP
american_scientific_journal-5305	83	81	relative	relative	ADJ
american_scientific_journal-5305	83	82	center	center	NOUN
american_scientific_journal-5305	83	83	of	of	ADP
american_scientific_journal-5305	83	84	mass	mass	PROPN
american_scientific_journal-5305	83	85	.	.	PUNCT
american_scientific_journal-5305	84	1	references	reference	NOUN
american_scientific_journal-5305	84	2	[	[	X
american_scientific_journal-5305	84	3	1	1	NUM
american_scientific_journal-5305	84	4	]	]	PUNCT
american_scientific_journal-5305	84	5	notes	note	NOUN
american_scientific_journal-5305	84	6	on	on	ADP
american_scientific_journal-5305	84	7	lie	lie	NOUN
american_scientific_journal-5305	84	8	groups	group	NOUN
american_scientific_journal-5305	84	9	–	–	PUNCT
american_scientific_journal-5305	84	10	eugene	eugene	PROPN
american_scientific_journal-5305	84	11	lerman	lerman	NOUN
american_scientific_journal-5305	84	12	–	–	PUNCT
american_scientific_journal-5305	84	13	february	february	PROPN
american_scientific_journal-5305	84	14	15	15	NUM
american_scientific_journal-5305	84	15	,	,	PUNCT
american_scientific_journal-5305	84	16	2012	2012	NUM
american_scientific_journal-5305	84	17	[	[	X
american_scientific_journal-5305	84	18	2	2	X
american_scientific_journal-5305	84	19	]	]	PUNCT
american_scientific_journal-5305	84	20	m.	m.	NOUN
american_scientific_journal-5305	84	21	a.	a.	NOUN
american_scientific_journal-5305	84	22	basher	basher	NOUN
american_scientific_journal-5305	84	23	:	:	PUNCT
american_scientific_journal-5305	84	24	lecture	lecture	NOUN
american_scientific_journal-5305	84	25	notes	note	NOUN
american_scientific_journal-5305	84	26	,	,	PUNCT
american_scientific_journal-5305	84	27	alneelain	alneelain	VERB
american_scientific_journal-5305	84	28	university2012	university2012	PROPN
american_scientific_journal-5305	85	1	[	[	X
american_scientific_journal-5305	85	2	3	3	X
american_scientific_journal-5305	85	3	]	]	X
american_scientific_journal-5305	85	4	an	an	DET
american_scientific_journal-5305	85	5	introduction	introduction	NOUN
american_scientific_journal-5305	85	6	to	to	PART
american_scientific_journal-5305	85	7	differentiable	differentiable	VERB
american_scientific_journal-5305	85	8	manifolds	manifold	NOUN
american_scientific_journal-5305	85	9	and	and	CCONJ
american_scientific_journal-5305	85	10	riemannian	riemannian	ADJ
american_scientific_journal-5305	85	11	geometry	geometry	NOUN
american_scientific_journal-5305	85	12	william.m	william.m	PROPN
american_scientific_journal-5305	85	13	.	.	PUNCT
american_scientific_journal-5305	86	1	boothby	boothby	VERB
american_scientific_journal-5305	87	1	[	[	X
american_scientific_journal-5305	87	2	4	4	NUM
american_scientific_journal-5305	87	3	]	]	ADJ
american_scientific_journal-5305	87	4	symmetry	symmetry	NOUN
american_scientific_journal-5305	87	5	and	and	CCONJ
american_scientific_journal-5305	87	6	conservation	conservation	NOUN
american_scientific_journal-5305	87	7	laws	law	NOUN
american_scientific_journal-5305	87	8	.	.	PUNCT
american_scientific_journal-5305	88	1	thesis	thesis	NOUN
american_scientific_journal-5305	88	2	for	for	ADP
american_scientific_journal-5305	88	3	the	the	DET
american_scientific_journal-5305	88	4	degree	degree	NOUN
american_scientific_journal-5305	88	5	of	of	ADP
american_scientific_journal-5305	88	6	doctor	doctor	NOUN
american_scientific_journal-5305	88	7	of	of	ADP
american_scientific_journal-5305	88	8	philosophy	philosophy	NOUN
american_scientific_journal-5305	88	9	–	–	PUNCT
american_scientific_journal-5305	88	10	växjö	växjö	NOUN
american_scientific_journal-5305	88	11	university	university	NOUN
american_scientific_journal-5305	88	12	,	,	PUNCT
american_scientific_journal-5305	88	13	sweeden2009	sweeden2009	PROPN
american_scientific_journal-5305	89	1	[	[	X
american_scientific_journal-5305	89	2	5	5	NUM
american_scientific_journal-5305	89	3	]	]	PUNCT
american_scientific_journal-5305	89	4	invariant	invariant	ADJ
american_scientific_journal-5305	89	5	variational	variational	ADJ
american_scientific_journal-5305	89	6	problems	problem	NOUN
american_scientific_journal-5305	89	7	.	.	PUNCT
american_scientific_journal-5305	90	1	(	(	PUNCT
american_scientific_journal-5305	90	2	f.klein	f.klein	ADV
american_scientific_journal-5305	90	3	on	on	ADP
american_scientific_journal-5305	90	4	his	his	PRON
american_scientific_journal-5305	90	5	fifty	fifty	NUM
american_scientific_journal-5305	90	6	-	-	PUNCT
american_scientific_journal-5305	90	7	year	year	NOUN
american_scientific_journal-5305	90	8	doctoral	doctoral	ADJ
american_scientific_journal-5305	90	9	jubile	jubile	NOUN
american_scientific_journal-5305	90	10	)	)	PUNCT
american_scientific_journal-5305	90	11	by	by	ADP
american_scientific_journal-5305	90	12	emmy	emmy	ADJ
american_scientific_journal-5305	90	13	noether	noether	PROPN
american_scientific_journal-5305	90	14	in	in	ADP
american_scientific_journal-5305	90	15	gottingan;translated	gottingan;translate	VERB
american_scientific_journal-5305	90	16	by	by	ADP
american_scientific_journal-5305	90	17	d.h	d.h	PROPN
american_scientific_journal-5305	90	18	.	.	PROPN
american_scientific_journal-5305	90	19	delpenich	delpenich	PROPN
american_scientific_journal-5305	91	1	[	[	X
american_scientific_journal-5305	91	2	6	6	NUM
american_scientific_journal-5305	91	3	]	]	PUNCT
american_scientific_journal-5305	91	4	symmetries	symmetry	NOUN
american_scientific_journal-5305	91	5	and	and	CCONJ
american_scientific_journal-5305	91	6	conservation	conservation	NOUN
american_scientific_journal-5305	91	7	laws	law	NOUN
american_scientific_journal-5305	91	8	obtained	obtain	VERB
american_scientific_journal-5305	91	9	by	by	ADP
american_scientific_journal-5305	91	10	lie	lie	NOUN
american_scientific_journal-5305	91	11	group	group	NOUN
american_scientific_journal-5305	91	12	analysis	analysis	NOUN
american_scientific_journal-5305	91	13	for	for	ADP
american_scientific_journal-5305	91	14	certain	certain	ADJ
american_scientific_journal-5305	91	15	physical	physical	ADJ
american_scientific_journal-5305	91	16	systems	system	NOUN
american_scientific_journal-5305	91	17	marcus	marcus	PROPN
american_scientific_journal-5305	91	18	erikssonuppsala	erikssonuppsala	PROPN
american_scientific_journal-5305	91	19	school	school	PROPN
american_scientific_journal-5305	91	20	of	of	ADP
american_scientific_journal-5305	91	21	engineering	engineering	NOUN
american_scientific_journal-5305	91	22	-	-	PUNCT
american_scientific_journal-5305	91	23	uppsala	uppsala	PROPN
american_scientific_journal-5305	91	24	university	university	PROPN
american_scientific_journal-5305	91	25	,	,	PUNCT
american_scientific_journal-5305	91	26	sweden	sweden	PROPN
american_scientific_journal-5305	92	1	[	[	X
american_scientific_journal-5305	92	2	7	7	NUM
american_scientific_journal-5305	92	3	]	]	ADJ
american_scientific_journal-5305	92	4	introduction	introduction	NOUN
american_scientific_journal-5305	92	5	to	to	ADP
american_scientific_journal-5305	92	6	differential	differential	ADJ
american_scientific_journal-5305	92	7	invariants	invariant	NOUN
american_scientific_journal-5305	92	8	–	–	PUNCT
american_scientific_journal-5305	92	9	valeriy	valeriy	NOUN
american_scientific_journal-5305	92	10	yumaguzhin	yumaguzhin	PROPN
american_scientific_journal-5305	92	11	opava	opava	NOUN
american_scientific_journal-5305	92	12	2005	2005	NUM
american_scientific_journal-5305	93	1	[	[	X
american_scientific_journal-5305	93	2	8	8	NUM
american_scientific_journal-5305	93	3	]	]	PUNCT
american_scientific_journal-5305	93	4	head	head	NOUN
american_scientific_journal-5305	93	5	a.	a.	NOUN
american_scientific_journal-5305	93	6	,	,	PUNCT
american_scientific_journal-5305	93	7	lie	lie	NOUN
american_scientific_journal-5305	93	8	,	,	PUNCT
american_scientific_journal-5305	93	9	a	a	DET
american_scientific_journal-5305	93	10	pc	pc	NOUN
american_scientific_journal-5305	93	11	program	program	NOUN
american_scientific_journal-5305	93	12	for	for	ADP
american_scientific_journal-5305	93	13	lie	lie	NOUN
american_scientific_journal-5305	93	14	analysis	analysis	NOUN
american_scientific_journal-5305	93	15	of	of	ADP
american_scientific_journal-5305	93	16	differential	differential	ADJ
american_scientific_journal-5305	93	17	equations	equation	NOUN
american_scientific_journal-5305	93	18	,	,	PUNCT
american_scientific_journal-5305	93	19	comp	comp	NOUN
american_scientific_journal-5305	93	20	.	.	PUNCT
american_scientific_journal-5305	94	1	phys	phy	NOUN
american_scientific_journal-5305	94	2	.	.	PUNCT
american_scientific_journal-5305	95	1	commun	commun	PROPN
american_scientific_journal-5305	95	2	.	.	PROPN
american_scientific_journal-5305	95	3	,	,	PUNCT
american_scientific_journal-5305	95	4	1993	1993	NUM
american_scientific_journal-5305	95	5	,	,	PUNCT
american_scientific_journal-5305	95	6	v.77	v.77	NOUN
american_scientific_journal-5305	95	7	,	,	PUNCT
american_scientific_journal-5305	95	8	24	24	NUM