id	sid	tid	token	lemma	pos
ejpam-6128	1	1	european	european	PROPN
ejpam-6128	1	2	journal	journal	PROPN
ejpam-6128	1	3	of	of	ADP
ejpam-6128	1	4	pure	pure	ADJ
ejpam-6128	1	5	and	and	CCONJ
ejpam-6128	1	6	applied	applied	ADJ
ejpam-6128	1	7	mathematics	mathematic	NOUN
ejpam-6128	1	8	2025	2025	NUM
ejpam-6128	1	9	,	,	PUNCT
ejpam-6128	1	10	vol	vol	NOUN
ejpam-6128	1	11	.	.	PROPN
ejpam-6128	1	12	18	18	NUM
ejpam-6128	1	13	,	,	PUNCT
ejpam-6128	1	14	issue	issue	NOUN
ejpam-6128	1	15	4	4	NUM
ejpam-6128	1	16	,	,	PUNCT
ejpam-6128	1	17	article	article	NOUN
ejpam-6128	1	18	number	number	NOUN
ejpam-6128	1	19	6128	6128	NUM
ejpam-6128	1	20	issn	issn	PROPN
ejpam-6128	1	21	1307	1307	NUM
ejpam-6128	1	22	-	-	SYM
ejpam-6128	1	23	5543	5543	NUM
ejpam-6128	1	24	–	–	PUNCT
ejpam-6128	1	25	ejpam.com	ejpam.com	X
ejpam-6128	1	26	published	publish	VERB
ejpam-6128	1	27	by	by	ADP
ejpam-6128	1	28	new	new	PROPN
ejpam-6128	1	29	york	york	PROPN
ejpam-6128	1	30	business	business	PROPN
ejpam-6128	1	31	global	global	PROPN
ejpam-6128	1	32	group	group	PROPN
ejpam-6128	1	33	analysis	analysis	NOUN
ejpam-6128	1	34	of	of	ADP
ejpam-6128	1	35	a	a	DET
ejpam-6128	1	36	class	class	NOUN
ejpam-6128	1	37	of	of	ADP
ejpam-6128	1	38	nonlinear	nonlinear	ADJ
ejpam-6128	1	39	wave	wave	NOUN
ejpam-6128	1	40	equations	equations	PROPN
ejpam-6128	1	41	m.	m.	PROPN
ejpam-6128	1	42	usman1	usman1	PROPN
ejpam-6128	1	43	,	,	PUNCT
ejpam-6128	1	44	akhtar	akhtar	PROPN
ejpam-6128	1	45	hussain2,∗	hussain2,∗	PROPN
ejpam-6128	1	46	,	,	PUNCT
ejpam-6128	1	47	m.	m.	NOUN
ejpam-6128	1	48	umar	umar	PROPN
ejpam-6128	1	49	farooq1	farooq1	PROPN
ejpam-6128	1	50	,	,	PUNCT
ejpam-6128	1	51	jorge	jorge	VERB
ejpam-6128	1	52	herrera3	herrera3	PROPN
ejpam-6128	2	1	1	1	NUM
ejpam-6128	2	2	college	college	NOUN
ejpam-6128	2	3	of	of	ADP
ejpam-6128	2	4	electrical	electrical	ADJ
ejpam-6128	2	5	and	and	CCONJ
ejpam-6128	2	6	mechanical	mechanical	ADJ
ejpam-6128	2	7	engineering	engineering	NOUN
ejpam-6128	2	8	(	(	PUNCT
ejpam-6128	2	9	ceme	ceme	NOUN
ejpam-6128	2	10	)	)	PUNCT
ejpam-6128	2	11	,	,	PUNCT
ejpam-6128	2	12	national	national	PROPN
ejpam-6128	2	13	university	university	PROPN
ejpam-6128	2	14	of	of	ADP
ejpam-6128	2	15	sciences	science	NOUN
ejpam-6128	2	16	and	and	CCONJ
ejpam-6128	2	17	technology	technology	NOUN
ejpam-6128	2	18	(	(	PUNCT
ejpam-6128	2	19	nust	nust	PROPN
ejpam-6128	2	20	)	)	PUNCT
ejpam-6128	2	21	,	,	PUNCT
ejpam-6128	2	22	h-12	h-12	NOUN
ejpam-6128	2	23	islamabad	islamabad	NOUN
ejpam-6128	2	24	44000	44000	NUM
ejpam-6128	2	25	,	,	PUNCT
ejpam-6128	2	26	pakistan	pakistan	PROPN
ejpam-6128	2	27	2	2	NUM
ejpam-6128	2	28	department	department	NOUN
ejpam-6128	2	29	of	of	ADP
ejpam-6128	2	30	mathematics	mathematic	NOUN
ejpam-6128	2	31	,	,	PUNCT
ejpam-6128	2	32	university	university	NOUN
ejpam-6128	2	33	of	of	ADP
ejpam-6128	2	34	management	management	NOUN
ejpam-6128	2	35	and	and	CCONJ
ejpam-6128	2	36	technology	technology	NOUN
ejpam-6128	2	37	,	,	PUNCT
ejpam-6128	2	38	lahore	lahore	NOUN
ejpam-6128	2	39	54770	54770	NUM
ejpam-6128	2	40	,	,	PUNCT
ejpam-6128	2	41	pakistan	pakistan	PROPN
ejpam-6128	2	42	3	3	NUM
ejpam-6128	2	43	facultad	facultad	PROPN
ejpam-6128	2	44	de	de	PROPN
ejpam-6128	2	45	ciencias	ciencias	PROPN
ejpam-6128	2	46	naturales	naturales	PROPN
ejpam-6128	2	47	e	e	PROPN
ejpam-6128	2	48	ingenieria	ingenieria	PROPN
ejpam-6128	2	49	,	,	PUNCT
ejpam-6128	2	50	universidad	universidad	PROPN
ejpam-6128	2	51	de	de	PROPN
ejpam-6128	2	52	bogota	bogota	PROPN
ejpam-6128	2	53	jorge	jorge	PROPN
ejpam-6128	2	54	tadeo	tadeo	PROPN
ejpam-6128	2	55	lozano	lozano	PROPN
ejpam-6128	2	56	,	,	PUNCT
ejpam-6128	2	57	bogota	bogota	PROPN
ejpam-6128	2	58	110311	110311	NUM
ejpam-6128	2	59	,	,	PUNCT
ejpam-6128	2	60	colombia	colombia	PROPN
ejpam-6128	2	61	abstract	abstract	NOUN
ejpam-6128	2	62	.	.	PUNCT
ejpam-6128	3	1	we	we	PRON
ejpam-6128	3	2	study	study	VERB
ejpam-6128	3	3	the	the	DET
ejpam-6128	3	4	nature	nature	NOUN
ejpam-6128	3	5	of	of	ADP
ejpam-6128	3	6	a	a	DET
ejpam-6128	3	7	(	(	PUNCT
ejpam-6128	3	8	2	2	NUM
ejpam-6128	3	9	+	+	NOUN
ejpam-6128	3	10	1)-dimensional	1)-dimensional	ADJ
ejpam-6128	3	11	nonlinear	nonlinear	ADJ
ejpam-6128	3	12	wave	wave	NOUN
ejpam-6128	3	13	equation	equation	NOUN
ejpam-6128	3	14	using	use	VERB
ejpam-6128	3	15	the	the	DET
ejpam-6128	3	16	lie	lie	NOUN
ejpam-6128	3	17	symmetry	symmetry	NOUN
ejpam-6128	3	18	analysis	analysis	NOUN
ejpam-6128	3	19	method	method	NOUN
ejpam-6128	3	20	.	.	PUNCT
ejpam-6128	4	1	this	this	DET
ejpam-6128	4	2	problem	problem	NOUN
ejpam-6128	4	3	is	be	AUX
ejpam-6128	4	4	reduced	reduce	VERB
ejpam-6128	4	5	to	to	ADP
ejpam-6128	4	6	ordinary	ordinary	ADJ
ejpam-6128	4	7	differential	differential	ADJ
ejpam-6128	4	8	equations	equation	NOUN
ejpam-6128	4	9	(	(	PUNCT
ejpam-6128	4	10	odes	ode	NOUN
ejpam-6128	4	11	)	)	PUNCT
ejpam-6128	4	12	using	use	VERB
ejpam-6128	4	13	non	non	ADJ
ejpam-6128	4	14	-	-	ADJ
ejpam-6128	4	15	similar	similar	ADJ
ejpam-6128	4	16	subalgebras	subalgebra	NOUN
ejpam-6128	4	17	of	of	ADP
ejpam-6128	4	18	lie	lie	NOUN
ejpam-6128	4	19	symmetries	symmetry	NOUN
ejpam-6128	4	20	.	.	PUNCT
ejpam-6128	5	1	we	we	PRON
ejpam-6128	5	2	presented	present	VERB
ejpam-6128	5	3	explicit	explicit	ADJ
ejpam-6128	5	4	solutions	solution	NOUN
ejpam-6128	5	5	by	by	ADP
ejpam-6128	5	6	solving	solve	VERB
ejpam-6128	5	7	the	the	DET
ejpam-6128	5	8	reduced	reduce	VERB
ejpam-6128	5	9	odes	ode	NOUN
ejpam-6128	5	10	.	.	PUNCT
ejpam-6128	6	1	the	the	DET
ejpam-6128	6	2	conserved	conserved	ADJ
ejpam-6128	6	3	vectors	vector	NOUN
ejpam-6128	6	4	were	be	AUX
ejpam-6128	6	5	constructed	construct	VERB
ejpam-6128	6	6	using	use	VERB
ejpam-6128	6	7	the	the	DET
ejpam-6128	6	8	lagrange	lagrange	NOUN
ejpam-6128	6	9	multiplier	multipli	ADJ
ejpam-6128	6	10	method	method	NOUN
ejpam-6128	6	11	.	.	PUNCT
ejpam-6128	7	1	using	use	VERB
ejpam-6128	7	2	these	these	DET
ejpam-6128	7	3	conserved	conserved	ADJ
ejpam-6128	7	4	vectors	vector	NOUN
ejpam-6128	7	5	,	,	PUNCT
ejpam-6128	7	6	we	we	PRON
ejpam-6128	7	7	also	also	ADV
ejpam-6128	7	8	derived	derive	VERB
ejpam-6128	7	9	the	the	DET
ejpam-6128	7	10	exact	exact	ADJ
ejpam-6128	7	11	solutions	solution	NOUN
ejpam-6128	7	12	of	of	ADP
ejpam-6128	7	13	the	the	DET
ejpam-6128	7	14	nonlinear	nonlinear	ADJ
ejpam-6128	7	15	wave	wave	NOUN
ejpam-6128	7	16	equation	equation	NOUN
ejpam-6128	7	17	.	.	PUNCT
ejpam-6128	8	1	consequently	consequently	ADV
ejpam-6128	8	2	,	,	PUNCT
ejpam-6128	8	3	3d	3d	PROPN
ejpam-6128	8	4	graphics	graphic	NOUN
ejpam-6128	8	5	were	be	AUX
ejpam-6128	8	6	used	use	VERB
ejpam-6128	8	7	to	to	PART
ejpam-6128	8	8	analyze	analyze	VERB
ejpam-6128	8	9	and	and	CCONJ
ejpam-6128	8	10	illustrate	illustrate	VERB
ejpam-6128	8	11	the	the	DET
ejpam-6128	8	12	graphical	graphical	ADJ
ejpam-6128	8	13	representations	representation	NOUN
ejpam-6128	8	14	of	of	ADP
ejpam-6128	8	15	the	the	DET
ejpam-6128	8	16	solutions	solution	NOUN
ejpam-6128	8	17	.	.	PUNCT
ejpam-6128	9	1	2020	2020	NUM
ejpam-6128	9	2	mathematics	mathematic	NOUN
ejpam-6128	9	3	subject	subject	NOUN
ejpam-6128	9	4	classifications	classification	NOUN
ejpam-6128	9	5	:	:	PUNCT
ejpam-6128	9	6	70g65	70g65	NUM
ejpam-6128	9	7	,	,	PUNCT
ejpam-6128	9	8	35	35	NUM
ejpam-6128	9	9	-	-	SYM
ejpam-6128	9	10	xx	xx	NUM
ejpam-6128	9	11	,	,	PUNCT
ejpam-6128	9	12	70s10	70s10	NUM
ejpam-6128	9	13	,	,	PUNCT
ejpam-6128	9	14	22e70	22e70	NUM
ejpam-6128	9	15	key	key	ADJ
ejpam-6128	9	16	words	word	NOUN
ejpam-6128	9	17	and	and	CCONJ
ejpam-6128	9	18	phrases	phrase	NOUN
ejpam-6128	9	19	:	:	PUNCT
ejpam-6128	9	20	lie	lie	NOUN
ejpam-6128	9	21	symmetries	symmetry	NOUN
ejpam-6128	9	22	,	,	PUNCT
ejpam-6128	9	23	conservation	conservation	NOUN
ejpam-6128	9	24	laws	law	NOUN
ejpam-6128	9	25	,	,	PUNCT
ejpam-6128	9	26	invariant	invariant	ADJ
ejpam-6128	9	27	solutions	solution	NOUN
ejpam-6128	9	28	,	,	PUNCT
ejpam-6128	9	29	nonlinear	nonlinear	ADJ
ejpam-6128	9	30	wave	wave	NOUN
ejpam-6128	9	31	equations	equation	NOUN
ejpam-6128	9	32	1	1	NUM
ejpam-6128	9	33	.	.	PUNCT
ejpam-6128	10	1	introduction	introduction	NOUN
ejpam-6128	10	2	the	the	DET
ejpam-6128	10	3	study	study	NOUN
ejpam-6128	10	4	of	of	ADP
ejpam-6128	10	5	nonlinear	nonlinear	ADJ
ejpam-6128	10	6	wave	wave	NOUN
ejpam-6128	10	7	phenomena	phenomena	PROPN
ejpam-6128	10	8	relies	rely	VERB
ejpam-6128	10	9	extensively	extensively	ADV
ejpam-6128	10	10	on	on	ADP
ejpam-6128	10	11	nonlinear	nonlinear	ADJ
ejpam-6128	10	12	partial	partial	ADJ
ejpam-6128	10	13	differential	differential	NOUN
ejpam-6128	10	14	equations	equation	NOUN
ejpam-6128	10	15	(	(	PUNCT
ejpam-6128	10	16	nlpdes	nlpde	NOUN
ejpam-6128	10	17	)	)	PUNCT
ejpam-6128	10	18	.	.	PUNCT
ejpam-6128	11	1	the	the	DET
ejpam-6128	11	2	interplay	interplay	NOUN
ejpam-6128	11	3	between	between	ADP
ejpam-6128	11	4	larger	large	ADJ
ejpam-6128	11	5	-	-	PUNCT
ejpam-6128	11	6	amplitude	amplitude	NOUN
ejpam-6128	11	7	waves	wave	NOUN
ejpam-6128	11	8	spreading	spread	VERB
ejpam-6128	11	9	with	with	ADP
ejpam-6128	11	10	lower	low	ADJ
ejpam-6128	11	11	-	-	PUNCT
ejpam-6128	11	12	amplitude	amplitude	NOUN
ejpam-6128	11	13	waves	wave	NOUN
ejpam-6128	11	14	is	be	AUX
ejpam-6128	11	15	the	the	DET
ejpam-6128	11	16	factor	factor	NOUN
ejpam-6128	11	17	that	that	PRON
ejpam-6128	11	18	causes	cause	VERB
ejpam-6128	11	19	the	the	DET
ejpam-6128	11	20	nonlinearity	nonlinearity	NOUN
ejpam-6128	11	21	.	.	PUNCT
ejpam-6128	12	1	finding	find	VERB
ejpam-6128	12	2	exact	exact	ADJ
ejpam-6128	12	3	solutions	solution	NOUN
ejpam-6128	12	4	is	be	AUX
ejpam-6128	12	5	an	an	DET
ejpam-6128	12	6	essential	essential	ADJ
ejpam-6128	12	7	problem	problem	NOUN
ejpam-6128	12	8	because	because	SCONJ
ejpam-6128	12	9	these	these	DET
ejpam-6128	12	10	equations	equation	NOUN
ejpam-6128	12	11	explain	explain	VERB
ejpam-6128	12	12	the	the	DET
ejpam-6128	12	13	characteristics	characteristic	NOUN
ejpam-6128	12	14	and	and	CCONJ
ejpam-6128	12	15	behaviors	behavior	NOUN
ejpam-6128	12	16	of	of	ADP
ejpam-6128	12	17	nonlinear	nonlinear	ADJ
ejpam-6128	12	18	phenomena	phenomenon	NOUN
ejpam-6128	12	19	.	.	PUNCT
ejpam-6128	13	1	it	it	PRON
ejpam-6128	13	2	is	be	AUX
ejpam-6128	13	3	important	important	ADJ
ejpam-6128	13	4	to	to	PART
ejpam-6128	13	5	mention	mention	VERB
ejpam-6128	13	6	that	that	SCONJ
ejpam-6128	13	7	various	various	ADJ
ejpam-6128	13	8	methods	method	NOUN
ejpam-6128	13	9	have	have	AUX
ejpam-6128	13	10	been	be	AUX
ejpam-6128	13	11	employed	employ	VERB
ejpam-6128	13	12	to	to	PART
ejpam-6128	13	13	address	address	VERB
ejpam-6128	13	14	these	these	DET
ejpam-6128	13	15	nonlinear	nonlinear	ADJ
ejpam-6128	13	16	problems	problem	NOUN
ejpam-6128	13	17	,	,	PUNCT
ejpam-6128	13	18	including	include	VERB
ejpam-6128	13	19	the	the	DET
ejpam-6128	13	20	φ6	φ6	NOUN
ejpam-6128	13	21	-	-	PUNCT
ejpam-6128	13	22	model	model	NOUN
ejpam-6128	13	23	expansion	expansion	NOUN
ejpam-6128	13	24	method	method	NOUN
ejpam-6128	13	25	[	[	X
ejpam-6128	13	26	1	1	NUM
ejpam-6128	13	27	]	]	PUNCT
ejpam-6128	13	28	,	,	PUNCT
ejpam-6128	13	29	the	the	DET
ejpam-6128	13	30	exp	exp	NOUN
ejpam-6128	13	31	-	-	PUNCT
ejpam-6128	13	32	function	function	NOUN
ejpam-6128	13	33	method	method	NOUN
ejpam-6128	13	34	[	[	X
ejpam-6128	13	35	2	2	NUM
ejpam-6128	13	36	]	]	PUNCT
ejpam-6128	13	37	,	,	PUNCT
ejpam-6128	13	38	the	the	DET
ejpam-6128	13	39	symmetry	symmetry	NOUN
ejpam-6128	13	40	method	method	NOUN
ejpam-6128	13	41	[	[	X
ejpam-6128	13	42	3	3	NUM
ejpam-6128	13	43	]	]	PUNCT
ejpam-6128	13	44	,	,	PUNCT
ejpam-6128	13	45	the	the	DET
ejpam-6128	13	46	residual	residual	ADJ
ejpam-6128	13	47	power	power	NOUN
ejpam-6128	13	48	series	series	PROPN
ejpam-6128	13	49	approach	approach	NOUN
ejpam-6128	13	50	[	[	X
ejpam-6128	13	51	4	4	NUM
ejpam-6128	13	52	]	]	PUNCT
ejpam-6128	13	53	,	,	PUNCT
ejpam-6128	13	54	the	the	DET
ejpam-6128	13	55	homogeneous	homogeneous	ADJ
ejpam-6128	13	56	balanced	balanced	ADJ
ejpam-6128	13	57	method	method	NOUN
ejpam-6128	13	58	[	[	X
ejpam-6128	13	59	5	5	NUM
ejpam-6128	13	60	]	]	PUNCT
ejpam-6128	13	61	,	,	PUNCT
ejpam-6128	13	62	the	the	DET
ejpam-6128	13	63	hyperbolic	hyperbolic	ADJ
ejpam-6128	13	64	tangent	tangent	NOUN
ejpam-6128	13	65	method	method	NOUN
ejpam-6128	13	66	[	[	X
ejpam-6128	13	67	6	6	NUM
ejpam-6128	13	68	]	]	PUNCT
ejpam-6128	13	69	,	,	PUNCT
ejpam-6128	13	70	f	f	X
ejpam-6128	13	71	-	-	PUNCT
ejpam-6128	13	72	expansion	expansion	NOUN
ejpam-6128	13	73	method	method	NOUN
ejpam-6128	13	74	[	[	X
ejpam-6128	13	75	7	7	NUM
ejpam-6128	13	76	]	]	PUNCT
ejpam-6128	13	77	,	,	PUNCT
ejpam-6128	13	78	the	the	DET
ejpam-6128	13	79	unified	unified	ADJ
ejpam-6128	13	80	method	method	NOUN
ejpam-6128	13	81	[	[	X
ejpam-6128	13	82	8	8	NUM
ejpam-6128	13	83	,	,	PUNCT
ejpam-6128	13	84	9	9	NUM
ejpam-6128	13	85	]	]	PUNCT
ejpam-6128	13	86	,	,	PUNCT
ejpam-6128	13	87	the	the	DET
ejpam-6128	13	88	new	new	ADJ
ejpam-6128	13	89	jacobi	jacobi	PROPN
ejpam-6128	13	90	elliptic	elliptic	ADJ
ejpam-6128	13	91	functions	function	NOUN
ejpam-6128	13	92	technique	technique	NOUN
ejpam-6128	13	93	[	[	X
ejpam-6128	13	94	10	10	NUM
ejpam-6128	13	95	]	]	PUNCT
ejpam-6128	13	96	and	and	CCONJ
ejpam-6128	13	97	the	the	DET
ejpam-6128	13	98	improved	improved	ADJ
ejpam-6128	13	99	sardar	sardar	NOUN
ejpam-6128	13	100	sub	sub	ADJ
ejpam-6128	13	101	-	-	ADJ
ejpam-6128	13	102	equation	equation	ADJ
ejpam-6128	13	103	approach	approach	NOUN
ejpam-6128	13	104	[	[	X
ejpam-6128	13	105	11	11	NUM
ejpam-6128	13	106	]	]	PUNCT
ejpam-6128	13	107	.	.	PUNCT
ejpam-6128	14	1	one	one	NUM
ejpam-6128	14	2	of	of	ADP
ejpam-6128	14	3	the	the	DET
ejpam-6128	14	4	most	most	ADV
ejpam-6128	14	5	effective	effective	ADJ
ejpam-6128	14	6	ways	way	NOUN
ejpam-6128	14	7	to	to	PART
ejpam-6128	14	8	obtain	obtain	VERB
ejpam-6128	14	9	analytical	analytical	ADJ
ejpam-6128	14	10	solutions	solution	NOUN
ejpam-6128	14	11	for	for	ADP
ejpam-6128	14	12	nlpdes	nlpde	NOUN
ejpam-6128	14	13	is	be	AUX
ejpam-6128	14	14	to	to	PART
ejpam-6128	14	15	apply	apply	VERB
ejpam-6128	14	16	lie	lie	NOUN
ejpam-6128	14	17	symmetry	symmetry	NOUN
ejpam-6128	14	18	[	[	X
ejpam-6128	14	19	3	3	NUM
ejpam-6128	14	20	]	]	PUNCT
ejpam-6128	14	21	.	.	PUNCT
ejpam-6128	15	1	any	any	DET
ejpam-6128	15	2	solution	solution	NOUN
ejpam-6128	15	3	to	to	ADP
ejpam-6128	15	4	an	an	DET
ejpam-6128	15	5	nlpde	nlpde	NOUN
ejpam-6128	15	6	can	can	AUX
ejpam-6128	15	7	be	be	AUX
ejpam-6128	15	8	converted	convert	VERB
ejpam-6128	15	9	into	into	ADP
ejpam-6128	15	10	a	a	DET
ejpam-6128	15	11	collection	collection	NOUN
ejpam-6128	15	12	of	of	ADP
ejpam-6128	15	13	solutions	solution	NOUN
ejpam-6128	15	14	to	to	ADP
ejpam-6128	15	15	∗corresponding	∗corresponde	VERB
ejpam-6128	15	16	author	author	NOUN
ejpam-6128	15	17	.	.	PUNCT
ejpam-6128	16	1	doi	doi	NOUN
ejpam-6128	16	2	:	:	PUNCT
ejpam-6128	16	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6128	https://doi.org/10.29020/nybg.ejpam.v18i4.6128	PROPN
ejpam-6128	16	4	email	email	NOUN
ejpam-6128	16	5	address	address	NOUN
ejpam-6128	16	6	:	:	PUNCT
ejpam-6128	16	7	akhtarhussain21@sms.edu.pk	akhtarhussain21@sms.edu.pk	PUNCT
ejpam-6128	16	8	(	(	PUNCT
ejpam-6128	16	9	a.	a.	NOUN
ejpam-6128	16	10	hussain	hussain	PROPN
ejpam-6128	16	11	)	)	PUNCT
ejpam-6128	16	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6128	17	1	1	1	NUM
ejpam-6128	17	2	copyright	copyright	NOUN
ejpam-6128	17	3	:	:	PUNCT
ejpam-6128	17	4	©	©	PROPN
ejpam-6128	17	5	2025	2025	NUM
ejpam-6128	17	6	the	the	DET
ejpam-6128	17	7	author(s	author(s	NOUN
ejpam-6128	17	8	)	)	PUNCT
ejpam-6128	17	9	.	.	PUNCT
ejpam-6128	18	1	(	(	PUNCT
ejpam-6128	18	2	cc	cc	NOUN
ejpam-6128	18	3	by	by	ADP
ejpam-6128	18	4	-	-	PUNCT
ejpam-6128	18	5	nc	nc	PROPN
ejpam-6128	18	6	4.0	4.0	NUM
ejpam-6128	18	7	)	)	PUNCT
ejpam-6128	18	8	m.	m.	NOUN
ejpam-6128	18	9	usman	usman	PROPN
ejpam-6128	18	10	,	,	PUNCT
ejpam-6128	18	11	a.	a.	NOUN
ejpam-6128	18	12	hussain	hussain	PROPN
ejpam-6128	18	13	,	,	PUNCT
ejpam-6128	18	14	m.	m.	PROPN
ejpam-6128	18	15	u.	u.	PROPN
ejpam-6128	18	16	farooq	farooq	PROPN
ejpam-6128	18	17	,	,	PUNCT
ejpam-6128	18	18	j.	j.	PROPN
ejpam-6128	18	19	herrera	herrera	PROPN
ejpam-6128	18	20	/	/	SYM
ejpam-6128	18	21	eur	eur	PROPN
ejpam-6128	18	22	.	.	PUNCT
ejpam-6128	19	1	j.	j.	PROPN
ejpam-6128	19	2	pure	pure	PROPN
ejpam-6128	19	3	appl	appl	PROPN
ejpam-6128	19	4	.	.	PROPN
ejpam-6128	19	5	math	math	PROPN
ejpam-6128	19	6	,	,	PUNCT
ejpam-6128	19	7	18	18	NUM
ejpam-6128	19	8	(	(	PUNCT
ejpam-6128	19	9	4	4	NUM
ejpam-6128	19	10	)	)	PUNCT
ejpam-6128	19	11	(	(	PUNCT
ejpam-6128	19	12	2025	2025	NUM
ejpam-6128	19	13	)	)	PUNCT
ejpam-6128	19	14	,	,	PUNCT
ejpam-6128	19	15	6128	6128	NUM
ejpam-6128	19	16	2	2	NUM
ejpam-6128	19	17	of	of	ADP
ejpam-6128	19	18	29	29	NUM
ejpam-6128	19	19	the	the	DET
ejpam-6128	19	20	same	same	ADJ
ejpam-6128	19	21	equation	equation	NOUN
ejpam-6128	19	22	via	via	ADP
ejpam-6128	19	23	symmetry	symmetry	NOUN
ejpam-6128	19	24	.	.	PUNCT
ejpam-6128	20	1	conservation	conservation	NOUN
ejpam-6128	20	2	laws	law	NOUN
ejpam-6128	20	3	play	play	VERB
ejpam-6128	20	4	a	a	DET
ejpam-6128	20	5	major	major	ADJ
ejpam-6128	20	6	role	role	NOUN
ejpam-6128	20	7	in	in	ADP
ejpam-6128	20	8	the	the	DET
ejpam-6128	20	9	development	development	NOUN
ejpam-6128	20	10	and	and	CCONJ
ejpam-6128	20	11	analysis	analysis	NOUN
ejpam-6128	20	12	of	of	ADP
ejpam-6128	20	13	various	various	ADJ
ejpam-6128	20	14	mathematical	mathematical	ADJ
ejpam-6128	20	15	models	model	NOUN
ejpam-6128	20	16	.	.	PUNCT
ejpam-6128	21	1	the	the	DET
ejpam-6128	21	2	most	most	ADV
ejpam-6128	21	3	efficient	efficient	ADJ
ejpam-6128	21	4	technique	technique	NOUN
ejpam-6128	21	5	for	for	ADP
ejpam-6128	21	6	determining	determine	VERB
ejpam-6128	21	7	the	the	DET
ejpam-6128	21	8	conservation	conservation	NOUN
ejpam-6128	21	9	laws	law	NOUN
ejpam-6128	21	10	for	for	ADP
ejpam-6128	21	11	nlpdes	nlpde	NOUN
ejpam-6128	21	12	is	be	AUX
ejpam-6128	21	13	the	the	DET
ejpam-6128	21	14	multiplier	multipli	ADJ
ejpam-6128	21	15	method	method	NOUN
ejpam-6128	21	16	[	[	X
ejpam-6128	21	17	3	3	NUM
ejpam-6128	21	18	,	,	PUNCT
ejpam-6128	21	19	12	12	NUM
ejpam-6128	21	20	]	]	PUNCT
ejpam-6128	21	21	.	.	PUNCT
ejpam-6128	22	1	it	it	PRON
ejpam-6128	22	2	is	be	AUX
ejpam-6128	22	3	commonly	commonly	ADV
ejpam-6128	22	4	recognized	recognize	VERB
ejpam-6128	22	5	that	that	SCONJ
ejpam-6128	22	6	the	the	DET
ejpam-6128	22	7	main	main	ADJ
ejpam-6128	22	8	objective	objective	NOUN
ejpam-6128	22	9	of	of	ADP
ejpam-6128	22	10	different	different	ADJ
ejpam-6128	22	11	linear	linear	NOUN
ejpam-6128	22	12	and	and	CCONJ
ejpam-6128	22	13	nonlinear	nonlinear	ADJ
ejpam-6128	22	14	wave	wave	NOUN
ejpam-6128	22	15	equations	equation	NOUN
ejpam-6128	22	16	is	be	AUX
ejpam-6128	22	17	to	to	PART
ejpam-6128	22	18	model	model	VERB
ejpam-6128	22	19	certain	certain	ADJ
ejpam-6128	22	20	wave	wave	NOUN
ejpam-6128	22	21	phenomena	phenomenon	NOUN
ejpam-6128	22	22	.	.	PUNCT
ejpam-6128	23	1	ames	ames	PROPN
ejpam-6128	23	2	et	et	PROPN
ejpam-6128	23	3	al	al	PROPN
ejpam-6128	23	4	.	.	PUNCT
ejpam-6128	24	1	[	[	X
ejpam-6128	24	2	13	13	NUM
ejpam-6128	24	3	]	]	PUNCT
ejpam-6128	24	4	used	use	VERB
ejpam-6128	24	5	the	the	DET
ejpam-6128	24	6	lie	lie	NOUN
ejpam-6128	24	7	group	group	NOUN
ejpam-6128	24	8	method	method	NOUN
ejpam-6128	24	9	to	to	PART
ejpam-6128	24	10	study	study	VERB
ejpam-6128	24	11	the	the	DET
ejpam-6128	24	12	general	general	ADJ
ejpam-6128	24	13	nonlinear	nonlinear	ADJ
ejpam-6128	24	14	form	form	NOUN
ejpam-6128	24	15	of	of	ADP
ejpam-6128	24	16	the	the	DET
ejpam-6128	24	17	(	(	PUNCT
ejpam-6128	24	18	1	1	NUM
ejpam-6128	24	19	+	+	NOUN
ejpam-6128	24	20	1)-dimensional	1)-dimensional	ADJ
ejpam-6128	24	21	wave	wave	NOUN
ejpam-6128	24	22	equation	equation	NOUN
ejpam-6128	24	23	given	give	VERB
ejpam-6128	24	24	by	by	ADP
ejpam-6128	24	25	utt	utt	ADJ
ejpam-6128	24	26	−	−	PROPN
ejpam-6128	24	27	(	(	PUNCT
ejpam-6128	24	28	k(u)ux)x	k(u)ux)x	X
ejpam-6128	24	29	=	=	SYM
ejpam-6128	24	30	0	0	NUM
ejpam-6128	24	31	.	.	PUNCT
ejpam-6128	25	1	(	(	PUNCT
ejpam-6128	25	2	1	1	X
ejpam-6128	25	3	)	)	PUNCT
ejpam-6128	25	4	bluman	bluman	NOUN
ejpam-6128	25	5	et	et	PROPN
ejpam-6128	25	6	al	al	PROPN
ejpam-6128	25	7	.	.	PUNCT
ejpam-6128	26	1	[	[	X
ejpam-6128	26	2	14	14	NUM
ejpam-6128	26	3	]	]	PUNCT
ejpam-6128	26	4	constructed	construct	VERB
ejpam-6128	26	5	the	the	DET
ejpam-6128	26	6	conserved	conserved	ADJ
ejpam-6128	26	7	vectors	vector	NOUN
ejpam-6128	26	8	for	for	ADP
ejpam-6128	26	9	(	(	PUNCT
ejpam-6128	26	10	1	1	NUM
ejpam-6128	26	11	)	)	PUNCT
ejpam-6128	26	12	,	,	PUNCT
ejpam-6128	26	13	while	while	SCONJ
ejpam-6128	26	14	the	the	DET
ejpam-6128	26	15	higher	high	ADJ
ejpam-6128	26	16	-	-	PUNCT
ejpam-6128	26	17	order	order	NOUN
ejpam-6128	26	18	conservation	conservation	NOUN
ejpam-6128	26	19	laws	law	NOUN
ejpam-6128	26	20	and	and	CCONJ
ejpam-6128	26	21	the	the	DET
ejpam-6128	26	22	complete	complete	ADJ
ejpam-6128	26	23	categorization	categorization	NOUN
ejpam-6128	26	24	of	of	ADP
ejpam-6128	26	25	lie	lie	NOUN
ejpam-6128	26	26	algebra	algebra	NOUN
ejpam-6128	26	27	for	for	ADP
ejpam-6128	26	28	(	(	PUNCT
ejpam-6128	26	29	1	1	X
ejpam-6128	26	30	)	)	PUNCT
ejpam-6128	26	31	are	be	AUX
ejpam-6128	26	32	presented	present	VERB
ejpam-6128	26	33	in	in	ADP
ejpam-6128	26	34	[	[	X
ejpam-6128	26	35	15	15	NUM
ejpam-6128	26	36	]	]	PUNCT
ejpam-6128	26	37	.	.	PUNCT
ejpam-6128	27	1	different	different	ADJ
ejpam-6128	27	2	types	type	NOUN
ejpam-6128	27	3	of	of	ADP
ejpam-6128	27	4	nonlinear	nonlinear	ADJ
ejpam-6128	27	5	wave	wave	NOUN
ejpam-6128	27	6	equations	equation	NOUN
ejpam-6128	27	7	are	be	AUX
ejpam-6128	27	8	presented	present	VERB
ejpam-6128	27	9	in	in	ADP
ejpam-6128	27	10	[	[	X
ejpam-6128	27	11	16–22	16–22	NUM
ejpam-6128	27	12	]	]	PUNCT
ejpam-6128	27	13	.	.	PUNCT
ejpam-6128	28	1	the	the	DET
ejpam-6128	28	2	general	general	ADJ
ejpam-6128	28	3	form	form	NOUN
ejpam-6128	28	4	of	of	ADP
ejpam-6128	28	5	(	(	PUNCT
ejpam-6128	28	6	2	2	NUM
ejpam-6128	28	7	+	+	NOUN
ejpam-6128	28	8	1)-dimensional	1)-dimensional	ADJ
ejpam-6128	28	9	nonlinear	nonlinear	ADJ
ejpam-6128	28	10	wave	wave	NOUN
ejpam-6128	28	11	equation	equation	NOUN
ejpam-6128	28	12	[	[	X
ejpam-6128	28	13	23	23	NUM
ejpam-6128	28	14	]	]	PUNCT
ejpam-6128	28	15	is	be	AUX
ejpam-6128	28	16	given	give	VERB
ejpam-6128	28	17	by	by	ADP
ejpam-6128	28	18	wtt	wtt	PROPN
ejpam-6128	28	19	−	−	PROPN
ejpam-6128	29	1	(	(	PUNCT
ejpam-6128	29	2	f(w)wx)x	f(w)wx)x	ADJ
ejpam-6128	29	3	−	−	PROPN
ejpam-6128	29	4	(	(	PUNCT
ejpam-6128	29	5	g(w)wy)y	g(w)wy)y	PROPN
ejpam-6128	29	6	=	=	SYM
ejpam-6128	29	7	0	0	PROPN
ejpam-6128	29	8	,	,	PUNCT
ejpam-6128	29	9	(	(	PUNCT
ejpam-6128	29	10	2	2	X
ejpam-6128	29	11	)	)	PUNCT
ejpam-6128	29	12	where	where	SCONJ
ejpam-6128	29	13	the	the	DET
ejpam-6128	29	14	nonlinear	nonlinear	ADJ
ejpam-6128	29	15	functions	function	NOUN
ejpam-6128	29	16	f(w	f(w	NOUN
ejpam-6128	29	17	)	)	PUNCT
ejpam-6128	29	18	and	and	CCONJ
ejpam-6128	29	19	g(w	g(w	PROPN
ejpam-6128	29	20	)	)	PUNCT
ejpam-6128	29	21	determine	determine	VERB
ejpam-6128	29	22	how	how	SCONJ
ejpam-6128	29	23	waves	wave	NOUN
ejpam-6128	29	24	propagate	propagate	VERB
ejpam-6128	29	25	.	.	PUNCT
ejpam-6128	30	1	usually	usually	ADV
ejpam-6128	30	2	,	,	PUNCT
ejpam-6128	30	3	this	this	DET
ejpam-6128	30	4	equation	equation	NOUN
ejpam-6128	30	5	simulates	simulate	VERB
ejpam-6128	30	6	the	the	DET
ejpam-6128	30	7	propagation	propagation	NOUN
ejpam-6128	30	8	of	of	ADP
ejpam-6128	30	9	waves	wave	NOUN
ejpam-6128	30	10	in	in	ADP
ejpam-6128	30	11	a	a	DET
ejpam-6128	30	12	nonlinear	nonlinear	ADJ
ejpam-6128	30	13	or	or	CCONJ
ejpam-6128	30	14	nonhomogeneous	nonhomogeneous	ADJ
ejpam-6128	30	15	mediums	medium	NOUN
ejpam-6128	30	16	,	,	PUNCT
ejpam-6128	30	17	where	where	SCONJ
ejpam-6128	30	18	the	the	DET
ejpam-6128	30	19	response	response	NOUN
ejpam-6128	30	20	of	of	ADP
ejpam-6128	30	21	the	the	DET
ejpam-6128	30	22	medium	medium	NOUN
ejpam-6128	30	23	is	be	AUX
ejpam-6128	30	24	determined	determine	VERB
ejpam-6128	30	25	by	by	ADP
ejpam-6128	30	26	the	the	DET
ejpam-6128	30	27	amplitude	amplitude	NOUN
ejpam-6128	30	28	of	of	ADP
ejpam-6128	30	29	the	the	DET
ejpam-6128	30	30	wave	wave	NOUN
ejpam-6128	30	31	.	.	PUNCT
ejpam-6128	31	1	twodimensional	twodimensional	ADJ
ejpam-6128	31	2	nonlinear	nonlinear	ADJ
ejpam-6128	31	3	acoustic	acoustic	ADJ
ejpam-6128	31	4	waves	wave	NOUN
ejpam-6128	31	5	,	,	PUNCT
ejpam-6128	31	6	surface	surface	NOUN
ejpam-6128	31	7	water	water	NOUN
ejpam-6128	31	8	waves	wave	NOUN
ejpam-6128	31	9	,	,	PUNCT
ejpam-6128	31	10	and	and	CCONJ
ejpam-6128	31	11	other	other	ADJ
ejpam-6128	31	12	waveforms	waveform	NOUN
ejpam-6128	31	13	capturing	capture	VERB
ejpam-6128	31	14	phenomena	phenomenon	NOUN
ejpam-6128	31	15	,	,	PUNCT
ejpam-6128	31	16	such	such	ADJ
ejpam-6128	31	17	as	as	ADP
ejpam-6128	31	18	wave	wave	NOUN
ejpam-6128	31	19	steepening	steepening	NOUN
ejpam-6128	31	20	and	and	CCONJ
ejpam-6128	31	21	shock	shock	NOUN
ejpam-6128	31	22	production	production	NOUN
ejpam-6128	31	23	,	,	PUNCT
ejpam-6128	31	24	can	can	AUX
ejpam-6128	31	25	be	be	AUX
ejpam-6128	31	26	modeled	model	VERB
ejpam-6128	31	27	using	use	VERB
ejpam-6128	31	28	(	(	PUNCT
ejpam-6128	31	29	2	2	NUM
ejpam-6128	31	30	)	)	PUNCT
ejpam-6128	31	31	.	.	PUNCT
ejpam-6128	32	1	the	the	DET
ejpam-6128	32	2	formulation	formulation	NOUN
ejpam-6128	32	3	f(w	f(w	NOUN
ejpam-6128	32	4	)	)	PUNCT
ejpam-6128	32	5	=	=	SYM
ejpam-6128	32	6	αw	αw	NOUN
ejpam-6128	32	7	,	,	PUNCT
ejpam-6128	32	8	g(w	g(w	ADJ
ejpam-6128	32	9	)	)	PUNCT
ejpam-6128	32	10	=	=	SYM
ejpam-6128	32	11	βw2	βw2	NOUN
ejpam-6128	32	12	in	in	ADP
ejpam-6128	32	13	(	(	PUNCT
ejpam-6128	32	14	2	2	X
ejpam-6128	32	15	)	)	PUNCT
ejpam-6128	32	16	can	can	AUX
ejpam-6128	32	17	simulate	simulate	VERB
ejpam-6128	32	18	the	the	DET
ejpam-6128	32	19	nonlinear	nonlinear	ADJ
ejpam-6128	32	20	dispersive	dispersive	ADJ
ejpam-6128	32	21	waves	wave	NOUN
ejpam-6128	32	22	including	include	VERB
ejpam-6128	32	23	solitons	soliton	NOUN
ejpam-6128	32	24	in	in	ADP
ejpam-6128	32	25	shallow	shallow	ADJ
ejpam-6128	32	26	water	water	NOUN
ejpam-6128	32	27	.	.	PUNCT
ejpam-6128	33	1	by	by	ADP
ejpam-6128	33	2	taking	take	VERB
ejpam-6128	33	3	f(w	f(w	NOUN
ejpam-6128	33	4	)	)	PUNCT
ejpam-6128	33	5	=	=	SYM
ejpam-6128	33	6	α	α	X
ejpam-6128	33	7	,	,	PUNCT
ejpam-6128	33	8	g(w	g(w	PROPN
ejpam-6128	33	9	)	)	PUNCT
ejpam-6128	33	10	=	=	SYM
ejpam-6128	33	11	βw	βw	ADP
ejpam-6128	33	12	in	in	ADP
ejpam-6128	33	13	(	(	PUNCT
ejpam-6128	33	14	2	2	NUM
ejpam-6128	33	15	)	)	PUNCT
ejpam-6128	33	16	,	,	PUNCT
ejpam-6128	33	17	the	the	DET
ejpam-6128	33	18	beam	beam	NOUN
ejpam-6128	33	19	dynamics	dynamic	NOUN
ejpam-6128	33	20	in	in	ADP
ejpam-6128	33	21	nonlinear	nonlinear	ADJ
ejpam-6128	33	22	elastic	elastic	ADJ
ejpam-6128	33	23	materials	material	NOUN
ejpam-6128	33	24	can	can	AUX
ejpam-6128	33	25	be	be	AUX
ejpam-6128	33	26	modeled	model	VERB
ejpam-6128	33	27	,	,	PUNCT
ejpam-6128	33	28	where	where	SCONJ
ejpam-6128	33	29	the	the	DET
ejpam-6128	33	30	response	response	NOUN
ejpam-6128	33	31	is	be	AUX
ejpam-6128	33	32	proportional	proportional	ADJ
ejpam-6128	33	33	to	to	ADP
ejpam-6128	33	34	the	the	DET
ejpam-6128	33	35	deformation	deformation	NOUN
ejpam-6128	33	36	.	.	PUNCT
ejpam-6128	34	1	in	in	ADP
ejpam-6128	34	2	[	[	X
ejpam-6128	34	3	23	23	NUM
ejpam-6128	34	4	]	]	PUNCT
ejpam-6128	34	5	,	,	PUNCT
ejpam-6128	34	6	the	the	DET
ejpam-6128	34	7	double	double	ADJ
ejpam-6128	34	8	reduction	reduction	NOUN
ejpam-6128	34	9	theory	theory	NOUN
ejpam-6128	34	10	is	be	AUX
ejpam-6128	34	11	applied	apply	VERB
ejpam-6128	34	12	on	on	ADP
ejpam-6128	34	13	(	(	PUNCT
ejpam-6128	34	14	2	2	NUM
ejpam-6128	34	15	)	)	PUNCT
ejpam-6128	34	16	based	base	VERB
ejpam-6128	34	17	on	on	ADP
ejpam-6128	34	18	the	the	DET
ejpam-6128	34	19	conserved	conserve	VERB
ejpam-6128	34	20	vectors	vector	NOUN
ejpam-6128	34	21	constructed	construct	VERB
ejpam-6128	34	22	using	use	VERB
ejpam-6128	34	23	a	a	DET
ejpam-6128	34	24	partial	partial	ADJ
ejpam-6128	34	25	lagrangian	lagrangian	NOUN
ejpam-6128	34	26	.	.	PUNCT
ejpam-6128	35	1	in	in	ADP
ejpam-6128	35	2	this	this	DET
ejpam-6128	35	3	study	study	NOUN
ejpam-6128	35	4	,	,	PUNCT
ejpam-6128	35	5	we	we	PRON
ejpam-6128	35	6	take	take	VERB
ejpam-6128	35	7	the	the	DET
ejpam-6128	35	8	nonlinear	nonlinear	ADJ
ejpam-6128	35	9	wave	wave	NOUN
ejpam-6128	35	10	equation	equation	NOUN
ejpam-6128	35	11	(	(	PUNCT
ejpam-6128	35	12	2	2	NUM
ejpam-6128	35	13	)	)	PUNCT
ejpam-6128	35	14	in	in	ADP
ejpam-6128	35	15	(	(	PUNCT
ejpam-6128	35	16	2	2	NUM
ejpam-6128	35	17	+	+	NOUN
ejpam-6128	35	18	1	1	NUM
ejpam-6128	35	19	)	)	PUNCT
ejpam-6128	35	20	dimensions	dimension	NOUN
ejpam-6128	35	21	and	and	CCONJ
ejpam-6128	35	22	use	use	VERB
ejpam-6128	35	23	the	the	DET
ejpam-6128	35	24	lie	lie	NOUN
ejpam-6128	35	25	group	group	NOUN
ejpam-6128	35	26	approach	approach	NOUN
ejpam-6128	35	27	to	to	PART
ejpam-6128	35	28	obtain	obtain	VERB
ejpam-6128	35	29	its	its	PRON
ejpam-6128	35	30	solutions	solution	NOUN
ejpam-6128	35	31	.	.	PUNCT
ejpam-6128	36	1	several	several	ADJ
ejpam-6128	36	2	interesting	interesting	ADJ
ejpam-6128	36	3	similarity	similarity	NOUN
ejpam-6128	36	4	reductions	reduction	NOUN
ejpam-6128	36	5	were	be	AUX
ejpam-6128	36	6	performed	perform	VERB
ejpam-6128	36	7	using	use	VERB
ejpam-6128	36	8	similar	similar	ADJ
ejpam-6128	36	9	conjugacy	conjugacy	ADJ
ejpam-6128	36	10	classes	class	NOUN
ejpam-6128	36	11	of	of	ADP
ejpam-6128	36	12	lie	lie	NOUN
ejpam-6128	36	13	algebra	algebra	PROPN
ejpam-6128	36	14	,	,	PUNCT
ejpam-6128	36	15	which	which	PRON
ejpam-6128	36	16	were	be	AUX
ejpam-6128	36	17	computed	compute	VERB
ejpam-6128	36	18	using	use	VERB
ejpam-6128	36	19	the	the	DET
ejpam-6128	36	20	matrix	matrix	NOUN
ejpam-6128	36	21	method	method	NOUN
ejpam-6128	36	22	.	.	PUNCT
ejpam-6128	37	1	invariant	invariant	ADJ
ejpam-6128	37	2	solutions	solution	NOUN
ejpam-6128	37	3	were	be	AUX
ejpam-6128	37	4	obtained	obtain	VERB
ejpam-6128	37	5	for	for	ADP
ejpam-6128	37	6	these	these	DET
ejpam-6128	37	7	symmetry	symmetry	NOUN
ejpam-6128	37	8	reductions	reduction	NOUN
ejpam-6128	37	9	.	.	PUNCT
ejpam-6128	38	1	the	the	DET
ejpam-6128	38	2	local	local	ADJ
ejpam-6128	38	3	conserved	conserved	ADJ
ejpam-6128	38	4	vectors	vector	NOUN
ejpam-6128	38	5	for	for	ADP
ejpam-6128	38	6	(	(	PUNCT
ejpam-6128	38	7	2	2	X
ejpam-6128	38	8	)	)	PUNCT
ejpam-6128	38	9	were	be	AUX
ejpam-6128	38	10	constructed	construct	VERB
ejpam-6128	38	11	and	and	CCONJ
ejpam-6128	38	12	utilized	utilize	VERB
ejpam-6128	38	13	to	to	PART
ejpam-6128	38	14	obtain	obtain	VERB
ejpam-6128	38	15	the	the	DET
ejpam-6128	38	16	exact	exact	ADJ
ejpam-6128	38	17	solutions	solution	NOUN
ejpam-6128	38	18	of	of	ADP
ejpam-6128	38	19	(	(	PUNCT
ejpam-6128	38	20	2	2	NUM
ejpam-6128	38	21	)	)	PUNCT
ejpam-6128	38	22	.	.	PUNCT
ejpam-6128	39	1	for	for	ADP
ejpam-6128	39	2	certain	certain	ADJ
ejpam-6128	39	3	parameter	parameter	NOUN
ejpam-6128	39	4	values	value	NOUN
ejpam-6128	39	5	,	,	PUNCT
ejpam-6128	39	6	3d	3d	NUM
ejpam-6128	39	7	images	image	NOUN
ejpam-6128	39	8	of	of	ADP
ejpam-6128	39	9	the	the	DET
ejpam-6128	39	10	solutions	solution	NOUN
ejpam-6128	39	11	in	in	ADP
ejpam-6128	39	12	various	various	ADJ
ejpam-6128	39	13	structures	structure	NOUN
ejpam-6128	39	14	were	be	AUX
ejpam-6128	39	15	created	create	VERB
ejpam-6128	39	16	to	to	PART
ejpam-6128	39	17	obtain	obtain	VERB
ejpam-6128	39	18	a	a	DET
ejpam-6128	39	19	better	well	ADJ
ejpam-6128	39	20	analysis	analysis	NOUN
ejpam-6128	39	21	of	of	ADP
ejpam-6128	39	22	the	the	DET
ejpam-6128	39	23	solutions	solution	NOUN
ejpam-6128	39	24	.	.	PUNCT
ejpam-6128	40	1	the	the	DET
ejpam-6128	40	2	remainder	remainder	NOUN
ejpam-6128	40	3	of	of	ADP
ejpam-6128	40	4	this	this	DET
ejpam-6128	40	5	paper	paper	NOUN
ejpam-6128	40	6	is	be	AUX
ejpam-6128	40	7	structured	structure	VERB
ejpam-6128	40	8	as	as	SCONJ
ejpam-6128	40	9	follows	follow	VERB
ejpam-6128	40	10	:	:	PUNCT
ejpam-6128	40	11	section	section	NOUN
ejpam-6128	40	12	2	2	NUM
ejpam-6128	40	13	is	be	AUX
ejpam-6128	40	14	devoted	devote	VERB
ejpam-6128	40	15	to	to	ADP
ejpam-6128	40	16	the	the	DET
ejpam-6128	40	17	classification	classification	NOUN
ejpam-6128	40	18	of	of	ADP
ejpam-6128	40	19	the	the	DET
ejpam-6128	40	20	lie	lie	NOUN
ejpam-6128	40	21	symmetries	symmetry	NOUN
ejpam-6128	40	22	and	and	CCONJ
ejpam-6128	40	23	the	the	DET
ejpam-6128	40	24	construction	construction	NOUN
ejpam-6128	40	25	of	of	ADP
ejpam-6128	40	26	the	the	DET
ejpam-6128	40	27	associated	associate	VERB
ejpam-6128	40	28	optimal	optimal	ADJ
ejpam-6128	40	29	set	set	NOUN
ejpam-6128	40	30	for	for	ADP
ejpam-6128	40	31	(	(	PUNCT
ejpam-6128	40	32	2	2	NUM
ejpam-6128	40	33	)	)	PUNCT
ejpam-6128	40	34	.	.	PUNCT
ejpam-6128	41	1	section	section	NOUN
ejpam-6128	41	2	3	3	NUM
ejpam-6128	41	3	addresses	address	NOUN
ejpam-6128	41	4	symmetry	symmetry	NOUN
ejpam-6128	41	5	reduction	reduction	NOUN
ejpam-6128	41	6	and	and	CCONJ
ejpam-6128	41	7	invariant	invariant	ADJ
ejpam-6128	41	8	solutions	solution	NOUN
ejpam-6128	41	9	.	.	PUNCT
ejpam-6128	42	1	the	the	DET
ejpam-6128	42	2	local	local	ADJ
ejpam-6128	42	3	conservation	conservation	NOUN
ejpam-6128	42	4	laws	law	NOUN
ejpam-6128	42	5	are	be	AUX
ejpam-6128	42	6	presented	present	VERB
ejpam-6128	42	7	in	in	ADP
ejpam-6128	42	8	section	section	NOUN
ejpam-6128	42	9	4	4	NUM
ejpam-6128	42	10	,	,	PUNCT
ejpam-6128	42	11	which	which	PRON
ejpam-6128	42	12	produce	produce	VERB
ejpam-6128	42	13	the	the	DET
ejpam-6128	42	14	exact	exact	ADJ
ejpam-6128	42	15	solutions	solution	NOUN
ejpam-6128	42	16	stated	state	VERB
ejpam-6128	42	17	in	in	ADP
ejpam-6128	42	18	section	section	NOUN
ejpam-6128	42	19	5	5	NUM
ejpam-6128	42	20	.	.	PUNCT
ejpam-6128	42	21	section	section	NOUN
ejpam-6128	42	22	6	6	NUM
ejpam-6128	42	23	presents	present	VERB
ejpam-6128	42	24	a	a	DET
ejpam-6128	42	25	geometric	geometric	ADJ
ejpam-6128	42	26	analysis	analysis	NOUN
ejpam-6128	42	27	of	of	ADP
ejpam-6128	42	28	the	the	DET
ejpam-6128	42	29	obtained	obtain	VERB
ejpam-6128	42	30	results	result	NOUN
ejpam-6128	42	31	.	.	PUNCT
ejpam-6128	43	1	2	2	X
ejpam-6128	43	2	.	.	X
ejpam-6128	43	3	lie	lie	NOUN
ejpam-6128	43	4	point	point	NOUN
ejpam-6128	43	5	symmetries	symmetry	NOUN
ejpam-6128	43	6	and	and	CCONJ
ejpam-6128	43	7	optimal	optimal	ADJ
ejpam-6128	43	8	system	system	NOUN
ejpam-6128	43	9	this	this	DET
ejpam-6128	43	10	section	section	NOUN
ejpam-6128	43	11	explains	explain	VERB
ejpam-6128	43	12	the	the	DET
ejpam-6128	43	13	fundamental	fundamental	ADJ
ejpam-6128	43	14	terms	term	NOUN
ejpam-6128	43	15	required	require	VERB
ejpam-6128	43	16	to	to	PART
ejpam-6128	43	17	calculate	calculate	VERB
ejpam-6128	43	18	the	the	DET
ejpam-6128	43	19	infinitesimals	infinitesimal	NOUN
ejpam-6128	43	20	of	of	ADP
ejpam-6128	43	21	(	(	PUNCT
ejpam-6128	43	22	2	2	NUM
ejpam-6128	43	23	)	)	PUNCT
ejpam-6128	43	24	.	.	PUNCT
ejpam-6128	44	1	we	we	PRON
ejpam-6128	44	2	take	take	VERB
ejpam-6128	44	3	a	a	DET
ejpam-6128	44	4	lie	lie	NOUN
ejpam-6128	44	5	group	group	NOUN
ejpam-6128	44	6	of	of	ADP
ejpam-6128	44	7	infinitesimal	infinitesimal	ADJ
ejpam-6128	44	8	transformations	transformation	NOUN
ejpam-6128	44	9	with	with	ADP
ejpam-6128	44	10	one	one	NUM
ejpam-6128	44	11	parameter	parameter	NOUN
ejpam-6128	44	12	that	that	PRON
ejpam-6128	44	13	acts	act	VERB
ejpam-6128	44	14	on	on	ADP
ejpam-6128	44	15	m.	m.	PROPN
ejpam-6128	44	16	usman	usman	PROPN
ejpam-6128	44	17	,	,	PUNCT
ejpam-6128	44	18	a.	a.	NOUN
ejpam-6128	44	19	hussain	hussain	PROPN
ejpam-6128	44	20	,	,	PUNCT
ejpam-6128	44	21	m.	m.	PROPN
ejpam-6128	44	22	u.	u.	PROPN
ejpam-6128	44	23	farooq	farooq	PROPN
ejpam-6128	44	24	,	,	PUNCT
ejpam-6128	44	25	j.	j.	PROPN
ejpam-6128	44	26	herrera	herrera	PROPN
ejpam-6128	44	27	/	/	SYM
ejpam-6128	44	28	eur	eur	PROPN
ejpam-6128	44	29	.	.	PUNCT
ejpam-6128	45	1	j.	j.	PROPN
ejpam-6128	45	2	pure	pure	PROPN
ejpam-6128	45	3	appl	appl	PROPN
ejpam-6128	45	4	.	.	PROPN
ejpam-6128	45	5	math	math	PROPN
ejpam-6128	45	6	,	,	PUNCT
ejpam-6128	45	7	18	18	NUM
ejpam-6128	45	8	(	(	PUNCT
ejpam-6128	45	9	4	4	NUM
ejpam-6128	45	10	)	)	PUNCT
ejpam-6128	45	11	(	(	PUNCT
ejpam-6128	45	12	2025	2025	NUM
ejpam-6128	45	13	)	)	PUNCT
ejpam-6128	45	14	,	,	PUNCT
ejpam-6128	45	15	6128	6128	NUM
ejpam-6128	45	16	3	3	NUM
ejpam-6128	45	17	of	of	ADP
ejpam-6128	45	18	29	29	NUM
ejpam-6128	45	19	the	the	DET
ejpam-6128	45	20	dependent	dependent	ADJ
ejpam-6128	45	21	variable	variable	NOUN
ejpam-6128	45	22	w	w	PROPN
ejpam-6128	45	23	and	and	CCONJ
ejpam-6128	45	24	the	the	DET
ejpam-6128	45	25	independent	independent	ADJ
ejpam-6128	45	26	variables	variable	NOUN
ejpam-6128	45	27	x	x	NOUN
ejpam-6128	45	28	,	,	PUNCT
ejpam-6128	45	29	y	y	PROPN
ejpam-6128	45	30	,	,	PUNCT
ejpam-6128	45	31	and	and	CCONJ
ejpam-6128	45	32	t	t	PROPN
ejpam-6128	45	33	of	of	ADP
ejpam-6128	45	34	eq	eq	PROPN
ejpam-6128	45	35	.	.	PUNCT
ejpam-6128	46	1	(	(	PUNCT
ejpam-6128	46	2	2	2	X
ejpam-6128	46	3	)	)	PUNCT
ejpam-6128	46	4	x̃	x̃	PROPN
ejpam-6128	46	5	→	→	SYM
ejpam-6128	46	6	x+	x+	ADJ
ejpam-6128	46	7	ςζ1(x	ςζ1(x	NOUN
ejpam-6128	46	8	,	,	PUNCT
ejpam-6128	46	9	y	y	PROPN
ejpam-6128	46	10	,	,	PUNCT
ejpam-6128	46	11	t	t	PROPN
ejpam-6128	46	12	,	,	PUNCT
ejpam-6128	46	13	w	w	NOUN
ejpam-6128	46	14	)	)	PUNCT
ejpam-6128	46	15	+	+	NOUN
ejpam-6128	46	16	o(ς2	o(ς2	NOUN
ejpam-6128	46	17	)	)	PUNCT
ejpam-6128	46	18	,	,	PUNCT
ejpam-6128	46	19	ỹ	ỹ	PROPN
ejpam-6128	46	20	→	→	SYM
ejpam-6128	46	21	y	y	PROPN
ejpam-6128	46	22	+	+	CCONJ
ejpam-6128	46	23	ςζ2(x	ςζ2(x	PROPN
ejpam-6128	46	24	,	,	PUNCT
ejpam-6128	46	25	y	y	PROPN
ejpam-6128	46	26	,	,	PUNCT
ejpam-6128	46	27	t	t	PROPN
ejpam-6128	46	28	,	,	PUNCT
ejpam-6128	46	29	w	w	NOUN
ejpam-6128	46	30	)	)	PUNCT
ejpam-6128	46	31	+	+	NOUN
ejpam-6128	46	32	o(ς2	o(ς2	NOUN
ejpam-6128	46	33	)	)	PUNCT
ejpam-6128	46	34	,	,	PUNCT
ejpam-6128	46	35	t̃	t̃	PROPN
ejpam-6128	46	36	→	→	SYM
ejpam-6128	46	37	t+	t+	NUM
ejpam-6128	46	38	ςζ3(x	ςζ3(x	PROPN
ejpam-6128	46	39	,	,	PUNCT
ejpam-6128	46	40	y	y	PROPN
ejpam-6128	46	41	,	,	PUNCT
ejpam-6128	46	42	t	t	PROPN
ejpam-6128	46	43	,	,	PUNCT
ejpam-6128	46	44	w	w	NOUN
ejpam-6128	46	45	)	)	PUNCT
ejpam-6128	46	46	+	+	NOUN
ejpam-6128	46	47	o(ς2	o(ς2	NOUN
ejpam-6128	46	48	)	)	PUNCT
ejpam-6128	46	49	,	,	PUNCT
ejpam-6128	46	50	w̃	w̃	PROPN
ejpam-6128	46	51	→	→	SYM
ejpam-6128	46	52	w	w	PROPN
ejpam-6128	46	53	+	+	NUM
ejpam-6128	46	54	ςφ(x	ςφ(x	NUM
ejpam-6128	46	55	,	,	PUNCT
ejpam-6128	46	56	y	y	PROPN
ejpam-6128	46	57	,	,	PUNCT
ejpam-6128	46	58	t	t	PROPN
ejpam-6128	46	59	,	,	PUNCT
ejpam-6128	46	60	w	w	NOUN
ejpam-6128	46	61	)	)	PUNCT
ejpam-6128	46	62	+	+	NOUN
ejpam-6128	46	63	o(ς2	o(ς2	NOUN
ejpam-6128	46	64	)	)	PUNCT
ejpam-6128	46	65	,	,	PUNCT
ejpam-6128	46	66	(	(	PUNCT
ejpam-6128	46	67	3	3	X
ejpam-6128	46	68	)	)	PUNCT
ejpam-6128	46	69	with	with	ADP
ejpam-6128	46	70	ς	ς	PROPN
ejpam-6128	46	71	�	�	PROPN
ejpam-6128	46	72	1	1	NUM
ejpam-6128	46	73	being	be	AUX
ejpam-6128	46	74	a	a	DET
ejpam-6128	46	75	parameter	parameter	NOUN
ejpam-6128	46	76	of	of	ADP
ejpam-6128	46	77	the	the	DET
ejpam-6128	46	78	group	group	NOUN
ejpam-6128	46	79	and	and	CCONJ
ejpam-6128	46	80	ζ1	ζ1	NOUN
ejpam-6128	46	81	,	,	PUNCT
ejpam-6128	46	82	ζ2	ζ2	NOUN
ejpam-6128	46	83	,	,	PUNCT
ejpam-6128	46	84	ζ3	ζ3	NOUN
ejpam-6128	46	85	and	and	CCONJ
ejpam-6128	46	86	φ	φ	PROPN
ejpam-6128	46	87	are	be	AUX
ejpam-6128	46	88	the	the	DET
ejpam-6128	46	89	infinitesimal	infinitesimal	ADJ
ejpam-6128	46	90	functions	function	NOUN
ejpam-6128	46	91	for	for	ADP
ejpam-6128	46	92	the	the	DET
ejpam-6128	46	93	variables	variable	NOUN
ejpam-6128	46	94	x	x	NOUN
ejpam-6128	46	95	,	,	PUNCT
ejpam-6128	46	96	y	y	PROPN
ejpam-6128	46	97	,	,	PUNCT
ejpam-6128	46	98	t	t	PROPN
ejpam-6128	46	99	and	and	CCONJ
ejpam-6128	46	100	w	w	NOUN
ejpam-6128	46	101	respectively	respectively	ADV
ejpam-6128	46	102	,	,	PUNCT
ejpam-6128	46	103	which	which	PRON
ejpam-6128	46	104	should	should	AUX
ejpam-6128	46	105	be	be	AUX
ejpam-6128	46	106	computed	compute	VERB
ejpam-6128	46	107	later	later	ADV
ejpam-6128	46	108	.	.	PUNCT
ejpam-6128	47	1	the	the	DET
ejpam-6128	47	2	vector	vector	NOUN
ejpam-6128	47	3	field	field	NOUN
ejpam-6128	47	4	associated	associate	VERB
ejpam-6128	47	5	with	with	ADP
ejpam-6128	47	6	the	the	DET
ejpam-6128	47	7	lie	lie	NOUN
ejpam-6128	47	8	group	group	NOUN
ejpam-6128	47	9	of	of	ADP
ejpam-6128	47	10	transformations	transformation	NOUN
ejpam-6128	47	11	(	(	PUNCT
ejpam-6128	47	12	3	3	NUM
ejpam-6128	47	13	)	)	PUNCT
ejpam-6128	47	14	takes	take	VERB
ejpam-6128	47	15	the	the	DET
ejpam-6128	47	16	form	form	NOUN
ejpam-6128	47	17	y	y	PROPN
ejpam-6128	47	18	=	=	SYM
ejpam-6128	47	19	ζ1	ζ1	PROPN
ejpam-6128	47	20	∂	∂	NOUN
ejpam-6128	47	21	∂x	∂x	PROPN
ejpam-6128	48	1	+	+	CCONJ
ejpam-6128	48	2	ζ2	ζ2	NOUN
ejpam-6128	48	3	∂	∂	NOUN
ejpam-6128	48	4	∂y	∂y	NOUN
ejpam-6128	48	5	+	+	PUNCT
ejpam-6128	48	6	ζ3	ζ3	NOUN
ejpam-6128	48	7	∂	∂	NOUN
ejpam-6128	48	8	∂t	∂t	PROPN
ejpam-6128	49	1	+	+	PROPN
ejpam-6128	49	2	φ	φ	PROPN
ejpam-6128	49	3	∂	∂	X
ejpam-6128	49	4	∂w	∂w	PROPN
ejpam-6128	49	5	·	·	PUNCT
ejpam-6128	49	6	(	(	PUNCT
ejpam-6128	49	7	4	4	X
ejpam-6128	49	8	)	)	PUNCT
ejpam-6128	49	9	the	the	DET
ejpam-6128	49	10	operator	operator	NOUN
ejpam-6128	49	11	y	y	PROPN
ejpam-6128	49	12	can	can	AUX
ejpam-6128	49	13	be	be	AUX
ejpam-6128	49	14	identified	identify	VERB
ejpam-6128	49	15	as	as	ADP
ejpam-6128	49	16	the	the	DET
ejpam-6128	49	17	lie	lie	NOUN
ejpam-6128	49	18	point	point	NOUN
ejpam-6128	49	19	symmetry	symmetry	NOUN
ejpam-6128	49	20	generator	generator	PROPN
ejpam-6128	49	21	of	of	ADP
ejpam-6128	49	22	(	(	PUNCT
ejpam-6128	49	23	2	2	X
ejpam-6128	49	24	)	)	PUNCT
ejpam-6128	49	25	if	if	SCONJ
ejpam-6128	49	26	it	it	PRON
ejpam-6128	49	27	meets	meet	VERB
ejpam-6128	49	28	the	the	DET
ejpam-6128	49	29	invariance	invariance	NOUN
ejpam-6128	49	30	criterion	criterion	NOUN
ejpam-6128	50	1	[	[	X
ejpam-6128	50	2	3	3	X
ejpam-6128	50	3	]	]	X
ejpam-6128	50	4	y	y	PROPN
ejpam-6128	51	1	[	[	X
ejpam-6128	51	2	2](wtt	2](wtt	NUM
ejpam-6128	51	3	−	−	PROPN
ejpam-6128	51	4	(	(	PUNCT
ejpam-6128	51	5	f(w)wx)x	f(w)wx)x	NUM
ejpam-6128	51	6	−	−	PROPN
ejpam-6128	51	7	(	(	PUNCT
ejpam-6128	51	8	g(w)wy)y)|(2	g(w)wy)y)|(2	NOUN
ejpam-6128	51	9	)	)	PUNCT
ejpam-6128	51	10	=	=	SYM
ejpam-6128	51	11	0	0	NUM
ejpam-6128	51	12	,	,	PUNCT
ejpam-6128	51	13	(	(	PUNCT
ejpam-6128	51	14	5	5	NUM
ejpam-6128	51	15	)	)	PUNCT
ejpam-6128	52	1	where	where	SCONJ
ejpam-6128	52	2	y	y	PROPN
ejpam-6128	52	3	[	[	X
ejpam-6128	52	4	2	2	X
ejpam-6128	52	5	]	]	PUNCT
ejpam-6128	52	6	denotes	denote	VERB
ejpam-6128	52	7	the	the	DET
ejpam-6128	52	8	prolongation	prolongation	NOUN
ejpam-6128	52	9	of	of	ADP
ejpam-6128	52	10	y	y	PROPN
ejpam-6128	52	11	up	up	ADP
ejpam-6128	52	12	to	to	PART
ejpam-6128	52	13	order	order	VERB
ejpam-6128	52	14	two	two	NUM
ejpam-6128	52	15	.	.	PUNCT
ejpam-6128	53	1	we	we	PRON
ejpam-6128	53	2	obtain	obtain	VERB
ejpam-6128	53	3	a	a	DET
ejpam-6128	53	4	system	system	NOUN
ejpam-6128	53	5	of	of	ADP
ejpam-6128	53	6	linear	linear	PROPN
ejpam-6128	53	7	coupled	couple	VERB
ejpam-6128	53	8	pdes	pde	NOUN
ejpam-6128	53	9	for	for	ADP
ejpam-6128	53	10	infinitesimals	infinitesimal	NOUN
ejpam-6128	53	11	by	by	ADP
ejpam-6128	53	12	setting	set	VERB
ejpam-6128	53	13	the	the	DET
ejpam-6128	53	14	coefficients	coefficient	NOUN
ejpam-6128	53	15	of	of	ADP
ejpam-6128	53	16	the	the	DET
ejpam-6128	53	17	dependent	dependent	ADJ
ejpam-6128	53	18	variable	variable	NOUN
ejpam-6128	53	19	and	and	CCONJ
ejpam-6128	53	20	its	its	PRON
ejpam-6128	53	21	differential	differential	NOUN
ejpam-6128	53	22	to	to	ADP
ejpam-6128	53	23	zero	zero	NUM
ejpam-6128	53	24	.	.	PUNCT
ejpam-6128	54	1	these	these	DET
ejpam-6128	54	2	coupled	couple	VERB
ejpam-6128	54	3	pdes	pde	NOUN
ejpam-6128	54	4	also	also	ADV
ejpam-6128	54	5	referred	refer	VERB
ejpam-6128	54	6	to	to	ADP
ejpam-6128	54	7	as	as	ADP
ejpam-6128	54	8	determining	determine	VERB
ejpam-6128	54	9	equations	equation	NOUN
ejpam-6128	54	10	,	,	PUNCT
ejpam-6128	54	11	are	be	AUX
ejpam-6128	54	12	solved	solve	VERB
ejpam-6128	54	13	to	to	PART
ejpam-6128	54	14	produce	produce	VERB
ejpam-6128	54	15	the	the	DET
ejpam-6128	54	16	infinitesimals	infinitesimal	NOUN
ejpam-6128	54	17	,	,	PUNCT
ejpam-6128	54	18	we	we	PRON
ejpam-6128	54	19	then	then	ADV
ejpam-6128	54	20	substitute	substitute	VERB
ejpam-6128	54	21	these	these	DET
ejpam-6128	54	22	infinitesimals	infinitesimal	NOUN
ejpam-6128	54	23	in	in	ADP
ejpam-6128	54	24	eq	eq	ADP
ejpam-6128	54	25	.	.	PUNCT
ejpam-6128	55	1	(	(	PUNCT
ejpam-6128	55	2	4	4	NUM
ejpam-6128	55	3	)	)	PUNCT
ejpam-6128	55	4	to	to	PART
ejpam-6128	55	5	extract	extract	VERB
ejpam-6128	55	6	the	the	DET
ejpam-6128	55	7	lie	lie	NOUN
ejpam-6128	55	8	point	point	NOUN
ejpam-6128	55	9	symmetries	symmetry	NOUN
ejpam-6128	55	10	for	for	ADP
ejpam-6128	55	11	(	(	PUNCT
ejpam-6128	55	12	2	2	NUM
ejpam-6128	55	13	)	)	PUNCT
ejpam-6128	55	14	,	,	PUNCT
ejpam-6128	55	15	which	which	PRON
ejpam-6128	55	16	are	be	AUX
ejpam-6128	55	17	stated	state	VERB
ejpam-6128	55	18	as	as	SCONJ
ejpam-6128	55	19	follows	follow	VERB
ejpam-6128	55	20	:	:	PUNCT
ejpam-6128	55	21	case-1	case-1	NUM
ejpam-6128	55	22	:	:	PUNCT
ejpam-6128	55	23	f(w),g(w	f(w),g(w	NUM
ejpam-6128	55	24	)	)	PUNCT
ejpam-6128	55	25	are	be	AUX
ejpam-6128	55	26	arbitrary	arbitrary	ADJ
ejpam-6128	55	27	[	[	X
ejpam-6128	55	28	23	23	NUM
ejpam-6128	55	29	]	]	PUNCT
ejpam-6128	55	30	.	.	PUNCT
ejpam-6128	56	1	in	in	ADP
ejpam-6128	56	2	this	this	DET
ejpam-6128	56	3	case	case	NOUN
ejpam-6128	56	4	,	,	PUNCT
ejpam-6128	56	5	the	the	DET
ejpam-6128	56	6	solution	solution	NOUN
ejpam-6128	56	7	of	of	ADP
ejpam-6128	56	8	(	(	PUNCT
ejpam-6128	56	9	5	5	NUM
ejpam-6128	56	10	)	)	PUNCT
ejpam-6128	56	11	provides	provide	VERB
ejpam-6128	56	12	a	a	DET
ejpam-6128	56	13	four	four	NUM
ejpam-6128	56	14	-	-	PUNCT
ejpam-6128	56	15	dimensional	dimensional	ADJ
ejpam-6128	56	16	lie	lie	NOUN
ejpam-6128	56	17	algebra	algebra	NOUN
ejpam-6128	56	18	of	of	ADP
ejpam-6128	56	19	(	(	PUNCT
ejpam-6128	56	20	2	2	NUM
ejpam-6128	56	21	)	)	PUNCT
ejpam-6128	56	22	spanned	span	VERB
ejpam-6128	56	23	by	by	ADP
ejpam-6128	56	24	the	the	DET
ejpam-6128	56	25	following	follow	VERB
ejpam-6128	56	26	vector	vector	NOUN
ejpam-6128	56	27	fields	field	NOUN
ejpam-6128	56	28	y1	y1	NOUN
ejpam-6128	56	29	=	=	SYM
ejpam-6128	56	30	∂	∂	NUM
ejpam-6128	56	31	∂x	∂x	PROPN
ejpam-6128	56	32	,	,	PUNCT
ejpam-6128	57	1	y2	y2	NOUN
ejpam-6128	57	2	=	=	SYM
ejpam-6128	57	3	∂	∂	NUM
ejpam-6128	58	1	∂y	∂y	NOUN
ejpam-6128	58	2	,	,	PUNCT
ejpam-6128	58	3	y3	y3	NOUN
ejpam-6128	58	4	=	=	SYM
ejpam-6128	58	5	∂	∂	NUM
ejpam-6128	58	6	∂t	∂t	PROPN
ejpam-6128	58	7	,	,	PUNCT
ejpam-6128	58	8	y4	y4	PROPN
ejpam-6128	58	9	=	=	SYM
ejpam-6128	58	10	x	x	SYM
ejpam-6128	58	11	∂	∂	NUM
ejpam-6128	58	12	∂x	∂x	PROPN
ejpam-6128	59	1	+	+	CCONJ
ejpam-6128	59	2	y	y	PROPN
ejpam-6128	59	3	∂	∂	NOUN
ejpam-6128	59	4	∂y	∂y	PROPN
ejpam-6128	59	5	+	+	PROPN
ejpam-6128	59	6	t	t	PROPN
ejpam-6128	59	7	∂	∂	X
ejpam-6128	59	8	∂t	∂t	PROPN
ejpam-6128	59	9	.	.	PUNCT
ejpam-6128	60	1	(	(	PUNCT
ejpam-6128	60	2	6	6	X
ejpam-6128	60	3	)	)	PUNCT
ejpam-6128	60	4	the	the	DET
ejpam-6128	60	5	lie	lie	NOUN
ejpam-6128	60	6	algebra	algebra	NOUN
ejpam-6128	60	7	for	for	ADP
ejpam-6128	60	8	(	(	PUNCT
ejpam-6128	60	9	2	2	NUM
ejpam-6128	60	10	)	)	PUNCT
ejpam-6128	60	11	is	be	AUX
ejpam-6128	60	12	extended	extend	VERB
ejpam-6128	60	13	for	for	ADP
ejpam-6128	60	14	the	the	DET
ejpam-6128	60	15	cases	case	NOUN
ejpam-6128	60	16	presented	present	VERB
ejpam-6128	60	17	as	as	SCONJ
ejpam-6128	60	18	follows	follow	VERB
ejpam-6128	60	19	:	:	PUNCT
ejpam-6128	60	20	case-2	case-2	NUM
ejpam-6128	60	21	:	:	PUNCT
ejpam-6128	60	22	f(w	f(w	X
ejpam-6128	60	23	)	)	PUNCT
ejpam-6128	60	24	=	=	SYM
ejpam-6128	60	25	αw	αw	NOUN
ejpam-6128	60	26	,	,	PUNCT
ejpam-6128	60	27	g(w	g(w	ADJ
ejpam-6128	60	28	)	)	PUNCT
ejpam-6128	60	29	=	=	PUNCT
ejpam-6128	61	1	βw2	βw2	NOUN
ejpam-6128	61	2	.	.	PUNCT
ejpam-6128	62	1	y1	y1	NOUN
ejpam-6128	62	2	=	=	SYM
ejpam-6128	62	3	∂	∂	NUM
ejpam-6128	62	4	∂x	∂x	PROPN
ejpam-6128	62	5	,	,	PUNCT
ejpam-6128	62	6	y2	y2	NOUN
ejpam-6128	62	7	=	=	SYM
ejpam-6128	62	8	∂	∂	NUM
ejpam-6128	62	9	∂y	∂y	NOUN
ejpam-6128	62	10	,	,	PUNCT
ejpam-6128	62	11	y3	y3	NOUN
ejpam-6128	62	12	=	=	SYM
ejpam-6128	62	13	∂	∂	NUM
ejpam-6128	62	14	∂t	∂t	PROPN
ejpam-6128	62	15	,	,	PUNCT
ejpam-6128	62	16	y4	y4	PROPN
ejpam-6128	62	17	=	=	SYM
ejpam-6128	62	18	x	x	SYM
ejpam-6128	62	19	∂	∂	NUM
ejpam-6128	62	20	∂x	∂x	NOUN
ejpam-6128	62	21	+	+	CCONJ
ejpam-6128	62	22	2	2	NUM
ejpam-6128	62	23	t	t	NOUN
ejpam-6128	62	24	∂	∂	NOUN
ejpam-6128	63	1	∂t	∂t	PROPN
ejpam-6128	63	2	−	−	PROPN
ejpam-6128	63	3	2w	2w	NUM
ejpam-6128	63	4	∂	∂	NOUN
ejpam-6128	63	5	∂w	∂w	PROPN
ejpam-6128	63	6	,	,	PUNCT
ejpam-6128	63	7	y5	y5	NOUN
ejpam-6128	63	8	=	=	SYM
ejpam-6128	63	9	y	y	PROPN
ejpam-6128	63	10	∂	∂	NOUN
ejpam-6128	63	11	∂y	∂y	NOUN
ejpam-6128	63	12	−	−	PROPN
ejpam-6128	63	13	t	t	NOUN
ejpam-6128	63	14	∂	∂	NOUN
ejpam-6128	64	1	∂t	∂t	PROPN
ejpam-6128	65	1	+	+	CCONJ
ejpam-6128	65	2	2w	2w	NUM
ejpam-6128	65	3	∂	∂	NOUN
ejpam-6128	65	4	∂w	∂w	PROPN
ejpam-6128	65	5	.	.	PUNCT
ejpam-6128	66	1	(	(	PUNCT
ejpam-6128	66	2	7	7	X
ejpam-6128	66	3	)	)	PUNCT
ejpam-6128	66	4	case-3	case-3	NUM
ejpam-6128	66	5	:	:	PUNCT
ejpam-6128	66	6	f(w	f(w	NOUN
ejpam-6128	66	7	)	)	PUNCT
ejpam-6128	67	1	=	=	SYM
ejpam-6128	67	2	α	α	X
ejpam-6128	67	3	,	,	PUNCT
ejpam-6128	67	4	g(w	g(w	PROPN
ejpam-6128	67	5	)	)	PUNCT
ejpam-6128	67	6	=	=	PUNCT
ejpam-6128	68	1	βw	βw	X
ejpam-6128	68	2	:	:	PUNCT
ejpam-6128	68	3	y1	y1	NOUN
ejpam-6128	68	4	=	=	SYM
ejpam-6128	68	5	∂	∂	NUM
ejpam-6128	68	6	∂x	∂x	PROPN
ejpam-6128	68	7	,	,	PUNCT
ejpam-6128	68	8	y2	y2	NOUN
ejpam-6128	68	9	=	=	SYM
ejpam-6128	68	10	∂	∂	NUM
ejpam-6128	68	11	∂y	∂y	NOUN
ejpam-6128	68	12	,	,	PUNCT
ejpam-6128	68	13	y3	y3	NOUN
ejpam-6128	68	14	=	=	SYM
ejpam-6128	68	15	∂	∂	NUM
ejpam-6128	68	16	∂t	∂t	PROPN
ejpam-6128	68	17	,	,	PUNCT
ejpam-6128	68	18	y4	y4	PROPN
ejpam-6128	68	19	=	=	SYM
ejpam-6128	68	20	t	t	PROPN
ejpam-6128	68	21	∂	∂	NOUN
ejpam-6128	68	22	∂x	∂x	PROPN
ejpam-6128	69	1	+	+	CCONJ
ejpam-6128	70	1	x	x	SYM
ejpam-6128	70	2	α	α	NOUN
ejpam-6128	70	3	∂	∂	NOUN
ejpam-6128	70	4	∂t	∂t	PROPN
ejpam-6128	70	5	,	,	PUNCT
ejpam-6128	70	6	y5	y5	NOUN
ejpam-6128	70	7	=	=	SYM
ejpam-6128	70	8	y	y	PROPN
ejpam-6128	70	9	∂	∂	NOUN
ejpam-6128	70	10	∂y	∂y	PROPN
ejpam-6128	71	1	+	+	NOUN
ejpam-6128	71	2	2w	2w	NUM
ejpam-6128	71	3	∂	∂	NOUN
ejpam-6128	71	4	∂w	∂w	PROPN
ejpam-6128	71	5	,	,	PUNCT
ejpam-6128	71	6	y6	y6	NOUN
ejpam-6128	71	7	=	=	SYM
ejpam-6128	71	8	x	x	SYM
ejpam-6128	71	9	∂	∂	NUM
ejpam-6128	72	1	∂x	∂x	PROPN
ejpam-6128	72	2	+	+	CCONJ
ejpam-6128	72	3	t	t	PROPN
ejpam-6128	72	4	∂	∂	NOUN
ejpam-6128	73	1	∂t	∂t	PROPN
ejpam-6128	73	2	−	−	PROPN
ejpam-6128	73	3	2w	2w	NUM
ejpam-6128	73	4	∂	∂	NOUN
ejpam-6128	73	5	∂w	∂w	PROPN
ejpam-6128	73	6	(	(	PUNCT
ejpam-6128	73	7	8)	8)	NUM
ejpam-6128	73	8	m.	m.	NOUN
ejpam-6128	73	9	usman	usman	PROPN
ejpam-6128	73	10	,	,	PUNCT
ejpam-6128	73	11	a.	a.	NOUN
ejpam-6128	73	12	hussain	hussain	PROPN
ejpam-6128	73	13	,	,	PUNCT
ejpam-6128	73	14	m.	m.	PROPN
ejpam-6128	73	15	u.	u.	PROPN
ejpam-6128	73	16	farooq	farooq	PROPN
ejpam-6128	73	17	,	,	PUNCT
ejpam-6128	73	18	j.	j.	PROPN
ejpam-6128	73	19	herrera	herrera	PROPN
ejpam-6128	73	20	/	/	SYM
ejpam-6128	73	21	eur	eur	PROPN
ejpam-6128	73	22	.	.	PUNCT
ejpam-6128	74	1	j.	j.	PROPN
ejpam-6128	74	2	pure	pure	PROPN
ejpam-6128	74	3	appl	appl	PROPN
ejpam-6128	74	4	.	.	PROPN
ejpam-6128	74	5	math	math	PROPN
ejpam-6128	74	6	,	,	PUNCT
ejpam-6128	74	7	18	18	NUM
ejpam-6128	74	8	(	(	PUNCT
ejpam-6128	74	9	4	4	NUM
ejpam-6128	74	10	)	)	PUNCT
ejpam-6128	74	11	(	(	PUNCT
ejpam-6128	74	12	2025	2025	NUM
ejpam-6128	74	13	)	)	PUNCT
ejpam-6128	74	14	,	,	PUNCT
ejpam-6128	74	15	6128	6128	NUM
ejpam-6128	74	16	4	4	NUM
ejpam-6128	74	17	of	of	ADP
ejpam-6128	74	18	29	29	NUM
ejpam-6128	74	19	case-4	case-4	NOUN
ejpam-6128	74	20	:	:	PUNCT
ejpam-6128	74	21	f(w	f(w	NUM
ejpam-6128	74	22	)	)	PUNCT
ejpam-6128	74	23	=	=	SYM
ejpam-6128	74	24	eαw	eαw	ADJ
ejpam-6128	74	25	,	,	PUNCT
ejpam-6128	74	26	g(w	g(w	PROPN
ejpam-6128	74	27	)	)	PUNCT
ejpam-6128	74	28	=	=	PUNCT
ejpam-6128	75	1	eβw	eβw	ADJ
ejpam-6128	75	2	:	:	PUNCT
ejpam-6128	75	3	y1	y1	NOUN
ejpam-6128	75	4	=	=	SYM
ejpam-6128	75	5	∂	∂	NUM
ejpam-6128	75	6	∂x	∂x	PROPN
ejpam-6128	75	7	,	,	PUNCT
ejpam-6128	75	8	y2	y2	NOUN
ejpam-6128	75	9	=	=	SYM
ejpam-6128	75	10	∂	∂	NUM
ejpam-6128	75	11	∂y	∂y	NOUN
ejpam-6128	75	12	,	,	PUNCT
ejpam-6128	75	13	y3	y3	NOUN
ejpam-6128	75	14	=	=	SYM
ejpam-6128	75	15	∂	∂	NUM
ejpam-6128	75	16	∂t	∂t	PROPN
ejpam-6128	75	17	,	,	PUNCT
ejpam-6128	75	18	y4	y4	PROPN
ejpam-6128	75	19	=	=	SYM
ejpam-6128	75	20	x	x	SYM
ejpam-6128	75	21	∂	∂	NUM
ejpam-6128	75	22	∂x	∂x	NOUN
ejpam-6128	76	1	+	+	CCONJ
ejpam-6128	76	2	βt	βt	PROPN
ejpam-6128	76	3	(	(	PUNCT
ejpam-6128	76	4	β	β	NOUN
ejpam-6128	76	5	−	−	NOUN
ejpam-6128	76	6	α	α	NUM
ejpam-6128	76	7	)	)	PUNCT
ejpam-6128	76	8	∂	∂	NOUN
ejpam-6128	77	1	∂t	∂t	PROPN
ejpam-6128	78	1	+	+	CCONJ
ejpam-6128	78	2	2	2	NUM
ejpam-6128	78	3	(	(	PUNCT
ejpam-6128	78	4	α−	α−	ADP
ejpam-6128	78	5	β	β	NOUN
ejpam-6128	78	6	)	)	PUNCT
ejpam-6128	78	7	∂	∂	NOUN
ejpam-6128	78	8	∂w	∂w	PROPN
ejpam-6128	78	9	,	,	PUNCT
ejpam-6128	78	10	y5	y5	NOUN
ejpam-6128	78	11	=	=	SYM
ejpam-6128	78	12	y	y	PROPN
ejpam-6128	78	13	∂	∂	NOUN
ejpam-6128	78	14	∂y	∂y	PROPN
ejpam-6128	79	1	+	+	NUM
ejpam-6128	79	2	αt	αt	PROPN
ejpam-6128	79	3	(	(	PUNCT
ejpam-6128	79	4	−β	−β	NOUN
ejpam-6128	79	5	+	+	CCONJ
ejpam-6128	79	6	α	α	NOUN
ejpam-6128	79	7	)	)	PUNCT
ejpam-6128	79	8	∂	∂	NOUN
ejpam-6128	80	1	∂t	∂t	PROPN
ejpam-6128	80	2	+	+	CCONJ
ejpam-6128	80	3	2	2	NUM
ejpam-6128	80	4	(	(	PUNCT
ejpam-6128	80	5	β	β	NOUN
ejpam-6128	80	6	−	−	NOUN
ejpam-6128	80	7	α	α	NUM
ejpam-6128	80	8	)	)	PUNCT
ejpam-6128	80	9	∂	∂	NOUN
ejpam-6128	81	1	∂w	∂w	PROPN
ejpam-6128	81	2	(	(	PUNCT
ejpam-6128	81	3	9	9	NUM
ejpam-6128	81	4	)	)	PUNCT
ejpam-6128	81	5	case-5	case-5	NOUN
ejpam-6128	81	6	:	:	PUNCT
ejpam-6128	81	7	f(w	f(w	NOUN
ejpam-6128	81	8	)	)	PUNCT
ejpam-6128	81	9	=	=	SYM
ejpam-6128	81	10	wα	wα	NOUN
ejpam-6128	81	11	,	,	PUNCT
ejpam-6128	81	12	g(w	g(w	PROPN
ejpam-6128	81	13	)	)	PUNCT
ejpam-6128	81	14	=	=	SYM
ejpam-6128	82	1	wβ	wβ	ADP
ejpam-6128	82	2	:	:	PUNCT
ejpam-6128	82	3	y1	y1	NOUN
ejpam-6128	82	4	=	=	SYM
ejpam-6128	82	5	∂	∂	NUM
ejpam-6128	82	6	∂x	∂x	PROPN
ejpam-6128	82	7	,	,	PUNCT
ejpam-6128	82	8	y2	y2	NOUN
ejpam-6128	82	9	=	=	SYM
ejpam-6128	82	10	∂	∂	NUM
ejpam-6128	82	11	∂y	∂y	NOUN
ejpam-6128	82	12	,	,	PUNCT
ejpam-6128	82	13	y3	y3	NOUN
ejpam-6128	82	14	=	=	SYM
ejpam-6128	82	15	∂	∂	NUM
ejpam-6128	82	16	∂t	∂t	PROPN
ejpam-6128	82	17	,	,	PUNCT
ejpam-6128	82	18	y4	y4	PROPN
ejpam-6128	82	19	=	=	SYM
ejpam-6128	82	20	x	x	SYM
ejpam-6128	82	21	∂	∂	NUM
ejpam-6128	82	22	∂x	∂x	NOUN
ejpam-6128	82	23	+	+	CCONJ
ejpam-6128	82	24	βt	βt	PROPN
ejpam-6128	82	25	(	(	PUNCT
ejpam-6128	82	26	β	β	NOUN
ejpam-6128	82	27	−	−	NOUN
ejpam-6128	82	28	α	α	NUM
ejpam-6128	82	29	)	)	PUNCT
ejpam-6128	82	30	∂	∂	NOUN
ejpam-6128	83	1	∂t	∂t	PROPN
ejpam-6128	83	2	−	−	PROPN
ejpam-6128	83	3	2w1+βw1+α	2w1+βw1+α	PROPN
ejpam-6128	83	4	wβ	wβ	ADP
ejpam-6128	83	5	(	(	PUNCT
ejpam-6128	83	6	β	β	X
ejpam-6128	83	7	−	−	PROPN
ejpam-6128	83	8	1)w1+α	1)w1+α	NUM
ejpam-6128	83	9	−	−	PROPN
ejpam-6128	83	10	w1+βwα	w1+βwα	INTJ
ejpam-6128	83	11	(	(	PUNCT
ejpam-6128	83	12	α−	α−	ADP
ejpam-6128	83	13	1	1	NUM
ejpam-6128	83	14	)	)	PUNCT
ejpam-6128	83	15	∂	∂	NOUN
ejpam-6128	83	16	∂w	∂w	PROPN
ejpam-6128	83	17	,	,	PUNCT
ejpam-6128	83	18	y5	y5	NOUN
ejpam-6128	83	19	=	=	SYM
ejpam-6128	83	20	y	y	PROPN
ejpam-6128	83	21	∂	∂	NOUN
ejpam-6128	83	22	∂y	∂y	PROPN
ejpam-6128	84	1	+	+	NUM
ejpam-6128	84	2	αt	αt	PROPN
ejpam-6128	84	3	(	(	PUNCT
ejpam-6128	84	4	−β	−β	NOUN
ejpam-6128	84	5	+	+	CCONJ
ejpam-6128	84	6	α	α	NOUN
ejpam-6128	84	7	)	)	PUNCT
ejpam-6128	84	8	∂	∂	NOUN
ejpam-6128	85	1	∂t	∂t	PROPN
ejpam-6128	85	2	+	+	CCONJ
ejpam-6128	85	3	2w1+βw1+α	2w1+βw1+α	PROPN
ejpam-6128	85	4	wβ	wβ	ADP
ejpam-6128	85	5	(	(	PUNCT
ejpam-6128	85	6	β	β	X
ejpam-6128	85	7	−	−	PROPN
ejpam-6128	85	8	1)w1+α	1)w1+α	NUM
ejpam-6128	85	9	−	−	PROPN
ejpam-6128	85	10	w1+βwα	w1+βwα	INTJ
ejpam-6128	85	11	(	(	PUNCT
ejpam-6128	85	12	α−	α−	ADP
ejpam-6128	85	13	1	1	NUM
ejpam-6128	85	14	)	)	PUNCT
ejpam-6128	85	15	∂	∂	NOUN
ejpam-6128	86	1	∂w	∂w	PROPN
ejpam-6128	86	2	(	(	PUNCT
ejpam-6128	86	3	10	10	NUM
ejpam-6128	86	4	)	)	PUNCT
ejpam-6128	86	5	case-6	case-6	PROPN
ejpam-6128	86	6	:	:	PUNCT
ejpam-6128	86	7	f(w	f(w	NUM
ejpam-6128	86	8	)	)	PUNCT
ejpam-6128	86	9	=	=	SYM
ejpam-6128	87	1	α	α	PROPN
ejpam-6128	87	2	lnw	lnw	ADJ
ejpam-6128	87	3	,	,	PUNCT
ejpam-6128	87	4	g(w	g(w	ADJ
ejpam-6128	87	5	)	)	PUNCT
ejpam-6128	87	6	=	=	PUNCT
ejpam-6128	88	1	β	β	X
ejpam-6128	88	2	lnw	lnw	ADJ
ejpam-6128	88	3	:	:	PUNCT
ejpam-6128	88	4	y1	y1	NOUN
ejpam-6128	88	5	=	=	SYM
ejpam-6128	88	6	∂	∂	NUM
ejpam-6128	88	7	∂x	∂x	PROPN
ejpam-6128	88	8	,	,	PUNCT
ejpam-6128	88	9	y2	y2	NOUN
ejpam-6128	88	10	=	=	SYM
ejpam-6128	88	11	∂	∂	NUM
ejpam-6128	88	12	∂y	∂y	NOUN
ejpam-6128	88	13	,	,	PUNCT
ejpam-6128	88	14	y3	y3	NOUN
ejpam-6128	88	15	=	=	SYM
ejpam-6128	88	16	∂	∂	NUM
ejpam-6128	88	17	∂t	∂t	PROPN
ejpam-6128	88	18	,	,	PUNCT
ejpam-6128	88	19	y4	y4	PROPN
ejpam-6128	88	20	=	=	SYM
ejpam-6128	88	21	x	x	SYM
ejpam-6128	88	22	∂	∂	NUM
ejpam-6128	88	23	∂x	∂x	PROPN
ejpam-6128	89	1	+	+	CCONJ
ejpam-6128	89	2	y	y	PROPN
ejpam-6128	89	3	∂	∂	NOUN
ejpam-6128	89	4	∂y	∂y	PROPN
ejpam-6128	89	5	+	+	PROPN
ejpam-6128	89	6	t	t	PROPN
ejpam-6128	89	7	∂	∂	NOUN
ejpam-6128	89	8	∂t	∂t	PROPN
ejpam-6128	89	9	,	,	PUNCT
ejpam-6128	89	10	y5	y5	NOUN
ejpam-6128	89	11	=	=	SYM
ejpam-6128	89	12	y	y	PROPN
ejpam-6128	89	13	∂	∂	NOUN
ejpam-6128	89	14	∂x	∂x	PROPN
ejpam-6128	90	1	−	−	PROPN
ejpam-6128	90	2	βx	βx	NOUN
ejpam-6128	90	3	α	α	NOUN
ejpam-6128	90	4	∂	∂	NOUN
ejpam-6128	90	5	∂y	∂y	X
ejpam-6128	90	6	(	(	PUNCT
ejpam-6128	90	7	11	11	NUM
ejpam-6128	90	8	)	)	PUNCT
ejpam-6128	90	9	case-7	case-7	NUM
ejpam-6128	90	10	:	:	PUNCT
ejpam-6128	90	11	f(w	f(w	NUM
ejpam-6128	90	12	)	)	PUNCT
ejpam-6128	90	13	=	=	SYM
ejpam-6128	90	14	α	α	X
ejpam-6128	90	15	,	,	PUNCT
ejpam-6128	90	16	g(w	g(w	PROPN
ejpam-6128	90	17	)	)	PUNCT
ejpam-6128	90	18	=	=	PUNCT
ejpam-6128	91	1	β	β	X
ejpam-6128	91	2	:	:	PUNCT
ejpam-6128	92	1	[	[	X
ejpam-6128	92	2	22	22	NUM
ejpam-6128	92	3	]	]	X
ejpam-6128	92	4	y1	y1	NOUN
ejpam-6128	92	5	=	=	SYM
ejpam-6128	92	6	∂	∂	NUM
ejpam-6128	92	7	∂x	∂x	PROPN
ejpam-6128	92	8	,	,	PUNCT
ejpam-6128	92	9	y2	y2	NOUN
ejpam-6128	92	10	=	=	SYM
ejpam-6128	92	11	∂	∂	NUM
ejpam-6128	92	12	∂y	∂y	NOUN
ejpam-6128	92	13	,	,	PUNCT
ejpam-6128	92	14	y3	y3	NOUN
ejpam-6128	92	15	=	=	SYM
ejpam-6128	92	16	∂	∂	NUM
ejpam-6128	92	17	∂t	∂t	PROPN
ejpam-6128	92	18	,	,	PUNCT
ejpam-6128	92	19	y4	y4	PROPN
ejpam-6128	92	20	=	=	SYM
ejpam-6128	92	21	x	x	SYM
ejpam-6128	92	22	∂	∂	NUM
ejpam-6128	92	23	∂x	∂x	PROPN
ejpam-6128	93	1	+	+	CCONJ
ejpam-6128	93	2	y	y	PROPN
ejpam-6128	93	3	∂	∂	NOUN
ejpam-6128	93	4	∂y	∂y	PROPN
ejpam-6128	93	5	+	+	PROPN
ejpam-6128	93	6	t	t	PROPN
ejpam-6128	93	7	∂	∂	NOUN
ejpam-6128	93	8	∂t	∂t	PROPN
ejpam-6128	93	9	,	,	PUNCT
ejpam-6128	93	10	y5	y5	PROPN
ejpam-6128	93	11	=	=	SYM
ejpam-6128	93	12	w	w	PROPN
ejpam-6128	93	13	∂	∂	NOUN
ejpam-6128	93	14	∂w	∂w	PROPN
ejpam-6128	93	15	,	,	PUNCT
ejpam-6128	93	16	y6	y6	NOUN
ejpam-6128	93	17	=	=	SYM
ejpam-6128	93	18	t	t	PROPN
ejpam-6128	93	19	∂	∂	NOUN
ejpam-6128	93	20	∂y	∂y	PROPN
ejpam-6128	94	1	+	+	CCONJ
ejpam-6128	94	2	y	y	PROPN
ejpam-6128	94	3	β	β	X
ejpam-6128	94	4	∂	∂	X
ejpam-6128	94	5	∂t	∂t	PROPN
ejpam-6128	94	6	,	,	PUNCT
ejpam-6128	94	7	y7	y7	PROPN
ejpam-6128	94	8	=	=	SYM
ejpam-6128	94	9	t	t	PROPN
ejpam-6128	94	10	∂	∂	NOUN
ejpam-6128	94	11	∂x	∂x	PROPN
ejpam-6128	95	1	+	+	CCONJ
ejpam-6128	96	1	x	x	SYM
ejpam-6128	96	2	α	α	NOUN
ejpam-6128	96	3	∂	∂	NOUN
ejpam-6128	96	4	∂t	∂t	PROPN
ejpam-6128	96	5	,	,	PUNCT
ejpam-6128	96	6	y8	y8	PROPN
ejpam-6128	96	7	=	=	PUNCT
ejpam-6128	96	8	y	y	PROPN
ejpam-6128	96	9	∂	∂	NOUN
ejpam-6128	96	10	∂x	∂x	PROPN
ejpam-6128	96	11	−	−	PROPN
ejpam-6128	96	12	βx	βx	NOUN
ejpam-6128	96	13	α	α	PROPN
ejpam-6128	96	14	∂	∂	NOUN
ejpam-6128	96	15	∂y	∂y	PROPN
ejpam-6128	96	16	,	,	PUNCT
ejpam-6128	96	17	y9	y9	PROPN
ejpam-6128	96	18	=	=	SYM
ejpam-6128	96	19	xt	xt	PROPN
ejpam-6128	96	20	∂	∂	NUM
ejpam-6128	96	21	∂x	∂x	PROPN
ejpam-6128	96	22	+	+	CCONJ
ejpam-6128	96	23	yt	yt	PROPN
ejpam-6128	96	24	∂	∂	NOUN
ejpam-6128	96	25	∂y	∂y	NOUN
ejpam-6128	97	1	+	+	CCONJ
ejpam-6128	97	2	(	(	PUNCT
ejpam-6128	97	3	y2	y2	INTJ
ejpam-6128	97	4	2β	2β	NOUN
ejpam-6128	97	5	+	+	CCONJ
ejpam-6128	97	6	x2	x2	ADJ
ejpam-6128	97	7	2α	2α	NOUN
ejpam-6128	97	8	+	+	CCONJ
ejpam-6128	97	9	t2	t2	PROPN
ejpam-6128	97	10	2	2	NUM
ejpam-6128	97	11	)	)	PUNCT
ejpam-6128	97	12	∂	∂	NOUN
ejpam-6128	98	1	∂t	∂t	PROPN
ejpam-6128	98	2	−	−	PROPN
ejpam-6128	98	3	tw	tw	PROPN
ejpam-6128	98	4	2	2	NUM
ejpam-6128	98	5	∂	∂	NOUN
ejpam-6128	98	6	∂w	∂w	PROPN
ejpam-6128	98	7	,	,	PUNCT
ejpam-6128	98	8	y10	y10	NOUN
ejpam-6128	98	9	=	=	SYM
ejpam-6128	98	10	xy	xy	NOUN
ejpam-6128	98	11	∂	∂	NOUN
ejpam-6128	98	12	∂x	∂x	PROPN
ejpam-6128	98	13	+	+	CCONJ
ejpam-6128	98	14	(	(	PUNCT
ejpam-6128	98	15	β	β	X
ejpam-6128	98	16	t2	t2	NOUN
ejpam-6128	98	17	+	+	CCONJ
ejpam-6128	98	18	y2	y2	INTJ
ejpam-6128	98	19	)	)	PUNCT
ejpam-6128	99	1	α−	α−	ADP
ejpam-6128	99	2	β	β	X
ejpam-6128	99	3	x2	x2	X
ejpam-6128	99	4	2α	2α	NOUN
ejpam-6128	99	5	∂	∂	X
ejpam-6128	99	6	∂y	∂y	NOUN
ejpam-6128	100	1	+	+	CCONJ
ejpam-6128	100	2	yt	yt	PROPN
ejpam-6128	100	3	∂	∂	NOUN
ejpam-6128	100	4	∂t	∂t	PROPN
ejpam-6128	100	5	−	−	PROPN
ejpam-6128	100	6	yw	yw	PROPN
ejpam-6128	100	7	2	2	NUM
ejpam-6128	100	8	∂	∂	NOUN
ejpam-6128	100	9	∂w	∂w	PROPN
ejpam-6128	100	10	,	,	PUNCT
ejpam-6128	100	11	y11	y11	NOUN
ejpam-6128	100	12	=	=	SYM
ejpam-6128	100	13	(	(	PUNCT
ejpam-6128	100	14	−β	−β	NOUN
ejpam-6128	100	15	t2	t2	PROPN
ejpam-6128	100	16	+	+	CCONJ
ejpam-6128	100	17	y2	y2	INTJ
ejpam-6128	100	18	)	)	PUNCT
ejpam-6128	101	1	α−	α−	ADP
ejpam-6128	101	2	β	β	X
ejpam-6128	101	3	x2	x2	X
ejpam-6128	101	4	2α	2α	NOUN
ejpam-6128	101	5	∂	∂	NOUN
ejpam-6128	101	6	∂x	∂x	PROPN
ejpam-6128	101	7	−	−	PROPN
ejpam-6128	101	8	βxy	βxy	NOUN
ejpam-6128	102	1	α	α	NOUN
ejpam-6128	102	2	∂	∂	NOUN
ejpam-6128	102	3	∂y	∂y	NOUN
ejpam-6128	102	4	−	−	PROPN
ejpam-6128	102	5	xβt	xβt	PROPN
ejpam-6128	102	6	α	α	PROPN
ejpam-6128	102	7	∂	∂	NOUN
ejpam-6128	102	8	∂t	∂t	PROPN
ejpam-6128	103	1	+	+	CCONJ
ejpam-6128	103	2	xβw	xβw	NOUN
ejpam-6128	103	3	2α	2α	NOUN
ejpam-6128	103	4	∂	∂	ADV
ejpam-6128	103	5	∂w	∂w	PROPN
ejpam-6128	103	6	(	(	PUNCT
ejpam-6128	103	7	12	12	NUM
ejpam-6128	103	8	)	)	PUNCT
ejpam-6128	103	9	2.1	2.1	NUM
ejpam-6128	103	10	.	.	PUNCT
ejpam-6128	104	1	optimal	optimal	ADJ
ejpam-6128	104	2	system	system	NOUN
ejpam-6128	104	3	the	the	DET
ejpam-6128	104	4	optimal	optimal	ADJ
ejpam-6128	104	5	systems	system	NOUN
ejpam-6128	104	6	for	for	ADP
ejpam-6128	104	7	the	the	DET
ejpam-6128	104	8	symmetry	symmetry	NOUN
ejpam-6128	104	9	generators	generator	NOUN
ejpam-6128	104	10	of	of	ADP
ejpam-6128	104	11	(	(	PUNCT
ejpam-6128	104	12	2	2	X
ejpam-6128	104	13	)	)	PUNCT
ejpam-6128	104	14	are	be	AUX
ejpam-6128	104	15	derived	derive	VERB
ejpam-6128	104	16	using	use	VERB
ejpam-6128	104	17	the	the	DET
ejpam-6128	104	18	algorithm	algorithm	NOUN
ejpam-6128	104	19	described	describe	VERB
ejpam-6128	104	20	in	in	ADP
ejpam-6128	104	21	[	[	X
ejpam-6128	104	22	3	3	NUM
ejpam-6128	104	23	]	]	PUNCT
ejpam-6128	104	24	.	.	PUNCT
ejpam-6128	105	1	the	the	DET
ejpam-6128	105	2	adjoint	adjoint	PROPN
ejpam-6128	105	3	action	action	NOUN
ejpam-6128	105	4	representation	representation	NOUN
ejpam-6128	105	5	[	[	X
ejpam-6128	105	6	15	15	NUM
ejpam-6128	105	7	]	]	PUNCT
ejpam-6128	105	8	is	be	AUX
ejpam-6128	105	9	written	write	VERB
ejpam-6128	105	10	as	as	SCONJ
ejpam-6128	105	11	follows	follow	VERB
ejpam-6128	105	12	ad(exp(ςyi)yj	ad(exp(ςyi)yj	PROPN
ejpam-6128	105	13	)	)	PUNCT
ejpam-6128	106	1	=	=	SYM
ejpam-6128	106	2	yj	yj	PROPN
ejpam-6128	106	3	−	−	PROPN
ejpam-6128	106	4	ς[yi	ς[yi	PROPN
ejpam-6128	106	5	,	,	PUNCT
ejpam-6128	106	6	yj	yj	PROPN
ejpam-6128	106	7	]	]	PUNCT
ejpam-6128	107	1	+	+	CCONJ
ejpam-6128	107	2	ς2	ς2	PROPN
ejpam-6128	107	3	2	2	NUM
ejpam-6128	107	4	!	!	PUNCT
ejpam-6128	108	1	[	[	X
ejpam-6128	108	2	yi	yi	X
ejpam-6128	108	3	,	,	PUNCT
ejpam-6128	108	4	[	[	X
ejpam-6128	108	5	yi	yi	X
ejpam-6128	108	6	,	,	PUNCT
ejpam-6128	108	7	yj	yj	X
ejpam-6128	108	8	]	]	X
ejpam-6128	108	9	]	]	X
ejpam-6128	108	10	−	−	PROPN
ejpam-6128	108	11	.	.	PUNCT
ejpam-6128	108	12	.	.	PUNCT
ejpam-6128	108	13	.	.	PUNCT
ejpam-6128	108	14	.	.	PUNCT
ejpam-6128	109	1	(	(	PUNCT
ejpam-6128	109	2	13	13	NUM
ejpam-6128	109	3	)	)	PUNCT
ejpam-6128	109	4	m.	m.	NOUN
ejpam-6128	109	5	usman	usman	PROPN
ejpam-6128	109	6	,	,	PUNCT
ejpam-6128	109	7	a.	a.	NOUN
ejpam-6128	109	8	hussain	hussain	PROPN
ejpam-6128	109	9	,	,	PUNCT
ejpam-6128	109	10	m.	m.	PROPN
ejpam-6128	109	11	u.	u.	PROPN
ejpam-6128	109	12	farooq	farooq	PROPN
ejpam-6128	109	13	,	,	PUNCT
ejpam-6128	109	14	j.	j.	PROPN
ejpam-6128	109	15	herrera	herrera	PROPN
ejpam-6128	109	16	/	/	SYM
ejpam-6128	109	17	eur	eur	PROPN
ejpam-6128	109	18	.	.	PUNCT
ejpam-6128	110	1	j.	j.	PROPN
ejpam-6128	110	2	pure	pure	PROPN
ejpam-6128	110	3	appl	appl	PROPN
ejpam-6128	110	4	.	.	PROPN
ejpam-6128	110	5	math	math	PROPN
ejpam-6128	110	6	,	,	PUNCT
ejpam-6128	110	7	18	18	NUM
ejpam-6128	110	8	(	(	PUNCT
ejpam-6128	110	9	4	4	NUM
ejpam-6128	110	10	)	)	PUNCT
ejpam-6128	110	11	(	(	PUNCT
ejpam-6128	110	12	2025	2025	NUM
ejpam-6128	110	13	)	)	PUNCT
ejpam-6128	110	14	,	,	PUNCT
ejpam-6128	110	15	6128	6128	NUM
ejpam-6128	110	16	5	5	NUM
ejpam-6128	110	17	of	of	ADP
ejpam-6128	110	18	29	29	NUM
ejpam-6128	110	19	computation	computation	NOUN
ejpam-6128	110	20	of	of	ADP
ejpam-6128	110	21	basic	basic	ADJ
ejpam-6128	110	22	invariants	invariant	NOUN
ejpam-6128	110	23	let	let	VERB
ejpam-6128	110	24	f	f	PRON
ejpam-6128	110	25	be	be	AUX
ejpam-6128	110	26	a	a	DET
ejpam-6128	110	27	function	function	NOUN
ejpam-6128	110	28	on	on	ADP
ejpam-6128	110	29	lie	lie	NOUN
ejpam-6128	110	30	algebra	algebra	PROPN
ejpam-6128	110	31	l	l	NOUN
ejpam-6128	110	32	such	such	ADJ
ejpam-6128	110	33	that	that	DET
ejpam-6128	110	34	f(ad(exp(ςy)x	f(ad(exp(ςy)x	PROPN
ejpam-6128	110	35	)	)	PUNCT
ejpam-6128	110	36	)	)	PUNCT
ejpam-6128	111	1	=	=	SYM
ejpam-6128	111	2	f(x	f(x	PROPN
ejpam-6128	111	3	)	)	PUNCT
ejpam-6128	111	4	∀	∀	PUNCT
ejpam-6128	112	1	y	y	PROPN
ejpam-6128	112	2	∈	∈	PROPN
ejpam-6128	112	3	l	l	NOUN
ejpam-6128	112	4	,	,	PUNCT
ejpam-6128	112	5	ς	ς	PROPN
ejpam-6128	112	6	∈	∈	PROPN
ejpam-6128	112	7	r.	r.	PROPN
ejpam-6128	112	8	(	(	PUNCT
ejpam-6128	112	9	14	14	NUM
ejpam-6128	112	10	)	)	PUNCT
ejpam-6128	112	11	now	now	ADV
ejpam-6128	112	12	,	,	PUNCT
ejpam-6128	112	13	if	if	SCONJ
ejpam-6128	112	14	we	we	PRON
ejpam-6128	112	15	write	write	VERB
ejpam-6128	112	16	f(y1y1	f(y1y1	NOUN
ejpam-6128	112	17	+	+	X
ejpam-6128	112	18	.	.	PUNCT
ejpam-6128	112	19	.	.	PUNCT
ejpam-6128	113	1	.+	.+	NOUN
ejpam-6128	113	2	ynyn	ynyn	NOUN
ejpam-6128	113	3	)	)	PUNCT
ejpam-6128	113	4	=	=	SYM
ejpam-6128	113	5	f(y1	f(y1	NOUN
ejpam-6128	113	6	+	+	X
ejpam-6128	113	7	.	.	PUNCT
ejpam-6128	113	8	.	.	PUNCT
ejpam-6128	114	1	.+	.+	PROPN
ejpam-6128	114	2	yn	yn	PROPN
ejpam-6128	114	3	)	)	PUNCT
ejpam-6128	114	4	,	,	PUNCT
ejpam-6128	114	5	then	then	ADV
ejpam-6128	114	6	for	for	ADP
ejpam-6128	114	7	the	the	DET
ejpam-6128	114	8	basis	basis	NOUN
ejpam-6128	114	9	{	{	PUNCT
ejpam-6128	114	10	y1	y1	NOUN
ejpam-6128	114	11	,	,	PUNCT
ejpam-6128	114	12	.	.	PUNCT
ejpam-6128	114	13	.	.	PUNCT
ejpam-6128	114	14	.	.	PUNCT
ejpam-6128	115	1	,	,	PUNCT
ejpam-6128	115	2	yn	yn	PROPN
ejpam-6128	115	3	}	}	PUNCT
ejpam-6128	115	4	,	,	PUNCT
ejpam-6128	115	5	we	we	PRON
ejpam-6128	115	6	get	get	VERB
ejpam-6128	115	7	[	[	X
ejpam-6128	115	8	24	24	NUM
ejpam-6128	115	9	]	]	PUNCT
ejpam-6128	115	10	∑	∑	PUNCT
ejpam-6128	115	11	1≤i	1≤i	NUM
ejpam-6128	115	12	,	,	PUNCT
ejpam-6128	115	13	i≤n	i≤n	ADP
ejpam-6128	115	14	yiθj([yk	yiθj([yk	NOUN
ejpam-6128	115	15	,	,	PUNCT
ejpam-6128	115	16	yi	yi	NOUN
ejpam-6128	115	17	]	]	PUNCT
ejpam-6128	115	18	)	)	PUNCT
ejpam-6128	116	1	∂f	∂f	PROPN
ejpam-6128	116	2	∂yi	∂yi	PROPN
ejpam-6128	116	3	=	=	SYM
ejpam-6128	116	4	0	0	PROPN
ejpam-6128	116	5	.	.	PUNCT
ejpam-6128	117	1	(	(	PUNCT
ejpam-6128	117	2	15	15	NUM
ejpam-6128	117	3	)	)	PUNCT
ejpam-6128	117	4	the	the	DET
ejpam-6128	117	5	basic	basic	ADJ
ejpam-6128	117	6	invariants	invariant	NOUN
ejpam-6128	117	7	in	in	ADP
ejpam-6128	117	8	the	the	DET
ejpam-6128	117	9	adjoint	adjoint	NOUN
ejpam-6128	117	10	representations	representation	NOUN
ejpam-6128	117	11	are	be	AUX
ejpam-6128	117	12	obtained	obtain	VERB
ejpam-6128	117	13	from	from	ADP
ejpam-6128	117	14	the	the	DET
ejpam-6128	117	15	solution	solution	NOUN
ejpam-6128	117	16	of	of	ADP
ejpam-6128	117	17	the	the	DET
ejpam-6128	117	18	linear	linear	ADJ
ejpam-6128	117	19	system	system	NOUN
ejpam-6128	117	20	of	of	ADP
ejpam-6128	117	21	pdes	pde	NOUN
ejpam-6128	117	22	(	(	PUNCT
ejpam-6128	117	23	15	15	NUM
ejpam-6128	117	24	)	)	PUNCT
ejpam-6128	117	25	.	.	PUNCT
ejpam-6128	118	1	the	the	DET
ejpam-6128	118	2	adjoint	adjoint	PROPN
ejpam-6128	118	3	transformation	transformation	NOUN
ejpam-6128	118	4	matrix	matrix	NOUN
ejpam-6128	118	5	[	[	X
ejpam-6128	118	6	24	24	NUM
ejpam-6128	118	7	]	]	PUNCT
ejpam-6128	118	8	is	be	AUX
ejpam-6128	118	9	given	give	VERB
ejpam-6128	118	10	by	by	ADP
ejpam-6128	118	11	a	a	DET
ejpam-6128	118	12	=	=	PROPN
ejpam-6128	118	13	n∏	n∏	PROPN
ejpam-6128	118	14	i=1	i=1	PROPN
ejpam-6128	118	15	ai	ai	PROPN
ejpam-6128	118	16	,	,	PUNCT
ejpam-6128	118	17	ai	ai	VERB
ejpam-6128	118	18	=	=	PUNCT
ejpam-6128	118	19	ad(eςiyi	ad(eςiyi	PROPN
ejpam-6128	118	20	)	)	PUNCT
ejpam-6128	118	21	.	.	PUNCT
ejpam-6128	119	1	(	(	PUNCT
ejpam-6128	119	2	16	16	X
ejpam-6128	119	3	)	)	PUNCT
ejpam-6128	119	4	let	let	VERB
ejpam-6128	119	5	y	y	PROPN
ejpam-6128	119	6	=	=	PUNCT
ejpam-6128	119	7	n∑	n∑	PROPN
ejpam-6128	119	8	i=1	i=1	PROPN
ejpam-6128	119	9	kiyi	kiyi	PROPN
ejpam-6128	119	10	,	,	PUNCT
ejpam-6128	119	11	ỹ	ỹ	PROPN
ejpam-6128	119	12	=	=	SYM
ejpam-6128	119	13	n∑	n∑	PROPN
ejpam-6128	119	14	i=1	i=1	PROPN
ejpam-6128	119	15	k̃iyi	k̃iyi	PROPN
ejpam-6128	119	16	∈	∈	PROPN
ejpam-6128	119	17	l.	l.	PROPN
ejpam-6128	119	18	for	for	ADP
ejpam-6128	119	19	simplicity	simplicity	NOUN
ejpam-6128	119	20	,	,	PUNCT
ejpam-6128	119	21	we	we	PRON
ejpam-6128	119	22	write	write	VERB
ejpam-6128	119	23	y	y	PROPN
ejpam-6128	119	24	=	=	PUNCT
ejpam-6128	119	25	(	(	PUNCT
ejpam-6128	119	26	k1	k1	PROPN
ejpam-6128	119	27	k2	k2	X
ejpam-6128	119	28	·	·	PUNCT
ejpam-6128	119	29	·	·	PUNCT
ejpam-6128	119	30	·	·	PUNCT
ejpam-6128	120	1	kn	kn	NOUN
ejpam-6128	120	2	)	)	PUNCT
ejpam-6128	120	3	,	,	PUNCT
ejpam-6128	120	4	ỹ	ỹ	PROPN
ejpam-6128	120	5	=	=	SYM
ejpam-6128	120	6	(	(	PUNCT
ejpam-6128	120	7	k̃1	k̃1	PROPN
ejpam-6128	120	8	k̃2	k̃2	PROPN
ejpam-6128	120	9	·	·	PUNCT
ejpam-6128	120	10	·	·	PUNCT
ejpam-6128	120	11	·	·	PUNCT
ejpam-6128	120	12	k̃n	k̃n	PROPN
ejpam-6128	120	13	)	)	PUNCT
ejpam-6128	120	14	.	.	PUNCT
ejpam-6128	121	1	then	then	ADV
ejpam-6128	121	2	,	,	PUNCT
ejpam-6128	121	3	y	y	PROPN
ejpam-6128	121	4	and	and	CCONJ
ejpam-6128	121	5	ỹ	ỹ	PROPN
ejpam-6128	121	6	are	be	AUX
ejpam-6128	121	7	in	in	ADP
ejpam-6128	121	8	the	the	DET
ejpam-6128	121	9	same	same	ADJ
ejpam-6128	121	10	conjugacy	conjugacy	ADJ
ejpam-6128	121	11	class	class	NOUN
ejpam-6128	121	12	,	,	PUNCT
ejpam-6128	121	13	if	if	SCONJ
ejpam-6128	121	14	we	we	PRON
ejpam-6128	121	15	have	have	VERB
ejpam-6128	121	16	[	[	X
ejpam-6128	121	17	24	24	NUM
ejpam-6128	121	18	]	]	PUNCT
ejpam-6128	121	19	ỹ	ỹ	PROPN
ejpam-6128	121	20	=	=	SYM
ejpam-6128	121	21	ya	ya	PROPN
ejpam-6128	121	22	.	.	PUNCT
ejpam-6128	122	1	(	(	PUNCT
ejpam-6128	122	2	17	17	NUM
ejpam-6128	122	3	)	)	PUNCT
ejpam-6128	122	4	the	the	DET
ejpam-6128	122	5	solution	solution	NOUN
ejpam-6128	122	6	of	of	ADP
ejpam-6128	122	7	(	(	PUNCT
ejpam-6128	122	8	17	17	NUM
ejpam-6128	122	9	)	)	PUNCT
ejpam-6128	122	10	gives	give	VERB
ejpam-6128	122	11	the	the	DET
ejpam-6128	122	12	values	value	NOUN
ejpam-6128	122	13	of	of	ADP
ejpam-6128	122	14	ςi	ςi	PROPN
ejpam-6128	122	15	in	in	ADP
ejpam-6128	122	16	terms	term	NOUN
ejpam-6128	122	17	of	of	ADP
ejpam-6128	122	18	ki	ki	PROPN
ejpam-6128	122	19	,	,	PUNCT
ejpam-6128	122	20	which	which	PRON
ejpam-6128	122	21	can	can	AUX
ejpam-6128	122	22	be	be	AUX
ejpam-6128	122	23	used	use	VERB
ejpam-6128	122	24	to	to	PART
ejpam-6128	122	25	simplify	simplify	VERB
ejpam-6128	122	26	k̃i	k̃i	NOUN
ejpam-6128	122	27	.	.	PUNCT
ejpam-6128	123	1	2.1.1	2.1.1	NUM
ejpam-6128	123	2	.	.	PUNCT
ejpam-6128	123	3	optimal	optimal	ADJ
ejpam-6128	123	4	system	system	NOUN
ejpam-6128	123	5	for	for	ADP
ejpam-6128	123	6	case	case	NOUN
ejpam-6128	123	7	1	1	NUM
ejpam-6128	123	8	the	the	DET
ejpam-6128	123	9	non	non	ADJ
ejpam-6128	123	10	-	-	ADJ
ejpam-6128	123	11	zero	zero	ADJ
ejpam-6128	123	12	commutators	commutator	NOUN
ejpam-6128	123	13	of	of	ADP
ejpam-6128	123	14	lie	lie	NOUN
ejpam-6128	123	15	algebra	algebra	PROPN
ejpam-6128	123	16	l4	l4	PROPN
ejpam-6128	123	17	presented	present	VERB
ejpam-6128	123	18	in	in	ADP
ejpam-6128	123	19	(	(	PUNCT
ejpam-6128	123	20	6	6	NUM
ejpam-6128	123	21	)	)	PUNCT
ejpam-6128	123	22	are	be	AUX
ejpam-6128	123	23	given	give	VERB
ejpam-6128	123	24	by	by	ADP
ejpam-6128	123	25	[	[	X
ejpam-6128	123	26	y1,y4	y1,y4	X
ejpam-6128	123	27	]	]	X
ejpam-6128	123	28	=	=	SYM
ejpam-6128	123	29	y1	y1	PROPN
ejpam-6128	123	30	,	,	PUNCT
ejpam-6128	123	31	[	[	X
ejpam-6128	123	32	y2,y4	y2,y4	X
ejpam-6128	123	33	]	]	X
ejpam-6128	123	34	=	=	SYM
ejpam-6128	123	35	y2	y2	PROPN
ejpam-6128	123	36	,	,	PUNCT
ejpam-6128	123	37	[	[	X
ejpam-6128	123	38	y3,y4	y3,y4	X
ejpam-6128	123	39	]	]	X
ejpam-6128	123	40	=	=	SYM
ejpam-6128	123	41	y3	y3	PROPN
ejpam-6128	123	42	.	.	PUNCT
ejpam-6128	124	1	(	(	PUNCT
ejpam-6128	124	2	18	18	NUM
ejpam-6128	124	3	)	)	PUNCT
ejpam-6128	124	4	the	the	DET
ejpam-6128	124	5	adjoint	adjoint	NOUN
ejpam-6128	124	6	action	action	NOUN
ejpam-6128	124	7	representations	representation	NOUN
ejpam-6128	124	8	of	of	ADP
ejpam-6128	124	9	lie	lie	NOUN
ejpam-6128	124	10	symmetries	symmetry	NOUN
ejpam-6128	124	11	(	(	PUNCT
ejpam-6128	124	12	6	6	NUM
ejpam-6128	124	13	)	)	PUNCT
ejpam-6128	124	14	are	be	AUX
ejpam-6128	124	15	obtained	obtain	VERB
ejpam-6128	124	16	using	use	VERB
ejpam-6128	124	17	(	(	PUNCT
ejpam-6128	124	18	13	13	NUM
ejpam-6128	124	19	)	)	PUNCT
ejpam-6128	124	20	and	and	CCONJ
ejpam-6128	124	21	are	be	AUX
ejpam-6128	124	22	presented	present	VERB
ejpam-6128	124	23	in	in	ADP
ejpam-6128	124	24	table	table	NOUN
ejpam-6128	124	25	1	1	NUM
ejpam-6128	124	26	.	.	PUNCT
ejpam-6128	124	27	table	table	NOUN
ejpam-6128	124	28	1	1	NUM
ejpam-6128	124	29	:	:	PUNCT
ejpam-6128	124	30	adjoint	adjoint	NOUN
ejpam-6128	124	31	table	table	NOUN
ejpam-6128	124	32	ad(eς	ad(eς	NOUN
ejpam-6128	124	33	)	)	PUNCT
ejpam-6128	124	34	y1	y1	NOUN
ejpam-6128	124	35	y2	y2	NOUN
ejpam-6128	124	36	y3	y3	NOUN
ejpam-6128	124	37	y4	y4	PROPN
ejpam-6128	124	38	y1	y1	NOUN
ejpam-6128	124	39	y1	y1	NOUN
ejpam-6128	124	40	y2	y2	NOUN
ejpam-6128	124	41	y3	y3	NOUN
ejpam-6128	124	42	y4	y4	PROPN
ejpam-6128	124	43	−	−	PROPN
ejpam-6128	125	1	ςy1	ςy1	PROPN
ejpam-6128	125	2	y2	y2	NOUN
ejpam-6128	125	3	y1	y1	INTJ
ejpam-6128	125	4	y2	y2	NOUN
ejpam-6128	125	5	y3	y3	NOUN
ejpam-6128	125	6	y4	y4	PROPN
ejpam-6128	125	7	−	−	PROPN
ejpam-6128	126	1	ςy2	ςy2	VERB
ejpam-6128	126	2	y3	y3	NOUN
ejpam-6128	126	3	y1	y1	ADJ
ejpam-6128	126	4	y2	y2	NOUN
ejpam-6128	126	5	y3	y3	NOUN
ejpam-6128	126	6	y4	y4	PROPN
ejpam-6128	126	7	−	−	PROPN
ejpam-6128	126	8	ςy3	ςy3	PROPN
ejpam-6128	126	9	y4	y4	PROPN
ejpam-6128	126	10	eςy1	eςy1	PROPN
ejpam-6128	126	11	eςy2	eςy2	PROPN
ejpam-6128	126	12	eςy3	eςy3	PROPN
ejpam-6128	126	13	y4	y4	PROPN
ejpam-6128	126	14	the	the	DET
ejpam-6128	126	15	adjoint	adjoint	PROPN
ejpam-6128	126	16	transformation	transformation	NOUN
ejpam-6128	126	17	matrix	matrix	NOUN
ejpam-6128	126	18	of	of	ADP
ejpam-6128	126	19	l4	l4	PROPN
ejpam-6128	126	20	is	be	AUX
ejpam-6128	126	21	constructed	construct	VERB
ejpam-6128	126	22	using	use	VERB
ejpam-6128	126	23	(	(	PUNCT
ejpam-6128	126	24	16	16	NUM
ejpam-6128	126	25	)	)	PUNCT
ejpam-6128	126	26	and	and	CCONJ
ejpam-6128	126	27	is	be	AUX
ejpam-6128	126	28	shown	show	VERB
ejpam-6128	126	29	below	below	ADP
ejpam-6128	126	30	m.	m.	PROPN
ejpam-6128	126	31	usman	usman	PROPN
ejpam-6128	126	32	,	,	PUNCT
ejpam-6128	126	33	a.	a.	NOUN
ejpam-6128	126	34	hussain	hussain	PROPN
ejpam-6128	126	35	,	,	PUNCT
ejpam-6128	126	36	m.	m.	PROPN
ejpam-6128	126	37	u.	u.	PROPN
ejpam-6128	126	38	farooq	farooq	PROPN
ejpam-6128	126	39	,	,	PUNCT
ejpam-6128	126	40	j.	j.	PROPN
ejpam-6128	126	41	herrera	herrera	PROPN
ejpam-6128	126	42	/	/	SYM
ejpam-6128	126	43	eur	eur	PROPN
ejpam-6128	126	44	.	.	PUNCT
ejpam-6128	127	1	j.	j.	PROPN
ejpam-6128	127	2	pure	pure	PROPN
ejpam-6128	127	3	appl	appl	PROPN
ejpam-6128	127	4	.	.	PROPN
ejpam-6128	127	5	math	math	PROPN
ejpam-6128	127	6	,	,	PUNCT
ejpam-6128	127	7	18	18	NUM
ejpam-6128	127	8	(	(	PUNCT
ejpam-6128	127	9	4	4	NUM
ejpam-6128	127	10	)	)	PUNCT
ejpam-6128	127	11	(	(	PUNCT
ejpam-6128	127	12	2025	2025	NUM
ejpam-6128	127	13	)	)	PUNCT
ejpam-6128	127	14	,	,	PUNCT
ejpam-6128	127	15	6128	6128	NUM
ejpam-6128	127	16	6	6	NUM
ejpam-6128	127	17	of	of	ADP
ejpam-6128	127	18	29	29	NUM
ejpam-6128	127	19	a	a	DET
ejpam-6128	127	20	=	=	NOUN
ejpam-6128	127	21			NOUN
ejpam-6128	127	22	eς4	eς4	NOUN
ejpam-6128	127	23	0	0	NUM
ejpam-6128	127	24	0	0	NUM
ejpam-6128	127	25	0	0	NUM
ejpam-6128	127	26	0	0	NUM
ejpam-6128	127	27	eς4	eς4	NOUN
ejpam-6128	127	28	0	0	NUM
ejpam-6128	127	29	0	0	NUM
ejpam-6128	127	30	0	0	NUM
ejpam-6128	127	31	0	0	NUM
ejpam-6128	127	32	eς4	eς4	NOUN
ejpam-6128	127	33	0	0	NUM
ejpam-6128	127	34	−ς1e	−ς1e	NUM
ejpam-6128	127	35	ς4	ς4	PROPN
ejpam-6128	127	36	−ς2e	−ς2e	ADP
ejpam-6128	127	37	ς4	ς4	PROPN
ejpam-6128	127	38	−ς3e	−ς3e	PROPN
ejpam-6128	127	39	ς4	ς4	NOUN
ejpam-6128	127	40	1	1	NUM
ejpam-6128	127	41			NOUN
ejpam-6128	127	42	using	use	VERB
ejpam-6128	127	43	(	(	PUNCT
ejpam-6128	127	44	17	17	NUM
ejpam-6128	127	45	)	)	PUNCT
ejpam-6128	127	46	,	,	PUNCT
ejpam-6128	127	47	we	we	PRON
ejpam-6128	127	48	obtain	obtain	VERB
ejpam-6128	127	49	the	the	DET
ejpam-6128	127	50	following	follow	VERB
ejpam-6128	127	51	system	system	NOUN
ejpam-6128	127	52	of	of	ADP
ejpam-6128	127	53	equations	equation	NOUN
ejpam-6128	127	54	,	,	PUNCT
ejpam-6128	127	55	which	which	PRON
ejpam-6128	127	56	is	be	AUX
ejpam-6128	127	57	used	use	VERB
ejpam-6128	127	58	to	to	PART
ejpam-6128	127	59	obtain	obtain	VERB
ejpam-6128	127	60	ςi	ςi	NOUN
ejpam-6128	127	61	:	:	PUNCT
ejpam-6128	127	62	k̃1	k̃1	PROPN
ejpam-6128	128	1	=	=	PUNCT
ejpam-6128	129	1	k1e	k1e	PROPN
ejpam-6128	129	2	ς4	ς4	PROPN
ejpam-6128	129	3	−	−	NOUN
ejpam-6128	129	4	k4ς1e	k4ς1e	NOUN
ejpam-6128	129	5	ς4	ς4	PROPN
ejpam-6128	129	6	,	,	PUNCT
ejpam-6128	129	7	k̃2	k̃2	PROPN
ejpam-6128	129	8	=	=	SYM
ejpam-6128	130	1	k2e	k2e	PROPN
ejpam-6128	130	2	ς4	ς4	PROPN
ejpam-6128	130	3	−	−	PROPN
ejpam-6128	130	4	k4ς2e	k4ς2e	SYM
ejpam-6128	131	1	ς4	ς4	VERB
ejpam-6128	131	2	,	,	PUNCT
ejpam-6128	131	3	k̃3	k̃3	PROPN
ejpam-6128	131	4	=	=	PUNCT
ejpam-6128	131	5	k3e	k3e	PROPN
ejpam-6128	131	6	ς4	ς4	PROPN
ejpam-6128	131	7	−	−	NOUN
ejpam-6128	131	8	k4ς3e	k4ς3e	NOUN
ejpam-6128	131	9	ς4	ς4	NOUN
ejpam-6128	131	10	,	,	PUNCT
ejpam-6128	131	11	k̃4	k̃4	PROPN
ejpam-6128	131	12	=	=	PUNCT
ejpam-6128	131	13	k4	k4	PROPN
ejpam-6128	131	14	.	.	PUNCT
ejpam-6128	132	1	(	(	PUNCT
ejpam-6128	132	2	19	19	NUM
ejpam-6128	132	3	)	)	PUNCT
ejpam-6128	132	4	the	the	DET
ejpam-6128	132	5	basic	basic	ADJ
ejpam-6128	132	6	invariants	invariant	NOUN
ejpam-6128	132	7	for	for	ADP
ejpam-6128	132	8	(	(	PUNCT
ejpam-6128	132	9	6	6	NUM
ejpam-6128	132	10	)	)	PUNCT
ejpam-6128	132	11	can	can	AUX
ejpam-6128	132	12	be	be	AUX
ejpam-6128	132	13	calculated	calculate	VERB
ejpam-6128	132	14	by	by	ADP
ejpam-6128	132	15	finding	find	VERB
ejpam-6128	132	16	a	a	DET
ejpam-6128	132	17	solution	solution	NOUN
ejpam-6128	132	18	of	of	ADP
ejpam-6128	132	19	the	the	DET
ejpam-6128	132	20	following	follow	VERB
ejpam-6128	132	21	system	system	NOUN
ejpam-6128	132	22	of	of	ADP
ejpam-6128	132	23	linear	linear	PROPN
ejpam-6128	132	24	pdes	pde	NOUN
ejpam-6128	132	25	,	,	PUNCT
ejpam-6128	132	26	which	which	PRON
ejpam-6128	132	27	is	be	AUX
ejpam-6128	132	28	derived	derive	VERB
ejpam-6128	132	29	using	use	VERB
ejpam-6128	132	30	(	(	PUNCT
ejpam-6128	132	31	15	15	NUM
ejpam-6128	132	32	)	)	PUNCT
ejpam-6128	132	33	.	.	PUNCT
ejpam-6128	133	1	k4	k4	PROPN
ejpam-6128	133	2	∂ϑ	∂ϑ	PROPN
ejpam-6128	133	3	∂k1	∂k1	PROPN
ejpam-6128	133	4	=	=	SYM
ejpam-6128	133	5	0	0	NUM
ejpam-6128	133	6	,	,	PUNCT
ejpam-6128	133	7	k4	k4	PROPN
ejpam-6128	133	8	∂ϑ	∂ϑ	PROPN
ejpam-6128	133	9	∂k2	∂k2	PROPN
ejpam-6128	133	10	=	=	SYM
ejpam-6128	133	11	0	0	NUM
ejpam-6128	133	12	,	,	PUNCT
ejpam-6128	133	13	k4	k4	PROPN
ejpam-6128	133	14	∂ϑ	∂ϑ	PROPN
ejpam-6128	133	15	∂k3	∂k3	PROPN
ejpam-6128	133	16	=	=	SYM
ejpam-6128	133	17	0	0	NUM
ejpam-6128	133	18	,	,	PUNCT
ejpam-6128	133	19	k1	k1	PROPN
ejpam-6128	133	20	∂ϑ	∂ϑ	PROPN
ejpam-6128	133	21	∂k1	∂k1	PROPN
ejpam-6128	133	22	+	+	NUM
ejpam-6128	134	1	k2	k2	PROPN
ejpam-6128	134	2	∂ϑ	∂ϑ	PROPN
ejpam-6128	134	3	∂k2	∂k2	PROPN
ejpam-6128	134	4	+	+	CCONJ
ejpam-6128	134	5	k3	k3	PROPN
ejpam-6128	134	6	∂ϑ	∂ϑ	PROPN
ejpam-6128	134	7	∂k3	∂k3	NOUN
ejpam-6128	134	8	=	=	SYM
ejpam-6128	134	9	0	0	PROPN
ejpam-6128	134	10	.	.	PUNCT
ejpam-6128	135	1	(	(	PUNCT
ejpam-6128	135	2	20	20	NUM
ejpam-6128	135	3	)	)	PUNCT
ejpam-6128	135	4	the	the	DET
ejpam-6128	135	5	solution	solution	NOUN
ejpam-6128	135	6	of	of	ADP
ejpam-6128	135	7	(	(	PUNCT
ejpam-6128	135	8	20	20	NUM
ejpam-6128	135	9	)	)	PUNCT
ejpam-6128	135	10	gives	give	VERB
ejpam-6128	135	11	ϑ(k1	ϑ(k1	NOUN
ejpam-6128	135	12	,	,	PUNCT
ejpam-6128	135	13	k2	k2	PROPN
ejpam-6128	135	14	,	,	PUNCT
ejpam-6128	135	15	k3	k3	PROPN
ejpam-6128	135	16	,	,	PUNCT
ejpam-6128	135	17	k4	k4	NOUN
ejpam-6128	135	18	)	)	PUNCT
ejpam-6128	136	1	=	=	SYM
ejpam-6128	136	2	f	f	PROPN
ejpam-6128	136	3	(	(	PUNCT
ejpam-6128	136	4	k4	k4	PROPN
ejpam-6128	136	5	)	)	PUNCT
ejpam-6128	136	6	.	.	PUNCT
ejpam-6128	137	1	so	so	ADV
ejpam-6128	137	2	,	,	PUNCT
ejpam-6128	137	3	the	the	DET
ejpam-6128	137	4	first	first	ADJ
ejpam-6128	137	5	basic	basic	ADJ
ejpam-6128	137	6	invariant	invariant	NOUN
ejpam-6128	137	7	is	be	AUX
ejpam-6128	137	8	k4	k4	NOUN
ejpam-6128	137	9	,	,	PUNCT
ejpam-6128	137	10	which	which	PRON
ejpam-6128	137	11	will	will	AUX
ejpam-6128	137	12	be	be	AUX
ejpam-6128	137	13	the	the	DET
ejpam-6128	137	14	first	first	ADJ
ejpam-6128	137	15	vertix	vertix	NOUN
ejpam-6128	137	16	of	of	ADP
ejpam-6128	137	17	the	the	DET
ejpam-6128	137	18	tree	tree	NOUN
ejpam-6128	137	19	.	.	PUNCT
ejpam-6128	138	1	k4	k4	ADJ
ejpam-6128	138	2	k4	k4	NOUN
ejpam-6128	138	3	=	=	SYM
ejpam-6128	138	4	0	0	NUM
ejpam-6128	139	1	k3	k3	ADJ
ejpam-6128	139	2	=	=	NOUN
ejpam-6128	139	3	0	0	NUM
ejpam-6128	139	4	,	,	PUNCT
ejpam-6128	139	5	k1	k1	X
ejpam-6128	139	6	6=	6=	SYM
ejpam-6128	139	7	0	0	NUM
ejpam-6128	139	8	k2	k2	NOUN
ejpam-6128	139	9	=	=	SYM
ejpam-6128	139	10	0	0	PUNCT
ejpam-6128	140	1	case-5	case-5	NUM
ejpam-6128	140	2	k2	k2	NOUN
ejpam-6128	140	3	6=	6=	ADP
ejpam-6128	140	4	0	0	NUM
ejpam-6128	140	5	case-4	case-4	NUM
ejpam-6128	140	6	k3	k3	ADJ
ejpam-6128	140	7	6=	6=	ADP
ejpam-6128	140	8	0	0	NUM
ejpam-6128	140	9	,	,	PUNCT
ejpam-6128	140	10	k1	k1	X
ejpam-6128	140	11	6=	6=	SYM
ejpam-6128	140	12	0	0	NUM
ejpam-6128	140	13	k2	k2	NOUN
ejpam-6128	140	14	=	=	SYM
ejpam-6128	140	15	0	0	PROPN
ejpam-6128	140	16	case-3	case-3	PROPN
ejpam-6128	140	17	k2	k2	PROPN
ejpam-6128	140	18	6=	6=	ADP
ejpam-6128	140	19	0	0	NUM
ejpam-6128	140	20	case-2	case-2	NUM
ejpam-6128	140	21	k4	k4	NOUN
ejpam-6128	140	22	6=	6=	ADP
ejpam-6128	140	23	0	0	NUM
ejpam-6128	140	24	case-1	case-1	NUM
ejpam-6128	140	25	case-1	case-1	NUM
ejpam-6128	140	26	:	:	PUNCT
ejpam-6128	140	27	for	for	ADP
ejpam-6128	140	28	k4	k4	PROPN
ejpam-6128	140	29	6=	6=	PROPN
ejpam-6128	140	30	0	0	NUM
ejpam-6128	140	31	,	,	PUNCT
ejpam-6128	140	32	the	the	DET
ejpam-6128	140	33	representative	representative	ADJ
ejpam-6128	140	34	element	element	NOUN
ejpam-6128	140	35	is	be	AUX
ejpam-6128	140	36	s1	s1	NOUN
ejpam-6128	140	37	=	=	SYM
ejpam-6128	140	38	y4	y4	PROPN
ejpam-6128	140	39	.	.	PUNCT
ejpam-6128	141	1	by	by	ADP
ejpam-6128	141	2	substituting	substitute	VERB
ejpam-6128	141	3	k̃4	k̃4	PROPN
ejpam-6128	141	4	=	=	PUNCT
ejpam-6128	141	5	1	1	NUM
ejpam-6128	141	6	in	in	ADP
ejpam-6128	141	7	(	(	PUNCT
ejpam-6128	141	8	19	19	NUM
ejpam-6128	141	9	)	)	PUNCT
ejpam-6128	141	10	,	,	PUNCT
ejpam-6128	141	11	we	we	PRON
ejpam-6128	141	12	get	get	VERB
ejpam-6128	141	13	ς1	ς1	NOUN
ejpam-6128	141	14	=	=	SYM
ejpam-6128	141	15	k1	k1	NOUN
ejpam-6128	141	16	k4	k4	NOUN
ejpam-6128	141	17	,	,	PUNCT
ejpam-6128	141	18	ς2	ς2	PROPN
ejpam-6128	141	19	=	=	SYM
ejpam-6128	141	20	k2	k2	ADJ
ejpam-6128	141	21	k4	k4	NOUN
ejpam-6128	141	22	,	,	PUNCT
ejpam-6128	141	23	ς3	ς3	NOUN
ejpam-6128	141	24	=	=	SYM
ejpam-6128	141	25	k3	k3	ADJ
ejpam-6128	141	26	k4	k4	NOUN
ejpam-6128	141	27	.	.	PUNCT
ejpam-6128	142	1	when	when	SCONJ
ejpam-6128	142	2	k4	k4	NOUN
ejpam-6128	142	3	=	=	NOUN
ejpam-6128	142	4	0	0	PROPN
ejpam-6128	142	5	,	,	PUNCT
ejpam-6128	142	6	the	the	DET
ejpam-6128	142	7	solution	solution	NOUN
ejpam-6128	142	8	of	of	ADP
ejpam-6128	142	9	(	(	PUNCT
ejpam-6128	142	10	20	20	NUM
ejpam-6128	142	11	)	)	PUNCT
ejpam-6128	142	12	provides	provide	VERB
ejpam-6128	142	13	ϑ(k1	ϑ(k1	NOUN
ejpam-6128	142	14	,	,	PUNCT
ejpam-6128	142	15	k2	k2	ADJ
ejpam-6128	142	16	,	,	PUNCT
ejpam-6128	142	17	k3	k3	PROPN
ejpam-6128	142	18	,	,	PUNCT
ejpam-6128	142	19	k4	k4	NOUN
ejpam-6128	142	20	)	)	PUNCT
ejpam-6128	142	21	=	=	SYM
ejpam-6128	142	22	f	f	PROPN
ejpam-6128	142	23	(	(	PUNCT
ejpam-6128	142	24	k2k1	k2k1	PROPN
ejpam-6128	142	25	,	,	PUNCT
ejpam-6128	142	26	k3	k3	ADJ
ejpam-6128	142	27	k1	k1	NOUN
ejpam-6128	142	28	,	,	PUNCT
ejpam-6128	142	29	k4	k4	PROPN
ejpam-6128	142	30	)	)	PUNCT
ejpam-6128	142	31	.	.	PUNCT
ejpam-6128	143	1	this	this	PRON
ejpam-6128	143	2	implies	imply	VERB
ejpam-6128	143	3	m.	m.	PROPN
ejpam-6128	143	4	usman	usman	PROPN
ejpam-6128	143	5	,	,	PUNCT
ejpam-6128	143	6	a.	a.	NOUN
ejpam-6128	143	7	hussain	hussain	PROPN
ejpam-6128	143	8	,	,	PUNCT
ejpam-6128	143	9	m.	m.	PROPN
ejpam-6128	143	10	u.	u.	PROPN
ejpam-6128	143	11	farooq	farooq	PROPN
ejpam-6128	143	12	,	,	PUNCT
ejpam-6128	143	13	j.	j.	PROPN
ejpam-6128	143	14	herrera	herrera	PROPN
ejpam-6128	143	15	/	/	SYM
ejpam-6128	143	16	eur	eur	PROPN
ejpam-6128	143	17	.	.	PUNCT
ejpam-6128	144	1	j.	j.	PROPN
ejpam-6128	144	2	pure	pure	PROPN
ejpam-6128	144	3	appl	appl	PROPN
ejpam-6128	144	4	.	.	PROPN
ejpam-6128	144	5	math	math	PROPN
ejpam-6128	144	6	,	,	PUNCT
ejpam-6128	144	7	18	18	NUM
ejpam-6128	144	8	(	(	PUNCT
ejpam-6128	144	9	4	4	NUM
ejpam-6128	144	10	)	)	PUNCT
ejpam-6128	144	11	(	(	PUNCT
ejpam-6128	144	12	2025	2025	NUM
ejpam-6128	144	13	)	)	PUNCT
ejpam-6128	144	14	,	,	PUNCT
ejpam-6128	144	15	6128	6128	NUM
ejpam-6128	144	16	7	7	NUM
ejpam-6128	144	17	of	of	ADP
ejpam-6128	144	18	29	29	NUM
ejpam-6128	144	19	that	that	SCONJ
ejpam-6128	144	20	the	the	DET
ejpam-6128	144	21	new	new	ADJ
ejpam-6128	144	22	invariants	invariant	NOUN
ejpam-6128	144	23	are	be	AUX
ejpam-6128	144	24	k2	k2	ADJ
ejpam-6128	144	25	k1	k1	NOUN
ejpam-6128	144	26	,	,	PUNCT
ejpam-6128	145	1	k3k1	k3k1	PROPN
ejpam-6128	145	2	.	.	PUNCT
ejpam-6128	146	1	since	since	SCONJ
ejpam-6128	146	2	k1	k1	PROPN
ejpam-6128	146	3	6=	6=	ADP
ejpam-6128	146	4	0	0	NUM
ejpam-6128	146	5	,	,	PUNCT
ejpam-6128	146	6	so	so	ADV
ejpam-6128	146	7	the	the	DET
ejpam-6128	146	8	next	next	ADJ
ejpam-6128	146	9	two	two	NUM
ejpam-6128	146	10	vertices	vertex	NOUN
ejpam-6128	146	11	will	will	AUX
ejpam-6128	146	12	be	be	AUX
ejpam-6128	146	13	k3	k3	VERB
ejpam-6128	146	14	and	and	CCONJ
ejpam-6128	146	15	k2	k2	NOUN
ejpam-6128	146	16	.	.	PUNCT
ejpam-6128	147	1	case-2	case-2	NUM
ejpam-6128	147	2	:	:	PUNCT
ejpam-6128	147	3	for	for	ADP
ejpam-6128	147	4	k4	k4	NOUN
ejpam-6128	147	5	=	=	SYM
ejpam-6128	147	6	0	0	NUM
ejpam-6128	147	7	,	,	PUNCT
ejpam-6128	147	8	k3	k3	VERB
ejpam-6128	147	9	6=	6=	ADP
ejpam-6128	147	10	0	0	NUM
ejpam-6128	147	11	,	,	PUNCT
ejpam-6128	147	12	k2	k2	PROPN
ejpam-6128	147	13	6=	6=	PROPN
ejpam-6128	147	14	0	0	NUM
ejpam-6128	147	15	,	,	PUNCT
ejpam-6128	147	16	k1	k1	PROPN
ejpam-6128	147	17	6=	6=	ADP
ejpam-6128	147	18	0	0	NUM
ejpam-6128	147	19	,	,	PUNCT
ejpam-6128	147	20	the	the	DET
ejpam-6128	147	21	corresponding	corresponding	ADJ
ejpam-6128	147	22	element	element	NOUN
ejpam-6128	147	23	of	of	ADP
ejpam-6128	147	24	the	the	DET
ejpam-6128	147	25	optimal	optimal	ADJ
ejpam-6128	147	26	system	system	NOUN
ejpam-6128	147	27	is	be	AUX
ejpam-6128	147	28	s2	s2	NOUN
ejpam-6128	147	29	=	=	SYM
ejpam-6128	147	30	y1	y1	PROPN
ejpam-6128	148	1	+	+	CCONJ
ejpam-6128	148	2	y2	y2	NOUN
ejpam-6128	148	3	+	+	NUM
ejpam-6128	148	4	y3	y3	NOUN
ejpam-6128	148	5	.	.	PUNCT
ejpam-6128	149	1	case-3	case-3	PROPN
ejpam-6128	149	2	:	:	PUNCT
ejpam-6128	149	3	for	for	ADP
ejpam-6128	149	4	k4	k4	NOUN
ejpam-6128	149	5	=	=	SYM
ejpam-6128	149	6	0	0	NUM
ejpam-6128	149	7	,	,	PUNCT
ejpam-6128	149	8	k3	k3	VERB
ejpam-6128	149	9	6=	6=	PRON
ejpam-6128	149	10	0	0	NUM
ejpam-6128	149	11	,	,	PUNCT
ejpam-6128	149	12	k1	k1	PROPN
ejpam-6128	149	13	6=	6=	ADP
ejpam-6128	149	14	0	0	NUM
ejpam-6128	149	15	,	,	PUNCT
ejpam-6128	149	16	k2	k2	NOUN
ejpam-6128	149	17	=	=	SYM
ejpam-6128	149	18	0	0	PROPN
ejpam-6128	149	19	,	,	PUNCT
ejpam-6128	149	20	the	the	DET
ejpam-6128	149	21	associated	associated	ADJ
ejpam-6128	149	22	element	element	NOUN
ejpam-6128	149	23	is	be	AUX
ejpam-6128	149	24	s3	s3	PROPN
ejpam-6128	149	25	=	=	PROPN
ejpam-6128	149	26	y1	y1	PROPN
ejpam-6128	149	27	+	+	NUM
ejpam-6128	149	28	y3	y3	NOUN
ejpam-6128	149	29	.	.	PUNCT
ejpam-6128	150	1	case-4	case-4	NOUN
ejpam-6128	150	2	:	:	PUNCT
ejpam-6128	150	3	for	for	ADP
ejpam-6128	150	4	k4	k4	NOUN
ejpam-6128	150	5	=	=	SYM
ejpam-6128	150	6	0	0	NUM
ejpam-6128	150	7	,	,	PUNCT
ejpam-6128	150	8	k3	k3	VERB
ejpam-6128	150	9	=	=	SYM
ejpam-6128	150	10	0	0	NUM
ejpam-6128	150	11	,	,	PUNCT
ejpam-6128	150	12	k1	k1	PROPN
ejpam-6128	150	13	6=	6=	ADP
ejpam-6128	150	14	0	0	NUM
ejpam-6128	150	15	,	,	PUNCT
ejpam-6128	150	16	k2	k2	PROPN
ejpam-6128	150	17	6=	6=	PROPN
ejpam-6128	150	18	0	0	NUM
ejpam-6128	150	19	,	,	PUNCT
ejpam-6128	150	20	the	the	DET
ejpam-6128	150	21	conjugacy	conjugacy	PROPN
ejpam-6128	150	22	class	class	NOUN
ejpam-6128	150	23	is	be	AUX
ejpam-6128	150	24	of	of	ADP
ejpam-6128	150	25	the	the	DET
ejpam-6128	150	26	form	form	NOUN
ejpam-6128	150	27	s4	s4	NOUN
ejpam-6128	150	28	=	=	SYM
ejpam-6128	150	29	y1+y2	y1+y2	PROPN
ejpam-6128	150	30	.	.	PUNCT
ejpam-6128	151	1	case-5	case-5	NOUN
ejpam-6128	151	2	:	:	PUNCT
ejpam-6128	151	3	for	for	ADP
ejpam-6128	151	4	k4	k4	NOUN
ejpam-6128	151	5	=	=	SYM
ejpam-6128	151	6	0	0	NUM
ejpam-6128	151	7	,	,	PUNCT
ejpam-6128	151	8	k3	k3	VERB
ejpam-6128	151	9	=	=	SYM
ejpam-6128	151	10	0	0	NUM
ejpam-6128	151	11	,	,	PUNCT
ejpam-6128	151	12	k1	k1	PROPN
ejpam-6128	151	13	6=	6=	ADP
ejpam-6128	151	14	0	0	NUM
ejpam-6128	151	15	,	,	PUNCT
ejpam-6128	151	16	k2	k2	NOUN
ejpam-6128	151	17	=	=	SYM
ejpam-6128	151	18	0	0	PROPN
ejpam-6128	151	19	,	,	PUNCT
ejpam-6128	151	20	the	the	DET
ejpam-6128	151	21	representative	representative	ADJ
ejpam-6128	151	22	element	element	NOUN
ejpam-6128	151	23	is	be	AUX
ejpam-6128	151	24	s5	s5	PROPN
ejpam-6128	151	25	=	=	SYM
ejpam-6128	151	26	y1	y1	PROPN
ejpam-6128	151	27	.	.	PUNCT
ejpam-6128	152	1	hence	hence	ADV
ejpam-6128	152	2	,	,	PUNCT
ejpam-6128	152	3	the	the	DET
ejpam-6128	152	4	one	one	NUM
ejpam-6128	152	5	-	-	PUNCT
ejpam-6128	152	6	dimensional	dimensional	ADJ
ejpam-6128	152	7	optimal	optimal	ADJ
ejpam-6128	152	8	system	system	NOUN
ejpam-6128	152	9	for	for	ADP
ejpam-6128	152	10	lie	lie	NOUN
ejpam-6128	152	11	algebra	algebra	NOUN
ejpam-6128	152	12	(	(	PUNCT
ejpam-6128	152	13	6	6	NUM
ejpam-6128	152	14	)	)	PUNCT
ejpam-6128	152	15	is	be	AUX
ejpam-6128	152	16	given	give	VERB
ejpam-6128	152	17	by	by	ADP
ejpam-6128	152	18	s1	s1	PROPN
ejpam-6128	152	19	=	=	SYM
ejpam-6128	152	20	y4	y4	PROPN
ejpam-6128	152	21	,	,	PUNCT
ejpam-6128	152	22	s2	s2	X
ejpam-6128	152	23	=	=	PUNCT
ejpam-6128	152	24	y1	y1	PROPN
ejpam-6128	152	25	+	+	CCONJ
ejpam-6128	152	26	y2	y2	NOUN
ejpam-6128	152	27	+	+	CCONJ
ejpam-6128	152	28	y3	y3	NOUN
ejpam-6128	152	29	,	,	PUNCT
ejpam-6128	152	30	s3	s3	PROPN
ejpam-6128	152	31	=	=	PROPN
ejpam-6128	152	32	y1	y1	PROPN
ejpam-6128	152	33	+	+	NUM
ejpam-6128	152	34	y3	y3	NOUN
ejpam-6128	152	35	,	,	PUNCT
ejpam-6128	152	36	s4	s4	PROPN
ejpam-6128	152	37	=	=	SYM
ejpam-6128	152	38	y1	y1	PROPN
ejpam-6128	152	39	+	+	CCONJ
ejpam-6128	152	40	y2	y2	PROPN
ejpam-6128	152	41	,	,	PUNCT
ejpam-6128	152	42	s5	s5	X
ejpam-6128	152	43	=	=	SYM
ejpam-6128	152	44	y1	y1	PROPN
ejpam-6128	152	45	.	.	PUNCT
ejpam-6128	153	1	(	(	PUNCT
ejpam-6128	153	2	21	21	NUM
ejpam-6128	153	3	)	)	PUNCT
ejpam-6128	153	4	2.1.2	2.1.2	NUM
ejpam-6128	153	5	.	.	PUNCT
ejpam-6128	153	6	optimal	optimal	ADJ
ejpam-6128	153	7	system	system	NOUN
ejpam-6128	153	8	for	for	ADP
ejpam-6128	153	9	case	case	NOUN
ejpam-6128	153	10	2	2	NUM
ejpam-6128	153	11	for	for	ADP
ejpam-6128	153	12	lie	lie	NOUN
ejpam-6128	153	13	algebra	algebra	NOUN
ejpam-6128	153	14	l5	l5	PROPN
ejpam-6128	153	15	given	give	VERB
ejpam-6128	153	16	in	in	ADP
ejpam-6128	153	17	(	(	PUNCT
ejpam-6128	153	18	7	7	NUM
ejpam-6128	153	19	)	)	PUNCT
ejpam-6128	154	1	,	,	PUNCT
ejpam-6128	154	2	we	we	PRON
ejpam-6128	154	3	have	have	VERB
ejpam-6128	154	4	the	the	DET
ejpam-6128	154	5	following	follow	VERB
ejpam-6128	154	6	non	non	ADJ
ejpam-6128	154	7	-	-	ADJ
ejpam-6128	154	8	zero	zero	ADJ
ejpam-6128	154	9	commutators	commutator	NOUN
ejpam-6128	154	10	[	[	X
ejpam-6128	154	11	y1,y4	y1,y4	X
ejpam-6128	154	12	]	]	X
ejpam-6128	154	13	=	=	SYM
ejpam-6128	154	14	y1	y1	PROPN
ejpam-6128	154	15	,	,	PUNCT
ejpam-6128	154	16	[	[	X
ejpam-6128	154	17	y2,y5	y2,y5	X
ejpam-6128	154	18	]	]	X
ejpam-6128	154	19	=	=	SYM
ejpam-6128	154	20	y2	y2	PROPN
ejpam-6128	154	21	,	,	PUNCT
ejpam-6128	154	22	[	[	X
ejpam-6128	154	23	y3,y4	y3,y4	X
ejpam-6128	154	24	]	]	X
ejpam-6128	154	25	=	=	SYM
ejpam-6128	154	26	2y3	2y3	NUM
ejpam-6128	154	27	,	,	PUNCT
ejpam-6128	154	28	[	[	X
ejpam-6128	154	29	y3,y5	y3,y5	X
ejpam-6128	154	30	]	]	X
ejpam-6128	154	31	=	=	SYM
ejpam-6128	154	32	−y3	−y3	NOUN
ejpam-6128	154	33	.	.	PUNCT
ejpam-6128	155	1	(	(	PUNCT
ejpam-6128	155	2	22	22	NUM
ejpam-6128	155	3	)	)	PUNCT
ejpam-6128	155	4	the	the	DET
ejpam-6128	155	5	adjoint	adjoint	NOUN
ejpam-6128	155	6	representations	representation	NOUN
ejpam-6128	155	7	of	of	ADP
ejpam-6128	155	8	(	(	PUNCT
ejpam-6128	155	9	7	7	NUM
ejpam-6128	155	10	)	)	PUNCT
ejpam-6128	155	11	are	be	AUX
ejpam-6128	155	12	given	give	VERB
ejpam-6128	155	13	in	in	ADP
ejpam-6128	155	14	table	table	NOUN
ejpam-6128	155	15	2	2	NUM
ejpam-6128	155	16	.	.	PUNCT
ejpam-6128	155	17	table	table	NOUN
ejpam-6128	155	18	2	2	NUM
ejpam-6128	155	19	:	:	PUNCT
ejpam-6128	155	20	adjoint	adjoint	NOUN
ejpam-6128	155	21	table	table	NOUN
ejpam-6128	155	22	ad(eς	ad(eς	NOUN
ejpam-6128	155	23	)	)	PUNCT
ejpam-6128	156	1	y1	y1	NOUN
ejpam-6128	156	2	y2	y2	NOUN
ejpam-6128	156	3	y3	y3	PROPN
ejpam-6128	156	4	y4	y4	NOUN
ejpam-6128	156	5	y5	y5	NOUN
ejpam-6128	156	6	y1	y1	NOUN
ejpam-6128	156	7	y1	y1	NOUN
ejpam-6128	156	8	y2	y2	NOUN
ejpam-6128	156	9	y3	y3	NOUN
ejpam-6128	156	10	y4	y4	PROPN
ejpam-6128	156	11	−	−	PROPN
ejpam-6128	156	12	ςy1	ςy1	PROPN
ejpam-6128	156	13	y5	y5	NOUN
ejpam-6128	157	1	y2	y2	NOUN
ejpam-6128	157	2	y1	y1	NOUN
ejpam-6128	157	3	y2	y2	NOUN
ejpam-6128	157	4	y3	y3	NOUN
ejpam-6128	157	5	y4	y4	PROPN
ejpam-6128	157	6	y5	y5	PROPN
ejpam-6128	157	7	−	−	PROPN
ejpam-6128	157	8	ςy2	ςy2	NOUN
ejpam-6128	157	9	y3	y3	NOUN
ejpam-6128	157	10	y1	y1	ADJ
ejpam-6128	157	11	y2	y2	NOUN
ejpam-6128	157	12	y3	y3	NOUN
ejpam-6128	157	13	y4	y4	NOUN
ejpam-6128	157	14	−	−	PROPN
ejpam-6128	157	15	2ςy3	2ςy3	NUM
ejpam-6128	157	16	y5	y5	NOUN
ejpam-6128	157	17	+	+	CCONJ
ejpam-6128	158	1	ςy3	ςy3	NOUN
ejpam-6128	158	2	y4	y4	NOUN
ejpam-6128	158	3	eςy1	eςy1	PROPN
ejpam-6128	158	4	y2	y2	PROPN
ejpam-6128	158	5	e2ςy3	e2ςy3	NOUN
ejpam-6128	158	6	y4	y4	VERB
ejpam-6128	158	7	y5	y5	PROPN
ejpam-6128	158	8	y5	y5	NOUN
ejpam-6128	158	9	y1	y1	PROPN
ejpam-6128	158	10	eςy2	eςy2	NOUN
ejpam-6128	158	11	e−ςy3	e−ςy3	NOUN
ejpam-6128	158	12	y4	y4	PROPN
ejpam-6128	158	13	y5	y5	PROPN
ejpam-6128	159	1	the	the	DET
ejpam-6128	159	2	adjoint	adjoint	NOUN
ejpam-6128	159	3	transformation	transformation	NOUN
ejpam-6128	159	4	matrix	matrix	NOUN
ejpam-6128	159	5	of	of	ADP
ejpam-6128	159	6	l5	l5	PROPN
ejpam-6128	159	7	is	be	AUX
ejpam-6128	159	8	given	give	VERB
ejpam-6128	159	9	as	as	ADP
ejpam-6128	159	10	a	a	DET
ejpam-6128	159	11	=	=	PUNCT
ejpam-6128	159	12			ADJ
ejpam-6128	159	13	eς4	eς4	NOUN
ejpam-6128	159	14	0	0	NUM
ejpam-6128	159	15	0	0	NUM
ejpam-6128	159	16	0	0	NUM
ejpam-6128	159	17	0	0	NUM
ejpam-6128	159	18	0	0	NUM
ejpam-6128	160	1	eς5	eς5	ADJ
ejpam-6128	160	2	0	0	NUM
ejpam-6128	160	3	0	0	NUM
ejpam-6128	160	4	0	0	NUM
ejpam-6128	160	5	0	0	NUM
ejpam-6128	160	6	0	0	NUM
ejpam-6128	160	7	e2ς4−ς5	e2ς4−ς5	NOUN
ejpam-6128	160	8	0	0	NUM
ejpam-6128	160	9	0	0	NUM
ejpam-6128	160	10	−ς1e	−ς1e	NUM
ejpam-6128	160	11	ς4	ς4	PROPN
ejpam-6128	160	12	0	0	NUM
ejpam-6128	160	13	−2ς3e	−2ς3e	NOUN
ejpam-6128	160	14	2ς4−ς5	2ς4−ς5	PROPN
ejpam-6128	160	15	1	1	NUM
ejpam-6128	160	16	0	0	NUM
ejpam-6128	160	17	0	0	NUM
ejpam-6128	161	1	−ς2e	−ς2e	NOUN
ejpam-6128	161	2	ς5	ς5	NOUN
ejpam-6128	161	3	ς3e	ς3e	NOUN
ejpam-6128	161	4	2ς4−ς5	2ς4−ς5	NOUN
ejpam-6128	161	5	0	0	NUM
ejpam-6128	161	6	1	1	NUM
ejpam-6128	161	7			NOUN
ejpam-6128	161	8	eq	eq	NOUN
ejpam-6128	161	9	.	.	PUNCT
ejpam-6128	162	1	(	(	PUNCT
ejpam-6128	162	2	17	17	NUM
ejpam-6128	162	3	)	)	PUNCT
ejpam-6128	162	4	yields	yield	VERB
ejpam-6128	162	5	the	the	DET
ejpam-6128	162	6	following	follow	VERB
ejpam-6128	162	7	system	system	NOUN
ejpam-6128	162	8	of	of	ADP
ejpam-6128	162	9	equations	equation	NOUN
ejpam-6128	163	1	k̃1	k̃1	PROPN
ejpam-6128	164	1	=	=	PUNCT
ejpam-6128	165	1	k1e	k1e	PROPN
ejpam-6128	165	2	ς4	ς4	PROPN
ejpam-6128	165	3	−	−	NOUN
ejpam-6128	165	4	k4ς1e	k4ς1e	NOUN
ejpam-6128	165	5	ς4	ς4	PROPN
ejpam-6128	165	6	,	,	PUNCT
ejpam-6128	165	7	k̃2	k̃2	PROPN
ejpam-6128	165	8	=	=	SYM
ejpam-6128	166	1	k2e	k2e	PROPN
ejpam-6128	166	2	ς5	ς5	PROPN
ejpam-6128	166	3	−	−	PROPN
ejpam-6128	166	4	k5ς2e	k5ς2e	X
ejpam-6128	166	5	ς5	ς5	NOUN
ejpam-6128	166	6	,	,	PUNCT
ejpam-6128	166	7	k̃3	k̃3	PROPN
ejpam-6128	166	8	=	=	PUNCT
ejpam-6128	166	9	k3e	k3e	PROPN
ejpam-6128	166	10	2ς4−ς5	2ς4−ς5	PROPN
ejpam-6128	166	11	−	−	NOUN
ejpam-6128	166	12	2k4ς3e	2k4ς3e	NUM
ejpam-6128	166	13	2ς4−ς5	2ς4−ς5	PROPN
ejpam-6128	167	1	+	+	CCONJ
ejpam-6128	167	2	k5ς3e	k5ς3e	X
ejpam-6128	167	3	2ς4−ς5	2ς4−ς5	NUM
ejpam-6128	167	4	,	,	PUNCT
ejpam-6128	167	5	k̃4	k̃4	PROPN
ejpam-6128	167	6	=	=	PUNCT
ejpam-6128	167	7	k4	k4	PROPN
ejpam-6128	167	8	,	,	PUNCT
ejpam-6128	167	9	k̃5	k̃5	PROPN
ejpam-6128	167	10	=	=	SYM
ejpam-6128	167	11	k5	k5	PROPN
ejpam-6128	167	12	.	.	PUNCT
ejpam-6128	168	1	(	(	PUNCT
ejpam-6128	168	2	23	23	NUM
ejpam-6128	168	3	)	)	PUNCT
ejpam-6128	168	4	m.	m.	NOUN
ejpam-6128	168	5	usman	usman	PROPN
ejpam-6128	168	6	,	,	PUNCT
ejpam-6128	168	7	a.	a.	NOUN
ejpam-6128	168	8	hussain	hussain	PROPN
ejpam-6128	168	9	,	,	PUNCT
ejpam-6128	168	10	m.	m.	PROPN
ejpam-6128	168	11	u.	u.	PROPN
ejpam-6128	168	12	farooq	farooq	PROPN
ejpam-6128	168	13	,	,	PUNCT
ejpam-6128	168	14	j.	j.	PROPN
ejpam-6128	168	15	herrera	herrera	PROPN
ejpam-6128	168	16	/	/	SYM
ejpam-6128	168	17	eur	eur	PROPN
ejpam-6128	168	18	.	.	PUNCT
ejpam-6128	169	1	j.	j.	PROPN
ejpam-6128	169	2	pure	pure	PROPN
ejpam-6128	169	3	appl	appl	PROPN
ejpam-6128	169	4	.	.	PROPN
ejpam-6128	169	5	math	math	PROPN
ejpam-6128	169	6	,	,	PUNCT
ejpam-6128	169	7	18	18	NUM
ejpam-6128	169	8	(	(	PUNCT
ejpam-6128	169	9	4	4	NUM
ejpam-6128	169	10	)	)	PUNCT
ejpam-6128	169	11	(	(	PUNCT
ejpam-6128	169	12	2025	2025	NUM
ejpam-6128	169	13	)	)	PUNCT
ejpam-6128	169	14	,	,	PUNCT
ejpam-6128	169	15	6128	6128	NUM
ejpam-6128	169	16	8	8	NUM
ejpam-6128	169	17	of	of	ADP
ejpam-6128	169	18	29	29	NUM
ejpam-6128	169	19	by	by	ADP
ejpam-6128	169	20	using	use	VERB
ejpam-6128	169	21	the	the	DET
ejpam-6128	169	22	formula	formula	NOUN
ejpam-6128	169	23	(	(	PUNCT
ejpam-6128	169	24	15	15	NUM
ejpam-6128	169	25	)	)	PUNCT
ejpam-6128	169	26	,	,	PUNCT
ejpam-6128	169	27	we	we	PRON
ejpam-6128	169	28	obtain	obtain	VERB
ejpam-6128	169	29	the	the	DET
ejpam-6128	169	30	following	follow	VERB
ejpam-6128	169	31	system	system	NOUN
ejpam-6128	169	32	of	of	ADP
ejpam-6128	169	33	linear	linear	PROPN
ejpam-6128	169	34	pdes	pde	NOUN
ejpam-6128	169	35	k4	k4	PROPN
ejpam-6128	169	36	∂ϑ	∂ϑ	PROPN
ejpam-6128	169	37	∂k1	∂k1	PROPN
ejpam-6128	169	38	=	=	SYM
ejpam-6128	169	39	0	0	NUM
ejpam-6128	169	40	,	,	PUNCT
ejpam-6128	169	41	k5	k5	PROPN
ejpam-6128	169	42	∂ϑ	∂ϑ	PROPN
ejpam-6128	169	43	∂k2	∂k2	PROPN
ejpam-6128	169	44	=	=	SYM
ejpam-6128	169	45	0	0	NUM
ejpam-6128	169	46	,	,	PUNCT
ejpam-6128	169	47	k5	k5	PROPN
ejpam-6128	169	48	∂ϑ	∂ϑ	PROPN
ejpam-6128	169	49	∂k3	∂k3	PROPN
ejpam-6128	170	1	−	−	PROPN
ejpam-6128	170	2	2k4	2k4	NUM
ejpam-6128	171	1	∂ϑ	∂ϑ	PROPN
ejpam-6128	171	2	∂k3	∂k3	NOUN
ejpam-6128	171	3	=	=	SYM
ejpam-6128	171	4	0	0	NUM
ejpam-6128	171	5	,	,	PUNCT
ejpam-6128	171	6	k1	k1	PROPN
ejpam-6128	171	7	∂ϑ	∂ϑ	PROPN
ejpam-6128	171	8	∂k1	∂k1	VERB
ejpam-6128	172	1	+	+	NUM
ejpam-6128	172	2	2k3	2k3	NUM
ejpam-6128	172	3	∂ϑ	∂ϑ	PROPN
ejpam-6128	172	4	∂k3	∂k3	NOUN
ejpam-6128	172	5	=	=	SYM
ejpam-6128	172	6	0	0	PROPN
ejpam-6128	172	7	,	,	PUNCT
ejpam-6128	172	8	k2	k2	PROPN
ejpam-6128	172	9	∂ϑ	∂ϑ	PROPN
ejpam-6128	172	10	∂k2	∂k2	PROPN
ejpam-6128	172	11	+	+	CCONJ
ejpam-6128	172	12	k3	k3	PROPN
ejpam-6128	172	13	∂ϑ	∂ϑ	PROPN
ejpam-6128	172	14	∂k3	∂k3	NOUN
ejpam-6128	172	15	=	=	SYM
ejpam-6128	172	16	0	0	PROPN
ejpam-6128	172	17	.	.	PUNCT
ejpam-6128	173	1	(	(	PUNCT
ejpam-6128	173	2	24	24	NUM
ejpam-6128	173	3	)	)	PUNCT
ejpam-6128	173	4	by	by	ADP
ejpam-6128	173	5	solving	solve	VERB
ejpam-6128	173	6	equation	equation	NOUN
ejpam-6128	173	7	(	(	PUNCT
ejpam-6128	173	8	24	24	NUM
ejpam-6128	173	9	)	)	PUNCT
ejpam-6128	173	10	,	,	PUNCT
ejpam-6128	173	11	we	we	PRON
ejpam-6128	173	12	get	get	VERB
ejpam-6128	173	13	φ(k1	φ(k1	ADJ
ejpam-6128	173	14	,	,	PUNCT
ejpam-6128	173	15	k2	k2	ADJ
ejpam-6128	173	16	,	,	PUNCT
ejpam-6128	173	17	k3	k3	PROPN
ejpam-6128	173	18	,	,	PUNCT
ejpam-6128	173	19	k4	k4	PROPN
ejpam-6128	173	20	,	,	PUNCT
ejpam-6128	173	21	k5	k5	PROPN
ejpam-6128	173	22	)	)	PUNCT
ejpam-6128	174	1	=	=	SYM
ejpam-6128	174	2	f	f	PROPN
ejpam-6128	174	3	(	(	PUNCT
ejpam-6128	174	4	k4	k4	PROPN
ejpam-6128	174	5	,	,	PUNCT
ejpam-6128	174	6	k5	k5	PROPN
ejpam-6128	174	7	)	)	PUNCT
ejpam-6128	174	8	.	.	PUNCT
ejpam-6128	175	1	so	so	ADV
ejpam-6128	175	2	,	,	PUNCT
ejpam-6128	175	3	the	the	DET
ejpam-6128	175	4	first	first	ADJ
ejpam-6128	175	5	two	two	NUM
ejpam-6128	175	6	vertices	vertex	NOUN
ejpam-6128	175	7	of	of	ADP
ejpam-6128	175	8	the	the	DET
ejpam-6128	175	9	tree	tree	NOUN
ejpam-6128	175	10	are	be	AUX
ejpam-6128	175	11	k4	k4	ADJ
ejpam-6128	175	12	and	and	CCONJ
ejpam-6128	175	13	k5	k5	PROPN
ejpam-6128	175	14	.	.	PUNCT
ejpam-6128	176	1	k5	k5	PROPN
ejpam-6128	176	2	k5	k5	PROPN
ejpam-6128	176	3	=	=	PROPN
ejpam-6128	176	4	0	0	NUM
ejpam-6128	176	5	k4	k4	NOUN
ejpam-6128	176	6	=	=	SYM
ejpam-6128	176	7	0	0	NUM
ejpam-6128	176	8	k2	k2	NOUN
ejpam-6128	176	9	=	=	SYM
ejpam-6128	176	10	0	0	NUM
ejpam-6128	176	11	,	,	PUNCT
ejpam-6128	176	12	k1	k1	X
ejpam-6128	176	13	6=	6=	ADP
ejpam-6128	176	14	0	0	NUM
ejpam-6128	176	15	k3	k3	ADJ
ejpam-6128	176	16	=	=	SYM
ejpam-6128	176	17	0	0	NUM
ejpam-6128	176	18	case-7	case-7	NOUN
ejpam-6128	176	19	k3	k3	VERB
ejpam-6128	176	20	6=	6=	PRON
ejpam-6128	176	21	0	0	SYM
ejpam-6128	177	1	case-6	case-6	VERB
ejpam-6128	177	2	k2	k2	PROPN
ejpam-6128	177	3	6=	6=	PROPN
ejpam-6128	177	4	0	0	NUM
ejpam-6128	177	5	,	,	PUNCT
ejpam-6128	177	6	k1	k1	X
ejpam-6128	177	7	6=	6=	ADP
ejpam-6128	177	8	0	0	NUM
ejpam-6128	177	9	k3	k3	ADJ
ejpam-6128	177	10	=	=	SYM
ejpam-6128	177	11	0	0	PUNCT
ejpam-6128	178	1	case-5	case-5	NOUN
ejpam-6128	178	2	k3	k3	VERB
ejpam-6128	178	3	6=	6=	PRON
ejpam-6128	178	4	0	0	SYM
ejpam-6128	178	5	case-4	case-4	NUM
ejpam-6128	178	6	k4	k4	NOUN
ejpam-6128	178	7	6=	6=	ADP
ejpam-6128	178	8	0	0	NUM
ejpam-6128	178	9	case-3	case-3	NUM
ejpam-6128	178	10	k5	k5	PROPN
ejpam-6128	178	11	6=	6=	ADP
ejpam-6128	178	12	0	0	NUM
ejpam-6128	178	13	k4	k4	NOUN
ejpam-6128	178	14	=	=	NOUN
ejpam-6128	178	15	0	0	PUNCT
ejpam-6128	178	16	case-2	case-2	NUM
ejpam-6128	178	17	k4	k4	NOUN
ejpam-6128	178	18	6=	6=	ADP
ejpam-6128	178	19	0	0	NUM
ejpam-6128	178	20	case-1	case-1	NUM
ejpam-6128	178	21	case-1	case-1	NUM
ejpam-6128	178	22	:	:	PUNCT
ejpam-6128	178	23	for	for	ADP
ejpam-6128	178	24	k5	k5	PROPN
ejpam-6128	178	25	6=	6=	ADP
ejpam-6128	178	26	0	0	NUM
ejpam-6128	178	27	,	,	PUNCT
ejpam-6128	178	28	k4	k4	PROPN
ejpam-6128	178	29	6=	6=	ADP
ejpam-6128	178	30	0	0	NUM
ejpam-6128	178	31	,	,	PUNCT
ejpam-6128	178	32	we	we	PRON
ejpam-6128	178	33	have	have	VERB
ejpam-6128	178	34	m1	m1	NOUN
ejpam-6128	178	35	=	=	SYM
ejpam-6128	178	36	y4	y4	PROPN
ejpam-6128	178	37	+	+	CCONJ
ejpam-6128	178	38	y5	y5	NOUN
ejpam-6128	178	39	.	.	PUNCT
ejpam-6128	179	1	by	by	ADP
ejpam-6128	179	2	substituting	substitute	VERB
ejpam-6128	179	3	k̃4	k̃4	PROPN
ejpam-6128	179	4	=	=	PUNCT
ejpam-6128	179	5	k̃5	k̃5	PROPN
ejpam-6128	179	6	=	=	NOUN
ejpam-6128	179	7	1	1	NUM
ejpam-6128	179	8	in	in	ADP
ejpam-6128	179	9	(	(	PUNCT
ejpam-6128	179	10	23	23	NUM
ejpam-6128	179	11	)	)	PUNCT
ejpam-6128	179	12	,	,	PUNCT
ejpam-6128	179	13	we	we	PRON
ejpam-6128	179	14	obtain	obtain	VERB
ejpam-6128	179	15	ς1	ς1	NOUN
ejpam-6128	179	16	=	=	SYM
ejpam-6128	179	17	k1	k1	NOUN
ejpam-6128	179	18	k4	k4	NOUN
ejpam-6128	179	19	,	,	PUNCT
ejpam-6128	179	20	ς2	ς2	PROPN
ejpam-6128	179	21	=	=	PROPN
ejpam-6128	179	22	k2	k2	PROPN
ejpam-6128	179	23	k5	k5	PROPN
ejpam-6128	179	24	,	,	PUNCT
ejpam-6128	179	25	ς3	ς3	NOUN
ejpam-6128	179	26	=	=	PUNCT
ejpam-6128	179	27	k3	k3	VERB
ejpam-6128	179	28	2k4−k5	2k4−k5	NOUN
ejpam-6128	179	29	.	.	PUNCT
ejpam-6128	180	1	case-2	case-2	ADV
ejpam-6128	180	2	:	:	PUNCT
ejpam-6128	180	3	for	for	ADP
ejpam-6128	180	4	k5	k5	PROPN
ejpam-6128	180	5	6=	6=	ADP
ejpam-6128	180	6	0	0	NUM
ejpam-6128	180	7	,	,	PUNCT
ejpam-6128	180	8	k4	k4	NOUN
ejpam-6128	180	9	=	=	SYM
ejpam-6128	180	10	0	0	NUM
ejpam-6128	180	11	,	,	PUNCT
ejpam-6128	180	12	we	we	PRON
ejpam-6128	180	13	have	have	VERB
ejpam-6128	180	14	m2	m2	PROPN
ejpam-6128	180	15	=	=	PROPN
ejpam-6128	180	16	y5	y5	PROPN
ejpam-6128	180	17	+	+	CCONJ
ejpam-6128	180	18	ay1	ay1	PROPN
ejpam-6128	180	19	,	,	PUNCT
ejpam-6128	180	20	a	a	DET
ejpam-6128	180	21	∈	∈	PROPN
ejpam-6128	180	22	r.	r.	NOUN
ejpam-6128	180	23	by	by	ADP
ejpam-6128	180	24	substituting	substitute	VERB
ejpam-6128	180	25	k̃1	k̃1	PROPN
ejpam-6128	180	26	=	=	PUNCT
ejpam-6128	180	27	k̃5	k̃5	PROPN
ejpam-6128	180	28	=	=	NOUN
ejpam-6128	180	29	1	1	NUM
ejpam-6128	180	30	in	in	ADP
ejpam-6128	180	31	(	(	PUNCT
ejpam-6128	180	32	23	23	NUM
ejpam-6128	180	33	)	)	PUNCT
ejpam-6128	180	34	,	,	PUNCT
ejpam-6128	180	35	we	we	PRON
ejpam-6128	180	36	obtain	obtain	VERB
ejpam-6128	180	37	ς2	ς2	PROPN
ejpam-6128	180	38	=	=	SYM
ejpam-6128	180	39	k2	k2	PROPN
ejpam-6128	180	40	k5	k5	PROPN
ejpam-6128	180	41	,	,	PUNCT
ejpam-6128	180	42	ς3	ς3	NOUN
ejpam-6128	180	43	=	=	PUNCT
ejpam-6128	180	44	k3	k3	VERB
ejpam-6128	180	45	2k4−k5	2k4−k5	NUM
ejpam-6128	180	46	.	.	PUNCT
ejpam-6128	181	1	case-3	case-3	NUM
ejpam-6128	181	2	:	:	PUNCT
ejpam-6128	181	3	for	for	ADP
ejpam-6128	181	4	k5	k5	PROPN
ejpam-6128	181	5	=	=	SYM
ejpam-6128	181	6	0	0	PROPN
ejpam-6128	181	7	,	,	PUNCT
ejpam-6128	181	8	k4	k4	PROPN
ejpam-6128	181	9	6=	6=	ADP
ejpam-6128	181	10	0	0	NUM
ejpam-6128	181	11	,	,	PUNCT
ejpam-6128	181	12	we	we	PRON
ejpam-6128	181	13	have	have	VERB
ejpam-6128	181	14	m3	m3	PROPN
ejpam-6128	181	15	=	=	PUNCT
ejpam-6128	181	16	y4	y4	PROPN
ejpam-6128	182	1	+	+	CCONJ
ejpam-6128	182	2	ay2	ay2	PROPN
ejpam-6128	182	3	,	,	PUNCT
ejpam-6128	182	4	a	a	DET
ejpam-6128	182	5	∈	∈	PROPN
ejpam-6128	182	6	r.	r.	NOUN
ejpam-6128	182	7	by	by	ADP
ejpam-6128	182	8	substituting	substitute	VERB
ejpam-6128	182	9	k̃2	k̃2	PROPN
ejpam-6128	182	10	=	=	SYM
ejpam-6128	182	11	k̃4	k̃4	PROPN
ejpam-6128	182	12	=	=	NOUN
ejpam-6128	182	13	1	1	NUM
ejpam-6128	182	14	in	in	ADP
ejpam-6128	182	15	(	(	PUNCT
ejpam-6128	182	16	23	23	NUM
ejpam-6128	182	17	)	)	PUNCT
ejpam-6128	182	18	,	,	PUNCT
ejpam-6128	182	19	we	we	PRON
ejpam-6128	182	20	obtain	obtain	VERB
ejpam-6128	182	21	ς1	ς1	NOUN
ejpam-6128	182	22	=	=	SYM
ejpam-6128	182	23	k1	k1	NOUN
ejpam-6128	182	24	k4	k4	NOUN
ejpam-6128	182	25	,	,	PUNCT
ejpam-6128	182	26	ς3	ς3	NOUN
ejpam-6128	182	27	=	=	PUNCT
ejpam-6128	182	28	k3	k3	VERB
ejpam-6128	182	29	2k4−k5	2k4−k5	NOUN
ejpam-6128	182	30	.	.	PUNCT
ejpam-6128	183	1	when	when	SCONJ
ejpam-6128	183	2	k4	k4	PROPN
ejpam-6128	183	3	=	=	PROPN
ejpam-6128	183	4	k5	k5	PROPN
ejpam-6128	183	5	=	=	SYM
ejpam-6128	183	6	0	0	PROPN
ejpam-6128	183	7	,	,	PUNCT
ejpam-6128	183	8	the	the	DET
ejpam-6128	183	9	solution	solution	NOUN
ejpam-6128	183	10	of	of	ADP
ejpam-6128	183	11	(	(	PUNCT
ejpam-6128	183	12	24	24	NUM
ejpam-6128	183	13	)	)	PUNCT
ejpam-6128	183	14	gives	give	VERB
ejpam-6128	183	15	ϑ(k1	ϑ(k1	NOUN
ejpam-6128	183	16	,	,	PUNCT
ejpam-6128	183	17	k2	k2	PROPN
ejpam-6128	183	18	,	,	PUNCT
ejpam-6128	183	19	k3	k3	PROPN
ejpam-6128	183	20	,	,	PUNCT
ejpam-6128	183	21	k4	k4	PROPN
ejpam-6128	183	22	,	,	PUNCT
ejpam-6128	183	23	k5	k5	PROPN
ejpam-6128	183	24	)	)	PUNCT
ejpam-6128	184	1	=	=	SYM
ejpam-6128	184	2	f	f	PROPN
ejpam-6128	184	3	(	(	PUNCT
ejpam-6128	184	4	k2k3	k2k3	X
ejpam-6128	184	5	k21	k21	X
ejpam-6128	184	6	,	,	PUNCT
ejpam-6128	184	7	k4	k4	PROPN
ejpam-6128	184	8	,	,	PUNCT
ejpam-6128	184	9	k5	k5	PROPN
ejpam-6128	184	10	)	)	PUNCT
ejpam-6128	184	11	.	.	PUNCT
ejpam-6128	185	1	this	this	PRON
ejpam-6128	185	2	means	mean	VERB
ejpam-6128	185	3	that	that	SCONJ
ejpam-6128	185	4	the	the	DET
ejpam-6128	185	5	new	new	ADJ
ejpam-6128	185	6	invariant	invariant	NOUN
ejpam-6128	185	7	is	be	AUX
ejpam-6128	185	8	k2k3	k2k3	INTJ
ejpam-6128	185	9	k21	k21	NOUN
ejpam-6128	185	10	.	.	PUNCT
ejpam-6128	186	1	since	since	SCONJ
ejpam-6128	186	2	k1	k1	PROPN
ejpam-6128	186	3	6=	6=	ADP
ejpam-6128	186	4	0	0	NUM
ejpam-6128	186	5	,	,	PUNCT
ejpam-6128	186	6	so	so	ADV
ejpam-6128	186	7	the	the	DET
ejpam-6128	186	8	next	next	ADJ
ejpam-6128	186	9	two	two	NUM
ejpam-6128	186	10	vertices	vertex	NOUN
ejpam-6128	186	11	will	will	AUX
ejpam-6128	186	12	be	be	AUX
ejpam-6128	186	13	k2	k2	ADJ
ejpam-6128	186	14	and	and	CCONJ
ejpam-6128	186	15	k3	k3	PROPN
ejpam-6128	186	16	.	.	PUNCT
ejpam-6128	187	1	case-4	case-4	NOUN
ejpam-6128	187	2	:	:	PUNCT
ejpam-6128	187	3	for	for	ADP
ejpam-6128	187	4	k4	k4	NOUN
ejpam-6128	187	5	=	=	SYM
ejpam-6128	187	6	k5	k5	PROPN
ejpam-6128	187	7	=	=	SYM
ejpam-6128	187	8	0	0	PROPN
ejpam-6128	187	9	,	,	PUNCT
ejpam-6128	187	10	k3	k3	VERB
ejpam-6128	187	11	6=	6=	ADP
ejpam-6128	187	12	0	0	NUM
ejpam-6128	187	13	,	,	PUNCT
ejpam-6128	187	14	k2	k2	PROPN
ejpam-6128	187	15	6=	6=	PROPN
ejpam-6128	187	16	0	0	NUM
ejpam-6128	187	17	,	,	PUNCT
ejpam-6128	187	18	k1	k1	PROPN
ejpam-6128	187	19	6=	6=	ADP
ejpam-6128	187	20	0	0	NUM
ejpam-6128	187	21	,	,	PUNCT
ejpam-6128	187	22	we	we	PRON
ejpam-6128	187	23	have	have	VERB
ejpam-6128	187	24	m4	m4	NOUN
ejpam-6128	187	25	=	=	SYM
ejpam-6128	187	26	y1	y1	NOUN
ejpam-6128	187	27	+	+	CCONJ
ejpam-6128	188	1	y2	y2	NOUN
ejpam-6128	188	2	+	+	NUM
ejpam-6128	188	3	y3	y3	NOUN
ejpam-6128	188	4	.	.	PUNCT
ejpam-6128	189	1	case-5	case-5	NOUN
ejpam-6128	189	2	:	:	PUNCT
ejpam-6128	189	3	for	for	ADP
ejpam-6128	189	4	k4	k4	NOUN
ejpam-6128	189	5	=	=	SYM
ejpam-6128	189	6	k5	k5	PROPN
ejpam-6128	189	7	=	=	SYM
ejpam-6128	189	8	0	0	PROPN
ejpam-6128	189	9	,	,	PUNCT
ejpam-6128	189	10	k3	k3	VERB
ejpam-6128	189	11	=	=	SYM
ejpam-6128	189	12	0	0	NUM
ejpam-6128	189	13	,	,	PUNCT
ejpam-6128	189	14	k2	k2	PROPN
ejpam-6128	189	15	6=	6=	PROPN
ejpam-6128	189	16	0	0	NUM
ejpam-6128	189	17	,	,	PUNCT
ejpam-6128	189	18	k1	k1	PROPN
ejpam-6128	189	19	6=	6=	ADP
ejpam-6128	189	20	0	0	NUM
ejpam-6128	189	21	,	,	PUNCT
ejpam-6128	189	22	we	we	PRON
ejpam-6128	189	23	have	have	VERB
ejpam-6128	189	24	m5	m5	NOUN
ejpam-6128	189	25	=	=	SYM
ejpam-6128	189	26	y1	y1	PROPN
ejpam-6128	189	27	+	+	CCONJ
ejpam-6128	189	28	y2	y2	NOUN
ejpam-6128	189	29	.	.	PUNCT
ejpam-6128	190	1	case-6	case-6	NOUN
ejpam-6128	190	2	:	:	PUNCT
ejpam-6128	190	3	for	for	ADP
ejpam-6128	190	4	k4	k4	NOUN
ejpam-6128	190	5	=	=	SYM
ejpam-6128	190	6	k5	k5	PROPN
ejpam-6128	190	7	=	=	SYM
ejpam-6128	190	8	0	0	PROPN
ejpam-6128	190	9	,	,	PUNCT
ejpam-6128	190	10	k3	k3	VERB
ejpam-6128	190	11	6=	6=	PRON
ejpam-6128	190	12	0	0	NUM
ejpam-6128	190	13	,	,	PUNCT
ejpam-6128	190	14	k2	k2	NOUN
ejpam-6128	190	15	=	=	SYM
ejpam-6128	190	16	0	0	NUM
ejpam-6128	190	17	,	,	PUNCT
ejpam-6128	190	18	k1	k1	PROPN
ejpam-6128	190	19	6=	6=	ADP
ejpam-6128	190	20	0	0	NUM
ejpam-6128	190	21	,	,	PUNCT
ejpam-6128	190	22	we	we	PRON
ejpam-6128	190	23	have	have	VERB
ejpam-6128	190	24	m6	m6	VERB
ejpam-6128	190	25	=	=	SYM
ejpam-6128	190	26	y1	y1	PROPN
ejpam-6128	190	27	+	+	NUM
ejpam-6128	190	28	y3	y3	NOUN
ejpam-6128	190	29	.	.	PUNCT
ejpam-6128	191	1	m.	m.	PROPN
ejpam-6128	191	2	usman	usman	PROPN
ejpam-6128	191	3	,	,	PUNCT
ejpam-6128	191	4	a.	a.	NOUN
ejpam-6128	191	5	hussain	hussain	PROPN
ejpam-6128	191	6	,	,	PUNCT
ejpam-6128	191	7	m.	m.	PROPN
ejpam-6128	191	8	u.	u.	PROPN
ejpam-6128	191	9	farooq	farooq	PROPN
ejpam-6128	191	10	,	,	PUNCT
ejpam-6128	191	11	j.	j.	PROPN
ejpam-6128	191	12	herrera	herrera	PROPN
ejpam-6128	191	13	/	/	SYM
ejpam-6128	191	14	eur	eur	PROPN
ejpam-6128	191	15	.	.	PUNCT
ejpam-6128	192	1	j.	j.	PROPN
ejpam-6128	192	2	pure	pure	PROPN
ejpam-6128	192	3	appl	appl	PROPN
ejpam-6128	192	4	.	.	PROPN
ejpam-6128	192	5	math	math	PROPN
ejpam-6128	192	6	,	,	PUNCT
ejpam-6128	192	7	18	18	NUM
ejpam-6128	192	8	(	(	PUNCT
ejpam-6128	192	9	4	4	NUM
ejpam-6128	192	10	)	)	PUNCT
ejpam-6128	192	11	(	(	PUNCT
ejpam-6128	192	12	2025	2025	NUM
ejpam-6128	192	13	)	)	PUNCT
ejpam-6128	192	14	,	,	PUNCT
ejpam-6128	192	15	6128	6128	NUM
ejpam-6128	192	16	9	9	NUM
ejpam-6128	192	17	of	of	ADP
ejpam-6128	192	18	29	29	NUM
ejpam-6128	192	19	case-7	case-7	NOUN
ejpam-6128	192	20	:	:	PUNCT
ejpam-6128	192	21	for	for	ADP
ejpam-6128	192	22	k4	k4	NOUN
ejpam-6128	192	23	=	=	SYM
ejpam-6128	192	24	k5	k5	PROPN
ejpam-6128	192	25	=	=	SYM
ejpam-6128	192	26	0	0	PROPN
ejpam-6128	192	27	,	,	PUNCT
ejpam-6128	192	28	k2	k2	NOUN
ejpam-6128	192	29	=	=	SYM
ejpam-6128	192	30	k3	k3	PROPN
ejpam-6128	192	31	=	=	NOUN
ejpam-6128	192	32	0	0	NUM
ejpam-6128	192	33	,	,	PUNCT
ejpam-6128	192	34	k1	k1	PROPN
ejpam-6128	192	35	6=	6=	ADP
ejpam-6128	192	36	0	0	NUM
ejpam-6128	192	37	,	,	PUNCT
ejpam-6128	192	38	we	we	PRON
ejpam-6128	192	39	have	have	VERB
ejpam-6128	192	40	m7	m7	PROPN
ejpam-6128	192	41	=	=	SYM
ejpam-6128	192	42	y1	y1	PROPN
ejpam-6128	192	43	.	.	PUNCT
ejpam-6128	193	1	so	so	ADV
ejpam-6128	193	2	,	,	PUNCT
ejpam-6128	193	3	the	the	DET
ejpam-6128	193	4	one	one	NUM
ejpam-6128	193	5	-	-	PUNCT
ejpam-6128	193	6	dimensional	dimensional	ADJ
ejpam-6128	193	7	optimal	optimal	ADJ
ejpam-6128	193	8	system	system	NOUN
ejpam-6128	193	9	of	of	ADP
ejpam-6128	193	10	subalgebras	subalgebra	NOUN
ejpam-6128	193	11	of	of	ADP
ejpam-6128	193	12	lie	lie	NOUN
ejpam-6128	193	13	algebra	algebra	NOUN
ejpam-6128	193	14	(	(	PUNCT
ejpam-6128	193	15	7	7	NUM
ejpam-6128	193	16	)	)	PUNCT
ejpam-6128	193	17	is	be	AUX
ejpam-6128	193	18	presented	present	VERB
ejpam-6128	193	19	as	as	ADP
ejpam-6128	193	20	m1	m1	PROPN
ejpam-6128	193	21	=	=	PROPN
ejpam-6128	193	22	y4	y4	PROPN
ejpam-6128	193	23	+	+	CCONJ
ejpam-6128	193	24	y5	y5	PROPN
ejpam-6128	193	25	,	,	PUNCT
ejpam-6128	193	26	m2	m2	PROPN
ejpam-6128	193	27	=	=	PROPN
ejpam-6128	193	28	y5	y5	PROPN
ejpam-6128	193	29	+	+	CCONJ
ejpam-6128	193	30	ay1	ay1	PROPN
ejpam-6128	193	31	,	,	PUNCT
ejpam-6128	193	32	a	a	DET
ejpam-6128	193	33	∈	∈	PROPN
ejpam-6128	193	34	r	r	NOUN
ejpam-6128	193	35	,	,	PUNCT
ejpam-6128	193	36	m3	m3	PROPN
ejpam-6128	193	37	=	=	PUNCT
ejpam-6128	193	38	y4	y4	PROPN
ejpam-6128	193	39	+	+	CCONJ
ejpam-6128	194	1	ay2	ay2	PROPN
ejpam-6128	194	2	,	,	PUNCT
ejpam-6128	194	3	a	a	DET
ejpam-6128	194	4	∈	∈	PROPN
ejpam-6128	194	5	r	r	NOUN
ejpam-6128	194	6	,	,	PUNCT
ejpam-6128	194	7	m4	m4	PROPN
ejpam-6128	194	8	=	=	SYM
ejpam-6128	194	9	y1	y1	PROPN
ejpam-6128	194	10	+	+	CCONJ
ejpam-6128	194	11	y2	y2	NOUN
ejpam-6128	194	12	+	+	CCONJ
ejpam-6128	194	13	y3	y3	NOUN
ejpam-6128	194	14	,	,	PUNCT
ejpam-6128	194	15	m5	m5	NOUN
ejpam-6128	194	16	=	=	SYM
ejpam-6128	194	17	y1	y1	PROPN
ejpam-6128	194	18	+	+	CCONJ
ejpam-6128	194	19	y2	y2	PROPN
ejpam-6128	194	20	,	,	PUNCT
ejpam-6128	194	21	m6	m6	ADJ
ejpam-6128	194	22	=	=	SYM
ejpam-6128	194	23	y1	y1	PROPN
ejpam-6128	194	24	+	+	NUM
ejpam-6128	194	25	y3	y3	NOUN
ejpam-6128	194	26	,	,	PUNCT
ejpam-6128	194	27	m7	m7	PROPN
ejpam-6128	194	28	=	=	SYM
ejpam-6128	194	29	y1	y1	PROPN
ejpam-6128	194	30	.	.	PUNCT
ejpam-6128	195	1	(	(	PUNCT
ejpam-6128	195	2	25	25	NUM
ejpam-6128	195	3	)	)	PUNCT
ejpam-6128	195	4	2.1.3	2.1.3	NUM
ejpam-6128	195	5	.	.	PUNCT
ejpam-6128	195	6	optimal	optimal	ADJ
ejpam-6128	195	7	system	system	NOUN
ejpam-6128	195	8	for	for	ADP
ejpam-6128	195	9	case	case	NOUN
ejpam-6128	195	10	3	3	NUM
ejpam-6128	195	11	for	for	ADP
ejpam-6128	195	12	lie	lie	NOUN
ejpam-6128	195	13	algebra	algebra	PROPN
ejpam-6128	195	14	l6	l6	PROPN
ejpam-6128	195	15	presented	present	VERB
ejpam-6128	195	16	in	in	ADP
ejpam-6128	195	17	(	(	PUNCT
ejpam-6128	195	18	8)	8)	NUM
ejpam-6128	195	19	,	,	PUNCT
ejpam-6128	195	20	the	the	DET
ejpam-6128	195	21	non	non	ADJ
ejpam-6128	195	22	-	-	ADJ
ejpam-6128	195	23	zero	zero	ADJ
ejpam-6128	195	24	commutators	commutator	NOUN
ejpam-6128	195	25	are	be	AUX
ejpam-6128	195	26	provided	provide	VERB
ejpam-6128	195	27	by	by	ADP
ejpam-6128	195	28	[	[	X
ejpam-6128	195	29	y1,y4	y1,y4	X
ejpam-6128	195	30	]	]	X
ejpam-6128	195	31	=	=	SYM
ejpam-6128	195	32	y3	y3	PROPN
ejpam-6128	195	33	α	α	NOUN
ejpam-6128	195	34	,	,	PUNCT
ejpam-6128	195	35	[	[	X
ejpam-6128	195	36	y1,y6	y1,y6	X
ejpam-6128	195	37	]	]	X
ejpam-6128	195	38	=	=	SYM
ejpam-6128	195	39	y1	y1	PROPN
ejpam-6128	195	40	,	,	PUNCT
ejpam-6128	195	41	[	[	X
ejpam-6128	195	42	y2,y5	y2,y5	X
ejpam-6128	195	43	]	]	X
ejpam-6128	195	44	=	=	SYM
ejpam-6128	195	45	y2	y2	PROPN
ejpam-6128	195	46	,	,	PUNCT
ejpam-6128	195	47	[	[	X
ejpam-6128	195	48	y3,y4	y3,y4	X
ejpam-6128	195	49	]	]	X
ejpam-6128	195	50	=	=	SYM
ejpam-6128	195	51	y1	y1	PROPN
ejpam-6128	195	52	,	,	PUNCT
ejpam-6128	195	53	[	[	X
ejpam-6128	195	54	y3,y6	y3,y6	X
ejpam-6128	195	55	]	]	X
ejpam-6128	195	56	=	=	SYM
ejpam-6128	195	57	y3	y3	PROPN
ejpam-6128	195	58	.	.	PUNCT
ejpam-6128	196	1	(	(	PUNCT
ejpam-6128	196	2	26	26	NUM
ejpam-6128	196	3	)	)	PUNCT
ejpam-6128	196	4	in	in	ADP
ejpam-6128	196	5	table	table	NOUN
ejpam-6128	196	6	3	3	NUM
ejpam-6128	196	7	,	,	PUNCT
ejpam-6128	196	8	the	the	DET
ejpam-6128	196	9	adjoint	adjoint	PROPN
ejpam-6128	196	10	actions	action	NOUN
ejpam-6128	196	11	of	of	ADP
ejpam-6128	196	12	(	(	PUNCT
ejpam-6128	196	13	8)	8)	NUM
ejpam-6128	196	14	are	be	AUX
ejpam-6128	196	15	presented	present	VERB
ejpam-6128	196	16	.	.	PUNCT
ejpam-6128	197	1	table	table	NOUN
ejpam-6128	197	2	3	3	NUM
ejpam-6128	197	3	:	:	PUNCT
ejpam-6128	197	4	adjoint	adjoint	NOUN
ejpam-6128	197	5	table	table	NOUN
ejpam-6128	197	6	ad(eς	ad(eς	NOUN
ejpam-6128	197	7	)	)	PUNCT
ejpam-6128	198	1	y1	y1	NOUN
ejpam-6128	198	2	y2	y2	NOUN
ejpam-6128	198	3	y3	y3	PROPN
ejpam-6128	198	4	y4	y4	NOUN
ejpam-6128	198	5	y5	y5	NOUN
ejpam-6128	198	6	y6	y6	ADJ
ejpam-6128	198	7	y1	y1	NOUN
ejpam-6128	198	8	y1	y1	NOUN
ejpam-6128	198	9	y2	y2	NOUN
ejpam-6128	198	10	y3	y3	NOUN
ejpam-6128	198	11	y4	y4	PROPN
ejpam-6128	198	12	−	−	PROPN
ejpam-6128	198	13	ς	ς	PROPN
ejpam-6128	198	14	α	α	NOUN
ejpam-6128	198	15	y3	y3	NOUN
ejpam-6128	198	16	y5	y5	NOUN
ejpam-6128	198	17	y6	y6	ADJ
ejpam-6128	198	18	−	−	PROPN
ejpam-6128	198	19	ςy1	ςy1	PROPN
ejpam-6128	198	20	y2	y2	NOUN
ejpam-6128	199	1	y1	y1	INTJ
ejpam-6128	199	2	y2	y2	NOUN
ejpam-6128	199	3	y3	y3	PROPN
ejpam-6128	199	4	y4	y4	PROPN
ejpam-6128	199	5	y5	y5	PROPN
ejpam-6128	199	6	−	−	PROPN
ejpam-6128	199	7	ςy2	ςy2	INTJ
ejpam-6128	199	8	y6	y6	NOUN
ejpam-6128	199	9	y3	y3	NOUN
ejpam-6128	199	10	y1	y1	ADJ
ejpam-6128	199	11	y2	y2	NOUN
ejpam-6128	199	12	y3	y3	NOUN
ejpam-6128	199	13	y4	y4	PROPN
ejpam-6128	199	14	−	−	PROPN
ejpam-6128	199	15	ςy1	ςy1	PROPN
ejpam-6128	199	16	y5	y5	NOUN
ejpam-6128	199	17	y6	y6	ADJ
ejpam-6128	199	18	−	−	PROPN
ejpam-6128	199	19	ςy3	ςy3	PROPN
ejpam-6128	199	20	y4	y4	NOUN
ejpam-6128	199	21	(	(	PUNCT
ejpam-6128	199	22	e	e	PROPN
ejpam-6128	199	23	ς√	ς√	NUM
ejpam-6128	199	24	α	α	NOUN
ejpam-6128	199	25	−e	−e	NOUN
ejpam-6128	199	26	−ς√	−ς√	ADP
ejpam-6128	199	27	α	α	NUM
ejpam-6128	199	28	)	)	PUNCT
ejpam-6128	199	29	2	2	NUM
ejpam-6128	199	30	√	√	NUM
ejpam-6128	199	31	α	α	PRON
ejpam-6128	199	32	y3	y3	NOUN
ejpam-6128	199	33	+	+	X
ejpam-6128	199	34	(	(	PUNCT
ejpam-6128	199	35	e	e	PROPN
ejpam-6128	199	36	ς√	ς√	NUM
ejpam-6128	199	37	α	α	NOUN
ejpam-6128	199	38	+	+	PROPN
ejpam-6128	199	39	e	e	X
ejpam-6128	199	40	−ς√	−ς√	NOUN
ejpam-6128	199	41	α	α	PROPN
ejpam-6128	199	42	)	)	PUNCT
ejpam-6128	199	43	2	2	NUM
ejpam-6128	199	44	y1	y1	NOUN
ejpam-6128	199	45	y2	y2	INTJ
ejpam-6128	199	46	(	(	PUNCT
ejpam-6128	199	47	e	e	PROPN
ejpam-6128	199	48	ς√	ς√	NUM
ejpam-6128	199	49	α	α	NOUN
ejpam-6128	199	50	+	+	PROPN
ejpam-6128	199	51	e	e	X
ejpam-6128	199	52	−ς√	−ς√	NOUN
ejpam-6128	199	53	α	α	PROPN
ejpam-6128	199	54	)	)	PUNCT
ejpam-6128	199	55	2	2	NUM
ejpam-6128	199	56	y3	y3	NOUN
ejpam-6128	199	57	−	−	PROPN
ejpam-6128	200	1	(	(	PUNCT
ejpam-6128	200	2	e	e	NOUN
ejpam-6128	200	3	−ς√	−ς√	ADP
ejpam-6128	200	4	α	α	PROPN
ejpam-6128	200	5	−e	−e	NOUN
ejpam-6128	200	6	ς√	ς√	NUM
ejpam-6128	200	7	α	α	NOUN
ejpam-6128	200	8	)	)	PUNCT
ejpam-6128	200	9	√	√	NOUN
ejpam-6128	200	10	α	α	PRON
ejpam-6128	200	11	2	2	NUM
ejpam-6128	200	12	y1	y1	NOUN
ejpam-6128	200	13	y4	y4	NOUN
ejpam-6128	200	14	y5	y5	NOUN
ejpam-6128	200	15	y6	y6	ADJ
ejpam-6128	200	16	y5	y5	NOUN
ejpam-6128	200	17	y1	y1	ADJ
ejpam-6128	200	18	eςy2	eςy2	NOUN
ejpam-6128	200	19	y3	y3	NOUN
ejpam-6128	200	20	y4	y4	PROPN
ejpam-6128	200	21	y5	y5	PROPN
ejpam-6128	200	22	y6	y6	ADJ
ejpam-6128	200	23	y6	y6	NOUN
ejpam-6128	200	24	eςy1	eςy1	PROPN
ejpam-6128	200	25	y2	y2	NOUN
ejpam-6128	200	26	eςy3	eςy3	VERB
ejpam-6128	200	27	y4	y4	VERB
ejpam-6128	200	28	y5	y5	NOUN
ejpam-6128	200	29	y6	y6	ADJ
ejpam-6128	200	30	for	for	ADP
ejpam-6128	200	31	lie	lie	NOUN
ejpam-6128	200	32	algebra	algebra	NOUN
ejpam-6128	200	33	(	(	PUNCT
ejpam-6128	200	34	8)	8)	NUM
ejpam-6128	200	35	,	,	PUNCT
ejpam-6128	200	36	the	the	DET
ejpam-6128	200	37	adjoint	adjoint	PROPN
ejpam-6128	200	38	transformation	transformation	NOUN
ejpam-6128	200	39	matrix	matrix	NOUN
ejpam-6128	200	40	is	be	AUX
ejpam-6128	200	41	presented	present	VERB
ejpam-6128	200	42	as	as	SCONJ
ejpam-6128	200	43	follows	follow	VERB
ejpam-6128	200	44	a	a	DET
ejpam-6128	200	45	=	=	NOUN
ejpam-6128	200	46			NOUN
ejpam-6128	200	47	(	(	PUNCT
ejpam-6128	200	48	e	e	PROPN
ejpam-6128	200	49	ς4√	ς4√	PROPN
ejpam-6128	200	50	α+e	α+e	NUM
ejpam-6128	200	51	−ς4√	−ς4√	PRON
ejpam-6128	200	52	α	α	NOUN
ejpam-6128	200	53	)	)	PUNCT
ejpam-6128	200	54	eς6	eς6	NOUN
ejpam-6128	200	55	2	2	NUM
ejpam-6128	200	56	0	0	NUM
ejpam-6128	200	57	(	(	PUNCT
ejpam-6128	200	58	e	e	NOUN
ejpam-6128	200	59	ς4√	ς4√	NUM
ejpam-6128	200	60	α−e	α−e	NUM
ejpam-6128	200	61	−ς4√	−ς4√	PRON
ejpam-6128	200	62	α	α	NOUN
ejpam-6128	200	63	)	)	PUNCT
ejpam-6128	200	64	eς6	eς6	NOUN
ejpam-6128	201	1	2	2	NUM
ejpam-6128	201	2	0	0	NUM
ejpam-6128	201	3	0	0	NUM
ejpam-6128	201	4	0	0	NUM
ejpam-6128	201	5	0	0	NUM
ejpam-6128	201	6	eς5	eς5	ADJ
ejpam-6128	201	7	0	0	NUM
ejpam-6128	201	8	0	0	NUM
ejpam-6128	201	9	0	0	NUM
ejpam-6128	201	10	0	0	NUM
ejpam-6128	201	11	−	−	NOUN
ejpam-6128	201	12	√	√	NUM
ejpam-6128	201	13	α(e	α(e	PROPN
ejpam-6128	202	1	−ς4√	−ς4√	PROPN
ejpam-6128	202	2	α	α	NOUN
ejpam-6128	202	3	−e	−e	VERB
ejpam-6128	202	4	ς4√	ς4√	PROPN
ejpam-6128	202	5	α	α	NOUN
ejpam-6128	202	6	)	)	PUNCT
ejpam-6128	202	7	eς6	eς6	NOUN
ejpam-6128	202	8	2	2	NUM
ejpam-6128	202	9	0	0	NUM
ejpam-6128	202	10	(	(	PUNCT
ejpam-6128	202	11	e	e	PROPN
ejpam-6128	202	12	ς4√	ς4√	PROPN
ejpam-6128	202	13	α+e	α+e	NUM
ejpam-6128	202	14	−ς4√	−ς4√	PRON
ejpam-6128	202	15	α	α	NOUN
ejpam-6128	202	16	)	)	PUNCT
ejpam-6128	202	17	eς6	eς6	NOUN
ejpam-6128	202	18	2	2	NUM
ejpam-6128	202	19	0	0	NUM
ejpam-6128	202	20	0	0	NUM
ejpam-6128	202	21	0	0	NUM
ejpam-6128	202	22	−ς3(e	−ς3(e	NOUN
ejpam-6128	202	23	ς4√	ς4√	PROPN
ejpam-6128	202	24	α+e	α+e	NUM
ejpam-6128	202	25	−ς4√	−ς4√	PRON
ejpam-6128	202	26	α	α	NOUN
ejpam-6128	202	27	)	)	PUNCT
ejpam-6128	202	28	eς6	eς6	NOUN
ejpam-6128	202	29	2	2	NUM
ejpam-6128	203	1	+	+	CCONJ
ejpam-6128	203	2	ς1(e	ς1(e	AUX
ejpam-6128	203	3	−ς4√	−ς4√	PROPN
ejpam-6128	203	4	α	α	NOUN
ejpam-6128	203	5	−e	−e	NOUN
ejpam-6128	203	6	ς4√	ς4√	PROPN
ejpam-6128	203	7	α	α	NOUN
ejpam-6128	203	8	)	)	PUNCT
ejpam-6128	203	9	eς6	eς6	PROPN
ejpam-6128	204	1	2	2	NUM
ejpam-6128	204	2	√	√	NOUN
ejpam-6128	204	3	α	α	NOUN
ejpam-6128	204	4	0	0	NUM
ejpam-6128	204	5	−ς3(e	−ς3(e	NOUN
ejpam-6128	204	6	ς4√	ς4√	PROPN
ejpam-6128	204	7	α−e	α−e	NUM
ejpam-6128	204	8	−ς4√	−ς4√	PRON
ejpam-6128	204	9	α	α	NOUN
ejpam-6128	204	10	)	)	PUNCT
ejpam-6128	204	11	eς6	eς6	PROPN
ejpam-6128	204	12	2	2	NUM
ejpam-6128	204	13	√	√	NUM
ejpam-6128	204	14	α	α	NOUN
ejpam-6128	204	15	−	−	NOUN
ejpam-6128	204	16	ς1(e	ς1(e	PROPN
ejpam-6128	204	17	ς4√	ς4√	PROPN
ejpam-6128	204	18	α+e	α+e	NUM
ejpam-6128	204	19	−ς4√	−ς4√	PRON
ejpam-6128	204	20	α	α	NOUN
ejpam-6128	204	21	)	)	PUNCT
ejpam-6128	205	1	eς6	eς6	NOUN
ejpam-6128	205	2	2α	2α	NOUN
ejpam-6128	205	3	1	1	NUM
ejpam-6128	205	4	0	0	NUM
ejpam-6128	205	5	0	0	NUM
ejpam-6128	205	6	0	0	NUM
ejpam-6128	206	1	−ς2e	−ς2e	NOUN
ejpam-6128	207	1	ς5	ς5	NOUN
ejpam-6128	207	2	0	0	NUM
ejpam-6128	207	3	0	0	NUM
ejpam-6128	207	4	1	1	NUM
ejpam-6128	207	5	0	0	NUM
ejpam-6128	207	6	−ς1(e	−ς1(e	PROPN
ejpam-6128	207	7	ς4√	ς4√	PROPN
ejpam-6128	207	8	α+e	α+e	NUM
ejpam-6128	207	9	−ς4√	−ς4√	PRON
ejpam-6128	207	10	α	α	NOUN
ejpam-6128	207	11	)	)	PUNCT
ejpam-6128	207	12	eς6	eς6	NOUN
ejpam-6128	207	13	2	2	NUM
ejpam-6128	207	14	+	+	NOUN
ejpam-6128	207	15	ς3	ς3	NOUN
ejpam-6128	207	16	√	√	ADP
ejpam-6128	207	17	α(e	α(e	PROPN
ejpam-6128	207	18	−ς4√	−ς4√	PROPN
ejpam-6128	207	19	α	α	NOUN
ejpam-6128	207	20	−e	−e	VERB
ejpam-6128	207	21	ς4√	ς4√	PROPN
ejpam-6128	207	22	α	α	NOUN
ejpam-6128	207	23	)	)	PUNCT
ejpam-6128	207	24	eς6	eς6	NOUN
ejpam-6128	207	25	2	2	NUM
ejpam-6128	207	26	0	0	NUM
ejpam-6128	207	27	−ς1(e	−ς1(e	PROPN
ejpam-6128	207	28	ς4√	ς4√	PROPN
ejpam-6128	207	29	α−e	α−e	NUM
ejpam-6128	207	30	−ς4√	−ς4√	PRON
ejpam-6128	207	31	α	α	NOUN
ejpam-6128	207	32	)	)	PUNCT
ejpam-6128	207	33	eς6	eς6	PROPN
ejpam-6128	207	34	2	2	NUM
ejpam-6128	207	35	√	√	NUM
ejpam-6128	207	36	α	α	PRON
ejpam-6128	207	37	−	−	NOUN
ejpam-6128	207	38	ς3	ς3	NOUN
ejpam-6128	207	39	√	√	ADP
ejpam-6128	207	40	α(e	α(e	PROPN
ejpam-6128	207	41	ς4√	ς4√	PROPN
ejpam-6128	207	42	α+e	α+e	NUM
ejpam-6128	207	43	−	−	NOUN
ejpam-6128	207	44	ς4√	ς4√	PROPN
ejpam-6128	207	45	α	α	NOUN
ejpam-6128	207	46	)	)	PUNCT
ejpam-6128	207	47	eς6	eς6	NOUN
ejpam-6128	207	48	2	2	NUM
ejpam-6128	207	49	0	0	NUM
ejpam-6128	207	50	0	0	NUM
ejpam-6128	207	51	1	1	NUM
ejpam-6128	207	52			NUM
ejpam-6128	207	53	by	by	ADP
ejpam-6128	207	54	using	use	VERB
ejpam-6128	207	55	adjoint	adjoint	NOUN
ejpam-6128	207	56	transformation	transformation	NOUN
ejpam-6128	207	57	matrix	matrix	NOUN
ejpam-6128	207	58	in	in	ADP
ejpam-6128	207	59	(	(	PUNCT
ejpam-6128	207	60	17	17	NUM
ejpam-6128	207	61	)	)	PUNCT
ejpam-6128	207	62	,	,	PUNCT
ejpam-6128	207	63	we	we	PRON
ejpam-6128	207	64	obtain	obtain	VERB
ejpam-6128	207	65	the	the	DET
ejpam-6128	207	66	following	follow	VERB
ejpam-6128	207	67	system	system	NOUN
ejpam-6128	207	68	of	of	ADP
ejpam-6128	207	69	equations	equation	NOUN
ejpam-6128	207	70	m.	m.	PROPN
ejpam-6128	207	71	usman	usman	PROPN
ejpam-6128	207	72	,	,	PUNCT
ejpam-6128	207	73	a.	a.	NOUN
ejpam-6128	207	74	hussain	hussain	PROPN
ejpam-6128	207	75	,	,	PUNCT
ejpam-6128	207	76	m.	m.	PROPN
ejpam-6128	207	77	u.	u.	PROPN
ejpam-6128	207	78	farooq	farooq	PROPN
ejpam-6128	207	79	,	,	PUNCT
ejpam-6128	207	80	j.	j.	PROPN
ejpam-6128	207	81	herrera	herrera	PROPN
ejpam-6128	207	82	/	/	SYM
ejpam-6128	207	83	eur	eur	PROPN
ejpam-6128	207	84	.	.	PUNCT
ejpam-6128	208	1	j.	j.	PROPN
ejpam-6128	208	2	pure	pure	PROPN
ejpam-6128	208	3	appl	appl	PROPN
ejpam-6128	208	4	.	.	PROPN
ejpam-6128	208	5	math	math	PROPN
ejpam-6128	208	6	,	,	PUNCT
ejpam-6128	208	7	18	18	NUM
ejpam-6128	208	8	(	(	PUNCT
ejpam-6128	208	9	4	4	NUM
ejpam-6128	208	10	)	)	PUNCT
ejpam-6128	208	11	(	(	PUNCT
ejpam-6128	208	12	2025	2025	NUM
ejpam-6128	208	13	)	)	PUNCT
ejpam-6128	208	14	,	,	PUNCT
ejpam-6128	208	15	6128	6128	NUM
ejpam-6128	208	16	10	10	NUM
ejpam-6128	208	17	of	of	ADP
ejpam-6128	208	18	29	29	NUM
ejpam-6128	208	19	k̃1	k̃1	PROPN
ejpam-6128	208	20	=	=	SYM
ejpam-6128	208	21	k1	k1	PROPN
ejpam-6128	208	22	(	(	PUNCT
ejpam-6128	208	23	e	e	NOUN
ejpam-6128	208	24	ς4√	ς4√	PROPN
ejpam-6128	208	25	α	α	NOUN
ejpam-6128	208	26	+	+	X
ejpam-6128	208	27	e	e	NOUN
ejpam-6128	208	28	−ς4√	−ς4√	PROPN
ejpam-6128	208	29	α	α	NOUN
ejpam-6128	208	30	)	)	PUNCT
ejpam-6128	209	1	eς6	eς6	NOUN
ejpam-6128	209	2	2	2	NUM
ejpam-6128	209	3	−	−	NOUN
ejpam-6128	209	4	k3	k3	VERB
ejpam-6128	209	5	√	√	PROPN
ejpam-6128	209	6	α(e	α(e	PROPN
ejpam-6128	209	7	−ς4√	−ς4√	NOUN
ejpam-6128	209	8	α	α	NOUN
ejpam-6128	209	9	−	−	NOUN
ejpam-6128	209	10	e	e	NOUN
ejpam-6128	209	11	ς4√	ς4√	PROPN
ejpam-6128	209	12	α	α	NOUN
ejpam-6128	209	13	)	)	PUNCT
ejpam-6128	209	14	eς6	eς6	NOUN
ejpam-6128	209	15	2	2	NUM
ejpam-6128	209	16	+	+	CCONJ
ejpam-6128	209	17	k4	k4	ADJ
ejpam-6128	209	18	(	(	PUNCT
ejpam-6128	209	19	−ς3(e	−ς3(e	NOUN
ejpam-6128	209	20	ς4√	ς4√	PROPN
ejpam-6128	209	21	α	α	NOUN
ejpam-6128	209	22	+	+	X
ejpam-6128	209	23	e	e	NOUN
ejpam-6128	209	24	−ς4√	−ς4√	PROPN
ejpam-6128	209	25	α	α	NOUN
ejpam-6128	209	26	)	)	PUNCT
ejpam-6128	209	27	eς6	eς6	NOUN
ejpam-6128	209	28	2	2	NUM
ejpam-6128	209	29	+	+	CCONJ
ejpam-6128	209	30	ς1(e	ς1(e	PROPN
ejpam-6128	210	1	−ς4√	−ς4√	NOUN
ejpam-6128	210	2	α	α	NOUN
ejpam-6128	210	3	−	−	NOUN
ejpam-6128	210	4	e	e	NOUN
ejpam-6128	210	5	ς4√	ς4√	PROPN
ejpam-6128	210	6	α	α	NOUN
ejpam-6128	210	7	)	)	PUNCT
ejpam-6128	210	8	eς6	eς6	PROPN
ejpam-6128	210	9	2	2	NUM
ejpam-6128	210	10	√	√	PROPN
ejpam-6128	210	11	α	α	NOUN
ejpam-6128	210	12	)	)	PUNCT
ejpam-6128	211	1	+	+	CCONJ
ejpam-6128	211	2	k6	k6	NOUN
ejpam-6128	211	3	(	(	PUNCT
ejpam-6128	211	4	−ς1(e	−ς1(e	VERB
ejpam-6128	211	5	ς4√	ς4√	PROPN
ejpam-6128	211	6	α	α	NOUN
ejpam-6128	211	7	+	+	X
ejpam-6128	211	8	e	e	NOUN
ejpam-6128	211	9	−ς4√	−ς4√	PROPN
ejpam-6128	211	10	α	α	NOUN
ejpam-6128	211	11	)	)	PUNCT
ejpam-6128	211	12	eς6	eς6	NOUN
ejpam-6128	211	13	2	2	NUM
ejpam-6128	211	14	+	+	NOUN
ejpam-6128	211	15	ς3	ς3	NOUN
ejpam-6128	211	16	√	√	ADP
ejpam-6128	211	17	α(e	α(e	PROPN
ejpam-6128	211	18	−ς4√	−ς4√	NOUN
ejpam-6128	211	19	α	α	NOUN
ejpam-6128	211	20	−	−	NOUN
ejpam-6128	211	21	e	e	NOUN
ejpam-6128	211	22	ς4√	ς4√	PROPN
ejpam-6128	211	23	α	α	NOUN
ejpam-6128	211	24	)	)	PUNCT
ejpam-6128	211	25	eς6	eς6	NOUN
ejpam-6128	211	26	2	2	NUM
ejpam-6128	211	27	)	)	PUNCT
ejpam-6128	211	28	,	,	PUNCT
ejpam-6128	212	1	k̃2	k̃2	PROPN
ejpam-6128	212	2	=	=	SYM
ejpam-6128	212	3	k2e	k2e	PROPN
ejpam-6128	212	4	ς5	ς5	PROPN
ejpam-6128	212	5	−	−	PROPN
ejpam-6128	212	6	k5ς2e	k5ς2e	X
ejpam-6128	212	7	ς5	ς5	NOUN
ejpam-6128	212	8	,	,	PUNCT
ejpam-6128	212	9	k̃3	k̃3	PROPN
ejpam-6128	212	10	=	=	SYM
ejpam-6128	212	11	k1	k1	NOUN
ejpam-6128	212	12	(	(	PUNCT
ejpam-6128	212	13	e	e	NOUN
ejpam-6128	212	14	ς4√	ς4√	PROPN
ejpam-6128	212	15	α	α	NOUN
ejpam-6128	212	16	−	−	NOUN
ejpam-6128	212	17	e	e	NOUN
ejpam-6128	212	18	−ς4√	−ς4√	PROPN
ejpam-6128	212	19	α	α	NOUN
ejpam-6128	212	20	)	)	PUNCT
ejpam-6128	212	21	eς6	eς6	NOUN
ejpam-6128	212	22	2	2	NUM
ejpam-6128	212	23	+	+	CCONJ
ejpam-6128	212	24	k3	k3	X
ejpam-6128	212	25	(	(	PUNCT
ejpam-6128	212	26	e	e	NOUN
ejpam-6128	212	27	ς4√	ς4√	PROPN
ejpam-6128	212	28	α	α	NOUN
ejpam-6128	212	29	+	+	X
ejpam-6128	212	30	e	e	NOUN
ejpam-6128	212	31	−ς4√	−ς4√	PROPN
ejpam-6128	212	32	α	α	NOUN
ejpam-6128	212	33	)	)	PUNCT
ejpam-6128	212	34	eς6	eς6	NOUN
ejpam-6128	212	35	2	2	NUM
ejpam-6128	212	36	+	+	CCONJ
ejpam-6128	212	37	k4	k4	ADJ
ejpam-6128	212	38	(	(	PUNCT
ejpam-6128	212	39	−ς3(e	−ς3(e	NOUN
ejpam-6128	212	40	ς4√	ς4√	PROPN
ejpam-6128	212	41	α	α	NOUN
ejpam-6128	212	42	−	−	NOUN
ejpam-6128	212	43	e	e	NOUN
ejpam-6128	212	44	−ς4√	−ς4√	PROPN
ejpam-6128	212	45	α	α	NOUN
ejpam-6128	212	46	)	)	PUNCT
ejpam-6128	212	47	eς6	eς6	PROPN
ejpam-6128	212	48	2	2	NUM
ejpam-6128	212	49	√	√	NUM
ejpam-6128	212	50	α	α	NOUN
ejpam-6128	212	51	−	−	NOUN
ejpam-6128	212	52	ς1(e	ς1(e	PROPN
ejpam-6128	212	53	ς4√	ς4√	SYM
ejpam-6128	212	54	α	α	NOUN
ejpam-6128	212	55	+	+	X
ejpam-6128	212	56	e	e	NOUN
ejpam-6128	212	57	−ς4√	−ς4√	PROPN
ejpam-6128	212	58	α	α	NOUN
ejpam-6128	212	59	)	)	PUNCT
ejpam-6128	212	60	eς6	eς6	PROPN
ejpam-6128	212	61	2α	2α	NOUN
ejpam-6128	212	62	)	)	PUNCT
ejpam-6128	213	1	+	+	CCONJ
ejpam-6128	213	2	k6	k6	NOUN
ejpam-6128	213	3	(	(	PUNCT
ejpam-6128	213	4	−ς1(e	−ς1(e	VERB
ejpam-6128	213	5	ς4√	ς4√	PROPN
ejpam-6128	213	6	α	α	NOUN
ejpam-6128	213	7	−	−	NOUN
ejpam-6128	213	8	e	e	NOUN
ejpam-6128	213	9	−ς4√	−ς4√	PROPN
ejpam-6128	213	10	α	α	NOUN
ejpam-6128	213	11	)	)	PUNCT
ejpam-6128	213	12	eς6	eς6	PROPN
ejpam-6128	213	13	2	2	NUM
ejpam-6128	213	14	√	√	NUM
ejpam-6128	213	15	α	α	PRON
ejpam-6128	213	16	−	−	NOUN
ejpam-6128	213	17	ς3	ς3	NOUN
ejpam-6128	213	18	√	√	ADP
ejpam-6128	213	19	α(e	α(e	PROPN
ejpam-6128	213	20	ς4√	ς4√	PROPN
ejpam-6128	213	21	α	α	NOUN
ejpam-6128	214	1	+	+	NOUN
ejpam-6128	214	2	e	e	NOUN
ejpam-6128	214	3	−	−	PROPN
ejpam-6128	214	4	ς4√	ς4√	PROPN
ejpam-6128	214	5	α	α	NOUN
ejpam-6128	214	6	)	)	PUNCT
ejpam-6128	214	7	eς6	eς6	NOUN
ejpam-6128	214	8	2	2	NUM
ejpam-6128	214	9	)	)	PUNCT
ejpam-6128	214	10	,	,	PUNCT
ejpam-6128	214	11	k̃4	k̃4	PROPN
ejpam-6128	214	12	=	=	PUNCT
ejpam-6128	214	13	k4	k4	PROPN
ejpam-6128	214	14	,	,	PUNCT
ejpam-6128	214	15	k̃5	k̃5	PROPN
ejpam-6128	214	16	=	=	SYM
ejpam-6128	214	17	k5	k5	PROPN
ejpam-6128	214	18	,	,	PUNCT
ejpam-6128	214	19	k̃6	k̃6	PROPN
ejpam-6128	214	20	=	=	PUNCT
ejpam-6128	214	21	k6	k6	PROPN
ejpam-6128	214	22	.	.	PUNCT
ejpam-6128	215	1	(	(	PUNCT
ejpam-6128	215	2	27	27	NUM
ejpam-6128	215	3	)	)	PUNCT
ejpam-6128	215	4	for	for	ADP
ejpam-6128	215	5	the	the	DET
ejpam-6128	215	6	computation	computation	NOUN
ejpam-6128	215	7	of	of	ADP
ejpam-6128	215	8	basic	basic	ADJ
ejpam-6128	215	9	invariants	invariant	NOUN
ejpam-6128	215	10	,	,	PUNCT
ejpam-6128	215	11	we	we	PRON
ejpam-6128	215	12	have	have	VERB
ejpam-6128	215	13	the	the	DET
ejpam-6128	215	14	following	follow	VERB
ejpam-6128	215	15	system	system	NOUN
ejpam-6128	215	16	of	of	ADP
ejpam-6128	215	17	linear	linear	ADJ
ejpam-6128	215	18	pdes	pde	NOUN
ejpam-6128	215	19	derived	derive	VERB
ejpam-6128	215	20	from	from	ADP
ejpam-6128	215	21	(	(	PUNCT
ejpam-6128	215	22	15	15	NUM
ejpam-6128	215	23	)	)	PUNCT
ejpam-6128	215	24	.	.	PUNCT
ejpam-6128	216	1	k6	k6	PROPN
ejpam-6128	216	2	∂ϑ	∂ϑ	PROPN
ejpam-6128	216	3	∂k1	∂k1	PROPN
ejpam-6128	216	4	+	+	CCONJ
ejpam-6128	216	5	k4	k4	ADJ
ejpam-6128	216	6	α	α	PROPN
ejpam-6128	216	7	∂ϑ	∂ϑ	PROPN
ejpam-6128	216	8	∂k3	∂k3	PROPN
ejpam-6128	216	9	=	=	SYM
ejpam-6128	216	10	0	0	PROPN
ejpam-6128	216	11	,	,	PUNCT
ejpam-6128	216	12	k5	k5	PROPN
ejpam-6128	216	13	∂ϑ	∂ϑ	PROPN
ejpam-6128	216	14	∂k2	∂k2	PROPN
ejpam-6128	216	15	=	=	NOUN
ejpam-6128	216	16	0	0	NUM
ejpam-6128	216	17	,	,	PUNCT
ejpam-6128	216	18	k4	k4	PROPN
ejpam-6128	216	19	∂ϑ	∂ϑ	PROPN
ejpam-6128	216	20	∂k1	∂k1	PROPN
ejpam-6128	216	21	+	+	NUM
ejpam-6128	216	22	k6	k6	PROPN
ejpam-6128	216	23	∂ϑ	∂ϑ	PROPN
ejpam-6128	216	24	∂k3	∂k3	PROPN
ejpam-6128	216	25	=	=	SYM
ejpam-6128	216	26	0	0	NUM
ejpam-6128	216	27	,	,	PUNCT
ejpam-6128	216	28	k3	k3	AUX
ejpam-6128	216	29	∂ϑ	∂ϑ	PROPN
ejpam-6128	216	30	∂k1	∂k1	VERB
ejpam-6128	217	1	+	+	CCONJ
ejpam-6128	217	2	k1	k1	PROPN
ejpam-6128	217	3	α	α	PROPN
ejpam-6128	217	4	∂ϑ	∂ϑ	PROPN
ejpam-6128	217	5	∂k3	∂k3	NOUN
ejpam-6128	217	6	=	=	SYM
ejpam-6128	217	7	0	0	PROPN
ejpam-6128	217	8	,	,	PUNCT
ejpam-6128	217	9	k2	k2	PROPN
ejpam-6128	217	10	∂ϑ	∂ϑ	PROPN
ejpam-6128	217	11	∂k2	∂k2	PROPN
ejpam-6128	217	12	=	=	SYM
ejpam-6128	217	13	0	0	NUM
ejpam-6128	217	14	,	,	PUNCT
ejpam-6128	217	15	k1	k1	PROPN
ejpam-6128	217	16	∂ϑ	∂ϑ	PROPN
ejpam-6128	217	17	∂k1	∂k1	VERB
ejpam-6128	217	18	+	+	CCONJ
ejpam-6128	217	19	k3	k3	PROPN
ejpam-6128	217	20	∂ϑ	∂ϑ	PROPN
ejpam-6128	217	21	∂k3	∂k3	NOUN
ejpam-6128	217	22	=	=	SYM
ejpam-6128	217	23	0	0	PROPN
ejpam-6128	217	24	.	.	PUNCT
ejpam-6128	218	1	(	(	PUNCT
ejpam-6128	218	2	28	28	NUM
ejpam-6128	218	3	)	)	PUNCT
ejpam-6128	218	4	this	this	PRON
ejpam-6128	218	5	implies	imply	VERB
ejpam-6128	218	6	φ(k1	φ(k1	PROPN
ejpam-6128	218	7	,	,	PUNCT
ejpam-6128	218	8	k2	k2	ADJ
ejpam-6128	218	9	,	,	PUNCT
ejpam-6128	218	10	k3	k3	PROPN
ejpam-6128	218	11	,	,	PUNCT
ejpam-6128	218	12	k4	k4	PROPN
ejpam-6128	218	13	,	,	PUNCT
ejpam-6128	218	14	k5	k5	PROPN
ejpam-6128	218	15	,	,	PUNCT
ejpam-6128	218	16	k6	k6	NOUN
ejpam-6128	218	17	)	)	PUNCT
ejpam-6128	218	18	=	=	SYM
ejpam-6128	218	19	f	f	PROPN
ejpam-6128	218	20	(	(	PUNCT
ejpam-6128	218	21	k4	k4	PROPN
ejpam-6128	218	22	,	,	PUNCT
ejpam-6128	218	23	k5	k5	PROPN
ejpam-6128	218	24	,	,	PUNCT
ejpam-6128	218	25	k6	k6	PROPN
ejpam-6128	218	26	)	)	PUNCT
ejpam-6128	218	27	.	.	PUNCT
ejpam-6128	219	1	so	so	ADV
ejpam-6128	219	2	,	,	PUNCT
ejpam-6128	219	3	the	the	DET
ejpam-6128	219	4	invariants	invariant	NOUN
ejpam-6128	219	5	k4	k4	PROPN
ejpam-6128	219	6	,	,	PUNCT
ejpam-6128	219	7	k5	k5	PROPN
ejpam-6128	219	8	and	and	CCONJ
ejpam-6128	219	9	k6	k6	PROPN
ejpam-6128	219	10	are	be	AUX
ejpam-6128	219	11	the	the	DET
ejpam-6128	219	12	vertices	vertex	NOUN
ejpam-6128	219	13	of	of	ADP
ejpam-6128	219	14	the	the	DET
ejpam-6128	219	15	tree	tree	NOUN
ejpam-6128	219	16	.	.	PUNCT
ejpam-6128	220	1	m.	m.	PROPN
ejpam-6128	220	2	usman	usman	PROPN
ejpam-6128	220	3	,	,	PUNCT
ejpam-6128	220	4	a.	a.	NOUN
ejpam-6128	220	5	hussain	hussain	PROPN
ejpam-6128	220	6	,	,	PUNCT
ejpam-6128	220	7	m.	m.	PROPN
ejpam-6128	220	8	u.	u.	PROPN
ejpam-6128	220	9	farooq	farooq	PROPN
ejpam-6128	220	10	,	,	PUNCT
ejpam-6128	220	11	j.	j.	PROPN
ejpam-6128	220	12	herrera	herrera	PROPN
ejpam-6128	220	13	/	/	SYM
ejpam-6128	220	14	eur	eur	PROPN
ejpam-6128	220	15	.	.	PUNCT
ejpam-6128	221	1	j.	j.	PROPN
ejpam-6128	221	2	pure	pure	PROPN
ejpam-6128	221	3	appl	appl	PROPN
ejpam-6128	221	4	.	.	PROPN
ejpam-6128	221	5	math	math	PROPN
ejpam-6128	221	6	,	,	PUNCT
ejpam-6128	221	7	18	18	NUM
ejpam-6128	221	8	(	(	PUNCT
ejpam-6128	221	9	4	4	NUM
ejpam-6128	221	10	)	)	PUNCT
ejpam-6128	221	11	(	(	PUNCT
ejpam-6128	221	12	2025	2025	NUM
ejpam-6128	221	13	)	)	PUNCT
ejpam-6128	221	14	,	,	PUNCT
ejpam-6128	221	15	6128	6128	NUM
ejpam-6128	221	16	11	11	NUM
ejpam-6128	221	17	of	of	ADP
ejpam-6128	221	18	29	29	NUM
ejpam-6128	221	19	k6	k6	NOUN
ejpam-6128	221	20	k6	k6	NOUN
ejpam-6128	221	21	=	=	SYM
ejpam-6128	221	22	0	0	NUM
ejpam-6128	221	23	k5	k5	PROPN
ejpam-6128	221	24	=	=	SYM
ejpam-6128	221	25	0	0	NUM
ejpam-6128	221	26	k4	k4	NOUN
ejpam-6128	221	27	=	=	SYM
ejpam-6128	221	28	0	0	NUM
ejpam-6128	221	29	case-8	case-8	PROPN
ejpam-6128	221	30	k4	k4	NOUN
ejpam-6128	221	31	6=	6=	SYM
ejpam-6128	221	32	0	0	NUM
ejpam-6128	221	33	case-7	case-7	NUM
ejpam-6128	221	34	k5	k5	PROPN
ejpam-6128	221	35	6=	6=	ADP
ejpam-6128	221	36	0	0	NUM
ejpam-6128	221	37	k4	k4	NOUN
ejpam-6128	221	38	=	=	SYM
ejpam-6128	221	39	0	0	PUNCT
ejpam-6128	222	1	case-6	case-6	VERB
ejpam-6128	222	2	k4	k4	NOUN
ejpam-6128	222	3	6=	6=	ADP
ejpam-6128	222	4	0	0	NUM
ejpam-6128	223	1	case-5	case-5	NUM
ejpam-6128	223	2	k6	k6	NOUN
ejpam-6128	223	3	6=	6=	SYM
ejpam-6128	223	4	0	0	NUM
ejpam-6128	223	5	k5	k5	PROPN
ejpam-6128	223	6	=	=	SYM
ejpam-6128	223	7	0	0	NUM
ejpam-6128	223	8	k4	k4	NOUN
ejpam-6128	223	9	=	=	NOUN
ejpam-6128	223	10	0	0	NUM
ejpam-6128	223	11	case-4	case-4	NUM
ejpam-6128	223	12	k4	k4	NOUN
ejpam-6128	223	13	6=	6=	ADP
ejpam-6128	223	14	0	0	NUM
ejpam-6128	223	15	case-3	case-3	NUM
ejpam-6128	223	16	k5	k5	PROPN
ejpam-6128	223	17	6=	6=	ADP
ejpam-6128	223	18	0	0	NUM
ejpam-6128	223	19	k4	k4	NOUN
ejpam-6128	223	20	=	=	NOUN
ejpam-6128	223	21	0	0	PUNCT
ejpam-6128	223	22	case-2	case-2	NUM
ejpam-6128	223	23	k4	k4	NOUN
ejpam-6128	223	24	6=	6=	ADP
ejpam-6128	223	25	0	0	NUM
ejpam-6128	223	26	case-1	case-1	NUM
ejpam-6128	223	27	case-1	case-1	NUM
ejpam-6128	223	28	:	:	PUNCT
ejpam-6128	223	29	for	for	ADP
ejpam-6128	223	30	k6	k6	PROPN
ejpam-6128	223	31	6=	6=	ADP
ejpam-6128	223	32	0	0	NUM
ejpam-6128	223	33	,	,	PUNCT
ejpam-6128	223	34	k5	k5	PROPN
ejpam-6128	223	35	6=	6=	ADP
ejpam-6128	223	36	0	0	NUM
ejpam-6128	223	37	,	,	PUNCT
ejpam-6128	223	38	k4	k4	PROPN
ejpam-6128	223	39	6=	6=	ADP
ejpam-6128	223	40	0	0	NUM
ejpam-6128	223	41	,	,	PUNCT
ejpam-6128	223	42	we	we	PRON
ejpam-6128	223	43	have	have	VERB
ejpam-6128	223	44	n1	n1	PROPN
ejpam-6128	223	45	=	=	SYM
ejpam-6128	223	46	y4+y5+y6	y4+y5+y6	PROPN
ejpam-6128	223	47	.	.	PUNCT
ejpam-6128	224	1	by	by	ADP
ejpam-6128	224	2	substituting	substitute	VERB
ejpam-6128	224	3	k̃4	k̃4	PROPN
ejpam-6128	224	4	=	=	PUNCT
ejpam-6128	224	5	k̃5	k̃5	PROPN
ejpam-6128	224	6	=	=	PUNCT
ejpam-6128	224	7	k̃6	k̃6	PROPN
ejpam-6128	224	8	=	=	NOUN
ejpam-6128	224	9	1	1	NUM
ejpam-6128	224	10	in	in	ADP
ejpam-6128	224	11	(	(	PUNCT
ejpam-6128	224	12	27	27	NUM
ejpam-6128	224	13	)	)	PUNCT
ejpam-6128	224	14	,	,	PUNCT
ejpam-6128	224	15	we	we	PRON
ejpam-6128	224	16	obtain	obtain	VERB
ejpam-6128	224	17	ς1	ς1	NOUN
ejpam-6128	224	18	=	=	SYM
ejpam-6128	224	19	√	√	NUM
ejpam-6128	225	1	αk1k6+k3	αk1k6+k3	NUM
ejpam-6128	226	1	(	(	PUNCT
ejpam-6128	226	2	k4	k4	NOUN
ejpam-6128	226	3	α	α	PROPN
ejpam-6128	226	4	+	+	NOUN
ejpam-6128	226	5	√	√	ADJ
ejpam-6128	226	6	α	α	NUM
ejpam-6128	226	7	2	2	NUM
ejpam-6128	226	8	k6	k6	NOUN
ejpam-6128	226	9	2	2	NUM
ejpam-6128	226	10	)	)	PUNCT
ejpam-6128	226	11	,	,	PUNCT
ejpam-6128	226	12	ς2	ς2	PROPN
ejpam-6128	226	13	=	=	SYM
ejpam-6128	226	14	k2	k2	PROPN
ejpam-6128	226	15	k5	k5	PROPN
ejpam-6128	226	16	,	,	PUNCT
ejpam-6128	226	17	ς3	ς3	NOUN
ejpam-6128	226	18	=	=	SYM
ejpam-6128	226	19	k1	k1	NOUN
ejpam-6128	226	20	k4	k4	NOUN
ejpam-6128	226	21	−	−	PROPN
ejpam-6128	226	22	k6	k6	NOUN
ejpam-6128	226	23	2k4	2k4	NUM
ejpam-6128	226	24	(	(	PUNCT
ejpam-6128	226	25	√	√	NUM
ejpam-6128	226	26	αk1k6+k3	αk1k6+k3	NUM
ejpam-6128	226	27	(	(	PUNCT
ejpam-6128	226	28	k4	k4	NOUN
ejpam-6128	226	29	α	α	PROPN
ejpam-6128	226	30	+	+	NOUN
ejpam-6128	226	31	√	√	ADJ
ejpam-6128	226	32	α	α	NUM
ejpam-6128	226	33	2	2	NUM
ejpam-6128	226	34	k6	k6	NOUN
ejpam-6128	226	35	2	2	NUM
ejpam-6128	226	36	)	)	PUNCT
ejpam-6128	226	37	)	)	PUNCT
ejpam-6128	226	38	,	,	PUNCT
ejpam-6128	226	39	ς4	ς4	NOUN
ejpam-6128	226	40	=	=	SYM
ejpam-6128	226	41	0	0	NUM
ejpam-6128	226	42	.	.	PUNCT
ejpam-6128	227	1	case-2	case-2	NUM
ejpam-6128	227	2	:	:	PUNCT
ejpam-6128	227	3	for	for	SCONJ
ejpam-6128	227	4	k6	k6	PROPN
ejpam-6128	227	5	6=	6=	ADP
ejpam-6128	227	6	0	0	NUM
ejpam-6128	227	7	,	,	PUNCT
ejpam-6128	227	8	k5	k5	PROPN
ejpam-6128	227	9	6=	6=	ADP
ejpam-6128	227	10	0	0	NUM
ejpam-6128	227	11	,	,	PUNCT
ejpam-6128	227	12	k4	k4	NOUN
ejpam-6128	227	13	=	=	SYM
ejpam-6128	227	14	0	0	NUM
ejpam-6128	227	15	,	,	PUNCT
ejpam-6128	227	16	we	we	PRON
ejpam-6128	227	17	have	have	VERB
ejpam-6128	227	18	n2	n2	NOUN
ejpam-6128	227	19	=	=	PUNCT
ejpam-6128	227	20	y5	y5	NOUN
ejpam-6128	227	21	+	+	CCONJ
ejpam-6128	227	22	y6	y6	ADJ
ejpam-6128	227	23	.	.	PUNCT
ejpam-6128	228	1	by	by	ADP
ejpam-6128	228	2	substituting	substitute	VERB
ejpam-6128	228	3	k̃5	k̃5	PROPN
ejpam-6128	228	4	=	=	PUNCT
ejpam-6128	228	5	k̃6	k̃6	PROPN
ejpam-6128	228	6	=	=	NOUN
ejpam-6128	228	7	1	1	NUM
ejpam-6128	228	8	in	in	ADP
ejpam-6128	228	9	(	(	PUNCT
ejpam-6128	228	10	27	27	NUM
ejpam-6128	228	11	)	)	PUNCT
ejpam-6128	228	12	,	,	PUNCT
ejpam-6128	228	13	we	we	PRON
ejpam-6128	228	14	obtain	obtain	VERB
ejpam-6128	228	15	ς1	ς1	NOUN
ejpam-6128	228	16	=	=	SYM
ejpam-6128	228	17	2k1	2k1	NUM
ejpam-6128	228	18	k6	k6	NOUN
ejpam-6128	228	19	,	,	PUNCT
ejpam-6128	228	20	ς2	ς2	PROPN
ejpam-6128	228	21	=	=	PROPN
ejpam-6128	228	22	k2	k2	PROPN
ejpam-6128	228	23	k5	k5	PROPN
ejpam-6128	228	24	,	,	PUNCT
ejpam-6128	228	25	ς3	ς3	NOUN
ejpam-6128	228	26	=	=	SYM
ejpam-6128	228	27	k3√	k3√	ADJ
ejpam-6128	228	28	αk6	αk6	NOUN
ejpam-6128	228	29	,	,	PUNCT
ejpam-6128	228	30	ς4	ς4	PROPN
ejpam-6128	228	31	=	=	SYM
ejpam-6128	228	32	0	0	NUM
ejpam-6128	228	33	.	.	PUNCT
ejpam-6128	229	1	case-3	case-3	PROPN
ejpam-6128	229	2	:	:	PUNCT
ejpam-6128	229	3	for	for	ADP
ejpam-6128	229	4	k6	k6	PROPN
ejpam-6128	229	5	6=	6=	ADP
ejpam-6128	229	6	0	0	NUM
ejpam-6128	229	7	,	,	PUNCT
ejpam-6128	229	8	k5	k5	PROPN
ejpam-6128	229	9	=	=	SYM
ejpam-6128	229	10	0	0	PROPN
ejpam-6128	229	11	,	,	PUNCT
ejpam-6128	229	12	k4	k4	PROPN
ejpam-6128	229	13	6=	6=	ADP
ejpam-6128	229	14	0	0	NUM
ejpam-6128	229	15	,	,	PUNCT
ejpam-6128	229	16	we	we	PRON
ejpam-6128	229	17	have	have	VERB
ejpam-6128	229	18	n3	n3	NOUN
ejpam-6128	229	19	=	=	PUNCT
ejpam-6128	229	20	y6	y6	PROPN
ejpam-6128	230	1	+	+	NOUN
ejpam-6128	230	2	y4	y4	ADJ
ejpam-6128	230	3	+	+	X
ejpam-6128	230	4	ay2	ay2	PROPN
ejpam-6128	230	5	,	,	PUNCT
ejpam-6128	230	6	a	a	DET
ejpam-6128	230	7	∈	∈	PROPN
ejpam-6128	230	8	r.	r.	NOUN
ejpam-6128	230	9	by	by	ADP
ejpam-6128	230	10	substituting	substitute	VERB
ejpam-6128	230	11	k̃2	k̃2	PROPN
ejpam-6128	230	12	=	=	SYM
ejpam-6128	230	13	k̃4	k̃4	PROPN
ejpam-6128	230	14	=	=	PUNCT
ejpam-6128	230	15	k̃6	k̃6	PROPN
ejpam-6128	230	16	=	=	NOUN
ejpam-6128	230	17	1	1	NUM
ejpam-6128	230	18	in	in	ADP
ejpam-6128	230	19	(	(	PUNCT
ejpam-6128	230	20	27	27	NUM
ejpam-6128	230	21	)	)	PUNCT
ejpam-6128	230	22	,	,	PUNCT
ejpam-6128	230	23	we	we	PRON
ejpam-6128	230	24	obtain	obtain	VERB
ejpam-6128	230	25	ς1	ς1	NOUN
ejpam-6128	230	26	=	=	SYM
ejpam-6128	230	27	√	√	NUM
ejpam-6128	231	1	αk1k6+k3	αk1k6+k3	NUM
ejpam-6128	232	1	(	(	PUNCT
ejpam-6128	232	2	k4	k4	NOUN
ejpam-6128	232	3	α	α	PROPN
ejpam-6128	232	4	+	+	NOUN
ejpam-6128	232	5	√	√	ADJ
ejpam-6128	232	6	α	α	NUM
ejpam-6128	232	7	2	2	NUM
ejpam-6128	232	8	k6	k6	NOUN
ejpam-6128	232	9	2	2	NUM
ejpam-6128	232	10	)	)	PUNCT
ejpam-6128	232	11	,	,	PUNCT
ejpam-6128	232	12	ς3	ς3	NOUN
ejpam-6128	232	13	=	=	SYM
ejpam-6128	232	14	k1	k1	NOUN
ejpam-6128	232	15	k4	k4	NOUN
ejpam-6128	232	16	−	−	PROPN
ejpam-6128	232	17	k6	k6	NOUN
ejpam-6128	232	18	2k4	2k4	NUM
ejpam-6128	232	19	(	(	PUNCT
ejpam-6128	232	20	√	√	NUM
ejpam-6128	232	21	αk1k6+k3	αk1k6+k3	NUM
ejpam-6128	232	22	(	(	PUNCT
ejpam-6128	232	23	k4	k4	NOUN
ejpam-6128	232	24	α	α	PROPN
ejpam-6128	232	25	+	+	NOUN
ejpam-6128	232	26	√	√	ADJ
ejpam-6128	232	27	α	α	NUM
ejpam-6128	232	28	2	2	NUM
ejpam-6128	232	29	k6	k6	NOUN
ejpam-6128	232	30	2	2	NUM
ejpam-6128	232	31	)	)	PUNCT
ejpam-6128	232	32	)	)	PUNCT
ejpam-6128	232	33	,	,	PUNCT
ejpam-6128	232	34	ς4	ς4	PROPN
ejpam-6128	232	35	=	=	SYM
ejpam-6128	232	36	0	0	NUM
ejpam-6128	232	37	.	.	PUNCT
ejpam-6128	233	1	case-4	case-4	NOUN
ejpam-6128	233	2	:	:	PUNCT
ejpam-6128	233	3	for	for	ADP
ejpam-6128	233	4	k6	k6	PROPN
ejpam-6128	233	5	6=	6=	ADP
ejpam-6128	233	6	0	0	NUM
ejpam-6128	233	7	,	,	PUNCT
ejpam-6128	233	8	k5	k5	PROPN
ejpam-6128	233	9	=	=	SYM
ejpam-6128	233	10	0	0	PROPN
ejpam-6128	233	11	,	,	PUNCT
ejpam-6128	233	12	k4	k4	NOUN
ejpam-6128	233	13	=	=	SYM
ejpam-6128	233	14	0	0	NUM
ejpam-6128	233	15	,	,	PUNCT
ejpam-6128	233	16	we	we	PRON
ejpam-6128	233	17	have	have	VERB
ejpam-6128	233	18	n4	n4	PROPN
ejpam-6128	233	19	=	=	PUNCT
ejpam-6128	233	20	y6	y6	PROPN
ejpam-6128	234	1	+	+	CCONJ
ejpam-6128	234	2	ay2	ay2	PROPN
ejpam-6128	234	3	,	,	PUNCT
ejpam-6128	234	4	a	a	DET
ejpam-6128	234	5	∈	∈	PROPN
ejpam-6128	234	6	r.	r.	NOUN
ejpam-6128	234	7	by	by	ADP
ejpam-6128	234	8	substituting	substitute	VERB
ejpam-6128	234	9	k̃2	k̃2	PROPN
ejpam-6128	234	10	=	=	SYM
ejpam-6128	234	11	k̃6	k̃6	PROPN
ejpam-6128	234	12	=	=	NOUN
ejpam-6128	234	13	1	1	NUM
ejpam-6128	234	14	in	in	ADP
ejpam-6128	234	15	(	(	PUNCT
ejpam-6128	234	16	27	27	NUM
ejpam-6128	234	17	)	)	PUNCT
ejpam-6128	234	18	,	,	PUNCT
ejpam-6128	234	19	we	we	PRON
ejpam-6128	234	20	obtain	obtain	VERB
ejpam-6128	234	21	ς1	ς1	NOUN
ejpam-6128	234	22	=	=	SYM
ejpam-6128	234	23	2k1	2k1	NUM
ejpam-6128	234	24	k6	k6	NOUN
ejpam-6128	234	25	,	,	PUNCT
ejpam-6128	234	26	ς3	ς3	NOUN
ejpam-6128	234	27	=	=	SYM
ejpam-6128	234	28	k3√	k3√	ADJ
ejpam-6128	234	29	αk6	αk6	NOUN
ejpam-6128	234	30	,	,	PUNCT
ejpam-6128	234	31	ς4	ς4	PROPN
ejpam-6128	234	32	=	=	SYM
ejpam-6128	234	33	0	0	NUM
ejpam-6128	234	34	.	.	PUNCT
ejpam-6128	235	1	case-5	case-5	NOUN
ejpam-6128	235	2	:	:	PUNCT
ejpam-6128	235	3	for	for	ADP
ejpam-6128	235	4	k6	k6	NOUN
ejpam-6128	235	5	=	=	SYM
ejpam-6128	235	6	0	0	PROPN
ejpam-6128	235	7	,	,	PUNCT
ejpam-6128	235	8	k5	k5	PROPN
ejpam-6128	235	9	6=	6=	ADP
ejpam-6128	235	10	0	0	NUM
ejpam-6128	235	11	,	,	PUNCT
ejpam-6128	235	12	k4	k4	PROPN
ejpam-6128	235	13	6=	6=	ADP
ejpam-6128	235	14	0	0	NUM
ejpam-6128	235	15	,	,	PUNCT
ejpam-6128	235	16	we	we	PRON
ejpam-6128	235	17	have	have	VERB
ejpam-6128	235	18	n5	n5	NOUN
ejpam-6128	235	19	=	=	PUNCT
ejpam-6128	235	20	y4	y4	PROPN
ejpam-6128	235	21	+	+	CCONJ
ejpam-6128	235	22	y5	y5	NOUN
ejpam-6128	235	23	.	.	PUNCT
ejpam-6128	236	1	by	by	ADP
ejpam-6128	236	2	substituting	substitute	VERB
ejpam-6128	236	3	k̃4	k̃4	PROPN
ejpam-6128	236	4	=	=	PUNCT
ejpam-6128	236	5	k̃5	k̃5	PROPN
ejpam-6128	236	6	=	=	NOUN
ejpam-6128	236	7	1	1	NUM
ejpam-6128	236	8	in	in	ADP
ejpam-6128	236	9	(	(	PUNCT
ejpam-6128	236	10	27	27	NUM
ejpam-6128	236	11	)	)	PUNCT
ejpam-6128	236	12	,	,	PUNCT
ejpam-6128	236	13	we	we	PRON
ejpam-6128	236	14	obtain	obtain	VERB
ejpam-6128	236	15	ς1	ς1	NOUN
ejpam-6128	236	16	=	=	SYM
ejpam-6128	236	17	αk3	αk3	NOUN
ejpam-6128	237	1	k4	k4	NOUN
ejpam-6128	237	2	,	,	PUNCT
ejpam-6128	237	3	ς2	ς2	PROPN
ejpam-6128	237	4	=	=	PROPN
ejpam-6128	237	5	k2	k2	PROPN
ejpam-6128	237	6	k5	k5	PROPN
ejpam-6128	237	7	,	,	PUNCT
ejpam-6128	237	8	ς3	ς3	NOUN
ejpam-6128	237	9	=	=	SYM
ejpam-6128	237	10	k1	k1	NOUN
ejpam-6128	237	11	k4	k4	NOUN
ejpam-6128	237	12	,	,	PUNCT
ejpam-6128	237	13	ς4	ς4	PROPN
ejpam-6128	237	14	=	=	SYM
ejpam-6128	237	15	0	0	NUM
ejpam-6128	237	16	.	.	PUNCT
ejpam-6128	238	1	case-6	case-6	NOUN
ejpam-6128	238	2	:	:	PUNCT
ejpam-6128	238	3	k6	k6	PROPN
ejpam-6128	238	4	=	=	SYM
ejpam-6128	238	5	0	0	PROPN
ejpam-6128	238	6	,	,	PUNCT
ejpam-6128	238	7	k5	k5	PROPN
ejpam-6128	238	8	6=	6=	ADP
ejpam-6128	238	9	0	0	NUM
ejpam-6128	238	10	,	,	PUNCT
ejpam-6128	238	11	k4	k4	NOUN
ejpam-6128	238	12	=	=	NOUN
ejpam-6128	238	13	0	0	NUM
ejpam-6128	238	14	.	.	PUNCT
ejpam-6128	239	1	for	for	ADP
ejpam-6128	239	2	ς2	ς2	PROPN
ejpam-6128	239	3	=	=	SYM
ejpam-6128	239	4	k2	k2	PROPN
ejpam-6128	239	5	k5	k5	PROPN
ejpam-6128	239	6	,	,	PUNCT
ejpam-6128	239	7	ς4	ς4	PROPN
ejpam-6128	239	8	=	=	SYM
ejpam-6128	239	9	(	(	PUNCT
ejpam-6128	239	10	ln	ln	X
ejpam-6128	239	11	(	(	PUNCT
ejpam-6128	239	12	k1−k3	k1−k3	PROPN
ejpam-6128	239	13	k1+k3	k1+k3	PROPN
ejpam-6128	239	14	)	)	PUNCT
ejpam-6128	239	15	)	)	PUNCT
ejpam-6128	239	16	√	√	ADP
ejpam-6128	239	17	α	α	PRON
ejpam-6128	239	18	2	2	NUM
ejpam-6128	239	19	,	,	PUNCT
ejpam-6128	239	20	we	we	PRON
ejpam-6128	239	21	get	get	VERB
ejpam-6128	239	22	n6	n6	NOUN
ejpam-6128	239	23	=	=	PROPN
ejpam-6128	239	24	y5	y5	PROPN
ejpam-6128	239	25	+	+	CCONJ
ejpam-6128	239	26	ay1	ay1	PROPN
ejpam-6128	239	27	,	,	PUNCT
ejpam-6128	239	28	a	a	DET
ejpam-6128	239	29	∈	∈	PROPN
ejpam-6128	239	30	r.	r.	NOUN
ejpam-6128	239	31	if	if	SCONJ
ejpam-6128	239	32	we	we	PRON
ejpam-6128	239	33	choose	choose	VERB
ejpam-6128	239	34	ς2	ς2	PROPN
ejpam-6128	239	35	=	=	SYM
ejpam-6128	239	36	k2	k2	PROPN
ejpam-6128	239	37	k5	k5	PROPN
ejpam-6128	239	38	,	,	PUNCT
ejpam-6128	239	39	ς4	ς4	PROPN
ejpam-6128	239	40	=	=	SYM
ejpam-6128	239	41	(	(	PUNCT
ejpam-6128	239	42	ln	ln	X
ejpam-6128	239	43	(	(	PUNCT
ejpam-6128	239	44	√	√	NOUN
ejpam-6128	239	45	αk3−k1√	αk3−k1√	NUM
ejpam-6128	239	46	αk3+k1	αk3+k1	NOUN
ejpam-6128	239	47	)	)	PUNCT
ejpam-6128	239	48	)	)	PUNCT
ejpam-6128	240	1	√	√	ADP
ejpam-6128	240	2	α	α	PRON
ejpam-6128	240	3	2	2	NUM
ejpam-6128	240	4	,	,	PUNCT
ejpam-6128	240	5	we	we	PRON
ejpam-6128	240	6	get	get	VERB
ejpam-6128	240	7	n7	n7	PROPN
ejpam-6128	240	8	=	=	SYM
ejpam-6128	240	9	y5	y5	PROPN
ejpam-6128	240	10	+	+	NUM
ejpam-6128	240	11	ay3	ay3	NOUN
ejpam-6128	240	12	,	,	PUNCT
ejpam-6128	240	13	a	a	DET
ejpam-6128	240	14	∈	∈	PROPN
ejpam-6128	240	15	r.	r.	NOUN
ejpam-6128	240	16	case-7	case-7	PROPN
ejpam-6128	240	17	:	:	PUNCT
ejpam-6128	240	18	for	for	ADP
ejpam-6128	240	19	k6	k6	NOUN
ejpam-6128	240	20	=	=	SYM
ejpam-6128	240	21	0	0	PROPN
ejpam-6128	240	22	,	,	PUNCT
ejpam-6128	240	23	k5	k5	PROPN
ejpam-6128	240	24	=	=	SYM
ejpam-6128	240	25	0	0	PROPN
ejpam-6128	240	26	,	,	PUNCT
ejpam-6128	240	27	k4	k4	PROPN
ejpam-6128	240	28	6=	6=	ADP
ejpam-6128	240	29	0	0	NUM
ejpam-6128	240	30	,	,	PUNCT
ejpam-6128	240	31	we	we	PRON
ejpam-6128	240	32	have	have	VERB
ejpam-6128	240	33	n8	n8	NOUN
ejpam-6128	240	34	=	=	SYM
ejpam-6128	240	35	y4	y4	PROPN
ejpam-6128	240	36	+	+	CCONJ
ejpam-6128	240	37	ay2	ay2	PROPN
ejpam-6128	240	38	,	,	PUNCT
ejpam-6128	240	39	a	a	DET
ejpam-6128	240	40	∈	∈	PROPN
ejpam-6128	240	41	r.	r.	NOUN
ejpam-6128	240	42	by	by	ADP
ejpam-6128	240	43	substituting	substitute	VERB
ejpam-6128	240	44	k̃2	k̃2	PROPN
ejpam-6128	240	45	=	=	SYM
ejpam-6128	240	46	k̃4	k̃4	PROPN
ejpam-6128	240	47	=	=	NOUN
ejpam-6128	240	48	1	1	NUM
ejpam-6128	240	49	in	in	ADP
ejpam-6128	240	50	(	(	PUNCT
ejpam-6128	240	51	27	27	NUM
ejpam-6128	240	52	)	)	PUNCT
ejpam-6128	240	53	,	,	PUNCT
ejpam-6128	240	54	we	we	PRON
ejpam-6128	240	55	obtain	obtain	VERB
ejpam-6128	240	56	ς1	ς1	NOUN
ejpam-6128	240	57	=	=	SYM
ejpam-6128	240	58	αk3	αk3	ADV
ejpam-6128	241	1	k4	k4	NOUN
ejpam-6128	241	2	,	,	PUNCT
ejpam-6128	241	3	ς3	ς3	NOUN
ejpam-6128	241	4	=	=	SYM
ejpam-6128	241	5	k1	k1	NOUN
ejpam-6128	241	6	k4	k4	NOUN
ejpam-6128	241	7	,	,	PUNCT
ejpam-6128	241	8	ς4	ς4	PROPN
ejpam-6128	241	9	=	=	SYM
ejpam-6128	241	10	0	0	NUM
ejpam-6128	241	11	.	.	PUNCT
ejpam-6128	242	1	case-8	case-8	NOUN
ejpam-6128	242	2	:	:	PUNCT
ejpam-6128	242	3	k6	k6	PROPN
ejpam-6128	242	4	=	=	SYM
ejpam-6128	242	5	0	0	PROPN
ejpam-6128	242	6	,	,	PUNCT
ejpam-6128	242	7	k5	k5	PROPN
ejpam-6128	242	8	=	=	SYM
ejpam-6128	242	9	0	0	PROPN
ejpam-6128	242	10	,	,	PUNCT
ejpam-6128	242	11	k4	k4	NOUN
ejpam-6128	242	12	=	=	NOUN
ejpam-6128	242	13	0	0	NUM
ejpam-6128	242	14	.	.	PUNCT
ejpam-6128	243	1	for	for	ADP
ejpam-6128	243	2	ς4	ς4	PROPN
ejpam-6128	243	3	=	=	SYM
ejpam-6128	243	4	(	(	PUNCT
ejpam-6128	243	5	ln	ln	X
ejpam-6128	243	6	(	(	PUNCT
ejpam-6128	243	7	k1−k3	k1−k3	PROPN
ejpam-6128	243	8	k1+k3	k1+k3	PROPN
ejpam-6128	243	9	)	)	PUNCT
ejpam-6128	243	10	)	)	PUNCT
ejpam-6128	243	11	√	√	ADP
ejpam-6128	243	12	α	α	PRON
ejpam-6128	243	13	2	2	NUM
ejpam-6128	243	14	,	,	PUNCT
ejpam-6128	243	15	we	we	PRON
ejpam-6128	243	16	get	get	VERB
ejpam-6128	243	17	n9	n9	X
ejpam-6128	243	18	=	=	PUNCT
ejpam-6128	243	19	y2	y2	PROPN
ejpam-6128	243	20	+	+	CCONJ
ejpam-6128	243	21	ay1	ay1	PROPN
ejpam-6128	243	22	,	,	PUNCT
ejpam-6128	243	23	a	a	DET
ejpam-6128	243	24	∈	∈	PROPN
ejpam-6128	243	25	r.	r.	NOUN
ejpam-6128	243	26	if	if	SCONJ
ejpam-6128	243	27	we	we	PRON
ejpam-6128	243	28	choose	choose	VERB
ejpam-6128	243	29	ς4	ς4	PROPN
ejpam-6128	243	30	=	=	PUNCT
ejpam-6128	243	31	(	(	PUNCT
ejpam-6128	243	32	ln	ln	X
ejpam-6128	243	33	(	(	PUNCT
ejpam-6128	243	34	√	√	NOUN
ejpam-6128	243	35	αk3−k1√	αk3−k1√	NUM
ejpam-6128	243	36	αk3+k1	αk3+k1	NOUN
ejpam-6128	243	37	)	)	PUNCT
ejpam-6128	243	38	)	)	PUNCT
ejpam-6128	244	1	√	√	ADP
ejpam-6128	244	2	α	α	PRON
ejpam-6128	244	3	2	2	NUM
ejpam-6128	244	4	,	,	PUNCT
ejpam-6128	244	5	we	we	PRON
ejpam-6128	244	6	get	get	VERB
ejpam-6128	244	7	n10	n10	NOUN
ejpam-6128	244	8	=	=	PUNCT
ejpam-6128	244	9	y2	y2	PROPN
ejpam-6128	244	10	+	+	NUM
ejpam-6128	244	11	ay3	ay3	NOUN
ejpam-6128	244	12	,	,	PUNCT
ejpam-6128	244	13	a	a	DET
ejpam-6128	244	14	∈	∈	PROPN
ejpam-6128	244	15	r.	r.	PROPN
ejpam-6128	244	16	m.	m.	PROPN
ejpam-6128	244	17	usman	usman	PROPN
ejpam-6128	244	18	,	,	PUNCT
ejpam-6128	244	19	a.	a.	NOUN
ejpam-6128	244	20	hussain	hussain	PROPN
ejpam-6128	244	21	,	,	PUNCT
ejpam-6128	244	22	m.	m.	PROPN
ejpam-6128	244	23	u.	u.	PROPN
ejpam-6128	244	24	farooq	farooq	PROPN
ejpam-6128	244	25	,	,	PUNCT
ejpam-6128	244	26	j.	j.	PROPN
ejpam-6128	244	27	herrera	herrera	PROPN
ejpam-6128	244	28	/	/	SYM
ejpam-6128	244	29	eur	eur	PROPN
ejpam-6128	244	30	.	.	PUNCT
ejpam-6128	245	1	j.	j.	PROPN
ejpam-6128	245	2	pure	pure	PROPN
ejpam-6128	245	3	appl	appl	PROPN
ejpam-6128	245	4	.	.	PROPN
ejpam-6128	245	5	math	math	PROPN
ejpam-6128	245	6	,	,	PUNCT
ejpam-6128	245	7	18	18	NUM
ejpam-6128	245	8	(	(	PUNCT
ejpam-6128	245	9	4	4	NUM
ejpam-6128	245	10	)	)	PUNCT
ejpam-6128	245	11	(	(	PUNCT
ejpam-6128	245	12	2025	2025	NUM
ejpam-6128	245	13	)	)	PUNCT
ejpam-6128	245	14	,	,	PUNCT
ejpam-6128	245	15	6128	6128	NUM
ejpam-6128	245	16	12	12	NUM
ejpam-6128	245	17	of	of	ADP
ejpam-6128	245	18	29	29	NUM
ejpam-6128	246	1	so	so	ADV
ejpam-6128	246	2	,	,	PUNCT
ejpam-6128	246	3	the	the	DET
ejpam-6128	246	4	one	one	NUM
ejpam-6128	246	5	-	-	PUNCT
ejpam-6128	246	6	dimensional	dimensional	ADJ
ejpam-6128	246	7	optimal	optimal	ADJ
ejpam-6128	246	8	system	system	NOUN
ejpam-6128	246	9	of	of	ADP
ejpam-6128	246	10	subalgebras	subalgebra	NOUN
ejpam-6128	246	11	of	of	ADP
ejpam-6128	246	12	lie	lie	NOUN
ejpam-6128	246	13	algebra	algebra	PROPN
ejpam-6128	246	14	(	(	PUNCT
ejpam-6128	246	15	8)	8)	NUM
ejpam-6128	246	16	is	be	AUX
ejpam-6128	246	17	presented	present	VERB
ejpam-6128	246	18	as	as	ADP
ejpam-6128	246	19	n1	n1	NOUN
ejpam-6128	246	20	=	=	PUNCT
ejpam-6128	246	21	y4	y4	PROPN
ejpam-6128	246	22	+	+	CCONJ
ejpam-6128	246	23	y5	y5	NOUN
ejpam-6128	246	24	+	+	CCONJ
ejpam-6128	246	25	y6	y6	ADJ
ejpam-6128	246	26	,	,	PUNCT
ejpam-6128	246	27	n2	n2	ADJ
ejpam-6128	246	28	=	=	PUNCT
ejpam-6128	246	29	y5	y5	NOUN
ejpam-6128	246	30	+	+	CCONJ
ejpam-6128	246	31	y6	y6	ADJ
ejpam-6128	246	32	,	,	PUNCT
ejpam-6128	246	33	n3	n3	NOUN
ejpam-6128	246	34	=	=	PUNCT
ejpam-6128	246	35	y6	y6	PROPN
ejpam-6128	246	36	+	+	CCONJ
ejpam-6128	246	37	y4	y4	PROPN
ejpam-6128	246	38	+	+	CCONJ
ejpam-6128	247	1	ay2	ay2	PROPN
ejpam-6128	247	2	,	,	PUNCT
ejpam-6128	247	3	a	a	PRON
ejpam-6128	247	4	∈	∈	PROPN
ejpam-6128	247	5	r	r	NOUN
ejpam-6128	247	6	,	,	PUNCT
ejpam-6128	247	7	n4	n4	PROPN
ejpam-6128	247	8	=	=	PROPN
ejpam-6128	247	9	y6	y6	PROPN
ejpam-6128	247	10	+	+	CCONJ
ejpam-6128	248	1	ay2	ay2	PROPN
ejpam-6128	248	2	,	,	PUNCT
ejpam-6128	248	3	a	a	DET
ejpam-6128	248	4	∈	∈	PROPN
ejpam-6128	248	5	r	r	NOUN
ejpam-6128	248	6	,	,	PUNCT
ejpam-6128	248	7	n5	n5	PROPN
ejpam-6128	248	8	=	=	PUNCT
ejpam-6128	248	9	y4	y4	PROPN
ejpam-6128	248	10	+	+	CCONJ
ejpam-6128	248	11	y5	y5	PROPN
ejpam-6128	248	12	,	,	PUNCT
ejpam-6128	248	13	n6	n6	NOUN
ejpam-6128	248	14	=	=	PROPN
ejpam-6128	248	15	y5	y5	PROPN
ejpam-6128	249	1	+	+	CCONJ
ejpam-6128	249	2	ay1	ay1	PROPN
ejpam-6128	249	3	,	,	PUNCT
ejpam-6128	249	4	a	a	DET
ejpam-6128	249	5	∈	∈	PROPN
ejpam-6128	249	6	r	r	NOUN
ejpam-6128	249	7	,	,	PUNCT
ejpam-6128	249	8	n7	n7	PROPN
ejpam-6128	249	9	=	=	SYM
ejpam-6128	249	10	y5	y5	PROPN
ejpam-6128	249	11	+	+	NUM
ejpam-6128	249	12	ay3	ay3	NOUN
ejpam-6128	249	13	,	,	PUNCT
ejpam-6128	249	14	a	a	DET
ejpam-6128	249	15	∈	∈	PROPN
ejpam-6128	249	16	r	r	NOUN
ejpam-6128	249	17	,	,	PUNCT
ejpam-6128	249	18	n8	n8	NOUN
ejpam-6128	249	19	=	=	SYM
ejpam-6128	250	1	y4	y4	PROPN
ejpam-6128	250	2	+	+	CCONJ
ejpam-6128	250	3	ay2	ay2	PROPN
ejpam-6128	250	4	,	,	PUNCT
ejpam-6128	250	5	a	a	DET
ejpam-6128	250	6	∈	∈	PROPN
ejpam-6128	250	7	r	r	NOUN
ejpam-6128	250	8	,	,	PUNCT
ejpam-6128	250	9	n9	n9	X
ejpam-6128	251	1	=	=	PUNCT
ejpam-6128	251	2	y2	y2	PROPN
ejpam-6128	251	3	+	+	CCONJ
ejpam-6128	251	4	ay1	ay1	PROPN
ejpam-6128	251	5	,	,	PUNCT
ejpam-6128	251	6	a	a	DET
ejpam-6128	251	7	∈	∈	PROPN
ejpam-6128	251	8	r	r	NOUN
ejpam-6128	251	9	,	,	PUNCT
ejpam-6128	251	10	n10	n10	X
ejpam-6128	251	11	=	=	SYM
ejpam-6128	251	12	y2	y2	PROPN
ejpam-6128	251	13	+	+	NUM
ejpam-6128	251	14	ay3	ay3	NOUN
ejpam-6128	251	15	,	,	PUNCT
ejpam-6128	251	16	a	a	DET
ejpam-6128	251	17	∈	∈	PROPN
ejpam-6128	251	18	r.	r.	NOUN
ejpam-6128	251	19	(	(	PUNCT
ejpam-6128	251	20	29	29	NUM
ejpam-6128	251	21	)	)	SYM
ejpam-6128	251	22	3	3	NUM
ejpam-6128	251	23	.	.	X
ejpam-6128	251	24	group	group	NOUN
ejpam-6128	251	25	invariant	invariant	PROPN
ejpam-6128	251	26	solutions	solution	NOUN
ejpam-6128	251	27	3.1	3.1	NUM
ejpam-6128	251	28	.	.	PUNCT
ejpam-6128	252	1	similarity	similarity	NOUN
ejpam-6128	252	2	reductions	reduction	NOUN
ejpam-6128	252	3	for	for	ADP
ejpam-6128	252	4	case	case	NOUN
ejpam-6128	252	5	1	1	NUM
ejpam-6128	252	6	case	case	NOUN
ejpam-6128	252	7	-	-	PUNCT
ejpam-6128	252	8	a	a	NOUN
ejpam-6128	252	9	:	:	PUNCT
ejpam-6128	252	10	consider	consider	VERB
ejpam-6128	252	11	y1	y1	NOUN
ejpam-6128	252	12	=	=	SYM
ejpam-6128	252	13	∂	∂	NUM
ejpam-6128	253	1	∂x	∂x	PROPN
ejpam-6128	253	2	.	.	PUNCT
ejpam-6128	254	1	the	the	DET
ejpam-6128	254	2	solution	solution	NOUN
ejpam-6128	254	3	of	of	ADP
ejpam-6128	254	4	the	the	DET
ejpam-6128	254	5	characteristic	characteristic	ADJ
ejpam-6128	254	6	equation	equation	NOUN
ejpam-6128	254	7	for	for	ADP
ejpam-6128	254	8	y1	y1	NOUN
ejpam-6128	254	9	provides	provide	VERB
ejpam-6128	254	10	the	the	DET
ejpam-6128	254	11	symmetry	symmetry	NOUN
ejpam-6128	254	12	invariants	invariant	NOUN
ejpam-6128	254	13	p	p	NOUN
ejpam-6128	254	14	=	=	SYM
ejpam-6128	254	15	y	y	PROPN
ejpam-6128	254	16	,	,	PUNCT
ejpam-6128	254	17	q	q	PROPN
ejpam-6128	254	18	=	=	SYM
ejpam-6128	254	19	t	t	PROPN
ejpam-6128	254	20	,	,	PUNCT
ejpam-6128	254	21	w(x	w(x	PROPN
ejpam-6128	254	22	,	,	PUNCT
ejpam-6128	254	23	y	y	PROPN
ejpam-6128	254	24	,	,	PUNCT
ejpam-6128	254	25	t	t	PROPN
ejpam-6128	254	26	)	)	PUNCT
ejpam-6128	255	1	=	=	SYM
ejpam-6128	255	2	h(p	h(p	PROPN
ejpam-6128	255	3	,	,	PUNCT
ejpam-6128	255	4	q	q	NOUN
ejpam-6128	255	5	)	)	PUNCT
ejpam-6128	255	6	.	.	PUNCT
ejpam-6128	256	1	(	(	PUNCT
ejpam-6128	256	2	30	30	NUM
ejpam-6128	256	3	)	)	PUNCT
ejpam-6128	256	4	by	by	ADP
ejpam-6128	256	5	inserting	insert	VERB
ejpam-6128	256	6	(	(	PUNCT
ejpam-6128	256	7	30	30	NUM
ejpam-6128	256	8	)	)	PUNCT
ejpam-6128	256	9	in	in	ADP
ejpam-6128	256	10	(	(	PUNCT
ejpam-6128	256	11	2	2	NUM
ejpam-6128	256	12	)	)	PUNCT
ejpam-6128	256	13	,	,	PUNCT
ejpam-6128	256	14	we	we	PRON
ejpam-6128	256	15	get	get	VERB
ejpam-6128	256	16	hqq	hqq	NOUN
ejpam-6128	256	17	−	−	PROPN
ejpam-6128	256	18	g′hp	g′hp	NOUN
ejpam-6128	256	19	2	2	NUM
ejpam-6128	256	20	−	−	NOUN
ejpam-6128	256	21	ghpp	ghpp	NOUN
ejpam-6128	256	22	=	=	NOUN
ejpam-6128	256	23	0	0	PROPN
ejpam-6128	256	24	.	.	PUNCT
ejpam-6128	257	1	(	(	PUNCT
ejpam-6128	257	2	31	31	NUM
ejpam-6128	257	3	)	)	PUNCT
ejpam-6128	257	4	infinitesimals	infinitesimal	NOUN
ejpam-6128	257	5	for	for	ADP
ejpam-6128	257	6	(	(	PUNCT
ejpam-6128	257	7	31	31	NUM
ejpam-6128	257	8	)	)	PUNCT
ejpam-6128	257	9	are	be	AUX
ejpam-6128	257	10	as	as	SCONJ
ejpam-6128	257	11	follows	follow	VERB
ejpam-6128	257	12	ζp	ζp	ADJ
ejpam-6128	257	13	=	=	PUNCT
ejpam-6128	257	14	c1p+	c1p+	PROPN
ejpam-6128	257	15	c2	c2	PROPN
ejpam-6128	257	16	,	,	PUNCT
ejpam-6128	257	17	ζq	ζq	NOUN
ejpam-6128	257	18	=	=	PUNCT
ejpam-6128	257	19	c1q	c1q	PROPN
ejpam-6128	257	20	+	+	CCONJ
ejpam-6128	257	21	c3	c3	NOUN
ejpam-6128	257	22	,	,	PUNCT
ejpam-6128	257	23	φh	φh	ADP
ejpam-6128	257	24	=	=	NOUN
ejpam-6128	257	25	0	0	NUM
ejpam-6128	257	26	.	.	PUNCT
ejpam-6128	258	1	(	(	PUNCT
ejpam-6128	258	2	32	32	NUM
ejpam-6128	258	3	)	)	PUNCT
ejpam-6128	258	4	case	case	NOUN
ejpam-6128	258	5	-	-	PUNCT
ejpam-6128	258	6	a1	a1	NOUN
ejpam-6128	258	7	:	:	PUNCT
ejpam-6128	258	8	in	in	ADP
ejpam-6128	258	9	(	(	PUNCT
ejpam-6128	258	10	32	32	NUM
ejpam-6128	258	11	)	)	PUNCT
ejpam-6128	258	12	,	,	PUNCT
ejpam-6128	258	13	set	set	VERB
ejpam-6128	258	14	c3	c3	NOUN
ejpam-6128	258	15	=	=	SYM
ejpam-6128	258	16	1	1	NUM
ejpam-6128	258	17	and	and	CCONJ
ejpam-6128	258	18	ci	ci	NOUN
ejpam-6128	258	19	=	=	NOUN
ejpam-6128	258	20	0	0	PROPN
ejpam-6128	258	21	for	for	ADP
ejpam-6128	258	22	i	i	PRON
ejpam-6128	258	23	=	=	NOUN
ejpam-6128	258	24	1	1	NUM
ejpam-6128	258	25	,	,	PUNCT
ejpam-6128	258	26	2	2	NUM
ejpam-6128	258	27	.	.	PUNCT
ejpam-6128	259	1	then	then	ADV
ejpam-6128	259	2	we	we	PRON
ejpam-6128	259	3	obtain	obtain	VERB
ejpam-6128	259	4	the	the	DET
ejpam-6128	259	5	symmetry	symmetry	NOUN
ejpam-6128	259	6	invariants	invariant	NOUN
ejpam-6128	259	7	r	r	NOUN
ejpam-6128	259	8	=	=	SYM
ejpam-6128	259	9	p	p	NOUN
ejpam-6128	259	10	,	,	PUNCT
ejpam-6128	259	11	h(p	h(p	PROPN
ejpam-6128	259	12	,	,	PUNCT
ejpam-6128	259	13	q	q	NOUN
ejpam-6128	259	14	)	)	PUNCT
ejpam-6128	259	15	=	=	SYM
ejpam-6128	259	16	µ(r	µ(r	NOUN
ejpam-6128	259	17	)	)	PUNCT
ejpam-6128	259	18	.	.	PUNCT
ejpam-6128	260	1	(	(	PUNCT
ejpam-6128	260	2	33	33	NUM
ejpam-6128	260	3	)	)	PUNCT
ejpam-6128	260	4	the	the	DET
ejpam-6128	260	5	substitution	substitution	NOUN
ejpam-6128	260	6	of	of	ADP
ejpam-6128	260	7	(	(	PUNCT
ejpam-6128	260	8	33	33	NUM
ejpam-6128	260	9	)	)	PUNCT
ejpam-6128	260	10	in	in	ADP
ejpam-6128	260	11	(	(	PUNCT
ejpam-6128	260	12	31	31	NUM
ejpam-6128	260	13	)	)	PUNCT
ejpam-6128	260	14	yields	yield	VERB
ejpam-6128	260	15	the	the	DET
ejpam-6128	260	16	following	follow	VERB
ejpam-6128	260	17	ode	ode	PROPN
ejpam-6128	260	18	gµ′′	gµ′′	PROPN
ejpam-6128	260	19	+	+	CCONJ
ejpam-6128	260	20	g′µ′2	g′µ′2	NOUN
ejpam-6128	260	21	=	=	SYM
ejpam-6128	260	22	0	0	X
ejpam-6128	260	23	.	.	PUNCT
ejpam-6128	261	1	(	(	PUNCT
ejpam-6128	261	2	34	34	NUM
ejpam-6128	261	3	)	)	PUNCT
ejpam-6128	261	4	m.	m.	NOUN
ejpam-6128	261	5	usman	usman	PROPN
ejpam-6128	261	6	,	,	PUNCT
ejpam-6128	261	7	a.	a.	NOUN
ejpam-6128	261	8	hussain	hussain	PROPN
ejpam-6128	261	9	,	,	PUNCT
ejpam-6128	261	10	m.	m.	PROPN
ejpam-6128	261	11	u.	u.	PROPN
ejpam-6128	261	12	farooq	farooq	PROPN
ejpam-6128	261	13	,	,	PUNCT
ejpam-6128	261	14	j.	j.	PROPN
ejpam-6128	261	15	herrera	herrera	PROPN
ejpam-6128	261	16	/	/	SYM
ejpam-6128	261	17	eur	eur	PROPN
ejpam-6128	261	18	.	.	PUNCT
ejpam-6128	262	1	j.	j.	PROPN
ejpam-6128	262	2	pure	pure	PROPN
ejpam-6128	262	3	appl	appl	PROPN
ejpam-6128	262	4	.	.	PROPN
ejpam-6128	262	5	math	math	PROPN
ejpam-6128	262	6	,	,	PUNCT
ejpam-6128	262	7	18	18	NUM
ejpam-6128	262	8	(	(	PUNCT
ejpam-6128	262	9	4	4	NUM
ejpam-6128	262	10	)	)	PUNCT
ejpam-6128	262	11	(	(	PUNCT
ejpam-6128	262	12	2025	2025	NUM
ejpam-6128	262	13	)	)	PUNCT
ejpam-6128	262	14	,	,	PUNCT
ejpam-6128	262	15	6128	6128	NUM
ejpam-6128	262	16	13	13	NUM
ejpam-6128	262	17	of	of	ADP
ejpam-6128	262	18	29	29	NUM
ejpam-6128	262	19	if	if	SCONJ
ejpam-6128	262	20	we	we	PRON
ejpam-6128	262	21	take	take	VERB
ejpam-6128	262	22	g	g	NOUN
ejpam-6128	262	23	=	=	SYM
ejpam-6128	262	24	b1µ+	b1µ+	NOUN
ejpam-6128	262	25	b2	b2	NOUN
ejpam-6128	262	26	,	,	PUNCT
ejpam-6128	262	27	then	then	ADV
ejpam-6128	262	28	the	the	DET
ejpam-6128	262	29	solution	solution	NOUN
ejpam-6128	262	30	of	of	ADP
ejpam-6128	262	31	(	(	PUNCT
ejpam-6128	262	32	34	34	NUM
ejpam-6128	262	33	)	)	PUNCT
ejpam-6128	262	34	takes	take	VERB
ejpam-6128	262	35	the	the	DET
ejpam-6128	262	36	form	form	NOUN
ejpam-6128	262	37	µ(r	µ(r	NOUN
ejpam-6128	262	38	)	)	PUNCT
ejpam-6128	263	1	=	=	SYM
ejpam-6128	264	1	−b2	−b2	PROPN
ejpam-6128	264	2	+	+	CCONJ
ejpam-6128	264	3	√	√	NUM
ejpam-6128	264	4	2c1b1r	2c1b1r	NUM
ejpam-6128	264	5	+	+	CCONJ
ejpam-6128	264	6	2c2b1	2c2b1	NUM
ejpam-6128	264	7	+	+	NUM
ejpam-6128	264	8	b2	b2	NOUN
ejpam-6128	264	9	2	2	NUM
ejpam-6128	264	10	b1	b1	NOUN
ejpam-6128	264	11	,	,	PUNCT
ejpam-6128	264	12	(	(	PUNCT
ejpam-6128	264	13	35	35	NUM
ejpam-6128	264	14	)	)	PUNCT
ejpam-6128	264	15	which	which	PRON
ejpam-6128	264	16	implies	imply	VERB
ejpam-6128	264	17	h(p	h(p	NOUN
ejpam-6128	264	18	,	,	PUNCT
ejpam-6128	264	19	q	q	X
ejpam-6128	264	20	)	)	PUNCT
ejpam-6128	264	21	=	=	SYM
ejpam-6128	265	1	−b2	−b2	PROPN
ejpam-6128	265	2	+	+	CCONJ
ejpam-6128	265	3	√	√	VERB
ejpam-6128	265	4	2c1b1p+	2c1b1p+	NUM
ejpam-6128	265	5	2c2b1	2c2b1	NUM
ejpam-6128	265	6	+	+	CCONJ
ejpam-6128	265	7	b2	b2	NOUN
ejpam-6128	265	8	2	2	NUM
ejpam-6128	265	9	b1	b1	NOUN
ejpam-6128	265	10	.	.	PUNCT
ejpam-6128	266	1	(	(	PUNCT
ejpam-6128	266	2	36	36	NUM
ejpam-6128	266	3	)	)	PUNCT
ejpam-6128	266	4	hence	hence	ADV
ejpam-6128	266	5	,	,	PUNCT
ejpam-6128	266	6	the	the	DET
ejpam-6128	266	7	solution	solution	NOUN
ejpam-6128	266	8	of	of	ADP
ejpam-6128	266	9	(	(	PUNCT
ejpam-6128	266	10	2	2	NUM
ejpam-6128	266	11	)	)	PUNCT
ejpam-6128	266	12	is	be	AUX
ejpam-6128	266	13	w(x	w(x	PROPN
ejpam-6128	266	14	,	,	PUNCT
ejpam-6128	266	15	y	y	PROPN
ejpam-6128	266	16	,	,	PUNCT
ejpam-6128	266	17	t	t	PROPN
ejpam-6128	266	18	)	)	PUNCT
ejpam-6128	266	19	=	=	SYM
ejpam-6128	267	1	−b2	−b2	PROPN
ejpam-6128	267	2	+	+	CCONJ
ejpam-6128	267	3	√	√	NUM
ejpam-6128	267	4	2c1b1y	2c1b1y	NUM
ejpam-6128	267	5	+	+	CCONJ
ejpam-6128	267	6	2c2b1	2c2b1	NUM
ejpam-6128	267	7	+	+	NUM
ejpam-6128	267	8	b2	b2	NOUN
ejpam-6128	267	9	2	2	NUM
ejpam-6128	267	10	b1	b1	NOUN
ejpam-6128	267	11	,	,	PUNCT
ejpam-6128	267	12	(	(	PUNCT
ejpam-6128	267	13	37	37	NUM
ejpam-6128	267	14	)	)	PUNCT
ejpam-6128	267	15	where	where	SCONJ
ejpam-6128	267	16	c1	c1	PROPN
ejpam-6128	267	17	and	and	CCONJ
ejpam-6128	267	18	c2	c2	PROPN
ejpam-6128	267	19	are	be	AUX
ejpam-6128	267	20	constants	constant	NOUN
ejpam-6128	267	21	of	of	ADP
ejpam-6128	267	22	integration	integration	NOUN
ejpam-6128	267	23	.	.	PUNCT
ejpam-6128	268	1	this	this	DET
ejpam-6128	268	2	solution	solution	NOUN
ejpam-6128	268	3	is	be	AUX
ejpam-6128	268	4	same	same	ADJ
ejpam-6128	268	5	,	,	PUNCT
ejpam-6128	268	6	as	as	SCONJ
ejpam-6128	268	7	obtained	obtain	VERB
ejpam-6128	268	8	in	in	ADP
ejpam-6128	268	9	[	[	X
ejpam-6128	268	10	22	22	NUM
ejpam-6128	268	11	]	]	PUNCT
ejpam-6128	268	12	.	.	PUNCT
ejpam-6128	269	1	case	case	NOUN
ejpam-6128	269	2	-	-	PUNCT
ejpam-6128	269	3	b	b	NOUN
ejpam-6128	269	4	:	:	PUNCT
ejpam-6128	269	5	consider	consider	VERB
ejpam-6128	269	6	y1	y1	NOUN
ejpam-6128	270	1	+	+	CCONJ
ejpam-6128	270	2	y2	y2	NOUN
ejpam-6128	270	3	=	=	SYM
ejpam-6128	270	4	∂	∂	NUM
ejpam-6128	270	5	∂x	∂x	PROPN
ejpam-6128	270	6	+	+	CCONJ
ejpam-6128	270	7	∂	∂	X
ejpam-6128	270	8	∂y	∂y	NOUN
ejpam-6128	270	9	.	.	PUNCT
ejpam-6128	271	1	the	the	DET
ejpam-6128	271	2	solution	solution	NOUN
ejpam-6128	271	3	of	of	ADP
ejpam-6128	271	4	the	the	DET
ejpam-6128	271	5	characteristic	characteristic	ADJ
ejpam-6128	271	6	equation	equation	NOUN
ejpam-6128	271	7	for	for	ADP
ejpam-6128	271	8	y1	y1	NOUN
ejpam-6128	271	9	+	+	CCONJ
ejpam-6128	271	10	y2	y2	PROPN
ejpam-6128	271	11	provides	provide	VERB
ejpam-6128	271	12	the	the	DET
ejpam-6128	271	13	symmetry	symmetry	NOUN
ejpam-6128	271	14	invariants	invariant	NOUN
ejpam-6128	271	15	p	p	PROPN
ejpam-6128	271	16	=	=	PROPN
ejpam-6128	271	17	t	t	PROPN
ejpam-6128	271	18	,	,	PUNCT
ejpam-6128	271	19	q	q	NOUN
ejpam-6128	272	1	=	=	PUNCT
ejpam-6128	272	2	y	y	PROPN
ejpam-6128	272	3	−	−	PROPN
ejpam-6128	272	4	x	x	SYM
ejpam-6128	272	5	,	,	PUNCT
ejpam-6128	272	6	w(x	w(x	PROPN
ejpam-6128	272	7	,	,	PUNCT
ejpam-6128	272	8	y	y	PROPN
ejpam-6128	272	9	,	,	PUNCT
ejpam-6128	272	10	t	t	PROPN
ejpam-6128	272	11	)	)	PUNCT
ejpam-6128	272	12	=	=	SYM
ejpam-6128	272	13	h(p	h(p	PROPN
ejpam-6128	272	14	,	,	PUNCT
ejpam-6128	272	15	q	q	NOUN
ejpam-6128	272	16	)	)	PUNCT
ejpam-6128	272	17	.	.	PUNCT
ejpam-6128	273	1	(	(	PUNCT
ejpam-6128	273	2	38	38	NUM
ejpam-6128	273	3	)	)	PUNCT
ejpam-6128	273	4	by	by	ADP
ejpam-6128	273	5	inserting	insert	VERB
ejpam-6128	273	6	(	(	PUNCT
ejpam-6128	273	7	38	38	NUM
ejpam-6128	273	8	)	)	PUNCT
ejpam-6128	273	9	in	in	ADP
ejpam-6128	273	10	(	(	PUNCT
ejpam-6128	273	11	2	2	NUM
ejpam-6128	273	12	)	)	PUNCT
ejpam-6128	273	13	,	,	PUNCT
ejpam-6128	273	14	we	we	PRON
ejpam-6128	273	15	get	get	VERB
ejpam-6128	273	16	hpp	hpp	PROPN
ejpam-6128	274	1	−	−	PROPN
ejpam-6128	275	1	(	(	PUNCT
ejpam-6128	275	2	f	f	NOUN
ejpam-6128	275	3	′	′	NUM
ejpam-6128	276	1	+	+	CCONJ
ejpam-6128	276	2	g′)hq	g′)hq	NOUN
ejpam-6128	276	3	2	2	NUM
ejpam-6128	276	4	−	−	NOUN
ejpam-6128	276	5	(	(	PUNCT
ejpam-6128	276	6	f	f	PROPN
ejpam-6128	276	7	+	+	CCONJ
ejpam-6128	276	8	g)hqq	g)hqq	PROPN
ejpam-6128	276	9	=	=	PUNCT
ejpam-6128	276	10	0	0	X
ejpam-6128	276	11	.	.	PUNCT
ejpam-6128	277	1	(	(	PUNCT
ejpam-6128	277	2	39	39	NUM
ejpam-6128	277	3	)	)	PUNCT
ejpam-6128	277	4	infinitesimals	infinitesimal	NOUN
ejpam-6128	277	5	for	for	ADP
ejpam-6128	277	6	(	(	PUNCT
ejpam-6128	277	7	39	39	NUM
ejpam-6128	277	8	)	)	PUNCT
ejpam-6128	277	9	are	be	AUX
ejpam-6128	277	10	as	as	SCONJ
ejpam-6128	277	11	follows	follow	VERB
ejpam-6128	277	12	ζp	ζp	ADJ
ejpam-6128	277	13	=	=	PUNCT
ejpam-6128	277	14	c1p+	c1p+	PROPN
ejpam-6128	277	15	c2	c2	PROPN
ejpam-6128	277	16	,	,	PUNCT
ejpam-6128	277	17	ζq	ζq	NOUN
ejpam-6128	277	18	=	=	PUNCT
ejpam-6128	277	19	c1q	c1q	PROPN
ejpam-6128	277	20	+	+	CCONJ
ejpam-6128	277	21	c3	c3	NOUN
ejpam-6128	277	22	,	,	PUNCT
ejpam-6128	277	23	φh	φh	ADP
ejpam-6128	277	24	=	=	NOUN
ejpam-6128	277	25	0	0	NUM
ejpam-6128	277	26	.	.	PUNCT
ejpam-6128	278	1	(	(	PUNCT
ejpam-6128	278	2	40	40	NUM
ejpam-6128	278	3	)	)	PUNCT
ejpam-6128	278	4	case	case	NOUN
ejpam-6128	278	5	-	-	PUNCT
ejpam-6128	278	6	b1	b1	NOUN
ejpam-6128	278	7	:	:	PUNCT
ejpam-6128	278	8	in	in	ADP
ejpam-6128	278	9	(	(	PUNCT
ejpam-6128	278	10	40	40	NUM
ejpam-6128	278	11	)	)	PUNCT
ejpam-6128	278	12	,	,	PUNCT
ejpam-6128	278	13	set	set	VERB
ejpam-6128	278	14	c2	c2	PROPN
ejpam-6128	278	15	=	=	SYM
ejpam-6128	278	16	1	1	NUM
ejpam-6128	278	17	and	and	CCONJ
ejpam-6128	278	18	ci	ci	NOUN
ejpam-6128	278	19	=	=	NOUN
ejpam-6128	278	20	0	0	PROPN
ejpam-6128	278	21	for	for	ADP
ejpam-6128	278	22	i	i	PRON
ejpam-6128	278	23	=	=	SYM
ejpam-6128	278	24	1	1	NUM
ejpam-6128	278	25	,	,	PUNCT
ejpam-6128	278	26	3	3	NUM
ejpam-6128	278	27	.	.	PUNCT
ejpam-6128	279	1	then	then	ADV
ejpam-6128	279	2	we	we	PRON
ejpam-6128	279	3	obtain	obtain	VERB
ejpam-6128	279	4	the	the	DET
ejpam-6128	279	5	symmetry	symmetry	NOUN
ejpam-6128	279	6	invariants	invariant	NOUN
ejpam-6128	279	7	r	r	NOUN
ejpam-6128	279	8	=	=	SYM
ejpam-6128	279	9	q	q	ADJ
ejpam-6128	279	10	,	,	PUNCT
ejpam-6128	279	11	h(p	h(p	PROPN
ejpam-6128	279	12	,	,	PUNCT
ejpam-6128	279	13	q	q	NOUN
ejpam-6128	279	14	)	)	PUNCT
ejpam-6128	279	15	=	=	SYM
ejpam-6128	279	16	µ(r	µ(r	NOUN
ejpam-6128	279	17	)	)	PUNCT
ejpam-6128	279	18	.	.	PUNCT
ejpam-6128	280	1	(	(	PUNCT
ejpam-6128	280	2	41	41	NUM
ejpam-6128	280	3	)	)	PUNCT
ejpam-6128	280	4	the	the	DET
ejpam-6128	280	5	substitution	substitution	NOUN
ejpam-6128	280	6	of	of	ADP
ejpam-6128	280	7	(	(	PUNCT
ejpam-6128	280	8	41	41	NUM
ejpam-6128	280	9	)	)	PUNCT
ejpam-6128	280	10	in	in	ADP
ejpam-6128	280	11	(	(	PUNCT
ejpam-6128	280	12	39	39	NUM
ejpam-6128	280	13	)	)	PUNCT
ejpam-6128	280	14	yields	yield	VERB
ejpam-6128	280	15	the	the	DET
ejpam-6128	280	16	following	follow	VERB
ejpam-6128	280	17	ode	ode	PROPN
ejpam-6128	280	18	(	(	PUNCT
ejpam-6128	280	19	f	f	NOUN
ejpam-6128	280	20	+	+	X
ejpam-6128	280	21	g)µ′′	g)µ′′	NOUN
ejpam-6128	281	1	+	+	CCONJ
ejpam-6128	281	2	(	(	PUNCT
ejpam-6128	281	3	f	f	NOUN
ejpam-6128	281	4	′	′	VERB
ejpam-6128	281	5	+	+	CCONJ
ejpam-6128	281	6	g′)µ′2	g′)µ′2	X
ejpam-6128	281	7	=	=	PUNCT
ejpam-6128	281	8	0	0	NUM
ejpam-6128	281	9	.	.	PUNCT
ejpam-6128	282	1	(	(	PUNCT
ejpam-6128	282	2	42	42	NUM
ejpam-6128	282	3	)	)	PUNCT
ejpam-6128	282	4	m.	m.	NOUN
ejpam-6128	282	5	usman	usman	PROPN
ejpam-6128	282	6	,	,	PUNCT
ejpam-6128	282	7	a.	a.	NOUN
ejpam-6128	282	8	hussain	hussain	PROPN
ejpam-6128	282	9	,	,	PUNCT
ejpam-6128	282	10	m.	m.	PROPN
ejpam-6128	282	11	u.	u.	PROPN
ejpam-6128	282	12	farooq	farooq	PROPN
ejpam-6128	282	13	,	,	PUNCT
ejpam-6128	282	14	j.	j.	PROPN
ejpam-6128	282	15	herrera	herrera	PROPN
ejpam-6128	282	16	/	/	SYM
ejpam-6128	282	17	eur	eur	PROPN
ejpam-6128	282	18	.	.	PUNCT
ejpam-6128	283	1	j.	j.	PROPN
ejpam-6128	283	2	pure	pure	PROPN
ejpam-6128	283	3	appl	appl	PROPN
ejpam-6128	283	4	.	.	PROPN
ejpam-6128	283	5	math	math	PROPN
ejpam-6128	283	6	,	,	PUNCT
ejpam-6128	283	7	18	18	NUM
ejpam-6128	283	8	(	(	PUNCT
ejpam-6128	283	9	4	4	NUM
ejpam-6128	283	10	)	)	PUNCT
ejpam-6128	283	11	(	(	PUNCT
ejpam-6128	283	12	2025	2025	NUM
ejpam-6128	283	13	)	)	PUNCT
ejpam-6128	283	14	,	,	PUNCT
ejpam-6128	283	15	6128	6128	NUM
ejpam-6128	283	16	14	14	NUM
ejpam-6128	283	17	of	of	ADP
ejpam-6128	283	18	29	29	NUM
ejpam-6128	283	19	if	if	SCONJ
ejpam-6128	283	20	we	we	PRON
ejpam-6128	283	21	take	take	VERB
ejpam-6128	283	22	f	f	NOUN
ejpam-6128	283	23	=	=	SYM
ejpam-6128	283	24	a1µ	a1µ	PROPN
ejpam-6128	283	25	2	2	NUM
ejpam-6128	283	26	+	+	NUM
ejpam-6128	283	27	a2	a2	NOUN
ejpam-6128	283	28	,	,	PUNCT
ejpam-6128	283	29	g	g	PROPN
ejpam-6128	283	30	=	=	PROPN
ejpam-6128	283	31	b1µ	b1µ	PROPN
ejpam-6128	283	32	,	,	PUNCT
ejpam-6128	283	33	then	then	ADV
ejpam-6128	283	34	the	the	DET
ejpam-6128	283	35	solution	solution	NOUN
ejpam-6128	283	36	of	of	ADP
ejpam-6128	283	37	(	(	PUNCT
ejpam-6128	283	38	42	42	NUM
ejpam-6128	283	39	)	)	PUNCT
ejpam-6128	283	40	takes	take	VERB
ejpam-6128	283	41	the	the	DET
ejpam-6128	283	42	form	form	NOUN
ejpam-6128	283	43	µ(r	µ(r	NOUN
ejpam-6128	283	44	)	)	PUNCT
ejpam-6128	283	45	=	=	SYM
ejpam-6128	283	46	1	1	NUM
ejpam-6128	283	47	2a1	2a1	NUM
ejpam-6128	283	48	(	(	PUNCT
ejpam-6128	283	49	12c1ra1	12c1ra1	NUM
ejpam-6128	283	50	2	2	NUM
ejpam-6128	283	51	+	+	NUM
ejpam-6128	283	52	12c2a1	12c2a1	NUM
ejpam-6128	283	53	2	2	NUM
ejpam-6128	283	54	+	+	CCONJ
ejpam-6128	283	55	6a1a2b1	6a1a2b1	NUM
ejpam-6128	283	56	−	−	NOUN
ejpam-6128	283	57	b1	b1	NOUN
ejpam-6128	283	58	3	3	NUM
ejpam-6128	283	59	+	+	CCONJ
ejpam-6128	283	60	2(36c1	2(36c1	NUM
ejpam-6128	283	61	2r2a1	2r2a1	NOUN
ejpam-6128	283	62	2	2	NUM
ejpam-6128	283	63	+	+	NUM
ejpam-6128	283	64	72c1c2ra1	72c1c2ra1	NOUN
ejpam-6128	283	65	2	2	NUM
ejpam-6128	283	66	+	+	CCONJ
ejpam-6128	283	67	36c1ra1a2b1	36c1ra1a2b1	NUM
ejpam-6128	283	68	−	−	NOUN
ejpam-6128	284	1	6c1rb1	6c1rb1	NUM
ejpam-6128	284	2	3	3	NUM
ejpam-6128	285	1	+	+	CCONJ
ejpam-6128	285	2	36c2	36c2	NUM
ejpam-6128	285	3	2a1	2a1	NUM
ejpam-6128	285	4	2	2	NUM
ejpam-6128	285	5	+	+	CCONJ
ejpam-6128	285	6	36c2a1a2b1	36c2a1a2b1	NUM
ejpam-6128	285	7	−	−	NOUN
ejpam-6128	285	8	6c2b1	6c2b1	NUM
ejpam-6128	285	9	3	3	NUM
ejpam-6128	285	10	+	+	CCONJ
ejpam-6128	285	11	16a1a2	16a1a2	NUM
ejpam-6128	285	12	3	3	NUM
ejpam-6128	285	13	−	−	PROPN
ejpam-6128	285	14	3a2	3a2	NUM
ejpam-6128	285	15	2b1	2b1	NUM
ejpam-6128	285	16	2	2	NUM
ejpam-6128	285	17	)	)	PUNCT
ejpam-6128	285	18	1	1	NUM
ejpam-6128	285	19	2a1	2a1	NUM
ejpam-6128	285	20	)	)	PUNCT
ejpam-6128	285	21	1	1	NUM
ejpam-6128	285	22	3	3	NUM
ejpam-6128	285	23	−	−	PROPN
ejpam-6128	285	24	(	(	PUNCT
ejpam-6128	285	25	4a1a2	4a1a2	INTJ
ejpam-6128	285	26	−	−	NOUN
ejpam-6128	285	27	b1	b1	NOUN
ejpam-6128	285	28	2	2	NUM
ejpam-6128	285	29	)	)	PUNCT
ejpam-6128	285	30	/	/	PUNCT
ejpam-6128	285	31	(	(	PUNCT
ejpam-6128	285	32	2a1(12c1ra1	2a1(12c1ra1	NUM
ejpam-6128	285	33	2	2	NUM
ejpam-6128	285	34	+	+	NUM
ejpam-6128	285	35	12c2a1	12c2a1	NUM
ejpam-6128	285	36	2	2	NUM
ejpam-6128	285	37	+	+	CCONJ
ejpam-6128	285	38	6a1a2b1	6a1a2b1	NUM
ejpam-6128	285	39	−	−	NOUN
ejpam-6128	285	40	b1	b1	NOUN
ejpam-6128	285	41	3	3	NUM
ejpam-6128	285	42	+	+	CCONJ
ejpam-6128	285	43	2(36c1	2(36c1	NUM
ejpam-6128	285	44	2r2a1	2r2a1	NOUN
ejpam-6128	285	45	2	2	NUM
ejpam-6128	285	46	+	+	NUM
ejpam-6128	285	47	72c1c2ra1	72c1c2ra1	NOUN
ejpam-6128	285	48	2	2	NUM
ejpam-6128	285	49	+	+	CCONJ
ejpam-6128	285	50	36c1ra1a2b1	36c1ra1a2b1	NUM
ejpam-6128	285	51	−	−	NOUN
ejpam-6128	285	52	6c1rb1	6c1rb1	NUM
ejpam-6128	285	53	3	3	NUM
ejpam-6128	286	1	+	+	CCONJ
ejpam-6128	286	2	36c2	36c2	NUM
ejpam-6128	286	3	2a1	2a1	NUM
ejpam-6128	286	4	2	2	NUM
ejpam-6128	286	5	+	+	CCONJ
ejpam-6128	286	6	36c2a1a2b1	36c2a1a2b1	NUM
ejpam-6128	286	7	−	−	NOUN
ejpam-6128	286	8	6c2b1	6c2b1	NUM
ejpam-6128	286	9	3	3	NUM
ejpam-6128	286	10	+	+	CCONJ
ejpam-6128	286	11	16a1a2	16a1a2	NUM
ejpam-6128	286	12	3	3	NUM
ejpam-6128	286	13	−	−	PROPN
ejpam-6128	286	14	3a2	3a2	NUM
ejpam-6128	286	15	2b1	2b1	NUM
ejpam-6128	286	16	2	2	NUM
ejpam-6128	286	17	)	)	PUNCT
ejpam-6128	286	18	1	1	NUM
ejpam-6128	286	19	2a1	2a1	NUM
ejpam-6128	286	20	)	)	PUNCT
ejpam-6128	286	21	1	1	NUM
ejpam-6128	286	22	3	3	NUM
ejpam-6128	286	23	)	)	PUNCT
ejpam-6128	286	24	−	−	PROPN
ejpam-6128	286	25	b1	b1	NOUN
ejpam-6128	286	26	2a1	2a1	NUM
ejpam-6128	286	27	,	,	PUNCT
ejpam-6128	286	28	(	(	PUNCT
ejpam-6128	286	29	43	43	NUM
ejpam-6128	286	30	)	)	PUNCT
ejpam-6128	286	31	which	which	PRON
ejpam-6128	286	32	implies	imply	VERB
ejpam-6128	286	33	h(p	h(p	NOUN
ejpam-6128	286	34	,	,	PUNCT
ejpam-6128	286	35	q	q	X
ejpam-6128	286	36	)	)	PUNCT
ejpam-6128	286	37	=	=	SYM
ejpam-6128	286	38	1	1	NUM
ejpam-6128	286	39	2a1	2a1	NUM
ejpam-6128	286	40	(	(	PUNCT
ejpam-6128	286	41	12c1qa1	12c1qa1	NOUN
ejpam-6128	286	42	2	2	NUM
ejpam-6128	286	43	+	+	CCONJ
ejpam-6128	286	44	12c2a1	12c2a1	NUM
ejpam-6128	286	45	2	2	NUM
ejpam-6128	286	46	+	+	CCONJ
ejpam-6128	286	47	6a1a2b1	6a1a2b1	NUM
ejpam-6128	286	48	−	−	NOUN
ejpam-6128	286	49	b1	b1	NOUN
ejpam-6128	286	50	3	3	NUM
ejpam-6128	286	51	+	+	CCONJ
ejpam-6128	286	52	2(36c1	2(36c1	NUM
ejpam-6128	286	53	2q2a1	2q2a1	NOUN
ejpam-6128	286	54	2	2	NUM
ejpam-6128	286	55	+	+	SYM
ejpam-6128	286	56	72c1c2qa1	72c1c2qa1	NOUN
ejpam-6128	286	57	2	2	NUM
ejpam-6128	286	58	+	+	CCONJ
ejpam-6128	287	1	36c1qa1a2b1	36c1qa1a2b1	NUM
ejpam-6128	287	2	−	−	NOUN
ejpam-6128	287	3	6c1qb1	6c1qb1	NUM
ejpam-6128	288	1	3	3	NUM
ejpam-6128	289	1	+	+	CCONJ
ejpam-6128	289	2	36c2	36c2	NUM
ejpam-6128	289	3	2a1	2a1	NUM
ejpam-6128	289	4	2	2	NUM
ejpam-6128	290	1	+	+	CCONJ
ejpam-6128	290	2	36c2a1a2b1	36c2a1a2b1	NUM
ejpam-6128	290	3	−	−	NOUN
ejpam-6128	290	4	6c2b1	6c2b1	NUM
ejpam-6128	290	5	3	3	NUM
ejpam-6128	290	6	+	+	CCONJ
ejpam-6128	290	7	16a1a2	16a1a2	NUM
ejpam-6128	290	8	3	3	NUM
ejpam-6128	290	9	−	−	PROPN
ejpam-6128	290	10	3a2	3a2	NUM
ejpam-6128	290	11	2b1	2b1	NUM
ejpam-6128	290	12	2	2	NUM
ejpam-6128	290	13	)	)	PUNCT
ejpam-6128	290	14	1	1	NUM
ejpam-6128	290	15	2a1	2a1	NUM
ejpam-6128	290	16	)	)	PUNCT
ejpam-6128	290	17	1	1	NUM
ejpam-6128	290	18	3	3	NUM
ejpam-6128	290	19	−	−	PROPN
ejpam-6128	290	20	(	(	PUNCT
ejpam-6128	290	21	4a1a2	4a1a2	INTJ
ejpam-6128	290	22	−	−	NOUN
ejpam-6128	290	23	b1	b1	NOUN
ejpam-6128	290	24	2	2	NUM
ejpam-6128	290	25	)	)	PUNCT
ejpam-6128	290	26	/	/	PUNCT
ejpam-6128	291	1	(	(	PUNCT
ejpam-6128	291	2	2a1(12c1qa1	2a1(12c1qa1	NUM
ejpam-6128	291	3	2	2	NUM
ejpam-6128	292	1	+	+	NUM
ejpam-6128	292	2	12c2a1	12c2a1	NUM
ejpam-6128	292	3	2	2	NUM
ejpam-6128	292	4	+	+	CCONJ
ejpam-6128	292	5	6a1a2b1	6a1a2b1	NUM
ejpam-6128	292	6	−	−	NOUN
ejpam-6128	292	7	b1	b1	NOUN
ejpam-6128	292	8	3	3	NUM
ejpam-6128	292	9	+	+	CCONJ
ejpam-6128	292	10	2(36c1	2(36c1	NUM
ejpam-6128	292	11	2q2a1	2q2a1	NOUN
ejpam-6128	292	12	2	2	NUM
ejpam-6128	292	13	+	+	SYM
ejpam-6128	292	14	72c1c2qa1	72c1c2qa1	NOUN
ejpam-6128	292	15	2	2	NUM
ejpam-6128	292	16	+	+	CCONJ
ejpam-6128	292	17	36c1qa1a2b1	36c1qa1a2b1	NUM
ejpam-6128	292	18	−	−	NOUN
ejpam-6128	292	19	6c1qb1	6c1qb1	NUM
ejpam-6128	292	20	3	3	NUM
ejpam-6128	293	1	+	+	CCONJ
ejpam-6128	293	2	36c2	36c2	NUM
ejpam-6128	293	3	2a1	2a1	NUM
ejpam-6128	293	4	2	2	NUM
ejpam-6128	294	1	+	+	CCONJ
ejpam-6128	294	2	36c2a1a2b1	36c2a1a2b1	NUM
ejpam-6128	294	3	−	−	NOUN
ejpam-6128	294	4	6c2b1	6c2b1	NUM
ejpam-6128	294	5	3	3	NUM
ejpam-6128	295	1	+	+	CCONJ
ejpam-6128	295	2	16a1a2	16a1a2	NUM
ejpam-6128	295	3	3	3	NUM
ejpam-6128	295	4	−	−	PROPN
ejpam-6128	295	5	3a2	3a2	NUM
ejpam-6128	295	6	2b1	2b1	NUM
ejpam-6128	295	7	2	2	NUM
ejpam-6128	295	8	)	)	PUNCT
ejpam-6128	295	9	1	1	NUM
ejpam-6128	295	10	2a1	2a1	NUM
ejpam-6128	295	11	)	)	PUNCT
ejpam-6128	295	12	1	1	NUM
ejpam-6128	295	13	3	3	NUM
ejpam-6128	295	14	)	)	PUNCT
ejpam-6128	295	15	−	−	PROPN
ejpam-6128	295	16	b1	b1	NOUN
ejpam-6128	295	17	2a1	2a1	NUM
ejpam-6128	295	18	.	.	PUNCT
ejpam-6128	296	1	(	(	PUNCT
ejpam-6128	296	2	44	44	NUM
ejpam-6128	296	3	)	)	PUNCT
ejpam-6128	296	4	hence	hence	ADV
ejpam-6128	296	5	,	,	PUNCT
ejpam-6128	296	6	the	the	DET
ejpam-6128	296	7	solution	solution	NOUN
ejpam-6128	296	8	of	of	ADP
ejpam-6128	296	9	(	(	PUNCT
ejpam-6128	296	10	2	2	NUM
ejpam-6128	296	11	)	)	PUNCT
ejpam-6128	296	12	is	be	AUX
ejpam-6128	296	13	w(x	w(x	PROPN
ejpam-6128	296	14	,	,	PUNCT
ejpam-6128	296	15	y	y	PROPN
ejpam-6128	296	16	,	,	PUNCT
ejpam-6128	296	17	t	t	PROPN
ejpam-6128	296	18	)	)	PUNCT
ejpam-6128	296	19	=	=	SYM
ejpam-6128	297	1	1	1	NUM
ejpam-6128	297	2	2a1	2a1	NUM
ejpam-6128	297	3	(	(	PUNCT
ejpam-6128	297	4	12c1qa1	12c1qa1	NOUN
ejpam-6128	297	5	2	2	NUM
ejpam-6128	297	6	+	+	CCONJ
ejpam-6128	297	7	12c2a1	12c2a1	NUM
ejpam-6128	297	8	2	2	NUM
ejpam-6128	297	9	+	+	CCONJ
ejpam-6128	297	10	6a1a2b1	6a1a2b1	NUM
ejpam-6128	297	11	−	−	NOUN
ejpam-6128	297	12	b1	b1	NOUN
ejpam-6128	297	13	3	3	NUM
ejpam-6128	297	14	+	+	CCONJ
ejpam-6128	297	15	2(36c1	2(36c1	NUM
ejpam-6128	297	16	2q2a1	2q2a1	NOUN
ejpam-6128	297	17	2	2	NUM
ejpam-6128	297	18	+	+	SYM
ejpam-6128	297	19	72c1c2qa1	72c1c2qa1	NOUN
ejpam-6128	297	20	2	2	NUM
ejpam-6128	297	21	+	+	CCONJ
ejpam-6128	297	22	36c1qa1a2b1	36c1qa1a2b1	NUM
ejpam-6128	297	23	−	−	NOUN
ejpam-6128	297	24	6c1qb1	6c1qb1	NUM
ejpam-6128	297	25	3	3	NUM
ejpam-6128	297	26	+	+	CCONJ
ejpam-6128	297	27	36c2	36c2	NUM
ejpam-6128	297	28	2a1	2a1	NUM
ejpam-6128	297	29	2	2	NUM
ejpam-6128	297	30	+	+	CCONJ
ejpam-6128	297	31	36c2a1a2b1	36c2a1a2b1	NUM
ejpam-6128	297	32	−	−	NOUN
ejpam-6128	297	33	6c2b1	6c2b1	NUM
ejpam-6128	297	34	3	3	NUM
ejpam-6128	297	35	+	+	CCONJ
ejpam-6128	297	36	16a1a2	16a1a2	NUM
ejpam-6128	297	37	3	3	NUM
ejpam-6128	297	38	−	−	PROPN
ejpam-6128	297	39	3a2	3a2	NUM
ejpam-6128	297	40	2b1	2b1	NUM
ejpam-6128	297	41	2	2	NUM
ejpam-6128	297	42	)	)	PUNCT
ejpam-6128	297	43	1	1	NUM
ejpam-6128	297	44	2a1	2a1	NUM
ejpam-6128	297	45	)	)	PUNCT
ejpam-6128	297	46	1	1	NUM
ejpam-6128	297	47	3	3	NUM
ejpam-6128	297	48	−	−	PROPN
ejpam-6128	297	49	(	(	PUNCT
ejpam-6128	297	50	4a1a2	4a1a2	INTJ
ejpam-6128	297	51	−	−	NOUN
ejpam-6128	297	52	b1	b1	NOUN
ejpam-6128	297	53	2	2	NUM
ejpam-6128	297	54	)	)	PUNCT
ejpam-6128	297	55	/	/	PUNCT
ejpam-6128	297	56	(	(	PUNCT
ejpam-6128	297	57	2a1(12c1qa1	2a1(12c1qa1	NUM
ejpam-6128	297	58	2	2	NUM
ejpam-6128	297	59	+	+	NUM
ejpam-6128	297	60	12c2a1	12c2a1	NUM
ejpam-6128	297	61	2	2	NUM
ejpam-6128	297	62	+	+	CCONJ
ejpam-6128	297	63	6a1a2b1	6a1a2b1	NUM
ejpam-6128	297	64	−	−	NOUN
ejpam-6128	297	65	b1	b1	NOUN
ejpam-6128	297	66	3	3	NUM
ejpam-6128	297	67	+	+	CCONJ
ejpam-6128	297	68	2(36c1	2(36c1	NUM
ejpam-6128	297	69	2q2a1	2q2a1	NOUN
ejpam-6128	297	70	2	2	NUM
ejpam-6128	297	71	+	+	SYM
ejpam-6128	297	72	72c1c2qa1	72c1c2qa1	NOUN
ejpam-6128	297	73	2	2	NUM
ejpam-6128	297	74	+	+	CCONJ
ejpam-6128	297	75	36c1qa1a2b1	36c1qa1a2b1	NUM
ejpam-6128	297	76	−	−	NOUN
ejpam-6128	297	77	6c1qb1	6c1qb1	NUM
ejpam-6128	297	78	3	3	NUM
ejpam-6128	297	79	+	+	CCONJ
ejpam-6128	297	80	36c2	36c2	NUM
ejpam-6128	297	81	2a1	2a1	NUM
ejpam-6128	297	82	2	2	NUM
ejpam-6128	297	83	+	+	CCONJ
ejpam-6128	297	84	36c2a1a2b1	36c2a1a2b1	NUM
ejpam-6128	297	85	−	−	NOUN
ejpam-6128	297	86	6c2b1	6c2b1	NUM
ejpam-6128	297	87	3	3	NUM
ejpam-6128	297	88	+	+	CCONJ
ejpam-6128	297	89	16a1a2	16a1a2	NUM
ejpam-6128	297	90	3	3	NUM
ejpam-6128	297	91	−	−	PROPN
ejpam-6128	297	92	3a2	3a2	NUM
ejpam-6128	297	93	2b1	2b1	NUM
ejpam-6128	297	94	2	2	NUM
ejpam-6128	297	95	)	)	PUNCT
ejpam-6128	297	96	1	1	NUM
ejpam-6128	297	97	2a1	2a1	NUM
ejpam-6128	297	98	)	)	PUNCT
ejpam-6128	297	99	1	1	NUM
ejpam-6128	297	100	3	3	NUM
ejpam-6128	297	101	)	)	PUNCT
ejpam-6128	297	102	−	−	PROPN
ejpam-6128	297	103	b1	b1	NOUN
ejpam-6128	297	104	2a1	2a1	NUM
ejpam-6128	297	105	,	,	PUNCT
ejpam-6128	297	106	(	(	PUNCT
ejpam-6128	297	107	45	45	NUM
ejpam-6128	297	108	)	)	PUNCT
ejpam-6128	297	109	where	where	SCONJ
ejpam-6128	297	110	c1	c1	PROPN
ejpam-6128	297	111	and	and	CCONJ
ejpam-6128	297	112	c2	c2	PROPN
ejpam-6128	297	113	are	be	AUX
ejpam-6128	297	114	constants	constant	NOUN
ejpam-6128	297	115	of	of	ADP
ejpam-6128	297	116	integration	integration	NOUN
ejpam-6128	297	117	.	.	PUNCT
ejpam-6128	298	1	3.2	3.2	NUM
ejpam-6128	298	2	.	.	PUNCT
ejpam-6128	299	1	similarity	similarity	NOUN
ejpam-6128	299	2	reductions	reduction	NOUN
ejpam-6128	299	3	for	for	ADP
ejpam-6128	299	4	case	case	NOUN
ejpam-6128	299	5	2	2	NUM
ejpam-6128	299	6	case	case	NOUN
ejpam-6128	299	7	-	-	PUNCT
ejpam-6128	299	8	a	a	NOUN
ejpam-6128	299	9	:	:	PUNCT
ejpam-6128	299	10	consider	consider	VERB
ejpam-6128	299	11	y1	y1	NOUN
ejpam-6128	299	12	+	+	NOUN
ejpam-6128	299	13	y3	y3	NOUN
ejpam-6128	299	14	=	=	SYM
ejpam-6128	299	15	∂	∂	NOUN
ejpam-6128	300	1	∂x	∂x	PROPN
ejpam-6128	301	1	+	+	CCONJ
ejpam-6128	301	2	∂	∂	NUM
ejpam-6128	301	3	∂t	∂t	PROPN
ejpam-6128	301	4	.	.	PUNCT
ejpam-6128	302	1	the	the	DET
ejpam-6128	302	2	solution	solution	NOUN
ejpam-6128	302	3	of	of	ADP
ejpam-6128	302	4	the	the	DET
ejpam-6128	302	5	characteristic	characteristic	ADJ
ejpam-6128	302	6	equation	equation	NOUN
ejpam-6128	302	7	for	for	ADP
ejpam-6128	302	8	y1	y1	NOUN
ejpam-6128	302	9	+	+	NOUN
ejpam-6128	302	10	y3	y3	NOUN
ejpam-6128	302	11	provides	provide	VERB
ejpam-6128	302	12	the	the	DET
ejpam-6128	302	13	symmetry	symmetry	NOUN
ejpam-6128	302	14	invariants	invariant	NOUN
ejpam-6128	302	15	p	p	NOUN
ejpam-6128	302	16	=	=	SYM
ejpam-6128	302	17	y	y	PROPN
ejpam-6128	302	18	,	,	PUNCT
ejpam-6128	302	19	q	q	NOUN
ejpam-6128	302	20	=	=	PUNCT
ejpam-6128	302	21	−x+	−x+	NOUN
ejpam-6128	302	22	t	t	PROPN
ejpam-6128	302	23	,	,	PUNCT
ejpam-6128	302	24	w(x	w(x	PROPN
ejpam-6128	302	25	,	,	PUNCT
ejpam-6128	302	26	y	y	PROPN
ejpam-6128	302	27	,	,	PUNCT
ejpam-6128	302	28	t	t	PROPN
ejpam-6128	302	29	)	)	PUNCT
ejpam-6128	302	30	=	=	SYM
ejpam-6128	302	31	h(p	h(p	PROPN
ejpam-6128	302	32	,	,	PUNCT
ejpam-6128	302	33	q	q	NOUN
ejpam-6128	302	34	)	)	PUNCT
ejpam-6128	302	35	.	.	PUNCT
ejpam-6128	303	1	(	(	PUNCT
ejpam-6128	303	2	46	46	X
ejpam-6128	303	3	)	)	PUNCT
ejpam-6128	303	4	m.	m.	NOUN
ejpam-6128	303	5	usman	usman	PROPN
ejpam-6128	303	6	,	,	PUNCT
ejpam-6128	303	7	a.	a.	NOUN
ejpam-6128	303	8	hussain	hussain	PROPN
ejpam-6128	303	9	,	,	PUNCT
ejpam-6128	303	10	m.	m.	PROPN
ejpam-6128	303	11	u.	u.	PROPN
ejpam-6128	303	12	farooq	farooq	PROPN
ejpam-6128	303	13	,	,	PUNCT
ejpam-6128	303	14	j.	j.	PROPN
ejpam-6128	303	15	herrera	herrera	PROPN
ejpam-6128	303	16	/	/	SYM
ejpam-6128	303	17	eur	eur	PROPN
ejpam-6128	303	18	.	.	PUNCT
ejpam-6128	304	1	j.	j.	PROPN
ejpam-6128	304	2	pure	pure	PROPN
ejpam-6128	304	3	appl	appl	PROPN
ejpam-6128	304	4	.	.	PROPN
ejpam-6128	304	5	math	math	PROPN
ejpam-6128	304	6	,	,	PUNCT
ejpam-6128	304	7	18	18	NUM
ejpam-6128	304	8	(	(	PUNCT
ejpam-6128	304	9	4	4	NUM
ejpam-6128	304	10	)	)	PUNCT
ejpam-6128	304	11	(	(	PUNCT
ejpam-6128	304	12	2025	2025	NUM
ejpam-6128	304	13	)	)	PUNCT
ejpam-6128	304	14	,	,	PUNCT
ejpam-6128	304	15	6128	6128	NUM
ejpam-6128	304	16	15	15	NUM
ejpam-6128	304	17	of	of	ADP
ejpam-6128	304	18	29	29	NUM
ejpam-6128	304	19	by	by	ADP
ejpam-6128	304	20	inserting	insert	VERB
ejpam-6128	304	21	(	(	PUNCT
ejpam-6128	304	22	46	46	NUM
ejpam-6128	304	23	)	)	PUNCT
ejpam-6128	304	24	in	in	ADP
ejpam-6128	304	25	(	(	PUNCT
ejpam-6128	304	26	2	2	NUM
ejpam-6128	304	27	)	)	PUNCT
ejpam-6128	304	28	,	,	PUNCT
ejpam-6128	304	29	we	we	PRON
ejpam-6128	304	30	get	get	VERB
ejpam-6128	304	31	hqq	hqq	NOUN
ejpam-6128	305	1	−	−	PUNCT
ejpam-6128	306	1	αhhqq	αhhqq	NOUN
ejpam-6128	307	1	−	−	NOUN
ejpam-6128	308	1	αhq	αhq	NOUN
ejpam-6128	308	2	2	2	NUM
ejpam-6128	308	3	−	−	PROPN
ejpam-6128	308	4	βh2hpp	βh2hpp	NOUN
ejpam-6128	308	5	−	−	PROPN
ejpam-6128	309	1	2βhhp	2βhhp	NUM
ejpam-6128	309	2	2	2	NUM
ejpam-6128	309	3	=	=	SYM
ejpam-6128	309	4	0	0	NUM
ejpam-6128	309	5	.	.	PUNCT
ejpam-6128	310	1	(	(	PUNCT
ejpam-6128	310	2	47	47	NUM
ejpam-6128	310	3	)	)	PUNCT
ejpam-6128	310	4	infinitesimals	infinitesimal	NOUN
ejpam-6128	310	5	for	for	ADP
ejpam-6128	310	6	(	(	PUNCT
ejpam-6128	310	7	47	47	NUM
ejpam-6128	310	8	)	)	PUNCT
ejpam-6128	310	9	are	be	AUX
ejpam-6128	310	10	as	as	SCONJ
ejpam-6128	310	11	follows	follow	VERB
ejpam-6128	310	12	ζp	ζp	ADJ
ejpam-6128	310	13	=	=	PUNCT
ejpam-6128	310	14	c1p+	c1p+	PROPN
ejpam-6128	310	15	c2	c2	PROPN
ejpam-6128	310	16	,	,	PUNCT
ejpam-6128	310	17	ζq	ζq	NOUN
ejpam-6128	310	18	=	=	PUNCT
ejpam-6128	310	19	c1q	c1q	PROPN
ejpam-6128	310	20	+	+	CCONJ
ejpam-6128	310	21	c3	c3	NOUN
ejpam-6128	310	22	,	,	PUNCT
ejpam-6128	310	23	φh	φh	ADP
ejpam-6128	310	24	=	=	NOUN
ejpam-6128	310	25	0	0	NUM
ejpam-6128	310	26	.	.	PUNCT
ejpam-6128	311	1	(	(	PUNCT
ejpam-6128	311	2	48	48	NUM
ejpam-6128	311	3	)	)	PUNCT
ejpam-6128	311	4	case	case	NOUN
ejpam-6128	311	5	-	-	PUNCT
ejpam-6128	311	6	a1	a1	NOUN
ejpam-6128	311	7	:	:	PUNCT
ejpam-6128	311	8	in	in	ADP
ejpam-6128	311	9	(	(	PUNCT
ejpam-6128	311	10	48	48	NUM
ejpam-6128	311	11	)	)	PUNCT
ejpam-6128	311	12	,	,	PUNCT
ejpam-6128	311	13	set	set	VERB
ejpam-6128	311	14	c2	c2	PROPN
ejpam-6128	311	15	=	=	SYM
ejpam-6128	311	16	1	1	NUM
ejpam-6128	311	17	and	and	CCONJ
ejpam-6128	311	18	ci	ci	NOUN
ejpam-6128	311	19	=	=	NOUN
ejpam-6128	311	20	0	0	PROPN
ejpam-6128	311	21	for	for	ADP
ejpam-6128	311	22	i	i	PRON
ejpam-6128	311	23	=	=	SYM
ejpam-6128	311	24	1	1	NUM
ejpam-6128	311	25	,	,	PUNCT
ejpam-6128	311	26	3	3	NUM
ejpam-6128	311	27	.	.	PUNCT
ejpam-6128	312	1	then	then	ADV
ejpam-6128	312	2	we	we	PRON
ejpam-6128	312	3	obtain	obtain	VERB
ejpam-6128	312	4	the	the	DET
ejpam-6128	312	5	symmetry	symmetry	NOUN
ejpam-6128	312	6	invariants	invariant	NOUN
ejpam-6128	312	7	r	r	NOUN
ejpam-6128	312	8	=	=	SYM
ejpam-6128	312	9	q	q	ADJ
ejpam-6128	312	10	,	,	PUNCT
ejpam-6128	312	11	h(p	h(p	PROPN
ejpam-6128	312	12	,	,	PUNCT
ejpam-6128	312	13	q	q	NOUN
ejpam-6128	312	14	)	)	PUNCT
ejpam-6128	312	15	=	=	SYM
ejpam-6128	312	16	µ(r	µ(r	NOUN
ejpam-6128	312	17	)	)	PUNCT
ejpam-6128	312	18	.	.	PUNCT
ejpam-6128	313	1	(	(	PUNCT
ejpam-6128	313	2	49	49	NUM
ejpam-6128	313	3	)	)	PUNCT
ejpam-6128	313	4	the	the	DET
ejpam-6128	313	5	substitution	substitution	NOUN
ejpam-6128	313	6	of	of	ADP
ejpam-6128	313	7	(	(	PUNCT
ejpam-6128	313	8	49	49	NUM
ejpam-6128	313	9	)	)	PUNCT
ejpam-6128	313	10	in	in	ADP
ejpam-6128	313	11	(	(	PUNCT
ejpam-6128	313	12	47	47	NUM
ejpam-6128	313	13	)	)	PUNCT
ejpam-6128	313	14	yields	yield	VERB
ejpam-6128	313	15	the	the	DET
ejpam-6128	313	16	following	follow	VERB
ejpam-6128	313	17	ode	ode	PROPN
ejpam-6128	313	18	µ′′	µ′′	PROPN
ejpam-6128	313	19	−	−	NOUN
ejpam-6128	313	20	αµµ′′	αµµ′′	ADJ
ejpam-6128	313	21	−	−	NOUN
ejpam-6128	313	22	αµ′2	αµ′2	NOUN
ejpam-6128	313	23	=	=	NOUN
ejpam-6128	313	24	0	0	NUM
ejpam-6128	313	25	.	.	PUNCT
ejpam-6128	314	1	(	(	PUNCT
ejpam-6128	314	2	50	50	NUM
ejpam-6128	314	3	)	)	PUNCT
ejpam-6128	314	4	the	the	DET
ejpam-6128	314	5	solution	solution	NOUN
ejpam-6128	314	6	of	of	ADP
ejpam-6128	314	7	(	(	PUNCT
ejpam-6128	314	8	50	50	NUM
ejpam-6128	314	9	)	)	PUNCT
ejpam-6128	314	10	takes	take	VERB
ejpam-6128	314	11	the	the	DET
ejpam-6128	314	12	form	form	NOUN
ejpam-6128	314	13	µ(r	µ(r	NOUN
ejpam-6128	314	14	)	)	PUNCT
ejpam-6128	314	15	=	=	SYM
ejpam-6128	315	1	1−	1−	NUM
ejpam-6128	316	1	√	√	NUM
ejpam-6128	316	2	1	1	NUM
ejpam-6128	317	1	+	+	CCONJ
ejpam-6128	317	2	(	(	PUNCT
ejpam-6128	317	3	2c1r	2c1r	NOUN
ejpam-6128	317	4	+	+	CCONJ
ejpam-6128	317	5	2c2)α	2c2)α	NUM
ejpam-6128	317	6	α	α	NOUN
ejpam-6128	317	7	,	,	PUNCT
ejpam-6128	317	8	(	(	PUNCT
ejpam-6128	317	9	51	51	NUM
ejpam-6128	317	10	)	)	PUNCT
ejpam-6128	317	11	which	which	PRON
ejpam-6128	317	12	implies	imply	VERB
ejpam-6128	317	13	h(p	h(p	NOUN
ejpam-6128	317	14	,	,	PUNCT
ejpam-6128	317	15	q	q	X
ejpam-6128	317	16	)	)	PUNCT
ejpam-6128	317	17	=	=	SYM
ejpam-6128	318	1	1−	1−	NUM
ejpam-6128	318	2	√	√	NUM
ejpam-6128	318	3	1	1	NUM
ejpam-6128	318	4	+	+	CCONJ
ejpam-6128	318	5	(	(	PUNCT
ejpam-6128	318	6	2c1q	2c1q	NOUN
ejpam-6128	318	7	+	+	PUNCT
ejpam-6128	319	1	2c2)α	2c2)α	NUM
ejpam-6128	319	2	α	α	NOUN
ejpam-6128	319	3	.	.	PUNCT
ejpam-6128	320	1	(	(	PUNCT
ejpam-6128	320	2	52	52	NUM
ejpam-6128	320	3	)	)	PUNCT
ejpam-6128	320	4	hence	hence	ADV
ejpam-6128	320	5	,	,	PUNCT
ejpam-6128	320	6	the	the	DET
ejpam-6128	320	7	solution	solution	NOUN
ejpam-6128	320	8	of	of	ADP
ejpam-6128	320	9	(	(	PUNCT
ejpam-6128	320	10	2	2	NUM
ejpam-6128	320	11	)	)	PUNCT
ejpam-6128	320	12	is	be	AUX
ejpam-6128	320	13	w(x	w(x	PROPN
ejpam-6128	320	14	,	,	PUNCT
ejpam-6128	320	15	y	y	PROPN
ejpam-6128	320	16	,	,	PUNCT
ejpam-6128	320	17	t	t	PROPN
ejpam-6128	320	18	)	)	PUNCT
ejpam-6128	320	19	=	=	SYM
ejpam-6128	321	1	1−	1−	NUM
ejpam-6128	321	2	√	√	NUM
ejpam-6128	321	3	1	1	NUM
ejpam-6128	322	1	+	+	CCONJ
ejpam-6128	322	2	(	(	PUNCT
ejpam-6128	322	3	2c1(t−	2c1(t−	NUM
ejpam-6128	322	4	x	x	NOUN
ejpam-6128	322	5	)	)	PUNCT
ejpam-6128	323	1	+	+	CCONJ
ejpam-6128	323	2	2c2)α	2c2)α	NUM
ejpam-6128	323	3	α	α	NOUN
ejpam-6128	323	4	,	,	PUNCT
ejpam-6128	323	5	(	(	PUNCT
ejpam-6128	323	6	53	53	NUM
ejpam-6128	323	7	)	)	PUNCT
ejpam-6128	323	8	where	where	SCONJ
ejpam-6128	323	9	c1	c1	PROPN
ejpam-6128	323	10	and	and	CCONJ
ejpam-6128	323	11	c2	c2	PROPN
ejpam-6128	323	12	are	be	AUX
ejpam-6128	323	13	constants	constant	NOUN
ejpam-6128	323	14	of	of	ADP
ejpam-6128	323	15	integration	integration	NOUN
ejpam-6128	323	16	.	.	PUNCT
ejpam-6128	324	1	case	case	NOUN
ejpam-6128	324	2	-	-	PUNCT
ejpam-6128	324	3	a2	a2	NOUN
ejpam-6128	324	4	:	:	PUNCT
ejpam-6128	324	5	in	in	ADP
ejpam-6128	324	6	(	(	PUNCT
ejpam-6128	324	7	48	48	NUM
ejpam-6128	324	8	)	)	PUNCT
ejpam-6128	324	9	,	,	PUNCT
ejpam-6128	324	10	set	set	VERB
ejpam-6128	324	11	c3	c3	NOUN
ejpam-6128	324	12	=	=	SYM
ejpam-6128	324	13	1	1	NUM
ejpam-6128	324	14	and	and	CCONJ
ejpam-6128	324	15	ci	ci	NOUN
ejpam-6128	324	16	=	=	NOUN
ejpam-6128	324	17	0	0	PROPN
ejpam-6128	324	18	for	for	ADP
ejpam-6128	324	19	i	i	PRON
ejpam-6128	324	20	=	=	NOUN
ejpam-6128	324	21	1	1	NUM
ejpam-6128	324	22	,	,	PUNCT
ejpam-6128	324	23	2	2	NUM
ejpam-6128	324	24	.	.	PUNCT
ejpam-6128	325	1	then	then	ADV
ejpam-6128	325	2	we	we	PRON
ejpam-6128	325	3	obtain	obtain	VERB
ejpam-6128	325	4	the	the	DET
ejpam-6128	325	5	symmetry	symmetry	NOUN
ejpam-6128	325	6	invariants	invariant	NOUN
ejpam-6128	325	7	r	r	NOUN
ejpam-6128	325	8	=	=	SYM
ejpam-6128	325	9	p	p	NOUN
ejpam-6128	325	10	,	,	PUNCT
ejpam-6128	325	11	h(p	h(p	PROPN
ejpam-6128	325	12	,	,	PUNCT
ejpam-6128	325	13	q	q	NOUN
ejpam-6128	325	14	)	)	PUNCT
ejpam-6128	325	15	=	=	SYM
ejpam-6128	325	16	µ(r	µ(r	NOUN
ejpam-6128	325	17	)	)	PUNCT
ejpam-6128	325	18	.	.	PUNCT
ejpam-6128	326	1	(	(	PUNCT
ejpam-6128	326	2	54	54	NUM
ejpam-6128	326	3	)	)	PUNCT
ejpam-6128	326	4	the	the	DET
ejpam-6128	326	5	substitution	substitution	NOUN
ejpam-6128	326	6	of	of	ADP
ejpam-6128	326	7	(	(	PUNCT
ejpam-6128	326	8	54	54	NUM
ejpam-6128	326	9	)	)	PUNCT
ejpam-6128	326	10	in	in	ADP
ejpam-6128	326	11	(	(	PUNCT
ejpam-6128	326	12	47	47	NUM
ejpam-6128	326	13	)	)	PUNCT
ejpam-6128	326	14	yields	yield	VERB
ejpam-6128	326	15	the	the	DET
ejpam-6128	326	16	following	follow	VERB
ejpam-6128	326	17	ode	ode	PROPN
ejpam-6128	326	18	µ2µ′′	µ2µ′′	PROPN
ejpam-6128	327	1	+	+	CCONJ
ejpam-6128	327	2	2µµ′2	2µµ′2	NUM
ejpam-6128	327	3	=	=	SYM
ejpam-6128	327	4	0	0	NUM
ejpam-6128	327	5	.	.	PUNCT
ejpam-6128	328	1	(	(	PUNCT
ejpam-6128	328	2	55	55	NUM
ejpam-6128	328	3	)	)	PUNCT
ejpam-6128	328	4	the	the	DET
ejpam-6128	328	5	solution	solution	NOUN
ejpam-6128	328	6	of	of	ADP
ejpam-6128	328	7	(	(	PUNCT
ejpam-6128	328	8	55	55	NUM
ejpam-6128	328	9	)	)	PUNCT
ejpam-6128	328	10	takes	take	VERB
ejpam-6128	328	11	the	the	DET
ejpam-6128	328	12	form	form	NOUN
ejpam-6128	328	13	µ(r	µ(r	NOUN
ejpam-6128	328	14	)	)	PUNCT
ejpam-6128	328	15	=	=	SYM
ejpam-6128	328	16	(	(	PUNCT
ejpam-6128	329	1	3c1r	3c1r	NUM
ejpam-6128	330	1	+	+	NOUN
ejpam-6128	330	2	3c2	3c2	NUM
ejpam-6128	330	3	)	)	PUNCT
ejpam-6128	330	4	1	1	NUM
ejpam-6128	330	5	3	3	NUM
ejpam-6128	330	6	,	,	PUNCT
ejpam-6128	330	7	(	(	PUNCT
ejpam-6128	330	8	56	56	NUM
ejpam-6128	330	9	)	)	PUNCT
ejpam-6128	330	10	m.	m.	NOUN
ejpam-6128	330	11	usman	usman	PROPN
ejpam-6128	330	12	,	,	PUNCT
ejpam-6128	330	13	a.	a.	NOUN
ejpam-6128	330	14	hussain	hussain	PROPN
ejpam-6128	330	15	,	,	PUNCT
ejpam-6128	330	16	m.	m.	PROPN
ejpam-6128	330	17	u.	u.	PROPN
ejpam-6128	330	18	farooq	farooq	PROPN
ejpam-6128	330	19	,	,	PUNCT
ejpam-6128	330	20	j.	j.	PROPN
ejpam-6128	330	21	herrera	herrera	PROPN
ejpam-6128	330	22	/	/	SYM
ejpam-6128	330	23	eur	eur	PROPN
ejpam-6128	330	24	.	.	PUNCT
ejpam-6128	331	1	j.	j.	PROPN
ejpam-6128	331	2	pure	pure	PROPN
ejpam-6128	331	3	appl	appl	PROPN
ejpam-6128	331	4	.	.	PROPN
ejpam-6128	331	5	math	math	PROPN
ejpam-6128	331	6	,	,	PUNCT
ejpam-6128	331	7	18	18	NUM
ejpam-6128	331	8	(	(	PUNCT
ejpam-6128	331	9	4	4	NUM
ejpam-6128	331	10	)	)	PUNCT
ejpam-6128	331	11	(	(	PUNCT
ejpam-6128	331	12	2025	2025	NUM
ejpam-6128	331	13	)	)	PUNCT
ejpam-6128	331	14	,	,	PUNCT
ejpam-6128	331	15	6128	6128	NUM
ejpam-6128	331	16	16	16	NUM
ejpam-6128	331	17	of	of	ADP
ejpam-6128	331	18	29	29	NUM
ejpam-6128	331	19	which	which	PRON
ejpam-6128	331	20	implies	imply	VERB
ejpam-6128	331	21	h(p	h(p	NOUN
ejpam-6128	331	22	,	,	PUNCT
ejpam-6128	331	23	q	q	X
ejpam-6128	331	24	)	)	PUNCT
ejpam-6128	331	25	=	=	SYM
ejpam-6128	331	26	(	(	PUNCT
ejpam-6128	331	27	3c1p+	3c1p+	NUM
ejpam-6128	331	28	3c2	3c2	NUM
ejpam-6128	331	29	)	)	PUNCT
ejpam-6128	331	30	1	1	NUM
ejpam-6128	331	31	3	3	NUM
ejpam-6128	331	32	.	.	PUNCT
ejpam-6128	332	1	(	(	PUNCT
ejpam-6128	332	2	57	57	NUM
ejpam-6128	332	3	)	)	PUNCT
ejpam-6128	332	4	hence	hence	ADV
ejpam-6128	332	5	,	,	PUNCT
ejpam-6128	332	6	the	the	DET
ejpam-6128	332	7	solution	solution	NOUN
ejpam-6128	332	8	of	of	ADP
ejpam-6128	332	9	(	(	PUNCT
ejpam-6128	332	10	2	2	NUM
ejpam-6128	332	11	)	)	PUNCT
ejpam-6128	332	12	is	be	AUX
ejpam-6128	332	13	w(x	w(x	PROPN
ejpam-6128	332	14	,	,	PUNCT
ejpam-6128	332	15	y	y	PROPN
ejpam-6128	332	16	,	,	PUNCT
ejpam-6128	332	17	t	t	PROPN
ejpam-6128	332	18	)	)	PUNCT
ejpam-6128	332	19	=	=	PUNCT
ejpam-6128	333	1	(	(	PUNCT
ejpam-6128	333	2	3c1y	3c1y	NOUN
ejpam-6128	333	3	+	+	PUNCT
ejpam-6128	333	4	3c2	3c2	NUM
ejpam-6128	333	5	)	)	PUNCT
ejpam-6128	333	6	1	1	NUM
ejpam-6128	333	7	3	3	NUM
ejpam-6128	333	8	,	,	PUNCT
ejpam-6128	333	9	(	(	PUNCT
ejpam-6128	333	10	58	58	NUM
ejpam-6128	333	11	)	)	PUNCT
ejpam-6128	333	12	where	where	SCONJ
ejpam-6128	333	13	c1	c1	PROPN
ejpam-6128	333	14	and	and	CCONJ
ejpam-6128	333	15	c2	c2	PROPN
ejpam-6128	333	16	are	be	AUX
ejpam-6128	333	17	constants	constant	NOUN
ejpam-6128	333	18	of	of	ADP
ejpam-6128	333	19	integration	integration	NOUN
ejpam-6128	333	20	.	.	PUNCT
ejpam-6128	334	1	case	case	NOUN
ejpam-6128	334	2	-	-	PUNCT
ejpam-6128	334	3	a3	a3	NOUN
ejpam-6128	334	4	:	:	PUNCT
ejpam-6128	334	5	in	in	ADP
ejpam-6128	334	6	(	(	PUNCT
ejpam-6128	334	7	48	48	NUM
ejpam-6128	334	8	)	)	PUNCT
ejpam-6128	334	9	,	,	PUNCT
ejpam-6128	334	10	set	set	VERB
ejpam-6128	334	11	c2	c2	PROPN
ejpam-6128	334	12	=	=	SYM
ejpam-6128	334	13	c3	c3	PROPN
ejpam-6128	334	14	=	=	SYM
ejpam-6128	334	15	1	1	NUM
ejpam-6128	334	16	and	and	CCONJ
ejpam-6128	334	17	c1	c1	NOUN
ejpam-6128	334	18	=	=	PUNCT
ejpam-6128	335	1	0	0	X
ejpam-6128	335	2	.	.	PUNCT
ejpam-6128	336	1	then	then	ADV
ejpam-6128	336	2	we	we	PRON
ejpam-6128	336	3	obtain	obtain	VERB
ejpam-6128	336	4	the	the	DET
ejpam-6128	336	5	symmetry	symmetry	NOUN
ejpam-6128	336	6	invariants	invariant	NOUN
ejpam-6128	336	7	r	r	NOUN
ejpam-6128	336	8	=	=	PUNCT
ejpam-6128	336	9	q	q	NOUN
ejpam-6128	336	10	−	−	PROPN
ejpam-6128	336	11	p	p	X
ejpam-6128	336	12	,	,	PUNCT
ejpam-6128	336	13	h(p	h(p	PROPN
ejpam-6128	336	14	,	,	PUNCT
ejpam-6128	336	15	q	q	NOUN
ejpam-6128	336	16	)	)	PUNCT
ejpam-6128	336	17	=	=	SYM
ejpam-6128	336	18	µ(r	µ(r	NOUN
ejpam-6128	336	19	)	)	PUNCT
ejpam-6128	336	20	.	.	PUNCT
ejpam-6128	337	1	(	(	PUNCT
ejpam-6128	337	2	59	59	NUM
ejpam-6128	337	3	)	)	PUNCT
ejpam-6128	337	4	the	the	DET
ejpam-6128	337	5	substitution	substitution	NOUN
ejpam-6128	337	6	of	of	ADP
ejpam-6128	337	7	(	(	PUNCT
ejpam-6128	337	8	59	59	NUM
ejpam-6128	337	9	)	)	PUNCT
ejpam-6128	337	10	in	in	ADP
ejpam-6128	337	11	(	(	PUNCT
ejpam-6128	337	12	47	47	NUM
ejpam-6128	337	13	)	)	PUNCT
ejpam-6128	337	14	yields	yield	VERB
ejpam-6128	337	15	the	the	DET
ejpam-6128	337	16	following	follow	VERB
ejpam-6128	337	17	ode	ode	ADJ
ejpam-6128	337	18	−βµ2µ′′	−βµ2µ′′	PROPN
ejpam-6128	337	19	−	−	PROPN
ejpam-6128	337	20	2βµµ′2	2βµµ′2	NOUN
ejpam-6128	337	21	−	−	NOUN
ejpam-6128	337	22	αµµ′′	αµµ′′	ADJ
ejpam-6128	337	23	−	−	NOUN
ejpam-6128	337	24	αµ′2	αµ′2	NOUN
ejpam-6128	337	25	+	+	NUM
ejpam-6128	337	26	µ′′	µ′′	NOUN
ejpam-6128	337	27	=	=	SYM
ejpam-6128	337	28	0	0	NUM
ejpam-6128	337	29	.	.	PUNCT
ejpam-6128	338	1	(	(	PUNCT
ejpam-6128	338	2	60	60	NUM
ejpam-6128	338	3	)	)	PUNCT
ejpam-6128	338	4	the	the	DET
ejpam-6128	338	5	solution	solution	NOUN
ejpam-6128	338	6	of	of	ADP
ejpam-6128	338	7	(	(	PUNCT
ejpam-6128	338	8	60	60	NUM
ejpam-6128	338	9	)	)	PUNCT
ejpam-6128	338	10	takes	take	VERB
ejpam-6128	338	11	the	the	DET
ejpam-6128	338	12	form	form	NOUN
ejpam-6128	338	13	µ(r	µ(r	NOUN
ejpam-6128	338	14	)	)	PUNCT
ejpam-6128	338	15	=	=	SYM
ejpam-6128	338	16	1	1	NUM
ejpam-6128	338	17	2β	2β	NOUN
ejpam-6128	338	18	(	(	PUNCT
ejpam-6128	338	19	12c1β	12c1β	PROPN
ejpam-6128	338	20	2r+12c2β	2r+12c2β	NUM
ejpam-6128	338	21	2−α3	2−α3	NUM
ejpam-6128	338	22	+	+	NOUN
ejpam-6128	338	23	2(36c1	2(36c1	NUM
ejpam-6128	338	24	2β2r2	2β2r2	NOUN
ejpam-6128	338	25	+	+	ADJ
ejpam-6128	338	26	72c1c2β	72c1c2β	NUM
ejpam-6128	338	27	2r−6c1α	2r−6c1α	NUM
ejpam-6128	338	28	3r−36c1αβr+36c2	3r−36c1αβr+36c2	NUM
ejpam-6128	338	29	2β2−	2β2−	NUM
ejpam-6128	338	30	6c2α	6c2α	NOUN
ejpam-6128	338	31	3	3	NUM
ejpam-6128	338	32	−	−	PROPN
ejpam-6128	338	33	36c2αβ	36c2αβ	NOUN
ejpam-6128	339	1	−	−	PROPN
ejpam-6128	339	2	3α2	3α2	NUM
ejpam-6128	339	3	−	−	PROPN
ejpam-6128	339	4	16β	16β	NOUN
ejpam-6128	339	5	)	)	PUNCT
ejpam-6128	339	6	1	1	NUM
ejpam-6128	339	7	2β	2β	NOUN
ejpam-6128	339	8	−	−	PROPN
ejpam-6128	339	9	6αβ	6αβ	NOUN
ejpam-6128	339	10	)	)	PUNCT
ejpam-6128	339	11	1	1	NUM
ejpam-6128	339	12	3	3	NUM
ejpam-6128	339	13	+	+	CCONJ
ejpam-6128	339	14	(	(	PUNCT
ejpam-6128	339	15	α2	α2	ADJ
ejpam-6128	339	16	+	+	CCONJ
ejpam-6128	339	17	4β	4β	NOUN
ejpam-6128	339	18	)	)	PUNCT
ejpam-6128	339	19	/	/	SYM
ejpam-6128	339	20	(	(	PUNCT
ejpam-6128	339	21	2β(12c1β	2β(12c1β	NUM
ejpam-6128	339	22	2r	2r	NUM
ejpam-6128	339	23	+	+	CCONJ
ejpam-6128	339	24	12c2β	12c2β	NUM
ejpam-6128	339	25	2	2	NUM
ejpam-6128	339	26	−	−	NOUN
ejpam-6128	339	27	α3	α3	NOUN
ejpam-6128	339	28	+	+	NOUN
ejpam-6128	339	29	2(36c1	2(36c1	NUM
ejpam-6128	339	30	2β2r2	2β2r2	NOUN
ejpam-6128	339	31	+	+	ADJ
ejpam-6128	339	32	72c1c2β	72c1c2β	NUM
ejpam-6128	339	33	2r−6c1α	2r−6c1α	NUM
ejpam-6128	339	34	3r−36c1αβr+36c2	3r−36c1αβr+36c2	NUM
ejpam-6128	339	35	2β2−6c2α	2β2−6c2α	NOUN
ejpam-6128	339	36	3−36c2αβ−3α2−16β	3−36c2αβ−3α2−16β	NUM
ejpam-6128	339	37	)	)	PUNCT
ejpam-6128	339	38	1	1	NUM
ejpam-6128	339	39	2β−	2β−	PROPN
ejpam-6128	339	40	6αβ	6αβ	NOUN
ejpam-6128	339	41	)	)	PUNCT
ejpam-6128	339	42	1	1	NUM
ejpam-6128	339	43	3	3	NUM
ejpam-6128	339	44	)	)	PUNCT
ejpam-6128	339	45	−	−	NOUN
ejpam-6128	340	1	α	α	NOUN
ejpam-6128	340	2	2β	2β	NOUN
ejpam-6128	340	3	,	,	PUNCT
ejpam-6128	340	4	which	which	PRON
ejpam-6128	340	5	implies	imply	VERB
ejpam-6128	340	6	h(p	h(p	NOUN
ejpam-6128	340	7	,	,	PUNCT
ejpam-6128	340	8	q	q	X
ejpam-6128	340	9	)	)	PUNCT
ejpam-6128	340	10	=	=	SYM
ejpam-6128	340	11	1	1	NUM
ejpam-6128	340	12	2β	2β	NOUN
ejpam-6128	340	13	(	(	PUNCT
ejpam-6128	340	14	12c1β	12c1β	NUM
ejpam-6128	340	15	2(q	2(q	NUM
ejpam-6128	340	16	−	−	PROPN
ejpam-6128	341	1	p	p	X
ejpam-6128	341	2	)	)	PUNCT
ejpam-6128	341	3	+	+	CCONJ
ejpam-6128	341	4	12c2β	12c2β	NUM
ejpam-6128	341	5	2	2	NUM
ejpam-6128	341	6	−	−	NOUN
ejpam-6128	341	7	α3	α3	NOUN
ejpam-6128	341	8	+	+	NOUN
ejpam-6128	341	9	2(36c1	2(36c1	NUM
ejpam-6128	341	10	2β2(q	2β2(q	NUM
ejpam-6128	341	11	−	−	NOUN
ejpam-6128	341	12	p)2	p)2	NOUN
ejpam-6128	341	13	+	+	CCONJ
ejpam-6128	341	14	72c1c2β	72c1c2β	NUM
ejpam-6128	341	15	2(q	2(q	NUM
ejpam-6128	341	16	−	−	ADP
ejpam-6128	342	1	p	p	X
ejpam-6128	342	2	)	)	PUNCT
ejpam-6128	342	3	−	−	PROPN
ejpam-6128	342	4	6c1α	6c1α	NOUN
ejpam-6128	343	1	3(q	3(q	NUM
ejpam-6128	343	2	−	−	PROPN
ejpam-6128	344	1	p	p	X
ejpam-6128	344	2	)	)	PUNCT
ejpam-6128	345	1	−	−	PROPN
ejpam-6128	345	2	36c1αβ(q	36c1αβ(q	NUM
ejpam-6128	345	3	−	−	NOUN
ejpam-6128	346	1	p	p	X
ejpam-6128	346	2	)	)	PUNCT
ejpam-6128	346	3	+	+	CCONJ
ejpam-6128	347	1	36c2	36c2	NUM
ejpam-6128	347	2	2β2	2β2	NUM
ejpam-6128	347	3	−	−	NOUN
ejpam-6128	347	4	6c2α	6c2α	NOUN
ejpam-6128	347	5	3	3	NUM
ejpam-6128	347	6	−	−	PROPN
ejpam-6128	347	7	36c2αβ	36c2αβ	NOUN
ejpam-6128	347	8	−	−	PROPN
ejpam-6128	347	9	3α2	3α2	NUM
ejpam-6128	347	10	−	−	PROPN
ejpam-6128	347	11	16β	16β	NOUN
ejpam-6128	347	12	)	)	PUNCT
ejpam-6128	347	13	1	1	NUM
ejpam-6128	347	14	2β	2β	NOUN
ejpam-6128	347	15	−	−	PROPN
ejpam-6128	347	16	6αβ	6αβ	NOUN
ejpam-6128	347	17	)	)	PUNCT
ejpam-6128	347	18	1	1	NUM
ejpam-6128	347	19	3	3	NUM
ejpam-6128	347	20	+	+	ADJ
ejpam-6128	347	21	(	(	PUNCT
ejpam-6128	347	22	α2	α2	ADJ
ejpam-6128	347	23	+	+	CCONJ
ejpam-6128	347	24	4β	4β	NOUN
ejpam-6128	347	25	)	)	PUNCT
ejpam-6128	347	26	/	/	SYM
ejpam-6128	347	27	(	(	PUNCT
ejpam-6128	347	28	2β(12c1β	2β(12c1β	NUM
ejpam-6128	347	29	2(q	2(q	NUM
ejpam-6128	347	30	−	−	PROPN
ejpam-6128	348	1	p	p	X
ejpam-6128	348	2	)	)	PUNCT
ejpam-6128	348	3	+	+	CCONJ
ejpam-6128	348	4	12c2β	12c2β	NUM
ejpam-6128	348	5	2	2	NUM
ejpam-6128	348	6	−	−	NOUN
ejpam-6128	348	7	α3	α3	NOUN
ejpam-6128	348	8	+	+	NOUN
ejpam-6128	348	9	2(36c1	2(36c1	NUM
ejpam-6128	348	10	2β2(q	2β2(q	NUM
ejpam-6128	348	11	−	−	NOUN
ejpam-6128	348	12	p)2	p)2	NOUN
ejpam-6128	348	13	+	+	CCONJ
ejpam-6128	348	14	72c1c2β	72c1c2β	NUM
ejpam-6128	348	15	2(q	2(q	NUM
ejpam-6128	348	16	−	−	ADP
ejpam-6128	349	1	p	p	X
ejpam-6128	349	2	)	)	PUNCT
ejpam-6128	349	3	−	−	PROPN
ejpam-6128	349	4	6c1α	6c1α	NOUN
ejpam-6128	349	5	3(q−	3(q−	NUM
ejpam-6128	349	6	p)−	p)−	NOUN
ejpam-6128	349	7	36c1αβ(q−	36c1αβ(q−	NOUN
ejpam-6128	349	8	p	p	NOUN
ejpam-6128	349	9	)	)	PUNCT
ejpam-6128	349	10	+	+	CCONJ
ejpam-6128	350	1	36c2	36c2	NUM
ejpam-6128	350	2	2β2	2β2	NUM
ejpam-6128	350	3	−	−	NOUN
ejpam-6128	350	4	6c2α	6c2α	NOUN
ejpam-6128	350	5	3	3	NUM
ejpam-6128	350	6	−	−	PROPN
ejpam-6128	350	7	36c2αβ	36c2αβ	NOUN
ejpam-6128	350	8	−	−	PROPN
ejpam-6128	350	9	3α2	3α2	NUM
ejpam-6128	350	10	−	−	PROPN
ejpam-6128	350	11	16β	16β	NOUN
ejpam-6128	350	12	)	)	PUNCT
ejpam-6128	350	13	1	1	NUM
ejpam-6128	350	14	2β	2β	NOUN
ejpam-6128	350	15	−	−	PROPN
ejpam-6128	350	16	6αβ	6αβ	NOUN
ejpam-6128	350	17	)	)	PUNCT
ejpam-6128	350	18	1	1	NUM
ejpam-6128	350	19	3	3	NUM
ejpam-6128	350	20	)	)	PUNCT
ejpam-6128	350	21	−	−	NOUN
ejpam-6128	351	1	α	α	NOUN
ejpam-6128	351	2	2β	2β	NOUN
ejpam-6128	351	3	.	.	PUNCT
ejpam-6128	352	1	hence	hence	ADV
ejpam-6128	352	2	,	,	PUNCT
ejpam-6128	352	3	the	the	DET
ejpam-6128	352	4	solution	solution	NOUN
ejpam-6128	352	5	of	of	ADP
ejpam-6128	352	6	(	(	PUNCT
ejpam-6128	352	7	2	2	NUM
ejpam-6128	352	8	)	)	PUNCT
ejpam-6128	352	9	is	be	AUX
ejpam-6128	352	10	w(x	w(x	PROPN
ejpam-6128	352	11	,	,	PUNCT
ejpam-6128	352	12	y	y	PROPN
ejpam-6128	352	13	,	,	PUNCT
ejpam-6128	352	14	t	t	PROPN
ejpam-6128	352	15	)	)	PUNCT
ejpam-6128	352	16	=	=	SYM
ejpam-6128	352	17	1	1	NUM
ejpam-6128	352	18	2β	2β	NOUN
ejpam-6128	352	19	(	(	PUNCT
ejpam-6128	352	20	12c1β	12c1β	NUM
ejpam-6128	352	21	2(t−x−y)+12c2β	2(t−x−y)+12c2β	NUM
ejpam-6128	352	22	2−α3	2−α3	NUM
ejpam-6128	352	23	+	+	SYM
ejpam-6128	352	24	2(36c1	2(36c1	NUM
ejpam-6128	352	25	2β2(t−x−y)2	2β2(t−x−y)2	ADV
ejpam-6128	352	26	+	+	ADJ
ejpam-6128	352	27	72c1c2β	72c1c2β	NUM
ejpam-6128	352	28	2(t−x−y)−	2(t−x−y)−	NUM
ejpam-6128	352	29	6c1α	6c1α	NOUN
ejpam-6128	352	30	3(t−x−y)−36c1αβ(t−x−y)+36c2	3(t−x−y)−36c1αβ(t−x−y)+36c2	NUM
ejpam-6128	352	31	2β2−6c2α	2β2−6c2α	NOUN
ejpam-6128	352	32	3−36c2αβ−3α2−16β	3−36c2αβ−3α2−16β	NUM
ejpam-6128	352	33	)	)	PUNCT
ejpam-6128	352	34	1	1	NUM
ejpam-6128	352	35	2β−6αβ	2β−6αβ	NUM
ejpam-6128	352	36	)	)	PUNCT
ejpam-6128	352	37	1	1	NUM
ejpam-6128	352	38	3	3	NUM
ejpam-6128	352	39	+	+	ADJ
ejpam-6128	352	40	(	(	PUNCT
ejpam-6128	352	41	α2	α2	ADJ
ejpam-6128	352	42	+	+	CCONJ
ejpam-6128	352	43	4β	4β	NOUN
ejpam-6128	352	44	)	)	PUNCT
ejpam-6128	352	45	/	/	SYM
ejpam-6128	352	46	(	(	PUNCT
ejpam-6128	352	47	2β(12c1β	2β(12c1β	NUM
ejpam-6128	352	48	2(t−x−y)+12c2β	2(t−x−y)+12c2β	NUM
ejpam-6128	352	49	2−α3	2−α3	NUM
ejpam-6128	352	50	+	+	SYM
ejpam-6128	352	51	2(36c1	2(36c1	NUM
ejpam-6128	352	52	2β2(t−x−y)2	2β2(t−x−y)2	ADV
ejpam-6128	352	53	+	+	ADJ
ejpam-6128	352	54	72c1c2β	72c1c2β	NUM
ejpam-6128	352	55	2(t−x−y)−	2(t−x−y)−	NUM
ejpam-6128	352	56	6c1α	6c1α	NOUN
ejpam-6128	352	57	3(t−x−y)−36c1αβ(t−x−y)+36c2	3(t−x−y)−36c1αβ(t−x−y)+36c2	NUM
ejpam-6128	352	58	2β2−6c2α	2β2−6c2α	NOUN
ejpam-6128	352	59	3−36c2αβ−3α2−16β	3−36c2αβ−3α2−16β	NUM
ejpam-6128	352	60	)	)	PUNCT
ejpam-6128	352	61	1	1	NUM
ejpam-6128	352	62	2β−6αβ	2β−6αβ	NUM
ejpam-6128	352	63	)	)	PUNCT
ejpam-6128	352	64	1	1	NUM
ejpam-6128	352	65	3	3	NUM
ejpam-6128	352	66	)	)	PUNCT
ejpam-6128	352	67	−	−	NOUN
ejpam-6128	353	1	α	α	NOUN
ejpam-6128	353	2	2β	2β	NOUN
ejpam-6128	353	3	,	,	PUNCT
ejpam-6128	353	4	where	where	SCONJ
ejpam-6128	353	5	c1	c1	PROPN
ejpam-6128	353	6	and	and	CCONJ
ejpam-6128	353	7	c2	c2	PROPN
ejpam-6128	353	8	are	be	AUX
ejpam-6128	353	9	constants	constant	NOUN
ejpam-6128	353	10	of	of	ADP
ejpam-6128	353	11	integration	integration	NOUN
ejpam-6128	353	12	.	.	PUNCT
ejpam-6128	354	1	m.	m.	PROPN
ejpam-6128	354	2	usman	usman	PROPN
ejpam-6128	354	3	,	,	PUNCT
ejpam-6128	354	4	a.	a.	NOUN
ejpam-6128	354	5	hussain	hussain	PROPN
ejpam-6128	354	6	,	,	PUNCT
ejpam-6128	354	7	m.	m.	PROPN
ejpam-6128	354	8	u.	u.	PROPN
ejpam-6128	354	9	farooq	farooq	PROPN
ejpam-6128	354	10	,	,	PUNCT
ejpam-6128	354	11	j.	j.	PROPN
ejpam-6128	354	12	herrera	herrera	PROPN
ejpam-6128	354	13	/	/	SYM
ejpam-6128	354	14	eur	eur	PROPN
ejpam-6128	354	15	.	.	PUNCT
ejpam-6128	355	1	j.	j.	PROPN
ejpam-6128	355	2	pure	pure	PROPN
ejpam-6128	355	3	appl	appl	PROPN
ejpam-6128	355	4	.	.	PROPN
ejpam-6128	355	5	math	math	PROPN
ejpam-6128	355	6	,	,	PUNCT
ejpam-6128	355	7	18	18	NUM
ejpam-6128	355	8	(	(	PUNCT
ejpam-6128	355	9	4	4	NUM
ejpam-6128	355	10	)	)	PUNCT
ejpam-6128	355	11	(	(	PUNCT
ejpam-6128	355	12	2025	2025	NUM
ejpam-6128	355	13	)	)	PUNCT
ejpam-6128	355	14	,	,	PUNCT
ejpam-6128	355	15	6128	6128	NUM
ejpam-6128	355	16	17	17	NUM
ejpam-6128	355	17	of	of	ADP
ejpam-6128	355	18	29	29	NUM
ejpam-6128	355	19	case	case	NOUN
ejpam-6128	355	20	-	-	PUNCT
ejpam-6128	355	21	b	b	NOUN
ejpam-6128	355	22	:	:	PUNCT
ejpam-6128	355	23	consider	consider	VERB
ejpam-6128	355	24	y1	y1	NOUN
ejpam-6128	355	25	=	=	SYM
ejpam-6128	355	26	∂	∂	NUM
ejpam-6128	356	1	∂x	∂x	PROPN
ejpam-6128	357	1	.	.	PUNCT
ejpam-6128	358	1	the	the	DET
ejpam-6128	358	2	solution	solution	NOUN
ejpam-6128	358	3	of	of	ADP
ejpam-6128	358	4	the	the	DET
ejpam-6128	358	5	characteristic	characteristic	ADJ
ejpam-6128	358	6	equation	equation	NOUN
ejpam-6128	358	7	for	for	ADP
ejpam-6128	358	8	y1	y1	NOUN
ejpam-6128	358	9	provides	provide	VERB
ejpam-6128	358	10	the	the	DET
ejpam-6128	358	11	symmetry	symmetry	NOUN
ejpam-6128	358	12	invariants	invariant	NOUN
ejpam-6128	358	13	p	p	PROPN
ejpam-6128	358	14	=	=	PROPN
ejpam-6128	358	15	t	t	PROPN
ejpam-6128	358	16	,	,	PUNCT
ejpam-6128	358	17	q	q	NOUN
ejpam-6128	358	18	=	=	SYM
ejpam-6128	358	19	y	y	PROPN
ejpam-6128	358	20	,	,	PUNCT
ejpam-6128	358	21	w(x	w(x	PROPN
ejpam-6128	358	22	,	,	PUNCT
ejpam-6128	358	23	y	y	PROPN
ejpam-6128	358	24	,	,	PUNCT
ejpam-6128	358	25	t	t	PROPN
ejpam-6128	358	26	)	)	PUNCT
ejpam-6128	358	27	=	=	SYM
ejpam-6128	358	28	h(p	h(p	PROPN
ejpam-6128	358	29	,	,	PUNCT
ejpam-6128	358	30	q	q	NOUN
ejpam-6128	358	31	)	)	PUNCT
ejpam-6128	358	32	.	.	PUNCT
ejpam-6128	359	1	(	(	PUNCT
ejpam-6128	359	2	61	61	NUM
ejpam-6128	359	3	)	)	PUNCT
ejpam-6128	359	4	by	by	ADP
ejpam-6128	359	5	inserting	insert	VERB
ejpam-6128	359	6	(	(	PUNCT
ejpam-6128	359	7	61	61	NUM
ejpam-6128	359	8	)	)	PUNCT
ejpam-6128	359	9	in	in	ADP
ejpam-6128	359	10	(	(	PUNCT
ejpam-6128	359	11	2	2	NUM
ejpam-6128	359	12	)	)	PUNCT
ejpam-6128	359	13	,	,	PUNCT
ejpam-6128	359	14	we	we	PRON
ejpam-6128	359	15	get	get	VERB
ejpam-6128	359	16	hpp	hpp	PROPN
ejpam-6128	359	17	−	−	PROPN
ejpam-6128	360	1	βh2hqq	βh2hqq	PROPN
ejpam-6128	361	1	−	−	NUM
ejpam-6128	361	2	2βhhq	2βhhq	NUM
ejpam-6128	361	3	2	2	NUM
ejpam-6128	361	4	=	=	SYM
ejpam-6128	361	5	0	0	NUM
ejpam-6128	361	6	.	.	PUNCT
ejpam-6128	362	1	(	(	PUNCT
ejpam-6128	362	2	62	62	NUM
ejpam-6128	362	3	)	)	PUNCT
ejpam-6128	362	4	infinitesimals	infinitesimal	NOUN
ejpam-6128	362	5	for	for	ADP
ejpam-6128	362	6	(	(	PUNCT
ejpam-6128	362	7	62	62	NUM
ejpam-6128	362	8	)	)	PUNCT
ejpam-6128	362	9	are	be	AUX
ejpam-6128	362	10	as	as	SCONJ
ejpam-6128	362	11	follows	follow	VERB
ejpam-6128	362	12	ζp	ζp	ADJ
ejpam-6128	362	13	=	=	PUNCT
ejpam-6128	362	14	c1p+	c1p+	PROPN
ejpam-6128	362	15	c2	c2	PROPN
ejpam-6128	362	16	,	,	PUNCT
ejpam-6128	362	17	ζq	ζq	NOUN
ejpam-6128	362	18	=	=	PUNCT
ejpam-6128	362	19	c3q	c3q	PROPN
ejpam-6128	362	20	+	+	NUM
ejpam-6128	362	21	c4	c4	NOUN
ejpam-6128	362	22	,	,	PUNCT
ejpam-6128	362	23	φh	φh	ADP
ejpam-6128	362	24	=	=	SYM
ejpam-6128	362	25	−h(c1	−h(c1	PROPN
ejpam-6128	362	26	−	−	PROPN
ejpam-6128	362	27	c3	c3	PROPN
ejpam-6128	362	28	)	)	PUNCT
ejpam-6128	362	29	.	.	PUNCT
ejpam-6128	363	1	(	(	PUNCT
ejpam-6128	363	2	63	63	NUM
ejpam-6128	363	3	)	)	PUNCT
ejpam-6128	363	4	case	case	NOUN
ejpam-6128	363	5	-	-	PUNCT
ejpam-6128	363	6	b1	b1	NOUN
ejpam-6128	363	7	:	:	PUNCT
ejpam-6128	363	8	in	in	ADP
ejpam-6128	363	9	(	(	PUNCT
ejpam-6128	363	10	63	63	NUM
ejpam-6128	363	11	)	)	PUNCT
ejpam-6128	363	12	,	,	PUNCT
ejpam-6128	363	13	set	set	VERB
ejpam-6128	363	14	c4	c4	NOUN
ejpam-6128	363	15	=	=	SYM
ejpam-6128	363	16	1	1	NUM
ejpam-6128	363	17	and	and	CCONJ
ejpam-6128	363	18	ci	ci	NOUN
ejpam-6128	363	19	=	=	NOUN
ejpam-6128	363	20	0	0	PROPN
ejpam-6128	364	1	for	for	ADP
ejpam-6128	364	2	i	i	PRON
ejpam-6128	364	3	=	=	NOUN
ejpam-6128	364	4	1	1	NUM
ejpam-6128	364	5	,	,	PUNCT
ejpam-6128	364	6	2	2	NUM
ejpam-6128	364	7	,	,	PUNCT
ejpam-6128	364	8	3	3	NUM
ejpam-6128	364	9	.	.	PUNCT
ejpam-6128	364	10	then	then	ADV
ejpam-6128	364	11	we	we	PRON
ejpam-6128	364	12	obtain	obtain	VERB
ejpam-6128	364	13	the	the	DET
ejpam-6128	364	14	symmetry	symmetry	NOUN
ejpam-6128	364	15	invariants	invariant	NOUN
ejpam-6128	364	16	r	r	NOUN
ejpam-6128	364	17	=	=	SYM
ejpam-6128	364	18	p	p	NOUN
ejpam-6128	364	19	,	,	PUNCT
ejpam-6128	364	20	h(p	h(p	PROPN
ejpam-6128	364	21	,	,	PUNCT
ejpam-6128	364	22	q	q	NOUN
ejpam-6128	364	23	)	)	PUNCT
ejpam-6128	364	24	=	=	SYM
ejpam-6128	364	25	µ(r	µ(r	NOUN
ejpam-6128	364	26	)	)	PUNCT
ejpam-6128	364	27	.	.	PUNCT
ejpam-6128	365	1	(	(	PUNCT
ejpam-6128	365	2	64	64	NUM
ejpam-6128	365	3	)	)	PUNCT
ejpam-6128	365	4	the	the	DET
ejpam-6128	365	5	substitution	substitution	NOUN
ejpam-6128	365	6	of	of	ADP
ejpam-6128	365	7	(	(	PUNCT
ejpam-6128	365	8	64	64	NUM
ejpam-6128	365	9	)	)	PUNCT
ejpam-6128	365	10	in	in	ADP
ejpam-6128	365	11	(	(	PUNCT
ejpam-6128	365	12	62	62	NUM
ejpam-6128	365	13	)	)	PUNCT
ejpam-6128	365	14	yields	yield	VERB
ejpam-6128	365	15	the	the	DET
ejpam-6128	365	16	following	follow	VERB
ejpam-6128	365	17	ode	ode	PROPN
ejpam-6128	365	18	µ′′	µ′′	PROPN
ejpam-6128	365	19	=	=	SYM
ejpam-6128	365	20	0	0	NUM
ejpam-6128	365	21	.	.	PUNCT
ejpam-6128	366	1	(	(	PUNCT
ejpam-6128	366	2	65	65	NUM
ejpam-6128	366	3	)	)	PUNCT
ejpam-6128	366	4	the	the	DET
ejpam-6128	366	5	solution	solution	NOUN
ejpam-6128	366	6	of	of	ADP
ejpam-6128	366	7	(	(	PUNCT
ejpam-6128	366	8	65	65	NUM
ejpam-6128	366	9	)	)	PUNCT
ejpam-6128	366	10	takes	take	VERB
ejpam-6128	366	11	the	the	DET
ejpam-6128	366	12	form	form	NOUN
ejpam-6128	366	13	µ(r	µ(r	NOUN
ejpam-6128	366	14	)	)	PUNCT
ejpam-6128	367	1	=	=	SYM
ejpam-6128	367	2	c1r	c1r	PROPN
ejpam-6128	368	1	+	+	PROPN
ejpam-6128	368	2	c2	c2	PROPN
ejpam-6128	368	3	,	,	PUNCT
ejpam-6128	368	4	(	(	PUNCT
ejpam-6128	368	5	66	66	NUM
ejpam-6128	368	6	)	)	PUNCT
ejpam-6128	368	7	which	which	PRON
ejpam-6128	368	8	implies	imply	VERB
ejpam-6128	368	9	h(p	h(p	NOUN
ejpam-6128	368	10	,	,	PUNCT
ejpam-6128	368	11	q	q	X
ejpam-6128	368	12	)	)	PUNCT
ejpam-6128	368	13	=	=	SYM
ejpam-6128	368	14	c1p+	c1p+	PROPN
ejpam-6128	368	15	c2	c2	PROPN
ejpam-6128	368	16	.	.	PUNCT
ejpam-6128	369	1	(	(	PUNCT
ejpam-6128	369	2	67	67	NUM
ejpam-6128	369	3	)	)	PUNCT
ejpam-6128	369	4	hence	hence	ADV
ejpam-6128	369	5	,	,	PUNCT
ejpam-6128	369	6	the	the	DET
ejpam-6128	369	7	solution	solution	NOUN
ejpam-6128	369	8	of	of	ADP
ejpam-6128	369	9	(	(	PUNCT
ejpam-6128	369	10	2	2	NUM
ejpam-6128	369	11	)	)	PUNCT
ejpam-6128	369	12	is	be	AUX
ejpam-6128	369	13	w(x	w(x	PROPN
ejpam-6128	369	14	,	,	PUNCT
ejpam-6128	369	15	y	y	PROPN
ejpam-6128	369	16	,	,	PUNCT
ejpam-6128	369	17	t	t	PROPN
ejpam-6128	369	18	)	)	PUNCT
ejpam-6128	370	1	=	=	SYM
ejpam-6128	370	2	c1t+	c1t+	PROPN
ejpam-6128	370	3	c2	c2	PROPN
ejpam-6128	370	4	,	,	PUNCT
ejpam-6128	370	5	(	(	PUNCT
ejpam-6128	370	6	68	68	NUM
ejpam-6128	370	7	)	)	PUNCT
ejpam-6128	370	8	where	where	SCONJ
ejpam-6128	370	9	c1	c1	PROPN
ejpam-6128	370	10	and	and	CCONJ
ejpam-6128	370	11	c2	c2	PROPN
ejpam-6128	370	12	are	be	AUX
ejpam-6128	370	13	constants	constant	NOUN
ejpam-6128	370	14	of	of	ADP
ejpam-6128	370	15	integration	integration	NOUN
ejpam-6128	370	16	.	.	PUNCT
ejpam-6128	371	1	this	this	DET
ejpam-6128	371	2	solution	solution	NOUN
ejpam-6128	371	3	is	be	AUX
ejpam-6128	371	4	also	also	ADV
ejpam-6128	371	5	obtained	obtain	VERB
ejpam-6128	371	6	in	in	ADP
ejpam-6128	371	7	[	[	X
ejpam-6128	371	8	22	22	NUM
ejpam-6128	371	9	]	]	PUNCT
ejpam-6128	371	10	.	.	PUNCT
ejpam-6128	372	1	case	case	NOUN
ejpam-6128	372	2	-	-	PUNCT
ejpam-6128	372	3	b2	b2	NOUN
ejpam-6128	372	4	:	:	PUNCT
ejpam-6128	372	5	in	in	ADP
ejpam-6128	372	6	(	(	PUNCT
ejpam-6128	372	7	63	63	NUM
ejpam-6128	372	8	)	)	PUNCT
ejpam-6128	372	9	,	,	PUNCT
ejpam-6128	372	10	set	set	VERB
ejpam-6128	372	11	c2	c2	PROPN
ejpam-6128	372	12	=	=	SYM
ejpam-6128	372	13	c4	c4	NOUN
ejpam-6128	372	14	=	=	SYM
ejpam-6128	372	15	1	1	NUM
ejpam-6128	372	16	and	and	CCONJ
ejpam-6128	372	17	ci	ci	NOUN
ejpam-6128	373	1	=	=	NOUN
ejpam-6128	373	2	0	0	PROPN
ejpam-6128	374	1	for	for	ADP
ejpam-6128	374	2	i	i	PRON
ejpam-6128	374	3	=	=	SYM
ejpam-6128	374	4	1	1	NUM
ejpam-6128	374	5	,	,	PUNCT
ejpam-6128	374	6	3	3	NUM
ejpam-6128	374	7	.	.	PUNCT
ejpam-6128	374	8	then	then	ADV
ejpam-6128	374	9	we	we	PRON
ejpam-6128	374	10	obtain	obtain	VERB
ejpam-6128	374	11	the	the	DET
ejpam-6128	374	12	symmetry	symmetry	NOUN
ejpam-6128	374	13	invariants	invariant	NOUN
ejpam-6128	374	14	r	r	NOUN
ejpam-6128	374	15	=	=	PUNCT
ejpam-6128	374	16	q	q	NOUN
ejpam-6128	374	17	−	−	PROPN
ejpam-6128	374	18	p	p	X
ejpam-6128	374	19	,	,	PUNCT
ejpam-6128	374	20	h(p	h(p	PROPN
ejpam-6128	374	21	,	,	PUNCT
ejpam-6128	374	22	q	q	NOUN
ejpam-6128	374	23	)	)	PUNCT
ejpam-6128	374	24	=	=	SYM
ejpam-6128	374	25	µ(r	µ(r	NOUN
ejpam-6128	374	26	)	)	PUNCT
ejpam-6128	374	27	.	.	PUNCT
ejpam-6128	375	1	(	(	PUNCT
ejpam-6128	375	2	69	69	NUM
ejpam-6128	375	3	)	)	PUNCT
ejpam-6128	375	4	the	the	DET
ejpam-6128	375	5	substitution	substitution	NOUN
ejpam-6128	375	6	of	of	ADP
ejpam-6128	375	7	(	(	PUNCT
ejpam-6128	375	8	69	69	NUM
ejpam-6128	375	9	)	)	PUNCT
ejpam-6128	375	10	in	in	ADP
ejpam-6128	375	11	(	(	PUNCT
ejpam-6128	375	12	62	62	NUM
ejpam-6128	375	13	)	)	PUNCT
ejpam-6128	375	14	yields	yield	VERB
ejpam-6128	375	15	the	the	DET
ejpam-6128	375	16	following	follow	VERB
ejpam-6128	375	17	ode	ode	PROPN
ejpam-6128	375	18	µ′′	µ′′	PROPN
ejpam-6128	375	19	−	−	NOUN
ejpam-6128	375	20	βµ2µ′′	βµ2µ′′	ADP
ejpam-6128	375	21	−	−	PROPN
ejpam-6128	375	22	2βµµ′2	2βµµ′2	NOUN
ejpam-6128	375	23	=	=	SYM
ejpam-6128	375	24	0	0	NUM
ejpam-6128	375	25	.	.	PUNCT
ejpam-6128	376	1	(	(	PUNCT
ejpam-6128	376	2	70	70	X
ejpam-6128	376	3	)	)	PUNCT
ejpam-6128	376	4	m.	m.	NOUN
ejpam-6128	376	5	usman	usman	PROPN
ejpam-6128	376	6	,	,	PUNCT
ejpam-6128	376	7	a.	a.	NOUN
ejpam-6128	376	8	hussain	hussain	PROPN
ejpam-6128	376	9	,	,	PUNCT
ejpam-6128	376	10	m.	m.	PROPN
ejpam-6128	376	11	u.	u.	PROPN
ejpam-6128	376	12	farooq	farooq	PROPN
ejpam-6128	376	13	,	,	PUNCT
ejpam-6128	376	14	j.	j.	PROPN
ejpam-6128	376	15	herrera	herrera	PROPN
ejpam-6128	376	16	/	/	SYM
ejpam-6128	376	17	eur	eur	PROPN
ejpam-6128	376	18	.	.	PUNCT
ejpam-6128	377	1	j.	j.	PROPN
ejpam-6128	377	2	pure	pure	PROPN
ejpam-6128	377	3	appl	appl	PROPN
ejpam-6128	377	4	.	.	PROPN
ejpam-6128	377	5	math	math	PROPN
ejpam-6128	377	6	,	,	PUNCT
ejpam-6128	377	7	18	18	NUM
ejpam-6128	377	8	(	(	PUNCT
ejpam-6128	377	9	4	4	NUM
ejpam-6128	377	10	)	)	PUNCT
ejpam-6128	377	11	(	(	PUNCT
ejpam-6128	377	12	2025	2025	NUM
ejpam-6128	377	13	)	)	PUNCT
ejpam-6128	377	14	,	,	PUNCT
ejpam-6128	377	15	6128	6128	NUM
ejpam-6128	377	16	18	18	NUM
ejpam-6128	377	17	of	of	ADP
ejpam-6128	377	18	29	29	NUM
ejpam-6128	377	19	the	the	DET
ejpam-6128	377	20	solution	solution	NOUN
ejpam-6128	377	21	of	of	ADP
ejpam-6128	377	22	(	(	PUNCT
ejpam-6128	377	23	70	70	NUM
ejpam-6128	377	24	)	)	PUNCT
ejpam-6128	377	25	takes	take	VERB
ejpam-6128	377	26	the	the	DET
ejpam-6128	377	27	form	form	NOUN
ejpam-6128	377	28	µ(r	µ(r	NOUN
ejpam-6128	377	29	)	)	PUNCT
ejpam-6128	377	30	=	=	PUNCT
ejpam-6128	377	31	(	(	PUNCT
ejpam-6128	377	32	2	2	NUM
ejpam-6128	377	33	1	1	NUM
ejpam-6128	377	34	3	3	NUM
ejpam-6128	377	35	(	(	PUNCT
ejpam-6128	377	36	2	2	NUM
ejpam-6128	377	37	1	1	NUM
ejpam-6128	377	38	3	3	NUM
ejpam-6128	377	39	(	(	PUNCT
ejpam-6128	377	40	√	√	ADP
ejpam-6128	377	41	−4	−4	PROPN
ejpam-6128	378	1	+	+	SYM
ejpam-6128	379	1	9(−c1r	9(−c1r	NUM
ejpam-6128	379	2	−	−	NOUN
ejpam-6128	379	3	c2)2β	c2)2β	ADJ
ejpam-6128	379	4	+	+	CCONJ
ejpam-6128	379	5	(	(	PUNCT
ejpam-6128	379	6	3c1r	3c1r	NOUN
ejpam-6128	379	7	+	+	NOUN
ejpam-6128	379	8	3c2	3c2	NUM
ejpam-6128	379	9	)	)	PUNCT
ejpam-6128	379	10	√	√	NUM
ejpam-6128	379	11	β	β	NOUN
ejpam-6128	379	12	)	)	PUNCT
ejpam-6128	379	13	2	2	NUM
ejpam-6128	379	14	3	3	NUM
ejpam-6128	379	15	+	+	CCONJ
ejpam-6128	379	16	2	2	NUM
ejpam-6128	379	17	)	)	PUNCT
ejpam-6128	379	18	)	)	PUNCT
ejpam-6128	379	19	/	/	SYM
ejpam-6128	379	20	(	(	PUNCT
ejpam-6128	379	21	2	2	NUM
ejpam-6128	379	22	√	√	NUM
ejpam-6128	379	23	β	β	NOUN
ejpam-6128	379	24	(	(	PUNCT
ejpam-6128	379	25	√	√	ADP
ejpam-6128	379	26	−4	−4	PROPN
ejpam-6128	380	1	+	+	SYM
ejpam-6128	381	1	9(−c1r	9(−c1r	NUM
ejpam-6128	381	2	−	−	NOUN
ejpam-6128	381	3	c2)2β	c2)2β	ADJ
ejpam-6128	381	4	+	+	CCONJ
ejpam-6128	381	5	(	(	PUNCT
ejpam-6128	381	6	3c1r	3c1r	NOUN
ejpam-6128	381	7	+	+	NOUN
ejpam-6128	381	8	3c2	3c2	NUM
ejpam-6128	381	9	)	)	PUNCT
ejpam-6128	381	10	√	√	NUM
ejpam-6128	381	11	β	β	X
ejpam-6128	381	12	)	)	PUNCT
ejpam-6128	381	13	1	1	NUM
ejpam-6128	381	14	3	3	NUM
ejpam-6128	381	15	)	)	PUNCT
ejpam-6128	381	16	.	.	PUNCT
ejpam-6128	382	1	(	(	PUNCT
ejpam-6128	382	2	71	71	NUM
ejpam-6128	382	3	)	)	PUNCT
ejpam-6128	382	4	which	which	PRON
ejpam-6128	382	5	implies	imply	VERB
ejpam-6128	382	6	h(p	h(p	NOUN
ejpam-6128	382	7	,	,	PUNCT
ejpam-6128	382	8	q	q	X
ejpam-6128	382	9	)	)	PUNCT
ejpam-6128	382	10	=	=	SYM
ejpam-6128	382	11	(	(	PUNCT
ejpam-6128	382	12	2	2	NUM
ejpam-6128	382	13	1	1	NUM
ejpam-6128	382	14	3	3	NUM
ejpam-6128	382	15	(	(	PUNCT
ejpam-6128	382	16	2	2	NUM
ejpam-6128	382	17	1	1	NUM
ejpam-6128	382	18	3	3	NUM
ejpam-6128	382	19	(	(	PUNCT
ejpam-6128	382	20	√	√	ADP
ejpam-6128	382	21	−4	−4	PROPN
ejpam-6128	382	22	+	+	SYM
ejpam-6128	382	23	9(−c1(q	9(−c1(q	NUM
ejpam-6128	382	24	−	−	PROPN
ejpam-6128	382	25	p)−	p)−	PROPN
ejpam-6128	382	26	c2)2β	c2)2β	PROPN
ejpam-6128	382	27	+	+	CCONJ
ejpam-6128	382	28	(	(	PUNCT
ejpam-6128	382	29	3c1(q	3c1(q	NUM
ejpam-6128	382	30	−	−	NOUN
ejpam-6128	382	31	p	p	X
ejpam-6128	382	32	)	)	PUNCT
ejpam-6128	382	33	+	+	CCONJ
ejpam-6128	382	34	3c2	3c2	NUM
ejpam-6128	382	35	)	)	PUNCT
ejpam-6128	382	36	√	√	NUM
ejpam-6128	382	37	β	β	NOUN
ejpam-6128	382	38	)	)	PUNCT
ejpam-6128	382	39	2	2	NUM
ejpam-6128	382	40	3	3	NUM
ejpam-6128	382	41	+	+	CCONJ
ejpam-6128	382	42	2	2	NUM
ejpam-6128	382	43	)	)	PUNCT
ejpam-6128	382	44	)	)	PUNCT
ejpam-6128	382	45	/	/	SYM
ejpam-6128	383	1	(	(	PUNCT
ejpam-6128	383	2	2	2	NUM
ejpam-6128	383	3	√	√	PROPN
ejpam-6128	383	4	β	β	NOUN
ejpam-6128	383	5	(	(	PUNCT
ejpam-6128	383	6	√	√	ADP
ejpam-6128	383	7	−4	−4	PROPN
ejpam-6128	383	8	+	+	SYM
ejpam-6128	383	9	9(−c1(q	9(−c1(q	NUM
ejpam-6128	383	10	−	−	PROPN
ejpam-6128	383	11	p)−	p)−	PROPN
ejpam-6128	383	12	c2)2β	c2)2β	PROPN
ejpam-6128	383	13	+	+	CCONJ
ejpam-6128	383	14	(	(	PUNCT
ejpam-6128	383	15	3c1(q	3c1(q	NUM
ejpam-6128	383	16	−	−	NOUN
ejpam-6128	383	17	p	p	X
ejpam-6128	383	18	)	)	PUNCT
ejpam-6128	383	19	+	+	CCONJ
ejpam-6128	383	20	3c2	3c2	NUM
ejpam-6128	383	21	)	)	PUNCT
ejpam-6128	383	22	√	√	NUM
ejpam-6128	383	23	β	β	X
ejpam-6128	383	24	)	)	PUNCT
ejpam-6128	383	25	1	1	NUM
ejpam-6128	383	26	3	3	NUM
ejpam-6128	383	27	)	)	PUNCT
ejpam-6128	383	28	.	.	PUNCT
ejpam-6128	384	1	(	(	PUNCT
ejpam-6128	384	2	72	72	NUM
ejpam-6128	384	3	)	)	PUNCT
ejpam-6128	384	4	hence	hence	ADV
ejpam-6128	384	5	,	,	PUNCT
ejpam-6128	384	6	the	the	DET
ejpam-6128	384	7	solution	solution	NOUN
ejpam-6128	384	8	of	of	ADP
ejpam-6128	384	9	(	(	PUNCT
ejpam-6128	384	10	2	2	NUM
ejpam-6128	384	11	)	)	PUNCT
ejpam-6128	384	12	is	be	AUX
ejpam-6128	384	13	w(x	w(x	PROPN
ejpam-6128	384	14	,	,	PUNCT
ejpam-6128	384	15	y	y	PROPN
ejpam-6128	384	16	,	,	PUNCT
ejpam-6128	384	17	t	t	PROPN
ejpam-6128	384	18	)	)	PUNCT
ejpam-6128	384	19	=	=	PUNCT
ejpam-6128	385	1	(	(	PUNCT
ejpam-6128	385	2	2	2	NUM
ejpam-6128	385	3	1	1	NUM
ejpam-6128	385	4	3	3	NUM
ejpam-6128	385	5	(	(	PUNCT
ejpam-6128	385	6	2	2	NUM
ejpam-6128	385	7	1	1	NUM
ejpam-6128	385	8	3	3	NUM
ejpam-6128	385	9	(	(	PUNCT
ejpam-6128	385	10	√	√	ADP
ejpam-6128	385	11	−4	−4	PROPN
ejpam-6128	386	1	+	+	SYM
ejpam-6128	386	2	9(−c1(y	9(−c1(y	NUM
ejpam-6128	387	1	−	−	NOUN
ejpam-6128	387	2	t)−	t)−	PROPN
ejpam-6128	387	3	c2)2β	c2)2β	PROPN
ejpam-6128	387	4	+	+	CCONJ
ejpam-6128	387	5	(	(	PUNCT
ejpam-6128	387	6	3c1(y	3c1(y	NUM
ejpam-6128	387	7	−	−	PROPN
ejpam-6128	387	8	t	t	PROPN
ejpam-6128	387	9	)	)	PUNCT
ejpam-6128	387	10	+	+	NUM
ejpam-6128	387	11	3c2	3c2	NUM
ejpam-6128	387	12	)	)	PUNCT
ejpam-6128	387	13	√	√	NUM
ejpam-6128	387	14	β	β	NOUN
ejpam-6128	387	15	)	)	PUNCT
ejpam-6128	387	16	2	2	NUM
ejpam-6128	387	17	3	3	NUM
ejpam-6128	387	18	+	+	CCONJ
ejpam-6128	387	19	2	2	NUM
ejpam-6128	387	20	)	)	PUNCT
ejpam-6128	387	21	)	)	PUNCT
ejpam-6128	387	22	/	/	SYM
ejpam-6128	388	1	(	(	PUNCT
ejpam-6128	388	2	2	2	NUM
ejpam-6128	388	3	√	√	PROPN
ejpam-6128	388	4	β	β	NOUN
ejpam-6128	388	5	(	(	PUNCT
ejpam-6128	388	6	√	√	ADP
ejpam-6128	388	7	−4	−4	PROPN
ejpam-6128	388	8	+	+	SYM
ejpam-6128	388	9	9(−c1(y	9(−c1(y	NUM
ejpam-6128	388	10	−	−	NOUN
ejpam-6128	389	1	t)−	t)−	PROPN
ejpam-6128	389	2	c2)2β	c2)2β	PROPN
ejpam-6128	389	3	+	+	CCONJ
ejpam-6128	389	4	(	(	PUNCT
ejpam-6128	389	5	3c1(y	3c1(y	NUM
ejpam-6128	389	6	−	−	PROPN
ejpam-6128	389	7	t	t	PROPN
ejpam-6128	389	8	)	)	PUNCT
ejpam-6128	389	9	+	+	NUM
ejpam-6128	389	10	3c2	3c2	NUM
ejpam-6128	389	11	)	)	PUNCT
ejpam-6128	389	12	√	√	NUM
ejpam-6128	389	13	β	β	X
ejpam-6128	389	14	)	)	PUNCT
ejpam-6128	389	15	1	1	NUM
ejpam-6128	389	16	3	3	NUM
ejpam-6128	389	17	)	)	PUNCT
ejpam-6128	389	18	,	,	PUNCT
ejpam-6128	389	19	(	(	PUNCT
ejpam-6128	389	20	73	73	NUM
ejpam-6128	389	21	)	)	PUNCT
ejpam-6128	389	22	where	where	SCONJ
ejpam-6128	389	23	c1	c1	PROPN
ejpam-6128	389	24	and	and	CCONJ
ejpam-6128	389	25	c2	c2	PROPN
ejpam-6128	389	26	are	be	AUX
ejpam-6128	389	27	constants	constant	NOUN
ejpam-6128	389	28	of	of	ADP
ejpam-6128	389	29	integration	integration	NOUN
ejpam-6128	389	30	.	.	PUNCT
ejpam-6128	390	1	case	case	NOUN
ejpam-6128	390	2	-	-	PUNCT
ejpam-6128	390	3	b3	b3	NOUN
ejpam-6128	390	4	:	:	PUNCT
ejpam-6128	390	5	in	in	ADP
ejpam-6128	390	6	(	(	PUNCT
ejpam-6128	390	7	63	63	NUM
ejpam-6128	390	8	)	)	PUNCT
ejpam-6128	390	9	,	,	PUNCT
ejpam-6128	390	10	set	set	VERB
ejpam-6128	390	11	c3	c3	NOUN
ejpam-6128	390	12	=	=	SYM
ejpam-6128	390	13	1	1	NUM
ejpam-6128	390	14	and	and	CCONJ
ejpam-6128	390	15	ci	ci	NOUN
ejpam-6128	390	16	=	=	NOUN
ejpam-6128	390	17	0	0	PROPN
ejpam-6128	390	18	for	for	ADP
ejpam-6128	390	19	i	i	PRON
ejpam-6128	390	20	=	=	NOUN
ejpam-6128	390	21	1	1	NUM
ejpam-6128	390	22	,	,	PUNCT
ejpam-6128	390	23	2	2	NUM
ejpam-6128	390	24	,	,	PUNCT
ejpam-6128	390	25	4	4	NUM
ejpam-6128	390	26	.	.	PUNCT
ejpam-6128	391	1	then	then	ADV
ejpam-6128	391	2	we	we	PRON
ejpam-6128	391	3	obtain	obtain	VERB
ejpam-6128	391	4	the	the	DET
ejpam-6128	391	5	symmetry	symmetry	NOUN
ejpam-6128	391	6	invariants	invariant	NOUN
ejpam-6128	391	7	r	r	NOUN
ejpam-6128	391	8	=	=	SYM
ejpam-6128	391	9	p	p	NOUN
ejpam-6128	391	10	,	,	PUNCT
ejpam-6128	391	11	h(p	h(p	PROPN
ejpam-6128	391	12	,	,	PUNCT
ejpam-6128	391	13	q	q	X
ejpam-6128	391	14	)	)	PUNCT
ejpam-6128	391	15	=	=	SYM
ejpam-6128	391	16	qµ(r	qµ(r	NOUN
ejpam-6128	391	17	)	)	PUNCT
ejpam-6128	391	18	.	.	PUNCT
ejpam-6128	392	1	(	(	PUNCT
ejpam-6128	392	2	74	74	X
ejpam-6128	392	3	)	)	PUNCT
ejpam-6128	392	4	the	the	DET
ejpam-6128	392	5	substitution	substitution	NOUN
ejpam-6128	392	6	of	of	ADP
ejpam-6128	392	7	(	(	PUNCT
ejpam-6128	392	8	74	74	NUM
ejpam-6128	392	9	)	)	PUNCT
ejpam-6128	392	10	in	in	ADP
ejpam-6128	392	11	(	(	PUNCT
ejpam-6128	392	12	62	62	NUM
ejpam-6128	392	13	)	)	PUNCT
ejpam-6128	392	14	yields	yield	VERB
ejpam-6128	392	15	the	the	DET
ejpam-6128	392	16	following	follow	VERB
ejpam-6128	392	17	ode	ode	PROPN
ejpam-6128	392	18	µ′′	µ′′	PROPN
ejpam-6128	392	19	−	−	PROPN
ejpam-6128	392	20	2βµ3	2βµ3	NUM
ejpam-6128	392	21	=	=	SYM
ejpam-6128	392	22	0	0	NUM
ejpam-6128	392	23	.	.	PUNCT
ejpam-6128	393	1	(	(	PUNCT
ejpam-6128	393	2	75	75	NUM
ejpam-6128	393	3	)	)	PUNCT
ejpam-6128	393	4	the	the	DET
ejpam-6128	393	5	solution	solution	NOUN
ejpam-6128	393	6	of	of	ADP
ejpam-6128	393	7	(	(	PUNCT
ejpam-6128	393	8	75	75	NUM
ejpam-6128	393	9	)	)	PUNCT
ejpam-6128	393	10	takes	take	VERB
ejpam-6128	393	11	the	the	DET
ejpam-6128	393	12	form	form	NOUN
ejpam-6128	393	13	µ(r	µ(r	NOUN
ejpam-6128	393	14	)	)	PUNCT
ejpam-6128	394	1	=	=	SYM
ejpam-6128	394	2	c2	c2	PROPN
ejpam-6128	394	3	jacobisn	jacobisn	PROPN
ejpam-6128	394	4	(	(	PUNCT
ejpam-6128	394	5	(	(	PUNCT
ejpam-6128	394	6	ι	ι	INTJ
ejpam-6128	394	7	√	√	ADP
ejpam-6128	394	8	βr	βr	NOUN
ejpam-6128	394	9	+	+	NUM
ejpam-6128	394	10	c1)c2	c1)c2	PROPN
ejpam-6128	394	11	,	,	PUNCT
ejpam-6128	394	12	ι	ι	PROPN
ejpam-6128	394	13	)	)	PUNCT
ejpam-6128	394	14	,	,	PUNCT
ejpam-6128	394	15	(	(	PUNCT
ejpam-6128	394	16	76	76	NUM
ejpam-6128	394	17	)	)	PUNCT
ejpam-6128	394	18	which	which	PRON
ejpam-6128	394	19	implies	imply	VERB
ejpam-6128	394	20	h(p	h(p	NOUN
ejpam-6128	394	21	,	,	PUNCT
ejpam-6128	394	22	q	q	X
ejpam-6128	394	23	)	)	PUNCT
ejpam-6128	394	24	=	=	SYM
ejpam-6128	395	1	c2	c2	PROPN
ejpam-6128	395	2	jacobisn	jacobisn	PROPN
ejpam-6128	395	3	(	(	PUNCT
ejpam-6128	395	4	(	(	PUNCT
ejpam-6128	395	5	ι	ι	PART
ejpam-6128	395	6	√	√	PROPN
ejpam-6128	395	7	βp+	βp+	NUM
ejpam-6128	395	8	c1)c2	c1)c2	PROPN
ejpam-6128	395	9	,	,	PUNCT
ejpam-6128	395	10	ι	ι	PROPN
ejpam-6128	395	11	)	)	PUNCT
ejpam-6128	395	12	q.	q.	PROPN
ejpam-6128	395	13	(	(	PUNCT
ejpam-6128	395	14	77	77	NUM
ejpam-6128	395	15	)	)	PUNCT
ejpam-6128	395	16	hence	hence	ADV
ejpam-6128	395	17	,	,	PUNCT
ejpam-6128	395	18	the	the	DET
ejpam-6128	395	19	solution	solution	NOUN
ejpam-6128	395	20	of	of	ADP
ejpam-6128	395	21	(	(	PUNCT
ejpam-6128	395	22	2	2	NUM
ejpam-6128	395	23	)	)	PUNCT
ejpam-6128	395	24	is	be	AUX
ejpam-6128	395	25	w(x	w(x	PROPN
ejpam-6128	395	26	,	,	PUNCT
ejpam-6128	395	27	y	y	PROPN
ejpam-6128	395	28	,	,	PUNCT
ejpam-6128	395	29	t	t	PROPN
ejpam-6128	395	30	)	)	PUNCT
ejpam-6128	396	1	=	=	SYM
ejpam-6128	397	1	c2	c2	PROPN
ejpam-6128	397	2	jacobisn	jacobisn	PROPN
ejpam-6128	397	3	(	(	PUNCT
ejpam-6128	397	4	(	(	PUNCT
ejpam-6128	397	5	ι	ι	PART
ejpam-6128	397	6	√	√	PROPN
ejpam-6128	397	7	βt+	βt+	ADJ
ejpam-6128	397	8	c1)c2	c1)c2	PROPN
ejpam-6128	397	9	,	,	PUNCT
ejpam-6128	397	10	ι	ι	PROPN
ejpam-6128	397	11	)	)	PUNCT
ejpam-6128	397	12	y	y	NOUN
ejpam-6128	397	13	,	,	PUNCT
ejpam-6128	397	14	(	(	PUNCT
ejpam-6128	397	15	78	78	NUM
ejpam-6128	397	16	)	)	PUNCT
ejpam-6128	397	17	where	where	SCONJ
ejpam-6128	397	18	c1	c1	PROPN
ejpam-6128	397	19	and	and	CCONJ
ejpam-6128	397	20	c2	c2	PROPN
ejpam-6128	397	21	are	be	AUX
ejpam-6128	397	22	constants	constant	NOUN
ejpam-6128	397	23	of	of	ADP
ejpam-6128	397	24	integration	integration	NOUN
ejpam-6128	397	25	.	.	PUNCT
ejpam-6128	398	1	m.	m.	PROPN
ejpam-6128	398	2	usman	usman	PROPN
ejpam-6128	398	3	,	,	PUNCT
ejpam-6128	398	4	a.	a.	NOUN
ejpam-6128	398	5	hussain	hussain	PROPN
ejpam-6128	398	6	,	,	PUNCT
ejpam-6128	398	7	m.	m.	PROPN
ejpam-6128	398	8	u.	u.	PROPN
ejpam-6128	398	9	farooq	farooq	PROPN
ejpam-6128	398	10	,	,	PUNCT
ejpam-6128	398	11	j.	j.	PROPN
ejpam-6128	398	12	herrera	herrera	PROPN
ejpam-6128	398	13	/	/	SYM
ejpam-6128	398	14	eur	eur	PROPN
ejpam-6128	398	15	.	.	PUNCT
ejpam-6128	399	1	j.	j.	PROPN
ejpam-6128	399	2	pure	pure	PROPN
ejpam-6128	399	3	appl	appl	PROPN
ejpam-6128	399	4	.	.	PROPN
ejpam-6128	399	5	math	math	PROPN
ejpam-6128	399	6	,	,	PUNCT
ejpam-6128	399	7	18	18	NUM
ejpam-6128	399	8	(	(	PUNCT
ejpam-6128	399	9	4	4	NUM
ejpam-6128	399	10	)	)	PUNCT
ejpam-6128	399	11	(	(	PUNCT
ejpam-6128	399	12	2025	2025	NUM
ejpam-6128	399	13	)	)	PUNCT
ejpam-6128	399	14	,	,	PUNCT
ejpam-6128	399	15	6128	6128	NUM
ejpam-6128	399	16	19	19	NUM
ejpam-6128	399	17	of	of	ADP
ejpam-6128	399	18	29	29	NUM
ejpam-6128	399	19	3.3	3.3	NUM
ejpam-6128	399	20	.	.	PUNCT
ejpam-6128	400	1	similarity	similarity	NOUN
ejpam-6128	400	2	reductions	reduction	NOUN
ejpam-6128	400	3	for	for	ADP
ejpam-6128	400	4	case	case	NOUN
ejpam-6128	400	5	3	3	NUM
ejpam-6128	400	6	case	case	NOUN
ejpam-6128	400	7	-	-	PUNCT
ejpam-6128	400	8	a	a	NOUN
ejpam-6128	400	9	:	:	PUNCT
ejpam-6128	400	10	consider	consider	VERB
ejpam-6128	400	11	y2	y2	NOUN
ejpam-6128	400	12	=	=	SYM
ejpam-6128	400	13	∂	∂	NUM
ejpam-6128	400	14	∂y	∂y	NOUN
ejpam-6128	400	15	.	.	PUNCT
ejpam-6128	401	1	the	the	DET
ejpam-6128	401	2	solution	solution	NOUN
ejpam-6128	401	3	of	of	ADP
ejpam-6128	401	4	the	the	DET
ejpam-6128	401	5	characteristic	characteristic	ADJ
ejpam-6128	401	6	equation	equation	NOUN
ejpam-6128	401	7	for	for	ADP
ejpam-6128	401	8	y2	y2	PROPN
ejpam-6128	401	9	provides	provide	VERB
ejpam-6128	401	10	the	the	DET
ejpam-6128	401	11	symmetry	symmetry	NOUN
ejpam-6128	401	12	invariants	invariant	NOUN
ejpam-6128	401	13	p	p	PROPN
ejpam-6128	401	14	=	=	PROPN
ejpam-6128	401	15	t	t	PROPN
ejpam-6128	401	16	,	,	PUNCT
ejpam-6128	401	17	q	q	NOUN
ejpam-6128	401	18	=	=	SYM
ejpam-6128	401	19	x	x	NOUN
ejpam-6128	401	20	,	,	PUNCT
ejpam-6128	401	21	w(x	w(x	PROPN
ejpam-6128	401	22	,	,	PUNCT
ejpam-6128	401	23	y	y	PROPN
ejpam-6128	401	24	,	,	PUNCT
ejpam-6128	401	25	t	t	PROPN
ejpam-6128	401	26	)	)	PUNCT
ejpam-6128	401	27	=	=	SYM
ejpam-6128	401	28	h(p	h(p	PROPN
ejpam-6128	401	29	,	,	PUNCT
ejpam-6128	401	30	q	q	NOUN
ejpam-6128	401	31	)	)	PUNCT
ejpam-6128	401	32	.	.	PUNCT
ejpam-6128	402	1	(	(	PUNCT
ejpam-6128	402	2	79	79	NUM
ejpam-6128	402	3	)	)	PUNCT
ejpam-6128	402	4	by	by	ADP
ejpam-6128	402	5	inserting	insert	VERB
ejpam-6128	402	6	(	(	PUNCT
ejpam-6128	402	7	79	79	NUM
ejpam-6128	402	8	)	)	PUNCT
ejpam-6128	402	9	in	in	ADP
ejpam-6128	402	10	(	(	PUNCT
ejpam-6128	402	11	2	2	NUM
ejpam-6128	402	12	)	)	PUNCT
ejpam-6128	402	13	,	,	PUNCT
ejpam-6128	402	14	we	we	PRON
ejpam-6128	402	15	get	get	VERB
ejpam-6128	402	16	hpp	hpp	PROPN
ejpam-6128	402	17	−	−	NOUN
ejpam-6128	402	18	αhqq	αhqq	NOUN
ejpam-6128	402	19	=	=	NOUN
ejpam-6128	402	20	0	0	PROPN
ejpam-6128	402	21	.	.	PUNCT
ejpam-6128	403	1	(	(	PUNCT
ejpam-6128	403	2	80	80	NUM
ejpam-6128	403	3	)	)	PUNCT
ejpam-6128	403	4	infinitesimals	infinitesimal	NOUN
ejpam-6128	403	5	for	for	ADP
ejpam-6128	403	6	(	(	PUNCT
ejpam-6128	403	7	80	80	NUM
ejpam-6128	403	8	)	)	PUNCT
ejpam-6128	403	9	are	be	AUX
ejpam-6128	403	10	as	as	SCONJ
ejpam-6128	403	11	follows	follow	VERB
ejpam-6128	403	12	ζp	ζp	ADJ
ejpam-6128	403	13	=	=	PUNCT
ejpam-6128	403	14	f5(q	f5(q	PROPN
ejpam-6128	403	15	+	+	CCONJ
ejpam-6128	403	16	√	√	NUM
ejpam-6128	403	17	αp	αp	NOUN
ejpam-6128	403	18	)	)	PUNCT
ejpam-6128	403	19	+	+	CCONJ
ejpam-6128	404	1	f6(q	f6(q	NUM
ejpam-6128	404	2	−	−	NOUN
ejpam-6128	404	3	√	√	NUM
ejpam-6128	404	4	αp	αp	NOUN
ejpam-6128	404	5	)	)	PUNCT
ejpam-6128	404	6	,	,	PUNCT
ejpam-6128	404	7	ζq	ζq	NOUN
ejpam-6128	404	8	=	=	PUNCT
ejpam-6128	404	9	√	√	NUM
ejpam-6128	404	10	αf5(q	αf5(q	PROPN
ejpam-6128	405	1	+	+	CCONJ
ejpam-6128	405	2	√	√	ADV
ejpam-6128	405	3	αp)−	αp)−	NUM
ejpam-6128	405	4	√	√	ADJ
ejpam-6128	405	5	αf6(q	αf6(q	NUM
ejpam-6128	405	6	−	−	NOUN
ejpam-6128	405	7	√	√	NUM
ejpam-6128	405	8	αp	αp	NOUN
ejpam-6128	405	9	)	)	PUNCT
ejpam-6128	406	1	+	+	CCONJ
ejpam-6128	406	2	c2	c2	PROPN
ejpam-6128	406	3	,	,	PUNCT
ejpam-6128	406	4	φh	φh	NOUN
ejpam-6128	406	5	=	=	NOUN
ejpam-6128	406	6	c1h+	c1h+	NOUN
ejpam-6128	406	7	f3(q	f3(q	PROPN
ejpam-6128	406	8	+	+	CCONJ
ejpam-6128	406	9	√	√	NUM
ejpam-6128	406	10	αp	αp	NOUN
ejpam-6128	406	11	)	)	PUNCT
ejpam-6128	406	12	+	+	PUNCT
ejpam-6128	406	13	f4(q	f4(q	ADP
ejpam-6128	406	14	−	−	PROPN
ejpam-6128	406	15	√	√	NUM
ejpam-6128	406	16	αp	αp	NOUN
ejpam-6128	406	17	)	)	PUNCT
ejpam-6128	406	18	.	.	PUNCT
ejpam-6128	407	1	(	(	PUNCT
ejpam-6128	407	2	81	81	NUM
ejpam-6128	407	3	)	)	PUNCT
ejpam-6128	407	4	case	case	NOUN
ejpam-6128	407	5	-	-	PUNCT
ejpam-6128	407	6	a1	a1	NOUN
ejpam-6128	407	7	:	:	PUNCT
ejpam-6128	407	8	in	in	ADP
ejpam-6128	407	9	(	(	PUNCT
ejpam-6128	407	10	81	81	NUM
ejpam-6128	407	11	)	)	PUNCT
ejpam-6128	407	12	,	,	PUNCT
ejpam-6128	407	13	set	set	VERB
ejpam-6128	407	14	c2	c2	PROPN
ejpam-6128	407	15	=	=	SYM
ejpam-6128	407	16	1	1	PROPN
ejpam-6128	407	17	,	,	PUNCT
ejpam-6128	407	18	c1	c1	NOUN
ejpam-6128	407	19	=	=	PROPN
ejpam-6128	407	20	0	0	PUNCT
ejpam-6128	407	21	and	and	CCONJ
ejpam-6128	407	22	all	all	DET
ejpam-6128	407	23	arbitrary	arbitrary	ADJ
ejpam-6128	407	24	functions	function	NOUN
ejpam-6128	407	25	zero	zero	NUM
ejpam-6128	407	26	.	.	PUNCT
ejpam-6128	408	1	then	then	ADV
ejpam-6128	408	2	we	we	PRON
ejpam-6128	408	3	obtain	obtain	VERB
ejpam-6128	408	4	the	the	DET
ejpam-6128	408	5	symmetry	symmetry	NOUN
ejpam-6128	408	6	invariants	invariant	NOUN
ejpam-6128	408	7	r	r	NOUN
ejpam-6128	408	8	=	=	SYM
ejpam-6128	408	9	p	p	NOUN
ejpam-6128	408	10	,	,	PUNCT
ejpam-6128	408	11	h(p	h(p	PROPN
ejpam-6128	408	12	,	,	PUNCT
ejpam-6128	408	13	q	q	NOUN
ejpam-6128	408	14	)	)	PUNCT
ejpam-6128	408	15	=	=	SYM
ejpam-6128	408	16	µ(r	µ(r	NOUN
ejpam-6128	408	17	)	)	PUNCT
ejpam-6128	408	18	.	.	PUNCT
ejpam-6128	409	1	(	(	PUNCT
ejpam-6128	409	2	82	82	NUM
ejpam-6128	409	3	)	)	PUNCT
ejpam-6128	409	4	the	the	DET
ejpam-6128	409	5	substitution	substitution	NOUN
ejpam-6128	409	6	of	of	ADP
ejpam-6128	409	7	(	(	PUNCT
ejpam-6128	409	8	82	82	NUM
ejpam-6128	409	9	)	)	PUNCT
ejpam-6128	409	10	in	in	ADP
ejpam-6128	409	11	(	(	PUNCT
ejpam-6128	409	12	80	80	NUM
ejpam-6128	409	13	)	)	PUNCT
ejpam-6128	409	14	yields	yield	VERB
ejpam-6128	409	15	the	the	DET
ejpam-6128	409	16	following	follow	VERB
ejpam-6128	409	17	ode	ode	PROPN
ejpam-6128	409	18	µ′′	µ′′	PROPN
ejpam-6128	409	19	=	=	SYM
ejpam-6128	409	20	0	0	NUM
ejpam-6128	409	21	.	.	PUNCT
ejpam-6128	410	1	(	(	PUNCT
ejpam-6128	410	2	83	83	NUM
ejpam-6128	410	3	)	)	PUNCT
ejpam-6128	410	4	the	the	DET
ejpam-6128	410	5	solution	solution	NOUN
ejpam-6128	410	6	of	of	ADP
ejpam-6128	410	7	(	(	PUNCT
ejpam-6128	410	8	83	83	NUM
ejpam-6128	410	9	)	)	PUNCT
ejpam-6128	410	10	takes	take	VERB
ejpam-6128	410	11	the	the	DET
ejpam-6128	410	12	form	form	NOUN
ejpam-6128	410	13	µ(r	µ(r	NOUN
ejpam-6128	410	14	)	)	PUNCT
ejpam-6128	411	1	=	=	SYM
ejpam-6128	411	2	c1r	c1r	PROPN
ejpam-6128	412	1	+	+	PROPN
ejpam-6128	412	2	c2	c2	PROPN
ejpam-6128	412	3	,	,	PUNCT
ejpam-6128	412	4	(	(	PUNCT
ejpam-6128	412	5	84	84	NUM
ejpam-6128	412	6	)	)	PUNCT
ejpam-6128	412	7	which	which	PRON
ejpam-6128	412	8	implies	imply	VERB
ejpam-6128	412	9	h(p	h(p	NOUN
ejpam-6128	412	10	,	,	PUNCT
ejpam-6128	412	11	q	q	X
ejpam-6128	412	12	)	)	PUNCT
ejpam-6128	412	13	=	=	SYM
ejpam-6128	412	14	c1p+	c1p+	PROPN
ejpam-6128	412	15	c2	c2	PROPN
ejpam-6128	412	16	.	.	PUNCT
ejpam-6128	413	1	(	(	PUNCT
ejpam-6128	413	2	85	85	NUM
ejpam-6128	413	3	)	)	PUNCT
ejpam-6128	413	4	hence	hence	ADV
ejpam-6128	413	5	,	,	PUNCT
ejpam-6128	413	6	the	the	DET
ejpam-6128	413	7	solution	solution	NOUN
ejpam-6128	413	8	of	of	ADP
ejpam-6128	413	9	(	(	PUNCT
ejpam-6128	413	10	2	2	NUM
ejpam-6128	413	11	)	)	PUNCT
ejpam-6128	413	12	is	be	AUX
ejpam-6128	413	13	w(x	w(x	PROPN
ejpam-6128	413	14	,	,	PUNCT
ejpam-6128	413	15	y	y	PROPN
ejpam-6128	413	16	,	,	PUNCT
ejpam-6128	413	17	t	t	PROPN
ejpam-6128	413	18	)	)	PUNCT
ejpam-6128	413	19	=	=	SYM
ejpam-6128	414	1	c1t+	c1t+	PROPN
ejpam-6128	414	2	c2	c2	PROPN
ejpam-6128	414	3	,	,	PUNCT
ejpam-6128	414	4	(	(	PUNCT
ejpam-6128	414	5	86	86	NUM
ejpam-6128	414	6	)	)	PUNCT
ejpam-6128	414	7	where	where	SCONJ
ejpam-6128	414	8	c1	c1	PROPN
ejpam-6128	414	9	and	and	CCONJ
ejpam-6128	414	10	c2	c2	PROPN
ejpam-6128	414	11	are	be	AUX
ejpam-6128	414	12	constants	constant	NOUN
ejpam-6128	414	13	of	of	ADP
ejpam-6128	414	14	integration	integration	NOUN
ejpam-6128	414	15	.	.	PUNCT
ejpam-6128	415	1	case	case	NOUN
ejpam-6128	415	2	-	-	PUNCT
ejpam-6128	415	3	a2	a2	NOUN
ejpam-6128	415	4	:	:	PUNCT
ejpam-6128	415	5	in	in	ADP
ejpam-6128	415	6	(	(	PUNCT
ejpam-6128	415	7	81	81	NUM
ejpam-6128	415	8	)	)	PUNCT
ejpam-6128	415	9	,	,	PUNCT
ejpam-6128	415	10	set	set	VERB
ejpam-6128	415	11	c1	c1	PROPN
ejpam-6128	415	12	=	=	PROPN
ejpam-6128	415	13	c2	c2	PROPN
ejpam-6128	415	14	=	=	SYM
ejpam-6128	415	15	1	1	NUM
ejpam-6128	415	16	and	and	CCONJ
ejpam-6128	415	17	all	all	DET
ejpam-6128	415	18	arbitrary	arbitrary	ADJ
ejpam-6128	415	19	functions	function	NOUN
ejpam-6128	415	20	zero	zero	NUM
ejpam-6128	415	21	.	.	PUNCT
ejpam-6128	416	1	then	then	ADV
ejpam-6128	416	2	we	we	PRON
ejpam-6128	416	3	obtain	obtain	VERB
ejpam-6128	416	4	the	the	DET
ejpam-6128	416	5	symmetry	symmetry	NOUN
ejpam-6128	416	6	invariants	invariant	NOUN
ejpam-6128	416	7	r	r	NOUN
ejpam-6128	416	8	=	=	SYM
ejpam-6128	416	9	p	p	NOUN
ejpam-6128	416	10	,	,	PUNCT
ejpam-6128	416	11	h(p	h(p	PROPN
ejpam-6128	416	12	,	,	PUNCT
ejpam-6128	416	13	q	q	X
ejpam-6128	416	14	)	)	PUNCT
ejpam-6128	416	15	=	=	SYM
ejpam-6128	416	16	eqµ(r	eqµ(r	PROPN
ejpam-6128	416	17	)	)	PUNCT
ejpam-6128	416	18	.	.	PUNCT
ejpam-6128	417	1	(	(	PUNCT
ejpam-6128	417	2	87	87	NUM
ejpam-6128	417	3	)	)	PUNCT
ejpam-6128	417	4	the	the	DET
ejpam-6128	417	5	substitution	substitution	NOUN
ejpam-6128	417	6	of	of	ADP
ejpam-6128	417	7	(	(	PUNCT
ejpam-6128	417	8	87	87	NUM
ejpam-6128	417	9	)	)	PUNCT
ejpam-6128	417	10	in	in	ADP
ejpam-6128	417	11	(	(	PUNCT
ejpam-6128	417	12	80	80	NUM
ejpam-6128	417	13	)	)	PUNCT
ejpam-6128	417	14	yields	yield	VERB
ejpam-6128	417	15	the	the	DET
ejpam-6128	417	16	following	follow	VERB
ejpam-6128	417	17	ode	ode	PROPN
ejpam-6128	417	18	µ′′	µ′′	PROPN
ejpam-6128	417	19	−	−	PROPN
ejpam-6128	417	20	αµ	αµ	PROPN
ejpam-6128	417	21	=	=	SYM
ejpam-6128	417	22	0	0	PROPN
ejpam-6128	417	23	.	.	PUNCT
ejpam-6128	418	1	(	(	PUNCT
ejpam-6128	418	2	88	88	NUM
ejpam-6128	418	3	)	)	PUNCT
ejpam-6128	418	4	m.	m.	NOUN
ejpam-6128	418	5	usman	usman	PROPN
ejpam-6128	418	6	,	,	PUNCT
ejpam-6128	418	7	a.	a.	NOUN
ejpam-6128	418	8	hussain	hussain	PROPN
ejpam-6128	418	9	,	,	PUNCT
ejpam-6128	418	10	m.	m.	PROPN
ejpam-6128	418	11	u.	u.	PROPN
ejpam-6128	418	12	farooq	farooq	PROPN
ejpam-6128	418	13	,	,	PUNCT
ejpam-6128	418	14	j.	j.	PROPN
ejpam-6128	418	15	herrera	herrera	PROPN
ejpam-6128	418	16	/	/	SYM
ejpam-6128	418	17	eur	eur	PROPN
ejpam-6128	418	18	.	.	PUNCT
ejpam-6128	419	1	j.	j.	PROPN
ejpam-6128	419	2	pure	pure	PROPN
ejpam-6128	419	3	appl	appl	PROPN
ejpam-6128	419	4	.	.	PROPN
ejpam-6128	419	5	math	math	PROPN
ejpam-6128	419	6	,	,	PUNCT
ejpam-6128	419	7	18	18	NUM
ejpam-6128	419	8	(	(	PUNCT
ejpam-6128	419	9	4	4	NUM
ejpam-6128	419	10	)	)	PUNCT
ejpam-6128	419	11	(	(	PUNCT
ejpam-6128	419	12	2025	2025	NUM
ejpam-6128	419	13	)	)	PUNCT
ejpam-6128	419	14	,	,	PUNCT
ejpam-6128	419	15	6128	6128	NUM
ejpam-6128	419	16	20	20	NUM
ejpam-6128	419	17	of	of	ADP
ejpam-6128	419	18	29	29	NUM
ejpam-6128	419	19	the	the	DET
ejpam-6128	419	20	solution	solution	NOUN
ejpam-6128	419	21	of	of	ADP
ejpam-6128	419	22	(	(	PUNCT
ejpam-6128	419	23	88	88	NUM
ejpam-6128	419	24	)	)	PUNCT
ejpam-6128	419	25	takes	take	VERB
ejpam-6128	419	26	the	the	DET
ejpam-6128	419	27	form	form	NOUN
ejpam-6128	419	28	µ(r	µ(r	NOUN
ejpam-6128	419	29	)	)	PUNCT
ejpam-6128	419	30	=	=	SYM
ejpam-6128	419	31	(	(	PUNCT
ejpam-6128	419	32	c1e	c1e	PROPN
ejpam-6128	419	33	2	2	NUM
ejpam-6128	419	34	√	√	NUM
ejpam-6128	419	35	αr	αr	NUM
ejpam-6128	419	36	+	+	CCONJ
ejpam-6128	419	37	c2)e	c2)e	PROPN
ejpam-6128	419	38	−	−	PROPN
ejpam-6128	419	39	√	√	NUM
ejpam-6128	419	40	αr	αr	PROPN
ejpam-6128	419	41	,	,	PUNCT
ejpam-6128	419	42	(	(	PUNCT
ejpam-6128	419	43	89	89	NUM
ejpam-6128	419	44	)	)	PUNCT
ejpam-6128	419	45	which	which	PRON
ejpam-6128	419	46	implies	imply	VERB
ejpam-6128	419	47	h(p	h(p	NOUN
ejpam-6128	419	48	,	,	PUNCT
ejpam-6128	419	49	q	q	X
ejpam-6128	419	50	)	)	PUNCT
ejpam-6128	419	51	=	=	SYM
ejpam-6128	419	52	(	(	PUNCT
ejpam-6128	419	53	c1e	c1e	PROPN
ejpam-6128	419	54	2	2	NUM
ejpam-6128	419	55	√	√	NUM
ejpam-6128	419	56	αp	αp	NOUN
ejpam-6128	420	1	+	+	CCONJ
ejpam-6128	420	2	c2)e	c2)e	PROPN
ejpam-6128	420	3	q−	q−	PROPN
ejpam-6128	420	4	√	√	PROPN
ejpam-6128	420	5	αp	αp	INTJ
ejpam-6128	420	6	.	.	PUNCT
ejpam-6128	421	1	(	(	PUNCT
ejpam-6128	421	2	90	90	NUM
ejpam-6128	421	3	)	)	PUNCT
ejpam-6128	421	4	hence	hence	ADV
ejpam-6128	421	5	,	,	PUNCT
ejpam-6128	421	6	the	the	DET
ejpam-6128	421	7	solution	solution	NOUN
ejpam-6128	421	8	of	of	ADP
ejpam-6128	421	9	(	(	PUNCT
ejpam-6128	421	10	2	2	NUM
ejpam-6128	421	11	)	)	PUNCT
ejpam-6128	421	12	is	be	AUX
ejpam-6128	421	13	w(x	w(x	PROPN
ejpam-6128	421	14	,	,	PUNCT
ejpam-6128	421	15	y	y	PROPN
ejpam-6128	421	16	,	,	PUNCT
ejpam-6128	421	17	t	t	PROPN
ejpam-6128	421	18	)	)	PUNCT
ejpam-6128	421	19	=	=	PUNCT
ejpam-6128	422	1	(	(	PUNCT
ejpam-6128	422	2	c1e	c1e	PROPN
ejpam-6128	422	3	2	2	NUM
ejpam-6128	422	4	√	√	NUM
ejpam-6128	422	5	αt	αt	NOUN
ejpam-6128	422	6	+	+	CCONJ
ejpam-6128	422	7	c2)e	c2)e	PROPN
ejpam-6128	422	8	x−	x−	PROPN
ejpam-6128	422	9	√	√	PROPN
ejpam-6128	422	10	αt	αt	PROPN
ejpam-6128	422	11	,	,	PUNCT
ejpam-6128	422	12	(	(	PUNCT
ejpam-6128	422	13	91	91	NUM
ejpam-6128	422	14	)	)	PUNCT
ejpam-6128	422	15	where	where	SCONJ
ejpam-6128	422	16	c1	c1	PROPN
ejpam-6128	422	17	and	and	CCONJ
ejpam-6128	422	18	c2	c2	PROPN
ejpam-6128	422	19	are	be	AUX
ejpam-6128	422	20	constants	constant	NOUN
ejpam-6128	422	21	of	of	ADP
ejpam-6128	422	22	integration	integration	NOUN
ejpam-6128	422	23	.	.	PUNCT
ejpam-6128	423	1	case	case	NOUN
ejpam-6128	423	2	-	-	PUNCT
ejpam-6128	423	3	b	b	NOUN
ejpam-6128	423	4	:	:	PUNCT
ejpam-6128	423	5	consider	consider	VERB
ejpam-6128	423	6	y5	y5	NOUN
ejpam-6128	423	7	+	+	NUM
ejpam-6128	423	8	ay3	ay3	NOUN
ejpam-6128	423	9	=	=	SYM
ejpam-6128	423	10	y	y	PROPN
ejpam-6128	423	11	∂	∂	NOUN
ejpam-6128	423	12	∂y	∂y	PROPN
ejpam-6128	424	1	+	+	NOUN
ejpam-6128	424	2	2w	2w	NUM
ejpam-6128	424	3	∂	∂	NOUN
ejpam-6128	424	4	∂w	∂w	NOUN
ejpam-6128	425	1	+	+	CCONJ
ejpam-6128	425	2	a	a	DET
ejpam-6128	425	3	∂	∂	NOUN
ejpam-6128	425	4	∂t	∂t	PROPN
ejpam-6128	425	5	.	.	PUNCT
ejpam-6128	426	1	the	the	DET
ejpam-6128	426	2	solution	solution	NOUN
ejpam-6128	426	3	of	of	ADP
ejpam-6128	426	4	the	the	DET
ejpam-6128	426	5	characteristic	characteristic	ADJ
ejpam-6128	426	6	equation	equation	NOUN
ejpam-6128	426	7	for	for	ADP
ejpam-6128	426	8	y5	y5	NOUN
ejpam-6128	426	9	+	+	NUM
ejpam-6128	426	10	ay3	ay3	NOUN
ejpam-6128	426	11	provides	provide	VERB
ejpam-6128	426	12	the	the	DET
ejpam-6128	426	13	symmetry	symmetry	NOUN
ejpam-6128	426	14	invariants	invariant	NOUN
ejpam-6128	426	15	p	p	NOUN
ejpam-6128	426	16	=	=	NOUN
ejpam-6128	426	17	x	x	NOUN
ejpam-6128	426	18	,	,	PUNCT
ejpam-6128	426	19	q	q	X
ejpam-6128	427	1	=	=	PUNCT
ejpam-6128	427	2	t−	t−	PRON
ejpam-6128	427	3	a	a	DET
ejpam-6128	427	4	ln	ln	ADJ
ejpam-6128	427	5	(	(	PUNCT
ejpam-6128	427	6	y	y	NOUN
ejpam-6128	427	7	)	)	PUNCT
ejpam-6128	427	8	,	,	PUNCT
ejpam-6128	427	9	w(x	w(x	PROPN
ejpam-6128	427	10	,	,	PUNCT
ejpam-6128	427	11	y	y	PROPN
ejpam-6128	427	12	,	,	PUNCT
ejpam-6128	427	13	t	t	PROPN
ejpam-6128	427	14	)	)	PUNCT
ejpam-6128	427	15	=	=	SYM
ejpam-6128	427	16	y2h(p	y2h(p	NOUN
ejpam-6128	427	17	,	,	PUNCT
ejpam-6128	427	18	q	q	NOUN
ejpam-6128	427	19	)	)	PUNCT
ejpam-6128	427	20	.	.	PUNCT
ejpam-6128	428	1	(	(	PUNCT
ejpam-6128	428	2	92	92	NUM
ejpam-6128	428	3	)	)	PUNCT
ejpam-6128	428	4	by	by	ADP
ejpam-6128	428	5	inserting	insert	VERB
ejpam-6128	428	6	(	(	PUNCT
ejpam-6128	428	7	92	92	NUM
ejpam-6128	428	8	)	)	PUNCT
ejpam-6128	428	9	in	in	ADP
ejpam-6128	428	10	(	(	PUNCT
ejpam-6128	428	11	2	2	NUM
ejpam-6128	428	12	)	)	PUNCT
ejpam-6128	428	13	,	,	PUNCT
ejpam-6128	428	14	we	we	PRON
ejpam-6128	428	15	get	get	VERB
ejpam-6128	428	16	−a2βhhqq	−a2βhhqq	NOUN
ejpam-6128	428	17	−	−	NOUN
ejpam-6128	429	1	6βh2	6βh2	NUM
ejpam-6128	430	1	+	+	CCONJ
ejpam-6128	430	2	7βhhq	7βhhq	NUM
ejpam-6128	430	3	−	−	NOUN
ejpam-6128	430	4	βa2hq	βa2hq	NUM
ejpam-6128	430	5	2	2	NUM
ejpam-6128	430	6	−	−	NOUN
ejpam-6128	430	7	αhpp	αhpp	NOUN
ejpam-6128	430	8	+	+	NOUN
ejpam-6128	430	9	hqq	hqq	X
ejpam-6128	430	10	=	=	SYM
ejpam-6128	430	11	0	0	PROPN
ejpam-6128	430	12	.	.	PUNCT
ejpam-6128	431	1	(	(	PUNCT
ejpam-6128	431	2	93	93	NUM
ejpam-6128	431	3	)	)	PUNCT
ejpam-6128	431	4	infinitesimals	infinitesimal	NOUN
ejpam-6128	431	5	for	for	ADP
ejpam-6128	431	6	(	(	PUNCT
ejpam-6128	431	7	93	93	NUM
ejpam-6128	431	8	)	)	PUNCT
ejpam-6128	431	9	are	be	AUX
ejpam-6128	431	10	as	as	SCONJ
ejpam-6128	431	11	follows	follow	VERB
ejpam-6128	431	12	ζp	ζp	ADJ
ejpam-6128	431	13	=	=	PROPN
ejpam-6128	431	14	c1	c1	NOUN
ejpam-6128	431	15	,	,	PUNCT
ejpam-6128	431	16	ζq	ζq	ADP
ejpam-6128	431	17	=	=	PROPN
ejpam-6128	431	18	c2	c2	PROPN
ejpam-6128	431	19	,	,	PUNCT
ejpam-6128	431	20	φh	φh	NOUN
ejpam-6128	431	21	=	=	NOUN
ejpam-6128	431	22	0	0	NUM
ejpam-6128	431	23	.	.	PUNCT
ejpam-6128	432	1	(	(	PUNCT
ejpam-6128	432	2	94	94	X
ejpam-6128	432	3	)	)	PUNCT
ejpam-6128	432	4	case	case	NOUN
ejpam-6128	432	5	-	-	PUNCT
ejpam-6128	432	6	b1	b1	NOUN
ejpam-6128	432	7	:	:	PUNCT
ejpam-6128	432	8	in	in	ADP
ejpam-6128	432	9	(	(	PUNCT
ejpam-6128	432	10	94	94	NUM
ejpam-6128	432	11	)	)	PUNCT
ejpam-6128	432	12	,	,	PUNCT
ejpam-6128	432	13	set	set	VERB
ejpam-6128	432	14	c2	c2	PROPN
ejpam-6128	432	15	=	=	SYM
ejpam-6128	432	16	1	1	NUM
ejpam-6128	432	17	and	and	CCONJ
ejpam-6128	432	18	c1	c1	NOUN
ejpam-6128	432	19	=	=	PUNCT
ejpam-6128	433	1	0	0	X
ejpam-6128	433	2	.	.	PUNCT
ejpam-6128	434	1	then	then	ADV
ejpam-6128	434	2	we	we	PRON
ejpam-6128	434	3	obtain	obtain	VERB
ejpam-6128	434	4	the	the	DET
ejpam-6128	434	5	symmetry	symmetry	NOUN
ejpam-6128	434	6	invariants	invariant	NOUN
ejpam-6128	434	7	r	r	NOUN
ejpam-6128	434	8	=	=	SYM
ejpam-6128	434	9	p	p	NOUN
ejpam-6128	434	10	,	,	PUNCT
ejpam-6128	434	11	h(p	h(p	PROPN
ejpam-6128	434	12	,	,	PUNCT
ejpam-6128	434	13	q	q	NOUN
ejpam-6128	434	14	)	)	PUNCT
ejpam-6128	434	15	=	=	SYM
ejpam-6128	434	16	µ(r	µ(r	NOUN
ejpam-6128	434	17	)	)	PUNCT
ejpam-6128	434	18	.	.	PUNCT
ejpam-6128	435	1	(	(	PUNCT
ejpam-6128	435	2	95	95	NUM
ejpam-6128	435	3	)	)	PUNCT
ejpam-6128	435	4	the	the	DET
ejpam-6128	435	5	substitution	substitution	NOUN
ejpam-6128	435	6	of	of	ADP
ejpam-6128	435	7	(	(	PUNCT
ejpam-6128	435	8	95	95	NUM
ejpam-6128	435	9	)	)	PUNCT
ejpam-6128	435	10	in	in	ADP
ejpam-6128	435	11	(	(	PUNCT
ejpam-6128	435	12	93	93	NUM
ejpam-6128	435	13	)	)	PUNCT
ejpam-6128	435	14	yields	yield	VERB
ejpam-6128	435	15	the	the	DET
ejpam-6128	435	16	following	follow	VERB
ejpam-6128	435	17	ode	ode	PROPN
ejpam-6128	435	18	αµ′′	αµ′′	ADJ
ejpam-6128	435	19	+	+	ADP
ejpam-6128	435	20	6βµ2	6βµ2	NUM
ejpam-6128	435	21	=	=	SYM
ejpam-6128	435	22	0	0	NUM
ejpam-6128	435	23	.	.	PUNCT
ejpam-6128	436	1	(	(	PUNCT
ejpam-6128	436	2	96	96	NUM
ejpam-6128	436	3	)	)	PUNCT
ejpam-6128	436	4	the	the	DET
ejpam-6128	436	5	solution	solution	NOUN
ejpam-6128	436	6	of	of	ADP
ejpam-6128	436	7	(	(	PUNCT
ejpam-6128	436	8	96	96	NUM
ejpam-6128	436	9	)	)	PUNCT
ejpam-6128	436	10	takes	take	VERB
ejpam-6128	436	11	the	the	DET
ejpam-6128	436	12	form	form	NOUN
ejpam-6128	436	13	µ(r	µ(r	NOUN
ejpam-6128	436	14	)	)	PUNCT
ejpam-6128	437	1	=	=	SYM
ejpam-6128	438	1	−weierstrassp	−weierstrassp	NOUN
ejpam-6128	438	2	(	(	PUNCT
ejpam-6128	438	3	r	r	NOUN
ejpam-6128	438	4	+	+	NUM
ejpam-6128	438	5	c1	c1	PROPN
ejpam-6128	438	6	,	,	PUNCT
ejpam-6128	438	7	0	0	NUM
ejpam-6128	438	8	,	,	PUNCT
ejpam-6128	438	9	c2)α	c2)α	PROPN
ejpam-6128	438	10	β	β	X
ejpam-6128	438	11	,	,	PUNCT
ejpam-6128	438	12	(	(	PUNCT
ejpam-6128	438	13	97	97	NUM
ejpam-6128	438	14	)	)	PUNCT
ejpam-6128	438	15	which	which	PRON
ejpam-6128	438	16	implies	imply	VERB
ejpam-6128	438	17	h(p	h(p	NOUN
ejpam-6128	438	18	,	,	PUNCT
ejpam-6128	438	19	q	q	X
ejpam-6128	438	20	)	)	PUNCT
ejpam-6128	438	21	=	=	SYM
ejpam-6128	439	1	−weierstrassp	−weierstrassp	NOUN
ejpam-6128	439	2	(	(	PUNCT
ejpam-6128	439	3	p+	p+	NOUN
ejpam-6128	439	4	c1	c1	NOUN
ejpam-6128	439	5	,	,	PUNCT
ejpam-6128	439	6	0	0	NUM
ejpam-6128	439	7	,	,	PUNCT
ejpam-6128	439	8	c2)α	c2)α	PROPN
ejpam-6128	439	9	β	β	X
ejpam-6128	439	10	.	.	PUNCT
ejpam-6128	440	1	(	(	PUNCT
ejpam-6128	440	2	98	98	NUM
ejpam-6128	440	3	)	)	PUNCT
ejpam-6128	440	4	m.	m.	NOUN
ejpam-6128	440	5	usman	usman	PROPN
ejpam-6128	440	6	,	,	PUNCT
ejpam-6128	440	7	a.	a.	NOUN
ejpam-6128	440	8	hussain	hussain	PROPN
ejpam-6128	440	9	,	,	PUNCT
ejpam-6128	440	10	m.	m.	PROPN
ejpam-6128	440	11	u.	u.	PROPN
ejpam-6128	440	12	farooq	farooq	PROPN
ejpam-6128	440	13	,	,	PUNCT
ejpam-6128	440	14	j.	j.	PROPN
ejpam-6128	440	15	herrera	herrera	PROPN
ejpam-6128	440	16	/	/	SYM
ejpam-6128	440	17	eur	eur	PROPN
ejpam-6128	440	18	.	.	PUNCT
ejpam-6128	441	1	j.	j.	PROPN
ejpam-6128	441	2	pure	pure	PROPN
ejpam-6128	441	3	appl	appl	PROPN
ejpam-6128	441	4	.	.	PROPN
ejpam-6128	441	5	math	math	PROPN
ejpam-6128	441	6	,	,	PUNCT
ejpam-6128	441	7	18	18	NUM
ejpam-6128	441	8	(	(	PUNCT
ejpam-6128	441	9	4	4	NUM
ejpam-6128	441	10	)	)	PUNCT
ejpam-6128	441	11	(	(	PUNCT
ejpam-6128	441	12	2025	2025	NUM
ejpam-6128	441	13	)	)	PUNCT
ejpam-6128	441	14	,	,	PUNCT
ejpam-6128	441	15	6128	6128	NUM
ejpam-6128	441	16	21	21	NUM
ejpam-6128	441	17	of	of	ADP
ejpam-6128	441	18	29	29	NUM
ejpam-6128	441	19	hence	hence	ADV
ejpam-6128	441	20	,	,	PUNCT
ejpam-6128	441	21	the	the	DET
ejpam-6128	441	22	solution	solution	NOUN
ejpam-6128	441	23	of	of	ADP
ejpam-6128	441	24	(	(	PUNCT
ejpam-6128	441	25	2	2	NUM
ejpam-6128	441	26	)	)	PUNCT
ejpam-6128	441	27	is	be	AUX
ejpam-6128	441	28	w(x	w(x	PROPN
ejpam-6128	441	29	,	,	PUNCT
ejpam-6128	441	30	y	y	PROPN
ejpam-6128	441	31	,	,	PUNCT
ejpam-6128	441	32	t	t	PROPN
ejpam-6128	441	33	)	)	PUNCT
ejpam-6128	441	34	=	=	SYM
ejpam-6128	442	1	−weierstrassp	−weierstrassp	X
ejpam-6128	442	2	(	(	PUNCT
ejpam-6128	442	3	x+	x+	PROPN
ejpam-6128	442	4	c1	c1	NOUN
ejpam-6128	442	5	,	,	PUNCT
ejpam-6128	442	6	0	0	NUM
ejpam-6128	442	7	,	,	PUNCT
ejpam-6128	442	8	c2)αy	c2)αy	NOUN
ejpam-6128	442	9	2	2	NUM
ejpam-6128	442	10	β	β	NOUN
ejpam-6128	442	11	,	,	PUNCT
ejpam-6128	442	12	(	(	PUNCT
ejpam-6128	442	13	99	99	NUM
ejpam-6128	442	14	)	)	PUNCT
ejpam-6128	442	15	where	where	SCONJ
ejpam-6128	442	16	c1	c1	PROPN
ejpam-6128	442	17	and	and	CCONJ
ejpam-6128	442	18	c2	c2	PROPN
ejpam-6128	442	19	are	be	AUX
ejpam-6128	442	20	constants	constant	NOUN
ejpam-6128	442	21	of	of	ADP
ejpam-6128	442	22	integration	integration	NOUN
ejpam-6128	442	23	.	.	PUNCT
ejpam-6128	443	1	case	case	NOUN
ejpam-6128	443	2	-	-	PUNCT
ejpam-6128	443	3	c	c	NOUN
ejpam-6128	443	4	:	:	PUNCT
ejpam-6128	443	5	consider	consider	VERB
ejpam-6128	443	6	y2	y2	NOUN
ejpam-6128	443	7	+	+	NUM
ejpam-6128	443	8	ay3	ay3	NOUN
ejpam-6128	443	9	=	=	SYM
ejpam-6128	443	10	∂	∂	NUM
ejpam-6128	443	11	∂y	∂y	NOUN
ejpam-6128	444	1	+	+	CCONJ
ejpam-6128	444	2	a	a	DET
ejpam-6128	444	3	∂	∂	NOUN
ejpam-6128	444	4	∂t	∂t	PROPN
ejpam-6128	444	5	.	.	PUNCT
ejpam-6128	445	1	the	the	DET
ejpam-6128	445	2	solution	solution	NOUN
ejpam-6128	445	3	of	of	ADP
ejpam-6128	445	4	the	the	DET
ejpam-6128	445	5	characteristic	characteristic	ADJ
ejpam-6128	445	6	equation	equation	NOUN
ejpam-6128	445	7	for	for	ADP
ejpam-6128	445	8	y2	y2	PROPN
ejpam-6128	445	9	+	+	CCONJ
ejpam-6128	445	10	ay3	ay3	NOUN
ejpam-6128	445	11	provides	provide	VERB
ejpam-6128	445	12	the	the	DET
ejpam-6128	445	13	symmetry	symmetry	NOUN
ejpam-6128	445	14	invariants	invariant	NOUN
ejpam-6128	445	15	p	p	NOUN
ejpam-6128	445	16	=	=	NOUN
ejpam-6128	445	17	x	x	NOUN
ejpam-6128	445	18	,	,	PUNCT
ejpam-6128	445	19	q	q	X
ejpam-6128	445	20	=	=	PUNCT
ejpam-6128	445	21	t−	t−	PROPN
ejpam-6128	445	22	ay	ay	PROPN
ejpam-6128	445	23	,	,	PUNCT
ejpam-6128	445	24	w(x	w(x	PROPN
ejpam-6128	445	25	,	,	PUNCT
ejpam-6128	445	26	y	y	PROPN
ejpam-6128	445	27	,	,	PUNCT
ejpam-6128	445	28	t	t	PROPN
ejpam-6128	445	29	)	)	PUNCT
ejpam-6128	445	30	=	=	SYM
ejpam-6128	445	31	h(p	h(p	PROPN
ejpam-6128	445	32	,	,	PUNCT
ejpam-6128	445	33	q	q	NOUN
ejpam-6128	445	34	)	)	PUNCT
ejpam-6128	445	35	.	.	PUNCT
ejpam-6128	446	1	(	(	PUNCT
ejpam-6128	446	2	100	100	NUM
ejpam-6128	446	3	)	)	PUNCT
ejpam-6128	446	4	by	by	ADP
ejpam-6128	446	5	inserting	insert	VERB
ejpam-6128	446	6	(	(	PUNCT
ejpam-6128	446	7	100	100	NUM
ejpam-6128	446	8	)	)	PUNCT
ejpam-6128	446	9	in	in	ADP
ejpam-6128	446	10	(	(	PUNCT
ejpam-6128	446	11	2	2	NUM
ejpam-6128	446	12	)	)	PUNCT
ejpam-6128	446	13	,	,	PUNCT
ejpam-6128	446	14	we	we	PRON
ejpam-6128	446	15	get	get	VERB
ejpam-6128	446	16	hqq	hqq	PROPN
ejpam-6128	446	17	−	−	PROPN
ejpam-6128	446	18	αhpp	αhpp	NOUN
ejpam-6128	446	19	−	−	PROPN
ejpam-6128	446	20	a2βhhqq	a2βhhqq	PROPN
ejpam-6128	447	1	−	−	PROPN
ejpam-6128	447	2	a2βhq	a2βhq	NOUN
ejpam-6128	447	3	2	2	NUM
ejpam-6128	447	4	=	=	SYM
ejpam-6128	447	5	0	0	NUM
ejpam-6128	447	6	.	.	PUNCT
ejpam-6128	448	1	(	(	PUNCT
ejpam-6128	448	2	101	101	NUM
ejpam-6128	448	3	)	)	PUNCT
ejpam-6128	448	4	infinitesimals	infinitesimal	NOUN
ejpam-6128	448	5	for	for	ADP
ejpam-6128	448	6	(	(	PUNCT
ejpam-6128	448	7	101	101	NUM
ejpam-6128	448	8	)	)	PUNCT
ejpam-6128	448	9	are	be	AUX
ejpam-6128	448	10	as	as	SCONJ
ejpam-6128	448	11	follows	follow	VERB
ejpam-6128	448	12	ζp	ζp	ADJ
ejpam-6128	448	13	=	=	PUNCT
ejpam-6128	448	14	c1p+	c1p+	PROPN
ejpam-6128	448	15	c2	c2	PROPN
ejpam-6128	448	16	,	,	PUNCT
ejpam-6128	448	17	ζq	ζq	NOUN
ejpam-6128	448	18	=	=	PUNCT
ejpam-6128	448	19	c3q	c3q	PROPN
ejpam-6128	448	20	+	+	NUM
ejpam-6128	448	21	c4	c4	NOUN
ejpam-6128	448	22	,	,	PUNCT
ejpam-6128	448	23	φh	φh	NOUN
ejpam-6128	448	24	=	=	PUNCT
ejpam-6128	448	25	−2(c1	−2(c1	PUNCT
ejpam-6128	448	26	−	−	PROPN
ejpam-6128	449	1	c3)(a	c3)(a	NOUN
ejpam-6128	449	2	2βh−	2βh−	NOUN
ejpam-6128	449	3	1	1	X
ejpam-6128	449	4	)	)	PUNCT
ejpam-6128	449	5	a2β	a2β	PUNCT
ejpam-6128	449	6	.	.	PUNCT
ejpam-6128	450	1	(	(	PUNCT
ejpam-6128	450	2	102	102	X
ejpam-6128	450	3	)	)	PUNCT
ejpam-6128	450	4	case	case	NOUN
ejpam-6128	450	5	-	-	PUNCT
ejpam-6128	450	6	c1	c1	NOUN
ejpam-6128	450	7	:	:	PUNCT
ejpam-6128	450	8	in	in	ADP
ejpam-6128	450	9	(	(	PUNCT
ejpam-6128	450	10	102	102	NUM
ejpam-6128	450	11	)	)	PUNCT
ejpam-6128	450	12	,	,	PUNCT
ejpam-6128	450	13	set	set	VERB
ejpam-6128	450	14	c2	c2	PROPN
ejpam-6128	450	15	=	=	SYM
ejpam-6128	450	16	1	1	NUM
ejpam-6128	450	17	and	and	CCONJ
ejpam-6128	450	18	other	other	ADJ
ejpam-6128	450	19	constants	constant	NOUN
ejpam-6128	450	20	zero	zero	NUM
ejpam-6128	450	21	.	.	PUNCT
ejpam-6128	451	1	then	then	ADV
ejpam-6128	451	2	we	we	PRON
ejpam-6128	451	3	obtain	obtain	VERB
ejpam-6128	451	4	the	the	DET
ejpam-6128	451	5	symmetry	symmetry	NOUN
ejpam-6128	451	6	invariants	invariant	NOUN
ejpam-6128	451	7	r	r	NOUN
ejpam-6128	451	8	=	=	SYM
ejpam-6128	451	9	q	q	ADJ
ejpam-6128	451	10	,	,	PUNCT
ejpam-6128	451	11	h(p	h(p	PROPN
ejpam-6128	451	12	,	,	PUNCT
ejpam-6128	451	13	q	q	NOUN
ejpam-6128	451	14	)	)	PUNCT
ejpam-6128	451	15	=	=	SYM
ejpam-6128	451	16	µ(r	µ(r	NOUN
ejpam-6128	451	17	)	)	PUNCT
ejpam-6128	451	18	.	.	PUNCT
ejpam-6128	452	1	(	(	PUNCT
ejpam-6128	452	2	103	103	NUM
ejpam-6128	452	3	)	)	PUNCT
ejpam-6128	452	4	the	the	DET
ejpam-6128	452	5	substitution	substitution	NOUN
ejpam-6128	452	6	of	of	ADP
ejpam-6128	452	7	(	(	PUNCT
ejpam-6128	452	8	103	103	NUM
ejpam-6128	452	9	)	)	PUNCT
ejpam-6128	452	10	in	in	ADP
ejpam-6128	452	11	(	(	PUNCT
ejpam-6128	452	12	101	101	NUM
ejpam-6128	452	13	)	)	PUNCT
ejpam-6128	452	14	yields	yield	VERB
ejpam-6128	452	15	the	the	DET
ejpam-6128	452	16	following	follow	VERB
ejpam-6128	452	17	ode	ode	PROPN
ejpam-6128	452	18	µ′′	µ′′	PROPN
ejpam-6128	452	19	−	−	PROPN
ejpam-6128	452	20	a2βµµ′′	a2βµµ′′	ADV
ejpam-6128	452	21	−	−	NOUN
ejpam-6128	452	22	a2βµ′2	a2βµ′2	ADP
ejpam-6128	453	1	=	=	NOUN
ejpam-6128	454	1	0	0	PROPN
ejpam-6128	454	2	.	.	PUNCT
ejpam-6128	455	1	(	(	PUNCT
ejpam-6128	455	2	104	104	X
ejpam-6128	455	3	)	)	PUNCT
ejpam-6128	455	4	the	the	DET
ejpam-6128	455	5	solution	solution	NOUN
ejpam-6128	455	6	of	of	ADP
ejpam-6128	455	7	(	(	PUNCT
ejpam-6128	455	8	104	104	NUM
ejpam-6128	455	9	)	)	PUNCT
ejpam-6128	455	10	takes	take	VERB
ejpam-6128	455	11	the	the	DET
ejpam-6128	455	12	form	form	NOUN
ejpam-6128	455	13	µ(r	µ(r	NOUN
ejpam-6128	455	14	)	)	PUNCT
ejpam-6128	455	15	=	=	SYM
ejpam-6128	456	1	1−	1−	NUM
ejpam-6128	456	2	√	√	NUM
ejpam-6128	456	3	1	1	NUM
ejpam-6128	457	1	+	+	NUM
ejpam-6128	457	2	2a2β(c1r	2a2β(c1r	PROPN
ejpam-6128	457	3	+	+	CCONJ
ejpam-6128	457	4	c2	c2	PROPN
ejpam-6128	457	5	)	)	PUNCT
ejpam-6128	457	6	a2β	a2β	PUNCT
ejpam-6128	457	7	,	,	PUNCT
ejpam-6128	457	8	(	(	PUNCT
ejpam-6128	457	9	105	105	NUM
ejpam-6128	457	10	)	)	PUNCT
ejpam-6128	457	11	which	which	PRON
ejpam-6128	457	12	implies	imply	VERB
ejpam-6128	457	13	h(p	h(p	NOUN
ejpam-6128	457	14	,	,	PUNCT
ejpam-6128	457	15	q	q	X
ejpam-6128	457	16	)	)	PUNCT
ejpam-6128	457	17	=	=	SYM
ejpam-6128	458	1	1−	1−	NUM
ejpam-6128	458	2	√	√	NUM
ejpam-6128	458	3	1	1	NUM
ejpam-6128	459	1	+	+	NUM
ejpam-6128	459	2	2a2β(c1q	2a2β(c1q	NOUN
ejpam-6128	459	3	+	+	CCONJ
ejpam-6128	459	4	c2	c2	PROPN
ejpam-6128	459	5	)	)	PUNCT
ejpam-6128	459	6	a2β	a2β	PUNCT
ejpam-6128	459	7	.	.	PUNCT
ejpam-6128	460	1	(	(	PUNCT
ejpam-6128	460	2	106	106	NUM
ejpam-6128	460	3	)	)	PUNCT
ejpam-6128	460	4	hence	hence	ADV
ejpam-6128	460	5	,	,	PUNCT
ejpam-6128	460	6	the	the	DET
ejpam-6128	460	7	solution	solution	NOUN
ejpam-6128	460	8	of	of	ADP
ejpam-6128	460	9	(	(	PUNCT
ejpam-6128	460	10	2	2	NUM
ejpam-6128	460	11	)	)	PUNCT
ejpam-6128	460	12	is	be	AUX
ejpam-6128	460	13	w(x	w(x	PROPN
ejpam-6128	460	14	,	,	PUNCT
ejpam-6128	460	15	y	y	PROPN
ejpam-6128	460	16	,	,	PUNCT
ejpam-6128	460	17	t	t	PROPN
ejpam-6128	460	18	)	)	PUNCT
ejpam-6128	460	19	=	=	SYM
ejpam-6128	461	1	1−	1−	NUM
ejpam-6128	461	2	√	√	NUM
ejpam-6128	461	3	1	1	NUM
ejpam-6128	462	1	+	+	NUM
ejpam-6128	462	2	2a2β(c1(t−	2a2β(c1(t−	NUM
ejpam-6128	462	3	ay	ay	NOUN
ejpam-6128	462	4	)	)	PUNCT
ejpam-6128	462	5	+	+	CCONJ
ejpam-6128	462	6	c2	c2	PROPN
ejpam-6128	462	7	)	)	PUNCT
ejpam-6128	462	8	a2β	a2β	PUNCT
ejpam-6128	462	9	,	,	PUNCT
ejpam-6128	462	10	(	(	PUNCT
ejpam-6128	462	11	107	107	X
ejpam-6128	462	12	)	)	PUNCT
ejpam-6128	462	13	m.	m.	NOUN
ejpam-6128	462	14	usman	usman	PROPN
ejpam-6128	462	15	,	,	PUNCT
ejpam-6128	462	16	a.	a.	NOUN
ejpam-6128	462	17	hussain	hussain	PROPN
ejpam-6128	462	18	,	,	PUNCT
ejpam-6128	462	19	m.	m.	PROPN
ejpam-6128	462	20	u.	u.	PROPN
ejpam-6128	462	21	farooq	farooq	PROPN
ejpam-6128	462	22	,	,	PUNCT
ejpam-6128	462	23	j.	j.	PROPN
ejpam-6128	462	24	herrera	herrera	PROPN
ejpam-6128	462	25	/	/	SYM
ejpam-6128	462	26	eur	eur	PROPN
ejpam-6128	462	27	.	.	PUNCT
ejpam-6128	463	1	j.	j.	PROPN
ejpam-6128	463	2	pure	pure	PROPN
ejpam-6128	463	3	appl	appl	PROPN
ejpam-6128	463	4	.	.	PROPN
ejpam-6128	463	5	math	math	PROPN
ejpam-6128	463	6	,	,	PUNCT
ejpam-6128	463	7	18	18	NUM
ejpam-6128	463	8	(	(	PUNCT
ejpam-6128	463	9	4	4	NUM
ejpam-6128	463	10	)	)	PUNCT
ejpam-6128	463	11	(	(	PUNCT
ejpam-6128	463	12	2025	2025	NUM
ejpam-6128	463	13	)	)	PUNCT
ejpam-6128	463	14	,	,	PUNCT
ejpam-6128	463	15	6128	6128	NUM
ejpam-6128	463	16	22	22	NUM
ejpam-6128	463	17	of	of	ADP
ejpam-6128	463	18	29	29	NUM
ejpam-6128	463	19	where	where	SCONJ
ejpam-6128	463	20	c1	c1	PROPN
ejpam-6128	463	21	and	and	CCONJ
ejpam-6128	463	22	c2	c2	PROPN
ejpam-6128	463	23	are	be	AUX
ejpam-6128	463	24	constants	constant	NOUN
ejpam-6128	463	25	of	of	ADP
ejpam-6128	463	26	integration	integration	NOUN
ejpam-6128	463	27	.	.	PUNCT
ejpam-6128	464	1	case	case	NOUN
ejpam-6128	464	2	-	-	PUNCT
ejpam-6128	464	3	c2	c2	PROPN
ejpam-6128	464	4	:	:	PUNCT
ejpam-6128	464	5	in	in	ADP
ejpam-6128	464	6	(	(	PUNCT
ejpam-6128	464	7	102	102	NUM
ejpam-6128	464	8	)	)	PUNCT
ejpam-6128	464	9	,	,	PUNCT
ejpam-6128	464	10	set	set	VERB
ejpam-6128	464	11	c4	c4	NOUN
ejpam-6128	464	12	=	=	SYM
ejpam-6128	464	13	1	1	NUM
ejpam-6128	464	14	and	and	CCONJ
ejpam-6128	464	15	other	other	ADJ
ejpam-6128	464	16	constants	constant	NOUN
ejpam-6128	464	17	zero	zero	NUM
ejpam-6128	464	18	.	.	PUNCT
ejpam-6128	465	1	then	then	ADV
ejpam-6128	465	2	we	we	PRON
ejpam-6128	465	3	obtain	obtain	VERB
ejpam-6128	465	4	the	the	DET
ejpam-6128	465	5	symmetry	symmetry	NOUN
ejpam-6128	465	6	invariants	invariant	NOUN
ejpam-6128	465	7	r	r	NOUN
ejpam-6128	465	8	=	=	SYM
ejpam-6128	465	9	p	p	NOUN
ejpam-6128	465	10	,	,	PUNCT
ejpam-6128	465	11	h(p	h(p	PROPN
ejpam-6128	465	12	,	,	PUNCT
ejpam-6128	465	13	q	q	NOUN
ejpam-6128	465	14	)	)	PUNCT
ejpam-6128	465	15	=	=	SYM
ejpam-6128	465	16	µ(r	µ(r	NOUN
ejpam-6128	465	17	)	)	PUNCT
ejpam-6128	465	18	.	.	PUNCT
ejpam-6128	466	1	(	(	PUNCT
ejpam-6128	466	2	108	108	NUM
ejpam-6128	466	3	)	)	PUNCT
ejpam-6128	466	4	the	the	DET
ejpam-6128	466	5	substitution	substitution	NOUN
ejpam-6128	466	6	of	of	ADP
ejpam-6128	466	7	(	(	PUNCT
ejpam-6128	466	8	108	108	NUM
ejpam-6128	466	9	)	)	PUNCT
ejpam-6128	466	10	in	in	ADP
ejpam-6128	466	11	(	(	PUNCT
ejpam-6128	466	12	101	101	NUM
ejpam-6128	466	13	)	)	PUNCT
ejpam-6128	466	14	yields	yield	VERB
ejpam-6128	466	15	the	the	DET
ejpam-6128	466	16	following	follow	VERB
ejpam-6128	466	17	ode	ode	PROPN
ejpam-6128	466	18	µ′′	µ′′	PROPN
ejpam-6128	466	19	=	=	SYM
ejpam-6128	466	20	0	0	NUM
ejpam-6128	466	21	.	.	PUNCT
ejpam-6128	467	1	(	(	PUNCT
ejpam-6128	467	2	109	109	NUM
ejpam-6128	467	3	)	)	PUNCT
ejpam-6128	467	4	the	the	DET
ejpam-6128	467	5	solution	solution	NOUN
ejpam-6128	467	6	of	of	ADP
ejpam-6128	467	7	(	(	PUNCT
ejpam-6128	467	8	109	109	NUM
ejpam-6128	467	9	)	)	PUNCT
ejpam-6128	467	10	takes	take	VERB
ejpam-6128	467	11	the	the	DET
ejpam-6128	467	12	form	form	NOUN
ejpam-6128	467	13	µ(r	µ(r	NOUN
ejpam-6128	467	14	)	)	PUNCT
ejpam-6128	468	1	=	=	SYM
ejpam-6128	468	2	c1r	c1r	PROPN
ejpam-6128	469	1	+	+	PROPN
ejpam-6128	469	2	c2	c2	PROPN
ejpam-6128	469	3	,	,	PUNCT
ejpam-6128	469	4	(	(	PUNCT
ejpam-6128	469	5	110	110	NUM
ejpam-6128	469	6	)	)	PUNCT
ejpam-6128	469	7	which	which	PRON
ejpam-6128	469	8	implies	imply	VERB
ejpam-6128	469	9	h(p	h(p	NOUN
ejpam-6128	469	10	,	,	PUNCT
ejpam-6128	469	11	q	q	X
ejpam-6128	469	12	)	)	PUNCT
ejpam-6128	469	13	=	=	SYM
ejpam-6128	469	14	c1p+	c1p+	PROPN
ejpam-6128	469	15	c2	c2	PROPN
ejpam-6128	469	16	.	.	PUNCT
ejpam-6128	470	1	(	(	PUNCT
ejpam-6128	470	2	111	111	NUM
ejpam-6128	470	3	)	)	PUNCT
ejpam-6128	470	4	hence	hence	ADV
ejpam-6128	470	5	,	,	PUNCT
ejpam-6128	470	6	the	the	DET
ejpam-6128	470	7	solution	solution	NOUN
ejpam-6128	470	8	of	of	ADP
ejpam-6128	470	9	(	(	PUNCT
ejpam-6128	470	10	2	2	NUM
ejpam-6128	470	11	)	)	PUNCT
ejpam-6128	470	12	is	be	AUX
ejpam-6128	470	13	w(x	w(x	PROPN
ejpam-6128	470	14	,	,	PUNCT
ejpam-6128	470	15	y	y	PROPN
ejpam-6128	470	16	,	,	PUNCT
ejpam-6128	470	17	t	t	PROPN
ejpam-6128	470	18	)	)	PUNCT
ejpam-6128	470	19	=	=	SYM
ejpam-6128	470	20	c1x+	c1x+	PROPN
ejpam-6128	470	21	c2	c2	PROPN
ejpam-6128	470	22	,	,	PUNCT
ejpam-6128	470	23	(	(	PUNCT
ejpam-6128	470	24	112	112	NUM
ejpam-6128	470	25	)	)	PUNCT
ejpam-6128	470	26	where	where	SCONJ
ejpam-6128	470	27	c1	c1	PROPN
ejpam-6128	470	28	and	and	CCONJ
ejpam-6128	470	29	c2	c2	PROPN
ejpam-6128	470	30	are	be	AUX
ejpam-6128	470	31	constants	constant	NOUN
ejpam-6128	470	32	of	of	ADP
ejpam-6128	470	33	integration	integration	NOUN
ejpam-6128	470	34	.	.	PUNCT
ejpam-6128	471	1	case	case	NOUN
ejpam-6128	471	2	-	-	PUNCT
ejpam-6128	471	3	c3	c3	NOUN
ejpam-6128	471	4	:	:	PUNCT
ejpam-6128	471	5	in	in	ADP
ejpam-6128	471	6	(	(	PUNCT
ejpam-6128	471	7	102	102	NUM
ejpam-6128	471	8	)	)	PUNCT
ejpam-6128	471	9	,	,	PUNCT
ejpam-6128	471	10	set	set	VERB
ejpam-6128	471	11	c2	c2	PROPN
ejpam-6128	471	12	=	=	SYM
ejpam-6128	471	13	c4	c4	NOUN
ejpam-6128	471	14	=	=	SYM
ejpam-6128	471	15	1	1	NUM
ejpam-6128	471	16	and	and	CCONJ
ejpam-6128	471	17	other	other	ADJ
ejpam-6128	471	18	constants	constant	NOUN
ejpam-6128	471	19	zero	zero	NUM
ejpam-6128	471	20	.	.	PUNCT
ejpam-6128	472	1	then	then	ADV
ejpam-6128	472	2	we	we	PRON
ejpam-6128	472	3	obtain	obtain	VERB
ejpam-6128	472	4	the	the	DET
ejpam-6128	472	5	symmetry	symmetry	NOUN
ejpam-6128	472	6	invariants	invariant	NOUN
ejpam-6128	472	7	r	r	NOUN
ejpam-6128	472	8	=	=	PUNCT
ejpam-6128	472	9	q	q	NOUN
ejpam-6128	472	10	−	−	PROPN
ejpam-6128	472	11	p	p	X
ejpam-6128	472	12	,	,	PUNCT
ejpam-6128	472	13	h(p	h(p	PROPN
ejpam-6128	472	14	,	,	PUNCT
ejpam-6128	472	15	q	q	NOUN
ejpam-6128	472	16	)	)	PUNCT
ejpam-6128	472	17	=	=	SYM
ejpam-6128	472	18	µ(r	µ(r	NOUN
ejpam-6128	472	19	)	)	PUNCT
ejpam-6128	472	20	.	.	PUNCT
ejpam-6128	473	1	(	(	PUNCT
ejpam-6128	473	2	113	113	NUM
ejpam-6128	473	3	)	)	PUNCT
ejpam-6128	473	4	the	the	DET
ejpam-6128	473	5	substitution	substitution	NOUN
ejpam-6128	473	6	of	of	ADP
ejpam-6128	473	7	(	(	PUNCT
ejpam-6128	473	8	113	113	NUM
ejpam-6128	473	9	)	)	PUNCT
ejpam-6128	473	10	in	in	ADP
ejpam-6128	473	11	(	(	PUNCT
ejpam-6128	473	12	101	101	NUM
ejpam-6128	473	13	)	)	PUNCT
ejpam-6128	473	14	yields	yield	VERB
ejpam-6128	473	15	the	the	DET
ejpam-6128	473	16	following	follow	VERB
ejpam-6128	473	17	ode	ode	PROPN
ejpam-6128	473	18	(	(	PUNCT
ejpam-6128	473	19	−a2βµ−	−a2βµ−	X
ejpam-6128	473	20	α+	α+	X
ejpam-6128	473	21	1)µ′′	1)µ′′	NUM
ejpam-6128	473	22	−	−	NOUN
ejpam-6128	474	1	a2βµ′2	a2βµ′2	ADP
ejpam-6128	475	1	=	=	NOUN
ejpam-6128	476	1	0	0	PROPN
ejpam-6128	476	2	.	.	PUNCT
ejpam-6128	477	1	(	(	PUNCT
ejpam-6128	477	2	114	114	NUM
ejpam-6128	477	3	)	)	PUNCT
ejpam-6128	477	4	the	the	DET
ejpam-6128	477	5	solution	solution	NOUN
ejpam-6128	477	6	of	of	ADP
ejpam-6128	477	7	(	(	PUNCT
ejpam-6128	477	8	114	114	NUM
ejpam-6128	477	9	)	)	PUNCT
ejpam-6128	477	10	takes	take	VERB
ejpam-6128	477	11	the	the	DET
ejpam-6128	477	12	form	form	NOUN
ejpam-6128	477	13	µ(r	µ(r	NOUN
ejpam-6128	477	14	)	)	PUNCT
ejpam-6128	478	1	=	=	PUNCT
ejpam-6128	479	1	−α+	−α+	NOUN
ejpam-6128	480	1	1−	1−	NUM
ejpam-6128	480	2	√	√	NUM
ejpam-6128	481	1	2(c1r	2(c1r	NOUN
ejpam-6128	481	2	+	+	PUNCT
ejpam-6128	482	1	c2)a2β	c2)a2β	CCONJ
ejpam-6128	483	1	+	+	CCONJ
ejpam-6128	483	2	(	(	PUNCT
ejpam-6128	483	3	α−	α−	ADP
ejpam-6128	483	4	1)2	1)2	NUM
ejpam-6128	483	5	a2β	a2β	PUNCT
ejpam-6128	483	6	,	,	PUNCT
ejpam-6128	483	7	(	(	PUNCT
ejpam-6128	483	8	115	115	NUM
ejpam-6128	483	9	)	)	PUNCT
ejpam-6128	483	10	which	which	PRON
ejpam-6128	483	11	implies	imply	VERB
ejpam-6128	483	12	h(p	h(p	NOUN
ejpam-6128	483	13	,	,	PUNCT
ejpam-6128	483	14	q	q	X
ejpam-6128	483	15	)	)	PUNCT
ejpam-6128	483	16	=	=	VERB
ejpam-6128	484	1	−α+	−α+	NOUN
ejpam-6128	484	2	1−	1−	NUM
ejpam-6128	485	1	√	√	NUM
ejpam-6128	485	2	2(c1(q	2(c1(q	NUM
ejpam-6128	485	3	−	−	PROPN
ejpam-6128	486	1	p	p	X
ejpam-6128	486	2	)	)	PUNCT
ejpam-6128	486	3	+	+	PUNCT
ejpam-6128	486	4	c2)a2β	c2)a2β	X
ejpam-6128	487	1	+	+	CCONJ
ejpam-6128	487	2	(	(	PUNCT
ejpam-6128	487	3	α−	α−	ADP
ejpam-6128	487	4	1)2	1)2	NUM
ejpam-6128	487	5	a2β	a2β	PUNCT
ejpam-6128	487	6	.	.	PUNCT
ejpam-6128	488	1	(	(	PUNCT
ejpam-6128	488	2	116	116	NUM
ejpam-6128	488	3	)	)	PUNCT
ejpam-6128	488	4	hence	hence	ADV
ejpam-6128	488	5	,	,	PUNCT
ejpam-6128	488	6	the	the	DET
ejpam-6128	488	7	solution	solution	NOUN
ejpam-6128	488	8	of	of	ADP
ejpam-6128	488	9	(	(	PUNCT
ejpam-6128	488	10	2	2	NUM
ejpam-6128	488	11	)	)	PUNCT
ejpam-6128	488	12	is	be	AUX
ejpam-6128	488	13	w(x	w(x	PROPN
ejpam-6128	488	14	,	,	PUNCT
ejpam-6128	488	15	y	y	PROPN
ejpam-6128	488	16	,	,	PUNCT
ejpam-6128	488	17	t	t	PROPN
ejpam-6128	488	18	)	)	PUNCT
ejpam-6128	488	19	=	=	PUNCT
ejpam-6128	489	1	−α+	−α+	NOUN
ejpam-6128	490	1	1−	1−	NUM
ejpam-6128	490	2	√	√	INTJ
ejpam-6128	491	1	2(c1(t−	2(c1(t−	NUM
ejpam-6128	491	2	ay	ay	NOUN
ejpam-6128	491	3	−	−	NOUN
ejpam-6128	492	1	x	x	NOUN
ejpam-6128	492	2	)	)	PUNCT
ejpam-6128	493	1	+	+	CCONJ
ejpam-6128	493	2	c2)a2β	c2)a2β	X
ejpam-6128	494	1	+	+	CCONJ
ejpam-6128	494	2	(	(	PUNCT
ejpam-6128	494	3	α−	α−	ADP
ejpam-6128	494	4	1)2	1)2	NUM
ejpam-6128	494	5	a2β	a2β	PUNCT
ejpam-6128	494	6	,	,	PUNCT
ejpam-6128	494	7	(	(	PUNCT
ejpam-6128	494	8	117	117	NUM
ejpam-6128	494	9	)	)	PUNCT
ejpam-6128	494	10	where	where	SCONJ
ejpam-6128	494	11	c1	c1	PROPN
ejpam-6128	494	12	and	and	CCONJ
ejpam-6128	494	13	c2	c2	PROPN
ejpam-6128	494	14	are	be	AUX
ejpam-6128	494	15	constants	constant	NOUN
ejpam-6128	494	16	of	of	ADP
ejpam-6128	494	17	integration	integration	NOUN
ejpam-6128	494	18	.	.	PUNCT
ejpam-6128	495	1	m.	m.	PROPN
ejpam-6128	495	2	usman	usman	PROPN
ejpam-6128	495	3	,	,	PUNCT
ejpam-6128	495	4	a.	a.	NOUN
ejpam-6128	495	5	hussain	hussain	PROPN
ejpam-6128	495	6	,	,	PUNCT
ejpam-6128	495	7	m.	m.	PROPN
ejpam-6128	495	8	u.	u.	PROPN
ejpam-6128	495	9	farooq	farooq	PROPN
ejpam-6128	495	10	,	,	PUNCT
ejpam-6128	495	11	j.	j.	PROPN
ejpam-6128	495	12	herrera	herrera	PROPN
ejpam-6128	495	13	/	/	SYM
ejpam-6128	495	14	eur	eur	PROPN
ejpam-6128	495	15	.	.	PUNCT
ejpam-6128	496	1	j.	j.	PROPN
ejpam-6128	496	2	pure	pure	PROPN
ejpam-6128	496	3	appl	appl	PROPN
ejpam-6128	496	4	.	.	PROPN
ejpam-6128	496	5	math	math	PROPN
ejpam-6128	496	6	,	,	PUNCT
ejpam-6128	496	7	18	18	NUM
ejpam-6128	496	8	(	(	PUNCT
ejpam-6128	496	9	4	4	NUM
ejpam-6128	496	10	)	)	PUNCT
ejpam-6128	496	11	(	(	PUNCT
ejpam-6128	496	12	2025	2025	NUM
ejpam-6128	496	13	)	)	PUNCT
ejpam-6128	496	14	,	,	PUNCT
ejpam-6128	496	15	6128	6128	NUM
ejpam-6128	496	16	23	23	NUM
ejpam-6128	496	17	of	of	ADP
ejpam-6128	496	18	29	29	NUM
ejpam-6128	496	19	4	4	NUM
ejpam-6128	496	20	.	.	PUNCT
ejpam-6128	497	1	conservation	conservation	NOUN
ejpam-6128	497	2	laws	law	NOUN
ejpam-6128	497	3	this	this	DET
ejpam-6128	497	4	section	section	NOUN
ejpam-6128	497	5	demonstrates	demonstrate	VERB
ejpam-6128	497	6	how	how	SCONJ
ejpam-6128	497	7	to	to	PART
ejpam-6128	497	8	use	use	VERB
ejpam-6128	497	9	the	the	DET
ejpam-6128	497	10	multiplier	multipli	ADJ
ejpam-6128	497	11	approach	approach	NOUN
ejpam-6128	497	12	[	[	X
ejpam-6128	497	13	12	12	NUM
ejpam-6128	497	14	]	]	PUNCT
ejpam-6128	497	15	to	to	PART
ejpam-6128	497	16	compute	compute	VERB
ejpam-6128	497	17	conservation	conservation	NOUN
ejpam-6128	497	18	laws	law	NOUN
ejpam-6128	497	19	for	for	ADP
ejpam-6128	497	20	(	(	PUNCT
ejpam-6128	497	21	2	2	NUM
ejpam-6128	497	22	)	)	PUNCT
ejpam-6128	497	23	.	.	PUNCT
ejpam-6128	498	1	the	the	DET
ejpam-6128	498	2	multipliers	multiplier	NOUN
ejpam-6128	498	3	q(x	q(x	PROPN
ejpam-6128	498	4	,	,	PUNCT
ejpam-6128	498	5	y	y	PROPN
ejpam-6128	498	6	,	,	PUNCT
ejpam-6128	498	7	t	t	PROPN
ejpam-6128	498	8	,	,	PUNCT
ejpam-6128	498	9	w	w	NOUN
ejpam-6128	498	10	)	)	PUNCT
ejpam-6128	498	11	for	for	ADP
ejpam-6128	498	12	(	(	PUNCT
ejpam-6128	498	13	2	2	X
ejpam-6128	498	14	)	)	PUNCT
ejpam-6128	498	15	can	can	AUX
ejpam-6128	498	16	be	be	AUX
ejpam-6128	498	17	computed	compute	VERB
ejpam-6128	498	18	by	by	ADP
ejpam-6128	498	19	solving	solve	VERB
ejpam-6128	498	20	the	the	DET
ejpam-6128	498	21	equation	equation	NOUN
ejpam-6128	498	22	given	give	VERB
ejpam-6128	498	23	by	by	ADP
ejpam-6128	498	24	[	[	PUNCT
ejpam-6128	498	25	25	25	NUM
ejpam-6128	498	26	]	]	X
ejpam-6128	498	27	δ	δ	NOUN
ejpam-6128	498	28	δw	δw	NOUN
ejpam-6128	498	29	(	(	PUNCT
ejpam-6128	498	30	q	q	PROPN
ejpam-6128	498	31	(	(	PUNCT
ejpam-6128	498	32	wtt	wtt	PROPN
ejpam-6128	498	33	−	−	PROPN
ejpam-6128	498	34	(	(	PUNCT
ejpam-6128	498	35	f(w)wx)x	f(w)wx)x	ADJ
ejpam-6128	498	36	−	−	PROPN
ejpam-6128	498	37	(	(	PUNCT
ejpam-6128	498	38	g(w)wy)y	g(w)wy)y	NUM
ejpam-6128	498	39	)	)	PUNCT
ejpam-6128	498	40	)	)	PUNCT
ejpam-6128	499	1	=	=	PUNCT
ejpam-6128	499	2	0	0	X
ejpam-6128	499	3	.	.	PUNCT
ejpam-6128	499	4	(	(	PUNCT
ejpam-6128	499	5	118	118	NUM
ejpam-6128	499	6	)	)	PUNCT
ejpam-6128	499	7	equation	equation	NOUN
ejpam-6128	499	8	(	(	PUNCT
ejpam-6128	499	9	118	118	NUM
ejpam-6128	499	10	)	)	PUNCT
ejpam-6128	499	11	yields	yield	VERB
ejpam-6128	499	12	the	the	DET
ejpam-6128	499	13	following	follow	VERB
ejpam-6128	499	14	multiplier	multipli	ADJ
ejpam-6128	499	15	functions	function	NOUN
ejpam-6128	499	16	q1	q1	PROPN
ejpam-6128	499	17	=	=	SYM
ejpam-6128	499	18	xyt	xyt	PROPN
ejpam-6128	499	19	,	,	PUNCT
ejpam-6128	499	20	q2	q2	PROPN
ejpam-6128	499	21	=	=	SYM
ejpam-6128	499	22	xt	xt	PROPN
ejpam-6128	499	23	,	,	PUNCT
ejpam-6128	499	24	q3	q3	PROPN
ejpam-6128	499	25	=	=	SYM
ejpam-6128	499	26	xy	xy	PROPN
ejpam-6128	499	27	,	,	PUNCT
ejpam-6128	499	28	q4	q4	PROPN
ejpam-6128	499	29	=	=	SYM
ejpam-6128	499	30	x	x	PROPN
ejpam-6128	499	31	,	,	PUNCT
ejpam-6128	499	32	q5	q5	PROPN
ejpam-6128	499	33	=	=	SYM
ejpam-6128	499	34	yt	yt	PROPN
ejpam-6128	499	35	,	,	PUNCT
ejpam-6128	499	36	q6	q6	PROPN
ejpam-6128	499	37	=	=	SYM
ejpam-6128	499	38	t	t	PROPN
ejpam-6128	499	39	,	,	PUNCT
ejpam-6128	499	40	q7	q7	PROPN
ejpam-6128	499	41	=	=	SYM
ejpam-6128	499	42	y	y	PROPN
ejpam-6128	499	43	,	,	PUNCT
ejpam-6128	499	44	q8	q8	PROPN
ejpam-6128	499	45	=	=	NOUN
ejpam-6128	499	46	1	1	X
ejpam-6128	499	47	.	.	PUNCT
ejpam-6128	500	1	(	(	PUNCT
ejpam-6128	500	2	119	119	NUM
ejpam-6128	500	3	)	)	PUNCT
ejpam-6128	500	4	the	the	DET
ejpam-6128	500	5	conserved	conserve	VERB
ejpam-6128	500	6	vectors	vector	NOUN
ejpam-6128	500	7	for	for	ADP
ejpam-6128	500	8	(	(	PUNCT
ejpam-6128	500	9	2	2	X
ejpam-6128	500	10	)	)	PUNCT
ejpam-6128	500	11	can	can	AUX
ejpam-6128	500	12	be	be	AUX
ejpam-6128	500	13	derived	derive	VERB
ejpam-6128	500	14	by	by	ADP
ejpam-6128	500	15	substituting	substitute	VERB
ejpam-6128	500	16	the	the	DET
ejpam-6128	500	17	multipliers	multiplier	NOUN
ejpam-6128	500	18	(	(	PUNCT
ejpam-6128	500	19	119	119	NUM
ejpam-6128	500	20	)	)	PUNCT
ejpam-6128	500	21	in	in	ADP
ejpam-6128	500	22	the	the	DET
ejpam-6128	500	23	following	follow	VERB
ejpam-6128	500	24	relation	relation	NOUN
ejpam-6128	500	25	[	[	X
ejpam-6128	500	26	25	25	NUM
ejpam-6128	500	27	]	]	PUNCT
ejpam-6128	500	28	q(wtt	q(wtt	PROPN
ejpam-6128	500	29	−	−	PROPN
ejpam-6128	501	1	(	(	PUNCT
ejpam-6128	501	2	f(w)wx)x	f(w)wx)x	INTJ
ejpam-6128	501	3	−	−	PROPN
ejpam-6128	501	4	(	(	PUNCT
ejpam-6128	501	5	g(w)wy)y	g(w)wy)y	NUM
ejpam-6128	501	6	)	)	PUNCT
ejpam-6128	501	7	=	=	PUNCT
ejpam-6128	502	1	dtγ	dtγ	PROPN
ejpam-6128	502	2	t	t	NOUN
ejpam-6128	503	1	+	+	CCONJ
ejpam-6128	503	2	dxγ	dxγ	NOUN
ejpam-6128	503	3	x	x	PUNCT
ejpam-6128	504	1	+	+	NOUN
ejpam-6128	504	2	dyγ	dyγ	NOUN
ejpam-6128	504	3	y	y	NOUN
ejpam-6128	504	4	,	,	PUNCT
ejpam-6128	504	5	(	(	PUNCT
ejpam-6128	504	6	120	120	NUM
ejpam-6128	504	7	)	)	PUNCT
ejpam-6128	504	8	and	and	CCONJ
ejpam-6128	504	9	are	be	AUX
ejpam-6128	504	10	formulated	formulate	VERB
ejpam-6128	504	11	as	as	SCONJ
ejpam-6128	504	12	follows	follow	VERB
ejpam-6128	504	13	γ1	γ1	PROPN
ejpam-6128	504	14	=	=	SYM
ejpam-6128	504	15			PROPN
ejpam-6128	504	16	γ1	γ1	PROPN
ejpam-6128	504	17	t	t	NOUN
ejpam-6128	504	18	=	=	PUNCT
ejpam-6128	504	19	xy(twt	xy(twt	PROPN
ejpam-6128	504	20	−	−	PROPN
ejpam-6128	504	21	w	w	NOUN
ejpam-6128	504	22	)	)	PUNCT
ejpam-6128	504	23	,	,	PUNCT
ejpam-6128	504	24	γ1	γ1	NOUN
ejpam-6128	504	25	x	x	PUNCT
ejpam-6128	504	26	=	=	SYM
ejpam-6128	504	27	t	t	PROPN
ejpam-6128	504	28	2(x	2(x	NUM
ejpam-6128	504	29	2g(w)wy	2g(w)wy	ADJ
ejpam-6128	504	30	−	−	PROPN
ejpam-6128	504	31	2xyf(w)wx	2xyf(w)wx	NUM
ejpam-6128	504	32	+	+	NUM
ejpam-6128	504	33	2y	2y	PROPN
ejpam-6128	504	34	∫	∫	PROPN
ejpam-6128	504	35	fdw	fdw	NOUN
ejpam-6128	504	36	)	)	PUNCT
ejpam-6128	504	37	,	,	PUNCT
ejpam-6128	504	38	γ1	γ1	NOUN
ejpam-6128	504	39	y	y	PROPN
ejpam-6128	504	40	=	=	SYM
ejpam-6128	504	41	−xt	−xt	PROPN
ejpam-6128	504	42	2	2	NUM
ejpam-6128	504	43	g(w)(xwx	g(w)(xwx	NOUN
ejpam-6128	504	44	+	+	CCONJ
ejpam-6128	504	45	2ywy	2ywy	NUM
ejpam-6128	504	46	)	)	PUNCT
ejpam-6128	504	47	.	.	PUNCT
ejpam-6128	505	1	(	(	PUNCT
ejpam-6128	505	2	121	121	NUM
ejpam-6128	505	3	)	)	PUNCT
ejpam-6128	505	4	γ2	γ2	NOUN
ejpam-6128	505	5	=	=	PUNCT
ejpam-6128	505	6			PUNCT
ejpam-6128	505	7	γ2	γ2	NOUN
ejpam-6128	505	8	t	t	PROPN
ejpam-6128	505	9	=	=	PUNCT
ejpam-6128	506	1	x(twt	x(twt	PUNCT
ejpam-6128	506	2	−	−	PROPN
ejpam-6128	506	3	w	w	NOUN
ejpam-6128	506	4	)	)	PUNCT
ejpam-6128	506	5	,	,	PUNCT
ejpam-6128	506	6	γ2	γ2	PROPN
ejpam-6128	506	7	x	x	PUNCT
ejpam-6128	506	8	=	=	PRON
ejpam-6128	507	1	t(−xf(w)wx	t(−xf(w)wx	ADJ
ejpam-6128	507	2	+	+	CCONJ
ejpam-6128	507	3	∫	∫	PROPN
ejpam-6128	507	4	fdw	fdw	NOUN
ejpam-6128	507	5	)	)	PUNCT
ejpam-6128	507	6	,	,	PUNCT
ejpam-6128	507	7	γ2	γ2	PROPN
ejpam-6128	507	8	y	y	PROPN
ejpam-6128	507	9	=	=	PUNCT
ejpam-6128	508	1	−xtg(w)wy	−xtg(w)wy	PROPN
ejpam-6128	508	2	.	.	PUNCT
ejpam-6128	509	1	(	(	PUNCT
ejpam-6128	509	2	122	122	NUM
ejpam-6128	509	3	)	)	PUNCT
ejpam-6128	509	4	γ3	γ3	NOUN
ejpam-6128	509	5	=	=	PUNCT
ejpam-6128	509	6			PUNCT
ejpam-6128	509	7	γ3	γ3	NOUN
ejpam-6128	509	8	t	t	NOUN
ejpam-6128	509	9	=	=	SYM
ejpam-6128	509	10	xywt	xywt	NOUN
ejpam-6128	509	11	,	,	PUNCT
ejpam-6128	509	12	γ3	γ3	NOUN
ejpam-6128	509	13	x	x	PUNCT
ejpam-6128	509	14	=	=	PUNCT
ejpam-6128	510	1	y	y	PROPN
ejpam-6128	510	2	∫	∫	PROPN
ejpam-6128	510	3	fdw	fdw	NOUN
ejpam-6128	510	4	−	−	PROPN
ejpam-6128	510	5	xyf(w)wx	xyf(w)wx	PUNCT
ejpam-6128	511	1	+	+	CCONJ
ejpam-6128	511	2	x2	x2	PROPN
ejpam-6128	511	3	2	2	NUM
ejpam-6128	511	4	g(w)wy	g(w)wy	NOUN
ejpam-6128	511	5	,	,	PUNCT
ejpam-6128	511	6	γ3	γ3	NOUN
ejpam-6128	511	7	y	y	NOUN
ejpam-6128	511	8	=	=	PUNCT
ejpam-6128	512	1	−x	−x	PRON
ejpam-6128	512	2	2g(w)(xwx	2g(w)(xwx	NOUN
ejpam-6128	512	3	+	+	CCONJ
ejpam-6128	512	4	2ywy	2ywy	NUM
ejpam-6128	512	5	)	)	PUNCT
ejpam-6128	512	6	.	.	PUNCT
ejpam-6128	513	1	(	(	PUNCT
ejpam-6128	513	2	123	123	NUM
ejpam-6128	513	3	)	)	PUNCT
ejpam-6128	513	4	γ4	γ4	NOUN
ejpam-6128	513	5	=	=	PUNCT
ejpam-6128	513	6			PUNCT
ejpam-6128	513	7	γ4	γ4	NOUN
ejpam-6128	513	8	t	t	NOUN
ejpam-6128	513	9	=	=	SYM
ejpam-6128	513	10	xwt	xwt	ADJ
ejpam-6128	513	11	,	,	PUNCT
ejpam-6128	513	12	γ4	γ4	NOUN
ejpam-6128	513	13	x	x	SYM
ejpam-6128	513	14	=	=	PUNCT
ejpam-6128	514	1	−xf(w)wx	−xf(w)wx	PROPN
ejpam-6128	515	1	+	+	NUM
ejpam-6128	515	2	∫	∫	PROPN
ejpam-6128	515	3	fdw	fdw	PROPN
ejpam-6128	515	4	,	,	PUNCT
ejpam-6128	516	1	γ4	γ4	NOUN
ejpam-6128	516	2	y	y	NOUN
ejpam-6128	516	3	=	=	PUNCT
ejpam-6128	516	4	−xg(w)wy	−xg(w)wy	PROPN
ejpam-6128	516	5	.	.	PUNCT
ejpam-6128	517	1	(	(	PUNCT
ejpam-6128	517	2	124	124	NUM
ejpam-6128	517	3	)	)	PUNCT
ejpam-6128	517	4	γ5	γ5	NOUN
ejpam-6128	517	5	=	=	PUNCT
ejpam-6128	517	6			PUNCT
ejpam-6128	517	7	γ5	γ5	NOUN
ejpam-6128	517	8	t	t	NOUN
ejpam-6128	517	9	=	=	PUNCT
ejpam-6128	517	10	y(twt	y(twt	NOUN
ejpam-6128	517	11	−	−	PROPN
ejpam-6128	517	12	w	w	NOUN
ejpam-6128	517	13	)	)	PUNCT
ejpam-6128	517	14	,	,	PUNCT
ejpam-6128	517	15	γ5	γ5	NOUN
ejpam-6128	517	16	x	x	X
ejpam-6128	518	1	=	=	PUNCT
ejpam-6128	519	1	t(xg(w)wy	t(xg(w)wy	DET
ejpam-6128	519	2	−	−	NOUN
ejpam-6128	519	3	yf(w)wx	yf(w)wx	ADJ
ejpam-6128	519	4	)	)	PUNCT
ejpam-6128	520	1	,	,	PUNCT
ejpam-6128	520	2	γ5	γ5	VERB
ejpam-6128	520	3	y	y	NOUN
ejpam-6128	520	4	=	=	PUNCT
ejpam-6128	521	1	−t(xwx	−t(xwx	PROPN
ejpam-6128	521	2	+	+	NUM
ejpam-6128	521	3	ywy)g(w	ywy)g(w	PROPN
ejpam-6128	521	4	)	)	PUNCT
ejpam-6128	521	5	.	.	PUNCT
ejpam-6128	522	1	(	(	PUNCT
ejpam-6128	522	2	125	125	NUM
ejpam-6128	522	3	)	)	PUNCT
ejpam-6128	522	4	γ6	γ6	NOUN
ejpam-6128	522	5	=	=	PUNCT
ejpam-6128	522	6			PROPN
ejpam-6128	522	7	γ6	γ6	PROPN
ejpam-6128	522	8	t	t	PROPN
ejpam-6128	522	9	=	=	PUNCT
ejpam-6128	522	10	twt	twt	NOUN
ejpam-6128	522	11	−	−	PROPN
ejpam-6128	522	12	w	w	PROPN
ejpam-6128	522	13	,	,	PUNCT
ejpam-6128	522	14	γ6	γ6	NOUN
ejpam-6128	522	15	x	x	PUNCT
ejpam-6128	522	16	=	=	SYM
ejpam-6128	522	17	−tf(w)wx	−tf(w)wx	PROPN
ejpam-6128	522	18	,	,	PUNCT
ejpam-6128	522	19	γ6	γ6	PROPN
ejpam-6128	522	20	y	y	PROPN
ejpam-6128	522	21	=	=	PUNCT
ejpam-6128	522	22	−tg(w)wy	−tg(w)wy	PROPN
ejpam-6128	522	23	.	.	PUNCT
ejpam-6128	523	1	(	(	PUNCT
ejpam-6128	523	2	126	126	X
ejpam-6128	523	3	)	)	PUNCT
ejpam-6128	523	4	γ7	γ7	NOUN
ejpam-6128	523	5	=	=	SYM
ejpam-6128	523	6			PROPN
ejpam-6128	523	7	γ7	γ7	PROPN
ejpam-6128	523	8	t	t	NOUN
ejpam-6128	523	9	=	=	SYM
ejpam-6128	523	10	ywt	ywt	NOUN
ejpam-6128	523	11	,	,	PUNCT
ejpam-6128	523	12	γ7	γ7	INTJ
ejpam-6128	523	13	x	x	X
ejpam-6128	523	14	=	=	SYM
ejpam-6128	523	15	xg(w)wy	xg(w)wy	PROPN
ejpam-6128	524	1	−	−	PROPN
ejpam-6128	524	2	yf(w)wx	yf(w)wx	ADJ
ejpam-6128	524	3	,	,	PUNCT
ejpam-6128	524	4	γ7	γ7	VERB
ejpam-6128	524	5	y	y	PROPN
ejpam-6128	524	6	=	=	PUNCT
ejpam-6128	524	7	−g(w)(xwx	−g(w)(xwx	PROPN
ejpam-6128	525	1	+	+	NUM
ejpam-6128	525	2	ywy	ywy	NOUN
ejpam-6128	525	3	)	)	PUNCT
ejpam-6128	525	4	.	.	PUNCT
ejpam-6128	526	1	(	(	PUNCT
ejpam-6128	526	2	127	127	NUM
ejpam-6128	526	3	)	)	PUNCT
ejpam-6128	526	4	m.	m.	NOUN
ejpam-6128	526	5	usman	usman	PROPN
ejpam-6128	526	6	,	,	PUNCT
ejpam-6128	526	7	a.	a.	NOUN
ejpam-6128	526	8	hussain	hussain	PROPN
ejpam-6128	526	9	,	,	PUNCT
ejpam-6128	526	10	m.	m.	PROPN
ejpam-6128	526	11	u.	u.	PROPN
ejpam-6128	526	12	farooq	farooq	PROPN
ejpam-6128	526	13	,	,	PUNCT
ejpam-6128	526	14	j.	j.	PROPN
ejpam-6128	526	15	herrera	herrera	PROPN
ejpam-6128	526	16	/	/	SYM
ejpam-6128	526	17	eur	eur	PROPN
ejpam-6128	526	18	.	.	PUNCT
ejpam-6128	527	1	j.	j.	PROPN
ejpam-6128	527	2	pure	pure	PROPN
ejpam-6128	527	3	appl	appl	PROPN
ejpam-6128	527	4	.	.	PROPN
ejpam-6128	527	5	math	math	PROPN
ejpam-6128	527	6	,	,	PUNCT
ejpam-6128	527	7	18	18	NUM
ejpam-6128	527	8	(	(	PUNCT
ejpam-6128	527	9	4	4	NUM
ejpam-6128	527	10	)	)	PUNCT
ejpam-6128	527	11	(	(	PUNCT
ejpam-6128	527	12	2025	2025	NUM
ejpam-6128	527	13	)	)	PUNCT
ejpam-6128	527	14	,	,	PUNCT
ejpam-6128	527	15	6128	6128	NUM
ejpam-6128	527	16	24	24	NUM
ejpam-6128	527	17	of	of	ADP
ejpam-6128	527	18	29	29	NUM
ejpam-6128	527	19	γ8	γ8	NOUN
ejpam-6128	527	20	=	=	PUNCT
ejpam-6128	527	21			PUNCT
ejpam-6128	527	22	γ8	γ8	PROPN
ejpam-6128	527	23	t	t	NOUN
ejpam-6128	527	24	=	=	SYM
ejpam-6128	527	25	wt	wt	PROPN
ejpam-6128	527	26	,	,	PUNCT
ejpam-6128	527	27	γ8	γ8	NOUN
ejpam-6128	527	28	x	x	NOUN
ejpam-6128	527	29	=	=	SYM
ejpam-6128	527	30	−f(w)wx	−f(w)wx	PROPN
ejpam-6128	527	31	,	,	PUNCT
ejpam-6128	528	1	γ8	γ8	NOUN
ejpam-6128	528	2	y	y	PROPN
ejpam-6128	528	3	=	=	SYM
ejpam-6128	528	4	−g(w)wy	−g(w)wy	PROPN
ejpam-6128	528	5	.	.	PUNCT
ejpam-6128	529	1	(	(	PUNCT
ejpam-6128	529	2	128	128	NUM
ejpam-6128	529	3	)	)	PUNCT
ejpam-6128	529	4	the	the	DET
ejpam-6128	529	5	conserved	conserved	ADJ
ejpam-6128	529	6	vectors	vector	NOUN
ejpam-6128	529	7	γ2,γ4,γ6,γ8	γ2,γ4,γ6,γ8	VERB
ejpam-6128	529	8	are	be	AUX
ejpam-6128	529	9	same	same	ADJ
ejpam-6128	529	10	,	,	PUNCT
ejpam-6128	529	11	which	which	PRON
ejpam-6128	529	12	are	be	AUX
ejpam-6128	529	13	derived	derive	VERB
ejpam-6128	529	14	in	in	ADP
ejpam-6128	529	15	[	[	X
ejpam-6128	529	16	23	23	NUM
ejpam-6128	529	17	]	]	PUNCT
ejpam-6128	529	18	by	by	ADP
ejpam-6128	529	19	using	use	VERB
ejpam-6128	529	20	a	a	DET
ejpam-6128	529	21	partial	partial	ADJ
ejpam-6128	529	22	lagrangian	lagrangian	NOUN
ejpam-6128	529	23	.	.	PUNCT
ejpam-6128	530	1	5	5	NUM
ejpam-6128	530	2	.	.	NOUN
ejpam-6128	530	3	exact	exact	ADJ
ejpam-6128	530	4	solutions	solution	NOUN
ejpam-6128	530	5	via	via	ADP
ejpam-6128	530	6	conservation	conservation	NOUN
ejpam-6128	530	7	laws	law	NOUN
ejpam-6128	530	8	this	this	DET
ejpam-6128	530	9	section	section	NOUN
ejpam-6128	530	10	deals	deal	VERB
ejpam-6128	530	11	with	with	ADP
ejpam-6128	530	12	the	the	DET
ejpam-6128	530	13	obtention	obtention	NOUN
ejpam-6128	530	14	of	of	ADP
ejpam-6128	530	15	exact	exact	ADJ
ejpam-6128	530	16	solutions	solution	NOUN
ejpam-6128	530	17	for	for	ADP
ejpam-6128	530	18	(	(	PUNCT
ejpam-6128	530	19	2	2	NUM
ejpam-6128	530	20	)	)	PUNCT
ejpam-6128	530	21	by	by	ADP
ejpam-6128	530	22	using	use	VERB
ejpam-6128	530	23	its	its	PRON
ejpam-6128	530	24	conserved	conserved	ADJ
ejpam-6128	530	25	vectors	vector	NOUN
ejpam-6128	530	26	.	.	PUNCT
ejpam-6128	531	1	by	by	ADP
ejpam-6128	531	2	using	use	VERB
ejpam-6128	531	3	the	the	DET
ejpam-6128	531	4	technique	technique	NOUN
ejpam-6128	531	5	explained	explain	VERB
ejpam-6128	531	6	in	in	ADP
ejpam-6128	531	7	[	[	X
ejpam-6128	531	8	26	26	NUM
ejpam-6128	531	9	,	,	PUNCT
ejpam-6128	531	10	27	27	NUM
ejpam-6128	531	11	]	]	PUNCT
ejpam-6128	531	12	,	,	PUNCT
ejpam-6128	531	13	the	the	DET
ejpam-6128	531	14	conserved	conserved	ADJ
ejpam-6128	531	15	vector	vector	NOUN
ejpam-6128	531	16	(	(	PUNCT
ejpam-6128	531	17	γt	γt	NOUN
ejpam-6128	531	18	,	,	PUNCT
ejpam-6128	531	19	γx	γx	NOUN
ejpam-6128	531	20	,	,	PUNCT
ejpam-6128	531	21	γy	γy	NOUN
ejpam-6128	531	22	)	)	PUNCT
ejpam-6128	531	23	of	of	ADP
ejpam-6128	531	24	(	(	PUNCT
ejpam-6128	531	25	2	2	X
ejpam-6128	531	26	)	)	PUNCT
ejpam-6128	531	27	satisfies	satisfy	VERB
ejpam-6128	531	28	the	the	DET
ejpam-6128	531	29	condition	condition	NOUN
ejpam-6128	531	30	stated	state	VERB
ejpam-6128	531	31	as	as	ADP
ejpam-6128	531	32	dtγ	dtγ	PROPN
ejpam-6128	531	33	t	t	NOUN
ejpam-6128	531	34	=	=	SYM
ejpam-6128	531	35	0	0	NUM
ejpam-6128	531	36	,	,	PUNCT
ejpam-6128	531	37	dxγ	dxγ	NOUN
ejpam-6128	531	38	x	x	PUNCT
ejpam-6128	532	1	=	=	SYM
ejpam-6128	532	2	0	0	NUM
ejpam-6128	532	3	,	,	PUNCT
ejpam-6128	532	4	dyγ	dyγ	NOUN
ejpam-6128	532	5	y	y	NOUN
ejpam-6128	533	1	=	=	SYM
ejpam-6128	533	2	0	0	PROPN
ejpam-6128	533	3	.	.	PUNCT
ejpam-6128	534	1	(	(	PUNCT
ejpam-6128	534	2	129	129	NUM
ejpam-6128	534	3	)	)	PUNCT
ejpam-6128	534	4	for	for	ADP
ejpam-6128	534	5	f(w	f(w	NOUN
ejpam-6128	534	6	)	)	PUNCT
ejpam-6128	534	7	=	=	SYM
ejpam-6128	534	8	αw	αw	NOUN
ejpam-6128	534	9	,	,	PUNCT
ejpam-6128	534	10	g(w	g(w	ADJ
ejpam-6128	534	11	)	)	PUNCT
ejpam-6128	534	12	=	=	SYM
ejpam-6128	535	1	βw2	βw2	NOUN
ejpam-6128	535	2	,	,	PUNCT
ejpam-6128	535	3	the	the	DET
ejpam-6128	535	4	conserved	conserved	ADJ
ejpam-6128	535	5	vector	vector	NOUN
ejpam-6128	535	6	(	(	PUNCT
ejpam-6128	535	7	122	122	NUM
ejpam-6128	535	8	)	)	PUNCT
ejpam-6128	535	9	becomes	become	VERB
ejpam-6128	535	10	γ2	γ2	NOUN
ejpam-6128	535	11	=	=	PUNCT
ejpam-6128	535	12			PUNCT
ejpam-6128	535	13	γ2	γ2	NOUN
ejpam-6128	535	14	t	t	PROPN
ejpam-6128	535	15	=	=	PUNCT
ejpam-6128	536	1	x(twt	x(twt	PUNCT
ejpam-6128	536	2	−	−	PROPN
ejpam-6128	536	3	w	w	NOUN
ejpam-6128	536	4	)	)	PUNCT
ejpam-6128	536	5	,	,	PUNCT
ejpam-6128	536	6	γ2	γ2	PROPN
ejpam-6128	536	7	x	x	PUNCT
ejpam-6128	537	1	=	=	PUNCT
ejpam-6128	537	2	αtw	αtw	NUM
ejpam-6128	537	3	2	2	NUM
ejpam-6128	537	4	(	(	PUNCT
ejpam-6128	537	5	w	w	NOUN
ejpam-6128	537	6	−	−	PROPN
ejpam-6128	537	7	2xwx	2xwx	NUM
ejpam-6128	537	8	)	)	PUNCT
ejpam-6128	537	9	,	,	PUNCT
ejpam-6128	537	10	γ2	γ2	PROPN
ejpam-6128	537	11	y	y	PROPN
ejpam-6128	537	12	=	=	SYM
ejpam-6128	537	13	−βxtw2wy	−βxtw2wy	PROPN
ejpam-6128	537	14	.	.	PUNCT
ejpam-6128	538	1	(	(	PUNCT
ejpam-6128	538	2	130	130	NUM
ejpam-6128	538	3	)	)	PUNCT
ejpam-6128	538	4	the	the	DET
ejpam-6128	538	5	following	follow	VERB
ejpam-6128	538	6	system	system	NOUN
ejpam-6128	538	7	is	be	AUX
ejpam-6128	538	8	acquired	acquire	VERB
ejpam-6128	538	9	by	by	ADP
ejpam-6128	538	10	the	the	DET
ejpam-6128	538	11	insertion	insertion	NOUN
ejpam-6128	538	12	of	of	ADP
ejpam-6128	538	13	conserved	conserved	ADJ
ejpam-6128	538	14	vector	vector	NOUN
ejpam-6128	538	15	(	(	PUNCT
ejpam-6128	538	16	130	130	NUM
ejpam-6128	538	17	)	)	PUNCT
ejpam-6128	538	18	in	in	ADP
ejpam-6128	538	19	(	(	PUNCT
ejpam-6128	538	20	129	129	NUM
ejpam-6128	538	21	)	)	PUNCT
ejpam-6128	538	22	.	.	PUNCT
ejpam-6128	539	1	wtt	wtt	X
ejpam-6128	540	1	=	=	SYM
ejpam-6128	540	2	0	0	PROPN
ejpam-6128	540	3	,	,	PUNCT
ejpam-6128	540	4	wx(−2xwx	wx(−2xwx	PROPN
ejpam-6128	540	5	+	+	CCONJ
ejpam-6128	540	6	w	w	X
ejpam-6128	540	7	)	)	PUNCT
ejpam-6128	540	8	+	+	CCONJ
ejpam-6128	540	9	w(−wx	w(−wx	VERB
ejpam-6128	540	10	−	−	PROPN
ejpam-6128	540	11	2xwxx	2xwxx	NUM
ejpam-6128	540	12	)	)	PUNCT
ejpam-6128	540	13	=	=	SYM
ejpam-6128	540	14	0	0	NUM
ejpam-6128	540	15	,	,	PUNCT
ejpam-6128	540	16	2wy	2wy	NOUN
ejpam-6128	540	17	2	2	NUM
ejpam-6128	540	18	+	+	NUM
ejpam-6128	540	19	wwyy	wwyy	NOUN
ejpam-6128	540	20	=	=	SYM
ejpam-6128	540	21	0	0	NUM
ejpam-6128	540	22	.	.	PUNCT
ejpam-6128	541	1	(	(	PUNCT
ejpam-6128	541	2	131	131	NUM
ejpam-6128	541	3	)	)	PUNCT
ejpam-6128	541	4	the	the	DET
ejpam-6128	541	5	exact	exact	ADJ
ejpam-6128	541	6	solution	solution	NOUN
ejpam-6128	541	7	of	of	ADP
ejpam-6128	541	8	(	(	PUNCT
ejpam-6128	541	9	2	2	NUM
ejpam-6128	541	10	)	)	PUNCT
ejpam-6128	541	11	is	be	AUX
ejpam-6128	541	12	founded	found	VERB
ejpam-6128	541	13	by	by	ADP
ejpam-6128	541	14	solving	solve	VERB
ejpam-6128	541	15	the	the	DET
ejpam-6128	541	16	system	system	NOUN
ejpam-6128	541	17	(	(	PUNCT
ejpam-6128	541	18	131	131	NUM
ejpam-6128	541	19	)	)	PUNCT
ejpam-6128	541	20	and	and	CCONJ
ejpam-6128	541	21	is	be	AUX
ejpam-6128	541	22	described	describe	VERB
ejpam-6128	541	23	as	as	SCONJ
ejpam-6128	541	24	follows	follow	VERB
ejpam-6128	541	25	w(x	w(x	PROPN
ejpam-6128	541	26	,	,	PUNCT
ejpam-6128	541	27	y	y	PROPN
ejpam-6128	541	28	,	,	PUNCT
ejpam-6128	541	29	t	t	PROPN
ejpam-6128	541	30	)	)	PUNCT
ejpam-6128	541	31	=	=	SYM
ejpam-6128	541	32	√√√√2c3(c1y	√√√√2c3(c1y	NOUN
ejpam-6128	541	33	+	+	CCONJ
ejpam-6128	541	34	c2	c2	PROPN
ejpam-6128	541	35	)	)	PUNCT
ejpam-6128	541	36	2	2	NUM
ejpam-6128	541	37	3x+	3x+	NUM
ejpam-6128	541	38	2	2	NUM
ejpam-6128	541	39	(	(	PUNCT
ejpam-6128	541	40	−(12c1y	−(12c1y	NUM
ejpam-6128	541	41	+	+	NOUN
ejpam-6128	541	42	12c2	12c2	NUM
ejpam-6128	541	43	)	)	PUNCT
ejpam-6128	541	44	1	1	NUM
ejpam-6128	541	45	3	3	NUM
ejpam-6128	541	46	4	4	NUM
ejpam-6128	541	47	+	+	CCONJ
ejpam-6128	541	48	ι	ι	PART
ejpam-6128	541	49	√	√	ADV
ejpam-6128	541	50	3(12c1y	3(12c1y	PROPN
ejpam-6128	542	1	+	+	CCONJ
ejpam-6128	543	1	12c2	12c2	NUM
ejpam-6128	543	2	)	)	PUNCT
ejpam-6128	543	3	1	1	NUM
ejpam-6128	543	4	3	3	NUM
ejpam-6128	543	5	4	4	NUM
ejpam-6128	543	6	)	)	SYM
ejpam-6128	543	7	2	2	NUM
ejpam-6128	543	8	t	t	NOUN
ejpam-6128	543	9	+	+	CCONJ
ejpam-6128	543	10	2c4(c1y	2c4(c1y	PROPN
ejpam-6128	543	11	+	+	CCONJ
ejpam-6128	543	12	c2	c2	PROPN
ejpam-6128	543	13	)	)	PUNCT
ejpam-6128	543	14	1	1	NUM
ejpam-6128	543	15	3	3	NUM
ejpam-6128	543	16	(	(	PUNCT
ejpam-6128	543	17	312	312	NUM
ejpam-6128	543	18	1	1	NUM
ejpam-6128	543	19	3	3	NUM
ejpam-6128	543	20	−	−	NOUN
ejpam-6128	543	21	2c3(18	2c3(18	NUM
ejpam-6128	543	22	)	)	PUNCT
ejpam-6128	543	23	1	1	NUM
ejpam-6128	543	24	3x+	3x+	NUM
ejpam-6128	543	25	4c3	4c3	NUM
ejpam-6128	543	26	2x2	2x2	NUM
ejpam-6128	543	27	)	)	PUNCT
ejpam-6128	543	28	1	1	NUM
ejpam-6128	544	1	4√	4√	PRON
ejpam-6128	544	2	−	−	NOUN
ejpam-6128	544	3	53073	53073	NUM
ejpam-6128	544	4	6692	6692	NUM
ejpam-6128	544	5	ιc3x+3ι	ιc3x+3ι	VERB
ejpam-6128	544	6	√	√	NOUN
ejpam-6128	544	7	3	3	NUM
ejpam-6128	544	8	+	+	NOUN
ejpam-6128	544	9	9	9	NUM
ejpam-6128	544	10	6c32(18	6c32(18	NUM
ejpam-6128	544	11	)	)	PUNCT
ejpam-6128	544	12	1	1	NUM
ejpam-6128	544	13	3	3	NUM
ejpam-6128	544	14	x2−318	x2−318	ADP
ejpam-6128	544	15	2	2	NUM
ejpam-6128	544	16	3	3	NUM
ejpam-6128	544	17	c3x+27	c3x+27	NUM
ejpam-6128	544	18	.	.	PUNCT
ejpam-6128	545	1	(	(	PUNCT
ejpam-6128	545	2	132	132	NUM
ejpam-6128	545	3	)	)	PUNCT
ejpam-6128	545	4	for	for	ADP
ejpam-6128	545	5	f(w	f(w	NOUN
ejpam-6128	545	6	)	)	PUNCT
ejpam-6128	545	7	=	=	SYM
ejpam-6128	545	8	α	α	X
ejpam-6128	545	9	,	,	PUNCT
ejpam-6128	545	10	g(w	g(w	PROPN
ejpam-6128	545	11	)	)	PUNCT
ejpam-6128	545	12	=	=	SYM
ejpam-6128	546	1	βw	βw	ADV
ejpam-6128	546	2	,	,	PUNCT
ejpam-6128	546	3	the	the	DET
ejpam-6128	546	4	conserved	conserved	ADJ
ejpam-6128	546	5	vector	vector	NOUN
ejpam-6128	546	6	(	(	PUNCT
ejpam-6128	546	7	121	121	NUM
ejpam-6128	546	8	)	)	PUNCT
ejpam-6128	546	9	takes	take	VERB
ejpam-6128	546	10	the	the	DET
ejpam-6128	546	11	following	follow	VERB
ejpam-6128	546	12	form	form	NOUN
ejpam-6128	546	13	γ1	γ1	NOUN
ejpam-6128	546	14	=	=	SYM
ejpam-6128	546	15			PROPN
ejpam-6128	546	16	γ1	γ1	PROPN
ejpam-6128	546	17	t	t	PROPN
ejpam-6128	546	18	=	=	SYM
ejpam-6128	546	19	wt	wt	PROPN
ejpam-6128	546	20	,	,	PUNCT
ejpam-6128	546	21	γ1	γ1	NOUN
ejpam-6128	546	22	x	x	NOUN
ejpam-6128	546	23	=	=	SYM
ejpam-6128	546	24	−αwx	−αwx	NOUN
ejpam-6128	546	25	,	,	PUNCT
ejpam-6128	547	1	γ1	γ1	NOUN
ejpam-6128	547	2	y	y	PROPN
ejpam-6128	547	3	=	=	PUNCT
ejpam-6128	547	4	−βwwy	−βwwy	PROPN
ejpam-6128	547	5	.	.	PUNCT
ejpam-6128	548	1	(	(	PUNCT
ejpam-6128	548	2	133	133	NUM
ejpam-6128	548	3	)	)	PUNCT
ejpam-6128	548	4	m.	m.	NOUN
ejpam-6128	548	5	usman	usman	PROPN
ejpam-6128	548	6	,	,	PUNCT
ejpam-6128	548	7	a.	a.	NOUN
ejpam-6128	548	8	hussain	hussain	PROPN
ejpam-6128	548	9	,	,	PUNCT
ejpam-6128	548	10	m.	m.	PROPN
ejpam-6128	548	11	u.	u.	PROPN
ejpam-6128	548	12	farooq	farooq	PROPN
ejpam-6128	548	13	,	,	PUNCT
ejpam-6128	548	14	j.	j.	PROPN
ejpam-6128	548	15	herrera	herrera	PROPN
ejpam-6128	548	16	/	/	SYM
ejpam-6128	548	17	eur	eur	PROPN
ejpam-6128	548	18	.	.	PUNCT
ejpam-6128	549	1	j.	j.	PROPN
ejpam-6128	549	2	pure	pure	PROPN
ejpam-6128	549	3	appl	appl	PROPN
ejpam-6128	549	4	.	.	PROPN
ejpam-6128	549	5	math	math	PROPN
ejpam-6128	549	6	,	,	PUNCT
ejpam-6128	549	7	18	18	NUM
ejpam-6128	549	8	(	(	PUNCT
ejpam-6128	549	9	4	4	NUM
ejpam-6128	549	10	)	)	PUNCT
ejpam-6128	549	11	(	(	PUNCT
ejpam-6128	549	12	2025	2025	NUM
ejpam-6128	549	13	)	)	PUNCT
ejpam-6128	549	14	,	,	PUNCT
ejpam-6128	549	15	6128	6128	NUM
ejpam-6128	549	16	25	25	NUM
ejpam-6128	549	17	of	of	ADP
ejpam-6128	549	18	29	29	NUM
ejpam-6128	549	19	by	by	ADP
ejpam-6128	549	20	substituting	substitute	VERB
ejpam-6128	549	21	the	the	DET
ejpam-6128	549	22	conserved	conserved	ADJ
ejpam-6128	549	23	vector	vector	NOUN
ejpam-6128	549	24	(	(	PUNCT
ejpam-6128	549	25	133	133	NUM
ejpam-6128	549	26	)	)	PUNCT
ejpam-6128	549	27	in	in	ADP
ejpam-6128	549	28	(	(	PUNCT
ejpam-6128	549	29	129	129	NUM
ejpam-6128	549	30	)	)	PUNCT
ejpam-6128	549	31	,	,	PUNCT
ejpam-6128	549	32	we	we	PRON
ejpam-6128	549	33	get	get	VERB
ejpam-6128	549	34	wtt	wtt	PROPN
ejpam-6128	549	35	=	=	SYM
ejpam-6128	549	36	0	0	PROPN
ejpam-6128	549	37	,	,	PUNCT
ejpam-6128	549	38	wxx	wxx	VERB
ejpam-6128	549	39	=	=	SYM
ejpam-6128	549	40	0	0	NUM
ejpam-6128	549	41	,	,	PUNCT
ejpam-6128	549	42	wy	wy	PROPN
ejpam-6128	549	43	2	2	NUM
ejpam-6128	549	44	+	+	NUM
ejpam-6128	549	45	wwyy	wwyy	NOUN
ejpam-6128	549	46	=	=	SYM
ejpam-6128	549	47	0	0	NUM
ejpam-6128	549	48	.	.	PUNCT
ejpam-6128	550	1	(	(	PUNCT
ejpam-6128	550	2	134	134	NUM
ejpam-6128	550	3	)	)	PUNCT
ejpam-6128	550	4	this	this	PRON
ejpam-6128	550	5	provides	provide	VERB
ejpam-6128	550	6	the	the	DET
ejpam-6128	550	7	solution	solution	NOUN
ejpam-6128	550	8	of	of	ADP
ejpam-6128	550	9	(	(	PUNCT
ejpam-6128	550	10	2	2	NUM
ejpam-6128	550	11	)	)	PUNCT
ejpam-6128	550	12	given	give	VERB
ejpam-6128	550	13	by	by	ADP
ejpam-6128	550	14	w(x	w(x	PROPN
ejpam-6128	550	15	,	,	PUNCT
ejpam-6128	550	16	y	y	PROPN
ejpam-6128	550	17	,	,	PUNCT
ejpam-6128	550	18	t	t	PROPN
ejpam-6128	550	19	)	)	PUNCT
ejpam-6128	550	20	=	=	SYM
ejpam-6128	550	21	−xt	−xt	PART
ejpam-6128	550	22	√	√	NUM
ejpam-6128	550	23	2c1y	2c1y	NOUN
ejpam-6128	551	1	+	+	CCONJ
ejpam-6128	552	1	2c2	2c2	NUM
ejpam-6128	552	2	+	+	CCONJ
ejpam-6128	552	3	√	√	VERB
ejpam-6128	552	4	c1y	c1y	NOUN
ejpam-6128	552	5	+	+	CCONJ
ejpam-6128	552	6	c2(c3x+	c2(c3x+	PROPN
ejpam-6128	552	7	c4t+	c4t+	NOUN
ejpam-6128	552	8	c5	c5	PROPN
ejpam-6128	552	9	)	)	PUNCT
ejpam-6128	552	10	.	.	PUNCT
ejpam-6128	553	1	(	(	PUNCT
ejpam-6128	553	2	135	135	NUM
ejpam-6128	553	3	)	)	PUNCT
ejpam-6128	553	4	the	the	DET
ejpam-6128	553	5	solutions	solution	NOUN
ejpam-6128	553	6	obtained	obtain	VERB
ejpam-6128	553	7	in	in	ADP
ejpam-6128	553	8	this	this	DET
ejpam-6128	553	9	section	section	NOUN
ejpam-6128	553	10	are	be	AUX
ejpam-6128	553	11	not	not	PART
ejpam-6128	553	12	invariant	invariant	ADJ
ejpam-6128	553	13	under	under	ADP
ejpam-6128	553	14	the	the	DET
ejpam-6128	553	15	lie	lie	NOUN
ejpam-6128	553	16	algebra	algebra	NOUN
ejpam-6128	553	17	.	.	PUNCT
ejpam-6128	554	1	6	6	NUM
ejpam-6128	554	2	.	.	X
ejpam-6128	554	3	graphical	graphical	ADJ
ejpam-6128	554	4	representation	representation	NOUN
ejpam-6128	554	5	of	of	ADP
ejpam-6128	554	6	solutions	solution	NOUN
ejpam-6128	554	7	in	in	ADP
ejpam-6128	554	8	the	the	DET
ejpam-6128	554	9	present	present	ADJ
ejpam-6128	554	10	section	section	NOUN
ejpam-6128	554	11	,	,	PUNCT
ejpam-6128	554	12	3d	3d	NUM
ejpam-6128	554	13	graphical	graphical	ADJ
ejpam-6128	554	14	representations	representation	NOUN
ejpam-6128	554	15	of	of	ADP
ejpam-6128	554	16	the	the	DET
ejpam-6128	554	17	obtained	obtain	VERB
ejpam-6128	554	18	findings	finding	NOUN
ejpam-6128	554	19	are	be	AUX
ejpam-6128	554	20	given	give	VERB
ejpam-6128	554	21	.	.	PUNCT
ejpam-6128	555	1	geometrical	geometrical	ADJ
ejpam-6128	555	2	analysis	analysis	NOUN
ejpam-6128	555	3	is	be	AUX
ejpam-6128	555	4	provided	provide	VERB
ejpam-6128	555	5	because	because	SCONJ
ejpam-6128	555	6	mathematical	mathematical	ADJ
ejpam-6128	555	7	expressions	expression	NOUN
ejpam-6128	555	8	are	be	AUX
ejpam-6128	555	9	insufficient	insufficient	ADJ
ejpam-6128	555	10	to	to	PART
ejpam-6128	555	11	describe	describe	VERB
ejpam-6128	555	12	the	the	DET
ejpam-6128	555	13	physical	physical	ADJ
ejpam-6128	555	14	wave	wave	NOUN
ejpam-6128	555	15	patterns	pattern	NOUN
ejpam-6128	555	16	.	.	PUNCT
ejpam-6128	556	1	figure	figure	NOUN
ejpam-6128	556	2	1	1	NUM
ejpam-6128	556	3	describes	describe	VERB
ejpam-6128	556	4	the	the	DET
ejpam-6128	556	5	3d	3d	PROPN
ejpam-6128	556	6	graphics	graphic	NOUN
ejpam-6128	556	7	of	of	ADP
ejpam-6128	556	8	(	(	PUNCT
ejpam-6128	556	9	73	73	NUM
ejpam-6128	556	10	)	)	PUNCT
ejpam-6128	556	11	in	in	ADP
ejpam-6128	556	12	the	the	DET
ejpam-6128	556	13	range	range	NOUN
ejpam-6128	556	14	of	of	ADP
ejpam-6128	556	15	variables	variable	NOUN
ejpam-6128	556	16	1	1	NUM
ejpam-6128	556	17	≤	≤	NUM
ejpam-6128	556	18	t	t	NOUN
ejpam-6128	556	19	≤	≤	NOUN
ejpam-6128	556	20	2	2	NUM
ejpam-6128	556	21	,	,	PUNCT
ejpam-6128	556	22	1	1	NUM
ejpam-6128	556	23	≤	≤	NUM
ejpam-6128	556	24	y	y	NOUN
ejpam-6128	556	25	≤	≤	NUM
ejpam-6128	556	26	3	3	NUM
ejpam-6128	556	27	and	and	CCONJ
ejpam-6128	556	28	1	1	NUM
ejpam-6128	556	29	≤	≤	NOUN
ejpam-6128	556	30	t	t	NOUN
ejpam-6128	556	31	≤	≤	NOUN
ejpam-6128	556	32	2	2	NUM
ejpam-6128	556	33	,	,	PUNCT
ejpam-6128	556	34	1	1	NUM
ejpam-6128	556	35	≤	≤	NUM
ejpam-6128	556	36	y	y	PROPN
ejpam-6128	556	37	≤	≤	NUM
ejpam-6128	556	38	25	25	NUM
ejpam-6128	556	39	by	by	ADP
ejpam-6128	556	40	assuming	assume	VERB
ejpam-6128	556	41	c1	c1	PROPN
ejpam-6128	556	42	=	=	PROPN
ejpam-6128	556	43	c2	c2	PROPN
ejpam-6128	556	44	=	=	SYM
ejpam-6128	556	45	1	1	NUM
ejpam-6128	556	46	and	and	CCONJ
ejpam-6128	556	47	β	β	X
ejpam-6128	556	48	=	=	NOUN
ejpam-6128	556	49	1	1	X
ejpam-6128	556	50	.	.	PUNCT
ejpam-6128	557	1	in	in	ADP
ejpam-6128	557	2	figure	figure	NOUN
ejpam-6128	557	3	2	2	NUM
ejpam-6128	557	4	,	,	PUNCT
ejpam-6128	557	5	an	an	DET
ejpam-6128	557	6	exponential	exponential	ADJ
ejpam-6128	557	7	wave	wave	NOUN
ejpam-6128	557	8	pattern	pattern	NOUN
ejpam-6128	557	9	of	of	ADP
ejpam-6128	557	10	(	(	PUNCT
ejpam-6128	557	11	91	91	NUM
ejpam-6128	557	12	)	)	PUNCT
ejpam-6128	557	13	is	be	AUX
ejpam-6128	557	14	shown	show	VERB
ejpam-6128	557	15	in	in	ADP
ejpam-6128	557	16	the	the	DET
ejpam-6128	557	17	range	range	NOUN
ejpam-6128	557	18	of	of	ADP
ejpam-6128	557	19	variables	variable	NOUN
ejpam-6128	557	20	1	1	NUM
ejpam-6128	557	21	≤	≤	NUM
ejpam-6128	557	22	t	t	NOUN
ejpam-6128	557	23	≤	≤	NOUN
ejpam-6128	557	24	2	2	NUM
ejpam-6128	557	25	,	,	PUNCT
ejpam-6128	557	26	1	1	NUM
ejpam-6128	557	27	≤	≤	NUM
ejpam-6128	557	28	x	x	SYM
ejpam-6128	557	29	≤	≤	NUM
ejpam-6128	557	30	30	30	NUM
ejpam-6128	557	31	and	and	CCONJ
ejpam-6128	557	32	1	1	NUM
ejpam-6128	557	33	≤	≤	NOUN
ejpam-6128	557	34	t	t	NOUN
ejpam-6128	557	35	≤	≤	NUM
ejpam-6128	557	36	20	20	NUM
ejpam-6128	557	37	,	,	PUNCT
ejpam-6128	557	38	1	1	NUM
ejpam-6128	557	39	≤	≤	NUM
ejpam-6128	557	40	x	x	SYM
ejpam-6128	557	41	≤	≤	NUM
ejpam-6128	557	42	4	4	NUM
ejpam-6128	557	43	by	by	ADP
ejpam-6128	557	44	assuming	assume	VERB
ejpam-6128	557	45	c1	c1	PROPN
ejpam-6128	557	46	=	=	PROPN
ejpam-6128	557	47	c2	c2	PROPN
ejpam-6128	557	48	=	=	SYM
ejpam-6128	557	49	1	1	NUM
ejpam-6128	557	50	and	and	CCONJ
ejpam-6128	557	51	α	α	NOUN
ejpam-6128	557	52	=	=	SYM
ejpam-6128	557	53	1	1	X
ejpam-6128	557	54	.	.	PUNCT
ejpam-6128	557	55	figure	figure	NOUN
ejpam-6128	557	56	3	3	NUM
ejpam-6128	557	57	describes	describe	VERB
ejpam-6128	557	58	the	the	DET
ejpam-6128	557	59	3d	3d	PROPN
ejpam-6128	557	60	graphics	graphic	NOUN
ejpam-6128	557	61	of	of	ADP
ejpam-6128	557	62	(	(	PUNCT
ejpam-6128	557	63	135	135	NUM
ejpam-6128	557	64	)	)	PUNCT
ejpam-6128	557	65	in	in	ADP
ejpam-6128	557	66	the	the	DET
ejpam-6128	557	67	range	range	NOUN
ejpam-6128	557	68	of	of	ADP
ejpam-6128	557	69	variables	variable	NOUN
ejpam-6128	557	70	1	1	NUM
ejpam-6128	557	71	≤	≤	NUM
ejpam-6128	557	72	x	x	PUNCT
ejpam-6128	557	73	≤	≤	NUM
ejpam-6128	557	74	2	2	NUM
ejpam-6128	557	75	,	,	PUNCT
ejpam-6128	557	76	1	1	NUM
ejpam-6128	557	77	≤	≤	NUM
ejpam-6128	557	78	y	y	PROPN
ejpam-6128	557	79	≤	≤	NUM
ejpam-6128	557	80	2	2	NUM
ejpam-6128	557	81	,	,	PUNCT
ejpam-6128	557	82	t	t	NOUN
ejpam-6128	557	83	=	=	SYM
ejpam-6128	557	84	2	2	NUM
ejpam-6128	557	85	and	and	CCONJ
ejpam-6128	557	86	1	1	NUM
ejpam-6128	557	87	≤	≤	NUM
ejpam-6128	557	88	x	x	SYM
ejpam-6128	557	89	≤	≤	NUM
ejpam-6128	557	90	20	20	NUM
ejpam-6128	557	91	,	,	PUNCT
ejpam-6128	557	92	1	1	NUM
ejpam-6128	557	93	≤	≤	NUM
ejpam-6128	557	94	y	y	PROPN
ejpam-6128	557	95	≤	≤	NUM
ejpam-6128	557	96	60	60	NUM
ejpam-6128	557	97	,	,	PUNCT
ejpam-6128	557	98	t	t	NOUN
ejpam-6128	557	99	=	=	NUM
ejpam-6128	557	100	40	40	NUM
ejpam-6128	557	101	by	by	ADP
ejpam-6128	557	102	assuming	assume	VERB
ejpam-6128	557	103	c1	c1	PROPN
ejpam-6128	557	104	=	=	PROPN
ejpam-6128	557	105	c2	c2	PROPN
ejpam-6128	557	106	=	=	SYM
ejpam-6128	557	107	c3	c3	PROPN
ejpam-6128	557	108	=	=	PROPN
ejpam-6128	557	109	c4	c4	PROPN
ejpam-6128	557	110	=	=	SYM
ejpam-6128	557	111	c5	c5	PROPN
ejpam-6128	557	112	=	=	PUNCT
ejpam-6128	558	1	1	1	X
ejpam-6128	558	2	.	.	PUNCT
ejpam-6128	558	3	(	(	PUNCT
ejpam-6128	558	4	a	a	X
ejpam-6128	558	5	)	)	PUNCT
ejpam-6128	558	6	(	(	PUNCT
ejpam-6128	558	7	b	b	X
ejpam-6128	558	8	)	)	PUNCT
ejpam-6128	558	9	figure	figure	NOUN
ejpam-6128	558	10	1	1	NUM
ejpam-6128	558	11	:	:	PUNCT
ejpam-6128	558	12	3d	3d	NUM
ejpam-6128	558	13	graphic	graphic	ADJ
ejpam-6128	558	14	depictions	depiction	NOUN
ejpam-6128	558	15	of	of	ADP
ejpam-6128	558	16	(	(	PUNCT
ejpam-6128	558	17	73	73	NUM
ejpam-6128	558	18	)	)	PUNCT
ejpam-6128	558	19	,	,	PUNCT
ejpam-6128	558	20	by	by	ADP
ejpam-6128	558	21	considering	consider	VERB
ejpam-6128	558	22	c1	c1	PROPN
ejpam-6128	558	23	=	=	PROPN
ejpam-6128	558	24	c2	c2	PROPN
ejpam-6128	558	25	=	=	SYM
ejpam-6128	558	26	1	1	NUM
ejpam-6128	558	27	and	and	CCONJ
ejpam-6128	558	28	β	β	X
ejpam-6128	558	29	=	=	SYM
ejpam-6128	558	30	1	1	X
ejpam-6128	558	31	.	.	PUNCT
ejpam-6128	558	32	m.	m.	PROPN
ejpam-6128	558	33	usman	usman	PROPN
ejpam-6128	558	34	,	,	PUNCT
ejpam-6128	558	35	a.	a.	NOUN
ejpam-6128	558	36	hussain	hussain	PROPN
ejpam-6128	558	37	,	,	PUNCT
ejpam-6128	558	38	m.	m.	PROPN
ejpam-6128	558	39	u.	u.	PROPN
ejpam-6128	558	40	farooq	farooq	PROPN
ejpam-6128	558	41	,	,	PUNCT
ejpam-6128	558	42	j.	j.	PROPN
ejpam-6128	558	43	herrera	herrera	PROPN
ejpam-6128	558	44	/	/	SYM
ejpam-6128	558	45	eur	eur	PROPN
ejpam-6128	558	46	.	.	PUNCT
ejpam-6128	559	1	j.	j.	PROPN
ejpam-6128	559	2	pure	pure	PROPN
ejpam-6128	559	3	appl	appl	PROPN
ejpam-6128	559	4	.	.	PROPN
ejpam-6128	559	5	math	math	PROPN
ejpam-6128	559	6	,	,	PUNCT
ejpam-6128	559	7	18	18	NUM
ejpam-6128	559	8	(	(	PUNCT
ejpam-6128	559	9	4	4	NUM
ejpam-6128	559	10	)	)	PUNCT
ejpam-6128	559	11	(	(	PUNCT
ejpam-6128	559	12	2025	2025	NUM
ejpam-6128	559	13	)	)	PUNCT
ejpam-6128	559	14	,	,	PUNCT
ejpam-6128	559	15	6128	6128	NUM
ejpam-6128	559	16	26	26	NUM
ejpam-6128	559	17	of	of	ADP
ejpam-6128	559	18	29	29	NUM
ejpam-6128	559	19	(	(	PUNCT
ejpam-6128	559	20	a	a	NOUN
ejpam-6128	559	21	)	)	PUNCT
ejpam-6128	559	22	(	(	PUNCT
ejpam-6128	559	23	b	b	X
ejpam-6128	559	24	)	)	PUNCT
ejpam-6128	559	25	figure	figure	NOUN
ejpam-6128	559	26	2	2	NUM
ejpam-6128	559	27	:	:	PUNCT
ejpam-6128	559	28	3d	3d	NUM
ejpam-6128	559	29	graphic	graphic	ADJ
ejpam-6128	559	30	depictions	depiction	NOUN
ejpam-6128	559	31	of	of	ADP
ejpam-6128	559	32	(	(	PUNCT
ejpam-6128	559	33	91	91	NUM
ejpam-6128	559	34	)	)	PUNCT
ejpam-6128	559	35	by	by	ADP
ejpam-6128	559	36	considering	consider	VERB
ejpam-6128	559	37	c1	c1	PROPN
ejpam-6128	559	38	=	=	PROPN
ejpam-6128	559	39	c2	c2	PROPN
ejpam-6128	559	40	=	=	SYM
ejpam-6128	559	41	1	1	NUM
ejpam-6128	559	42	and	and	CCONJ
ejpam-6128	559	43	α	α	NOUN
ejpam-6128	559	44	=	=	SYM
ejpam-6128	559	45	1	1	X
ejpam-6128	559	46	.	.	PUNCT
ejpam-6128	560	1	(	(	PUNCT
ejpam-6128	560	2	a	a	X
ejpam-6128	560	3	)	)	PUNCT
ejpam-6128	560	4	t=2	t=2	PROPN
ejpam-6128	560	5	(	(	PUNCT
ejpam-6128	560	6	b	b	X
ejpam-6128	560	7	)	)	PUNCT
ejpam-6128	560	8	t=40	t=40	NOUN
ejpam-6128	560	9	figure	figure	NOUN
ejpam-6128	560	10	3	3	NUM
ejpam-6128	560	11	:	:	SYM
ejpam-6128	560	12	3d	3d	NUM
ejpam-6128	560	13	graphic	graphic	ADJ
ejpam-6128	560	14	depictions	depiction	NOUN
ejpam-6128	560	15	of	of	ADP
ejpam-6128	560	16	(	(	PUNCT
ejpam-6128	560	17	135	135	NUM
ejpam-6128	560	18	)	)	PUNCT
ejpam-6128	560	19	by	by	ADP
ejpam-6128	560	20	considering	consider	VERB
ejpam-6128	560	21	c1	c1	PROPN
ejpam-6128	560	22	=	=	PROPN
ejpam-6128	560	23	c2	c2	PROPN
ejpam-6128	560	24	=	=	SYM
ejpam-6128	560	25	c3	c3	PROPN
ejpam-6128	560	26	=	=	PROPN
ejpam-6128	560	27	c4	c4	PROPN
ejpam-6128	560	28	=	=	SYM
ejpam-6128	560	29	c5	c5	PROPN
ejpam-6128	560	30	=	=	PUNCT
ejpam-6128	560	31	1	1	NUM
ejpam-6128	560	32	.	.	NOUN
ejpam-6128	560	33	7	7	NUM
ejpam-6128	560	34	.	.	X
ejpam-6128	560	35	conclusions	conclusion	NOUN
ejpam-6128	560	36	through	through	ADP
ejpam-6128	560	37	the	the	DET
ejpam-6128	560	38	implementation	implementation	NOUN
ejpam-6128	560	39	of	of	ADP
ejpam-6128	560	40	the	the	DET
ejpam-6128	560	41	lie	lie	NOUN
ejpam-6128	560	42	group	group	NOUN
ejpam-6128	560	43	analysis	analysis	NOUN
ejpam-6128	560	44	method	method	NOUN
ejpam-6128	560	45	,	,	PUNCT
ejpam-6128	560	46	we	we	PRON
ejpam-6128	560	47	investigated	investigate	VERB
ejpam-6128	560	48	the	the	DET
ejpam-6128	560	49	characteristics	characteristic	NOUN
ejpam-6128	560	50	of	of	ADP
ejpam-6128	560	51	a	a	DET
ejpam-6128	560	52	(	(	PUNCT
ejpam-6128	560	53	2	2	NUM
ejpam-6128	560	54	+	+	NOUN
ejpam-6128	560	55	1)-dimensional	1)-dimensional	ADJ
ejpam-6128	560	56	nonlinear	nonlinear	ADJ
ejpam-6128	560	57	wave	wave	NOUN
ejpam-6128	560	58	equation	equation	NOUN
ejpam-6128	560	59	.	.	PUNCT
ejpam-6128	561	1	we	we	PRON
ejpam-6128	561	2	built	build	VERB
ejpam-6128	561	3	an	an	DET
ejpam-6128	561	4	optimal	optimal	ADJ
ejpam-6128	561	5	set	set	NOUN
ejpam-6128	561	6	of	of	ADP
ejpam-6128	561	7	subalgebras	subalgebra	NOUN
ejpam-6128	561	8	of	of	ADP
ejpam-6128	561	9	lie	lie	NOUN
ejpam-6128	561	10	algebra	algebra	PROPN
ejpam-6128	561	11	,	,	PUNCT
ejpam-6128	561	12	which	which	PRON
ejpam-6128	561	13	are	be	AUX
ejpam-6128	561	14	one	one	NUM
ejpam-6128	561	15	-	-	PUNCT
ejpam-6128	561	16	dimensional	dimensional	ADJ
ejpam-6128	561	17	,	,	PUNCT
ejpam-6128	561	18	and	and	CCONJ
ejpam-6128	561	19	inspected	inspect	VERB
ejpam-6128	561	20	its	its	PRON
ejpam-6128	561	21	representatives	representative	NOUN
ejpam-6128	561	22	in	in	ADP
ejpam-6128	561	23	order	order	NOUN
ejpam-6128	561	24	to	to	PART
ejpam-6128	561	25	investigate	investigate	VERB
ejpam-6128	561	26	invariant	invariant	ADJ
ejpam-6128	561	27	solutions	solution	NOUN
ejpam-6128	561	28	and	and	CCONJ
ejpam-6128	561	29	similarity	similarity	NOUN
ejpam-6128	561	30	reductions	reduction	NOUN
ejpam-6128	561	31	,	,	PUNCT
ejpam-6128	561	32	which	which	PRON
ejpam-6128	561	33	provide	provide	VERB
ejpam-6128	561	34	a	a	DET
ejpam-6128	561	35	mulm	mulm	NOUN
ejpam-6128	561	36	.	.	PUNCT
ejpam-6128	562	1	usman	usman	PROPN
ejpam-6128	562	2	,	,	PUNCT
ejpam-6128	562	3	a.	a.	NOUN
ejpam-6128	562	4	hussain	hussain	PROPN
ejpam-6128	562	5	,	,	PUNCT
ejpam-6128	562	6	m.	m.	PROPN
ejpam-6128	562	7	u.	u.	PROPN
ejpam-6128	562	8	farooq	farooq	PROPN
ejpam-6128	562	9	,	,	PUNCT
ejpam-6128	562	10	j.	j.	PROPN
ejpam-6128	562	11	herrera	herrera	PROPN
ejpam-6128	562	12	/	/	SYM
ejpam-6128	562	13	eur	eur	PROPN
ejpam-6128	562	14	.	.	PUNCT
ejpam-6128	563	1	j.	j.	PROPN
ejpam-6128	563	2	pure	pure	PROPN
ejpam-6128	563	3	appl	appl	PROPN
ejpam-6128	563	4	.	.	PROPN
ejpam-6128	563	5	math	math	PROPN
ejpam-6128	563	6	,	,	PUNCT
ejpam-6128	563	7	18	18	NUM
ejpam-6128	563	8	(	(	PUNCT
ejpam-6128	563	9	4	4	NUM
ejpam-6128	563	10	)	)	PUNCT
ejpam-6128	563	11	(	(	PUNCT
ejpam-6128	563	12	2025	2025	NUM
ejpam-6128	563	13	)	)	PUNCT
ejpam-6128	563	14	,	,	PUNCT
ejpam-6128	563	15	6128	6128	NUM
ejpam-6128	563	16	27	27	NUM
ejpam-6128	563	17	of	of	ADP
ejpam-6128	563	18	29	29	NUM
ejpam-6128	563	19	titude	titude	NOUN
ejpam-6128	563	20	of	of	ADP
ejpam-6128	563	21	explicit	explicit	ADJ
ejpam-6128	563	22	exact	exact	ADJ
ejpam-6128	563	23	solutions	solution	NOUN
ejpam-6128	563	24	using	use	VERB
ejpam-6128	563	25	computerized	computerized	ADJ
ejpam-6128	563	26	symbolic	symbolic	ADJ
ejpam-6128	563	27	computation	computation	NOUN
ejpam-6128	563	28	.	.	PUNCT
ejpam-6128	564	1	we	we	PRON
ejpam-6128	564	2	applied	apply	VERB
ejpam-6128	564	3	the	the	DET
ejpam-6128	564	4	lagrange	lagrange	NOUN
ejpam-6128	564	5	multiplier	multipli	ADJ
ejpam-6128	564	6	approach	approach	NOUN
ejpam-6128	564	7	to	to	PART
ejpam-6128	564	8	generate	generate	VERB
ejpam-6128	564	9	conserved	conserved	ADJ
ejpam-6128	564	10	vectors	vector	NOUN
ejpam-6128	564	11	.	.	PUNCT
ejpam-6128	565	1	we	we	PRON
ejpam-6128	565	2	have	have	AUX
ejpam-6128	565	3	also	also	ADV
ejpam-6128	565	4	obtained	obtain	VERB
ejpam-6128	565	5	precise	precise	ADJ
ejpam-6128	565	6	solutions	solution	NOUN
ejpam-6128	565	7	to	to	ADP
ejpam-6128	565	8	the	the	DET
ejpam-6128	565	9	nonlinear	nonlinear	ADJ
ejpam-6128	565	10	wave	wave	NOUN
ejpam-6128	565	11	equation	equation	NOUN
ejpam-6128	565	12	through	through	ADP
ejpam-6128	565	13	the	the	DET
ejpam-6128	565	14	use	use	NOUN
ejpam-6128	565	15	of	of	ADP
ejpam-6128	565	16	these	these	DET
ejpam-6128	565	17	conserved	conserved	ADJ
ejpam-6128	565	18	vectors	vector	NOUN
ejpam-6128	565	19	.	.	PUNCT
ejpam-6128	566	1	consequently	consequently	ADV
ejpam-6128	566	2	,	,	PUNCT
ejpam-6128	566	3	graphical	graphical	ADJ
ejpam-6128	566	4	representations	representation	NOUN
ejpam-6128	566	5	of	of	ADP
ejpam-6128	566	6	the	the	DET
ejpam-6128	566	7	answers	answer	NOUN
ejpam-6128	566	8	are	be	AUX
ejpam-6128	566	9	analyzed	analyze	VERB
ejpam-6128	566	10	and	and	CCONJ
ejpam-6128	566	11	illustrated	illustrate	VERB
ejpam-6128	566	12	using	use	VERB
ejpam-6128	566	13	3d	3d	NUM
ejpam-6128	566	14	visuals	visual	NOUN
ejpam-6128	566	15	.	.	PUNCT
ejpam-6128	567	1	ethics	ethic	NOUN
ejpam-6128	567	2	approval	approval	NOUN
ejpam-6128	567	3	and	and	CCONJ
ejpam-6128	567	4	consent	consent	NOUN
ejpam-6128	567	5	to	to	PART
ejpam-6128	567	6	participate	participate	VERB
ejpam-6128	567	7	:	:	PUNCT
ejpam-6128	567	8	all	all	DET
ejpam-6128	567	9	the	the	DET
ejpam-6128	567	10	authors	author	NOUN
ejpam-6128	567	11	approve	approve	VERB
ejpam-6128	567	12	their	their	PRON
ejpam-6128	567	13	consent	consent	NOUN
ejpam-6128	567	14	.	.	PUNCT
ejpam-6128	568	1	consent	consent	NOUN
ejpam-6128	568	2	for	for	ADP
ejpam-6128	568	3	publication	publication	NOUN
ejpam-6128	568	4	:	:	PUNCT
ejpam-6128	568	5	the	the	DET
ejpam-6128	568	6	authors	author	NOUN
ejpam-6128	568	7	approve	approve	VERB
ejpam-6128	568	8	this	this	DET
ejpam-6128	568	9	version	version	NOUN
ejpam-6128	568	10	for	for	ADP
ejpam-6128	568	11	publication	publication	NOUN
ejpam-6128	568	12	.	.	PUNCT
ejpam-6128	569	1	availability	availability	NOUN
ejpam-6128	569	2	of	of	ADP
ejpam-6128	569	3	data	datum	NOUN
ejpam-6128	569	4	and	and	CCONJ
ejpam-6128	569	5	materials	material	NOUN
ejpam-6128	569	6	:	:	PUNCT
ejpam-6128	569	7	all	all	DET
ejpam-6128	569	8	data	datum	NOUN
ejpam-6128	569	9	generated	generate	VERB
ejpam-6128	569	10	or	or	CCONJ
ejpam-6128	569	11	analyzed	analyze	VERB
ejpam-6128	569	12	during	during	ADP
ejpam-6128	569	13	this	this	DET
ejpam-6128	569	14	study	study	NOUN
ejpam-6128	569	15	are	be	AUX
ejpam-6128	569	16	included	include	VERB
ejpam-6128	569	17	in	in	ADP
ejpam-6128	569	18	this	this	DET
ejpam-6128	569	19	published	publish	VERB
ejpam-6128	569	20	article	article	NOUN
ejpam-6128	569	21	.	.	PUNCT
ejpam-6128	570	1	competing	compete	VERB
ejpam-6128	570	2	interests	interest	NOUN
ejpam-6128	570	3	:	:	PUNCT
ejpam-6128	570	4	the	the	DET
ejpam-6128	570	5	authors	author	NOUN
ejpam-6128	570	6	professed	profess	VERB
ejpam-6128	570	7	no	no	DET
ejpam-6128	570	8	conflicts	conflict	NOUN
ejpam-6128	570	9	of	of	ADP
ejpam-6128	570	10	interest	interest	NOUN
ejpam-6128	570	11	.	.	PUNCT
ejpam-6128	571	1	funding	funding	NOUN
ejpam-6128	571	2	:	:	PUNCT
ejpam-6128	571	3	no	no	DET
ejpam-6128	571	4	external	external	ADJ
ejpam-6128	571	5	funding	funding	NOUN
ejpam-6128	571	6	received	receive	VERB
ejpam-6128	571	7	.	.	PUNCT
ejpam-6128	572	1	references	reference	NOUN
ejpam-6128	572	2	[	[	X
ejpam-6128	572	3	1	1	NUM
ejpam-6128	572	4	]	]	X
ejpam-6128	572	5	f	f	PROPN
ejpam-6128	572	6	ali	ali	PROPN
ejpam-6128	572	7	,	,	PUNCT
ejpam-6128	572	8	a	a	DET
ejpam-6128	572	9	jhangeer	jhangeer	NOUN
ejpam-6128	572	10	,	,	PUNCT
ejpam-6128	572	11	m	m	NOUN
ejpam-6128	572	12	muddasser	muddasser	NOUN
ejpam-6128	572	13	,	,	PUNCT
ejpam-6128	572	14	and	and	CCONJ
ejpam-6128	572	15	h	h	NOUN
ejpam-6128	572	16	almusawa	almusawa	NOUN
ejpam-6128	572	17	.	.	PUNCT
ejpam-6128	573	1	solitonic	solitonic	NOUN
ejpam-6128	573	2	,	,	PUNCT
ejpam-6128	573	3	quasi	quasi	ADJ
ejpam-6128	573	4	-	-	NOUN
ejpam-6128	573	5	periodic	periodic	ADJ
ejpam-6128	573	6	,	,	PUNCT
ejpam-6128	573	7	super	super	ADJ
ejpam-6128	573	8	nonlinear	nonlinear	ADJ
ejpam-6128	573	9	and	and	CCONJ
ejpam-6128	573	10	chaotic	chaotic	ADJ
ejpam-6128	573	11	behaviors	behavior	NOUN
ejpam-6128	573	12	of	of	ADP
ejpam-6128	573	13	a	a	DET
ejpam-6128	573	14	dispersive	dispersive	ADJ
ejpam-6128	573	15	extended	extended	ADJ
ejpam-6128	573	16	nonlinear	nonlinear	ADJ
ejpam-6128	573	17	schrödinger	schrödinger	ADJ
ejpam-6128	573	18	equation	equation	NOUN
ejpam-6128	573	19	in	in	ADP
ejpam-6128	573	20	an	an	DET
ejpam-6128	573	21	optical	optical	ADJ
ejpam-6128	573	22	fiber	fiber	NOUN
ejpam-6128	573	23	.	.	PUNCT
ejpam-6128	574	1	results	result	NOUN
ejpam-6128	574	2	in	in	ADP
ejpam-6128	574	3	physics	physics	NOUN
ejpam-6128	574	4	,	,	PUNCT
ejpam-6128	574	5	page	page	NOUN
ejpam-6128	574	6	104921	104921	NUM
ejpam-6128	574	7	,	,	PUNCT
ejpam-6128	574	8	2021	2021	NUM
ejpam-6128	574	9	.	.	PUNCT
ejpam-6128	575	1	[	[	X
ejpam-6128	575	2	2	2	NUM
ejpam-6128	575	3	]	]	X
ejpam-6128	575	4	k	k	PROPN
ejpam-6128	575	5	muhamad	muhamad	PROPN
ejpam-6128	575	6	,	,	PUNCT
ejpam-6128	575	7	t	t	PROPN
ejpam-6128	575	8	tanriverdi	tanriverdi	PROPN
ejpam-6128	575	9	,	,	PUNCT
ejpam-6128	575	10	a	a	DET
ejpam-6128	575	11	mahmud	mahmud	PROPN
ejpam-6128	575	12	,	,	PUNCT
ejpam-6128	575	13	and	and	CCONJ
ejpam-6128	575	14	h	h	NOUN
ejpam-6128	575	15	baskonus	baskonus	NOUN
ejpam-6128	575	16	.	.	PUNCT
ejpam-6128	576	1	interaction	interaction	NOUN
ejpam-6128	576	2	characteristics	characteristic	NOUN
ejpam-6128	576	3	of	of	ADP
ejpam-6128	576	4	the	the	DET
ejpam-6128	576	5	riemann	riemann	PROPN
ejpam-6128	576	6	wave	wave	PROPN
ejpam-6128	576	7	propagation	propagation	NOUN
ejpam-6128	576	8	in	in	ADP
ejpam-6128	576	9	the	the	DET
ejpam-6128	576	10	(	(	PUNCT
ejpam-6128	576	11	2	2	NUM
ejpam-6128	576	12	+	+	NUM
ejpam-6128	576	13	1)-dimensional	1)-dimensional	NUM
ejpam-6128	576	14	generalized	generalized	ADJ
ejpam-6128	576	15	breaking	break	VERB
ejpam-6128	576	16	soliton	soliton	NOUN
ejpam-6128	576	17	system	system	NOUN
ejpam-6128	576	18	.	.	PUNCT
ejpam-6128	577	1	int	int	NOUN
ejpam-6128	577	2	.	.	PUNCT
ejpam-6128	578	1	j.	j.	PROPN
ejpam-6128	578	2	comput	comput	PROPN
ejpam-6128	578	3	.	.	PUNCT
ejpam-6128	579	1	math	math	NOUN
ejpam-6128	579	2	.	.	PUNCT
ejpam-6128	579	3	,	,	PUNCT
ejpam-6128	579	4	100:1355	100:1355	NUM
ejpam-6128	579	5	,	,	PUNCT
ejpam-6128	579	6	2023	2023	NUM
ejpam-6128	579	7	.	.	PUNCT
ejpam-6128	580	1	[	[	X
ejpam-6128	580	2	3	3	X
ejpam-6128	580	3	]	]	X
ejpam-6128	580	4	p	p	X
ejpam-6128	580	5	olver	olver	NOUN
ejpam-6128	580	6	.	.	PUNCT
ejpam-6128	581	1	applications	application	NOUN
ejpam-6128	581	2	of	of	ADP
ejpam-6128	581	3	lie	lie	NOUN
ejpam-6128	581	4	groups	group	NOUN
ejpam-6128	581	5	to	to	PART
ejpam-6128	581	6	differential	differential	VERB
ejpam-6128	581	7	equations	equation	NOUN
ejpam-6128	581	8	.	.	PUNCT
ejpam-6128	582	1	springer	springer	NOUN
ejpam-6128	582	2	science	science	PROPN
ejpam-6128	582	3	&	&	CCONJ
ejpam-6128	582	4	business	business	NOUN
ejpam-6128	582	5	media	medium	NOUN
ejpam-6128	582	6	,	,	PUNCT
ejpam-6128	582	7	2000	2000	NUM
ejpam-6128	582	8	.	.	PUNCT
ejpam-6128	583	1	[	[	X
ejpam-6128	583	2	4	4	NUM
ejpam-6128	583	3	]	]	SYM
ejpam-6128	583	4	b	b	PROPN
ejpam-6128	583	5	kour	kour	NOUN
ejpam-6128	583	6	and	and	CCONJ
ejpam-6128	583	7	s	s	PROPN
ejpam-6128	583	8	kumar	kumar	PROPN
ejpam-6128	583	9	.	.	PROPN
ejpam-6128	583	10	symmetry	symmetry	PROPN
ejpam-6128	583	11	analysis	analysis	NOUN
ejpam-6128	583	12	,	,	PUNCT
ejpam-6128	583	13	explicit	explicit	ADJ
ejpam-6128	583	14	power	power	NOUN
ejpam-6128	583	15	series	series	NOUN
ejpam-6128	583	16	solutions	solution	NOUN
ejpam-6128	583	17	and	and	CCONJ
ejpam-6128	583	18	conservation	conservation	NOUN
ejpam-6128	583	19	laws	law	NOUN
ejpam-6128	583	20	of	of	ADP
ejpam-6128	583	21	the	the	DET
ejpam-6128	583	22	space	space	NOUN
ejpam-6128	583	23	-	-	PUNCT
ejpam-6128	583	24	time	time	NOUN
ejpam-6128	583	25	fractional	fractional	ADJ
ejpam-6128	583	26	variant	variant	ADJ
ejpam-6128	583	27	boussinesq	boussinesq	NOUN
ejpam-6128	583	28	system	system	NOUN
ejpam-6128	583	29	.	.	PUNCT
ejpam-6128	584	1	euro	euro	NOUN
ejpam-6128	584	2	.	.	PUNCT
ejpam-6128	585	1	phys	phy	NOUN
ejpam-6128	585	2	.	.	PUNCT
ejpam-6128	586	1	j.	j.	PROPN
ejpam-6128	586	2	plus	plus	PROPN
ejpam-6128	586	3	,	,	PUNCT
ejpam-6128	586	4	520:2018	520:2018	NUM
ejpam-6128	586	5	,	,	PUNCT
ejpam-6128	586	6	133	133	NUM
ejpam-6128	586	7	.	.	PUNCT
ejpam-6128	587	1	[	[	X
ejpam-6128	587	2	5	5	NUM
ejpam-6128	587	3	]	]	PUNCT
ejpam-6128	587	4	e	e	X
ejpam-6128	587	5	fan	fan	NOUN
ejpam-6128	587	6	and	and	CCONJ
ejpam-6128	587	7	h	h	PROPN
ejpam-6128	587	8	zhang	zhang	PROPN
ejpam-6128	587	9	.	.	PUNCT
ejpam-6128	588	1	a	a	DET
ejpam-6128	588	2	note	note	NOUN
ejpam-6128	588	3	on	on	ADP
ejpam-6128	588	4	the	the	DET
ejpam-6128	588	5	homogeneous	homogeneous	ADJ
ejpam-6128	588	6	balance	balance	NOUN
ejpam-6128	588	7	method	method	NOUN
ejpam-6128	588	8	.	.	PUNCT
ejpam-6128	589	1	physics	physics	NOUN
ejpam-6128	589	2	letters	letter	NOUN
ejpam-6128	589	3	a	a	PRON
ejpam-6128	589	4	,	,	PUNCT
ejpam-6128	589	5	1998	1998	NUM
ejpam-6128	589	6	.	.	PUNCT
ejpam-6128	590	1	[	[	X
ejpam-6128	590	2	6	6	NUM
ejpam-6128	590	3	]	]	PUNCT
ejpam-6128	590	4	a	a	DET
ejpam-6128	590	5	wazwaz	wazwaz	NOUN
ejpam-6128	590	6	.	.	PUNCT
ejpam-6128	591	1	the	the	DET
ejpam-6128	591	2	tan	tan	PROPN
ejpam-6128	591	3	h	h	NOUN
ejpam-6128	591	4	method	method	NOUN
ejpam-6128	591	5	:	:	PUNCT
ejpam-6128	591	6	solitons	soliton	NOUN
ejpam-6128	591	7	and	and	CCONJ
ejpam-6128	591	8	periodic	periodic	ADJ
ejpam-6128	591	9	solutions	solution	NOUN
ejpam-6128	591	10	for	for	ADP
ejpam-6128	591	11	the	the	DET
ejpam-6128	591	12	dodd	dodd	NOUN
ejpam-6128	591	13	–	–	PUNCT
ejpam-6128	591	14	bullough	bullough	ADJ
ejpam-6128	591	15	–	–	PUNCT
ejpam-6128	591	16	mikhailov	mikhailov	NOUN
ejpam-6128	591	17	and	and	CCONJ
ejpam-6128	591	18	the	the	DET
ejpam-6128	591	19	tzitzeica	tzitzeica	PROPN
ejpam-6128	591	20	–	–	PUNCT
ejpam-6128	591	21	dodd	dodd	NOUN
ejpam-6128	591	22	–	–	PUNCT
ejpam-6128	591	23	bullough	bullough	ADJ
ejpam-6128	591	24	equations	equation	NOUN
ejpam-6128	591	25	.	.	PUNCT
ejpam-6128	592	1	chaos	chaos	NOUN
ejpam-6128	592	2	,	,	PUNCT
ejpam-6128	592	3	solitons	soliton	NOUN
ejpam-6128	592	4	&	&	CCONJ
ejpam-6128	592	5	fractals	fractal	NOUN
ejpam-6128	592	6	,	,	PUNCT
ejpam-6128	592	7	2005	2005	NUM
ejpam-6128	592	8	.	.	PUNCT
ejpam-6128	593	1	[	[	X
ejpam-6128	593	2	7	7	NUM
ejpam-6128	593	3	]	]	X
ejpam-6128	593	4	h	h	PROPN
ejpam-6128	593	5	kumar	kumar	PROPN
ejpam-6128	593	6	,	,	PUNCT
ejpam-6128	593	7	a	a	DET
ejpam-6128	593	8	malik	malik	NOUN
ejpam-6128	593	9	,	,	PUNCT
ejpam-6128	593	10	and	and	CCONJ
ejpam-6128	593	11	f	f	PROPN
ejpam-6128	593	12	chand	chand	PROPN
ejpam-6128	593	13	.	.	PUNCT
ejpam-6128	594	1	analytical	analytical	ADJ
ejpam-6128	594	2	spatiotemporal	spatiotemporal	ADJ
ejpam-6128	594	3	soliton	soliton	NOUN
ejpam-6128	594	4	solutions	solution	NOUN
ejpam-6128	594	5	to	to	ADP
ejpam-6128	594	6	(	(	PUNCT
ejpam-6128	594	7	3	3	NUM
ejpam-6128	594	8	+	+	NUM
ejpam-6128	594	9	1)-dimensional	1)-dimensional	NUM
ejpam-6128	594	10	cubic	cubic	ADJ
ejpam-6128	594	11	-	-	PUNCT
ejpam-6128	594	12	quintic	quintic	ADJ
ejpam-6128	594	13	nonlinear	nonlinear	ADJ
ejpam-6128	594	14	schrödinger	schrödinger	ADJ
ejpam-6128	594	15	equation	equation	NOUN
ejpam-6128	594	16	with	with	ADP
ejpam-6128	594	17	distributed	distribute	VERB
ejpam-6128	594	18	coefficients	coefficient	NOUN
ejpam-6128	594	19	.	.	PUNCT
ejpam-6128	595	1	journal	journal	NOUN
ejpam-6128	595	2	of	of	ADP
ejpam-6128	595	3	mathematical	mathematical	ADJ
ejpam-6128	595	4	physics	physics	NOUN
ejpam-6128	595	5	,	,	PUNCT
ejpam-6128	595	6	2012	2012	NUM
ejpam-6128	595	7	.	.	PUNCT
ejpam-6128	596	1	[	[	X
ejpam-6128	596	2	8	8	NUM
ejpam-6128	596	3	]	]	X
ejpam-6128	596	4	m	m	VERB
ejpam-6128	596	5	bilal	bilal	PROPN
ejpam-6128	596	6	,	,	PUNCT
ejpam-6128	596	7	h	h	PROPN
ejpam-6128	596	8	haris	haris	PROPN
ejpam-6128	596	9	,	,	PUNCT
ejpam-6128	596	10	a	a	DET
ejpam-6128	596	11	waheed	waheed	NOUN
ejpam-6128	596	12	,	,	PUNCT
ejpam-6128	596	13	and	and	CCONJ
ejpam-6128	596	14	m	m	PROPN
ejpam-6128	596	15	faheem	faheem	NOUN
ejpam-6128	596	16	.	.	PUNCT
ejpam-6128	597	1	the	the	DET
ejpam-6128	597	2	analysis	analysis	NOUN
ejpam-6128	597	3	of	of	ADP
ejpam-6128	597	4	exact	exact	ADJ
ejpam-6128	597	5	solitons	soliton	NOUN
ejpam-6128	597	6	solutions	solution	NOUN
ejpam-6128	597	7	in	in	ADP
ejpam-6128	597	8	monomode	monomode	ADJ
ejpam-6128	597	9	optical	optical	ADJ
ejpam-6128	597	10	fibers	fiber	NOUN
ejpam-6128	597	11	to	to	ADP
ejpam-6128	597	12	the	the	DET
ejpam-6128	597	13	generalized	generalized	ADJ
ejpam-6128	597	14	nonlinear	nonlinear	ADJ
ejpam-6128	597	15	schrödinger	schrödinger	ADJ
ejpam-6128	597	16	system	system	NOUN
ejpam-6128	597	17	by	by	ADP
ejpam-6128	597	18	the	the	DET
ejpam-6128	597	19	compatible	compatible	ADJ
ejpam-6128	597	20	techniques	technique	NOUN
ejpam-6128	597	21	.	.	PUNCT
ejpam-6128	598	1	int	int	NOUN
ejpam-6128	598	2	.	.	PUNCT
ejpam-6128	599	1	j.	j.	PROPN
ejpam-6128	599	2	math	math	PROPN
ejpam-6128	599	3	.	.	PUNCT
ejpam-6128	600	1	comput	comput	NOUN
ejpam-6128	600	2	.	.	PUNCT
ejpam-6128	601	1	eng	eng	PROPN
ejpam-6128	601	2	.	.	PROPN
ejpam-6128	601	3	,	,	PUNCT
ejpam-6128	601	4	1:170	1:170	NUM
ejpam-6128	601	5	,	,	PUNCT
ejpam-6128	601	6	2023	2023	NUM
ejpam-6128	601	7	.	.	PUNCT
ejpam-6128	602	1	[	[	X
ejpam-6128	602	2	9	9	NUM
ejpam-6128	602	3	]	]	PUNCT
ejpam-6128	602	4	a	a	DET
ejpam-6128	602	5	kumar	kumar	PROPN
ejpam-6128	602	6	and	and	CCONJ
ejpam-6128	602	7	s	s	PROPN
ejpam-6128	602	8	kumar	kumar	PROPN
ejpam-6128	602	9	.	.	PUNCT
ejpam-6128	602	10	dynamic	dynamic	ADJ
ejpam-6128	602	11	nature	nature	NOUN
ejpam-6128	602	12	of	of	ADP
ejpam-6128	602	13	analytical	analytical	ADJ
ejpam-6128	602	14	soliton	soliton	NOUN
ejpam-6128	602	15	solutions	solution	NOUN
ejpam-6128	602	16	of	of	ADP
ejpam-6128	602	17	the	the	DET
ejpam-6128	602	18	(	(	PUNCT
ejpam-6128	602	19	1	1	NUM
ejpam-6128	602	20	+	+	NUM
ejpam-6128	602	21	1)-dimensional	1)-dimensional	ADJ
ejpam-6128	602	22	mikhailov	mikhailov	ADJ
ejpam-6128	602	23	-	-	PUNCT
ejpam-6128	602	24	novikov	novikov	NOUN
ejpam-6128	602	25	-	-	PUNCT
ejpam-6128	602	26	wang	wang	PROPN
ejpam-6128	602	27	equation	equation	NOUN
ejpam-6128	602	28	using	use	VERB
ejpam-6128	602	29	the	the	DET
ejpam-6128	602	30	unified	unified	ADJ
ejpam-6128	602	31	approach	approach	NOUN
ejpam-6128	602	32	.	.	PUNCT
ejpam-6128	603	1	int	int	NOUN
ejpam-6128	603	2	.	.	PUNCT
ejpam-6128	604	1	j.	j.	PROPN
ejpam-6128	604	2	math	math	PROPN
ejpam-6128	604	3	.	.	PUNCT
ejpam-6128	605	1	comput	comput	NOUN
ejpam-6128	605	2	.	.	PUNCT
ejpam-6128	606	1	eng	eng	PROPN
ejpam-6128	606	2	.	.	PROPN
ejpam-6128	606	3	,	,	PUNCT
ejpam-6128	606	4	2:228	2:228	NUM
ejpam-6128	606	5	,	,	PUNCT
ejpam-6128	606	6	2023	2023	NUM
ejpam-6128	606	7	.	.	PUNCT
ejpam-6128	607	1	[	[	X
ejpam-6128	607	2	10	10	NUM
ejpam-6128	607	3	]	]	X
ejpam-6128	607	4	e	e	X
ejpam-6128	607	5	zayed	zayed	NOUN
ejpam-6128	607	6	and	and	CCONJ
ejpam-6128	607	7	k	k	PROPN
ejpam-6128	607	8	alurrfi	alurrfi	PROPN
ejpam-6128	607	9	.	.	PUNCT
ejpam-6128	608	1	a	a	DET
ejpam-6128	608	2	new	new	ADJ
ejpam-6128	608	3	jacobi	jacobi	PROPN
ejpam-6128	608	4	elliptic	elliptic	ADJ
ejpam-6128	608	5	function	function	NOUN
ejpam-6128	608	6	expansion	expansion	NOUN
ejpam-6128	608	7	method	method	NOUN
ejpam-6128	608	8	for	for	ADP
ejpam-6128	608	9	solving	solve	VERB
ejpam-6128	608	10	m.	m.	NOUN
ejpam-6128	608	11	usman	usman	PROPN
ejpam-6128	608	12	,	,	PUNCT
ejpam-6128	608	13	a.	a.	NOUN
ejpam-6128	608	14	hussain	hussain	PROPN
ejpam-6128	608	15	,	,	PUNCT
ejpam-6128	608	16	m.	m.	PROPN
ejpam-6128	608	17	u.	u.	PROPN
ejpam-6128	608	18	farooq	farooq	PROPN
ejpam-6128	608	19	,	,	PUNCT
ejpam-6128	608	20	j.	j.	PROPN
ejpam-6128	608	21	herrera	herrera	PROPN
ejpam-6128	608	22	/	/	SYM
ejpam-6128	608	23	eur	eur	PROPN
ejpam-6128	608	24	.	.	PUNCT
ejpam-6128	609	1	j.	j.	PROPN
ejpam-6128	609	2	pure	pure	PROPN
ejpam-6128	609	3	appl	appl	PROPN
ejpam-6128	609	4	.	.	PROPN
ejpam-6128	609	5	math	math	PROPN
ejpam-6128	609	6	,	,	PUNCT
ejpam-6128	609	7	18	18	NUM
ejpam-6128	609	8	(	(	PUNCT
ejpam-6128	609	9	4	4	NUM
ejpam-6128	609	10	)	)	PUNCT
ejpam-6128	609	11	(	(	PUNCT
ejpam-6128	609	12	2025	2025	NUM
ejpam-6128	609	13	)	)	PUNCT
ejpam-6128	609	14	,	,	PUNCT
ejpam-6128	609	15	6128	6128	NUM
ejpam-6128	609	16	28	28	NUM
ejpam-6128	609	17	of	of	ADP
ejpam-6128	609	18	29	29	NUM
ejpam-6128	609	19	a	a	DET
ejpam-6128	609	20	nonlinear	nonlinear	ADJ
ejpam-6128	609	21	pde	pde	NOUN
ejpam-6128	609	22	describing	describe	VERB
ejpam-6128	609	23	the	the	DET
ejpam-6128	609	24	nonlinear	nonlinear	ADJ
ejpam-6128	609	25	low	low	ADJ
ejpam-6128	609	26	-	-	PUNCT
ejpam-6128	609	27	pass	pass	NOUN
ejpam-6128	609	28	electrical	electrical	ADJ
ejpam-6128	609	29	lines	line	NOUN
ejpam-6128	609	30	.	.	PUNCT
ejpam-6128	610	1	chaos	chaos	NOUN
ejpam-6128	610	2	solitons	soliton	NOUN
ejpam-6128	610	3	and	and	CCONJ
ejpam-6128	610	4	fractals	fractal	NOUN
ejpam-6128	610	5	,	,	PUNCT
ejpam-6128	610	6	78:55	78:55	NUM
ejpam-6128	610	7	,	,	PUNCT
ejpam-6128	610	8	2015	2015	NUM
ejpam-6128	610	9	.	.	PUNCT
ejpam-6128	611	1	[	[	X
ejpam-6128	611	2	11	11	NUM
ejpam-6128	611	3	]	]	X
ejpam-6128	611	4	l	l	NOUN
ejpam-6128	611	5	akinyemi	akinyemi	ADV
ejpam-6128	611	6	,	,	PUNCT
ejpam-6128	611	7	h	h	NOUN
ejpam-6128	611	8	rezazadeh	rezazadeh	PROPN
ejpam-6128	611	9	,	,	PUNCT
ejpam-6128	611	10	q	q	PROPN
ejpam-6128	611	11	shi	shi	PROPN
ejpam-6128	611	12	,	,	PUNCT
ejpam-6128	611	13	m	m	PROPN
ejpam-6128	611	14	inc	inc	PROPN
ejpam-6128	611	15	,	,	PUNCT
ejpam-6128	611	16	m	m	NOUN
ejpam-6128	611	17	khater	khater	ADJ
ejpam-6128	611	18	,	,	PUNCT
ejpam-6128	611	19	h	h	PROPN
ejpam-6128	611	20	ahmad	ahmad	PROPN
ejpam-6128	611	21	,	,	PUNCT
ejpam-6128	611	22	a	a	DET
ejpam-6128	611	23	jhangeer	jhangeer	NOUN
ejpam-6128	611	24	,	,	PUNCT
ejpam-6128	611	25	and	and	CCONJ
ejpam-6128	611	26	m	m	NOUN
ejpam-6128	611	27	akbar	akbar	NOUN
ejpam-6128	611	28	.	.	PUNCT
ejpam-6128	612	1	new	new	ADJ
ejpam-6128	612	2	optical	optical	ADJ
ejpam-6128	612	3	solitons	soliton	NOUN
ejpam-6128	612	4	of	of	ADP
ejpam-6128	612	5	perturbed	perturb	VERB
ejpam-6128	612	6	nonlinear	nonlinear	ADJ
ejpam-6128	612	7	schrödinger	schrödinger	ADJ
ejpam-6128	612	8	–	–	PUNCT
ejpam-6128	612	9	hirota	hirota	NOUN
ejpam-6128	612	10	equation	equation	NOUN
ejpam-6128	612	11	with	with	ADP
ejpam-6128	612	12	spatio	spatio	PROPN
ejpam-6128	612	13	-	-	PUNCT
ejpam-6128	612	14	temporal	temporal	ADJ
ejpam-6128	612	15	dispersion	dispersion	NOUN
ejpam-6128	612	16	.	.	PUNCT
ejpam-6128	613	1	results	result	NOUN
ejpam-6128	613	2	in	in	ADP
ejpam-6128	613	3	physics	physics	NOUN
ejpam-6128	613	4	,	,	PUNCT
ejpam-6128	613	5	29:104656	29:104656	NUM
ejpam-6128	613	6	,	,	PUNCT
ejpam-6128	613	7	2021	2021	NUM
ejpam-6128	613	8	.	.	PUNCT
ejpam-6128	614	1	[	[	X
ejpam-6128	614	2	12	12	NUM
ejpam-6128	614	3	]	]	X
ejpam-6128	614	4	s	s	PART
ejpam-6128	614	5	anco	anco	NOUN
ejpam-6128	614	6	and	and	CCONJ
ejpam-6128	614	7	g	g	PROPN
ejpam-6128	614	8	bluman	bluman	NOUN
ejpam-6128	614	9	.	.	PUNCT
ejpam-6128	615	1	direct	direct	ADJ
ejpam-6128	615	2	construction	construction	NOUN
ejpam-6128	615	3	method	method	NOUN
ejpam-6128	615	4	for	for	ADP
ejpam-6128	615	5	conservation	conservation	NOUN
ejpam-6128	615	6	laws	law	NOUN
ejpam-6128	615	7	of	of	ADP
ejpam-6128	615	8	partial	partial	ADJ
ejpam-6128	615	9	differential	differential	ADJ
ejpam-6128	615	10	equations	equation	NOUN
ejpam-6128	615	11	.	.	PUNCT
ejpam-6128	616	1	part	part	NOUN
ejpam-6128	617	1	i	i	NOUN
ejpam-6128	617	2	:	:	PUNCT
ejpam-6128	617	3	examples	example	NOUN
ejpam-6128	617	4	of	of	ADP
ejpam-6128	617	5	conservation	conservation	NOUN
ejpam-6128	617	6	law	law	NOUN
ejpam-6128	617	7	classifications	classification	NOUN
ejpam-6128	617	8	.	.	PUNCT
ejpam-6128	618	1	eur	eur	PROPN
ejpam-6128	618	2	j	j	PROPN
ejpam-6128	618	3	appl	appl	PROPN
ejpam-6128	618	4	math	math	PROPN
ejpam-6128	618	5	,	,	PUNCT
ejpam-6128	618	6	13:545–66	13:545–66	NOUN
ejpam-6128	618	7	,	,	PUNCT
ejpam-6128	618	8	2002	2002	NUM
ejpam-6128	618	9	.	.	PUNCT
ejpam-6128	619	1	[	[	X
ejpam-6128	619	2	13	13	NUM
ejpam-6128	619	3	]	]	X
ejpam-6128	619	4	w	w	PROPN
ejpam-6128	619	5	ames	ame	NOUN
ejpam-6128	619	6	,	,	PUNCT
ejpam-6128	619	7	r	r	NOUN
ejpam-6128	619	8	lohner	lohner	NOUN
ejpam-6128	619	9	,	,	PUNCT
ejpam-6128	619	10	and	and	CCONJ
ejpam-6128	619	11	e	e	PROPN
ejpam-6128	619	12	adams	adams	PROPN
ejpam-6128	619	13	.	.	PUNCT
ejpam-6128	620	1	group	group	NOUN
ejpam-6128	620	2	properties	property	NOUN
ejpam-6128	620	3	of	of	ADP
ejpam-6128	620	4	utt	utt	NOUN
ejpam-6128	620	5	=	=	SYM
ejpam-6128	620	6	(	(	PUNCT
ejpam-6128	620	7	f(u)ux)x	f(u)ux)x	NOUN
ejpam-6128	620	8	.	.	PUNCT
ejpam-6128	621	1	int	int	NOUN
ejpam-6128	621	2	.	.	PUNCT
ejpam-6128	622	1	j.	j.	PROPN
ejpam-6128	622	2	non	non	ADJ
ejpam-6128	622	3	-	-	ADJ
ejpam-6128	622	4	linear	linear	ADJ
ejpam-6128	622	5	mech	mech	NOUN
ejpam-6128	622	6	.	.	PUNCT
ejpam-6128	622	7	,	,	PUNCT
ejpam-6128	622	8	16:439–447	16:439–447	NUM
ejpam-6128	622	9	,	,	PUNCT
ejpam-6128	622	10	1981	1981	NUM
ejpam-6128	622	11	.	.	PUNCT
ejpam-6128	623	1	[	[	X
ejpam-6128	623	2	14	14	NUM
ejpam-6128	623	3	]	]	X
ejpam-6128	623	4	g	g	PROPN
ejpam-6128	623	5	bluman	bluman	NOUN
ejpam-6128	623	6	and	and	CCONJ
ejpam-6128	623	7	a	a	DET
ejpam-6128	623	8	cheviakov	cheviakov	NOUN
ejpam-6128	623	9	.	.	PUNCT
ejpam-6128	624	1	nonlocally	nonlocally	ADV
ejpam-6128	624	2	related	relate	VERB
ejpam-6128	624	3	systems	system	NOUN
ejpam-6128	624	4	,	,	PUNCT
ejpam-6128	624	5	linearization	linearization	NOUN
ejpam-6128	624	6	and	and	CCONJ
ejpam-6128	624	7	nonlocal	nonlocal	ADJ
ejpam-6128	624	8	symmetries	symmetry	NOUN
ejpam-6128	624	9	for	for	ADP
ejpam-6128	624	10	the	the	DET
ejpam-6128	624	11	nonlinear	nonlinear	ADJ
ejpam-6128	624	12	wave	wave	NOUN
ejpam-6128	624	13	equation	equation	NOUN
ejpam-6128	624	14	.	.	PUNCT
ejpam-6128	625	1	journal	journal	PROPN
ejpam-6128	625	2	of	of	ADP
ejpam-6128	625	3	mathematical	mathematical	ADJ
ejpam-6128	625	4	analysis	analysis	NOUN
ejpam-6128	625	5	and	and	CCONJ
ejpam-6128	625	6	applications	application	NOUN
ejpam-6128	625	7	,	,	PUNCT
ejpam-6128	625	8	2007	2007	NUM
ejpam-6128	625	9	.	.	PUNCT
ejpam-6128	626	1	[	[	X
ejpam-6128	626	2	15	15	NUM
ejpam-6128	626	3	]	]	X
ejpam-6128	626	4	a	a	DET
ejpam-6128	626	5	raza	raza	NOUN
ejpam-6128	626	6	,	,	PUNCT
ejpam-6128	626	7	f	f	PROPN
ejpam-6128	626	8	mahomed	mahome	VERB
ejpam-6128	626	9	,	,	PUNCT
ejpam-6128	626	10	f	f	PROPN
ejpam-6128	626	11	zaman	zaman	PROPN
ejpam-6128	626	12	,	,	PUNCT
ejpam-6128	626	13	and	and	CCONJ
ejpam-6128	626	14	a	a	DET
ejpam-6128	626	15	kara	kara	NOUN
ejpam-6128	626	16	.	.	PUNCT
ejpam-6128	627	1	optimal	optimal	ADJ
ejpam-6128	627	2	system	system	NOUN
ejpam-6128	627	3	and	and	CCONJ
ejpam-6128	627	4	classification	classification	NOUN
ejpam-6128	627	5	of	of	ADP
ejpam-6128	627	6	invariant	invariant	ADJ
ejpam-6128	627	7	solutions	solution	NOUN
ejpam-6128	627	8	of	of	ADP
ejpam-6128	627	9	nonlinear	nonlinear	ADJ
ejpam-6128	627	10	class	class	NOUN
ejpam-6128	627	11	of	of	ADP
ejpam-6128	627	12	wave	wave	NOUN
ejpam-6128	627	13	equations	equation	NOUN
ejpam-6128	627	14	and	and	CCONJ
ejpam-6128	627	15	their	their	PRON
ejpam-6128	627	16	conservation	conservation	NOUN
ejpam-6128	627	17	laws	law	NOUN
ejpam-6128	627	18	.	.	PUNCT
ejpam-6128	628	1	journal	journal	NOUN
ejpam-6128	628	2	of	of	ADP
ejpam-6128	628	3	mathematical	mathematical	ADJ
ejpam-6128	628	4	analysis	analysis	NOUN
ejpam-6128	628	5	and	and	CCONJ
ejpam-6128	628	6	applications	application	NOUN
ejpam-6128	628	7	,	,	PUNCT
ejpam-6128	628	8	2022	2022	NUM
ejpam-6128	628	9	.	.	PUNCT
ejpam-6128	629	1	[	[	X
ejpam-6128	629	2	16	16	NUM
ejpam-6128	629	3	]	]	X
ejpam-6128	629	4	u	u	PROPN
ejpam-6128	629	5	ali	ali	PROPN
ejpam-6128	629	6	,	,	PUNCT
ejpam-6128	629	7	a	a	DET
ejpam-6128	629	8	bokhari	bokhari	NOUN
ejpam-6128	629	9	,	,	PUNCT
ejpam-6128	629	10	a	a	DET
ejpam-6128	629	11	kara	kara	NOUN
ejpam-6128	629	12	,	,	PUNCT
ejpam-6128	629	13	and	and	CCONJ
ejpam-6128	629	14	f	f	PROPN
ejpam-6128	629	15	zaman	zaman	PROPN
ejpam-6128	629	16	.	.	PUNCT
ejpam-6128	630	1	on	on	ADP
ejpam-6128	630	2	the	the	DET
ejpam-6128	630	3	symmetries	symmetry	NOUN
ejpam-6128	630	4	and	and	CCONJ
ejpam-6128	630	5	conservation	conservation	NOUN
ejpam-6128	630	6	laws	law	NOUN
ejpam-6128	630	7	of	of	ADP
ejpam-6128	630	8	the	the	DET
ejpam-6128	630	9	multidimensional	multidimensional	ADJ
ejpam-6128	630	10	nonlinear	nonlinear	ADJ
ejpam-6128	630	11	damped	damp	VERB
ejpam-6128	630	12	wave	wave	NOUN
ejpam-6128	630	13	equations	equation	NOUN
ejpam-6128	630	14	.	.	PUNCT
ejpam-6128	631	1	advances	advance	NOUN
ejpam-6128	631	2	in	in	ADP
ejpam-6128	631	3	mathematical	mathematical	ADJ
ejpam-6128	631	4	physics	physics	NOUN
ejpam-6128	631	5	,	,	PUNCT
ejpam-6128	631	6	2017	2017	NUM
ejpam-6128	631	7	.	.	PUNCT
ejpam-6128	632	1	[	[	X
ejpam-6128	632	2	17	17	NUM
ejpam-6128	632	3	]	]	X
ejpam-6128	632	4	u	u	PROPN
ejpam-6128	632	5	ali	ali	PROPN
ejpam-6128	632	6	,	,	PUNCT
ejpam-6128	632	7	a	a	DET
ejpam-6128	632	8	bokhari	bokhari	NOUN
ejpam-6128	632	9	,	,	PUNCT
ejpam-6128	632	10	a	a	DET
ejpam-6128	632	11	kara	kara	NOUN
ejpam-6128	632	12	,	,	PUNCT
ejpam-6128	632	13	and	and	CCONJ
ejpam-6128	632	14	f	f	PROPN
ejpam-6128	632	15	zaman	zaman	PROPN
ejpam-6128	632	16	.	.	PROPN
ejpam-6128	632	17	symmetry	symmetry	NOUN
ejpam-6128	632	18	analysis	analysis	NOUN
ejpam-6128	632	19	and	and	CCONJ
ejpam-6128	632	20	exact	exact	ADJ
ejpam-6128	632	21	solutions	solution	NOUN
ejpam-6128	632	22	of	of	ADP
ejpam-6128	632	23	the	the	DET
ejpam-6128	632	24	damped	damp	VERB
ejpam-6128	632	25	wave	wave	NOUN
ejpam-6128	632	26	equation	equation	NOUN
ejpam-6128	632	27	on	on	ADP
ejpam-6128	632	28	the	the	DET
ejpam-6128	632	29	surface	surface	NOUN
ejpam-6128	632	30	of	of	ADP
ejpam-6128	632	31	the	the	DET
ejpam-6128	632	32	sphere	sphere	NOUN
ejpam-6128	632	33	.	.	PUNCT
ejpam-6128	633	1	advances	advance	NOUN
ejpam-6128	633	2	in	in	ADP
ejpam-6128	633	3	differential	differential	ADJ
ejpam-6128	633	4	equations	equation	NOUN
ejpam-6128	633	5	and	and	CCONJ
ejpam-6128	633	6	control	control	NOUN
ejpam-6128	633	7	processes	process	NOUN
ejpam-6128	633	8	,	,	PUNCT
ejpam-6128	633	9	2016	2016	NUM
ejpam-6128	633	10	.	.	PUNCT
ejpam-6128	634	1	[	[	X
ejpam-6128	634	2	18	18	NUM
ejpam-6128	634	3	]	]	X
ejpam-6128	634	4	w	w	NOUN
ejpam-6128	634	5	ahmed	ahmed	PROPN
ejpam-6128	634	6	,	,	PUNCT
ejpam-6128	634	7	f	f	PROPN
ejpam-6128	634	8	zaman	zaman	PROPN
ejpam-6128	634	9	,	,	PUNCT
ejpam-6128	634	10	and	and	CCONJ
ejpam-6128	634	11	k	k	PROPN
ejpam-6128	634	12	saleh	saleh	NOUN
ejpam-6128	634	13	.	.	PUNCT
ejpam-6128	635	1	invariant	invariant	ADJ
ejpam-6128	635	2	solutions	solution	NOUN
ejpam-6128	635	3	for	for	ADP
ejpam-6128	635	4	a	a	DET
ejpam-6128	635	5	class	class	NOUN
ejpam-6128	635	6	of	of	ADP
ejpam-6128	635	7	perturbed	perturb	VERB
ejpam-6128	635	8	nonlinear	nonlinear	ADJ
ejpam-6128	635	9	wave	wave	NOUN
ejpam-6128	635	10	equations	equation	NOUN
ejpam-6128	635	11	.	.	PUNCT
ejpam-6128	636	1	mathematics	mathematic	NOUN
ejpam-6128	636	2	,	,	PUNCT
ejpam-6128	636	3	2017	2017	NUM
ejpam-6128	636	4	.	.	PUNCT
ejpam-6128	637	1	[	[	X
ejpam-6128	637	2	19	19	NUM
ejpam-6128	637	3	]	]	X
ejpam-6128	637	4	u	u	PROPN
ejpam-6128	637	5	ali	ali	PROPN
ejpam-6128	637	6	,	,	PUNCT
ejpam-6128	637	7	a	a	DET
ejpam-6128	637	8	bokhari	bokhari	NOUN
ejpam-6128	637	9	,	,	PUNCT
ejpam-6128	637	10	a	a	DET
ejpam-6128	637	11	kara	kara	NOUN
ejpam-6128	637	12	,	,	PUNCT
ejpam-6128	637	13	and	and	CCONJ
ejpam-6128	637	14	f	f	PROPN
ejpam-6128	637	15	zaman	zaman	PROPN
ejpam-6128	637	16	.	.	PUNCT
ejpam-6128	638	1	invariance	invariance	NOUN
ejpam-6128	638	2	properties	property	NOUN
ejpam-6128	638	3	and	and	CCONJ
ejpam-6128	638	4	conservation	conservation	NOUN
ejpam-6128	638	5	laws	law	NOUN
ejpam-6128	638	6	of	of	ADP
ejpam-6128	638	7	the	the	DET
ejpam-6128	638	8	nonlinear	nonlinear	ADJ
ejpam-6128	638	9	damped	damp	VERB
ejpam-6128	638	10	wave	wave	NOUN
ejpam-6128	638	11	equation	equation	NOUN
ejpam-6128	638	12	with	with	ADP
ejpam-6128	638	13	power	power	NOUN
ejpam-6128	638	14	law	law	NOUN
ejpam-6128	638	15	nonlinearities	nonlinearitie	NOUN
ejpam-6128	638	16	.	.	PUNCT
ejpam-6128	639	1	results	result	NOUN
ejpam-6128	639	2	in	in	ADP
ejpam-6128	639	3	physics	physics	NOUN
ejpam-6128	639	4	,	,	PUNCT
ejpam-6128	639	5	2017	2017	NUM
ejpam-6128	639	6	.	.	PUNCT
ejpam-6128	640	1	[	[	X
ejpam-6128	640	2	20	20	NUM
ejpam-6128	640	3	]	]	PUNCT
ejpam-6128	640	4	a	a	DET
ejpam-6128	640	5	ahmad	ahmad	PROPN
ejpam-6128	640	6	,	,	PUNCT
ejpam-6128	640	7	a	a	DET
ejpam-6128	640	8	bokhari	bokhari	NOUN
ejpam-6128	640	9	,	,	PUNCT
ejpam-6128	640	10	a	a	DET
ejpam-6128	640	11	kara	kara	NOUN
ejpam-6128	640	12	,	,	PUNCT
ejpam-6128	640	13	and	and	CCONJ
ejpam-6128	640	14	f	f	PROPN
ejpam-6128	640	15	zaman	zaman	PROPN
ejpam-6128	640	16	.	.	PUNCT
ejpam-6128	641	1	a	a	DET
ejpam-6128	641	2	complete	complete	ADJ
ejpam-6128	641	3	symmetry	symmetry	NOUN
ejpam-6128	641	4	classification	classification	NOUN
ejpam-6128	641	5	and	and	CCONJ
ejpam-6128	641	6	reduction	reduction	NOUN
ejpam-6128	641	7	of	of	ADP
ejpam-6128	641	8	some	some	DET
ejpam-6128	641	9	classes	class	NOUN
ejpam-6128	641	10	of	of	ADP
ejpam-6128	641	11	the	the	DET
ejpam-6128	641	12	nonlinear	nonlinear	ADJ
ejpam-6128	641	13	(	(	PUNCT
ejpam-6128	641	14	1	1	NUM
ejpam-6128	641	15	-	-	SYM
ejpam-6128	641	16	2	2	NUM
ejpam-6128	641	17	)	)	PUNCT
ejpam-6128	641	18	wave	wave	NOUN
ejpam-6128	641	19	equation	equation	NOUN
ejpam-6128	641	20	.	.	PUNCT
ejpam-6128	642	1	quaestiones	quaestione	NOUN
ejpam-6128	642	2	mathematicae	mathematicae	PROPN
ejpam-6128	642	3	,	,	PUNCT
ejpam-6128	642	4	2010	2010	NUM
ejpam-6128	642	5	.	.	PUNCT
ejpam-6128	643	1	[	[	X
ejpam-6128	643	2	21	21	NUM
ejpam-6128	643	3	]	]	X
ejpam-6128	643	4	a	a	DET
ejpam-6128	643	5	bokhari	bokhari	NOUN
ejpam-6128	643	6	,	,	PUNCT
ejpam-6128	643	7	a	a	DET
ejpam-6128	643	8	al	al	PROPN
ejpam-6128	643	9	-	-	PUNCT
ejpam-6128	643	10	dweik	dweik	NOUN
ejpam-6128	643	11	,	,	PUNCT
ejpam-6128	643	12	a	a	DET
ejpam-6128	643	13	kara	kara	NOUN
ejpam-6128	643	14	,	,	PUNCT
ejpam-6128	643	15	m	m	PROPN
ejpam-6128	643	16	karim	karim	PROPN
ejpam-6128	643	17	,	,	PUNCT
ejpam-6128	643	18	and	and	CCONJ
ejpam-6128	643	19	f	f	PROPN
ejpam-6128	643	20	zaman	zaman	PROPN
ejpam-6128	643	21	.	.	PROPN
ejpam-6128	643	22	wave	wave	PROPN
ejpam-6128	643	23	equation	equation	NOUN
ejpam-6128	643	24	on	on	ADP
ejpam-6128	643	25	spherically	spherically	PROPN
ejpam-6128	643	26	symmetric	symmetric	ADJ
ejpam-6128	643	27	lorentzian	lorentzian	ADJ
ejpam-6128	643	28	metrics	metric	NOUN
ejpam-6128	643	29	.	.	PUNCT
ejpam-6128	644	1	journal	journal	PROPN
ejpam-6128	644	2	of	of	ADP
ejpam-6128	644	3	mathematical	mathematical	ADJ
ejpam-6128	644	4	physics	physics	NOUN
ejpam-6128	644	5	,	,	PUNCT
ejpam-6128	644	6	2011	2011	NUM
ejpam-6128	644	7	.	.	PUNCT
ejpam-6128	645	1	[	[	X
ejpam-6128	645	2	22	22	NUM
ejpam-6128	645	3	]	]	X
ejpam-6128	645	4	a	a	DET
ejpam-6128	645	5	hussain	hussain	PROPN
ejpam-6128	645	6	,	,	PUNCT
ejpam-6128	645	7	m	m	PROPN
ejpam-6128	645	8	usman	usman	PROPN
ejpam-6128	645	9	,	,	PUNCT
ejpam-6128	645	10	f	f	PROPN
ejpam-6128	645	11	zaman	zaman	PROPN
ejpam-6128	645	12	,	,	PUNCT
ejpam-6128	645	13	and	and	CCONJ
ejpam-6128	645	14	a	a	DET
ejpam-6128	645	15	zidan	zidan	PROPN
ejpam-6128	645	16	.	.	PUNCT
ejpam-6128	646	1	lie	lie	PROPN
ejpam-6128	646	2	group	group	NOUN
ejpam-6128	646	3	analysis	analysis	NOUN
ejpam-6128	646	4	and	and	CCONJ
ejpam-6128	646	5	its	its	PRON
ejpam-6128	646	6	invariants	invariant	NOUN
ejpam-6128	646	7	for	for	ADP
ejpam-6128	646	8	the	the	DET
ejpam-6128	646	9	class	class	NOUN
ejpam-6128	646	10	of	of	ADP
ejpam-6128	646	11	multidimensional	multidimensional	ADJ
ejpam-6128	646	12	nonlinear	nonlinear	ADJ
ejpam-6128	646	13	wave	wave	NOUN
ejpam-6128	646	14	equations	equation	NOUN
ejpam-6128	646	15	.	.	PUNCT
ejpam-6128	647	1	nonlinear	nonlinear	ADJ
ejpam-6128	647	2	analysis	analysis	NOUN
ejpam-6128	647	3	:	:	PUNCT
ejpam-6128	647	4	modelling	modelling	NOUN
ejpam-6128	647	5	and	and	CCONJ
ejpam-6128	647	6	control	control	NOUN
ejpam-6128	647	7	,	,	PUNCT
ejpam-6128	647	8	29:1161–79	29:1161–79	ADV
ejpam-6128	647	9	,	,	PUNCT
ejpam-6128	647	10	2024	2024	NUM
ejpam-6128	647	11	.	.	PUNCT
ejpam-6128	648	1	[	[	X
ejpam-6128	648	2	23	23	NUM
ejpam-6128	648	3	]	]	PUNCT
ejpam-6128	648	4	a	a	DET
ejpam-6128	648	5	bokhari	bokhari	NOUN
ejpam-6128	648	6	,	,	PUNCT
ejpam-6128	648	7	a	a	DET
ejpam-6128	648	8	al	al	PROPN
ejpam-6128	648	9	-	-	PUNCT
ejpam-6128	648	10	dweik	dweik	NOUN
ejpam-6128	648	11	,	,	PUNCT
ejpam-6128	648	12	a	a	DET
ejpam-6128	648	13	kara	kara	NOUN
ejpam-6128	648	14	,	,	PUNCT
ejpam-6128	648	15	f	f	PROPN
ejpam-6128	648	16	mahomed	mahome	VERB
ejpam-6128	648	17	,	,	PUNCT
ejpam-6128	648	18	and	and	CCONJ
ejpam-6128	648	19	f	f	PROPN
ejpam-6128	648	20	zaman	zaman	PROPN
ejpam-6128	648	21	.	.	PUNCT
ejpam-6128	649	1	double	double	ADJ
ejpam-6128	649	2	reduction	reduction	NOUN
ejpam-6128	649	3	of	of	ADP
ejpam-6128	649	4	a	a	DET
ejpam-6128	649	5	nonlinear	nonlinear	NOUN
ejpam-6128	649	6	(	(	PUNCT
ejpam-6128	649	7	2	2	NUM
ejpam-6128	649	8	+	+	NUM
ejpam-6128	649	9	1	1	NUM
ejpam-6128	649	10	)	)	PUNCT
ejpam-6128	649	11	wave	wave	NOUN
ejpam-6128	649	12	equation	equation	NOUN
ejpam-6128	649	13	via	via	ADP
ejpam-6128	649	14	conservation	conservation	NOUN
ejpam-6128	649	15	laws	law	NOUN
ejpam-6128	649	16	.	.	PUNCT
ejpam-6128	650	1	communications	communication	NOUN
ejpam-6128	650	2	in	in	ADP
ejpam-6128	650	3	nonlinear	nonlinear	ADJ
ejpam-6128	650	4	science	science	NOUN
ejpam-6128	650	5	and	and	CCONJ
ejpam-6128	650	6	numerical	numerical	PROPN
ejpam-6128	650	7	simulation	simulation	PROPN
ejpam-6128	650	8	,	,	PUNCT
ejpam-6128	650	9	2011	2011	NUM
ejpam-6128	650	10	.	.	PUNCT
ejpam-6128	651	1	[	[	X
ejpam-6128	651	2	24	24	NUM
ejpam-6128	651	3	]	]	X
ejpam-6128	651	4	s	s	PART
ejpam-6128	651	5	al	al	PROPN
ejpam-6128	651	6	-	-	PUNCT
ejpam-6128	651	7	omari	omari	PROPN
ejpam-6128	651	8	,	,	PUNCT
ejpam-6128	651	9	f	f	PROPN
ejpam-6128	651	10	zaman	zaman	PROPN
ejpam-6128	651	11	,	,	PUNCT
ejpam-6128	651	12	and	and	CCONJ
ejpam-6128	651	13	h	h	PROPN
ejpam-6128	651	14	azad	azad	PROPN
ejpam-6128	651	15	.	.	PUNCT
ejpam-6128	652	1	lie	lie	PROPN
ejpam-6128	652	2	symmetries	symmetry	NOUN
ejpam-6128	652	3	,	,	PUNCT
ejpam-6128	652	4	optimal	optimal	ADJ
ejpam-6128	652	5	system	system	NOUN
ejpam-6128	652	6	and	and	CCONJ
ejpam-6128	652	7	invariant	invariant	ADJ
ejpam-6128	652	8	reductions	reduction	NOUN
ejpam-6128	652	9	to	to	ADP
ejpam-6128	652	10	a	a	DET
ejpam-6128	652	11	nonlinear	nonlinear	ADJ
ejpam-6128	652	12	timoshenko	timoshenko	ADJ
ejpam-6128	652	13	system	system	NOUN
ejpam-6128	652	14	.	.	PUNCT
ejpam-6128	653	1	mathematics	mathematic	NOUN
ejpam-6128	653	2	,	,	PUNCT
ejpam-6128	653	3	2017	2017	NUM
ejpam-6128	653	4	.	.	PUNCT
ejpam-6128	654	1	[	[	X
ejpam-6128	654	2	25	25	NUM
ejpam-6128	654	3	]	]	X
ejpam-6128	654	4	r	r	NOUN
ejpam-6128	654	5	naz	naz	PROPN
ejpam-6128	654	6	,	,	PUNCT
ejpam-6128	654	7	f	f	PROPN
ejpam-6128	654	8	mahomed	mahome	VERB
ejpam-6128	654	9	,	,	PUNCT
ejpam-6128	654	10	and	and	CCONJ
ejpam-6128	654	11	d	d	PROPN
ejpam-6128	654	12	mason	mason	PROPN
ejpam-6128	654	13	.	.	PUNCT
ejpam-6128	655	1	comparison	comparison	NOUN
ejpam-6128	655	2	of	of	ADP
ejpam-6128	655	3	different	different	ADJ
ejpam-6128	655	4	approaches	approach	NOUN
ejpam-6128	655	5	to	to	ADP
ejpam-6128	655	6	conservation	conservation	NOUN
ejpam-6128	655	7	laws	law	NOUN
ejpam-6128	655	8	for	for	ADP
ejpam-6128	655	9	some	some	DET
ejpam-6128	655	10	partial	partial	ADJ
ejpam-6128	655	11	differential	differential	ADJ
ejpam-6128	655	12	equations	equation	NOUN
ejpam-6128	655	13	in	in	ADP
ejpam-6128	655	14	fluid	fluid	ADJ
ejpam-6128	655	15	mechanics	mechanic	NOUN
ejpam-6128	655	16	.	.	PUNCT
ejpam-6128	656	1	applied	apply	VERB
ejpam-6128	656	2	mathematics	mathematic	NOUN
ejpam-6128	656	3	and	and	CCONJ
ejpam-6128	656	4	computation	computation	NOUN
ejpam-6128	656	5	,	,	PUNCT
ejpam-6128	656	6	2008	2008	NUM
ejpam-6128	656	7	.	.	PUNCT
ejpam-6128	657	1	m.	m.	PROPN
ejpam-6128	657	2	usman	usman	PROPN
ejpam-6128	657	3	,	,	PUNCT
ejpam-6128	657	4	a.	a.	NOUN
ejpam-6128	657	5	hussain	hussain	PROPN
ejpam-6128	657	6	,	,	PUNCT
ejpam-6128	657	7	m.	m.	PROPN
ejpam-6128	657	8	u.	u.	PROPN
ejpam-6128	657	9	farooq	farooq	PROPN
ejpam-6128	657	10	,	,	PUNCT
ejpam-6128	657	11	j.	j.	PROPN
ejpam-6128	657	12	herrera	herrera	PROPN
ejpam-6128	657	13	/	/	SYM
ejpam-6128	657	14	eur	eur	PROPN
ejpam-6128	657	15	.	.	PUNCT
ejpam-6128	658	1	j.	j.	PROPN
ejpam-6128	658	2	pure	pure	PROPN
ejpam-6128	658	3	appl	appl	PROPN
ejpam-6128	658	4	.	.	PROPN
ejpam-6128	658	5	math	math	PROPN
ejpam-6128	658	6	,	,	PUNCT
ejpam-6128	658	7	18	18	NUM
ejpam-6128	658	8	(	(	PUNCT
ejpam-6128	658	9	4	4	NUM
ejpam-6128	658	10	)	)	PUNCT
ejpam-6128	658	11	(	(	PUNCT
ejpam-6128	658	12	2025	2025	NUM
ejpam-6128	658	13	)	)	PUNCT
ejpam-6128	658	14	,	,	PUNCT
ejpam-6128	658	15	6128	6128	NUM
ejpam-6128	658	16	29	29	NUM
ejpam-6128	658	17	of	of	ADP
ejpam-6128	658	18	29	29	NUM
ejpam-6128	659	1	[	[	SYM
ejpam-6128	659	2	26	26	NUM
ejpam-6128	659	3	]	]	PUNCT
ejpam-6128	659	4	n	n	CCONJ
ejpam-6128	659	5	ibragimov	ibragimov	ADJ
ejpam-6128	659	6	and	and	CCONJ
ejpam-6128	659	7	e	e	NOUN
ejpam-6128	659	8	avdonina	avdonina	NOUN
ejpam-6128	659	9	.	.	PUNCT
ejpam-6128	660	1	nonlinear	nonlinear	ADJ
ejpam-6128	660	2	self	self	NOUN
ejpam-6128	660	3	-	-	PUNCT
ejpam-6128	660	4	adjointness	adjointness	NOUN
ejpam-6128	660	5	,	,	PUNCT
ejpam-6128	660	6	conservation	conservation	NOUN
ejpam-6128	660	7	laws	law	NOUN
ejpam-6128	660	8	,	,	PUNCT
ejpam-6128	660	9	and	and	CCONJ
ejpam-6128	660	10	the	the	DET
ejpam-6128	660	11	construction	construction	NOUN
ejpam-6128	660	12	of	of	ADP
ejpam-6128	660	13	solutions	solution	NOUN
ejpam-6128	660	14	of	of	ADP
ejpam-6128	660	15	partial	partial	ADJ
ejpam-6128	660	16	differential	differential	ADJ
ejpam-6128	660	17	equations	equation	NOUN
ejpam-6128	660	18	using	use	VERB
ejpam-6128	660	19	conservation	conservation	NOUN
ejpam-6128	660	20	laws	law	NOUN
ejpam-6128	660	21	.	.	PUNCT
ejpam-6128	661	1	russian	russian	ADJ
ejpam-6128	661	2	mathematical	mathematical	ADJ
ejpam-6128	661	3	surveys	survey	NOUN
ejpam-6128	661	4	,	,	PUNCT
ejpam-6128	661	5	page	page	NOUN
ejpam-6128	661	6	889	889	NUM
ejpam-6128	661	7	,	,	PUNCT
ejpam-6128	661	8	2013	2013	NUM
ejpam-6128	661	9	.	.	PUNCT
ejpam-6128	662	1	[	[	X
ejpam-6128	662	2	27	27	NUM
ejpam-6128	662	3	]	]	PUNCT
ejpam-6128	662	4	n	n	CCONJ
ejpam-6128	662	5	ibragimov	ibragimov	NOUN
ejpam-6128	662	6	.	.	PUNCT
ejpam-6128	663	1	conservation	conservation	NOUN
ejpam-6128	663	2	laws	law	NOUN
ejpam-6128	663	3	and	and	CCONJ
ejpam-6128	663	4	non	non	ADJ
ejpam-6128	663	5	-	-	ADJ
ejpam-6128	663	6	invariant	invariant	ADJ
ejpam-6128	663	7	solutions	solution	NOUN
ejpam-6128	663	8	of	of	ADP
ejpam-6128	663	9	anisotropic	anisotropic	NOUN
ejpam-6128	663	10	wave	wave	NOUN
ejpam-6128	663	11	equations	equation	NOUN
ejpam-6128	663	12	with	with	ADP
ejpam-6128	663	13	a	a	DET
ejpam-6128	663	14	source	source	NOUN
ejpam-6128	663	15	.	.	PUNCT
ejpam-6128	664	1	nonlinear	nonlinear	ADJ
ejpam-6128	664	2	analysis	analysis	NOUN
ejpam-6128	664	3	:	:	PUNCT
ejpam-6128	664	4	real	real	ADJ
ejpam-6128	664	5	world	world	NOUN
ejpam-6128	664	6	applications	application	NOUN
ejpam-6128	664	7	,	,	PUNCT
ejpam-6128	664	8	pages	page	NOUN
ejpam-6128	664	9	82–94	82–94	NUM
ejpam-6128	664	10	,	,	PUNCT
ejpam-6128	664	11	2018	2018	NUM
ejpam-6128	664	12	.	.	PUNCT