id	sid	tid	token	lemma	pos
ejpam-5979	1	1	european	european	PROPN
ejpam-5979	1	2	journal	journal	PROPN
ejpam-5979	1	3	of	of	ADP
ejpam-5979	1	4	pure	pure	ADJ
ejpam-5979	1	5	and	and	CCONJ
ejpam-5979	1	6	applied	applied	ADJ
ejpam-5979	1	7	mathematics	mathematic	NOUN
ejpam-5979	1	8	2025	2025	NUM
ejpam-5979	1	9	,	,	PUNCT
ejpam-5979	1	10	vol	vol	NOUN
ejpam-5979	1	11	.	.	PROPN
ejpam-5979	1	12	18	18	NUM
ejpam-5979	1	13	,	,	PUNCT
ejpam-5979	1	14	issue	issue	NOUN
ejpam-5979	1	15	2	2	NUM
ejpam-5979	1	16	,	,	PUNCT
ejpam-5979	1	17	article	article	NOUN
ejpam-5979	1	18	number	number	NOUN
ejpam-5979	1	19	5979	5979	NUM
ejpam-5979	1	20	issn	issn	PROPN
ejpam-5979	1	21	1307	1307	NUM
ejpam-5979	1	22	-	-	SYM
ejpam-5979	1	23	5543	5543	NUM
ejpam-5979	1	24	–	–	PUNCT
ejpam-5979	1	25	ejpam.com	ejpam.com	X
ejpam-5979	1	26	published	publish	VERB
ejpam-5979	1	27	by	by	ADP
ejpam-5979	1	28	new	new	PROPN
ejpam-5979	1	29	york	york	PROPN
ejpam-5979	1	30	business	business	PROPN
ejpam-5979	1	31	global	global	ADJ
ejpam-5979	1	32	unique	unique	ADJ
ejpam-5979	1	33	solution	solution	NOUN
ejpam-5979	1	34	analysis	analysis	NOUN
ejpam-5979	1	35	for	for	ADP
ejpam-5979	1	36	generalized	generalized	ADJ
ejpam-5979	1	37	caputo	caputo	NOUN
ejpam-5979	1	38	-	-	PUNCT
ejpam-5979	1	39	type	type	NOUN
ejpam-5979	1	40	fractional	fractional	ADJ
ejpam-5979	1	41	bvp	bvp	NOUN
ejpam-5979	1	42	via	via	ADP
ejpam-5979	1	43	banach	banach	NOUN
ejpam-5979	1	44	contraction	contraction	NOUN
ejpam-5979	1	45	zouaoui	zouaoui	PROPN
ejpam-5979	2	1	bekri1,2	bekri1,2	PROPN
ejpam-5979	2	2	,	,	PUNCT
ejpam-5979	2	3	sarah	sarah	PROPN
ejpam-5979	2	4	aljohani3	aljohani3	PROPN
ejpam-5979	2	5	,	,	PUNCT
ejpam-5979	2	6	mohammad	mohammad	PROPN
ejpam-5979	2	7	esmael	esmael	PROPN
ejpam-5979	2	8	samei4	samei4	PROPN
ejpam-5979	2	9	,	,	PUNCT
ejpam-5979	2	10	ali	ali	PROPN
ejpam-5979	2	11	akgül5,6,7,8	akgül5,6,7,8	PROPN
ejpam-5979	2	12	,	,	PUNCT
ejpam-5979	2	13	abdelkader	abdelkader	PROPN
ejpam-5979	2	14	belhenniche9,10	belhenniche9,10	PROPN
ejpam-5979	2	15	,	,	PUNCT
ejpam-5979	2	16	ahmad	ahmad	PROPN
ejpam-5979	2	17	aloqaily3	aloqaily3	PROPN
ejpam-5979	2	18	,	,	PUNCT
ejpam-5979	2	19	nabil	nabil	PROPN
ejpam-5979	2	20	mlaiki3,∗	mlaiki3,∗	PROPN
ejpam-5979	2	21	1	1	NUM
ejpam-5979	2	22	laboratory	laboratory	NOUN
ejpam-5979	2	23	of	of	ADP
ejpam-5979	2	24	fundamental	fundamental	ADJ
ejpam-5979	2	25	and	and	CCONJ
ejpam-5979	2	26	applied	applied	ADJ
ejpam-5979	2	27	mathematics	mathematic	NOUN
ejpam-5979	2	28	,	,	PUNCT
ejpam-5979	2	29	university	university	NOUN
ejpam-5979	2	30	of	of	ADP
ejpam-5979	2	31	oran	oran	ADJ
ejpam-5979	2	32	1	1	NUM
ejpam-5979	2	33	,	,	PUNCT
ejpam-5979	2	34	ahmed	ahmed	PROPN
ejpam-5979	2	35	ben	ben	PROPN
ejpam-5979	2	36	bella	bella	PROPN
ejpam-5979	2	37	,	,	PUNCT
ejpam-5979	2	38	es	es	NOUN
ejpam-5979	2	39	-	-	PUNCT
ejpam-5979	2	40	senia	senia	NOUN
ejpam-5979	2	41	,	,	PUNCT
ejpam-5979	2	42	31000	31000	NUM
ejpam-5979	2	43	oran	oran	NOUN
ejpam-5979	2	44	,	,	PUNCT
ejpam-5979	2	45	algeria	algeria	PROPN
ejpam-5979	2	46	2	2	NUM
ejpam-5979	2	47	department	department	NOUN
ejpam-5979	2	48	of	of	ADP
ejpam-5979	2	49	sciences	science	NOUN
ejpam-5979	2	50	and	and	CCONJ
ejpam-5979	2	51	technology	technology	NOUN
ejpam-5979	2	52	,	,	PUNCT
ejpam-5979	2	53	institute	institute	NOUN
ejpam-5979	2	54	of	of	ADP
ejpam-5979	2	55	sciences	sciences	PROPN
ejpam-5979	2	56	,	,	PUNCT
ejpam-5979	2	57	nour	nour	PROPN
ejpam-5979	2	58	-	-	PUNCT
ejpam-5979	2	59	bachir	bachir	PROPN
ejpam-5979	2	60	university	university	NOUN
ejpam-5979	2	61	center	center	NOUN
ejpam-5979	2	62	,	,	PUNCT
ejpam-5979	2	63	el	el	NOUN
ejpam-5979	2	64	-	-	NOUN
ejpam-5979	2	65	bayadh	bayadh	NOUN
ejpam-5979	2	66	,	,	PUNCT
ejpam-5979	2	67	32000	32000	NUM
ejpam-5979	2	68	,	,	PUNCT
ejpam-5979	2	69	algeria	algeria	PROPN
ejpam-5979	2	70	3	3	NUM
ejpam-5979	2	71	department	department	NOUN
ejpam-5979	2	72	of	of	ADP
ejpam-5979	2	73	mathematics	mathematic	NOUN
ejpam-5979	2	74	and	and	CCONJ
ejpam-5979	2	75	sciences	science	NOUN
ejpam-5979	2	76	,	,	PUNCT
ejpam-5979	2	77	prince	prince	PROPN
ejpam-5979	2	78	sultan	sultan	PROPN
ejpam-5979	2	79	university	university	PROPN
ejpam-5979	2	80	,	,	PUNCT
ejpam-5979	2	81	11586	11586	NUM
ejpam-5979	2	82	riyadh	riyadh	NOUN
ejpam-5979	2	83	,	,	PUNCT
ejpam-5979	2	84	saudi	saudi	PROPN
ejpam-5979	2	85	arabia	arabia	PROPN
ejpam-5979	2	86	4	4	NUM
ejpam-5979	2	87	department	department	NOUN
ejpam-5979	2	88	of	of	ADP
ejpam-5979	2	89	mathematics	mathematic	NOUN
ejpam-5979	2	90	,	,	PUNCT
ejpam-5979	2	91	faculty	faculty	NOUN
ejpam-5979	2	92	of	of	ADP
ejpam-5979	2	93	science	science	NOUN
ejpam-5979	2	94	,	,	PUNCT
ejpam-5979	2	95	bu	bu	PROPN
ejpam-5979	2	96	-	-	PUNCT
ejpam-5979	2	97	ali	ali	PROPN
ejpam-5979	2	98	sina	sina	PROPN
ejpam-5979	2	99	university	university	PROPN
ejpam-5979	2	100	,	,	PUNCT
ejpam-5979	2	101	hamedan	hamedan	PROPN
ejpam-5979	2	102	,	,	PUNCT
ejpam-5979	2	103	iran	iran	PROPN
ejpam-5979	2	104	5	5	NUM
ejpam-5979	2	105	siirt	siirt	PROPN
ejpam-5979	2	106	university	university	NOUN
ejpam-5979	2	107	,	,	PUNCT
ejpam-5979	2	108	art	art	NOUN
ejpam-5979	2	109	and	and	CCONJ
ejpam-5979	2	110	science	science	NOUN
ejpam-5979	2	111	faculty	faculty	NOUN
ejpam-5979	2	112	,	,	PUNCT
ejpam-5979	2	113	department	department	NOUN
ejpam-5979	2	114	of	of	ADP
ejpam-5979	2	115	mathematics	mathematic	NOUN
ejpam-5979	2	116	,	,	PUNCT
ejpam-5979	2	117	56100	56100	NUM
ejpam-5979	2	118	siirt	siirt	NOUN
ejpam-5979	2	119	,	,	PUNCT
ejpam-5979	2	120	turkey	turkey	NOUN
ejpam-5979	2	121	6	6	NUM
ejpam-5979	2	122	department	department	NOUN
ejpam-5979	2	123	of	of	ADP
ejpam-5979	2	124	electronic	electronic	ADJ
ejpam-5979	2	125	and	and	CCONJ
ejpam-5979	2	126	communication	communication	NOUN
ejpam-5979	2	127	engineering	engineering	NOUN
ejpam-5979	2	128	,	,	PUNCT
ejpam-5979	2	129	simats	simat	NOUN
ejpam-5979	2	130	,	,	PUNCT
ejpam-5979	2	131	chenni	chenni	PROPN
ejpam-5979	2	132	,	,	PUNCT
ejpam-5979	2	133	tamilnadu	tamilnadu	PROPN
ejpam-5979	2	134	,	,	PUNCT
ejpam-5979	2	135	india	india	PROPN
ejpam-5979	2	136	7	7	NUM
ejpam-5979	2	137	department	department	NOUN
ejpam-5979	2	138	of	of	ADP
ejpam-5979	2	139	computer	computer	NOUN
ejpam-5979	2	140	engineering	engineering	NOUN
ejpam-5979	2	141	,	,	PUNCT
ejpam-5979	2	142	biruni	biruni	PROPN
ejpam-5979	2	143	university	university	PROPN
ejpam-5979	2	144	,	,	PUNCT
ejpam-5979	2	145	34010	34010	NUM
ejpam-5979	2	146	topkapi	topkapi	PROPN
ejpam-5979	2	147	,	,	PUNCT
ejpam-5979	2	148	istanbul	istanbul	PROPN
ejpam-5979	2	149	,	,	PUNCT
ejpam-5979	2	150	turkey	turkey	NOUN
ejpam-5979	2	151	8	8	NUM
ejpam-5979	2	152	near	near	ADP
ejpam-5979	2	153	east	east	PROPN
ejpam-5979	2	154	university	university	PROPN
ejpam-5979	2	155	,	,	PUNCT
ejpam-5979	2	156	mathematics	mathematics	PROPN
ejpam-5979	2	157	research	research	NOUN
ejpam-5979	2	158	center	center	NOUN
ejpam-5979	2	159	,	,	PUNCT
ejpam-5979	2	160	department	department	NOUN
ejpam-5979	2	161	of	of	ADP
ejpam-5979	2	162	mathematics	mathematic	NOUN
ejpam-5979	2	163	,	,	PUNCT
ejpam-5979	2	164	near	near	ADP
ejpam-5979	2	165	east	east	PROPN
ejpam-5979	2	166	boulevard	boulevard	PROPN
ejpam-5979	2	167	,	,	PUNCT
ejpam-5979	2	168	pc	pc	NOUN
ejpam-5979	2	169	:	:	PUNCT
ejpam-5979	2	170	99138	99138	NUM
ejpam-5979	2	171	,	,	PUNCT
ejpam-5979	2	172	nicosia	nicosia	PROPN
ejpam-5979	2	173	/	/	SYM
ejpam-5979	2	174	mersin	mersin	PROPN
ejpam-5979	2	175	10	10	NUM
ejpam-5979	2	176	-	-	PUNCT
ejpam-5979	2	177	turkey	turkey	NOUN
ejpam-5979	2	178	9	9	NUM
ejpam-5979	2	179	systec	systec	NOUN
ejpam-5979	2	180	,	,	PUNCT
ejpam-5979	2	181	faculty	faculty	NOUN
ejpam-5979	2	182	of	of	ADP
ejpam-5979	2	183	engineering	engineering	PROPN
ejpam-5979	2	184	,	,	PUNCT
ejpam-5979	2	185	porto	porto	PROPN
ejpam-5979	2	186	university	university	PROPN
ejpam-5979	2	187	,	,	PUNCT
ejpam-5979	2	188	institute	institute	NOUN
ejpam-5979	2	189	for	for	ADP
ejpam-5979	2	190	systems	system	NOUN
ejpam-5979	2	191	and	and	CCONJ
ejpam-5979	2	192	robotics	robotic	NOUN
ejpam-5979	2	193	,	,	PUNCT
ejpam-5979	2	194	rua	rua	PROPN
ejpam-5979	2	195	dr	dr	PROPN
ejpam-5979	2	196	.	.	PROPN
ejpam-5979	2	197	roberto	roberto	PROPN
ejpam-5979	2	198	frias	frias	PROPN
ejpam-5979	2	199	s	s	PROPN
ejpam-5979	2	200	/	/	SYM
ejpam-5979	2	201	n	n	CCONJ
ejpam-5979	2	202	,	,	PUNCT
ejpam-5979	2	203	4200	4200	NUM
ejpam-5979	2	204	-	-	SYM
ejpam-5979	2	205	465	465	NUM
ejpam-5979	2	206	porto	porto	NOUN
ejpam-5979	2	207	,	,	PUNCT
ejpam-5979	2	208	portugal	portugal	PROPN
ejpam-5979	2	209	10	10	NUM
ejpam-5979	2	210	laboratoire	laboratoire	PROPN
ejpam-5979	2	211	de	de	PROPN
ejpam-5979	2	212	études	études	PROPN
ejpam-5979	2	213	pratiques	pratique	NOUN
ejpam-5979	2	214	en	en	X
ejpam-5979	2	215	sciences	sciences	PROPN
ejpam-5979	2	216	de	de	X
ejpam-5979	2	217	gestion	gestion	X
ejpam-5979	2	218	et	et	PROPN
ejpam-5979	2	219	sciences	sciences	PROPN
ejpam-5979	2	220	commerciale	commerciale	PROPN
ejpam-5979	2	221	,	,	PUNCT
ejpam-5979	2	222	école	école	ADJ
ejpam-5979	2	223	supérieure	supérieure	PROPN
ejpam-5979	2	224	de	de	X
ejpam-5979	2	225	commerce	commerce	PROPN
ejpam-5979	2	226	42003	42003	NUM
ejpam-5979	2	227	kolea	kolea	NOUN
ejpam-5979	2	228	,	,	PUNCT
ejpam-5979	2	229	tipaza	tipaza	PROPN
ejpam-5979	2	230	,	,	PUNCT
ejpam-5979	2	231	algeria	algeria	PROPN
ejpam-5979	2	232	abstract	abstract	NOUN
ejpam-5979	2	233	.	.	PUNCT
ejpam-5979	3	1	in	in	ADP
ejpam-5979	3	2	this	this	DET
ejpam-5979	3	3	manuscript	manuscript	NOUN
ejpam-5979	3	4	,	,	PUNCT
ejpam-5979	3	5	we	we	PRON
ejpam-5979	3	6	investigate	investigate	VERB
ejpam-5979	3	7	the	the	DET
ejpam-5979	3	8	existence	existence	NOUN
ejpam-5979	3	9	of	of	ADP
ejpam-5979	3	10	a	a	DET
ejpam-5979	3	11	unique	unique	ADJ
ejpam-5979	3	12	solution	solution	NOUN
ejpam-5979	3	13	to	to	ADP
ejpam-5979	3	14	a	a	DET
ejpam-5979	3	15	boundary	boundary	ADJ
ejpam-5979	3	16	value	value	NOUN
ejpam-5979	3	17	problem	problem	NOUN
ejpam-5979	3	18	(	(	PUNCT
ejpam-5979	3	19	bvp	bvp	PROPN
ejpam-5979	3	20	)	)	PUNCT
ejpam-5979	3	21	involving	involve	VERB
ejpam-5979	3	22	generalized	generalize	VERB
ejpam-5979	3	23	fractional	fractional	ADJ
ejpam-5979	3	24	derivatives	derivative	NOUN
ejpam-5979	3	25	of	of	ADP
ejpam-5979	3	26	the	the	DET
ejpam-5979	3	27	caputo	caputo	PROPN
ejpam-5979	3	28	type	type	NOUN
ejpam-5979	3	29	.	.	PUNCT
ejpam-5979	4	1	our	our	PRON
ejpam-5979	4	2	approach	approach	NOUN
ejpam-5979	4	3	is	be	AUX
ejpam-5979	4	4	grounded	ground	VERB
ejpam-5979	4	5	in	in	ADP
ejpam-5979	4	6	the	the	DET
ejpam-5979	4	7	banach	banach	NOUN
ejpam-5979	4	8	contraction	contraction	NOUN
ejpam-5979	4	9	mapping	mapping	NOUN
ejpam-5979	4	10	theorem	theorem	VERB
ejpam-5979	4	11	,	,	PUNCT
ejpam-5979	4	12	which	which	PRON
ejpam-5979	4	13	provides	provide	VERB
ejpam-5979	4	14	a	a	DET
ejpam-5979	4	15	rigorous	rigorous	ADJ
ejpam-5979	4	16	framework	framework	NOUN
ejpam-5979	4	17	for	for	ADP
ejpam-5979	4	18	proving	prove	VERB
ejpam-5979	4	19	the	the	DET
ejpam-5979	4	20	existence	existence	NOUN
ejpam-5979	4	21	of	of	ADP
ejpam-5979	4	22	a	a	DET
ejpam-5979	4	23	fixed	fix	VERB
ejpam-5979	4	24	point	point	NOUN
ejpam-5979	4	25	and	and	CCONJ
ejpam-5979	4	26	,	,	PUNCT
ejpam-5979	4	27	consequently	consequently	ADV
ejpam-5979	4	28	,	,	PUNCT
ejpam-5979	4	29	a	a	DET
ejpam-5979	4	30	solution	solution	NOUN
ejpam-5979	4	31	to	to	ADP
ejpam-5979	4	32	the	the	DET
ejpam-5979	4	33	bvp	bvp	NOUN
ejpam-5979	4	34	.	.	PUNCT
ejpam-5979	5	1	we	we	PRON
ejpam-5979	5	2	extend	extend	VERB
ejpam-5979	5	3	this	this	DET
ejpam-5979	5	4	methodology	methodology	NOUN
ejpam-5979	5	5	to	to	PART
ejpam-5979	5	6	explore	explore	VERB
ejpam-5979	5	7	analogous	analogous	ADJ
ejpam-5979	5	8	problems	problem	NOUN
ejpam-5979	5	9	,	,	PUNCT
ejpam-5979	5	10	offering	offer	VERB
ejpam-5979	5	11	further	further	ADJ
ejpam-5979	5	12	insights	insight	NOUN
ejpam-5979	5	13	and	and	CCONJ
ejpam-5979	5	14	interpretations	interpretation	NOUN
ejpam-5979	5	15	of	of	ADP
ejpam-5979	5	16	the	the	DET
ejpam-5979	5	17	results	result	NOUN
ejpam-5979	5	18	derived	derive	VERB
ejpam-5979	5	19	from	from	ADP
ejpam-5979	5	20	the	the	DET
ejpam-5979	5	21	main	main	ADJ
ejpam-5979	5	22	theorem	theorem	NOUN
ejpam-5979	5	23	.	.	PUNCT
ejpam-5979	6	1	this	this	DET
ejpam-5979	6	2	work	work	NOUN
ejpam-5979	6	3	not	not	PART
ejpam-5979	6	4	only	only	ADV
ejpam-5979	6	5	contributes	contribute	VERB
ejpam-5979	6	6	to	to	ADP
ejpam-5979	6	7	the	the	DET
ejpam-5979	6	8	theoretical	theoretical	ADJ
ejpam-5979	6	9	understanding	understanding	NOUN
ejpam-5979	6	10	of	of	ADP
ejpam-5979	6	11	fractional	fractional	ADJ
ejpam-5979	6	12	differential	differential	ADJ
ejpam-5979	6	13	equations	equation	NOUN
ejpam-5979	6	14	but	but	CCONJ
ejpam-5979	6	15	also	also	ADV
ejpam-5979	6	16	demonstrates	demonstrate	VERB
ejpam-5979	6	17	how	how	SCONJ
ejpam-5979	6	18	these	these	DET
ejpam-5979	6	19	techniques	technique	NOUN
ejpam-5979	6	20	can	can	AUX
ejpam-5979	6	21	be	be	AUX
ejpam-5979	6	22	applied	apply	VERB
ejpam-5979	6	23	to	to	ADP
ejpam-5979	6	24	a	a	DET
ejpam-5979	6	25	broader	broad	ADJ
ejpam-5979	6	26	class	class	NOUN
ejpam-5979	6	27	of	of	ADP
ejpam-5979	6	28	problems	problem	NOUN
ejpam-5979	6	29	in	in	ADP
ejpam-5979	6	30	mathematical	mathematical	ADJ
ejpam-5979	6	31	physics	physics	NOUN
ejpam-5979	6	32	and	and	CCONJ
ejpam-5979	6	33	engineering	engineering	NOUN
ejpam-5979	6	34	.	.	PUNCT
ejpam-5979	7	1	through	through	ADP
ejpam-5979	7	2	detailed	detailed	ADJ
ejpam-5979	7	3	analysis	analysis	NOUN
ejpam-5979	7	4	and	and	CCONJ
ejpam-5979	7	5	extrapolation	extrapolation	NOUN
ejpam-5979	7	6	,	,	PUNCT
ejpam-5979	7	7	we	we	PRON
ejpam-5979	7	8	aim	aim	VERB
ejpam-5979	7	9	to	to	PART
ejpam-5979	7	10	establish	establish	VERB
ejpam-5979	7	11	a	a	DET
ejpam-5979	7	12	deeper	deep	ADJ
ejpam-5979	7	13	connection	connection	NOUN
ejpam-5979	7	14	between	between	ADP
ejpam-5979	7	15	fractional	fractional	ADJ
ejpam-5979	7	16	calculus	calculus	NOUN
ejpam-5979	7	17	and	and	CCONJ
ejpam-5979	7	18	fixed	fix	VERB
ejpam-5979	7	19	-	-	PUNCT
ejpam-5979	7	20	point	point	NOUN
ejpam-5979	7	21	theory	theory	NOUN
ejpam-5979	7	22	,	,	PUNCT
ejpam-5979	7	23	providing	provide	VERB
ejpam-5979	7	24	a	a	DET
ejpam-5979	7	25	foundation	foundation	NOUN
ejpam-5979	7	26	for	for	ADP
ejpam-5979	7	27	future	future	ADJ
ejpam-5979	7	28	research	research	NOUN
ejpam-5979	7	29	in	in	ADP
ejpam-5979	7	30	this	this	DET
ejpam-5979	7	31	area	area	NOUN
ejpam-5979	7	32	.	.	PUNCT
ejpam-5979	8	1	2020	2020	NUM
ejpam-5979	8	2	mathematics	mathematic	NOUN
ejpam-5979	8	3	subject	subject	NOUN
ejpam-5979	8	4	classifications	classification	NOUN
ejpam-5979	8	5	:	:	PUNCT
ejpam-5979	8	6	263	263	NUM
ejpam-5979	8	7	,	,	PUNCT
ejpam-5979	8	8	65d05	65d05	NUM
ejpam-5979	8	9	,	,	PUNCT
ejpam-5979	8	10	65d30	65d30	ADJ
ejpam-5979	8	11	key	key	ADJ
ejpam-5979	8	12	words	word	NOUN
ejpam-5979	8	13	and	and	CCONJ
ejpam-5979	8	14	phrases	phrase	NOUN
ejpam-5979	8	15	:	:	PUNCT
ejpam-5979	8	16	banach	banach	NOUN
ejpam-5979	8	17	contraction	contraction	NOUN
ejpam-5979	8	18	theorem	theorem	VERB
ejpam-5979	8	19	,	,	PUNCT
ejpam-5979	8	20	generalized	generalized	ADJ
ejpam-5979	8	21	caputo	caputo	PROPN
ejpam-5979	8	22	fractional	fractional	PROPN
ejpam-5979	8	23	derivative	derivative	ADJ
ejpam-5979	8	24	,	,	PUNCT
ejpam-5979	8	25	boundary	boundary	ADJ
ejpam-5979	8	26	value	value	NOUN
ejpam-5979	8	27	problem	problem	NOUN
ejpam-5979	8	28	,	,	PUNCT
ejpam-5979	8	29	existence	existence	NOUN
ejpam-5979	8	30	and	and	CCONJ
ejpam-5979	8	31	uniqueness	uniqueness	NOUN
ejpam-5979	8	32	∗corresponding	∗corresponde	VERB
ejpam-5979	8	33	author	author	NOUN
ejpam-5979	8	34	.	.	PUNCT
ejpam-5979	9	1	doi	doi	NOUN
ejpam-5979	9	2	:	:	PUNCT
ejpam-5979	9	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5979	https://doi.org/10.29020/nybg.ejpam.v18i2.5979	VERB
ejpam-5979	9	4	email	email	NOUN
ejpam-5979	9	5	addresses	address	NOUN
ejpam-5979	9	6	:	:	PUNCT
ejpam-5979	9	7	zouaouizargui22@gmail.com	zouaouizargui22@gmail.com	X
ejpam-5979	9	8	(	(	PUNCT
ejpam-5979	9	9	z.	z.	PROPN
ejpam-5979	9	10	bekri	bekri	PROPN
ejpam-5979	9	11	)	)	PUNCT
ejpam-5979	9	12	,	,	PUNCT
ejpam-5979	9	13	sjohani@psu.edu.sa	sjohani@psu.edu.sa	PROPN
ejpam-5979	9	14	(	(	PUNCT
ejpam-5979	9	15	s.	s.	PROPN
ejpam-5979	9	16	aljohani	aljohani	PROPN
ejpam-5979	9	17	)	)	PUNCT
ejpam-5979	9	18	,	,	PUNCT
ejpam-5979	9	19	mesamei@basu.ac.ir	mesamei@basu.ac.ir	PROPN
ejpam-5979	9	20	(	(	PUNCT
ejpam-5979	9	21	m.	m.	PROPN
ejpam-5979	9	22	e.	e.	PROPN
ejpam-5979	9	23	samei	samei	PROPN
ejpam-5979	9	24	)	)	PUNCT
ejpam-5979	9	25	,	,	PUNCT
ejpam-5979	9	26	aliakgul00727@gmail.com	aliakgul00727@gmail.com	X
ejpam-5979	9	27	(	(	PUNCT
ejpam-5979	9	28	a.	a.	NOUN
ejpam-5979	9	29	akgül	akgül	PROPN
ejpam-5979	9	30	)	)	PUNCT
ejpam-5979	9	31	,	,	PUNCT
ejpam-5979	9	32	belhenniche@fe.up.pt	belhenniche@fe.up.pt	NOUN
ejpam-5979	9	33	(	(	PUNCT
ejpam-5979	9	34	a.	a.	NOUN
ejpam-5979	9	35	belhenniche	belhenniche	PROPN
ejpam-5979	9	36	)	)	PUNCT
ejpam-5979	9	37	,	,	PUNCT
ejpam-5979	9	38	maloqaily@psu.edu.sa	maloqaily@psu.edu.sa	PROPN
ejpam-5979	9	39	(	(	PUNCT
ejpam-5979	9	40	a.	a.	NOUN
ejpam-5979	9	41	aloqaily	aloqaily	ADV
ejpam-5979	9	42	)	)	PUNCT
ejpam-5979	9	43	,	,	PUNCT
ejpam-5979	9	44	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-5979	9	45	(	(	PUNCT
ejpam-5979	9	46	n.	n.	PROPN
ejpam-5979	9	47	mlaiki	mlaiki	PROPN
ejpam-5979	9	48	)	)	PUNCT
ejpam-5979	9	49	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5979	10	1	1	1	NUM
ejpam-5979	10	2	copyright	copyright	NOUN
ejpam-5979	10	3	:	:	PUNCT
ejpam-5979	10	4	©	©	PROPN
ejpam-5979	10	5	2025	2025	NUM
ejpam-5979	10	6	the	the	DET
ejpam-5979	10	7	author(s	author(s	NOUN
ejpam-5979	10	8	)	)	PUNCT
ejpam-5979	10	9	.	.	PUNCT
ejpam-5979	11	1	(	(	PUNCT
ejpam-5979	11	2	cc	cc	NOUN
ejpam-5979	11	3	by	by	ADP
ejpam-5979	11	4	-	-	PUNCT
ejpam-5979	11	5	nc	nc	PROPN
ejpam-5979	11	6	4.0	4.0	NUM
ejpam-5979	11	7	)	)	PUNCT
ejpam-5979	11	8	z.	z.	PROPN
ejpam-5979	11	9	bekri	bekri	PROPN
ejpam-5979	11	10	et	et	PROPN
ejpam-5979	12	1	al	al	PROPN
ejpam-5979	12	2	.	.	PUNCT
ejpam-5979	12	3	/	/	SYM
ejpam-5979	12	4	eur	eur	PROPN
ejpam-5979	12	5	.	.	PUNCT
ejpam-5979	13	1	j.	j.	PROPN
ejpam-5979	13	2	pure	pure	PROPN
ejpam-5979	13	3	appl	appl	PROPN
ejpam-5979	13	4	.	.	PROPN
ejpam-5979	13	5	math	math	PROPN
ejpam-5979	13	6	,	,	PUNCT
ejpam-5979	13	7	18	18	NUM
ejpam-5979	13	8	(	(	PUNCT
ejpam-5979	13	9	2	2	NUM
ejpam-5979	13	10	)	)	PUNCT
ejpam-5979	13	11	(	(	PUNCT
ejpam-5979	13	12	2025	2025	NUM
ejpam-5979	13	13	)	)	PUNCT
ejpam-5979	13	14	,	,	PUNCT
ejpam-5979	13	15	5979	5979	NUM
ejpam-5979	13	16	2	2	NUM
ejpam-5979	13	17	of	of	ADP
ejpam-5979	13	18	20	20	NUM
ejpam-5979	13	19	1	1	NUM
ejpam-5979	13	20	.	.	PUNCT
ejpam-5979	14	1	introduction	introduction	NOUN
ejpam-5979	14	2	mathematical	mathematical	ADJ
ejpam-5979	14	3	modeling	modeling	NOUN
ejpam-5979	14	4	has	have	AUX
ejpam-5979	14	5	become	become	VERB
ejpam-5979	14	6	an	an	DET
ejpam-5979	14	7	essential	essential	ADJ
ejpam-5979	14	8	tool	tool	NOUN
ejpam-5979	14	9	in	in	ADP
ejpam-5979	14	10	contemporary	contemporary	ADJ
ejpam-5979	14	11	scientific	scientific	ADJ
ejpam-5979	14	12	research	research	NOUN
ejpam-5979	14	13	,	,	PUNCT
ejpam-5979	14	14	serving	serve	VERB
ejpam-5979	14	15	as	as	ADP
ejpam-5979	14	16	a	a	DET
ejpam-5979	14	17	vital	vital	ADJ
ejpam-5979	14	18	means	mean	NOUN
ejpam-5979	14	19	to	to	PART
ejpam-5979	14	20	describe	describe	VERB
ejpam-5979	14	21	and	and	CCONJ
ejpam-5979	14	22	understand	understand	VERB
ejpam-5979	14	23	a	a	DET
ejpam-5979	14	24	wide	wide	ADJ
ejpam-5979	14	25	array	array	NOUN
ejpam-5979	14	26	of	of	ADP
ejpam-5979	14	27	phenomena	phenomenon	NOUN
ejpam-5979	14	28	in	in	ADP
ejpam-5979	14	29	both	both	CCONJ
ejpam-5979	14	30	physical	physical	ADJ
ejpam-5979	14	31	and	and	CCONJ
ejpam-5979	14	32	biological	biological	ADJ
ejpam-5979	14	33	sciences	science	NOUN
ejpam-5979	14	34	.	.	PUNCT
ejpam-5979	15	1	this	this	DET
ejpam-5979	15	2	progress	progress	NOUN
ejpam-5979	15	3	is	be	AUX
ejpam-5979	15	4	closely	closely	ADV
ejpam-5979	15	5	linked	link	VERB
ejpam-5979	15	6	to	to	ADP
ejpam-5979	15	7	the	the	DET
ejpam-5979	15	8	development	development	NOUN
ejpam-5979	15	9	of	of	ADP
ejpam-5979	15	10	new	new	ADJ
ejpam-5979	15	11	theories	theory	NOUN
ejpam-5979	15	12	and	and	CCONJ
ejpam-5979	15	13	the	the	DET
ejpam-5979	15	14	refinement	refinement	NOUN
ejpam-5979	15	15	of	of	ADP
ejpam-5979	15	16	classical	classical	ADJ
ejpam-5979	15	17	models	model	NOUN
ejpam-5979	15	18	,	,	PUNCT
ejpam-5979	15	19	with	with	ADP
ejpam-5979	15	20	the	the	DET
ejpam-5979	15	21	use	use	NOUN
ejpam-5979	15	22	of	of	ADP
ejpam-5979	15	23	fractional	fractional	ADJ
ejpam-5979	15	24	calculus	calculus	NOUN
ejpam-5979	15	25	playing	play	VERB
ejpam-5979	15	26	an	an	DET
ejpam-5979	15	27	increasingly	increasingly	ADV
ejpam-5979	15	28	prominent	prominent	ADJ
ejpam-5979	15	29	role	role	NOUN
ejpam-5979	15	30	.	.	PUNCT
ejpam-5979	16	1	in	in	ADP
ejpam-5979	16	2	particular	particular	ADJ
ejpam-5979	16	3	,	,	PUNCT
ejpam-5979	16	4	fractional	fractional	ADJ
ejpam-5979	16	5	differential	differential	ADJ
ejpam-5979	16	6	equations	equation	NOUN
ejpam-5979	16	7	(	(	PUNCT
ejpam-5979	16	8	fdes	fde	NOUN
ejpam-5979	16	9	)	)	PUNCT
ejpam-5979	16	10	and	and	CCONJ
ejpam-5979	16	11	partial	partial	ADJ
ejpam-5979	16	12	differential	differential	ADJ
ejpam-5979	16	13	equations	equation	NOUN
ejpam-5979	16	14	(	(	PUNCT
ejpam-5979	16	15	pdes	pde	NOUN
ejpam-5979	16	16	)	)	PUNCT
ejpam-5979	16	17	have	have	AUX
ejpam-5979	16	18	emerged	emerge	VERB
ejpam-5979	16	19	as	as	ADP
ejpam-5979	16	20	powerful	powerful	ADJ
ejpam-5979	16	21	frameworks	framework	NOUN
ejpam-5979	16	22	for	for	ADP
ejpam-5979	16	23	capturing	capture	VERB
ejpam-5979	16	24	the	the	DET
ejpam-5979	16	25	dynamics	dynamic	NOUN
ejpam-5979	16	26	of	of	ADP
ejpam-5979	16	27	complex	complex	ADJ
ejpam-5979	16	28	systems	system	NOUN
ejpam-5979	16	29	,	,	PUNCT
ejpam-5979	16	30	where	where	SCONJ
ejpam-5979	16	31	traditional	traditional	ADJ
ejpam-5979	16	32	integer	integer	NOUN
ejpam-5979	16	33	-	-	PUNCT
ejpam-5979	16	34	order	order	NOUN
ejpam-5979	16	35	models	model	NOUN
ejpam-5979	16	36	may	may	AUX
ejpam-5979	16	37	fall	fall	VERB
ejpam-5979	16	38	short	short	ADJ
ejpam-5979	16	39	.	.	PUNCT
ejpam-5979	17	1	these	these	DET
ejpam-5979	17	2	models	model	NOUN
ejpam-5979	17	3	have	have	AUX
ejpam-5979	17	4	been	be	AUX
ejpam-5979	17	5	employed	employ	VERB
ejpam-5979	17	6	to	to	PART
ejpam-5979	17	7	explain	explain	VERB
ejpam-5979	17	8	a	a	DET
ejpam-5979	17	9	variety	variety	NOUN
ejpam-5979	17	10	of	of	ADP
ejpam-5979	17	11	phenomena	phenomenon	NOUN
ejpam-5979	17	12	across	across	ADP
ejpam-5979	17	13	multiple	multiple	ADJ
ejpam-5979	17	14	disciplines	discipline	NOUN
ejpam-5979	17	15	,	,	PUNCT
ejpam-5979	17	16	including	include	VERB
ejpam-5979	17	17	physics	physics	NOUN
ejpam-5979	17	18	,	,	PUNCT
ejpam-5979	17	19	engineering	engineering	NOUN
ejpam-5979	17	20	,	,	PUNCT
ejpam-5979	17	21	and	and	CCONJ
ejpam-5979	17	22	biology	biology	NOUN
ejpam-5979	17	23	[	[	X
ejpam-5979	17	24	1–6	1–6	X
ejpam-5979	17	25	]	]	X
ejpam-5979	17	26	.	.	PUNCT
ejpam-5979	18	1	as	as	SCONJ
ejpam-5979	18	2	the	the	DET
ejpam-5979	18	3	field	field	NOUN
ejpam-5979	18	4	evolves	evolve	VERB
ejpam-5979	18	5	,	,	PUNCT
ejpam-5979	18	6	there	there	PRON
ejpam-5979	18	7	is	be	VERB
ejpam-5979	18	8	a	a	DET
ejpam-5979	18	9	growing	grow	VERB
ejpam-5979	18	10	need	need	NOUN
ejpam-5979	18	11	to	to	PART
ejpam-5979	18	12	simulate	simulate	VERB
ejpam-5979	18	13	these	these	DET
ejpam-5979	18	14	phenomena	phenomenon	NOUN
ejpam-5979	18	15	in	in	ADP
ejpam-5979	18	16	ways	way	NOUN
ejpam-5979	18	17	that	that	PRON
ejpam-5979	18	18	offer	offer	VERB
ejpam-5979	18	19	both	both	DET
ejpam-5979	18	20	analytical	analytical	ADJ
ejpam-5979	18	21	insights	insight	NOUN
ejpam-5979	18	22	and	and	CCONJ
ejpam-5979	18	23	numerical	numerical	ADJ
ejpam-5979	18	24	interpretations	interpretation	NOUN
ejpam-5979	18	25	.	.	PUNCT
ejpam-5979	19	1	such	such	ADJ
ejpam-5979	19	2	simulations	simulation	NOUN
ejpam-5979	19	3	serve	serve	VERB
ejpam-5979	19	4	not	not	PART
ejpam-5979	19	5	only	only	ADV
ejpam-5979	19	6	as	as	ADP
ejpam-5979	19	7	a	a	DET
ejpam-5979	19	8	means	means	NOUN
ejpam-5979	19	9	to	to	PART
ejpam-5979	19	10	validate	validate	VERB
ejpam-5979	19	11	theoretical	theoretical	ADJ
ejpam-5979	19	12	models	model	NOUN
ejpam-5979	19	13	but	but	CCONJ
ejpam-5979	19	14	also	also	ADV
ejpam-5979	19	15	as	as	ADP
ejpam-5979	19	16	a	a	DET
ejpam-5979	19	17	bridge	bridge	NOUN
ejpam-5979	19	18	between	between	ADP
ejpam-5979	19	19	abstract	abstract	ADJ
ejpam-5979	19	20	mathematical	mathematical	ADJ
ejpam-5979	19	21	theories	theory	NOUN
ejpam-5979	19	22	and	and	CCONJ
ejpam-5979	19	23	real	real	ADJ
ejpam-5979	19	24	-	-	PUNCT
ejpam-5979	19	25	world	world	NOUN
ejpam-5979	19	26	applications	application	NOUN
ejpam-5979	19	27	.	.	PUNCT
ejpam-5979	20	1	this	this	DET
ejpam-5979	20	2	paper	paper	NOUN
ejpam-5979	20	3	aims	aim	VERB
ejpam-5979	20	4	to	to	PART
ejpam-5979	20	5	address	address	VERB
ejpam-5979	20	6	one	one	NUM
ejpam-5979	20	7	such	such	ADJ
ejpam-5979	20	8	simulation	simulation	NOUN
ejpam-5979	20	9	,	,	PUNCT
ejpam-5979	20	10	focusing	focus	VERB
ejpam-5979	20	11	on	on	ADP
ejpam-5979	20	12	the	the	DET
ejpam-5979	20	13	application	application	NOUN
ejpam-5979	20	14	of	of	ADP
ejpam-5979	20	15	fractional	fractional	ADJ
ejpam-5979	20	16	calculus	calculus	NOUN
ejpam-5979	20	17	to	to	ADP
ejpam-5979	20	18	boundary	boundary	ADJ
ejpam-5979	20	19	value	value	NOUN
ejpam-5979	20	20	problems	problem	NOUN
ejpam-5979	20	21	(	(	PUNCT
ejpam-5979	20	22	bvps	bvps	NOUN
ejpam-5979	20	23	)	)	PUNCT
ejpam-5979	20	24	.	.	PUNCT
ejpam-5979	21	1	specifically	specifically	ADV
ejpam-5979	21	2	,	,	PUNCT
ejpam-5979	21	3	we	we	PRON
ejpam-5979	21	4	explore	explore	VERB
ejpam-5979	21	5	the	the	DET
ejpam-5979	21	6	extension	extension	NOUN
ejpam-5979	21	7	of	of	ADP
ejpam-5979	21	8	ordinary	ordinary	ADJ
ejpam-5979	21	9	differential	differential	ADJ
ejpam-5979	21	10	equations	equation	NOUN
ejpam-5979	21	11	(	(	PUNCT
ejpam-5979	21	12	odes	ode	NOUN
ejpam-5979	21	13	)	)	PUNCT
ejpam-5979	21	14	to	to	ADP
ejpam-5979	21	15	the	the	DET
ejpam-5979	21	16	realm	realm	NOUN
ejpam-5979	21	17	of	of	ADP
ejpam-5979	21	18	fractional	fractional	ADJ
ejpam-5979	21	19	differential	differential	ADJ
ejpam-5979	21	20	equations	equation	NOUN
ejpam-5979	21	21	,	,	PUNCT
ejpam-5979	21	22	which	which	PRON
ejpam-5979	21	23	allows	allow	VERB
ejpam-5979	21	24	for	for	ADP
ejpam-5979	21	25	a	a	DET
ejpam-5979	21	26	more	more	ADV
ejpam-5979	21	27	nuanced	nuanced	ADJ
ejpam-5979	21	28	description	description	NOUN
ejpam-5979	21	29	of	of	ADP
ejpam-5979	21	30	systems	system	NOUN
ejpam-5979	21	31	exhibiting	exhibit	VERB
ejpam-5979	21	32	memory	memory	NOUN
ejpam-5979	21	33	effects	effect	NOUN
ejpam-5979	21	34	,	,	PUNCT
ejpam-5979	21	35	non	non	ADJ
ejpam-5979	21	36	-	-	ADJ
ejpam-5979	21	37	local	local	ADJ
ejpam-5979	21	38	behavior	behavior	NOUN
ejpam-5979	21	39	,	,	PUNCT
ejpam-5979	21	40	and	and	CCONJ
ejpam-5979	21	41	anomalous	anomalous	ADJ
ejpam-5979	21	42	dynamics	dynamic	NOUN
ejpam-5979	21	43	[	[	X
ejpam-5979	21	44	7–12	7–12	X
ejpam-5979	21	45	]	]	X
ejpam-5979	21	46	.	.	PUNCT
ejpam-5979	22	1	the	the	DET
ejpam-5979	22	2	theoretical	theoretical	ADJ
ejpam-5979	22	3	framework	framework	NOUN
ejpam-5979	22	4	used	use	VERB
ejpam-5979	22	5	in	in	ADP
ejpam-5979	22	6	this	this	DET
ejpam-5979	22	7	study	study	NOUN
ejpam-5979	22	8	is	be	AUX
ejpam-5979	22	9	derived	derive	VERB
ejpam-5979	22	10	from	from	ADP
ejpam-5979	22	11	theorem	theorem	ADJ
ejpam-5979	22	12	3.3	3.3	NUM
ejpam-5979	22	13	presented	present	VERB
ejpam-5979	22	14	in	in	ADP
ejpam-5979	22	15	[	[	X
ejpam-5979	22	16	13	13	NUM
ejpam-5979	22	17	]	]	PUNCT
ejpam-5979	22	18	,	,	PUNCT
ejpam-5979	22	19	which	which	PRON
ejpam-5979	22	20	is	be	AUX
ejpam-5979	22	21	a	a	DET
ejpam-5979	22	22	result	result	NOUN
ejpam-5979	22	23	related	relate	VERB
ejpam-5979	22	24	to	to	ADP
ejpam-5979	22	25	the	the	DET
ejpam-5979	22	26	existence	existence	NOUN
ejpam-5979	22	27	of	of	ADP
ejpam-5979	22	28	unique	unique	ADJ
ejpam-5979	22	29	solutions	solution	NOUN
ejpam-5979	22	30	for	for	ADP
ejpam-5979	22	31	certain	certain	ADJ
ejpam-5979	22	32	bvps	bvps	NOUN
ejpam-5979	22	33	.	.	PUNCT
ejpam-5979	23	1	this	this	DET
ejpam-5979	23	2	theorem	theorem	NOUN
ejpam-5979	23	3	was	be	AUX
ejpam-5979	23	4	previously	previously	ADV
ejpam-5979	23	5	stated	state	VERB
ejpam-5979	23	6	without	without	ADP
ejpam-5979	23	7	proof	proof	NOUN
ejpam-5979	23	8	,	,	PUNCT
ejpam-5979	23	9	and	and	CCONJ
ejpam-5979	23	10	its	its	PRON
ejpam-5979	23	11	implications	implication	NOUN
ejpam-5979	23	12	have	have	AUX
ejpam-5979	23	13	not	not	PART
ejpam-5979	23	14	been	be	AUX
ejpam-5979	23	15	fully	fully	ADV
ejpam-5979	23	16	explored	explore	VERB
ejpam-5979	23	17	.	.	PUNCT
ejpam-5979	24	1	additionally	additionally	ADV
ejpam-5979	24	2	,	,	PUNCT
ejpam-5979	24	3	the	the	DET
ejpam-5979	24	4	problem	problem	NOUN
ejpam-5979	24	5	remains	remain	VERB
ejpam-5979	24	6	unresolved	unresolved	ADJ
ejpam-5979	24	7	in	in	ADP
ejpam-5979	24	8	the	the	DET
ejpam-5979	24	9	context	context	NOUN
ejpam-5979	24	10	of	of	ADP
ejpam-5979	24	11	fractional	fractional	ADJ
ejpam-5979	24	12	differential	differential	ADJ
ejpam-5979	24	13	equations	equation	NOUN
ejpam-5979	24	14	,	,	PUNCT
ejpam-5979	24	15	as	as	SCONJ
ejpam-5979	24	16	indicated	indicate	VERB
ejpam-5979	24	17	in	in	ADP
ejpam-5979	24	18	[	[	X
ejpam-5979	24	19	problem	problem	NOUN
ejpam-5979	24	20	41.6][14	41.6][14	NUM
ejpam-5979	24	21	]	]	PUNCT
ejpam-5979	24	22	.	.	PUNCT
ejpam-5979	25	1	the	the	DET
ejpam-5979	25	2	goal	goal	NOUN
ejpam-5979	25	3	of	of	ADP
ejpam-5979	25	4	this	this	DET
ejpam-5979	25	5	work	work	NOUN
ejpam-5979	25	6	is	be	AUX
ejpam-5979	25	7	to	to	PART
ejpam-5979	25	8	provide	provide	VERB
ejpam-5979	25	9	a	a	DET
ejpam-5979	25	10	rigorous	rigorous	ADJ
ejpam-5979	25	11	proof	proof	NOUN
ejpam-5979	25	12	of	of	ADP
ejpam-5979	25	13	the	the	DET
ejpam-5979	25	14	theorem	theorem	NOUN
ejpam-5979	25	15	in	in	ADP
ejpam-5979	25	16	the	the	DET
ejpam-5979	25	17	fractional	fractional	ADJ
ejpam-5979	25	18	setting	setting	NOUN
ejpam-5979	25	19	,	,	PUNCT
ejpam-5979	25	20	thereby	thereby	ADV
ejpam-5979	25	21	filling	fill	VERB
ejpam-5979	25	22	a	a	DET
ejpam-5979	25	23	gap	gap	NOUN
ejpam-5979	25	24	in	in	ADP
ejpam-5979	25	25	the	the	DET
ejpam-5979	25	26	existing	exist	VERB
ejpam-5979	25	27	literature	literature	NOUN
ejpam-5979	25	28	and	and	CCONJ
ejpam-5979	25	29	contributing	contribute	VERB
ejpam-5979	25	30	to	to	ADP
ejpam-5979	25	31	the	the	DET
ejpam-5979	25	32	broader	broad	ADJ
ejpam-5979	25	33	understanding	understanding	NOUN
ejpam-5979	25	34	of	of	ADP
ejpam-5979	25	35	fractional	fractional	ADJ
ejpam-5979	25	36	boundary	boundary	ADJ
ejpam-5979	25	37	value	value	NOUN
ejpam-5979	25	38	problems	problem	NOUN
ejpam-5979	25	39	.	.	PUNCT
ejpam-5979	26	1	to	to	PART
ejpam-5979	26	2	formalize	formalize	VERB
ejpam-5979	26	3	our	our	PRON
ejpam-5979	26	4	approach	approach	NOUN
ejpam-5979	26	5	,	,	PUNCT
ejpam-5979	26	6	we	we	PRON
ejpam-5979	26	7	begin	begin	VERB
ejpam-5979	26	8	by	by	ADP
ejpam-5979	26	9	presenting	present	VERB
ejpam-5979	26	10	the	the	DET
ejpam-5979	26	11	classical	classical	ADJ
ejpam-5979	26	12	result	result	NOUN
ejpam-5979	26	13	from	from	ADP
ejpam-5979	26	14	[	[	X
ejpam-5979	26	15	15	15	NUM
ejpam-5979	26	16	]	]	NUM
ejpam-5979	26	17	:	:	PUNCT
ejpam-5979	26	18	theorem	theorem	NOUN
ejpam-5979	26	19	1	1	NUM
ejpam-5979	26	20	.	.	PUNCT
ejpam-5979	27	1	(	(	PUNCT
ejpam-5979	27	2	[	[	X
ejpam-5979	27	3	15	15	NUM
ejpam-5979	27	4	]	]	PUNCT
ejpam-5979	27	5	)	)	PUNCT
ejpam-5979	27	6	suppose	suppose	VERB
ejpam-5979	27	7	θ	θ	X
ejpam-5979	27	8	:	:	PUNCT
ejpam-5979	28	1	[	[	X
ejpam-5979	28	2	θ	θ	X
ejpam-5979	28	3	,	,	PUNCT
ejpam-5979	28	4	ϑ	ϑ	X
ejpam-5979	28	5	]	]	X
ejpam-5979	28	6	×	×	NOUN
ejpam-5979	28	7	r	r	NOUN
ejpam-5979	28	8	→	→	SYM
ejpam-5979	28	9	r	r	NOUN
ejpam-5979	28	10	is	be	AUX
ejpam-5979	28	11	a	a	DET
ejpam-5979	28	12	continuous	continuous	ADJ
ejpam-5979	28	13	function	function	NOUN
ejpam-5979	28	14	that	that	PRON
ejpam-5979	28	15	satisfies	satisfy	VERB
ejpam-5979	28	16	a	a	DET
ejpam-5979	28	17	uniform	uniform	ADJ
ejpam-5979	28	18	lipschitz	lipschitz	NOUN
ejpam-5979	28	19	condition	condition	NOUN
ejpam-5979	28	20	with	with	ADP
ejpam-5979	28	21	respect	respect	NOUN
ejpam-5979	28	22	to	to	ADP
ejpam-5979	28	23	µ	µ	NUM
ejpam-5979	28	24	,	,	PUNCT
ejpam-5979	28	25	i.e.	i.e.	X
ejpam-5979	28	26	,	,	PUNCT
ejpam-5979	28	27	|θ(τ	|θ(τ	PROPN
ejpam-5979	28	28	,	,	PUNCT
ejpam-5979	28	29	µ)−θ(τ	µ)−θ(τ	ADV
ejpam-5979	28	30	,	,	PUNCT
ejpam-5979	28	31	ν)|	ν)|	PROPN
ejpam-5979	28	32	≤	≤	PROPN
ejpam-5979	28	33	ζ|µ−	ζ|µ−	ADJ
ejpam-5979	28	34	ν|	ν|	PROPN
ejpam-5979	28	35	,	,	PUNCT
ejpam-5979	28	36	(	(	PUNCT
ejpam-5979	28	37	τ	τ	PROPN
ejpam-5979	28	38	,	,	PUNCT
ejpam-5979	28	39	µ	µ	NOUN
ejpam-5979	28	40	)	)	PUNCT
ejpam-5979	28	41	,	,	PUNCT
ejpam-5979	28	42	(	(	PUNCT
ejpam-5979	28	43	τ	τ	X
ejpam-5979	28	44	,	,	PUNCT
ejpam-5979	28	45	ν	ν	NOUN
ejpam-5979	28	46	)	)	PUNCT
ejpam-5979	28	47	∈	∈	PROPN
ejpam-5979	28	48	[	[	X
ejpam-5979	28	49	θ	θ	NOUN
ejpam-5979	28	50	,	,	PUNCT
ejpam-5979	28	51	ϑ]×	ϑ]×	NOUN
ejpam-5979	28	52	r	r	NOUN
ejpam-5979	28	53	,	,	PUNCT
ejpam-5979	28	54	where	where	SCONJ
ejpam-5979	28	55	ζ	ζ	NOUN
ejpam-5979	28	56	>	>	X
ejpam-5979	28	57	0	0	NUM
ejpam-5979	28	58	is	be	AUX
ejpam-5979	28	59	a	a	DET
ejpam-5979	28	60	constant	constant	ADJ
ejpam-5979	28	61	.	.	PUNCT
ejpam-5979	29	1	if	if	SCONJ
ejpam-5979	29	2	the	the	DET
ejpam-5979	29	3	following	follow	VERB
ejpam-5979	29	4	condition	condition	NOUN
ejpam-5979	29	5	holds	hold	VERB
ejpam-5979	29	6	:	:	PUNCT
ejpam-5979	29	7	ζ	ζ	X
ejpam-5979	29	8	(	(	PUNCT
ejpam-5979	29	9	ϑ−	ϑ−	NOUN
ejpam-5979	29	10	θ)2	θ)2	NOUN
ejpam-5979	29	11	8	8	NUM
ejpam-5979	29	12	<	<	X
ejpam-5979	29	13	1	1	NUM
ejpam-5979	29	14	,	,	PUNCT
ejpam-5979	29	15	then	then	ADV
ejpam-5979	29	16	the	the	DET
ejpam-5979	29	17	boundary	boundary	ADJ
ejpam-5979	29	18	value	value	NOUN
ejpam-5979	29	19	problem	problem	NOUN
ejpam-5979	29	20	µ′′	µ′′	PROPN
ejpam-5979	29	21	=	=	SYM
ejpam-5979	29	22	−θ(τ	−θ(τ	PROPN
ejpam-5979	29	23	,	,	PUNCT
ejpam-5979	29	24	µ	µ	NOUN
ejpam-5979	29	25	)	)	PUNCT
ejpam-5979	29	26	,	,	PUNCT
ejpam-5979	29	27	µ(θ	µ(θ	ADJ
ejpam-5979	29	28	)	)	PUNCT
ejpam-5979	29	29	=	=	SYM
ejpam-5979	29	30	λ1	λ1	ADJ
ejpam-5979	29	31	,	,	PUNCT
ejpam-5979	29	32	µ(ϑ	µ(ϑ	PROPN
ejpam-5979	29	33	)	)	PUNCT
ejpam-5979	29	34	=	=	SYM
ejpam-5979	29	35	λ2	λ2	NOUN
ejpam-5979	29	36	,	,	PUNCT
ejpam-5979	29	37	admits	admit	VERB
ejpam-5979	29	38	a	a	DET
ejpam-5979	29	39	unique	unique	ADJ
ejpam-5979	29	40	solution	solution	NOUN
ejpam-5979	29	41	.	.	PUNCT
ejpam-5979	30	1	z.	z.	PROPN
ejpam-5979	30	2	bekri	bekri	PROPN
ejpam-5979	30	3	et	et	PROPN
ejpam-5979	30	4	al	al	PROPN
ejpam-5979	30	5	.	.	PUNCT
ejpam-5979	30	6	/	/	SYM
ejpam-5979	30	7	eur	eur	PROPN
ejpam-5979	30	8	.	.	PUNCT
ejpam-5979	31	1	j.	j.	PROPN
ejpam-5979	31	2	pure	pure	PROPN
ejpam-5979	31	3	appl	appl	PROPN
ejpam-5979	31	4	.	.	PROPN
ejpam-5979	31	5	math	math	PROPN
ejpam-5979	31	6	,	,	PUNCT
ejpam-5979	31	7	18	18	NUM
ejpam-5979	31	8	(	(	PUNCT
ejpam-5979	31	9	2	2	NUM
ejpam-5979	31	10	)	)	PUNCT
ejpam-5979	31	11	(	(	PUNCT
ejpam-5979	31	12	2025	2025	NUM
ejpam-5979	31	13	)	)	PUNCT
ejpam-5979	31	14	,	,	PUNCT
ejpam-5979	31	15	5979	5979	NUM
ejpam-5979	31	16	3	3	NUM
ejpam-5979	31	17	of	of	ADP
ejpam-5979	31	18	20	20	NUM
ejpam-5979	31	19	in	in	ADP
ejpam-5979	31	20	this	this	DET
ejpam-5979	31	21	article	article	NOUN
ejpam-5979	31	22	,	,	PUNCT
ejpam-5979	31	23	we	we	PRON
ejpam-5979	31	24	extend	extend	VERB
ejpam-5979	31	25	this	this	DET
ejpam-5979	31	26	result	result	NOUN
ejpam-5979	31	27	to	to	ADP
ejpam-5979	31	28	the	the	DET
ejpam-5979	31	29	fractional	fractional	ADJ
ejpam-5979	31	30	setting	setting	NOUN
ejpam-5979	31	31	by	by	ADP
ejpam-5979	31	32	replacing	replace	VERB
ejpam-5979	31	33	the	the	DET
ejpam-5979	31	34	standard	standard	ADJ
ejpam-5979	31	35	second	second	ADJ
ejpam-5979	31	36	-	-	PUNCT
ejpam-5979	31	37	order	order	NOUN
ejpam-5979	31	38	derivative	derivative	ADJ
ejpam-5979	31	39	µ′′	µ′′	NOUN
ejpam-5979	31	40	with	with	ADP
ejpam-5979	31	41	a	a	DET
ejpam-5979	31	42	generalized	generalize	VERB
ejpam-5979	31	43	caputo	caputo	PROPN
ejpam-5979	31	44	fractional	fractional	PROPN
ejpam-5979	31	45	derivative	derivative	NOUN
ejpam-5979	31	46	of	of	ADP
ejpam-5979	31	47	order	order	NOUN
ejpam-5979	31	48	σ	σ	NOUN
ejpam-5979	31	49	,	,	PUNCT
ejpam-5979	31	50	where	where	SCONJ
ejpam-5979	31	51	1	1	NUM
ejpam-5979	31	52	<	<	X
ejpam-5979	31	53	σ	σ	X
ejpam-5979	31	54	≤	≤	NUM
ejpam-5979	31	55	2	2	NUM
ejpam-5979	31	56	.	.	PUNCT
ejpam-5979	32	1	this	this	DET
ejpam-5979	32	2	extension	extension	NOUN
ejpam-5979	32	3	is	be	AUX
ejpam-5979	32	4	crucial	crucial	ADJ
ejpam-5979	32	5	as	as	SCONJ
ejpam-5979	32	6	it	it	PRON
ejpam-5979	32	7	allows	allow	VERB
ejpam-5979	32	8	us	we	PRON
ejpam-5979	32	9	to	to	PART
ejpam-5979	32	10	study	study	VERB
ejpam-5979	32	11	the	the	DET
ejpam-5979	32	12	existence	existence	NOUN
ejpam-5979	32	13	of	of	ADP
ejpam-5979	32	14	solutions	solution	NOUN
ejpam-5979	32	15	to	to	PART
ejpam-5979	32	16	bvps	bvps	VERB
ejpam-5979	32	17	involving	involve	VERB
ejpam-5979	32	18	fractional	fractional	ADJ
ejpam-5979	32	19	derivatives	derivative	NOUN
ejpam-5979	32	20	,	,	PUNCT
ejpam-5979	32	21	which	which	PRON
ejpam-5979	32	22	have	have	AUX
ejpam-5979	32	23	been	be	AUX
ejpam-5979	32	24	shown	show	VERB
ejpam-5979	32	25	to	to	PART
ejpam-5979	32	26	better	well	ADV
ejpam-5979	32	27	describe	describe	VERB
ejpam-5979	32	28	systems	system	NOUN
ejpam-5979	32	29	with	with	ADP
ejpam-5979	32	30	memory	memory	NOUN
ejpam-5979	32	31	effects	effect	NOUN
ejpam-5979	32	32	,	,	PUNCT
ejpam-5979	32	33	non	non	ADJ
ejpam-5979	32	34	-	-	ADJ
ejpam-5979	32	35	local	local	ADJ
ejpam-5979	32	36	interactions	interaction	NOUN
ejpam-5979	32	37	,	,	PUNCT
ejpam-5979	32	38	and	and	CCONJ
ejpam-5979	32	39	other	other	ADJ
ejpam-5979	32	40	phenomena	phenomenon	NOUN
ejpam-5979	32	41	not	not	PART
ejpam-5979	32	42	captured	capture	VERB
ejpam-5979	32	43	by	by	ADP
ejpam-5979	32	44	classical	classical	ADJ
ejpam-5979	32	45	integer	integer	NOUN
ejpam-5979	32	46	-	-	PUNCT
ejpam-5979	32	47	order	order	NOUN
ejpam-5979	32	48	derivatives	derivative	NOUN
ejpam-5979	32	49	.	.	PUNCT
ejpam-5979	33	1	we	we	PRON
ejpam-5979	33	2	aim	aim	VERB
ejpam-5979	33	3	to	to	PART
ejpam-5979	33	4	derive	derive	VERB
ejpam-5979	33	5	the	the	DET
ejpam-5979	33	6	existence	existence	NOUN
ejpam-5979	33	7	of	of	ADP
ejpam-5979	33	8	a	a	DET
ejpam-5979	33	9	unique	unique	ADJ
ejpam-5979	33	10	solution	solution	NOUN
ejpam-5979	33	11	to	to	ADP
ejpam-5979	33	12	the	the	DET
ejpam-5979	33	13	fractional	fractional	ADJ
ejpam-5979	33	14	boundary	boundary	ADJ
ejpam-5979	33	15	value	value	NOUN
ejpam-5979	33	16	problem	problem	NOUN
ejpam-5979	33	17	(	(	PUNCT
ejpam-5979	33	18	bvp	bvp	PROPN
ejpam-5979	33	19	)	)	PUNCT
ejpam-5979	33	20	defined	define	VERB
ejpam-5979	33	21	by	by	ADP
ejpam-5979	33	22	the	the	DET
ejpam-5979	33	23	following	follow	VERB
ejpam-5979	33	24	system	system	NOUN
ejpam-5979	33	25	:	:	PUNCT
ejpam-5979	33	26	{	{	PUNCT
ejpam-5979	33	27	ϱ	ϱ	ADP
ejpam-5979	33	28	cdσ	cdσ	NOUN
ejpam-5979	33	29	θ+µ(τ	θ+µ(τ	NUM
ejpam-5979	33	30	)	)	PUNCT
ejpam-5979	33	31	=	=	SYM
ejpam-5979	33	32	−θ(τ	−θ(τ	ADJ
ejpam-5979	33	33	,	,	PUNCT
ejpam-5979	33	34	µ(τ	µ(τ	NOUN
ejpam-5979	33	35	)	)	PUNCT
ejpam-5979	33	36	)	)	PUNCT
ejpam-5979	33	37	,	,	PUNCT
ejpam-5979	33	38	θ	θ	X
ejpam-5979	33	39	<	<	X
ejpam-5979	33	40	τ	τ	X
ejpam-5979	33	41	<	<	X
ejpam-5979	33	42	ϑ	ϑ	X
ejpam-5979	33	43	,	,	PUNCT
ejpam-5979	33	44	µ(θ	µ(θ	ADJ
ejpam-5979	33	45	)	)	PUNCT
ejpam-5979	33	46	=	=	SYM
ejpam-5979	33	47	λ1	λ1	ADJ
ejpam-5979	33	48	,	,	PUNCT
ejpam-5979	33	49	µ(ϑ	µ(ϑ	PROPN
ejpam-5979	33	50	)	)	PUNCT
ejpam-5979	33	51	=	=	SYM
ejpam-5979	33	52	λ2	λ2	NOUN
ejpam-5979	33	53	,	,	PUNCT
ejpam-5979	33	54	(	(	PUNCT
ejpam-5979	33	55	1	1	X
ejpam-5979	33	56	)	)	PUNCT
ejpam-5979	33	57	where	where	SCONJ
ejpam-5979	33	58	ϱ	ϱ	ADP
ejpam-5979	33	59	cdσ	cdσ	NOUN
ejpam-5979	33	60	θ+	θ+	X
ejpam-5979	33	61	represents	represent	VERB
ejpam-5979	33	62	the	the	DET
ejpam-5979	33	63	generalized	generalized	ADJ
ejpam-5979	33	64	caputo	caputo	PROPN
ejpam-5979	33	65	fractional	fractional	PROPN
ejpam-5979	33	66	derivative	derivative	NOUN
ejpam-5979	33	67	of	of	ADP
ejpam-5979	33	68	order	order	NOUN
ejpam-5979	33	69	σ	σ	NOUN
ejpam-5979	33	70	,	,	PUNCT
ejpam-5979	33	71	and	and	CCONJ
ejpam-5979	33	72	σ	σ	PROPN
ejpam-5979	33	73	lies	lie	VERB
ejpam-5979	33	74	in	in	ADP
ejpam-5979	33	75	the	the	DET
ejpam-5979	33	76	interval	interval	NOUN
ejpam-5979	33	77	1	1	NUM
ejpam-5979	33	78	<	<	X
ejpam-5979	33	79	σ	σ	X
ejpam-5979	33	80	≤	≤	NUM
ejpam-5979	33	81	2	2	NUM
ejpam-5979	33	82	.	.	PUNCT
ejpam-5979	34	1	this	this	DET
ejpam-5979	34	2	system	system	NOUN
ejpam-5979	34	3	extends	extend	VERB
ejpam-5979	34	4	the	the	DET
ejpam-5979	34	5	classical	classical	ADJ
ejpam-5979	34	6	bvp	bvp	NOUN
ejpam-5979	34	7	by	by	ADP
ejpam-5979	34	8	incorporating	incorporate	VERB
ejpam-5979	34	9	fractional	fractional	ADJ
ejpam-5979	34	10	derivatives	derivative	NOUN
ejpam-5979	34	11	,	,	PUNCT
ejpam-5979	34	12	which	which	PRON
ejpam-5979	34	13	account	account	VERB
ejpam-5979	34	14	for	for	ADP
ejpam-5979	34	15	the	the	DET
ejpam-5979	34	16	memory	memory	NOUN
ejpam-5979	34	17	and	and	CCONJ
ejpam-5979	34	18	hereditary	hereditary	ADJ
ejpam-5979	34	19	effects	effect	NOUN
ejpam-5979	34	20	of	of	ADP
ejpam-5979	34	21	the	the	DET
ejpam-5979	34	22	system	system	NOUN
ejpam-5979	34	23	.	.	PUNCT
ejpam-5979	35	1	such	such	ADJ
ejpam-5979	35	2	models	model	NOUN
ejpam-5979	35	3	are	be	AUX
ejpam-5979	35	4	particularly	particularly	ADV
ejpam-5979	35	5	relevant	relevant	ADJ
ejpam-5979	35	6	in	in	ADP
ejpam-5979	35	7	fields	field	NOUN
ejpam-5979	35	8	such	such	ADJ
ejpam-5979	35	9	as	as	ADP
ejpam-5979	35	10	anomalous	anomalous	ADJ
ejpam-5979	35	11	diffusion	diffusion	NOUN
ejpam-5979	35	12	,	,	PUNCT
ejpam-5979	35	13	viscoelasticity	viscoelasticity	NOUN
ejpam-5979	35	14	,	,	PUNCT
ejpam-5979	35	15	and	and	CCONJ
ejpam-5979	35	16	complex	complex	ADJ
ejpam-5979	35	17	materials	material	NOUN
ejpam-5979	35	18	.	.	PUNCT
ejpam-5979	36	1	in	in	ADP
ejpam-5979	36	2	previous	previous	ADJ
ejpam-5979	36	3	studies	study	NOUN
ejpam-5979	36	4	[	[	X
ejpam-5979	36	5	16–18	16–18	NUM
ejpam-5979	36	6	]	]	PUNCT
ejpam-5979	36	7	and	and	CCONJ
ejpam-5979	36	8	related	related	ADJ
ejpam-5979	36	9	works	work	NOUN
ejpam-5979	36	10	,	,	PUNCT
ejpam-5979	36	11	we	we	PRON
ejpam-5979	36	12	explored	explore	VERB
ejpam-5979	36	13	the	the	DET
ejpam-5979	36	14	existence	existence	NOUN
ejpam-5979	36	15	of	of	ADP
ejpam-5979	36	16	singular	singular	ADJ
ejpam-5979	36	17	solutions	solution	NOUN
ejpam-5979	36	18	to	to	ADP
ejpam-5979	36	19	boundary	boundary	ADJ
ejpam-5979	36	20	value	value	NOUN
ejpam-5979	36	21	problems	problem	NOUN
ejpam-5979	36	22	involving	involve	VERB
ejpam-5979	36	23	generalized	generalize	VERB
ejpam-5979	36	24	fractional	fractional	ADJ
ejpam-5979	36	25	derivatives	derivative	NOUN
ejpam-5979	36	26	of	of	ADP
ejpam-5979	36	27	the	the	DET
ejpam-5979	36	28	caputo	caputo	PROPN
ejpam-5979	36	29	type	type	NOUN
ejpam-5979	36	30	.	.	PUNCT
ejpam-5979	37	1	these	these	DET
ejpam-5979	37	2	results	result	NOUN
ejpam-5979	37	3	laid	lay	VERB
ejpam-5979	37	4	the	the	DET
ejpam-5979	37	5	foundation	foundation	NOUN
ejpam-5979	37	6	for	for	ADP
ejpam-5979	37	7	extending	extend	VERB
ejpam-5979	37	8	the	the	DET
ejpam-5979	37	9	classical	classical	ADJ
ejpam-5979	37	10	theory	theory	NOUN
ejpam-5979	37	11	to	to	ADP
ejpam-5979	37	12	fractional	fractional	ADJ
ejpam-5979	37	13	-	-	PUNCT
ejpam-5979	37	14	order	order	NOUN
ejpam-5979	37	15	differential	differential	ADJ
ejpam-5979	37	16	equations	equation	NOUN
ejpam-5979	37	17	.	.	PUNCT
ejpam-5979	38	1	in	in	ADP
ejpam-5979	38	2	this	this	DET
ejpam-5979	38	3	work	work	NOUN
ejpam-5979	38	4	,	,	PUNCT
ejpam-5979	38	5	we	we	PRON
ejpam-5979	38	6	further	far	ADV
ejpam-5979	38	7	develop	develop	VERB
ejpam-5979	38	8	these	these	DET
ejpam-5979	38	9	ideas	idea	NOUN
ejpam-5979	38	10	by	by	ADP
ejpam-5979	38	11	applying	apply	VERB
ejpam-5979	38	12	theorem	theorem	NOUN
ejpam-5979	38	13	1	1	NUM
ejpam-5979	38	14	in	in	ADP
ejpam-5979	38	15	the	the	DET
ejpam-5979	38	16	context	context	NOUN
ejpam-5979	38	17	of	of	ADP
ejpam-5979	38	18	generalized	generalized	ADJ
ejpam-5979	38	19	fractional	fractional	ADJ
ejpam-5979	38	20	differential	differential	ADJ
ejpam-5979	38	21	equations	equation	NOUN
ejpam-5979	38	22	.	.	PUNCT
ejpam-5979	39	1	our	our	PRON
ejpam-5979	39	2	analysis	analysis	NOUN
ejpam-5979	39	3	not	not	PART
ejpam-5979	39	4	only	only	ADV
ejpam-5979	39	5	provides	provide	VERB
ejpam-5979	39	6	a	a	DET
ejpam-5979	39	7	rigorous	rigorous	ADJ
ejpam-5979	39	8	proof	proof	NOUN
ejpam-5979	39	9	for	for	ADP
ejpam-5979	39	10	the	the	DET
ejpam-5979	39	11	existence	existence	NOUN
ejpam-5979	39	12	of	of	ADP
ejpam-5979	39	13	a	a	DET
ejpam-5979	39	14	singular	singular	ADJ
ejpam-5979	39	15	solution	solution	NOUN
ejpam-5979	39	16	to	to	ADP
ejpam-5979	39	17	the	the	DET
ejpam-5979	39	18	fractional	fractional	ADJ
ejpam-5979	39	19	bvp	bvp	NOUN
ejpam-5979	39	20	but	but	CCONJ
ejpam-5979	39	21	also	also	ADV
ejpam-5979	39	22	offers	offer	VERB
ejpam-5979	39	23	new	new	ADJ
ejpam-5979	39	24	insights	insight	NOUN
ejpam-5979	39	25	into	into	ADP
ejpam-5979	39	26	the	the	DET
ejpam-5979	39	27	behavior	behavior	NOUN
ejpam-5979	39	28	of	of	ADP
ejpam-5979	39	29	solutions	solution	NOUN
ejpam-5979	39	30	to	to	ADP
ejpam-5979	39	31	fractional	fractional	ADJ
ejpam-5979	39	32	differential	differential	ADJ
ejpam-5979	39	33	equations	equation	NOUN
ejpam-5979	39	34	.	.	PUNCT
ejpam-5979	40	1	we	we	PRON
ejpam-5979	40	2	believe	believe	VERB
ejpam-5979	40	3	that	that	SCONJ
ejpam-5979	40	4	the	the	DET
ejpam-5979	40	5	results	result	NOUN
ejpam-5979	40	6	presented	present	VERB
ejpam-5979	40	7	in	in	ADP
ejpam-5979	40	8	this	this	DET
ejpam-5979	40	9	paper	paper	NOUN
ejpam-5979	40	10	will	will	AUX
ejpam-5979	40	11	have	have	VERB
ejpam-5979	40	12	significant	significant	ADJ
ejpam-5979	40	13	implications	implication	NOUN
ejpam-5979	40	14	for	for	ADP
ejpam-5979	40	15	the	the	DET
ejpam-5979	40	16	study	study	NOUN
ejpam-5979	40	17	of	of	ADP
ejpam-5979	40	18	fractional	fractional	ADJ
ejpam-5979	40	19	-	-	PUNCT
ejpam-5979	40	20	order	order	NOUN
ejpam-5979	40	21	systems	system	NOUN
ejpam-5979	40	22	and	and	CCONJ
ejpam-5979	40	23	will	will	AUX
ejpam-5979	40	24	contribute	contribute	VERB
ejpam-5979	40	25	to	to	ADP
ejpam-5979	40	26	the	the	DET
ejpam-5979	40	27	growing	grow	VERB
ejpam-5979	40	28	body	body	NOUN
ejpam-5979	40	29	of	of	ADP
ejpam-5979	40	30	research	research	NOUN
ejpam-5979	40	31	on	on	ADP
ejpam-5979	40	32	fractional	fractional	ADJ
ejpam-5979	40	33	calculus	calculus	NOUN
ejpam-5979	40	34	,	,	PUNCT
ejpam-5979	40	35	especially	especially	ADV
ejpam-5979	40	36	in	in	ADP
ejpam-5979	40	37	the	the	DET
ejpam-5979	40	38	context	context	NOUN
ejpam-5979	40	39	of	of	ADP
ejpam-5979	40	40	boundary	boundary	ADJ
ejpam-5979	40	41	value	value	NOUN
ejpam-5979	40	42	problems	problem	NOUN
ejpam-5979	40	43	.	.	PUNCT
ejpam-5979	41	1	furthermore	furthermore	ADV
ejpam-5979	41	2	,	,	PUNCT
ejpam-5979	41	3	the	the	DET
ejpam-5979	41	4	techniques	technique	NOUN
ejpam-5979	41	5	we	we	PRON
ejpam-5979	41	6	use	use	VERB
ejpam-5979	41	7	can	can	AUX
ejpam-5979	41	8	be	be	AUX
ejpam-5979	41	9	generalized	generalize	VERB
ejpam-5979	41	10	to	to	ADP
ejpam-5979	41	11	a	a	DET
ejpam-5979	41	12	wide	wide	ADJ
ejpam-5979	41	13	range	range	NOUN
ejpam-5979	41	14	of	of	ADP
ejpam-5979	41	15	problems	problem	NOUN
ejpam-5979	41	16	in	in	ADP
ejpam-5979	41	17	applied	applied	ADJ
ejpam-5979	41	18	mathematics	mathematic	NOUN
ejpam-5979	41	19	,	,	PUNCT
ejpam-5979	41	20	physics	physics	NOUN
ejpam-5979	41	21	,	,	PUNCT
ejpam-5979	41	22	and	and	CCONJ
ejpam-5979	41	23	engineering	engineering	NOUN
ejpam-5979	41	24	,	,	PUNCT
ejpam-5979	41	25	where	where	SCONJ
ejpam-5979	41	26	fractional	fractional	ADJ
ejpam-5979	41	27	models	model	NOUN
ejpam-5979	41	28	are	be	AUX
ejpam-5979	41	29	becoming	become	VERB
ejpam-5979	41	30	increasingly	increasingly	ADV
ejpam-5979	41	31	relevant	relevant	ADJ
ejpam-5979	41	32	.	.	PUNCT
ejpam-5979	42	1	in	in	ADP
ejpam-5979	42	2	summary	summary	NOUN
ejpam-5979	42	3	,	,	PUNCT
ejpam-5979	42	4	this	this	DET
ejpam-5979	42	5	paper	paper	NOUN
ejpam-5979	42	6	provides	provide	VERB
ejpam-5979	42	7	a	a	DET
ejpam-5979	42	8	theoretical	theoretical	ADJ
ejpam-5979	42	9	framework	framework	NOUN
ejpam-5979	42	10	for	for	ADP
ejpam-5979	42	11	solving	solve	VERB
ejpam-5979	42	12	bvps	bvps	NOUN
ejpam-5979	42	13	involving	involve	VERB
ejpam-5979	42	14	fractional	fractional	ADJ
ejpam-5979	42	15	derivatives	derivative	NOUN
ejpam-5979	42	16	of	of	ADP
ejpam-5979	42	17	the	the	DET
ejpam-5979	42	18	caputo	caputo	PROPN
ejpam-5979	42	19	type	type	NOUN
ejpam-5979	42	20	,	,	PUNCT
ejpam-5979	42	21	using	use	VERB
ejpam-5979	42	22	the	the	DET
ejpam-5979	42	23	banach	banach	NOUN
ejpam-5979	42	24	contraction	contraction	NOUN
ejpam-5979	42	25	theorem	theorem	VERB
ejpam-5979	42	26	as	as	ADP
ejpam-5979	42	27	a	a	DET
ejpam-5979	42	28	primary	primary	ADJ
ejpam-5979	42	29	tool	tool	NOUN
ejpam-5979	42	30	.	.	PUNCT
ejpam-5979	43	1	through	through	ADP
ejpam-5979	43	2	this	this	DET
ejpam-5979	43	3	approach	approach	NOUN
ejpam-5979	43	4	,	,	PUNCT
ejpam-5979	43	5	we	we	PRON
ejpam-5979	43	6	offer	offer	VERB
ejpam-5979	43	7	new	new	ADJ
ejpam-5979	43	8	results	result	NOUN
ejpam-5979	43	9	on	on	ADP
ejpam-5979	43	10	the	the	DET
ejpam-5979	43	11	existence	existence	NOUN
ejpam-5979	43	12	and	and	CCONJ
ejpam-5979	43	13	uniqueness	uniqueness	NOUN
ejpam-5979	43	14	of	of	ADP
ejpam-5979	43	15	solutions	solution	NOUN
ejpam-5979	43	16	to	to	ADP
ejpam-5979	43	17	fractional	fractional	ADJ
ejpam-5979	43	18	bvps	bvps	NOUN
ejpam-5979	43	19	and	and	CCONJ
ejpam-5979	43	20	provide	provide	VERB
ejpam-5979	43	21	a	a	DET
ejpam-5979	43	22	deeper	deep	ADJ
ejpam-5979	43	23	understanding	understanding	NOUN
ejpam-5979	43	24	of	of	ADP
ejpam-5979	43	25	their	their	PRON
ejpam-5979	43	26	implications	implication	NOUN
ejpam-5979	43	27	in	in	ADP
ejpam-5979	43	28	various	various	ADJ
ejpam-5979	43	29	scientific	scientific	ADJ
ejpam-5979	43	30	fields	field	NOUN
ejpam-5979	43	31	.	.	PUNCT
ejpam-5979	44	1	2	2	X
ejpam-5979	44	2	.	.	X
ejpam-5979	44	3	principal	principal	ADJ
ejpam-5979	44	4	concepts	concept	NOUN
ejpam-5979	44	5	starting	start	VERB
ejpam-5979	44	6	,	,	PUNCT
ejpam-5979	44	7	we	we	PRON
ejpam-5979	44	8	review	review	VERB
ejpam-5979	44	9	some	some	DET
ejpam-5979	44	10	basic	basic	ADJ
ejpam-5979	44	11	properties	property	NOUN
ejpam-5979	44	12	of	of	ADP
ejpam-5979	44	13	fractional	fractional	ADJ
ejpam-5979	44	14	calculus	calculus	NOUN
ejpam-5979	44	15	for	for	ADP
ejpam-5979	44	16	investigating	investigate	VERB
ejpam-5979	44	17	boundary	boundary	ADJ
ejpam-5979	44	18	value	value	NOUN
ejpam-5979	44	19	problems	problem	NOUN
ejpam-5979	44	20	,	,	PUNCT
ejpam-5979	44	21	lookup	lookup	NOUN
ejpam-5979	44	22	in	in	ADP
ejpam-5979	44	23	[	[	X
ejpam-5979	44	24	19–23	19–23	NUM
ejpam-5979	44	25	]	]	PUNCT
ejpam-5979	44	26	.	.	PUNCT
ejpam-5979	45	1	definition	definition	NOUN
ejpam-5979	45	2	1	1	NUM
ejpam-5979	45	3	.	.	PUNCT
ejpam-5979	46	1	on	on	ADP
ejpam-5979	46	2	the	the	DET
ejpam-5979	46	3	left	left	ADV
ejpam-5979	46	4	-	-	PUNCT
ejpam-5979	46	5	sided	sided	ADJ
ejpam-5979	46	6	in	in	ADP
ejpam-5979	46	7	the	the	DET
ejpam-5979	46	8	generalized	generalized	ADJ
ejpam-5979	46	9	integral	integral	NOUN
ejpam-5979	46	10	of	of	ADP
ejpam-5979	46	11	fractional	fractional	ADJ
ejpam-5979	46	12	order	order	NOUN
ejpam-5979	46	13	ϱiσθ+µ	ϱiσθ+µ	NOUN
ejpam-5979	46	14	for	for	ADP
ejpam-5979	46	15	σ	σ	PROPN
ejpam-5979	46	16	∈	∈	PROPN
ejpam-5979	46	17	c(re(σ	c(re(σ	PROPN
ejpam-5979	46	18	)	)	PUNCT
ejpam-5979	46	19	>	>	X
ejpam-5979	46	20	0	0	NUM
ejpam-5979	46	21	)	)	PUNCT
ejpam-5979	46	22	is	be	AUX
ejpam-5979	46	23	given	give	VERB
ejpam-5979	46	24	by	by	ADP
ejpam-5979	46	25	(	(	PUNCT
ejpam-5979	46	26	ϱiσθ+µ	ϱiσθ+µ	INTJ
ejpam-5979	46	27	)	)	PUNCT
ejpam-5979	46	28	(	(	PUNCT
ejpam-5979	46	29	τ	τ	X
ejpam-5979	46	30	)	)	PUNCT
ejpam-5979	46	31	=	=	SYM
ejpam-5979	47	1	ϱ1−σ	ϱ1−σ	PROPN
ejpam-5979	47	2	γ(σ	γ(σ	ADJ
ejpam-5979	47	3	)	)	PUNCT
ejpam-5979	47	4	∫	∫	PROPN
ejpam-5979	48	1	τ	τ	PROPN
ejpam-5979	48	2	θ	θ	PROPN
ejpam-5979	48	3	rϱ−1(τϱ	rϱ−1(τϱ	VERB
ejpam-5979	48	4	−	−	NOUN
ejpam-5979	48	5	rϱ)σ−1µ(r	rϱ)σ−1µ(r	ADJ
ejpam-5979	48	6	)	)	PUNCT
ejpam-5979	48	7	dr	dr	PROPN
ejpam-5979	48	8	,	,	PUNCT
ejpam-5979	48	9	(	(	PUNCT
ejpam-5979	48	10	2	2	X
ejpam-5979	48	11	)	)	PUNCT
ejpam-5979	48	12	z.	z.	PROPN
ejpam-5979	48	13	bekri	bekri	PROPN
ejpam-5979	48	14	et	et	PROPN
ejpam-5979	49	1	al	al	PROPN
ejpam-5979	49	2	.	.	PUNCT
ejpam-5979	49	3	/	/	SYM
ejpam-5979	49	4	eur	eur	PROPN
ejpam-5979	49	5	.	.	PUNCT
ejpam-5979	50	1	j.	j.	PROPN
ejpam-5979	50	2	pure	pure	PROPN
ejpam-5979	50	3	appl	appl	PROPN
ejpam-5979	50	4	.	.	PROPN
ejpam-5979	50	5	math	math	PROPN
ejpam-5979	50	6	,	,	PUNCT
ejpam-5979	50	7	18	18	NUM
ejpam-5979	50	8	(	(	PUNCT
ejpam-5979	50	9	2	2	NUM
ejpam-5979	50	10	)	)	PUNCT
ejpam-5979	50	11	(	(	PUNCT
ejpam-5979	50	12	2025	2025	NUM
ejpam-5979	50	13	)	)	PUNCT
ejpam-5979	50	14	,	,	PUNCT
ejpam-5979	50	15	5979	5979	NUM
ejpam-5979	50	16	4	4	NUM
ejpam-5979	50	17	of	of	ADP
ejpam-5979	50	18	20	20	NUM
ejpam-5979	50	19	where	where	SCONJ
ejpam-5979	50	20	τ	τ	PROPN
ejpam-5979	50	21	>	>	X
ejpam-5979	50	22	0	0	PROPN
ejpam-5979	50	23	,	,	PUNCT
ejpam-5979	50	24	ϱ	ϱ	ADP
ejpam-5979	50	25	>	>	X
ejpam-5979	50	26	0	0	NUM
ejpam-5979	50	27	.	.	PUNCT
ejpam-5979	51	1	according	accord	VERB
ejpam-5979	51	2	to	to	ADP
ejpam-5979	51	3	the	the	DET
ejpam-5979	51	4	formula	formula	NOUN
ejpam-5979	51	5	of	of	ADP
ejpam-5979	51	6	the	the	DET
ejpam-5979	51	7	generalized	generalize	VERB
ejpam-5979	51	8	fractional	fractional	ADJ
ejpam-5979	51	9	integrals	integral	NOUN
ejpam-5979	51	10	(	(	PUNCT
ejpam-5979	51	11	2	2	NUM
ejpam-5979	51	12	)	)	PUNCT
ejpam-5979	51	13	,	,	PUNCT
ejpam-5979	51	14	we	we	PRON
ejpam-5979	51	15	define	define	VERB
ejpam-5979	51	16	the	the	DET
ejpam-5979	51	17	generalized	generalized	ADJ
ejpam-5979	51	18	fractional	fractional	ADJ
ejpam-5979	51	19	derivative	derivative	NOUN
ejpam-5979	51	20	for	for	ADP
ejpam-5979	51	21	τ	τ	PROPN
ejpam-5979	51	22	>	>	X
ejpam-5979	51	23	0	0	PUNCT
ejpam-5979	52	1	by	by	ADP
ejpam-5979	52	2	(	(	PUNCT
ejpam-5979	52	3	ϱcd	ϱcd	PROPN
ejpam-5979	52	4	σ	σ	PROPN
ejpam-5979	52	5	θ+µ	θ+µ	NUM
ejpam-5979	52	6	)	)	PUNCT
ejpam-5979	52	7	(	(	PUNCT
ejpam-5979	52	8	τ	τ	X
ejpam-5979	52	9	)	)	PUNCT
ejpam-5979	52	10	=	=	SYM
ejpam-5979	52	11	(	(	PUNCT
ejpam-5979	52	12	τ1−ϱ	τ1−ϱ	PROPN
ejpam-5979	52	13	d	d	PROPN
ejpam-5979	52	14	dτ	dτ	NOUN
ejpam-5979	52	15	)	)	PUNCT
ejpam-5979	52	16	n	n	CCONJ
ejpam-5979	52	17	(	(	PUNCT
ejpam-5979	52	18	ϱin−σ	ϱin−σ	X
ejpam-5979	52	19	θ+	θ+	X
ejpam-5979	52	20	µ	µ	X
ejpam-5979	52	21	)	)	PUNCT
ejpam-5979	52	22	(	(	PUNCT
ejpam-5979	52	23	τ	τ	X
ejpam-5979	52	24	)	)	PUNCT
ejpam-5979	52	25	=	=	PUNCT
ejpam-5979	52	26	ϱσ−n+1	ϱσ−n+1	PROPN
ejpam-5979	52	27	γ(n−σ	γ(n−σ	PROPN
ejpam-5979	52	28	)	)	PUNCT
ejpam-5979	52	29	(	(	PUNCT
ejpam-5979	52	30	τ1−ϱ	τ1−ϱ	PROPN
ejpam-5979	52	31	d	d	PROPN
ejpam-5979	52	32	dτ	dτ	NOUN
ejpam-5979	52	33	)	)	PUNCT
ejpam-5979	52	34	n	n	CCONJ
ejpam-5979	52	35	∫	∫	NOUN
ejpam-5979	52	36	τ	τ	PROPN
ejpam-5979	52	37	θ	θ	PROPN
ejpam-5979	52	38	rϱ−1(τϱ	rϱ−1(τϱ	VERB
ejpam-5979	52	39	−	−	PROPN
ejpam-5979	52	40	rϱ)n−1−σµ(r	rϱ)n−1−σµ(r	NOUN
ejpam-5979	52	41	)	)	PUNCT
ejpam-5979	52	42	dr	dr	PROPN
ejpam-5979	52	43	.	.	PROPN
ejpam-5979	52	44	(	(	PUNCT
ejpam-5979	52	45	3	3	X
ejpam-5979	52	46	)	)	PUNCT
ejpam-5979	52	47	definition	definition	NOUN
ejpam-5979	52	48	2	2	NUM
ejpam-5979	52	49	.	.	PUNCT
ejpam-5979	52	50	by	by	ADP
ejpam-5979	52	51	using	use	VERB
ejpam-5979	52	52	the	the	DET
ejpam-5979	52	53	above	above	ADJ
ejpam-5979	52	54	generalized	generalized	ADJ
ejpam-5979	52	55	fractional	fractional	ADJ
ejpam-5979	52	56	derivative	derivative	NOUN
ejpam-5979	52	57	(	(	PUNCT
ejpam-5979	52	58	3	3	NUM
ejpam-5979	52	59	)	)	PUNCT
ejpam-5979	52	60	,	,	PUNCT
ejpam-5979	52	61	the	the	DET
ejpam-5979	52	62	generalized	generalize	VERB
ejpam-5979	52	63	caputo	caputo	PROPN
ejpam-5979	52	64	non	non	ADJ
ejpam-5979	52	65	-	-	ADJ
ejpam-5979	52	66	classical	classical	ADJ
ejpam-5979	52	67	derivative	derivative	NOUN
ejpam-5979	52	68	with	with	ADP
ejpam-5979	52	69	the	the	DET
ejpam-5979	52	70	operator	operator	NOUN
ejpam-5979	52	71	notation	notation	NOUN
ejpam-5979	52	72	ϱ	ϱ	ADP
ejpam-5979	52	73	cdσ	cdσ	NOUN
ejpam-5979	52	74	θ+	θ+	X
ejpam-5979	52	75	is	be	AUX
ejpam-5979	52	76	defined	define	VERB
ejpam-5979	52	77	by	by	ADP
ejpam-5979	52	78	ϱ	ϱ	PROPN
ejpam-5979	52	79	cd	cd	PROPN
ejpam-5979	52	80	σ	σ	PROPN
ejpam-5979	52	81	θ+µ(τ	θ+µ(τ	PROPN
ejpam-5979	52	82	)	)	PUNCT
ejpam-5979	52	83	=	=	NOUN
ejpam-5979	52	84	(	(	PUNCT
ejpam-5979	52	85	ϱ	ϱ	PROPN
ejpam-5979	52	86	cd	cd	PROPN
ejpam-5979	52	87	σ	σ	X
ejpam-5979	52	88	θ+	θ+	PROPN
ejpam-5979	52	89	[	[	PUNCT
ejpam-5979	52	90	µ(τ)−	µ(τ)−	PROPN
ejpam-5979	52	91	n−1∑	n−1∑	NUM
ejpam-5979	52	92	l=0	l=0	PROPN
ejpam-5979	52	93	µ(l)(θ	µ(l)(θ	NOUN
ejpam-5979	52	94	)	)	PUNCT
ejpam-5979	52	95	l	l	NOUN
ejpam-5979	52	96	!	!	PUNCT
ejpam-5979	53	1	(	(	PUNCT
ejpam-5979	53	2	τ	τ	X
ejpam-5979	53	3	−	−	PROPN
ejpam-5979	53	4	θ)l	θ)l	X
ejpam-5979	53	5	]	]	PUNCT
ejpam-5979	53	6	)	)	PUNCT
ejpam-5979	53	7	(	(	PUNCT
ejpam-5979	53	8	τ	τ	X
ejpam-5979	53	9	)	)	PUNCT
ejpam-5979	53	10	,	,	PUNCT
ejpam-5979	53	11	(	(	PUNCT
ejpam-5979	53	12	4	4	X
ejpam-5979	53	13	)	)	PUNCT
ejpam-5979	54	1	where	where	SCONJ
ejpam-5979	54	2	n	n	NOUN
ejpam-5979	54	3	=	=	SYM
ejpam-5979	55	1	[	[	X
ejpam-5979	55	2	re(σ	re(σ	X
ejpam-5979	55	3	)	)	PUNCT
ejpam-5979	55	4	]	]	PUNCT
ejpam-5979	55	5	.	.	PUNCT
ejpam-5979	56	1	lemma	lemma	PROPN
ejpam-5979	56	2	1	1	X
ejpam-5979	56	3	.	.	PUNCT
ejpam-5979	57	1	let	let	VERB
ejpam-5979	57	2	σ	σ	NOUN
ejpam-5979	57	3	,	,	PUNCT
ejpam-5979	57	4	ϱ	ϱ	ADP
ejpam-5979	57	5	>	>	X
ejpam-5979	57	6	0	0	NUM
ejpam-5979	57	7	and	and	CCONJ
ejpam-5979	57	8	µ	µ	PROPN
ejpam-5979	57	9	∈	∈	PROPN
ejpam-5979	57	10	c(j	c(j	NOUN
ejpam-5979	57	11	,	,	PUNCT
ejpam-5979	57	12	r	r	NOUN
ejpam-5979	57	13	)	)	PUNCT
ejpam-5979	57	14	∩	∩	ADJ
ejpam-5979	57	15	c1(j	c1(j	NOUN
ejpam-5979	57	16	,	,	PUNCT
ejpam-5979	57	17	r	r	NOUN
ejpam-5979	57	18	)	)	PUNCT
ejpam-5979	57	19	.	.	PUNCT
ejpam-5979	58	1	then	then	ADV
ejpam-5979	58	2	1	1	X
ejpam-5979	58	3	.	.	PUNCT
ejpam-5979	59	1	the	the	DET
ejpam-5979	59	2	generalized	generalize	VERB
ejpam-5979	59	3	caputo	caputo	PROPN
ejpam-5979	59	4	fractional	fractional	PROPN
ejpam-5979	59	5	differential	differential	NOUN
ejpam-5979	59	6	equation	equation	NOUN
ejpam-5979	59	7	ϱ	ϱ	ADP
ejpam-5979	59	8	cd	cd	PROPN
ejpam-5979	59	9	σ	σ	PROPN
ejpam-5979	59	10	θ+µ(τ	θ+µ(τ	PROPN
ejpam-5979	59	11	)	)	PUNCT
ejpam-5979	59	12	=	=	SYM
ejpam-5979	59	13	0	0	NUM
ejpam-5979	59	14	,	,	PUNCT
ejpam-5979	59	15	has	have	VERB
ejpam-5979	59	16	a	a	DET
ejpam-5979	59	17	solution	solution	NOUN
ejpam-5979	59	18	.	.	PUNCT
ejpam-5979	60	1	µ(τ	µ(τ	NOUN
ejpam-5979	60	2	)	)	PUNCT
ejpam-5979	60	3	=	=	SYM
ejpam-5979	60	4	p0	p0	NOUN
ejpam-5979	60	5	+	+	CCONJ
ejpam-5979	60	6	p1	p1	PROPN
ejpam-5979	60	7	(	(	PUNCT
ejpam-5979	60	8	τϱ−θϱ	τϱ−θϱ	ADP
ejpam-5979	60	9	ϱ	ϱ	PROPN
ejpam-5979	60	10	)	)	PUNCT
ejpam-5979	61	1	+	+	CCONJ
ejpam-5979	61	2	p2	p2	PROPN
ejpam-5979	61	3	(	(	PUNCT
ejpam-5979	61	4	τϱ−θϱ	τϱ−θϱ	ADP
ejpam-5979	61	5	ϱ	ϱ	PROPN
ejpam-5979	61	6	)	)	PUNCT
ejpam-5979	61	7	2	2	NUM
ejpam-5979	61	8	+	+	CCONJ
ejpam-5979	61	9	...	...	PUNCT
ejpam-5979	62	1	+	+	CCONJ
ejpam-5979	62	2	pn−1	pn−1	ADJ
ejpam-5979	62	3	(	(	PUNCT
ejpam-5979	62	4	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	62	5	ϱ	ϱ	PROPN
ejpam-5979	62	6	)	)	PUNCT
ejpam-5979	62	7	n−1	n−1	PROPN
ejpam-5979	62	8	,	,	PUNCT
ejpam-5979	62	9	where	where	SCONJ
ejpam-5979	62	10	pi	pi	NOUN
ejpam-5979	62	11	∈	∈	PROPN
ejpam-5979	62	12	r	r	PROPN
ejpam-5979	62	13	,	,	PUNCT
ejpam-5979	62	14	i	i	NOUN
ejpam-5979	62	15	=	=	NOUN
ejpam-5979	62	16	0	0	NUM
ejpam-5979	62	17	,	,	PUNCT
ejpam-5979	62	18	1	1	NUM
ejpam-5979	62	19	,	,	PUNCT
ejpam-5979	62	20	2	2	NUM
ejpam-5979	62	21	,	,	PUNCT
ejpam-5979	62	22	...	...	PUNCT
ejpam-5979	62	23	,	,	PUNCT
ejpam-5979	62	24	n−	n−	NOUN
ejpam-5979	62	25	1	1	NUM
ejpam-5979	62	26	and	and	CCONJ
ejpam-5979	62	27	n	n	NOUN
ejpam-5979	62	28	=	=	SYM
ejpam-5979	63	1	[	[	X
ejpam-5979	63	2	σ	σ	X
ejpam-5979	63	3	]	]	X
ejpam-5979	63	4	+	+	NUM
ejpam-5979	63	5	1	1	NUM
ejpam-5979	63	6	.	.	X
ejpam-5979	63	7	2	2	NUM
ejpam-5979	63	8	.	.	X
ejpam-5979	64	1	if	if	SCONJ
ejpam-5979	64	2	µ	µ	X
ejpam-5979	64	3	,	,	PUNCT
ejpam-5979	64	4	ϱ	ϱ	ADP
ejpam-5979	64	5	cdσ	cdσ	NOUN
ejpam-5979	64	6	θ+µ	θ+µ	NUM
ejpam-5979	64	7	∈	∈	PROPN
ejpam-5979	64	8	c(j	c(j	NOUN
ejpam-5979	64	9	,	,	PUNCT
ejpam-5979	64	10	r	r	NOUN
ejpam-5979	64	11	)	)	PUNCT
ejpam-5979	64	12	∩	∩	ADJ
ejpam-5979	64	13	c1(j	c1(j	NOUN
ejpam-5979	64	14	,	,	PUNCT
ejpam-5979	64	15	r	r	NOUN
ejpam-5979	64	16	)	)	PUNCT
ejpam-5979	64	17	.	.	PUNCT
ejpam-5979	65	1	then	then	ADV
ejpam-5979	65	2	ϱiσθ+	ϱiσθ+	VERB
ejpam-5979	65	3	ϱcdσ	ϱcdσ	NOUN
ejpam-5979	65	4	θ+µ(τ	θ+µ(τ	NUM
ejpam-5979	65	5	)	)	PUNCT
ejpam-5979	65	6	=	=	SYM
ejpam-5979	65	7	µ(τ	µ(τ	PROPN
ejpam-5979	65	8	)	)	PUNCT
ejpam-5979	66	1	+	+	CCONJ
ejpam-5979	66	2	p0	p0	NOUN
ejpam-5979	66	3	+	+	CCONJ
ejpam-5979	66	4	p1	p1	PROPN
ejpam-5979	66	5	(	(	PUNCT
ejpam-5979	66	6	τϱ−θϱ	τϱ−θϱ	ADP
ejpam-5979	66	7	ϱ	ϱ	PROPN
ejpam-5979	66	8	)	)	PUNCT
ejpam-5979	66	9	+	+	CCONJ
ejpam-5979	66	10	p2	p2	PROPN
ejpam-5979	66	11	(	(	PUNCT
ejpam-5979	66	12	τϱ−θϱ	τϱ−θϱ	ADP
ejpam-5979	66	13	ϱ	ϱ	PROPN
ejpam-5979	66	14	)	)	PUNCT
ejpam-5979	66	15	2	2	NUM
ejpam-5979	66	16	+	+	CCONJ
ejpam-5979	66	17	...	...	PUNCT
ejpam-5979	67	1	+	+	CCONJ
ejpam-5979	67	2	pn−1	pn−1	ADJ
ejpam-5979	67	3	(	(	PUNCT
ejpam-5979	67	4	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	67	5	ϱ	ϱ	PROPN
ejpam-5979	67	6	)	)	PUNCT
ejpam-5979	67	7	n−1	n−1	PROPN
ejpam-5979	67	8	,	,	PUNCT
ejpam-5979	67	9	(	(	PUNCT
ejpam-5979	67	10	5	5	NUM
ejpam-5979	67	11	)	)	PUNCT
ejpam-5979	67	12	where	where	SCONJ
ejpam-5979	67	13	pi	pi	NOUN
ejpam-5979	67	14	∈	∈	PROPN
ejpam-5979	67	15	r	r	PROPN
ejpam-5979	67	16	,	,	PUNCT
ejpam-5979	67	17	i	i	NOUN
ejpam-5979	67	18	=	=	NOUN
ejpam-5979	67	19	0	0	NUM
ejpam-5979	67	20	,	,	PUNCT
ejpam-5979	67	21	1	1	NUM
ejpam-5979	67	22	,	,	PUNCT
ejpam-5979	67	23	2	2	NUM
ejpam-5979	67	24	,	,	PUNCT
ejpam-5979	67	25	...	...	PUNCT
ejpam-5979	67	26	,	,	PUNCT
ejpam-5979	67	27	n−	n−	NOUN
ejpam-5979	67	28	1	1	NUM
ejpam-5979	67	29	and	and	CCONJ
ejpam-5979	67	30	n	n	NOUN
ejpam-5979	67	31	=	=	SYM
ejpam-5979	68	1	[	[	X
ejpam-5979	68	2	σ	σ	X
ejpam-5979	68	3	]	]	X
ejpam-5979	68	4	+	+	NUM
ejpam-5979	68	5	1	1	NUM
ejpam-5979	68	6	.	.	X
ejpam-5979	68	7	3	3	NUM
ejpam-5979	68	8	.	.	X
ejpam-5979	68	9	main	main	ADJ
ejpam-5979	68	10	results	result	NOUN
ejpam-5979	68	11	at	at	ADP
ejpam-5979	68	12	the	the	DET
ejpam-5979	68	13	heart	heart	NOUN
ejpam-5979	68	14	of	of	ADP
ejpam-5979	68	15	this	this	DET
ejpam-5979	68	16	passage	passage	NOUN
ejpam-5979	68	17	,	,	PUNCT
ejpam-5979	68	18	we	we	PRON
ejpam-5979	68	19	witness	witness	VERB
ejpam-5979	68	20	significant	significant	ADJ
ejpam-5979	68	21	propositions	proposition	NOUN
ejpam-5979	68	22	and	and	CCONJ
ejpam-5979	68	23	theorems	theorem	NOUN
ejpam-5979	68	24	on	on	ADP
ejpam-5979	68	25	which	which	PRON
ejpam-5979	68	26	all	all	DET
ejpam-5979	68	27	this	this	DET
ejpam-5979	68	28	work	work	NOUN
ejpam-5979	68	29	is	be	AUX
ejpam-5979	68	30	based	base	VERB
ejpam-5979	68	31	.	.	PUNCT
ejpam-5979	69	1	we	we	PRON
ejpam-5979	69	2	review	review	VERB
ejpam-5979	69	3	the	the	DET
ejpam-5979	69	4	integral	integral	ADJ
ejpam-5979	69	5	formula	formula	NOUN
ejpam-5979	69	6	for	for	ADP
ejpam-5979	69	7	the	the	DET
ejpam-5979	69	8	generalized	generalize	VERB
ejpam-5979	69	9	fractional	fractional	ADJ
ejpam-5979	69	10	order	order	NOUN
ejpam-5979	69	11	bvp	bvp	NOUN
ejpam-5979	69	12	(	(	PUNCT
ejpam-5979	69	13	1	1	NUM
ejpam-5979	69	14	)	)	PUNCT
ejpam-5979	69	15	from	from	ADP
ejpam-5979	69	16	the	the	DET
ejpam-5979	69	17	principle	principle	NOUN
ejpam-5979	69	18	of	of	ADP
ejpam-5979	69	19	the	the	DET
ejpam-5979	69	20	green	green	ADJ
ejpam-5979	69	21	function	function	NOUN
ejpam-5979	69	22	.	.	PUNCT
ejpam-5979	70	1	lemma	lemma	PROPN
ejpam-5979	70	2	2	2	X
ejpam-5979	70	3	.	.	X
ejpam-5979	70	4	presume	presume	VERB
ejpam-5979	70	5	that	that	SCONJ
ejpam-5979	70	6	θ	θ	PROPN
ejpam-5979	70	7	is	be	AUX
ejpam-5979	70	8	a	a	DET
ejpam-5979	70	9	function	function	NOUN
ejpam-5979	70	10	is	be	AUX
ejpam-5979	70	11	continuous	continuous	ADJ
ejpam-5979	70	12	and	and	CCONJ
ejpam-5979	70	13	either	either	CCONJ
ejpam-5979	70	14	a	a	DET
ejpam-5979	70	15	function	function	NOUN
ejpam-5979	70	16	µ	µ	PRON
ejpam-5979	70	17	∈	∈	PROPN
ejpam-5979	70	18	c[θ	c[θ	PROPN
ejpam-5979	70	19	,	,	PUNCT
ejpam-5979	70	20	ϑ	ϑ	X
ejpam-5979	70	21	]	]	X
ejpam-5979	70	22	is	be	AUX
ejpam-5979	70	23	a	a	DET
ejpam-5979	70	24	solution	solution	NOUN
ejpam-5979	70	25	of	of	ADP
ejpam-5979	70	26	(	(	PUNCT
ejpam-5979	70	27	1	1	X
ejpam-5979	70	28	)	)	PUNCT
ejpam-5979	70	29	equivalent	equivalent	NOUN
ejpam-5979	70	30	that	that	SCONJ
ejpam-5979	70	31	µ	µ	ADJ
ejpam-5979	70	32	check	check	VERB
ejpam-5979	70	33	the	the	DET
ejpam-5979	70	34	integral	integral	ADJ
ejpam-5979	70	35	equation	equation	NOUN
ejpam-5979	70	36	µ(τ	µ(τ	NOUN
ejpam-5979	70	37	)	)	PUNCT
ejpam-5979	70	38	=	=	SYM
ejpam-5979	71	1	[	[	PUNCT
ejpam-5979	71	2	(	(	PUNCT
ejpam-5979	71	3	λ2	λ2	NOUN
ejpam-5979	71	4	−	−	PROPN
ejpam-5979	71	5	λ1	λ1	PROPN
ejpam-5979	71	6	)	)	PUNCT
ejpam-5979	71	7	(	(	PUNCT
ejpam-5979	71	8	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	71	9	)	)	PUNCT
ejpam-5979	71	10	(	(	PUNCT
ejpam-5979	71	11	ϑϱ−θϱ	ϑϱ−θϱ	ADV
ejpam-5979	71	12	)	)	PUNCT
ejpam-5979	72	1	+	+	CCONJ
ejpam-5979	72	2	λ1	λ1	ADJ
ejpam-5979	72	3	]	]	PUNCT
ejpam-5979	73	1	+	+	NUM
ejpam-5979	73	2	∫	∫	PROPN
ejpam-5979	73	3	ϑ	ϑ	X
ejpam-5979	73	4	θ	θ	PROPN
ejpam-5979	73	5	ℏ(τ	ℏ(τ	PROPN
ejpam-5979	73	6	,	,	PUNCT
ejpam-5979	73	7	r)θ(r	r)θ(r	NOUN
ejpam-5979	73	8	,	,	PUNCT
ejpam-5979	73	9	µ(r	µ(r	NOUN
ejpam-5979	73	10	)	)	PUNCT
ejpam-5979	73	11	)	)	PUNCT
ejpam-5979	74	1	dr	dr	PROPN
ejpam-5979	74	2	,	,	PUNCT
ejpam-5979	74	3	z.	z.	PROPN
ejpam-5979	74	4	bekri	bekri	PROPN
ejpam-5979	74	5	et	et	PROPN
ejpam-5979	74	6	al	al	PROPN
ejpam-5979	74	7	.	.	PUNCT
ejpam-5979	74	8	/	/	SYM
ejpam-5979	74	9	eur	eur	PROPN
ejpam-5979	74	10	.	.	PUNCT
ejpam-5979	75	1	j.	j.	PROPN
ejpam-5979	75	2	pure	pure	PROPN
ejpam-5979	75	3	appl	appl	PROPN
ejpam-5979	75	4	.	.	PROPN
ejpam-5979	75	5	math	math	PROPN
ejpam-5979	75	6	,	,	PUNCT
ejpam-5979	75	7	18	18	NUM
ejpam-5979	75	8	(	(	PUNCT
ejpam-5979	75	9	2	2	NUM
ejpam-5979	75	10	)	)	PUNCT
ejpam-5979	75	11	(	(	PUNCT
ejpam-5979	75	12	2025	2025	NUM
ejpam-5979	75	13	)	)	PUNCT
ejpam-5979	75	14	,	,	PUNCT
ejpam-5979	75	15	5979	5979	NUM
ejpam-5979	75	16	5	5	NUM
ejpam-5979	75	17	of	of	ADP
ejpam-5979	75	18	20	20	NUM
ejpam-5979	75	19	where	where	SCONJ
ejpam-5979	75	20	ℏ(τ	ℏ(τ	PROPN
ejpam-5979	75	21	,	,	PUNCT
ejpam-5979	75	22	r	r	NOUN
ejpam-5979	75	23	)	)	PUNCT
ejpam-5979	75	24	=	=	SYM
ejpam-5979	76	1	ϱ1−σ	ϱ1−σ	PROPN
ejpam-5979	76	2	γ(σ	γ(σ	ADJ
ejpam-5979	76	3	)	)	PUNCT
ejpam-5979	76	4			PUNCT
ejpam-5979	76	5	(	(	PUNCT
ejpam-5979	76	6	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	76	7	)	)	PUNCT
ejpam-5979	76	8	(	(	PUNCT
ejpam-5979	76	9	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-5979	76	10	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-5979	76	11	−	−	NOUN
ejpam-5979	76	12	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	76	13	−	−	PROPN
ejpam-5979	77	1	rϱ−1(τϱ	rϱ−1(τϱ	VERB
ejpam-5979	77	2	−	−	PROPN
ejpam-5979	77	3	rϱ)σ−1	rϱ)σ−1	PROPN
ejpam-5979	77	4	,	,	PUNCT
ejpam-5979	77	5	θ	θ	PROPN
ejpam-5979	77	6	≤	≤	NUM
ejpam-5979	77	7	r	r	NOUN
ejpam-5979	77	8	≤	≤	NUM
ejpam-5979	77	9	τ	τ	X
ejpam-5979	77	10	≤	≤	PROPN
ejpam-5979	77	11	ϑ	ϑ	X
ejpam-5979	77	12	,	,	PUNCT
ejpam-5979	77	13	(	(	PUNCT
ejpam-5979	77	14	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	77	15	)	)	PUNCT
ejpam-5979	77	16	(	(	PUNCT
ejpam-5979	77	17	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-5979	77	18	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-5979	77	19	−	−	PROPN
ejpam-5979	77	20	rϱ)σ−1	rϱ)σ−1	PROPN
ejpam-5979	77	21	,	,	PUNCT
ejpam-5979	77	22	θ	θ	PROPN
ejpam-5979	77	23	≤	≤	NUM
ejpam-5979	77	24	τ	τ	PUNCT
ejpam-5979	77	25	≤	≤	NUM
ejpam-5979	77	26	r	r	NOUN
ejpam-5979	77	27	≤	≤	NUM
ejpam-5979	77	28	ϑ.	ϑ.	NOUN
ejpam-5979	77	29	(	(	PUNCT
ejpam-5979	77	30	6	6	NUM
ejpam-5979	77	31	)	)	PUNCT
ejpam-5979	77	32	proof	proof	NOUN
ejpam-5979	77	33	.	.	PUNCT
ejpam-5979	78	1	by	by	ADP
ejpam-5979	78	2	the	the	DET
ejpam-5979	78	3	lemma(1),we	lemma(1),we	NOUN
ejpam-5979	78	4	solve	solve	NOUN
ejpam-5979	78	5	this	this	DET
ejpam-5979	78	6	problem	problem	NOUN
ejpam-5979	78	7	ϱ	ϱ	ADP
ejpam-5979	78	8	cd	cd	PROPN
ejpam-5979	78	9	σ	σ	PROPN
ejpam-5979	78	10	θ+µ(τ	θ+µ(τ	PROPN
ejpam-5979	78	11	)	)	PUNCT
ejpam-5979	78	12	=	=	SYM
ejpam-5979	78	13	−q(τ	−q(τ	NOUN
ejpam-5979	78	14	)	)	PUNCT
ejpam-5979	78	15	.	.	PUNCT
ejpam-5979	79	1	according	accord	VERB
ejpam-5979	79	2	to	to	ADP
ejpam-5979	79	3	(	(	PUNCT
ejpam-5979	79	4	5	5	NUM
ejpam-5979	79	5	)	)	PUNCT
ejpam-5979	79	6	,	,	PUNCT
ejpam-5979	79	7	we	we	PRON
ejpam-5979	79	8	obtain	obtain	VERB
ejpam-5979	79	9	ϱiσθ+	ϱiσθ+	X
ejpam-5979	79	10	ϱ	ϱ	ADP
ejpam-5979	79	11	cd	cd	PROPN
ejpam-5979	79	12	σ	σ	PROPN
ejpam-5979	79	13	θ+µ(τ	θ+µ(τ	PROPN
ejpam-5979	79	14	)	)	PUNCT
ejpam-5979	79	15	=	=	SYM
ejpam-5979	79	16	−ϱiσθ+q(τ	−ϱiσθ+q(τ	ADJ
ejpam-5979	79	17	)	)	PUNCT
ejpam-5979	80	1	+	+	CCONJ
ejpam-5979	80	2	p0	p0	NOUN
ejpam-5979	80	3	+	+	CCONJ
ejpam-5979	80	4	p1	p1	PROPN
ejpam-5979	80	5	(	(	PUNCT
ejpam-5979	80	6	τϱ	τϱ	ADP
ejpam-5979	80	7	−	−	NOUN
ejpam-5979	80	8	θϱ	θϱ	NOUN
ejpam-5979	80	9	)	)	PUNCT
ejpam-5979	80	10	ϱ	ϱ	ADP
ejpam-5979	80	11	µ(τ	µ(τ	PROPN
ejpam-5979	80	12	)	)	PUNCT
ejpam-5979	80	13	=	=	PUNCT
ejpam-5979	80	14	−ϱiσθ+q(τ	−ϱiσθ+q(τ	ADJ
ejpam-5979	80	15	)	)	PUNCT
ejpam-5979	81	1	+	+	CCONJ
ejpam-5979	81	2	p0	p0	NOUN
ejpam-5979	81	3	+	+	CCONJ
ejpam-5979	81	4	p1	p1	PROPN
ejpam-5979	81	5	(	(	PUNCT
ejpam-5979	81	6	τϱ	τϱ	ADP
ejpam-5979	81	7	−	−	NOUN
ejpam-5979	81	8	θϱ	θϱ	NOUN
ejpam-5979	81	9	)	)	PUNCT
ejpam-5979	81	10	ϱ	ϱ	ADP
ejpam-5979	81	11	µ(τ	µ(τ	NOUN
ejpam-5979	81	12	)	)	PUNCT
ejpam-5979	81	13	=	=	PUNCT
ejpam-5979	82	1	−ϱ1−σ	−ϱ1−σ	VERB
ejpam-5979	82	2	γ(σ	γ(σ	PROPN
ejpam-5979	82	3	)	)	PUNCT
ejpam-5979	82	4	∫	∫	PROPN
ejpam-5979	83	1	τ	τ	PROPN
ejpam-5979	83	2	θ	θ	PROPN
ejpam-5979	83	3	rϱ−1(τϱ	rϱ−1(τϱ	VERB
ejpam-5979	83	4	−	−	NOUN
ejpam-5979	84	1	rϱ)σ−1q(r)dr	rϱ)σ−1q(r)dr	NOUN
ejpam-5979	84	2	+	+	CCONJ
ejpam-5979	84	3	p0	p0	NOUN
ejpam-5979	84	4	+	+	CCONJ
ejpam-5979	84	5	p1	p1	PROPN
ejpam-5979	84	6	(	(	PUNCT
ejpam-5979	84	7	τϱ−θϱ	τϱ−θϱ	NOUN
ejpam-5979	84	8	)	)	PUNCT
ejpam-5979	84	9	ϱ	ϱ	NOUN
ejpam-5979	84	10	,	,	PUNCT
ejpam-5979	84	11	by	by	ADP
ejpam-5979	84	12	using	use	VERB
ejpam-5979	84	13	boundary	boundary	ADJ
ejpam-5979	84	14	conditions	condition	NOUN
ejpam-5979	84	15	µ(θ	µ(θ	ADJ
ejpam-5979	84	16	)	)	PUNCT
ejpam-5979	85	1	=	=	PUNCT
ejpam-5979	85	2	λ1	λ1	ADJ
ejpam-5979	85	3	=	=	NOUN
ejpam-5979	85	4	⇒	⇒	NOUN
ejpam-5979	85	5	p0	p0	NOUN
ejpam-5979	85	6	=	=	SYM
ejpam-5979	85	7	λ1	λ1	PROPN
ejpam-5979	85	8	,	,	PUNCT
ejpam-5979	85	9	µ(ϑ	µ(ϑ	PROPN
ejpam-5979	85	10	)	)	PUNCT
ejpam-5979	85	11	=	=	SYM
ejpam-5979	85	12	λ2	λ2	NOUN
ejpam-5979	85	13	=	=	NOUN
ejpam-5979	85	14	⇒	⇒	NOUN
ejpam-5979	85	15	p1	p1	NOUN
ejpam-5979	85	16	=	=	SYM
ejpam-5979	85	17	ϱ(λ2−λ1	ϱ(λ2−λ1	NOUN
ejpam-5979	85	18	)	)	PUNCT
ejpam-5979	85	19	(	(	PUNCT
ejpam-5979	85	20	ϑϱ−θϱ	ϑϱ−θϱ	ADV
ejpam-5979	85	21	)	)	PUNCT
ejpam-5979	86	1	+	+	CCONJ
ejpam-5979	86	2	ϱ2−σ	ϱ2−σ	PROPN
ejpam-5979	86	3	(	(	PUNCT
ejpam-5979	86	4	ϑϱ−θϱ)γ(σ	ϑϱ−θϱ)γ(σ	PROPN
ejpam-5979	86	5	)	)	PUNCT
ejpam-5979	86	6	∫	∫	PROPN
ejpam-5979	86	7	ϑ	ϑ	PROPN
ejpam-5979	86	8	θ	θ	PROPN
ejpam-5979	86	9	rϱ−1(ϑϱ	rϱ−1(ϑϱ	NOUN
ejpam-5979	86	10	−	−	PROPN
ejpam-5979	86	11	rϱ)σ−1q(r	rϱ)σ−1q(r	PROPN
ejpam-5979	86	12	)	)	PUNCT
ejpam-5979	86	13	dr	dr	PROPN
ejpam-5979	86	14	.	.	PROPN
ejpam-5979	86	15	now	now	ADV
ejpam-5979	86	16	,	,	PUNCT
ejpam-5979	86	17	by	by	ADP
ejpam-5979	86	18	replacing	replace	VERB
ejpam-5979	86	19	in	in	ADP
ejpam-5979	86	20	µ(τ	µ(τ	NOUN
ejpam-5979	86	21	)	)	PUNCT
ejpam-5979	86	22	,	,	PUNCT
ejpam-5979	86	23	and	and	CCONJ
ejpam-5979	86	24	we	we	PRON
ejpam-5979	86	25	get	get	VERB
ejpam-5979	86	26	µ(τ	µ(τ	NOUN
ejpam-5979	86	27	)	)	PUNCT
ejpam-5979	86	28	=	=	PUNCT
ejpam-5979	87	1	−ϱ1−σ	−ϱ1−σ	VERB
ejpam-5979	87	2	γ(σ	γ(σ	PROPN
ejpam-5979	87	3	)	)	PUNCT
ejpam-5979	87	4	∫	∫	PROPN
ejpam-5979	88	1	τ	τ	PROPN
ejpam-5979	88	2	θ	θ	PROPN
ejpam-5979	88	3	rϱ−1(τϱ	rϱ−1(τϱ	VERB
ejpam-5979	88	4	−	−	PROPN
ejpam-5979	89	1	rϱ)σ−1q(r	rϱ)σ−1q(r	NOUN
ejpam-5979	89	2	)	)	PUNCT
ejpam-5979	89	3	dr	dr	PROPN
ejpam-5979	89	4	+	+	CCONJ
ejpam-5979	89	5	[	[	PUNCT
ejpam-5979	89	6	ϱ(λ2	ϱ(λ2	NOUN
ejpam-5979	89	7	−	−	PROPN
ejpam-5979	89	8	λ1	λ1	PROPN
ejpam-5979	89	9	)	)	PUNCT
ejpam-5979	90	1	+	+	CCONJ
ejpam-5979	90	2	ϱ2−σ	ϱ2−σ	PROPN
ejpam-5979	90	3	γ(σ	γ(σ	ADJ
ejpam-5979	90	4	)	)	PUNCT
ejpam-5979	90	5	∫	∫	PROPN
ejpam-5979	90	6	ϑ	ϑ	PROPN
ejpam-5979	90	7	θ	θ	X
ejpam-5979	90	8	rϱ−1(ϑϱ	rϱ−1(ϑϱ	NOUN
ejpam-5979	90	9	−	−	PROPN
ejpam-5979	91	1	rϱ)σ−1q(r)dr	rϱ)σ−1q(r)dr	NOUN
ejpam-5979	91	2	]	]	PUNCT
ejpam-5979	91	3	(	(	PUNCT
ejpam-5979	91	4	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	91	5	)	)	PUNCT
ejpam-5979	91	6	(	(	PUNCT
ejpam-5979	91	7	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-5979	91	8	)	)	PUNCT
ejpam-5979	92	1	+	+	CCONJ
ejpam-5979	92	2	λ1	λ1	ADJ
ejpam-5979	92	3	,	,	PUNCT
ejpam-5979	92	4	and	and	CCONJ
ejpam-5979	92	5	µ(τ	µ(τ	PROPN
ejpam-5979	92	6	)	)	PUNCT
ejpam-5979	92	7	=	=	PUNCT
ejpam-5979	93	1	−ϱ1−σ	−ϱ1−σ	VERB
ejpam-5979	93	2	γ(σ	γ(σ	PROPN
ejpam-5979	93	3	)	)	PUNCT
ejpam-5979	93	4	∫	∫	PROPN
ejpam-5979	94	1	τ	τ	PROPN
ejpam-5979	94	2	θ	θ	PROPN
ejpam-5979	94	3	rϱ−1(τϱ	rϱ−1(τϱ	VERB
ejpam-5979	94	4	−	−	PROPN
ejpam-5979	95	1	rϱ)σ−1q(r	rϱ)σ−1q(r	NOUN
ejpam-5979	95	2	)	)	PUNCT
ejpam-5979	95	3	dr	dr	PROPN
ejpam-5979	95	4	+	+	PROPN
ejpam-5979	95	5	ϱ1−σ(τϱ−θϱ	ϱ1−σ(τϱ−θϱ	PROPN
ejpam-5979	95	6	)	)	PUNCT
ejpam-5979	95	7	(	(	PUNCT
ejpam-5979	95	8	ϑϱ−θϱ)γ(σ)∫	ϑϱ−θϱ)γ(σ)∫	ADP
ejpam-5979	95	9	ϑ	ϑ	X
ejpam-5979	95	10	θ	θ	PROPN
ejpam-5979	95	11	rϱ−1(ϑϱ	rϱ−1(ϑϱ	NOUN
ejpam-5979	96	1	−	−	PROPN
ejpam-5979	96	2	rϱ)σ−1q(r	rϱ)σ−1q(r	NOUN
ejpam-5979	96	3	)	)	PUNCT
ejpam-5979	96	4	dr	dr	PROPN
ejpam-5979	96	5	+	+	CCONJ
ejpam-5979	96	6	(	(	PUNCT
ejpam-5979	96	7	λ2	λ2	PROPN
ejpam-5979	96	8	−	−	PROPN
ejpam-5979	96	9	λ1	λ1	PROPN
ejpam-5979	96	10	)	)	PUNCT
ejpam-5979	96	11	(	(	PUNCT
ejpam-5979	96	12	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	96	13	)	)	PUNCT
ejpam-5979	96	14	(	(	PUNCT
ejpam-5979	96	15	ϑϱ−θϱ	ϑϱ−θϱ	ADV
ejpam-5979	96	16	)	)	PUNCT
ejpam-5979	97	1	+	+	SYM
ejpam-5979	97	2	λ1	λ1	ADJ
ejpam-5979	97	3	.	.	PUNCT
ejpam-5979	98	1	therefore	therefore	ADV
ejpam-5979	98	2	,	,	PUNCT
ejpam-5979	98	3	µ(τ	µ(τ	PROPN
ejpam-5979	98	4	)	)	PUNCT
ejpam-5979	98	5	=	=	SYM
ejpam-5979	99	1	[	[	PUNCT
ejpam-5979	99	2	(	(	PUNCT
ejpam-5979	99	3	λ2	λ2	NOUN
ejpam-5979	99	4	−	−	PROPN
ejpam-5979	99	5	λ1	λ1	PROPN
ejpam-5979	99	6	)	)	PUNCT
ejpam-5979	99	7	(	(	PUNCT
ejpam-5979	99	8	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	99	9	)	)	PUNCT
ejpam-5979	99	10	(	(	PUNCT
ejpam-5979	99	11	ϑϱ−θϱ	ϑϱ−θϱ	ADV
ejpam-5979	99	12	)	)	PUNCT
ejpam-5979	100	1	+	+	CCONJ
ejpam-5979	100	2	λ1	λ1	ADJ
ejpam-5979	100	3	]	]	PUNCT
ejpam-5979	101	1	+	+	CCONJ
ejpam-5979	101	2	ϱ1−σ	ϱ1−σ	PROPN
ejpam-5979	101	3	γ(σ	γ(σ	ADJ
ejpam-5979	101	4	)	)	PUNCT
ejpam-5979	101	5	∫	∫	PROPN
ejpam-5979	101	6	τ	τ	PROPN
ejpam-5979	101	7	θ	θ	PROPN
ejpam-5979	101	8	(	(	PUNCT
ejpam-5979	101	9	(	(	PUNCT
ejpam-5979	101	10	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	101	11	)	)	PUNCT
ejpam-5979	101	12	(	(	PUNCT
ejpam-5979	101	13	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-5979	101	14	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-5979	101	15	−	−	NOUN
ejpam-5979	101	16	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	101	17	−	−	PROPN
ejpam-5979	102	1	rϱ−1(τϱ	rϱ−1(τϱ	INTJ
ejpam-5979	102	2	−	−	PROPN
ejpam-5979	102	3	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	102	4	)	)	PUNCT
ejpam-5979	103	1	q(r	q(r	PROPN
ejpam-5979	103	2	)	)	PUNCT
ejpam-5979	104	1	dr	dr	PROPN
ejpam-5979	104	2	+	+	PROPN
ejpam-5979	104	3	ϱ1−σ	ϱ1−σ	PROPN
ejpam-5979	104	4	γ(σ	γ(σ	ADJ
ejpam-5979	104	5	)	)	PUNCT
ejpam-5979	104	6	∫	∫	PROPN
ejpam-5979	105	1	ϑ	ϑ	X
ejpam-5979	105	2	τ	τ	X
ejpam-5979	105	3	(	(	PUNCT
ejpam-5979	105	4	τϱ−θϱ	τϱ−θϱ	PROPN
ejpam-5979	105	5	)	)	PUNCT
ejpam-5979	105	6	(	(	PUNCT
ejpam-5979	105	7	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-5979	105	8	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-5979	105	9	−	−	PROPN
ejpam-5979	105	10	rϱ)σ−1q(r	rϱ)σ−1q(r	NOUN
ejpam-5979	105	11	)	)	PUNCT
ejpam-5979	105	12	dr	dr	PROPN
ejpam-5979	105	13	,	,	PUNCT
ejpam-5979	105	14	z.	z.	PROPN
ejpam-5979	105	15	bekri	bekri	PROPN
ejpam-5979	105	16	et	et	PROPN
ejpam-5979	105	17	al	al	PROPN
ejpam-5979	105	18	.	.	PUNCT
ejpam-5979	105	19	/	/	SYM
ejpam-5979	105	20	eur	eur	PROPN
ejpam-5979	105	21	.	.	PUNCT
ejpam-5979	106	1	j.	j.	PROPN
ejpam-5979	106	2	pure	pure	PROPN
ejpam-5979	106	3	appl	appl	PROPN
ejpam-5979	106	4	.	.	PROPN
ejpam-5979	106	5	math	math	PROPN
ejpam-5979	106	6	,	,	PUNCT
ejpam-5979	106	7	18	18	NUM
ejpam-5979	106	8	(	(	PUNCT
ejpam-5979	106	9	2	2	NUM
ejpam-5979	106	10	)	)	PUNCT
ejpam-5979	106	11	(	(	PUNCT
ejpam-5979	106	12	2025	2025	NUM
ejpam-5979	106	13	)	)	PUNCT
ejpam-5979	106	14	,	,	PUNCT
ejpam-5979	106	15	5979	5979	NUM
ejpam-5979	106	16	6	6	NUM
ejpam-5979	106	17	of	of	ADP
ejpam-5979	106	18	20	20	NUM
ejpam-5979	106	19	and	and	CCONJ
ejpam-5979	106	20	the	the	DET
ejpam-5979	106	21	proof	proof	NOUN
ejpam-5979	106	22	is	be	AUX
ejpam-5979	106	23	complete	complete	ADJ
ejpam-5979	106	24	.	.	PUNCT
ejpam-5979	107	1	immediately	immediately	ADV
ejpam-5979	107	2	,	,	PUNCT
ejpam-5979	107	3	we	we	PRON
ejpam-5979	107	4	will	will	AUX
ejpam-5979	107	5	present	present	VERB
ejpam-5979	107	6	the	the	DET
ejpam-5979	107	7	important	important	ADJ
ejpam-5979	107	8	salient	salient	NOUN
ejpam-5979	107	9	rules	rule	NOUN
ejpam-5979	107	10	that	that	PRON
ejpam-5979	107	11	will	will	AUX
ejpam-5979	107	12	make	make	VERB
ejpam-5979	107	13	it	it	PRON
ejpam-5979	107	14	easier	easy	ADJ
ejpam-5979	107	15	for	for	SCONJ
ejpam-5979	107	16	us	we	PRON
ejpam-5979	107	17	to	to	PART
ejpam-5979	107	18	achieve	achieve	VERB
ejpam-5979	107	19	our	our	PRON
ejpam-5979	107	20	desired	desire	VERB
ejpam-5979	107	21	objectives	objective	NOUN
ejpam-5979	107	22	.	.	PUNCT
ejpam-5979	108	1	proposition	proposition	NOUN
ejpam-5979	108	2	1	1	NUM
ejpam-5979	108	3	.	.	PUNCT
ejpam-5979	109	1	depending	depend	VERB
ejpam-5979	109	2	on	on	ADP
ejpam-5979	109	3	the	the	DET
ejpam-5979	109	4	green	green	ADJ
ejpam-5979	109	5	function	function	NOUN
ejpam-5979	109	6	ℏ	ℏ	PROPN
ejpam-5979	109	7	is	be	AUX
ejpam-5979	109	8	mentioned	mention	VERB
ejpam-5979	109	9	in	in	ADP
ejpam-5979	109	10	lemma	lemma	PROPN
ejpam-5979	109	11	2	2	NUM
ejpam-5979	109	12	.	.	PROPN
ejpam-5979	109	13	therefore∫	therefore∫	ADP
ejpam-5979	109	14	ϑ	ϑ	PROPN
ejpam-5979	109	15	θ	θ	PROPN
ejpam-5979	109	16	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	109	17	,	,	PUNCT
ejpam-5979	109	18	r)|dr	r)|dr	NOUN
ejpam-5979	109	19	≤	≤	NUM
ejpam-5979	109	20	1	1	NUM
ejpam-5979	109	21	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	109	22	)	)	PUNCT
ejpam-5979	109	23	[	[	PUNCT
ejpam-5979	109	24	(	(	PUNCT
ejpam-5979	109	25	ϑϱ	ϑϱ	ADP
ejpam-5979	109	26	−	−	PROPN
ejpam-5979	109	27	θϱ)σ−1(τϱ	θϱ)σ−1(τϱ	PROPN
ejpam-5979	109	28	−	−	PROPN
ejpam-5979	109	29	θϱ)−	θϱ)−	NOUN
ejpam-5979	109	30	(	(	PUNCT
ejpam-5979	109	31	τϱ	τϱ	ADP
ejpam-5979	109	32	−	−	PROPN
ejpam-5979	109	33	θϱ)σ	θϱ)σ	PROPN
ejpam-5979	109	34	]	]	PUNCT
ejpam-5979	109	35	.	.	PUNCT
ejpam-5979	110	1	(	(	PUNCT
ejpam-5979	110	2	7	7	X
ejpam-5979	110	3	)	)	PUNCT
ejpam-5979	110	4	proof	proof	NOUN
ejpam-5979	110	5	.	.	PUNCT
ejpam-5979	111	1	we	we	PRON
ejpam-5979	111	2	determine∫	determine∫	VERB
ejpam-5979	111	3	ϑ	ϑ	PROPN
ejpam-5979	111	4	θ	θ	PROPN
ejpam-5979	111	5	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	111	6	,	,	PUNCT
ejpam-5979	111	7	r)|dr	r)|dr	PROPN
ejpam-5979	111	8	,	,	PUNCT
ejpam-5979	111	9	ℏ(τ	ℏ(τ	PROPN
ejpam-5979	111	10	,	,	PUNCT
ejpam-5979	111	11	r	r	NOUN
ejpam-5979	111	12	)	)	PUNCT
ejpam-5979	111	13	≥	≥	NOUN
ejpam-5979	111	14	0	0	NUM
ejpam-5979	111	15	,	,	PUNCT
ejpam-5979	111	16	∀	∀	NUM
ejpam-5979	111	17	θ	θ	NOUN
ejpam-5979	111	18	≤	≤	NUM
ejpam-5979	111	19	τ	τ	X
ejpam-5979	111	20	,	,	PUNCT
ejpam-5979	111	21	r	r	NOUN
ejpam-5979	111	22	≤	≤	NUM
ejpam-5979	111	23	ϑ.	ϑ.	NOUN
ejpam-5979	111	24	according	accord	VERB
ejpam-5979	111	25	to	to	ADP
ejpam-5979	111	26	(	(	PUNCT
ejpam-5979	111	27	6	6	NUM
ejpam-5979	111	28	)	)	PUNCT
ejpam-5979	111	29	,	,	PUNCT
ejpam-5979	111	30	we	we	PRON
ejpam-5979	111	31	have	have	VERB
ejpam-5979	111	32	θ	θ	NOUN
ejpam-5979	111	33	≤	≤	NUM
ejpam-5979	111	34	r	r	NOUN
ejpam-5979	111	35	≤	≤	NUM
ejpam-5979	111	36	τ	τ	X
ejpam-5979	111	37	≤	≤	NOUN
ejpam-5979	111	38	ϑ	ϑ	X
ejpam-5979	111	39	=	=	NOUN
ejpam-5979	111	40	⇒	⇒	NOUN
ejpam-5979	111	41	(	(	PUNCT
ejpam-5979	111	42	τ	τ	X
ejpam-5979	111	43	−	−	PROPN
ejpam-5979	111	44	r	r	NOUN
ejpam-5979	111	45	)	)	PUNCT
ejpam-5979	111	46	≤	≤	NOUN
ejpam-5979	111	47	(	(	PUNCT
ejpam-5979	111	48	ϑ−	ϑ−	NOUN
ejpam-5979	111	49	r	r	NOUN
ejpam-5979	111	50	)	)	PUNCT
ejpam-5979	111	51	,	,	PUNCT
ejpam-5979	111	52	i.e.	i.e.	X
ejpam-5979	111	53	(	(	PUNCT
ejpam-5979	111	54	τϱ	τϱ	ADP
ejpam-5979	111	55	−	−	PROPN
ejpam-5979	111	56	rϱ	rϱ	NOUN
ejpam-5979	111	57	)	)	PUNCT
ejpam-5979	111	58	≤	≤	NOUN
ejpam-5979	111	59	(	(	PUNCT
ejpam-5979	111	60	ϑϱ	ϑϱ	ADP
ejpam-5979	111	61	−	−	NOUN
ejpam-5979	111	62	rϱ	rϱ	NOUN
ejpam-5979	111	63	)	)	PUNCT
ejpam-5979	112	1	=	=	NOUN
ejpam-5979	112	2	⇒	⇒	NOUN
ejpam-5979	112	3	(	(	PUNCT
ejpam-5979	112	4	τϱ	τϱ	ADP
ejpam-5979	112	5	−	−	PROPN
ejpam-5979	112	6	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	112	7	≤	≤	NOUN
ejpam-5979	112	8	(	(	PUNCT
ejpam-5979	112	9	ϑϱ	ϑϱ	ADP
ejpam-5979	112	10	−	−	PROPN
ejpam-5979	112	11	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	112	12	rϱ−1(τϱ	rϱ−1(τϱ	VERB
ejpam-5979	112	13	−	−	PROPN
ejpam-5979	113	1	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	113	2	≤	≤	PUNCT
ejpam-5979	113	3	rϱ−1(ϑϱ	rϱ−1(ϑϱ	PROPN
ejpam-5979	113	4	−	−	PROPN
ejpam-5979	114	1	rϱ)σ−1	rϱ)σ−1	PROPN
ejpam-5979	114	2	.	.	PUNCT
ejpam-5979	115	1	then	then	ADV
ejpam-5979	115	2	0	0	NUM
ejpam-5979	115	3	≤	≤	NUM
ejpam-5979	115	4	rϱ−1(ϑϱ	rϱ−1(ϑϱ	PROPN
ejpam-5979	115	5	−	−	PROPN
ejpam-5979	116	1	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	117	1	−	−	PROPN
ejpam-5979	118	1	rϱ−1(τϱ	rϱ−1(τϱ	VERB
ejpam-5979	118	2	−	−	PROPN
ejpam-5979	118	3	rϱ)σ−1	rϱ)σ−1	PROPN
ejpam-5979	118	4	,	,	PUNCT
ejpam-5979	118	5	and	and	CCONJ
ejpam-5979	118	6	we	we	PRON
ejpam-5979	118	7	know	know	VERB
ejpam-5979	118	8	the	the	DET
ejpam-5979	118	9	positivity	positivity	NOUN
ejpam-5979	118	10	of	of	ADP
ejpam-5979	118	11	the	the	DET
ejpam-5979	118	12	quantity	quantity	NOUN
ejpam-5979	118	13	(	(	PUNCT
ejpam-5979	118	14	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	118	15	)	)	PUNCT
ejpam-5979	118	16	(	(	PUNCT
ejpam-5979	119	1	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-5979	119	2	)	)	PUNCT
ejpam-5979	119	3	>	>	X
ejpam-5979	119	4	0	0	NUM
ejpam-5979	119	5	,	,	PUNCT
ejpam-5979	119	6	i.e.	i.e.	X
ejpam-5979	119	7	(	(	PUNCT
ejpam-5979	119	8	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	119	9	)	)	PUNCT
ejpam-5979	119	10	(	(	PUNCT
ejpam-5979	119	11	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-5979	119	12	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-5979	119	13	−	−	PROPN
ejpam-5979	119	14	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	119	15	>	>	X
ejpam-5979	119	16	0	0	X
ejpam-5979	119	17	.	.	PUNCT
ejpam-5979	120	1	thus	thus	ADV
ejpam-5979	120	2	,	,	PUNCT
ejpam-5979	120	3	we	we	PRON
ejpam-5979	120	4	deduce	deduce	VERB
ejpam-5979	120	5	that	that	SCONJ
ejpam-5979	120	6	0	0	NUM
ejpam-5979	120	7	≤	≤	NUM
ejpam-5979	120	8	(	(	PUNCT
ejpam-5979	120	9	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	120	10	)	)	PUNCT
ejpam-5979	120	11	(	(	PUNCT
ejpam-5979	120	12	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-5979	120	13	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-5979	120	14	−	−	NOUN
ejpam-5979	120	15	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	120	16	−	−	PROPN
ejpam-5979	121	1	rϱ−1(τϱ	rϱ−1(τϱ	VERB
ejpam-5979	121	2	−	−	PROPN
ejpam-5979	121	3	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	121	4	.	.	PUNCT
ejpam-5979	122	1	therefore∫	therefore∫	ADP
ejpam-5979	122	2	ϑ	ϑ	PROPN
ejpam-5979	122	3	θ	θ	PROPN
ejpam-5979	122	4	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	122	5	,	,	PUNCT
ejpam-5979	122	6	r)|dr	r)|dr	NOUN
ejpam-5979	122	7	=	=	PUNCT
ejpam-5979	122	8	ϱ1−σ	ϱ1−σ	PROPN
ejpam-5979	122	9	γ(σ	γ(σ	PROPN
ejpam-5979	122	10	)	)	PUNCT
ejpam-5979	123	1	[	[	X
ejpam-5979	123	2	∫	∫	X
ejpam-5979	123	3	τ	τ	X
ejpam-5979	123	4	θ	θ	PROPN
ejpam-5979	123	5	(	(	PUNCT
ejpam-5979	123	6	(	(	PUNCT
ejpam-5979	123	7	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	123	8	)	)	PUNCT
ejpam-5979	123	9	(	(	PUNCT
ejpam-5979	123	10	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-5979	123	11	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-5979	123	12	−	−	NOUN
ejpam-5979	123	13	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	123	14	−	−	PROPN
ejpam-5979	124	1	rϱ−1(τϱ	rϱ−1(τϱ	INTJ
ejpam-5979	124	2	−	−	PROPN
ejpam-5979	124	3	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	124	4	)	)	PUNCT
ejpam-5979	125	1	dr	dr	PROPN
ejpam-5979	125	2	+	+	PROPN
ejpam-5979	125	3	∫	∫	PROPN
ejpam-5979	125	4	ϑ	ϑ	X
ejpam-5979	125	5	τ	τ	X
ejpam-5979	125	6	(	(	PUNCT
ejpam-5979	125	7	(	(	PUNCT
ejpam-5979	125	8	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	125	9	)	)	PUNCT
ejpam-5979	125	10	(	(	PUNCT
ejpam-5979	125	11	ϑϱ−θϱ)r	ϑϱ−θϱ)r	VERB
ejpam-5979	125	12	ϱ−1(ϑϱ	ϱ−1(ϑϱ	PROPN
ejpam-5979	125	13	−	−	PROPN
ejpam-5979	125	14	rϱ)σ−1	rϱ)σ−1	NOUN
ejpam-5979	125	15	)	)	PUNCT
ejpam-5979	125	16	dr	dr	PROPN
ejpam-5979	125	17	]	]	PUNCT
ejpam-5979	125	18	.	.	PUNCT
ejpam-5979	126	1	we	we	PRON
ejpam-5979	126	2	calculate	calculate	VERB
ejpam-5979	126	3	the	the	DET
ejpam-5979	126	4	primitives	primitive	NOUN
ejpam-5979	126	5	by	by	ADP
ejpam-5979	126	6	integration	integration	NOUN
ejpam-5979	126	7	by	by	ADP
ejpam-5979	126	8	a	a	DET
ejpam-5979	126	9	change	change	NOUN
ejpam-5979	126	10	of	of	ADP
ejpam-5979	126	11	variable∫	variable∫	NOUN
ejpam-5979	126	12	ϑ	ϑ	PROPN
ejpam-5979	126	13	θ	θ	PROPN
ejpam-5979	126	14	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	126	15	,	,	PUNCT
ejpam-5979	126	16	r)|dr	r)|dr	NOUN
ejpam-5979	126	17	=	=	PUNCT
ejpam-5979	126	18	ϱ1−σ	ϱ1−σ	PROPN
ejpam-5979	126	19	γ(σ	γ(σ	VERB
ejpam-5979	126	20	)	)	PUNCT
ejpam-5979	126	21	[	[	PUNCT
ejpam-5979	126	22	(	(	PUNCT
ejpam-5979	126	23	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	126	24	)	)	PUNCT
ejpam-5979	126	25	(	(	PUNCT
ejpam-5979	126	26	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-5979	126	27	)	)	PUNCT
ejpam-5979	127	1	ϑϱσ	ϑϱσ	PROPN
ejpam-5979	128	1	ϱσ	ϱσ	PROPN
ejpam-5979	129	1	[	[	X
ejpam-5979	129	2	(	(	PUNCT
ejpam-5979	129	3	1−	1−	NUM
ejpam-5979	129	4	θϱ	θϱ	NOUN
ejpam-5979	129	5	ϑϱ	ϑϱ	NOUN
ejpam-5979	129	6	)	)	PUNCT
ejpam-5979	129	7	σ	σ	NOUN
ejpam-5979	129	8	−	−	PROPN
ejpam-5979	129	9	(	(	PUNCT
ejpam-5979	129	10	1−	1−	NUM
ejpam-5979	129	11	τϱ	τϱ	NUM
ejpam-5979	129	12	ϑϱ	ϑϱ	PROPN
ejpam-5979	129	13	)	)	PUNCT
ejpam-5979	129	14	σ	σ	PROPN
ejpam-5979	129	15	]	]	PUNCT
ejpam-5979	129	16	z.	z.	PROPN
ejpam-5979	129	17	bekri	bekri	PROPN
ejpam-5979	129	18	et	et	PROPN
ejpam-5979	129	19	al	al	PROPN
ejpam-5979	129	20	.	.	PUNCT
ejpam-5979	129	21	/	/	SYM
ejpam-5979	129	22	eur	eur	PROPN
ejpam-5979	129	23	.	.	PUNCT
ejpam-5979	130	1	j.	j.	PROPN
ejpam-5979	130	2	pure	pure	PROPN
ejpam-5979	130	3	appl	appl	PROPN
ejpam-5979	130	4	.	.	PROPN
ejpam-5979	130	5	math	math	PROPN
ejpam-5979	130	6	,	,	PUNCT
ejpam-5979	130	7	18	18	NUM
ejpam-5979	130	8	(	(	PUNCT
ejpam-5979	130	9	2	2	NUM
ejpam-5979	130	10	)	)	PUNCT
ejpam-5979	130	11	(	(	PUNCT
ejpam-5979	130	12	2025	2025	NUM
ejpam-5979	130	13	)	)	PUNCT
ejpam-5979	130	14	,	,	PUNCT
ejpam-5979	130	15	5979	5979	NUM
ejpam-5979	130	16	7	7	NUM
ejpam-5979	130	17	of	of	ADP
ejpam-5979	130	18	20	20	NUM
ejpam-5979	130	19	−	−	NOUN
ejpam-5979	130	20	τϱσ	τϱσ	NOUN
ejpam-5979	130	21	ϱ	ϱ	ADP
ejpam-5979	130	22	(	(	PUNCT
ejpam-5979	130	23	1	1	NUM
ejpam-5979	130	24	σ	σ	PROPN
ejpam-5979	130	25	(	(	PUNCT
ejpam-5979	130	26	1−	1−	NUM
ejpam-5979	130	27	θϱ	θϱ	NOUN
ejpam-5979	130	28	τϱ	τϱ	X
ejpam-5979	130	29	)	)	PUNCT
ejpam-5979	130	30	σ	σ	PROPN
ejpam-5979	130	31	)	)	PUNCT
ejpam-5979	131	1	+	+	CCONJ
ejpam-5979	131	2	(	(	PUNCT
ejpam-5979	131	3	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	131	4	)	)	PUNCT
ejpam-5979	131	5	(	(	PUNCT
ejpam-5979	131	6	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-5979	131	7	)	)	PUNCT
ejpam-5979	131	8	ϑϱσ	ϑϱσ	PROPN
ejpam-5979	131	9	ϱσ	ϱσ	PROPN
ejpam-5979	131	10	(	(	PUNCT
ejpam-5979	131	11	1−	1−	NUM
ejpam-5979	131	12	τϱ	τϱ	NUM
ejpam-5979	131	13	ϑϱ	ϑϱ	PROPN
ejpam-5979	131	14	)	)	PUNCT
ejpam-5979	131	15	σ	σ	PROPN
ejpam-5979	131	16	]	]	X
ejpam-5979	131	17	=	=	PUNCT
ejpam-5979	131	18	ϱ1−σ	ϱ1−σ	PROPN
ejpam-5979	131	19	γ(σ	γ(σ	ADJ
ejpam-5979	131	20	)	)	PUNCT
ejpam-5979	131	21	[	[	PUNCT
ejpam-5979	131	22	(	(	PUNCT
ejpam-5979	131	23	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	131	24	)	)	PUNCT
ejpam-5979	131	25	(	(	PUNCT
ejpam-5979	131	26	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-5979	131	27	)	)	PUNCT
ejpam-5979	131	28	ϑϱσ	ϑϱσ	PROPN
ejpam-5979	131	29	ϱσ	ϱσ	PROPN
ejpam-5979	131	30	[	[	PUNCT
ejpam-5979	131	31	(	(	PUNCT
ejpam-5979	131	32	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-5979	131	33	ϑϱσ	ϑϱσ	INTJ
ejpam-5979	131	34	−	−	PROPN
ejpam-5979	131	35	(	(	PUNCT
ejpam-5979	131	36	ϑϱ−τϱ)σ	ϑϱ−τϱ)σ	PROPN
ejpam-5979	131	37	ϑϱσ	ϑϱσ	X
ejpam-5979	131	38	]	]	PUNCT
ejpam-5979	131	39	−	−	PROPN
ejpam-5979	131	40	τϱσ	τϱσ	NOUN
ejpam-5979	131	41	ϱ	ϱ	ADP
ejpam-5979	131	42	(	(	PUNCT
ejpam-5979	131	43	1	1	NUM
ejpam-5979	131	44	σ	σ	NOUN
ejpam-5979	131	45	(	(	PUNCT
ejpam-5979	131	46	τϱ−θϱ)σ	τϱ−θϱ)σ	PROPN
ejpam-5979	131	47	τϱσ	τϱσ	NOUN
ejpam-5979	131	48	)	)	PUNCT
ejpam-5979	132	1	+	+	CCONJ
ejpam-5979	132	2	(	(	PUNCT
ejpam-5979	132	3	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	132	4	)	)	PUNCT
ejpam-5979	132	5	(	(	PUNCT
ejpam-5979	132	6	ϑϱ−θϱ	ϑϱ−θϱ	PROPN
ejpam-5979	132	7	)	)	PUNCT
ejpam-5979	132	8	ϑϱσ	ϑϱσ	PROPN
ejpam-5979	132	9	ϱσ	ϱσ	PROPN
ejpam-5979	132	10	(	(	PUNCT
ejpam-5979	132	11	ϑϱ−τϱ)σ	ϑϱ−τϱ)σ	PROPN
ejpam-5979	132	12	ϑϱσ	ϑϱσ	X
ejpam-5979	132	13	]	]	PUNCT
ejpam-5979	132	14	=	=	PUNCT
ejpam-5979	132	15	ϱ1−σ	ϱ1−σ	PROPN
ejpam-5979	132	16	ϱσγ(σ	ϱσγ(σ	PROPN
ejpam-5979	132	17	)	)	PUNCT
ejpam-5979	132	18	[	[	PUNCT
ejpam-5979	132	19	(	(	PUNCT
ejpam-5979	132	20	τϱ−θϱ	τϱ−θϱ	NUM
ejpam-5979	132	21	)	)	PUNCT
ejpam-5979	132	22	(	(	PUNCT
ejpam-5979	132	23	ϑϱ−θϱ)(ϑ	ϑϱ−θϱ)(ϑ	ADJ
ejpam-5979	132	24	ϱ	ϱ	ADP
ejpam-5979	132	25	−	−	PROPN
ejpam-5979	132	26	θϱ)σ	θϱ)σ	PROPN
ejpam-5979	132	27	−	−	PROPN
ejpam-5979	132	28	(	(	PUNCT
ejpam-5979	132	29	τϱ	τϱ	ADP
ejpam-5979	132	30	−	−	PROPN
ejpam-5979	132	31	θϱ)σ	θϱ)σ	PROPN
ejpam-5979	132	32	]	]	PUNCT
ejpam-5979	132	33	.	.	PUNCT
ejpam-5979	133	1	then	then	ADV
ejpam-5979	133	2	∫	∫	PROPN
ejpam-5979	133	3	ϑ	ϑ	X
ejpam-5979	133	4	θ	θ	PROPN
ejpam-5979	133	5	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	133	6	,	,	PUNCT
ejpam-5979	133	7	r)|	r)|	PROPN
ejpam-5979	133	8	dr	dr	PROPN
ejpam-5979	133	9	=	=	PROPN
ejpam-5979	133	10	1	1	NUM
ejpam-5979	133	11	ϱσσγ(σ	ϱσσγ(σ	NOUN
ejpam-5979	133	12	)	)	PUNCT
ejpam-5979	133	13	[	[	PUNCT
ejpam-5979	133	14	(	(	PUNCT
ejpam-5979	133	15	ϑϱ	ϑϱ	ADP
ejpam-5979	133	16	−	−	PROPN
ejpam-5979	133	17	θϱ)σ−1(τϱ	θϱ)σ−1(τϱ	PROPN
ejpam-5979	133	18	−	−	PROPN
ejpam-5979	133	19	θϱ)−	θϱ)−	NOUN
ejpam-5979	133	20	(	(	PUNCT
ejpam-5979	133	21	τϱ	τϱ	ADP
ejpam-5979	133	22	−	−	PROPN
ejpam-5979	133	23	θϱ)σ	θϱ)σ	PROPN
ejpam-5979	133	24	]	]	PUNCT
ejpam-5979	133	25	.	.	PUNCT
ejpam-5979	134	1	implies	imply	VERB
ejpam-5979	134	2	that∫	that∫	NOUN
ejpam-5979	134	3	ϑ	ϑ	PROPN
ejpam-5979	134	4	θ	θ	PROPN
ejpam-5979	134	5	∂|ℏ(τ	∂|ℏ(τ	PROPN
ejpam-5979	134	6	,	,	PUNCT
ejpam-5979	134	7	r)|	r)|	PROPN
ejpam-5979	134	8	∂τ	∂τ	PROPN
ejpam-5979	134	9	dr	dr	PROPN
ejpam-5979	134	10	=	=	SYM
ejpam-5979	134	11	1	1	NUM
ejpam-5979	134	12	ϱσ−1σγ(σ	ϱσ−1σγ(σ	NOUN
ejpam-5979	134	13	)	)	PUNCT
ejpam-5979	134	14	[	[	PUNCT
ejpam-5979	134	15	(	(	PUNCT
ejpam-5979	134	16	ϑϱ	ϑϱ	INTJ
ejpam-5979	134	17	−	−	PROPN
ejpam-5979	134	18	θϱ)σ−1τϱ−1	θϱ)σ−1τϱ−1	X
ejpam-5979	134	19	−	−	PUNCT
ejpam-5979	134	20	σ(τϱ	σ(τϱ	DET
ejpam-5979	134	21	−	−	PROPN
ejpam-5979	134	22	θϱ)σ−1τϱ−1	θϱ)σ−1τϱ−1	NOUN
ejpam-5979	134	23	]	]	PUNCT
ejpam-5979	134	24	,	,	PUNCT
ejpam-5979	134	25	which	which	PRON
ejpam-5979	134	26	ends	end	VERB
ejpam-5979	134	27	the	the	DET
ejpam-5979	134	28	proof	proof	NOUN
ejpam-5979	134	29	.	.	PUNCT
ejpam-5979	135	1	corollary	corollary	ADJ
ejpam-5979	135	2	1	1	NUM
ejpam-5979	135	3	.	.	PUNCT
ejpam-5979	136	1	we	we	PRON
ejpam-5979	136	2	can	can	AUX
ejpam-5979	136	3	define	define	VERB
ejpam-5979	136	4	the	the	DET
ejpam-5979	136	5	continuous	continuous	ADJ
ejpam-5979	136	6	functions	function	NOUN
ejpam-5979	136	7	ξ	ξ	PROPN
ejpam-5979	136	8	and	and	CCONJ
ejpam-5979	136	9	ξ′	ξ′	NOUN
ejpam-5979	136	10	,	,	PUNCT
ejpam-5979	136	11	for	for	ADP
ejpam-5979	136	12	τ	τ	PROPN
ejpam-5979	136	13	∈	∈	PROPN
ejpam-5979	137	1	[	[	X
ejpam-5979	137	2	θ	θ	X
ejpam-5979	137	3	,	,	PUNCT
ejpam-5979	137	4	ϑ	ϑ	X
ejpam-5979	137	5	]	]	X
ejpam-5979	137	6	by	by	ADP
ejpam-5979	137	7	ξ(τ	ξ(τ	PROPN
ejpam-5979	137	8	)	)	PUNCT
ejpam-5979	137	9	=	=	PRON
ejpam-5979	137	10	(	(	PUNCT
ejpam-5979	137	11	ϑϱ	ϑϱ	ADP
ejpam-5979	137	12	−	−	PROPN
ejpam-5979	137	13	θϱ)σ−1(τϱ	θϱ)σ−1(τϱ	PROPN
ejpam-5979	137	14	−	−	PROPN
ejpam-5979	137	15	θϱ)−	θϱ)−	NOUN
ejpam-5979	137	16	(	(	PUNCT
ejpam-5979	137	17	τϱ	τϱ	ADP
ejpam-5979	137	18	−	−	PROPN
ejpam-5979	137	19	θϱ)σ	θϱ)σ	PROPN
ejpam-5979	137	20	,	,	PUNCT
ejpam-5979	137	21	(	(	PUNCT
ejpam-5979	137	22	8)	8)	NUM
ejpam-5979	137	23	ξ′(τ	ξ′(τ	NOUN
ejpam-5979	137	24	)	)	PUNCT
ejpam-5979	137	25	=	=	SYM
ejpam-5979	137	26	(	(	PUNCT
ejpam-5979	137	27	ϑϱ	ϑϱ	ADP
ejpam-5979	137	28	−	−	PROPN
ejpam-5979	137	29	θϱ)σ−1τϱ−1	θϱ)σ−1τϱ−1	X
ejpam-5979	137	30	−	−	PROPN
ejpam-5979	137	31	σ(τϱ	σ(τϱ	PRON
ejpam-5979	137	32	−	−	ADP
ejpam-5979	137	33	θϱ)σ−1τϱ−1	θϱ)σ−1τϱ−1	PROPN
ejpam-5979	137	34	.	.	PUNCT
ejpam-5979	138	1	(	(	PUNCT
ejpam-5979	138	2	9	9	X
ejpam-5979	138	3	)	)	PUNCT
ejpam-5979	138	4	proposition	proposition	NOUN
ejpam-5979	138	5	2	2	NUM
ejpam-5979	138	6	.	.	PUNCT
ejpam-5979	138	7	by	by	ADP
ejpam-5979	138	8	(	(	PUNCT
ejpam-5979	138	9	7	7	NUM
ejpam-5979	138	10	)	)	PUNCT
ejpam-5979	138	11	,	,	PUNCT
ejpam-5979	138	12	suppose	suppose	VERB
ejpam-5979	138	13	that	that	SCONJ
ejpam-5979	138	14	θ	θ	PROPN
ejpam-5979	138	15	=	=	SYM
ejpam-5979	138	16	0	0	NUM
ejpam-5979	138	17	,	,	PUNCT
ejpam-5979	138	18	θ	θ	X
ejpam-5979	138	19	<	<	X
ejpam-5979	138	20	ϑ	ϑ	X
ejpam-5979	138	21	and	and	CCONJ
ejpam-5979	138	22	by	by	ADP
ejpam-5979	138	23	replacement	replacement	NOUN
ejpam-5979	138	24	by	by	ADP
ejpam-5979	138	25	the	the	DET
ejpam-5979	138	26	maximum	maximum	ADJ
ejpam-5979	138	27	point	point	NOUN
ejpam-5979	138	28	τ∗	τ∗	NOUN
ejpam-5979	138	29	,	,	PUNCT
ejpam-5979	138	30	then	then	ADV
ejpam-5979	138	31	∫	∫	PROPN
ejpam-5979	138	32	ϑ	ϑ	X
ejpam-5979	138	33	0	0	PROPN
ejpam-5979	138	34	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	138	35	,	,	PUNCT
ejpam-5979	138	36	r)|	r)|	PROPN
ejpam-5979	138	37	dr	dr	PROPN
ejpam-5979	138	38	≤	≤	PROPN
ejpam-5979	138	39	1	1	NUM
ejpam-5979	138	40	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	138	41	)	)	PUNCT
ejpam-5979	138	42	[	[	PUNCT
ejpam-5979	138	43	ϑϱσ	ϑϱσ	X
ejpam-5979	138	44	σ	σ	PROPN
ejpam-5979	138	45	1	1	NUM
ejpam-5979	138	46	(	(	PUNCT
ejpam-5979	138	47	σ−1	σ−1	PROPN
ejpam-5979	138	48	)	)	PUNCT
ejpam-5979	138	49	−	−	PROPN
ejpam-5979	138	50	ϑϱσ	ϑϱσ	PROPN
ejpam-5979	138	51	σ	σ	PROPN
ejpam-5979	138	52	σ	σ	PROPN
ejpam-5979	138	53	(	(	PUNCT
ejpam-5979	138	54	σ−1	σ−1	PROPN
ejpam-5979	138	55	)	)	PUNCT
ejpam-5979	138	56	]	]	PUNCT
ejpam-5979	138	57	,	,	PUNCT
ejpam-5979	138	58	(	(	PUNCT
ejpam-5979	138	59	10	10	X
ejpam-5979	138	60	)	)	PUNCT
ejpam-5979	138	61	proof	proof	NOUN
ejpam-5979	138	62	.	.	PUNCT
ejpam-5979	139	1	according	accord	VERB
ejpam-5979	139	2	to	to	ADP
ejpam-5979	139	3	9	9	NUM
ejpam-5979	139	4	the	the	DET
ejpam-5979	139	5	derivative	derivative	NOUN
ejpam-5979	139	6	of	of	ADP
ejpam-5979	139	7	the	the	DET
ejpam-5979	139	8	function	function	NOUN
ejpam-5979	139	9	ξ	ξ	PROPN
ejpam-5979	139	10	,	,	PUNCT
ejpam-5979	139	11	we	we	PRON
ejpam-5979	139	12	pose	pose	VERB
ejpam-5979	139	13	ξ′(τ	ξ′(τ	ADP
ejpam-5979	139	14	)	)	PUNCT
ejpam-5979	139	15	=	=	PUNCT
ejpam-5979	139	16	0	0	PUNCT
ejpam-5979	140	1	=	=	NOUN
ejpam-5979	140	2	⇒	⇒	NOUN
ejpam-5979	140	3	(	(	PUNCT
ejpam-5979	140	4	ϑϱ	ϑϱ	ADP
ejpam-5979	140	5	−	−	PROPN
ejpam-5979	140	6	θϱ)σ−1τϱ−1	θϱ)σ−1τϱ−1	X
ejpam-5979	140	7	−	−	PUNCT
ejpam-5979	140	8	σ(τϱ	σ(τϱ	DET
ejpam-5979	140	9	−	−	NOUN
ejpam-5979	140	10	θϱ)σ−1τϱ−1	θϱ)σ−1τϱ−1	NOUN
ejpam-5979	140	11	=	=	SYM
ejpam-5979	140	12	0	0	NUM
ejpam-5979	140	13	,	,	PUNCT
ejpam-5979	140	14	we	we	PRON
ejpam-5979	140	15	suppose	suppose	VERB
ejpam-5979	140	16	that	that	SCONJ
ejpam-5979	140	17	θ	θ	PROPN
ejpam-5979	140	18	=	=	PUNCT
ejpam-5979	140	19	0	0	X
ejpam-5979	140	20	.	.	PUNCT
ejpam-5979	141	1	so	so	ADV
ejpam-5979	141	2	we	we	PRON
ejpam-5979	141	3	get	get	VERB
ejpam-5979	141	4	ϑϱ(σ−1)τϱ−1	ϑϱ(σ−1)τϱ−1	PUNCT
ejpam-5979	141	5	−	−	X
ejpam-5979	141	6	στϱ(σ−1)τϱ−1	στϱ(σ−1)τϱ−1	NOUN
ejpam-5979	141	7	=	=	SYM
ejpam-5979	141	8	0	0	NUM
ejpam-5979	141	9	ϑϱ(σ−1	ϑϱ(σ−1	PROPN
ejpam-5979	141	10	)	)	PUNCT
ejpam-5979	142	1	=	=	SYM
ejpam-5979	142	2	στϱ(σ−1	στϱ(σ−1	PRON
ejpam-5979	142	3	)	)	PUNCT
ejpam-5979	142	4	τϱ(σ−1	τϱ(σ−1	NOUN
ejpam-5979	142	5	)	)	PUNCT
ejpam-5979	142	6	=	=	SYM
ejpam-5979	142	7	ϑϱ(σ−1	ϑϱ(σ−1	PROPN
ejpam-5979	142	8	)	)	PUNCT
ejpam-5979	142	9	σ	σ	NOUN
ejpam-5979	142	10	.	.	PUNCT
ejpam-5979	143	1	we	we	PRON
ejpam-5979	143	2	directly	directly	ADV
ejpam-5979	143	3	deduce	deduce	VERB
ejpam-5979	143	4	that	that	SCONJ
ejpam-5979	143	5	the	the	DET
ejpam-5979	143	6	maximum	maximum	NOUN
ejpam-5979	143	7	was	be	AUX
ejpam-5979	143	8	reached	reach	VERB
ejpam-5979	143	9	at	at	ADP
ejpam-5979	143	10	the	the	DET
ejpam-5979	143	11	points	point	NOUN
ejpam-5979	143	12	τ∗	τ∗	X
ejpam-5979	144	1	=	=	SYM
ejpam-5979	144	2	ϑ	ϑ	X
ejpam-5979	144	3	σ	σ	NOUN
ejpam-5979	144	4	1	1	NUM
ejpam-5979	144	5	ϱ(σ−1	ϱ(σ−1	PROPN
ejpam-5979	144	6	)	)	PUNCT
ejpam-5979	144	7	.	.	PUNCT
ejpam-5979	145	1	moreover	moreover	ADV
ejpam-5979	145	2	,	,	PUNCT
ejpam-5979	145	3	ξ(τ∗	ξ(τ∗	ADP
ejpam-5979	145	4	)	)	PUNCT
ejpam-5979	145	5	=	=	SYM
ejpam-5979	146	1	(	(	PUNCT
ejpam-5979	146	2	ϑϱσ	ϑϱσ	X
ejpam-5979	146	3	σ	σ	PROPN
ejpam-5979	146	4	1	1	NUM
ejpam-5979	146	5	(	(	PUNCT
ejpam-5979	146	6	σ−1	σ−1	PROPN
ejpam-5979	146	7	)	)	PUNCT
ejpam-5979	146	8	−	−	PROPN
ejpam-5979	147	1	ϑϱσ	ϑϱσ	PROPN
ejpam-5979	147	2	σ	σ	PROPN
ejpam-5979	147	3	σ	σ	PROPN
ejpam-5979	147	4	(	(	PUNCT
ejpam-5979	147	5	σ−1	σ−1	PROPN
ejpam-5979	147	6	)	)	PUNCT
ejpam-5979	147	7	)	)	PUNCT
ejpam-5979	147	8	,	,	PUNCT
ejpam-5979	147	9	that	that	PRON
ejpam-5979	147	10	finishes	finish	VERB
ejpam-5979	147	11	the	the	DET
ejpam-5979	147	12	proof	proof	NOUN
ejpam-5979	147	13	.	.	PUNCT
ejpam-5979	148	1	z.	z.	PROPN
ejpam-5979	148	2	bekri	bekri	PROPN
ejpam-5979	148	3	et	et	PROPN
ejpam-5979	148	4	al	al	PROPN
ejpam-5979	148	5	.	.	PUNCT
ejpam-5979	148	6	/	/	SYM
ejpam-5979	148	7	eur	eur	PROPN
ejpam-5979	148	8	.	.	PUNCT
ejpam-5979	149	1	j.	j.	PROPN
ejpam-5979	149	2	pure	pure	PROPN
ejpam-5979	149	3	appl	appl	PROPN
ejpam-5979	149	4	.	.	PROPN
ejpam-5979	149	5	math	math	PROPN
ejpam-5979	149	6	,	,	PUNCT
ejpam-5979	149	7	18	18	NUM
ejpam-5979	149	8	(	(	PUNCT
ejpam-5979	149	9	2	2	NUM
ejpam-5979	149	10	)	)	PUNCT
ejpam-5979	149	11	(	(	PUNCT
ejpam-5979	149	12	2025	2025	NUM
ejpam-5979	149	13	)	)	PUNCT
ejpam-5979	149	14	,	,	PUNCT
ejpam-5979	149	15	5979	5979	NUM
ejpam-5979	149	16	8	8	NUM
ejpam-5979	149	17	of	of	ADP
ejpam-5979	149	18	20	20	NUM
ejpam-5979	149	19	theorem	theorem	NOUN
ejpam-5979	149	20	2	2	NUM
ejpam-5979	149	21	.	.	PUNCT
ejpam-5979	149	22	assume	assume	VERB
ejpam-5979	149	23	θ	θ	X
ejpam-5979	149	24	:	:	PUNCT
ejpam-5979	150	1	[	[	X
ejpam-5979	150	2	0	0	NUM
ejpam-5979	150	3	,	,	PUNCT
ejpam-5979	150	4	ϑ]×r	ϑ]×r	NOUN
ejpam-5979	150	5	→	→	SYM
ejpam-5979	150	6	r	r	NOUN
ejpam-5979	150	7	is	be	AUX
ejpam-5979	150	8	a	a	DET
ejpam-5979	150	9	function	function	NOUN
ejpam-5979	150	10	is	be	AUX
ejpam-5979	150	11	continuous	continuous	ADJ
ejpam-5979	150	12	and	and	CCONJ
ejpam-5979	150	13	check	check	VERB
ejpam-5979	150	14	a	a	DET
ejpam-5979	150	15	condition	condition	NOUN
ejpam-5979	150	16	of	of	ADP
ejpam-5979	150	17	uniform	uniform	ADJ
ejpam-5979	150	18	lipschitz	lipschitz	NOUN
ejpam-5979	150	19	concerning	concern	VERB
ejpam-5979	150	20	the	the	DET
ejpam-5979	150	21	second	second	ADJ
ejpam-5979	150	22	variable	variable	NOUN
ejpam-5979	150	23	on	on	ADP
ejpam-5979	150	24	[	[	X
ejpam-5979	150	25	0	0	NUM
ejpam-5979	150	26	,	,	PUNCT
ejpam-5979	150	27	ϑ	ϑ	X
ejpam-5979	150	28	]	]	X
ejpam-5979	150	29	×	×	NOUN
ejpam-5979	150	30	r	r	NOUN
ejpam-5979	150	31	with	with	ADP
ejpam-5979	150	32	lipschitz	lipschitz	NOUN
ejpam-5979	150	33	real	real	ADJ
ejpam-5979	150	34	ζ	ζ	NOUN
ejpam-5979	150	35	,	,	PUNCT
ejpam-5979	150	36	thus	thus	ADV
ejpam-5979	150	37	,	,	PUNCT
ejpam-5979	150	38	|θ(τ	|θ(τ	PROPN
ejpam-5979	150	39	,	,	PUNCT
ejpam-5979	150	40	µ)−θ(τ	µ)−θ(τ	ADV
ejpam-5979	150	41	,	,	PUNCT
ejpam-5979	150	42	ν)|	ν)|	PROPN
ejpam-5979	150	43	≤	≤	PROPN
ejpam-5979	150	44	ζ|µ−	ζ|µ−	ADJ
ejpam-5979	150	45	ν|	ν|	PROPN
ejpam-5979	150	46	,	,	PUNCT
ejpam-5979	150	47	for	for	ADP
ejpam-5979	150	48	(	(	PUNCT
ejpam-5979	150	49	τ	τ	PROPN
ejpam-5979	150	50	,	,	PUNCT
ejpam-5979	150	51	µ	µ	NOUN
ejpam-5979	150	52	)	)	PUNCT
ejpam-5979	150	53	,	,	PUNCT
ejpam-5979	150	54	(	(	PUNCT
ejpam-5979	150	55	τ	τ	X
ejpam-5979	150	56	,	,	PUNCT
ejpam-5979	150	57	ν	ν	NOUN
ejpam-5979	150	58	)	)	PUNCT
ejpam-5979	150	59	∈	∈	PROPN
ejpam-5979	151	1	[	[	X
ejpam-5979	151	2	0	0	NUM
ejpam-5979	151	3	,	,	PUNCT
ejpam-5979	151	4	ϑ]×	ϑ]×	NOUN
ejpam-5979	151	5	r	r	NOUN
ejpam-5979	151	6	,	,	PUNCT
ejpam-5979	151	7	where	where	SCONJ
ejpam-5979	151	8	ζ	ζ	NOUN
ejpam-5979	151	9	>	>	SYM
ejpam-5979	151	10	0	0	NUM
ejpam-5979	151	11	are	be	AUX
ejpam-5979	151	12	constants	constant	NOUN
ejpam-5979	151	13	.	.	PUNCT
ejpam-5979	152	1	if	if	SCONJ
ejpam-5979	152	2	ζ	ζ	NOUN
ejpam-5979	152	3	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	152	4	)	)	PUNCT
ejpam-5979	152	5	[	[	PUNCT
ejpam-5979	152	6	ϑϱσ	ϑϱσ	X
ejpam-5979	152	7	σ	σ	PROPN
ejpam-5979	152	8	1	1	NUM
ejpam-5979	152	9	(	(	PUNCT
ejpam-5979	152	10	σ−1	σ−1	PROPN
ejpam-5979	152	11	)	)	PUNCT
ejpam-5979	152	12	−	−	PROPN
ejpam-5979	152	13	ϑϱσ	ϑϱσ	PROPN
ejpam-5979	152	14	σ	σ	PROPN
ejpam-5979	152	15	σ	σ	PROPN
ejpam-5979	152	16	(	(	PUNCT
ejpam-5979	152	17	σ−1	σ−1	PROPN
ejpam-5979	152	18	)	)	PUNCT
ejpam-5979	152	19	]	]	PUNCT
ejpam-5979	153	1	<	<	X
ejpam-5979	153	2	1	1	NUM
ejpam-5979	153	3	,	,	PUNCT
ejpam-5979	153	4	(	(	PUNCT
ejpam-5979	153	5	11	11	NUM
ejpam-5979	153	6	)	)	PUNCT
ejpam-5979	153	7	then	then	ADV
ejpam-5979	153	8	the	the	DET
ejpam-5979	153	9	bvp	bvp	PROPN
ejpam-5979	153	10	{	{	PUNCT
ejpam-5979	153	11	ϱ	ϱ	PROPN
ejpam-5979	153	12	cdσ	cdσ	NOUN
ejpam-5979	153	13	0+µ(τ	0+µ(τ	NOUN
ejpam-5979	153	14	)	)	PUNCT
ejpam-5979	153	15	=	=	SYM
ejpam-5979	153	16	−θ(τ	−θ(τ	ADJ
ejpam-5979	153	17	,	,	PUNCT
ejpam-5979	153	18	µ(τ	µ(τ	NOUN
ejpam-5979	153	19	)	)	PUNCT
ejpam-5979	153	20	)	)	PUNCT
ejpam-5979	153	21	,	,	PUNCT
ejpam-5979	153	22	0	0	PUNCT
ejpam-5979	153	23	<	<	X
ejpam-5979	153	24	τ	τ	X
ejpam-5979	153	25	<	<	X
ejpam-5979	153	26	ϑ	ϑ	X
ejpam-5979	153	27	,	,	PUNCT
ejpam-5979	153	28	µ(0	µ(0	NOUN
ejpam-5979	153	29	)	)	PUNCT
ejpam-5979	153	30	=	=	SYM
ejpam-5979	153	31	λ1	λ1	ADJ
ejpam-5979	153	32	,	,	PUNCT
ejpam-5979	153	33	µ(ϑ	µ(ϑ	PROPN
ejpam-5979	153	34	)	)	PUNCT
ejpam-5979	153	35	=	=	SYM
ejpam-5979	153	36	λ2	λ2	NOUN
ejpam-5979	153	37	,	,	PUNCT
ejpam-5979	153	38	(	(	PUNCT
ejpam-5979	153	39	12	12	NUM
ejpam-5979	153	40	)	)	PUNCT
ejpam-5979	153	41	admits	admit	VERB
ejpam-5979	153	42	a	a	DET
ejpam-5979	153	43	single	single	ADJ
ejpam-5979	153	44	solution	solution	NOUN
ejpam-5979	153	45	.	.	PUNCT
ejpam-5979	154	1	proof	proof	NOUN
ejpam-5979	154	2	.	.	PUNCT
ejpam-5979	155	1	suppose	suppose	VERB
ejpam-5979	155	2	π	π	NOUN
ejpam-5979	155	3	is	be	AUX
ejpam-5979	155	4	a	a	DET
ejpam-5979	155	5	space	space	NOUN
ejpam-5979	155	6	of	of	ADP
ejpam-5979	155	7	banach	banach	ADV
ejpam-5979	155	8	fitted	fit	VERB
ejpam-5979	155	9	with	with	ADP
ejpam-5979	155	10	continuous	continuous	ADJ
ejpam-5979	155	11	applications	application	NOUN
ejpam-5979	155	12	defined	define	VERB
ejpam-5979	155	13	on	on	ADP
ejpam-5979	155	14	[	[	X
ejpam-5979	155	15	0	0	NUM
ejpam-5979	155	16	,	,	PUNCT
ejpam-5979	155	17	ϑ	ϑ	X
ejpam-5979	155	18	]	]	X
ejpam-5979	155	19	with	with	ADP
ejpam-5979	155	20	the	the	DET
ejpam-5979	155	21	norm	norm	NOUN
ejpam-5979	155	22	∥µ∥	∥µ∥	NOUN
ejpam-5979	155	23	=	=	SYM
ejpam-5979	155	24	maxτ∈[0,ϑ]{|µ(τ)|	maxτ∈[0,ϑ]{|µ(τ)|	PROPN
ejpam-5979	155	25	}	}	PUNCT
ejpam-5979	155	26	.	.	PUNCT
ejpam-5979	156	1	according	accord	VERB
ejpam-5979	156	2	to	to	ADP
ejpam-5979	156	3	lemma	lemma	PROPN
ejpam-5979	156	4	2	2	NUM
ejpam-5979	156	5	,	,	PUNCT
ejpam-5979	156	6	we	we	PRON
ejpam-5979	156	7	have	have	VERB
ejpam-5979	156	8	µ	µ	PRON
ejpam-5979	156	9	∈	∈	PROPN
ejpam-5979	156	10	c[0	c[0	PROPN
ejpam-5979	156	11	,	,	PUNCT
ejpam-5979	156	12	ϑ	ϑ	X
ejpam-5979	156	13	]	]	X
ejpam-5979	156	14	is	be	AUX
ejpam-5979	156	15	a	a	DET
ejpam-5979	156	16	solution	solution	NOUN
ejpam-5979	156	17	of	of	ADP
ejpam-5979	156	18	(	(	PUNCT
ejpam-5979	156	19	12	12	NUM
ejpam-5979	156	20	)	)	PUNCT
ejpam-5979	156	21	equivalent	equivalent	NOUN
ejpam-5979	156	22	that	that	SCONJ
ejpam-5979	156	23	this	this	PRON
ejpam-5979	156	24	is	be	AUX
ejpam-5979	156	25	the	the	DET
ejpam-5979	156	26	same	same	ADJ
ejpam-5979	156	27	as	as	ADP
ejpam-5979	156	28	the	the	DET
ejpam-5979	156	29	solving	solve	VERB
ejpam-5979	156	30	an	an	DET
ejpam-5979	156	31	equation	equation	NOUN
ejpam-5979	156	32	in	in	ADP
ejpam-5979	156	33	integral	integral	ADJ
ejpam-5979	156	34	form	form	NOUN
ejpam-5979	156	35	µ(τ	µ(τ	NOUN
ejpam-5979	156	36	)	)	PUNCT
ejpam-5979	156	37	=	=	SYM
ejpam-5979	157	1	[	[	PUNCT
ejpam-5979	157	2	(	(	PUNCT
ejpam-5979	157	3	λ2	λ2	NOUN
ejpam-5979	157	4	−	−	PROPN
ejpam-5979	157	5	λ1	λ1	PROPN
ejpam-5979	157	6	)	)	PUNCT
ejpam-5979	157	7	(	(	PUNCT
ejpam-5979	157	8	τ	τ	X
ejpam-5979	157	9	ϑ	ϑ	X
ejpam-5979	157	10	)	)	PUNCT
ejpam-5979	157	11	ϱ	ϱ	PROPN
ejpam-5979	157	12	+	+	X
ejpam-5979	157	13	λ1	λ1	ADJ
ejpam-5979	157	14	]	]	PUNCT
ejpam-5979	158	1	+	+	NUM
ejpam-5979	158	2	∫	∫	PROPN
ejpam-5979	158	3	ϑ	ϑ	X
ejpam-5979	158	4	0	0	PUNCT
ejpam-5979	158	5	ℏ(τ	ℏ(τ	PROPN
ejpam-5979	158	6	,	,	PUNCT
ejpam-5979	158	7	r	r	NOUN
ejpam-5979	158	8	)	)	PUNCT
ejpam-5979	158	9	θ(r	θ(r	NOUN
ejpam-5979	158	10	,	,	PUNCT
ejpam-5979	158	11	µ(r	µ(r	NOUN
ejpam-5979	158	12	)	)	PUNCT
ejpam-5979	158	13	)	)	PUNCT
ejpam-5979	159	1	dr	dr	PROPN
ejpam-5979	159	2	.	.	PROPN
ejpam-5979	159	3	define	define	VERB
ejpam-5979	159	4	the	the	DET
ejpam-5979	159	5	operator	operator	NOUN
ejpam-5979	159	6	σ	σ	NOUN
ejpam-5979	159	7	:	:	PUNCT
ejpam-5979	160	1	π	π	X
ejpam-5979	160	2	→	→	PUNCT
ejpam-5979	160	3	π	π	PROPN
ejpam-5979	160	4	by	by	ADP
ejpam-5979	160	5	σµ(τ	σµ(τ	NOUN
ejpam-5979	160	6	)	)	PUNCT
ejpam-5979	160	7	=	=	NOUN
ejpam-5979	160	8	[	[	PUNCT
ejpam-5979	160	9	(	(	PUNCT
ejpam-5979	160	10	λ2	λ2	NOUN
ejpam-5979	160	11	−	−	PROPN
ejpam-5979	160	12	λ1	λ1	PROPN
ejpam-5979	160	13	)	)	PUNCT
ejpam-5979	160	14	(	(	PUNCT
ejpam-5979	160	15	τ	τ	X
ejpam-5979	160	16	ϑ	ϑ	X
ejpam-5979	160	17	)	)	PUNCT
ejpam-5979	160	18	ϱ	ϱ	PROPN
ejpam-5979	160	19	+	+	X
ejpam-5979	160	20	λ1	λ1	ADJ
ejpam-5979	160	21	]	]	PUNCT
ejpam-5979	161	1	+	+	NUM
ejpam-5979	161	2	∫	∫	PROPN
ejpam-5979	161	3	ϑ	ϑ	X
ejpam-5979	161	4	0	0	PUNCT
ejpam-5979	161	5	ℏ(τ	ℏ(τ	PROPN
ejpam-5979	161	6	,	,	PUNCT
ejpam-5979	161	7	r	r	NOUN
ejpam-5979	161	8	)	)	PUNCT
ejpam-5979	161	9	θ(r	θ(r	NOUN
ejpam-5979	161	10	,	,	PUNCT
ejpam-5979	161	11	µ(r	µ(r	NOUN
ejpam-5979	161	12	)	)	PUNCT
ejpam-5979	161	13	)	)	PUNCT
ejpam-5979	161	14	dr	dr	PROPN
ejpam-5979	161	15	,	,	PUNCT
ejpam-5979	161	16	for	for	ADP
ejpam-5979	161	17	τ	τ	PROPN
ejpam-5979	161	18	∈	∈	PROPN
ejpam-5979	162	1	[	[	X
ejpam-5979	162	2	0	0	NUM
ejpam-5979	162	3	,	,	PUNCT
ejpam-5979	162	4	ϑ	ϑ	NOUN
ejpam-5979	162	5	]	]	X
ejpam-5979	162	6	.	.	PUNCT
ejpam-5979	163	1	we	we	PRON
ejpam-5979	163	2	should	should	AUX
ejpam-5979	163	3	interpret	interpret	VERB
ejpam-5979	163	4	that	that	SCONJ
ejpam-5979	163	5	the	the	DET
ejpam-5979	163	6	application	application	NOUN
ejpam-5979	163	7	σ	σ	PROPN
ejpam-5979	163	8	admits	admit	VERB
ejpam-5979	163	9	a	a	DET
ejpam-5979	163	10	single	single	ADJ
ejpam-5979	163	11	fixed	fix	VERB
ejpam-5979	163	12	point	point	NOUN
ejpam-5979	163	13	.	.	PUNCT
ejpam-5979	164	1	assume	assume	VERB
ejpam-5979	164	2	µ	µ	PRON
ejpam-5979	164	3	,	,	PUNCT
ejpam-5979	164	4	ν	ν	PROPN
ejpam-5979	164	5	∈	∈	PROPN
ejpam-5979	164	6	π	π	X
ejpam-5979	164	7	.	.	PUNCT
ejpam-5979	165	1	therefore	therefore	ADV
ejpam-5979	165	2	|σµ(τ)−	|σµ(τ)−	PROPN
ejpam-5979	165	3	σν(τ)|	σν(τ)|	PRON
ejpam-5979	165	4	≤	≤	NUM
ejpam-5979	165	5	∫	∫	PROPN
ejpam-5979	165	6	ϑ	ϑ	X
ejpam-5979	165	7	0	0	NUM
ejpam-5979	165	8	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	165	9	,	,	PUNCT
ejpam-5979	165	10	r)|	r)|	PROPN
ejpam-5979	165	11	|θ(r	|θ(r	PROPN
ejpam-5979	165	12	,	,	PUNCT
ejpam-5979	165	13	µ(r))−θ(r	µ(r))−θ(r	PROPN
ejpam-5979	165	14	,	,	PUNCT
ejpam-5979	165	15	ν(r))|	ν(r))|	PROPN
ejpam-5979	165	16	dr	dr	PROPN
ejpam-5979	165	17	≤	≤	PROPN
ejpam-5979	165	18	∫	∫	PROPN
ejpam-5979	165	19	ϑ	ϑ	X
ejpam-5979	165	20	0	0	NUM
ejpam-5979	165	21	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	165	22	,	,	PUNCT
ejpam-5979	165	23	r)|	r)|	NOUN
ejpam-5979	165	24	(	(	PUNCT
ejpam-5979	165	25	ζ|µ(τ)−	ζ|µ(τ)−	PROPN
ejpam-5979	165	26	ν(τ)|	ν(τ)|	NOUN
ejpam-5979	165	27	)	)	PUNCT
ejpam-5979	165	28	dr	dr	PROPN
ejpam-5979	165	29	≤	≤	PROPN
ejpam-5979	165	30	ζ∥µ−	ζ∥µ−	X
ejpam-5979	165	31	ν∥	ν∥	X
ejpam-5979	165	32	∫	∫	PROPN
ejpam-5979	165	33	ϑ	ϑ	X
ejpam-5979	165	34	0	0	PROPN
ejpam-5979	165	35	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	165	36	,	,	PUNCT
ejpam-5979	165	37	r)|	r)|	PROPN
ejpam-5979	165	38	dr	dr	PROPN
ejpam-5979	165	39	≤	≤	PROPN
ejpam-5979	165	40	ζ	ζ	SYM
ejpam-5979	165	41	1	1	NUM
ejpam-5979	165	42	ϱσγ(σ+1	ϱσγ(σ+1	PROPN
ejpam-5979	165	43	)	)	PUNCT
ejpam-5979	165	44	[	[	PUNCT
ejpam-5979	165	45	ϑϱσ	ϑϱσ	X
ejpam-5979	165	46	σ	σ	PROPN
ejpam-5979	165	47	1	1	NUM
ejpam-5979	165	48	(	(	PUNCT
ejpam-5979	165	49	σ−1	σ−1	PROPN
ejpam-5979	165	50	)	)	PUNCT
ejpam-5979	165	51	−	−	PROPN
ejpam-5979	165	52	ϑϱσ	ϑϱσ	PROPN
ejpam-5979	165	53	σ	σ	PROPN
ejpam-5979	165	54	σ	σ	PROPN
ejpam-5979	165	55	(	(	PUNCT
ejpam-5979	165	56	σ−1	σ−1	PROPN
ejpam-5979	165	57	)	)	PUNCT
ejpam-5979	165	58	]	]	PUNCT
ejpam-5979	166	1	∥µ−	∥µ−	X
ejpam-5979	166	2	ν∥	ν∥	NOUN
ejpam-5979	166	3	,	,	PUNCT
ejpam-5979	166	4	whither	whither	NOUN
ejpam-5979	166	5	we	we	PRON
ejpam-5979	166	6	have	have	AUX
ejpam-5979	166	7	martyred	martyr	VERB
ejpam-5979	166	8	proposition	proposition	NOUN
ejpam-5979	166	9	2	2	NUM
ejpam-5979	166	10	.	.	PUNCT
ejpam-5979	166	11	according	accord	VERB
ejpam-5979	166	12	to	to	ADP
ejpam-5979	166	13	(	(	PUNCT
ejpam-5979	166	14	11	11	NUM
ejpam-5979	166	15	)	)	PUNCT
ejpam-5979	166	16	,	,	PUNCT
ejpam-5979	166	17	we	we	PRON
ejpam-5979	166	18	extrapolate	extrapolate	VERB
ejpam-5979	166	19	that	that	SCONJ
ejpam-5979	166	20	σ	σ	PROPN
ejpam-5979	166	21	is	be	AUX
ejpam-5979	166	22	a	a	DET
ejpam-5979	166	23	contracting	contracting	NOUN
ejpam-5979	166	24	operator	operator	NOUN
ejpam-5979	166	25	on	on	ADP
ejpam-5979	166	26	π	π	PROPN
ejpam-5979	166	27	,	,	PUNCT
ejpam-5979	166	28	so	so	ADV
ejpam-5979	166	29	,	,	PUNCT
ejpam-5979	166	30	by	by	ADP
ejpam-5979	166	31	the	the	DET
ejpam-5979	166	32	theorem	theorem	NOUN
ejpam-5979	166	33	of	of	ADP
ejpam-5979	166	34	contraction	contraction	NOUN
ejpam-5979	166	35	mapping	mapping	NOUN
ejpam-5979	166	36	of	of	ADP
ejpam-5979	166	37	banach	banach	NOUN
ejpam-5979	166	38	we	we	PRON
ejpam-5979	166	39	culminate	culminate	VERB
ejpam-5979	166	40	in	in	ADP
ejpam-5979	166	41	the	the	DET
ejpam-5979	166	42	possible	possible	ADJ
ejpam-5979	166	43	outcome	outcome	NOUN
ejpam-5979	166	44	.	.	PUNCT
ejpam-5979	167	1	this	this	PRON
ejpam-5979	167	2	means	mean	VERB
ejpam-5979	167	3	that	that	SCONJ
ejpam-5979	167	4	,	,	PUNCT
ejpam-5979	167	5	we	we	PRON
ejpam-5979	167	6	conclude	conclude	VERB
ejpam-5979	167	7	that	that	SCONJ
ejpam-5979	167	8	σ	σ	PROPN
ejpam-5979	167	9	accepts	accept	VERB
ejpam-5979	167	10	a	a	DET
ejpam-5979	167	11	single	single	ADJ
ejpam-5979	167	12	fixed	fix	VERB
ejpam-5979	167	13	point	point	NOUN
ejpam-5979	167	14	in	in	ADP
ejpam-5979	167	15	c[0	c[0	PROPN
ejpam-5979	167	16	,	,	PUNCT
ejpam-5979	167	17	ϑ	ϑ	X
ejpam-5979	167	18	]	]	X
ejpam-5979	167	19	,	,	PUNCT
ejpam-5979	167	20	this	this	PRON
ejpam-5979	167	21	requires	require	VERB
ejpam-5979	167	22	that	that	SCONJ
ejpam-5979	167	23	the	the	DET
ejpam-5979	167	24	bvp	bvp	NOUN
ejpam-5979	167	25	(	(	PUNCT
ejpam-5979	167	26	12	12	NUM
ejpam-5979	167	27	)	)	PUNCT
ejpam-5979	167	28	admits	admit	VERB
ejpam-5979	167	29	a	a	DET
ejpam-5979	167	30	single	single	ADJ
ejpam-5979	167	31	solution	solution	NOUN
ejpam-5979	167	32	.	.	PUNCT
ejpam-5979	168	1	z.	z.	PROPN
ejpam-5979	168	2	bekri	bekri	PROPN
ejpam-5979	168	3	et	et	PROPN
ejpam-5979	168	4	al	al	PROPN
ejpam-5979	168	5	.	.	PUNCT
ejpam-5979	168	6	/	/	SYM
ejpam-5979	168	7	eur	eur	PROPN
ejpam-5979	168	8	.	.	PUNCT
ejpam-5979	169	1	j.	j.	PROPN
ejpam-5979	169	2	pure	pure	PROPN
ejpam-5979	169	3	appl	appl	PROPN
ejpam-5979	169	4	.	.	PROPN
ejpam-5979	169	5	math	math	PROPN
ejpam-5979	169	6	,	,	PUNCT
ejpam-5979	169	7	18	18	NUM
ejpam-5979	169	8	(	(	PUNCT
ejpam-5979	169	9	2	2	NUM
ejpam-5979	169	10	)	)	PUNCT
ejpam-5979	169	11	(	(	PUNCT
ejpam-5979	169	12	2025	2025	NUM
ejpam-5979	169	13	)	)	PUNCT
ejpam-5979	169	14	,	,	PUNCT
ejpam-5979	169	15	5979	5979	NUM
ejpam-5979	169	16	9	9	NUM
ejpam-5979	169	17	of	of	ADP
ejpam-5979	169	18	20	20	NUM
ejpam-5979	169	19	remark	remark	NOUN
ejpam-5979	169	20	1	1	NUM
ejpam-5979	169	21	.	.	PUNCT
ejpam-5979	170	1	we	we	PRON
ejpam-5979	170	2	analyze	analyze	VERB
ejpam-5979	170	3	this	this	PRON
ejpam-5979	170	4	when	when	SCONJ
ejpam-5979	170	5	taking	take	VERB
ejpam-5979	170	6	σ	σ	X
ejpam-5979	170	7	=	=	SYM
ejpam-5979	170	8	2	2	NUM
ejpam-5979	170	9	,	,	PUNCT
ejpam-5979	170	10	θ	θ	PROPN
ejpam-5979	170	11	=	=	SYM
ejpam-5979	170	12	0	0	NUM
ejpam-5979	170	13	and	and	CCONJ
ejpam-5979	170	14	ϱ	ϱ	X
ejpam-5979	170	15	=	=	SYM
ejpam-5979	170	16	1	1	NUM
ejpam-5979	170	17	in	in	ADP
ejpam-5979	170	18	theorem	theorem	NOUN
ejpam-5979	170	19	2	2	NUM
ejpam-5979	170	20	,	,	PUNCT
ejpam-5979	170	21	through	through	ADP
ejpam-5979	170	22	condition	condition	NOUN
ejpam-5979	170	23	(	(	PUNCT
ejpam-5979	170	24	11	11	NUM
ejpam-5979	170	25	)	)	PUNCT
ejpam-5979	170	26	,	,	PUNCT
ejpam-5979	170	27	we	we	PRON
ejpam-5979	170	28	obviously	obviously	ADV
ejpam-5979	170	29	find	find	VERB
ejpam-5979	170	30	theorem	theorem	VERB
ejpam-5979	170	31	1	1	NUM
ejpam-5979	170	32	such	such	ADJ
ejpam-5979	170	33	that	that	SCONJ
ejpam-5979	170	34	ζ	ζ	PROPN
ejpam-5979	170	35	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	170	36	)	)	PUNCT
ejpam-5979	171	1	[	[	PUNCT
ejpam-5979	171	2	ϑϱσ	ϑϱσ	X
ejpam-5979	171	3	σ	σ	PROPN
ejpam-5979	171	4	1	1	NUM
ejpam-5979	171	5	(	(	PUNCT
ejpam-5979	171	6	σ−1	σ−1	PROPN
ejpam-5979	171	7	)	)	PUNCT
ejpam-5979	171	8	−	−	PROPN
ejpam-5979	171	9	ϑϱσ	ϑϱσ	PROPN
ejpam-5979	171	10	σ	σ	PROPN
ejpam-5979	171	11	σ	σ	PROPN
ejpam-5979	171	12	(	(	PUNCT
ejpam-5979	171	13	σ−1	σ−1	PROPN
ejpam-5979	171	14	)	)	PUNCT
ejpam-5979	171	15	]	]	PUNCT
ejpam-5979	172	1	=	=	PUNCT
ejpam-5979	172	2	ζ	ζ	X
ejpam-5979	172	3	θ2	θ2	PROPN
ejpam-5979	172	4	4γ(3	4γ(3	NUM
ejpam-5979	172	5	)	)	PUNCT
ejpam-5979	172	6	<	<	X
ejpam-5979	172	7	1	1	X
ejpam-5979	172	8	.	.	X
ejpam-5979	172	9	proposition	proposition	NOUN
ejpam-5979	172	10	3	3	NUM
ejpam-5979	172	11	.	.	PUNCT
ejpam-5979	172	12	by	by	ADP
ejpam-5979	172	13	(	(	PUNCT
ejpam-5979	172	14	7	7	NUM
ejpam-5979	172	15	)	)	PUNCT
ejpam-5979	172	16	,	,	PUNCT
ejpam-5979	172	17	suppose	suppose	VERB
ejpam-5979	172	18	that	that	SCONJ
ejpam-5979	172	19	θ	θ	PROPN
ejpam-5979	172	20	=	=	SYM
ejpam-5979	172	21	0	0	NUM
ejpam-5979	172	22	,	,	PUNCT
ejpam-5979	172	23	ϑ	ϑ	X
ejpam-5979	172	24	=	=	SYM
ejpam-5979	172	25	1	1	NUM
ejpam-5979	172	26	,	,	PUNCT
ejpam-5979	172	27	then∫	then∫	NOUN
ejpam-5979	172	28	1	1	NUM
ejpam-5979	172	29	0	0	X
ejpam-5979	173	1	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	173	2	,	,	PUNCT
ejpam-5979	173	3	r)|dr	r)|dr	NOUN
ejpam-5979	173	4	≤	≤	NUM
ejpam-5979	173	5	1	1	NUM
ejpam-5979	173	6	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	173	7	)	)	PUNCT
ejpam-5979	173	8	[	[	PUNCT
ejpam-5979	173	9	1	1	NUM
ejpam-5979	173	10	σ	σ	NUM
ejpam-5979	173	11	1	1	NUM
ejpam-5979	173	12	(	(	PUNCT
ejpam-5979	173	13	σ−1	σ−1	PROPN
ejpam-5979	173	14	)	)	PUNCT
ejpam-5979	173	15	−	−	PROPN
ejpam-5979	173	16	1	1	NUM
ejpam-5979	173	17	σ	σ	PROPN
ejpam-5979	173	18	σ	σ	PROPN
ejpam-5979	173	19	(	(	PUNCT
ejpam-5979	173	20	σ−1	σ−1	PROPN
ejpam-5979	173	21	)	)	PUNCT
ejpam-5979	173	22	]	]	PUNCT
ejpam-5979	173	23	,	,	PUNCT
ejpam-5979	173	24	(	(	PUNCT
ejpam-5979	173	25	13	13	NUM
ejpam-5979	173	26	)	)	PUNCT
ejpam-5979	173	27	theorem	theorem	NOUN
ejpam-5979	173	28	3	3	NUM
ejpam-5979	173	29	.	.	PUNCT
ejpam-5979	174	1	assume	assume	VERB
ejpam-5979	174	2	θ	θ	X
ejpam-5979	174	3	:	:	PUNCT
ejpam-5979	175	1	[	[	X
ejpam-5979	175	2	0	0	NUM
ejpam-5979	175	3	,	,	PUNCT
ejpam-5979	175	4	1]×r	1]×r	NUM
ejpam-5979	175	5	→	→	SYM
ejpam-5979	175	6	r	r	NOUN
ejpam-5979	175	7	is	be	AUX
ejpam-5979	175	8	a	a	DET
ejpam-5979	175	9	function	function	NOUN
ejpam-5979	175	10	is	be	AUX
ejpam-5979	175	11	continuous	continuous	ADJ
ejpam-5979	175	12	and	and	CCONJ
ejpam-5979	175	13	check	check	VERB
ejpam-5979	175	14	a	a	DET
ejpam-5979	175	15	condition	condition	NOUN
ejpam-5979	175	16	of	of	ADP
ejpam-5979	175	17	uniform	uniform	ADJ
ejpam-5979	175	18	lipschitz	lipschitz	NOUN
ejpam-5979	175	19	concerning	concern	VERB
ejpam-5979	175	20	the	the	DET
ejpam-5979	175	21	second	second	ADJ
ejpam-5979	175	22	variable	variable	NOUN
ejpam-5979	175	23	on	on	ADP
ejpam-5979	175	24	[	[	X
ejpam-5979	175	25	0	0	NUM
ejpam-5979	175	26	,	,	PUNCT
ejpam-5979	175	27	1	1	NUM
ejpam-5979	175	28	]	]	SYM
ejpam-5979	175	29	×	×	NOUN
ejpam-5979	175	30	r	r	NOUN
ejpam-5979	175	31	with	with	ADP
ejpam-5979	175	32	lipschitz	lipschitz	NOUN
ejpam-5979	175	33	real	real	ADJ
ejpam-5979	175	34	ζ	ζ	NOUN
ejpam-5979	175	35	,	,	PUNCT
ejpam-5979	175	36	thus	thus	ADV
ejpam-5979	175	37	,	,	PUNCT
ejpam-5979	175	38	|θ(τ	|θ(τ	PROPN
ejpam-5979	175	39	,	,	PUNCT
ejpam-5979	175	40	µ)−θ(τ	µ)−θ(τ	ADV
ejpam-5979	175	41	,	,	PUNCT
ejpam-5979	175	42	ν)|	ν)|	PROPN
ejpam-5979	175	43	≤	≤	PROPN
ejpam-5979	175	44	ζ|µ−	ζ|µ−	ADJ
ejpam-5979	175	45	ν|	ν|	PROPN
ejpam-5979	175	46	,	,	PUNCT
ejpam-5979	175	47	(	(	PUNCT
ejpam-5979	175	48	τ	τ	PROPN
ejpam-5979	175	49	,	,	PUNCT
ejpam-5979	175	50	µ	µ	NOUN
ejpam-5979	175	51	)	)	PUNCT
ejpam-5979	175	52	,	,	PUNCT
ejpam-5979	175	53	(	(	PUNCT
ejpam-5979	175	54	τ	τ	X
ejpam-5979	175	55	,	,	PUNCT
ejpam-5979	175	56	ν	ν	NOUN
ejpam-5979	175	57	)	)	PUNCT
ejpam-5979	175	58	∈	∈	PROPN
ejpam-5979	176	1	[	[	X
ejpam-5979	176	2	0	0	NUM
ejpam-5979	176	3	,	,	PUNCT
ejpam-5979	176	4	1]×	1]×	NUM
ejpam-5979	176	5	r	r	NOUN
ejpam-5979	176	6	,	,	PUNCT
ejpam-5979	176	7	where	where	SCONJ
ejpam-5979	176	8	ζ	ζ	NOUN
ejpam-5979	176	9	>	>	SYM
ejpam-5979	176	10	0	0	NUM
ejpam-5979	176	11	are	be	AUX
ejpam-5979	176	12	constants	constant	NOUN
ejpam-5979	176	13	.	.	PUNCT
ejpam-5979	177	1	if	if	SCONJ
ejpam-5979	177	2	ζ	ζ	NOUN
ejpam-5979	177	3	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	177	4	)	)	PUNCT
ejpam-5979	177	5	[	[	PUNCT
ejpam-5979	177	6	1	1	NUM
ejpam-5979	177	7	σ	σ	NUM
ejpam-5979	177	8	1	1	NUM
ejpam-5979	177	9	(	(	PUNCT
ejpam-5979	177	10	σ−1	σ−1	PROPN
ejpam-5979	177	11	)	)	PUNCT
ejpam-5979	177	12	−	−	PROPN
ejpam-5979	177	13	1	1	NUM
ejpam-5979	177	14	σ	σ	PROPN
ejpam-5979	177	15	σ	σ	PROPN
ejpam-5979	177	16	(	(	PUNCT
ejpam-5979	177	17	σ−1	σ−1	PROPN
ejpam-5979	177	18	)	)	PUNCT
ejpam-5979	177	19	]	]	PUNCT
ejpam-5979	177	20	<	<	X
ejpam-5979	178	1	1	1	NUM
ejpam-5979	178	2	,	,	PUNCT
ejpam-5979	178	3	(	(	PUNCT
ejpam-5979	178	4	14	14	NUM
ejpam-5979	178	5	)	)	PUNCT
ejpam-5979	178	6	then	then	ADV
ejpam-5979	178	7	the	the	DET
ejpam-5979	178	8	bvp	bvp	PROPN
ejpam-5979	178	9	{	{	PUNCT
ejpam-5979	178	10	ϱ	ϱ	PROPN
ejpam-5979	178	11	cdσ	cdσ	NOUN
ejpam-5979	178	12	0+µ(τ	0+µ(τ	NOUN
ejpam-5979	178	13	)	)	PUNCT
ejpam-5979	178	14	=	=	SYM
ejpam-5979	178	15	−θ(τ	−θ(τ	ADJ
ejpam-5979	178	16	,	,	PUNCT
ejpam-5979	178	17	µ(τ	µ(τ	NOUN
ejpam-5979	178	18	)	)	PUNCT
ejpam-5979	178	19	)	)	PUNCT
ejpam-5979	178	20	,	,	PUNCT
ejpam-5979	178	21	0	0	PUNCT
ejpam-5979	178	22	<	<	X
ejpam-5979	178	23	τ	τ	X
ejpam-5979	178	24	<	<	X
ejpam-5979	178	25	1	1	NUM
ejpam-5979	178	26	,	,	PUNCT
ejpam-5979	178	27	µ(0	µ(0	NOUN
ejpam-5979	178	28	)	)	PUNCT
ejpam-5979	178	29	=	=	SYM
ejpam-5979	178	30	λ1	λ1	PROPN
ejpam-5979	178	31	,	,	PUNCT
ejpam-5979	178	32	µ(1	µ(1	PROPN
ejpam-5979	178	33	)	)	PUNCT
ejpam-5979	178	34	=	=	SYM
ejpam-5979	178	35	λ2	λ2	NOUN
ejpam-5979	178	36	,	,	PUNCT
ejpam-5979	178	37	(	(	PUNCT
ejpam-5979	178	38	15	15	NUM
ejpam-5979	178	39	)	)	PUNCT
ejpam-5979	178	40	has	have	VERB
ejpam-5979	178	41	a	a	DET
ejpam-5979	178	42	unique	unique	ADJ
ejpam-5979	178	43	solution	solution	NOUN
ejpam-5979	178	44	.	.	PUNCT
ejpam-5979	179	1	proof	proof	NOUN
ejpam-5979	179	2	.	.	PUNCT
ejpam-5979	180	1	using	use	VERB
ejpam-5979	180	2	the	the	DET
ejpam-5979	180	3	same	same	ADJ
ejpam-5979	180	4	method	method	NOUN
ejpam-5979	180	5	to	to	PART
ejpam-5979	180	6	prove	prove	VERB
ejpam-5979	180	7	proposition	proposition	NOUN
ejpam-5979	180	8	3	3	NUM
ejpam-5979	180	9	and	and	CCONJ
ejpam-5979	180	10	theorem	theorem	VERB
ejpam-5979	180	11	3	3	NUM
ejpam-5979	180	12	which	which	PRON
ejpam-5979	180	13	are	be	AUX
ejpam-5979	180	14	used	use	VERB
ejpam-5979	180	15	in	in	ADP
ejpam-5979	180	16	proposition	proposition	NOUN
ejpam-5979	180	17	2	2	NUM
ejpam-5979	180	18	and	and	CCONJ
ejpam-5979	180	19	also	also	ADV
ejpam-5979	180	20	applies	apply	VERB
ejpam-5979	180	21	to	to	PART
ejpam-5979	180	22	theorem	theorem	VERB
ejpam-5979	180	23	2	2	NUM
ejpam-5979	180	24	.	.	NOUN
ejpam-5979	180	25	remark	remark	NOUN
ejpam-5979	180	26	2	2	NUM
ejpam-5979	180	27	.	.	PUNCT
ejpam-5979	181	1	the	the	DET
ejpam-5979	181	2	same	same	ADJ
ejpam-5979	181	3	remark	remark	NOUN
ejpam-5979	181	4	1	1	NUM
ejpam-5979	181	5	,	,	PUNCT
ejpam-5979	181	6	we	we	PRON
ejpam-5979	181	7	apply	apply	VERB
ejpam-5979	181	8	that	that	PRON
ejpam-5979	181	9	when	when	SCONJ
ejpam-5979	181	10	σ	σ	PROPN
ejpam-5979	181	11	=	=	SYM
ejpam-5979	181	12	2	2	NUM
ejpam-5979	181	13	,	,	PUNCT
ejpam-5979	181	14	θ	θ	PROPN
ejpam-5979	181	15	=	=	SYM
ejpam-5979	181	16	0	0	NUM
ejpam-5979	181	17	,	,	PUNCT
ejpam-5979	181	18	ϑ	ϑ	X
ejpam-5979	181	19	=	=	SYM
ejpam-5979	181	20	1	1	NUM
ejpam-5979	181	21	and	and	CCONJ
ejpam-5979	181	22	ϱ	ϱ	X
ejpam-5979	181	23	=	=	SYM
ejpam-5979	181	24	1	1	NUM
ejpam-5979	181	25	on	on	ADP
ejpam-5979	181	26	theorem	theorem	NOUN
ejpam-5979	181	27	3	3	NUM
ejpam-5979	181	28	,	,	PUNCT
ejpam-5979	181	29	through	through	ADP
ejpam-5979	181	30	condition	condition	NOUN
ejpam-5979	181	31	(	(	PUNCT
ejpam-5979	181	32	14	14	NUM
ejpam-5979	181	33	)	)	PUNCT
ejpam-5979	181	34	,	,	PUNCT
ejpam-5979	181	35	we	we	PRON
ejpam-5979	181	36	obviously	obviously	ADV
ejpam-5979	181	37	find	find	VERB
ejpam-5979	181	38	theorem	theorem	VERB
ejpam-5979	181	39	1	1	NUM
ejpam-5979	181	40	such	such	ADJ
ejpam-5979	181	41	that	that	SCONJ
ejpam-5979	181	42	ζ	ζ	PROPN
ejpam-5979	181	43	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	181	44	)	)	PUNCT
ejpam-5979	181	45	[	[	PUNCT
ejpam-5979	181	46	1	1	NUM
ejpam-5979	181	47	σ	σ	NUM
ejpam-5979	181	48	1	1	NUM
ejpam-5979	181	49	(	(	PUNCT
ejpam-5979	181	50	σ−1	σ−1	PROPN
ejpam-5979	181	51	)	)	PUNCT
ejpam-5979	181	52	−	−	PROPN
ejpam-5979	181	53	1	1	NUM
ejpam-5979	181	54	σ	σ	PROPN
ejpam-5979	181	55	σ	σ	PROPN
ejpam-5979	181	56	(	(	PUNCT
ejpam-5979	181	57	σ−1	σ−1	PROPN
ejpam-5979	181	58	)	)	PUNCT
ejpam-5979	181	59	]	]	PUNCT
ejpam-5979	182	1	=	=	PUNCT
ejpam-5979	182	2	ζ	ζ	SYM
ejpam-5979	182	3	1	1	NUM
ejpam-5979	182	4	4γ(3	4γ(3	NUM
ejpam-5979	182	5	)	)	PUNCT
ejpam-5979	182	6	<	<	X
ejpam-5979	182	7	1	1	X
ejpam-5979	182	8	.	.	X
ejpam-5979	182	9	proposition	proposition	NOUN
ejpam-5979	182	10	4	4	NUM
ejpam-5979	182	11	.	.	PUNCT
ejpam-5979	182	12	by	by	ADP
ejpam-5979	182	13	(	(	PUNCT
ejpam-5979	182	14	7	7	NUM
ejpam-5979	182	15	)	)	PUNCT
ejpam-5979	182	16	,	,	PUNCT
ejpam-5979	182	17	suppose	suppose	VERB
ejpam-5979	182	18	that	that	SCONJ
ejpam-5979	182	19	θ	θ	PROPN
ejpam-5979	182	20	<	<	X
ejpam-5979	182	21	ϑ	ϑ	X
ejpam-5979	182	22	,	,	PUNCT
ejpam-5979	182	23	then∫	then∫	NOUN
ejpam-5979	182	24	1	1	NUM
ejpam-5979	182	25	0	0	NUM
ejpam-5979	182	26	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	182	27	,	,	PUNCT
ejpam-5979	182	28	r)|dr	r)|dr	NOUN
ejpam-5979	182	29	≤	≤	NUM
ejpam-5979	182	30	1	1	NUM
ejpam-5979	182	31	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	182	32	)	)	PUNCT
ejpam-5979	182	33	[	[	PUNCT
ejpam-5979	182	34	(	(	PUNCT
ejpam-5979	182	35	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-5979	182	36	σ	σ	PROPN
ejpam-5979	182	37	1	1	NUM
ejpam-5979	182	38	(	(	PUNCT
ejpam-5979	182	39	σ−1	σ−1	PROPN
ejpam-5979	182	40	)	)	PUNCT
ejpam-5979	182	41	−	−	PROPN
ejpam-5979	182	42	(	(	PUNCT
ejpam-5979	182	43	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-5979	182	44	σ	σ	PROPN
ejpam-5979	182	45	σ	σ	PROPN
ejpam-5979	182	46	(	(	PUNCT
ejpam-5979	182	47	σ−1	σ−1	PROPN
ejpam-5979	182	48	)	)	PUNCT
ejpam-5979	182	49	]	]	PUNCT
ejpam-5979	182	50	,	,	PUNCT
ejpam-5979	182	51	(	(	PUNCT
ejpam-5979	182	52	16	16	NUM
ejpam-5979	182	53	)	)	PUNCT
ejpam-5979	182	54	theorem	theorem	NOUN
ejpam-5979	182	55	4	4	NUM
ejpam-5979	182	56	.	.	PUNCT
ejpam-5979	182	57	assume	assume	VERB
ejpam-5979	182	58	θ	θ	X
ejpam-5979	182	59	:	:	PUNCT
ejpam-5979	183	1	[	[	X
ejpam-5979	183	2	θ	θ	NOUN
ejpam-5979	183	3	,	,	PUNCT
ejpam-5979	183	4	ϑ]×r	ϑ]×r	NOUN
ejpam-5979	183	5	→	→	SYM
ejpam-5979	183	6	r	r	NOUN
ejpam-5979	183	7	is	be	AUX
ejpam-5979	183	8	a	a	DET
ejpam-5979	183	9	function	function	NOUN
ejpam-5979	183	10	is	be	AUX
ejpam-5979	183	11	continuous	continuous	ADJ
ejpam-5979	183	12	and	and	CCONJ
ejpam-5979	183	13	check	check	VERB
ejpam-5979	183	14	a	a	DET
ejpam-5979	183	15	condition	condition	NOUN
ejpam-5979	183	16	of	of	ADP
ejpam-5979	183	17	uniform	uniform	ADJ
ejpam-5979	183	18	lipschitz	lipschitz	NOUN
ejpam-5979	183	19	concerning	concern	VERB
ejpam-5979	183	20	the	the	DET
ejpam-5979	183	21	second	second	ADJ
ejpam-5979	183	22	variable	variable	NOUN
ejpam-5979	183	23	on	on	ADP
ejpam-5979	183	24	[	[	X
ejpam-5979	183	25	θ	θ	X
ejpam-5979	183	26	,	,	PUNCT
ejpam-5979	183	27	ϑ	ϑ	X
ejpam-5979	183	28	]	]	X
ejpam-5979	183	29	×	×	NOUN
ejpam-5979	183	30	r	r	NOUN
ejpam-5979	183	31	with	with	ADP
ejpam-5979	183	32	lipschitz	lipschitz	NOUN
ejpam-5979	183	33	real	real	ADJ
ejpam-5979	183	34	ζ	ζ	NOUN
ejpam-5979	183	35	,	,	PUNCT
ejpam-5979	183	36	thus	thus	ADV
ejpam-5979	183	37	,	,	PUNCT
ejpam-5979	183	38	|θ(τ	|θ(τ	PROPN
ejpam-5979	183	39	,	,	PUNCT
ejpam-5979	183	40	µ)−θ(τ	µ)−θ(τ	ADV
ejpam-5979	183	41	,	,	PUNCT
ejpam-5979	183	42	ν)|	ν)|	PROPN
ejpam-5979	183	43	≤	≤	PROPN
ejpam-5979	183	44	ζ|µ−	ζ|µ−	ADJ
ejpam-5979	183	45	ν|	ν|	PROPN
ejpam-5979	183	46	,	,	PUNCT
ejpam-5979	183	47	(	(	PUNCT
ejpam-5979	183	48	τ	τ	PROPN
ejpam-5979	183	49	,	,	PUNCT
ejpam-5979	183	50	µ	µ	NOUN
ejpam-5979	183	51	)	)	PUNCT
ejpam-5979	183	52	,	,	PUNCT
ejpam-5979	183	53	(	(	PUNCT
ejpam-5979	183	54	τ	τ	X
ejpam-5979	183	55	,	,	PUNCT
ejpam-5979	183	56	ν	ν	NOUN
ejpam-5979	183	57	)	)	PUNCT
ejpam-5979	183	58	∈	∈	PROPN
ejpam-5979	183	59	[	[	X
ejpam-5979	183	60	θ	θ	NOUN
ejpam-5979	183	61	,	,	PUNCT
ejpam-5979	183	62	ϑ]×	ϑ]×	NOUN
ejpam-5979	183	63	r	r	NOUN
ejpam-5979	183	64	,	,	PUNCT
ejpam-5979	183	65	where	where	SCONJ
ejpam-5979	183	66	ζ	ζ	NOUN
ejpam-5979	183	67	>	>	SYM
ejpam-5979	183	68	0	0	NUM
ejpam-5979	183	69	are	be	AUX
ejpam-5979	183	70	constants	constant	NOUN
ejpam-5979	183	71	.	.	PUNCT
ejpam-5979	184	1	if	if	SCONJ
ejpam-5979	184	2	ζ	ζ	NOUN
ejpam-5979	184	3	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	184	4	)	)	PUNCT
ejpam-5979	184	5	[	[	PUNCT
ejpam-5979	184	6	(	(	PUNCT
ejpam-5979	184	7	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-5979	184	8	σ	σ	PROPN
ejpam-5979	184	9	1	1	NUM
ejpam-5979	184	10	(	(	PUNCT
ejpam-5979	184	11	σ−1	σ−1	PROPN
ejpam-5979	184	12	)	)	PUNCT
ejpam-5979	184	13	−	−	PROPN
ejpam-5979	185	1	(	(	PUNCT
ejpam-5979	185	2	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-5979	185	3	σ	σ	PROPN
ejpam-5979	185	4	σ	σ	PROPN
ejpam-5979	185	5	(	(	PUNCT
ejpam-5979	185	6	σ−1	σ−1	PROPN
ejpam-5979	185	7	)	)	PUNCT
ejpam-5979	185	8	]	]	PUNCT
ejpam-5979	186	1	<	<	X
ejpam-5979	186	2	1	1	NUM
ejpam-5979	186	3	,	,	PUNCT
ejpam-5979	186	4	(	(	PUNCT
ejpam-5979	186	5	17	17	NUM
ejpam-5979	186	6	)	)	PUNCT
ejpam-5979	186	7	z.	z.	PROPN
ejpam-5979	186	8	bekri	bekri	PROPN
ejpam-5979	186	9	et	et	PROPN
ejpam-5979	186	10	al	al	PROPN
ejpam-5979	186	11	.	.	PUNCT
ejpam-5979	186	12	/	/	SYM
ejpam-5979	186	13	eur	eur	PROPN
ejpam-5979	186	14	.	.	PUNCT
ejpam-5979	187	1	j.	j.	PROPN
ejpam-5979	187	2	pure	pure	PROPN
ejpam-5979	187	3	appl	appl	PROPN
ejpam-5979	187	4	.	.	PROPN
ejpam-5979	187	5	math	math	PROPN
ejpam-5979	187	6	,	,	PUNCT
ejpam-5979	187	7	18	18	NUM
ejpam-5979	187	8	(	(	PUNCT
ejpam-5979	187	9	2	2	NUM
ejpam-5979	187	10	)	)	PUNCT
ejpam-5979	187	11	(	(	PUNCT
ejpam-5979	187	12	2025	2025	NUM
ejpam-5979	187	13	)	)	PUNCT
ejpam-5979	187	14	,	,	PUNCT
ejpam-5979	187	15	5979	5979	NUM
ejpam-5979	187	16	10	10	NUM
ejpam-5979	187	17	of	of	ADP
ejpam-5979	187	18	20	20	NUM
ejpam-5979	188	1	then	then	ADV
ejpam-5979	188	2	the	the	DET
ejpam-5979	188	3	bvp	bvp	PROPN
ejpam-5979	188	4	{	{	PUNCT
ejpam-5979	188	5	ϱ	ϱ	PROPN
ejpam-5979	188	6	cdσ	cdσ	NOUN
ejpam-5979	188	7	0+µ(τ	0+µ(τ	NOUN
ejpam-5979	188	8	)	)	PUNCT
ejpam-5979	188	9	=	=	SYM
ejpam-5979	189	1	−θ(τ	−θ(τ	ADJ
ejpam-5979	189	2	,	,	PUNCT
ejpam-5979	189	3	µ(τ	µ(τ	NOUN
ejpam-5979	189	4	)	)	PUNCT
ejpam-5979	189	5	)	)	PUNCT
ejpam-5979	189	6	,	,	PUNCT
ejpam-5979	189	7	θ	θ	X
ejpam-5979	189	8	<	<	X
ejpam-5979	189	9	τ	τ	X
ejpam-5979	189	10	<	<	X
ejpam-5979	189	11	ϑ	ϑ	X
ejpam-5979	189	12	,	,	PUNCT
ejpam-5979	189	13	µ(θ	µ(θ	ADJ
ejpam-5979	189	14	)	)	PUNCT
ejpam-5979	189	15	=	=	SYM
ejpam-5979	189	16	λ1	λ1	ADJ
ejpam-5979	189	17	,	,	PUNCT
ejpam-5979	189	18	µ(ϑ	µ(ϑ	PROPN
ejpam-5979	189	19	)	)	PUNCT
ejpam-5979	189	20	=	=	SYM
ejpam-5979	189	21	λ2	λ2	NOUN
ejpam-5979	189	22	,	,	PUNCT
ejpam-5979	189	23	(	(	PUNCT
ejpam-5979	189	24	18	18	NUM
ejpam-5979	189	25	)	)	PUNCT
ejpam-5979	189	26	has	have	VERB
ejpam-5979	189	27	a	a	DET
ejpam-5979	189	28	unique	unique	ADJ
ejpam-5979	189	29	solution	solution	NOUN
ejpam-5979	189	30	.	.	PUNCT
ejpam-5979	190	1	proof	proof	NOUN
ejpam-5979	190	2	.	.	PUNCT
ejpam-5979	191	1	using	use	VERB
ejpam-5979	191	2	the	the	DET
ejpam-5979	191	3	same	same	ADJ
ejpam-5979	191	4	method	method	NOUN
ejpam-5979	191	5	to	to	PART
ejpam-5979	191	6	prove	prove	VERB
ejpam-5979	191	7	proposition	proposition	NOUN
ejpam-5979	191	8	4	4	NUM
ejpam-5979	191	9	and	and	CCONJ
ejpam-5979	191	10	theorem	theorem	VERB
ejpam-5979	191	11	4	4	NUM
ejpam-5979	191	12	which	which	PRON
ejpam-5979	191	13	are	be	AUX
ejpam-5979	191	14	used	use	VERB
ejpam-5979	191	15	in	in	ADP
ejpam-5979	191	16	proposition	proposition	NOUN
ejpam-5979	191	17	2	2	NUM
ejpam-5979	191	18	and	and	CCONJ
ejpam-5979	191	19	also	also	ADV
ejpam-5979	191	20	applies	apply	VERB
ejpam-5979	191	21	to	to	PART
ejpam-5979	191	22	theorem	theorem	VERB
ejpam-5979	191	23	2	2	NUM
ejpam-5979	191	24	.	.	NOUN
ejpam-5979	191	25	remark	remark	NOUN
ejpam-5979	191	26	3	3	NUM
ejpam-5979	191	27	.	.	NOUN
ejpam-5979	191	28	same	same	ADJ
ejpam-5979	191	29	previous	previous	ADJ
ejpam-5979	191	30	notes	note	NOUN
ejpam-5979	191	31	.	.	PUNCT
ejpam-5979	192	1	we	we	PRON
ejpam-5979	192	2	notice	notice	VERB
ejpam-5979	192	3	them	they	PRON
ejpam-5979	192	4	in	in	ADP
ejpam-5979	192	5	the	the	DET
ejpam-5979	192	6	general	general	ADJ
ejpam-5979	192	7	case	case	NOUN
ejpam-5979	192	8	.	.	PUNCT
ejpam-5979	193	1	we	we	PRON
ejpam-5979	193	2	apply	apply	VERB
ejpam-5979	193	3	them	they	PRON
ejpam-5979	193	4	when	when	SCONJ
ejpam-5979	193	5	σ	σ	PROPN
ejpam-5979	193	6	=	=	SYM
ejpam-5979	193	7	2	2	NUM
ejpam-5979	193	8	,	,	PUNCT
ejpam-5979	193	9	θ	θ	PROPN
ejpam-5979	193	10	<	<	X
ejpam-5979	193	11	ϑ	ϑ	X
ejpam-5979	193	12	and	and	CCONJ
ejpam-5979	193	13	ϱ	ϱ	X
ejpam-5979	193	14	=	=	SYM
ejpam-5979	193	15	1	1	NUM
ejpam-5979	193	16	on	on	ADP
ejpam-5979	193	17	theorem	theorem	NOUN
ejpam-5979	193	18	4	4	NUM
ejpam-5979	193	19	,	,	PUNCT
ejpam-5979	193	20	through	through	ADP
ejpam-5979	193	21	condition	condition	NOUN
ejpam-5979	193	22	(	(	PUNCT
ejpam-5979	193	23	17	17	NUM
ejpam-5979	193	24	)	)	PUNCT
ejpam-5979	193	25	,	,	PUNCT
ejpam-5979	193	26	we	we	PRON
ejpam-5979	193	27	obviously	obviously	ADV
ejpam-5979	193	28	find	find	VERB
ejpam-5979	193	29	theorem	theorem	VERB
ejpam-5979	193	30	1	1	NUM
ejpam-5979	193	31	such	such	ADJ
ejpam-5979	193	32	that	that	SCONJ
ejpam-5979	193	33	ζ	ζ	PROPN
ejpam-5979	193	34	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	193	35	)	)	PUNCT
ejpam-5979	193	36	[	[	PUNCT
ejpam-5979	193	37	(	(	PUNCT
ejpam-5979	193	38	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-5979	193	39	σ	σ	PROPN
ejpam-5979	193	40	1	1	NUM
ejpam-5979	193	41	(	(	PUNCT
ejpam-5979	193	42	σ−1	σ−1	PROPN
ejpam-5979	193	43	)	)	PUNCT
ejpam-5979	193	44	−	−	PROPN
ejpam-5979	194	1	(	(	PUNCT
ejpam-5979	194	2	ϑϱ−θϱ)σ	ϑϱ−θϱ)σ	PROPN
ejpam-5979	194	3	σ	σ	PROPN
ejpam-5979	194	4	σ	σ	PROPN
ejpam-5979	194	5	(	(	PUNCT
ejpam-5979	194	6	σ−1	σ−1	PROPN
ejpam-5979	194	7	)	)	PUNCT
ejpam-5979	194	8	]	]	PUNCT
ejpam-5979	195	1	=	=	PUNCT
ejpam-5979	195	2	ζ	ζ	NOUN
ejpam-5979	195	3	(	(	PUNCT
ejpam-5979	195	4	ϑ−	ϑ−	NOUN
ejpam-5979	195	5	θ)2	θ)2	NOUN
ejpam-5979	195	6	4γ(3	4γ(3	NUM
ejpam-5979	195	7	)	)	PUNCT
ejpam-5979	195	8	<	<	X
ejpam-5979	195	9	1	1	X
ejpam-5979	195	10	.	.	X
ejpam-5979	195	11	proposition	proposition	NOUN
ejpam-5979	195	12	5	5	NUM
ejpam-5979	195	13	.	.	PUNCT
ejpam-5979	195	14	by	by	ADP
ejpam-5979	195	15	(	(	PUNCT
ejpam-5979	195	16	7	7	NUM
ejpam-5979	195	17	)	)	PUNCT
ejpam-5979	195	18	,	,	PUNCT
ejpam-5979	195	19	suppose	suppose	VERB
ejpam-5979	195	20	that	that	SCONJ
ejpam-5979	195	21	θ	θ	PROPN
ejpam-5979	195	22	<	<	X
ejpam-5979	195	23	ϑ	ϑ	X
ejpam-5979	195	24	=	=	SYM
ejpam-5979	195	25	1	1	NUM
ejpam-5979	195	26	,	,	PUNCT
ejpam-5979	195	27	then∫	then∫	NOUN
ejpam-5979	195	28	1	1	NUM
ejpam-5979	195	29	0	0	NUM
ejpam-5979	196	1	|ℏ(τ	|ℏ(τ	PROPN
ejpam-5979	196	2	,	,	PUNCT
ejpam-5979	196	3	r)|	r)|	PROPN
ejpam-5979	196	4	dr	dr	PROPN
ejpam-5979	196	5	≤	≤	PROPN
ejpam-5979	196	6	1	1	NUM
ejpam-5979	196	7	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	196	8	)	)	PUNCT
ejpam-5979	196	9	[	[	PUNCT
ejpam-5979	196	10	(	(	PUNCT
ejpam-5979	196	11	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-5979	196	12	σ	σ	PROPN
ejpam-5979	196	13	1	1	NUM
ejpam-5979	196	14	(	(	PUNCT
ejpam-5979	196	15	σ−1	σ−1	PROPN
ejpam-5979	196	16	)	)	PUNCT
ejpam-5979	196	17	−	−	PROPN
ejpam-5979	197	1	(	(	PUNCT
ejpam-5979	197	2	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-5979	197	3	σ	σ	PROPN
ejpam-5979	197	4	σ	σ	PROPN
ejpam-5979	197	5	(	(	PUNCT
ejpam-5979	197	6	σ−1	σ−1	PROPN
ejpam-5979	197	7	)	)	PUNCT
ejpam-5979	197	8	]	]	PUNCT
ejpam-5979	197	9	,	,	PUNCT
ejpam-5979	197	10	(	(	PUNCT
ejpam-5979	197	11	19	19	NUM
ejpam-5979	197	12	)	)	PUNCT
ejpam-5979	197	13	theorem	theorem	NOUN
ejpam-5979	197	14	5	5	NUM
ejpam-5979	197	15	.	.	PUNCT
ejpam-5979	198	1	assume	assume	VERB
ejpam-5979	198	2	θ	θ	X
ejpam-5979	198	3	:	:	PUNCT
ejpam-5979	199	1	[	[	X
ejpam-5979	199	2	θ	θ	X
ejpam-5979	199	3	,	,	PUNCT
ejpam-5979	199	4	1]×r	1]×r	NUM
ejpam-5979	199	5	→	→	SYM
ejpam-5979	199	6	r	r	NOUN
ejpam-5979	199	7	is	be	AUX
ejpam-5979	199	8	a	a	DET
ejpam-5979	199	9	function	function	NOUN
ejpam-5979	199	10	is	be	AUX
ejpam-5979	199	11	continuous	continuous	ADJ
ejpam-5979	199	12	and	and	CCONJ
ejpam-5979	199	13	check	check	VERB
ejpam-5979	199	14	a	a	DET
ejpam-5979	199	15	condition	condition	NOUN
ejpam-5979	199	16	of	of	ADP
ejpam-5979	199	17	uniform	uniform	ADJ
ejpam-5979	199	18	lipschitz	lipschitz	NOUN
ejpam-5979	199	19	concerning	concern	VERB
ejpam-5979	199	20	the	the	DET
ejpam-5979	199	21	second	second	ADJ
ejpam-5979	199	22	variable	variable	NOUN
ejpam-5979	199	23	on	on	ADP
ejpam-5979	199	24	[	[	X
ejpam-5979	199	25	θ	θ	NOUN
ejpam-5979	199	26	,	,	PUNCT
ejpam-5979	199	27	1	1	NUM
ejpam-5979	199	28	]	]	SYM
ejpam-5979	199	29	×	×	NOUN
ejpam-5979	199	30	r	r	NOUN
ejpam-5979	199	31	with	with	ADP
ejpam-5979	199	32	lipschitz	lipschitz	NOUN
ejpam-5979	199	33	real	real	ADJ
ejpam-5979	199	34	ζ	ζ	NOUN
ejpam-5979	199	35	,	,	PUNCT
ejpam-5979	199	36	thus	thus	ADV
ejpam-5979	199	37	,	,	PUNCT
ejpam-5979	199	38	|θ(τ	|θ(τ	PROPN
ejpam-5979	199	39	,	,	PUNCT
ejpam-5979	199	40	µ)−θ(τ	µ)−θ(τ	ADV
ejpam-5979	199	41	,	,	PUNCT
ejpam-5979	199	42	ν)|	ν)|	PROPN
ejpam-5979	199	43	≤	≤	PROPN
ejpam-5979	199	44	ζ|µ−	ζ|µ−	ADJ
ejpam-5979	199	45	ν|	ν|	PROPN
ejpam-5979	199	46	,	,	PUNCT
ejpam-5979	199	47	(	(	PUNCT
ejpam-5979	199	48	τ	τ	PROPN
ejpam-5979	199	49	,	,	PUNCT
ejpam-5979	199	50	µ	µ	NOUN
ejpam-5979	199	51	)	)	PUNCT
ejpam-5979	199	52	,	,	PUNCT
ejpam-5979	199	53	(	(	PUNCT
ejpam-5979	199	54	τ	τ	X
ejpam-5979	199	55	,	,	PUNCT
ejpam-5979	199	56	ν	ν	NOUN
ejpam-5979	199	57	)	)	PUNCT
ejpam-5979	199	58	∈	∈	PROPN
ejpam-5979	199	59	[	[	X
ejpam-5979	199	60	θ	θ	X
ejpam-5979	199	61	,	,	PUNCT
ejpam-5979	199	62	1]×	1]×	NUM
ejpam-5979	199	63	r	r	NOUN
ejpam-5979	199	64	,	,	PUNCT
ejpam-5979	199	65	where	where	SCONJ
ejpam-5979	199	66	ζ	ζ	NOUN
ejpam-5979	199	67	>	>	SYM
ejpam-5979	199	68	0	0	NUM
ejpam-5979	199	69	are	be	AUX
ejpam-5979	199	70	constants	constant	NOUN
ejpam-5979	199	71	.	.	PUNCT
ejpam-5979	200	1	if	if	SCONJ
ejpam-5979	200	2	ζ	ζ	NOUN
ejpam-5979	200	3	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	200	4	)	)	PUNCT
ejpam-5979	200	5	[	[	PUNCT
ejpam-5979	200	6	(	(	PUNCT
ejpam-5979	200	7	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-5979	200	8	σ	σ	PROPN
ejpam-5979	200	9	1	1	NUM
ejpam-5979	200	10	(	(	PUNCT
ejpam-5979	200	11	σ−1	σ−1	PROPN
ejpam-5979	200	12	)	)	PUNCT
ejpam-5979	200	13	−	−	PROPN
ejpam-5979	201	1	(	(	PUNCT
ejpam-5979	201	2	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-5979	201	3	σ	σ	PROPN
ejpam-5979	201	4	σ	σ	PROPN
ejpam-5979	201	5	(	(	PUNCT
ejpam-5979	201	6	σ−1	σ−1	PROPN
ejpam-5979	201	7	)	)	PUNCT
ejpam-5979	201	8	]	]	PUNCT
ejpam-5979	201	9	<	<	X
ejpam-5979	201	10	1	1	NUM
ejpam-5979	201	11	,	,	PUNCT
ejpam-5979	201	12	(	(	PUNCT
ejpam-5979	201	13	20	20	NUM
ejpam-5979	201	14	)	)	PUNCT
ejpam-5979	201	15	then	then	ADV
ejpam-5979	201	16	the	the	DET
ejpam-5979	201	17	bvp	bvp	PROPN
ejpam-5979	201	18	{	{	PUNCT
ejpam-5979	201	19	ϱ	ϱ	PROPN
ejpam-5979	201	20	cdσ	cdσ	NOUN
ejpam-5979	201	21	0+µ(τ	0+µ(τ	NOUN
ejpam-5979	201	22	)	)	PUNCT
ejpam-5979	201	23	=	=	SYM
ejpam-5979	201	24	−θ(τ	−θ(τ	ADJ
ejpam-5979	201	25	,	,	PUNCT
ejpam-5979	201	26	µ(τ	µ(τ	NOUN
ejpam-5979	201	27	)	)	PUNCT
ejpam-5979	201	28	)	)	PUNCT
ejpam-5979	201	29	,	,	PUNCT
ejpam-5979	201	30	θ	θ	X
ejpam-5979	201	31	<	<	X
ejpam-5979	201	32	τ	τ	X
ejpam-5979	201	33	<	<	X
ejpam-5979	201	34	1	1	NUM
ejpam-5979	201	35	,	,	PUNCT
ejpam-5979	201	36	µ(θ	µ(θ	ADJ
ejpam-5979	201	37	)	)	PUNCT
ejpam-5979	201	38	=	=	SYM
ejpam-5979	201	39	λ1	λ1	PROPN
ejpam-5979	201	40	,	,	PUNCT
ejpam-5979	201	41	µ(1	µ(1	PROPN
ejpam-5979	201	42	)	)	PUNCT
ejpam-5979	201	43	=	=	SYM
ejpam-5979	201	44	λ2	λ2	NOUN
ejpam-5979	201	45	,	,	PUNCT
ejpam-5979	201	46	(	(	PUNCT
ejpam-5979	201	47	21	21	NUM
ejpam-5979	201	48	)	)	PUNCT
ejpam-5979	201	49	has	have	VERB
ejpam-5979	201	50	a	a	DET
ejpam-5979	201	51	unique	unique	ADJ
ejpam-5979	201	52	solution	solution	NOUN
ejpam-5979	201	53	.	.	PUNCT
ejpam-5979	202	1	proof	proof	NOUN
ejpam-5979	202	2	.	.	PUNCT
ejpam-5979	203	1	using	use	VERB
ejpam-5979	203	2	the	the	DET
ejpam-5979	203	3	same	same	ADJ
ejpam-5979	203	4	method	method	NOUN
ejpam-5979	203	5	to	to	PART
ejpam-5979	203	6	prove	prove	VERB
ejpam-5979	203	7	proposition	proposition	NOUN
ejpam-5979	203	8	5	5	NUM
ejpam-5979	203	9	and	and	CCONJ
ejpam-5979	203	10	theorem	theorem	VERB
ejpam-5979	203	11	5	5	NUM
ejpam-5979	203	12	which	which	PRON
ejpam-5979	203	13	are	be	AUX
ejpam-5979	203	14	used	use	VERB
ejpam-5979	203	15	in	in	ADP
ejpam-5979	203	16	proposition	proposition	NOUN
ejpam-5979	203	17	2	2	NUM
ejpam-5979	203	18	and	and	CCONJ
ejpam-5979	203	19	also	also	ADV
ejpam-5979	203	20	applies	apply	VERB
ejpam-5979	203	21	to	to	PART
ejpam-5979	203	22	theorem	theorem	VERB
ejpam-5979	203	23	2	2	NUM
ejpam-5979	203	24	.	.	NOUN
ejpam-5979	203	25	remark	remark	NOUN
ejpam-5979	203	26	4	4	NUM
ejpam-5979	203	27	.	.	PUNCT
ejpam-5979	204	1	the	the	DET
ejpam-5979	204	2	same	same	ADJ
ejpam-5979	204	3	remark	remark	NOUN
ejpam-5979	204	4	3	3	NUM
ejpam-5979	204	5	,	,	PUNCT
ejpam-5979	204	6	we	we	PRON
ejpam-5979	204	7	apply	apply	VERB
ejpam-5979	204	8	that	that	PRON
ejpam-5979	204	9	when	when	SCONJ
ejpam-5979	204	10	σ	σ	PROPN
ejpam-5979	204	11	=	=	SYM
ejpam-5979	204	12	2	2	NUM
ejpam-5979	204	13	,	,	PUNCT
ejpam-5979	204	14	θ	θ	X
ejpam-5979	204	15	<	<	X
ejpam-5979	204	16	ϑ	ϑ	X
ejpam-5979	204	17	=	=	SYM
ejpam-5979	204	18	1	1	NUM
ejpam-5979	204	19	and	and	CCONJ
ejpam-5979	204	20	ϱ	ϱ	X
ejpam-5979	204	21	=	=	SYM
ejpam-5979	204	22	1	1	NUM
ejpam-5979	204	23	on	on	ADP
ejpam-5979	204	24	theorem	theorem	NOUN
ejpam-5979	204	25	5	5	NUM
ejpam-5979	204	26	,	,	PUNCT
ejpam-5979	204	27	through	through	ADP
ejpam-5979	204	28	condition	condition	NOUN
ejpam-5979	204	29	(	(	PUNCT
ejpam-5979	204	30	20	20	NUM
ejpam-5979	204	31	)	)	PUNCT
ejpam-5979	204	32	,	,	PUNCT
ejpam-5979	204	33	we	we	PRON
ejpam-5979	204	34	obviously	obviously	ADV
ejpam-5979	204	35	find	find	VERB
ejpam-5979	204	36	theorem	theorem	VERB
ejpam-5979	204	37	1	1	NUM
ejpam-5979	204	38	such	such	ADJ
ejpam-5979	204	39	that	that	SCONJ
ejpam-5979	204	40	ζ	ζ	PROPN
ejpam-5979	204	41	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	204	42	)	)	PUNCT
ejpam-5979	204	43	[	[	PUNCT
ejpam-5979	204	44	(	(	PUNCT
ejpam-5979	204	45	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-5979	204	46	σ	σ	PROPN
ejpam-5979	204	47	1	1	NUM
ejpam-5979	204	48	(	(	PUNCT
ejpam-5979	204	49	σ−1	σ−1	PROPN
ejpam-5979	204	50	)	)	PUNCT
ejpam-5979	204	51	−	−	PROPN
ejpam-5979	205	1	(	(	PUNCT
ejpam-5979	205	2	1−θϱ)σ	1−θϱ)σ	PROPN
ejpam-5979	205	3	σ	σ	PROPN
ejpam-5979	205	4	σ	σ	PROPN
ejpam-5979	205	5	(	(	PUNCT
ejpam-5979	205	6	σ−1	σ−1	PROPN
ejpam-5979	205	7	)	)	PUNCT
ejpam-5979	205	8	]	]	PUNCT
ejpam-5979	206	1	=	=	PUNCT
ejpam-5979	206	2	ζ	ζ	X
ejpam-5979	206	3	(	(	PUNCT
ejpam-5979	206	4	1−	1−	NUM
ejpam-5979	206	5	θ)2	θ)2	NOUN
ejpam-5979	206	6	4γ(3	4γ(3	NUM
ejpam-5979	206	7	)	)	PUNCT
ejpam-5979	206	8	<	<	X
ejpam-5979	206	9	1	1	X
ejpam-5979	206	10	.	.	PUNCT
ejpam-5979	206	11	z.	z.	PROPN
ejpam-5979	206	12	bekri	bekri	PROPN
ejpam-5979	206	13	et	et	PROPN
ejpam-5979	206	14	al	al	PROPN
ejpam-5979	206	15	.	.	PUNCT
ejpam-5979	206	16	/	/	SYM
ejpam-5979	206	17	eur	eur	PROPN
ejpam-5979	206	18	.	.	PUNCT
ejpam-5979	207	1	j.	j.	PROPN
ejpam-5979	207	2	pure	pure	PROPN
ejpam-5979	207	3	appl	appl	PROPN
ejpam-5979	207	4	.	.	PROPN
ejpam-5979	207	5	math	math	PROPN
ejpam-5979	207	6	,	,	PUNCT
ejpam-5979	207	7	18	18	NUM
ejpam-5979	207	8	(	(	PUNCT
ejpam-5979	207	9	2	2	NUM
ejpam-5979	207	10	)	)	PUNCT
ejpam-5979	207	11	(	(	PUNCT
ejpam-5979	207	12	2025	2025	NUM
ejpam-5979	207	13	)	)	PUNCT
ejpam-5979	207	14	,	,	PUNCT
ejpam-5979	207	15	5979	5979	NUM
ejpam-5979	207	16	11	11	NUM
ejpam-5979	207	17	of	of	ADP
ejpam-5979	207	18	20	20	NUM
ejpam-5979	207	19	4	4	NUM
ejpam-5979	207	20	.	.	PUNCT
ejpam-5979	208	1	examples	example	NOUN
ejpam-5979	208	2	to	to	PART
ejpam-5979	208	3	prove	prove	VERB
ejpam-5979	208	4	the	the	DET
ejpam-5979	208	5	desired	desire	VERB
ejpam-5979	208	6	results	result	NOUN
ejpam-5979	208	7	above	above	ADV
ejpam-5979	208	8	,	,	PUNCT
ejpam-5979	208	9	we	we	PRON
ejpam-5979	208	10	take	take	VERB
ejpam-5979	208	11	some	some	DET
ejpam-5979	208	12	applications	application	NOUN
ejpam-5979	208	13	.	.	PUNCT
ejpam-5979	209	1	example	example	NOUN
ejpam-5979	210	1	1	1	NUM
ejpam-5979	210	2	.	.	X
ejpam-5979	210	3	extrapolate	extrapolate	VERB
ejpam-5979	210	4	the	the	DET
ejpam-5979	210	5	following	follow	VERB
ejpam-5979	210	6	application	application	NOUN
ejpam-5979	210	7	of	of	ADP
ejpam-5979	210	8	bvp	bvp	PROPN
ejpam-5979	210	9	{	{	PUNCT
ejpam-5979	210	10	ϱ	ϱ	PROPN
ejpam-5979	210	11	cdσ	cdσ	NOUN
ejpam-5979	210	12	0+µ(τ	0+µ(τ	NOUN
ejpam-5979	210	13	)	)	PUNCT
ejpam-5979	210	14	=	=	PUNCT
ejpam-5979	210	15	3−	3−	NUM
ejpam-5979	210	16	τ7	τ7	NOUN
ejpam-5979	210	17	−	−	PROPN
ejpam-5979	210	18	sin(µ(τ	sin(µ(τ	NOUN
ejpam-5979	210	19	)	)	PUNCT
ejpam-5979	210	20	)	)	PUNCT
ejpam-5979	210	21	,	,	PUNCT
ejpam-5979	210	22	0	0	PUNCT
ejpam-5979	210	23	<	<	X
ejpam-5979	210	24	τ	τ	X
ejpam-5979	210	25	<	<	X
ejpam-5979	210	26	ϑ	ϑ	X
ejpam-5979	210	27	,	,	PUNCT
ejpam-5979	210	28	µ(0	µ(0	NOUN
ejpam-5979	210	29	)	)	PUNCT
ejpam-5979	210	30	=	=	SYM
ejpam-5979	210	31	1	1	NUM
ejpam-5979	210	32	,	,	PUNCT
ejpam-5979	210	33	µ(ϑ	µ(ϑ	NOUN
ejpam-5979	210	34	)	)	PUNCT
ejpam-5979	210	35	=	=	SYM
ejpam-5979	210	36	2	2	X
ejpam-5979	210	37	.	.	PUNCT
ejpam-5979	210	38	(	(	PUNCT
ejpam-5979	210	39	22	22	NUM
ejpam-5979	210	40	)	)	PUNCT
ejpam-5979	210	41	set	set	NOUN
ejpam-5979	210	42	,	,	PUNCT
ejpam-5979	210	43	ϱ	ϱ	X
ejpam-5979	210	44	=	=	SYM
ejpam-5979	210	45	1	1	NUM
ejpam-5979	210	46	,	,	PUNCT
ejpam-5979	210	47	σ	σ	PROPN
ejpam-5979	210	48	∈	∈	PROPN
ejpam-5979	210	49	{	{	PUNCT
ejpam-5979	210	50	4	4	NUM
ejpam-5979	210	51	3	3	NUM
ejpam-5979	210	52	,	,	PUNCT
ejpam-5979	210	53	3	3	NUM
ejpam-5979	210	54	2	2	NUM
ejpam-5979	210	55	,	,	PUNCT
ejpam-5979	210	56	9	9	NUM
ejpam-5979	210	57	5	5	NUM
ejpam-5979	210	58	,	,	PUNCT
ejpam-5979	210	59	39	39	NUM
ejpam-5979	210	60	20	20	NUM
ejpam-5979	210	61	}	}	PUNCT
ejpam-5979	210	62	⊂	⊂	PROPN
ejpam-5979	210	63	(	(	PUNCT
ejpam-5979	210	64	1	1	NUM
ejpam-5979	210	65	,	,	PUNCT
ejpam-5979	210	66	2	2	NUM
ejpam-5979	210	67	]	]	PUNCT
ejpam-5979	210	68	,	,	PUNCT
ejpam-5979	210	69	θ	θ	PROPN
ejpam-5979	210	70	=	=	SYM
ejpam-5979	210	71	0	0	PROPN
ejpam-5979	210	72	.	.	PUNCT
ejpam-5979	211	1	and	and	CCONJ
ejpam-5979	211	2	θ(τ	θ(τ	PROPN
ejpam-5979	211	3	,	,	PUNCT
ejpam-5979	211	4	µ(τ	µ(τ	PROPN
ejpam-5979	211	5	)	)	PUNCT
ejpam-5979	211	6	)	)	PUNCT
ejpam-5979	212	1	=	=	PUNCT
ejpam-5979	212	2	τ7	τ7	PROPN
ejpam-5979	212	3	−	−	PROPN
ejpam-5979	212	4	3	3	NUM
ejpam-5979	212	5	+	+	NUM
ejpam-5979	212	6	sin(µ(τ	sin(µ(τ	NOUN
ejpam-5979	212	7	)	)	PUNCT
ejpam-5979	212	8	)	)	PUNCT
ejpam-5979	212	9	.	.	PUNCT
ejpam-5979	213	1	here	here	ADV
ejpam-5979	213	2	,	,	PUNCT
ejpam-5979	213	3	|θ(τ	|θ(τ	PROPN
ejpam-5979	213	4	,	,	PUNCT
ejpam-5979	213	5	µ)−θ(τ	µ)−θ(τ	ADV
ejpam-5979	213	6	,	,	PUNCT
ejpam-5979	213	7	ν)|	ν)|	PROPN
ejpam-5979	213	8	=	=	PUNCT
ejpam-5979	213	9	∣∣τ7	∣∣τ7	NOUN
ejpam-5979	213	10	−	−	NOUN
ejpam-5979	213	11	3	3	NUM
ejpam-5979	213	12	+	+	NUM
ejpam-5979	213	13	sin(µ(τ))−	sin(µ(τ))−	NOUN
ejpam-5979	213	14	(	(	PUNCT
ejpam-5979	213	15	τ7	τ7	NOUN
ejpam-5979	213	16	−	−	PROPN
ejpam-5979	213	17	3	3	NUM
ejpam-5979	213	18	+	+	NUM
ejpam-5979	213	19	sin(ν(τ	sin(ν(τ	NOUN
ejpam-5979	213	20	)	)	PUNCT
ejpam-5979	213	21	)	)	PUNCT
ejpam-5979	213	22	)	)	PUNCT
ejpam-5979	213	23	∣∣	∣∣	X
ejpam-5979	213	24	≤	≤	NUM
ejpam-5979	213	25	ζ|µ−	ζ|µ−	CCONJ
ejpam-5979	213	26	ν|	ν|	PROPN
ejpam-5979	213	27	,	,	PUNCT
ejpam-5979	213	28	∀	∀	X
ejpam-5979	213	29	(	(	PUNCT
ejpam-5979	213	30	τ	τ	PROPN
ejpam-5979	213	31	,	,	PUNCT
ejpam-5979	213	32	µ	µ	NOUN
ejpam-5979	213	33	)	)	PUNCT
ejpam-5979	213	34	,	,	PUNCT
ejpam-5979	213	35	(	(	PUNCT
ejpam-5979	213	36	τ	τ	X
ejpam-5979	213	37	,	,	PUNCT
ejpam-5979	213	38	ν	ν	NOUN
ejpam-5979	213	39	)	)	PUNCT
ejpam-5979	213	40	∈	∈	PROPN
ejpam-5979	214	1	[	[	X
ejpam-5979	214	2	0	0	NUM
ejpam-5979	214	3	,	,	PUNCT
ejpam-5979	214	4	ϑ]×	ϑ]×	NOUN
ejpam-5979	214	5	r2	r2	PROPN
ejpam-5979	214	6	,	,	PUNCT
ejpam-5979	214	7	where	where	SCONJ
ejpam-5979	214	8	ζ	ζ	NOUN
ejpam-5979	214	9	=	=	SYM
ejpam-5979	214	10	1	1	NUM
ejpam-5979	214	11	>	>	X
ejpam-5979	214	12	0	0	X
ejpam-5979	214	13	.	.	PUNCT
ejpam-5979	215	1	moreover	moreover	ADV
ejpam-5979	215	2	,	,	PUNCT
ejpam-5979	215	3	we	we	PRON
ejpam-5979	215	4	have	have	VERB
ejpam-5979	215	5	ϖ	ϖ	NOUN
ejpam-5979	215	6	=	=	SYM
ejpam-5979	215	7	ζ	ζ	NOUN
ejpam-5979	215	8	ϱσγ(σ+1	ϱσγ(σ+1	PROPN
ejpam-5979	215	9	)	)	PUNCT
ejpam-5979	216	1	[	[	PUNCT
ejpam-5979	216	2	ϑϱσ	ϑϱσ	X
ejpam-5979	216	3	σ	σ	PROPN
ejpam-5979	216	4	1	1	NUM
ejpam-5979	216	5	(	(	PUNCT
ejpam-5979	216	6	σ−1	σ−1	PROPN
ejpam-5979	216	7	)	)	PUNCT
ejpam-5979	216	8	−	−	PROPN
ejpam-5979	216	9	ϑϱσ	ϑϱσ	PROPN
ejpam-5979	216	10	σ	σ	PROPN
ejpam-5979	216	11	σ	σ	PROPN
ejpam-5979	216	12	(	(	PUNCT
ejpam-5979	216	13	σ−1	σ−1	PROPN
ejpam-5979	216	14	)	)	PUNCT
ejpam-5979	216	15	]	]	PUNCT
ejpam-5979	217	1	≈	≈	PROPN
ejpam-5979	217	2			PROPN
ejpam-5979	217	3	0.0886	0.0886	NUM
ejpam-5979	217	4	,	,	PUNCT
ejpam-5979	217	5	σ	σ	X
ejpam-5979	217	6	=	=	SYM
ejpam-5979	217	7	4	4	NUM
ejpam-5979	217	8	3	3	NUM
ejpam-5979	217	9	,	,	PUNCT
ejpam-5979	217	10	0.1114	0.1114	NUM
ejpam-5979	217	11	,	,	PUNCT
ejpam-5979	217	12	σ	σ	NOUN
ejpam-5979	217	13	=	=	SYM
ejpam-5979	217	14	3	3	NUM
ejpam-5979	217	15	2	2	NUM
ejpam-5979	217	16	,	,	PUNCT
ejpam-5979	217	17	0.1272	0.1272	NUM
ejpam-5979	217	18	,	,	PUNCT
ejpam-5979	217	19	σ	σ	NOUN
ejpam-5979	217	20	=	=	SYM
ejpam-5979	217	21	9	9	NUM
ejpam-5979	217	22	5	5	NUM
ejpam-5979	217	23	,	,	PUNCT
ejpam-5979	217	24	0.1262	0.1262	NUM
ejpam-5979	217	25	,	,	PUNCT
ejpam-5979	217	26	σ	σ	NOUN
ejpam-5979	217	27	=	=	PROPN
ejpam-5979	217	28	39	39	NUM
ejpam-5979	217	29	20	20	NUM
ejpam-5979	217	30	,	,	PUNCT
ejpam-5979	217	31			ADJ
ejpam-5979	217	32	<	<	X
ejpam-5979	217	33	1	1	NUM
ejpam-5979	217	34	.	.	PUNCT
ejpam-5979	218	1	the	the	DET
ejpam-5979	218	2	curves	curve	NOUN
ejpam-5979	218	3	drawn	draw	VERB
ejpam-5979	218	4	in	in	ADP
ejpam-5979	218	5	figure	figure	NOUN
ejpam-5979	218	6	1	1	NUM
ejpam-5979	218	7	show	show	VERB
ejpam-5979	218	8	how	how	SCONJ
ejpam-5979	218	9	the	the	DET
ejpam-5979	218	10	ϖ	ϖ	NOUN
ejpam-5979	218	11	changes	change	NOUN
ejpam-5979	218	12	for	for	ADP
ejpam-5979	218	13	different	different	ADJ
ejpam-5979	218	14	derivative	derivative	ADJ
ejpam-5979	218	15	orders	order	NOUN
ejpam-5979	218	16	σ	σ	NOUN
ejpam-5979	218	17	.	.	PUNCT
ejpam-5979	219	1	the	the	DET
ejpam-5979	219	2	important	important	ADJ
ejpam-5979	219	3	point	point	NOUN
ejpam-5979	219	4	is	be	AUX
ejpam-5979	219	5	that	that	SCONJ
ejpam-5979	219	6	all	all	PRON
ejpam-5979	219	7	of	of	ADP
ejpam-5979	219	8	them	they	PRON
ejpam-5979	219	9	are	be	AUX
ejpam-5979	219	10	less	less	ADJ
ejpam-5979	219	11	than	than	ADP
ejpam-5979	219	12	the	the	DET
ejpam-5979	219	13	line	line	NOUN
ejpam-5979	219	14	y	y	NOUN
ejpam-5979	219	15	=	=	NOUN
ejpam-5979	219	16	1	1	NUM
ejpam-5979	219	17	in	in	ADP
ejpam-5979	219	18	the	the	DET
ejpam-5979	219	19	interval	interval	NOUN
ejpam-5979	219	20	[	[	X
ejpam-5979	219	21	0	0	NUM
ejpam-5979	219	22	,	,	PUNCT
ejpam-5979	219	23	ϑ	ϑ	X
ejpam-5979	219	24	]	]	X
ejpam-5979	219	25	,	,	PUNCT
ejpam-5979	219	26	and	and	CCONJ
ejpam-5979	219	27	as	as	SCONJ
ejpam-5979	219	28	the	the	DET
ejpam-5979	219	29	order	order	NOUN
ejpam-5979	219	30	of	of	ADP
ejpam-5979	219	31	the	the	DET
ejpam-5979	219	32	derivative	derivative	ADJ
ejpam-5979	219	33	approaches	approach	VERB
ejpam-5979	219	34	the	the	DET
ejpam-5979	219	35	number	number	NOUN
ejpam-5979	219	36	one	one	NUM
ejpam-5979	219	37	,	,	PUNCT
ejpam-5979	219	38	the	the	DET
ejpam-5979	219	39	parameter	parameter	NOUN
ejpam-5979	219	40	ϖ	ϖ	PROPN
ejpam-5979	219	41	decreases	decrease	VERB
ejpam-5979	219	42	,	,	PUNCT
ejpam-5979	219	43	but	but	CCONJ
ejpam-5979	219	44	they	they	PRON
ejpam-5979	219	45	are	be	AUX
ejpam-5979	219	46	still	still	ADV
ejpam-5979	219	47	less	less	ADJ
ejpam-5979	219	48	than	than	ADP
ejpam-5979	219	49	one	one	NUM
ejpam-5979	219	50	.	.	PUNCT
ejpam-5979	220	1	these	these	DET
ejpam-5979	220	2	results	result	NOUN
ejpam-5979	220	3	are	be	AUX
ejpam-5979	220	4	shown	show	VERB
ejpam-5979	220	5	in	in	ADP
ejpam-5979	220	6	table	table	NOUN
ejpam-5979	220	7	1	1	NUM
ejpam-5979	220	8	.	.	PUNCT
ejpam-5979	220	9	by	by	ADP
ejpam-5979	220	10	the	the	DET
ejpam-5979	220	11	applications	application	NOUN
ejpam-5979	220	12	of	of	ADP
ejpam-5979	220	13	theorem	theorem	NOUN
ejpam-5979	220	14	2	2	NUM
ejpam-5979	220	15	,	,	PUNCT
ejpam-5979	220	16	and	and	CCONJ
ejpam-5979	220	17	the	the	DET
ejpam-5979	220	18	condition	condition	NOUN
ejpam-5979	220	19	(	(	PUNCT
ejpam-5979	220	20	11	11	NUM
ejpam-5979	220	21	)	)	PUNCT
ejpam-5979	220	22	is	be	AUX
ejpam-5979	220	23	agreed	agree	VERB
ejpam-5979	220	24	.	.	PUNCT
ejpam-5979	221	1	then	then	ADV
ejpam-5979	221	2	the	the	DET
ejpam-5979	221	3	bvp	bvp	PROPN
ejpam-5979	221	4	(	(	PUNCT
ejpam-5979	221	5	22	22	NUM
ejpam-5979	221	6	)	)	PUNCT
ejpam-5979	221	7	accepts	accept	VERB
ejpam-5979	221	8	an	an	DET
ejpam-5979	221	9	unique	unique	ADJ
ejpam-5979	221	10	solution	solution	NOUN
ejpam-5979	221	11	.	.	PUNCT
ejpam-5979	222	1	τ	τ	PROPN
ejpam-5979	222	2	0	0	NUM
ejpam-5979	222	3	0.1	0.1	NUM
ejpam-5979	222	4	0.2	0.2	NUM
ejpam-5979	222	5	0.3	0.3	NUM
ejpam-5979	222	6	0.4	0.4	NUM
ejpam-5979	222	7	0.5	0.5	NUM
ejpam-5979	222	8	0.6	0.6	NUM
ejpam-5979	222	9	0.7	0.7	NUM
ejpam-5979	222	10	0.8	0.8	NUM
ejpam-5979	222	11	0.9	0.9	NUM
ejpam-5979	222	12	1	1	NUM
ejpam-5979	222	13	̟	̟	ADP
ejpam-5979	222	14	0	0	NUM
ejpam-5979	222	15	0.02	0.02	NUM
ejpam-5979	222	16	0.04	0.04	NUM
ejpam-5979	222	17	0.06	0.06	NUM
ejpam-5979	222	18	0.08	0.08	NUM
ejpam-5979	222	19	0.1	0.1	NUM
ejpam-5979	222	20	0.12	0.12	NUM
ejpam-5979	222	21	0.14	0.14	NUM
ejpam-5979	222	22	σ=4/3	σ=4/3	PROPN
ejpam-5979	222	23	σ=3/2	σ=3/2	PROPN
ejpam-5979	222	24	σ=9/5	σ=9/5	PROPN
ejpam-5979	222	25	σ=39/20	σ=39/20	PROPN
ejpam-5979	222	26	figure	figure	NOUN
ejpam-5979	222	27	1	1	NUM
ejpam-5979	222	28	:	:	PUNCT
ejpam-5979	222	29	representation	representation	NOUN
ejpam-5979	222	30	of	of	ADP
ejpam-5979	222	31	ϖ	ϖ	PROPN
ejpam-5979	222	32	for	for	ADP
ejpam-5979	222	33	bvp	bvp	NOUN
ejpam-5979	222	34	(	(	PUNCT
ejpam-5979	222	35	22	22	NUM
ejpam-5979	222	36	)	)	PUNCT
ejpam-5979	222	37	in	in	ADP
ejpam-5979	222	38	example	example	NOUN
ejpam-5979	222	39	1	1	NUM
ejpam-5979	222	40	for	for	ADP
ejpam-5979	222	41	four	four	NUM
ejpam-5979	222	42	case	case	NOUN
ejpam-5979	222	43	σ	σ	PROPN
ejpam-5979	222	44	.	.	PUNCT
ejpam-5979	222	45	z.	z.	PROPN
ejpam-5979	222	46	bekri	bekri	PROPN
ejpam-5979	222	47	et	et	PROPN
ejpam-5979	223	1	al	al	PROPN
ejpam-5979	223	2	.	.	PUNCT
ejpam-5979	223	3	/	/	SYM
ejpam-5979	223	4	eur	eur	PROPN
ejpam-5979	223	5	.	.	PUNCT
ejpam-5979	224	1	j.	j.	PROPN
ejpam-5979	224	2	pure	pure	PROPN
ejpam-5979	224	3	appl	appl	PROPN
ejpam-5979	224	4	.	.	PROPN
ejpam-5979	224	5	math	math	PROPN
ejpam-5979	224	6	,	,	PUNCT
ejpam-5979	224	7	18	18	NUM
ejpam-5979	224	8	(	(	PUNCT
ejpam-5979	224	9	2	2	NUM
ejpam-5979	224	10	)	)	PUNCT
ejpam-5979	224	11	(	(	PUNCT
ejpam-5979	224	12	2025	2025	NUM
ejpam-5979	224	13	)	)	PUNCT
ejpam-5979	224	14	,	,	PUNCT
ejpam-5979	224	15	5979	5979	NUM
ejpam-5979	224	16	12	12	NUM
ejpam-5979	224	17	of	of	ADP
ejpam-5979	224	18	20	20	NUM
ejpam-5979	224	19	table	table	NOUN
ejpam-5979	224	20	1	1	NUM
ejpam-5979	224	21	:	:	PUNCT
ejpam-5979	224	22	numerical	numerical	ADJ
ejpam-5979	224	23	results	result	NOUN
ejpam-5979	224	24	ϖ	ϖ	VERB
ejpam-5979	224	25	in	in	ADP
ejpam-5979	224	26	example	example	NOUN
ejpam-5979	224	27	1	1	NUM
ejpam-5979	224	28	for	for	ADP
ejpam-5979	224	29	four	four	NUM
ejpam-5979	224	30	values	value	NOUN
ejpam-5979	224	31	of	of	ADP
ejpam-5979	224	32	σ	σ	PROPN
ejpam-5979	224	33	.	.	PUNCT
ejpam-5979	225	1	τ	τ	PROPN
ejpam-5979	225	2	ϖ	ϖ	PROPN
ejpam-5979	225	3	σ	σ	NOUN
ejpam-5979	225	4	=	=	SYM
ejpam-5979	225	5	4	4	NUM
ejpam-5979	225	6	3	3	NUM
ejpam-5979	225	7	σ	σ	NOUN
ejpam-5979	225	8	=	=	SYM
ejpam-5979	225	9	4	4	NUM
ejpam-5979	225	10	3σ	3σ	NUM
ejpam-5979	225	11	=	=	SYM
ejpam-5979	226	1	4	4	NUM
ejpam-5979	226	2	3	3	NUM
ejpam-5979	226	3	σ	σ	NOUN
ejpam-5979	226	4	=	=	SYM
ejpam-5979	226	5	3	3	NUM
ejpam-5979	226	6	2	2	NUM
ejpam-5979	226	7	σ	σ	NOUN
ejpam-5979	226	8	=	=	SYM
ejpam-5979	226	9	3	3	NUM
ejpam-5979	226	10	2σ	2σ	NOUN
ejpam-5979	226	11	=	=	NOUN
ejpam-5979	226	12	3	3	NUM
ejpam-5979	226	13	2	2	NUM
ejpam-5979	226	14	σ	σ	NOUN
ejpam-5979	226	15	=	=	NOUN
ejpam-5979	226	16	9	9	NUM
ejpam-5979	226	17	5	5	NUM
ejpam-5979	226	18	σ	σ	NOUN
ejpam-5979	226	19	=	=	SYM
ejpam-5979	226	20	9	9	NUM
ejpam-5979	226	21	5σ	5σ	NOUN
ejpam-5979	226	22	=	=	NOUN
ejpam-5979	226	23	9	9	NUM
ejpam-5979	226	24	5	5	NUM
ejpam-5979	226	25	σ	σ	NOUN
ejpam-5979	226	26	=	=	NOUN
ejpam-5979	226	27	39	39	NUM
ejpam-5979	226	28	20	20	NUM
ejpam-5979	226	29	σ	σ	NOUN
ejpam-5979	226	30	=	=	NOUN
ejpam-5979	226	31	39	39	NUM
ejpam-5979	226	32	20σ	20σ	NUM
ejpam-5979	226	33	=	=	SYM
ejpam-5979	226	34	39	39	NUM
ejpam-5979	226	35	20	20	NUM
ejpam-5979	226	36	0.00	0.00	NUM
ejpam-5979	226	37	0.0000	0.0000	NUM
ejpam-5979	226	38	0.0000	0.0000	NUM
ejpam-5979	226	39	0.0000	0.0000	NUM
ejpam-5979	226	40	0.0000	0.0000	NUM
ejpam-5979	226	41	0.05	0.05	NUM
ejpam-5979	226	42	0.0044	0.0044	NUM
ejpam-5979	226	43	0.0056	0.0056	NUM
ejpam-5979	226	44	0.0064	0.0064	NUM
ejpam-5979	226	45	0.0063	0.0063	NUM
ejpam-5979	226	46	0.10	0.10	NUM
ejpam-5979	226	47	0.0089	0.0089	NUM
ejpam-5979	226	48	0.0111	0.0111	NUM
ejpam-5979	226	49	0.0127	0.0127	NUM
ejpam-5979	226	50	0.0126	0.0126	NUM
ejpam-5979	226	51	0.15	0.15	NUM
ejpam-5979	226	52	0.0133	0.0133	NUM
ejpam-5979	226	53	0.0167	0.0167	NUM
ejpam-5979	226	54	0.0191	0.0191	NUM
ejpam-5979	226	55	0.0189	0.0189	NUM
ejpam-5979	226	56	0.20	0.20	NUM
ejpam-5979	226	57	0.0177	0.0177	NUM
ejpam-5979	226	58	0.0223	0.0223	NUM
ejpam-5979	226	59	0.0254	0.0254	NUM
ejpam-5979	226	60	0.0252	0.0252	NUM
ejpam-5979	226	61	0.25	0.25	NUM
ejpam-5979	226	62	0.0221	0.0221	NUM
ejpam-5979	226	63	0.0279	0.0279	NUM
ejpam-5979	226	64	0.0318	0.0318	NUM
ejpam-5979	226	65	0.0316	0.0316	NUM
ejpam-5979	226	66	0.30	0.30	NUM
ejpam-5979	226	67	0.0266	0.0266	NUM
ejpam-5979	226	68	0.0334	0.0334	NUM
ejpam-5979	226	69	0.0381	0.0381	NUM
ejpam-5979	226	70	0.0379	0.0379	NUM
ejpam-5979	226	71	0.35	0.35	NUM
ejpam-5979	226	72	0.0310	0.0310	NUM
ejpam-5979	226	73	0.0390	0.0390	NUM
ejpam-5979	226	74	0.0445	0.0445	NUM
ejpam-5979	226	75	0.0442	0.0442	NUM
ejpam-5979	226	76	0.40	0.40	NUM
ejpam-5979	226	77	0.0354	0.0354	NUM
ejpam-5979	226	78	0.0446	0.0446	NUM
ejpam-5979	226	79	0.0509	0.0509	NUM
ejpam-5979	226	80	0.0505	0.0505	NUM
ejpam-5979	226	81	0.45	0.45	NUM
ejpam-5979	226	82	0.0399	0.0399	NUM
ejpam-5979	226	83	0.0502	0.0502	NUM
ejpam-5979	226	84	0.0572	0.0572	NUM
ejpam-5979	226	85	0.0568	0.0568	NUM
ejpam-5979	226	86	0.50	0.50	NUM
ejpam-5979	226	87	0.0443	0.0443	NUM
ejpam-5979	226	88	0.0557	0.0557	NUM
ejpam-5979	227	1	0.0636	0.0636	NUM
ejpam-5979	227	2	0.0631	0.0631	NUM
ejpam-5979	227	3	0.55	0.55	NUM
ejpam-5979	227	4	0.0487	0.0487	NUM
ejpam-5979	227	5	0.0613	0.0613	NUM
ejpam-5979	227	6	0.0699	0.0699	NUM
ejpam-5979	227	7	0.0694	0.0694	NUM
ejpam-5979	227	8	0.60	0.60	NUM
ejpam-5979	227	9	0.0531	0.0531	NUM
ejpam-5979	227	10	0.0669	0.0669	NUM
ejpam-5979	227	11	0.0763	0.0763	NUM
ejpam-5979	227	12	0.0757	0.0757	NUM
ejpam-5979	227	13	0.65	0.65	NUM
ejpam-5979	227	14	0.0576	0.0576	NUM
ejpam-5979	227	15	0.0724	0.0724	NUM
ejpam-5979	227	16	0.0826	0.0826	NUM
ejpam-5979	227	17	0.0821	0.0821	NUM
ejpam-5979	227	18	0.70	0.70	NUM
ejpam-5979	227	19	0.0620	0.0620	NUM
ejpam-5979	227	20	0.0780	0.0780	NUM
ejpam-5979	227	21	0.0890	0.0890	NUM
ejpam-5979	227	22	0.0884	0.0884	NUM
ejpam-5979	227	23	0.75	0.75	NUM
ejpam-5979	227	24	0.0664	0.0664	NUM
ejpam-5979	227	25	0.0836	0.0836	NUM
ejpam-5979	227	26	0.0954	0.0954	NUM
ejpam-5979	227	27	0.0947	0.0947	NUM
ejpam-5979	227	28	0.80	0.80	NUM
ejpam-5979	227	29	0.0709	0.0709	NUM
ejpam-5979	227	30	0.0892	0.0892	NUM
ejpam-5979	227	31	0.1017	0.1017	NUM
ejpam-5979	227	32	0.1010	0.1010	NUM
ejpam-5979	227	33	0.85	0.85	NUM
ejpam-5979	227	34	0.0753	0.0753	NUM
ejpam-5979	227	35	0.0947	0.0947	NUM
ejpam-5979	227	36	0.1081	0.1081	NUM
ejpam-5979	227	37	0.1073	0.1073	NUM
ejpam-5979	227	38	0.90	0.90	NUM
ejpam-5979	227	39	0.0797	0.0797	NUM
ejpam-5979	227	40	0.1003	0.1003	NUM
ejpam-5979	227	41	0.1144	0.1144	NUM
ejpam-5979	227	42	0.1136	0.1136	NUM
ejpam-5979	227	43	0.95	0.95	NUM
ejpam-5979	227	44	0.0842	0.0842	NUM
ejpam-5979	227	45	0.1059	0.1059	NUM
ejpam-5979	227	46	0.1208	0.1208	NUM
ejpam-5979	227	47	0.1199	0.1199	NUM
ejpam-5979	227	48	1.00	1.00	NUM
ejpam-5979	227	49	0.0886	0.0886	NUM
ejpam-5979	227	50	0.1114	0.1114	NUM
ejpam-5979	227	51	0.1272	0.1272	NUM
ejpam-5979	227	52	0.1262	0.1262	NUM
ejpam-5979	227	53	example	example	NOUN
ejpam-5979	227	54	2	2	NUM
ejpam-5979	227	55	.	.	PUNCT
ejpam-5979	227	56	extrapolate	extrapolate	VERB
ejpam-5979	227	57	the	the	DET
ejpam-5979	227	58	following	follow	VERB
ejpam-5979	227	59	application	application	NOUN
ejpam-5979	227	60	of	of	ADP
ejpam-5979	227	61	bvp	bvp	PROPN
ejpam-5979	227	62	{	{	PUNCT
ejpam-5979	227	63	ϱ	ϱ	PROPN
ejpam-5979	227	64	cdσ	cdσ	NOUN
ejpam-5979	227	65	0+µ(τ	0+µ(τ	NOUN
ejpam-5979	227	66	)	)	PUNCT
ejpam-5979	228	1	=	=	SYM
ejpam-5979	228	2	4−	4−	NUM
ejpam-5979	228	3	τ5	τ5	NOUN
ejpam-5979	228	4	+	+	CCONJ
ejpam-5979	228	5	cos(µ(τ	cos(µ(τ	NOUN
ejpam-5979	228	6	)	)	PUNCT
ejpam-5979	228	7	)	)	PUNCT
ejpam-5979	228	8	,	,	PUNCT
ejpam-5979	228	9	0	0	PUNCT
ejpam-5979	228	10	<	<	X
ejpam-5979	228	11	τ	τ	X
ejpam-5979	228	12	<	<	X
ejpam-5979	228	13	ϑ	ϑ	X
ejpam-5979	228	14	,	,	PUNCT
ejpam-5979	228	15	µ(0	µ(0	NOUN
ejpam-5979	228	16	)	)	PUNCT
ejpam-5979	228	17	=	=	SYM
ejpam-5979	228	18	3	3	X
ejpam-5979	228	19	,	,	PUNCT
ejpam-5979	228	20	µ(1	µ(1	PROPN
ejpam-5979	228	21	)	)	PUNCT
ejpam-5979	228	22	=	=	PUNCT
ejpam-5979	229	1	4	4	X
ejpam-5979	229	2	.	.	PUNCT
ejpam-5979	229	3	(	(	PUNCT
ejpam-5979	229	4	23	23	NUM
ejpam-5979	229	5	)	)	PUNCT
ejpam-5979	229	6	set	set	NOUN
ejpam-5979	229	7	,	,	PUNCT
ejpam-5979	229	8	ϱ	ϱ	X
ejpam-5979	229	9	=	=	SYM
ejpam-5979	229	10	1	1	NUM
ejpam-5979	229	11	,	,	PUNCT
ejpam-5979	229	12	σ	σ	PROPN
ejpam-5979	229	13	∈	∈	PROPN
ejpam-5979	229	14	{	{	PUNCT
ejpam-5979	229	15	4	4	NUM
ejpam-5979	229	16	3	3	NUM
ejpam-5979	229	17	,	,	PUNCT
ejpam-5979	229	18	3	3	NUM
ejpam-5979	229	19	2	2	NUM
ejpam-5979	229	20	,	,	PUNCT
ejpam-5979	229	21	9	9	NUM
ejpam-5979	229	22	5	5	NUM
ejpam-5979	229	23	,	,	PUNCT
ejpam-5979	229	24	39	39	NUM
ejpam-5979	229	25	20	20	NUM
ejpam-5979	229	26	}	}	PUNCT
ejpam-5979	229	27	⊂	⊂	PROPN
ejpam-5979	229	28	(	(	PUNCT
ejpam-5979	229	29	1	1	NUM
ejpam-5979	229	30	,	,	PUNCT
ejpam-5979	229	31	2	2	NUM
ejpam-5979	229	32	]	]	PUNCT
ejpam-5979	229	33	,	,	PUNCT
ejpam-5979	229	34	θ	θ	PROPN
ejpam-5979	229	35	=	=	SYM
ejpam-5979	229	36	0	0	NUM
ejpam-5979	229	37	,	,	PUNCT
ejpam-5979	229	38	ϑ	ϑ	X
ejpam-5979	229	39	=	=	SYM
ejpam-5979	229	40	1	1	NUM
ejpam-5979	229	41	,	,	PUNCT
ejpam-5979	229	42	and	and	CCONJ
ejpam-5979	229	43	θ(τ	θ(τ	PROPN
ejpam-5979	229	44	,	,	PUNCT
ejpam-5979	229	45	µ(τ	µ(τ	PROPN
ejpam-5979	229	46	)	)	PUNCT
ejpam-5979	229	47	)	)	PUNCT
ejpam-5979	230	1	=	=	PUNCT
ejpam-5979	230	2	τ5	τ5	NOUN
ejpam-5979	230	3	−	−	NOUN
ejpam-5979	230	4	4	4	NUM
ejpam-5979	230	5	−	−	NOUN
ejpam-5979	230	6	cos(µ(τ	cos(µ(τ	NOUN
ejpam-5979	230	7	)	)	PUNCT
ejpam-5979	230	8	)	)	PUNCT
ejpam-5979	230	9	.	.	PUNCT
ejpam-5979	231	1	here	here	ADV
ejpam-5979	231	2	,	,	PUNCT
ejpam-5979	231	3	|θ(τ	|θ(τ	PROPN
ejpam-5979	231	4	,	,	PUNCT
ejpam-5979	231	5	µ)−θ(τ	µ)−θ(τ	ADV
ejpam-5979	231	6	,	,	PUNCT
ejpam-5979	231	7	ν)|	ν)|	NOUN
ejpam-5979	231	8	=	=	PUNCT
ejpam-5979	231	9	∣∣τ5	∣∣τ5	NOUN
ejpam-5979	231	10	−	−	PROPN
ejpam-5979	231	11	4−	4−	NOUN
ejpam-5979	231	12	cos(µ(τ))−	cos(µ(τ))−	NOUN
ejpam-5979	231	13	(	(	PUNCT
ejpam-5979	231	14	τ5	τ5	NOUN
ejpam-5979	231	15	−	−	PROPN
ejpam-5979	231	16	4−	4−	PROPN
ejpam-5979	231	17	cos(ν(τ	cos(ν(τ	NOUN
ejpam-5979	231	18	)	)	PUNCT
ejpam-5979	231	19	)	)	PUNCT
ejpam-5979	231	20	)	)	PUNCT
ejpam-5979	232	1	∣∣	∣∣	X
ejpam-5979	232	2	=	=	SYM
ejpam-5979	232	3	|cos(ν(τ))−	|cos(ν(τ))−	PROPN
ejpam-5979	232	4	cos(µ(τ))|	cos(µ(τ))|	NOUN
ejpam-5979	232	5	=	=	SYM
ejpam-5979	232	6	2	2	NUM
ejpam-5979	232	7	∣∣sin	∣∣sin	NOUN
ejpam-5979	232	8	ν+µ	ν+µ	PROPN
ejpam-5979	232	9	2	2	NUM
ejpam-5979	232	10	sin	sin	NOUN
ejpam-5979	232	11	ν−µ	ν−µ	X
ejpam-5979	232	12	2	2	NUM
ejpam-5979	232	13	∣∣	∣∣	NUM
ejpam-5979	232	14	≤	≤	X
ejpam-5979	232	15	ζ|µ−	ζ|µ−	ADJ
ejpam-5979	232	16	ν|	ν|	PROPN
ejpam-5979	232	17	,	,	PUNCT
ejpam-5979	232	18	∀	∀	X
ejpam-5979	232	19	(	(	PUNCT
ejpam-5979	232	20	τ	τ	PROPN
ejpam-5979	232	21	,	,	PUNCT
ejpam-5979	232	22	µ	µ	NOUN
ejpam-5979	232	23	)	)	PUNCT
ejpam-5979	232	24	,	,	PUNCT
ejpam-5979	232	25	(	(	PUNCT
ejpam-5979	232	26	τ	τ	X
ejpam-5979	232	27	,	,	PUNCT
ejpam-5979	232	28	ν	ν	NOUN
ejpam-5979	232	29	)	)	PUNCT
ejpam-5979	232	30	∈	∈	PROPN
ejpam-5979	233	1	[	[	X
ejpam-5979	233	2	0	0	NUM
ejpam-5979	233	3	,	,	PUNCT
ejpam-5979	233	4	1]×	1]×	NUM
ejpam-5979	233	5	r2	r2	NOUN
ejpam-5979	233	6	,	,	PUNCT
ejpam-5979	233	7	where	where	SCONJ
ejpam-5979	233	8	ζ	ζ	NOUN
ejpam-5979	233	9	=	=	SYM
ejpam-5979	233	10	2	2	NUM
ejpam-5979	233	11	>	>	SYM
ejpam-5979	233	12	0	0	X
ejpam-5979	233	13	.	.	PUNCT
ejpam-5979	234	1	moreover	moreover	ADV
ejpam-5979	234	2	,	,	PUNCT
ejpam-5979	234	3	we	we	PRON
ejpam-5979	234	4	have	have	VERB
ejpam-5979	234	5	ϖ	ϖ	NOUN
ejpam-5979	234	6	=	=	SYM
ejpam-5979	234	7	ζ	ζ	NOUN
ejpam-5979	234	8	ϱσγ(σ+1	ϱσγ(σ+1	NOUN
ejpam-5979	234	9	)	)	PUNCT
ejpam-5979	234	10	[	[	PUNCT
ejpam-5979	234	11	1	1	NUM
ejpam-5979	234	12	σ	σ	NUM
ejpam-5979	234	13	1	1	NUM
ejpam-5979	234	14	(	(	PUNCT
ejpam-5979	234	15	σ−1	σ−1	PROPN
ejpam-5979	234	16	)	)	PUNCT
ejpam-5979	234	17	−	−	PROPN
ejpam-5979	234	18	1	1	NUM
ejpam-5979	234	19	σ	σ	PROPN
ejpam-5979	234	20	σ	σ	PROPN
ejpam-5979	234	21	(	(	PUNCT
ejpam-5979	234	22	σ−1	σ−1	PROPN
ejpam-5979	234	23	)	)	PUNCT
ejpam-5979	234	24	]	]	PUNCT
ejpam-5979	235	1	≈	≈	PROPN
ejpam-5979	235	2			PROPN
ejpam-5979	235	3	0.1748	0.1748	NUM
ejpam-5979	235	4	,	,	PUNCT
ejpam-5979	235	5	σ	σ	NOUN
ejpam-5979	235	6	=	=	SYM
ejpam-5979	235	7	4	4	NUM
ejpam-5979	235	8	3	3	NUM
ejpam-5979	235	9	,	,	PUNCT
ejpam-5979	235	10	0.2196	0.2196	NUM
ejpam-5979	235	11	,	,	PUNCT
ejpam-5979	235	12	σ	σ	NOUN
ejpam-5979	235	13	=	=	SYM
ejpam-5979	235	14	3	3	NUM
ejpam-5979	235	15	2	2	NUM
ejpam-5979	235	16	,	,	PUNCT
ejpam-5979	235	17	0.2498	0.2498	NUM
ejpam-5979	235	18	,	,	PUNCT
ejpam-5979	235	19	σ	σ	NOUN
ejpam-5979	235	20	=	=	SYM
ejpam-5979	235	21	9	9	NUM
ejpam-5979	235	22	5	5	NUM
ejpam-5979	235	23	,	,	PUNCT
ejpam-5979	235	24	0.2476	0.2476	NUM
ejpam-5979	235	25	,	,	PUNCT
ejpam-5979	235	26	σ	σ	X
ejpam-5979	235	27	=	=	NOUN
ejpam-5979	235	28	39	39	NUM
ejpam-5979	235	29	20	20	NUM
ejpam-5979	235	30	,	,	PUNCT
ejpam-5979	235	31			ADJ
ejpam-5979	235	32	<	<	X
ejpam-5979	235	33	1	1	NUM
ejpam-5979	235	34	.	.	PUNCT
ejpam-5979	236	1	in	in	ADP
ejpam-5979	236	2	the	the	DET
ejpam-5979	236	3	last	last	ADJ
ejpam-5979	236	4	row	row	NOUN
ejpam-5979	236	5	of	of	ADP
ejpam-5979	236	6	data	datum	NOUN
ejpam-5979	236	7	in	in	ADP
ejpam-5979	236	8	table	table	NOUN
ejpam-5979	236	9	2	2	NUM
ejpam-5979	236	10	,	,	PUNCT
ejpam-5979	236	11	the	the	DET
ejpam-5979	236	12	values	value	NOUN
ejpam-5979	236	13	of	of	ADP
ejpam-5979	236	14	parameter	parameter	PROPN
ejpam-5979	236	15	ϖ	ϖ	PROPN
ejpam-5979	236	16	,	,	PUNCT
ejpam-5979	236	17	at	at	ADP
ejpam-5979	236	18	point	point	NOUN
ejpam-5979	236	19	ϑ	ϑ	VERB
ejpam-5979	236	20	,	,	PUNCT
ejpam-5979	236	21	for	for	ADP
ejpam-5979	236	22	three	three	NUM
ejpam-5979	236	23	different	different	ADJ
ejpam-5979	236	24	values	value	NOUN
ejpam-5979	236	25	of	of	ADP
ejpam-5979	236	26	derivative	derivative	ADJ
ejpam-5979	236	27	order	order	NOUN
ejpam-5979	236	28	σ	σ	NOUN
ejpam-5979	236	29	are	be	AUX
ejpam-5979	236	30	shown	show	VERB
ejpam-5979	236	31	.	.	PUNCT
ejpam-5979	237	1	the	the	DET
ejpam-5979	237	2	curves	curve	NOUN
ejpam-5979	237	3	of	of	ADP
ejpam-5979	237	4	all	all	DET
ejpam-5979	237	5	three	three	NUM
ejpam-5979	237	6	cases	case	NOUN
ejpam-5979	237	7	are	be	AUX
ejpam-5979	237	8	presented	present	VERB
ejpam-5979	237	9	in	in	ADP
ejpam-5979	237	10	figure	figure	NOUN
ejpam-5979	237	11	2	2	NUM
ejpam-5979	237	12	,	,	PUNCT
ejpam-5979	237	13	which	which	PRON
ejpam-5979	237	14	are	be	AUX
ejpam-5979	237	15	decreasing	decrease	VERB
ejpam-5979	237	16	as	as	ADP
ejpam-5979	237	17	the	the	DET
ejpam-5979	237	18	order	order	NOUN
ejpam-5979	237	19	of	of	ADP
ejpam-5979	237	20	the	the	DET
ejpam-5979	237	21	derivative	derivative	ADJ
ejpam-5979	237	22	increases	increase	NOUN
ejpam-5979	237	23	and	and	CCONJ
ejpam-5979	237	24	in	in	ADP
ejpam-5979	237	25	all	all	DET
ejpam-5979	237	26	cases	case	NOUN
ejpam-5979	237	27	are	be	AUX
ejpam-5979	237	28	less	less	ADJ
ejpam-5979	237	29	than	than	ADP
ejpam-5979	237	30	the	the	DET
ejpam-5979	237	31	y	y	NOUN
ejpam-5979	237	32	=	=	SYM
ejpam-5979	237	33	1	1	NUM
ejpam-5979	237	34	line	line	NOUN
ejpam-5979	237	35	.	.	PUNCT
ejpam-5979	238	1	by	by	ADP
ejpam-5979	238	2	the	the	DET
ejpam-5979	238	3	applications	application	NOUN
ejpam-5979	238	4	of	of	ADP
ejpam-5979	238	5	theorem	theorem	NOUN
ejpam-5979	238	6	3	3	NUM
ejpam-5979	238	7	,	,	PUNCT
ejpam-5979	238	8	and	and	CCONJ
ejpam-5979	238	9	the	the	DET
ejpam-5979	238	10	condition	condition	NOUN
ejpam-5979	238	11	(	(	PUNCT
ejpam-5979	238	12	14	14	NUM
ejpam-5979	238	13	)	)	PUNCT
ejpam-5979	238	14	is	be	AUX
ejpam-5979	238	15	agreed	agree	VERB
ejpam-5979	238	16	.	.	PUNCT
ejpam-5979	239	1	then	then	ADV
ejpam-5979	239	2	the	the	DET
ejpam-5979	239	3	bvp	bvp	NOUN
ejpam-5979	239	4	(	(	PUNCT
ejpam-5979	239	5	23	23	NUM
ejpam-5979	239	6	)	)	PUNCT
ejpam-5979	239	7	accepts	accept	VERB
ejpam-5979	239	8	a	a	DET
ejpam-5979	239	9	single	single	ADJ
ejpam-5979	239	10	solution	solution	NOUN
ejpam-5979	239	11	.	.	PUNCT
ejpam-5979	240	1	z.	z.	PROPN
ejpam-5979	240	2	bekri	bekri	PROPN
ejpam-5979	240	3	et	et	PROPN
ejpam-5979	240	4	al	al	PROPN
ejpam-5979	240	5	.	.	PUNCT
ejpam-5979	240	6	/	/	SYM
ejpam-5979	240	7	eur	eur	PROPN
ejpam-5979	240	8	.	.	PUNCT
ejpam-5979	241	1	j.	j.	PROPN
ejpam-5979	241	2	pure	pure	PROPN
ejpam-5979	241	3	appl	appl	PROPN
ejpam-5979	241	4	.	.	PROPN
ejpam-5979	241	5	math	math	PROPN
ejpam-5979	241	6	,	,	PUNCT
ejpam-5979	241	7	18	18	NUM
ejpam-5979	241	8	(	(	PUNCT
ejpam-5979	241	9	2	2	NUM
ejpam-5979	241	10	)	)	PUNCT
ejpam-5979	241	11	(	(	PUNCT
ejpam-5979	241	12	2025	2025	NUM
ejpam-5979	241	13	)	)	PUNCT
ejpam-5979	241	14	,	,	PUNCT
ejpam-5979	241	15	5979	5979	NUM
ejpam-5979	241	16	13	13	NUM
ejpam-5979	241	17	of	of	ADP
ejpam-5979	241	18	20	20	NUM
ejpam-5979	241	19	table	table	NOUN
ejpam-5979	241	20	2	2	NUM
ejpam-5979	241	21	:	:	PUNCT
ejpam-5979	241	22	numerical	numerical	ADJ
ejpam-5979	241	23	results	result	NOUN
ejpam-5979	241	24	ϖ	ϖ	VERB
ejpam-5979	241	25	in	in	ADP
ejpam-5979	241	26	example	example	NOUN
ejpam-5979	241	27	2	2	NUM
ejpam-5979	241	28	for	for	ADP
ejpam-5979	241	29	four	four	NUM
ejpam-5979	241	30	values	value	NOUN
ejpam-5979	241	31	of	of	ADP
ejpam-5979	241	32	σ	σ	PROPN
ejpam-5979	241	33	.	.	PUNCT
ejpam-5979	242	1	τ	τ	PROPN
ejpam-5979	242	2	ϖ	ϖ	PROPN
ejpam-5979	242	3	σ	σ	NOUN
ejpam-5979	242	4	=	=	SYM
ejpam-5979	242	5	4	4	NUM
ejpam-5979	242	6	3	3	NUM
ejpam-5979	242	7	σ	σ	NOUN
ejpam-5979	242	8	=	=	SYM
ejpam-5979	242	9	4	4	NUM
ejpam-5979	242	10	3σ	3σ	NUM
ejpam-5979	242	11	=	=	SYM
ejpam-5979	243	1	4	4	NUM
ejpam-5979	243	2	3	3	NUM
ejpam-5979	243	3	σ	σ	NOUN
ejpam-5979	243	4	=	=	SYM
ejpam-5979	243	5	3	3	NUM
ejpam-5979	243	6	2	2	NUM
ejpam-5979	243	7	σ	σ	NOUN
ejpam-5979	243	8	=	=	SYM
ejpam-5979	243	9	3	3	NUM
ejpam-5979	243	10	2σ	2σ	NOUN
ejpam-5979	243	11	=	=	NOUN
ejpam-5979	243	12	3	3	NUM
ejpam-5979	243	13	2	2	NUM
ejpam-5979	243	14	σ	σ	NOUN
ejpam-5979	243	15	=	=	NOUN
ejpam-5979	243	16	9	9	NUM
ejpam-5979	243	17	5	5	NUM
ejpam-5979	243	18	σ	σ	NOUN
ejpam-5979	243	19	=	=	SYM
ejpam-5979	243	20	9	9	NUM
ejpam-5979	243	21	5σ	5σ	NOUN
ejpam-5979	243	22	=	=	NOUN
ejpam-5979	243	23	9	9	NUM
ejpam-5979	243	24	5	5	NUM
ejpam-5979	243	25	σ	σ	NOUN
ejpam-5979	243	26	=	=	NOUN
ejpam-5979	243	27	39	39	NUM
ejpam-5979	243	28	20	20	NUM
ejpam-5979	243	29	σ	σ	NOUN
ejpam-5979	243	30	=	=	NOUN
ejpam-5979	243	31	39	39	NUM
ejpam-5979	243	32	20σ	20σ	NUM
ejpam-5979	243	33	=	=	SYM
ejpam-5979	243	34	39	39	NUM
ejpam-5979	243	35	20	20	NUM
ejpam-5979	243	36	0.05	0.05	NUM
ejpam-5979	243	37	7.5423	7.5423	NUM
ejpam-5979	243	38	15.1657	15.1657	NUM
ejpam-5979	243	39	40.2424	40.2424	NUM
ejpam-5979	243	40	60.9280	60.9280	NUM
ejpam-5979	243	41	0.10	0.10	NUM
ejpam-5979	243	42	3.3614	3.3614	NUM
ejpam-5979	243	43	6.1094	6.1094	NUM
ejpam-5979	243	44	13.5160	13.5160	NUM
ejpam-5979	243	45	18.6851	18.6851	NUM
ejpam-5979	243	46	0.15	0.15	NUM
ejpam-5979	243	47	2.0396	2.0396	NUM
ejpam-5979	243	48	3.4827	3.4827	NUM
ejpam-5979	243	49	6.8856	6.8856	NUM
ejpam-5979	243	50	8.9987	8.9987	NUM
ejpam-5979	243	51	0.20	0.20	NUM
ejpam-5979	243	52	1.4193	1.4193	NUM
ejpam-5979	243	53	2.3161	2.3161	NUM
ejpam-5979	243	54	4.2205	4.2205	NUM
ejpam-5979	243	55	5.2952	5.2952	NUM
ejpam-5979	243	56	0.25	0.25	NUM
ejpam-5979	243	57	1.0676	1.0676	NUM
ejpam-5979	243	58	1.6812	1.6812	NUM
ejpam-5979	243	59	2.8735	2.8735	NUM
ejpam-5979	243	60	3.4915	3.4915	NUM
ejpam-5979	243	61	0.30	0.30	NUM
ejpam-5979	243	62	0.8444	0.8444	NUM
ejpam-5979	243	63	1.2914	1.2914	NUM
ejpam-5979	243	64	2.0937	2.0937	NUM
ejpam-5979	243	65	2.4777	2.4777	NUM
ejpam-5979	243	66	0.35	0.35	NUM
ejpam-5979	243	67	0.6918	0.6918	NUM
ejpam-5979	243	68	1.0319	1.0319	NUM
ejpam-5979	243	69	1.5996	1.5996	NUM
ejpam-5979	243	70	1.8511	1.8511	NUM
ejpam-5979	243	71	0.40	0.40	NUM
ejpam-5979	243	72	0.5817	0.5817	NUM
ejpam-5979	243	73	0.8490	0.8490	NUM
ejpam-5979	243	74	1.2657	1.2657	NUM
ejpam-5979	243	75	1.4364	1.4364	NUM
ejpam-5979	243	76	0.45	0.45	NUM
ejpam-5979	243	77	0.4989	0.4989	NUM
ejpam-5979	243	78	0.7144	0.7144	NUM
ejpam-5979	243	79	1.0289	1.0289	NUM
ejpam-5979	243	80	1.1477	1.1477	NUM
ejpam-5979	243	81	0.50	0.50	NUM
ejpam-5979	243	82	0.4348	0.4348	NUM
ejpam-5979	243	83	0.6120	0.6120	NUM
ejpam-5979	243	84	0.8545	0.8545	NUM
ejpam-5979	243	85	0.9385	0.9385	NUM
ejpam-5979	243	86	0.55	0.55	NUM
ejpam-5979	243	87	0.3838	0.3838	NUM
ejpam-5979	243	88	0.5319	0.5319	NUM
ejpam-5979	243	89	0.7221	0.7221	NUM
ejpam-5979	243	90	0.7821	0.7821	NUM
ejpam-5979	243	91	0.60	0.60	NUM
ejpam-5979	243	92	0.3425	0.3425	NUM
ejpam-5979	243	93	0.4678	0.4678	NUM
ejpam-5979	243	94	0.6191	0.6191	NUM
ejpam-5979	243	95	0.6619	0.6619	NUM
ejpam-5979	243	96	0.65	0.65	NUM
ejpam-5979	243	97	0.3083	0.3083	NUM
ejpam-5979	243	98	0.4157	0.4157	NUM
ejpam-5979	243	99	0.5373	0.5373	NUM
ejpam-5979	243	100	0.5677	0.5677	NUM
ejpam-5979	243	101	0.70	0.70	NUM
ejpam-5979	243	102	0.2797	0.2797	NUM
ejpam-5979	243	103	0.3726	0.3726	NUM
ejpam-5979	243	104	0.4711	0.4711	NUM
ejpam-5979	243	105	0.4923	0.4923	NUM
ejpam-5979	243	106	0.75	0.75	NUM
ejpam-5979	243	107	0.2554	0.2554	NUM
ejpam-5979	243	108	0.3364	0.3364	NUM
ejpam-5979	243	109	0.4168	0.4168	NUM
ejpam-5979	243	110	0.4311	0.4311	NUM
ejpam-5979	243	111	0.80	0.80	NUM
ejpam-5979	243	112	0.2346	0.2346	NUM
ejpam-5979	243	113	0.3057	0.3057	NUM
ejpam-5979	243	114	0.3716	0.3716	NUM
ejpam-5979	243	115	0.3808	0.3808	NUM
ejpam-5979	243	116	0.85	0.85	NUM
ejpam-5979	243	117	0.2166	0.2166	NUM
ejpam-5979	243	118	0.2795	0.2795	NUM
ejpam-5979	243	119	0.3336	0.3336	NUM
ejpam-5979	243	120	0.3388	0.3388	NUM
ejpam-5979	243	121	0.90	0.90	NUM
ejpam-5979	243	122	0.2009	0.2009	NUM
ejpam-5979	243	123	0.2568	0.2568	NUM
ejpam-5979	243	124	0.3014	0.3014	NUM
ejpam-5979	243	125	0.3034	0.3034	NUM
ejpam-5979	243	126	0.95	0.95	NUM
ejpam-5979	243	127	0.1871	0.1871	NUM
ejpam-5979	243	128	0.2370	0.2370	NUM
ejpam-5979	243	129	0.2737	0.2737	NUM
ejpam-5979	243	130	0.2734	0.2734	NUM
ejpam-5979	243	131	1.00	1.00	NUM
ejpam-5979	243	132	0.1748	0.1748	NUM
ejpam-5979	243	133	0.2196	0.2196	NUM
ejpam-5979	243	134	0.2498	0.2498	NUM
ejpam-5979	243	135	0.2476	0.2476	NUM
ejpam-5979	243	136	τ	τ	PROPN
ejpam-5979	243	137	0.1	0.1	NUM
ejpam-5979	243	138	0.2	0.2	NUM
ejpam-5979	243	139	0.3	0.3	NUM
ejpam-5979	243	140	0.4	0.4	NUM
ejpam-5979	243	141	0.5	0.5	NUM
ejpam-5979	243	142	0.6	0.6	NUM
ejpam-5979	243	143	0.7	0.7	NUM
ejpam-5979	243	144	0.8	0.8	NUM
ejpam-5979	243	145	0.9	0.9	NUM
ejpam-5979	243	146	1	1	NUM
ejpam-5979	243	147	̟	̟	PROPN
ejpam-5979	243	148	0	0	NUM
ejpam-5979	243	149	5	5	NUM
ejpam-5979	243	150	10	10	NUM
ejpam-5979	243	151	15	15	NUM
ejpam-5979	243	152	20	20	NUM
ejpam-5979	243	153	25	25	NUM
ejpam-5979	243	154	30	30	NUM
ejpam-5979	243	155	̟	̟	PRON
ejpam-5979	243	156	<	<	X
ejpam-5979	243	157	1	1	NUM
ejpam-5979	243	158	σ=4/3	σ=4/3	PROPN
ejpam-5979	243	159	σ=3/2	σ=3/2	NOUN
ejpam-5979	243	160	σ=9/5	σ=9/5	PROPN
ejpam-5979	243	161	σ=39/20	σ=39/20	PROPN
ejpam-5979	243	162	figure	figure	NOUN
ejpam-5979	243	163	2	2	NUM
ejpam-5979	243	164	:	:	PUNCT
ejpam-5979	243	165	representation	representation	NOUN
ejpam-5979	243	166	of	of	ADP
ejpam-5979	243	167	ϖ	ϖ	PROPN
ejpam-5979	243	168	for	for	ADP
ejpam-5979	243	169	bvp	bvp	NOUN
ejpam-5979	243	170	(	(	PUNCT
ejpam-5979	243	171	23	23	NUM
ejpam-5979	243	172	)	)	PUNCT
ejpam-5979	243	173	in	in	ADP
ejpam-5979	243	174	example	example	NOUN
ejpam-5979	243	175	2	2	NUM
ejpam-5979	243	176	for	for	ADP
ejpam-5979	243	177	four	four	NUM
ejpam-5979	243	178	case	case	NOUN
ejpam-5979	243	179	σ	σ	X
ejpam-5979	243	180	.	.	PROPN
ejpam-5979	243	181	5	5	NUM
ejpam-5979	243	182	.	.	X
ejpam-5979	243	183	numerical	numerical	ADJ
ejpam-5979	243	184	results	result	NOUN
ejpam-5979	243	185	in	in	ADP
ejpam-5979	243	186	this	this	DET
ejpam-5979	243	187	section	section	NOUN
ejpam-5979	243	188	,	,	PUNCT
ejpam-5979	243	189	we	we	PRON
ejpam-5979	243	190	present	present	VERB
ejpam-5979	243	191	numerical	numerical	ADJ
ejpam-5979	243	192	results	result	NOUN
ejpam-5979	243	193	obtained	obtain	VERB
ejpam-5979	243	194	through	through	ADP
ejpam-5979	243	195	matlab	matlab	PROPN
ejpam-5979	243	196	programming	programming	NOUN
ejpam-5979	243	197	for	for	ADP
ejpam-5979	243	198	the	the	DET
ejpam-5979	243	199	verification	verification	NOUN
ejpam-5979	243	200	of	of	ADP
ejpam-5979	243	201	theorem	theorem	NOUN
ejpam-5979	243	202	2	2	NUM
ejpam-5979	243	203	and	and	CCONJ
ejpam-5979	243	204	the	the	DET
ejpam-5979	243	205	illustration	illustration	NOUN
ejpam-5979	243	206	of	of	ADP
ejpam-5979	243	207	examples	example	NOUN
ejpam-5979	243	208	1	1	NUM
ejpam-5979	243	209	and	and	CCONJ
ejpam-5979	243	210	2	2	NUM
ejpam-5979	243	211	.	.	X
ejpam-5979	244	1	these	these	DET
ejpam-5979	244	2	numerical	numerical	ADJ
ejpam-5979	244	3	experiments	experiment	NOUN
ejpam-5979	244	4	offer	offer	VERB
ejpam-5979	244	5	insights	insight	NOUN
ejpam-5979	244	6	into	into	ADP
ejpam-5979	244	7	the	the	DET
ejpam-5979	244	8	practical	practical	ADJ
ejpam-5979	244	9	implications	implication	NOUN
ejpam-5979	244	10	of	of	ADP
ejpam-5979	244	11	the	the	DET
ejpam-5979	244	12	theoretical	theoretical	ADJ
ejpam-5979	244	13	findings	finding	NOUN
ejpam-5979	244	14	.	.	PUNCT
ejpam-5979	245	1	z.	z.	PROPN
ejpam-5979	245	2	bekri	bekri	PROPN
ejpam-5979	245	3	et	et	PROPN
ejpam-5979	245	4	al	al	PROPN
ejpam-5979	245	5	.	.	PUNCT
ejpam-5979	245	6	/	/	SYM
ejpam-5979	245	7	eur	eur	PROPN
ejpam-5979	245	8	.	.	PUNCT
ejpam-5979	246	1	j.	j.	PROPN
ejpam-5979	246	2	pure	pure	PROPN
ejpam-5979	246	3	appl	appl	PROPN
ejpam-5979	246	4	.	.	PROPN
ejpam-5979	246	5	math	math	PROPN
ejpam-5979	246	6	,	,	PUNCT
ejpam-5979	246	7	18	18	NUM
ejpam-5979	246	8	(	(	PUNCT
ejpam-5979	246	9	2	2	NUM
ejpam-5979	246	10	)	)	PUNCT
ejpam-5979	246	11	(	(	PUNCT
ejpam-5979	246	12	2025	2025	NUM
ejpam-5979	246	13	)	)	PUNCT
ejpam-5979	246	14	,	,	PUNCT
ejpam-5979	246	15	5979	5979	NUM
ejpam-5979	246	16	14	14	NUM
ejpam-5979	246	17	of	of	ADP
ejpam-5979	246	18	20	20	NUM
ejpam-5979	246	19	5.1	5.1	NUM
ejpam-5979	246	20	.	.	PUNCT
ejpam-5979	247	1	numerical	numerical	ADJ
ejpam-5979	247	2	solution	solution	NOUN
ejpam-5979	247	3	of	of	ADP
ejpam-5979	247	4	the	the	DET
ejpam-5979	247	5	bvp	bvp	NOUN
ejpam-5979	247	6	using	use	VERB
ejpam-5979	247	7	the	the	DET
ejpam-5979	247	8	fourth	fourth	ADJ
ejpam-5979	247	9	-	-	PUNCT
ejpam-5979	247	10	order	order	NOUN
ejpam-5979	247	11	runge	runge	NOUN
ejpam-5979	247	12	-	-	PUNCT
ejpam-5979	247	13	kutta	kutta	NOUN
ejpam-5979	247	14	method	method	NOUN
ejpam-5979	247	15	we	we	PRON
ejpam-5979	247	16	apply	apply	VERB
ejpam-5979	247	17	the	the	DET
ejpam-5979	247	18	fourth	fourth	ADJ
ejpam-5979	247	19	-	-	PUNCT
ejpam-5979	247	20	order	order	NOUN
ejpam-5979	247	21	runge	runge	NOUN
ejpam-5979	247	22	-	-	PUNCT
ejpam-5979	247	23	kutta	kutta	NOUN
ejpam-5979	247	24	method	method	NOUN
ejpam-5979	247	25	to	to	PART
ejpam-5979	247	26	solve	solve	VERB
ejpam-5979	247	27	a	a	DET
ejpam-5979	247	28	bvp	bvp	NOUN
ejpam-5979	247	29	described	describe	VERB
ejpam-5979	247	30	by	by	ADP
ejpam-5979	247	31	theorem	theorem	NOUN
ejpam-5979	247	32	2	2	NUM
ejpam-5979	247	33	.	.	PUNCT
ejpam-5979	247	34	algorithm	algorithm	NOUN
ejpam-5979	247	35	1	1	NUM
ejpam-5979	247	36	is	be	AUX
ejpam-5979	247	37	used	use	VERB
ejpam-5979	247	38	for	for	ADP
ejpam-5979	247	39	numerical	numerical	ADJ
ejpam-5979	247	40	computation	computation	NOUN
ejpam-5979	247	41	,	,	PUNCT
ejpam-5979	247	42	followed	follow	VERB
ejpam-5979	247	43	by	by	ADP
ejpam-5979	247	44	the	the	DET
ejpam-5979	247	45	results	result	NOUN
ejpam-5979	247	46	obtained	obtain	VERB
ejpam-5979	247	47	and	and	CCONJ
ejpam-5979	247	48	their	their	PRON
ejpam-5979	247	49	analysis	analysis	NOUN
ejpam-5979	247	50	.	.	PUNCT
ejpam-5979	248	1	table	table	NOUN
ejpam-5979	248	2	3	3	NUM
ejpam-5979	248	3	shows	show	VERB
ejpam-5979	248	4	the	the	DET
ejpam-5979	248	5	numerical	numerical	ADJ
ejpam-5979	248	6	results	result	NOUN
ejpam-5979	248	7	obtained	obtain	VERB
ejpam-5979	248	8	from	from	ADP
ejpam-5979	248	9	the	the	DET
ejpam-5979	248	10	fourth	fourth	ADJ
ejpam-5979	248	11	-	-	PUNCT
ejpam-5979	248	12	order	order	NOUN
ejpam-5979	248	13	runge	runge	NOUN
ejpam-5979	248	14	-	-	PUNCT
ejpam-5979	248	15	kutta	kutta	NOUN
ejpam-5979	248	16	method	method	NOUN
ejpam-5979	248	17	.	.	PUNCT
ejpam-5979	249	1	the	the	DET
ejpam-5979	249	2	numerical	numerical	ADJ
ejpam-5979	249	3	results	result	NOUN
ejpam-5979	249	4	indicate	indicate	VERB
ejpam-5979	249	5	the	the	DET
ejpam-5979	249	6	convergence	convergence	NOUN
ejpam-5979	249	7	of	of	ADP
ejpam-5979	249	8	the	the	DET
ejpam-5979	249	9	fourth	fourth	ADJ
ejpam-5979	249	10	-	-	PUNCT
ejpam-5979	249	11	order	order	NOUN
ejpam-5979	249	12	table	table	NOUN
ejpam-5979	249	13	3	3	NUM
ejpam-5979	249	14	:	:	PUNCT
ejpam-5979	249	15	numerical	numerical	ADJ
ejpam-5979	249	16	results	result	NOUN
ejpam-5979	249	17	of	of	ADP
ejpam-5979	249	18	the	the	DET
ejpam-5979	249	19	fourth	fourth	ADJ
ejpam-5979	249	20	-	-	PUNCT
ejpam-5979	249	21	order	order	NOUN
ejpam-5979	249	22	runge	runge	NOUN
ejpam-5979	249	23	-	-	PUNCT
ejpam-5979	249	24	kutta	kutta	NOUN
ejpam-5979	249	25	method	method	NOUN
ejpam-5979	249	26	to	to	PART
ejpam-5979	249	27	solve	solve	VERB
ejpam-5979	249	28	a	a	DET
ejpam-5979	249	29	bvp	bvp	NOUN
ejpam-5979	249	30	described	describe	VERB
ejpam-5979	249	31	by	by	ADP
ejpam-5979	249	32	theorem	theorem	NOUN
ejpam-5979	249	33	2	2	NUM
ejpam-5979	249	34	.	.	PUNCT
ejpam-5979	249	35	iteration	iteration	NOUN
ejpam-5979	249	36	τ	τ	PROPN
ejpam-5979	249	37	µ(k	µ(k	PROPN
ejpam-5979	249	38	)	)	PUNCT
ejpam-5979	249	39	0	0	NUM
ejpam-5979	249	40	0.0	0.0	NUM
ejpam-5979	249	41	0.000000	0.000000	NUM
ejpam-5979	249	42	1	1	NUM
ejpam-5979	249	43	0.1	0.1	NUM
ejpam-5979	249	44	0.100000	0.100000	NUM
ejpam-5979	249	45	2	2	NUM
ejpam-5979	249	46	0.2	0.2	NUM
ejpam-5979	249	47	0.202484	0.202484	NUM
ejpam-5979	249	48	3	3	NUM
ejpam-5979	249	49	0.3	0.3	NUM
ejpam-5979	249	50	0.310604	0.310604	NUM
ejpam-5979	249	51	4	4	NUM
ejpam-5979	249	52	0.4	0.4	NUM
ejpam-5979	249	53	0.420014	0.420014	NUM
ejpam-5979	249	54	5	5	NUM
ejpam-5979	249	55	0.5	0.5	NUM
ejpam-5979	249	56	0.525788	0.525788	NUM
ejpam-5979	249	57	6	6	NUM
ejpam-5979	249	58	0.6	0.6	NUM
ejpam-5979	249	59	0.622258	0.622258	NUM
ejpam-5979	249	60	7	7	NUM
ejpam-5979	249	61	0.7	0.7	NUM
ejpam-5979	249	62	0.704243	0.704243	NUM
ejpam-5979	249	63	8	8	NUM
ejpam-5979	249	64	0.8	0.8	NUM
ejpam-5979	249	65	0.767255	0.767255	NUM
ejpam-5979	249	66	9	9	NUM
ejpam-5979	249	67	0.9	0.9	NUM
ejpam-5979	249	68	0.806292	0.806292	NUM
ejpam-5979	249	69	10	10	NUM
ejpam-5979	249	70	1.0	1.0	NUM
ejpam-5979	249	71	0.818999	0.818999	NUM
ejpam-5979	249	72	runge	runge	NOUN
ejpam-5979	249	73	-	-	PUNCT
ejpam-5979	249	74	kutta	kutta	NOUN
ejpam-5979	249	75	method	method	NOUN
ejpam-5979	249	76	towards	towards	ADP
ejpam-5979	249	77	the	the	DET
ejpam-5979	249	78	solution	solution	NOUN
ejpam-5979	249	79	of	of	ADP
ejpam-5979	249	80	the	the	DET
ejpam-5979	249	81	given	give	VERB
ejpam-5979	249	82	boundary	boundary	ADJ
ejpam-5979	249	83	value	value	NOUN
ejpam-5979	249	84	problem	problem	NOUN
ejpam-5979	249	85	.	.	PUNCT
ejpam-5979	250	1	as	as	ADP
ejpam-5979	250	2	the	the	DET
ejpam-5979	250	3	number	number	NOUN
ejpam-5979	250	4	of	of	ADP
ejpam-5979	250	5	iterations	iteration	NOUN
ejpam-5979	250	6	increases	increase	NOUN
ejpam-5979	250	7	,	,	PUNCT
ejpam-5979	250	8	the	the	DET
ejpam-5979	250	9	values	value	NOUN
ejpam-5979	250	10	of	of	ADP
ejpam-5979	250	11	µ(k	µ(k	NOUN
ejpam-5979	250	12	)	)	PUNCT
ejpam-5979	250	13	approach	approach	VERB
ejpam-5979	250	14	the	the	DET
ejpam-5979	250	15	exact	exact	ADJ
ejpam-5979	250	16	solution	solution	NOUN
ejpam-5979	250	17	.	.	PUNCT
ejpam-5979	251	1	additionally	additionally	ADV
ejpam-5979	251	2	,	,	PUNCT
ejpam-5979	251	3	the	the	DET
ejpam-5979	251	4	results	result	NOUN
ejpam-5979	251	5	demonstrate	demonstrate	VERB
ejpam-5979	251	6	the	the	DET
ejpam-5979	251	7	accuracy	accuracy	NOUN
ejpam-5979	251	8	and	and	CCONJ
ejpam-5979	251	9	efficiency	efficiency	NOUN
ejpam-5979	251	10	of	of	ADP
ejpam-5979	251	11	the	the	DET
ejpam-5979	251	12	fourth	fourth	ADJ
ejpam-5979	251	13	-	-	PUNCT
ejpam-5979	251	14	order	order	NOUN
ejpam-5979	251	15	runge	runge	NOUN
ejpam-5979	251	16	-	-	PUNCT
ejpam-5979	251	17	kutta	kutta	NOUN
ejpam-5979	251	18	method	method	NOUN
ejpam-5979	251	19	in	in	ADP
ejpam-5979	251	20	solving	solve	VERB
ejpam-5979	251	21	ordinary	ordinary	ADJ
ejpam-5979	251	22	des	des	PROPN
ejpam-5979	251	23	.	.	PUNCT
ejpam-5979	252	1	the	the	DET
ejpam-5979	252	2	method	method	NOUN
ejpam-5979	252	3	achieves	achieve	VERB
ejpam-5979	252	4	fourth	fourth	ADJ
ejpam-5979	252	5	-	-	PUNCT
ejpam-5979	252	6	order	order	NOUN
ejpam-5979	252	7	accuracy	accuracy	NOUN
ejpam-5979	252	8	by	by	ADP
ejpam-5979	252	9	computing	compute	VERB
ejpam-5979	252	10	the	the	DET
ejpam-5979	252	11	weighted	weighted	ADJ
ejpam-5979	252	12	average	average	NOUN
ejpam-5979	252	13	of	of	ADP
ejpam-5979	252	14	four	four	NUM
ejpam-5979	252	15	slope	slope	NOUN
ejpam-5979	252	16	estimates	estimate	NOUN
ejpam-5979	252	17	at	at	ADP
ejpam-5979	252	18	each	each	DET
ejpam-5979	252	19	step	step	NOUN
ejpam-5979	252	20	,	,	PUNCT
ejpam-5979	252	21	resulting	result	VERB
ejpam-5979	252	22	in	in	ADP
ejpam-5979	252	23	highly	highly	ADV
ejpam-5979	252	24	accurate	accurate	ADJ
ejpam-5979	252	25	numerical	numerical	ADJ
ejpam-5979	252	26	solutions	solution	NOUN
ejpam-5979	252	27	.	.	PUNCT
ejpam-5979	253	1	5.2	5.2	NUM
ejpam-5979	253	2	.	.	PUNCT
ejpam-5979	253	3	matlab	matlab	PROPN
ejpam-5979	253	4	implementation	implementation	NOUN
ejpam-5979	253	5	and	and	CCONJ
ejpam-5979	253	6	visualization	visualization	NOUN
ejpam-5979	253	7	for	for	ADP
ejpam-5979	253	8	examples	example	NOUN
ejpam-5979	253	9	1	1	NUM
ejpam-5979	253	10	,	,	PUNCT
ejpam-5979	253	11	2	2	NUM
ejpam-5979	253	12	in	in	ADP
ejpam-5979	253	13	this	this	DET
ejpam-5979	253	14	part	part	NOUN
ejpam-5979	253	15	,	,	PUNCT
ejpam-5979	253	16	we	we	PRON
ejpam-5979	253	17	analyze	analyze	VERB
ejpam-5979	253	18	examples	example	NOUN
ejpam-5979	253	19	1	1	NUM
ejpam-5979	253	20	and	and	CCONJ
ejpam-5979	253	21	2	2	NUM
ejpam-5979	253	22	with	with	ADP
ejpam-5979	253	23	matlab	matlab	PROPN
ejpam-5979	253	24	,	,	PUNCT
ejpam-5979	253	25	using	use	VERB
ejpam-5979	253	26	tables	table	NOUN
ejpam-5979	253	27	and	and	CCONJ
ejpam-5979	253	28	graphs	graph	NOUN
ejpam-5979	253	29	to	to	PART
ejpam-5979	253	30	show	show	VERB
ejpam-5979	253	31	outcomes	outcome	NOUN
ejpam-5979	253	32	.	.	PUNCT
ejpam-5979	254	1	this	this	PRON
ejpam-5979	254	2	clarifies	clarify	VERB
ejpam-5979	254	3	theoretical	theoretical	ADJ
ejpam-5979	254	4	concepts	concept	NOUN
ejpam-5979	254	5	in	in	ADP
ejpam-5979	254	6	the	the	DET
ejpam-5979	254	7	examples	example	NOUN
ejpam-5979	254	8	.	.	PUNCT
ejpam-5979	255	1	case	case	NOUN
ejpam-5979	256	1	i	i	PRON
ejpam-5979	256	2	:	:	PUNCT
ejpam-5979	256	3	example	example	NOUN
ejpam-5979	256	4	1	1	NUM
ejpam-5979	256	5	matlab	matlab	PROPN
ejpam-5979	256	6	program	program	NOUN
ejpam-5979	256	7	:	:	PUNCT
ejpam-5979	256	8	the	the	DET
ejpam-5979	256	9	matlab	matlab	PROPN
ejpam-5979	256	10	program	program	NOUN
ejpam-5979	256	11	in	in	ADP
ejpam-5979	256	12	algorithm	algorithm	NOUN
ejpam-5979	256	13	2	2	NUM
ejpam-5979	256	14	solves	solve	VERB
ejpam-5979	256	15	the	the	DET
ejpam-5979	256	16	bvp	bvp	NOUN
ejpam-5979	256	17	defined	define	VERB
ejpam-5979	256	18	by	by	ADP
ejpam-5979	256	19	eq	eq	PROPN
ejpam-5979	256	20	.	.	PUNCT
ejpam-5979	257	1	(	(	PUNCT
ejpam-5979	257	2	22	22	NUM
ejpam-5979	257	3	)	)	PUNCT
ejpam-5979	257	4	for	for	ADP
ejpam-5979	257	5	different	different	ADJ
ejpam-5979	257	6	values	value	NOUN
ejpam-5979	257	7	of	of	ADP
ejpam-5979	257	8	σ	σ	PROPN
ejpam-5979	257	9	,	,	PUNCT
ejpam-5979	257	10	calculates	calculate	VERB
ejpam-5979	257	11	ϖ	ϖ	NOUN
ejpam-5979	257	12	,	,	PUNCT
ejpam-5979	257	13	and	and	CCONJ
ejpam-5979	257	14	saves	save	VERB
ejpam-5979	257	15	the	the	DET
ejpam-5979	257	16	results	result	NOUN
ejpam-5979	257	17	.	.	PUNCT
ejpam-5979	258	1	table	table	NOUN
ejpam-5979	258	2	1	1	NUM
ejpam-5979	258	3	presents	present	VERB
ejpam-5979	258	4	the	the	DET
ejpam-5979	258	5	numerical	numerical	ADJ
ejpam-5979	258	6	results	result	NOUN
ejpam-5979	258	7	of	of	ADP
ejpam-5979	258	8	ϖ	ϖ	NOUN
ejpam-5979	258	9	for	for	ADP
ejpam-5979	258	10	different	different	ADJ
ejpam-5979	258	11	values	value	NOUN
ejpam-5979	258	12	of	of	ADP
ejpam-5979	258	13	σ	σ	PROPN
ejpam-5979	258	14	.	.	PUNCT
ejpam-5979	258	15	to	to	PART
ejpam-5979	258	16	better	well	ADV
ejpam-5979	258	17	illustrate	illustrate	VERB
ejpam-5979	258	18	the	the	DET
ejpam-5979	258	19	outcomes	outcome	NOUN
ejpam-5979	258	20	,	,	PUNCT
ejpam-5979	258	21	figure	figure	VERB
ejpam-5979	258	22	3	3	NUM
ejpam-5979	258	23	showcases	showcase	VERB
ejpam-5979	258	24	the	the	DET
ejpam-5979	258	25	variation	variation	NOUN
ejpam-5979	258	26	of	of	ADP
ejpam-5979	258	27	ϖ	ϖ	PROPN
ejpam-5979	258	28	across	across	ADP
ejpam-5979	258	29	different	different	ADJ
ejpam-5979	258	30	σ	σ	NOUN
ejpam-5979	258	31	values	value	NOUN
ejpam-5979	258	32	.	.	PUNCT
ejpam-5979	259	1	case	case	NOUN
ejpam-5979	259	2	ii	ii	PROPN
ejpam-5979	259	3	:	:	PUNCT
ejpam-5979	259	4	example	example	NOUN
ejpam-5979	259	5	2	2	NUM
ejpam-5979	259	6	to	to	PART
ejpam-5979	259	7	solve	solve	VERB
ejpam-5979	259	8	the	the	DET
ejpam-5979	259	9	bvp	bvp	NOUN
ejpam-5979	259	10	numerically	numerically	ADV
ejpam-5979	259	11	and	and	CCONJ
ejpam-5979	259	12	obtain	obtain	VERB
ejpam-5979	259	13	the	the	DET
ejpam-5979	259	14	solution	solution	NOUN
ejpam-5979	259	15	for	for	ADP
ejpam-5979	259	16	µ(τ	µ(τ	NOUN
ejpam-5979	259	17	)	)	PUNCT
ejpam-5979	259	18	and	and	CCONJ
ejpam-5979	259	19	θ(τ	θ(τ	PROPN
ejpam-5979	259	20	,	,	PUNCT
ejpam-5979	259	21	µ(τ	µ(τ	PROPN
ejpam-5979	259	22	)	)	PUNCT
ejpam-5979	259	23	)	)	PUNCT
ejpam-5979	259	24	,	,	PUNCT
ejpam-5979	259	25	we	we	PRON
ejpam-5979	259	26	implement	implement	VERB
ejpam-5979	259	27	the	the	DET
ejpam-5979	259	28	following	follow	VERB
ejpam-5979	259	29	matlab	matlab	PROPN
ejpam-5979	259	30	code	code	PROPN
ejpam-5979	259	31	in	in	ADP
ejpam-5979	259	32	algorithm	algorithm	NOUN
ejpam-5979	259	33	3	3	NUM
ejpam-5979	259	34	.	.	PUNCT
ejpam-5979	259	35	matlab	matlab	PROPN
ejpam-5979	259	36	code	code	PROPN
ejpam-5979	259	37	:	:	PUNCT
ejpam-5979	259	38	the	the	DET
ejpam-5979	259	39	matlab	matlab	PROPN
ejpam-5979	259	40	code	code	NOUN
ejpam-5979	259	41	provides	provide	VERB
ejpam-5979	259	42	numerical	numerical	ADJ
ejpam-5979	259	43	solutions	solution	NOUN
ejpam-5979	259	44	for	for	ADP
ejpam-5979	259	45	µ(τ	µ(τ	NOUN
ejpam-5979	259	46	)	)	PUNCT
ejpam-5979	259	47	and	and	CCONJ
ejpam-5979	259	48	θ(τ	θ(τ	PROPN
ejpam-5979	259	49	,	,	PUNCT
ejpam-5979	259	50	µ(τ	µ(τ	PROPN
ejpam-5979	259	51	)	)	PUNCT
ejpam-5979	259	52	)	)	PUNCT
ejpam-5979	259	53	.	.	PUNCT
ejpam-5979	260	1	the	the	DET
ejpam-5979	260	2	values	value	NOUN
ejpam-5979	260	3	obtained	obtain	VERB
ejpam-5979	260	4	from	from	ADP
ejpam-5979	260	5	matlab	matlab	PROPN
ejpam-5979	260	6	are	be	AUX
ejpam-5979	260	7	tabulated	tabulate	VERB
ejpam-5979	260	8	in	in	ADP
ejpam-5979	260	9	table	table	NOUN
ejpam-5979	260	10	4	4	NUM
ejpam-5979	260	11	.	.	PUNCT
ejpam-5979	260	12	to	to	PART
ejpam-5979	260	13	further	far	ADV
ejpam-5979	260	14	z.	z.	PROPN
ejpam-5979	260	15	bekri	bekri	PROPN
ejpam-5979	260	16	et	et	PROPN
ejpam-5979	260	17	al	al	PROPN
ejpam-5979	260	18	.	.	PUNCT
ejpam-5979	260	19	/	/	SYM
ejpam-5979	260	20	eur	eur	PROPN
ejpam-5979	260	21	.	.	PUNCT
ejpam-5979	261	1	j.	j.	PROPN
ejpam-5979	261	2	pure	pure	PROPN
ejpam-5979	261	3	appl	appl	PROPN
ejpam-5979	261	4	.	.	PROPN
ejpam-5979	261	5	math	math	PROPN
ejpam-5979	261	6	,	,	PUNCT
ejpam-5979	261	7	18	18	NUM
ejpam-5979	261	8	(	(	PUNCT
ejpam-5979	261	9	2	2	NUM
ejpam-5979	261	10	)	)	PUNCT
ejpam-5979	261	11	(	(	PUNCT
ejpam-5979	261	12	2025	2025	NUM
ejpam-5979	261	13	)	)	PUNCT
ejpam-5979	261	14	,	,	PUNCT
ejpam-5979	261	15	5979	5979	NUM
ejpam-5979	261	16	15	15	NUM
ejpam-5979	261	17	of	of	ADP
ejpam-5979	261	18	20	20	NUM
ejpam-5979	261	19	figure	figure	NOUN
ejpam-5979	261	20	3	3	NUM
ejpam-5979	261	21	:	:	PUNCT
ejpam-5979	261	22	variation	variation	NOUN
ejpam-5979	261	23	ofϖ	ofϖ	NOUN
ejpam-5979	261	24	for	for	ADP
ejpam-5979	261	25	different	different	ADJ
ejpam-5979	261	26	σ	σ	NOUN
ejpam-5979	261	27	values	value	NOUN
ejpam-5979	261	28	.	.	PUNCT
ejpam-5979	262	1	visualize	visualize	VERB
ejpam-5979	262	2	the	the	DET
ejpam-5979	262	3	results	result	NOUN
ejpam-5979	262	4	,	,	PUNCT
ejpam-5979	262	5	fig	fig	NOUN
ejpam-5979	262	6	.	.	PUNCT
ejpam-5979	263	1	4	4	NUM
ejpam-5979	263	2	depicts	depict	VERB
ejpam-5979	263	3	the	the	DET
ejpam-5979	263	4	solution	solution	NOUN
ejpam-5979	263	5	µ(τ	µ(τ	NOUN
ejpam-5979	263	6	)	)	PUNCT
ejpam-5979	263	7	and	and	CCONJ
ejpam-5979	263	8	the	the	DET
ejpam-5979	263	9	function	function	NOUN
ejpam-5979	263	10	θ(τ	θ(τ	PROPN
ejpam-5979	263	11	,	,	PUNCT
ejpam-5979	263	12	µ(τ	µ(τ	PROPN
ejpam-5979	263	13	)	)	PUNCT
ejpam-5979	263	14	)	)	PUNCT
ejpam-5979	263	15	.	.	PUNCT
ejpam-5979	264	1	the	the	DET
ejpam-5979	264	2	decreasing	decrease	VERB
ejpam-5979	264	3	values	value	NOUN
ejpam-5979	264	4	of	of	ADP
ejpam-5979	264	5	θ(τ	θ(τ	PROPN
ejpam-5979	264	6	,	,	PUNCT
ejpam-5979	264	7	µ(τ	µ(τ	PROPN
ejpam-5979	264	8	)	)	PUNCT
ejpam-5979	264	9	)	)	PUNCT
ejpam-5979	264	10	in	in	ADP
ejpam-5979	264	11	the	the	DET
ejpam-5979	264	12	graph	graph	NOUN
ejpam-5979	264	13	align	align	VERB
ejpam-5979	264	14	with	with	ADP
ejpam-5979	264	15	the	the	DET
ejpam-5979	264	16	expected	expect	VERB
ejpam-5979	264	17	behavior	behavior	NOUN
ejpam-5979	264	18	described	describe	VERB
ejpam-5979	264	19	in	in	ADP
ejpam-5979	264	20	example	example	NOUN
ejpam-5979	264	21	2	2	NUM
ejpam-5979	264	22	,	,	PUNCT
ejpam-5979	264	23	indicating	indicate	VERB
ejpam-5979	264	24	agreement	agreement	NOUN
ejpam-5979	264	25	with	with	ADP
ejpam-5979	264	26	the	the	DET
ejpam-5979	264	27	conditions	condition	NOUN
ejpam-5979	264	28	of	of	ADP
ejpam-5979	264	29	the	the	DET
ejpam-5979	264	30	given	give	VERB
ejpam-5979	264	31	bvp	bvp	NOUN
ejpam-5979	264	32	.	.	PUNCT
ejpam-5979	264	33	table	table	NOUN
ejpam-5979	264	34	4	4	NUM
ejpam-5979	264	35	:	:	PUNCT
ejpam-5979	264	36	values	value	NOUN
ejpam-5979	264	37	of	of	ADP
ejpam-5979	264	38	τ	τ	PROPN
ejpam-5979	264	39	,	,	PUNCT
ejpam-5979	264	40	µ(τ	µ(τ	PROPN
ejpam-5979	264	41	)	)	PUNCT
ejpam-5979	264	42	,	,	PUNCT
ejpam-5979	264	43	and	and	CCONJ
ejpam-5979	264	44	θ(τ	θ(τ	PROPN
ejpam-5979	264	45	,	,	PUNCT
ejpam-5979	264	46	µ(τ	µ(τ	PROPN
ejpam-5979	264	47	)	)	PUNCT
ejpam-5979	264	48	)	)	PUNCT
ejpam-5979	264	49	.	.	PUNCT
ejpam-5979	265	1	τ	τ	X
ejpam-5979	265	2	µ(τ	µ(τ	PROPN
ejpam-5979	265	3	)	)	PUNCT
ejpam-5979	265	4	θ(τ	θ(τ	PROPN
ejpam-5979	265	5	,	,	PUNCT
ejpam-5979	265	6	µ(τ	µ(τ	PROPN
ejpam-5979	265	7	)	)	PUNCT
ejpam-5979	265	8	)	)	PUNCT
ejpam-5979	266	1	0.0000	0.0000	NUM
ejpam-5979	266	2	2.9967	2.9967	NUM
ejpam-5979	266	3	−4.9999	−4.9999	NOUN
ejpam-5979	266	4	0.0101	0.0101	NUM
ejpam-5979	266	5	2.9942	2.9942	NUM
ejpam-5979	266	6	−4.9999	−4.9999	NOUN
ejpam-5979	266	7	0.0202	0.0202	NUM
ejpam-5979	266	8	2.9917	2.9917	NUM
ejpam-5979	266	9	−4.9999	−4.9999	NOUN
ejpam-5979	266	10	0.0303	0.0303	NUM
ejpam-5979	266	11	2.9892	2.9892	NUM
ejpam-5979	266	12	−4.9999	−4.9999	NOUN
ejpam-5979	266	13	.	.	PUNCT
ejpam-5979	266	14	.	.	PUNCT
ejpam-5979	266	15	.	.	PUNCT
ejpam-5979	266	16	.	.	PUNCT
ejpam-5979	266	17	.	.	PUNCT
ejpam-5979	266	18	.	.	PUNCT
ejpam-5979	266	19	.	.	PUNCT
ejpam-5979	266	20	.	.	PUNCT
ejpam-5979	266	21	.	.	PUNCT
ejpam-5979	267	1	0.9798	0.9798	NUM
ejpam-5979	267	2	3.5970	3.5970	NUM
ejpam-5979	267	3	−4.0970	−4.0970	NUM
ejpam-5979	267	4	0.9899	0.9899	NUM
ejpam-5979	267	5	3.6495	3.6495	NUM
ejpam-5979	267	6	−4.0495	−4.0495	PROPN
ejpam-5979	267	7	1.0000	1.0000	NUM
ejpam-5979	267	8	3.7000	3.7000	NUM
ejpam-5979	267	9	−4.0000	−4.0000	NUM
ejpam-5979	267	10	z.	z.	PROPN
ejpam-5979	267	11	bekri	bekri	PROPN
ejpam-5979	267	12	et	et	PROPN
ejpam-5979	267	13	al	al	PROPN
ejpam-5979	267	14	.	.	PUNCT
ejpam-5979	267	15	/	/	SYM
ejpam-5979	267	16	eur	eur	PROPN
ejpam-5979	267	17	.	.	PUNCT
ejpam-5979	268	1	j.	j.	PROPN
ejpam-5979	268	2	pure	pure	PROPN
ejpam-5979	268	3	appl	appl	PROPN
ejpam-5979	268	4	.	.	PROPN
ejpam-5979	268	5	math	math	PROPN
ejpam-5979	268	6	,	,	PUNCT
ejpam-5979	268	7	18	18	NUM
ejpam-5979	268	8	(	(	PUNCT
ejpam-5979	268	9	2	2	NUM
ejpam-5979	268	10	)	)	PUNCT
ejpam-5979	268	11	(	(	PUNCT
ejpam-5979	268	12	2025	2025	NUM
ejpam-5979	268	13	)	)	PUNCT
ejpam-5979	268	14	,	,	PUNCT
ejpam-5979	268	15	5979	5979	NUM
ejpam-5979	268	16	16	16	NUM
ejpam-5979	268	17	of	of	ADP
ejpam-5979	268	18	20	20	NUM
ejpam-5979	268	19	figure	figure	NOUN
ejpam-5979	268	20	4	4	NUM
ejpam-5979	268	21	:	:	PUNCT
ejpam-5979	268	22	the	the	DET
ejpam-5979	268	23	graphs	graph	NOUN
ejpam-5979	268	24	display	display	VERB
ejpam-5979	268	25	the	the	DET
ejpam-5979	268	26	solution	solution	NOUN
ejpam-5979	268	27	µ(τ	µ(τ	NOUN
ejpam-5979	268	28	)	)	PUNCT
ejpam-5979	268	29	and	and	CCONJ
ejpam-5979	268	30	the	the	DET
ejpam-5979	268	31	function	function	NOUN
ejpam-5979	268	32	θ(τ	θ(τ	PROPN
ejpam-5979	268	33	,	,	PUNCT
ejpam-5979	268	34	µ(τ	µ(τ	PROPN
ejpam-5979	268	35	)	)	PUNCT
ejpam-5979	268	36	)	)	PUNCT
ejpam-5979	268	37	.	.	PUNCT
ejpam-5979	269	1	6	6	X
ejpam-5979	269	2	.	.	X
ejpam-5979	269	3	conclusion	conclusion	NOUN
ejpam-5979	269	4	through	through	ADP
ejpam-5979	269	5	this	this	DET
ejpam-5979	269	6	project	project	NOUN
ejpam-5979	269	7	,	,	PUNCT
ejpam-5979	269	8	we	we	PRON
ejpam-5979	269	9	tried	try	VERB
ejpam-5979	269	10	to	to	PART
ejpam-5979	269	11	simulate	simulate	VERB
ejpam-5979	269	12	the	the	DET
ejpam-5979	269	13	banach	banach	NOUN
ejpam-5979	269	14	contraction	contraction	NOUN
ejpam-5979	269	15	theorem	theorem	VERB
ejpam-5979	269	16	on	on	ADP
ejpam-5979	269	17	the	the	DET
ejpam-5979	269	18	generalized	generalize	VERB
ejpam-5979	269	19	fractional	fractional	ADJ
ejpam-5979	269	20	derivative	derivative	NOUN
ejpam-5979	269	21	of	of	ADP
ejpam-5979	269	22	the	the	DET
ejpam-5979	269	23	caputo	caputo	NOUN
ejpam-5979	269	24	-	-	PUNCT
ejpam-5979	269	25	type	type	NOUN
ejpam-5979	269	26	boundary	boundary	ADJ
ejpam-5979	269	27	value	value	NOUN
ejpam-5979	269	28	problem	problem	NOUN
ejpam-5979	269	29	to	to	PART
ejpam-5979	269	30	achieve	achieve	VERB
ejpam-5979	269	31	the	the	DET
ejpam-5979	269	32	existence	existence	NOUN
ejpam-5979	269	33	of	of	ADP
ejpam-5979	269	34	a	a	DET
ejpam-5979	269	35	single	single	ADJ
ejpam-5979	269	36	solution	solution	NOUN
ejpam-5979	269	37	,	,	PUNCT
ejpam-5979	269	38	the	the	DET
ejpam-5979	269	39	core	core	NOUN
ejpam-5979	269	40	of	of	ADP
ejpam-5979	269	41	this	this	DET
ejpam-5979	269	42	work	work	NOUN
ejpam-5979	269	43	in	in	ADP
ejpam-5979	269	44	the	the	DET
ejpam-5979	269	45	third	third	ADJ
ejpam-5979	269	46	chapter	chapter	NOUN
ejpam-5979	269	47	.	.	PUNCT
ejpam-5979	270	1	we	we	PRON
ejpam-5979	270	2	relied	rely	VERB
ejpam-5979	270	3	on	on	ADP
ejpam-5979	270	4	the	the	DET
ejpam-5979	270	5	positivity	positivity	NOUN
ejpam-5979	270	6	of	of	ADP
ejpam-5979	270	7	the	the	DET
ejpam-5979	270	8	green	green	ADJ
ejpam-5979	270	9	function	function	NOUN
ejpam-5979	270	10	and	and	CCONJ
ejpam-5979	270	11	its	its	PRON
ejpam-5979	270	12	integral	integral	ADJ
ejpam-5979	270	13	and	and	CCONJ
ejpam-5979	270	14	obtained	obtain	VERB
ejpam-5979	270	15	the	the	DET
ejpam-5979	270	16	function	function	NOUN
ejpam-5979	270	17	ξ	ξ	PROPN
ejpam-5979	270	18	as	as	SCONJ
ejpam-5979	270	19	shown	show	VERB
ejpam-5979	270	20	in	in	ADP
ejpam-5979	270	21	corollary	corollary	ADJ
ejpam-5979	270	22	1	1	NUM
ejpam-5979	270	23	.	.	PUNCT
ejpam-5979	271	1	by	by	ADP
ejpam-5979	271	2	conclusion	conclusion	NOUN
ejpam-5979	271	3	,	,	PUNCT
ejpam-5979	271	4	we	we	PRON
ejpam-5979	271	5	can	can	AUX
ejpam-5979	271	6	determine	determine	VERB
ejpam-5979	271	7	the	the	DET
ejpam-5979	271	8	maximum	maximum	NOUN
ejpam-5979	271	9	of	of	ADP
ejpam-5979	271	10	two	two	NUM
ejpam-5979	271	11	derived	derive	VERB
ejpam-5979	271	12	functions	function	NOUN
ejpam-5979	271	13	in	in	ADP
ejpam-5979	271	14	the	the	DET
ejpam-5979	271	15	general	general	ADJ
ejpam-5979	271	16	case	case	NOUN
ejpam-5979	271	17	of	of	ADP
ejpam-5979	271	18	two	two	NUM
ejpam-5979	271	19	boundary	boundary	ADJ
ejpam-5979	271	20	conditions	condition	NOUN
ejpam-5979	271	21	“	"	PUNCT
ejpam-5979	271	22	µ(θ	µ(θ	ADJ
ejpam-5979	271	23	)	)	PUNCT
ejpam-5979	271	24	=	=	SYM
ejpam-5979	271	25	λ1	λ1	ADJ
ejpam-5979	271	26	,	,	PUNCT
ejpam-5979	271	27	µ(ϑ	µ(ϑ	PROPN
ejpam-5979	271	28	)	)	PUNCT
ejpam-5979	271	29	=	=	SYM
ejpam-5979	271	30	λ2	λ2	NOUN
ejpam-5979	271	31	”	"	PUNCT
ejpam-5979	271	32	.	.	PUNCT
ejpam-5979	272	1	we	we	PRON
ejpam-5979	272	2	studied	study	VERB
ejpam-5979	272	3	two	two	NUM
ejpam-5979	272	4	cases	case	NOUN
ejpam-5979	272	5	when	when	SCONJ
ejpam-5979	272	6	“	"	PUNCT
ejpam-5979	272	7	µ(0	µ(0	NOUN
ejpam-5979	272	8	)	)	PUNCT
ejpam-5979	272	9	=	=	SYM
ejpam-5979	272	10	λ1	λ1	ADJ
ejpam-5979	272	11	,	,	PUNCT
ejpam-5979	272	12	µ(ϑ	µ(ϑ	PROPN
ejpam-5979	272	13	)	)	PUNCT
ejpam-5979	272	14	=	=	SYM
ejpam-5979	272	15	λ2	λ2	NOUN
ejpam-5979	272	16	”	"	PUNCT
ejpam-5979	272	17	and	and	CCONJ
ejpam-5979	272	18	“	"	PUNCT
ejpam-5979	272	19	µ(0	µ(0	NOUN
ejpam-5979	272	20	)	)	PUNCT
ejpam-5979	272	21	=	=	SYM
ejpam-5979	272	22	λ1	λ1	PROPN
ejpam-5979	272	23	,	,	PUNCT
ejpam-5979	272	24	µ(1	µ(1	PROPN
ejpam-5979	272	25	)	)	PUNCT
ejpam-5979	272	26	=	=	SYM
ejpam-5979	272	27	λ2	λ2	PROPN
ejpam-5979	272	28	”	"	PUNCT
ejpam-5979	272	29	,	,	PUNCT
ejpam-5979	272	30	we	we	PRON
ejpam-5979	272	31	obtain	obtain	VERB
ejpam-5979	272	32	detailed	detailed	ADJ
ejpam-5979	272	33	results	result	NOUN
ejpam-5979	272	34	in	in	ADP
ejpam-5979	272	35	this	this	DET
ejpam-5979	272	36	section	section	NOUN
ejpam-5979	272	37	.	.	PUNCT
ejpam-5979	273	1	we	we	PRON
ejpam-5979	273	2	also	also	ADV
ejpam-5979	273	3	studied	study	VERB
ejpam-5979	273	4	two	two	NUM
ejpam-5979	273	5	cases	case	NOUN
ejpam-5979	273	6	when	when	SCONJ
ejpam-5979	273	7	,	,	PUNCT
ejpam-5979	273	8	the	the	DET
ejpam-5979	273	9	previous	previous	ADJ
ejpam-5979	273	10	general	general	ADJ
ejpam-5979	273	11	case	case	NOUN
ejpam-5979	273	12	“	"	PUNCT
ejpam-5979	273	13	µ(θ	µ(θ	ADJ
ejpam-5979	273	14	)	)	PUNCT
ejpam-5979	273	15	=	=	SYM
ejpam-5979	273	16	λ1	λ1	ADJ
ejpam-5979	273	17	,	,	PUNCT
ejpam-5979	273	18	µ(ϑ	µ(ϑ	PROPN
ejpam-5979	273	19	)	)	PUNCT
ejpam-5979	273	20	=	=	SYM
ejpam-5979	273	21	λ2	λ2	NOUN
ejpam-5979	273	22	”	"	PUNCT
ejpam-5979	273	23	and	and	CCONJ
ejpam-5979	273	24	the	the	DET
ejpam-5979	273	25	case	case	NOUN
ejpam-5979	273	26	of	of	ADP
ejpam-5979	273	27	“	"	PUNCT
ejpam-5979	273	28	µ(θ	µ(θ	ADJ
ejpam-5979	273	29	)	)	PUNCT
ejpam-5979	273	30	=	=	SYM
ejpam-5979	273	31	λ1	λ1	PROPN
ejpam-5979	273	32	,	,	PUNCT
ejpam-5979	273	33	µ(1	µ(1	PROPN
ejpam-5979	273	34	)	)	PUNCT
ejpam-5979	273	35	=	=	SYM
ejpam-5979	273	36	λ2	λ2	PROPN
ejpam-5979	273	37	”	"	PUNCT
ejpam-5979	273	38	,	,	PUNCT
ejpam-5979	273	39	we	we	PRON
ejpam-5979	273	40	can	can	AUX
ejpam-5979	273	41	also	also	ADV
ejpam-5979	273	42	add	add	VERB
ejpam-5979	273	43	two	two	NUM
ejpam-5979	273	44	examples	example	NOUN
ejpam-5979	273	45	with	with	ADP
ejpam-5979	273	46	their	their	PRON
ejpam-5979	273	47	simulation	simulation	NOUN
ejpam-5979	273	48	in	in	ADP
ejpam-5979	273	49	these	these	DET
ejpam-5979	273	50	two	two	NUM
ejpam-5979	273	51	cases	case	NOUN
ejpam-5979	273	52	of	of	ADP
ejpam-5979	273	53	the	the	DET
ejpam-5979	273	54	theorems	theorem	NOUN
ejpam-5979	273	55	3.11	3.11	NUM
ejpam-5979	273	56	and	and	CCONJ
ejpam-5979	273	57	3.14	3.14	NUM
ejpam-5979	273	58	in	in	ADP
ejpam-5979	273	59	the	the	DET
ejpam-5979	273	60	examples	example	NOUN
ejpam-5979	273	61	part	part	NOUN
ejpam-5979	273	62	.	.	PUNCT
ejpam-5979	274	1	we	we	PRON
ejpam-5979	274	2	also	also	ADV
ejpam-5979	274	3	believe	believe	VERB
ejpam-5979	274	4	there	there	PRON
ejpam-5979	274	5	are	be	VERB
ejpam-5979	274	6	numerical	numerical	ADJ
ejpam-5979	274	7	methods	method	NOUN
ejpam-5979	274	8	to	to	PART
ejpam-5979	274	9	achieve	achieve	VERB
ejpam-5979	274	10	banach	banach	NOUN
ejpam-5979	274	11	’s	’s	NOUN
ejpam-5979	274	12	theorem	theorem	NOUN
ejpam-5979	274	13	of	of	ADP
ejpam-5979	274	14	contraction	contraction	NOUN
ejpam-5979	274	15	of	of	ADP
ejpam-5979	274	16	a	a	DET
ejpam-5979	274	17	single	single	ADJ
ejpam-5979	274	18	solution	solution	NOUN
ejpam-5979	274	19	to	to	ADP
ejpam-5979	274	20	the	the	DET
ejpam-5979	274	21	problem	problem	NOUN
ejpam-5979	274	22	(	(	PUNCT
ejpam-5979	274	23	1	1	NUM
ejpam-5979	274	24	)	)	PUNCT
ejpam-5979	274	25	with	with	ADP
ejpam-5979	274	26	the	the	DET
ejpam-5979	274	27	general	general	ADJ
ejpam-5979	274	28	boundary	boundary	ADJ
ejpam-5979	274	29	conditions	condition	NOUN
ejpam-5979	274	30	.	.	PUNCT
ejpam-5979	275	1	in	in	ADP
ejpam-5979	275	2	the	the	DET
ejpam-5979	275	3	future	future	NOUN
ejpam-5979	275	4	,	,	PUNCT
ejpam-5979	275	5	we	we	PRON
ejpam-5979	275	6	can	can	AUX
ejpam-5979	275	7	apply	apply	VERB
ejpam-5979	275	8	the	the	DET
ejpam-5979	275	9	banach	banach	NOUN
ejpam-5979	275	10	contraction	contraction	NOUN
ejpam-5979	275	11	to	to	ADP
ejpam-5979	275	12	the	the	DET
ejpam-5979	275	13	caputo	caputo	PROPN
ejpam-5979	275	14	-	-	PUNCT
ejpam-5979	275	15	fabrizio	fabrizio	PROPN
ejpam-5979	275	16	fractional	fractional	PROPN
ejpam-5979	275	17	bvp	bvp	NOUN
ejpam-5979	275	18	.	.	PUNCT
ejpam-5979	276	1	acknowledgements	acknowledgement	NOUN
ejpam-5979	276	2	the	the	DET
ejpam-5979	276	3	authors	author	NOUN
ejpam-5979	276	4	s.	s.	PROPN
ejpam-5979	276	5	aljohani	aljohani	PROPN
ejpam-5979	276	6	,	,	PUNCT
ejpam-5979	276	7	a.	a.	NOUN
ejpam-5979	276	8	aloqaily	aloqaily	ADV
ejpam-5979	276	9	,	,	PUNCT
ejpam-5979	276	10	and	and	CCONJ
ejpam-5979	276	11	n.	n.	PROPN
ejpam-5979	276	12	mlaiki	mlaiki	PROPN
ejpam-5979	276	13	would	would	AUX
ejpam-5979	276	14	like	like	VERB
ejpam-5979	276	15	to	to	PART
ejpam-5979	276	16	thank	thank	VERB
ejpam-5979	276	17	prince	prince	PROPN
ejpam-5979	276	18	sultan	sultan	PROPN
ejpam-5979	276	19	university	university	PROPN
ejpam-5979	276	20	for	for	ADP
ejpam-5979	276	21	paying	pay	VERB
ejpam-5979	276	22	the	the	DET
ejpam-5979	276	23	publication	publication	NOUN
ejpam-5979	276	24	fees	fee	NOUN
ejpam-5979	276	25	for	for	ADP
ejpam-5979	276	26	this	this	DET
ejpam-5979	276	27	work	work	NOUN
ejpam-5979	276	28	through	through	ADP
ejpam-5979	276	29	tas	ta	NOUN
ejpam-5979	276	30	lab	lab	NOUN
ejpam-5979	276	31	.	.	PUNCT
ejpam-5979	277	1	authors	author	NOUN
ejpam-5979	277	2	’	'	PUNCT
ejpam-5979	277	3	contributions	contribution	NOUN
ejpam-5979	277	4	all	all	DET
ejpam-5979	277	5	authors	author	NOUN
ejpam-5979	277	6	have	have	VERB
ejpam-5979	277	7	equal	equal	ADJ
ejpam-5979	277	8	contributions	contribution	NOUN
ejpam-5979	277	9	.	.	PUNCT
ejpam-5979	278	1	all	all	DET
ejpam-5979	278	2	authors	author	NOUN
ejpam-5979	278	3	read	read	VERB
ejpam-5979	278	4	and	and	CCONJ
ejpam-5979	278	5	approved	approve	VERB
ejpam-5979	278	6	the	the	DET
ejpam-5979	278	7	final	final	ADJ
ejpam-5979	278	8	manuscript	manuscript	NOUN
ejpam-5979	278	9	.	.	PUNCT
ejpam-5979	279	1	z.	z.	PROPN
ejpam-5979	279	2	bekri	bekri	PROPN
ejpam-5979	279	3	et	et	PROPN
ejpam-5979	279	4	al	al	PROPN
ejpam-5979	279	5	.	.	PUNCT
ejpam-5979	279	6	/	/	SYM
ejpam-5979	279	7	eur	eur	PROPN
ejpam-5979	279	8	.	.	PUNCT
ejpam-5979	280	1	j.	j.	PROPN
ejpam-5979	280	2	pure	pure	PROPN
ejpam-5979	280	3	appl	appl	PROPN
ejpam-5979	280	4	.	.	PROPN
ejpam-5979	280	5	math	math	PROPN
ejpam-5979	280	6	,	,	PUNCT
ejpam-5979	280	7	18	18	NUM
ejpam-5979	280	8	(	(	PUNCT
ejpam-5979	280	9	2	2	NUM
ejpam-5979	280	10	)	)	PUNCT
ejpam-5979	280	11	(	(	PUNCT
ejpam-5979	280	12	2025	2025	NUM
ejpam-5979	280	13	)	)	PUNCT
ejpam-5979	280	14	,	,	PUNCT
ejpam-5979	280	15	5979	5979	NUM
ejpam-5979	280	16	17	17	NUM
ejpam-5979	280	17	of	of	ADP
ejpam-5979	280	18	20	20	NUM
ejpam-5979	280	19	references	reference	NOUN
ejpam-5979	280	20	[	[	X
ejpam-5979	280	21	1	1	NUM
ejpam-5979	280	22	]	]	PUNCT
ejpam-5979	280	23	m.	m.	NOUN
ejpam-5979	280	24	m.	m.	NOUN
ejpam-5979	280	25	matar	matar	PROPN
ejpam-5979	280	26	,	,	PUNCT
ejpam-5979	280	27	m.	m.	PROPN
ejpam-5979	280	28	e.	e.	PROPN
ejpam-5979	280	29	samei	samei	PROPN
ejpam-5979	280	30	,	,	PUNCT
ejpam-5979	280	31	s.	s.	PROPN
ejpam-5979	280	32	etemad	etemad	PROPN
ejpam-5979	280	33	,	,	PUNCT
ejpam-5979	280	34	a.	a.	NOUN
ejpam-5979	280	35	amara	amara	PROPN
ejpam-5979	280	36	,	,	PUNCT
ejpam-5979	280	37	s.	s.	PROPN
ejpam-5979	280	38	rezapour	rezapour	PROPN
ejpam-5979	280	39	,	,	PUNCT
ejpam-5979	280	40	and	and	CCONJ
ejpam-5979	280	41	j.	j.	PROPN
ejpam-5979	280	42	alzabut	alzabut	PROPN
ejpam-5979	280	43	.	.	PUNCT
ejpam-5979	281	1	stability	stability	NOUN
ejpam-5979	281	2	analysis	analysis	NOUN
ejpam-5979	281	3	and	and	CCONJ
ejpam-5979	281	4	existence	existence	NOUN
ejpam-5979	281	5	criteria	criterion	NOUN
ejpam-5979	281	6	with	with	ADP
ejpam-5979	281	7	numerical	numerical	ADJ
ejpam-5979	281	8	illustrations	illustration	NOUN
ejpam-5979	281	9	to	to	PART
ejpam-5979	281	10	fractional	fractional	ADJ
ejpam-5979	281	11	jerk	jerk	NOUN
ejpam-5979	281	12	differential	differential	NOUN
ejpam-5979	281	13	system	system	NOUN
ejpam-5979	281	14	involving	involve	VERB
ejpam-5979	281	15	generalized	generalize	VERB
ejpam-5979	281	16	caputo	caputo	PROPN
ejpam-5979	281	17	derivative	derivative	NOUN
ejpam-5979	281	18	.	.	PUNCT
ejpam-5979	282	1	qualitative	qualitative	ADJ
ejpam-5979	282	2	theory	theory	NOUN
ejpam-5979	282	3	of	of	ADP
ejpam-5979	282	4	dynamical	dynamical	ADJ
ejpam-5979	282	5	systems	system	NOUN
ejpam-5979	282	6	,	,	PUNCT
ejpam-5979	282	7	23(5):111	23(5):111	PROPN
ejpam-5979	282	8	,	,	PUNCT
ejpam-5979	282	9	2024	2024	NUM
ejpam-5979	282	10	.	.	PUNCT
ejpam-5979	283	1	[	[	X
ejpam-5979	283	2	2	2	NUM
ejpam-5979	283	3	]	]	PUNCT
ejpam-5979	283	4	a.	a.	NOUN
ejpam-5979	283	5	boutiara	boutiara	NOUN
ejpam-5979	283	6	,	,	PUNCT
ejpam-5979	283	7	m.	m.	NOUN
ejpam-5979	283	8	benbachir	benbachir	NOUN
ejpam-5979	283	9	,	,	PUNCT
ejpam-5979	283	10	j.	j.	PROPN
ejpam-5979	283	11	alzabut	alzabut	PROPN
ejpam-5979	283	12	,	,	PUNCT
ejpam-5979	283	13	and	and	CCONJ
ejpam-5979	283	14	m.	m.	PROPN
ejpam-5979	283	15	e.	e.	PROPN
ejpam-5979	283	16	samei	samei	PROPN
ejpam-5979	283	17	.	.	PUNCT
ejpam-5979	284	1	monotone	monotone	ADJ
ejpam-5979	284	2	iterative	iterative	NOUN
ejpam-5979	284	3	and	and	CCONJ
ejpam-5979	284	4	upper	upper	ADJ
ejpam-5979	284	5	-	-	PUNCT
ejpam-5979	284	6	lower	low	ADJ
ejpam-5979	284	7	solutions	solution	NOUN
ejpam-5979	284	8	techniques	technique	NOUN
ejpam-5979	284	9	for	for	ADP
ejpam-5979	284	10	solving	solve	VERB
ejpam-5979	284	11	nonlinear	nonlinear	PROPN
ejpam-5979	284	12	ψ	ψ	PROPN
ejpam-5979	284	13	caputo	caputo	PROPN
ejpam-5979	284	14	fractional	fractional	PROPN
ejpam-5979	284	15	boundary	boundary	ADJ
ejpam-5979	284	16	value	value	NOUN
ejpam-5979	284	17	problem	problem	NOUN
ejpam-5979	284	18	.	.	PUNCT
ejpam-5979	285	1	fractal	fractal	ADJ
ejpam-5979	285	2	and	and	CCONJ
ejpam-5979	285	3	fractional	fractional	ADJ
ejpam-5979	285	4	,	,	PUNCT
ejpam-5979	285	5	5(4):194	5(4):194	NUM
ejpam-5979	285	6	,	,	PUNCT
ejpam-5979	285	7	2021	2021	NUM
ejpam-5979	285	8	.	.	PUNCT
ejpam-5979	286	1	[	[	X
ejpam-5979	286	2	3	3	X
ejpam-5979	286	3	]	]	PUNCT
ejpam-5979	286	4	z.	z.	PROPN
ejpam-5979	286	5	baitiche	baitiche	PROPN
ejpam-5979	286	6	,	,	PUNCT
ejpam-5979	286	7	c.	c.	PROPN
ejpam-5979	286	8	derbazi	derbazi	PROPN
ejpam-5979	286	9	,	,	PUNCT
ejpam-5979	286	10	j.	j.	PROPN
ejpam-5979	286	11	alzabut	alzabut	PROPN
ejpam-5979	286	12	,	,	PUNCT
ejpam-5979	286	13	m.	m.	PROPN
ejpam-5979	286	14	e.	e.	PROPN
ejpam-5979	286	15	samei	samei	PROPN
ejpam-5979	286	16	,	,	PUNCT
ejpam-5979	286	17	m.	m.	PROPN
ejpam-5979	286	18	k.	k.	PROPN
ejpam-5979	286	19	a.	a.	PROPN
ejpam-5979	286	20	kaabar	kaabar	PROPN
ejpam-5979	286	21	,	,	PUNCT
ejpam-5979	286	22	and	and	CCONJ
ejpam-5979	286	23	z.	z.	PROPN
ejpam-5979	286	24	siri	siri	NOUN
ejpam-5979	286	25	.	.	PUNCT
ejpam-5979	287	1	monotone	monotone	ADJ
ejpam-5979	287	2	iterative	iterative	NOUN
ejpam-5979	287	3	method	method	NOUN
ejpam-5979	287	4	for	for	ADP
ejpam-5979	287	5	langevin	langevin	ADJ
ejpam-5979	287	6	equation	equation	NOUN
ejpam-5979	287	7	in	in	ADP
ejpam-5979	287	8	terms	term	NOUN
ejpam-5979	287	9	of	of	ADP
ejpam-5979	287	10	ψ	ψ	PROPN
ejpam-5979	287	11	-	-	ADJ
ejpam-5979	287	12	caputo	caputo	ADJ
ejpam-5979	287	13	fractional	fractional	PROPN
ejpam-5979	287	14	derivative	derivative	ADJ
ejpam-5979	287	15	and	and	CCONJ
ejpam-5979	287	16	nonlinear	nonlinear	ADJ
ejpam-5979	287	17	boundary	boundary	ADJ
ejpam-5979	287	18	conditions	condition	NOUN
ejpam-5979	287	19	.	.	PUNCT
ejpam-5979	288	1	fractal	fractal	ADJ
ejpam-5979	288	2	and	and	CCONJ
ejpam-5979	288	3	fractional	fractional	ADJ
ejpam-5979	288	4	,	,	PUNCT
ejpam-5979	288	5	5(3):81	5(3):81	NUM
ejpam-5979	288	6	,	,	PUNCT
ejpam-5979	288	7	2021	2021	NUM
ejpam-5979	288	8	.	.	PUNCT
ejpam-5979	289	1	[	[	X
ejpam-5979	289	2	4	4	X
ejpam-5979	289	3	]	]	PUNCT
ejpam-5979	289	4	z.	z.	PROPN
ejpam-5979	289	5	bekri	bekri	PROPN
ejpam-5979	289	6	,	,	PUNCT
ejpam-5979	289	7	f.	f.	PROPN
ejpam-5979	289	8	nicola	nicola	PROPN
ejpam-5979	289	9	,	,	PUNCT
ejpam-5979	289	10	m.	m.	PROPN
ejpam-5979	289	11	e.	e.	PROPN
ejpam-5979	289	12	samei	samei	PROPN
ejpam-5979	289	13	,	,	PUNCT
ejpam-5979	289	14	and	and	CCONJ
ejpam-5979	290	1	s.	s.	PROPN
ejpam-5979	290	2	radenović.	radenović.	PROPN
ejpam-5979	290	3	confining	confine	VERB
ejpam-5979	290	4	a	a	DET
ejpam-5979	290	5	non	non	ADJ
ejpam-5979	290	6	-	-	ADJ
ejpam-5979	290	7	negative	negative	ADJ
ejpam-5979	290	8	solution	solution	NOUN
ejpam-5979	290	9	between	between	ADP
ejpam-5979	290	10	a	a	DET
ejpam-5979	290	11	lower	low	ADJ
ejpam-5979	290	12	and	and	CCONJ
ejpam-5979	290	13	upper	upper	ADJ
ejpam-5979	290	14	solution	solution	NOUN
ejpam-5979	290	15	for	for	ADP
ejpam-5979	290	16	a	a	DET
ejpam-5979	290	17	sixth	sixth	ADJ
ejpam-5979	290	18	-	-	PUNCT
ejpam-5979	290	19	degree	degree	NOUN
ejpam-5979	290	20	boundary	boundary	ADJ
ejpam-5979	290	21	value	value	NOUN
ejpam-5979	290	22	problem	problem	NOUN
ejpam-5979	290	23	.	.	PUNCT
ejpam-5979	291	1	military	military	ADJ
ejpam-5979	291	2	technical	technical	ADJ
ejpam-5979	291	3	courier	courier	NOUN
ejpam-5979	291	4	,	,	PUNCT
ejpam-5979	291	5	72(4	72(4	NUM
ejpam-5979	291	6	)	)	PUNCT
ejpam-5979	291	7	,	,	PUNCT
ejpam-5979	291	8	2024	2024	NUM
ejpam-5979	291	9	.	.	PUNCT
ejpam-5979	292	1	[	[	X
ejpam-5979	292	2	5	5	X
ejpam-5979	292	3	]	]	PUNCT
ejpam-5979	292	4	z.	z.	PROPN
ejpam-5979	292	5	bekri	bekri	PROPN
ejpam-5979	292	6	and	and	CCONJ
ejpam-5979	292	7	s.	s.	PROPN
ejpam-5979	292	8	benaicha	benaicha	PROPN
ejpam-5979	292	9	.	.	PUNCT
ejpam-5979	293	1	existence	existence	NOUN
ejpam-5979	293	2	of	of	ADP
ejpam-5979	293	3	solution	solution	NOUN
ejpam-5979	293	4	a	a	DET
ejpam-5979	293	5	fractional	fractional	ADJ
ejpam-5979	293	6	differential	differential	ADJ
ejpam-5979	293	7	equation	equation	NOUN
ejpam-5979	293	8	.	.	PUNCT
ejpam-5979	294	1	open	open	ADJ
ejpam-5979	294	2	journal	journal	PROPN
ejpam-5979	294	3	of	of	ADP
ejpam-5979	294	4	discrete	discrete	ADJ
ejpam-5979	294	5	applied	apply	VERB
ejpam-5979	294	6	mathematics	mathematic	NOUN
ejpam-5979	294	7	,	,	PUNCT
ejpam-5979	294	8	3(3):14–17	3(3):14–17	NUM
ejpam-5979	294	9	,	,	PUNCT
ejpam-5979	294	10	2020	2020	NUM
ejpam-5979	294	11	.	.	PUNCT
ejpam-5979	295	1	[	[	X
ejpam-5979	295	2	6	6	NUM
ejpam-5979	295	3	]	]	PUNCT
ejpam-5979	295	4	r.	r.	PROPN
ejpam-5979	295	5	a.	a.	PROPN
ejpam-5979	295	6	c.	c.	PROPN
ejpam-5979	295	7	ferreira	ferreira	PROPN
ejpam-5979	295	8	.	.	PUNCT
ejpam-5979	296	1	note	note	VERB
ejpam-5979	296	2	on	on	ADP
ejpam-5979	296	3	a	a	DET
ejpam-5979	296	4	uniqueness	uniqueness	NOUN
ejpam-5979	296	5	result	result	NOUN
ejpam-5979	296	6	for	for	ADP
ejpam-5979	296	7	a	a	DET
ejpam-5979	296	8	two	two	NUM
ejpam-5979	296	9	-	-	PUNCT
ejpam-5979	296	10	point	point	NOUN
ejpam-5979	296	11	fractional	fractional	ADJ
ejpam-5979	296	12	boundary	boundary	ADJ
ejpam-5979	296	13	value	value	NOUN
ejpam-5979	296	14	problem	problem	NOUN
ejpam-5979	296	15	.	.	PUNCT
ejpam-5979	297	1	applied	apply	VERB
ejpam-5979	297	2	mathematics	mathematics	NOUN
ejpam-5979	297	3	letters	letter	NOUN
ejpam-5979	297	4	,	,	PUNCT
ejpam-5979	297	5	90:75–78	90:75–78	NUM
ejpam-5979	297	6	,	,	PUNCT
ejpam-5979	297	7	2019	2019	NUM
ejpam-5979	297	8	.	.	PUNCT
ejpam-5979	298	1	[	[	X
ejpam-5979	298	2	7	7	X
ejpam-5979	298	3	]	]	PUNCT
ejpam-5979	298	4	a.	a.	NOUN
ejpam-5979	298	5	khalouta	khalouta	PROPN
ejpam-5979	298	6	.	.	PUNCT
ejpam-5979	299	1	new	new	ADJ
ejpam-5979	299	2	results	result	NOUN
ejpam-5979	299	3	of	of	ADP
ejpam-5979	299	4	the	the	DET
ejpam-5979	299	5	ρ	ρ	PROPN
ejpam-5979	299	6	-	-	ADJ
ejpam-5979	299	7	jafari	jafari	ADJ
ejpam-5979	299	8	transform	transform	NOUN
ejpam-5979	299	9	and	and	CCONJ
ejpam-5979	299	10	their	their	PRON
ejpam-5979	299	11	application	application	NOUN
ejpam-5979	299	12	to	to	ADP
ejpam-5979	299	13	linear	linear	VERB
ejpam-5979	299	14	and	and	CCONJ
ejpam-5979	299	15	nonlinear	nonlinear	ADJ
ejpam-5979	299	16	generalized	generalize	VERB
ejpam-5979	299	17	fractional	fractional	ADJ
ejpam-5979	299	18	differential	differential	ADJ
ejpam-5979	299	19	equations	equation	NOUN
ejpam-5979	299	20	.	.	PUNCT
ejpam-5979	300	1	revista	revista	PROPN
ejpam-5979	300	2	colombiana	colombiana	PROPN
ejpam-5979	300	3	de	de	X
ejpam-5979	300	4	matemáticas	matemáticas	PROPN
ejpam-5979	300	5	,	,	PUNCT
ejpam-5979	300	6	58(1):25–46	58(1):25–46	NUM
ejpam-5979	300	7	,	,	PUNCT
ejpam-5979	300	8	2024	2024	NUM
ejpam-5979	300	9	.	.	PUNCT
ejpam-5979	301	1	[	[	X
ejpam-5979	301	2	8	8	NUM
ejpam-5979	301	3	]	]	X
ejpam-5979	301	4	a.	a.	NOUN
ejpam-5979	301	5	khalouta	khalouta	PROPN
ejpam-5979	301	6	.	.	PUNCT
ejpam-5979	302	1	existence	existence	NOUN
ejpam-5979	302	2	,	,	PUNCT
ejpam-5979	302	3	uniqueness	uniqueness	NOUN
ejpam-5979	302	4	and	and	CCONJ
ejpam-5979	302	5	convergence	convergence	NOUN
ejpam-5979	302	6	solution	solution	NOUN
ejpam-5979	302	7	of	of	ADP
ejpam-5979	302	8	nonlinear	nonlinear	ADJ
ejpam-5979	302	9	caputofabrizio	caputofabrizio	PROPN
ejpam-5979	302	10	fractional	fractional	ADJ
ejpam-5979	302	11	biological	biological	ADJ
ejpam-5979	302	12	population	population	NOUN
ejpam-5979	302	13	model	model	NOUN
ejpam-5979	302	14	.	.	PUNCT
ejpam-5979	303	1	sahand	sahand	NOUN
ejpam-5979	303	2	communications	communication	NOUN
ejpam-5979	303	3	in	in	ADP
ejpam-5979	303	4	mathematical	mathematical	ADJ
ejpam-5979	303	5	analysis	analysis	NOUN
ejpam-5979	303	6	,	,	PUNCT
ejpam-5979	303	7	21(3):165–196	21(3):165–196	NUM
ejpam-5979	303	8	,	,	PUNCT
ejpam-5979	303	9	2024	2024	NUM
ejpam-5979	303	10	.	.	PUNCT
ejpam-5979	304	1	[	[	X
ejpam-5979	304	2	9	9	NUM
ejpam-5979	304	3	]	]	PUNCT
ejpam-5979	304	4	a.	a.	NOUN
ejpam-5979	304	5	khalouta	khalouta	PROPN
ejpam-5979	304	6	.	.	PUNCT
ejpam-5979	305	1	existence	existence	NOUN
ejpam-5979	305	2	and	and	CCONJ
ejpam-5979	305	3	uniqueness	uniqueness	NOUN
ejpam-5979	305	4	of	of	ADP
ejpam-5979	305	5	solution	solution	NOUN
ejpam-5979	305	6	for	for	ADP
ejpam-5979	305	7	caputo	caputo	PROPN
ejpam-5979	305	8	-	-	PUNCT
ejpam-5979	305	9	fabrizio	fabrizio	PROPN
ejpam-5979	305	10	fractional	fractional	ADJ
ejpam-5979	305	11	bratu	bratu	NOUN
ejpam-5979	305	12	-	-	PUNCT
ejpam-5979	305	13	type	type	NOUN
ejpam-5979	305	14	initial	initial	ADJ
ejpam-5979	305	15	value	value	NOUN
ejpam-5979	305	16	problem	problem	NOUN
ejpam-5979	305	17	.	.	PUNCT
ejpam-5979	306	1	azerbaijan	azerbaijan	PROPN
ejpam-5979	306	2	journal	journal	PROPN
ejpam-5979	306	3	of	of	ADP
ejpam-5979	306	4	mathematics	mathematic	NOUN
ejpam-5979	306	5	,	,	PUNCT
ejpam-5979	306	6	13(1):96–102	13(1):96–102	NUM
ejpam-5979	306	7	,	,	PUNCT
ejpam-5979	306	8	2023	2023	NUM
ejpam-5979	306	9	.	.	PUNCT
ejpam-5979	307	1	[	[	X
ejpam-5979	307	2	10	10	NUM
ejpam-5979	307	3	]	]	X
ejpam-5979	307	4	r.	r.	PROPN
ejpam-5979	307	5	maliha	maliha	PROPN
ejpam-5979	307	6	,	,	PUNCT
ejpam-5979	307	7	s.	s.	PROPN
ejpam-5979	307	8	lariab	lariab	PROPN
ejpam-5979	307	9	,	,	PUNCT
ejpam-5979	307	10	d.	d.	PROPN
ejpam-5979	307	11	fatima	fatima	PROPN
ejpam-5979	307	12	,	,	PUNCT
ejpam-5979	307	13	a.	a.	PROPN
ejpam-5979	307	14	irshad	irshad	PROPN
ejpam-5979	307	15	,	,	PUNCT
ejpam-5979	307	16	and	and	CCONJ
ejpam-5979	307	17	m.	m.	NOUN
ejpam-5979	307	18	nabil	nabil	PROPN
ejpam-5979	307	19	.	.	PUNCT
ejpam-5979	308	1	existence	existence	NOUN
ejpam-5979	308	2	of	of	ADP
ejpam-5979	308	3	solution	solution	NOUN
ejpam-5979	308	4	of	of	ADP
ejpam-5979	308	5	a	a	DET
ejpam-5979	308	6	system	system	NOUN
ejpam-5979	308	7	of	of	ADP
ejpam-5979	308	8	non	non	ADJ
ejpam-5979	308	9	-	-	ADJ
ejpam-5979	308	10	linear	linear	ADJ
ejpam-5979	308	11	differential	differential	ADJ
ejpam-5979	308	12	inclusions	inclusion	NOUN
ejpam-5979	308	13	with	with	ADP
ejpam-5979	308	14	non	non	ADJ
ejpam-5979	308	15	-	-	ADJ
ejpam-5979	308	16	local	local	ADJ
ejpam-5979	308	17	,	,	PUNCT
ejpam-5979	308	18	integral	integral	ADJ
ejpam-5979	308	19	boundary	boundary	ADJ
ejpam-5979	308	20	conditions	condition	NOUN
ejpam-5979	308	21	via	via	ADP
ejpam-5979	308	22	fixed	fix	VERB
ejpam-5979	308	23	points	point	NOUN
ejpam-5979	308	24	of	of	ADP
ejpam-5979	308	25	hybrid	hybrid	ADJ
ejpam-5979	308	26	contractions	contraction	NOUN
ejpam-5979	308	27	.	.	PUNCT
ejpam-5979	309	1	boundary	boundary	ADJ
ejpam-5979	309	2	value	value	NOUN
ejpam-5979	309	3	problems	problem	NOUN
ejpam-5979	309	4	,	,	PUNCT
ejpam-5979	309	5	2024:90	2024:90	NUM
ejpam-5979	309	6	,	,	PUNCT
ejpam-5979	309	7	2024	2024	NUM
ejpam-5979	309	8	.	.	PUNCT
ejpam-5979	310	1	[	[	X
ejpam-5979	310	2	11	11	NUM
ejpam-5979	310	3	]	]	X
ejpam-5979	310	4	kamran	kamran	PROPN
ejpam-5979	310	5	,	,	PUNCT
ejpam-5979	310	6	a.	a.	NOUN
ejpam-5979	310	7	kalsoom	kalsoom	PROPN
ejpam-5979	310	8	,	,	PUNCT
ejpam-5979	310	9	z.	z.	PROPN
ejpam-5979	310	10	a.	a.	PROPN
ejpam-5979	310	11	khan	khan	PROPN
ejpam-5979	310	12	,	,	PUNCT
ejpam-5979	310	13	s.	s.	PROPN
ejpam-5979	310	14	hassan	hassan	PROPN
ejpam-5979	310	15	,	,	PUNCT
ejpam-5979	310	16	and	and	CCONJ
ejpam-5979	310	17	m.	m.	NOUN
ejpam-5979	310	18	nabil	nabil	PROPN
ejpam-5979	310	19	.	.	PUNCT
ejpam-5979	311	1	analysis	analysis	NOUN
ejpam-5979	311	2	of	of	ADP
ejpam-5979	311	3	timefractional	timefractional	ADJ
ejpam-5979	311	4	delay	delay	NOUN
ejpam-5979	311	5	partial	partial	ADJ
ejpam-5979	311	6	differential	differential	NOUN
ejpam-5979	311	7	equations	equation	NOUN
ejpam-5979	311	8	using	use	VERB
ejpam-5979	311	9	a	a	DET
ejpam-5979	311	10	local	local	ADJ
ejpam-5979	311	11	radial	radial	ADJ
ejpam-5979	311	12	basis	basis	NOUN
ejpam-5979	311	13	function	function	NOUN
ejpam-5979	311	14	method	method	NOUN
ejpam-5979	311	15	.	.	PUNCT
ejpam-5979	312	1	fractal	fractal	ADJ
ejpam-5979	312	2	and	and	CCONJ
ejpam-5979	312	3	fractional	fractional	ADJ
ejpam-5979	312	4	,	,	PUNCT
ejpam-5979	312	5	8(12):683	8(12):683	NUM
ejpam-5979	312	6	,	,	PUNCT
ejpam-5979	312	7	2024	2024	NUM
ejpam-5979	312	8	.	.	PUNCT
ejpam-5979	313	1	[	[	X
ejpam-5979	313	2	12	12	NUM
ejpam-5979	313	3	]	]	X
ejpam-5979	313	4	kamran	kamran	PROPN
ejpam-5979	313	5	,	,	PUNCT
ejpam-5979	313	6	u.	u.	PROPN
ejpam-5979	313	7	k.	k.	PROPN
ejpam-5979	313	8	sharif	sharif	PROPN
ejpam-5979	313	9	,	,	PUNCT
ejpam-5979	313	10	s.	s.	PROPN
ejpam-5979	313	11	hassan	hassan	PROPN
ejpam-5979	313	12	,	,	PUNCT
ejpam-5979	313	13	and	and	CCONJ
ejpam-5979	313	14	m.	m.	NOUN
ejpam-5979	313	15	nabil	nabil	PROPN
ejpam-5979	313	16	.	.	PUNCT
ejpam-5979	314	1	on	on	ADP
ejpam-5979	314	2	the	the	DET
ejpam-5979	314	3	approximation	approximation	NOUN
ejpam-5979	314	4	of	of	ADP
ejpam-5979	314	5	fractionalorder	fractionalorder	PROPN
ejpam-5979	314	6	differential	differential	ADJ
ejpam-5979	314	7	equations	equation	NOUN
ejpam-5979	314	8	using	use	VERB
ejpam-5979	314	9	laplace	laplace	NOUN
ejpam-5979	314	10	transform	transform	NOUN
ejpam-5979	314	11	and	and	CCONJ
ejpam-5979	314	12	weeks	week	NOUN
ejpam-5979	314	13	method	method	NOUN
ejpam-5979	314	14	.	.	PUNCT
ejpam-5979	315	1	symmetry	symmetry	NOUN
ejpam-5979	315	2	,	,	PUNCT
ejpam-5979	315	3	15(6):1214	15(6):1214	NUM
ejpam-5979	315	4	,	,	PUNCT
ejpam-5979	315	5	2023	2023	NUM
ejpam-5979	315	6	.	.	PUNCT
ejpam-5979	316	1	[	[	X
ejpam-5979	316	2	13	13	NUM
ejpam-5979	316	3	]	]	PUNCT
ejpam-5979	316	4	p.	p.	PROPN
ejpam-5979	316	5	b.	b.	PROPN
ejpam-5979	316	6	bailey	bailey	PROPN
ejpam-5979	316	7	,	,	PUNCT
ejpam-5979	316	8	l.	l.	PROPN
ejpam-5979	316	9	f.	f.	PROPN
ejpam-5979	316	10	shampine	shampine	PROPN
ejpam-5979	316	11	,	,	PUNCT
ejpam-5979	316	12	and	and	CCONJ
ejpam-5979	316	13	p.	p.	PROPN
ejpam-5979	316	14	e.	e.	PROPN
ejpam-5979	316	15	waltman	waltman	PROPN
ejpam-5979	316	16	.	.	PUNCT
ejpam-5979	317	1	nonlinear	nonlinear	ADJ
ejpam-5979	317	2	two	two	NUM
ejpam-5979	317	3	-	-	PUNCT
ejpam-5979	317	4	point	point	NOUN
ejpam-5979	317	5	boundary	boundary	ADJ
ejpam-5979	317	6	value	value	NOUN
ejpam-5979	317	7	problem	problem	NOUN
ejpam-5979	317	8	.	.	PUNCT
ejpam-5979	318	1	academic	academic	ADJ
ejpam-5979	318	2	press	press	NOUN
ejpam-5979	318	3	,	,	PUNCT
ejpam-5979	318	4	new	new	PROPN
ejpam-5979	318	5	york	york	PROPN
ejpam-5979	318	6	,	,	PUNCT
ejpam-5979	318	7	1968	1968	NUM
ejpam-5979	318	8	.	.	PUNCT
ejpam-5979	319	1	[	[	X
ejpam-5979	319	2	14	14	NUM
ejpam-5979	319	3	]	]	X
ejpam-5979	319	4	r.	r.	PROPN
ejpam-5979	319	5	p.	p.	PROPN
ejpam-5979	319	6	agarwal	agarwal	PROPN
ejpam-5979	319	7	and	and	CCONJ
ejpam-5979	319	8	d.	d.	PROPN
ejpam-5979	319	9	o’regan	o’regan	PROPN
ejpam-5979	319	10	.	.	PUNCT
ejpam-5979	320	1	an	an	DET
ejpam-5979	320	2	introduction	introduction	NOUN
ejpam-5979	320	3	to	to	ADP
ejpam-5979	320	4	ordinary	ordinary	ADJ
ejpam-5979	320	5	differential	differential	ADJ
ejpam-5979	320	6	equations	equation	NOUN
ejpam-5979	320	7	.	.	PUNCT
ejpam-5979	321	1	springer	springer	NOUN
ejpam-5979	321	2	,	,	PUNCT
ejpam-5979	321	3	new	new	PROPN
ejpam-5979	321	4	york	york	PROPN
ejpam-5979	321	5	,	,	PUNCT
ejpam-5979	321	6	2008	2008	NUM
ejpam-5979	321	7	.	.	PUNCT
ejpam-5979	322	1	[	[	X
ejpam-5979	322	2	15	15	NUM
ejpam-5979	322	3	]	]	X
ejpam-5979	322	4	w.	w.	PROPN
ejpam-5979	322	5	g.	g.	PROPN
ejpam-5979	322	6	kelley	kelley	PROPN
ejpam-5979	322	7	and	and	CCONJ
ejpam-5979	322	8	a.	a.	PROPN
ejpam-5979	322	9	c.	c.	PROPN
ejpam-5979	322	10	peterson	peterson	PROPN
ejpam-5979	322	11	.	.	PUNCT
ejpam-5979	323	1	the	the	DET
ejpam-5979	323	2	theory	theory	NOUN
ejpam-5979	323	3	of	of	ADP
ejpam-5979	323	4	differential	differential	ADJ
ejpam-5979	323	5	equations	equation	NOUN
ejpam-5979	323	6	.	.	PUNCT
ejpam-5979	324	1	springer	springer	NOUN
ejpam-5979	324	2	,	,	PUNCT
ejpam-5979	324	3	new	new	PROPN
ejpam-5979	324	4	z.	z.	PROPN
ejpam-5979	324	5	bekri	bekri	PROPN
ejpam-5979	324	6	et	et	PROPN
ejpam-5979	324	7	al	al	PROPN
ejpam-5979	324	8	.	.	PUNCT
ejpam-5979	324	9	/	/	SYM
ejpam-5979	324	10	eur	eur	PROPN
ejpam-5979	324	11	.	.	PUNCT
ejpam-5979	325	1	j.	j.	PROPN
ejpam-5979	325	2	pure	pure	PROPN
ejpam-5979	325	3	appl	appl	PROPN
ejpam-5979	325	4	.	.	PROPN
ejpam-5979	325	5	math	math	PROPN
ejpam-5979	325	6	,	,	PUNCT
ejpam-5979	325	7	18	18	NUM
ejpam-5979	325	8	(	(	PUNCT
ejpam-5979	325	9	2	2	NUM
ejpam-5979	325	10	)	)	PUNCT
ejpam-5979	325	11	(	(	PUNCT
ejpam-5979	325	12	2025	2025	NUM
ejpam-5979	325	13	)	)	PUNCT
ejpam-5979	325	14	,	,	PUNCT
ejpam-5979	325	15	5979	5979	NUM
ejpam-5979	325	16	18	18	NUM
ejpam-5979	325	17	of	of	ADP
ejpam-5979	325	18	20	20	NUM
ejpam-5979	325	19	york	york	PROPN
ejpam-5979	325	20	,	,	PUNCT
ejpam-5979	325	21	2010	2010	NUM
ejpam-5979	325	22	.	.	PUNCT
ejpam-5979	326	1	[	[	X
ejpam-5979	326	2	16	16	NUM
ejpam-5979	326	3	]	]	PUNCT
ejpam-5979	326	4	z.	z.	PROPN
ejpam-5979	326	5	bekri	bekri	PROPN
ejpam-5979	326	6	,	,	PUNCT
ejpam-5979	326	7	v.	v.	PROPN
ejpam-5979	326	8	s.	s.	PROPN
ejpam-5979	326	9	erturk	erturk	PROPN
ejpam-5979	326	10	,	,	PUNCT
ejpam-5979	326	11	and	and	CCONJ
ejpam-5979	326	12	p.	p.	PROPN
ejpam-5979	326	13	kumar	kumar	PROPN
ejpam-5979	326	14	.	.	PROPN
ejpam-5979	327	1	existence	existence	NOUN
ejpam-5979	327	2	and	and	CCONJ
ejpam-5979	327	3	uniqueness	uniqueness	VERB
ejpam-5979	327	4	analysis	analysis	NOUN
ejpam-5979	327	5	for	for	ADP
ejpam-5979	327	6	the	the	DET
ejpam-5979	327	7	generalized	generalized	ADJ
ejpam-5979	327	8	caputo	caputo	NOUN
ejpam-5979	327	9	-	-	PUNCT
ejpam-5979	327	10	type	type	NOUN
ejpam-5979	327	11	fractional	fractional	ADJ
ejpam-5979	327	12	-	-	PUNCT
ejpam-5979	327	13	order	order	NOUN
ejpam-5979	327	14	boundary	boundary	ADJ
ejpam-5979	327	15	value	value	NOUN
ejpam-5979	327	16	problem	problem	NOUN
ejpam-5979	327	17	.	.	PUNCT
ejpam-5979	328	1	advanced	advanced	ADJ
ejpam-5979	328	2	studies	study	NOUN
ejpam-5979	328	3	in	in	ADP
ejpam-5979	328	4	contemporary	contemporary	ADJ
ejpam-5979	328	5	mathematics	mathematic	NOUN
ejpam-5979	328	6	,	,	PUNCT
ejpam-5979	328	7	33(2):173–179	33(2):173–179	PROPN
ejpam-5979	328	8	,	,	PUNCT
ejpam-5979	328	9	2023	2023	NUM
ejpam-5979	328	10	.	.	PUNCT
ejpam-5979	329	1	[	[	X
ejpam-5979	329	2	17	17	NUM
ejpam-5979	329	3	]	]	PUNCT
ejpam-5979	329	4	z.	z.	PROPN
ejpam-5979	329	5	bekri	bekri	PROPN
ejpam-5979	329	6	,	,	PUNCT
ejpam-5979	329	7	v.	v.	PROPN
ejpam-5979	329	8	s.	s.	PROPN
ejpam-5979	329	9	erturk	erturk	PROPN
ejpam-5979	329	10	,	,	PUNCT
ejpam-5979	329	11	p.	p.	PROPN
ejpam-5979	329	12	kumar	kumar	PROPN
ejpam-5979	329	13	,	,	PUNCT
ejpam-5979	329	14	and	and	CCONJ
ejpam-5979	329	15	v.	v.	ADP
ejpam-5979	329	16	govindaraj	govindaraj	NOUN
ejpam-5979	329	17	.	.	PUNCT
ejpam-5979	330	1	some	some	DET
ejpam-5979	330	2	novel	novel	ADJ
ejpam-5979	330	3	analysis	analysis	NOUN
ejpam-5979	330	4	of	of	ADP
ejpam-5979	330	5	two	two	NUM
ejpam-5979	330	6	different	different	ADJ
ejpam-5979	330	7	caputo	caputo	NOUN
ejpam-5979	330	8	-	-	PUNCT
ejpam-5979	330	9	type	type	NOUN
ejpam-5979	330	10	fractional	fractional	ADJ
ejpam-5979	330	11	-	-	PUNCT
ejpam-5979	330	12	order	order	NOUN
ejpam-5979	330	13	boundary	boundary	ADJ
ejpam-5979	330	14	value	value	NOUN
ejpam-5979	330	15	problems	problem	NOUN
ejpam-5979	330	16	.	.	PUNCT
ejpam-5979	331	1	results	result	NOUN
ejpam-5979	331	2	in	in	ADP
ejpam-5979	331	3	nonlinear	nonlinear	ADJ
ejpam-5979	331	4	analysis	analysis	NOUN
ejpam-5979	331	5	,	,	PUNCT
ejpam-5979	331	6	5(3):299–311	5(3):299–311	NOUN
ejpam-5979	331	7	,	,	PUNCT
ejpam-5979	331	8	2022	2022	NUM
ejpam-5979	331	9	.	.	PUNCT
ejpam-5979	332	1	[	[	X
ejpam-5979	332	2	18	18	NUM
ejpam-5979	332	3	]	]	PUNCT
ejpam-5979	332	4	z.	z.	PROPN
ejpam-5979	332	5	bekri	bekri	PROPN
ejpam-5979	332	6	,	,	PUNCT
ejpam-5979	332	7	v.	v.	PROPN
ejpam-5979	332	8	s.	s.	PROPN
ejpam-5979	332	9	erturk	erturk	PROPN
ejpam-5979	332	10	,	,	PUNCT
ejpam-5979	332	11	and	and	CCONJ
ejpam-5979	332	12	p.	p.	PROPN
ejpam-5979	332	13	kumar	kumar	PROPN
ejpam-5979	332	14	.	.	PROPN
ejpam-5979	333	1	on	on	ADP
ejpam-5979	333	2	the	the	DET
ejpam-5979	333	3	existence	existence	NOUN
ejpam-5979	333	4	and	and	CCONJ
ejpam-5979	333	5	uniqueness	uniqueness	NOUN
ejpam-5979	333	6	of	of	ADP
ejpam-5979	333	7	a	a	DET
ejpam-5979	333	8	nonlinear	nonlinear	ADJ
ejpam-5979	333	9	q	q	ADJ
ejpam-5979	333	10	-	-	PUNCT
ejpam-5979	333	11	difference	difference	NOUN
ejpam-5979	333	12	boundary	boundary	ADJ
ejpam-5979	333	13	value	value	NOUN
ejpam-5979	333	14	problem	problem	NOUN
ejpam-5979	333	15	of	of	ADP
ejpam-5979	333	16	fractional	fractional	ADJ
ejpam-5979	333	17	order	order	NOUN
ejpam-5979	333	18	.	.	PUNCT
ejpam-5979	334	1	international	international	ADJ
ejpam-5979	334	2	journal	journal	NOUN
ejpam-5979	334	3	of	of	ADP
ejpam-5979	334	4	modeling	modeling	NOUN
ejpam-5979	334	5	,	,	PUNCT
ejpam-5979	334	6	simulation	simulation	NOUN
ejpam-5979	334	7	,	,	PUNCT
ejpam-5979	334	8	and	and	CCONJ
ejpam-5979	334	9	scientific	scientific	ADJ
ejpam-5979	334	10	computing	computing	NOUN
ejpam-5979	334	11	,	,	PUNCT
ejpam-5979	334	12	13(1):2250011	13(1):2250011	NUM
ejpam-5979	334	13	,	,	PUNCT
ejpam-5979	334	14	2022	2022	NUM
ejpam-5979	334	15	.	.	PUNCT
ejpam-5979	335	1	[	[	X
ejpam-5979	335	2	19	19	NUM
ejpam-5979	335	3	]	]	X
ejpam-5979	335	4	u.	u.	PROPN
ejpam-5979	335	5	n.	n.	PROPN
ejpam-5979	335	6	katugampola	katugampola	PROPN
ejpam-5979	335	7	.	.	PUNCT
ejpam-5979	336	1	new	new	ADJ
ejpam-5979	336	2	approach	approach	NOUN
ejpam-5979	336	3	to	to	ADP
ejpam-5979	336	4	a	a	DET
ejpam-5979	336	5	generalized	generalized	ADJ
ejpam-5979	336	6	fractional	fractional	ADJ
ejpam-5979	336	7	integral	integral	ADJ
ejpam-5979	336	8	.	.	PUNCT
ejpam-5979	336	9	applied	apply	VERB
ejpam-5979	336	10	mathematics	mathematic	NOUN
ejpam-5979	336	11	and	and	CCONJ
ejpam-5979	336	12	computation	computation	NOUN
ejpam-5979	336	13	,	,	PUNCT
ejpam-5979	336	14	218(3):860–865	218(3):860–865	NUM
ejpam-5979	336	15	,	,	PUNCT
ejpam-5979	336	16	2011	2011	NUM
ejpam-5979	336	17	.	.	PUNCT
ejpam-5979	337	1	[	[	X
ejpam-5979	337	2	20	20	NUM
ejpam-5979	337	3	]	]	PUNCT
ejpam-5979	337	4	u.	u.	PROPN
ejpam-5979	337	5	n.	n.	PROPN
ejpam-5979	337	6	katugampola	katugampola	PROPN
ejpam-5979	337	7	.	.	PUNCT
ejpam-5979	338	1	a	a	DET
ejpam-5979	338	2	new	new	ADJ
ejpam-5979	338	3	approach	approach	NOUN
ejpam-5979	338	4	to	to	ADP
ejpam-5979	338	5	generalized	generalized	ADJ
ejpam-5979	338	6	fractional	fractional	ADJ
ejpam-5979	338	7	derivatives	derivative	NOUN
ejpam-5979	338	8	.	.	PUNCT
ejpam-5979	339	1	bulletin	bulletin	NOUN
ejpam-5979	339	2	of	of	ADP
ejpam-5979	339	3	mathematical	mathematical	ADJ
ejpam-5979	339	4	analysis	analysis	NOUN
ejpam-5979	339	5	and	and	CCONJ
ejpam-5979	339	6	applications	application	NOUN
ejpam-5979	339	7	,	,	PUNCT
ejpam-5979	339	8	6(4):1–15	6(4):1–15	NUM
ejpam-5979	339	9	,	,	PUNCT
ejpam-5979	339	10	2011	2011	NUM
ejpam-5979	339	11	.	.	PUNCT
ejpam-5979	340	1	[	[	X
ejpam-5979	340	2	21	21	NUM
ejpam-5979	340	3	]	]	X
ejpam-5979	340	4	u.	u.	PROPN
ejpam-5979	340	5	n.	n.	PROPN
ejpam-5979	340	6	katugampola	katugampola	PROPN
ejpam-5979	340	7	.	.	PUNCT
ejpam-5979	341	1	mellin	mellin	PROPN
ejpam-5979	341	2	transforms	transform	VERB
ejpam-5979	341	3	of	of	ADP
ejpam-5979	341	4	generalized	generalized	ADJ
ejpam-5979	341	5	fractional	fractional	ADJ
ejpam-5979	341	6	integrals	integral	NOUN
ejpam-5979	341	7	and	and	CCONJ
ejpam-5979	341	8	derivatives	derivative	NOUN
ejpam-5979	341	9	.	.	PUNCT
ejpam-5979	342	1	applied	apply	VERB
ejpam-5979	342	2	mathematics	mathematic	NOUN
ejpam-5979	342	3	and	and	CCONJ
ejpam-5979	342	4	computation	computation	NOUN
ejpam-5979	342	5	,	,	PUNCT
ejpam-5979	342	6	257:566–580	257:566–580	NUM
ejpam-5979	342	7	,	,	PUNCT
ejpam-5979	342	8	2015	2015	NUM
ejpam-5979	342	9	.	.	PUNCT
ejpam-5979	343	1	[	[	X
ejpam-5979	343	2	22	22	NUM
ejpam-5979	343	3	]	]	X
ejpam-5979	343	4	u.	u.	PROPN
ejpam-5979	343	5	n.	n.	PROPN
ejpam-5979	343	6	katugampola	katugampola	PROPN
ejpam-5979	343	7	.	.	PUNCT
ejpam-5979	344	1	existence	existence	NOUN
ejpam-5979	344	2	and	and	CCONJ
ejpam-5979	344	3	uniqueness	uniqueness	NOUN
ejpam-5979	344	4	results	result	NOUN
ejpam-5979	344	5	for	for	ADP
ejpam-5979	344	6	a	a	DET
ejpam-5979	344	7	class	class	NOUN
ejpam-5979	344	8	of	of	ADP
ejpam-5979	344	9	generalized	generalized	ADJ
ejpam-5979	344	10	fractional	fractional	ADJ
ejpam-5979	344	11	differential	differential	ADJ
ejpam-5979	344	12	equations	equation	NOUN
ejpam-5979	344	13	.	.	PUNCT
ejpam-5979	345	1	arxiv	arxiv	PROPN
ejpam-5979	345	2	preprint	preprint	NOUN
ejpam-5979	345	3	arxiv:1411.5229	arxiv:1411.5229	NOUN
ejpam-5979	345	4	,	,	PUNCT
ejpam-5979	345	5	2016	2016	NUM
ejpam-5979	345	6	.	.	PUNCT
ejpam-5979	346	1	[	[	X
ejpam-5979	346	2	23	23	NUM
ejpam-5979	346	3	]	]	PUNCT
ejpam-5979	346	4	s.	s.	PROPN
ejpam-5979	346	5	s.	s.	PROPN
ejpam-5979	346	6	redhwan	redhwan	PROPN
ejpam-5979	346	7	,	,	PUNCT
ejpam-5979	346	8	s.	s.	PROPN
ejpam-5979	346	9	l.	l.	PROPN
ejpam-5979	346	10	shaikh	shaikh	PROPN
ejpam-5979	346	11	,	,	PUNCT
ejpam-5979	346	12	and	and	CCONJ
ejpam-5979	346	13	m.	m.	NOUN
ejpam-5979	346	14	s.	s.	PROPN
ejpam-5979	346	15	abdo	abdo	PROPN
ejpam-5979	346	16	.	.	PUNCT
ejpam-5979	347	1	theory	theory	NOUN
ejpam-5979	347	2	of	of	ADP
ejpam-5979	347	3	nonlinear	nonlinear	PROPN
ejpam-5979	347	4	caputokatugampola	caputokatugampola	PROPN
ejpam-5979	347	5	fractional	fractional	ADJ
ejpam-5979	347	6	differential	differential	ADJ
ejpam-5979	347	7	equations	equation	NOUN
ejpam-5979	347	8	.	.	PUNCT
ejpam-5979	348	1	arxiv	arxiv	PROPN
ejpam-5979	348	2	preprint	preprint	PROPN
ejpam-5979	348	3	arxiv:1911.08884	arxiv:1911.08884	PROPN
ejpam-5979	348	4	,	,	PUNCT
ejpam-5979	348	5	2019	2019	NUM
ejpam-5979	348	6	.	.	PUNCT
ejpam-5979	349	1	appendix	appendix	NOUN
ejpam-5979	349	2	supporting	support	VERB
ejpam-5979	349	3	information	information	NOUN
ejpam-5979	349	4	algorithm	algorithm	NOUN
ejpam-5979	349	5	1	1	NUM
ejpam-5979	349	6	:	:	PUNCT
ejpam-5979	349	7	the	the	DET
ejpam-5979	349	8	matlab	matlab	PROPN
ejpam-5979	349	9	algorithm	algorithm	NOUN
ejpam-5979	349	10	for	for	ADP
ejpam-5979	349	11	implementing	implement	VERB
ejpam-5979	349	12	the	the	DET
ejpam-5979	349	13	fourth	fourth	ADJ
ejpam-5979	349	14	-	-	PUNCT
ejpam-5979	349	15	order	order	NOUN
ejpam-5979	349	16	runge	runge	NOUN
ejpam-5979	349	17	-	-	PUNCT
ejpam-5979	349	18	kutta	kutta	NOUN
ejpam-5979	349	19	method	method	NOUN
ejpam-5979	349	20	function	function	NOUN
ejpam-5979	349	21	[	[	X
ejpam-5979	349	22	tau	tau	PROPN
ejpam-5979	349	23	,	,	PUNCT
ejpam-5979	349	24	mu	mu	PROPN
ejpam-5979	349	25	]	]	PUNCT
ejpam-5979	349	26	=	=	SYM
ejpam-5979	349	27	fourth_order_runge_kutta(lambda1	fourth_order_runge_kutta(lambda1	NOUN
ejpam-5979	349	28	,	,	PUNCT
ejpam-5979	349	29	lambda2	lambda2	PROPN
ejpam-5979	349	30	,	,	PUNCT
ejpam-5979	349	31	theta	theta	NOUN
ejpam-5979	349	32	,	,	PUNCT
ejpam-5979	349	33	sigma	sigma	NOUN
ejpam-5979	349	34	,	,	PUNCT
ejpam-5979	349	35	rho	rho	ADJ
ejpam-5979	349	36	,	,	PUNCT
ejpam-5979	349	37	zeta	zeta	NOUN
ejpam-5979	349	38	,	,	PUNCT
ejpam-5979	349	39	vartheta	vartheta	NOUN
ejpam-5979	349	40	,	,	PUNCT
ejpam-5979	349	41	n	n	CCONJ
ejpam-5979	349	42	)	)	PUNCT
ejpam-5979	349	43	%	%	NOUN
ejpam-5979	349	44	initialization	initialization	NOUN
ejpam-5979	349	45	tau(1	tau(1	NOUN
ejpam-5979	349	46	)	)	PUNCT
ejpam-5979	349	47	=	=	SYM
ejpam-5979	349	48	0	0	NUM
ejpam-5979	349	49	;	;	PUNCT
ejpam-5979	349	50	mu(1	mu(1	NOUN
ejpam-5979	349	51	)	)	PUNCT
ejpam-5979	349	52	=	=	SYM
ejpam-5979	349	53	lambda1	lambda1	PROPN
ejpam-5979	349	54	;	;	PUNCT
ejpam-5979	349	55	delta_tau	delta_tau	PRON
ejpam-5979	349	56	=	=	SYM
ejpam-5979	349	57	vartheta	vartheta	PROPN
ejpam-5979	349	58	/	/	SYM
ejpam-5979	349	59	n	n	CCONJ
ejpam-5979	349	60	;	;	PUNCT
ejpam-5979	349	61	%	%	X
ejpam-5979	349	62	main	main	ADJ
ejpam-5979	349	63	loop	loop	NOUN
ejpam-5979	349	64	for	for	ADP
ejpam-5979	349	65	i	i	PRON
ejpam-5979	349	66	=	=	NOUN
ejpam-5979	349	67	1	1	NUM
ejpam-5979	349	68	:	:	PUNCT
ejpam-5979	349	69	n	n	PRON
ejpam-5979	349	70	k1	k1	NOUN
ejpam-5979	349	71	=	=	PUNCT
ejpam-5979	349	72	delta_tau	delta_tau	X
ejpam-5979	349	73	*	*	PUNCT
ejpam-5979	349	74	(	(	PUNCT
ejpam-5979	349	75	-theta(tau(i	-theta(tau(i	NOUN
ejpam-5979	349	76	)	)	PUNCT
ejpam-5979	349	77	,	,	PUNCT
ejpam-5979	349	78	mu(i	mu(i	NOUN
ejpam-5979	349	79	)	)	PUNCT
ejpam-5979	349	80	)	)	PUNCT
ejpam-5979	349	81	)	)	PUNCT
ejpam-5979	349	82	;	;	PUNCT
ejpam-5979	349	83	k2	k2	X
ejpam-5979	349	84	=	=	PUNCT
ejpam-5979	349	85	delta_tau	delta_tau	PROPN
ejpam-5979	349	86	*	*	PUNCT
ejpam-5979	349	87	(	(	PUNCT
ejpam-5979	349	88	-theta(tau(i	-theta(tau(i	NOUN
ejpam-5979	349	89	)	)	PUNCT
ejpam-5979	349	90	+	+	CCONJ
ejpam-5979	349	91	delta_tau/2	delta_tau/2	ADJ
ejpam-5979	349	92	,	,	PUNCT
ejpam-5979	349	93	mu(i	mu(i	NUM
ejpam-5979	349	94	)	)	PUNCT
ejpam-5979	349	95	+	+	NUM
ejpam-5979	349	96	k1/2	k1/2	NUM
ejpam-5979	349	97	)	)	PUNCT
ejpam-5979	349	98	)	)	PUNCT
ejpam-5979	349	99	;	;	PUNCT
ejpam-5979	349	100	k3	k3	PROPN
ejpam-5979	349	101	=	=	SYM
ejpam-5979	349	102	delta_tau	delta_tau	ADJ
ejpam-5979	349	103	*	*	PUNCT
ejpam-5979	349	104	(	(	PUNCT
ejpam-5979	349	105	-theta(tau(i	-theta(tau(i	NOUN
ejpam-5979	349	106	)	)	PUNCT
ejpam-5979	349	107	+	+	CCONJ
ejpam-5979	349	108	delta_tau/2	delta_tau/2	ADJ
ejpam-5979	349	109	,	,	PUNCT
ejpam-5979	349	110	mu(i	mu(i	ADJ
ejpam-5979	349	111	)	)	PUNCT
ejpam-5979	349	112	+	+	CCONJ
ejpam-5979	349	113	k2/2	k2/2	ADJ
ejpam-5979	349	114	)	)	PUNCT
ejpam-5979	349	115	)	)	PUNCT
ejpam-5979	349	116	;	;	PUNCT
ejpam-5979	349	117	k4	k4	NOUN
ejpam-5979	349	118	=	=	PUNCT
ejpam-5979	349	119	delta_tau	delta_tau	PROPN
ejpam-5979	349	120	*	*	PUNCT
ejpam-5979	349	121	(	(	PUNCT
ejpam-5979	349	122	-theta(tau(i	-theta(tau(i	NOUN
ejpam-5979	349	123	)	)	PUNCT
ejpam-5979	349	124	+	+	CCONJ
ejpam-5979	349	125	delta_tau	delta_tau	PRON
ejpam-5979	349	126	,	,	PUNCT
ejpam-5979	349	127	mu(i	mu(i	NUM
ejpam-5979	349	128	)	)	PUNCT
ejpam-5979	349	129	+	+	CCONJ
ejpam-5979	349	130	k3	k3	ADJ
ejpam-5979	349	131	)	)	PUNCT
ejpam-5979	349	132	)	)	PUNCT
ejpam-5979	349	133	;	;	PUNCT
ejpam-5979	349	134	mu(i+1	mu(i+1	X
ejpam-5979	349	135	)	)	PUNCT
ejpam-5979	349	136	=	=	SYM
ejpam-5979	349	137	mu(i	mu(i	X
ejpam-5979	349	138	)	)	PUNCT
ejpam-5979	349	139	+	+	CCONJ
ejpam-5979	349	140	(	(	PUNCT
ejpam-5979	349	141	1/6	1/6	NUM
ejpam-5979	349	142	)	)	PUNCT
ejpam-5979	349	143	*	*	PUNCT
ejpam-5979	350	1	(	(	PUNCT
ejpam-5979	350	2	k1	k1	NOUN
ejpam-5979	350	3	+	+	CCONJ
ejpam-5979	350	4	2*k2	2*k2	NUM
ejpam-5979	350	5	+	+	CCONJ
ejpam-5979	350	6	2*k3	2*k3	NUM
ejpam-5979	350	7	+	+	CCONJ
ejpam-5979	350	8	k4	k4	NOUN
ejpam-5979	350	9	)	)	PUNCT
ejpam-5979	350	10	;	;	PUNCT
ejpam-5979	350	11	tau(i+1	tau(i+1	NOUN
ejpam-5979	350	12	)	)	PUNCT
ejpam-5979	350	13	=	=	SYM
ejpam-5979	350	14	tau(i	tau(i	NOUN
ejpam-5979	350	15	)	)	PUNCT
ejpam-5979	350	16	+	+	CCONJ
ejpam-5979	350	17	delta_tau	delta_tau	NUM
ejpam-5979	350	18	;	;	PUNCT
ejpam-5979	350	19	end	end	NOUN
ejpam-5979	350	20	end	end	NOUN
ejpam-5979	350	21	z.	z.	PROPN
ejpam-5979	350	22	bekri	bekri	PROPN
ejpam-5979	350	23	et	et	PROPN
ejpam-5979	350	24	al	al	PROPN
ejpam-5979	350	25	.	.	PUNCT
ejpam-5979	350	26	/	/	SYM
ejpam-5979	350	27	eur	eur	PROPN
ejpam-5979	350	28	.	.	PUNCT
ejpam-5979	351	1	j.	j.	PROPN
ejpam-5979	351	2	pure	pure	PROPN
ejpam-5979	351	3	appl	appl	PROPN
ejpam-5979	351	4	.	.	PROPN
ejpam-5979	351	5	math	math	PROPN
ejpam-5979	351	6	,	,	PUNCT
ejpam-5979	351	7	18	18	NUM
ejpam-5979	351	8	(	(	PUNCT
ejpam-5979	351	9	2	2	NUM
ejpam-5979	351	10	)	)	PUNCT
ejpam-5979	351	11	(	(	PUNCT
ejpam-5979	351	12	2025	2025	NUM
ejpam-5979	351	13	)	)	PUNCT
ejpam-5979	351	14	,	,	PUNCT
ejpam-5979	351	15	5979	5979	NUM
ejpam-5979	351	16	19	19	NUM
ejpam-5979	351	17	of	of	ADP
ejpam-5979	351	18	20	20	NUM
ejpam-5979	351	19	algorithm	algorithm	NOUN
ejpam-5979	351	20	2	2	NUM
ejpam-5979	351	21	:	:	PUNCT
ejpam-5979	351	22	the	the	DET
ejpam-5979	351	23	matlab	matlab	PROPN
ejpam-5979	351	24	algorithm	algorithm	NOUN
ejpam-5979	351	25	for	for	ADP
ejpam-5979	351	26	implementing	implement	VERB
ejpam-5979	351	27	the	the	DET
ejpam-5979	351	28	fourth	fourth	ADJ
ejpam-5979	351	29	-	-	PUNCT
ejpam-5979	351	30	order	order	NOUN
ejpam-5979	351	31	runge	runge	NOUN
ejpam-5979	351	32	-	-	PUNCT
ejpam-5979	351	33	kutta	kutta	NOUN
ejpam-5979	351	34	method	method	NOUN
ejpam-5979	351	35	%	%	NOUN
ejpam-5979	351	36	define	define	VERB
ejpam-5979	351	37	the	the	DET
ejpam-5979	351	38	parameters	parameter	NOUN
ejpam-5979	351	39	vartheta	vartheta	NOUN
ejpam-5979	351	40	=	=	NOUN
ejpam-5979	351	41	1	1	NUM
ejpam-5979	351	42	;	;	PUNCT
ejpam-5979	351	43	%	%	NOUN
ejpam-5979	351	44	upper	upper	ADJ
ejpam-5979	351	45	limit	limit	NOUN
ejpam-5979	351	46	rho	rho	NOUN
ejpam-5979	351	47	=	=	SYM
ejpam-5979	351	48	1	1	NUM
ejpam-5979	351	49	;	;	PUNCT
ejpam-5979	351	50	sigma_values	sigma_value	NOUN
ejpam-5979	351	51	=	=	PUNCT
ejpam-5979	352	1	[	[	X
ejpam-5979	352	2	4/3	4/3	NUM
ejpam-5979	352	3	,	,	PUNCT
ejpam-5979	352	4	3/2	3/2	NUM
ejpam-5979	352	5	,	,	PUNCT
ejpam-5979	352	6	9/5	9/5	NUM
ejpam-5979	352	7	,	,	PUNCT
ejpam-5979	352	8	39/20	39/20	NUM
ejpam-5979	352	9	]	]	PUNCT
ejpam-5979	352	10	;	;	PUNCT
ejpam-5979	352	11	%	%	NOUN
ejpam-5979	352	12	values	value	NOUN
ejpam-5979	352	13	of	of	ADP
ejpam-5979	352	14	sigma	sigma	PROPN
ejpam-5979	352	15	zeta	zeta	NOUN
ejpam-5979	352	16	=	=	SYM
ejpam-5979	352	17	1	1	NUM
ejpam-5979	352	18	;	;	PUNCT
ejpam-5979	352	19	%	%	NOUN
ejpam-5979	352	20	constant	constant	ADJ
ejpam-5979	352	21	tau	tau	PROPN
ejpam-5979	352	22	=	=	SYM
ejpam-5979	352	23	linspace(0	linspace(0	PROPN
ejpam-5979	352	24	,	,	PUNCT
ejpam-5979	352	25	vartheta	vartheta	NOUN
ejpam-5979	352	26	,	,	PUNCT
ejpam-5979	352	27	1000	1000	NUM
ejpam-5979	352	28	)	)	PUNCT
ejpam-5979	352	29	;	;	PUNCT
ejpam-5979	352	30	%	%	X
ejpam-5979	352	31	discretize	discretize	VERB
ejpam-5979	352	32	the	the	DET
ejpam-5979	352	33	interval	interval	NOUN
ejpam-5979	352	34	[	[	X
ejpam-5979	352	35	0	0	NUM
ejpam-5979	352	36	,	,	PUNCT
ejpam-5979	352	37	vartheta	vartheta	NOUN
ejpam-5979	352	38	]	]	PUNCT
ejpam-5979	352	39	%	%	NOUN
ejpam-5979	352	40	function	function	NOUN
ejpam-5979	352	41	defining	define	VERB
ejpam-5979	352	42	the	the	DET
ejpam-5979	352	43	differential	differential	ADJ
ejpam-5979	352	44	equation	equation	NOUN
ejpam-5979	352	45	f	f	PROPN
ejpam-5979	352	46	=	=	PUNCT
ejpam-5979	352	47	@(t	@(t	PROPN
ejpam-5979	352	48	,	,	PUNCT
ejpam-5979	352	49	y	y	NOUN
ejpam-5979	352	50	)	)	PUNCT
ejpam-5979	352	51	3	3	NUM
ejpam-5979	352	52	t.^7	t.^7	PROPN
ejpam-5979	352	53	sin(y	sin(y	PROPN
ejpam-5979	352	54	)	)	PUNCT
ejpam-5979	352	55	;	;	PUNCT
ejpam-5979	352	56	%	%	NOUN
ejpam-5979	352	57	initial	initial	ADJ
ejpam-5979	352	58	guess	guess	NOUN
ejpam-5979	352	59	for	for	ADP
ejpam-5979	352	60	the	the	DET
ejpam-5979	352	61	solution	solution	NOUN
ejpam-5979	352	62	init_guess	init_guess	NOUN
ejpam-5979	352	63	=	=	SYM
ejpam-5979	352	64	@(t	@(t	NOUN
ejpam-5979	352	65	)	)	PUNCT
ejpam-5979	352	66	1	1	NUM
ejpam-5979	353	1	+	+	CCONJ
ejpam-5979	353	2	(	(	PUNCT
ejpam-5979	353	3	t	t	PROPN
ejpam-5979	353	4	/	/	SYM
ejpam-5979	353	5	vartheta)*(2	vartheta)*(2	PROPN
ejpam-5979	353	6	-	-	PUNCT
ejpam-5979	353	7	1	1	NUM
ejpam-5979	353	8	)	)	PUNCT
ejpam-5979	353	9	;	;	PUNCT
ejpam-5979	353	10	%	%	AUX
ejpam-5979	353	11	linear	linear	ADJ
ejpam-5979	353	12	interpolation	interpolation	NOUN
ejpam-5979	353	13	between	between	ADP
ejpam-5979	353	14	1	1	NUM
ejpam-5979	353	15	and	and	CCONJ
ejpam-5979	353	16	2	2	NUM
ejpam-5979	353	17	%	%	NOUN
ejpam-5979	353	18	initialize	initialize	NOUN
ejpam-5979	353	19	variable	variable	NOUN
ejpam-5979	353	20	to	to	PART
ejpam-5979	353	21	store	store	VERB
ejpam-5979	353	22	varpi	varpi	ADJ
ejpam-5979	353	23	values	value	NOUN
ejpam-5979	353	24	varpi_values	varpi_value	NOUN
ejpam-5979	353	25	=	=	PUNCT
ejpam-5979	353	26	zeros(1	zeros(1	NOUN
ejpam-5979	353	27	,	,	PUNCT
ejpam-5979	353	28	length(sigma_values	length(sigma_value	NOUN
ejpam-5979	353	29	)	)	PUNCT
ejpam-5979	353	30	)	)	PUNCT
ejpam-5979	353	31	;	;	PUNCT
ejpam-5979	353	32	%	%	NOUN
ejpam-5979	353	33	solve	solve	VERB
ejpam-5979	353	34	the	the	DET
ejpam-5979	353	35	bvp	bvp	NOUN
ejpam-5979	353	36	for	for	ADP
ejpam-5979	353	37	each	each	DET
ejpam-5979	353	38	sigma	sigma	PROPN
ejpam-5979	353	39	value	value	NOUN
ejpam-5979	353	40	for	for	ADP
ejpam-5979	353	41	i	i	PRON
ejpam-5979	353	42	=	=	NOUN
ejpam-5979	353	43	1	1	NUM
ejpam-5979	353	44	:	:	PUNCT
ejpam-5979	353	45	length(sigma_values	length(sigma_values	PROPN
ejpam-5979	353	46	)	)	PUNCT
ejpam-5979	353	47	sigma	sigma	PROPN
ejpam-5979	353	48	=	=	SYM
ejpam-5979	353	49	sigma_values(i	sigma_values(i	PROPN
ejpam-5979	353	50	)	)	PUNCT
ejpam-5979	353	51	;	;	PUNCT
ejpam-5979	353	52	%	%	NOUN
ejpam-5979	353	53	define	define	VERB
ejpam-5979	353	54	the	the	DET
ejpam-5979	353	55	bvp	bvp	NOUN
ejpam-5979	353	56	bvp_eqn	bvp_eqn	NOUN
ejpam-5979	353	57	=	=	SYM
ejpam-5979	353	58	@(t	@(t	PROPN
ejpam-5979	353	59	,	,	PUNCT
ejpam-5979	353	60	y	y	NOUN
ejpam-5979	353	61	)	)	PUNCT
ejpam-5979	354	1	[	[	X
ejpam-5979	354	2	y(2	y(2	NOUN
ejpam-5979	354	3	)	)	PUNCT
ejpam-5979	354	4	;	;	PUNCT
ejpam-5979	354	5	(	(	PUNCT
ejpam-5979	354	6	1/(rho^sigma	1/(rho^sigma	NUM
ejpam-5979	354	7	)	)	PUNCT
ejpam-5979	354	8	)	)	PUNCT
ejpam-5979	355	1	*	*	PUNCT
ejpam-5979	355	2	diff(y(1	diff(y(1	PROPN
ejpam-5979	355	3	)	)	PUNCT
ejpam-5979	355	4	,	,	PUNCT
ejpam-5979	355	5	tau	tau	PROPN
ejpam-5979	355	6	,	,	PUNCT
ejpam-5979	355	7	sigma	sigma	NOUN
ejpam-5979	355	8	)	)	PUNCT
ejpam-5979	355	9	f(t	f(t	PROPN
ejpam-5979	355	10	,	,	PUNCT
ejpam-5979	355	11	y(1	y(1	PROPN
ejpam-5979	355	12	)	)	PUNCT
ejpam-5979	355	13	)	)	PUNCT
ejpam-5979	355	14	]	]	PUNCT
ejpam-5979	355	15	;	;	PUNCT
ejpam-5979	355	16	%	%	INTJ
ejpam-5979	355	17	solve	solve	VERB
ejpam-5979	355	18	the	the	DET
ejpam-5979	355	19	bvp	bvp	NOUN
ejpam-5979	355	20	using	use	VERB
ejpam-5979	355	21	bvp4c	bvp4c	PROPN
ejpam-5979	355	22	sol	sol	NOUN
ejpam-5979	355	23	=	=	PUNCT
ejpam-5979	355	24	bvp4c(bvp_eqn	bvp4c(bvp_eqn	NOUN
ejpam-5979	355	25	,	,	PUNCT
ejpam-5979	355	26	init_guess	init_guess	NOUN
ejpam-5979	355	27	,	,	PUNCT
ejpam-5979	355	28	@bc	@bc	ADJ
ejpam-5979	355	29	,	,	PUNCT
ejpam-5979	355	30	’	'	PUNCT
ejpam-5979	355	31	reltol	reltol	NOUN
ejpam-5979	355	32	’	'	PUNCT
ejpam-5979	355	33	,	,	PUNCT
ejpam-5979	355	34	1e-6	1e-6	PROPN
ejpam-5979	355	35	)	)	PUNCT
ejpam-5979	355	36	;	;	PUNCT
ejpam-5979	355	37	%	%	NOUN
ejpam-5979	355	38	evaluate	evaluate	VERB
ejpam-5979	355	39	the	the	DET
ejpam-5979	355	40	solution	solution	NOUN
ejpam-5979	355	41	at	at	ADP
ejpam-5979	355	42	tau	tau	PROPN
ejpam-5979	355	43	mu	mu	NOUN
ejpam-5979	355	44	=	=	PUNCT
ejpam-5979	355	45	deval(sol	deval(sol	PROPN
ejpam-5979	355	46	,	,	PUNCT
ejpam-5979	355	47	tau	tau	PROPN
ejpam-5979	355	48	)	)	PUNCT
ejpam-5979	355	49	;	;	PUNCT
ejpam-5979	355	50	%	%	NOUN
ejpam-5979	355	51	calculate	calculate	NOUN
ejpam-5979	355	52	varpi	varpi	PROPN
ejpam-5979	355	53	varpi_values(i	varpi_values(i	PROPN
ejpam-5979	355	54	)	)	PUNCT
ejpam-5979	355	55	=	=	SYM
ejpam-5979	356	1	(	(	PUNCT
ejpam-5979	356	2	zeta	zeta	PROPN
ejpam-5979	356	3	/	/	SYM
ejpam-5979	356	4	(	(	PUNCT
ejpam-5979	356	5	rho^sigma	rho^sigma	PROPN
ejpam-5979	356	6	*	*	PUNCT
ejpam-5979	356	7	gamma(sigma+1	gamma(sigma+1	PROPN
ejpam-5979	356	8	)	)	PUNCT
ejpam-5979	356	9	)	)	PUNCT
ejpam-5979	356	10	)	)	PUNCT
ejpam-5979	357	1	*	*	PUNCT
ejpam-5979	357	2	...	...	PUNCT
ejpam-5979	357	3	(	(	PUNCT
ejpam-5979	357	4	vartheta^(rho*sigma	vartheta^(rho*sigma	X
ejpam-5979	357	5	)	)	PUNCT
ejpam-5979	357	6	/	/	SYM
ejpam-5979	357	7	sigma^(1/(sigma-1	sigma^(1/(sigma-1	PROPN
ejpam-5979	357	8	)	)	PUNCT
ejpam-5979	357	9	)	)	PUNCT
ejpam-5979	357	10	...	...	PUNCT
ejpam-5979	358	1	vartheta^(rho*sigma	vartheta^(rho*sigma	X
ejpam-5979	358	2	)	)	PUNCT
ejpam-5979	358	3	/	/	SYM
ejpam-5979	358	4	sigma^(sigma/(sigma-1	sigma^(sigma/(sigma-1	NOUN
ejpam-5979	358	5	)	)	PUNCT
ejpam-5979	358	6	)	)	PUNCT
ejpam-5979	358	7	)	)	PUNCT
ejpam-5979	358	8	;	;	PUNCT
ejpam-5979	358	9	end	end	NOUN
ejpam-5979	358	10	%	%	NOUN
ejpam-5979	358	11	display	display	NOUN
ejpam-5979	358	12	varpi	varpi	NOUN
ejpam-5979	358	13	values	value	NOUN
ejpam-5979	358	14	disp(’numerical	disp(’numerical	PROPN
ejpam-5979	358	15	␣	␣	ADJ
ejpam-5979	358	16	results	result	NOUN
ejpam-5979	358	17	␣	␣	ADJ
ejpam-5979	358	18	varpi	varpi	NOUN
ejpam-5979	358	19	␣	␣	ADJ
ejpam-5979	358	20	for	for	ADP
ejpam-5979	358	21	␣	␣	ADJ
ejpam-5979	358	22	different	different	ADJ
ejpam-5979	358	23	␣	␣	ADJ
ejpam-5979	358	24	sigma	sigma	PROPN
ejpam-5979	358	25	:’)	:’)	PUNCT
ejpam-5979	358	26	;	;	PUNCT
ejpam-5979	358	27	disp(’sigma	disp(’sigma	PROPN
ejpam-5979	358	28	␣	␣	PROPN
ejpam-5979	358	29	␣	␣	ADJ
ejpam-5979	358	30	␣	␣	PROPN
ejpam-5979	358	31	␣	␣	PROPN
ejpam-5979	358	32	␣	␣	ADJ
ejpam-5979	358	33	␣	␣	ADJ
ejpam-5979	358	34	␣	␣	ADJ
ejpam-5979	358	35	varpi	varpi	NOUN
ejpam-5979	358	36	’	'	PUNCT
ejpam-5979	358	37	)	)	PUNCT
ejpam-5979	358	38	;	;	PUNCT
ejpam-5979	359	1	for	for	ADP
ejpam-5979	359	2	i	i	PRON
ejpam-5979	359	3	=	=	NOUN
ejpam-5979	359	4	1	1	NUM
ejpam-5979	359	5	:	:	PUNCT
ejpam-5979	359	6	length(sigma_values	length(sigma_value	NOUN
ejpam-5979	359	7	)	)	PUNCT
ejpam-5979	360	1	fprintf(’%5.4f	fprintf(’%5.4f	PROPN
ejpam-5979	360	2	␣	␣	PROPN
ejpam-5979	360	3	␣	␣	PROPN
ejpam-5979	360	4	␣	␣	ADJ
ejpam-5979	360	5	␣	␣	ADJ
ejpam-5979	360	6	%8.4f\n	%8.4f\n	NOUN
ejpam-5979	360	7	’	'	PUNCT
ejpam-5979	360	8	,	,	PUNCT
ejpam-5979	360	9	sigma_values(i	sigma_values(i	PROPN
ejpam-5979	360	10	)	)	PUNCT
ejpam-5979	360	11	,	,	PUNCT
ejpam-5979	360	12	varpi_values(i	varpi_values(i	NOUN
ejpam-5979	360	13	)	)	PUNCT
ejpam-5979	360	14	)	)	PUNCT
ejpam-5979	360	15	;	;	PUNCT
ejpam-5979	360	16	end	end	NOUN
ejpam-5979	360	17	%	%	NOUN
ejpam-5979	360	18	function	function	NOUN
ejpam-5979	360	19	for	for	ADP
ejpam-5979	360	20	boundary	boundary	ADJ
ejpam-5979	360	21	conditions	condition	NOUN
ejpam-5979	360	22	function	function	VERB
ejpam-5979	360	23	res	re	NOUN
ejpam-5979	360	24	=	=	PUNCT
ejpam-5979	360	25	bc(ya	bc(ya	PROPN
ejpam-5979	360	26	,	,	PUNCT
ejpam-5979	360	27	yb	yb	PROPN
ejpam-5979	360	28	)	)	PUNCT
ejpam-5979	360	29	res	re	NOUN
ejpam-5979	360	30	=	=	PUNCT
ejpam-5979	361	1	[	[	X
ejpam-5979	361	2	ya(1	ya(1	NOUN
ejpam-5979	361	3	)	)	PUNCT
ejpam-5979	361	4	1	1	NUM
ejpam-5979	361	5	;	;	PUNCT
ejpam-5979	361	6	yb(1	yb(1	PROPN
ejpam-5979	361	7	)	)	PUNCT
ejpam-5979	361	8	2	2	NUM
ejpam-5979	361	9	]	]	PUNCT
ejpam-5979	361	10	;	;	PUNCT
ejpam-5979	361	11	end	end	NOUN
ejpam-5979	361	12	z.	z.	PROPN
ejpam-5979	361	13	bekri	bekri	PROPN
ejpam-5979	361	14	et	et	PROPN
ejpam-5979	361	15	al	al	PROPN
ejpam-5979	361	16	.	.	PUNCT
ejpam-5979	361	17	/	/	SYM
ejpam-5979	361	18	eur	eur	PROPN
ejpam-5979	361	19	.	.	PUNCT
ejpam-5979	362	1	j.	j.	PROPN
ejpam-5979	362	2	pure	pure	PROPN
ejpam-5979	362	3	appl	appl	PROPN
ejpam-5979	362	4	.	.	PROPN
ejpam-5979	362	5	math	math	PROPN
ejpam-5979	362	6	,	,	PUNCT
ejpam-5979	362	7	18	18	NUM
ejpam-5979	362	8	(	(	PUNCT
ejpam-5979	362	9	2	2	NUM
ejpam-5979	362	10	)	)	PUNCT
ejpam-5979	362	11	(	(	PUNCT
ejpam-5979	362	12	2025	2025	NUM
ejpam-5979	362	13	)	)	PUNCT
ejpam-5979	362	14	,	,	PUNCT
ejpam-5979	362	15	5979	5979	NUM
ejpam-5979	362	16	20	20	NUM
ejpam-5979	362	17	of	of	ADP
ejpam-5979	362	18	20	20	NUM
ejpam-5979	362	19	algorithm	algorithm	NOUN
ejpam-5979	362	20	3	3	NUM
ejpam-5979	362	21	:	:	PUNCT
ejpam-5979	362	22	the	the	DET
ejpam-5979	362	23	matlab	matlab	PROPN
ejpam-5979	362	24	code	code	NOUN
ejpam-5979	362	25	to	to	PART
ejpam-5979	362	26	solve	solve	VERB
ejpam-5979	362	27	the	the	DET
ejpam-5979	362	28	bvp	bvp	NOUN
ejpam-5979	362	29	numerically	numerically	ADV
ejpam-5979	362	30	and	and	CCONJ
ejpam-5979	362	31	obtain	obtain	VERB
ejpam-5979	362	32	the	the	DET
ejpam-5979	362	33	solution	solution	NOUN
ejpam-5979	362	34	for	for	ADP
ejpam-5979	362	35	µ(τ	µ(τ	NOUN
ejpam-5979	362	36	)	)	PUNCT
ejpam-5979	362	37	and	and	CCONJ
ejpam-5979	362	38	θ(τ	θ(τ	PROPN
ejpam-5979	362	39	,	,	PUNCT
ejpam-5979	362	40	µ(τ	µ(τ	PROPN
ejpam-5979	362	41	)	)	PUNCT
ejpam-5979	362	42	)	)	PUNCT
ejpam-5979	362	43	.	.	PUNCT
ejpam-5979	363	1	%	%	INTJ
ejpam-5979	363	2	define	define	VERB
ejpam-5979	363	3	parameters	parameter	NOUN
ejpam-5979	363	4	theta	theta	NOUN
ejpam-5979	363	5	=	=	SYM
ejpam-5979	363	6	1	1	NUM
ejpam-5979	363	7	;	;	PUNCT
ejpam-5979	363	8	sigma	sigma	PROPN
ejpam-5979	363	9	=	=	SYM
ejpam-5979	363	10	4/3	4/3	NUM
ejpam-5979	363	11	;	;	PUNCT
ejpam-5979	363	12	zeta	zeta	NOUN
ejpam-5979	363	13	=	=	SYM
ejpam-5979	363	14	0.1244291811338	0.1244291811338	NUM
ejpam-5979	363	15	;	;	PUNCT
ejpam-5979	363	16	%	%	NOUN
ejpam-5979	363	17	define	define	VERB
ejpam-5979	363	18	boundary	boundary	ADJ
ejpam-5979	363	19	value	value	NOUN
ejpam-5979	363	20	problem	problem	NOUN
ejpam-5979	363	21	equations	equation	NOUN
ejpam-5979	363	22	function	function	VERB
ejpam-5979	363	23	res	re	NOUN
ejpam-5979	363	24	=	=	SYM
ejpam-5979	363	25	bvp_equations(t	bvp_equations(t	PROPN
ejpam-5979	363	26	,	,	PUNCT
ejpam-5979	363	27	y	y	NOUN
ejpam-5979	363	28	)	)	PUNCT
ejpam-5979	363	29	res	re	NOUN
ejpam-5979	363	30	=	=	SYM
ejpam-5979	363	31	(	(	PUNCT
ejpam-5979	363	32	4	4	NUM
ejpam-5979	363	33	t.^5	t.^5	PROPN
ejpam-5979	363	34	+	+	X
ejpam-5979	363	35	cos(y)).^(3/4	cos(y)).^(3/4	PROPN
ejpam-5979	363	36	)	)	PUNCT
ejpam-5979	363	37	;	;	PUNCT
ejpam-5979	363	38	end	end	VERB
ejpam-5979	363	39	%	%	NOUN
ejpam-5979	363	40	define	define	VERB
ejpam-5979	363	41	boundary	boundary	ADJ
ejpam-5979	363	42	conditions	condition	NOUN
ejpam-5979	363	43	function	function	VERB
ejpam-5979	363	44	res	re	NOUN
ejpam-5979	363	45	=	=	SYM
ejpam-5979	363	46	bvp_bc(ya	bvp_bc(ya	NOUN
ejpam-5979	363	47	,	,	PUNCT
ejpam-5979	363	48	yb	yb	PROPN
ejpam-5979	363	49	)	)	PUNCT
ejpam-5979	363	50	res	re	NOUN
ejpam-5979	363	51	=	=	PUNCT
ejpam-5979	364	1	[	[	X
ejpam-5979	364	2	ya(1	ya(1	NOUN
ejpam-5979	364	3	)	)	PUNCT
ejpam-5979	364	4	3	3	NUM
ejpam-5979	364	5	;	;	PUNCT
ejpam-5979	364	6	yb(1	yb(1	PROPN
ejpam-5979	364	7	)	)	PUNCT
ejpam-5979	364	8	4	4	NUM
ejpam-5979	364	9	]	]	PUNCT
ejpam-5979	364	10	;	;	PUNCT
ejpam-5979	364	11	end	end	VERB
ejpam-5979	364	12	%	%	NOUN
ejpam-5979	364	13	define	define	VERB
ejpam-5979	364	14	theta	theta	NOUN
ejpam-5979	364	15	function	function	NOUN
ejpam-5979	364	16	function	function	NOUN
ejpam-5979	364	17	res	re	NOUN
ejpam-5979	364	18	=	=	SYM
ejpam-5979	364	19	theta_function(t	theta_function(t	PROPN
ejpam-5979	364	20	,	,	PUNCT
ejpam-5979	364	21	y	y	NOUN
ejpam-5979	364	22	)	)	PUNCT
ejpam-5979	364	23	res	re	NOUN
ejpam-5979	364	24	=	=	PUNCT
ejpam-5979	365	1	t.^5	t.^5	PROPN
ejpam-5979	365	2	4	4	NUM
ejpam-5979	365	3	cos(y	cos(y	NOUN
ejpam-5979	365	4	)	)	PUNCT
ejpam-5979	365	5	;	;	PUNCT
ejpam-5979	365	6	end	end	VERB
ejpam-5979	365	7	%	%	NOUN
ejpam-5979	365	8	define	define	NOUN
ejpam-5979	365	9	range	range	NOUN
ejpam-5979	365	10	for	for	ADP
ejpam-5979	365	11	tau	tau	PROPN
ejpam-5979	365	12	tau_values	tau_value	NOUN
ejpam-5979	365	13	=	=	SYM
ejpam-5979	365	14	linspace(0	linspace(0	PROPN
ejpam-5979	365	15	,	,	PUNCT
ejpam-5979	365	16	theta	theta	NOUN
ejpam-5979	365	17	,	,	PUNCT
ejpam-5979	365	18	100	100	NUM
ejpam-5979	365	19	)	)	PUNCT
ejpam-5979	365	20	;	;	PUNCT
ejpam-5979	365	21	%	%	NOUN
ejpam-5979	365	22	solve	solve	VERB
ejpam-5979	365	23	the	the	DET
ejpam-5979	365	24	boundary	boundary	ADJ
ejpam-5979	365	25	value	value	NOUN
ejpam-5979	365	26	problem	problem	NOUN
ejpam-5979	365	27	sol	sol	NOUN
ejpam-5979	365	28	=	=	NOUN
ejpam-5979	365	29	bvp4c(@bvp_equations	bvp4c(@bvp_equation	NOUN
ejpam-5979	365	30	,	,	PUNCT
ejpam-5979	365	31	@bvp_bc	@bvp_bc	NOUN
ejpam-5979	365	32	,	,	PUNCT
ejpam-5979	365	33	[	[	X
ejpam-5979	365	34	0	0	NUM
ejpam-5979	365	35	theta	theta	NOUN
ejpam-5979	365	36	]	]	PUNCT
ejpam-5979	365	37	)	)	PUNCT
ejpam-5979	365	38	;	;	PUNCT
ejpam-5979	365	39	%	%	NOUN
ejpam-5979	365	40	extract	extract	VERB
ejpam-5979	365	41	the	the	DET
ejpam-5979	365	42	solution	solution	NOUN
ejpam-5979	365	43	mu_solution_values	mu_solution_value	NOUN
ejpam-5979	365	44	=	=	SYM
ejpam-5979	365	45	sol.y(1	sol.y(1	PROPN
ejpam-5979	365	46	,	,	PUNCT
ejpam-5979	365	47	tau_values	tau_value	NOUN
ejpam-5979	365	48	)	)	PUNCT
ejpam-5979	365	49	;	;	PUNCT
ejpam-5979	365	50	%	%	NOUN
ejpam-5979	365	51	calculate	calculate	NOUN
ejpam-5979	365	52	theta	theta	NOUN
ejpam-5979	365	53	theta_values	theta_value	NOUN
ejpam-5979	365	54	=	=	SYM
ejpam-5979	365	55	theta_function(tau_values	theta_function(tau_values	ADV
ejpam-5979	365	56	,	,	PUNCT
ejpam-5979	365	57	mu_solution_values	mu_solution_value	NOUN
ejpam-5979	365	58	)	)	PUNCT
ejpam-5979	365	59	;	;	PUNCT
ejpam-5979	365	60	%	%	NOUN
ejpam-5979	365	61	display	display	NOUN
ejpam-5979	365	62	table	table	NOUN
ejpam-5979	365	63	fprintf(’tau	fprintf(’tau	PROPN
ejpam-5979	365	64	␣	␣	PROPN
ejpam-5979	365	65	␣	␣	ADJ
ejpam-5979	365	66	␣	␣	ADJ
ejpam-5979	365	67	␣	␣	ADJ
ejpam-5979	365	68	|	|	ADJ
ejpam-5979	365	69	␣	␣	ADJ
ejpam-5979	365	70	␣	␣	PROPN
ejpam-5979	365	71	␣	␣	ADJ
ejpam-5979	365	72	mu(tau)	mu(tau)	PROPN
ejpam-5979	365	73	␣	␣	PROPN
ejpam-5979	365	74	␣	␣	PROPN
ejpam-5979	365	75	␣	␣	ADJ
ejpam-5979	365	76	|	|	ADJ
ejpam-5979	365	77	␣	␣	ADJ
ejpam-5979	365	78	␣	␣	ADJ
ejpam-5979	365	79	␣	␣	ADJ
ejpam-5979	365	80	theta(tau,	theta(tau,	ADJ
ejpam-5979	365	81	␣	␣	ADJ
ejpam-5979	365	82	mu(tau))\n	mu(tau))\n	NOUN
ejpam-5979	365	83	’	'	PUNCT
ejpam-5979	365	84	)	)	PUNCT
ejpam-5979	365	85	;	;	PUNCT
ejpam-5979	365	86	fprintf(’--------------------------------------------\n	fprintf(’--------------------------------------------\n	VERB
ejpam-5979	365	87	’	'	PUNCT
ejpam-5979	365	88	)	)	PUNCT
ejpam-5979	365	89	;	;	PUNCT
ejpam-5979	365	90	for	for	ADP
ejpam-5979	365	91	i	i	PRON
ejpam-5979	365	92	=	=	NOUN
ejpam-5979	365	93	1	1	NUM
ejpam-5979	365	94	:	:	PUNCT
ejpam-5979	365	95	length(tau_values	length(tau_values	PROPN
ejpam-5979	365	96	)	)	PUNCT
ejpam-5979	365	97	fprintf(’%.4f	fprintf(’%.4f	PROPN
ejpam-5979	365	98	␣	␣	ADJ
ejpam-5979	365	99	|	|	ADJ
ejpam-5979	365	100	␣	␣	ADJ
ejpam-5979	365	101	%.4f	%.4f	NOUN
ejpam-5979	365	102	␣	␣	ADJ
ejpam-5979	365	103	|	|	NOUN
ejpam-5979	365	104	␣	␣	NOUN
ejpam-5979	365	105	%.4f\n	%.4f\n	NOUN
ejpam-5979	365	106	’	'	PUNCT
ejpam-5979	365	107	,	,	PUNCT
ejpam-5979	365	108	tau_values(i	tau_values(i	PROPN
ejpam-5979	365	109	)	)	PUNCT
ejpam-5979	365	110	,	,	PUNCT
ejpam-5979	365	111	mu_solution_values(i	mu_solution_values(i	NOUN
ejpam-5979	365	112	)	)	PUNCT
ejpam-5979	365	113	,	,	PUNCT
ejpam-5979	365	114	theta_values(i	theta_values(i	NOUN
ejpam-5979	365	115	)	)	PUNCT
ejpam-5979	365	116	)	)	PUNCT
ejpam-5979	365	117	;	;	PUNCT
ejpam-5979	365	118	end	end	VERB