id	sid	tid	token	lemma	pos
ejpam-6617	1	1	european	european	PROPN
ejpam-6617	1	2	journal	journal	PROPN
ejpam-6617	1	3	of	of	ADP
ejpam-6617	1	4	pure	pure	ADJ
ejpam-6617	1	5	and	and	CCONJ
ejpam-6617	1	6	applied	applied	ADJ
ejpam-6617	1	7	mathematics	mathematic	NOUN
ejpam-6617	1	8	2025	2025	NUM
ejpam-6617	1	9	,	,	PUNCT
ejpam-6617	1	10	vol	vol	NOUN
ejpam-6617	1	11	.	.	PROPN
ejpam-6617	1	12	18	18	NUM
ejpam-6617	1	13	,	,	PUNCT
ejpam-6617	1	14	issue	issue	NOUN
ejpam-6617	1	15	3	3	NUM
ejpam-6617	1	16	,	,	PUNCT
ejpam-6617	1	17	article	article	NOUN
ejpam-6617	1	18	number	number	NOUN
ejpam-6617	1	19	6617	6617	NUM
ejpam-6617	1	20	issn	issn	PROPN
ejpam-6617	1	21	1307	1307	NUM
ejpam-6617	1	22	-	-	SYM
ejpam-6617	1	23	5543	5543	NUM
ejpam-6617	1	24	–	–	PUNCT
ejpam-6617	1	25	ejpam.com	ejpam.com	X
ejpam-6617	1	26	published	publish	VERB
ejpam-6617	1	27	by	by	ADP
ejpam-6617	1	28	new	new	PROPN
ejpam-6617	1	29	york	york	PROPN
ejpam-6617	1	30	business	business	PROPN
ejpam-6617	1	31	global	global	PROPN
ejpam-6617	1	32	a	a	DET
ejpam-6617	1	33	fractional	fractional	ADJ
ejpam-6617	1	34	calculus	calculus	NOUN
ejpam-6617	1	35	approach	approach	NOUN
ejpam-6617	1	36	to	to	ADP
ejpam-6617	1	37	interval	interval	NOUN
ejpam-6617	1	38	-	-	PUNCT
ejpam-6617	1	39	valued	value	VERB
ejpam-6617	1	40	variational	variational	ADJ
ejpam-6617	1	41	programming	programming	NOUN
ejpam-6617	1	42	problems	problem	NOUN
ejpam-6617	1	43	vivekananda	vivekananda	PROPN
ejpam-6617	1	44	rayanki1	rayanki1	PROPN
ejpam-6617	1	45	,	,	PUNCT
ejpam-6617	1	46	krishna	krishna	PROPN
ejpam-6617	1	47	kummari2	kummari2	PROPN
ejpam-6617	1	48	,	,	PUNCT
ejpam-6617	1	49	izhar	izhar	PROPN
ejpam-6617	1	50	ahmad3,4	ahmad3,4	PROPN
ejpam-6617	1	51	,	,	PUNCT
ejpam-6617	1	52	thiti	thiti	PROPN
ejpam-6617	1	53	gaketem5,∗	gaketem5,∗	PROPN
ejpam-6617	1	54	1	1	NUM
ejpam-6617	1	55	department	department	NOUN
ejpam-6617	1	56	of	of	ADP
ejpam-6617	1	57	mathematics	mathematic	NOUN
ejpam-6617	1	58	,	,	PUNCT
ejpam-6617	1	59	vallurupalli	vallurupalli	VERB
ejpam-6617	1	60	nageswara	nageswara	PROPN
ejpam-6617	1	61	rao	rao	PROPN
ejpam-6617	1	62	vignana	vignana	PROPN
ejpam-6617	1	63	jyothi	jyothi	PROPN
ejpam-6617	1	64	institute	institute	PROPN
ejpam-6617	1	65	of	of	ADP
ejpam-6617	1	66	engineering	engineering	NOUN
ejpam-6617	1	67	and	and	CCONJ
ejpam-6617	1	68	technology	technology	NOUN
ejpam-6617	1	69	,	,	PUNCT
ejpam-6617	1	70	vignana	vignana	PROPN
ejpam-6617	1	71	jyothi	jyothi	PROPN
ejpam-6617	1	72	nagar	nagar	PROPN
ejpam-6617	1	73	,	,	PUNCT
ejpam-6617	1	74	pragathi	pragathi	NOUN
ejpam-6617	1	75	nagar	nagar	NOUN
ejpam-6617	1	76	,	,	PUNCT
ejpam-6617	1	77	hyderabad	hyderabad	PROPN
ejpam-6617	1	78	500090	500090	NUM
ejpam-6617	1	79	,	,	PUNCT
ejpam-6617	1	80	telangana	telangana	PROPN
ejpam-6617	1	81	,	,	PUNCT
ejpam-6617	1	82	india	india	PROPN
ejpam-6617	1	83	2	2	NUM
ejpam-6617	1	84	department	department	NOUN
ejpam-6617	1	85	of	of	ADP
ejpam-6617	1	86	mathematics	mathematic	NOUN
ejpam-6617	1	87	,	,	PUNCT
ejpam-6617	1	88	school	school	NOUN
ejpam-6617	1	89	of	of	ADP
ejpam-6617	1	90	science	science	NOUN
ejpam-6617	1	91	,	,	PUNCT
ejpam-6617	1	92	gitam	gitam	NOUN
ejpam-6617	1	93	-	-	PUNCT
ejpam-6617	1	94	hyderabad	hyderabad	NOUN
ejpam-6617	1	95	campus	campus	NOUN
ejpam-6617	1	96	,	,	PUNCT
ejpam-6617	1	97	hyderabad-502329	hyderabad-502329	PROPN
ejpam-6617	1	98	,	,	PUNCT
ejpam-6617	1	99	india	india	PROPN
ejpam-6617	1	100	.	.	PROPN
ejpam-6617	1	101	3	3	NUM
ejpam-6617	1	102	department	department	NOUN
ejpam-6617	1	103	of	of	ADP
ejpam-6617	1	104	mathematics	mathematic	NOUN
ejpam-6617	1	105	,	,	PUNCT
ejpam-6617	1	106	king	king	PROPN
ejpam-6617	1	107	fahd	fahd	PROPN
ejpam-6617	1	108	university	university	PROPN
ejpam-6617	1	109	of	of	ADP
ejpam-6617	1	110	petroleum	petroleum	NOUN
ejpam-6617	1	111	and	and	CCONJ
ejpam-6617	1	112	minerals	mineral	NOUN
ejpam-6617	1	113	,	,	PUNCT
ejpam-6617	1	114	dhahran	dhahran	ADJ
ejpam-6617	1	115	31261	31261	NUM
ejpam-6617	1	116	,	,	PUNCT
ejpam-6617	1	117	saudi	saudi	PROPN
ejpam-6617	1	118	arabia	arabia	PROPN
ejpam-6617	1	119	4	4	NUM
ejpam-6617	1	120	center	center	NOUN
ejpam-6617	1	121	for	for	ADP
ejpam-6617	1	122	intelligent	intelligent	ADJ
ejpam-6617	1	123	secure	secure	ADJ
ejpam-6617	1	124	systems	system	NOUN
ejpam-6617	1	125	,	,	PUNCT
ejpam-6617	1	126	king	king	PROPN
ejpam-6617	1	127	fahd	fahd	PROPN
ejpam-6617	1	128	university	university	PROPN
ejpam-6617	1	129	of	of	ADP
ejpam-6617	1	130	petroleum	petroleum	NOUN
ejpam-6617	1	131	and	and	CCONJ
ejpam-6617	1	132	minerals	mineral	NOUN
ejpam-6617	1	133	,	,	PUNCT
ejpam-6617	1	134	dhahran	dhahran	ADJ
ejpam-6617	1	135	31261	31261	NUM
ejpam-6617	1	136	,	,	PUNCT
ejpam-6617	1	137	saudi	saudi	PROPN
ejpam-6617	1	138	arabia	arabia	PROPN
ejpam-6617	1	139	5	5	NUM
ejpam-6617	1	140	department	department	NOUN
ejpam-6617	1	141	of	of	ADP
ejpam-6617	1	142	mathematics	mathematic	NOUN
ejpam-6617	1	143	,	,	PUNCT
ejpam-6617	1	144	school	school	NOUN
ejpam-6617	1	145	of	of	ADP
ejpam-6617	1	146	science	science	NOUN
ejpam-6617	1	147	,	,	PUNCT
ejpam-6617	1	148	university	university	NOUN
ejpam-6617	1	149	of	of	ADP
ejpam-6617	1	150	phayao	phayao	NOUN
ejpam-6617	1	151	,	,	PUNCT
ejpam-6617	1	152	phayao	phayao	NOUN
ejpam-6617	1	153	56000	56000	NUM
ejpam-6617	1	154	,	,	PUNCT
ejpam-6617	1	155	thailand	thailand	PROPN
ejpam-6617	1	156	abstract	abstract	NOUN
ejpam-6617	1	157	.	.	PUNCT
ejpam-6617	2	1	this	this	DET
ejpam-6617	2	2	study	study	NOUN
ejpam-6617	2	3	explores	explore	VERB
ejpam-6617	2	4	a	a	DET
ejpam-6617	2	5	class	class	NOUN
ejpam-6617	2	6	of	of	ADP
ejpam-6617	2	7	fractional	fractional	ADJ
ejpam-6617	2	8	interval	interval	NOUN
ejpam-6617	2	9	-	-	PUNCT
ejpam-6617	2	10	valued	value	VERB
ejpam-6617	2	11	variational	variational	ADJ
ejpam-6617	2	12	programming	programming	NOUN
ejpam-6617	2	13	problems	problem	NOUN
ejpam-6617	2	14	involving	involve	VERB
ejpam-6617	2	15	the	the	DET
ejpam-6617	2	16	caputo	caputo	PROPN
ejpam-6617	2	17	-	-	PUNCT
ejpam-6617	2	18	fabrizio	fabrizio	PROPN
ejpam-6617	2	19	(	(	PUNCT
ejpam-6617	2	20	c	c	NOUN
ejpam-6617	2	21	-	-	PUNCT
ejpam-6617	2	22	f	f	ADJ
ejpam-6617	2	23	)	)	PUNCT
ejpam-6617	2	24	fractional	fractional	ADJ
ejpam-6617	2	25	derivative	derivative	NOUN
ejpam-6617	2	26	.	.	PUNCT
ejpam-6617	3	1	by	by	ADP
ejpam-6617	3	2	employing	employ	VERB
ejpam-6617	3	3	the	the	DET
ejpam-6617	3	4	concepts	concept	NOUN
ejpam-6617	3	5	of	of	ADP
ejpam-6617	3	6	invex	invex	NOUN
ejpam-6617	3	7	and	and	CCONJ
ejpam-6617	3	8	generalized	generalized	ADJ
ejpam-6617	3	9	invex	invex	NOUN
ejpam-6617	3	10	functions	function	NOUN
ejpam-6617	3	11	,	,	PUNCT
ejpam-6617	3	12	we	we	PRON
ejpam-6617	3	13	establish	establish	VERB
ejpam-6617	3	14	sufficient	sufficient	ADJ
ejpam-6617	3	15	optimality	optimality	NOUN
ejpam-6617	3	16	conditions	condition	NOUN
ejpam-6617	3	17	for	for	ADP
ejpam-6617	3	18	these	these	DET
ejpam-6617	3	19	problems	problem	NOUN
ejpam-6617	3	20	.	.	PUNCT
ejpam-6617	4	1	additionally	additionally	ADV
ejpam-6617	4	2	,	,	PUNCT
ejpam-6617	4	3	we	we	PRON
ejpam-6617	4	4	develop	develop	VERB
ejpam-6617	4	5	a	a	DET
ejpam-6617	4	6	wolfe	wolfe	NOUN
ejpam-6617	4	7	-	-	PUNCT
ejpam-6617	4	8	type	type	NOUN
ejpam-6617	4	9	dual	dual	ADJ
ejpam-6617	4	10	formulation	formulation	NOUN
ejpam-6617	4	11	and	and	CCONJ
ejpam-6617	4	12	investigate	investigate	VERB
ejpam-6617	4	13	the	the	DET
ejpam-6617	4	14	corresponding	corresponding	ADJ
ejpam-6617	4	15	duality	duality	NOUN
ejpam-6617	4	16	relationships	relationship	NOUN
ejpam-6617	4	17	.	.	PUNCT
ejpam-6617	5	1	in	in	ADP
ejpam-6617	5	2	particular	particular	ADJ
ejpam-6617	5	3	,	,	PUNCT
ejpam-6617	5	4	we	we	PRON
ejpam-6617	5	5	derive	derive	VERB
ejpam-6617	5	6	and	and	CCONJ
ejpam-6617	5	7	prove	prove	VERB
ejpam-6617	5	8	the	the	DET
ejpam-6617	5	9	weak	weak	ADJ
ejpam-6617	5	10	,	,	PUNCT
ejpam-6617	5	11	strong	strong	ADJ
ejpam-6617	5	12	,	,	PUNCT
ejpam-6617	5	13	and	and	CCONJ
ejpam-6617	5	14	converse	converse	NOUN
ejpam-6617	5	15	duality	duality	NOUN
ejpam-6617	5	16	theorems	theorem	VERB
ejpam-6617	5	17	to	to	PART
ejpam-6617	5	18	establish	establish	VERB
ejpam-6617	5	19	a	a	DET
ejpam-6617	5	20	connection	connection	NOUN
ejpam-6617	5	21	between	between	ADP
ejpam-6617	5	22	the	the	DET
ejpam-6617	5	23	primal	primal	ADJ
ejpam-6617	5	24	and	and	CCONJ
ejpam-6617	5	25	dual	dual	ADJ
ejpam-6617	5	26	problems	problem	NOUN
ejpam-6617	5	27	.	.	PUNCT
ejpam-6617	6	1	the	the	DET
ejpam-6617	6	2	theoretical	theoretical	ADJ
ejpam-6617	6	3	findings	finding	NOUN
ejpam-6617	6	4	are	be	AUX
ejpam-6617	6	5	further	far	ADV
ejpam-6617	6	6	illustrated	illustrate	VERB
ejpam-6617	6	7	through	through	ADP
ejpam-6617	6	8	carefully	carefully	ADV
ejpam-6617	6	9	constructed	construct	VERB
ejpam-6617	6	10	numerical	numerical	ADJ
ejpam-6617	6	11	examples	example	NOUN
ejpam-6617	6	12	,	,	PUNCT
ejpam-6617	6	13	demonstrating	demonstrate	VERB
ejpam-6617	6	14	the	the	DET
ejpam-6617	6	15	applicability	applicability	NOUN
ejpam-6617	6	16	and	and	CCONJ
ejpam-6617	6	17	effectiveness	effectiveness	NOUN
ejpam-6617	6	18	of	of	ADP
ejpam-6617	6	19	the	the	DET
ejpam-6617	6	20	proposed	propose	VERB
ejpam-6617	6	21	approach	approach	NOUN
ejpam-6617	6	22	.	.	PUNCT
ejpam-6617	7	1	2020	2020	NUM
ejpam-6617	7	2	mathematics	mathematic	NOUN
ejpam-6617	7	3	subject	subject	NOUN
ejpam-6617	7	4	classifications	classification	NOUN
ejpam-6617	7	5	:	:	PUNCT
ejpam-6617	7	6	26a51	26a51	NUM
ejpam-6617	7	7	,	,	PUNCT
ejpam-6617	7	8	49j40	49j40	NUM
ejpam-6617	7	9	,	,	PUNCT
ejpam-6617	7	10	49k99	49k99	NUM
ejpam-6617	7	11	,	,	PUNCT
ejpam-6617	7	12	90c46	90c46	NUM
ejpam-6617	7	13	key	key	ADJ
ejpam-6617	7	14	words	word	NOUN
ejpam-6617	7	15	and	and	CCONJ
ejpam-6617	7	16	phrases	phrase	NOUN
ejpam-6617	7	17	:	:	PUNCT
ejpam-6617	7	18	variational	variational	ADJ
ejpam-6617	7	19	programming	programming	NOUN
ejpam-6617	7	20	problem	problem	NOUN
ejpam-6617	7	21	,	,	PUNCT
ejpam-6617	7	22	sufficient	sufficient	ADJ
ejpam-6617	7	23	optimality	optimality	NOUN
ejpam-6617	7	24	conditions	condition	NOUN
ejpam-6617	7	25	,	,	PUNCT
ejpam-6617	7	26	lu	lu	NOUN
ejpam-6617	7	27	-	-	PUNCT
ejpam-6617	7	28	optimality	optimality	NOUN
ejpam-6617	7	29	,	,	PUNCT
ejpam-6617	7	30	caputo	caputo	PROPN
ejpam-6617	7	31	-	-	PUNCT
ejpam-6617	7	32	fabrizio	fabrizio	PROPN
ejpam-6617	7	33	fractional	fractional	PROPN
ejpam-6617	7	34	derivative	derivative	NOUN
ejpam-6617	7	35	,	,	PUNCT
ejpam-6617	7	36	wolfe	wolfe	PROPN
ejpam-6617	7	37	-	-	PUNCT
ejpam-6617	7	38	type	type	NOUN
ejpam-6617	7	39	duality	duality	NOUN
ejpam-6617	7	40	.	.	PUNCT
ejpam-6617	8	1	1	1	X
ejpam-6617	8	2	.	.	X
ejpam-6617	8	3	introduction	introduction	NOUN
ejpam-6617	8	4	the	the	DET
ejpam-6617	8	5	optimization	optimization	NOUN
ejpam-6617	8	6	theory	theory	NOUN
ejpam-6617	8	7	acknowledges	acknowledge	VERB
ejpam-6617	8	8	interval	interval	NOUN
ejpam-6617	8	9	-	-	PUNCT
ejpam-6617	8	10	valued	value	VERB
ejpam-6617	8	11	programming	programming	NOUN
ejpam-6617	8	12	as	as	ADP
ejpam-6617	8	13	a	a	DET
ejpam-6617	8	14	crucial	crucial	ADJ
ejpam-6617	8	15	component	component	NOUN
ejpam-6617	8	16	.	.	PUNCT
ejpam-6617	9	1	in	in	ADP
ejpam-6617	9	2	various	various	ADJ
ejpam-6617	9	3	scientific	scientific	ADJ
ejpam-6617	9	4	and	and	CCONJ
ejpam-6617	9	5	mathematical	mathematical	ADJ
ejpam-6617	9	6	domains	domain	NOUN
ejpam-6617	9	7	,	,	PUNCT
ejpam-6617	9	8	interval	interval	NOUN
ejpam-6617	9	9	-	-	PUNCT
ejpam-6617	9	10	valued	value	VERB
ejpam-6617	9	11	optimization	optimization	NOUN
ejpam-6617	9	12	has	have	AUX
ejpam-6617	9	13	recently	recently	ADV
ejpam-6617	9	14	gained	gain	VERB
ejpam-6617	9	15	popularity	popularity	NOUN
ejpam-6617	9	16	.	.	PUNCT
ejpam-6617	10	1	due	due	ADP
ejpam-6617	10	2	to	to	ADP
ejpam-6617	10	3	the	the	DET
ejpam-6617	10	4	uncertainty	uncertainty	NOUN
ejpam-6617	10	5	of	of	ADP
ejpam-6617	10	6	the	the	DET
ejpam-6617	10	7	theory	theory	NOUN
ejpam-6617	10	8	underpinning	underpin	VERB
ejpam-6617	10	9	the	the	DET
ejpam-6617	10	10	parameters	parameter	NOUN
ejpam-6617	10	11	,	,	PUNCT
ejpam-6617	10	12	estimating	estimate	VERB
ejpam-6617	10	13	a	a	DET
ejpam-6617	10	14	physical	physical	ADJ
ejpam-6617	10	15	world	world	NOUN
ejpam-6617	10	16	system	system	NOUN
ejpam-6617	10	17	’s	’s	PART
ejpam-6617	10	18	parameters	parameter	NOUN
ejpam-6617	10	19	is	be	AUX
ejpam-6617	10	20	challenging	challenging	ADJ
ejpam-6617	10	21	.	.	PUNCT
ejpam-6617	11	1	we	we	PRON
ejpam-6617	11	2	can	can	AUX
ejpam-6617	11	3	see	see	VERB
ejpam-6617	11	4	that	that	SCONJ
ejpam-6617	11	5	∗corresponding	∗corresponde	VERB
ejpam-6617	11	6	author	author	NOUN
ejpam-6617	11	7	.	.	PUNCT
ejpam-6617	12	1	doi	doi	NOUN
ejpam-6617	12	2	:	:	PUNCT
ejpam-6617	12	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6617	https://doi.org/10.29020/nybg.ejpam.v18i3.6617	PROPN
ejpam-6617	12	4	email	email	NOUN
ejpam-6617	12	5	addresses	address	NOUN
ejpam-6617	12	6	:	:	PUNCT
ejpam-6617	12	7	rayankee@gmail.com	rayankee@gmail.com	X
ejpam-6617	12	8	(	(	PUNCT
ejpam-6617	12	9	r.	r.	PROPN
ejpam-6617	12	10	vivekananda	vivekananda	PROPN
ejpam-6617	12	11	)	)	PUNCT
ejpam-6617	12	12	,	,	PUNCT
ejpam-6617	12	13	krishna.maths@gmail.com	krishna.maths@gmail.com	X
ejpam-6617	12	14	(	(	PUNCT
ejpam-6617	12	15	k.	k.	PROPN
ejpam-6617	12	16	kummari	kummari	PROPN
ejpam-6617	12	17	)	)	PUNCT
ejpam-6617	12	18	,	,	PUNCT
ejpam-6617	12	19	drizhar@kfupm.edu.sa	drizhar@kfupm.edu.sa	NOUN
ejpam-6617	12	20	(	(	PUNCT
ejpam-6617	12	21	i.	i.	PROPN
ejpam-6617	12	22	ahmad	ahmad	PROPN
ejpam-6617	12	23	)	)	PUNCT
ejpam-6617	13	1	thiti.ga@up.ac.th	thiti.ga@up.ac.th	PROPN
ejpam-6617	13	2	(	(	PUNCT
ejpam-6617	13	3	t.	t.	NOUN
ejpam-6617	13	4	gaketem	gaketem	PROPN
ejpam-6617	13	5	)	)	PUNCT
ejpam-6617	13	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6617	14	1	1	1	NUM
ejpam-6617	14	2	copyright	copyright	NOUN
ejpam-6617	14	3	:	:	PUNCT
ejpam-6617	14	4	©	©	PROPN
ejpam-6617	14	5	2025	2025	NUM
ejpam-6617	14	6	the	the	DET
ejpam-6617	14	7	author(s	author(s	NOUN
ejpam-6617	14	8	)	)	PUNCT
ejpam-6617	14	9	.	.	PUNCT
ejpam-6617	15	1	(	(	PUNCT
ejpam-6617	15	2	cc	cc	NOUN
ejpam-6617	15	3	by	by	ADP
ejpam-6617	15	4	-	-	PUNCT
ejpam-6617	15	5	nc	nc	PROPN
ejpam-6617	15	6	4.0	4.0	NUM
ejpam-6617	15	7	)	)	PUNCT
ejpam-6617	15	8	v.	v.	ADP
ejpam-6617	15	9	rayanki	rayanki	NOUN
ejpam-6617	15	10	et	et	PROPN
ejpam-6617	15	11	al	al	PROPN
ejpam-6617	15	12	.	.	PUNCT
ejpam-6617	15	13	/	/	SYM
ejpam-6617	15	14	eur	eur	PROPN
ejpam-6617	15	15	.	.	PUNCT
ejpam-6617	16	1	j.	j.	PROPN
ejpam-6617	16	2	pure	pure	PROPN
ejpam-6617	16	3	appl	appl	PROPN
ejpam-6617	16	4	.	.	PROPN
ejpam-6617	16	5	math	math	PROPN
ejpam-6617	16	6	,	,	PUNCT
ejpam-6617	16	7	18	18	NUM
ejpam-6617	16	8	(	(	PUNCT
ejpam-6617	16	9	3	3	NUM
ejpam-6617	16	10	)	)	PUNCT
ejpam-6617	16	11	(	(	PUNCT
ejpam-6617	16	12	2025	2025	NUM
ejpam-6617	16	13	)	)	PUNCT
ejpam-6617	16	14	,	,	PUNCT
ejpam-6617	16	15	6617	6617	NUM
ejpam-6617	16	16	2	2	NUM
ejpam-6617	16	17	of	of	ADP
ejpam-6617	16	18	38	38	NUM
ejpam-6617	16	19	there	there	PRON
ejpam-6617	16	20	are	be	VERB
ejpam-6617	16	21	several	several	ADJ
ejpam-6617	16	22	applications	application	NOUN
ejpam-6617	16	23	in	in	ADP
ejpam-6617	16	24	many	many	ADJ
ejpam-6617	16	25	different	different	ADJ
ejpam-6617	16	26	fields	field	NOUN
ejpam-6617	16	27	,	,	PUNCT
ejpam-6617	16	28	including	include	VERB
ejpam-6617	16	29	decision	decision	NOUN
ejpam-6617	16	30	-	-	PUNCT
ejpam-6617	16	31	making	making	NOUN
ejpam-6617	16	32	[	[	X
ejpam-6617	16	33	1	1	NUM
ejpam-6617	16	34	]	]	PUNCT
ejpam-6617	16	35	,	,	PUNCT
ejpam-6617	16	36	diagnostic	diagnostic	ADJ
ejpam-6617	16	37	[	[	X
ejpam-6617	16	38	2	2	NUM
ejpam-6617	16	39	]	]	PUNCT
ejpam-6617	16	40	,	,	PUNCT
ejpam-6617	16	41	portfolio	portfolio	NOUN
ejpam-6617	16	42	optimization	optimization	NOUN
ejpam-6617	16	43	[	[	X
ejpam-6617	16	44	3	3	NUM
ejpam-6617	16	45	]	]	PUNCT
ejpam-6617	16	46	,	,	PUNCT
ejpam-6617	16	47	financial	financial	ADJ
ejpam-6617	16	48	planning	planning	NOUN
ejpam-6617	16	49	,	,	PUNCT
ejpam-6617	16	50	business	business	NOUN
ejpam-6617	16	51	planning	planning	NOUN
ejpam-6617	16	52	,	,	PUNCT
ejpam-6617	16	53	healthcare	healthcare	PROPN
ejpam-6617	16	54	,	,	PUNCT
ejpam-6617	16	55	production	production	NOUN
ejpam-6617	16	56	,	,	PUNCT
ejpam-6617	16	57	hospital	hospital	NOUN
ejpam-6617	16	58	planning	planning	NOUN
ejpam-6617	16	59	and	and	CCONJ
ejpam-6617	16	60	management	management	NOUN
ejpam-6617	16	61	,	,	PUNCT
ejpam-6617	16	62	and	and	CCONJ
ejpam-6617	16	63	many	many	ADJ
ejpam-6617	16	64	more	more	ADJ
ejpam-6617	16	65	.	.	PUNCT
ejpam-6617	17	1	in	in	ADP
ejpam-6617	17	2	the	the	DET
ejpam-6617	17	3	very	very	ADV
ejpam-6617	17	4	recent	recent	ADJ
ejpam-6617	17	5	work	work	NOUN
ejpam-6617	17	6	,	,	PUNCT
ejpam-6617	17	7	[	[	X
ejpam-6617	17	8	4	4	X
ejpam-6617	17	9	]	]	PUNCT
ejpam-6617	17	10	studied	study	VERB
ejpam-6617	17	11	a	a	DET
ejpam-6617	17	12	new	new	ADJ
ejpam-6617	17	13	class	class	NOUN
ejpam-6617	17	14	of	of	ADP
ejpam-6617	17	15	optimization	optimization	NOUN
ejpam-6617	17	16	problems	problem	NOUN
ejpam-6617	17	17	governed	govern	VERB
ejpam-6617	17	18	by	by	ADP
ejpam-6617	17	19	interval	interval	NOUN
ejpam-6617	17	20	-	-	PUNCT
ejpam-6617	17	21	valued	value	VERB
ejpam-6617	17	22	variational	variational	ADJ
ejpam-6617	17	23	programming	programming	NOUN
ejpam-6617	17	24	and	and	CCONJ
ejpam-6617	17	25	inequalities	inequality	NOUN
ejpam-6617	17	26	.	.	PUNCT
ejpam-6617	18	1	its	its	PRON
ejpam-6617	18	2	results	result	NOUN
ejpam-6617	18	3	work	work	VERB
ejpam-6617	18	4	in	in	ADP
ejpam-6617	18	5	applications	application	NOUN
ejpam-6617	18	6	of	of	ADP
ejpam-6617	18	7	control	control	NOUN
ejpam-6617	18	8	and	and	CCONJ
ejpam-6617	18	9	optimization	optimization	NOUN
ejpam-6617	18	10	problems	problem	NOUN
ejpam-6617	18	11	.	.	PUNCT
ejpam-6617	19	1	and	and	CCONJ
ejpam-6617	19	2	at	at	ADP
ejpam-6617	19	3	the	the	DET
ejpam-6617	19	4	same	same	ADJ
ejpam-6617	19	5	time	time	NOUN
ejpam-6617	19	6	,	,	PUNCT
ejpam-6617	19	7	[	[	X
ejpam-6617	19	8	5	5	NUM
ejpam-6617	19	9	]	]	PUNCT
ejpam-6617	19	10	discussed	discuss	VERB
ejpam-6617	19	11	some	some	DET
ejpam-6617	19	12	results	result	NOUN
ejpam-6617	19	13	on	on	ADP
ejpam-6617	19	14	solutions	solution	NOUN
ejpam-6617	19	15	associated	associate	VERB
ejpam-6617	19	16	with	with	ADP
ejpam-6617	19	17	interval	interval	NOUN
ejpam-6617	19	18	-	-	PUNCT
ejpam-6617	19	19	valued	value	VERB
ejpam-6617	19	20	optimal	optimal	ADJ
ejpam-6617	19	21	control	control	NOUN
ejpam-6617	19	22	problems	problem	NOUN
ejpam-6617	19	23	driven	drive	VERB
ejpam-6617	19	24	by	by	ADP
ejpam-6617	19	25	generalized	generalized	ADJ
ejpam-6617	19	26	invariant	invariant	ADJ
ejpam-6617	19	27	convex	convex	NOUN
ejpam-6617	19	28	(	(	PUNCT
ejpam-6617	19	29	invex	invex	NOUN
ejpam-6617	19	30	)	)	PUNCT
ejpam-6617	19	31	functionals	functional	NOUN
ejpam-6617	19	32	and	and	CCONJ
ejpam-6617	19	33	also	also	ADV
ejpam-6617	19	34	investigated	investigate	VERB
ejpam-6617	19	35	necessary	necessary	ADJ
ejpam-6617	19	36	and	and	CCONJ
ejpam-6617	19	37	sufficient	sufficient	ADJ
ejpam-6617	19	38	optimality	optimality	NOUN
ejpam-6617	19	39	conditions	condition	NOUN
ejpam-6617	19	40	for	for	ADP
ejpam-6617	19	41	the	the	DET
ejpam-6617	19	42	considered	consider	VERB
ejpam-6617	19	43	optimization	optimization	NOUN
ejpam-6617	19	44	problem	problem	NOUN
ejpam-6617	19	45	.	.	PUNCT
ejpam-6617	20	1	before	before	ADP
ejpam-6617	20	2	them,[6	them,[6	NUM
ejpam-6617	20	3	]	]	PUNCT
ejpam-6617	20	4	developed	develop	VERB
ejpam-6617	20	5	a	a	DET
ejpam-6617	20	6	framework	framework	NOUN
ejpam-6617	20	7	for	for	ADP
ejpam-6617	20	8	analyzing	analyze	VERB
ejpam-6617	20	9	problems	problem	NOUN
ejpam-6617	20	10	involving	involve	VERB
ejpam-6617	20	11	interval	interval	NOUN
ejpam-6617	20	12	-	-	PUNCT
ejpam-6617	20	13	valued	value	VERB
ejpam-6617	20	14	optimization	optimization	NOUN
ejpam-6617	20	15	.	.	PUNCT
ejpam-6617	21	1	reading	read	VERB
ejpam-6617	21	2	the	the	DET
ejpam-6617	21	3	books	book	NOUN
ejpam-6617	22	1	[	[	X
ejpam-6617	22	2	7–9	7–9	X
ejpam-6617	22	3	]	]	X
ejpam-6617	22	4	and	and	CCONJ
ejpam-6617	22	5	some	some	DET
ejpam-6617	22	6	recent	recent	ADJ
ejpam-6617	22	7	articles	article	NOUN
ejpam-6617	22	8	[	[	X
ejpam-6617	22	9	4–6	4–6	NOUN
ejpam-6617	22	10	,	,	PUNCT
ejpam-6617	22	11	10	10	NUM
ejpam-6617	22	12	,	,	PUNCT
ejpam-6617	22	13	11	11	NUM
ejpam-6617	22	14	]	]	PUNCT
ejpam-6617	22	15	will	will	AUX
ejpam-6617	22	16	help	help	VERB
ejpam-6617	22	17	to	to	PART
ejpam-6617	22	18	learn	learn	VERB
ejpam-6617	22	19	the	the	DET
ejpam-6617	22	20	basics	basic	NOUN
ejpam-6617	22	21	of	of	ADP
ejpam-6617	22	22	intervalvalued	intervalvalue	VERB
ejpam-6617	22	23	optimization	optimization	NOUN
ejpam-6617	22	24	.	.	PUNCT
ejpam-6617	23	1	problems	problem	NOUN
ejpam-6617	23	2	with	with	ADP
ejpam-6617	23	3	variational	variational	ADJ
ejpam-6617	23	4	programming	programming	NOUN
ejpam-6617	23	5	start	start	VERB
ejpam-6617	23	6	with	with	ADP
ejpam-6617	23	7	the	the	DET
ejpam-6617	23	8	calculus	calculus	NOUN
ejpam-6617	23	9	of	of	ADP
ejpam-6617	23	10	variations	variation	NOUN
ejpam-6617	23	11	.	.	PUNCT
ejpam-6617	24	1	recent	recent	ADJ
ejpam-6617	24	2	advances	advance	NOUN
ejpam-6617	24	3	in	in	ADP
ejpam-6617	24	4	variational	variational	ADJ
ejpam-6617	24	5	calculus	calculus	NOUN
ejpam-6617	24	6	and	and	CCONJ
ejpam-6617	24	7	optimization	optimization	NOUN
ejpam-6617	24	8	theory	theory	NOUN
ejpam-6617	24	9	have	have	AUX
ejpam-6617	24	10	given	give	VERB
ejpam-6617	24	11	us	we	PRON
ejpam-6617	24	12	a	a	DET
ejpam-6617	24	13	cogent	cogent	NOUN
ejpam-6617	24	14	framework	framework	NOUN
ejpam-6617	24	15	for	for	ADP
ejpam-6617	24	16	analyzing	analyze	VERB
ejpam-6617	24	17	a	a	DET
ejpam-6617	24	18	range	range	NOUN
ejpam-6617	24	19	of	of	ADP
ejpam-6617	24	20	issues	issue	NOUN
ejpam-6617	24	21	in	in	ADP
ejpam-6617	24	22	numerous	numerous	ADJ
ejpam-6617	24	23	other	other	ADJ
ejpam-6617	24	24	fields	field	NOUN
ejpam-6617	24	25	of	of	ADP
ejpam-6617	24	26	pure	pure	ADJ
ejpam-6617	24	27	and	and	CCONJ
ejpam-6617	24	28	applied	applied	ADJ
ejpam-6617	24	29	mathematics	mathematic	NOUN
ejpam-6617	24	30	.	.	PUNCT
ejpam-6617	25	1	the	the	DET
ejpam-6617	25	2	dynamics	dynamic	NOUN
ejpam-6617	25	3	of	of	ADP
ejpam-6617	25	4	rigid	rigid	ADJ
ejpam-6617	25	5	bodies	body	NOUN
ejpam-6617	25	6	,	,	PUNCT
ejpam-6617	25	7	orbit	orbit	NOUN
ejpam-6617	25	8	optimization	optimization	NOUN
ejpam-6617	25	9	[	[	X
ejpam-6617	25	10	12	12	NUM
ejpam-6617	25	11	]	]	PUNCT
ejpam-6617	25	12	,	,	PUNCT
ejpam-6617	25	13	flight	flight	NOUN
ejpam-6617	25	14	design	design	NOUN
ejpam-6617	25	15	[	[	X
ejpam-6617	25	16	13	13	NUM
ejpam-6617	25	17	,	,	PUNCT
ejpam-6617	25	18	14	14	NUM
ejpam-6617	25	19	]	]	PUNCT
ejpam-6617	25	20	,	,	PUNCT
ejpam-6617	25	21	and	and	CCONJ
ejpam-6617	25	22	other	other	ADJ
ejpam-6617	25	23	problems	problem	NOUN
ejpam-6617	25	24	are	be	AUX
ejpam-6617	25	25	among	among	ADP
ejpam-6617	25	26	the	the	DET
ejpam-6617	25	27	areas	area	NOUN
ejpam-6617	25	28	where	where	SCONJ
ejpam-6617	25	29	the	the	DET
ejpam-6617	25	30	calculus	calculus	NOUN
ejpam-6617	25	31	of	of	ADP
ejpam-6617	25	32	variations	variation	NOUN
ejpam-6617	25	33	is	be	AUX
ejpam-6617	25	34	utilized	utilize	VERB
ejpam-6617	25	35	to	to	PART
ejpam-6617	25	36	address	address	VERB
ejpam-6617	25	37	problems	problem	NOUN
ejpam-6617	25	38	.	.	PUNCT
ejpam-6617	26	1	using	use	VERB
ejpam-6617	26	2	invexity	invexity	NOUN
ejpam-6617	26	3	assumptions	assumption	NOUN
ejpam-6617	26	4	,	,	PUNCT
ejpam-6617	26	5	[	[	X
ejpam-6617	26	6	15	15	NUM
ejpam-6617	26	7	]	]	PUNCT
ejpam-6617	26	8	developed	develop	VERB
ejpam-6617	26	9	some	some	DET
ejpam-6617	26	10	optimality	optimality	NOUN
ejpam-6617	26	11	requirements	requirement	NOUN
ejpam-6617	26	12	and	and	CCONJ
ejpam-6617	26	13	theorems	theorem	NOUN
ejpam-6617	26	14	of	of	ADP
ejpam-6617	26	15	duality	duality	NOUN
ejpam-6617	26	16	for	for	ADP
ejpam-6617	26	17	interval	interval	NOUN
ejpam-6617	26	18	-	-	PUNCT
ejpam-6617	26	19	valued	value	VERB
ejpam-6617	26	20	optimization	optimization	NOUN
ejpam-6617	26	21	problems	problem	NOUN
ejpam-6617	26	22	.	.	PUNCT
ejpam-6617	27	1	later	later	ADV
ejpam-6617	27	2	,	,	PUNCT
ejpam-6617	27	3	[	[	X
ejpam-6617	27	4	11	11	NUM
ejpam-6617	27	5	]	]	PUNCT
ejpam-6617	27	6	modified	modify	VERB
ejpam-6617	27	7	the	the	DET
ejpam-6617	27	8	definitions	definition	NOUN
ejpam-6617	27	9	of	of	ADP
ejpam-6617	27	10	pre	pre	ADJ
ejpam-6617	27	11	-	-	NOUN
ejpam-6617	27	12	invexity	invexity	ADJ
ejpam-6617	27	13	and	and	CCONJ
ejpam-6617	27	14	generalized	generalized	ADJ
ejpam-6617	27	15	invexity	invexity	NOUN
ejpam-6617	27	16	in	in	ADP
ejpam-6617	27	17	interval	interval	NOUN
ejpam-6617	27	18	-	-	PUNCT
ejpam-6617	27	19	valued	value	VERB
ejpam-6617	27	20	functions	function	NOUN
ejpam-6617	27	21	and	and	CCONJ
ejpam-6617	27	22	additionally	additionally	ADV
ejpam-6617	27	23	developed	develop	VERB
ejpam-6617	27	24	karush	karush	PROPN
ejpam-6617	27	25	-	-	PUNCT
ejpam-6617	27	26	kuhn	kuhn	PROPN
ejpam-6617	27	27	-	-	PUNCT
ejpam-6617	27	28	tucker	tucker	PROPN
ejpam-6617	27	29	optimality	optimality	NOUN
ejpam-6617	27	30	requirements	requirement	NOUN
ejpam-6617	27	31	for	for	ADP
ejpam-6617	27	32	the	the	DET
ejpam-6617	27	33	optimization	optimization	NOUN
ejpam-6617	27	34	problem	problem	NOUN
ejpam-6617	27	35	under	under	ADP
ejpam-6617	27	36	consideration	consideration	NOUN
ejpam-6617	27	37	,	,	PUNCT
ejpam-6617	27	38	where	where	SCONJ
ejpam-6617	27	39	the	the	DET
ejpam-6617	27	40	objective	objective	ADJ
ejpam-6617	27	41	function	function	NOUN
ejpam-6617	27	42	was	be	AUX
ejpam-6617	27	43	assumed	assume	VERB
ejpam-6617	27	44	to	to	PART
ejpam-6617	27	45	be	be	AUX
ejpam-6617	27	46	interval	interval	NOUN
ejpam-6617	27	47	-	-	PUNCT
ejpam-6617	27	48	valued	value	VERB
ejpam-6617	27	49	.	.	PUNCT
ejpam-6617	28	1	recently	recently	ADV
ejpam-6617	28	2	,	,	PUNCT
ejpam-6617	28	3	[	[	X
ejpam-6617	28	4	16	16	NUM
ejpam-6617	28	5	]	]	PUNCT
ejpam-6617	28	6	used	use	VERB
ejpam-6617	28	7	extended	extend	VERB
ejpam-6617	28	8	(	(	PUNCT
ejpam-6617	28	9	p	p	NOUN
ejpam-6617	28	10	,	,	PUNCT
ejpam-6617	28	11	r)−ρ−	r)−ρ−	VERB
ejpam-6617	28	12	(	(	PUNCT
ejpam-6617	28	13	ℵ	ℵ	NOUN
ejpam-6617	28	14	,	,	PUNCT
ejpam-6617	28	15	θ)-invexity	θ)-invexity	NOUN
ejpam-6617	28	16	for	for	ADP
ejpam-6617	28	17	a	a	DET
ejpam-6617	28	18	problem	problem	NOUN
ejpam-6617	28	19	of	of	ADP
ejpam-6617	28	20	interval	interval	NOUN
ejpam-6617	28	21	-	-	PUNCT
ejpam-6617	28	22	valued	value	VERB
ejpam-6617	28	23	optimization	optimization	NOUN
ejpam-6617	28	24	to	to	PART
ejpam-6617	28	25	study	study	VERB
ejpam-6617	28	26	optimality	optimality	NOUN
ejpam-6617	28	27	and	and	CCONJ
ejpam-6617	28	28	duality	duality	NOUN
ejpam-6617	28	29	.	.	PUNCT
ejpam-6617	29	1	[	[	X
ejpam-6617	29	2	17	17	NUM
ejpam-6617	29	3	]	]	PUNCT
ejpam-6617	29	4	established	establish	VERB
ejpam-6617	29	5	duality	duality	NOUN
ejpam-6617	29	6	conclusions	conclusion	NOUN
ejpam-6617	29	7	for	for	ADP
ejpam-6617	29	8	cases	case	NOUN
ejpam-6617	29	9	involving	involve	VERB
ejpam-6617	29	10	variational	variational	ADJ
ejpam-6617	29	11	programming	programming	NOUN
ejpam-6617	29	12	.	.	PUNCT
ejpam-6617	30	1	jimenez	jimenez	PROPN
ejpam-6617	30	2	et	et	PROPN
ejpam-6617	30	3	al	al	PROPN
ejpam-6617	30	4	.	.	PROPN
ejpam-6617	30	5	,	,	PUNCT
ejpam-6617	31	1	[	[	X
ejpam-6617	31	2	18	18	NUM
ejpam-6617	31	3	]	]	PUNCT
ejpam-6617	31	4	,	,	PUNCT
ejpam-6617	31	5	developed	develop	VERB
ejpam-6617	31	6	some	some	DET
ejpam-6617	31	7	duality	duality	NOUN
ejpam-6617	31	8	solutions	solution	NOUN
ejpam-6617	31	9	for	for	ADP
ejpam-6617	31	10	the	the	DET
ejpam-6617	31	11	multiobjective	multiobjective	ADJ
ejpam-6617	31	12	variational	variational	ADJ
ejpam-6617	31	13	issue	issue	NOUN
ejpam-6617	31	14	utilizing	utilize	VERB
ejpam-6617	31	15	the	the	DET
ejpam-6617	31	16	pseudo	pseudo	NOUN
ejpam-6617	31	17	-	-	NOUN
ejpam-6617	31	18	invexity	invexity	NOUN
ejpam-6617	31	19	notion	notion	NOUN
ejpam-6617	31	20	.	.	PUNCT
ejpam-6617	32	1	treanctua	treanctua	PROPN
ejpam-6617	32	2	et	et	PROPN
ejpam-6617	32	3	al	al	PROPN
ejpam-6617	32	4	.	.	PUNCT
ejpam-6617	33	1	[	[	X
ejpam-6617	33	2	19	19	NUM
ejpam-6617	33	3	]	]	PUNCT
ejpam-6617	33	4	investigated	investigate	VERB
ejpam-6617	33	5	efficiency	efficiency	NOUN
ejpam-6617	33	6	conditions	condition	NOUN
ejpam-6617	33	7	in	in	ADP
ejpam-6617	33	8	interval	interval	NOUN
ejpam-6617	33	9	-	-	PUNCT
ejpam-6617	33	10	valued	value	VERB
ejpam-6617	33	11	control	control	NOUN
ejpam-6617	33	12	models	model	NOUN
ejpam-6617	33	13	using	use	VERB
ejpam-6617	33	14	a	a	DET
ejpam-6617	33	15	modified	modify	VERB
ejpam-6617	33	16	objective	objective	ADJ
ejpam-6617	33	17	functional	functional	ADJ
ejpam-6617	33	18	and	and	CCONJ
ejpam-6617	33	19	saddle	saddle	NOUN
ejpam-6617	33	20	-	-	PUNCT
ejpam-6617	33	21	point	point	NOUN
ejpam-6617	33	22	criteria	criterion	NOUN
ejpam-6617	33	23	.	.	PUNCT
ejpam-6617	34	1	numerous	numerous	ADJ
ejpam-6617	34	2	additional	additional	ADJ
ejpam-6617	34	3	studies	study	NOUN
ejpam-6617	34	4	have	have	AUX
ejpam-6617	34	5	discussed	discuss	VERB
ejpam-6617	34	6	the	the	DET
ejpam-6617	34	7	issues	issue	NOUN
ejpam-6617	34	8	with	with	ADP
ejpam-6617	34	9	variational	variational	ADJ
ejpam-6617	34	10	programming	programming	NOUN
ejpam-6617	34	11	(	(	PUNCT
ejpam-6617	34	12	see	see	VERB
ejpam-6617	34	13	,	,	PUNCT
ejpam-6617	34	14	for	for	ADP
ejpam-6617	34	15	example	example	NOUN
ejpam-6617	34	16	,	,	PUNCT
ejpam-6617	34	17	[	[	X
ejpam-6617	34	18	20	20	NUM
ejpam-6617	34	19	,	,	PUNCT
ejpam-6617	34	20	21	21	NUM
ejpam-6617	34	21	]	]	PUNCT
ejpam-6617	34	22	)	)	PUNCT
ejpam-6617	34	23	.	.	PUNCT
ejpam-6617	35	1	fractional	fractional	ADJ
ejpam-6617	35	2	calculus	calculus	NOUN
ejpam-6617	35	3	(	(	PUNCT
ejpam-6617	35	4	fc	fc	INTJ
ejpam-6617	35	5	)	)	PUNCT
ejpam-6617	35	6	is	be	AUX
ejpam-6617	35	7	currently	currently	ADV
ejpam-6617	35	8	recognized	recognize	VERB
ejpam-6617	35	9	as	as	ADP
ejpam-6617	35	10	a	a	DET
ejpam-6617	35	11	fascinating	fascinating	ADJ
ejpam-6617	35	12	subject	subject	NOUN
ejpam-6617	35	13	by	by	ADP
ejpam-6617	35	14	the	the	DET
ejpam-6617	35	15	community	community	NOUN
ejpam-6617	35	16	of	of	ADP
ejpam-6617	35	17	practical	practical	ADJ
ejpam-6617	35	18	engineers	engineer	NOUN
ejpam-6617	35	19	.	.	PUNCT
ejpam-6617	36	1	it	it	PRON
ejpam-6617	36	2	is	be	AUX
ejpam-6617	36	3	a	a	DET
ejpam-6617	36	4	generalization	generalization	NOUN
ejpam-6617	36	5	of	of	ADP
ejpam-6617	36	6	conventional	conventional	ADJ
ejpam-6617	36	7	calculus	calculus	NOUN
ejpam-6617	36	8	because	because	SCONJ
ejpam-6617	36	9	derivatives	derivative	NOUN
ejpam-6617	36	10	and	and	CCONJ
ejpam-6617	36	11	integrals	integral	NOUN
ejpam-6617	36	12	are	be	AUX
ejpam-6617	36	13	employed	employ	VERB
ejpam-6617	36	14	outside	outside	ADV
ejpam-6617	36	15	of	of	ADP
ejpam-6617	36	16	integer	integer	NOUN
ejpam-6617	36	17	orders	order	NOUN
ejpam-6617	36	18	.	.	PUNCT
ejpam-6617	37	1	fractional	fractional	ADJ
ejpam-6617	37	2	calculus	calculus	NOUN
ejpam-6617	37	3	has	have	VERB
ejpam-6617	37	4	numerous	numerous	ADJ
ejpam-6617	37	5	uses	use	NOUN
ejpam-6617	37	6	in	in	ADP
ejpam-6617	37	7	science	science	NOUN
ejpam-6617	37	8	and	and	CCONJ
ejpam-6617	37	9	engineering	engineering	NOUN
ejpam-6617	38	1	[	[	X
ejpam-6617	38	2	22	22	NUM
ejpam-6617	38	3	]	]	PUNCT
ejpam-6617	38	4	,	,	PUNCT
ejpam-6617	38	5	and	and	CCONJ
ejpam-6617	38	6	it	it	PRON
ejpam-6617	38	7	has	have	AUX
ejpam-6617	38	8	grown	grow	VERB
ejpam-6617	38	9	in	in	ADP
ejpam-6617	38	10	popularity	popularity	NOUN
ejpam-6617	38	11	in	in	ADP
ejpam-6617	38	12	recent	recent	ADJ
ejpam-6617	38	13	years	year	NOUN
ejpam-6617	38	14	as	as	ADP
ejpam-6617	38	15	a	a	DET
ejpam-6617	38	16	tool	tool	NOUN
ejpam-6617	38	17	for	for	ADP
ejpam-6617	38	18	researching	research	VERB
ejpam-6617	38	19	the	the	DET
ejpam-6617	38	20	dynamics	dynamic	NOUN
ejpam-6617	38	21	of	of	ADP
ejpam-6617	38	22	practical	practical	ADJ
ejpam-6617	38	23	problems	problem	NOUN
ejpam-6617	38	24	.	.	PUNCT
ejpam-6617	39	1	[	[	X
ejpam-6617	39	2	23	23	NUM
ejpam-6617	39	3	,	,	PUNCT
ejpam-6617	39	4	24	24	NUM
ejpam-6617	39	5	]	]	PUNCT
ejpam-6617	39	6	looked	look	VERB
ejpam-6617	39	7	into	into	ADP
ejpam-6617	39	8	a	a	DET
ejpam-6617	39	9	few	few	ADJ
ejpam-6617	39	10	common	common	ADJ
ejpam-6617	39	11	variational	variational	ADJ
ejpam-6617	39	12	issues	issue	NOUN
ejpam-6617	39	13	by	by	ADP
ejpam-6617	39	14	incorporating	incorporate	VERB
ejpam-6617	39	15	fractional	fractional	ADJ
ejpam-6617	39	16	derivatives	derivative	NOUN
ejpam-6617	39	17	of	of	ADP
ejpam-6617	39	18	riemann	riemann	PROPN
ejpam-6617	39	19	-	-	PUNCT
ejpam-6617	39	20	liouville	liouville	NOUN
ejpam-6617	39	21	[	[	X
ejpam-6617	39	22	25	25	NUM
ejpam-6617	39	23	]	]	PUNCT
ejpam-6617	39	24	,	,	PUNCT
ejpam-6617	39	25	caputo	caputo	PROPN
ejpam-6617	39	26	,	,	PUNCT
ejpam-6617	39	27	and	and	CCONJ
ejpam-6617	39	28	riesz	riesz	PROPN
ejpam-6617	39	29	types	type	NOUN
ejpam-6617	39	30	.	.	PUNCT
ejpam-6617	40	1	in	in	ADP
ejpam-6617	40	2	other	other	ADJ
ejpam-6617	40	3	research	research	NOUN
ejpam-6617	40	4	work	work	NOUN
ejpam-6617	40	5	[	[	X
ejpam-6617	40	6	26	26	NUM
ejpam-6617	40	7	]	]	PUNCT
ejpam-6617	40	8	,	,	PUNCT
ejpam-6617	40	9	variational	variational	ADJ
ejpam-6617	40	10	problems	problem	NOUN
ejpam-6617	40	11	pertaining	pertain	VERB
ejpam-6617	40	12	to	to	ADP
ejpam-6617	40	13	a	a	DET
ejpam-6617	40	14	lagrangian	lagrangian	ADJ
ejpam-6617	40	15	function	function	NOUN
ejpam-6617	40	16	given	give	VERB
ejpam-6617	40	17	fractional	fractional	ADJ
ejpam-6617	40	18	derivatives	derivative	NOUN
ejpam-6617	40	19	have	have	AUX
ejpam-6617	40	20	been	be	AUX
ejpam-6617	40	21	analyzed	analyze	VERB
ejpam-6617	40	22	to	to	PART
ejpam-6617	40	23	determine	determine	VERB
ejpam-6617	40	24	optimality	optimality	NOUN
ejpam-6617	40	25	conditions	condition	NOUN
ejpam-6617	40	26	.	.	PUNCT
ejpam-6617	41	1	shalini	shalini	PROPN
ejpam-6617	41	2	et	et	PROPN
ejpam-6617	41	3	al	al	PROPN
ejpam-6617	41	4	.	.	PUNCT
ejpam-6617	42	1	[	[	X
ejpam-6617	42	2	27	27	NUM
ejpam-6617	42	3	]	]	PUNCT
ejpam-6617	42	4	investigate	investigate	VERB
ejpam-6617	42	5	dynamical	dynamical	ADJ
ejpam-6617	42	6	control	control	NOUN
ejpam-6617	42	7	systems	system	NOUN
ejpam-6617	42	8	using	use	VERB
ejpam-6617	42	9	a	a	DET
ejpam-6617	42	10	fuzzy	fuzzy	ADJ
ejpam-6617	42	11	modeling	modeling	NOUN
ejpam-6617	42	12	framework	framework	NOUN
ejpam-6617	42	13	,	,	PUNCT
ejpam-6617	42	14	wherein	wherein	SCONJ
ejpam-6617	42	15	the	the	DET
ejpam-6617	42	16	system	system	NOUN
ejpam-6617	42	17	dynamics	dynamic	NOUN
ejpam-6617	42	18	are	be	AUX
ejpam-6617	42	19	governed	govern	VERB
ejpam-6617	42	20	by	by	ADP
ejpam-6617	42	21	a	a	DET
ejpam-6617	42	22	fuzzy	fuzzy	ADJ
ejpam-6617	42	23	stochastic	stochastic	ADJ
ejpam-6617	42	24	process	process	NOUN
ejpam-6617	42	25	(	(	PUNCT
ejpam-6617	42	26	fsp	fsp	NOUN
ejpam-6617	42	27	)	)	PUNCT
ejpam-6617	42	28	driven	drive	VERB
ejpam-6617	42	29	by	by	ADP
ejpam-6617	42	30	fuzzy	fuzzy	ADJ
ejpam-6617	42	31	brownian	brownian	ADJ
ejpam-6617	42	32	motion	motion	NOUN
ejpam-6617	42	33	(	(	PUNCT
ejpam-6617	42	34	fbm	fbm	NOUN
ejpam-6617	42	35	)	)	PUNCT
ejpam-6617	42	36	.	.	PUNCT
ejpam-6617	43	1	fuzzy	fuzzy	ADJ
ejpam-6617	43	2	fractional	fractional	ADJ
ejpam-6617	43	3	variational	variational	ADJ
ejpam-6617	43	4	problems	problem	NOUN
ejpam-6617	43	5	(	(	PUNCT
ejpam-6617	43	6	fvps	fvps	NOUN
ejpam-6617	43	7	)	)	PUNCT
ejpam-6617	43	8	have	have	AUX
ejpam-6617	43	9	been	be	AUX
ejpam-6617	43	10	explored	explore	VERB
ejpam-6617	43	11	in	in	ADP
ejpam-6617	43	12	the	the	DET
ejpam-6617	43	13	literature	literature	NOUN
ejpam-6617	43	14	for	for	ADP
ejpam-6617	43	15	necv	necv	NOUN
ejpam-6617	43	16	.	.	PUNCT
ejpam-6617	44	1	rayanki	rayanki	PROPN
ejpam-6617	44	2	et	et	PROPN
ejpam-6617	44	3	al	al	PROPN
ejpam-6617	44	4	.	.	PUNCT
ejpam-6617	44	5	/	/	SYM
ejpam-6617	44	6	eur	eur	PROPN
ejpam-6617	44	7	.	.	PUNCT
ejpam-6617	45	1	j.	j.	PROPN
ejpam-6617	45	2	pure	pure	PROPN
ejpam-6617	45	3	appl	appl	PROPN
ejpam-6617	45	4	.	.	PROPN
ejpam-6617	45	5	math	math	PROPN
ejpam-6617	45	6	,	,	PUNCT
ejpam-6617	45	7	18	18	NUM
ejpam-6617	45	8	(	(	PUNCT
ejpam-6617	45	9	3	3	NUM
ejpam-6617	45	10	)	)	PUNCT
ejpam-6617	45	11	(	(	PUNCT
ejpam-6617	45	12	2025	2025	NUM
ejpam-6617	45	13	)	)	PUNCT
ejpam-6617	45	14	,	,	PUNCT
ejpam-6617	45	15	6617	6617	NUM
ejpam-6617	45	16	3	3	NUM
ejpam-6617	45	17	of	of	ADP
ejpam-6617	45	18	38	38	NUM
ejpam-6617	45	19	essary	essary	ADJ
ejpam-6617	45	20	optimality	optimality	NOUN
ejpam-6617	45	21	conditions	condition	NOUN
ejpam-6617	45	22	,	,	PUNCT
ejpam-6617	45	23	as	as	SCONJ
ejpam-6617	45	24	seen	see	VERB
ejpam-6617	45	25	in	in	ADP
ejpam-6617	45	26	the	the	DET
ejpam-6617	45	27	works	work	NOUN
ejpam-6617	45	28	of	of	ADP
ejpam-6617	45	29	[	[	X
ejpam-6617	45	30	28	28	NUM
ejpam-6617	45	31	]	]	PUNCT
ejpam-6617	45	32	and	and	CCONJ
ejpam-6617	45	33	[	[	X
ejpam-6617	45	34	29	29	NUM
ejpam-6617	45	35	]	]	PUNCT
ejpam-6617	45	36	.	.	PUNCT
ejpam-6617	46	1	these	these	DET
ejpam-6617	46	2	studies	study	NOUN
ejpam-6617	46	3	provide	provide	VERB
ejpam-6617	46	4	foundational	foundational	ADJ
ejpam-6617	46	5	insights	insight	NOUN
ejpam-6617	46	6	into	into	ADP
ejpam-6617	46	7	the	the	DET
ejpam-6617	46	8	interplay	interplay	NOUN
ejpam-6617	46	9	between	between	ADP
ejpam-6617	46	10	fuzzy	fuzzy	ADJ
ejpam-6617	46	11	logic	logic	NOUN
ejpam-6617	46	12	and	and	CCONJ
ejpam-6617	46	13	fractional	fractional	ADJ
ejpam-6617	46	14	calculus	calculus	NOUN
ejpam-6617	46	15	,	,	PUNCT
ejpam-6617	46	16	particularly	particularly	ADV
ejpam-6617	46	17	in	in	ADP
ejpam-6617	46	18	variational	variational	ADJ
ejpam-6617	46	19	settings	setting	NOUN
ejpam-6617	46	20	.	.	PUNCT
ejpam-6617	47	1	caputo	caputo	PROPN
ejpam-6617	47	2	and	and	CCONJ
ejpam-6617	47	3	fabrizio	fabrizio	PROPN
ejpam-6617	47	4	[	[	X
ejpam-6617	47	5	30	30	NUM
ejpam-6617	47	6	]	]	PUNCT
ejpam-6617	47	7	introduced	introduce	VERB
ejpam-6617	47	8	a	a	DET
ejpam-6617	47	9	novel	novel	ADJ
ejpam-6617	47	10	fractional	fractional	ADJ
ejpam-6617	47	11	derivative	derivative	NOUN
ejpam-6617	47	12	,	,	PUNCT
ejpam-6617	47	13	characterized	characterize	VERB
ejpam-6617	47	14	by	by	ADP
ejpam-6617	47	15	the	the	DET
ejpam-6617	47	16	order	order	NOUN
ejpam-6617	47	17	θ•	θ•	PROPN
ejpam-6617	47	18	∈	∈	PROPN
ejpam-6617	47	19	(	(	PUNCT
ejpam-6617	47	20	0	0	NUM
ejpam-6617	47	21	,	,	PUNCT
ejpam-6617	47	22	1	1	NUM
ejpam-6617	47	23	)	)	PUNCT
ejpam-6617	47	24	,	,	PUNCT
ejpam-6617	47	25	defined	define	VERB
ejpam-6617	47	26	using	use	VERB
ejpam-6617	47	27	an	an	DET
ejpam-6617	47	28	exponential	exponential	ADJ
ejpam-6617	47	29	kernel	kernel	NOUN
ejpam-6617	47	30	.	.	PUNCT
ejpam-6617	48	1	this	this	DET
ejpam-6617	48	2	derivative	derivative	ADJ
ejpam-6617	48	3	avoids	avoid	VERB
ejpam-6617	48	4	singular	singular	ADJ
ejpam-6617	48	5	kernels	kernel	NOUN
ejpam-6617	48	6	and	and	CCONJ
ejpam-6617	48	7	is	be	AUX
ejpam-6617	48	8	well	well	ADV
ejpam-6617	48	9	-	-	PUNCT
ejpam-6617	48	10	suited	suit	VERB
ejpam-6617	48	11	for	for	ADP
ejpam-6617	48	12	modeling	model	VERB
ejpam-6617	48	13	systems	system	NOUN
ejpam-6617	48	14	with	with	ADP
ejpam-6617	48	15	memory	memory	NOUN
ejpam-6617	48	16	effects	effect	NOUN
ejpam-6617	48	17	,	,	PUNCT
ejpam-6617	48	18	which	which	PRON
ejpam-6617	48	19	marks	mark	VERB
ejpam-6617	48	20	a	a	DET
ejpam-6617	48	21	significant	significant	ADJ
ejpam-6617	48	22	departure	departure	NOUN
ejpam-6617	48	23	from	from	ADP
ejpam-6617	48	24	classical	classical	ADJ
ejpam-6617	48	25	riemann	riemann	PROPN
ejpam-6617	48	26	–	–	PUNCT
ejpam-6617	48	27	liouville	liouville	PROPN
ejpam-6617	48	28	and	and	CCONJ
ejpam-6617	48	29	caputo	caputo	PROPN
ejpam-6617	48	30	definitions	definition	NOUN
ejpam-6617	48	31	that	that	PRON
ejpam-6617	48	32	employ	employ	VERB
ejpam-6617	48	33	singular	singular	ADJ
ejpam-6617	48	34	kernels	kernel	NOUN
ejpam-6617	48	35	.	.	PUNCT
ejpam-6617	49	1	jayswal	jayswal	NOUN
ejpam-6617	49	2	and	and	CCONJ
ejpam-6617	49	3	uniyal	uniyal	ADJ
ejpam-6617	49	4	[	[	X
ejpam-6617	49	5	31	31	NUM
ejpam-6617	49	6	]	]	PUNCT
ejpam-6617	49	7	presented	present	VERB
ejpam-6617	49	8	necessary	necessary	ADJ
ejpam-6617	49	9	and	and	CCONJ
ejpam-6617	49	10	sufficient	sufficient	ADJ
ejpam-6617	49	11	optimality	optimality	NOUN
ejpam-6617	49	12	conditions	condition	NOUN
ejpam-6617	49	13	and	and	CCONJ
ejpam-6617	49	14	mond	mond	NOUN
ejpam-6617	49	15	-	-	PUNCT
ejpam-6617	49	16	weir	weir	PROPN
ejpam-6617	49	17	duality	duality	NOUN
ejpam-6617	49	18	results	result	NOUN
ejpam-6617	49	19	for	for	ADP
ejpam-6617	49	20	semi	semi	ADJ
ejpam-6617	49	21	-	-	ADJ
ejpam-6617	49	22	infinite	infinite	ADJ
ejpam-6617	49	23	variational	variational	ADJ
ejpam-6617	49	24	programming	programming	NOUN
ejpam-6617	49	25	(	(	PUNCT
ejpam-6617	49	26	sivp	sivp	NOUN
ejpam-6617	49	27	)	)	PUNCT
ejpam-6617	49	28	problems	problem	NOUN
ejpam-6617	49	29	involving	involve	VERB
ejpam-6617	49	30	caputo	caputo	PROPN
ejpam-6617	49	31	-	-	PUNCT
ejpam-6617	49	32	fabrizio	fabrizio	PROPN
ejpam-6617	49	33	fractional	fractional	ADJ
ejpam-6617	49	34	derivatives	derivative	NOUN
ejpam-6617	49	35	.	.	PUNCT
ejpam-6617	50	1	their	their	PRON
ejpam-6617	50	2	analysis	analysis	NOUN
ejpam-6617	50	3	leveraged	leverage	VERB
ejpam-6617	50	4	slater	slater	NOUN
ejpam-6617	50	5	-	-	PUNCT
ejpam-6617	50	6	type	type	NOUN
ejpam-6617	50	7	constraint	constraint	NOUN
ejpam-6617	50	8	qualifications	qualification	NOUN
ejpam-6617	50	9	and	and	CCONJ
ejpam-6617	50	10	generalized	generalized	ADJ
ejpam-6617	50	11	convexity	convexity	NOUN
ejpam-6617	50	12	assumptions	assumption	NOUN
ejpam-6617	50	13	.	.	PUNCT
ejpam-6617	51	1	in	in	ADP
ejpam-6617	51	2	a	a	DET
ejpam-6617	51	3	follow	follow	VERB
ejpam-6617	51	4	-	-	PUNCT
ejpam-6617	51	5	up	up	ADP
ejpam-6617	51	6	work	work	NOUN
ejpam-6617	51	7	[	[	X
ejpam-6617	51	8	32	32	NUM
ejpam-6617	51	9	]	]	PUNCT
ejpam-6617	51	10	,	,	PUNCT
ejpam-6617	51	11	they	they	PRON
ejpam-6617	51	12	extended	extend	VERB
ejpam-6617	51	13	this	this	DET
ejpam-6617	51	14	framework	framework	NOUN
ejpam-6617	51	15	to	to	PART
ejpam-6617	51	16	investigate	investigate	VERB
ejpam-6617	51	17	optimality	optimality	NOUN
ejpam-6617	51	18	conditions	condition	NOUN
ejpam-6617	51	19	for	for	ADP
ejpam-6617	51	20	broader	broad	ADJ
ejpam-6617	51	21	classes	class	NOUN
ejpam-6617	51	22	of	of	ADP
ejpam-6617	51	23	semi	semi	ADJ
ejpam-6617	51	24	-	-	ADJ
ejpam-6617	51	25	infinite	infinite	ADJ
ejpam-6617	51	26	fractional	fractional	ADJ
ejpam-6617	51	27	variational	variational	ADJ
ejpam-6617	51	28	problems	problem	NOUN
ejpam-6617	51	29	with	with	ADP
ejpam-6617	51	30	similar	similar	ADJ
ejpam-6617	51	31	structural	structural	ADJ
ejpam-6617	51	32	features	feature	NOUN
ejpam-6617	51	33	.	.	PUNCT
ejpam-6617	52	1	the	the	DET
ejpam-6617	52	2	present	present	ADJ
ejpam-6617	52	3	study	study	NOUN
ejpam-6617	52	4	advances	advance	VERB
ejpam-6617	52	5	the	the	DET
ejpam-6617	52	6	existing	exist	VERB
ejpam-6617	52	7	literature	literature	NOUN
ejpam-6617	52	8	by	by	ADP
ejpam-6617	52	9	considering	consider	VERB
ejpam-6617	52	10	interval	interval	NOUN
ejpam-6617	52	11	-	-	PUNCT
ejpam-6617	52	12	valued	value	VERB
ejpam-6617	52	13	variational	variational	ADJ
ejpam-6617	52	14	programming	programming	NOUN
ejpam-6617	52	15	problems	problem	NOUN
ejpam-6617	52	16	(	(	PUNCT
ejpam-6617	52	17	p	p	NOUN
ejpam-6617	52	18	)	)	PUNCT
ejpam-6617	52	19	governed	govern	VERB
ejpam-6617	52	20	by	by	ADP
ejpam-6617	52	21	caputo	caputo	PROPN
ejpam-6617	52	22	-	-	PUNCT
ejpam-6617	52	23	fabrizio	fabrizio	PROPN
ejpam-6617	52	24	fractional	fractional	ADJ
ejpam-6617	52	25	derivatives	derivative	NOUN
ejpam-6617	52	26	.	.	PUNCT
ejpam-6617	53	1	in	in	ADP
ejpam-6617	53	2	contrast	contrast	NOUN
ejpam-6617	53	3	to	to	ADP
ejpam-6617	53	4	previous	previous	ADJ
ejpam-6617	53	5	works	work	NOUN
ejpam-6617	53	6	that	that	PRON
ejpam-6617	53	7	primarily	primarily	ADV
ejpam-6617	53	8	address	address	VERB
ejpam-6617	53	9	crisp	crisp	ADV
ejpam-6617	53	10	-	-	PUNCT
ejpam-6617	53	11	valued	value	VERB
ejpam-6617	53	12	problems	problem	NOUN
ejpam-6617	53	13	,	,	PUNCT
ejpam-6617	53	14	the	the	DET
ejpam-6617	53	15	incorporation	incorporation	NOUN
ejpam-6617	53	16	of	of	ADP
ejpam-6617	53	17	interval	interval	NOUN
ejpam-6617	53	18	-	-	PUNCT
ejpam-6617	53	19	valued	value	VERB
ejpam-6617	53	20	objective	objective	ADJ
ejpam-6617	53	21	and	and	CCONJ
ejpam-6617	53	22	constraint	constraint	NOUN
ejpam-6617	53	23	functions	function	NOUN
ejpam-6617	53	24	introduces	introduce	VERB
ejpam-6617	53	25	a	a	DET
ejpam-6617	53	26	layer	layer	NOUN
ejpam-6617	53	27	of	of	ADP
ejpam-6617	53	28	uncertainty	uncertainty	NOUN
ejpam-6617	53	29	and	and	CCONJ
ejpam-6617	53	30	imprecision	imprecision	NOUN
ejpam-6617	53	31	,	,	PUNCT
ejpam-6617	53	32	which	which	PRON
ejpam-6617	53	33	is	be	AUX
ejpam-6617	53	34	more	more	ADV
ejpam-6617	53	35	reflective	reflective	ADJ
ejpam-6617	53	36	of	of	ADP
ejpam-6617	53	37	real	real	ADJ
ejpam-6617	53	38	-	-	PUNCT
ejpam-6617	53	39	world	world	NOUN
ejpam-6617	53	40	systems	system	NOUN
ejpam-6617	53	41	.	.	PUNCT
ejpam-6617	54	1	moreover	moreover	ADV
ejpam-6617	54	2	,	,	PUNCT
ejpam-6617	54	3	unlike	unlike	ADP
ejpam-6617	54	4	earlier	early	ADJ
ejpam-6617	54	5	criteria	criterion	NOUN
ejpam-6617	54	6	that	that	PRON
ejpam-6617	54	7	focus	focus	VERB
ejpam-6617	54	8	on	on	ADP
ejpam-6617	54	9	classical	classical	ADJ
ejpam-6617	54	10	convexity	convexity	NOUN
ejpam-6617	54	11	,	,	PUNCT
ejpam-6617	54	12	this	this	DET
ejpam-6617	54	13	work	work	NOUN
ejpam-6617	54	14	applies	apply	VERB
ejpam-6617	54	15	lu	lu	NOUN
ejpam-6617	54	16	-	-	PUNCT
ejpam-6617	54	17	optimality	optimality	NOUN
ejpam-6617	54	18	conditions	condition	NOUN
ejpam-6617	54	19	and	and	CCONJ
ejpam-6617	54	20	generalized	generalize	VERB
ejpam-6617	54	21	-	-	PUNCT
ejpam-6617	54	22	invexity	invexity	NOUN
ejpam-6617	54	23	criteria	criterion	NOUN
ejpam-6617	54	24	that	that	PRON
ejpam-6617	54	25	offer	offer	VERB
ejpam-6617	54	26	a	a	DET
ejpam-6617	54	27	broader	broad	ADJ
ejpam-6617	54	28	,	,	PUNCT
ejpam-6617	54	29	more	more	ADV
ejpam-6617	54	30	flexible	flexible	ADJ
ejpam-6617	54	31	framework	framework	NOUN
ejpam-6617	54	32	for	for	ADP
ejpam-6617	54	33	establishing	establish	VERB
ejpam-6617	54	34	optimality	optimality	NOUN
ejpam-6617	54	35	in	in	ADP
ejpam-6617	54	36	uncertain	uncertain	ADJ
ejpam-6617	54	37	fractional	fractional	ADJ
ejpam-6617	54	38	variational	variational	ADJ
ejpam-6617	54	39	environments	environment	NOUN
ejpam-6617	54	40	.	.	PUNCT
ejpam-6617	55	1	the	the	DET
ejpam-6617	55	2	proposed	propose	VERB
ejpam-6617	55	3	approach	approach	NOUN
ejpam-6617	55	4	also	also	ADV
ejpam-6617	55	5	contributes	contribute	VERB
ejpam-6617	55	6	by	by	ADP
ejpam-6617	55	7	establishing	establish	VERB
ejpam-6617	55	8	karush	karush	ADJ
ejpam-6617	55	9	-	-	PUNCT
ejpam-6617	55	10	kuhn	kuhn	PROPN
ejpam-6617	55	11	-	-	PUNCT
ejpam-6617	55	12	tucker	tucker	NOUN
ejpam-6617	55	13	-	-	PUNCT
ejpam-6617	55	14	type	type	NOUN
ejpam-6617	55	15	sufficient	sufficient	ADJ
ejpam-6617	55	16	optimality	optimality	NOUN
ejpam-6617	55	17	conditions	condition	NOUN
ejpam-6617	55	18	and	and	CCONJ
ejpam-6617	55	19	analyzing	analyze	VERB
ejpam-6617	55	20	wolfe	wolfe	PROPN
ejpam-6617	55	21	-	-	PUNCT
ejpam-6617	55	22	type	type	NOUN
ejpam-6617	55	23	duality	duality	NOUN
ejpam-6617	55	24	in	in	ADP
ejpam-6617	55	25	the	the	DET
ejpam-6617	55	26	context	context	NOUN
ejpam-6617	55	27	of	of	ADP
ejpam-6617	55	28	intervalvalued	intervalvalue	VERB
ejpam-6617	55	29	programming	programming	NOUN
ejpam-6617	55	30	problems	problem	NOUN
ejpam-6617	55	31	with	with	ADP
ejpam-6617	55	32	caputo	caputo	PROPN
ejpam-6617	55	33	-	-	PUNCT
ejpam-6617	55	34	fabrizio	fabrizio	PROPN
ejpam-6617	55	35	derivatives	derivative	NOUN
ejpam-6617	55	36	.	.	PUNCT
ejpam-6617	56	1	these	these	DET
ejpam-6617	56	2	enhancements	enhancement	NOUN
ejpam-6617	56	3	allow	allow	VERB
ejpam-6617	56	4	for	for	ADP
ejpam-6617	56	5	a	a	DET
ejpam-6617	56	6	more	more	ADV
ejpam-6617	56	7	generalized	generalized	ADJ
ejpam-6617	56	8	efficiency	efficiency	NOUN
ejpam-6617	56	9	framework	framework	NOUN
ejpam-6617	56	10	than	than	ADP
ejpam-6617	56	11	those	those	PRON
ejpam-6617	56	12	discussed	discuss	VERB
ejpam-6617	56	13	in	in	ADP
ejpam-6617	56	14	[	[	X
ejpam-6617	56	15	28	28	NUM
ejpam-6617	56	16	]	]	X
ejpam-6617	57	1	[	[	X
ejpam-6617	57	2	31	31	NUM
ejpam-6617	57	3	]	]	PUNCT
ejpam-6617	57	4	,	,	PUNCT
ejpam-6617	57	5	and	and	CCONJ
ejpam-6617	57	6	[	[	X
ejpam-6617	57	7	29	29	NUM
ejpam-6617	57	8	]	]	PUNCT
ejpam-6617	57	9	,	,	PUNCT
ejpam-6617	57	10	and	and	CCONJ
ejpam-6617	57	11	facilitate	facilitate	VERB
ejpam-6617	57	12	a	a	DET
ejpam-6617	57	13	better	well	ADJ
ejpam-6617	57	14	understanding	understanding	NOUN
ejpam-6617	57	15	of	of	ADP
ejpam-6617	57	16	solution	solution	NOUN
ejpam-6617	57	17	robustness	robustness	NOUN
ejpam-6617	57	18	under	under	ADP
ejpam-6617	57	19	fuzzy	fuzzy	ADJ
ejpam-6617	57	20	uncertainty	uncertainty	NOUN
ejpam-6617	57	21	and	and	CCONJ
ejpam-6617	57	22	memory	memory	NOUN
ejpam-6617	57	23	effects	effect	NOUN
ejpam-6617	57	24	introduced	introduce	VERB
ejpam-6617	57	25	by	by	ADP
ejpam-6617	57	26	the	the	DET
ejpam-6617	57	27	exponential	exponential	ADJ
ejpam-6617	57	28	kernel	kernel	NOUN
ejpam-6617	57	29	.	.	PUNCT
ejpam-6617	58	1	we	we	PRON
ejpam-6617	58	2	will	will	AUX
ejpam-6617	58	3	now	now	ADV
ejpam-6617	58	4	continue	continue	VERB
ejpam-6617	58	5	to	to	PART
ejpam-6617	58	6	discuss	discuss	VERB
ejpam-6617	58	7	this	this	DET
ejpam-6617	58	8	article	article	NOUN
ejpam-6617	58	9	’s	’s	PART
ejpam-6617	58	10	contents	content	NOUN
ejpam-6617	58	11	.	.	PUNCT
ejpam-6617	59	1	several	several	ADJ
ejpam-6617	59	2	fractional	fractional	ADJ
ejpam-6617	59	3	calculus	calculus	NOUN
ejpam-6617	59	4	ideas	idea	NOUN
ejpam-6617	59	5	,	,	PUNCT
ejpam-6617	59	6	concepts	concept	NOUN
ejpam-6617	59	7	,	,	PUNCT
ejpam-6617	59	8	and	and	CCONJ
ejpam-6617	59	9	features	feature	NOUN
ejpam-6617	59	10	were	be	AUX
ejpam-6617	59	11	reviewed	review	VERB
ejpam-6617	59	12	in	in	ADP
ejpam-6617	59	13	preliminary	preliminary	ADJ
ejpam-6617	59	14	section	section	NOUN
ejpam-6617	59	15	2	2	NUM
ejpam-6617	59	16	.	.	PUNCT
ejpam-6617	60	1	we	we	PRON
ejpam-6617	60	2	also	also	ADV
ejpam-6617	60	3	go	go	VERB
ejpam-6617	60	4	through	through	ADP
ejpam-6617	60	5	the	the	DET
ejpam-6617	60	6	lu	lu	NOUN
ejpam-6617	60	7	-	-	ADJ
ejpam-6617	60	8	optimal	optimal	ADJ
ejpam-6617	60	9	approach	approach	NOUN
ejpam-6617	60	10	to	to	ADP
ejpam-6617	60	11	the	the	DET
ejpam-6617	60	12	programming	programming	NOUN
ejpam-6617	60	13	problem	problem	NOUN
ejpam-6617	60	14	of	of	ADP
ejpam-6617	60	15	variational	variational	ADJ
ejpam-6617	60	16	calculus	calculus	NOUN
ejpam-6617	60	17	.	.	PUNCT
ejpam-6617	61	1	we	we	PRON
ejpam-6617	61	2	examine	examine	VERB
ejpam-6617	61	3	the	the	DET
ejpam-6617	61	4	fractional	fractional	ADJ
ejpam-6617	61	5	derivative	derivative	ADJ
ejpam-6617	61	6	c	c	NOUN
ejpam-6617	61	7	-	-	PUNCT
ejpam-6617	61	8	f	f	PROPN
ejpam-6617	61	9	for	for	ADP
ejpam-6617	61	10	the	the	DET
ejpam-6617	61	11	kkt	kkt	NOUN
ejpam-6617	61	12	-	-	PUNCT
ejpam-6617	61	13	type	type	NOUN
ejpam-6617	61	14	sufficient	sufficient	ADJ
ejpam-6617	61	15	optimality	optimality	NOUN
ejpam-6617	61	16	conditions	condition	NOUN
ejpam-6617	61	17	in	in	ADP
ejpam-6617	61	18	section	section	NOUN
ejpam-6617	61	19	3	3	NUM
ejpam-6617	61	20	.	.	PUNCT
ejpam-6617	62	1	we	we	PRON
ejpam-6617	62	2	establish	establish	VERB
ejpam-6617	62	3	and	and	CCONJ
ejpam-6617	62	4	verify	verify	VERB
ejpam-6617	62	5	weak	weak	ADJ
ejpam-6617	62	6	,	,	PUNCT
ejpam-6617	62	7	strong	strong	ADJ
ejpam-6617	62	8	,	,	PUNCT
ejpam-6617	62	9	and	and	CCONJ
ejpam-6617	62	10	strict	strict	ADJ
ejpam-6617	62	11	converse	converse	NOUN
ejpam-6617	62	12	duality	duality	NOUN
ejpam-6617	62	13	theorems	theorem	VERB
ejpam-6617	62	14	for	for	ADP
ejpam-6617	62	15	the	the	DET
ejpam-6617	62	16	wolfe	wolfe	PROPN
ejpam-6617	62	17	-	-	PUNCT
ejpam-6617	62	18	type	type	NOUN
ejpam-6617	62	19	dual	dual	ADJ
ejpam-6617	62	20	model	model	NOUN
ejpam-6617	62	21	in	in	ADP
ejpam-6617	62	22	section	section	NOUN
ejpam-6617	62	23	4	4	NUM
ejpam-6617	62	24	and	and	CCONJ
ejpam-6617	62	25	section	section	NOUN
ejpam-6617	62	26	5	5	NUM
ejpam-6617	62	27	contains	contain	VERB
ejpam-6617	62	28	the	the	DET
ejpam-6617	62	29	article	article	NOUN
ejpam-6617	62	30	’s	’s	PART
ejpam-6617	62	31	conclusion	conclusion	NOUN
ejpam-6617	62	32	and	and	CCONJ
ejpam-6617	62	33	future	future	ADJ
ejpam-6617	62	34	direction	direction	NOUN
ejpam-6617	62	35	.	.	PUNCT
ejpam-6617	63	1	2	2	X
ejpam-6617	63	2	.	.	X
ejpam-6617	63	3	preliminaries	preliminary	NOUN
ejpam-6617	63	4	this	this	DET
ejpam-6617	63	5	section	section	NOUN
ejpam-6617	63	6	recollects	recollect	VERB
ejpam-6617	63	7	some	some	DET
ejpam-6617	63	8	notations	notation	NOUN
ejpam-6617	63	9	,	,	PUNCT
ejpam-6617	63	10	symbols	symbol	NOUN
ejpam-6617	63	11	,	,	PUNCT
ejpam-6617	63	12	and	and	CCONJ
ejpam-6617	63	13	definitions	definition	NOUN
ejpam-6617	63	14	that	that	PRON
ejpam-6617	63	15	will	will	AUX
ejpam-6617	63	16	be	be	AUX
ejpam-6617	63	17	important	important	ADJ
ejpam-6617	63	18	in	in	ADP
ejpam-6617	63	19	the	the	DET
ejpam-6617	63	20	follow	follow	NOUN
ejpam-6617	63	21	-	-	PUNCT
ejpam-6617	63	22	up	up	NOUN
ejpam-6617	63	23	to	to	ADP
ejpam-6617	63	24	this	this	DET
ejpam-6617	63	25	work	work	NOUN
ejpam-6617	63	26	.	.	PUNCT
ejpam-6617	64	1	for	for	ADP
ejpam-6617	64	2	any	any	DET
ejpam-6617	64	3	number	number	NOUN
ejpam-6617	64	4	of	of	ADP
ejpam-6617	64	5	intervals	interval	NOUN
ejpam-6617	64	6	a	a	DET
ejpam-6617	64	7	=	=	X
ejpam-6617	64	8	[	[	PUNCT
ejpam-6617	64	9	al	al	PROPN
ejpam-6617	64	10	,	,	PUNCT
ejpam-6617	64	11	au	au	X
ejpam-6617	64	12	]	]	PUNCT
ejpam-6617	64	13	and	and	CCONJ
ejpam-6617	64	14	b	b	X
ejpam-6617	64	15	=	=	PRON
ejpam-6617	64	16	[	[	PUNCT
ejpam-6617	64	17	bl	bl	INTJ
ejpam-6617	64	18	,	,	PUNCT
ejpam-6617	64	19	bu	bu	PROPN
ejpam-6617	64	20	]	]	PUNCT
ejpam-6617	64	21	where	where	SCONJ
ejpam-6617	64	22	al	al	PROPN
ejpam-6617	64	23	,	,	PUNCT
ejpam-6617	64	24	au	au	ADV
ejpam-6617	64	25	,	,	PUNCT
ejpam-6617	64	26	bl	bl	INTJ
ejpam-6617	64	27	,	,	PUNCT
ejpam-6617	64	28	bu	bu	PROPN
ejpam-6617	64	29	∈	∈	PROPN
ejpam-6617	64	30	r	r	NOUN
ejpam-6617	64	31	,	,	PUNCT
ejpam-6617	64	32	we	we	PRON
ejpam-6617	64	33	define	define	VERB
ejpam-6617	64	34	the	the	DET
ejpam-6617	64	35	following	follow	VERB
ejpam-6617	64	36	partial	partial	ADJ
ejpam-6617	64	37	ordering	ordering	NOUN
ejpam-6617	64	38	relations	relation	NOUN
ejpam-6617	64	39	on	on	ADP
ejpam-6617	64	40	the	the	DET
ejpam-6617	64	41	lines	line	NOUN
ejpam-6617	64	42	of	of	ADP
ejpam-6617	64	43	[	[	X
ejpam-6617	64	44	33	33	NUM
ejpam-6617	64	45	]	]	PUNCT
ejpam-6617	64	46	and	and	CCONJ
ejpam-6617	64	47	[	[	X
ejpam-6617	64	48	21	21	NUM
ejpam-6617	64	49	]	]	X
ejpam-6617	64	50	:	:	PUNCT
ejpam-6617	64	51	(	(	PUNCT
ejpam-6617	64	52	i	i	NOUN
ejpam-6617	64	53	)	)	PUNCT
ejpam-6617	64	54	a	a	DET
ejpam-6617	64	55	⪯lu	⪯lu	NUM
ejpam-6617	64	56	b	b	X
ejpam-6617	64	57	⇐	⇐	ADJ
ejpam-6617	64	58	⇒	⇒	PROPN
ejpam-6617	64	59	al	al	PROPN
ejpam-6617	64	60	≤	≤	PROPN
ejpam-6617	64	61	bland	bland	ADJ
ejpam-6617	64	62	au	au	ADJ
ejpam-6617	64	63	≤	≤	NOUN
ejpam-6617	64	64	bu	bu	ADV
ejpam-6617	64	65	.	.	PUNCT
ejpam-6617	65	1	v.	v.	CCONJ
ejpam-6617	65	2	rayanki	rayanki	PROPN
ejpam-6617	65	3	et	et	PROPN
ejpam-6617	65	4	al	al	PROPN
ejpam-6617	65	5	.	.	PUNCT
ejpam-6617	65	6	/	/	SYM
ejpam-6617	65	7	eur	eur	PROPN
ejpam-6617	65	8	.	.	PUNCT
ejpam-6617	66	1	j.	j.	PROPN
ejpam-6617	66	2	pure	pure	PROPN
ejpam-6617	66	3	appl	appl	PROPN
ejpam-6617	66	4	.	.	PROPN
ejpam-6617	66	5	math	math	PROPN
ejpam-6617	66	6	,	,	PUNCT
ejpam-6617	66	7	18	18	NUM
ejpam-6617	66	8	(	(	PUNCT
ejpam-6617	66	9	3	3	NUM
ejpam-6617	66	10	)	)	PUNCT
ejpam-6617	66	11	(	(	PUNCT
ejpam-6617	66	12	2025	2025	NUM
ejpam-6617	66	13	)	)	PUNCT
ejpam-6617	66	14	,	,	PUNCT
ejpam-6617	66	15	6617	6617	NUM
ejpam-6617	66	16	4	4	NUM
ejpam-6617	66	17	of	of	ADP
ejpam-6617	66	18	38	38	NUM
ejpam-6617	66	19	(	(	PUNCT
ejpam-6617	66	20	ii	ii	NOUN
ejpam-6617	66	21	)	)	PUNCT
ejpam-6617	66	22	a	a	DET
ejpam-6617	66	23	≺lu	≺lu	PROPN
ejpam-6617	66	24	b	b	NUM
ejpam-6617	66	25	⇐	⇐	PROPN
ejpam-6617	66	26	⇒	⇒	PROPN
ejpam-6617	66	27	al	al	PROPN
ejpam-6617	66	28	<	<	X
ejpam-6617	66	29	bl	bl	PROPN
ejpam-6617	66	30	,	,	PUNCT
ejpam-6617	66	31	au	au	X
ejpam-6617	66	32	≤	≤	PROPN
ejpam-6617	66	33	bu	bu	ADV
ejpam-6617	66	34	,	,	PUNCT
ejpam-6617	66	35	or	or	CCONJ
ejpam-6617	66	36	al	al	PROPN
ejpam-6617	66	37	≤	≤	PROPN
ejpam-6617	66	38	bl	bl	PROPN
ejpam-6617	66	39	,	,	PUNCT
ejpam-6617	66	40	au	au	X
ejpam-6617	66	41	<	<	X
ejpam-6617	66	42	bu	bu	INTJ
ejpam-6617	66	43	,	,	PUNCT
ejpam-6617	66	44	or	or	CCONJ
ejpam-6617	66	45	al	al	PROPN
ejpam-6617	66	46	<	<	X
ejpam-6617	66	47	bl	bl	PROPN
ejpam-6617	66	48	,	,	PUNCT
ejpam-6617	66	49	au	au	X
ejpam-6617	66	50	<	<	X
ejpam-6617	66	51	bu	bu	INTJ
ejpam-6617	66	52	.	.	PUNCT
ejpam-6617	67	1	throughout	throughout	ADP
ejpam-6617	67	2	the	the	DET
ejpam-6617	67	3	paper	paper	NOUN
ejpam-6617	67	4	,	,	PUNCT
ejpam-6617	67	5	κ	κ	X
ejpam-6617	67	6	:	:	PUNCT
ejpam-6617	68	1	[	[	X
ejpam-6617	68	2	a1	a1	NOUN
ejpam-6617	68	3	,	,	PUNCT
ejpam-6617	68	4	a2	a2	PROPN
ejpam-6617	68	5	]	]	PUNCT
ejpam-6617	68	6	→	→	SYM
ejpam-6617	68	7	r	r	NOUN
ejpam-6617	68	8	is	be	AUX
ejpam-6617	68	9	a	a	DET
ejpam-6617	68	10	function	function	NOUN
ejpam-6617	68	11	of	of	ADP
ejpam-6617	68	12	class	class	NOUN
ejpam-6617	68	13	c1	c1	PROPN
ejpam-6617	68	14	and	and	CCONJ
ejpam-6617	68	15	θ•	θ•	PROPN
ejpam-6617	68	16	∈	∈	PROPN
ejpam-6617	68	17	(	(	PUNCT
ejpam-6617	68	18	0	0	NUM
ejpam-6617	68	19	,	,	PUNCT
ejpam-6617	68	20	1	1	NUM
ejpam-6617	68	21	)	)	PUNCT
ejpam-6617	68	22	.	.	PUNCT
ejpam-6617	69	1	definition	definition	NOUN
ejpam-6617	69	2	1	1	NUM
ejpam-6617	69	3	.	.	PUNCT
ejpam-6617	70	1	[	[	X
ejpam-6617	70	2	8	8	NUM
ejpam-6617	70	3	]	]	PUNCT
ejpam-6617	70	4	left	left	ADJ
ejpam-6617	70	5	and	and	CCONJ
ejpam-6617	70	6	right	right	ADJ
ejpam-6617	70	7	fractional	fractional	ADJ
ejpam-6617	70	8	derivatives	derivative	NOUN
ejpam-6617	70	9	of	of	ADP
ejpam-6617	70	10	riemann	riemann	PROPN
ejpam-6617	70	11	-	-	PUNCT
ejpam-6617	70	12	liouville	liouville	NOUN
ejpam-6617	70	13	of	of	ADP
ejpam-6617	70	14	order	order	NOUN
ejpam-6617	70	15	θ•	θ•	NOUN
ejpam-6617	70	16	are	be	AUX
ejpam-6617	70	17	defined	define	VERB
ejpam-6617	70	18	by	by	ADP
ejpam-6617	70	19	a1dθ•	a1dθ•	PROPN
ejpam-6617	70	20	ς	ς	PROPN
ejpam-6617	70	21	κ(ς	κ(ς	PROPN
ejpam-6617	70	22	)	)	PUNCT
ejpam-6617	70	23	=	=	SYM
ejpam-6617	70	24	1	1	NUM
ejpam-6617	70	25	γ(1−	γ(1−	NOUN
ejpam-6617	70	26	θ•	θ•	NOUN
ejpam-6617	70	27	)	)	PUNCT
ejpam-6617	71	1	d	d	NOUN
ejpam-6617	71	2	dς	dς	X
ejpam-6617	71	3	∫	∫	PROPN
ejpam-6617	71	4	ς	ς	PROPN
ejpam-6617	71	5	a1	a1	PROPN
ejpam-6617	71	6	(	(	PUNCT
ejpam-6617	71	7	ς	ς	PROPN
ejpam-6617	71	8	−	−	PROPN
ejpam-6617	71	9	ν)−θ•κ(ν)dν	ν)−θ•κ(ν)dν	ADJ
ejpam-6617	71	10	,	,	PUNCT
ejpam-6617	71	11	ςdθ•	ςdθ•	PROPN
ejpam-6617	71	12	a2κ(θ	a2κ(θ	PROPN
ejpam-6617	71	13	•	•	NUM
ejpam-6617	71	14	)	)	PUNCT
ejpam-6617	71	15	=	=	SYM
ejpam-6617	72	1	−	−	PROPN
ejpam-6617	72	2	1	1	NUM
ejpam-6617	72	3	γ(1−	γ(1−	NOUN
ejpam-6617	72	4	θ•	θ•	NOUN
ejpam-6617	72	5	)	)	PUNCT
ejpam-6617	73	1	d	d	PROPN
ejpam-6617	73	2	dς	dς	X
ejpam-6617	73	3	∫	∫	PROPN
ejpam-6617	73	4	a2	a2	PROPN
ejpam-6617	73	5	ς	ς	PROPN
ejpam-6617	73	6	(	(	PUNCT
ejpam-6617	73	7	ν	ν	X
ejpam-6617	73	8	−	−	NOUN
ejpam-6617	73	9	ς)−θ•κ(ν)dν	ς)−θ•κ(ν)dν	ADJ
ejpam-6617	73	10	,	,	PUNCT
ejpam-6617	73	11	θ•	θ•	PROPN
ejpam-6617	73	12	∈	∈	PROPN
ejpam-6617	73	13	(	(	PUNCT
ejpam-6617	73	14	0	0	NUM
ejpam-6617	73	15	,	,	PUNCT
ejpam-6617	73	16	1	1	NUM
ejpam-6617	73	17	)	)	PUNCT
ejpam-6617	73	18	.	.	PUNCT
ejpam-6617	74	1	definition	definition	NOUN
ejpam-6617	74	2	2	2	NUM
ejpam-6617	74	3	.	.	PUNCT
ejpam-6617	75	1	[	[	X
ejpam-6617	75	2	34	34	NUM
ejpam-6617	75	3	]	]	PUNCT
ejpam-6617	75	4	the	the	DET
ejpam-6617	75	5	fractional	fractional	ADJ
ejpam-6617	75	6	derivative	derivative	NOUN
ejpam-6617	75	7	of	of	ADP
ejpam-6617	75	8	caputo	caputo	PROPN
ejpam-6617	75	9	,	,	PUNCT
ejpam-6617	75	10	κ(ς	κ(ς	PROPN
ejpam-6617	75	11	)	)	PUNCT
ejpam-6617	75	12	:	:	PUNCT
ejpam-6617	76	1	[	[	X
ejpam-6617	76	2	a1	a1	NOUN
ejpam-6617	76	3	,	,	PUNCT
ejpam-6617	76	4	a2	a2	PROPN
ejpam-6617	76	5	]	]	PUNCT
ejpam-6617	76	6	→	→	PUNCT
ejpam-6617	76	7	r	r	NOUN
ejpam-6617	76	8	of	of	ADP
ejpam-6617	76	9	order	order	NOUN
ejpam-6617	76	10	θ•	θ•	PROPN
ejpam-6617	76	11	∈	∈	PROPN
ejpam-6617	76	12	(	(	PUNCT
ejpam-6617	76	13	0	0	NUM
ejpam-6617	76	14	,	,	PUNCT
ejpam-6617	76	15	1	1	NUM
ejpam-6617	76	16	)	)	PUNCT
ejpam-6617	76	17	is	be	AUX
ejpam-6617	76	18	stated	state	VERB
ejpam-6617	76	19	to	to	PART
ejpam-6617	76	20	be	be	AUX
ejpam-6617	76	21	cdθ•	cdθ•	ADJ
ejpam-6617	76	22	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	76	23	)	)	PUNCT
ejpam-6617	77	1	=	=	SYM
ejpam-6617	77	2	1	1	NUM
ejpam-6617	77	3	γ(1−	γ(1−	NOUN
ejpam-6617	77	4	θ•	θ•	NOUN
ejpam-6617	77	5	)	)	PUNCT
ejpam-6617	78	1	d	d	NOUN
ejpam-6617	78	2	dς	dς	X
ejpam-6617	78	3	∫	∫	PROPN
ejpam-6617	78	4	ς	ς	PROPN
ejpam-6617	78	5	a1	a1	PROPN
ejpam-6617	78	6	1	1	NUM
ejpam-6617	78	7	(	(	PUNCT
ejpam-6617	78	8	ς	ς	PROPN
ejpam-6617	78	9	−	−	PROPN
ejpam-6617	79	1	ν)θ•	ν)θ•	PRON
ejpam-6617	79	2	[	[	PUNCT
ejpam-6617	79	3	κ(ν)−	κ(ν)−	NOUN
ejpam-6617	79	4	κ(a)]dν	κ(a)]dν	NOUN
ejpam-6617	79	5	.	.	PUNCT
ejpam-6617	80	1	if	if	SCONJ
ejpam-6617	80	2	κ	κ	PROPN
ejpam-6617	80	3	∈	∈	PROPN
ejpam-6617	80	4	c1	c1	NOUN
ejpam-6617	80	5	,	,	PUNCT
ejpam-6617	80	6	then	then	ADV
ejpam-6617	80	7	cdθ•	cdθ•	PROPN
ejpam-6617	80	8	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	80	9	)	)	PUNCT
ejpam-6617	80	10	=	=	SYM
ejpam-6617	80	11	1	1	NUM
ejpam-6617	80	12	γ(1−	γ(1−	NOUN
ejpam-6617	80	13	θ•	θ•	NOUN
ejpam-6617	80	14	)	)	PUNCT
ejpam-6617	81	1	d	d	NOUN
ejpam-6617	81	2	dς	dς	X
ejpam-6617	81	3	∫	∫	PROPN
ejpam-6617	81	4	ς	ς	PROPN
ejpam-6617	81	5	a1	a1	PROPN
ejpam-6617	81	6	1	1	NUM
ejpam-6617	81	7	(	(	PUNCT
ejpam-6617	81	8	ς	ς	PROPN
ejpam-6617	81	9	−	−	PROPN
ejpam-6617	81	10	ν)θ•	ν)θ•	PROPN
ejpam-6617	81	11	κ′(ν)dν	κ′(ν)dν	PROPN
ejpam-6617	81	12	.	.	PROPN
ejpam-6617	82	1	as	as	ADP
ejpam-6617	82	2	θ•	θ•	PROPN
ejpam-6617	82	3	→	→	SYM
ejpam-6617	82	4	1	1	NUM
ejpam-6617	82	5	,	,	PUNCT
ejpam-6617	82	6	cdθ•	cdθ•	ADJ
ejpam-6617	82	7	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	82	8	)	)	PUNCT
ejpam-6617	82	9	approaches	approach	NOUN
ejpam-6617	82	10	to	to	ADP
ejpam-6617	82	11	κ′(ς	κ′(ς	PUNCT
ejpam-6617	82	12	)	)	PUNCT
ejpam-6617	82	13	.	.	PUNCT
ejpam-6617	83	1	definition	definition	NOUN
ejpam-6617	83	2	3	3	NUM
ejpam-6617	83	3	.	.	PUNCT
ejpam-6617	84	1	[	[	X
ejpam-6617	84	2	30	30	NUM
ejpam-6617	84	3	]	]	PUNCT
ejpam-6617	84	4	the	the	DET
ejpam-6617	84	5	operator	operator	NOUN
ejpam-6617	84	6	of	of	ADP
ejpam-6617	84	7	new	new	ADJ
ejpam-6617	84	8	caputo	caputo	PROPN
ejpam-6617	84	9	-	-	PUNCT
ejpam-6617	84	10	fabrizio	fabrizio	PROPN
ejpam-6617	84	11	(	(	PUNCT
ejpam-6617	84	12	cf	cf	NOUN
ejpam-6617	84	13	)	)	PUNCT
ejpam-6617	84	14	fractional	fractional	ADJ
ejpam-6617	84	15	derivative	derivative	NOUN
ejpam-6617	84	16	is	be	AUX
ejpam-6617	84	17	described	describe	VERB
ejpam-6617	84	18	as	as	ADP
ejpam-6617	84	19	cfdθ•	cfdθ•	PROPN
ejpam-6617	84	20	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	84	21	)	)	PUNCT
ejpam-6617	85	1	=	=	SYM
ejpam-6617	85	2	κ(θ•	κ(θ•	NOUN
ejpam-6617	85	3	)	)	PUNCT
ejpam-6617	85	4	(	(	PUNCT
ejpam-6617	85	5	1−	1−	NUM
ejpam-6617	85	6	θ•	θ•	NOUN
ejpam-6617	85	7	)	)	PUNCT
ejpam-6617	85	8	∫	∫	PROPN
ejpam-6617	86	1	ς	ς	PROPN
ejpam-6617	86	2	a1	a1	PROPN
ejpam-6617	86	3	exp	exp	NOUN
ejpam-6617	86	4	(	(	PUNCT
ejpam-6617	86	5	−	−	PROPN
ejpam-6617	86	6	θ•(ς	θ•(ς	ADJ
ejpam-6617	86	7	−	−	NOUN
ejpam-6617	86	8	ν	ν	NOUN
ejpam-6617	86	9	)	)	PUNCT
ejpam-6617	86	10	(	(	PUNCT
ejpam-6617	86	11	1−	1−	NUM
ejpam-6617	86	12	θ•	θ•	NOUN
ejpam-6617	86	13	)	)	PUNCT
ejpam-6617	86	14	)	)	PUNCT
ejpam-6617	87	1	κ′(ν)dν	κ′(ν)dν	PROPN
ejpam-6617	87	2	,	,	PUNCT
ejpam-6617	87	3	θ•	θ•	PROPN
ejpam-6617	87	4	∈	∈	PROPN
ejpam-6617	87	5	(	(	PUNCT
ejpam-6617	87	6	0	0	NUM
ejpam-6617	87	7	,	,	PUNCT
ejpam-6617	87	8	1	1	NUM
ejpam-6617	87	9	)	)	PUNCT
ejpam-6617	87	10	,	,	PUNCT
ejpam-6617	87	11	where	where	SCONJ
ejpam-6617	87	12	κ(θ•	κ(θ•	NOUN
ejpam-6617	87	13	)	)	PUNCT
ejpam-6617	87	14	signifies	signify	VERB
ejpam-6617	87	15	the	the	DET
ejpam-6617	87	16	normalization	normalization	NOUN
ejpam-6617	87	17	function	function	NOUN
ejpam-6617	87	18	(	(	PUNCT
ejpam-6617	87	19	1−	1−	NUM
ejpam-6617	87	20	θ•)+	θ•)+	ADJ
ejpam-6617	87	21	θ•	θ•	PROPN
ejpam-6617	87	22	γ(θ•	γ(θ•	NOUN
ejpam-6617	87	23	)	)	PUNCT
ejpam-6617	87	24	with	with	ADP
ejpam-6617	87	25	the	the	DET
ejpam-6617	87	26	property	property	NOUN
ejpam-6617	87	27	κ(0	κ(0	NOUN
ejpam-6617	87	28	)	)	PUNCT
ejpam-6617	87	29	=	=	SYM
ejpam-6617	87	30	κ(1	κ(1	PROPN
ejpam-6617	87	31	)	)	PUNCT
ejpam-6617	87	32	=	=	SYM
ejpam-6617	88	1	1	1	X
ejpam-6617	88	2	.	.	PUNCT
ejpam-6617	88	3	clearly	clearly	ADV
ejpam-6617	88	4	cfdθ•	cfdθ•	PROPN
ejpam-6617	88	5	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	88	6	)	)	PUNCT
ejpam-6617	89	1	=	=	PUNCT
ejpam-6617	89	2	0	0	NUM
ejpam-6617	89	3	,	,	PUNCT
ejpam-6617	89	4	if	if	SCONJ
ejpam-6617	89	5	κ(ς	κ(ς	PROPN
ejpam-6617	89	6	)	)	PUNCT
ejpam-6617	89	7	is	be	AUX
ejpam-6617	89	8	a	a	DET
ejpam-6617	89	9	constant	constant	ADJ
ejpam-6617	89	10	function	function	NOUN
ejpam-6617	89	11	,	,	PUNCT
ejpam-6617	89	12	i.e	i.e	PRON
ejpam-6617	89	13	,	,	PUNCT
ejpam-6617	89	14	a	a	DET
ejpam-6617	89	15	constant	constant	ADJ
ejpam-6617	89	16	function	function	NOUN
ejpam-6617	89	17	’s	’s	PART
ejpam-6617	89	18	cf	cf	NOUN
ejpam-6617	89	19	derivative	derivative	NOUN
ejpam-6617	89	20	equals	equal	VERB
ejpam-6617	89	21	zero	zero	NUM
ejpam-6617	89	22	,	,	PUNCT
ejpam-6617	89	23	but	but	CCONJ
ejpam-6617	89	24	the	the	DET
ejpam-6617	89	25	cf	cf	NOUN
ejpam-6617	89	26	derivative	derivative	NOUN
ejpam-6617	89	27	lacks	lack	VERB
ejpam-6617	89	28	a	a	DET
ejpam-6617	89	29	unique	unique	ADJ
ejpam-6617	89	30	kernel	kernel	NOUN
ejpam-6617	89	31	for	for	ADP
ejpam-6617	89	32	ς	ς	PROPN
ejpam-6617	89	33	=	=	SYM
ejpam-6617	89	34	ν	ν	NOUN
ejpam-6617	89	35	,	,	PUNCT
ejpam-6617	89	36	like	like	ADP
ejpam-6617	89	37	the	the	DET
ejpam-6617	89	38	caputo	caputo	PROPN
ejpam-6617	89	39	derivative	derivative	PROPN
ejpam-6617	89	40	.	.	PUNCT
ejpam-6617	90	1	remark	remark	PROPN
ejpam-6617	90	2	1	1	NUM
ejpam-6617	90	3	.	.	PUNCT
ejpam-6617	91	1	as	as	ADP
ejpam-6617	91	2	θ•	θ•	PROPN
ejpam-6617	91	3	→	→	SYM
ejpam-6617	91	4	1	1	NUM
ejpam-6617	91	5	,	,	PUNCT
ejpam-6617	91	6	cfdθ•	cfdθ•	PROPN
ejpam-6617	91	7	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	91	8	)	)	PUNCT
ejpam-6617	91	9	⇒	⇒	NOUN
ejpam-6617	91	10	κ′(ς	κ′(ς	PUNCT
ejpam-6617	91	11	)	)	PUNCT
ejpam-6617	91	12	and	and	CCONJ
ejpam-6617	91	13	as	as	ADP
ejpam-6617	91	14	θ•	θ•	PROPN
ejpam-6617	91	15	→	→	SYM
ejpam-6617	91	16	0	0	NUM
ejpam-6617	91	17	,	,	PUNCT
ejpam-6617	91	18	cfdθ•	cfdθ•	PROPN
ejpam-6617	91	19	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	91	20	)	)	PUNCT
ejpam-6617	91	21	⇒	⇒	NOUN
ejpam-6617	91	22	κ(ς)−κ(a1	κ(ς)−κ(a1	PROPN
ejpam-6617	91	23	)	)	PUNCT
ejpam-6617	91	24	.	.	PUNCT
ejpam-6617	92	1	definition	definition	NOUN
ejpam-6617	92	2	4	4	NUM
ejpam-6617	92	3	.	.	PUNCT
ejpam-6617	93	1	[	[	X
ejpam-6617	93	2	1	1	X
ejpam-6617	93	3	]	]	PUNCT
ejpam-6617	93	4	the	the	DET
ejpam-6617	93	5	right	right	PROPN
ejpam-6617	93	6	caputo	caputo	PROPN
ejpam-6617	93	7	-	-	PUNCT
ejpam-6617	93	8	fabrizio	fabrizio	PROPN
ejpam-6617	93	9	fractional	fractional	ADJ
ejpam-6617	93	10	derivative	derivative	NOUN
ejpam-6617	93	11	is	be	AUX
ejpam-6617	93	12	defined	define	VERB
ejpam-6617	93	13	as	as	ADP
ejpam-6617	93	14	cfdθ•	cfdθ•	PROPN
ejpam-6617	93	15	a2−κ(ς	a2−κ(ς	NOUN
ejpam-6617	93	16	)	)	PUNCT
ejpam-6617	94	1	=	=	SYM
ejpam-6617	94	2	κ(θ•	κ(θ•	NOUN
ejpam-6617	94	3	)	)	PUNCT
ejpam-6617	94	4	(	(	PUNCT
ejpam-6617	94	5	1−	1−	NUM
ejpam-6617	94	6	θ•	θ•	NOUN
ejpam-6617	94	7	)	)	PUNCT
ejpam-6617	94	8	∫	∫	PROPN
ejpam-6617	94	9	a2	a2	PROPN
ejpam-6617	94	10	ς	ς	PROPN
ejpam-6617	94	11	exp	exp	NOUN
ejpam-6617	94	12	(	(	PUNCT
ejpam-6617	94	13	−	−	PROPN
ejpam-6617	94	14	θ•(ς	θ•(ς	ADJ
ejpam-6617	94	15	−	−	NOUN
ejpam-6617	94	16	ν	ν	NOUN
ejpam-6617	94	17	)	)	PUNCT
ejpam-6617	94	18	(	(	PUNCT
ejpam-6617	94	19	1−	1−	NUM
ejpam-6617	94	20	θ•	θ•	NOUN
ejpam-6617	94	21	)	)	PUNCT
ejpam-6617	94	22	)	)	PUNCT
ejpam-6617	95	1	κ′(ν)dν	κ′(ν)dν	PROPN
ejpam-6617	95	2	,	,	PUNCT
ejpam-6617	95	3	θ•	θ•	PROPN
ejpam-6617	95	4	∈	∈	PROPN
ejpam-6617	95	5	(	(	PUNCT
ejpam-6617	95	6	0	0	NUM
ejpam-6617	95	7	,	,	PUNCT
ejpam-6617	95	8	1	1	NUM
ejpam-6617	95	9	)	)	PUNCT
ejpam-6617	95	10	.	.	PUNCT
ejpam-6617	96	1	definition	definition	NOUN
ejpam-6617	96	2	5	5	NUM
ejpam-6617	96	3	.	.	PUNCT
ejpam-6617	97	1	the	the	DET
ejpam-6617	97	2	order	order	NOUN
ejpam-6617	97	3	of	of	ADP
ejpam-6617	97	4	sobolev	sobolev	ADJ
ejpam-6617	97	5	space	space	NOUN
ejpam-6617	97	6	1	1	NUM
ejpam-6617	97	7	∈	∈	PROPN
ejpam-6617	97	8	(	(	PUNCT
ejpam-6617	97	9	a1	a1	NOUN
ejpam-6617	97	10	,	,	PUNCT
ejpam-6617	97	11	a2	a2	PROPN
ejpam-6617	97	12	)	)	PUNCT
ejpam-6617	97	13	is	be	AUX
ejpam-6617	97	14	defined	define	VERB
ejpam-6617	97	15	:	:	PUNCT
ejpam-6617	97	16	h1(a1	h1(a1	ADJ
ejpam-6617	97	17	,	,	PUNCT
ejpam-6617	97	18	a2	a2	NOUN
ejpam-6617	97	19	)	)	PUNCT
ejpam-6617	97	20	=	=	PRON
ejpam-6617	98	1	{	{	PUNCT
ejpam-6617	98	2	y	y	PROPN
ejpam-6617	98	3	∈	∈	PROPN
ejpam-6617	98	4	l2(a1	l2(a1	NOUN
ejpam-6617	98	5	,	,	PUNCT
ejpam-6617	98	6	a2	a2	PROPN
ejpam-6617	98	7	)	)	PUNCT
ejpam-6617	99	1	|	|	ADV
ejpam-6617	100	1	y	y	PROPN
ejpam-6617	100	2	′	′	NUM
ejpam-6617	100	3	∈	∈	PROPN
ejpam-6617	100	4	l2(a1	l2(a1	NOUN
ejpam-6617	100	5	,	,	PUNCT
ejpam-6617	100	6	a2	a2	PROPN
ejpam-6617	100	7	)	)	PUNCT
ejpam-6617	100	8	}	}	PUNCT
ejpam-6617	100	9	,	,	PUNCT
ejpam-6617	100	10	y′	y′	ADV
ejpam-6617	100	11	is	be	AUX
ejpam-6617	100	12	the	the	DET
ejpam-6617	100	13	weak	weak	ADJ
ejpam-6617	100	14	derivative	derivative	NOUN
ejpam-6617	100	15	of	of	ADP
ejpam-6617	100	16	y.	y.	PROPN
ejpam-6617	100	17	v.	v.	PROPN
ejpam-6617	100	18	rayanki	rayanki	PROPN
ejpam-6617	100	19	et	et	PROPN
ejpam-6617	100	20	al	al	PROPN
ejpam-6617	100	21	.	.	PUNCT
ejpam-6617	100	22	/	/	SYM
ejpam-6617	100	23	eur	eur	PROPN
ejpam-6617	100	24	.	.	PUNCT
ejpam-6617	101	1	j.	j.	PROPN
ejpam-6617	101	2	pure	pure	PROPN
ejpam-6617	101	3	appl	appl	PROPN
ejpam-6617	101	4	.	.	PROPN
ejpam-6617	101	5	math	math	PROPN
ejpam-6617	101	6	,	,	PUNCT
ejpam-6617	101	7	18	18	NUM
ejpam-6617	101	8	(	(	PUNCT
ejpam-6617	101	9	3	3	NUM
ejpam-6617	101	10	)	)	PUNCT
ejpam-6617	101	11	(	(	PUNCT
ejpam-6617	101	12	2025	2025	NUM
ejpam-6617	101	13	)	)	PUNCT
ejpam-6617	101	14	,	,	PUNCT
ejpam-6617	101	15	6617	6617	NUM
ejpam-6617	101	16	5	5	NUM
ejpam-6617	101	17	of	of	ADP
ejpam-6617	101	18	38	38	NUM
ejpam-6617	101	19	definition	definition	NOUN
ejpam-6617	101	20	6	6	NUM
ejpam-6617	101	21	.	.	PUNCT
ejpam-6617	102	1	[	[	X
ejpam-6617	102	2	30	30	NUM
ejpam-6617	102	3	]	]	PUNCT
ejpam-6617	102	4	let	let	VERB
ejpam-6617	102	5	κ	κ	PROPN
ejpam-6617	102	6	∈	∈	PROPN
ejpam-6617	102	7	h1(a1	h1(a1	NOUN
ejpam-6617	102	8	,	,	PUNCT
ejpam-6617	102	9	a2	a2	PROPN
ejpam-6617	102	10	)	)	PUNCT
ejpam-6617	102	11	,	,	PUNCT
ejpam-6617	102	12	a2	a2	PROPN
ejpam-6617	102	13	>	>	X
ejpam-6617	102	14	a1	a1	PROPN
ejpam-6617	102	15	,	,	PUNCT
ejpam-6617	102	16	0	0	PUNCT
ejpam-6617	102	17	<	<	X
ejpam-6617	102	18	θ•	θ•	X
ejpam-6617	102	19	<	<	X
ejpam-6617	102	20	1	1	NUM
ejpam-6617	102	21	.	.	PUNCT
ejpam-6617	103	1	the	the	DET
ejpam-6617	103	2	fractional	fractional	ADJ
ejpam-6617	103	3	derivative	derivative	NOUN
ejpam-6617	103	4	of	of	ADP
ejpam-6617	103	5	cf	cf	NOUN
ejpam-6617	103	6	is	be	AUX
ejpam-6617	103	7	therefore	therefore	ADV
ejpam-6617	103	8	given	give	VERB
ejpam-6617	103	9	as	as	ADP
ejpam-6617	103	10	in	in	ADP
ejpam-6617	103	11	definition	definition	NOUN
ejpam-6617	103	12	3	3	NUM
ejpam-6617	103	13	,	,	PUNCT
ejpam-6617	103	14	where	where	SCONJ
ejpam-6617	103	15	κ(θ•	κ(θ•	NOUN
ejpam-6617	103	16	)	)	PUNCT
ejpam-6617	103	17	specifies	specify	VERB
ejpam-6617	103	18	the	the	DET
ejpam-6617	103	19	function	function	NOUN
ejpam-6617	103	20	of	of	ADP
ejpam-6617	103	21	normalization	normalization	NOUN
ejpam-6617	103	22	characterized	characterize	VERB
ejpam-6617	103	23	by	by	ADP
ejpam-6617	103	24	κ(0	κ(0	PROPN
ejpam-6617	103	25	)	)	PUNCT
ejpam-6617	103	26	=	=	SYM
ejpam-6617	103	27	κ(1	κ(1	PROPN
ejpam-6617	103	28	)	)	PUNCT
ejpam-6617	103	29	=	=	PUNCT
ejpam-6617	104	1	1	1	X
ejpam-6617	104	2	.	.	PUNCT
ejpam-6617	104	3	if	if	SCONJ
ejpam-6617	104	4	the	the	DET
ejpam-6617	104	5	function	function	NOUN
ejpam-6617	104	6	is	be	AUX
ejpam-6617	104	7	κ	κ	NOUN
ejpam-6617	104	8	/∈	/∈	PUNCT
ejpam-6617	104	9	h1(a1	h1(a1	NOUN
ejpam-6617	104	10	,	,	PUNCT
ejpam-6617	104	11	a2	a2	PROPN
ejpam-6617	104	12	)	)	PUNCT
ejpam-6617	104	13	,	,	PUNCT
ejpam-6617	104	14	then	then	ADV
ejpam-6617	104	15	the	the	DET
ejpam-6617	104	16	derivative	derivative	NOUN
ejpam-6617	104	17	is	be	AUX
ejpam-6617	104	18	written	write	VERB
ejpam-6617	104	19	in	in	ADP
ejpam-6617	104	20	the	the	DET
ejpam-6617	104	21	following	following	ADJ
ejpam-6617	104	22	manner	manner	NOUN
ejpam-6617	104	23	:	:	PUNCT
ejpam-6617	104	24	cfdθ•	cfdθ•	PROPN
ejpam-6617	104	25	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	104	26	)	)	PUNCT
ejpam-6617	104	27	=	=	SYM
ejpam-6617	104	28	θ•κ(θ•	θ•κ(θ•	PROPN
ejpam-6617	104	29	)	)	PUNCT
ejpam-6617	104	30	(	(	PUNCT
ejpam-6617	104	31	1−	1−	NUM
ejpam-6617	104	32	θ•	θ•	NOUN
ejpam-6617	104	33	)	)	PUNCT
ejpam-6617	104	34	∫	∫	PROPN
ejpam-6617	105	1	ς	ς	PROPN
ejpam-6617	105	2	a1	a1	PROPN
ejpam-6617	105	3	exp	exp	NOUN
ejpam-6617	105	4	(	(	PUNCT
ejpam-6617	105	5	−	−	PROPN
ejpam-6617	105	6	θ•(ς	θ•(ς	ADJ
ejpam-6617	105	7	−	−	NOUN
ejpam-6617	105	8	ν	ν	NOUN
ejpam-6617	105	9	)	)	PUNCT
ejpam-6617	105	10	(	(	PUNCT
ejpam-6617	105	11	1−	1−	NUM
ejpam-6617	105	12	θ•	θ•	NOUN
ejpam-6617	105	13	)	)	PUNCT
ejpam-6617	105	14	)	)	PUNCT
ejpam-6617	106	1	[	[	X
ejpam-6617	106	2	κ(ς)−	κ(ς)−	NOUN
ejpam-6617	106	3	κ(ν	κ(ν	PROPN
ejpam-6617	106	4	)	)	PUNCT
ejpam-6617	106	5	]	]	PUNCT
ejpam-6617	106	6	dν	dν	VERB
ejpam-6617	106	7	,	,	PUNCT
ejpam-6617	106	8	where	where	SCONJ
ejpam-6617	106	9	cf	cf	NOUN
ejpam-6617	106	10	has	have	VERB
ejpam-6617	106	11	an	an	DET
ejpam-6617	106	12	exponential	exponential	ADJ
ejpam-6617	106	13	kernel	kernel	NOUN
ejpam-6617	106	14	.	.	PUNCT
ejpam-6617	107	1	definition	definition	NOUN
ejpam-6617	107	2	7	7	NUM
ejpam-6617	107	3	.	.	PUNCT
ejpam-6617	108	1	[	[	X
ejpam-6617	108	2	1	1	NUM
ejpam-6617	108	3	,	,	PUNCT
ejpam-6617	108	4	35	35	NUM
ejpam-6617	108	5	]	]	PUNCT
ejpam-6617	108	6	let	let	VERB
ejpam-6617	108	7	κ	κ	PART
ejpam-6617	108	8	be	be	AUX
ejpam-6617	108	9	a	a	DET
ejpam-6617	108	10	function	function	NOUN
ejpam-6617	108	11	with	with	ADP
ejpam-6617	108	12	the	the	DET
ejpam-6617	108	13	property	property	NOUN
ejpam-6617	108	14	that	that	PRON
ejpam-6617	108	15	κ	κ	PROPN
ejpam-6617	108	16	∈	∈	PROPN
ejpam-6617	108	17	h	h	NOUN
ejpam-6617	108	18	′	′	PRON
ejpam-6617	108	19	(	(	PUNCT
ejpam-6617	108	20	a1	a1	PROPN
ejpam-6617	108	21	,	,	PUNCT
ejpam-6617	108	22	a2	a2	PROPN
ejpam-6617	108	23	)	)	PUNCT
ejpam-6617	108	24	,	,	PUNCT
ejpam-6617	108	25	a1	a1	NOUN
ejpam-6617	108	26	<	<	X
ejpam-6617	108	27	a2	a2	PROPN
ejpam-6617	108	28	.	.	PUNCT
ejpam-6617	109	1	in	in	ADP
ejpam-6617	109	2	the	the	DET
ejpam-6617	109	3	caputo	caputo	PROPN
ejpam-6617	109	4	-	-	PUNCT
ejpam-6617	109	5	fabrizio	fabrizio	PROPN
ejpam-6617	109	6	sense	sense	NOUN
ejpam-6617	109	7	,	,	PUNCT
ejpam-6617	109	8	the	the	DET
ejpam-6617	109	9	order	order	NOUN
ejpam-6617	109	10	of	of	ADP
ejpam-6617	109	11	the	the	DET
ejpam-6617	109	12	left	left	ADJ
ejpam-6617	109	13	riemann	riemann	PROPN
ejpam-6617	109	14	fractional	fractional	PROPN
ejpam-6617	109	15	derivative	derivative	ADJ
ejpam-6617	109	16	θ•	θ•	NOUN
ejpam-6617	109	17	is	be	AUX
ejpam-6617	109	18	expressed	express	VERB
ejpam-6617	109	19	as	as	ADP
ejpam-6617	109	20	cfrdθ•	cfrdθ•	PROPN
ejpam-6617	109	21	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	109	22	)	)	PUNCT
ejpam-6617	110	1	=	=	SYM
ejpam-6617	110	2	κ(θ•	κ(θ•	NOUN
ejpam-6617	110	3	)	)	PUNCT
ejpam-6617	110	4	(	(	PUNCT
ejpam-6617	110	5	1−	1−	NUM
ejpam-6617	110	6	θ•	θ•	NOUN
ejpam-6617	110	7	)	)	PUNCT
ejpam-6617	111	1	d	d	NOUN
ejpam-6617	111	2	dς	dς	X
ejpam-6617	111	3	∫	∫	PROPN
ejpam-6617	111	4	ς	ς	PROPN
ejpam-6617	111	5	a1	a1	NOUN
ejpam-6617	111	6	exp	exp	NOUN
ejpam-6617	111	7	(	(	PUNCT
ejpam-6617	111	8	−	−	PROPN
ejpam-6617	111	9	θ•(ς	θ•(ς	ADJ
ejpam-6617	111	10	−	−	NOUN
ejpam-6617	111	11	ν	ν	NOUN
ejpam-6617	111	12	)	)	PUNCT
ejpam-6617	111	13	(	(	PUNCT
ejpam-6617	111	14	1−	1−	NUM
ejpam-6617	111	15	θ•	θ•	NOUN
ejpam-6617	111	16	)	)	PUNCT
ejpam-6617	111	17	)	)	PUNCT
ejpam-6617	112	1	κ(ν)dν	κ(ν)dν	X
ejpam-6617	112	2	,	,	PUNCT
ejpam-6617	112	3	(	(	PUNCT
ejpam-6617	112	4	1	1	X
ejpam-6617	112	5	)	)	PUNCT
ejpam-6617	112	6	where	where	SCONJ
ejpam-6617	112	7	a1	a1	NOUN
ejpam-6617	112	8	≤	≤	PUNCT
ejpam-6617	112	9	ς	ς	PROPN
ejpam-6617	112	10	,	,	PUNCT
ejpam-6617	112	11	θ•	θ•	PROPN
ejpam-6617	112	12	(	(	PUNCT
ejpam-6617	112	13	0	0	PUNCT
ejpam-6617	112	14	<	<	X
ejpam-6617	112	15	θ•	θ•	X
ejpam-6617	112	16	<	<	X
ejpam-6617	112	17	1	1	NUM
ejpam-6617	112	18	)	)	PUNCT
ejpam-6617	112	19	is	be	AUX
ejpam-6617	112	20	a	a	DET
ejpam-6617	112	21	real	real	ADJ
ejpam-6617	112	22	number	number	NOUN
ejpam-6617	112	23	and	and	CCONJ
ejpam-6617	112	24	κ(θ•	κ(θ•	NOUN
ejpam-6617	112	25	)	)	PUNCT
ejpam-6617	112	26	is	be	AUX
ejpam-6617	112	27	a	a	DET
ejpam-6617	112	28	normalization	normalization	NOUN
ejpam-6617	112	29	function	function	NOUN
ejpam-6617	112	30	that	that	PRON
ejpam-6617	112	31	depends	depend	VERB
ejpam-6617	112	32	on	on	ADP
ejpam-6617	112	33	θ•	θ•	NOUN
ejpam-6617	112	34	such	such	ADJ
ejpam-6617	112	35	that	that	PRON
ejpam-6617	112	36	κ(0	κ(0	NOUN
ejpam-6617	112	37	)	)	PUNCT
ejpam-6617	112	38	=	=	SYM
ejpam-6617	112	39	κ(1	κ(1	PROPN
ejpam-6617	112	40	)	)	PUNCT
ejpam-6617	112	41	=	=	PUNCT
ejpam-6617	113	1	1	1	X
ejpam-6617	113	2	.	.	PUNCT
ejpam-6617	113	3	similarly	similarly	ADV
ejpam-6617	113	4	,	,	PUNCT
ejpam-6617	113	5	in	in	ADP
ejpam-6617	113	6	the	the	DET
ejpam-6617	113	7	caputo	caputo	PROPN
ejpam-6617	113	8	-	-	PUNCT
ejpam-6617	113	9	fabrizio	fabrizio	PROPN
ejpam-6617	113	10	sense	sense	NOUN
ejpam-6617	113	11	,	,	PUNCT
ejpam-6617	113	12	the	the	DET
ejpam-6617	113	13	order	order	NOUN
ejpam-6617	113	14	of	of	ADP
ejpam-6617	113	15	right	right	ADJ
ejpam-6617	113	16	riemann	riemann	PROPN
ejpam-6617	113	17	fractional	fractional	PROPN
ejpam-6617	113	18	derivative	derivative	ADJ
ejpam-6617	113	19	θ•	θ•	NOUN
ejpam-6617	113	20	can	can	AUX
ejpam-6617	113	21	be	be	AUX
ejpam-6617	113	22	stated	state	VERB
ejpam-6617	113	23	as	as	SCONJ
ejpam-6617	113	24	follows	follow	VERB
ejpam-6617	113	25	:	:	PUNCT
ejpam-6617	113	26	cfrdθ•	cfrdθ•	PROPN
ejpam-6617	113	27	a2−κ(ς	a2−κ(ς	NOUN
ejpam-6617	113	28	)	)	PUNCT
ejpam-6617	114	1	=	=	SYM
ejpam-6617	114	2	κ(θ•	κ(θ•	NOUN
ejpam-6617	114	3	)	)	PUNCT
ejpam-6617	114	4	(	(	PUNCT
ejpam-6617	114	5	1−	1−	NUM
ejpam-6617	114	6	θ•	θ•	NOUN
ejpam-6617	114	7	)	)	PUNCT
ejpam-6617	115	1	d	d	PROPN
ejpam-6617	115	2	dς	dς	X
ejpam-6617	115	3	∫	∫	PROPN
ejpam-6617	115	4	a2	a2	PROPN
ejpam-6617	115	5	ς	ς	PROPN
ejpam-6617	115	6	exp	exp	NOUN
ejpam-6617	115	7	(	(	PUNCT
ejpam-6617	115	8	−	−	PROPN
ejpam-6617	115	9	θ•(ς	θ•(ς	ADJ
ejpam-6617	115	10	−	−	NOUN
ejpam-6617	115	11	ν	ν	NOUN
ejpam-6617	115	12	)	)	PUNCT
ejpam-6617	115	13	(	(	PUNCT
ejpam-6617	115	14	1−	1−	NUM
ejpam-6617	115	15	θ•	θ•	NOUN
ejpam-6617	115	16	)	)	PUNCT
ejpam-6617	115	17	)	)	PUNCT
ejpam-6617	116	1	κ(ν)dν	κ(ν)dν	X
ejpam-6617	116	2	,	,	PUNCT
ejpam-6617	116	3	where	where	SCONJ
ejpam-6617	116	4	ς	ς	PROPN
ejpam-6617	116	5	≤	≤	PROPN
ejpam-6617	116	6	a2	a2	PROPN
ejpam-6617	116	7	.	.	PUNCT
ejpam-6617	117	1	remark	remark	PROPN
ejpam-6617	118	1	2	2	NUM
ejpam-6617	119	1	.	.	PUNCT
ejpam-6617	120	1	when	when	SCONJ
ejpam-6617	120	2	θ•	θ•	PROPN
ejpam-6617	120	3	→	→	SYM
ejpam-6617	120	4	0	0	NUM
ejpam-6617	120	5	,	,	PUNCT
ejpam-6617	120	6	(	(	PUNCT
ejpam-6617	120	7	1	1	X
ejpam-6617	120	8	)	)	PUNCT
ejpam-6617	120	9	becomes	become	VERB
ejpam-6617	120	10	lim	lim	PROPN
ejpam-6617	120	11	θ•→0	θ•→0	PROPN
ejpam-6617	120	12	cfrdθ•	cfrdθ•	PROPN
ejpam-6617	120	13	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	120	14	)	)	PUNCT
ejpam-6617	121	1	=	=	PUNCT
ejpam-6617	122	1	d	d	X
ejpam-6617	122	2	dς	dς	X
ejpam-6617	122	3	∫	∫	PROPN
ejpam-6617	122	4	ς	ς	PROPN
ejpam-6617	122	5	a1	a1	NOUN
ejpam-6617	122	6	κ(ν)dν	κ(ν)dν	NOUN
ejpam-6617	122	7	=	=	SYM
ejpam-6617	122	8	κ(ς	κ(ς	PROPN
ejpam-6617	122	9	)	)	PUNCT
ejpam-6617	122	10	.	.	PUNCT
ejpam-6617	123	1	proposition	proposition	NOUN
ejpam-6617	123	2	1	1	NUM
ejpam-6617	123	3	(	(	PUNCT
ejpam-6617	123	4	abdeljawad	abdeljawad	NOUN
ejpam-6617	123	5	and	and	CCONJ
ejpam-6617	123	6	baleanu	baleanu	NOUN
ejpam-6617	124	1	[	[	X
ejpam-6617	124	2	1	1	NUM
ejpam-6617	124	3	]	]	PUNCT
ejpam-6617	124	4	)	)	PUNCT
ejpam-6617	124	5	.	.	PUNCT
ejpam-6617	125	1	let	let	VERB
ejpam-6617	125	2	θ•	θ•	PROPN
ejpam-6617	125	3	∈	∈	PROPN
ejpam-6617	125	4	(	(	PUNCT
ejpam-6617	125	5	0	0	NUM
ejpam-6617	125	6	,	,	PUNCT
ejpam-6617	125	7	1	1	NUM
ejpam-6617	125	8	)	)	PUNCT
ejpam-6617	125	9	and	and	CCONJ
ejpam-6617	125	10	κ	κ	NOUN
ejpam-6617	125	11	,	,	PUNCT
ejpam-6617	125	12	z	z	NOUN
ejpam-6617	125	13	:	:	PUNCT
ejpam-6617	126	1	[	[	X
ejpam-6617	126	2	a1	a1	NOUN
ejpam-6617	126	3	,	,	PUNCT
ejpam-6617	126	4	a2	a2	PROPN
ejpam-6617	126	5	]	]	PUNCT
ejpam-6617	126	6	→	→	PUNCT
ejpam-6617	126	7	r	r	NOUN
ejpam-6617	126	8	be	be	VERB
ejpam-6617	126	9	two	two	NUM
ejpam-6617	126	10	continuous	continuous	ADJ
ejpam-6617	126	11	functions	function	NOUN
ejpam-6617	126	12	of	of	ADP
ejpam-6617	126	13	class	class	NOUN
ejpam-6617	126	14	c1[a1	c1[a1	VERB
ejpam-6617	126	15	,	,	PUNCT
ejpam-6617	126	16	a2	a2	PROPN
ejpam-6617	126	17	]	]	PUNCT
ejpam-6617	126	18	.	.	PUNCT
ejpam-6617	127	1	then	then	ADV
ejpam-6617	127	2	the	the	DET
ejpam-6617	127	3	following	follow	VERB
ejpam-6617	127	4	integration	integration	NOUN
ejpam-6617	127	5	by	by	ADP
ejpam-6617	127	6	parts	part	NOUN
ejpam-6617	127	7	formula	formula	NOUN
ejpam-6617	127	8	holds	hold	VERB
ejpam-6617	127	9	true:∫	true:∫	PROPN
ejpam-6617	127	10	a2	a2	PROPN
ejpam-6617	127	11	a1	a1	PROPN
ejpam-6617	127	12	κ(ς)cfdθ•	κ(ς)cfdθ•	NOUN
ejpam-6617	127	13	a1+z(ς)dς	a1+z(ς)dς	PROPN
ejpam-6617	127	14	=	=	PUNCT
ejpam-6617	128	1	[	[	X
ejpam-6617	128	2	z(ς)i1−θ•	z(ς)i1−θ•	NOUN
ejpam-6617	128	3	a2−	a2−	PROPN
ejpam-6617	128	4	κ(ς	κ(ς	PROPN
ejpam-6617	128	5	)	)	PUNCT
ejpam-6617	128	6	]	]	PUNCT
ejpam-6617	129	1	∣∣∣∣ς	∣∣∣∣ς	NOUN
ejpam-6617	129	2	=	=	NOUN
ejpam-6617	129	3	a2	a2	PROPN
ejpam-6617	129	4	ς	ς	NOUN
ejpam-6617	129	5	=	=	NOUN
ejpam-6617	129	6	a1	a1	NOUN
ejpam-6617	129	7	+	+	CCONJ
ejpam-6617	129	8	∫	∫	PROPN
ejpam-6617	129	9	a2	a2	PROPN
ejpam-6617	129	10	a1	a1	PROPN
ejpam-6617	129	11	z(ς)cfrdθ•	z(ς)cfrdθ•	PROPN
ejpam-6617	129	12	a2−κ(ς)dς	a2−κ(ς)dς	NOUN
ejpam-6617	129	13	,	,	PUNCT
ejpam-6617	129	14	where	where	SCONJ
ejpam-6617	129	15	i1−θ•	i1−θ•	VERB
ejpam-6617	129	16	a2−	a2−	PROPN
ejpam-6617	129	17	κ(ς	κ(ς	PROPN
ejpam-6617	129	18	)	)	PUNCT
ejpam-6617	129	19	=	=	SYM
ejpam-6617	129	20	k(θ•	k(θ•	ADJ
ejpam-6617	129	21	)	)	PUNCT
ejpam-6617	129	22	(	(	PUNCT
ejpam-6617	129	23	1−	1−	NUM
ejpam-6617	129	24	θ•	θ•	NOUN
ejpam-6617	129	25	)	)	PUNCT
ejpam-6617	129	26	∫	∫	PROPN
ejpam-6617	129	27	a2	a2	PROPN
ejpam-6617	129	28	ς	ς	PROPN
ejpam-6617	129	29	exp	exp	NOUN
ejpam-6617	129	30	(	(	PUNCT
ejpam-6617	129	31	−	−	PROPN
ejpam-6617	129	32	θ•	θ•	PROPN
ejpam-6617	129	33	(	(	PUNCT
ejpam-6617	129	34	1−	1−	NUM
ejpam-6617	129	35	θ•	θ•	NOUN
ejpam-6617	129	36	)	)	PUNCT
ejpam-6617	129	37	(	(	PUNCT
ejpam-6617	129	38	ν	ν	X
ejpam-6617	129	39	−	−	PROPN
ejpam-6617	129	40	ς	ς	PROPN
ejpam-6617	129	41	)	)	PUNCT
ejpam-6617	129	42	)	)	PUNCT
ejpam-6617	130	1	κ(ν)dν	κ(ν)dν	X
ejpam-6617	130	2	.	.	PUNCT
ejpam-6617	131	1	let	let	VERB
ejpam-6617	131	2	𭟋	𭟋	VERB
ejpam-6617	131	3	:	:	PUNCT
ejpam-6617	131	4	ℑ	ℑ	PROPN
ejpam-6617	131	5	×	×	PROPN
ejpam-6617	131	6	rn	rn	PROPN
ejpam-6617	131	7	×	×	PROPN
ejpam-6617	131	8	rn	rn	PROPN
ejpam-6617	131	9	→	→	SYM
ejpam-6617	131	10	r	r	NOUN
ejpam-6617	131	11	be	be	AUX
ejpam-6617	131	12	a	a	DET
ejpam-6617	131	13	continuously	continuously	ADV
ejpam-6617	131	14	differentiable	differentiable	ADJ
ejpam-6617	131	15	function	function	NOUN
ejpam-6617	131	16	where	where	SCONJ
ejpam-6617	131	17	ℑ	ℑ	PROPN
ejpam-6617	131	18	=	=	SYM
ejpam-6617	132	1	[	[	X
ejpam-6617	132	2	a1	a1	NOUN
ejpam-6617	132	3	,	,	PUNCT
ejpam-6617	132	4	a2	a2	PROPN
ejpam-6617	132	5	]	]	PUNCT
ejpam-6617	132	6	is	be	AUX
ejpam-6617	132	7	real	real	ADV
ejpam-6617	132	8	valued	value	VERB
ejpam-6617	132	9	interval	interval	NOUN
ejpam-6617	132	10	.	.	PUNCT
ejpam-6617	133	1	now	now	ADV
ejpam-6617	133	2	,	,	PUNCT
ejpam-6617	133	3	we	we	PRON
ejpam-6617	133	4	are	be	AUX
ejpam-6617	133	5	dealing	deal	VERB
ejpam-6617	133	6	with	with	ADP
ejpam-6617	133	7	the	the	DET
ejpam-6617	133	8	function	function	NOUN
ejpam-6617	133	9	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	133	10	,	,	PUNCT
ejpam-6617	133	11	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	133	12	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	133	13	)	)	PUNCT
ejpam-6617	133	14	)	)	PUNCT
ejpam-6617	133	15	,	,	PUNCT
ejpam-6617	133	16	where	where	SCONJ
ejpam-6617	133	17	κ	κ	NOUN
ejpam-6617	133	18	:	:	PUNCT
ejpam-6617	133	19	ℑ	ℑ	PROPN
ejpam-6617	133	20	→	→	SYM
ejpam-6617	133	21	rn	rn	PROPN
ejpam-6617	133	22	is	be	AUX
ejpam-6617	133	23	an	an	DET
ejpam-6617	133	24	n	n	ADV
ejpam-6617	133	25	-	-	PUNCT
ejpam-6617	133	26	dimensional	dimensional	ADJ
ejpam-6617	133	27	function	function	NOUN
ejpam-6617	133	28	of	of	ADP
ejpam-6617	133	29	class	class	NOUN
ejpam-6617	133	30	c1[a1	c1[a1	VERB
ejpam-6617	133	31	,	,	PUNCT
ejpam-6617	133	32	a2	a2	PROPN
ejpam-6617	133	33	]	]	PUNCT
ejpam-6617	133	34	and	and	CCONJ
ejpam-6617	133	35	cfdθ•	cfdθ•	PROPN
ejpam-6617	133	36	a1+κ	a1+κ	PROPN
ejpam-6617	133	37	represents	represent	VERB
ejpam-6617	133	38	the	the	DET
ejpam-6617	133	39	caputo	caputo	PROPN
ejpam-6617	133	40	-	-	PUNCT
ejpam-6617	133	41	fabrizio	fabrizio	PROPN
ejpam-6617	133	42	derivative	derivative	NOUN
ejpam-6617	133	43	of	of	ADP
ejpam-6617	133	44	order	order	NOUN
ejpam-6617	133	45	0	0	PUNCT
ejpam-6617	133	46	<	<	X
ejpam-6617	133	47	θ•	θ•	X
ejpam-6617	133	48	<	<	X
ejpam-6617	133	49	1	1	NUM
ejpam-6617	133	50	for	for	ADP
ejpam-6617	133	51	a	a	DET
ejpam-6617	133	52	function	function	NOUN
ejpam-6617	133	53	κ	κ	NOUN
ejpam-6617	133	54	.	.	PUNCT
ejpam-6617	134	1	the	the	DET
ejpam-6617	134	2	partial	partial	ADJ
ejpam-6617	134	3	derivatives	derivative	NOUN
ejpam-6617	134	4	of	of	ADP
ejpam-6617	134	5	𭟋	𭟋	PROPN
ejpam-6617	134	6	are	be	AUX
ejpam-6617	134	7	represented	represent	VERB
ejpam-6617	134	8	by	by	ADP
ejpam-6617	134	9	𭟋ς	𭟋ς	PROPN
ejpam-6617	134	10	=	=	SYM
ejpam-6617	135	1	∂𭟋	∂𭟋	ADP
ejpam-6617	135	2	∂ς	∂ς	PROPN
ejpam-6617	135	3	,	,	PUNCT
ejpam-6617	135	4	𭟋κ	𭟋κ	NOUN
ejpam-6617	135	5	=	=	PUNCT
ejpam-6617	136	1	[	[	PUNCT
ejpam-6617	136	2	∂𭟋	∂𭟋	ADP
ejpam-6617	136	3	∂κ1	∂κ1	NOUN
ejpam-6617	136	4	,	,	PUNCT
ejpam-6617	136	5	∂𭟋	∂𭟋	ADP
ejpam-6617	136	6	∂κ2	∂κ2	NOUN
ejpam-6617	136	7	,	,	PUNCT
ejpam-6617	136	8	∂𭟋	∂𭟋	ADP
ejpam-6617	136	9	∂κ3	∂κ3	NOUN
ejpam-6617	136	10	,	,	PUNCT
ejpam-6617	136	11	...	...	PUNCT
ejpam-6617	136	12	,	,	PUNCT
ejpam-6617	136	13	∂𭟋	∂𭟋	ADP
ejpam-6617	136	14	∂κn	∂κn	PROPN
ejpam-6617	136	15	]	]	PUNCT
ejpam-6617	136	16	,	,	PUNCT
ejpam-6617	136	17	v.	v.	CCONJ
ejpam-6617	136	18	rayanki	rayanki	PROPN
ejpam-6617	136	19	et	et	PROPN
ejpam-6617	136	20	al	al	PROPN
ejpam-6617	136	21	.	.	PUNCT
ejpam-6617	136	22	/	/	SYM
ejpam-6617	136	23	eur	eur	PROPN
ejpam-6617	136	24	.	.	PUNCT
ejpam-6617	137	1	j.	j.	PROPN
ejpam-6617	137	2	pure	pure	PROPN
ejpam-6617	137	3	appl	appl	PROPN
ejpam-6617	137	4	.	.	PROPN
ejpam-6617	137	5	math	math	PROPN
ejpam-6617	137	6	,	,	PUNCT
ejpam-6617	137	7	18	18	NUM
ejpam-6617	137	8	(	(	PUNCT
ejpam-6617	137	9	3	3	NUM
ejpam-6617	137	10	)	)	PUNCT
ejpam-6617	137	11	(	(	PUNCT
ejpam-6617	137	12	2025	2025	NUM
ejpam-6617	137	13	)	)	PUNCT
ejpam-6617	137	14	,	,	PUNCT
ejpam-6617	137	15	6617	6617	NUM
ejpam-6617	137	16	6	6	NUM
ejpam-6617	137	17	of	of	ADP
ejpam-6617	137	18	38	38	NUM
ejpam-6617	137	19	𭟋	𭟋	ADP
ejpam-6617	137	20	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	137	21	+	+	CCONJ
ejpam-6617	137	22	κ	κ	NOUN
ejpam-6617	137	23	=	=	PUNCT
ejpam-6617	137	24	[	[	PUNCT
ejpam-6617	137	25	∂𭟋	∂𭟋	ADP
ejpam-6617	137	26	∂(cfdθ•	∂(cfdθ•	PROPN
ejpam-6617	137	27	a1	a1	NOUN
ejpam-6617	137	28	+	+	X
ejpam-6617	137	29	κ1	κ1	NOUN
ejpam-6617	137	30	)	)	PUNCT
ejpam-6617	137	31	,	,	PUNCT
ejpam-6617	138	1	∂𭟋	∂𭟋	ADP
ejpam-6617	138	2	∂(cfdθ•	∂(cfdθ•	PROPN
ejpam-6617	138	3	a1	a1	PROPN
ejpam-6617	138	4	+	+	X
ejpam-6617	138	5	κ2	κ2	NOUN
ejpam-6617	138	6	)	)	PUNCT
ejpam-6617	138	7	,	,	PUNCT
ejpam-6617	138	8	∂𭟋	∂𭟋	ADP
ejpam-6617	138	9	∂(cfdθ•	∂(cfdθ•	PROPN
ejpam-6617	138	10	a1	a1	PROPN
ejpam-6617	138	11	+	+	CCONJ
ejpam-6617	138	12	κ3	κ3	PROPN
ejpam-6617	138	13	)	)	PUNCT
ejpam-6617	138	14	,	,	PUNCT
ejpam-6617	138	15	...	...	PUNCT
ejpam-6617	138	16	,	,	PUNCT
ejpam-6617	138	17	∂𭟋	∂𭟋	ADP
ejpam-6617	138	18	∂(cfdθ•	∂(cfdθ•	PROPN
ejpam-6617	138	19	a1	a1	PROPN
ejpam-6617	138	20	+	+	CCONJ
ejpam-6617	138	21	κn	κn	NOUN
ejpam-6617	138	22	)	)	PUNCT
ejpam-6617	138	23	]	]	PUNCT
ejpam-6617	138	24	.	.	PUNCT
ejpam-6617	139	1	where	where	SCONJ
ejpam-6617	139	2	κ1,κ2,κ3	κ1,κ2,κ3	PROPN
ejpam-6617	139	3	,	,	PUNCT
ejpam-6617	139	4	...	...	PUNCT
ejpam-6617	139	5	,	,	PUNCT
ejpam-6617	139	6	κn	κn	NOUN
ejpam-6617	139	7	are	be	AUX
ejpam-6617	139	8	components	component	NOUN
ejpam-6617	139	9	of	of	ADP
ejpam-6617	139	10	κ	κ	PROPN
ejpam-6617	139	11	.	.	PUNCT
ejpam-6617	139	12	consider	consider	VERB
ejpam-6617	139	13	the	the	DET
ejpam-6617	139	14	space	space	NOUN
ejpam-6617	139	15	of	of	ADP
ejpam-6617	139	16	piecewise	piecewise	NOUN
ejpam-6617	139	17	smooth	smooth	ADJ
ejpam-6617	139	18	functions	function	NOUN
ejpam-6617	139	19	to	to	PART
ejpam-6617	139	20	be	be	AUX
ejpam-6617	139	21	κ	κ	NOUN
ejpam-6617	139	22	:	:	PUNCT
ejpam-6617	139	23	ℑ	ℑ	PROPN
ejpam-6617	139	24	→	→	SYM
ejpam-6617	139	25	rn	rn	NOUN
ejpam-6617	139	26	along	along	ADV
ejpam-6617	139	27	with	with	ADP
ejpam-6617	139	28	the	the	DET
ejpam-6617	139	29	norm	norm	NOUN
ejpam-6617	139	30	∥κ∥	∥κ∥	NOUN
ejpam-6617	139	31	=	=	SYM
ejpam-6617	139	32	∥κ∥∞	∥κ∥∞	X
ejpam-6617	139	33	+	+	SYM
ejpam-6617	139	34	∥dκ∥∞	∥dκ∥∞	NOUN
ejpam-6617	139	35	,	,	PUNCT
ejpam-6617	139	36	where	where	SCONJ
ejpam-6617	139	37	the	the	DET
ejpam-6617	139	38	differential	differential	ADJ
ejpam-6617	139	39	operator	operator	NOUN
ejpam-6617	139	40	d	d	NOUN
ejpam-6617	139	41	is	be	AUX
ejpam-6617	139	42	described	describe	VERB
ejpam-6617	139	43	as	as	SCONJ
ejpam-6617	139	44	follows	follow	VERB
ejpam-6617	139	45	:	:	PUNCT
ejpam-6617	139	46	v	v	NOUN
ejpam-6617	139	47	=	=	SYM
ejpam-6617	139	48	dκ	dκ	ADP
ejpam-6617	139	49	⇐	⇐	ADJ
ejpam-6617	139	50	⇒	⇒	PROPN
ejpam-6617	139	51	κ(ς	κ(ς	PROPN
ejpam-6617	139	52	)	)	PUNCT
ejpam-6617	140	1	=	=	SYM
ejpam-6617	141	1	κ0	κ0	NOUN
ejpam-6617	141	2	+	+	CCONJ
ejpam-6617	141	3	∫	∫	PROPN
ejpam-6617	141	4	ς	ς	PROPN
ejpam-6617	141	5	a1	a1	PROPN
ejpam-6617	141	6	v(s)ds	v(s)ds	PROPN
ejpam-6617	141	7	,	,	PUNCT
ejpam-6617	141	8	where	where	SCONJ
ejpam-6617	141	9	κ0	κ0	PROPN
ejpam-6617	141	10	signifies	signify	VERB
ejpam-6617	141	11	the	the	DET
ejpam-6617	141	12	boundary	boundary	ADJ
ejpam-6617	141	13	value	value	NOUN
ejpam-6617	141	14	.	.	PUNCT
ejpam-6617	142	1	let	let	VERB
ejpam-6617	142	2	𭟋	𭟋	VERB
ejpam-6617	142	3	:	:	PUNCT
ejpam-6617	142	4	x	x	X
ejpam-6617	142	5	→	→	SYM
ejpam-6617	142	6	r	r	NOUN
ejpam-6617	142	7	defined	define	VERB
ejpam-6617	142	8	by	by	ADP
ejpam-6617	142	9	𭟋(κ	𭟋(κ	PROPN
ejpam-6617	142	10	)	)	PUNCT
ejpam-6617	143	1	=	=	SYM
ejpam-6617	143	2	∫	∫	PROPN
ejpam-6617	143	3	a2	a2	PROPN
ejpam-6617	143	4	a1	a1	PROPN
ejpam-6617	143	5	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	143	6	,	,	PUNCT
ejpam-6617	143	7	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	143	8	a1+κ(ς))dς	a1+κ(ς))dς	ADV
ejpam-6617	143	9	be	be	AUX
ejpam-6617	143	10	differentiable	differentiable	ADJ
ejpam-6617	143	11	.	.	PUNCT
ejpam-6617	144	1	for	for	ADP
ejpam-6617	144	2	notational	notational	ADJ
ejpam-6617	144	3	convenience	convenience	NOUN
ejpam-6617	144	4	,	,	PUNCT
ejpam-6617	144	5	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	144	6	,	,	PUNCT
ejpam-6617	144	7	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	144	8	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	144	9	)	)	PUNCT
ejpam-6617	144	10	)	)	PUNCT
ejpam-6617	144	11	will	will	AUX
ejpam-6617	144	12	be	be	AUX
ejpam-6617	144	13	written	write	VERB
ejpam-6617	144	14	as	as	ADP
ejpam-6617	144	15	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	144	16	,	,	PUNCT
ejpam-6617	144	17	κ	κ	NOUN
ejpam-6617	144	18	,	,	PUNCT
ejpam-6617	144	19	cfdθ•	cfdθ•	PROPN
ejpam-6617	144	20	a1+κ	a1+κ	PROPN
ejpam-6617	144	21	)	)	PUNCT
ejpam-6617	144	22	.	.	PUNCT
ejpam-6617	145	1	now	now	ADV
ejpam-6617	145	2	,	,	PUNCT
ejpam-6617	145	3	we	we	PRON
ejpam-6617	145	4	define	define	VERB
ejpam-6617	145	5	the	the	DET
ejpam-6617	145	6	concept	concept	NOUN
ejpam-6617	145	7	of	of	ADP
ejpam-6617	145	8	invex	invex	NOUN
ejpam-6617	145	9	and	and	CCONJ
ejpam-6617	145	10	generalized	generalized	ADJ
ejpam-6617	145	11	invex	invex	NOUN
ejpam-6617	145	12	functions	function	NOUN
ejpam-6617	145	13	by	by	ADP
ejpam-6617	145	14	using	use	VERB
ejpam-6617	145	15	the	the	DET
ejpam-6617	145	16	caputofabrizio	caputofabrizio	NOUN
ejpam-6617	145	17	(	(	PUNCT
ejpam-6617	145	18	cf	cf	NOUN
ejpam-6617	145	19	)	)	PUNCT
ejpam-6617	145	20	fractional	fractional	ADJ
ejpam-6617	145	21	derivative	derivative	NOUN
ejpam-6617	145	22	of	of	ADP
ejpam-6617	145	23	order	order	NOUN
ejpam-6617	145	24	0	0	PUNCT
ejpam-6617	145	25	<	<	X
ejpam-6617	145	26	θ•	θ•	X
ejpam-6617	145	27	<	<	X
ejpam-6617	145	28	1	1	NUM
ejpam-6617	145	29	,	,	PUNCT
ejpam-6617	145	30	in	in	ADP
ejpam-6617	145	31	the	the	DET
ejpam-6617	145	32	following	following	ADJ
ejpam-6617	145	33	way	way	NOUN
ejpam-6617	145	34	:	:	PUNCT
ejpam-6617	145	35	definition	definition	NOUN
ejpam-6617	145	36	8	8	NUM
ejpam-6617	145	37	.	.	PUNCT
ejpam-6617	146	1	the	the	DET
ejpam-6617	146	2	functional	functional	ADJ
ejpam-6617	146	3	𭟋	𭟋	NOUN
ejpam-6617	146	4	is	be	AUX
ejpam-6617	146	5	stated	state	VERB
ejpam-6617	146	6	as	as	ADP
ejpam-6617	146	7	invex	invex	NOUN
ejpam-6617	146	8	(	(	PUNCT
ejpam-6617	146	9	strictly	strictly	ADV
ejpam-6617	146	10	invex	invex	VERB
ejpam-6617	146	11	)	)	PUNCT
ejpam-6617	146	12	with	with	ADP
ejpam-6617	146	13	respect	respect	NOUN
ejpam-6617	146	14	to	to	ADP
ejpam-6617	146	15	ℵ	ℵ	NOUN
ejpam-6617	146	16	if	if	SCONJ
ejpam-6617	146	17	a	a	DET
ejpam-6617	146	18	differentiable	differentiable	ADJ
ejpam-6617	146	19	vector	vector	NOUN
ejpam-6617	146	20	function	function	NOUN
ejpam-6617	146	21	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	146	22	,	,	PUNCT
ejpam-6617	146	23	κ	κ	NOUN
ejpam-6617	146	24	,	,	PUNCT
ejpam-6617	146	25	κ̄	κ̄	NOUN
ejpam-6617	146	26	)	)	PUNCT
ejpam-6617	146	27	∈	∈	PROPN
ejpam-6617	146	28	c1[a1	c1[a1	NUM
ejpam-6617	146	29	,	,	PUNCT
ejpam-6617	146	30	a2	a2	PROPN
ejpam-6617	146	31	]	]	PUNCT
ejpam-6617	146	32	with	with	ADP
ejpam-6617	146	33	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	146	34	,	,	PUNCT
ejpam-6617	146	35	κ	κ	NOUN
ejpam-6617	146	36	,	,	PUNCT
ejpam-6617	146	37	κ	κ	NOUN
ejpam-6617	146	38	)	)	PUNCT
ejpam-6617	146	39	=	=	SYM
ejpam-6617	146	40	0	0	NUM
ejpam-6617	146	41	occurs	occur	VERB
ejpam-6617	146	42	such	such	ADJ
ejpam-6617	146	43	that	that	DET
ejpam-6617	146	44	forall	forall	NOUN
ejpam-6617	146	45	κ	κ	NOUN
ejpam-6617	146	46	,	,	PUNCT
ejpam-6617	147	1	κ̄	κ̄	NOUN
ejpam-6617	147	2	∈	∈	PROPN
ejpam-6617	147	3	x	x	NOUN
ejpam-6617	147	4	,	,	PUNCT
ejpam-6617	147	5	a2∫	a2∫	X
ejpam-6617	147	6	a1	a1	VERB
ejpam-6617	147	7	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	147	8	,	,	PUNCT
ejpam-6617	147	9	κ	κ	NOUN
ejpam-6617	147	10	,	,	PUNCT
ejpam-6617	147	11	cfdθ•	cfdθ•	PROPN
ejpam-6617	147	12	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	147	13	−	−	NOUN
ejpam-6617	147	14	a2∫	a2∫	NOUN
ejpam-6617	147	15	a1	a1	VERB
ejpam-6617	147	16	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	147	17	,	,	PUNCT
ejpam-6617	147	18	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	147	19	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	147	20	≥	≥	X
ejpam-6617	147	21	(	(	PUNCT
ejpam-6617	147	22	>	>	PUNCT
ejpam-6617	147	23	)	)	PUNCT
ejpam-6617	147	24	∫	∫	PROPN
ejpam-6617	147	25	a2	a2	PROPN
ejpam-6617	147	26	a1	a1	PROPN
ejpam-6617	147	27	[	[	PUNCT
ejpam-6617	147	28	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	147	29	,	,	PUNCT
ejpam-6617	147	30	κ	κ	NOUN
ejpam-6617	147	31	,	,	PUNCT
ejpam-6617	147	32	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	147	33	,	,	PUNCT
ejpam-6617	147	34	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	147	35	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	147	36	)	)	PUNCT
ejpam-6617	147	37	+	+	CCONJ
ejpam-6617	147	38	(	(	PUNCT
ejpam-6617	147	39	cfdθ•	cfdθ•	PROPN
ejpam-6617	147	40	a1+ℵ(ς	a1+ℵ(ς	NUM
ejpam-6617	147	41	,	,	PUNCT
ejpam-6617	147	42	κ	κ	NOUN
ejpam-6617	147	43	,	,	PUNCT
ejpam-6617	147	44	κ̄))𭟋cfdθ•a1	κ̄))𭟋cfdθ•a1	PROPN
ejpam-6617	147	45	+	+	CCONJ
ejpam-6617	147	46	κ̄	κ̄	NOUN
ejpam-6617	147	47	(	(	PUNCT
ejpam-6617	147	48	ς	ς	PROPN
ejpam-6617	147	49	,	,	PUNCT
ejpam-6617	147	50	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	147	51	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	147	52	)	)	PUNCT
ejpam-6617	147	53	]	]	PUNCT
ejpam-6617	148	1	dς	dς	PROPN
ejpam-6617	148	2	.	.	PUNCT
ejpam-6617	149	1	the	the	DET
ejpam-6617	149	2	following	follow	VERB
ejpam-6617	149	3	example	example	NOUN
ejpam-6617	149	4	demonstrates	demonstrate	VERB
ejpam-6617	149	5	that	that	SCONJ
ejpam-6617	149	6	,	,	PUNCT
ejpam-6617	149	7	the	the	DET
ejpam-6617	149	8	function	function	NOUN
ejpam-6617	149	9	𭟋	𭟋	NOUN
ejpam-6617	149	10	is	be	AUX
ejpam-6617	149	11	invex	invex	NOUN
ejpam-6617	149	12	under	under	ADP
ejpam-6617	149	13	caputo	caputo	PROPN
ejpam-6617	149	14	-	-	PUNCT
ejpam-6617	149	15	fabrizio	fabrizio	PROPN
ejpam-6617	149	16	fractional	fractional	PROPN
ejpam-6617	149	17	derivative	derivative	NOUN
ejpam-6617	149	18	.	.	PUNCT
ejpam-6617	149	19	example	example	NOUN
ejpam-6617	150	1	1	1	NUM
ejpam-6617	150	2	.	.	PUNCT
ejpam-6617	150	3	:	:	PUNCT
ejpam-6617	150	4	let	let	VERB
ejpam-6617	150	5	𭟋(κ	𭟋(κ	PRON
ejpam-6617	150	6	)	)	PUNCT
ejpam-6617	150	7	:	:	PUNCT
ejpam-6617	151	1	x	x	X
ejpam-6617	151	2	=	=	PUNCT
ejpam-6617	152	1	[	[	X
ejpam-6617	152	2	0	0	NUM
ejpam-6617	152	3	,	,	PUNCT
ejpam-6617	152	4	1	1	NUM
ejpam-6617	152	5	]	]	PUNCT
ejpam-6617	152	6	→	→	PUNCT
ejpam-6617	152	7	r	r	NOUN
ejpam-6617	152	8	be	be	AUX
ejpam-6617	152	9	defined	define	VERB
ejpam-6617	152	10	by	by	ADP
ejpam-6617	152	11	𭟋(κ	𭟋(κ	PROPN
ejpam-6617	152	12	)	)	PUNCT
ejpam-6617	152	13	=	=	PUNCT
ejpam-6617	153	1	1∫	1∫	NUM
ejpam-6617	153	2	0	0	NUM
ejpam-6617	153	3	{	{	PUNCT
ejpam-6617	153	4	−κ(ς	−κ(ς	NOUN
ejpam-6617	153	5	)	)	PUNCT
ejpam-6617	153	6	+	+	CCONJ
ejpam-6617	154	1	6.5514ς	6.5514ς	NUM
ejpam-6617	154	2	−	−	NOUN
ejpam-6617	154	3	16.3785e	16.3785e	NUM
ejpam-6617	154	4	−	−	NOUN
ejpam-6617	154	5	ς	ς	PROPN
ejpam-6617	154	6	3	3	NUM
ejpam-6617	154	7	+	+	CCONJ
ejpam-6617	154	8	22.9299)}dς	22.9299)}dς	NUM
ejpam-6617	154	9	and	and	CCONJ
ejpam-6617	154	10	κ(ς	κ(ς	NUM
ejpam-6617	154	11	)	)	PUNCT
ejpam-6617	154	12	=	=	PUNCT
ejpam-6617	155	1	−ς2	−ς2	PROPN
ejpam-6617	156	1	+	+	CCONJ
ejpam-6617	156	2	ς	ς	PROPN
ejpam-6617	156	3	+	+	CCONJ
ejpam-6617	156	4	1	1	NUM
ejpam-6617	156	5	∈	∈	NOUN
ejpam-6617	156	6	x	x	NOUN
ejpam-6617	156	7	,	,	PUNCT
ejpam-6617	156	8	forall	forall	NOUN
ejpam-6617	156	9	ς	ς	PROPN
ejpam-6617	156	10	∈	∈	PROPN
ejpam-6617	157	1	[	[	X
ejpam-6617	157	2	0	0	NUM
ejpam-6617	157	3	,	,	PUNCT
ejpam-6617	157	4	1	1	NUM
ejpam-6617	157	5	]	]	PUNCT
ejpam-6617	157	6	and	and	CCONJ
ejpam-6617	157	7	note	note	VERB
ejpam-6617	157	8	that	that	PRON
ejpam-6617	157	9	(	(	PUNCT
ejpam-6617	157	10	κ	κ	PROPN
ejpam-6617	157	11	̸=	̸=	PROPN
ejpam-6617	157	12	κ̄	κ̄	NOUN
ejpam-6617	157	13	)	)	PUNCT
ejpam-6617	157	14	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	157	15	)	)	PUNCT
ejpam-6617	157	16	=	=	SYM
ejpam-6617	157	17	1	1	NUM
ejpam-6617	157	18	∈	∈	NOUN
ejpam-6617	157	19	x	x	PUNCT
ejpam-6617	157	20	in	in	ADP
ejpam-6617	157	21	such	such	ADJ
ejpam-6617	157	22	way	way	NOUN
ejpam-6617	157	23	that	that	SCONJ
ejpam-6617	157	24	,	,	PUNCT
ejpam-6617	157	25	a2∫	a2∫	NOUN
ejpam-6617	157	26	a1	a1	VERB
ejpam-6617	157	27	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	157	28	,	,	PUNCT
ejpam-6617	157	29	κ	κ	NOUN
ejpam-6617	157	30	,	,	PUNCT
ejpam-6617	157	31	cfdθ•	cfdθ•	PROPN
ejpam-6617	157	32	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	157	33	−	−	NOUN
ejpam-6617	157	34	a2∫	a2∫	NOUN
ejpam-6617	157	35	a1	a1	VERB
ejpam-6617	157	36	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	157	37	,	,	PUNCT
ejpam-6617	157	38	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	157	39	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	157	40	>	>	PUNCT
ejpam-6617	157	41	a2∫	a2∫	VERB
ejpam-6617	157	42	a1	a1	NOUN
ejpam-6617	157	43	{	{	PUNCT
ejpam-6617	157	44	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	157	45	,	,	PUNCT
ejpam-6617	157	46	κ	κ	NOUN
ejpam-6617	157	47	,	,	PUNCT
ejpam-6617	157	48	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	157	49	,	,	PUNCT
ejpam-6617	157	50	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	157	51	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	157	52	)	)	PUNCT
ejpam-6617	157	53	+	+	CCONJ
ejpam-6617	157	54	cfdθ•	cfdθ•	PROPN
ejpam-6617	157	55	a1+(ℵ(ς	a1+(ℵ(ς	PROPN
ejpam-6617	157	56	,	,	PUNCT
ejpam-6617	157	57	κ	κ	NOUN
ejpam-6617	157	58	,	,	PUNCT
ejpam-6617	157	59	κ̄	κ̄	NOUN
ejpam-6617	157	60	)	)	PUNCT
ejpam-6617	157	61	)	)	PUNCT
ejpam-6617	157	62	𭟋cfdθ•	𭟋cfdθ•	PRON
ejpam-6617	157	63	a1	a1	NOUN
ejpam-6617	157	64	+	+	X
ejpam-6617	157	65	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	157	66	,	,	PUNCT
ejpam-6617	157	67	κ̄	κ̄	NOUN
ejpam-6617	157	68	,	,	PUNCT
ejpam-6617	157	69	cfdθ•	cfdθ•	PROPN
ejpam-6617	157	70	a1+κ̄)}dς	a1+κ̄)}dς	PROPN
ejpam-6617	157	71	.	.	PUNCT
ejpam-6617	158	1	in	in	ADP
ejpam-6617	158	2	this	this	DET
ejpam-6617	158	3	example	example	NOUN
ejpam-6617	158	4	,	,	PUNCT
ejpam-6617	158	5	θ•	θ•	NOUN
ejpam-6617	158	6	=	=	SYM
ejpam-6617	158	7	1	1	NUM
ejpam-6617	158	8	4	4	NUM
ejpam-6617	158	9	,	,	PUNCT
ejpam-6617	158	10	a1	a1	NOUN
ejpam-6617	158	11	=	=	SYM
ejpam-6617	158	12	0	0	NUM
ejpam-6617	158	13	,	,	PUNCT
ejpam-6617	158	14	a2	a2	PROPN
ejpam-6617	158	15	=	=	SYM
ejpam-6617	158	16	1	1	NUM
ejpam-6617	158	17	,	,	PUNCT
ejpam-6617	158	18	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	158	19	,	,	PUNCT
ejpam-6617	158	20	κ	κ	NOUN
ejpam-6617	158	21	,	,	PUNCT
ejpam-6617	158	22	κ̄	κ̄	NOUN
ejpam-6617	158	23	)	)	PUNCT
ejpam-6617	158	24	=	=	SYM
ejpam-6617	159	1	κ	κ	PRON
ejpam-6617	159	2	−	−	PROPN
ejpam-6617	159	3	κ̄	κ̄	NOUN
ejpam-6617	159	4	and	and	CCONJ
ejpam-6617	159	5	κ(ς	κ(ς	NUM
ejpam-6617	159	6	)	)	PUNCT
ejpam-6617	160	1	=	=	PUNCT
ejpam-6617	161	1	−ς2	−ς2	PROPN
ejpam-6617	162	1	+	+	CCONJ
ejpam-6617	162	2	ς	ς	PROPN
ejpam-6617	163	1	+	+	CCONJ
ejpam-6617	163	2	1	1	NUM
ejpam-6617	163	3	are	be	AUX
ejpam-6617	163	4	v.	v.	ADP
ejpam-6617	163	5	rayanki	rayanki	NOUN
ejpam-6617	163	6	et	et	PROPN
ejpam-6617	163	7	al	al	PROPN
ejpam-6617	163	8	.	.	PUNCT
ejpam-6617	163	9	/	/	SYM
ejpam-6617	163	10	eur	eur	PROPN
ejpam-6617	163	11	.	.	PUNCT
ejpam-6617	164	1	j.	j.	PROPN
ejpam-6617	164	2	pure	pure	PROPN
ejpam-6617	164	3	appl	appl	PROPN
ejpam-6617	164	4	.	.	PROPN
ejpam-6617	164	5	math	math	PROPN
ejpam-6617	164	6	,	,	PUNCT
ejpam-6617	164	7	18	18	NUM
ejpam-6617	164	8	(	(	PUNCT
ejpam-6617	164	9	3	3	NUM
ejpam-6617	164	10	)	)	PUNCT
ejpam-6617	164	11	(	(	PUNCT
ejpam-6617	164	12	2025	2025	NUM
ejpam-6617	164	13	)	)	PUNCT
ejpam-6617	164	14	,	,	PUNCT
ejpam-6617	164	15	6617	6617	NUM
ejpam-6617	164	16	7	7	NUM
ejpam-6617	164	17	of	of	ADP
ejpam-6617	164	18	38	38	NUM
ejpam-6617	164	19	figure	figure	NOUN
ejpam-6617	164	20	1	1	NUM
ejpam-6617	164	21	:	:	PUNCT
ejpam-6617	164	22	graphical	graphical	ADJ
ejpam-6617	164	23	view	view	NOUN
ejpam-6617	164	24	of	of	ADP
ejpam-6617	164	25	the	the	DET
ejpam-6617	164	26	function	function	NOUN
ejpam-6617	164	27	𭟋	𭟋	PROPN
ejpam-6617	164	28	=	=	SYM
ejpam-6617	164	29	−κ(ς	−κ(ς	PROPN
ejpam-6617	164	30	)	)	PUNCT
ejpam-6617	165	1	+	+	CCONJ
ejpam-6617	166	1	6.5514ς	6.5514ς	NUM
ejpam-6617	166	2	−	−	NOUN
ejpam-6617	166	3	16.3785e	16.3785e	NUM
ejpam-6617	166	4	−	−	NOUN
ejpam-6617	166	5	ς	ς	PROPN
ejpam-6617	166	6	3	3	NUM
ejpam-6617	166	7	+	+	NUM
ejpam-6617	166	8	22.9299	22.9299	NUM
ejpam-6617	166	9	taken	take	VERB
ejpam-6617	166	10	relevantly	relevantly	ADV
ejpam-6617	166	11	and	and	CCONJ
ejpam-6617	166	12	deduce	deduce	PROPN
ejpam-6617	166	13	cfdθ•	cfdθ•	PROPN
ejpam-6617	166	14	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	166	15	)	)	PUNCT
ejpam-6617	166	16	=	=	PUNCT
ejpam-6617	166	17	−6.5514ς−22.9299e−ς/3	−6.5514ς−22.9299e−ς/3	PROPN
ejpam-6617	166	18	+	+	NOUN
ejpam-6617	166	19	22.9299	22.9299	NUM
ejpam-6617	166	20	.	.	PUNCT
ejpam-6617	167	1	but	but	CCONJ
ejpam-6617	167	2	in	in	ADP
ejpam-6617	167	3	the	the	DET
ejpam-6617	167	4	given	give	VERB
ejpam-6617	167	5	example	example	NOUN
ejpam-6617	167	6	,	,	PUNCT
ejpam-6617	167	7	the	the	DET
ejpam-6617	167	8	function	function	NOUN
ejpam-6617	167	9	is	be	AUX
ejpam-6617	167	10	not	not	PART
ejpam-6617	167	11	convex	convex	ADJ
ejpam-6617	167	12	for	for	ADP
ejpam-6617	167	13	the	the	DET
ejpam-6617	167	14	differentiable	differentiable	ADJ
ejpam-6617	167	15	function	function	NOUN
ejpam-6617	167	16	(	(	PUNCT
ejpam-6617	167	17	κ−	κ−	PROPN
ejpam-6617	167	18	κ̄)t	κ̄)t	NOUN
ejpam-6617	167	19	=	=	SYM
ejpam-6617	167	20	κ+	κ+	NOUN
ejpam-6617	167	21	κ̄.	κ̄.	PUNCT
ejpam-6617	167	22	definition	definition	NOUN
ejpam-6617	167	23	9	9	NUM
ejpam-6617	167	24	.	.	PUNCT
ejpam-6617	168	1	the	the	DET
ejpam-6617	168	2	functional	functional	ADJ
ejpam-6617	168	3	𭟋	𭟋	NOUN
ejpam-6617	168	4	is	be	AUX
ejpam-6617	168	5	stated	state	VERB
ejpam-6617	168	6	as	as	ADP
ejpam-6617	168	7	pseudo	pseudo	NOUN
ejpam-6617	168	8	-	-	NOUN
ejpam-6617	168	9	invex	invex	NOUN
ejpam-6617	168	10	with	with	ADP
ejpam-6617	168	11	regard	regard	NOUN
ejpam-6617	168	12	to	to	ADP
ejpam-6617	168	13	ℵ	ℵ	NOUN
ejpam-6617	168	14	if	if	SCONJ
ejpam-6617	168	15	a	a	DET
ejpam-6617	168	16	differentiable	differentiable	ADJ
ejpam-6617	168	17	function	function	NOUN
ejpam-6617	168	18	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	168	19	,	,	PUNCT
ejpam-6617	168	20	κ	κ	NOUN
ejpam-6617	168	21	,	,	PUNCT
ejpam-6617	168	22	κ̄	κ̄	NOUN
ejpam-6617	168	23	)	)	PUNCT
ejpam-6617	168	24	∈	∈	PROPN
ejpam-6617	168	25	c1[a1	c1[a1	NUM
ejpam-6617	168	26	,	,	PUNCT
ejpam-6617	168	27	a2	a2	PROPN
ejpam-6617	168	28	]	]	PUNCT
ejpam-6617	168	29	with	with	ADP
ejpam-6617	168	30	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	168	31	,	,	PUNCT
ejpam-6617	168	32	κ	κ	NOUN
ejpam-6617	168	33	,	,	PUNCT
ejpam-6617	168	34	κ	κ	NOUN
ejpam-6617	168	35	)	)	PUNCT
ejpam-6617	168	36	=	=	SYM
ejpam-6617	168	37	0	0	NUM
ejpam-6617	168	38	occurs	occur	VERB
ejpam-6617	168	39	such	such	ADJ
ejpam-6617	168	40	that	that	SCONJ
ejpam-6617	168	41	∀κ	∀κ	NOUN
ejpam-6617	168	42	,	,	PUNCT
ejpam-6617	168	43	κ̄	κ̄	NOUN
ejpam-6617	168	44	∈	∈	PROPN
ejpam-6617	168	45	x,∫	x,∫	NOUN
ejpam-6617	168	46	a2	a2	PROPN
ejpam-6617	168	47	a1	a1	PROPN
ejpam-6617	168	48	[	[	PUNCT
ejpam-6617	168	49	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	168	50	,	,	PUNCT
ejpam-6617	168	51	κ	κ	NOUN
ejpam-6617	168	52	,	,	PUNCT
ejpam-6617	168	53	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	168	54	,	,	PUNCT
ejpam-6617	168	55	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	168	56	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	168	57	)	)	PUNCT
ejpam-6617	168	58	+	+	CCONJ
ejpam-6617	168	59	(	(	PUNCT
ejpam-6617	168	60	cfdθ•	cfdθ•	INTJ
ejpam-6617	168	61	a1ℵ(ς	a1ℵ(ς	PROPN
ejpam-6617	168	62	,	,	PUNCT
ejpam-6617	168	63	κ	κ	PROPN
ejpam-6617	168	64	,	,	PUNCT
ejpam-6617	168	65	κ̄))𭟋cfdθ•a+κ̄	κ̄))𭟋cfdθ•a+κ̄	PROPN
ejpam-6617	168	66	(	(	PUNCT
ejpam-6617	168	67	ς	ς	PROPN
ejpam-6617	168	68	,	,	PUNCT
ejpam-6617	168	69	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	168	70	a1κ̄	a1κ̄	NUM
ejpam-6617	168	71	)	)	PUNCT
ejpam-6617	168	72	]	]	PUNCT
ejpam-6617	168	73	dς	dς	X
ejpam-6617	168	74	≥	≥	X
ejpam-6617	168	75	0	0	NUM
ejpam-6617	168	76	⇒	⇒	NOUN
ejpam-6617	168	77	a2∫	a2∫	NOUN
ejpam-6617	168	78	a1	a1	PROPN
ejpam-6617	168	79	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	168	80	,	,	PUNCT
ejpam-6617	168	81	κ	κ	NOUN
ejpam-6617	168	82	,	,	PUNCT
ejpam-6617	168	83	cfdθ•	cfdθ•	PROPN
ejpam-6617	168	84	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	168	85	≥	≥	VERB
ejpam-6617	168	86	a2∫	a2∫	NOUN
ejpam-6617	168	87	a1	a1	VERB
ejpam-6617	168	88	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	168	89	,	,	PUNCT
ejpam-6617	168	90	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	168	91	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	168	92	,	,	PUNCT
ejpam-6617	168	93	or	or	CCONJ
ejpam-6617	168	94	equivalently	equivalently	ADV
ejpam-6617	168	95	,	,	PUNCT
ejpam-6617	168	96	a2∫	a2∫	NOUN
ejpam-6617	168	97	a1	a1	VERB
ejpam-6617	168	98	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	168	99	,	,	PUNCT
ejpam-6617	168	100	κ	κ	NOUN
ejpam-6617	168	101	,	,	PUNCT
ejpam-6617	168	102	cfdθ•	cfdθ•	PROPN
ejpam-6617	168	103	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	168	104	<	<	X
ejpam-6617	168	105	a2∫	a2∫	X
ejpam-6617	168	106	a1	a1	NOUN
ejpam-6617	168	107	g(ς	g(ς	PROPN
ejpam-6617	168	108	,	,	PUNCT
ejpam-6617	168	109	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	168	110	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	168	111	⇒	⇒	VERB
ejpam-6617	168	112	∫	∫	PROPN
ejpam-6617	168	113	a2	a2	PROPN
ejpam-6617	168	114	a1	a1	PROPN
ejpam-6617	168	115	[	[	PUNCT
ejpam-6617	168	116	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	168	117	,	,	PUNCT
ejpam-6617	168	118	κ	κ	NOUN
ejpam-6617	168	119	,	,	PUNCT
ejpam-6617	168	120	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	168	121	,	,	PUNCT
ejpam-6617	168	122	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	168	123	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	168	124	)	)	PUNCT
ejpam-6617	168	125	+	+	PROPN
ejpam-6617	168	126	cfdθ•	cfdθ•	PROPN
ejpam-6617	168	127	a1+ℵ(ς	a1+ℵ(ς	PRON
ejpam-6617	168	128	,	,	PUNCT
ejpam-6617	168	129	κ	κ	NOUN
ejpam-6617	168	130	,	,	PUNCT
ejpam-6617	168	131	κ̄))𭟋cfdθ•a1	κ̄))𭟋cfdθ•a1	PROPN
ejpam-6617	168	132	+	+	CCONJ
ejpam-6617	168	133	κ̄	κ̄	NOUN
ejpam-6617	168	134	(	(	PUNCT
ejpam-6617	168	135	ς	ς	PROPN
ejpam-6617	168	136	,	,	PUNCT
ejpam-6617	168	137	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	168	138	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	168	139	)	)	PUNCT
ejpam-6617	168	140	]	]	PUNCT
ejpam-6617	168	141	dς	dς	X
ejpam-6617	168	142	<	<	X
ejpam-6617	168	143	0	0	X
ejpam-6617	168	144	.	.	PUNCT
ejpam-6617	169	1	v.	v.	ADP
ejpam-6617	169	2	rayanki	rayanki	PROPN
ejpam-6617	169	3	et	et	PROPN
ejpam-6617	169	4	al	al	PROPN
ejpam-6617	169	5	.	.	PUNCT
ejpam-6617	169	6	/	/	SYM
ejpam-6617	169	7	eur	eur	PROPN
ejpam-6617	169	8	.	.	PUNCT
ejpam-6617	170	1	j.	j.	PROPN
ejpam-6617	170	2	pure	pure	PROPN
ejpam-6617	170	3	appl	appl	PROPN
ejpam-6617	170	4	.	.	PROPN
ejpam-6617	170	5	math	math	PROPN
ejpam-6617	170	6	,	,	PUNCT
ejpam-6617	170	7	18	18	NUM
ejpam-6617	170	8	(	(	PUNCT
ejpam-6617	170	9	3	3	NUM
ejpam-6617	170	10	)	)	PUNCT
ejpam-6617	170	11	(	(	PUNCT
ejpam-6617	170	12	2025	2025	NUM
ejpam-6617	170	13	)	)	PUNCT
ejpam-6617	170	14	,	,	PUNCT
ejpam-6617	170	15	6617	6617	NUM
ejpam-6617	170	16	8	8	NUM
ejpam-6617	170	17	of	of	ADP
ejpam-6617	170	18	38	38	NUM
ejpam-6617	170	19	the	the	DET
ejpam-6617	170	20	following	follow	VERB
ejpam-6617	170	21	example	example	NOUN
ejpam-6617	170	22	illustrates	illustrate	VERB
ejpam-6617	170	23	that	that	SCONJ
ejpam-6617	170	24	,	,	PUNCT
ejpam-6617	170	25	the	the	DET
ejpam-6617	170	26	function	function	NOUN
ejpam-6617	170	27	g	g	PROPN
ejpam-6617	170	28	is	be	AUX
ejpam-6617	170	29	pseudo	pseudo	NOUN
ejpam-6617	170	30	-	-	NOUN
ejpam-6617	170	31	invex	invex	ADJ
ejpam-6617	170	32	,	,	PUNCT
ejpam-6617	170	33	but	but	CCONJ
ejpam-6617	170	34	not	not	PART
ejpam-6617	170	35	a	a	DET
ejpam-6617	170	36	invex	invex	NOUN
ejpam-6617	170	37	under	under	ADP
ejpam-6617	170	38	caputo	caputo	PROPN
ejpam-6617	170	39	-	-	PUNCT
ejpam-6617	170	40	fabrizio	fabrizio	PROPN
ejpam-6617	170	41	fractional	fractional	PROPN
ejpam-6617	170	42	derivative	derivative	NOUN
ejpam-6617	170	43	.	.	PUNCT
ejpam-6617	170	44	example	example	NOUN
ejpam-6617	171	1	2	2	NUM
ejpam-6617	171	2	.	.	PUNCT
ejpam-6617	171	3	:	:	PUNCT
ejpam-6617	171	4	let	let	VERB
ejpam-6617	171	5	𭟋(κ	𭟋(κ	PRON
ejpam-6617	171	6	)	)	PUNCT
ejpam-6617	171	7	:	:	PUNCT
ejpam-6617	172	1	x	x	X
ejpam-6617	172	2	=	=	PUNCT
ejpam-6617	173	1	[	[	X
ejpam-6617	173	2	0	0	NUM
ejpam-6617	173	3	,	,	PUNCT
ejpam-6617	173	4	1	1	NUM
ejpam-6617	173	5	]	]	PUNCT
ejpam-6617	173	6	→	→	PUNCT
ejpam-6617	173	7	r	r	NOUN
ejpam-6617	173	8	be	be	AUX
ejpam-6617	173	9	defined	define	VERB
ejpam-6617	173	10	by	by	ADP
ejpam-6617	173	11	𭟋(κ	𭟋(κ	PROPN
ejpam-6617	173	12	)	)	PUNCT
ejpam-6617	173	13	=	=	PUNCT
ejpam-6617	174	1	1∫	1∫	NUM
ejpam-6617	174	2	0	0	NUM
ejpam-6617	174	3	{	{	PUNCT
ejpam-6617	174	4	−κ(ς	−κ(ς	NOUN
ejpam-6617	174	5	)	)	PUNCT
ejpam-6617	175	1	+	+	CCONJ
ejpam-6617	176	1	2.1838ς	2.1838ς	NUM
ejpam-6617	176	2	+	+	CCONJ
ejpam-6617	176	3	9.8272e	9.8272e	NUM
ejpam-6617	176	4	−	−	ADP
ejpam-6617	176	5	ς	ς	PROPN
ejpam-6617	176	6	3	3	NUM
ejpam-6617	176	7	−	−	NOUN
ejpam-6617	176	8	7.6459)}dς	7.6459)}dς	NUM
ejpam-6617	176	9	and	and	CCONJ
ejpam-6617	176	10	κ(ς	κ(ς	NUM
ejpam-6617	176	11	)	)	PUNCT
ejpam-6617	176	12	=	=	SYM
ejpam-6617	176	13	1	1	NUM
ejpam-6617	176	14	3	3	NUM
ejpam-6617	176	15	ς2	ς2	NOUN
ejpam-6617	176	16	−	−	PROPN
ejpam-6617	176	17	3.6666667	3.6666667	NUM
ejpam-6617	176	18	11	11	NUM
ejpam-6617	176	19	ς	ς	PROPN
ejpam-6617	176	20	+1	+1	PROPN
ejpam-6617	176	21	∈	∈	PROPN
ejpam-6617	176	22	x	x	NOUN
ejpam-6617	176	23	,	,	PUNCT
ejpam-6617	176	24	forall	forall	VERB
ejpam-6617	176	25	ς	ς	PROPN
ejpam-6617	176	26	∈	∈	PROPN
ejpam-6617	177	1	[	[	X
ejpam-6617	177	2	0	0	NUM
ejpam-6617	177	3	,	,	PUNCT
ejpam-6617	177	4	1	1	NUM
ejpam-6617	177	5	]	]	PUNCT
ejpam-6617	177	6	and	and	CCONJ
ejpam-6617	177	7	note	note	VERB
ejpam-6617	177	8	that	that	PRON
ejpam-6617	177	9	(	(	PUNCT
ejpam-6617	177	10	κ	κ	PROPN
ejpam-6617	177	11	̸=	̸=	PROPN
ejpam-6617	177	12	κ̄	κ̄	NOUN
ejpam-6617	177	13	)	)	PUNCT
ejpam-6617	177	14	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	177	15	)	)	PUNCT
ejpam-6617	177	16	=	=	SYM
ejpam-6617	177	17	1	1	NUM
ejpam-6617	177	18	∈	∈	NOUN
ejpam-6617	177	19	x	x	PUNCT
ejpam-6617	177	20	in	in	ADP
ejpam-6617	177	21	such	such	ADJ
ejpam-6617	177	22	way	way	NOUN
ejpam-6617	177	23	that	that	SCONJ
ejpam-6617	177	24	,	,	PUNCT
ejpam-6617	177	25	a2∫	a2∫	NOUN
ejpam-6617	177	26	a1	a1	NOUN
ejpam-6617	177	27	{	{	PUNCT
ejpam-6617	177	28	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	177	29	,	,	PUNCT
ejpam-6617	177	30	κ	κ	NOUN
ejpam-6617	177	31	,	,	PUNCT
ejpam-6617	177	32	κ̄)𭟋κ̄	κ̄)𭟋κ̄	PROPN
ejpam-6617	177	33	(	(	PUNCT
ejpam-6617	177	34	ς	ς	PROPN
ejpam-6617	177	35	,	,	PUNCT
ejpam-6617	177	36	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	177	37	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	177	38	)	)	PUNCT
ejpam-6617	177	39	+	+	CCONJ
ejpam-6617	177	40	cfdθ•	cfdθ•	PROPN
ejpam-6617	177	41	a1+(ℵ(ς	a1+(ℵ(ς	PROPN
ejpam-6617	177	42	,	,	PUNCT
ejpam-6617	177	43	κ	κ	NOUN
ejpam-6617	177	44	,	,	PUNCT
ejpam-6617	177	45	κ̄	κ̄	NOUN
ejpam-6617	177	46	)	)	PUNCT
ejpam-6617	177	47	)	)	PUNCT
ejpam-6617	177	48	𭟋cfdθ•	𭟋cfdθ•	PRON
ejpam-6617	177	49	a1	a1	NOUN
ejpam-6617	177	50	+	+	X
ejpam-6617	177	51	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	177	52	,	,	PUNCT
ejpam-6617	177	53	κ̄	κ̄	NOUN
ejpam-6617	177	54	,	,	PUNCT
ejpam-6617	177	55	cf	cf	NOUN
ejpam-6617	177	56	dθ•	dθ•	PROPN
ejpam-6617	177	57	a1	a1	NOUN
ejpam-6617	177	58	+	+	X
ejpam-6617	177	59	κ̄	κ̄	NOUN
ejpam-6617	177	60	)	)	PUNCT
ejpam-6617	177	61	}	}	PUNCT
ejpam-6617	177	62	dς	dς	VERB
ejpam-6617	177	63	>	>	X
ejpam-6617	177	64	0	0	PUNCT
ejpam-6617	178	1	⇒	⇒	NOUN
ejpam-6617	178	2	a2∫	a2∫	NOUN
ejpam-6617	178	3	a1	a1	PROPN
ejpam-6617	178	4	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	178	5	,	,	PUNCT
ejpam-6617	178	6	κ	κ	NOUN
ejpam-6617	178	7	,	,	PUNCT
ejpam-6617	178	8	cfdθ•	cfdθ•	PROPN
ejpam-6617	178	9	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	178	10	>	>	PUNCT
ejpam-6617	178	11	a2∫	a2∫	NOUN
ejpam-6617	178	12	a1	a1	PROPN
ejpam-6617	178	13	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	178	14	,	,	PUNCT
ejpam-6617	178	15	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	178	16	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	178	17	.	.	PUNCT
ejpam-6617	179	1	but	but	CCONJ
ejpam-6617	179	2	,	,	PUNCT
ejpam-6617	179	3	𭟋	𭟋	PROPN
ejpam-6617	179	4	=	=	SYM
ejpam-6617	179	5	1∫	1∫	NUM
ejpam-6617	179	6	0	0	NUM
ejpam-6617	179	7	{	{	PUNCT
ejpam-6617	179	8	−κ(ς	−κ(ς	NOUN
ejpam-6617	179	9	)	)	PUNCT
ejpam-6617	180	1	+	+	CCONJ
ejpam-6617	180	2	2.1838ς	2.1838ς	NUM
ejpam-6617	180	3	+	+	NUM
ejpam-6617	180	4	figure	figure	NOUN
ejpam-6617	180	5	2	2	NUM
ejpam-6617	180	6	:	:	PUNCT
ejpam-6617	180	7	graphical	graphical	ADJ
ejpam-6617	180	8	view	view	NOUN
ejpam-6617	180	9	of	of	ADP
ejpam-6617	180	10	the	the	DET
ejpam-6617	180	11	function	function	NOUN
ejpam-6617	180	12	𭟋	𭟋	PROPN
ejpam-6617	180	13	=	=	SYM
ejpam-6617	180	14	−κ(ς	−κ(ς	PROPN
ejpam-6617	180	15	)	)	PUNCT
ejpam-6617	181	1	+	+	CCONJ
ejpam-6617	182	1	2.1838ς	2.1838ς	NUM
ejpam-6617	182	2	+	+	CCONJ
ejpam-6617	182	3	9.8272e	9.8272e	NUM
ejpam-6617	182	4	−	−	ADP
ejpam-6617	182	5	ς	ς	PROPN
ejpam-6617	182	6	3	3	NUM
ejpam-6617	182	7	−	−	PROPN
ejpam-6617	182	8	7.6459	7.6459	NUM
ejpam-6617	182	9	9.8272e	9.8272e	NOUN
ejpam-6617	182	10	−	−	NUM
ejpam-6617	182	11	ς	ς	PROPN
ejpam-6617	182	12	3	3	NUM
ejpam-6617	182	13	−	−	PROPN
ejpam-6617	182	14	7.6459}dς	7.6459}dς	NUM
ejpam-6617	182	15	is	be	AUX
ejpam-6617	182	16	not	not	PART
ejpam-6617	182	17	invex	invex	NOUN
ejpam-6617	182	18	at	at	ADP
ejpam-6617	182	19	κ̄	κ̄	NOUN
ejpam-6617	182	20	=	=	SYM
ejpam-6617	182	21	1	1	NUM
ejpam-6617	182	22	∈	∈	PROPN
ejpam-6617	182	23	x	x	NOUN
ejpam-6617	182	24	,	,	PUNCT
ejpam-6617	182	25	that	that	PRON
ejpam-6617	182	26	is	be	AUX
ejpam-6617	182	27	a2∫	a2∫	NOUN
ejpam-6617	182	28	a1	a1	PROPN
ejpam-6617	182	29	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	182	30	,	,	PUNCT
ejpam-6617	182	31	κ	κ	NOUN
ejpam-6617	182	32	,	,	PUNCT
ejpam-6617	182	33	cfdθ•	cfdθ•	PROPN
ejpam-6617	182	34	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	182	35	−	−	NOUN
ejpam-6617	182	36	a2∫	a2∫	NOUN
ejpam-6617	182	37	a1	a1	VERB
ejpam-6617	182	38	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	182	39	,	,	PUNCT
ejpam-6617	182	40	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	182	41	a1+κ̄)dς	a1+κ̄)dς	NOUN
ejpam-6617	182	42	≯	≯	VERB
ejpam-6617	182	43	a2∫	a2∫	NOUN
ejpam-6617	182	44	a1	a1	NOUN
ejpam-6617	182	45	{	{	PUNCT
ejpam-6617	182	46	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	182	47	,	,	PUNCT
ejpam-6617	182	48	κ	κ	NOUN
ejpam-6617	182	49	,	,	PUNCT
ejpam-6617	182	50	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	182	51	,	,	PUNCT
ejpam-6617	182	52	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	182	53	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	182	54	)	)	PUNCT
ejpam-6617	183	1	+	+	PROPN
ejpam-6617	183	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	183	3	a1+(ℵ(ς	a1+(ℵ(ς	PROPN
ejpam-6617	183	4	,	,	PUNCT
ejpam-6617	183	5	κ	κ	NOUN
ejpam-6617	183	6	,	,	PUNCT
ejpam-6617	183	7	κ̄))𭟋cfdθ•	κ̄))𭟋cfdθ•	NOUN
ejpam-6617	183	8	a1	a1	NOUN
ejpam-6617	183	9	+	+	X
ejpam-6617	183	10	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	183	11	,	,	PUNCT
ejpam-6617	183	12	κ̄	κ̄	NOUN
ejpam-6617	183	13	,	,	PUNCT
ejpam-6617	183	14	cfdθ•	cfdθ•	PROPN
ejpam-6617	183	15	a1+κ̄)}dς	a1+κ̄)}dς	PROPN
ejpam-6617	183	16	.	.	PUNCT
ejpam-6617	184	1	this	this	DET
ejpam-6617	184	2	example	example	NOUN
ejpam-6617	184	3	provided	provide	VERB
ejpam-6617	184	4	,	,	PUNCT
ejpam-6617	184	5	on	on	ADP
ejpam-6617	184	6	taking	take	VERB
ejpam-6617	184	7	θ•	θ•	NOUN
ejpam-6617	184	8	=	=	NOUN
ejpam-6617	184	9	1	1	NUM
ejpam-6617	184	10	4	4	NUM
ejpam-6617	184	11	,	,	PUNCT
ejpam-6617	184	12	a1	a1	NOUN
ejpam-6617	184	13	=	=	SYM
ejpam-6617	184	14	0	0	NUM
ejpam-6617	184	15	,	,	PUNCT
ejpam-6617	184	16	a2	a2	PROPN
ejpam-6617	184	17	=	=	SYM
ejpam-6617	184	18	1	1	NUM
ejpam-6617	184	19	,	,	PUNCT
ejpam-6617	184	20	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	184	21	,	,	PUNCT
ejpam-6617	184	22	κ	κ	NOUN
ejpam-6617	184	23	,	,	PUNCT
ejpam-6617	184	24	κ̄	κ̄	NOUN
ejpam-6617	184	25	)	)	PUNCT
ejpam-6617	185	1	=	=	SYM
ejpam-6617	185	2	κ	κ	PROPN
ejpam-6617	185	3	−	−	PROPN
ejpam-6617	185	4	κ̄	κ̄	NOUN
ejpam-6617	185	5	,	,	PUNCT
ejpam-6617	185	6	κ(ς	κ(ς	PROPN
ejpam-6617	185	7	)	)	PUNCT
ejpam-6617	185	8	=	=	PUNCT
ejpam-6617	186	1	v.	v.	ADP
ejpam-6617	186	2	rayanki	rayanki	NOUN
ejpam-6617	186	3	et	et	PROPN
ejpam-6617	186	4	al	al	PROPN
ejpam-6617	186	5	.	.	PUNCT
ejpam-6617	186	6	/	/	SYM
ejpam-6617	186	7	eur	eur	PROPN
ejpam-6617	186	8	.	.	PUNCT
ejpam-6617	187	1	j.	j.	PROPN
ejpam-6617	187	2	pure	pure	PROPN
ejpam-6617	187	3	appl	appl	PROPN
ejpam-6617	187	4	.	.	PROPN
ejpam-6617	187	5	math	math	PROPN
ejpam-6617	187	6	,	,	PUNCT
ejpam-6617	187	7	18	18	NUM
ejpam-6617	187	8	(	(	PUNCT
ejpam-6617	187	9	3	3	NUM
ejpam-6617	187	10	)	)	PUNCT
ejpam-6617	187	11	(	(	PUNCT
ejpam-6617	187	12	2025	2025	NUM
ejpam-6617	187	13	)	)	PUNCT
ejpam-6617	187	14	,	,	PUNCT
ejpam-6617	187	15	6617	6617	NUM
ejpam-6617	187	16	9	9	NUM
ejpam-6617	187	17	of	of	ADP
ejpam-6617	187	18	38	38	NUM
ejpam-6617	187	19	1	1	NUM
ejpam-6617	187	20	3	3	NUM
ejpam-6617	187	21	ς2	ς2	PROPN
ejpam-6617	187	22	−	−	PROPN
ejpam-6617	187	23	3.6666667	3.6666667	NUM
ejpam-6617	187	24	11	11	NUM
ejpam-6617	187	25	ς	ς	PROPN
ejpam-6617	187	26	+	+	CCONJ
ejpam-6617	187	27	1	1	NUM
ejpam-6617	187	28	and	and	CCONJ
ejpam-6617	187	29	deduce	deduce	PROPN
ejpam-6617	187	30	cfdθ•	cfdθ•	PROPN
ejpam-6617	187	31	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	187	32	)	)	PUNCT
ejpam-6617	188	1	=	=	PUNCT
ejpam-6617	189	1	2.1838ς	2.1838ς	NUM
ejpam-6617	189	2	+	+	NUM
ejpam-6617	189	3	10.919e−ς/3	10.919e−ς/3	NUM
ejpam-6617	189	4	−	−	PROPN
ejpam-6617	189	5	7.6459	7.6459	NUM
ejpam-6617	189	6	.	.	PUNCT
ejpam-6617	190	1	definition	definition	NOUN
ejpam-6617	190	2	10	10	NUM
ejpam-6617	190	3	.	.	PUNCT
ejpam-6617	191	1	the	the	DET
ejpam-6617	191	2	functional	functional	ADJ
ejpam-6617	191	3	𭟋	𭟋	NOUN
ejpam-6617	191	4	is	be	AUX
ejpam-6617	191	5	stated	state	VERB
ejpam-6617	191	6	as	as	ADP
ejpam-6617	191	7	strictly	strictly	ADV
ejpam-6617	191	8	pseudo	pseudo	NOUN
ejpam-6617	191	9	-	-	NOUN
ejpam-6617	191	10	invex	invex	ADJ
ejpam-6617	191	11	with	with	ADP
ejpam-6617	191	12	regards	regard	NOUN
ejpam-6617	191	13	to	to	ADP
ejpam-6617	191	14	ℵ	ℵ	NOUN
ejpam-6617	191	15	if	if	SCONJ
ejpam-6617	191	16	a	a	DET
ejpam-6617	191	17	differentiable	differentiable	ADJ
ejpam-6617	191	18	function	function	NOUN
ejpam-6617	191	19	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	191	20	,	,	PUNCT
ejpam-6617	191	21	κ	κ	NOUN
ejpam-6617	191	22	,	,	PUNCT
ejpam-6617	191	23	κ̄	κ̄	NOUN
ejpam-6617	191	24	)	)	PUNCT
ejpam-6617	191	25	∈	∈	PROPN
ejpam-6617	191	26	c1[a1	c1[a1	NUM
ejpam-6617	191	27	,	,	PUNCT
ejpam-6617	191	28	a2	a2	PROPN
ejpam-6617	191	29	]	]	PUNCT
ejpam-6617	191	30	with	with	ADP
ejpam-6617	191	31	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	191	32	,	,	PUNCT
ejpam-6617	191	33	κ	κ	NOUN
ejpam-6617	191	34	,	,	PUNCT
ejpam-6617	191	35	κ	κ	NOUN
ejpam-6617	191	36	)	)	PUNCT
ejpam-6617	191	37	=	=	SYM
ejpam-6617	191	38	0	0	NUM
ejpam-6617	191	39	occurs	occur	VERB
ejpam-6617	191	40	such	such	ADJ
ejpam-6617	191	41	that	that	PRON
ejpam-6617	191	42	∀	∀	NOUN
ejpam-6617	191	43	κ	κ	NOUN
ejpam-6617	191	44	,	,	PUNCT
ejpam-6617	191	45	κ̄	κ̄	NOUN
ejpam-6617	191	46	∈	∈	PROPN
ejpam-6617	191	47	x	x	SYM
ejpam-6617	191	48	,	,	PUNCT
ejpam-6617	191	49	∫	∫	PROPN
ejpam-6617	191	50	a2	a2	PROPN
ejpam-6617	191	51	a1	a1	PROPN
ejpam-6617	191	52	[	[	PUNCT
ejpam-6617	191	53	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	191	54	,	,	PUNCT
ejpam-6617	191	55	κ	κ	NOUN
ejpam-6617	191	56	,	,	PUNCT
ejpam-6617	191	57	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	191	58	,	,	PUNCT
ejpam-6617	191	59	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	191	60	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	191	61	)	)	PUNCT
ejpam-6617	192	1	+	+	PROPN
ejpam-6617	192	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	192	3	a1+ℵ(ς	a1+ℵ(ς	PRON
ejpam-6617	192	4	,	,	PUNCT
ejpam-6617	192	5	κ	κ	NOUN
ejpam-6617	192	6	,	,	PUNCT
ejpam-6617	192	7	κ̄))𭟋cfdθ•a1	κ̄))𭟋cfdθ•a1	PROPN
ejpam-6617	192	8	+	+	CCONJ
ejpam-6617	192	9	κ̄	κ̄	NOUN
ejpam-6617	192	10	(	(	PUNCT
ejpam-6617	192	11	ς	ς	PROPN
ejpam-6617	192	12	,	,	PUNCT
ejpam-6617	192	13	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	192	14	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	192	15	)	)	PUNCT
ejpam-6617	192	16	]	]	PUNCT
ejpam-6617	192	17	dς	dς	X
ejpam-6617	192	18	≥	≥	X
ejpam-6617	192	19	0	0	NUM
ejpam-6617	192	20	⇒	⇒	NOUN
ejpam-6617	192	21	a2∫	a2∫	NOUN
ejpam-6617	192	22	a1	a1	PROPN
ejpam-6617	192	23	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	192	24	,	,	PUNCT
ejpam-6617	192	25	κ	κ	NOUN
ejpam-6617	192	26	,	,	PUNCT
ejpam-6617	192	27	cfdθ•	cfdθ•	PROPN
ejpam-6617	192	28	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	192	29	>	>	PUNCT
ejpam-6617	192	30	a2∫	a2∫	NOUN
ejpam-6617	192	31	a1	a1	PROPN
ejpam-6617	192	32	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	192	33	,	,	PUNCT
ejpam-6617	192	34	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	192	35	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	192	36	,	,	PUNCT
ejpam-6617	192	37	or	or	CCONJ
ejpam-6617	192	38	,	,	PUNCT
ejpam-6617	192	39	alternatively	alternatively	ADV
ejpam-6617	192	40	a2∫	a2∫	NOUN
ejpam-6617	192	41	a1	a1	PROPN
ejpam-6617	192	42	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	192	43	,	,	PUNCT
ejpam-6617	192	44	κ	κ	NOUN
ejpam-6617	192	45	,	,	PUNCT
ejpam-6617	192	46	cfdθ•	cfdθ•	X
ejpam-6617	192	47	a1+𭟋)dς	a1+𭟋)dς	NOUN
ejpam-6617	192	48	≤	≤	NUM
ejpam-6617	192	49	a2∫	a2∫	NOUN
ejpam-6617	192	50	a1	a1	NOUN
ejpam-6617	192	51	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	192	52	,	,	PUNCT
ejpam-6617	192	53	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	192	54	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	192	55	⇒	⇒	VERB
ejpam-6617	192	56	∫	∫	PROPN
ejpam-6617	192	57	a2	a2	PROPN
ejpam-6617	192	58	a1	a1	PROPN
ejpam-6617	192	59	[	[	PUNCT
ejpam-6617	192	60	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	192	61	,	,	PUNCT
ejpam-6617	192	62	κ	κ	NOUN
ejpam-6617	192	63	,	,	PUNCT
ejpam-6617	192	64	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	192	65	,	,	PUNCT
ejpam-6617	192	66	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	192	67	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	192	68	)	)	PUNCT
ejpam-6617	193	1	+	+	PROPN
ejpam-6617	193	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	193	3	a1+ℵ(ς	a1+ℵ(ς	PRON
ejpam-6617	193	4	,	,	PUNCT
ejpam-6617	193	5	κ	κ	PROPN
ejpam-6617	193	6	,	,	PUNCT
ejpam-6617	193	7	κ̄))𭟋cfdθ•a+κ̄	κ̄))𭟋cfdθ•a+κ̄	PROPN
ejpam-6617	193	8	(	(	PUNCT
ejpam-6617	193	9	ς	ς	PROPN
ejpam-6617	193	10	,	,	PUNCT
ejpam-6617	193	11	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	193	12	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	193	13	)	)	PUNCT
ejpam-6617	193	14	]	]	PUNCT
ejpam-6617	193	15	dς	dς	X
ejpam-6617	193	16	<	<	X
ejpam-6617	193	17	0	0	X
ejpam-6617	193	18	.	.	PUNCT
ejpam-6617	194	1	definition	definition	NOUN
ejpam-6617	194	2	11	11	NUM
ejpam-6617	194	3	.	.	PUNCT
ejpam-6617	195	1	the	the	DET
ejpam-6617	195	2	functional	functional	ADJ
ejpam-6617	195	3	𭟋	𭟋	NOUN
ejpam-6617	195	4	is	be	AUX
ejpam-6617	195	5	stated	state	VERB
ejpam-6617	195	6	as	as	ADP
ejpam-6617	195	7	quasi	quasi	NOUN
ejpam-6617	195	8	-	-	NOUN
ejpam-6617	195	9	invex	invex	ADJ
ejpam-6617	195	10	in	in	ADP
ejpam-6617	195	11	respect	respect	NOUN
ejpam-6617	195	12	to	to	ADP
ejpam-6617	195	13	ℵ	ℵ	NOUN
ejpam-6617	195	14	if	if	SCONJ
ejpam-6617	195	15	a	a	DET
ejpam-6617	195	16	differentiable	differentiable	ADJ
ejpam-6617	195	17	function	function	NOUN
ejpam-6617	195	18	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	195	19	,	,	PUNCT
ejpam-6617	195	20	κ	κ	NOUN
ejpam-6617	195	21	,	,	PUNCT
ejpam-6617	195	22	κ̄	κ̄	NOUN
ejpam-6617	195	23	)	)	PUNCT
ejpam-6617	195	24	∈	∈	PROPN
ejpam-6617	195	25	c1[a1	c1[a1	NUM
ejpam-6617	195	26	,	,	PUNCT
ejpam-6617	195	27	a2	a2	PROPN
ejpam-6617	195	28	]	]	PUNCT
ejpam-6617	195	29	with	with	ADP
ejpam-6617	195	30	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	195	31	,	,	PUNCT
ejpam-6617	195	32	κ	κ	NOUN
ejpam-6617	195	33	,	,	PUNCT
ejpam-6617	195	34	κ	κ	NOUN
ejpam-6617	195	35	)	)	PUNCT
ejpam-6617	195	36	=	=	SYM
ejpam-6617	195	37	0	0	NUM
ejpam-6617	195	38	occurs	occur	VERB
ejpam-6617	195	39	in	in	ADP
ejpam-6617	195	40	such	such	ADJ
ejpam-6617	195	41	way	way	NOUN
ejpam-6617	195	42	that	that	SCONJ
ejpam-6617	195	43	∀	∀	NOUN
ejpam-6617	195	44	κ	κ	NOUN
ejpam-6617	195	45	,	,	PUNCT
ejpam-6617	195	46	κ̄	κ̄	NOUN
ejpam-6617	195	47	∈	∈	PROPN
ejpam-6617	195	48	x,∫	x,∫	NOUN
ejpam-6617	195	49	a2	a2	PROPN
ejpam-6617	195	50	a1	a1	PROPN
ejpam-6617	195	51	[	[	PUNCT
ejpam-6617	195	52	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	195	53	,	,	PUNCT
ejpam-6617	195	54	κ	κ	NOUN
ejpam-6617	195	55	,	,	PUNCT
ejpam-6617	195	56	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	195	57	,	,	PUNCT
ejpam-6617	195	58	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	195	59	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	195	60	)	)	PUNCT
ejpam-6617	196	1	+	+	PROPN
ejpam-6617	196	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	196	3	a1+ℵ(ς	a1+ℵ(ς	PRON
ejpam-6617	196	4	,	,	PUNCT
ejpam-6617	196	5	κ	κ	NOUN
ejpam-6617	196	6	,	,	PUNCT
ejpam-6617	196	7	κ̄))𭟋cfdθ•a1	κ̄))𭟋cfdθ•a1	PROPN
ejpam-6617	196	8	+	+	CCONJ
ejpam-6617	196	9	κ̄	κ̄	NOUN
ejpam-6617	196	10	(	(	PUNCT
ejpam-6617	196	11	ς	ς	PROPN
ejpam-6617	196	12	,	,	PUNCT
ejpam-6617	196	13	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	196	14	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	196	15	)	)	PUNCT
ejpam-6617	196	16	]	]	PUNCT
ejpam-6617	196	17	dς	dς	X
ejpam-6617	196	18	>	>	X
ejpam-6617	196	19	0	0	PUNCT
ejpam-6617	196	20	⇒	⇒	NOUN
ejpam-6617	196	21	a2∫	a2∫	NOUN
ejpam-6617	196	22	a1	a1	PROPN
ejpam-6617	196	23	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	196	24	,	,	PUNCT
ejpam-6617	196	25	κ	κ	NOUN
ejpam-6617	196	26	,	,	PUNCT
ejpam-6617	196	27	cfdθ•	cfdθ•	PROPN
ejpam-6617	196	28	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	196	29	>	>	PUNCT
ejpam-6617	196	30	a2∫	a2∫	NOUN
ejpam-6617	196	31	a1	a1	PROPN
ejpam-6617	196	32	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	196	33	,	,	PUNCT
ejpam-6617	196	34	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	196	35	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	196	36	,	,	PUNCT
ejpam-6617	196	37	or	or	CCONJ
ejpam-6617	196	38	equivalently	equivalently	ADV
ejpam-6617	196	39	,	,	PUNCT
ejpam-6617	196	40	a2∫	a2∫	NOUN
ejpam-6617	196	41	a1	a1	VERB
ejpam-6617	196	42	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	196	43	,	,	PUNCT
ejpam-6617	196	44	κ	κ	NOUN
ejpam-6617	196	45	,	,	PUNCT
ejpam-6617	196	46	cfdθ•	cfdθ•	PROPN
ejpam-6617	196	47	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	196	48	≤	≤	NUM
ejpam-6617	196	49	a2∫	a2∫	NOUN
ejpam-6617	196	50	a1	a1	NOUN
ejpam-6617	196	51	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	196	52	,	,	PUNCT
ejpam-6617	196	53	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	196	54	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	196	55	⇒	⇒	VERB
ejpam-6617	196	56	∫	∫	PROPN
ejpam-6617	196	57	a2	a2	PROPN
ejpam-6617	196	58	a1	a1	PROPN
ejpam-6617	196	59	[	[	PUNCT
ejpam-6617	196	60	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	196	61	,	,	PUNCT
ejpam-6617	196	62	κ	κ	NOUN
ejpam-6617	196	63	,	,	PUNCT
ejpam-6617	196	64	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	196	65	,	,	PUNCT
ejpam-6617	196	66	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	196	67	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	196	68	)	)	PUNCT
ejpam-6617	197	1	+	+	PROPN
ejpam-6617	197	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	197	3	a1+ℵ(ς	a1+ℵ(ς	PRON
ejpam-6617	197	4	,	,	PUNCT
ejpam-6617	197	5	κ	κ	NOUN
ejpam-6617	197	6	,	,	PUNCT
ejpam-6617	197	7	κ̄))𭟋cfdθ•a1	κ̄))𭟋cfdθ•a1	PROPN
ejpam-6617	197	8	+	+	CCONJ
ejpam-6617	197	9	κ̄	κ̄	NOUN
ejpam-6617	197	10	(	(	PUNCT
ejpam-6617	197	11	ς	ς	PROPN
ejpam-6617	197	12	,	,	PUNCT
ejpam-6617	197	13	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	197	14	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	197	15	)	)	PUNCT
ejpam-6617	197	16	]	]	PUNCT
ejpam-6617	197	17	dς	dς	VERB
ejpam-6617	197	18	≤	≤	NUM
ejpam-6617	197	19	0	0	NUM
ejpam-6617	197	20	.	.	PUNCT
ejpam-6617	198	1	v.	v.	ADP
ejpam-6617	198	2	rayanki	rayanki	PROPN
ejpam-6617	198	3	et	et	PROPN
ejpam-6617	198	4	al	al	PROPN
ejpam-6617	198	5	.	.	PUNCT
ejpam-6617	198	6	/	/	SYM
ejpam-6617	198	7	eur	eur	PROPN
ejpam-6617	198	8	.	.	PUNCT
ejpam-6617	199	1	j.	j.	PROPN
ejpam-6617	199	2	pure	pure	PROPN
ejpam-6617	199	3	appl	appl	PROPN
ejpam-6617	199	4	.	.	PROPN
ejpam-6617	199	5	math	math	PROPN
ejpam-6617	199	6	,	,	PUNCT
ejpam-6617	199	7	18	18	NUM
ejpam-6617	199	8	(	(	PUNCT
ejpam-6617	199	9	3	3	NUM
ejpam-6617	199	10	)	)	PUNCT
ejpam-6617	199	11	(	(	PUNCT
ejpam-6617	199	12	2025	2025	NUM
ejpam-6617	199	13	)	)	PUNCT
ejpam-6617	199	14	,	,	PUNCT
ejpam-6617	199	15	6617	6617	NUM
ejpam-6617	199	16	10	10	NUM
ejpam-6617	199	17	of	of	ADP
ejpam-6617	199	18	38	38	NUM
ejpam-6617	199	19	the	the	DET
ejpam-6617	199	20	following	follow	VERB
ejpam-6617	199	21	example	example	NOUN
ejpam-6617	199	22	shows	show	VERB
ejpam-6617	199	23	that	that	SCONJ
ejpam-6617	199	24	g	g	PROPN
ejpam-6617	199	25	is	be	AUX
ejpam-6617	199	26	a	a	DET
ejpam-6617	199	27	quasi	quasi	ADJ
ejpam-6617	199	28	-	-	ADJ
ejpam-6617	199	29	invex	invex	ADJ
ejpam-6617	199	30	function	function	NOUN
ejpam-6617	199	31	but	but	CCONJ
ejpam-6617	199	32	neither	neither	CCONJ
ejpam-6617	199	33	invex	invex	NOUN
ejpam-6617	199	34	nor	nor	CCONJ
ejpam-6617	199	35	pseudoinvex	pseudoinvex	NOUN
ejpam-6617	199	36	.	.	PROPN
ejpam-6617	199	37	example	example	NOUN
ejpam-6617	199	38	3	3	NUM
ejpam-6617	199	39	.	.	PUNCT
ejpam-6617	199	40	:	:	PUNCT
ejpam-6617	199	41	let	let	VERB
ejpam-6617	199	42	𭟋(κ	𭟋(κ	PRON
ejpam-6617	199	43	)	)	PUNCT
ejpam-6617	199	44	:	:	PUNCT
ejpam-6617	199	45	x	x	X
ejpam-6617	199	46	=	=	PUNCT
ejpam-6617	200	1	[	[	X
ejpam-6617	200	2	0	0	NUM
ejpam-6617	200	3	,	,	PUNCT
ejpam-6617	200	4	1	1	NUM
ejpam-6617	200	5	]	]	PUNCT
ejpam-6617	200	6	→	→	PUNCT
ejpam-6617	200	7	r	r	NOUN
ejpam-6617	200	8	be	be	AUX
ejpam-6617	200	9	defined	define	VERB
ejpam-6617	200	10	by	by	ADP
ejpam-6617	200	11	𭟋(κ	𭟋(κ	PROPN
ejpam-6617	200	12	)	)	PUNCT
ejpam-6617	200	13	=	=	PUNCT
ejpam-6617	201	1	1∫	1∫	NUM
ejpam-6617	201	2	0	0	NUM
ejpam-6617	201	3	{	{	PUNCT
ejpam-6617	201	4	−κ(ς	−κ(ς	NOUN
ejpam-6617	201	5	)	)	PUNCT
ejpam-6617	201	6	+	+	CCONJ
ejpam-6617	202	1	1.871822ς	1.871822ς	NUM
ejpam-6617	202	2	+	+	SYM
ejpam-6617	202	3	6.5514e	6.5514e	NUM
ejpam-6617	202	4	−	−	NOUN
ejpam-6617	202	5	ς	ς	PROPN
ejpam-6617	202	6	3	3	NUM
ejpam-6617	202	7	−	−	PROPN
ejpam-6617	202	8	5.6154}dς	5.6154}dς	NUM
ejpam-6617	202	9	and	and	CCONJ
ejpam-6617	202	10	κ(ς	κ(ς	NUM
ejpam-6617	202	11	)	)	PUNCT
ejpam-6617	202	12	=	=	SYM
ejpam-6617	203	1	2	2	NUM
ejpam-6617	203	2	7	7	NUM
ejpam-6617	203	3	ς2	ς2	PROPN
ejpam-6617	203	4	−	−	PROPN
ejpam-6617	203	5	3.1428	3.1428	NUM
ejpam-6617	203	6	11	11	NUM
ejpam-6617	203	7	ς	ς	PROPN
ejpam-6617	203	8	+	+	CCONJ
ejpam-6617	203	9	1	1	NUM
ejpam-6617	203	10	∈	∈	NOUN
ejpam-6617	203	11	x	x	NOUN
ejpam-6617	203	12	,	,	PUNCT
ejpam-6617	203	13	forall	forall	NOUN
ejpam-6617	203	14	ς	ς	PROPN
ejpam-6617	203	15	∈	∈	PROPN
ejpam-6617	204	1	[	[	X
ejpam-6617	204	2	0	0	NUM
ejpam-6617	204	3	,	,	PUNCT
ejpam-6617	204	4	1	1	NUM
ejpam-6617	204	5	]	]	PUNCT
ejpam-6617	204	6	and	and	CCONJ
ejpam-6617	204	7	note	note	VERB
ejpam-6617	204	8	that	that	PRON
ejpam-6617	204	9	(	(	PUNCT
ejpam-6617	204	10	κ	κ	PROPN
ejpam-6617	204	11	̸=	̸=	PROPN
ejpam-6617	204	12	κ̄	κ̄	NOUN
ejpam-6617	204	13	)	)	PUNCT
ejpam-6617	204	14	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	204	15	)	)	PUNCT
ejpam-6617	204	16	=	=	SYM
ejpam-6617	204	17	1	1	NUM
ejpam-6617	204	18	∈	∈	NOUN
ejpam-6617	204	19	x	x	PUNCT
ejpam-6617	204	20	such	such	ADJ
ejpam-6617	204	21	that	that	SCONJ
ejpam-6617	204	22	,	,	PUNCT
ejpam-6617	204	23	a2∫	a2∫	NOUN
ejpam-6617	204	24	a1	a1	NOUN
ejpam-6617	204	25	{	{	PUNCT
ejpam-6617	204	26	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	204	27	,	,	PUNCT
ejpam-6617	204	28	κ	κ	NOUN
ejpam-6617	204	29	,	,	PUNCT
ejpam-6617	204	30	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	204	31	,	,	PUNCT
ejpam-6617	204	32	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	204	33	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	204	34	)	)	PUNCT
ejpam-6617	205	1	+	+	PROPN
ejpam-6617	205	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	205	3	a1+(ℵ(ς	a1+(ℵ(ς	PROPN
ejpam-6617	205	4	,	,	PUNCT
ejpam-6617	205	5	κ	κ	NOUN
ejpam-6617	205	6	,	,	PUNCT
ejpam-6617	205	7	κ̄))𭟋cfdθ•	κ̄))𭟋cfdθ•	NOUN
ejpam-6617	205	8	a1	a1	NOUN
ejpam-6617	205	9	+	+	X
ejpam-6617	205	10	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	205	11	,	,	PUNCT
ejpam-6617	205	12	κ̄	κ̄	NOUN
ejpam-6617	205	13	,	,	PUNCT
ejpam-6617	205	14	cfdγ	cfdγ	ADJ
ejpam-6617	205	15	a+κ̄)}dς	a+κ̄)}dς	PROPN
ejpam-6617	205	16	>	>	SYM
ejpam-6617	205	17	0	0	PUNCT
ejpam-6617	205	18	⇒	⇒	NOUN
ejpam-6617	205	19	a2∫	a2∫	NOUN
ejpam-6617	205	20	a1	a1	PROPN
ejpam-6617	205	21	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	205	22	,	,	PUNCT
ejpam-6617	205	23	κ	κ	NOUN
ejpam-6617	205	24	,	,	PUNCT
ejpam-6617	205	25	cfdθ•	cfdθ•	PROPN
ejpam-6617	205	26	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	205	27	>	>	PUNCT
ejpam-6617	205	28	a2∫	a2∫	NOUN
ejpam-6617	205	29	a1	a1	PROPN
ejpam-6617	205	30	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	205	31	,	,	PUNCT
ejpam-6617	205	32	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	205	33	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	205	34	.	.	PUNCT
ejpam-6617	206	1	but	but	CCONJ
ejpam-6617	206	2	,	,	PUNCT
ejpam-6617	206	3	𭟋	𭟋	PROPN
ejpam-6617	206	4	is	be	AUX
ejpam-6617	206	5	neither	neither	CCONJ
ejpam-6617	206	6	invex	invex	NOUN
ejpam-6617	206	7	nor	nor	CCONJ
ejpam-6617	206	8	pseudo	pseudo	NOUN
ejpam-6617	206	9	-	-	NOUN
ejpam-6617	206	10	invex	invex	ADJ
ejpam-6617	206	11	,	,	PUNCT
ejpam-6617	206	12	that	that	PRON
ejpam-6617	206	13	is	be	AUX
ejpam-6617	206	14	a2∫	a2∫	NOUN
ejpam-6617	206	15	a1	a1	PROPN
ejpam-6617	206	16	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	206	17	,	,	PUNCT
ejpam-6617	206	18	κ	κ	NOUN
ejpam-6617	206	19	,	,	PUNCT
ejpam-6617	206	20	cfdθ•	cfdθ•	PROPN
ejpam-6617	206	21	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	206	22	−	−	NOUN
ejpam-6617	206	23	a2∫	a2∫	NOUN
ejpam-6617	206	24	a1	a1	VERB
ejpam-6617	206	25	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	206	26	,	,	PUNCT
ejpam-6617	206	27	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	206	28	a1+κ̄)dς	a1+κ̄)dς	NOUN
ejpam-6617	206	29	≯	≯	VERB
ejpam-6617	206	30	a2∫	a2∫	NOUN
ejpam-6617	206	31	a1	a1	NOUN
ejpam-6617	206	32	{	{	PUNCT
ejpam-6617	206	33	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	206	34	,	,	PUNCT
ejpam-6617	206	35	κ	κ	NOUN
ejpam-6617	206	36	,	,	PUNCT
ejpam-6617	206	37	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	206	38	,	,	PUNCT
ejpam-6617	206	39	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	206	40	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	206	41	)	)	PUNCT
ejpam-6617	207	1	+	+	PROPN
ejpam-6617	207	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	207	3	a1+(ℵ(ς	a1+(ℵ(ς	PROPN
ejpam-6617	207	4	,	,	PUNCT
ejpam-6617	207	5	κ	κ	NOUN
ejpam-6617	207	6	,	,	PUNCT
ejpam-6617	207	7	κ̄))𭟋cfdθ•	κ̄))𭟋cfdθ•	NOUN
ejpam-6617	207	8	a1	a1	NOUN
ejpam-6617	207	9	+	+	X
ejpam-6617	207	10	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	207	11	,	,	PUNCT
ejpam-6617	207	12	κ̄	κ̄	NOUN
ejpam-6617	207	13	,	,	PUNCT
ejpam-6617	207	14	cfdθ•	cfdθ•	PROPN
ejpam-6617	207	15	a1+κ̄)}dς	a1+κ̄)}dς	X
ejpam-6617	207	16	.	.	PUNCT
ejpam-6617	208	1	and	and	CCONJ
ejpam-6617	208	2	a2∫	a2∫	NOUN
ejpam-6617	208	3	a1	a1	VERB
ejpam-6617	208	4	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	208	5	,	,	PUNCT
ejpam-6617	208	6	κ	κ	NOUN
ejpam-6617	208	7	,	,	PUNCT
ejpam-6617	208	8	cfdθ•	cfdθ•	PROPN
ejpam-6617	208	9	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	208	10	≮	≮	VERB
ejpam-6617	208	11	a2∫	a2∫	NOUN
ejpam-6617	208	12	a1	a1	NOUN
ejpam-6617	208	13	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	208	14	,	,	PUNCT
ejpam-6617	208	15	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	208	16	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	208	17	⇒	⇒	VERB
ejpam-6617	208	18	a2∫	a2∫	VERB
ejpam-6617	208	19	a1	a1	NOUN
ejpam-6617	208	20	{	{	PUNCT
ejpam-6617	208	21	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	208	22	,	,	PUNCT
ejpam-6617	208	23	κ	κ	NOUN
ejpam-6617	208	24	,	,	PUNCT
ejpam-6617	208	25	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	208	26	,	,	PUNCT
ejpam-6617	208	27	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	208	28	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	208	29	)	)	PUNCT
ejpam-6617	208	30	+	+	PROPN
ejpam-6617	208	31	cfdθ•	cfdθ•	PROPN
ejpam-6617	208	32	a1+(ℵ(ς	a1+(ℵ(ς	PROPN
ejpam-6617	208	33	,	,	PUNCT
ejpam-6617	208	34	κ	κ	NOUN
ejpam-6617	208	35	,	,	PUNCT
ejpam-6617	208	36	κ̄))𭟋cfdθ•	κ̄))𭟋cfdθ•	NOUN
ejpam-6617	208	37	a1	a1	NOUN
ejpam-6617	208	38	+	+	X
ejpam-6617	208	39	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	208	40	,	,	PUNCT
ejpam-6617	208	41	κ̄	κ̄	NOUN
ejpam-6617	208	42	,	,	PUNCT
ejpam-6617	208	43	cfdθ•	cfdθ•	PROPN
ejpam-6617	208	44	a1+κ̄)}dς	a1+κ̄)}dς	PROPN
ejpam-6617	208	45	≮	≮	VERB
ejpam-6617	208	46	0	0	NUM
ejpam-6617	208	47	.	.	PUNCT
ejpam-6617	209	1	in	in	ADP
ejpam-6617	209	2	construction	construction	NOUN
ejpam-6617	209	3	of	of	ADP
ejpam-6617	209	4	this	this	DET
ejpam-6617	209	5	example	example	NOUN
ejpam-6617	209	6	,	,	PUNCT
ejpam-6617	209	7	relevantly	relevantly	ADV
ejpam-6617	209	8	taken	take	VERB
ejpam-6617	209	9	θ•	θ•	NOUN
ejpam-6617	209	10	=	=	NOUN
ejpam-6617	209	11	1	1	NUM
ejpam-6617	209	12	4	4	NUM
ejpam-6617	209	13	,	,	PUNCT
ejpam-6617	209	14	a1	a1	NOUN
ejpam-6617	209	15	=	=	SYM
ejpam-6617	209	16	0	0	NUM
ejpam-6617	209	17	,	,	PUNCT
ejpam-6617	209	18	a2	a2	PROPN
ejpam-6617	209	19	=	=	SYM
ejpam-6617	209	20	1	1	NUM
ejpam-6617	209	21	,	,	PUNCT
ejpam-6617	209	22	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	209	23	,	,	PUNCT
ejpam-6617	209	24	κ	κ	NOUN
ejpam-6617	209	25	,	,	PUNCT
ejpam-6617	209	26	κ̄	κ̄	NOUN
ejpam-6617	209	27	)	)	PUNCT
ejpam-6617	209	28	=	=	SYM
ejpam-6617	209	29	κ−κ̄	κ−κ̄	NOUN
ejpam-6617	209	30	,	,	PUNCT
ejpam-6617	209	31	κ(ς	κ(ς	PROPN
ejpam-6617	209	32	)	)	PUNCT
ejpam-6617	209	33	=	=	SYM
ejpam-6617	210	1	2	2	NUM
ejpam-6617	210	2	7	7	NUM
ejpam-6617	210	3	ς2−	ς2−	NOUN
ejpam-6617	210	4	3.1428	3.1428	NUM
ejpam-6617	210	5	11	11	NUM
ejpam-6617	210	6	ς+1	ς+1	NUM
ejpam-6617	210	7	and	and	CCONJ
ejpam-6617	210	8	deduce	deduce	PROPN
ejpam-6617	210	9	cfdθ•	cfdθ•	PROPN
ejpam-6617	210	10	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	210	11	)	)	PUNCT
ejpam-6617	211	1	=	=	SYM
ejpam-6617	212	1	1.871822ς+6.5514e	1.871822ς+6.5514e	NUM
ejpam-6617	212	2	−	−	NOUN
ejpam-6617	212	3	ς	ς	PROPN
ejpam-6617	212	4	3−5.6154	3−5.6154	PROPN
ejpam-6617	212	5	.	.	PUNCT
ejpam-6617	213	1	v.	v.	ADP
ejpam-6617	213	2	rayanki	rayanki	PROPN
ejpam-6617	213	3	et	et	PROPN
ejpam-6617	213	4	al	al	PROPN
ejpam-6617	213	5	.	.	PUNCT
ejpam-6617	213	6	/	/	SYM
ejpam-6617	213	7	eur	eur	PROPN
ejpam-6617	213	8	.	.	PUNCT
ejpam-6617	214	1	j.	j.	PROPN
ejpam-6617	214	2	pure	pure	PROPN
ejpam-6617	214	3	appl	appl	PROPN
ejpam-6617	214	4	.	.	PROPN
ejpam-6617	214	5	math	math	PROPN
ejpam-6617	214	6	,	,	PUNCT
ejpam-6617	214	7	18	18	NUM
ejpam-6617	214	8	(	(	PUNCT
ejpam-6617	214	9	3	3	NUM
ejpam-6617	214	10	)	)	PUNCT
ejpam-6617	214	11	(	(	PUNCT
ejpam-6617	214	12	2025	2025	NUM
ejpam-6617	214	13	)	)	PUNCT
ejpam-6617	214	14	,	,	PUNCT
ejpam-6617	214	15	6617	6617	NUM
ejpam-6617	214	16	11	11	NUM
ejpam-6617	214	17	of	of	ADP
ejpam-6617	214	18	38	38	NUM
ejpam-6617	214	19	figure	figure	NOUN
ejpam-6617	214	20	3	3	NUM
ejpam-6617	214	21	:	:	PUNCT
ejpam-6617	214	22	graphical	graphical	ADJ
ejpam-6617	214	23	view	view	NOUN
ejpam-6617	214	24	of	of	ADP
ejpam-6617	214	25	the	the	DET
ejpam-6617	214	26	function	function	NOUN
ejpam-6617	214	27	𭟋	𭟋	PROPN
ejpam-6617	214	28	=	=	SYM
ejpam-6617	214	29	−κ(ς	−κ(ς	PROPN
ejpam-6617	214	30	)	)	PUNCT
ejpam-6617	215	1	+	+	CCONJ
ejpam-6617	215	2	1.871822ς	1.871822ς	NUM
ejpam-6617	215	3	+	+	SYM
ejpam-6617	215	4	6.5514e	6.5514e	NUM
ejpam-6617	215	5	−	−	NOUN
ejpam-6617	215	6	ς	ς	PROPN
ejpam-6617	215	7	3	3	NUM
ejpam-6617	215	8	−	−	PROPN
ejpam-6617	215	9	5.6154	5.6154	NUM
ejpam-6617	215	10	in	in	ADP
ejpam-6617	215	11	the	the	DET
ejpam-6617	215	12	above	above	ADJ
ejpam-6617	215	13	definitions	definition	NOUN
ejpam-6617	215	14	(	(	PUNCT
ejpam-6617	215	15	8)	8)	NUM
ejpam-6617	215	16	(	(	PUNCT
ejpam-6617	215	17	11	11	NUM
ejpam-6617	215	18	)	)	PUNCT
ejpam-6617	215	19	,	,	PUNCT
ejpam-6617	215	20	cfdθ•	cfdθ•	PROPN
ejpam-6617	215	21	a1+ℵ(ς	a1+ℵ(ς	X
ejpam-6617	215	22	,	,	PUNCT
ejpam-6617	215	23	κ	κ	NOUN
ejpam-6617	215	24	,	,	PUNCT
ejpam-6617	215	25	κ̄	κ̄	NOUN
ejpam-6617	215	26	)	)	PUNCT
ejpam-6617	215	27	is	be	AUX
ejpam-6617	215	28	the	the	DET
ejpam-6617	215	29	vector	vector	NOUN
ejpam-6617	215	30	whose	whose	DET
ejpam-6617	215	31	i	i	PRON
ejpam-6617	215	32	th	th	NUM
ejpam-6617	215	33	component	component	NOUN
ejpam-6617	215	34	is	be	AUX
ejpam-6617	215	35	dθ	dθ	PROPN
ejpam-6617	215	36	•	•	NUM
ejpam-6617	215	37	dςθ•	dςθ•	PROPN
ejpam-6617	215	38	ℵi(ς	ℵi(ς	NOUN
ejpam-6617	215	39	,	,	PUNCT
ejpam-6617	215	40	κ	κ	NOUN
ejpam-6617	215	41	,	,	PUNCT
ejpam-6617	215	42	κ̄	κ̄	NOUN
ejpam-6617	215	43	)	)	PUNCT
ejpam-6617	215	44	.	.	PUNCT
ejpam-6617	216	1	let	let	VERB
ejpam-6617	216	2	ϕ(ς	ϕ(ς	PROPN
ejpam-6617	216	3	,	,	PUNCT
ejpam-6617	216	4	κ	κ	PROPN
ejpam-6617	216	5	,	,	PUNCT
ejpam-6617	216	6	cfdθ•	cfdθ•	PROPN
ejpam-6617	216	7	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	216	8	)	)	PUNCT
ejpam-6617	216	9	)	)	PUNCT
ejpam-6617	217	1	=	=	PUNCT
ejpam-6617	217	2	[	[	PUNCT
ejpam-6617	217	3	ϕl(ς	ϕl(ς	NOUN
ejpam-6617	217	4	,	,	PUNCT
ejpam-6617	217	5	κ	κ	NOUN
ejpam-6617	217	6	,	,	PUNCT
ejpam-6617	217	7	cfdθ•	cfdθ•	PROPN
ejpam-6617	217	8	a1+y(ς	a1+y(ς	NOUN
ejpam-6617	217	9	)	)	PUNCT
ejpam-6617	217	10	)	)	PUNCT
ejpam-6617	217	11	,	,	PUNCT
ejpam-6617	217	12	ϕu	ϕu	INTJ
ejpam-6617	217	13	(	(	PUNCT
ejpam-6617	217	14	ς	ς	PROPN
ejpam-6617	217	15	,	,	PUNCT
ejpam-6617	217	16	κ	κ	NOUN
ejpam-6617	217	17	,	,	PUNCT
ejpam-6617	217	18	cfdθ•	cfdθ•	PROPN
ejpam-6617	217	19	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	217	20	)	)	PUNCT
ejpam-6617	217	21	)	)	PUNCT
ejpam-6617	217	22	]	]	PUNCT
ejpam-6617	217	23	be	be	AUX
ejpam-6617	217	24	an	an	DET
ejpam-6617	217	25	interval	interval	NOUN
ejpam-6617	217	26	-	-	PUNCT
ejpam-6617	217	27	valued	value	VERB
ejpam-6617	217	28	function	function	NOUN
ejpam-6617	217	29	and	and	CCONJ
ejpam-6617	217	30	h(ς	h(ς	PROPN
ejpam-6617	217	31	,	,	PUNCT
ejpam-6617	217	32	κ	κ	NOUN
ejpam-6617	217	33	,	,	PUNCT
ejpam-6617	217	34	cfdθ•	cfdθ•	PROPN
ejpam-6617	217	35	a1+y(ς	a1+y(ς	NOUN
ejpam-6617	217	36	)	)	PUNCT
ejpam-6617	217	37	)	)	PUNCT
ejpam-6617	217	38	be	be	AUX
ejpam-6617	217	39	a	a	DET
ejpam-6617	217	40	m	m	ADJ
ejpam-6617	217	41	-	-	ADJ
ejpam-6617	217	42	dimensional	dimensional	ADJ
ejpam-6617	217	43	function	function	NOUN
ejpam-6617	217	44	having	have	VERB
ejpam-6617	217	45	continuous	continuous	ADJ
ejpam-6617	217	46	derivatives	derivative	NOUN
ejpam-6617	217	47	up	up	ADP
ejpam-6617	217	48	to	to	ADP
ejpam-6617	217	49	the	the	DET
ejpam-6617	217	50	second	second	ADJ
ejpam-6617	217	51	order	order	NOUN
ejpam-6617	217	52	with	with	ADP
ejpam-6617	217	53	regard	regard	NOUN
ejpam-6617	217	54	to	to	ADP
ejpam-6617	217	55	each	each	PRON
ejpam-6617	217	56	of	of	ADP
ejpam-6617	217	57	its	its	PRON
ejpam-6617	217	58	parameters	parameter	NOUN
ejpam-6617	217	59	.	.	PUNCT
ejpam-6617	218	1	here	here	ADV
ejpam-6617	218	2	,	,	PUNCT
ejpam-6617	218	3	κ	κ	PROPN
ejpam-6617	218	4	is	be	AUX
ejpam-6617	218	5	a	a	DET
ejpam-6617	218	6	n	n	ADV
ejpam-6617	218	7	-	-	PUNCT
ejpam-6617	218	8	dimensional	dimensional	ADJ
ejpam-6617	218	9	function	function	NOUN
ejpam-6617	218	10	of	of	ADP
ejpam-6617	218	11	ς	ς	PROPN
ejpam-6617	218	12	,	,	PUNCT
ejpam-6617	218	13	and	and	CCONJ
ejpam-6617	218	14	cfdθ•	cfdθ•	PROPN
ejpam-6617	218	15	a1+y(ς	a1+y(ς	NOUN
ejpam-6617	218	16	)	)	PUNCT
ejpam-6617	218	17	is	be	AUX
ejpam-6617	218	18	the	the	DET
ejpam-6617	218	19	cf	cf	NOUN
ejpam-6617	218	20	fractional	fractional	ADJ
ejpam-6617	218	21	derivative	derivative	NOUN
ejpam-6617	218	22	of	of	ADP
ejpam-6617	218	23	order	order	NOUN
ejpam-6617	218	24	θ•	θ•	NOUN
ejpam-6617	218	25	with	with	ADP
ejpam-6617	218	26	respect	respect	NOUN
ejpam-6617	218	27	to	to	ADP
ejpam-6617	218	28	ς	ς	NOUN
ejpam-6617	218	29	,	,	PUNCT
ejpam-6617	218	30	where	where	SCONJ
ejpam-6617	218	31	0	0	X
ejpam-6617	218	32	<	<	X
ejpam-6617	218	33	θ•	θ•	X
ejpam-6617	218	34	<	<	X
ejpam-6617	218	35	1	1	NUM
ejpam-6617	218	36	.	.	PUNCT
ejpam-6617	219	1	let	let	VERB
ejpam-6617	219	2	us	we	PRON
ejpam-6617	219	3	consider	consider	VERB
ejpam-6617	219	4	the	the	DET
ejpam-6617	219	5	following	follow	VERB
ejpam-6617	219	6	problem	problem	NOUN
ejpam-6617	219	7	(	(	PUNCT
ejpam-6617	219	8	p	p	NOUN
ejpam-6617	219	9	)	)	PUNCT
ejpam-6617	219	10	under	under	ADP
ejpam-6617	219	11	caputo	caputo	PROPN
ejpam-6617	219	12	-	-	PUNCT
ejpam-6617	219	13	fabrizio	fabrizio	PROPN
ejpam-6617	219	14	fractional	fractional	ADJ
ejpam-6617	219	15	derivative	derivative	NOUN
ejpam-6617	219	16	:	:	PUNCT
ejpam-6617	219	17	(	(	PUNCT
ejpam-6617	219	18	p	p	NOUN
ejpam-6617	219	19	)	)	PUNCT
ejpam-6617	219	20	:	:	PUNCT
ejpam-6617	219	21	minφ(κ)κ∈x	minφ(κ)κ∈x	X
ejpam-6617	220	1	=	=	PUNCT
ejpam-6617	220	2			NOUN
ejpam-6617	220	3	a2∫	a2∫	NOUN
ejpam-6617	220	4	a1	a1	NOUN
ejpam-6617	220	5	ϕl(ς	ϕl(ς	PUNCT
ejpam-6617	220	6	,	,	PUNCT
ejpam-6617	220	7	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	220	8	a1+κ(ς))dς	a1+κ(ς))dς	ADV
ejpam-6617	220	9	,	,	PUNCT
ejpam-6617	220	10	a2∫	a2∫	X
ejpam-6617	220	11	a1	a1	VERB
ejpam-6617	220	12	ϕu	ϕu	X
ejpam-6617	220	13	(	(	PUNCT
ejpam-6617	220	14	ς	ς	PROPN
ejpam-6617	220	15	,	,	PUNCT
ejpam-6617	220	16	y(ς),cfdθ•	y(ς),cfdθ•	PROPN
ejpam-6617	220	17	a1+κ(ς))dς	a1+κ(ς))dς	PUNCT
ejpam-6617	220	18			NOUN
ejpam-6617	220	19	subject	subject	ADJ
ejpam-6617	220	20	to	to	ADP
ejpam-6617	220	21	,	,	PUNCT
ejpam-6617	220	22	κ(a1	κ(a1	NOUN
ejpam-6617	220	23	)	)	PUNCT
ejpam-6617	220	24	=	=	SYM
ejpam-6617	220	25	α	α	NUM
ejpam-6617	220	26	,	,	PUNCT
ejpam-6617	220	27	κ(a2	κ(a2	NOUN
ejpam-6617	220	28	)	)	PUNCT
ejpam-6617	220	29	=	=	SYM
ejpam-6617	221	1	β	β	X
ejpam-6617	221	2	,	,	PUNCT
ejpam-6617	221	3	(	(	PUNCT
ejpam-6617	221	4	2	2	X
ejpam-6617	221	5	)	)	PUNCT
ejpam-6617	221	6	h(ς	h(ς	PROPN
ejpam-6617	221	7	,	,	PUNCT
ejpam-6617	221	8	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	221	9	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	221	10	)	)	PUNCT
ejpam-6617	221	11	)	)	PUNCT
ejpam-6617	222	1	≤	≤	ADV
ejpam-6617	222	2	0	0	NUM
ejpam-6617	222	3	,	,	PUNCT
ejpam-6617	222	4	ς	ς	PROPN
ejpam-6617	222	5	∈	∈	PROPN
ejpam-6617	222	6	ℑ.	ℑ.	PROPN
ejpam-6617	222	7	(	(	PUNCT
ejpam-6617	222	8	3	3	NUM
ejpam-6617	222	9	)	)	PUNCT
ejpam-6617	222	10	the	the	DET
ejpam-6617	222	11	region	region	NOUN
ejpam-6617	222	12	(	(	PUNCT
ejpam-6617	222	13	feasibility	feasibility	NOUN
ejpam-6617	222	14	region	region	NOUN
ejpam-6617	222	15	)	)	PUNCT
ejpam-6617	222	16	,	,	PUNCT
ejpam-6617	222	17	where	where	SCONJ
ejpam-6617	222	18	the	the	DET
ejpam-6617	222	19	restrictions	restriction	NOUN
ejpam-6617	222	20	are	be	AUX
ejpam-6617	222	21	satisfied	satisfied	ADJ
ejpam-6617	222	22	,	,	PUNCT
ejpam-6617	222	23	is	be	AUX
ejpam-6617	222	24	provided	provide	VERB
ejpam-6617	222	25	by	by	ADP
ejpam-6617	222	26	φ	φ	PROPN
ejpam-6617	222	27	=	=	SYM
ejpam-6617	222	28	{	{	PUNCT
ejpam-6617	222	29	κ	κ	NOUN
ejpam-6617	222	30	∈	∈	PROPN
ejpam-6617	222	31	x	x	X
ejpam-6617	222	32	:	:	PUNCT
ejpam-6617	222	33	κ(a1	κ(a1	NOUN
ejpam-6617	222	34	)	)	PUNCT
ejpam-6617	222	35	=	=	SYM
ejpam-6617	222	36	α	α	NUM
ejpam-6617	222	37	,	,	PUNCT
ejpam-6617	222	38	κ(a2	κ(a2	NOUN
ejpam-6617	222	39	)	)	PUNCT
ejpam-6617	222	40	=	=	SYM
ejpam-6617	222	41	β	β	X
ejpam-6617	222	42	,	,	PUNCT
ejpam-6617	222	43	h(ς	h(ς	PROPN
ejpam-6617	222	44	,	,	PUNCT
ejpam-6617	222	45	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	222	46	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	222	47	)	)	PUNCT
ejpam-6617	222	48	)	)	PUNCT
ejpam-6617	223	1	≤	≤	ADV
ejpam-6617	223	2	0	0	NUM
ejpam-6617	223	3	,	,	PUNCT
ejpam-6617	223	4	ς	ς	PROPN
ejpam-6617	223	5	∈	∈	PROPN
ejpam-6617	223	6	ℑ	ℑ	PROPN
ejpam-6617	223	7	=	=	PUNCT
ejpam-6617	224	1	[	[	X
ejpam-6617	224	2	a1	a1	NOUN
ejpam-6617	224	3	,	,	PUNCT
ejpam-6617	224	4	a2	a2	PROPN
ejpam-6617	224	5	]	]	PUNCT
ejpam-6617	224	6	}	}	PUNCT
ejpam-6617	224	7	.	.	PUNCT
ejpam-6617	225	1	definition	definition	NOUN
ejpam-6617	225	2	12	12	NUM
ejpam-6617	225	3	.	.	PUNCT
ejpam-6617	226	1	a	a	DET
ejpam-6617	226	2	feasible	feasible	ADJ
ejpam-6617	226	3	point	point	NOUN
ejpam-6617	226	4	κ̄	κ̄	NOUN
ejpam-6617	226	5	is	be	AUX
ejpam-6617	226	6	said	say	VERB
ejpam-6617	226	7	to	to	PART
ejpam-6617	226	8	be	be	AUX
ejpam-6617	226	9	a	a	DET
ejpam-6617	226	10	lu	lu	NOUN
ejpam-6617	226	11	optimal	optimal	ADJ
ejpam-6617	226	12	solution	solution	NOUN
ejpam-6617	226	13	of	of	ADP
ejpam-6617	226	14	the	the	DET
ejpam-6617	226	15	problem	problem	NOUN
ejpam-6617	226	16	(	(	PUNCT
ejpam-6617	226	17	p	p	NOUN
ejpam-6617	226	18	)	)	PUNCT
ejpam-6617	226	19	,	,	PUNCT
ejpam-6617	226	20	v.	v.	ADP
ejpam-6617	226	21	rayanki	rayanki	PROPN
ejpam-6617	226	22	et	et	PROPN
ejpam-6617	226	23	al	al	PROPN
ejpam-6617	226	24	.	.	PUNCT
ejpam-6617	226	25	/	/	SYM
ejpam-6617	226	26	eur	eur	PROPN
ejpam-6617	226	27	.	.	PUNCT
ejpam-6617	227	1	j.	j.	PROPN
ejpam-6617	227	2	pure	pure	PROPN
ejpam-6617	227	3	appl	appl	PROPN
ejpam-6617	227	4	.	.	PROPN
ejpam-6617	227	5	math	math	PROPN
ejpam-6617	227	6	,	,	PUNCT
ejpam-6617	227	7	18	18	NUM
ejpam-6617	227	8	(	(	PUNCT
ejpam-6617	227	9	3	3	NUM
ejpam-6617	227	10	)	)	PUNCT
ejpam-6617	227	11	(	(	PUNCT
ejpam-6617	227	12	2025	2025	NUM
ejpam-6617	227	13	)	)	PUNCT
ejpam-6617	227	14	,	,	PUNCT
ejpam-6617	227	15	6617	6617	NUM
ejpam-6617	227	16	12	12	NUM
ejpam-6617	227	17	of	of	ADP
ejpam-6617	227	18	38	38	NUM
ejpam-6617	227	19	if	if	SCONJ
ejpam-6617	227	20	there	there	PRON
ejpam-6617	227	21	is	be	VERB
ejpam-6617	227	22	no	no	DET
ejpam-6617	227	23	feasible	feasible	ADJ
ejpam-6617	227	24	point	point	NOUN
ejpam-6617	227	25	κ	κ	ADP
ejpam-6617	227	26	∈	∈	PROPN
ejpam-6617	228	1	f	f	PROPN
ejpam-6617	228	2	such	such	ADJ
ejpam-6617	228	3	that,	that,	NOUN
ejpam-6617	228	4	a2∫	a2∫	VERB
ejpam-6617	228	5	a1	a1	NOUN
ejpam-6617	228	6	ϕl(ς	ϕl(ς	ADJ
ejpam-6617	228	7	,	,	PUNCT
ejpam-6617	228	8	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	228	9	a1+κ(ς)dς	a1+κ(ς)dς	NOUN
ejpam-6617	228	10	,	,	PUNCT
ejpam-6617	228	11	a2∫	a2∫	X
ejpam-6617	228	12	a1	a1	VERB
ejpam-6617	228	13	ϕu	ϕu	X
ejpam-6617	228	14	(	(	PUNCT
ejpam-6617	228	15	ς	ς	PROPN
ejpam-6617	228	16	,	,	PUNCT
ejpam-6617	228	17	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	228	18	a1+κ(ς)dς	a1+κ(ς)dς	NOUN
ejpam-6617	228	19			NOUN
ejpam-6617	228	20	≺lu	≺lu	VERB
ejpam-6617	228	21			NOUN
ejpam-6617	228	22	a2∫	a2∫	NOUN
ejpam-6617	228	23	a1	a1	NOUN
ejpam-6617	228	24	ϕl(ς	ϕl(ς	PRON
ejpam-6617	228	25	,	,	PUNCT
ejpam-6617	228	26	κ̄(ς),cfdθ•	κ̄(ς),cfdθ•	ADJ
ejpam-6617	228	27	a1+κ̄(ς)dς	a1+κ̄(ς)dς	PROPN
ejpam-6617	228	28	,	,	PUNCT
ejpam-6617	228	29	a2∫	a2∫	X
ejpam-6617	228	30	a1	a1	VERB
ejpam-6617	228	31	ϕu	ϕu	X
ejpam-6617	228	32	(	(	PUNCT
ejpam-6617	228	33	ς	ς	PROPN
ejpam-6617	228	34	,	,	PUNCT
ejpam-6617	228	35	κ̄(ς),cfdθ•	κ̄(ς),cfdθ•	NOUN
ejpam-6617	228	36	a1+κ̄(ς)dς	a1+κ̄(ς)dς	NOUN
ejpam-6617	228	37			NOUN
ejpam-6617	228	38	.	.	PUNCT
ejpam-6617	229	1	for	for	ADP
ejpam-6617	229	2	convenience	convenience	NOUN
ejpam-6617	229	3	we	we	PRON
ejpam-6617	229	4	write	write	VERB
ejpam-6617	229	5	as	as	ADP
ejpam-6617	229	6	,	,	PUNCT
ejpam-6617	229	7	ϕ(ς	ϕ(ς	PROPN
ejpam-6617	229	8	,	,	PUNCT
ejpam-6617	229	9	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	229	10	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	229	11	)	)	PUNCT
ejpam-6617	229	12	in	in	ADP
ejpam-6617	229	13	the	the	DET
ejpam-6617	229	14	place	place	NOUN
ejpam-6617	229	15	of	of	ADP
ejpam-6617	229	16	ϕ(ς	ϕ(ς	PROPN
ejpam-6617	229	17	,	,	PUNCT
ejpam-6617	229	18	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	229	19	)	)	PUNCT
ejpam-6617	229	20	,	,	PUNCT
ejpam-6617	229	21	cfdθ•	cfdθ•	PROPN
ejpam-6617	229	22	a1	a1	PROPN
ejpam-6617	229	23	+	+	X
ejpam-6617	229	24	κ̄(ς	κ̄(ς	NOUN
ejpam-6617	229	25	)	)	PUNCT
ejpam-6617	229	26	)	)	PUNCT
ejpam-6617	229	27	.	.	PUNCT
ejpam-6617	230	1	3	3	X
ejpam-6617	230	2	.	.	X
ejpam-6617	230	3	optimality	optimality	NOUN
ejpam-6617	230	4	conditions	condition	NOUN
ejpam-6617	230	5	the	the	DET
ejpam-6617	230	6	following	follow	VERB
ejpam-6617	230	7	kkt	kkt	PROPN
ejpam-6617	230	8	necessary	necessary	ADJ
ejpam-6617	230	9	optimality	optimality	NOUN
ejpam-6617	230	10	conditions	condition	NOUN
ejpam-6617	230	11	were	be	AUX
ejpam-6617	230	12	established	establish	VERB
ejpam-6617	230	13	in	in	ADP
ejpam-6617	230	14	[	[	X
ejpam-6617	230	15	36	36	NUM
ejpam-6617	230	16	]	]	PUNCT
ejpam-6617	230	17	for	for	ADP
ejpam-6617	230	18	the	the	DET
ejpam-6617	230	19	problem(p	problem(p	NOUN
ejpam-6617	230	20	)	)	PUNCT
ejpam-6617	230	21	,	,	PUNCT
ejpam-6617	230	22	which	which	PRON
ejpam-6617	230	23	will	will	AUX
ejpam-6617	230	24	be	be	AUX
ejpam-6617	230	25	used	use	VERB
ejpam-6617	230	26	to	to	PART
ejpam-6617	230	27	demonstrate	demonstrate	VERB
ejpam-6617	230	28	the	the	DET
ejpam-6617	230	29	sufficient	sufficient	ADJ
ejpam-6617	230	30	conditions	condition	NOUN
ejpam-6617	230	31	and	and	CCONJ
ejpam-6617	230	32	strong	strong	ADJ
ejpam-6617	230	33	duality	duality	NOUN
ejpam-6617	230	34	in	in	ADP
ejpam-6617	230	35	the	the	DET
ejpam-6617	230	36	subsequent	subsequent	ADJ
ejpam-6617	230	37	sections	section	NOUN
ejpam-6617	230	38	of	of	ADP
ejpam-6617	230	39	the	the	DET
ejpam-6617	230	40	paper	paper	NOUN
ejpam-6617	230	41	.	.	PUNCT
ejpam-6617	231	1	theorem	theorem	ADJ
ejpam-6617	231	2	1	1	NUM
ejpam-6617	231	3	(	(	PUNCT
ejpam-6617	231	4	karush	karush	PROPN
ejpam-6617	231	5	-	-	PUNCT
ejpam-6617	231	6	kuhn	kuhn	PROPN
ejpam-6617	231	7	-	-	PUNCT
ejpam-6617	231	8	tucker	tucker	PROPN
ejpam-6617	231	9	necessary	necessary	ADJ
ejpam-6617	231	10	optimaliy	optimaliy	ADJ
ejpam-6617	231	11	conditions	condition	NOUN
ejpam-6617	231	12	)	)	PUNCT
ejpam-6617	231	13	.	.	PUNCT
ejpam-6617	232	1	let	let	VERB
ejpam-6617	232	2	κ̄	κ̄	NOUN
ejpam-6617	232	3	be	be	AUX
ejpam-6617	232	4	the	the	DET
ejpam-6617	232	5	lu	lu	NOUN
ejpam-6617	232	6	optimum	optimum	ADJ
ejpam-6617	232	7	solution	solution	NOUN
ejpam-6617	232	8	of	of	ADP
ejpam-6617	232	9	(	(	PUNCT
ejpam-6617	232	10	p	p	NOUN
ejpam-6617	232	11	)	)	PUNCT
ejpam-6617	232	12	with	with	ADP
ejpam-6617	232	13	slater	slater	PROPN
ejpam-6617	232	14	’s	’s	PART
ejpam-6617	232	15	constraint	constraint	NOUN
ejpam-6617	232	16	qualification	qualification	NOUN
ejpam-6617	232	17	satisfied	satisfy	VERB
ejpam-6617	232	18	at	at	ADP
ejpam-6617	232	19	κ̄.	κ̄.	X
ejpam-6617	232	20	then	then	ADV
ejpam-6617	232	21	,	,	PUNCT
ejpam-6617	232	22	∃	∃	PROPN
ejpam-6617	232	23	a	a	DET
ejpam-6617	232	24	function	function	NOUN
ejpam-6617	232	25	that	that	PRON
ejpam-6617	232	26	is	be	AUX
ejpam-6617	232	27	piecewise	piecewise	NOUN
ejpam-6617	232	28	smooth	smooth	ADJ
ejpam-6617	232	29	,	,	PUNCT
ejpam-6617	232	30	θ̄	θ̄	ADJ
ejpam-6617	232	31	:	:	PUNCT
ejpam-6617	232	32	ℑ	ℑ	PROPN
ejpam-6617	232	33	→	→	SYM
ejpam-6617	232	34	rm	rm	PROPN
ejpam-6617	232	35	,	,	PUNCT
ejpam-6617	232	36	such	such	ADJ
ejpam-6617	232	37	that	that	SCONJ
ejpam-6617	232	38	(	(	PUNCT
ejpam-6617	232	39	κ̄	κ̄	NOUN
ejpam-6617	232	40	,	,	PUNCT
ejpam-6617	232	41	θ̄	θ̄	ADJ
ejpam-6617	232	42	)	)	PUNCT
ejpam-6617	232	43	satisfies	satisfie	NOUN
ejpam-6617	232	44	,	,	PUNCT
ejpam-6617	232	45	ϕl	ϕl	PROPN
ejpam-6617	232	46	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	232	47	,	,	PUNCT
ejpam-6617	232	48	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	232	49	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	232	50	)	)	PUNCT
ejpam-6617	232	51	+	+	CCONJ
ejpam-6617	232	52	ϕu	ϕu	ADP
ejpam-6617	232	53	κ̄	κ̄	NOUN
ejpam-6617	232	54	(	(	PUNCT
ejpam-6617	232	55	ς	ς	PROPN
ejpam-6617	232	56	,	,	PUNCT
ejpam-6617	232	57	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	232	58	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	232	59	)	)	PUNCT
ejpam-6617	233	1	+	+	CCONJ
ejpam-6617	233	2	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	233	3	,	,	PUNCT
ejpam-6617	233	4	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	233	5	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	233	6	)	)	PUNCT
ejpam-6617	233	7	=	=	SYM
ejpam-6617	233	8	−cfrdθ•	−cfrdθ•	ADJ
ejpam-6617	233	9	b−	b−	PROPN
ejpam-6617	233	10	[	[	PUNCT
ejpam-6617	233	11	ϕl	ϕl	PROPN
ejpam-6617	233	12	cfdθ•a+κ̄(ς	cfdθ•a+κ̄(ς	PROPN
ejpam-6617	233	13	)	)	PUNCT
ejpam-6617	233	14	(	(	PUNCT
ejpam-6617	233	15	ς	ς	PROPN
ejpam-6617	233	16	,	,	PUNCT
ejpam-6617	233	17	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	233	18	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	233	19	)	)	PUNCT
ejpam-6617	233	20	+	+	CCONJ
ejpam-6617	233	21	ϕu	ϕu	PROPN
ejpam-6617	233	22	cfdθ•a+κ̄(ς	cfdθ•a+κ̄(ς	NOUN
ejpam-6617	233	23	)	)	PUNCT
ejpam-6617	233	24	(	(	PUNCT
ejpam-6617	233	25	ς	ς	PROPN
ejpam-6617	233	26	,	,	PUNCT
ejpam-6617	233	27	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	233	28	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	233	29	)	)	PUNCT
ejpam-6617	233	30	+	+	PROPN
ejpam-6617	233	31	θ̄(ς)hcfdθ•	θ̄(ς)hcfdθ•	PROPN
ejpam-6617	233	32	a1	a1	PROPN
ejpam-6617	233	33	+	+	CCONJ
ejpam-6617	233	34	κ̄(ς)(ς	κ̄(ς)(ς	PROPN
ejpam-6617	233	35	,	,	PUNCT
ejpam-6617	233	36	κ̄	κ̄	NOUN
ejpam-6617	233	37	,	,	PUNCT
ejpam-6617	233	38	cfdθ•	cfdθ•	PROPN
ejpam-6617	233	39	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	233	40	)	)	PUNCT
ejpam-6617	233	41	]	]	PUNCT
ejpam-6617	233	42	,	,	PUNCT
ejpam-6617	233	43	(	(	PUNCT
ejpam-6617	233	44	4	4	X
ejpam-6617	233	45	)	)	PUNCT
ejpam-6617	233	46	θ̄(ς)h(ς	θ̄(ς)h(ς	PROPN
ejpam-6617	233	47	,	,	PUNCT
ejpam-6617	233	48	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	233	49	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	233	50	)	)	PUNCT
ejpam-6617	233	51	=	=	SYM
ejpam-6617	233	52	0	0	NUM
ejpam-6617	233	53	,	,	PUNCT
ejpam-6617	233	54	θ̄(ς	θ̄(ς	NOUN
ejpam-6617	233	55	)	)	PUNCT
ejpam-6617	233	56	≥	≥	NOUN
ejpam-6617	233	57	0	0	NUM
ejpam-6617	233	58	.	.	PUNCT
ejpam-6617	234	1	(	(	PUNCT
ejpam-6617	234	2	5	5	X
ejpam-6617	234	3	)	)	PUNCT
ejpam-6617	234	4	theorem	theorem	NOUN
ejpam-6617	234	5	2	2	NUM
ejpam-6617	234	6	(	(	PUNCT
ejpam-6617	234	7	sufficient	sufficient	ADJ
ejpam-6617	234	8	optimality	optimality	NOUN
ejpam-6617	234	9	conditions	condition	NOUN
ejpam-6617	234	10	)	)	PUNCT
ejpam-6617	234	11	.	.	PUNCT
ejpam-6617	235	1	let	let	VERB
ejpam-6617	235	2	κ̄	κ̄	NOUN
ejpam-6617	235	3	∈	∈	PROPN
ejpam-6617	235	4	x	x	PUNCT
ejpam-6617	235	5	be	be	AUX
ejpam-6617	235	6	a	a	DET
ejpam-6617	235	7	feasible	feasible	ADJ
ejpam-6617	235	8	solution	solution	NOUN
ejpam-6617	235	9	of	of	ADP
ejpam-6617	235	10	(	(	PUNCT
ejpam-6617	235	11	p	p	NOUN
ejpam-6617	235	12	)	)	PUNCT
ejpam-6617	235	13	and	and	CCONJ
ejpam-6617	235	14	there	there	PRON
ejpam-6617	235	15	is	be	VERB
ejpam-6617	235	16	a	a	DET
ejpam-6617	235	17	piecewise	piecewise	NOUN
ejpam-6617	235	18	smooth	smooth	ADJ
ejpam-6617	235	19	function	function	NOUN
ejpam-6617	235	20	θ̄	θ̄	ADJ
ejpam-6617	235	21	:	:	PUNCT
ejpam-6617	235	22	ℑ	ℑ	PROPN
ejpam-6617	235	23	→	→	SYM
ejpam-6617	235	24	rm	rm	PROPN
ejpam-6617	235	25	,	,	PUNCT
ejpam-6617	235	26	θ̄(ς	θ̄(ς	PROPN
ejpam-6617	235	27	)	)	PUNCT
ejpam-6617	235	28	≥	≥	NOUN
ejpam-6617	235	29	0	0	NUM
ejpam-6617	235	30	such	such	ADJ
ejpam-6617	235	31	that	that	SCONJ
ejpam-6617	235	32	equations	equation	NOUN
ejpam-6617	235	33	(	(	PUNCT
ejpam-6617	235	34	4	4	NUM
ejpam-6617	235	35	)	)	PUNCT
ejpam-6617	235	36	and	and	CCONJ
ejpam-6617	235	37	(	(	PUNCT
ejpam-6617	235	38	5	5	X
ejpam-6617	235	39	)	)	PUNCT
ejpam-6617	235	40	are	be	AUX
ejpam-6617	235	41	satisfied	satisfied	ADJ
ejpam-6617	235	42	at	at	ADP
ejpam-6617	235	43	(	(	PUNCT
ejpam-6617	235	44	κ̄	κ̄	NOUN
ejpam-6617	235	45	,	,	PUNCT
ejpam-6617	235	46	θ̄	θ̄	ADJ
ejpam-6617	235	47	)	)	PUNCT
ejpam-6617	235	48	.	.	PUNCT
ejpam-6617	236	1	also	also	ADV
ejpam-6617	236	2	,	,	PUNCT
ejpam-6617	236	3	assume	assume	VERB
ejpam-6617	236	4	that	that	SCONJ
ejpam-6617	236	5	(	(	PUNCT
ejpam-6617	236	6	i	i	NOUN
ejpam-6617	236	7	)	)	PUNCT
ejpam-6617	236	8	the	the	DET
ejpam-6617	236	9	functional	functional	ADJ
ejpam-6617	236	10	a2∫	a2∫	NOUN
ejpam-6617	236	11	a1	a1	NOUN
ejpam-6617	236	12	(	(	PUNCT
ejpam-6617	236	13	ϕl	ϕl	PROPN
ejpam-6617	237	1	+	+	NOUN
ejpam-6617	237	2	ϕu	ϕu	NOUN
ejpam-6617	237	3	)	)	PUNCT
ejpam-6617	237	4	(	(	PUNCT
ejpam-6617	237	5	ς	ς	PROPN
ejpam-6617	237	6	,	,	PUNCT
ejpam-6617	237	7	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	237	8	a1+κ(ς))dς	a1+κ(ς))dς	PROPN
ejpam-6617	237	9	is	be	AUX
ejpam-6617	237	10	invex	invex	NOUN
ejpam-6617	237	11	at	at	ADP
ejpam-6617	237	12	κ̄	κ̄	NOUN
ejpam-6617	237	13	on	on	ADP
ejpam-6617	237	14	x	x	X
ejpam-6617	237	15	,	,	PUNCT
ejpam-6617	237	16	(	(	PUNCT
ejpam-6617	237	17	ii	ii	NOUN
ejpam-6617	237	18	)	)	PUNCT
ejpam-6617	237	19	the	the	DET
ejpam-6617	237	20	functional	functional	ADJ
ejpam-6617	237	21	a2∫	a2∫	NOUN
ejpam-6617	237	22	a1	a1	NOUN
ejpam-6617	237	23	θ̄(ς)h(ς	θ̄(ς)h(ς	NOUN
ejpam-6617	237	24	,	,	PUNCT
ejpam-6617	237	25	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	237	26	a+κ̄)dς	a+κ̄)dς	PROPN
ejpam-6617	237	27	is	be	AUX
ejpam-6617	237	28	invex	invex	NOUN
ejpam-6617	237	29	at	at	ADP
ejpam-6617	237	30	κ̄	κ̄	NOUN
ejpam-6617	237	31	on	on	ADP
ejpam-6617	237	32	x	x	X
ejpam-6617	237	33	,	,	PUNCT
ejpam-6617	237	34	then	then	ADV
ejpam-6617	237	35	κ̄	κ̄	NOUN
ejpam-6617	237	36	is	be	AUX
ejpam-6617	237	37	a	a	DET
ejpam-6617	237	38	lu	lu	NOUN
ejpam-6617	237	39	optimal	optimal	ADJ
ejpam-6617	237	40	solution	solution	NOUN
ejpam-6617	237	41	for	for	ADP
ejpam-6617	237	42	(	(	PUNCT
ejpam-6617	237	43	p	p	NOUN
ejpam-6617	237	44	)	)	PUNCT
ejpam-6617	237	45	.	.	PUNCT
ejpam-6617	238	1	proof	proof	NOUN
ejpam-6617	238	2	.	.	PUNCT
ejpam-6617	239	1	if	if	SCONJ
ejpam-6617	239	2	κ̄	κ̄	NOUN
ejpam-6617	239	3	is	be	AUX
ejpam-6617	239	4	not	not	PART
ejpam-6617	239	5	a	a	DET
ejpam-6617	239	6	lu	lu	NOUN
ejpam-6617	239	7	optimum	optimum	ADJ
ejpam-6617	239	8	solution	solution	NOUN
ejpam-6617	239	9	for	for	ADP
ejpam-6617	239	10	(	(	PUNCT
ejpam-6617	239	11	p	p	NOUN
ejpam-6617	239	12	)	)	PUNCT
ejpam-6617	239	13	,	,	PUNCT
ejpam-6617	239	14	then	then	ADV
ejpam-6617	239	15	by	by	ADP
ejpam-6617	239	16	definition	definition	NOUN
ejpam-6617	239	17	12	12	NUM
ejpam-6617	239	18	another	another	DET
ejpam-6617	239	19	feasible	feasible	ADJ
ejpam-6617	239	20	solution	solution	NOUN
ejpam-6617	239	21	κ	κ	X
ejpam-6617	239	22	for	for	ADP
ejpam-6617	239	23	(	(	PUNCT
ejpam-6617	239	24	p	p	NOUN
ejpam-6617	239	25	)	)	PUNCT
ejpam-6617	239	26	exists	exist	VERB
ejpam-6617	239	27	,	,	PUNCT
ejpam-6617	239	28	such	such	ADJ
ejpam-6617	239	29	that	that	X
ejpam-6617	239	30	a2∫	a2∫	NOUN
ejpam-6617	239	31	a1	a1	NOUN
ejpam-6617	239	32	ϕl(ς	ϕl(ς	X
ejpam-6617	239	33	,	,	PUNCT
ejpam-6617	239	34	κ	κ	NOUN
ejpam-6617	239	35	,	,	PUNCT
ejpam-6617	239	36	cfdθ•	cfdθ•	PROPN
ejpam-6617	239	37	a1+κ)dς	a1+κ)dς	NUM
ejpam-6617	239	38	,	,	PUNCT
ejpam-6617	239	39	a2∫	a2∫	X
ejpam-6617	239	40	a1	a1	VERB
ejpam-6617	239	41	ϕu	ϕu	X
ejpam-6617	239	42	(	(	PUNCT
ejpam-6617	239	43	ς	ς	PROPN
ejpam-6617	239	44	,	,	PUNCT
ejpam-6617	239	45	κ	κ	NOUN
ejpam-6617	239	46	,	,	PUNCT
ejpam-6617	239	47	cfdγ	cfdγ	NOUN
ejpam-6617	239	48	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	239	49			NOUN
ejpam-6617	239	50	v.	v.	ADP
ejpam-6617	239	51	rayanki	rayanki	NOUN
ejpam-6617	239	52	et	et	PROPN
ejpam-6617	239	53	al	al	PROPN
ejpam-6617	239	54	.	.	PUNCT
ejpam-6617	239	55	/	/	SYM
ejpam-6617	239	56	eur	eur	PROPN
ejpam-6617	239	57	.	.	PUNCT
ejpam-6617	240	1	j.	j.	PROPN
ejpam-6617	240	2	pure	pure	PROPN
ejpam-6617	240	3	appl	appl	PROPN
ejpam-6617	240	4	.	.	PROPN
ejpam-6617	240	5	math	math	PROPN
ejpam-6617	240	6	,	,	PUNCT
ejpam-6617	240	7	18	18	NUM
ejpam-6617	240	8	(	(	PUNCT
ejpam-6617	240	9	3	3	NUM
ejpam-6617	240	10	)	)	PUNCT
ejpam-6617	240	11	(	(	PUNCT
ejpam-6617	240	12	2025	2025	NUM
ejpam-6617	240	13	)	)	PUNCT
ejpam-6617	240	14	,	,	PUNCT
ejpam-6617	240	15	6617	6617	NUM
ejpam-6617	240	16	13	13	NUM
ejpam-6617	240	17	of	of	ADP
ejpam-6617	240	18	38	38	NUM
ejpam-6617	240	19	≺lu	≺lu	PROPN
ejpam-6617	240	20			NOUN
ejpam-6617	240	21	a2∫	a2∫	NOUN
ejpam-6617	240	22	a1	a1	NOUN
ejpam-6617	240	23	ϕl(ς	ϕl(ς	PRON
ejpam-6617	240	24	,	,	PUNCT
ejpam-6617	240	25	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	240	26	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	240	27	,	,	PUNCT
ejpam-6617	240	28	a2∫	a2∫	X
ejpam-6617	240	29	a1	a1	VERB
ejpam-6617	240	30	ϕu	ϕu	X
ejpam-6617	240	31	(	(	PUNCT
ejpam-6617	240	32	ς	ς	PROPN
ejpam-6617	240	33	,	,	PUNCT
ejpam-6617	240	34	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	240	35	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	240	36			NOUN
ejpam-6617	240	37	.	.	PUNCT
ejpam-6617	241	1	thus	thus	ADV
ejpam-6617	241	2	,	,	PUNCT
ejpam-6617	241	3	we	we	PRON
ejpam-6617	241	4	have	have	VERB
ejpam-6617	241	5			NUM
ejpam-6617	241	6	a2∫	a2∫	VERB
ejpam-6617	241	7	a1	a1	NOUN
ejpam-6617	241	8	ϕl(ς	ϕl(ς	X
ejpam-6617	241	9	,	,	PUNCT
ejpam-6617	241	10	κ	κ	NOUN
ejpam-6617	241	11	,	,	PUNCT
ejpam-6617	241	12	cfdθ•	cfdθ•	PROPN
ejpam-6617	241	13	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	241	14	<	<	X
ejpam-6617	241	15	a2∫	a2∫	X
ejpam-6617	241	16	a1	a1	NOUN
ejpam-6617	241	17	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	241	18	,	,	PUNCT
ejpam-6617	241	19	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	241	20	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	241	21	a2∫	a2∫	VERB
ejpam-6617	241	22	a1	a1	NOUN
ejpam-6617	241	23	ϕu	ϕu	X
ejpam-6617	241	24	(	(	PUNCT
ejpam-6617	241	25	ς	ς	PROPN
ejpam-6617	241	26	,	,	PUNCT
ejpam-6617	241	27	κ	κ	NOUN
ejpam-6617	241	28	,	,	PUNCT
ejpam-6617	241	29	cfdθ•	cfdθ•	PROPN
ejpam-6617	241	30	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	241	31	≤	≤	NUM
ejpam-6617	241	32	a2∫	a2∫	NOUN
ejpam-6617	241	33	a1	a1	NOUN
ejpam-6617	241	34	ϕu	ϕu	X
ejpam-6617	241	35	(	(	PUNCT
ejpam-6617	241	36	ς	ς	PROPN
ejpam-6617	241	37	,	,	PUNCT
ejpam-6617	241	38	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	241	39	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	241	40	,	,	PUNCT
ejpam-6617	241	41	or	or	CCONJ
ejpam-6617	241	42			NUM
ejpam-6617	241	43	a2∫	a2∫	NOUN
ejpam-6617	241	44	a1	a1	NOUN
ejpam-6617	241	45	ϕl(ς	ϕl(ς	X
ejpam-6617	241	46	,	,	PUNCT
ejpam-6617	241	47	κ	κ	NOUN
ejpam-6617	241	48	,	,	PUNCT
ejpam-6617	241	49	cfdθ•	cfdθ•	PROPN
ejpam-6617	241	50	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	241	51	≤	≤	NUM
ejpam-6617	241	52	a2∫	a2∫	NOUN
ejpam-6617	241	53	a1	a1	NOUN
ejpam-6617	241	54	ϕl(ς	ϕl(ς	PUNCT
ejpam-6617	241	55	,	,	PUNCT
ejpam-6617	241	56	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	241	57	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	241	58	a2∫	a2∫	VERB
ejpam-6617	241	59	a1	a1	NOUN
ejpam-6617	241	60	ϕu	ϕu	X
ejpam-6617	241	61	(	(	PUNCT
ejpam-6617	241	62	ς	ς	PROPN
ejpam-6617	241	63	,	,	PUNCT
ejpam-6617	241	64	κ	κ	NOUN
ejpam-6617	241	65	,	,	PUNCT
ejpam-6617	241	66	cfdθ•	cfdθ•	PROPN
ejpam-6617	241	67	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	241	68	<	<	X
ejpam-6617	241	69	a2∫	a2∫	X
ejpam-6617	241	70	a1	a1	NOUN
ejpam-6617	241	71	ϕu	ϕu	X
ejpam-6617	241	72	(	(	PUNCT
ejpam-6617	241	73	ς	ς	PROPN
ejpam-6617	241	74	,	,	PUNCT
ejpam-6617	241	75	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	241	76	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	241	77	,	,	PUNCT
ejpam-6617	241	78	or	or	CCONJ
ejpam-6617	241	79			NUM
ejpam-6617	241	80	a2∫	a2∫	NOUN
ejpam-6617	241	81	a1	a1	NOUN
ejpam-6617	241	82	ϕl(ς	ϕl(ς	X
ejpam-6617	241	83	,	,	PUNCT
ejpam-6617	241	84	κ	κ	NOUN
ejpam-6617	241	85	,	,	PUNCT
ejpam-6617	241	86	cfdθ•	cfdθ•	PROPN
ejpam-6617	241	87	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	241	88	<	<	X
ejpam-6617	241	89	a2∫	a2∫	X
ejpam-6617	241	90	a1	a1	NOUN
ejpam-6617	241	91	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	241	92	,	,	PUNCT
ejpam-6617	241	93	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	241	94	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	241	95	a2∫	a2∫	VERB
ejpam-6617	241	96	a1	a1	NOUN
ejpam-6617	241	97	ϕu	ϕu	X
ejpam-6617	241	98	(	(	PUNCT
ejpam-6617	241	99	ς	ς	PROPN
ejpam-6617	241	100	,	,	PUNCT
ejpam-6617	241	101	κ	κ	NOUN
ejpam-6617	241	102	,	,	PUNCT
ejpam-6617	241	103	cfdθ•	cfdθ•	PROPN
ejpam-6617	241	104	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	241	105	<	<	X
ejpam-6617	241	106	a2∫	a2∫	X
ejpam-6617	241	107	a1	a1	NOUN
ejpam-6617	241	108	ϕu	ϕu	X
ejpam-6617	241	109	(	(	PUNCT
ejpam-6617	241	110	ς	ς	PROPN
ejpam-6617	241	111	,	,	PUNCT
ejpam-6617	241	112	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	241	113	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	241	114	.	.	PUNCT
ejpam-6617	242	1	from	from	ADP
ejpam-6617	242	2	the	the	DET
ejpam-6617	242	3	above	above	ADJ
ejpam-6617	242	4	inequalities	inequality	NOUN
ejpam-6617	242	5	,	,	PUNCT
ejpam-6617	242	6	we	we	PRON
ejpam-6617	242	7	get	get	VERB
ejpam-6617	242	8	a2∫	a2∫	NOUN
ejpam-6617	242	9	a1	a1	NOUN
ejpam-6617	242	10	[	[	PUNCT
ejpam-6617	242	11	ϕl	ϕl	PROPN
ejpam-6617	243	1	+	+	X
ejpam-6617	243	2	ϕu	ϕu	X
ejpam-6617	243	3	]	]	X
ejpam-6617	243	4	(	(	PUNCT
ejpam-6617	243	5	ς	ς	PROPN
ejpam-6617	243	6	,	,	PUNCT
ejpam-6617	243	7	κ	κ	NOUN
ejpam-6617	243	8	,	,	PUNCT
ejpam-6617	243	9	cfdθ•	cfdθ•	PROPN
ejpam-6617	243	10	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	243	11	<	<	X
ejpam-6617	243	12	a2∫	a2∫	ADJ
ejpam-6617	243	13	a1	a1	NOUN
ejpam-6617	243	14	[	[	PUNCT
ejpam-6617	243	15	ϕl	ϕl	PROPN
ejpam-6617	244	1	+	+	X
ejpam-6617	244	2	ϕu	ϕu	X
ejpam-6617	244	3	]	]	X
ejpam-6617	244	4	(	(	PUNCT
ejpam-6617	244	5	ς	ς	PROPN
ejpam-6617	244	6	,	,	PUNCT
ejpam-6617	244	7	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	244	8	a1+κ̄)dς	a1+κ̄)dς	NOUN
ejpam-6617	244	9	(	(	PUNCT
ejpam-6617	244	10	6	6	NUM
ejpam-6617	244	11	)	)	PUNCT
ejpam-6617	244	12	by	by	ADP
ejpam-6617	244	13	hypothesis(i	hypothesis(i	NOUN
ejpam-6617	244	14	)	)	PUNCT
ejpam-6617	244	15	,	,	PUNCT
ejpam-6617	244	16	the	the	DET
ejpam-6617	244	17	functional	functional	ADJ
ejpam-6617	244	18	a2∫	a2∫	NOUN
ejpam-6617	244	19	a1	a1	NOUN
ejpam-6617	244	20	(	(	PUNCT
ejpam-6617	244	21	ϕl	ϕl	PROPN
ejpam-6617	245	1	+	+	NOUN
ejpam-6617	245	2	ϕu	ϕu	NOUN
ejpam-6617	245	3	)	)	PUNCT
ejpam-6617	245	4	(	(	PUNCT
ejpam-6617	245	5	ς	ς	PROPN
ejpam-6617	245	6	,	,	PUNCT
ejpam-6617	245	7	κ	κ	NOUN
ejpam-6617	245	8	,	,	PUNCT
ejpam-6617	245	9	cfdθ•	cfdθ•	PROPN
ejpam-6617	245	10	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	245	11	is	be	AUX
ejpam-6617	245	12	invex	invex	NOUN
ejpam-6617	245	13	at	at	ADP
ejpam-6617	245	14	κ̄	κ̄	PROPN
ejpam-6617	245	15	∈	∈	PROPN
ejpam-6617	245	16	x.	x.	NOUN
ejpam-6617	246	1	thus	thus	ADV
ejpam-6617	246	2	,	,	PUNCT
ejpam-6617	246	3	from	from	ADP
ejpam-6617	246	4	the	the	DET
ejpam-6617	246	5	definition	definition	NOUN
ejpam-6617	246	6	8	8	NUM
ejpam-6617	246	7	,	,	PUNCT
ejpam-6617	246	8	we	we	PRON
ejpam-6617	246	9	have	have	VERB
ejpam-6617	246	10	a2∫	a2∫	NOUN
ejpam-6617	246	11	a1	a1	VERB
ejpam-6617	246	12	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	246	13	,	,	PUNCT
ejpam-6617	246	14	κ	κ	NOUN
ejpam-6617	246	15	,	,	PUNCT
ejpam-6617	246	16	cfdθ•	cfdθ•	PROPN
ejpam-6617	246	17	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	246	18	−	−	NOUN
ejpam-6617	246	19	a2∫	a2∫	NOUN
ejpam-6617	246	20	a1	a1	VERB
ejpam-6617	246	21	𭟋(ς	𭟋(ς	PROPN
ejpam-6617	246	22	,	,	PUNCT
ejpam-6617	246	23	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	246	24	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	246	25	≥	≥	X
ejpam-6617	246	26	(	(	PUNCT
ejpam-6617	246	27	>	>	PUNCT
ejpam-6617	246	28	)	)	PUNCT
ejpam-6617	246	29	∫	∫	PROPN
ejpam-6617	246	30	a2	a2	PROPN
ejpam-6617	246	31	a1	a1	PROPN
ejpam-6617	246	32	[	[	PUNCT
ejpam-6617	246	33	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	246	34	,	,	PUNCT
ejpam-6617	246	35	κ	κ	NOUN
ejpam-6617	246	36	,	,	PUNCT
ejpam-6617	246	37	κ̄)𭟋κ̄(ς	κ̄)𭟋κ̄(ς	PROPN
ejpam-6617	246	38	,	,	PUNCT
ejpam-6617	246	39	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	246	40	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	246	41	)	)	PUNCT
ejpam-6617	247	1	+	+	PROPN
ejpam-6617	247	2	(	(	PUNCT
ejpam-6617	247	3	cfdθ•	cfdθ•	PROPN
ejpam-6617	247	4	a1+ℵ(ς	a1+ℵ(ς	PROPN
ejpam-6617	247	5	,	,	PUNCT
ejpam-6617	247	6	κ	κ	NOUN
ejpam-6617	247	7	,	,	PUNCT
ejpam-6617	247	8	κ̄))𭟋cfdθ•a1	κ̄))𭟋cfdθ•a1	PROPN
ejpam-6617	247	9	+	+	CCONJ
ejpam-6617	247	10	κ̄	κ̄	NOUN
ejpam-6617	247	11	(	(	PUNCT
ejpam-6617	247	12	ς	ς	PROPN
ejpam-6617	247	13	,	,	PUNCT
ejpam-6617	247	14	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	247	15	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	247	16	)	)	PUNCT
ejpam-6617	247	17	]	]	PUNCT
ejpam-6617	248	1	dς	dς	PROPN
ejpam-6617	248	2	,	,	PUNCT
ejpam-6617	248	3	which	which	PRON
ejpam-6617	248	4	along	along	ADP
ejpam-6617	248	5	with	with	ADP
ejpam-6617	248	6	(	(	PUNCT
ejpam-6617	248	7	6	6	NUM
ejpam-6617	248	8	)	)	PUNCT
ejpam-6617	248	9	,	,	PUNCT
ejpam-6617	248	10	gives	give	VERB
ejpam-6617	248	11	a2∫	a2∫	NOUN
ejpam-6617	248	12	a1	a1	NOUN
ejpam-6617	248	13	{	{	PUNCT
ejpam-6617	248	14	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	248	15	,	,	PUNCT
ejpam-6617	248	16	κ	κ	NOUN
ejpam-6617	248	17	,	,	PUNCT
ejpam-6617	248	18	κ̄	κ̄	NOUN
ejpam-6617	248	19	)	)	PUNCT
ejpam-6617	248	20	[	[	PUNCT
ejpam-6617	248	21	ϕl	ϕl	NUM
ejpam-6617	248	22	κ̄	κ̄	NOUN
ejpam-6617	248	23	+	+	CCONJ
ejpam-6617	248	24	ϕu	ϕu	ADP
ejpam-6617	248	25	κ̄	κ̄	NOUN
ejpam-6617	248	26	]	]	PUNCT
ejpam-6617	248	27	(	(	PUNCT
ejpam-6617	248	28	ς	ς	PROPN
ejpam-6617	248	29	,	,	PUNCT
ejpam-6617	248	30	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	248	31	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	248	32	)	)	PUNCT
ejpam-6617	248	33	v.	v.	ADP
ejpam-6617	248	34	rayanki	rayanki	NOUN
ejpam-6617	248	35	et	et	PROPN
ejpam-6617	248	36	al	al	PROPN
ejpam-6617	248	37	.	.	PUNCT
ejpam-6617	248	38	/	/	SYM
ejpam-6617	248	39	eur	eur	PROPN
ejpam-6617	248	40	.	.	PUNCT
ejpam-6617	249	1	j.	j.	PROPN
ejpam-6617	249	2	pure	pure	PROPN
ejpam-6617	249	3	appl	appl	PROPN
ejpam-6617	249	4	.	.	PROPN
ejpam-6617	249	5	math	math	PROPN
ejpam-6617	249	6	,	,	PUNCT
ejpam-6617	249	7	18	18	NUM
ejpam-6617	249	8	(	(	PUNCT
ejpam-6617	249	9	3	3	NUM
ejpam-6617	249	10	)	)	PUNCT
ejpam-6617	249	11	(	(	PUNCT
ejpam-6617	249	12	2025	2025	NUM
ejpam-6617	249	13	)	)	PUNCT
ejpam-6617	249	14	,	,	PUNCT
ejpam-6617	249	15	6617	6617	NUM
ejpam-6617	249	16	14	14	NUM
ejpam-6617	249	17	of	of	ADP
ejpam-6617	249	18	38	38	NUM
ejpam-6617	249	19	+	+	PROPN
ejpam-6617	249	20	cfdθ•	cfdθ•	PROPN
ejpam-6617	249	21	a1+ℵ(ς	a1+ℵ(ς	PRON
ejpam-6617	249	22	,	,	PUNCT
ejpam-6617	249	23	κ	κ	NOUN
ejpam-6617	249	24	,	,	PUNCT
ejpam-6617	249	25	κ̄	κ̄	NOUN
ejpam-6617	249	26	)	)	PUNCT
ejpam-6617	249	27	[	[	PUNCT
ejpam-6617	249	28	ϕl	ϕl	PROPN
ejpam-6617	249	29	cfdθ•	cfdθ•	PROPN
ejpam-6617	249	30	a1	a1	PROPN
ejpam-6617	249	31	+	+	CCONJ
ejpam-6617	249	32	κ̄	κ̄	NOUN
ejpam-6617	249	33	+	+	CCONJ
ejpam-6617	249	34	ϕu	ϕu	PROPN
ejpam-6617	249	35	cfdθ•	cfdθ•	PROPN
ejpam-6617	249	36	a1	a1	PROPN
ejpam-6617	249	37	+	+	CCONJ
ejpam-6617	249	38	κ̄	κ̄	NOUN
ejpam-6617	249	39	]	]	X
ejpam-6617	249	40	(	(	PUNCT
ejpam-6617	249	41	ς	ς	PROPN
ejpam-6617	249	42	,	,	PUNCT
ejpam-6617	249	43	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	249	44	a1+κ̄)}dς	a1+κ̄)}dς	X
ejpam-6617	249	45	<	<	X
ejpam-6617	249	46	0	0	NUM
ejpam-6617	249	47	(	(	PUNCT
ejpam-6617	249	48	7	7	NUM
ejpam-6617	249	49	)	)	PUNCT
ejpam-6617	249	50	on	on	ADP
ejpam-6617	249	51	the	the	DET
ejpam-6617	249	52	other	other	ADJ
ejpam-6617	249	53	hand	hand	NOUN
ejpam-6617	249	54	,	,	PUNCT
ejpam-6617	249	55	from	from	ADP
ejpam-6617	249	56	(	(	PUNCT
ejpam-6617	249	57	4	4	NUM
ejpam-6617	249	58	)	)	PUNCT
ejpam-6617	249	59	together	together	ADV
ejpam-6617	249	60	with	with	ADP
ejpam-6617	249	61	proposition	proposition	NOUN
ejpam-6617	249	62	1	1	NUM
ejpam-6617	249	63	,	,	PUNCT
ejpam-6617	249	64	yields	yield	VERB
ejpam-6617	249	65	a2∫	a2∫	PRON
ejpam-6617	249	66	a1	a1	NOUN
ejpam-6617	249	67	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	249	68	,	,	PUNCT
ejpam-6617	249	69	κ	κ	NOUN
ejpam-6617	249	70	,	,	PUNCT
ejpam-6617	249	71	κ̄)[ϕl	κ̄)[ϕl	ADJ
ejpam-6617	249	72	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	249	73	,	,	PUNCT
ejpam-6617	249	74	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	249	75	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	249	76	)	)	PUNCT
ejpam-6617	250	1	+	+	CCONJ
ejpam-6617	250	2	ϕu	ϕu	ADP
ejpam-6617	250	3	κ̄	κ̄	NOUN
ejpam-6617	250	4	(	(	PUNCT
ejpam-6617	250	5	ς	ς	PROPN
ejpam-6617	250	6	,	,	PUNCT
ejpam-6617	250	7	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	250	8	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	250	9	)	)	PUNCT
ejpam-6617	250	10	+	+	CCONJ
ejpam-6617	250	11	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	250	12	,	,	PUNCT
ejpam-6617	250	13	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	250	14	a1+κ̄)]dς	a1+κ̄)]dς	PROPN
ejpam-6617	250	15	=	=	PUNCT
ejpam-6617	250	16	a2∫	a2∫	X
ejpam-6617	250	17	a1	a1	NOUN
ejpam-6617	250	18	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	250	19	,	,	PUNCT
ejpam-6617	250	20	κ	κ	NOUN
ejpam-6617	250	21	,	,	PUNCT
ejpam-6617	250	22	κ̄)(−cfdθ•	κ̄)(−cfdθ•	ADJ
ejpam-6617	250	23	b−)[ϕ	b−)[ϕ	PROPN
ejpam-6617	250	24	l	l	PROPN
ejpam-6617	250	25	cfdθ•	cfdθ•	PROPN
ejpam-6617	250	26	a1	a1	PROPN
ejpam-6617	250	27	+	+	X
ejpam-6617	250	28	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	250	29	,	,	PUNCT
ejpam-6617	250	30	κ̄	κ̄	NOUN
ejpam-6617	250	31	,	,	PUNCT
ejpam-6617	250	32	cfdθ•	cfdθ•	PROPN
ejpam-6617	250	33	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	250	34	)	)	PUNCT
ejpam-6617	250	35	+	+	CCONJ
ejpam-6617	250	36	ϕu	ϕu	PROPN
ejpam-6617	250	37	cfdθ•	cfdθ•	PROPN
ejpam-6617	250	38	a1	a1	PROPN
ejpam-6617	250	39	+	+	X
ejpam-6617	250	40	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	250	41	,	,	PUNCT
ejpam-6617	250	42	κ̄	κ̄	NOUN
ejpam-6617	250	43	,	,	PUNCT
ejpam-6617	250	44	cfdθ•	cfdθ•	PROPN
ejpam-6617	250	45	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	250	46	)	)	PUNCT
ejpam-6617	250	47	+	+	CCONJ
ejpam-6617	250	48	θ̄(ς)hcfdθ•	θ̄(ς)hcfdθ•	CCONJ
ejpam-6617	250	49	a1	a1	PROPN
ejpam-6617	250	50	+	+	X
ejpam-6617	250	51	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	250	52	,	,	PUNCT
ejpam-6617	250	53	κ̄	κ̄	NOUN
ejpam-6617	250	54	,	,	PUNCT
ejpam-6617	250	55	cfdθ•	cfdθ•	PROPN
ejpam-6617	250	56	a1+κ̄)]dς	a1+κ̄)]dς	PROPN
ejpam-6617	250	57	=	=	PRON
ejpam-6617	250	58	{	{	PUNCT
ejpam-6617	250	59	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	250	60	,	,	PUNCT
ejpam-6617	250	61	κ	κ	NOUN
ejpam-6617	250	62	,	,	PUNCT
ejpam-6617	250	63	κ̄)i1−θ•	κ̄)i1−θ•	VERB
ejpam-6617	250	64	b−	b−	PROPN
ejpam-6617	250	65	[	[	X
ejpam-6617	250	66	ϕl	ϕl	PROPN
ejpam-6617	250	67	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	250	68	,	,	PUNCT
ejpam-6617	250	69	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	250	70	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	250	71	)	)	PUNCT
ejpam-6617	251	1	+	+	CCONJ
ejpam-6617	251	2	ϕu	ϕu	ADP
ejpam-6617	251	3	κ̄	κ̄	NOUN
ejpam-6617	251	4	(	(	PUNCT
ejpam-6617	251	5	ς	ς	PROPN
ejpam-6617	251	6	,	,	PUNCT
ejpam-6617	251	7	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	251	8	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	251	9	)	)	PUNCT
ejpam-6617	251	10	+	+	CCONJ
ejpam-6617	251	11	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	251	12	,	,	PUNCT
ejpam-6617	252	1	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	252	2	a1+κ̄)]}|	a1+κ̄)]}|	PROPN
ejpam-6617	252	3	b	b	PROPN
ejpam-6617	252	4	a	a	DET
ejpam-6617	252	5	−	−	NOUN
ejpam-6617	252	6	a2∫	a2∫	NOUN
ejpam-6617	252	7	a1	a1	NOUN
ejpam-6617	252	8	{	{	PUNCT
ejpam-6617	252	9	ϕl	ϕl	PROPN
ejpam-6617	252	10	cfdθ•	cfdθ•	PROPN
ejpam-6617	252	11	a1	a1	PROPN
ejpam-6617	252	12	+	+	X
ejpam-6617	252	13	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	252	14	,	,	PUNCT
ejpam-6617	252	15	κ̄	κ̄	NOUN
ejpam-6617	252	16	,	,	PUNCT
ejpam-6617	252	17	cfdθ•	cfdθ•	PROPN
ejpam-6617	252	18	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	252	19	)	)	PUNCT
ejpam-6617	253	1	+	+	CCONJ
ejpam-6617	253	2	ϕu	ϕu	PROPN
ejpam-6617	253	3	cfdθ•	cfdθ•	PROPN
ejpam-6617	253	4	a1	a1	PROPN
ejpam-6617	253	5	+	+	X
ejpam-6617	253	6	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	253	7	,	,	PUNCT
ejpam-6617	253	8	κ̄	κ̄	NOUN
ejpam-6617	253	9	,	,	PUNCT
ejpam-6617	253	10	cfdθ•	cfdθ•	PROPN
ejpam-6617	253	11	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	253	12	)	)	PUNCT
ejpam-6617	254	1	+	+	CCONJ
ejpam-6617	254	2	θ̄(ς)hcfdθ•	θ̄(ς)hcfdθ•	CCONJ
ejpam-6617	254	3	a1	a1	PROPN
ejpam-6617	254	4	+	+	X
ejpam-6617	254	5	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	254	6	,	,	PUNCT
ejpam-6617	254	7	κ̄	κ̄	NOUN
ejpam-6617	254	8	,	,	PUNCT
ejpam-6617	254	9	cfdθ•	cfdθ•	PROPN
ejpam-6617	254	10	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	254	11	)	)	PUNCT
ejpam-6617	254	12	}	}	PUNCT
ejpam-6617	254	13	.	.	PUNCT
ejpam-6617	255	1	by	by	ADP
ejpam-6617	255	2	using	use	VERB
ejpam-6617	255	3	(	(	PUNCT
ejpam-6617	255	4	2	2	NUM
ejpam-6617	255	5	)	)	PUNCT
ejpam-6617	255	6	,	,	PUNCT
ejpam-6617	255	7	we	we	PRON
ejpam-6617	255	8	get	get	VERB
ejpam-6617	255	9	a2∫	a2∫	NOUN
ejpam-6617	255	10	a1	a1	NOUN
ejpam-6617	255	11	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	255	12	,	,	PUNCT
ejpam-6617	255	13	κ	κ	NOUN
ejpam-6617	255	14	,	,	PUNCT
ejpam-6617	255	15	κ̄)[ϕl	κ̄)[ϕl	ADJ
ejpam-6617	255	16	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	255	17	,	,	PUNCT
ejpam-6617	255	18	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	255	19	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	255	20	)	)	PUNCT
ejpam-6617	256	1	+	+	CCONJ
ejpam-6617	256	2	ϕu	ϕu	ADP
ejpam-6617	256	3	κ̄	κ̄	NOUN
ejpam-6617	256	4	(	(	PUNCT
ejpam-6617	256	5	ς	ς	PROPN
ejpam-6617	256	6	,	,	PUNCT
ejpam-6617	256	7	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	256	8	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	256	9	)	)	PUNCT
ejpam-6617	257	1	+	+	PROPN
ejpam-6617	257	2	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	257	3	,	,	PUNCT
ejpam-6617	257	4	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	257	5	a1+κ̄)]dς	a1+κ̄)]dς	PROPN
ejpam-6617	257	6	=	=	PUNCT
ejpam-6617	257	7	−	−	NOUN
ejpam-6617	257	8	a2∫	a2∫	NOUN
ejpam-6617	257	9	a1	a1	NOUN
ejpam-6617	257	10	{	{	PUNCT
ejpam-6617	257	11	ϕl	ϕl	PROPN
ejpam-6617	257	12	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	257	13	+	+	CCONJ
ejpam-6617	257	14	κ̄	κ̄	NOUN
ejpam-6617	257	15	(	(	PUNCT
ejpam-6617	257	16	ς	ς	PROPN
ejpam-6617	257	17	,	,	PUNCT
ejpam-6617	257	18	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	257	19	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	257	20	)	)	PUNCT
ejpam-6617	257	21	+	+	CCONJ
ejpam-6617	258	1	ϕu	ϕu	PROPN
ejpam-6617	258	2	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	258	3	+	+	CCONJ
ejpam-6617	258	4	κ̄	κ̄	NOUN
ejpam-6617	258	5	(	(	PUNCT
ejpam-6617	258	6	ς	ς	PROPN
ejpam-6617	258	7	,	,	PUNCT
ejpam-6617	258	8	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	258	9	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	258	10	)	)	PUNCT
ejpam-6617	258	11	+	+	ADJ
ejpam-6617	258	12	θ̄(ς)h	θ̄(ς)h	ADJ
ejpam-6617	258	13	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	258	14	+	+	SYM
ejpam-6617	258	15	κ̄	κ̄	NOUN
ejpam-6617	258	16	(	(	PUNCT
ejpam-6617	258	17	ς	ς	PROPN
ejpam-6617	258	18	,	,	PUNCT
ejpam-6617	258	19	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	258	20	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	258	21	)	)	PUNCT
ejpam-6617	258	22	}	}	PUNCT
ejpam-6617	258	23	cfdθ•	cfdθ•	PROPN
ejpam-6617	258	24	a1+ℵ(ς	a1+ℵ(ς	NUM
ejpam-6617	258	25	,	,	PUNCT
ejpam-6617	258	26	κ	κ	PROPN
ejpam-6617	258	27	,	,	PUNCT
ejpam-6617	258	28	κ̄))dς	κ̄))dς	NOUN
ejpam-6617	258	29	,	,	PUNCT
ejpam-6617	258	30	that	that	PRON
ejpam-6617	258	31	is	be	AUX
ejpam-6617	258	32	a2∫	a2∫	NOUN
ejpam-6617	258	33	a1	a1	NOUN
ejpam-6617	258	34	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	258	35	,	,	PUNCT
ejpam-6617	258	36	κ	κ	NOUN
ejpam-6617	258	37	,	,	PUNCT
ejpam-6617	258	38	κ̄	κ̄	NOUN
ejpam-6617	258	39	)	)	PUNCT
ejpam-6617	258	40	[	[	PUNCT
ejpam-6617	258	41	ϕl	ϕl	PROPN
ejpam-6617	258	42	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	258	43	,	,	PUNCT
ejpam-6617	258	44	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	258	45	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	258	46	)	)	PUNCT
ejpam-6617	258	47	+	+	CCONJ
ejpam-6617	259	1	ϕu	ϕu	ADP
ejpam-6617	259	2	κ̄	κ̄	NOUN
ejpam-6617	259	3	(	(	PUNCT
ejpam-6617	259	4	ς	ς	PROPN
ejpam-6617	259	5	,	,	PUNCT
ejpam-6617	259	6	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	259	7	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	259	8	)	)	PUNCT
ejpam-6617	259	9	+	+	PROPN
ejpam-6617	259	10	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	259	11	,	,	PUNCT
ejpam-6617	259	12	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	259	13	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	259	14	)	)	PUNCT
ejpam-6617	259	15	]	]	PUNCT
ejpam-6617	259	16	dς	dς	X
ejpam-6617	259	17	+	+	PUNCT
ejpam-6617	259	18	a2∫	a2∫	NOUN
ejpam-6617	259	19	a1	a1	NOUN
ejpam-6617	259	20	{	{	PUNCT
ejpam-6617	259	21	ϕl	ϕl	PROPN
ejpam-6617	259	22	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	259	23	+	+	CCONJ
ejpam-6617	259	24	κ̄	κ̄	NOUN
ejpam-6617	259	25	(	(	PUNCT
ejpam-6617	259	26	ς	ς	PROPN
ejpam-6617	259	27	,	,	PUNCT
ejpam-6617	259	28	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	259	29	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	259	30	)	)	PUNCT
ejpam-6617	259	31	+	+	CCONJ
ejpam-6617	259	32	ϕu	ϕu	PROPN
ejpam-6617	259	33	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	259	34	+	+	CCONJ
ejpam-6617	259	35	κ̄	κ̄	NOUN
ejpam-6617	259	36	(	(	PUNCT
ejpam-6617	259	37	ς	ς	PROPN
ejpam-6617	259	38	,	,	PUNCT
ejpam-6617	259	39	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	259	40	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	259	41	)	)	PUNCT
ejpam-6617	259	42	v.	v.	ADP
ejpam-6617	259	43	rayanki	rayanki	NOUN
ejpam-6617	259	44	et	et	PROPN
ejpam-6617	259	45	al	al	PROPN
ejpam-6617	259	46	.	.	PUNCT
ejpam-6617	259	47	/	/	SYM
ejpam-6617	259	48	eur	eur	PROPN
ejpam-6617	259	49	.	.	PUNCT
ejpam-6617	260	1	j.	j.	PROPN
ejpam-6617	260	2	pure	pure	PROPN
ejpam-6617	260	3	appl	appl	PROPN
ejpam-6617	260	4	.	.	PROPN
ejpam-6617	260	5	math	math	PROPN
ejpam-6617	260	6	,	,	PUNCT
ejpam-6617	260	7	18	18	NUM
ejpam-6617	260	8	(	(	PUNCT
ejpam-6617	260	9	3	3	NUM
ejpam-6617	260	10	)	)	PUNCT
ejpam-6617	260	11	(	(	PUNCT
ejpam-6617	260	12	2025	2025	NUM
ejpam-6617	260	13	)	)	PUNCT
ejpam-6617	260	14	,	,	PUNCT
ejpam-6617	260	15	6617	6617	NUM
ejpam-6617	260	16	15	15	NUM
ejpam-6617	260	17	of	of	ADP
ejpam-6617	260	18	38	38	NUM
ejpam-6617	260	19	+	+	ADJ
ejpam-6617	260	20	θ̄(ς)h	θ̄(ς)h	ADJ
ejpam-6617	260	21	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	260	22	+	+	SYM
ejpam-6617	260	23	κ̄	κ̄	NOUN
ejpam-6617	260	24	(	(	PUNCT
ejpam-6617	260	25	ς	ς	PROPN
ejpam-6617	260	26	,	,	PUNCT
ejpam-6617	260	27	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	260	28	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	260	29	)	)	PUNCT
ejpam-6617	260	30	}	}	PUNCT
ejpam-6617	260	31	cfdθ•	cfdθ•	PROPN
ejpam-6617	260	32	a1+ℵ(ς	a1+ℵ(ς	NUM
ejpam-6617	260	33	,	,	PUNCT
ejpam-6617	260	34	κ	κ	PROPN
ejpam-6617	260	35	,	,	PUNCT
ejpam-6617	260	36	κ̄)dς	κ̄)dς	PROPN
ejpam-6617	260	37	=	=	PROPN
ejpam-6617	260	38	0	0	PROPN
ejpam-6617	260	39	.	.	PUNCT
ejpam-6617	261	1	(	(	PUNCT
ejpam-6617	261	2	8)	8)	NUM
ejpam-6617	261	3	for	for	ADP
ejpam-6617	261	4	the	the	DET
ejpam-6617	261	5	feasibility	feasibility	NOUN
ejpam-6617	261	6	of	of	ADP
ejpam-6617	261	7	κ	κ	PROPN
ejpam-6617	261	8	of	of	ADP
ejpam-6617	261	9	(	(	PUNCT
ejpam-6617	261	10	p	p	NOUN
ejpam-6617	261	11	)	)	PUNCT
ejpam-6617	261	12	,	,	PUNCT
ejpam-6617	261	13	we	we	PRON
ejpam-6617	261	14	have	have	VERB
ejpam-6617	261	15	h(ς	h(ς	PROPN
ejpam-6617	261	16	,	,	PUNCT
ejpam-6617	261	17	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	261	18	a+κ(ς	a+κ(ς	NOUN
ejpam-6617	261	19	)	)	PUNCT
ejpam-6617	261	20	)	)	PUNCT
ejpam-6617	261	21	≤	≤	ADV
ejpam-6617	261	22	0	0	NUM
ejpam-6617	261	23	,	,	PUNCT
ejpam-6617	261	24	ς	ς	PROPN
ejpam-6617	261	25	∈	∈	PROPN
ejpam-6617	261	26	ℑ	ℑ	PROPN
ejpam-6617	261	27	,	,	PUNCT
ejpam-6617	261	28	wherein	wherein	ADJ
ejpam-6617	261	29	,	,	PUNCT
ejpam-6617	261	30	by	by	ADP
ejpam-6617	261	31	utilising	utilise	VERB
ejpam-6617	261	32	the	the	DET
ejpam-6617	261	33	fact	fact	NOUN
ejpam-6617	261	34	θ̄(ς	θ̄(ς	NOUN
ejpam-6617	261	35	)	)	PUNCT
ejpam-6617	261	36	∈	∈	PROPN
ejpam-6617	261	37	rm	rm	PROPN
ejpam-6617	261	38	,	,	PUNCT
ejpam-6617	261	39	θ̄(ς	θ̄(ς	PROPN
ejpam-6617	261	40	)	)	PUNCT
ejpam-6617	261	41	≥	≥	NOUN
ejpam-6617	261	42	0	0	NUM
ejpam-6617	261	43	and	and	CCONJ
ejpam-6617	261	44	(	(	PUNCT
ejpam-6617	261	45	5	5	NUM
ejpam-6617	261	46	)	)	PUNCT
ejpam-6617	261	47	,	,	PUNCT
ejpam-6617	261	48	we	we	PRON
ejpam-6617	261	49	have	have	VERB
ejpam-6617	261	50	a2∫	a2∫	NOUN
ejpam-6617	261	51	a1	a1	NOUN
ejpam-6617	261	52	θ̄(ς)h(ς	θ̄(ς)h(ς	NOUN
ejpam-6617	261	53	,	,	PUNCT
ejpam-6617	261	54	κ	κ	NOUN
ejpam-6617	261	55	,	,	PUNCT
ejpam-6617	261	56	cfdθ•	cfdθ•	PROPN
ejpam-6617	261	57	a1+)dς	a1+)dς	PROPN
ejpam-6617	261	58	−	−	PROPN
ejpam-6617	261	59	a2∫	a2∫	PRON
ejpam-6617	261	60	a1	a1	NOUN
ejpam-6617	261	61	θ̄(ς)h(ς	θ̄(ς)h(ς	NOUN
ejpam-6617	261	62	,	,	PUNCT
ejpam-6617	261	63	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	261	64	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	261	65	≤	≤	ADV
ejpam-6617	261	66	0	0	NUM
ejpam-6617	261	67	,	,	PUNCT
ejpam-6617	261	68	which	which	PRON
ejpam-6617	261	69	along	along	ADP
ejpam-6617	261	70	with	with	ADP
ejpam-6617	261	71	the	the	DET
ejpam-6617	261	72	hypothesis(ii	hypothesis(ii	NOUN
ejpam-6617	261	73	)	)	PUNCT
ejpam-6617	261	74	,	,	PUNCT
ejpam-6617	261	75	invexity	invexity	NOUN
ejpam-6617	261	76	of	of	ADP
ejpam-6617	261	77	a2∫	a2∫	NOUN
ejpam-6617	261	78	a1	a1	NOUN
ejpam-6617	261	79	θ̄(ς)h(ς	θ̄(ς)h(ς	NOUN
ejpam-6617	261	80	,	,	PUNCT
ejpam-6617	261	81	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	261	82	a+κ̄)dς	a+κ̄)dς	PROPN
ejpam-6617	261	83	at	at	ADP
ejpam-6617	261	84	κ̄	κ̄	NOUN
ejpam-6617	261	85	∈	∈	PROPN
ejpam-6617	261	86	x	x	X
ejpam-6617	261	87	,	,	PUNCT
ejpam-6617	261	88	yeilds	yeild	VERB
ejpam-6617	261	89	0	0	NUM
ejpam-6617	261	90	≥	≥	NOUN
ejpam-6617	261	91	a2∫	a2∫	VERB
ejpam-6617	261	92	a1	a1	PROPN
ejpam-6617	261	93	θ̄(ς	θ̄(ς	NOUN
ejpam-6617	261	94	)	)	PUNCT
ejpam-6617	261	95	[	[	PUNCT
ejpam-6617	261	96	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	261	97	,	,	PUNCT
ejpam-6617	261	98	κ	κ	NOUN
ejpam-6617	261	99	,	,	PUNCT
ejpam-6617	261	100	κ̄)hκ̄(ς	κ̄)hκ̄(ς	PROPN
ejpam-6617	261	101	,	,	PUNCT
ejpam-6617	261	102	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	261	103	a1+κ̄)+	a1+κ̄)+	PROPN
ejpam-6617	261	104	cfdθ•	cfdθ•	PROPN
ejpam-6617	261	105	a1+ℵ(ς	a1+ℵ(ς	X
ejpam-6617	261	106	,	,	PUNCT
ejpam-6617	261	107	κ	κ	NOUN
ejpam-6617	261	108	,	,	PUNCT
ejpam-6617	261	109	κ̄)hcfdθ•a1	κ̄)hcfdθ•a1	PROPN
ejpam-6617	261	110	+	+	SYM
ejpam-6617	261	111	κ̄	κ̄	NOUN
ejpam-6617	261	112	(	(	PUNCT
ejpam-6617	261	113	ς	ς	PROPN
ejpam-6617	261	114	,	,	PUNCT
ejpam-6617	261	115	κ̄(ς),cfdθ•	κ̄(ς),cfdθ•	ADJ
ejpam-6617	261	116	a1+κ̄(ς	a1+κ̄(ς	PROPN
ejpam-6617	261	117	)	)	PUNCT
ejpam-6617	261	118	)	)	PUNCT
ejpam-6617	261	119	]	]	PUNCT
ejpam-6617	262	1	dς	dς	X
ejpam-6617	262	2	.	.	PUNCT
ejpam-6617	263	1	(	(	PUNCT
ejpam-6617	263	2	9	9	NUM
ejpam-6617	263	3	)	)	PUNCT
ejpam-6617	263	4	on	on	ADP
ejpam-6617	263	5	adding	add	VERB
ejpam-6617	263	6	(	(	PUNCT
ejpam-6617	263	7	7	7	NUM
ejpam-6617	263	8	)	)	PUNCT
ejpam-6617	263	9	and	and	CCONJ
ejpam-6617	263	10	(	(	PUNCT
ejpam-6617	263	11	9	9	NUM
ejpam-6617	263	12	)	)	PUNCT
ejpam-6617	263	13	,	,	PUNCT
ejpam-6617	263	14	we	we	PRON
ejpam-6617	263	15	get	get	VERB
ejpam-6617	263	16	a2∫	a2∫	NOUN
ejpam-6617	263	17	a1	a1	NOUN
ejpam-6617	263	18	{	{	PUNCT
ejpam-6617	263	19	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	263	20	,	,	PUNCT
ejpam-6617	263	21	κ	κ	NOUN
ejpam-6617	263	22	,	,	PUNCT
ejpam-6617	263	23	κ̄	κ̄	NOUN
ejpam-6617	263	24	)	)	PUNCT
ejpam-6617	263	25	[	[	PUNCT
ejpam-6617	263	26	ϕl	ϕl	PROPN
ejpam-6617	263	27	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	263	28	,	,	PUNCT
ejpam-6617	263	29	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	263	30	a+κ̄	a+κ̄	NOUN
ejpam-6617	263	31	)	)	PUNCT
ejpam-6617	264	1	+	+	CCONJ
ejpam-6617	264	2	ϕu	ϕu	ADP
ejpam-6617	264	3	κ̄	κ̄	NOUN
ejpam-6617	264	4	(	(	PUNCT
ejpam-6617	264	5	ς	ς	PROPN
ejpam-6617	264	6	,	,	PUNCT
ejpam-6617	264	7	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	264	8	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	264	9	)	)	PUNCT
ejpam-6617	265	1	+	+	PROPN
ejpam-6617	265	2	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	265	3	,	,	PUNCT
ejpam-6617	265	4	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	265	5	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	265	6	)	)	PUNCT
ejpam-6617	265	7	]	]	PUNCT
ejpam-6617	266	1	+	+	PROPN
ejpam-6617	266	2	(	(	PUNCT
ejpam-6617	266	3	cfdθ•	cfdθ•	PROPN
ejpam-6617	266	4	a1+ℵ(ς	a1+ℵ(ς	PROPN
ejpam-6617	266	5	,	,	PUNCT
ejpam-6617	266	6	κ	κ	NOUN
ejpam-6617	266	7	,	,	PUNCT
ejpam-6617	266	8	κ̄))[ϕ	κ̄))[ϕ	VERB
ejpam-6617	266	9	l	l	PROPN
ejpam-6617	266	10	cfdθ•	cfdθ•	PROPN
ejpam-6617	266	11	a1	a1	PROPN
ejpam-6617	266	12	+	+	CCONJ
ejpam-6617	266	13	κ̄	κ̄	NOUN
ejpam-6617	266	14	(	(	PUNCT
ejpam-6617	266	15	ς	ς	PROPN
ejpam-6617	266	16	,	,	PUNCT
ejpam-6617	266	17	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	266	18	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	266	19	)	)	PUNCT
ejpam-6617	267	1	+	+	PROPN
ejpam-6617	267	2	ϕu	ϕu	PROPN
ejpam-6617	267	3	cfdθ•	cfdθ•	PROPN
ejpam-6617	267	4	a+κ̄	a+κ̄	NOUN
ejpam-6617	267	5	(	(	PUNCT
ejpam-6617	267	6	ς	ς	PROPN
ejpam-6617	267	7	,	,	PUNCT
ejpam-6617	267	8	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	267	9	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	267	10	)	)	PUNCT
ejpam-6617	268	1	+	+	CCONJ
ejpam-6617	268	2	θ̄(ς)h	θ̄(ς)h	ADJ
ejpam-6617	268	3	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	268	4	+	+	CCONJ
ejpam-6617	268	5	κ̄	κ̄	NOUN
ejpam-6617	268	6	(	(	PUNCT
ejpam-6617	268	7	ς	ς	PROPN
ejpam-6617	268	8	,	,	PUNCT
ejpam-6617	268	9	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	268	10	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	268	11	)	)	PUNCT
ejpam-6617	268	12	]	]	PUNCT
ejpam-6617	268	13	}	}	PUNCT
ejpam-6617	268	14	dς	dς	X
ejpam-6617	268	15	<	<	X
ejpam-6617	268	16	0	0	NUM
ejpam-6617	268	17	,	,	PUNCT
ejpam-6617	268	18	which	which	PRON
ejpam-6617	268	19	is	be	AUX
ejpam-6617	268	20	a	a	DET
ejpam-6617	268	21	contradiction	contradiction	NOUN
ejpam-6617	268	22	to	to	ADP
ejpam-6617	268	23	(	(	PUNCT
ejpam-6617	268	24	8)	8)	NUM
ejpam-6617	268	25	.	.	PUNCT
ejpam-6617	269	1	hence	hence	ADV
ejpam-6617	269	2	the	the	DET
ejpam-6617	269	3	theorem	theorem	NOUN
ejpam-6617	269	4	.	.	PUNCT
ejpam-6617	270	1	we	we	PRON
ejpam-6617	270	2	provide	provide	VERB
ejpam-6617	270	3	an	an	DET
ejpam-6617	270	4	algorithm	algorithm	NOUN
ejpam-6617	270	5	for	for	ADP
ejpam-6617	270	6	the	the	DET
ejpam-6617	270	7	theorem	theorem	ADJ
ejpam-6617	270	8	3.2	3.2	NUM
ejpam-6617	270	9	in	in	ADP
ejpam-6617	270	10	the	the	DET
ejpam-6617	270	11	following	following	ADJ
ejpam-6617	270	12	way	way	NOUN
ejpam-6617	270	13	:	:	PUNCT
ejpam-6617	270	14	•algorithm	•algorithm	NUM
ejpam-6617	270	15	:	:	PUNCT
ejpam-6617	270	16	input	input	NOUN
ejpam-6617	270	17	:	:	PUNCT
ejpam-6617	270	18	•	•	ADP
ejpam-6617	270	19	primal	primal	ADJ
ejpam-6617	270	20	objective	objective	ADJ
ejpam-6617	270	21	functional	functional	NOUN
ejpam-6617	270	22	:	:	PUNCT
ejpam-6617	270	23	(	(	PUNCT
ejpam-6617	270	24	p-2	p-2	NOUN
ejpam-6617	270	25	):	):	PUNCT
ejpam-6617	270	26	min	min	PROPN
ejpam-6617	270	27			NOUN
ejpam-6617	270	28	a2∫	a2∫	VERB
ejpam-6617	270	29	a1	a1	NOUN
ejpam-6617	270	30	ϕl(ς	ϕl(ς	PUNCT
ejpam-6617	270	31	,	,	PUNCT
ejpam-6617	270	32	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	270	33	a1+κ(ς))dς	a1+κ(ς))dς	ADV
ejpam-6617	270	34	,	,	PUNCT
ejpam-6617	270	35	a2∫	a2∫	X
ejpam-6617	270	36	a1	a1	VERB
ejpam-6617	270	37	ϕu	ϕu	X
ejpam-6617	270	38	(	(	PUNCT
ejpam-6617	270	39	ς	ς	PROPN
ejpam-6617	270	40	,	,	PUNCT
ejpam-6617	270	41	κ(ς),cfdθ•	κ(ς),cfdθ•	NOUN
ejpam-6617	270	42	a1+κ(ς))dς	a1+κ(ς))dς	PRON
ejpam-6617	270	43			NOUN
ejpam-6617	270	44	v.	v.	ADP
ejpam-6617	270	45	rayanki	rayanki	NOUN
ejpam-6617	270	46	et	et	PROPN
ejpam-6617	270	47	al	al	PROPN
ejpam-6617	270	48	.	.	PUNCT
ejpam-6617	270	49	/	/	SYM
ejpam-6617	270	50	eur	eur	PROPN
ejpam-6617	270	51	.	.	PUNCT
ejpam-6617	271	1	j.	j.	PROPN
ejpam-6617	271	2	pure	pure	PROPN
ejpam-6617	271	3	appl	appl	PROPN
ejpam-6617	271	4	.	.	PROPN
ejpam-6617	271	5	math	math	PROPN
ejpam-6617	271	6	,	,	PUNCT
ejpam-6617	271	7	18	18	NUM
ejpam-6617	271	8	(	(	PUNCT
ejpam-6617	271	9	3	3	NUM
ejpam-6617	271	10	)	)	PUNCT
ejpam-6617	271	11	(	(	PUNCT
ejpam-6617	271	12	2025	2025	NUM
ejpam-6617	271	13	)	)	PUNCT
ejpam-6617	271	14	,	,	PUNCT
ejpam-6617	271	15	6617	6617	NUM
ejpam-6617	271	16	16	16	NUM
ejpam-6617	271	17	of	of	ADP
ejpam-6617	271	18	38	38	NUM
ejpam-6617	271	19	•	•	NOUN
ejpam-6617	271	20	set	set	NOUN
ejpam-6617	271	21	of	of	ADP
ejpam-6617	271	22	constraints	constraint	NOUN
ejpam-6617	271	23	:	:	PUNCT
ejpam-6617	271	24	h(ς	h(ς	PROPN
ejpam-6617	271	25	,	,	PUNCT
ejpam-6617	271	26	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	271	27	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	271	28	)	)	PUNCT
ejpam-6617	271	29	)	)	PUNCT
ejpam-6617	272	1	≤	≤	ADV
ejpam-6617	272	2	0	0	NUM
ejpam-6617	272	3	,	,	PUNCT
ejpam-6617	272	4	κ(a1	κ(a1	NOUN
ejpam-6617	272	5	)	)	PUNCT
ejpam-6617	272	6	=	=	SYM
ejpam-6617	272	7	α	α	NUM
ejpam-6617	272	8	,	,	PUNCT
ejpam-6617	272	9	κ(a2	κ(a2	NOUN
ejpam-6617	272	10	)	)	PUNCT
ejpam-6617	272	11	=	=	SYM
ejpam-6617	273	1	β	β	X
ejpam-6617	273	2	,	,	PUNCT
ejpam-6617	273	3	ς	ς	PROPN
ejpam-6617	273	4	∈	∈	PROPN
ejpam-6617	273	5	[	[	X
ejpam-6617	273	6	a1	a1	NOUN
ejpam-6617	273	7	,	,	PUNCT
ejpam-6617	273	8	a2	a2	PROPN
ejpam-6617	273	9	]	]	PUNCT
ejpam-6617	273	10	.	.	PUNCT
ejpam-6617	274	1	•	•	NUM
ejpam-6617	274	2	set	set	NOUN
ejpam-6617	274	3	of	of	ADP
ejpam-6617	274	4	feasible	feasible	ADJ
ejpam-6617	274	5	point	point	NOUN
ejpam-6617	274	6	:	:	PUNCT
ejpam-6617	274	7	φ2	φ2	PROPN
ejpam-6617	274	8	=	=	PUNCT
ejpam-6617	274	9	{	{	PUNCT
ejpam-6617	274	10	κ	κ	NOUN
ejpam-6617	274	11	∈	∈	PROPN
ejpam-6617	274	12	x	x	X
ejpam-6617	274	13	:	:	PUNCT
ejpam-6617	274	14	h(ς	h(ς	NOUN
ejpam-6617	274	15	,	,	PUNCT
ejpam-6617	274	16	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	274	17	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	274	18	)	)	PUNCT
ejpam-6617	274	19	)	)	PUNCT
ejpam-6617	275	1	≤	≤	NUM
ejpam-6617	275	2	0,κ(a1	0,κ(a1	NUM
ejpam-6617	275	3	)	)	PUNCT
ejpam-6617	275	4	=	=	SYM
ejpam-6617	275	5	α	α	X
ejpam-6617	275	6	,	,	PUNCT
ejpam-6617	275	7	κ(a2	κ(a2	NOUN
ejpam-6617	275	8	)	)	PUNCT
ejpam-6617	275	9	=	=	PUNCT
ejpam-6617	275	10	β	β	X
ejpam-6617	275	11	}	}	PUNCT
ejpam-6617	275	12	.	.	PUNCT
ejpam-6617	276	1	•	•	NUM
ejpam-6617	276	2	set	set	NOUN
ejpam-6617	276	3	of	of	ADP
ejpam-6617	276	4	self	self	NOUN
ejpam-6617	276	5	data	datum	NOUN
ejpam-6617	276	6	:	:	PUNCT
ejpam-6617	276	7	ϕl(ς	ϕl(ς	NUM
ejpam-6617	276	8	,	,	PUNCT
ejpam-6617	276	9	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	276	10	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	276	11	)	)	PUNCT
ejpam-6617	276	12	)	)	PUNCT
ejpam-6617	276	13	,	,	PUNCT
ejpam-6617	276	14	ϕu	ϕu	INTJ
ejpam-6617	276	15	(	(	PUNCT
ejpam-6617	276	16	ς	ς	PROPN
ejpam-6617	276	17	,	,	PUNCT
ejpam-6617	276	18	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	276	19	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	276	20	)	)	PUNCT
ejpam-6617	276	21	)	)	PUNCT
ejpam-6617	276	22	,	,	PUNCT
ejpam-6617	276	23	h(ς	h(ς	PROPN
ejpam-6617	276	24	,	,	PUNCT
ejpam-6617	276	25	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	276	26	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	276	27	)	)	PUNCT
ejpam-6617	276	28	)	)	PUNCT
ejpam-6617	276	29	.	.	PUNCT
ejpam-6617	277	1	the	the	DET
ejpam-6617	277	2	above	above	ADJ
ejpam-6617	277	3	functions	function	NOUN
ejpam-6617	277	4	are	be	AUX
ejpam-6617	277	5	continuous	continuous	ADJ
ejpam-6617	277	6	differetiable	differetiable	ADJ
ejpam-6617	277	7	andare	andare	PROPN
ejpam-6617	277	8	invexity	invexity	NOUN
ejpam-6617	277	9	for	for	ADP
ejpam-6617	277	10	ς	ς	PROPN
ejpam-6617	277	11	∈	∈	PROPN
ejpam-6617	277	12	φ2	φ2	PROPN
ejpam-6617	277	13	.	.	PUNCT
ejpam-6617	278	1	output	output	NOUN
ejpam-6617	278	2	:	:	PUNCT
ejpam-6617	278	3	•	•	NUM
ejpam-6617	278	4	verification	verification	NOUN
ejpam-6617	278	5	of	of	ADP
ejpam-6617	278	6	invexity	invexity	NOUN
ejpam-6617	278	7	:	:	PUNCT
ejpam-6617	278	8	ϕl(ς	ϕl(ς	NUM
ejpam-6617	278	9	,	,	PUNCT
ejpam-6617	278	10	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	278	11	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	278	12	)	)	PUNCT
ejpam-6617	278	13	)	)	PUNCT
ejpam-6617	278	14	,	,	PUNCT
ejpam-6617	278	15	ϕu	ϕu	INTJ
ejpam-6617	278	16	(	(	PUNCT
ejpam-6617	278	17	ς	ς	PROPN
ejpam-6617	278	18	,	,	PUNCT
ejpam-6617	278	19	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	278	20	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	278	21	)	)	PUNCT
ejpam-6617	278	22	)	)	PUNCT
ejpam-6617	278	23	,	,	PUNCT
ejpam-6617	278	24	h(ς	h(ς	PROPN
ejpam-6617	278	25	,	,	PUNCT
ejpam-6617	278	26	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	278	27	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	278	28	)	)	PUNCT
ejpam-6617	278	29	)	)	PUNCT
ejpam-6617	278	30	,	,	PUNCT
ejpam-6617	278	31	ς	ς	PROPN
ejpam-6617	278	32	∈	∈	PROPN
ejpam-6617	278	33	φ2	φ2	PROPN
ejpam-6617	278	34	.	.	PUNCT
ejpam-6617	279	1	the	the	DET
ejpam-6617	279	2	point	point	NOUN
ejpam-6617	279	3	κ̄	κ̄	NOUN
ejpam-6617	279	4	is	be	AUX
ejpam-6617	279	5	satisfying	satisfy	VERB
ejpam-6617	279	6	the	the	DET
ejpam-6617	279	7	definition12	definition12	NOUN
ejpam-6617	279	8	.	.	PUNCT
ejpam-6617	280	1	set	set	NOUN
ejpam-6617	280	2	of	of	ADP
ejpam-6617	280	3	self	self	NOUN
ejpam-6617	280	4	data	datum	NOUN
ejpam-6617	280	5	.	.	PUNCT
ejpam-6617	281	1	begin	begin	VERB
ejpam-6617	281	2	:	:	PUNCT
ejpam-6617	281	3	•	•	NUM
ejpam-6617	281	4	selective	selective	ADJ
ejpam-6617	281	5	stage	stage	NOUN
ejpam-6617	281	6	:	:	PUNCT
ejpam-6617	281	7	select	select	VERB
ejpam-6617	281	8	a	a	DET
ejpam-6617	281	9	point	point	NOUN
ejpam-6617	281	10	that	that	PRON
ejpam-6617	281	11	κ̄	κ̄	PROPN
ejpam-6617	281	12	∈	∈	PROPN
ejpam-6617	281	13	φ2	φ2	PROPN
ejpam-6617	281	14	if	if	SCONJ
ejpam-6617	281	15	slater	slater	PROPN
ejpam-6617	281	16	’s	’s	PART
ejpam-6617	281	17	constraint	constraint	PROPN
ejpam-6617	281	18	qualification	qualification	NOUN
ejpam-6617	281	19	satisfied	satisfied	ADJ
ejpam-6617	281	20	atκ̄	atκ̄	PROPN
ejpam-6617	281	21	;	;	PUNCT
ejpam-6617	281	22	then	then	ADV
ejpam-6617	281	23	continue	continue	VERB
ejpam-6617	281	24	to	to	ADP
ejpam-6617	281	25	the	the	DET
ejpam-6617	281	26	next	next	ADJ
ejpam-6617	281	27	,	,	PUNCT
ejpam-6617	281	28	if	if	SCONJ
ejpam-6617	281	29	kkt	kkt	PROPN
ejpam-6617	281	30	necessary	necessary	ADJ
ejpam-6617	281	31	optimality	optimality	NOUN
ejpam-6617	281	32	conditions	condition	NOUN
ejpam-6617	281	33	(	(	PUNCT
ejpam-6617	281	34	4	4	NUM
ejpam-6617	281	35	)	)	PUNCT
ejpam-6617	281	36	and	and	CCONJ
ejpam-6617	281	37	(	(	PUNCT
ejpam-6617	281	38	5	5	X
ejpam-6617	281	39	)	)	PUNCT
ejpam-6617	281	40	holds	hold	VERB
ejpam-6617	281	41	at	at	ADP
ejpam-6617	281	42	κ̄	κ̄	NOUN
ejpam-6617	281	43	;	;	PUNCT
ejpam-6617	281	44	v.	v.	CCONJ
ejpam-6617	281	45	rayanki	rayanki	PROPN
ejpam-6617	281	46	et	et	PROPN
ejpam-6617	281	47	al	al	PROPN
ejpam-6617	281	48	.	.	PUNCT
ejpam-6617	281	49	/	/	SYM
ejpam-6617	281	50	eur	eur	PROPN
ejpam-6617	281	51	.	.	PUNCT
ejpam-6617	282	1	j.	j.	PROPN
ejpam-6617	282	2	pure	pure	PROPN
ejpam-6617	282	3	appl	appl	PROPN
ejpam-6617	282	4	.	.	PROPN
ejpam-6617	282	5	math	math	PROPN
ejpam-6617	282	6	,	,	PUNCT
ejpam-6617	282	7	18	18	NUM
ejpam-6617	282	8	(	(	PUNCT
ejpam-6617	282	9	3	3	NUM
ejpam-6617	282	10	)	)	PUNCT
ejpam-6617	282	11	(	(	PUNCT
ejpam-6617	282	12	2025	2025	NUM
ejpam-6617	282	13	)	)	PUNCT
ejpam-6617	282	14	,	,	PUNCT
ejpam-6617	282	15	6617	6617	NUM
ejpam-6617	282	16	17	17	NUM
ejpam-6617	282	17	of	of	ADP
ejpam-6617	282	18	38	38	NUM
ejpam-6617	282	19	else	else	ADV
ejpam-6617	282	20	stop	stop	NOUN
ejpam-6617	282	21	;	;	PUNCT
ejpam-6617	282	22	end	end	VERB
ejpam-6617	282	23	if	if	SCONJ
ejpam-6617	282	24	;	;	PUNCT
ejpam-6617	282	25	•	•	NUM
ejpam-6617	282	26	screening	screening	NOUN
ejpam-6617	282	27	stage	stage	NOUN
ejpam-6617	282	28	:	:	PUNCT
ejpam-6617	282	29	detecting	detect	VERB
ejpam-6617	282	30	piece	piece	NOUN
ejpam-6617	282	31	-	-	PUNCT
ejpam-6617	282	32	wise	wise	ADJ
ejpam-6617	282	33	smooth	smooth	ADJ
ejpam-6617	282	34	function	function	NOUN
ejpam-6617	282	35	θ̄	θ̄	ADV
ejpam-6617	282	36	if	if	SCONJ
ejpam-6617	282	37	self	self	NOUN
ejpam-6617	282	38	data	datum	NOUN
ejpam-6617	282	39	holds	hold	VERB
ejpam-6617	282	40	at	at	ADP
ejpam-6617	282	41	κ̄for	κ̄for	PROPN
ejpam-6617	282	42	(	(	PUNCT
ejpam-6617	282	43	p	p	NOUN
ejpam-6617	282	44	−	−	PROPN
ejpam-6617	282	45	2	2	NUM
ejpam-6617	282	46	)	)	PUNCT
ejpam-6617	282	47	;	;	PUNCT
ejpam-6617	282	48	else	else	ADV
ejpam-6617	282	49	stop	stop	VERB
ejpam-6617	282	50	;	;	PUNCT
ejpam-6617	282	51	end	end	VERB
ejpam-6617	282	52	if	if	SCONJ
ejpam-6617	282	53	;	;	PUNCT
ejpam-6617	282	54	•	•	NUM
ejpam-6617	282	55	conclusive	conclusive	ADJ
ejpam-6617	282	56	stage	stage	NOUN
ejpam-6617	282	57	:	:	PUNCT
ejpam-6617	282	58	detecting	detect	VERB
ejpam-6617	282	59	the	the	DET
ejpam-6617	282	60	point	point	NOUN
ejpam-6617	282	61	κ̄	κ̄	NOUN
ejpam-6617	282	62	=	=	SYM
ejpam-6617	282	63	0	0	NUM
ejpam-6617	282	64	,	,	PUNCT
ejpam-6617	282	65	is	be	AUX
ejpam-6617	282	66	optimal	optimal	ADJ
ejpam-6617	282	67	solution	solution	NOUN
ejpam-6617	282	68	for	for	ADP
ejpam-6617	282	69	the	the	DET
ejpam-6617	282	70	problem	problem	NOUN
ejpam-6617	282	71	(	(	PUNCT
ejpam-6617	282	72	p-2	p-2	NOUN
ejpam-6617	282	73	)	)	PUNCT
ejpam-6617	282	74	.	.	PUNCT
ejpam-6617	283	1	else	else	ADV
ejpam-6617	283	2	stop	stop	VERB
ejpam-6617	283	3	;	;	PUNCT
ejpam-6617	283	4	end	end	NOUN
ejpam-6617	283	5	;	;	PUNCT
ejpam-6617	283	6	the	the	DET
ejpam-6617	283	7	following	follow	VERB
ejpam-6617	283	8	example	example	NOUN
ejpam-6617	283	9	illustrates	illustrate	VERB
ejpam-6617	283	10	theorem	theorem	VERB
ejpam-6617	283	11	3.2	3.2	NUM
ejpam-6617	283	12	.	.	PUNCT
ejpam-6617	283	13	example	example	NOUN
ejpam-6617	284	1	4	4	NUM
ejpam-6617	284	2	.	.	PUNCT
ejpam-6617	284	3	consider	consider	VERB
ejpam-6617	284	4	the	the	DET
ejpam-6617	284	5	following	follow	VERB
ejpam-6617	284	6	interval	interval	NOUN
ejpam-6617	284	7	-	-	PUNCT
ejpam-6617	284	8	valued	value	VERB
ejpam-6617	284	9	variational	variational	ADJ
ejpam-6617	284	10	programming	programming	NOUN
ejpam-6617	284	11	problem	problem	NOUN
ejpam-6617	284	12	under	under	ADP
ejpam-6617	284	13	caputo	caputo	PROPN
ejpam-6617	284	14	-	-	PUNCT
ejpam-6617	284	15	fabrizio	fabrizio	PROPN
ejpam-6617	284	16	fractional	fractional	ADJ
ejpam-6617	284	17	derivative	derivative	NOUN
ejpam-6617	284	18	:	:	PUNCT
ejpam-6617	284	19	(	(	PUNCT
ejpam-6617	284	20	p-2	p-2	NOUN
ejpam-6617	284	21	)	)	PUNCT
ejpam-6617	284	22	:	:	PUNCT
ejpam-6617	284	23	min	min	PROPN
ejpam-6617	284	24			NOUN
ejpam-6617	284	25	a2∫	a2∫	VERB
ejpam-6617	284	26	a1	a1	NOUN
ejpam-6617	284	27	ϕl(ς	ϕl(ς	PUNCT
ejpam-6617	284	28	,	,	PUNCT
ejpam-6617	284	29	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	284	30	a1+κ(ς))dς	a1+κ(ς))dς	ADV
ejpam-6617	284	31	,	,	PUNCT
ejpam-6617	284	32	a2∫	a2∫	X
ejpam-6617	284	33	a1	a1	VERB
ejpam-6617	284	34	ϕu	ϕu	X
ejpam-6617	284	35	(	(	PUNCT
ejpam-6617	284	36	ς	ς	PROPN
ejpam-6617	284	37	,	,	PUNCT
ejpam-6617	284	38	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	284	39	a1+κ(ς))dς	a1+κ(ς))dς	PRON
ejpam-6617	284	40			NOUN
ejpam-6617	284	41	subject	subject	ADJ
ejpam-6617	284	42	to	to	ADP
ejpam-6617	284	43	,	,	PUNCT
ejpam-6617	284	44	ln2−	ln2−	X
ejpam-6617	284	45	ln(ς	ln(ς	PUNCT
ejpam-6617	285	1	+	+	CCONJ
ejpam-6617	285	2	2	2	X
ejpam-6617	285	3	)	)	PUNCT
ejpam-6617	285	4	≤	≤	NOUN
ejpam-6617	285	5	0	0	NUM
ejpam-6617	285	6	,	,	PUNCT
ejpam-6617	285	7	κ(0	κ(0	NOUN
ejpam-6617	285	8	)	)	PUNCT
ejpam-6617	286	1	=	=	SYM
ejpam-6617	286	2	0	0	NUM
ejpam-6617	286	3	,	,	PUNCT
ejpam-6617	286	4	κ(1	κ(1	PROPN
ejpam-6617	286	5	)	)	PUNCT
ejpam-6617	286	6	=	=	PUNCT
ejpam-6617	287	1	1	1	NUM
ejpam-6617	287	2	,	,	PUNCT
ejpam-6617	287	3	ς	ς	PROPN
ejpam-6617	287	4	∈	∈	PROPN
ejpam-6617	288	1	[	[	X
ejpam-6617	288	2	0	0	NUM
ejpam-6617	288	3	,	,	PUNCT
ejpam-6617	288	4	1	1	NUM
ejpam-6617	288	5	]	]	PUNCT
ejpam-6617	288	6	,	,	PUNCT
ejpam-6617	288	7	where	where	SCONJ
ejpam-6617	288	8	,	,	PUNCT
ejpam-6617	288	9	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	288	10	,	,	PUNCT
ejpam-6617	288	11	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	288	12	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	288	13	)	)	PUNCT
ejpam-6617	288	14	)	)	PUNCT
ejpam-6617	289	1	=	=	PUNCT
ejpam-6617	289	2	ς3	ς3	NOUN
ejpam-6617	289	3	+	+	CCONJ
ejpam-6617	289	4	ς	ς	NOUN
ejpam-6617	289	5	,	,	PUNCT
ejpam-6617	289	6	ϕu	ϕu	X
ejpam-6617	289	7	(	(	PUNCT
ejpam-6617	289	8	ς	ς	PROPN
ejpam-6617	289	9	,	,	PUNCT
ejpam-6617	289	10	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	289	11	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	289	12	)	)	PUNCT
ejpam-6617	289	13	)	)	PUNCT
ejpam-6617	290	1	=	=	PUNCT
ejpam-6617	290	2	3ς3	3ς3	NUM
ejpam-6617	291	1	+	+	CCONJ
ejpam-6617	291	2	3	3	X
ejpam-6617	291	3	.	.	X
ejpam-6617	291	4	take	take	VERB
ejpam-6617	291	5	a	a	DET
ejpam-6617	291	6	note	note	NOUN
ejpam-6617	291	7	that	that	SCONJ
ejpam-6617	291	8	κ̄	κ̄	NOUN
ejpam-6617	291	9	=	=	SYM
ejpam-6617	291	10	0	0	NUM
ejpam-6617	291	11	is	be	AUX
ejpam-6617	291	12	a	a	DET
ejpam-6617	291	13	feasible	feasible	ADJ
ejpam-6617	291	14	solution	solution	NOUN
ejpam-6617	291	15	of	of	ADP
ejpam-6617	291	16	(	(	PUNCT
ejpam-6617	291	17	p-2	p-2	NOUN
ejpam-6617	291	18	)	)	PUNCT
ejpam-6617	291	19	and	and	CCONJ
ejpam-6617	291	20	it	it	PRON
ejpam-6617	291	21	can	can	AUX
ejpam-6617	291	22	be	be	AUX
ejpam-6617	291	23	easily	easily	ADV
ejpam-6617	291	24	observed	observe	VERB
ejpam-6617	291	25	that	that	SCONJ
ejpam-6617	291	26	there	there	PRON
ejpam-6617	291	27	is	be	VERB
ejpam-6617	291	28	θ	θ	PROPN
ejpam-6617	291	29	∈	∈	PROPN
ejpam-6617	291	30	r	r	NOUN
ejpam-6617	291	31	and	and	CCONJ
ejpam-6617	291	32	θ̄	θ̄	NOUN
ejpam-6617	291	33	=	=	SYM
ejpam-6617	291	34	0	0	NUM
ejpam-6617	291	35	,	,	PUNCT
ejpam-6617	291	36	such	such	ADJ
ejpam-6617	291	37	that	that	SCONJ
ejpam-6617	291	38	the	the	DET
ejpam-6617	291	39	relations	relation	NOUN
ejpam-6617	291	40	(	(	PUNCT
ejpam-6617	291	41	4	4	NUM
ejpam-6617	291	42	)	)	PUNCT
ejpam-6617	291	43	and	and	CCONJ
ejpam-6617	291	44	(	(	PUNCT
ejpam-6617	291	45	5	5	X
ejpam-6617	291	46	)	)	PUNCT
ejpam-6617	291	47	hold	hold	NOUN
ejpam-6617	291	48	for	for	ADP
ejpam-6617	291	49	the	the	DET
ejpam-6617	291	50	problem	problem	NOUN
ejpam-6617	291	51	(	(	PUNCT
ejpam-6617	291	52	p2	p2	PROPN
ejpam-6617	291	53	)	)	PUNCT
ejpam-6617	291	54	.	.	PUNCT
ejpam-6617	292	1	also	also	ADV
ejpam-6617	292	2	,	,	PUNCT
ejpam-6617	292	3	it	it	PRON
ejpam-6617	292	4	is	be	AUX
ejpam-6617	292	5	observed	observe	VERB
ejpam-6617	292	6	that	that	SCONJ
ejpam-6617	292	7	a2∫	a2∫	NOUN
ejpam-6617	292	8	a1	a1	NOUN
ejpam-6617	292	9	(	(	PUNCT
ejpam-6617	292	10	ϕl	ϕl	PROPN
ejpam-6617	293	1	+	+	NOUN
ejpam-6617	293	2	ϕu	ϕu	NOUN
ejpam-6617	293	3	)	)	PUNCT
ejpam-6617	293	4	(	(	PUNCT
ejpam-6617	293	5	ς	ς	PROPN
ejpam-6617	293	6	,	,	PUNCT
ejpam-6617	293	7	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	293	8	a1+κ(ς))dς	a1+κ(ς))dς	PROPN
ejpam-6617	293	9	is	be	AUX
ejpam-6617	293	10	invex	invex	NOUN
ejpam-6617	293	11	at	at	ADP
ejpam-6617	293	12	κ̄	κ̄	NOUN
ejpam-6617	293	13	on	on	ADP
ejpam-6617	293	14	φ2	φ2	PROPN
ejpam-6617	293	15	and	and	CCONJ
ejpam-6617	293	16	a2∫	a2∫	NOUN
ejpam-6617	293	17	a1	a1	NOUN
ejpam-6617	293	18	θ̄(ς)h(ς	θ̄(ς)h(ς	NOUN
ejpam-6617	293	19	,	,	PUNCT
ejpam-6617	293	20	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	293	21	a+κ̄)dς	a+κ̄)dς	PROPN
ejpam-6617	293	22	is	be	AUX
ejpam-6617	293	23	invex	invex	NOUN
ejpam-6617	293	24	at	at	ADP
ejpam-6617	293	25	κ̄	κ̄	NOUN
ejpam-6617	293	26	on	on	ADP
ejpam-6617	293	27	φ2	φ2	PROPN
ejpam-6617	293	28	.	.	PUNCT
ejpam-6617	294	1	since	since	SCONJ
ejpam-6617	294	2	all	all	PRON
ejpam-6617	294	3	of	of	ADP
ejpam-6617	294	4	the	the	DET
ejpam-6617	294	5	observations	observation	NOUN
ejpam-6617	294	6	of	of	ADP
ejpam-6617	294	7	theorem	theorem	ADJ
ejpam-6617	294	8	3.2	3.2	NUM
ejpam-6617	294	9	are	be	AUX
ejpam-6617	294	10	satisfied	satisfied	ADJ
ejpam-6617	294	11	,	,	PUNCT
ejpam-6617	294	12	then	then	ADV
ejpam-6617	294	13	(	(	PUNCT
ejpam-6617	294	14	θ̄	θ̄	X
ejpam-6617	294	15	=	=	SYM
ejpam-6617	294	16	0	0	NUM
ejpam-6617	294	17	,	,	PUNCT
ejpam-6617	294	18	κ̄	κ̄	NOUN
ejpam-6617	294	19	=	=	SYM
ejpam-6617	294	20	0	0	NUM
ejpam-6617	294	21	)	)	PUNCT
ejpam-6617	294	22	is	be	AUX
ejpam-6617	294	23	the	the	DET
ejpam-6617	294	24	lu	lu	NOUN
ejpam-6617	294	25	optimum	optimum	ADJ
ejpam-6617	294	26	solution	solution	NOUN
ejpam-6617	294	27	to	to	ADP
ejpam-6617	294	28	the	the	DET
ejpam-6617	294	29	problem	problem	NOUN
ejpam-6617	294	30	(	(	PUNCT
ejpam-6617	294	31	p-2	p-2	NOUN
ejpam-6617	294	32	)	)	PUNCT
ejpam-6617	294	33	.	.	PUNCT
ejpam-6617	295	1	v.	v.	CCONJ
ejpam-6617	295	2	rayanki	rayanki	PROPN
ejpam-6617	295	3	et	et	PROPN
ejpam-6617	295	4	al	al	PROPN
ejpam-6617	295	5	.	.	PUNCT
ejpam-6617	295	6	/	/	SYM
ejpam-6617	295	7	eur	eur	PROPN
ejpam-6617	295	8	.	.	PUNCT
ejpam-6617	296	1	j.	j.	PROPN
ejpam-6617	296	2	pure	pure	PROPN
ejpam-6617	296	3	appl	appl	PROPN
ejpam-6617	296	4	.	.	PROPN
ejpam-6617	296	5	math	math	PROPN
ejpam-6617	296	6	,	,	PUNCT
ejpam-6617	296	7	18	18	NUM
ejpam-6617	296	8	(	(	PUNCT
ejpam-6617	296	9	3	3	NUM
ejpam-6617	296	10	)	)	PUNCT
ejpam-6617	296	11	(	(	PUNCT
ejpam-6617	296	12	2025	2025	NUM
ejpam-6617	296	13	)	)	PUNCT
ejpam-6617	296	14	,	,	PUNCT
ejpam-6617	296	15	6617	6617	NUM
ejpam-6617	296	16	18	18	NUM
ejpam-6617	296	17	of	of	ADP
ejpam-6617	296	18	38	38	NUM
ejpam-6617	296	19	figure	figure	NOUN
ejpam-6617	296	20	4	4	NUM
ejpam-6617	296	21	:	:	PUNCT
ejpam-6617	296	22	graphical	graphical	ADJ
ejpam-6617	296	23	view	view	NOUN
ejpam-6617	296	24	of	of	ADP
ejpam-6617	296	25	the	the	DET
ejpam-6617	296	26	example	example	NOUN
ejpam-6617	296	27	problem	problem	NOUN
ejpam-6617	296	28	(	(	PUNCT
ejpam-6617	296	29	p-2	p-2	PROPN
ejpam-6617	296	30	)	)	PUNCT
ejpam-6617	296	31	the	the	DET
ejpam-6617	296	32	problem	problem	NOUN
ejpam-6617	296	33	(	(	PUNCT
ejpam-6617	296	34	p-2	p-2	NOUN
ejpam-6617	296	35	)	)	PUNCT
ejpam-6617	296	36	has	have	VERB
ejpam-6617	296	37	a	a	DET
ejpam-6617	296	38	feasible	feasible	ADJ
ejpam-6617	296	39	region	region	NOUN
ejpam-6617	296	40	,	,	PUNCT
ejpam-6617	296	41	φ2	φ2	PROPN
ejpam-6617	296	42	=	=	PUNCT
ejpam-6617	296	43	{	{	PUNCT
ejpam-6617	296	44	κ	κ	NOUN
ejpam-6617	296	45	∈	∈	PROPN
ejpam-6617	296	46	x	x	PUNCT
ejpam-6617	296	47	:	:	PUNCT
ejpam-6617	296	48	ln2	ln2	ADJ
ejpam-6617	296	49	−	−	NOUN
ejpam-6617	296	50	ln(ς	ln(ς	PUNCT
ejpam-6617	296	51	+	+	CCONJ
ejpam-6617	296	52	2	2	X
ejpam-6617	296	53	)	)	PUNCT
ejpam-6617	296	54	≤	≤	NOUN
ejpam-6617	296	55	0,κ(0	0,κ(0	NUM
ejpam-6617	296	56	)	)	PUNCT
ejpam-6617	297	1	=	=	PUNCT
ejpam-6617	297	2	0,κ(1	0,κ(1	X
ejpam-6617	297	3	)	)	PUNCT
ejpam-6617	297	4	=	=	SYM
ejpam-6617	298	1	1	1	NUM
ejpam-6617	298	2	}	}	PUNCT
ejpam-6617	298	3	.	.	PUNCT
ejpam-6617	299	1	theorem	theorem	ADJ
ejpam-6617	299	2	3	3	NUM
ejpam-6617	299	3	(	(	PUNCT
ejpam-6617	299	4	sufficient	sufficient	ADJ
ejpam-6617	299	5	optimality	optimality	NOUN
ejpam-6617	299	6	conditions	condition	NOUN
ejpam-6617	299	7	)	)	PUNCT
ejpam-6617	299	8	.	.	PUNCT
ejpam-6617	300	1	let	let	VERB
ejpam-6617	300	2	κ̄	κ̄	NOUN
ejpam-6617	300	3	∈	∈	PROPN
ejpam-6617	300	4	x	x	PUNCT
ejpam-6617	300	5	be	be	AUX
ejpam-6617	300	6	a	a	DET
ejpam-6617	300	7	feasible	feasible	ADJ
ejpam-6617	300	8	solution	solution	NOUN
ejpam-6617	300	9	of	of	ADP
ejpam-6617	300	10	(	(	PUNCT
ejpam-6617	300	11	p	p	NOUN
ejpam-6617	300	12	)	)	PUNCT
ejpam-6617	300	13	and	and	CCONJ
ejpam-6617	300	14	there	there	PRON
ejpam-6617	300	15	is	be	VERB
ejpam-6617	300	16	a	a	DET
ejpam-6617	300	17	function	function	NOUN
ejpam-6617	300	18	that	that	PRON
ejpam-6617	300	19	is	be	AUX
ejpam-6617	300	20	piecewise	piecewise	NOUN
ejpam-6617	300	21	smooth	smooth	ADJ
ejpam-6617	300	22	,	,	PUNCT
ejpam-6617	300	23	θ̄	θ̄	ADJ
ejpam-6617	300	24	:	:	PUNCT
ejpam-6617	300	25	ℑ	ℑ	PROPN
ejpam-6617	300	26	→	→	SYM
ejpam-6617	300	27	rm	rm	PROPN
ejpam-6617	300	28	,	,	PUNCT
ejpam-6617	300	29	θ̄(ς	θ̄(ς	PROPN
ejpam-6617	300	30	)	)	PUNCT
ejpam-6617	300	31	≥	≥	NOUN
ejpam-6617	300	32	0	0	NUM
ejpam-6617	300	33	in	in	ADP
ejpam-6617	300	34	such	such	ADJ
ejpam-6617	300	35	way	way	NOUN
ejpam-6617	300	36	that	that	SCONJ
ejpam-6617	300	37	(	(	PUNCT
ejpam-6617	300	38	4	4	NUM
ejpam-6617	300	39	)	)	PUNCT
ejpam-6617	300	40	and	and	CCONJ
ejpam-6617	300	41	(	(	PUNCT
ejpam-6617	300	42	5	5	X
ejpam-6617	300	43	)	)	PUNCT
ejpam-6617	300	44	are	be	AUX
ejpam-6617	300	45	satisfied	satisfied	ADJ
ejpam-6617	300	46	at	at	ADP
ejpam-6617	300	47	(	(	PUNCT
ejpam-6617	300	48	κ̄	κ̄	NOUN
ejpam-6617	300	49	,	,	PUNCT
ejpam-6617	300	50	θ̄	θ̄	ADJ
ejpam-6617	300	51	)	)	PUNCT
ejpam-6617	300	52	.	.	PUNCT
ejpam-6617	301	1	also	also	ADV
ejpam-6617	301	2	,	,	PUNCT
ejpam-6617	301	3	assume	assume	VERB
ejpam-6617	301	4	that	that	SCONJ
ejpam-6617	301	5	(	(	PUNCT
ejpam-6617	301	6	i	i	NOUN
ejpam-6617	301	7	)	)	PUNCT
ejpam-6617	301	8	the	the	DET
ejpam-6617	301	9	functional	functional	ADJ
ejpam-6617	301	10	a2∫	a2∫	NOUN
ejpam-6617	301	11	a1	a1	NOUN
ejpam-6617	301	12	(	(	PUNCT
ejpam-6617	301	13	ϕl	ϕl	PROPN
ejpam-6617	302	1	+	+	NOUN
ejpam-6617	302	2	ϕu	ϕu	NOUN
ejpam-6617	302	3	)	)	PUNCT
ejpam-6617	302	4	(	(	PUNCT
ejpam-6617	302	5	ς	ς	PROPN
ejpam-6617	302	6	,	,	PUNCT
ejpam-6617	302	7	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	302	8	a1+κ(ς))dς	a1+κ(ς))dς	PROPN
ejpam-6617	302	9	is	be	AUX
ejpam-6617	302	10	pseudo	pseudo	NOUN
ejpam-6617	302	11	-	-	NOUN
ejpam-6617	302	12	invex	invex	NOUN
ejpam-6617	302	13	at	at	ADP
ejpam-6617	302	14	κ̄	κ̄	NOUN
ejpam-6617	302	15	on	on	ADP
ejpam-6617	302	16	x	x	X
ejpam-6617	302	17	,	,	PUNCT
ejpam-6617	302	18	(	(	PUNCT
ejpam-6617	302	19	ii	ii	NOUN
ejpam-6617	302	20	)	)	PUNCT
ejpam-6617	302	21	the	the	DET
ejpam-6617	302	22	functional	functional	ADJ
ejpam-6617	302	23	a2∫	a2∫	NOUN
ejpam-6617	302	24	a1	a1	NOUN
ejpam-6617	302	25	θ̄(ς)h(ς	θ̄(ς)h(ς	NOUN
ejpam-6617	302	26	,	,	PUNCT
ejpam-6617	302	27	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	302	28	a+κ̄)dς	a+κ̄)dς	PROPN
ejpam-6617	302	29	is	be	AUX
ejpam-6617	302	30	quasi	quasi	ADJ
ejpam-6617	302	31	-	-	NOUN
ejpam-6617	302	32	invex	invex	ADJ
ejpam-6617	302	33	at	at	ADP
ejpam-6617	302	34	κ̄	κ̄	NOUN
ejpam-6617	302	35	on	on	ADP
ejpam-6617	302	36	x	x	X
ejpam-6617	302	37	,	,	PUNCT
ejpam-6617	302	38	then	then	ADV
ejpam-6617	302	39	κ̄	κ̄	NOUN
ejpam-6617	302	40	is	be	AUX
ejpam-6617	302	41	a	a	DET
ejpam-6617	302	42	lu	lu	NOUN
ejpam-6617	302	43	optimal	optimal	ADJ
ejpam-6617	302	44	solution	solution	NOUN
ejpam-6617	302	45	for	for	ADP
ejpam-6617	302	46	(	(	PUNCT
ejpam-6617	302	47	p	p	NOUN
ejpam-6617	302	48	)	)	PUNCT
ejpam-6617	302	49	.	.	PUNCT
ejpam-6617	303	1	proof	proof	NOUN
ejpam-6617	303	2	.	.	PUNCT
ejpam-6617	304	1	if	if	SCONJ
ejpam-6617	304	2	κ̄	κ̄	NOUN
ejpam-6617	304	3	is	be	AUX
ejpam-6617	304	4	not	not	PART
ejpam-6617	304	5	a	a	DET
ejpam-6617	304	6	lu	lu	NOUN
ejpam-6617	304	7	optimal	optimal	ADJ
ejpam-6617	304	8	solution	solution	NOUN
ejpam-6617	304	9	for	for	ADP
ejpam-6617	304	10	(	(	PUNCT
ejpam-6617	304	11	p	p	NOUN
ejpam-6617	304	12	)	)	PUNCT
ejpam-6617	304	13	,	,	PUNCT
ejpam-6617	304	14	then	then	ADV
ejpam-6617	304	15	by	by	ADP
ejpam-6617	304	16	definition	definition	NOUN
ejpam-6617	304	17	12	12	NUM
ejpam-6617	304	18	there	there	PRON
ejpam-6617	304	19	is	be	VERB
ejpam-6617	304	20	another	another	DET
ejpam-6617	304	21	feasible	feasible	ADJ
ejpam-6617	304	22	solution	solution	NOUN
ejpam-6617	304	23	κ	κ	X
ejpam-6617	304	24	for	for	ADP
ejpam-6617	304	25	(	(	PUNCT
ejpam-6617	304	26	p	p	NOUN
ejpam-6617	304	27	)	)	PUNCT
ejpam-6617	304	28	,	,	PUNCT
ejpam-6617	304	29	such	such	ADJ
ejpam-6617	304	30	that	that	X
ejpam-6617	304	31	a2∫	a2∫	NOUN
ejpam-6617	304	32	a1	a1	NOUN
ejpam-6617	304	33	ϕl(ς	ϕl(ς	X
ejpam-6617	304	34	,	,	PUNCT
ejpam-6617	304	35	κ	κ	NOUN
ejpam-6617	304	36	,	,	PUNCT
ejpam-6617	304	37	cfdθ•	cfdθ•	PROPN
ejpam-6617	304	38	a1+κ)dς	a1+κ)dς	NUM
ejpam-6617	304	39	,	,	PUNCT
ejpam-6617	304	40	a2∫	a2∫	X
ejpam-6617	304	41	a1	a1	VERB
ejpam-6617	304	42	ϕu	ϕu	X
ejpam-6617	304	43	(	(	PUNCT
ejpam-6617	304	44	ς	ς	PROPN
ejpam-6617	304	45	,	,	PUNCT
ejpam-6617	304	46	κ	κ	NOUN
ejpam-6617	304	47	,	,	PUNCT
ejpam-6617	304	48	cfdθ•	cfdθ•	X
ejpam-6617	304	49	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	304	50			NOUN
ejpam-6617	304	51	≺lu	≺lu	VERB
ejpam-6617	304	52			NOUN
ejpam-6617	304	53	a2∫	a2∫	NOUN
ejpam-6617	304	54	a1	a1	NOUN
ejpam-6617	304	55	ϕl(ς	ϕl(ς	PRON
ejpam-6617	304	56	,	,	PUNCT
ejpam-6617	304	57	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	304	58	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	304	59	,	,	PUNCT
ejpam-6617	304	60	a2∫	a2∫	X
ejpam-6617	304	61	a1	a1	VERB
ejpam-6617	304	62	ϕu	ϕu	X
ejpam-6617	304	63	(	(	PUNCT
ejpam-6617	304	64	ς	ς	PROPN
ejpam-6617	304	65	,	,	PUNCT
ejpam-6617	304	66	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	304	67	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	304	68			NOUN
ejpam-6617	304	69	.	.	PUNCT
ejpam-6617	305	1	v.	v.	CCONJ
ejpam-6617	305	2	rayanki	rayanki	PROPN
ejpam-6617	305	3	et	et	PROPN
ejpam-6617	305	4	al	al	PROPN
ejpam-6617	305	5	.	.	PUNCT
ejpam-6617	305	6	/	/	SYM
ejpam-6617	305	7	eur	eur	PROPN
ejpam-6617	305	8	.	.	PUNCT
ejpam-6617	306	1	j.	j.	PROPN
ejpam-6617	306	2	pure	pure	PROPN
ejpam-6617	306	3	appl	appl	PROPN
ejpam-6617	306	4	.	.	PROPN
ejpam-6617	306	5	math	math	PROPN
ejpam-6617	306	6	,	,	PUNCT
ejpam-6617	306	7	18	18	NUM
ejpam-6617	306	8	(	(	PUNCT
ejpam-6617	306	9	3	3	NUM
ejpam-6617	306	10	)	)	PUNCT
ejpam-6617	306	11	(	(	PUNCT
ejpam-6617	306	12	2025	2025	NUM
ejpam-6617	306	13	)	)	PUNCT
ejpam-6617	306	14	,	,	PUNCT
ejpam-6617	306	15	6617	6617	NUM
ejpam-6617	306	16	19	19	NUM
ejpam-6617	306	17	of	of	ADP
ejpam-6617	306	18	38	38	NUM
ejpam-6617	306	19	thus	thus	ADV
ejpam-6617	306	20	,	,	PUNCT
ejpam-6617	306	21	we	we	PRON
ejpam-6617	306	22	have	have	AUX
ejpam-6617	306	23			NUM
ejpam-6617	306	24	a2∫	a2∫	VERB
ejpam-6617	306	25	a1	a1	NOUN
ejpam-6617	306	26	ϕl(ς	ϕl(ς	X
ejpam-6617	306	27	,	,	PUNCT
ejpam-6617	306	28	κ	κ	NOUN
ejpam-6617	306	29	,	,	PUNCT
ejpam-6617	306	30	cfdθ•	cfdθ•	PROPN
ejpam-6617	306	31	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	306	32	<	<	X
ejpam-6617	306	33	a2∫	a2∫	X
ejpam-6617	306	34	a1	a1	NOUN
ejpam-6617	306	35	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	306	36	,	,	PUNCT
ejpam-6617	306	37	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	306	38	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	306	39	a2∫	a2∫	VERB
ejpam-6617	306	40	a1	a1	NOUN
ejpam-6617	306	41	ϕu	ϕu	X
ejpam-6617	306	42	(	(	PUNCT
ejpam-6617	306	43	ς	ς	PROPN
ejpam-6617	306	44	,	,	PUNCT
ejpam-6617	306	45	κ	κ	NOUN
ejpam-6617	306	46	,	,	PUNCT
ejpam-6617	306	47	cfdθ•	cfdθ•	PROPN
ejpam-6617	306	48	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	306	49	≤	≤	NUM
ejpam-6617	306	50	a2∫	a2∫	NOUN
ejpam-6617	306	51	a1	a1	NOUN
ejpam-6617	306	52	ϕu	ϕu	X
ejpam-6617	306	53	(	(	PUNCT
ejpam-6617	306	54	ς	ς	PROPN
ejpam-6617	306	55	,	,	PUNCT
ejpam-6617	306	56	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	306	57	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	306	58	,	,	PUNCT
ejpam-6617	306	59	or	or	CCONJ
ejpam-6617	306	60			NUM
ejpam-6617	306	61	a2∫	a2∫	NOUN
ejpam-6617	306	62	a1	a1	NOUN
ejpam-6617	306	63	ϕl(ς	ϕl(ς	X
ejpam-6617	306	64	,	,	PUNCT
ejpam-6617	306	65	κ	κ	NOUN
ejpam-6617	306	66	,	,	PUNCT
ejpam-6617	306	67	cfdθ•	cfdθ•	PROPN
ejpam-6617	306	68	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	306	69	≤	≤	NUM
ejpam-6617	306	70	a2∫	a2∫	NOUN
ejpam-6617	306	71	a1	a1	NOUN
ejpam-6617	306	72	ϕl(ς	ϕl(ς	PUNCT
ejpam-6617	306	73	,	,	PUNCT
ejpam-6617	306	74	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	306	75	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	306	76	a2∫	a2∫	VERB
ejpam-6617	306	77	a1	a1	NOUN
ejpam-6617	306	78	ϕu	ϕu	X
ejpam-6617	306	79	(	(	PUNCT
ejpam-6617	306	80	ς	ς	PROPN
ejpam-6617	306	81	,	,	PUNCT
ejpam-6617	306	82	κ	κ	NOUN
ejpam-6617	306	83	,	,	PUNCT
ejpam-6617	306	84	cfdθ•	cfdθ•	PROPN
ejpam-6617	306	85	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	306	86	<	<	X
ejpam-6617	306	87	a2∫	a2∫	X
ejpam-6617	306	88	a1	a1	NOUN
ejpam-6617	306	89	ϕu	ϕu	X
ejpam-6617	306	90	(	(	PUNCT
ejpam-6617	306	91	ς	ς	PROPN
ejpam-6617	306	92	,	,	PUNCT
ejpam-6617	306	93	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	306	94	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	306	95	,	,	PUNCT
ejpam-6617	306	96	or	or	CCONJ
ejpam-6617	306	97			NUM
ejpam-6617	306	98	a2∫	a2∫	NOUN
ejpam-6617	306	99	a1	a1	NOUN
ejpam-6617	306	100	ϕl(ς	ϕl(ς	X
ejpam-6617	306	101	,	,	PUNCT
ejpam-6617	306	102	κ	κ	NOUN
ejpam-6617	306	103	,	,	PUNCT
ejpam-6617	306	104	cfdθ•	cfdθ•	PROPN
ejpam-6617	306	105	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	306	106	<	<	X
ejpam-6617	306	107	a2∫	a2∫	X
ejpam-6617	306	108	a1	a1	NOUN
ejpam-6617	306	109	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	306	110	,	,	PUNCT
ejpam-6617	306	111	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	306	112	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	306	113	a2∫	a2∫	VERB
ejpam-6617	306	114	a1	a1	NOUN
ejpam-6617	306	115	ϕu	ϕu	X
ejpam-6617	306	116	(	(	PUNCT
ejpam-6617	306	117	ς	ς	PROPN
ejpam-6617	306	118	,	,	PUNCT
ejpam-6617	306	119	κ	κ	NOUN
ejpam-6617	306	120	,	,	PUNCT
ejpam-6617	306	121	cfdθ•	cfdθ•	PROPN
ejpam-6617	306	122	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	306	123	<	<	X
ejpam-6617	306	124	a2∫	a2∫	X
ejpam-6617	306	125	a1	a1	NOUN
ejpam-6617	306	126	ϕu	ϕu	X
ejpam-6617	306	127	(	(	PUNCT
ejpam-6617	306	128	ς	ς	PROPN
ejpam-6617	306	129	,	,	PUNCT
ejpam-6617	306	130	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	306	131	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	306	132	.	.	PUNCT
ejpam-6617	307	1	from	from	ADP
ejpam-6617	307	2	the	the	DET
ejpam-6617	307	3	above	above	ADJ
ejpam-6617	307	4	inequalities	inequality	NOUN
ejpam-6617	307	5	,	,	PUNCT
ejpam-6617	307	6	we	we	PRON
ejpam-6617	307	7	get	get	VERB
ejpam-6617	307	8	a2∫	a2∫	NOUN
ejpam-6617	307	9	a1	a1	NOUN
ejpam-6617	307	10	[	[	PUNCT
ejpam-6617	307	11	ϕl	ϕl	PROPN
ejpam-6617	308	1	+	+	X
ejpam-6617	308	2	ϕu	ϕu	X
ejpam-6617	308	3	]	]	X
ejpam-6617	308	4	(	(	PUNCT
ejpam-6617	308	5	ς	ς	PROPN
ejpam-6617	308	6	,	,	PUNCT
ejpam-6617	308	7	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	308	8	a1+κ(ς))dς	a1+κ(ς))dς	ADV
ejpam-6617	308	9	<	<	X
ejpam-6617	308	10	a2∫	a2∫	ADJ
ejpam-6617	308	11	a1	a1	NOUN
ejpam-6617	308	12	[	[	PUNCT
ejpam-6617	308	13	ϕl	ϕl	PROPN
ejpam-6617	309	1	+	+	X
ejpam-6617	309	2	ϕu	ϕu	X
ejpam-6617	309	3	]	]	X
ejpam-6617	309	4	(	(	PUNCT
ejpam-6617	309	5	ς	ς	PROPN
ejpam-6617	309	6	,	,	PUNCT
ejpam-6617	309	7	κ̄(ς),cfdθ•	κ̄(ς),cfdθ•	NOUN
ejpam-6617	309	8	a1+κ̄(ς))dς	a1+κ̄(ς))dς	PROPN
ejpam-6617	309	9	,	,	PUNCT
ejpam-6617	309	10	which	which	PRON
ejpam-6617	309	11	,	,	PUNCT
ejpam-6617	309	12	according	accord	VERB
ejpam-6617	309	13	to	to	ADP
ejpam-6617	309	14	the	the	DET
ejpam-6617	309	15	hypothesis	hypothesis	NOUN
ejpam-6617	309	16	(	(	PUNCT
ejpam-6617	309	17	i	i	NOUN
ejpam-6617	309	18	)	)	PUNCT
ejpam-6617	309	19	,	,	PUNCT
ejpam-6617	309	20	there	there	PRON
ejpam-6617	309	21	exists	exist	VERB
ejpam-6617	309	22	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	309	23	,	,	PUNCT
ejpam-6617	309	24	κ	κ	NOUN
ejpam-6617	309	25	,	,	PUNCT
ejpam-6617	309	26	κ̄	κ̄	NOUN
ejpam-6617	309	27	)	)	PUNCT
ejpam-6617	309	28	∈	∈	PROPN
ejpam-6617	309	29	c1[a	c1[a	NOUN
ejpam-6617	309	30	,	,	PUNCT
ejpam-6617	310	1	b	b	X
ejpam-6617	310	2	]	]	X
ejpam-6617	311	1	such	such	ADJ
ejpam-6617	311	2	that	that	SCONJ
ejpam-6617	311	3	a2∫	a2∫	ADJ
ejpam-6617	311	4	a1	a1	NOUN
ejpam-6617	311	5	{	{	PUNCT
ejpam-6617	311	6	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	311	7	,	,	PUNCT
ejpam-6617	311	8	κ	κ	NOUN
ejpam-6617	311	9	,	,	PUNCT
ejpam-6617	311	10	κ̄	κ̄	NOUN
ejpam-6617	311	11	)	)	PUNCT
ejpam-6617	311	12	[	[	PUNCT
ejpam-6617	311	13	ϕl	ϕl	NUM
ejpam-6617	311	14	κ̄	κ̄	NOUN
ejpam-6617	311	15	+	+	CCONJ
ejpam-6617	311	16	ϕu	ϕu	ADP
ejpam-6617	311	17	κ̄	κ̄	NOUN
ejpam-6617	311	18	]	]	PUNCT
ejpam-6617	311	19	(	(	PUNCT
ejpam-6617	311	20	ς	ς	PROPN
ejpam-6617	311	21	,	,	PUNCT
ejpam-6617	311	22	κ̄(ς),cfdθ•	κ̄(ς),cfdθ•	ADJ
ejpam-6617	311	23	a1+κ̄(ς	a1+κ̄(ς	PROPN
ejpam-6617	311	24	)	)	PUNCT
ejpam-6617	311	25	)	)	PUNCT
ejpam-6617	312	1	+	+	PROPN
ejpam-6617	312	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	312	3	a1+ℵ(ς	a1+ℵ(ς	PRON
ejpam-6617	312	4	,	,	PUNCT
ejpam-6617	312	5	κ	κ	X
ejpam-6617	312	6	,	,	PUNCT
ejpam-6617	312	7	κ̄)(ϕ	κ̄)(ϕ	PROPN
ejpam-6617	312	8	l	l	PROPN
ejpam-6617	312	9	cfdθ•	cfdθ•	PROPN
ejpam-6617	312	10	a1	a1	PROPN
ejpam-6617	312	11	+	+	CCONJ
ejpam-6617	312	12	κ̄	κ̄	NOUN
ejpam-6617	312	13	+	+	CCONJ
ejpam-6617	312	14	ϕu	ϕu	PROPN
ejpam-6617	312	15	cfdθ•	cfdθ•	PROPN
ejpam-6617	312	16	a1	a1	PROPN
ejpam-6617	312	17	+	+	X
ejpam-6617	312	18	κ̄)(ς	κ̄)(ς	PROPN
ejpam-6617	312	19	,	,	PUNCT
ejpam-6617	312	20	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	312	21	)	)	PUNCT
ejpam-6617	312	22	,	,	PUNCT
ejpam-6617	312	23	cfdθ•	cfdθ•	PROPN
ejpam-6617	312	24	a1+κ̄(ς	a1+κ̄(ς	PROPN
ejpam-6617	312	25	)	)	PUNCT
ejpam-6617	312	26	)	)	PUNCT
ejpam-6617	312	27	}	}	PUNCT
ejpam-6617	312	28	dς	dς	VERB
ejpam-6617	312	29	<	<	X
ejpam-6617	312	30	0	0	NUM
ejpam-6617	312	31	.	.	PUNCT
ejpam-6617	313	1	(	(	PUNCT
ejpam-6617	313	2	10	10	NUM
ejpam-6617	313	3	)	)	PUNCT
ejpam-6617	313	4	on	on	ADP
ejpam-6617	313	5	the	the	DET
ejpam-6617	313	6	other	other	ADJ
ejpam-6617	313	7	hand	hand	NOUN
ejpam-6617	313	8	,	,	PUNCT
ejpam-6617	313	9	from	from	ADP
ejpam-6617	313	10	(	(	PUNCT
ejpam-6617	313	11	4	4	NUM
ejpam-6617	313	12	)	)	PUNCT
ejpam-6617	313	13	,	,	PUNCT
ejpam-6617	313	14	we	we	PRON
ejpam-6617	313	15	have	have	VERB
ejpam-6617	313	16	a2∫	a2∫	NOUN
ejpam-6617	313	17	a1	a1	NOUN
ejpam-6617	313	18	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	313	19	,	,	PUNCT
ejpam-6617	313	20	κ	κ	NOUN
ejpam-6617	313	21	,	,	PUNCT
ejpam-6617	313	22	κ̄	κ̄	NOUN
ejpam-6617	313	23	)	)	PUNCT
ejpam-6617	313	24	[	[	PUNCT
ejpam-6617	313	25	ϕl	ϕl	PROPN
ejpam-6617	313	26	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	313	27	,	,	PUNCT
ejpam-6617	313	28	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	313	29	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	313	30	)	)	PUNCT
ejpam-6617	313	31	+	+	CCONJ
ejpam-6617	313	32	ϕu	ϕu	ADP
ejpam-6617	313	33	κ̄	κ̄	NOUN
ejpam-6617	313	34	(	(	PUNCT
ejpam-6617	313	35	ς	ς	PROPN
ejpam-6617	313	36	,	,	PUNCT
ejpam-6617	313	37	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	313	38	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	313	39	)	)	PUNCT
ejpam-6617	314	1	+	+	PROPN
ejpam-6617	314	2	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	314	3	,	,	PUNCT
ejpam-6617	314	4	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	314	5	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	314	6	)	)	PUNCT
ejpam-6617	314	7	]	]	PUNCT
ejpam-6617	314	8	dς	dς	PROPN
ejpam-6617	315	1	v.	v.	ADP
ejpam-6617	315	2	rayanki	rayanki	PROPN
ejpam-6617	315	3	et	et	PROPN
ejpam-6617	315	4	al	al	PROPN
ejpam-6617	315	5	.	.	PUNCT
ejpam-6617	315	6	/	/	SYM
ejpam-6617	315	7	eur	eur	PROPN
ejpam-6617	315	8	.	.	PUNCT
ejpam-6617	316	1	j.	j.	PROPN
ejpam-6617	316	2	pure	pure	PROPN
ejpam-6617	316	3	appl	appl	PROPN
ejpam-6617	316	4	.	.	PROPN
ejpam-6617	316	5	math	math	PROPN
ejpam-6617	316	6	,	,	PUNCT
ejpam-6617	316	7	18	18	NUM
ejpam-6617	316	8	(	(	PUNCT
ejpam-6617	316	9	3	3	NUM
ejpam-6617	316	10	)	)	PUNCT
ejpam-6617	316	11	(	(	PUNCT
ejpam-6617	316	12	2025	2025	NUM
ejpam-6617	316	13	)	)	PUNCT
ejpam-6617	316	14	,	,	PUNCT
ejpam-6617	316	15	6617	6617	NUM
ejpam-6617	316	16	20	20	NUM
ejpam-6617	316	17	of	of	ADP
ejpam-6617	316	18	38	38	NUM
ejpam-6617	316	19	=	=	NOUN
ejpam-6617	316	20	a2∫	a2∫	NOUN
ejpam-6617	316	21	a1	a1	NOUN
ejpam-6617	316	22	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	316	23	,	,	PUNCT
ejpam-6617	316	24	κ	κ	NOUN
ejpam-6617	316	25	,	,	PUNCT
ejpam-6617	316	26	κ̄)(−cfdθ•	κ̄)(−cfdθ•	ADV
ejpam-6617	316	27	a2−){ϕ	a2−){ϕ	PROPN
ejpam-6617	316	28	l	l	PROPN
ejpam-6617	316	29	cfdθ•	cfdθ•	PROPN
ejpam-6617	316	30	a1	a1	PROPN
ejpam-6617	316	31	+	+	CCONJ
ejpam-6617	316	32	κ̄(ς)(ς	κ̄(ς)(ς	PROPN
ejpam-6617	316	33	,	,	PUNCT
ejpam-6617	316	34	κ̄	κ̄	NOUN
ejpam-6617	316	35	,	,	PUNCT
ejpam-6617	316	36	cfdθ•	cfdθ•	PROPN
ejpam-6617	316	37	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	316	38	)	)	PUNCT
ejpam-6617	317	1	+	+	PROPN
ejpam-6617	317	2	ϕu	ϕu	PROPN
ejpam-6617	317	3	cfdθ•	cfdθ•	PROPN
ejpam-6617	317	4	a1	a1	PROPN
ejpam-6617	317	5	+	+	CCONJ
ejpam-6617	317	6	κ̄(ς)(ς	κ̄(ς)(ς	PROPN
ejpam-6617	317	7	,	,	PUNCT
ejpam-6617	317	8	κ̄	κ̄	NOUN
ejpam-6617	317	9	,	,	PUNCT
ejpam-6617	317	10	cfdθ•	cfdθ•	PROPN
ejpam-6617	317	11	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	317	12	)	)	PUNCT
ejpam-6617	317	13	+	+	CCONJ
ejpam-6617	317	14	θ̄(ς)hcfdθ•	θ̄(ς)hcfdθ•	CCONJ
ejpam-6617	317	15	a1	a1	PROPN
ejpam-6617	317	16	+	+	CCONJ
ejpam-6617	317	17	κ̄(ς)(ς	κ̄(ς)(ς	PROPN
ejpam-6617	317	18	,	,	PUNCT
ejpam-6617	317	19	κ̄	κ̄	NOUN
ejpam-6617	317	20	,	,	PUNCT
ejpam-6617	317	21	cfdθ•	cfdθ•	ADJ
ejpam-6617	317	22	a1+κ̄)}dς	a1+κ̄)}dς	VERB
ejpam-6617	317	23	=	=	PRON
ejpam-6617	317	24	{	{	PUNCT
ejpam-6617	317	25	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	317	26	,	,	PUNCT
ejpam-6617	317	27	κ	κ	NOUN
ejpam-6617	317	28	,	,	PUNCT
ejpam-6617	317	29	κ̄)i1−θ•	κ̄)i1−θ•	PROPN
ejpam-6617	317	30	b−	b−	PROPN
ejpam-6617	317	31	[	[	PUNCT
ejpam-6617	317	32	ϕl	ϕl	PROPN
ejpam-6617	317	33	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	317	34	+	+	CCONJ
ejpam-6617	317	35	κ̄	κ̄	NOUN
ejpam-6617	317	36	(	(	PUNCT
ejpam-6617	317	37	ς	ς	PROPN
ejpam-6617	317	38	,	,	PUNCT
ejpam-6617	317	39	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	317	40	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	317	41	)	)	PUNCT
ejpam-6617	317	42	+	+	CCONJ
ejpam-6617	318	1	ϕu	ϕu	PROPN
ejpam-6617	318	2	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	318	3	+	+	CCONJ
ejpam-6617	318	4	κ̄	κ̄	NOUN
ejpam-6617	318	5	(	(	PUNCT
ejpam-6617	318	6	ς	ς	PROPN
ejpam-6617	318	7	,	,	PUNCT
ejpam-6617	318	8	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	318	9	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	318	10	)	)	PUNCT
ejpam-6617	319	1	+	+	PROPN
ejpam-6617	319	2	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	319	3	,	,	PUNCT
ejpam-6617	319	4	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	319	5	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	319	6	)	)	PUNCT
ejpam-6617	319	7	]	]	PUNCT
ejpam-6617	319	8	}	}	PUNCT
ejpam-6617	319	9	∣∣∣∣a2	∣∣∣∣a2	PROPN
ejpam-6617	319	10	a1	a1	NOUN
ejpam-6617	319	11	−	−	NOUN
ejpam-6617	319	12	a2∫	a2∫	NOUN
ejpam-6617	319	13	a1	a1	NOUN
ejpam-6617	319	14	{	{	PUNCT
ejpam-6617	319	15	ϕl	ϕl	PROPN
ejpam-6617	319	16	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	319	17	+	+	CCONJ
ejpam-6617	319	18	κ̄	κ̄	NOUN
ejpam-6617	319	19	(	(	PUNCT
ejpam-6617	319	20	ς	ς	PROPN
ejpam-6617	319	21	,	,	PUNCT
ejpam-6617	319	22	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	319	23	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	319	24	)	)	PUNCT
ejpam-6617	319	25	+	+	CCONJ
ejpam-6617	319	26	ϕu	ϕu	PROPN
ejpam-6617	319	27	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	319	28	+	+	CCONJ
ejpam-6617	319	29	κ̄	κ̄	NOUN
ejpam-6617	319	30	(	(	PUNCT
ejpam-6617	319	31	ς	ς	PROPN
ejpam-6617	319	32	,	,	PUNCT
ejpam-6617	319	33	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	319	34	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	319	35	)	)	PUNCT
ejpam-6617	319	36	+	+	ADJ
ejpam-6617	319	37	θ̄(ς)h	θ̄(ς)h	ADJ
ejpam-6617	319	38	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	319	39	+	+	SYM
ejpam-6617	319	40	κ̄	κ̄	NOUN
ejpam-6617	319	41	(	(	PUNCT
ejpam-6617	319	42	ς	ς	PROPN
ejpam-6617	319	43	,	,	PUNCT
ejpam-6617	319	44	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	319	45	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	319	46	)	)	PUNCT
ejpam-6617	319	47	}	}	PUNCT
ejpam-6617	319	48	cfdθ•	cfdθ•	PROPN
ejpam-6617	319	49	a1+ℵ(ς	a1+ℵ(ς	NUM
ejpam-6617	319	50	,	,	PUNCT
ejpam-6617	319	51	κ	κ	PROPN
ejpam-6617	319	52	,	,	PUNCT
ejpam-6617	319	53	κ̄)dς	κ̄)dς	PROPN
ejpam-6617	319	54	.	.	PUNCT
ejpam-6617	320	1	(	(	PUNCT
ejpam-6617	320	2	by	by	ADP
ejpam-6617	320	3	proposition	proposition	NOUN
ejpam-6617	320	4	1	1	NUM
ejpam-6617	320	5	)	)	PUNCT
ejpam-6617	320	6	by	by	ADP
ejpam-6617	320	7	using	use	VERB
ejpam-6617	320	8	(	(	PUNCT
ejpam-6617	320	9	2	2	NUM
ejpam-6617	320	10	)	)	PUNCT
ejpam-6617	320	11	,	,	PUNCT
ejpam-6617	320	12	we	we	PRON
ejpam-6617	320	13	get	get	VERB
ejpam-6617	320	14	a2∫	a2∫	NOUN
ejpam-6617	320	15	a1	a1	NOUN
ejpam-6617	320	16	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	320	17	,	,	PUNCT
ejpam-6617	320	18	κ	κ	NOUN
ejpam-6617	320	19	,	,	PUNCT
ejpam-6617	320	20	κ̄)[ϕl	κ̄)[ϕl	ADJ
ejpam-6617	320	21	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	320	22	,	,	PUNCT
ejpam-6617	320	23	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	320	24	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	320	25	)	)	PUNCT
ejpam-6617	321	1	+	+	CCONJ
ejpam-6617	321	2	ϕu	ϕu	ADP
ejpam-6617	321	3	κ̄	κ̄	NOUN
ejpam-6617	321	4	(	(	PUNCT
ejpam-6617	321	5	ς	ς	PROPN
ejpam-6617	321	6	,	,	PUNCT
ejpam-6617	321	7	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	321	8	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	321	9	)	)	PUNCT
ejpam-6617	322	1	+	+	PROPN
ejpam-6617	322	2	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	322	3	,	,	PUNCT
ejpam-6617	322	4	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	322	5	a1+κ̄)]dς	a1+κ̄)]dς	PROPN
ejpam-6617	322	6	=	=	PUNCT
ejpam-6617	322	7	−	−	NOUN
ejpam-6617	322	8	a2∫	a2∫	NOUN
ejpam-6617	322	9	a1	a1	NOUN
ejpam-6617	322	10	{	{	PUNCT
ejpam-6617	322	11	ϕl	ϕl	PROPN
ejpam-6617	322	12	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	322	13	+	+	CCONJ
ejpam-6617	322	14	κ̄	κ̄	NOUN
ejpam-6617	322	15	(	(	PUNCT
ejpam-6617	322	16	ς	ς	PROPN
ejpam-6617	322	17	,	,	PUNCT
ejpam-6617	322	18	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	322	19	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	322	20	)	)	PUNCT
ejpam-6617	322	21	+	+	CCONJ
ejpam-6617	323	1	ϕu	ϕu	PROPN
ejpam-6617	323	2	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	323	3	+	+	CCONJ
ejpam-6617	323	4	κ̄	κ̄	NOUN
ejpam-6617	323	5	(	(	PUNCT
ejpam-6617	323	6	ς	ς	PROPN
ejpam-6617	323	7	,	,	PUNCT
ejpam-6617	323	8	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	323	9	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	323	10	)	)	PUNCT
ejpam-6617	323	11	+	+	ADJ
ejpam-6617	323	12	θ̄(ς)h	θ̄(ς)h	ADJ
ejpam-6617	323	13	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	323	14	+	+	SYM
ejpam-6617	323	15	κ̄	κ̄	NOUN
ejpam-6617	323	16	(	(	PUNCT
ejpam-6617	323	17	ς	ς	PROPN
ejpam-6617	323	18	,	,	PUNCT
ejpam-6617	323	19	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	323	20	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	323	21	)	)	PUNCT
ejpam-6617	323	22	}	}	PUNCT
ejpam-6617	323	23	cfdθ•	cfdθ•	PROPN
ejpam-6617	323	24	a1+ℵ(ς	a1+ℵ(ς	NUM
ejpam-6617	323	25	,	,	PUNCT
ejpam-6617	323	26	κ	κ	PROPN
ejpam-6617	323	27	,	,	PUNCT
ejpam-6617	323	28	κ̄))dς	κ̄))dς	NOUN
ejpam-6617	323	29	,	,	PUNCT
ejpam-6617	323	30	that	that	PRON
ejpam-6617	323	31	is	be	AUX
ejpam-6617	323	32	a2∫	a2∫	NOUN
ejpam-6617	323	33	a1	a1	NOUN
ejpam-6617	323	34	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	323	35	,	,	PUNCT
ejpam-6617	323	36	κ	κ	NOUN
ejpam-6617	323	37	,	,	PUNCT
ejpam-6617	323	38	κ̄	κ̄	NOUN
ejpam-6617	323	39	)	)	PUNCT
ejpam-6617	323	40	[	[	PUNCT
ejpam-6617	323	41	ϕl	ϕl	PROPN
ejpam-6617	323	42	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	323	43	,	,	PUNCT
ejpam-6617	323	44	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	323	45	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	323	46	)	)	PUNCT
ejpam-6617	323	47	+	+	CCONJ
ejpam-6617	324	1	ϕu	ϕu	ADP
ejpam-6617	324	2	κ̄	κ̄	NOUN
ejpam-6617	324	3	(	(	PUNCT
ejpam-6617	324	4	ς	ς	PROPN
ejpam-6617	324	5	,	,	PUNCT
ejpam-6617	324	6	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	324	7	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	324	8	)	)	PUNCT
ejpam-6617	324	9	+	+	PROPN
ejpam-6617	324	10	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	324	11	,	,	PUNCT
ejpam-6617	324	12	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	324	13	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	324	14	)	)	PUNCT
ejpam-6617	324	15	]	]	PUNCT
ejpam-6617	324	16	dς	dς	X
ejpam-6617	324	17	+	+	PUNCT
ejpam-6617	324	18	a2∫	a2∫	NOUN
ejpam-6617	324	19	a1	a1	NOUN
ejpam-6617	324	20	{	{	PUNCT
ejpam-6617	324	21	ϕl	ϕl	PROPN
ejpam-6617	324	22	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	324	23	+	+	CCONJ
ejpam-6617	324	24	κ̄	κ̄	NOUN
ejpam-6617	324	25	(	(	PUNCT
ejpam-6617	324	26	ς	ς	PROPN
ejpam-6617	324	27	,	,	PUNCT
ejpam-6617	324	28	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	324	29	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	324	30	)	)	PUNCT
ejpam-6617	324	31	+	+	CCONJ
ejpam-6617	324	32	ϕu	ϕu	ADP
ejpam-6617	324	33	cfdςa+κ̄	cfdςa+κ̄	NOUN
ejpam-6617	324	34	(	(	PUNCT
ejpam-6617	324	35	ς	ς	PROPN
ejpam-6617	324	36	,	,	PUNCT
ejpam-6617	324	37	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	324	38	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	324	39	)	)	PUNCT
ejpam-6617	325	1	+	+	ADP
ejpam-6617	325	2	θ̄(κ)h	θ̄(κ)h	NOUN
ejpam-6617	325	3	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	325	4	+	+	CCONJ
ejpam-6617	325	5	κ̄	κ̄	NOUN
ejpam-6617	325	6	(	(	PUNCT
ejpam-6617	325	7	ς	ς	PROPN
ejpam-6617	325	8	,	,	PUNCT
ejpam-6617	325	9	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	325	10	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	325	11	)	)	PUNCT
ejpam-6617	325	12	}	}	PUNCT
ejpam-6617	325	13	cfdθ•	cfdθ•	PROPN
ejpam-6617	325	14	a1+ℵ(ς	a1+ℵ(ς	NUM
ejpam-6617	325	15	,	,	PUNCT
ejpam-6617	325	16	κ	κ	NOUN
ejpam-6617	325	17	,	,	PUNCT
ejpam-6617	325	18	κ̄)dξ	κ̄)dξ	PROPN
ejpam-6617	325	19	=	=	NOUN
ejpam-6617	325	20	0	0	NUM
ejpam-6617	325	21	.	.	PUNCT
ejpam-6617	326	1	(	(	PUNCT
ejpam-6617	326	2	11	11	NUM
ejpam-6617	326	3	)	)	PUNCT
ejpam-6617	326	4	v.	v.	ADP
ejpam-6617	326	5	rayanki	rayanki	X
ejpam-6617	326	6	et	et	PROPN
ejpam-6617	326	7	al	al	PROPN
ejpam-6617	326	8	.	.	PUNCT
ejpam-6617	326	9	/	/	SYM
ejpam-6617	326	10	eur	eur	PROPN
ejpam-6617	326	11	.	.	PUNCT
ejpam-6617	327	1	j.	j.	PROPN
ejpam-6617	327	2	pure	pure	PROPN
ejpam-6617	327	3	appl	appl	PROPN
ejpam-6617	327	4	.	.	PROPN
ejpam-6617	327	5	math	math	PROPN
ejpam-6617	327	6	,	,	PUNCT
ejpam-6617	327	7	18	18	NUM
ejpam-6617	327	8	(	(	PUNCT
ejpam-6617	327	9	3	3	NUM
ejpam-6617	327	10	)	)	PUNCT
ejpam-6617	327	11	(	(	PUNCT
ejpam-6617	327	12	2025	2025	NUM
ejpam-6617	327	13	)	)	PUNCT
ejpam-6617	327	14	,	,	PUNCT
ejpam-6617	327	15	6617	6617	NUM
ejpam-6617	327	16	21	21	NUM
ejpam-6617	327	17	of	of	ADP
ejpam-6617	327	18	38	38	NUM
ejpam-6617	327	19	in	in	ADP
ejpam-6617	327	20	order	order	NOUN
ejpam-6617	327	21	to	to	PART
ejpam-6617	327	22	determine	determine	VERB
ejpam-6617	327	23	the	the	DET
ejpam-6617	327	24	feasibility	feasibility	NOUN
ejpam-6617	327	25	of	of	ADP
ejpam-6617	327	26	κ	κ	PROPN
ejpam-6617	327	27	in	in	ADP
ejpam-6617	327	28	the	the	DET
ejpam-6617	327	29	problem	problem	NOUN
ejpam-6617	327	30	(	(	PUNCT
ejpam-6617	327	31	p	p	X
ejpam-6617	327	32	)	)	PUNCT
ejpam-6617	327	33	,	,	PUNCT
ejpam-6617	327	34	we	we	PRON
ejpam-6617	327	35	have	have	VERB
ejpam-6617	327	36	h(ς	h(ς	PROPN
ejpam-6617	327	37	,	,	PUNCT
ejpam-6617	327	38	κ(ς	κ(ς	PROPN
ejpam-6617	327	39	)	)	PUNCT
ejpam-6617	327	40	,	,	PUNCT
ejpam-6617	327	41	cfdθ•	cfdθ•	PROPN
ejpam-6617	327	42	a+κ(ς	a+κ(ς	NOUN
ejpam-6617	327	43	)	)	PUNCT
ejpam-6617	327	44	)	)	PUNCT
ejpam-6617	327	45	≤	≤	ADV
ejpam-6617	327	46	0	0	NUM
ejpam-6617	327	47	,	,	PUNCT
ejpam-6617	327	48	ς	ς	PROPN
ejpam-6617	327	49	∈	∈	PROPN
ejpam-6617	327	50	ℑ	ℑ	PROPN
ejpam-6617	327	51	,	,	PUNCT
ejpam-6617	327	52	which	which	PRON
ejpam-6617	327	53	by	by	ADP
ejpam-6617	327	54	using	use	VERB
ejpam-6617	327	55	the	the	DET
ejpam-6617	327	56	fact	fact	NOUN
ejpam-6617	327	57	θ̄(ς	θ̄(ς	NOUN
ejpam-6617	327	58	)	)	PUNCT
ejpam-6617	327	59	∈	∈	PROPN
ejpam-6617	327	60	rm	rm	PROPN
ejpam-6617	327	61	,	,	PUNCT
ejpam-6617	327	62	θ̄(ς	θ̄(ς	PROPN
ejpam-6617	327	63	)	)	PUNCT
ejpam-6617	327	64	≥	≥	NOUN
ejpam-6617	327	65	0	0	NUM
ejpam-6617	327	66	and	and	CCONJ
ejpam-6617	327	67	(	(	PUNCT
ejpam-6617	327	68	5	5	X
ejpam-6617	327	69	)	)	PUNCT
ejpam-6617	327	70	we	we	PRON
ejpam-6617	327	71	have	have	VERB
ejpam-6617	327	72	a2∫	a2∫	NOUN
ejpam-6617	327	73	a1	a1	NOUN
ejpam-6617	327	74	θ̄(ς)h(ς	θ̄(ς)h(ς	NOUN
ejpam-6617	327	75	,	,	PUNCT
ejpam-6617	327	76	κ	κ	NOUN
ejpam-6617	327	77	,	,	PUNCT
ejpam-6617	327	78	cfdθ•	cfdθ•	PROPN
ejpam-6617	327	79	a1+)dς	a1+)dς	PROPN
ejpam-6617	327	80	≤	≤	NOUN
ejpam-6617	327	81	a2∫	a2∫	NOUN
ejpam-6617	327	82	a1	a1	NOUN
ejpam-6617	327	83	θ̄(ς)h(ς	θ̄(ς)h(ς	NOUN
ejpam-6617	327	84	,	,	PUNCT
ejpam-6617	327	85	ς̄	ς̄	PROPN
ejpam-6617	327	86	,	,	PUNCT
ejpam-6617	327	87	cfdθ•	cfdθ•	PROPN
ejpam-6617	327	88	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	327	89	.	.	PUNCT
ejpam-6617	328	1	on	on	ADP
ejpam-6617	328	2	the	the	DET
ejpam-6617	328	3	basis	basis	NOUN
ejpam-6617	328	4	of	of	ADP
ejpam-6617	328	5	hypothesis	hypothesis	NOUN
ejpam-6617	328	6	(	(	PUNCT
ejpam-6617	328	7	ii	ii	NOUN
ejpam-6617	328	8	)	)	PUNCT
ejpam-6617	328	9	,	,	PUNCT
ejpam-6617	328	10	there	there	PRON
ejpam-6617	328	11	exists	exist	VERB
ejpam-6617	328	12	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	328	13	,	,	PUNCT
ejpam-6617	328	14	κ	κ	NOUN
ejpam-6617	328	15	,	,	PUNCT
ejpam-6617	328	16	κ̄	κ̄	NOUN
ejpam-6617	328	17	)	)	PUNCT
ejpam-6617	328	18	∈	∈	PROPN
ejpam-6617	328	19	c1[a	c1[a	NOUN
ejpam-6617	328	20	,	,	PUNCT
ejpam-6617	328	21	b	b	X
ejpam-6617	328	22	]	]	X
ejpam-6617	328	23	such	such	ADJ
ejpam-6617	328	24	that	that	SCONJ
ejpam-6617	328	25	a2∫	a2∫	NOUN
ejpam-6617	328	26	a1	a1	NOUN
ejpam-6617	328	27	θ̄(ς	θ̄(ς	NOUN
ejpam-6617	328	28	)	)	PUNCT
ejpam-6617	328	29	[	[	PUNCT
ejpam-6617	328	30	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	328	31	,	,	PUNCT
ejpam-6617	328	32	κ	κ	NOUN
ejpam-6617	328	33	,	,	PUNCT
ejpam-6617	328	34	κ̄)hκ̄(ς	κ̄)hκ̄(ς	PROPN
ejpam-6617	328	35	,	,	PUNCT
ejpam-6617	328	36	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	328	37	a1+κ̄)+	a1+κ̄)+	PROPN
ejpam-6617	328	38	cfdθ•	cfdθ•	PROPN
ejpam-6617	328	39	a1+ℵ(ς	a1+ℵ(ς	X
ejpam-6617	328	40	,	,	PUNCT
ejpam-6617	328	41	κ	κ	NOUN
ejpam-6617	328	42	,	,	PUNCT
ejpam-6617	328	43	κ̄)hcfdθ•a1	κ̄)hcfdθ•a1	PROPN
ejpam-6617	328	44	+	+	SYM
ejpam-6617	328	45	κ̄	κ̄	NOUN
ejpam-6617	328	46	(	(	PUNCT
ejpam-6617	328	47	ς	ς	PROPN
ejpam-6617	328	48	,	,	PUNCT
ejpam-6617	328	49	κ̄(ς),cfdθ•	κ̄(ς),cfdθ•	ADJ
ejpam-6617	328	50	a1+κ̄(ς	a1+κ̄(ς	PROPN
ejpam-6617	328	51	)	)	PUNCT
ejpam-6617	328	52	)	)	PUNCT
ejpam-6617	328	53	]	]	PUNCT
ejpam-6617	329	1	dς	dς	VERB
ejpam-6617	329	2	≤	≤	NUM
ejpam-6617	329	3	0	0	NUM
ejpam-6617	329	4	.	.	PUNCT
ejpam-6617	330	1	(	(	PUNCT
ejpam-6617	330	2	12	12	NUM
ejpam-6617	330	3	)	)	PUNCT
ejpam-6617	330	4	on	on	ADP
ejpam-6617	330	5	adding	add	VERB
ejpam-6617	330	6	(	(	PUNCT
ejpam-6617	330	7	10	10	NUM
ejpam-6617	330	8	)	)	PUNCT
ejpam-6617	330	9	and	and	CCONJ
ejpam-6617	330	10	(	(	PUNCT
ejpam-6617	330	11	12	12	NUM
ejpam-6617	330	12	)	)	PUNCT
ejpam-6617	330	13	,	,	PUNCT
ejpam-6617	330	14	we	we	PRON
ejpam-6617	330	15	get	get	VERB
ejpam-6617	330	16	a2∫	a2∫	NOUN
ejpam-6617	330	17	a1	a1	NOUN
ejpam-6617	330	18	{	{	PUNCT
ejpam-6617	330	19	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	330	20	,	,	PUNCT
ejpam-6617	330	21	κ	κ	NOUN
ejpam-6617	330	22	,	,	PUNCT
ejpam-6617	330	23	κ̄	κ̄	NOUN
ejpam-6617	330	24	)	)	PUNCT
ejpam-6617	330	25	[	[	PUNCT
ejpam-6617	330	26	ϕl	ϕl	PROPN
ejpam-6617	330	27	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	330	28	,	,	PUNCT
ejpam-6617	330	29	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	330	30	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	330	31	)	)	PUNCT
ejpam-6617	331	1	+	+	CCONJ
ejpam-6617	331	2	ϕu	ϕu	ADP
ejpam-6617	331	3	κ̄	κ̄	NOUN
ejpam-6617	331	4	(	(	PUNCT
ejpam-6617	331	5	ς	ς	PROPN
ejpam-6617	331	6	,	,	PUNCT
ejpam-6617	331	7	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	331	8	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	331	9	)	)	PUNCT
ejpam-6617	332	1	+	+	PROPN
ejpam-6617	332	2	θ̄(ς)hκ̄(ς	θ̄(ς)hκ̄(ς	PROPN
ejpam-6617	332	3	,	,	PUNCT
ejpam-6617	332	4	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	332	5	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	332	6	)	)	PUNCT
ejpam-6617	332	7	]	]	PUNCT
ejpam-6617	333	1	+	+	PROPN
ejpam-6617	333	2	(	(	PUNCT
ejpam-6617	333	3	cfdθ•	cfdθ•	PROPN
ejpam-6617	333	4	a1+ℵ(ς	a1+ℵ(ς	PROPN
ejpam-6617	333	5	,	,	PUNCT
ejpam-6617	333	6	κ	κ	NOUN
ejpam-6617	333	7	,	,	PUNCT
ejpam-6617	333	8	κ̄))[ϕ	κ̄))[ϕ	VERB
ejpam-6617	333	9	l	l	PROPN
ejpam-6617	333	10	cfdθ•	cfdθ•	PROPN
ejpam-6617	333	11	a1	a1	PROPN
ejpam-6617	333	12	+	+	CCONJ
ejpam-6617	333	13	κ̄	κ̄	NOUN
ejpam-6617	333	14	(	(	PUNCT
ejpam-6617	333	15	ς	ς	PROPN
ejpam-6617	333	16	,	,	PUNCT
ejpam-6617	333	17	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	333	18	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	333	19	)	)	PUNCT
ejpam-6617	333	20	+	+	CCONJ
ejpam-6617	333	21	ϕu	ϕu	PROPN
ejpam-6617	333	22	cfdθ•	cfdθ•	PROPN
ejpam-6617	333	23	a+κ̄	a+κ̄	NOUN
ejpam-6617	333	24	(	(	PUNCT
ejpam-6617	333	25	ς	ς	PROPN
ejpam-6617	333	26	,	,	PUNCT
ejpam-6617	333	27	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	333	28	a+κ̄)+	a+κ̄)+	NOUN
ejpam-6617	333	29	θ̄(ς)h	θ̄(ς)h	PROPN
ejpam-6617	333	30	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	333	31	+	+	CCONJ
ejpam-6617	333	32	κ̄	κ̄	NOUN
ejpam-6617	333	33	(	(	PUNCT
ejpam-6617	333	34	ς	ς	PROPN
ejpam-6617	333	35	,	,	PUNCT
ejpam-6617	333	36	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	333	37	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	333	38	)	)	PUNCT
ejpam-6617	333	39	]	]	PUNCT
ejpam-6617	333	40	}	}	PUNCT
ejpam-6617	333	41	dς	dς	X
ejpam-6617	333	42	<	<	X
ejpam-6617	333	43	0	0	NUM
ejpam-6617	333	44	,	,	PUNCT
ejpam-6617	333	45	which	which	PRON
ejpam-6617	333	46	is	be	AUX
ejpam-6617	333	47	a	a	DET
ejpam-6617	333	48	contradiction	contradiction	NOUN
ejpam-6617	333	49	to	to	ADP
ejpam-6617	333	50	(	(	PUNCT
ejpam-6617	333	51	11	11	NUM
ejpam-6617	333	52	)	)	PUNCT
ejpam-6617	333	53	.	.	PUNCT
ejpam-6617	334	1	hence	hence	ADV
ejpam-6617	334	2	the	the	DET
ejpam-6617	334	3	theorem	theorem	NOUN
ejpam-6617	334	4	.	.	PUNCT
ejpam-6617	335	1	the	the	DET
ejpam-6617	335	2	following	follow	VERB
ejpam-6617	335	3	example	example	NOUN
ejpam-6617	335	4	illustrates	illustrate	VERB
ejpam-6617	335	5	theorem	theorem	VERB
ejpam-6617	335	6	3.3	3.3	NUM
ejpam-6617	335	7	.	.	PUNCT
ejpam-6617	335	8	example	example	NOUN
ejpam-6617	335	9	5	5	NUM
ejpam-6617	335	10	.	.	PUNCT
ejpam-6617	336	1	consider	consider	VERB
ejpam-6617	336	2	the	the	DET
ejpam-6617	336	3	following	follow	VERB
ejpam-6617	336	4	problem	problem	NOUN
ejpam-6617	336	5	(	(	PUNCT
ejpam-6617	336	6	p-3	p-3	NOUN
ejpam-6617	336	7	):	):	PUNCT
ejpam-6617	336	8	(	(	PUNCT
ejpam-6617	336	9	p-3	p-3	X
ejpam-6617	336	10	)	)	PUNCT
ejpam-6617	336	11	=	=	SYM
ejpam-6617	336	12	min	min	NOUN
ejpam-6617	336	13			NOUN
ejpam-6617	336	14	a2∫	a2∫	X
ejpam-6617	336	15	a1	a1	NOUN
ejpam-6617	336	16	ϕl(ς	ϕl(ς	PUNCT
ejpam-6617	336	17	,	,	PUNCT
ejpam-6617	336	18	y(ς),cfdθ•	y(ς),cfdθ•	PROPN
ejpam-6617	336	19	a1+κ(ς))dς	a1+κ(ς))dς	PROPN
ejpam-6617	336	20	,	,	PUNCT
ejpam-6617	336	21	a2∫	a2∫	X
ejpam-6617	336	22	a1	a1	VERB
ejpam-6617	336	23	ϕu	ϕu	X
ejpam-6617	336	24	(	(	PUNCT
ejpam-6617	336	25	ς	ς	PROPN
ejpam-6617	336	26	,	,	PUNCT
ejpam-6617	336	27	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	336	28	a1+κ(ς))dς	a1+κ(ς))dς	PRON
ejpam-6617	336	29			NOUN
ejpam-6617	336	30	subject	subject	ADJ
ejpam-6617	336	31	to	to	ADP
ejpam-6617	336	32	,	,	PUNCT
ejpam-6617	336	33	−	−	PROPN
ejpam-6617	336	34	y(ς	y(ς	NOUN
ejpam-6617	336	35	)	)	PUNCT
ejpam-6617	337	1	+	+	CCONJ
ejpam-6617	337	2	1.871822ς	1.871822ς	NUM
ejpam-6617	337	3	+	+	SYM
ejpam-6617	337	4	6.5514e	6.5514e	NUM
ejpam-6617	337	5	−	−	NOUN
ejpam-6617	337	6	ς	ς	PROPN
ejpam-6617	337	7	3	3	NUM
ejpam-6617	337	8	−	−	PROPN
ejpam-6617	337	9	5.6154	5.6154	NUM
ejpam-6617	337	10	≤	≤	NUM
ejpam-6617	337	11	0	0	NUM
ejpam-6617	337	12	,	,	PUNCT
ejpam-6617	337	13	κ(0	κ(0	NOUN
ejpam-6617	337	14	)	)	PUNCT
ejpam-6617	337	15	=	=	SYM
ejpam-6617	337	16	1	1	NUM
ejpam-6617	337	17	,	,	PUNCT
ejpam-6617	337	18	κ(1	κ(1	PROPN
ejpam-6617	337	19	)	)	PUNCT
ejpam-6617	337	20	=	=	PUNCT
ejpam-6617	338	1	1	1	NUM
ejpam-6617	338	2	,	,	PUNCT
ejpam-6617	338	3	ς	ς	PROPN
ejpam-6617	338	4	∈	∈	PROPN
ejpam-6617	339	1	[	[	X
ejpam-6617	339	2	0	0	NUM
ejpam-6617	339	3	,	,	PUNCT
ejpam-6617	339	4	1	1	NUM
ejpam-6617	339	5	]	]	PUNCT
ejpam-6617	339	6	,	,	PUNCT
ejpam-6617	339	7	where	where	SCONJ
ejpam-6617	339	8	,	,	PUNCT
ejpam-6617	339	9	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	339	10	,	,	PUNCT
ejpam-6617	339	11	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	339	12	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	339	13	)	)	PUNCT
ejpam-6617	339	14	)	)	PUNCT
ejpam-6617	340	1	=	=	PUNCT
ejpam-6617	340	2	−κ(ς	−κ(ς	PROPN
ejpam-6617	340	3	)	)	PUNCT
ejpam-6617	341	1	+	+	CCONJ
ejpam-6617	342	1	6.5514ς	6.5514ς	NUM
ejpam-6617	342	2	−	−	PROPN
ejpam-6617	342	3	16.37859e	16.37859e	NUM
ejpam-6617	342	4	−	−	NOUN
ejpam-6617	342	5	ς	ς	PROPN
ejpam-6617	342	6	3	3	NUM
ejpam-6617	342	7	+	+	CCONJ
ejpam-6617	342	8	23.9299	23.9299	NUM
ejpam-6617	342	9	,	,	PUNCT
ejpam-6617	342	10	v.	v.	ADP
ejpam-6617	342	11	rayanki	rayanki	PROPN
ejpam-6617	342	12	et	et	PROPN
ejpam-6617	342	13	al	al	PROPN
ejpam-6617	342	14	.	.	PUNCT
ejpam-6617	342	15	/	/	SYM
ejpam-6617	342	16	eur	eur	PROPN
ejpam-6617	342	17	.	.	PUNCT
ejpam-6617	343	1	j.	j.	PROPN
ejpam-6617	343	2	pure	pure	PROPN
ejpam-6617	343	3	appl	appl	PROPN
ejpam-6617	343	4	.	.	PROPN
ejpam-6617	343	5	math	math	PROPN
ejpam-6617	343	6	,	,	PUNCT
ejpam-6617	343	7	18	18	NUM
ejpam-6617	343	8	(	(	PUNCT
ejpam-6617	343	9	3	3	NUM
ejpam-6617	343	10	)	)	PUNCT
ejpam-6617	343	11	(	(	PUNCT
ejpam-6617	343	12	2025	2025	NUM
ejpam-6617	343	13	)	)	PUNCT
ejpam-6617	343	14	,	,	PUNCT
ejpam-6617	343	15	6617	6617	NUM
ejpam-6617	343	16	22	22	NUM
ejpam-6617	343	17	of	of	ADP
ejpam-6617	343	18	38	38	NUM
ejpam-6617	343	19	ϕu	ϕu	NOUN
ejpam-6617	343	20	(	(	PUNCT
ejpam-6617	343	21	ς	ς	PROPN
ejpam-6617	343	22	,	,	PUNCT
ejpam-6617	343	23	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	343	24	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	343	25	)	)	PUNCT
ejpam-6617	343	26	)	)	PUNCT
ejpam-6617	344	1	=	=	SYM
ejpam-6617	344	2	−κ2(ς	−κ2(ς	NOUN
ejpam-6617	344	3	)	)	PUNCT
ejpam-6617	345	1	+	+	CCONJ
ejpam-6617	345	2	6.5514ς	6.5514ς	NUM
ejpam-6617	345	3	−	−	NOUN
ejpam-6617	345	4	16.3785e	16.3785e	NUM
ejpam-6617	345	5	−	−	NOUN
ejpam-6617	345	6	ς	ς	PROPN
ejpam-6617	345	7	3	3	NUM
ejpam-6617	345	8	+	+	NOUN
ejpam-6617	345	9	22.9299	22.9299	NUM
ejpam-6617	345	10	)	)	PUNCT
ejpam-6617	345	11	,	,	PUNCT
ejpam-6617	345	12	and	and	CCONJ
ejpam-6617	345	13	κ(ς	κ(ς	NUM
ejpam-6617	345	14	)	)	PUNCT
ejpam-6617	345	15	=	=	PUNCT
ejpam-6617	346	1	−ς2	−ς2	PROPN
ejpam-6617	347	1	+	+	CCONJ
ejpam-6617	347	2	ς	ς	PROPN
ejpam-6617	347	3	+	+	CCONJ
ejpam-6617	347	4	1	1	NUM
ejpam-6617	347	5	∈	∈	NOUN
ejpam-6617	347	6	x.	x.	NOUN
ejpam-6617	348	1	the	the	DET
ejpam-6617	348	2	feasible	feasible	ADJ
ejpam-6617	348	3	region	region	NOUN
ejpam-6617	348	4	of	of	ADP
ejpam-6617	348	5	(	(	PUNCT
ejpam-6617	348	6	p-3	p-3	NOUN
ejpam-6617	348	7	)	)	PUNCT
ejpam-6617	348	8	is	be	AUX
ejpam-6617	348	9	φ3	φ3	NOUN
ejpam-6617	348	10	=	=	PUNCT
ejpam-6617	348	11	{	{	PUNCT
ejpam-6617	348	12	κ	κ	NOUN
ejpam-6617	348	13	∈	∈	PROPN
ejpam-6617	348	14	x	x	PUNCT
ejpam-6617	348	15	:	:	PUNCT
ejpam-6617	348	16	−κ(ς)+	−κ(ς)+	PROPN
ejpam-6617	348	17	1.871822ς	1.871822ς	NUM
ejpam-6617	349	1	+6.5514e	+6.5514e	SYM
ejpam-6617	349	2	−	−	PUNCT
ejpam-6617	350	1	ς	ς	PROPN
ejpam-6617	350	2	3−	3−	NUM
ejpam-6617	350	3	5.6154	5.6154	NUM
ejpam-6617	350	4	)	)	PUNCT
ejpam-6617	350	5	≤	≤	NOUN
ejpam-6617	350	6	0,κ(0	0,κ(0	NUM
ejpam-6617	350	7	)	)	PUNCT
ejpam-6617	350	8	=	=	SYM
ejpam-6617	351	1	1,κ(1	1,κ(1	NUM
ejpam-6617	351	2	)	)	PUNCT
ejpam-6617	351	3	=	=	SYM
ejpam-6617	351	4	1	1	NUM
ejpam-6617	351	5	}	}	PUNCT
ejpam-6617	351	6	.	.	PUNCT
ejpam-6617	352	1	note	note	VERB
ejpam-6617	352	2	that	that	SCONJ
ejpam-6617	352	3	κ̄	κ̄	NOUN
ejpam-6617	352	4	=	=	SYM
ejpam-6617	352	5	1	1	NUM
ejpam-6617	352	6	is	be	AUX
ejpam-6617	352	7	a	a	DET
ejpam-6617	352	8	feasible	feasible	ADJ
ejpam-6617	352	9	solution	solution	NOUN
ejpam-6617	352	10	of	of	ADP
ejpam-6617	352	11	(	(	PUNCT
ejpam-6617	352	12	p-3	p-3	NOUN
ejpam-6617	352	13	)	)	PUNCT
ejpam-6617	352	14	and	and	CCONJ
ejpam-6617	352	15	it	it	PRON
ejpam-6617	352	16	can	can	AUX
ejpam-6617	352	17	be	be	AUX
ejpam-6617	352	18	easily	easily	ADV
ejpam-6617	352	19	observe	observe	VERB
ejpam-6617	352	20	that	that	SCONJ
ejpam-6617	352	21	there	there	PRON
ejpam-6617	352	22	is	be	VERB
ejpam-6617	352	23	θ	θ	PROPN
ejpam-6617	352	24	∈	∈	PROPN
ejpam-6617	352	25	r	r	NOUN
ejpam-6617	352	26	and	and	CCONJ
ejpam-6617	352	27	θ̄	θ̄	NOUN
ejpam-6617	352	28	=	=	SYM
ejpam-6617	352	29	0	0	NUM
ejpam-6617	352	30	,	,	PUNCT
ejpam-6617	352	31	such	such	ADJ
ejpam-6617	352	32	that	that	SCONJ
ejpam-6617	352	33	the	the	DET
ejpam-6617	352	34	relations	relation	NOUN
ejpam-6617	352	35	(	(	PUNCT
ejpam-6617	352	36	4	4	NUM
ejpam-6617	352	37	)	)	PUNCT
ejpam-6617	352	38	and	and	CCONJ
ejpam-6617	352	39	(	(	PUNCT
ejpam-6617	352	40	5	5	X
ejpam-6617	352	41	)	)	PUNCT
ejpam-6617	352	42	holds	hold	VERB
ejpam-6617	352	43	for	for	ADP
ejpam-6617	352	44	(	(	PUNCT
ejpam-6617	352	45	p-3	p-3	NOUN
ejpam-6617	352	46	)	)	PUNCT
ejpam-6617	352	47	.	.	PUNCT
ejpam-6617	353	1	also	also	ADV
ejpam-6617	353	2	it	it	PRON
ejpam-6617	353	3	is	be	AUX
ejpam-6617	353	4	observed	observe	VERB
ejpam-6617	353	5	that	that	SCONJ
ejpam-6617	353	6	a2∫	a2∫	NOUN
ejpam-6617	353	7	a1	a1	NOUN
ejpam-6617	353	8	(	(	PUNCT
ejpam-6617	353	9	ϕl	ϕl	PROPN
ejpam-6617	354	1	+	+	NOUN
ejpam-6617	354	2	ϕu	ϕu	NOUN
ejpam-6617	354	3	)	)	PUNCT
ejpam-6617	354	4	(	(	PUNCT
ejpam-6617	354	5	ς	ς	PROPN
ejpam-6617	354	6	,	,	PUNCT
ejpam-6617	354	7	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	354	8	a1+κ(ς))dς	a1+κ(ς))dς	PROPN
ejpam-6617	354	9	is	be	AUX
ejpam-6617	354	10	pseudo	pseudo	NOUN
ejpam-6617	354	11	-	-	NOUN
ejpam-6617	354	12	convex	convex	NOUN
ejpam-6617	354	13	at	at	ADP
ejpam-6617	354	14	κ̄	κ̄	NOUN
ejpam-6617	354	15	on	on	ADP
ejpam-6617	354	16	φ3	φ3	NOUN
ejpam-6617	354	17	and	and	CCONJ
ejpam-6617	354	18	a2∫	a2∫	NOUN
ejpam-6617	354	19	a1	a1	NOUN
ejpam-6617	354	20	θ̄(ς)h(ς	θ̄(ς)h(ς	NOUN
ejpam-6617	354	21	,	,	PUNCT
ejpam-6617	354	22	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	354	23	a+κ̄)dς	a+κ̄)dς	PROPN
ejpam-6617	354	24	is	be	AUX
ejpam-6617	354	25	quasi	quasi	ADJ
ejpam-6617	354	26	-	-	VERB
ejpam-6617	354	27	convex	convex	ADJ
ejpam-6617	354	28	at	at	ADP
ejpam-6617	354	29	κ̄	κ̄	NOUN
ejpam-6617	354	30	on	on	ADP
ejpam-6617	354	31	φ3	φ3	NOUN
ejpam-6617	354	32	.	.	PUNCT
ejpam-6617	355	1	since	since	SCONJ
ejpam-6617	355	2	all	all	DET
ejpam-6617	355	3	the	the	DET
ejpam-6617	355	4	observations	observation	NOUN
ejpam-6617	355	5	of	of	ADP
ejpam-6617	355	6	theorem	theorem	ADJ
ejpam-6617	355	7	3	3	NUM
ejpam-6617	355	8	are	be	AUX
ejpam-6617	355	9	satisfied	satisfied	ADJ
ejpam-6617	355	10	,	,	PUNCT
ejpam-6617	355	11	then	then	ADV
ejpam-6617	355	12	(	(	PUNCT
ejpam-6617	355	13	θ̄	θ̄	X
ejpam-6617	355	14	=	=	SYM
ejpam-6617	355	15	0	0	NUM
ejpam-6617	355	16	,	,	PUNCT
ejpam-6617	355	17	κ̄	κ̄	NOUN
ejpam-6617	355	18	=	=	SYM
ejpam-6617	355	19	1	1	X
ejpam-6617	355	20	)	)	PUNCT
ejpam-6617	355	21	is	be	AUX
ejpam-6617	355	22	a	a	DET
ejpam-6617	355	23	lu	lu	NOUN
ejpam-6617	355	24	optimal	optimal	ADJ
ejpam-6617	355	25	solution	solution	NOUN
ejpam-6617	355	26	(	(	PUNCT
ejpam-6617	355	27	p-3	p-3	NOUN
ejpam-6617	355	28	)	)	PUNCT
ejpam-6617	355	29	.	.	PUNCT
ejpam-6617	356	1	4	4	X
ejpam-6617	356	2	.	.	X
ejpam-6617	356	3	wolfe	wolfe	PROPN
ejpam-6617	356	4	-	-	PUNCT
ejpam-6617	356	5	type	type	NOUN
ejpam-6617	356	6	dual	dual	ADJ
ejpam-6617	356	7	model	model	NOUN
ejpam-6617	356	8	we	we	PRON
ejpam-6617	356	9	are	be	AUX
ejpam-6617	356	10	concerned	concerned	ADJ
ejpam-6617	356	11	in	in	ADP
ejpam-6617	356	12	this	this	DET
ejpam-6617	356	13	part	part	NOUN
ejpam-6617	356	14	with	with	ADP
ejpam-6617	356	15	the	the	DET
ejpam-6617	356	16	wolfe	wolfe	NOUN
ejpam-6617	356	17	-	-	PUNCT
ejpam-6617	356	18	type	type	NOUN
ejpam-6617	356	19	dual	dual	ADJ
ejpam-6617	356	20	problem	problem	NOUN
ejpam-6617	356	21	(	(	PUNCT
ejpam-6617	356	22	wd	wd	PROPN
ejpam-6617	356	23	)	)	PUNCT
ejpam-6617	356	24	with	with	ADP
ejpam-6617	356	25	the	the	DET
ejpam-6617	356	26	cf	cf	NOUN
ejpam-6617	356	27	derivative	derivative	ADJ
ejpam-6617	356	28	operator	operator	NOUN
ejpam-6617	356	29	in	in	ADP
ejpam-6617	356	30	relation	relation	NOUN
ejpam-6617	356	31	to	to	ADP
ejpam-6617	356	32	the	the	DET
ejpam-6617	356	33	primary	primary	ADJ
ejpam-6617	356	34	problem	problem	NOUN
ejpam-6617	356	35	(	(	PUNCT
ejpam-6617	356	36	p	p	NOUN
ejpam-6617	356	37	)	)	PUNCT
ejpam-6617	356	38	,	,	PUNCT
ejpam-6617	356	39	it	it	PRON
ejpam-6617	356	40	is	be	AUX
ejpam-6617	356	41	as	as	SCONJ
ejpam-6617	356	42	follows	follow	VERB
ejpam-6617	356	43	:	:	PUNCT
ejpam-6617	356	44	(	(	PUNCT
ejpam-6617	356	45	wd	wd	PROPN
ejpam-6617	356	46	)	)	PUNCT
ejpam-6617	356	47	maxg(ε	maxg(ε	NOUN
ejpam-6617	356	48	,	,	PUNCT
ejpam-6617	356	49	θ̄	θ̄	ADJ
ejpam-6617	356	50	)	)	PUNCT
ejpam-6617	356	51	=	=	NOUN
ejpam-6617	356	52	a2∫	a2∫	X
ejpam-6617	356	53	a1	a1	NOUN
ejpam-6617	356	54	[	[	PUNCT
ejpam-6617	356	55	[	[	PUNCT
ejpam-6617	356	56	ϕl(ς	ϕl(ς	X
ejpam-6617	356	57	,	,	PUNCT
ejpam-6617	356	58	ε	ε	PROPN
ejpam-6617	356	59	,	,	PUNCT
ejpam-6617	356	60	cfdθ•	cfdθ•	PROPN
ejpam-6617	356	61	a1+ε	a1+ε	PROPN
ejpam-6617	356	62	)	)	PUNCT
ejpam-6617	356	63	,	,	PUNCT
ejpam-6617	356	64	ϕ	ϕ	PROPN
ejpam-6617	356	65	u	u	X
ejpam-6617	356	66	(	(	PUNCT
ejpam-6617	356	67	ς	ς	PROPN
ejpam-6617	356	68	,	,	PUNCT
ejpam-6617	356	69	ε	ε	PROPN
ejpam-6617	356	70	,	,	PUNCT
ejpam-6617	356	71	cfdθ•	cfdθ•	PROPN
ejpam-6617	356	72	a1+ε	a1+ε	PROPN
ejpam-6617	356	73	)	)	PUNCT
ejpam-6617	356	74	]	]	PUNCT
ejpam-6617	357	1	+	+	CCONJ
ejpam-6617	357	2	(	(	PUNCT
ejpam-6617	357	3	θ̄)th(ς	θ̄)th(ς	PROPN
ejpam-6617	357	4	,	,	PUNCT
ejpam-6617	357	5	ε	ε	PROPN
ejpam-6617	357	6	,	,	PUNCT
ejpam-6617	357	7	cfdθ•	cfdθ•	PROPN
ejpam-6617	357	8	a1+ε(ς	a1+ε(ς	X
ejpam-6617	357	9	)	)	PUNCT
ejpam-6617	357	10	)	)	PUNCT
ejpam-6617	357	11	]	]	PUNCT
ejpam-6617	358	1	dς	dς	PROPN
ejpam-6617	358	2	,	,	PUNCT
ejpam-6617	358	3	subject	subject	ADJ
ejpam-6617	358	4	to	to	ADP
ejpam-6617	358	5	,	,	PUNCT
ejpam-6617	358	6	ε(a1	ε(a1	X
ejpam-6617	358	7	)	)	PUNCT
ejpam-6617	358	8	=	=	SYM
ejpam-6617	358	9	α	α	NOUN
ejpam-6617	358	10	,	,	PUNCT
ejpam-6617	358	11	ε(a2	ε(a2	NOUN
ejpam-6617	358	12	)	)	PUNCT
ejpam-6617	358	13	=	=	SYM
ejpam-6617	358	14	β	β	X
ejpam-6617	358	15	,	,	PUNCT
ejpam-6617	358	16	(	(	PUNCT
ejpam-6617	358	17	13	13	NUM
ejpam-6617	358	18	)	)	PUNCT
ejpam-6617	358	19	ϕl	ϕl	INTJ
ejpam-6617	358	20	ε	ε	PROPN
ejpam-6617	358	21	(	(	PUNCT
ejpam-6617	358	22	ς	ς	PROPN
ejpam-6617	358	23	,	,	PUNCT
ejpam-6617	358	24	ε	ε	PROPN
ejpam-6617	358	25	,	,	PUNCT
ejpam-6617	358	26	cfdθ•	cfdθ•	PROPN
ejpam-6617	358	27	a1+ε	a1+ε	PROPN
ejpam-6617	358	28	)	)	PUNCT
ejpam-6617	359	1	+	+	CCONJ
ejpam-6617	359	2	ϕu	ϕu	PROPN
ejpam-6617	359	3	ε	ε	PROPN
ejpam-6617	359	4	(	(	PUNCT
ejpam-6617	359	5	ς	ς	PROPN
ejpam-6617	359	6	,	,	PUNCT
ejpam-6617	359	7	ε	ε	PROPN
ejpam-6617	359	8	,	,	PUNCT
ejpam-6617	359	9	cfdθ•	cfdθ•	PROPN
ejpam-6617	359	10	a1+ε	a1+ε	PROPN
ejpam-6617	359	11	)	)	PUNCT
ejpam-6617	359	12	+	+	CCONJ
ejpam-6617	359	13	(	(	PUNCT
ejpam-6617	359	14	θ̄)t	θ̄)t	NOUN
ejpam-6617	359	15	(	(	PUNCT
ejpam-6617	359	16	ς)hε(ς	ς)hε(ς	PROPN
ejpam-6617	359	17	,	,	PUNCT
ejpam-6617	359	18	ε	ε	PROPN
ejpam-6617	359	19	,	,	PUNCT
ejpam-6617	359	20	cfdθ•	cfdθ•	PROPN
ejpam-6617	359	21	a1+ε(ς	a1+ε(ς	X
ejpam-6617	359	22	)	)	PUNCT
ejpam-6617	359	23	)	)	PUNCT
ejpam-6617	360	1	=	=	PUNCT
ejpam-6617	360	2	−cfdθ•	−cfdθ•	NOUN
ejpam-6617	360	3	a2−	a2−	PROPN
ejpam-6617	360	4	{	{	PUNCT
ejpam-6617	360	5	ϕl	ϕl	PROPN
ejpam-6617	360	6	cfdθ•	cfdθ•	PROPN
ejpam-6617	360	7	a1	a1	PROPN
ejpam-6617	360	8	+	+	X
ejpam-6617	360	9	ε(ς	ε(ς	NOUN
ejpam-6617	360	10	)	)	PUNCT
ejpam-6617	360	11	(	(	PUNCT
ejpam-6617	360	12	ς	ς	PROPN
ejpam-6617	360	13	,	,	PUNCT
ejpam-6617	360	14	ε	ε	PROPN
ejpam-6617	360	15	,	,	PUNCT
ejpam-6617	360	16	cfdθ•	cfdθ•	PROPN
ejpam-6617	360	17	a1+ε	a1+ε	PROPN
ejpam-6617	360	18	)	)	PUNCT
ejpam-6617	360	19	+	+	PROPN
ejpam-6617	360	20	ϕu	ϕu	PROPN
ejpam-6617	360	21	cfdθ•	cfdθ•	PROPN
ejpam-6617	360	22	a1	a1	PROPN
ejpam-6617	360	23	+	+	X
ejpam-6617	360	24	ε(ς	ε(ς	NOUN
ejpam-6617	360	25	)	)	PUNCT
ejpam-6617	360	26	(	(	PUNCT
ejpam-6617	360	27	ς	ς	PROPN
ejpam-6617	360	28	,	,	PUNCT
ejpam-6617	360	29	ε	ε	PROPN
ejpam-6617	360	30	,	,	PUNCT
ejpam-6617	360	31	cfdθ•	cfdθ•	PROPN
ejpam-6617	360	32	a1+ε	a1+ε	PROPN
ejpam-6617	360	33	)	)	PUNCT
ejpam-6617	360	34	+	+	PROPN
ejpam-6617	360	35	(	(	PUNCT
ejpam-6617	360	36	θ̄)t	θ̄)t	PROPN
ejpam-6617	360	37	(	(	PUNCT
ejpam-6617	360	38	ς)hcfdθ•	ς)hcfdθ•	NOUN
ejpam-6617	360	39	a1	a1	NOUN
ejpam-6617	360	40	+	+	CCONJ
ejpam-6617	360	41	ε(ς)(ς	ε(ς)(ς	PROPN
ejpam-6617	360	42	,	,	PUNCT
ejpam-6617	360	43	ε	ε	PROPN
ejpam-6617	360	44	,	,	PUNCT
ejpam-6617	360	45	cfdθ•	cfdθ•	PROPN
ejpam-6617	360	46	a1+ε(ς	a1+ε(ς	X
ejpam-6617	360	47	)	)	PUNCT
ejpam-6617	360	48	)	)	PUNCT
ejpam-6617	360	49	}	}	PUNCT
ejpam-6617	360	50	,	,	PUNCT
ejpam-6617	360	51	(	(	PUNCT
ejpam-6617	360	52	14	14	NUM
ejpam-6617	360	53	)	)	PUNCT
ejpam-6617	360	54	a2∫	a2∫	NOUN
ejpam-6617	360	55	a1	a1	NOUN
ejpam-6617	360	56	(	(	PUNCT
ejpam-6617	360	57	θ̄)t	θ̄)t	NOUN
ejpam-6617	360	58	(	(	PUNCT
ejpam-6617	360	59	ς)h(ς	ς)h(ς	X
ejpam-6617	360	60	,	,	PUNCT
ejpam-6617	360	61	ε(ς),cfdθ•	ε(ς),cfdθ•	PROPN
ejpam-6617	360	62	a1+ε(ς))dς	a1+ε(ς))dς	PROPN
ejpam-6617	360	63	≤	≤	ADV
ejpam-6617	360	64	0	0	NUM
ejpam-6617	360	65	,	,	PUNCT
ejpam-6617	360	66	(	(	PUNCT
ejpam-6617	360	67	15	15	NUM
ejpam-6617	360	68	)	)	PUNCT
ejpam-6617	360	69	θ̄(ξ	θ̄(ξ	NOUN
ejpam-6617	360	70	)	)	PUNCT
ejpam-6617	360	71	≥	≥	NOUN
ejpam-6617	360	72	0	0	NUM
ejpam-6617	360	73	,	,	PUNCT
ejpam-6617	360	74	ς	ς	PROPN
ejpam-6617	360	75	∈	∈	PROPN
ejpam-6617	360	76	ℑ.	ℑ.	PROPN
ejpam-6617	360	77	(	(	PUNCT
ejpam-6617	360	78	16	16	NUM
ejpam-6617	360	79	)	)	PUNCT
ejpam-6617	360	80	here	here	ADV
ejpam-6617	360	81	,	,	PUNCT
ejpam-6617	360	82	ε(ς	ε(ς	NOUN
ejpam-6617	360	83	)	)	PUNCT
ejpam-6617	360	84	signifies	signify	VERB
ejpam-6617	360	85	an	an	DET
ejpam-6617	360	86	n	n	ADV
ejpam-6617	360	87	-	-	PUNCT
ejpam-6617	360	88	dimensional	dimensional	ADJ
ejpam-6617	360	89	function	function	NOUN
ejpam-6617	360	90	,	,	PUNCT
ejpam-6617	360	91	θ̄(ς	θ̄(ς	NOUN
ejpam-6617	360	92	)	)	PUNCT
ejpam-6617	360	93	denotes	denote	VERB
ejpam-6617	360	94	an	an	DET
ejpam-6617	360	95	m	m	ADJ
ejpam-6617	360	96	-	-	ADJ
ejpam-6617	360	97	dimensional	dimensional	ADJ
ejpam-6617	360	98	function	function	NOUN
ejpam-6617	360	99	.	.	PUNCT
ejpam-6617	361	1	let	let	VERB
ejpam-6617	361	2	θ(ε̄	θ(ε̄	NOUN
ejpam-6617	361	3	)	)	PUNCT
ejpam-6617	361	4	=	=	SYM
ejpam-6617	361	5	{	{	PUNCT
ejpam-6617	361	6	(	(	PUNCT
ejpam-6617	361	7	θ̄	θ̄	ADJ
ejpam-6617	361	8	,	,	PUNCT
ejpam-6617	361	9	ε̄	ε̄	NOUN
ejpam-6617	361	10	)	)	PUNCT
ejpam-6617	361	11	:	:	PUNCT
ejpam-6617	361	12	θ̄	θ̄	PROPN
ejpam-6617	361	13	∈	∈	PROPN
ejpam-6617	361	14	rm	rm	PROPN
ejpam-6617	361	15	,	,	PUNCT
ejpam-6617	361	16	ε̄	ε̄	ADJ
ejpam-6617	361	17	∈	∈	PROPN
ejpam-6617	361	18	x	x	NOUN
ejpam-6617	361	19	:	:	PUNCT
ejpam-6617	361	20	satisfying	satisfy	VERB
ejpam-6617	361	21	the	the	DET
ejpam-6617	361	22	constraints	constraint	NOUN
ejpam-6617	361	23	of	of	ADP
ejpam-6617	361	24	(	(	PUNCT
ejpam-6617	361	25	wd	wd	PROPN
ejpam-6617	361	26	)	)	PUNCT
ejpam-6617	361	27	,	,	PUNCT
ejpam-6617	361	28	forall	forall	VERB
ejpam-6617	361	29	ς	ς	PROPN
ejpam-6617	361	30	∈	∈	PROPN
ejpam-6617	361	31	ℑ	ℑ	PROPN
ejpam-6617	361	32	}	}	PUNCT
ejpam-6617	361	33	be	be	VERB
ejpam-6617	361	34	the	the	DET
ejpam-6617	361	35	collection	collection	NOUN
ejpam-6617	361	36	of	of	ADP
ejpam-6617	361	37	all	all	DET
ejpam-6617	361	38	feasible	feasible	ADJ
ejpam-6617	361	39	points	point	NOUN
ejpam-6617	361	40	to	to	ADP
ejpam-6617	361	41	(	(	PUNCT
ejpam-6617	361	42	wd	wd	PROPN
ejpam-6617	361	43	)	)	PUNCT
ejpam-6617	361	44	.	.	PUNCT
ejpam-6617	362	1	v.	v.	CCONJ
ejpam-6617	362	2	rayanki	rayanki	PROPN
ejpam-6617	362	3	et	et	PROPN
ejpam-6617	362	4	al	al	PROPN
ejpam-6617	362	5	.	.	PUNCT
ejpam-6617	362	6	/	/	SYM
ejpam-6617	362	7	eur	eur	PROPN
ejpam-6617	362	8	.	.	PUNCT
ejpam-6617	363	1	j.	j.	PROPN
ejpam-6617	363	2	pure	pure	PROPN
ejpam-6617	363	3	appl	appl	PROPN
ejpam-6617	363	4	.	.	PROPN
ejpam-6617	363	5	math	math	PROPN
ejpam-6617	363	6	,	,	PUNCT
ejpam-6617	363	7	18	18	NUM
ejpam-6617	363	8	(	(	PUNCT
ejpam-6617	363	9	3	3	NUM
ejpam-6617	363	10	)	)	PUNCT
ejpam-6617	363	11	(	(	PUNCT
ejpam-6617	363	12	2025	2025	NUM
ejpam-6617	363	13	)	)	PUNCT
ejpam-6617	363	14	,	,	PUNCT
ejpam-6617	363	15	6617	6617	NUM
ejpam-6617	363	16	23	23	NUM
ejpam-6617	363	17	of	of	ADP
ejpam-6617	363	18	38	38	NUM
ejpam-6617	363	19	definition	definition	NOUN
ejpam-6617	363	20	13	13	NUM
ejpam-6617	363	21	.	.	PUNCT
ejpam-6617	364	1	a	a	DET
ejpam-6617	364	2	feasible	feasible	ADJ
ejpam-6617	364	3	point	point	NOUN
ejpam-6617	364	4	(	(	PUNCT
ejpam-6617	364	5	ε̄	ε̄	ADJ
ejpam-6617	364	6	,	,	PUNCT
ejpam-6617	364	7	θ̄	θ̄	PRON
ejpam-6617	364	8	)	)	PUNCT
ejpam-6617	364	9	is	be	AUX
ejpam-6617	364	10	stated	state	VERB
ejpam-6617	364	11	to	to	PART
ejpam-6617	364	12	be	be	AUX
ejpam-6617	364	13	an	an	DET
ejpam-6617	364	14	lu	lu	NOUN
ejpam-6617	364	15	optimal	optimal	ADJ
ejpam-6617	364	16	point	point	NOUN
ejpam-6617	364	17	of	of	ADP
ejpam-6617	364	18	a	a	DET
ejpam-6617	364	19	maximum	maximum	ADJ
ejpam-6617	364	20	type	type	NOUN
ejpam-6617	364	21	for	for	ADP
ejpam-6617	364	22	(	(	PUNCT
ejpam-6617	364	23	wd	wd	PROPN
ejpam-6617	364	24	)	)	PUNCT
ejpam-6617	364	25	,	,	PUNCT
ejpam-6617	364	26	if	if	SCONJ
ejpam-6617	364	27	there	there	PRON
ejpam-6617	364	28	is	be	VERB
ejpam-6617	364	29	no	no	DET
ejpam-6617	364	30	feasible	feasible	ADJ
ejpam-6617	364	31	point	point	NOUN
ejpam-6617	364	32	(	(	PUNCT
ejpam-6617	364	33	ε	ε	PROPN
ejpam-6617	364	34	,	,	PUNCT
ejpam-6617	364	35	θ	θ	PROPN
ejpam-6617	364	36	)	)	PUNCT
ejpam-6617	364	37	,	,	PUNCT
ejpam-6617	364	38	such	such	ADJ
ejpam-6617	364	39	that	that	X
ejpam-6617	364	40	a2∫	a2∫	NOUN
ejpam-6617	364	41	a1	a1	NOUN
ejpam-6617	364	42	ϕl(ς	ϕl(ς	ADJ
ejpam-6617	364	43	,	,	PUNCT
ejpam-6617	364	44	ε̄,cfdθ•	ε̄,cfdθ•	PROPN
ejpam-6617	364	45	a+ε̄)dς	a+ε̄)dς	PROPN
ejpam-6617	364	46	,	,	PUNCT
ejpam-6617	364	47	a2∫	a2∫	X
ejpam-6617	364	48	a1	a1	VERB
ejpam-6617	364	49	ϕu	ϕu	X
ejpam-6617	364	50	(	(	PUNCT
ejpam-6617	364	51	ς	ς	PROPN
ejpam-6617	364	52	,	,	PUNCT
ejpam-6617	364	53	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	364	54	a1+ε̄)dθ	a1+ε̄)dθ	NOUN
ejpam-6617	364	55	•	•	NOUN
ejpam-6617	364	56	+	+	PROPN
ejpam-6617	364	57	a2∫	a2∫	NOUN
ejpam-6617	364	58	a1	a1	NOUN
ejpam-6617	364	59	(	(	PUNCT
ejpam-6617	364	60	θ̄)th(ς	θ̄)th(ς	PROPN
ejpam-6617	364	61	,	,	PUNCT
ejpam-6617	364	62	ε̄,cfdθ•	ε̄,cfdθ•	PROPN
ejpam-6617	364	63	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	364	64	≺lu	≺lu	VERB
ejpam-6617	364	65			NOUN
ejpam-6617	364	66	a2∫	a2∫	NOUN
ejpam-6617	364	67	a1	a1	NOUN
ejpam-6617	364	68	ϕl(ς	ϕl(ς	X
ejpam-6617	364	69	,	,	PUNCT
ejpam-6617	364	70	ε	ε	PROPN
ejpam-6617	364	71	,	,	PUNCT
ejpam-6617	364	72	cfdθ•	cfdθ•	PROPN
ejpam-6617	364	73	a1+ε)dς	a1+ε)dς	NOUN
ejpam-6617	364	74	,	,	PUNCT
ejpam-6617	364	75	a2∫	a2∫	X
ejpam-6617	364	76	a1	a1	VERB
ejpam-6617	364	77	ϕu	ϕu	X
ejpam-6617	364	78	(	(	PUNCT
ejpam-6617	364	79	ς	ς	PROPN
ejpam-6617	364	80	,	,	PUNCT
ejpam-6617	364	81	ν	ν	NOUN
ejpam-6617	364	82	,	,	PUNCT
ejpam-6617	364	83	cfdθ•	cfdθ•	PROPN
ejpam-6617	364	84	a1+ε)dς	a1+ε)dς	PRON
ejpam-6617	364	85			NOUN
ejpam-6617	364	86	+	+	CCONJ
ejpam-6617	364	87	a2∫	a2∫	NOUN
ejpam-6617	364	88	a1	a1	NOUN
ejpam-6617	364	89	(	(	PUNCT
ejpam-6617	364	90	θ̄)th(ς	θ̄)th(ς	PROPN
ejpam-6617	364	91	,	,	PUNCT
ejpam-6617	364	92	ε	ε	PROPN
ejpam-6617	364	93	,	,	PUNCT
ejpam-6617	364	94	cfdθ•	cfdθ•	PROPN
ejpam-6617	364	95	a1+ε)dς	a1+ε)dς	PROPN
ejpam-6617	364	96	.	.	PUNCT
ejpam-6617	365	1	the	the	DET
ejpam-6617	365	2	weak	weak	ADJ
ejpam-6617	365	3	,	,	PUNCT
ejpam-6617	365	4	strong	strong	ADJ
ejpam-6617	365	5	,	,	PUNCT
ejpam-6617	365	6	and	and	CCONJ
ejpam-6617	365	7	strict	strict	ADJ
ejpam-6617	365	8	converse	converse	NOUN
ejpam-6617	365	9	duality	duality	NOUN
ejpam-6617	365	10	theorems	theorem	NOUN
ejpam-6617	365	11	are	be	AUX
ejpam-6617	365	12	studied	study	VERB
ejpam-6617	365	13	for	for	ADP
ejpam-6617	365	14	(	(	PUNCT
ejpam-6617	365	15	wd	wd	PROPN
ejpam-6617	365	16	)	)	PUNCT
ejpam-6617	365	17	from	from	ADP
ejpam-6617	365	18	the	the	DET
ejpam-6617	365	19	standpoint	standpoint	NOUN
ejpam-6617	365	20	of	of	ADP
ejpam-6617	365	21	the	the	DET
ejpam-6617	365	22	cf	cf	NOUN
ejpam-6617	365	23	fractional	fractional	ADJ
ejpam-6617	365	24	derivative	derivative	ADJ
ejpam-6617	365	25	operator	operator	NOUN
ejpam-6617	365	26	:	:	PUNCT
ejpam-6617	365	27	theorem	theorem	NOUN
ejpam-6617	365	28	4	4	NUM
ejpam-6617	365	29	(	(	PUNCT
ejpam-6617	365	30	weak	weak	ADJ
ejpam-6617	365	31	duality	duality	NOUN
ejpam-6617	365	32	)	)	PUNCT
ejpam-6617	365	33	.	.	PUNCT
ejpam-6617	366	1	let	let	AUX
ejpam-6617	366	2	(	(	PUNCT
ejpam-6617	366	3	θ̄	θ̄	ADJ
ejpam-6617	366	4	,	,	PUNCT
ejpam-6617	366	5	κ̄	κ̄	NOUN
ejpam-6617	366	6	)	)	PUNCT
ejpam-6617	366	7	and	and	CCONJ
ejpam-6617	366	8	(	(	PUNCT
ejpam-6617	366	9	θ̄	θ̄	ADJ
ejpam-6617	366	10	,	,	PUNCT
ejpam-6617	366	11	ε̄	ε̄	NOUN
ejpam-6617	366	12	)	)	PUNCT
ejpam-6617	366	13	be	be	VERB
ejpam-6617	366	14	the	the	DET
ejpam-6617	366	15	feasible	feasible	ADJ
ejpam-6617	366	16	points	point	NOUN
ejpam-6617	366	17	for	for	ADP
ejpam-6617	366	18	(	(	PUNCT
ejpam-6617	366	19	p	p	NOUN
ejpam-6617	366	20	)	)	PUNCT
ejpam-6617	366	21	and	and	CCONJ
ejpam-6617	366	22	(	(	PUNCT
ejpam-6617	366	23	wd	wd	PROPN
ejpam-6617	366	24	)	)	PUNCT
ejpam-6617	366	25	,	,	PUNCT
ejpam-6617	366	26	respectively	respectively	ADV
ejpam-6617	366	27	.	.	PUNCT
ejpam-6617	367	1	suppose	suppose	VERB
ejpam-6617	367	2	that	that	SCONJ
ejpam-6617	367	3	,	,	PUNCT
ejpam-6617	367	4	(	(	PUNCT
ejpam-6617	367	5	θ̄)t	θ̄)t	X
ejpam-6617	367	6	>	>	X
ejpam-6617	367	7	0	0	PUNCT
ejpam-6617	367	8	and	and	CCONJ
ejpam-6617	367	9	the	the	DET
ejpam-6617	367	10	functional	functional	ADJ
ejpam-6617	367	11	(	(	PUNCT
ejpam-6617	367	12	ϕl	ϕl	INTJ
ejpam-6617	367	13	+	+	NOUN
ejpam-6617	367	14	ϕu	ϕu	PROPN
ejpam-6617	368	1	+	+	CCONJ
ejpam-6617	368	2	(	(	PUNCT
ejpam-6617	368	3	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	368	4	,	,	PUNCT
ejpam-6617	368	5	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	368	6	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	368	7	)	)	PUNCT
ejpam-6617	368	8	is	be	AUX
ejpam-6617	368	9	invex	invex	NOUN
ejpam-6617	368	10	at	at	ADP
ejpam-6617	368	11	ε̄	ε̄	ADJ
ejpam-6617	368	12	on	on	ADP
ejpam-6617	368	13	x	x	X
ejpam-6617	368	14	,	,	PUNCT
ejpam-6617	368	15	then	then	ADV
ejpam-6617	368	16	the	the	DET
ejpam-6617	368	17	following	follow	VERB
ejpam-6617	368	18	ca	can	AUX
ejpam-6617	368	19	n’t	not	PART
ejpam-6617	368	20	hold	hold	ADJ
ejpam-6617	368	21	a2∫	a2∫	PUNCT
ejpam-6617	368	22	a1	a1	NOUN
ejpam-6617	368	23	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	368	24	,	,	PUNCT
ejpam-6617	368	25	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	368	26	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	368	27	,	,	PUNCT
ejpam-6617	368	28	a2∫	a2∫	X
ejpam-6617	368	29	a1	a1	VERB
ejpam-6617	368	30	ϕu	ϕu	X
ejpam-6617	368	31	(	(	PUNCT
ejpam-6617	368	32	ς	ς	PROPN
ejpam-6617	368	33	,	,	PUNCT
ejpam-6617	368	34	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	368	35	a1+κ̄)dς	a1+κ̄)dς	PRON
ejpam-6617	368	36			NOUN
ejpam-6617	368	37	≺lu	≺lu	VERB
ejpam-6617	368	38			NOUN
ejpam-6617	368	39	a2∫	a2∫	NOUN
ejpam-6617	368	40	a1	a1	NOUN
ejpam-6617	368	41	(	(	PUNCT
ejpam-6617	368	42	ϕl	ϕl	PROPN
ejpam-6617	368	43	+	+	PROPN
ejpam-6617	368	44	(	(	PUNCT
ejpam-6617	368	45	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	368	46	,	,	PUNCT
ejpam-6617	368	47	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	368	48	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	368	49	,	,	PUNCT
ejpam-6617	368	50	a2∫	a2∫	X
ejpam-6617	368	51	a1	a1	NOUN
ejpam-6617	368	52	(	(	PUNCT
ejpam-6617	368	53	ϕu	ϕu	NOUN
ejpam-6617	368	54	+	+	CCONJ
ejpam-6617	368	55	(	(	PUNCT
ejpam-6617	368	56	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	368	57	,	,	PUNCT
ejpam-6617	368	58	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	368	59	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	368	60			NOUN
ejpam-6617	368	61	.	.	PUNCT
ejpam-6617	369	1	proof	proof	NOUN
ejpam-6617	369	2	.	.	PUNCT
ejpam-6617	370	1	assume	assume	VERB
ejpam-6617	370	2	,	,	PUNCT
ejpam-6617	370	3	contrary	contrary	ADJ
ejpam-6617	370	4	to	to	ADP
ejpam-6617	370	5	the	the	DET
ejpam-6617	370	6	outcome,	outcome,	NOUN
ejpam-6617	370	7	a2∫	a2∫	NOUN
ejpam-6617	370	8	a1	a1	NOUN
ejpam-6617	370	9	ϕl(ς	ϕl(ς	PRON
ejpam-6617	370	10	,	,	PUNCT
ejpam-6617	370	11	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	370	12	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	370	13	,	,	PUNCT
ejpam-6617	370	14	a2∫	a2∫	X
ejpam-6617	370	15	a1	a1	VERB
ejpam-6617	370	16	ϕu	ϕu	X
ejpam-6617	370	17	(	(	PUNCT
ejpam-6617	370	18	ς	ς	PROPN
ejpam-6617	370	19	,	,	PUNCT
ejpam-6617	370	20	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	370	21	a1+κ̄)dς	a1+κ̄)dς	PRON
ejpam-6617	370	22			NOUN
ejpam-6617	370	23	≺lu	≺lu	VERB
ejpam-6617	370	24			NOUN
ejpam-6617	370	25	a2∫	a2∫	NOUN
ejpam-6617	370	26	a1	a1	NOUN
ejpam-6617	370	27	(	(	PUNCT
ejpam-6617	370	28	ϕl	ϕl	PROPN
ejpam-6617	370	29	+	+	PROPN
ejpam-6617	370	30	(	(	PUNCT
ejpam-6617	370	31	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	370	32	,	,	PUNCT
ejpam-6617	370	33	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	370	34	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	370	35	,	,	PUNCT
ejpam-6617	370	36	a2∫	a2∫	X
ejpam-6617	370	37	a1	a1	NOUN
ejpam-6617	370	38	(	(	PUNCT
ejpam-6617	370	39	ϕu	ϕu	NOUN
ejpam-6617	370	40	+	+	CCONJ
ejpam-6617	370	41	(	(	PUNCT
ejpam-6617	370	42	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	370	43	,	,	PUNCT
ejpam-6617	370	44	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	370	45	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	370	46			NOUN
ejpam-6617	370	47	.	.	PUNCT
ejpam-6617	371	1	from	from	ADP
ejpam-6617	371	2	(	(	PUNCT
ejpam-6617	371	3	p	p	NOUN
ejpam-6617	371	4	)	)	PUNCT
ejpam-6617	371	5	,	,	PUNCT
ejpam-6617	371	6	h(ς	h(ς	PROPN
ejpam-6617	371	7	,	,	PUNCT
ejpam-6617	371	8	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	371	9	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	371	10	)	)	PUNCT
ejpam-6617	371	11	)	)	PUNCT
ejpam-6617	371	12	≤	≤	NUM
ejpam-6617	371	13	0	0	NUM
ejpam-6617	372	1	and	and	CCONJ
ejpam-6617	372	2	h	h	NOUN
ejpam-6617	372	3	is	be	AUX
ejpam-6617	372	4	continuously	continuously	ADV
ejpam-6617	372	5	differential	differential	ADJ
ejpam-6617	372	6	function	function	NOUN
ejpam-6617	372	7	.	.	PUNCT
ejpam-6617	373	1	moreover	moreover	ADV
ejpam-6617	373	2	(	(	PUNCT
ejpam-6617	373	3	θ̄)t	θ̄)t	NOUN
ejpam-6617	373	4	≥	≥	NUM
ejpam-6617	373	5	0	0	NUM
ejpam-6617	373	6	.	.	PUNCT
ejpam-6617	374	1	then	then	ADV
ejpam-6617	374	2	,	,	PUNCT
ejpam-6617	374	3	it	it	PRON
ejpam-6617	374	4	follows	follow	VERB
ejpam-6617	374	5	that	that	NUM
ejpam-6617	374	6	a2∫	a2∫	NOUN
ejpam-6617	374	7	a1	a1	NOUN
ejpam-6617	374	8	(	(	PUNCT
ejpam-6617	374	9	ϕl	ϕl	PROPN
ejpam-6617	374	10	+	+	X
ejpam-6617	374	11	(	(	PUNCT
ejpam-6617	374	12	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	374	13	,	,	PUNCT
ejpam-6617	374	14	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	374	15	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	374	16	<	<	X
ejpam-6617	374	17	a2∫	a2∫	NOUN
ejpam-6617	374	18	a1	a1	NOUN
ejpam-6617	374	19	(	(	PUNCT
ejpam-6617	374	20	ϕl	ϕl	PROPN
ejpam-6617	374	21	+	+	PROPN
ejpam-6617	374	22	(	(	PUNCT
ejpam-6617	374	23	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	374	24	,	,	PUNCT
ejpam-6617	374	25	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	374	26	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	374	27	a2∫	a2∫	VERB
ejpam-6617	374	28	a1	a1	NOUN
ejpam-6617	374	29	(	(	PUNCT
ejpam-6617	374	30	ϕu	ϕu	NOUN
ejpam-6617	374	31	+	+	CCONJ
ejpam-6617	374	32	(	(	PUNCT
ejpam-6617	374	33	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	374	34	,	,	PUNCT
ejpam-6617	374	35	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	374	36	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	374	37	≤	≤	NUM
ejpam-6617	374	38	a2∫	a2∫	NOUN
ejpam-6617	374	39	a1	a1	NOUN
ejpam-6617	374	40	(	(	PUNCT
ejpam-6617	374	41	ϕu	ϕu	NOUN
ejpam-6617	374	42	+	+	CCONJ
ejpam-6617	374	43	(	(	PUNCT
ejpam-6617	374	44	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	374	45	,	,	PUNCT
ejpam-6617	374	46	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	374	47	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	374	48	,	,	PUNCT
ejpam-6617	374	49	v.	v.	ADP
ejpam-6617	374	50	rayanki	rayanki	PROPN
ejpam-6617	374	51	et	et	PROPN
ejpam-6617	374	52	al	al	PROPN
ejpam-6617	374	53	.	.	PUNCT
ejpam-6617	374	54	/	/	SYM
ejpam-6617	374	55	eur	eur	PROPN
ejpam-6617	374	56	.	.	PUNCT
ejpam-6617	375	1	j.	j.	PROPN
ejpam-6617	375	2	pure	pure	PROPN
ejpam-6617	375	3	appl	appl	PROPN
ejpam-6617	375	4	.	.	PROPN
ejpam-6617	375	5	math	math	PROPN
ejpam-6617	375	6	,	,	PUNCT
ejpam-6617	375	7	18	18	NUM
ejpam-6617	375	8	(	(	PUNCT
ejpam-6617	375	9	3	3	NUM
ejpam-6617	375	10	)	)	PUNCT
ejpam-6617	375	11	(	(	PUNCT
ejpam-6617	375	12	2025	2025	NUM
ejpam-6617	375	13	)	)	PUNCT
ejpam-6617	375	14	,	,	PUNCT
ejpam-6617	375	15	6617	6617	NUM
ejpam-6617	375	16	24	24	NUM
ejpam-6617	375	17	of	of	ADP
ejpam-6617	375	18	38	38	NUM
ejpam-6617	375	19	or	or	CCONJ
ejpam-6617	375	20			NUM
ejpam-6617	375	21	a2∫	a2∫	NOUN
ejpam-6617	375	22	a1	a1	NOUN
ejpam-6617	375	23	(	(	PUNCT
ejpam-6617	375	24	ϕl	ϕl	PROPN
ejpam-6617	375	25	+	+	X
ejpam-6617	375	26	(	(	PUNCT
ejpam-6617	375	27	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	375	28	,	,	PUNCT
ejpam-6617	375	29	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	375	30	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	375	31	≤	≤	NUM
ejpam-6617	375	32	a2∫	a2∫	NOUN
ejpam-6617	375	33	a1	a1	NOUN
ejpam-6617	375	34	(	(	PUNCT
ejpam-6617	375	35	ϕl	ϕl	PROPN
ejpam-6617	375	36	+	+	PROPN
ejpam-6617	375	37	(	(	PUNCT
ejpam-6617	375	38	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	375	39	,	,	PUNCT
ejpam-6617	375	40	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	375	41	a1+ν̄)dς	a1+ν̄)dς	NOUN
ejpam-6617	375	42	a2∫	a2∫	VERB
ejpam-6617	375	43	a1	a1	NOUN
ejpam-6617	375	44	(	(	PUNCT
ejpam-6617	375	45	ϕu	ϕu	NOUN
ejpam-6617	375	46	+	+	CCONJ
ejpam-6617	375	47	(	(	PUNCT
ejpam-6617	375	48	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	375	49	,	,	PUNCT
ejpam-6617	375	50	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	375	51	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	375	52	<	<	X
ejpam-6617	375	53	a2∫	a2∫	NOUN
ejpam-6617	375	54	a1	a1	NOUN
ejpam-6617	375	55	(	(	PUNCT
ejpam-6617	375	56	ϕu	ϕu	NOUN
ejpam-6617	375	57	+	+	CCONJ
ejpam-6617	375	58	(	(	PUNCT
ejpam-6617	375	59	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	375	60	,	,	PUNCT
ejpam-6617	375	61	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	375	62	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	375	63	,	,	PUNCT
ejpam-6617	375	64	or	or	CCONJ
ejpam-6617	375	65			NUM
ejpam-6617	375	66	a2∫	a2∫	NOUN
ejpam-6617	375	67	a1	a1	NOUN
ejpam-6617	375	68	(	(	PUNCT
ejpam-6617	375	69	ϕl	ϕl	PROPN
ejpam-6617	375	70	+	+	X
ejpam-6617	375	71	(	(	PUNCT
ejpam-6617	375	72	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	375	73	,	,	PUNCT
ejpam-6617	375	74	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	375	75	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	375	76	<	<	X
ejpam-6617	375	77	a2∫	a2∫	NOUN
ejpam-6617	375	78	a1	a1	NOUN
ejpam-6617	375	79	(	(	PUNCT
ejpam-6617	375	80	ϕl	ϕl	PROPN
ejpam-6617	375	81	+	+	PROPN
ejpam-6617	375	82	(	(	PUNCT
ejpam-6617	375	83	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	375	84	,	,	PUNCT
ejpam-6617	375	85	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	375	86	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	375	87	a2∫	a2∫	VERB
ejpam-6617	375	88	a1	a1	NOUN
ejpam-6617	375	89	(	(	PUNCT
ejpam-6617	375	90	ϕu	ϕu	NOUN
ejpam-6617	375	91	+	+	CCONJ
ejpam-6617	375	92	(	(	PUNCT
ejpam-6617	375	93	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	375	94	,	,	PUNCT
ejpam-6617	375	95	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	375	96	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	375	97	<	<	X
ejpam-6617	375	98	a2∫	a2∫	NOUN
ejpam-6617	375	99	a1	a1	NOUN
ejpam-6617	375	100	(	(	PUNCT
ejpam-6617	375	101	ϕu	ϕu	NOUN
ejpam-6617	375	102	+	+	CCONJ
ejpam-6617	375	103	(	(	PUNCT
ejpam-6617	375	104	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	375	105	,	,	PUNCT
ejpam-6617	375	106	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	375	107	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	375	108	.	.	PUNCT
ejpam-6617	376	1	from	from	ADP
ejpam-6617	376	2	the	the	DET
ejpam-6617	376	3	above	above	ADJ
ejpam-6617	376	4	inequalities	inequality	NOUN
ejpam-6617	376	5	,	,	PUNCT
ejpam-6617	376	6	we	we	PRON
ejpam-6617	376	7	get	get	VERB
ejpam-6617	376	8	a2∫	a2∫	NOUN
ejpam-6617	376	9	a1	a1	NOUN
ejpam-6617	376	10	(	(	PUNCT
ejpam-6617	376	11	ϕl	ϕl	PROPN
ejpam-6617	377	1	+	+	NOUN
ejpam-6617	377	2	ϕu	ϕu	PROPN
ejpam-6617	378	1	+	+	CCONJ
ejpam-6617	378	2	(	(	PUNCT
ejpam-6617	378	3	θ̄)th))(ς	θ̄)th))(ς	PROPN
ejpam-6617	378	4	,	,	PUNCT
ejpam-6617	378	5	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	378	6	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	378	7	−	−	NOUN
ejpam-6617	378	8	a2∫	a2∫	NOUN
ejpam-6617	378	9	a1	a1	NOUN
ejpam-6617	378	10	(	(	PUNCT
ejpam-6617	378	11	ϕl	ϕl	PROPN
ejpam-6617	379	1	+	+	NOUN
ejpam-6617	379	2	ϕu	ϕu	PROPN
ejpam-6617	380	1	+	+	CCONJ
ejpam-6617	380	2	(	(	PUNCT
ejpam-6617	380	3	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	380	4	,	,	PUNCT
ejpam-6617	380	5	ε̄,cfdθ•	ε̄,cfdθ•	PROPN
ejpam-6617	380	6	a1+ε̄)dς	a1+ε̄)dς	ADV
ejpam-6617	380	7	<	<	X
ejpam-6617	380	8	0	0	NUM
ejpam-6617	380	9	,	,	PUNCT
ejpam-6617	380	10	hence	hence	ADV
ejpam-6617	380	11	,	,	PUNCT
ejpam-6617	380	12	taking	take	VERB
ejpam-6617	380	13	the	the	DET
ejpam-6617	380	14	invexity	invexity	NOUN
ejpam-6617	380	15	assumption	assumption	NOUN
ejpam-6617	380	16	on	on	ADP
ejpam-6617	380	17	a2∫	a2∫	NOUN
ejpam-6617	380	18	a1	a1	NOUN
ejpam-6617	380	19	(	(	PUNCT
ejpam-6617	380	20	ϕl	ϕl	PROPN
ejpam-6617	381	1	+	+	NOUN
ejpam-6617	381	2	ϕu	ϕu	PROPN
ejpam-6617	382	1	+	+	CCONJ
ejpam-6617	382	2	(	(	PUNCT
ejpam-6617	382	3	θ̄)th))(ς	θ̄)th))(ς	PROPN
ejpam-6617	382	4	,	,	PUNCT
ejpam-6617	382	5	.	.	PUNCT
ejpam-6617	382	6	,	,	PUNCT
ejpam-6617	382	7	.)dς	.)dς	PUNCT
ejpam-6617	383	1	at	at	ADP
ejpam-6617	383	2	ε̄	ε̄	NOUN
ejpam-6617	383	3	on	on	ADP
ejpam-6617	383	4	x	x	NOUN
ejpam-6617	383	5	,	,	PUNCT
ejpam-6617	383	6	there	there	PRON
ejpam-6617	383	7	exists	exist	VERB
ejpam-6617	383	8	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	383	9	,	,	PUNCT
ejpam-6617	383	10	κ̄	κ̄	NOUN
ejpam-6617	383	11	,	,	PUNCT
ejpam-6617	383	12	ε̄	ε̄	ADJ
ejpam-6617	383	13	)	)	PUNCT
ejpam-6617	383	14	∈	∈	PROPN
ejpam-6617	383	15	c1[a1	c1[a1	VERB
ejpam-6617	383	16	,	,	PUNCT
ejpam-6617	383	17	a2	a2	PROPN
ejpam-6617	383	18	]	]	PUNCT
ejpam-6617	383	19	such	such	ADJ
ejpam-6617	383	20	that	that	SCONJ
ejpam-6617	383	21	a2∫	a2∫	ADJ
ejpam-6617	383	22	a1	a1	NOUN
ejpam-6617	383	23	{	{	PUNCT
ejpam-6617	383	24	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	383	25	,	,	PUNCT
ejpam-6617	383	26	κ̄	κ̄	NOUN
ejpam-6617	383	27	,	,	PUNCT
ejpam-6617	383	28	ε̄)t	ε̄)t	PUNCT
ejpam-6617	383	29	[	[	PUNCT
ejpam-6617	383	30	ϕl	ϕl	PRON
ejpam-6617	383	31	ε̄	ε̄	NOUN
ejpam-6617	383	32	+	+	CCONJ
ejpam-6617	383	33	ϕu	ϕu	ADP
ejpam-6617	383	34	ε̄	ε̄	ADJ
ejpam-6617	384	1	+	+	CCONJ
ejpam-6617	384	2	(	(	PUNCT
ejpam-6617	384	3	θ̄)th	θ̄)th	X
ejpam-6617	384	4	]	]	X
ejpam-6617	384	5	(	(	PUNCT
ejpam-6617	384	6	ς	ς	NOUN
ejpam-6617	384	7	,	,	PUNCT
ejpam-6617	384	8	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	384	9	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	384	10	)	)	PUNCT
ejpam-6617	385	1	+	+	ADP
ejpam-6617	385	2	cfdγ	cfdγ	NOUN
ejpam-6617	385	3	a1+ℵ(ς	a1+ℵ(ς	PRON
ejpam-6617	385	4	,	,	PUNCT
ejpam-6617	385	5	κ̄	κ̄	NOUN
ejpam-6617	385	6	,	,	PUNCT
ejpam-6617	385	7	ε̄	ε̄	NOUN
ejpam-6617	385	8	)	)	PUNCT
ejpam-6617	385	9	t	t	NOUN
ejpam-6617	385	10	[	[	PUNCT
ejpam-6617	385	11	ϕl	ϕl	PROPN
ejpam-6617	385	12	cfdθ•	cfdθ•	PROPN
ejpam-6617	385	13	a1	a1	PROPN
ejpam-6617	385	14	+	+	CCONJ
ejpam-6617	385	15	ε̄	ε̄	ADJ
ejpam-6617	385	16	+	+	PROPN
ejpam-6617	385	17	ϕu	ϕu	PROPN
ejpam-6617	385	18	cfdθ•	cfdθ•	PROPN
ejpam-6617	385	19	a1	a1	PROPN
ejpam-6617	385	20	+	+	CCONJ
ejpam-6617	385	21	ε̄	ε̄	ADJ
ejpam-6617	385	22	+	+	PROPN
ejpam-6617	385	23	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	385	24	,	,	PUNCT
ejpam-6617	385	25	κ̄	κ̄	NOUN
ejpam-6617	385	26	,	,	PUNCT
ejpam-6617	385	27	ε̄)thcfdθ•	ε̄)thcfdθ•	X
ejpam-6617	385	28	a1	a1	NOUN
ejpam-6617	385	29	+	+	CCONJ
ejpam-6617	385	30	ε̄	ε̄	NOUN
ejpam-6617	385	31	]	]	PUNCT
ejpam-6617	385	32	(	(	PUNCT
ejpam-6617	385	33	ς	ς	NOUN
ejpam-6617	385	34	,	,	PUNCT
ejpam-6617	385	35	ε̄,cfdθ•	ε̄,cfdθ•	PROPN
ejpam-6617	385	36	a1+ε̄)}dς	a1+ε̄)}dς	NOUN
ejpam-6617	385	37	<	<	X
ejpam-6617	385	38	0	0	NUM
ejpam-6617	385	39	.	.	PUNCT
ejpam-6617	386	1	(	(	PUNCT
ejpam-6617	386	2	17	17	NUM
ejpam-6617	386	3	)	)	PUNCT
ejpam-6617	386	4	further	far	ADV
ejpam-6617	386	5	,	,	PUNCT
ejpam-6617	386	6	from	from	ADP
ejpam-6617	386	7	the	the	DET
ejpam-6617	386	8	dual	dual	ADJ
ejpam-6617	386	9	constraint	constraint	NOUN
ejpam-6617	386	10	(	(	PUNCT
ejpam-6617	386	11	14	14	NUM
ejpam-6617	386	12	)	)	PUNCT
ejpam-6617	386	13	and	and	CCONJ
ejpam-6617	386	14	the	the	DET
ejpam-6617	386	15	proposition	proposition	NOUN
ejpam-6617	386	16	2.1	2.1	NUM
ejpam-6617	386	17	,	,	PUNCT
ejpam-6617	386	18	we	we	PRON
ejpam-6617	386	19	get	get	VERB
ejpam-6617	386	20	a2∫	a2∫	NOUN
ejpam-6617	386	21	a1	a1	NOUN
ejpam-6617	386	22	{	{	PUNCT
ejpam-6617	386	23	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	386	24	,	,	PUNCT
ejpam-6617	386	25	κ̄	κ̄	NOUN
ejpam-6617	386	26	,	,	PUNCT
ejpam-6617	386	27	ε̄)t	ε̄)t	PUNCT
ejpam-6617	386	28	[	[	PUNCT
ejpam-6617	386	29	ϕl	ϕl	PRON
ejpam-6617	386	30	ε̄	ε̄	PROPN
ejpam-6617	386	31	(	(	PUNCT
ejpam-6617	386	32	ς	ς	NOUN
ejpam-6617	386	33	,	,	PUNCT
ejpam-6617	386	34	ε̄	ε̄	ADJ
ejpam-6617	386	35	,	,	PUNCT
ejpam-6617	386	36	cfdθ•	cfdθ•	NOUN
ejpam-6617	386	37	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	386	38	)	)	PUNCT
ejpam-6617	387	1	+	+	CCONJ
ejpam-6617	387	2	ϕu	ϕu	ADP
ejpam-6617	387	3	ε̄	ε̄	ADJ
ejpam-6617	387	4	(	(	PUNCT
ejpam-6617	387	5	ς	ς	NOUN
ejpam-6617	387	6	,	,	PUNCT
ejpam-6617	387	7	ε̄	ε̄	ADJ
ejpam-6617	387	8	,	,	PUNCT
ejpam-6617	387	9	cfdθ•	cfdθ•	NOUN
ejpam-6617	387	10	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	387	11	)	)	PUNCT
ejpam-6617	388	1	(	(	PUNCT
ejpam-6617	388	2	18	18	NUM
ejpam-6617	388	3	)	)	PUNCT
ejpam-6617	388	4	+	+	PROPN
ejpam-6617	388	5	(	(	PUNCT
ejpam-6617	388	6	θ̄)t	θ̄)t	NOUN
ejpam-6617	388	7	(	(	PUNCT
ejpam-6617	388	8	ς)hε̄(ς	ς)hε̄(ς	PROPN
ejpam-6617	388	9	,	,	PUNCT
ejpam-6617	388	10	ε̄	ε̄	NOUN
ejpam-6617	388	11	,	,	PUNCT
ejpam-6617	388	12	cfdθ•	cfdθ•	PROPN
ejpam-6617	388	13	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	388	14	)	)	PUNCT
ejpam-6617	388	15	]	]	PUNCT
ejpam-6617	388	16	}	}	PUNCT
ejpam-6617	388	17	dς	dς	VERB
ejpam-6617	388	18	=	=	SYM
ejpam-6617	388	19	a2∫	a2∫	X
ejpam-6617	388	20	a1	a1	NOUN
ejpam-6617	388	21	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	388	22	,	,	PUNCT
ejpam-6617	388	23	κ̄	κ̄	NOUN
ejpam-6617	388	24	,	,	PUNCT
ejpam-6617	388	25	ε̄)t	ε̄)t	PUNCT
ejpam-6617	388	26	[	[	PUNCT
ejpam-6617	388	27	−	−	PROPN
ejpam-6617	388	28	cfdθ•	cfdθ•	PROPN
ejpam-6617	388	29	a1−	a1−	PROPN
ejpam-6617	388	30	{	{	PUNCT
ejpam-6617	388	31	ϕl	ϕl	PROPN
ejpam-6617	388	32	cfdθ•	cfdθ•	PROPN
ejpam-6617	388	33	a1	a1	PROPN
ejpam-6617	388	34	+	+	CCONJ
ejpam-6617	388	35	ε̄	ε̄	ADJ
ejpam-6617	388	36	(	(	PUNCT
ejpam-6617	388	37	ς	ς	PROPN
ejpam-6617	388	38	,	,	PUNCT
ejpam-6617	388	39	ε̄,cfdς	ε̄,cfdς	PROPN
ejpam-6617	388	40	a1+ε̄	a1+ε̄	PROPN
ejpam-6617	388	41	)	)	PUNCT
ejpam-6617	389	1	v.	v.	CCONJ
ejpam-6617	389	2	rayanki	rayanki	PROPN
ejpam-6617	389	3	et	et	PROPN
ejpam-6617	389	4	al	al	PROPN
ejpam-6617	389	5	.	.	PUNCT
ejpam-6617	389	6	/	/	SYM
ejpam-6617	389	7	eur	eur	PROPN
ejpam-6617	389	8	.	.	PUNCT
ejpam-6617	390	1	j.	j.	PROPN
ejpam-6617	390	2	pure	pure	PROPN
ejpam-6617	390	3	appl	appl	PROPN
ejpam-6617	390	4	.	.	PROPN
ejpam-6617	390	5	math	math	PROPN
ejpam-6617	390	6	,	,	PUNCT
ejpam-6617	390	7	18	18	NUM
ejpam-6617	390	8	(	(	PUNCT
ejpam-6617	390	9	3	3	NUM
ejpam-6617	390	10	)	)	PUNCT
ejpam-6617	390	11	(	(	PUNCT
ejpam-6617	390	12	2025	2025	NUM
ejpam-6617	390	13	)	)	PUNCT
ejpam-6617	390	14	,	,	PUNCT
ejpam-6617	390	15	6617	6617	NUM
ejpam-6617	390	16	25	25	NUM
ejpam-6617	390	17	of	of	ADP
ejpam-6617	390	18	38	38	NUM
ejpam-6617	390	19	+	+	CCONJ
ejpam-6617	390	20	ϕu	ϕu	PROPN
ejpam-6617	390	21	cfdθ•	cfdθ•	PROPN
ejpam-6617	390	22	a1	a1	PROPN
ejpam-6617	390	23	+	+	CCONJ
ejpam-6617	390	24	ε̄	ε̄	ADJ
ejpam-6617	390	25	(	(	PUNCT
ejpam-6617	390	26	ς	ς	NOUN
ejpam-6617	390	27	,	,	PUNCT
ejpam-6617	390	28	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	390	29	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	390	30	)	)	PUNCT
ejpam-6617	390	31	}	}	PUNCT
ejpam-6617	391	1	+	+	CCONJ
ejpam-6617	391	2	(	(	PUNCT
ejpam-6617	391	3	θ̄)t	θ̄)t	NOUN
ejpam-6617	391	4	(	(	PUNCT
ejpam-6617	391	5	ς)hcfdγ	ς)hcfdγ	PROPN
ejpam-6617	391	6	a+ε̄(ς	a+ε̄(ς	ADJ
ejpam-6617	391	7	,	,	PUNCT
ejpam-6617	391	8	ε̄	ε̄	ADJ
ejpam-6617	391	9	,	,	PUNCT
ejpam-6617	391	10	cfdθ•	cfdθ•	NOUN
ejpam-6617	391	11	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	391	12	)	)	PUNCT
ejpam-6617	391	13	]	]	PUNCT
ejpam-6617	391	14	dς	dς	X
ejpam-6617	392	1	=	=	SYM
ejpam-6617	392	2	[	[	PUNCT
ejpam-6617	392	3	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	392	4	,	,	PUNCT
ejpam-6617	392	5	κ̄	κ̄	NOUN
ejpam-6617	392	6	,	,	PUNCT
ejpam-6617	392	7	ε̄)t	ε̄)t	ADJ
ejpam-6617	392	8	i1−θ•	i1−θ•	VERB
ejpam-6617	392	9	b−	b−	PROPN
ejpam-6617	392	10	{	{	PUNCT
ejpam-6617	392	11	ϕl	ϕl	PROPN
ejpam-6617	392	12	cfdθ•	cfdθ•	PROPN
ejpam-6617	392	13	a1	a1	PROPN
ejpam-6617	392	14	+	+	CCONJ
ejpam-6617	392	15	ε̄	ε̄	ADJ
ejpam-6617	392	16	+	+	CCONJ
ejpam-6617	392	17	ϕu	ϕu	PROPN
ejpam-6617	392	18	cfdθ•	cfdθ•	PROPN
ejpam-6617	392	19	a1	a1	PROPN
ejpam-6617	392	20	+	+	CCONJ
ejpam-6617	392	21	ε̄	ε̄	ADJ
ejpam-6617	392	22	}	}	PUNCT
ejpam-6617	392	23	(	(	PUNCT
ejpam-6617	392	24	ς	ς	NOUN
ejpam-6617	392	25	,	,	PUNCT
ejpam-6617	392	26	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	392	27	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	392	28	)	)	PUNCT
ejpam-6617	393	1	+	+	CCONJ
ejpam-6617	393	2	(	(	PUNCT
ejpam-6617	393	3	θ̄)t	θ̄)t	NOUN
ejpam-6617	393	4	(	(	PUNCT
ejpam-6617	393	5	ς)hcfdθ•	ς)hcfdθ•	NOUN
ejpam-6617	393	6	a1	a1	PROPN
ejpam-6617	393	7	+	+	CCONJ
ejpam-6617	393	8	ε̄(ς	ε̄(ς	PROPN
ejpam-6617	393	9	,	,	PUNCT
ejpam-6617	393	10	ε̄	ε̄	NOUN
ejpam-6617	393	11	,	,	PUNCT
ejpam-6617	393	12	cfdθ•	cfdθ•	NOUN
ejpam-6617	393	13	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	393	14	)	)	PUNCT
ejpam-6617	394	1	]	]	X
ejpam-6617	394	2	b	b	X
ejpam-6617	394	3	a	a	DET
ejpam-6617	394	4	−	−	NOUN
ejpam-6617	394	5	a2∫	a2∫	X
ejpam-6617	394	6	a1	a1	NOUN
ejpam-6617	394	7	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	394	8	,	,	PUNCT
ejpam-6617	394	9	κ̄	κ̄	NOUN
ejpam-6617	394	10	,	,	PUNCT
ejpam-6617	394	11	ε̄)t	ε̄)t	PUNCT
ejpam-6617	394	12	[	[	PUNCT
ejpam-6617	394	13	cfdθ•	cfdθ•	NOUN
ejpam-6617	394	14	a1	a1	NOUN
ejpam-6617	394	15	+	+	CCONJ
ejpam-6617	394	16	{	{	PUNCT
ejpam-6617	394	17	ϕl	ϕl	PROPN
ejpam-6617	394	18	cfdθ•	cfdθ•	PROPN
ejpam-6617	394	19	a1	a1	PROPN
ejpam-6617	394	20	+	+	CCONJ
ejpam-6617	394	21	ε̄	ε̄	ADJ
ejpam-6617	394	22	+	+	ADJ
ejpam-6617	394	23	+	+	ADJ
ejpam-6617	394	24	ϕu	ϕu	PROPN
ejpam-6617	394	25	cfdθ•	cfdθ•	PROPN
ejpam-6617	394	26	a1	a1	PROPN
ejpam-6617	394	27	+	+	CCONJ
ejpam-6617	394	28	ε̄	ε̄	ADJ
ejpam-6617	394	29	}	}	PUNCT
ejpam-6617	394	30	(	(	PUNCT
ejpam-6617	394	31	ς	ς	NOUN
ejpam-6617	394	32	,	,	PUNCT
ejpam-6617	394	33	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	394	34	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	394	35	)	)	PUNCT
ejpam-6617	395	1	+	+	CCONJ
ejpam-6617	395	2	(	(	PUNCT
ejpam-6617	395	3	θ̄)t	θ̄)t	NOUN
ejpam-6617	395	4	(	(	PUNCT
ejpam-6617	395	5	ς)hcfdθ•	ς)hcfdθ•	NOUN
ejpam-6617	395	6	a1	a1	PROPN
ejpam-6617	395	7	+	+	CCONJ
ejpam-6617	395	8	ε̄(ς	ε̄(ς	PROPN
ejpam-6617	395	9	,	,	PUNCT
ejpam-6617	395	10	ε̄	ε̄	NOUN
ejpam-6617	395	11	,	,	PUNCT
ejpam-6617	395	12	cfdθ•	cfdθ•	PROPN
ejpam-6617	395	13	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	395	14	)	)	PUNCT
ejpam-6617	395	15	]	]	PUNCT
ejpam-6617	396	1	dς	dς	X
ejpam-6617	396	2	.	.	PUNCT
ejpam-6617	396	3	by	by	ADP
ejpam-6617	396	4	using	use	VERB
ejpam-6617	396	5	(	(	PUNCT
ejpam-6617	396	6	13	13	NUM
ejpam-6617	396	7	)	)	PUNCT
ejpam-6617	396	8	,	,	PUNCT
ejpam-6617	396	9	it	it	PRON
ejpam-6617	396	10	gives	give	VERB
ejpam-6617	396	11	a2∫	a2∫	NOUN
ejpam-6617	396	12	a1	a1	NOUN
ejpam-6617	396	13	[	[	PUNCT
ejpam-6617	396	14	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	396	15	,	,	PUNCT
ejpam-6617	396	16	κ̄	κ̄	NOUN
ejpam-6617	396	17	,	,	PUNCT
ejpam-6617	396	18	ε̄)t	ε̄)t	NUM
ejpam-6617	396	19	{	{	PUNCT
ejpam-6617	396	20	ϕl	ϕl	INTJ
ejpam-6617	396	21	ε̄	ε̄	PROPN
ejpam-6617	396	22	(	(	PUNCT
ejpam-6617	396	23	ς	ς	NOUN
ejpam-6617	396	24	,	,	PUNCT
ejpam-6617	396	25	ε̄	ε̄	ADJ
ejpam-6617	396	26	,	,	PUNCT
ejpam-6617	396	27	cfdθ•	cfdθ•	NOUN
ejpam-6617	396	28	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	396	29	)	)	PUNCT
ejpam-6617	397	1	+	+	CCONJ
ejpam-6617	397	2	ϕu	ϕu	ADP
ejpam-6617	397	3	ε̄	ε̄	ADJ
ejpam-6617	397	4	(	(	PUNCT
ejpam-6617	397	5	ς	ς	NOUN
ejpam-6617	397	6	,	,	PUNCT
ejpam-6617	397	7	ε̄	ε̄	ADJ
ejpam-6617	397	8	,	,	PUNCT
ejpam-6617	397	9	cfdθ•	cfdθ•	NOUN
ejpam-6617	397	10	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	397	11	)	)	PUNCT
ejpam-6617	398	1	+	+	PROPN
ejpam-6617	398	2	(	(	PUNCT
ejpam-6617	398	3	θ̄)t	θ̄)t	NOUN
ejpam-6617	398	4	(	(	PUNCT
ejpam-6617	398	5	ς)hε̄(ς	ς)hε̄(ς	PROPN
ejpam-6617	398	6	,	,	PUNCT
ejpam-6617	398	7	ε̄	ε̄	NOUN
ejpam-6617	398	8	,	,	PUNCT
ejpam-6617	398	9	cfdθ•	cfdθ•	NOUN
ejpam-6617	398	10	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	398	11	)	)	PUNCT
ejpam-6617	398	12	}	}	PUNCT
ejpam-6617	398	13	]	]	PUNCT
ejpam-6617	398	14	dς	dς	X
ejpam-6617	399	1	=	=	PUNCT
ejpam-6617	399	2	−	−	NOUN
ejpam-6617	399	3	a2∫	a2∫	X
ejpam-6617	399	4	a1	a1	NOUN
ejpam-6617	399	5	[	[	PUNCT
ejpam-6617	399	6	cfdθ•	cfdθ•	NOUN
ejpam-6617	399	7	a1+(ε−	a1+(ε−	PROPN
ejpam-6617	399	8	ε̄	ε̄	NOUN
ejpam-6617	399	9	)	)	PUNCT
ejpam-6617	399	10	{	{	PUNCT
ejpam-6617	399	11	ϕl	ϕl	PROPN
ejpam-6617	399	12	cfdθ•	cfdθ•	PROPN
ejpam-6617	399	13	a1	a1	PROPN
ejpam-6617	399	14	+	+	CCONJ
ejpam-6617	399	15	ε̄	ε̄	ADJ
ejpam-6617	399	16	+	+	CCONJ
ejpam-6617	399	17	ϕu	ϕu	PROPN
ejpam-6617	399	18	cfdθ•	cfdθ•	PROPN
ejpam-6617	399	19	a1	a1	PROPN
ejpam-6617	399	20	+	+	CCONJ
ejpam-6617	399	21	ε̄	ε̄	ADJ
ejpam-6617	399	22	}	}	PUNCT
ejpam-6617	399	23	(	(	PUNCT
ejpam-6617	399	24	ς	ς	NOUN
ejpam-6617	399	25	,	,	PUNCT
ejpam-6617	399	26	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	399	27	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	399	28	)	)	PUNCT
ejpam-6617	400	1	+	+	PROPN
ejpam-6617	400	2	(	(	PUNCT
ejpam-6617	400	3	θ̄)t	θ̄)t	PROPN
ejpam-6617	400	4	(	(	PUNCT
ejpam-6617	400	5	ς)hcfdθ•	ς)hcfdθ•	NOUN
ejpam-6617	400	6	a1	a1	NOUN
ejpam-6617	400	7	+	+	X
ejpam-6617	400	8	ε̄(ξ	ε̄(ξ	ADJ
ejpam-6617	400	9	,	,	PUNCT
ejpam-6617	400	10	ε̄	ε̄	ADJ
ejpam-6617	400	11	,	,	PUNCT
ejpam-6617	400	12	cfdθ•	cfdθ•	NOUN
ejpam-6617	400	13	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	400	14	)	)	PUNCT
ejpam-6617	400	15	]	]	PUNCT
ejpam-6617	401	1	dς	dς	PROPN
ejpam-6617	401	2	.	.	PUNCT
ejpam-6617	402	1	that	that	PRON
ejpam-6617	402	2	is	be	AUX
ejpam-6617	402	3	a2∫	a2∫	NOUN
ejpam-6617	402	4	a1	a1	NOUN
ejpam-6617	402	5	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	402	6	,	,	PUNCT
ejpam-6617	402	7	κ̄	κ̄	NOUN
ejpam-6617	402	8	,	,	PUNCT
ejpam-6617	402	9	ε̄)t	ε̄)t	NUM
ejpam-6617	402	10	{	{	PUNCT
ejpam-6617	402	11	ϕl	ϕl	INTJ
ejpam-6617	402	12	ε̄	ε̄	PROPN
ejpam-6617	402	13	(	(	PUNCT
ejpam-6617	402	14	ς	ς	NOUN
ejpam-6617	402	15	,	,	PUNCT
ejpam-6617	402	16	ε̄	ε̄	ADJ
ejpam-6617	402	17	,	,	PUNCT
ejpam-6617	402	18	cfdθ•	cfdθ•	NOUN
ejpam-6617	402	19	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	402	20	)	)	PUNCT
ejpam-6617	403	1	+	+	CCONJ
ejpam-6617	403	2	ϕu	ϕu	ADP
ejpam-6617	403	3	ε̄	ε̄	ADJ
ejpam-6617	403	4	(	(	PUNCT
ejpam-6617	403	5	ς	ς	NOUN
ejpam-6617	403	6	,	,	PUNCT
ejpam-6617	403	7	ε̄	ε̄	ADJ
ejpam-6617	403	8	,	,	PUNCT
ejpam-6617	403	9	cfdθ•	cfdθ•	NOUN
ejpam-6617	403	10	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	403	11	)	)	PUNCT
ejpam-6617	404	1	+	+	PROPN
ejpam-6617	404	2	(	(	PUNCT
ejpam-6617	404	3	θ̄)t	θ̄)t	NOUN
ejpam-6617	404	4	(	(	PUNCT
ejpam-6617	404	5	ς)hε̄(ς	ς)hε̄(ς	PROPN
ejpam-6617	404	6	,	,	PUNCT
ejpam-6617	404	7	ε̄	ε̄	NOUN
ejpam-6617	404	8	,	,	PUNCT
ejpam-6617	404	9	cfdθ•	cfdθ•	PROPN
ejpam-6617	404	10	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	404	11	)	)	PUNCT
ejpam-6617	404	12	}	}	PUNCT
ejpam-6617	404	13	dς	dς	VERB
ejpam-6617	404	14	+	+	PUNCT
ejpam-6617	404	15	a2∫	a2∫	NOUN
ejpam-6617	404	16	a1	a1	NOUN
ejpam-6617	404	17	cfdθ•	cfdθ•	NOUN
ejpam-6617	404	18	a1+(ε−	a1+(ε−	PROPN
ejpam-6617	404	19	ε̄)t	ε̄)t	PROPN
ejpam-6617	404	20	{	{	PUNCT
ejpam-6617	404	21	ϕl	ϕl	PROPN
ejpam-6617	404	22	cfdθ•	cfdθ•	PROPN
ejpam-6617	404	23	a1	a1	PROPN
ejpam-6617	404	24	+	+	CCONJ
ejpam-6617	404	25	ε̄	ε̄	ADJ
ejpam-6617	404	26	(	(	PUNCT
ejpam-6617	404	27	ς	ς	NOUN
ejpam-6617	404	28	,	,	PUNCT
ejpam-6617	404	29	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	404	30	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	404	31	)	)	PUNCT
ejpam-6617	405	1	+	+	CCONJ
ejpam-6617	405	2	ϕu	ϕu	PROPN
ejpam-6617	405	3	cfdθ•	cfdθ•	PROPN
ejpam-6617	405	4	a1	a1	PROPN
ejpam-6617	405	5	+	+	CCONJ
ejpam-6617	405	6	ε̄	ε̄	ADJ
ejpam-6617	405	7	(	(	PUNCT
ejpam-6617	405	8	ς	ς	NOUN
ejpam-6617	405	9	,	,	PUNCT
ejpam-6617	405	10	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	405	11	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	405	12	)	)	PUNCT
ejpam-6617	406	1	+	+	PROPN
ejpam-6617	406	2	(	(	PUNCT
ejpam-6617	406	3	θ̄)t	θ̄)t	PROPN
ejpam-6617	406	4	(	(	PUNCT
ejpam-6617	406	5	ς)hcfdθ•	ς)hcfdθ•	NOUN
ejpam-6617	406	6	a1	a1	PROPN
ejpam-6617	406	7	+	+	CCONJ
ejpam-6617	406	8	ε̄(ς	ε̄(ς	PROPN
ejpam-6617	406	9	,	,	PUNCT
ejpam-6617	406	10	ε̄	ε̄	NOUN
ejpam-6617	406	11	,	,	PUNCT
ejpam-6617	406	12	cfdθ•	cfdθ•	PROPN
ejpam-6617	406	13	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	406	14	)	)	PUNCT
ejpam-6617	406	15	}	}	PUNCT
ejpam-6617	406	16	dς	dς	VERB
ejpam-6617	406	17	=	=	SYM
ejpam-6617	406	18	0	0	NUM
ejpam-6617	406	19	,	,	PUNCT
ejpam-6617	406	20	(	(	PUNCT
ejpam-6617	406	21	19	19	NUM
ejpam-6617	406	22	)	)	PUNCT
ejpam-6617	406	23	which	which	PRON
ejpam-6617	406	24	contradicts	contradict	VERB
ejpam-6617	406	25	(	(	PUNCT
ejpam-6617	406	26	17	17	NUM
ejpam-6617	406	27	)	)	PUNCT
ejpam-6617	406	28	.	.	PUNCT
ejpam-6617	407	1	hence	hence	ADV
ejpam-6617	407	2	the	the	DET
ejpam-6617	407	3	theorem	theorem	NOUN
ejpam-6617	407	4	.	.	PUNCT
ejpam-6617	408	1	we	we	PRON
ejpam-6617	408	2	provide	provide	VERB
ejpam-6617	408	3	an	an	DET
ejpam-6617	408	4	algorithm	algorithm	NOUN
ejpam-6617	408	5	for	for	ADP
ejpam-6617	408	6	the	the	DET
ejpam-6617	408	7	weak	weak	ADJ
ejpam-6617	408	8	duality	duality	NOUN
ejpam-6617	408	9	theorem	theorem	VERB
ejpam-6617	408	10	in	in	ADP
ejpam-6617	408	11	the	the	DET
ejpam-6617	408	12	following	following	ADJ
ejpam-6617	408	13	way	way	NOUN
ejpam-6617	408	14	:	:	PUNCT
ejpam-6617	408	15	v.	v.	ADP
ejpam-6617	408	16	rayanki	rayanki	VERB
ejpam-6617	408	17	et	et	PROPN
ejpam-6617	408	18	al	al	PROPN
ejpam-6617	408	19	.	.	PUNCT
ejpam-6617	408	20	/	/	SYM
ejpam-6617	408	21	eur	eur	PROPN
ejpam-6617	408	22	.	.	PUNCT
ejpam-6617	409	1	j.	j.	PROPN
ejpam-6617	409	2	pure	pure	PROPN
ejpam-6617	409	3	appl	appl	PROPN
ejpam-6617	409	4	.	.	PROPN
ejpam-6617	409	5	math	math	PROPN
ejpam-6617	409	6	,	,	PUNCT
ejpam-6617	409	7	18	18	NUM
ejpam-6617	409	8	(	(	PUNCT
ejpam-6617	409	9	3	3	NUM
ejpam-6617	409	10	)	)	PUNCT
ejpam-6617	409	11	(	(	PUNCT
ejpam-6617	409	12	2025	2025	NUM
ejpam-6617	409	13	)	)	PUNCT
ejpam-6617	409	14	,	,	PUNCT
ejpam-6617	409	15	6617	6617	NUM
ejpam-6617	409	16	26	26	NUM
ejpam-6617	409	17	of	of	ADP
ejpam-6617	409	18	38	38	NUM
ejpam-6617	409	19	algorithm	algorithm	NOUN
ejpam-6617	409	20	of	of	ADP
ejpam-6617	409	21	weak	weak	ADJ
ejpam-6617	409	22	duality	duality	NOUN
ejpam-6617	409	23	input	input	NOUN
ejpam-6617	409	24	:	:	PUNCT
ejpam-6617	409	25	•	•	ADP
ejpam-6617	409	26	primal	primal	ADJ
ejpam-6617	409	27	objective	objective	ADJ
ejpam-6617	409	28	functional	functional	NOUN
ejpam-6617	409	29	:	:	PUNCT
ejpam-6617	409	30	(	(	PUNCT
ejpam-6617	409	31	p-4	p-4	NOUN
ejpam-6617	409	32	):	):	PUNCT
ejpam-6617	409	33	min	min	PROPN
ejpam-6617	409	34			NOUN
ejpam-6617	409	35	a2∫	a2∫	VERB
ejpam-6617	409	36	a1	a1	NOUN
ejpam-6617	409	37	ϕl(ς	ϕl(ς	PUNCT
ejpam-6617	409	38	,	,	PUNCT
ejpam-6617	409	39	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	409	40	a1+κ(ς))dς	a1+κ(ς))dς	ADV
ejpam-6617	409	41	,	,	PUNCT
ejpam-6617	409	42	a2∫	a2∫	X
ejpam-6617	409	43	a1	a1	VERB
ejpam-6617	409	44	ϕu	ϕu	X
ejpam-6617	409	45	(	(	PUNCT
ejpam-6617	409	46	ς	ς	PROPN
ejpam-6617	409	47	,	,	PUNCT
ejpam-6617	409	48	κ(ς),cfdθ•	κ(ς),cfdθ•	NOUN
ejpam-6617	409	49	a1+κ(ς))dς	a1+κ(ς))dς	ADV
ejpam-6617	409	50			NOUN
ejpam-6617	409	51	•	•	NOUN
ejpam-6617	409	52	set	set	NOUN
ejpam-6617	409	53	of	of	ADP
ejpam-6617	409	54	constraints	constraint	NOUN
ejpam-6617	409	55	:	:	PUNCT
ejpam-6617	409	56	h(ς	h(ς	PROPN
ejpam-6617	409	57	,	,	PUNCT
ejpam-6617	409	58	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	409	59	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	409	60	)	)	PUNCT
ejpam-6617	409	61	)	)	PUNCT
ejpam-6617	410	1	≤	≤	ADV
ejpam-6617	410	2	0	0	NUM
ejpam-6617	410	3	,	,	PUNCT
ejpam-6617	410	4	κ(a1	κ(a1	NOUN
ejpam-6617	410	5	)	)	PUNCT
ejpam-6617	410	6	=	=	SYM
ejpam-6617	410	7	α	α	NUM
ejpam-6617	410	8	,	,	PUNCT
ejpam-6617	410	9	κ(a2	κ(a2	NOUN
ejpam-6617	410	10	)	)	PUNCT
ejpam-6617	410	11	=	=	SYM
ejpam-6617	411	1	β	β	X
ejpam-6617	411	2	,	,	PUNCT
ejpam-6617	411	3	ς	ς	PROPN
ejpam-6617	411	4	∈	∈	PROPN
ejpam-6617	411	5	[	[	X
ejpam-6617	411	6	a1	a1	NOUN
ejpam-6617	411	7	,	,	PUNCT
ejpam-6617	411	8	a2	a2	PROPN
ejpam-6617	411	9	]	]	PUNCT
ejpam-6617	411	10	.	.	PUNCT
ejpam-6617	412	1	•	•	NUM
ejpam-6617	412	2	set	set	NOUN
ejpam-6617	412	3	of	of	ADP
ejpam-6617	412	4	feasible	feasible	ADJ
ejpam-6617	412	5	point	point	NOUN
ejpam-6617	412	6	for	for	ADP
ejpam-6617	412	7	(	(	PUNCT
ejpam-6617	412	8	p-4	p-4	NOUN
ejpam-6617	412	9	):	):	PUNCT
ejpam-6617	412	10	φ3	φ3	NOUN
ejpam-6617	412	11	=	=	PUNCT
ejpam-6617	412	12	{	{	PUNCT
ejpam-6617	412	13	h(ς	h(ς	PROPN
ejpam-6617	412	14	,	,	PUNCT
ejpam-6617	412	15	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	412	16	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	412	17	)	)	PUNCT
ejpam-6617	412	18	)	)	PUNCT
ejpam-6617	413	1	≤	≤	NUM
ejpam-6617	413	2	0,κ(a1	0,κ(a1	NUM
ejpam-6617	413	3	)	)	PUNCT
ejpam-6617	413	4	=	=	SYM
ejpam-6617	413	5	α	α	X
ejpam-6617	413	6	,	,	PUNCT
ejpam-6617	413	7	κ(a2	κ(a2	NOUN
ejpam-6617	413	8	)	)	PUNCT
ejpam-6617	413	9	=	=	PUNCT
ejpam-6617	413	10	β	β	X
ejpam-6617	413	11	}	}	PUNCT
ejpam-6617	413	12	.	.	PUNCT
ejpam-6617	414	1	•	•	NUM
ejpam-6617	414	2	wolfe	wolfe	PROPN
ejpam-6617	414	3	dual	dual	ADJ
ejpam-6617	414	4	objective	objective	ADJ
ejpam-6617	414	5	functional	functional	ADJ
ejpam-6617	414	6	corresponding	corresponding	NOUN
ejpam-6617	414	7	to	to	ADP
ejpam-6617	414	8	the	the	DET
ejpam-6617	414	9	primal	primal	ADJ
ejpam-6617	414	10	(	(	PUNCT
ejpam-6617	414	11	p-4	p-4	NOUN
ejpam-6617	414	12	):	):	PUNCT
ejpam-6617	414	13	(	(	PUNCT
ejpam-6617	414	14	wd-1	wd-1	X
ejpam-6617	414	15	)	)	PUNCT
ejpam-6617	414	16	=	=	SYM
ejpam-6617	415	1	max	max	NOUN
ejpam-6617	415	2	a2∫	a2∫	NOUN
ejpam-6617	415	3	a1	a1	NOUN
ejpam-6617	415	4	[	[	PUNCT
ejpam-6617	415	5	[	[	PUNCT
ejpam-6617	415	6	ϕl(ς	ϕl(ς	X
ejpam-6617	415	7	,	,	PUNCT
ejpam-6617	415	8	ε	ε	PROPN
ejpam-6617	415	9	,	,	PUNCT
ejpam-6617	415	10	cfdθ•	cfdθ•	PROPN
ejpam-6617	415	11	a1+ε	a1+ε	PROPN
ejpam-6617	415	12	)	)	PUNCT
ejpam-6617	415	13	,	,	PUNCT
ejpam-6617	415	14	ϕu	ϕu	X
ejpam-6617	415	15	(	(	PUNCT
ejpam-6617	415	16	ς	ς	PROPN
ejpam-6617	415	17	,	,	PUNCT
ejpam-6617	415	18	ε	ε	PROPN
ejpam-6617	415	19	,	,	PUNCT
ejpam-6617	415	20	cfdθ•	cfdθ•	PROPN
ejpam-6617	415	21	a1+ε	a1+ε	PROPN
ejpam-6617	415	22	)	)	PUNCT
ejpam-6617	415	23	]	]	PUNCT
ejpam-6617	416	1	+	+	CCONJ
ejpam-6617	416	2	(	(	PUNCT
ejpam-6617	416	3	θ̄)th(ς	θ̄)th(ς	PROPN
ejpam-6617	416	4	,	,	PUNCT
ejpam-6617	416	5	ε	ε	PROPN
ejpam-6617	416	6	,	,	PUNCT
ejpam-6617	416	7	cfdθ•	cfdθ•	PROPN
ejpam-6617	416	8	a1+ε(ς	a1+ε(ς	X
ejpam-6617	416	9	)	)	PUNCT
ejpam-6617	416	10	)	)	PUNCT
ejpam-6617	416	11	]	]	PUNCT
ejpam-6617	417	1	dς	dς	X
ejpam-6617	417	2	,	,	PUNCT
ejpam-6617	417	3	•	•	NOUN
ejpam-6617	417	4	set	set	NOUN
ejpam-6617	417	5	of	of	ADP
ejpam-6617	417	6	constraints	constraint	NOUN
ejpam-6617	417	7	for	for	ADP
ejpam-6617	417	8	(	(	PUNCT
ejpam-6617	417	9	wd-1	wd-1	X
ejpam-6617	417	10	):	):	PUNCT
ejpam-6617	417	11	ϕl	ϕl	PROPN
ejpam-6617	417	12	ε	ε	PROPN
ejpam-6617	417	13	(	(	PUNCT
ejpam-6617	417	14	ς	ς	PROPN
ejpam-6617	417	15	,	,	PUNCT
ejpam-6617	417	16	ε	ε	PROPN
ejpam-6617	417	17	,	,	PUNCT
ejpam-6617	417	18	cfdθ•	cfdθ•	PROPN
ejpam-6617	417	19	a1+ε	a1+ε	PROPN
ejpam-6617	417	20	)	)	PUNCT
ejpam-6617	417	21	+	+	CCONJ
ejpam-6617	417	22	ϕu	ϕu	PROPN
ejpam-6617	417	23	ε	ε	PROPN
ejpam-6617	417	24	(	(	PUNCT
ejpam-6617	417	25	ς	ς	PROPN
ejpam-6617	417	26	,	,	PUNCT
ejpam-6617	417	27	ε	ε	PROPN
ejpam-6617	417	28	,	,	PUNCT
ejpam-6617	417	29	cfdθ•	cfdθ•	PROPN
ejpam-6617	417	30	a1+ε	a1+ε	PROPN
ejpam-6617	417	31	)	)	PUNCT
ejpam-6617	417	32	+	+	CCONJ
ejpam-6617	417	33	(	(	PUNCT
ejpam-6617	417	34	θ̄)t	θ̄)t	NOUN
ejpam-6617	417	35	(	(	PUNCT
ejpam-6617	417	36	ς)hε(ς	ς)hε(ς	PROPN
ejpam-6617	417	37	,	,	PUNCT
ejpam-6617	417	38	ε	ε	PROPN
ejpam-6617	417	39	,	,	PUNCT
ejpam-6617	417	40	cfdθ•	cfdθ•	PROPN
ejpam-6617	417	41	a1+ε(ς	a1+ε(ς	X
ejpam-6617	417	42	)	)	PUNCT
ejpam-6617	417	43	)	)	PUNCT
ejpam-6617	418	1	=	=	PUNCT
ejpam-6617	418	2	−cfdθ•	−cfdθ•	NOUN
ejpam-6617	418	3	a2−	a2−	PROPN
ejpam-6617	418	4	{	{	PUNCT
ejpam-6617	418	5	ϕl	ϕl	PROPN
ejpam-6617	418	6	cfdθ•	cfdθ•	PROPN
ejpam-6617	418	7	a1	a1	PROPN
ejpam-6617	418	8	+	+	X
ejpam-6617	418	9	ε(ς	ε(ς	NOUN
ejpam-6617	418	10	)	)	PUNCT
ejpam-6617	418	11	(	(	PUNCT
ejpam-6617	418	12	ς	ς	PROPN
ejpam-6617	418	13	,	,	PUNCT
ejpam-6617	418	14	ε	ε	PROPN
ejpam-6617	418	15	,	,	PUNCT
ejpam-6617	418	16	cfdθ•	cfdθ•	PROPN
ejpam-6617	418	17	a1+ε	a1+ε	PROPN
ejpam-6617	418	18	)	)	PUNCT
ejpam-6617	418	19	+	+	PROPN
ejpam-6617	418	20	ϕu	ϕu	PROPN
ejpam-6617	418	21	cfdθ•	cfdθ•	PROPN
ejpam-6617	418	22	a1	a1	PROPN
ejpam-6617	418	23	+	+	X
ejpam-6617	418	24	ε(ς	ε(ς	NOUN
ejpam-6617	418	25	)	)	PUNCT
ejpam-6617	418	26	(	(	PUNCT
ejpam-6617	418	27	ς	ς	PROPN
ejpam-6617	418	28	,	,	PUNCT
ejpam-6617	418	29	ε	ε	PROPN
ejpam-6617	418	30	,	,	PUNCT
ejpam-6617	418	31	cfdθ•	cfdθ•	PROPN
ejpam-6617	418	32	a1+ε	a1+ε	PROPN
ejpam-6617	418	33	)	)	PUNCT
ejpam-6617	418	34	+	+	PROPN
ejpam-6617	418	35	(	(	PUNCT
ejpam-6617	418	36	θ̄)t	θ̄)t	PROPN
ejpam-6617	418	37	(	(	PUNCT
ejpam-6617	418	38	ς)hcfdθ•	ς)hcfdθ•	NOUN
ejpam-6617	418	39	a1	a1	NOUN
ejpam-6617	418	40	+	+	CCONJ
ejpam-6617	418	41	ε(ς)(ς	ε(ς)(ς	PROPN
ejpam-6617	418	42	,	,	PUNCT
ejpam-6617	418	43	ε	ε	PROPN
ejpam-6617	418	44	,	,	PUNCT
ejpam-6617	418	45	cfdθ•	cfdθ•	PROPN
ejpam-6617	418	46	a1+ε(ς	a1+ε(ς	X
ejpam-6617	418	47	)	)	PUNCT
ejpam-6617	418	48	)	)	PUNCT
ejpam-6617	418	49	}	}	PUNCT
ejpam-6617	418	50	,	,	PUNCT
ejpam-6617	418	51	a2∫	a2∫	NOUN
ejpam-6617	418	52	a1	a1	NOUN
ejpam-6617	418	53	(	(	PUNCT
ejpam-6617	418	54	θ̄)t	θ̄)t	NOUN
ejpam-6617	418	55	(	(	PUNCT
ejpam-6617	418	56	ς)h(ς	ς)h(ς	X
ejpam-6617	418	57	,	,	PUNCT
ejpam-6617	418	58	ε(ς),cfdθ•	ε(ς),cfdθ•	PROPN
ejpam-6617	418	59	a1+ε(ς))dς	a1+ε(ς))dς	PROPN
ejpam-6617	418	60	≤	≤	ADV
ejpam-6617	418	61	0	0	NUM
ejpam-6617	418	62	,	,	PUNCT
ejpam-6617	418	63	θ̄(ξ	θ̄(ξ	PROPN
ejpam-6617	418	64	)	)	PUNCT
ejpam-6617	418	65	≥	≥	NOUN
ejpam-6617	418	66	0	0	NUM
ejpam-6617	418	67	,	,	PUNCT
ejpam-6617	418	68	ς	ς	PROPN
ejpam-6617	418	69	∈	∈	PROPN
ejpam-6617	418	70	ℑ,where	ℑ,where	X
ejpam-6617	418	71	a1	a1	NOUN
ejpam-6617	418	72	=	=	SYM
ejpam-6617	418	73	0	0	NUM
ejpam-6617	418	74	,	,	PUNCT
ejpam-6617	418	75	a2	a2	PROPN
ejpam-6617	418	76	=	=	NOUN
ejpam-6617	418	77	1	1	X
ejpam-6617	418	78	.	.	PUNCT
ejpam-6617	419	1	v.	v.	CCONJ
ejpam-6617	419	2	rayanki	rayanki	PROPN
ejpam-6617	419	3	et	et	PROPN
ejpam-6617	419	4	al	al	PROPN
ejpam-6617	419	5	.	.	PUNCT
ejpam-6617	419	6	/	/	SYM
ejpam-6617	419	7	eur	eur	PROPN
ejpam-6617	419	8	.	.	PUNCT
ejpam-6617	420	1	j.	j.	PROPN
ejpam-6617	420	2	pure	pure	PROPN
ejpam-6617	420	3	appl	appl	PROPN
ejpam-6617	420	4	.	.	PROPN
ejpam-6617	420	5	math	math	PROPN
ejpam-6617	420	6	,	,	PUNCT
ejpam-6617	420	7	18	18	NUM
ejpam-6617	420	8	(	(	PUNCT
ejpam-6617	420	9	3	3	NUM
ejpam-6617	420	10	)	)	PUNCT
ejpam-6617	420	11	(	(	PUNCT
ejpam-6617	420	12	2025	2025	NUM
ejpam-6617	420	13	)	)	PUNCT
ejpam-6617	420	14	,	,	PUNCT
ejpam-6617	420	15	6617	6617	NUM
ejpam-6617	420	16	27	27	NUM
ejpam-6617	420	17	of	of	ADP
ejpam-6617	420	18	38	38	NUM
ejpam-6617	420	19	•	•	NOUN
ejpam-6617	420	20	set	set	NOUN
ejpam-6617	420	21	of	of	ADP
ejpam-6617	420	22	feasible	feasible	ADJ
ejpam-6617	420	23	point	point	NOUN
ejpam-6617	420	24	for	for	ADP
ejpam-6617	420	25	(	(	PUNCT
ejpam-6617	420	26	wd-1	wd-1	X
ejpam-6617	420	27	):	):	PUNCT
ejpam-6617	420	28	w3	w3	PROPN
ejpam-6617	420	29	=	=	SYM
ejpam-6617	420	30	{	{	PUNCT
ejpam-6617	420	31	(	(	PUNCT
ejpam-6617	420	32	θ̄	θ̄	ADJ
ejpam-6617	420	33	,	,	PUNCT
ejpam-6617	420	34	ε̄	ε̄	NOUN
ejpam-6617	420	35	)	)	PUNCT
ejpam-6617	420	36	:	:	PUNCT
ejpam-6617	420	37	θ̄	θ̄	PROPN
ejpam-6617	420	38	∈	∈	PROPN
ejpam-6617	420	39	rm	rm	PROPN
ejpam-6617	420	40	,	,	PUNCT
ejpam-6617	420	41	ε	ε	PROPN
ejpam-6617	420	42	∈	∈	PROPN
ejpam-6617	420	43	x	x	X
ejpam-6617	420	44	:	:	PUNCT
ejpam-6617	420	45	satisfying	satisfy	VERB
ejpam-6617	420	46	constraints	constraint	NOUN
ejpam-6617	420	47	of	of	ADP
ejpam-6617	420	48	(	(	PUNCT
ejpam-6617	420	49	wd-1	wd-1	X
ejpam-6617	420	50	)	)	PUNCT
ejpam-6617	420	51	,	,	PUNCT
ejpam-6617	420	52	forall	forall	VERB
ejpam-6617	420	53	ς	ς	PROPN
ejpam-6617	420	54	∈	∈	PROPN
ejpam-6617	420	55	ℑ	ℑ	PROPN
ejpam-6617	420	56	}	}	PUNCT
ejpam-6617	420	57	•	•	NOUN
ejpam-6617	420	58	set	set	NOUN
ejpam-6617	420	59	of	of	ADP
ejpam-6617	420	60	self	self	NOUN
ejpam-6617	420	61	data	datum	NOUN
ejpam-6617	420	62	:	:	PUNCT
ejpam-6617	420	63	where	where	SCONJ
ejpam-6617	420	64	,	,	PUNCT
ejpam-6617	420	65	ϕlς	ϕlς	PROPN
ejpam-6617	420	66	,	,	PUNCT
ejpam-6617	420	67	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	420	68	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	420	69	)	)	PUNCT
ejpam-6617	420	70	)	)	PUNCT
ejpam-6617	420	71	,	,	PUNCT
ejpam-6617	420	72	ϕu	ϕu	INTJ
ejpam-6617	420	73	(	(	PUNCT
ejpam-6617	420	74	ς	ς	PROPN
ejpam-6617	420	75	,	,	PUNCT
ejpam-6617	420	76	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	420	77	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	420	78	)	)	PUNCT
ejpam-6617	420	79	)	)	PUNCT
ejpam-6617	420	80	,	,	PUNCT
ejpam-6617	420	81	h(ς	h(ς	PROPN
ejpam-6617	420	82	,	,	PUNCT
ejpam-6617	420	83	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	420	84	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	420	85	)	)	PUNCT
ejpam-6617	420	86	)	)	PUNCT
ejpam-6617	420	87	and	and	CCONJ
ejpam-6617	420	88	κ(ς)are	κ(ς)are	VERB
ejpam-6617	420	89	continuously	continuously	ADV
ejpam-6617	420	90	differentiable	differentiable	ADJ
ejpam-6617	420	91	functions	function	NOUN
ejpam-6617	420	92	and	and	CCONJ
ejpam-6617	420	93	are	be	AUX
ejpam-6617	420	94	invexity	invexity	NOUN
ejpam-6617	420	95	for	for	ADP
ejpam-6617	420	96	.	.	PUNCT
ejpam-6617	421	1	ς	ς	PROPN
ejpam-6617	421	2	∈	∈	PROPN
ejpam-6617	421	3	φ3	φ3	NOUN
ejpam-6617	421	4	.	.	PUNCT
ejpam-6617	422	1	output	output	NOUN
ejpam-6617	422	2	:	:	PUNCT
ejpam-6617	422	3	•	•	NUM
ejpam-6617	422	4	verification	verification	NOUN
ejpam-6617	422	5	of	of	ADP
ejpam-6617	422	6	invexity	invexity	NOUN
ejpam-6617	422	7	:	:	PUNCT
ejpam-6617	422	8	ϕl(ς	ϕl(ς	NUM
ejpam-6617	422	9	,	,	PUNCT
ejpam-6617	422	10	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	422	11	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	422	12	)	)	PUNCT
ejpam-6617	422	13	)	)	PUNCT
ejpam-6617	423	1	ϕu	ϕu	INTJ
ejpam-6617	423	2	(	(	PUNCT
ejpam-6617	423	3	ς	ς	PROPN
ejpam-6617	423	4	,	,	PUNCT
ejpam-6617	423	5	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	423	6	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	423	7	)	)	PUNCT
ejpam-6617	423	8	ϕl(ς	ϕl(ς	PUNCT
ejpam-6617	423	9	,	,	PUNCT
ejpam-6617	423	10	ε(ς),cfdθ•	ε(ς),cfdθ•	PROPN
ejpam-6617	423	11	a1+ε(ς	a1+ε(ς	X
ejpam-6617	423	12	)	)	PUNCT
ejpam-6617	423	13	)	)	PUNCT
ejpam-6617	424	1	+	+	CCONJ
ejpam-6617	424	2	(	(	PUNCT
ejpam-6617	424	3	θ̄)t	θ̄)t	NOUN
ejpam-6617	424	4	(	(	PUNCT
ejpam-6617	424	5	ς)h(ς	ς)h(ς	X
ejpam-6617	424	6	,	,	PUNCT
ejpam-6617	424	7	ε(ς	ε(ς	NOUN
ejpam-6617	424	8	)	)	PUNCT
ejpam-6617	424	9	,	,	PUNCT
ejpam-6617	424	10	ϕu	ϕu	X
ejpam-6617	424	11	(	(	PUNCT
ejpam-6617	424	12	ς	ς	PROPN
ejpam-6617	424	13	,	,	PUNCT
ejpam-6617	424	14	ε(ς),cfdθ•	ε(ς),cfdθ•	PROPN
ejpam-6617	424	15	a1+ε(ς	a1+ε(ς	X
ejpam-6617	424	16	)	)	PUNCT
ejpam-6617	424	17	)	)	PUNCT
ejpam-6617	425	1	+	+	CCONJ
ejpam-6617	425	2	(	(	PUNCT
ejpam-6617	425	3	θ̄)t	θ̄)t	NOUN
ejpam-6617	425	4	(	(	PUNCT
ejpam-6617	425	5	ς)h(ς	ς)h(ς	X
ejpam-6617	425	6	,	,	PUNCT
ejpam-6617	425	7	ε(ς	ε(ς	NOUN
ejpam-6617	425	8	)	)	PUNCT
ejpam-6617	425	9	,	,	PUNCT
ejpam-6617	425	10	h(ς	h(ς	PROPN
ejpam-6617	425	11	,	,	PUNCT
ejpam-6617	425	12	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	425	13	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	425	14	)	)	PUNCT
ejpam-6617	425	15	)	)	PUNCT
ejpam-6617	425	16	,	,	PUNCT
ejpam-6617	425	17	ς	ς	PROPN
ejpam-6617	425	18	∈	∈	PROPN
ejpam-6617	425	19	φ3,w3	φ3,w3	PROPN
ejpam-6617	425	20	.	.	PUNCT
ejpam-6617	426	1	the	the	DET
ejpam-6617	426	2	point	point	NOUN
ejpam-6617	426	3	κ̄	κ̄	PROPN
ejpam-6617	426	4	,	,	PUNCT
ejpam-6617	426	5	the	the	DET
ejpam-6617	426	6	point	point	NOUN
ejpam-6617	426	7	ε̄	ε̄	NOUN
ejpam-6617	426	8	is	be	AUX
ejpam-6617	426	9	satisfying	satisfy	VERB
ejpam-6617	426	10	the	the	DET
ejpam-6617	426	11	definition12	definition12	NOUN
ejpam-6617	426	12	.	.	PUNCT
ejpam-6617	427	1	set	set	NOUN
ejpam-6617	427	2	of	of	ADP
ejpam-6617	427	3	self	self	NOUN
ejpam-6617	427	4	data	datum	NOUN
ejpam-6617	427	5	.	.	PUNCT
ejpam-6617	428	1	begin	begin	VERB
ejpam-6617	428	2	:	:	PUNCT
ejpam-6617	428	3	main	main	ADJ
ejpam-6617	428	4	optimization	optimization	NOUN
ejpam-6617	428	5	loop	loop	NOUN
ejpam-6617	428	6	:	:	PUNCT
ejpam-6617	428	7	primary	primary	ADJ
ejpam-6617	428	8	problem	problem	NOUN
ejpam-6617	428	9	solution	solution	NOUN
ejpam-6617	428	10	:	:	PUNCT
ejpam-6617	428	11	•	•	X
ejpam-6617	428	12	while	while	SCONJ
ejpam-6617	428	13	not	not	PART
ejpam-6617	428	14	converged	converge	VERB
ejpam-6617	428	15	:	:	PUNCT
ejpam-6617	428	16	•	•	NUM
ejpam-6617	428	17	compute	compute	PROPN
ejpam-6617	428	18	caputo	caputo	PROPN
ejpam-6617	428	19	-	-	PUNCT
ejpam-6617	428	20	fabrizio	fabrizio	PROPN
ejpam-6617	428	21	fractional	fractional	ADJ
ejpam-6617	428	22	derivative	derivative	NOUN
ejpam-6617	428	23	:	:	PUNCT
ejpam-6617	428	24	cfdθ•	cfdθ•	PROPN
ejpam-6617	428	25	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	428	26	)	)	PUNCT
ejpam-6617	428	27	•	•	X
ejpam-6617	428	28	evaluate	evaluate	VERB
ejpam-6617	428	29	objective	objective	ADJ
ejpam-6617	428	30	functions	function	NOUN
ejpam-6617	428	31	v.	v.	ADP
ejpam-6617	428	32	rayanki	rayanki	X
ejpam-6617	428	33	et	et	PROPN
ejpam-6617	428	34	al	al	PROPN
ejpam-6617	428	35	.	.	PUNCT
ejpam-6617	428	36	/	/	SYM
ejpam-6617	428	37	eur	eur	PROPN
ejpam-6617	428	38	.	.	PUNCT
ejpam-6617	429	1	j.	j.	PROPN
ejpam-6617	429	2	pure	pure	PROPN
ejpam-6617	429	3	appl	appl	PROPN
ejpam-6617	429	4	.	.	PROPN
ejpam-6617	429	5	math	math	PROPN
ejpam-6617	429	6	,	,	PUNCT
ejpam-6617	429	7	18	18	NUM
ejpam-6617	429	8	(	(	PUNCT
ejpam-6617	429	9	3	3	NUM
ejpam-6617	429	10	)	)	PUNCT
ejpam-6617	429	11	(	(	PUNCT
ejpam-6617	429	12	2025	2025	NUM
ejpam-6617	429	13	)	)	PUNCT
ejpam-6617	429	14	,	,	PUNCT
ejpam-6617	429	15	6617	6617	NUM
ejpam-6617	429	16	28	28	NUM
ejpam-6617	429	17	of	of	ADP
ejpam-6617	429	18	38	38	NUM
ejpam-6617	429	19	jl	jl	NOUN
ejpam-6617	429	20	=	=	PUNCT
ejpam-6617	429	21	a2∫	a2∫	X
ejpam-6617	429	22	a1	a1	NOUN
ejpam-6617	429	23	ϕl(ς	ϕl(ς	PUNCT
ejpam-6617	429	24	,	,	PUNCT
ejpam-6617	429	25	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	429	26	a1+κ(ς))dς	a1+κ(ς))dς	PROPN
ejpam-6617	429	27	,	,	PUNCT
ejpam-6617	429	28	ju	ju	NOUN
ejpam-6617	429	29	=	=	PUNCT
ejpam-6617	429	30	a2∫	a2∫	X
ejpam-6617	429	31	a1	a1	NOUN
ejpam-6617	429	32	ϕu	ϕu	X
ejpam-6617	429	33	(	(	PUNCT
ejpam-6617	429	34	ς	ς	PROPN
ejpam-6617	429	35	,	,	PUNCT
ejpam-6617	429	36	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	429	37	a1+κ(ς))dς	a1+κ(ς))dς	ADV
ejpam-6617	429	38	•	•	NOUN
ejpam-6617	429	39	check	check	NOUN
ejpam-6617	429	40	constraints	constraint	NOUN
ejpam-6617	429	41	h(ς	h(ς	PROPN
ejpam-6617	429	42	,	,	PUNCT
ejpam-6617	429	43	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	429	44	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	429	45	)	)	PUNCT
ejpam-6617	429	46	)	)	PUNCT
ejpam-6617	430	1	≤	≤	ADV
ejpam-6617	430	2	0	0	NUM
ejpam-6617	430	3	,	,	PUNCT
ejpam-6617	430	4	∀	∀	X
ejpam-6617	430	5	ς	ς	PROPN
ejpam-6617	430	6	∈	∈	PROPN
ejpam-6617	430	7	[	[	X
ejpam-6617	430	8	a1	a1	NOUN
ejpam-6617	430	9	,	,	PUNCT
ejpam-6617	430	10	a2	a2	PROPN
ejpam-6617	430	11	]	]	PUNCT
ejpam-6617	430	12	and	and	CCONJ
ejpam-6617	430	13	•	•	NOUN
ejpam-6617	430	14	boundary	boundary	ADJ
ejpam-6617	430	15	conditions	condition	NOUN
ejpam-6617	430	16	are	be	AUX
ejpam-6617	430	17	satisfied	satisfied	ADJ
ejpam-6617	430	18	:	:	PUNCT
ejpam-6617	430	19	•	•	NUM
ejpam-6617	430	20	solution	solution	NOUN
ejpam-6617	430	21	is	be	AUX
ejpam-6617	430	22	feasible	feasible	ADJ
ejpam-6617	430	23	•	•	NUM
ejpam-6617	430	24	store	store	NOUN
ejpam-6617	430	25	current	current	ADJ
ejpam-6617	430	26	solution	solution	NOUN
ejpam-6617	430	27	•	•	ADV
ejpam-6617	430	28	else	else	ADV
ejpam-6617	430	29	:	:	PUNCT
ejpam-6617	430	30	•	•	ADP
ejpam-6617	430	31	apply	apply	VERB
ejpam-6617	430	32	constraint	constraint	NOUN
ejpam-6617	430	33	projection	projection	NOUN
ejpam-6617	430	34	•	•	NOUN
ejpam-6617	430	35	update	update	NOUN
ejpam-6617	430	36	solution	solution	NOUN
ejpam-6617	430	37	using	use	VERB
ejpam-6617	430	38	gradient	gradient	ADJ
ejpam-6617	430	39	descent	descent	NOUN
ejpam-6617	430	40	or	or	CCONJ
ejpam-6617	430	41	other	other	ADJ
ejpam-6617	430	42	optimization	optimization	NOUN
ejpam-6617	430	43	κ̄k+1	κ̄k+1	NOUN
ejpam-6617	430	44	=	=	SYM
ejpam-6617	430	45	update	update	NOUN
ejpam-6617	430	46	solution(κ̄k	solution(κ̄k	PROPN
ejpam-6617	430	47	,	,	PUNCT
ejpam-6617	430	48	j	j	PROPN
ejpam-6617	430	49	l	l	PROPN
ejpam-6617	430	50	,	,	PUNCT
ejpam-6617	430	51	ju	ju	PROPN
ejpam-6617	430	52	,	,	PUNCT
ejpam-6617	430	53	constraints	constraint	NOUN
ejpam-6617	430	54	)	)	PUNCT
ejpam-6617	430	55	•	•	NUM
ejpam-6617	430	56	check	check	NOUN
ejpam-6617	430	57	convergence	convergence	NOUN
ejpam-6617	430	58	criteria	criterion	NOUN
ejpam-6617	430	59	wolfe	wolfe	PROPN
ejpam-6617	430	60	-	-	PUNCT
ejpam-6617	430	61	type	type	NOUN
ejpam-6617	430	62	dual	dual	ADJ
ejpam-6617	430	63	problem	problem	NOUN
ejpam-6617	430	64	(	(	PUNCT
ejpam-6617	430	65	wd-1	wd-1	X
ejpam-6617	430	66	)	)	PUNCT
ejpam-6617	430	67	solution	solution	NOUN
ejpam-6617	430	68	:	:	PUNCT
ejpam-6617	430	69	•	•	ADP
ejpam-6617	430	70	while	while	SCONJ
ejpam-6617	430	71	not	not	PART
ejpam-6617	430	72	converged	converge	VERB
ejpam-6617	430	73	:	:	PUNCT
ejpam-6617	430	74	•	•	NUM
ejpam-6617	430	75	compute	compute	NOUN
ejpam-6617	430	76	adjoint	adjoint	NOUN
ejpam-6617	430	77	system	system	NOUN
ejpam-6617	430	78	solve	solve	VERB
ejpam-6617	430	79	the	the	DET
ejpam-6617	430	80	euler	euler	NOUN
ejpam-6617	430	81	-	-	PUNCT
ejpam-6617	430	82	lagrange	lagrange	NOUN
ejpam-6617	430	83	type	type	NOUN
ejpam-6617	430	84	equation	equation	NOUN
ejpam-6617	430	85	:	:	PUNCT
ejpam-6617	430	86	ϕl	ϕl	PROPN
ejpam-6617	430	87	ε	ε	PROPN
ejpam-6617	430	88	(	(	PUNCT
ejpam-6617	430	89	ς	ς	PROPN
ejpam-6617	430	90	,	,	PUNCT
ejpam-6617	430	91	ε	ε	PROPN
ejpam-6617	430	92	,	,	PUNCT
ejpam-6617	430	93	cfdθ•	cfdθ•	PROPN
ejpam-6617	430	94	a1+ε	a1+ε	PROPN
ejpam-6617	430	95	)	)	PUNCT
ejpam-6617	430	96	+	+	CCONJ
ejpam-6617	430	97	ϕu	ϕu	PROPN
ejpam-6617	430	98	ε	ε	PROPN
ejpam-6617	430	99	(	(	PUNCT
ejpam-6617	430	100	ς	ς	PROPN
ejpam-6617	430	101	,	,	PUNCT
ejpam-6617	430	102	ε	ε	PROPN
ejpam-6617	430	103	,	,	PUNCT
ejpam-6617	430	104	cfdθ•	cfdθ•	PROPN
ejpam-6617	430	105	a1+ε	a1+ε	PROPN
ejpam-6617	430	106	)	)	PUNCT
ejpam-6617	430	107	+	+	CCONJ
ejpam-6617	430	108	(	(	PUNCT
ejpam-6617	430	109	θ̄)t	θ̄)t	NOUN
ejpam-6617	430	110	(	(	PUNCT
ejpam-6617	430	111	ς)hε(ς	ς)hε(ς	PROPN
ejpam-6617	430	112	,	,	PUNCT
ejpam-6617	430	113	ε	ε	PROPN
ejpam-6617	430	114	,	,	PUNCT
ejpam-6617	430	115	cfdθ•	cfdθ•	PROPN
ejpam-6617	430	116	a1+ε(ς	a1+ε(ς	X
ejpam-6617	430	117	)	)	PUNCT
ejpam-6617	430	118	)	)	PUNCT
ejpam-6617	431	1	+	+	CCONJ
ejpam-6617	431	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	431	3	a2−	a2−	PROPN
ejpam-6617	431	4	{	{	PUNCT
ejpam-6617	431	5	ϕl	ϕl	PROPN
ejpam-6617	431	6	cfdθ•	cfdθ•	PROPN
ejpam-6617	431	7	a1	a1	PROPN
ejpam-6617	431	8	+	+	X
ejpam-6617	431	9	ε(ς	ε(ς	NOUN
ejpam-6617	431	10	)	)	PUNCT
ejpam-6617	431	11	(	(	PUNCT
ejpam-6617	431	12	ς	ς	PROPN
ejpam-6617	431	13	,	,	PUNCT
ejpam-6617	431	14	ε	ε	PROPN
ejpam-6617	431	15	,	,	PUNCT
ejpam-6617	431	16	cfdθ•	cfdθ•	PROPN
ejpam-6617	431	17	a1+ε	a1+ε	PROPN
ejpam-6617	431	18	)	)	PUNCT
ejpam-6617	431	19	+	+	PROPN
ejpam-6617	431	20	ϕu	ϕu	PROPN
ejpam-6617	431	21	cfdθ•	cfdθ•	PROPN
ejpam-6617	431	22	a1	a1	PROPN
ejpam-6617	431	23	+	+	X
ejpam-6617	431	24	ε(ς	ε(ς	NOUN
ejpam-6617	431	25	)	)	PUNCT
ejpam-6617	431	26	(	(	PUNCT
ejpam-6617	431	27	ς	ς	PROPN
ejpam-6617	431	28	,	,	PUNCT
ejpam-6617	431	29	ε	ε	PROPN
ejpam-6617	431	30	,	,	PUNCT
ejpam-6617	431	31	cfdθ•	cfdθ•	PROPN
ejpam-6617	431	32	a1+ε	a1+ε	PROPN
ejpam-6617	431	33	)	)	PUNCT
ejpam-6617	431	34	+	+	PROPN
ejpam-6617	431	35	(	(	PUNCT
ejpam-6617	431	36	θ̄)t	θ̄)t	PROPN
ejpam-6617	431	37	(	(	PUNCT
ejpam-6617	431	38	ς)hcfdθ•	ς)hcfdθ•	NOUN
ejpam-6617	431	39	a1	a1	NOUN
ejpam-6617	431	40	+	+	CCONJ
ejpam-6617	431	41	ε(ς)(ς	ε(ς)(ς	PROPN
ejpam-6617	431	42	,	,	PUNCT
ejpam-6617	431	43	ε	ε	PROPN
ejpam-6617	431	44	,	,	PUNCT
ejpam-6617	431	45	cfdθ•	cfdθ•	PROPN
ejpam-6617	431	46	a1+ε(ς	a1+ε(ς	X
ejpam-6617	431	47	)	)	PUNCT
ejpam-6617	431	48	)	)	PUNCT
ejpam-6617	431	49	}	}	PUNCT
ejpam-6617	432	1	=	=	PUNCT
ejpam-6617	432	2	0	0	NUM
ejpam-6617	432	3	.	.	NOUN
ejpam-6617	432	4	•	•	NOUN
ejpam-6617	432	5	check	check	VERB
ejpam-6617	432	6	dual	dual	ADJ
ejpam-6617	432	7	constraints	constraint	NOUN
ejpam-6617	432	8	a2∫	a2∫	NOUN
ejpam-6617	432	9	a1	a1	NOUN
ejpam-6617	432	10	(	(	PUNCT
ejpam-6617	432	11	θ̄)t	θ̄)t	NOUN
ejpam-6617	432	12	(	(	PUNCT
ejpam-6617	432	13	ς)h(ς	ς)h(ς	X
ejpam-6617	432	14	,	,	PUNCT
ejpam-6617	432	15	ε(ς),cfdθ•	ε(ς),cfdθ•	PROPN
ejpam-6617	432	16	a1+ε(ς))dς	a1+ε(ς))dς	PROPN
ejpam-6617	432	17	≤	≤	ADV
ejpam-6617	432	18	0	0	NUM
ejpam-6617	432	19	,	,	PUNCT
ejpam-6617	432	20	•	•	NOUN
ejpam-6617	432	21	and	and	CCONJ
ejpam-6617	432	22	boundary	boundary	ADJ
ejpam-6617	432	23	conditions	condition	NOUN
ejpam-6617	432	24	θ̄(ξ	θ̄(ξ	PROPN
ejpam-6617	432	25	)	)	PUNCT
ejpam-6617	432	26	≥	≥	NOUN
ejpam-6617	432	27	0	0	NUM
ejpam-6617	432	28	,	,	PUNCT
ejpam-6617	432	29	ς	ς	PROPN
ejpam-6617	432	30	∈	∈	PROPN
ejpam-6617	432	31	ℑ	ℑ	PROPN
ejpam-6617	432	32	=	=	PUNCT
ejpam-6617	433	1	[	[	X
ejpam-6617	433	2	a1	a1	NOUN
ejpam-6617	433	3	,	,	PUNCT
ejpam-6617	433	4	a2	a2	PROPN
ejpam-6617	433	5	]	]	PUNCT
ejpam-6617	433	6	.	.	PUNCT
ejpam-6617	434	1	v.	v.	CCONJ
ejpam-6617	434	2	rayanki	rayanki	PROPN
ejpam-6617	434	3	et	et	PROPN
ejpam-6617	434	4	al	al	PROPN
ejpam-6617	434	5	.	.	PUNCT
ejpam-6617	434	6	/	/	SYM
ejpam-6617	434	7	eur	eur	PROPN
ejpam-6617	434	8	.	.	PUNCT
ejpam-6617	435	1	j.	j.	PROPN
ejpam-6617	435	2	pure	pure	PROPN
ejpam-6617	435	3	appl	appl	PROPN
ejpam-6617	435	4	.	.	PROPN
ejpam-6617	435	5	math	math	PROPN
ejpam-6617	435	6	,	,	PUNCT
ejpam-6617	435	7	18	18	NUM
ejpam-6617	435	8	(	(	PUNCT
ejpam-6617	435	9	3	3	NUM
ejpam-6617	435	10	)	)	PUNCT
ejpam-6617	435	11	(	(	PUNCT
ejpam-6617	435	12	2025	2025	NUM
ejpam-6617	435	13	)	)	PUNCT
ejpam-6617	435	14	,	,	PUNCT
ejpam-6617	435	15	6617	6617	NUM
ejpam-6617	435	16	29	29	NUM
ejpam-6617	435	17	of	of	ADP
ejpam-6617	435	18	38	38	NUM
ejpam-6617	435	19	solution	solution	NOUN
ejpam-6617	435	20	is	be	AUX
ejpam-6617	435	21	feasible	feasible	ADJ
ejpam-6617	435	22	store	store	NOUN
ejpam-6617	435	23	current	current	ADJ
ejpam-6617	435	24	dual	dual	ADJ
ejpam-6617	435	25	solution	solution	NOUN
ejpam-6617	435	26	else	else	ADV
ejpam-6617	435	27	;	;	PUNCT
ejpam-6617	435	28	•	•	NUM
ejpam-6617	435	29	apply	apply	VERB
ejpam-6617	435	30	constraint	constraint	NOUN
ejpam-6617	435	31	projection	projection	NOUN
ejpam-6617	435	32	•	•	NOUN
ejpam-6617	435	33	update	update	NOUN
ejpam-6617	435	34	solution	solution	NOUN
ejpam-6617	435	35	using	use	VERB
ejpam-6617	435	36	gradient	gradient	ADJ
ejpam-6617	435	37	descent	descent	NOUN
ejpam-6617	435	38	or	or	CCONJ
ejpam-6617	435	39	other	other	ADJ
ejpam-6617	435	40	optimization	optimization	NOUN
ejpam-6617	435	41	(	(	PUNCT
ejpam-6617	435	42	θ̄k+1	θ̄k+1	VERB
ejpam-6617	435	43	,	,	PUNCT
ejpam-6617	435	44	ε̄k+1	ε̄k+1	ADJ
ejpam-6617	435	45	)	)	PUNCT
ejpam-6617	435	46	=	=	SYM
ejpam-6617	435	47	update	update	NOUN
ejpam-6617	435	48	dual	dual	ADJ
ejpam-6617	435	49	variables(θ̄k	variables(θ̄k	PROPN
ejpam-6617	435	50	,	,	PUNCT
ejpam-6617	435	51	ε̄k	ε̄k	PROPN
ejpam-6617	435	52	)	)	PUNCT
ejpam-6617	435	53	•	•	NUM
ejpam-6617	435	54	check	check	NOUN
ejpam-6617	435	55	convergence	convergence	NOUN
ejpam-6617	435	56	criteria	criterion	NOUN
ejpam-6617	435	57	verification	verification	NOUN
ejpam-6617	435	58	and	and	CCONJ
ejpam-6617	435	59	duality	duality	NOUN
ejpam-6617	435	60	check	check	NOUN
ejpam-6617	435	61	:	:	PUNCT
ejpam-6617	435	62	•	•	NUM
ejpam-6617	435	63	duality	duality	NOUN
ejpam-6617	435	64	verification	verification	NOUN
ejpam-6617	435	65	:	:	PUNCT
ejpam-6617	435	66	for	for	ADP
ejpam-6617	435	67	feasible	feasible	ADJ
ejpam-6617	435	68	solutions	solution	NOUN
ejpam-6617	435	69	(	(	PUNCT
ejpam-6617	435	70	θ̄k+1	θ̄k+1	VERB
ejpam-6617	435	71	,	,	PUNCT
ejpam-6617	435	72	ς̄k+1	ς̄k+1	X
ejpam-6617	435	73	)	)	PUNCT
ejpam-6617	435	74	,	,	PUNCT
ejpam-6617	435	75	for	for	ADP
ejpam-6617	435	76	the	the	DET
ejpam-6617	435	77	primal	primal	ADJ
ejpam-6617	435	78	problem	problem	NOUN
ejpam-6617	435	79	(	(	PUNCT
ejpam-6617	435	80	p-4	p-4	NOUN
ejpam-6617	435	81	)	)	PUNCT
ejpam-6617	435	82	and(θ̄k+1	and(θ̄k+1	VERB
ejpam-6617	435	83	,	,	PUNCT
ejpam-6617	435	84	ε̄k+1)for	ε̄k+1)for	ADP
ejpam-6617	435	85	dual	dual	ADJ
ejpam-6617	435	86	problem	problem	NOUN
ejpam-6617	435	87	(	(	PUNCT
ejpam-6617	435	88	wd-1	wd-1	X
ejpam-6617	435	89	)	)	PUNCT
ejpam-6617	435	90	verify	verify	VERB
ejpam-6617	435	91	that	that	SCONJ
ejpam-6617	435	92	the	the	DET
ejpam-6617	435	93	interval	interval	NOUN
ejpam-6617	435	94	objective	objective	ADJ
ejpam-6617	435	95	values	value	NOUN
ejpam-6617	435	96	are	be	AUX
ejpam-6617	435	97	not	not	PART
ejpam-6617	435	98	comparable	comparable	ADJ
ejpam-6617	435	99	under	under	ADP
ejpam-6617	435	100	the	the	DET
ejpam-6617	435	101	⪯lu	⪯lu	NOUN
ejpam-6617	435	102	else	else	ADV
ejpam-6617	435	103	stop	stop	NOUN
ejpam-6617	435	104	;	;	PUNCT
ejpam-6617	435	105	end	end	NOUN
ejpam-6617	435	106	;	;	PUNCT
ejpam-6617	435	107	we	we	PRON
ejpam-6617	435	108	provide	provide	VERB
ejpam-6617	435	109	an	an	DET
ejpam-6617	435	110	example	example	NOUN
ejpam-6617	435	111	for	for	SCONJ
ejpam-6617	435	112	the	the	DET
ejpam-6617	435	113	weak	weak	ADJ
ejpam-6617	435	114	duality	duality	NOUN
ejpam-6617	435	115	theorem	theorem	VERB
ejpam-6617	435	116	in	in	ADP
ejpam-6617	435	117	the	the	DET
ejpam-6617	435	118	following	following	ADJ
ejpam-6617	435	119	way	way	NOUN
ejpam-6617	435	120	:	:	PUNCT
ejpam-6617	435	121	example	example	NOUN
ejpam-6617	436	1	6	6	NUM
ejpam-6617	436	2	.	.	PUNCT
ejpam-6617	437	1	let	let	VERB
ejpam-6617	437	2	us	we	PRON
ejpam-6617	437	3	consider	consider	VERB
ejpam-6617	437	4	the	the	DET
ejpam-6617	437	5	following	follow	VERB
ejpam-6617	437	6	interval	interval	NOUN
ejpam-6617	437	7	-	-	PUNCT
ejpam-6617	437	8	valued	value	VERB
ejpam-6617	437	9	variational	variational	ADJ
ejpam-6617	437	10	programming	programming	NOUN
ejpam-6617	437	11	problem	problem	NOUN
ejpam-6617	437	12	under	under	ADP
ejpam-6617	437	13	caputo	caputo	PROPN
ejpam-6617	437	14	-	-	PUNCT
ejpam-6617	437	15	fabrizio	fabrizio	PROPN
ejpam-6617	437	16	fractional	fractional	ADJ
ejpam-6617	437	17	derivative	derivative	NOUN
ejpam-6617	437	18	:	:	PUNCT
ejpam-6617	437	19	(	(	PUNCT
ejpam-6617	437	20	p-4	p-4	NOUN
ejpam-6617	437	21	)	)	PUNCT
ejpam-6617	437	22	:	:	PUNCT
ejpam-6617	437	23	min	min	PROPN
ejpam-6617	437	24			NOUN
ejpam-6617	437	25	a2∫	a2∫	VERB
ejpam-6617	437	26	a1	a1	NOUN
ejpam-6617	437	27	ϕl(ς	ϕl(ς	PUNCT
ejpam-6617	437	28	,	,	PUNCT
ejpam-6617	437	29	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	437	30	a1+κ(ς))dς	a1+κ(ς))dς	ADV
ejpam-6617	437	31	,	,	PUNCT
ejpam-6617	437	32	a2∫	a2∫	X
ejpam-6617	437	33	a1	a1	VERB
ejpam-6617	437	34	ϕu	ϕu	X
ejpam-6617	437	35	(	(	PUNCT
ejpam-6617	437	36	ς	ς	PROPN
ejpam-6617	437	37	,	,	PUNCT
ejpam-6617	437	38	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	437	39	a1+κ(ς))dς	a1+κ(ς))dς	PRON
ejpam-6617	437	40			NOUN
ejpam-6617	437	41	subject	subject	ADJ
ejpam-6617	437	42	to	to	ADP
ejpam-6617	437	43	,	,	PUNCT
ejpam-6617	437	44	−	−	PROPN
ejpam-6617	437	45	2κ2(ς)−	2κ2(ς)−	NUM
ejpam-6617	437	46	4κ(ς	4κ(ς	NUM
ejpam-6617	437	47	)	)	PUNCT
ejpam-6617	438	1	+	+	CCONJ
ejpam-6617	438	2	3	3	NUM
ejpam-6617	438	3	√	√	NUM
ejpam-6617	438	4	(	(	PUNCT
ejpam-6617	438	5	π	π	NOUN
ejpam-6617	438	6	)	)	PUNCT
ejpam-6617	438	7	+	+	NUM
ejpam-6617	438	8	1√	1√	PROPN
ejpam-6617	438	9	(	(	PUNCT
ejpam-6617	438	10	π	π	NOUN
ejpam-6617	438	11	)	)	PUNCT
ejpam-6617	438	12	(	(	PUNCT
ejpam-6617	438	13	1−	1−	NUM
ejpam-6617	438	14	e−ς	e−ς	NOUN
ejpam-6617	438	15	)	)	PUNCT
ejpam-6617	438	16	≤	≤	NOUN
ejpam-6617	438	17	0	0	NUM
ejpam-6617	438	18	,	,	PUNCT
ejpam-6617	438	19	κ(0	κ(0	NOUN
ejpam-6617	438	20	)	)	PUNCT
ejpam-6617	438	21	=	=	SYM
ejpam-6617	438	22	1	1	NUM
ejpam-6617	438	23	,	,	PUNCT
ejpam-6617	438	24	κ(1	κ(1	PROPN
ejpam-6617	438	25	)	)	PUNCT
ejpam-6617	438	26	=	=	PUNCT
ejpam-6617	438	27	1	1	NUM
ejpam-6617	438	28	,	,	PUNCT
ejpam-6617	438	29	ς	ς	PROPN
ejpam-6617	438	30	∈	∈	PROPN
ejpam-6617	439	1	[	[	X
ejpam-6617	439	2	0	0	NUM
ejpam-6617	439	3	,	,	PUNCT
ejpam-6617	439	4	1	1	NUM
ejpam-6617	439	5	]	]	PUNCT
ejpam-6617	439	6	,	,	PUNCT
ejpam-6617	439	7	where	where	SCONJ
ejpam-6617	439	8	,	,	PUNCT
ejpam-6617	439	9	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	439	10	,	,	PUNCT
ejpam-6617	439	11	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	439	12	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	439	13	)	)	PUNCT
ejpam-6617	439	14	)	)	PUNCT
ejpam-6617	440	1	=	=	SYM
ejpam-6617	440	2	κ(ς	κ(ς	PROPN
ejpam-6617	440	3	)	)	PUNCT
ejpam-6617	441	1	+	+	CCONJ
ejpam-6617	441	2	1	1	NUM
ejpam-6617	441	3	2	2	NUM
ejpam-6617	441	4	√	√	NUM
ejpam-6617	441	5	(	(	PUNCT
ejpam-6617	441	6	π	π	NOUN
ejpam-6617	441	7	)	)	PUNCT
ejpam-6617	441	8	+	+	NUM
ejpam-6617	441	9	1√	1√	PROPN
ejpam-6617	441	10	(	(	PUNCT
ejpam-6617	441	11	π	π	NOUN
ejpam-6617	441	12	)	)	PUNCT
ejpam-6617	441	13	(	(	PUNCT
ejpam-6617	441	14	1−	1−	NUM
ejpam-6617	441	15	e−ς	e−ς	NOUN
ejpam-6617	441	16	)	)	PUNCT
ejpam-6617	441	17	,	,	PUNCT
ejpam-6617	441	18	ϕu	ϕu	X
ejpam-6617	441	19	(	(	PUNCT
ejpam-6617	441	20	ς	ς	PROPN
ejpam-6617	441	21	,	,	PUNCT
ejpam-6617	441	22	κ(ς),cfdθ•	κ(ς),cfdθ•	PROPN
ejpam-6617	441	23	a1+κ(ς	a1+κ(ς	NOUN
ejpam-6617	441	24	)	)	PUNCT
ejpam-6617	441	25	)	)	PUNCT
ejpam-6617	442	1	=	=	PUNCT
ejpam-6617	442	2	1	1	NUM
ejpam-6617	442	3	3	3	NUM
ejpam-6617	442	4	κ2(ς	κ2(ς	NOUN
ejpam-6617	442	5	)	)	PUNCT
ejpam-6617	442	6	+	+	CCONJ
ejpam-6617	442	7	3	3	NUM
ejpam-6617	442	8	√	√	NUM
ejpam-6617	442	9	(	(	PUNCT
ejpam-6617	442	10	π	π	NOUN
ejpam-6617	442	11	)	)	PUNCT
ejpam-6617	442	12	+	+	NUM
ejpam-6617	442	13	1√	1√	PROPN
ejpam-6617	442	14	(	(	PUNCT
ejpam-6617	442	15	π	π	NOUN
ejpam-6617	442	16	)	)	PUNCT
ejpam-6617	442	17	(	(	PUNCT
ejpam-6617	442	18	1−	1−	NUM
ejpam-6617	442	19	e−ς	e−ς	NOUN
ejpam-6617	442	20	)	)	PUNCT
ejpam-6617	442	21	,	,	PUNCT
ejpam-6617	442	22	and	and	CCONJ
ejpam-6617	442	23	κ(ς	κ(ς	NUM
ejpam-6617	442	24	)	)	PUNCT
ejpam-6617	442	25	=	=	NOUN
ejpam-6617	442	26	7	7	NUM
ejpam-6617	442	27	2	2	NUM
ejpam-6617	442	28	ς2	ς2	NOUN
ejpam-6617	442	29	−	−	PROPN
ejpam-6617	442	30	5.5636	5.5636	NUM
ejpam-6617	442	31	1.5896	1.5896	NUM
ejpam-6617	442	32	ς	ς	NOUN
ejpam-6617	442	33	+	+	PROPN
ejpam-6617	442	34	1	1	X
ejpam-6617	442	35	.	.	X
ejpam-6617	443	1	v.	v.	ADP
ejpam-6617	443	2	rayanki	rayanki	PROPN
ejpam-6617	443	3	et	et	PROPN
ejpam-6617	443	4	al	al	PROPN
ejpam-6617	443	5	.	.	PUNCT
ejpam-6617	443	6	/	/	SYM
ejpam-6617	443	7	eur	eur	PROPN
ejpam-6617	443	8	.	.	PUNCT
ejpam-6617	444	1	j.	j.	PROPN
ejpam-6617	444	2	pure	pure	PROPN
ejpam-6617	444	3	appl	appl	PROPN
ejpam-6617	444	4	.	.	PROPN
ejpam-6617	444	5	math	math	PROPN
ejpam-6617	444	6	,	,	PUNCT
ejpam-6617	444	7	18	18	NUM
ejpam-6617	444	8	(	(	PUNCT
ejpam-6617	444	9	3	3	NUM
ejpam-6617	444	10	)	)	PUNCT
ejpam-6617	444	11	(	(	PUNCT
ejpam-6617	444	12	2025	2025	NUM
ejpam-6617	444	13	)	)	PUNCT
ejpam-6617	444	14	,	,	PUNCT
ejpam-6617	444	15	6617	6617	NUM
ejpam-6617	444	16	30	30	NUM
ejpam-6617	444	17	of	of	ADP
ejpam-6617	444	18	38	38	NUM
ejpam-6617	444	19	the	the	DET
ejpam-6617	444	20	feasible	feasible	ADJ
ejpam-6617	444	21	region	region	NOUN
ejpam-6617	444	22	of	of	ADP
ejpam-6617	444	23	(	(	PUNCT
ejpam-6617	444	24	p-4	p-4	NOUN
ejpam-6617	444	25	)	)	PUNCT
ejpam-6617	444	26	is	be	AUX
ejpam-6617	444	27	φ3	φ3	NOUN
ejpam-6617	444	28	=	=	PUNCT
ejpam-6617	444	29	{	{	PUNCT
ejpam-6617	444	30	κ	κ	NOUN
ejpam-6617	444	31	∈	∈	PROPN
ejpam-6617	444	32	x	x	X
ejpam-6617	444	33	:	:	PUNCT
ejpam-6617	444	34	−2κ2(ς	−2κ2(ς	NOUN
ejpam-6617	444	35	)	)	PUNCT
ejpam-6617	444	36	−	−	PROPN
ejpam-6617	444	37	4κ(ς	4κ(ς	NOUN
ejpam-6617	444	38	)	)	PUNCT
ejpam-6617	445	1	+	+	CCONJ
ejpam-6617	445	2	3	3	NUM
ejpam-6617	445	3	√	√	NUM
ejpam-6617	445	4	(	(	PUNCT
ejpam-6617	445	5	π	π	NOUN
ejpam-6617	445	6	)	)	PUNCT
ejpam-6617	445	7	+	+	NUM
ejpam-6617	445	8	1√	1√	PROPN
ejpam-6617	445	9	(	(	PUNCT
ejpam-6617	445	10	π	π	NOUN
ejpam-6617	445	11	)	)	PUNCT
ejpam-6617	445	12	(	(	PUNCT
ejpam-6617	445	13	1	1	NUM
ejpam-6617	445	14	−	−	NOUN
ejpam-6617	445	15	e−ς	e−ς	NOUN
ejpam-6617	445	16	)	)	PUNCT
ejpam-6617	445	17	≤	≤	NOUN
ejpam-6617	445	18	0,κ(0	0,κ(0	NUM
ejpam-6617	445	19	)	)	PUNCT
ejpam-6617	445	20	=	=	SYM
ejpam-6617	446	1	1,κ(1	1,κ(1	NUM
ejpam-6617	446	2	)	)	PUNCT
ejpam-6617	446	3	=	=	SYM
ejpam-6617	446	4	1	1	NUM
ejpam-6617	446	5	}	}	PUNCT
ejpam-6617	446	6	.	.	PUNCT
ejpam-6617	447	1	for	for	ADP
ejpam-6617	447	2	κ	κ	PROPN
ejpam-6617	447	3	∈	∈	PROPN
ejpam-6617	447	4	φ3	φ3	NOUN
ejpam-6617	447	5	,	,	PUNCT
ejpam-6617	447	6	the	the	DET
ejpam-6617	447	7	wolfe	wolfe	NOUN
ejpam-6617	447	8	-	-	PUNCT
ejpam-6617	447	9	type	type	NOUN
ejpam-6617	447	10	dual	dual	ADJ
ejpam-6617	447	11	problem	problem	NOUN
ejpam-6617	447	12	for	for	ADP
ejpam-6617	447	13	the	the	DET
ejpam-6617	447	14	primary	primary	ADJ
ejpam-6617	447	15	problem	problem	NOUN
ejpam-6617	447	16	(	(	PUNCT
ejpam-6617	447	17	p-4	p-4	NOUN
ejpam-6617	447	18	)	)	PUNCT
ejpam-6617	447	19	is	be	AUX
ejpam-6617	447	20	given	give	VERB
ejpam-6617	447	21	by	by	ADP
ejpam-6617	447	22	(	(	PUNCT
ejpam-6617	447	23	wd-1	wd-1	X
ejpam-6617	447	24	)	)	PUNCT
ejpam-6617	447	25	:	:	PUNCT
ejpam-6617	447	26	max	max	PROPN
ejpam-6617	447	27	a2∫	a2∫	NOUN
ejpam-6617	447	28	a1	a1	NOUN
ejpam-6617	447	29	[	[	PUNCT
ejpam-6617	447	30	{	{	PUNCT
ejpam-6617	447	31	ϕl(ς	ϕl(ς	NOUN
ejpam-6617	447	32	,	,	PUNCT
ejpam-6617	447	33	ε(ς),cfdθ•	ε(ς),cfdθ•	PROPN
ejpam-6617	447	34	a1+ε(ς))dς	a1+ε(ς))dς	PROPN
ejpam-6617	447	35	,	,	PUNCT
ejpam-6617	447	36	ϕu	ϕu	X
ejpam-6617	447	37	(	(	PUNCT
ejpam-6617	447	38	ς	ς	PROPN
ejpam-6617	447	39	,	,	PUNCT
ejpam-6617	447	40	ε(ς),cfdθ•	ε(ς),cfdθ•	PROPN
ejpam-6617	447	41	a1+ε(ς	a1+ε(ς	X
ejpam-6617	447	42	)	)	PUNCT
ejpam-6617	447	43	)	)	PUNCT
ejpam-6617	447	44	}	}	PUNCT
ejpam-6617	448	1	+	+	CCONJ
ejpam-6617	448	2	(	(	PUNCT
ejpam-6617	448	3	θ̄)th(ς	θ̄)th(ς	PROPN
ejpam-6617	448	4	,	,	PUNCT
ejpam-6617	448	5	ε	ε	PROPN
ejpam-6617	448	6	,	,	PUNCT
ejpam-6617	448	7	cfdθ•	cfdθ•	PROPN
ejpam-6617	448	8	a1+ε(ς	a1+ε(ς	X
ejpam-6617	448	9	)	)	PUNCT
ejpam-6617	448	10	)	)	PUNCT
ejpam-6617	448	11	]	]	PUNCT
ejpam-6617	449	1	dς	dς	PROPN
ejpam-6617	449	2	,	,	PUNCT
ejpam-6617	449	3	subject	subject	ADJ
ejpam-6617	449	4	to	to	ADP
ejpam-6617	449	5	,	,	PUNCT
ejpam-6617	449	6	ε(0	ε(0	PROPN
ejpam-6617	449	7	)	)	PUNCT
ejpam-6617	449	8	=	=	SYM
ejpam-6617	449	9	1	1	NUM
ejpam-6617	449	10	,	,	PUNCT
ejpam-6617	449	11	ε(1	ε(1	NOUN
ejpam-6617	449	12	)	)	PUNCT
ejpam-6617	449	13	=	=	SYM
ejpam-6617	449	14	1	1	NUM
ejpam-6617	449	15	,	,	PUNCT
ejpam-6617	449	16	(	(	PUNCT
ejpam-6617	449	17	1	1	NUM
ejpam-6617	449	18	+	+	NUM
ejpam-6617	449	19	0.7825e−ς	0.7825e−ς	NUM
ejpam-6617	449	20	)	)	PUNCT
ejpam-6617	450	1	+	+	CCONJ
ejpam-6617	450	2	(	(	PUNCT
ejpam-6617	450	3	2	2	NUM
ejpam-6617	450	4	3	3	NUM
ejpam-6617	450	5	ε+	ε+	NOUN
ejpam-6617	450	6	4.7688e−ς	4.7688e−ς	NOUN
ejpam-6617	450	7	)	)	PUNCT
ejpam-6617	451	1	+	+	CCONJ
ejpam-6617	451	2	(	(	PUNCT
ejpam-6617	451	3	θ̄)t	θ̄)t	NOUN
ejpam-6617	451	4	(	(	PUNCT
ejpam-6617	451	5	−4ε−	−4ε−	VERB
ejpam-6617	451	6	4	4	NUM
ejpam-6617	451	7	+	+	NUM
ejpam-6617	451	8	4.7688e−ς	4.7688e−ς	NUM
ejpam-6617	451	9	)	)	PUNCT
ejpam-6617	452	1	+	+	CCONJ
ejpam-6617	452	2	0.9292	0.9292	NUM
ejpam-6617	452	3	d	d	NOUN
ejpam-6617	452	4	dς	dς	PROPN
ejpam-6617	452	5	{	{	PUNCT
ejpam-6617	452	6	1∫	1∫	NUM
ejpam-6617	452	7	ς	ς	PROPN
ejpam-6617	452	8	{	{	PUNCT
ejpam-6617	452	9	(	(	PUNCT
ejpam-6617	452	10	1	1	NUM
ejpam-6617	452	11	+	+	NUM
ejpam-6617	452	12	2	2	NUM
ejpam-6617	452	13	3	3	NUM
ejpam-6617	452	14	ε+	ε+	NOUN
ejpam-6617	452	15	5.5513e−ς	5.5513e−ς	NUM
ejpam-6617	452	16	)	)	PUNCT
ejpam-6617	452	17	+	+	CCONJ
ejpam-6617	452	18	(	(	PUNCT
ejpam-6617	452	19	θ̄)t	θ̄)t	NOUN
ejpam-6617	452	20	(	(	PUNCT
ejpam-6617	452	21	−2ε−	−2ε−	X
ejpam-6617	452	22	4	4	NUM
ejpam-6617	452	23	+	+	SYM
ejpam-6617	452	24	1.5641e−ς)}dς	1.5641e−ς)}dς	NUM
ejpam-6617	452	25	}	}	PUNCT
ejpam-6617	452	26	=	=	PUNCT
ejpam-6617	452	27	0	0	NUM
ejpam-6617	453	1	1∫	1∫	NUM
ejpam-6617	453	2	ς	ς	NOUN
ejpam-6617	453	3	{	{	PUNCT
ejpam-6617	453	4	(	(	PUNCT
ejpam-6617	453	5	θ̄)t	θ̄)t	NOUN
ejpam-6617	453	6	(	(	PUNCT
ejpam-6617	453	7	−4ε−	−4ε−	VERB
ejpam-6617	453	8	4	4	NUM
ejpam-6617	453	9	+	+	CCONJ
ejpam-6617	453	10	4.7688e−ς)}dς	4.7688e−ς)}dς	NUM
ejpam-6617	453	11	≤	≤	NOUN
ejpam-6617	453	12	0	0	NUM
ejpam-6617	453	13	.	.	PUNCT
ejpam-6617	454	1	let	let	VERB
ejpam-6617	454	2	w3	w3	PROPN
ejpam-6617	454	3	be	be	AUX
ejpam-6617	454	4	the	the	DET
ejpam-6617	454	5	collection	collection	NOUN
ejpam-6617	454	6	of	of	ADP
ejpam-6617	454	7	all	all	DET
ejpam-6617	454	8	feasible	feasible	ADJ
ejpam-6617	454	9	solutions	solution	NOUN
ejpam-6617	454	10	of	of	ADP
ejpam-6617	454	11	the	the	DET
ejpam-6617	454	12	problem	problem	NOUN
ejpam-6617	454	13	(	(	PUNCT
ejpam-6617	454	14	wd-1	wd-1	X
ejpam-6617	454	15	)	)	PUNCT
ejpam-6617	454	16	,	,	PUNCT
ejpam-6617	454	17	that	that	PRON
ejpam-6617	454	18	is	be	AUX
ejpam-6617	454	19	w3	w3	PROPN
ejpam-6617	454	20	=	=	SYM
ejpam-6617	454	21	{	{	PUNCT
ejpam-6617	454	22	(	(	PUNCT
ejpam-6617	454	23	θ̄	θ̄	ADJ
ejpam-6617	454	24	,	,	PUNCT
ejpam-6617	454	25	ε̄	ε̄	NOUN
ejpam-6617	454	26	)	)	PUNCT
ejpam-6617	454	27	:	:	PUNCT
ejpam-6617	454	28	θ̄	θ̄	PROPN
ejpam-6617	454	29	∈	∈	PROPN
ejpam-6617	454	30	rm	rm	PROPN
ejpam-6617	454	31	,	,	PUNCT
ejpam-6617	454	32	ε	ε	PROPN
ejpam-6617	454	33	∈	∈	PROPN
ejpam-6617	454	34	x	x	PRON
ejpam-6617	454	35	:	:	PUNCT
ejpam-6617	454	36	satisfying	satisfy	VERB
ejpam-6617	454	37	constraints	constraint	NOUN
ejpam-6617	454	38	of	of	ADP
ejpam-6617	454	39	(	(	PUNCT
ejpam-6617	454	40	wd-1	wd-1	X
ejpam-6617	454	41	)	)	PUNCT
ejpam-6617	454	42	,	,	PUNCT
ejpam-6617	454	43	forall	forall	VERB
ejpam-6617	454	44	ς	ς	PROPN
ejpam-6617	454	45	∈	∈	PROPN
ejpam-6617	454	46	ℑ	ℑ	PROPN
ejpam-6617	454	47	}	}	PUNCT
ejpam-6617	454	48	.	.	PUNCT
ejpam-6617	455	1	for	for	ADP
ejpam-6617	455	2	the	the	DET
ejpam-6617	455	3	feasible	feasible	ADJ
ejpam-6617	455	4	solutions	solution	NOUN
ejpam-6617	455	5	(	(	PUNCT
ejpam-6617	455	6	θ̄	θ̄	X
ejpam-6617	455	7	=	=	SYM
ejpam-6617	455	8	0	0	NUM
ejpam-6617	455	9	,	,	PUNCT
ejpam-6617	455	10	κ̄	κ̄	NOUN
ejpam-6617	455	11	=	=	SYM
ejpam-6617	455	12	1	1	NUM
ejpam-6617	455	13	)	)	PUNCT
ejpam-6617	455	14	of	of	ADP
ejpam-6617	455	15	(	(	PUNCT
ejpam-6617	455	16	p	p	NOUN
ejpam-6617	455	17	−	−	PROPN
ejpam-6617	455	18	4	4	NUM
ejpam-6617	455	19	)	)	PUNCT
ejpam-6617	455	20	and	and	CCONJ
ejpam-6617	455	21	(	(	PUNCT
ejpam-6617	455	22	θ̄	θ̄	X
ejpam-6617	455	23	=	=	SYM
ejpam-6617	455	24	0	0	NUM
ejpam-6617	455	25	,	,	PUNCT
ejpam-6617	455	26	ε̄	ε̄	ADJ
ejpam-6617	455	27	=	=	SYM
ejpam-6617	455	28	1	1	NUM
ejpam-6617	455	29	)	)	PUNCT
ejpam-6617	455	30	of	of	ADP
ejpam-6617	455	31	(	(	PUNCT
ejpam-6617	455	32	wd-1	wd-1	X
ejpam-6617	455	33	)	)	PUNCT
ejpam-6617	455	34	,	,	PUNCT
ejpam-6617	455	35	one	one	PRON
ejpam-6617	455	36	can	can	AUX
ejpam-6617	455	37	easily	easily	ADV
ejpam-6617	455	38	verify	verify	VERB
ejpam-6617	455	39	that	that	SCONJ
ejpam-6617	455	40	a2∫	a2∫	NOUN
ejpam-6617	455	41	a1	a1	NOUN
ejpam-6617	455	42	[	[	PUNCT
ejpam-6617	455	43	{	{	PUNCT
ejpam-6617	455	44	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	455	45	,	,	PUNCT
ejpam-6617	455	46	ε(ς),cfdθ•	ε(ς),cfdθ•	PROPN
ejpam-6617	455	47	a1+ε(ς	a1+ε(ς	X
ejpam-6617	455	48	)	)	PUNCT
ejpam-6617	455	49	)	)	PUNCT
ejpam-6617	455	50	,	,	PUNCT
ejpam-6617	455	51	ϕu	ϕu	INTJ
ejpam-6617	455	52	(	(	PUNCT
ejpam-6617	455	53	ς	ς	PROPN
ejpam-6617	455	54	,	,	PUNCT
ejpam-6617	455	55	ε(ς),cfdθ•	ε(ς),cfdθ•	PROPN
ejpam-6617	455	56	a1+ε(ς	a1+ε(ς	X
ejpam-6617	455	57	)	)	PUNCT
ejpam-6617	455	58	)	)	PUNCT
ejpam-6617	455	59	}	}	PUNCT
ejpam-6617	456	1	+	+	ADJ
ejpam-6617	456	2	(	(	PUNCT
ejpam-6617	456	3	θ̄)th(ς	θ̄)th(ς	PROPN
ejpam-6617	456	4	,	,	PUNCT
ejpam-6617	456	5	ε	ε	PROPN
ejpam-6617	456	6	,	,	PUNCT
ejpam-6617	456	7	cfdθ•	cfdθ•	PROPN
ejpam-6617	456	8	a1+ε(ς	a1+ε(ς	X
ejpam-6617	456	9	)	)	PUNCT
ejpam-6617	456	10	)	)	PUNCT
ejpam-6617	456	11	]	]	PUNCT
ejpam-6617	456	12	dς	dς	X
ejpam-6617	456	13	,	,	PUNCT
ejpam-6617	456	14	is	be	AUX
ejpam-6617	456	15	invex	invex	NOUN
ejpam-6617	456	16	at	at	ADP
ejpam-6617	456	17	ε̄	ε̄	ADJ
ejpam-6617	456	18	on	on	ADP
ejpam-6617	456	19	φ3	φ3	NOUN
ejpam-6617	456	20	∪w3	∪w3	VERB
ejpam-6617	456	21	,	,	PUNCT
ejpam-6617	456	22	we	we	PRON
ejpam-6617	456	23	observe	observe	VERB
ejpam-6617	456	24	that	that	X
ejpam-6617	456	25	a2∫	a2∫	NOUN
ejpam-6617	456	26	a1	a1	NOUN
ejpam-6617	456	27	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	456	28	,	,	PUNCT
ejpam-6617	456	29	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	456	30	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	456	31	,	,	PUNCT
ejpam-6617	456	32	a2∫	a2∫	X
ejpam-6617	456	33	a1	a1	VERB
ejpam-6617	456	34	ϕu	ϕu	X
ejpam-6617	456	35	(	(	PUNCT
ejpam-6617	456	36	ς	ς	PROPN
ejpam-6617	456	37	,	,	PUNCT
ejpam-6617	456	38	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	456	39	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	456	40			VERB
ejpam-6617	456	41	⊀lu	⊀lu	PROPN
ejpam-6617	456	42			PROPN
ejpam-6617	456	43	a2∫	a2∫	VERB
ejpam-6617	456	44	a1	a1	NOUN
ejpam-6617	456	45	(	(	PUNCT
ejpam-6617	456	46	ϕl	ϕl	PROPN
ejpam-6617	456	47	+	+	PROPN
ejpam-6617	456	48	(	(	PUNCT
ejpam-6617	456	49	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	456	50	,	,	PUNCT
ejpam-6617	456	51	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	456	52	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	456	53	,	,	PUNCT
ejpam-6617	456	54	a2∫	a2∫	X
ejpam-6617	456	55	a1	a1	NOUN
ejpam-6617	456	56	(	(	PUNCT
ejpam-6617	456	57	ϕu	ϕu	NOUN
ejpam-6617	456	58	+	+	CCONJ
ejpam-6617	456	59	(	(	PUNCT
ejpam-6617	456	60	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	456	61	,	,	PUNCT
ejpam-6617	456	62	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	456	63	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	456	64			NOUN
ejpam-6617	456	65	.	.	PUNCT
ejpam-6617	457	1	v.	v.	CCONJ
ejpam-6617	457	2	rayanki	rayanki	PROPN
ejpam-6617	457	3	et	et	PROPN
ejpam-6617	457	4	al	al	PROPN
ejpam-6617	457	5	.	.	PUNCT
ejpam-6617	457	6	/	/	SYM
ejpam-6617	457	7	eur	eur	PROPN
ejpam-6617	457	8	.	.	PUNCT
ejpam-6617	458	1	j.	j.	PROPN
ejpam-6617	458	2	pure	pure	PROPN
ejpam-6617	458	3	appl	appl	PROPN
ejpam-6617	458	4	.	.	PROPN
ejpam-6617	458	5	math	math	PROPN
ejpam-6617	458	6	,	,	PUNCT
ejpam-6617	458	7	18	18	NUM
ejpam-6617	458	8	(	(	PUNCT
ejpam-6617	458	9	3	3	NUM
ejpam-6617	458	10	)	)	PUNCT
ejpam-6617	458	11	(	(	PUNCT
ejpam-6617	458	12	2025	2025	NUM
ejpam-6617	458	13	)	)	PUNCT
ejpam-6617	458	14	,	,	PUNCT
ejpam-6617	458	15	6617	6617	NUM
ejpam-6617	458	16	31	31	NUM
ejpam-6617	458	17	of	of	ADP
ejpam-6617	458	18	38	38	NUM
ejpam-6617	458	19	theorem	theorem	ADJ
ejpam-6617	458	20	5	5	NUM
ejpam-6617	458	21	(	(	PUNCT
ejpam-6617	458	22	strong	strong	ADJ
ejpam-6617	458	23	duality	duality	NOUN
ejpam-6617	458	24	)	)	PUNCT
ejpam-6617	458	25	.	.	PUNCT
ejpam-6617	459	1	let	let	VERB
ejpam-6617	459	2	κ̄	κ̄	NOUN
ejpam-6617	459	3	be	be	AUX
ejpam-6617	459	4	an	an	DET
ejpam-6617	459	5	lu	lu	NOUN
ejpam-6617	459	6	optimal	optimal	ADJ
ejpam-6617	459	7	point	point	NOUN
ejpam-6617	459	8	for	for	ADP
ejpam-6617	459	9	(	(	PUNCT
ejpam-6617	459	10	p	p	NOUN
ejpam-6617	459	11	)	)	PUNCT
ejpam-6617	459	12	,	,	PUNCT
ejpam-6617	459	13	and	and	CCONJ
ejpam-6617	459	14	the	the	DET
ejpam-6617	459	15	slater	slater	NOUN
ejpam-6617	459	16	’s	’s	PART
ejpam-6617	459	17	constraint	constraint	NOUN
ejpam-6617	459	18	qualification	qualification	NOUN
ejpam-6617	459	19	is	be	AUX
ejpam-6617	459	20	satisfied	satisfied	ADJ
ejpam-6617	459	21	at	at	ADP
ejpam-6617	459	22	κ̄.	κ̄.	X
ejpam-6617	459	23	then	then	ADV
ejpam-6617	459	24	there	there	PRON
ejpam-6617	459	25	are	be	VERB
ejpam-6617	459	26	piecewise	piecewise	NOUN
ejpam-6617	459	27	smooth	smooth	ADJ
ejpam-6617	459	28	functions	function	NOUN
ejpam-6617	459	29	θ̄	θ̄	ADJ
ejpam-6617	459	30	:	:	PUNCT
ejpam-6617	459	31	ℑ	ℑ	PROPN
ejpam-6617	459	32	→	→	SYM
ejpam-6617	459	33	rm	rm	PROPN
ejpam-6617	459	34	,	,	PUNCT
ejpam-6617	459	35	θ̄	θ̄	X
ejpam-6617	459	36	≥	≥	NOUN
ejpam-6617	459	37	0	0	NUM
ejpam-6617	459	38	,	,	PUNCT
ejpam-6617	459	39	such	such	ADJ
ejpam-6617	459	40	that	that	SCONJ
ejpam-6617	459	41	(	(	PUNCT
ejpam-6617	459	42	κ̄	κ̄	NOUN
ejpam-6617	459	43	,	,	PUNCT
ejpam-6617	459	44	θ̄	θ̄	ADJ
ejpam-6617	459	45	)	)	PUNCT
ejpam-6617	459	46	is	be	AUX
ejpam-6617	459	47	a	a	DET
ejpam-6617	459	48	feasible	feasible	ADJ
ejpam-6617	459	49	point	point	NOUN
ejpam-6617	459	50	for	for	ADP
ejpam-6617	459	51	(	(	PUNCT
ejpam-6617	459	52	wd	wd	PROPN
ejpam-6617	459	53	)	)	PUNCT
ejpam-6617	459	54	and	and	CCONJ
ejpam-6617	459	55	the	the	DET
ejpam-6617	459	56	two	two	NUM
ejpam-6617	459	57	objective	objective	ADJ
ejpam-6617	459	58	functions	function	NOUN
ejpam-6617	459	59	are	be	AUX
ejpam-6617	459	60	equivalent	equivalent	ADJ
ejpam-6617	459	61	at	at	ADP
ejpam-6617	459	62	κ̄	κ̄	NOUN
ejpam-6617	459	63	and	and	CCONJ
ejpam-6617	459	64	(	(	PUNCT
ejpam-6617	459	65	κ̄	κ̄	NOUN
ejpam-6617	459	66	,	,	PUNCT
ejpam-6617	459	67	θ̄	θ̄	ADJ
ejpam-6617	459	68	)	)	PUNCT
ejpam-6617	459	69	for	for	ADP
ejpam-6617	459	70	(	(	PUNCT
ejpam-6617	459	71	p	p	NOUN
ejpam-6617	459	72	)	)	PUNCT
ejpam-6617	459	73	and	and	CCONJ
ejpam-6617	459	74	(	(	PUNCT
ejpam-6617	459	75	wd	wd	PROPN
ejpam-6617	459	76	)	)	PUNCT
ejpam-6617	459	77	,	,	PUNCT
ejpam-6617	459	78	respectively	respectively	ADV
ejpam-6617	459	79	.	.	PUNCT
ejpam-6617	460	1	furthermore	furthermore	ADV
ejpam-6617	460	2	,	,	PUNCT
ejpam-6617	460	3	if	if	SCONJ
ejpam-6617	460	4	weak	weak	ADJ
ejpam-6617	460	5	duality	duality	NOUN
ejpam-6617	460	6	theorem	theorem	VERB
ejpam-6617	460	7	4	4	NUM
ejpam-6617	460	8	holds	hold	VERB
ejpam-6617	460	9	between	between	ADP
ejpam-6617	460	10	(	(	PUNCT
ejpam-6617	460	11	p	p	NOUN
ejpam-6617	460	12	)	)	PUNCT
ejpam-6617	460	13	and	and	CCONJ
ejpam-6617	460	14	(	(	PUNCT
ejpam-6617	460	15	wd	wd	PROPN
ejpam-6617	460	16	)	)	PUNCT
ejpam-6617	460	17	,	,	PUNCT
ejpam-6617	460	18	then	then	ADV
ejpam-6617	460	19	(	(	PUNCT
ejpam-6617	460	20	κ̄	κ̄	NOUN
ejpam-6617	460	21	,	,	PUNCT
ejpam-6617	460	22	θ̄	θ̄	ADJ
ejpam-6617	460	23	)	)	PUNCT
ejpam-6617	460	24	is	be	AUX
ejpam-6617	460	25	lu	lu	NOUN
ejpam-6617	460	26	-	-	PUNCT
ejpam-6617	460	27	optimality	optimality	NOUN
ejpam-6617	460	28	for	for	ADP
ejpam-6617	460	29	(	(	PUNCT
ejpam-6617	460	30	wd	wd	PROPN
ejpam-6617	460	31	)	)	PUNCT
ejpam-6617	460	32	.	.	PUNCT
ejpam-6617	461	1	proof	proof	NOUN
ejpam-6617	461	2	.	.	PUNCT
ejpam-6617	462	1	according	accord	VERB
ejpam-6617	462	2	to	to	ADP
ejpam-6617	462	3	the	the	DET
ejpam-6617	462	4	hypothesis	hypothesis	NOUN
ejpam-6617	462	5	of	of	ADP
ejpam-6617	462	6	the	the	DET
ejpam-6617	462	7	theorem	theorem	NOUN
ejpam-6617	462	8	,	,	PUNCT
ejpam-6617	462	9	κ̄	κ̄	NOUN
ejpam-6617	462	10	is	be	AUX
ejpam-6617	462	11	a	a	DET
ejpam-6617	462	12	lu	lu	NOUN
ejpam-6617	462	13	optimum	optimum	ADJ
ejpam-6617	462	14	point	point	NOUN
ejpam-6617	462	15	for	for	ADP
ejpam-6617	462	16	(	(	PUNCT
ejpam-6617	462	17	p	p	NOUN
ejpam-6617	462	18	)	)	PUNCT
ejpam-6617	462	19	,	,	PUNCT
ejpam-6617	462	20	hence	hence	ADV
ejpam-6617	462	21	according	accord	VERB
ejpam-6617	462	22	to	to	ADP
ejpam-6617	462	23	theorem	theorem	NOUN
ejpam-6617	462	24	1	1	NUM
ejpam-6617	462	25	,	,	PUNCT
ejpam-6617	462	26	there	there	PRON
ejpam-6617	462	27	exist	exist	VERB
ejpam-6617	462	28	piecewise	piecewise	NOUN
ejpam-6617	462	29	smooth	smooth	ADJ
ejpam-6617	462	30	functions	function	NOUN
ejpam-6617	462	31	θ̄	θ̄	ADJ
ejpam-6617	462	32	:	:	PUNCT
ejpam-6617	462	33	ℑ	ℑ	PROPN
ejpam-6617	462	34	→	→	SYM
ejpam-6617	462	35	rm	rm	NOUN
ejpam-6617	462	36	such	such	ADJ
ejpam-6617	462	37	that	that	SCONJ
ejpam-6617	462	38	ϕl	ϕl	PROPN
ejpam-6617	462	39	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	462	40	,	,	PUNCT
ejpam-6617	462	41	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	462	42	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	462	43	)	)	PUNCT
ejpam-6617	463	1	+	+	CCONJ
ejpam-6617	463	2	ϕu	ϕu	ADP
ejpam-6617	463	3	κ̄	κ̄	NOUN
ejpam-6617	463	4	(	(	PUNCT
ejpam-6617	463	5	ς	ς	PROPN
ejpam-6617	463	6	,	,	PUNCT
ejpam-6617	463	7	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	463	8	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	463	9	)	)	PUNCT
ejpam-6617	463	10	+	+	CCONJ
ejpam-6617	463	11	(	(	PUNCT
ejpam-6617	463	12	θ̄)t	θ̄)t	NOUN
ejpam-6617	463	13	(	(	PUNCT
ejpam-6617	463	14	ς)hκ̄(ς	ς)hκ̄(ς	PROPN
ejpam-6617	463	15	,	,	PUNCT
ejpam-6617	463	16	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	463	17	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	463	18	)	)	PUNCT
ejpam-6617	463	19	=	=	PUNCT
ejpam-6617	463	20	−cfrdθ•	−cfrdθ•	ADJ
ejpam-6617	463	21	a2−	a2−	PROPN
ejpam-6617	463	22	[	[	PUNCT
ejpam-6617	463	23	ϕl	ϕl	PROPN
ejpam-6617	463	24	cfdθ•a+κ̄(ς	cfdθ•a+κ̄(ς	PROPN
ejpam-6617	463	25	)	)	PUNCT
ejpam-6617	463	26	(	(	PUNCT
ejpam-6617	463	27	ς	ς	PROPN
ejpam-6617	463	28	,	,	PUNCT
ejpam-6617	463	29	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	463	30	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	463	31	)	)	PUNCT
ejpam-6617	463	32	+	+	CCONJ
ejpam-6617	463	33	ϕu	ϕu	PROPN
ejpam-6617	463	34	cfdθ•a1	cfdθ•a1	PROPN
ejpam-6617	463	35	+	+	CCONJ
ejpam-6617	463	36	κ̄(ς	κ̄(ς	PROPN
ejpam-6617	463	37	)	)	PUNCT
ejpam-6617	463	38	(	(	PUNCT
ejpam-6617	463	39	ς	ς	PROPN
ejpam-6617	463	40	,	,	PUNCT
ejpam-6617	463	41	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	463	42	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	463	43	)	)	PUNCT
ejpam-6617	463	44	+	+	PROPN
ejpam-6617	463	45	(	(	PUNCT
ejpam-6617	463	46	θ̄)t	θ̄)t	PROPN
ejpam-6617	463	47	(	(	PUNCT
ejpam-6617	463	48	ς)hcfdθ•	ς)hcfdθ•	NOUN
ejpam-6617	463	49	a1	a1	PROPN
ejpam-6617	463	50	+	+	CCONJ
ejpam-6617	463	51	κ̄(ς)(ς	κ̄(ς)(ς	PROPN
ejpam-6617	463	52	,	,	PUNCT
ejpam-6617	463	53	κ̄	κ̄	NOUN
ejpam-6617	463	54	,	,	PUNCT
ejpam-6617	463	55	cfdθ•	cfdθ•	PROPN
ejpam-6617	463	56	a+κ̄	a+κ̄	NOUN
ejpam-6617	463	57	)	)	PUNCT
ejpam-6617	463	58	]	]	PUNCT
ejpam-6617	463	59	,	,	PUNCT
ejpam-6617	463	60	(	(	PUNCT
ejpam-6617	463	61	θ̄)t	θ̄)t	X
ejpam-6617	463	62	(	(	PUNCT
ejpam-6617	463	63	ς)h(ς	ς)h(ς	PROPN
ejpam-6617	463	64	,	,	PUNCT
ejpam-6617	463	65	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	463	66	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	463	67	)	)	PUNCT
ejpam-6617	463	68	=	=	SYM
ejpam-6617	463	69	0	0	NUM
ejpam-6617	463	70	,	,	PUNCT
ejpam-6617	463	71	(	(	PUNCT
ejpam-6617	463	72	θ̄)(ς	θ̄)(ς	PROPN
ejpam-6617	463	73	)	)	PUNCT
ejpam-6617	463	74	≥	≥	NOUN
ejpam-6617	463	75	0	0	NUM
ejpam-6617	463	76	.	.	PUNCT
ejpam-6617	464	1	it	it	PRON
ejpam-6617	464	2	follows	follow	VERB
ejpam-6617	464	3	that	that	SCONJ
ejpam-6617	464	4	(	(	PUNCT
ejpam-6617	464	5	κ̄	κ̄	NOUN
ejpam-6617	464	6	,	,	PUNCT
ejpam-6617	464	7	θ̄	θ̄	ADJ
ejpam-6617	464	8	)	)	PUNCT
ejpam-6617	464	9	is	be	AUX
ejpam-6617	464	10	a	a	DET
ejpam-6617	464	11	feasible	feasible	ADJ
ejpam-6617	464	12	point	point	NOUN
ejpam-6617	464	13	for	for	ADP
ejpam-6617	464	14	(	(	PUNCT
ejpam-6617	464	15	wd	wd	PROPN
ejpam-6617	464	16	)	)	PUNCT
ejpam-6617	464	17	and	and	CCONJ
ejpam-6617	464	18	the	the	DET
ejpam-6617	464	19	objective	objective	ADJ
ejpam-6617	464	20	values	value	NOUN
ejpam-6617	464	21	of	of	ADP
ejpam-6617	464	22	(	(	PUNCT
ejpam-6617	464	23	p	p	NOUN
ejpam-6617	464	24	)	)	PUNCT
ejpam-6617	464	25	and	and	CCONJ
ejpam-6617	464	26	(	(	PUNCT
ejpam-6617	464	27	wd	wd	X
ejpam-6617	464	28	)	)	PUNCT
ejpam-6617	464	29	are	be	AUX
ejpam-6617	464	30	equal	equal	ADJ
ejpam-6617	464	31	.	.	PUNCT
ejpam-6617	465	1	according	accord	VERB
ejpam-6617	465	2	to	to	ADP
ejpam-6617	465	3	theorem	theorem	ADJ
ejpam-6617	465	4	4	4	NUM
ejpam-6617	465	5	,	,	PUNCT
ejpam-6617	465	6	(	(	PUNCT
ejpam-6617	465	7	κ̄	κ̄	NOUN
ejpam-6617	465	8	,	,	PUNCT
ejpam-6617	465	9	θ̄	θ̄	ADJ
ejpam-6617	465	10	)	)	PUNCT
ejpam-6617	465	11	is	be	AUX
ejpam-6617	465	12	the	the	DET
ejpam-6617	465	13	optimal	optimal	ADJ
ejpam-6617	465	14	point	point	NOUN
ejpam-6617	465	15	for	for	ADP
ejpam-6617	465	16	(	(	PUNCT
ejpam-6617	465	17	wd	wd	PROPN
ejpam-6617	465	18	)	)	PUNCT
ejpam-6617	465	19	.	.	PUNCT
ejpam-6617	466	1	theorem	theorem	NOUN
ejpam-6617	466	2	6	6	NUM
ejpam-6617	466	3	(	(	PUNCT
ejpam-6617	466	4	strict	strict	ADJ
ejpam-6617	466	5	converse	converse	NOUN
ejpam-6617	466	6	duality	duality	NOUN
ejpam-6617	466	7	)	)	PUNCT
ejpam-6617	466	8	.	.	PUNCT
ejpam-6617	467	1	let	let	VERB
ejpam-6617	467	2	κ̄	κ̄	NOUN
ejpam-6617	467	3	and	and	CCONJ
ejpam-6617	467	4	(	(	PUNCT
ejpam-6617	467	5	θ̄	θ̄	ADJ
ejpam-6617	467	6	,	,	PUNCT
ejpam-6617	467	7	ε̄	ε̄	NOUN
ejpam-6617	467	8	)	)	PUNCT
ejpam-6617	467	9	be	be	VERB
ejpam-6617	467	10	the	the	DET
ejpam-6617	467	11	feasibile	feasibile	NOUN
ejpam-6617	467	12	points	point	NOUN
ejpam-6617	467	13	for	for	ADP
ejpam-6617	467	14	(	(	PUNCT
ejpam-6617	467	15	p	p	NOUN
ejpam-6617	467	16	)	)	PUNCT
ejpam-6617	467	17	and	and	CCONJ
ejpam-6617	467	18	(	(	PUNCT
ejpam-6617	467	19	wd	wd	PROPN
ejpam-6617	467	20	)	)	PUNCT
ejpam-6617	467	21	respectively	respectively	ADV
ejpam-6617	467	22	,	,	PUNCT
ejpam-6617	467	23	such	such	ADJ
ejpam-6617	467	24	that	that	X
ejpam-6617	467	25	a2∫	a2∫	NOUN
ejpam-6617	467	26	a1	a1	NOUN
ejpam-6617	467	27	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	467	28	,	,	PUNCT
ejpam-6617	467	29	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	467	30	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	467	31	,	,	PUNCT
ejpam-6617	467	32	a2∫	a2∫	X
ejpam-6617	467	33	a1	a1	VERB
ejpam-6617	467	34	ϕu	ϕu	X
ejpam-6617	467	35	(	(	PUNCT
ejpam-6617	467	36	ς	ς	PROPN
ejpam-6617	467	37	,	,	PUNCT
ejpam-6617	467	38	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	467	39	a1+κ̄)dς	a1+κ̄)dς	PRON
ejpam-6617	467	40			NOUN
ejpam-6617	467	41	+	+	NUM
ejpam-6617	467	42	a2∫	a2∫	NOUN
ejpam-6617	467	43	a1	a1	NOUN
ejpam-6617	467	44	(	(	PUNCT
ejpam-6617	467	45	θ̄)t	θ̄)t	NOUN
ejpam-6617	467	46	(	(	PUNCT
ejpam-6617	467	47	ς)h(ξ	ς)h(ξ	NOUN
ejpam-6617	467	48	,	,	PUNCT
ejpam-6617	467	49	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	467	50	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	468	1	=	=	SYM
ejpam-6617	468	2			NOUN
ejpam-6617	468	3	a2∫	a2∫	X
ejpam-6617	468	4	a1	a1	NOUN
ejpam-6617	468	5	ϕl(ς	ϕl(ς	X
ejpam-6617	468	6	,	,	PUNCT
ejpam-6617	468	7	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	468	8	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	468	9	,	,	PUNCT
ejpam-6617	468	10	a2∫	a2∫	X
ejpam-6617	468	11	a1	a1	VERB
ejpam-6617	468	12	ϕu	ϕu	X
ejpam-6617	468	13	(	(	PUNCT
ejpam-6617	468	14	ς	ς	NOUN
ejpam-6617	468	15	,	,	PUNCT
ejpam-6617	468	16	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	468	17	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	468	18			NOUN
ejpam-6617	468	19	+	+	NUM
ejpam-6617	468	20	a2∫	a2∫	NOUN
ejpam-6617	468	21	a1	a1	NOUN
ejpam-6617	468	22	(	(	PUNCT
ejpam-6617	468	23	θ̄)t	θ̄)t	NOUN
ejpam-6617	468	24	(	(	PUNCT
ejpam-6617	468	25	ς)h(ς	ς)h(ς	NOUN
ejpam-6617	468	26	,	,	PUNCT
ejpam-6617	468	27	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	468	28	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	468	29	.	.	PUNCT
ejpam-6617	469	1	(	(	PUNCT
ejpam-6617	469	2	20	20	NUM
ejpam-6617	469	3	)	)	PUNCT
ejpam-6617	469	4	further	far	ADV
ejpam-6617	469	5	,	,	PUNCT
ejpam-6617	469	6	suppose	suppose	VERB
ejpam-6617	469	7	that	that	SCONJ
ejpam-6617	469	8	ε(ς	ε(ς	NOUN
ejpam-6617	469	9	)	)	PUNCT
ejpam-6617	469	10	∈	∈	PROPN
ejpam-6617	469	11	x	x	X
ejpam-6617	469	12	,	,	PUNCT
ejpam-6617	469	13	ε(ς	ε(ς	NOUN
ejpam-6617	469	14	)	)	PUNCT
ejpam-6617	469	15	≥	≥	NOUN
ejpam-6617	469	16	0	0	NUM
ejpam-6617	469	17	and	and	CCONJ
ejpam-6617	469	18	the	the	DET
ejpam-6617	469	19	functional	functional	ADJ
ejpam-6617	469	20	a2∫	a2∫	NOUN
ejpam-6617	469	21	a1	a1	NOUN
ejpam-6617	470	1	[	[	X
ejpam-6617	470	2	ϕl	ϕl	X
ejpam-6617	471	1	+	+	NOUN
ejpam-6617	471	2	ϕu	ϕu	PROPN
ejpam-6617	472	1	+	+	CCONJ
ejpam-6617	472	2	(	(	PUNCT
ejpam-6617	472	3	θ̄)th](ς	θ̄)th](ς	PROPN
ejpam-6617	472	4	,	,	PUNCT
ejpam-6617	472	5	ε̄(ς	ε̄(ς	PROPN
ejpam-6617	472	6	)	)	PUNCT
ejpam-6617	472	7	,	,	PUNCT
ejpam-6617	472	8	cfdθ•	cfdθ•	PROPN
ejpam-6617	472	9	a1	a1	PROPN
ejpam-6617	472	10	+	+	CCONJ
ejpam-6617	472	11	ε̄(ς	ε̄(ς	NOUN
ejpam-6617	472	12	)	)	PUNCT
ejpam-6617	472	13	)	)	PUNCT
ejpam-6617	473	1	dς	dς	PUNCT
ejpam-6617	473	2	is	be	AUX
ejpam-6617	473	3	strictly	strictly	ADV
ejpam-6617	473	4	-	-	PUNCT
ejpam-6617	473	5	invex	invex	NOUN
ejpam-6617	473	6	at	at	ADP
ejpam-6617	473	7	ε̄	ε̄	ADJ
ejpam-6617	473	8	on	on	ADP
ejpam-6617	473	9	x.	x.	NOUN
ejpam-6617	473	10	then	then	ADV
ejpam-6617	473	11	,	,	PUNCT
ejpam-6617	473	12	κ̄	κ̄	NOUN
ejpam-6617	473	13	=	=	SYM
ejpam-6617	473	14	ε̄	ε̄	ADJ
ejpam-6617	473	15	and	and	CCONJ
ejpam-6617	473	16	ε̄	ε̄	ADJ
ejpam-6617	473	17	is	be	AUX
ejpam-6617	473	18	an	an	DET
ejpam-6617	473	19	lu	lu	NOUN
ejpam-6617	473	20	optimal	optimal	ADJ
ejpam-6617	473	21	point	point	NOUN
ejpam-6617	473	22	for	for	ADP
ejpam-6617	473	23	(	(	PUNCT
ejpam-6617	473	24	p	p	NOUN
ejpam-6617	473	25	)	)	PUNCT
ejpam-6617	473	26	.	.	PUNCT
ejpam-6617	474	1	v.	v.	CCONJ
ejpam-6617	474	2	rayanki	rayanki	PROPN
ejpam-6617	474	3	et	et	PROPN
ejpam-6617	474	4	al	al	PROPN
ejpam-6617	474	5	.	.	PUNCT
ejpam-6617	474	6	/	/	SYM
ejpam-6617	474	7	eur	eur	PROPN
ejpam-6617	474	8	.	.	PUNCT
ejpam-6617	475	1	j.	j.	PROPN
ejpam-6617	475	2	pure	pure	PROPN
ejpam-6617	475	3	appl	appl	PROPN
ejpam-6617	475	4	.	.	PROPN
ejpam-6617	475	5	math	math	PROPN
ejpam-6617	475	6	,	,	PUNCT
ejpam-6617	475	7	18	18	NUM
ejpam-6617	475	8	(	(	PUNCT
ejpam-6617	475	9	3	3	NUM
ejpam-6617	475	10	)	)	PUNCT
ejpam-6617	475	11	(	(	PUNCT
ejpam-6617	475	12	2025	2025	NUM
ejpam-6617	475	13	)	)	PUNCT
ejpam-6617	475	14	,	,	PUNCT
ejpam-6617	475	15	6617	6617	NUM
ejpam-6617	475	16	32	32	NUM
ejpam-6617	475	17	of	of	ADP
ejpam-6617	475	18	38	38	NUM
ejpam-6617	475	19	proof	proof	NOUN
ejpam-6617	475	20	.	.	PUNCT
ejpam-6617	476	1	assume	assume	VERB
ejpam-6617	476	2	,	,	PUNCT
ejpam-6617	476	3	contrary	contrary	ADJ
ejpam-6617	476	4	to	to	ADP
ejpam-6617	476	5	the	the	DET
ejpam-6617	476	6	outcome	outcome	NOUN
ejpam-6617	476	7	,	,	PUNCT
ejpam-6617	476	8	κ̄	κ̄	VERB
ejpam-6617	476	9	̸=	̸=	PROPN
ejpam-6617	476	10	ε̄.	ε̄.	PUNCT
ejpam-6617	476	11	by	by	ADP
ejpam-6617	476	12	(	(	PUNCT
ejpam-6617	476	13	20	20	NUM
ejpam-6617	476	14	)	)	PUNCT
ejpam-6617	476	15	,	,	PUNCT
ejpam-6617	476	16	we	we	PRON
ejpam-6617	476	17	have	have	VERB
ejpam-6617	476	18	[	[	PUNCT
ejpam-6617	476	19	a2∫	a2∫	X
ejpam-6617	476	20	a1	a1	NOUN
ejpam-6617	476	21	ϕl(ς	ϕl(ς	PROPN
ejpam-6617	476	22	,	,	PUNCT
ejpam-6617	476	23	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	476	24	a+κ̄)dς	a+κ̄)dς	PROPN
ejpam-6617	476	25	,	,	PUNCT
ejpam-6617	476	26	a2∫	a2∫	X
ejpam-6617	476	27	a1	a1	VERB
ejpam-6617	476	28	ϕu	ϕu	X
ejpam-6617	476	29	(	(	PUNCT
ejpam-6617	476	30	ς	ς	PROPN
ejpam-6617	476	31	,	,	PUNCT
ejpam-6617	476	32	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	476	33	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	476	34	]	]	PUNCT
ejpam-6617	477	1	+	+	CCONJ
ejpam-6617	477	2	a2∫	a2∫	NOUN
ejpam-6617	477	3	a1	a1	NOUN
ejpam-6617	477	4	(	(	PUNCT
ejpam-6617	477	5	θ̄)t	θ̄)t	NOUN
ejpam-6617	477	6	(	(	PUNCT
ejpam-6617	477	7	ς)h(ς	ς)h(ς	PROPN
ejpam-6617	477	8	,	,	PUNCT
ejpam-6617	477	9	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	477	10	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	477	11	=	=	PUNCT
ejpam-6617	477	12	[	[	PUNCT
ejpam-6617	477	13	a2∫	a2∫	X
ejpam-6617	477	14	a1	a1	NOUN
ejpam-6617	477	15	ϕl(ς	ϕl(ς	PRON
ejpam-6617	477	16	,	,	PUNCT
ejpam-6617	477	17	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	477	18	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	477	19	,	,	PUNCT
ejpam-6617	477	20	a2∫	a2∫	X
ejpam-6617	477	21	a1	a1	VERB
ejpam-6617	477	22	ϕu	ϕu	X
ejpam-6617	477	23	(	(	PUNCT
ejpam-6617	477	24	ς	ς	NOUN
ejpam-6617	477	25	,	,	PUNCT
ejpam-6617	477	26	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	477	27	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	477	28	]	]	PUNCT
ejpam-6617	477	29	+	+	CCONJ
ejpam-6617	477	30	a2∫	a2∫	NOUN
ejpam-6617	477	31	a1	a1	NOUN
ejpam-6617	477	32	(	(	PUNCT
ejpam-6617	477	33	θ̄)t	θ̄)t	NOUN
ejpam-6617	477	34	(	(	PUNCT
ejpam-6617	477	35	ς)h(ς	ς)h(ς	NOUN
ejpam-6617	477	36	,	,	PUNCT
ejpam-6617	477	37	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	477	38	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	477	39	.	.	PUNCT
ejpam-6617	478	1	that	that	PRON
ejpam-6617	478	2	is	is	ADV
ejpam-6617	478	3	,	,	PUNCT
ejpam-6617	478	4	a2∫	a2∫	NOUN
ejpam-6617	478	5	a1	a1	NOUN
ejpam-6617	478	6	(	(	PUNCT
ejpam-6617	478	7	ϕl	ϕl	PROPN
ejpam-6617	478	8	+	+	X
ejpam-6617	478	9	(	(	PUNCT
ejpam-6617	478	10	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	478	11	,	,	PUNCT
ejpam-6617	478	12	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	478	13	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	478	14	=	=	PUNCT
ejpam-6617	478	15	a2∫	a2∫	VERB
ejpam-6617	478	16	a1	a1	NOUN
ejpam-6617	478	17	(	(	PUNCT
ejpam-6617	478	18	ϕl	ϕl	PROPN
ejpam-6617	478	19	+	+	PROPN
ejpam-6617	478	20	(	(	PUNCT
ejpam-6617	478	21	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	478	22	,	,	PUNCT
ejpam-6617	478	23	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	478	24	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	478	25	,	,	PUNCT
ejpam-6617	478	26	(	(	PUNCT
ejpam-6617	478	27	21	21	NUM
ejpam-6617	478	28	)	)	PUNCT
ejpam-6617	478	29	a2∫	a2∫	NOUN
ejpam-6617	478	30	a1	a1	NOUN
ejpam-6617	478	31	(	(	PUNCT
ejpam-6617	478	32	ϕu	ϕu	NOUN
ejpam-6617	478	33	+	+	CCONJ
ejpam-6617	478	34	(	(	PUNCT
ejpam-6617	478	35	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	478	36	,	,	PUNCT
ejpam-6617	478	37	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	478	38	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	478	39	=	=	PUNCT
ejpam-6617	478	40	a2∫	a2∫	VERB
ejpam-6617	478	41	a1	a1	NOUN
ejpam-6617	478	42	(	(	PUNCT
ejpam-6617	478	43	ϕu	ϕu	NOUN
ejpam-6617	478	44	+	+	CCONJ
ejpam-6617	478	45	(	(	PUNCT
ejpam-6617	478	46	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	478	47	,	,	PUNCT
ejpam-6617	478	48	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	478	49	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	478	50	.	.	PUNCT
ejpam-6617	479	1	(	(	PUNCT
ejpam-6617	479	2	22	22	NUM
ejpam-6617	479	3	)	)	PUNCT
ejpam-6617	479	4	on	on	ADP
ejpam-6617	479	5	adding	add	VERB
ejpam-6617	479	6	(	(	PUNCT
ejpam-6617	479	7	21	21	NUM
ejpam-6617	479	8	)	)	PUNCT
ejpam-6617	479	9	and	and	CCONJ
ejpam-6617	479	10	(	(	PUNCT
ejpam-6617	479	11	22	22	NUM
ejpam-6617	479	12	)	)	PUNCT
ejpam-6617	479	13	,	,	PUNCT
ejpam-6617	479	14	we	we	PRON
ejpam-6617	479	15	get	get	VERB
ejpam-6617	479	16	a2∫	a2∫	NOUN
ejpam-6617	479	17	a1	a1	NOUN
ejpam-6617	479	18	[	[	PUNCT
ejpam-6617	479	19	ϕl	ϕl	PROPN
ejpam-6617	480	1	+	+	CCONJ
ejpam-6617	480	2	ϕu	ϕu	PROPN
ejpam-6617	481	1	+	+	CCONJ
ejpam-6617	481	2	(	(	PUNCT
ejpam-6617	481	3	θ̄)th	θ̄)th	X
ejpam-6617	481	4	]	]	X
ejpam-6617	481	5	(	(	PUNCT
ejpam-6617	481	6	ς	ς	PROPN
ejpam-6617	481	7	,	,	PUNCT
ejpam-6617	481	8	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	481	9	a1+κ̄)dς	a1+κ̄)dς	X
ejpam-6617	481	10	=	=	PUNCT
ejpam-6617	481	11	a2∫	a2∫	VERB
ejpam-6617	481	12	a1	a1	NOUN
ejpam-6617	481	13	[	[	PUNCT
ejpam-6617	481	14	ϕl	ϕl	PROPN
ejpam-6617	482	1	+	+	CCONJ
ejpam-6617	482	2	ϕu	ϕu	PROPN
ejpam-6617	483	1	+	+	CCONJ
ejpam-6617	483	2	(	(	PUNCT
ejpam-6617	483	3	θ̄)th	θ̄)th	X
ejpam-6617	483	4	]	]	X
ejpam-6617	483	5	(	(	PUNCT
ejpam-6617	483	6	ς	ς	NOUN
ejpam-6617	483	7	,	,	PUNCT
ejpam-6617	483	8	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	483	9	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	483	10	.	.	PUNCT
ejpam-6617	484	1	(	(	PUNCT
ejpam-6617	484	2	23	23	NUM
ejpam-6617	484	3	)	)	PUNCT
ejpam-6617	484	4	on	on	ADP
ejpam-6617	484	5	the	the	DET
ejpam-6617	484	6	other	other	ADJ
ejpam-6617	484	7	hand	hand	NOUN
ejpam-6617	484	8	,	,	PUNCT
ejpam-6617	484	9	by	by	ADP
ejpam-6617	484	10	using	use	VERB
ejpam-6617	484	11	strictly	strictly	ADV
ejpam-6617	484	12	-	-	PUNCT
ejpam-6617	484	13	invex	invex	NOUN
ejpam-6617	484	14	of	of	ADP
ejpam-6617	484	15	(	(	PUNCT
ejpam-6617	484	16	ϕl	ϕl	INTJ
ejpam-6617	485	1	+	+	NOUN
ejpam-6617	485	2	ϕu	ϕu	PROPN
ejpam-6617	486	1	+	+	CCONJ
ejpam-6617	486	2	(	(	PUNCT
ejpam-6617	486	3	θ̄)th)(ς	θ̄)th)(ς	PROPN
ejpam-6617	486	4	,	,	PUNCT
ejpam-6617	486	5	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	486	6	a1+κ̄	a1+κ̄	NOUN
ejpam-6617	486	7	)	)	PUNCT
ejpam-6617	486	8	at	at	ADP
ejpam-6617	486	9	ε̄	ε̄	NOUN
ejpam-6617	486	10	on	on	ADP
ejpam-6617	486	11	κ	κ	NOUN
ejpam-6617	486	12	,	,	PUNCT
ejpam-6617	486	13	we	we	PRON
ejpam-6617	486	14	have	have	VERB
ejpam-6617	486	15	a2∫	a2∫	NOUN
ejpam-6617	486	16	a1	a1	NOUN
ejpam-6617	486	17	[	[	PUNCT
ejpam-6617	486	18	ϕl	ϕl	PROPN
ejpam-6617	487	1	+	+	CCONJ
ejpam-6617	487	2	ϕu	ϕu	PROPN
ejpam-6617	488	1	+	+	CCONJ
ejpam-6617	488	2	(	(	PUNCT
ejpam-6617	488	3	θ̄)th	θ̄)th	X
ejpam-6617	488	4	]	]	X
ejpam-6617	488	5	(	(	PUNCT
ejpam-6617	488	6	ς	ς	PROPN
ejpam-6617	488	7	,	,	PUNCT
ejpam-6617	488	8	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	488	9	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	488	10	−	−	NOUN
ejpam-6617	488	11	a2∫	a2∫	NOUN
ejpam-6617	488	12	a1	a1	NOUN
ejpam-6617	488	13	[	[	PUNCT
ejpam-6617	488	14	ϕl	ϕl	PROPN
ejpam-6617	489	1	+	+	CCONJ
ejpam-6617	489	2	ϕu	ϕu	PROPN
ejpam-6617	490	1	+	+	CCONJ
ejpam-6617	490	2	(	(	PUNCT
ejpam-6617	490	3	θ̄)th	θ̄)th	X
ejpam-6617	490	4	]	]	X
ejpam-6617	490	5	(	(	PUNCT
ejpam-6617	490	6	ς	ς	NOUN
ejpam-6617	490	7	,	,	PUNCT
ejpam-6617	490	8	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	490	9	a1+ε̄)dς	a1+ε̄)dς	PROPN
ejpam-6617	490	10	>	>	SYM
ejpam-6617	490	11	a2∫	a2∫	X
ejpam-6617	490	12	a1	a1	PROPN
ejpam-6617	490	13	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	490	14	,	,	PUNCT
ejpam-6617	490	15	κ̄	κ̄	NOUN
ejpam-6617	490	16	,	,	PUNCT
ejpam-6617	490	17	ε̄)t	ε̄)t	PUNCT
ejpam-6617	490	18	[	[	PUNCT
ejpam-6617	490	19	ϕl	ϕl	PRON
ejpam-6617	490	20	ε̄	ε̄	NOUN
ejpam-6617	490	21	+	+	CCONJ
ejpam-6617	490	22	ϕu	ϕu	ADP
ejpam-6617	490	23	ε̄	ε̄	NOUN
ejpam-6617	490	24	+	+	CCONJ
ejpam-6617	490	25	(	(	PUNCT
ejpam-6617	490	26	θ̄)thε̄	θ̄)thε̄	X
ejpam-6617	490	27	]	]	PUNCT
ejpam-6617	490	28	(	(	PUNCT
ejpam-6617	490	29	ς	ς	NOUN
ejpam-6617	490	30	,	,	PUNCT
ejpam-6617	490	31	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	490	32	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	490	33	)	)	PUNCT
ejpam-6617	491	1	+	+	PROPN
ejpam-6617	491	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	491	3	a1+ℵ(ς	a1+ℵ(ς	PRON
ejpam-6617	491	4	,	,	PUNCT
ejpam-6617	491	5	κ̄	κ̄	NOUN
ejpam-6617	491	6	,	,	PUNCT
ejpam-6617	491	7	ε̄	ε̄	NOUN
ejpam-6617	491	8	)	)	PUNCT
ejpam-6617	491	9	t	t	NOUN
ejpam-6617	491	10	[	[	PUNCT
ejpam-6617	491	11	ϕl	ϕl	PROPN
ejpam-6617	491	12	cfdθ•	cfdθ•	PROPN
ejpam-6617	491	13	a1	a1	PROPN
ejpam-6617	491	14	+	+	CCONJ
ejpam-6617	491	15	ε̄	ε̄	ADJ
ejpam-6617	491	16	+	+	PROPN
ejpam-6617	491	17	ϕu	ϕu	PROPN
ejpam-6617	491	18	cfdθ•	cfdθ•	PROPN
ejpam-6617	491	19	a1	a1	PROPN
ejpam-6617	491	20	+	+	CCONJ
ejpam-6617	491	21	ε̄	ε̄	ADJ
ejpam-6617	491	22	v.	v.	ADP
ejpam-6617	491	23	rayanki	rayanki	NOUN
ejpam-6617	491	24	et	et	PROPN
ejpam-6617	491	25	al	al	PROPN
ejpam-6617	491	26	.	.	PUNCT
ejpam-6617	491	27	/	/	SYM
ejpam-6617	491	28	eur	eur	PROPN
ejpam-6617	491	29	.	.	PUNCT
ejpam-6617	492	1	j.	j.	PROPN
ejpam-6617	492	2	pure	pure	PROPN
ejpam-6617	492	3	appl	appl	PROPN
ejpam-6617	492	4	.	.	PROPN
ejpam-6617	492	5	math	math	PROPN
ejpam-6617	492	6	,	,	PUNCT
ejpam-6617	492	7	18	18	NUM
ejpam-6617	492	8	(	(	PUNCT
ejpam-6617	492	9	3	3	NUM
ejpam-6617	492	10	)	)	PUNCT
ejpam-6617	492	11	(	(	PUNCT
ejpam-6617	492	12	2025	2025	NUM
ejpam-6617	492	13	)	)	PUNCT
ejpam-6617	492	14	,	,	PUNCT
ejpam-6617	492	15	6617	6617	NUM
ejpam-6617	492	16	33	33	NUM
ejpam-6617	492	17	of	of	ADP
ejpam-6617	492	18	38	38	NUM
ejpam-6617	492	19	+	+	ADJ
ejpam-6617	492	20	(	(	PUNCT
ejpam-6617	492	21	θ̄)thcfdθ•	θ̄)thcfdθ•	NOUN
ejpam-6617	492	22	a1	a1	PROPN
ejpam-6617	492	23	+	+	X
ejpam-6617	492	24	ε̄	ε̄	NOUN
ejpam-6617	492	25	]	]	PUNCT
ejpam-6617	492	26	(	(	PUNCT
ejpam-6617	492	27	ς	ς	NOUN
ejpam-6617	492	28	,	,	PUNCT
ejpam-6617	492	29	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	492	30	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	492	31	.	.	PUNCT
ejpam-6617	493	1	(	(	PUNCT
ejpam-6617	493	2	24	24	NUM
ejpam-6617	493	3	)	)	PUNCT
ejpam-6617	493	4	by	by	ADP
ejpam-6617	493	5	using	use	VERB
ejpam-6617	493	6	dual	dual	ADJ
ejpam-6617	493	7	constraints	constraint	NOUN
ejpam-6617	493	8	(	(	PUNCT
ejpam-6617	493	9	13	13	NUM
ejpam-6617	493	10	)	)	PUNCT
ejpam-6617	493	11	,	,	PUNCT
ejpam-6617	493	12	(	(	PUNCT
ejpam-6617	493	13	14	14	NUM
ejpam-6617	493	14	)	)	PUNCT
ejpam-6617	493	15	with	with	ADP
ejpam-6617	493	16	proposition	proposition	NOUN
ejpam-6617	493	17	2.1	2.1	NUM
ejpam-6617	493	18	,	,	PUNCT
ejpam-6617	493	19	in	in	ADP
ejpam-6617	493	20	view	view	NOUN
ejpam-6617	493	21	of	of	ADP
ejpam-6617	493	22	the	the	DET
ejpam-6617	493	23	weak	weak	ADJ
ejpam-6617	493	24	-	-	PUNCT
ejpam-6617	493	25	duality	duality	NOUN
ejpam-6617	493	26	theorem	theorem	NOUN
ejpam-6617	493	27	4	4	NUM
ejpam-6617	493	28	,	,	PUNCT
ejpam-6617	493	29	we	we	PRON
ejpam-6617	493	30	get	get	VERB
ejpam-6617	493	31	a2∫	a2∫	NOUN
ejpam-6617	493	32	a1	a1	NOUN
ejpam-6617	493	33	ℵ(ς	ℵ(ς	PROPN
ejpam-6617	493	34	,	,	PUNCT
ejpam-6617	493	35	κ̄	κ̄	NOUN
ejpam-6617	493	36	,	,	PUNCT
ejpam-6617	493	37	ε̄)t	ε̄)t	PUNCT
ejpam-6617	493	38	[	[	PUNCT
ejpam-6617	493	39	ϕl	ϕl	PRON
ejpam-6617	493	40	ε̄	ε̄	NOUN
ejpam-6617	493	41	+	+	CCONJ
ejpam-6617	493	42	ϕu	ϕu	ADP
ejpam-6617	493	43	ε̄	ε̄	NOUN
ejpam-6617	494	1	+	+	CCONJ
ejpam-6617	494	2	(	(	PUNCT
ejpam-6617	494	3	θ̄)thε̄	θ̄)thε̄	X
ejpam-6617	494	4	]	]	PUNCT
ejpam-6617	494	5	(	(	PUNCT
ejpam-6617	494	6	ς	ς	NOUN
ejpam-6617	494	7	,	,	PUNCT
ejpam-6617	494	8	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	494	9	a1+ε̄	a1+ε̄	NOUN
ejpam-6617	494	10	)	)	PUNCT
ejpam-6617	495	1	+	+	CCONJ
ejpam-6617	495	2	cfdθ•	cfdθ•	PROPN
ejpam-6617	495	3	a1+ℵ(ς	a1+ℵ(ς	PRON
ejpam-6617	495	4	,	,	PUNCT
ejpam-6617	495	5	κ̄	κ̄	NOUN
ejpam-6617	495	6	,	,	PUNCT
ejpam-6617	495	7	ε̄	ε̄	NOUN
ejpam-6617	495	8	)	)	PUNCT
ejpam-6617	495	9	t	t	NOUN
ejpam-6617	495	10	[	[	PUNCT
ejpam-6617	495	11	ϕl	ϕl	PROPN
ejpam-6617	495	12	cfdθ•	cfdθ•	PROPN
ejpam-6617	495	13	a1	a1	PROPN
ejpam-6617	495	14	+	+	CCONJ
ejpam-6617	495	15	ε̄	ε̄	ADJ
ejpam-6617	495	16	+	+	PROPN
ejpam-6617	495	17	ϕu	ϕu	PROPN
ejpam-6617	495	18	cfdθ•	cfdθ•	PROPN
ejpam-6617	495	19	a1	a1	PROPN
ejpam-6617	495	20	+	+	CCONJ
ejpam-6617	495	21	ε̄	ε̄	ADJ
ejpam-6617	495	22	+	+	CCONJ
ejpam-6617	495	23	(	(	PUNCT
ejpam-6617	495	24	θ̄)thcfdθ•	θ̄)thcfdθ•	NOUN
ejpam-6617	495	25	a1	a1	PROPN
ejpam-6617	495	26	+	+	X
ejpam-6617	495	27	ε̄	ε̄	NOUN
ejpam-6617	495	28	]	]	PUNCT
ejpam-6617	495	29	(	(	PUNCT
ejpam-6617	495	30	ς	ς	NOUN
ejpam-6617	495	31	,	,	PUNCT
ejpam-6617	495	32	ε̄,cfdθ•	ε̄,cfdθ•	NOUN
ejpam-6617	495	33	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	495	34	=	=	SYM
ejpam-6617	495	35	0	0	X
ejpam-6617	495	36	.	.	PUNCT
ejpam-6617	496	1	(	(	PUNCT
ejpam-6617	496	2	25	25	NUM
ejpam-6617	496	3	)	)	PUNCT
ejpam-6617	496	4	(	(	PUNCT
ejpam-6617	496	5	24	24	NUM
ejpam-6617	496	6	)	)	PUNCT
ejpam-6617	496	7	and	and	CCONJ
ejpam-6617	496	8	(	(	PUNCT
ejpam-6617	496	9	25	25	NUM
ejpam-6617	496	10	)	)	PUNCT
ejpam-6617	496	11	,	,	PUNCT
ejpam-6617	496	12	give	give	VERB
ejpam-6617	496	13	us	we	PRON
ejpam-6617	496	14	a2∫	a2∫	NOUN
ejpam-6617	496	15	a1	a1	NOUN
ejpam-6617	496	16	[	[	PUNCT
ejpam-6617	496	17	ϕl	ϕl	PROPN
ejpam-6617	497	1	+	+	CCONJ
ejpam-6617	497	2	ϕu	ϕu	PROPN
ejpam-6617	498	1	+	+	CCONJ
ejpam-6617	498	2	(	(	PUNCT
ejpam-6617	498	3	θ̄)th	θ̄)th	X
ejpam-6617	498	4	]	]	X
ejpam-6617	498	5	(	(	PUNCT
ejpam-6617	498	6	ς	ς	PROPN
ejpam-6617	498	7	,	,	PUNCT
ejpam-6617	498	8	κ̄,cfdθ•	κ̄,cfdθ•	PROPN
ejpam-6617	498	9	a1+κ̄)dς	a1+κ̄)dς	PROPN
ejpam-6617	498	10	−	−	NOUN
ejpam-6617	498	11	a2∫	a2∫	NOUN
ejpam-6617	498	12	a1	a1	NOUN
ejpam-6617	498	13	[	[	PUNCT
ejpam-6617	498	14	ϕl	ϕl	PROPN
ejpam-6617	499	1	+	+	CCONJ
ejpam-6617	499	2	ϕu	ϕu	PROPN
ejpam-6617	500	1	+	+	CCONJ
ejpam-6617	500	2	(	(	PUNCT
ejpam-6617	500	3	θ̄)th	θ̄)th	X
ejpam-6617	500	4	]	]	X
ejpam-6617	500	5	(	(	PUNCT
ejpam-6617	500	6	ς	ς	NOUN
ejpam-6617	500	7	,	,	PUNCT
ejpam-6617	500	8	ε̄,cfdθ•	ε̄,cfdθ•	PROPN
ejpam-6617	500	9	a1+ε̄)dς	a1+ε̄)dς	PROPN
ejpam-6617	500	10	>	>	X
ejpam-6617	500	11	0	0	NUM
ejpam-6617	500	12	which	which	PRON
ejpam-6617	500	13	contradicts	contradict	VERB
ejpam-6617	500	14	(	(	PUNCT
ejpam-6617	500	15	23	23	NUM
ejpam-6617	500	16	)	)	PUNCT
ejpam-6617	500	17	.	.	PUNCT
ejpam-6617	501	1	hence	hence	ADV
ejpam-6617	501	2	κ̄	κ̄	VERB
ejpam-6617	501	3	=	=	PUNCT
ejpam-6617	501	4	ε̄.	ε̄.	PUNCT
ejpam-6617	501	5	further	far	ADV
ejpam-6617	501	6	,	,	PUNCT
ejpam-6617	501	7	if	if	SCONJ
ejpam-6617	501	8	κ̄	κ̄	NOUN
ejpam-6617	501	9	is	be	AUX
ejpam-6617	501	10	not	not	PART
ejpam-6617	501	11	an	an	DET
ejpam-6617	501	12	lu	lu	NOUN
ejpam-6617	501	13	optimal	optimal	ADJ
ejpam-6617	501	14	point	point	NOUN
ejpam-6617	501	15	for	for	ADP
ejpam-6617	501	16	(	(	PUNCT
ejpam-6617	501	17	p	p	NOUN
ejpam-6617	501	18	)	)	PUNCT
ejpam-6617	501	19	,	,	PUNCT
ejpam-6617	501	20	then	then	ADV
ejpam-6617	501	21	there	there	PRON
ejpam-6617	501	22	is	be	VERB
ejpam-6617	501	23	another	another	DET
ejpam-6617	501	24	feasible	feasible	ADJ
ejpam-6617	501	25	point	point	NOUN
ejpam-6617	501	26	κ	κ	NOUN
ejpam-6617	501	27	for	for	ADP
ejpam-6617	501	28	(	(	PUNCT
ejpam-6617	501	29	p	p	NOUN
ejpam-6617	501	30	)	)	PUNCT
ejpam-6617	501	31	such	such	ADJ
ejpam-6617	501	32	that	that	SCONJ
ejpam-6617	501	33			NOUN
ejpam-6617	501	34	a2∫	a2∫	VERB
ejpam-6617	501	35	a1	a1	NOUN
ejpam-6617	501	36	ϕl(ς	ϕl(ς	X
ejpam-6617	501	37	,	,	PUNCT
ejpam-6617	501	38	κ	κ	NOUN
ejpam-6617	501	39	,	,	PUNCT
ejpam-6617	501	40	cfdγ	cfdγ	PROPN
ejpam-6617	501	41	a+κ)dς	a+κ)dς	PROPN
ejpam-6617	501	42	,	,	PUNCT
ejpam-6617	501	43	a2∫	a2∫	X
ejpam-6617	501	44	a1	a1	VERB
ejpam-6617	501	45	ϕu	ϕu	X
ejpam-6617	501	46	(	(	PUNCT
ejpam-6617	501	47	ς	ς	PROPN
ejpam-6617	501	48	,	,	PUNCT
ejpam-6617	501	49	κ	κ	NOUN
ejpam-6617	501	50	,	,	PUNCT
ejpam-6617	501	51	cfdθ•	cfdθ•	PROPN
ejpam-6617	501	52	a1+κ)dℵ	a1+κ)dℵ	NOUN
ejpam-6617	501	53			NOUN
ejpam-6617	501	54	≺lu	≺lu	VERB
ejpam-6617	501	55			NOUN
ejpam-6617	501	56	a2∫	a2∫	NOUN
ejpam-6617	501	57	a1	a1	NOUN
ejpam-6617	501	58	ϕl(ς	ϕl(ς	X
ejpam-6617	501	59	,	,	PUNCT
ejpam-6617	501	60	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	501	61	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	501	62	,	,	PUNCT
ejpam-6617	501	63	a2∫	a2∫	X
ejpam-6617	501	64	a1	a1	VERB
ejpam-6617	501	65	ϕu	ϕu	X
ejpam-6617	501	66	(	(	PUNCT
ejpam-6617	501	67	ς	ς	PROPN
ejpam-6617	501	68	,	,	PUNCT
ejpam-6617	501	69	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	501	70	a1+ν̄)dς	a1+ν̄)dς	NOUN
ejpam-6617	501	71			NOUN
ejpam-6617	501	72	.	.	PUNCT
ejpam-6617	502	1	since	since	SCONJ
ejpam-6617	502	2	κ	κ	PROPN
ejpam-6617	502	3	and	and	CCONJ
ejpam-6617	502	4	(	(	PUNCT
ejpam-6617	502	5	θ̄	θ̄	ADJ
ejpam-6617	502	6	,	,	PUNCT
ejpam-6617	502	7	ν̄	ν̄	NOUN
ejpam-6617	502	8	)	)	PUNCT
ejpam-6617	502	9	represent	represent	VERB
ejpam-6617	502	10	the	the	DET
ejpam-6617	502	11	respective	respective	ADJ
ejpam-6617	502	12	feasibility	feasibility	NOUN
ejpam-6617	502	13	points	point	NOUN
ejpam-6617	502	14	for	for	ADP
ejpam-6617	502	15	(	(	PUNCT
ejpam-6617	502	16	p	p	NOUN
ejpam-6617	502	17	)	)	PUNCT
ejpam-6617	502	18	and	and	CCONJ
ejpam-6617	502	19	(	(	PUNCT
ejpam-6617	502	20	wd	wd	PROPN
ejpam-6617	502	21	)	)	PUNCT
ejpam-6617	502	22	,	,	PUNCT
ejpam-6617	502	23	then	then	ADV
ejpam-6617	502	24	from	from	ADP
ejpam-6617	502	25	the	the	DET
ejpam-6617	502	26	theorem	theorem	NOUN
ejpam-6617	502	27	4	4	NUM
ejpam-6617	502	28	,	,	PUNCT
ejpam-6617	502	29	we	we	PRON
ejpam-6617	502	30	have	have	VERB
ejpam-6617	502	31	a2∫	a2∫	NOUN
ejpam-6617	502	32	a1	a1	NOUN
ejpam-6617	502	33	ϕl(ς	ϕl(ς	X
ejpam-6617	502	34	,	,	PUNCT
ejpam-6617	502	35	κ	κ	NOUN
ejpam-6617	502	36	,	,	PUNCT
ejpam-6617	502	37	cfdθ•	cfdθ•	PROPN
ejpam-6617	502	38	a1+κ)dς	a1+κ)dς	NUM
ejpam-6617	502	39	,	,	PUNCT
ejpam-6617	502	40	a2∫	a2∫	X
ejpam-6617	502	41	a1	a1	VERB
ejpam-6617	502	42	ϕu	ϕu	X
ejpam-6617	502	43	(	(	PUNCT
ejpam-6617	502	44	ς	ς	PROPN
ejpam-6617	502	45	,	,	PUNCT
ejpam-6617	502	46	κ	κ	NOUN
ejpam-6617	502	47	,	,	PUNCT
ejpam-6617	502	48	cfdθ•	cfdθ•	X
ejpam-6617	502	49	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	502	50			VERB
ejpam-6617	502	51	⊀lu	⊀lu	PROPN
ejpam-6617	502	52			NOUN
ejpam-6617	502	53	a2∫	a2∫	VERB
ejpam-6617	502	54	a1	a1	NOUN
ejpam-6617	502	55	ϕl(ς	ϕl(ς	X
ejpam-6617	502	56	,	,	PUNCT
ejpam-6617	502	57	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	502	58	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	502	59	,	,	PUNCT
ejpam-6617	502	60	a2∫	a2∫	X
ejpam-6617	502	61	a1	a1	VERB
ejpam-6617	502	62	ϕu	ϕu	X
ejpam-6617	502	63	(	(	PUNCT
ejpam-6617	502	64	ς	ς	NOUN
ejpam-6617	502	65	,	,	PUNCT
ejpam-6617	502	66	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	502	67	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	502	68			NOUN
ejpam-6617	502	69	+	+	NUM
ejpam-6617	502	70	a2∫	a2∫	NOUN
ejpam-6617	502	71	a1	a1	NOUN
ejpam-6617	502	72	(	(	PUNCT
ejpam-6617	502	73	θ̄)t	θ̄)t	NOUN
ejpam-6617	502	74	(	(	PUNCT
ejpam-6617	502	75	ς)h(ς	ς)h(ς	NOUN
ejpam-6617	502	76	,	,	PUNCT
ejpam-6617	502	77	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	502	78	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	502	79	.	.	PUNCT
ejpam-6617	503	1	v.	v.	CCONJ
ejpam-6617	503	2	rayanki	rayanki	PROPN
ejpam-6617	503	3	et	et	PROPN
ejpam-6617	503	4	al	al	PROPN
ejpam-6617	503	5	.	.	PUNCT
ejpam-6617	503	6	/	/	SYM
ejpam-6617	503	7	eur	eur	PROPN
ejpam-6617	503	8	.	.	PUNCT
ejpam-6617	504	1	j.	j.	PROPN
ejpam-6617	504	2	pure	pure	PROPN
ejpam-6617	504	3	appl	appl	PROPN
ejpam-6617	504	4	.	.	PROPN
ejpam-6617	504	5	math	math	PROPN
ejpam-6617	504	6	,	,	PUNCT
ejpam-6617	504	7	18	18	NUM
ejpam-6617	504	8	(	(	PUNCT
ejpam-6617	504	9	3	3	NUM
ejpam-6617	504	10	)	)	PUNCT
ejpam-6617	504	11	(	(	PUNCT
ejpam-6617	504	12	2025	2025	NUM
ejpam-6617	504	13	)	)	PUNCT
ejpam-6617	504	14	,	,	PUNCT
ejpam-6617	504	15	6617	6617	NUM
ejpam-6617	504	16	34	34	NUM
ejpam-6617	504	17	of	of	ADP
ejpam-6617	504	18	38	38	NUM
ejpam-6617	504	19	considering	consider	VERB
ejpam-6617	504	20	the	the	DET
ejpam-6617	504	21	feasibility	feasibility	NOUN
ejpam-6617	504	22	of	of	ADP
ejpam-6617	504	23	κ	κ	PROPN
ejpam-6617	504	24	for	for	ADP
ejpam-6617	504	25	(	(	PUNCT
ejpam-6617	504	26	p	p	NOUN
ejpam-6617	504	27	)	)	PUNCT
ejpam-6617	505	1	,	,	PUNCT
ejpam-6617	505	2	it	it	PRON
ejpam-6617	505	3	follows	follow	VERB
ejpam-6617	505	4	that	that	X
ejpam-6617	505	5	a2∫	a2∫	NOUN
ejpam-6617	505	6	a1	a1	NOUN
ejpam-6617	505	7	ϕl(ς	ϕl(ς	X
ejpam-6617	505	8	,	,	PUNCT
ejpam-6617	505	9	κ	κ	NOUN
ejpam-6617	505	10	,	,	PUNCT
ejpam-6617	505	11	cfdγ	cfdγ	NOUN
ejpam-6617	505	12	a1+κ)dς	a1+κ)dς	NUM
ejpam-6617	505	13	,	,	PUNCT
ejpam-6617	505	14	a2∫	a2∫	X
ejpam-6617	505	15	a1	a1	VERB
ejpam-6617	505	16	ϕu	ϕu	X
ejpam-6617	505	17	(	(	PUNCT
ejpam-6617	505	18	ς	ς	PROPN
ejpam-6617	505	19	,	,	PUNCT
ejpam-6617	505	20	κ	κ	NOUN
ejpam-6617	505	21	,	,	PUNCT
ejpam-6617	505	22	cfdθ•	cfdθ•	X
ejpam-6617	505	23	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	505	24			NOUN
ejpam-6617	505	25	+	+	NUM
ejpam-6617	505	26	a2∫	a2∫	NOUN
ejpam-6617	505	27	a1	a1	NOUN
ejpam-6617	505	28	(	(	PUNCT
ejpam-6617	505	29	θ̄)t	θ̄)t	NOUN
ejpam-6617	505	30	(	(	PUNCT
ejpam-6617	505	31	ς)h(ς	ς)h(ς	NUM
ejpam-6617	505	32	,	,	PUNCT
ejpam-6617	505	33	κ	κ	NOUN
ejpam-6617	505	34	,	,	PUNCT
ejpam-6617	505	35	cfdθ•	cfdθ•	PROPN
ejpam-6617	505	36	a1+κ)dς	a1+κ)dς	PRON
ejpam-6617	505	37	⊀lu	⊀lu	PROPN
ejpam-6617	505	38			PROPN
ejpam-6617	505	39	a2∫	a2∫	VERB
ejpam-6617	505	40	a1	a1	NOUN
ejpam-6617	505	41	ϕl(ς	ϕl(ς	X
ejpam-6617	505	42	,	,	PUNCT
ejpam-6617	505	43	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	505	44	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	505	45	,	,	PUNCT
ejpam-6617	505	46	a2∫	a2∫	X
ejpam-6617	505	47	a1	a1	VERB
ejpam-6617	505	48	ϕu	ϕu	X
ejpam-6617	505	49	(	(	PUNCT
ejpam-6617	505	50	ς	ς	NOUN
ejpam-6617	505	51	,	,	PUNCT
ejpam-6617	505	52	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	505	53	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	505	54			NOUN
ejpam-6617	505	55	+	+	NUM
ejpam-6617	505	56	a2∫	a2∫	NOUN
ejpam-6617	505	57	a1	a1	NOUN
ejpam-6617	505	58	(	(	PUNCT
ejpam-6617	505	59	θ̄)t	θ̄)t	NOUN
ejpam-6617	505	60	(	(	PUNCT
ejpam-6617	505	61	ς)h(ς	ς)h(ς	NOUN
ejpam-6617	505	62	,	,	PUNCT
ejpam-6617	505	63	ε̄,cfdθ•	ε̄,cfdθ•	ADJ
ejpam-6617	505	64	a1+ε̄)dς	a1+ε̄)dς	NOUN
ejpam-6617	505	65	,	,	PUNCT
ejpam-6617	505	66	it	it	PRON
ejpam-6617	505	67	is	be	AUX
ejpam-6617	505	68	in	in	ADP
ejpam-6617	505	69	contradiction	contradiction	NOUN
ejpam-6617	505	70	with	with	ADP
ejpam-6617	505	71	(	(	PUNCT
ejpam-6617	505	72	20	20	NUM
ejpam-6617	505	73	)	)	PUNCT
ejpam-6617	505	74	.	.	PUNCT
ejpam-6617	506	1	this	this	PRON
ejpam-6617	506	2	implies	imply	VERB
ejpam-6617	506	3	that	that	SCONJ
ejpam-6617	506	4	ε̄	ε̄	NOUN
ejpam-6617	506	5	is	be	AUX
ejpam-6617	506	6	a	a	DET
ejpam-6617	506	7	lu	lu	NOUN
ejpam-6617	506	8	optimum	optimum	ADJ
ejpam-6617	506	9	point	point	NOUN
ejpam-6617	506	10	for	for	ADP
ejpam-6617	506	11	(	(	PUNCT
ejpam-6617	506	12	p	p	NOUN
ejpam-6617	506	13	)	)	PUNCT
ejpam-6617	506	14	and	and	CCONJ
ejpam-6617	506	15	hence	hence	ADV
ejpam-6617	506	16	the	the	DET
ejpam-6617	506	17	proof	proof	NOUN
ejpam-6617	506	18	.	.	PUNCT
ejpam-6617	507	1	5	5	X
ejpam-6617	507	2	.	.	X
ejpam-6617	507	3	conclusion	conclusion	NOUN
ejpam-6617	507	4	lu	lu	NOUN
ejpam-6617	507	5	optimality	optimality	NOUN
ejpam-6617	507	6	and	and	CCONJ
ejpam-6617	507	7	generalized	generalize	VERB
ejpam-6617	507	8	-	-	PUNCT
ejpam-6617	507	9	invexity	invexity	NOUN
ejpam-6617	507	10	are	be	AUX
ejpam-6617	507	11	employed	employ	VERB
ejpam-6617	507	12	to	to	PART
ejpam-6617	507	13	establish	establish	VERB
ejpam-6617	507	14	optimality	optimality	NOUN
ejpam-6617	507	15	conditions	condition	NOUN
ejpam-6617	507	16	for	for	ADP
ejpam-6617	507	17	a	a	DET
ejpam-6617	507	18	broader	broad	ADJ
ejpam-6617	507	19	class	class	NOUN
ejpam-6617	507	20	of	of	ADP
ejpam-6617	507	21	interval	interval	NOUN
ejpam-6617	507	22	-	-	PUNCT
ejpam-6617	507	23	valued	value	VERB
ejpam-6617	507	24	variational	variational	ADJ
ejpam-6617	507	25	programming	programming	NOUN
ejpam-6617	507	26	problems	problem	NOUN
ejpam-6617	507	27	involving	involve	VERB
ejpam-6617	507	28	objective	objective	ADJ
ejpam-6617	507	29	functions	function	NOUN
ejpam-6617	507	30	with	with	ADP
ejpam-6617	507	31	caputo	caputo	PROPN
ejpam-6617	507	32	-	-	PUNCT
ejpam-6617	507	33	fabrizio	fabrizio	PROPN
ejpam-6617	507	34	fractional	fractional	ADJ
ejpam-6617	507	35	derivatives	derivative	NOUN
ejpam-6617	507	36	.	.	PUNCT
ejpam-6617	508	1	for	for	ADP
ejpam-6617	508	2	the	the	DET
ejpam-6617	508	3	associated	associated	ADJ
ejpam-6617	508	4	wolfe	wolfe	PROPN
ejpam-6617	508	5	-	-	PUNCT
ejpam-6617	508	6	type	type	NOUN
ejpam-6617	508	7	dual	dual	ADJ
ejpam-6617	508	8	problems	problem	NOUN
ejpam-6617	508	9	,	,	PUNCT
ejpam-6617	508	10	we	we	PRON
ejpam-6617	508	11	have	have	AUX
ejpam-6617	508	12	derived	derive	VERB
ejpam-6617	508	13	results	result	NOUN
ejpam-6617	508	14	pertaining	pertain	VERB
ejpam-6617	508	15	to	to	ADP
ejpam-6617	508	16	weak	weak	ADJ
ejpam-6617	508	17	,	,	PUNCT
ejpam-6617	508	18	strong	strong	ADJ
ejpam-6617	508	19	,	,	PUNCT
ejpam-6617	508	20	and	and	CCONJ
ejpam-6617	508	21	strict	strict	ADJ
ejpam-6617	508	22	converse	converse	NOUN
ejpam-6617	508	23	duality	duality	NOUN
ejpam-6617	508	24	.	.	PUNCT
ejpam-6617	509	1	these	these	DET
ejpam-6617	509	2	theoretical	theoretical	ADJ
ejpam-6617	509	3	developments	development	NOUN
ejpam-6617	509	4	are	be	AUX
ejpam-6617	509	5	further	far	ADV
ejpam-6617	509	6	substantiated	substantiate	VERB
ejpam-6617	509	7	through	through	ADP
ejpam-6617	509	8	illustrative	illustrative	ADJ
ejpam-6617	509	9	examples	example	NOUN
ejpam-6617	509	10	.	.	PUNCT
ejpam-6617	510	1	the	the	DET
ejpam-6617	510	2	utilization	utilization	NOUN
ejpam-6617	510	3	of	of	ADP
ejpam-6617	510	4	the	the	DET
ejpam-6617	510	5	caputo	caputo	PROPN
ejpam-6617	510	6	-	-	PUNCT
ejpam-6617	510	7	fabrizio	fabrizio	PROPN
ejpam-6617	510	8	fractional	fractional	ADJ
ejpam-6617	510	9	derivative	derivative	ADJ
ejpam-6617	510	10	introduces	introduce	NOUN
ejpam-6617	510	11	memory	memory	NOUN
ejpam-6617	510	12	effects	effect	NOUN
ejpam-6617	510	13	without	without	ADP
ejpam-6617	510	14	involving	involve	VERB
ejpam-6617	510	15	singular	singular	ADJ
ejpam-6617	510	16	kernels	kernel	NOUN
ejpam-6617	510	17	,	,	PUNCT
ejpam-6617	510	18	thereby	thereby	ADV
ejpam-6617	510	19	enabling	enable	VERB
ejpam-6617	510	20	more	more	ADV
ejpam-6617	510	21	accurate	accurate	ADJ
ejpam-6617	510	22	modeling	modeling	NOUN
ejpam-6617	510	23	of	of	ADP
ejpam-6617	510	24	physical	physical	ADJ
ejpam-6617	510	25	and	and	CCONJ
ejpam-6617	510	26	engineering	engineering	NOUN
ejpam-6617	510	27	systems	system	NOUN
ejpam-6617	510	28	.	.	PUNCT
ejpam-6617	511	1	meanwhile	meanwhile	ADV
ejpam-6617	511	2	,	,	PUNCT
ejpam-6617	511	3	incorporating	incorporate	VERB
ejpam-6617	511	4	interval	interval	NOUN
ejpam-6617	511	5	-	-	PUNCT
ejpam-6617	511	6	valued	value	VERB
ejpam-6617	511	7	objective	objective	ADJ
ejpam-6617	511	8	functions	function	NOUN
ejpam-6617	511	9	strengthens	strengthen	VERB
ejpam-6617	511	10	the	the	DET
ejpam-6617	511	11	robustness	robustness	NOUN
ejpam-6617	511	12	of	of	ADP
ejpam-6617	511	13	the	the	DET
ejpam-6617	511	14	model	model	NOUN
ejpam-6617	511	15	in	in	ADP
ejpam-6617	511	16	handling	handle	VERB
ejpam-6617	511	17	uncertainties	uncertainty	NOUN
ejpam-6617	511	18	that	that	PRON
ejpam-6617	511	19	frequently	frequently	ADV
ejpam-6617	511	20	arise	arise	VERB
ejpam-6617	511	21	in	in	ADP
ejpam-6617	511	22	real	real	ADJ
ejpam-6617	511	23	-	-	PUNCT
ejpam-6617	511	24	world	world	NOUN
ejpam-6617	511	25	scenarios	scenario	NOUN
ejpam-6617	511	26	.	.	PUNCT
ejpam-6617	512	1	the	the	DET
ejpam-6617	512	2	introduction	introduction	NOUN
ejpam-6617	512	3	of	of	ADP
ejpam-6617	512	4	generalized	generalize	VERB
ejpam-6617	512	5	-	-	PUNCT
ejpam-6617	512	6	invexity	invexity	NOUN
ejpam-6617	512	7	significantly	significantly	ADV
ejpam-6617	512	8	extends	extend	VERB
ejpam-6617	512	9	the	the	DET
ejpam-6617	512	10	framework	framework	NOUN
ejpam-6617	512	11	of	of	ADP
ejpam-6617	512	12	optimality	optimality	NOUN
ejpam-6617	512	13	and	and	CCONJ
ejpam-6617	512	14	duality	duality	NOUN
ejpam-6617	512	15	,	,	PUNCT
ejpam-6617	512	16	surpassing	surpass	VERB
ejpam-6617	512	17	traditional	traditional	ADJ
ejpam-6617	512	18	convexity	convexity	NOUN
ejpam-6617	512	19	assumptions	assumption	NOUN
ejpam-6617	512	20	and	and	CCONJ
ejpam-6617	512	21	offering	offer	VERB
ejpam-6617	512	22	greater	great	ADJ
ejpam-6617	512	23	flexibility	flexibility	NOUN
ejpam-6617	512	24	and	and	CCONJ
ejpam-6617	512	25	generality	generality	NOUN
ejpam-6617	512	26	.	.	PUNCT
ejpam-6617	513	1	the	the	DET
ejpam-6617	513	2	proposed	propose	VERB
ejpam-6617	513	3	framework	framework	NOUN
ejpam-6617	513	4	relies	rely	VERB
ejpam-6617	513	5	on	on	ADP
ejpam-6617	513	6	the	the	DET
ejpam-6617	513	7	assumption	assumption	NOUN
ejpam-6617	513	8	that	that	SCONJ
ejpam-6617	513	9	the	the	DET
ejpam-6617	513	10	interval	interval	NOUN
ejpam-6617	513	11	-	-	PUNCT
ejpam-6617	513	12	valued	value	VERB
ejpam-6617	513	13	objective	objective	ADJ
ejpam-6617	513	14	and	and	CCONJ
ejpam-6617	513	15	constraint	constraint	NOUN
ejpam-6617	513	16	functions	function	NOUN
ejpam-6617	513	17	are	be	AUX
ejpam-6617	513	18	both	both	PRON
ejpam-6617	513	19	well	well	ADV
ejpam-6617	513	20	-	-	PUNCT
ejpam-6617	513	21	defined	define	VERB
ejpam-6617	513	22	and	and	CCONJ
ejpam-6617	513	23	bounded	bound	VERB
ejpam-6617	513	24	.	.	PUNCT
ejpam-6617	514	1	however	however	ADV
ejpam-6617	514	2	,	,	PUNCT
ejpam-6617	514	3	in	in	ADP
ejpam-6617	514	4	real	real	ADJ
ejpam-6617	514	5	-	-	PUNCT
ejpam-6617	514	6	world	world	NOUN
ejpam-6617	514	7	scenarios	scenario	NOUN
ejpam-6617	514	8	characterized	characterize	VERB
ejpam-6617	514	9	by	by	ADP
ejpam-6617	514	10	high	high	ADJ
ejpam-6617	514	11	volatility	volatility	NOUN
ejpam-6617	514	12	or	or	CCONJ
ejpam-6617	514	13	deep	deep	ADJ
ejpam-6617	514	14	uncertainty	uncertainty	NOUN
ejpam-6617	514	15	,	,	PUNCT
ejpam-6617	514	16	these	these	DET
ejpam-6617	514	17	assumptions	assumption	NOUN
ejpam-6617	514	18	may	may	AUX
ejpam-6617	514	19	not	not	PART
ejpam-6617	514	20	always	always	ADV
ejpam-6617	514	21	hold	hold	VERB
ejpam-6617	514	22	,	,	PUNCT
ejpam-6617	514	23	potentially	potentially	ADV
ejpam-6617	514	24	affecting	affect	VERB
ejpam-6617	514	25	the	the	DET
ejpam-6617	514	26	model	model	NOUN
ejpam-6617	514	27	’s	’s	PART
ejpam-6617	514	28	accuracy	accuracy	NOUN
ejpam-6617	514	29	and	and	CCONJ
ejpam-6617	514	30	reliability	reliability	NOUN
ejpam-6617	514	31	.	.	PUNCT
ejpam-6617	515	1	additionally	additionally	ADV
ejpam-6617	515	2	,	,	PUNCT
ejpam-6617	515	3	the	the	DET
ejpam-6617	515	4	use	use	NOUN
ejpam-6617	515	5	of	of	ADP
ejpam-6617	515	6	caputo	caputo	PROPN
ejpam-6617	515	7	-	-	PUNCT
ejpam-6617	515	8	fabrizio	fabrizio	PROPN
ejpam-6617	515	9	fractional	fractional	ADJ
ejpam-6617	515	10	derivatives	derivative	NOUN
ejpam-6617	515	11	,	,	PUNCT
ejpam-6617	515	12	though	though	SCONJ
ejpam-6617	515	13	beneficial	beneficial	ADJ
ejpam-6617	515	14	for	for	ADP
ejpam-6617	515	15	capturing	capture	VERB
ejpam-6617	515	16	memory	memory	NOUN
ejpam-6617	515	17	effects	effect	NOUN
ejpam-6617	515	18	without	without	ADP
ejpam-6617	515	19	singularities	singularity	NOUN
ejpam-6617	515	20	,	,	PUNCT
ejpam-6617	515	21	may	may	AUX
ejpam-6617	515	22	not	not	PART
ejpam-6617	515	23	be	be	AUX
ejpam-6617	515	24	appropriate	appropriate	ADJ
ejpam-6617	515	25	for	for	ADP
ejpam-6617	515	26	systems	system	NOUN
ejpam-6617	515	27	where	where	SCONJ
ejpam-6617	515	28	long	long	ADJ
ejpam-6617	515	29	-	-	PUNCT
ejpam-6617	515	30	range	range	NOUN
ejpam-6617	515	31	memory	memory	NOUN
ejpam-6617	515	32	behavior	behavior	NOUN
ejpam-6617	515	33	is	be	AUX
ejpam-6617	515	34	best	well	ADV
ejpam-6617	515	35	modeled	model	VERB
ejpam-6617	515	36	using	use	VERB
ejpam-6617	515	37	singular	singular	ADJ
ejpam-6617	515	38	kernels	kernel	NOUN
ejpam-6617	515	39	(	(	PUNCT
ejpam-6617	515	40	e.g.	e.g.	ADV
ejpam-6617	515	41	,	,	PUNCT
ejpam-6617	515	42	power	power	NOUN
ejpam-6617	515	43	-	-	PUNCT
ejpam-6617	515	44	law	law	NOUN
ejpam-6617	515	45	decay	decay	NOUN
ejpam-6617	515	46	)	)	PUNCT
ejpam-6617	515	47	,	,	PUNCT
ejpam-6617	515	48	thereby	thereby	ADV
ejpam-6617	515	49	limiting	limit	VERB
ejpam-6617	515	50	its	its	PRON
ejpam-6617	515	51	applicability	applicability	NOUN
ejpam-6617	515	52	in	in	ADP
ejpam-6617	515	53	certain	certain	ADJ
ejpam-6617	515	54	contexts	context	NOUN
ejpam-6617	515	55	.	.	PUNCT
ejpam-6617	516	1	v.	v.	ADP
ejpam-6617	516	2	rayanki	rayanki	PROPN
ejpam-6617	516	3	et	et	PROPN
ejpam-6617	516	4	al	al	PROPN
ejpam-6617	516	5	.	.	PUNCT
ejpam-6617	516	6	/	/	SYM
ejpam-6617	516	7	eur	eur	PROPN
ejpam-6617	516	8	.	.	PUNCT
ejpam-6617	517	1	j.	j.	PROPN
ejpam-6617	517	2	pure	pure	PROPN
ejpam-6617	517	3	appl	appl	PROPN
ejpam-6617	517	4	.	.	PROPN
ejpam-6617	517	5	math	math	PROPN
ejpam-6617	517	6	,	,	PUNCT
ejpam-6617	517	7	18	18	NUM
ejpam-6617	517	8	(	(	PUNCT
ejpam-6617	517	9	3	3	NUM
ejpam-6617	517	10	)	)	PUNCT
ejpam-6617	517	11	(	(	PUNCT
ejpam-6617	517	12	2025	2025	NUM
ejpam-6617	517	13	)	)	PUNCT
ejpam-6617	517	14	,	,	PUNCT
ejpam-6617	517	15	6617	6617	NUM
ejpam-6617	517	16	35	35	NUM
ejpam-6617	517	17	of	of	ADP
ejpam-6617	517	18	38	38	NUM
ejpam-6617	517	19	this	this	DET
ejpam-6617	517	20	model	model	NOUN
ejpam-6617	517	21	is	be	AUX
ejpam-6617	517	22	well	well	ADV
ejpam-6617	517	23	-	-	PUNCT
ejpam-6617	517	24	suited	suited	ADJ
ejpam-6617	517	25	for	for	ADP
ejpam-6617	517	26	addressing	address	VERB
ejpam-6617	517	27	resource	resource	NOUN
ejpam-6617	517	28	allocation	allocation	NOUN
ejpam-6617	517	29	problems	problem	NOUN
ejpam-6617	517	30	in	in	ADP
ejpam-6617	517	31	uncertain	uncertain	ADJ
ejpam-6617	517	32	market	market	NOUN
ejpam-6617	517	33	environments	environment	NOUN
ejpam-6617	517	34	,	,	PUNCT
ejpam-6617	517	35	particularly	particularly	ADV
ejpam-6617	517	36	when	when	SCONJ
ejpam-6617	517	37	costs	cost	NOUN
ejpam-6617	517	38	or	or	CCONJ
ejpam-6617	517	39	returns	return	NOUN
ejpam-6617	517	40	exhibit	exhibit	VERB
ejpam-6617	517	41	memory	memory	NOUN
ejpam-6617	517	42	-	-	PUNCT
ejpam-6617	517	43	dependent	dependent	ADJ
ejpam-6617	517	44	behavior	behavior	NOUN
ejpam-6617	517	45	and	and	CCONJ
ejpam-6617	517	46	are	be	AUX
ejpam-6617	517	47	best	well	ADV
ejpam-6617	517	48	represented	represent	VERB
ejpam-6617	517	49	using	use	VERB
ejpam-6617	517	50	interval	interval	NOUN
ejpam-6617	517	51	values	value	NOUN
ejpam-6617	517	52	.	.	PUNCT
ejpam-6617	518	1	it	it	PRON
ejpam-6617	518	2	also	also	ADV
ejpam-6617	518	3	has	have	VERB
ejpam-6617	518	4	relevance	relevance	NOUN
ejpam-6617	518	5	in	in	ADP
ejpam-6617	518	6	control	control	NOUN
ejpam-6617	518	7	system	system	NOUN
ejpam-6617	518	8	design	design	NOUN
ejpam-6617	518	9	and	and	CCONJ
ejpam-6617	518	10	structural	structural	ADJ
ejpam-6617	518	11	optimization	optimization	NOUN
ejpam-6617	518	12	,	,	PUNCT
ejpam-6617	518	13	where	where	SCONJ
ejpam-6617	518	14	degradation	degradation	NOUN
ejpam-6617	518	15	of	of	ADP
ejpam-6617	518	16	material	material	NOUN
ejpam-6617	518	17	properties	property	NOUN
ejpam-6617	518	18	over	over	ADP
ejpam-6617	518	19	time	time	NOUN
ejpam-6617	518	20	and	and	CCONJ
ejpam-6617	518	21	underlying	underlying	ADJ
ejpam-6617	518	22	uncertainty	uncertainty	NOUN
ejpam-6617	518	23	play	play	VERB
ejpam-6617	518	24	a	a	DET
ejpam-6617	518	25	critical	critical	ADJ
ejpam-6617	518	26	role	role	NOUN
ejpam-6617	518	27	.	.	PUNCT
ejpam-6617	519	1	the	the	DET
ejpam-6617	519	2	framework	framework	NOUN
ejpam-6617	519	3	’s	’s	PART
ejpam-6617	519	4	flexibility	flexibility	NOUN
ejpam-6617	519	5	in	in	ADP
ejpam-6617	519	6	handling	handle	VERB
ejpam-6617	519	7	both	both	CCONJ
ejpam-6617	519	8	interval	interval	NOUN
ejpam-6617	519	9	uncertainty	uncertainty	NOUN
ejpam-6617	519	10	and	and	CCONJ
ejpam-6617	519	11	memory	memory	NOUN
ejpam-6617	519	12	effects	effect	NOUN
ejpam-6617	519	13	makes	make	VERB
ejpam-6617	519	14	it	it	PRON
ejpam-6617	519	15	applicable	applicable	ADJ
ejpam-6617	519	16	across	across	ADP
ejpam-6617	519	17	various	various	ADJ
ejpam-6617	519	18	engineering	engineering	NOUN
ejpam-6617	519	19	,	,	PUNCT
ejpam-6617	519	20	economic	economic	ADJ
ejpam-6617	519	21	,	,	PUNCT
ejpam-6617	519	22	and	and	CCONJ
ejpam-6617	519	23	decision	decision	NOUN
ejpam-6617	519	24	-	-	PUNCT
ejpam-6617	519	25	making	make	VERB
ejpam-6617	519	26	problems	problem	NOUN
ejpam-6617	519	27	involving	involve	VERB
ejpam-6617	519	28	complex	complex	ADJ
ejpam-6617	519	29	dynamic	dynamic	ADJ
ejpam-6617	519	30	systems	system	NOUN
ejpam-6617	519	31	.	.	PUNCT
ejpam-6617	520	1	future	future	ADJ
ejpam-6617	520	2	research	research	NOUN
ejpam-6617	520	3	may	may	AUX
ejpam-6617	520	4	extend	extend	VERB
ejpam-6617	520	5	this	this	DET
ejpam-6617	520	6	work	work	NOUN
ejpam-6617	520	7	by	by	ADP
ejpam-6617	520	8	exploring	explore	VERB
ejpam-6617	520	9	fuzzy	fuzzy	ADJ
ejpam-6617	520	10	interval	interval	NOUN
ejpam-6617	520	11	level	level	NOUN
ejpam-6617	520	12	sets	set	NOUN
ejpam-6617	520	13	,	,	PUNCT
ejpam-6617	520	14	closed	closed	ADJ
ejpam-6617	520	15	and	and	CCONJ
ejpam-6617	520	16	bounded	bound	VERB
ejpam-6617	520	17	intervals	interval	NOUN
ejpam-6617	520	18	of	of	ADP
ejpam-6617	520	19	real	real	ADJ
ejpam-6617	520	20	numbers	number	NOUN
ejpam-6617	520	21	that	that	PRON
ejpam-6617	520	22	act	act	VERB
ejpam-6617	520	23	as	as	ADP
ejpam-6617	520	24	a	a	DET
ejpam-6617	520	25	bridge	bridge	NOUN
ejpam-6617	520	26	between	between	ADP
ejpam-6617	520	27	fuzzy	fuzzy	ADJ
ejpam-6617	520	28	set	set	NOUN
ejpam-6617	520	29	theory	theory	NOUN
ejpam-6617	520	30	and	and	CCONJ
ejpam-6617	520	31	classical	classical	ADJ
ejpam-6617	520	32	mathematical	mathematical	ADJ
ejpam-6617	520	33	analysis	analysis	NOUN
ejpam-6617	520	34	.	.	PUNCT
ejpam-6617	521	1	based	base	VERB
ejpam-6617	521	2	on	on	ADP
ejpam-6617	521	3	existing	exist	VERB
ejpam-6617	521	4	literature	literature	NOUN
ejpam-6617	521	5	,	,	PUNCT
ejpam-6617	521	6	such	such	ADJ
ejpam-6617	521	7	as	as	ADP
ejpam-6617	521	8	[	[	X
ejpam-6617	521	9	34	34	NUM
ejpam-6617	521	10	]	]	PUNCT
ejpam-6617	521	11	and	and	CCONJ
ejpam-6617	521	12	[	[	X
ejpam-6617	521	13	17	17	NUM
ejpam-6617	521	14	]	]	PUNCT
ejpam-6617	521	15	,	,	PUNCT
ejpam-6617	521	16	which	which	PRON
ejpam-6617	521	17	describe	describe	VERB
ejpam-6617	521	18	applications	application	NOUN
ejpam-6617	521	19	of	of	ADP
ejpam-6617	521	20	fuzzy	fuzzy	ADJ
ejpam-6617	521	21	set	set	NOUN
ejpam-6617	521	22	theory	theory	NOUN
ejpam-6617	521	23	in	in	ADP
ejpam-6617	521	24	system	system	NOUN
ejpam-6617	521	25	analysis	analysis	NOUN
ejpam-6617	521	26	,	,	PUNCT
ejpam-6617	521	27	the	the	DET
ejpam-6617	521	28	concept	concept	NOUN
ejpam-6617	521	29	of	of	ADP
ejpam-6617	521	30	fuzzy	fuzzy	ADJ
ejpam-6617	521	31	interval	interval	NOUN
ejpam-6617	521	32	level	level	NOUN
ejpam-6617	521	33	sets	set	NOUN
ejpam-6617	521	34	can	can	AUX
ejpam-6617	521	35	be	be	AUX
ejpam-6617	521	36	used	use	VERB
ejpam-6617	521	37	to	to	PART
ejpam-6617	521	38	extend	extend	VERB
ejpam-6617	521	39	results	result	NOUN
ejpam-6617	521	40	from	from	ADP
ejpam-6617	521	41	interval	interval	NOUN
ejpam-6617	521	42	spaces	space	NOUN
ejpam-6617	521	43	to	to	ADP
ejpam-6617	521	44	fuzzy	fuzzy	ADJ
ejpam-6617	521	45	intervals	interval	NOUN
ejpam-6617	521	46	.	.	PUNCT
ejpam-6617	522	1	consequently	consequently	ADV
ejpam-6617	522	2	,	,	PUNCT
ejpam-6617	522	3	this	this	DET
ejpam-6617	522	4	line	line	NOUN
ejpam-6617	522	5	of	of	ADP
ejpam-6617	522	6	inquiry	inquiry	NOUN
ejpam-6617	522	7	could	could	AUX
ejpam-6617	522	8	pave	pave	VERB
ejpam-6617	522	9	the	the	DET
ejpam-6617	522	10	way	way	NOUN
ejpam-6617	522	11	for	for	ADP
ejpam-6617	522	12	developing	develop	VERB
ejpam-6617	522	13	optimality	optimality	NOUN
ejpam-6617	522	14	conditions	condition	NOUN
ejpam-6617	522	15	for	for	ADP
ejpam-6617	522	16	fuzzy	fuzzy	ADJ
ejpam-6617	522	17	interval	interval	NOUN
ejpam-6617	522	18	-	-	PUNCT
ejpam-6617	522	19	valued	value	VERB
ejpam-6617	522	20	variational	variational	ADJ
ejpam-6617	522	21	programming	programming	NOUN
ejpam-6617	522	22	problems	problem	NOUN
ejpam-6617	522	23	with	with	ADP
ejpam-6617	522	24	caputo	caputo	PROPN
ejpam-6617	522	25	-	-	PUNCT
ejpam-6617	522	26	fabrizio	fabrizio	PROPN
ejpam-6617	522	27	fractional	fractional	ADJ
ejpam-6617	522	28	derivatives	derivative	NOUN
ejpam-6617	522	29	,	,	PUNCT
ejpam-6617	522	30	marking	mark	VERB
ejpam-6617	522	31	a	a	DET
ejpam-6617	522	32	novel	novel	ADJ
ejpam-6617	522	33	direction	direction	NOUN
ejpam-6617	522	34	in	in	ADP
ejpam-6617	522	35	this	this	DET
ejpam-6617	522	36	field	field	NOUN
ejpam-6617	522	37	of	of	ADP
ejpam-6617	522	38	study	study	NOUN
ejpam-6617	522	39	.	.	PUNCT
ejpam-6617	523	1	conflicts	conflict	NOUN
ejpam-6617	523	2	of	of	ADP
ejpam-6617	523	3	interest	interest	NOUN
ejpam-6617	523	4	or	or	CCONJ
ejpam-6617	523	5	competing	compete	VERB
ejpam-6617	523	6	interests	interest	NOUN
ejpam-6617	523	7	the	the	DET
ejpam-6617	523	8	authors	author	NOUN
ejpam-6617	523	9	declare	declare	VERB
ejpam-6617	523	10	that	that	SCONJ
ejpam-6617	523	11	they	they	PRON
ejpam-6617	523	12	have	have	VERB
ejpam-6617	523	13	no	no	DET
ejpam-6617	523	14	conflicts	conflict	NOUN
ejpam-6617	523	15	of	of	ADP
ejpam-6617	523	16	interest	interest	NOUN
ejpam-6617	523	17	.	.	PUNCT
ejpam-6617	524	1	data	datum	NOUN
ejpam-6617	524	2	and	and	CCONJ
ejpam-6617	524	3	code	code	NOUN
ejpam-6617	524	4	availability	availability	NOUN
ejpam-6617	524	5	no	no	DET
ejpam-6617	524	6	data	datum	NOUN
ejpam-6617	524	7	were	be	AUX
ejpam-6617	524	8	used	use	VERB
ejpam-6617	524	9	to	to	PART
ejpam-6617	524	10	support	support	VERB
ejpam-6617	524	11	this	this	DET
ejpam-6617	524	12	study	study	NOUN
ejpam-6617	524	13	supplementary	supplementary	ADJ
ejpam-6617	524	14	information	information	NOUN
ejpam-6617	524	15	not	not	PART
ejpam-6617	524	16	applicable	applicable	ADJ
ejpam-6617	524	17	ethical	ethical	ADJ
ejpam-6617	524	18	approval	approval	NOUN
ejpam-6617	524	19	this	this	DET
ejpam-6617	524	20	article	article	NOUN
ejpam-6617	524	21	does	do	AUX
ejpam-6617	524	22	not	not	PART
ejpam-6617	524	23	contain	contain	VERB
ejpam-6617	524	24	any	any	DET
ejpam-6617	524	25	studies	study	NOUN
ejpam-6617	524	26	with	with	ADP
ejpam-6617	524	27	human	human	ADJ
ejpam-6617	524	28	participants	participant	NOUN
ejpam-6617	524	29	or	or	CCONJ
ejpam-6617	524	30	animals	animal	NOUN
ejpam-6617	524	31	performed	perform	VERB
ejpam-6617	524	32	by	by	ADP
ejpam-6617	524	33	any	any	PRON
ejpam-6617	524	34	of	of	ADP
ejpam-6617	524	35	the	the	DET
ejpam-6617	524	36	authors	author	NOUN
ejpam-6617	524	37	informed	inform	VERB
ejpam-6617	524	38	consent	consent	VERB
ejpam-6617	524	39	the	the	DET
ejpam-6617	524	40	authors	author	NOUN
ejpam-6617	524	41	are	be	AUX
ejpam-6617	524	42	fully	fully	ADV
ejpam-6617	524	43	aware	aware	ADJ
ejpam-6617	524	44	and	and	CCONJ
ejpam-6617	524	45	satisfied	satisfied	ADJ
ejpam-6617	524	46	with	with	ADP
ejpam-6617	524	47	the	the	DET
ejpam-6617	524	48	contents	content	NOUN
ejpam-6617	524	49	of	of	ADP
ejpam-6617	524	50	the	the	DET
ejpam-6617	524	51	article	article	NOUN
ejpam-6617	524	52	.	.	PUNCT
ejpam-6617	525	1	acknowledgements	acknowledgement	NOUN
ejpam-6617	525	2	we	we	PRON
ejpam-6617	525	3	sincerely	sincerely	ADV
ejpam-6617	525	4	thank	thank	VERB
ejpam-6617	525	5	the	the	DET
ejpam-6617	525	6	anonymous	anonymous	ADJ
ejpam-6617	525	7	reviewers	reviewer	NOUN
ejpam-6617	525	8	for	for	ADP
ejpam-6617	525	9	their	their	PRON
ejpam-6617	525	10	insightful	insightful	ADJ
ejpam-6617	525	11	comments	comment	NOUN
ejpam-6617	525	12	and	and	CCONJ
ejpam-6617	525	13	constructive	constructive	ADJ
ejpam-6617	525	14	suggestions	suggestion	NOUN
ejpam-6617	525	15	,	,	PUNCT
ejpam-6617	525	16	which	which	PRON
ejpam-6617	525	17	have	have	AUX
ejpam-6617	525	18	greatly	greatly	ADV
ejpam-6617	525	19	enhanced	enhance	VERB
ejpam-6617	525	20	the	the	DET
ejpam-6617	525	21	quality	quality	NOUN
ejpam-6617	525	22	and	and	CCONJ
ejpam-6617	525	23	clarity	clarity	NOUN
ejpam-6617	525	24	of	of	ADP
ejpam-6617	525	25	our	our	PRON
ejpam-6617	525	26	paper	paper	NOUN
ejpam-6617	525	27	.	.	PUNCT
ejpam-6617	526	1	v.	v.	CCONJ
ejpam-6617	526	2	rayanki	rayanki	PROPN
ejpam-6617	526	3	et	et	PROPN
ejpam-6617	526	4	al	al	PROPN
ejpam-6617	526	5	.	.	PUNCT
ejpam-6617	526	6	/	/	SYM
ejpam-6617	526	7	eur	eur	PROPN
ejpam-6617	526	8	.	.	PUNCT
ejpam-6617	527	1	j.	j.	PROPN
ejpam-6617	527	2	pure	pure	PROPN
ejpam-6617	527	3	appl	appl	PROPN
ejpam-6617	527	4	.	.	PROPN
ejpam-6617	527	5	math	math	PROPN
ejpam-6617	527	6	,	,	PUNCT
ejpam-6617	527	7	18	18	NUM
ejpam-6617	527	8	(	(	PUNCT
ejpam-6617	527	9	3	3	NUM
ejpam-6617	527	10	)	)	PUNCT
ejpam-6617	527	11	(	(	PUNCT
ejpam-6617	527	12	2025	2025	NUM
ejpam-6617	527	13	)	)	PUNCT
ejpam-6617	527	14	,	,	PUNCT
ejpam-6617	527	15	6617	6617	NUM
ejpam-6617	527	16	36	36	NUM
ejpam-6617	527	17	of	of	ADP
ejpam-6617	527	18	38	38	NUM
ejpam-6617	527	19	references	reference	NOUN
ejpam-6617	527	20	[	[	X
ejpam-6617	527	21	1	1	NUM
ejpam-6617	527	22	]	]	PUNCT
ejpam-6617	527	23	t	t	NOUN
ejpam-6617	527	24	abdeljawad	abdeljawad	NOUN
ejpam-6617	527	25	and	and	CCONJ
ejpam-6617	527	26	d	d	X
ejpam-6617	527	27	baleanu	baleanu	NOUN
ejpam-6617	527	28	.	.	PUNCT
ejpam-6617	528	1	on	on	ADP
ejpam-6617	528	2	fractional	fractional	ADJ
ejpam-6617	528	3	derivatives	derivative	NOUN
ejpam-6617	528	4	with	with	ADP
ejpam-6617	528	5	exponential	exponential	ADJ
ejpam-6617	528	6	kernel	kernel	NOUN
ejpam-6617	528	7	and	and	CCONJ
ejpam-6617	528	8	their	their	PRON
ejpam-6617	528	9	discrete	discrete	ADJ
ejpam-6617	528	10	versions	version	NOUN
ejpam-6617	528	11	.	.	PUNCT
ejpam-6617	529	1	reports	report	NOUN
ejpam-6617	529	2	on	on	ADP
ejpam-6617	529	3	mathematical	mathematical	ADJ
ejpam-6617	529	4	physics	physics	NOUN
ejpam-6617	529	5	,	,	PUNCT
ejpam-6617	529	6	80(1):11–27	80(1):11–27	NUM
ejpam-6617	529	7	,	,	PUNCT
ejpam-6617	529	8	2017	2017	NUM
ejpam-6617	529	9	.	.	PUNCT
ejpam-6617	530	1	[	[	X
ejpam-6617	530	2	2	2	NUM
ejpam-6617	530	3	]	]	SYM
ejpam-6617	530	4	b	b	X
ejpam-6617	530	5	chetia	chetia	PROPN
ejpam-6617	530	6	and	and	CCONJ
ejpam-6617	530	7	p	p	PROPN
ejpam-6617	530	8	k	k	PROPN
ejpam-6617	530	9	das	das	PROPN
ejpam-6617	530	10	.	.	PUNCT
ejpam-6617	531	1	an	an	DET
ejpam-6617	531	2	application	application	NOUN
ejpam-6617	531	3	of	of	ADP
ejpam-6617	531	4	interval	interval	NOUN
ejpam-6617	531	5	-	-	PUNCT
ejpam-6617	531	6	valued	value	VERB
ejpam-6617	531	7	fuzzy	fuzzy	ADJ
ejpam-6617	531	8	soft	soft	ADJ
ejpam-6617	531	9	.	.	PUNCT
ejpam-6617	532	1	international	international	ADJ
ejpam-6617	532	2	journal	journal	PROPN
ejpam-6617	532	3	of	of	ADP
ejpam-6617	532	4	contemporary	contemporary	PROPN
ejpam-6617	532	5	mathematical	mathematical	PROPN
ejpam-6617	532	6	sciences	sciences	PROPN
ejpam-6617	532	7	,	,	PUNCT
ejpam-6617	532	8	5(38):1887–1894	5(38):1887–1894	NUM
ejpam-6617	532	9	,	,	PUNCT
ejpam-6617	532	10	2010	2010	NUM
ejpam-6617	532	11	.	.	PUNCT
ejpam-6617	533	1	[	[	X
ejpam-6617	533	2	3	3	NUM
ejpam-6617	533	3	]	]	X
ejpam-6617	533	4	d	d	X
ejpam-6617	533	5	yin	yin	PROPN
ejpam-6617	533	6	et	et	PROPN
ejpam-6617	533	7	al	al	PROPN
ejpam-6617	533	8	.	.	PROPN
ejpam-6617	533	9	application	application	NOUN
ejpam-6617	533	10	of	of	ADP
ejpam-6617	533	11	interval	interval	NOUN
ejpam-6617	533	12	valued	value	VERB
ejpam-6617	533	13	fuzzy	fuzzy	ADJ
ejpam-6617	533	14	linear	linear	ADJ
ejpam-6617	533	15	programming	programming	NOUN
ejpam-6617	533	16	for	for	ADP
ejpam-6617	533	17	stock	stock	NOUN
ejpam-6617	533	18	portfolio	portfolio	NOUN
ejpam-6617	533	19	optimization	optimization	NOUN
ejpam-6617	533	20	.	.	PUNCT
ejpam-6617	534	1	applied	apply	VERB
ejpam-6617	534	2	mathematics	mathematic	NOUN
ejpam-6617	534	3	,	,	PUNCT
ejpam-6617	534	4	9(02):101	9(02):101	NUM
ejpam-6617	534	5	,	,	PUNCT
ejpam-6617	534	6	2018	2018	NUM
ejpam-6617	534	7	.	.	PUNCT
ejpam-6617	535	1	[	[	X
ejpam-6617	535	2	4	4	NUM
ejpam-6617	535	3	]	]	PUNCT
ejpam-6617	535	4	t	t	PROPN
ejpam-6617	535	5	saeed	saeed	PROPN
ejpam-6617	535	6	and	and	CCONJ
ejpam-6617	535	7	s	s	PROPN
ejpam-6617	535	8	treanctua	treanctua	NOUN
ejpam-6617	535	9	.	.	PUNCT
ejpam-6617	536	1	new	new	ADJ
ejpam-6617	536	2	classes	class	NOUN
ejpam-6617	536	3	of	of	ADP
ejpam-6617	536	4	interval	interval	NOUN
ejpam-6617	536	5	-	-	PUNCT
ejpam-6617	536	6	valued	value	VERB
ejpam-6617	536	7	variational	variational	ADJ
ejpam-6617	536	8	problems	problem	NOUN
ejpam-6617	536	9	and	and	CCONJ
ejpam-6617	536	10	inequalities	inequality	NOUN
ejpam-6617	536	11	.	.	PUNCT
ejpam-6617	537	1	results	result	NOUN
ejpam-6617	537	2	in	in	ADP
ejpam-6617	537	3	control	control	NOUN
ejpam-6617	537	4	and	and	CCONJ
ejpam-6617	537	5	optimization	optimization	NOUN
ejpam-6617	537	6	,	,	PUNCT
ejpam-6617	537	7	13:100324	13:100324	NUM
ejpam-6617	537	8	,	,	PUNCT
ejpam-6617	537	9	2023	2023	NUM
ejpam-6617	537	10	.	.	PUNCT
ejpam-6617	538	1	[	[	X
ejpam-6617	538	2	5	5	NUM
ejpam-6617	538	3	]	]	PUNCT
ejpam-6617	538	4	s	s	VERB
ejpam-6617	538	5	treanta	treanta	NOUN
ejpam-6617	538	6	and	and	CCONJ
ejpam-6617	538	7	marilena	marilena	PROPN
ejpam-6617	538	8	ciontescu	ciontescu	PROPN
ejpam-6617	538	9	.	.	PUNCT
ejpam-6617	539	1	on	on	ADP
ejpam-6617	539	2	optimal	optimal	ADJ
ejpam-6617	539	3	control	control	NOUN
ejpam-6617	539	4	problems	problem	NOUN
ejpam-6617	539	5	with	with	ADP
ejpam-6617	539	6	generalized	generalized	ADJ
ejpam-6617	539	7	invariant	invariant	ADJ
ejpam-6617	539	8	convex	convex	NOUN
ejpam-6617	539	9	interval	interval	NOUN
ejpam-6617	539	10	-	-	PUNCT
ejpam-6617	539	11	valued	value	VERB
ejpam-6617	539	12	functionals	functional	NOUN
ejpam-6617	539	13	.	.	PUNCT
ejpam-6617	540	1	journal	journal	NOUN
ejpam-6617	540	2	of	of	ADP
ejpam-6617	540	3	industrial	industrial	ADJ
ejpam-6617	540	4	and	and	CCONJ
ejpam-6617	540	5	management	management	NOUN
ejpam-6617	540	6	optimization	optimization	NOUN
ejpam-6617	540	7	,	,	PUNCT
ejpam-6617	540	8	20:3317–3336	20:3317–3336	NUM
ejpam-6617	540	9	,	,	PUNCT
ejpam-6617	540	10	2024	2024	NUM
ejpam-6617	540	11	.	.	PUNCT
ejpam-6617	541	1	[	[	X
ejpam-6617	541	2	6	6	NUM
ejpam-6617	541	3	]	]	PUNCT
ejpam-6617	541	4	a	a	DET
ejpam-6617	541	5	k	k	PROPN
ejpam-6617	541	6	bhurjee	bhurjee	NOUN
ejpam-6617	541	7	and	and	CCONJ
ejpam-6617	541	8	g	g	NOUN
ejpam-6617	541	9	panda	panda	NOUN
ejpam-6617	541	10	.	.	PUNCT
ejpam-6617	542	1	sufficient	sufficient	ADJ
ejpam-6617	542	2	optimality	optimality	NOUN
ejpam-6617	542	3	conditions	condition	NOUN
ejpam-6617	542	4	and	and	CCONJ
ejpam-6617	542	5	duality	duality	NOUN
ejpam-6617	542	6	theory	theory	NOUN
ejpam-6617	542	7	for	for	ADP
ejpam-6617	542	8	interval	interval	NOUN
ejpam-6617	542	9	optimization	optimization	NOUN
ejpam-6617	542	10	problem	problem	NOUN
ejpam-6617	542	11	.	.	PUNCT
ejpam-6617	543	1	annals	annal	NOUN
ejpam-6617	543	2	of	of	ADP
ejpam-6617	543	3	operations	operation	NOUN
ejpam-6617	543	4	research	research	NOUN
ejpam-6617	543	5	,	,	PUNCT
ejpam-6617	543	6	243(1):335–348	243(1):335–348	PROPN
ejpam-6617	543	7	,	,	PUNCT
ejpam-6617	543	8	2016	2016	NUM
ejpam-6617	543	9	.	.	PUNCT
ejpam-6617	544	1	[	[	X
ejpam-6617	544	2	7	7	X
ejpam-6617	544	3	]	]	X
ejpam-6617	544	4	r	r	NOUN
ejpam-6617	544	5	e	e	X
ejpam-6617	544	6	moore	moore	PROPN
ejpam-6617	544	7	.	.	PUNCT
ejpam-6617	545	1	interval	interval	NOUN
ejpam-6617	545	2	analysis	analysis	NOUN
ejpam-6617	545	3	.	.	PUNCT
ejpam-6617	546	1	prentice	prentice	NOUN
ejpam-6617	546	2	-	-	PUNCT
ejpam-6617	546	3	hall	hall	NOUN
ejpam-6617	546	4	,	,	PUNCT
ejpam-6617	546	5	1966	1966	NUM
ejpam-6617	546	6	.	.	PUNCT
ejpam-6617	547	1	[	[	X
ejpam-6617	547	2	8	8	X
ejpam-6617	547	3	]	]	PUNCT
ejpam-6617	547	4	a	a	DET
ejpam-6617	547	5	neumaier	neumaier	NOUN
ejpam-6617	547	6	.	.	PUNCT
ejpam-6617	548	1	interval	interval	NOUN
ejpam-6617	548	2	methods	method	NOUN
ejpam-6617	548	3	for	for	ADP
ejpam-6617	548	4	systems	system	NOUN
ejpam-6617	548	5	of	of	ADP
ejpam-6617	548	6	equations	equation	NOUN
ejpam-6617	548	7	.	.	PUNCT
ejpam-6617	549	1	number	number	NOUN
ejpam-6617	549	2	37	37	NUM
ejpam-6617	549	3	.	.	PUNCT
ejpam-6617	550	1	cambridge	cambridge	PROPN
ejpam-6617	550	2	university	university	PROPN
ejpam-6617	550	3	press	press	NOUN
ejpam-6617	550	4	,	,	PUNCT
ejpam-6617	550	5	1990	1990	NUM
ejpam-6617	550	6	.	.	PUNCT
ejpam-6617	551	1	[	[	X
ejpam-6617	551	2	9	9	NUM
ejpam-6617	551	3	]	]	X
ejpam-6617	551	4	i	i	PRON
ejpam-6617	551	5	m	m	VERB
ejpam-6617	551	6	stancu	stancu	NOUN
ejpam-6617	551	7	-	-	PUNCT
ejpam-6617	551	8	minasian	minasian	ADJ
ejpam-6617	551	9	.	.	PUNCT
ejpam-6617	552	1	stochastic	stochastic	ADJ
ejpam-6617	552	2	programming	programming	NOUN
ejpam-6617	552	3	with	with	ADP
ejpam-6617	552	4	multiple	multiple	ADJ
ejpam-6617	552	5	objective	objective	ADJ
ejpam-6617	552	6	functions	function	NOUN
ejpam-6617	552	7	,	,	PUNCT
ejpam-6617	552	8	volume	volume	NOUN
ejpam-6617	552	9	13	13	NUM
ejpam-6617	552	10	.	.	PUNCT
ejpam-6617	552	11	springer	springer	NOUN
ejpam-6617	552	12	,	,	PUNCT
ejpam-6617	552	13	1984	1984	NUM
ejpam-6617	552	14	.	.	PUNCT
ejpam-6617	553	1	[	[	X
ejpam-6617	553	2	10	10	NUM
ejpam-6617	553	3	]	]	X
ejpam-6617	553	4	r	r	NOUN
ejpam-6617	553	5	osuna	osuna	PROPN
ejpam-6617	553	6	-	-	PUNCT
ejpam-6617	553	7	gómez	gómez	PROPN
ejpam-6617	553	8	,	,	PUNCT
ejpam-6617	553	9	b	b	PROPN
ejpam-6617	553	10	hernández	hernández	PROPN
ejpam-6617	553	11	-	-	PUNCT
ejpam-6617	553	12	jiménez	jiménez	PROPN
ejpam-6617	553	13	,	,	PUNCT
ejpam-6617	553	14	y	y	PROPN
ejpam-6617	553	15	chalco	chalco	PROPN
ejpam-6617	553	16	-	-	PUNCT
ejpam-6617	553	17	cano	cano	PROPN
ejpam-6617	553	18	,	,	PUNCT
ejpam-6617	553	19	and	and	CCONJ
ejpam-6617	553	20	g	g	ADP
ejpam-6617	553	21	ruiz	ruiz	NOUN
ejpam-6617	553	22	-	-	PUNCT
ejpam-6617	553	23	garzón	garzón	PROPN
ejpam-6617	553	24	.	.	PUNCT
ejpam-6617	553	25	new	new	ADJ
ejpam-6617	553	26	efficiency	efficiency	NOUN
ejpam-6617	553	27	conditions	condition	NOUN
ejpam-6617	553	28	for	for	ADP
ejpam-6617	553	29	multiobjective	multiobjective	ADJ
ejpam-6617	553	30	interval	interval	NOUN
ejpam-6617	553	31	-	-	PUNCT
ejpam-6617	553	32	valued	value	VERB
ejpam-6617	553	33	programming	programming	NOUN
ejpam-6617	553	34	problems	problem	NOUN
ejpam-6617	553	35	.	.	PUNCT
ejpam-6617	554	1	information	information	NOUN
ejpam-6617	554	2	sciences	sciences	PROPN
ejpam-6617	554	3	,	,	PUNCT
ejpam-6617	554	4	420:235–248	420:235–248	NUM
ejpam-6617	554	5	,	,	PUNCT
ejpam-6617	554	6	2017	2017	NUM
ejpam-6617	554	7	.	.	PUNCT
ejpam-6617	555	1	[	[	X
ejpam-6617	555	2	11	11	NUM
ejpam-6617	555	3	]	]	X
ejpam-6617	555	4	y	y	PROPN
ejpam-6617	555	5	sun	sun	PROPN
ejpam-6617	555	6	and	and	CCONJ
ejpam-6617	555	7	l	l	PROPN
ejpam-6617	555	8	wang	wang	PROPN
ejpam-6617	555	9	.	.	PUNCT
ejpam-6617	556	1	optimality	optimality	NOUN
ejpam-6617	556	2	conditions	condition	NOUN
ejpam-6617	556	3	and	and	CCONJ
ejpam-6617	556	4	duality	duality	NOUN
ejpam-6617	556	5	in	in	ADP
ejpam-6617	556	6	nondifferentiable	nondifferentiable	ADJ
ejpam-6617	556	7	intervalvalued	intervalvalue	VERB
ejpam-6617	556	8	programming	programming	NOUN
ejpam-6617	556	9	.	.	PUNCT
ejpam-6617	557	1	journal	journal	PROPN
ejpam-6617	557	2	of	of	ADP
ejpam-6617	557	3	industrial	industrial	PROPN
ejpam-6617	557	4	&	&	CCONJ
ejpam-6617	557	5	management	management	NOUN
ejpam-6617	557	6	optimization	optimization	NOUN
ejpam-6617	557	7	,	,	PUNCT
ejpam-6617	557	8	9(1	9(1	NUM
ejpam-6617	557	9	)	)	PUNCT
ejpam-6617	557	10	,	,	PUNCT
ejpam-6617	557	11	2013	2013	NUM
ejpam-6617	557	12	.	.	PUNCT
ejpam-6617	558	1	[	[	X
ejpam-6617	558	2	12	12	NUM
ejpam-6617	558	3	]	]	X
ejpam-6617	558	4	r	r	NOUN
ejpam-6617	558	5	esmaelzadeh	esmaelzadeh	NOUN
ejpam-6617	558	6	.	.	PUNCT
ejpam-6617	559	1	low	low	ADJ
ejpam-6617	559	2	-	-	PUNCT
ejpam-6617	559	3	thrust	thrust	NOUN
ejpam-6617	559	4	orbit	orbit	NOUN
ejpam-6617	559	5	transfer	transfer	NOUN
ejpam-6617	559	6	optimization	optimization	NOUN
ejpam-6617	559	7	using	use	VERB
ejpam-6617	559	8	a	a	DET
ejpam-6617	559	9	combined	combine	VERB
ejpam-6617	559	10	method	method	NOUN
ejpam-6617	559	11	.	.	PUNCT
ejpam-6617	560	1	international	international	ADJ
ejpam-6617	560	2	journal	journal	PROPN
ejpam-6617	560	3	of	of	ADP
ejpam-6617	560	4	computer	computer	NOUN
ejpam-6617	560	5	applications	application	NOUN
ejpam-6617	560	6	,	,	PUNCT
ejpam-6617	560	7	89(4	89(4	NOUN
ejpam-6617	560	8	)	)	PUNCT
ejpam-6617	560	9	,	,	PUNCT
ejpam-6617	560	10	2014	2014	NUM
ejpam-6617	560	11	.	.	PUNCT
ejpam-6617	561	1	[	[	X
ejpam-6617	561	2	13	13	NUM
ejpam-6617	561	3	]	]	SYM
ejpam-6617	561	4	l	l	NOUN
ejpam-6617	561	5	blasi	blasi	NOUN
ejpam-6617	561	6	,	,	PUNCT
ejpam-6617	561	7	s	s	PART
ejpam-6617	561	8	barbato	barbato	NOUN
ejpam-6617	561	9	,	,	PUNCT
ejpam-6617	561	10	and	and	CCONJ
ejpam-6617	561	11	mmattei	mmattei	NOUN
ejpam-6617	561	12	.	.	PUNCT
ejpam-6617	562	1	a	a	DET
ejpam-6617	562	2	particle	particle	NOUN
ejpam-6617	562	3	swarm	swarm	NOUN
ejpam-6617	562	4	approach	approach	NOUN
ejpam-6617	562	5	for	for	ADP
ejpam-6617	562	6	flight	flight	NOUN
ejpam-6617	562	7	path	path	NOUN
ejpam-6617	562	8	optimization	optimization	NOUN
ejpam-6617	562	9	in	in	ADP
ejpam-6617	562	10	a	a	DET
ejpam-6617	562	11	constrained	constrain	VERB
ejpam-6617	562	12	environment	environment	NOUN
ejpam-6617	562	13	.	.	PUNCT
ejpam-6617	563	1	aerospace	aerospace	NOUN
ejpam-6617	563	2	science	science	NOUN
ejpam-6617	563	3	and	and	CCONJ
ejpam-6617	563	4	technology	technology	NOUN
ejpam-6617	563	5	,	,	PUNCT
ejpam-6617	563	6	26(1):128–137	26(1):128–137	PROPN
ejpam-6617	563	7	,	,	PUNCT
ejpam-6617	563	8	2013	2013	NUM
ejpam-6617	563	9	.	.	PUNCT
ejpam-6617	564	1	[	[	X
ejpam-6617	564	2	14	14	NUM
ejpam-6617	564	3	]	]	X
ejpam-6617	564	4	s	s	PART
ejpam-6617	564	5	khardi	khardi	NOUN
ejpam-6617	564	6	.	.	PUNCT
ejpam-6617	565	1	aircraft	aircraft	NOUN
ejpam-6617	565	2	flight	flight	NOUN
ejpam-6617	565	3	path	path	NOUN
ejpam-6617	565	4	optimization	optimization	NOUN
ejpam-6617	565	5	.	.	PUNCT
ejpam-6617	566	1	the	the	DET
ejpam-6617	566	2	hamilton	hamilton	PROPN
ejpam-6617	566	3	-	-	PUNCT
ejpam-6617	566	4	jacobi	jacobi	PROPN
ejpam-6617	566	5	-	-	PUNCT
ejpam-6617	566	6	bellman	bellman	PROPN
ejpam-6617	566	7	considerations	consideration	NOUN
ejpam-6617	566	8	.	.	PUNCT
ejpam-6617	567	1	applied	apply	VERB
ejpam-6617	567	2	mathematical	mathematical	ADJ
ejpam-6617	567	3	sciences	science	NOUN
ejpam-6617	567	4	,	,	PUNCT
ejpam-6617	567	5	6(25):pp–1221	6(25):pp–1221	NUM
ejpam-6617	567	6	,	,	PUNCT
ejpam-6617	567	7	2012	2012	NUM
ejpam-6617	567	8	.	.	PUNCT
ejpam-6617	568	1	[	[	X
ejpam-6617	568	2	15	15	NUM
ejpam-6617	568	3	]	]	X
ejpam-6617	568	4	i	i	PROPN
ejpam-6617	568	5	ahmad	ahmad	PROPN
ejpam-6617	568	6	,	,	PUNCT
ejpam-6617	568	7	a	a	DET
ejpam-6617	568	8	jayswal	jayswal	NOUN
ejpam-6617	568	9	,	,	PUNCT
ejpam-6617	568	10	s	s	PROPN
ejpam-6617	568	11	al	al	PROPN
ejpam-6617	568	12	-	-	PROPN
ejpam-6617	568	13	homidan	homidan	PROPN
ejpam-6617	568	14	,	,	PUNCT
ejpam-6617	568	15	and	and	CCONJ
ejpam-6617	568	16	j	j	PROPN
ejpam-6617	568	17	banerjee	banerjee	PROPN
ejpam-6617	568	18	.	.	PUNCT
ejpam-6617	569	1	sufficiency	sufficiency	NOUN
ejpam-6617	569	2	and	and	CCONJ
ejpam-6617	569	3	duality	duality	NOUN
ejpam-6617	569	4	in	in	ADP
ejpam-6617	569	5	interval	interval	NOUN
ejpam-6617	569	6	-	-	PUNCT
ejpam-6617	569	7	valued	value	VERB
ejpam-6617	569	8	variational	variational	ADJ
ejpam-6617	569	9	programming	programming	NOUN
ejpam-6617	569	10	.	.	PUNCT
ejpam-6617	570	1	neural	neural	ADJ
ejpam-6617	570	2	computing	computing	NOUN
ejpam-6617	570	3	and	and	CCONJ
ejpam-6617	570	4	applications	application	NOUN
ejpam-6617	570	5	,	,	PUNCT
ejpam-6617	570	6	31(8):4423–4433	31(8):4423–4433	NUM
ejpam-6617	570	7	,	,	PUNCT
ejpam-6617	570	8	2019	2019	NUM
ejpam-6617	570	9	.	.	PUNCT
ejpam-6617	571	1	[	[	X
ejpam-6617	571	2	16	16	NUM
ejpam-6617	571	3	]	]	X
ejpam-6617	571	4	i	i	PROPN
ejpam-6617	571	5	ahmad	ahmad	PROPN
ejpam-6617	571	6	,	,	PUNCT
ejpam-6617	571	7	a	a	DET
ejpam-6617	571	8	jayswal	jayswal	NOUN
ejpam-6617	571	9	,	,	PUNCT
ejpam-6617	571	10	and	and	CCONJ
ejpam-6617	571	11	j	j	PROPN
ejpam-6617	571	12	banerjee	banerjee	PROPN
ejpam-6617	571	13	.	.	PUNCT
ejpam-6617	572	1	on	on	ADP
ejpam-6617	572	2	interval	interval	NOUN
ejpam-6617	572	3	-	-	PUNCT
ejpam-6617	572	4	valued	value	VERB
ejpam-6617	572	5	optimization	optimization	NOUN
ejpam-6617	572	6	problems	problem	NOUN
ejpam-6617	572	7	with	with	ADP
ejpam-6617	572	8	generalized	generalized	ADJ
ejpam-6617	572	9	invex	invex	NOUN
ejpam-6617	572	10	functions	function	NOUN
ejpam-6617	572	11	.	.	PUNCT
ejpam-6617	573	1	journal	journal	PROPN
ejpam-6617	573	2	of	of	ADP
ejpam-6617	573	3	inequalities	inequality	NOUN
ejpam-6617	573	4	and	and	CCONJ
ejpam-6617	573	5	applications	application	NOUN
ejpam-6617	573	6	,	,	PUNCT
ejpam-6617	573	7	2013(1):313	2013(1):313	NUM
ejpam-6617	573	8	,	,	PUNCT
ejpam-6617	573	9	2013	2013	NUM
ejpam-6617	573	10	.	.	PUNCT
ejpam-6617	574	1	[	[	X
ejpam-6617	574	2	17	17	NUM
ejpam-6617	574	3	]	]	X
ejpam-6617	574	4	i	i	PRON
ejpam-6617	574	5	husain	husain	VERB
ejpam-6617	574	6	and	and	CCONJ
ejpam-6617	574	7	m	m	PROPN
ejpam-6617	574	8	masoodi	masoodi	NOUN
ejpam-6617	574	9	.	.	PUNCT
ejpam-6617	575	1	second	second	ADJ
ejpam-6617	575	2	-	-	PUNCT
ejpam-6617	575	3	order	order	NOUN
ejpam-6617	575	4	duality	duality	NOUN
ejpam-6617	575	5	for	for	ADP
ejpam-6617	575	6	continuous	continuous	ADJ
ejpam-6617	575	7	programming	programming	NOUN
ejpam-6617	575	8	containing	contain	VERB
ejpam-6617	575	9	support	support	NOUN
ejpam-6617	575	10	functions	function	NOUN
ejpam-6617	575	11	.	.	PUNCT
ejpam-6617	576	1	applied	apply	VERB
ejpam-6617	576	2	mathematics	mathematic	NOUN
ejpam-6617	576	3	,	,	PUNCT
ejpam-6617	576	4	1(6):534–541	1(6):534–541	NUM
ejpam-6617	576	5	,	,	PUNCT
ejpam-6617	576	6	2010	2010	NUM
ejpam-6617	576	7	.	.	PUNCT
ejpam-6617	577	1	[	[	X
ejpam-6617	577	2	18	18	NUM
ejpam-6617	577	3	]	]	X
ejpam-6617	577	4	m	m	PROPN
ejpam-6617	577	5	arana	arana	PROPN
ejpam-6617	577	6	-	-	PUNCT
ejpam-6617	577	7	jiménez	jiménez	PROPN
ejpam-6617	577	8	,	,	PUNCT
ejpam-6617	577	9	g	g	PROPN
ejpam-6617	577	10	ruiz	ruiz	NOUN
ejpam-6617	577	11	-	-	PUNCT
ejpam-6617	577	12	garzón	garzón	PROPN
ejpam-6617	577	13	,	,	PUNCT
ejpam-6617	577	14	a	a	DET
ejpam-6617	577	15	rufián	rufián	NOUN
ejpam-6617	577	16	-	-	PUNCT
ejpam-6617	577	17	lizana	lizana	PROPN
ejpam-6617	577	18	,	,	PUNCT
ejpam-6617	577	19	and	and	CCONJ
ejpam-6617	577	20	r	r	NOUN
ejpam-6617	577	21	osuna	osuna	PROPN
ejpam-6617	577	22	-	-	PUNCT
ejpam-6617	577	23	gómez	gómez	NOUN
ejpam-6617	577	24	.	.	PUNCT
ejpam-6617	578	1	a	a	DET
ejpam-6617	578	2	necessary	necessary	ADJ
ejpam-6617	578	3	and	and	CCONJ
ejpam-6617	578	4	sufficient	sufficient	ADJ
ejpam-6617	578	5	condition	condition	NOUN
ejpam-6617	578	6	for	for	ADP
ejpam-6617	578	7	duality	duality	NOUN
ejpam-6617	578	8	in	in	ADP
ejpam-6617	578	9	multiobjective	multiobjective	ADJ
ejpam-6617	578	10	variational	variational	ADJ
ejpam-6617	578	11	problems	problem	NOUN
ejpam-6617	578	12	.	.	PUNCT
ejpam-6617	579	1	european	european	ADJ
ejpam-6617	579	2	journal	journal	PROPN
ejpam-6617	579	3	of	of	ADP
ejpam-6617	579	4	operational	operational	ADJ
ejpam-6617	579	5	research	research	NOUN
ejpam-6617	579	6	,	,	PUNCT
ejpam-6617	579	7	201(3):672–681	201(3):672–681	NUM
ejpam-6617	579	8	,	,	PUNCT
ejpam-6617	579	9	2010	2010	NUM
ejpam-6617	579	10	.	.	PUNCT
ejpam-6617	580	1	v.	v.	CCONJ
ejpam-6617	580	2	rayanki	rayanki	PROPN
ejpam-6617	580	3	et	et	PROPN
ejpam-6617	580	4	al	al	PROPN
ejpam-6617	580	5	.	.	PUNCT
ejpam-6617	580	6	/	/	SYM
ejpam-6617	580	7	eur	eur	PROPN
ejpam-6617	580	8	.	.	PUNCT
ejpam-6617	581	1	j.	j.	PROPN
ejpam-6617	581	2	pure	pure	PROPN
ejpam-6617	581	3	appl	appl	PROPN
ejpam-6617	581	4	.	.	PROPN
ejpam-6617	581	5	math	math	PROPN
ejpam-6617	581	6	,	,	PUNCT
ejpam-6617	581	7	18	18	NUM
ejpam-6617	581	8	(	(	PUNCT
ejpam-6617	581	9	3	3	NUM
ejpam-6617	581	10	)	)	PUNCT
ejpam-6617	581	11	(	(	PUNCT
ejpam-6617	581	12	2025	2025	NUM
ejpam-6617	581	13	)	)	PUNCT
ejpam-6617	581	14	,	,	PUNCT
ejpam-6617	581	15	6617	6617	NUM
ejpam-6617	581	16	37	37	NUM
ejpam-6617	581	17	of	of	ADP
ejpam-6617	581	18	38	38	NUM
ejpam-6617	582	1	[	[	X
ejpam-6617	582	2	19	19	NUM
ejpam-6617	582	3	]	]	PUNCT
ejpam-6617	582	4	s	s	PART
ejpam-6617	582	5	treanta	treanta	NOUN
ejpam-6617	582	6	,	,	PUNCT
ejpam-6617	582	7	c	c	PROPN
ejpam-6617	582	8	f	f	PROPN
ejpam-6617	582	9	pırje	pırje	PROPN
ejpam-6617	582	10	,	,	PUNCT
ejpam-6617	582	11	j	j	PROPN
ejpam-6617	582	12	c	c	PROPN
ejpam-6617	582	13	yao	yao	PROPN
ejpam-6617	582	14	,	,	PUNCT
ejpam-6617	582	15	and	and	CCONJ
ejpam-6617	582	16	b	b	X
ejpam-6617	582	17	b	b	PROPN
ejpam-6617	582	18	upadhyay	upadhyay	PROPN
ejpam-6617	582	19	.	.	PUNCT
ejpam-6617	582	20	efficiency	efficiency	NOUN
ejpam-6617	582	21	conditions	condition	NOUN
ejpam-6617	582	22	in	in	ADP
ejpam-6617	582	23	new	new	ADJ
ejpam-6617	582	24	interval	interval	NOUN
ejpam-6617	582	25	-	-	PUNCT
ejpam-6617	582	26	valued	value	VERB
ejpam-6617	582	27	control	control	NOUN
ejpam-6617	582	28	models	model	NOUN
ejpam-6617	582	29	via	via	ADP
ejpam-6617	582	30	modified	modify	VERB
ejpam-6617	582	31	t	t	PROPN
ejpam-6617	582	32	-	-	PUNCT
ejpam-6617	582	33	objective	objective	ADJ
ejpam-6617	582	34	functional	functional	ADJ
ejpam-6617	582	35	approach	approach	NOUN
ejpam-6617	582	36	and	and	CCONJ
ejpam-6617	582	37	saddle	saddle	NOUN
ejpam-6617	582	38	-	-	PUNCT
ejpam-6617	582	39	point	point	NOUN
ejpam-6617	582	40	criteria	criterion	NOUN
ejpam-6617	582	41	.	.	PUNCT
ejpam-6617	583	1	mathematical	mathematical	ADJ
ejpam-6617	583	2	modelling	modelling	NOUN
ejpam-6617	583	3	and	and	CCONJ
ejpam-6617	583	4	control	control	NOUN
ejpam-6617	583	5	,	,	PUNCT
ejpam-6617	583	6	2025	2025	NUM
ejpam-6617	583	7	.	.	PUNCT
ejpam-6617	584	1	[	[	X
ejpam-6617	584	2	20	20	NUM
ejpam-6617	584	3	]	]	X
ejpam-6617	584	4	k	k	PROPN
ejpam-6617	584	5	khazafi	khazafi	PROPN
ejpam-6617	584	6	,	,	PUNCT
ejpam-6617	584	7	n	n	CCONJ
ejpam-6617	584	8	rueda	rueda	NOUN
ejpam-6617	584	9	,	,	PUNCT
ejpam-6617	584	10	and	and	CCONJ
ejpam-6617	584	11	p	p	PROPN
ejpam-6617	584	12	enflo	enflo	PROPN
ejpam-6617	584	13	.	.	PUNCT
ejpam-6617	585	1	sufficiency	sufficiency	PROPN
ejpam-6617	585	2	and	and	CCONJ
ejpam-6617	585	3	duality	duality	NOUN
ejpam-6617	585	4	for	for	ADP
ejpam-6617	585	5	multiobjective	multiobjective	ADJ
ejpam-6617	585	6	control	control	NOUN
ejpam-6617	585	7	problems	problem	NOUN
ejpam-6617	585	8	under	under	ADP
ejpam-6617	585	9	generalized	generalized	ADJ
ejpam-6617	585	10	(	(	PUNCT
ejpam-6617	585	11	b	b	NOUN
ejpam-6617	585	12	,	,	PUNCT
ejpam-6617	585	13	ρ)-type	ρ)-type	PUNCT
ejpam-6617	585	14	i	i	PRON
ejpam-6617	585	15	functions	function	NOUN
ejpam-6617	585	16	.	.	PUNCT
ejpam-6617	586	1	journal	journal	NOUN
ejpam-6617	586	2	of	of	ADP
ejpam-6617	586	3	global	global	ADJ
ejpam-6617	586	4	optimization	optimization	NOUN
ejpam-6617	586	5	,	,	PUNCT
ejpam-6617	586	6	46(1):111–132	46(1):111–132	PROPN
ejpam-6617	586	7	,	,	PUNCT
ejpam-6617	586	8	2010	2010	NUM
ejpam-6617	586	9	.	.	PUNCT
ejpam-6617	587	1	[	[	X
ejpam-6617	587	2	21	21	NUM
ejpam-6617	587	3	]	]	SYM
ejpam-6617	587	4	s	s	PART
ejpam-6617	587	5	mititelu	mititelu	NOUN
ejpam-6617	587	6	and	and	CCONJ
ejpam-6617	587	7	m	m	PROPN
ejpam-6617	587	8	postolache	postolache	NOUN
ejpam-6617	587	9	.	.	PUNCT
ejpam-6617	588	1	mond	mond	PROPN
ejpam-6617	588	2	-	-	PUNCT
ejpam-6617	588	3	weir	weir	PROPN
ejpam-6617	588	4	dualities	duality	NOUN
ejpam-6617	588	5	with	with	ADP
ejpam-6617	588	6	lagrangians	lagrangian	NOUN
ejpam-6617	588	7	for	for	ADP
ejpam-6617	588	8	multiobjective	multiobjective	ADJ
ejpam-6617	588	9	fractional	fractional	ADJ
ejpam-6617	588	10	and	and	CCONJ
ejpam-6617	588	11	non	non	ADJ
ejpam-6617	588	12	-	-	ADJ
ejpam-6617	588	13	fractional	fractional	ADJ
ejpam-6617	588	14	variational	variational	ADJ
ejpam-6617	588	15	problems	problem	NOUN
ejpam-6617	588	16	.	.	PUNCT
ejpam-6617	589	1	journal	journal	NOUN
ejpam-6617	589	2	of	of	ADP
ejpam-6617	589	3	advanced	advanced	ADJ
ejpam-6617	589	4	mathematical	mathematical	ADJ
ejpam-6617	589	5	studies	study	NOUN
ejpam-6617	589	6	,	,	PUNCT
ejpam-6617	589	7	3(1	3(1	NUM
ejpam-6617	589	8	)	)	PUNCT
ejpam-6617	589	9	,	,	PUNCT
ejpam-6617	589	10	2010	2010	NUM
ejpam-6617	589	11	.	.	PUNCT
ejpam-6617	590	1	[	[	X
ejpam-6617	590	2	22	22	NUM
ejpam-6617	590	3	]	]	PUNCT
ejpam-6617	590	4	n	n	CCONJ
ejpam-6617	590	5	pokharna	pokharna	VERB
ejpam-6617	590	6	and	and	CCONJ
ejpam-6617	590	7	i	i	PRON
ejpam-6617	590	8	p	p	PROPN
ejpam-6617	590	9	tripathi	tripathi	PROPN
ejpam-6617	590	10	.	.	PUNCT
ejpam-6617	591	1	a	a	DET
ejpam-6617	591	2	generalized	generalized	ADJ
ejpam-6617	591	3	division	division	NOUN
ejpam-6617	591	4	approach	approach	NOUN
ejpam-6617	591	5	for	for	ADP
ejpam-6617	591	6	interval	interval	NOUN
ejpam-6617	591	7	fractional	fractional	ADJ
ejpam-6617	591	8	programming	programming	NOUN
ejpam-6617	591	9	problems	problem	NOUN
ejpam-6617	591	10	.	.	PUNCT
ejpam-6617	592	1	applied	apply	VERB
ejpam-6617	592	2	mathematical	mathematical	ADJ
ejpam-6617	592	3	modelling	modelling	NOUN
ejpam-6617	592	4	,	,	PUNCT
ejpam-6617	592	5	144:116048	144:116048	NUM
ejpam-6617	592	6	,	,	PUNCT
ejpam-6617	592	7	2025	2025	NUM
ejpam-6617	592	8	.	.	PUNCT
ejpam-6617	593	1	[	[	X
ejpam-6617	593	2	23	23	NUM
ejpam-6617	593	3	]	]	X
ejpam-6617	593	4	om	om	PROPN
ejpam-6617	593	5	p	p	PROPN
ejpam-6617	593	6	agrawal	agrawal	PROPN
ejpam-6617	593	7	.	.	PUNCT
ejpam-6617	594	1	formulation	formulation	NOUN
ejpam-6617	594	2	of	of	ADP
ejpam-6617	594	3	euler	euler	PROPN
ejpam-6617	594	4	–	–	PUNCT
ejpam-6617	594	5	lagrange	lagrange	NOUN
ejpam-6617	594	6	equations	equation	NOUN
ejpam-6617	594	7	for	for	ADP
ejpam-6617	594	8	fractional	fractional	ADJ
ejpam-6617	594	9	variational	variational	ADJ
ejpam-6617	594	10	problems	problem	NOUN
ejpam-6617	594	11	.	.	PUNCT
ejpam-6617	595	1	journal	journal	PROPN
ejpam-6617	595	2	of	of	ADP
ejpam-6617	595	3	mathematical	mathematical	ADJ
ejpam-6617	595	4	analysis	analysis	NOUN
ejpam-6617	595	5	and	and	CCONJ
ejpam-6617	595	6	applications	application	NOUN
ejpam-6617	595	7	,	,	PUNCT
ejpam-6617	595	8	272(1):368–379	272(1):368–379	NUM
ejpam-6617	595	9	,	,	PUNCT
ejpam-6617	595	10	2002	2002	NUM
ejpam-6617	595	11	.	.	PUNCT
ejpam-6617	596	1	[	[	X
ejpam-6617	596	2	24	24	NUM
ejpam-6617	596	3	]	]	PUNCT
ejpam-6617	596	4	op	op	NOUN
ejpam-6617	596	5	agrawal	agrawal	PROPN
ejpam-6617	596	6	.	.	PUNCT
ejpam-6617	597	1	fractional	fractional	ADJ
ejpam-6617	597	2	variational	variational	ADJ
ejpam-6617	597	3	calculus	calculus	NOUN
ejpam-6617	597	4	and	and	CCONJ
ejpam-6617	597	5	the	the	DET
ejpam-6617	597	6	transversality	transversality	NOUN
ejpam-6617	597	7	conditions	condition	NOUN
ejpam-6617	597	8	.	.	PUNCT
ejpam-6617	598	1	journal	journal	PROPN
ejpam-6617	598	2	of	of	ADP
ejpam-6617	598	3	physics	physics	PROPN
ejpam-6617	598	4	a	a	PRON
ejpam-6617	598	5	:	:	PUNCT
ejpam-6617	598	6	mathematical	mathematical	ADJ
ejpam-6617	598	7	and	and	CCONJ
ejpam-6617	598	8	general	general	ADJ
ejpam-6617	598	9	,	,	PUNCT
ejpam-6617	598	10	39(33):10375	39(33):10375	NUM
ejpam-6617	598	11	,	,	PUNCT
ejpam-6617	598	12	2006	2006	NUM
ejpam-6617	598	13	.	.	PUNCT
ejpam-6617	599	1	[	[	X
ejpam-6617	599	2	25	25	NUM
ejpam-6617	599	3	]	]	X
ejpam-6617	599	4	s	s	PART
ejpam-6617	599	5	g	g	NOUN
ejpam-6617	599	6	samko	samko	NOUN
ejpam-6617	599	7	.	.	PUNCT
ejpam-6617	600	1	fractional	fractional	ADJ
ejpam-6617	600	2	integrals	integral	NOUN
ejpam-6617	600	3	and	and	CCONJ
ejpam-6617	600	4	derivatives	derivative	NOUN
ejpam-6617	600	5	.	.	PUNCT
ejpam-6617	601	1	theory	theory	NOUN
ejpam-6617	601	2	and	and	CCONJ
ejpam-6617	601	3	applications	application	NOUN
ejpam-6617	601	4	,	,	PUNCT
ejpam-6617	601	5	1993	1993	NUM
ejpam-6617	601	6	.	.	PUNCT
ejpam-6617	602	1	[	[	X
ejpam-6617	602	2	26	26	NUM
ejpam-6617	602	3	]	]	X
ejpam-6617	602	4	r	r	PROPN
ejpam-6617	602	5	almeida	almeida	PROPN
ejpam-6617	602	6	.	.	PUNCT
ejpam-6617	603	1	variational	variational	ADJ
ejpam-6617	603	2	problems	problem	NOUN
ejpam-6617	603	3	involving	involve	VERB
ejpam-6617	603	4	a	a	DET
ejpam-6617	603	5	caputo	caputo	NOUN
ejpam-6617	603	6	-	-	PUNCT
ejpam-6617	603	7	type	type	NOUN
ejpam-6617	603	8	fractional	fractional	ADJ
ejpam-6617	603	9	derivative	derivative	NOUN
ejpam-6617	603	10	.	.	PUNCT
ejpam-6617	604	1	journal	journal	PROPN
ejpam-6617	604	2	of	of	ADP
ejpam-6617	604	3	optimization	optimization	NOUN
ejpam-6617	604	4	theory	theory	NOUN
ejpam-6617	604	5	and	and	CCONJ
ejpam-6617	604	6	applications	application	NOUN
ejpam-6617	604	7	,	,	PUNCT
ejpam-6617	604	8	174(1):276–294	174(1):276–294	NUM
ejpam-6617	604	9	,	,	PUNCT
ejpam-6617	604	10	2017	2017	NUM
ejpam-6617	604	11	.	.	PUNCT
ejpam-6617	605	1	[	[	X
ejpam-6617	605	2	27	27	NUM
ejpam-6617	605	3	]	]	X
ejpam-6617	605	4	m	m	VERB
ejpam-6617	605	5	m	m	NOUN
ejpam-6617	605	6	shalini	shalini	PROPN
ejpam-6617	605	7	,	,	PUNCT
ejpam-6617	605	8	b	b	PROPN
ejpam-6617	605	9	kandasamy	kandasamy	NOUN
ejpam-6617	605	10	,	,	PUNCT
ejpam-6617	605	11	m	m	PROPN
ejpam-6617	605	12	rangasamy	rangasamy	NOUN
ejpam-6617	605	13	,	,	PUNCT
ejpam-6617	605	14	p	p	PROPN
ejpam-6617	605	15	b	b	PROPN
ejpam-6617	605	16	dhandapani	dhandapani	NOUN
ejpam-6617	605	17	,	,	PUNCT
ejpam-6617	605	18	a	a	DET
ejpam-6617	605	19	zeb	zeb	NOUN
ejpam-6617	605	20	,	,	PUNCT
ejpam-6617	605	21	i	i	PROPN
ejpam-6617	605	22	khan	khan	PROPN
ejpam-6617	605	23	,	,	PUNCT
ejpam-6617	605	24	and	and	CCONJ
ejpam-6617	605	25	abdoalrahman	abdoalrahman	PROPN
ejpam-6617	605	26	sa	sa	PROPN
ejpam-6617	605	27	omer	omer	PROPN
ejpam-6617	605	28	.	.	PUNCT
ejpam-6617	606	1	feasibility	feasibility	NOUN
ejpam-6617	606	2	of	of	ADP
ejpam-6617	606	3	variable	variable	ADJ
ejpam-6617	606	4	delay	delay	NOUN
ejpam-6617	606	5	fuzzy	fuzzy	ADJ
ejpam-6617	606	6	fractional	fractional	ADJ
ejpam-6617	606	7	stochastic	stochastic	ADJ
ejpam-6617	606	8	differential	differential	NOUN
ejpam-6617	606	9	system	system	NOUN
ejpam-6617	606	10	with	with	ADP
ejpam-6617	606	11	non	non	ADJ
ejpam-6617	606	12	-	-	ADJ
ejpam-6617	606	13	instantaneous	instantaneous	ADJ
ejpam-6617	606	14	impulses	impulse	NOUN
ejpam-6617	606	15	.	.	PUNCT
ejpam-6617	607	1	applied	apply	VERB
ejpam-6617	607	2	mathematics	mathematic	NOUN
ejpam-6617	607	3	in	in	ADP
ejpam-6617	607	4	science	science	NOUN
ejpam-6617	607	5	and	and	CCONJ
ejpam-6617	607	6	engineering	engineering	NOUN
ejpam-6617	607	7	,	,	PUNCT
ejpam-6617	607	8	33(1):2458612	33(1):2458612	NUM
ejpam-6617	607	9	,	,	PUNCT
ejpam-6617	607	10	2025	2025	NUM
ejpam-6617	607	11	.	.	PUNCT
ejpam-6617	608	1	[	[	X
ejpam-6617	608	2	28	28	NUM
ejpam-6617	608	3	]	]	X
ejpam-6617	608	4	o	o	X
ejpam-6617	608	5	s	s	X
ejpam-6617	608	6	fard	fard	NOUN
ejpam-6617	608	7	and	and	CCONJ
ejpam-6617	608	8	m	m	NOUN
ejpam-6617	608	9	salehi	salehi	NOUN
ejpam-6617	608	10	.	.	PUNCT
ejpam-6617	609	1	a	a	DET
ejpam-6617	609	2	survey	survey	NOUN
ejpam-6617	609	3	on	on	ADP
ejpam-6617	609	4	fuzzy	fuzzy	ADJ
ejpam-6617	609	5	fractional	fractional	ADJ
ejpam-6617	609	6	variational	variational	ADJ
ejpam-6617	609	7	problems	problem	NOUN
ejpam-6617	609	8	.	.	PUNCT
ejpam-6617	610	1	journal	journal	NOUN
ejpam-6617	610	2	of	of	ADP
ejpam-6617	610	3	computational	computational	ADJ
ejpam-6617	610	4	and	and	CCONJ
ejpam-6617	610	5	applied	applied	ADJ
ejpam-6617	610	6	mathematics	mathematic	NOUN
ejpam-6617	610	7	,	,	PUNCT
ejpam-6617	610	8	271:71–82	271:71–82	NUM
ejpam-6617	610	9	,	,	PUNCT
ejpam-6617	610	10	2014	2014	NUM
ejpam-6617	610	11	.	.	PUNCT
ejpam-6617	611	1	[	[	X
ejpam-6617	611	2	29	29	NUM
ejpam-6617	611	3	]	]	X
ejpam-6617	611	4	j	j	PROPN
ejpam-6617	611	5	soolaki	soolaki	NOUN
ejpam-6617	611	6	,	,	PUNCT
ejpam-6617	611	7	o	o	NOUN
ejpam-6617	611	8	s	s	PART
ejpam-6617	611	9	fard	fard	NOUN
ejpam-6617	611	10	,	,	PUNCT
ejpam-6617	611	11	and	and	CCONJ
ejpam-6617	611	12	a	a	DET
ejpam-6617	611	13	h	h	NOUN
ejpam-6617	611	14	borzabadi	borzabadi	NOUN
ejpam-6617	611	15	.	.	PUNCT
ejpam-6617	612	1	generalized	generalize	VERB
ejpam-6617	612	2	euler	euler	PROPN
ejpam-6617	612	3	–	–	PUNCT
ejpam-6617	612	4	lagrange	lagrange	NOUN
ejpam-6617	612	5	equations	equation	NOUN
ejpam-6617	612	6	for	for	ADP
ejpam-6617	612	7	fuzzy	fuzzy	ADJ
ejpam-6617	612	8	variational	variational	ADJ
ejpam-6617	612	9	problems	problem	NOUN
ejpam-6617	612	10	.	.	PUNCT
ejpam-6617	613	1	sema	sema	PROPN
ejpam-6617	613	2	journal	journal	PROPN
ejpam-6617	613	3	,	,	PUNCT
ejpam-6617	613	4	73(2):131–148	73(2):131–148	PROPN
ejpam-6617	613	5	,	,	PUNCT
ejpam-6617	613	6	2016	2016	NUM
ejpam-6617	613	7	.	.	PUNCT
ejpam-6617	614	1	[	[	X
ejpam-6617	614	2	30	30	NUM
ejpam-6617	614	3	]	]	X
ejpam-6617	614	4	m	m	PROPN
ejpam-6617	614	5	caputo	caputo	PROPN
ejpam-6617	614	6	and	and	CCONJ
ejpam-6617	614	7	m	m	PROPN
ejpam-6617	614	8	fabrizio	fabrizio	PROPN
ejpam-6617	614	9	.	.	PUNCT
ejpam-6617	615	1	a	a	DET
ejpam-6617	615	2	new	new	ADJ
ejpam-6617	615	3	definition	definition	NOUN
ejpam-6617	615	4	of	of	ADP
ejpam-6617	615	5	fractional	fractional	ADJ
ejpam-6617	615	6	derivative	derivative	NOUN
ejpam-6617	615	7	without	without	ADP
ejpam-6617	615	8	singular	singular	ADJ
ejpam-6617	615	9	kernel	kernel	PROPN
ejpam-6617	615	10	.	.	PUNCT
ejpam-6617	616	1	progress	progress	NOUN
ejpam-6617	616	2	in	in	ADP
ejpam-6617	616	3	fractional	fractional	ADJ
ejpam-6617	616	4	differentiation	differentiation	NOUN
ejpam-6617	616	5	&	&	CCONJ
ejpam-6617	616	6	applications	application	NOUN
ejpam-6617	616	7	,	,	PUNCT
ejpam-6617	616	8	1(2):73–85	1(2):73–85	NUM
ejpam-6617	616	9	,	,	PUNCT
ejpam-6617	616	10	2015	2015	NUM
ejpam-6617	616	11	.	.	PUNCT
ejpam-6617	617	1	[	[	X
ejpam-6617	617	2	31	31	NUM
ejpam-6617	617	3	]	]	PUNCT
ejpam-6617	617	4	a	a	DET
ejpam-6617	617	5	jayswal	jayswal	NOUN
ejpam-6617	617	6	and	and	CCONJ
ejpam-6617	617	7	g	g	NOUN
ejpam-6617	617	8	uniyal	uniyal	ADJ
ejpam-6617	617	9	.	.	PUNCT
ejpam-6617	618	1	optimal	optimal	ADJ
ejpam-6617	618	2	conditions	condition	NOUN
ejpam-6617	618	3	and	and	CCONJ
ejpam-6617	618	4	duality	duality	NOUN
ejpam-6617	618	5	results	result	NOUN
ejpam-6617	618	6	for	for	ADP
ejpam-6617	618	7	a	a	DET
ejpam-6617	618	8	semiinfinite	semiinfinite	ADJ
ejpam-6617	618	9	variational	variational	ADJ
ejpam-6617	618	10	programming	programming	NOUN
ejpam-6617	618	11	problem	problem	NOUN
ejpam-6617	618	12	and	and	CCONJ
ejpam-6617	618	13	its	its	PRON
ejpam-6617	618	14	mond	mond	NOUN
ejpam-6617	618	15	–	–	PUNCT
ejpam-6617	618	16	weir	weir	NOUN
ejpam-6617	618	17	dual	dual	ADJ
ejpam-6617	618	18	involving	involve	VERB
ejpam-6617	618	19	caputo	caputo	PROPN
ejpam-6617	618	20	–	–	PUNCT
ejpam-6617	618	21	fabrizio	fabrizio	NOUN
ejpam-6617	618	22	fractional	fractional	ADJ
ejpam-6617	618	23	derivatives	derivative	NOUN
ejpam-6617	618	24	.	.	PUNCT
ejpam-6617	619	1	journal	journal	NOUN
ejpam-6617	619	2	of	of	ADP
ejpam-6617	619	3	computational	computational	ADJ
ejpam-6617	619	4	and	and	CCONJ
ejpam-6617	619	5	applied	applied	ADJ
ejpam-6617	619	6	mathematics	mathematic	NOUN
ejpam-6617	619	7	,	,	PUNCT
ejpam-6617	619	8	468:116628	468:116628	NUM
ejpam-6617	619	9	,	,	PUNCT
ejpam-6617	619	10	2025	2025	NUM
ejpam-6617	619	11	.	.	PUNCT
ejpam-6617	620	1	[	[	X
ejpam-6617	620	2	32	32	NUM
ejpam-6617	620	3	]	]	PUNCT
ejpam-6617	620	4	a	a	DET
ejpam-6617	620	5	jayswal	jayswal	NOUN
ejpam-6617	620	6	and	and	CCONJ
ejpam-6617	620	7	g	g	NOUN
ejpam-6617	620	8	uniyal	uniyal	ADJ
ejpam-6617	620	9	.	.	PUNCT
ejpam-6617	621	1	lagrange	lagrange	NOUN
ejpam-6617	621	2	duality	duality	NOUN
ejpam-6617	621	3	and	and	CCONJ
ejpam-6617	621	4	saddle	saddle	NOUN
ejpam-6617	621	5	point	point	NOUN
ejpam-6617	621	6	criteria	criterion	NOUN
ejpam-6617	621	7	for	for	ADP
ejpam-6617	621	8	semi	semi	ADJ
ejpam-6617	621	9	-	-	ADJ
ejpam-6617	621	10	infinite	infinite	ADJ
ejpam-6617	621	11	variational	variational	ADJ
ejpam-6617	621	12	programming	programming	NOUN
ejpam-6617	621	13	problem	problem	NOUN
ejpam-6617	621	14	with	with	ADP
ejpam-6617	621	15	caputo	caputo	PROPN
ejpam-6617	621	16	-	-	PUNCT
ejpam-6617	621	17	fabrizio	fabrizio	PROPN
ejpam-6617	621	18	fractional	fractional	PROPN
ejpam-6617	621	19	derivative	derivative	NOUN
ejpam-6617	621	20	.	.	PUNCT
ejpam-6617	622	1	journal	journal	PROPN
ejpam-6617	622	2	of	of	ADP
ejpam-6617	622	3	applied	apply	VERB
ejpam-6617	622	4	mathematics	mathematic	NOUN
ejpam-6617	622	5	and	and	CCONJ
ejpam-6617	622	6	computing	computing	NOUN
ejpam-6617	622	7	,	,	PUNCT
ejpam-6617	622	8	pages	page	NOUN
ejpam-6617	622	9	1–21	1–21	PROPN
ejpam-6617	622	10	,	,	PUNCT
ejpam-6617	622	11	2025	2025	NUM
ejpam-6617	622	12	.	.	PUNCT
ejpam-6617	623	1	[	[	X
ejpam-6617	623	2	33	33	NUM
ejpam-6617	623	3	]	]	PUNCT
ejpam-6617	623	4	h	h	NOUN
ejpam-6617	623	5	ishibuchi	ishibuchi	NOUN
ejpam-6617	623	6	and	and	CCONJ
ejpam-6617	623	7	h	h	NOUN
ejpam-6617	623	8	tanaka	tanaka	PROPN
ejpam-6617	623	9	.	.	PUNCT
ejpam-6617	624	1	multiobjective	multiobjective	ADJ
ejpam-6617	624	2	programming	programming	NOUN
ejpam-6617	624	3	in	in	ADP
ejpam-6617	624	4	optimization	optimization	NOUN
ejpam-6617	624	5	of	of	ADP
ejpam-6617	624	6	the	the	DET
ejpam-6617	624	7	interval	interval	NOUN
ejpam-6617	624	8	objective	objective	ADJ
ejpam-6617	624	9	function	function	NOUN
ejpam-6617	624	10	.	.	PUNCT
ejpam-6617	625	1	european	european	ADJ
ejpam-6617	625	2	journal	journal	PROPN
ejpam-6617	625	3	of	of	ADP
ejpam-6617	625	4	operational	operational	ADJ
ejpam-6617	625	5	research	research	NOUN
ejpam-6617	625	6	,	,	PUNCT
ejpam-6617	625	7	48(2):219–225	48(2):219–225	NOUN
ejpam-6617	625	8	,	,	PUNCT
ejpam-6617	625	9	1990	1990	NUM
ejpam-6617	625	10	.	.	PUNCT
ejpam-6617	626	1	[	[	X
ejpam-6617	626	2	34	34	NUM
ejpam-6617	626	3	]	]	X
ejpam-6617	626	4	a	a	DET
ejpam-6617	626	5	a	a	DET
ejpam-6617	626	6	kilbas	kilbas	NOUN
ejpam-6617	626	7	,	,	PUNCT
ejpam-6617	626	8	h	h	PROPN
ejpam-6617	626	9	m	m	PROPN
ejpam-6617	626	10	srivastava	srivastava	PROPN
ejpam-6617	626	11	,	,	PUNCT
ejpam-6617	626	12	and	and	CCONJ
ejpam-6617	626	13	j	j	PROPN
ejpam-6617	626	14	j	j	PROPN
ejpam-6617	626	15	trujillo	trujillo	PROPN
ejpam-6617	626	16	.	.	PUNCT
ejpam-6617	626	17	theory	theory	NOUN
ejpam-6617	626	18	and	and	CCONJ
ejpam-6617	626	19	applications	application	NOUN
ejpam-6617	626	20	of	of	ADP
ejpam-6617	626	21	fractional	fractional	ADJ
ejpam-6617	626	22	differential	differential	ADJ
ejpam-6617	626	23	equations	equation	NOUN
ejpam-6617	626	24	,	,	PUNCT
ejpam-6617	626	25	volume	volume	NOUN
ejpam-6617	626	26	204	204	NUM
ejpam-6617	626	27	.	.	PUNCT
ejpam-6617	627	1	elsevier	elsevier	NOUN
ejpam-6617	627	2	,	,	PUNCT
ejpam-6617	627	3	2006	2006	NUM
ejpam-6617	627	4	.	.	PUNCT
ejpam-6617	628	1	[	[	X
ejpam-6617	628	2	35	35	NUM
ejpam-6617	628	3	]	]	X
ejpam-6617	628	4	e	e	X
ejpam-6617	628	5	f	f	PROPN
ejpam-6617	628	6	d	d	X
ejpam-6617	628	7	goufo	goufo	NOUN
ejpam-6617	628	8	and	and	CCONJ
ejpam-6617	628	9	a	a	DET
ejpam-6617	628	10	atangana	atangana	PROPN
ejpam-6617	628	11	.	.	PUNCT
ejpam-6617	629	1	analytical	analytical	ADJ
ejpam-6617	629	2	and	and	CCONJ
ejpam-6617	629	3	numerical	numerical	ADJ
ejpam-6617	629	4	schemes	scheme	NOUN
ejpam-6617	629	5	for	for	ADP
ejpam-6617	629	6	a	a	DET
ejpam-6617	629	7	derivative	derivative	NOUN
ejpam-6617	629	8	with	with	ADP
ejpam-6617	629	9	filtering	filter	VERB
ejpam-6617	629	10	property	property	NOUN
ejpam-6617	629	11	and	and	CCONJ
ejpam-6617	629	12	no	no	DET
ejpam-6617	629	13	singular	singular	ADJ
ejpam-6617	629	14	kernel	kernel	NOUN
ejpam-6617	629	15	with	with	ADP
ejpam-6617	629	16	applications	application	NOUN
ejpam-6617	629	17	to	to	ADP
ejpam-6617	629	18	diffusion	diffusion	NOUN
ejpam-6617	629	19	.	.	PUNCT
ejpam-6617	630	1	the	the	DET
ejpam-6617	630	2	european	european	PROPN
ejpam-6617	630	3	physical	physical	PROPN
ejpam-6617	630	4	journal	journal	PROPN
ejpam-6617	630	5	plus	plus	CCONJ
ejpam-6617	630	6	,	,	PUNCT
ejpam-6617	630	7	131(8):269	131(8):269	NUM
ejpam-6617	630	8	,	,	PUNCT
ejpam-6617	630	9	2016	2016	NUM
ejpam-6617	630	10	.	.	PUNCT
ejpam-6617	631	1	v.	v.	CCONJ
ejpam-6617	631	2	rayanki	rayanki	PROPN
ejpam-6617	631	3	et	et	PROPN
ejpam-6617	631	4	al	al	PROPN
ejpam-6617	631	5	.	.	PUNCT
ejpam-6617	631	6	/	/	SYM
ejpam-6617	631	7	eur	eur	PROPN
ejpam-6617	631	8	.	.	PUNCT
ejpam-6617	632	1	j.	j.	PROPN
ejpam-6617	632	2	pure	pure	PROPN
ejpam-6617	632	3	appl	appl	PROPN
ejpam-6617	632	4	.	.	PROPN
ejpam-6617	632	5	math	math	PROPN
ejpam-6617	632	6	,	,	PUNCT
ejpam-6617	632	7	18	18	NUM
ejpam-6617	632	8	(	(	PUNCT
ejpam-6617	632	9	3	3	NUM
ejpam-6617	632	10	)	)	PUNCT
ejpam-6617	632	11	(	(	PUNCT
ejpam-6617	632	12	2025	2025	NUM
ejpam-6617	632	13	)	)	PUNCT
ejpam-6617	632	14	,	,	PUNCT
ejpam-6617	632	15	6617	6617	NUM
ejpam-6617	632	16	38	38	NUM
ejpam-6617	632	17	of	of	ADP
ejpam-6617	632	18	38	38	NUM
ejpam-6617	633	1	[	[	SYM
ejpam-6617	633	2	36	36	NUM
ejpam-6617	633	3	]	]	SYM
ejpam-6617	633	4	v	v	X
ejpam-6617	633	5	rayanki	rayanki	NOUN
ejpam-6617	633	6	,	,	PUNCT
ejpam-6617	633	7	i	i	PRON
ejpam-6617	633	8	ahmad	ahmad	PROPN
ejpam-6617	633	9	,	,	PUNCT
ejpam-6617	633	10	and	and	CCONJ
ejpam-6617	633	11	k	k	PROPN
ejpam-6617	633	12	kummari	kummari	PROPN
ejpam-6617	633	13	.	.	PUNCT
ejpam-6617	634	1	interval	interval	NOUN
ejpam-6617	634	2	-	-	PUNCT
ejpam-6617	634	3	valued	value	VERB
ejpam-6617	634	4	variational	variational	ADJ
ejpam-6617	634	5	programming	programming	NOUN
ejpam-6617	634	6	problem	problem	NOUN
ejpam-6617	634	7	with	with	ADP
ejpam-6617	634	8	caputo	caputo	PROPN
ejpam-6617	634	9	–	–	PUNCT
ejpam-6617	634	10	fabrizio	fabrizio	PROPN
ejpam-6617	634	11	fractional	fractional	PROPN
ejpam-6617	634	12	derivative	derivative	NOUN
ejpam-6617	634	13	.	.	PUNCT
ejpam-6617	635	1	mathematical	mathematical	ADJ
ejpam-6617	635	2	methods	method	NOUN
ejpam-6617	635	3	in	in	ADP
ejpam-6617	635	4	the	the	DET
ejpam-6617	635	5	applied	apply	VERB
ejpam-6617	635	6	sciences	science	NOUN
ejpam-6617	635	7	,	,	PUNCT
ejpam-6617	635	8	46(16):17485–17510	46(16):17485–17510	NUM
ejpam-6617	635	9	,	,	PUNCT
ejpam-6617	635	10	2023	2023	NUM
ejpam-6617	635	11	.	.	PUNCT