id	sid	tid	token	lemma	pos
ejpam-7112	1	1	european	european	PROPN
ejpam-7112	1	2	journal	journal	PROPN
ejpam-7112	1	3	of	of	ADP
ejpam-7112	1	4	pure	pure	ADJ
ejpam-7112	1	5	and	and	CCONJ
ejpam-7112	1	6	applied	applied	ADJ
ejpam-7112	1	7	mathematics	mathematic	NOUN
ejpam-7112	1	8	2025	2025	NUM
ejpam-7112	1	9	,	,	PUNCT
ejpam-7112	1	10	vol	vol	NOUN
ejpam-7112	1	11	.	.	PROPN
ejpam-7112	1	12	18	18	NUM
ejpam-7112	1	13	,	,	PUNCT
ejpam-7112	1	14	issue	issue	NOUN
ejpam-7112	1	15	4	4	NUM
ejpam-7112	1	16	,	,	PUNCT
ejpam-7112	1	17	article	article	NOUN
ejpam-7112	1	18	number	number	NOUN
ejpam-7112	1	19	7112	7112	NUM
ejpam-7112	1	20	issn	issn	PROPN
ejpam-7112	1	21	1307	1307	NUM
ejpam-7112	1	22	-	-	SYM
ejpam-7112	1	23	5543	5543	NUM
ejpam-7112	1	24	–	–	PUNCT
ejpam-7112	1	25	ejpam.com	ejpam.com	X
ejpam-7112	1	26	published	publish	VERB
ejpam-7112	1	27	by	by	ADP
ejpam-7112	1	28	new	new	PROPN
ejpam-7112	1	29	york	york	PROPN
ejpam-7112	1	30	business	business	PROPN
ejpam-7112	1	31	global	global	ADJ
ejpam-7112	1	32	approximating	approximate	VERB
ejpam-7112	1	33	riemann	riemann	PROPN
ejpam-7112	1	34	-	-	PUNCT
ejpam-7112	1	35	stieltjes	stieltjes	NOUN
ejpam-7112	1	36	integral	integral	ADJ
ejpam-7112	1	37	using	use	VERB
ejpam-7112	1	38	new	new	ADJ
ejpam-7112	1	39	time	time	NOUN
ejpam-7112	1	40	and	and	CCONJ
ejpam-7112	1	41	cost	cost	VERB
ejpam-7112	1	42	efficient	efficient	ADJ
ejpam-7112	1	43	trapezoid	trapezoid	ADJ
ejpam-7112	1	44	-	-	PUNCT
ejpam-7112	1	45	type	type	NOUN
ejpam-7112	1	46	quadrature	quadrature	NOUN
ejpam-7112	1	47	kashif	kashif	PROPN
ejpam-7112	1	48	memon1	memon1	PROPN
ejpam-7112	1	49	,	,	PUNCT
ejpam-7112	1	50	muhammad	muhammad	PROPN
ejpam-7112	1	51	mujtaba	mujtaba	PROPN
ejpam-7112	1	52	shaikh2	shaikh2	PROPN
ejpam-7112	1	53	,	,	PUNCT
ejpam-7112	1	54	sara	sara	PROPN
ejpam-7112	1	55	mahesar2	mahesar2	PROPN
ejpam-7112	1	56	,	,	PUNCT
ejpam-7112	1	57	kamran	kamran	PROPN
ejpam-7112	1	58	malik3	malik3	PROPN
ejpam-7112	1	59	,	,	PUNCT
ejpam-7112	1	60	hijaz	hijaz	PROPN
ejpam-7112	1	61	ahmad4,5,6,∗	ahmad4,5,6,∗	PROPN
ejpam-7112	1	62	,	,	PUNCT
ejpam-7112	1	63	berna	berna	NOUN
ejpam-7112	1	64	uzun4	uzun4	NOUN
ejpam-7112	1	65	,	,	PUNCT
ejpam-7112	1	66	ilker	ilker	VERB
ejpam-7112	1	67	ozsahin4,7	ozsahin4,7	PROPN
ejpam-7112	1	68	,	,	PUNCT
ejpam-7112	1	69	waleed	waleed	PROPN
ejpam-7112	1	70	mohammed	mohammed	PROPN
ejpam-7112	1	71	abdelfattah8,9	abdelfattah8,9	PROPN
ejpam-7112	1	72	1	1	NUM
ejpam-7112	1	73	institute	institute	NOUN
ejpam-7112	1	74	of	of	ADP
ejpam-7112	1	75	mathematics	mathematics	PROPN
ejpam-7112	1	76	and	and	CCONJ
ejpam-7112	1	77	computer	computer	NOUN
ejpam-7112	1	78	science	science	NOUN
ejpam-7112	1	79	,	,	PUNCT
ejpam-7112	1	80	university	university	NOUN
ejpam-7112	1	81	of	of	ADP
ejpam-7112	1	82	sindh	sindh	PROPN
ejpam-7112	1	83	,	,	PUNCT
ejpam-7112	1	84	jamshoro	jamshoro	PROPN
ejpam-7112	1	85	,	,	PUNCT
ejpam-7112	1	86	sindh	sindh	PROPN
ejpam-7112	1	87	,	,	PUNCT
ejpam-7112	1	88	pakistan	pakistan	PROPN
ejpam-7112	1	89	2	2	NUM
ejpam-7112	1	90	department	department	NOUN
ejpam-7112	1	91	of	of	ADP
ejpam-7112	1	92	basic	basic	ADJ
ejpam-7112	1	93	sciences	science	NOUN
ejpam-7112	1	94	and	and	CCONJ
ejpam-7112	1	95	related	related	ADJ
ejpam-7112	1	96	studies	study	NOUN
ejpam-7112	1	97	,	,	PUNCT
ejpam-7112	1	98	mehran	mehran	PROPN
ejpam-7112	1	99	university	university	PROPN
ejpam-7112	1	100	of	of	ADP
ejpam-7112	1	101	engineering	engineering	NOUN
ejpam-7112	1	102	and	and	CCONJ
ejpam-7112	1	103	technology	technology	NOUN
ejpam-7112	1	104	,	,	PUNCT
ejpam-7112	1	105	jamshoro	jamshoro	PROPN
ejpam-7112	1	106	,	,	PUNCT
ejpam-7112	1	107	sindh	sindh	PROPN
ejpam-7112	1	108	,	,	PUNCT
ejpam-7112	1	109	pakistan	pakistan	PROPN
ejpam-7112	1	110	3	3	NUM
ejpam-7112	1	111	department	department	NOUN
ejpam-7112	1	112	of	of	ADP
ejpam-7112	1	113	mathematics	mathematic	NOUN
ejpam-7112	1	114	,	,	PUNCT
ejpam-7112	1	115	government	government	NOUN
ejpam-7112	1	116	college	college	PROPN
ejpam-7112	1	117	university	university	PROPN
ejpam-7112	1	118	,	,	PUNCT
ejpam-7112	1	119	hyderabad	hyderabad	PROPN
ejpam-7112	1	120	,	,	PUNCT
ejpam-7112	1	121	pakistan	pakistan	PROPN
ejpam-7112	1	122	4	4	NUM
ejpam-7112	1	123	operational	operational	ADJ
ejpam-7112	1	124	research	research	NOUN
ejpam-7112	1	125	center	center	NOUN
ejpam-7112	1	126	in	in	ADP
ejpam-7112	1	127	healthcare	healthcare	PROPN
ejpam-7112	1	128	,	,	PUNCT
ejpam-7112	1	129	near	near	ADP
ejpam-7112	1	130	east	east	PROPN
ejpam-7112	1	131	university	university	PROPN
ejpam-7112	1	132	,	,	PUNCT
ejpam-7112	1	133	nicosia	nicosia	PROPN
ejpam-7112	1	134	/	/	SYM
ejpam-7112	1	135	trnc	trnc	PROPN
ejpam-7112	1	136	,	,	PUNCT
ejpam-7112	1	137	99138	99138	NUM
ejpam-7112	1	138	mersin	mersin	PROPN
ejpam-7112	1	139	10	10	NUM
ejpam-7112	1	140	,	,	PUNCT
ejpam-7112	1	141	turkey	turkey	NOUN
ejpam-7112	1	142	5	5	NUM
ejpam-7112	1	143	sustainability	sustainability	NOUN
ejpam-7112	1	144	competence	competence	NOUN
ejpam-7112	1	145	centre	centre	NOUN
ejpam-7112	1	146	,	,	PUNCT
ejpam-7112	1	147	széchenyi	széchenyi	PROPN
ejpam-7112	1	148	istván	istván	PROPN
ejpam-7112	1	149	university	university	PROPN
ejpam-7112	1	150	,	,	PUNCT
ejpam-7112	1	151	egyetem	egyetem	NOUN
ejpam-7112	1	152	tér	tér	PROPN
ejpam-7112	1	153	1	1	NUM
ejpam-7112	1	154	,	,	PUNCT
ejpam-7112	1	155	h-9026	h-9026	PROPN
ejpam-7112	1	156	győr	győr	PROPN
ejpam-7112	1	157	,	,	PUNCT
ejpam-7112	1	158	hungary	hungary	PROPN
ejpam-7112	1	159	6	6	NUM
ejpam-7112	1	160	department	department	NOUN
ejpam-7112	1	161	of	of	ADP
ejpam-7112	1	162	mathematics	mathematic	NOUN
ejpam-7112	1	163	,	,	PUNCT
ejpam-7112	1	164	college	college	NOUN
ejpam-7112	1	165	of	of	ADP
ejpam-7112	1	166	science	science	PROPN
ejpam-7112	1	167	,	,	PUNCT
ejpam-7112	1	168	korea	korea	PROPN
ejpam-7112	1	169	university	university	PROPN
ejpam-7112	1	170	,	,	PUNCT
ejpam-7112	1	171	145	145	NUM
ejpam-7112	1	172	anam	anam	PROPN
ejpam-7112	1	173	-	-	PUNCT
ejpam-7112	1	174	ro	ro	ADJ
ejpam-7112	1	175	,	,	PUNCT
ejpam-7112	1	176	seongbuk	seongbuk	NOUN
ejpam-7112	1	177	-	-	PUNCT
ejpam-7112	1	178	gu	gu	NOUN
ejpam-7112	1	179	,	,	PUNCT
ejpam-7112	1	180	seoul	seoul	PROPN
ejpam-7112	1	181	02841	02841	PROPN
ejpam-7112	1	182	,	,	PUNCT
ejpam-7112	1	183	south	south	PROPN
ejpam-7112	1	184	korea	korea	PROPN
ejpam-7112	1	185	7	7	NUM
ejpam-7112	1	186	department	department	PROPN
ejpam-7112	1	187	of	of	ADP
ejpam-7112	1	188	mathematical	mathematical	ADJ
ejpam-7112	1	189	sciences	sciences	PROPN
ejpam-7112	1	190	,	,	PUNCT
ejpam-7112	1	191	saveetha	saveetha	PROPN
ejpam-7112	1	192	school	school	NOUN
ejpam-7112	1	193	of	of	ADP
ejpam-7112	1	194	engineering	engineering	NOUN
ejpam-7112	1	195	,	,	PUNCT
ejpam-7112	1	196	simats	simat	NOUN
ejpam-7112	1	197	,	,	PUNCT
ejpam-7112	1	198	chennai	chennai	PROPN
ejpam-7112	1	199	,	,	PUNCT
ejpam-7112	1	200	tamilnadu	tamilnadu	NOUN
ejpam-7112	1	201	,	,	PUNCT
ejpam-7112	1	202	india	india	PROPN
ejpam-7112	1	203	8	8	NUM
ejpam-7112	1	204	college	college	NOUN
ejpam-7112	1	205	of	of	ADP
ejpam-7112	1	206	engineering	engineering	NOUN
ejpam-7112	1	207	,	,	PUNCT
ejpam-7112	1	208	university	university	NOUN
ejpam-7112	1	209	of	of	ADP
ejpam-7112	1	210	business	business	NOUN
ejpam-7112	1	211	and	and	CCONJ
ejpam-7112	1	212	technology	technology	NOUN
ejpam-7112	1	213	,	,	PUNCT
ejpam-7112	1	214	jeddah	jeddah	PROPN
ejpam-7112	1	215	23435	23435	NUM
ejpam-7112	1	216	,	,	PUNCT
ejpam-7112	1	217	saudi	saudi	PROPN
ejpam-7112	1	218	arabia	arabia	PROPN
ejpam-7112	1	219	9	9	NUM
ejpam-7112	1	220	department	department	NOUN
ejpam-7112	1	221	of	of	ADP
ejpam-7112	1	222	engineering	engineering	NOUN
ejpam-7112	1	223	mathematics	mathematic	NOUN
ejpam-7112	1	224	and	and	CCONJ
ejpam-7112	1	225	physics	physics	NOUN
ejpam-7112	1	226	,	,	PUNCT
ejpam-7112	1	227	faculty	faculty	NOUN
ejpam-7112	1	228	of	of	ADP
ejpam-7112	1	229	engineering	engineering	PROPN
ejpam-7112	1	230	,	,	PUNCT
ejpam-7112	1	231	zagazig	zagazig	PROPN
ejpam-7112	1	232	university	university	PROPN
ejpam-7112	1	233	,	,	PUNCT
ejpam-7112	1	234	p.o	p.o	PROPN
ejpam-7112	1	235	.	.	PROPN
ejpam-7112	1	236	44519	44519	NUM
ejpam-7112	1	237	,	,	PUNCT
ejpam-7112	1	238	egypt	egypt	PROPN
ejpam-7112	1	239	abstract	abstract	PROPN
ejpam-7112	1	240	.	.	PUNCT
ejpam-7112	2	1	engineers	engineer	NOUN
ejpam-7112	2	2	and	and	CCONJ
ejpam-7112	2	3	scientists	scientist	NOUN
ejpam-7112	2	4	adopt	adopt	VERB
ejpam-7112	2	5	numerical	numerical	ADJ
ejpam-7112	2	6	integration	integration	NOUN
ejpam-7112	2	7	to	to	PART
ejpam-7112	2	8	achieve	achieve	VERB
ejpam-7112	2	9	an	an	DET
ejpam-7112	2	10	approximate	approximate	ADJ
ejpam-7112	2	11	solution	solution	NOUN
ejpam-7112	2	12	for	for	ADP
ejpam-7112	2	13	definite	definite	ADJ
ejpam-7112	2	14	integrals	integral	NOUN
ejpam-7112	2	15	that	that	PRON
ejpam-7112	2	16	have	have	VERB
ejpam-7112	2	17	no	no	DET
ejpam-7112	2	18	analytic	analytic	ADJ
ejpam-7112	2	19	solution	solution	NOUN
ejpam-7112	2	20	.	.	PUNCT
ejpam-7112	3	1	this	this	DET
ejpam-7112	3	2	research	research	NOUN
ejpam-7112	3	3	focuses	focus	VERB
ejpam-7112	3	4	on	on	ADP
ejpam-7112	3	5	developing	develop	VERB
ejpam-7112	3	6	some	some	DET
ejpam-7112	3	7	new	new	ADJ
ejpam-7112	3	8	derivativebased	derivativebase	VERB
ejpam-7112	3	9	quadrature	quadrature	NOUN
ejpam-7112	3	10	schemes	scheme	NOUN
ejpam-7112	3	11	for	for	ADP
ejpam-7112	3	12	numerically	numerically	ADV
ejpam-7112	3	13	integrating	integrate	VERB
ejpam-7112	3	14	the	the	DET
ejpam-7112	3	15	integral	integral	ADJ
ejpam-7112	3	16	of	of	ADP
ejpam-7112	3	17	riemann	riemann	PROPN
ejpam-7112	3	18	-	-	PUNCT
ejpam-7112	3	19	stieltjes	stieltjes	PROPN
ejpam-7112	3	20	(	(	PUNCT
ejpam-7112	3	21	rs	rs	ADJ
ejpam-7112	3	22	-	-	ADJ
ejpam-7112	3	23	integral	integral	ADJ
ejpam-7112	3	24	)	)	PUNCT
ejpam-7112	3	25	by	by	ADP
ejpam-7112	3	26	proposing	propose	VERB
ejpam-7112	3	27	new	new	ADJ
ejpam-7112	3	28	schemes	scheme	NOUN
ejpam-7112	3	29	which	which	PRON
ejpam-7112	3	30	are	be	AUX
ejpam-7112	3	31	based	base	VERB
ejpam-7112	3	32	on	on	ADP
ejpam-7112	3	33	trapezoid	trapezoid	ADJ
ejpam-7112	3	34	-	-	PUNCT
ejpam-7112	3	35	type	type	NOUN
ejpam-7112	3	36	quadrature	quadrature	NOUN
ejpam-7112	3	37	.	.	PUNCT
ejpam-7112	4	1	the	the	DET
ejpam-7112	4	2	process	process	NOUN
ejpam-7112	4	3	of	of	ADP
ejpam-7112	4	4	undetermined	undetermined	ADJ
ejpam-7112	4	5	coefficients	coefficient	NOUN
ejpam-7112	4	6	has	have	AUX
ejpam-7112	4	7	been	be	AUX
ejpam-7112	4	8	used	use	VERB
ejpam-7112	4	9	for	for	ADP
ejpam-7112	4	10	the	the	DET
ejpam-7112	4	11	derivation	derivation	NOUN
ejpam-7112	4	12	of	of	ADP
ejpam-7112	4	13	proposed	propose	VERB
ejpam-7112	4	14	schemes	scheme	NOUN
ejpam-7112	4	15	.	.	PUNCT
ejpam-7112	5	1	the	the	DET
ejpam-7112	5	2	theoretical	theoretical	ADJ
ejpam-7112	5	3	derivation	derivation	NOUN
ejpam-7112	5	4	and	and	CCONJ
ejpam-7112	5	5	numerical	numerical	ADJ
ejpam-7112	5	6	verification	verification	NOUN
ejpam-7112	5	7	of	of	ADP
ejpam-7112	5	8	orders	order	NOUN
ejpam-7112	5	9	of	of	ADP
ejpam-7112	5	10	accuracy	accuracy	NOUN
ejpam-7112	5	11	have	have	AUX
ejpam-7112	5	12	been	be	AUX
ejpam-7112	5	13	addressed	address	VERB
ejpam-7112	5	14	in	in	ADP
ejpam-7112	5	15	line	line	NOUN
ejpam-7112	5	16	with	with	ADP
ejpam-7112	5	17	the	the	DET
ejpam-7112	5	18	degrees	degree	NOUN
ejpam-7112	5	19	of	of	ADP
ejpam-7112	5	20	precision	precision	NOUN
ejpam-7112	5	21	,	,	PUNCT
ejpam-7112	5	22	and	and	CCONJ
ejpam-7112	5	23	a	a	DET
ejpam-7112	5	24	sufficient	sufficient	ADJ
ejpam-7112	5	25	improvement	improvement	NOUN
ejpam-7112	5	26	has	have	AUX
ejpam-7112	5	27	been	be	AUX
ejpam-7112	5	28	demonstrated	demonstrate	VERB
ejpam-7112	5	29	over	over	ADP
ejpam-7112	5	30	the	the	DET
ejpam-7112	5	31	existing	exist	VERB
ejpam-7112	5	32	schemes	scheme	NOUN
ejpam-7112	5	33	.	.	PUNCT
ejpam-7112	6	1	the	the	DET
ejpam-7112	6	2	theorems	theorem	NOUN
ejpam-7112	6	3	regarding	regard	VERB
ejpam-7112	6	4	single	single	ADJ
ejpam-7112	6	5	and	and	CCONJ
ejpam-7112	6	6	multiple	multiple	ADJ
ejpam-7112	6	7	use	use	NOUN
ejpam-7112	6	8	of	of	ADP
ejpam-7112	6	9	the	the	DET
ejpam-7112	6	10	suggested	suggest	VERB
ejpam-7112	6	11	schemes	scheme	NOUN
ejpam-7112	6	12	in	in	ADP
ejpam-7112	6	13	a	a	DET
ejpam-7112	6	14	finite	finite	ADJ
ejpam-7112	6	15	interval	interval	NOUN
ejpam-7112	6	16	have	have	AUX
ejpam-7112	6	17	been	be	AUX
ejpam-7112	6	18	proved	prove	VERB
ejpam-7112	6	19	along	along	ADP
ejpam-7112	6	20	with	with	ADP
ejpam-7112	6	21	the	the	DET
ejpam-7112	6	22	theoretical	theoretical	ADJ
ejpam-7112	6	23	results	result	NOUN
ejpam-7112	6	24	on	on	ADP
ejpam-7112	6	25	residual	residual	ADJ
ejpam-7112	6	26	terms	term	NOUN
ejpam-7112	6	27	,	,	PUNCT
ejpam-7112	6	28	both	both	CCONJ
ejpam-7112	6	29	locally	locally	ADV
ejpam-7112	6	30	and	and	CCONJ
ejpam-7112	6	31	globally	globally	ADV
ejpam-7112	6	32	.	.	PUNCT
ejpam-7112	7	1	all	all	PRON
ejpam-7112	7	2	suggested	suggest	VERB
ejpam-7112	7	3	schemes	scheme	NOUN
ejpam-7112	7	4	have	have	AUX
ejpam-7112	7	5	been	be	AUX
ejpam-7112	7	6	verified	verify	VERB
ejpam-7112	7	7	to	to	PART
ejpam-7112	7	8	reduce	reduce	VERB
ejpam-7112	7	9	to	to	ADP
ejpam-7112	7	10	corresponding	correspond	VERB
ejpam-7112	7	11	variants	variant	NOUN
ejpam-7112	7	12	for	for	ADP
ejpam-7112	7	13	the	the	DET
ejpam-7112	7	14	riemann	riemann	PROPN
ejpam-7112	7	15	integral	integral	PROPN
ejpam-7112	7	16	in	in	ADP
ejpam-7112	7	17	the	the	DET
ejpam-7112	7	18	case	case	NOUN
ejpam-7112	7	19	when	when	SCONJ
ejpam-7112	7	20	integrator	integrator	PROPN
ejpam-7112	7	21	g(t	g(t	PROPN
ejpam-7112	7	22	)	)	PUNCT
ejpam-7112	8	1	=	=	SYM
ejpam-7112	8	2	t.	t.	PROPN
ejpam-7112	8	3	numerical	numerical	ADJ
ejpam-7112	8	4	experiments	experiment	NOUN
ejpam-7112	8	5	have	have	AUX
ejpam-7112	8	6	been	be	AUX
ejpam-7112	8	7	performed	perform	VERB
ejpam-7112	8	8	on	on	ADP
ejpam-7112	8	9	all	all	DET
ejpam-7112	8	10	the	the	DET
ejpam-7112	8	11	discussed	discuss	VERB
ejpam-7112	8	12	schemes	scheme	NOUN
ejpam-7112	8	13	with	with	ADP
ejpam-7112	8	14	the	the	DET
ejpam-7112	8	15	help	help	NOUN
ejpam-7112	8	16	of	of	ADP
ejpam-7112	8	17	matlab	matlab	PROPN
ejpam-7112	8	18	coding	coding	NOUN
ejpam-7112	8	19	.	.	PUNCT
ejpam-7112	9	1	the	the	DET
ejpam-7112	9	2	experimental	experimental	ADJ
ejpam-7112	9	3	results	result	NOUN
ejpam-7112	9	4	assure	assure	VERB
ejpam-7112	9	5	the	the	DET
ejpam-7112	9	6	smaller	small	ADJ
ejpam-7112	9	7	numerical	numerical	ADJ
ejpam-7112	9	8	errors	error	NOUN
ejpam-7112	9	9	by	by	ADP
ejpam-7112	9	10	the	the	DET
ejpam-7112	9	11	proposed	propose	VERB
ejpam-7112	9	12	schemes	scheme	NOUN
ejpam-7112	9	13	in	in	ADP
ejpam-7112	9	14	the	the	DET
ejpam-7112	9	15	comparison	comparison	NOUN
ejpam-7112	9	16	of	of	ADP
ejpam-7112	9	17	existing	exist	VERB
ejpam-7112	9	18	schemes	scheme	NOUN
ejpam-7112	9	19	.	.	PUNCT
ejpam-7112	10	1	the	the	DET
ejpam-7112	10	2	obtained	obtain	VERB
ejpam-7112	10	3	results	result	NOUN
ejpam-7112	10	4	show	show	VERB
ejpam-7112	10	5	the	the	DET
ejpam-7112	10	6	efficiency	efficiency	NOUN
ejpam-7112	10	7	of	of	ADP
ejpam-7112	10	8	proposed	propose	VERB
ejpam-7112	10	9	schemes	scheme	NOUN
ejpam-7112	10	10	in	in	ADP
ejpam-7112	10	11	light	light	NOUN
ejpam-7112	10	12	of	of	ADP
ejpam-7112	10	13	computational	computational	ADJ
ejpam-7112	10	14	burden	burden	NOUN
ejpam-7112	10	15	and	and	CCONJ
ejpam-7112	10	16	cpu	cpu	NOUN
ejpam-7112	10	17	time	time	NOUN
ejpam-7112	10	18	(	(	PUNCT
ejpam-7112	10	19	in	in	ADP
ejpam-7112	10	20	seconds	second	NOUN
ejpam-7112	10	21	)	)	PUNCT
ejpam-7112	10	22	with	with	ADP
ejpam-7112	10	23	reference	reference	NOUN
ejpam-7112	10	24	to	to	ADP
ejpam-7112	10	25	the	the	DET
ejpam-7112	10	26	existing	exist	VERB
ejpam-7112	10	27	quadrature	quadrature	NOUN
ejpam-7112	10	28	.	.	PUNCT
ejpam-7112	11	1	the	the	DET
ejpam-7112	11	2	proposed	propose	VERB
ejpam-7112	11	3	work	work	NOUN
ejpam-7112	11	4	substantially	substantially	ADV
ejpam-7112	11	5	advances	advance	VERB
ejpam-7112	11	6	the	the	DET
ejpam-7112	11	7	existing	exist	VERB
ejpam-7112	11	8	knowledge	knowledge	NOUN
ejpam-7112	11	9	with	with	ADP
ejpam-7112	11	10	an	an	DET
ejpam-7112	11	11	addition	addition	NOUN
ejpam-7112	11	12	of	of	ADP
ejpam-7112	11	13	derivative	derivative	NOUN
ejpam-7112	11	14	-	-	PUNCT
ejpam-7112	11	15	based	base	VERB
ejpam-7112	11	16	correction	correction	NOUN
ejpam-7112	11	17	terms	term	NOUN
ejpam-7112	11	18	in	in	ADP
ejpam-7112	11	19	the	the	DET
ejpam-7112	11	20	usual	usual	ADJ
ejpam-7112	11	21	quadrature	quadrature	NOUN
ejpam-7112	11	22	in	in	ADP
ejpam-7112	11	23	a	a	DET
ejpam-7112	11	24	way	way	NOUN
ejpam-7112	11	25	that	that	PRON
ejpam-7112	11	26	the	the	DET
ejpam-7112	11	27	consequent	consequent	ADJ
ejpam-7112	11	28	computational	computational	ADJ
ejpam-7112	11	29	costs	cost	NOUN
ejpam-7112	11	30	and	and	CCONJ
ejpam-7112	11	31	execution	execution	NOUN
ejpam-7112	11	32	times	time	NOUN
ejpam-7112	11	33	are	be	AUX
ejpam-7112	11	34	also	also	ADV
ejpam-7112	11	35	minimized	minimize	VERB
ejpam-7112	11	36	.	.	PUNCT
ejpam-7112	12	1	2020	2020	NUM
ejpam-7112	12	2	mathematics	mathematic	NOUN
ejpam-7112	12	3	subject	subject	NOUN
ejpam-7112	12	4	classifications	classification	NOUN
ejpam-7112	12	5	:	:	PUNCT
ejpam-7112	12	6	65d30	65d30	NUM
ejpam-7112	12	7	,	,	PUNCT
ejpam-7112	12	8	65d32	65d32	NUM
ejpam-7112	12	9	key	key	ADJ
ejpam-7112	12	10	words	word	NOUN
ejpam-7112	12	11	and	and	CCONJ
ejpam-7112	12	12	phrases	phrase	NOUN
ejpam-7112	12	13	:	:	PUNCT
ejpam-7112	12	14	quadrature	quadrature	NOUN
ejpam-7112	12	15	rule	rule	NOUN
ejpam-7112	12	16	,	,	PUNCT
ejpam-7112	12	17	riemann	riemann	PROPN
ejpam-7112	12	18	-	-	PUNCT
ejpam-7112	12	19	stieltjes	stieltjes	PROPN
ejpam-7112	12	20	integral	integral	ADJ
ejpam-7112	12	21	,	,	PUNCT
ejpam-7112	12	22	trapezoidal	trapezoidal	ADJ
ejpam-7112	12	23	rule	rule	NOUN
ejpam-7112	12	24	,	,	PUNCT
ejpam-7112	12	25	derivativebased	derivativebase	VERB
ejpam-7112	12	26	schemes	scheme	NOUN
ejpam-7112	12	27	,	,	PUNCT
ejpam-7112	12	28	midpoint	midpoint	NOUN
ejpam-7112	12	29	methods	method	NOUN
ejpam-7112	12	30	,	,	PUNCT
ejpam-7112	12	31	means	mean	VERB
ejpam-7112	12	32	∗corresponding	∗corresponde	VERB
ejpam-7112	12	33	author	author	NOUN
ejpam-7112	12	34	.	.	PUNCT
ejpam-7112	13	1	doi	doi	NOUN
ejpam-7112	13	2	:	:	PUNCT
ejpam-7112	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7112	https://doi.org/10.29020/nybg.ejpam.v18i4.7112	ADJ
ejpam-7112	13	4	email	email	NOUN
ejpam-7112	13	5	addresses	address	NOUN
ejpam-7112	13	6	:	:	PUNCT
ejpam-7112	13	7	hijaz.ahmad@neu.edu.tr	hijaz.ahmad@neu.edu.tr	PROPN
ejpam-7112	13	8	(	(	PUNCT
ejpam-7112	13	9	h.	h.	PROPN
ejpam-7112	13	10	ahmad	ahmad	PROPN
ejpam-7112	13	11	)	)	PUNCT
ejpam-7112	13	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7112	14	1	1	1	NUM
ejpam-7112	14	2	copyright	copyright	NOUN
ejpam-7112	14	3	:	:	PUNCT
ejpam-7112	14	4	©	©	PROPN
ejpam-7112	14	5	2025	2025	NUM
ejpam-7112	14	6	the	the	DET
ejpam-7112	14	7	author(s	author(s	NOUN
ejpam-7112	14	8	)	)	PUNCT
ejpam-7112	14	9	.	.	PUNCT
ejpam-7112	15	1	(	(	PUNCT
ejpam-7112	15	2	cc	cc	NOUN
ejpam-7112	15	3	by	by	ADP
ejpam-7112	15	4	-	-	PUNCT
ejpam-7112	15	5	nc	nc	PROPN
ejpam-7112	15	6	4.0	4.0	NUM
ejpam-7112	15	7	)	)	PUNCT
ejpam-7112	15	8	k.	k.	PROPN
ejpam-7112	15	9	memon	memon	PROPN
ejpam-7112	15	10	et	et	PROPN
ejpam-7112	15	11	al	al	PROPN
ejpam-7112	15	12	.	.	PUNCT
ejpam-7112	15	13	/	/	SYM
ejpam-7112	15	14	eur	eur	PROPN
ejpam-7112	15	15	.	.	PUNCT
ejpam-7112	16	1	j.	j.	PROPN
ejpam-7112	16	2	pure	pure	PROPN
ejpam-7112	16	3	appl	appl	PROPN
ejpam-7112	16	4	.	.	PROPN
ejpam-7112	16	5	math	math	PROPN
ejpam-7112	16	6	,	,	PUNCT
ejpam-7112	16	7	18	18	NUM
ejpam-7112	16	8	(	(	PUNCT
ejpam-7112	16	9	4	4	NUM
ejpam-7112	16	10	)	)	PUNCT
ejpam-7112	16	11	(	(	PUNCT
ejpam-7112	16	12	2025	2025	NUM
ejpam-7112	16	13	)	)	PUNCT
ejpam-7112	16	14	,	,	PUNCT
ejpam-7112	16	15	7112	7112	NUM
ejpam-7112	16	16	2	2	NUM
ejpam-7112	16	17	of	of	ADP
ejpam-7112	16	18	38	38	NUM
ejpam-7112	16	19	1	1	NUM
ejpam-7112	16	20	.	.	PUNCT
ejpam-7112	17	1	introduction	introduction	NOUN
ejpam-7112	17	2	one	one	NUM
ejpam-7112	17	3	of	of	ADP
ejpam-7112	17	4	the	the	DET
ejpam-7112	17	5	oldest	old	ADJ
ejpam-7112	17	6	and	and	CCONJ
ejpam-7112	17	7	most	most	ADV
ejpam-7112	17	8	attractive	attractive	ADJ
ejpam-7112	17	9	concepts	concept	NOUN
ejpam-7112	17	10	in	in	ADP
ejpam-7112	17	11	numerical	numerical	ADJ
ejpam-7112	17	12	analysis	analysis	NOUN
ejpam-7112	17	13	is	be	AUX
ejpam-7112	17	14	numerical	numerical	ADJ
ejpam-7112	17	15	integration	integration	NOUN
ejpam-7112	17	16	.	.	PUNCT
ejpam-7112	18	1	when	when	SCONJ
ejpam-7112	18	2	integrating	integrate	VERB
ejpam-7112	18	3	f(x	f(x	PROPN
ejpam-7112	18	4	)	)	PUNCT
ejpam-7112	18	5	analytically	analytically	ADV
ejpam-7112	18	6	is	be	AUX
ejpam-7112	18	7	difficult	difficult	ADJ
ejpam-7112	18	8	or	or	CCONJ
ejpam-7112	18	9	impossible	impossible	ADJ
ejpam-7112	18	10	,	,	PUNCT
ejpam-7112	18	11	or	or	CCONJ
ejpam-7112	18	12	if	if	SCONJ
ejpam-7112	18	13	the	the	DET
ejpam-7112	18	14	values	value	NOUN
ejpam-7112	18	15	of	of	ADP
ejpam-7112	18	16	f(x	f(x	PROPN
ejpam-7112	18	17	)	)	PUNCT
ejpam-7112	18	18	are	be	AUX
ejpam-7112	18	19	defined	define	VERB
ejpam-7112	18	20	in	in	ADP
ejpam-7112	18	21	tabular	tabular	NOUN
ejpam-7112	18	22	form	form	NOUN
ejpam-7112	18	23	,	,	PUNCT
ejpam-7112	18	24	then	then	ADV
ejpam-7112	18	25	the	the	DET
ejpam-7112	18	26	numerical	numerical	ADJ
ejpam-7112	18	27	integration	integration	NOUN
ejpam-7112	18	28	methods	method	NOUN
ejpam-7112	18	29	are	be	AUX
ejpam-7112	18	30	applied	apply	VERB
ejpam-7112	18	31	.	.	PUNCT
ejpam-7112	19	1	however	however	ADV
ejpam-7112	19	2	,	,	PUNCT
ejpam-7112	19	3	numerical	numerical	ADJ
ejpam-7112	19	4	integration	integration	NOUN
ejpam-7112	19	5	gives	give	VERB
ejpam-7112	19	6	only	only	ADV
ejpam-7112	19	7	the	the	DET
ejpam-7112	19	8	approximate	approximate	ADJ
ejpam-7112	19	9	value	value	NOUN
ejpam-7112	19	10	of	of	ADP
ejpam-7112	19	11	the	the	DET
ejpam-7112	19	12	integral	integral	ADJ
ejpam-7112	19	13	with	with	ADP
ejpam-7112	19	14	given	give	VERB
ejpam-7112	19	15	parameters	parameter	NOUN
ejpam-7112	19	16	.	.	PUNCT
ejpam-7112	20	1	numerical	numerical	ADJ
ejpam-7112	20	2	integration	integration	NOUN
ejpam-7112	20	3	generates	generate	VERB
ejpam-7112	20	4	better	well	ADJ
ejpam-7112	20	5	results	result	NOUN
ejpam-7112	20	6	when	when	SCONJ
ejpam-7112	20	7	it	it	PRON
ejpam-7112	20	8	is	be	AUX
ejpam-7112	20	9	solved	solve	VERB
ejpam-7112	20	10	properly	properly	ADV
ejpam-7112	20	11	with	with	ADP
ejpam-7112	20	12	appropriate	appropriate	ADJ
ejpam-7112	20	13	methods	method	NOUN
ejpam-7112	20	14	.	.	PUNCT
ejpam-7112	21	1	the	the	DET
ejpam-7112	21	2	term	term	NOUN
ejpam-7112	21	3	quadrature	quadrature	NOUN
ejpam-7112	21	4	is	be	AUX
ejpam-7112	21	5	used	use	VERB
ejpam-7112	21	6	to	to	PART
ejpam-7112	21	7	describe	describe	VERB
ejpam-7112	21	8	numerical	numerical	ADJ
ejpam-7112	21	9	integration	integration	NOUN
ejpam-7112	21	10	in	in	ADP
ejpam-7112	21	11	one	one	NUM
ejpam-7112	21	12	dimension	dimension	NOUN
ejpam-7112	21	13	.	.	PUNCT
ejpam-7112	22	1	quadrature	quadrature	NOUN
ejpam-7112	22	2	formulas	formula	NOUN
ejpam-7112	22	3	are	be	AUX
ejpam-7112	22	4	usually	usually	ADV
ejpam-7112	22	5	based	base	VERB
ejpam-7112	22	6	on	on	ADP
ejpam-7112	22	7	polynomial	polynomial	ADJ
ejpam-7112	22	8	interpolation	interpolation	NOUN
ejpam-7112	22	9	.	.	PUNCT
ejpam-7112	23	1	mostly	mostly	ADV
ejpam-7112	23	2	,	,	PUNCT
ejpam-7112	23	3	the	the	DET
ejpam-7112	23	4	conventional	conventional	PROPN
ejpam-7112	23	5	newton	newton	PROPN
ejpam-7112	23	6	-	-	PUNCT
ejpam-7112	23	7	cotes	cote	NOUN
ejpam-7112	23	8	quadrature	quadrature	NOUN
ejpam-7112	23	9	formulae	formulae	ADJ
ejpam-7112	23	10	work	work	NOUN
ejpam-7112	23	11	well	well	ADV
ejpam-7112	23	12	for	for	ADP
ejpam-7112	23	13	definite	definite	ADJ
ejpam-7112	23	14	integrals	integral	NOUN
ejpam-7112	23	15	.	.	PUNCT
ejpam-7112	24	1	different	different	ADJ
ejpam-7112	24	2	types	type	NOUN
ejpam-7112	24	3	of	of	ADP
ejpam-7112	24	4	newton	newton	PROPN
ejpam-7112	24	5	-	-	PUNCT
ejpam-7112	24	6	cotes	cote	NOUN
ejpam-7112	24	7	formulas	formula	NOUN
ejpam-7112	24	8	are	be	AUX
ejpam-7112	24	9	known	know	VERB
ejpam-7112	24	10	that	that	PRON
ejpam-7112	24	11	are	be	AUX
ejpam-7112	24	12	based	base	VERB
ejpam-7112	24	13	on	on	ADP
ejpam-7112	24	14	the	the	DET
ejpam-7112	24	15	range	range	NOUN
ejpam-7112	24	16	of	of	ADP
ejpam-7112	24	17	the	the	DET
ejpam-7112	24	18	limits	limit	NOUN
ejpam-7112	24	19	a	a	PRON
ejpam-7112	24	20	and	and	CCONJ
ejpam-7112	24	21	b.	b.	PROPN
ejpam-7112	24	22	the	the	DET
ejpam-7112	24	23	newton	newton	PROPN
ejpam-7112	24	24	-	-	PUNCT
ejpam-7112	24	25	cotes	cote	NOUN
ejpam-7112	24	26	formulae	formulae	NOUN
ejpam-7112	24	27	of	of	ADP
ejpam-7112	24	28	closed	closed	ADJ
ejpam-7112	24	29	type	type	NOUN
ejpam-7112	24	30	,	,	PUNCT
ejpam-7112	24	31	which	which	PRON
ejpam-7112	24	32	include	include	VERB
ejpam-7112	24	33	both	both	DET
ejpam-7112	24	34	endpoints	endpoint	NOUN
ejpam-7112	24	35	,	,	PUNCT
ejpam-7112	24	36	can	can	AUX
ejpam-7112	24	37	be	be	AUX
ejpam-7112	24	38	regarded	regard	VERB
ejpam-7112	24	39	as	as	ADP
ejpam-7112	24	40	a	a	DET
ejpam-7112	24	41	bulk	bulk	NOUN
ejpam-7112	24	42	of	of	ADP
ejpam-7112	24	43	essential	essential	ADJ
ejpam-7112	24	44	formulas	formula	NOUN
ejpam-7112	24	45	.	.	PUNCT
ejpam-7112	25	1	the	the	DET
ejpam-7112	25	2	closed	closed	PROPN
ejpam-7112	25	3	newton	newton	PROPN
ejpam-7112	25	4	-	-	PUNCT
ejpam-7112	25	5	cotes	cote	NOUN
ejpam-7112	25	6	integration	integration	NOUN
ejpam-7112	25	7	formulae	formulae	NOUN
ejpam-7112	25	8	include	include	VERB
ejpam-7112	25	9	the	the	DET
ejpam-7112	25	10	trapezoid	trapezoid	ADJ
ejpam-7112	25	11	rule	rule	NOUN
ejpam-7112	25	12	as	as	ADP
ejpam-7112	25	13	a	a	DET
ejpam-7112	25	14	specific	specific	ADJ
ejpam-7112	25	15	case	case	NOUN
ejpam-7112	25	16	.	.	PUNCT
ejpam-7112	26	1	the	the	DET
ejpam-7112	26	2	integrand	integrand	PROPN
ejpam-7112	26	3	function	function	NOUN
ejpam-7112	26	4	is	be	AUX
ejpam-7112	26	5	fitted	fit	VERB
ejpam-7112	26	6	with	with	ADP
ejpam-7112	26	7	nth	nth	NOUN
ejpam-7112	26	8	degree	degree	NOUN
ejpam-7112	26	9	polynomials	polynomial	NOUN
ejpam-7112	26	10	at	at	ADP
ejpam-7112	26	11	n	n	PROPN
ejpam-7112	26	12	+	+	CCONJ
ejpam-7112	26	13	1	1	NUM
ejpam-7112	26	14	control	control	NOUN
ejpam-7112	26	15	points	point	NOUN
ejpam-7112	26	16	to	to	PART
ejpam-7112	26	17	obtain	obtain	VERB
ejpam-7112	26	18	this	this	DET
ejpam-7112	26	19	formula	formula	NOUN
ejpam-7112	26	20	.	.	PUNCT
ejpam-7112	27	1	mostly	mostly	ADV
ejpam-7112	27	2	,	,	PUNCT
ejpam-7112	27	3	attention	attention	NOUN
ejpam-7112	27	4	of	of	ADP
ejpam-7112	27	5	research	research	NOUN
ejpam-7112	27	6	works	work	NOUN
ejpam-7112	27	7	in	in	ADP
ejpam-7112	27	8	the	the	DET
ejpam-7112	27	9	field	field	NOUN
ejpam-7112	27	10	of	of	ADP
ejpam-7112	27	11	numerical	numerical	ADJ
ejpam-7112	27	12	integration	integration	NOUN
ejpam-7112	27	13	was	be	AUX
ejpam-7112	27	14	focused	focus	VERB
ejpam-7112	27	15	on	on	ADP
ejpam-7112	27	16	the	the	DET
ejpam-7112	27	17	riemann	riemann	PROPN
ejpam-7112	27	18	integral	integral	PROPN
ejpam-7112	27	19	.	.	PUNCT
ejpam-7112	28	1	similar	similar	ADJ
ejpam-7112	28	2	progress	progress	NOUN
ejpam-7112	28	3	may	may	AUX
ejpam-7112	28	4	be	be	AUX
ejpam-7112	28	5	achieved	achieve	VERB
ejpam-7112	28	6	for	for	ADP
ejpam-7112	28	7	the	the	DET
ejpam-7112	28	8	rs	rs	NOUN
ejpam-7112	28	9	-	-	ADJ
ejpam-7112	28	10	integral	integral	ADJ
ejpam-7112	28	11	.	.	PUNCT
ejpam-7112	29	1	the	the	DET
ejpam-7112	29	2	evaluation	evaluation	NOUN
ejpam-7112	29	3	of	of	ADP
ejpam-7112	29	4	rs	rs	NOUN
ejpam-7112	29	5	-	-	ADJ
ejpam-7112	29	6	integral	integral	ADJ
ejpam-7112	29	7	,	,	PUNCT
ejpam-7112	29	8	in	in	ADP
ejpam-7112	29	9	which	which	PRON
ejpam-7112	29	10	the	the	DET
ejpam-7112	29	11	integrand	integrand	NOUN
ejpam-7112	29	12	is	be	AUX
ejpam-7112	29	13	f(x	f(x	PROPN
ejpam-7112	29	14	)	)	PUNCT
ejpam-7112	29	15	and	and	CCONJ
ejpam-7112	29	16	the	the	DET
ejpam-7112	29	17	integrator	integrator	NOUN
ejpam-7112	29	18	is	be	AUX
ejpam-7112	29	19	another	another	DET
ejpam-7112	29	20	function	function	NOUN
ejpam-7112	29	21	of	of	ADP
ejpam-7112	29	22	x	x	PROPN
ejpam-7112	29	23	,	,	PUNCT
ejpam-7112	29	24	α(x	α(x	PROPN
ejpam-7112	29	25	)	)	PUNCT
ejpam-7112	29	26	,	,	PUNCT
ejpam-7112	29	27	develops	develop	VERB
ejpam-7112	29	28	a	a	DET
ejpam-7112	29	29	mainstream	mainstream	NOUN
ejpam-7112	29	30	part	part	NOUN
ejpam-7112	29	31	in	in	ADP
ejpam-7112	29	32	mathematics	mathematic	NOUN
ejpam-7112	29	33	[	[	X
ejpam-7112	29	34	1	1	NUM
ejpam-7112	29	35	]	]	PUNCT
ejpam-7112	29	36	.	.	PUNCT
ejpam-7112	30	1	rs	rs	ADJ
ejpam-7112	30	2	-	-	ADJ
ejpam-7112	30	3	integral	integral	ADJ
ejpam-7112	30	4	may	may	AUX
ejpam-7112	30	5	be	be	AUX
ejpam-7112	30	6	applied	apply	VERB
ejpam-7112	30	7	in	in	ADP
ejpam-7112	30	8	the	the	DET
ejpam-7112	30	9	areas	area	NOUN
ejpam-7112	30	10	of	of	ADP
ejpam-7112	30	11	statistics	statistic	NOUN
ejpam-7112	30	12	and	and	CCONJ
ejpam-7112	30	13	probability	probability	NOUN
ejpam-7112	30	14	theory	theory	NOUN
ejpam-7112	30	15	of	of	ADP
ejpam-7112	30	16	operators	operator	NOUN
ejpam-7112	30	17	,	,	PUNCT
ejpam-7112	30	18	mathematical	mathematical	ADJ
ejpam-7112	30	19	analysis	analysis	NOUN
ejpam-7112	30	20	,	,	PUNCT
ejpam-7112	30	21	etc	etc	X
ejpam-7112	30	22	.	.	X
ejpam-7112	31	1	obviously	obviously	ADV
ejpam-7112	31	2	,	,	PUNCT
ejpam-7112	31	3	the	the	DET
ejpam-7112	31	4	rs	rs	ADJ
ejpam-7112	31	5	-	-	ADJ
ejpam-7112	31	6	integral	integral	ADJ
ejpam-7112	31	7	can	can	AUX
ejpam-7112	31	8	be	be	AUX
ejpam-7112	31	9	regarded	regard	VERB
ejpam-7112	31	10	as	as	ADP
ejpam-7112	31	11	an	an	DET
ejpam-7112	31	12	enhancement	enhancement	NOUN
ejpam-7112	31	13	of	of	ADP
ejpam-7112	31	14	the	the	DET
ejpam-7112	31	15	usual	usual	ADJ
ejpam-7112	31	16	integration	integration	NOUN
ejpam-7112	31	17	by	by	ADP
ejpam-7112	31	18	riemann	riemann	PROPN
ejpam-7112	31	19	,	,	PUNCT
ejpam-7112	31	20	in	in	ADP
ejpam-7112	31	21	a	a	DET
ejpam-7112	31	22	way	way	NOUN
ejpam-7112	31	23	that	that	SCONJ
ejpam-7112	31	24	besides	besides	SCONJ
ejpam-7112	31	25	the	the	DET
ejpam-7112	31	26	integrand	integrand	PROPN
ejpam-7112	31	27	f	f	PROPN
ejpam-7112	31	28	,	,	PUNCT
ejpam-7112	31	29	the	the	DET
ejpam-7112	31	30	integrator	integrator	NOUN
ejpam-7112	31	31	also	also	ADV
ejpam-7112	31	32	depends	depend	VERB
ejpam-7112	31	33	on	on	ADP
ejpam-7112	31	34	x.	x.	NOUN
ejpam-7112	31	35	while	while	SCONJ
ejpam-7112	31	36	a	a	DET
ejpam-7112	31	37	considerable	considerable	ADJ
ejpam-7112	31	38	effort	effort	NOUN
ejpam-7112	31	39	in	in	ADP
ejpam-7112	31	40	literature	literature	NOUN
ejpam-7112	31	41	has	have	AUX
ejpam-7112	31	42	been	be	AUX
ejpam-7112	31	43	done	do	VERB
ejpam-7112	31	44	on	on	ADP
ejpam-7112	31	45	enhancing	enhance	VERB
ejpam-7112	31	46	quadrature	quadrature	NOUN
ejpam-7112	31	47	rules	rule	NOUN
ejpam-7112	31	48	for	for	ADP
ejpam-7112	31	49	the	the	DET
ejpam-7112	31	50	classical	classical	ADJ
ejpam-7112	31	51	riemann	riemann	PROPN
ejpam-7112	31	52	integrals	integral	NOUN
ejpam-7112	31	53	as	as	SCONJ
ejpam-7112	31	54	compared	compare	VERB
ejpam-7112	31	55	to	to	ADP
ejpam-7112	31	56	the	the	DET
ejpam-7112	31	57	rs	r	NOUN
ejpam-7112	31	58	-	-	PUNCT
ejpam-7112	31	59	integrals	integral	NOUN
ejpam-7112	31	60	,	,	PUNCT
ejpam-7112	31	61	only	only	ADV
ejpam-7112	31	62	some	some	DET
ejpam-7112	31	63	investigations	investigation	NOUN
ejpam-7112	31	64	have	have	AUX
ejpam-7112	31	65	been	be	AUX
ejpam-7112	31	66	attempted	attempt	VERB
ejpam-7112	31	67	to	to	PART
ejpam-7112	31	68	approximate	approximate	VERB
ejpam-7112	31	69	the	the	DET
ejpam-7112	31	70	rs	rs	NOUN
ejpam-7112	31	71	-	-	ADJ
ejpam-7112	31	72	integral	integral	ADJ
ejpam-7112	31	73	.	.	PUNCT
ejpam-7112	32	1	in	in	ADP
ejpam-7112	32	2	2008	2008	NUM
ejpam-7112	32	3	,	,	PUNCT
ejpam-7112	32	4	mercer	mercer	PROPN
ejpam-7112	33	1	[	[	X
ejpam-7112	33	2	2	2	NUM
ejpam-7112	33	3	]	]	PUNCT
ejpam-7112	33	4	offered	offer	VERB
ejpam-7112	33	5	the	the	DET
ejpam-7112	33	6	trapezoidal	trapezoidal	ADJ
ejpam-7112	33	7	rule	rule	NOUN
ejpam-7112	33	8	extension	extension	NOUN
ejpam-7112	33	9	which	which	PRON
ejpam-7112	33	10	addressed	address	VERB
ejpam-7112	33	11	the	the	DET
ejpam-7112	33	12	applicability	applicability	NOUN
ejpam-7112	33	13	of	of	ADP
ejpam-7112	33	14	the	the	DET
ejpam-7112	33	15	hadamard	hadamard	ADJ
ejpam-7112	33	16	integral	integral	ADJ
ejpam-7112	33	17	inequality	inequality	NOUN
ejpam-7112	33	18	for	for	ADP
ejpam-7112	33	19	the	the	DET
ejpam-7112	33	20	rs	rs	NOUN
ejpam-7112	33	21	-	-	ADJ
ejpam-7112	33	22	integral	integral	ADJ
ejpam-7112	33	23	.	.	PUNCT
ejpam-7112	34	1	moreover	moreover	ADV
ejpam-7112	34	2	,	,	PUNCT
ejpam-7112	34	3	in	in	ADP
ejpam-7112	34	4	2012	2012	NUM
ejpam-7112	34	5	,	,	PUNCT
ejpam-7112	34	6	mercer	mercer	PROPN
ejpam-7112	34	7	[	[	X
ejpam-7112	34	8	3	3	NUM
ejpam-7112	34	9	]	]	PUNCT
ejpam-7112	34	10	introduced	introduce	VERB
ejpam-7112	34	11	a	a	DET
ejpam-7112	34	12	new	new	ADJ
ejpam-7112	34	13	approach	approach	NOUN
ejpam-7112	34	14	for	for	ADP
ejpam-7112	34	15	midpoint	midpoint	NOUN
ejpam-7112	34	16	and	and	CCONJ
ejpam-7112	34	17	simpson	simpson	PROPN
ejpam-7112	34	18	’s	’s	PART
ejpam-7112	34	19	schemes	scheme	NOUN
ejpam-7112	34	20	on	on	ADP
ejpam-7112	34	21	the	the	DET
ejpam-7112	34	22	rs	rs	ADJ
ejpam-7112	34	23	-	-	ADJ
ejpam-7112	34	24	integral	integral	ADJ
ejpam-7112	34	25	,	,	PUNCT
ejpam-7112	34	26	based	base	VERB
ejpam-7112	34	27	on	on	ADP
ejpam-7112	34	28	the	the	DET
ejpam-7112	34	29	concept	concept	NOUN
ejpam-7112	34	30	of	of	ADP
ejpam-7112	34	31	relative	relative	ADJ
ejpam-7112	34	32	convexity	convexity	NOUN
ejpam-7112	34	33	.	.	PUNCT
ejpam-7112	35	1	in	in	ADP
ejpam-7112	35	2	2013	2013	NUM
ejpam-7112	35	3	,	,	PUNCT
ejpam-7112	35	4	zhao	zhao	PROPN
ejpam-7112	35	5	and	and	CCONJ
ejpam-7112	35	6	li	li	NOUN
ejpam-7112	35	7	[	[	X
ejpam-7112	35	8	4	4	X
ejpam-7112	35	9	]	]	PUNCT
ejpam-7112	35	10	developed	develop	VERB
ejpam-7112	35	11	a	a	DET
ejpam-7112	35	12	novel	novel	ADJ
ejpam-7112	35	13	midpoint	midpoint	NOUN
ejpam-7112	35	14	derivative	derivative	NOUN
ejpam-7112	35	15	-	-	PUNCT
ejpam-7112	35	16	based	base	VERB
ejpam-7112	35	17	family	family	NOUN
ejpam-7112	35	18	of	of	ADP
ejpam-7112	35	19	closed	closed	PROPN
ejpam-7112	35	20	newton	newton	PROPN
ejpam-7112	35	21	-	-	PUNCT
ejpam-7112	35	22	cotes	cote	NOUN
ejpam-7112	35	23	quadrature	quadrature	NOUN
ejpam-7112	35	24	rules	rule	NOUN
ejpam-7112	35	25	.	.	PUNCT
ejpam-7112	36	1	afterwards	afterwards	ADV
ejpam-7112	36	2	in	in	ADP
ejpam-7112	36	3	2014	2014	NUM
ejpam-7112	36	4	,	,	PUNCT
ejpam-7112	36	5	zhao	zhao	PROPN
ejpam-7112	36	6	et	et	PROPN
ejpam-7112	36	7	al	al	PROPN
ejpam-7112	36	8	.	.	PUNCT
ejpam-7112	37	1	[	[	X
ejpam-7112	37	2	5	5	NUM
ejpam-7112	37	3	]	]	PUNCT
ejpam-7112	37	4	proposed	propose	VERB
ejpam-7112	37	5	a	a	DET
ejpam-7112	37	6	trapezoid	trapezoid	ADJ
ejpam-7112	37	7	rule	rule	NOUN
ejpam-7112	37	8	for	for	ADP
ejpam-7112	37	9	the	the	DET
ejpam-7112	37	10	rs	rs	ADJ
ejpam-7112	37	11	-	-	ADJ
ejpam-7112	37	12	integral	integral	ADJ
ejpam-7112	37	13	based	base	VERB
ejpam-7112	37	14	on	on	ADP
ejpam-7112	37	15	the	the	DET
ejpam-7112	37	16	midpoint	midpoint	NOUN
ejpam-7112	37	17	derivative	derivative	NOUN
ejpam-7112	37	18	,	,	PUNCT
ejpam-7112	37	19	in	in	ADP
ejpam-7112	37	20	which	which	PRON
ejpam-7112	37	21	the	the	DET
ejpam-7112	37	22	function	function	NOUN
ejpam-7112	37	23	derivative	derivative	NOUN
ejpam-7112	37	24	was	be	AUX
ejpam-7112	37	25	computed	compute	VERB
ejpam-7112	37	26	using	use	VERB
ejpam-7112	37	27	the	the	DET
ejpam-7112	37	28	midpoint	midpoint	NOUN
ejpam-7112	37	29	.	.	PUNCT
ejpam-7112	38	1	in	in	ADP
ejpam-7112	38	2	2016	2016	NUM
ejpam-7112	38	3	,	,	PUNCT
ejpam-7112	38	4	shaikh	shaikh	PROPN
ejpam-7112	38	5	et	et	PROPN
ejpam-7112	38	6	al	al	PROPN
ejpam-7112	38	7	.	.	PUNCT
ejpam-7112	39	1	[	[	X
ejpam-7112	39	2	6	6	NUM
ejpam-7112	39	3	]	]	PUNCT
ejpam-7112	39	4	improved	improve	VERB
ejpam-7112	39	5	with	with	ADP
ejpam-7112	39	6	the	the	DET
ejpam-7112	39	7	second	second	ADJ
ejpam-7112	39	8	-	-	PUNCT
ejpam-7112	39	9	order	order	NOUN
ejpam-7112	39	10	derivative	derivative	NOUN
ejpam-7112	39	11	-	-	PUNCT
ejpam-7112	39	12	based	base	VERB
ejpam-7112	39	13	rule	rule	NOUN
ejpam-7112	39	14	with	with	ADP
ejpam-7112	39	15	the	the	DET
ejpam-7112	39	16	help	help	NOUN
ejpam-7112	39	17	of	of	ADP
ejpam-7112	39	18	midpoint	midpoint	NOUN
ejpam-7112	39	19	,	,	PUNCT
ejpam-7112	39	20	the	the	DET
ejpam-7112	39	21	zhao	zhao	PROPN
ejpam-7112	39	22	and	and	CCONJ
ejpam-7112	39	23	li	li	PROPN
ejpam-7112	39	24	’s	’s	PART
ejpam-7112	39	25	[	[	X
ejpam-7112	39	26	4	4	NUM
ejpam-7112	39	27	]	]	SYM
ejpam-7112	39	28	scheme	scheme	NOUN
ejpam-7112	39	29	of	of	ADP
ejpam-7112	39	30	simpson	simpson	PROPN
ejpam-7112	39	31	’s	’s	PART
ejpam-7112	39	32	3/8	3/8	NUM
ejpam-7112	39	33	-	-	PUNCT
ejpam-7112	39	34	type	type	NOUN
ejpam-7112	39	35	,	,	PUNCT
ejpam-7112	39	36	which	which	PRON
ejpam-7112	39	37	had	have	AUX
ejpam-7112	39	38	used	use	VERB
ejpam-7112	39	39	fourth	fourth	ADJ
ejpam-7112	39	40	-	-	PUNCT
ejpam-7112	39	41	order	order	NOUN
ejpam-7112	39	42	derivative	derivative	NOUN
ejpam-7112	39	43	.	.	PUNCT
ejpam-7112	40	1	there	there	PRON
ejpam-7112	40	2	are	be	VERB
ejpam-7112	40	3	so	so	ADV
ejpam-7112	40	4	many	many	ADJ
ejpam-7112	40	5	works	work	NOUN
ejpam-7112	40	6	that	that	PRON
ejpam-7112	40	7	have	have	AUX
ejpam-7112	40	8	been	be	AUX
ejpam-7112	40	9	done	do	VERB
ejpam-7112	40	10	on	on	ADP
ejpam-7112	40	11	the	the	DET
ejpam-7112	40	12	numerical	numerical	ADJ
ejpam-7112	40	13	enhancement	enhancement	NOUN
ejpam-7112	40	14	of	of	ADP
ejpam-7112	40	15	the	the	DET
ejpam-7112	40	16	usual	usual	ADJ
ejpam-7112	40	17	integration	integration	NOUN
ejpam-7112	40	18	formulas	formula	NOUN
ejpam-7112	40	19	of	of	ADP
ejpam-7112	40	20	newton	newton	PROPN
ejpam-7112	40	21	and	and	CCONJ
ejpam-7112	40	22	cotes	cotes	PROPN
ejpam-7112	40	23	.	.	PUNCT
ejpam-7112	41	1	in	in	ADP
ejpam-7112	41	2	2016	2016	NUM
ejpam-7112	41	3	,	,	PUNCT
ejpam-7112	41	4	ramachandran	ramachandran	PROPN
ejpam-7112	41	5	et	et	PROPN
ejpam-7112	41	6	al	al	PROPN
ejpam-7112	41	7	.	.	PUNCT
ejpam-7112	42	1	[	[	X
ejpam-7112	42	2	7	7	NUM
ejpam-7112	42	3	]	]	PUNCT
ejpam-7112	42	4	developed	develop	VERB
ejpam-7112	42	5	a	a	DET
ejpam-7112	42	6	novel	novel	ADJ
ejpam-7112	42	7	quadrature	quadrature	NOUN
ejpam-7112	42	8	of	of	ADP
ejpam-7112	42	9	the	the	DET
ejpam-7112	42	10	closed	closed	ADJ
ejpam-7112	42	11	form	form	NOUN
ejpam-7112	42	12	that	that	PRON
ejpam-7112	42	13	used	use	VERB
ejpam-7112	42	14	the	the	DET
ejpam-7112	42	15	geometric	geometric	ADJ
ejpam-7112	42	16	mean	mean	NOUN
ejpam-7112	42	17	value	value	NOUN
ejpam-7112	42	18	to	to	PART
ejpam-7112	42	19	compute	compute	VERB
ejpam-7112	42	20	the	the	DET
ejpam-7112	42	21	derivative	derivative	NOUN
ejpam-7112	42	22	.	.	PUNCT
ejpam-7112	43	1	they	they	PRON
ejpam-7112	43	2	proved	prove	VERB
ejpam-7112	43	3	that	that	SCONJ
ejpam-7112	43	4	this	this	DET
ejpam-7112	43	5	novel	novel	ADJ
ejpam-7112	43	6	quadrature	quadrature	NOUN
ejpam-7112	43	7	scheme	scheme	NOUN
ejpam-7112	43	8	provided	provide	VERB
ejpam-7112	43	9	an	an	DET
ejpam-7112	43	10	improvement	improvement	NOUN
ejpam-7112	43	11	of	of	ADP
ejpam-7112	43	12	a	a	DET
ejpam-7112	43	13	single	single	ADJ
ejpam-7112	43	14	order	order	NOUN
ejpam-7112	43	15	in	in	ADP
ejpam-7112	43	16	precision	precision	NOUN
ejpam-7112	43	17	against	against	ADP
ejpam-7112	43	18	the	the	DET
ejpam-7112	43	19	traditional	traditional	ADJ
ejpam-7112	43	20	closed	closed	ADJ
ejpam-7112	43	21	quadrature	quadrature	NOUN
ejpam-7112	43	22	by	by	ADP
ejpam-7112	43	23	newton	newton	PROPN
ejpam-7112	43	24	and	and	CCONJ
ejpam-7112	43	25	cotes	cotes	PROPN
ejpam-7112	43	26	.	.	PUNCT
ejpam-7112	44	1	in	in	ADP
ejpam-7112	44	2	2016	2016	NUM
ejpam-7112	44	3	,	,	PUNCT
ejpam-7112	44	4	ramachandran	ramachandran	PROPN
ejpam-7112	44	5	et	et	PROPN
ejpam-7112	44	6	al	al	PROPN
ejpam-7112	44	7	.	.	PUNCT
ejpam-7112	45	1	[	[	X
ejpam-7112	45	2	8	8	NUM
ejpam-7112	45	3	]	]	PUNCT
ejpam-7112	45	4	developed	develop	VERB
ejpam-7112	45	5	another	another	DET
ejpam-7112	45	6	closed	closed	ADJ
ejpam-7112	45	7	-	-	PUNCT
ejpam-7112	45	8	form	form	NOUN
ejpam-7112	45	9	novel	novel	NOUN
ejpam-7112	45	10	quadrature	quadrature	NOUN
ejpam-7112	45	11	approach	approach	NOUN
ejpam-7112	45	12	that	that	PRON
ejpam-7112	45	13	used	use	VERB
ejpam-7112	45	14	the	the	DET
ejpam-7112	45	15	harmonic	harmonic	ADJ
ejpam-7112	45	16	mean	mean	NOUN
ejpam-7112	45	17	value	value	NOUN
ejpam-7112	45	18	to	to	PART
ejpam-7112	45	19	compute	compute	VERB
ejpam-7112	45	20	the	the	DET
ejpam-7112	45	21	derivative	derivative	NOUN
ejpam-7112	45	22	.	.	PUNCT
ejpam-7112	46	1	they	they	PRON
ejpam-7112	46	2	proved	prove	VERB
ejpam-7112	46	3	that	that	SCONJ
ejpam-7112	46	4	this	this	DET
ejpam-7112	46	5	novel	novel	ADJ
ejpam-7112	46	6	quadrature	quadrature	NOUN
ejpam-7112	46	7	scheme	scheme	NOUN
ejpam-7112	46	8	provided	provide	VERB
ejpam-7112	46	9	an	an	DET
ejpam-7112	46	10	improvement	improvement	NOUN
ejpam-7112	46	11	of	of	ADP
ejpam-7112	46	12	a	a	DET
ejpam-7112	46	13	single	single	ADJ
ejpam-7112	46	14	order	order	NOUN
ejpam-7112	46	15	in	in	ADP
ejpam-7112	46	16	precision	precision	NOUN
ejpam-7112	46	17	over	over	ADP
ejpam-7112	46	18	the	the	DET
ejpam-7112	46	19	closed	closed	ADJ
ejpam-7112	46	20	newton	newton	PROPN
ejpam-7112	46	21	-	-	PUNCT
ejpam-7112	46	22	cotes	cote	NOUN
ejpam-7112	46	23	quadrature	quadrature	NOUN
ejpam-7112	46	24	formula	formula	NOUN
ejpam-7112	46	25	.	.	PUNCT
ejpam-7112	47	1	ramachandran	ramachandran	PROPN
ejpam-7112	47	2	et	et	PROPN
ejpam-7112	47	3	al	al	PROPN
ejpam-7112	47	4	.	.	PUNCT
ejpam-7112	48	1	[	[	X
ejpam-7112	48	2	9	9	NUM
ejpam-7112	48	3	]	]	PUNCT
ejpam-7112	48	4	performed	perform	VERB
ejpam-7112	48	5	a	a	DET
ejpam-7112	48	6	test	test	NOUN
ejpam-7112	48	7	k.	k.	PROPN
ejpam-7112	48	8	memon	memon	PROPN
ejpam-7112	48	9	et	et	PROPN
ejpam-7112	48	10	al	al	PROPN
ejpam-7112	48	11	.	.	PUNCT
ejpam-7112	48	12	/	/	SYM
ejpam-7112	48	13	eur	eur	PROPN
ejpam-7112	48	14	.	.	PUNCT
ejpam-7112	49	1	j.	j.	PROPN
ejpam-7112	49	2	pure	pure	PROPN
ejpam-7112	49	3	appl	appl	PROPN
ejpam-7112	49	4	.	.	PROPN
ejpam-7112	49	5	math	math	PROPN
ejpam-7112	49	6	,	,	PUNCT
ejpam-7112	49	7	18	18	NUM
ejpam-7112	49	8	(	(	PUNCT
ejpam-7112	49	9	4	4	NUM
ejpam-7112	49	10	)	)	PUNCT
ejpam-7112	49	11	(	(	PUNCT
ejpam-7112	49	12	2025	2025	NUM
ejpam-7112	49	13	)	)	PUNCT
ejpam-7112	49	14	,	,	PUNCT
ejpam-7112	49	15	7112	7112	NUM
ejpam-7112	49	16	3	3	NUM
ejpam-7112	49	17	of	of	ADP
ejpam-7112	49	18	38	38	NUM
ejpam-7112	49	19	among	among	ADP
ejpam-7112	49	20	three	three	NUM
ejpam-7112	49	21	derivative	derivative	NOUN
ejpam-7112	49	22	-	-	PUNCT
ejpam-7112	49	23	based	base	VERB
ejpam-7112	49	24	closed	closed	ADJ
ejpam-7112	49	25	newton	newton	PROPN
ejpam-7112	49	26	-	-	PUNCT
ejpam-7112	49	27	cotes	cote	NOUN
ejpam-7112	49	28	quadrature	quadrature	NOUN
ejpam-7112	49	29	schemes	scheme	NOUN
ejpam-7112	49	30	which	which	PRON
ejpam-7112	49	31	were	be	AUX
ejpam-7112	49	32	proposed	propose	VERB
ejpam-7112	49	33	in	in	ADP
ejpam-7112	49	34	[	[	X
ejpam-7112	49	35	4	4	NUM
ejpam-7112	49	36	,	,	PUNCT
ejpam-7112	49	37	7	7	NUM
ejpam-7112	49	38	,	,	PUNCT
ejpam-7112	49	39	8	8	NUM
ejpam-7112	49	40	]	]	PUNCT
ejpam-7112	49	41	.	.	PUNCT
ejpam-7112	50	1	according	accord	VERB
ejpam-7112	50	2	to	to	ADP
ejpam-7112	50	3	the	the	DET
ejpam-7112	50	4	comparison	comparison	NOUN
ejpam-7112	50	5	,	,	PUNCT
ejpam-7112	50	6	the	the	DET
ejpam-7112	50	7	arithmetic	arithmetic	ADJ
ejpam-7112	50	8	mean	mean	NOUN
ejpam-7112	50	9	derivative	derivative	NOUN
ejpam-7112	50	10	-	-	PUNCT
ejpam-7112	50	11	based	base	VERB
ejpam-7112	50	12	rule	rule	NOUN
ejpam-7112	50	13	was	be	AUX
ejpam-7112	50	14	much	much	ADV
ejpam-7112	50	15	more	more	ADV
ejpam-7112	50	16	effective	effective	ADJ
ejpam-7112	50	17	than	than	ADP
ejpam-7112	50	18	the	the	DET
ejpam-7112	50	19	other	other	ADJ
ejpam-7112	50	20	schemes	scheme	NOUN
ejpam-7112	50	21	.	.	PUNCT
ejpam-7112	51	1	moreover	moreover	ADV
ejpam-7112	51	2	,	,	PUNCT
ejpam-7112	51	3	ramachandran	ramachandran	PROPN
ejpam-7112	51	4	et	et	PROPN
ejpam-7112	51	5	al	al	PROPN
ejpam-7112	51	6	.	.	PUNCT
ejpam-7112	52	1	[	[	X
ejpam-7112	52	2	10]-[11	10]-[11	X
ejpam-7112	52	3	]	]	PUNCT
ejpam-7112	52	4	developed	develop	VERB
ejpam-7112	52	5	the	the	DET
ejpam-7112	52	6	closed	closed	ADJ
ejpam-7112	52	7	newton	newton	PROPN
ejpam-7112	52	8	-	-	PUNCT
ejpam-7112	52	9	cotes	cotes	PROPN
ejpam-7112	52	10	scheme	scheme	NOUN
ejpam-7112	52	11	to	to	PART
ejpam-7112	52	12	evaluate	evaluate	VERB
ejpam-7112	52	13	function	function	NOUN
ejpam-7112	52	14	derivatives	derivative	NOUN
ejpam-7112	52	15	using	use	VERB
ejpam-7112	52	16	heronian	heronian	ADJ
ejpam-7112	52	17	mean	mean	NOUN
ejpam-7112	52	18	and	and	CCONJ
ejpam-7112	52	19	centroidal	centroidal	PROPN
ejpam-7112	52	20	mean	mean	NOUN
ejpam-7112	52	21	.	.	PUNCT
ejpam-7112	53	1	they	they	PRON
ejpam-7112	53	2	proved	prove	VERB
ejpam-7112	53	3	that	that	SCONJ
ejpam-7112	53	4	these	these	DET
ejpam-7112	53	5	novel	novel	ADJ
ejpam-7112	53	6	quadrature	quadrature	NOUN
ejpam-7112	53	7	schemes	scheme	NOUN
ejpam-7112	53	8	provide	provide	VERB
ejpam-7112	53	9	an	an	DET
ejpam-7112	53	10	improvement	improvement	NOUN
ejpam-7112	53	11	of	of	ADP
ejpam-7112	53	12	a	a	DET
ejpam-7112	53	13	single	single	ADJ
ejpam-7112	53	14	order	order	NOUN
ejpam-7112	53	15	in	in	ADP
ejpam-7112	53	16	precision	precision	NOUN
ejpam-7112	53	17	over	over	ADP
ejpam-7112	53	18	the	the	DET
ejpam-7112	53	19	closed	closed	ADJ
ejpam-7112	53	20	newton	newton	PROPN
ejpam-7112	53	21	-	-	PUNCT
ejpam-7112	53	22	cotes	cote	NOUN
ejpam-7112	53	23	quadrature	quadrature	NOUN
ejpam-7112	53	24	formula	formula	NOUN
ejpam-7112	53	25	.	.	PUNCT
ejpam-7112	54	1	the	the	DET
ejpam-7112	54	2	work	work	NOUN
ejpam-7112	54	3	in	in	ADP
ejpam-7112	54	4	[	[	X
ejpam-7112	54	5	12	12	NUM
ejpam-7112	54	6	]	]	X
ejpam-7112	54	7	encouraged	encouraged	ADJ
ejpam-7112	54	8	proposition	proposition	NOUN
ejpam-7112	54	9	of	of	ADP
ejpam-7112	54	10	time	time	NOUN
ejpam-7112	54	11	and	and	CCONJ
ejpam-7112	54	12	cost	cost	VERB
ejpam-7112	54	13	effective	effective	ADJ
ejpam-7112	54	14	quadrature	quadrature	NOUN
ejpam-7112	54	15	schemes	scheme	NOUN
ejpam-7112	54	16	by	by	ADP
ejpam-7112	54	17	utilizing	utilize	VERB
ejpam-7112	54	18	derivative	derivative	ADJ
ejpam-7112	54	19	corrections	correction	NOUN
ejpam-7112	54	20	as	as	ADP
ejpam-7112	54	21	a	a	DET
ejpam-7112	54	22	better	well	ADJ
ejpam-7112	54	23	and	and	CCONJ
ejpam-7112	54	24	efficient	efficient	ADJ
ejpam-7112	54	25	way	way	NOUN
ejpam-7112	54	26	to	to	PART
ejpam-7112	54	27	enhance	enhance	VERB
ejpam-7112	54	28	the	the	DET
ejpam-7112	54	29	accuracy	accuracy	NOUN
ejpam-7112	54	30	and	and	CCONJ
ejpam-7112	54	31	precision	precision	NOUN
ejpam-7112	54	32	of	of	ADP
ejpam-7112	54	33	riemann	riemann	PROPN
ejpam-7112	54	34	integral	integral	ADJ
ejpam-7112	54	35	approximations	approximation	NOUN
ejpam-7112	54	36	as	as	ADV
ejpam-7112	54	37	well	well	ADV
ejpam-7112	54	38	.	.	PUNCT
ejpam-7112	55	1	in	in	ADP
ejpam-7112	55	2	recent	recent	ADJ
ejpam-7112	55	3	years	year	NOUN
ejpam-7112	55	4	,	,	PUNCT
ejpam-7112	55	5	some	some	DET
ejpam-7112	55	6	work	work	NOUN
ejpam-7112	55	7	has	have	AUX
ejpam-7112	55	8	been	be	AUX
ejpam-7112	55	9	focused	focus	VERB
ejpam-7112	55	10	on	on	ADP
ejpam-7112	55	11	the	the	DET
ejpam-7112	55	12	approximation	approximation	NOUN
ejpam-7112	55	13	of	of	ADP
ejpam-7112	55	14	rs	rs	ADJ
ejpam-7112	55	15	-	-	ADJ
ejpam-7112	55	16	integral	integral	ADJ
ejpam-7112	55	17	using	use	VERB
ejpam-7112	55	18	different	different	ADJ
ejpam-7112	55	19	means	mean	NOUN
ejpam-7112	55	20	,	,	PUNCT
ejpam-7112	55	21	but	but	CCONJ
ejpam-7112	55	22	with	with	ADP
ejpam-7112	55	23	more	more	ADJ
ejpam-7112	55	24	nodal	nodal	NOUN
ejpam-7112	55	25	points	point	NOUN
ejpam-7112	55	26	in	in	ADP
ejpam-7112	55	27	the	the	DET
ejpam-7112	55	28	sense	sense	NOUN
ejpam-7112	55	29	of	of	ADP
ejpam-7112	55	30	simpson	simpson	PROPN
ejpam-7112	55	31	’s	’s	PART
ejpam-7112	55	32	quadrature	quadrature	NOUN
ejpam-7112	55	33	,	,	PUNCT
ejpam-7112	55	34	for	for	ADP
ejpam-7112	55	35	example	example	NOUN
ejpam-7112	56	1	[	[	X
ejpam-7112	56	2	13	13	NUM
ejpam-7112	56	3	]	]	PUNCT
ejpam-7112	56	4	,	,	PUNCT
ejpam-7112	56	5	[	[	X
ejpam-7112	56	6	14	14	NUM
ejpam-7112	56	7	]	]	PUNCT
ejpam-7112	56	8	and	and	CCONJ
ejpam-7112	56	9	[	[	X
ejpam-7112	56	10	15	15	NUM
ejpam-7112	56	11	]	]	PUNCT
ejpam-7112	56	12	.	.	PUNCT
ejpam-7112	57	1	the	the	DET
ejpam-7112	57	2	applications	application	NOUN
ejpam-7112	57	3	of	of	ADP
ejpam-7112	57	4	the	the	DET
ejpam-7112	57	5	rs	rs	ADJ
ejpam-7112	57	6	-	-	ADJ
ejpam-7112	57	7	integral	integral	ADJ
ejpam-7112	57	8	can	can	AUX
ejpam-7112	57	9	be	be	AUX
ejpam-7112	57	10	further	far	ADV
ejpam-7112	57	11	studied	study	VERB
ejpam-7112	57	12	through	through	ADP
ejpam-7112	57	13	[	[	X
ejpam-7112	57	14	16	16	NUM
ejpam-7112	57	15	]	]	PUNCT
ejpam-7112	57	16	,	,	PUNCT
ejpam-7112	57	17	whereas	whereas	SCONJ
ejpam-7112	57	18	the	the	DET
ejpam-7112	57	19	studies	study	NOUN
ejpam-7112	57	20	[	[	X
ejpam-7112	57	21	17	17	NUM
ejpam-7112	57	22	]	]	PUNCT
ejpam-7112	57	23	and	and	CCONJ
ejpam-7112	57	24	[	[	X
ejpam-7112	57	25	18	18	NUM
ejpam-7112	57	26	]	]	PUNCT
ejpam-7112	57	27	provide	provide	VERB
ejpam-7112	57	28	a	a	DET
ejpam-7112	57	29	way	way	NOUN
ejpam-7112	57	30	forward	forward	ADV
ejpam-7112	57	31	to	to	PART
ejpam-7112	57	32	apply	apply	VERB
ejpam-7112	57	33	the	the	DET
ejpam-7112	57	34	numerical	numerical	ADJ
ejpam-7112	57	35	procedures	procedure	NOUN
ejpam-7112	57	36	in	in	ADP
ejpam-7112	57	37	the	the	DET
ejpam-7112	57	38	mesh	mesh	NOUN
ejpam-7112	57	39	-	-	PUNCT
ejpam-7112	57	40	free	free	ADJ
ejpam-7112	57	41	sense	sense	NOUN
ejpam-7112	57	42	to	to	PART
ejpam-7112	57	43	better	well	ADV
ejpam-7112	57	44	deal	deal	VERB
ejpam-7112	57	45	with	with	ADP
ejpam-7112	57	46	some	some	DET
ejpam-7112	57	47	case	case	NOUN
ejpam-7112	57	48	studies	study	NOUN
ejpam-7112	57	49	in	in	ADP
ejpam-7112	57	50	engineering	engineering	NOUN
ejpam-7112	57	51	science	science	NOUN
ejpam-7112	57	52	.	.	PUNCT
ejpam-7112	58	1	this	this	DET
ejpam-7112	58	2	research	research	NOUN
ejpam-7112	58	3	extends	extend	VERB
ejpam-7112	58	4	some	some	DET
ejpam-7112	58	5	recent	recent	ADJ
ejpam-7112	58	6	derivative	derivative	ADJ
ejpam-7112	58	7	-	-	PUNCT
ejpam-7112	58	8	based	base	VERB
ejpam-7112	58	9	quadrature	quadrature	NOUN
ejpam-7112	58	10	schemes	scheme	NOUN
ejpam-7112	58	11	of	of	ADP
ejpam-7112	58	12	the	the	DET
ejpam-7112	58	13	riemann	riemann	PROPN
ejpam-7112	58	14	integral	integral	PROPN
ejpam-7112	58	15	into	into	ADP
ejpam-7112	58	16	corresponding	correspond	VERB
ejpam-7112	58	17	efficient	efficient	ADJ
ejpam-7112	58	18	derivative	derivative	NOUN
ejpam-7112	58	19	-	-	PUNCT
ejpam-7112	58	20	based	base	VERB
ejpam-7112	58	21	quadrature	quadrature	NOUN
ejpam-7112	58	22	schemes	scheme	NOUN
ejpam-7112	58	23	for	for	ADP
ejpam-7112	58	24	the	the	DET
ejpam-7112	58	25	rs	rs	ADJ
ejpam-7112	58	26	-	-	ADJ
ejpam-7112	58	27	integral	integral	ADJ
ejpam-7112	58	28	using	use	VERB
ejpam-7112	58	29	different	different	ADJ
ejpam-7112	58	30	means	mean	NOUN
ejpam-7112	58	31	.	.	PUNCT
ejpam-7112	59	1	further	far	ADV
ejpam-7112	59	2	,	,	PUNCT
ejpam-7112	59	3	the	the	DET
ejpam-7112	59	4	suggested	suggest	VERB
ejpam-7112	59	5	schemes	scheme	NOUN
ejpam-7112	59	6	include	include	VERB
ejpam-7112	59	7	the	the	DET
ejpam-7112	59	8	work	work	NOUN
ejpam-7112	59	9	of	of	ADP
ejpam-7112	59	10	zhao	zhao	PROPN
ejpam-7112	59	11	et	et	PROPN
ejpam-7112	59	12	al	al	PROPN
ejpam-7112	59	13	.	.	PUNCT
ejpam-7112	60	1	[	[	X
ejpam-7112	60	2	5	5	NUM
ejpam-7112	60	3	]	]	PUNCT
ejpam-7112	60	4	for	for	ADP
ejpam-7112	60	5	the	the	DET
ejpam-7112	60	6	rs	rs	NOUN
ejpam-7112	60	7	-	-	ADJ
ejpam-7112	60	8	integral	integral	ADJ
ejpam-7112	60	9	with	with	ADP
ejpam-7112	60	10	modification	modification	NOUN
ejpam-7112	60	11	.	.	PUNCT
ejpam-7112	61	1	the	the	DET
ejpam-7112	61	2	suggested	suggest	VERB
ejpam-7112	61	3	schemes	scheme	NOUN
ejpam-7112	61	4	are	be	AUX
ejpam-7112	61	5	much	much	ADV
ejpam-7112	61	6	more	more	ADV
ejpam-7112	61	7	effective	effective	ADJ
ejpam-7112	61	8	than	than	ADP
ejpam-7112	61	9	the	the	DET
ejpam-7112	61	10	zhao	zhao	PROPN
ejpam-7112	61	11	et	et	PROPN
ejpam-7112	61	12	al	al	PROPN
ejpam-7112	61	13	.	.	PUNCT
ejpam-7112	62	1	[	[	X
ejpam-7112	62	2	5	5	NUM
ejpam-7112	62	3	]	]	PUNCT
ejpam-7112	62	4	scheme	scheme	NOUN
ejpam-7112	62	5	in	in	ADP
ejpam-7112	62	6	comparison	comparison	NOUN
ejpam-7112	62	7	.	.	PUNCT
ejpam-7112	63	1	the	the	DET
ejpam-7112	63	2	composite	composite	ADJ
ejpam-7112	63	3	form	form	NOUN
ejpam-7112	63	4	is	be	AUX
ejpam-7112	63	5	involved	involve	VERB
ejpam-7112	63	6	for	for	ADP
ejpam-7112	63	7	the	the	DET
ejpam-7112	63	8	purpose	purpose	NOUN
ejpam-7112	63	9	of	of	ADP
ejpam-7112	63	10	reducing	reduce	VERB
ejpam-7112	63	11	errors	error	NOUN
ejpam-7112	63	12	.	.	PUNCT
ejpam-7112	64	1	the	the	DET
ejpam-7112	64	2	derivations	derivation	NOUN
ejpam-7112	64	3	of	of	ADP
ejpam-7112	64	4	suggested	suggest	VERB
ejpam-7112	64	5	schemes	scheme	NOUN
ejpam-7112	64	6	are	be	AUX
ejpam-7112	64	7	proved	prove	VERB
ejpam-7112	64	8	in	in	ADP
ejpam-7112	64	9	composite	composite	ADJ
ejpam-7112	64	10	form	form	NOUN
ejpam-7112	64	11	for	for	ADP
ejpam-7112	64	12	the	the	DET
ejpam-7112	64	13	rs	rs	ADJ
ejpam-7112	64	14	-	-	ADJ
ejpam-7112	64	15	integral	integral	ADJ
ejpam-7112	64	16	and	and	CCONJ
ejpam-7112	64	17	used	use	VERB
ejpam-7112	64	18	for	for	ADP
ejpam-7112	64	19	the	the	DET
ejpam-7112	64	20	numerical	numerical	ADJ
ejpam-7112	64	21	experiments	experiment	NOUN
ejpam-7112	64	22	.	.	PUNCT
ejpam-7112	65	1	finally	finally	ADV
ejpam-7112	65	2	,	,	PUNCT
ejpam-7112	65	3	the	the	DET
ejpam-7112	65	4	theoretical	theoretical	ADJ
ejpam-7112	65	5	and	and	CCONJ
ejpam-7112	65	6	numerical	numerical	ADJ
ejpam-7112	65	7	results	result	NOUN
ejpam-7112	65	8	tailor	tailor	VERB
ejpam-7112	65	9	the	the	DET
ejpam-7112	65	10	time	time	NOUN
ejpam-7112	65	11	and	and	CCONJ
ejpam-7112	65	12	cost	cost	NOUN
ejpam-7112	65	13	effectiveness	effectiveness	NOUN
ejpam-7112	65	14	of	of	ADP
ejpam-7112	65	15	the	the	DET
ejpam-7112	65	16	proposed	propose	VERB
ejpam-7112	65	17	quadrature	quadrature	NOUN
ejpam-7112	65	18	in	in	ADP
ejpam-7112	65	19	terms	term	NOUN
ejpam-7112	65	20	of	of	ADP
ejpam-7112	65	21	standard	standard	ADJ
ejpam-7112	65	22	parameters	parameter	NOUN
ejpam-7112	65	23	,	,	PUNCT
ejpam-7112	65	24	like	like	ADP
ejpam-7112	65	25	:	:	PUNCT
ejpam-7112	65	26	absolute	absolute	ADJ
ejpam-7112	65	27	error	error	NOUN
ejpam-7112	65	28	,	,	PUNCT
ejpam-7112	65	29	cost	cost	NOUN
ejpam-7112	65	30	,	,	PUNCT
ejpam-7112	65	31	and	and	CCONJ
ejpam-7112	65	32	cpu	cpu	NOUN
ejpam-7112	65	33	times	time	NOUN
ejpam-7112	65	34	.	.	PUNCT
ejpam-7112	66	1	2	2	X
ejpam-7112	66	2	.	.	X
ejpam-7112	66	3	materials	material	NOUN
ejpam-7112	66	4	and	and	CCONJ
ejpam-7112	66	5	methods	method	NOUN
ejpam-7112	66	6	2.1	2.1	NUM
ejpam-7112	66	7	.	.	PUNCT
ejpam-7112	67	1	basics	basic	NOUN
ejpam-7112	67	2	of	of	ADP
ejpam-7112	67	3	riemann	riemann	PROPN
ejpam-7112	67	4	and	and	CCONJ
ejpam-7112	67	5	riemann	riemann	PROPN
ejpam-7112	67	6	-	-	PUNCT
ejpam-7112	67	7	stieltjes	stieltjes	PROPN
ejpam-7112	67	8	integrals	integral	NOUN
ejpam-7112	67	9	and	and	CCONJ
ejpam-7112	67	10	their	their	PRON
ejpam-7112	67	11	existing	exist	VERB
ejpam-7112	67	12	quadrature	quadrature	NOUN
ejpam-7112	67	13	for	for	ADP
ejpam-7112	67	14	integrating	integrate	VERB
ejpam-7112	67	15	a	a	DET
ejpam-7112	67	16	function	function	NOUN
ejpam-7112	67	17	f(x	f(x	PROPN
ejpam-7112	67	18	)	)	PUNCT
ejpam-7112	67	19	from	from	ADP
ejpam-7112	67	20	x	x	X
ejpam-7112	67	21	=	=	PUNCT
ejpam-7112	67	22	a	a	PRON
ejpam-7112	67	23	to	to	PART
ejpam-7112	67	24	x	x	PROPN
ejpam-7112	67	25	=	=	SYM
ejpam-7112	67	26	b	b	PROPN
ejpam-7112	67	27	,	,	PUNCT
ejpam-7112	67	28	the	the	DET
ejpam-7112	67	29	basic	basic	ADJ
ejpam-7112	67	30	riemann	riemann	PROPN
ejpam-7112	67	31	notation	notation	NOUN
ejpam-7112	67	32	is	be	AUX
ejpam-7112	67	33	:	:	PUNCT
ejpam-7112	67	34	i(f	i(f	NOUN
ejpam-7112	67	35	;	;	PUNCT
ejpam-7112	67	36	a	a	DET
ejpam-7112	67	37	,	,	PUNCT
ejpam-7112	67	38	b	b	NOUN
ejpam-7112	67	39	)	)	PUNCT
ejpam-7112	67	40	=	=	SYM
ejpam-7112	68	1	∫	∫	PROPN
ejpam-7112	68	2	b	b	PROPN
ejpam-7112	68	3	a	a	DET
ejpam-7112	68	4	f(x	f(x	PROPN
ejpam-7112	68	5	)	)	PUNCT
ejpam-7112	68	6	dx	dx	PROPN
ejpam-7112	68	7	(	(	PUNCT
ejpam-7112	68	8	1	1	NUM
ejpam-7112	68	9	)	)	PUNCT
ejpam-7112	68	10	geometrically	geometrically	ADV
ejpam-7112	68	11	,	,	PUNCT
ejpam-7112	68	12	i(f	i(f	PROPN
ejpam-7112	68	13	;	;	PUNCT
ejpam-7112	68	14	a	a	DET
ejpam-7112	68	15	,	,	PUNCT
ejpam-7112	68	16	b)represents	b)represents	NUM
ejpam-7112	68	17	area	area	NOUN
ejpam-7112	68	18	bounded	bound	VERB
ejpam-7112	68	19	between	between	ADP
ejpam-7112	68	20	f(x	f(x	PROPN
ejpam-7112	68	21	)	)	PUNCT
ejpam-7112	68	22	and	and	CCONJ
ejpam-7112	68	23	x	x	NOUN
ejpam-7112	68	24	-	-	NOUN
ejpam-7112	68	25	axis	axis	ADJ
ejpam-7112	68	26	when	when	SCONJ
ejpam-7112	68	27	x	x	PRON
ejpam-7112	68	28	varies	vary	VERB
ejpam-7112	68	29	from	from	ADP
ejpam-7112	68	30	a	a	PRON
ejpam-7112	68	31	to	to	AUX
ejpam-7112	68	32	b.	b.	PROPN
ejpam-7112	68	33	the	the	DET
ejpam-7112	68	34	rs	rs	ADJ
ejpam-7112	68	35	-	-	ADJ
ejpam-7112	68	36	integral	integral	ADJ
ejpam-7112	68	37	advances	advance	NOUN
ejpam-7112	68	38	the	the	DET
ejpam-7112	68	39	riemann	riemann	PROPN
ejpam-7112	68	40	concept	concept	NOUN
ejpam-7112	68	41	of	of	ADP
ejpam-7112	68	42	integration	integration	NOUN
ejpam-7112	68	43	,	,	PUNCT
ejpam-7112	68	44	which	which	PRON
ejpam-7112	68	45	was	be	AUX
ejpam-7112	68	46	limited	limit	VERB
ejpam-7112	68	47	to	to	ADP
ejpam-7112	68	48	integrating	integrate	VERB
ejpam-7112	68	49	a	a	DET
ejpam-7112	68	50	function	function	NOUN
ejpam-7112	68	51	f(x	f(x	PROPN
ejpam-7112	68	52	)	)	PUNCT
ejpam-7112	68	53	in	in	ADP
ejpam-7112	68	54	a	a	DET
ejpam-7112	68	55	segment	segment	NOUN
ejpam-7112	68	56	of	of	ADP
ejpam-7112	68	57	the	the	DET
ejpam-7112	68	58	set	set	NOUN
ejpam-7112	68	59	of	of	ADP
ejpam-7112	68	60	real	real	ADJ
ejpam-7112	68	61	numbers	number	NOUN
ejpam-7112	68	62	.	.	PUNCT
ejpam-7112	69	1	the	the	DET
ejpam-7112	69	2	rsintegral	rsintegral	ADJ
ejpam-7112	69	3	utilizes	utilizes	ADJ
ejpam-7112	69	4	integrator	integrator	NOUN
ejpam-7112	69	5	which	which	PRON
ejpam-7112	69	6	is	be	AUX
ejpam-7112	69	7	another	another	DET
ejpam-7112	69	8	function	function	NOUN
ejpam-7112	69	9	of	of	ADP
ejpam-7112	69	10	x	x	X
ejpam-7112	69	11	,	,	PUNCT
ejpam-7112	69	12	and	and	CCONJ
ejpam-7112	69	13	also	also	ADV
ejpam-7112	69	14	monotonic	monotonic	ADJ
ejpam-7112	69	15	rising	rise	VERB
ejpam-7112	69	16	but	but	CCONJ
ejpam-7112	69	17	bounded	bound	VERB
ejpam-7112	69	18	.	.	PUNCT
ejpam-7112	70	1	therefore	therefore	ADV
ejpam-7112	70	2	,	,	PUNCT
ejpam-7112	70	3	it	it	PRON
ejpam-7112	70	4	is	be	AUX
ejpam-7112	70	5	important	important	ADJ
ejpam-7112	70	6	to	to	PART
ejpam-7112	70	7	frame	frame	VERB
ejpam-7112	70	8	and	and	CCONJ
ejpam-7112	70	9	analyze	analyze	VERB
ejpam-7112	70	10	the	the	DET
ejpam-7112	70	11	latter	latter	ADJ
ejpam-7112	70	12	instance	instance	NOUN
ejpam-7112	70	13	geometrically	geometrically	ADV
ejpam-7112	70	14	in	in	ADP
ejpam-7112	70	15	three	three	NUM
ejpam-7112	70	16	dimensions	dimension	NOUN
ejpam-7112	70	17	.	.	PUNCT
ejpam-7112	71	1	the	the	DET
ejpam-7112	71	2	rs	rs	ADJ
ejpam-7112	71	3	-	-	ADJ
ejpam-7112	71	4	integral	integral	ADJ
ejpam-7112	71	5	notation	notation	NOUN
ejpam-7112	71	6	can	can	AUX
ejpam-7112	71	7	be	be	AUX
ejpam-7112	71	8	describes	describe	NOUN
ejpam-7112	71	9	as	as	ADP
ejpam-7112	71	10	:	:	PUNCT
ejpam-7112	71	11	rs(f	rs(f	NUM
ejpam-7112	71	12	;	;	PUNCT
ejpam-7112	72	1	g	g	NOUN
ejpam-7112	72	2	;	;	PUNCT
ejpam-7112	72	3	a	a	DET
ejpam-7112	72	4	,	,	PUNCT
ejpam-7112	72	5	b	b	NOUN
ejpam-7112	72	6	)	)	PUNCT
ejpam-7112	72	7	=	=	SYM
ejpam-7112	73	1	∫	∫	PROPN
ejpam-7112	73	2	b	b	PROPN
ejpam-7112	73	3	a	a	DET
ejpam-7112	73	4	f(t	f(t	PROPN
ejpam-7112	73	5	)	)	PUNCT
ejpam-7112	73	6	dα(t	dα(t	NOUN
ejpam-7112	73	7	)	)	PUNCT
ejpam-7112	73	8	(	(	PUNCT
ejpam-7112	73	9	2	2	X
ejpam-7112	73	10	)	)	PUNCT
ejpam-7112	73	11	k.	k.	PROPN
ejpam-7112	73	12	memon	memon	PROPN
ejpam-7112	73	13	et	et	PROPN
ejpam-7112	73	14	al	al	PROPN
ejpam-7112	73	15	.	.	PUNCT
ejpam-7112	73	16	/	/	SYM
ejpam-7112	73	17	eur	eur	PROPN
ejpam-7112	73	18	.	.	PUNCT
ejpam-7112	74	1	j.	j.	PROPN
ejpam-7112	74	2	pure	pure	PROPN
ejpam-7112	74	3	appl	appl	PROPN
ejpam-7112	74	4	.	.	PROPN
ejpam-7112	74	5	math	math	PROPN
ejpam-7112	74	6	,	,	PUNCT
ejpam-7112	74	7	18	18	NUM
ejpam-7112	74	8	(	(	PUNCT
ejpam-7112	74	9	4	4	NUM
ejpam-7112	74	10	)	)	PUNCT
ejpam-7112	74	11	(	(	PUNCT
ejpam-7112	74	12	2025	2025	NUM
ejpam-7112	74	13	)	)	PUNCT
ejpam-7112	74	14	,	,	PUNCT
ejpam-7112	74	15	7112	7112	NUM
ejpam-7112	74	16	4	4	NUM
ejpam-7112	74	17	of	of	ADP
ejpam-7112	74	18	38	38	NUM
ejpam-7112	74	19	figure	figure	NOUN
ejpam-7112	74	20	1	1	NUM
ejpam-7112	74	21	:	:	PUNCT
ejpam-7112	74	22	geometrical	geometrical	ADJ
ejpam-7112	74	23	representation	representation	NOUN
ejpam-7112	74	24	of	of	ADP
ejpam-7112	74	25	riemann	riemann	PROPN
ejpam-7112	74	26	integral	integral	PROPN
ejpam-7112	74	27	where	where	SCONJ
ejpam-7112	74	28	integrator	integrator	NOUN
ejpam-7112	74	29	is	be	AUX
ejpam-7112	74	30	increasing	increase	VERB
ejpam-7112	74	31	there	there	ADV
ejpam-7112	74	32	with	with	ADP
ejpam-7112	74	33	both	both	CCONJ
ejpam-7112	74	34	continuous	continuous	ADJ
ejpam-7112	74	35	integrand	integrand	NOUN
ejpam-7112	74	36	and	and	CCONJ
ejpam-7112	74	37	integrator	integrator	NOUN
ejpam-7112	74	38	in	in	ADP
ejpam-7112	74	39	the	the	DET
ejpam-7112	74	40	interval	interval	NOUN
ejpam-7112	74	41	of	of	ADP
ejpam-7112	74	42	integration	integration	NOUN
ejpam-7112	74	43	.	.	PUNCT
ejpam-7112	75	1	the	the	DET
ejpam-7112	75	2	width	width	NOUN
ejpam-7112	75	3	of	of	ADP
ejpam-7112	75	4	a	a	DET
ejpam-7112	75	5	sub	sub	NOUN
ejpam-7112	75	6	-	-	ADJ
ejpam-7112	75	7	rectangle	rectangle	NOUN
ejpam-7112	75	8	can	can	AUX
ejpam-7112	75	9	be	be	AUX
ejpam-7112	75	10	computed	compute	VERB
ejpam-7112	75	11	by	by	ADP
ejpam-7112	75	12	differences	difference	NOUN
ejpam-7112	75	13	in	in	ADP
ejpam-7112	75	14	the	the	DET
ejpam-7112	75	15	precise	precise	ADJ
ejpam-7112	75	16	values	value	NOUN
ejpam-7112	75	17	of	of	ADP
ejpam-7112	75	18	x	x	PUNCT
ejpam-7112	75	19	in	in	ADP
ejpam-7112	75	20	that	that	DET
ejpam-7112	75	21	sub	sub	NOUN
ejpam-7112	75	22	-	-	NOUN
ejpam-7112	75	23	interval	interval	NOUN
ejpam-7112	75	24	,	,	PUNCT
ejpam-7112	75	25	which	which	PRON
ejpam-7112	75	26	are	be	AUX
ejpam-7112	75	27	the	the	DET
ejpam-7112	75	28	interval	interval	NOUN
ejpam-7112	75	29	’s	’s	PART
ejpam-7112	75	30	end	end	NOUN
ejpam-7112	75	31	points	point	NOUN
ejpam-7112	75	32	in	in	ADP
ejpam-7112	75	33	the	the	DET
ejpam-7112	75	34	riemann	riemann	PROPN
ejpam-7112	75	35	integral	integral	PROPN
ejpam-7112	75	36	.	.	PUNCT
ejpam-7112	76	1	however	however	ADV
ejpam-7112	76	2	,	,	PUNCT
ejpam-7112	76	3	the	the	DET
ejpam-7112	76	4	similar	similar	ADJ
ejpam-7112	76	5	partitioning	partitioning	NOUN
ejpam-7112	76	6	is	be	AUX
ejpam-7112	76	7	done	do	VERB
ejpam-7112	76	8	using	use	VERB
ejpam-7112	76	9	the	the	DET
ejpam-7112	76	10	differences	difference	NOUN
ejpam-7112	76	11	in	in	ADP
ejpam-7112	76	12	the	the	DET
ejpam-7112	76	13	integrator	integrator	NOUN
ejpam-7112	76	14	increasing	increase	VERB
ejpam-7112	76	15	function	function	NOUN
ejpam-7112	76	16	’s	’s	PART
ejpam-7112	76	17	values	value	NOUN
ejpam-7112	76	18	in	in	ADP
ejpam-7112	76	19	the	the	DET
ejpam-7112	76	20	rs	rs	NOUN
ejpam-7112	76	21	-	-	ADJ
ejpam-7112	76	22	integral	integral	ADJ
ejpam-7112	76	23	.	.	PUNCT
ejpam-7112	77	1	the	the	DET
ejpam-7112	77	2	geometrical	geometrical	ADJ
ejpam-7112	77	3	form	form	NOUN
ejpam-7112	77	4	of	of	ADP
ejpam-7112	77	5	the	the	DET
ejpam-7112	77	6	riemann	riemann	PROPN
ejpam-7112	77	7	integral	integral	PROPN
ejpam-7112	77	8	is	be	AUX
ejpam-7112	77	9	shown	show	VERB
ejpam-7112	77	10	in	in	ADP
ejpam-7112	77	11	fig	fig	NOUN
ejpam-7112	77	12	.	.	PUNCT
ejpam-7112	78	1	1	1	NUM
ejpam-7112	78	2	,	,	PUNCT
ejpam-7112	78	3	where	where	SCONJ
ejpam-7112	78	4	the	the	DET
ejpam-7112	78	5	x	x	X
ejpam-7112	78	6	-	-	NOUN
ejpam-7112	78	7	axis	axis	NOUN
ejpam-7112	78	8	is	be	AUX
ejpam-7112	78	9	used	use	VERB
ejpam-7112	78	10	to	to	PART
ejpam-7112	78	11	divide	divide	VERB
ejpam-7112	78	12	the	the	DET
ejpam-7112	78	13	area	area	NOUN
ejpam-7112	78	14	into	into	ADP
ejpam-7112	78	15	rectangles	rectangle	NOUN
ejpam-7112	78	16	,	,	PUNCT
ejpam-7112	78	17	and	and	CCONJ
ejpam-7112	78	18	limiting	limit	VERB
ejpam-7112	78	19	case	case	NOUN
ejpam-7112	78	20	of	of	ADP
ejpam-7112	78	21	areas	area	NOUN
ejpam-7112	78	22	summed	sum	VERB
ejpam-7112	78	23	-	-	PUNCT
ejpam-7112	78	24	up	up	ADP
ejpam-7112	78	25	define	define	VERB
ejpam-7112	78	26	the	the	DET
ejpam-7112	78	27	integral	integral	NOUN
ejpam-7112	78	28	.	.	PUNCT
ejpam-7112	79	1	the	the	DET
ejpam-7112	79	2	similar	similar	ADJ
ejpam-7112	79	3	explanation	explanation	NOUN
ejpam-7112	79	4	on	on	ADP
ejpam-7112	79	5	the	the	DET
ejpam-7112	79	6	rs	rs	ADJ
ejpam-7112	79	7	-	-	ADJ
ejpam-7112	79	8	integral	integral	ADJ
ejpam-7112	79	9	is	be	AUX
ejpam-7112	79	10	explained	explain	VERB
ejpam-7112	79	11	in	in	ADP
ejpam-7112	79	12	fig.2	fig.2	PROPN
ejpam-7112	79	13	.	.	PUNCT
ejpam-7112	80	1	the	the	DET
ejpam-7112	80	2	graphs	graph	NOUN
ejpam-7112	80	3	of	of	ADP
ejpam-7112	80	4	integrator	integrator	NOUN
ejpam-7112	80	5	and	and	CCONJ
ejpam-7112	80	6	integrand	integrand	NOUN
ejpam-7112	80	7	can	can	AUX
ejpam-7112	80	8	be	be	AUX
ejpam-7112	80	9	seen	see	VERB
ejpam-7112	80	10	initially	initially	ADV
ejpam-7112	80	11	in	in	ADP
ejpam-7112	80	12	2d	2d	NUM
ejpam-7112	80	13	plane	plane	NOUN
ejpam-7112	80	14	,	,	PUNCT
ejpam-7112	80	15	each	each	PRON
ejpam-7112	80	16	versus	versus	ADP
ejpam-7112	80	17	the	the	DET
ejpam-7112	80	18	x	x	NOUN
ejpam-7112	80	19	-	-	NOUN
ejpam-7112	80	20	axis	axis	ADJ
ejpam-7112	80	21	,	,	PUNCT
ejpam-7112	80	22	and	and	CCONJ
ejpam-7112	80	23	then	then	ADV
ejpam-7112	80	24	the	the	DET
ejpam-7112	80	25	rectangular	rectangular	ADJ
ejpam-7112	80	26	regions	region	NOUN
ejpam-7112	80	27	that	that	PRON
ejpam-7112	80	28	cover	cover	VERB
ejpam-7112	80	29	the	the	DET
ejpam-7112	80	30	surface	surface	NOUN
ejpam-7112	80	31	area	area	NOUN
ejpam-7112	80	32	using	use	VERB
ejpam-7112	80	33	the	the	DET
ejpam-7112	80	34	rs	rs	ADJ
ejpam-7112	80	35	-	-	ADJ
ejpam-7112	80	36	integral	integral	ADJ
ejpam-7112	80	37	are	be	AUX
ejpam-7112	80	38	identified	identify	VERB
ejpam-7112	80	39	on	on	ADP
ejpam-7112	80	40	the	the	DET
ejpam-7112	80	41	three	three	NUM
ejpam-7112	80	42	-	-	PUNCT
ejpam-7112	80	43	dimensional	dimensional	ADJ
ejpam-7112	80	44	graph	graph	NOUN
ejpam-7112	80	45	.	.	PUNCT
ejpam-7112	81	1	figure	figure	NOUN
ejpam-7112	81	2	2	2	NUM
ejpam-7112	81	3	:	:	PUNCT
ejpam-7112	81	4	geometrical	geometrical	ADJ
ejpam-7112	81	5	representation	representation	NOUN
ejpam-7112	81	6	of	of	ADP
ejpam-7112	81	7	riemann	riemann	PROPN
ejpam-7112	81	8	-	-	PUNCT
ejpam-7112	81	9	stieltjes	stieltjes	NOUN
ejpam-7112	81	10	integral	integral	ADJ
ejpam-7112	81	11	[	[	X
ejpam-7112	81	12	19	19	NUM
ejpam-7112	81	13	]	]	PUNCT
ejpam-7112	81	14	the	the	DET
ejpam-7112	81	15	riemann	riemann	PROPN
ejpam-7112	81	16	notion	notion	NOUN
ejpam-7112	81	17	of	of	ADP
ejpam-7112	81	18	integral	integral	ADJ
ejpam-7112	81	19	i(f	i(f	NOUN
ejpam-7112	81	20	;	;	PUNCT
ejpam-7112	81	21	a	a	DET
ejpam-7112	81	22	,	,	PUNCT
ejpam-7112	81	23	b	b	NOUN
ejpam-7112	81	24	)	)	PUNCT
ejpam-7112	81	25	through	through	ADP
ejpam-7112	81	26	(	(	PUNCT
ejpam-7112	81	27	1	1	NUM
ejpam-7112	81	28	)	)	PUNCT
ejpam-7112	81	29	,	,	PUNCT
ejpam-7112	81	30	when	when	SCONJ
ejpam-7112	81	31	evaluated	evaluated	AUX
ejpam-7112	81	32	numerically	numerically	ADV
ejpam-7112	81	33	using	use	VERB
ejpam-7112	81	34	a	a	DET
ejpam-7112	81	35	quadrature	quadrature	NOUN
ejpam-7112	81	36	scheme	scheme	NOUN
ejpam-7112	81	37	,	,	PUNCT
ejpam-7112	81	38	is	be	AUX
ejpam-7112	81	39	the	the	DET
ejpam-7112	81	40	sum	sum	NOUN
ejpam-7112	81	41	of	of	ADP
ejpam-7112	81	42	products	product	NOUN
ejpam-7112	81	43	of	of	ADP
ejpam-7112	81	44	the	the	DET
ejpam-7112	81	45	integrand	integrand	NOUN
ejpam-7112	81	46	evaluated	evaluate	VERB
ejpam-7112	81	47	at	at	ADP
ejpam-7112	81	48	some	some	DET
ejpam-7112	81	49	finite	finite	ADJ
ejpam-7112	81	50	discrete	discrete	ADJ
ejpam-7112	81	51	points	point	NOUN
ejpam-7112	81	52	and	and	CCONJ
ejpam-7112	81	53	the	the	DET
ejpam-7112	81	54	corresponding	corresponding	ADJ
ejpam-7112	81	55	weights	weight	NOUN
ejpam-7112	81	56	.	.	PUNCT
ejpam-7112	82	1	we	we	PRON
ejpam-7112	82	2	can	can	AUX
ejpam-7112	82	3	write	write	VERB
ejpam-7112	82	4	with	with	ADP
ejpam-7112	82	5	reference	reference	NOUN
ejpam-7112	82	6	to	to	ADP
ejpam-7112	82	7	[	[	X
ejpam-7112	82	8	1	1	NUM
ejpam-7112	82	9	]	]	PUNCT
ejpam-7112	82	10	:	:	PUNCT
ejpam-7112	83	1	i(f	i(f	NOUN
ejpam-7112	83	2	;	;	PUNCT
ejpam-7112	83	3	a	a	DET
ejpam-7112	83	4	,	,	PUNCT
ejpam-7112	83	5	b	b	NOUN
ejpam-7112	83	6	)	)	PUNCT
ejpam-7112	83	7	=	=	SYM
ejpam-7112	83	8	∫	∫	PROPN
ejpam-7112	83	9	b	b	PROPN
ejpam-7112	83	10	a	a	DET
ejpam-7112	83	11	f(x	f(x	PROPN
ejpam-7112	83	12	)	)	PUNCT
ejpam-7112	83	13	dx	dx	PROPN
ejpam-7112	83	14	≈	≈	PROPN
ejpam-7112	83	15	n∑	n∑	PROPN
ejpam-7112	83	16	i=0	i=0	PROPN
ejpam-7112	83	17	wif(xi	wif(xi	X
ejpam-7112	83	18	)	)	PUNCT
ejpam-7112	83	19	(	(	PUNCT
ejpam-7112	83	20	3	3	X
ejpam-7112	83	21	)	)	PUNCT
ejpam-7112	83	22	the	the	DET
ejpam-7112	83	23	quantities	quantity	NOUN
ejpam-7112	83	24	wi	wi	PROPN
ejpam-7112	83	25	and	and	CCONJ
ejpam-7112	83	26	xi	xi	X
ejpam-7112	83	27	=	=	PUNCT
ejpam-7112	84	1	a	a	PRON
ejpam-7112	85	1	+	+	X
ejpam-7112	85	2	ih	ih	NOUN
ejpam-7112	85	3	are	be	AUX
ejpam-7112	85	4	,	,	PUNCT
ejpam-7112	85	5	respectively	respectively	ADV
ejpam-7112	85	6	,	,	PUNCT
ejpam-7112	85	7	the	the	DET
ejpam-7112	85	8	weights	weight	NOUN
ejpam-7112	85	9	and	and	CCONJ
ejpam-7112	85	10	abscissas	abscissa	NOUN
ejpam-7112	85	11	/	/	SYM
ejpam-7112	85	12	nodes	node	NOUN
ejpam-7112	85	13	,	,	PUNCT
ejpam-7112	85	14	where	where	SCONJ
ejpam-7112	85	15	h	h	NOUN
ejpam-7112	85	16	=	=	SYM
ejpam-7112	85	17	b−a	b−a	PROPN
ejpam-7112	85	18	n	n	PROPN
ejpam-7112	85	19	and	and	CCONJ
ejpam-7112	85	20	the	the	DET
ejpam-7112	85	21	index	index	NOUN
ejpam-7112	85	22	i	i	PRON
ejpam-7112	85	23	varies	vary	VERB
ejpam-7112	85	24	from	from	ADP
ejpam-7112	85	25	0	0	NUM
ejpam-7112	85	26	to	to	PART
ejpam-7112	85	27	n.	n.	VERB
ejpam-7112	85	28	the	the	DET
ejpam-7112	85	29	nodes	node	NOUN
ejpam-7112	85	30	can	can	AUX
ejpam-7112	85	31	be	be	AUX
ejpam-7112	85	32	the	the	DET
ejpam-7112	85	33	equally	equally	ADV
ejpam-7112	85	34	-	-	PUNCT
ejpam-7112	85	35	spaced	space	VERB
ejpam-7112	85	36	points	point	NOUN
ejpam-7112	85	37	in	in	ADP
ejpam-7112	85	38	the	the	DET
ejpam-7112	85	39	interval	interval	NOUN
ejpam-7112	85	40	of	of	ADP
ejpam-7112	85	41	integration	integration	NOUN
ejpam-7112	85	42	–	–	PUNCT
ejpam-7112	85	43	as	as	ADP
ejpam-7112	85	44	the	the	DET
ejpam-7112	85	45	case	case	NOUN
ejpam-7112	85	46	of	of	ADP
ejpam-7112	85	47	widely	widely	ADV
ejpam-7112	85	48	used	use	VERB
ejpam-7112	85	49	quadrature	quadrature	NOUN
ejpam-7112	85	50	by	by	ADP
ejpam-7112	85	51	newton	newton	PROPN
ejpam-7112	85	52	and	and	CCONJ
ejpam-7112	85	53	cotes	cotes	PROPN
ejpam-7112	85	54	–	–	PUNCT
ejpam-7112	85	55	or	or	CCONJ
ejpam-7112	85	56	also	also	ADV
ejpam-7112	85	57	zeros	zero	NOUN
ejpam-7112	85	58	of	of	ADP
ejpam-7112	85	59	orthogonal	orthogonal	ADJ
ejpam-7112	85	60	polynomials	polynomial	NOUN
ejpam-7112	85	61	in	in	ADP
ejpam-7112	85	62	the	the	DET
ejpam-7112	85	63	sense	sense	NOUN
ejpam-7112	85	64	of	of	ADP
ejpam-7112	85	65	quadrature	quadrature	NOUN
ejpam-7112	85	66	introduced	introduce	VERB
ejpam-7112	85	67	by	by	ADP
ejpam-7112	85	68	gauss	gauss	PROPN
ejpam-7112	85	69	.	.	PUNCT
ejpam-7112	86	1	the	the	DET
ejpam-7112	86	2	most	most	ADV
ejpam-7112	86	3	basic	basic	ADJ
ejpam-7112	86	4	techniques	technique	NOUN
ejpam-7112	86	5	are	be	AUX
ejpam-7112	86	6	the	the	DET
ejpam-7112	86	7	newton	newton	PROPN
ejpam-7112	86	8	-	-	PUNCT
ejpam-7112	86	9	cotes	cote	NOUN
ejpam-7112	86	10	quadrature	quadrature	NOUN
ejpam-7112	86	11	formulas	formula	NOUN
ejpam-7112	86	12	.	.	PUNCT
ejpam-7112	87	1	the	the	DET
ejpam-7112	87	2	closed	closed	PROPN
ejpam-7112	87	3	newton	newton	PROPN
ejpam-7112	87	4	-	-	PUNCT
ejpam-7112	87	5	cotes	cote	NOUN
ejpam-7112	87	6	quadrature	quadrature	NOUN
ejpam-7112	87	7	formulas	formula	NOUN
ejpam-7112	87	8	include	include	VERB
ejpam-7112	87	9	the	the	DET
ejpam-7112	87	10	end	end	NOUN
ejpam-7112	87	11	points	point	NOUN
ejpam-7112	87	12	of	of	ADP
ejpam-7112	87	13	integration	integration	NOUN
ejpam-7112	87	14	interval	interval	NOUN
ejpam-7112	87	15	[	[	X
ejpam-7112	87	16	a	a	X
ejpam-7112	87	17	,	,	PUNCT
ejpam-7112	87	18	b	b	NOUN
ejpam-7112	87	19	]	]	X
ejpam-7112	87	20	for	for	ADP
ejpam-7112	87	21	evaluating	evaluate	VERB
ejpam-7112	87	22	the	the	DET
ejpam-7112	87	23	integral	integral	NOUN
ejpam-7112	87	24	that	that	PRON
ejpam-7112	87	25	is	be	AUX
ejpam-7112	87	26	described	describe	VERB
ejpam-7112	87	27	as	as	ADP
ejpam-7112	87	28	:	:	PUNCT
ejpam-7112	87	29	i(f	i(f	PROPN
ejpam-7112	87	30	;	;	PUNCT
ejpam-7112	87	31	a	a	DET
ejpam-7112	87	32	,	,	PUNCT
ejpam-7112	87	33	b	b	NOUN
ejpam-7112	87	34	)	)	PUNCT
ejpam-7112	87	35	=	=	SYM
ejpam-7112	88	1	∫	∫	PROPN
ejpam-7112	88	2	b	b	PROPN
ejpam-7112	88	3	a	a	DET
ejpam-7112	88	4	f(x	f(x	PROPN
ejpam-7112	88	5	)	)	PUNCT
ejpam-7112	89	1	dx	dx	PROPN
ejpam-7112	90	1	≈	≈	PROPN
ejpam-7112	90	2	n∑	n∑	PROPN
ejpam-7112	90	3	i=0	i=0	PROPN
ejpam-7112	90	4	wif(x0	wif(x0	PROPN
ejpam-7112	90	5	+	+	CCONJ
ejpam-7112	90	6	ih	ih	NOUN
ejpam-7112	90	7	)	)	PUNCT
ejpam-7112	91	1	(	(	PUNCT
ejpam-7112	91	2	4	4	X
ejpam-7112	91	3	)	)	PUNCT
ejpam-7112	91	4	k.	k.	PROPN
ejpam-7112	91	5	memon	memon	PROPN
ejpam-7112	91	6	et	et	PROPN
ejpam-7112	91	7	al	al	PROPN
ejpam-7112	91	8	.	.	PUNCT
ejpam-7112	91	9	/	/	SYM
ejpam-7112	91	10	eur	eur	PROPN
ejpam-7112	91	11	.	.	PUNCT
ejpam-7112	92	1	j.	j.	PROPN
ejpam-7112	92	2	pure	pure	PROPN
ejpam-7112	92	3	appl	appl	PROPN
ejpam-7112	92	4	.	.	PROPN
ejpam-7112	92	5	math	math	PROPN
ejpam-7112	92	6	,	,	PUNCT
ejpam-7112	92	7	18	18	NUM
ejpam-7112	92	8	(	(	PUNCT
ejpam-7112	92	9	4	4	NUM
ejpam-7112	92	10	)	)	PUNCT
ejpam-7112	92	11	(	(	PUNCT
ejpam-7112	92	12	2025	2025	NUM
ejpam-7112	92	13	)	)	PUNCT
ejpam-7112	92	14	,	,	PUNCT
ejpam-7112	92	15	7112	7112	NUM
ejpam-7112	92	16	5	5	NUM
ejpam-7112	92	17	of	of	ADP
ejpam-7112	92	18	38	38	NUM
ejpam-7112	92	19	there	there	PRON
ejpam-7112	92	20	are	be	VERB
ejpam-7112	92	21	several	several	ADJ
ejpam-7112	92	22	methods	method	NOUN
ejpam-7112	92	23	for	for	ADP
ejpam-7112	92	24	calculating	calculate	VERB
ejpam-7112	92	25	the	the	DET
ejpam-7112	92	26	weighting	weighting	NOUN
ejpam-7112	92	27	coefficients	coefficient	NOUN
ejpam-7112	92	28	in	in	ADP
ejpam-7112	92	29	equation	equation	NOUN
ejpam-7112	92	30	(	(	PUNCT
ejpam-7112	92	31	4	4	NUM
ejpam-7112	92	32	)	)	PUNCT
ejpam-7112	92	33	.	.	PUNCT
ejpam-7112	93	1	one	one	NUM
ejpam-7112	93	2	basic	basic	ADJ
ejpam-7112	93	3	approach	approach	NOUN
ejpam-7112	93	4	of	of	ADP
ejpam-7112	93	5	a	a	DET
ejpam-7112	93	6	quadrature	quadrature	NOUN
ejpam-7112	93	7	formula	formula	NOUN
ejpam-7112	93	8	is	be	AUX
ejpam-7112	93	9	concerned	concern	VERB
ejpam-7112	93	10	with	with	ADP
ejpam-7112	93	11	the	the	DET
ejpam-7112	93	12	precision	precision	NOUN
ejpam-7112	93	13	,	,	PUNCT
ejpam-7112	93	14	in	in	ADP
ejpam-7112	93	15	which	which	PRON
ejpam-7112	93	16	the	the	DET
ejpam-7112	93	17	weight	weight	NOUN
ejpam-7112	93	18	values	value	NOUN
ejpam-7112	93	19	w0	w0	PROPN
ejpam-7112	93	20	,	,	PUNCT
ejpam-7112	93	21	w1	w1	NOUN
ejpam-7112	93	22	,	,	PUNCT
ejpam-7112	93	23	,	,	PUNCT
ejpam-7112	93	24	wnare	wnare	PROPN
ejpam-7112	93	25	considered	consider	VERB
ejpam-7112	93	26	to	to	PART
ejpam-7112	93	27	have	have	VERB
ejpam-7112	93	28	a	a	DET
ejpam-7112	93	29	zero	zero	NUM
ejpam-7112	93	30	approximation	approximation	NOUN
ejpam-7112	93	31	error	error	NOUN
ejpam-7112	93	32	in	in	ADP
ejpam-7112	93	33	equation	equation	NOUN
ejpam-7112	93	34	(	(	PUNCT
ejpam-7112	93	35	4	4	NUM
ejpam-7112	93	36	)	)	PUNCT
ejpam-7112	93	37	,	,	PUNCT
ejpam-7112	93	38	i.e.	i.e.	X
ejpam-7112	93	39	e(f	e(f	PROPN
ejpam-7112	93	40	)	)	PUNCT
ejpam-7112	94	1	=	=	SYM
ejpam-7112	95	1	∫	∫	PROPN
ejpam-7112	95	2	b	b	PROPN
ejpam-7112	95	3	a	a	DET
ejpam-7112	95	4	f(x	f(x	PROPN
ejpam-7112	95	5	)	)	PUNCT
ejpam-7112	95	6	dx−	dx−	NUM
ejpam-7112	95	7	n∑	n∑	PROPN
ejpam-7112	95	8	i=0	i=0	PROPN
ejpam-7112	95	9	wif(xi	wif(xi	X
ejpam-7112	95	10	)	)	PUNCT
ejpam-7112	96	1	=	=	SYM
ejpam-7112	96	2	0	0	PUNCT
ejpam-7112	96	3	(	(	PUNCT
ejpam-7112	96	4	5	5	NUM
ejpam-7112	96	5	)	)	PUNCT
ejpam-7112	96	6	where	where	SCONJ
ejpam-7112	96	7	f(x	f(x	PROPN
ejpam-7112	96	8	)	)	PUNCT
ejpam-7112	96	9	are	be	AUX
ejpam-7112	96	10	monic	monic	ADJ
ejpam-7112	96	11	polynomials	polynomial	NOUN
ejpam-7112	96	12	,	,	PUNCT
ejpam-7112	96	13	where	where	SCONJ
ejpam-7112	96	14	degree	degree	NOUN
ejpam-7112	96	15	j	j	PROPN
ejpam-7112	96	16	varies	vary	VERB
ejpam-7112	96	17	from	from	ADP
ejpam-7112	96	18	0	0	NUM
ejpam-7112	96	19	to	to	PART
ejpam-7112	96	20	n.	n.	VERB
ejpam-7112	96	21	a	a	DET
ejpam-7112	96	22	few	few	ADJ
ejpam-7112	96	23	important	important	ADJ
ejpam-7112	96	24	metrics	metric	NOUN
ejpam-7112	96	25	related	relate	VERB
ejpam-7112	96	26	to	to	ADP
ejpam-7112	96	27	accuracy	accuracy	NOUN
ejpam-7112	96	28	and	and	CCONJ
ejpam-7112	96	29	errors	error	NOUN
ejpam-7112	96	30	associated	associate	VERB
ejpam-7112	96	31	to	to	ADP
ejpam-7112	96	32	quadrature	quadrature	NOUN
ejpam-7112	96	33	rules	rule	NOUN
ejpam-7112	96	34	are	be	AUX
ejpam-7112	96	35	explained	explain	VERB
ejpam-7112	96	36	here	here	ADV
ejpam-7112	96	37	for	for	ADP
ejpam-7112	96	38	accommodating	accommodate	VERB
ejpam-7112	96	39	better	well	ADJ
ejpam-7112	96	40	understanding	understanding	NOUN
ejpam-7112	96	41	of	of	ADP
ejpam-7112	96	42	the	the	DET
ejpam-7112	96	43	forthcoming	forthcoming	ADJ
ejpam-7112	96	44	sections	section	NOUN
ejpam-7112	96	45	.	.	PUNCT
ejpam-7112	97	1	definition	definition	NOUN
ejpam-7112	97	2	1	1	NUM
ejpam-7112	97	3	.	.	PUNCT
ejpam-7112	98	1	if	if	SCONJ
ejpam-7112	98	2	a	a	DET
ejpam-7112	98	3	quadrature	quadrature	NOUN
ejpam-7112	98	4	formula	formula	NOUN
ejpam-7112	98	5	is	be	AUX
ejpam-7112	98	6	able	able	ADJ
ejpam-7112	98	7	to	to	PART
ejpam-7112	98	8	exactly	exactly	ADV
ejpam-7112	98	9	integrate	integrate	VERB
ejpam-7112	98	10	all	all	DET
ejpam-7112	98	11	polynomials	polynomial	NOUN
ejpam-7112	98	12	of	of	ADP
ejpam-7112	98	13	degree	degree	NOUN
ejpam-7112	98	14	up	up	ADP
ejpam-7112	98	15	to	to	ADP
ejpam-7112	98	16	n	n	CCONJ
ejpam-7112	98	17	,	,	PUNCT
ejpam-7112	98	18	but	but	CCONJ
ejpam-7112	98	19	not	not	PART
ejpam-7112	98	20	onward	onward	ADV
ejpam-7112	98	21	,	,	PUNCT
ejpam-7112	98	22	then	then	ADV
ejpam-7112	98	23	we	we	PRON
ejpam-7112	98	24	say	say	VERB
ejpam-7112	98	25	that	that	SCONJ
ejpam-7112	98	26	it	it	PRON
ejpam-7112	98	27	has	have	VERB
ejpam-7112	98	28	a	a	DET
ejpam-7112	98	29	degree	degree	NOUN
ejpam-7112	98	30	of	of	ADP
ejpam-7112	98	31	exactness	exactness	NOUN
ejpam-7112	98	32	/	/	SYM
ejpam-7112	98	33	precision	precision	NOUN
ejpam-7112	98	34	of	of	ADP
ejpam-7112	98	35	n.	n.	NOUN
ejpam-7112	98	36	definition	definition	NOUN
ejpam-7112	98	37	2	2	NUM
ejpam-7112	98	38	.	.	PUNCT
ejpam-7112	99	1	order	order	NOUN
ejpam-7112	99	2	of	of	ADP
ejpam-7112	99	3	accuracy	accuracy	NOUN
ejpam-7112	99	4	of	of	ADP
ejpam-7112	99	5	a	a	DET
ejpam-7112	99	6	quadrature	quadrature	NOUN
ejpam-7112	99	7	formula	formula	NOUN
ejpam-7112	99	8	refers	refer	VERB
ejpam-7112	99	9	to	to	ADP
ejpam-7112	99	10	the	the	DET
ejpam-7112	99	11	exponent	exponent	NOUN
ejpam-7112	99	12	of	of	ADP
ejpam-7112	99	13	the	the	DET
ejpam-7112	99	14	truncation	truncation	NOUN
ejpam-7112	99	15	error	error	NOUN
ejpam-7112	99	16	term	term	NOUN
ejpam-7112	99	17	,	,	PUNCT
ejpam-7112	99	18	and	and	CCONJ
ejpam-7112	99	19	it	it	PRON
ejpam-7112	99	20	indicates	indicate	VERB
ejpam-7112	99	21	decrease	decrease	NOUN
ejpam-7112	99	22	of	of	ADP
ejpam-7112	99	23	error	error	NOUN
ejpam-7112	99	24	as	as	ADP
ejpam-7112	99	25	step	step	NOUN
ejpam-7112	99	26	-	-	PUNCT
ejpam-7112	99	27	size	size	NOUN
ejpam-7112	99	28	decreases	decrease	VERB
ejpam-7112	99	29	.	.	PUNCT
ejpam-7112	100	1	definition	definition	NOUN
ejpam-7112	100	2	3	3	NUM
ejpam-7112	100	3	.	.	PUNCT
ejpam-7112	100	4	general	general	ADJ
ejpam-7112	100	5	truncation	truncation	NOUN
ejpam-7112	100	6	error	error	NOUN
ejpam-7112	100	7	in	in	ADP
ejpam-7112	100	8	a	a	DET
ejpam-7112	100	9	quadrature	quadrature	NOUN
ejpam-7112	100	10	rule	rule	NOUN
ejpam-7112	100	11	which	which	PRON
ejpam-7112	100	12	has	have	VERB
ejpam-7112	100	13	degree	degree	NOUN
ejpam-7112	100	14	of	of	ADP
ejpam-7112	100	15	exactness	exactness	NOUN
ejpam-7112	100	16	of	of	ADP
ejpam-7112	100	17	p	p	PROPN
ejpam-7112	100	18	can	can	AUX
ejpam-7112	100	19	be	be	AUX
ejpam-7112	100	20	expressed	express	VERB
ejpam-7112	100	21	as	as	ADP
ejpam-7112	100	22	:	:	PUNCT
ejpam-7112	100	23	r[f	r[f	NOUN
ejpam-7112	100	24	]	]	PUNCT
ejpam-7112	101	1	=	=	SYM
ejpam-7112	101	2	ch(p+1)f	ch(p+1)f	NUM
ejpam-7112	101	3	(	(	PUNCT
ejpam-7112	101	4	p+1)(ϵ	p+1)(ϵ	PROPN
ejpam-7112	101	5	)	)	PUNCT
ejpam-7112	101	6	(	(	PUNCT
ejpam-7112	101	7	6	6	NUM
ejpam-7112	101	8	)	)	PUNCT
ejpam-7112	101	9	where	where	SCONJ
ejpam-7112	101	10	c	c	NOUN
ejpam-7112	101	11	is	be	AUX
ejpam-7112	101	12	a	a	DET
ejpam-7112	101	13	nonzero	nonzero	NOUN
ejpam-7112	101	14	constant	constant	ADJ
ejpam-7112	101	15	,	,	PUNCT
ejpam-7112	101	16	h	h	NOUN
ejpam-7112	101	17	is	be	AUX
ejpam-7112	101	18	the	the	DET
ejpam-7112	101	19	width	width	NOUN
ejpam-7112	101	20	of	of	ADP
ejpam-7112	101	21	interval	interval	NOUN
ejpam-7112	101	22	and	and	CCONJ
ejpam-7112	101	23	p	p	NOUN
ejpam-7112	101	24	+	+	CCONJ
ejpam-7112	101	25	1is	1is	ADJ
ejpam-7112	101	26	the	the	DET
ejpam-7112	101	27	order	order	NOUN
ejpam-7112	101	28	of	of	ADP
ejpam-7112	101	29	error	error	NOUN
ejpam-7112	101	30	term	term	NOUN
ejpam-7112	101	31	with	with	ADP
ejpam-7112	101	32	precision	precision	NOUN
ejpam-7112	101	33	p.	p.	NOUN
ejpam-7112	101	34	listed	list	VERB
ejpam-7112	101	35	below	below	ADV
ejpam-7112	101	36	are	be	AUX
ejpam-7112	101	37	a	a	DET
ejpam-7112	101	38	few	few	ADJ
ejpam-7112	101	39	recognized	recognize	VERB
ejpam-7112	101	40	members	member	NOUN
ejpam-7112	101	41	of	of	ADP
ejpam-7112	101	42	the	the	DET
ejpam-7112	101	43	closed	closed	ADJ
ejpam-7112	101	44	-	-	PUNCT
ejpam-7112	101	45	form	form	NOUN
ejpam-7112	101	46	quadrature	quadrature	NOUN
ejpam-7112	101	47	by	by	ADP
ejpam-7112	101	48	newton	newton	PROPN
ejpam-7112	101	49	and	and	CCONJ
ejpam-7112	101	50	cotes	cote	NOUN
ejpam-7112	101	51	for	for	ADP
ejpam-7112	101	52	approximating	approximate	VERB
ejpam-7112	101	53	riemann	riemann	PROPN
ejpam-7112	101	54	integration	integration	NOUN
ejpam-7112	101	55	[	[	X
ejpam-7112	101	56	1	1	X
ejpam-7112	101	57	]	]	PUNCT
ejpam-7112	101	58	with	with	ADP
ejpam-7112	101	59	local	local	ADJ
ejpam-7112	101	60	approximations	approximation	NOUN
ejpam-7112	101	61	and	and	CCONJ
ejpam-7112	101	62	truncation	truncation	NOUN
ejpam-7112	101	63	errors:∫	errors:∫	NOUN
ejpam-7112	101	64	b	b	PROPN
ejpam-7112	101	65	a	a	DET
ejpam-7112	101	66	f(x	f(x	PROPN
ejpam-7112	101	67	)	)	PUNCT
ejpam-7112	101	68	dx	dx	PROPN
ejpam-7112	102	1	=	=	PUNCT
ejpam-7112	102	2	b−	b−	PROPN
ejpam-7112	102	3	a	a	DET
ejpam-7112	102	4	2	2	NUM
ejpam-7112	102	5	[	[	NOUN
ejpam-7112	102	6	f(a	f(a	NOUN
ejpam-7112	102	7	)	)	PUNCT
ejpam-7112	103	1	+	+	CCONJ
ejpam-7112	103	2	f(b)]−	f(b)]−	ADV
ejpam-7112	103	3	(	(	PUNCT
ejpam-7112	103	4	b−	b−	PROPN
ejpam-7112	103	5	a)3	a)3	VERB
ejpam-7112	103	6	12	12	NUM
ejpam-7112	103	7	f	f	PROPN
ejpam-7112	103	8	′′(ξ	′′(ξ	NUM
ejpam-7112	103	9	)	)	PUNCT
ejpam-7112	103	10	(	(	PUNCT
ejpam-7112	103	11	7	7	X
ejpam-7112	103	12	)	)	PUNCT
ejpam-7112	103	13	∫	∫	PROPN
ejpam-7112	104	1	b	b	PROPN
ejpam-7112	105	1	a	a	DET
ejpam-7112	105	2	f(x	f(x	PROPN
ejpam-7112	105	3	)	)	PUNCT
ejpam-7112	105	4	dx	dx	PROPN
ejpam-7112	106	1	=	=	PUNCT
ejpam-7112	106	2	b−	b−	PROPN
ejpam-7112	106	3	a	a	DET
ejpam-7112	106	4	6	6	NUM
ejpam-7112	106	5	[	[	PUNCT
ejpam-7112	106	6	f(a	f(a	NOUN
ejpam-7112	106	7	)	)	PUNCT
ejpam-7112	107	1	+	+	NUM
ejpam-7112	107	2	4f	4f	NUM
ejpam-7112	107	3	(	(	PUNCT
ejpam-7112	107	4	a+	a+	PUNCT
ejpam-7112	107	5	b	b	PROPN
ejpam-7112	107	6	2	2	NUM
ejpam-7112	107	7	)	)	PUNCT
ejpam-7112	107	8	+	+	CCONJ
ejpam-7112	107	9	f(b	f(b	X
ejpam-7112	107	10	)	)	PUNCT
ejpam-7112	107	11	]	]	PUNCT
ejpam-7112	108	1	−	−	PROPN
ejpam-7112	108	2	(	(	PUNCT
ejpam-7112	108	3	b−	b−	NOUN
ejpam-7112	108	4	a)5	a)5	VERB
ejpam-7112	108	5	2880	2880	NUM
ejpam-7112	108	6	f	f	PROPN
ejpam-7112	108	7	(	(	PUNCT
ejpam-7112	108	8	4)(ξ	4)(ξ	NUM
ejpam-7112	108	9	)	)	PUNCT
ejpam-7112	108	10	(	(	PUNCT
ejpam-7112	108	11	8)∫	8)∫	PROPN
ejpam-7112	108	12	b	b	PROPN
ejpam-7112	108	13	a	a	DET
ejpam-7112	108	14	f(x	f(x	PROPN
ejpam-7112	108	15	)	)	PUNCT
ejpam-7112	108	16	dx	dx	PROPN
ejpam-7112	109	1	=	=	PUNCT
ejpam-7112	109	2	b−	b−	PROPN
ejpam-7112	109	3	a	a	DET
ejpam-7112	109	4	8	8	NUM
ejpam-7112	109	5	[	[	PUNCT
ejpam-7112	109	6	f(a	f(a	NOUN
ejpam-7112	109	7	)	)	PUNCT
ejpam-7112	110	1	+	+	CCONJ
ejpam-7112	110	2	3f	3f	PROPN
ejpam-7112	110	3	(	(	PUNCT
ejpam-7112	110	4	2a+	2a+	NUM
ejpam-7112	110	5	b	b	PROPN
ejpam-7112	110	6	3	3	NUM
ejpam-7112	110	7	)	)	PUNCT
ejpam-7112	110	8	+	+	CCONJ
ejpam-7112	110	9	3f	3f	PROPN
ejpam-7112	110	10	(	(	PUNCT
ejpam-7112	110	11	a+	a+	X
ejpam-7112	110	12	2b	2b	NUM
ejpam-7112	110	13	3	3	NUM
ejpam-7112	110	14	)	)	PUNCT
ejpam-7112	110	15	+	+	CCONJ
ejpam-7112	110	16	f(b	f(b	X
ejpam-7112	110	17	)	)	PUNCT
ejpam-7112	110	18	]	]	PUNCT
ejpam-7112	111	1	−	−	PROPN
ejpam-7112	111	2	(	(	PUNCT
ejpam-7112	111	3	b−	b−	NOUN
ejpam-7112	111	4	a)5	a)5	PROPN
ejpam-7112	111	5	6480	6480	NUM
ejpam-7112	111	6	f	f	X
ejpam-7112	111	7	(	(	PUNCT
ejpam-7112	111	8	4)(ξ	4)(ξ	NUM
ejpam-7112	111	9	)	)	PUNCT
ejpam-7112	111	10	(	(	PUNCT
ejpam-7112	111	11	9	9	X
ejpam-7112	111	12	)	)	PUNCT
ejpam-7112	111	13	whereξ	whereξ	NOUN
ejpam-7112	111	14	∈	∈	PROPN
ejpam-7112	111	15	(	(	PUNCT
ejpam-7112	111	16	a	a	DET
ejpam-7112	111	17	,	,	PUNCT
ejpam-7112	111	18	b	b	NOUN
ejpam-7112	111	19	)	)	PUNCT
ejpam-7112	111	20	.	.	PUNCT
ejpam-7112	112	1	the	the	DET
ejpam-7112	112	2	precision	precision	NOUN
ejpam-7112	112	3	of	of	ADP
ejpam-7112	112	4	the	the	DET
ejpam-7112	112	5	trapezoidal	trapezoidal	ADJ
ejpam-7112	112	6	rule	rule	NOUN
ejpam-7112	112	7	is	be	AUX
ejpam-7112	112	8	1	1	NUM
ejpam-7112	112	9	,	,	PUNCT
ejpam-7112	112	10	and	and	CCONJ
ejpam-7112	112	11	its	its	PRON
ejpam-7112	112	12	order	order	NOUN
ejpam-7112	112	13	of	of	ADP
ejpam-7112	112	14	accuracy	accuracy	NOUN
ejpam-7112	112	15	is	be	AUX
ejpam-7112	112	16	2	2	NUM
ejpam-7112	112	17	,	,	PUNCT
ejpam-7112	112	18	as	as	SCONJ
ejpam-7112	112	19	it	it	PRON
ejpam-7112	112	20	gives	give	VERB
ejpam-7112	112	21	an	an	DET
ejpam-7112	112	22	exact	exact	ADJ
ejpam-7112	112	23	proper	proper	ADJ
ejpam-7112	112	24	integral	integral	NOUN
ejpam-7112	112	25	of	of	ADP
ejpam-7112	112	26	polynomials	polynomial	NOUN
ejpam-7112	112	27	of	of	ADP
ejpam-7112	112	28	degree	degree	NOUN
ejpam-7112	112	29	one	one	NUM
ejpam-7112	112	30	or	or	CCONJ
ejpam-7112	112	31	less	less	ADJ
ejpam-7112	112	32	.	.	PUNCT
ejpam-7112	113	1	the	the	DET
ejpam-7112	113	2	precision	precision	NOUN
ejpam-7112	113	3	of	of	ADP
ejpam-7112	113	4	the	the	DET
ejpam-7112	113	5	simpson	simpson	PROPN
ejpam-7112	113	6	’s	’s	PART
ejpam-7112	113	7	3	3	NUM
ejpam-7112	113	8	-	-	PUNCT
ejpam-7112	113	9	point	point	NOUN
ejpam-7112	113	10	(	(	PUNCT
ejpam-7112	113	11	1/3	1/3	NUM
ejpam-7112	113	12	)	)	PUNCT
ejpam-7112	113	13	rule	rule	NOUN
ejpam-7112	113	14	is	be	AUX
ejpam-7112	113	15	3	3	NUM
ejpam-7112	113	16	,	,	PUNCT
ejpam-7112	113	17	and	and	CCONJ
ejpam-7112	113	18	its	its	PRON
ejpam-7112	113	19	order	order	NOUN
ejpam-7112	113	20	of	of	ADP
ejpam-7112	113	21	accuracy	accuracy	NOUN
ejpam-7112	113	22	is	be	AUX
ejpam-7112	113	23	4	4	NUM
ejpam-7112	113	24	,	,	PUNCT
ejpam-7112	113	25	as	as	SCONJ
ejpam-7112	113	26	it	it	PRON
ejpam-7112	113	27	gives	give	VERB
ejpam-7112	113	28	an	an	DET
ejpam-7112	113	29	exact	exact	ADJ
ejpam-7112	113	30	proper	proper	ADJ
ejpam-7112	113	31	integral	integral	NOUN
ejpam-7112	113	32	of	of	ADP
ejpam-7112	113	33	polynomials	polynomial	NOUN
ejpam-7112	113	34	of	of	ADP
ejpam-7112	113	35	degree	degree	NOUN
ejpam-7112	113	36	three	three	NUM
ejpam-7112	113	37	or	or	CCONJ
ejpam-7112	113	38	less	less	ADJ
ejpam-7112	113	39	.	.	PUNCT
ejpam-7112	114	1	the	the	DET
ejpam-7112	114	2	rule	rule	NOUN
ejpam-7112	114	3	(	(	PUNCT
ejpam-7112	114	4	9	9	NUM
ejpam-7112	114	5	)	)	PUNCT
ejpam-7112	114	6	has	have	VERB
ejpam-7112	114	7	same	same	ADJ
ejpam-7112	114	8	precision	precision	NOUN
ejpam-7112	114	9	3	3	NUM
ejpam-7112	114	10	as	as	ADP
ejpam-7112	114	11	of	of	ADP
ejpam-7112	114	12	(	(	PUNCT
ejpam-7112	114	13	8)	8)	NUM
ejpam-7112	114	14	,	,	PUNCT
ejpam-7112	114	15	and	and	CCONJ
ejpam-7112	114	16	order	order	NOUN
ejpam-7112	114	17	of	of	ADP
ejpam-7112	114	18	accuracy	accuracy	NOUN
ejpam-7112	114	19	4	4	NUM
ejpam-7112	114	20	.	.	PUNCT
ejpam-7112	115	1	besides	besides	SCONJ
ejpam-7112	115	2	the	the	DET
ejpam-7112	115	3	usual	usual	ADJ
ejpam-7112	115	4	closed	closed	ADJ
ejpam-7112	115	5	-	-	PUNCT
ejpam-7112	115	6	form	form	NOUN
ejpam-7112	115	7	rules	rule	NOUN
ejpam-7112	115	8	by	by	ADP
ejpam-7112	115	9	newton	newton	PROPN
ejpam-7112	115	10	and	and	CCONJ
ejpam-7112	115	11	cotes	cotes	PROPN
ejpam-7112	115	12	,	,	PUNCT
ejpam-7112	115	13	there	there	PRON
ejpam-7112	115	14	exist	exist	VERB
ejpam-7112	115	15	quadrature	quadrature	NOUN
ejpam-7112	115	16	proposed	propose	VERB
ejpam-7112	115	17	in	in	ADP
ejpam-7112	115	18	last	last	ADJ
ejpam-7112	115	19	decade	decade	NOUN
ejpam-7112	115	20	which	which	PRON
ejpam-7112	115	21	use	use	VERB
ejpam-7112	115	22	derivatives	derivative	NOUN
ejpam-7112	115	23	and	and	CCONJ
ejpam-7112	115	24	correction	correction	NOUN
ejpam-7112	115	25	terms	term	NOUN
ejpam-7112	115	26	in	in	ADP
ejpam-7112	115	27	the	the	DET
ejpam-7112	115	28	usual	usual	ADJ
ejpam-7112	115	29	closed	closed	NOUN
ejpam-7112	115	30	-	-	PUNCT
ejpam-7112	115	31	from	from	ADP
ejpam-7112	115	32	rules	rule	NOUN
ejpam-7112	115	33	[	[	X
ejpam-7112	115	34	4	4	NUM
ejpam-7112	115	35	]	]	PUNCT
ejpam-7112	115	36	,	,	PUNCT
ejpam-7112	115	37	[	[	X
ejpam-7112	115	38	7	7	NUM
ejpam-7112	115	39	]	]	PUNCT
ejpam-7112	115	40	,	,	PUNCT
ejpam-7112	115	41	[	[	X
ejpam-7112	115	42	8	8	NUM
ejpam-7112	115	43	]	]	PUNCT
ejpam-7112	115	44	,	,	PUNCT
ejpam-7112	115	45	[	[	X
ejpam-7112	115	46	10	10	NUM
ejpam-7112	115	47	]	]	PUNCT
ejpam-7112	115	48	,	,	PUNCT
ejpam-7112	115	49	[	[	X
ejpam-7112	115	50	11	11	NUM
ejpam-7112	115	51	]	]	PUNCT
ejpam-7112	115	52	.	.	PUNCT
ejpam-7112	116	1	here	here	ADV
ejpam-7112	116	2	,	,	PUNCT
ejpam-7112	116	3	we	we	PRON
ejpam-7112	116	4	refer	refer	VERB
ejpam-7112	116	5	to	to	ADP
ejpam-7112	116	6	the	the	DET
ejpam-7112	116	7	local	local	ADJ
ejpam-7112	116	8	approximations	approximation	NOUN
ejpam-7112	116	9	and	and	CCONJ
ejpam-7112	116	10	truncation	truncation	NOUN
ejpam-7112	116	11	error	error	NOUN
ejpam-7112	116	12	terms	term	NOUN
ejpam-7112	116	13	of	of	ADP
ejpam-7112	116	14	such	such	ADJ
ejpam-7112	116	15	quadrature	quadrature	NOUN
ejpam-7112	116	16	.	.	PUNCT
ejpam-7112	117	1	the	the	DET
ejpam-7112	117	2	arithmetic	arithmetic	ADJ
ejpam-7112	117	3	mean	mean	NOUN
ejpam-7112	117	4	derivative	derivative	NOUN
ejpam-7112	117	5	-	-	PUNCT
ejpam-7112	117	6	based	base	VERB
ejpam-7112	117	7	trapezoidal	trapezoidal	ADJ
ejpam-7112	117	8	rule	rule	NOUN
ejpam-7112	117	9	[	[	X
ejpam-7112	117	10	4	4	X
ejpam-7112	117	11	]	]	PUNCT
ejpam-7112	117	12	has	have	VERB
ejpam-7112	117	13	exactness	exactness	ADJ
ejpam-7112	117	14	degree	degree	NOUN
ejpam-7112	117	15	of	of	ADP
ejpam-7112	117	16	3	3	NUM
ejpam-7112	117	17	,	,	PUNCT
ejpam-7112	117	18	and	and	CCONJ
ejpam-7112	117	19	is	be	AUX
ejpam-7112	117	20	described	describe	VERB
ejpam-7112	117	21	as:∫	as:∫	PROPN
ejpam-7112	117	22	b	b	PROPN
ejpam-7112	117	23	a	a	DET
ejpam-7112	117	24	f(t	f(t	NOUN
ejpam-7112	117	25	)	)	PUNCT
ejpam-7112	117	26	dt	dt	NOUN
ejpam-7112	118	1	=	=	PUNCT
ejpam-7112	118	2	b−	b−	PROPN
ejpam-7112	118	3	a	a	DET
ejpam-7112	118	4	2	2	NUM
ejpam-7112	118	5	[	[	NOUN
ejpam-7112	118	6	f(a	f(a	NOUN
ejpam-7112	118	7	)	)	PUNCT
ejpam-7112	119	1	+	+	CCONJ
ejpam-7112	119	2	f(b)]−	f(b)]−	ADV
ejpam-7112	119	3	(	(	PUNCT
ejpam-7112	119	4	b−	b−	NOUN
ejpam-7112	119	5	a)3	a)3	VERB
ejpam-7112	119	6	12	12	NUM
ejpam-7112	119	7	f	f	X
ejpam-7112	120	1	′′	′′	PROPN
ejpam-7112	120	2	(	(	PUNCT
ejpam-7112	120	3	a+	a+	PROPN
ejpam-7112	120	4	b	b	PROPN
ejpam-7112	120	5	2	2	NUM
ejpam-7112	120	6	)	)	PUNCT
ejpam-7112	120	7	−	−	PROPN
ejpam-7112	120	8	(	(	PUNCT
ejpam-7112	120	9	b−	b−	NOUN
ejpam-7112	120	10	a)5	a)5	VERB
ejpam-7112	120	11	480	480	NUM
ejpam-7112	120	12	f	f	X
ejpam-7112	120	13	(	(	PUNCT
ejpam-7112	120	14	4)(ξ	4)(ξ	NUM
ejpam-7112	120	15	)	)	PUNCT
ejpam-7112	120	16	,	,	PUNCT
ejpam-7112	120	17	(	(	PUNCT
ejpam-7112	120	18	10	10	NUM
ejpam-7112	120	19	)	)	PUNCT
ejpam-7112	120	20	k.	k.	PROPN
ejpam-7112	120	21	memon	memon	PROPN
ejpam-7112	120	22	et	et	PROPN
ejpam-7112	120	23	al	al	PROPN
ejpam-7112	120	24	.	.	PUNCT
ejpam-7112	120	25	/	/	SYM
ejpam-7112	120	26	eur	eur	PROPN
ejpam-7112	120	27	.	.	PUNCT
ejpam-7112	121	1	j.	j.	PROPN
ejpam-7112	121	2	pure	pure	PROPN
ejpam-7112	121	3	appl	appl	PROPN
ejpam-7112	121	4	.	.	PROPN
ejpam-7112	121	5	math	math	PROPN
ejpam-7112	121	6	,	,	PUNCT
ejpam-7112	121	7	18	18	NUM
ejpam-7112	121	8	(	(	PUNCT
ejpam-7112	121	9	4	4	NUM
ejpam-7112	121	10	)	)	PUNCT
ejpam-7112	121	11	(	(	PUNCT
ejpam-7112	121	12	2025	2025	NUM
ejpam-7112	121	13	)	)	PUNCT
ejpam-7112	121	14	,	,	PUNCT
ejpam-7112	121	15	7112	7112	NUM
ejpam-7112	121	16	6	6	NUM
ejpam-7112	121	17	of	of	ADP
ejpam-7112	121	18	38	38	NUM
ejpam-7112	121	19	the	the	DET
ejpam-7112	121	20	geometric	geometric	ADJ
ejpam-7112	121	21	mean	mean	NOUN
ejpam-7112	121	22	derivative	derivative	NOUN
ejpam-7112	121	23	-	-	PUNCT
ejpam-7112	121	24	based	base	VERB
ejpam-7112	121	25	trapezoidal	trapezoidal	ADJ
ejpam-7112	121	26	rule	rule	NOUN
ejpam-7112	122	1	[	[	X
ejpam-7112	122	2	7	7	X
ejpam-7112	122	3	]	]	PUNCT
ejpam-7112	122	4	with	with	ADP
ejpam-7112	122	5	degree	degree	NOUN
ejpam-7112	122	6	of	of	ADP
ejpam-7112	122	7	exactness	exactness	NOUN
ejpam-7112	122	8	2	2	NUM
ejpam-7112	122	9	is	be	AUX
ejpam-7112	122	10	described	describe	VERB
ejpam-7112	122	11	as:∫	as:∫	PROPN
ejpam-7112	122	12	b	b	PROPN
ejpam-7112	122	13	a	a	DET
ejpam-7112	122	14	f(t	f(t	NOUN
ejpam-7112	122	15	)	)	PUNCT
ejpam-7112	122	16	dt	dt	NOUN
ejpam-7112	123	1	=	=	PUNCT
ejpam-7112	123	2	b−	b−	PROPN
ejpam-7112	123	3	a	a	DET
ejpam-7112	123	4	2	2	NUM
ejpam-7112	123	5	[	[	NOUN
ejpam-7112	123	6	f(a	f(a	NOUN
ejpam-7112	123	7	)	)	PUNCT
ejpam-7112	124	1	+	+	CCONJ
ejpam-7112	124	2	f(b)]−	f(b)]−	ADV
ejpam-7112	124	3	(	(	PUNCT
ejpam-7112	124	4	b−	b−	NOUN
ejpam-7112	124	5	a)3	a)3	VERB
ejpam-7112	124	6	12	12	NUM
ejpam-7112	124	7	f	f	X
ejpam-7112	125	1	′′	′′	PROPN
ejpam-7112	125	2	(	(	PUNCT
ejpam-7112	125	3	√	√	PROPN
ejpam-7112	125	4	ab	ab	PROPN
ejpam-7112	125	5	)	)	PUNCT
ejpam-7112	125	6	−	−	PROPN
ejpam-7112	125	7	(	(	PUNCT
ejpam-7112	125	8	b−	b−	PROPN
ejpam-7112	125	9	a)3	a)3	ADJ
ejpam-7112	125	10	24	24	NUM
ejpam-7112	125	11	(	(	PUNCT
ejpam-7112	125	12	√	√	NUM
ejpam-7112	125	13	b−	b−	PROPN
ejpam-7112	125	14	√	√	NUM
ejpam-7112	125	15	a	a	PRON
ejpam-7112	125	16	)	)	PUNCT
ejpam-7112	125	17	2	2	NUM
ejpam-7112	125	18	f	f	NOUN
ejpam-7112	125	19	(	(	PUNCT
ejpam-7112	125	20	3)(ξ	3)(ξ	NUM
ejpam-7112	125	21	)	)	PUNCT
ejpam-7112	125	22	,	,	PUNCT
ejpam-7112	125	23	(	(	PUNCT
ejpam-7112	125	24	11	11	X
ejpam-7112	125	25	)	)	PUNCT
ejpam-7112	125	26	the	the	DET
ejpam-7112	125	27	harmonic	harmonic	ADJ
ejpam-7112	125	28	mean	mean	VERB
ejpam-7112	125	29	derivative	derivative	NOUN
ejpam-7112	125	30	-	-	PUNCT
ejpam-7112	125	31	based	base	VERB
ejpam-7112	125	32	trapezoidal	trapezoidal	ADJ
ejpam-7112	125	33	rule	rule	NOUN
ejpam-7112	125	34	[	[	X
ejpam-7112	125	35	8	8	NUM
ejpam-7112	125	36	]	]	PUNCT
ejpam-7112	125	37	with	with	ADP
ejpam-7112	125	38	degree	degree	NOUN
ejpam-7112	125	39	of	of	ADP
ejpam-7112	125	40	exactness	exactness	NOUN
ejpam-7112	125	41	2	2	NUM
ejpam-7112	125	42	is	be	AUX
ejpam-7112	125	43	described	describe	VERB
ejpam-7112	125	44	as	as	ADP
ejpam-7112	125	45	:	:	PUNCT
ejpam-7112	125	46	∫	∫	PROPN
ejpam-7112	125	47	b	b	PROPN
ejpam-7112	125	48	a	a	DET
ejpam-7112	125	49	f(t	f(t	NOUN
ejpam-7112	125	50	)	)	PUNCT
ejpam-7112	125	51	dt	dt	NOUN
ejpam-7112	126	1	=	=	PUNCT
ejpam-7112	126	2	b−	b−	PROPN
ejpam-7112	126	3	a	a	DET
ejpam-7112	126	4	2	2	NUM
ejpam-7112	126	5	[	[	NOUN
ejpam-7112	126	6	f(a	f(a	NOUN
ejpam-7112	126	7	)	)	PUNCT
ejpam-7112	127	1	+	+	CCONJ
ejpam-7112	127	2	f(b)]−	f(b)]−	ADV
ejpam-7112	127	3	(	(	PUNCT
ejpam-7112	127	4	b−	b−	NOUN
ejpam-7112	127	5	a)3	a)3	VERB
ejpam-7112	127	6	12	12	NUM
ejpam-7112	127	7	f	f	X
ejpam-7112	128	1	′′	′′	PROPN
ejpam-7112	128	2	(	(	PUNCT
ejpam-7112	128	3	2ab	2ab	ADJ
ejpam-7112	128	4	a+	a+	PRON
ejpam-7112	128	5	b	b	NOUN
ejpam-7112	128	6	)	)	PUNCT
ejpam-7112	128	7	−	−	PROPN
ejpam-7112	128	8	(	(	PUNCT
ejpam-7112	128	9	b−	b−	NOUN
ejpam-7112	128	10	a)5	a)5	PROPN
ejpam-7112	128	11	24(a+	24(a+	PROPN
ejpam-7112	128	12	b	b	NOUN
ejpam-7112	128	13	)	)	PUNCT
ejpam-7112	128	14	f	f	PROPN
ejpam-7112	128	15	(	(	PUNCT
ejpam-7112	128	16	4)(ξ	4)(ξ	NUM
ejpam-7112	128	17	)	)	PUNCT
ejpam-7112	128	18	,	,	PUNCT
ejpam-7112	128	19	(	(	PUNCT
ejpam-7112	128	20	12	12	NUM
ejpam-7112	128	21	)	)	PUNCT
ejpam-7112	128	22	the	the	DET
ejpam-7112	128	23	heronian	heronian	ADJ
ejpam-7112	128	24	mean	mean	VERB
ejpam-7112	128	25	derivative	derivative	NOUN
ejpam-7112	128	26	-	-	PUNCT
ejpam-7112	128	27	based	base	VERB
ejpam-7112	128	28	trapezoidal	trapezoidal	ADJ
ejpam-7112	128	29	rule	rule	NOUN
ejpam-7112	128	30	[	[	X
ejpam-7112	128	31	10	10	NUM
ejpam-7112	128	32	]	]	PUNCT
ejpam-7112	128	33	with	with	ADP
ejpam-7112	128	34	degree	degree	NOUN
ejpam-7112	128	35	of	of	ADP
ejpam-7112	128	36	exactness	exactness	NOUN
ejpam-7112	128	37	2	2	NUM
ejpam-7112	128	38	is	be	AUX
ejpam-7112	128	39	described	describe	VERB
ejpam-7112	128	40	as:∫	as:∫	PROPN
ejpam-7112	128	41	b	b	PROPN
ejpam-7112	128	42	a	a	DET
ejpam-7112	128	43	f(t	f(t	NOUN
ejpam-7112	128	44	)	)	PUNCT
ejpam-7112	128	45	dt	dt	NOUN
ejpam-7112	129	1	=	=	PUNCT
ejpam-7112	129	2	b−	b−	PROPN
ejpam-7112	129	3	a	a	DET
ejpam-7112	129	4	2	2	NUM
ejpam-7112	129	5	[	[	NOUN
ejpam-7112	129	6	f(a	f(a	NOUN
ejpam-7112	129	7	)	)	PUNCT
ejpam-7112	130	1	+	+	NUM
ejpam-7112	130	2	f(b)]−(b−	f(b)]−(b−	NOUN
ejpam-7112	130	3	a)3	a)3	ADJ
ejpam-7112	130	4	12	12	NUM
ejpam-7112	130	5	f	f	X
ejpam-7112	131	1	′′	′′	PROPN
ejpam-7112	131	2	(	(	PUNCT
ejpam-7112	131	3	a+	a+	PUNCT
ejpam-7112	131	4	√	√	PROPN
ejpam-7112	131	5	ab+	ab+	PROPN
ejpam-7112	131	6	b	b	PROPN
ejpam-7112	131	7	3	3	NUM
ejpam-7112	131	8	)	)	PUNCT
ejpam-7112	131	9	−(b−	−(b−	NOUN
ejpam-7112	131	10	a)3	a)3	ADJ
ejpam-7112	131	11	72	72	NUM
ejpam-7112	131	12	(	(	PUNCT
ejpam-7112	131	13	√	√	NUM
ejpam-7112	131	14	b−	b−	PROPN
ejpam-7112	131	15	√	√	NUM
ejpam-7112	131	16	a	a	PRON
ejpam-7112	131	17	)	)	PUNCT
ejpam-7112	131	18	2	2	NUM
ejpam-7112	131	19	f	f	NOUN
ejpam-7112	131	20	(	(	PUNCT
ejpam-7112	131	21	3)(ξ	3)(ξ	NUM
ejpam-7112	131	22	)	)	PUNCT
ejpam-7112	131	23	,	,	PUNCT
ejpam-7112	131	24	(	(	PUNCT
ejpam-7112	131	25	13	13	X
ejpam-7112	131	26	)	)	PUNCT
ejpam-7112	131	27	the	the	DET
ejpam-7112	131	28	centroidal	centroidal	NOUN
ejpam-7112	131	29	mean	mean	VERB
ejpam-7112	131	30	derivative	derivative	NOUN
ejpam-7112	131	31	-	-	PUNCT
ejpam-7112	131	32	based	base	VERB
ejpam-7112	131	33	trapezoidal	trapezoidal	ADJ
ejpam-7112	131	34	rule	rule	NOUN
ejpam-7112	131	35	[	[	X
ejpam-7112	131	36	11	11	NUM
ejpam-7112	131	37	]	]	PUNCT
ejpam-7112	131	38	with	with	ADP
ejpam-7112	131	39	degree	degree	NOUN
ejpam-7112	131	40	of	of	ADP
ejpam-7112	131	41	exactness	exactness	NOUN
ejpam-7112	131	42	2	2	NUM
ejpam-7112	131	43	is	be	AUX
ejpam-7112	131	44	described	describe	VERB
ejpam-7112	131	45	as	as	ADP
ejpam-7112	131	46	:	:	PUNCT
ejpam-7112	131	47	∫	∫	PROPN
ejpam-7112	131	48	b	b	PROPN
ejpam-7112	131	49	a	a	DET
ejpam-7112	131	50	f(t	f(t	NOUN
ejpam-7112	131	51	)	)	PUNCT
ejpam-7112	131	52	dt	dt	NOUN
ejpam-7112	132	1	=	=	PUNCT
ejpam-7112	132	2	b−	b−	PROPN
ejpam-7112	132	3	a	a	DET
ejpam-7112	132	4	2	2	NUM
ejpam-7112	132	5	[	[	NOUN
ejpam-7112	132	6	f(a	f(a	NOUN
ejpam-7112	132	7	)	)	PUNCT
ejpam-7112	133	1	+	+	CCONJ
ejpam-7112	133	2	f(b)]−	f(b)]−	ADV
ejpam-7112	133	3	(	(	PUNCT
ejpam-7112	133	4	b−	b−	NOUN
ejpam-7112	133	5	a)3	a)3	VERB
ejpam-7112	133	6	12	12	NUM
ejpam-7112	133	7	f	f	X
ejpam-7112	134	1	′′	′′	PROPN
ejpam-7112	134	2	(	(	PUNCT
ejpam-7112	134	3	2	2	NUM
ejpam-7112	134	4	(	(	PUNCT
ejpam-7112	134	5	a2	a2	PROPN
ejpam-7112	134	6	+	+	CCONJ
ejpam-7112	134	7	ab+	ab+	NOUN
ejpam-7112	134	8	b2	b2	PROPN
ejpam-7112	134	9	)	)	PUNCT
ejpam-7112	134	10	3(a+	3(a+	PROPN
ejpam-7112	134	11	b	b	NOUN
ejpam-7112	134	12	)	)	PUNCT
ejpam-7112	134	13	)	)	PUNCT
ejpam-7112	135	1	+	+	CCONJ
ejpam-7112	135	2	(	(	PUNCT
ejpam-7112	135	3	b−	b−	NOUN
ejpam-7112	135	4	a)5	a)5	PROPN
ejpam-7112	135	5	72(a+	72(a+	PROPN
ejpam-7112	135	6	b	b	NOUN
ejpam-7112	135	7	)	)	PUNCT
ejpam-7112	135	8	f	f	PROPN
ejpam-7112	135	9	(	(	PUNCT
ejpam-7112	135	10	4)(ξ	4)(ξ	NUM
ejpam-7112	135	11	)	)	PUNCT
ejpam-7112	135	12	,	,	PUNCT
ejpam-7112	135	13	(	(	PUNCT
ejpam-7112	135	14	14	14	X
ejpam-7112	135	15	)	)	PUNCT
ejpam-7112	135	16	one	one	NOUN
ejpam-7112	135	17	can	can	AUX
ejpam-7112	135	18	note	note	VERB
ejpam-7112	135	19	that	that	SCONJ
ejpam-7112	135	20	the	the	DET
ejpam-7112	135	21	formula	formula	NOUN
ejpam-7112	135	22	(	(	PUNCT
ejpam-7112	135	23	10	10	NUM
ejpam-7112	135	24	)	)	PUNCT
ejpam-7112	135	25	can	can	AUX
ejpam-7112	135	26	be	be	AUX
ejpam-7112	135	27	said	say	VERB
ejpam-7112	135	28	,	,	PUNCT
ejpam-7112	135	29	comparatively	comparatively	ADV
ejpam-7112	135	30	in	in	ADP
ejpam-7112	135	31	contrast	contrast	NOUN
ejpam-7112	135	32	with	with	ADP
ejpam-7112	135	33	others	other	NOUN
ejpam-7112	135	34	(	(	PUNCT
ejpam-7112	135	35	11)-(14	11)-(14	NOUN
ejpam-7112	135	36	)	)	PUNCT
ejpam-7112	135	37	,	,	PUNCT
ejpam-7112	135	38	to	to	PART
ejpam-7112	135	39	have	have	VERB
ejpam-7112	135	40	no	no	DET
ejpam-7112	135	41	limitations	limitation	NOUN
ejpam-7112	135	42	on	on	ADP
ejpam-7112	135	43	the	the	DET
ejpam-7112	135	44	choice	choice	NOUN
ejpam-7112	135	45	of	of	ADP
ejpam-7112	135	46	limits	limit	NOUN
ejpam-7112	135	47	of	of	ADP
ejpam-7112	135	48	integration	integration	NOUN
ejpam-7112	135	49	.	.	PUNCT
ejpam-7112	136	1	on	on	ADP
ejpam-7112	136	2	the	the	DET
ejpam-7112	136	3	other	other	ADJ
ejpam-7112	136	4	hand	hand	NOUN
ejpam-7112	136	5	,	,	PUNCT
ejpam-7112	136	6	methods	method	NOUN
ejpam-7112	136	7	(	(	PUNCT
ejpam-7112	136	8	11)-(14	11)-(14	NOUN
ejpam-7112	136	9	)	)	PUNCT
ejpam-7112	136	10	,	,	PUNCT
ejpam-7112	136	11	are	be	AUX
ejpam-7112	136	12	prone	prone	ADJ
ejpam-7112	136	13	to	to	ADP
ejpam-7112	136	14	limitations	limitation	NOUN
ejpam-7112	136	15	based	base	VERB
ejpam-7112	136	16	on	on	ADP
ejpam-7112	136	17	the	the	DET
ejpam-7112	136	18	limits	limit	NOUN
ejpam-7112	136	19	of	of	ADP
ejpam-7112	136	20	integration	integration	NOUN
ejpam-7112	136	21	.	.	PUNCT
ejpam-7112	137	1	for	for	ADP
ejpam-7112	137	2	example	example	NOUN
ejpam-7112	137	3	,	,	PUNCT
ejpam-7112	137	4	(	(	PUNCT
ejpam-7112	137	5	11	11	NUM
ejpam-7112	137	6	)	)	PUNCT
ejpam-7112	137	7	and	and	CCONJ
ejpam-7112	137	8	(	(	PUNCT
ejpam-7112	137	9	13	13	NUM
ejpam-7112	137	10	)	)	PUNCT
ejpam-7112	137	11	lead	lead	NOUN
ejpam-7112	137	12	to	to	ADP
ejpam-7112	137	13	complex	complex	ADJ
ejpam-7112	137	14	number	number	NOUN
ejpam-7112	137	15	arithmetic	arithmetic	ADJ
ejpam-7112	137	16	if	if	SCONJ
ejpam-7112	137	17	limits	limit	NOUN
ejpam-7112	137	18	of	of	ADP
ejpam-7112	137	19	integration	integration	NOUN
ejpam-7112	137	20	are	be	AUX
ejpam-7112	137	21	opposite	opposite	ADJ
ejpam-7112	137	22	in	in	ADP
ejpam-7112	137	23	sign	sign	NOUN
ejpam-7112	137	24	.	.	PUNCT
ejpam-7112	138	1	in	in	ADP
ejpam-7112	138	2	this	this	DET
ejpam-7112	138	3	way	way	NOUN
ejpam-7112	138	4	,	,	PUNCT
ejpam-7112	138	5	(	(	PUNCT
ejpam-7112	138	6	12	12	NUM
ejpam-7112	138	7	)	)	PUNCT
ejpam-7112	138	8	and	and	CCONJ
ejpam-7112	138	9	(	(	PUNCT
ejpam-7112	138	10	14	14	NUM
ejpam-7112	138	11	)	)	PUNCT
ejpam-7112	138	12	lead	lead	NOUN
ejpam-7112	138	13	to	to	PART
ejpam-7112	138	14	indeterminate	indeterminate	VERB
ejpam-7112	138	15	and	and	CCONJ
ejpam-7112	138	16	undefined	undefined	ADJ
ejpam-7112	138	17	forms	form	NOUN
ejpam-7112	138	18	when	when	SCONJ
ejpam-7112	138	19	limits	limit	NOUN
ejpam-7112	138	20	of	of	ADP
ejpam-7112	138	21	integration	integration	NOUN
ejpam-7112	138	22	add	add	VERB
ejpam-7112	138	23	up	up	ADP
ejpam-7112	138	24	to	to	ADP
ejpam-7112	138	25	zero	zero	NUM
ejpam-7112	138	26	.	.	PUNCT
ejpam-7112	139	1	it	it	PRON
ejpam-7112	139	2	should	should	AUX
ejpam-7112	139	3	also	also	ADV
ejpam-7112	139	4	be	be	AUX
ejpam-7112	139	5	noted	note	VERB
ejpam-7112	139	6	that	that	SCONJ
ejpam-7112	139	7	the	the	PRON
ejpam-7112	139	8	*	*	X
ejpam-7112	139	9	in	in	ADP
ejpam-7112	139	10	(	(	PUNCT
ejpam-7112	139	11	12	12	NUM
ejpam-7112	139	12	)	)	PUNCT
ejpam-7112	139	13	and	and	CCONJ
ejpam-7112	139	14	(	(	PUNCT
ejpam-7112	139	15	14	14	NUM
ejpam-7112	139	16	)	)	PUNCT
ejpam-7112	139	17	refers	refer	VERB
ejpam-7112	139	18	to	to	ADP
ejpam-7112	139	19	the	the	DET
ejpam-7112	139	20	studies	study	NOUN
ejpam-7112	139	21	[	[	X
ejpam-7112	139	22	8	8	NUM
ejpam-7112	139	23	]	]	PUNCT
ejpam-7112	139	24	and	and	CCONJ
ejpam-7112	139	25	[	[	X
ejpam-7112	139	26	11	11	NUM
ejpam-7112	139	27	]	]	PUNCT
ejpam-7112	139	28	,	,	PUNCT
ejpam-7112	139	29	respectively	respectively	ADV
ejpam-7112	139	30	,	,	PUNCT
ejpam-7112	139	31	where	where	SCONJ
ejpam-7112	139	32	authors	author	NOUN
ejpam-7112	139	33	put	put	VERB
ejpam-7112	139	34	fourth	fourth	ADJ
ejpam-7112	139	35	-	-	PUNCT
ejpam-7112	139	36	order	order	NOUN
ejpam-7112	139	37	derivative	derivative	NOUN
ejpam-7112	139	38	in	in	ADP
ejpam-7112	139	39	the	the	DET
ejpam-7112	139	40	error	error	NOUN
ejpam-7112	139	41	term	term	NOUN
ejpam-7112	139	42	,	,	PUNCT
ejpam-7112	139	43	whereas	whereas	SCONJ
ejpam-7112	139	44	it	it	PRON
ejpam-7112	139	45	is	be	AUX
ejpam-7112	139	46	expected	expect	VERB
ejpam-7112	139	47	that	that	SCONJ
ejpam-7112	139	48	an	an	DET
ejpam-7112	139	49	interpolatory	interpolatory	NOUN
ejpam-7112	139	50	quadrature	quadrature	NOUN
ejpam-7112	139	51	has	have	VERB
ejpam-7112	139	52	(	(	PUNCT
ejpam-7112	139	53	p	p	NOUN
ejpam-7112	139	54	+	+	NOUN
ejpam-7112	139	55	2)nd	2)nd	NUM
ejpam-7112	139	56	order	order	NOUN
ejpam-7112	139	57	derivative	derivative	NOUN
ejpam-7112	139	58	in	in	ADP
ejpam-7112	139	59	the	the	DET
ejpam-7112	139	60	local	local	ADJ
ejpam-7112	139	61	error	error	NOUN
ejpam-7112	139	62	term	term	NOUN
ejpam-7112	139	63	if	if	SCONJ
ejpam-7112	139	64	its	its	PRON
ejpam-7112	139	65	precision	precision	NOUN
ejpam-7112	139	66	is	be	AUX
ejpam-7112	139	67	p.	p.	NOUN
ejpam-7112	139	68	the	the	DET
ejpam-7112	139	69	extension	extension	NOUN
ejpam-7112	139	70	of	of	ADP
ejpam-7112	139	71	the	the	DET
ejpam-7112	139	72	conventional	conventional	ADJ
ejpam-7112	139	73	trapezoid	trapezoid	ADJ
ejpam-7112	139	74	rule	rule	NOUN
ejpam-7112	139	75	of	of	ADP
ejpam-7112	139	76	the	the	DET
ejpam-7112	139	77	riemann	riemann	PROPN
ejpam-7112	139	78	integral	integral	PROPN
ejpam-7112	139	79	is	be	AUX
ejpam-7112	139	80	discussed	discuss	VERB
ejpam-7112	139	81	in	in	ADP
ejpam-7112	139	82	[	[	X
ejpam-7112	139	83	20	20	NUM
ejpam-7112	139	84	]	]	PUNCT
ejpam-7112	139	85	for	for	ADP
ejpam-7112	139	86	the	the	DET
ejpam-7112	139	87	approximation	approximation	NOUN
ejpam-7112	139	88	of	of	ADP
ejpam-7112	139	89	rs	rs	ADJ
ejpam-7112	139	90	-	-	ADJ
ejpam-7112	139	91	integral	integral	ADJ
ejpam-7112	139	92	.	.	PUNCT
ejpam-7112	140	1	so	so	ADV
ejpam-7112	140	2	,	,	PUNCT
ejpam-7112	140	3	its	its	PRON
ejpam-7112	140	4	resulting	result	VERB
ejpam-7112	140	5	conventional	conventional	ADJ
ejpam-7112	140	6	trapezoid	trapezoid	ADJ
ejpam-7112	140	7	rule	rule	NOUN
ejpam-7112	140	8	without	without	ADP
ejpam-7112	140	9	derivative	derivative	NOUN
ejpam-7112	140	10	for	for	ADP
ejpam-7112	140	11	rs	r	NOUN
ejpam-7112	140	12	integral	integral	ADJ
ejpam-7112	140	13	with	with	ADP
ejpam-7112	140	14	local	local	ADJ
ejpam-7112	140	15	error	error	NOUN
ejpam-7112	140	16	term	term	NOUN
ejpam-7112	140	17	is	be	AUX
ejpam-7112	140	18	as	as	SCONJ
ejpam-7112	140	19	follows	follow	VERB
ejpam-7112	140	20	:	:	PUNCT
ejpam-7112	140	21	rs(f	rs(f	NUM
ejpam-7112	140	22	;	;	PUNCT
ejpam-7112	140	23	g;α	g;α	PROPN
ejpam-7112	140	24	,	,	PUNCT
ejpam-7112	140	25	β	β	NOUN
ejpam-7112	140	26	)	)	PUNCT
ejpam-7112	140	27	=	=	SYM
ejpam-7112	141	1	∫	∫	PROPN
ejpam-7112	141	2	β	β	PROPN
ejpam-7112	141	3	α	α	PROPN
ejpam-7112	141	4	f(x	f(x	PROPN
ejpam-7112	141	5	)	)	PUNCT
ejpam-7112	141	6	dg	dg	PROPN
ejpam-7112	142	1	=	=	SYM
ejpam-7112	142	2	t	t	PROPN
ejpam-7112	142	3	+	+	PROPN
ejpam-7112	142	4	rt	rt	PROPN
ejpam-7112	143	1	[	[	X
ejpam-7112	143	2	f	f	X
ejpam-7112	143	3	]	]	X
ejpam-7112	143	4	=	=	PUNCT
ejpam-7112	143	5	(	(	PUNCT
ejpam-7112	143	6	1	1	NUM
ejpam-7112	143	7	β	β	X
ejpam-7112	143	8	−	−	PROPN
ejpam-7112	143	9	α	α	PRON
ejpam-7112	143	10	∫	∫	PROPN
ejpam-7112	143	11	β	β	PROPN
ejpam-7112	143	12	α	α	PROPN
ejpam-7112	143	13	g(t	g(t	PROPN
ejpam-7112	143	14	)	)	PUNCT
ejpam-7112	143	15	dt−	dt−	PUNCT
ejpam-7112	143	16	g(α	g(α	PROPN
ejpam-7112	143	17	)	)	PUNCT
ejpam-7112	143	18	)	)	PUNCT
ejpam-7112	144	1	f(α	f(α	NOUN
ejpam-7112	144	2	)	)	PUNCT
ejpam-7112	145	1	+	+	CCONJ
ejpam-7112	145	2	(	(	PUNCT
ejpam-7112	145	3	g(β)−	g(β)−	PROPN
ejpam-7112	145	4	1	1	NUM
ejpam-7112	145	5	β	β	NOUN
ejpam-7112	145	6	−	−	PROPN
ejpam-7112	145	7	α	α	PRON
ejpam-7112	145	8	∫	∫	PROPN
ejpam-7112	145	9	β	β	PROPN
ejpam-7112	145	10	α	α	PROPN
ejpam-7112	145	11	g(t)dt	g(t)dt	PROPN
ejpam-7112	145	12	)	)	PUNCT
ejpam-7112	145	13	f(β)−	f(β)−	PROPN
ejpam-7112	145	14	(	(	PUNCT
ejpam-7112	145	15	β	β	X
ejpam-7112	145	16	−	−	X
ejpam-7112	145	17	α)3	α)3	NOUN
ejpam-7112	145	18	12	12	NUM
ejpam-7112	145	19	f	f	PROPN
ejpam-7112	145	20	′′(ξ)g′(η	′′(ξ)g′(η	PROPN
ejpam-7112	145	21	)	)	PUNCT
ejpam-7112	145	22	,	,	PUNCT
ejpam-7112	145	23	(	(	PUNCT
ejpam-7112	145	24	15	15	NUM
ejpam-7112	145	25	)	)	PUNCT
ejpam-7112	145	26	k.	k.	PROPN
ejpam-7112	145	27	memon	memon	PROPN
ejpam-7112	145	28	et	et	PROPN
ejpam-7112	145	29	al	al	PROPN
ejpam-7112	145	30	.	.	PUNCT
ejpam-7112	145	31	/	/	SYM
ejpam-7112	145	32	eur	eur	PROPN
ejpam-7112	145	33	.	.	PUNCT
ejpam-7112	146	1	j.	j.	PROPN
ejpam-7112	146	2	pure	pure	PROPN
ejpam-7112	146	3	appl	appl	PROPN
ejpam-7112	146	4	.	.	PROPN
ejpam-7112	146	5	math	math	PROPN
ejpam-7112	146	6	,	,	PUNCT
ejpam-7112	146	7	18	18	NUM
ejpam-7112	146	8	(	(	PUNCT
ejpam-7112	146	9	4	4	NUM
ejpam-7112	146	10	)	)	PUNCT
ejpam-7112	146	11	(	(	PUNCT
ejpam-7112	146	12	2025	2025	NUM
ejpam-7112	146	13	)	)	PUNCT
ejpam-7112	146	14	,	,	PUNCT
ejpam-7112	146	15	7112	7112	NUM
ejpam-7112	146	16	7	7	NUM
ejpam-7112	146	17	of	of	ADP
ejpam-7112	146	18	38	38	NUM
ejpam-7112	146	19	where	where	SCONJ
ejpam-7112	146	20	ξ	ξ	PROPN
ejpam-7112	146	21	,	,	PUNCT
ejpam-7112	146	22	η	η	PROPN
ejpam-7112	146	23	∈	∈	PROPN
ejpam-7112	146	24	(	(	PUNCT
ejpam-7112	146	25	α	α	NOUN
ejpam-7112	146	26	,	,	PUNCT
ejpam-7112	146	27	β	β	NOUN
ejpam-7112	146	28	)	)	PUNCT
ejpam-7112	146	29	the	the	DET
ejpam-7112	146	30	rule	rule	NOUN
ejpam-7112	146	31	(	(	PUNCT
ejpam-7112	146	32	15	15	NUM
ejpam-7112	146	33	)	)	PUNCT
ejpam-7112	146	34	describes	describe	VERB
ejpam-7112	146	35	the	the	DET
ejpam-7112	146	36	formula	formula	NOUN
ejpam-7112	146	37	of	of	ADP
ejpam-7112	146	38	two	two	NUM
ejpam-7112	146	39	points	point	NOUN
ejpam-7112	146	40	,	,	PUNCT
ejpam-7112	146	41	so	so	ADV
ejpam-7112	146	42	its	its	PRON
ejpam-7112	146	43	performance	performance	NOUN
ejpam-7112	146	44	of	of	ADP
ejpam-7112	146	45	large	large	ADJ
ejpam-7112	146	46	integration	integration	NOUN
ejpam-7112	146	47	intervals	interval	NOUN
ejpam-7112	146	48	is	be	AUX
ejpam-7112	146	49	not	not	PART
ejpam-7112	146	50	appropriate	appropriate	ADJ
ejpam-7112	146	51	.	.	PUNCT
ejpam-7112	147	1	in	in	ADP
ejpam-7112	147	2	order	order	NOUN
ejpam-7112	147	3	to	to	PART
ejpam-7112	147	4	get	get	VERB
ejpam-7112	147	5	smaller	small	ADJ
ejpam-7112	147	6	local	local	ADJ
ejpam-7112	147	7	errors	error	NOUN
ejpam-7112	147	8	in	in	ADP
ejpam-7112	147	9	each	each	DET
ejpam-7112	147	10	approximation	approximation	NOUN
ejpam-7112	147	11	,	,	PUNCT
ejpam-7112	147	12	the	the	DET
ejpam-7112	147	13	composite	composite	ADJ
ejpam-7112	147	14	scheme	scheme	NOUN
ejpam-7112	147	15	of	of	ADP
ejpam-7112	147	16	original	original	ADJ
ejpam-7112	147	17	trapezoid	trapezoid	ADJ
ejpam-7112	147	18	rule	rule	NOUN
ejpam-7112	147	19	,	,	PUNCT
ejpam-7112	147	20	referred	refer	VERB
ejpam-7112	147	21	here	here	ADV
ejpam-7112	147	22	as	as	ADP
ejpam-7112	147	23	ct	ct	NUM
ejpam-7112	147	24	scheme	scheme	NOUN
ejpam-7112	147	25	with	with	ADP
ejpam-7112	147	26	global	global	ADJ
ejpam-7112	147	27	error	error	NOUN
ejpam-7112	147	28	term	term	NOUN
ejpam-7112	147	29	,	,	PUNCT
ejpam-7112	147	30	for	for	ADP
ejpam-7112	147	31	rs	rs	NOUN
ejpam-7112	147	32	integrals	integral	NOUN
ejpam-7112	147	33	given	give	VERB
ejpam-7112	147	34	in	in	ADP
ejpam-7112	147	35	[	[	NOUN
ejpam-7112	147	36	20	20	NUM
ejpam-7112	147	37	]	]	PUNCT
ejpam-7112	147	38	is	be	AUX
ejpam-7112	147	39	:	:	PUNCT
ejpam-7112	147	40	∫	∫	PROPN
ejpam-7112	147	41	β	β	PROPN
ejpam-7112	147	42	α	α	DET
ejpam-7112	147	43	f(t	f(t	NOUN
ejpam-7112	147	44	)	)	PUNCT
ejpam-7112	148	1	dg	dg	VERB
ejpam-7112	149	1	=	=	SYM
ejpam-7112	149	2	ct	ct	PROPN
ejpam-7112	149	3	+	+	NUM
ejpam-7112	149	4	rct	rct	PROPN
ejpam-7112	150	1	[	[	X
ejpam-7112	150	2	f	f	X
ejpam-7112	150	3	]	]	X
ejpam-7112	150	4	=	=	PUNCT
ejpam-7112	150	5	[	[	PUNCT
ejpam-7112	150	6	η	η	X
ejpam-7112	150	7	β	β	X
ejpam-7112	150	8	−	−	PROPN
ejpam-7112	151	1	α	α	PRON
ejpam-7112	151	2	∫	∫	PROPN
ejpam-7112	152	1	x1	x1	PROPN
ejpam-7112	152	2	α	α	PROPN
ejpam-7112	152	3	g(t	g(t	PROPN
ejpam-7112	152	4	)	)	PUNCT
ejpam-7112	152	5	dt−	dt−	PUNCT
ejpam-7112	152	6	g(α	g(α	PROPN
ejpam-7112	152	7	)	)	PUNCT
ejpam-7112	152	8	]	]	PUNCT
ejpam-7112	153	1	f(α	f(α	NOUN
ejpam-7112	153	2	)	)	PUNCT
ejpam-7112	153	3	+	+	CCONJ
ejpam-7112	153	4	η	η	PROPN
ejpam-7112	153	5	β	β	X
ejpam-7112	153	6	−	−	PROPN
ejpam-7112	153	7	α	α	PROPN
ejpam-7112	153	8	n−1∑	n−1∑	PROPN
ejpam-7112	154	1	k=1	k=1	PUNCT
ejpam-7112	155	1	[	[	X
ejpam-7112	155	2	∫	∫	X
ejpam-7112	155	3	xk+1	xk+1	PROPN
ejpam-7112	155	4	xk	xk	PROPN
ejpam-7112	156	1	g(t)dt−	g(t)dt−	PROPN
ejpam-7112	156	2	∫	∫	PROPN
ejpam-7112	156	3	xk	xk	PROPN
ejpam-7112	156	4	xk−1	xk−1	PROPN
ejpam-7112	156	5	g(t)dt	g(t)dt	PROPN
ejpam-7112	156	6	]	]	PUNCT
ejpam-7112	156	7	f(xk	f(xk	X
ejpam-7112	156	8	)	)	PUNCT
ejpam-7112	156	9	+	+	CCONJ
ejpam-7112	156	10	[	[	PUNCT
ejpam-7112	156	11	g(β)−	g(β)−	PROPN
ejpam-7112	156	12	η	η	PROPN
ejpam-7112	156	13	β	β	NOUN
ejpam-7112	156	14	−	−	PROPN
ejpam-7112	157	1	α	α	PRON
ejpam-7112	157	2	∫	∫	PROPN
ejpam-7112	157	3	β	β	X
ejpam-7112	157	4	xn−1	xn−1	PROPN
ejpam-7112	157	5	g(t)dt	g(t)dt	PROPN
ejpam-7112	157	6	]	]	PUNCT
ejpam-7112	157	7	f(β)−	f(β)−	PROPN
ejpam-7112	157	8	(	(	PUNCT
ejpam-7112	157	9	β	β	X
ejpam-7112	157	10	−	−	X
ejpam-7112	157	11	α)3	α)3	NOUN
ejpam-7112	157	12	12n2	12n2	NUM
ejpam-7112	157	13	f	f	NOUN
ejpam-7112	157	14	′′(µ)g′′(η	′′(µ)g′′(η	NUM
ejpam-7112	157	15	)	)	PUNCT
ejpam-7112	157	16	,	,	PUNCT
ejpam-7112	157	17	(	(	PUNCT
ejpam-7112	157	18	16	16	NUM
ejpam-7112	157	19	)	)	PUNCT
ejpam-7112	157	20	where	where	SCONJ
ejpam-7112	157	21	,	,	PUNCT
ejpam-7112	157	22	µ	µ	NOUN
ejpam-7112	157	23	,	,	PUNCT
ejpam-7112	157	24	η	η	PROPN
ejpam-7112	157	25	∈	∈	PROPN
ejpam-7112	157	26	(	(	PUNCT
ejpam-7112	157	27	α	α	NOUN
ejpam-7112	157	28	,	,	PUNCT
ejpam-7112	157	29	β	β	NOUN
ejpam-7112	157	30	)	)	PUNCT
ejpam-7112	157	31	zhao	zhao	PROPN
ejpam-7112	157	32	et	et	PROPN
ejpam-7112	157	33	al	al	PROPN
ejpam-7112	157	34	.	.	PUNCT
ejpam-7112	158	1	[	[	X
ejpam-7112	158	2	21	21	NUM
ejpam-7112	158	3	]	]	PUNCT
ejpam-7112	158	4	discussed	discuss	VERB
ejpam-7112	158	5	the	the	DET
ejpam-7112	158	6	conventional	conventional	ADJ
ejpam-7112	158	7	trapezoidal	trapezoidal	ADJ
ejpam-7112	158	8	rule	rule	NOUN
ejpam-7112	158	9	with	with	ADP
ejpam-7112	158	10	the	the	DET
ejpam-7112	158	11	midpoint	midpoint	NOUN
ejpam-7112	158	12	derivative	derivative	NOUN
ejpam-7112	158	13	for	for	ADP
ejpam-7112	158	14	the	the	DET
ejpam-7112	158	15	rs	rs	NOUN
ejpam-7112	158	16	integral	integral	NOUN
ejpam-7112	158	17	.	.	PUNCT
ejpam-7112	159	1	so	so	ADV
ejpam-7112	159	2	,	,	PUNCT
ejpam-7112	159	3	its	its	PRON
ejpam-7112	159	4	resulting	result	VERB
ejpam-7112	159	5	scheme	scheme	NOUN
ejpam-7112	159	6	is	be	AUX
ejpam-7112	159	7	as	as	SCONJ
ejpam-7112	159	8	follows:∫	follows:∫	NOUN
ejpam-7112	159	9	β	β	NOUN
ejpam-7112	159	10	a	a	DET
ejpam-7112	159	11	f(x	f(x	PROPN
ejpam-7112	159	12	)	)	PUNCT
ejpam-7112	159	13	dg	dg	PROPN
ejpam-7112	159	14	≈	≈	PROPN
ejpam-7112	159	15	zt	zt	PROPN
ejpam-7112	159	16	=	=	PROPN
ejpam-7112	159	17	t	t	PROPN
ejpam-7112	160	1	+	+	CCONJ
ejpam-7112	160	2	(	(	PUNCT
ejpam-7112	160	3	∫	∫	PROPN
ejpam-7112	160	4	β	β	X
ejpam-7112	160	5	a	a	DET
ejpam-7112	160	6	∫	∫	PROPN
ejpam-7112	160	7	t	t	PROPN
ejpam-7112	160	8	a	a	DET
ejpam-7112	160	9	g(x	g(x	NOUN
ejpam-7112	160	10	)	)	PUNCT
ejpam-7112	160	11	dx	dx	PROPN
ejpam-7112	160	12	dt−	dt−	PROPN
ejpam-7112	160	13	β	β	X
ejpam-7112	160	14	−	−	PROPN
ejpam-7112	160	15	a	a	DET
ejpam-7112	160	16	2	2	NUM
ejpam-7112	160	17	∫	∫	NOUN
ejpam-7112	160	18	β	β	PROPN
ejpam-7112	160	19	a	a	DET
ejpam-7112	160	20	g(t	g(t	PROPN
ejpam-7112	160	21	)	)	PUNCT
ejpam-7112	160	22	dt	dt	NOUN
ejpam-7112	160	23	)	)	PUNCT
ejpam-7112	161	1	f	f	PROPN
ejpam-7112	161	2	′′(c	′′(c	ADV
ejpam-7112	161	3	)	)	PUNCT
ejpam-7112	162	1	,	,	PUNCT
ejpam-7112	162	2	(	(	PUNCT
ejpam-7112	162	3	17	17	NUM
ejpam-7112	162	4	)	)	PUNCT
ejpam-7112	162	5	where	where	SCONJ
ejpam-7112	162	6	,	,	PUNCT
ejpam-7112	162	7	c	c	NOUN
ejpam-7112	162	8	=	=	SYM
ejpam-7112	162	9	(	(	PUNCT
ejpam-7112	162	10	−2β2	−2β2	NUM
ejpam-7112	162	11	+	+	CCONJ
ejpam-7112	162	12	α2	α2	ADJ
ejpam-7112	162	13	−	−	PROPN
ejpam-7112	162	14	αβ	αβ	INTJ
ejpam-7112	162	15	)	)	PUNCT
ejpam-7112	162	16	∫	∫	PROPN
ejpam-7112	162	17	β	β	PROPN
ejpam-7112	162	18	α	α	PROPN
ejpam-7112	162	19	g(t	g(t	PROPN
ejpam-7112	162	20	)	)	PUNCT
ejpam-7112	162	21	dt+	dt+	NOUN
ejpam-7112	162	22	6β	6β	NOUN
ejpam-7112	162	23	∫	∫	PROPN
ejpam-7112	162	24	β	β	PROPN
ejpam-7112	162	25	α	α	PROPN
ejpam-7112	162	26	∫	∫	PROPN
ejpam-7112	162	27	t	t	PROPN
ejpam-7112	162	28	α	α	PROPN
ejpam-7112	162	29	g(x	g(x	PROPN
ejpam-7112	162	30	)	)	PUNCT
ejpam-7112	162	31	dx	dx	PROPN
ejpam-7112	163	1	dt−	dt−	NUM
ejpam-7112	163	2	6	6	NUM
ejpam-7112	163	3	∫	∫	PROPN
ejpam-7112	163	4	β	β	PROPN
ejpam-7112	163	5	α	α	PROPN
ejpam-7112	163	6	∫	∫	PROPN
ejpam-7112	163	7	t	t	PROPN
ejpam-7112	163	8	α	α	NOUN
ejpam-7112	163	9	∫	∫	PROPN
ejpam-7112	163	10	y	y	PROPN
ejpam-7112	163	11	α	α	PROPN
ejpam-7112	163	12	g(x	g(x	PROPN
ejpam-7112	163	13	)	)	PUNCT
ejpam-7112	163	14	dx	dx	PROPN
ejpam-7112	163	15	dy	dy	NOUN
ejpam-7112	163	16	dt	dt	PROPN
ejpam-7112	163	17	6	6	NUM
ejpam-7112	163	18	∫	∫	PROPN
ejpam-7112	163	19	β	β	PROPN
ejpam-7112	164	1	α	α	PROPN
ejpam-7112	164	2	∫	∫	PROPN
ejpam-7112	164	3	t	t	PROPN
ejpam-7112	164	4	α	α	PROPN
ejpam-7112	164	5	g(x	g(x	PROPN
ejpam-7112	164	6	)	)	PUNCT
ejpam-7112	164	7	dx	dx	PROPN
ejpam-7112	165	1	dt−	dt−	NUM
ejpam-7112	165	2	3(β	3(β	NUM
ejpam-7112	165	3	−	−	PROPN
ejpam-7112	165	4	α	α	NUM
ejpam-7112	165	5	)	)	PUNCT
ejpam-7112	165	6	∫	∫	PROPN
ejpam-7112	165	7	β	β	PROPN
ejpam-7112	165	8	α	α	PROPN
ejpam-7112	165	9	g(t	g(t	PROPN
ejpam-7112	165	10	)	)	PUNCT
ejpam-7112	165	11	dt	dt	X
ejpam-7112	165	12	,	,	PUNCT
ejpam-7112	165	13	(	(	PUNCT
ejpam-7112	165	14	18	18	NUM
ejpam-7112	165	15	)	)	PUNCT
ejpam-7112	165	16	this	this	DET
ejpam-7112	165	17	method	method	NOUN
ejpam-7112	165	18	has	have	VERB
ejpam-7112	165	19	precision	precision	NOUN
ejpam-7112	165	20	3	3	NUM
ejpam-7112	165	21	and	and	CCONJ
ejpam-7112	165	22	its	its	PRON
ejpam-7112	165	23	error	error	NOUN
ejpam-7112	165	24	term	term	NOUN
ejpam-7112	165	25	r[f	r[f	NOUN
ejpam-7112	165	26	]	]	PUNCT
ejpam-7112	165	27	is	be	AUX
ejpam-7112	165	28	as	as	SCONJ
ejpam-7112	165	29	follows	follow	VERB
ejpam-7112	165	30	:	:	PUNCT
ejpam-7112	166	1	α3	α3	PROPN
ejpam-7112	166	2	+	+	CCONJ
ejpam-7112	166	3	αβ2	αβ2	ADJ
ejpam-7112	166	4	+	+	NOUN
ejpam-7112	166	5	α2β2	α2β2	ADP
ejpam-7112	166	6	−	−	PROPN
ejpam-7112	166	7	3β3	3β3	NUM
ejpam-7112	166	8	+	+	CCONJ
ejpam-7112	166	9	6(β	6(β	NUM
ejpam-7112	166	10	−	−	NOUN
ejpam-7112	167	1	α)c2	α)c2	NOUN
ejpam-7112	167	2	24	24	NUM
ejpam-7112	167	3	[	[	X
ejpam-7112	167	4	∫	∫	X
ejpam-7112	167	5	β	β	PROPN
ejpam-7112	167	6	α	α	PROPN
ejpam-7112	167	7	g(t	g(t	PROPN
ejpam-7112	167	8	)	)	PUNCT
ejpam-7112	167	9	dt+	dt+	NOUN
ejpam-7112	167	10	β2	β2	NOUN
ejpam-7112	167	11	−	−	PROPN
ejpam-7112	167	12	α2	α2	ADJ
ejpam-7112	167	13	2	2	NUM
ejpam-7112	167	14	(	(	PUNCT
ejpam-7112	167	15	∫	∫	PROPN
ejpam-7112	167	16	β	β	PROPN
ejpam-7112	167	17	α	α	PROPN
ejpam-7112	167	18	∫	∫	PROPN
ejpam-7112	167	19	t	t	PROPN
ejpam-7112	167	20	α	α	PROPN
ejpam-7112	167	21	g(x	g(x	PROPN
ejpam-7112	167	22	)	)	PUNCT
ejpam-7112	167	23	dx	dx	PROPN
ejpam-7112	167	24	dt	dt	NOUN
ejpam-7112	167	25	)	)	PUNCT
ejpam-7112	168	1	−	−	PROPN
ejpam-7112	168	2	β	β	X
ejpam-7112	168	3	∫	∫	PROPN
ejpam-7112	168	4	β	β	X
ejpam-7112	168	5	α	α	PROPN
ejpam-7112	168	6	∫	∫	PROPN
ejpam-7112	168	7	t	t	PROPN
ejpam-7112	169	1	α	α	NOUN
ejpam-7112	169	2	∫	∫	PROPN
ejpam-7112	169	3	y	y	PROPN
ejpam-7112	169	4	α	α	PROPN
ejpam-7112	169	5	g(x	g(x	PROPN
ejpam-7112	169	6	)	)	PUNCT
ejpam-7112	170	1	dx	dx	PROPN
ejpam-7112	170	2	dt+	dt+	NOUN
ejpam-7112	170	3	∫	∫	PROPN
ejpam-7112	170	4	β	β	X
ejpam-7112	170	5	α	α	PROPN
ejpam-7112	170	6	∫	∫	PROPN
ejpam-7112	171	1	t	t	PROPN
ejpam-7112	171	2	α	α	PROPN
ejpam-7112	171	3	∫	∫	PROPN
ejpam-7112	171	4	z	z	PROPN
ejpam-7112	172	1	α	α	PRON
ejpam-7112	172	2	∫	∫	PROPN
ejpam-7112	172	3	y	y	PROPN
ejpam-7112	172	4	α	α	PROPN
ejpam-7112	172	5	g(x	g(x	PROPN
ejpam-7112	172	6	)	)	PUNCT
ejpam-7112	172	7	dx	dx	PROPN
ejpam-7112	172	8	dy	dy	PROPN
ejpam-7112	172	9	dz	dz	PROPN
ejpam-7112	172	10	dtf	dtf	PROPN
ejpam-7112	172	11	(	(	PUNCT
ejpam-7112	172	12	4)(ξ	4)(ξ	NUM
ejpam-7112	172	13	)	)	PUNCT
ejpam-7112	172	14	,	,	PUNCT
ejpam-7112	172	15	(	(	PUNCT
ejpam-7112	172	16	19	19	NUM
ejpam-7112	172	17	)	)	PUNCT
ejpam-7112	172	18	where	where	SCONJ
ejpam-7112	172	19	ξ	ξ	PROPN
ejpam-7112	172	20	∈	∈	PROPN
ejpam-7112	172	21	(	(	PUNCT
ejpam-7112	172	22	α	α	NOUN
ejpam-7112	172	23	,	,	PUNCT
ejpam-7112	172	24	β	β	NOUN
ejpam-7112	172	25	)	)	PUNCT
ejpam-7112	172	26	while	while	SCONJ
ejpam-7112	172	27	in	in	SCONJ
ejpam-7112	172	28	[	[	X
ejpam-7112	172	29	5	5	NUM
ejpam-7112	172	30	]	]	X
ejpam-7112	172	31	zhao	zhao	PROPN
ejpam-7112	172	32	et	et	PROPN
ejpam-7112	172	33	al	al	PROPN
ejpam-7112	172	34	.	.	PROPN
ejpam-7112	172	35	attempted	attempt	VERB
ejpam-7112	172	36	to	to	PART
ejpam-7112	172	37	modify	modify	VERB
ejpam-7112	172	38	the	the	DET
ejpam-7112	172	39	existing	exist	VERB
ejpam-7112	172	40	trapezoidtype	trapezoidtype	NOUN
ejpam-7112	172	41	scheme	scheme	NOUN
ejpam-7112	172	42	without	without	ADP
ejpam-7112	172	43	derivatives	derivative	NOUN
ejpam-7112	172	44	by	by	ADP
ejpam-7112	172	45	introducing	introduce	VERB
ejpam-7112	172	46	derivative	derivative	NOUN
ejpam-7112	172	47	of	of	ADP
ejpam-7112	172	48	second	second	ADJ
ejpam-7112	172	49	-	-	PUNCT
ejpam-7112	172	50	order	order	NOUN
ejpam-7112	172	51	at	at	ADP
ejpam-7112	172	52	point	point	NOUN
ejpam-7112	172	53	c	c	NOUN
ejpam-7112	172	54	,	,	PUNCT
ejpam-7112	172	55	the	the	DET
ejpam-7112	172	56	improvement	improvement	NOUN
ejpam-7112	172	57	happens	happen	VERB
ejpam-7112	172	58	to	to	PART
ejpam-7112	172	59	be	be	AUX
ejpam-7112	172	60	quite	quite	ADV
ejpam-7112	172	61	complicated	complicated	ADJ
ejpam-7112	172	62	and	and	CCONJ
ejpam-7112	172	63	demands	demand	VERB
ejpam-7112	172	64	a	a	DET
ejpam-7112	172	65	lot	lot	NOUN
ejpam-7112	172	66	of	of	ADP
ejpam-7112	172	67	computational	computational	ADJ
ejpam-7112	172	68	effort	effort	NOUN
ejpam-7112	172	69	due	due	ADP
ejpam-7112	172	70	to	to	ADP
ejpam-7112	172	71	complicated	complicated	ADJ
ejpam-7112	172	72	formula	formula	NOUN
ejpam-7112	172	73	of	of	ADP
ejpam-7112	172	74	c	c	PROPN
ejpam-7112	172	75	in	in	ADP
ejpam-7112	172	76	the	the	DET
ejpam-7112	172	77	complete	complete	ADJ
ejpam-7112	172	78	formula	formula	NOUN
ejpam-7112	172	79	.	.	PUNCT
ejpam-7112	173	1	further	far	ADV
ejpam-7112	173	2	,	,	PUNCT
ejpam-7112	173	3	in	in	ADP
ejpam-7112	173	4	scheme	scheme	NOUN
ejpam-7112	173	5	(	(	PUNCT
ejpam-7112	173	6	17	17	NUM
ejpam-7112	173	7	)	)	PUNCT
ejpam-7112	173	8	,	,	PUNCT
ejpam-7112	173	9	when	when	SCONJ
ejpam-7112	173	10	g(t	g(t	PROPN
ejpam-7112	173	11	)	)	PUNCT
ejpam-7112	173	12	=	=	SYM
ejpam-7112	173	13	t	t	PROPN
ejpam-7112	173	14	,	,	PUNCT
ejpam-7112	173	15	then	then	ADV
ejpam-7112	173	16	expression	expression	NOUN
ejpam-7112	173	17	of	of	ADP
ejpam-7112	173	18	c	c	NOUN
ejpam-7112	173	19	reduces	reduce	VERB
ejpam-7112	173	20	to	to	PART
ejpam-7112	173	21	(	(	PUNCT
ejpam-7112	173	22	α+β)3	α+β)3	PROPN
ejpam-7112	173	23	2(α−β)2	2(α−β)2	PROPN
ejpam-7112	173	24	instead	instead	ADV
ejpam-7112	173	25	of	of	ADP
ejpam-7112	173	26	(	(	PUNCT
ejpam-7112	173	27	α+β	α+β	PROPN
ejpam-7112	173	28	)	)	PUNCT
ejpam-7112	173	29	2	2	NUM
ejpam-7112	173	30	.	.	PUNCT
ejpam-7112	174	1	consequently	consequently	ADV
ejpam-7112	174	2	,	,	PUNCT
ejpam-7112	174	3	the	the	DET
ejpam-7112	174	4	scheme	scheme	NOUN
ejpam-7112	174	5	of	of	ADP
ejpam-7112	174	6	zhao	zhao	PROPN
ejpam-7112	174	7	et	et	PROPN
ejpam-7112	174	8	al	al	PROPN
ejpam-7112	174	9	.	.	PUNCT
ejpam-7112	175	1	[	[	X
ejpam-7112	175	2	5	5	NUM
ejpam-7112	175	3	]	]	PUNCT
ejpam-7112	175	4	was	be	AUX
ejpam-7112	175	5	rectified	rectify	VERB
ejpam-7112	175	6	by	by	ADP
ejpam-7112	175	7	modified	modify	VERB
ejpam-7112	175	8	zhao	zhao	PROPN
ejpam-7112	175	9	trapezoidal	trapezoidal	ADJ
ejpam-7112	175	10	rule	rule	NOUN
ejpam-7112	175	11	(	(	PUNCT
ejpam-7112	175	12	mzt	mzt	PROPN
ejpam-7112	175	13	)	)	PUNCT
ejpam-7112	175	14	in	in	ADP
ejpam-7112	175	15	[	[	X
ejpam-7112	175	16	22	22	NUM
ejpam-7112	175	17	]	]	PUNCT
ejpam-7112	175	18	.	.	PUNCT
ejpam-7112	176	1	the	the	DET
ejpam-7112	176	2	mzt	mzt	PROPN
ejpam-7112	176	3	scheme	scheme	NOUN
ejpam-7112	176	4	is	be	AUX
ejpam-7112	176	5	:	:	PUNCT
ejpam-7112	176	6	k.	k.	PROPN
ejpam-7112	176	7	memon	memon	PROPN
ejpam-7112	176	8	et	et	PROPN
ejpam-7112	176	9	al	al	PROPN
ejpam-7112	176	10	.	.	PUNCT
ejpam-7112	176	11	/	/	SYM
ejpam-7112	176	12	eur	eur	PROPN
ejpam-7112	176	13	.	.	PUNCT
ejpam-7112	177	1	j.	j.	PROPN
ejpam-7112	177	2	pure	pure	PROPN
ejpam-7112	177	3	appl	appl	PROPN
ejpam-7112	177	4	.	.	PROPN
ejpam-7112	177	5	math	math	PROPN
ejpam-7112	177	6	,	,	PUNCT
ejpam-7112	177	7	18	18	NUM
ejpam-7112	177	8	(	(	PUNCT
ejpam-7112	177	9	4	4	NUM
ejpam-7112	177	10	)	)	PUNCT
ejpam-7112	177	11	(	(	PUNCT
ejpam-7112	177	12	2025	2025	NUM
ejpam-7112	177	13	)	)	PUNCT
ejpam-7112	177	14	,	,	PUNCT
ejpam-7112	177	15	7112	7112	NUM
ejpam-7112	177	16	8	8	NUM
ejpam-7112	177	17	of	of	ADP
ejpam-7112	177	18	38∫	38∫	NUM
ejpam-7112	177	19	β	β	NOUN
ejpam-7112	177	20	a	a	DET
ejpam-7112	177	21	f(x	f(x	PROPN
ejpam-7112	177	22	)	)	PUNCT
ejpam-7112	177	23	dg	dg	PROPN
ejpam-7112	178	1	≈	≈	PROPN
ejpam-7112	178	2	mzt	mzt	PROPN
ejpam-7112	178	3	=	=	PUNCT
ejpam-7112	178	4	(	(	PUNCT
ejpam-7112	178	5	1	1	NUM
ejpam-7112	178	6	β	β	X
ejpam-7112	178	7	−	−	PROPN
ejpam-7112	178	8	a	a	DET
ejpam-7112	178	9	∫	∫	PROPN
ejpam-7112	178	10	β	β	PROPN
ejpam-7112	178	11	α	α	PROPN
ejpam-7112	178	12	g(t	g(t	PROPN
ejpam-7112	178	13	)	)	PUNCT
ejpam-7112	178	14	dt−	dt−	PROPN
ejpam-7112	178	15	g(a	g(a	PROPN
ejpam-7112	178	16	)	)	PUNCT
ejpam-7112	178	17	)	)	PUNCT
ejpam-7112	179	1	f(a)+	f(a)+	NOUN
ejpam-7112	179	2	(	(	PUNCT
ejpam-7112	179	3	g(β)−	g(β)−	PROPN
ejpam-7112	179	4	1	1	NUM
ejpam-7112	179	5	β	β	NOUN
ejpam-7112	179	6	−	−	PROPN
ejpam-7112	179	7	a	a	DET
ejpam-7112	179	8	∫	∫	PROPN
ejpam-7112	179	9	β	β	X
ejpam-7112	179	10	a	a	DET
ejpam-7112	179	11	g(t	g(t	PROPN
ejpam-7112	179	12	)	)	PUNCT
ejpam-7112	179	13	dt	dt	NOUN
ejpam-7112	179	14	)	)	PUNCT
ejpam-7112	179	15	f(β	f(β	PROPN
ejpam-7112	179	16	)	)	PUNCT
ejpam-7112	180	1	+	+	CCONJ
ejpam-7112	180	2	(	(	PUNCT
ejpam-7112	180	3	∫	∫	PROPN
ejpam-7112	180	4	β	β	X
ejpam-7112	180	5	a	a	DET
ejpam-7112	180	6	∫	∫	PROPN
ejpam-7112	180	7	t	t	PROPN
ejpam-7112	180	8	a	a	DET
ejpam-7112	180	9	g(x	g(x	NOUN
ejpam-7112	180	10	)	)	PUNCT
ejpam-7112	180	11	dx	dx	PROPN
ejpam-7112	180	12	dt−	dt−	PROPN
ejpam-7112	180	13	β	β	X
ejpam-7112	180	14	−	−	PROPN
ejpam-7112	180	15	a	a	DET
ejpam-7112	180	16	2	2	NUM
ejpam-7112	180	17	∫	∫	NOUN
ejpam-7112	180	18	β	β	PROPN
ejpam-7112	180	19	a	a	DET
ejpam-7112	180	20	g(t	g(t	PROPN
ejpam-7112	180	21	)	)	PUNCT
ejpam-7112	180	22	dt	dt	NOUN
ejpam-7112	180	23	)	)	PUNCT
ejpam-7112	181	1	f	f	PROPN
ejpam-7112	181	2	′′(c	′′(c	ADV
ejpam-7112	181	3	)	)	PUNCT
ejpam-7112	182	1	,	,	PUNCT
ejpam-7112	182	2	(	(	PUNCT
ejpam-7112	182	3	20	20	NUM
ejpam-7112	182	4	)	)	PUNCT
ejpam-7112	182	5	where	where	SCONJ
ejpam-7112	182	6	c	c	NOUN
ejpam-7112	182	7	=	=	SYM
ejpam-7112	182	8	(	(	PUNCT
ejpam-7112	182	9	−2β2	−2β2	NUM
ejpam-7112	182	10	+	+	CCONJ
ejpam-7112	182	11	α2	α2	ADJ
ejpam-7112	182	12	+	+	CCONJ
ejpam-7112	182	13	αβ	αβ	X
ejpam-7112	182	14	)	)	PUNCT
ejpam-7112	182	15	∫	∫	PROPN
ejpam-7112	182	16	β	β	PROPN
ejpam-7112	182	17	α	α	PROPN
ejpam-7112	182	18	g(t	g(t	PROPN
ejpam-7112	182	19	)	)	PUNCT
ejpam-7112	182	20	dt+	dt+	NOUN
ejpam-7112	182	21	6β	6β	NOUN
ejpam-7112	182	22	∫	∫	PROPN
ejpam-7112	182	23	β	β	PROPN
ejpam-7112	182	24	α	α	PROPN
ejpam-7112	182	25	∫	∫	PROPN
ejpam-7112	182	26	t	t	PROPN
ejpam-7112	182	27	α	α	PROPN
ejpam-7112	182	28	g(x	g(x	PROPN
ejpam-7112	182	29	)	)	PUNCT
ejpam-7112	182	30	dx	dx	PROPN
ejpam-7112	183	1	dt−	dt−	NUM
ejpam-7112	183	2	6	6	NUM
ejpam-7112	183	3	∫	∫	PROPN
ejpam-7112	183	4	β	β	PROPN
ejpam-7112	183	5	α	α	PROPN
ejpam-7112	183	6	∫	∫	PROPN
ejpam-7112	183	7	t	t	PROPN
ejpam-7112	183	8	α	α	NOUN
ejpam-7112	183	9	∫	∫	PROPN
ejpam-7112	183	10	y	y	PROPN
ejpam-7112	183	11	α	α	PROPN
ejpam-7112	183	12	g(x	g(x	PROPN
ejpam-7112	183	13	)	)	PUNCT
ejpam-7112	183	14	dx	dx	PROPN
ejpam-7112	183	15	dy	dy	NOUN
ejpam-7112	183	16	dt	dt	PROPN
ejpam-7112	183	17	6	6	NUM
ejpam-7112	183	18	∫	∫	PROPN
ejpam-7112	183	19	β	β	PROPN
ejpam-7112	184	1	α	α	PROPN
ejpam-7112	184	2	∫	∫	PROPN
ejpam-7112	184	3	t	t	PROPN
ejpam-7112	184	4	α	α	PROPN
ejpam-7112	184	5	g(x	g(x	PROPN
ejpam-7112	184	6	)	)	PUNCT
ejpam-7112	184	7	dx	dx	PROPN
ejpam-7112	185	1	dt−	dt−	NUM
ejpam-7112	185	2	3(β	3(β	NUM
ejpam-7112	185	3	−	−	PROPN
ejpam-7112	185	4	α	α	NUM
ejpam-7112	185	5	)	)	PUNCT
ejpam-7112	185	6	∫	∫	PROPN
ejpam-7112	185	7	β	β	PROPN
ejpam-7112	185	8	α	α	PROPN
ejpam-7112	185	9	g(t	g(t	PROPN
ejpam-7112	185	10	)	)	PUNCT
ejpam-7112	185	11	dt	dt	X
ejpam-7112	185	12	,	,	PUNCT
ejpam-7112	185	13	(	(	PUNCT
ejpam-7112	185	14	21	21	NUM
ejpam-7112	185	15	)	)	PUNCT
ejpam-7112	185	16	this	this	DET
ejpam-7112	185	17	mzt	mzt	NOUN
ejpam-7112	185	18	method	method	NOUN
ejpam-7112	185	19	has	have	VERB
ejpam-7112	185	20	precision	precision	NOUN
ejpam-7112	185	21	3	3	NUM
ejpam-7112	185	22	and	and	CCONJ
ejpam-7112	185	23	its	its	PRON
ejpam-7112	185	24	error	error	NOUN
ejpam-7112	185	25	term	term	NOUN
ejpam-7112	185	26	r[f	r[f	NOUN
ejpam-7112	185	27	]	]	PUNCT
ejpam-7112	185	28	is	be	AUX
ejpam-7112	185	29	as	as	SCONJ
ejpam-7112	185	30	follows	follow	VERB
ejpam-7112	185	31	:	:	PUNCT
ejpam-7112	186	1	α2	α2	ADJ
ejpam-7112	186	2	+	+	CCONJ
ejpam-7112	186	3	αβ2	αβ2	ADJ
ejpam-7112	186	4	+	+	CCONJ
ejpam-7112	186	5	α2β	α2β	PROPN
ejpam-7112	186	6	−	−	PROPN
ejpam-7112	186	7	3β3	3β3	NUM
ejpam-7112	186	8	+	+	CCONJ
ejpam-7112	186	9	6(β	6(β	NUM
ejpam-7112	186	10	−	−	NOUN
ejpam-7112	186	11	α)c2	α)c2	NOUN
ejpam-7112	186	12	24	24	NUM
ejpam-7112	186	13	(	(	PUNCT
ejpam-7112	186	14	∫	∫	PROPN
ejpam-7112	186	15	β	β	PROPN
ejpam-7112	186	16	α	α	PROPN
ejpam-7112	186	17	g(t	g(t	PROPN
ejpam-7112	186	18	)	)	PUNCT
ejpam-7112	186	19	dt+	dt+	NOUN
ejpam-7112	186	20	β2	β2	NOUN
ejpam-7112	186	21	−	−	PROPN
ejpam-7112	186	22	c2	c2	PROPN
ejpam-7112	186	23	2	2	NUM
ejpam-7112	187	1	[	[	X
ejpam-7112	187	2	∫	∫	X
ejpam-7112	187	3	β	β	X
ejpam-7112	187	4	α	α	PROPN
ejpam-7112	187	5	∫	∫	PROPN
ejpam-7112	187	6	t	t	PROPN
ejpam-7112	187	7	α	α	PROPN
ejpam-7112	187	8	g(x	g(x	PROPN
ejpam-7112	187	9	)	)	PUNCT
ejpam-7112	188	1	dx	dx	PROPN
ejpam-7112	189	1	dt	dt	X
ejpam-7112	189	2	−	−	PROPN
ejpam-7112	190	1	β	β	X
ejpam-7112	190	2	∫	∫	PROPN
ejpam-7112	190	3	β	β	X
ejpam-7112	190	4	α	α	PROPN
ejpam-7112	190	5	∫	∫	PROPN
ejpam-7112	190	6	t	t	PROPN
ejpam-7112	191	1	α	α	NOUN
ejpam-7112	191	2	∫	∫	PROPN
ejpam-7112	191	3	y	y	PROPN
ejpam-7112	191	4	α	α	PROPN
ejpam-7112	191	5	g(x	g(x	PROPN
ejpam-7112	191	6	)	)	PUNCT
ejpam-7112	191	7	dx	dx	PROPN
ejpam-7112	191	8	dy	dy	NOUN
ejpam-7112	191	9	dt+	dt+	NOUN
ejpam-7112	191	10	∫	∫	PROPN
ejpam-7112	192	1	β	β	PROPN
ejpam-7112	192	2	α	α	PROPN
ejpam-7112	192	3	∫	∫	PROPN
ejpam-7112	192	4	t	t	PROPN
ejpam-7112	193	1	α	α	NOUN
ejpam-7112	193	2	∫	∫	PROPN
ejpam-7112	193	3	x	x	PUNCT
ejpam-7112	194	1	α	α	PRON
ejpam-7112	194	2	∫	∫	PROPN
ejpam-7112	194	3	y	y	PROPN
ejpam-7112	194	4	α	α	PROPN
ejpam-7112	194	5	g(x	g(x	PROPN
ejpam-7112	194	6	)	)	PUNCT
ejpam-7112	194	7	dx	dx	PROPN
ejpam-7112	194	8	dy	dy	PROPN
ejpam-7112	194	9	dz	dz	PROPN
ejpam-7112	194	10	dtf∗(4)(ξ	dtf∗(4)(ξ	PROPN
ejpam-7112	194	11	)	)	PUNCT
ejpam-7112	194	12	,	,	PUNCT
ejpam-7112	194	13	(	(	PUNCT
ejpam-7112	194	14	22	22	NUM
ejpam-7112	194	15	)	)	PUNCT
ejpam-7112	195	1	where	where	SCONJ
ejpam-7112	195	2	,	,	PUNCT
ejpam-7112	195	3	ξ	ξ	PROPN
ejpam-7112	195	4	∈	∈	PROPN
ejpam-7112	195	5	(	(	PUNCT
ejpam-7112	195	6	α	α	NOUN
ejpam-7112	195	7	,	,	PUNCT
ejpam-7112	195	8	β	β	NOUN
ejpam-7112	195	9	)	)	PUNCT
ejpam-7112	195	10	2.2	2.2	NUM
ejpam-7112	195	11	.	.	PUNCT
ejpam-7112	195	12	proposed	propose	VERB
ejpam-7112	195	13	trapezoid	trapezoid	ADJ
ejpam-7112	195	14	-	-	PUNCT
ejpam-7112	195	15	type	type	NOUN
ejpam-7112	195	16	quadrature	quadrature	NOUN
ejpam-7112	195	17	for	for	ADP
ejpam-7112	195	18	approximating	approximate	VERB
ejpam-7112	195	19	riemannstieltjes	riemannstieltjes	NOUN
ejpam-7112	195	20	integral	integral	ADJ
ejpam-7112	195	21	the	the	DET
ejpam-7112	195	22	main	main	ADJ
ejpam-7112	195	23	motivation	motivation	NOUN
ejpam-7112	195	24	in	in	ADP
ejpam-7112	195	25	the	the	DET
ejpam-7112	195	26	present	present	ADJ
ejpam-7112	195	27	study	study	NOUN
ejpam-7112	195	28	lies	lie	VERB
ejpam-7112	195	29	on	on	ADP
ejpam-7112	195	30	proposing	propose	VERB
ejpam-7112	195	31	time	time	NOUN
ejpam-7112	195	32	and	and	CCONJ
ejpam-7112	195	33	cost	cost	VERB
ejpam-7112	195	34	efficient	efficient	ADJ
ejpam-7112	195	35	trapezoid	trapezoid	ADJ
ejpam-7112	195	36	-	-	PUNCT
ejpam-7112	195	37	type	type	NOUN
ejpam-7112	195	38	quadrature	quadrature	NOUN
ejpam-7112	195	39	basing	base	VERB
ejpam-7112	195	40	the	the	DET
ejpam-7112	195	41	contributions	contribution	NOUN
ejpam-7112	195	42	around	around	ADP
ejpam-7112	195	43	the	the	DET
ejpam-7112	195	44	simplicity	simplicity	NOUN
ejpam-7112	195	45	of	of	ADP
ejpam-7112	195	46	c	c	PROPN
ejpam-7112	195	47	in	in	ADP
ejpam-7112	195	48	the	the	DET
ejpam-7112	195	49	formula	formula	NOUN
ejpam-7112	195	50	introduced	introduce	VERB
ejpam-7112	195	51	in	in	ADP
ejpam-7112	195	52	[	[	X
ejpam-7112	195	53	5	5	NUM
ejpam-7112	195	54	]	]	PUNCT
ejpam-7112	195	55	.	.	PUNCT
ejpam-7112	196	1	because	because	SCONJ
ejpam-7112	196	2	of	of	ADP
ejpam-7112	196	3	the	the	DET
ejpam-7112	196	4	complicated	complicated	ADJ
ejpam-7112	196	5	c	c	NOUN
ejpam-7112	196	6	in	in	ADP
ejpam-7112	196	7	(	(	PUNCT
ejpam-7112	196	8	17	17	NUM
ejpam-7112	196	9	)	)	PUNCT
ejpam-7112	196	10	,	,	PUNCT
ejpam-7112	196	11	its	its	PRON
ejpam-7112	196	12	dependence	dependence	NOUN
ejpam-7112	196	13	on	on	ADP
ejpam-7112	196	14	the	the	DET
ejpam-7112	196	15	integrand	integrand	NOUN
ejpam-7112	196	16	and	and	CCONJ
ejpam-7112	196	17	integrator	integrator	NOUN
ejpam-7112	196	18	functions	function	NOUN
ejpam-7112	196	19	,	,	PUNCT
ejpam-7112	196	20	its	its	PRON
ejpam-7112	196	21	dependence	dependence	NOUN
ejpam-7112	196	22	on	on	ADP
ejpam-7112	196	23	derivatives	derivative	NOUN
ejpam-7112	196	24	of	of	ADP
ejpam-7112	196	25	integrator	integrator	NOUN
ejpam-7112	196	26	and	and	CCONJ
ejpam-7112	196	27	integrals	integral	NOUN
ejpam-7112	196	28	of	of	ADP
ejpam-7112	196	29	integrator	integrator	NOUN
ejpam-7112	196	30	,	,	PUNCT
ejpam-7112	196	31	it	it	PRON
ejpam-7112	196	32	is	be	AUX
ejpam-7112	196	33	imperative	imperative	ADJ
ejpam-7112	196	34	to	to	PART
ejpam-7112	196	35	think	think	VERB
ejpam-7112	196	36	of	of	ADP
ejpam-7112	196	37	precise	precise	ADJ
ejpam-7112	196	38	and	and	CCONJ
ejpam-7112	196	39	simple	simple	ADJ
ejpam-7112	196	40	cin	cin	PROPN
ejpam-7112	196	41	(	(	PUNCT
ejpam-7112	196	42	17	17	NUM
ejpam-7112	196	43	)	)	PUNCT
ejpam-7112	196	44	.	.	PUNCT
ejpam-7112	197	1	in	in	ADP
ejpam-7112	197	2	this	this	DET
ejpam-7112	197	3	attempt	attempt	NOUN
ejpam-7112	197	4	,	,	PUNCT
ejpam-7112	197	5	we	we	PRON
ejpam-7112	197	6	consider	consider	VERB
ejpam-7112	197	7	the	the	DET
ejpam-7112	197	8	analogies	analogy	NOUN
ejpam-7112	197	9	from	from	ADP
ejpam-7112	197	10	recent	recent	ADJ
ejpam-7112	197	11	advancements	advancement	NOUN
ejpam-7112	197	12	in	in	ADP
ejpam-7112	197	13	the	the	DET
ejpam-7112	197	14	case	case	NOUN
ejpam-7112	197	15	of	of	ADP
ejpam-7112	197	16	riemann	riemann	PROPN
ejpam-7112	197	17	integrals	integral	NOUN
ejpam-7112	197	18	where	where	SCONJ
ejpam-7112	197	19	the	the	DET
ejpam-7112	197	20	derivatives	derivative	NOUN
ejpam-7112	197	21	were	be	AUX
ejpam-7112	197	22	used	use	VERB
ejpam-7112	197	23	in	in	ADP
ejpam-7112	197	24	addition	addition	NOUN
ejpam-7112	197	25	to	to	ADP
ejpam-7112	197	26	the	the	DET
ejpam-7112	197	27	actual	actual	ADJ
ejpam-7112	197	28	trapezoid	trapezoid	ADJ
ejpam-7112	197	29	approximations	approximation	NOUN
ejpam-7112	197	30	to	to	PART
ejpam-7112	197	31	enhance	enhance	VERB
ejpam-7112	197	32	the	the	DET
ejpam-7112	197	33	accuracy	accuracy	NOUN
ejpam-7112	197	34	[	[	X
ejpam-7112	197	35	4	4	NUM
ejpam-7112	197	36	]	]	PUNCT
ejpam-7112	197	37	,	,	PUNCT
ejpam-7112	197	38	[	[	X
ejpam-7112	197	39	7	7	NUM
ejpam-7112	197	40	]	]	PUNCT
ejpam-7112	197	41	,	,	PUNCT
ejpam-7112	197	42	[	[	X
ejpam-7112	197	43	8	8	NUM
ejpam-7112	197	44	]	]	PUNCT
ejpam-7112	197	45	,	,	PUNCT
ejpam-7112	197	46	[	[	X
ejpam-7112	197	47	10	10	NUM
ejpam-7112	197	48	]	]	PUNCT
ejpam-7112	197	49	,	,	PUNCT
ejpam-7112	197	50	[	[	X
ejpam-7112	197	51	11	11	NUM
ejpam-7112	197	52	]	]	PUNCT
ejpam-7112	197	53	.	.	PUNCT
ejpam-7112	198	1	the	the	DET
ejpam-7112	198	2	points	point	NOUN
ejpam-7112	198	3	at	at	ADP
ejpam-7112	198	4	which	which	PRON
ejpam-7112	198	5	derivatives	derivative	NOUN
ejpam-7112	198	6	where	where	SCONJ
ejpam-7112	198	7	used	use	VERB
ejpam-7112	198	8	in	in	ADP
ejpam-7112	198	9	these	these	DET
ejpam-7112	198	10	studies	study	NOUN
ejpam-7112	198	11	were	be	AUX
ejpam-7112	198	12	statistical	statistical	ADJ
ejpam-7112	198	13	averages	average	NOUN
ejpam-7112	198	14	of	of	ADP
ejpam-7112	198	15	the	the	DET
ejpam-7112	198	16	limits	limit	NOUN
ejpam-7112	198	17	of	of	ADP
ejpam-7112	198	18	the	the	DET
ejpam-7112	198	19	interval	interval	NOUN
ejpam-7112	198	20	of	of	ADP
ejpam-7112	198	21	integration	integration	NOUN
ejpam-7112	198	22	.	.	PUNCT
ejpam-7112	199	1	selecting	select	VERB
ejpam-7112	199	2	such	such	ADJ
ejpam-7112	199	3	means	mean	NOUN
ejpam-7112	199	4	in	in	ADP
ejpam-7112	199	5	the	the	DET
ejpam-7112	199	6	proposed	propose	VERB
ejpam-7112	199	7	trapezoid	trapezoid	ADJ
ejpam-7112	199	8	-	-	PUNCT
ejpam-7112	199	9	type	type	NOUN
ejpam-7112	199	10	quadrature	quadrature	NOUN
ejpam-7112	199	11	for	for	ADP
ejpam-7112	199	12	the	the	DET
ejpam-7112	199	13	rs	rs	NOUN
ejpam-7112	199	14	-	-	ADJ
ejpam-7112	199	15	integral	integral	ADJ
ejpam-7112	199	16	to	to	PART
ejpam-7112	199	17	evaluate	evaluate	VERB
ejpam-7112	199	18	derivatives	derivative	NOUN
ejpam-7112	199	19	in	in	ADP
ejpam-7112	199	20	advance	advance	NOUN
ejpam-7112	199	21	minimizes	minimize	VERB
ejpam-7112	199	22	the	the	DET
ejpam-7112	199	23	computational	computational	ADJ
ejpam-7112	199	24	cost	cost	NOUN
ejpam-7112	199	25	and	and	CCONJ
ejpam-7112	199	26	execution	execution	NOUN
ejpam-7112	199	27	times	time	NOUN
ejpam-7112	199	28	,	,	PUNCT
ejpam-7112	199	29	without	without	ADP
ejpam-7112	199	30	compromising	compromise	VERB
ejpam-7112	199	31	on	on	ADP
ejpam-7112	199	32	the	the	DET
ejpam-7112	199	33	accuracy	accuracy	NOUN
ejpam-7112	199	34	of	of	ADP
ejpam-7112	199	35	the	the	DET
ejpam-7112	199	36	quadrature	quadrature	NOUN
ejpam-7112	199	37	.	.	PUNCT
ejpam-7112	200	1	it	it	PRON
ejpam-7112	200	2	will	will	AUX
ejpam-7112	200	3	be	be	AUX
ejpam-7112	200	4	demonstrated	demonstrate	VERB
ejpam-7112	200	5	that	that	SCONJ
ejpam-7112	200	6	our	our	PRON
ejpam-7112	200	7	enhancements	enhancement	NOUN
ejpam-7112	200	8	prove	prove	VERB
ejpam-7112	200	9	to	to	PART
ejpam-7112	200	10	be	be	AUX
ejpam-7112	200	11	efficient	efficient	ADJ
ejpam-7112	200	12	than	than	ADP
ejpam-7112	200	13	those	those	PRON
ejpam-7112	200	14	suggested	suggest	VERB
ejpam-7112	200	15	and	and	CCONJ
ejpam-7112	200	16	used	use	VERB
ejpam-7112	200	17	on	on	ADP
ejpam-7112	200	18	this	this	DET
ejpam-7112	200	19	subject	subject	NOUN
ejpam-7112	200	20	through	through	ADP
ejpam-7112	200	21	[	[	X
ejpam-7112	200	22	5	5	NUM
ejpam-7112	200	23	]	]	PUNCT
ejpam-7112	200	24	and	and	CCONJ
ejpam-7112	200	25	[	[	X
ejpam-7112	200	26	22	22	NUM
ejpam-7112	200	27	]	]	PUNCT
ejpam-7112	200	28	.	.	PUNCT
ejpam-7112	201	1	the	the	DET
ejpam-7112	201	2	contributions	contribution	NOUN
ejpam-7112	201	3	are	be	AUX
ejpam-7112	201	4	divided	divide	VERB
ejpam-7112	201	5	in	in	ADP
ejpam-7112	201	6	two	two	NUM
ejpam-7112	201	7	sections	section	NOUN
ejpam-7112	201	8	here	here	ADV
ejpam-7112	201	9	:	:	PUNCT
ejpam-7112	201	10	firstly	firstly	ADV
ejpam-7112	201	11	we	we	PRON
ejpam-7112	201	12	derive	derive	VERB
ejpam-7112	201	13	and	and	CCONJ
ejpam-7112	201	14	prove	prove	VERB
ejpam-7112	201	15	theorems	theorem	NOUN
ejpam-7112	201	16	on	on	ADP
ejpam-7112	201	17	the	the	DET
ejpam-7112	201	18	proposed	propose	VERB
ejpam-7112	201	19	trapezoid	trapezoid	ADJ
ejpam-7112	201	20	-	-	PUNCT
ejpam-7112	201	21	type	type	NOUN
ejpam-7112	201	22	quadrature	quadrature	NOUN
ejpam-7112	201	23	using	use	VERB
ejpam-7112	201	24	arithmetic	arithmetic	ADJ
ejpam-7112	201	25	mean	mean	NOUN
ejpam-7112	201	26	,	,	PUNCT
ejpam-7112	201	27	and	and	CCONJ
ejpam-7112	201	28	secondly	secondly	ADV
ejpam-7112	201	29	the	the	DET
ejpam-7112	201	30	similar	similar	ADJ
ejpam-7112	201	31	discussion	discussion	NOUN
ejpam-7112	201	32	in	in	ADP
ejpam-7112	201	33	precisely	precisely	ADV
ejpam-7112	201	34	extended	extended	ADJ
ejpam-7112	201	35	to	to	ADP
ejpam-7112	201	36	other	other	ADJ
ejpam-7112	201	37	averages	average	NOUN
ejpam-7112	201	38	.	.	PUNCT
ejpam-7112	202	1	2.2.1	2.2.1	NUM
ejpam-7112	202	2	.	.	PUNCT
ejpam-7112	202	3	approximating	approximate	VERB
ejpam-7112	202	4	riemann	riemann	PROPN
ejpam-7112	202	5	-	-	PUNCT
ejpam-7112	202	6	stieltjes	stieltjes	NOUN
ejpam-7112	202	7	integral	integral	ADJ
ejpam-7112	202	8	using	use	VERB
ejpam-7112	202	9	arithmetic	arithmetic	ADJ
ejpam-7112	202	10	mean	mean	ADJ
ejpam-7112	202	11	trapezoidtype	trapezoidtype	NOUN
ejpam-7112	202	12	quadrature	quadrature	NOUN
ejpam-7112	202	13	in	in	ADP
ejpam-7112	202	14	the	the	DET
ejpam-7112	202	15	formula	formula	NOUN
ejpam-7112	202	16	(	(	PUNCT
ejpam-7112	202	17	17	17	NUM
ejpam-7112	202	18	)	)	PUNCT
ejpam-7112	202	19	,	,	PUNCT
ejpam-7112	202	20	we	we	PRON
ejpam-7112	202	21	restrict	restrict	VERB
ejpam-7112	202	22	c	c	NOUN
ejpam-7112	202	23	to	to	PART
ejpam-7112	202	24	be	be	AUX
ejpam-7112	202	25	the	the	DET
ejpam-7112	202	26	mid	mid	NOUN
ejpam-7112	202	27	-	-	NOUN
ejpam-7112	202	28	point	point	NOUN
ejpam-7112	202	29	of	of	ADP
ejpam-7112	202	30	the	the	DET
ejpam-7112	202	31	limits	limit	NOUN
ejpam-7112	202	32	of	of	ADP
ejpam-7112	202	33	integration	integration	NOUN
ejpam-7112	202	34	,	,	PUNCT
ejpam-7112	202	35	or	or	CCONJ
ejpam-7112	202	36	in	in	ADP
ejpam-7112	202	37	other	other	ADJ
ejpam-7112	202	38	words	word	NOUN
ejpam-7112	202	39	,	,	PUNCT
ejpam-7112	202	40	arithmetic	arithmetic	ADJ
ejpam-7112	202	41	average	average	NOUN
ejpam-7112	202	42	of	of	ADP
ejpam-7112	202	43	the	the	DET
ejpam-7112	202	44	limits	limit	NOUN
ejpam-7112	202	45	,	,	PUNCT
ejpam-7112	202	46	then	then	ADV
ejpam-7112	202	47	consequent	consequent	ADJ
ejpam-7112	202	48	trapezoid	trapezoid	ADJ
ejpam-7112	202	49	-	-	PUNCT
ejpam-7112	202	50	type	type	NOUN
ejpam-7112	202	51	approximation	approximation	NOUN
ejpam-7112	202	52	so	so	ADV
ejpam-7112	202	53	obtained	obtain	VERB
ejpam-7112	202	54	is	be	AUX
ejpam-7112	202	55	referred	refer	VERB
ejpam-7112	202	56	as	as	ADP
ejpam-7112	202	57	amt	amt	PROPN
ejpam-7112	202	58	,	,	PUNCT
ejpam-7112	202	59	and	and	CCONJ
ejpam-7112	202	60	the	the	DET
ejpam-7112	202	61	quadrature	quadrature	NOUN
ejpam-7112	202	62	is	be	AUX
ejpam-7112	202	63	derived	derive	VERB
ejpam-7112	202	64	in	in	ADP
ejpam-7112	202	65	theorem	theorem	NOUN
ejpam-7112	202	66	1	1	NUM
ejpam-7112	202	67	.	.	PUNCT
ejpam-7112	203	1	k.	k.	PROPN
ejpam-7112	203	2	memon	memon	PROPN
ejpam-7112	203	3	et	et	PROPN
ejpam-7112	203	4	al	al	PROPN
ejpam-7112	203	5	.	.	PUNCT
ejpam-7112	203	6	/	/	SYM
ejpam-7112	203	7	eur	eur	PROPN
ejpam-7112	203	8	.	.	PUNCT
ejpam-7112	204	1	j.	j.	PROPN
ejpam-7112	204	2	pure	pure	PROPN
ejpam-7112	204	3	appl	appl	PROPN
ejpam-7112	204	4	.	.	PROPN
ejpam-7112	204	5	math	math	PROPN
ejpam-7112	204	6	,	,	PUNCT
ejpam-7112	204	7	18	18	NUM
ejpam-7112	204	8	(	(	PUNCT
ejpam-7112	204	9	4	4	NUM
ejpam-7112	204	10	)	)	PUNCT
ejpam-7112	204	11	(	(	PUNCT
ejpam-7112	204	12	2025	2025	NUM
ejpam-7112	204	13	)	)	PUNCT
ejpam-7112	204	14	,	,	PUNCT
ejpam-7112	204	15	7112	7112	NUM
ejpam-7112	204	16	9	9	NUM
ejpam-7112	204	17	of	of	ADP
ejpam-7112	204	18	38	38	NUM
ejpam-7112	204	19	theorem	theorem	NOUN
ejpam-7112	204	20	1	1	NUM
ejpam-7112	204	21	.	.	PUNCT
ejpam-7112	204	22	assuming	assume	VERB
ejpam-7112	204	23	continuity	continuity	NOUN
ejpam-7112	204	24	of	of	ADP
ejpam-7112	204	25	f(t	f(t	PROPN
ejpam-7112	204	26	)	)	PUNCT
ejpam-7112	204	27	and	and	CCONJ
ejpam-7112	204	28	g(t	g(t	PROPN
ejpam-7112	204	29	)	)	PUNCT
ejpam-7112	204	30	in	in	ADP
ejpam-7112	204	31	along	along	ADP
ejpam-7112	204	32	with	with	ADP
ejpam-7112	204	33	g(t	g(t	PROPN
ejpam-7112	204	34	)	)	PUNCT
ejpam-7112	204	35	being	be	AUX
ejpam-7112	204	36	monotonically	monotonically	ADV
ejpam-7112	204	37	rising	rise	VERB
ejpam-7112	204	38	in	in	ADP
ejpam-7112	204	39	the	the	DET
ejpam-7112	204	40	same	same	ADJ
ejpam-7112	204	41	interval	interval	NOUN
ejpam-7112	204	42	,	,	PUNCT
ejpam-7112	204	43	amt	amt	PROPN
ejpam-7112	204	44	quadrature	quadrature	NOUN
ejpam-7112	204	45	for	for	ADP
ejpam-7112	204	46	the	the	DET
ejpam-7112	204	47	rs	rs	ADJ
ejpam-7112	204	48	-	-	ADJ
ejpam-7112	204	49	integral	integral	ADJ
ejpam-7112	204	50	is:∫	is:∫	NOUN
ejpam-7112	204	51	β	β	NOUN
ejpam-7112	204	52	α	α	PRON
ejpam-7112	204	53	f(t	f(t	NOUN
ejpam-7112	204	54	)	)	PUNCT
ejpam-7112	204	55	dg	dg	PROPN
ejpam-7112	205	1	≈	≈	PROPN
ejpam-7112	205	2	amt	amt	PROPN
ejpam-7112	205	3	=	=	SYM
ejpam-7112	206	1	(	(	PUNCT
ejpam-7112	206	2	1	1	NUM
ejpam-7112	206	3	β	β	NOUN
ejpam-7112	206	4	−	−	PROPN
ejpam-7112	206	5	α	α	PROPN
ejpam-7112	206	6	i1	i1	PROPN
ejpam-7112	206	7	−	−	PROPN
ejpam-7112	206	8	g(α	g(α	PROPN
ejpam-7112	206	9	)	)	PUNCT
ejpam-7112	206	10	)	)	PUNCT
ejpam-7112	207	1	f(α	f(α	NOUN
ejpam-7112	207	2	)	)	PUNCT
ejpam-7112	208	1	+	+	CCONJ
ejpam-7112	208	2	(	(	PUNCT
ejpam-7112	208	3	g(β)−	g(β)−	PROPN
ejpam-7112	208	4	1	1	NUM
ejpam-7112	208	5	β	β	NOUN
ejpam-7112	208	6	−	−	PROPN
ejpam-7112	208	7	α	α	PROPN
ejpam-7112	208	8	i1	i1	PROPN
ejpam-7112	208	9	)	)	PUNCT
ejpam-7112	208	10	f(β	f(β	PROPN
ejpam-7112	208	11	)	)	PUNCT
ejpam-7112	209	1	+	+	CCONJ
ejpam-7112	209	2	(	(	PUNCT
ejpam-7112	209	3	i2	i2	PROPN
ejpam-7112	209	4	−	−	PROPN
ejpam-7112	209	5	β	β	NOUN
ejpam-7112	209	6	−	−	PROPN
ejpam-7112	209	7	α	α	PROPN
ejpam-7112	209	8	2	2	NUM
ejpam-7112	209	9	i1	i1	PROPN
ejpam-7112	209	10	)	)	PUNCT
ejpam-7112	210	1	f	f	X
ejpam-7112	211	1	′	′	NUM
ejpam-7112	211	2	(	(	PUNCT
ejpam-7112	211	3	α+	α+	X
ejpam-7112	211	4	β	β	X
ejpam-7112	211	5	2	2	NUM
ejpam-7112	211	6	)	)	PUNCT
ejpam-7112	211	7	,	,	PUNCT
ejpam-7112	211	8	(	(	PUNCT
ejpam-7112	211	9	23	23	NUM
ejpam-7112	211	10	)	)	PUNCT
ejpam-7112	211	11	where	where	SCONJ
ejpam-7112	211	12	i1	i1	PROPN
ejpam-7112	211	13	=	=	PUNCT
ejpam-7112	211	14	∫	∫	PROPN
ejpam-7112	211	15	β	β	PROPN
ejpam-7112	211	16	α	α	PROPN
ejpam-7112	211	17	g(t	g(t	PROPN
ejpam-7112	211	18	)	)	PUNCT
ejpam-7112	212	1	dt	dt	PROPN
ejpam-7112	212	2	,	,	PUNCT
ejpam-7112	212	3	i2	i2	PROPN
ejpam-7112	212	4	=	=	SYM
ejpam-7112	212	5	∫	∫	PROPN
ejpam-7112	212	6	β	β	PROPN
ejpam-7112	212	7	α	α	PROPN
ejpam-7112	212	8	∫	∫	PROPN
ejpam-7112	212	9	t	t	PROPN
ejpam-7112	212	10	α	α	PROPN
ejpam-7112	212	11	g(x	g(x	PROPN
ejpam-7112	212	12	)	)	PUNCT
ejpam-7112	212	13	dx	dx	PROPN
ejpam-7112	213	1	dt	dt	NOUN
ejpam-7112	213	2	,	,	PUNCT
ejpam-7112	213	3	i3	i3	NOUN
ejpam-7112	213	4	=	=	SYM
ejpam-7112	213	5	∫	∫	PROPN
ejpam-7112	213	6	β	β	X
ejpam-7112	213	7	α	α	PROPN
ejpam-7112	213	8	∫	∫	PROPN
ejpam-7112	214	1	t	t	PROPN
ejpam-7112	214	2	α	α	NOUN
ejpam-7112	214	3	∫	∫	PROPN
ejpam-7112	214	4	y	y	PROPN
ejpam-7112	214	5	α	α	PROPN
ejpam-7112	214	6	g	g	PROPN
ejpam-7112	214	7	(	(	PUNCT
ejpam-7112	214	8	)	)	PUNCT
ejpam-7112	214	9	dx	dx	PROPN
ejpam-7112	214	10	dy	dy	NOUN
ejpam-7112	214	11	dt	dt	PROPN
ejpam-7112	214	12	,	,	PUNCT
ejpam-7112	214	13	and	and	CCONJ
ejpam-7112	214	14	i4	i4	PROPN
ejpam-7112	214	15	=	=	SYM
ejpam-7112	215	1	∫	∫	PROPN
ejpam-7112	215	2	β	β	PROPN
ejpam-7112	215	3	α	α	PROPN
ejpam-7112	215	4	∫	∫	PROPN
ejpam-7112	215	5	t	t	PROPN
ejpam-7112	216	1	α	α	PROPN
ejpam-7112	216	2	∫	∫	PROPN
ejpam-7112	216	3	z	z	PROPN
ejpam-7112	217	1	α	α	PRON
ejpam-7112	217	2	∫	∫	PROPN
ejpam-7112	217	3	y	y	PROPN
ejpam-7112	217	4	α	α	PROPN
ejpam-7112	217	5	g(x	g(x	PROPN
ejpam-7112	217	6	)	)	PUNCT
ejpam-7112	217	7	dx	dx	PROPN
ejpam-7112	217	8	dy	dy	X
ejpam-7112	217	9	dz	dz	PROPN
ejpam-7112	217	10	dt	dt	PROPN
ejpam-7112	217	11	.	.	PUNCT
ejpam-7112	218	1	proof	proof	NOUN
ejpam-7112	218	2	.	.	PUNCT
ejpam-7112	219	1	referencing	reference	VERB
ejpam-7112	219	2	to	to	ADP
ejpam-7112	219	3	the	the	DET
ejpam-7112	219	4	amt	amt	PROPN
ejpam-7112	219	5	scheme	scheme	NOUN
ejpam-7112	219	6	for	for	ADP
ejpam-7112	219	7	the	the	DET
ejpam-7112	219	8	riemann	riemann	PROPN
ejpam-7112	219	9	integral	integral	PROPN
ejpam-7112	219	10	as	as	ADP
ejpam-7112	219	11	in	in	ADP
ejpam-7112	219	12	[	[	X
ejpam-7112	219	13	4	4	NUM
ejpam-7112	219	14	]	]	PUNCT
ejpam-7112	219	15	,	,	PUNCT
ejpam-7112	219	16	the	the	DET
ejpam-7112	219	17	proposed	propose	VERB
ejpam-7112	219	18	amt	amt	PROPN
ejpam-7112	219	19	quadrature	quadrature	NOUN
ejpam-7112	219	20	for	for	ADP
ejpam-7112	219	21	the	the	DET
ejpam-7112	219	22	rs	rs	ADJ
ejpam-7112	219	23	-	-	ADJ
ejpam-7112	219	24	integral	integral	ADJ
ejpam-7112	219	25	can	can	AUX
ejpam-7112	219	26	be	be	AUX
ejpam-7112	219	27	described	describe	VERB
ejpam-7112	219	28	generally	generally	ADV
ejpam-7112	219	29	as:∫	as:∫	PROPN
ejpam-7112	219	30	β	β	PROPN
ejpam-7112	219	31	α	α	DET
ejpam-7112	219	32	f(t	f(t	NOUN
ejpam-7112	219	33	)	)	PUNCT
ejpam-7112	219	34	dg	dg	VERB
ejpam-7112	219	35	≈	≈	PROPN
ejpam-7112	219	36	a0f(α	a0f(α	PROPN
ejpam-7112	219	37	)	)	PUNCT
ejpam-7112	220	1	+	+	CCONJ
ejpam-7112	220	2	b0f(β	b0f(β	PROPN
ejpam-7112	220	3	)	)	PUNCT
ejpam-7112	221	1	+	+	CCONJ
ejpam-7112	222	1	c0f	c0f	NOUN
ejpam-7112	222	2	′	′	NOUN
ejpam-7112	222	3	(	(	PUNCT
ejpam-7112	222	4	α+	α+	X
ejpam-7112	222	5	β	β	X
ejpam-7112	222	6	2	2	NUM
ejpam-7112	222	7	)	)	PUNCT
ejpam-7112	222	8	.	.	PUNCT
ejpam-7112	223	1	(	(	PUNCT
ejpam-7112	223	2	24	24	NUM
ejpam-7112	223	3	)	)	PUNCT
ejpam-7112	223	4	looking	look	VERB
ejpam-7112	223	5	at	at	ADP
ejpam-7112	223	6	the	the	DET
ejpam-7112	223	7	precision	precision	NOUN
ejpam-7112	223	8	of	of	ADP
ejpam-7112	223	9	(	(	PUNCT
ejpam-7112	223	10	1	1	X
ejpam-7112	223	11	)	)	PUNCT
ejpam-7112	223	12	[	[	X
ejpam-7112	223	13	4	4	NUM
ejpam-7112	223	14	]	]	PUNCT
ejpam-7112	223	15	,	,	PUNCT
ejpam-7112	223	16	we	we	PRON
ejpam-7112	223	17	can	can	AUX
ejpam-7112	223	18	expect	expect	VERB
ejpam-7112	223	19	the	the	DET
ejpam-7112	223	20	degree	degree	NOUN
ejpam-7112	223	21	of	of	ADP
ejpam-7112	223	22	exactness	exactness	NOUN
ejpam-7112	223	23	of	of	ADP
ejpam-7112	223	24	(	(	PUNCT
ejpam-7112	223	25	24	24	NUM
ejpam-7112	223	26	)	)	PUNCT
ejpam-7112	223	27	to	to	PART
ejpam-7112	223	28	be	be	AUX
ejpam-7112	223	29	3	3	NUM
ejpam-7112	223	30	as	as	ADV
ejpam-7112	223	31	well	well	ADV
ejpam-7112	223	32	.	.	PUNCT
ejpam-7112	224	1	amt	amt	PROPN
ejpam-7112	224	2	quadrature	quadrature	NOUN
ejpam-7112	224	3	in	in	ADP
ejpam-7112	224	4	(	(	PUNCT
ejpam-7112	224	5	24	24	NUM
ejpam-7112	224	6	)	)	PUNCT
ejpam-7112	224	7	when	when	SCONJ
ejpam-7112	224	8	integrand	integrand	NOUN
ejpam-7112	224	9	is	be	AUX
ejpam-7112	224	10	allowed	allow	VERB
ejpam-7112	224	11	to	to	PART
ejpam-7112	224	12	be	be	AUX
ejpam-7112	224	13	a	a	DET
ejpam-7112	224	14	monomial	monomial	NOUN
ejpam-7112	224	15	of	of	ADP
ejpam-7112	224	16	degree	degree	NOUN
ejpam-7112	224	17	at	at	ADP
ejpam-7112	224	18	most	most	ADJ
ejpam-7112	224	19	3	3	NUM
ejpam-7112	224	20	leads	lead	VERB
ejpam-7112	224	21	to	to	ADP
ejpam-7112	224	22	four	four	NUM
ejpam-7112	224	23	equations:∫	equations:∫	NOUN
ejpam-7112	224	24	β	β	ADP
ejpam-7112	224	25	α	α	NOUN
ejpam-7112	224	26	1dg	1dg	NOUN
ejpam-7112	224	27	=	=	SYM
ejpam-7112	224	28	a0	a0	PROPN
ejpam-7112	224	29	+	+	CCONJ
ejpam-7112	224	30	b0,∫	b0,∫	PROPN
ejpam-7112	224	31	β	β	PROPN
ejpam-7112	224	32	α	α	PROPN
ejpam-7112	224	33	tdg	tdg	PROPN
ejpam-7112	224	34	=	=	PROPN
ejpam-7112	224	35	a0α+	a0α+	PROPN
ejpam-7112	224	36	b0β,∫	b0β,∫	PROPN
ejpam-7112	224	37	β	β	X
ejpam-7112	224	38	α	α	NOUN
ejpam-7112	224	39	t2dg	t2dg	NOUN
ejpam-7112	224	40	=	=	PUNCT
ejpam-7112	224	41	a0α	a0α	NOUN
ejpam-7112	224	42	2	2	NUM
ejpam-7112	224	43	+	+	CCONJ
ejpam-7112	224	44	b0β	b0β	PROPN
ejpam-7112	224	45	2	2	NUM
ejpam-7112	224	46	+	+	CCONJ
ejpam-7112	224	47	2c0,∫	2c0,∫	ADJ
ejpam-7112	224	48	β	β	X
ejpam-7112	224	49	α	α	NOUN
ejpam-7112	224	50	t3dg	t3dg	PUNCT
ejpam-7112	224	51	=	=	PUNCT
ejpam-7112	224	52	a0α	a0α	NOUN
ejpam-7112	224	53	3	3	NUM
ejpam-7112	224	54	+	+	CCONJ
ejpam-7112	224	55	b0β	b0β	PROPN
ejpam-7112	224	56	3	3	NUM
ejpam-7112	224	57	+	+	SYM
ejpam-7112	224	58	3c0(α+	3c0(α+	NUM
ejpam-7112	224	59	β	β	NOUN
ejpam-7112	224	60	)	)	PUNCT
ejpam-7112	224	61	.	.	PUNCT
ejpam-7112	225	1	the	the	DET
ejpam-7112	225	2	following	follow	VERB
ejpam-7112	225	3	system	system	NOUN
ejpam-7112	225	4	of	of	ADP
ejpam-7112	225	5	equations	equation	NOUN
ejpam-7112	225	6	(	(	PUNCT
ejpam-7112	225	7	25)-(29	25)-(29	NUM
ejpam-7112	225	8	)	)	PUNCT
ejpam-7112	225	9	has	have	AUX
ejpam-7112	225	10	been	be	AUX
ejpam-7112	225	11	obtained	obtain	VERB
ejpam-7112	225	12	using	use	VERB
ejpam-7112	225	13	the	the	DET
ejpam-7112	225	14	integration	integration	NOUN
ejpam-7112	225	15	technique	technique	NOUN
ejpam-7112	225	16	by	by	ADP
ejpam-7112	225	17	parts	part	NOUN
ejpam-7112	225	18	of	of	ADP
ejpam-7112	225	19	the	the	DET
ejpam-7112	225	20	rs	rs	ADJ
ejpam-7112	225	21	integral	integral	NOUN
ejpam-7112	225	22	.	.	PUNCT
ejpam-7112	226	1	a0	a0	PROPN
ejpam-7112	226	2	+	+	CCONJ
ejpam-7112	226	3	b0	b0	PROPN
ejpam-7112	226	4	=	=	SYM
ejpam-7112	226	5	g(α	g(α	PROPN
ejpam-7112	226	6	)	)	PUNCT
ejpam-7112	227	1	+	+	CCONJ
ejpam-7112	227	2	(	(	PUNCT
ejpam-7112	227	3	β	β	NOUN
ejpam-7112	227	4	)	)	PUNCT
ejpam-7112	227	5	,	,	PUNCT
ejpam-7112	227	6	(	(	PUNCT
ejpam-7112	227	7	25	25	NUM
ejpam-7112	227	8	)	)	PUNCT
ejpam-7112	227	9	a0α+	a0α+	PROPN
ejpam-7112	227	10	b0β	b0β	PROPN
ejpam-7112	227	11	=	=	SYM
ejpam-7112	227	12	α	α	PROPN
ejpam-7112	227	13	β−αi1	β−αi1	ADP
ejpam-7112	227	14	−	−	NOUN
ejpam-7112	227	15	αg(α	αg(α	NUM
ejpam-7112	227	16	)	)	PUNCT
ejpam-7112	228	1	+	+	CCONJ
ejpam-7112	228	2	βg(β)−	βg(β)−	ADJ
ejpam-7112	228	3	β	β	X
ejpam-7112	228	4	β−αi1	β−αi1	ADP
ejpam-7112	228	5	⇒	⇒	PROPN
ejpam-7112	228	6	a0α+	a0α+	PROPN
ejpam-7112	228	7	b0β	b0β	PROPN
ejpam-7112	228	8	=	=	PRON
ejpam-7112	228	9	βg(β)−	βg(β)−	NOUN
ejpam-7112	228	10	αg(α)−	αg(α)−	VERB
ejpam-7112	228	11	i1	i1	NOUN
ejpam-7112	228	12	(	(	PUNCT
ejpam-7112	228	13	26	26	NUM
ejpam-7112	228	14	)	)	PUNCT
ejpam-7112	228	15	aα2	aα2	NOUN
ejpam-7112	228	16	+	+	CCONJ
ejpam-7112	228	17	bβ2	bβ2	NOUN
ejpam-7112	229	1	+	+	CCONJ
ejpam-7112	229	2	2c0	2c0	NUM
ejpam-7112	229	3	=	=	SYM
ejpam-7112	229	4	(	(	PUNCT
ejpam-7112	229	5	α2	α2	ADV
ejpam-7112	229	6	β	β	X
ejpam-7112	229	7	−	−	X
ejpam-7112	229	8	α	α	PRON
ejpam-7112	229	9	−	−	PROPN
ejpam-7112	230	1	β2	β2	NOUN
ejpam-7112	230	2	β	β	NOUN
ejpam-7112	230	3	−	−	PROPN
ejpam-7112	230	4	α	α	PROPN
ejpam-7112	230	5	)	)	PUNCT
ejpam-7112	230	6	i1	i1	PROPN
ejpam-7112	230	7	−	−	PROPN
ejpam-7112	230	8	αz2g(α	αz2g(α	NUM
ejpam-7112	230	9	)	)	PUNCT
ejpam-7112	231	1	+	+	CCONJ
ejpam-7112	231	2	β2g(β	β2g(β	PROPN
ejpam-7112	231	3	)	)	PUNCT
ejpam-7112	232	1	+	+	CCONJ
ejpam-7112	232	2	2i1	2i1	NUM
ejpam-7112	232	3	−	−	NOUN
ejpam-7112	232	4	(	(	PUNCT
ejpam-7112	232	5	β	β	X
ejpam-7112	232	6	−	−	NOUN
ejpam-7112	232	7	α)2i1	α)2i1	ADJ
ejpam-7112	232	8	(	(	PUNCT
ejpam-7112	232	9	27	27	NUM
ejpam-7112	232	10	)	)	PUNCT
ejpam-7112	232	11	⇒	⇒	VERB
ejpam-7112	232	12	aα2	aα2	PROPN
ejpam-7112	232	13	+	+	CCONJ
ejpam-7112	232	14	b0β	b0β	PROPN
ejpam-7112	232	15	2	2	NUM
ejpam-7112	232	16	+	+	NUM
ejpam-7112	232	17	2c0	2c0	NUM
ejpam-7112	232	18	=	=	SYM
ejpam-7112	232	19	β2g(β)−	β2g(β)−	NUM
ejpam-7112	232	20	2βi	2βi	NOUN
ejpam-7112	232	21	+	+	CCONJ
ejpam-7112	232	22	2i2	2i2	NUM
ejpam-7112	232	23	(	(	PUNCT
ejpam-7112	232	24	28	28	NUM
ejpam-7112	232	25	)	)	PUNCT
ejpam-7112	232	26	a0α	a0α	NOUN
ejpam-7112	232	27	3+b20β	3+b20β	NUM
ejpam-7112	232	28	3	3	NUM
ejpam-7112	232	29	+	+	NOUN
ejpam-7112	232	30	3c0(α+β	3c0(α+β	NOUN
ejpam-7112	232	31	)	)	PUNCT
ejpam-7112	233	1	=	=	SYM
ejpam-7112	233	2	α3	α3	NOUN
ejpam-7112	233	3	β−αi1−α3g(α)−β3g(β)−	β−αi1−α3g(α)−β3g(β)−	AUX
ejpam-7112	233	4	β3	β3	AUX
ejpam-7112	233	5	β−αi1	β−αi1	VERB
ejpam-7112	233	6	+	+	PROPN
ejpam-7112	233	7	3(α+β)i2−	3(α+β)i2−	NUM
ejpam-7112	233	8	3	3	NUM
ejpam-7112	233	9	2(β	2(β	NUM
ejpam-7112	233	10	2−α2)i1	2−α2)i1	NUM
ejpam-7112	233	11	⇒	⇒	NOUN
ejpam-7112	233	12	a0α	a0α	NOUN
ejpam-7112	233	13	3	3	NUM
ejpam-7112	234	1	+	+	CCONJ
ejpam-7112	234	2	b0β	b0β	PROPN
ejpam-7112	234	3	3	3	NUM
ejpam-7112	234	4	+	+	SYM
ejpam-7112	234	5	3c0(α+	3c0(α+	NUM
ejpam-7112	234	6	β	β	X
ejpam-7112	234	7	)	)	PUNCT
ejpam-7112	234	8	=	=	SYM
ejpam-7112	234	9	β3g(β)−	β3g(β)−	PUNCT
ejpam-7112	234	10	α3g(α)−	α3g(α)−	PROPN
ejpam-7112	234	11	3β2i1	3β2i1	NUM
ejpam-7112	234	12	+	+	CCONJ
ejpam-7112	234	13	6βi2	6βi2	NUM
ejpam-7112	234	14	−	−	PRON
ejpam-7112	234	15	6i3	6i3	NUM
ejpam-7112	234	16	(	(	PUNCT
ejpam-7112	234	17	29	29	NUM
ejpam-7112	234	18	)	)	PUNCT
ejpam-7112	234	19	the	the	DET
ejpam-7112	234	20	following	follow	VERB
ejpam-7112	234	21	matrix	matrix	NOUN
ejpam-7112	234	22	is	be	AUX
ejpam-7112	234	23	obtained	obtain	VERB
ejpam-7112	234	24	from	from	ADP
ejpam-7112	234	25	the	the	DET
ejpam-7112	234	26	system	system	NOUN
ejpam-7112	234	27	of	of	ADP
ejpam-7112	234	28	linear	linear	PROPN
ejpam-7112	234	29	equations	equation	NOUN
ejpam-7112	234	30	(	(	PUNCT
ejpam-7112	234	31	25)-(29	25)-(29	NUM
ejpam-7112	234	32	)	)	PUNCT
ejpam-7112	234	33	in	in	ADP
ejpam-7112	234	34	the	the	DET
ejpam-7112	234	35	unknowns	unknown	NOUN
ejpam-7112	234	36	:	:	PUNCT
ejpam-7112	234	37	k.	k.	PROPN
ejpam-7112	234	38	memon	memon	PROPN
ejpam-7112	234	39	et	et	PROPN
ejpam-7112	234	40	al	al	PROPN
ejpam-7112	234	41	.	.	PUNCT
ejpam-7112	234	42	/	/	SYM
ejpam-7112	234	43	eur	eur	PROPN
ejpam-7112	234	44	.	.	PUNCT
ejpam-7112	235	1	j.	j.	PROPN
ejpam-7112	235	2	pure	pure	PROPN
ejpam-7112	235	3	appl	appl	PROPN
ejpam-7112	235	4	.	.	PROPN
ejpam-7112	235	5	math	math	PROPN
ejpam-7112	235	6	,	,	PUNCT
ejpam-7112	235	7	18	18	NUM
ejpam-7112	235	8	(	(	PUNCT
ejpam-7112	235	9	4	4	NUM
ejpam-7112	235	10	)	)	PUNCT
ejpam-7112	235	11	(	(	PUNCT
ejpam-7112	235	12	2025	2025	NUM
ejpam-7112	235	13	)	)	PUNCT
ejpam-7112	235	14	,	,	PUNCT
ejpam-7112	235	15	7112	7112	NUM
ejpam-7112	235	16	10	10	NUM
ejpam-7112	235	17	of	of	ADP
ejpam-7112	235	18	38	38	NUM
ejpam-7112	235	19	m	m	NOUN
ejpam-7112	235	20	=	=	NOUN
ejpam-7112	235	21			NOUN
ejpam-7112	235	22	1	1	NUM
ejpam-7112	235	23	1	1	NUM
ejpam-7112	235	24	0	0	NUM
ejpam-7112	236	1	α	α	PRON
ejpam-7112	236	2	β	β	X
ejpam-7112	236	3	0	0	NUM
ejpam-7112	237	1	α2	α2	ADJ
ejpam-7112	237	2	β2	β2	NOUN
ejpam-7112	237	3	2	2	NUM
ejpam-7112	237	4	α3	α3	NOUN
ejpam-7112	237	5	β3	β3	VERB
ejpam-7112	237	6	3(α+	3(α+	PRON
ejpam-7112	237	7	β	β	NOUN
ejpam-7112	237	8	)	)	PUNCT
ejpam-7112	237	9			NOUN
ejpam-7112	237	10	the	the	DET
ejpam-7112	237	11	above	above	ADJ
ejpam-7112	237	12	matrix	matrix	NOUN
ejpam-7112	237	13	m	m	VERB
ejpam-7112	237	14	is	be	AUX
ejpam-7112	237	15	further	far	ADV
ejpam-7112	237	16	written	write	VERB
ejpam-7112	237	17	in	in	ADP
ejpam-7112	237	18	reduced	reduce	VERB
ejpam-7112	237	19	row	row	NOUN
ejpam-7112	237	20	echelon	echelon	NOUN
ejpam-7112	237	21	form	form	NOUN
ejpam-7112	237	22	as	as	ADP
ejpam-7112	237	23	:	:	PUNCT
ejpam-7112	237	24	m	m	VERB
ejpam-7112	237	25	≈	≈	NOUN
ejpam-7112	237	26	mr	mr	NOUN
ejpam-7112	237	27	=	=	NOUN
ejpam-7112	237	28			NOUN
ejpam-7112	238	1	1	1	NUM
ejpam-7112	238	2	0	0	NUM
ejpam-7112	238	3	0	0	NUM
ejpam-7112	238	4	0	0	NUM
ejpam-7112	238	5	1	1	NUM
ejpam-7112	238	6	0	0	NUM
ejpam-7112	238	7	0	0	NUM
ejpam-7112	238	8	0	0	NUM
ejpam-7112	238	9	1	1	NUM
ejpam-7112	238	10	0	0	NUM
ejpam-7112	238	11	0	0	NUM
ejpam-7112	238	12	0	0	NUM
ejpam-7112	238	13			NOUN
ejpam-7112	238	14	it	it	PRON
ejpam-7112	238	15	is	be	AUX
ejpam-7112	238	16	observed	observe	VERB
ejpam-7112	238	17	frommr	frommr	ADV
ejpam-7112	238	18	that	that	SCONJ
ejpam-7112	238	19	the	the	DET
ejpam-7112	238	20	rank(m	rank(m	NOUN
ejpam-7112	238	21	)	)	PUNCT
ejpam-7112	238	22	=	=	SYM
ejpam-7112	239	1	3	3	NUM
ejpam-7112	239	2	,	,	PUNCT
ejpam-7112	239	3	since	since	SCONJ
ejpam-7112	239	4	the	the	DET
ejpam-7112	239	5	reduced	reduce	VERB
ejpam-7112	239	6	row	row	NOUN
ejpam-7112	239	7	echelon	echelon	NOUN
ejpam-7112	239	8	form	form	NOUN
ejpam-7112	239	9	has	have	VERB
ejpam-7112	239	10	three	three	NUM
ejpam-7112	239	11	nonzero	nonzero	NOUN
ejpam-7112	239	12	rows	row	NOUN
ejpam-7112	239	13	.	.	PUNCT
ejpam-7112	240	1	so	so	ADV
ejpam-7112	240	2	,	,	PUNCT
ejpam-7112	240	3	we	we	PRON
ejpam-7112	240	4	solve	solve	VERB
ejpam-7112	240	5	the	the	DET
ejpam-7112	240	6	above	above	ADJ
ejpam-7112	240	7	equations	equation	NOUN
ejpam-7112	240	8	(	(	PUNCT
ejpam-7112	240	9	25	25	NUM
ejpam-7112	240	10	)	)	PUNCT
ejpam-7112	240	11	,	,	PUNCT
ejpam-7112	240	12	(	(	PUNCT
ejpam-7112	240	13	26	26	NUM
ejpam-7112	240	14	)	)	PUNCT
ejpam-7112	240	15	,	,	PUNCT
ejpam-7112	240	16	and	and	CCONJ
ejpam-7112	240	17	(	(	PUNCT
ejpam-7112	240	18	28	28	NUM
ejpam-7112	240	19	)	)	PUNCT
ejpam-7112	240	20	simultaneously	simultaneously	ADV
ejpam-7112	240	21	to	to	PART
ejpam-7112	240	22	determine	determine	VERB
ejpam-7112	240	23	the	the	DET
ejpam-7112	240	24	coefficients	coefficient	NOUN
ejpam-7112	240	25	a0	a0	PROPN
ejpam-7112	240	26	,	,	PUNCT
ejpam-7112	241	1	b0andc0	b0andc0	PROPN
ejpam-7112	241	2	.	.	PROPN
ejpam-7112	241	3	a0	a0	PROPN
ejpam-7112	241	4	=	=	PROPN
ejpam-7112	241	5	1	1	NUM
ejpam-7112	241	6	β−αi1g(α	β−αi1g(α	NOUN
ejpam-7112	241	7	)	)	PUNCT
ejpam-7112	241	8	b0	b0	NOUN
ejpam-7112	241	9	=	=	SYM
ejpam-7112	241	10	g(β)−	g(β)−	PROPN
ejpam-7112	241	11	1	1	NUM
ejpam-7112	241	12	β−αi1	β−αi1	PROPN
ejpam-7112	241	13	c0	c0	PROPN
ejpam-7112	241	14	=	=	SYM
ejpam-7112	241	15	(	(	PUNCT
ejpam-7112	241	16	β−α	β−α	X
ejpam-7112	241	17	2	2	NUM
ejpam-7112	241	18	)	)	PUNCT
ejpam-7112	241	19	i1	i1	PROPN
ejpam-7112	241	20	+	+	CCONJ
ejpam-7112	241	21	i2	i2	PROPN
ejpam-7112	241	22	putting	put	VERB
ejpam-7112	241	23	the	the	DET
ejpam-7112	241	24	values	value	NOUN
ejpam-7112	241	25	of	of	ADP
ejpam-7112	241	26	coefficients	coefficient	NOUN
ejpam-7112	241	27	a0	a0	PROPN
ejpam-7112	241	28	,	,	PUNCT
ejpam-7112	241	29	b0andc0	b0andc0	PROPN
ejpam-7112	241	30	in	in	ADP
ejpam-7112	241	31	(	(	PUNCT
ejpam-7112	241	32	24	24	NUM
ejpam-7112	241	33	)	)	PUNCT
ejpam-7112	241	34	,	,	PUNCT
ejpam-7112	241	35	we	we	PRON
ejpam-7112	241	36	have:∫	have:∫	VERB
ejpam-7112	241	37	β	β	PROPN
ejpam-7112	241	38	α	α	DET
ejpam-7112	241	39	f(t	f(t	NOUN
ejpam-7112	241	40	)	)	PUNCT
ejpam-7112	241	41	dg	dg	VERB
ejpam-7112	242	1	≈	≈	PROPN
ejpam-7112	242	2	[	[	PUNCT
ejpam-7112	242	3	1	1	NUM
ejpam-7112	242	4	β	β	NOUN
ejpam-7112	242	5	−	−	PROPN
ejpam-7112	242	6	α	α	PROPN
ejpam-7112	242	7	i1	i1	PROPN
ejpam-7112	242	8	−	−	PROPN
ejpam-7112	242	9	g(α)]f(α	g(α)]f(α	PROPN
ejpam-7112	242	10	)	)	PUNCT
ejpam-7112	243	1	+	+	CCONJ
ejpam-7112	244	1	[	[	X
ejpam-7112	244	2	g(β)−	g(β)−	PROPN
ejpam-7112	244	3	1	1	NUM
ejpam-7112	244	4	β	β	NOUN
ejpam-7112	244	5	−	−	PROPN
ejpam-7112	244	6	α	α	PROPN
ejpam-7112	244	7	i1]f(β	i1]f(β	PROPN
ejpam-7112	244	8	)	)	PUNCT
ejpam-7112	244	9	+	+	CCONJ
ejpam-7112	245	1	[	[	X
ejpam-7112	245	2	(	(	PUNCT
ejpam-7112	245	3	β	β	X
ejpam-7112	245	4	−	−	NOUN
ejpam-7112	245	5	α	α	NOUN
ejpam-7112	245	6	2	2	X
ejpam-7112	245	7	)	)	PUNCT
ejpam-7112	245	8	i1	i1	NOUN
ejpam-7112	246	1	+	+	CCONJ
ejpam-7112	247	1	i2]f	i2]f	PROPN
ejpam-7112	247	2	′	′	NUM
ejpam-7112	247	3	(	(	PUNCT
ejpam-7112	247	4	α+	α+	X
ejpam-7112	247	5	β	β	X
ejpam-7112	247	6	2	2	NUM
ejpam-7112	247	7	)	)	PUNCT
ejpam-7112	247	8	.	.	PUNCT
ejpam-7112	248	1	(	(	PUNCT
ejpam-7112	248	2	30	30	X
ejpam-7112	248	3	)	)	PUNCT
ejpam-7112	248	4	this	this	DET
ejpam-7112	248	5	formula	formula	NOUN
ejpam-7112	248	6	is	be	AUX
ejpam-7112	248	7	the	the	DET
ejpam-7112	248	8	required	require	VERB
ejpam-7112	248	9	amt	amt	PROPN
ejpam-7112	248	10	quadrature	quadrature	NOUN
ejpam-7112	248	11	,	,	PUNCT
ejpam-7112	248	12	as	as	ADP
ejpam-7112	248	13	in	in	ADP
ejpam-7112	248	14	(	(	PUNCT
ejpam-7112	248	15	23	23	NUM
ejpam-7112	248	16	)	)	PUNCT
ejpam-7112	248	17	.	.	PUNCT
ejpam-7112	249	1	theorem	theorem	VERB
ejpam-7112	249	2	2	2	NUM
ejpam-7112	249	3	presents	present	NOUN
ejpam-7112	249	4	truncation	truncation	NOUN
ejpam-7112	249	5	error	error	NOUN
ejpam-7112	249	6	in	in	ADP
ejpam-7112	249	7	the	the	DET
ejpam-7112	249	8	amt	amt	PROPN
ejpam-7112	249	9	quadrature	quadrature	NOUN
ejpam-7112	249	10	locally	locally	ADV
ejpam-7112	249	11	.	.	PUNCT
ejpam-7112	250	1	theorem	theorem	NOUN
ejpam-7112	250	2	2	2	NUM
ejpam-7112	250	3	.	.	PUNCT
ejpam-7112	250	4	assuming	assume	VERB
ejpam-7112	250	5	continuity	continuity	NOUN
ejpam-7112	250	6	of	of	ADP
ejpam-7112	250	7	f(t	f(t	PROPN
ejpam-7112	250	8	)	)	PUNCT
ejpam-7112	250	9	and	and	CCONJ
ejpam-7112	250	10	g(t	g(t	PROPN
ejpam-7112	250	11	)	)	PUNCT
ejpam-7112	250	12	in	in	ADP
ejpam-7112	250	13	along	along	ADP
ejpam-7112	250	14	with	with	ADP
ejpam-7112	250	15	g(t	g(t	PROPN
ejpam-7112	250	16	)	)	PUNCT
ejpam-7112	250	17	being	be	AUX
ejpam-7112	250	18	monotonically	monotonically	ADV
ejpam-7112	250	19	rising	rise	VERB
ejpam-7112	250	20	in	in	ADP
ejpam-7112	250	21	the	the	DET
ejpam-7112	250	22	same	same	ADJ
ejpam-7112	250	23	interval	interval	NOUN
ejpam-7112	250	24	[	[	X
ejpam-7112	250	25	α	α	X
ejpam-7112	250	26	,	,	PUNCT
ejpam-7112	250	27	β	β	X
ejpam-7112	250	28	]	]	X
ejpam-7112	250	29	,	,	PUNCT
ejpam-7112	250	30	amt	amt	PROPN
ejpam-7112	250	31	quadrature	quadrature	NOUN
ejpam-7112	250	32	’s	’s	PART
ejpam-7112	250	33	truncation	truncation	NOUN
ejpam-7112	250	34	error	error	NOUN
ejpam-7112	250	35	for	for	ADP
ejpam-7112	250	36	the	the	DET
ejpam-7112	250	37	rs	rs	ADJ
ejpam-7112	250	38	-	-	ADJ
ejpam-7112	250	39	integral	integral	ADJ
ejpam-7112	250	40	is	be	AUX
ejpam-7112	250	41	:	:	PUNCT
ejpam-7112	250	42	ramt[f	ramt[f	X
ejpam-7112	250	43	]	]	PUNCT
ejpam-7112	251	1	=	=	SYM
ejpam-7112	251	2	(	(	PUNCT
ejpam-7112	251	3	2α3	2α3	NUM
ejpam-7112	251	4	+	+	CCONJ
ejpam-7112	251	5	2αβ2	2αβ2	NUM
ejpam-7112	251	6	−	−	NOUN
ejpam-7112	251	7	6β3	6β3	NUM
ejpam-7112	251	8	+	+	CCONJ
ejpam-7112	251	9	3(β	3(β	NUM
ejpam-7112	251	10	−	−	NOUN
ejpam-7112	251	11	α)(α+	α)(α+	NOUN
ejpam-7112	251	12	β)2	β)2	X
ejpam-7112	251	13	48	48	NUM
ejpam-7112	251	14	i1	i1	PROPN
ejpam-7112	251	15	)	)	PUNCT
ejpam-7112	251	16	f	f	PROPN
ejpam-7112	251	17	(	(	PUNCT
ejpam-7112	251	18	4)(ξ)g(η	4)(ξ)g(η	NUM
ejpam-7112	251	19	)	)	PUNCT
ejpam-7112	251	20	+	+	CCONJ
ejpam-7112	251	21	(	(	PUNCT
ejpam-7112	251	22	4β2	4β2	NUM
ejpam-7112	251	23	−	−	NOUN
ejpam-7112	251	24	(	(	PUNCT
ejpam-7112	251	25	α+	α+	X
ejpam-7112	251	26	β)2	β)2	X
ejpam-7112	251	27	8	8	NUM
ejpam-7112	251	28	i2	i2	PROPN
ejpam-7112	251	29	−	−	PROPN
ejpam-7112	251	30	i2	i2	PROPN
ejpam-7112	251	31	βi3	βi3	PROPN
ejpam-7112	252	1	+	+	CCONJ
ejpam-7112	252	2	i4	i4	PROPN
ejpam-7112	252	3	)	)	PUNCT
ejpam-7112	252	4	f	f	PROPN
ejpam-7112	252	5	(	(	PUNCT
ejpam-7112	252	6	4)(ξ)g(η	4)(ξ)g(η	NUM
ejpam-7112	252	7	)	)	PUNCT
ejpam-7112	252	8	(	(	PUNCT
ejpam-7112	252	9	31	31	NUM
ejpam-7112	252	10	)	)	PUNCT
ejpam-7112	252	11	proof	proof	NOUN
ejpam-7112	252	12	.	.	PUNCT
ejpam-7112	253	1	taking	take	VERB
ejpam-7112	253	2	for	for	ADP
ejpam-7112	253	3	the	the	DET
ejpam-7112	253	4	truncation	truncation	NOUN
ejpam-7112	253	5	error	error	NOUN
ejpam-7112	253	6	,	,	PUNCT
ejpam-7112	253	7	as	as	SCONJ
ejpam-7112	253	8	degree	degree	NOUN
ejpam-7112	253	9	of	of	ADP
ejpam-7112	253	10	exactness	exactness	NOUN
ejpam-7112	253	11	of	of	ADP
ejpam-7112	253	12	(	(	PUNCT
ejpam-7112	253	13	23	23	NUM
ejpam-7112	253	14	)	)	PUNCT
ejpam-7112	253	15	is	be	AUX
ejpam-7112	253	16	3	3	NUM
ejpam-7112	253	17	,	,	PUNCT
ejpam-7112	253	18	we	we	PRON
ejpam-7112	253	19	have	have	AUX
ejpam-7112	253	20	:	:	PUNCT
ejpam-7112	253	21	ramt[f	ramt[f	X
ejpam-7112	253	22	]	]	PUNCT
ejpam-7112	253	23	=	=	SYM
ejpam-7112	253	24	1	1	NUM
ejpam-7112	253	25	4	4	NUM
ejpam-7112	253	26	!	!	PUNCT
ejpam-7112	253	27	∫	∫	PROPN
ejpam-7112	254	1	β	β	PROPN
ejpam-7112	254	2	α	α	PROPN
ejpam-7112	254	3	t4	t4	PROPN
ejpam-7112	254	4	dg	dg	PROPN
ejpam-7112	254	5	−amt	−amt	PROPN
ejpam-7112	254	6	(	(	PUNCT
ejpam-7112	254	7	t4	t4	PROPN
ejpam-7112	254	8	;	;	PUNCT
ejpam-7112	254	9	g;α	g;α	PROPN
ejpam-7112	254	10	,	,	PUNCT
ejpam-7112	254	11	β	β	NOUN
ejpam-7112	254	12	)	)	PUNCT
ejpam-7112	254	13	(	(	PUNCT
ejpam-7112	254	14	32	32	NUM
ejpam-7112	254	15	)	)	PUNCT
ejpam-7112	254	16	from	from	ADP
ejpam-7112	254	17	[	[	X
ejpam-7112	254	18	4	4	NUM
ejpam-7112	254	19	]	]	PUNCT
ejpam-7112	254	20	,	,	PUNCT
ejpam-7112	254	21	we	we	PRON
ejpam-7112	254	22	know	know	VERB
ejpam-7112	254	23	that	that	PRON
ejpam-7112	254	24	:	:	PUNCT
ejpam-7112	254	25	1	1	NUM
ejpam-7112	254	26	4	4	NUM
ejpam-7112	254	27	!	!	PUNCT
ejpam-7112	254	28	∫	∫	PROPN
ejpam-7112	254	29	β	β	PROPN
ejpam-7112	254	30	α	α	PROPN
ejpam-7112	254	31	t4	t4	PROPN
ejpam-7112	254	32	dg	dg	PROPN
ejpam-7112	254	33	=	=	SYM
ejpam-7112	254	34	1	1	NUM
ejpam-7112	254	35	24	24	NUM
ejpam-7112	254	36	(	(	PUNCT
ejpam-7112	254	37	(	(	PUNCT
ejpam-7112	254	38	β4g(β))−	β4g(β))−	ADP
ejpam-7112	254	39	α4g(α))−	α4g(α))−	AUX
ejpam-7112	254	40	β3	β3	VERB
ejpam-7112	254	41	6	6	NUM
ejpam-7112	254	42	i1	i1	PROPN
ejpam-7112	254	43	−	−	PROPN
ejpam-7112	255	1	βi3	βi3	PROPN
ejpam-7112	256	1	+	+	CCONJ
ejpam-7112	256	2	i4	i4	PROPN
ejpam-7112	256	3	(	(	PUNCT
ejpam-7112	256	4	33	33	NUM
ejpam-7112	256	5	)	)	PUNCT
ejpam-7112	256	6	k.	k.	PROPN
ejpam-7112	256	7	memon	memon	PROPN
ejpam-7112	256	8	et	et	PROPN
ejpam-7112	256	9	al	al	PROPN
ejpam-7112	256	10	.	.	PUNCT
ejpam-7112	256	11	/	/	SYM
ejpam-7112	256	12	eur	eur	PROPN
ejpam-7112	256	13	.	.	PUNCT
ejpam-7112	257	1	j.	j.	PROPN
ejpam-7112	257	2	pure	pure	PROPN
ejpam-7112	257	3	appl	appl	PROPN
ejpam-7112	257	4	.	.	PROPN
ejpam-7112	257	5	math	math	PROPN
ejpam-7112	257	6	,	,	PUNCT
ejpam-7112	257	7	18	18	NUM
ejpam-7112	257	8	(	(	PUNCT
ejpam-7112	257	9	4	4	NUM
ejpam-7112	257	10	)	)	PUNCT
ejpam-7112	257	11	(	(	PUNCT
ejpam-7112	257	12	2025	2025	NUM
ejpam-7112	257	13	)	)	PUNCT
ejpam-7112	257	14	,	,	PUNCT
ejpam-7112	257	15	7112	7112	NUM
ejpam-7112	257	16	11	11	NUM
ejpam-7112	257	17	of	of	ADP
ejpam-7112	257	18	38	38	NUM
ejpam-7112	257	19	by	by	ADP
ejpam-7112	257	20	theorem	theorem	ADJ
ejpam-7112	257	21	1	1	NUM
ejpam-7112	257	22	and	and	CCONJ
ejpam-7112	257	23	scheme	scheme	NOUN
ejpam-7112	257	24	(	(	PUNCT
ejpam-7112	257	25	23	23	NUM
ejpam-7112	257	26	)	)	PUNCT
ejpam-7112	257	27	,	,	PUNCT
ejpam-7112	257	28	we	we	PRON
ejpam-7112	257	29	have	have	VERB
ejpam-7112	257	30	:	:	PUNCT
ejpam-7112	257	31	amt	amt	PROPN
ejpam-7112	257	32	(	(	PUNCT
ejpam-7112	257	33	t4	t4	PROPN
ejpam-7112	257	34	;	;	PUNCT
ejpam-7112	257	35	g;α	g;α	PROPN
ejpam-7112	257	36	,	,	PUNCT
ejpam-7112	257	37	β	β	NOUN
ejpam-7112	257	38	)	)	PUNCT
ejpam-7112	257	39	=	=	VERB
ejpam-7112	258	1	α2	α2	ADJ
ejpam-7112	258	2	4	4	NUM
ejpam-7112	258	3	!	!	PUNCT
ejpam-7112	259	1	(	(	PUNCT
ejpam-7112	259	2	1	1	NUM
ejpam-7112	259	3	β	β	X
ejpam-7112	259	4	−	−	PROPN
ejpam-7112	259	5	α	α	PROPN
ejpam-7112	259	6	i1	i1	PROPN
ejpam-7112	259	7	−	−	PROPN
ejpam-7112	259	8	g(α	g(α	PROPN
ejpam-7112	259	9	)	)	PUNCT
ejpam-7112	259	10	)	)	PUNCT
ejpam-7112	260	1	+	+	CCONJ
ejpam-7112	260	2	β2	β2	VERB
ejpam-7112	260	3	4	4	NUM
ejpam-7112	260	4	!	!	PUNCT
ejpam-7112	261	1	(	(	PUNCT
ejpam-7112	261	2	g(β)−	g(β)−	PROPN
ejpam-7112	261	3	1	1	NUM
ejpam-7112	261	4	β	β	NOUN
ejpam-7112	261	5	−	−	PROPN
ejpam-7112	261	6	α	α	PROPN
ejpam-7112	261	7	i1	i1	PROPN
ejpam-7112	261	8	)	)	PUNCT
ejpam-7112	262	1	+	+	CCONJ
ejpam-7112	262	2	(	(	PUNCT
ejpam-7112	262	3	α+	α+	X
ejpam-7112	262	4	β)2	β)2	X
ejpam-7112	262	5	8	8	NUM
ejpam-7112	262	6	(	(	PUNCT
ejpam-7112	262	7	i2	i2	PROPN
ejpam-7112	262	8	−	−	PROPN
ejpam-7112	262	9	β	β	NOUN
ejpam-7112	262	10	−	−	PROPN
ejpam-7112	262	11	α	α	PROPN
ejpam-7112	262	12	2	2	NUM
ejpam-7112	262	13	i1	i1	NOUN
ejpam-7112	262	14	)	)	PUNCT
ejpam-7112	262	15	1	1	NUM
ejpam-7112	262	16	2	2	NUM
ejpam-7112	262	17	!	!	PUNCT
ejpam-7112	263	1	(	(	PUNCT
ejpam-7112	263	2	α+	α+	X
ejpam-7112	263	3	β	β	X
ejpam-7112	263	4	2	2	NUM
ejpam-7112	263	5	)	)	PUNCT
ejpam-7112	263	6	2	2	NUM
ejpam-7112	263	7	(	(	PUNCT
ejpam-7112	263	8	34	34	NUM
ejpam-7112	263	9	)	)	PUNCT
ejpam-7112	263	10	ramt	ramt	VERB
ejpam-7112	264	1	[	[	X
ejpam-7112	264	2	f	f	X
ejpam-7112	264	3	]	]	X
ejpam-7112	264	4	=	=	SYM
ejpam-7112	264	5	1	1	NUM
ejpam-7112	264	6	24	24	NUM
ejpam-7112	264	7	[	[	X
ejpam-7112	264	8	(	(	PUNCT
ejpam-7112	264	9	β4g(β)−α4g(α))−	β4g(β)−α4g(α))−	NOUN
ejpam-7112	264	10	(	(	PUNCT
ejpam-7112	264	11	β)3	β)3	PROPN
ejpam-7112	264	12	6	6	NUM
ejpam-7112	264	13	i1	i1	NOUN
ejpam-7112	264	14	+	+	CCONJ
ejpam-7112	264	15	(	(	PUNCT
ejpam-7112	264	16	β)2	β)2	X
ejpam-7112	264	17	2	2	NUM
ejpam-7112	264	18	i2−βi3	i2−βi3	PROPN
ejpam-7112	264	19	+	+	NUM
ejpam-7112	264	20	i4	i4	PROPN
ejpam-7112	264	21	+	+	CCONJ
ejpam-7112	264	22	α4	α4	NOUN
ejpam-7112	264	23	24(β	24(β	NUM
ejpam-7112	264	24	−	−	PROPN
ejpam-7112	264	25	α	α	X
ejpam-7112	264	26	)	)	PUNCT
ejpam-7112	264	27	i1	i1	NOUN
ejpam-7112	264	28	+	+	CCONJ
ejpam-7112	264	29	α4g(α	α4g(α	PROPN
ejpam-7112	264	30	)	)	PUNCT
ejpam-7112	264	31	24	24	NUM
ejpam-7112	264	32	−	−	PROPN
ejpam-7112	264	33	β4g(β	β4g(β	PROPN
ejpam-7112	264	34	)	)	PUNCT
ejpam-7112	264	35	24	24	NUM
ejpam-7112	265	1	+	+	CCONJ
ejpam-7112	265	2	β4	β4	PROPN
ejpam-7112	265	3	24(β	24(β	NUM
ejpam-7112	265	4	−	−	PROPN
ejpam-7112	265	5	α	α	X
ejpam-7112	265	6	)	)	PUNCT
ejpam-7112	265	7	i1	i1	PROPN
ejpam-7112	265	8	−	−	PROPN
ejpam-7112	266	1	(	(	PUNCT
ejpam-7112	266	2	α+	α+	X
ejpam-7112	266	3	β)2	β)2	X
ejpam-7112	266	4	8	8	NUM
ejpam-7112	266	5	i2	i2	NOUN
ejpam-7112	266	6	+	+	CCONJ
ejpam-7112	266	7	(	(	PUNCT
ejpam-7112	266	8	β	β	X
ejpam-7112	266	9	−	−	NOUN
ejpam-7112	266	10	α)(α+	α)(α+	NOUN
ejpam-7112	266	11	β)2	β)2	X
ejpam-7112	266	12	16	16	NUM
ejpam-7112	266	13	]	]	SYM
ejpam-7112	266	14	f	f	X
ejpam-7112	266	15	(	(	PUNCT
ejpam-7112	266	16	4)(ξ)g(η	4)(ξ)g(η	NUM
ejpam-7112	266	17	)	)	PUNCT
ejpam-7112	266	18	(	(	PUNCT
ejpam-7112	266	19	35	35	NUM
ejpam-7112	266	20	)	)	PUNCT
ejpam-7112	266	21	ramt	ramt	VERB
ejpam-7112	267	1	[	[	X
ejpam-7112	267	2	f	f	X
ejpam-7112	267	3	]	]	X
ejpam-7112	267	4	=	=	PUNCT
ejpam-7112	267	5	(	(	PUNCT
ejpam-7112	267	6	2α3	2α3	NUM
ejpam-7112	267	7	+	+	CCONJ
ejpam-7112	267	8	2αβ2	2αβ2	NUM
ejpam-7112	267	9	+	+	CCONJ
ejpam-7112	267	10	2α2β	2α2β	ADJ
ejpam-7112	267	11	−	−	NOUN
ejpam-7112	267	12	6β3	6β3	NUM
ejpam-7112	267	13	+	+	CCONJ
ejpam-7112	267	14	3(β	3(β	NUM
ejpam-7112	267	15	−	−	NOUN
ejpam-7112	267	16	α)(α+	α)(α+	NOUN
ejpam-7112	267	17	β)2	β)2	X
ejpam-7112	267	18	48	48	NUM
ejpam-7112	267	19	)	)	PUNCT
ejpam-7112	267	20	i1	i1	PROPN
ejpam-7112	267	21	+	+	CCONJ
ejpam-7112	267	22	[	[	PUNCT
ejpam-7112	267	23	4β2	4β2	NUM
ejpam-7112	267	24	−	−	PROPN
ejpam-7112	267	25	(	(	PUNCT
ejpam-7112	267	26	α−	α−	ADP
ejpam-7112	267	27	β)2	β)2	X
ejpam-7112	267	28	8	8	NUM
ejpam-7112	267	29	i2	i2	NOUN
ejpam-7112	267	30	−	−	NOUN
ejpam-7112	267	31	βj3	βj3	NOUN
ejpam-7112	267	32	+	+	CCONJ
ejpam-7112	267	33	i4	i4	PROPN
ejpam-7112	267	34	]	]	PUNCT
ejpam-7112	267	35	f	f	PROPN
ejpam-7112	267	36	(	(	PUNCT
ejpam-7112	267	37	4)(ξ)g(η	4)(ξ)g(η	NUM
ejpam-7112	267	38	)	)	PUNCT
ejpam-7112	267	39	(	(	PUNCT
ejpam-7112	267	40	36	36	NUM
ejpam-7112	267	41	)	)	PUNCT
ejpam-7112	267	42	theorem	theorem	NOUN
ejpam-7112	267	43	3	3	NUM
ejpam-7112	267	44	.	.	PUNCT
ejpam-7112	268	1	if	if	SCONJ
ejpam-7112	268	2	g(t	g(t	PROPN
ejpam-7112	268	3	)	)	PUNCT
ejpam-7112	269	1	=	=	SYM
ejpam-7112	269	2	t	t	PROPN
ejpam-7112	269	3	,	,	PUNCT
ejpam-7112	269	4	then	then	ADV
ejpam-7112	269	5	amt	amt	PROPN
ejpam-7112	269	6	quadrature	quadrature	NOUN
ejpam-7112	269	7	and	and	CCONJ
ejpam-7112	269	8	its	its	PRON
ejpam-7112	269	9	truncation	truncation	NOUN
ejpam-7112	269	10	error	error	NOUN
ejpam-7112	269	11	term	term	NOUN
ejpam-7112	269	12	as	as	ADP
ejpam-7112	269	13	in	in	ADP
ejpam-7112	269	14	(	(	PUNCT
ejpam-7112	269	15	23)-(24	23)-(24	NUM
ejpam-7112	269	16	)	)	PUNCT
ejpam-7112	269	17	for	for	ADP
ejpam-7112	269	18	rs	rs	X
ejpam-7112	269	19	integral	integral	ADJ
ejpam-7112	269	20	reduces	reduce	NOUN
ejpam-7112	269	21	to	to	ADP
ejpam-7112	269	22	simple	simple	ADJ
ejpam-7112	269	23	amt	amt	PROPN
ejpam-7112	269	24	quadrature	quadrature	NOUN
ejpam-7112	269	25	(	(	PUNCT
ejpam-7112	269	26	10	10	NUM
ejpam-7112	269	27	)	)	PUNCT
ejpam-7112	270	1	[	[	X
ejpam-7112	270	2	4	4	NUM
ejpam-7112	270	3	]	]	PUNCT
ejpam-7112	270	4	.	.	PUNCT
ejpam-7112	271	1	proof	proof	NOUN
ejpam-7112	271	2	.	.	PUNCT
ejpam-7112	272	1	obtaining	obtain	VERB
ejpam-7112	272	2	the	the	DET
ejpam-7112	272	3	following	following	NOUN
ejpam-7112	272	4	using	use	VERB
ejpam-7112	272	5	the	the	DET
ejpam-7112	272	6	theorem	theorem	ADJ
ejpam-7112	272	7	2:∫	2:∫	NUM
ejpam-7112	272	8	β	β	NOUN
ejpam-7112	272	9	a	a	DET
ejpam-7112	272	10	f(t	f(t	PROPN
ejpam-7112	272	11	)	)	PUNCT
ejpam-7112	272	12	dg	dg	PART
ejpam-7112	272	13	=	=	SYM
ejpam-7112	272	14	∫	∫	PROPN
ejpam-7112	272	15	β	β	PROPN
ejpam-7112	272	16	a	a	DET
ejpam-7112	272	17	f(t	f(t	PROPN
ejpam-7112	272	18	)	)	PUNCT
ejpam-7112	272	19	dt	dt	NOUN
ejpam-7112	273	1	=	=	PUNCT
ejpam-7112	273	2	(	(	PUNCT
ejpam-7112	273	3	1	1	NUM
ejpam-7112	273	4	β	β	X
ejpam-7112	273	5	−	−	PROPN
ejpam-7112	274	1	α	α	X
ejpam-7112	274	2	∫	∫	PROPN
ejpam-7112	274	3	β	β	PROPN
ejpam-7112	274	4	a	a	PRON
ejpam-7112	274	5	t	t	PROPN
ejpam-7112	274	6	dt−	dt−	X
ejpam-7112	274	7	g(α	g(α	PROPN
ejpam-7112	274	8	)	)	PUNCT
ejpam-7112	274	9	)	)	PUNCT
ejpam-7112	274	10	f(α	f(α	NOUN
ejpam-7112	274	11	)	)	PUNCT
ejpam-7112	275	1	+	+	CCONJ
ejpam-7112	275	2	(	(	PUNCT
ejpam-7112	275	3	g(β)−	g(β)−	PROPN
ejpam-7112	275	4	1	1	NUM
ejpam-7112	275	5	β	β	NOUN
ejpam-7112	275	6	−	−	PROPN
ejpam-7112	275	7	α	α	DET
ejpam-7112	275	8	∫	∫	PROPN
ejpam-7112	275	9	β	β	X
ejpam-7112	275	10	a	a	PROPN
ejpam-7112	275	11	t	t	NOUN
ejpam-7112	275	12	dt	dt	PUNCT
ejpam-7112	275	13	)	)	PUNCT
ejpam-7112	276	1	f(β	f(β	PROPN
ejpam-7112	276	2	)	)	PUNCT
ejpam-7112	277	1	+	+	CCONJ
ejpam-7112	277	2	(	(	PUNCT
ejpam-7112	277	3	∫	∫	PROPN
ejpam-7112	277	4	β	β	X
ejpam-7112	277	5	a	a	DET
ejpam-7112	277	6	∫	∫	PROPN
ejpam-7112	277	7	t	t	PROPN
ejpam-7112	277	8	a	a	X
ejpam-7112	277	9	x	x	SYM
ejpam-7112	277	10	dx	dx	PROPN
ejpam-7112	277	11	dt−	dt−	PROPN
ejpam-7112	277	12	β	β	X
ejpam-7112	277	13	−	−	X
ejpam-7112	277	14	α	α	NOUN
ejpam-7112	277	15	2	2	NUM
ejpam-7112	277	16	∫	∫	PROPN
ejpam-7112	277	17	β	β	PROPN
ejpam-7112	277	18	a	a	PROPN
ejpam-7112	277	19	t	t	NOUN
ejpam-7112	277	20	dt	dt	NOUN
ejpam-7112	277	21	)	)	PUNCT
ejpam-7112	278	1	f	f	PROPN
ejpam-7112	278	2	′′	′′	PROPN
ejpam-7112	278	3	(	(	PUNCT
ejpam-7112	278	4	α+	α+	X
ejpam-7112	278	5	β	β	X
ejpam-7112	278	6	2	2	NUM
ejpam-7112	278	7	)	)	PUNCT
ejpam-7112	278	8	+	+	CCONJ
ejpam-7112	278	9	2α3	2α3	NUM
ejpam-7112	278	10	+	+	CCONJ
ejpam-7112	278	11	2αβ2	2αβ2	NUM
ejpam-7112	278	12	+	+	CCONJ
ejpam-7112	278	13	2α2β	2α2β	ADJ
ejpam-7112	278	14	−	−	NOUN
ejpam-7112	278	15	6β3	6β3	NUM
ejpam-7112	278	16	+	+	CCONJ
ejpam-7112	278	17	3(β	3(β	NUM
ejpam-7112	278	18	−	−	NOUN
ejpam-7112	278	19	α)(α+	α)(α+	NOUN
ejpam-7112	278	20	β)2	β)2	X
ejpam-7112	278	21	48	48	NUM
ejpam-7112	278	22	∫	∫	PROPN
ejpam-7112	278	23	β	β	PROPN
ejpam-7112	278	24	a	a	PROPN
ejpam-7112	278	25	t	t	X
ejpam-7112	278	26	dt	dt	NOUN
ejpam-7112	278	27	+	+	CCONJ
ejpam-7112	278	28	4β2	4β2	NUM
ejpam-7112	278	29	−	−	NOUN
ejpam-7112	278	30	(	(	PUNCT
ejpam-7112	278	31	α+	α+	X
ejpam-7112	278	32	β)2	β)2	X
ejpam-7112	278	33	8	8	NUM
ejpam-7112	278	34	(	(	PUNCT
ejpam-7112	278	35	∫	∫	PROPN
ejpam-7112	278	36	β	β	PROPN
ejpam-7112	278	37	a	a	DET
ejpam-7112	278	38	∫	∫	PROPN
ejpam-7112	278	39	t	t	PROPN
ejpam-7112	278	40	a	a	X
ejpam-7112	278	41	x	x	SYM
ejpam-7112	278	42	dx	dx	PROPN
ejpam-7112	278	43	dt−	dt−	PROPN
ejpam-7112	278	44	β	β	X
ejpam-7112	278	45	∫	∫	PROPN
ejpam-7112	278	46	β	β	X
ejpam-7112	278	47	a	a	DET
ejpam-7112	278	48	∫	∫	PROPN
ejpam-7112	278	49	t	t	PROPN
ejpam-7112	278	50	a	a	DET
ejpam-7112	278	51	∫	∫	PROPN
ejpam-7112	278	52	y	y	PROPN
ejpam-7112	278	53	a	a	X
ejpam-7112	278	54	x	x	X
ejpam-7112	278	55	dx	dx	PROPN
ejpam-7112	278	56	dy	dy	X
ejpam-7112	278	57	dz	dz	PROPN
ejpam-7112	278	58	)	)	PUNCT
ejpam-7112	278	59	f	f	PROPN
ejpam-7112	278	60	(	(	PUNCT
ejpam-7112	278	61	4)(ξ)g′(η	4)(ξ)g′(η	NUM
ejpam-7112	278	62	)	)	PUNCT
ejpam-7112	278	63	+	+	CCONJ
ejpam-7112	278	64	(	(	PUNCT
ejpam-7112	278	65	∫	∫	PROPN
ejpam-7112	278	66	β	β	X
ejpam-7112	278	67	a	a	DET
ejpam-7112	278	68	∫	∫	PROPN
ejpam-7112	278	69	t	t	PROPN
ejpam-7112	278	70	a	a	DET
ejpam-7112	278	71	∫	∫	PROPN
ejpam-7112	278	72	z	z	PROPN
ejpam-7112	278	73	a	a	DET
ejpam-7112	278	74	∫	∫	PROPN
ejpam-7112	278	75	y	y	PROPN
ejpam-7112	278	76	a	a	X
ejpam-7112	278	77	x	x	X
ejpam-7112	278	78	dx	dx	PROPN
ejpam-7112	278	79	dy	dy	X
ejpam-7112	278	80	dz	dz	PROPN
ejpam-7112	278	81	dt	dt	PROPN
ejpam-7112	278	82	)	)	PUNCT
ejpam-7112	278	83	f	f	PROPN
ejpam-7112	278	84	(	(	PUNCT
ejpam-7112	278	85	4)(ξ)g′(η	4)(ξ)g′(η	NUM
ejpam-7112	278	86	)	)	PUNCT
ejpam-7112	278	87	(	(	PUNCT
ejpam-7112	278	88	37	37	NUM
ejpam-7112	278	89	)	)	PUNCT
ejpam-7112	278	90	k.	k.	PROPN
ejpam-7112	278	91	memon	memon	PROPN
ejpam-7112	278	92	et	et	PROPN
ejpam-7112	278	93	al	al	PROPN
ejpam-7112	278	94	.	.	PUNCT
ejpam-7112	278	95	/	/	SYM
ejpam-7112	278	96	eur	eur	PROPN
ejpam-7112	278	97	.	.	PUNCT
ejpam-7112	279	1	j.	j.	PROPN
ejpam-7112	279	2	pure	pure	PROPN
ejpam-7112	279	3	appl	appl	PROPN
ejpam-7112	279	4	.	.	PROPN
ejpam-7112	279	5	math	math	PROPN
ejpam-7112	279	6	,	,	PUNCT
ejpam-7112	279	7	18	18	NUM
ejpam-7112	279	8	(	(	PUNCT
ejpam-7112	279	9	4	4	NUM
ejpam-7112	279	10	)	)	PUNCT
ejpam-7112	279	11	(	(	PUNCT
ejpam-7112	279	12	2025	2025	NUM
ejpam-7112	279	13	)	)	PUNCT
ejpam-7112	279	14	,	,	PUNCT
ejpam-7112	279	15	7112	7112	NUM
ejpam-7112	279	16	12	12	NUM
ejpam-7112	279	17	of	of	ADP
ejpam-7112	279	18	38	38	NUM
ejpam-7112	279	19	now	now	ADV
ejpam-7112	279	20	,	,	PUNCT
ejpam-7112	279	21	it	it	PRON
ejpam-7112	279	22	is	be	AUX
ejpam-7112	279	23	easy	easy	ADJ
ejpam-7112	279	24	to	to	PART
ejpam-7112	279	25	obtain:∫	obtain:∫	VERB
ejpam-7112	279	26	β	β	X
ejpam-7112	279	27	a	a	DET
ejpam-7112	279	28	t	t	NOUN
ejpam-7112	279	29	dt	dt	NOUN
ejpam-7112	280	1	=	=	SYM
ejpam-7112	280	2	β2−α2	β2−α2	NUM
ejpam-7112	280	3	2∫	2∫	NUM
ejpam-7112	280	4	β	β	NOUN
ejpam-7112	280	5	a	a	DET
ejpam-7112	280	6	∫	∫	PROPN
ejpam-7112	280	7	t	t	PROPN
ejpam-7112	280	8	a	a	X
ejpam-7112	280	9	x	x	X
ejpam-7112	280	10	dx	dx	PROPN
ejpam-7112	280	11	dt	dt	NOUN
ejpam-7112	281	1	=	=	SYM
ejpam-7112	281	2	β3	β3	PROPN
ejpam-7112	281	3	6	6	NUM
ejpam-7112	281	4	−	−	NUM
ejpam-7112	281	5	α2β	α2β	PROPN
ejpam-7112	281	6	2	2	NUM
ejpam-7112	281	7	+	+	CCONJ
ejpam-7112	281	8	α3	α3	NOUN
ejpam-7112	281	9	3∫	3∫	NUM
ejpam-7112	281	10	β	β	NOUN
ejpam-7112	281	11	a	a	DET
ejpam-7112	281	12	∫	∫	PROPN
ejpam-7112	281	13	t	t	PROPN
ejpam-7112	281	14	a	a	DET
ejpam-7112	281	15	∫	∫	PROPN
ejpam-7112	281	16	y	y	PROPN
ejpam-7112	281	17	a	a	X
ejpam-7112	281	18	x	x	X
ejpam-7112	281	19	dx	dx	PROPN
ejpam-7112	281	20	dy	dy	NOUN
ejpam-7112	281	21	dt	dt	PROPN
ejpam-7112	282	1	=	=	SYM
ejpam-7112	282	2	β4	β4	PROPN
ejpam-7112	282	3	24	24	NUM
ejpam-7112	282	4	−	−	NOUN
ejpam-7112	282	5	α2β2	α2β2	SYM
ejpam-7112	282	6	4	4	NUM
ejpam-7112	282	7	+	+	CCONJ
ejpam-7112	282	8	α3β	α3β	ADJ
ejpam-7112	282	9	3	3	NUM
ejpam-7112	282	10	−	−	NOUN
ejpam-7112	282	11	α4	α4	NOUN
ejpam-7112	282	12	8	8	NUM
ejpam-7112	282	13	.	.	PUNCT
ejpam-7112	283	1	and	and	CCONJ
ejpam-7112	283	2	,	,	PUNCT
ejpam-7112	283	3	using	use	VERB
ejpam-7112	283	4	these	these	PRON
ejpam-7112	283	5	in	in	ADP
ejpam-7112	283	6	(	(	PUNCT
ejpam-7112	283	7	37	37	NUM
ejpam-7112	283	8	)	)	PUNCT
ejpam-7112	283	9	,	,	PUNCT
ejpam-7112	283	10	we	we	PRON
ejpam-7112	283	11	finally	finally	ADV
ejpam-7112	283	12	get:∫	get:∫	VERB
ejpam-7112	283	13	β	β	X
ejpam-7112	283	14	a	a	DET
ejpam-7112	283	15	f(t	f(t	PROPN
ejpam-7112	283	16	)	)	PUNCT
ejpam-7112	283	17	dt	dt	NOUN
ejpam-7112	284	1	=	=	PUNCT
ejpam-7112	284	2	β	β	X
ejpam-7112	284	3	−	−	NOUN
ejpam-7112	285	1	α	α	NOUN
ejpam-7112	285	2	2	2	NUM
ejpam-7112	286	1	[	[	X
ejpam-7112	286	2	f(α	f(α	NOUN
ejpam-7112	286	3	)	)	PUNCT
ejpam-7112	287	1	+	+	NUM
ejpam-7112	287	2	f(β)]−	f(β)]−	X
ejpam-7112	287	3	(	(	PUNCT
ejpam-7112	287	4	β	β	X
ejpam-7112	287	5	−	−	X
ejpam-7112	287	6	α)3	α)3	NOUN
ejpam-7112	287	7	12	12	NUM
ejpam-7112	287	8	f	f	X
ejpam-7112	288	1	′′	′′	PROPN
ejpam-7112	288	2	(	(	PUNCT
ejpam-7112	288	3	α+	α+	X
ejpam-7112	288	4	β	β	PROPN
ejpam-7112	288	5	2	2	NUM
ejpam-7112	288	6	)	)	PUNCT
ejpam-7112	288	7	−	−	PROPN
ejpam-7112	288	8	(	(	PUNCT
ejpam-7112	288	9	β	β	X
ejpam-7112	288	10	−	−	PROPN
ejpam-7112	288	11	α)5	α)5	PROPN
ejpam-7112	288	12	480	480	NUM
ejpam-7112	288	13	f	f	X
ejpam-7112	288	14	(	(	PUNCT
ejpam-7112	288	15	4)(ξ	4)(ξ	NUM
ejpam-7112	288	16	)	)	PUNCT
ejpam-7112	288	17	,	,	PUNCT
ejpam-7112	288	18	(	(	PUNCT
ejpam-7112	288	19	38	38	NUM
ejpam-7112	288	20	)	)	PUNCT
ejpam-7112	288	21	where	where	SCONJ
ejpam-7112	288	22	which	which	PRON
ejpam-7112	288	23	show	show	VERB
ejpam-7112	288	24	the	the	DET
ejpam-7112	288	25	reducibility	reducibility	NOUN
ejpam-7112	288	26	of	of	ADP
ejpam-7112	288	27	proposed	propose	VERB
ejpam-7112	288	28	amt	amt	PROPN
ejpam-7112	288	29	quadrature	quadrature	NOUN
ejpam-7112	288	30	its	its	PRON
ejpam-7112	288	31	simple	simple	ADJ
ejpam-7112	288	32	counterpart	counterpart	NOUN
ejpam-7112	288	33	(	(	PUNCT
ejpam-7112	288	34	10	10	NUM
ejpam-7112	288	35	)	)	PUNCT
ejpam-7112	288	36	[	[	X
ejpam-7112	288	37	4	4	NUM
ejpam-7112	288	38	]	]	PUNCT
ejpam-7112	288	39	.	.	PUNCT
ejpam-7112	289	1	it	it	PRON
ejpam-7112	289	2	is	be	AUX
ejpam-7112	289	3	a	a	DET
ejpam-7112	289	4	fact	fact	NOUN
ejpam-7112	289	5	that	that	SCONJ
ejpam-7112	289	6	the	the	DET
ejpam-7112	289	7	composite	composite	ADJ
ejpam-7112	289	8	quadrature	quadrature	NOUN
ejpam-7112	289	9	rules	rule	NOUN
ejpam-7112	289	10	provides	provide	VERB
ejpam-7112	289	11	greater	great	ADJ
ejpam-7112	289	12	accuracy	accuracy	NOUN
ejpam-7112	289	13	than	than	ADP
ejpam-7112	289	14	the	the	DET
ejpam-7112	289	15	basic	basic	ADJ
ejpam-7112	289	16	formulae	formulae	NOUN
ejpam-7112	289	17	.	.	PUNCT
ejpam-7112	290	1	to	to	PART
ejpam-7112	290	2	reduce	reduce	VERB
ejpam-7112	290	3	truncation	truncation	NOUN
ejpam-7112	290	4	error	error	NOUN
ejpam-7112	290	5	further	far	ADV
ejpam-7112	290	6	from	from	ADP
ejpam-7112	290	7	local	local	ADJ
ejpam-7112	290	8	to	to	ADP
ejpam-7112	290	9	global	global	ADJ
ejpam-7112	290	10	application	application	NOUN
ejpam-7112	290	11	of	of	ADP
ejpam-7112	290	12	amt	amt	PROPN
ejpam-7112	290	13	quadrature	quadrature	NOUN
ejpam-7112	290	14	,	,	PUNCT
ejpam-7112	290	15	the	the	DET
ejpam-7112	290	16	composite	composite	ADJ
ejpam-7112	290	17	quadrature	quadrature	NOUN
ejpam-7112	290	18	to	to	ADP
ejpam-7112	290	19	(	(	PUNCT
ejpam-7112	290	20	23	23	NUM
ejpam-7112	290	21	)	)	PUNCT
ejpam-7112	290	22	is	be	AUX
ejpam-7112	290	23	referred	refer	VERB
ejpam-7112	290	24	here	here	ADV
ejpam-7112	290	25	as	as	ADP
ejpam-7112	290	26	amct	amct	ADJ
ejpam-7112	290	27	,	,	PUNCT
ejpam-7112	290	28	and	and	CCONJ
ejpam-7112	290	29	with	with	ADP
ejpam-7112	290	30	b−a	b−a	NOUN
ejpam-7112	290	31	n	n	NOUN
ejpam-7112	290	32	=	=	NOUN
ejpam-7112	290	33	h	h	NOUN
ejpam-7112	290	34	keeping	keep	VERB
ejpam-7112	290	35	the	the	DET
ejpam-7112	290	36	assumptions	assumption	NOUN
ejpam-7112	290	37	of	of	ADP
ejpam-7112	290	38	theorems	theorem	NOUN
ejpam-7112	290	39	1	1	NUM
ejpam-7112	290	40	-	-	SYM
ejpam-7112	290	41	2	2	NUM
ejpam-7112	290	42	it	it	PRON
ejpam-7112	290	43	can	can	AUX
ejpam-7112	290	44	be	be	AUX
ejpam-7112	290	45	written	write	VERB
ejpam-7112	290	46	as:∫	as:∫	NOUN
ejpam-7112	290	47	β	β	PROPN
ejpam-7112	290	48	a	a	DET
ejpam-7112	290	49	f(t	f(t	PROPN
ejpam-7112	290	50	)	)	PUNCT
ejpam-7112	290	51	dg	dg	PART
ejpam-7112	291	1	≈	≈	PROPN
ejpam-7112	291	2	amct	amct	VERB
ejpam-7112	291	3	=	=	PUNCT
ejpam-7112	291	4	[	[	PUNCT
ejpam-7112	291	5	n	n	X
ejpam-7112	291	6	β	β	NOUN
ejpam-7112	291	7	−	−	PROPN
ejpam-7112	292	1	α	α	PRON
ejpam-7112	292	2	∫	∫	PROPN
ejpam-7112	292	3	x1	x1	PROPN
ejpam-7112	293	1	a	a	DET
ejpam-7112	293	2	g(t	g(t	PROPN
ejpam-7112	293	3	)	)	PUNCT
ejpam-7112	293	4	dt−	dt−	PUNCT
ejpam-7112	293	5	g(α	g(α	PROPN
ejpam-7112	293	6	)	)	PUNCT
ejpam-7112	293	7	]	]	PUNCT
ejpam-7112	294	1	f(α	f(α	NOUN
ejpam-7112	294	2	)	)	PUNCT
ejpam-7112	295	1	+	+	NUM
ejpam-7112	296	1	n	n	CCONJ
ejpam-7112	296	2	β	β	NOUN
ejpam-7112	296	3	−	−	NOUN
ejpam-7112	296	4	α	α	PROPN
ejpam-7112	296	5	n−1∑	n−1∑	PROPN
ejpam-7112	296	6	k=1	k=1	PUNCT
ejpam-7112	297	1	[	[	X
ejpam-7112	297	2	∫	∫	X
ejpam-7112	297	3	xk+1	xk+1	PROPN
ejpam-7112	297	4	xk	xk	PROPN
ejpam-7112	297	5	g(t	g(t	PROPN
ejpam-7112	297	6	)	)	PUNCT
ejpam-7112	297	7	dt−	dt−	NUM
ejpam-7112	297	8	∫	∫	PROPN
ejpam-7112	297	9	xk	xk	PROPN
ejpam-7112	297	10	xk−1	xk−1	PROPN
ejpam-7112	297	11	g(t	g(t	PROPN
ejpam-7112	297	12	)	)	PUNCT
ejpam-7112	297	13	dxi	dxi	NOUN
ejpam-7112	297	14	]	]	PUNCT
ejpam-7112	297	15	f(xk	f(xk	X
ejpam-7112	297	16	)	)	PUNCT
ejpam-7112	297	17	+	+	CCONJ
ejpam-7112	297	18	[	[	PUNCT
ejpam-7112	297	19	g(β)−	g(β)−	PROPN
ejpam-7112	297	20	n	n	PROPN
ejpam-7112	297	21	β	β	NOUN
ejpam-7112	297	22	−	−	PROPN
ejpam-7112	298	1	α	α	PRON
ejpam-7112	298	2	∫	∫	PROPN
ejpam-7112	298	3	β	β	X
ejpam-7112	298	4	xn−1	xn−1	PROPN
ejpam-7112	298	5	g(t	g(t	PROPN
ejpam-7112	298	6	)	)	PUNCT
ejpam-7112	299	1	dt	dt	X
ejpam-7112	299	2	]	]	PUNCT
ejpam-7112	299	3	f(β	f(β	PROPN
ejpam-7112	299	4	)	)	PUNCT
ejpam-7112	300	1	+	+	CCONJ
ejpam-7112	301	1	n−1∑	n−1∑	NUM
ejpam-7112	301	2	i=1	i=1	PUNCT
ejpam-7112	302	1	[	[	X
ejpam-7112	302	2	∫	∫	X
ejpam-7112	302	3	xk	xk	PROPN
ejpam-7112	302	4	xk−1	xk−1	PROPN
ejpam-7112	302	5	∫	∫	PROPN
ejpam-7112	302	6	t	t	PROPN
ejpam-7112	302	7	xk−1	xk−1	PROPN
ejpam-7112	302	8	g(x	g(x	PROPN
ejpam-7112	302	9	)	)	PUNCT
ejpam-7112	302	10	dx	dx	PROPN
ejpam-7112	303	1	dt−	dt−	PROPN
ejpam-7112	303	2	h	h	PROPN
ejpam-7112	303	3	2	2	NUM
ejpam-7112	303	4	∫	∫	PROPN
ejpam-7112	303	5	k	k	PROPN
ejpam-7112	303	6	xk−1	xk−1	PROPN
ejpam-7112	303	7	g(t	g(t	PROPN
ejpam-7112	303	8	)	)	PUNCT
ejpam-7112	303	9	dt	dt	X
ejpam-7112	303	10	]	]	PUNCT
ejpam-7112	304	1	f	f	X
ejpam-7112	304	2	′′	′′	PROPN
ejpam-7112	304	3	(	(	PUNCT
ejpam-7112	304	4	xk−1	xk−1	PROPN
ejpam-7112	304	5	+	+	CCONJ
ejpam-7112	304	6	xk	xk	PROPN
ejpam-7112	304	7	2	2	NUM
ejpam-7112	304	8	)	)	PUNCT
ejpam-7112	304	9	(	(	PUNCT
ejpam-7112	304	10	39	39	NUM
ejpam-7112	304	11	)	)	PUNCT
ejpam-7112	304	12	theorem	theorem	NOUN
ejpam-7112	304	13	4	4	NUM
ejpam-7112	304	14	.	.	PUNCT
ejpam-7112	304	15	assuming	assume	VERB
ejpam-7112	304	16	continuity	continuity	NOUN
ejpam-7112	304	17	of	of	ADP
ejpam-7112	304	18	f(t	f(t	PROPN
ejpam-7112	304	19	)	)	PUNCT
ejpam-7112	304	20	and	and	CCONJ
ejpam-7112	304	21	g(t	g(t	PROPN
ejpam-7112	304	22	)	)	PUNCT
ejpam-7112	304	23	in	in	ADP
ejpam-7112	304	24	β−α	β−α	NOUN
ejpam-7112	304	25	2	2	NUM
ejpam-7112	304	26	along	along	ADP
ejpam-7112	304	27	with	with	ADP
ejpam-7112	304	28	g(t	g(t	PROPN
ejpam-7112	304	29	)	)	PUNCT
ejpam-7112	304	30	being	be	AUX
ejpam-7112	304	31	monotonically	monotonically	ADV
ejpam-7112	304	32	rising	rise	VERB
ejpam-7112	304	33	in	in	ADP
ejpam-7112	304	34	the	the	DET
ejpam-7112	304	35	same	same	ADJ
ejpam-7112	304	36	interval	interval	NOUN
ejpam-7112	304	37	.	.	PUNCT
ejpam-7112	305	1	suppose	suppose	VERB
ejpam-7112	305	2	that	that	SCONJ
ejpam-7112	305	3	[	[	X
ejpam-7112	305	4	α.β	α.β	X
ejpam-7112	305	5	]	]	X
ejpam-7112	305	6	partitioned	partition	VERB
ejpam-7112	305	7	in	in	ADP
ejpam-7112	305	8	n	n	PRON
ejpam-7112	305	9	sub	sub	NOUN
ejpam-7112	305	10	-	-	NOUN
ejpam-7112	305	11	intervals	interval	NOUN
ejpam-7112	305	12	[	[	X
ejpam-7112	305	13	xk	xk	X
ejpam-7112	305	14	,	,	PUNCT
ejpam-7112	305	15	xk−1	xk−1	PROPN
ejpam-7112	305	16	]	]	PUNCT
ejpam-7112	305	17	of	of	ADP
ejpam-7112	305	18	size	size	NOUN
ejpam-7112	305	19	h	h	NOUN
ejpam-7112	305	20	=	=	NOUN
ejpam-7112	305	21	β−α	β−α	NOUN
ejpam-7112	305	22	2	2	NUM
ejpam-7112	305	23	in	in	ADP
ejpam-7112	305	24	form	form	NOUN
ejpam-7112	305	25	of	of	ADP
ejpam-7112	305	26	uniformly	uniformly	ADV
ejpam-7112	305	27	-	-	PUNCT
ejpam-7112	305	28	spaced	space	VERB
ejpam-7112	305	29	integration	integration	NOUN
ejpam-7112	305	30	points	point	NOUN
ejpam-7112	305	31	:	:	PUNCT
ejpam-7112	305	32	,	,	PUNCT
ejpam-7112	305	33	for	for	ADP
ejpam-7112	305	34	k	k	PROPN
ejpam-7112	305	35	=	=	SYM
ejpam-7112	305	36	0	0	NUM
ejpam-7112	305	37	,	,	PUNCT
ejpam-7112	305	38	1	1	NUM
ejpam-7112	305	39	,	,	PUNCT
ejpam-7112	305	40	,	,	PUNCT
ejpam-7112	305	41	n.	n.	NOUN
ejpam-7112	305	42	the	the	DET
ejpam-7112	305	43	amct	amct	ADJ
ejpam-7112	305	44	quadrature	quadrature	NOUN
ejpam-7112	305	45	with	with	ADP
ejpam-7112	305	46	global	global	ADJ
ejpam-7112	305	47	truncation	truncation	NOUN
ejpam-7112	305	48	error	error	NOUN
ejpam-7112	305	49	ramct	ramct	VERB
ejpam-7112	305	50	[	[	X
ejpam-7112	305	51	f	f	X
ejpam-7112	305	52	]	]	X
ejpam-7112	305	53	is	be	AUX
ejpam-7112	305	54	:	:	PUNCT
ejpam-7112	305	55	∫	∫	PROPN
ejpam-7112	305	56	β	β	PROPN
ejpam-7112	305	57	a	a	DET
ejpam-7112	305	58	f(t	f(t	PROPN
ejpam-7112	305	59	)	)	PUNCT
ejpam-7112	305	60	dg	dg	NOUN
ejpam-7112	305	61	=	=	PRON
ejpam-7112	305	62	amct	amct	VERB
ejpam-7112	306	1	+	+	ADV
ejpam-7112	306	2	ramct	ramct	ADJ
ejpam-7112	307	1	[	[	X
ejpam-7112	307	2	f	f	X
ejpam-7112	307	3	]	]	X
ejpam-7112	307	4	=	=	PUNCT
ejpam-7112	307	5	[	[	PUNCT
ejpam-7112	307	6	n	n	X
ejpam-7112	307	7	β	β	NOUN
ejpam-7112	307	8	−	−	PROPN
ejpam-7112	307	9	α	α	PRON
ejpam-7112	307	10	∫	∫	PROPN
ejpam-7112	307	11	x1	x1	PROPN
ejpam-7112	307	12	a	a	DET
ejpam-7112	307	13	g(t	g(t	PROPN
ejpam-7112	307	14	)	)	PUNCT
ejpam-7112	307	15	dt−	dt−	PUNCT
ejpam-7112	307	16	g(α	g(α	PROPN
ejpam-7112	307	17	)	)	PUNCT
ejpam-7112	307	18	]	]	PUNCT
ejpam-7112	307	19	f(α	f(α	NOUN
ejpam-7112	307	20	)	)	PUNCT
ejpam-7112	307	21	+	+	NUM
ejpam-7112	308	1	n	n	CCONJ
ejpam-7112	308	2	β	β	NOUN
ejpam-7112	308	3	−	−	NOUN
ejpam-7112	308	4	α	α	PROPN
ejpam-7112	308	5	n−1∑	n−1∑	PROPN
ejpam-7112	308	6	k=1	k=1	PUNCT
ejpam-7112	309	1	[	[	X
ejpam-7112	309	2	∫	∫	X
ejpam-7112	309	3	xk+1	xk+1	PROPN
ejpam-7112	309	4	xk	xk	PROPN
ejpam-7112	309	5	g(t	g(t	PROPN
ejpam-7112	309	6	)	)	PUNCT
ejpam-7112	309	7	dt−	dt−	NUM
ejpam-7112	309	8	∫	∫	PROPN
ejpam-7112	309	9	xk	xk	PROPN
ejpam-7112	309	10	xk−1	xk−1	PROPN
ejpam-7112	309	11	g(t	g(t	PROPN
ejpam-7112	309	12	)	)	PUNCT
ejpam-7112	309	13	dxi	dxi	NOUN
ejpam-7112	309	14	]	]	PUNCT
ejpam-7112	309	15	f(xk	f(xk	X
ejpam-7112	309	16	)	)	PUNCT
ejpam-7112	309	17	+	+	CCONJ
ejpam-7112	309	18	[	[	PUNCT
ejpam-7112	309	19	g(β)−	g(β)−	PROPN
ejpam-7112	309	20	n	n	PROPN
ejpam-7112	309	21	β	β	NOUN
ejpam-7112	309	22	−	−	PROPN
ejpam-7112	310	1	α	α	PRON
ejpam-7112	310	2	∫	∫	PROPN
ejpam-7112	310	3	β	β	X
ejpam-7112	310	4	xn−1	xn−1	PROPN
ejpam-7112	310	5	g(t	g(t	PROPN
ejpam-7112	310	6	)	)	PUNCT
ejpam-7112	311	1	dt	dt	X
ejpam-7112	311	2	]	]	PUNCT
ejpam-7112	311	3	f(β	f(β	PROPN
ejpam-7112	311	4	)	)	PUNCT
ejpam-7112	311	5	k.	k.	PROPN
ejpam-7112	312	1	memon	memon	PROPN
ejpam-7112	312	2	et	et	PROPN
ejpam-7112	312	3	al	al	PROPN
ejpam-7112	312	4	.	.	PUNCT
ejpam-7112	312	5	/	/	SYM
ejpam-7112	312	6	eur	eur	PROPN
ejpam-7112	312	7	.	.	PUNCT
ejpam-7112	313	1	j.	j.	PROPN
ejpam-7112	313	2	pure	pure	PROPN
ejpam-7112	313	3	appl	appl	PROPN
ejpam-7112	313	4	.	.	PROPN
ejpam-7112	313	5	math	math	PROPN
ejpam-7112	313	6	,	,	PUNCT
ejpam-7112	313	7	18	18	NUM
ejpam-7112	313	8	(	(	PUNCT
ejpam-7112	313	9	4	4	NUM
ejpam-7112	313	10	)	)	PUNCT
ejpam-7112	313	11	(	(	PUNCT
ejpam-7112	313	12	2025	2025	NUM
ejpam-7112	313	13	)	)	PUNCT
ejpam-7112	313	14	,	,	PUNCT
ejpam-7112	313	15	7112	7112	NUM
ejpam-7112	313	16	13	13	NUM
ejpam-7112	313	17	of	of	ADP
ejpam-7112	313	18	38	38	NUM
ejpam-7112	313	19	+	+	CCONJ
ejpam-7112	313	20	n−1∑	n−1∑	NUM
ejpam-7112	313	21	k=1	k=1	PUNCT
ejpam-7112	314	1	[	[	X
ejpam-7112	314	2	∫	∫	X
ejpam-7112	314	3	xk	xk	PROPN
ejpam-7112	314	4	xk−1	xk−1	PROPN
ejpam-7112	314	5	∫	∫	PROPN
ejpam-7112	314	6	xt	xt	PROPN
ejpam-7112	314	7	xk−1	xk−1	PROPN
ejpam-7112	314	8	g(x	g(x	PROPN
ejpam-7112	314	9	)	)	PUNCT
ejpam-7112	315	1	dx	dx	PROPN
ejpam-7112	315	2	dt−	dt−	PROPN
ejpam-7112	315	3	h	h	PROPN
ejpam-7112	315	4	2	2	NUM
ejpam-7112	315	5	∫	∫	PROPN
ejpam-7112	315	6	xk	xk	PROPN
ejpam-7112	315	7	xk−1	xk−1	PROPN
ejpam-7112	315	8	g(t	g(t	PROPN
ejpam-7112	315	9	)	)	PUNCT
ejpam-7112	316	1	dt	dt	X
ejpam-7112	316	2	]	]	PUNCT
ejpam-7112	317	1	f	f	X
ejpam-7112	317	2	′′	′′	PROPN
ejpam-7112	317	3	(	(	PUNCT
ejpam-7112	317	4	xi+1	xi+1	NUM
ejpam-7112	317	5	+	+	CCONJ
ejpam-7112	317	6	xi	xi	ADP
ejpam-7112	317	7	2	2	NUM
ejpam-7112	317	8	)	)	PUNCT
ejpam-7112	317	9	+	+	NUM
ejpam-7112	317	10	n	n	CCONJ
ejpam-7112	317	11	[	[	PUNCT
ejpam-7112	317	12	2α3	2α3	NUM
ejpam-7112	317	13	+	+	CCONJ
ejpam-7112	317	14	2αβ2	2αβ2	NUM
ejpam-7112	317	15	+	+	CCONJ
ejpam-7112	317	16	2α2β	2α2β	ADJ
ejpam-7112	317	17	−	−	NOUN
ejpam-7112	317	18	6β3	6β3	NUM
ejpam-7112	317	19	+	+	CCONJ
ejpam-7112	317	20	3(β	3(β	NUM
ejpam-7112	317	21	−	−	NOUN
ejpam-7112	317	22	α)(α+	α)(α+	NOUN
ejpam-7112	317	23	β)2	β)2	X
ejpam-7112	317	24	48	48	NUM
ejpam-7112	317	25	∫	∫	PROPN
ejpam-7112	317	26	β	β	PROPN
ejpam-7112	317	27	a	a	DET
ejpam-7112	317	28	g(t	g(t	PROPN
ejpam-7112	317	29	)	)	PUNCT
ejpam-7112	317	30	dt	dt	PUNCT
ejpam-7112	318	1	+	+	CCONJ
ejpam-7112	318	2	4β2	4β2	NUM
ejpam-7112	318	3	−	−	NOUN
ejpam-7112	318	4	(	(	PUNCT
ejpam-7112	318	5	α+	α+	X
ejpam-7112	318	6	β)2	β)2	X
ejpam-7112	318	7	8	8	NUM
ejpam-7112	318	8	∫	∫	PROPN
ejpam-7112	318	9	β	β	PROPN
ejpam-7112	318	10	a	a	DET
ejpam-7112	318	11	∫	∫	PROPN
ejpam-7112	318	12	t	t	PROPN
ejpam-7112	318	13	a	a	DET
ejpam-7112	318	14	g(x	g(x	NOUN
ejpam-7112	318	15	)	)	PUNCT
ejpam-7112	319	1	dx	dx	PROPN
ejpam-7112	320	1	dt	dt	PROPN
ejpam-7112	320	2	−β	−β	PROPN
ejpam-7112	320	3	∫	∫	PROPN
ejpam-7112	320	4	β	β	PROPN
ejpam-7112	320	5	a	a	DET
ejpam-7112	320	6	∫	∫	PROPN
ejpam-7112	320	7	t	t	PROPN
ejpam-7112	320	8	a	a	DET
ejpam-7112	320	9	∫	∫	PROPN
ejpam-7112	320	10	y	y	PROPN
ejpam-7112	320	11	a	a	DET
ejpam-7112	320	12	g(x	g(x	NOUN
ejpam-7112	320	13	)	)	PUNCT
ejpam-7112	320	14	dx	dx	PROPN
ejpam-7112	320	15	dy	dy	NOUN
ejpam-7112	320	16	dt+	dt+	NOUN
ejpam-7112	320	17	∫	∫	PROPN
ejpam-7112	320	18	β	β	PROPN
ejpam-7112	320	19	a	a	DET
ejpam-7112	320	20	∫	∫	PROPN
ejpam-7112	320	21	t	t	PROPN
ejpam-7112	320	22	a	a	DET
ejpam-7112	320	23	∫	∫	PROPN
ejpam-7112	320	24	y	y	PROPN
ejpam-7112	320	25	a	a	DET
ejpam-7112	320	26	∫	∫	PROPN
ejpam-7112	320	27	z	z	PROPN
ejpam-7112	320	28	a	a	DET
ejpam-7112	320	29	g(x	g(x	NOUN
ejpam-7112	320	30	)	)	PUNCT
ejpam-7112	320	31	dx	dx	PROPN
ejpam-7112	320	32	dy	dy	X
ejpam-7112	320	33	dz	dz	PROPN
ejpam-7112	320	34	dt	dt	X
ejpam-7112	320	35	]	]	X
ejpam-7112	320	36	f	f	X
ejpam-7112	320	37	(	(	PUNCT
ejpam-7112	320	38	4)(ξ)g′(η	4)(ξ)g′(η	NUM
ejpam-7112	320	39	)	)	PUNCT
ejpam-7112	320	40	(	(	PUNCT
ejpam-7112	320	41	40	40	NUM
ejpam-7112	320	42	)	)	PUNCT
ejpam-7112	320	43	whereξ	whereξ	PROPN
ejpam-7112	320	44	,	,	PUNCT
ejpam-7112	320	45	η	η	PROPN
ejpam-7112	320	46	∈	∈	PROPN
ejpam-7112	320	47	(	(	PUNCT
ejpam-7112	320	48	α	α	NOUN
ejpam-7112	320	49	,	,	PUNCT
ejpam-7112	320	50	β	β	NOUN
ejpam-7112	320	51	)	)	PUNCT
ejpam-7112	320	52	proof	proof	NOUN
ejpam-7112	320	53	.	.	PUNCT
ejpam-7112	321	1	refereeing	referee	VERB
ejpam-7112	321	2	to	to	ADP
ejpam-7112	321	3	a	a	DET
ejpam-7112	321	4	local	local	ADJ
ejpam-7112	321	5	truncation	truncation	NOUN
ejpam-7112	321	6	error	error	NOUN
ejpam-7112	321	7	from	from	ADP
ejpam-7112	321	8	(	(	PUNCT
ejpam-7112	321	9	24	24	NUM
ejpam-7112	321	10	)	)	PUNCT
ejpam-7112	321	11	for	for	ADP
ejpam-7112	321	12	the	the	DET
ejpam-7112	321	13	amt	amt	PROPN
ejpam-7112	321	14	quadrature	quadrature	NOUN
ejpam-7112	321	15	,	,	PUNCT
ejpam-7112	321	16	we	we	PRON
ejpam-7112	321	17	have	have	VERB
ejpam-7112	321	18	:	:	PUNCT
ejpam-7112	321	19	[	[	PUNCT
ejpam-7112	321	20	2x3p−1	2x3p−1	NUM
ejpam-7112	321	21	+	+	NUM
ejpam-7112	321	22	2xp−1x	2xp−1x	NUM
ejpam-7112	321	23	2	2	NUM
ejpam-7112	321	24	p	p	NOUN
ejpam-7112	321	25	+	+	CCONJ
ejpam-7112	321	26	2x2p−1xp	2x2p−1xp	NUM
ejpam-7112	321	27	−	−	NOUN
ejpam-7112	321	28	6x3p	6x3p	NOUN
ejpam-7112	322	1	+	+	CCONJ
ejpam-7112	322	2	3(xp	3(xp	NUM
ejpam-7112	322	3	−	−	PROPN
ejpam-7112	322	4	xp−1)(xp−1	xp−1)(xp−1	PROPN
ejpam-7112	323	1	+	+	NUM
ejpam-7112	323	2	xp	xp	PROPN
ejpam-7112	323	3	)	)	PUNCT
ejpam-7112	323	4	2	2	NUM
ejpam-7112	323	5	48	48	NUM
ejpam-7112	323	6	∫	∫	NOUN
ejpam-7112	323	7	xp	xp	PROPN
ejpam-7112	323	8	xp−1	xp−1	PROPN
ejpam-7112	323	9	g(t	g(t	PROPN
ejpam-7112	323	10	)	)	PUNCT
ejpam-7112	324	1	dt	dt	PUNCT
ejpam-7112	325	1	+	+	CCONJ
ejpam-7112	326	1	4x2p	4x2p	NOUN
ejpam-7112	326	2	−	−	PROPN
ejpam-7112	327	1	(	(	PUNCT
ejpam-7112	327	2	xp−1	xp−1	PROPN
ejpam-7112	327	3	+	+	CCONJ
ejpam-7112	327	4	xp	xp	X
ejpam-7112	327	5	)	)	PUNCT
ejpam-7112	327	6	2	2	NUM
ejpam-7112	327	7	8	8	NUM
ejpam-7112	327	8	∫	∫	NOUN
ejpam-7112	327	9	xp	xp	INTJ
ejpam-7112	328	1	xp−1	xp−1	PROPN
ejpam-7112	328	2	∫	∫	PROPN
ejpam-7112	329	1	t	t	PROPN
ejpam-7112	329	2	xp−1	xp−1	INTJ
ejpam-7112	330	1	g(x	g(x	NOUN
ejpam-7112	330	2	)	)	PUNCT
ejpam-7112	330	3	dx	dx	PROPN
ejpam-7112	331	1	dt−	dt−	PROPN
ejpam-7112	331	2	xp	xp	INTJ
ejpam-7112	331	3	∫	∫	PROPN
ejpam-7112	331	4	xp	xp	INTJ
ejpam-7112	332	1	xp−1	xp−1	PROPN
ejpam-7112	332	2	∫	∫	PROPN
ejpam-7112	333	1	t	t	PROPN
ejpam-7112	334	1	xp−1	xp−1	INTJ
ejpam-7112	334	2	∫	∫	PROPN
ejpam-7112	335	1	y	y	PROPN
ejpam-7112	335	2	xp−1	xp−1	PROPN
ejpam-7112	336	1	g(x	g(x	PROPN
ejpam-7112	336	2	)	)	PUNCT
ejpam-7112	337	1	dx	dx	PROPN
ejpam-7112	337	2	dy	dy	INTJ
ejpam-7112	337	3	dt	dt	PROPN
ejpam-7112	338	1	+	+	CCONJ
ejpam-7112	338	2	∫	∫	PROPN
ejpam-7112	338	3	xp	xp	INTJ
ejpam-7112	339	1	xp−1	xp−1	PROPN
ejpam-7112	339	2	∫	∫	PROPN
ejpam-7112	340	1	t	t	PROPN
ejpam-7112	341	1	xp−1	xp−1	INTJ
ejpam-7112	341	2	∫	∫	PROPN
ejpam-7112	342	1	y	y	PROPN
ejpam-7112	343	1	xp−1	xp−1	PROPN
ejpam-7112	343	2	∫	∫	PROPN
ejpam-7112	344	1	z	z	X
ejpam-7112	345	1	xp−1	xp−1	PROPN
ejpam-7112	346	1	g(x	g(x	NOUN
ejpam-7112	346	2	)	)	PUNCT
ejpam-7112	347	1	dx	dx	PROPN
ejpam-7112	347	2	dy	dy	X
ejpam-7112	347	3	dz	dz	PROPN
ejpam-7112	348	1	dt	dt	X
ejpam-7112	348	2	]	]	X
ejpam-7112	348	3	f	f	X
ejpam-7112	348	4	(	(	PUNCT
ejpam-7112	348	5	4)(ξp	4)(ξp	NUM
ejpam-7112	348	6	)	)	PUNCT
ejpam-7112	348	7	g	g	ADP
ejpam-7112	348	8	′(ηp	′(ηp	ADJ
ejpam-7112	348	9	)	)	PUNCT
ejpam-7112	348	10	(	(	PUNCT
ejpam-7112	348	11	41	41	NUM
ejpam-7112	348	12	)	)	PUNCT
ejpam-7112	348	13	where	where	SCONJ
ejpam-7112	348	14	ξp	ξp	X
ejpam-7112	348	15	,	,	PUNCT
ejpam-7112	348	16	η	η	PROPN
ejpam-7112	348	17	∈	∈	PROPN
ejpam-7112	348	18	(	(	PUNCT
ejpam-7112	348	19	α	α	NOUN
ejpam-7112	348	20	,	,	PUNCT
ejpam-7112	348	21	β	β	NOUN
ejpam-7112	348	22	)	)	PUNCT
ejpam-7112	348	23	adding	add	VERB
ejpam-7112	348	24	n	n	CCONJ
ejpam-7112	348	25	such	such	ADJ
ejpam-7112	348	26	local	local	ADJ
ejpam-7112	348	27	truncation	truncation	NOUN
ejpam-7112	348	28	errors	error	NOUN
ejpam-7112	348	29	leads	lead	VERB
ejpam-7112	348	30	to	to	ADP
ejpam-7112	348	31	the	the	DET
ejpam-7112	348	32	global	global	ADJ
ejpam-7112	348	33	truncation	truncation	NOUN
ejpam-7112	348	34	error	error	NOUN
ejpam-7112	348	35	as	as	ADP
ejpam-7112	348	36	:	:	PUNCT
ejpam-7112	348	37	n−1∑	n−1∑	NUM
ejpam-7112	348	38	k=1	k=1	PUNCT
ejpam-7112	349	1	[	[	PUNCT
ejpam-7112	349	2	2x3k−1	2x3k−1	NUM
ejpam-7112	349	3	+	+	NUM
ejpam-7112	349	4	2xk−1x	2xk−1x	NUM
ejpam-7112	349	5	2	2	NUM
ejpam-7112	349	6	k	k	NOUN
ejpam-7112	349	7	+	+	NUM
ejpam-7112	349	8	2x2k−1xk	2x2k−1xk	NUM
ejpam-7112	349	9	−	−	NOUN
ejpam-7112	349	10	6x3k	6x3k	NOUN
ejpam-7112	350	1	+	+	NOUN
ejpam-7112	350	2	3(xk	3(xk	NUM
ejpam-7112	350	3	−	−	NOUN
ejpam-7112	350	4	xk−1)(xk−1	xk−1)(xk−1	PROPN
ejpam-7112	351	1	+	+	CCONJ
ejpam-7112	351	2	xk	xk	PROPN
ejpam-7112	351	3	)	)	PUNCT
ejpam-7112	351	4	2	2	NUM
ejpam-7112	351	5	48	48	NUM
ejpam-7112	351	6	∫	∫	PROPN
ejpam-7112	351	7	xk	xk	PROPN
ejpam-7112	351	8	xk−1	xk−1	PROPN
ejpam-7112	351	9	g(t	g(t	PROPN
ejpam-7112	351	10	)	)	PUNCT
ejpam-7112	352	1	dt	dt	PART
ejpam-7112	353	1	+	+	NUM
ejpam-7112	353	2	4x2k	4x2k	NOUN
ejpam-7112	353	3	−	−	PROPN
ejpam-7112	354	1	(	(	PUNCT
ejpam-7112	354	2	xk−1	xk−1	PROPN
ejpam-7112	354	3	+	+	CCONJ
ejpam-7112	354	4	xk	xk	PROPN
ejpam-7112	354	5	)	)	PUNCT
ejpam-7112	354	6	2	2	NUM
ejpam-7112	354	7	8	8	NUM
ejpam-7112	354	8	∫	∫	PROPN
ejpam-7112	354	9	xk	xk	PROPN
ejpam-7112	354	10	xk−1	xk−1	PROPN
ejpam-7112	354	11	∫	∫	PROPN
ejpam-7112	354	12	t	t	PROPN
ejpam-7112	354	13	xk−1	xk−1	PROPN
ejpam-7112	354	14	g(x	g(x	PROPN
ejpam-7112	354	15	)	)	PUNCT
ejpam-7112	355	1	dx	dx	PROPN
ejpam-7112	356	1	dt−	dt−	PROPN
ejpam-7112	356	2	xk	xk	PROPN
ejpam-7112	356	3	∫	∫	PROPN
ejpam-7112	356	4	xk	xk	PROPN
ejpam-7112	357	1	xk−1	xk−1	PROPN
ejpam-7112	357	2	∫	∫	PROPN
ejpam-7112	358	1	t	t	PROPN
ejpam-7112	358	2	xk−1	xk−1	PROPN
ejpam-7112	358	3	∫	∫	PROPN
ejpam-7112	358	4	y	y	PROPN
ejpam-7112	358	5	xk−1	xk−1	PROPN
ejpam-7112	358	6	g(x	g(x	PROPN
ejpam-7112	358	7	)	)	PUNCT
ejpam-7112	359	1	dx	dx	PROPN
ejpam-7112	359	2	dy	dy	INTJ
ejpam-7112	359	3	dt	dt	PROPN
ejpam-7112	360	1	+	+	CCONJ
ejpam-7112	360	2	∫	∫	PROPN
ejpam-7112	360	3	xk	xk	PROPN
ejpam-7112	360	4	xk−1	xk−1	PROPN
ejpam-7112	360	5	∫	∫	PROPN
ejpam-7112	360	6	t	t	PROPN
ejpam-7112	360	7	xk−1	xk−1	PROPN
ejpam-7112	360	8	∫	∫	PROPN
ejpam-7112	360	9	y	y	PROPN
ejpam-7112	360	10	xk−1	xk−1	PROPN
ejpam-7112	360	11	∫	∫	PROPN
ejpam-7112	360	12	z	z	PROPN
ejpam-7112	360	13	xk−1	xk−1	PROPN
ejpam-7112	360	14	g(x	g(x	PROPN
ejpam-7112	360	15	)	)	PUNCT
ejpam-7112	361	1	dx	dx	PROPN
ejpam-7112	361	2	dy	dy	X
ejpam-7112	361	3	dz	dz	PROPN
ejpam-7112	362	1	dt	dt	X
ejpam-7112	362	2	]	]	X
ejpam-7112	362	3	f	f	X
ejpam-7112	362	4	(	(	PUNCT
ejpam-7112	362	5	4)(ξk	4)(ξk	NUM
ejpam-7112	362	6	)	)	PUNCT
ejpam-7112	362	7	g	g	PROPN
ejpam-7112	362	8	′(η	′(η	NOUN
ejpam-7112	362	9	)	)	PUNCT
ejpam-7112	362	10	(	(	PUNCT
ejpam-7112	362	11	42	42	NUM
ejpam-7112	362	12	)	)	PUNCT
ejpam-7112	362	13	=	=	SYM
ejpam-7112	363	1	n	n	PROPN
ejpam-7112	363	2	(	(	PUNCT
ejpam-7112	363	3	2α3	2α3	NUM
ejpam-7112	363	4	+	+	CCONJ
ejpam-7112	363	5	2αβ2	2αβ2	NUM
ejpam-7112	363	6	+	+	CCONJ
ejpam-7112	363	7	2α2β	2α2β	ADJ
ejpam-7112	363	8	−	−	NOUN
ejpam-7112	363	9	6β3	6β3	NUM
ejpam-7112	364	1	+	+	CCONJ
ejpam-7112	364	2	3(β	3(β	NUM
ejpam-7112	364	3	−	−	NOUN
ejpam-7112	364	4	α)(α+	α)(α+	NOUN
ejpam-7112	364	5	β)2	β)2	X
ejpam-7112	364	6	48	48	NUM
ejpam-7112	364	7	∫	∫	PROPN
ejpam-7112	364	8	β	β	PROPN
ejpam-7112	364	9	a	a	DET
ejpam-7112	364	10	g(t	g(t	PROPN
ejpam-7112	364	11	)	)	PUNCT
ejpam-7112	364	12	dt	dt	PUNCT
ejpam-7112	365	1	+	+	CCONJ
ejpam-7112	365	2	4β2	4β2	NUM
ejpam-7112	365	3	−	−	NOUN
ejpam-7112	365	4	(	(	PUNCT
ejpam-7112	365	5	α+	α+	X
ejpam-7112	365	6	β)2	β)2	X
ejpam-7112	365	7	8	8	NUM
ejpam-7112	365	8	∫	∫	PROPN
ejpam-7112	365	9	β	β	PROPN
ejpam-7112	365	10	a	a	DET
ejpam-7112	365	11	∫	∫	PROPN
ejpam-7112	365	12	β	β	X
ejpam-7112	365	13	a	a	DET
ejpam-7112	365	14	g(x	g(x	NOUN
ejpam-7112	365	15	)	)	PUNCT
ejpam-7112	365	16	dx	dx	PROPN
ejpam-7112	366	1	dt	dt	X
ejpam-7112	366	2	−	−	PROPN
ejpam-7112	367	1	β	β	X
ejpam-7112	367	2	∫	∫	PROPN
ejpam-7112	367	3	β	β	X
ejpam-7112	367	4	a	a	DET
ejpam-7112	367	5	∫	∫	PROPN
ejpam-7112	367	6	t	t	PROPN
ejpam-7112	367	7	a	a	DET
ejpam-7112	367	8	∫	∫	PROPN
ejpam-7112	367	9	y	y	PROPN
ejpam-7112	367	10	a	a	DET
ejpam-7112	367	11	g(x	g(x	NOUN
ejpam-7112	367	12	)	)	PUNCT
ejpam-7112	367	13	dx	dx	PROPN
ejpam-7112	368	1	dy	dy	INTJ
ejpam-7112	368	2	dt	dt	PROPN
ejpam-7112	369	1	+	+	CCONJ
ejpam-7112	369	2	∫	∫	PROPN
ejpam-7112	369	3	β	β	X
ejpam-7112	369	4	a	a	DET
ejpam-7112	369	5	∫	∫	PROPN
ejpam-7112	369	6	t	t	PROPN
ejpam-7112	369	7	a	a	DET
ejpam-7112	369	8	∫	∫	PROPN
ejpam-7112	369	9	y	y	PROPN
ejpam-7112	369	10	a	a	DET
ejpam-7112	369	11	∫	∫	PROPN
ejpam-7112	369	12	z	z	PROPN
ejpam-7112	369	13	a	a	DET
ejpam-7112	369	14	g(x	g(x	NOUN
ejpam-7112	369	15	)	)	PUNCT
ejpam-7112	369	16	dx	dx	PROPN
ejpam-7112	369	17	dy	dy	X
ejpam-7112	369	18	dz	dz	PROPN
ejpam-7112	369	19	dt	dt	PROPN
ejpam-7112	369	20	)	)	PUNCT
ejpam-7112	369	21	[	[	PUNCT
ejpam-7112	369	22	1	1	NUM
ejpam-7112	369	23	n	n	NUM
ejpam-7112	369	24	n∑	n∑	NOUN
ejpam-7112	369	25	k=1	k=1	X
ejpam-7112	370	1	f	f	PROPN
ejpam-7112	370	2	(	(	PUNCT
ejpam-7112	370	3	4)(ξk	4)(ξk	PROPN
ejpam-7112	370	4	)	)	PUNCT
ejpam-7112	370	5	g	g	PROPN
ejpam-7112	370	6	′(η	′(η	NOUN
ejpam-7112	370	7	)	)	PUNCT
ejpam-7112	370	8	]	]	PUNCT
ejpam-7112	371	1	(	(	PUNCT
ejpam-7112	371	2	43	43	NUM
ejpam-7112	371	3	)	)	PUNCT
ejpam-7112	371	4	let	let	VERB
ejpam-7112	371	5	m	m	VERB
ejpam-7112	371	6	=	=	PUNCT
ejpam-7112	372	1	[	[	PUNCT
ejpam-7112	372	2	1	1	NUM
ejpam-7112	372	3	n	n	NOUN
ejpam-7112	372	4	∑n	∑n	PROPN
ejpam-7112	373	1	k=1	k=1	X
ejpam-7112	373	2	f	f	PROPN
ejpam-7112	373	3	(	(	PUNCT
ejpam-7112	373	4	4)(ξk	4)(ξk	PROPN
ejpam-7112	373	5	)	)	PUNCT
ejpam-7112	373	6	g	g	PROPN
ejpam-7112	373	7	′(η	′(η	NOUN
ejpam-7112	373	8	)	)	PUNCT
ejpam-7112	373	9	]	]	PUNCT
ejpam-7112	374	1	k.	k.	PROPN
ejpam-7112	374	2	memon	memon	PROPN
ejpam-7112	374	3	et	et	PROPN
ejpam-7112	374	4	al	al	PROPN
ejpam-7112	374	5	.	.	PUNCT
ejpam-7112	374	6	/	/	SYM
ejpam-7112	374	7	eur	eur	PROPN
ejpam-7112	374	8	.	.	PUNCT
ejpam-7112	375	1	j.	j.	PROPN
ejpam-7112	375	2	pure	pure	PROPN
ejpam-7112	375	3	appl	appl	PROPN
ejpam-7112	375	4	.	.	PROPN
ejpam-7112	375	5	math	math	PROPN
ejpam-7112	375	6	,	,	PUNCT
ejpam-7112	375	7	18	18	NUM
ejpam-7112	375	8	(	(	PUNCT
ejpam-7112	375	9	4	4	NUM
ejpam-7112	375	10	)	)	PUNCT
ejpam-7112	375	11	(	(	PUNCT
ejpam-7112	375	12	2025	2025	NUM
ejpam-7112	375	13	)	)	PUNCT
ejpam-7112	375	14	,	,	PUNCT
ejpam-7112	375	15	7112	7112	NUM
ejpam-7112	375	16	14	14	NUM
ejpam-7112	375	17	of	of	ADP
ejpam-7112	375	18	38	38	NUM
ejpam-7112	375	19	clearly	clearly	ADV
ejpam-7112	375	20	,	,	PUNCT
ejpam-7112	375	21	minx∈[α	minx∈[α	NOUN
ejpam-7112	375	22	,	,	PUNCT
ejpam-7112	375	23	β	β	X
ejpam-7112	375	24	]	]	X
ejpam-7112	375	25	{	{	PUNCT
ejpam-7112	375	26	f	f	X
ejpam-7112	375	27	(	(	PUNCT
ejpam-7112	375	28	4)(x)g(4)(x	4)(x)g(4)(x	NUM
ejpam-7112	375	29	)	)	PUNCT
ejpam-7112	375	30	}	}	PUNCT
ejpam-7112	375	31	≤	≤	NUM
ejpam-7112	375	32	m	m	VERB
ejpam-7112	375	33	≤	≤	NOUN
ejpam-7112	375	34	maxx∈[α	maxx∈[α	NOUN
ejpam-7112	375	35	,	,	PUNCT
ejpam-7112	375	36	β	β	X
ejpam-7112	375	37	]	]	X
ejpam-7112	375	38	{	{	PUNCT
ejpam-7112	375	39	f	f	X
ejpam-7112	375	40	(	(	PUNCT
ejpam-7112	375	41	4)(x)g(4)(x	4)(x)g(4)(x	NUM
ejpam-7112	375	42	)	)	PUNCT
ejpam-7112	375	43	}	}	PUNCT
ejpam-7112	375	44	.	.	PUNCT
ejpam-7112	376	1	because	because	SCONJ
ejpam-7112	376	2	f	f	PROPN
ejpam-7112	376	3	(	(	PUNCT
ejpam-7112	376	4	4)(x)and	4)(x)and	NUM
ejpam-7112	376	5	g′(x	g′(x	NOUN
ejpam-7112	376	6	)	)	PUNCT
ejpam-7112	376	7	in	in	ADP
ejpam-7112	376	8	[	[	X
ejpam-7112	376	9	α	α	X
ejpam-7112	376	10	,	,	PUNCT
ejpam-7112	376	11	β	β	X
ejpam-7112	376	12	]	]	X
ejpam-7112	376	13	are	be	AUX
ejpam-7112	376	14	continuous	continuous	ADJ
ejpam-7112	376	15	,	,	PUNCT
ejpam-7112	376	16	so	so	CCONJ
ejpam-7112	376	17	there	there	PRON
ejpam-7112	376	18	is	be	VERB
ejpam-7112	376	19	a	a	DET
ejpam-7112	376	20	point	point	NOUN
ejpam-7112	376	21	µ	µ	PRON
ejpam-7112	376	22	such	such	ADJ
ejpam-7112	376	23	thatm	thatm	NOUN
ejpam-7112	376	24	=	=	SYM
ejpam-7112	376	25	f	f	PROPN
ejpam-7112	376	26	(	(	PUNCT
ejpam-7112	376	27	4)(µ)g′(η	4)(µ)g′(η	NUM
ejpam-7112	376	28	)	)	PUNCT
ejpam-7112	376	29	.	.	PUNCT
ejpam-7112	377	1	finally	finally	ADV
ejpam-7112	377	2	,	,	PUNCT
ejpam-7112	377	3	the	the	DET
ejpam-7112	377	4	global	global	ADJ
ejpam-7112	377	5	truncation	truncation	NOUN
ejpam-7112	377	6	error	error	NOUN
ejpam-7112	377	7	ramct	ramct	VERB
ejpam-7112	377	8	[	[	X
ejpam-7112	377	9	f	f	X
ejpam-7112	377	10	]	]	X
ejpam-7112	377	11	takes	take	VERB
ejpam-7112	377	12	the	the	DET
ejpam-7112	377	13	form	form	NOUN
ejpam-7112	377	14	:	:	PUNCT
ejpam-7112	378	1	=	=	SYM
ejpam-7112	378	2	n	n	CCONJ
ejpam-7112	378	3	(	(	PUNCT
ejpam-7112	378	4	2α3	2α3	NUM
ejpam-7112	378	5	+	+	CCONJ
ejpam-7112	378	6	2αβ2	2αβ2	NUM
ejpam-7112	378	7	+	+	CCONJ
ejpam-7112	378	8	2α2β	2α2β	ADJ
ejpam-7112	378	9	−	−	NOUN
ejpam-7112	378	10	6β3	6β3	NUM
ejpam-7112	378	11	+	+	CCONJ
ejpam-7112	378	12	3(β	3(β	NUM
ejpam-7112	378	13	−	−	NOUN
ejpam-7112	378	14	α)(α+	α)(α+	NOUN
ejpam-7112	378	15	β)2	β)2	X
ejpam-7112	378	16	48	48	NUM
ejpam-7112	378	17	∫	∫	PROPN
ejpam-7112	378	18	β	β	PROPN
ejpam-7112	378	19	a	a	DET
ejpam-7112	378	20	g(t	g(t	PROPN
ejpam-7112	378	21	)	)	PUNCT
ejpam-7112	378	22	dt+	dt+	NOUN
ejpam-7112	378	23	4β2	4β2	NUM
ejpam-7112	378	24	−	−	PROPN
ejpam-7112	378	25	(	(	PUNCT
ejpam-7112	378	26	α+	α+	X
ejpam-7112	378	27	β)2	β)2	X
ejpam-7112	378	28	8	8	NUM
ejpam-7112	378	29	∫	∫	PROPN
ejpam-7112	378	30	β	β	PROPN
ejpam-7112	378	31	a	a	DET
ejpam-7112	378	32	∫	∫	PROPN
ejpam-7112	378	33	β	β	X
ejpam-7112	378	34	a	a	DET
ejpam-7112	378	35	g(x	g(x	NOUN
ejpam-7112	378	36	)	)	PUNCT
ejpam-7112	378	37	dx	dx	PROPN
ejpam-7112	379	1	dt	dt	X
ejpam-7112	379	2	−	−	PROPN
ejpam-7112	380	1	β	β	X
ejpam-7112	380	2	∫	∫	PROPN
ejpam-7112	380	3	β	β	X
ejpam-7112	380	4	a	a	DET
ejpam-7112	380	5	∫	∫	PROPN
ejpam-7112	380	6	t	t	PROPN
ejpam-7112	380	7	a	a	DET
ejpam-7112	380	8	∫	∫	PROPN
ejpam-7112	380	9	y	y	PROPN
ejpam-7112	380	10	a	a	DET
ejpam-7112	380	11	g(x	g(x	NOUN
ejpam-7112	380	12	)	)	PUNCT
ejpam-7112	380	13	dx	dx	PROPN
ejpam-7112	381	1	dy	dy	NOUN
ejpam-7112	381	2	dt+	dt+	NOUN
ejpam-7112	381	3	∫	∫	PROPN
ejpam-7112	381	4	β	β	PROPN
ejpam-7112	381	5	a	a	DET
ejpam-7112	381	6	∫	∫	PROPN
ejpam-7112	381	7	t	t	PROPN
ejpam-7112	381	8	a	a	DET
ejpam-7112	381	9	∫	∫	PROPN
ejpam-7112	381	10	y	y	PROPN
ejpam-7112	381	11	a	a	DET
ejpam-7112	381	12	∫	∫	PROPN
ejpam-7112	381	13	z	z	PROPN
ejpam-7112	381	14	a	a	DET
ejpam-7112	381	15	g(x	g(x	NOUN
ejpam-7112	381	16	)	)	PUNCT
ejpam-7112	381	17	dx	dx	PROPN
ejpam-7112	382	1	dy	dy	X
ejpam-7112	382	2	dz	dz	PROPN
ejpam-7112	382	3	dt	dt	PROPN
ejpam-7112	382	4	)	)	PUNCT
ejpam-7112	382	5	f	f	PROPN
ejpam-7112	382	6	(	(	PUNCT
ejpam-7112	382	7	4)(µ)g′(η	4)(µ)g′(η	NUM
ejpam-7112	382	8	)	)	PUNCT
ejpam-7112	382	9	(	(	PUNCT
ejpam-7112	382	10	44	44	NUM
ejpam-7112	382	11	)	)	PUNCT
ejpam-7112	382	12	where	where	SCONJ
ejpam-7112	382	13	µ	µ	X
ejpam-7112	382	14	,	,	PUNCT
ejpam-7112	382	15	η	η	PROPN
ejpam-7112	382	16	∈	∈	PROPN
ejpam-7112	382	17	(	(	PUNCT
ejpam-7112	382	18	α	α	NOUN
ejpam-7112	382	19	,	,	PUNCT
ejpam-7112	382	20	β	β	NOUN
ejpam-7112	382	21	)	)	PUNCT
ejpam-7112	382	22	and	and	CCONJ
ejpam-7112	382	23	h	h	NOUN
ejpam-7112	382	24	=	=	NOUN
ejpam-7112	382	25	β−α	β−α	NOUN
ejpam-7112	382	26	n	n	PRON
ejpam-7112	382	27	2.2.2	2.2.2	NUM
ejpam-7112	382	28	.	.	PUNCT
ejpam-7112	382	29	proposed	propose	VERB
ejpam-7112	382	30	derivative	derivative	NOUN
ejpam-7112	382	31	-	-	PUNCT
ejpam-7112	382	32	based	base	VERB
ejpam-7112	382	33	rules	rule	NOUN
ejpam-7112	382	34	for	for	ADP
ejpam-7112	382	35	the	the	DET
ejpam-7112	382	36	riemann	riemann	PROPN
ejpam-7112	382	37	-	-	PUNCT
ejpam-7112	382	38	stieltjes	stieltjes	NOUN
ejpam-7112	382	39	integral	integral	ADJ
ejpam-7112	382	40	using	use	VERB
ejpam-7112	382	41	other	other	ADJ
ejpam-7112	382	42	means	mean	VERB
ejpam-7112	382	43	some	some	DET
ejpam-7112	382	44	other	other	ADJ
ejpam-7112	382	45	schemes	scheme	NOUN
ejpam-7112	382	46	are	be	AUX
ejpam-7112	382	47	derived	derive	VERB
ejpam-7112	382	48	in	in	ADP
ejpam-7112	382	49	terms	term	NOUN
ejpam-7112	382	50	of	of	ADP
ejpam-7112	382	51	geometric	geometric	ADJ
ejpam-7112	382	52	,	,	PUNCT
ejpam-7112	382	53	harmonic	harmonic	ADJ
ejpam-7112	382	54	,	,	PUNCT
ejpam-7112	382	55	heronian	heronian	ADJ
ejpam-7112	382	56	and	and	CCONJ
ejpam-7112	382	57	centroidal	centroidal	PROPN
ejpam-7112	382	58	means	mean	VERB
ejpam-7112	382	59	for	for	ADP
ejpam-7112	382	60	rs	rs	ADJ
ejpam-7112	382	61	-	-	ADJ
ejpam-7112	382	62	integral	integral	ADJ
ejpam-7112	382	63	using	use	VERB
ejpam-7112	382	64	the	the	DET
ejpam-7112	382	65	approach	approach	NOUN
ejpam-7112	382	66	discussed	discuss	VERB
ejpam-7112	382	67	in	in	ADP
ejpam-7112	382	68	section	section	NOUN
ejpam-7112	382	69	2.2.1	2.2.1	NUM
ejpam-7112	382	70	.	.	PUNCT
ejpam-7112	383	1	the	the	DET
ejpam-7112	383	2	derivation	derivation	NOUN
ejpam-7112	383	3	of	of	ADP
ejpam-7112	383	4	the	the	DET
ejpam-7112	383	5	quadrature	quadrature	NOUN
ejpam-7112	383	6	scheme	scheme	NOUN
ejpam-7112	383	7	,	,	PUNCT
ejpam-7112	383	8	its	its	PRON
ejpam-7112	383	9	error	error	NOUN
ejpam-7112	383	10	term	term	NOUN
ejpam-7112	383	11	and	and	CCONJ
ejpam-7112	383	12	the	the	DET
ejpam-7112	383	13	consequent	consequent	ADJ
ejpam-7112	383	14	reduction	reduction	NOUN
ejpam-7112	383	15	to	to	ADP
ejpam-7112	383	16	the	the	DET
ejpam-7112	383	17	classical	classical	ADJ
ejpam-7112	383	18	riemann	riemann	PROPN
ejpam-7112	383	19	integral	integral	ADJ
ejpam-7112	383	20	case	case	NOUN
ejpam-7112	383	21	are	be	AUX
ejpam-7112	383	22	in	in	ADP
ejpam-7112	383	23	a	a	DET
ejpam-7112	383	24	same	same	ADJ
ejpam-7112	383	25	pattern	pattern	NOUN
ejpam-7112	383	26	as	as	SCONJ
ejpam-7112	383	27	proved	prove	VERB
ejpam-7112	383	28	in	in	ADP
ejpam-7112	383	29	theorems	theorem	NOUN
ejpam-7112	383	30	1	1	NUM
ejpam-7112	383	31	-	-	SYM
ejpam-7112	383	32	4	4	NUM
ejpam-7112	383	33	,	,	PUNCT
ejpam-7112	383	34	respectively	respectively	ADV
ejpam-7112	383	35	.	.	PUNCT
ejpam-7112	384	1	for	for	ADP
ejpam-7112	384	2	brevity	brevity	NOUN
ejpam-7112	384	3	,	,	PUNCT
ejpam-7112	384	4	we	we	PRON
ejpam-7112	384	5	discuss	discuss	VERB
ejpam-7112	384	6	the	the	DET
ejpam-7112	384	7	main	main	ADJ
ejpam-7112	384	8	results	result	NOUN
ejpam-7112	384	9	in	in	ADP
ejpam-7112	384	10	form	form	NOUN
ejpam-7112	384	11	of	of	ADP
ejpam-7112	384	12	corollaries	corollary	NOUN
ejpam-7112	384	13	here	here	ADV
ejpam-7112	384	14	that	that	PRON
ejpam-7112	384	15	have	have	VERB
ejpam-7112	384	16	similar	similar	ADJ
ejpam-7112	384	17	proofs	proof	NOUN
ejpam-7112	384	18	to	to	ADP
ejpam-7112	384	19	theorems	theorem	NOUN
ejpam-7112	384	20	1	1	NUM
ejpam-7112	384	21	-	-	SYM
ejpam-7112	384	22	4	4	NUM
ejpam-7112	384	23	,	,	PUNCT
ejpam-7112	384	24	and	and	CCONJ
ejpam-7112	384	25	can	can	AUX
ejpam-7112	384	26	also	also	ADV
ejpam-7112	384	27	be	be	AUX
ejpam-7112	384	28	considered	consider	VERB
ejpam-7112	384	29	immediate	immediate	ADJ
ejpam-7112	384	30	consequences	consequence	NOUN
ejpam-7112	384	31	of	of	ADP
ejpam-7112	384	32	the	the	DET
ejpam-7112	384	33	process	process	NOUN
ejpam-7112	384	34	followed	follow	VERB
ejpam-7112	384	35	therein	therein	ADV
ejpam-7112	384	36	.	.	PUNCT
ejpam-7112	385	1	in	in	ADP
ejpam-7112	385	2	scheme	scheme	NOUN
ejpam-7112	385	3	(	(	PUNCT
ejpam-7112	385	4	17	17	NUM
ejpam-7112	385	5	)	)	PUNCT
ejpam-7112	385	6	,	,	PUNCT
ejpam-7112	385	7	selecting	select	VERB
ejpam-7112	385	8	the	the	DET
ejpam-7112	385	9	expression	expression	NOUN
ejpam-7112	385	10	of	of	ADP
ejpam-7112	385	11	c	c	PROPN
ejpam-7112	385	12	as	as	ADP
ejpam-7112	385	13	the	the	DET
ejpam-7112	385	14	geometric	geometric	ADJ
ejpam-7112	385	15	,	,	PUNCT
ejpam-7112	385	16	harmonic	harmonic	ADJ
ejpam-7112	385	17	,	,	PUNCT
ejpam-7112	385	18	heronian	heronian	ADJ
ejpam-7112	385	19	and	and	CCONJ
ejpam-7112	385	20	centroidal	centroidal	ADJ
ejpam-7112	385	21	means	mean	NOUN
ejpam-7112	385	22	of	of	ADP
ejpam-7112	385	23	the	the	DET
ejpam-7112	385	24	limits	limit	NOUN
ejpam-7112	385	25	of	of	ADP
ejpam-7112	385	26	integration	integration	NOUN
ejpam-7112	385	27	,	,	PUNCT
ejpam-7112	385	28	then	then	ADV
ejpam-7112	385	29	the	the	DET
ejpam-7112	385	30	corresponding	corresponding	ADJ
ejpam-7112	385	31	new	new	ADJ
ejpam-7112	385	32	trapezoid	trapezoid	ADJ
ejpam-7112	385	33	-	-	PUNCT
ejpam-7112	385	34	type	type	NOUN
ejpam-7112	385	35	schemes	scheme	NOUN
ejpam-7112	385	36	for	for	ADP
ejpam-7112	385	37	the	the	DET
ejpam-7112	385	38	rs	rs	ADJ
ejpam-7112	385	39	integrals	integral	NOUN
ejpam-7112	385	40	,	,	PUNCT
ejpam-7112	385	41	labeled	label	VERB
ejpam-7112	385	42	as	as	ADP
ejpam-7112	385	43	:	:	PUNCT
ejpam-7112	385	44	gmt	gmt	X
ejpam-7112	385	45	,	,	PUNCT
ejpam-7112	385	46	hamt	hamt	PROPN
ejpam-7112	385	47	,	,	PUNCT
ejpam-7112	385	48	hemt	hemt	PROPN
ejpam-7112	385	49	and	and	CCONJ
ejpam-7112	385	50	cmt	cmt	PROPN
ejpam-7112	385	51	,	,	PUNCT
ejpam-7112	385	52	respectively	respectively	ADV
ejpam-7112	385	53	,	,	PUNCT
ejpam-7112	385	54	are	be	AUX
ejpam-7112	385	55	described	describe	VERB
ejpam-7112	385	56	in	in	ADP
ejpam-7112	385	57	corollaries	corollary	NOUN
ejpam-7112	385	58	1	1	NUM
ejpam-7112	385	59	-	-	SYM
ejpam-7112	385	60	4	4	NUM
ejpam-7112	385	61	with	with	ADP
ejpam-7112	385	62	error	error	NOUN
ejpam-7112	385	63	terms	term	NOUN
ejpam-7112	385	64	in	in	ADP
ejpam-7112	385	65	basic	basic	ADJ
ejpam-7112	385	66	form	form	NOUN
ejpam-7112	385	67	.	.	PUNCT
ejpam-7112	386	1	corollary	corollary	ADJ
ejpam-7112	386	2	1	1	NUM
ejpam-7112	386	3	.	.	PUNCT
ejpam-7112	387	1	assuming	assume	VERB
ejpam-7112	387	2	continuity	continuity	NOUN
ejpam-7112	387	3	of	of	ADP
ejpam-7112	387	4	f(t	f(t	PROPN
ejpam-7112	387	5	)	)	PUNCT
ejpam-7112	387	6	and	and	CCONJ
ejpam-7112	387	7	g(t	g(t	PROPN
ejpam-7112	387	8	)	)	PUNCT
ejpam-7112	387	9	in	in	ADP
ejpam-7112	387	10	[	[	X
ejpam-7112	387	11	α	α	X
ejpam-7112	387	12	,	,	PUNCT
ejpam-7112	387	13	β	β	X
ejpam-7112	387	14	]	]	PUNCT
ejpam-7112	387	15	along	along	ADP
ejpam-7112	387	16	withg(t	withg(t	PROPN
ejpam-7112	387	17	)	)	PUNCT
ejpam-7112	387	18	being	be	AUX
ejpam-7112	387	19	monotonically	monotonically	ADV
ejpam-7112	387	20	rising	rise	VERB
ejpam-7112	387	21	in	in	ADP
ejpam-7112	387	22	the	the	DET
ejpam-7112	387	23	same	same	ADJ
ejpam-7112	387	24	interval	interval	NOUN
ejpam-7112	387	25	,	,	PUNCT
ejpam-7112	387	26	gmt	gmt	X
ejpam-7112	387	27	quadrature	quadrature	NOUN
ejpam-7112	387	28	for	for	ADP
ejpam-7112	387	29	the	the	DET
ejpam-7112	387	30	rs	rs	ADJ
ejpam-7112	387	31	-	-	ADJ
ejpam-7112	387	32	integral	integral	ADJ
ejpam-7112	387	33	is:∫	is:∫	NOUN
ejpam-7112	387	34	β	β	ADP
ejpam-7112	387	35	a	a	DET
ejpam-7112	387	36	f(x	f(x	PROPN
ejpam-7112	387	37	)	)	PUNCT
ejpam-7112	387	38	dg	dg	PROPN
ejpam-7112	388	1	≈	≈	PROPN
ejpam-7112	388	2	gmt	gmt	PROPN
ejpam-7112	388	3	=	=	PUNCT
ejpam-7112	388	4	(	(	PUNCT
ejpam-7112	388	5	1	1	NUM
ejpam-7112	388	6	β	β	X
ejpam-7112	388	7	−	−	PROPN
ejpam-7112	388	8	α	α	X
ejpam-7112	388	9	∫	∫	PROPN
ejpam-7112	388	10	β	β	PROPN
ejpam-7112	388	11	a	a	DET
ejpam-7112	388	12	g(t	g(t	PROPN
ejpam-7112	388	13	)	)	PUNCT
ejpam-7112	388	14	dt−	dt−	PUNCT
ejpam-7112	388	15	g(α	g(α	PROPN
ejpam-7112	388	16	)	)	PUNCT
ejpam-7112	388	17	)	)	PUNCT
ejpam-7112	389	1	f(α	f(α	NOUN
ejpam-7112	389	2	)	)	PUNCT
ejpam-7112	390	1	+	+	CCONJ
ejpam-7112	390	2	(	(	PUNCT
ejpam-7112	390	3	g(β)−	g(β)−	PROPN
ejpam-7112	390	4	1	1	NUM
ejpam-7112	390	5	β	β	NOUN
ejpam-7112	390	6	−	−	PROPN
ejpam-7112	390	7	α	α	DET
ejpam-7112	390	8	∫	∫	PROPN
ejpam-7112	390	9	β	β	PROPN
ejpam-7112	390	10	a	a	DET
ejpam-7112	390	11	g(t	g(t	PROPN
ejpam-7112	390	12	)	)	PUNCT
ejpam-7112	390	13	dt	dt	NOUN
ejpam-7112	390	14	)	)	PUNCT
ejpam-7112	390	15	f(β	f(β	PROPN
ejpam-7112	390	16	)	)	PUNCT
ejpam-7112	391	1	+	+	CCONJ
ejpam-7112	391	2	(	(	PUNCT
ejpam-7112	391	3	∫	∫	PROPN
ejpam-7112	391	4	β	β	X
ejpam-7112	391	5	a	a	DET
ejpam-7112	391	6	∫	∫	PROPN
ejpam-7112	391	7	t	t	PROPN
ejpam-7112	391	8	a	a	DET
ejpam-7112	391	9	g(x	g(x	NOUN
ejpam-7112	391	10	)	)	PUNCT
ejpam-7112	391	11	dx	dx	PROPN
ejpam-7112	392	1	dt−	dt−	PROPN
ejpam-7112	392	2	β	β	X
ejpam-7112	392	3	−	−	X
ejpam-7112	392	4	α	α	NOUN
ejpam-7112	392	5	2	2	NUM
ejpam-7112	392	6	∫	∫	PROPN
ejpam-7112	392	7	β	β	PROPN
ejpam-7112	392	8	a	a	DET
ejpam-7112	392	9	g(t	g(t	PROPN
ejpam-7112	392	10	)	)	PUNCT
ejpam-7112	392	11	dt	dt	NOUN
ejpam-7112	392	12	)	)	PUNCT
ejpam-7112	393	1	f	f	PROPN
ejpam-7112	393	2	′′	′′	PROPN
ejpam-7112	393	3	(	(	PUNCT
ejpam-7112	393	4	√	√	NUM
ejpam-7112	393	5	αβ	αβ	INTJ
ejpam-7112	393	6	)	)	PUNCT
ejpam-7112	393	7	(	(	PUNCT
ejpam-7112	393	8	45	45	NUM
ejpam-7112	393	9	)	)	PUNCT
ejpam-7112	393	10	with	with	ADP
ejpam-7112	393	11	precision	precision	NOUN
ejpam-7112	393	12	2	2	NUM
ejpam-7112	393	13	.	.	PUNCT
ejpam-7112	394	1	the	the	DET
ejpam-7112	394	2	error	error	NOUN
ejpam-7112	394	3	term	term	NOUN
ejpam-7112	394	4	rgmt	rgmt	ADJ
ejpam-7112	394	5	[	[	X
ejpam-7112	394	6	f	f	X
ejpam-7112	394	7	]	]	X
ejpam-7112	394	8	is	be	AUX
ejpam-7112	394	9	:(	:(	PUNCT
ejpam-7112	394	10	α2	α2	ADJ
ejpam-7112	395	1	+	+	CCONJ
ejpam-7112	396	1	αβ	αβ	ADP
ejpam-7112	396	2	−	−	ADP
ejpam-7112	396	3	2β2	2β2	NUM
ejpam-7112	396	4	+	+	CCONJ
ejpam-7112	396	5	3	3	NUM
ejpam-7112	396	6	√	√	NUM
ejpam-7112	396	7	αβ(β	αβ(β	NUM
ejpam-7112	396	8	−	−	PROPN
ejpam-7112	396	9	α	α	NOUN
ejpam-7112	396	10	)	)	PUNCT
ejpam-7112	396	11	6	6	NUM
ejpam-7112	396	12	∫	∫	PROPN
ejpam-7112	396	13	β	β	PROPN
ejpam-7112	396	14	α	α	PROPN
ejpam-7112	396	15	g(t	g(t	PROPN
ejpam-7112	396	16	)	)	PUNCT
ejpam-7112	396	17	dt+	dt+	NOUN
ejpam-7112	396	18	(	(	PUNCT
ejpam-7112	396	19	β	β	NOUN
ejpam-7112	396	20	−	−	NOUN
ejpam-7112	396	21	√	√	INTJ
ejpam-7112	396	22	αβ	αβ	INTJ
ejpam-7112	396	23	)	)	PUNCT
ejpam-7112	396	24	∫	∫	PROPN
ejpam-7112	396	25	β	β	PROPN
ejpam-7112	396	26	α	α	PROPN
ejpam-7112	396	27	∫	∫	PROPN
ejpam-7112	396	28	t	t	PROPN
ejpam-7112	396	29	α	α	PROPN
ejpam-7112	396	30	g(x	g(x	PROPN
ejpam-7112	396	31	)	)	PUNCT
ejpam-7112	396	32	dx	dx	PROPN
ejpam-7112	397	1	dt	dt	X
ejpam-7112	398	1	−	−	PROPN
ejpam-7112	398	2	∫	∫	PROPN
ejpam-7112	398	3	β	β	PROPN
ejpam-7112	398	4	α	α	PROPN
ejpam-7112	398	5	∫	∫	PROPN
ejpam-7112	398	6	t	t	PROPN
ejpam-7112	399	1	α	α	NOUN
ejpam-7112	399	2	∫	∫	PROPN
ejpam-7112	399	3	y	y	PROPN
ejpam-7112	399	4	α	α	PROPN
ejpam-7112	399	5	g(x	g(x	PROPN
ejpam-7112	399	6	)	)	PUNCT
ejpam-7112	399	7	dx	dx	PROPN
ejpam-7112	399	8	dy	dy	NOUN
ejpam-7112	400	1	dt	dt	NOUN
ejpam-7112	400	2	)	)	PUNCT
ejpam-7112	400	3	f	f	PROPN
ejpam-7112	400	4	(	(	PUNCT
ejpam-7112	400	5	3)(ξ	3)(ξ	NUM
ejpam-7112	400	6	)	)	PUNCT
ejpam-7112	400	7	,	,	PUNCT
ejpam-7112	400	8	k.	k.	PROPN
ejpam-7112	400	9	memon	memon	PROPN
ejpam-7112	400	10	et	et	PROPN
ejpam-7112	400	11	al	al	PROPN
ejpam-7112	400	12	.	.	PUNCT
ejpam-7112	400	13	/	/	SYM
ejpam-7112	400	14	eur	eur	PROPN
ejpam-7112	400	15	.	.	PUNCT
ejpam-7112	401	1	j.	j.	PROPN
ejpam-7112	401	2	pure	pure	PROPN
ejpam-7112	401	3	appl	appl	PROPN
ejpam-7112	401	4	.	.	PROPN
ejpam-7112	401	5	math	math	PROPN
ejpam-7112	401	6	,	,	PUNCT
ejpam-7112	401	7	18	18	NUM
ejpam-7112	401	8	(	(	PUNCT
ejpam-7112	401	9	4	4	NUM
ejpam-7112	401	10	)	)	PUNCT
ejpam-7112	401	11	(	(	PUNCT
ejpam-7112	401	12	2025	2025	NUM
ejpam-7112	401	13	)	)	PUNCT
ejpam-7112	401	14	,	,	PUNCT
ejpam-7112	401	15	7112	7112	NUM
ejpam-7112	401	16	15	15	NUM
ejpam-7112	401	17	of	of	ADP
ejpam-7112	401	18	38	38	NUM
ejpam-7112	401	19	where	where	SCONJ
ejpam-7112	401	20	ξ	ξ	PROPN
ejpam-7112	401	21	∈	∈	PROPN
ejpam-7112	401	22	(	(	PUNCT
ejpam-7112	401	23	α	α	NOUN
ejpam-7112	401	24	,	,	PUNCT
ejpam-7112	401	25	β	β	NOUN
ejpam-7112	401	26	)	)	PUNCT
ejpam-7112	401	27	corollary	corollary	ADJ
ejpam-7112	401	28	2	2	NUM
ejpam-7112	401	29	.	.	PUNCT
ejpam-7112	401	30	assuming	assume	VERB
ejpam-7112	401	31	continuity	continuity	NOUN
ejpam-7112	401	32	of	of	ADP
ejpam-7112	401	33	f(t	f(t	PROPN
ejpam-7112	401	34	)	)	PUNCT
ejpam-7112	401	35	and	and	CCONJ
ejpam-7112	401	36	g(t	g(t	PROPN
ejpam-7112	401	37	)	)	PUNCT
ejpam-7112	401	38	in	in	ADP
ejpam-7112	401	39	[	[	X
ejpam-7112	401	40	α	α	X
ejpam-7112	401	41	,	,	PUNCT
ejpam-7112	401	42	β	β	X
ejpam-7112	401	43	]	]	PUNCT
ejpam-7112	401	44	along	along	ADP
ejpam-7112	401	45	with	with	ADP
ejpam-7112	401	46	g(t	g(t	PROPN
ejpam-7112	401	47	)	)	PUNCT
ejpam-7112	401	48	being	be	AUX
ejpam-7112	401	49	monotonically	monotonically	ADV
ejpam-7112	401	50	rising	rise	VERB
ejpam-7112	401	51	in	in	ADP
ejpam-7112	401	52	the	the	DET
ejpam-7112	401	53	same	same	ADJ
ejpam-7112	401	54	interval	interval	NOUN
ejpam-7112	401	55	,	,	PUNCT
ejpam-7112	401	56	hamt	hamt	NOUN
ejpam-7112	401	57	quadrature	quadrature	NOUN
ejpam-7112	401	58	for	for	ADP
ejpam-7112	401	59	the	the	DET
ejpam-7112	401	60	rs	rs	ADJ
ejpam-7112	401	61	-	-	ADJ
ejpam-7112	401	62	integral	integral	ADJ
ejpam-7112	401	63	is:∫	is:∫	NOUN
ejpam-7112	401	64	β	β	ADP
ejpam-7112	401	65	a	a	DET
ejpam-7112	401	66	f(x	f(x	PROPN
ejpam-7112	401	67	)	)	PUNCT
ejpam-7112	401	68	dg	dg	PROPN
ejpam-7112	402	1	≈	≈	PROPN
ejpam-7112	402	2	hamt	hamt	NOUN
ejpam-7112	402	3	=	=	PUNCT
ejpam-7112	403	1	(	(	PUNCT
ejpam-7112	403	2	1	1	NUM
ejpam-7112	403	3	β	β	X
ejpam-7112	403	4	−	−	PROPN
ejpam-7112	403	5	α	α	X
ejpam-7112	403	6	∫	∫	PROPN
ejpam-7112	403	7	β	β	PROPN
ejpam-7112	403	8	a	a	DET
ejpam-7112	403	9	g(t	g(t	PROPN
ejpam-7112	403	10	)	)	PUNCT
ejpam-7112	403	11	dt−	dt−	PUNCT
ejpam-7112	403	12	g(α	g(α	PROPN
ejpam-7112	403	13	)	)	PUNCT
ejpam-7112	403	14	)	)	PUNCT
ejpam-7112	403	15	f(α	f(α	NOUN
ejpam-7112	403	16	)	)	PUNCT
ejpam-7112	404	1	+	+	CCONJ
ejpam-7112	404	2	(	(	PUNCT
ejpam-7112	404	3	g(β)−	g(β)−	PROPN
ejpam-7112	404	4	1	1	NUM
ejpam-7112	404	5	β	β	NOUN
ejpam-7112	404	6	−	−	PROPN
ejpam-7112	404	7	α	α	DET
ejpam-7112	404	8	∫	∫	PROPN
ejpam-7112	404	9	β	β	PROPN
ejpam-7112	404	10	a	a	DET
ejpam-7112	404	11	g(t	g(t	PROPN
ejpam-7112	404	12	)	)	PUNCT
ejpam-7112	404	13	dt	dt	NOUN
ejpam-7112	404	14	)	)	PUNCT
ejpam-7112	404	15	f(β	f(β	PROPN
ejpam-7112	404	16	)	)	PUNCT
ejpam-7112	405	1	+	+	CCONJ
ejpam-7112	405	2	(	(	PUNCT
ejpam-7112	405	3	∫	∫	PROPN
ejpam-7112	405	4	β	β	X
ejpam-7112	405	5	a	a	DET
ejpam-7112	405	6	∫	∫	PROPN
ejpam-7112	405	7	t	t	PROPN
ejpam-7112	405	8	a	a	DET
ejpam-7112	405	9	g(x	g(x	NOUN
ejpam-7112	405	10	)	)	PUNCT
ejpam-7112	405	11	dx	dx	PROPN
ejpam-7112	406	1	dt−	dt−	PROPN
ejpam-7112	406	2	β	β	X
ejpam-7112	406	3	−	−	X
ejpam-7112	406	4	α	α	NOUN
ejpam-7112	406	5	2	2	NUM
ejpam-7112	406	6	∫	∫	PROPN
ejpam-7112	406	7	β	β	PROPN
ejpam-7112	406	8	a	a	DET
ejpam-7112	406	9	g(t	g(t	PROPN
ejpam-7112	406	10	)	)	PUNCT
ejpam-7112	406	11	dt	dt	NOUN
ejpam-7112	406	12	)	)	PUNCT
ejpam-7112	407	1	f	f	PROPN
ejpam-7112	407	2	′′	′′	PROPN
ejpam-7112	407	3	(	(	PUNCT
ejpam-7112	407	4	2αβ	2αβ	ADJ
ejpam-7112	407	5	α+	α+	NUM
ejpam-7112	407	6	β	β	NOUN
ejpam-7112	407	7	)	)	PUNCT
ejpam-7112	407	8	(	(	PUNCT
ejpam-7112	407	9	46	46	NUM
ejpam-7112	407	10	)	)	PUNCT
ejpam-7112	407	11	with	with	ADP
ejpam-7112	407	12	precision	precision	NOUN
ejpam-7112	407	13	2	2	NUM
ejpam-7112	407	14	.	.	PUNCT
ejpam-7112	408	1	the	the	DET
ejpam-7112	408	2	truncation	truncation	NOUN
ejpam-7112	408	3	error	error	NOUN
ejpam-7112	408	4	rhamt	rhamt	VERB
ejpam-7112	408	5	[	[	X
ejpam-7112	408	6	f	f	X
ejpam-7112	408	7	]	]	X
ejpam-7112	408	8	is	be	AUX
ejpam-7112	408	9	:(	:(	PUNCT
ejpam-7112	408	10	α3	α3	ADJ
ejpam-7112	408	11	−	−	PROPN
ejpam-7112	408	12	4α2β	4α2β	PROPN
ejpam-7112	409	1	+	+	CCONJ
ejpam-7112	409	2	5αβ2	5αβ2	NUM
ejpam-7112	409	3	−	−	NOUN
ejpam-7112	410	1	2β3	2β3	NUM
ejpam-7112	410	2	6(α+	6(α+	NUM
ejpam-7112	410	3	β	β	NOUN
ejpam-7112	410	4	)	)	PUNCT
ejpam-7112	410	5	∫	∫	PROPN
ejpam-7112	410	6	β	β	PROPN
ejpam-7112	410	7	α	α	PROPN
ejpam-7112	410	8	g(t	g(t	PROPN
ejpam-7112	410	9	)	)	PUNCT
ejpam-7112	410	10	dt+	dt+	NOUN
ejpam-7112	410	11	(	(	PUNCT
ejpam-7112	410	12	β2	β2	NOUN
ejpam-7112	410	13	−	−	PROPN
ejpam-7112	411	1	αβ	αβ	INTJ
ejpam-7112	411	2	α+	α+	NOUN
ejpam-7112	411	3	β	β	X
ejpam-7112	411	4	)	)	PUNCT
ejpam-7112	411	5	∫	∫	PROPN
ejpam-7112	411	6	β	β	PROPN
ejpam-7112	411	7	α	α	PROPN
ejpam-7112	411	8	∫	∫	PROPN
ejpam-7112	411	9	t	t	PROPN
ejpam-7112	411	10	α	α	PROPN
ejpam-7112	411	11	g(x	g(x	PROPN
ejpam-7112	411	12	)	)	PUNCT
ejpam-7112	412	1	dx	dx	PROPN
ejpam-7112	413	1	dt	dt	X
ejpam-7112	414	1	−	−	PROPN
ejpam-7112	414	2	∫	∫	PROPN
ejpam-7112	414	3	β	β	PROPN
ejpam-7112	414	4	α	α	PROPN
ejpam-7112	414	5	∫	∫	PROPN
ejpam-7112	414	6	t	t	PROPN
ejpam-7112	415	1	α	α	NOUN
ejpam-7112	415	2	∫	∫	PROPN
ejpam-7112	415	3	y	y	PROPN
ejpam-7112	415	4	α	α	PROPN
ejpam-7112	415	5	g(x	g(x	PROPN
ejpam-7112	415	6	)	)	PUNCT
ejpam-7112	415	7	dx	dx	PROPN
ejpam-7112	415	8	dy	dy	NOUN
ejpam-7112	416	1	dt	dt	NOUN
ejpam-7112	416	2	)	)	PUNCT
ejpam-7112	416	3	f	f	PROPN
ejpam-7112	416	4	(	(	PUNCT
ejpam-7112	416	5	4)(ξ	4)(ξ	NUM
ejpam-7112	416	6	)	)	PUNCT
ejpam-7112	416	7	,	,	PUNCT
ejpam-7112	416	8	(	(	PUNCT
ejpam-7112	416	9	47	47	NUM
ejpam-7112	416	10	)	)	PUNCT
ejpam-7112	416	11	where	where	SCONJ
ejpam-7112	416	12	ξ	ξ	X
ejpam-7112	416	13	∈	∈	PROPN
ejpam-7112	416	14	(	(	PUNCT
ejpam-7112	416	15	α	α	NOUN
ejpam-7112	416	16	,	,	PUNCT
ejpam-7112	416	17	β	β	NOUN
ejpam-7112	416	18	)	)	PUNCT
ejpam-7112	416	19	corollary	corollary	ADJ
ejpam-7112	416	20	3	3	NUM
ejpam-7112	416	21	.	.	PUNCT
ejpam-7112	417	1	assuming	assume	VERB
ejpam-7112	417	2	continuity	continuity	NOUN
ejpam-7112	417	3	of	of	ADP
ejpam-7112	417	4	f(t	f(t	PROPN
ejpam-7112	417	5	)	)	PUNCT
ejpam-7112	417	6	and	and	CCONJ
ejpam-7112	417	7	g(t	g(t	PROPN
ejpam-7112	417	8	)	)	PUNCT
ejpam-7112	417	9	in	in	ADP
ejpam-7112	417	10	[	[	X
ejpam-7112	417	11	α	α	X
ejpam-7112	417	12	,	,	PUNCT
ejpam-7112	417	13	β	β	X
ejpam-7112	417	14	]	]	PUNCT
ejpam-7112	417	15	along	along	ADP
ejpam-7112	417	16	with	with	ADP
ejpam-7112	417	17	g(t	g(t	PROPN
ejpam-7112	417	18	)	)	PUNCT
ejpam-7112	417	19	being	be	AUX
ejpam-7112	417	20	monotonically	monotonically	ADV
ejpam-7112	417	21	rising	rise	VERB
ejpam-7112	417	22	in	in	ADP
ejpam-7112	417	23	the	the	DET
ejpam-7112	417	24	same	same	ADJ
ejpam-7112	417	25	interval	interval	NOUN
ejpam-7112	418	1	,	,	PUNCT
ejpam-7112	418	2	hemt	hemt	NOUN
ejpam-7112	418	3	quadrature	quadrature	NOUN
ejpam-7112	418	4	for	for	ADP
ejpam-7112	418	5	the	the	DET
ejpam-7112	418	6	rs	rs	ADJ
ejpam-7112	418	7	-	-	ADJ
ejpam-7112	418	8	integral	integral	ADJ
ejpam-7112	418	9	is:∫	is:∫	NOUN
ejpam-7112	418	10	β	β	ADP
ejpam-7112	418	11	a	a	DET
ejpam-7112	418	12	f(x	f(x	PROPN
ejpam-7112	418	13	)	)	PUNCT
ejpam-7112	418	14	dg	dg	PROPN
ejpam-7112	419	1	≈	≈	PROPN
ejpam-7112	419	2	hemt	hemt	PROPN
ejpam-7112	419	3	=	=	PUNCT
ejpam-7112	419	4	(	(	PUNCT
ejpam-7112	419	5	1	1	NUM
ejpam-7112	419	6	β	β	X
ejpam-7112	419	7	−	−	PROPN
ejpam-7112	420	1	α	α	X
ejpam-7112	420	2	∫	∫	PROPN
ejpam-7112	420	3	β	β	PROPN
ejpam-7112	420	4	a	a	DET
ejpam-7112	420	5	g(t	g(t	PROPN
ejpam-7112	420	6	)	)	PUNCT
ejpam-7112	420	7	dt−	dt−	PUNCT
ejpam-7112	420	8	g(α	g(α	PROPN
ejpam-7112	420	9	)	)	PUNCT
ejpam-7112	420	10	)	)	PUNCT
ejpam-7112	421	1	f(α	f(α	NOUN
ejpam-7112	421	2	)	)	PUNCT
ejpam-7112	422	1	+	+	CCONJ
ejpam-7112	422	2	(	(	PUNCT
ejpam-7112	422	3	g(β)−	g(β)−	PROPN
ejpam-7112	422	4	1	1	NUM
ejpam-7112	422	5	β	β	NOUN
ejpam-7112	422	6	−	−	PROPN
ejpam-7112	422	7	α	α	DET
ejpam-7112	422	8	∫	∫	PROPN
ejpam-7112	422	9	β	β	PROPN
ejpam-7112	422	10	a	a	DET
ejpam-7112	422	11	g(t	g(t	PROPN
ejpam-7112	422	12	)	)	PUNCT
ejpam-7112	422	13	dt	dt	NOUN
ejpam-7112	422	14	)	)	PUNCT
ejpam-7112	422	15	f(β	f(β	PROPN
ejpam-7112	422	16	)	)	PUNCT
ejpam-7112	423	1	+	+	CCONJ
ejpam-7112	423	2	(	(	PUNCT
ejpam-7112	423	3	∫	∫	PROPN
ejpam-7112	423	4	β	β	X
ejpam-7112	423	5	a	a	DET
ejpam-7112	423	6	∫	∫	PROPN
ejpam-7112	423	7	t	t	PROPN
ejpam-7112	423	8	a	a	DET
ejpam-7112	423	9	g(x	g(x	NOUN
ejpam-7112	423	10	)	)	PUNCT
ejpam-7112	423	11	dx	dx	PROPN
ejpam-7112	424	1	dt−	dt−	PROPN
ejpam-7112	424	2	β	β	X
ejpam-7112	424	3	−	−	X
ejpam-7112	424	4	α	α	NOUN
ejpam-7112	424	5	2	2	NUM
ejpam-7112	424	6	∫	∫	PROPN
ejpam-7112	424	7	β	β	PROPN
ejpam-7112	424	8	a	a	DET
ejpam-7112	424	9	g(t	g(t	PROPN
ejpam-7112	424	10	)	)	PUNCT
ejpam-7112	424	11	dt	dt	NOUN
ejpam-7112	424	12	)	)	PUNCT
ejpam-7112	425	1	f	f	PROPN
ejpam-7112	425	2	′′	′′	PROPN
ejpam-7112	425	3	(	(	PUNCT
ejpam-7112	425	4	α+	α+	ADP
ejpam-7112	425	5	√	√	INTJ
ejpam-7112	425	6	αβ	αβ	INTJ
ejpam-7112	425	7	+	+	X
ejpam-7112	425	8	β	β	X
ejpam-7112	425	9	3	3	NUM
ejpam-7112	425	10	)	)	PUNCT
ejpam-7112	425	11	(	(	PUNCT
ejpam-7112	425	12	48	48	NUM
ejpam-7112	425	13	)	)	PUNCT
ejpam-7112	425	14	with	with	ADP
ejpam-7112	425	15	precision	precision	NOUN
ejpam-7112	425	16	2	2	NUM
ejpam-7112	425	17	.	.	PUNCT
ejpam-7112	426	1	the	the	DET
ejpam-7112	426	2	error	error	NOUN
ejpam-7112	426	3	term	term	NOUN
ejpam-7112	426	4	rhemt	rhemt	NOUN
ejpam-7112	426	5	[	[	X
ejpam-7112	426	6	f	f	X
ejpam-7112	426	7	]	]	X
ejpam-7112	426	8	is	be	AUX
ejpam-7112	426	9	(	(	PUNCT
ejpam-7112	426	10	(	(	PUNCT
ejpam-7112	426	11	β	β	X
ejpam-7112	426	12	−	−	NOUN
ejpam-7112	426	13	α	α	NOUN
ejpam-7112	426	14	)	)	PUNCT
ejpam-7112	426	15	(	(	PUNCT
ejpam-7112	426	16	√	√	NUM
ejpam-7112	427	1	αβ	αβ	INTJ
ejpam-7112	427	2	−	−	NOUN
ejpam-7112	428	1	β	β	NOUN
ejpam-7112	428	2	)	)	PUNCT
ejpam-7112	428	3	6	6	NUM
ejpam-7112	428	4	∫	∫	PROPN
ejpam-7112	428	5	β	β	PROPN
ejpam-7112	428	6	a	a	DET
ejpam-7112	428	7	g(t	g(t	PROPN
ejpam-7112	428	8	)	)	PUNCT
ejpam-7112	428	9	dt+	dt+	NOUN
ejpam-7112	428	10	2β	2β	NOUN
ejpam-7112	428	11	−	−	NOUN
ejpam-7112	428	12	α−	α−	ADP
ejpam-7112	428	13	√	√	ADV
ejpam-7112	428	14	αβ	αβ	PRON
ejpam-7112	428	15	3	3	NUM
ejpam-7112	428	16	∫	∫	PROPN
ejpam-7112	428	17	β	β	PROPN
ejpam-7112	428	18	a	a	DET
ejpam-7112	428	19	∫	∫	PROPN
ejpam-7112	428	20	t	t	PROPN
ejpam-7112	428	21	a	a	DET
ejpam-7112	428	22	g(x	g(x	NOUN
ejpam-7112	428	23	)	)	PUNCT
ejpam-7112	428	24	dx	dx	PROPN
ejpam-7112	429	1	dt	dt	X
ejpam-7112	430	1	−	−	PROPN
ejpam-7112	430	2	∫	∫	PROPN
ejpam-7112	430	3	β	β	PROPN
ejpam-7112	430	4	a	a	DET
ejpam-7112	430	5	∫	∫	PROPN
ejpam-7112	430	6	t	t	PROPN
ejpam-7112	430	7	a	a	DET
ejpam-7112	430	8	∫	∫	PROPN
ejpam-7112	430	9	y	y	PROPN
ejpam-7112	430	10	a	a	DET
ejpam-7112	430	11	g(x	g(x	NOUN
ejpam-7112	430	12	)	)	PUNCT
ejpam-7112	430	13	dx	dx	PROPN
ejpam-7112	431	1	dy	dy	NOUN
ejpam-7112	431	2	dt	dt	NOUN
ejpam-7112	431	3	)	)	PUNCT
ejpam-7112	431	4	f	f	PROPN
ejpam-7112	431	5	(	(	PUNCT
ejpam-7112	431	6	3)(ξ	3)(ξ	NUM
ejpam-7112	431	7	)	)	PUNCT
ejpam-7112	431	8	,	,	PUNCT
ejpam-7112	431	9	(	(	PUNCT
ejpam-7112	431	10	49	49	NUM
ejpam-7112	431	11	)	)	PUNCT
ejpam-7112	431	12	where	where	SCONJ
ejpam-7112	431	13	ξ	ξ	X
ejpam-7112	431	14	∈	∈	PROPN
ejpam-7112	431	15	(	(	PUNCT
ejpam-7112	431	16	α	α	NOUN
ejpam-7112	431	17	,	,	PUNCT
ejpam-7112	431	18	β	β	NOUN
ejpam-7112	431	19	)	)	PUNCT
ejpam-7112	431	20	corollary	corollary	ADJ
ejpam-7112	431	21	4	4	NUM
ejpam-7112	431	22	.	.	PUNCT
ejpam-7112	431	23	assuming	assume	VERB
ejpam-7112	431	24	continuity	continuity	NOUN
ejpam-7112	431	25	of	of	ADP
ejpam-7112	431	26	f(t)andg(t	f(t)andg(t	NOUN
ejpam-7112	431	27	)	)	PUNCT
ejpam-7112	431	28	in	in	ADP
ejpam-7112	431	29	[	[	X
ejpam-7112	431	30	α	α	X
ejpam-7112	431	31	,	,	PUNCT
ejpam-7112	431	32	β	β	X
ejpam-7112	431	33	]	]	PUNCT
ejpam-7112	431	34	along	along	ADP
ejpam-7112	431	35	with	with	ADP
ejpam-7112	431	36	g(t	g(t	PROPN
ejpam-7112	431	37	)	)	PUNCT
ejpam-7112	431	38	being	be	AUX
ejpam-7112	431	39	monotonically	monotonically	ADV
ejpam-7112	431	40	rising	rise	VERB
ejpam-7112	431	41	in	in	ADP
ejpam-7112	431	42	the	the	DET
ejpam-7112	431	43	same	same	ADJ
ejpam-7112	431	44	interval	interval	NOUN
ejpam-7112	431	45	,	,	PUNCT
ejpam-7112	431	46	cmt	cmt	PROPN
ejpam-7112	431	47	quadrature	quadrature	NOUN
ejpam-7112	431	48	for	for	ADP
ejpam-7112	431	49	the	the	DET
ejpam-7112	431	50	rs	rs	ADJ
ejpam-7112	431	51	-	-	ADJ
ejpam-7112	431	52	integral	integral	ADJ
ejpam-7112	431	53	is:∫	is:∫	NOUN
ejpam-7112	431	54	β	β	ADP
ejpam-7112	431	55	a	a	DET
ejpam-7112	431	56	f(x	f(x	PROPN
ejpam-7112	431	57	)	)	PUNCT
ejpam-7112	431	58	dg	dg	PROPN
ejpam-7112	432	1	≈	≈	PROPN
ejpam-7112	432	2	cmt	cmt	PROPN
ejpam-7112	432	3	=	=	PUNCT
ejpam-7112	432	4	(	(	PUNCT
ejpam-7112	432	5	1	1	NUM
ejpam-7112	432	6	β	β	X
ejpam-7112	432	7	−	−	PROPN
ejpam-7112	432	8	α	α	X
ejpam-7112	432	9	∫	∫	PROPN
ejpam-7112	432	10	β	β	PROPN
ejpam-7112	432	11	a	a	DET
ejpam-7112	432	12	g(t	g(t	PROPN
ejpam-7112	432	13	)	)	PUNCT
ejpam-7112	432	14	dt−	dt−	PUNCT
ejpam-7112	432	15	g(α	g(α	PROPN
ejpam-7112	432	16	)	)	PUNCT
ejpam-7112	432	17	)	)	PUNCT
ejpam-7112	433	1	f(α	f(α	NOUN
ejpam-7112	433	2	)	)	PUNCT
ejpam-7112	434	1	+	+	CCONJ
ejpam-7112	434	2	(	(	PUNCT
ejpam-7112	434	3	g(β)−	g(β)−	PROPN
ejpam-7112	434	4	1	1	NUM
ejpam-7112	434	5	β	β	NOUN
ejpam-7112	434	6	−	−	PROPN
ejpam-7112	434	7	α	α	DET
ejpam-7112	434	8	∫	∫	PROPN
ejpam-7112	434	9	β	β	PROPN
ejpam-7112	434	10	a	a	DET
ejpam-7112	434	11	g(t	g(t	PROPN
ejpam-7112	434	12	)	)	PUNCT
ejpam-7112	434	13	dt	dt	NOUN
ejpam-7112	434	14	)	)	PUNCT
ejpam-7112	434	15	f(β	f(β	PROPN
ejpam-7112	434	16	)	)	PUNCT
ejpam-7112	435	1	+	+	CCONJ
ejpam-7112	435	2	(	(	PUNCT
ejpam-7112	435	3	∫	∫	PROPN
ejpam-7112	435	4	β	β	X
ejpam-7112	435	5	a	a	DET
ejpam-7112	435	6	∫	∫	PROPN
ejpam-7112	435	7	t	t	PROPN
ejpam-7112	435	8	a	a	DET
ejpam-7112	435	9	g(x	g(x	NOUN
ejpam-7112	435	10	)	)	PUNCT
ejpam-7112	435	11	dx	dx	PROPN
ejpam-7112	436	1	dt−	dt−	PROPN
ejpam-7112	436	2	β	β	X
ejpam-7112	436	3	−	−	X
ejpam-7112	436	4	α	α	NOUN
ejpam-7112	436	5	2	2	NUM
ejpam-7112	436	6	∫	∫	PROPN
ejpam-7112	436	7	β	β	PROPN
ejpam-7112	436	8	a	a	DET
ejpam-7112	436	9	g(t	g(t	PROPN
ejpam-7112	436	10	)	)	PUNCT
ejpam-7112	436	11	dt	dt	NOUN
ejpam-7112	436	12	)	)	PUNCT
ejpam-7112	437	1	f	f	PROPN
ejpam-7112	437	2	′′	′′	PROPN
ejpam-7112	437	3	(	(	PUNCT
ejpam-7112	437	4	2(α2	2(α2	NUM
ejpam-7112	438	1	+	+	CCONJ
ejpam-7112	438	2	αβ	αβ	NOUN
ejpam-7112	438	3	+	+	CCONJ
ejpam-7112	438	4	β2	β2	ADJ
ejpam-7112	438	5	)	)	PUNCT
ejpam-7112	438	6	3(α+	3(α+	NUM
ejpam-7112	439	1	β	β	NOUN
ejpam-7112	439	2	)	)	PUNCT
ejpam-7112	439	3	)	)	PUNCT
ejpam-7112	440	1	(	(	PUNCT
ejpam-7112	440	2	50	50	NUM
ejpam-7112	440	3	)	)	PUNCT
ejpam-7112	440	4	k.	k.	PROPN
ejpam-7112	440	5	memon	memon	PROPN
ejpam-7112	440	6	et	et	PROPN
ejpam-7112	440	7	al	al	PROPN
ejpam-7112	440	8	.	.	PUNCT
ejpam-7112	440	9	/	/	SYM
ejpam-7112	440	10	eur	eur	PROPN
ejpam-7112	440	11	.	.	PUNCT
ejpam-7112	441	1	j.	j.	PROPN
ejpam-7112	441	2	pure	pure	PROPN
ejpam-7112	441	3	appl	appl	PROPN
ejpam-7112	441	4	.	.	PROPN
ejpam-7112	441	5	math	math	PROPN
ejpam-7112	441	6	,	,	PUNCT
ejpam-7112	441	7	18	18	NUM
ejpam-7112	441	8	(	(	PUNCT
ejpam-7112	441	9	4	4	NUM
ejpam-7112	441	10	)	)	PUNCT
ejpam-7112	441	11	(	(	PUNCT
ejpam-7112	441	12	2025	2025	NUM
ejpam-7112	441	13	)	)	PUNCT
ejpam-7112	441	14	,	,	PUNCT
ejpam-7112	441	15	7112	7112	NUM
ejpam-7112	441	16	16	16	NUM
ejpam-7112	441	17	of	of	ADP
ejpam-7112	441	18	38	38	NUM
ejpam-7112	441	19	with	with	ADP
ejpam-7112	441	20	precision	precision	NOUN
ejpam-7112	441	21	2	2	NUM
ejpam-7112	441	22	.	.	PUNCT
ejpam-7112	442	1	the	the	DET
ejpam-7112	442	2	error	error	NOUN
ejpam-7112	442	3	term	term	NOUN
ejpam-7112	442	4	rcmt	rcmt	VERB
ejpam-7112	442	5	[	[	X
ejpam-7112	442	6	f	f	X
ejpam-7112	442	7	]	]	X
ejpam-7112	442	8	is	be	AUX
ejpam-7112	442	9	:(	:(	PUNCT
ejpam-7112	442	10	2α2β	2α2β	ADV
ejpam-7112	442	11	−	−	PROPN
ejpam-7112	443	1	αβ2	αβ2	ADJ
ejpam-7112	444	1	−	−	PROPN
ejpam-7112	445	1	α3	α3	NOUN
ejpam-7112	445	2	6(α+	6(α+	NUM
ejpam-7112	445	3	β	β	NOUN
ejpam-7112	445	4	)	)	PUNCT
ejpam-7112	445	5	∫	∫	PROPN
ejpam-7112	445	6	β	β	PROPN
ejpam-7112	445	7	α	α	PROPN
ejpam-7112	445	8	g(t	g(t	PROPN
ejpam-7112	445	9	)	)	PUNCT
ejpam-7112	445	10	dt+	dt+	NOUN
ejpam-7112	445	11	αβ	αβ	INTJ
ejpam-7112	446	1	+	+	CCONJ
ejpam-7112	446	2	β2	β2	VERB
ejpam-7112	446	3	−	−	PROPN
ejpam-7112	446	4	2α2	2α2	NUM
ejpam-7112	446	5	3(α+	3(α+	PRON
ejpam-7112	446	6	β	β	X
ejpam-7112	446	7	)	)	PUNCT
ejpam-7112	446	8	∫	∫	PROPN
ejpam-7112	447	1	β	β	PROPN
ejpam-7112	447	2	α	α	PROPN
ejpam-7112	447	3	∫	∫	PROPN
ejpam-7112	447	4	t	t	PROPN
ejpam-7112	447	5	α	α	PROPN
ejpam-7112	447	6	g(x	g(x	PROPN
ejpam-7112	447	7	)	)	PUNCT
ejpam-7112	448	1	dx	dx	PROPN
ejpam-7112	449	1	dt	dt	X
ejpam-7112	450	1	−	−	PROPN
ejpam-7112	450	2	∫	∫	PROPN
ejpam-7112	450	3	β	β	PROPN
ejpam-7112	450	4	α	α	PROPN
ejpam-7112	450	5	∫	∫	PROPN
ejpam-7112	450	6	t	t	PROPN
ejpam-7112	451	1	α	α	NOUN
ejpam-7112	451	2	∫	∫	PROPN
ejpam-7112	451	3	y	y	PROPN
ejpam-7112	451	4	α	α	PROPN
ejpam-7112	451	5	g(x	g(x	PROPN
ejpam-7112	451	6	)	)	PUNCT
ejpam-7112	451	7	dx	dx	PROPN
ejpam-7112	451	8	dy	dy	NOUN
ejpam-7112	452	1	dt	dt	NOUN
ejpam-7112	452	2	)	)	PUNCT
ejpam-7112	452	3	f	f	PROPN
ejpam-7112	452	4	(	(	PUNCT
ejpam-7112	452	5	3)(ξ	3)(ξ	NUM
ejpam-7112	452	6	)	)	PUNCT
ejpam-7112	452	7	,	,	PUNCT
ejpam-7112	452	8	(	(	PUNCT
ejpam-7112	452	9	51	51	NUM
ejpam-7112	452	10	)	)	PUNCT
ejpam-7112	452	11	where	where	SCONJ
ejpam-7112	452	12	ξ	ξ	X
ejpam-7112	452	13	∈	∈	PROPN
ejpam-7112	452	14	(	(	PUNCT
ejpam-7112	452	15	α	α	NOUN
ejpam-7112	452	16	,	,	PUNCT
ejpam-7112	452	17	β	β	X
ejpam-7112	452	18	)	)	PUNCT
ejpam-7112	452	19	it	it	PRON
ejpam-7112	452	20	is	be	AUX
ejpam-7112	452	21	trivial	trivial	ADJ
ejpam-7112	452	22	to	to	PART
ejpam-7112	452	23	verify	verify	VERB
ejpam-7112	452	24	the	the	DET
ejpam-7112	452	25	reduction	reduction	NOUN
ejpam-7112	452	26	of	of	ADP
ejpam-7112	452	27	the	the	DET
ejpam-7112	452	28	gmt	gmt	PROPN
ejpam-7112	452	29	,	,	PUNCT
ejpam-7112	452	30	hamt	hamt	PROPN
ejpam-7112	452	31	,	,	PUNCT
ejpam-7112	452	32	hemt	hemt	PROPN
ejpam-7112	452	33	and	and	CCONJ
ejpam-7112	452	34	cmt	cmt	PROPN
ejpam-7112	452	35	rules	rule	NOUN
ejpam-7112	452	36	for	for	ADP
ejpam-7112	452	37	the	the	DET
ejpam-7112	452	38	rs	rs	NOUN
ejpam-7112	452	39	integral	integral	NOUN
ejpam-7112	452	40	to	to	ADP
ejpam-7112	452	41	the	the	DET
ejpam-7112	452	42	classical	classical	ADJ
ejpam-7112	452	43	riemann	riemann	PROPN
ejpam-7112	452	44	integral	integral	ADJ
ejpam-7112	452	45	by	by	ADP
ejpam-7112	452	46	choosing	choose	VERB
ejpam-7112	452	47	g(t	g(t	PROPN
ejpam-7112	452	48	)	)	PUNCT
ejpam-7112	453	1	=	=	SYM
ejpam-7112	453	2	t	t	PROPN
ejpam-7112	453	3	in	in	ADP
ejpam-7112	453	4	context	context	NOUN
ejpam-7112	453	5	of	of	ADP
ejpam-7112	453	6	the	the	DET
ejpam-7112	453	7	proof	proof	NOUN
ejpam-7112	453	8	of	of	ADP
ejpam-7112	453	9	theorem	theorem	NOUN
ejpam-7112	453	10	3	3	NUM
ejpam-7112	453	11	for	for	ADP
ejpam-7112	453	12	the	the	DET
ejpam-7112	453	13	amt	amt	PROPN
ejpam-7112	453	14	rule	rule	NOUN
ejpam-7112	453	15	.	.	PUNCT
ejpam-7112	454	1	using	use	VERB
ejpam-7112	454	2	g(t	g(t	PROPN
ejpam-7112	454	3	)	)	PUNCT
ejpam-7112	455	1	=	=	SYM
ejpam-7112	455	2	t	t	PROPN
ejpam-7112	455	3	in	in	ADP
ejpam-7112	455	4	(	(	PUNCT
ejpam-7112	455	5	44	44	NUM
ejpam-7112	455	6	)	)	PUNCT
ejpam-7112	455	7	,	,	PUNCT
ejpam-7112	455	8	(	(	PUNCT
ejpam-7112	455	9	46	46	NUM
ejpam-7112	455	10	)	)	PUNCT
ejpam-7112	455	11	,	,	PUNCT
ejpam-7112	455	12	(	(	PUNCT
ejpam-7112	455	13	48	48	NUM
ejpam-7112	455	14	)	)	PUNCT
ejpam-7112	455	15	and	and	CCONJ
ejpam-7112	455	16	(	(	PUNCT
ejpam-7112	455	17	50	50	NUM
ejpam-7112	455	18	)	)	PUNCT
ejpam-7112	455	19	along	along	ADP
ejpam-7112	455	20	with	with	ADP
ejpam-7112	455	21	in	in	ADP
ejpam-7112	455	22	the	the	DET
ejpam-7112	455	23	error	error	NOUN
ejpam-7112	455	24	terms	term	NOUN
ejpam-7112	455	25	(	(	PUNCT
ejpam-7112	455	26	1	1	NUM
ejpam-7112	455	27	)	)	PUNCT
ejpam-7112	455	28	,	,	PUNCT
ejpam-7112	455	29	(	(	PUNCT
ejpam-7112	455	30	47	47	NUM
ejpam-7112	455	31	)	)	PUNCT
ejpam-7112	455	32	,	,	PUNCT
ejpam-7112	455	33	(	(	PUNCT
ejpam-7112	455	34	49	49	NUM
ejpam-7112	455	35	)	)	PUNCT
ejpam-7112	455	36	and	and	CCONJ
ejpam-7112	455	37	(	(	PUNCT
ejpam-7112	455	38	51	51	NUM
ejpam-7112	455	39	)	)	PUNCT
ejpam-7112	455	40	,	,	PUNCT
ejpam-7112	455	41	we	we	PRON
ejpam-7112	455	42	obtain	obtain	VERB
ejpam-7112	455	43	the	the	DET
ejpam-7112	455	44	corresponding	corresponding	ADJ
ejpam-7112	455	45	schemes	scheme	NOUN
ejpam-7112	455	46	(	(	PUNCT
ejpam-7112	455	47	11)-(14	11)-(14	NOUN
ejpam-7112	455	48	)	)	PUNCT
ejpam-7112	455	49	for	for	ADP
ejpam-7112	455	50	the	the	DET
ejpam-7112	455	51	riemann	riemann	PROPN
ejpam-7112	455	52	integral	integral	ADJ
ejpam-7112	455	53	[	[	X
ejpam-7112	455	54	7	7	NUM
ejpam-7112	455	55	]	]	PUNCT
ejpam-7112	455	56	.	.	PUNCT
ejpam-7112	456	1	the	the	DET
ejpam-7112	456	2	successful	successful	ADJ
ejpam-7112	456	3	reducibility	reducibility	NOUN
ejpam-7112	456	4	of	of	ADP
ejpam-7112	456	5	proposed	propose	VERB
ejpam-7112	456	6	derivativebased	derivativebase	VERB
ejpam-7112	456	7	rules	rule	NOUN
ejpam-7112	456	8	to	to	ADP
ejpam-7112	456	9	the	the	DET
ejpam-7112	456	10	counterparts	counterpart	NOUN
ejpam-7112	456	11	for	for	ADP
ejpam-7112	456	12	riemann	riemann	PROPN
ejpam-7112	456	13	integral	integral	ADJ
ejpam-7112	456	14	show	show	NOUN
ejpam-7112	456	15	that	that	SCONJ
ejpam-7112	456	16	the	the	DET
ejpam-7112	456	17	proposed	propose	VERB
ejpam-7112	456	18	rules	rule	NOUN
ejpam-7112	456	19	defined	define	VERB
ejpam-7112	456	20	in	in	ADP
ejpam-7112	456	21	theorems	theorem	NOUN
ejpam-7112	456	22	1	1	NUM
ejpam-7112	456	23	-	-	SYM
ejpam-7112	456	24	5	5	NUM
ejpam-7112	456	25	and	and	CCONJ
ejpam-7112	456	26	corollaries	corollary	NOUN
ejpam-7112	456	27	1	1	NUM
ejpam-7112	456	28	-	-	SYM
ejpam-7112	456	29	4	4	NUM
ejpam-7112	456	30	are	be	AUX
ejpam-7112	456	31	a	a	DET
ejpam-7112	456	32	sensible	sensible	ADJ
ejpam-7112	456	33	modification	modification	NOUN
ejpam-7112	456	34	to	to	ADP
ejpam-7112	456	35	the	the	DET
ejpam-7112	456	36	existing	exist	VERB
ejpam-7112	456	37	rules	rule	NOUN
ejpam-7112	456	38	,	,	PUNCT
ejpam-7112	456	39	the	the	DET
ejpam-7112	456	40	classical	classical	ADJ
ejpam-7112	456	41	trapezoid	trapezoid	NOUN
ejpam-7112	456	42	and	and	CCONJ
ejpam-7112	456	43	zhao	zhao	PROPN
ejpam-7112	456	44	et	et	PROPN
ejpam-7112	456	45	al	al	PROPN
ejpam-7112	456	46	.	.	PUNCT
ejpam-7112	457	1	[	[	X
ejpam-7112	457	2	5	5	NUM
ejpam-7112	457	3	]	]	ADJ
ejpam-7112	457	4	rules	rule	NOUN
ejpam-7112	457	5	.	.	PUNCT
ejpam-7112	458	1	to	to	PART
ejpam-7112	458	2	guarantee	guarantee	VERB
ejpam-7112	458	3	higher	high	ADJ
ejpam-7112	458	4	accuracy	accuracy	NOUN
ejpam-7112	458	5	and	and	CCONJ
ejpam-7112	458	6	lower	low	ADJ
ejpam-7112	458	7	errors	error	NOUN
ejpam-7112	458	8	,	,	PUNCT
ejpam-7112	458	9	the	the	DET
ejpam-7112	458	10	global	global	ADJ
ejpam-7112	458	11	/	/	SYM
ejpam-7112	458	12	composite	composite	ADJ
ejpam-7112	458	13	quadrature	quadrature	NOUN
ejpam-7112	458	14	through	through	ADP
ejpam-7112	458	15	(	(	PUNCT
ejpam-7112	458	16	44	44	NUM
ejpam-7112	458	17	)	)	PUNCT
ejpam-7112	458	18	,	,	PUNCT
ejpam-7112	458	19	(	(	PUNCT
ejpam-7112	458	20	46	46	NUM
ejpam-7112	458	21	)	)	PUNCT
ejpam-7112	458	22	,	,	PUNCT
ejpam-7112	458	23	(	(	PUNCT
ejpam-7112	458	24	48	48	NUM
ejpam-7112	458	25	)	)	PUNCT
ejpam-7112	458	26	and	and	CCONJ
ejpam-7112	458	27	(	(	PUNCT
ejpam-7112	458	28	50	50	NUM
ejpam-7112	458	29	)	)	PUNCT
ejpam-7112	458	30	are	be	AUX
ejpam-7112	458	31	referred	refer	VERB
ejpam-7112	458	32	as	as	ADP
ejpam-7112	458	33	gmct	gmct	ADJ
ejpam-7112	458	34	,	,	PUNCT
ejpam-7112	458	35	hamct	hamct	PROPN
ejpam-7112	458	36	,	,	PUNCT
ejpam-7112	458	37	hemct	hemct	ADJ
ejpam-7112	458	38	and	and	CCONJ
ejpam-7112	458	39	cmct	cmct	ADJ
ejpam-7112	458	40	,	,	PUNCT
ejpam-7112	458	41	and	and	CCONJ
ejpam-7112	458	42	are	be	AUX
ejpam-7112	458	43	presented	present	VERB
ejpam-7112	458	44	in	in	ADP
ejpam-7112	458	45	corollary	corollary	ADJ
ejpam-7112	458	46	5	5	NUM
ejpam-7112	458	47	.	.	PUNCT
ejpam-7112	458	48	corollary	corollary	ADJ
ejpam-7112	458	49	5	5	NUM
ejpam-7112	458	50	.	.	PUNCT
ejpam-7112	458	51	assuming	assume	VERB
ejpam-7112	458	52	continuity	continuity	NOUN
ejpam-7112	458	53	of	of	ADP
ejpam-7112	458	54	f(t	f(t	PROPN
ejpam-7112	458	55	)	)	PUNCT
ejpam-7112	458	56	and	and	CCONJ
ejpam-7112	458	57	g(t)in	g(t)in	PRON
ejpam-7112	459	1	[	[	X
ejpam-7112	459	2	α	α	X
ejpam-7112	459	3	,	,	PUNCT
ejpam-7112	459	4	β	β	X
ejpam-7112	459	5	]	]	PUNCT
ejpam-7112	459	6	along	along	ADP
ejpam-7112	459	7	with	with	ADP
ejpam-7112	459	8	g(t	g(t	PROPN
ejpam-7112	459	9	)	)	PUNCT
ejpam-7112	459	10	being	be	AUX
ejpam-7112	459	11	monotonically	monotonically	ADV
ejpam-7112	459	12	rising	rise	VERB
ejpam-7112	459	13	in	in	ADP
ejpam-7112	459	14	the	the	DET
ejpam-7112	459	15	same	same	ADJ
ejpam-7112	459	16	interval	interval	NOUN
ejpam-7112	459	17	,	,	PUNCT
ejpam-7112	459	18	and	and	CCONJ
ejpam-7112	459	19	with	with	ADP
ejpam-7112	459	20	,	,	PUNCT
ejpam-7112	459	21	the	the	DET
ejpam-7112	459	22	composite	composite	ADJ
ejpam-7112	459	23	form	form	NOUN
ejpam-7112	459	24	of	of	ADP
ejpam-7112	459	25	the	the	DET
ejpam-7112	459	26	proposed	propose	VERB
ejpam-7112	459	27	schemes	scheme	NOUN
ejpam-7112	459	28	(	(	PUNCT
ejpam-7112	459	29	45	45	NUM
ejpam-7112	459	30	)	)	PUNCT
ejpam-7112	459	31	,	,	PUNCT
ejpam-7112	459	32	(	(	PUNCT
ejpam-7112	459	33	46	46	NUM
ejpam-7112	459	34	)	)	PUNCT
ejpam-7112	459	35	,	,	PUNCT
ejpam-7112	459	36	(	(	PUNCT
ejpam-7112	459	37	48	48	NUM
ejpam-7112	459	38	)	)	PUNCT
ejpam-7112	459	39	and	and	CCONJ
ejpam-7112	459	40	(	(	PUNCT
ejpam-7112	459	41	50	50	NUM
ejpam-7112	459	42	)	)	PUNCT
ejpam-7112	459	43	are	be	AUX
ejpam-7112	459	44	given	give	VERB
ejpam-7112	459	45	in	in	ADP
ejpam-7112	459	46	(	(	PUNCT
ejpam-7112	459	47	52)-(55).∫	52)-(55).∫	NOUN
ejpam-7112	459	48	β	β	NOUN
ejpam-7112	459	49	a	a	DET
ejpam-7112	459	50	f(t	f(t	PROPN
ejpam-7112	459	51	)	)	PUNCT
ejpam-7112	459	52	dg	dg	VERB
ejpam-7112	460	1	≈	≈	NUM
ejpam-7112	460	2	gmct	gmct	ADJ
ejpam-7112	460	3	=	=	SYM
ejpam-7112	461	1	[	[	PUNCT
ejpam-7112	461	2	n	n	X
ejpam-7112	461	3	β	β	NOUN
ejpam-7112	461	4	−	−	PROPN
ejpam-7112	462	1	α	α	PRON
ejpam-7112	462	2	∫	∫	PROPN
ejpam-7112	462	3	x1	x1	PROPN
ejpam-7112	463	1	a	a	DET
ejpam-7112	463	2	g(t	g(t	PROPN
ejpam-7112	463	3	)	)	PUNCT
ejpam-7112	463	4	dt−	dt−	PUNCT
ejpam-7112	463	5	g(α	g(α	PROPN
ejpam-7112	463	6	)	)	PUNCT
ejpam-7112	463	7	]	]	PUNCT
ejpam-7112	464	1	f(α	f(α	NOUN
ejpam-7112	464	2	)	)	PUNCT
ejpam-7112	465	1	+	+	NUM
ejpam-7112	466	1	n	n	CCONJ
ejpam-7112	466	2	β	β	NOUN
ejpam-7112	466	3	−	−	NOUN
ejpam-7112	466	4	α	α	PROPN
ejpam-7112	466	5	n−1∑	n−1∑	PROPN
ejpam-7112	466	6	k=1	k=1	PUNCT
ejpam-7112	467	1	[	[	X
ejpam-7112	467	2	∫	∫	X
ejpam-7112	467	3	xk+1	xk+1	PROPN
ejpam-7112	467	4	xk	xk	PROPN
ejpam-7112	467	5	g(t	g(t	PROPN
ejpam-7112	467	6	)	)	PUNCT
ejpam-7112	467	7	dt−	dt−	NUM
ejpam-7112	467	8	∫	∫	PROPN
ejpam-7112	467	9	xk	xk	PROPN
ejpam-7112	467	10	xk−1	xk−1	PROPN
ejpam-7112	467	11	g(t	g(t	PROPN
ejpam-7112	467	12	)	)	PUNCT
ejpam-7112	467	13	dt	dt	X
ejpam-7112	467	14	]	]	PUNCT
ejpam-7112	467	15	f(xk	f(xk	X
ejpam-7112	467	16	)	)	PUNCT
ejpam-7112	467	17	+	+	CCONJ
ejpam-7112	467	18	[	[	PUNCT
ejpam-7112	467	19	g(β)−	g(β)−	PROPN
ejpam-7112	467	20	n	n	PROPN
ejpam-7112	467	21	β	β	NOUN
ejpam-7112	467	22	−	−	PROPN
ejpam-7112	468	1	α	α	PRON
ejpam-7112	468	2	∫	∫	PROPN
ejpam-7112	468	3	β	β	X
ejpam-7112	468	4	xn−1	xn−1	PROPN
ejpam-7112	468	5	g(t	g(t	PROPN
ejpam-7112	468	6	)	)	PUNCT
ejpam-7112	469	1	dt	dt	X
ejpam-7112	469	2	]	]	PUNCT
ejpam-7112	469	3	f(β	f(β	PROPN
ejpam-7112	469	4	)	)	PUNCT
ejpam-7112	470	1	+	+	NUM
ejpam-7112	471	1	n∑	n∑	INTJ
ejpam-7112	471	2	k=1	k=1	PUNCT
ejpam-7112	472	1	[	[	X
ejpam-7112	472	2	∫	∫	X
ejpam-7112	472	3	xk	xk	PROPN
ejpam-7112	472	4	xk−1	xk−1	PROPN
ejpam-7112	472	5	∫	∫	PROPN
ejpam-7112	472	6	t	t	PROPN
ejpam-7112	472	7	xk−1	xk−1	PROPN
ejpam-7112	472	8	g(x	g(x	PROPN
ejpam-7112	472	9	)	)	PUNCT
ejpam-7112	472	10	dx	dx	PROPN
ejpam-7112	473	1	dt−	dt−	PROPN
ejpam-7112	473	2	h	h	PROPN
ejpam-7112	473	3	2	2	NUM
ejpam-7112	473	4	∫	∫	PROPN
ejpam-7112	473	5	xk	xk	PROPN
ejpam-7112	473	6	xk−1	xk−1	PROPN
ejpam-7112	473	7	g(t	g(t	PROPN
ejpam-7112	473	8	)	)	PUNCT
ejpam-7112	474	1	dt	dt	PUNCT
ejpam-7112	474	2	]	]	X
ejpam-7112	475	1	f	f	X
ejpam-7112	475	2	′′(√xkxk−1	′′(√xkxk−1	PROPN
ejpam-7112	475	3	)	)	PUNCT
ejpam-7112	475	4	(	(	PUNCT
ejpam-7112	475	5	52	52	NUM
ejpam-7112	475	6	)	)	PUNCT
ejpam-7112	475	7	∫	∫	PROPN
ejpam-7112	475	8	β	β	PROPN
ejpam-7112	475	9	a	a	DET
ejpam-7112	475	10	f(t	f(t	PROPN
ejpam-7112	475	11	)	)	PUNCT
ejpam-7112	475	12	dg	dg	PROPN
ejpam-7112	476	1	≈	≈	NUM
ejpam-7112	476	2	hamct	hamct	PROPN
ejpam-7112	476	3	=	=	PUNCT
ejpam-7112	476	4	[	[	PUNCT
ejpam-7112	476	5	n	n	X
ejpam-7112	476	6	β	β	NOUN
ejpam-7112	476	7	−	−	PROPN
ejpam-7112	477	1	α	α	PRON
ejpam-7112	477	2	∫	∫	PROPN
ejpam-7112	477	3	x1	x1	PROPN
ejpam-7112	478	1	a	a	DET
ejpam-7112	478	2	g(t	g(t	PROPN
ejpam-7112	478	3	)	)	PUNCT
ejpam-7112	478	4	dt−	dt−	PUNCT
ejpam-7112	478	5	g(α	g(α	PROPN
ejpam-7112	478	6	)	)	PUNCT
ejpam-7112	478	7	]	]	PUNCT
ejpam-7112	479	1	f(α	f(α	NOUN
ejpam-7112	479	2	)	)	PUNCT
ejpam-7112	480	1	+	+	NUM
ejpam-7112	481	1	n	n	CCONJ
ejpam-7112	481	2	β	β	NOUN
ejpam-7112	481	3	−	−	NOUN
ejpam-7112	481	4	α	α	PROPN
ejpam-7112	481	5	n−1∑	n−1∑	PROPN
ejpam-7112	481	6	k=1	k=1	PUNCT
ejpam-7112	482	1	[	[	X
ejpam-7112	482	2	∫	∫	X
ejpam-7112	482	3	xk+1	xk+1	PROPN
ejpam-7112	482	4	xk	xk	PROPN
ejpam-7112	482	5	g(t	g(t	PROPN
ejpam-7112	482	6	)	)	PUNCT
ejpam-7112	482	7	dt−	dt−	NUM
ejpam-7112	482	8	∫	∫	PROPN
ejpam-7112	482	9	xk	xk	PROPN
ejpam-7112	482	10	xk−1	xk−1	PROPN
ejpam-7112	482	11	g(t	g(t	PROPN
ejpam-7112	482	12	)	)	PUNCT
ejpam-7112	482	13	dt	dt	X
ejpam-7112	482	14	]	]	PUNCT
ejpam-7112	482	15	f(xk	f(xk	X
ejpam-7112	482	16	)	)	PUNCT
ejpam-7112	482	17	+	+	CCONJ
ejpam-7112	482	18	[	[	PUNCT
ejpam-7112	482	19	g(β)−	g(β)−	PROPN
ejpam-7112	482	20	n	n	PROPN
ejpam-7112	482	21	β	β	NOUN
ejpam-7112	482	22	−	−	PROPN
ejpam-7112	483	1	α	α	PRON
ejpam-7112	483	2	∫	∫	PROPN
ejpam-7112	483	3	β	β	X
ejpam-7112	483	4	xn−1	xn−1	PROPN
ejpam-7112	483	5	g(t	g(t	PROPN
ejpam-7112	483	6	)	)	PUNCT
ejpam-7112	484	1	dt	dt	X
ejpam-7112	484	2	]	]	PUNCT
ejpam-7112	484	3	f(β	f(β	PROPN
ejpam-7112	484	4	)	)	PUNCT
ejpam-7112	485	1	+	+	NUM
ejpam-7112	486	1	n∑	n∑	INTJ
ejpam-7112	486	2	k=1	k=1	PUNCT
ejpam-7112	487	1	[	[	X
ejpam-7112	487	2	∫	∫	X
ejpam-7112	487	3	xk	xk	PROPN
ejpam-7112	487	4	xk−1	xk−1	PROPN
ejpam-7112	487	5	∫	∫	PROPN
ejpam-7112	487	6	t	t	PROPN
ejpam-7112	487	7	xk−1	xk−1	PROPN
ejpam-7112	487	8	g(x	g(x	PROPN
ejpam-7112	487	9	)	)	PUNCT
ejpam-7112	487	10	dx	dx	PROPN
ejpam-7112	487	11	dt−	dt−	PROPN
ejpam-7112	487	12	h	h	PROPN
ejpam-7112	487	13	2	2	NUM
ejpam-7112	487	14	∫	∫	PROPN
ejpam-7112	487	15	xk	xk	PROPN
ejpam-7112	487	16	xk−1	xk−1	PROPN
ejpam-7112	487	17	g(t	g(t	PROPN
ejpam-7112	487	18	)	)	PUNCT
ejpam-7112	487	19	dt	dt	X
ejpam-7112	487	20	]	]	PUNCT
ejpam-7112	488	1	f	f	X
ejpam-7112	488	2	′′	′′	PROPN
ejpam-7112	488	3	(	(	PUNCT
ejpam-7112	488	4	2xkxk−1	2xkxk−1	NUM
ejpam-7112	488	5	xk−1	xk−1	PROPN
ejpam-7112	488	6	+	+	NUM
ejpam-7112	488	7	xk	xk	PROPN
ejpam-7112	488	8	)	)	PUNCT
ejpam-7112	488	9	(	(	PUNCT
ejpam-7112	488	10	53	53	NUM
ejpam-7112	488	11	)	)	PUNCT
ejpam-7112	488	12	k.	k.	PROPN
ejpam-7112	488	13	memon	memon	PROPN
ejpam-7112	488	14	et	et	PROPN
ejpam-7112	488	15	al	al	PROPN
ejpam-7112	488	16	.	.	PUNCT
ejpam-7112	488	17	/	/	SYM
ejpam-7112	488	18	eur	eur	PROPN
ejpam-7112	488	19	.	.	PUNCT
ejpam-7112	489	1	j.	j.	PROPN
ejpam-7112	489	2	pure	pure	PROPN
ejpam-7112	489	3	appl	appl	PROPN
ejpam-7112	489	4	.	.	PROPN
ejpam-7112	489	5	math	math	PROPN
ejpam-7112	489	6	,	,	PUNCT
ejpam-7112	489	7	18	18	NUM
ejpam-7112	489	8	(	(	PUNCT
ejpam-7112	489	9	4	4	NUM
ejpam-7112	489	10	)	)	PUNCT
ejpam-7112	489	11	(	(	PUNCT
ejpam-7112	489	12	2025	2025	NUM
ejpam-7112	489	13	)	)	PUNCT
ejpam-7112	489	14	,	,	PUNCT
ejpam-7112	489	15	7112	7112	NUM
ejpam-7112	489	16	17	17	NUM
ejpam-7112	489	17	of	of	ADP
ejpam-7112	489	18	38	38	NUM
ejpam-7112	489	19	∫	∫	PROPN
ejpam-7112	489	20	β	β	NOUN
ejpam-7112	489	21	a	a	DET
ejpam-7112	489	22	f(t	f(t	PROPN
ejpam-7112	489	23	)	)	PUNCT
ejpam-7112	489	24	dg	dg	PROPN
ejpam-7112	489	25	≈	≈	PROPN
ejpam-7112	489	26	hemct	hemct	PROPN
ejpam-7112	490	1	=	=	PUNCT
ejpam-7112	490	2	[	[	PUNCT
ejpam-7112	490	3	n	n	X
ejpam-7112	490	4	β	β	NOUN
ejpam-7112	490	5	−	−	PROPN
ejpam-7112	491	1	α	α	PRON
ejpam-7112	491	2	∫	∫	PROPN
ejpam-7112	491	3	x1	x1	PROPN
ejpam-7112	492	1	a	a	DET
ejpam-7112	492	2	g(t	g(t	PROPN
ejpam-7112	492	3	)	)	PUNCT
ejpam-7112	492	4	dt−	dt−	PUNCT
ejpam-7112	492	5	g(α	g(α	PROPN
ejpam-7112	492	6	)	)	PUNCT
ejpam-7112	492	7	]	]	PUNCT
ejpam-7112	493	1	f(α	f(α	NOUN
ejpam-7112	493	2	)	)	PUNCT
ejpam-7112	494	1	+	+	NUM
ejpam-7112	495	1	n	n	CCONJ
ejpam-7112	495	2	β	β	X
ejpam-7112	495	3	−	−	NOUN
ejpam-7112	496	1	α	α	PROPN
ejpam-7112	496	2	n−1∑	n−1∑	PROPN
ejpam-7112	497	1	i	i	PROPN
ejpam-7112	497	2	=	=	PROPN
ejpam-7112	497	3	k	k	PROPN
ejpam-7112	498	1	[	[	X
ejpam-7112	498	2	∫	∫	X
ejpam-7112	498	3	xk+1	xk+1	PROPN
ejpam-7112	498	4	xk	xk	PROPN
ejpam-7112	498	5	g(t	g(t	PROPN
ejpam-7112	498	6	)	)	PUNCT
ejpam-7112	498	7	dt−	dt−	NUM
ejpam-7112	498	8	∫	∫	PROPN
ejpam-7112	498	9	xk	xk	PROPN
ejpam-7112	498	10	xk−1	xk−1	PROPN
ejpam-7112	498	11	g(t	g(t	PROPN
ejpam-7112	498	12	)	)	PUNCT
ejpam-7112	498	13	dt	dt	X
ejpam-7112	498	14	]	]	PUNCT
ejpam-7112	498	15	f(xk	f(xk	X
ejpam-7112	498	16	)	)	PUNCT
ejpam-7112	498	17	+	+	CCONJ
ejpam-7112	498	18	[	[	PUNCT
ejpam-7112	498	19	g(β)−	g(β)−	PROPN
ejpam-7112	498	20	n	n	PROPN
ejpam-7112	498	21	β	β	NOUN
ejpam-7112	498	22	−	−	PROPN
ejpam-7112	499	1	α	α	PRON
ejpam-7112	499	2	∫	∫	PROPN
ejpam-7112	499	3	β	β	X
ejpam-7112	499	4	xn−1	xn−1	PROPN
ejpam-7112	499	5	g(t	g(t	PROPN
ejpam-7112	499	6	)	)	PUNCT
ejpam-7112	500	1	dt	dt	X
ejpam-7112	500	2	]	]	PUNCT
ejpam-7112	500	3	f(β	f(β	PROPN
ejpam-7112	500	4	)	)	PUNCT
ejpam-7112	501	1	+	+	NUM
ejpam-7112	502	1	n∑	n∑	INTJ
ejpam-7112	502	2	k=1	k=1	PUNCT
ejpam-7112	503	1	[	[	X
ejpam-7112	503	2	∫	∫	X
ejpam-7112	503	3	xk	xk	PROPN
ejpam-7112	503	4	xk−1	xk−1	PROPN
ejpam-7112	503	5	∫	∫	PROPN
ejpam-7112	503	6	t	t	PROPN
ejpam-7112	503	7	xk−1	xk−1	PROPN
ejpam-7112	503	8	g(x	g(x	PROPN
ejpam-7112	503	9	)	)	PUNCT
ejpam-7112	503	10	dx	dx	PROPN
ejpam-7112	504	1	dt−	dt−	PROPN
ejpam-7112	504	2	h	h	PROPN
ejpam-7112	504	3	2	2	NUM
ejpam-7112	504	4	∫	∫	NOUN
ejpam-7112	504	5	xi	xi	PROPN
ejpam-7112	504	6	xk−1	xk−1	PROPN
ejpam-7112	504	7	g(t	g(t	PROPN
ejpam-7112	504	8	)	)	PUNCT
ejpam-7112	505	1	dt	dt	X
ejpam-7112	505	2	]	]	PUNCT
ejpam-7112	506	1	f	f	X
ejpam-7112	506	2	′′	′′	PROPN
ejpam-7112	506	3	(	(	PUNCT
ejpam-7112	506	4	xk−1	xk−1	PROPN
ejpam-7112	506	5	+	+	CCONJ
ejpam-7112	506	6	√	√	PROPN
ejpam-7112	506	7	xk−1xi	xk−1xi	PROPN
ejpam-7112	506	8	+	+	CCONJ
ejpam-7112	506	9	xk	xk	PROPN
ejpam-7112	506	10	3	3	NUM
ejpam-7112	506	11	)	)	PUNCT
ejpam-7112	506	12	(	(	PUNCT
ejpam-7112	506	13	54	54	NUM
ejpam-7112	506	14	)	)	PUNCT
ejpam-7112	506	15	∫	∫	PROPN
ejpam-7112	506	16	β	β	PROPN
ejpam-7112	506	17	a	a	DET
ejpam-7112	506	18	f(t	f(t	PROPN
ejpam-7112	506	19	)	)	PUNCT
ejpam-7112	506	20	dg	dg	PROPN
ejpam-7112	506	21	≈	≈	PROPN
ejpam-7112	506	22	cmct	cmct	ADJ
ejpam-7112	507	1	=	=	PUNCT
ejpam-7112	508	1	[	[	PUNCT
ejpam-7112	508	2	n	n	X
ejpam-7112	508	3	β	β	NOUN
ejpam-7112	508	4	−	−	PROPN
ejpam-7112	509	1	α	α	PRON
ejpam-7112	509	2	∫	∫	PROPN
ejpam-7112	509	3	x1	x1	PROPN
ejpam-7112	510	1	a	a	DET
ejpam-7112	510	2	g(t	g(t	PROPN
ejpam-7112	510	3	)	)	PUNCT
ejpam-7112	510	4	dt−	dt−	PUNCT
ejpam-7112	510	5	g(α	g(α	PROPN
ejpam-7112	510	6	)	)	PUNCT
ejpam-7112	510	7	]	]	PUNCT
ejpam-7112	511	1	f(α	f(α	NOUN
ejpam-7112	511	2	)	)	PUNCT
ejpam-7112	512	1	+	+	NUM
ejpam-7112	513	1	n	n	CCONJ
ejpam-7112	513	2	β	β	NOUN
ejpam-7112	513	3	−	−	NOUN
ejpam-7112	513	4	α	α	PROPN
ejpam-7112	513	5	n−1∑	n−1∑	PROPN
ejpam-7112	513	6	k=1	k=1	PUNCT
ejpam-7112	514	1	[	[	X
ejpam-7112	514	2	∫	∫	X
ejpam-7112	514	3	xk+1	xk+1	PROPN
ejpam-7112	514	4	xk	xk	PROPN
ejpam-7112	514	5	g(t	g(t	PROPN
ejpam-7112	514	6	)	)	PUNCT
ejpam-7112	514	7	dt−	dt−	NUM
ejpam-7112	514	8	∫	∫	PROPN
ejpam-7112	514	9	xk	xk	PROPN
ejpam-7112	514	10	xk−1	xk−1	PROPN
ejpam-7112	514	11	g(t	g(t	PROPN
ejpam-7112	514	12	)	)	PUNCT
ejpam-7112	514	13	dt	dt	X
ejpam-7112	514	14	]	]	PUNCT
ejpam-7112	514	15	f(xk	f(xk	X
ejpam-7112	514	16	)	)	PUNCT
ejpam-7112	514	17	+	+	CCONJ
ejpam-7112	514	18	[	[	PUNCT
ejpam-7112	514	19	g(β)−	g(β)−	PROPN
ejpam-7112	514	20	n	n	PROPN
ejpam-7112	514	21	β	β	NOUN
ejpam-7112	514	22	−	−	PROPN
ejpam-7112	515	1	α	α	PRON
ejpam-7112	515	2	∫	∫	PROPN
ejpam-7112	515	3	β	β	X
ejpam-7112	515	4	xn−1	xn−1	PROPN
ejpam-7112	515	5	g(t	g(t	PROPN
ejpam-7112	515	6	)	)	PUNCT
ejpam-7112	516	1	dt	dt	X
ejpam-7112	516	2	]	]	PUNCT
ejpam-7112	516	3	f(β	f(β	PROPN
ejpam-7112	516	4	)	)	PUNCT
ejpam-7112	517	1	+	+	NUM
ejpam-7112	518	1	n∑	n∑	INTJ
ejpam-7112	518	2	k=1	k=1	PUNCT
ejpam-7112	519	1	[	[	X
ejpam-7112	519	2	∫	∫	X
ejpam-7112	519	3	xk	xk	PROPN
ejpam-7112	519	4	xk−1	xk−1	PROPN
ejpam-7112	519	5	∫	∫	PROPN
ejpam-7112	519	6	t	t	PROPN
ejpam-7112	519	7	xk−1	xk−1	PROPN
ejpam-7112	519	8	g(x	g(x	PROPN
ejpam-7112	519	9	)	)	PUNCT
ejpam-7112	519	10	dx	dx	PROPN
ejpam-7112	520	1	dt−	dt−	PROPN
ejpam-7112	520	2	h	h	PROPN
ejpam-7112	520	3	2	2	NUM
ejpam-7112	520	4	∫	∫	NOUN
ejpam-7112	520	5	xi	xi	PROPN
ejpam-7112	520	6	xk−1	xk−1	PROPN
ejpam-7112	520	7	g(t	g(t	PROPN
ejpam-7112	520	8	)	)	PUNCT
ejpam-7112	521	1	dt	dt	X
ejpam-7112	521	2	]	]	PUNCT
ejpam-7112	522	1	f	f	X
ejpam-7112	522	2	′′	′′	PROPN
ejpam-7112	522	3	(	(	PUNCT
ejpam-7112	522	4	2	2	NUM
ejpam-7112	522	5	(	(	PUNCT
ejpam-7112	522	6	x2k−1	x2k−1	PROPN
ejpam-7112	522	7	+	+	NUM
ejpam-7112	522	8	xk−1xk	xk−1xk	PROPN
ejpam-7112	522	9	+	+	CCONJ
ejpam-7112	522	10	x2k	x2k	NOUN
ejpam-7112	522	11	)	)	PUNCT
ejpam-7112	522	12	3	3	NUM
ejpam-7112	522	13	(	(	PUNCT
ejpam-7112	522	14	xk−1	xk−1	PROPN
ejpam-7112	522	15	+	+	CCONJ
ejpam-7112	522	16	xk	xk	PROPN
ejpam-7112	522	17	)	)	PUNCT
ejpam-7112	522	18	)	)	PUNCT
ejpam-7112	522	19	(	(	PUNCT
ejpam-7112	522	20	55	55	NUM
ejpam-7112	522	21	)	)	PUNCT
ejpam-7112	522	22	unlike	unlike	ADP
ejpam-7112	522	23	the	the	DET
ejpam-7112	522	24	standard	standard	ADJ
ejpam-7112	522	25	form	form	NOUN
ejpam-7112	522	26	of	of	ADP
ejpam-7112	522	27	the	the	DET
ejpam-7112	522	28	truncation	truncation	NOUN
ejpam-7112	522	29	error	error	NOUN
ejpam-7112	522	30	(	(	PUNCT
ejpam-7112	522	31	43	43	NUM
ejpam-7112	522	32	)	)	PUNCT
ejpam-7112	522	33	of	of	ADP
ejpam-7112	522	34	the	the	DET
ejpam-7112	522	35	proposed	propose	VERB
ejpam-7112	522	36	amct	amct	ADJ
ejpam-7112	522	37	quadrature	quadrature	NOUN
ejpam-7112	522	38	,	,	PUNCT
ejpam-7112	522	39	the	the	DET
ejpam-7112	522	40	same	same	ADJ
ejpam-7112	522	41	can	can	AUX
ejpam-7112	522	42	not	not	PART
ejpam-7112	522	43	be	be	AUX
ejpam-7112	522	44	expected	expect	VERB
ejpam-7112	522	45	for	for	ADP
ejpam-7112	522	46	the	the	DET
ejpam-7112	522	47	case	case	NOUN
ejpam-7112	522	48	of	of	ADP
ejpam-7112	522	49	proposed	propose	VERB
ejpam-7112	522	50	trapezoid	trapezoid	ADJ
ejpam-7112	522	51	-	-	PUNCT
ejpam-7112	522	52	type	type	NOUN
ejpam-7112	522	53	quadrature	quadrature	NOUN
ejpam-7112	522	54	with	with	ADP
ejpam-7112	522	55	other	other	ADJ
ejpam-7112	522	56	averages	average	NOUN
ejpam-7112	522	57	.	.	PUNCT
ejpam-7112	523	1	this	this	PRON
ejpam-7112	523	2	is	be	AUX
ejpam-7112	523	3	because	because	SCONJ
ejpam-7112	523	4	of	of	ADP
ejpam-7112	523	5	the	the	DET
ejpam-7112	523	6	non	non	ADJ
ejpam-7112	523	7	-	-	ADJ
ejpam-7112	523	8	conventional	conventional	ADJ
ejpam-7112	523	9	expressions	expression	NOUN
ejpam-7112	523	10	of	of	ADP
ejpam-7112	523	11	type	type	NOUN
ejpam-7112	523	12	(	(	PUNCT
ejpam-7112	523	13	√	√	NUM
ejpam-7112	523	14	(	(	PUNCT
ejpam-7112	523	15	b)−	b)−	PROPN
ejpam-7112	523	16	√	√	PROPN
ejpam-7112	523	17	(	(	PUNCT
ejpam-7112	523	18	a	a	NOUN
ejpam-7112	523	19	)	)	PUNCT
ejpam-7112	523	20	)	)	PUNCT
ejpam-7112	523	21	,	,	PUNCT
ejpam-7112	523	22	(	(	PUNCT
ejpam-7112	523	23	α+	α+	X
ejpam-7112	523	24	β	β	NOUN
ejpam-7112	523	25	)	)	PUNCT
ejpam-7112	523	26	,	,	PUNCT
ejpam-7112	523	27	etc	etc	X
ejpam-7112	523	28	.	.	X
ejpam-7112	524	1	in	in	ADP
ejpam-7112	524	2	local	local	ADJ
ejpam-7112	524	3	truncation	truncation	NOUN
ejpam-7112	524	4	errors	error	NOUN
ejpam-7112	524	5	in	in	ADP
ejpam-7112	524	6	addition	addition	NOUN
ejpam-7112	524	7	to	to	ADP
ejpam-7112	524	8	the	the	DET
ejpam-7112	524	9	usual	usual	ADJ
ejpam-7112	524	10	conventional	conventional	ADJ
ejpam-7112	524	11	exponents	exponent	NOUN
ejpam-7112	524	12	of	of	ADP
ejpam-7112	524	13	(	(	PUNCT
ejpam-7112	524	14	β	β	X
ejpam-7112	524	15	−	−	NOUN
ejpam-7112	524	16	α	α	NOUN
ejpam-7112	524	17	)	)	PUNCT
ejpam-7112	524	18	;	;	PUNCT
ejpam-7112	524	19	as	as	ADV
ejpam-7112	524	20	also	also	ADV
ejpam-7112	524	21	obvious	obvious	ADJ
ejpam-7112	524	22	from	from	ADP
ejpam-7112	524	23	the	the	DET
ejpam-7112	524	24	definition	definition	NOUN
ejpam-7112	524	25	3	3	NUM
ejpam-7112	524	26	.	.	PUNCT
ejpam-7112	525	1	however	however	ADV
ejpam-7112	525	2	,	,	PUNCT
ejpam-7112	525	3	the	the	DET
ejpam-7112	525	4	zct	zct	NOUN
ejpam-7112	525	5	[	[	X
ejpam-7112	525	6	5	5	NUM
ejpam-7112	525	7	]	]	PUNCT
ejpam-7112	525	8	quadrature	quadrature	NOUN
ejpam-7112	525	9	’s	’s	PART
ejpam-7112	525	10	composite	composite	ADJ
ejpam-7112	525	11	form	form	NOUN
ejpam-7112	525	12	,	,	PUNCT
ejpam-7112	525	13	though	though	SCONJ
ejpam-7112	525	14	not	not	PART
ejpam-7112	525	15	presented	present	VERB
ejpam-7112	525	16	in	in	ADP
ejpam-7112	525	17	[	[	X
ejpam-7112	525	18	5	5	NUM
ejpam-7112	525	19	]	]	PUNCT
ejpam-7112	525	20	,	,	PUNCT
ejpam-7112	525	21	takes	take	VERB
ejpam-7112	525	22	the	the	DET
ejpam-7112	525	23	form	form	NOUN
ejpam-7112	525	24	:	:	PUNCT
ejpam-7112	525	25	k.	k.	PROPN
ejpam-7112	525	26	memon	memon	PROPN
ejpam-7112	525	27	et	et	PROPN
ejpam-7112	525	28	al	al	PROPN
ejpam-7112	525	29	.	.	PUNCT
ejpam-7112	525	30	/	/	SYM
ejpam-7112	525	31	eur	eur	PROPN
ejpam-7112	525	32	.	.	PUNCT
ejpam-7112	526	1	j.	j.	PROPN
ejpam-7112	526	2	pure	pure	PROPN
ejpam-7112	526	3	appl	appl	PROPN
ejpam-7112	526	4	.	.	PROPN
ejpam-7112	526	5	math	math	PROPN
ejpam-7112	526	6	,	,	PUNCT
ejpam-7112	526	7	18	18	NUM
ejpam-7112	526	8	(	(	PUNCT
ejpam-7112	526	9	4	4	NUM
ejpam-7112	526	10	)	)	PUNCT
ejpam-7112	526	11	(	(	PUNCT
ejpam-7112	526	12	2025	2025	NUM
ejpam-7112	526	13	)	)	PUNCT
ejpam-7112	526	14	,	,	PUNCT
ejpam-7112	526	15	7112	7112	NUM
ejpam-7112	526	16	18	18	NUM
ejpam-7112	526	17	of	of	ADP
ejpam-7112	526	18	38	38	NUM
ejpam-7112	526	19	∫	∫	PROPN
ejpam-7112	526	20	β	β	NOUN
ejpam-7112	526	21	a	a	DET
ejpam-7112	526	22	f(t	f(t	PROPN
ejpam-7112	526	23	)	)	PUNCT
ejpam-7112	526	24	dg	dg	VERB
ejpam-7112	526	25	≈	≈	NOUN
ejpam-7112	526	26	zct	zct	NOUN
ejpam-7112	527	1	=	=	PUNCT
ejpam-7112	528	1	[	[	PUNCT
ejpam-7112	528	2	n	n	X
ejpam-7112	528	3	β	β	NOUN
ejpam-7112	528	4	−	−	PROPN
ejpam-7112	529	1	α	α	PRON
ejpam-7112	529	2	∫	∫	PROPN
ejpam-7112	529	3	x1	x1	PROPN
ejpam-7112	530	1	a	a	DET
ejpam-7112	530	2	g(t	g(t	PROPN
ejpam-7112	530	3	)	)	PUNCT
ejpam-7112	530	4	dt−	dt−	PUNCT
ejpam-7112	530	5	g(α	g(α	PROPN
ejpam-7112	530	6	)	)	PUNCT
ejpam-7112	530	7	]	]	PUNCT
ejpam-7112	531	1	f(α	f(α	NOUN
ejpam-7112	531	2	)	)	PUNCT
ejpam-7112	532	1	+	+	NUM
ejpam-7112	533	1	n	n	CCONJ
ejpam-7112	533	2	β	β	NOUN
ejpam-7112	533	3	−	−	NOUN
ejpam-7112	533	4	α	α	PROPN
ejpam-7112	533	5	n−1∑	n−1∑	PROPN
ejpam-7112	533	6	k=1	k=1	PUNCT
ejpam-7112	534	1	[	[	X
ejpam-7112	534	2	∫	∫	X
ejpam-7112	534	3	xk+1	xk+1	PROPN
ejpam-7112	534	4	xk	xk	PROPN
ejpam-7112	534	5	g(t	g(t	PROPN
ejpam-7112	534	6	)	)	PUNCT
ejpam-7112	534	7	dt−	dt−	NUM
ejpam-7112	534	8	∫	∫	PROPN
ejpam-7112	534	9	xk	xk	PROPN
ejpam-7112	534	10	xk−1	xk−1	PROPN
ejpam-7112	534	11	g(t	g(t	PROPN
ejpam-7112	534	12	)	)	PUNCT
ejpam-7112	534	13	dt	dt	X
ejpam-7112	534	14	]	]	PUNCT
ejpam-7112	534	15	f(xk	f(xk	X
ejpam-7112	534	16	)	)	PUNCT
ejpam-7112	534	17	+	+	CCONJ
ejpam-7112	534	18	[	[	PUNCT
ejpam-7112	534	19	g(β)−	g(β)−	PROPN
ejpam-7112	534	20	n	n	PROPN
ejpam-7112	534	21	β	β	NOUN
ejpam-7112	534	22	−	−	PROPN
ejpam-7112	535	1	α	α	PRON
ejpam-7112	535	2	∫	∫	PROPN
ejpam-7112	535	3	β	β	X
ejpam-7112	535	4	xn−1	xn−1	PROPN
ejpam-7112	535	5	g(t	g(t	PROPN
ejpam-7112	535	6	)	)	PUNCT
ejpam-7112	536	1	dt	dt	X
ejpam-7112	536	2	]	]	PUNCT
ejpam-7112	536	3	f(β	f(β	PROPN
ejpam-7112	536	4	)	)	PUNCT
ejpam-7112	537	1	+	+	NUM
ejpam-7112	538	1	n∑	n∑	INTJ
ejpam-7112	538	2	k=1	k=1	PUNCT
ejpam-7112	539	1	[	[	X
ejpam-7112	539	2	∫	∫	X
ejpam-7112	539	3	xk	xk	PROPN
ejpam-7112	539	4	xk−1	xk−1	PROPN
ejpam-7112	539	5	∫	∫	PROPN
ejpam-7112	539	6	t	t	PROPN
ejpam-7112	539	7	xk−1	xk−1	PROPN
ejpam-7112	539	8	g(x	g(x	PROPN
ejpam-7112	539	9	)	)	PUNCT
ejpam-7112	539	10	dx	dx	PROPN
ejpam-7112	539	11	dt−	dt−	PROPN
ejpam-7112	539	12	h	h	PROPN
ejpam-7112	539	13	2	2	NUM
ejpam-7112	539	14	∫	∫	PROPN
ejpam-7112	539	15	xk	xk	PROPN
ejpam-7112	539	16	xk−1	xk−1	PROPN
ejpam-7112	539	17	g(t	g(t	PROPN
ejpam-7112	539	18	)	)	PUNCT
ejpam-7112	540	1	dt	dt	PUNCT
ejpam-7112	540	2	]	]	PUNCT
ejpam-7112	541	1	g(t)f	g(t)f	PROPN
ejpam-7112	541	2	′′(εk	′′(εk	PROPN
ejpam-7112	541	3	)	)	PUNCT
ejpam-7112	541	4	(	(	PUNCT
ejpam-7112	541	5	56	56	NUM
ejpam-7112	541	6	)	)	PUNCT
ejpam-7112	541	7	n	n	PROPN
ejpam-7112	541	8	(	(	PUNCT
ejpam-7112	541	9	α3	α3	PROPN
ejpam-7112	541	10	+	+	CCONJ
ejpam-7112	541	11	αβ2	αβ2	ADJ
ejpam-7112	541	12	+	+	CCONJ
ejpam-7112	541	13	α2β	α2β	PROPN
ejpam-7112	541	14	−	−	PROPN
ejpam-7112	541	15	3β3	3β3	NUM
ejpam-7112	541	16	+	+	CCONJ
ejpam-7112	541	17	6(β	6(β	NUM
ejpam-7112	541	18	−	−	NOUN
ejpam-7112	541	19	α)c2	α)c2	NOUN
ejpam-7112	541	20	24	24	NUM
ejpam-7112	541	21	∫	∫	PROPN
ejpam-7112	541	22	β	β	PROPN
ejpam-7112	541	23	α	α	PROPN
ejpam-7112	541	24	g(t	g(t	PROPN
ejpam-7112	541	25	)	)	PUNCT
ejpam-7112	541	26	dt+	dt+	NOUN
ejpam-7112	541	27	β2	β2	NOUN
ejpam-7112	541	28	−	−	PROPN
ejpam-7112	541	29	c2	c2	PROPN
ejpam-7112	541	30	2	2	NUM
ejpam-7112	541	31	∫	∫	PROPN
ejpam-7112	541	32	β	β	PROPN
ejpam-7112	541	33	α	α	PROPN
ejpam-7112	541	34	∫	∫	PROPN
ejpam-7112	541	35	t	t	PROPN
ejpam-7112	541	36	α	α	PROPN
ejpam-7112	541	37	g(x	g(x	PROPN
ejpam-7112	541	38	)	)	PUNCT
ejpam-7112	541	39	dx	dx	PROPN
ejpam-7112	542	1	dt	dt	X
ejpam-7112	542	2	−	−	PROPN
ejpam-7112	543	1	β	β	X
ejpam-7112	543	2	∫	∫	PROPN
ejpam-7112	543	3	β	β	X
ejpam-7112	543	4	α	α	PROPN
ejpam-7112	543	5	∫	∫	PROPN
ejpam-7112	543	6	t	t	PROPN
ejpam-7112	544	1	α	α	NOUN
ejpam-7112	544	2	∫	∫	PROPN
ejpam-7112	544	3	y	y	PROPN
ejpam-7112	544	4	α	α	PROPN
ejpam-7112	544	5	g(x	g(x	PROPN
ejpam-7112	544	6	)	)	PUNCT
ejpam-7112	544	7	dx	dx	PROPN
ejpam-7112	544	8	dy	dy	NOUN
ejpam-7112	544	9	dt+	dt+	NOUN
ejpam-7112	544	10	∫	∫	PROPN
ejpam-7112	545	1	β	β	PROPN
ejpam-7112	545	2	α	α	PROPN
ejpam-7112	545	3	∫	∫	PROPN
ejpam-7112	545	4	t	t	PROPN
ejpam-7112	546	1	α	α	NOUN
ejpam-7112	546	2	∫	∫	PROPN
ejpam-7112	546	3	y	y	PROPN
ejpam-7112	546	4	α	α	PROPN
ejpam-7112	547	1	∫	∫	PROPN
ejpam-7112	547	2	z	z	PROPN
ejpam-7112	547	3	α	α	PROPN
ejpam-7112	547	4	g(x	g(x	PROPN
ejpam-7112	547	5	)	)	PUNCT
ejpam-7112	548	1	dx	dx	PROPN
ejpam-7112	548	2	dy	dy	X
ejpam-7112	548	3	dz	dz	PROPN
ejpam-7112	548	4	dt	dt	PROPN
ejpam-7112	548	5	)	)	PUNCT
ejpam-7112	548	6	f	f	PROPN
ejpam-7112	548	7	(	(	PUNCT
ejpam-7112	548	8	4)(ξ	4)(ξ	NUM
ejpam-7112	548	9	)	)	PUNCT
ejpam-7112	548	10	g′(η	g′(η	NOUN
ejpam-7112	548	11	)	)	PUNCT
ejpam-7112	548	12	(	(	PUNCT
ejpam-7112	548	13	57	57	NUM
ejpam-7112	548	14	)	)	PUNCT
ejpam-7112	548	15	where	where	SCONJ
ejpam-7112	548	16	µ	µ	X
ejpam-7112	548	17	,	,	PUNCT
ejpam-7112	548	18	η	η	PROPN
ejpam-7112	548	19	∈	∈	PROPN
ejpam-7112	548	20	[	[	X
ejpam-7112	548	21	α	α	X
ejpam-7112	548	22	,	,	PUNCT
ejpam-7112	548	23	β	β	X
ejpam-7112	548	24	]	]	PUNCT
ejpam-7112	548	25	.	.	PUNCT
ejpam-7112	549	1	now	now	ADV
ejpam-7112	549	2	,	,	PUNCT
ejpam-7112	549	3	we	we	PRON
ejpam-7112	549	4	describe	describe	VERB
ejpam-7112	549	5	the	the	DET
ejpam-7112	549	6	composite	composite	ADJ
ejpam-7112	549	7	form	form	NOUN
ejpam-7112	549	8	mzct	mzct	NOUN
ejpam-7112	549	9	of	of	ADP
ejpam-7112	549	10	mzt	mzt	NOUN
ejpam-7112	550	1	[	[	X
ejpam-7112	550	2	22	22	NUM
ejpam-7112	550	3	]	]	PUNCT
ejpam-7112	550	4	in	in	ADP
ejpam-7112	550	5	(	(	PUNCT
ejpam-7112	550	6	57	57	NUM
ejpam-7112	550	7	)	)	PUNCT
ejpam-7112	550	8	.	.	PUNCT
ejpam-7112	551	1	∫	∫	PROPN
ejpam-7112	551	2	β	β	X
ejpam-7112	551	3	a	a	DET
ejpam-7112	551	4	f(t	f(t	PROPN
ejpam-7112	551	5	)	)	PUNCT
ejpam-7112	551	6	dg	dg	PART
ejpam-7112	551	7	≈	≈	NUM
ejpam-7112	551	8	mzct	mzct	NOUN
ejpam-7112	551	9	=	=	PUNCT
ejpam-7112	551	10	[	[	PUNCT
ejpam-7112	551	11	n	n	X
ejpam-7112	551	12	β	β	NOUN
ejpam-7112	551	13	−	−	PROPN
ejpam-7112	552	1	α	α	PRON
ejpam-7112	552	2	∫	∫	PROPN
ejpam-7112	552	3	x1	x1	PROPN
ejpam-7112	553	1	a	a	DET
ejpam-7112	553	2	g(t	g(t	PROPN
ejpam-7112	553	3	)	)	PUNCT
ejpam-7112	553	4	dt−	dt−	PUNCT
ejpam-7112	553	5	g(α	g(α	PROPN
ejpam-7112	553	6	)	)	PUNCT
ejpam-7112	553	7	]	]	PUNCT
ejpam-7112	554	1	f(α	f(α	NOUN
ejpam-7112	554	2	)	)	PUNCT
ejpam-7112	555	1	+	+	NUM
ejpam-7112	556	1	n	n	CCONJ
ejpam-7112	556	2	β	β	NOUN
ejpam-7112	556	3	−	−	NOUN
ejpam-7112	556	4	α	α	PROPN
ejpam-7112	556	5	n−1∑	n−1∑	PROPN
ejpam-7112	556	6	k=1	k=1	PUNCT
ejpam-7112	557	1	[	[	X
ejpam-7112	557	2	∫	∫	X
ejpam-7112	557	3	xk+1	xk+1	PROPN
ejpam-7112	557	4	xk	xk	PROPN
ejpam-7112	557	5	g(t	g(t	PROPN
ejpam-7112	557	6	)	)	PUNCT
ejpam-7112	557	7	dt−	dt−	NUM
ejpam-7112	557	8	∫	∫	PROPN
ejpam-7112	557	9	xk	xk	PROPN
ejpam-7112	557	10	xk−1	xk−1	PROPN
ejpam-7112	557	11	g(t	g(t	PROPN
ejpam-7112	557	12	)	)	PUNCT
ejpam-7112	557	13	dt	dt	X
ejpam-7112	557	14	]	]	PUNCT
ejpam-7112	557	15	f(xi	f(xi	X
ejpam-7112	557	16	)	)	PUNCT
ejpam-7112	557	17	+	+	CCONJ
ejpam-7112	557	18	[	[	PUNCT
ejpam-7112	557	19	g(β)−	g(β)−	PROPN
ejpam-7112	557	20	n	n	PROPN
ejpam-7112	557	21	β	β	NOUN
ejpam-7112	557	22	−	−	PROPN
ejpam-7112	558	1	α	α	PRON
ejpam-7112	558	2	∫	∫	PROPN
ejpam-7112	558	3	β	β	X
ejpam-7112	558	4	xn−1	xn−1	PROPN
ejpam-7112	558	5	g(t	g(t	PROPN
ejpam-7112	558	6	)	)	PUNCT
ejpam-7112	559	1	dt	dt	X
ejpam-7112	559	2	]	]	PUNCT
ejpam-7112	559	3	f(β	f(β	PROPN
ejpam-7112	559	4	)	)	PUNCT
ejpam-7112	560	1	+	+	NUM
ejpam-7112	561	1	n∑	n∑	INTJ
ejpam-7112	561	2	k=1	k=1	PUNCT
ejpam-7112	562	1	[	[	X
ejpam-7112	562	2	∫	∫	X
ejpam-7112	562	3	xk	xk	PROPN
ejpam-7112	562	4	xk−1	xk−1	PROPN
ejpam-7112	562	5	∫	∫	PROPN
ejpam-7112	562	6	t	t	PROPN
ejpam-7112	562	7	xk−1	xk−1	PROPN
ejpam-7112	562	8	g(x	g(x	PROPN
ejpam-7112	562	9	)	)	PUNCT
ejpam-7112	562	10	dx	dx	PROPN
ejpam-7112	562	11	dt−	dt−	PROPN
ejpam-7112	562	12	h	h	PROPN
ejpam-7112	562	13	2	2	NUM
ejpam-7112	562	14	∫	∫	PROPN
ejpam-7112	562	15	xk	xk	PROPN
ejpam-7112	562	16	xk−1	xk−1	PROPN
ejpam-7112	562	17	g(t	g(t	PROPN
ejpam-7112	562	18	)	)	PUNCT
ejpam-7112	562	19	dt	dt	PUNCT
ejpam-7112	562	20	]	]	PUNCT
ejpam-7112	562	21	g(t)f	g(t)f	PROPN
ejpam-7112	562	22	′′(εi	′′(εi	NOUN
ejpam-7112	562	23	)	)	PUNCT
ejpam-7112	562	24	(	(	PUNCT
ejpam-7112	562	25	58	58	NUM
ejpam-7112	562	26	)	)	PUNCT
ejpam-7112	562	27	k.	k.	PROPN
ejpam-7112	562	28	memon	memon	PROPN
ejpam-7112	562	29	et	et	PROPN
ejpam-7112	562	30	al	al	PROPN
ejpam-7112	562	31	.	.	PUNCT
ejpam-7112	562	32	/	/	SYM
ejpam-7112	562	33	eur	eur	PROPN
ejpam-7112	562	34	.	.	PUNCT
ejpam-7112	563	1	j.	j.	PROPN
ejpam-7112	563	2	pure	pure	PROPN
ejpam-7112	563	3	appl	appl	PROPN
ejpam-7112	563	4	.	.	PROPN
ejpam-7112	563	5	math	math	PROPN
ejpam-7112	563	6	,	,	PUNCT
ejpam-7112	563	7	18	18	NUM
ejpam-7112	563	8	(	(	PUNCT
ejpam-7112	563	9	4	4	NUM
ejpam-7112	563	10	)	)	PUNCT
ejpam-7112	563	11	(	(	PUNCT
ejpam-7112	563	12	2025	2025	NUM
ejpam-7112	563	13	)	)	PUNCT
ejpam-7112	563	14	,	,	PUNCT
ejpam-7112	563	15	7112	7112	NUM
ejpam-7112	563	16	19	19	NUM
ejpam-7112	563	17	of	of	ADP
ejpam-7112	563	18	38	38	NUM
ejpam-7112	563	19	n	n	CCONJ
ejpam-7112	563	20	(	(	PUNCT
ejpam-7112	563	21	α3	α3	PROPN
ejpam-7112	563	22	+	+	CCONJ
ejpam-7112	563	23	αβ2	αβ2	ADJ
ejpam-7112	563	24	+	+	CCONJ
ejpam-7112	563	25	α2β	α2β	PROPN
ejpam-7112	563	26	−	−	PROPN
ejpam-7112	563	27	3β3	3β3	NUM
ejpam-7112	563	28	+	+	CCONJ
ejpam-7112	563	29	6(β	6(β	NUM
ejpam-7112	563	30	−	−	NOUN
ejpam-7112	564	1	α)c2	α)c2	NOUN
ejpam-7112	564	2	24	24	NUM
ejpam-7112	564	3	∫	∫	PROPN
ejpam-7112	564	4	β	β	PROPN
ejpam-7112	564	5	α	α	PROPN
ejpam-7112	564	6	g(t	g(t	PROPN
ejpam-7112	564	7	)	)	PUNCT
ejpam-7112	564	8	dt+	dt+	NOUN
ejpam-7112	564	9	β2	β2	NOUN
ejpam-7112	564	10	−	−	PROPN
ejpam-7112	564	11	c2	c2	PROPN
ejpam-7112	564	12	2	2	NUM
ejpam-7112	564	13	∫	∫	PROPN
ejpam-7112	564	14	β	β	PROPN
ejpam-7112	564	15	α	α	PROPN
ejpam-7112	564	16	∫	∫	PROPN
ejpam-7112	564	17	t	t	PROPN
ejpam-7112	564	18	α	α	PROPN
ejpam-7112	564	19	g(x	g(x	PROPN
ejpam-7112	564	20	)	)	PUNCT
ejpam-7112	564	21	dx	dx	PROPN
ejpam-7112	565	1	dt	dt	X
ejpam-7112	565	2	−	−	PROPN
ejpam-7112	566	1	β	β	X
ejpam-7112	566	2	∫	∫	PROPN
ejpam-7112	566	3	β	β	X
ejpam-7112	566	4	α	α	PROPN
ejpam-7112	566	5	∫	∫	PROPN
ejpam-7112	566	6	t	t	PROPN
ejpam-7112	567	1	α	α	NOUN
ejpam-7112	567	2	∫	∫	PROPN
ejpam-7112	567	3	y	y	PROPN
ejpam-7112	567	4	α	α	PROPN
ejpam-7112	567	5	g(x	g(x	PROPN
ejpam-7112	567	6	)	)	PUNCT
ejpam-7112	567	7	dx	dx	PROPN
ejpam-7112	567	8	dy	dy	NOUN
ejpam-7112	567	9	dt+	dt+	NOUN
ejpam-7112	567	10	∫	∫	PROPN
ejpam-7112	568	1	β	β	PROPN
ejpam-7112	568	2	α	α	PROPN
ejpam-7112	568	3	∫	∫	PROPN
ejpam-7112	568	4	t	t	PROPN
ejpam-7112	569	1	α	α	NOUN
ejpam-7112	569	2	∫	∫	PROPN
ejpam-7112	569	3	y	y	PROPN
ejpam-7112	569	4	α	α	PROPN
ejpam-7112	570	1	∫	∫	PROPN
ejpam-7112	570	2	z	z	PROPN
ejpam-7112	570	3	α	α	PROPN
ejpam-7112	570	4	g(x	g(x	PROPN
ejpam-7112	570	5	)	)	PUNCT
ejpam-7112	571	1	dx	dx	PROPN
ejpam-7112	571	2	dy	dy	X
ejpam-7112	571	3	dz	dz	PROPN
ejpam-7112	571	4	dt	dt	PROPN
ejpam-7112	571	5	)	)	PUNCT
ejpam-7112	571	6	f	f	PROPN
ejpam-7112	571	7	(	(	PUNCT
ejpam-7112	571	8	4)(ξ	4)(ξ	NUM
ejpam-7112	571	9	)	)	PUNCT
ejpam-7112	571	10	g′(η	g′(η	NOUN
ejpam-7112	571	11	)	)	PUNCT
ejpam-7112	571	12	(	(	PUNCT
ejpam-7112	571	13	59	59	NUM
ejpam-7112	571	14	)	)	PUNCT
ejpam-7112	571	15	where	where	SCONJ
ejpam-7112	571	16	µ	µ	X
ejpam-7112	571	17	,	,	PUNCT
ejpam-7112	571	18	η	η	PROPN
ejpam-7112	571	19	∈	∈	PROPN
ejpam-7112	571	20	(	(	PUNCT
ejpam-7112	571	21	α	α	NOUN
ejpam-7112	571	22	,	,	PUNCT
ejpam-7112	571	23	β	β	NOUN
ejpam-7112	571	24	)	)	PUNCT
ejpam-7112	571	25	.	.	PUNCT
ejpam-7112	572	1	3	3	X
ejpam-7112	572	2	.	.	X
ejpam-7112	572	3	results	result	NOUN
ejpam-7112	572	4	of	of	ADP
ejpam-7112	572	5	the	the	DET
ejpam-7112	572	6	numerical	numerical	ADJ
ejpam-7112	572	7	experiments	experiment	NOUN
ejpam-7112	572	8	and	and	CCONJ
ejpam-7112	572	9	their	their	PRON
ejpam-7112	572	10	discussion	discussion	NOUN
ejpam-7112	572	11	we	we	PRON
ejpam-7112	572	12	examine	examine	VERB
ejpam-7112	572	13	the	the	DET
ejpam-7112	572	14	performance	performance	NOUN
ejpam-7112	572	15	of	of	ADP
ejpam-7112	572	16	the	the	DET
ejpam-7112	572	17	proposed	propose	VERB
ejpam-7112	572	18	quadrature	quadrature	NOUN
ejpam-7112	572	19	of	of	ADP
ejpam-7112	572	20	trapezoid	trapezoid	NOUN
ejpam-7112	572	21	-	-	PUNCT
ejpam-7112	572	22	type	type	NOUN
ejpam-7112	572	23	for	for	ADP
ejpam-7112	572	24	rsintegral	rsintegral	ADJ
ejpam-7112	572	25	over	over	ADP
ejpam-7112	572	26	original	original	ADJ
ejpam-7112	572	27	trapezoid	trapezoid	NOUN
ejpam-7112	572	28	,	,	PUNCT
ejpam-7112	572	29	zhao	zhao	PROPN
ejpam-7112	572	30	et	et	NOUN
ejpam-7112	572	31	al	al	PROPN
ejpam-7112	572	32	.	.	PUNCT
ejpam-7112	573	1	[	[	X
ejpam-7112	573	2	5	5	NUM
ejpam-7112	573	3	]	]	PUNCT
ejpam-7112	573	4	and	and	CCONJ
ejpam-7112	573	5	modified	modify	VERB
ejpam-7112	573	6	zhao	zhao	NOUN
ejpam-7112	573	7	-	-	PUNCT
ejpam-7112	573	8	trapezoid	trapezoid	NOUN
ejpam-7112	573	9	(	(	PUNCT
ejpam-7112	573	10	mzt	mzt	PROPN
ejpam-7112	573	11	)	)	PUNCT
ejpam-7112	574	1	[	[	X
ejpam-7112	574	2	22	22	NUM
ejpam-7112	574	3	]	]	PUNCT
ejpam-7112	574	4	rules	rule	NOUN
ejpam-7112	574	5	in	in	ADP
ejpam-7112	574	6	terms	term	NOUN
ejpam-7112	574	7	of	of	ADP
ejpam-7112	574	8	absolute	absolute	ADJ
ejpam-7112	574	9	error	error	NOUN
ejpam-7112	574	10	distributions	distribution	NOUN
ejpam-7112	574	11	when	when	SCONJ
ejpam-7112	574	12	integration	integration	NOUN
ejpam-7112	574	13	strips	strip	NOUN
ejpam-7112	574	14	are	be	AUX
ejpam-7112	574	15	increased	increase	VERB
ejpam-7112	574	16	.	.	PUNCT
ejpam-7112	575	1	in	in	ADP
ejpam-7112	575	2	addition	addition	NOUN
ejpam-7112	575	3	,	,	PUNCT
ejpam-7112	575	4	we	we	PRON
ejpam-7112	575	5	also	also	ADV
ejpam-7112	575	6	compute	compute	VERB
ejpam-7112	575	7	computational	computational	ADJ
ejpam-7112	575	8	/	/	SYM
ejpam-7112	575	9	observed	observed	ADJ
ejpam-7112	575	10	order	order	NOUN
ejpam-7112	575	11	of	of	ADP
ejpam-7112	575	12	accuracy	accuracy	NOUN
ejpam-7112	575	13	/	/	SYM
ejpam-7112	575	14	exactness	exactness	NOUN
ejpam-7112	575	15	of	of	ADP
ejpam-7112	575	16	proposed	propose	VERB
ejpam-7112	575	17	quadrature	quadrature	NOUN
ejpam-7112	575	18	so	so	SCONJ
ejpam-7112	575	19	that	that	SCONJ
ejpam-7112	575	20	the	the	DET
ejpam-7112	575	21	theoretical	theoretical	ADJ
ejpam-7112	575	22	expressions	expression	NOUN
ejpam-7112	575	23	in	in	ADP
ejpam-7112	575	24	theorems	theorem	NOUN
ejpam-7112	575	25	1	1	NUM
ejpam-7112	575	26	-	-	SYM
ejpam-7112	575	27	4	4	NUM
ejpam-7112	575	28	and	and	CCONJ
ejpam-7112	575	29	corollaries	corollary	NOUN
ejpam-7112	575	30	1	1	NUM
ejpam-7112	575	31	-	-	SYM
ejpam-7112	575	32	5	5	NUM
ejpam-7112	575	33	are	be	AUX
ejpam-7112	575	34	verified	verify	VERB
ejpam-7112	575	35	.	.	PUNCT
ejpam-7112	576	1	it	it	PRON
ejpam-7112	576	2	should	should	AUX
ejpam-7112	576	3	be	be	AUX
ejpam-7112	576	4	noted	note	VERB
ejpam-7112	576	5	that	that	SCONJ
ejpam-7112	576	6	in	in	ADP
ejpam-7112	576	7	the	the	DET
ejpam-7112	576	8	previous	previous	ADJ
ejpam-7112	576	9	studies	study	NOUN
ejpam-7112	576	10	[	[	X
ejpam-7112	576	11	3	3	NUM
ejpam-7112	576	12	]	]	PUNCT
ejpam-7112	576	13	,	,	PUNCT
ejpam-7112	576	14	[	[	X
ejpam-7112	576	15	5	5	NUM
ejpam-7112	576	16	]	]	PUNCT
ejpam-7112	576	17	,	,	PUNCT
ejpam-7112	576	18	the	the	DET
ejpam-7112	576	19	numerical	numerical	ADJ
ejpam-7112	576	20	experiments	experiment	NOUN
ejpam-7112	576	21	were	be	AUX
ejpam-7112	576	22	not	not	PART
ejpam-7112	576	23	performed	perform	VERB
ejpam-7112	576	24	on	on	ADP
ejpam-7112	576	25	the	the	DET
ejpam-7112	576	26	quadrature	quadrature	NOUN
ejpam-7112	576	27	schemes	scheme	NOUN
ejpam-7112	576	28	for	for	ADP
ejpam-7112	576	29	the	the	DET
ejpam-7112	576	30	rs	rs	NOUN
ejpam-7112	576	31	-	-	ADJ
ejpam-7112	576	32	integral	integral	ADJ
ejpam-7112	576	33	;	;	PUNCT
ejpam-7112	576	34	however	however	ADV
ejpam-7112	576	35	,	,	PUNCT
ejpam-7112	576	36	this	this	DET
ejpam-7112	576	37	research	research	NOUN
ejpam-7112	576	38	verifies	verify	VERB
ejpam-7112	576	39	the	the	DET
ejpam-7112	576	40	theoretical	theoretical	ADJ
ejpam-7112	576	41	results	result	NOUN
ejpam-7112	576	42	by	by	ADP
ejpam-7112	576	43	experimental	experimental	ADJ
ejpam-7112	576	44	results	result	NOUN
ejpam-7112	576	45	solving	solve	VERB
ejpam-7112	576	46	five	five	NUM
ejpam-7112	576	47	different	different	ADJ
ejpam-7112	576	48	examples	example	NOUN
ejpam-7112	576	49	.	.	PUNCT
ejpam-7112	577	1	five	five	NUM
ejpam-7112	577	2	problems	problem	NOUN
ejpam-7112	577	3	are	be	AUX
ejpam-7112	577	4	taken	take	VERB
ejpam-7112	577	5	from	from	ADP
ejpam-7112	577	6	[	[	X
ejpam-7112	577	7	21	21	NUM
ejpam-7112	577	8	]	]	PUNCT
ejpam-7112	577	9	,	,	PUNCT
ejpam-7112	577	10	[	[	X
ejpam-7112	577	11	23],[24	23],[24	NOUN
ejpam-7112	577	12	]	]	X
ejpam-7112	577	13	,	,	PUNCT
ejpam-7112	577	14	[	[	X
ejpam-7112	577	15	13	13	NUM
ejpam-7112	577	16	]	]	PUNCT
ejpam-7112	577	17	and	and	CCONJ
ejpam-7112	577	18	[	[	X
ejpam-7112	577	19	14	14	NUM
ejpam-7112	577	20	]	]	PUNCT
ejpam-7112	577	21	,	,	PUNCT
ejpam-7112	577	22	and	and	CCONJ
ejpam-7112	577	23	these	these	PRON
ejpam-7112	577	24	are	be	AUX
ejpam-7112	577	25	tested	test	VERB
ejpam-7112	577	26	in	in	ADP
ejpam-7112	577	27	approximations	approximation	NOUN
ejpam-7112	577	28	up	up	ADP
ejpam-7112	577	29	to	to	PART
ejpam-7112	577	30	16	16	NUM
ejpam-7112	577	31	decimal	decimal	ADJ
ejpam-7112	577	32	places	place	NOUN
ejpam-7112	577	33	of	of	ADP
ejpam-7112	577	34	accuracy	accuracy	NOUN
ejpam-7112	577	35	using	use	VERB
ejpam-7112	577	36	the	the	DET
ejpam-7112	577	37	matlab	matlab	PROPN
ejpam-7112	577	38	software	software	NOUN
ejpam-7112	577	39	.	.	PUNCT
ejpam-7112	578	1	the	the	DET
ejpam-7112	578	2	results	result	NOUN
ejpam-7112	578	3	were	be	AUX
ejpam-7112	578	4	noted	note	VERB
ejpam-7112	578	5	using	use	VERB
ejpam-7112	578	6	the	the	DET
ejpam-7112	578	7	intel	intel	PROPN
ejpam-7112	578	8	(	(	PUNCT
ejpam-7112	578	9	r	r	NOUN
ejpam-7112	578	10	)	)	PUNCT
ejpam-7112	578	11	core	core	NOUN
ejpam-7112	578	12	(	(	PUNCT
ejpam-7112	578	13	tm	tm	NOUN
ejpam-7112	578	14	)	)	PUNCT
ejpam-7112	578	15	laptop	laptop	NOUN
ejpam-7112	578	16	using	use	VERB
ejpam-7112	578	17	4	4	NUM
ejpam-7112	578	18	gb	gb	NOUN
ejpam-7112	578	19	ram	ram	NOUN
ejpam-7112	578	20	operating	operate	VERB
ejpam-7112	578	21	at	at	ADP
ejpam-7112	578	22	speed	speed	NOUN
ejpam-7112	578	23	of	of	ADP
ejpam-7112	578	24	0.80	0.80	NUM
ejpam-7112	578	25	ghz	ghz	NOUN
ejpam-7112	578	26	–	–	PUNCT
ejpam-7112	578	27	1.00	1.00	NUM
ejpam-7112	578	28	ghz	ghz	NOUN
ejpam-7112	578	29	.	.	PUNCT
ejpam-7112	579	1	also	also	ADV
ejpam-7112	579	2	,	,	PUNCT
ejpam-7112	579	3	the	the	DET
ejpam-7112	579	4	double	double	ADJ
ejpam-7112	579	5	precision	precision	NOUN
ejpam-7112	579	6	default	default	NOUN
ejpam-7112	579	7	arithmetic	arithmetic	NOUN
ejpam-7112	579	8	of	of	ADP
ejpam-7112	579	9	matlab	matlab	PROPN
ejpam-7112	579	10	is	be	AUX
ejpam-7112	579	11	utilized	utilize	VERB
ejpam-7112	579	12	for	for	ADP
ejpam-7112	579	13	the	the	DET
ejpam-7112	579	14	results	result	NOUN
ejpam-7112	579	15	.	.	PUNCT
ejpam-7112	580	1	(	(	PUNCT
ejpam-7112	580	2	i	i	NOUN
ejpam-7112	580	3	)	)	PUNCT
ejpam-7112	580	4	example	example	NOUN
ejpam-7112	580	5	1	1	NUM
ejpam-7112	580	6	∫	∫	PROPN
ejpam-7112	580	7	3.5	3.5	NUM
ejpam-7112	580	8	4.5	4.5	NUM
ejpam-7112	580	9	sin	sin	NOUN
ejpam-7112	580	10	5x	5x	NUM
ejpam-7112	580	11	d(cosx	d(cosx	NOUN
ejpam-7112	580	12	)	)	PUNCT
ejpam-7112	580	13	=	=	SYM
ejpam-7112	580	14	0.227676016130689	0.227676016130689	NUM
ejpam-7112	580	15	(	(	PUNCT
ejpam-7112	580	16	ii	ii	NOUN
ejpam-7112	580	17	)	)	PUNCT
ejpam-7112	580	18	example	example	NOUN
ejpam-7112	580	19	2	2	NUM
ejpam-7112	580	20	∫	∫	NOUN
ejpam-7112	580	21	6	6	NUM
ejpam-7112	580	22	5	5	NUM
ejpam-7112	580	23	sinx	sinx	NOUN
ejpam-7112	580	24	d(x3	d(x3	X
ejpam-7112	580	25	)	)	PUNCT
ejpam-7112	581	1	=	=	SYM
ejpam-7112	581	2	59.655908136641912	59.655908136641912	NUM
ejpam-7112	581	3	(	(	PUNCT
ejpam-7112	581	4	iii	iii	NOUN
ejpam-7112	581	5	)	)	PUNCT
ejpam-7112	581	6	example	example	NOUN
ejpam-7112	581	7	3	3	NUM
ejpam-7112	581	8	∫	∫	NOUN
ejpam-7112	581	9	6	6	NUM
ejpam-7112	581	10	5	5	NUM
ejpam-7112	581	11	ex	ex	X
ejpam-7112	581	12	d(sinx	d(sinx	NOUN
ejpam-7112	581	13	)	)	PUNCT
ejpam-7112	581	14	=	=	SYM
ejpam-7112	582	1	187.4269314248657	187.4269314248657	NUM
ejpam-7112	582	2	(	(	PUNCT
ejpam-7112	582	3	iv	iv	NUM
ejpam-7112	582	4	)	)	PUNCT
ejpam-7112	582	5	example	example	NOUN
ejpam-7112	582	6	4	4	NUM
ejpam-7112	582	7	∫	∫	NOUN
ejpam-7112	582	8	pi	pi	NOUN
ejpam-7112	582	9	0	0	NUM
ejpam-7112	582	10	x3	x3	ADJ
ejpam-7112	582	11	d(sinx	d(sinx	NOUN
ejpam-7112	582	12	)	)	PUNCT
ejpam-7112	582	13	=	=	SYM
ejpam-7112	583	1	−17.608813203268074	−17.608813203268074	PROPN
ejpam-7112	583	2	(	(	PUNCT
ejpam-7112	583	3	v	v	NOUN
ejpam-7112	583	4	)	)	PUNCT
ejpam-7112	583	5	example	example	NOUN
ejpam-7112	583	6	5	5	NUM
ejpam-7112	583	7	∫	∫	PROPN
ejpam-7112	583	8	1	1	NUM
ejpam-7112	583	9	−1	−1	NOUN
ejpam-7112	583	10	x	x	SYM
ejpam-7112	583	11	3	3	NUM
ejpam-7112	583	12	d(ex	d(ex	NOUN
ejpam-7112	583	13	)	)	PUNCT
ejpam-7112	583	14	=	=	SYM
ejpam-7112	584	1	−17.608813203268074	−17.608813203268074	PROPN
ejpam-7112	584	2	the	the	DET
ejpam-7112	584	3	formula	formula	NOUN
ejpam-7112	584	4	of	of	ADP
ejpam-7112	584	5	absolute	absolute	ADJ
ejpam-7112	584	6	error	error	NOUN
ejpam-7112	584	7	drop	drop	NOUN
ejpam-7112	584	8	(	(	PUNCT
ejpam-7112	584	9	aed	aed	NOUN
ejpam-7112	584	10	)	)	PUNCT
ejpam-7112	585	1	[	[	X
ejpam-7112	585	2	9	9	NUM
ejpam-7112	585	3	]	]	PUNCT
ejpam-7112	585	4	is	be	AUX
ejpam-7112	585	5	:	:	PUNCT
ejpam-7112	585	6	aed	aed	NOUN
ejpam-7112	585	7	=	=	PUNCT
ejpam-7112	585	8	|ev	|ev	X
ejpam-7112	585	9	av	av	PROPN
ejpam-7112	586	1	|	|	ADV
ejpam-7112	586	2	(	(	PUNCT
ejpam-7112	586	3	60	60	NUM
ejpam-7112	586	4	)	)	PUNCT
ejpam-7112	587	1	k.	k.	PROPN
ejpam-7112	587	2	memon	memon	PROPN
ejpam-7112	587	3	et	et	PROPN
ejpam-7112	587	4	al	al	PROPN
ejpam-7112	587	5	.	.	PUNCT
ejpam-7112	587	6	/	/	SYM
ejpam-7112	587	7	eur	eur	PROPN
ejpam-7112	587	8	.	.	PUNCT
ejpam-7112	588	1	j.	j.	PROPN
ejpam-7112	588	2	pure	pure	PROPN
ejpam-7112	588	3	appl	appl	PROPN
ejpam-7112	588	4	.	.	PROPN
ejpam-7112	588	5	math	math	PROPN
ejpam-7112	588	6	,	,	PUNCT
ejpam-7112	588	7	18	18	NUM
ejpam-7112	588	8	(	(	PUNCT
ejpam-7112	588	9	4	4	NUM
ejpam-7112	588	10	)	)	PUNCT
ejpam-7112	588	11	(	(	PUNCT
ejpam-7112	588	12	2025	2025	NUM
ejpam-7112	588	13	)	)	PUNCT
ejpam-7112	588	14	,	,	PUNCT
ejpam-7112	588	15	7112	7112	NUM
ejpam-7112	588	16	20	20	NUM
ejpam-7112	588	17	of	of	ADP
ejpam-7112	588	18	38	38	NUM
ejpam-7112	588	19	in	in	ADP
ejpam-7112	588	20	(	(	PUNCT
ejpam-7112	588	21	60	60	NUM
ejpam-7112	588	22	)	)	PUNCT
ejpam-7112	588	23	,	,	PUNCT
ejpam-7112	588	24	ae	ae	PROPN
ejpam-7112	588	25	and	and	CCONJ
ejpam-7112	588	26	av	av	PRON
ejpam-7112	588	27	refer	refer	VERB
ejpam-7112	588	28	to	to	ADP
ejpam-7112	588	29	exact	exact	ADJ
ejpam-7112	588	30	and	and	CCONJ
ejpam-7112	588	31	approximate	approximate	ADJ
ejpam-7112	588	32	values	value	NOUN
ejpam-7112	588	33	of	of	ADP
ejpam-7112	588	34	integrals	integral	NOUN
ejpam-7112	588	35	,	,	PUNCT
ejpam-7112	588	36	respectively	respectively	ADV
ejpam-7112	588	37	.	.	PUNCT
ejpam-7112	589	1	the	the	DET
ejpam-7112	589	2	formula	formula	NOUN
ejpam-7112	589	3	for	for	ADP
ejpam-7112	589	4	the	the	DET
ejpam-7112	589	5	observed	observe	VERB
ejpam-7112	589	6	/	/	SYM
ejpam-7112	589	7	computational	computational	ADJ
ejpam-7112	589	8	order	order	NOUN
ejpam-7112	589	9	of	of	ADP
ejpam-7112	589	10	accuracy	accuracy	NOUN
ejpam-7112	589	11	is	be	AUX
ejpam-7112	589	12	defined	define	VERB
ejpam-7112	589	13	in	in	ADP
ejpam-7112	589	14	[	[	X
ejpam-7112	589	15	25	25	NUM
ejpam-7112	589	16	]	]	PUNCT
ejpam-7112	589	17	,	,	PUNCT
ejpam-7112	589	18	[	[	X
ejpam-7112	589	19	24	24	NUM
ejpam-7112	589	20	]	]	PUNCT
ejpam-7112	589	21	,	,	PUNCT
ejpam-7112	589	22	[	[	X
ejpam-7112	589	23	13	13	NUM
ejpam-7112	589	24	]	]	PUNCT
ejpam-7112	589	25	,	,	PUNCT
ejpam-7112	589	26	[	[	X
ejpam-7112	589	27	14	14	NUM
ejpam-7112	589	28	]	]	PUNCT
ejpam-7112	589	29	as	as	ADP
ejpam-7112	589	30	:	:	PUNCT
ejpam-7112	589	31	p	p	X
ejpam-7112	589	32	=	=	NOUN
ejpam-7112	589	33	ln	ln	ADJ
ejpam-7112	589	34	(	(	PUNCT
ejpam-7112	589	35	|n(2h)−n(0)|	|n(2h)−n(0)|	NOUN
ejpam-7112	589	36	|n(h)−n(0)|	|n(h)−n(0)|	NUM
ejpam-7112	589	37	)	)	PUNCT
ejpam-7112	590	1	ln	ln	ADV
ejpam-7112	590	2	2	2	NUM
ejpam-7112	590	3	.	.	PUNCT
ejpam-7112	591	1	(	(	PUNCT
ejpam-7112	591	2	61	61	NUM
ejpam-7112	591	3	)	)	PUNCT
ejpam-7112	591	4	where	where	SCONJ
ejpam-7112	591	5	n	n	PRON
ejpam-7112	591	6	indicates	indicate	VERB
ejpam-7112	591	7	approximate	approximate	ADJ
ejpam-7112	591	8	quadrature	quadrature	NOUN
ejpam-7112	591	9	result	result	NOUN
ejpam-7112	591	10	at	at	ADP
ejpam-7112	591	11	the	the	DET
ejpam-7112	591	12	step	step	NOUN
ejpam-7112	591	13	-	-	PUNCT
ejpam-7112	591	14	size	size	NOUN
ejpam-7112	591	15	indicated	indicate	VERB
ejpam-7112	591	16	in	in	ADP
ejpam-7112	591	17	the	the	DET
ejpam-7112	591	18	parenthesis	parenthesis	NOUN
ejpam-7112	591	19	,	,	PUNCT
ejpam-7112	591	20	and	and	CCONJ
ejpam-7112	591	21	with	with	ADP
ejpam-7112	591	22	0	0	NUM
ejpam-7112	591	23	inside	inside	ADP
ejpam-7112	591	24	the	the	DET
ejpam-7112	591	25	base	base	NOUN
ejpam-7112	591	26	result	result	NOUN
ejpam-7112	591	27	–	–	PUNCT
ejpam-7112	591	28	the	the	DET
ejpam-7112	591	29	exact	exact	ADJ
ejpam-7112	591	30	integral	integral	ADJ
ejpam-7112	591	31	value	value	NOUN
ejpam-7112	591	32	–	–	PUNCT
ejpam-7112	591	33	is	be	AUX
ejpam-7112	591	34	intended	intend	VERB
ejpam-7112	591	35	.	.	PUNCT
ejpam-7112	592	1	figs	fig	NOUN
ejpam-7112	592	2	.	.	PUNCT
ejpam-7112	593	1	(	(	PUNCT
ejpam-7112	593	2	3)-(7	3)-(7	NUM
ejpam-7112	593	3	)	)	PUNCT
ejpam-7112	593	4	,	,	PUNCT
ejpam-7112	593	5	respectively	respectively	ADV
ejpam-7112	593	6	,	,	PUNCT
ejpam-7112	593	7	display	display	NOUN
ejpam-7112	593	8	aeds	aed	NOUN
ejpam-7112	593	9	for	for	ADP
ejpam-7112	593	10	the	the	DET
ejpam-7112	593	11	case	case	NOUN
ejpam-7112	593	12	of	of	ADP
ejpam-7112	593	13	examples	example	NOUN
ejpam-7112	593	14	1	1	NUM
ejpam-7112	593	15	-	-	SYM
ejpam-7112	593	16	5	5	NUM
ejpam-7112	593	17	for	for	ADP
ejpam-7112	593	18	the	the	DET
ejpam-7112	593	19	quadrature	quadrature	NOUN
ejpam-7112	593	20	approximations	approximation	NOUN
ejpam-7112	593	21	of	of	ADP
ejpam-7112	593	22	previous	previous	ADJ
ejpam-7112	593	23	quadrature	quadrature	NOUN
ejpam-7112	593	24	:	:	PUNCT
ejpam-7112	593	25	trapezoid	trapezoid	NOUN
ejpam-7112	593	26	ct	ct	PROPN
ejpam-7112	594	1	[	[	X
ejpam-7112	594	2	20	20	NUM
ejpam-7112	594	3	]	]	PUNCT
ejpam-7112	594	4	,	,	PUNCT
ejpam-7112	594	5	zct	zct	NOUN
ejpam-7112	594	6	[	[	X
ejpam-7112	594	7	5	5	NUM
ejpam-7112	594	8	]	]	PUNCT
ejpam-7112	594	9	and	and	CCONJ
ejpam-7112	594	10	mzct	mzct	NOUN
ejpam-7112	594	11	[	[	X
ejpam-7112	594	12	22	22	NUM
ejpam-7112	594	13	]	]	PUNCT
ejpam-7112	594	14	,	,	PUNCT
ejpam-7112	594	15	and	and	CCONJ
ejpam-7112	594	16	the	the	DET
ejpam-7112	594	17	new	new	ADJ
ejpam-7112	594	18	trapezoid	trapezoid	ADJ
ejpam-7112	594	19	-	-	PUNCT
ejpam-7112	594	20	type	type	NOUN
ejpam-7112	594	21	quadrature	quadrature	NOUN
ejpam-7112	594	22	:	:	PUNCT
ejpam-7112	594	23	amct	amct	ADJ
ejpam-7112	594	24	,	,	PUNCT
ejpam-7112	594	25	gmct	gmct	ADJ
ejpam-7112	594	26	,	,	PUNCT
ejpam-7112	594	27	hmct	hmct	NOUN
ejpam-7112	594	28	,	,	PUNCT
ejpam-7112	594	29	hemct	hemct	ADJ
ejpam-7112	594	30	and	and	CCONJ
ejpam-7112	594	31	cmct	cmct	ADJ
ejpam-7112	594	32	.	.	PUNCT
ejpam-7112	595	1	for	for	ADP
ejpam-7112	595	2	numerical	numerical	ADJ
ejpam-7112	595	3	test	test	NOUN
ejpam-7112	595	4	integrals	integral	NOUN
ejpam-7112	595	5	1	1	NUM
ejpam-7112	595	6	-	-	SYM
ejpam-7112	595	7	3	3	NUM
ejpam-7112	595	8	through	through	ADP
ejpam-7112	595	9	figs.(3)-(5	figs.(3)-(5	NOUN
ejpam-7112	595	10	)	)	PUNCT
ejpam-7112	595	11	,	,	PUNCT
ejpam-7112	595	12	it	it	PRON
ejpam-7112	595	13	is	be	AUX
ejpam-7112	595	14	obvious	obvious	ADJ
ejpam-7112	595	15	to	to	PART
ejpam-7112	595	16	note	note	VERB
ejpam-7112	595	17	the	the	DET
ejpam-7112	595	18	ascending	ascend	VERB
ejpam-7112	595	19	performance	performance	NOUN
ejpam-7112	595	20	of	of	ADP
ejpam-7112	595	21	the	the	DET
ejpam-7112	595	22	proposed	propose	VERB
ejpam-7112	595	23	quadrature	quadrature	NOUN
ejpam-7112	595	24	.	.	PUNCT
ejpam-7112	596	1	the	the	DET
ejpam-7112	596	2	aeds	aed	NOUN
ejpam-7112	596	3	for	for	ADP
ejpam-7112	596	4	the	the	DET
ejpam-7112	596	5	cmct	cmct	ADJ
ejpam-7112	596	6	quadrature	quadrature	NOUN
ejpam-7112	596	7	are	be	AUX
ejpam-7112	596	8	lowest	low	ADJ
ejpam-7112	596	9	of	of	ADP
ejpam-7112	596	10	all	all	PRON
ejpam-7112	596	11	for	for	ADP
ejpam-7112	596	12	test	test	NOUN
ejpam-7112	596	13	numerical	numerical	ADJ
ejpam-7112	596	14	integrals	integral	NOUN
ejpam-7112	596	15	1	1	NUM
ejpam-7112	596	16	-	-	SYM
ejpam-7112	596	17	3	3	NUM
ejpam-7112	596	18	,	,	PUNCT
ejpam-7112	596	19	and	and	CCONJ
ejpam-7112	596	20	the	the	DET
ejpam-7112	596	21	aeds	aed	NOUN
ejpam-7112	596	22	in	in	ADP
ejpam-7112	596	23	the	the	DET
ejpam-7112	596	24	case	case	NOUN
ejpam-7112	596	25	of	of	ADP
ejpam-7112	596	26	existing	exist	VERB
ejpam-7112	596	27	quadrature	quadrature	NOUN
ejpam-7112	596	28	ct	ct	NOUN
ejpam-7112	596	29	and	and	CCONJ
ejpam-7112	596	30	zct	zct	NOUN
ejpam-7112	596	31	are	be	AUX
ejpam-7112	596	32	much	much	ADV
ejpam-7112	596	33	slower	slow	ADJ
ejpam-7112	596	34	(	(	PUNCT
ejpam-7112	596	35	3)-(5	3)-(5	NUM
ejpam-7112	596	36	)	)	PUNCT
ejpam-7112	596	37	.	.	PUNCT
ejpam-7112	597	1	the	the	DET
ejpam-7112	597	2	zct	zct	NOUN
ejpam-7112	597	3	quadrature	quadrature	NOUN
ejpam-7112	597	4	[	[	X
ejpam-7112	597	5	5	5	NUM
ejpam-7112	597	6	]	]	PUNCT
ejpam-7112	597	7	is	be	AUX
ejpam-7112	597	8	less	less	ADV
ejpam-7112	597	9	likely	likely	ADJ
ejpam-7112	597	10	to	to	PART
ejpam-7112	597	11	assure	assure	VERB
ejpam-7112	597	12	the	the	DET
ejpam-7112	597	13	claimed	claim	VERB
ejpam-7112	597	14	units	unit	NOUN
ejpam-7112	597	15	of	of	ADP
ejpam-7112	597	16	precision	precision	NOUN
ejpam-7112	597	17	and	and	CCONJ
ejpam-7112	597	18	accuracy	accuracy	NOUN
ejpam-7112	597	19	as	as	ADP
ejpam-7112	597	20	in	in	ADP
ejpam-7112	597	21	[	[	X
ejpam-7112	597	22	5	5	NUM
ejpam-7112	597	23	]	]	PUNCT
ejpam-7112	597	24	,	,	PUNCT
ejpam-7112	597	25	but	but	CCONJ
ejpam-7112	597	26	mzct	mzct	NOUN
ejpam-7112	597	27	quadrature	quadrature	NOUN
ejpam-7112	597	28	[	[	X
ejpam-7112	597	29	22	22	NUM
ejpam-7112	597	30	]	]	PUNCT
ejpam-7112	597	31	exhibits	exhibit	VERB
ejpam-7112	597	32	obvious	obvious	ADJ
ejpam-7112	597	33	improvement	improvement	NOUN
ejpam-7112	597	34	over	over	ADP
ejpam-7112	597	35	the	the	DET
ejpam-7112	597	36	zct	zct	NOUN
ejpam-7112	597	37	quadrature	quadrature	NOUN
ejpam-7112	597	38	in	in	ADP
ejpam-7112	597	39	all	all	DET
ejpam-7112	597	40	test	test	NOUN
ejpam-7112	597	41	integrals	integral	NOUN
ejpam-7112	597	42	.	.	PUNCT
ejpam-7112	598	1	the	the	DET
ejpam-7112	598	2	zct	zct	NOUN
ejpam-7112	598	3	quadrature	quadrature	NOUN
ejpam-7112	598	4	behaves	behave	VERB
ejpam-7112	598	5	poorest	poor	ADJ
ejpam-7112	598	6	of	of	ADP
ejpam-7112	598	7	all	all	PRON
ejpam-7112	598	8	in	in	ADP
ejpam-7112	598	9	the	the	DET
ejpam-7112	598	10	case	case	NOUN
ejpam-7112	598	11	of	of	ADP
ejpam-7112	598	12	problems	problem	NOUN
ejpam-7112	598	13	4	4	NUM
ejpam-7112	598	14	-	-	SYM
ejpam-7112	598	15	5	5	NUM
ejpam-7112	598	16	.	.	PUNCT
ejpam-7112	599	1	in	in	ADP
ejpam-7112	599	2	problems	problem	NOUN
ejpam-7112	599	3	4	4	NUM
ejpam-7112	599	4	-	-	SYM
ejpam-7112	599	5	5	5	NUM
ejpam-7112	599	6	(	(	PUNCT
ejpam-7112	599	7	see	see	VERB
ejpam-7112	599	8	figs	fig	NOUN
ejpam-7112	599	9	.	.	PUNCT
ejpam-7112	600	1	(	(	PUNCT
ejpam-7112	600	2	6)-(7	6)-(7	NUM
ejpam-7112	600	3	)	)	PUNCT
ejpam-7112	600	4	)	)	PUNCT
ejpam-7112	600	5	,	,	PUNCT
ejpam-7112	600	6	the	the	DET
ejpam-7112	600	7	new	new	ADJ
ejpam-7112	600	8	quadrature	quadrature	NOUN
ejpam-7112	600	9	proposed	propose	VERB
ejpam-7112	600	10	in	in	ADP
ejpam-7112	600	11	this	this	DET
ejpam-7112	600	12	study	study	NOUN
ejpam-7112	600	13	result	result	NOUN
ejpam-7112	600	14	in	in	ADP
ejpam-7112	600	15	smaller	small	ADJ
ejpam-7112	600	16	aeds	aed	NOUN
ejpam-7112	600	17	when	when	SCONJ
ejpam-7112	600	18	compared	compare	VERB
ejpam-7112	600	19	with	with	ADP
ejpam-7112	600	20	zct	zct	NOUN
ejpam-7112	600	21	and	and	CCONJ
ejpam-7112	600	22	ct	ct	NUM
ejpam-7112	600	23	quadrature	quadrature	NOUN
ejpam-7112	600	24	.	.	PUNCT
ejpam-7112	601	1	also	also	ADV
ejpam-7112	601	2	,	,	PUNCT
ejpam-7112	601	3	the	the	DET
ejpam-7112	601	4	mzct	mzct	NOUN
ejpam-7112	601	5	quadrature	quadrature	NOUN
ejpam-7112	601	6	[	[	X
ejpam-7112	601	7	22	22	NUM
ejpam-7112	601	8	]	]	X
ejpam-7112	601	9	assures	assure	VERB
ejpam-7112	601	10	smallest	small	ADJ
ejpam-7112	601	11	aed	aed	NOUN
ejpam-7112	601	12	than	than	ADP
ejpam-7112	601	13	what	what	PRON
ejpam-7112	601	14	was	be	AUX
ejpam-7112	601	15	expected	expect	VERB
ejpam-7112	601	16	in	in	ADP
ejpam-7112	601	17	single	single	ADJ
ejpam-7112	601	18	strip	strip	NOUN
ejpam-7112	601	19	,	,	PUNCT
ejpam-7112	601	20	but	but	CCONJ
ejpam-7112	601	21	then	then	ADV
ejpam-7112	601	22	the	the	DET
ejpam-7112	601	23	aeds	aed	NOUN
ejpam-7112	601	24	do	do	AUX
ejpam-7112	601	25	not	not	PART
ejpam-7112	601	26	get	get	VERB
ejpam-7112	601	27	smaller	small	ADJ
ejpam-7112	601	28	rapidly	rapidly	ADV
ejpam-7112	601	29	since	since	SCONJ
ejpam-7112	601	30	we	we	PRON
ejpam-7112	601	31	used	use	VERB
ejpam-7112	601	32	double	double	ADJ
ejpam-7112	601	33	precision	precision	NOUN
ejpam-7112	601	34	default	default	NOUN
ejpam-7112	601	35	in	in	ADP
ejpam-7112	601	36	matlab	matlab	PROPN
ejpam-7112	601	37	.	.	PUNCT
ejpam-7112	602	1	to	to	PART
ejpam-7112	602	2	avoid	avoid	VERB
ejpam-7112	602	3	the	the	DET
ejpam-7112	602	4	distrubance	distrubance	NOUN
ejpam-7112	602	5	in	in	ADP
ejpam-7112	602	6	results	result	NOUN
ejpam-7112	602	7	due	due	ADP
ejpam-7112	602	8	to	to	ADP
ejpam-7112	602	9	zct	zct	NOUN
ejpam-7112	602	10	oscillations	oscillation	NOUN
ejpam-7112	602	11	in	in	ADP
ejpam-7112	602	12	decreasing	decrease	VERB
ejpam-7112	602	13	errors	error	NOUN
ejpam-7112	602	14	,	,	PUNCT
ejpam-7112	602	15	the	the	DET
ejpam-7112	602	16	aeds	aed	NOUN
ejpam-7112	602	17	for	for	ADP
ejpam-7112	602	18	examples	example	NOUN
ejpam-7112	602	19	1	1	NUM
ejpam-7112	602	20	-	-	SYM
ejpam-7112	602	21	5	5	NUM
ejpam-7112	602	22	are	be	AUX
ejpam-7112	602	23	also	also	ADV
ejpam-7112	602	24	displayed	display	VERB
ejpam-7112	602	25	in	in	ADP
ejpam-7112	602	26	figs	fig	NOUN
ejpam-7112	602	27	.	.	PUNCT
ejpam-7112	603	1	(	(	PUNCT
ejpam-7112	603	2	8)-(12	8)-(12	NUM
ejpam-7112	603	3	)	)	PUNCT
ejpam-7112	603	4	without	without	ADP
ejpam-7112	603	5	the	the	DET
ejpam-7112	603	6	zct	zct	NOUN
ejpam-7112	603	7	errors	error	NOUN
ejpam-7112	603	8	.	.	PUNCT
ejpam-7112	604	1	the	the	DET
ejpam-7112	604	2	figs	fig	NOUN
ejpam-7112	604	3	.	.	PUNCT
ejpam-7112	605	1	(	(	PUNCT
ejpam-7112	605	2	8)-(12	8)-(12	X
ejpam-7112	605	3	)	)	PUNCT
ejpam-7112	605	4	provide	provide	VERB
ejpam-7112	605	5	more	more	ADV
ejpam-7112	605	6	comprehensive	comprehensive	ADJ
ejpam-7112	605	7	and	and	CCONJ
ejpam-7112	605	8	clearer	clear	ADJ
ejpam-7112	605	9	picture	picture	NOUN
ejpam-7112	605	10	of	of	ADP
ejpam-7112	605	11	the	the	DET
ejpam-7112	605	12	performance	performance	NOUN
ejpam-7112	605	13	of	of	ADP
ejpam-7112	605	14	the	the	DET
ejpam-7112	605	15	new	new	ADJ
ejpam-7112	605	16	proposed	propose	VERB
ejpam-7112	605	17	rules	rule	NOUN
ejpam-7112	605	18	with	with	ADP
ejpam-7112	605	19	each	each	DET
ejpam-7112	605	20	other	other	ADJ
ejpam-7112	605	21	and	and	CCONJ
ejpam-7112	605	22	the	the	DET
ejpam-7112	605	23	ct	ct	NOUN
ejpam-7112	605	24	in	in	ADP
ejpam-7112	605	25	terms	term	NOUN
ejpam-7112	605	26	of	of	ADP
ejpam-7112	605	27	decreasing	decrease	VERB
ejpam-7112	605	28	aeds	aed	NOUN
ejpam-7112	605	29	.	.	PUNCT
ejpam-7112	606	1	table	table	NOUN
ejpam-7112	606	2	(	(	PUNCT
ejpam-7112	606	3	1	1	NUM
ejpam-7112	606	4	)	)	PUNCT
ejpam-7112	606	5	summarizes	summarize	NOUN
ejpam-7112	606	6	quadrature	quadrature	NOUN
ejpam-7112	606	7	results	result	NOUN
ejpam-7112	606	8	for	for	ADP
ejpam-7112	606	9	problems	problem	NOUN
ejpam-7112	606	10	1	1	NUM
ejpam-7112	606	11	-	-	SYM
ejpam-7112	606	12	5	5	NUM
ejpam-7112	606	13	and	and	CCONJ
ejpam-7112	606	14	corresponding	correspond	VERB
ejpam-7112	606	15	aeds	aed	NOUN
ejpam-7112	606	16	at	at	ADP
ejpam-7112	606	17	the	the	DET
ejpam-7112	606	18	final	final	ADJ
ejpam-7112	606	19	integration	integration	NOUN
ejpam-7112	606	20	strip	strip	NOUN
ejpam-7112	606	21	,	,	PUNCT
ejpam-7112	606	22	which	which	PRON
ejpam-7112	606	23	evidently	evidently	ADV
ejpam-7112	606	24	confirms	confirm	VERB
ejpam-7112	606	25	that	that	SCONJ
ejpam-7112	606	26	the	the	DET
ejpam-7112	606	27	proposed	propose	VERB
ejpam-7112	606	28	quadrature	quadrature	NOUN
ejpam-7112	606	29	assures	assure	VERB
ejpam-7112	606	30	smaller	small	ADJ
ejpam-7112	606	31	aeds	aed	NOUN
ejpam-7112	606	32	against	against	ADP
ejpam-7112	606	33	zct	zct	NOUN
ejpam-7112	606	34	and	and	CCONJ
ejpam-7112	606	35	ct	ct	NUM
ejpam-7112	606	36	in	in	ADP
ejpam-7112	606	37	all	all	DET
ejpam-7112	606	38	problems	problem	NOUN
ejpam-7112	606	39	taken	take	VERB
ejpam-7112	606	40	;	;	PUNCT
ejpam-7112	606	41	the	the	DET
ejpam-7112	606	42	cmct	cmct	ADJ
ejpam-7112	606	43	quadrature	quadrature	NOUN
ejpam-7112	606	44	being	be	AUX
ejpam-7112	606	45	the	the	DET
ejpam-7112	606	46	best	good	ADJ
ejpam-7112	606	47	in	in	ADP
ejpam-7112	606	48	problems	problem	NOUN
ejpam-7112	606	49	1	1	NUM
ejpam-7112	606	50	-	-	SYM
ejpam-7112	606	51	3	3	NUM
ejpam-7112	606	52	.	.	PUNCT
ejpam-7112	607	1	the	the	DET
ejpam-7112	607	2	results	result	NOUN
ejpam-7112	607	3	of	of	ADP
ejpam-7112	607	4	mzct	mzct	NOUN
ejpam-7112	607	5	quadrature	quadrature	NOUN
ejpam-7112	607	6	[	[	X
ejpam-7112	607	7	22	22	NUM
ejpam-7112	607	8	]	]	PUNCT
ejpam-7112	607	9	are	be	AUX
ejpam-7112	607	10	pretty	pretty	ADV
ejpam-7112	607	11	inclined	inclined	ADJ
ejpam-7112	607	12	near	near	ADP
ejpam-7112	607	13	the	the	DET
ejpam-7112	607	14	proposed	propose	VERB
ejpam-7112	607	15	quadrature	quadrature	NOUN
ejpam-7112	607	16	for	for	ADP
ejpam-7112	607	17	problems	problem	NOUN
ejpam-7112	607	18	1	1	NUM
ejpam-7112	607	19	-	-	SYM
ejpam-7112	607	20	3	3	NUM
ejpam-7112	607	21	,	,	PUNCT
ejpam-7112	607	22	but	but	CCONJ
ejpam-7112	607	23	the	the	DET
ejpam-7112	607	24	default	default	NOUN
ejpam-7112	607	25	double	double	ADJ
ejpam-7112	607	26	precision	precision	NOUN
ejpam-7112	607	27	limit	limit	NOUN
ejpam-7112	607	28	in	in	ADP
ejpam-7112	607	29	problems	problem	NOUN
ejpam-7112	607	30	4	4	NUM
ejpam-7112	607	31	-	-	SYM
ejpam-7112	607	32	5	5	NUM
ejpam-7112	607	33	restricts	restrict	VERB
ejpam-7112	607	34	mzct	mzct	NOUN
ejpam-7112	607	35	quadrature	quadrature	NOUN
ejpam-7112	607	36	to	to	PART
ejpam-7112	607	37	rapidly	rapidly	ADV
ejpam-7112	607	38	reduce	reduce	VERB
ejpam-7112	607	39	errors	error	NOUN
ejpam-7112	607	40	ahead	ahead	ADV
ejpam-7112	607	41	.	.	PUNCT
ejpam-7112	608	1	hence	hence	ADV
ejpam-7112	608	2	,	,	PUNCT
ejpam-7112	608	3	the	the	DET
ejpam-7112	608	4	proposed	propose	VERB
ejpam-7112	608	5	quadrature	quadrature	NOUN
ejpam-7112	608	6	exhibit	exhibit	VERB
ejpam-7112	608	7	stable	stable	ADJ
ejpam-7112	608	8	pattern	pattern	NOUN
ejpam-7112	608	9	of	of	ADP
ejpam-7112	608	10	aeds	aed	NOUN
ejpam-7112	608	11	.	.	PUNCT
ejpam-7112	609	1	in	in	ADP
ejpam-7112	609	2	tables	table	NOUN
ejpam-7112	609	3	(	(	PUNCT
ejpam-7112	609	4	2)-(6	2)-(6	NUM
ejpam-7112	609	5	)	)	PUNCT
ejpam-7112	609	6	,	,	PUNCT
ejpam-7112	609	7	we	we	PRON
ejpam-7112	609	8	present	present	VERB
ejpam-7112	609	9	the	the	DET
ejpam-7112	609	10	computational	computational	ADJ
ejpam-7112	609	11	/	/	SYM
ejpam-7112	609	12	observed	observe	VERB
ejpam-7112	609	13	results	result	NOUN
ejpam-7112	609	14	on	on	ADP
ejpam-7112	609	15	the	the	DET
ejpam-7112	609	16	orders	order	NOUN
ejpam-7112	609	17	of	of	ADP
ejpam-7112	609	18	exactness	exactness	NOUN
ejpam-7112	609	19	/	/	SYM
ejpam-7112	609	20	accuracy	accuracy	NOUN
ejpam-7112	609	21	for	for	ADP
ejpam-7112	609	22	all	all	DET
ejpam-7112	609	23	used	use	VERB
ejpam-7112	609	24	quadrature	quadrature	NOUN
ejpam-7112	609	25	for	for	ADP
ejpam-7112	609	26	the	the	DET
ejpam-7112	609	27	case	case	NOUN
ejpam-7112	609	28	of	of	ADP
ejpam-7112	609	29	problems	problem	NOUN
ejpam-7112	609	30	1	1	NUM
ejpam-7112	609	31	-	-	SYM
ejpam-7112	609	32	5	5	NUM
ejpam-7112	609	33	through	through	ADP
ejpam-7112	609	34	the	the	DET
ejpam-7112	609	35	methodology	methodology	NOUN
ejpam-7112	609	36	described	describe	VERB
ejpam-7112	609	37	in	in	ADP
ejpam-7112	609	38	[	[	X
ejpam-7112	609	39	22	22	NUM
ejpam-7112	609	40	]	]	PUNCT
ejpam-7112	609	41	.	.	PUNCT
ejpam-7112	610	1	for	for	ADP
ejpam-7112	610	2	the	the	DET
ejpam-7112	610	3	case	case	NOUN
ejpam-7112	610	4	of	of	ADP
ejpam-7112	610	5	zct	zct	NOUN
ejpam-7112	610	6	quadrature	quadrature	NOUN
ejpam-7112	610	7	with	with	ADP
ejpam-7112	610	8	reference	reference	NOUN
ejpam-7112	610	9	to	to	ADP
ejpam-7112	610	10	the	the	DET
ejpam-7112	610	11	tables	table	NOUN
ejpam-7112	610	12	(	(	PUNCT
ejpam-7112	610	13	2)-(4	2)-(4	NUM
ejpam-7112	610	14	)	)	PUNCT
ejpam-7112	610	15	,	,	PUNCT
ejpam-7112	610	16	the	the	DET
ejpam-7112	610	17	numerical	numerical	ADJ
ejpam-7112	610	18	results	result	NOUN
ejpam-7112	610	19	on	on	ADP
ejpam-7112	610	20	order	order	NOUN
ejpam-7112	610	21	of	of	ADP
ejpam-7112	610	22	exactness	exactness	NOUN
ejpam-7112	610	23	are	be	AUX
ejpam-7112	610	24	not	not	PART
ejpam-7112	610	25	in	in	ADP
ejpam-7112	610	26	line	line	NOUN
ejpam-7112	610	27	with	with	ADP
ejpam-7112	610	28	what	what	PRON
ejpam-7112	610	29	was	be	AUX
ejpam-7112	610	30	expected	expect	VERB
ejpam-7112	610	31	through	through	ADP
ejpam-7112	610	32	[	[	X
ejpam-7112	610	33	5	5	NUM
ejpam-7112	610	34	]	]	PUNCT
ejpam-7112	610	35	.	.	PUNCT
ejpam-7112	611	1	however	however	ADV
ejpam-7112	611	2	,	,	PUNCT
ejpam-7112	611	3	the	the	DET
ejpam-7112	611	4	mzct	mzct	NOUN
ejpam-7112	611	5	and	and	CCONJ
ejpam-7112	611	6	all	all	DET
ejpam-7112	611	7	the	the	DET
ejpam-7112	611	8	proposed	propose	VERB
ejpam-7112	611	9	quadrature	quadrature	NOUN
ejpam-7112	611	10	results	result	NOUN
ejpam-7112	611	11	tend	tend	VERB
ejpam-7112	611	12	to	to	ADP
ejpam-7112	611	13	the	the	DET
ejpam-7112	611	14	expected	expect	VERB
ejpam-7112	611	15	theoretical	theoretical	ADJ
ejpam-7112	611	16	results	result	NOUN
ejpam-7112	611	17	.	.	PUNCT
ejpam-7112	612	1	the	the	DET
ejpam-7112	612	2	mzct	mzct	NOUN
ejpam-7112	612	3	quadrature	quadrature	NOUN
ejpam-7112	612	4	results	result	NOUN
ejpam-7112	612	5	on	on	ADP
ejpam-7112	612	6	numerical	numerical	ADJ
ejpam-7112	612	7	order	order	NOUN
ejpam-7112	612	8	of	of	ADP
ejpam-7112	612	9	accuracy	accuracy	NOUN
ejpam-7112	612	10	can	can	AUX
ejpam-7112	612	11	not	not	PART
ejpam-7112	612	12	be	be	AUX
ejpam-7112	612	13	actualized	actualize	VERB
ejpam-7112	612	14	because	because	SCONJ
ejpam-7112	612	15	of	of	ADP
ejpam-7112	612	16	precision	precision	NOUN
ejpam-7112	612	17	limits	limit	NOUN
ejpam-7112	612	18	in	in	ADP
ejpam-7112	612	19	the	the	DET
ejpam-7112	612	20	case	case	NOUN
ejpam-7112	612	21	of	of	ADP
ejpam-7112	612	22	problems	problem	NOUN
ejpam-7112	612	23	4	4	NUM
ejpam-7112	612	24	-	-	SYM
ejpam-7112	612	25	5	5	NUM
ejpam-7112	612	26	;	;	PUNCT
ejpam-7112	612	27	act	act	VERB
ejpam-7112	612	28	quadrature	quadrature	NOUN
ejpam-7112	612	29	also	also	ADV
ejpam-7112	612	30	did	do	AUX
ejpam-7112	612	31	not	not	PART
ejpam-7112	612	32	result	result	VERB
ejpam-7112	612	33	in	in	ADP
ejpam-7112	612	34	expected	expect	VERB
ejpam-7112	612	35	accuracy	accuracy	NOUN
ejpam-7112	612	36	in	in	ADP
ejpam-7112	612	37	[	[	X
ejpam-7112	612	38	5	5	NUM
ejpam-7112	612	39	]	]	PUNCT
ejpam-7112	612	40	.	.	PUNCT
ejpam-7112	613	1	on	on	ADP
ejpam-7112	613	2	the	the	DET
ejpam-7112	613	3	other	other	ADJ
ejpam-7112	613	4	hand	hand	NOUN
ejpam-7112	613	5	,	,	PUNCT
ejpam-7112	613	6	all	all	DET
ejpam-7112	613	7	the	the	DET
ejpam-7112	613	8	proposed	propose	VERB
ejpam-7112	613	9	quadrature	quadrature	NOUN
ejpam-7112	613	10	actualize	actualize	VERB
ejpam-7112	613	11	the	the	DET
ejpam-7112	613	12	theoretically	theoretically	ADV
ejpam-7112	613	13	expected	expect	VERB
ejpam-7112	613	14	results	result	NOUN
ejpam-7112	613	15	in	in	ADP
ejpam-7112	613	16	terms	term	NOUN
ejpam-7112	613	17	of	of	ADP
ejpam-7112	613	18	the	the	DET
ejpam-7112	613	19	numerical	numerical	ADJ
ejpam-7112	613	20	results	result	NOUN
ejpam-7112	613	21	presented	present	VERB
ejpam-7112	613	22	in	in	ADP
ejpam-7112	613	23	tables	table	NOUN
ejpam-7112	613	24	(	(	PUNCT
ejpam-7112	613	25	2)-(6	2)-(6	NUM
ejpam-7112	613	26	)	)	PUNCT
ejpam-7112	613	27	,	,	PUNCT
ejpam-7112	613	28	with	with	ADP
ejpam-7112	613	29	the	the	DET
ejpam-7112	613	30	only	only	ADJ
ejpam-7112	613	31	exception	exception	NOUN
ejpam-7112	613	32	of	of	ADP
ejpam-7112	613	33	the	the	DET
ejpam-7112	613	34	two	two	NUM
ejpam-7112	613	35	:	:	PUNCT
ejpam-7112	613	36	gmct	gmct	ADJ
ejpam-7112	613	37	and	and	CCONJ
ejpam-7112	613	38	hemct	hemct	ADJ
ejpam-7112	613	39	for	for	ADP
ejpam-7112	613	40	the	the	DET
ejpam-7112	613	41	problem	problem	NOUN
ejpam-7112	613	42	5	5	NUM
ejpam-7112	613	43	alone	alone	ADJ
ejpam-7112	613	44	through	through	ADP
ejpam-7112	613	45	table	table	NOUN
ejpam-7112	613	46	6	6	NUM
ejpam-7112	613	47	.	.	PUNCT
ejpam-7112	614	1	the	the	DET
ejpam-7112	614	2	exception	exception	NOUN
ejpam-7112	614	3	is	be	AUX
ejpam-7112	614	4	result	result	NOUN
ejpam-7112	614	5	of	of	ADP
ejpam-7112	614	6	the	the	DET
ejpam-7112	614	7	fact	fact	NOUN
ejpam-7112	614	8	that	that	SCONJ
ejpam-7112	614	9	these	these	DET
ejpam-7112	614	10	two	two	NUM
ejpam-7112	614	11	rules	rule	NOUN
ejpam-7112	614	12	have	have	AUX
ejpam-7112	614	13	k.	k.	PROPN
ejpam-7112	614	14	memon	memon	PROPN
ejpam-7112	615	1	et	et	PROPN
ejpam-7112	615	2	al	al	PROPN
ejpam-7112	615	3	.	.	PUNCT
ejpam-7112	615	4	/	/	SYM
ejpam-7112	615	5	eur	eur	PROPN
ejpam-7112	615	6	.	.	PUNCT
ejpam-7112	616	1	j.	j.	PROPN
ejpam-7112	616	2	pure	pure	PROPN
ejpam-7112	616	3	appl	appl	PROPN
ejpam-7112	616	4	.	.	PROPN
ejpam-7112	616	5	math	math	PROPN
ejpam-7112	616	6	,	,	PUNCT
ejpam-7112	616	7	18	18	NUM
ejpam-7112	616	8	(	(	PUNCT
ejpam-7112	616	9	4	4	NUM
ejpam-7112	616	10	)	)	PUNCT
ejpam-7112	616	11	(	(	PUNCT
ejpam-7112	616	12	2025	2025	NUM
ejpam-7112	616	13	)	)	PUNCT
ejpam-7112	616	14	,	,	PUNCT
ejpam-7112	616	15	7112	7112	NUM
ejpam-7112	616	16	21	21	NUM
ejpam-7112	616	17	of	of	ADP
ejpam-7112	616	18	38	38	NUM
ejpam-7112	616	19	limitation	limitation	NOUN
ejpam-7112	616	20	for	for	ADP
ejpam-7112	616	21	the	the	DET
ejpam-7112	616	22	limits	limit	NOUN
ejpam-7112	616	23	of	of	ADP
ejpam-7112	616	24	integration	integration	NOUN
ejpam-7112	616	25	being	be	AUX
ejpam-7112	616	26	different	different	ADJ
ejpam-7112	616	27	signs	sign	NOUN
ejpam-7112	616	28	;	;	PUNCT
ejpam-7112	616	29	this	this	PRON
ejpam-7112	616	30	was	be	AUX
ejpam-7112	616	31	the	the	DET
ejpam-7112	616	32	case	case	NOUN
ejpam-7112	616	33	in	in	ADP
ejpam-7112	616	34	problem	problem	NOUN
ejpam-7112	616	35	5	5	NUM
ejpam-7112	616	36	.	.	PUNCT
ejpam-7112	616	37	similarly	similarly	ADV
ejpam-7112	616	38	,	,	PUNCT
ejpam-7112	616	39	there	there	PRON
ejpam-7112	616	40	is	be	VERB
ejpam-7112	616	41	an	an	DET
ejpam-7112	616	42	exception	exception	NOUN
ejpam-7112	616	43	for	for	ADP
ejpam-7112	616	44	the	the	DET
ejpam-7112	616	45	two	two	NUM
ejpam-7112	616	46	quadrature	quadrature	NOUN
ejpam-7112	616	47	formulae	formulae	NOUN
ejpam-7112	616	48	:	:	PUNCT
ejpam-7112	616	49	hmct	hmct	NOUN
ejpam-7112	616	50	and	and	CCONJ
ejpam-7112	616	51	cmct	cmct	VERB
ejpam-7112	616	52	for	for	ADP
ejpam-7112	616	53	the	the	DET
ejpam-7112	616	54	problem	problem	NOUN
ejpam-7112	616	55	5	5	NUM
ejpam-7112	616	56	as	as	SCONJ
ejpam-7112	616	57	zero	zero	NUM
ejpam-7112	616	58	denominators	denominator	NOUN
ejpam-7112	616	59	are	be	AUX
ejpam-7112	616	60	caused	cause	VERB
ejpam-7112	616	61	since	since	SCONJ
ejpam-7112	616	62	limits	limit	NOUN
ejpam-7112	616	63	add	add	VERB
ejpam-7112	616	64	to	to	ADP
ejpam-7112	616	65	zero	zero	NUM
ejpam-7112	616	66	,	,	PUNCT
ejpam-7112	616	67	but	but	CCONJ
ejpam-7112	616	68	only	only	ADV
ejpam-7112	616	69	for	for	ADP
ejpam-7112	616	70	odd	odd	ADJ
ejpam-7112	616	71	strips	strip	NOUN
ejpam-7112	616	72	.	.	PUNCT
ejpam-7112	617	1	both	both	CCONJ
ejpam-7112	617	2	the	the	DET
ejpam-7112	617	3	rules	rule	NOUN
ejpam-7112	617	4	are	be	AUX
ejpam-7112	617	5	applicable	applicable	ADJ
ejpam-7112	617	6	safely	safely	ADV
ejpam-7112	617	7	in	in	ADP
ejpam-7112	617	8	the	the	DET
ejpam-7112	617	9	alternate	alternate	ADJ
ejpam-7112	617	10	cases	case	NOUN
ejpam-7112	617	11	with	with	ADP
ejpam-7112	617	12	even	even	ADV
ejpam-7112	617	13	strips	strip	NOUN
ejpam-7112	617	14	.	.	PUNCT
ejpam-7112	618	1	we	we	PRON
ejpam-7112	618	2	highlight	highlight	VERB
ejpam-7112	618	3	that	that	SCONJ
ejpam-7112	618	4	the	the	DET
ejpam-7112	618	5	selection	selection	NOUN
ejpam-7112	618	6	of	of	ADP
ejpam-7112	618	7	numerical	numerical	ADJ
ejpam-7112	618	8	problems	problem	NOUN
ejpam-7112	618	9	in	in	ADP
ejpam-7112	618	10	this	this	DET
ejpam-7112	618	11	study	study	NOUN
ejpam-7112	618	12	was	be	AUX
ejpam-7112	618	13	done	do	VERB
ejpam-7112	618	14	in	in	ADP
ejpam-7112	618	15	the	the	DET
ejpam-7112	618	16	form	form	NOUN
ejpam-7112	618	17	of	of	ADP
ejpam-7112	618	18	problems	problem	NOUN
ejpam-7112	618	19	1	1	NUM
ejpam-7112	618	20	-	-	SYM
ejpam-7112	618	21	5	5	NUM
ejpam-7112	618	22	intentionally	intentionally	ADV
ejpam-7112	618	23	from	from	ADP
ejpam-7112	618	24	the	the	DET
ejpam-7112	618	25	literature	literature	NOUN
ejpam-7112	618	26	so	so	SCONJ
ejpam-7112	618	27	that	that	SCONJ
ejpam-7112	618	28	the	the	DET
ejpam-7112	618	29	best	good	ADJ
ejpam-7112	618	30	coverage	coverage	NOUN
ejpam-7112	618	31	of	of	ADP
ejpam-7112	618	32	use	use	NOUN
ejpam-7112	618	33	,	,	PUNCT
ejpam-7112	618	34	restrictions	restriction	NOUN
ejpam-7112	618	35	and	and	CCONJ
ejpam-7112	618	36	performance	performance	NOUN
ejpam-7112	618	37	of	of	ADP
ejpam-7112	618	38	all	all	DET
ejpam-7112	618	39	the	the	DET
ejpam-7112	618	40	quadrature	quadrature	NOUN
ejpam-7112	618	41	used	use	VERB
ejpam-7112	618	42	can	can	AUX
ejpam-7112	618	43	be	be	AUX
ejpam-7112	618	44	done	do	VERB
ejpam-7112	618	45	sufficiently	sufficiently	ADV
ejpam-7112	618	46	.	.	PUNCT
ejpam-7112	619	1	the	the	DET
ejpam-7112	619	2	quadrature	quadrature	NOUN
ejpam-7112	619	3	formulae	formulae	NOUN
ejpam-7112	619	4	in	in	ADP
ejpam-7112	619	5	the	the	DET
ejpam-7112	619	6	case	case	NOUN
ejpam-7112	619	7	compared	compare	VERB
ejpam-7112	619	8	previous	previous	ADJ
ejpam-7112	619	9	and	and	CCONJ
ejpam-7112	619	10	new	new	ADJ
ejpam-7112	619	11	rules	rule	NOUN
ejpam-7112	619	12	differ	differ	VERB
ejpam-7112	619	13	in	in	ADP
ejpam-7112	619	14	the	the	DET
ejpam-7112	619	15	fact	fact	NOUN
ejpam-7112	619	16	that	that	SCONJ
ejpam-7112	619	17	these	these	PRON
ejpam-7112	619	18	utilize	utilize	VERB
ejpam-7112	619	19	different	different	ADJ
ejpam-7112	619	20	information	information	NOUN
ejpam-7112	619	21	of	of	ADP
ejpam-7112	619	22	integrand	integrand	NOUN
ejpam-7112	619	23	and	and	CCONJ
ejpam-7112	619	24	integrator	integrator	NOUN
ejpam-7112	619	25	functions	function	NOUN
ejpam-7112	619	26	,	,	PUNCT
ejpam-7112	619	27	their	their	PRON
ejpam-7112	619	28	derivatives	derivative	NOUN
ejpam-7112	619	29	and	and	CCONJ
ejpam-7112	619	30	integrations	integration	NOUN
ejpam-7112	619	31	.	.	PUNCT
ejpam-7112	620	1	hence	hence	ADV
ejpam-7112	620	2	,	,	PUNCT
ejpam-7112	620	3	it	it	PRON
ejpam-7112	620	4	is	be	AUX
ejpam-7112	620	5	mandatory	mandatory	ADJ
ejpam-7112	620	6	to	to	PART
ejpam-7112	620	7	observe	observe	VERB
ejpam-7112	620	8	the	the	DET
ejpam-7112	620	9	computational	computational	ADJ
ejpam-7112	620	10	overhead	overhead	NOUN
ejpam-7112	620	11	/	/	PUNCT
ejpam-7112	620	12	cost	cost	NOUN
ejpam-7112	620	13	through	through	ADP
ejpam-7112	620	14	the	the	DET
ejpam-7112	620	15	information	information	NOUN
ejpam-7112	620	16	content	content	NOUN
ejpam-7112	620	17	used	use	VERB
ejpam-7112	620	18	in	in	ADP
ejpam-7112	620	19	the	the	DET
ejpam-7112	620	20	formulae	formulae	NOUN
ejpam-7112	620	21	and	and	CCONJ
ejpam-7112	620	22	also	also	ADV
ejpam-7112	620	23	discuss	discuss	VERB
ejpam-7112	620	24	the	the	DET
ejpam-7112	620	25	cpu	cpu	NOUN
ejpam-7112	620	26	usage	usage	NOUN
ejpam-7112	620	27	time	time	NOUN
ejpam-7112	620	28	(	(	PUNCT
ejpam-7112	620	29	in	in	ADP
ejpam-7112	620	30	seconds	second	NOUN
ejpam-7112	620	31	)	)	PUNCT
ejpam-7112	620	32	when	when	SCONJ
ejpam-7112	620	33	all	all	DET
ejpam-7112	620	34	the	the	DET
ejpam-7112	620	35	quadrature	quadrature	NOUN
ejpam-7112	620	36	formulae	formulae	NOUN
ejpam-7112	620	37	are	be	AUX
ejpam-7112	620	38	applied	apply	VERB
ejpam-7112	620	39	to	to	PART
ejpam-7112	620	40	solve	solve	VERB
ejpam-7112	620	41	problems	problem	NOUN
ejpam-7112	620	42	1	1	NUM
ejpam-7112	620	43	-	-	SYM
ejpam-7112	620	44	5	5	NUM
ejpam-7112	620	45	under	under	ADP
ejpam-7112	620	46	similar	similar	ADJ
ejpam-7112	620	47	conditions	condition	NOUN
ejpam-7112	620	48	to	to	PART
ejpam-7112	620	49	achieve	achieve	VERB
ejpam-7112	620	50	a	a	DET
ejpam-7112	620	51	given	give	VERB
ejpam-7112	620	52	error	error	NOUN
ejpam-7112	620	53	bound	bind	VERB
ejpam-7112	620	54	.	.	PUNCT
ejpam-7112	621	1	table	table	NOUN
ejpam-7112	621	2	(	(	PUNCT
ejpam-7112	621	3	7	7	X
ejpam-7112	621	4	)	)	PUNCT
ejpam-7112	621	5	presents	present	VERB
ejpam-7112	621	6	the	the	DET
ejpam-7112	621	7	distribution	distribution	NOUN
ejpam-7112	621	8	of	of	ADP
ejpam-7112	621	9	evaluations	evaluation	NOUN
ejpam-7112	621	10	in	in	ADP
ejpam-7112	621	11	the	the	DET
ejpam-7112	621	12	formulae	formulae	NOUN
ejpam-7112	621	13	of	of	ADP
ejpam-7112	621	14	all	all	DET
ejpam-7112	621	15	used	used	ADJ
ejpam-7112	621	16	quadrature	quadrature	NOUN
ejpam-7112	621	17	.	.	PUNCT
ejpam-7112	622	1	tables	table	NOUN
ejpam-7112	622	2	(	(	PUNCT
ejpam-7112	622	3	8)-(12	8)-(12	X
ejpam-7112	622	4	)	)	PUNCT
ejpam-7112	622	5	summarize	summarize	VERB
ejpam-7112	622	6	distribution	distribution	NOUN
ejpam-7112	622	7	of	of	ADP
ejpam-7112	622	8	computational	computational	ADJ
ejpam-7112	622	9	cost	cost	NOUN
ejpam-7112	622	10	for	for	ADP
ejpam-7112	622	11	all	all	DET
ejpam-7112	622	12	used	use	VERB
ejpam-7112	622	13	quadrature	quadrature	NOUN
ejpam-7112	622	14	when	when	SCONJ
ejpam-7112	622	15	the	the	DET
ejpam-7112	622	16	preset	preset	ADJ
ejpam-7112	622	17	error	error	NOUN
ejpam-7112	622	18	tolerance	tolerance	NOUN
ejpam-7112	622	19	was	be	AUX
ejpam-7112	622	20	kept	keep	VERB
ejpam-7112	622	21	at	at	ADP
ejpam-7112	622	22	10−5	10−5	NUM
ejpam-7112	622	23	for	for	ADP
ejpam-7112	622	24	problems	problem	NOUN
ejpam-7112	622	25	1	1	NUM
ejpam-7112	622	26	-	-	SYM
ejpam-7112	622	27	5	5	NUM
ejpam-7112	622	28	.	.	PUNCT
ejpam-7112	623	1	also	also	ADV
ejpam-7112	623	2	,	,	PUNCT
ejpam-7112	623	3	the	the	DET
ejpam-7112	623	4	net	net	ADJ
ejpam-7112	623	5	computational	computational	ADJ
ejpam-7112	623	6	costs	cost	NOUN
ejpam-7112	623	7	for	for	ADP
ejpam-7112	623	8	problems	problem	NOUN
ejpam-7112	623	9	1	1	NUM
ejpam-7112	623	10	-	-	SYM
ejpam-7112	623	11	5	5	NUM
ejpam-7112	623	12	are	be	AUX
ejpam-7112	623	13	displayed	display	VERB
ejpam-7112	623	14	in	in	ADP
ejpam-7112	623	15	tables	table	NOUN
ejpam-7112	623	16	(	(	PUNCT
ejpam-7112	623	17	8)-(12	8)-(12	NUM
ejpam-7112	623	18	)	)	PUNCT
ejpam-7112	623	19	.	.	PUNCT
ejpam-7112	624	1	the	the	DET
ejpam-7112	624	2	results	result	NOUN
ejpam-7112	624	3	in	in	ADP
ejpam-7112	624	4	tables	table	NOUN
ejpam-7112	624	5	(	(	PUNCT
ejpam-7112	624	6	8)-(12	8)-(12	NUM
ejpam-7112	624	7	)	)	PUNCT
ejpam-7112	624	8	and	and	CCONJ
ejpam-7112	624	9	corresponding	correspond	VERB
ejpam-7112	624	10	last	last	ADJ
ejpam-7112	624	11	columns	column	NOUN
ejpam-7112	624	12	in	in	ADP
ejpam-7112	624	13	these	these	PRON
ejpam-7112	624	14	highlight	highlight	VERB
ejpam-7112	624	15	the	the	DET
ejpam-7112	624	16	cost	cost	NOUN
ejpam-7112	624	17	effectiveness	effectiveness	NOUN
ejpam-7112	624	18	of	of	ADP
ejpam-7112	624	19	the	the	DET
ejpam-7112	624	20	proposed	propose	VERB
ejpam-7112	624	21	quadrature	quadrature	NOUN
ejpam-7112	624	22	formulae	formulae	NOUN
ejpam-7112	624	23	over	over	ADP
ejpam-7112	624	24	zct	zct	NOUN
ejpam-7112	624	25	,	,	PUNCT
ejpam-7112	624	26	ct	ct	PRON
ejpam-7112	624	27	and	and	CCONJ
ejpam-7112	624	28	mzct	mzct	NOUN
ejpam-7112	624	29	in	in	ADP
ejpam-7112	624	30	all	all	DET
ejpam-7112	624	31	problems	problem	NOUN
ejpam-7112	624	32	,	,	PUNCT
ejpam-7112	624	33	but	but	CCONJ
ejpam-7112	624	34	with	with	ADP
ejpam-7112	624	35	exception	exception	NOUN
ejpam-7112	624	36	for	for	ADP
ejpam-7112	624	37	for	for	ADP
ejpam-7112	624	38	gmct	gmct	ADJ
ejpam-7112	624	39	and	and	CCONJ
ejpam-7112	624	40	hemct	hemct	ADJ
ejpam-7112	624	41	quadrature	quadrature	NOUN
ejpam-7112	624	42	for	for	ADP
ejpam-7112	624	43	problem	problem	NOUN
ejpam-7112	624	44	5	5	NUM
ejpam-7112	624	45	only	only	ADV
ejpam-7112	624	46	.	.	PUNCT
ejpam-7112	625	1	from	from	ADP
ejpam-7112	625	2	tables	table	NOUN
ejpam-7112	625	3	(	(	PUNCT
ejpam-7112	625	4	11)-(12	11)-(12	NOUN
ejpam-7112	625	5	)	)	PUNCT
ejpam-7112	625	6	in	in	ADP
ejpam-7112	625	7	the	the	DET
ejpam-7112	625	8	case	case	NOUN
ejpam-7112	625	9	of	of	ADP
ejpam-7112	625	10	problems	problem	NOUN
ejpam-7112	625	11	4	4	NUM
ejpam-7112	625	12	-	-	SYM
ejpam-7112	625	13	5	5	NUM
ejpam-7112	625	14	,	,	PUNCT
ejpam-7112	625	15	it	it	PRON
ejpam-7112	625	16	is	be	AUX
ejpam-7112	625	17	again	again	ADV
ejpam-7112	625	18	reconfirmed	reconfirm	VERB
ejpam-7112	625	19	that	that	SCONJ
ejpam-7112	625	20	the	the	DET
ejpam-7112	625	21	zct	zct	NOUN
ejpam-7112	625	22	quadrature	quadrature	NOUN
ejpam-7112	625	23	is	be	AUX
ejpam-7112	625	24	not	not	PART
ejpam-7112	625	25	applicable	applicable	ADJ
ejpam-7112	625	26	;	;	PUNCT
ejpam-7112	625	27	the	the	DET
ejpam-7112	625	28	mzct	mzct	NOUN
ejpam-7112	625	29	quadrature	quadrature	NOUN
ejpam-7112	625	30	restrict	restrict	VERB
ejpam-7112	625	31	to	to	ADP
ejpam-7112	625	32	first	first	ADJ
ejpam-7112	625	33	strip	strip	NOUN
ejpam-7112	625	34	of	of	ADP
ejpam-7112	625	35	integration	integration	NOUN
ejpam-7112	625	36	only	only	ADV
ejpam-7112	625	37	and	and	CCONJ
ejpam-7112	625	38	all	all	DET
ejpam-7112	625	39	the	the	DET
ejpam-7112	625	40	new	new	ADJ
ejpam-7112	625	41	quadrature	quadrature	NOUN
ejpam-7112	625	42	show	show	VERB
ejpam-7112	625	43	better	well	ADJ
ejpam-7112	625	44	performance	performance	NOUN
ejpam-7112	625	45	for	for	ADP
ejpam-7112	625	46	the	the	DET
ejpam-7112	625	47	cost	cost	NOUN
ejpam-7112	625	48	efficiency	efficiency	NOUN
ejpam-7112	625	49	.	.	PUNCT
ejpam-7112	626	1	in	in	ADP
ejpam-7112	626	2	the	the	DET
ejpam-7112	626	3	same	same	ADJ
ejpam-7112	626	4	way	way	NOUN
ejpam-7112	626	5	to	to	PART
ejpam-7112	626	6	achieve	achieve	VERB
ejpam-7112	626	7	a	a	DET
ejpam-7112	626	8	preset	preset	ADJ
ejpam-7112	626	9	aed	aed	NOUN
ejpam-7112	626	10	of	of	ADP
ejpam-7112	626	11	at	at	ADV
ejpam-7112	626	12	most	most	ADJ
ejpam-7112	626	13	10−5	10−5	NUM
ejpam-7112	626	14	,	,	PUNCT
ejpam-7112	626	15	the	the	DET
ejpam-7112	626	16	performance	performance	NOUN
ejpam-7112	626	17	of	of	ADP
ejpam-7112	626	18	all	all	DET
ejpam-7112	626	19	the	the	DET
ejpam-7112	626	20	used	use	VERB
ejpam-7112	626	21	quadrature	quadrature	NOUN
ejpam-7112	626	22	was	be	AUX
ejpam-7112	626	23	tested	test	VERB
ejpam-7112	626	24	with	with	ADP
ejpam-7112	626	25	regards	regard	NOUN
ejpam-7112	626	26	to	to	ADP
ejpam-7112	626	27	the	the	DET
ejpam-7112	626	28	time	time	NOUN
ejpam-7112	626	29	efficiency	efficiency	NOUN
ejpam-7112	626	30	,	,	PUNCT
ejpam-7112	626	31	and	and	CCONJ
ejpam-7112	626	32	these	these	DET
ejpam-7112	626	33	results	result	NOUN
ejpam-7112	626	34	are	be	AUX
ejpam-7112	626	35	presented	present	VERB
ejpam-7112	626	36	in	in	ADP
ejpam-7112	626	37	table	table	NOUN
ejpam-7112	626	38	(	(	PUNCT
ejpam-7112	626	39	13	13	NUM
ejpam-7112	626	40	)	)	PUNCT
ejpam-7112	626	41	for	for	ADP
ejpam-7112	626	42	all	all	DET
ejpam-7112	626	43	problems	problem	NOUN
ejpam-7112	626	44	in	in	ADP
ejpam-7112	626	45	form	form	NOUN
ejpam-7112	626	46	of	of	ADP
ejpam-7112	626	47	execution	execution	NOUN
ejpam-7112	626	48	times	time	NOUN
ejpam-7112	626	49	(	(	PUNCT
ejpam-7112	626	50	in	in	ADP
ejpam-7112	626	51	seconds	second	NOUN
ejpam-7112	626	52	)	)	PUNCT
ejpam-7112	626	53	.	.	PUNCT
ejpam-7112	627	1	table	table	NOUN
ejpam-7112	627	2	13	13	NUM
ejpam-7112	627	3	highlights	highlight	NOUN
ejpam-7112	627	4	that	that	PRON
ejpam-7112	627	5	the	the	DET
ejpam-7112	627	6	amct	amct	ADJ
ejpam-7112	627	7	and	and	CCONJ
ejpam-7112	627	8	cmct	cmct	ADJ
ejpam-7112	627	9	quadrature	quadrature	NOUN
ejpam-7112	627	10	exhibit	exhibit	NOUN
ejpam-7112	627	11	smallest	small	ADJ
ejpam-7112	627	12	times	time	NOUN
ejpam-7112	627	13	mostly	mostly	ADV
ejpam-7112	627	14	,	,	PUNCT
ejpam-7112	627	15	except	except	SCONJ
ejpam-7112	627	16	for	for	ADP
ejpam-7112	627	17	problems	problem	NOUN
ejpam-7112	627	18	4	4	NUM
ejpam-7112	627	19	-	-	SYM
ejpam-7112	627	20	5	5	NUM
ejpam-7112	627	21	than	than	ADP
ejpam-7112	627	22	mzct	mzct	NOUN
ejpam-7112	627	23	quadrature	quadrature	NOUN
ejpam-7112	627	24	,	,	PUNCT
ejpam-7112	627	25	which	which	PRON
ejpam-7112	627	26	is	be	AUX
ejpam-7112	627	27	restricted	restrict	VERB
ejpam-7112	627	28	to	to	PART
ejpam-7112	627	29	frit	frit	VERB
ejpam-7112	627	30	strip	strip	PROPN
ejpam-7112	627	31	only	only	ADV
ejpam-7112	627	32	.	.	PUNCT
ejpam-7112	628	1	finally	finally	ADV
ejpam-7112	628	2	,	,	PUNCT
ejpam-7112	628	3	it	it	PRON
ejpam-7112	628	4	can	can	AUX
ejpam-7112	628	5	be	be	AUX
ejpam-7112	628	6	safely	safely	ADV
ejpam-7112	628	7	concluded	conclude	VERB
ejpam-7112	628	8	that	that	SCONJ
ejpam-7112	628	9	the	the	DET
ejpam-7112	628	10	proposed	propose	VERB
ejpam-7112	628	11	quadrature	quadrature	NOUN
ejpam-7112	628	12	exhibit	exhibit	VERB
ejpam-7112	628	13	encouraging	encouraging	ADJ
ejpam-7112	628	14	and	and	CCONJ
ejpam-7112	628	15	better	well	ADJ
ejpam-7112	628	16	performance	performance	NOUN
ejpam-7112	628	17	overall	overall	ADV
ejpam-7112	628	18	than	than	ADP
ejpam-7112	628	19	the	the	DET
ejpam-7112	628	20	previous	previous	ADJ
ejpam-7112	628	21	ct	ct	NOUN
ejpam-7112	628	22	and	and	CCONJ
ejpam-7112	628	23	zct	zct	NOUN
ejpam-7112	628	24	quadrature	quadrature	NOUN
ejpam-7112	628	25	.	.	PUNCT
ejpam-7112	629	1	k.	k.	PROPN
ejpam-7112	629	2	memon	memon	PROPN
ejpam-7112	629	3	et	et	PROPN
ejpam-7112	629	4	al	al	PROPN
ejpam-7112	629	5	.	.	PUNCT
ejpam-7112	629	6	/	/	SYM
ejpam-7112	629	7	eur	eur	PROPN
ejpam-7112	629	8	.	.	PUNCT
ejpam-7112	630	1	j.	j.	PROPN
ejpam-7112	630	2	pure	pure	PROPN
ejpam-7112	630	3	appl	appl	PROPN
ejpam-7112	630	4	.	.	PROPN
ejpam-7112	630	5	math	math	PROPN
ejpam-7112	630	6	,	,	PUNCT
ejpam-7112	630	7	18	18	NUM
ejpam-7112	630	8	(	(	PUNCT
ejpam-7112	630	9	4	4	NUM
ejpam-7112	630	10	)	)	PUNCT
ejpam-7112	630	11	(	(	PUNCT
ejpam-7112	630	12	2025	2025	NUM
ejpam-7112	630	13	)	)	PUNCT
ejpam-7112	630	14	,	,	PUNCT
ejpam-7112	630	15	7112	7112	NUM
ejpam-7112	630	16	22	22	NUM
ejpam-7112	630	17	of	of	ADP
ejpam-7112	630	18	38	38	NUM
ejpam-7112	630	19	table	table	NOUN
ejpam-7112	630	20	1	1	NUM
ejpam-7112	630	21	:	:	PUNCT
ejpam-7112	630	22	absolute	absolute	ADJ
ejpam-7112	630	23	errors	error	NOUN
ejpam-7112	630	24	are	be	AUX
ejpam-7112	630	25	compared	compare	VERB
ejpam-7112	630	26	to	to	ADP
ejpam-7112	630	27	all	all	DET
ejpam-7112	630	28	schemes	scheme	NOUN
ejpam-7112	630	29	for	for	ADP
ejpam-7112	630	30	examples	example	NOUN
ejpam-7112	630	31	1	1	NUM
ejpam-7112	630	32	-	-	SYM
ejpam-7112	630	33	5	5	NUM
ejpam-7112	630	34	trapezoid	trapezoid	ADJ
ejpam-7112	630	35	variant	variant	ADJ
ejpam-7112	630	36	example	example	NOUN
ejpam-7112	630	37	1	1	NUM
ejpam-7112	630	38	(	(	PUNCT
ejpam-7112	630	39	n	n	NOUN
ejpam-7112	630	40	=	=	SYM
ejpam-7112	630	41	50	50	NUM
ejpam-7112	630	42	)	)	PUNCT
ejpam-7112	630	43	example	example	NOUN
ejpam-7112	630	44	2	2	NUM
ejpam-7112	630	45	(	(	PUNCT
ejpam-7112	630	46	n	n	NOUN
ejpam-7112	630	47	=	=	SYM
ejpam-7112	630	48	200	200	NUM
ejpam-7112	630	49	)	)	PUNCT
ejpam-7112	630	50	example	example	NOUN
ejpam-7112	630	51	3	3	NUM
ejpam-7112	630	52	(	(	PUNCT
ejpam-7112	630	53	n	n	NOUN
ejpam-7112	630	54	=	=	SYM
ejpam-7112	630	55	50	50	NUM
ejpam-7112	630	56	)	)	PUNCT
ejpam-7112	630	57	example	example	NOUN
ejpam-7112	630	58	4	4	NUM
ejpam-7112	630	59	(	(	PUNCT
ejpam-7112	630	60	n	n	NOUN
ejpam-7112	630	61	=	=	SYM
ejpam-7112	630	62	50	50	NUM
ejpam-7112	630	63	)	)	PUNCT
ejpam-7112	630	64	example	example	NOUN
ejpam-7112	630	65	5	5	NUM
ejpam-7112	630	66	(	(	PUNCT
ejpam-7112	630	67	n	n	NOUN
ejpam-7112	630	68	=	=	SYM
ejpam-7112	630	69	50	50	NUM
ejpam-7112	630	70	)	)	PUNCT
ejpam-7112	630	71	ct	ct	PROPN
ejpam-7112	630	72	0.227486276308570	0.227486276308570	NUM
ejpam-7112	631	1	−59.655783853372625	−59.655783853372625	PROPN
ejpam-7112	631	2	187.4331788489458	187.4331788489458	NUM
ejpam-7112	631	3	−17.612760265633682	−17.612760265633682	PROPN
ejpam-7112	631	4	0.450095792679060	0.450095792679060	NUM
ejpam-7112	631	5	(	(	PUNCT
ejpam-7112	631	6	1.8974×	1.8974×	NUM
ejpam-7112	631	7	10−4	10−4	NUM
ejpam-7112	631	8	)	)	PUNCT
ejpam-7112	631	9	(	(	PUNCT
ejpam-7112	631	10	1.2428×	1.2428×	NUM
ejpam-7112	631	11	10−4	10−4	NUM
ejpam-7112	631	12	)	)	PUNCT
ejpam-7112	631	13	(	(	PUNCT
ejpam-7112	631	14	6.2474×	6.2474×	NOUN
ejpam-7112	631	15	10−3	10−3	NUM
ejpam-7112	631	16	)	)	PUNCT
ejpam-7112	631	17	(	(	PUNCT
ejpam-7112	631	18	3.9471×	3.9471×	NUM
ejpam-7112	631	19	10−3	10−3	NUM
ejpam-7112	631	20	)	)	PUNCT
ejpam-7112	631	21	(	(	PUNCT
ejpam-7112	631	22	5.8839×	5.8839×	NUM
ejpam-7112	631	23	10−4	10−4	NUM
ejpam-7112	631	24	)	)	PUNCT
ejpam-7112	631	25	zct	zct	NOUN
ejpam-7112	631	26	0.227524664135771	0.227524664135771	NUM
ejpam-7112	631	27	−59.655762104211938	−59.655762104211938	PROPN
ejpam-7112	631	28	187.4331788489458	187.4331788489458	NUM
ejpam-7112	631	29	−29.345389591343285	−29.345389591343285	PROPN
ejpam-7112	631	30	−1.30536248.6941216	−1.30536248.6941216	PROPN
ejpam-7112	631	31	(	(	PUNCT
ejpam-7112	631	32	1.5135×	1.5135×	NUM
ejpam-7112	631	33	10−4	10−4	NUM
ejpam-7112	631	34	)	)	PUNCT
ejpam-7112	631	35	(	(	PUNCT
ejpam-7112	631	36	1.4603×	1.4603×	PROPN
ejpam-7112	631	37	10−4	10−4	NUM
ejpam-7112	631	38	)	)	PUNCT
ejpam-7112	631	39	(	(	PUNCT
ejpam-7112	631	40	6.2474×	6.2474×	NOUN
ejpam-7112	631	41	10−3	10−3	NUM
ejpam-7112	631	42	)	)	PUNCT
ejpam-7112	631	43	(	(	PUNCT
ejpam-7112	631	44	1.1737×	1.1737×	NUM
ejpam-7112	631	45	10	10	NUM
ejpam-7112	631	46	+	+	NOUN
ejpam-7112	631	47	1	1	NUM
ejpam-7112	631	48	)	)	PUNCT
ejpam-7112	631	49	(	(	PUNCT
ejpam-7112	631	50	1.7549×	1.7549×	NUM
ejpam-7112	631	51	10	10	NUM
ejpam-7112	631	52	+	+	NOUN
ejpam-7112	631	53	0	0	NUM
ejpam-7112	631	54	)	)	PUNCT
ejpam-7112	631	55	mzct	mzct	NOUN
ejpam-7112	631	56	0.227676063572853	0.227676063572853	NUM
ejpam-7112	631	57	−59.655908136719574	−59.655908136719574	PROPN
ejpam-7112	631	58	1.874269314873392	1.874269314873392	NUM
ejpam-7112	631	59	−17.608813203268074	−17.608813203268074	PROPN
ejpam-7112	631	60	0.449507401824980	0.449507401824980	NUM
ejpam-7112	631	61	(	(	PUNCT
ejpam-7112	631	62	4.7442×	4.7442×	NUM
ejpam-7112	631	63	10−8	10−8	NUM
ejpam-7112	631	64	)	)	PUNCT
ejpam-7112	631	65	(	(	PUNCT
ejpam-7112	631	66	7.7648×	7.7648×	NUM
ejpam-7112	631	67	10−11	10−11	NUM
ejpam-7112	631	68	)	)	PUNCT
ejpam-7112	631	69	(	(	PUNCT
ejpam-7112	631	70	6.2473×	6.2473×	NOUN
ejpam-7112	631	71	10−8	10−8	NUM
ejpam-7112	631	72	)	)	PUNCT
ejpam-7112	631	73	(	(	PUNCT
ejpam-7112	631	74	1.9201×	1.9201×	NUM
ejpam-7112	631	75	10−15	10−15	NOUN
ejpam-7112	631	76	)	)	PUNCT
ejpam-7112	631	77	(	(	PUNCT
ejpam-7112	631	78	−7.1054×	−7.1054×	CCONJ
ejpam-7112	631	79	10−15	10−15	NOUN
ejpam-7112	631	80	)	)	PUNCT
ejpam-7112	631	81	amct	amct	VERB
ejpam-7112	631	82	0.227676057801290	0.227676057801290	NUM
ejpam-7112	631	83	−59.655908136739335	−59.655908136739335	PROPN
ejpam-7112	631	84	187.4269315224149	187.4269315224149	NUM
ejpam-7112	631	85	−17.608813463050069	−17.608813463050069	PROPN
ejpam-7112	631	86	0.449507451964994	0.449507451964994	NUM
ejpam-7112	631	87	(	(	PUNCT
ejpam-7112	631	88	4.1671×	4.1671×	NUM
ejpam-7112	631	89	10−8	10−8	NUM
ejpam-7112	631	90	)	)	PUNCT
ejpam-7112	631	91	(	(	PUNCT
ejpam-7112	631	92	9.7423×	9.7423×	NOUN
ejpam-7112	631	93	10−11	10−11	NUM
ejpam-7112	631	94	)	)	PUNCT
ejpam-7112	631	95	(	(	PUNCT
ejpam-7112	631	96	9.7549×	9.7549×	NOUN
ejpam-7112	631	97	10−8	10−8	NUM
ejpam-7112	631	98	)	)	PUNCT
ejpam-7112	631	99	(	(	PUNCT
ejpam-7112	631	100	2.5978×	2.5978×	NUM
ejpam-7112	631	101	10−7	10−7	NUM
ejpam-7112	631	102	)	)	PUNCT
ejpam-7112	631	103	(	(	PUNCT
ejpam-7112	631	104	5.0140×	5.0140×	NUM
ejpam-7112	631	105	10−8	10−8	NUM
ejpam-7112	631	106	)	)	PUNCT
ejpam-7112	631	107	gmct	gmct	ADJ
ejpam-7112	631	108	0.227676058321505	0.227676058321505	NUM
ejpam-7112	631	109	−59.655908136813444	−59.655908136813444	NOUN
ejpam-7112	631	110	187.4269315777802	187.4269315777802	NUM
ejpam-7112	631	111	−17.608807372830086	−17.608807372830086	NOUN
ejpam-7112	631	112	0.449086933331309	0.449086933331309	NUM
ejpam-7112	631	113	(	(	PUNCT
ejpam-7112	631	114	4.2191×	4.2191×	NUM
ejpam-7112	631	115	10−8	10−8	NUM
ejpam-7112	631	116	)	)	PUNCT
ejpam-7112	631	117	(	(	PUNCT
ejpam-7112	631	118	1.7153×	1.7153×	NOUN
ejpam-7112	631	119	10−10	10−10	NUM
ejpam-7112	631	120	)	)	PUNCT
ejpam-7112	631	121	(	(	PUNCT
ejpam-7112	631	122	1.5291×	1.5291×	NUM
ejpam-7112	631	123	10−7	10−7	NUM
ejpam-7112	631	124	)	)	PUNCT
ejpam-7112	631	125	(	(	PUNCT
ejpam-7112	631	126	5.8304×	5.8304×	NUM
ejpam-7112	631	127	10−6	10−6	NUM
ejpam-7112	631	128	)	)	PUNCT
ejpam-7112	631	129	(	(	PUNCT
ejpam-7112	631	130	4.2047×	4.2047×	PROPN
ejpam-7112	631	131	10−4	10−4	NUM
ejpam-7112	631	132	)	)	PUNCT
ejpam-7112	631	133	hamct	hamct	VERB
ejpam-7112	631	134	0.227676058841074	0.227676058841074	NUM
ejpam-7112	631	135	−59.655908136887568	−59.655908136887568	PROPN
ejpam-7112	631	136	187.4269316331454	187.4269316331454	NUM
ejpam-7112	631	137	−17.608805228593440	−17.608805228593440	PROPN
ejpam-7112	631	138	0.449508128616925	0.449508128616925	NUM
ejpam-7112	631	139	(	(	PUNCT
ejpam-7112	631	140	4.2710×	4.2710×	NOUN
ejpam-7112	631	141	10−8	10−8	NUM
ejpam-7112	631	142	)	)	PUNCT
ejpam-7112	631	143	(	(	PUNCT
ejpam-7112	631	144	2.4566×	2.4566×	NOUN
ejpam-7112	631	145	10−10	10−10	NUM
ejpam-7112	631	146	)	)	PUNCT
ejpam-7112	631	147	(	(	PUNCT
ejpam-7112	631	148	2.0828×	2.0828×	NUM
ejpam-7112	631	149	10−7	10−7	NUM
ejpam-7112	631	150	)	)	PUNCT
ejpam-7112	631	151	(	(	PUNCT
ejpam-7112	631	152	7.9747×	7.9747×	X
ejpam-7112	631	153	10−6	10−6	NUM
ejpam-7112	631	154	)	)	PUNCT
ejpam-7112	631	155	(	(	PUNCT
ejpam-7112	631	156	7.2679×	7.2679×	NUM
ejpam-7112	631	157	10−7	10−7	NUM
ejpam-7112	631	158	)	)	PUNCT
ejpam-7112	631	159	hemct	hemct	ADJ
ejpam-7112	631	160	0.227676057974770	0.227676057974770	NUM
ejpam-7112	631	161	−59.655908136764033	−59.655908136764033	VERB
ejpam-7112	631	162	187.4269315408704	187.4269315408704	NUM
ejpam-7112	631	163	−17.608811432976740	−17.608811432976740	NOUN
ejpam-7112	631	164	0.449367279087097	0.449367279087097	NUM
ejpam-7112	631	165	(	(	PUNCT
ejpam-7112	631	166	4.1844×	4.1844×	NOUN
ejpam-7112	631	167	10−8	10−8	NUM
ejpam-7112	631	168	)	)	PUNCT
ejpam-7112	631	169	(	(	PUNCT
ejpam-7112	631	170	1.2212×	1.2212×	NUM
ejpam-7112	631	171	10−10	10−10	NUM
ejpam-7112	631	172	)	)	PUNCT
ejpam-7112	631	173	(	(	PUNCT
ejpam-7112	631	174	1.1600×	1.1600×	NUM
ejpam-7112	631	175	10−7	10−7	NUM
ejpam-7112	631	176	)	)	PUNCT
ejpam-7112	631	177	(	(	PUNCT
ejpam-7112	631	178	1.7703×	1.7703×	NUM
ejpam-7112	631	179	10−6	10−6	NUM
ejpam-7112	631	180	)	)	PUNCT
ejpam-7112	631	181	(	(	PUNCT
ejpam-7112	631	182	1.4012×	1.4012×	NUM
ejpam-7112	631	183	10−4	10−4	NUM
ejpam-7112	631	184	)	)	PUNCT
ejpam-7112	631	185	cmct	cmct	NOUN
ejpam-7112	632	1	0.227676057454114	0.227676057454114	NUM
ejpam-7112	632	2	−59.655908136689931	−59.655908136689931	PROPN
ejpam-7112	632	3	187.4269314855043	187.4269314855043	NUM
ejpam-7112	633	1	−17.608816207868944	−17.608816207868944	PROPN
ejpam-7112	633	2	0.449507226414350	0.449507226414350	PROPN
ejpam-7112	633	3	(	(	PUNCT
ejpam-7112	633	4	4.1323×	4.1323×	NUM
ejpam-7112	633	5	10−8	10−8	NUM
ejpam-7112	633	6	)	)	PUNCT
ejpam-7112	633	7	(	(	PUNCT
ejpam-7112	633	8	4.8018×	4.8018×	NUM
ejpam-7112	633	9	10−11	10−11	NUM
ejpam-7112	633	10	)	)	PUNCT
ejpam-7112	633	11	(	(	PUNCT
ejpam-7112	633	12	6.0639×	6.0639×	NUM
ejpam-7112	633	13	10−8	10−8	NUM
ejpam-7112	633	14	)	)	PUNCT
ejpam-7112	633	15	(	(	PUNCT
ejpam-7112	633	16	3.0046×	3.0046×	NUM
ejpam-7112	633	17	10−6	10−6	NUM
ejpam-7112	633	18	)	)	PUNCT
ejpam-7112	633	19	(	(	PUNCT
ejpam-7112	633	20	1.7541×	1.7541×	PROPN
ejpam-7112	633	21	10−7	10−7	NUM
ejpam-7112	633	22	)	)	PUNCT
ejpam-7112	633	23	k.	k.	PROPN
ejpam-7112	634	1	memon	memon	PROPN
ejpam-7112	634	2	et	et	PROPN
ejpam-7112	634	3	al	al	PROPN
ejpam-7112	634	4	.	.	PUNCT
ejpam-7112	634	5	/	/	SYM
ejpam-7112	634	6	eur	eur	PROPN
ejpam-7112	634	7	.	.	PUNCT
ejpam-7112	635	1	j.	j.	PROPN
ejpam-7112	635	2	pure	pure	PROPN
ejpam-7112	635	3	appl	appl	PROPN
ejpam-7112	635	4	.	.	PROPN
ejpam-7112	635	5	math	math	PROPN
ejpam-7112	635	6	,	,	PUNCT
ejpam-7112	635	7	18	18	NUM
ejpam-7112	635	8	(	(	PUNCT
ejpam-7112	635	9	4	4	NUM
ejpam-7112	635	10	)	)	PUNCT
ejpam-7112	635	11	(	(	PUNCT
ejpam-7112	635	12	2025	2025	NUM
ejpam-7112	635	13	)	)	PUNCT
ejpam-7112	635	14	,	,	PUNCT
ejpam-7112	635	15	7112	7112	NUM
ejpam-7112	635	16	23	23	NUM
ejpam-7112	635	17	of	of	ADP
ejpam-7112	635	18	38	38	NUM
ejpam-7112	635	19	figure	figure	NOUN
ejpam-7112	635	20	3	3	NUM
ejpam-7112	635	21	:	:	PUNCT
ejpam-7112	635	22	distributions	distribution	NOUN
ejpam-7112	635	23	of	of	ADP
ejpam-7112	635	24	absolute	absolute	ADJ
ejpam-7112	635	25	-	-	PUNCT
ejpam-7112	635	26	error	error	NOUN
ejpam-7112	635	27	-	-	PUNCT
ejpam-7112	635	28	drops	drop	NOUN
ejpam-7112	635	29	in	in	ADP
ejpam-7112	635	30	example	example	NOUN
ejpam-7112	635	31	1	1	NUM
ejpam-7112	635	32	k.	k.	PROPN
ejpam-7112	635	33	memon	memon	PROPN
ejpam-7112	635	34	et	et	PROPN
ejpam-7112	635	35	al	al	PROPN
ejpam-7112	635	36	.	.	PUNCT
ejpam-7112	635	37	/	/	SYM
ejpam-7112	635	38	eur	eur	PROPN
ejpam-7112	635	39	.	.	PUNCT
ejpam-7112	636	1	j.	j.	PROPN
ejpam-7112	636	2	pure	pure	PROPN
ejpam-7112	636	3	appl	appl	PROPN
ejpam-7112	636	4	.	.	PROPN
ejpam-7112	636	5	math	math	PROPN
ejpam-7112	636	6	,	,	PUNCT
ejpam-7112	636	7	18	18	NUM
ejpam-7112	636	8	(	(	PUNCT
ejpam-7112	636	9	4	4	NUM
ejpam-7112	636	10	)	)	PUNCT
ejpam-7112	636	11	(	(	PUNCT
ejpam-7112	636	12	2025	2025	NUM
ejpam-7112	636	13	)	)	PUNCT
ejpam-7112	636	14	,	,	PUNCT
ejpam-7112	636	15	7112	7112	NUM
ejpam-7112	636	16	24	24	NUM
ejpam-7112	636	17	of	of	ADP
ejpam-7112	636	18	38	38	NUM
ejpam-7112	636	19	figure	figure	NOUN
ejpam-7112	636	20	4	4	NUM
ejpam-7112	636	21	:	:	PUNCT
ejpam-7112	636	22	distributions	distribution	NOUN
ejpam-7112	636	23	of	of	ADP
ejpam-7112	636	24	absolute	absolute	ADJ
ejpam-7112	636	25	-	-	PUNCT
ejpam-7112	636	26	error	error	NOUN
ejpam-7112	636	27	-	-	PUNCT
ejpam-7112	636	28	drops	drop	NOUN
ejpam-7112	636	29	in	in	ADP
ejpam-7112	636	30	example	example	NOUN
ejpam-7112	636	31	2	2	NUM
ejpam-7112	636	32	k.	k.	PROPN
ejpam-7112	636	33	memon	memon	PROPN
ejpam-7112	636	34	et	et	PROPN
ejpam-7112	636	35	al	al	PROPN
ejpam-7112	636	36	.	.	PUNCT
ejpam-7112	636	37	/	/	SYM
ejpam-7112	636	38	eur	eur	PROPN
ejpam-7112	636	39	.	.	PUNCT
ejpam-7112	637	1	j.	j.	PROPN
ejpam-7112	637	2	pure	pure	PROPN
ejpam-7112	637	3	appl	appl	PROPN
ejpam-7112	637	4	.	.	PROPN
ejpam-7112	637	5	math	math	PROPN
ejpam-7112	637	6	,	,	PUNCT
ejpam-7112	637	7	18	18	NUM
ejpam-7112	637	8	(	(	PUNCT
ejpam-7112	637	9	4	4	NUM
ejpam-7112	637	10	)	)	PUNCT
ejpam-7112	637	11	(	(	PUNCT
ejpam-7112	637	12	2025	2025	NUM
ejpam-7112	637	13	)	)	PUNCT
ejpam-7112	637	14	,	,	PUNCT
ejpam-7112	637	15	7112	7112	NUM
ejpam-7112	637	16	25	25	NUM
ejpam-7112	637	17	of	of	ADP
ejpam-7112	637	18	38	38	NUM
ejpam-7112	637	19	figure	figure	NOUN
ejpam-7112	637	20	5	5	NUM
ejpam-7112	637	21	:	:	PUNCT
ejpam-7112	637	22	distributions	distribution	NOUN
ejpam-7112	637	23	of	of	ADP
ejpam-7112	637	24	absolute	absolute	ADJ
ejpam-7112	637	25	-	-	PUNCT
ejpam-7112	637	26	error	error	NOUN
ejpam-7112	637	27	-	-	PUNCT
ejpam-7112	637	28	drops	drop	NOUN
ejpam-7112	637	29	in	in	ADP
ejpam-7112	637	30	example	example	NOUN
ejpam-7112	637	31	3	3	NUM
ejpam-7112	637	32	k.	k.	PROPN
ejpam-7112	637	33	memon	memon	PROPN
ejpam-7112	637	34	et	et	PROPN
ejpam-7112	637	35	al	al	PROPN
ejpam-7112	637	36	.	.	PUNCT
ejpam-7112	637	37	/	/	SYM
ejpam-7112	637	38	eur	eur	PROPN
ejpam-7112	637	39	.	.	PUNCT
ejpam-7112	638	1	j.	j.	PROPN
ejpam-7112	638	2	pure	pure	PROPN
ejpam-7112	638	3	appl	appl	PROPN
ejpam-7112	638	4	.	.	PROPN
ejpam-7112	638	5	math	math	PROPN
ejpam-7112	638	6	,	,	PUNCT
ejpam-7112	638	7	18	18	NUM
ejpam-7112	638	8	(	(	PUNCT
ejpam-7112	638	9	4	4	NUM
ejpam-7112	638	10	)	)	PUNCT
ejpam-7112	638	11	(	(	PUNCT
ejpam-7112	638	12	2025	2025	NUM
ejpam-7112	638	13	)	)	PUNCT
ejpam-7112	638	14	,	,	PUNCT
ejpam-7112	638	15	7112	7112	NUM
ejpam-7112	638	16	26	26	NUM
ejpam-7112	638	17	of	of	ADP
ejpam-7112	638	18	38	38	NUM
ejpam-7112	638	19	figure	figure	NOUN
ejpam-7112	638	20	6	6	NUM
ejpam-7112	638	21	:	:	PUNCT
ejpam-7112	638	22	distributions	distribution	NOUN
ejpam-7112	638	23	of	of	ADP
ejpam-7112	638	24	absolute	absolute	ADJ
ejpam-7112	638	25	-	-	PUNCT
ejpam-7112	638	26	error	error	NOUN
ejpam-7112	638	27	-	-	PUNCT
ejpam-7112	638	28	drops	drop	NOUN
ejpam-7112	638	29	in	in	ADP
ejpam-7112	638	30	example	example	NOUN
ejpam-7112	638	31	4	4	NUM
ejpam-7112	638	32	k.	k.	PROPN
ejpam-7112	638	33	memon	memon	PROPN
ejpam-7112	638	34	et	et	PROPN
ejpam-7112	638	35	al	al	PROPN
ejpam-7112	638	36	.	.	PUNCT
ejpam-7112	638	37	/	/	SYM
ejpam-7112	638	38	eur	eur	PROPN
ejpam-7112	638	39	.	.	PUNCT
ejpam-7112	639	1	j.	j.	PROPN
ejpam-7112	639	2	pure	pure	PROPN
ejpam-7112	639	3	appl	appl	PROPN
ejpam-7112	639	4	.	.	PROPN
ejpam-7112	639	5	math	math	PROPN
ejpam-7112	639	6	,	,	PUNCT
ejpam-7112	639	7	18	18	NUM
ejpam-7112	639	8	(	(	PUNCT
ejpam-7112	639	9	4	4	NUM
ejpam-7112	639	10	)	)	PUNCT
ejpam-7112	639	11	(	(	PUNCT
ejpam-7112	639	12	2025	2025	NUM
ejpam-7112	639	13	)	)	PUNCT
ejpam-7112	639	14	,	,	PUNCT
ejpam-7112	639	15	7112	7112	NUM
ejpam-7112	639	16	27	27	NUM
ejpam-7112	639	17	of	of	ADP
ejpam-7112	639	18	38	38	NUM
ejpam-7112	639	19	figure	figure	NOUN
ejpam-7112	639	20	7	7	NUM
ejpam-7112	639	21	:	:	PUNCT
ejpam-7112	639	22	distributions	distribution	NOUN
ejpam-7112	639	23	of	of	ADP
ejpam-7112	639	24	absolute	absolute	ADJ
ejpam-7112	639	25	-	-	PUNCT
ejpam-7112	639	26	error	error	NOUN
ejpam-7112	639	27	-	-	PUNCT
ejpam-7112	639	28	drops	drop	NOUN
ejpam-7112	639	29	in	in	ADP
ejpam-7112	639	30	example	example	NOUN
ejpam-7112	639	31	5	5	NUM
ejpam-7112	639	32	k.	k.	PROPN
ejpam-7112	639	33	memon	memon	PROPN
ejpam-7112	639	34	et	et	PROPN
ejpam-7112	639	35	al	al	PROPN
ejpam-7112	639	36	.	.	PUNCT
ejpam-7112	639	37	/	/	SYM
ejpam-7112	639	38	eur	eur	PROPN
ejpam-7112	639	39	.	.	PUNCT
ejpam-7112	640	1	j.	j.	PROPN
ejpam-7112	640	2	pure	pure	PROPN
ejpam-7112	640	3	appl	appl	PROPN
ejpam-7112	640	4	.	.	PROPN
ejpam-7112	640	5	math	math	PROPN
ejpam-7112	640	6	,	,	PUNCT
ejpam-7112	640	7	18	18	NUM
ejpam-7112	640	8	(	(	PUNCT
ejpam-7112	640	9	4	4	NUM
ejpam-7112	640	10	)	)	PUNCT
ejpam-7112	640	11	(	(	PUNCT
ejpam-7112	640	12	2025	2025	NUM
ejpam-7112	640	13	)	)	PUNCT
ejpam-7112	640	14	,	,	PUNCT
ejpam-7112	640	15	7112	7112	NUM
ejpam-7112	640	16	28	28	NUM
ejpam-7112	640	17	of	of	ADP
ejpam-7112	640	18	38	38	NUM
ejpam-7112	640	19	figure	figure	NOUN
ejpam-7112	640	20	8	8	NUM
ejpam-7112	640	21	:	:	PUNCT
ejpam-7112	640	22	distributions	distribution	NOUN
ejpam-7112	640	23	of	of	ADP
ejpam-7112	640	24	absolute	absolute	ADJ
ejpam-7112	640	25	-	-	PUNCT
ejpam-7112	640	26	error	error	NOUN
ejpam-7112	640	27	-	-	PUNCT
ejpam-7112	640	28	drops	drop	NOUN
ejpam-7112	640	29	without	without	ADP
ejpam-7112	640	30	zct	zct	NOUN
ejpam-7112	640	31	in	in	ADP
ejpam-7112	640	32	example	example	NOUN
ejpam-7112	640	33	1	1	NUM
ejpam-7112	640	34	k.	k.	PROPN
ejpam-7112	640	35	memon	memon	PROPN
ejpam-7112	640	36	et	et	PROPN
ejpam-7112	640	37	al	al	PROPN
ejpam-7112	640	38	.	.	PUNCT
ejpam-7112	640	39	/	/	SYM
ejpam-7112	640	40	eur	eur	PROPN
ejpam-7112	640	41	.	.	PUNCT
ejpam-7112	641	1	j.	j.	PROPN
ejpam-7112	641	2	pure	pure	PROPN
ejpam-7112	641	3	appl	appl	PROPN
ejpam-7112	641	4	.	.	PROPN
ejpam-7112	641	5	math	math	PROPN
ejpam-7112	641	6	,	,	PUNCT
ejpam-7112	641	7	18	18	NUM
ejpam-7112	641	8	(	(	PUNCT
ejpam-7112	641	9	4	4	NUM
ejpam-7112	641	10	)	)	PUNCT
ejpam-7112	641	11	(	(	PUNCT
ejpam-7112	641	12	2025	2025	NUM
ejpam-7112	641	13	)	)	PUNCT
ejpam-7112	641	14	,	,	PUNCT
ejpam-7112	641	15	7112	7112	NUM
ejpam-7112	641	16	29	29	NUM
ejpam-7112	641	17	of	of	ADP
ejpam-7112	641	18	38	38	NUM
ejpam-7112	641	19	figure	figure	NOUN
ejpam-7112	641	20	9	9	NUM
ejpam-7112	641	21	:	:	PUNCT
ejpam-7112	641	22	distributions	distribution	NOUN
ejpam-7112	641	23	of	of	ADP
ejpam-7112	641	24	absolute	absolute	ADJ
ejpam-7112	641	25	-	-	PUNCT
ejpam-7112	641	26	error	error	NOUN
ejpam-7112	641	27	-	-	PUNCT
ejpam-7112	641	28	drops	drop	NOUN
ejpam-7112	641	29	without	without	ADP
ejpam-7112	641	30	zct	zct	NOUN
ejpam-7112	641	31	in	in	ADP
ejpam-7112	641	32	example	example	NOUN
ejpam-7112	641	33	2	2	NUM
ejpam-7112	641	34	k.	k.	PROPN
ejpam-7112	641	35	memon	memon	PROPN
ejpam-7112	641	36	et	et	PROPN
ejpam-7112	641	37	al	al	PROPN
ejpam-7112	641	38	.	.	PUNCT
ejpam-7112	641	39	/	/	SYM
ejpam-7112	641	40	eur	eur	PROPN
ejpam-7112	641	41	.	.	PUNCT
ejpam-7112	642	1	j.	j.	PROPN
ejpam-7112	642	2	pure	pure	PROPN
ejpam-7112	642	3	appl	appl	PROPN
ejpam-7112	642	4	.	.	PROPN
ejpam-7112	642	5	math	math	PROPN
ejpam-7112	642	6	,	,	PUNCT
ejpam-7112	642	7	18	18	NUM
ejpam-7112	642	8	(	(	PUNCT
ejpam-7112	642	9	4	4	NUM
ejpam-7112	642	10	)	)	PUNCT
ejpam-7112	642	11	(	(	PUNCT
ejpam-7112	642	12	2025	2025	NUM
ejpam-7112	642	13	)	)	PUNCT
ejpam-7112	642	14	,	,	PUNCT
ejpam-7112	642	15	7112	7112	NUM
ejpam-7112	642	16	30	30	NUM
ejpam-7112	642	17	of	of	ADP
ejpam-7112	642	18	38	38	NUM
ejpam-7112	642	19	figure	figure	NOUN
ejpam-7112	642	20	10	10	NUM
ejpam-7112	642	21	:	:	PUNCT
ejpam-7112	642	22	distributions	distribution	NOUN
ejpam-7112	642	23	of	of	ADP
ejpam-7112	642	24	absolute	absolute	ADJ
ejpam-7112	642	25	-	-	PUNCT
ejpam-7112	642	26	error	error	NOUN
ejpam-7112	642	27	-	-	PUNCT
ejpam-7112	642	28	drops	drop	NOUN
ejpam-7112	642	29	without	without	ADP
ejpam-7112	642	30	zct	zct	NOUN
ejpam-7112	642	31	in	in	ADP
ejpam-7112	642	32	example	example	NOUN
ejpam-7112	642	33	3	3	NUM
ejpam-7112	642	34	k.	k.	PROPN
ejpam-7112	642	35	memon	memon	PROPN
ejpam-7112	642	36	et	et	PROPN
ejpam-7112	642	37	al	al	PROPN
ejpam-7112	642	38	.	.	PUNCT
ejpam-7112	642	39	/	/	SYM
ejpam-7112	642	40	eur	eur	PROPN
ejpam-7112	642	41	.	.	PUNCT
ejpam-7112	643	1	j.	j.	PROPN
ejpam-7112	643	2	pure	pure	PROPN
ejpam-7112	643	3	appl	appl	PROPN
ejpam-7112	643	4	.	.	PROPN
ejpam-7112	643	5	math	math	PROPN
ejpam-7112	643	6	,	,	PUNCT
ejpam-7112	643	7	18	18	NUM
ejpam-7112	643	8	(	(	PUNCT
ejpam-7112	643	9	4	4	NUM
ejpam-7112	643	10	)	)	PUNCT
ejpam-7112	643	11	(	(	PUNCT
ejpam-7112	643	12	2025	2025	NUM
ejpam-7112	643	13	)	)	PUNCT
ejpam-7112	643	14	,	,	PUNCT
ejpam-7112	643	15	7112	7112	NUM
ejpam-7112	643	16	31	31	NUM
ejpam-7112	643	17	of	of	ADP
ejpam-7112	643	18	38	38	NUM
ejpam-7112	643	19	figure	figure	NOUN
ejpam-7112	643	20	11	11	NUM
ejpam-7112	643	21	:	:	PUNCT
ejpam-7112	643	22	distributions	distribution	NOUN
ejpam-7112	643	23	of	of	ADP
ejpam-7112	643	24	absolute	absolute	ADJ
ejpam-7112	643	25	-	-	PUNCT
ejpam-7112	643	26	error	error	NOUN
ejpam-7112	643	27	-	-	PUNCT
ejpam-7112	643	28	drops	drop	NOUN
ejpam-7112	643	29	without	without	ADP
ejpam-7112	643	30	zct	zct	NOUN
ejpam-7112	643	31	in	in	ADP
ejpam-7112	643	32	example	example	NOUN
ejpam-7112	643	33	4	4	NUM
ejpam-7112	643	34	k.	k.	PROPN
ejpam-7112	643	35	memon	memon	PROPN
ejpam-7112	643	36	et	et	PROPN
ejpam-7112	643	37	al	al	PROPN
ejpam-7112	643	38	.	.	PUNCT
ejpam-7112	643	39	/	/	SYM
ejpam-7112	643	40	eur	eur	PROPN
ejpam-7112	643	41	.	.	PUNCT
ejpam-7112	644	1	j.	j.	PROPN
ejpam-7112	644	2	pure	pure	PROPN
ejpam-7112	644	3	appl	appl	PROPN
ejpam-7112	644	4	.	.	PROPN
ejpam-7112	644	5	math	math	PROPN
ejpam-7112	644	6	,	,	PUNCT
ejpam-7112	644	7	18	18	NUM
ejpam-7112	644	8	(	(	PUNCT
ejpam-7112	644	9	4	4	NUM
ejpam-7112	644	10	)	)	PUNCT
ejpam-7112	644	11	(	(	PUNCT
ejpam-7112	644	12	2025	2025	NUM
ejpam-7112	644	13	)	)	PUNCT
ejpam-7112	644	14	,	,	PUNCT
ejpam-7112	644	15	7112	7112	NUM
ejpam-7112	644	16	32	32	NUM
ejpam-7112	644	17	of	of	ADP
ejpam-7112	644	18	38	38	NUM
ejpam-7112	644	19	figure	figure	NOUN
ejpam-7112	644	20	12	12	NUM
ejpam-7112	644	21	:	:	PUNCT
ejpam-7112	644	22	distributions	distribution	NOUN
ejpam-7112	644	23	of	of	ADP
ejpam-7112	644	24	absolute	absolute	ADJ
ejpam-7112	644	25	-	-	PUNCT
ejpam-7112	644	26	error	error	NOUN
ejpam-7112	644	27	-	-	PUNCT
ejpam-7112	644	28	drops	drop	NOUN
ejpam-7112	644	29	without	without	ADP
ejpam-7112	644	30	zct	zct	NOUN
ejpam-7112	644	31	in	in	ADP
ejpam-7112	644	32	example	example	NOUN
ejpam-7112	644	33	5	5	NUM
ejpam-7112	644	34	table	table	NOUN
ejpam-7112	644	35	2	2	NUM
ejpam-7112	644	36	:	:	PUNCT
ejpam-7112	644	37	.	.	PUNCT
ejpam-7112	645	1	representation	representation	NOUN
ejpam-7112	645	2	of	of	ADP
ejpam-7112	645	3	the	the	DET
ejpam-7112	645	4	order	order	NOUN
ejpam-7112	645	5	of	of	ADP
ejpam-7112	645	6	accuracy	accuracy	NOUN
ejpam-7112	645	7	to	to	ADP
ejpam-7112	645	8	all	all	DET
ejpam-7112	645	9	schemes	scheme	NOUN
ejpam-7112	645	10	for	for	ADP
ejpam-7112	645	11	example	example	NOUN
ejpam-7112	645	12	1	1	NUM
ejpam-7112	645	13	m	m	NOUN
ejpam-7112	645	14	n	n	NUM
ejpam-7112	645	15	ct	ct	NOUN
ejpam-7112	645	16	zct	zct	NOUN
ejpam-7112	645	17	mzct	mzct	NOUN
ejpam-7112	645	18	amct	amct	VERB
ejpam-7112	645	19	gmct	gmct	ADJ
ejpam-7112	645	20	hamct	hamct	NOUN
ejpam-7112	645	21	hemct	hemct	ADJ
ejpam-7112	645	22	cmct	cmct	ADJ
ejpam-7112	645	23	1	1	NUM
ejpam-7112	645	24	1	1	NUM
ejpam-7112	645	25	na	na	NOUN
ejpam-7112	645	26	na	na	NOUN
ejpam-7112	645	27	na	na	INTJ
ejpam-7112	645	28	na	na	VERB
ejpam-7112	645	29	na	na	VERB
ejpam-7112	645	30	na	na	VERB
ejpam-7112	645	31	na	na	ADV
ejpam-7112	645	32	na	na	SYM
ejpam-7112	645	33	2	2	NUM
ejpam-7112	645	34	2	2	NUM
ejpam-7112	645	35	2.5728	2.5728	NUM
ejpam-7112	645	36	3.3788	3.3788	NUM
ejpam-7112	645	37	5.0724	5.0724	NUM
ejpam-7112	645	38	5.1766	5.1766	NUM
ejpam-7112	645	39	4.9006	4.9006	NUM
ejpam-7112	645	40	4.4721	4.4721	NUM
ejpam-7112	645	41	5.0970	5.0970	NUM
ejpam-7112	645	42	5.3064	5.3064	NUM
ejpam-7112	645	43	4	4	NUM
ejpam-7112	645	44	4	4	NUM
ejpam-7112	645	45	2.0420	2.0420	NUM
ejpam-7112	645	46	4.3106	4.3106	NUM
ejpam-7112	645	47	4.1474	4.1474	NUM
ejpam-7112	645	48	4.1447	4.1447	NUM
ejpam-7112	645	49	4.1338	4.1338	NUM
ejpam-7112	645	50	4.1124	4.1124	NUM
ejpam-7112	646	1	4.1422	4.1422	NUM
ejpam-7112	646	2	4.1459	4.1459	NUM
ejpam-7112	646	3	8	8	NUM
ejpam-7112	646	4	8	8	NUM
ejpam-7112	646	5	2.0091	2.0091	NUM
ejpam-7112	646	6	-0.8154	-0.8154	NOUN
ejpam-7112	646	7	4.0348	4.0348	NUM
ejpam-7112	646	8	4.0338	4.0338	NUM
ejpam-7112	646	9	4.0317	4.0317	NUM
ejpam-7112	646	10	4.0272	4.0272	NUM
ejpam-7112	646	11	4.0334	4.0334	NUM
ejpam-7112	646	12	4.0338	4.0338	NUM
ejpam-7112	646	13	16	16	NUM
ejpam-7112	646	14	16	16	NUM
ejpam-7112	646	15	2.0022	2.0022	NUM
ejpam-7112	646	16	2.1713	2.1713	NUM
ejpam-7112	646	17	4.0086	4.0086	NUM
ejpam-7112	646	18	4.0083	4.0083	NUM
ejpam-7112	647	1	4.0078	4.0078	NUM
ejpam-7112	647	2	4.0067	4.0067	NUM
ejpam-7112	647	3	4.0082	4.0082	NUM
ejpam-7112	647	4	4.0083	4.0083	NUM
ejpam-7112	647	5	32	32	NUM
ejpam-7112	647	6	32	32	NUM
ejpam-7112	647	7	2.0006	2.0006	NUM
ejpam-7112	647	8	3.2118	3.2118	NUM
ejpam-7112	647	9	4.0021	4.0021	NUM
ejpam-7112	647	10	4.0021	4.0021	NUM
ejpam-7112	647	11	4.0020	4.0020	NUM
ejpam-7112	647	12	4.0017	4.0017	NUM
ejpam-7112	647	13	4.0021	4.0021	NUM
ejpam-7112	647	14	4.0021	4.0021	NUM
ejpam-7112	647	15	64	64	NUM
ejpam-7112	647	16	64	64	NUM
ejpam-7112	647	17	2.0001	2.0001	NUM
ejpam-7112	647	18	1.1185	1.1185	NUM
ejpam-7112	647	19	4.0006	4.0006	NUM
ejpam-7112	647	20	4.0006	4.0006	NUM
ejpam-7112	648	1	4.0005	4.0005	NUM
ejpam-7112	648	2	4.0004	4.0004	NUM
ejpam-7112	648	3	4.0005	4.0005	NUM
ejpam-7112	648	4	4.0005	4.0005	NUM
ejpam-7112	648	5	k.	k.	PROPN
ejpam-7112	648	6	memon	memon	PROPN
ejpam-7112	648	7	et	et	PROPN
ejpam-7112	648	8	al	al	PROPN
ejpam-7112	648	9	.	.	PUNCT
ejpam-7112	648	10	/	/	SYM
ejpam-7112	648	11	eur	eur	PROPN
ejpam-7112	648	12	.	.	PUNCT
ejpam-7112	649	1	j.	j.	PROPN
ejpam-7112	649	2	pure	pure	PROPN
ejpam-7112	649	3	appl	appl	PROPN
ejpam-7112	649	4	.	.	PROPN
ejpam-7112	649	5	math	math	PROPN
ejpam-7112	649	6	,	,	PUNCT
ejpam-7112	649	7	18	18	NUM
ejpam-7112	649	8	(	(	PUNCT
ejpam-7112	649	9	4	4	NUM
ejpam-7112	649	10	)	)	PUNCT
ejpam-7112	649	11	(	(	PUNCT
ejpam-7112	649	12	2025	2025	NUM
ejpam-7112	649	13	)	)	PUNCT
ejpam-7112	649	14	,	,	PUNCT
ejpam-7112	649	15	7112	7112	NUM
ejpam-7112	649	16	33	33	NUM
ejpam-7112	649	17	of	of	ADP
ejpam-7112	649	18	38	38	NUM
ejpam-7112	649	19	table	table	NOUN
ejpam-7112	649	20	3	3	NUM
ejpam-7112	649	21	:	:	PUNCT
ejpam-7112	649	22	representation	representation	NOUN
ejpam-7112	649	23	of	of	ADP
ejpam-7112	649	24	the	the	DET
ejpam-7112	649	25	order	order	NOUN
ejpam-7112	649	26	of	of	ADP
ejpam-7112	649	27	accuracy	accuracy	NOUN
ejpam-7112	649	28	to	to	ADP
ejpam-7112	649	29	all	all	DET
ejpam-7112	649	30	schemes	scheme	NOUN
ejpam-7112	649	31	for	for	ADP
ejpam-7112	649	32	example	example	NOUN
ejpam-7112	649	33	2	2	NUM
ejpam-7112	649	34	m	m	NOUN
ejpam-7112	649	35	n	n	NUM
ejpam-7112	649	36	ct	ct	NOUN
ejpam-7112	649	37	zct	zct	NOUN
ejpam-7112	649	38	mzct	mzct	NOUN
ejpam-7112	649	39	amct	amct	VERB
ejpam-7112	649	40	gmct	gmct	ADJ
ejpam-7112	649	41	hamct	hamct	NOUN
ejpam-7112	649	42	hemct	hemct	ADJ
ejpam-7112	649	43	cmct	cmct	ADJ
ejpam-7112	649	44	5	5	NUM
ejpam-7112	649	45	5	5	NUM
ejpam-7112	649	46	na	na	NOUN
ejpam-7112	649	47	na	na	NOUN
ejpam-7112	649	48	na	na	NOUN
ejpam-7112	649	49	na	na	VERB
ejpam-7112	649	50	na	na	VERB
ejpam-7112	649	51	na	na	VERB
ejpam-7112	649	52	na	na	ADV
ejpam-7112	649	53	na	na	PART
ejpam-7112	649	54	10	10	NUM
ejpam-7112	649	55	10	10	NUM
ejpam-7112	649	56	2.0018	2.0018	NUM
ejpam-7112	649	57	1.9243	1.9243	NUM
ejpam-7112	649	58	4.0025	4.0025	NUM
ejpam-7112	649	59	4.0022	4.0022	NUM
ejpam-7112	649	60	4.0017	4.0017	NUM
ejpam-7112	649	61	4.0010	4.0010	NUM
ejpam-7112	649	62	4.0020	4.0020	NUM
ejpam-7112	649	63	4.0030	4.0030	NUM
ejpam-7112	649	64	20	20	NUM
ejpam-7112	649	65	20	20	NUM
ejpam-7112	649	66	2.0004	2.0004	NUM
ejpam-7112	649	67	2.4487	2.4487	NUM
ejpam-7112	649	68	4.0007	4.0007	NUM
ejpam-7112	649	69	4.0006	4.0006	NUM
ejpam-7112	649	70	4.0004	4.0004	NUM
ejpam-7112	649	71	4.0003	4.0003	NUM
ejpam-7112	649	72	4.0005	4.0005	NUM
ejpam-7112	649	73	4.0008	4.0008	NUM
ejpam-7112	649	74	40	40	NUM
ejpam-7112	649	75	40	40	NUM
ejpam-7112	649	76	2.0001	2.0001	NUM
ejpam-7112	649	77	2.3985	2.3985	NUM
ejpam-7112	649	78	4.0001	4.0001	NUM
ejpam-7112	649	79	4.0002	4.0002	NUM
ejpam-7112	649	80	4.0002	4.0002	NUM
ejpam-7112	649	81	4.0000	4.0000	NUM
ejpam-7112	649	82	4.0001	4.0001	NUM
ejpam-7112	649	83	4.0002	4.0002	NUM
ejpam-7112	649	84	80	80	NUM
ejpam-7112	649	85	80	80	NUM
ejpam-7112	649	86	2.0001	2.0001	NUM
ejpam-7112	649	87	1.4026	1.4026	NUM
ejpam-7112	649	88	4.0000	4.0000	NUM
ejpam-7112	649	89	4.0000	4.0000	NUM
ejpam-7112	649	90	4.0000	4.0000	NUM
ejpam-7112	649	91	4.0001	4.0001	NUM
ejpam-7112	649	92	4.0000	4.0000	NUM
ejpam-7112	650	1	4.0001	4.0001	NUM
ejpam-7112	650	2	160	160	NUM
ejpam-7112	650	3	160	160	NUM
ejpam-7112	650	4	2.0000	2.0000	NUM
ejpam-7112	650	5	2.4557	2.4557	NUM
ejpam-7112	650	6	3.9998	3.9998	NUM
ejpam-7112	650	7	4.0001	4.0001	NUM
ejpam-7112	650	8	4.0001	4.0001	NUM
ejpam-7112	650	9	4.0001	4.0001	NUM
ejpam-7112	650	10	4.0001	4.0001	NUM
ejpam-7112	650	11	4.0002	4.0002	NUM
ejpam-7112	650	12	table	table	NOUN
ejpam-7112	650	13	4	4	NUM
ejpam-7112	650	14	:	:	PUNCT
ejpam-7112	650	15	representation	representation	NOUN
ejpam-7112	650	16	of	of	ADP
ejpam-7112	650	17	the	the	DET
ejpam-7112	650	18	order	order	NOUN
ejpam-7112	650	19	of	of	ADP
ejpam-7112	650	20	accuracy	accuracy	NOUN
ejpam-7112	650	21	to	to	ADP
ejpam-7112	650	22	all	all	DET
ejpam-7112	650	23	schemes	scheme	NOUN
ejpam-7112	650	24	for	for	ADP
ejpam-7112	650	25	example	example	NOUN
ejpam-7112	650	26	3	3	NUM
ejpam-7112	650	27	m	m	NOUN
ejpam-7112	650	28	n	n	NUM
ejpam-7112	650	29	ct	ct	NOUN
ejpam-7112	650	30	zct	zct	NOUN
ejpam-7112	650	31	mzct	mzct	NOUN
ejpam-7112	650	32	amct	amct	VERB
ejpam-7112	650	33	gmct	gmct	ADJ
ejpam-7112	650	34	hamct	hamct	NOUN
ejpam-7112	650	35	hemct	hemct	ADJ
ejpam-7112	650	36	cmct	cmct	ADJ
ejpam-7112	650	37	1	1	NUM
ejpam-7112	650	38	1	1	NUM
ejpam-7112	650	39	na	na	NOUN
ejpam-7112	650	40	na	na	NOUN
ejpam-7112	650	41	na	na	INTJ
ejpam-7112	650	42	na	na	VERB
ejpam-7112	650	43	na	na	VERB
ejpam-7112	650	44	na	na	VERB
ejpam-7112	650	45	na	na	ADV
ejpam-7112	650	46	na	na	PART
ejpam-7112	650	47	2	2	NUM
ejpam-7112	650	48	2	2	NUM
ejpam-7112	650	49	1.9319	1.9319	NUM
ejpam-7112	650	50	1.9319	1.9319	NUM
ejpam-7112	650	51	3.8984	3.8984	NUM
ejpam-7112	650	52	3.9697	3.9697	NUM
ejpam-7112	650	53	3.9467	3.9467	NUM
ejpam-7112	650	54	3.9283	3.9283	NUM
ejpam-7112	650	55	3.9610	3.9610	NUM
ejpam-7112	650	56	3.9970	3.9970	NUM
ejpam-7112	650	57	4	4	NUM
ejpam-7112	650	58	4	4	NUM
ejpam-7112	650	59	1.9844	1.9844	NUM
ejpam-7112	650	60	1.9844	1.9844	NUM
ejpam-7112	650	61	3.9761	3.9761	NUM
ejpam-7112	650	62	3.9935	3.9935	NUM
ejpam-7112	650	63	3.9878	3.9878	NUM
ejpam-7112	650	64	3.9832	3.9832	NUM
ejpam-7112	650	65	3.9913	3.9913	NUM
ejpam-7112	650	66	4.0003	4.0003	NUM
ejpam-7112	650	67	8	8	NUM
ejpam-7112	650	68	8	8	NUM
ejpam-7112	650	69	1.9962	1.9962	NUM
ejpam-7112	650	70	1.9962	1.9962	NUM
ejpam-7112	650	71	3.9941	3.9941	NUM
ejpam-7112	650	72	3.9984	3.9984	NUM
ejpam-7112	650	73	3.9971	3.9971	NUM
ejpam-7112	650	74	3.9958	3.9958	NUM
ejpam-7112	650	75	3.9979	3.9979	NUM
ejpam-7112	650	76	4.0002	4.0002	NUM
ejpam-7112	650	77	16	16	NUM
ejpam-7112	650	78	16	16	NUM
ejpam-7112	650	79	1.9990	1.9990	NUM
ejpam-7112	650	80	1.9990	1.9990	NUM
ejpam-7112	650	81	3.9985	3.9985	NUM
ejpam-7112	650	82	3.9996	3.9996	NUM
ejpam-7112	650	83	3.9992	3.9992	NUM
ejpam-7112	650	84	3.9990	3.9990	NUM
ejpam-7112	650	85	3.9995	3.9995	NUM
ejpam-7112	650	86	4.0000	4.0000	NUM
ejpam-7112	650	87	32	32	NUM
ejpam-7112	650	88	32	32	NUM
ejpam-7112	650	89	1.9998	1.9998	NUM
ejpam-7112	650	90	1.9998	1.9998	NUM
ejpam-7112	650	91	3.9996	3.9996	NUM
ejpam-7112	650	92	3.9999	3.9999	NUM
ejpam-7112	650	93	3.9998	3.9998	NUM
ejpam-7112	650	94	3.9998	3.9998	NUM
ejpam-7112	650	95	3.9999	3.9999	NUM
ejpam-7112	650	96	4.0000	4.0000	NUM
ejpam-7112	650	97	64	64	NUM
ejpam-7112	650	98	64	64	NUM
ejpam-7112	650	99	1.9999	1.9999	NUM
ejpam-7112	650	100	1.9999	1.9999	NUM
ejpam-7112	650	101	3.9999	3.9999	NUM
ejpam-7112	650	102	4.0000	4.0000	NUM
ejpam-7112	650	103	4.0000	4.0000	NUM
ejpam-7112	650	104	3.9999	3.9999	NUM
ejpam-7112	650	105	4.0000	4.0000	NUM
ejpam-7112	650	106	4.0000	4.0000	NUM
ejpam-7112	650	107	table	table	NOUN
ejpam-7112	650	108	5	5	NUM
ejpam-7112	650	109	:	:	PUNCT
ejpam-7112	650	110	representation	representation	NOUN
ejpam-7112	650	111	of	of	ADP
ejpam-7112	650	112	the	the	DET
ejpam-7112	650	113	order	order	NOUN
ejpam-7112	650	114	of	of	ADP
ejpam-7112	650	115	accuracy	accuracy	NOUN
ejpam-7112	650	116	to	to	ADP
ejpam-7112	650	117	all	all	DET
ejpam-7112	650	118	schemes	scheme	NOUN
ejpam-7112	650	119	for	for	ADP
ejpam-7112	650	120	example	example	NOUN
ejpam-7112	650	121	4	4	NUM
ejpam-7112	650	122	m	m	NOUN
ejpam-7112	650	123	n	n	NUM
ejpam-7112	650	124	ct	ct	NOUN
ejpam-7112	650	125	zct	zct	NOUN
ejpam-7112	650	126	mzct	mzct	NOUN
ejpam-7112	650	127	amct	amct	VERB
ejpam-7112	650	128	gmct	gmct	ADJ
ejpam-7112	650	129	hamct	hamct	NOUN
ejpam-7112	650	130	hemct	hemct	ADJ
ejpam-7112	650	131	cmct	cmct	ADJ
ejpam-7112	650	132	1	1	NUM
ejpam-7112	650	133	1	1	NUM
ejpam-7112	650	134	na	na	NOUN
ejpam-7112	650	135	na	na	NOUN
ejpam-7112	650	136	na	na	INTJ
ejpam-7112	650	137	na	na	VERB
ejpam-7112	650	138	na	na	VERB
ejpam-7112	650	139	na	na	VERB
ejpam-7112	650	140	na	na	ADV
ejpam-7112	650	141	na	na	SYM
ejpam-7112	650	142	2	2	NUM
ejpam-7112	650	143	2	2	NUM
ejpam-7112	650	144	0	0	NUM
ejpam-7112	650	145	na	na	NOUN
ejpam-7112	650	146	na	na	ADP
ejpam-7112	650	147	4.3044	4.3044	NUM
ejpam-7112	650	148	1.5452	1.5452	NUM
ejpam-7112	650	149	1.9113	1.9113	NUM
ejpam-7112	650	150	3.6353	3.6353	NUM
ejpam-7112	650	151	2.6795	2.6795	NUM
ejpam-7112	650	152	4	4	NUM
ejpam-7112	650	153	4	4	NUM
ejpam-7112	650	154	1.8345	1.8345	NUM
ejpam-7112	650	155	0.1972	0.1972	NUM
ejpam-7112	650	156	na	na	ADP
ejpam-7112	650	157	4.0662	4.0662	NUM
ejpam-7112	650	158	3.2559	3.2559	NUM
ejpam-7112	650	159	2.9653	2.9653	NUM
ejpam-7112	650	160	3.0169	3.0169	NUM
ejpam-7112	650	161	3.3438	3.3438	NUM
ejpam-7112	650	162	8	8	NUM
ejpam-7112	650	163	8	8	NUM
ejpam-7112	650	164	1.9649	1.9649	NUM
ejpam-7112	650	165	0.0404	0.0404	NUM
ejpam-7112	650	166	na	na	ADP
ejpam-7112	650	167	4.0160	4.0160	NUM
ejpam-7112	650	168	3.6533	3.6533	NUM
ejpam-7112	650	169	3.4400	3.4400	NUM
ejpam-7112	650	170	3.5898	3.5898	NUM
ejpam-7112	650	171	3.5701	3.5701	NUM
ejpam-7112	650	172	16	16	NUM
ejpam-7112	650	173	16	16	NUM
ejpam-7112	650	174	1.9916	1.9916	NUM
ejpam-7112	650	175	0.0095	0.0095	NUM
ejpam-7112	650	176	na	na	ADP
ejpam-7112	650	177	4.0040	4.0040	NUM
ejpam-7112	650	178	3.7589	3.7589	NUM
ejpam-7112	650	179	3.6076	3.6076	NUM
ejpam-7112	650	180	3.7252	3.7252	NUM
ejpam-7112	650	181	3.6758	3.6758	NUM
ejpam-7112	650	182	32	32	NUM
ejpam-7112	650	183	32	32	NUM
ejpam-7112	650	184	1.9979	1.9979	NUM
ejpam-7112	650	185	0.0025	0.0025	NUM
ejpam-7112	650	186	na	na	ADP
ejpam-7112	650	187	4.0010	4.0010	NUM
ejpam-7112	650	188	3.8029	3.8029	NUM
ejpam-7112	650	189	3.6944	3.6944	NUM
ejpam-7112	650	190	3.7801	3.7801	NUM
ejpam-7112	650	191	3.7374	3.7374	NUM
ejpam-7112	650	192	64	64	NUM
ejpam-7112	650	193	64	64	NUM
ejpam-7112	650	194	1.9995	1.9995	NUM
ejpam-7112	650	195	0.00061	0.00061	NUM
ejpam-7112	650	196	na	na	ADP
ejpam-7112	650	197	4.0002	4.0002	NUM
ejpam-7112	650	198	3.8289	3.8289	NUM
ejpam-7112	650	199	3.7487	3.7487	NUM
ejpam-7112	650	200	3.8118	3.8118	NUM
ejpam-7112	650	201	3.7784	3.7784	NUM
ejpam-7112	650	202	k.	k.	PROPN
ejpam-7112	650	203	memon	memon	PROPN
ejpam-7112	650	204	et	et	PROPN
ejpam-7112	650	205	al	al	PROPN
ejpam-7112	650	206	.	.	PUNCT
ejpam-7112	650	207	/	/	SYM
ejpam-7112	650	208	eur	eur	PROPN
ejpam-7112	650	209	.	.	PUNCT
ejpam-7112	651	1	j.	j.	PROPN
ejpam-7112	651	2	pure	pure	PROPN
ejpam-7112	651	3	appl	appl	PROPN
ejpam-7112	651	4	.	.	PROPN
ejpam-7112	651	5	math	math	PROPN
ejpam-7112	651	6	,	,	PUNCT
ejpam-7112	651	7	18	18	NUM
ejpam-7112	651	8	(	(	PUNCT
ejpam-7112	651	9	4	4	NUM
ejpam-7112	651	10	)	)	PUNCT
ejpam-7112	651	11	(	(	PUNCT
ejpam-7112	651	12	2025	2025	NUM
ejpam-7112	651	13	)	)	PUNCT
ejpam-7112	651	14	,	,	PUNCT
ejpam-7112	651	15	7112	7112	NUM
ejpam-7112	651	16	34	34	NUM
ejpam-7112	651	17	of	of	ADP
ejpam-7112	651	18	38	38	NUM
ejpam-7112	651	19	table	table	NOUN
ejpam-7112	651	20	6	6	NUM
ejpam-7112	651	21	:	:	PUNCT
ejpam-7112	651	22	representation	representation	NOUN
ejpam-7112	651	23	of	of	ADP
ejpam-7112	651	24	the	the	DET
ejpam-7112	651	25	order	order	NOUN
ejpam-7112	651	26	of	of	ADP
ejpam-7112	651	27	accuracy	accuracy	NOUN
ejpam-7112	651	28	to	to	ADP
ejpam-7112	651	29	all	all	DET
ejpam-7112	651	30	schemes	scheme	NOUN
ejpam-7112	651	31	for	for	ADP
ejpam-7112	651	32	example	example	NOUN
ejpam-7112	651	33	5	5	NUM
ejpam-7112	651	34	m	m	NOUN
ejpam-7112	651	35	n	n	NUM
ejpam-7112	651	36	ct	ct	NOUN
ejpam-7112	651	37	zct	zct	NOUN
ejpam-7112	651	38	mzct	mzct	NOUN
ejpam-7112	651	39	amct	amct	VERB
ejpam-7112	651	40	gmct	gmct	ADJ
ejpam-7112	651	41	hamct	hamct	NOUN
ejpam-7112	651	42	hemct	hemct	ADJ
ejpam-7112	651	43	cmct	cmct	ADJ
ejpam-7112	651	44	1	1	NUM
ejpam-7112	651	45	1	1	NUM
ejpam-7112	651	46	na	na	NOUN
ejpam-7112	651	47	na	na	NOUN
ejpam-7112	651	48	na	na	INTJ
ejpam-7112	651	49	na	na	VERB
ejpam-7112	651	50	na	na	VERB
ejpam-7112	651	51	na	na	VERB
ejpam-7112	651	52	na	na	ADV
ejpam-7112	651	53	na	na	SYM
ejpam-7112	651	54	2	2	NUM
ejpam-7112	651	55	2	2	NUM
ejpam-7112	651	56	0	0	NUM
ejpam-7112	651	57	53.7424	53.7424	NUM
ejpam-7112	651	58	1.0000	1.0000	NUM
ejpam-7112	651	59	3.9032	3.9032	NUM
ejpam-7112	651	60	3.9499	3.9499	NUM
ejpam-7112	651	61	na	na	ADP
ejpam-7112	651	62	3.7927	3.7927	NUM
ejpam-7112	651	63	na	na	PART
ejpam-7112	651	64	4	4	NUM
ejpam-7112	651	65	4	4	NUM
ejpam-7112	651	66	1.7226	1.7226	NUM
ejpam-7112	651	67	51.8971	51.8971	NUM
ejpam-7112	651	68	1.0000	1.0000	NUM
ejpam-7112	651	69	3.9747	3.9747	NUM
ejpam-7112	651	70	3.3325	3.3325	NUM
ejpam-7112	651	71	4.0089	4.0089	NUM
ejpam-7112	651	72	3.6427	3.6427	NUM
ejpam-7112	651	73	4.0217	4.0217	NUM
ejpam-7112	651	74	8	8	NUM
ejpam-7112	651	75	8	8	NUM
ejpam-7112	651	76	1.9363	1.9363	NUM
ejpam-7112	651	77	0.3302	0.3302	NUM
ejpam-7112	651	78	1.5850	1.5850	NUM
ejpam-7112	651	79	3.9936	3.9936	NUM
ejpam-7112	651	80	1.0357	1.0357	NUM
ejpam-7112	651	81	4.0023	4.0023	NUM
ejpam-7112	651	82	0.9225	0.9225	NUM
ejpam-7112	651	83	4.0055	4.0055	NUM
ejpam-7112	651	84	16	16	NUM
ejpam-7112	651	85	16	16	NUM
ejpam-7112	651	86	1.9844	1.9844	NUM
ejpam-7112	651	87	0.0725	0.0725	NUM
ejpam-7112	651	88	na	na	ADP
ejpam-7112	651	89	3.9984	3.9984	NUM
ejpam-7112	651	90	1.8139	1.8139	NUM
ejpam-7112	651	91	4.0005	4.0005	NUM
ejpam-7112	651	92	1.8014	1.8014	NUM
ejpam-7112	651	93	4.0014	4.0014	NUM
ejpam-7112	651	94	32	32	NUM
ejpam-7112	651	95	32	32	NUM
ejpam-7112	651	96	1.9962	1.9962	NUM
ejpam-7112	651	97	0.0176	0.0176	NUM
ejpam-7112	651	98	na	na	ADP
ejpam-7112	651	99	3.9996	3.9996	NUM
ejpam-7112	651	100	1.9516	1.9516	NUM
ejpam-7112	651	101	4.0001	4.0001	NUM
ejpam-7112	651	102	1.9489	1.9489	NUM
ejpam-7112	651	103	4.0003	4.0003	NUM
ejpam-7112	651	104	64	64	NUM
ejpam-7112	651	105	64	64	NUM
ejpam-7112	651	106	1.9990	1.9990	NUM
ejpam-7112	651	107	0.0044	0.0044	NUM
ejpam-7112	651	108	na	na	ADP
ejpam-7112	651	109	3.9999	3.9999	NUM
ejpam-7112	651	110	1.9867	1.9867	NUM
ejpam-7112	651	111	4.0000	4.0000	NUM
ejpam-7112	651	112	1.9861	1.9861	NUM
ejpam-7112	651	113	4.0001	4.0001	NUM
ejpam-7112	651	114	table	table	NOUN
ejpam-7112	651	115	7	7	NUM
ejpam-7112	651	116	:	:	PUNCT
ejpam-7112	651	117	total	total	ADJ
ejpam-7112	651	118	computational	computational	ADJ
ejpam-7112	651	119	cost	cost	NOUN
ejpam-7112	651	120	in	in	ADP
ejpam-7112	651	121	trapezoidal	trapezoidal	ADJ
ejpam-7112	651	122	variants	variant	NOUN
ejpam-7112	651	123	for	for	ADP
ejpam-7112	651	124	n	n	DET
ejpam-7112	651	125	sub	sub	ADJ
ejpam-7112	651	126	-	-	NOUN
ejpam-7112	651	127	intervals	interval	NOUN
ejpam-7112	651	128	trapezoidal	trapezoidal	ADJ
ejpam-7112	651	129	variants	variant	NOUN
ejpam-7112	651	130	f	f	PROPN
ejpam-7112	651	131	g	g	PROPN
ejpam-7112	651	132	f	f	PROPN
ejpam-7112	651	133	(	(	PUNCT
ejpam-7112	651	134	1	1	NUM
ejpam-7112	651	135	)	)	PUNCT
ejpam-7112	651	136	f	f	NOUN
ejpam-7112	651	137	(	(	PUNCT
ejpam-7112	651	138	2	2	X
ejpam-7112	651	139	)	)	PUNCT
ejpam-7112	651	140	i1	i1	PROPN
ejpam-7112	651	141	i2	i2	PROPN
ejpam-7112	651	142	i3	i3	PROPN
ejpam-7112	651	143	total	total	NOUN
ejpam-7112	651	144	evaluations	evaluation	NOUN
ejpam-7112	651	145	total	total	NOUN
ejpam-7112	651	146	(	(	PUNCT
ejpam-7112	651	147	n=1	n=1	PROPN
ejpam-7112	651	148	)	)	PUNCT
ejpam-7112	651	149	ct	ct	PROPN
ejpam-7112	651	150	n+	n+	NUM
ejpam-7112	652	1	1	1	NUM
ejpam-7112	652	2	2	2	NUM
ejpam-7112	652	3	0	0	NUM
ejpam-7112	652	4	0	0	NUM
ejpam-7112	652	5	n	n	CCONJ
ejpam-7112	652	6	0	0	NUM
ejpam-7112	652	7	0	0	NUM
ejpam-7112	652	8	2n+	2n+	NUM
ejpam-7112	652	9	3	3	NUM
ejpam-7112	652	10	5	5	NUM
ejpam-7112	652	11	zct	zct	NOUN
ejpam-7112	652	12	n+	n+	ADP
ejpam-7112	652	13	1	1	NUM
ejpam-7112	652	14	2	2	NUM
ejpam-7112	652	15	0	0	NUM
ejpam-7112	652	16	n	n	CCONJ
ejpam-7112	652	17	n	n	CCONJ
ejpam-7112	652	18	n	n	CCONJ
ejpam-7112	652	19	n	n	ADV
ejpam-7112	652	20	5n+	5n+	NUM
ejpam-7112	652	21	3	3	NUM
ejpam-7112	652	22	8	8	NUM
ejpam-7112	652	23	mzct	mzct	NOUN
ejpam-7112	652	24	n+	n+	ADP
ejpam-7112	652	25	1	1	NUM
ejpam-7112	652	26	2	2	NUM
ejpam-7112	652	27	0	0	NUM
ejpam-7112	652	28	n	n	CCONJ
ejpam-7112	652	29	n	n	CCONJ
ejpam-7112	652	30	n	n	CCONJ
ejpam-7112	652	31	n	n	ADV
ejpam-7112	652	32	5n+	5n+	NUM
ejpam-7112	652	33	3	3	NUM
ejpam-7112	652	34	8	8	NUM
ejpam-7112	652	35	amct	amct	ADJ
ejpam-7112	652	36	n+	n+	ADP
ejpam-7112	652	37	1	1	NUM
ejpam-7112	652	38	2	2	NUM
ejpam-7112	652	39	0	0	NUM
ejpam-7112	652	40	n	n	CCONJ
ejpam-7112	652	41	n	n	CCONJ
ejpam-7112	652	42	n	n	NOUN
ejpam-7112	652	43	0	0	NUM
ejpam-7112	652	44	4n+	4n+	NUM
ejpam-7112	652	45	3	3	NUM
ejpam-7112	652	46	7	7	NUM
ejpam-7112	652	47	gmct	gmct	ADJ
ejpam-7112	652	48	n+	n+	ADP
ejpam-7112	652	49	1	1	NUM
ejpam-7112	652	50	2	2	NUM
ejpam-7112	652	51	0	0	NUM
ejpam-7112	652	52	n	n	CCONJ
ejpam-7112	652	53	n	n	CCONJ
ejpam-7112	652	54	n	n	NOUN
ejpam-7112	652	55	0	0	NUM
ejpam-7112	652	56	4n+	4n+	NUM
ejpam-7112	652	57	3	3	NUM
ejpam-7112	652	58	7	7	NUM
ejpam-7112	652	59	hamct	hamct	NOUN
ejpam-7112	652	60	n+	n+	PUNCT
ejpam-7112	652	61	1	1	NUM
ejpam-7112	652	62	2	2	NUM
ejpam-7112	652	63	0	0	NUM
ejpam-7112	652	64	n	n	CCONJ
ejpam-7112	652	65	n	n	CCONJ
ejpam-7112	652	66	n	n	NOUN
ejpam-7112	652	67	0	0	NUM
ejpam-7112	652	68	4n+	4n+	NUM
ejpam-7112	652	69	3	3	NUM
ejpam-7112	652	70	7	7	NUM
ejpam-7112	652	71	hemct	hemct	ADJ
ejpam-7112	652	72	n+	n+	PUNCT
ejpam-7112	652	73	1	1	NUM
ejpam-7112	652	74	2	2	NUM
ejpam-7112	652	75	0	0	NUM
ejpam-7112	652	76	n	n	CCONJ
ejpam-7112	652	77	n	n	CCONJ
ejpam-7112	652	78	n	n	NOUN
ejpam-7112	652	79	0	0	NUM
ejpam-7112	652	80	4n+	4n+	NUM
ejpam-7112	652	81	3	3	NUM
ejpam-7112	652	82	7	7	NUM
ejpam-7112	652	83	cmct	cmct	NOUN
ejpam-7112	652	84	n+	n+	ADP
ejpam-7112	652	85	1	1	NUM
ejpam-7112	652	86	2	2	NUM
ejpam-7112	652	87	0	0	NUM
ejpam-7112	652	88	n	n	CCONJ
ejpam-7112	652	89	n	n	CCONJ
ejpam-7112	652	90	n	n	NOUN
ejpam-7112	652	91	0	0	NUM
ejpam-7112	652	92	4n+	4n+	NUM
ejpam-7112	652	93	3	3	NUM
ejpam-7112	652	94	7	7	NUM
ejpam-7112	652	95	table	table	NOUN
ejpam-7112	652	96	8	8	NUM
ejpam-7112	652	97	:	:	PUNCT
ejpam-7112	652	98	computational	computational	ADJ
ejpam-7112	652	99	cost	cost	NOUN
ejpam-7112	652	100	in	in	ADP
ejpam-7112	652	101	trapezoidal	trapezoidal	ADJ
ejpam-7112	652	102	variants	variant	NOUN
ejpam-7112	652	103	to	to	PART
ejpam-7112	652	104	achieve	achieve	VERB
ejpam-7112	652	105	ξ	ξ	PRON
ejpam-7112	652	106	≤	≤	NOUN
ejpam-7112	652	107	10−5	10−5	NUM
ejpam-7112	652	108	in	in	ADP
ejpam-7112	652	109	example	example	NOUN
ejpam-7112	652	110	1	1	NUM
ejpam-7112	652	111	trapezoidal	trapezoidal	ADJ
ejpam-7112	652	112	variants	variant	NOUN
ejpam-7112	652	113	f	f	PROPN
ejpam-7112	652	114	g	g	PROPN
ejpam-7112	652	115	f	f	PROPN
ejpam-7112	652	116	(	(	PUNCT
ejpam-7112	652	117	1	1	NUM
ejpam-7112	652	118	)	)	PUNCT
ejpam-7112	652	119	f	f	NOUN
ejpam-7112	652	120	(	(	PUNCT
ejpam-7112	652	121	2	2	X
ejpam-7112	652	122	)	)	PUNCT
ejpam-7112	652	123	i1	i1	PROPN
ejpam-7112	652	124	i2	i2	PROPN
ejpam-7112	652	125	i3	i3	PROPN
ejpam-7112	652	126	total	total	NOUN
ejpam-7112	652	127	evaluations	evaluation	NOUN
ejpam-7112	652	128	ct	ct	VERB
ejpam-7112	652	129	219	219	NUM
ejpam-7112	652	130	2	2	NUM
ejpam-7112	652	131	0	0	NUM
ejpam-7112	652	132	0	0	NUM
ejpam-7112	652	133	218	218	NUM
ejpam-7112	652	134	0	0	NUM
ejpam-7112	652	135	0	0	NUM
ejpam-7112	652	136	439	439	NUM
ejpam-7112	652	137	zct	zct	NOUN
ejpam-7112	652	138	209	209	NUM
ejpam-7112	652	139	2	2	NUM
ejpam-7112	652	140	0	0	NUM
ejpam-7112	652	141	208	208	NUM
ejpam-7112	652	142	208	208	NUM
ejpam-7112	652	143	208	208	NUM
ejpam-7112	652	144	208	208	NUM
ejpam-7112	652	145	1043	1043	NUM
ejpam-7112	652	146	mzct	mzct	NOUN
ejpam-7112	652	147	15	15	NUM
ejpam-7112	652	148	2	2	NUM
ejpam-7112	652	149	0	0	NUM
ejpam-7112	652	150	14	14	NUM
ejpam-7112	652	151	14	14	NUM
ejpam-7112	652	152	14	14	NUM
ejpam-7112	652	153	14	14	NUM
ejpam-7112	652	154	73	73	NUM
ejpam-7112	652	155	amct	amct	ADJ
ejpam-7112	652	156	14	14	NUM
ejpam-7112	652	157	2	2	NUM
ejpam-7112	652	158	0	0	NUM
ejpam-7112	652	159	13	13	NUM
ejpam-7112	652	160	13	13	NUM
ejpam-7112	652	161	13	13	NUM
ejpam-7112	652	162	0	0	NUM
ejpam-7112	652	163	55	55	NUM
ejpam-7112	652	164	gmct	gmct	ADJ
ejpam-7112	652	165	14	14	NUM
ejpam-7112	652	166	2	2	NUM
ejpam-7112	652	167	0	0	NUM
ejpam-7112	652	168	13	13	NUM
ejpam-7112	652	169	13	13	NUM
ejpam-7112	652	170	13	13	NUM
ejpam-7112	652	171	0	0	NUM
ejpam-7112	652	172	55	55	NUM
ejpam-7112	652	173	hamct	hamct	ADJ
ejpam-7112	652	174	14	14	NUM
ejpam-7112	652	175	2	2	NUM
ejpam-7112	652	176	0	0	NUM
ejpam-7112	652	177	13	13	NUM
ejpam-7112	652	178	13	13	NUM
ejpam-7112	652	179	13	13	NUM
ejpam-7112	652	180	0	0	NUM
ejpam-7112	652	181	55	55	NUM
ejpam-7112	652	182	hemct	hemct	ADJ
ejpam-7112	652	183	14	14	NUM
ejpam-7112	652	184	2	2	NUM
ejpam-7112	652	185	0	0	NUM
ejpam-7112	652	186	13	13	NUM
ejpam-7112	652	187	13	13	NUM
ejpam-7112	652	188	13	13	NUM
ejpam-7112	652	189	0	0	NUM
ejpam-7112	652	190	55	55	NUM
ejpam-7112	652	191	cmct	cmct	NUM
ejpam-7112	652	192	14	14	NUM
ejpam-7112	652	193	2	2	NUM
ejpam-7112	652	194	0	0	NUM
ejpam-7112	652	195	13	13	NUM
ejpam-7112	652	196	13	13	NUM
ejpam-7112	652	197	13	13	NUM
ejpam-7112	652	198	0	0	NUM
ejpam-7112	652	199	55	55	NUM
ejpam-7112	652	200	k.	k.	PROPN
ejpam-7112	652	201	memon	memon	PROPN
ejpam-7112	652	202	et	et	PROPN
ejpam-7112	652	203	al	al	PROPN
ejpam-7112	652	204	.	.	PUNCT
ejpam-7112	652	205	/	/	SYM
ejpam-7112	652	206	eur	eur	PROPN
ejpam-7112	652	207	.	.	PUNCT
ejpam-7112	653	1	j.	j.	PROPN
ejpam-7112	653	2	pure	pure	PROPN
ejpam-7112	653	3	appl	appl	PROPN
ejpam-7112	653	4	.	.	PROPN
ejpam-7112	653	5	math	math	PROPN
ejpam-7112	653	6	,	,	PUNCT
ejpam-7112	653	7	18	18	NUM
ejpam-7112	653	8	(	(	PUNCT
ejpam-7112	653	9	4	4	NUM
ejpam-7112	653	10	)	)	PUNCT
ejpam-7112	653	11	(	(	PUNCT
ejpam-7112	653	12	2025	2025	NUM
ejpam-7112	653	13	)	)	PUNCT
ejpam-7112	653	14	,	,	PUNCT
ejpam-7112	653	15	7112	7112	NUM
ejpam-7112	653	16	35	35	NUM
ejpam-7112	653	17	of	of	ADP
ejpam-7112	653	18	38	38	NUM
ejpam-7112	653	19	table	table	NOUN
ejpam-7112	653	20	9	9	NUM
ejpam-7112	653	21	:	:	PUNCT
ejpam-7112	653	22	computational	computational	ADJ
ejpam-7112	653	23	cost	cost	NOUN
ejpam-7112	653	24	in	in	ADP
ejpam-7112	653	25	trapezoidal	trapezoidal	ADJ
ejpam-7112	653	26	variants	variant	NOUN
ejpam-7112	653	27	to	to	PART
ejpam-7112	653	28	achieve	achieve	VERB
ejpam-7112	653	29	ξ	ξ	PRON
ejpam-7112	653	30	≤	≤	NOUN
ejpam-7112	653	31	10−5	10−5	NUM
ejpam-7112	653	32	in	in	ADP
ejpam-7112	653	33	example	example	NOUN
ejpam-7112	653	34	2	2	NUM
ejpam-7112	653	35	trapezoidal	trapezoidal	NOUN
ejpam-7112	653	36	variants	variant	NOUN
ejpam-7112	653	37	f	f	PROPN
ejpam-7112	653	38	g	g	PROPN
ejpam-7112	653	39	f	f	PROPN
ejpam-7112	653	40	(	(	PUNCT
ejpam-7112	653	41	1	1	NUM
ejpam-7112	653	42	)	)	PUNCT
ejpam-7112	653	43	f	f	NOUN
ejpam-7112	653	44	(	(	PUNCT
ejpam-7112	653	45	2	2	X
ejpam-7112	653	46	)	)	PUNCT
ejpam-7112	653	47	i1	i1	PROPN
ejpam-7112	653	48	i2	i2	PROPN
ejpam-7112	653	49	i3	i3	PROPN
ejpam-7112	653	50	total	total	NOUN
ejpam-7112	653	51	evaluations	evaluation	NOUN
ejpam-7112	653	52	ct	ct	NOUN
ejpam-7112	653	53	707	707	NUM
ejpam-7112	653	54	2	2	NUM
ejpam-7112	653	55	0	0	NUM
ejpam-7112	653	56	0	0	NUM
ejpam-7112	653	57	706	706	NUM
ejpam-7112	653	58	0	0	NUM
ejpam-7112	653	59	0	0	NUM
ejpam-7112	653	60	1415	1415	NUM
ejpam-7112	653	61	zct	zct	NOUN
ejpam-7112	653	62	701	701	NUM
ejpam-7112	653	63	2	2	NUM
ejpam-7112	653	64	0	0	NUM
ejpam-7112	653	65	700	700	NUM
ejpam-7112	653	66	700	700	NUM
ejpam-7112	653	67	700	700	NUM
ejpam-7112	653	68	700	700	NUM
ejpam-7112	653	69	3503	3503	NUM
ejpam-7112	653	70	mzct	mzct	NOUN
ejpam-7112	653	71	16	16	NUM
ejpam-7112	653	72	2	2	NUM
ejpam-7112	653	73	0	0	NUM
ejpam-7112	653	74	15	15	NUM
ejpam-7112	653	75	15	15	NUM
ejpam-7112	653	76	15	15	NUM
ejpam-7112	653	77	15	15	NUM
ejpam-7112	653	78	78	78	NUM
ejpam-7112	653	79	amct	amct	ADJ
ejpam-7112	653	80	13	13	NUM
ejpam-7112	653	81	2	2	NUM
ejpam-7112	653	82	0	0	NUM
ejpam-7112	653	83	12	12	NUM
ejpam-7112	653	84	12	12	NUM
ejpam-7112	653	85	12	12	NUM
ejpam-7112	653	86	0	0	NUM
ejpam-7112	653	87	51	51	NUM
ejpam-7112	653	88	gmct	gmct	ADJ
ejpam-7112	653	89	14	14	NUM
ejpam-7112	653	90	2	2	NUM
ejpam-7112	653	91	0	0	NUM
ejpam-7112	653	92	13	13	NUM
ejpam-7112	653	93	13	13	NUM
ejpam-7112	653	94	13	13	NUM
ejpam-7112	653	95	0	0	NUM
ejpam-7112	653	96	55	55	NUM
ejpam-7112	653	97	hamct	hamct	ADJ
ejpam-7112	653	98	16	16	NUM
ejpam-7112	653	99	2	2	NUM
ejpam-7112	653	100	0	0	NUM
ejpam-7112	653	101	15	15	NUM
ejpam-7112	653	102	15	15	NUM
ejpam-7112	653	103	15	15	NUM
ejpam-7112	653	104	0	0	NUM
ejpam-7112	653	105	63	63	NUM
ejpam-7112	653	106	hemct	hemct	ADJ
ejpam-7112	653	107	13	13	NUM
ejpam-7112	653	108	2	2	NUM
ejpam-7112	653	109	0	0	NUM
ejpam-7112	653	110	12	12	NUM
ejpam-7112	653	111	12	12	NUM
ejpam-7112	653	112	12	12	NUM
ejpam-7112	653	113	0	0	NUM
ejpam-7112	653	114	51	51	NUM
ejpam-7112	653	115	cmct	cmct	ADJ
ejpam-7112	653	116	11	11	NUM
ejpam-7112	653	117	2	2	NUM
ejpam-7112	653	118	0	0	NUM
ejpam-7112	653	119	10	10	NUM
ejpam-7112	653	120	10	10	NUM
ejpam-7112	653	121	10	10	NUM
ejpam-7112	653	122	0	0	NUM
ejpam-7112	653	123	43	43	NUM
ejpam-7112	653	124	table	table	NOUN
ejpam-7112	653	125	10	10	NUM
ejpam-7112	653	126	:	:	PUNCT
ejpam-7112	653	127	computational	computational	ADJ
ejpam-7112	653	128	cost	cost	NOUN
ejpam-7112	653	129	in	in	ADP
ejpam-7112	653	130	trapezoidal	trapezoidal	ADJ
ejpam-7112	653	131	variants	variant	NOUN
ejpam-7112	653	132	to	to	PART
ejpam-7112	653	133	achieve	achieve	VERB
ejpam-7112	653	134	ξ	ξ	PRON
ejpam-7112	653	135	≤	≤	NUM
ejpam-7112	653	136	10−5accuracy	10−5accuracy	NUM
ejpam-7112	653	137	in	in	ADP
ejpam-7112	653	138	example	example	NOUN
ejpam-7112	653	139	3	3	NUM
ejpam-7112	653	140	trapezoidal	trapezoidal	ADJ
ejpam-7112	653	141	variants	variant	NOUN
ejpam-7112	653	142	f	f	PROPN
ejpam-7112	653	143	g	g	PROPN
ejpam-7112	653	144	f	f	PROPN
ejpam-7112	653	145	(	(	PUNCT
ejpam-7112	653	146	1	1	NUM
ejpam-7112	653	147	)	)	PUNCT
ejpam-7112	653	148	f	f	NOUN
ejpam-7112	653	149	(	(	PUNCT
ejpam-7112	653	150	2	2	X
ejpam-7112	653	151	)	)	PUNCT
ejpam-7112	653	152	i1	i1	PROPN
ejpam-7112	653	153	i2	i2	PROPN
ejpam-7112	653	154	i3	i3	PROPN
ejpam-7112	653	155	total	total	NOUN
ejpam-7112	653	156	evaluations	evaluation	NOUN
ejpam-7112	653	157	ct	ct	NUM
ejpam-7112	653	158	1251	1251	NUM
ejpam-7112	653	159	2	2	NUM
ejpam-7112	653	160	0	0	NUM
ejpam-7112	653	161	0	0	NUM
ejpam-7112	653	162	1250	1250	NUM
ejpam-7112	653	163	0	0	NUM
ejpam-7112	653	164	0	0	NUM
ejpam-7112	653	165	2503	2503	NUM
ejpam-7112	653	166	zct	zct	NOUN
ejpam-7112	653	167	1251	1251	NUM
ejpam-7112	653	168	2	2	NUM
ejpam-7112	653	169	0	0	NUM
ejpam-7112	653	170	1250	1250	NUM
ejpam-7112	653	171	1250	1250	NUM
ejpam-7112	653	172	1250	1250	NUM
ejpam-7112	653	173	1250	1250	NUM
ejpam-7112	653	174	6253	6253	NUM
ejpam-7112	653	175	mzct	mzct	NOUN
ejpam-7112	653	176	16	16	NUM
ejpam-7112	653	177	2	2	NUM
ejpam-7112	653	178	0	0	NUM
ejpam-7112	653	179	15	15	NUM
ejpam-7112	653	180	15	15	NUM
ejpam-7112	653	181	15	15	NUM
ejpam-7112	653	182	15	15	NUM
ejpam-7112	653	183	78	78	NUM
ejpam-7112	653	184	amct	amct	ADJ
ejpam-7112	653	185	17	17	NUM
ejpam-7112	653	186	2	2	NUM
ejpam-7112	653	187	0	0	NUM
ejpam-7112	653	188	16	16	NUM
ejpam-7112	653	189	16	16	NUM
ejpam-7112	653	190	16	16	NUM
ejpam-7112	653	191	0	0	NUM
ejpam-7112	653	192	67	67	NUM
ejpam-7112	653	193	gmct	gmct	ADJ
ejpam-7112	653	194	19	19	NUM
ejpam-7112	653	195	2	2	NUM
ejpam-7112	653	196	0	0	NUM
ejpam-7112	653	197	18	18	NUM
ejpam-7112	653	198	18	18	NUM
ejpam-7112	653	199	18	18	NUM
ejpam-7112	653	200	0	0	NUM
ejpam-7112	653	201	75	75	NUM
ejpam-7112	653	202	hamct	hamct	PROPN
ejpam-7112	653	203	20	20	NUM
ejpam-7112	653	204	2	2	NUM
ejpam-7112	653	205	0	0	NUM
ejpam-7112	653	206	19	19	NUM
ejpam-7112	653	207	19	19	NUM
ejpam-7112	653	208	19	19	NUM
ejpam-7112	653	209	0	0	NUM
ejpam-7112	653	210	79	79	NUM
ejpam-7112	653	211	hemct	hemct	ADJ
ejpam-7112	653	212	18	18	NUM
ejpam-7112	653	213	2	2	NUM
ejpam-7112	653	214	0	0	NUM
ejpam-7112	653	215	17	17	NUM
ejpam-7112	653	216	17	17	NUM
ejpam-7112	653	217	17	17	NUM
ejpam-7112	653	218	0	0	NUM
ejpam-7112	653	219	71	71	NUM
ejpam-7112	653	220	cmct	cmct	ADJ
ejpam-7112	653	221	15	15	NUM
ejpam-7112	653	222	2	2	NUM
ejpam-7112	653	223	0	0	NUM
ejpam-7112	653	224	14	14	NUM
ejpam-7112	653	225	14	14	NUM
ejpam-7112	653	226	14	14	NUM
ejpam-7112	653	227	0	0	NUM
ejpam-7112	653	228	59	59	NUM
ejpam-7112	653	229	table	table	NOUN
ejpam-7112	653	230	11	11	NUM
ejpam-7112	653	231	:	:	PUNCT
ejpam-7112	653	232	computational	computational	ADJ
ejpam-7112	653	233	cost	cost	NOUN
ejpam-7112	653	234	in	in	ADP
ejpam-7112	653	235	trapezoidal	trapezoidal	ADJ
ejpam-7112	653	236	variants	variant	NOUN
ejpam-7112	653	237	to	to	PART
ejpam-7112	653	238	achieve	achieve	VERB
ejpam-7112	653	239	ξ	ξ	PRON
ejpam-7112	653	240	≤	≤	NUM
ejpam-7112	653	241	10−5accuracy	10−5accuracy	NUM
ejpam-7112	653	242	in	in	ADP
ejpam-7112	653	243	example	example	NOUN
ejpam-7112	653	244	4	4	NUM
ejpam-7112	653	245	trapezoidal	trapezoidal	ADJ
ejpam-7112	653	246	variants	variant	NOUN
ejpam-7112	653	247	f	f	PROPN
ejpam-7112	653	248	g	g	PROPN
ejpam-7112	653	249	f	f	PROPN
ejpam-7112	653	250	(	(	PUNCT
ejpam-7112	653	251	1	1	NUM
ejpam-7112	653	252	)	)	PUNCT
ejpam-7112	653	253	f	f	NOUN
ejpam-7112	653	254	(	(	PUNCT
ejpam-7112	653	255	2	2	X
ejpam-7112	653	256	)	)	PUNCT
ejpam-7112	653	257	i1	i1	PROPN
ejpam-7112	653	258	i2	i2	PROPN
ejpam-7112	653	259	i3	i3	PROPN
ejpam-7112	653	260	total	total	NOUN
ejpam-7112	653	261	evaluations	evaluation	NOUN
ejpam-7112	653	262	ct	ct	VERB
ejpam-7112	654	1	995	995	NUM
ejpam-7112	654	2	2	2	NUM
ejpam-7112	654	3	0	0	NUM
ejpam-7112	654	4	0	0	NUM
ejpam-7112	654	5	994	994	NUM
ejpam-7112	654	6	0	0	NUM
ejpam-7112	654	7	0	0	NUM
ejpam-7112	654	8	1991	1991	NUM
ejpam-7112	654	9	zct	zct	NOUN
ejpam-7112	654	10	–	–	PUNCT
ejpam-7112	654	11	–	–	PUNCT
ejpam-7112	654	12	–	–	PUNCT
ejpam-7112	654	13	–	–	PUNCT
ejpam-7112	654	14	–	–	PUNCT
ejpam-7112	654	15	–	–	PUNCT
ejpam-7112	654	16	–	–	PUNCT
ejpam-7112	654	17	–	–	PUNCT
ejpam-7112	654	18	mzct	mzct	NOUN
ejpam-7112	654	19	–	–	PUNCT
ejpam-7112	654	20	–	–	PUNCT
ejpam-7112	654	21	–	–	PUNCT
ejpam-7112	654	22	–	–	PUNCT
ejpam-7112	654	23	–	–	PUNCT
ejpam-7112	654	24	–	–	PUNCT
ejpam-7112	654	25	–	–	PUNCT
ejpam-7112	654	26	–	–	PUNCT
ejpam-7112	654	27	amct	amct	VERB
ejpam-7112	654	28	22	22	NUM
ejpam-7112	654	29	2	2	NUM
ejpam-7112	654	30	0	0	NUM
ejpam-7112	654	31	21	21	NUM
ejpam-7112	654	32	21	21	NUM
ejpam-7112	654	33	21	21	NUM
ejpam-7112	654	34	0	0	NUM
ejpam-7112	654	35	87	87	NUM
ejpam-7112	654	36	gmct	gmct	ADJ
ejpam-7112	654	37	45	45	NUM
ejpam-7112	654	38	2	2	NUM
ejpam-7112	654	39	0	0	NUM
ejpam-7112	654	40	44	44	NUM
ejpam-7112	654	41	44	44	NUM
ejpam-7112	654	42	44	44	NUM
ejpam-7112	654	43	0	0	NUM
ejpam-7112	654	44	179	179	NUM
ejpam-7112	654	45	hamct	hamct	PROPN
ejpam-7112	654	46	49	49	NUM
ejpam-7112	654	47	2	2	NUM
ejpam-7112	654	48	0	0	NUM
ejpam-7112	654	49	48	48	NUM
ejpam-7112	654	50	48	48	NUM
ejpam-7112	654	51	48	48	NUM
ejpam-7112	654	52	0	0	NUM
ejpam-7112	654	53	195	195	NUM
ejpam-7112	654	54	hemct	hemct	ADJ
ejpam-7112	654	55	33	33	NUM
ejpam-7112	654	56	2	2	NUM
ejpam-7112	654	57	0	0	NUM
ejpam-7112	654	58	32	32	NUM
ejpam-7112	654	59	32	32	NUM
ejpam-7112	654	60	32	32	NUM
ejpam-7112	654	61	0	0	NUM
ejpam-7112	654	62	131	131	NUM
ejpam-7112	654	63	cmct	cmct	ADJ
ejpam-7112	654	64	38	38	NUM
ejpam-7112	654	65	2	2	NUM
ejpam-7112	654	66	0	0	NUM
ejpam-7112	654	67	37	37	NUM
ejpam-7112	654	68	37	37	NUM
ejpam-7112	654	69	37	37	NUM
ejpam-7112	654	70	0	0	NUM
ejpam-7112	654	71	151	151	NUM
ejpam-7112	654	72	k.	k.	NOUN
ejpam-7112	654	73	memon	memon	PROPN
ejpam-7112	654	74	et	et	PROPN
ejpam-7112	654	75	al	al	PROPN
ejpam-7112	654	76	.	.	PUNCT
ejpam-7112	654	77	/	/	SYM
ejpam-7112	654	78	eur	eur	PROPN
ejpam-7112	654	79	.	.	PUNCT
ejpam-7112	655	1	j.	j.	PROPN
ejpam-7112	655	2	pure	pure	PROPN
ejpam-7112	655	3	appl	appl	PROPN
ejpam-7112	655	4	.	.	PROPN
ejpam-7112	655	5	math	math	PROPN
ejpam-7112	655	6	,	,	PUNCT
ejpam-7112	655	7	18	18	NUM
ejpam-7112	655	8	(	(	PUNCT
ejpam-7112	655	9	4	4	NUM
ejpam-7112	655	10	)	)	PUNCT
ejpam-7112	655	11	(	(	PUNCT
ejpam-7112	655	12	2025	2025	NUM
ejpam-7112	655	13	)	)	PUNCT
ejpam-7112	655	14	,	,	PUNCT
ejpam-7112	655	15	7112	7112	NUM
ejpam-7112	655	16	36	36	NUM
ejpam-7112	655	17	of	of	ADP
ejpam-7112	655	18	38	38	NUM
ejpam-7112	655	19	table	table	NOUN
ejpam-7112	655	20	12	12	NUM
ejpam-7112	655	21	:	:	PUNCT
ejpam-7112	655	22	computational	computational	ADJ
ejpam-7112	655	23	cost	cost	NOUN
ejpam-7112	655	24	in	in	ADP
ejpam-7112	655	25	trapezoidal	trapezoidal	ADJ
ejpam-7112	655	26	variants	variant	NOUN
ejpam-7112	655	27	to	to	PART
ejpam-7112	655	28	achieve	achieve	VERB
ejpam-7112	655	29	ξ	ξ	PRON
ejpam-7112	655	30	≤	≤	NOUN
ejpam-7112	655	31	10−5	10−5	NUM
ejpam-7112	655	32	accuracy	accuracy	NOUN
ejpam-7112	655	33	in	in	ADP
ejpam-7112	655	34	example	example	NOUN
ejpam-7112	655	35	5	5	NUM
ejpam-7112	655	36	trapezoidal	trapezoidal	ADJ
ejpam-7112	655	37	variants	variant	NOUN
ejpam-7112	655	38	f	f	PROPN
ejpam-7112	655	39	g	g	PROPN
ejpam-7112	655	40	f	f	PROPN
ejpam-7112	655	41	(	(	PUNCT
ejpam-7112	655	42	1	1	NUM
ejpam-7112	655	43	)	)	PUNCT
ejpam-7112	655	44	f	f	NOUN
ejpam-7112	655	45	(	(	PUNCT
ejpam-7112	655	46	2	2	X
ejpam-7112	655	47	)	)	PUNCT
ejpam-7112	655	48	i1	i1	PROPN
ejpam-7112	655	49	i2	i2	PROPN
ejpam-7112	655	50	i3	i3	PROPN
ejpam-7112	655	51	total	total	NOUN
ejpam-7112	655	52	evaluations	evaluation	NOUN
ejpam-7112	655	53	ct	ct	NOUN
ejpam-7112	655	54	285	285	NUM
ejpam-7112	655	55	2	2	NUM
ejpam-7112	655	56	0	0	NUM
ejpam-7112	655	57	0	0	NUM
ejpam-7112	655	58	284	284	NUM
ejpam-7112	655	59	0	0	NUM
ejpam-7112	655	60	0	0	NUM
ejpam-7112	655	61	571	571	NUM
ejpam-7112	655	62	zct	zct	NOUN
ejpam-7112	655	63	–	–	PUNCT
ejpam-7112	655	64	–	–	PUNCT
ejpam-7112	655	65	–	–	PUNCT
ejpam-7112	655	66	–	–	PUNCT
ejpam-7112	655	67	–	–	PUNCT
ejpam-7112	655	68	–	–	PUNCT
ejpam-7112	655	69	–	–	PUNCT
ejpam-7112	655	70	–	–	PUNCT
ejpam-7112	655	71	mzct	mzct	NOUN
ejpam-7112	655	72	–	–	PUNCT
ejpam-7112	655	73	–	–	PUNCT
ejpam-7112	655	74	–	–	PUNCT
ejpam-7112	655	75	–	–	PUNCT
ejpam-7112	655	76	–	–	PUNCT
ejpam-7112	655	77	–	–	PUNCT
ejpam-7112	655	78	–	–	PUNCT
ejpam-7112	655	79	–	–	PUNCT
ejpam-7112	655	80	amct	amct	VERB
ejpam-7112	655	81	15	15	NUM
ejpam-7112	655	82	2	2	NUM
ejpam-7112	655	83	0	0	NUM
ejpam-7112	655	84	14	14	NUM
ejpam-7112	655	85	14	14	NUM
ejpam-7112	655	86	14	14	NUM
ejpam-7112	655	87	0	0	NUM
ejpam-7112	655	88	59	59	NUM
ejpam-7112	655	89	gmct	gmct	ADJ
ejpam-7112	655	90	327	327	NUM
ejpam-7112	655	91	2	2	NUM
ejpam-7112	655	92	0	0	NUM
ejpam-7112	655	93	326	326	NUM
ejpam-7112	655	94	326	326	NUM
ejpam-7112	655	95	326	326	NUM
ejpam-7112	655	96	0	0	NUM
ejpam-7112	655	97	1307	1307	NUM
ejpam-7112	655	98	hamct	hamct	VERB
ejpam-7112	655	99	27	27	NUM
ejpam-7112	655	100	2	2	NUM
ejpam-7112	655	101	0	0	NUM
ejpam-7112	655	102	26	26	NUM
ejpam-7112	655	103	26	26	NUM
ejpam-7112	655	104	26	26	NUM
ejpam-7112	655	105	0	0	NUM
ejpam-7112	655	106	107	107	NUM
ejpam-7112	655	107	hemct	hemct	ADJ
ejpam-7112	655	108	189	189	NUM
ejpam-7112	655	109	2	2	NUM
ejpam-7112	655	110	0	0	NUM
ejpam-7112	655	111	188	188	NUM
ejpam-7112	655	112	188	188	NUM
ejpam-7112	655	113	188	188	NUM
ejpam-7112	655	114	0	0	NUM
ejpam-7112	655	115	755	755	NUM
ejpam-7112	655	116	cmct	cmct	NUM
ejpam-7112	655	117	21	21	NUM
ejpam-7112	655	118	2	2	NUM
ejpam-7112	655	119	0	0	NUM
ejpam-7112	655	120	20	20	NUM
ejpam-7112	655	121	20	20	NUM
ejpam-7112	655	122	20	20	NUM
ejpam-7112	655	123	0	0	NUM
ejpam-7112	655	124	83	83	NUM
ejpam-7112	655	125	table	table	NOUN
ejpam-7112	655	126	13	13	NUM
ejpam-7112	655	127	:	:	PUNCT
ejpam-7112	655	128	average	average	ADJ
ejpam-7112	655	129	cpu	cpu	NOUN
ejpam-7112	655	130	time	time	NOUN
ejpam-7112	655	131	(	(	PUNCT
ejpam-7112	655	132	in	in	ADP
ejpam-7112	655	133	seconds	second	NOUN
ejpam-7112	655	134	)	)	PUNCT
ejpam-7112	655	135	to	to	PART
ejpam-7112	655	136	achieve	achieve	VERB
ejpam-7112	655	137	|ε|	|ε|	DET
ejpam-7112	655	138	≤	≤	NOUN
ejpam-7112	655	139	10−5	10−5	NUM
ejpam-7112	655	140	in	in	ADP
ejpam-7112	655	141	examples	example	NOUN
ejpam-7112	655	142	1	1	NUM
ejpam-7112	655	143	-	-	SYM
ejpam-7112	655	144	5	5	NUM
ejpam-7112	655	145	trapezoidal	trapezoidal	ADJ
ejpam-7112	655	146	variants	variant	NOUN
ejpam-7112	655	147	example	example	NOUN
ejpam-7112	655	148	1	1	NUM
ejpam-7112	655	149	example	example	NOUN
ejpam-7112	655	150	2	2	NUM
ejpam-7112	655	151	example	example	NOUN
ejpam-7112	655	152	3	3	NUM
ejpam-7112	655	153	example	example	NOUN
ejpam-7112	655	154	4	4	NUM
ejpam-7112	655	155	example	example	NOUN
ejpam-7112	655	156	5	5	NUM
ejpam-7112	655	157	ct	ct	NUM
ejpam-7112	655	158	68.043837	68.043837	NUM
ejpam-7112	655	159	12.821123	12.821123	NUM
ejpam-7112	655	160	432.303629	432.303629	NUM
ejpam-7112	655	161	364.293037	364.293037	NUM
ejpam-7112	655	162	39.670771	39.670771	NUM
ejpam-7112	655	163	zct	zct	NOUN
ejpam-7112	655	164	552.603703	552.603703	NUM
ejpam-7112	655	165	153.984100	153.984100	NUM
ejpam-7112	655	166	6469.382491	6469.382491	NUM
ejpam-7112	655	167	–	–	PUNCT
ejpam-7112	655	168	–	–	PUNCT
ejpam-7112	655	169	mzct	mzct	NOUN
ejpam-7112	655	170	28.010080	28.010080	NUM
ejpam-7112	655	171	5.261296	5.261296	NUM
ejpam-7112	655	172	27.353811	27.353811	NUM
ejpam-7112	655	173	–	–	PUNCT
ejpam-7112	655	174	–	–	PUNCT
ejpam-7112	655	175	amct	amct	VERB
ejpam-7112	655	176	14.760520	14.760520	NUM
ejpam-7112	655	177	3.085717	3.085717	NUM
ejpam-7112	655	178	14.702231	14.702231	NUM
ejpam-7112	655	179	20.346118	20.346118	NUM
ejpam-7112	655	180	7.468816	7.468816	NUM
ejpam-7112	655	181	gmct	gmct	ADJ
ejpam-7112	655	182	14.929914	14.929914	NUM
ejpam-7112	655	183	3.146952	3.146952	NUM
ejpam-7112	655	184	16.340413	16.340413	NUM
ejpam-7112	655	185	42.374740	42.374740	NUM
ejpam-7112	655	186	203.371200	203.371200	NUM
ejpam-7112	655	187	hamct	hamct	ADJ
ejpam-7112	655	188	14.880674	14.880674	NUM
ejpam-7112	655	189	3.230150	3.230150	NUM
ejpam-7112	655	190	17.171850	17.171850	NUM
ejpam-7112	655	191	46.938636	46.938636	NUM
ejpam-7112	655	192	11.446324	11.446324	NUM
ejpam-7112	655	193	hemct	hemct	ADJ
ejpam-7112	655	194	14.782009	14.782009	NUM
ejpam-7112	655	195	3.061632	3.061632	NUM
ejpam-7112	655	196	15.484834	15.484834	NUM
ejpam-7112	655	197	30.986400	30.986400	NUM
ejpam-7112	655	198	105.331456	105.331456	NUM
ejpam-7112	655	199	cmct	cmct	VERB
ejpam-7112	655	200	14.773490	14.773490	NUM
ejpam-7112	655	201	2.944814	2.944814	NUM
ejpam-7112	655	202	13.170858	13.170858	NUM
ejpam-7112	655	203	35.370088	35.370088	NUM
ejpam-7112	655	204	9.399820	9.399820	NUM
ejpam-7112	655	205	4	4	NUM
ejpam-7112	655	206	.	.	PUNCT
ejpam-7112	656	1	conclusion	conclusion	NOUN
ejpam-7112	656	2	this	this	DET
ejpam-7112	656	3	study	study	NOUN
ejpam-7112	656	4	focused	focus	VERB
ejpam-7112	656	5	the	the	DET
ejpam-7112	656	6	development	development	NOUN
ejpam-7112	656	7	of	of	ADP
ejpam-7112	656	8	new	new	ADJ
ejpam-7112	656	9	variants	variant	NOUN
ejpam-7112	656	10	of	of	ADP
ejpam-7112	656	11	trapezoid	trapezoid	ADJ
ejpam-7112	656	12	-	-	PUNCT
ejpam-7112	656	13	type	type	NOUN
ejpam-7112	656	14	quadrature	quadrature	NOUN
ejpam-7112	656	15	keeping	keep	VERB
ejpam-7112	656	16	track	track	NOUN
ejpam-7112	656	17	on	on	ADP
ejpam-7112	656	18	the	the	DET
ejpam-7112	656	19	efficiency	efficiency	NOUN
ejpam-7112	656	20	in	in	ADP
ejpam-7112	656	21	terms	term	NOUN
ejpam-7112	656	22	of	of	ADP
ejpam-7112	656	23	time	time	NOUN
ejpam-7112	656	24	and	and	CCONJ
ejpam-7112	656	25	cost	cost	NOUN
ejpam-7112	656	26	effectiveness	effectiveness	NOUN
ejpam-7112	656	27	for	for	ADP
ejpam-7112	656	28	the	the	DET
ejpam-7112	656	29	rs	rs	ADJ
ejpam-7112	656	30	-	-	ADJ
ejpam-7112	656	31	integral	integral	ADJ
ejpam-7112	656	32	approximation	approximation	NOUN
ejpam-7112	656	33	.	.	PUNCT
ejpam-7112	657	1	the	the	DET
ejpam-7112	657	2	derivative	derivative	ADJ
ejpam-7112	657	3	corrections	correction	NOUN
ejpam-7112	657	4	have	have	AUX
ejpam-7112	657	5	been	be	AUX
ejpam-7112	657	6	utilized	utilize	VERB
ejpam-7112	657	7	at	at	ADP
ejpam-7112	657	8	the	the	DET
ejpam-7112	657	9	points	point	NOUN
ejpam-7112	657	10	which	which	PRON
ejpam-7112	657	11	were	be	AUX
ejpam-7112	657	12	averages	average	NOUN
ejpam-7112	657	13	of	of	ADP
ejpam-7112	657	14	the	the	DET
ejpam-7112	657	15	limits	limit	NOUN
ejpam-7112	657	16	of	of	ADP
ejpam-7112	657	17	integration	integration	NOUN
ejpam-7112	657	18	.	.	PUNCT
ejpam-7112	658	1	the	the	DET
ejpam-7112	658	2	derivation	derivation	NOUN
ejpam-7112	658	3	of	of	ADP
ejpam-7112	658	4	proposed	propose	VERB
ejpam-7112	658	5	rules	rule	NOUN
ejpam-7112	658	6	was	be	AUX
ejpam-7112	658	7	discussed	discuss	VERB
ejpam-7112	658	8	along	along	ADP
ejpam-7112	658	9	with	with	ADP
ejpam-7112	658	10	proved	prove	VERB
ejpam-7112	658	11	theorems	theorem	NOUN
ejpam-7112	658	12	on	on	ADP
ejpam-7112	658	13	the	the	DET
ejpam-7112	658	14	local	local	ADJ
ejpam-7112	658	15	and	and	CCONJ
ejpam-7112	658	16	global	global	ADJ
ejpam-7112	658	17	applications	application	NOUN
ejpam-7112	658	18	,	,	PUNCT
ejpam-7112	658	19	local	local	ADJ
ejpam-7112	658	20	and	and	CCONJ
ejpam-7112	658	21	global	global	ADJ
ejpam-7112	658	22	truncation	truncation	NOUN
ejpam-7112	658	23	errors	error	NOUN
ejpam-7112	658	24	and	and	CCONJ
ejpam-7112	658	25	reduction	reduction	NOUN
ejpam-7112	658	26	to	to	ADP
ejpam-7112	658	27	conventional	conventional	ADJ
ejpam-7112	658	28	forms	form	NOUN
ejpam-7112	658	29	.	.	PUNCT
ejpam-7112	659	1	an	an	DET
ejpam-7112	659	2	exhaustive	exhaustive	ADJ
ejpam-7112	659	3	numerical	numerical	ADJ
ejpam-7112	659	4	examination	examination	NOUN
ejpam-7112	659	5	was	be	AUX
ejpam-7112	659	6	conducted	conduct	VERB
ejpam-7112	659	7	for	for	ADP
ejpam-7112	659	8	the	the	DET
ejpam-7112	659	9	thorough	thorough	ADJ
ejpam-7112	659	10	performance	performance	NOUN
ejpam-7112	659	11	evaluation	evaluation	NOUN
ejpam-7112	659	12	of	of	ADP
ejpam-7112	659	13	the	the	DET
ejpam-7112	659	14	previous	previous	ADJ
ejpam-7112	659	15	and	and	CCONJ
ejpam-7112	659	16	new	new	ADJ
ejpam-7112	659	17	quadrature	quadrature	NOUN
ejpam-7112	659	18	by	by	ADP
ejpam-7112	659	19	considering	consider	VERB
ejpam-7112	659	20	varying	vary	VERB
ejpam-7112	659	21	nature	nature	NOUN
ejpam-7112	659	22	test	test	NOUN
ejpam-7112	659	23	rsintegrals	rsintegral	NOUN
ejpam-7112	659	24	from	from	ADP
ejpam-7112	659	25	literature	literature	NOUN
ejpam-7112	659	26	.	.	PUNCT
ejpam-7112	660	1	the	the	DET
ejpam-7112	660	2	new	new	ADJ
ejpam-7112	660	3	quadrature	quadrature	NOUN
ejpam-7112	660	4	enhance	enhance	VERB
ejpam-7112	660	5	precision	precision	NOUN
ejpam-7112	660	6	and	and	CCONJ
ejpam-7112	660	7	accuracy	accuracy	NOUN
ejpam-7112	660	8	of	of	ADP
ejpam-7112	660	9	the	the	DET
ejpam-7112	660	10	previously	previously	ADV
ejpam-7112	660	11	existing	exist	VERB
ejpam-7112	660	12	quadrature	quadrature	NOUN
ejpam-7112	660	13	.	.	PUNCT
ejpam-7112	661	1	the	the	DET
ejpam-7112	661	2	numerical	numerical	ADJ
ejpam-7112	661	3	results	result	NOUN
ejpam-7112	661	4	on	on	ADP
ejpam-7112	661	5	error	error	NOUN
ejpam-7112	661	6	drops	drop	NOUN
ejpam-7112	661	7	,	,	PUNCT
ejpam-7112	661	8	accuracy	accuracy	NOUN
ejpam-7112	661	9	(	(	PUNCT
ejpam-7112	661	10	orders	order	NOUN
ejpam-7112	661	11	observed	observe	VERB
ejpam-7112	661	12	computationally	computationally	ADV
ejpam-7112	661	13	)	)	PUNCT
ejpam-7112	661	14	,	,	PUNCT
ejpam-7112	661	15	execution	execution	NOUN
ejpam-7112	661	16	times	time	NOUN
ejpam-7112	661	17	and	and	CCONJ
ejpam-7112	661	18	computational	computational	ADJ
ejpam-7112	661	19	overheads	overhead	NOUN
ejpam-7112	661	20	in	in	ADP
ejpam-7112	661	21	all	all	DET
ejpam-7112	661	22	considered	consider	VERB
ejpam-7112	661	23	problems	problem	NOUN
ejpam-7112	661	24	reflected	reflect	VERB
ejpam-7112	661	25	encouraging	encourage	VERB
ejpam-7112	661	26	behavior	behavior	NOUN
ejpam-7112	661	27	and	and	CCONJ
ejpam-7112	661	28	application	application	NOUN
ejpam-7112	661	29	of	of	ADP
ejpam-7112	661	30	the	the	DET
ejpam-7112	661	31	proposed	propose	VERB
ejpam-7112	661	32	quadrature	quadrature	NOUN
ejpam-7112	661	33	over	over	ADP
ejpam-7112	661	34	existing	exist	VERB
ejpam-7112	661	35	ones	one	NOUN
ejpam-7112	661	36	.	.	PUNCT
ejpam-7112	662	1	besides	besides	SCONJ
ejpam-7112	662	2	,	,	PUNCT
ejpam-7112	662	3	we	we	PRON
ejpam-7112	662	4	also	also	ADV
ejpam-7112	662	5	highlighted	highlight	VERB
ejpam-7112	662	6	the	the	DET
ejpam-7112	662	7	critical	critical	ADJ
ejpam-7112	662	8	cases	case	NOUN
ejpam-7112	662	9	indicating	indicate	VERB
ejpam-7112	662	10	natural	natural	ADJ
ejpam-7112	662	11	limitations	limitation	NOUN
ejpam-7112	662	12	and	and	CCONJ
ejpam-7112	662	13	usability	usability	NOUN
ejpam-7112	662	14	of	of	ADP
ejpam-7112	662	15	the	the	DET
ejpam-7112	662	16	used	use	VERB
ejpam-7112	662	17	quadrature	quadrature	NOUN
ejpam-7112	662	18	for	for	ADP
ejpam-7112	662	19	the	the	DET
ejpam-7112	662	20	rs	r	NOUN
ejpam-7112	662	21	-	-	PUNCT
ejpam-7112	662	22	integrals	integral	NOUN
ejpam-7112	662	23	.	.	PUNCT
ejpam-7112	663	1	the	the	DET
ejpam-7112	663	2	proposed	propose	VERB
ejpam-7112	663	3	quadrature	quadrature	NOUN
ejpam-7112	663	4	appear	appear	VERB
ejpam-7112	663	5	to	to	PART
ejpam-7112	663	6	be	be	AUX
ejpam-7112	663	7	efficient	efficient	ADJ
ejpam-7112	663	8	enhancements	enhancement	NOUN
ejpam-7112	663	9	,	,	PUNCT
ejpam-7112	663	10	both	both	CCONJ
ejpam-7112	663	11	in	in	ADP
ejpam-7112	663	12	terms	term	NOUN
ejpam-7112	663	13	of	of	ADP
ejpam-7112	663	14	accuracy	accuracy	NOUN
ejpam-7112	663	15	and	and	CCONJ
ejpam-7112	663	16	computational	computational	ADJ
ejpam-7112	663	17	cost	cost	NOUN
ejpam-7112	663	18	,	,	PUNCT
ejpam-7112	663	19	over	over	ADP
ejpam-7112	663	20	the	the	DET
ejpam-7112	663	21	existing	exist	VERB
ejpam-7112	663	22	ones	one	NOUN
ejpam-7112	663	23	.	.	PUNCT
ejpam-7112	664	1	the	the	DET
ejpam-7112	664	2	contributions	contribution	NOUN
ejpam-7112	664	3	of	of	ADP
ejpam-7112	664	4	k.	k.	PROPN
ejpam-7112	664	5	memon	memon	PROPN
ejpam-7112	664	6	et	et	PROPN
ejpam-7112	664	7	al	al	PROPN
ejpam-7112	664	8	.	.	PUNCT
ejpam-7112	664	9	/	/	SYM
ejpam-7112	664	10	eur	eur	PROPN
ejpam-7112	664	11	.	.	PUNCT
ejpam-7112	665	1	j.	j.	PROPN
ejpam-7112	665	2	pure	pure	PROPN
ejpam-7112	665	3	appl	appl	PROPN
ejpam-7112	665	4	.	.	PROPN
ejpam-7112	665	5	math	math	PROPN
ejpam-7112	665	6	,	,	PUNCT
ejpam-7112	665	7	18	18	NUM
ejpam-7112	665	8	(	(	PUNCT
ejpam-7112	665	9	4	4	NUM
ejpam-7112	665	10	)	)	PUNCT
ejpam-7112	665	11	(	(	PUNCT
ejpam-7112	665	12	2025	2025	NUM
ejpam-7112	665	13	)	)	PUNCT
ejpam-7112	665	14	,	,	PUNCT
ejpam-7112	665	15	7112	7112	NUM
ejpam-7112	665	16	37	37	NUM
ejpam-7112	665	17	of	of	ADP
ejpam-7112	665	18	38	38	NUM
ejpam-7112	665	19	this	this	DET
ejpam-7112	665	20	study	study	NOUN
ejpam-7112	665	21	can	can	AUX
ejpam-7112	665	22	be	be	AUX
ejpam-7112	665	23	useful	useful	ADJ
ejpam-7112	665	24	in	in	ADP
ejpam-7112	665	25	future	future	ADJ
ejpam-7112	665	26	studies	study	NOUN
ejpam-7112	665	27	focusing	focus	VERB
ejpam-7112	665	28	the	the	DET
ejpam-7112	665	29	fractional	fractional	ADJ
ejpam-7112	665	30	integration	integration	NOUN
ejpam-7112	665	31	and	and	CCONJ
ejpam-7112	665	32	solving	solve	VERB
ejpam-7112	665	33	integral	integral	ADJ
ejpam-7112	665	34	and	and	CCONJ
ejpam-7112	665	35	integro	integro	ADJ
ejpam-7112	665	36	-	-	PUNCT
ejpam-7112	665	37	differential	differential	NOUN
ejpam-7112	665	38	equations	equation	NOUN
ejpam-7112	665	39	with	with	ADP
ejpam-7112	665	40	different	different	ADJ
ejpam-7112	665	41	weight	weight	NOUN
ejpam-7112	665	42	functions	function	NOUN
ejpam-7112	665	43	.	.	PUNCT
ejpam-7112	666	1	references	reference	NOUN
ejpam-7112	666	2	[	[	X
ejpam-7112	666	3	1	1	NUM
ejpam-7112	666	4	]	]	PUNCT
ejpam-7112	666	5	r.	r.	PROPN
ejpam-7112	666	6	l.	l.	PROPN
ejpam-7112	666	7	burden	burden	PROPN
ejpam-7112	666	8	and	and	CCONJ
ejpam-7112	666	9	j.	j.	PROPN
ejpam-7112	666	10	d.	d.	PROPN
ejpam-7112	666	11	faires	faires	PROPN
ejpam-7112	666	12	.	.	PUNCT
ejpam-7112	667	1	numerical	numerical	ADJ
ejpam-7112	667	2	analysis	analysis	NOUN
ejpam-7112	667	3	.	.	PUNCT
ejpam-7112	668	1	brooks	brooks	PROPN
ejpam-7112	668	2	/	/	SYM
ejpam-7112	668	3	cole	cole	PROPN
ejpam-7112	668	4	,	,	PUNCT
ejpam-7112	668	5	boston	boston	PROPN
ejpam-7112	668	6	,	,	PUNCT
ejpam-7112	668	7	ma	ma	PROPN
ejpam-7112	668	8	,	,	PUNCT
ejpam-7112	668	9	usa	usa	PROPN
ejpam-7112	668	10	,	,	PUNCT
ejpam-7112	668	11	9th	9th	ADJ
ejpam-7112	668	12	edition	edition	NOUN
ejpam-7112	668	13	,	,	PUNCT
ejpam-7112	668	14	2011	2011	NUM
ejpam-7112	668	15	.	.	PUNCT
ejpam-7112	669	1	[	[	X
ejpam-7112	669	2	2	2	X
ejpam-7112	669	3	]	]	PUNCT
ejpam-7112	669	4	p.	p.	PROPN
ejpam-7112	669	5	r.	r.	PROPN
ejpam-7112	669	6	mercer	mercer	PROPN
ejpam-7112	669	7	.	.	PUNCT
ejpam-7112	670	1	hadamard	hadamard	PROPN
ejpam-7112	670	2	’s	’s	PART
ejpam-7112	670	3	inequality	inequality	NOUN
ejpam-7112	670	4	and	and	CCONJ
ejpam-7112	670	5	trapezoid	trapezoid	ADJ
ejpam-7112	670	6	rules	rule	NOUN
ejpam-7112	670	7	for	for	ADP
ejpam-7112	670	8	the	the	DET
ejpam-7112	670	9	riemann	riemann	PROPN
ejpam-7112	670	10	-	-	PUNCT
ejpam-7112	670	11	stieltjes	stieltjes	PROPN
ejpam-7112	670	12	integral	integral	ADJ
ejpam-7112	670	13	.	.	PUNCT
ejpam-7112	670	14	journal	journal	PROPN
ejpam-7112	670	15	of	of	ADP
ejpam-7112	670	16	mathematical	mathematical	ADJ
ejpam-7112	670	17	analysis	analysis	NOUN
ejpam-7112	670	18	and	and	CCONJ
ejpam-7112	670	19	applications	application	NOUN
ejpam-7112	670	20	,	,	PUNCT
ejpam-7112	670	21	344:921–926	344:921–926	NUM
ejpam-7112	670	22	,	,	PUNCT
ejpam-7112	670	23	2008	2008	NUM
ejpam-7112	670	24	.	.	PUNCT
ejpam-7112	671	1	[	[	X
ejpam-7112	671	2	3	3	X
ejpam-7112	671	3	]	]	X
ejpam-7112	671	4	p.	p.	PROPN
ejpam-7112	671	5	r.	r.	PROPN
ejpam-7112	671	6	mercer	mercer	PROPN
ejpam-7112	671	7	.	.	PROPN
ejpam-7112	671	8	relative	relative	ADJ
ejpam-7112	671	9	convexity	convexity	NOUN
ejpam-7112	671	10	and	and	CCONJ
ejpam-7112	671	11	quadrature	quadrature	NOUN
ejpam-7112	671	12	rules	rule	NOUN
ejpam-7112	671	13	for	for	ADP
ejpam-7112	671	14	the	the	DET
ejpam-7112	671	15	riemann	riemann	PROPN
ejpam-7112	671	16	-	-	PUNCT
ejpam-7112	671	17	stieltjes	stieltjes	PROPN
ejpam-7112	671	18	integral	integral	ADJ
ejpam-7112	671	19	.	.	PUNCT
ejpam-7112	671	20	journal	journal	PROPN
ejpam-7112	671	21	of	of	ADP
ejpam-7112	671	22	mathematical	mathematical	ADJ
ejpam-7112	671	23	inequalities	inequality	NOUN
ejpam-7112	671	24	,	,	PUNCT
ejpam-7112	671	25	6:65–68	6:65–68	NOUN
ejpam-7112	671	26	,	,	PUNCT
ejpam-7112	671	27	2012	2012	NUM
ejpam-7112	671	28	.	.	PUNCT
ejpam-7112	672	1	[	[	X
ejpam-7112	672	2	4	4	X
ejpam-7112	672	3	]	]	PUNCT
ejpam-7112	672	4	w.	w.	PROPN
ejpam-7112	672	5	zhao	zhao	PROPN
ejpam-7112	672	6	and	and	CCONJ
ejpam-7112	672	7	h.	h.	PROPN
ejpam-7112	672	8	li	li	PROPN
ejpam-7112	672	9	.	.	PROPN
ejpam-7112	672	10	midpoint	midpoint	PROPN
ejpam-7112	672	11	derivative	derivative	NOUN
ejpam-7112	672	12	-	-	PUNCT
ejpam-7112	672	13	based	base	VERB
ejpam-7112	672	14	closed	closed	ADJ
ejpam-7112	672	15	newton	newton	PROPN
ejpam-7112	672	16	-	-	PUNCT
ejpam-7112	672	17	cotes	cote	NOUN
ejpam-7112	672	18	quadrature	quadrature	NOUN
ejpam-7112	672	19	.	.	PUNCT
ejpam-7112	673	1	abstract	abstract	ADJ
ejpam-7112	673	2	and	and	CCONJ
ejpam-7112	673	3	applied	apply	VERB
ejpam-7112	673	4	analysis	analysis	NOUN
ejpam-7112	673	5	,	,	PUNCT
ejpam-7112	673	6	2013	2013	NUM
ejpam-7112	673	7	.	.	PUNCT
ejpam-7112	674	1	article	article	NOUN
ejpam-7112	674	2	i	i	PROPN
ejpam-7112	674	3	d	d	PROPN
ejpam-7112	674	4	492507	492507	NUM
ejpam-7112	674	5	.	.	PUNCT
ejpam-7112	675	1	[	[	X
ejpam-7112	675	2	5	5	X
ejpam-7112	675	3	]	]	PUNCT
ejpam-7112	675	4	w.	w.	PROPN
ejpam-7112	675	5	zhao	zhao	PROPN
ejpam-7112	675	6	,	,	PUNCT
ejpam-7112	675	7	z.	z.	PROPN
ejpam-7112	675	8	zhang	zhang	PROPN
ejpam-7112	675	9	,	,	PUNCT
ejpam-7112	675	10	and	and	CCONJ
ejpam-7112	675	11	z.	z.	PROPN
ejpam-7112	675	12	ye	ye	PROPN
ejpam-7112	675	13	.	.	PROPN
ejpam-7112	675	14	midpoint	midpoint	PROPN
ejpam-7112	675	15	derivative	derivative	NOUN
ejpam-7112	675	16	-	-	PUNCT
ejpam-7112	675	17	based	base	VERB
ejpam-7112	675	18	trapezoid	trapezoid	ADJ
ejpam-7112	675	19	rule	rule	NOUN
ejpam-7112	675	20	for	for	ADP
ejpam-7112	675	21	the	the	DET
ejpam-7112	675	22	riemann	riemann	PROPN
ejpam-7112	675	23	-	-	PUNCT
ejpam-7112	675	24	stieltjes	stieltjes	PROPN
ejpam-7112	675	25	integral	integral	ADJ
ejpam-7112	675	26	.	.	PUNCT
ejpam-7112	675	27	italian	italian	ADJ
ejpam-7112	675	28	journal	journal	NOUN
ejpam-7112	675	29	of	of	ADP
ejpam-7112	675	30	pure	pure	ADJ
ejpam-7112	675	31	and	and	CCONJ
ejpam-7112	675	32	applied	applied	ADJ
ejpam-7112	675	33	mathematics	mathematic	NOUN
ejpam-7112	675	34	,	,	PUNCT
ejpam-7112	675	35	33:369	33:369	NUM
ejpam-7112	675	36	–	–	PUNCT
ejpam-7112	675	37	376	376	NUM
ejpam-7112	675	38	,	,	PUNCT
ejpam-7112	675	39	2014	2014	NUM
ejpam-7112	675	40	.	.	PUNCT
ejpam-7112	676	1	[	[	X
ejpam-7112	676	2	6	6	NUM
ejpam-7112	676	3	]	]	PUNCT
ejpam-7112	676	4	m.	m.	NOUN
ejpam-7112	676	5	m.	m.	NOUN
ejpam-7112	676	6	shaikh	shaikh	PROPN
ejpam-7112	676	7	,	,	PUNCT
ejpam-7112	676	8	m.	m.	NOUN
ejpam-7112	676	9	s.	s.	PROPN
ejpam-7112	676	10	chandio	chandio	PROPN
ejpam-7112	676	11	,	,	PUNCT
ejpam-7112	676	12	and	and	CCONJ
ejpam-7112	676	13	a.	a.	PROPN
ejpam-7112	676	14	s.	s.	PROPN
ejpam-7112	676	15	soomro	soomro	PROPN
ejpam-7112	676	16	.	.	PUNCT
ejpam-7112	677	1	a	a	DET
ejpam-7112	677	2	modified	modify	VERB
ejpam-7112	677	3	fourpoint	fourpoint	NOUN
ejpam-7112	677	4	closed	closed	ADJ
ejpam-7112	677	5	midpoint	midpoint	NOUN
ejpam-7112	677	6	derivative	derivative	NOUN
ejpam-7112	677	7	-	-	PUNCT
ejpam-7112	677	8	based	base	VERB
ejpam-7112	677	9	quadrature	quadrature	NOUN
ejpam-7112	677	10	rule	rule	NOUN
ejpam-7112	677	11	for	for	ADP
ejpam-7112	677	12	numerical	numerical	ADJ
ejpam-7112	677	13	integration	integration	NOUN
ejpam-7112	677	14	.	.	PUNCT
ejpam-7112	678	1	sindh	sindh	PROPN
ejpam-7112	678	2	university	university	PROPN
ejpam-7112	678	3	research	research	PROPN
ejpam-7112	678	4	journal	journal	PROPN
ejpam-7112	678	5	(	(	PUNCT
ejpam-7112	678	6	science	science	NOUN
ejpam-7112	678	7	series	series	PROPN
ejpam-7112	678	8	)	)	PUNCT
ejpam-7112	678	9	,	,	PUNCT
ejpam-7112	678	10	48(2	48(2	NUM
ejpam-7112	678	11	)	)	PUNCT
ejpam-7112	678	12	,	,	PUNCT
ejpam-7112	678	13	2016	2016	NUM
ejpam-7112	678	14	.	.	PUNCT
ejpam-7112	679	1	[	[	X
ejpam-7112	679	2	7	7	X
ejpam-7112	679	3	]	]	X
ejpam-7112	679	4	t.	t.	PROPN
ejpam-7112	679	5	ramachandran	ramachandran	PROPN
ejpam-7112	679	6	,	,	PUNCT
ejpam-7112	679	7	d.	d.	PROPN
ejpam-7112	679	8	udayakumar	udayakumar	PROPN
ejpam-7112	679	9	,	,	PUNCT
ejpam-7112	679	10	and	and	CCONJ
ejpam-7112	679	11	r.	r.	PROPN
ejpam-7112	679	12	parimala	parimala	PROPN
ejpam-7112	679	13	.	.	PUNCT
ejpam-7112	680	1	geometric	geometric	ADJ
ejpam-7112	680	2	mean	mean	NOUN
ejpam-7112	680	3	derivativebased	derivativebase	VERB
ejpam-7112	680	4	closed	closed	PROPN
ejpam-7112	680	5	newton	newton	PROPN
ejpam-7112	680	6	-	-	PUNCT
ejpam-7112	680	7	cotes	cote	NOUN
ejpam-7112	680	8	quadrature	quadrature	NOUN
ejpam-7112	680	9	.	.	PUNCT
ejpam-7112	681	1	international	international	ADJ
ejpam-7112	681	2	journal	journal	NOUN
ejpam-7112	681	3	of	of	ADP
ejpam-7112	681	4	pure	pure	ADJ
ejpam-7112	681	5	and	and	CCONJ
ejpam-7112	681	6	engineering	engineering	NOUN
ejpam-7112	681	7	mathematics	mathematic	NOUN
ejpam-7112	681	8	,	,	PUNCT
ejpam-7112	681	9	4:107–116	4:107–116	PROPN
ejpam-7112	681	10	,	,	PUNCT
ejpam-7112	681	11	2016	2016	NUM
ejpam-7112	681	12	.	.	PUNCT
ejpam-7112	682	1	[	[	X
ejpam-7112	682	2	8	8	X
ejpam-7112	682	3	]	]	PUNCT
ejpam-7112	682	4	t.	t.	PROPN
ejpam-7112	682	5	ramachandran	ramachandran	PROPN
ejpam-7112	682	6	,	,	PUNCT
ejpam-7112	682	7	d.	d.	PROPN
ejpam-7112	682	8	udayakumar	udayakumar	PROPN
ejpam-7112	682	9	,	,	PUNCT
ejpam-7112	682	10	and	and	CCONJ
ejpam-7112	682	11	r.	r.	PROPN
ejpam-7112	682	12	parimala	parimala	PROPN
ejpam-7112	682	13	.	.	PUNCT
ejpam-7112	683	1	harmonic	harmonic	PROPN
ejpam-7112	683	2	mean	mean	PROPN
ejpam-7112	683	3	derivativebased	derivativebase	VERB
ejpam-7112	683	4	closed	closed	PROPN
ejpam-7112	683	5	newton	newton	PROPN
ejpam-7112	683	6	-	-	PUNCT
ejpam-7112	683	7	cotes	cote	NOUN
ejpam-7112	683	8	quadrature	quadrature	NOUN
ejpam-7112	683	9	.	.	PUNCT
ejpam-7112	684	1	iosr	iosr	ADJ
ejpam-7112	684	2	journal	journal	PROPN
ejpam-7112	684	3	of	of	ADP
ejpam-7112	684	4	mathematics	mathematic	NOUN
ejpam-7112	684	5	,	,	PUNCT
ejpam-7112	684	6	12:36–41	12:36–41	NUM
ejpam-7112	684	7	,	,	PUNCT
ejpam-7112	684	8	2016	2016	NUM
ejpam-7112	684	9	.	.	PUNCT
ejpam-7112	685	1	[	[	X
ejpam-7112	685	2	9	9	NUM
ejpam-7112	685	3	]	]	PUNCT
ejpam-7112	685	4	t.	t.	PROPN
ejpam-7112	685	5	ramachandran	ramachandran	PROPN
ejpam-7112	685	6	,	,	PUNCT
ejpam-7112	685	7	d.	d.	PROPN
ejpam-7112	685	8	udayakumar	udayakumar	PROPN
ejpam-7112	685	9	,	,	PUNCT
ejpam-7112	685	10	and	and	CCONJ
ejpam-7112	685	11	r.	r.	PROPN
ejpam-7112	685	12	parimala	parimala	PROPN
ejpam-7112	685	13	.	.	PUNCT
ejpam-7112	686	1	comparison	comparison	NOUN
ejpam-7112	686	2	of	of	ADP
ejpam-7112	686	3	arithmetic	arithmetic	ADJ
ejpam-7112	686	4	mean	mean	NOUN
ejpam-7112	686	5	,	,	PUNCT
ejpam-7112	686	6	geometric	geometric	ADJ
ejpam-7112	686	7	mean	mean	NOUN
ejpam-7112	686	8	and	and	CCONJ
ejpam-7112	686	9	harmonic	harmonic	ADJ
ejpam-7112	686	10	mean	mean	NOUN
ejpam-7112	686	11	derivative	derivative	NOUN
ejpam-7112	686	12	-	-	PUNCT
ejpam-7112	686	13	based	base	VERB
ejpam-7112	686	14	closed	closed	ADJ
ejpam-7112	686	15	newton	newton	PROPN
ejpam-7112	686	16	-	-	PUNCT
ejpam-7112	686	17	cotes	cote	NOUN
ejpam-7112	686	18	quadrature	quadrature	NOUN
ejpam-7112	686	19	.	.	PUNCT
ejpam-7112	687	1	progress	progress	NOUN
ejpam-7112	687	2	in	in	ADP
ejpam-7112	687	3	nonlinear	nonlinear	ADJ
ejpam-7112	687	4	dynamics	dynamic	NOUN
ejpam-7112	687	5	and	and	CCONJ
ejpam-7112	687	6	chaos	chaos	NOUN
ejpam-7112	687	7	,	,	PUNCT
ejpam-7112	687	8	4:35–43	4:35–43	NUM
ejpam-7112	687	9	,	,	PUNCT
ejpam-7112	687	10	2016	2016	NUM
ejpam-7112	687	11	.	.	PUNCT
ejpam-7112	688	1	[	[	X
ejpam-7112	688	2	10	10	NUM
ejpam-7112	688	3	]	]	PUNCT
ejpam-7112	688	4	t.	t.	PROPN
ejpam-7112	688	5	ramachandran	ramachandran	PROPN
ejpam-7112	688	6	,	,	PUNCT
ejpam-7112	688	7	d.	d.	PROPN
ejpam-7112	688	8	udayakumar	udayakumar	PROPN
ejpam-7112	688	9	,	,	PUNCT
ejpam-7112	688	10	and	and	CCONJ
ejpam-7112	688	11	r.	r.	PROPN
ejpam-7112	688	12	parimala	parimala	PROPN
ejpam-7112	688	13	.	.	PUNCT
ejpam-7112	689	1	heronian	heronian	PROPN
ejpam-7112	689	2	mean	mean	PROPN
ejpam-7112	689	3	derivativebased	derivativebase	VERB
ejpam-7112	689	4	closed	closed	PROPN
ejpam-7112	689	5	newton	newton	PROPN
ejpam-7112	689	6	-	-	PUNCT
ejpam-7112	689	7	cotes	cote	NOUN
ejpam-7112	689	8	quadrature	quadrature	NOUN
ejpam-7112	689	9	.	.	PUNCT
ejpam-7112	690	1	international	international	ADJ
ejpam-7112	690	2	journal	journal	PROPN
ejpam-7112	690	3	of	of	ADP
ejpam-7112	690	4	mathematical	mathematical	ADJ
ejpam-7112	690	5	archive	archive	NOUN
ejpam-7112	690	6	,	,	PUNCT
ejpam-7112	690	7	7:53–58	7:53–58	NUM
ejpam-7112	690	8	,	,	PUNCT
ejpam-7112	690	9	2016	2016	NUM
ejpam-7112	690	10	.	.	PUNCT
ejpam-7112	691	1	[	[	X
ejpam-7112	691	2	11	11	NUM
ejpam-7112	691	3	]	]	PUNCT
ejpam-7112	691	4	t.	t.	PROPN
ejpam-7112	691	5	ramachandran	ramachandran	PROPN
ejpam-7112	691	6	,	,	PUNCT
ejpam-7112	691	7	d.	d.	PROPN
ejpam-7112	691	8	udayakumar	udayakumar	PROPN
ejpam-7112	691	9	,	,	PUNCT
ejpam-7112	691	10	and	and	CCONJ
ejpam-7112	691	11	r.	r.	PROPN
ejpam-7112	691	12	parimala	parimala	PROPN
ejpam-7112	691	13	.	.	PUNCT
ejpam-7112	692	1	centroidal	centroidal	PROPN
ejpam-7112	692	2	mean	mean	PROPN
ejpam-7112	692	3	derivativebased	derivativebase	VERB
ejpam-7112	692	4	closed	closed	PROPN
ejpam-7112	692	5	newton	newton	PROPN
ejpam-7112	692	6	-	-	PUNCT
ejpam-7112	692	7	cotes	cote	NOUN
ejpam-7112	692	8	quadrature	quadrature	NOUN
ejpam-7112	692	9	.	.	PUNCT
ejpam-7112	693	1	international	international	ADJ
ejpam-7112	693	2	journal	journal	PROPN
ejpam-7112	693	3	of	of	ADP
ejpam-7112	693	4	science	science	NOUN
ejpam-7112	693	5	and	and	CCONJ
ejpam-7112	693	6	research	research	NOUN
ejpam-7112	693	7	,	,	PUNCT
ejpam-7112	693	8	5:338–343	5:338–343	PROPN
ejpam-7112	693	9	,	,	PUNCT
ejpam-7112	693	10	2016	2016	NUM
ejpam-7112	693	11	.	.	PUNCT
ejpam-7112	694	1	[	[	X
ejpam-7112	694	2	12	12	NUM
ejpam-7112	694	3	]	]	PUNCT
ejpam-7112	694	4	sara	sara	PROPN
ejpam-7112	694	5	mahesar	mahesar	PROPN
ejpam-7112	694	6	,	,	PUNCT
ejpam-7112	694	7	muhammad	muhammad	PROPN
ejpam-7112	694	8	mujtaba	mujtaba	PROPN
ejpam-7112	694	9	shaikh	shaikh	PROPN
ejpam-7112	694	10	,	,	PUNCT
ejpam-7112	694	11	muhammad	muhammad	PROPN
ejpam-7112	694	12	saleem	saleem	PROPN
ejpam-7112	694	13	chandio	chandio	PROPN
ejpam-7112	694	14	,	,	PUNCT
ejpam-7112	694	15	and	and	CCONJ
ejpam-7112	694	16	abdul	abdul	PROPN
ejpam-7112	694	17	wasim	wasim	PROPN
ejpam-7112	694	18	shaikh	shaikh	PROPN
ejpam-7112	694	19	.	.	PUNCT
ejpam-7112	695	1	some	some	DET
ejpam-7112	695	2	new	new	ADJ
ejpam-7112	695	3	time	time	NOUN
ejpam-7112	695	4	and	and	CCONJ
ejpam-7112	695	5	cost	cost	VERB
ejpam-7112	695	6	efficient	efficient	ADJ
ejpam-7112	695	7	quadrature	quadrature	NOUN
ejpam-7112	695	8	formulas	formula	NOUN
ejpam-7112	695	9	to	to	PART
ejpam-7112	695	10	compute	compute	VERB
ejpam-7112	695	11	integrals	integral	NOUN
ejpam-7112	695	12	using	use	VERB
ejpam-7112	695	13	derivatives	derivative	NOUN
ejpam-7112	695	14	with	with	ADP
ejpam-7112	695	15	error	error	NOUN
ejpam-7112	695	16	analysis	analysis	NOUN
ejpam-7112	695	17	.	.	PUNCT
ejpam-7112	696	1	symmetry	symmetry	NOUN
ejpam-7112	696	2	,	,	PUNCT
ejpam-7112	696	3	14(12):2611	14(12):2611	NUM
ejpam-7112	696	4	,	,	PUNCT
ejpam-7112	696	5	2022	2022	NUM
ejpam-7112	696	6	.	.	PUNCT
ejpam-7112	697	1	[	[	X
ejpam-7112	697	2	13	13	NUM
ejpam-7112	697	3	]	]	PUNCT
ejpam-7112	697	4	kashif	kashif	PROPN
ejpam-7112	697	5	memon	memon	PROPN
ejpam-7112	697	6	,	,	PUNCT
ejpam-7112	697	7	muhammad	muhammad	PROPN
ejpam-7112	697	8	mujtaba	mujtaba	PROPN
ejpam-7112	697	9	shaikh	shaikh	PROPN
ejpam-7112	697	10	,	,	PUNCT
ejpam-7112	697	11	and	and	CCONJ
ejpam-7112	697	12	sara	sara	PROPN
ejpam-7112	697	13	mahesar	mahesar	PROPN
ejpam-7112	697	14	.	.	PUNCT
ejpam-7112	698	1	numerical	numerical	PROPN
ejpam-7112	698	2	investigation	investigation	NOUN
ejpam-7112	698	3	of	of	ADP
ejpam-7112	698	4	a	a	DET
ejpam-7112	698	5	four	four	NUM
ejpam-7112	698	6	-	-	PUNCT
ejpam-7112	698	7	point	point	NOUN
ejpam-7112	698	8	simpson	simpson	PROPN
ejpam-7112	698	9	’s	’s	PART
ejpam-7112	698	10	quadrature	quadrature	NOUN
ejpam-7112	698	11	for	for	ADP
ejpam-7112	698	12	computing	compute	VERB
ejpam-7112	698	13	riemann	riemann	PROPN
ejpam-7112	698	14	-	-	PUNCT
ejpam-7112	698	15	stieltjes	stieltjes	PROPN
ejpam-7112	698	16	integrals	integral	NOUN
ejpam-7112	698	17	.	.	PUNCT
ejpam-7112	699	1	ned	ned	PROPN
ejpam-7112	699	2	university	university	PROPN
ejpam-7112	699	3	journal	journal	NOUN
ejpam-7112	699	4	of	of	ADP
ejpam-7112	699	5	research	research	NOUN
ejpam-7112	699	6	,	,	PUNCT
ejpam-7112	699	7	22(1/2):27–44	22(1/2):27–44	NUM
ejpam-7112	699	8	,	,	PUNCT
ejpam-7112	699	9	2025	2025	NUM
ejpam-7112	699	10	.	.	PUNCT
ejpam-7112	700	1	[	[	X
ejpam-7112	700	2	14	14	NUM
ejpam-7112	700	3	]	]	X
ejpam-7112	700	4	kashif	kashif	PROPN
ejpam-7112	700	5	memon	memon	PROPN
ejpam-7112	700	6	,	,	PUNCT
ejpam-7112	700	7	muhammad	muhammad	PROPN
ejpam-7112	700	8	mujtaba	mujtaba	PROPN
ejpam-7112	700	9	shaikh	shaikh	PROPN
ejpam-7112	700	10	,	,	PUNCT
ejpam-7112	700	11	kamran	kamran	PROPN
ejpam-7112	700	12	malik	malik	PROPN
ejpam-7112	700	13	,	,	PUNCT
ejpam-7112	700	14	muhammad	muhammad	PROPN
ejpam-7112	700	15	saleem	saleem	PROPN
ejpam-7112	700	16	chandio	chandio	PROPN
ejpam-7112	700	17	,	,	PUNCT
ejpam-7112	700	18	and	and	CCONJ
ejpam-7112	700	19	abdul	abdul	PROPN
ejpam-7112	700	20	wasim	wasim	PROPN
ejpam-7112	700	21	shaikh	shaikh	PROPN
ejpam-7112	700	22	.	.	PUNCT
ejpam-7112	701	1	efficient	efficient	ADJ
ejpam-7112	701	2	derivative	derivative	NOUN
ejpam-7112	701	3	-	-	PUNCT
ejpam-7112	701	4	based	base	VERB
ejpam-7112	701	5	simpson	simpson	PROPN
ejpam-7112	701	6	’s	’s	PART
ejpam-7112	701	7	1/3	1/3	NUM
ejpam-7112	701	8	-	-	PUNCT
ejpam-7112	701	9	type	type	NOUN
ejpam-7112	701	10	scheme	scheme	NOUN
ejpam-7112	701	11	using	use	VERB
ejpam-7112	701	12	centroidal	centroidal	NOUN
ejpam-7112	701	13	mean	mean	PROPN
ejpam-7112	701	14	for	for	ADP
ejpam-7112	701	15	riemann	riemann	PROPN
ejpam-7112	701	16	-	-	PUNCT
ejpam-7112	701	17	stieltjes	stieltjes	PROPN
ejpam-7112	701	18	integral	integral	ADJ
ejpam-7112	701	19	.	.	PUNCT
ejpam-7112	702	1	journal	journal	PROPN
ejpam-7112	702	2	of	of	ADP
ejpam-7112	702	3	mechanics	mechanic	NOUN
ejpam-7112	702	4	of	of	ADP
ejpam-7112	702	5	continua	continua	PROPN
ejpam-7112	702	6	and	and	CCONJ
ejpam-7112	702	7	mathematical	mathematical	ADJ
ejpam-7112	702	8	sciences	science	NOUN
ejpam-7112	702	9	,	,	PUNCT
ejpam-7112	702	10	16(3):69–85	16(3):69–85	NUM
ejpam-7112	702	11	,	,	PUNCT
ejpam-7112	702	12	2021	2021	NUM
ejpam-7112	702	13	.	.	PUNCT
ejpam-7112	703	1	k.	k.	PROPN
ejpam-7112	703	2	memon	memon	PROPN
ejpam-7112	703	3	et	et	PROPN
ejpam-7112	703	4	al	al	PROPN
ejpam-7112	703	5	.	.	PUNCT
ejpam-7112	703	6	/	/	SYM
ejpam-7112	703	7	eur	eur	PROPN
ejpam-7112	703	8	.	.	PUNCT
ejpam-7112	704	1	j.	j.	PROPN
ejpam-7112	704	2	pure	pure	PROPN
ejpam-7112	704	3	appl	appl	PROPN
ejpam-7112	704	4	.	.	PROPN
ejpam-7112	704	5	math	math	PROPN
ejpam-7112	704	6	,	,	PUNCT
ejpam-7112	704	7	18	18	NUM
ejpam-7112	704	8	(	(	PUNCT
ejpam-7112	704	9	4	4	NUM
ejpam-7112	704	10	)	)	PUNCT
ejpam-7112	704	11	(	(	PUNCT
ejpam-7112	704	12	2025	2025	NUM
ejpam-7112	704	13	)	)	PUNCT
ejpam-7112	704	14	,	,	PUNCT
ejpam-7112	704	15	7112	7112	NUM
ejpam-7112	704	16	38	38	NUM
ejpam-7112	704	17	of	of	ADP
ejpam-7112	704	18	38	38	NUM
ejpam-7112	704	19	[	[	SYM
ejpam-7112	704	20	15	15	NUM
ejpam-7112	704	21	]	]	PUNCT
ejpam-7112	704	22	weijing	weije	VERB
ejpam-7112	704	23	zhao	zhao	PROPN
ejpam-7112	704	24	and	and	CCONJ
ejpam-7112	704	25	zhaoning	zhaoning	PROPN
ejpam-7112	704	26	zhang	zhang	PROPN
ejpam-7112	704	27	.	.	PUNCT
ejpam-7112	704	28	simpson	simpson	PROPN
ejpam-7112	704	29	’s	’s	PART
ejpam-7112	704	30	rule	rule	NOUN
ejpam-7112	704	31	for	for	ADP
ejpam-7112	704	32	the	the	DET
ejpam-7112	704	33	riemann	riemann	PROPN
ejpam-7112	704	34	-	-	PUNCT
ejpam-7112	704	35	stieltjes	stieltjes	PROPN
ejpam-7112	704	36	integral	integral	ADJ
ejpam-7112	704	37	.	.	PUNCT
ejpam-7112	704	38	journal	journal	PROPN
ejpam-7112	704	39	of	of	ADP
ejpam-7112	704	40	interdisciplinary	interdisciplinary	ADJ
ejpam-7112	704	41	mathematics	mathematic	NOUN
ejpam-7112	704	42	,	,	PUNCT
ejpam-7112	704	43	24(5):1305–1314	24(5):1305–1314	NUM
ejpam-7112	704	44	,	,	PUNCT
ejpam-7112	704	45	2021	2021	NUM
ejpam-7112	704	46	.	.	PUNCT
ejpam-7112	705	1	[	[	X
ejpam-7112	705	2	16	16	NUM
ejpam-7112	705	3	]	]	X
ejpam-7112	705	4	mohammad	mohammad	PROPN
ejpam-7112	705	5	alomari	alomari	PROPN
ejpam-7112	705	6	.	.	PUNCT
ejpam-7112	706	1	a	a	DET
ejpam-7112	706	2	companion	companion	NOUN
ejpam-7112	706	3	of	of	ADP
ejpam-7112	706	4	ostrowski	ostrowski	ADJ
ejpam-7112	706	5	inequality	inequality	NOUN
ejpam-7112	706	6	for	for	ADP
ejpam-7112	706	7	the	the	DET
ejpam-7112	706	8	stieltjes	stieltjes	NOUN
ejpam-7112	706	9	integral	integral	ADJ
ejpam-7112	706	10	of	of	ADP
ejpam-7112	706	11	monotonic	monotonic	ADJ
ejpam-7112	706	12	functions	function	NOUN
ejpam-7112	706	13	.	.	PUNCT
ejpam-7112	707	1	innovative	innovative	ADJ
ejpam-7112	707	2	journal	journal	NOUN
ejpam-7112	707	3	of	of	ADP
ejpam-7112	707	4	mathematics	mathematics	PROPN
ejpam-7112	707	5	(	(	PUNCT
ejpam-7112	707	6	ijm	ijm	PROPN
ejpam-7112	707	7	)	)	PUNCT
ejpam-7112	707	8	,	,	PUNCT
ejpam-7112	707	9	1(2):18–29	1(2):18–29	NUM
ejpam-7112	707	10	,	,	PUNCT
ejpam-7112	707	11	2022	2022	NUM
ejpam-7112	707	12	.	.	PUNCT
ejpam-7112	708	1	[	[	X
ejpam-7112	708	2	17	17	NUM
ejpam-7112	708	3	]	]	X
ejpam-7112	708	4	abdulrahman	abdulrahman	PROPN
ejpam-7112	708	5	obaid	obaid	PROPN
ejpam-7112	708	6	alshammari	alshammari	PROPN
ejpam-7112	708	7	,	,	PUNCT
ejpam-7112	708	8	muhammad	muhammad	PROPN
ejpam-7112	708	9	nawaz	nawaz	PROPN
ejpam-7112	708	10	khan	khan	PROPN
ejpam-7112	708	11	,	,	PUNCT
ejpam-7112	708	12	and	and	CCONJ
ejpam-7112	708	13	imtiaz	imtiaz	PROPN
ejpam-7112	708	14	ahmad	ahmad	PROPN
ejpam-7112	708	15	.	.	PUNCT
ejpam-7112	709	1	boundary	boundary	ADJ
ejpam-7112	709	2	layer	layer	NOUN
ejpam-7112	709	3	challenges	challenge	NOUN
ejpam-7112	709	4	:	:	PUNCT
ejpam-7112	709	5	a	a	DET
ejpam-7112	709	6	comparative	comparative	ADJ
ejpam-7112	709	7	analysis	analysis	NOUN
ejpam-7112	709	8	of	of	ADP
ejpam-7112	709	9	two	two	NUM
ejpam-7112	709	10	efficient	efficient	ADJ
ejpam-7112	709	11	meshless	meshless	ADJ
ejpam-7112	709	12	approaches	approach	NOUN
ejpam-7112	709	13	.	.	PUNCT
ejpam-7112	710	1	partial	partial	ADJ
ejpam-7112	710	2	differential	differential	ADJ
ejpam-7112	710	3	equations	equation	NOUN
ejpam-7112	710	4	in	in	ADP
ejpam-7112	710	5	applied	applied	ADJ
ejpam-7112	710	6	mathematics	mathematic	NOUN
ejpam-7112	710	7	,	,	PUNCT
ejpam-7112	710	8	10:100743	10:100743	NUM
ejpam-7112	710	9	,	,	PUNCT
ejpam-7112	710	10	2024	2024	NUM
ejpam-7112	710	11	.	.	PUNCT
ejpam-7112	711	1	[	[	X
ejpam-7112	711	2	18	18	NUM
ejpam-7112	711	3	]	]	X
ejpam-7112	711	4	shakeel	shakeel	PROPN
ejpam-7112	711	5	mehnaz	mehnaz	PROPN
ejpam-7112	711	6	,	,	PUNCT
ejpam-7112	711	7	muhammad	muhammad	PROPN
ejpam-7112	711	8	nawaz	nawaz	PROPN
ejpam-7112	711	9	khan	khan	PROPN
ejpam-7112	711	10	,	,	PUNCT
ejpam-7112	711	11	imtiaz	imtiaz	PROPN
ejpam-7112	711	12	ahmad	ahmad	PROPN
ejpam-7112	711	13	,	,	PUNCT
ejpam-7112	711	14	sayed	say	VERB
ejpam-7112	711	15	abdel	abdel	PROPN
ejpam-7112	711	16	-	-	PUNCT
ejpam-7112	711	17	khalek	khalek	PROPN
ejpam-7112	711	18	,	,	PUNCT
ejpam-7112	711	19	ahmed	ahmed	PROPN
ejpam-7112	711	20	mohammed	mohammed	PROPN
ejpam-7112	711	21	alghamdi	alghamdi	PROPN
ejpam-7112	711	22	,	,	PUNCT
ejpam-7112	711	23	and	and	CCONJ
ejpam-7112	711	24	mustafa	mustafa	PROPN
ejpam-7112	711	25	inc	inc	PROPN
ejpam-7112	711	26	.	.	PUNCT
ejpam-7112	712	1	the	the	DET
ejpam-7112	712	2	generalized	generalized	ADJ
ejpam-7112	712	3	time	time	NOUN
ejpam-7112	712	4	fractional	fractional	PROPN
ejpam-7112	712	5	gardner	gardner	NOUN
ejpam-7112	712	6	equation	equation	NOUN
ejpam-7112	712	7	via	via	ADP
ejpam-7112	712	8	numerical	numerical	ADJ
ejpam-7112	712	9	meshless	meshless	ADJ
ejpam-7112	712	10	collocation	collocation	NOUN
ejpam-7112	712	11	method	method	NOUN
ejpam-7112	712	12	.	.	PUNCT
ejpam-7112	713	1	thermal	thermal	ADJ
ejpam-7112	713	2	science	science	NOUN
ejpam-7112	713	3	,	,	PUNCT
ejpam-7112	713	4	26(spec	26(spec	NUM
ejpam-7112	713	5	.	.	PUNCT
ejpam-7112	714	1	issue	issue	NOUN
ejpam-7112	714	2	1):469–474	1):469–474	NUM
ejpam-7112	714	3	,	,	PUNCT
ejpam-7112	714	4	2022	2022	NUM
ejpam-7112	714	5	.	.	PUNCT
ejpam-7112	715	1	[	[	X
ejpam-7112	715	2	19	19	NUM
ejpam-7112	715	3	]	]	X
ejpam-7112	715	4	g.	g.	PROPN
ejpam-7112	715	5	l.	l.	PROPN
ejpam-7112	715	6	bullock	bullock	PROPN
ejpam-7112	715	7	.	.	PUNCT
ejpam-7112	716	1	a	a	DET
ejpam-7112	716	2	geometric	geometric	ADJ
ejpam-7112	716	3	interpretation	interpretation	NOUN
ejpam-7112	716	4	of	of	ADP
ejpam-7112	716	5	the	the	DET
ejpam-7112	716	6	riemann	riemann	PROPN
ejpam-7112	716	7	-	-	PUNCT
ejpam-7112	716	8	stieltjes	stieltjes	PROPN
ejpam-7112	716	9	integral	integral	ADJ
ejpam-7112	716	10	.	.	PUNCT
ejpam-7112	717	1	the	the	DET
ejpam-7112	717	2	american	american	PROPN
ejpam-7112	717	3	mathematical	mathematical	PROPN
ejpam-7112	717	4	monthly	monthly	ADV
ejpam-7112	717	5	,	,	PUNCT
ejpam-7112	717	6	95(5):448–455	95(5):448–455	PRON
ejpam-7112	717	7	,	,	PUNCT
ejpam-7112	717	8	1988	1988	NUM
ejpam-7112	717	9	.	.	PUNCT
ejpam-7112	718	1	[	[	X
ejpam-7112	718	2	20	20	NUM
ejpam-7112	718	3	]	]	PUNCT
ejpam-7112	718	4	w.	w.	PROPN
ejpam-7112	718	5	zhao	zhao	PROPN
ejpam-7112	718	6	,	,	PUNCT
ejpam-7112	718	7	z.	z.	PROPN
ejpam-7112	718	8	zhang	zhang	PROPN
ejpam-7112	718	9	,	,	PUNCT
ejpam-7112	718	10	and	and	CCONJ
ejpam-7112	718	11	z.	z.	PROPN
ejpam-7112	718	12	ye	ye	PROPN
ejpam-7112	718	13	.	.	PROPN
ejpam-7112	718	14	composite	composite	ADJ
ejpam-7112	718	15	trapezoid	trapezoid	ADJ
ejpam-7112	718	16	rule	rule	NOUN
ejpam-7112	718	17	for	for	ADP
ejpam-7112	718	18	the	the	DET
ejpam-7112	718	19	riemann	riemann	PROPN
ejpam-7112	718	20	-	-	PUNCT
ejpam-7112	718	21	stieltjes	stieltjes	NOUN
ejpam-7112	718	22	integral	integral	ADJ
ejpam-7112	718	23	and	and	CCONJ
ejpam-7112	718	24	its	its	PRON
ejpam-7112	718	25	richardson	richardson	PROPN
ejpam-7112	718	26	extrapolation	extrapolation	NOUN
ejpam-7112	718	27	formula	formula	NOUN
ejpam-7112	718	28	.	.	PUNCT
ejpam-7112	719	1	italian	italian	ADJ
ejpam-7112	719	2	journal	journal	NOUN
ejpam-7112	719	3	of	of	ADP
ejpam-7112	719	4	pure	pure	ADJ
ejpam-7112	719	5	and	and	CCONJ
ejpam-7112	719	6	applied	applied	ADJ
ejpam-7112	719	7	mathematics	mathematic	NOUN
ejpam-7112	719	8	,	,	PUNCT
ejpam-7112	719	9	35:311–318	35:311–318	PROPN
ejpam-7112	719	10	,	,	PUNCT
ejpam-7112	719	11	2015	2015	NUM
ejpam-7112	719	12	.	.	PUNCT
ejpam-7112	720	1	[	[	X
ejpam-7112	720	2	21	21	NUM
ejpam-7112	720	3	]	]	PUNCT
ejpam-7112	720	4	m.	m.	NOUN
ejpam-7112	720	5	h.	h.	PROPN
ejpam-7112	720	6	protter	protter	PROPN
ejpam-7112	720	7	and	and	CCONJ
ejpam-7112	720	8	c.	c.	PROPN
ejpam-7112	720	9	b.	b.	PROPN
ejpam-7112	720	10	morrey	morrey	PROPN
ejpam-7112	720	11	.	.	PUNCT
ejpam-7112	721	1	a	a	DET
ejpam-7112	721	2	first	first	ADJ
ejpam-7112	721	3	course	course	NOUN
ejpam-7112	721	4	in	in	ADP
ejpam-7112	721	5	real	real	ADJ
ejpam-7112	721	6	analysis	analysis	NOUN
ejpam-7112	721	7	.	.	PUNCT
ejpam-7112	722	1	springer	springer	NOUN
ejpam-7112	722	2	,	,	PUNCT
ejpam-7112	722	3	new	new	PROPN
ejpam-7112	722	4	york	york	PROPN
ejpam-7112	722	5	,	,	PUNCT
ejpam-7112	722	6	ny	ny	PROPN
ejpam-7112	722	7	,	,	PUNCT
ejpam-7112	722	8	1977	1977	NUM
ejpam-7112	722	9	.	.	PUNCT
ejpam-7112	723	1	[	[	X
ejpam-7112	723	2	22	22	NUM
ejpam-7112	723	3	]	]	PUNCT
ejpam-7112	723	4	k.	k.	PROPN
ejpam-7112	723	5	memon	memon	PROPN
ejpam-7112	723	6	et	et	PROPN
ejpam-7112	723	7	al	al	PROPN
ejpam-7112	723	8	.	.	PUNCT
ejpam-7112	724	1	a	a	DET
ejpam-7112	724	2	modified	modify	VERB
ejpam-7112	724	3	derivative	derivative	NOUN
ejpam-7112	724	4	-	-	PUNCT
ejpam-7112	724	5	based	base	VERB
ejpam-7112	724	6	scheme	scheme	NOUN
ejpam-7112	724	7	for	for	ADP
ejpam-7112	724	8	the	the	DET
ejpam-7112	724	9	riemann	riemann	PROPN
ejpam-7112	724	10	-	-	PUNCT
ejpam-7112	724	11	stieltjes	stieltjes	PROPN
ejpam-7112	724	12	integral	integral	ADJ
ejpam-7112	724	13	.	.	PUNCT
ejpam-7112	724	14	sindh	sindh	PROPN
ejpam-7112	724	15	university	university	PROPN
ejpam-7112	724	16	research	research	PROPN
ejpam-7112	724	17	journal	journal	PROPN
ejpam-7112	724	18	(	(	PUNCT
ejpam-7112	724	19	science	science	NOUN
ejpam-7112	724	20	series	series	PROPN
ejpam-7112	724	21	)	)	PUNCT
ejpam-7112	724	22	,	,	PUNCT
ejpam-7112	724	23	52(1	52(1	NOUN
ejpam-7112	724	24	)	)	PUNCT
ejpam-7112	724	25	,	,	PUNCT
ejpam-7112	724	26	2020	2020	NUM
ejpam-7112	724	27	.	.	PUNCT
ejpam-7112	725	1	[	[	X
ejpam-7112	725	2	23	23	NUM
ejpam-7112	725	3	]	]	X
ejpam-7112	725	4	r.	r.	PROPN
ejpam-7112	725	5	g.	g.	PROPN
ejpam-7112	725	6	bartle	bartle	PROPN
ejpam-7112	725	7	.	.	PUNCT
ejpam-7112	726	1	the	the	DET
ejpam-7112	726	2	elements	element	NOUN
ejpam-7112	726	3	of	of	ADP
ejpam-7112	726	4	real	real	ADJ
ejpam-7112	726	5	analysis	analysis	NOUN
ejpam-7112	726	6	.	.	PUNCT
ejpam-7112	727	1	john	john	PROPN
ejpam-7112	727	2	wiley	wiley	PROPN
ejpam-7112	727	3	&	&	CCONJ
ejpam-7112	727	4	sons	son	NOUN
ejpam-7112	727	5	,	,	PUNCT
ejpam-7112	727	6	2nd	2nd	PROPN
ejpam-7112	727	7	edition	edition	NOUN
ejpam-7112	727	8	,	,	PUNCT
ejpam-7112	727	9	1964	1964	NUM
ejpam-7112	727	10	.	.	PUNCT
ejpam-7112	728	1	[	[	X
ejpam-7112	728	2	24	24	NUM
ejpam-7112	728	3	]	]	PUNCT
ejpam-7112	728	4	kashif	kashif	PROPN
ejpam-7112	728	5	memon	memon	PROPN
ejpam-7112	728	6	,	,	PUNCT
ejpam-7112	728	7	muhammad	muhammad	PROPN
ejpam-7112	728	8	mujtaba	mujtaba	PROPN
ejpam-7112	728	9	shaikh	shaikh	PROPN
ejpam-7112	728	10	,	,	PUNCT
ejpam-7112	728	11	ms	ms	PROPN
ejpam-7112	728	12	chandio	chandio	NOUN
ejpam-7112	728	13	,	,	PUNCT
ejpam-7112	728	14	and	and	CCONJ
ejpam-7112	728	15	aw	aw	INTJ
ejpam-7112	728	16	shaikh	shaikh	PROPN
ejpam-7112	728	17	.	.	PUNCT
ejpam-7112	729	1	heronian	heronian	ADJ
ejpam-7112	729	2	mean	mean	VERB
ejpam-7112	729	3	derivative	derivative	NOUN
ejpam-7112	729	4	-	-	PUNCT
ejpam-7112	729	5	based	base	VERB
ejpam-7112	729	6	simpson’s	simpson’s	NOUN
ejpam-7112	729	7	-	-	PUNCT
ejpam-7112	729	8	type	type	NOUN
ejpam-7112	729	9	scheme	scheme	NOUN
ejpam-7112	729	10	for	for	ADP
ejpam-7112	729	11	riemann	riemann	PROPN
ejpam-7112	729	12	-	-	PUNCT
ejpam-7112	729	13	stieltjes	stieltjes	NOUN
ejpam-7112	729	14	integral	integral	ADJ
ejpam-7112	729	15	’	'	PUNCT
ejpam-7112	729	16	.	.	PUNCT
ejpam-7112	730	1	journal	journal	PROPN
ejpam-7112	730	2	of	of	ADP
ejpam-7112	730	3	mechanics	mechanic	NOUN
ejpam-7112	730	4	of	of	ADP
ejpam-7112	730	5	continua	continua	PROPN
ejpam-7112	730	6	and	and	CCONJ
ejpam-7112	730	7	mathematical	mathematical	ADJ
ejpam-7112	730	8	sciences	science	NOUN
ejpam-7112	730	9	,	,	PUNCT
ejpam-7112	730	10	16(3):55–68	16(3):55–68	NUM
ejpam-7112	730	11	,	,	PUNCT
ejpam-7112	730	12	2021	2021	NUM
ejpam-7112	730	13	.	.	PUNCT
ejpam-7112	731	1	[	[	X
ejpam-7112	731	2	25	25	NUM
ejpam-7112	731	3	]	]	X
ejpam-7112	731	4	f.	f.	PROPN
ejpam-7112	731	5	zafar	zafar	PROPN
ejpam-7112	731	6	,	,	PUNCT
ejpam-7112	731	7	s.	s.	PROPN
ejpam-7112	731	8	saleem	saleem	PROPN
ejpam-7112	731	9	,	,	PUNCT
ejpam-7112	731	10	and	and	CCONJ
ejpam-7112	731	11	c.	c.	PROPN
ejpam-7112	731	12	o.	o.	PROPN
ejpam-7112	731	13	e.	e.	PROPN
ejpam-7112	731	14	burg	burg	PROPN
ejpam-7112	731	15	.	.	PUNCT
ejpam-7112	732	1	new	new	ADJ
ejpam-7112	732	2	derivative	derivative	NOUN
ejpam-7112	732	3	-	-	PUNCT
ejpam-7112	732	4	based	base	VERB
ejpam-7112	732	5	open	open	PROPN
ejpam-7112	732	6	newton	newton	PROPN
ejpam-7112	732	7	-	-	PUNCT
ejpam-7112	732	8	cotes	cote	NOUN
ejpam-7112	732	9	quadrature	quadrature	NOUN
ejpam-7112	732	10	rules	rule	NOUN
ejpam-7112	732	11	.	.	PUNCT
ejpam-7112	733	1	abstract	abstract	ADJ
ejpam-7112	733	2	and	and	CCONJ
ejpam-7112	733	3	applied	apply	VERB
ejpam-7112	733	4	analysis	analysis	NOUN
ejpam-7112	733	5	,	,	PUNCT
ejpam-7112	733	6	2014	2014	NUM
ejpam-7112	733	7	,	,	PUNCT
ejpam-7112	733	8	2014	2014	NUM
ejpam-7112	733	9	.	.	PUNCT
ejpam-7112	734	1	article	article	NOUN
ejpam-7112	734	2	i	i	PROPN
ejpam-7112	734	3	d	d	PROPN
ejpam-7112	734	4	109138	109138	NUM
ejpam-7112	734	5	,	,	PUNCT
ejpam-7112	734	6	16	16	NUM
ejpam-7112	734	7	pages	page	NOUN
ejpam-7112	734	8	.	.	PUNCT