id	sid	tid	token	lemma	pos
ap-6103	1	1	acta	acta	PROPN
ap-6103	1	2	polytechnica	polytechnica	PROPN
ap-6103	1	3	doi:10.14311	doi:10.14311	PROPN
ap-6103	1	4	/	/	SYM
ap-6103	1	5	ap.2020.60.0428	ap.2020.60.0428	PROPN
ap-6103	1	6	acta	acta	PROPN
ap-6103	1	7	polytechnica	polytechnica	PROPN
ap-6103	1	8	60(5):428–434	60(5):428–434	PROPN
ap-6103	1	9	,	,	PUNCT
ap-6103	1	10	2020	2020	NUM
ap-6103	1	11	©	©	PROPN
ap-6103	1	12	czech	czech	PROPN
ap-6103	1	13	technical	technical	PROPN
ap-6103	1	14	university	university	PROPN
ap-6103	1	15	in	in	ADP
ap-6103	1	16	prague	prague	PROPN
ap-6103	1	17	,	,	PUNCT
ap-6103	1	18	2020	2020	NUM
ap-6103	1	19	available	available	ADJ
ap-6103	1	20	online	online	ADV
ap-6103	1	21	at	at	ADP
ap-6103	1	22	https://ojs.cvut.cz/ojs/index.php/ap	https://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-6103	1	23	properties	property	NOUN
ap-6103	1	24	of	of	ADP
ap-6103	1	25	a	a	DET
ap-6103	1	26	differential	differential	ADJ
ap-6103	1	27	sequence	sequence	NOUN
ap-6103	1	28	based	base	VERB
ap-6103	1	29	upon	upon	SCONJ
ap-6103	1	30	the	the	DET
ap-6103	1	31	kummer	kummer	NOUN
ap-6103	1	32	-	-	PUNCT
ap-6103	1	33	schwarz	schwarz	PROPN
ap-6103	1	34	equation	equation	NOUN
ap-6103	1	35	adhir	adhir	ADP
ap-6103	1	36	maharaja,∗	maharaja,∗	PROPN
ap-6103	1	37	,	,	PUNCT
ap-6103	1	38	kostis	kostis	PROPN
ap-6103	1	39	andriopoulosb	andriopoulosb	PROPN
ap-6103	1	40	,	,	PUNCT
ap-6103	1	41	peter	peter	PROPN
ap-6103	1	42	leacha	leacha	PROPN
ap-6103	1	43	,	,	PUNCT
ap-6103	1	44	b	b	PROPN
ap-6103	1	45	a	a	DET
ap-6103	1	46	durban	durban	PROPN
ap-6103	1	47	university	university	PROPN
ap-6103	1	48	of	of	ADP
ap-6103	1	49	technology	technology	NOUN
ap-6103	1	50	,	,	PUNCT
ap-6103	1	51	steve	steve	PROPN
ap-6103	1	52	biko	biko	PROPN
ap-6103	1	53	campus	campus	PROPN
ap-6103	1	54	,	,	PUNCT
ap-6103	1	55	department	department	NOUN
ap-6103	1	56	of	of	ADP
ap-6103	1	57	mathematics	mathematics	PROPN
ap-6103	1	58	,	,	PUNCT
ap-6103	1	59	durban	durban	NOUN
ap-6103	1	60	,	,	PUNCT
ap-6103	1	61	4000	4000	NUM
ap-6103	1	62	,	,	PUNCT
ap-6103	1	63	republic	republic	NOUN
ap-6103	1	64	of	of	ADP
ap-6103	1	65	south	south	PROPN
ap-6103	1	66	africa	africa	PROPN
ap-6103	1	67	b	b	PROPN
ap-6103	1	68	university	university	PROPN
ap-6103	1	69	of	of	ADP
ap-6103	1	70	kwazulu	kwazulu	PROPN
ap-6103	1	71	-	-	PUNCT
ap-6103	1	72	natal	natal	ADJ
ap-6103	1	73	,	,	PUNCT
ap-6103	1	74	school	school	NOUN
ap-6103	1	75	of	of	ADP
ap-6103	1	76	mathematical	mathematical	ADJ
ap-6103	1	77	sciences	science	NOUN
ap-6103	1	78	,	,	PUNCT
ap-6103	1	79	private	private	ADJ
ap-6103	1	80	bag	bag	NOUN
ap-6103	1	81	x54001	x54001	PROPN
ap-6103	1	82	,	,	PUNCT
ap-6103	1	83	durban,4000	durban,4000	NOUN
ap-6103	1	84	,	,	PUNCT
ap-6103	1	85	republic	republic	NOUN
ap-6103	1	86	of	of	ADP
ap-6103	1	87	south	south	PROPN
ap-6103	1	88	africa	africa	PROPN
ap-6103	1	89	∗	∗	PROPN
ap-6103	1	90	corresponding	correspond	VERB
ap-6103	1	91	author	author	NOUN
ap-6103	1	92	:	:	PUNCT
ap-6103	1	93	adhirm@dut.ac.za	adhirm@dut.ac.za	NOUN
ap-6103	1	94	abstract	abstract	NOUN
ap-6103	1	95	.	.	PUNCT
ap-6103	2	1	in	in	ADP
ap-6103	2	2	this	this	DET
ap-6103	2	3	paper	paper	NOUN
ap-6103	2	4	,	,	PUNCT
ap-6103	2	5	we	we	PRON
ap-6103	2	6	determine	determine	VERB
ap-6103	2	7	a	a	DET
ap-6103	2	8	recursion	recursion	NOUN
ap-6103	2	9	operator	operator	NOUN
ap-6103	2	10	for	for	ADP
ap-6103	2	11	the	the	DET
ap-6103	2	12	kummer	kummer	NOUN
ap-6103	2	13	-	-	PUNCT
ap-6103	2	14	schwarz	schwarz	PROPN
ap-6103	2	15	equation	equation	NOUN
ap-6103	2	16	,	,	PUNCT
ap-6103	2	17	which	which	PRON
ap-6103	2	18	leads	lead	VERB
ap-6103	2	19	to	to	ADP
ap-6103	2	20	a	a	DET
ap-6103	2	21	sequence	sequence	NOUN
ap-6103	2	22	with	with	ADP
ap-6103	2	23	unacceptable	unacceptable	ADJ
ap-6103	2	24	singularity	singularity	NOUN
ap-6103	2	25	properties	property	NOUN
ap-6103	2	26	.	.	PUNCT
ap-6103	3	1	a	a	DET
ap-6103	3	2	different	different	ADJ
ap-6103	3	3	sequence	sequence	NOUN
ap-6103	3	4	is	be	AUX
ap-6103	3	5	devised	devise	VERB
ap-6103	3	6	based	base	VERB
ap-6103	3	7	upon	upon	SCONJ
ap-6103	3	8	the	the	DET
ap-6103	3	9	relationship	relationship	NOUN
ap-6103	3	10	between	between	ADP
ap-6103	3	11	the	the	DET
ap-6103	3	12	kummer	kummer	NOUN
ap-6103	3	13	-	-	PUNCT
ap-6103	3	14	schwarz	schwarz	PROPN
ap-6103	3	15	equation	equation	NOUN
ap-6103	3	16	and	and	CCONJ
ap-6103	3	17	the	the	DET
ap-6103	3	18	first	first	ADJ
ap-6103	3	19	-	-	PUNCT
ap-6103	3	20	order	order	NOUN
ap-6103	3	21	riccati	riccati	NOUN
ap-6103	3	22	equation	equation	NOUN
ap-6103	3	23	for	for	ADP
ap-6103	3	24	which	which	PRON
ap-6103	3	25	a	a	DET
ap-6103	3	26	particular	particular	ADJ
ap-6103	3	27	generator	generator	NOUN
ap-6103	3	28	has	have	AUX
ap-6103	3	29	been	be	AUX
ap-6103	3	30	found	find	VERB
ap-6103	3	31	to	to	PART
ap-6103	3	32	give	give	VERB
ap-6103	3	33	interesting	interesting	ADJ
ap-6103	3	34	and	and	CCONJ
ap-6103	3	35	excellent	excellent	ADJ
ap-6103	3	36	properties	property	NOUN
ap-6103	3	37	.	.	PUNCT
ap-6103	4	1	we	we	PRON
ap-6103	4	2	examine	examine	VERB
ap-6103	4	3	the	the	DET
ap-6103	4	4	elements	element	NOUN
ap-6103	4	5	of	of	ADP
ap-6103	4	6	this	this	DET
ap-6103	4	7	sequence	sequence	NOUN
ap-6103	4	8	in	in	ADP
ap-6103	4	9	terms	term	NOUN
ap-6103	4	10	of	of	ADP
ap-6103	4	11	the	the	DET
ap-6103	4	12	usual	usual	ADJ
ap-6103	4	13	properties	property	NOUN
ap-6103	4	14	to	to	PART
ap-6103	4	15	be	be	AUX
ap-6103	4	16	investigated	investigate	VERB
ap-6103	4	17	–	–	PUNCT
ap-6103	4	18	symmetries	symmetry	NOUN
ap-6103	4	19	,	,	PUNCT
ap-6103	4	20	singularity	singularity	NOUN
ap-6103	4	21	properties	property	NOUN
ap-6103	4	22	,	,	PUNCT
ap-6103	4	23	integrability	integrability	NOUN
ap-6103	4	24	,	,	PUNCT
ap-6103	4	25	alternate	alternate	ADJ
ap-6103	4	26	sequence	sequence	NOUN
ap-6103	4	27	–	–	PUNCT
ap-6103	4	28	and	and	CCONJ
ap-6103	4	29	provide	provide	VERB
ap-6103	4	30	an	an	DET
ap-6103	4	31	explanation	explanation	NOUN
ap-6103	4	32	of	of	ADP
ap-6103	4	33	the	the	DET
ap-6103	4	34	curious	curious	ADJ
ap-6103	4	35	relationship	relationship	NOUN
ap-6103	4	36	between	between	ADP
ap-6103	4	37	the	the	DET
ap-6103	4	38	results	result	NOUN
ap-6103	4	39	of	of	ADP
ap-6103	4	40	the	the	DET
ap-6103	4	41	singularity	singularity	NOUN
ap-6103	4	42	analysis	analysis	NOUN
ap-6103	4	43	and	and	CCONJ
ap-6103	4	44	a	a	DET
ap-6103	4	45	consideration	consideration	NOUN
ap-6103	4	46	of	of	ADP
ap-6103	4	47	the	the	DET
ap-6103	4	48	solution	solution	NOUN
ap-6103	4	49	of	of	ADP
ap-6103	4	50	each	each	DET
ap-6103	4	51	element	element	NOUN
ap-6103	4	52	obtained	obtain	VERB
ap-6103	4	53	by	by	ADP
ap-6103	4	54	quadratures	quadrature	NOUN
ap-6103	4	55	.	.	PUNCT
ap-6103	5	1	keywords	keyword	NOUN
ap-6103	5	2	:	:	PUNCT
ap-6103	5	3	lie	lie	NOUN
ap-6103	5	4	symmetries	symmetry	NOUN
ap-6103	5	5	,	,	PUNCT
ap-6103	5	6	singularity	singularity	NOUN
ap-6103	5	7	analysis	analysis	NOUN
ap-6103	5	8	,	,	PUNCT
ap-6103	5	9	differential	differential	ADJ
ap-6103	5	10	sequence	sequence	NOUN
ap-6103	5	11	.	.	PUNCT
ap-6103	6	1	1	1	X
ap-6103	6	2	.	.	X
ap-6103	6	3	introduction	introduction	NOUN
ap-6103	6	4	in	in	ADP
ap-6103	6	5	a	a	DET
ap-6103	6	6	prescient	prescient	ADJ
ap-6103	6	7	paper	paper	NOUN
ap-6103	6	8	of	of	ADP
ap-6103	6	9	1977	1977	NUM
ap-6103	6	10	olver	olver	NOUN
ap-6103	7	1	[	[	X
ap-6103	7	2	1	1	NUM
ap-6103	7	3	]	]	PUNCT
ap-6103	7	4	,	,	PUNCT
ap-6103	7	5	the	the	DET
ap-6103	7	6	idea	idea	NOUN
ap-6103	7	7	of	of	ADP
ap-6103	7	8	a	a	DET
ap-6103	7	9	recursion	recursion	NOUN
ap-6103	7	10	operator	operator	NOUN
ap-6103	7	11	for	for	ADP
ap-6103	7	12	an	an	DET
ap-6103	7	13	evolution	evolution	NOUN
ap-6103	7	14	of	of	ADP
ap-6103	7	15	partial	partial	ADJ
ap-6103	7	16	differential	differential	NOUN
ap-6103	7	17	equations	equation	NOUN
ap-6103	7	18	,	,	PUNCT
ap-6103	7	19	but	but	CCONJ
ap-6103	7	20	with	with	ADP
ap-6103	7	21	definite	definite	ADJ
ap-6103	7	22	indication	indication	NOUN
ap-6103	7	23	of	of	ADP
ap-6103	7	24	extension	extension	NOUN
ap-6103	7	25	to	to	ADP
ap-6103	7	26	wider	wide	ADJ
ap-6103	7	27	classes	class	NOUN
ap-6103	7	28	of	of	ADP
ap-6103	7	29	partial	partial	ADJ
ap-6103	7	30	differential	differential	ADJ
ap-6103	7	31	equations	equation	NOUN
ap-6103	7	32	was	be	AUX
ap-6103	7	33	introduced1	introduced1	NOUN
ap-6103	7	34	.	.	PUNCT
ap-6103	8	1	given	give	VERB
ap-6103	8	2	an	an	DET
ap-6103	8	3	evolution	evolution	NOUN
ap-6103	8	4	differential	differential	NOUN
ap-6103	8	5	equation	equation	NOUN
ap-6103	8	6	,	,	PUNCT
ap-6103	8	7	ut	ut	PROPN
ap-6103	8	8	=	=	SYM
ap-6103	8	9	f	f	PROPN
ap-6103	8	10	(	(	PUNCT
ap-6103	8	11	t	t	PROPN
ap-6103	8	12	,	,	PUNCT
ap-6103	8	13	x	x	X
ap-6103	8	14	,	,	PUNCT
ap-6103	8	15	u	u	NOUN
ap-6103	8	16	,	,	PUNCT
ap-6103	8	17	ux	ux	PROPN
ap-6103	8	18	,	,	PUNCT
ap-6103	8	19	.	.	PUNCT
ap-6103	8	20	.	.	PUNCT
ap-6103	8	21	.	.	PUNCT
ap-6103	9	1	,	,	PUNCT
ap-6103	9	2	unx	unx	PROPN
ap-6103	9	3	)	)	PUNCT
ap-6103	9	4	,	,	PUNCT
ap-6103	9	5	(	(	PUNCT
ap-6103	9	6	1	1	X
ap-6103	9	7	)	)	PUNCT
ap-6103	9	8	r[u	r[u	NOUN
ap-6103	9	9	]	]	PUNCT
ap-6103	9	10	is	be	AUX
ap-6103	9	11	a	a	DET
ap-6103	9	12	recursion	recursion	NOUN
ap-6103	9	13	operator	operator	NOUN
ap-6103	9	14	for	for	ADP
ap-6103	9	15	(	(	PUNCT
ap-6103	9	16	1	1	X
ap-6103	9	17	)	)	PUNCT
ap-6103	9	18	if	if	SCONJ
ap-6103	9	19	it	it	PRON
ap-6103	9	20	satisfies	satisfy	VERB
ap-6103	9	21	the	the	DET
ap-6103	9	22	equation	equation	NOUN
ap-6103	9	23	[	[	X
ap-6103	9	24	1	1	X
ap-6103	9	25	]	]	PUNCT
ap-6103	9	26	[	[	X
ap-6103	9	27	p	p	NOUN
ap-6103	9	28	1213	1213	NUM
ap-6103	9	29	,	,	PUNCT
ap-6103	9	30	(	(	PUNCT
ap-6103	9	31	8)	8)	X
ap-6103	9	32	]	]	X
ap-6103	9	33	[	[	X
ap-6103	9	34	l[f	l[f	X
ap-6103	9	35	]	]	X
ap-6103	9	36	−dt	−dt	NUM
ap-6103	9	37	,	,	PUNCT
ap-6103	9	38	r[u]]lb	r[u]]lb	VERB
ap-6103	9	39	v	v	X
ap-6103	9	40	∈	∈	PROPN
ap-6103	9	41	(	(	PUNCT
ap-6103	9	42	ut	ut	PROPN
ap-6103	9	43	−	−	PROPN
ap-6103	9	44	f	f	PROPN
ap-6103	9	45	)	)	PUNCT
ap-6103	9	46	,	,	PUNCT
ap-6103	9	47	(	(	PUNCT
ap-6103	9	48	2	2	X
ap-6103	9	49	)	)	PUNCT
ap-6103	9	50	where	where	SCONJ
ap-6103	9	51	l[f	l[f	NOUN
ap-6103	9	52	]	]	X
ap-6103	9	53	is	be	AUX
ap-6103	9	54	the	the	DET
ap-6103	9	55	linearised	linearise	VERB
ap-6103	9	56	operator	operator	NOUN
ap-6103	9	57	l[f	l[f	NOUN
ap-6103	9	58	]	]	X
ap-6103	10	1	=	=	PUNCT
ap-6103	10	2	∂f	∂f	PROPN
ap-6103	10	3	∂unx	∂unx	VERB
ap-6103	10	4	dn	dn	NOUN
ap-6103	10	5	x	x	PUNCT
ap-6103	10	6	+	+	CCONJ
ap-6103	10	7	.	.	PUNCT
ap-6103	10	8	.	.	PUNCT
ap-6103	10	9	.	.	PUNCT
ap-6103	11	1	+	+	CCONJ
ap-6103	11	2	∂f	∂f	PROPN
ap-6103	11	3	∂ux	∂ux	ADJ
ap-6103	11	4	dx	dx	NOUN
ap-6103	12	1	+	+	CCONJ
ap-6103	12	2	∂f	∂f	PROPN
ap-6103	12	3	∂u	∂u	PROPN
ap-6103	12	4	,	,	PUNCT
ap-6103	12	5	(	(	PUNCT
ap-6103	12	6	3	3	X
ap-6103	12	7	)	)	PUNCT
ap-6103	12	8	dt	dt	NOUN
ap-6103	12	9	anddx	anddx	NOUN
ap-6103	12	10	denote	denote	VERB
ap-6103	12	11	the	the	DET
ap-6103	12	12	total	total	ADJ
ap-6103	12	13	differentiation	differentiation	NOUN
ap-6103	12	14	with	with	ADP
ap-6103	12	15	respect	respect	NOUN
ap-6103	12	16	to	to	ADP
ap-6103	12	17	t	t	NOUN
ap-6103	12	18	and	and	CCONJ
ap-6103	12	19	x	x	NOUN
ap-6103	12	20	,	,	PUNCT
ap-6103	12	21	respectively	respectively	ADV
ap-6103	12	22	,	,	PUNCT
ap-6103	12	23	and	and	CCONJ
ap-6103	12	24	v	v	NOUN
ap-6103	12	25	is	be	AUX
ap-6103	12	26	a	a	DET
ap-6103	12	27	solution	solution	NOUN
ap-6103	12	28	of	of	ADP
ap-6103	12	29	the	the	DET
ap-6103	12	30	linearised	linearise	VERB
ap-6103	12	31	equation	equation	NOUN
ap-6103	12	32	,	,	PUNCT
ap-6103	12	33	ie	ie	X
ap-6103	12	34	lv	lv	X
ap-6103	12	35	=	=	SYM
ap-6103	12	36	0	0	PROPN
ap-6103	12	37	.	.	PUNCT
ap-6103	13	1	over	over	ADP
ap-6103	13	2	the	the	DET
ap-6103	13	3	last	last	ADJ
ap-6103	13	4	thirty	thirty	NUM
ap-6103	13	5	years	year	NOUN
ap-6103	13	6	,	,	PUNCT
ap-6103	13	7	recursion	recursion	NOUN
ap-6103	13	8	operators	operator	NOUN
ap-6103	13	9	have	have	AUX
ap-6103	13	10	found	find	VERB
ap-6103	13	11	a	a	DET
ap-6103	13	12	wide	wide	ADJ
ap-6103	13	13	application	application	NOUN
ap-6103	13	14	in	in	ADP
ap-6103	13	15	the	the	DET
ap-6103	13	16	study	study	NOUN
ap-6103	13	17	of	of	ADP
ap-6103	13	18	nonlinear	nonlinear	ADJ
ap-6103	13	19	evolution	evolution	NOUN
ap-6103	13	20	partial	partial	ADJ
ap-6103	13	21	differential	differential	NOUN
ap-6103	13	22	equations	equation	NOUN
ap-6103	13	23	with	with	ADP
ap-6103	13	24	particular	particular	ADJ
ap-6103	13	25	reference	reference	NOUN
ap-6103	13	26	to	to	ADP
ap-6103	13	27	their	their	PRON
ap-6103	13	28	integrability	integrability	NOUN
ap-6103	13	29	in	in	ADP
ap-6103	13	30	terms	term	NOUN
ap-6103	13	31	of	of	ADP
ap-6103	13	32	the	the	DET
ap-6103	13	33	possession	possession	NOUN
ap-6103	13	34	of	of	ADP
ap-6103	13	35	an	an	DET
ap-6103	13	36	infinite	infinite	ADJ
ap-6103	13	37	number	number	NOUN
ap-6103	13	38	of	of	ADP
ap-6103	13	39	conservation	conservation	NOUN
ap-6103	13	40	laws	law	NOUN
ap-6103	13	41	.	.	PUNCT
ap-6103	14	1	more	more	ADV
ap-6103	14	2	recently	recently	ADV
ap-6103	14	3	,	,	PUNCT
ap-6103	14	4	euler	euler	PROPN
ap-6103	14	5	et	et	PROPN
ap-6103	14	6	al	al	PROPN
ap-6103	15	1	[	[	X
ap-6103	15	2	4	4	X
ap-6103	15	3	]	]	PUNCT
ap-6103	15	4	and	and	CCONJ
ap-6103	15	5	petersson	petersson	NOUN
ap-6103	15	6	et	et	PROPN
ap-6103	15	7	al	al	PROPN
ap-6103	16	1	[	[	X
ap-6103	16	2	5	5	NUM
ap-6103	16	3	]	]	PUNCT
ap-6103	16	4	examined	examine	VERB
ap-6103	16	5	the	the	DET
ap-6103	16	6	linearisability	linearisability	NOUN
ap-6103	16	7	of	of	ADP
ap-6103	16	8	nonlinear	nonlinear	ADJ
ap-6103	16	9	hierarchies	hierarchy	NOUN
ap-6103	16	10	of	of	ADP
ap-6103	16	11	evolution	evolution	NOUN
ap-6103	16	12	equations	equation	NOUN
ap-6103	16	13	in	in	ADP
ap-6103	16	14	(	(	PUNCT
ap-6103	16	15	1	1	NUM
ap-6103	16	16	+	+	NUM
ap-6103	16	17	1	1	X
ap-6103	16	18	)	)	PUNCT
ap-6103	16	19	dimensions	dimension	NOUN
ap-6103	16	20	with	with	ADP
ap-6103	16	21	a	a	DET
ap-6103	16	22	particular	particular	ADJ
ap-6103	16	23	reference	reference	NOUN
ap-6103	16	24	to	to	ADP
ap-6103	16	25	the	the	DET
ap-6103	16	26	generalised	generalised	ADJ
ap-6103	16	27	x	x	ADJ
ap-6103	16	28	-	-	ADJ
ap-6103	16	29	hodograph	hodograph	ADJ
ap-6103	16	30	transformation	transformation	NOUN
ap-6103	16	31	.	.	PUNCT
ap-6103	17	1	as	as	ADP
ap-6103	17	2	a	a	DET
ap-6103	17	3	natural	natural	ADJ
ap-6103	17	4	development	development	NOUN
ap-6103	17	5	from	from	ADP
ap-6103	17	6	this	this	DET
ap-6103	17	7	work	work	NOUN
ap-6103	17	8	,	,	PUNCT
ap-6103	17	9	euler	euler	PROPN
ap-6103	17	10	et	et	PROPN
ap-6103	17	11	al	al	PROPN
ap-6103	18	1	[	[	X
ap-6103	18	2	6	6	NUM
ap-6103	18	3	]	]	PUNCT
ap-6103	18	4	initiated	initiate	VERB
ap-6103	18	5	a	a	DET
ap-6103	18	6	parallel	parallel	ADJ
ap-6103	18	7	study	study	NOUN
ap-6103	18	8	of	of	ADP
ap-6103	18	9	recursion	recursion	NOUN
ap-6103	18	10	1	1	NUM
ap-6103	18	11	in	in	ADP
ap-6103	18	12	this	this	DET
ap-6103	18	13	respect	respect	NOUN
ap-6103	18	14	olver	olver	NOUN
ap-6103	18	15	made	make	VERB
ap-6103	18	16	use	use	NOUN
ap-6103	18	17	of	of	ADP
ap-6103	18	18	a	a	DET
ap-6103	18	19	number	number	NOUN
ap-6103	18	20	of	of	ADP
ap-6103	18	21	results	result	NOUN
ap-6103	18	22	due	due	ADP
ap-6103	18	23	to	to	ADP
ap-6103	18	24	various	various	ADJ
ap-6103	18	25	authors	author	NOUN
ap-6103	18	26	[	[	X
ap-6103	18	27	2	2	NUM
ap-6103	18	28	,	,	PUNCT
ap-6103	18	29	3	3	NUM
ap-6103	18	30	]	]	PUNCT
ap-6103	18	31	.	.	PUNCT
ap-6103	19	1	the	the	DET
ap-6103	19	2	beauty	beauty	NOUN
ap-6103	19	3	of	of	ADP
ap-6103	19	4	the	the	DET
ap-6103	19	5	subsequent	subsequent	ADJ
ap-6103	19	6	work	work	NOUN
ap-6103	19	7	is	be	AUX
ap-6103	19	8	in	in	ADP
ap-6103	19	9	his	his	PRON
ap-6103	19	10	synthesis	synthesis	NOUN
ap-6103	19	11	.	.	PUNCT
ap-6103	20	1	operators	operator	NOUN
ap-6103	20	2	applied	apply	VERB
ap-6103	20	3	to	to	ADP
ap-6103	20	4	ordinary	ordinary	ADJ
ap-6103	20	5	differential	differential	ADJ
ap-6103	20	6	equations	equation	NOUN
ap-6103	20	7	.	.	PUNCT
ap-6103	21	1	this	this	PRON
ap-6103	21	2	was	be	AUX
ap-6103	21	3	subsequently	subsequently	ADV
ap-6103	21	4	amplified	amplify	VERB
ap-6103	21	5	by	by	ADP
ap-6103	21	6	andriopoulos	andriopoulos	PROPN
ap-6103	21	7	et	et	PROPN
ap-6103	21	8	al	al	PROPN
ap-6103	22	1	[	[	X
ap-6103	22	2	7	7	X
ap-6103	22	3	]	]	PUNCT
ap-6103	22	4	in	in	ADP
ap-6103	22	5	their	their	PRON
ap-6103	22	6	detailed	detailed	ADJ
ap-6103	22	7	study	study	NOUN
ap-6103	22	8	of	of	ADP
ap-6103	22	9	the	the	DET
ap-6103	22	10	riccati	riccati	PROPN
ap-6103	22	11	differential	differential	PROPN
ap-6103	22	12	sequence2	sequence2	PROPN
ap-6103	22	13	.	.	PUNCT
ap-6103	23	1	a	a	DET
ap-6103	23	2	further	further	ADJ
ap-6103	23	3	development	development	NOUN
ap-6103	23	4	was	be	AUX
ap-6103	23	5	the	the	DET
ap-6103	23	6	introduction	introduction	NOUN
ap-6103	23	7	of	of	ADP
ap-6103	23	8	the	the	DET
ap-6103	23	9	concept	concept	NOUN
ap-6103	23	10	of	of	ADP
ap-6103	23	11	an	an	DET
ap-6103	23	12	alternate	alternate	ADJ
ap-6103	23	13	sequence	sequence	NOUN
ap-6103	23	14	[	[	X
ap-6103	23	15	8	8	NUM
ap-6103	23	16	]	]	PUNCT
ap-6103	23	17	.	.	PUNCT
ap-6103	24	1	in	in	ADP
ap-6103	24	2	this	this	DET
ap-6103	24	3	paper	paper	NOUN
ap-6103	24	4	,	,	PUNCT
ap-6103	24	5	we	we	PRON
ap-6103	24	6	construct	construct	VERB
ap-6103	24	7	a	a	DET
ap-6103	24	8	first	first	ADJ
ap-6103	24	9	-	-	PUNCT
ap-6103	24	10	order	order	NOUN
ap-6103	24	11	recursion	recursion	NOUN
ap-6103	24	12	operator	operator	NOUN
ap-6103	24	13	for	for	ADP
ap-6103	24	14	a	a	DET
ap-6103	24	15	sequence	sequence	NOUN
ap-6103	24	16	of	of	ADP
ap-6103	24	17	nonlinear	nonlinear	ADJ
ap-6103	24	18	ordinary	ordinary	ADJ
ap-6103	24	19	differential	differential	ADJ
ap-6103	24	20	equations	equation	NOUN
ap-6103	24	21	based	base	VERB
ap-6103	24	22	upon	upon	SCONJ
ap-6103	24	23	the	the	DET
ap-6103	24	24	schwarzian	schwarzian	PROPN
ap-6103	24	25	differential	differential	PROPN
ap-6103	24	26	invariant	invariant	ADJ
ap-6103	24	27	in	in	ADP
ap-6103	24	28	its	its	PRON
ap-6103	24	29	expression	expression	NOUN
ap-6103	24	30	as	as	ADP
ap-6103	24	31	the	the	DET
ap-6103	24	32	kummer	kummer	NOUN
ap-6103	24	33	-	-	PUNCT
ap-6103	24	34	schwarz	schwarz	PROPN
ap-6103	24	35	equation	equation	NOUN
ap-6103	24	36	and	and	CCONJ
ap-6103	24	37	investigate	investigate	VERB
ap-6103	24	38	the	the	DET
ap-6103	24	39	properties	property	NOUN
ap-6103	24	40	of	of	ADP
ap-6103	24	41	the	the	DET
ap-6103	24	42	higherorder	higherorder	NOUN
ap-6103	24	43	differential	differential	ADJ
ap-6103	24	44	equations	equation	NOUN
ap-6103	24	45	so	so	ADV
ap-6103	24	46	generated	generate	VERB
ap-6103	24	47	.	.	PUNCT
ap-6103	25	1	as	as	SCONJ
ap-6103	25	2	our	our	PRON
ap-6103	25	3	primary	primary	ADJ
ap-6103	25	4	interest	interest	NOUN
ap-6103	25	5	is	be	AUX
ap-6103	25	6	in	in	ADP
ap-6103	25	7	differential	differential	ADJ
ap-6103	25	8	equations	equation	NOUN
ap-6103	25	9	integrable	integrable	ADJ
ap-6103	25	10	in	in	ADP
ap-6103	25	11	the	the	DET
ap-6103	25	12	sense	sense	NOUN
ap-6103	25	13	of	of	ADP
ap-6103	25	14	poincaré	poincaré	PROPN
ap-6103	25	15	(	(	PUNCT
ap-6103	25	16	iewith	iewith	PROPN
ap-6103	25	17	solutions	solution	NOUN
ap-6103	25	18	which	which	PRON
ap-6103	25	19	are	be	AUX
ap-6103	25	20	analytically	analytically	ADV
ap-6103	25	21	away	away	ADV
ap-6103	25	22	from	from	ADP
ap-6103	25	23	isolated	isolated	ADJ
ap-6103	25	24	polelike	polelike	ADJ
ap-6103	25	25	singularities	singularity	NOUN
ap-6103	25	26	)	)	PUNCT
ap-6103	25	27	we	we	PRON
ap-6103	25	28	are	be	AUX
ap-6103	25	29	disappointed	disappoint	VERB
ap-6103	25	30	with	with	ADP
ap-6103	25	31	the	the	DET
ap-6103	25	32	results	result	NOUN
ap-6103	25	33	.	.	PUNCT
ap-6103	26	1	however	however	ADV
ap-6103	26	2	,	,	PUNCT
ap-6103	26	3	we	we	PRON
ap-6103	26	4	are	be	AUX
ap-6103	26	5	able	able	ADJ
ap-6103	26	6	to	to	PART
ap-6103	26	7	develop	develop	VERB
ap-6103	26	8	a	a	DET
ap-6103	26	9	sequence	sequence	NOUN
ap-6103	26	10	based	base	VERB
ap-6103	26	11	upon	upon	SCONJ
ap-6103	26	12	a	a	DET
ap-6103	26	13	different	different	ADJ
ap-6103	26	14	generator	generator	NOUN
ap-6103	26	15	and	and	CCONJ
ap-6103	26	16	find	find	VERB
ap-6103	26	17	that	that	SCONJ
ap-6103	26	18	the	the	DET
ap-6103	26	19	elements	element	NOUN
ap-6103	26	20	of	of	ADP
ap-6103	26	21	that	that	DET
ap-6103	26	22	sequence	sequence	NOUN
ap-6103	26	23	have	have	VERB
ap-6103	26	24	a	a	DET
ap-6103	26	25	combination	combination	NOUN
ap-6103	26	26	of	of	ADP
ap-6103	26	27	very	very	ADV
ap-6103	26	28	interesting	interesting	ADJ
ap-6103	26	29	properties	property	NOUN
ap-6103	26	30	,	,	PUNCT
ap-6103	26	31	which	which	PRON
ap-6103	26	32	help	help	VERB
ap-6103	26	33	to	to	PART
ap-6103	26	34	illustrate	illustrate	VERB
ap-6103	26	35	a	a	DET
ap-6103	26	36	facet	facet	NOUN
ap-6103	26	37	of	of	ADP
ap-6103	26	38	this	this	DET
ap-6103	26	39	type	type	NOUN
ap-6103	26	40	of	of	ADP
ap-6103	26	41	analysis	analysis	NOUN
ap-6103	26	42	not	not	PART
ap-6103	26	43	displayed	display	VERB
ap-6103	26	44	in	in	ADP
ap-6103	26	45	the	the	DET
ap-6103	26	46	literature	literature	NOUN
ap-6103	26	47	.	.	PUNCT
ap-6103	27	1	in	in	ADP
ap-6103	27	2	addition	addition	NOUN
ap-6103	27	3	to	to	ADP
ap-6103	27	4	the	the	DET
ap-6103	27	5	examination	examination	NOUN
ap-6103	27	6	of	of	ADP
ap-6103	27	7	the	the	DET
ap-6103	27	8	singularity	singularity	NOUN
ap-6103	27	9	properties	property	NOUN
ap-6103	27	10	of	of	ADP
ap-6103	27	11	this	this	DET
ap-6103	27	12	sequence	sequence	NOUN
ap-6103	27	13	,	,	PUNCT
ap-6103	27	14	we	we	PRON
ap-6103	27	15	also	also	ADV
ap-6103	27	16	demonstrate	demonstrate	VERB
ap-6103	27	17	its	its	PRON
ap-6103	27	18	complete	complete	ADJ
ap-6103	27	19	symmetry	symmetry	NOUN
ap-6103	27	20	group	group	NOUN
ap-6103	27	21	and	and	CCONJ
ap-6103	27	22	provide	provide	VERB
ap-6103	27	23	a	a	DET
ap-6103	27	24	differential	differential	ADJ
ap-6103	27	25	generator	generator	NOUN
ap-6103	27	26	for	for	ADP
ap-6103	27	27	an	an	DET
ap-6103	27	28	alternate	alternate	ADJ
ap-6103	27	29	representation	representation	NOUN
ap-6103	27	30	of	of	ADP
ap-6103	27	31	the	the	DET
ap-6103	27	32	elements	element	NOUN
ap-6103	27	33	of	of	ADP
ap-6103	27	34	the	the	DET
ap-6103	27	35	sequence	sequence	NOUN
ap-6103	27	36	.	.	PUNCT
ap-6103	28	1	2	2	X
ap-6103	28	2	.	.	X
ap-6103	28	3	the	the	DET
ap-6103	28	4	first	first	ADJ
ap-6103	28	5	-	-	PUNCT
ap-6103	28	6	order	order	NOUN
ap-6103	28	7	recursion	recursion	NOUN
ap-6103	28	8	operator	operator	NOUN
ap-6103	28	9	for	for	ADP
ap-6103	28	10	the	the	DET
ap-6103	28	11	kummer	kummer	NOUN
ap-6103	28	12	-	-	PUNCT
ap-6103	28	13	schwarz	schwarz	PROPN
ap-6103	28	14	equation	equation	NOUN
ap-6103	28	15	we	we	PRON
ap-6103	28	16	write	write	VERB
ap-6103	28	17	the	the	DET
ap-6103	28	18	kummer	kummer	NOUN
ap-6103	28	19	-	-	PUNCT
ap-6103	28	20	schwarz	schwarz	PROPN
ap-6103	28	21	equation	equation	NOUN
ap-6103	28	22	in	in	ADP
ap-6103	28	23	the	the	DET
ap-6103	28	24	form	form	NOUN
ap-6103	28	25	u′′′	u′′′	VERB
ap-6103	28	26	2u′	2u′	NUM
ap-6103	28	27	−	−	ADP
ap-6103	28	28	3u′′2	3u′′2	NUM
ap-6103	28	29	4u′2	4u′2	NUM
ap-6103	28	30	=	=	SYM
ap-6103	28	31	0	0	PROPN
ap-6103	28	32	,	,	PUNCT
ap-6103	28	33	(	(	PUNCT
ap-6103	28	34	4	4	X
ap-6103	28	35	)	)	PUNCT
ap-6103	28	36	2the	2the	NUM
ap-6103	28	37	change	change	NOUN
ap-6103	28	38	in	in	ADP
ap-6103	28	39	terminology	terminology	NOUN
ap-6103	28	40	is	be	AUX
ap-6103	28	41	justified	justify	VERB
ap-6103	28	42	in	in	ADP
ap-6103	28	43	that	that	DET
ap-6103	28	44	paper	paper	NOUN
ap-6103	28	45	.	.	PUNCT
ap-6103	29	1	428	428	NUM
ap-6103	29	2	https://doi.org/10.14311/ap.2020.60.0428	https://doi.org/10.14311/ap.2020.60.0428	NOUN
ap-6103	29	3	https://ojs.cvut.cz/ojs/index.php/ap	https://ojs.cvut.cz/ojs/index.php/ap	NUM
ap-6103	29	4	vol	vol	NOUN
ap-6103	29	5	.	.	PUNCT
ap-6103	30	1	60	60	NUM
ap-6103	30	2	no	no	NOUN
ap-6103	30	3	.	.	PUNCT
ap-6103	31	1	5/2020	5/2020	NUM
ap-6103	31	2	properties	property	NOUN
ap-6103	31	3	of	of	ADP
ap-6103	31	4	a	a	DET
ap-6103	31	5	differential	differential	ADJ
ap-6103	31	6	sequence	sequence	NOUN
ap-6103	31	7	based	base	VERB
ap-6103	31	8	upon	upon	SCONJ
ap-6103	31	9	the	the	DET
ap-6103	31	10	kummer	kummer	NOUN
ap-6103	31	11	-	-	PUNCT
ap-6103	31	12	schwarz	schwarz	PROPN
ap-6103	31	13	.	.	PUNCT
ap-6103	31	14	.	.	PUNCT
ap-6103	31	15	.	.	PUNCT
ap-6103	32	1	where	where	SCONJ
ap-6103	32	2	the	the	DET
ap-6103	32	3	prime	prime	ADJ
ap-6103	32	4	denotes	denote	VERB
ap-6103	32	5	the	the	DET
ap-6103	32	6	differentiation	differentiation	NOUN
ap-6103	32	7	with	with	ADP
ap-6103	32	8	respect	respect	NOUN
ap-6103	32	9	to	to	ADP
ap-6103	32	10	the	the	DET
ap-6103	32	11	independent	independent	ADJ
ap-6103	32	12	variable	variable	NOUN
ap-6103	32	13	,	,	PUNCT
ap-6103	32	14	x	x	X
ap-6103	32	15	,	,	PUNCT
ap-6103	32	16	to	to	PART
ap-6103	32	17	emphasise	emphasise	VERB
ap-6103	32	18	its	its	PRON
ap-6103	32	19	connection	connection	NOUN
ap-6103	32	20	with	with	ADP
ap-6103	32	21	the	the	DET
ap-6103	32	22	schwarzian	schwarzian	PROPN
ap-6103	32	23	derivative	derivative	NOUN
ap-6103	32	24	,	,	PUNCT
ap-6103	32	25	(	(	PUNCT
ap-6103	32	26	u′−1/2)′′.	u′−1/2)′′.	PROPN
ap-6103	32	27	we	we	PRON
ap-6103	32	28	construct	construct	VERB
ap-6103	32	29	a	a	DET
ap-6103	32	30	first	first	ADJ
ap-6103	32	31	-	-	PUNCT
ap-6103	32	32	order	order	NOUN
ap-6103	32	33	recursion	recursion	NOUN
ap-6103	32	34	operator	operator	NOUN
ap-6103	32	35	for	for	ADP
ap-6103	32	36	(	(	PUNCT
ap-6103	32	37	4	4	NUM
ap-6103	32	38	)	)	PUNCT
ap-6103	32	39	,	,	PUNCT
ap-6103	32	40	r	r	NOUN
ap-6103	32	41	=	=	SYM
ap-6103	32	42	d	d	PROPN
ap-6103	32	43	+	+	CCONJ
ap-6103	32	44	a	a	X
ap-6103	32	45	,	,	PUNCT
ap-6103	32	46	where	where	SCONJ
ap-6103	32	47	we	we	PRON
ap-6103	32	48	write	write	VERB
ap-6103	32	49	d	d	PROPN
ap-6103	32	50	as	as	ADP
ap-6103	32	51	the	the	DET
ap-6103	32	52	operator	operator	NOUN
ap-6103	32	53	of	of	ADP
ap-6103	32	54	the	the	DET
ap-6103	32	55	total	total	ADJ
ap-6103	32	56	differentiation	differentiation	NOUN
ap-6103	32	57	with	with	ADP
ap-6103	32	58	respect	respect	NOUN
ap-6103	32	59	to	to	ADP
ap-6103	32	60	the	the	DET
ap-6103	32	61	single	single	ADJ
ap-6103	32	62	independent	independent	ADJ
ap-6103	32	63	variable	variable	NOUN
ap-6103	32	64	,	,	PUNCT
ap-6103	32	65	x	x	PRON
ap-6103	32	66	,	,	PUNCT
ap-6103	32	67	and	and	CCONJ
ap-6103	32	68	a	a	PRON
ap-6103	32	69	is	be	AUX
ap-6103	32	70	a	a	DET
ap-6103	32	71	function	function	NOUN
ap-6103	32	72	to	to	PART
ap-6103	32	73	be	be	AUX
ap-6103	32	74	determined	determine	VERB
ap-6103	32	75	.	.	PUNCT
ap-6103	33	1	the	the	DET
ap-6103	33	2	linearised	linearise	VERB
ap-6103	33	3	operator	operator	NOUN
ap-6103	33	4	for	for	ADP
ap-6103	33	5	(	(	PUNCT
ap-6103	33	6	4	4	NUM
ap-6103	33	7	)	)	PUNCT
ap-6103	33	8	is	be	AUX
ap-6103	33	9	l[u	l[u	NOUN
ap-6103	33	10	]	]	X
ap-6103	33	11	=	=	SYM
ap-6103	34	1	1	1	NUM
ap-6103	34	2	2u′d	2u′d	NUM
ap-6103	34	3	3	3	NUM
ap-6103	34	4	−	−	PROPN
ap-6103	34	5	3u′′	3u′′	NUM
ap-6103	34	6	2u′2d	2u′2d	NUM
ap-6103	34	7	2	2	NUM
ap-6103	34	8	−	−	PROPN
ap-6103	34	9	(	(	PUNCT
ap-6103	34	10	u′′′	u′′′	PROPN
ap-6103	34	11	2u′2	2u′2	NUM
ap-6103	35	1	−	−	PROPN
ap-6103	35	2	3u′′2	3u′′2	NUM
ap-6103	35	3	2u′3	2u′3	NUM
ap-6103	35	4	)	)	PUNCT
ap-6103	35	5	d.	d.	NOUN
ap-6103	35	6	(	(	PUNCT
ap-6103	35	7	5	5	NUM
ap-6103	35	8	)	)	PUNCT
ap-6103	35	9	as	as	SCONJ
ap-6103	35	10	we	we	PRON
ap-6103	35	11	are	be	AUX
ap-6103	35	12	dealing	deal	VERB
ap-6103	35	13	with	with	ADP
ap-6103	35	14	an	an	DET
ap-6103	35	15	ordinary	ordinary	ADJ
ap-6103	35	16	differential	differential	ADJ
ap-6103	35	17	equation	equation	NOUN
ap-6103	35	18	,	,	PUNCT
ap-6103	35	19	(	(	PUNCT
ap-6103	35	20	2	2	X
ap-6103	35	21	)	)	PUNCT
ap-6103	35	22	is	be	AUX
ap-6103	35	23	somewhat	somewhat	ADV
ap-6103	35	24	simpler	simple	ADJ
ap-6103	35	25	.	.	PUNCT
ap-6103	36	1	we	we	PRON
ap-6103	36	2	calculate	calculate	VERB
ap-6103	36	3	the	the	DET
ap-6103	36	4	lie	lie	NOUN
ap-6103	36	5	bracket	bracket	NOUN
ap-6103	36	6	of	of	ADP
ap-6103	36	7	l	l	NOUN
ap-6103	36	8	and	and	CCONJ
ap-6103	36	9	r	r	NOUN
ap-6103	36	10	and	and	CCONJ
ap-6103	36	11	require	require	VERB
ap-6103	36	12	its	its	PRON
ap-6103	36	13	action	action	NOUN
ap-6103	36	14	upon	upon	SCONJ
ap-6103	36	15	v	v	NUM
ap-6103	36	16	to	to	PART
ap-6103	36	17	give	give	VERB
ap-6103	36	18	zero	zero	NUM
ap-6103	36	19	when	when	SCONJ
ap-6103	36	20	the	the	DET
ap-6103	36	21	(	(	PUNCT
ap-6103	36	22	linearised	linearised	ADJ
ap-6103	36	23	)	)	PUNCT
ap-6103	36	24	equation	equation	NOUN
ap-6103	36	25	for	for	ADP
ap-6103	36	26	v	v	NOUN
ap-6103	36	27	is	be	AUX
ap-6103	36	28	satisfied	satisfied	ADJ
ap-6103	36	29	.	.	PUNCT
ap-6103	37	1	this	this	PRON
ap-6103	37	2	gives	give	VERB
ap-6103	37	3	a	a	DET
ap-6103	37	4	large	large	ADJ
ap-6103	37	5	equation	equation	NOUN
ap-6103	37	6	with	with	ADP
ap-6103	37	7	terms	term	NOUN
ap-6103	37	8	in	in	ADP
ap-6103	37	9	v′′	v′′	NOUN
ap-6103	37	10	,	,	PUNCT
ap-6103	37	11	v′	v′	NOUN
ap-6103	37	12	and	and	CCONJ
ap-6103	37	13	v.	v.	ADP
ap-6103	37	14	the	the	DET
ap-6103	37	15	coefficient	coefficient	NOUN
ap-6103	37	16	of	of	ADP
ap-6103	37	17	each	each	PRON
ap-6103	37	18	of	of	ADP
ap-6103	37	19	these	these	DET
ap-6103	37	20	terms	term	NOUN
ap-6103	37	21	is	be	AUX
ap-6103	37	22	required	require	VERB
ap-6103	37	23	separately	separately	ADV
ap-6103	37	24	to	to	PART
ap-6103	37	25	be	be	AUX
ap-6103	37	26	zero	zero	NUM
ap-6103	37	27	.	.	PUNCT
ap-6103	38	1	that	that	PRON
ap-6103	38	2	of	of	ADP
ap-6103	38	3	v′′	v′′	NOUN
ap-6103	38	4	gives	give	VERB
ap-6103	38	5	6a′	6a′	NUM
ap-6103	38	6	u′	u′	PROPN
ap-6103	38	7	−	−	PROPN
ap-6103	38	8	6u′′2	6u′′2	NUM
ap-6103	38	9	u′3	u′3	ADJ
ap-6103	39	1	+	+	CCONJ
ap-6103	39	2	6u′′′	6u′′′	NUM
ap-6103	39	3	u′2	u′2	X
ap-6103	39	4	=	=	SYM
ap-6103	39	5	0	0	NUM
ap-6103	39	6	(	(	PUNCT
ap-6103	39	7	6	6	NUM
ap-6103	39	8	)	)	PUNCT
ap-6103	39	9	which	which	PRON
ap-6103	39	10	has	have	VERB
ap-6103	39	11	the	the	DET
ap-6103	39	12	solution	solution	NOUN
ap-6103	39	13	a	a	DET
ap-6103	39	14	=	=	SYM
ap-6103	39	15	−u	−u	PROPN
ap-6103	39	16	′′	′′	PROPN
ap-6103	39	17	u′	u′	PROPN
ap-6103	39	18	(	(	PUNCT
ap-6103	39	19	7	7	NUM
ap-6103	39	20	)	)	PUNCT
ap-6103	39	21	up	up	ADP
ap-6103	39	22	to	to	ADP
ap-6103	39	23	an	an	DET
ap-6103	39	24	arbitrary	arbitrary	ADJ
ap-6103	39	25	constant	constant	NOUN
ap-6103	39	26	of	of	ADP
ap-6103	39	27	integration	integration	NOUN
ap-6103	39	28	,	,	PUNCT
ap-6103	39	29	which	which	PRON
ap-6103	39	30	we	we	PRON
ap-6103	39	31	consider	consider	VERB
ap-6103	39	32	to	to	PART
ap-6103	39	33	be	be	AUX
ap-6103	39	34	zero	zero	NUM
ap-6103	39	35	.	.	PUNCT
ap-6103	40	1	when	when	SCONJ
ap-6103	40	2	the	the	DET
ap-6103	40	3	right	right	ADJ
ap-6103	40	4	side	side	NOUN
ap-6103	40	5	(	(	PUNCT
ap-6103	40	6	7	7	NUM
ap-6103	40	7	)	)	PUNCT
ap-6103	40	8	is	be	AUX
ap-6103	40	9	substituted	substitute	VERB
ap-6103	40	10	into	into	ADP
ap-6103	40	11	the	the	DET
ap-6103	40	12	remaining	remain	VERB
ap-6103	40	13	terms	term	NOUN
ap-6103	40	14	,	,	PUNCT
ap-6103	40	15	the	the	DET
ap-6103	40	16	result	result	NOUN
ap-6103	40	17	is	be	AUX
ap-6103	40	18	identically	identically	ADV
ap-6103	40	19	zero	zero	NUM
ap-6103	40	20	.	.	PUNCT
ap-6103	41	1	we	we	PRON
ap-6103	41	2	apply	apply	VERB
ap-6103	41	3	the	the	DET
ap-6103	41	4	recursion	recursion	NOUN
ap-6103	41	5	operator	operator	NOUN
ap-6103	41	6	r	r	NOUN
ap-6103	41	7	=	=	SYM
ap-6103	41	8	d	d	NOUN
ap-6103	41	9	−	−	PROPN
ap-6103	41	10	u′′	u′′	PROPN
ap-6103	41	11	u′	u′	PROPN
ap-6103	41	12	(	(	PUNCT
ap-6103	41	13	8)	8)	NUM
ap-6103	41	14	to	to	ADP
ap-6103	41	15	the	the	DET
ap-6103	41	16	kummer	kummer	NOUN
ap-6103	41	17	-	-	PUNCT
ap-6103	41	18	schwarz	schwarz	PROPN
ap-6103	41	19	equation	equation	NOUN
ap-6103	41	20	,	,	PUNCT
ap-6103	41	21	(	(	PUNCT
ap-6103	41	22	4	4	NUM
ap-6103	41	23	)	)	PUNCT
ap-6103	41	24	,	,	PUNCT
ap-6103	41	25	to	to	PART
ap-6103	41	26	initiate	initiate	VERB
ap-6103	41	27	the	the	DET
ap-6103	41	28	construction	construction	NOUN
ap-6103	41	29	of	of	ADP
ap-6103	41	30	the	the	DET
ap-6103	41	31	elements	element	NOUN
ap-6103	41	32	of	of	ADP
ap-6103	41	33	the	the	DET
ap-6103	41	34	sequence	sequence	NOUN
ap-6103	41	35	.	.	PUNCT
ap-6103	42	1	the	the	DET
ap-6103	42	2	first	first	ADJ
ap-6103	42	3	equation	equation	NOUN
ap-6103	42	4	we	we	PRON
ap-6103	42	5	obtain	obtain	VERB
ap-6103	42	6	is	be	AUX
ap-6103	42	7	u(4	u(4	PROPN
ap-6103	42	8	)	)	PUNCT
ap-6103	42	9	u′	u′	PROPN
ap-6103	42	10	−	−	PROPN
ap-6103	42	11	5u	5u	NUM
ap-6103	42	12	′′u(3	′′u(3	PROPN
ap-6103	42	13	)	)	PUNCT
ap-6103	42	14	u′2	u′2	NOUN
ap-6103	43	1	+	+	NOUN
ap-6103	43	2	9	9	NUM
ap-6103	43	3	u	u	NOUN
ap-6103	43	4	′′3	′′3	NOUN
ap-6103	43	5	2u′3	2u′3	NUM
ap-6103	43	6	=	=	SYM
ap-6103	43	7	0	0	X
ap-6103	43	8	.	.	PUNCT
ap-6103	44	1	(	(	PUNCT
ap-6103	44	2	9	9	NUM
ap-6103	44	3	)	)	PUNCT
ap-6103	44	4	when	when	SCONJ
ap-6103	44	5	we	we	PRON
ap-6103	44	6	seek	seek	VERB
ap-6103	44	7	the	the	DET
ap-6103	44	8	leading	lead	VERB
ap-6103	44	9	-	-	PUNCT
ap-6103	44	10	order	order	NOUN
ap-6103	44	11	behaviour	behaviour	NOUN
ap-6103	44	12	of	of	ADP
ap-6103	44	13	(	(	PUNCT
ap-6103	44	14	9	9	NUM
ap-6103	44	15	)	)	PUNCT
ap-6103	44	16	by	by	ADP
ap-6103	44	17	setting	set	VERB
ap-6103	44	18	u	u	NOUN
ap-6103	44	19	=	=	NOUN
ap-6103	44	20	αχp	αχp	PROPN
ap-6103	44	21	,	,	PUNCT
ap-6103	44	22	where	where	SCONJ
ap-6103	44	23	χ	χ	X
ap-6103	44	24	=	=	PUNCT
ap-6103	44	25	x−x0	x−x0	NOUN
ap-6103	44	26	and	and	CCONJ
ap-6103	44	27	x0	x0	PROPN
ap-6103	44	28	is	be	AUX
ap-6103	44	29	the	the	DET
ap-6103	44	30	location	location	NOUN
ap-6103	44	31	of	of	ADP
ap-6103	44	32	the	the	DET
ap-6103	44	33	putative	putative	ADJ
ap-6103	44	34	singularity	singularity	NOUN
ap-6103	44	35	,	,	PUNCT
ap-6103	44	36	we	we	PRON
ap-6103	44	37	find	find	VERB
ap-6103	44	38	that	that	SCONJ
ap-6103	44	39	p	p	X
ap-6103	44	40	=	=	PUNCT
ap-6103	44	41	−1(bis	−1(bis	PROPN
ap-6103	44	42	)	)	PUNCT
ap-6103	44	43	,	,	PUNCT
ap-6103	44	44	1	1	X
ap-6103	44	45	.	.	PUNCT
ap-6103	45	1	this	this	PRON
ap-6103	45	2	is	be	AUX
ap-6103	45	3	not	not	PART
ap-6103	45	4	acceptable	acceptable	ADJ
ap-6103	45	5	for	for	ADP
ap-6103	45	6	a	a	DET
ap-6103	45	7	scalar	scalar	ADJ
ap-6103	45	8	equation	equation	NOUN
ap-6103	45	9	!	!	PUNCT
ap-6103	46	1	we	we	PRON
ap-6103	46	2	recall	recall	VERB
ap-6103	46	3	that	that	SCONJ
ap-6103	46	4	the	the	DET
ap-6103	46	5	kummer	kummer	NOUN
ap-6103	46	6	-	-	PUNCT
ap-6103	46	7	schwarz	schwarz	PROPN
ap-6103	46	8	equation	equation	NOUN
ap-6103	46	9	is	be	AUX
ap-6103	46	10	closely	closely	ADV
ap-6103	46	11	related	relate	VERB
ap-6103	46	12	to	to	ADP
ap-6103	46	13	the	the	DET
ap-6103	46	14	equation	equation	NOUN
ap-6103	46	15	v′′	v′′	NOUN
ap-6103	46	16	+	+	CCONJ
ap-6103	46	17	v′2	v′2	NOUN
ap-6103	46	18	=	=	NOUN
ap-6103	46	19	0	0	NUM
ap-6103	46	20	(	(	PUNCT
ap-6103	46	21	10	10	NUM
ap-6103	46	22	)	)	PUNCT
ap-6103	46	23	which	which	PRON
ap-6103	46	24	is	be	AUX
ap-6103	46	25	the	the	DET
ap-6103	46	26	autonomous	autonomous	ADJ
ap-6103	46	27	version	version	NOUN
ap-6103	46	28	of	of	ADP
ap-6103	46	29	the	the	DET
ap-6103	46	30	potential	potential	ADJ
ap-6103	46	31	form	form	NOUN
ap-6103	46	32	of	of	ADP
ap-6103	46	33	burgers	burger	NOUN
ap-6103	46	34	equation	equation	NOUN
ap-6103	46	35	for	for	ADP
ap-6103	46	36	which	which	PRON
ap-6103	46	37	the	the	DET
ap-6103	46	38	first	first	ADJ
ap-6103	46	39	-	-	PUNCT
ap-6103	46	40	order	order	NOUN
ap-6103	46	41	recurrence	recurrence	NOUN
ap-6103	46	42	relation	relation	NOUN
ap-6103	46	43	is	be	AUX
ap-6103	46	44	d	d	X
ap-6103	46	45	+	+	CCONJ
ap-6103	46	46	v′.	v′.	ADP
ap-6103	46	47	this	this	DET
ap-6103	46	48	recurrence	recurrence	NOUN
ap-6103	46	49	relation	relation	NOUN
ap-6103	46	50	becomes	become	VERB
ap-6103	46	51	that	that	PRON
ap-6103	46	52	of	of	ADP
ap-6103	46	53	the	the	DET
ap-6103	46	54	kummer	kummer	NOUN
ap-6103	46	55	-	-	PUNCT
ap-6103	46	56	schwarz	schwarz	PROPN
ap-6103	46	57	equation	equation	NOUN
ap-6103	46	58	obtained	obtain	VERB
ap-6103	46	59	above	above	ADV
ap-6103	46	60	,	,	PUNCT
ap-6103	46	61	under	under	ADP
ap-6103	46	62	the	the	DET
ap-6103	46	63	transformation	transformation	NOUN
ap-6103	46	64	connecting	connect	VERB
ap-6103	46	65	the	the	DET
ap-6103	46	66	two	two	NUM
ap-6103	46	67	equations	equation	NOUN
ap-6103	46	68	.	.	PUNCT
ap-6103	47	1	equation	equation	NOUN
ap-6103	47	2	(	(	PUNCT
ap-6103	47	3	10	10	NUM
ap-6103	47	4	)	)	PUNCT
ap-6103	47	5	is	be	AUX
ap-6103	47	6	an	an	DET
ap-6103	47	7	elementary	elementary	ADJ
ap-6103	47	8	riccati	riccati	NOUN
ap-6103	47	9	equation	equation	NOUN
ap-6103	47	10	in	in	ADP
ap-6103	47	11	the	the	DET
ap-6103	47	12	dependent	dependent	ADJ
ap-6103	47	13	variable	variable	NOUN
ap-6103	47	14	v′.	v′.	ADV
ap-6103	47	15	in	in	ADP
ap-6103	47	16	terms	term	NOUN
ap-6103	47	17	of	of	ADP
ap-6103	47	18	y	y	PROPN
ap-6103	47	19	=	=	SYM
ap-6103	47	20	v′	v′	PROPN
ap-6103	47	21	it	it	PRON
ap-6103	47	22	is	be	AUX
ap-6103	47	23	y′	y′	NOUN
ap-6103	47	24	+	+	CCONJ
ap-6103	48	1	y2	y2	NOUN
ap-6103	48	2	=	=	SYM
ap-6103	48	3	0	0	PROPN
ap-6103	48	4	.	.	PUNCT
ap-6103	49	1	(	(	PUNCT
ap-6103	49	2	11	11	NUM
ap-6103	49	3	)	)	PUNCT
ap-6103	49	4	the	the	DET
ap-6103	49	5	connection	connection	NOUN
ap-6103	49	6	of	of	ADP
ap-6103	49	7	this	this	DET
ap-6103	49	8	form	form	NOUN
ap-6103	49	9	of	of	ADP
ap-6103	49	10	the	the	DET
ap-6103	49	11	riccati	riccati	PROPN
ap-6103	49	12	equation	equation	NOUN
ap-6103	49	13	to	to	ADP
ap-6103	49	14	the	the	DET
ap-6103	49	15	kummer	kummer	NOUN
ap-6103	49	16	-	-	PUNCT
ap-6103	49	17	schwarz	schwarz	PROPN
ap-6103	49	18	equation	equation	NOUN
ap-6103	49	19	is	be	AUX
ap-6103	49	20	well	well	ADV
ap-6103	49	21	known	know	VERB
ap-6103	49	22	.	.	PUNCT
ap-6103	50	1	it	it	PRON
ap-6103	50	2	is	be	AUX
ap-6103	50	3	a	a	DET
ap-6103	50	4	simple	simple	ADJ
ap-6103	50	5	calculation	calculation	NOUN
ap-6103	50	6	to	to	PART
ap-6103	50	7	show	show	VERB
ap-6103	50	8	that	that	SCONJ
ap-6103	50	9	the	the	DET
ap-6103	50	10	recursion	recursion	NOUN
ap-6103	50	11	operator	operator	NOUN
ap-6103	50	12	for	for	ADP
ap-6103	50	13	(	(	PUNCT
ap-6103	50	14	11	11	NUM
ap-6103	50	15	)	)	PUNCT
ap-6103	50	16	is	be	AUX
ap-6103	50	17	d	d	PROPN
ap-6103	50	18	+	+	NUM
ap-6103	50	19	2y	2y	NUM
ap-6103	50	20	.	.	PUNCT
ap-6103	51	1	however	however	ADV
ap-6103	51	2	,	,	PUNCT
ap-6103	51	3	it	it	PRON
ap-6103	51	4	has	have	AUX
ap-6103	51	5	been	be	AUX
ap-6103	51	6	shown	show	VERB
ap-6103	51	7	[	[	PUNCT
ap-6103	51	8	6	6	NUM
ap-6103	51	9	,	,	PUNCT
ap-6103	51	10	7	7	NUM
ap-6103	51	11	]	]	PUNCT
ap-6103	51	12	that	that	SCONJ
ap-6103	51	13	the	the	DET
ap-6103	51	14	operator	operator	NOUN
ap-6103	51	15	,	,	PUNCT
ap-6103	51	16	d	d	PROPN
ap-6103	51	17	+	+	NUM
ap-6103	51	18	y	y	NOUN
ap-6103	51	19	,	,	PUNCT
ap-6103	51	20	generates	generate	VERB
ap-6103	51	21	a	a	DET
ap-6103	51	22	sequence	sequence	NOUN
ap-6103	51	23	of	of	ADP
ap-6103	51	24	differential	differential	ADJ
ap-6103	51	25	equations	equation	NOUN
ap-6103	51	26	based	base	VERB
ap-6103	51	27	upon	upon	SCONJ
ap-6103	51	28	the	the	DET
ap-6103	51	29	riccati	riccati	PROPN
ap-6103	51	30	equation	equation	NOUN
ap-6103	51	31	,	,	PUNCT
ap-6103	51	32	which	which	PRON
ap-6103	51	33	has	have	VERB
ap-6103	51	34	very	very	ADV
ap-6103	51	35	satisfying	satisfying	ADJ
ap-6103	51	36	properties	property	NOUN
ap-6103	51	37	in	in	ADP
ap-6103	51	38	terms	term	NOUN
ap-6103	51	39	of	of	ADP
ap-6103	51	40	their	their	PRON
ap-6103	51	41	singularity	singularity	NOUN
ap-6103	51	42	characteristics	characteristic	NOUN
ap-6103	51	43	and	and	CCONJ
ap-6103	51	44	algebras	algebra	NOUN
ap-6103	51	45	.	.	PUNCT
ap-6103	52	1	there	there	PRON
ap-6103	52	2	is	be	VERB
ap-6103	52	3	a	a	DET
ap-6103	52	4	price	price	NOUN
ap-6103	52	5	to	to	PART
ap-6103	52	6	pay	pay	VERB
ap-6103	52	7	.	.	PUNCT
ap-6103	53	1	this	this	DET
ap-6103	53	2	operator	operator	NOUN
ap-6103	53	3	is	be	AUX
ap-6103	53	4	not	not	PART
ap-6103	53	5	a	a	DET
ap-6103	53	6	recursion	recursion	NOUN
ap-6103	53	7	operator	operator	NOUN
ap-6103	53	8	–	–	PUNCT
ap-6103	53	9	hence	hence	ADV
ap-6103	53	10	the	the	DET
ap-6103	53	11	descriptor	descriptor	NOUN
ap-6103	53	12	‘	'	PUNCT
ap-6103	53	13	generator	generator	NOUN
ap-6103	53	14	of	of	ADP
ap-6103	53	15	sequence	sequence	NOUN
ap-6103	53	16	’	'	PUNCT
ap-6103	54	1	[	[	X
ap-6103	54	2	7	7	NUM
ap-6103	54	3	]	]	PUNCT
ap-6103	54	4	to	to	PART
ap-6103	54	5	emphasise	emphasise	VERB
ap-6103	54	6	the	the	DET
ap-6103	54	7	distinction	distinction	NOUN
ap-6103	54	8	–	–	PUNCT
ap-6103	54	9	and	and	CCONJ
ap-6103	54	10	so	so	ADV
ap-6103	54	11	one	one	NOUN
ap-6103	54	12	can	can	AUX
ap-6103	54	13	not	not	PART
ap-6103	54	14	expect	expect	VERB
ap-6103	54	15	to	to	PART
ap-6103	54	16	obtain	obtain	VERB
ap-6103	54	17	the	the	DET
ap-6103	54	18	properties	property	NOUN
ap-6103	54	19	normally	normally	ADV
ap-6103	54	20	associated	associate	VERB
ap-6103	54	21	with	with	ADP
ap-6103	54	22	the	the	DET
ap-6103	54	23	recursion	recursion	NOUN
ap-6103	54	24	operator	operator	NOUN
ap-6103	54	25	for	for	ADP
ap-6103	54	26	an	an	DET
ap-6103	54	27	hierarchy	hierarchy	NOUN
ap-6103	54	28	of	of	ADP
ap-6103	54	29	evolution	evolution	NOUN
ap-6103	54	30	equations	equation	NOUN
ap-6103	54	31	.	.	PUNCT
ap-6103	55	1	however	however	ADV
ap-6103	55	2	,	,	PUNCT
ap-6103	55	3	there	there	PRON
ap-6103	55	4	is	be	VERB
ap-6103	55	5	much	much	ADJ
ap-6103	55	6	to	to	PART
ap-6103	55	7	be	be	AUX
ap-6103	55	8	said	say	VERB
ap-6103	55	9	for	for	ADP
ap-6103	55	10	the	the	DET
ap-6103	55	11	attractive	attractive	ADJ
ap-6103	55	12	properties	property	NOUN
ap-6103	55	13	which	which	PRON
ap-6103	55	14	we	we	PRON
ap-6103	55	15	do	do	AUX
ap-6103	55	16	find	find	VERB
ap-6103	55	17	.	.	PUNCT
ap-6103	56	1	in	in	ADP
ap-6103	56	2	terms	term	NOUN
ap-6103	56	3	of	of	ADP
ap-6103	56	4	the	the	DET
ap-6103	56	5	dependent	dependent	ADJ
ap-6103	56	6	variable	variable	NOUN
ap-6103	56	7	of	of	ADP
ap-6103	56	8	the	the	DET
ap-6103	56	9	kummerschwarz	kummerschwarz	PROPN
ap-6103	56	10	equation	equation	NOUN
ap-6103	56	11	,	,	PUNCT
ap-6103	56	12	the	the	DET
ap-6103	56	13	generator	generator	NOUN
ap-6103	56	14	of	of	ADP
ap-6103	56	15	the	the	DET
ap-6103	56	16	sequence	sequence	NOUN
ap-6103	56	17	,	,	PUNCT
ap-6103	56	18	d+y	d+y	PROPN
ap-6103	56	19	,	,	PUNCT
ap-6103	56	20	becomes	become	VERB
ap-6103	56	21	d	d	PROPN
ap-6103	56	22	−	−	PROPN
ap-6103	56	23	u′′/2u′	u′′/2u′	NOUN
ap-6103	57	1	and	and	CCONJ
ap-6103	57	2	it	it	PRON
ap-6103	57	3	is	be	AUX
ap-6103	57	4	this	this	DET
ap-6103	57	5	operator	operator	NOUN
ap-6103	57	6	which	which	PRON
ap-6103	57	7	we	we	PRON
ap-6103	57	8	employ	employ	VERB
ap-6103	57	9	henceforth	henceforth	ADV
ap-6103	57	10	.	.	PUNCT
ap-6103	58	1	3	3	X
ap-6103	58	2	.	.	X
ap-6103	58	3	the	the	DET
ap-6103	58	4	early	early	ADJ
ap-6103	58	5	elements	element	NOUN
ap-6103	58	6	of	of	ADP
ap-6103	58	7	the	the	DET
ap-6103	58	8	new	new	ADJ
ap-6103	58	9	sequence	sequence	NOUN
ap-6103	58	10	we	we	PRON
ap-6103	58	11	now	now	ADV
ap-6103	58	12	apply	apply	VERB
ap-6103	58	13	the	the	DET
ap-6103	58	14	generator	generator	NOUN
ap-6103	59	1	r	r	NOUN
ap-6103	59	2	=	=	SYM
ap-6103	59	3	d	d	NOUN
ap-6103	59	4	−	−	PROPN
ap-6103	59	5	u′′	u′′	PROPN
ap-6103	59	6	2u′	2u′	NUM
ap-6103	59	7	(	(	PUNCT
ap-6103	59	8	12	12	NUM
ap-6103	59	9	)	)	PUNCT
ap-6103	59	10	to	to	ADP
ap-6103	59	11	the	the	DET
ap-6103	59	12	kummer	kummer	NOUN
ap-6103	59	13	-	-	PUNCT
ap-6103	59	14	schwarz	schwarz	PROPN
ap-6103	59	15	equation	equation	NOUN
ap-6103	59	16	,	,	PUNCT
ap-6103	59	17	(	(	PUNCT
ap-6103	59	18	4	4	NUM
ap-6103	59	19	)	)	PUNCT
ap-6103	59	20	,	,	PUNCT
ap-6103	59	21	to	to	PART
ap-6103	59	22	initiate	initiate	VERB
ap-6103	59	23	the	the	DET
ap-6103	59	24	construction	construction	NOUN
ap-6103	59	25	of	of	ADP
ap-6103	59	26	the	the	DET
ap-6103	59	27	elements	element	NOUN
ap-6103	59	28	of	of	ADP
ap-6103	59	29	the	the	DET
ap-6103	59	30	sequence	sequence	NOUN
ap-6103	59	31	and	and	CCONJ
ap-6103	59	32	then	then	ADV
ap-6103	59	33	apply	apply	VERB
ap-6103	59	34	it	it	PRON
ap-6103	59	35	to	to	ADP
ap-6103	59	36	each	each	DET
ap-6103	59	37	new	new	ADJ
ap-6103	59	38	element	element	NOUN
ap-6103	59	39	in	in	ADP
ap-6103	59	40	turn	turn	NOUN
ap-6103	59	41	.	.	PUNCT
ap-6103	60	1	the	the	DET
ap-6103	60	2	process	process	NOUN
ap-6103	60	3	may	may	AUX
ap-6103	60	4	be	be	AUX
ap-6103	60	5	continued	continue	VERB
ap-6103	60	6	for	for	ADP
ap-6103	60	7	as	as	ADV
ap-6103	60	8	long	long	ADV
ap-6103	60	9	as	as	SCONJ
ap-6103	60	10	the	the	DET
ap-6103	60	11	memory	memory	NOUN
ap-6103	60	12	of	of	ADP
ap-6103	60	13	one	one	NUM
ap-6103	60	14	’s	’s	PART
ap-6103	60	15	symbolic	symbolic	ADJ
ap-6103	60	16	manipulator	manipulator	NOUN
ap-6103	60	17	can	can	AUX
ap-6103	60	18	contain	contain	VERB
ap-6103	60	19	the	the	DET
ap-6103	60	20	results	result	NOUN
ap-6103	60	21	.	.	PUNCT
ap-6103	61	1	we	we	PRON
ap-6103	61	2	simply	simply	ADV
ap-6103	61	3	list	list	VERB
ap-6103	61	4	the	the	DET
ap-6103	61	5	first	first	ADJ
ap-6103	61	6	few	few	ADJ
ap-6103	61	7	members	member	NOUN
ap-6103	61	8	to	to	PART
ap-6103	61	9	give	give	VERB
ap-6103	61	10	an	an	DET
ap-6103	61	11	indication	indication	NOUN
ap-6103	61	12	of	of	ADP
ap-6103	61	13	the	the	DET
ap-6103	61	14	structure	structure	NOUN
ap-6103	61	15	of	of	ADP
ap-6103	61	16	these	these	DET
ap-6103	61	17	equations	equation	NOUN
ap-6103	61	18	.	.	PUNCT
ap-6103	62	1	we	we	PRON
ap-6103	62	2	include	include	VERB
ap-6103	62	3	the	the	DET
ap-6103	62	4	first	first	ADJ
ap-6103	62	5	element	element	NOUN
ap-6103	62	6	,	,	PUNCT
ap-6103	62	7	the	the	DET
ap-6103	62	8	original	original	ADJ
ap-6103	62	9	kummer	kummer	NOUN
ap-6103	62	10	-	-	PUNCT
ap-6103	62	11	schwarz	schwarz	PROPN
ap-6103	62	12	equation	equation	NOUN
ap-6103	62	13	,	,	PUNCT
ap-6103	62	14	for	for	ADP
ap-6103	62	15	the	the	DET
ap-6103	62	16	sake	sake	NOUN
ap-6103	62	17	of	of	ADP
ap-6103	62	18	completeness	completeness	NOUN
ap-6103	62	19	in	in	ADP
ap-6103	62	20	terms	term	NOUN
ap-6103	62	21	of	of	ADP
ap-6103	62	22	the	the	DET
ap-6103	62	23	notation	notation	NOUN
ap-6103	62	24	used	use	VERB
ap-6103	62	25	.	.	PUNCT
ap-6103	63	1	the	the	DET
ap-6103	63	2	ks	ks	PROPN
ap-6103	63	3	should	should	AUX
ap-6103	63	4	need	need	VERB
ap-6103	63	5	no	no	DET
ap-6103	63	6	explanation	explanation	NOUN
ap-6103	63	7	.	.	PUNCT
ap-6103	64	1	the	the	DET
ap-6103	64	2	initial	initial	ADJ
ap-6103	64	3	‘	'	PUNCT
ap-6103	64	4	1	1	NUM
ap-6103	64	5	’	'	PUNCT
ap-6103	64	6	indicates	indicate	VERB
ap-6103	64	7	that	that	SCONJ
ap-6103	64	8	the	the	DET
ap-6103	64	9	sequence	sequence	NOUN
ap-6103	64	10	is	be	AUX
ap-6103	64	11	generated	generate	VERB
ap-6103	64	12	by	by	ADP
ap-6103	64	13	a	a	DET
ap-6103	64	14	firstorder	firstorder	NOUN
ap-6103	64	15	operator	operator	NOUN
ap-6103	64	16	.	.	PUNCT
ap-6103	65	1	the	the	DET
ap-6103	65	2	two	two	NUM
ap-6103	65	3	subsequent	subsequent	ADJ
ap-6103	65	4	digits	digit	NOUN
ap-6103	65	5	indicate	indicate	VERB
ap-6103	65	6	the	the	DET
ap-6103	65	7	place	place	NOUN
ap-6103	65	8	of	of	ADP
ap-6103	65	9	the	the	DET
ap-6103	65	10	particular	particular	ADJ
ap-6103	65	11	equation	equation	NOUN
ap-6103	65	12	as	as	ADP
ap-6103	65	13	an	an	DET
ap-6103	65	14	element	element	NOUN
ap-6103	65	15	of	of	ADP
ap-6103	65	16	the	the	DET
ap-6103	65	17	sequence	sequence	NOUN
ap-6103	65	18	.	.	PUNCT
ap-6103	66	1	we	we	PRON
ap-6103	66	2	obtain	obtain	VERB
ap-6103	66	3	the	the	DET
ap-6103	66	4	following	follow	VERB
ap-6103	66	5	sequence	sequence	NOUN
ap-6103	66	6	,	,	PUNCT
ap-6103	66	7	ks101	ks101	PROPN
ap-6103	66	8	:	:	PUNCT
ap-6103	66	9	=	=	PUNCT
ap-6103	66	10	u′′′	u′′′	PROPN
ap-6103	66	11	u′	u′	PROPN
ap-6103	66	12	−	−	PROPN
ap-6103	66	13	3u′′2	3u′′2	NUM
ap-6103	66	14	2u′2	2u′2	NOUN
ap-6103	67	1	=	=	SYM
ap-6103	67	2	0	0	PUNCT
ap-6103	67	3	ks102	ks102	PROPN
ap-6103	67	4	:	:	PUNCT
ap-6103	67	5	=	=	SYM
ap-6103	67	6	u′′′′	u′′′′	PROPN
ap-6103	67	7	u′	u′	X
ap-6103	67	8	−	−	PROPN
ap-6103	67	9	9u′′u′′′	9u′′u′′′	NUM
ap-6103	67	10	2u′2	2u′2	NOUN
ap-6103	68	1	+	+	CCONJ
ap-6103	68	2	15u′′3	15u′′3	NUM
ap-6103	68	3	4u′3	4u′3	ADJ
ap-6103	68	4	=	=	SYM
ap-6103	68	5	0	0	NUM
ap-6103	68	6	ks103	ks103	NOUN
ap-6103	68	7	:	:	PUNCT
ap-6103	69	1	=	=	SYM
ap-6103	69	2	u′′′′′	u′′′′′	PROPN
ap-6103	69	3	u′	u′	NUM
ap-6103	69	4	−	−	PROPN
ap-6103	70	1	6u′′u′′′′	6u′′u′′′′	NUM
ap-6103	70	2	u′2	u′2	NOUN
ap-6103	71	1	−	−	PROPN
ap-6103	71	2	9u′′′2	9u′′′2	NUM
ap-6103	71	3	2u′2	2u′2	NUM
ap-6103	72	1	+	+	CCONJ
ap-6103	72	2	45u′′2u′′′	45u′′2u′′′	NUM
ap-6103	72	3	2u′3	2u′3	NUM
ap-6103	72	4	−105u′′4	−105u′′4	X
ap-6103	72	5	8u′4	8u′4	NUM
ap-6103	73	1	=	=	SYM
ap-6103	73	2	0	0	NUM
ap-6103	73	3	ks104	ks104	NOUN
ap-6103	73	4	:	:	PUNCT
ap-6103	73	5	=	=	PUNCT
ap-6103	73	6	u′′′′′′	u′′′′′′	PROPN
ap-6103	73	7	u′	u′	X
ap-6103	73	8	−	−	PROPN
ap-6103	73	9	15u′′u′′′′′	15u′′u′′′′′	NUM
ap-6103	73	10	2u′2	2u′2	NUM
ap-6103	74	1	−	−	NUM
ap-6103	74	2	15u′′′u′′′′	15u′′′u′′′′	NUM
ap-6103	74	3	u′2	u′2	X
ap-6103	74	4	+75u′′2u′′′′	+75u′′2u′′′′	X
ap-6103	74	5	2u′3	2u′3	NUM
ap-6103	74	6	+	+	CCONJ
ap-6103	74	7	225u′′u′′′2	225u′′u′′′2	NUM
ap-6103	74	8	4u′3	4u′3	NUM
ap-6103	74	9	−525u′′3u′′′	−525u′′3u′′′	ADJ
ap-6103	74	10	4u′4	4u′4	NUM
ap-6103	75	1	+	+	CCONJ
ap-6103	75	2	945u′′5	945u′′5	NUM
ap-6103	75	3	16u′5	16u′5	NUM
ap-6103	75	4	=	=	SYM
ap-6103	75	5	0	0	NUM
ap-6103	75	6	...	...	PUNCT
ap-6103	75	7	429	429	NUM
ap-6103	75	8	a.	a.	NOUN
ap-6103	75	9	maharaj	maharaj	PROPN
ap-6103	75	10	,	,	PUNCT
ap-6103	75	11	k.	k.	PROPN
ap-6103	75	12	andriopoulos	andriopoulos	PROPN
ap-6103	75	13	,	,	PUNCT
ap-6103	75	14	p.	p.	NOUN
ap-6103	75	15	leach	leach	NOUN
ap-6103	75	16	acta	acta	PROPN
ap-6103	75	17	polytechnica	polytechnica	PROPN
ap-6103	75	18	ks10n:=	ks10n:=	PROPN
ap-6103	76	1	(	(	PUNCT
ap-6103	76	2	d	d	X
ap-6103	76	3	−	−	PROPN
ap-6103	76	4	u′′	u′′	PROPN
ap-6103	76	5	2u′	2u′	NUM
ap-6103	76	6	)	)	PUNCT
ap-6103	76	7	n	n	CCONJ
ap-6103	76	8	(	(	PUNCT
ap-6103	76	9	u′′′	u′′′	PROPN
ap-6103	76	10	u′	u′	PROPN
ap-6103	76	11	−	−	PROPN
ap-6103	76	12	3u′′2	3u′′2	NUM
ap-6103	76	13	2u′2	2u′2	NOUN
ap-6103	76	14	)	)	PUNCT
ap-6103	77	1	=	=	PUNCT
ap-6103	77	2	0	0	X
ap-6103	77	3	.	.	NOUN
ap-6103	77	4	4	4	NUM
ap-6103	77	5	.	.	X
ap-6103	77	6	singularity	singularity	NOUN
ap-6103	77	7	analysis	analysis	NOUN
ap-6103	77	8	we	we	PRON
ap-6103	77	9	perform	perform	VERB
ap-6103	77	10	the	the	DET
ap-6103	77	11	singularity	singularity	NOUN
ap-6103	77	12	analysis	analysis	NOUN
ap-6103	77	13	in	in	ADP
ap-6103	77	14	the	the	DET
ap-6103	77	15	usual	usual	ADJ
ap-6103	77	16	fashion	fashion	NOUN
ap-6103	77	17	by	by	ADP
ap-6103	77	18	firstly	firstly	ADV
ap-6103	77	19	making	make	VERB
ap-6103	77	20	the	the	DET
ap-6103	77	21	substitution	substitution	NOUN
ap-6103	77	22	u	u	NOUN
ap-6103	77	23	=	=	NOUN
ap-6103	77	24	αχp	αχp	PROPN
ap-6103	77	25	,	,	PUNCT
ap-6103	77	26	(	(	PUNCT
ap-6103	77	27	13	13	NUM
ap-6103	77	28	)	)	PUNCT
ap-6103	77	29	where	where	SCONJ
ap-6103	77	30	χ	χ	X
ap-6103	77	31	=	=	PUNCT
ap-6103	77	32	x−x0	x−x0	NOUN
ap-6103	77	33	and	and	CCONJ
ap-6103	77	34	x0	x0	PROPN
ap-6103	77	35	is	be	AUX
ap-6103	77	36	the	the	DET
ap-6103	77	37	location	location	NOUN
ap-6103	77	38	of	of	ADP
ap-6103	77	39	the	the	DET
ap-6103	77	40	putative	putative	ADJ
ap-6103	77	41	singularity	singularity	NOUN
ap-6103	77	42	,	,	PUNCT
ap-6103	77	43	to	to	PART
ap-6103	77	44	determine	determine	VERB
ap-6103	77	45	the	the	DET
ap-6103	77	46	possible	possible	ADJ
ap-6103	77	47	exponents	exponent	NOUN
ap-6103	77	48	of	of	ADP
ap-6103	77	49	the	the	DET
ap-6103	77	50	leading	lead	VERB
ap-6103	77	51	-	-	PUNCT
ap-6103	77	52	order	order	NOUN
ap-6103	77	53	term	term	NOUN
ap-6103	77	54	and	and	CCONJ
ap-6103	77	55	the	the	DET
ap-6103	77	56	corresponding	corresponding	ADJ
ap-6103	77	57	coefficients	coefficient	NOUN
ap-6103	77	58	.	.	PUNCT
ap-6103	78	1	the	the	DET
ap-6103	78	2	results	result	NOUN
ap-6103	78	3	for	for	ADP
ap-6103	78	4	the	the	DET
ap-6103	78	5	first	first	ADJ
ap-6103	78	6	few	few	ADJ
ap-6103	78	7	elements	element	NOUN
ap-6103	78	8	of	of	ADP
ap-6103	78	9	the	the	DET
ap-6103	78	10	sequence	sequence	NOUN
ap-6103	78	11	are	be	AUX
ap-6103	78	12	given	give	VERB
ap-6103	78	13	in	in	ADP
ap-6103	78	14	table	table	NOUN
ap-6103	78	15	1	1	NUM
ap-6103	78	16	.	.	PUNCT
ap-6103	79	1	there	there	PRON
ap-6103	79	2	are	be	VERB
ap-6103	79	3	three	three	NUM
ap-6103	79	4	points	point	NOUN
ap-6103	79	5	to	to	PART
ap-6103	79	6	note	note	VERB
ap-6103	79	7	.	.	PUNCT
ap-6103	80	1	firstly	firstly	ADV
ap-6103	80	2	,	,	PUNCT
ap-6103	80	3	the	the	DET
ap-6103	80	4	elements	element	NOUN
ap-6103	80	5	of	of	ADP
ap-6103	80	6	the	the	DET
ap-6103	80	7	sequence	sequence	NOUN
ap-6103	80	8	are	be	AUX
ap-6103	80	9	of	of	ADP
ap-6103	80	10	degree	degree	NOUN
ap-6103	80	11	zero	zero	NUM
ap-6103	80	12	in	in	ADP
ap-6103	80	13	u	u	NOUN
ap-6103	80	14	and	and	CCONJ
ap-6103	80	15	so	so	ADV
ap-6103	80	16	the	the	DET
ap-6103	80	17	coefficient	coefficient	NOUN
ap-6103	80	18	of	of	ADP
ap-6103	80	19	the	the	DET
ap-6103	80	20	leading	lead	VERB
ap-6103	80	21	-	-	PUNCT
ap-6103	80	22	order	order	NOUN
ap-6103	80	23	term	term	NOUN
ap-6103	80	24	is	be	AUX
ap-6103	80	25	arbitrary	arbitrary	ADJ
ap-6103	80	26	.	.	PUNCT
ap-6103	81	1	secondly	secondly	ADV
ap-6103	81	2	,	,	PUNCT
ap-6103	81	3	if	if	SCONJ
ap-6103	81	4	one	one	PRON
ap-6103	81	5	removes	remove	VERB
ap-6103	81	6	the	the	DET
ap-6103	81	7	fractions	fraction	NOUN
ap-6103	81	8	by	by	ADP
ap-6103	81	9	multiplying	multiply	VERB
ap-6103	81	10	by	by	ADP
ap-6103	81	11	the	the	DET
ap-6103	81	12	highest	high	ADJ
ap-6103	81	13	power	power	NOUN
ap-6103	81	14	of	of	ADP
ap-6103	81	15	u′	u′	PROPN
ap-6103	81	16	in	in	ADP
ap-6103	81	17	the	the	DET
ap-6103	81	18	denominator	denominator	NOUN
ap-6103	81	19	,	,	PUNCT
ap-6103	81	20	the	the	DET
ap-6103	81	21	possibility	possibility	NOUN
ap-6103	81	22	of	of	ADP
ap-6103	81	23	p	p	NOUN
ap-6103	81	24	=	=	SYM
ap-6103	81	25	0	0	NUM
ap-6103	81	26	has	have	VERB
ap-6103	81	27	multiple	multiple	ADJ
ap-6103	81	28	occurrences	occurrence	NOUN
ap-6103	81	29	.	.	PUNCT
ap-6103	82	1	for	for	ADP
ap-6103	82	2	the	the	DET
ap-6103	82	3	sequence	sequence	NOUN
ap-6103	82	4	as	as	SCONJ
ap-6103	82	5	we	we	PRON
ap-6103	82	6	have	have	AUX
ap-6103	82	7	written	write	VERB
ap-6103	82	8	it	it	PRON
ap-6103	82	9	,	,	PUNCT
ap-6103	82	10	these	these	DET
ap-6103	82	11	possibilities	possibility	NOUN
ap-6103	82	12	are	be	AUX
ap-6103	82	13	spurious	spurious	ADJ
ap-6103	82	14	.	.	PUNCT
ap-6103	83	1	as	as	SCONJ
ap-6103	83	2	further	further	ADJ
ap-6103	83	3	analysis	analysis	NOUN
ap-6103	83	4	is	be	AUX
ap-6103	83	5	more	more	ADV
ap-6103	83	6	convenient	convenient	ADJ
ap-6103	83	7	to	to	PART
ap-6103	83	8	perform	perform	VERB
ap-6103	83	9	when	when	SCONJ
ap-6103	83	10	the	the	DET
ap-6103	83	11	denominators	denominator	NOUN
ap-6103	83	12	are	be	AUX
ap-6103	83	13	removed	remove	VERB
ap-6103	83	14	,	,	PUNCT
ap-6103	83	15	we	we	PRON
ap-6103	83	16	ignore	ignore	VERB
ap-6103	83	17	these	these	DET
ap-6103	83	18	values	value	NOUN
ap-6103	83	19	.	.	PUNCT
ap-6103	84	1	thirdly	thirdly	ADV
ap-6103	84	2	,	,	PUNCT
ap-6103	84	3	there	there	PRON
ap-6103	84	4	is	be	VERB
ap-6103	84	5	always	always	ADV
ap-6103	84	6	the	the	DET
ap-6103	84	7	possibility	possibility	NOUN
ap-6103	84	8	that	that	SCONJ
ap-6103	84	9	p	p	X
ap-6103	84	10	=	=	NOUN
ap-6103	84	11	1	1	NUM
ap-6103	84	12	.	.	PUNCT
ap-6103	84	13	such	such	DET
ap-6103	84	14	a	a	DET
ap-6103	84	15	value	value	NOUN
ap-6103	84	16	is	be	AUX
ap-6103	84	17	without	without	ADP
ap-6103	84	18	the	the	DET
ap-6103	84	19	ambit	ambit	NOUN
ap-6103	84	20	of	of	ADP
ap-6103	84	21	the	the	DET
ap-6103	84	22	singularity	singularity	NOUN
ap-6103	84	23	analysis	analysis	NOUN
ap-6103	84	24	.	.	PUNCT
ap-6103	85	1	it	it	PRON
ap-6103	85	2	is	be	AUX
ap-6103	85	3	amusing	amusing	ADJ
ap-6103	85	4	to	to	PART
ap-6103	85	5	note	note	VERB
ap-6103	85	6	that	that	SCONJ
ap-6103	85	7	ks101	ks101	PROPN
ap-6103	85	8	is	be	AUX
ap-6103	85	9	invariant	invariant	ADJ
ap-6103	85	10	under	under	ADP
ap-6103	85	11	the	the	DET
ap-6103	85	12	transformation	transformation	NOUN
ap-6103	85	13	u	u	NOUN
ap-6103	85	14	−→	−→	ADJ
ap-6103	85	15	1	1	NUM
ap-6103	85	16	/	/	SYM
ap-6103	85	17	u.	u.	NOUN
ap-6103	85	18	this	this	DET
ap-6103	85	19	property	property	NOUN
ap-6103	85	20	does	do	AUX
ap-6103	85	21	not	not	PART
ap-6103	85	22	persist	persist	VERB
ap-6103	85	23	for	for	ADP
ap-6103	85	24	higher	high	ADJ
ap-6103	85	25	elements	element	NOUN
ap-6103	85	26	of	of	ADP
ap-6103	85	27	the	the	DET
ap-6103	85	28	sequence	sequence	NOUN
ap-6103	85	29	.	.	PUNCT
ap-6103	86	1	the	the	DET
ap-6103	86	2	second	second	ADJ
ap-6103	86	3	step	step	NOUN
ap-6103	86	4	in	in	ADP
ap-6103	86	5	the	the	DET
ap-6103	86	6	singularity	singularity	NOUN
ap-6103	86	7	analysis	analysis	NOUN
ap-6103	86	8	is	be	AUX
ap-6103	86	9	to	to	PART
ap-6103	86	10	determine	determine	VERB
ap-6103	86	11	at	at	ADP
ap-6103	86	12	what	what	PRON
ap-6103	86	13	powers	power	NOUN
ap-6103	86	14	of	of	ADP
ap-6103	86	15	χ	χ	PRON
ap-6103	86	16	the	the	DET
ap-6103	86	17	additional	additional	ADJ
ap-6103	86	18	constants	constant	NOUN
ap-6103	86	19	of	of	ADP
ap-6103	86	20	integration	integration	NOUN
ap-6103	86	21	occur	occur	VERB
ap-6103	86	22	.	.	PUNCT
ap-6103	87	1	the	the	DET
ap-6103	87	2	performance	performance	NOUN
ap-6103	87	3	of	of	ADP
ap-6103	87	4	this	this	DET
ap-6103	87	5	computation	computation	NOUN
ap-6103	87	6	is	be	AUX
ap-6103	87	7	greatly	greatly	ADV
ap-6103	87	8	facilitated	facilitate	VERB
ap-6103	87	9	by	by	ADP
ap-6103	87	10	the	the	DET
ap-6103	87	11	removal	removal	NOUN
ap-6103	87	12	of	of	ADP
ap-6103	87	13	the	the	DET
ap-6103	87	14	fractions	fraction	NOUN
ap-6103	87	15	involving	involve	VERB
ap-6103	87	16	the	the	DET
ap-6103	87	17	derivative	derivative	NOUN
ap-6103	87	18	of	of	ADP
ap-6103	87	19	the	the	DET
ap-6103	87	20	dependent	dependent	ADJ
ap-6103	87	21	variable	variable	NOUN
ap-6103	87	22	.	.	PUNCT
ap-6103	88	1	in	in	ADP
ap-6103	88	2	table	table	NOUN
ap-6103	88	3	2	2	NUM
ap-6103	88	4	,	,	PUNCT
ap-6103	88	5	we	we	PRON
ap-6103	88	6	list	list	VERB
ap-6103	88	7	the	the	DET
ap-6103	88	8	resonances	resonance	NOUN
ap-6103	88	9	for	for	ADP
ap-6103	88	10	the	the	DET
ap-6103	88	11	various	various	ADJ
ap-6103	88	12	permissible	permissible	ADJ
ap-6103	88	13	values	value	NOUN
ap-6103	88	14	of	of	ADP
ap-6103	88	15	the	the	DET
ap-6103	88	16	exponents	exponent	NOUN
ap-6103	88	17	,	,	PUNCT
ap-6103	88	18	p.	p.	NOUN
ap-6103	88	19	5	5	NUM
ap-6103	88	20	.	.	PUNCT
ap-6103	88	21	complete	complete	PROPN
ap-6103	88	22	symmetry	symmetry	NOUN
ap-6103	88	23	group	group	NOUN
ap-6103	88	24	the	the	DET
ap-6103	88	25	element	element	NOUN
ap-6103	88	26	ks101	ks101	PROPN
ap-6103	88	27	possesses	possess	VERB
ap-6103	88	28	six	six	NUM
ap-6103	88	29	lie	lie	NOUN
ap-6103	88	30	point	point	NOUN
ap-6103	88	31	symmetries	symmetry	NOUN
ap-6103	88	32	with	with	ADP
ap-6103	88	33	the	the	DET
ap-6103	88	34	algebra	algebra	PROPN
ap-6103	88	35	sl(2	sl(2	PROPN
ap-6103	88	36	,	,	PUNCT
ap-6103	88	37	r)⊕sl(2	r)⊕sl(2	NOUN
ap-6103	88	38	,	,	PUNCT
ap-6103	88	39	r	r	NOUN
ap-6103	88	40	)	)	PUNCT
ap-6103	88	41	.	.	PUNCT
ap-6103	89	1	all	all	DET
ap-6103	89	2	other	other	ADJ
ap-6103	89	3	elements	element	NOUN
ap-6103	89	4	of	of	ADP
ap-6103	89	5	the	the	DET
ap-6103	89	6	differential	differential	ADJ
ap-6103	89	7	sequence	sequence	NOUN
ap-6103	89	8	possess	possess	VERB
ap-6103	89	9	just	just	ADV
ap-6103	89	10	four	four	NUM
ap-6103	89	11	lie	lie	NOUN
ap-6103	89	12	point	point	NOUN
ap-6103	89	13	symmetries	symmetry	NOUN
ap-6103	89	14	,	,	PUNCT
ap-6103	89	15	namely	namely	ADV
ap-6103	89	16	γ1	γ1	NOUN
ap-6103	89	17	=	=	SYM
ap-6103	89	18	∂x	∂x	PROPN
ap-6103	89	19	,	,	PUNCT
ap-6103	89	20	γ2	γ2	NOUN
ap-6103	89	21	=	=	SYM
ap-6103	89	22	x∂x	x∂x	NOUN
ap-6103	89	23	,	,	PUNCT
ap-6103	89	24	γ3	γ3	NOUN
ap-6103	89	25	=	=	SYM
ap-6103	89	26	∂u	∂u	PROPN
ap-6103	89	27	and	and	CCONJ
ap-6103	89	28	γ4	γ4	PROPN
ap-6103	89	29	=	=	NOUN
ap-6103	89	30	u∂u	u∂u	NOUN
ap-6103	89	31	with	with	ADP
ap-6103	89	32	the	the	DET
ap-6103	89	33	algebra	algebra	NOUN
ap-6103	89	34	2a1	2a1	NUM
ap-6103	89	35	⊕	⊕	PROPN
ap-6103	89	36	2a1	2a1	NUM
ap-6103	89	37	.	.	PUNCT
ap-6103	90	1	neither	neither	DET
ap-6103	90	2	algebra	algebra	NOUN
ap-6103	90	3	is	be	AUX
ap-6103	90	4	sufficient	sufficient	ADJ
ap-6103	90	5	to	to	PART
ap-6103	90	6	specify	specify	VERB
ap-6103	90	7	the	the	DET
ap-6103	90	8	corresponding	correspond	VERB
ap-6103	90	9	equation	equation	NOUN
ap-6103	90	10	completely	completely	ADV
ap-6103	90	11	.	.	PUNCT
ap-6103	91	1	it	it	PRON
ap-6103	91	2	is	be	AUX
ap-6103	91	3	necessary	necessary	ADJ
ap-6103	91	4	to	to	PART
ap-6103	91	5	have	have	VERB
ap-6103	91	6	a	a	DET
ap-6103	91	7	recourse	recourse	NOUN
ap-6103	91	8	to	to	ADP
ap-6103	91	9	nonlocal	nonlocal	ADJ
ap-6103	91	10	symmetries	symmetry	NOUN
ap-6103	91	11	for	for	ADP
ap-6103	91	12	the	the	DET
ap-6103	91	13	complete	complete	ADJ
ap-6103	91	14	specification	specification	NOUN
ap-6103	91	15	.	.	PUNCT
ap-6103	92	1	the	the	DET
ap-6103	92	2	determination	determination	NOUN
ap-6103	92	3	of	of	ADP
ap-6103	92	4	the	the	DET
ap-6103	92	5	nonlocal	nonlocal	ADJ
ap-6103	92	6	symmetries	symmetry	NOUN
ap-6103	92	7	is	be	AUX
ap-6103	92	8	facilitated	facilitate	VERB
ap-6103	92	9	by	by	ADP
ap-6103	92	10	the	the	DET
ap-6103	92	11	fact	fact	NOUN
ap-6103	92	12	that	that	SCONJ
ap-6103	92	13	all	all	DET
ap-6103	92	14	elements	element	NOUN
ap-6103	92	15	of	of	ADP
ap-6103	92	16	the	the	DET
ap-6103	92	17	sequence	sequence	NOUN
ap-6103	92	18	may	may	AUX
ap-6103	92	19	be	be	AUX
ap-6103	92	20	linearised	linearise	VERB
ap-6103	92	21	by	by	ADP
ap-6103	92	22	means	mean	NOUN
ap-6103	92	23	of	of	ADP
ap-6103	92	24	the	the	DET
ap-6103	92	25	same	same	ADJ
ap-6103	92	26	transformation	transformation	NOUN
ap-6103	92	27	,	,	PUNCT
ap-6103	92	28	which	which	PRON
ap-6103	92	29	linearises	linearise	VERB
ap-6103	92	30	the	the	DET
ap-6103	92	31	kummer	kummer	NOUN
ap-6103	92	32	-	-	PUNCT
ap-6103	92	33	schwarz	schwarz	PROPN
ap-6103	92	34	equation	equation	NOUN
ap-6103	92	35	.	.	PUNCT
ap-6103	93	1	we	we	PRON
ap-6103	93	2	recall	recall	VERB
ap-6103	93	3	that	that	SCONJ
ap-6103	93	4	(	(	PUNCT
ap-6103	93	5	4	4	X
ap-6103	93	6	)	)	PUNCT
ap-6103	93	7	can	can	AUX
ap-6103	93	8	be	be	AUX
ap-6103	93	9	written	write	VERB
ap-6103	93	10	as	as	ADP
ap-6103	93	11	u′1/2(u′−1/2)′′	u′1/2(u′−1/2)′′	PROPN
ap-6103	93	12	=	=	NOUN
ap-6103	93	13	0	0	PROPN
ap-6103	93	14	.	.	PUNCT
ap-6103	94	1	consequently	consequently	ADV
ap-6103	94	2	the	the	DET
ap-6103	94	3	linearising	linearise	VERB
ap-6103	94	4	transformation	transformation	NOUN
ap-6103	94	5	is	be	AUX
ap-6103	94	6	u′	u′	PROPN
ap-6103	94	7	=	=	SYM
ap-6103	94	8	1	1	NUM
ap-6103	94	9	/	/	SYM
ap-6103	94	10	w2	w2	NOUN
ap-6103	94	11	.	.	PUNCT
ap-6103	95	1	the	the	DET
ap-6103	95	2	linear	linear	ADJ
ap-6103	95	3	equation	equation	NOUN
ap-6103	95	4	corresponding	correspond	VERB
ap-6103	95	5	to	to	ADP
ap-6103	95	6	the	the	DET
ap-6103	95	7	nth	nth	NOUN
ap-6103	95	8	element	element	NOUN
ap-6103	95	9	of	of	ADP
ap-6103	95	10	the	the	DET
ap-6103	95	11	sequence	sequence	NOUN
ap-6103	95	12	is3	is3	VERB
ap-6103	95	13	w(n+1	w(n+1	NUM
ap-6103	95	14	)	)	PUNCT
ap-6103	96	1	=	=	SYM
ap-6103	96	2	0	0	NUM
ap-6103	97	1	(	(	PUNCT
ap-6103	97	2	14	14	NUM
ap-6103	97	3	)	)	PUNCT
ap-6103	98	1	for	for	ADP
ap-6103	98	2	which	which	PRON
ap-6103	98	3	a	a	DET
ap-6103	98	4	representation	representation	NOUN
ap-6103	98	5	of	of	ADP
ap-6103	98	6	its	its	PRON
ap-6103	98	7	complete	complete	ADJ
ap-6103	98	8	symmetry	symmetry	NOUN
ap-6103	98	9	group	group	NOUN
ap-6103	98	10	[	[	X
ap-6103	98	11	9	9	NUM
ap-6103	98	12	,	,	PUNCT
ap-6103	98	13	10	10	NUM
ap-6103	98	14	]	]	PUNCT
ap-6103	98	15	is	be	AUX
ap-6103	98	16	σi	σi	NOUN
ap-6103	98	17	=	=	PUNCT
ap-6103	98	18	xi∂w	xi∂w	NOUN
ap-6103	98	19	,	,	PUNCT
ap-6103	98	20	i	i	NOUN
ap-6103	98	21	=	=	NOUN
ap-6103	98	22	0	0	NUM
ap-6103	98	23	,	,	PUNCT
ap-6103	98	24	n	n	CCONJ
ap-6103	98	25	,	,	PUNCT
ap-6103	98	26	and	and	CCONJ
ap-6103	98	27	σn+1	σn+1	PROPN
ap-6103	98	28	=	=	NOUN
ap-6103	98	29	w∂w	w∂w	NOUN
ap-6103	98	30	.	.	PUNCT
ap-6103	99	1	(	(	PUNCT
ap-6103	99	2	15	15	NUM
ap-6103	99	3	)	)	PUNCT
ap-6103	99	4	when	when	SCONJ
ap-6103	99	5	we	we	PRON
ap-6103	99	6	reverse	reverse	VERB
ap-6103	99	7	the	the	DET
ap-6103	99	8	transformation	transformation	NOUN
ap-6103	99	9	,	,	PUNCT
ap-6103	99	10	the	the	DET
ap-6103	99	11	symmetries	symmetry	NOUN
ap-6103	99	12	in	in	ADP
ap-6103	99	13	(	(	PUNCT
ap-6103	99	14	15	15	NUM
ap-6103	99	15	)	)	PUNCT
ap-6103	99	16	become	become	VERB
ap-6103	99	17	σ̄i	σ̄i	NOUN
ap-6103	99	18	=	=	SYM
ap-6103	99	19	{	{	PUNCT
ap-6103	99	20	∫	∫	PROPN
ap-6103	99	21	xiu′3/2dx	xiu′3/2dx	PROPN
ap-6103	99	22	}	}	SYM
ap-6103	99	23	∂u	∂u	PROPN
ap-6103	99	24	,	,	PUNCT
ap-6103	99	25	i	i	PRON
ap-6103	99	26	=	=	NOUN
ap-6103	99	27	0	0	NUM
ap-6103	99	28	,	,	PUNCT
ap-6103	99	29	n	n	CCONJ
ap-6103	99	30	,	,	PUNCT
ap-6103	99	31	and	and	CCONJ
ap-6103	99	32	σ̄n+1	σ̄n+1	X
ap-6103	99	33	=	=	SYM
ap-6103	99	34	u∂u	u∂u	NOUN
ap-6103	99	35	.	.	PUNCT
ap-6103	100	1	(	(	PUNCT
ap-6103	100	2	16	16	NUM
ap-6103	100	3	)	)	PUNCT
ap-6103	100	4	to	to	ADP
ap-6103	100	5	these	these	DET
ap-6103	100	6	n	n	CCONJ
ap-6103	100	7	+	+	CCONJ
ap-6103	100	8	2	2	NUM
ap-6103	100	9	symmetries	symmetry	NOUN
ap-6103	100	10	,	,	PUNCT
ap-6103	100	11	we	we	PRON
ap-6103	100	12	add	add	VERB
ap-6103	100	13	the	the	DET
ap-6103	100	14	symmetry	symmetry	NOUN
ap-6103	100	15	behind	behind	ADP
ap-6103	100	16	the	the	DET
ap-6103	100	17	reduction	reduction	NOUN
ap-6103	100	18	of	of	ADP
ap-6103	100	19	order	order	NOUN
ap-6103	100	20	to	to	PART
ap-6103	100	21	(	(	PUNCT
ap-6103	100	22	14	14	NUM
ap-6103	100	23	)	)	PUNCT
ap-6103	100	24	,	,	PUNCT
ap-6103	100	25	namely	namely	ADV
ap-6103	100	26	∂u	∂u	PROPN
ap-6103	100	27	.	.	PUNCT
ap-6103	101	1	it	it	PRON
ap-6103	101	2	is	be	AUX
ap-6103	101	3	a	a	DET
ap-6103	101	4	simple	simple	ADJ
ap-6103	101	5	matter	matter	NOUN
ap-6103	101	6	to	to	PART
ap-6103	101	7	demonstrate	demonstrate	VERB
ap-6103	101	8	that	that	SCONJ
ap-6103	101	9	this	this	PRON
ap-6103	101	10	indeed	indeed	ADV
ap-6103	101	11	is	be	AUX
ap-6103	101	12	a	a	DET
ap-6103	101	13	representation	representation	NOUN
ap-6103	101	14	of	of	ADP
ap-6103	101	15	the	the	DET
ap-6103	101	16	complete	complete	ADJ
ap-6103	101	17	symmetry	symmetry	NOUN
ap-6103	101	18	group	group	NOUN
ap-6103	101	19	.	.	PUNCT
ap-6103	102	1	the	the	DET
ap-6103	102	2	algebra	algebra	NOUN
ap-6103	102	3	is	be	AUX
ap-6103	102	4	a2	a2	PROPN
ap-6103	102	5	⊕s	⊕s	NOUN
ap-6103	102	6	(	(	PUNCT
ap-6103	102	7	n+	n+	NUM
ap-6103	102	8	1)a1	1)a1	NUM
ap-6103	102	9	.	.	PUNCT
ap-6103	103	1	the	the	DET
ap-6103	103	2	(	(	PUNCT
ap-6103	103	3	n+	n+	NUM
ap-6103	103	4	1)-dimensional	1)-dimensional	ADJ
ap-6103	103	5	abelian	abelian	ADJ
ap-6103	103	6	subalgebra	subalgebra	NOUN
ap-6103	103	7	is	be	AUX
ap-6103	103	8	comprised	comprise	VERB
ap-6103	103	9	of	of	ADP
ap-6103	103	10	the	the	DET
ap-6103	103	11	symmetries	symmetry	NOUN
ap-6103	103	12	σ̄i	σ̄i	NOUN
ap-6103	103	13	,	,	PUNCT
ap-6103	103	14	i	i	PROPN
ap-6103	103	15	=	=	NOUN
ap-6103	103	16	0	0	NUM
ap-6103	103	17	,	,	PUNCT
ap-6103	103	18	n.	n.	NOUN
ap-6103	103	19	6	6	NUM
ap-6103	103	20	.	.	PUNCT
ap-6103	104	1	the	the	DET
ap-6103	104	2	alternate	alternate	ADJ
ap-6103	104	3	sequence	sequence	NOUN
ap-6103	104	4	in	in	ADP
ap-6103	104	5	the	the	DET
ap-6103	104	6	introduction	introduction	NOUN
ap-6103	104	7	,	,	PUNCT
ap-6103	104	8	we	we	PRON
ap-6103	104	9	mention	mention	VERB
ap-6103	104	10	the	the	DET
ap-6103	104	11	work	work	NOUN
ap-6103	104	12	of	of	ADP
ap-6103	104	13	euler	euler	NOUN
ap-6103	104	14	and	and	CCONJ
ap-6103	104	15	leach	leach	NOUN
ap-6103	104	16	[	[	X
ap-6103	104	17	8	8	NUM
ap-6103	104	18	]	]	PUNCT
ap-6103	104	19	in	in	ADP
ap-6103	104	20	which	which	PRON
ap-6103	104	21	they	they	PRON
ap-6103	104	22	demonstrated	demonstrate	VERB
ap-6103	104	23	that	that	SCONJ
ap-6103	104	24	the	the	DET
ap-6103	104	25	elements	element	NOUN
ap-6103	104	26	of	of	ADP
ap-6103	104	27	a	a	DET
ap-6103	104	28	given	give	VERB
ap-6103	104	29	sequence	sequence	NOUN
ap-6103	104	30	of	of	ADP
ap-6103	104	31	ordinary	ordinary	ADJ
ap-6103	104	32	differential	differential	ADJ
ap-6103	104	33	equations	equation	NOUN
ap-6103	104	34	of	of	ADP
ap-6103	104	35	increasing	increase	VERB
ap-6103	104	36	order	order	NOUN
ap-6103	104	37	could	could	AUX
ap-6103	104	38	be	be	AUX
ap-6103	104	39	written	write	VERB
ap-6103	104	40	in	in	ADP
ap-6103	104	41	terms	term	NOUN
ap-6103	104	42	of	of	ADP
ap-6103	104	43	equations	equation	NOUN
ap-6103	104	44	of	of	ADP
ap-6103	104	45	a	a	DET
ap-6103	104	46	lower	low	ADJ
ap-6103	104	47	order	order	NOUN
ap-6103	104	48	with	with	ADP
ap-6103	104	49	a	a	DET
ap-6103	104	50	nonhomogeneous	nonhomogeneous	ADJ
ap-6103	104	51	term	term	NOUN
ap-6103	104	52	of	of	ADP
ap-6103	104	53	increasing	increase	VERB
ap-6103	104	54	complexity	complexity	NOUN
ap-6103	104	55	as	as	SCONJ
ap-6103	104	56	one	one	NUM
ap-6103	104	57	rose	rise	VERB
ap-6103	104	58	through	through	ADP
ap-6103	104	59	the	the	DET
ap-6103	104	60	sequence	sequence	NOUN
ap-6103	104	61	.	.	PUNCT
ap-6103	105	1	this	this	PRON
ap-6103	105	2	is	be	AUX
ap-6103	105	3	also	also	ADV
ap-6103	105	4	the	the	DET
ap-6103	105	5	case	case	NOUN
ap-6103	105	6	with	with	ADP
ap-6103	105	7	the	the	DET
ap-6103	105	8	present	present	ADJ
ap-6103	105	9	sequence	sequence	NOUN
ap-6103	105	10	.	.	PUNCT
ap-6103	106	1	we	we	PRON
ap-6103	106	2	illustrate	illustrate	VERB
ap-6103	106	3	the	the	DET
ap-6103	106	4	procedure	procedure	NOUN
ap-6103	106	5	with	with	ADP
ap-6103	106	6	the	the	DET
ap-6103	106	7	first	first	ADJ
ap-6103	106	8	few	few	ADJ
ap-6103	106	9	elements	element	NOUN
ap-6103	106	10	of	of	ADP
ap-6103	106	11	the	the	DET
ap-6103	106	12	sequence	sequence	NOUN
ap-6103	106	13	.	.	PUNCT
ap-6103	107	1	we	we	PRON
ap-6103	107	2	recall	recall	VERB
ap-6103	107	3	that	that	SCONJ
ap-6103	107	4	the	the	DET
ap-6103	107	5	principle	principle	NOUN
ap-6103	107	6	of	of	ADP
ap-6103	107	7	the	the	DET
ap-6103	107	8	construction	construction	NOUN
ap-6103	107	9	of	of	ADP
ap-6103	107	10	the	the	DET
ap-6103	107	11	alternate	alternate	ADJ
ap-6103	107	12	sequence	sequence	NOUN
ap-6103	107	13	is	be	AUX
ap-6103	107	14	based	base	VERB
ap-6103	107	15	upon	upon	SCONJ
ap-6103	107	16	the	the	DET
ap-6103	107	17	relationship	relationship	NOUN
ap-6103	107	18	between	between	ADP
ap-6103	107	19	one	one	NUM
ap-6103	107	20	member	member	NOUN
ap-6103	107	21	of	of	ADP
ap-6103	107	22	the	the	DET
ap-6103	107	23	sequence	sequence	NOUN
ap-6103	107	24	and	and	CCONJ
ap-6103	107	25	the	the	DET
ap-6103	107	26	next	next	ADJ
ap-6103	107	27	member	member	NOUN
ap-6103	107	28	through	through	ADP
ap-6103	107	29	the	the	DET
ap-6103	107	30	generator	generator	NOUN
ap-6103	107	31	of	of	ADP
ap-6103	107	32	sequences	sequence	NOUN
ap-6103	107	33	.	.	PUNCT
ap-6103	108	1	the	the	DET
ap-6103	108	2	initial	initial	ADJ
ap-6103	108	3	step	step	NOUN
ap-6103	108	4	is	be	AUX
ap-6103	108	5	to	to	PART
ap-6103	108	6	solve	solve	VERB
ap-6103	108	7	the	the	DET
ap-6103	108	8	equation	equation	NOUN
ap-6103	108	9	(	(	PUNCT
ap-6103	108	10	d	d	X
ap-6103	108	11	−	−	PROPN
ap-6103	108	12	u′′	u′′	PROPN
ap-6103	108	13	2u′	2u′	NUM
ap-6103	108	14	)	)	PUNCT
ap-6103	108	15	q1	q1	PROPN
ap-6103	108	16	=	=	SYM
ap-6103	108	17	0	0	NUM
ap-6103	108	18	.	.	PUNCT
ap-6103	109	1	(	(	PUNCT
ap-6103	109	2	17	17	NUM
ap-6103	109	3	)	)	PUNCT
ap-6103	109	4	thereafter	thereafter	ADV
ap-6103	109	5	,	,	PUNCT
ap-6103	109	6	one	one	NUM
ap-6103	109	7	proceeds	proceed	NOUN
ap-6103	109	8	in	in	ADP
ap-6103	109	9	a	a	DET
ap-6103	109	10	sequential	sequential	ADJ
ap-6103	109	11	manner	manner	NOUN
ap-6103	109	12	by	by	ADP
ap-6103	109	13	solving	solve	VERB
ap-6103	109	14	(	(	PUNCT
ap-6103	109	15	d	d	NOUN
ap-6103	109	16	−	−	PROPN
ap-6103	109	17	u′′	u′′	PROPN
ap-6103	109	18	2u′	2u′	NUM
ap-6103	109	19	)	)	PUNCT
ap-6103	110	1	qn	qn	NOUN
ap-6103	110	2	=	=	PUNCT
ap-6103	110	3	qn−1	qn−1	PROPN
ap-6103	110	4	,	,	PUNCT
ap-6103	110	5	n	n	NOUN
ap-6103	110	6	=	=	SYM
ap-6103	110	7	1	1	NUM
ap-6103	110	8	,	,	PUNCT
ap-6103	110	9	.	.	PUNCT
ap-6103	110	10	.	.	PUNCT
ap-6103	110	11	.	.	PUNCT
ap-6103	111	1	,	,	PUNCT
ap-6103	111	2	(	(	PUNCT
ap-6103	111	3	18	18	NUM
ap-6103	111	4	)	)	PUNCT
ap-6103	111	5	where	where	SCONJ
ap-6103	111	6	we	we	PRON
ap-6103	111	7	adopt	adopt	VERB
ap-6103	111	8	the	the	DET
ap-6103	111	9	convention	convention	NOUN
ap-6103	111	10	that	that	PRON
ap-6103	111	11	q0	q0	VERB
ap-6103	111	12	=	=	X
ap-6103	111	13	0	0	PROPN
ap-6103	111	14	.	.	PUNCT
ap-6103	112	1	the	the	DET
ap-6103	112	2	solution	solution	NOUN
ap-6103	112	3	of	of	ADP
ap-6103	112	4	(	(	PUNCT
ap-6103	112	5	17	17	NUM
ap-6103	112	6	)	)	PUNCT
ap-6103	112	7	is	be	AUX
ap-6103	112	8	q1	q1	PROPN
ap-6103	112	9	=	=	SYM
ap-6103	112	10	c0u	c0u	PROPN
ap-6103	112	11	′1/2	′1/2	PROPN
ap-6103	112	12	,	,	PUNCT
ap-6103	112	13	(	(	PUNCT
ap-6103	112	14	19	19	NUM
ap-6103	112	15	)	)	PUNCT
ap-6103	112	16	where	where	SCONJ
ap-6103	112	17	u′−1/2	u′−1/2	ADJ
ap-6103	112	18	is	be	AUX
ap-6103	112	19	an	an	DET
ap-6103	112	20	integrating	integrating	NOUN
ap-6103	112	21	factor	factor	NOUN
ap-6103	112	22	for	for	ADP
ap-6103	112	23	ks1014	ks1014	PROPN
ap-6103	112	24	.	.	PUNCT
ap-6103	113	1	the	the	DET
ap-6103	113	2	representation	representation	NOUN
ap-6103	113	3	of	of	ADP
ap-6103	113	4	the	the	DET
ap-6103	113	5	second	second	ADJ
ap-6103	113	6	member	member	NOUN
ap-6103	113	7	of	of	ADP
ap-6103	113	8	the	the	DET
ap-6103	113	9	sequence	sequence	NOUN
ap-6103	113	10	3	3	NUM
ap-6103	113	11	in	in	ADP
ap-6103	113	12	a	a	DET
ap-6103	113	13	usual	usual	ADJ
ap-6103	113	14	manner	manner	NOUN
ap-6103	113	15	of	of	ADP
ap-6103	113	16	dealing	deal	VERB
ap-6103	113	17	with	with	ADP
ap-6103	113	18	differential	differential	ADJ
ap-6103	113	19	equations	equation	NOUN
ap-6103	113	20	one	one	NUM
ap-6103	113	21	forgets	forget	VERB
ap-6103	113	22	about	about	ADP
ap-6103	113	23	the	the	DET
ap-6103	113	24	factor	factor	NOUN
ap-6103	113	25	1	1	NUM
ap-6103	113	26	/	/	SYM
ap-6103	113	27	w	w	NOUN
ap-6103	113	28	corresponding	correspond	VERB
ap-6103	113	29	to	to	ADP
ap-6103	113	30	the	the	DET
ap-6103	113	31	u′1/2	u′1/2	NOUN
ap-6103	113	32	.	.	PUNCT
ap-6103	114	1	when	when	SCONJ
ap-6103	114	2	it	it	PRON
ap-6103	114	3	comes	come	VERB
ap-6103	114	4	to	to	ADP
ap-6103	114	5	the	the	DET
ap-6103	114	6	generation	generation	NOUN
ap-6103	114	7	of	of	ADP
ap-6103	114	8	differential	differential	ADJ
ap-6103	114	9	sequences	sequence	NOUN
ap-6103	114	10	,	,	PUNCT
ap-6103	114	11	there	there	PRON
ap-6103	114	12	is	be	VERB
ap-6103	114	13	no	no	DET
ap-6103	114	14	place	place	NOUN
ap-6103	114	15	for	for	ADP
ap-6103	114	16	such	such	ADJ
ap-6103	114	17	slackness	slackness	NOUN
ap-6103	114	18	.	.	PUNCT
ap-6103	115	1	were	be	AUX
ap-6103	115	2	one	one	NUM
ap-6103	115	3	to	to	PART
ap-6103	115	4	wish	wish	VERB
ap-6103	115	5	to	to	PART
ap-6103	115	6	consider	consider	VERB
ap-6103	115	7	the	the	DET
ap-6103	115	8	differential	differential	ADJ
ap-6103	115	9	sequence	sequence	NOUN
ap-6103	115	10	corresponding	correspond	VERB
ap-6103	115	11	to	to	ADP
ap-6103	115	12	that	that	PRON
ap-6103	115	13	of	of	ADP
ap-6103	115	14	the	the	DET
ap-6103	115	15	kummerschwarz	kummerschwarz	PROPN
ap-6103	115	16	sequence	sequence	NOUN
ap-6103	115	17	,	,	PUNCT
ap-6103	115	18	the	the	DET
ap-6103	115	19	base	base	NOUN
ap-6103	115	20	equation	equation	NOUN
ap-6103	115	21	would	would	AUX
ap-6103	115	22	have	have	VERB
ap-6103	115	23	to	to	PART
ap-6103	115	24	be	be	AUX
ap-6103	115	25	w′′/w	w′′/w	NOUN
ap-6103	115	26	=	=	NOUN
ap-6103	115	27	0	0	NUM
ap-6103	115	28	.	.	PUNCT
ap-6103	116	1	as	as	SCONJ
ap-6103	116	2	we	we	PRON
ap-6103	116	3	see	see	VERB
ap-6103	116	4	below	below	ADV
ap-6103	116	5	,	,	PUNCT
ap-6103	116	6	the	the	DET
ap-6103	116	7	removal	removal	NOUN
ap-6103	116	8	of	of	ADP
ap-6103	116	9	denominators	denominator	NOUN
ap-6103	116	10	entails	entail	VERB
ap-6103	116	11	an	an	DET
ap-6103	116	12	adjustment	adjustment	NOUN
ap-6103	116	13	of	of	ADP
ap-6103	116	14	the	the	DET
ap-6103	116	15	generator	generator	NOUN
ap-6103	116	16	.	.	PUNCT
ap-6103	117	1	4this	4this	DET
ap-6103	117	2	property	property	NOUN
ap-6103	117	3	was	be	AUX
ap-6103	117	4	firstly	firstly	ADV
ap-6103	117	5	noted	note	VERB
ap-6103	117	6	in	in	ADP
ap-6103	117	7	the	the	DET
ap-6103	117	8	case	case	NOUN
ap-6103	117	9	of	of	ADP
ap-6103	117	10	recursion	recursion	NOUN
ap-6103	117	11	operators	operator	NOUN
ap-6103	117	12	.	.	PUNCT
ap-6103	118	1	it	it	PRON
ap-6103	118	2	appears	appear	VERB
ap-6103	118	3	to	to	PART
ap-6103	118	4	be	be	AUX
ap-6103	118	5	somewhat	somewhat	ADV
ap-6103	118	6	robust	robust	ADJ
ap-6103	118	7	!	!	PUNCT
ap-6103	119	1	430	430	NUM
ap-6103	119	2	vol	vol	NOUN
ap-6103	119	3	.	.	PUNCT
ap-6103	120	1	60	60	NUM
ap-6103	120	2	no	no	NOUN
ap-6103	120	3	.	.	PUNCT
ap-6103	121	1	5/2020	5/2020	NUM
ap-6103	121	2	properties	property	NOUN
ap-6103	121	3	of	of	ADP
ap-6103	121	4	a	a	DET
ap-6103	121	5	differential	differential	ADJ
ap-6103	121	6	sequence	sequence	NOUN
ap-6103	121	7	based	base	VERB
ap-6103	121	8	upon	upon	SCONJ
ap-6103	121	9	the	the	DET
ap-6103	121	10	kummer	kummer	NOUN
ap-6103	121	11	-	-	PUNCT
ap-6103	121	12	schwarz	schwarz	PROPN
ap-6103	121	13	.	.	PUNCT
ap-6103	121	14	.	.	PUNCT
ap-6103	121	15	.	.	PUNCT
ap-6103	122	1	element	element	NOUN
ap-6103	122	2	identifier	identifier	NOUN
ap-6103	122	3	possible	possible	ADJ
ap-6103	122	4	exponents	exponent	NOUN
ap-6103	122	5	ks101	ks101	PROPN
ap-6103	122	6	-1	-1	ADP
ap-6103	122	7	,	,	PUNCT
ap-6103	122	8	1	1	X
ap-6103	122	9	ks102	ks102	X
ap-6103	122	10	-3	-3	PUNCT
ap-6103	122	11	,	,	PUNCT
ap-6103	122	12	-1	-1	INTJ
ap-6103	122	13	,	,	PUNCT
ap-6103	122	14	1	1	NUM
ap-6103	122	15	ks103	ks103	NOUN
ap-6103	122	16	-5	-5	NOUN
ap-6103	122	17	,	,	PUNCT
ap-6103	122	18	-3	-3	INTJ
ap-6103	122	19	,	,	PUNCT
ap-6103	122	20	-1	-1	INTJ
ap-6103	122	21	,	,	PUNCT
ap-6103	122	22	1	1	NUM
ap-6103	122	23	ks104	ks104	NOUN
ap-6103	122	24	-7	-7	NOUN
ap-6103	122	25	,	,	PUNCT
ap-6103	122	26	-5	-5	INTJ
ap-6103	122	27	,	,	PUNCT
ap-6103	122	28	-3	-3	INTJ
ap-6103	122	29	,	,	PUNCT
ap-6103	122	30	-1	-1	INTJ
ap-6103	122	31	,	,	PUNCT
ap-6103	122	32	1	1	NUM
ap-6103	122	33	ks105	ks105	PROPN
ap-6103	122	34	-9	-9	PROPN
ap-6103	122	35	,	,	PUNCT
ap-6103	122	36	-7	-7	INTJ
ap-6103	122	37	,	,	PUNCT
ap-6103	122	38	-5	-5	INTJ
ap-6103	122	39	,	,	PUNCT
ap-6103	122	40	-3	-3	INTJ
ap-6103	122	41	,	,	PUNCT
ap-6103	122	42	-1	-1	INTJ
ap-6103	122	43	,	,	PUNCT
ap-6103	122	44	1	1	NUM
ap-6103	122	45	ks106	ks106	NOUN
ap-6103	122	46	-11	-11	PROPN
ap-6103	122	47	,	,	PUNCT
ap-6103	122	48	-9	-9	INTJ
ap-6103	122	49	,	,	PUNCT
ap-6103	122	50	-7	-7	INTJ
ap-6103	122	51	,	,	PUNCT
ap-6103	122	52	-5	-5	INTJ
ap-6103	122	53	,	,	PUNCT
ap-6103	122	54	-3	-3	INTJ
ap-6103	122	55	,	,	PUNCT
ap-6103	122	56	-1	-1	INTJ
ap-6103	122	57	,	,	PUNCT
ap-6103	122	58	1	1	NUM
ap-6103	122	59	ks107	ks107	NOUN
ap-6103	122	60	-13	-13	NUM
ap-6103	122	61	,	,	PUNCT
ap-6103	122	62	-11	-11	NUM
ap-6103	122	63	,	,	PUNCT
ap-6103	122	64	-9	-9	ADV
ap-6103	122	65	,	,	PUNCT
ap-6103	122	66	-7	-7	INTJ
ap-6103	122	67	,	,	PUNCT
ap-6103	122	68	-5	-5	INTJ
ap-6103	122	69	,	,	PUNCT
ap-6103	122	70	-3	-3	INTJ
ap-6103	122	71	,	,	PUNCT
ap-6103	122	72	-1	-1	INTJ
ap-6103	122	73	,	,	PUNCT
ap-6103	122	74	1	1	NUM
ap-6103	122	75	ks108	ks108	PROPN
ap-6103	122	76	-15	-15	NUM
ap-6103	122	77	,	,	PUNCT
ap-6103	122	78	-13	-13	NUM
ap-6103	122	79	,	,	PUNCT
ap-6103	122	80	-11	-11	NUM
ap-6103	122	81	,	,	PUNCT
ap-6103	122	82	-9	-9	ADV
ap-6103	122	83	,	,	PUNCT
ap-6103	122	84	-7	-7	INTJ
ap-6103	122	85	,	,	PUNCT
ap-6103	122	86	-5	-5	INTJ
ap-6103	122	87	,	,	PUNCT
ap-6103	122	88	-3	-3	INTJ
ap-6103	122	89	,	,	PUNCT
ap-6103	122	90	-1	-1	INTJ
ap-6103	122	91	,	,	PUNCT
ap-6103	122	92	1	1	NUM
ap-6103	122	93	...	...	PUNCT
ap-6103	122	94	ks10n	ks10n	X
ap-6103	122	95	-2n+1	-2n+1	PROPN
ap-6103	122	96	,	,	PUNCT
ap-6103	122	97	-2n+3	-2n+3	PUNCT
ap-6103	122	98	,	,	PUNCT
ap-6103	122	99	-2n+5	-2n+5	PUNCT
ap-6103	122	100	,	,	PUNCT
ap-6103	122	101	...	...	PUNCT
ap-6103	123	1	-7	-7	INTJ
ap-6103	123	2	,	,	PUNCT
ap-6103	123	3	-5	-5	INTJ
ap-6103	123	4	,	,	PUNCT
ap-6103	123	5	-3	-3	INTJ
ap-6103	123	6	,	,	PUNCT
ap-6103	123	7	-1	-1	INTJ
ap-6103	123	8	,	,	PUNCT
ap-6103	123	9	1	1	NUM
ap-6103	123	10	table	table	NOUN
ap-6103	123	11	1	1	NUM
ap-6103	123	12	.	.	PUNCT
ap-6103	123	13	kummer	kummer	NOUN
ap-6103	123	14	-	-	PUNCT
ap-6103	123	15	schwarz	schwarz	PROPN
ap-6103	123	16	sequence	sequence	NOUN
ap-6103	123	17	:	:	PUNCT
ap-6103	123	18	possible	possible	ADJ
ap-6103	123	19	exponents	exponent	NOUN
ap-6103	123	20	of	of	ADP
ap-6103	123	21	the	the	DET
ap-6103	123	22	leading	lead	VERB
ap-6103	123	23	-	-	PUNCT
ap-6103	123	24	order	order	NOUN
ap-6103	123	25	term	term	NOUN
ap-6103	123	26	for	for	ADP
ap-6103	123	27	the	the	DET
ap-6103	123	28	first	first	ADJ
ap-6103	123	29	eight	eight	NUM
ap-6103	123	30	elements	element	NOUN
ap-6103	123	31	is	be	AUX
ap-6103	123	32	then	then	ADV
ap-6103	123	33	ks102	ks102	PROPN
ap-6103	123	34	:	:	PUNCT
ap-6103	123	35	u′′′	u′′′	PROPN
ap-6103	123	36	u′	u′	PROPN
ap-6103	123	37	−	−	PROPN
ap-6103	123	38	3u′′2	3u′′2	NUM
ap-6103	123	39	2u′2	2u′2	NOUN
ap-6103	124	1	=	=	PUNCT
ap-6103	124	2	c0u	c0u	PROPN
ap-6103	124	3	′1/2	′1/2	PROPN
ap-6103	124	4	.	.	PUNCT
ap-6103	125	1	(	(	PUNCT
ap-6103	125	2	20	20	NUM
ap-6103	125	3	)	)	PUNCT
ap-6103	125	4	it	it	PRON
ap-6103	125	5	is	be	AUX
ap-6103	125	6	an	an	DET
ap-6103	125	7	easy	easy	ADJ
ap-6103	125	8	matter	matter	NOUN
ap-6103	125	9	to	to	PART
ap-6103	125	10	demonstrate	demonstrate	VERB
ap-6103	125	11	that	that	SCONJ
ap-6103	125	12	in	in	ADP
ap-6103	125	13	general	general	ADJ
ap-6103	125	14	ks10n	ks10n	NOUN
ap-6103	125	15	:	:	PUNCT
ap-6103	125	16	u′′′	u′′′	PROPN
ap-6103	125	17	u′	u′	PROPN
ap-6103	125	18	−	−	PROPN
ap-6103	125	19	3u′′2	3u′′2	NUM
ap-6103	125	20	2u′2	2u′2	NOUN
ap-6103	126	1	=	=	SYM
ap-6103	126	2	(	(	PUNCT
ap-6103	126	3	n−1∑	n−1∑	PROPN
ap-6103	126	4	i=0	i=0	PROPN
ap-6103	126	5	1	1	NUM
ap-6103	126	6	i!cn−1−ix	i!cn−1−ix	PROPN
ap-6103	126	7	i	i	PROPN
ap-6103	126	8	)	)	PUNCT
ap-6103	126	9	u′1/2	u′1/2	PROPN
ap-6103	126	10	.	.	PUNCT
ap-6103	127	1	(	(	PUNCT
ap-6103	127	2	21	21	NUM
ap-6103	127	3	)	)	PUNCT
ap-6103	127	4	7	7	NUM
ap-6103	127	5	.	.	PUNCT
ap-6103	127	6	conclusion	conclusion	NOUN
ap-6103	127	7	in	in	ADP
ap-6103	127	8	the	the	DET
ap-6103	127	9	article	article	NOUN
ap-6103	127	10	,	,	PUNCT
ap-6103	127	11	we	we	PRON
ap-6103	127	12	have	have	AUX
ap-6103	127	13	reported	report	VERB
ap-6103	127	14	the	the	DET
ap-6103	127	15	results	result	NOUN
ap-6103	127	16	of	of	ADP
ap-6103	127	17	our	our	PRON
ap-6103	127	18	analysis	analysis	NOUN
ap-6103	127	19	of	of	ADP
ap-6103	127	20	the	the	DET
ap-6103	127	21	elements	element	NOUN
ap-6103	127	22	of	of	ADP
ap-6103	127	23	this	this	DET
ap-6103	127	24	sequence	sequence	NOUN
ap-6103	127	25	.	.	PUNCT
ap-6103	128	1	it	it	PRON
ap-6103	128	2	remains	remain	VERB
ap-6103	128	3	to	to	PART
ap-6103	128	4	interpret	interpret	VERB
ap-6103	128	5	the	the	DET
ap-6103	128	6	results	result	NOUN
ap-6103	128	7	of	of	ADP
ap-6103	128	8	the	the	DET
ap-6103	128	9	singularity	singularity	NOUN
ap-6103	128	10	analysis	analysis	NOUN
ap-6103	128	11	in	in	ADP
ap-6103	128	12	the	the	DET
ap-6103	128	13	light	light	NOUN
ap-6103	128	14	of	of	ADP
ap-6103	128	15	our	our	PRON
ap-6103	128	16	knowledge	knowledge	NOUN
ap-6103	128	17	of	of	ADP
ap-6103	128	18	a	a	DET
ap-6103	128	19	route	route	NOUN
ap-6103	128	20	to	to	PART
ap-6103	128	21	obtain	obtain	VERB
ap-6103	128	22	the	the	DET
ap-6103	128	23	solution	solution	NOUN
ap-6103	128	24	of	of	ADP
ap-6103	128	25	each	each	DET
ap-6103	128	26	element	element	NOUN
ap-6103	128	27	of	of	ADP
ap-6103	128	28	the	the	DET
ap-6103	128	29	sequence	sequence	NOUN
ap-6103	128	30	in	in	ADP
ap-6103	128	31	terms	term	NOUN
ap-6103	128	32	of	of	ADP
ap-6103	128	33	a	a	DET
ap-6103	128	34	quadrature	quadrature	NOUN
ap-6103	128	35	.	.	PUNCT
ap-6103	129	1	the	the	DET
ap-6103	129	2	nth	nth	PROPN
ap-6103	129	3	element	element	NOUN
ap-6103	129	4	of	of	ADP
ap-6103	129	5	the	the	DET
ap-6103	129	6	sequence	sequence	NOUN
ap-6103	129	7	has	have	VERB
ap-6103	129	8	n	n	NUM
ap-6103	129	9	possible	possible	ADJ
ap-6103	129	10	values	value	NOUN
ap-6103	129	11	for	for	ADP
ap-6103	129	12	the	the	DET
ap-6103	129	13	exponent	exponent	NOUN
ap-6103	129	14	of	of	ADP
ap-6103	129	15	the	the	DET
ap-6103	129	16	leading	lead	VERB
ap-6103	129	17	-	-	PUNCT
ap-6103	129	18	order	order	NOUN
ap-6103	129	19	term	term	NOUN
ap-6103	129	20	,	,	PUNCT
ap-6103	129	21	which	which	PRON
ap-6103	129	22	are	be	AUX
ap-6103	129	23	acceptable	acceptable	ADJ
ap-6103	129	24	,	,	PUNCT
ap-6103	129	25	ie	ie	X
ap-6103	129	26	negative	negative	ADJ
ap-6103	129	27	integers	integer	NOUN
ap-6103	129	28	.	.	PUNCT
ap-6103	130	1	as	as	SCONJ
ap-6103	130	2	was	be	AUX
ap-6103	130	3	noted	note	VERB
ap-6103	130	4	in	in	ADP
ap-6103	130	5	table	table	NOUN
ap-6103	130	6	1	1	NUM
ap-6103	130	7	,	,	PUNCT
ap-6103	130	8	for	for	ADP
ap-6103	130	9	the	the	DET
ap-6103	130	10	first	first	ADJ
ap-6103	130	11	eight	eight	NUM
ap-6103	130	12	elements	element	NOUN
ap-6103	130	13	of	of	ADP
ap-6103	130	14	the	the	DET
ap-6103	130	15	sequence	sequence	NOUN
ap-6103	130	16	,	,	PUNCT
ap-6103	130	17	the	the	DET
ap-6103	130	18	precise	precise	ADJ
ap-6103	130	19	values	value	NOUN
ap-6103	130	20	are	be	AUX
ap-6103	130	21	−(2i	−(2i	X
ap-6103	130	22	−	−	NOUN
ap-6103	130	23	1	1	NUM
ap-6103	130	24	)	)	PUNCT
ap-6103	130	25	,	,	PUNCT
ap-6103	130	26	i	i	PRON
ap-6103	130	27	=	=	NOUN
ap-6103	130	28	1	1	NUM
ap-6103	130	29	,	,	PUNCT
ap-6103	130	30	2	2	NUM
ap-6103	130	31	,	,	PUNCT
ap-6103	130	32	.	.	PUNCT
ap-6103	130	33	.	.	PUNCT
ap-6103	131	1	.	.	PUNCT
ap-6103	132	1	,	,	PUNCT
ap-6103	132	2	n.	n.	NOUN
ap-6103	132	3	in	in	ADP
ap-6103	132	4	table	table	NOUN
ap-6103	132	5	2	2	NUM
ap-6103	132	6	,	,	PUNCT
ap-6103	132	7	the	the	DET
ap-6103	132	8	resonances	resonance	NOUN
ap-6103	132	9	for	for	ADP
ap-6103	132	10	each	each	PRON
ap-6103	132	11	of	of	ADP
ap-6103	132	12	the	the	DET
ap-6103	132	13	negative	negative	ADJ
ap-6103	132	14	exponents	exponent	NOUN
ap-6103	132	15	of	of	ADP
ap-6103	132	16	the	the	DET
ap-6103	132	17	leading	lead	VERB
ap-6103	132	18	-	-	PUNCT
ap-6103	132	19	order	order	NOUN
ap-6103	132	20	term	term	NOUN
ap-6103	132	21	are	be	AUX
ap-6103	132	22	given	give	VERB
ap-6103	132	23	.	.	PUNCT
ap-6103	133	1	several	several	ADJ
ap-6103	133	2	features	feature	NOUN
ap-6103	133	3	are	be	AUX
ap-6103	133	4	to	to	PART
ap-6103	133	5	be	be	AUX
ap-6103	133	6	noted	note	VERB
ap-6103	133	7	.	.	PUNCT
ap-6103	134	1	firstly	firstly	ADV
ap-6103	134	2	,	,	PUNCT
ap-6103	134	3	there	there	PRON
ap-6103	134	4	is	be	VERB
ap-6103	134	5	the	the	DET
ap-6103	134	6	possibility	possibility	NOUN
ap-6103	134	7	of	of	ADP
ap-6103	134	8	repeated	repeat	VERB
ap-6103	134	9	resonances	resonance	NOUN
ap-6103	134	10	,	,	PUNCT
ap-6103	134	11	which	which	PRON
ap-6103	134	12	indicates	indicate	VERB
ap-6103	134	13	the	the	DET
ap-6103	134	14	introduction	introduction	NOUN
ap-6103	134	15	of	of	ADP
ap-6103	134	16	a	a	DET
ap-6103	134	17	logarithmic	logarithmic	ADJ
ap-6103	134	18	term	term	NOUN
ap-6103	134	19	into	into	ADP
ap-6103	134	20	the	the	DET
ap-6103	134	21	laurent	laurent	NOUN
ap-6103	134	22	expansion	expansion	NOUN
ap-6103	134	23	for	for	ADP
ap-6103	134	24	the	the	DET
ap-6103	134	25	solution	solution	NOUN
ap-6103	134	26	.	.	PUNCT
ap-6103	135	1	the	the	DET
ap-6103	135	2	number	number	NOUN
ap-6103	135	3	of	of	ADP
ap-6103	135	4	exponents	exponent	NOUN
ap-6103	135	5	of	of	ADP
ap-6103	135	6	the	the	DET
ap-6103	135	7	leading	lead	VERB
ap-6103	135	8	-	-	PUNCT
ap-6103	135	9	order	order	NOUN
ap-6103	135	10	term	term	NOUN
ap-6103	135	11	for	for	ADP
ap-6103	135	12	which	which	PRON
ap-6103	135	13	this	this	PRON
ap-6103	135	14	happens	happen	VERB
ap-6103	135	15	increases	increase	NOUN
ap-6103	135	16	as	as	SCONJ
ap-6103	135	17	one	one	NUM
ap-6103	135	18	proceeds	proceed	VERB
ap-6103	135	19	down	down	ADP
ap-6103	135	20	the	the	DET
ap-6103	135	21	sequence	sequence	NOUN
ap-6103	135	22	.	.	PUNCT
ap-6103	136	1	secondly	secondly	ADV
ap-6103	136	2	,	,	PUNCT
ap-6103	136	3	the	the	DET
ap-6103	136	4	highest	high	ADJ
ap-6103	136	5	exponent	exponent	NOUN
ap-6103	136	6	leads	lead	VERB
ap-6103	136	7	to	to	ADP
ap-6103	136	8	a	a	DET
ap-6103	136	9	right	right	ADJ
ap-6103	136	10	painlevé	painlevé	NOUN
ap-6103	136	11	series	series	NOUN
ap-6103	136	12	,	,	PUNCT
ap-6103	136	13	albeit	albeit	SCONJ
ap-6103	136	14	with	with	ADP
ap-6103	136	15	the	the	DET
ap-6103	136	16	intrusion	intrusion	NOUN
ap-6103	136	17	of	of	ADP
ap-6103	136	18	the	the	DET
ap-6103	136	19	unhappy	unhappy	ADJ
ap-6103	136	20	logarithm	logarithm	NOUN
ap-6103	136	21	,	,	PUNCT
ap-6103	136	22	and	and	CCONJ
ap-6103	136	23	the	the	DET
ap-6103	136	24	lowest	low	ADJ
ap-6103	136	25	exponent	exponent	NOUN
ap-6103	136	26	to	to	ADP
ap-6103	136	27	what	what	PRON
ap-6103	136	28	would	would	AUX
ap-6103	136	29	be	be	AUX
ap-6103	136	30	a	a	DET
ap-6103	136	31	left	left	ADJ
ap-6103	136	32	painlevé	painlevé	NOUN
ap-6103	136	33	series	series	NOUN
ap-6103	136	34	were	be	AUX
ap-6103	136	35	it	it	PRON
ap-6103	136	36	not	not	PART
ap-6103	136	37	for	for	ADP
ap-6103	136	38	a	a	DET
ap-6103	136	39	single	single	ADJ
ap-6103	136	40	positive	positive	ADJ
ap-6103	136	41	resonance	resonance	NOUN
ap-6103	136	42	equal	equal	ADJ
ap-6103	136	43	in	in	ADP
ap-6103	136	44	value	value	NOUN
ap-6103	136	45	to	to	ADP
ap-6103	136	46	the	the	DET
ap-6103	136	47	negative	negative	NOUN
ap-6103	136	48	of	of	ADP
ap-6103	136	49	the	the	DET
ap-6103	136	50	exponent	exponent	NOUN
ap-6103	136	51	.	.	PUNCT
ap-6103	137	1	for	for	ADP
ap-6103	137	2	the	the	DET
ap-6103	137	3	exponents	exponent	NOUN
ap-6103	137	4	between	between	ADP
ap-6103	137	5	the	the	DET
ap-6103	137	6	highest	high	ADJ
ap-6103	137	7	and	and	CCONJ
ap-6103	137	8	the	the	DET
ap-6103	137	9	lowest	low	ADJ
ap-6103	137	10	,	,	PUNCT
ap-6103	137	11	one	one	PRON
ap-6103	137	12	sees	see	VERB
ap-6103	137	13	a	a	DET
ap-6103	137	14	selection	selection	NOUN
ap-6103	137	15	of	of	ADP
ap-6103	137	16	both	both	CCONJ
ap-6103	137	17	negative	negative	ADJ
ap-6103	137	18	and	and	CCONJ
ap-6103	137	19	positive	positive	ADJ
ap-6103	137	20	resonances	resonance	NOUN
ap-6103	137	21	(	(	PUNCT
ap-6103	137	22	apart	apart	ADV
ap-6103	137	23	from	from	ADP
ap-6103	137	24	the	the	DET
ap-6103	137	25	generic	generic	ADJ
ap-6103	137	26	−1	−1	NOUN
ap-6103	137	27	)	)	PUNCT
ap-6103	137	28	,	,	PUNCT
ap-6103	137	29	which	which	PRON
ap-6103	137	30	indicates	indicate	VERB
ap-6103	137	31	a	a	DET
ap-6103	137	32	full	full	ADJ
ap-6103	137	33	laurent	laurent	NOUN
ap-6103	137	34	expansion	expansion	NOUN
ap-6103	137	35	,	,	PUNCT
ap-6103	137	36	again	again	ADV
ap-6103	137	37	with	with	ADP
ap-6103	137	38	the	the	DET
ap-6103	137	39	possibility	possibility	NOUN
ap-6103	137	40	of	of	ADP
ap-6103	137	41	logarithmic	logarithmic	ADJ
ap-6103	137	42	terms	term	NOUN
ap-6103	137	43	occurring	occur	VERB
ap-6103	137	44	.	.	PUNCT
ap-6103	138	1	as	as	SCONJ
ap-6103	138	2	should	should	AUX
ap-6103	138	3	be	be	AUX
ap-6103	138	4	by	by	ADP
ap-6103	138	5	now	now	ADV
ap-6103	138	6	well	well	ADV
ap-6103	138	7	known	know	VERB
ap-6103	138	8	,	,	PUNCT
ap-6103	138	9	the	the	DET
ap-6103	138	10	right	right	ADJ
ap-6103	138	11	painlevé	painlevé	PROPN
ap-6103	138	12	series	series	PROPN
ap-6103	138	13	is	be	AUX
ap-6103	138	14	a	a	DET
ap-6103	138	15	laurent	laurent	ADJ
ap-6103	138	16	expansion	expansion	NOUN
ap-6103	138	17	in	in	ADP
ap-6103	138	18	the	the	DET
ap-6103	138	19	neighbourhood	neighbourhood	NOUN
ap-6103	138	20	of	of	ADP
ap-6103	138	21	the	the	DET
ap-6103	138	22	singularity	singularity	NOUN
ap-6103	138	23	convergent	convergent	NOUN
ap-6103	138	24	on	on	ADP
ap-6103	138	25	a	a	DET
ap-6103	138	26	punctured	punctured	ADJ
ap-6103	138	27	disc	disc	NOUN
ap-6103	138	28	and	and	CCONJ
ap-6103	138	29	the	the	DET
ap-6103	138	30	left	left	ADJ
ap-6103	138	31	painlevé	painlevé	NOUN
ap-6103	138	32	series	series	PROPN
ap-6103	138	33	has	have	VERB
ap-6103	138	34	the	the	DET
ap-6103	138	35	nature	nature	NOUN
ap-6103	138	36	of	of	ADP
ap-6103	138	37	an	an	DET
ap-6103	138	38	asymptotic	asymptotic	ADJ
ap-6103	138	39	expansion	expansion	NOUN
ap-6103	138	40	in	in	ADP
ap-6103	138	41	that	that	SCONJ
ap-6103	138	42	it	it	PRON
ap-6103	138	43	exists	exist	VERB
ap-6103	138	44	on	on	ADP
ap-6103	138	45	the	the	DET
ap-6103	138	46	exterior	exterior	NOUN
ap-6103	138	47	of	of	ADP
ap-6103	138	48	a	a	DET
ap-6103	138	49	disc	disc	NOUN
ap-6103	138	50	centred	centre	VERB
ap-6103	138	51	on	on	ADP
ap-6103	138	52	the	the	DET
ap-6103	138	53	singularity	singularity	NOUN
ap-6103	138	54	.	.	PUNCT
ap-6103	139	1	the	the	DET
ap-6103	139	2	full	full	ADJ
ap-6103	139	3	series	series	NOUN
ap-6103	139	4	is	be	AUX
ap-6103	139	5	defined	define	VERB
ap-6103	139	6	over	over	ADP
ap-6103	139	7	an	an	DET
ap-6103	139	8	annulus	annulus	NOUN
ap-6103	139	9	centred	centre	VERB
ap-6103	139	10	on	on	ADP
ap-6103	139	11	the	the	DET
ap-6103	139	12	similarity	similarity	NOUN
ap-6103	139	13	and	and	CCONJ
ap-6103	139	14	the	the	DET
ap-6103	139	15	existence	existence	NOUN
ap-6103	139	16	of	of	ADP
ap-6103	139	17	multiple	multiple	ADJ
ap-6103	139	18	instances	instance	NOUN
ap-6103	139	19	of	of	ADP
ap-6103	139	20	these	these	DET
ap-6103	139	21	series	series	NOUN
ap-6103	139	22	indicates	indicate	VERB
ap-6103	139	23	a	a	DET
ap-6103	139	24	succession	succession	NOUN
ap-6103	139	25	of	of	ADP
ap-6103	139	26	annuli	annuli	NOUN
ap-6103	139	27	,	,	PUNCT
ap-6103	139	28	the	the	DET
ap-6103	139	29	bounding	bounding	NOUN
ap-6103	139	30	circles	circle	NOUN
ap-6103	139	31	of	of	ADP
ap-6103	139	32	which	which	PRON
ap-6103	139	33	are	be	AUX
ap-6103	139	34	defined	define	VERB
ap-6103	139	35	by	by	ADP
ap-6103	139	36	successive	successive	ADJ
ap-6103	139	37	singularities	singularity	NOUN
ap-6103	139	38	.	.	PUNCT
ap-6103	140	1	thirdly	thirdly	ADV
ap-6103	140	2	,	,	PUNCT
ap-6103	140	3	the	the	DET
ap-6103	140	4	value	value	NOUN
ap-6103	140	5	of	of	ADP
ap-6103	140	6	the	the	DET
ap-6103	140	7	highest	high	ADJ
ap-6103	140	8	resonance	resonance	NOUN
ap-6103	140	9	shows	show	VERB
ap-6103	140	10	some	some	DET
ap-6103	140	11	variability	variability	NOUN
ap-6103	140	12	.	.	PUNCT
ap-6103	141	1	for	for	ADP
ap-6103	141	2	patterns	pattern	NOUN
ap-6103	141	3	of	of	ADP
ap-6103	141	4	resonances	resonance	NOUN
ap-6103	141	5	,	,	PUNCT
ap-6103	141	6	in	in	ADP
ap-6103	141	7	which	which	PRON
ap-6103	141	8	there	there	PRON
ap-6103	141	9	is	be	VERB
ap-6103	141	10	no	no	DET
ap-6103	141	11	repeated	repeat	VERB
ap-6103	141	12	resonance	resonance	NOUN
ap-6103	141	13	or	or	CCONJ
ap-6103	141	14	the	the	DET
ap-6103	141	15	repeated	repeat	VERB
ap-6103	141	16	resonance	resonance	NOUN
ap-6103	141	17	is	be	AUX
ap-6103	141	18	the	the	DET
ap-6103	141	19	highest	high	ADJ
ap-6103	141	20	resonance	resonance	NOUN
ap-6103	141	21	,	,	PUNCT
ap-6103	141	22	the	the	DET
ap-6103	141	23	highest	high	ADJ
ap-6103	141	24	resonance	resonance	NOUN
ap-6103	141	25	is	be	AUX
ap-6103	141	26	the	the	DET
ap-6103	141	27	negative	negative	ADJ
ap-6103	141	28	of	of	ADP
ap-6103	141	29	the	the	DET
ap-6103	141	30	exponent	exponent	NOUN
ap-6103	141	31	of	of	ADP
ap-6103	141	32	the	the	DET
ap-6103	141	33	leading	lead	VERB
ap-6103	141	34	-	-	PUNCT
ap-6103	141	35	order	order	NOUN
ap-6103	141	36	term	term	NOUN
ap-6103	141	37	.	.	PUNCT
ap-6103	142	1	for	for	ADP
ap-6103	142	2	the	the	DET
ap-6103	142	3	other	other	ADJ
ap-6103	142	4	patterns	pattern	NOUN
ap-6103	142	5	of	of	ADP
ap-6103	142	6	the	the	DET
ap-6103	142	7	resonances	resonance	NOUN
ap-6103	142	8	–	–	PUNCT
ap-6103	142	9	always	always	ADV
ap-6103	142	10	starting	start	VERB
ap-6103	142	11	from	from	ADP
ap-6103	142	12	the	the	DET
ap-6103	142	13	more	more	ADV
ap-6103	142	14	positive	positive	ADJ
ap-6103	142	15	exponents	exponent	NOUN
ap-6103	142	16	–	–	PUNCT
ap-6103	142	17	this	this	DET
ap-6103	142	18	value	value	NOUN
ap-6103	142	19	is	be	AUX
ap-6103	142	20	exceeded	exceed	VERB
ap-6103	142	21	to	to	ADP
ap-6103	142	22	the	the	DET
ap-6103	142	23	extent	extent	NOUN
ap-6103	142	24	that	that	SCONJ
ap-6103	142	25	it	it	PRON
ap-6103	142	26	is	be	AUX
ap-6103	142	27	necessary	necessary	ADJ
ap-6103	142	28	to	to	PART
ap-6103	142	29	provide	provide	VERB
ap-6103	142	30	a	a	DET
ap-6103	142	31	full	full	ADJ
ap-6103	142	32	number	number	NOUN
ap-6103	142	33	of	of	ADP
ap-6103	142	34	constants	constant	NOUN
ap-6103	142	35	of	of	ADP
ap-6103	142	36	integration	integration	NOUN
ap-6103	142	37	.	.	PUNCT
ap-6103	143	1	evidently	evidently	ADV
ap-6103	143	2	,	,	PUNCT
ap-6103	143	3	some	some	DET
ap-6103	143	4	explanation	explanation	NOUN
ap-6103	143	5	of	of	ADP
ap-6103	143	6	these	these	DET
ap-6103	143	7	features	feature	NOUN
ap-6103	143	8	is	be	AUX
ap-6103	143	9	required	require	VERB
ap-6103	143	10	!	!	PUNCT
ap-6103	144	1	fortunately	fortunately	ADV
ap-6103	144	2	,	,	PUNCT
ap-6103	144	3	we	we	PRON
ap-6103	144	4	are	be	AUX
ap-6103	144	5	in	in	ADP
ap-6103	144	6	a	a	DET
ap-6103	144	7	position	position	NOUN
ap-6103	144	8	to	to	PART
ap-6103	144	9	describe	describe	VERB
ap-6103	144	10	the	the	DET
ap-6103	144	11	solution	solution	NOUN
ap-6103	144	12	of	of	ADP
ap-6103	144	13	each	each	DET
ap-6103	144	14	element	element	NOUN
ap-6103	144	15	of	of	ADP
ap-6103	144	16	the	the	DET
ap-6103	144	17	sequence	sequence	NOUN
ap-6103	144	18	due	due	ADP
ap-6103	144	19	to	to	ADP
ap-6103	144	20	the	the	DET
ap-6103	144	21	property	property	NOUN
ap-6103	144	22	of	of	ADP
ap-6103	144	23	the	the	DET
ap-6103	144	24	linearisation	linearisation	NOUN
ap-6103	144	25	noted	note	VERB
ap-6103	144	26	in	in	ADP
ap-6103	144	27	§	§	PROPN
ap-6103	144	28	5	5	NUM
ap-6103	144	29	.	.	PUNCT
ap-6103	144	30	to	to	PART
ap-6103	144	31	provide	provide	VERB
ap-6103	144	32	the	the	DET
ap-6103	144	33	explanation	explanation	NOUN
ap-6103	144	34	,	,	PUNCT
ap-6103	144	35	we	we	PRON
ap-6103	144	36	make	make	VERB
ap-6103	144	37	use	use	NOUN
ap-6103	144	38	of	of	ADP
ap-6103	144	39	the	the	DET
ap-6103	144	40	third	third	ADJ
ap-6103	144	41	element	element	NOUN
ap-6103	144	42	of	of	ADP
ap-6103	144	43	the	the	DET
ap-6103	144	44	sequence	sequence	NOUN
ap-6103	144	45	,	,	PUNCT
ap-6103	144	46	which	which	PRON
ap-6103	144	47	has	have	VERB
ap-6103	144	48	the	the	DET
ap-6103	144	49	double	double	ADJ
ap-6103	144	50	merits	merit	NOUN
ap-6103	144	51	of	of	ADP
ap-6103	144	52	featuring	feature	VERB
ap-6103	144	53	in	in	ADP
ap-6103	144	54	almost	almost	ADV
ap-6103	144	55	every	every	PRON
ap-6103	144	56	property	property	NOUN
ap-6103	144	57	(	(	PUNCT
ap-6103	144	58	the	the	DET
ap-6103	144	59	repetition	repetition	NOUN
ap-6103	144	60	of	of	ADP
ap-6103	144	61	logarithms	logarithm	NOUN
ap-6103	144	62	is	be	AUX
ap-6103	144	63	not	not	PART
ap-6103	144	64	one	one	NUM
ap-6103	144	65	of	of	ADP
ap-6103	144	66	them	they	PRON
ap-6103	144	67	)	)	PUNCT
ap-6103	144	68	mentioned	mention	VERB
ap-6103	144	69	in	in	ADP
ap-6103	144	70	the	the	DET
ap-6103	144	71	previous	previous	ADJ
ap-6103	144	72	paragraph	paragraph	NOUN
ap-6103	144	73	.	.	PUNCT
ap-6103	145	1	the	the	DET
ap-6103	145	2	third	third	ADJ
ap-6103	145	3	element	element	NOUN
ap-6103	145	4	of	of	ADP
ap-6103	145	5	the	the	DET
ap-6103	145	6	sequence	sequence	NOUN
ap-6103	145	7	,	,	PUNCT
ap-6103	145	8	ks103	ks103	PROPN
ap-6103	145	9	,	,	PUNCT
ap-6103	145	10	u′′′′′	u′′′′′	PROPN
ap-6103	145	11	u′	u′	PRON
ap-6103	145	12	−	−	PROPN
ap-6103	146	1	6u′′u′′′′	6u′′u′′′′	NUM
ap-6103	146	2	u′2	u′2	NOUN
ap-6103	147	1	−	−	PROPN
ap-6103	147	2	9u′′′2	9u′′′2	NUM
ap-6103	147	3	2u′2	2u′2	NUM
ap-6103	148	1	+	+	CCONJ
ap-6103	148	2	45u′′2u′′′	45u′′2u′′′	NUM
ap-6103	148	3	2u′3	2u′3	NUM
ap-6103	149	1	−	−	NOUN
ap-6103	149	2	105u′′4	105u′′4	NUM
ap-6103	149	3	8u′4	8u′4	NUM
ap-6103	149	4	=	=	SYM
ap-6103	149	5	0	0	NUM
ap-6103	149	6	,	,	PUNCT
ap-6103	149	7	(	(	PUNCT
ap-6103	149	8	22	22	NUM
ap-6103	149	9	)	)	PUNCT
ap-6103	149	10	takes	take	VERB
ap-6103	149	11	the	the	DET
ap-6103	149	12	linear	linear	ADJ
ap-6103	149	13	form	form	NOUN
ap-6103	149	14	w(4	w(4	NOUN
ap-6103	149	15	)	)	PUNCT
ap-6103	149	16	=	=	SYM
ap-6103	149	17	0	0	NUM
ap-6103	150	1	(	(	PUNCT
ap-6103	150	2	23	23	NUM
ap-6103	150	3	)	)	PUNCT
ap-6103	150	4	under	under	ADP
ap-6103	150	5	the	the	DET
ap-6103	150	6	transformation	transformation	NOUN
ap-6103	150	7	u′	u′	PROPN
ap-6103	150	8	−→	−→	PROPN
ap-6103	150	9	w−2	w−2	PROPN
ap-6103	150	10	.	.	PUNCT
ap-6103	151	1	the	the	DET
ap-6103	151	2	solution	solution	NOUN
ap-6103	151	3	of	of	ADP
ap-6103	151	4	(	(	PUNCT
ap-6103	151	5	23	23	NUM
ap-6103	151	6	)	)	PUNCT
ap-6103	151	7	is	be	AUX
ap-6103	151	8	w(x	w(x	NOUN
ap-6103	151	9	)	)	PUNCT
ap-6103	152	1	=	=	SYM
ap-6103	152	2	p3(x	p3(x	PROPN
ap-6103	152	3	)	)	PUNCT
ap-6103	152	4	,	,	PUNCT
ap-6103	152	5	(	(	PUNCT
ap-6103	152	6	24	24	NUM
ap-6103	152	7	)	)	PUNCT
ap-6103	152	8	431	431	NUM
ap-6103	152	9	a.	a.	NOUN
ap-6103	152	10	maharaj	maharaj	PROPN
ap-6103	152	11	,	,	PUNCT
ap-6103	152	12	k.	k.	PROPN
ap-6103	152	13	andriopoulos	andriopoulos	PROPN
ap-6103	152	14	,	,	PUNCT
ap-6103	152	15	p.	p.	NOUN
ap-6103	152	16	leach	leach	NOUN
ap-6103	152	17	acta	acta	PROPN
ap-6103	152	18	polytechnica	polytechnica	PROPN
ap-6103	152	19	element	element	PROPN
ap-6103	152	20	identifier	identifier	NOUN
ap-6103	152	21	exponents	exponent	NOUN
ap-6103	152	22	resonances	resonance	VERB
ap-6103	152	23	ks101	ks101	PROPN
ap-6103	152	24	-1	-1	ADP
ap-6103	152	25	-1	-1	ADJ
ap-6103	152	26	,	,	PUNCT
ap-6103	152	27	0	0	NUM
ap-6103	152	28	,	,	PUNCT
ap-6103	152	29	1	1	NUM
ap-6103	152	30	ks102	ks102	PROPN
ap-6103	152	31	-1	-1	INTJ
ap-6103	152	32	-1	-1	INTJ
ap-6103	152	33	,	,	PUNCT
ap-6103	152	34	0	0	NUM
ap-6103	152	35	,	,	PUNCT
ap-6103	152	36	1	1	NUM
ap-6103	152	37	(	(	PUNCT
ap-6103	152	38	bis	bis	PROPN
ap-6103	152	39	)	)	PUNCT
ap-6103	152	40	-3	-3	PUNCT
ap-6103	152	41	-2	-2	INTJ
ap-6103	152	42	,	,	PUNCT
ap-6103	152	43	-1	-1	INTJ
ap-6103	152	44	,	,	PUNCT
ap-6103	152	45	0	0	NUM
ap-6103	152	46	,	,	PUNCT
ap-6103	152	47	3	3	NUM
ap-6103	152	48	ks103	ks103	NOUN
ap-6103	152	49	-1	-1	NOUN
ap-6103	152	50	-1	-1	NOUN
ap-6103	152	51	,	,	PUNCT
ap-6103	152	52	0	0	NUM
ap-6103	152	53	,	,	PUNCT
ap-6103	152	54	1	1	NUM
ap-6103	152	55	(	(	PUNCT
ap-6103	152	56	bis	bis	ADJ
ap-6103	152	57	)	)	PUNCT
ap-6103	152	58	,	,	PUNCT
ap-6103	152	59	2	2	NUM
ap-6103	152	60	-3	-3	NUM
ap-6103	152	61	-2	-2	INTJ
ap-6103	152	62	,	,	PUNCT
ap-6103	152	63	-1	-1	INTJ
ap-6103	152	64	,	,	PUNCT
ap-6103	152	65	0	0	NUM
ap-6103	152	66	,	,	PUNCT
ap-6103	152	67	1	1	NUM
ap-6103	152	68	,	,	PUNCT
ap-6103	152	69	3	3	NUM
ap-6103	152	70	-5	-5	NUM
ap-6103	152	71	-3	-3	INTJ
ap-6103	152	72	,	,	PUNCT
ap-6103	152	73	-2	-2	INTJ
ap-6103	152	74	,	,	PUNCT
ap-6103	152	75	-1	-1	INTJ
ap-6103	152	76	,	,	PUNCT
ap-6103	152	77	0	0	NUM
ap-6103	152	78	,	,	PUNCT
ap-6103	152	79	5	5	NUM
ap-6103	152	80	ks104	ks104	NOUN
ap-6103	152	81	-1	-1	INTJ
ap-6103	152	82	-1	-1	ADJ
ap-6103	152	83	,	,	PUNCT
ap-6103	152	84	0	0	NUM
ap-6103	152	85	,	,	PUNCT
ap-6103	152	86	1	1	NUM
ap-6103	152	87	(	(	PUNCT
ap-6103	152	88	bis	bis	ADJ
ap-6103	152	89	)	)	PUNCT
ap-6103	152	90	,	,	PUNCT
ap-6103	152	91	2	2	NUM
ap-6103	152	92	,	,	PUNCT
ap-6103	152	93	3	3	NUM
ap-6103	152	94	-3	-3	NOUN
ap-6103	152	95	-2	-2	INTJ
ap-6103	152	96	,	,	PUNCT
ap-6103	152	97	-1	-1	INTJ
ap-6103	152	98	,	,	PUNCT
ap-6103	152	99	0	0	NUM
ap-6103	152	100	,	,	PUNCT
ap-6103	152	101	1	1	NUM
ap-6103	152	102	,	,	PUNCT
ap-6103	152	103	2	2	NUM
ap-6103	152	104	,	,	PUNCT
ap-6103	152	105	3	3	NUM
ap-6103	152	106	-5	-5	NUM
ap-6103	152	107	-3	-3	INTJ
ap-6103	152	108	,	,	PUNCT
ap-6103	152	109	-2	-2	INTJ
ap-6103	152	110	,	,	PUNCT
ap-6103	152	111	-1	-1	INTJ
ap-6103	152	112	,	,	PUNCT
ap-6103	152	113	0	0	NUM
ap-6103	152	114	,	,	PUNCT
ap-6103	152	115	1	1	NUM
ap-6103	152	116	,	,	PUNCT
ap-6103	152	117	5	5	NUM
ap-6103	152	118	-7	-7	NOUN
ap-6103	152	119	-4	-4	PROPN
ap-6103	152	120	,	,	PUNCT
ap-6103	152	121	-3	-3	INTJ
ap-6103	152	122	,	,	PUNCT
ap-6103	152	123	2	2	NUM
ap-6103	152	124	,	,	PUNCT
ap-6103	152	125	-1	-1	ADJ
ap-6103	152	126	,	,	PUNCT
ap-6103	152	127	0	0	NUM
ap-6103	152	128	,	,	PUNCT
ap-6103	152	129	7	7	NUM
ap-6103	152	130	ks105	ks105	NOUN
ap-6103	152	131	-1	-1	INTJ
ap-6103	152	132	-1	-1	ADJ
ap-6103	152	133	,	,	PUNCT
ap-6103	152	134	0	0	NUM
ap-6103	152	135	,	,	PUNCT
ap-6103	152	136	1	1	NUM
ap-6103	152	137	(	(	PUNCT
ap-6103	152	138	bis	bis	ADJ
ap-6103	152	139	)	)	PUNCT
ap-6103	152	140	,	,	PUNCT
ap-6103	152	141	2	2	NUM
ap-6103	152	142	,	,	PUNCT
ap-6103	152	143	3	3	NUM
ap-6103	152	144	,	,	PUNCT
ap-6103	152	145	4	4	NUM
ap-6103	152	146	-3	-3	NOUN
ap-6103	152	147	-2	-2	INTJ
ap-6103	152	148	,	,	PUNCT
ap-6103	152	149	-1	-1	INTJ
ap-6103	152	150	,	,	PUNCT
ap-6103	152	151	0	0	NUM
ap-6103	152	152	,	,	PUNCT
ap-6103	152	153	1	1	NUM
ap-6103	152	154	,	,	PUNCT
ap-6103	152	155	2	2	NUM
ap-6103	152	156	,	,	PUNCT
ap-6103	152	157	3	3	NUM
ap-6103	152	158	(	(	PUNCT
ap-6103	152	159	bis	bis	ADJ
ap-6103	152	160	)	)	PUNCT
ap-6103	152	161	-5	-5	INTJ
ap-6103	152	162	-3	-3	INTJ
ap-6103	152	163	,	,	PUNCT
ap-6103	152	164	-2	-2	INTJ
ap-6103	152	165	,	,	PUNCT
ap-6103	152	166	-1	-1	INTJ
ap-6103	152	167	,	,	PUNCT
ap-6103	152	168	0	0	NUM
ap-6103	152	169	,	,	PUNCT
ap-6103	152	170	1	1	NUM
ap-6103	152	171	,	,	PUNCT
ap-6103	152	172	2	2	NUM
ap-6103	152	173	,	,	PUNCT
ap-6103	152	174	5	5	NUM
ap-6103	152	175	-7	-7	NOUN
ap-6103	152	176	-4	-4	PROPN
ap-6103	152	177	,	,	PUNCT
ap-6103	152	178	-3	-3	INTJ
ap-6103	152	179	,	,	PUNCT
ap-6103	152	180	-2	-2	INTJ
ap-6103	152	181	,	,	PUNCT
ap-6103	152	182	-1	-1	INTJ
ap-6103	152	183	,	,	PUNCT
ap-6103	152	184	0	0	NUM
ap-6103	152	185	,	,	PUNCT
ap-6103	152	186	1	1	NUM
ap-6103	152	187	,	,	PUNCT
ap-6103	152	188	7	7	NUM
ap-6103	152	189	-9	-9	NOUN
ap-6103	152	190	-5	-5	ADJ
ap-6103	152	191	,	,	PUNCT
ap-6103	152	192	-4	-4	INTJ
ap-6103	152	193	,	,	PUNCT
ap-6103	152	194	-3	-3	INTJ
ap-6103	152	195	,	,	PUNCT
ap-6103	152	196	-2	-2	INTJ
ap-6103	152	197	,	,	PUNCT
ap-6103	152	198	-1	-1	INTJ
ap-6103	152	199	,	,	PUNCT
ap-6103	152	200	0	0	NUM
ap-6103	152	201	,	,	PUNCT
ap-6103	152	202	9	9	NUM
ap-6103	152	203	ks106	ks106	NOUN
ap-6103	152	204	-1	-1	PROPN
ap-6103	152	205	-1	-1	INTJ
ap-6103	152	206	,	,	PUNCT
ap-6103	152	207	0	0	NUM
ap-6103	152	208	,	,	PUNCT
ap-6103	152	209	1	1	NUM
ap-6103	152	210	(	(	PUNCT
ap-6103	152	211	bis	bis	ADJ
ap-6103	152	212	)	)	PUNCT
ap-6103	152	213	,	,	PUNCT
ap-6103	152	214	2	2	NUM
ap-6103	152	215	,	,	PUNCT
ap-6103	152	216	3	3	NUM
ap-6103	152	217	,	,	PUNCT
ap-6103	152	218	4	4	NUM
ap-6103	152	219	,	,	PUNCT
ap-6103	152	220	5	5	NUM
ap-6103	152	221	-3	-3	NOUN
ap-6103	152	222	-2	-2	INTJ
ap-6103	152	223	,	,	PUNCT
ap-6103	152	224	-1	-1	INTJ
ap-6103	152	225	,	,	PUNCT
ap-6103	152	226	0	0	NUM
ap-6103	152	227	,	,	PUNCT
ap-6103	152	228	1	1	NUM
ap-6103	152	229	,	,	PUNCT
ap-6103	152	230	2	2	NUM
ap-6103	152	231	,	,	PUNCT
ap-6103	152	232	3	3	NUM
ap-6103	152	233	(	(	PUNCT
ap-6103	152	234	bis	bis	PROPN
ap-6103	152	235	)	)	PUNCT
ap-6103	152	236	,	,	PUNCT
ap-6103	152	237	4	4	NUM
ap-6103	152	238	-5	-5	NUM
ap-6103	152	239	-3	-3	INTJ
ap-6103	152	240	,	,	PUNCT
ap-6103	152	241	-2	-2	INTJ
ap-6103	152	242	,	,	PUNCT
ap-6103	152	243	-1	-1	INTJ
ap-6103	152	244	,	,	PUNCT
ap-6103	152	245	0	0	NUM
ap-6103	152	246	,	,	PUNCT
ap-6103	152	247	1	1	NUM
ap-6103	152	248	,	,	PUNCT
ap-6103	152	249	2	2	NUM
ap-6103	152	250	,	,	PUNCT
ap-6103	152	251	3	3	NUM
ap-6103	152	252	,	,	PUNCT
ap-6103	152	253	5	5	NUM
ap-6103	152	254	-7	-7	NOUN
ap-6103	152	255	-4	-4	PROPN
ap-6103	152	256	,	,	PUNCT
ap-6103	152	257	-3	-3	INTJ
ap-6103	152	258	,	,	PUNCT
ap-6103	152	259	-2	-2	INTJ
ap-6103	152	260	,	,	PUNCT
ap-6103	152	261	-1	-1	INTJ
ap-6103	152	262	,	,	PUNCT
ap-6103	152	263	0	0	NUM
ap-6103	152	264	,	,	PUNCT
ap-6103	152	265	1	1	NUM
ap-6103	152	266	,	,	PUNCT
ap-6103	152	267	2	2	NUM
ap-6103	152	268	,	,	PUNCT
ap-6103	152	269	7	7	NUM
ap-6103	152	270	-9	-9	NOUN
ap-6103	152	271	-5	-5	ADJ
ap-6103	152	272	,	,	PUNCT
ap-6103	152	273	-4	-4	INTJ
ap-6103	152	274	,	,	PUNCT
ap-6103	152	275	-3	-3	INTJ
ap-6103	152	276	,	,	PUNCT
ap-6103	152	277	-2	-2	INTJ
ap-6103	152	278	,	,	PUNCT
ap-6103	152	279	-1	-1	INTJ
ap-6103	152	280	,	,	PUNCT
ap-6103	152	281	0	0	NUM
ap-6103	152	282	,	,	PUNCT
ap-6103	152	283	1	1	NUM
ap-6103	152	284	,	,	PUNCT
ap-6103	152	285	9	9	NUM
ap-6103	152	286	-11	-11	PUNCT
ap-6103	152	287	-6	-6	ADV
ap-6103	152	288	,	,	PUNCT
ap-6103	152	289	-5	-5	INTJ
ap-6103	152	290	,	,	PUNCT
ap-6103	152	291	-4	-4	INTJ
ap-6103	152	292	,	,	PUNCT
ap-6103	152	293	-3	-3	INTJ
ap-6103	152	294	,	,	PUNCT
ap-6103	152	295	-2	-2	INTJ
ap-6103	152	296	,	,	PUNCT
ap-6103	152	297	-1	-1	INTJ
ap-6103	152	298	,	,	PUNCT
ap-6103	152	299	0	0	NUM
ap-6103	152	300	,	,	PUNCT
ap-6103	152	301	11	11	NUM
ap-6103	152	302	ks107	ks107	NOUN
ap-6103	152	303	-1	-1	INTJ
ap-6103	152	304	-1	-1	ADJ
ap-6103	152	305	,	,	PUNCT
ap-6103	152	306	0	0	NUM
ap-6103	152	307	,	,	PUNCT
ap-6103	152	308	1	1	NUM
ap-6103	152	309	(	(	PUNCT
ap-6103	152	310	bis	bis	ADJ
ap-6103	152	311	)	)	PUNCT
ap-6103	152	312	,	,	PUNCT
ap-6103	152	313	2	2	NUM
ap-6103	152	314	,	,	PUNCT
ap-6103	152	315	3	3	NUM
ap-6103	152	316	,	,	PUNCT
ap-6103	152	317	4	4	NUM
ap-6103	152	318	,	,	PUNCT
ap-6103	152	319	5	5	NUM
ap-6103	152	320	,	,	PUNCT
ap-6103	152	321	6	6	NUM
ap-6103	152	322	-3	-3	NOUN
ap-6103	152	323	-2	-2	NOUN
ap-6103	152	324	,	,	PUNCT
ap-6103	152	325	-1	-1	INTJ
ap-6103	152	326	,	,	PUNCT
ap-6103	152	327	0	0	NUM
ap-6103	152	328	,	,	PUNCT
ap-6103	152	329	1	1	NUM
ap-6103	152	330	,	,	PUNCT
ap-6103	152	331	2	2	NUM
ap-6103	152	332	,	,	PUNCT
ap-6103	152	333	3	3	NUM
ap-6103	152	334	(	(	PUNCT
ap-6103	152	335	bis	bis	PROPN
ap-6103	152	336	)	)	PUNCT
ap-6103	152	337	,	,	PUNCT
ap-6103	152	338	4	4	NUM
ap-6103	152	339	,	,	PUNCT
ap-6103	152	340	5	5	NUM
ap-6103	152	341	,	,	PUNCT
ap-6103	152	342	-5	-5	ADJ
ap-6103	152	343	-3	-3	ADJ
ap-6103	152	344	,	,	PUNCT
ap-6103	152	345	-2	-2	INTJ
ap-6103	152	346	,	,	PUNCT
ap-6103	152	347	-1	-1	INTJ
ap-6103	152	348	,	,	PUNCT
ap-6103	152	349	0	0	NUM
ap-6103	152	350	,	,	PUNCT
ap-6103	152	351	1	1	NUM
ap-6103	152	352	,	,	PUNCT
ap-6103	152	353	2	2	NUM
ap-6103	152	354	,	,	PUNCT
ap-6103	152	355	3	3	NUM
ap-6103	152	356	,	,	PUNCT
ap-6103	152	357	4	4	NUM
ap-6103	152	358	,	,	PUNCT
ap-6103	152	359	5	5	NUM
ap-6103	152	360	-7	-7	NOUN
ap-6103	152	361	-4	-4	PROPN
ap-6103	152	362	,	,	PUNCT
ap-6103	152	363	-3	-3	INTJ
ap-6103	152	364	,	,	PUNCT
ap-6103	152	365	-2	-2	INTJ
ap-6103	152	366	,	,	PUNCT
ap-6103	152	367	-1	-1	INTJ
ap-6103	152	368	,	,	PUNCT
ap-6103	152	369	0	0	NUM
ap-6103	152	370	,	,	PUNCT
ap-6103	152	371	1	1	NUM
ap-6103	152	372	,	,	PUNCT
ap-6103	152	373	2	2	NUM
ap-6103	152	374	,	,	PUNCT
ap-6103	152	375	3	3	NUM
ap-6103	152	376	,	,	PUNCT
ap-6103	152	377	7	7	NUM
ap-6103	152	378	-9	-9	NOUN
ap-6103	152	379	-5	-5	ADJ
ap-6103	152	380	,	,	PUNCT
ap-6103	152	381	-4	-4	INTJ
ap-6103	152	382	,	,	PUNCT
ap-6103	152	383	-3	-3	INTJ
ap-6103	152	384	,	,	PUNCT
ap-6103	152	385	-2	-2	INTJ
ap-6103	152	386	,	,	PUNCT
ap-6103	152	387	-1	-1	INTJ
ap-6103	152	388	,	,	PUNCT
ap-6103	152	389	0	0	NUM
ap-6103	152	390	,	,	PUNCT
ap-6103	152	391	1	1	NUM
ap-6103	152	392	,	,	PUNCT
ap-6103	152	393	2	2	NUM
ap-6103	152	394	,	,	PUNCT
ap-6103	152	395	9	9	NUM
ap-6103	152	396	-11	-11	PUNCT
ap-6103	152	397	-6	-6	ADV
ap-6103	152	398	,	,	PUNCT
ap-6103	152	399	-5	-5	INTJ
ap-6103	152	400	,	,	PUNCT
ap-6103	152	401	-4	-4	INTJ
ap-6103	152	402	,	,	PUNCT
ap-6103	152	403	-3	-3	INTJ
ap-6103	152	404	,	,	PUNCT
ap-6103	152	405	-2	-2	INTJ
ap-6103	152	406	,	,	PUNCT
ap-6103	152	407	-1	-1	INTJ
ap-6103	152	408	,	,	PUNCT
ap-6103	152	409	0	0	NUM
ap-6103	152	410	,	,	PUNCT
ap-6103	152	411	1	1	NUM
ap-6103	152	412	,	,	PUNCT
ap-6103	152	413	11	11	NUM
ap-6103	152	414	13	13	NUM
ap-6103	152	415	-7	-7	NOUN
ap-6103	152	416	,	,	PUNCT
ap-6103	152	417	-6	-6	INTJ
ap-6103	152	418	,	,	PUNCT
ap-6103	152	419	-5	-5	INTJ
ap-6103	152	420	,	,	PUNCT
ap-6103	152	421	-4	-4	INTJ
ap-6103	152	422	,	,	PUNCT
ap-6103	152	423	-3	-3	INTJ
ap-6103	152	424	,	,	PUNCT
ap-6103	152	425	-2	-2	INTJ
ap-6103	152	426	,	,	PUNCT
ap-6103	152	427	-1	-1	INTJ
ap-6103	152	428	,	,	PUNCT
ap-6103	152	429	0	0	NUM
ap-6103	152	430	,	,	PUNCT
ap-6103	152	431	13	13	NUM
ap-6103	152	432	ks108	ks108	NOUN
ap-6103	152	433	-1	-1	PUNCT
ap-6103	153	1	-1	-1	ADJ
ap-6103	153	2	,	,	PUNCT
ap-6103	153	3	0	0	NUM
ap-6103	153	4	,	,	PUNCT
ap-6103	153	5	1	1	NUM
ap-6103	153	6	(	(	PUNCT
ap-6103	153	7	bis	bis	ADJ
ap-6103	153	8	)	)	PUNCT
ap-6103	153	9	,	,	PUNCT
ap-6103	153	10	2	2	NUM
ap-6103	153	11	,	,	PUNCT
ap-6103	153	12	3	3	NUM
ap-6103	153	13	,	,	PUNCT
ap-6103	153	14	4	4	NUM
ap-6103	153	15	,	,	PUNCT
ap-6103	153	16	5	5	NUM
ap-6103	153	17	,	,	PUNCT
ap-6103	153	18	6	6	NUM
ap-6103	153	19	,	,	PUNCT
ap-6103	153	20	7	7	NUM
ap-6103	153	21	-3	-3	INTJ
ap-6103	153	22	-2	-2	INTJ
ap-6103	153	23	,	,	PUNCT
ap-6103	153	24	-1	-1	INTJ
ap-6103	153	25	,	,	PUNCT
ap-6103	153	26	0	0	NUM
ap-6103	153	27	,	,	PUNCT
ap-6103	153	28	1	1	NUM
ap-6103	153	29	,	,	PUNCT
ap-6103	153	30	2	2	NUM
ap-6103	153	31	,	,	PUNCT
ap-6103	153	32	3	3	NUM
ap-6103	153	33	(	(	PUNCT
ap-6103	153	34	bis	bis	PROPN
ap-6103	153	35	)	)	PUNCT
ap-6103	153	36	,	,	PUNCT
ap-6103	153	37	4	4	NUM
ap-6103	153	38	,	,	PUNCT
ap-6103	153	39	5	5	NUM
ap-6103	153	40	,	,	PUNCT
ap-6103	153	41	6	6	NUM
ap-6103	153	42	-5	-5	NOUN
ap-6103	153	43	-3	-3	INTJ
ap-6103	153	44	,	,	PUNCT
ap-6103	153	45	-2	-2	INTJ
ap-6103	153	46	,	,	PUNCT
ap-6103	153	47	-1	-1	INTJ
ap-6103	153	48	,	,	PUNCT
ap-6103	153	49	0	0	NUM
ap-6103	153	50	,	,	PUNCT
ap-6103	153	51	1	1	NUM
ap-6103	153	52	,	,	PUNCT
ap-6103	153	53	2	2	NUM
ap-6103	153	54	,	,	PUNCT
ap-6103	153	55	3	3	NUM
ap-6103	153	56	,	,	PUNCT
ap-6103	153	57	4	4	NUM
ap-6103	153	58	,	,	PUNCT
ap-6103	153	59	5	5	NUM
ap-6103	153	60	(	(	PUNCT
ap-6103	153	61	bis	bis	PROPN
ap-6103	153	62	)	)	PUNCT
ap-6103	153	63	-7	-7	NOUN
ap-6103	154	1	-4	-4	INTJ
ap-6103	154	2	,	,	PUNCT
ap-6103	154	3	-3	-3	INTJ
ap-6103	154	4	,	,	PUNCT
ap-6103	154	5	-2	-2	INTJ
ap-6103	154	6	,	,	PUNCT
ap-6103	154	7	-1	-1	INTJ
ap-6103	154	8	,	,	PUNCT
ap-6103	154	9	0	0	NUM
ap-6103	154	10	,	,	PUNCT
ap-6103	154	11	1	1	NUM
ap-6103	154	12	,	,	PUNCT
ap-6103	154	13	2	2	NUM
ap-6103	154	14	,	,	PUNCT
ap-6103	154	15	3	3	NUM
ap-6103	154	16	,	,	PUNCT
ap-6103	154	17	4	4	NUM
ap-6103	154	18	,	,	PUNCT
ap-6103	154	19	7	7	NUM
ap-6103	154	20	-9	-9	NOUN
ap-6103	154	21	-5	-5	ADJ
ap-6103	154	22	,	,	PUNCT
ap-6103	154	23	-4	-4	INTJ
ap-6103	154	24	,	,	PUNCT
ap-6103	154	25	-3	-3	INTJ
ap-6103	154	26	,	,	PUNCT
ap-6103	154	27	-2	-2	INTJ
ap-6103	154	28	,	,	PUNCT
ap-6103	154	29	-1	-1	INTJ
ap-6103	154	30	,	,	PUNCT
ap-6103	154	31	0	0	NUM
ap-6103	154	32	,	,	PUNCT
ap-6103	154	33	1	1	NUM
ap-6103	154	34	,	,	PUNCT
ap-6103	154	35	2	2	NUM
ap-6103	154	36	,	,	PUNCT
ap-6103	154	37	3	3	NUM
ap-6103	154	38	,	,	PUNCT
ap-6103	154	39	9	9	NUM
ap-6103	154	40	-11	-11	PUNCT
ap-6103	154	41	-6	-6	ADV
ap-6103	154	42	,	,	PUNCT
ap-6103	154	43	-5	-5	INTJ
ap-6103	154	44	,	,	PUNCT
ap-6103	154	45	-4	-4	INTJ
ap-6103	154	46	,	,	PUNCT
ap-6103	154	47	-3	-3	INTJ
ap-6103	154	48	,	,	PUNCT
ap-6103	154	49	-2	-2	INTJ
ap-6103	154	50	,	,	PUNCT
ap-6103	154	51	-1	-1	INTJ
ap-6103	154	52	,	,	PUNCT
ap-6103	154	53	0	0	NUM
ap-6103	154	54	,	,	PUNCT
ap-6103	154	55	1	1	NUM
ap-6103	154	56	,	,	PUNCT
ap-6103	154	57	2	2	NUM
ap-6103	154	58	,	,	PUNCT
ap-6103	154	59	11	11	NUM
ap-6103	154	60	13	13	NUM
ap-6103	154	61	-7	-7	NOUN
ap-6103	154	62	,	,	PUNCT
ap-6103	154	63	-6	-6	INTJ
ap-6103	154	64	,	,	PUNCT
ap-6103	154	65	-5	-5	INTJ
ap-6103	154	66	,	,	PUNCT
ap-6103	154	67	-4	-4	INTJ
ap-6103	154	68	,	,	PUNCT
ap-6103	154	69	-3	-3	INTJ
ap-6103	154	70	,	,	PUNCT
ap-6103	154	71	-2	-2	INTJ
ap-6103	154	72	,	,	PUNCT
ap-6103	154	73	-1	-1	INTJ
ap-6103	154	74	,	,	PUNCT
ap-6103	154	75	0	0	NUM
ap-6103	154	76	,	,	PUNCT
ap-6103	154	77	1	1	NUM
ap-6103	154	78	,	,	PUNCT
ap-6103	154	79	13	13	NUM
ap-6103	154	80	-15	-15	SYM
ap-6103	154	81	-8	-8	NOUN
ap-6103	154	82	,	,	PUNCT
ap-6103	154	83	-7	-7	INTJ
ap-6103	154	84	,	,	PUNCT
ap-6103	154	85	-6	-6	INTJ
ap-6103	154	86	,	,	PUNCT
ap-6103	154	87	-5	-5	INTJ
ap-6103	154	88	,	,	PUNCT
ap-6103	154	89	-4	-4	INTJ
ap-6103	154	90	,	,	PUNCT
ap-6103	154	91	-3	-3	INTJ
ap-6103	154	92	,	,	PUNCT
ap-6103	154	93	-2	-2	INTJ
ap-6103	154	94	,	,	PUNCT
ap-6103	154	95	-1	-1	INTJ
ap-6103	154	96	,	,	PUNCT
ap-6103	154	97	0	0	NUM
ap-6103	154	98	,	,	PUNCT
ap-6103	154	99	15	15	NUM
ap-6103	154	100	table	table	NOUN
ap-6103	154	101	2	2	NUM
ap-6103	154	102	.	.	PUNCT
ap-6103	154	103	kummer	kummer	NOUN
ap-6103	154	104	-	-	PUNCT
ap-6103	154	105	schwarz	schwarz	PROPN
ap-6103	154	106	sequence	sequence	NOUN
ap-6103	154	107	:	:	PUNCT
ap-6103	154	108	resonances	resonance	NOUN
ap-6103	154	109	for	for	ADP
ap-6103	154	110	the	the	DET
ap-6103	154	111	permissible	permissible	ADJ
ap-6103	154	112	values	value	NOUN
ap-6103	154	113	of	of	ADP
ap-6103	154	114	the	the	DET
ap-6103	154	115	exponent	exponent	NOUN
ap-6103	154	116	of	of	ADP
ap-6103	154	117	the	the	DET
ap-6103	154	118	leading	lead	VERB
ap-6103	154	119	-	-	PUNCT
ap-6103	154	120	order	order	NOUN
ap-6103	154	121	term	term	NOUN
ap-6103	154	122	432	432	NUM
ap-6103	154	123	vol	vol	NOUN
ap-6103	154	124	.	.	PUNCT
ap-6103	155	1	60	60	NUM
ap-6103	155	2	no	no	NOUN
ap-6103	155	3	.	.	PUNCT
ap-6103	156	1	5/2020	5/2020	NUM
ap-6103	156	2	properties	property	NOUN
ap-6103	156	3	of	of	ADP
ap-6103	156	4	a	a	DET
ap-6103	156	5	differential	differential	ADJ
ap-6103	156	6	sequence	sequence	NOUN
ap-6103	156	7	based	base	VERB
ap-6103	156	8	upon	upon	SCONJ
ap-6103	156	9	the	the	DET
ap-6103	156	10	kummer	kummer	NOUN
ap-6103	156	11	-	-	PUNCT
ap-6103	156	12	schwarz	schwarz	PROPN
ap-6103	156	13	.	.	PUNCT
ap-6103	156	14	.	.	PUNCT
ap-6103	156	15	.	.	PUNCT
ap-6103	157	1	where	where	SCONJ
ap-6103	157	2	p3(x	p3(x	X
ap-6103	157	3	)	)	PUNCT
ap-6103	157	4	is	be	AUX
ap-6103	157	5	a	a	DET
ap-6103	157	6	polynomial	polynomial	NOUN
ap-6103	157	7	of	of	ADP
ap-6103	157	8	degree	degree	NOUN
ap-6103	157	9	three	three	NUM
ap-6103	157	10	in	in	ADP
ap-6103	157	11	x.	x.	NOUN
ap-6103	157	12	consequently	consequently	ADV
ap-6103	157	13	,	,	PUNCT
ap-6103	157	14	the	the	DET
ap-6103	157	15	solution	solution	NOUN
ap-6103	157	16	of	of	ADP
ap-6103	157	17	(	(	PUNCT
ap-6103	157	18	22	22	NUM
ap-6103	157	19	)	)	PUNCT
ap-6103	157	20	can	can	AUX
ap-6103	157	21	be	be	AUX
ap-6103	157	22	written	write	VERB
ap-6103	157	23	in	in	ADP
ap-6103	157	24	terms	term	NOUN
ap-6103	157	25	of	of	ADP
ap-6103	157	26	the	the	DET
ap-6103	157	27	quadrature	quadrature	NOUN
ap-6103	157	28	,	,	PUNCT
ap-6103	157	29	u(x	u(x	PROPN
ap-6103	157	30	)	)	PUNCT
ap-6103	158	1	=	=	SYM
ap-6103	158	2	∫	∫	PROPN
ap-6103	158	3	dx	dx	PROPN
ap-6103	158	4	p3(x)2	p3(x)2	PROPN
ap-6103	158	5	+	+	CCONJ
ap-6103	158	6	m.	m.	NOUN
ap-6103	158	7	(	(	PUNCT
ap-6103	158	8	25	25	NUM
ap-6103	158	9	)	)	PUNCT
ap-6103	158	10	the	the	DET
ap-6103	158	11	evaluation	evaluation	NOUN
ap-6103	158	12	of	of	ADP
ap-6103	158	13	the	the	DET
ap-6103	158	14	quadrature	quadrature	NOUN
ap-6103	158	15	in	in	ADP
ap-6103	158	16	(	(	PUNCT
ap-6103	158	17	25	25	NUM
ap-6103	158	18	)	)	PUNCT
ap-6103	158	19	is	be	AUX
ap-6103	158	20	,	,	PUNCT
ap-6103	158	21	in	in	ADP
ap-6103	158	22	principle	principle	NOUN
ap-6103	158	23	,	,	PUNCT
ap-6103	158	24	a	a	DET
ap-6103	158	25	simple	simple	ADJ
ap-6103	158	26	matter	matter	NOUN
ap-6103	158	27	due	due	ADP
ap-6103	158	28	to	to	ADP
ap-6103	158	29	the	the	DET
ap-6103	158	30	fundamental	fundamental	ADJ
ap-6103	158	31	theorem	theorem	NOUN
ap-6103	158	32	of	of	ADP
ap-6103	158	33	algebra	algebra	NOUN
ap-6103	158	34	and	and	CCONJ
ap-6103	158	35	the	the	DET
ap-6103	158	36	use	use	NOUN
ap-6103	158	37	of	of	ADP
ap-6103	158	38	partial	partial	ADJ
ap-6103	158	39	fractions	fraction	NOUN
ap-6103	158	40	.	.	PUNCT
ap-6103	159	1	however	however	ADV
ap-6103	159	2	,	,	PUNCT
ap-6103	159	3	the	the	DET
ap-6103	159	4	interpretation	interpretation	NOUN
ap-6103	159	5	of	of	ADP
ap-6103	159	6	the	the	DET
ap-6103	159	7	results	result	NOUN
ap-6103	159	8	of	of	ADP
ap-6103	159	9	the	the	DET
ap-6103	159	10	singularity	singularity	NOUN
ap-6103	159	11	analysis	analysis	NOUN
ap-6103	159	12	obtained	obtain	VERB
ap-6103	159	13	above	above	ADV
ap-6103	159	14	requires	require	VERB
ap-6103	159	15	that	that	SCONJ
ap-6103	159	16	the	the	DET
ap-6103	159	17	quadrature	quadrature	NOUN
ap-6103	159	18	is	be	AUX
ap-6103	159	19	to	to	PART
ap-6103	159	20	be	be	AUX
ap-6103	159	21	approached	approach	VERB
ap-6103	159	22	with	with	ADP
ap-6103	159	23	a	a	DET
ap-6103	159	24	certain	certain	ADJ
ap-6103	159	25	degree	degree	NOUN
ap-6103	159	26	of	of	ADP
ap-6103	159	27	delicacy	delicacy	NOUN
ap-6103	159	28	to	to	PART
ap-6103	159	29	illustrate	illustrate	VERB
ap-6103	159	30	the	the	DET
ap-6103	159	31	different	different	ADJ
ap-6103	159	32	possibilities	possibility	NOUN
ap-6103	159	33	.	.	PUNCT
ap-6103	160	1	we	we	PRON
ap-6103	160	2	commence	commence	VERB
ap-6103	160	3	with	with	ADP
ap-6103	160	4	the	the	DET
ap-6103	160	5	case	case	NOUN
ap-6103	160	6	p	p	X
ap-6103	160	7	=	=	PUNCT
ap-6103	160	8	−1	−1	NOUN
ap-6103	160	9	and	and	CCONJ
ap-6103	160	10	write	write	VERB
ap-6103	160	11	the	the	DET
ap-6103	160	12	solution	solution	NOUN
ap-6103	160	13	in	in	ADP
ap-6103	160	14	terms	term	NOUN
ap-6103	160	15	of	of	ADP
ap-6103	160	16	a	a	DET
ap-6103	160	17	polynomial	polynomial	NOUN
ap-6103	160	18	about	about	ADP
ap-6103	160	19	the	the	DET
ap-6103	160	20	singularity	singularity	NOUN
ap-6103	160	21	at	at	ADP
ap-6103	160	22	x0	x0	PROPN
ap-6103	160	23	in	in	ADP
ap-6103	160	24	terms	term	NOUN
ap-6103	160	25	of	of	ADP
ap-6103	160	26	the	the	DET
ap-6103	160	27	variable	variable	ADJ
ap-6103	160	28	χ	χ	X
ap-6103	160	29	=	=	PUNCT
ap-6103	160	30	x−	x−	PROPN
ap-6103	160	31	x0	x0	PROPN
ap-6103	160	32	.	.	PUNCT
ap-6103	161	1	we	we	PRON
ap-6103	161	2	have	have	VERB
ap-6103	161	3	p3(x	p3(x	NOUN
ap-6103	161	4	)	)	PUNCT
ap-6103	161	5	=	=	PUNCT
ap-6103	161	6	kχ(χ−	kχ(χ−	VERB
ap-6103	161	7	a)(χ−	a)(χ−	NOUN
ap-6103	161	8	b	b	NOUN
ap-6103	161	9	)	)	PUNCT
ap-6103	161	10	,	,	PUNCT
ap-6103	161	11	(	(	PUNCT
ap-6103	161	12	26	26	NUM
ap-6103	161	13	)	)	PUNCT
ap-6103	161	14	where	where	SCONJ
ap-6103	161	15	we	we	PRON
ap-6103	161	16	have	have	AUX
ap-6103	161	17	written	write	VERB
ap-6103	161	18	the	the	DET
ap-6103	161	19	factors	factor	NOUN
ap-6103	161	20	in	in	ADP
ap-6103	161	21	the	the	DET
ap-6103	161	22	sense	sense	NOUN
ap-6103	161	23	that	that	SCONJ
ap-6103	161	24	0	0	PUNCT
ap-6103	161	25	<	<	X
ap-6103	161	26	|a|	|a|	NOUN
ap-6103	161	27	≤	≤	NOUN
ap-6103	161	28	|b|	|b|	VERB
ap-6103	161	29	to	to	PART
ap-6103	161	30	empathise	empathise	VERB
ap-6103	161	31	that	that	SCONJ
ap-6103	161	32	we	we	PRON
ap-6103	161	33	are	be	AUX
ap-6103	161	34	dealing	deal	VERB
ap-6103	161	35	with	with	ADP
ap-6103	161	36	a	a	DET
ap-6103	161	37	simple	simple	ADJ
ap-6103	161	38	pole	pole	NOUN
ap-6103	161	39	at	at	ADP
ap-6103	161	40	x0	x0	PROPN
ap-6103	161	41	.	.	PUNCT
ap-6103	162	1	when	when	SCONJ
ap-6103	162	2	we	we	PRON
ap-6103	162	3	substitute	substitute	VERB
ap-6103	162	4	(	(	PUNCT
ap-6103	162	5	26	26	NUM
ap-6103	162	6	)	)	PUNCT
ap-6103	162	7	into	into	ADP
ap-6103	162	8	(	(	PUNCT
ap-6103	162	9	25	25	NUM
ap-6103	162	10	)	)	PUNCT
ap-6103	162	11	,	,	PUNCT
ap-6103	162	12	we	we	PRON
ap-6103	162	13	obtain	obtain	VERB
ap-6103	162	14	u(x	u(x	NOUN
ap-6103	162	15	)	)	PUNCT
ap-6103	163	1	=	=	SYM
ap-6103	163	2	∫	∫	PROPN
ap-6103	163	3	dx	dx	PROPN
ap-6103	163	4	(	(	PUNCT
ap-6103	163	5	kχ(χ−	kχ(χ−	VERB
ap-6103	163	6	a)(χ−	a)(χ−	NOUN
ap-6103	163	7	b))2	b))2	NOUN
ap-6103	163	8	+	+	NOUN
ap-6103	163	9	m.	m.	NOUN
ap-6103	163	10	(	(	PUNCT
ap-6103	163	11	27	27	NUM
ap-6103	163	12	)	)	PUNCT
ap-6103	163	13	we	we	PRON
ap-6103	163	14	may	may	AUX
ap-6103	163	15	write	write	VERB
ap-6103	163	16	the	the	DET
ap-6103	163	17	integrand	integrand	NOUN
ap-6103	163	18	of	of	ADP
ap-6103	163	19	(	(	PUNCT
ap-6103	163	20	27	27	NUM
ap-6103	163	21	)	)	PUNCT
ap-6103	163	22	as	as	ADP
ap-6103	163	23	1	1	NUM
ap-6103	163	24	k2χ2a2b2	k2χ2a2b2	NOUN
ap-6103	163	25	(	(	PUNCT
ap-6103	163	26	1−	1−	NUM
ap-6103	163	27	χ	χ	DET
ap-6103	163	28	a	a	DET
ap-6103	163	29	)	)	PUNCT
ap-6103	163	30	−2	−2	NOUN
ap-6103	163	31	(	(	PUNCT
ap-6103	163	32	1−	1−	NUM
ap-6103	163	33	χ	χ	PRON
ap-6103	163	34	b	b	X
ap-6103	163	35	)	)	PUNCT
ap-6103	163	36	−2	−2	NOUN
ap-6103	163	37	.	.	PUNCT
ap-6103	164	1	(	(	PUNCT
ap-6103	164	2	28	28	NUM
ap-6103	164	3	)	)	PUNCT
ap-6103	164	4	after	after	ADP
ap-6103	164	5	applying	apply	VERB
ap-6103	164	6	the	the	DET
ap-6103	164	7	binomial	binomial	ADJ
ap-6103	164	8	expansion	expansion	NOUN
ap-6103	164	9	and	and	CCONJ
ap-6103	164	10	simplifying	simplifying	NOUN
ap-6103	164	11	,	,	PUNCT
ap-6103	164	12	we	we	PRON
ap-6103	164	13	may	may	AUX
ap-6103	164	14	write	write	VERB
ap-6103	164	15	(	(	PUNCT
ap-6103	164	16	28	28	NUM
ap-6103	164	17	)	)	PUNCT
ap-6103	164	18	as	as	ADP
ap-6103	164	19	1	1	NUM
ap-6103	164	20	k2a2b2	k2a2b2	NOUN
ap-6103	164	21	[	[	PUNCT
ap-6103	164	22	1	1	NUM
ap-6103	164	23	χ2	χ2	NOUN
ap-6103	164	24	−	−	PROPN
ap-6103	164	25	2	2	NUM
ap-6103	164	26	(	(	PUNCT
ap-6103	164	27	1	1	NUM
ap-6103	164	28	a	a	DET
ap-6103	164	29	+	+	NUM
ap-6103	164	30	1	1	NUM
ap-6103	164	31	b	b	NOUN
ap-6103	164	32	)	)	PUNCT
ap-6103	164	33	1	1	NUM
ap-6103	164	34	χ	χ	NOUN
ap-6103	164	35	+	+	CCONJ
ap-6103	164	36	(	(	PUNCT
ap-6103	164	37	3	3	NUM
ap-6103	164	38	a2	a2	PROPN
ap-6103	164	39	+	+	CCONJ
ap-6103	164	40	3	3	NUM
ap-6103	164	41	b2	b2	NOUN
ap-6103	164	42	+	+	CCONJ
ap-6103	164	43	4	4	NUM
ap-6103	164	44	ab	ab	NOUN
ap-6103	164	45	)	)	PUNCT
ap-6103	165	1	+2	+2	PROPN
ap-6103	165	2	(	(	PUNCT
ap-6103	165	3	2	2	NUM
ap-6103	165	4	a3	a3	NOUN
ap-6103	165	5	+	+	CCONJ
ap-6103	165	6	2	2	NUM
ap-6103	165	7	b3	b3	NOUN
ap-6103	165	8	−	−	NOUN
ap-6103	165	9	3	3	NUM
ap-6103	165	10	ab2	ab2	NOUN
ap-6103	165	11	−	−	PROPN
ap-6103	165	12	3	3	NUM
ap-6103	165	13	a2b	a2b	NOUN
ap-6103	165	14	)	)	PUNCT
ap-6103	165	15	χ	χ	ADP
ap-6103	165	16	...	...	PUNCT
ap-6103	165	17	]	]	PUNCT
ap-6103	165	18	.	.	PUNCT
ap-6103	166	1	(	(	PUNCT
ap-6103	166	2	29	29	NUM
ap-6103	166	3	)	)	PUNCT
ap-6103	166	4	when	when	SCONJ
ap-6103	166	5	we	we	PRON
ap-6103	166	6	substitute	substitute	VERB
ap-6103	166	7	(	(	PUNCT
ap-6103	166	8	29	29	NUM
ap-6103	166	9	)	)	PUNCT
ap-6103	166	10	into	into	ADP
ap-6103	166	11	(	(	PUNCT
ap-6103	166	12	27	27	NUM
ap-6103	166	13	)	)	PUNCT
ap-6103	166	14	and	and	CCONJ
ap-6103	166	15	perform	perform	VERB
ap-6103	166	16	the	the	DET
ap-6103	166	17	quadrature	quadrature	NOUN
ap-6103	166	18	,	,	PUNCT
ap-6103	166	19	we	we	PRON
ap-6103	166	20	obtain	obtain	VERB
ap-6103	166	21	u(x	u(x	NOUN
ap-6103	166	22	)	)	PUNCT
ap-6103	167	1	=	=	PUNCT
ap-6103	167	2	m	m	VERB
ap-6103	167	3	−	−	NUM
ap-6103	167	4	1	1	NUM
ap-6103	167	5	k2a2b2	k2a2b2	NOUN
ap-6103	167	6	[	[	PUNCT
ap-6103	167	7	1	1	NUM
ap-6103	167	8	χ	χ	NOUN
ap-6103	167	9	+	+	NOUN
ap-6103	167	10	2	2	NUM
ap-6103	167	11	(	(	PUNCT
ap-6103	167	12	1	1	NUM
ap-6103	167	13	a	a	DET
ap-6103	167	14	+	+	NUM
ap-6103	167	15	1	1	NUM
ap-6103	167	16	b	b	NOUN
ap-6103	167	17	)	)	PUNCT
ap-6103	167	18	logχ	logχ	NOUN
ap-6103	168	1	−	−	PROPN
ap-6103	168	2	(	(	PUNCT
ap-6103	168	3	3	3	NUM
ap-6103	168	4	a2	a2	PROPN
ap-6103	168	5	+	+	CCONJ
ap-6103	168	6	3	3	NUM
ap-6103	168	7	b2	b2	NOUN
ap-6103	168	8	−	−	PROPN
ap-6103	168	9	4	4	NUM
ap-6103	168	10	ab	ab	PROPN
ap-6103	168	11	)	)	PUNCT
ap-6103	169	1	χ	χ	PRON
ap-6103	169	2	−	−	PROPN
ap-6103	169	3	(	(	PUNCT
ap-6103	169	4	2	2	NUM
ap-6103	169	5	a3	a3	NOUN
ap-6103	169	6	+	+	CCONJ
ap-6103	169	7	2	2	NUM
ap-6103	169	8	b3	b3	NOUN
ap-6103	169	9	−	−	NOUN
ap-6103	169	10	3	3	NUM
ap-6103	169	11	ab2	ab2	NOUN
ap-6103	169	12	−	−	PROPN
ap-6103	169	13	3	3	NUM
ap-6103	169	14	a2b	a2b	PROPN
ap-6103	169	15	)	)	PUNCT
ap-6103	169	16	χ2	χ2	PROPN
ap-6103	169	17	...	...	PUNCT
ap-6103	169	18	]	]	PUNCT
ap-6103	169	19	.	.	PUNCT
ap-6103	170	1	(	(	PUNCT
ap-6103	170	2	30	30	NUM
ap-6103	170	3	)	)	PUNCT
ap-6103	170	4	the	the	DET
ap-6103	170	5	occurrence	occurrence	NOUN
ap-6103	170	6	of	of	ADP
ap-6103	170	7	the	the	DET
ap-6103	170	8	unfortunate	unfortunate	ADJ
ap-6103	170	9	logarithm	logarithm	NOUN
ap-6103	170	10	and	and	CCONJ
ap-6103	170	11	the	the	DET
ap-6103	170	12	requisite	requisite	ADJ
ap-6103	170	13	number	number	NOUN
ap-6103	170	14	of	of	ADP
ap-6103	170	15	constants	constant	NOUN
ap-6103	170	16	of	of	ADP
ap-6103	170	17	integration	integration	NOUN
ap-6103	170	18	(	(	PUNCT
ap-6103	170	19	five	five	NUM
ap-6103	170	20	in	in	ADP
ap-6103	170	21	this	this	DET
ap-6103	170	22	case	case	NOUN
ap-6103	170	23	,	,	PUNCT
ap-6103	170	24	k	k	NOUN
ap-6103	170	25	,	,	PUNCT
ap-6103	170	26	a	a	DET
ap-6103	170	27	,	,	PUNCT
ap-6103	170	28	b	b	NOUN
ap-6103	170	29	,	,	PUNCT
ap-6103	170	30	x0	x0	PROPN
ap-6103	170	31	and	and	CCONJ
ap-6103	170	32	m	m	NOUN
ap-6103	170	33	)	)	PUNCT
ap-6103	170	34	is	be	AUX
ap-6103	170	35	obvious	obvious	ADJ
ap-6103	170	36	.	.	PUNCT
ap-6103	171	1	the	the	DET
ap-6103	171	2	quadrature	quadrature	NOUN
ap-6103	171	3	evaluated	evaluate	VERB
ap-6103	171	4	above	above	ADV
ap-6103	171	5	is	be	AUX
ap-6103	171	6	valid	valid	ADJ
ap-6103	171	7	to	to	ADP
ap-6103	171	8	the	the	DET
ap-6103	171	9	next	next	ADJ
ap-6103	171	10	singularity	singularity	NOUN
ap-6103	171	11	at	at	ADP
ap-6103	171	12	χ	χ	NOUN
ap-6103	171	13	=	=	PUNCT
ap-6103	171	14	a.	a.	NOUN
ap-6103	171	15	for	for	ADP
ap-6103	171	16	the	the	DET
ap-6103	171	17	case	case	NOUN
ap-6103	171	18	p	p	X
ap-6103	171	19	=	=	NOUN
ap-6103	171	20	−5	−5	ADJ
ap-6103	171	21	,	,	PUNCT
ap-6103	171	22	we	we	PRON
ap-6103	171	23	may	may	AUX
ap-6103	171	24	write	write	VERB
ap-6103	171	25	the	the	DET
ap-6103	171	26	integrand	integrand	NOUN
ap-6103	171	27	of	of	ADP
ap-6103	171	28	(	(	PUNCT
ap-6103	171	29	27	27	NUM
ap-6103	171	30	)	)	PUNCT
ap-6103	171	31	as	as	ADP
ap-6103	171	32	1	1	NUM
ap-6103	171	33	k2χ6	k2χ6	PROPN
ap-6103	171	34	(	(	PUNCT
ap-6103	171	35	1−	1−	NUM
ap-6103	171	36	a	a	DET
ap-6103	171	37	k	k	NOUN
ap-6103	171	38	)	)	PUNCT
ap-6103	171	39	−2	−2	PROPN
ap-6103	171	40	(	(	PUNCT
ap-6103	171	41	1−	1−	NUM
ap-6103	171	42	b	b	X
ap-6103	171	43	k	k	NOUN
ap-6103	171	44	)	)	PUNCT
ap-6103	171	45	−2	−2	NOUN
ap-6103	171	46	.	.	PUNCT
ap-6103	172	1	(	(	PUNCT
ap-6103	172	2	31	31	NUM
ap-6103	172	3	)	)	PUNCT
ap-6103	172	4	after	after	ADP
ap-6103	172	5	the	the	DET
ap-6103	172	6	application	application	NOUN
ap-6103	172	7	of	of	ADP
ap-6103	172	8	the	the	DET
ap-6103	172	9	binomial	binomial	ADJ
ap-6103	172	10	expansion	expansion	NOUN
ap-6103	172	11	and	and	CCONJ
ap-6103	172	12	simplification	simplification	NOUN
ap-6103	172	13	of	of	ADP
ap-6103	172	14	(	(	PUNCT
ap-6103	172	15	31	31	NUM
ap-6103	172	16	)	)	PUNCT
ap-6103	172	17	,	,	PUNCT
ap-6103	172	18	we	we	PRON
ap-6103	172	19	obtain	obtain	VERB
ap-6103	172	20	1	1	NUM
ap-6103	172	21	k2χ6	k2χ6	PROPN
ap-6103	172	22	[	[	PUNCT
ap-6103	172	23	1−	1−	NUM
ap-6103	172	24	2(a+	2(a+	NUM
ap-6103	172	25	b	b	NOUN
ap-6103	172	26	)	)	PUNCT
ap-6103	172	27	χ	χ	NOUN
ap-6103	172	28	+	+	NUM
ap-6103	172	29	3(a2	3(a2	NUM
ap-6103	172	30	+	+	CCONJ
ap-6103	172	31	b2	b2	NOUN
ap-6103	172	32	)	)	PUNCT
ap-6103	172	33	+	+	NUM
ap-6103	172	34	4ab	4ab	ADJ
ap-6103	172	35	χ2	χ2	PROPN
ap-6103	172	36	−4(a3	−4(a3	X
ap-6103	172	37	+	+	PUNCT
ap-6103	172	38	b3	b3	NOUN
ap-6103	172	39	)	)	PUNCT
ap-6103	172	40	+	+	CCONJ
ap-6103	172	41	6a2b2	6a2b2	NUM
ap-6103	172	42	+	+	CCONJ
ap-6103	172	43	6ab2	6ab2	NUM
ap-6103	172	44	χ3	χ3	NOUN
ap-6103	172	45	...	...	PUNCT
ap-6103	172	46	]	]	PUNCT
ap-6103	172	47	.	.	PUNCT
ap-6103	173	1	(	(	PUNCT
ap-6103	173	2	32	32	NUM
ap-6103	173	3	)	)	PUNCT
ap-6103	173	4	when	when	SCONJ
ap-6103	173	5	we	we	PRON
ap-6103	173	6	substitute	substitute	VERB
ap-6103	173	7	(	(	PUNCT
ap-6103	173	8	32	32	NUM
ap-6103	173	9	)	)	PUNCT
ap-6103	173	10	into	into	ADP
ap-6103	173	11	(	(	PUNCT
ap-6103	173	12	27	27	NUM
ap-6103	173	13	)	)	PUNCT
ap-6103	173	14	and	and	CCONJ
ap-6103	173	15	perform	perform	VERB
ap-6103	173	16	the	the	DET
ap-6103	173	17	quadrature	quadrature	NOUN
ap-6103	173	18	,	,	PUNCT
ap-6103	173	19	we	we	PRON
ap-6103	173	20	have	have	VERB
ap-6103	173	21	u(x	u(x	NOUN
ap-6103	173	22	)	)	PUNCT
ap-6103	173	23	=	=	SYM
ap-6103	173	24	1	1	NUM
ap-6103	173	25	k2	k2	NOUN
ap-6103	173	26	[	[	PUNCT
ap-6103	173	27	−	−	PROPN
ap-6103	173	28	1	1	NUM
ap-6103	173	29	5χ5	5χ5	NUM
ap-6103	173	30	+	+	CCONJ
ap-6103	173	31	(	(	PUNCT
ap-6103	173	32	a+	a+	X
ap-6103	173	33	b	b	NOUN
ap-6103	173	34	)	)	PUNCT
ap-6103	173	35	4χ6	4χ6	NUM
ap-6103	173	36	−	−	NUM
ap-6103	173	37	3(a2	3(a2	NUM
ap-6103	173	38	+	+	NUM
ap-6103	173	39	b2	b2	NOUN
ap-6103	173	40	)	)	PUNCT
ap-6103	174	1	+	+	X
ap-6103	174	2	4ab	4ab	ADJ
ap-6103	174	3	7χ7	7χ7	NUM
ap-6103	174	4	+2(a3	+2(a3	X
ap-6103	175	1	+	+	CCONJ
ap-6103	175	2	b3	b3	NOUN
ap-6103	175	3	)	)	PUNCT
ap-6103	176	1	+	+	CCONJ
ap-6103	176	2	3a2b+	3a2b+	NUM
ap-6103	176	3	3ab2	3ab2	NUM
ap-6103	176	4	4χ8	4χ8	NUM
ap-6103	176	5	...	...	PUNCT
ap-6103	177	1	]	]	PUNCT
ap-6103	178	1	+	+	ADV
ap-6103	178	2	m	m	X
ap-6103	178	3	,	,	PUNCT
ap-6103	178	4	(	(	PUNCT
ap-6103	178	5	33	33	NUM
ap-6103	178	6	)	)	PUNCT
ap-6103	178	7	where	where	SCONJ
ap-6103	178	8	the	the	DET
ap-6103	178	9	requisite	requisite	ADJ
ap-6103	178	10	number	number	NOUN
ap-6103	178	11	of	of	ADP
ap-6103	178	12	constants	constant	NOUN
ap-6103	178	13	of	of	ADP
ap-6103	178	14	integration	integration	NOUN
ap-6103	178	15	is	be	AUX
ap-6103	178	16	also	also	ADV
ap-6103	178	17	obvious	obvious	ADJ
ap-6103	178	18	.	.	PUNCT
ap-6103	179	1	finally	finally	ADV
ap-6103	179	2	,	,	PUNCT
ap-6103	179	3	we	we	PRON
ap-6103	179	4	consider	consider	VERB
ap-6103	179	5	the	the	DET
ap-6103	179	6	case	case	NOUN
ap-6103	179	7	p	p	X
ap-6103	179	8	=	=	NOUN
ap-6103	179	9	−3	−3	ADJ
ap-6103	179	10	where	where	SCONJ
ap-6103	179	11	the	the	DET
ap-6103	179	12	full	full	ADJ
ap-6103	179	13	series	series	NOUN
ap-6103	179	14	is	be	AUX
ap-6103	179	15	defined	define	VERB
ap-6103	179	16	over	over	ADP
ap-6103	179	17	an	an	DET
ap-6103	179	18	annulus	annulus	NOUN
ap-6103	179	19	centred	centre	VERB
ap-6103	179	20	on	on	ADP
ap-6103	179	21	the	the	DET
ap-6103	179	22	singularity	singularity	NOUN
ap-6103	179	23	and	and	CCONJ
ap-6103	179	24	we	we	PRON
ap-6103	179	25	write	write	VERB
ap-6103	179	26	the	the	DET
ap-6103	179	27	factors	factor	NOUN
ap-6103	179	28	in	in	ADP
ap-6103	179	29	the	the	DET
ap-6103	179	30	sense	sense	NOUN
ap-6103	179	31	that	that	SCONJ
ap-6103	179	32	|a|	|a|	NOUN
ap-6103	179	33	<	<	X
ap-6103	179	34	|χ|	|χ|	X
ap-6103	179	35	<	<	X
ap-6103	179	36	|b|	|b|	PROPN
ap-6103	179	37	.	.	PUNCT
ap-6103	180	1	we	we	PRON
ap-6103	180	2	now	now	ADV
ap-6103	180	3	write	write	VERB
ap-6103	180	4	integrand	integrand	NOUN
ap-6103	180	5	of	of	ADP
ap-6103	180	6	(	(	PUNCT
ap-6103	180	7	27	27	NUM
ap-6103	180	8	)	)	PUNCT
ap-6103	180	9	as	as	ADP
ap-6103	180	10	1	1	NUM
ap-6103	180	11	k2b2χ4	k2b2χ4	NOUN
ap-6103	180	12	(	(	PUNCT
ap-6103	180	13	1−	1−	NUM
ap-6103	180	14	a	a	DET
ap-6103	180	15	χ	χ	NOUN
ap-6103	180	16	)	)	PUNCT
ap-6103	180	17	−2	−2	NOUN
ap-6103	180	18	(	(	PUNCT
ap-6103	180	19	1−	1−	NUM
ap-6103	180	20	χ	χ	PRON
ap-6103	180	21	b	b	X
ap-6103	180	22	)	)	PUNCT
ap-6103	180	23	−2	−2	NOUN
ap-6103	180	24	.	.	PUNCT
ap-6103	181	1	(	(	PUNCT
ap-6103	181	2	34	34	NUM
ap-6103	181	3	)	)	PUNCT
ap-6103	181	4	by	by	ADP
ap-6103	181	5	applying	apply	VERB
ap-6103	181	6	the	the	DET
ap-6103	181	7	above	above	ADJ
ap-6103	181	8	method	method	NOUN
ap-6103	181	9	to	to	ADP
ap-6103	181	10	(	(	PUNCT
ap-6103	181	11	34	34	NUM
ap-6103	181	12	)	)	PUNCT
ap-6103	181	13	we	we	PRON
ap-6103	181	14	obtain	obtain	VERB
ap-6103	181	15	u(x	u(x	NOUN
ap-6103	181	16	)	)	PUNCT
ap-6103	181	17	=	=	PUNCT
ap-6103	182	1	m	m	VERB
ap-6103	182	2	+	+	NOUN
ap-6103	182	3	1	1	NUM
ap-6103	182	4	b2k2	b2k2	NOUN
ap-6103	182	5	[	[	X
ap-6103	182	6	(	(	PUNCT
ap-6103	182	7	−	−	PROPN
ap-6103	182	8	4	4	NUM
ap-6103	182	9	b3	b3	NOUN
ap-6103	182	10	...	...	PUNCT
ap-6103	182	11	)	)	PUNCT
ap-6103	182	12	logχ−	logχ−	VERB
ap-6103	182	13	1	1	NUM
ap-6103	182	14	χ	χ	NOUN
ap-6103	182	15	(	(	PUNCT
ap-6103	182	16	3	3	NUM
ap-6103	182	17	b2	b2	NOUN
ap-6103	182	18	+	+	CCONJ
ap-6103	182	19	8a	8a	NUM
ap-6103	182	20	b3	b3	NOUN
ap-6103	182	21	...	...	PUNCT
ap-6103	182	22	)	)	PUNCT
ap-6103	183	1	−	−	ADP
ap-6103	183	2	1	1	NUM
ap-6103	183	3	2χ2	2χ2	NUM
ap-6103	183	4	(	(	PUNCT
ap-6103	183	5	−2	−2	NOUN
ap-6103	183	6	b	b	NOUN
ap-6103	183	7	−	−	PROPN
ap-6103	183	8	6a	6a	NOUN
ap-6103	183	9	b2	b2	NOUN
ap-6103	183	10	−	−	PROPN
ap-6103	183	11	12a2	12a2	NUM
ap-6103	183	12	b3	b3	PROPN
ap-6103	183	13	...	...	PUNCT
ap-6103	183	14	)	)	PUNCT
ap-6103	184	1	−	−	ADP
ap-6103	184	2	1	1	NUM
ap-6103	184	3	3χ3	3χ3	NUM
ap-6103	184	4	(	(	PUNCT
ap-6103	184	5	1	1	NUM
ap-6103	184	6	+	+	NUM
ap-6103	184	7	4a	4a	X
ap-6103	184	8	b	b	X
ap-6103	184	9	+	+	CCONJ
ap-6103	184	10	9a2	9a2	NUM
ap-6103	184	11	b2	b2	NOUN
ap-6103	184	12	+	+	CCONJ
ap-6103	184	13	16a3	16a3	NUM
ap-6103	184	14	b3	b3	NOUN
ap-6103	184	15	...	...	PUNCT
ap-6103	184	16	)	)	PUNCT
ap-6103	185	1	−	−	PROPN
ap-6103	185	2	1	1	NUM
ap-6103	185	3	4χ4	4χ4	NUM
ap-6103	185	4	(	(	PUNCT
ap-6103	185	5	−2a−	−2a−	NOUN
ap-6103	185	6	6a2	6a2	NUM
ap-6103	185	7	b	b	X
ap-6103	185	8	−	−	PROPN
ap-6103	185	9	12a3	12a3	NUM
ap-6103	185	10	b2	b2	NOUN
ap-6103	185	11	...	...	PUNCT
ap-6103	185	12	)	)	PUNCT
ap-6103	186	1	−	−	ADP
ap-6103	187	1	1	1	NUM
ap-6103	187	2	5χ5	5χ5	NUM
ap-6103	187	3	(	(	PUNCT
ap-6103	187	4	3a2	3a2	NUM
ap-6103	187	5	+	+	NUM
ap-6103	187	6	8a3	8a3	NUM
ap-6103	187	7	b	b	NOUN
ap-6103	187	8	...	...	PUNCT
ap-6103	187	9	)	)	PUNCT
ap-6103	187	10	]	]	PUNCT
ap-6103	187	11	.	.	PUNCT
ap-6103	188	1	(	(	PUNCT
ap-6103	188	2	35	35	NUM
ap-6103	188	3	)	)	PUNCT
ap-6103	188	4	we	we	PRON
ap-6103	188	5	observe	observe	VERB
ap-6103	188	6	that	that	SCONJ
ap-6103	188	7	(	(	PUNCT
ap-6103	188	8	35	35	NUM
ap-6103	188	9	)	)	PUNCT
ap-6103	188	10	contains	contain	VERB
ap-6103	188	11	an	an	DET
ap-6103	188	12	unfortunate	unfortunate	ADJ
ap-6103	188	13	logarithmic	logarithmic	ADJ
ap-6103	188	14	term	term	NOUN
ap-6103	188	15	,	,	PUNCT
ap-6103	188	16	which	which	PRON
ap-6103	188	17	is	be	AUX
ap-6103	188	18	not	not	PART
ap-6103	188	19	indicated	indicate	VERB
ap-6103	188	20	in	in	ADP
ap-6103	188	21	the	the	DET
ap-6103	188	22	resonances	resonance	NOUN
ap-6103	188	23	for	for	ADP
ap-6103	188	24	p	p	NOUN
ap-6103	189	1	=	=	NOUN
ap-6103	189	2	−3	−3	PROPN
ap-6103	189	3	.	.	PUNCT
ap-6103	190	1	this	this	PRON
ap-6103	190	2	is	be	AUX
ap-6103	190	3	possible	possible	ADJ
ap-6103	190	4	since	since	SCONJ
ap-6103	190	5	we	we	PRON
ap-6103	190	6	have	have	VERB
ap-6103	190	7	a	a	DET
ap-6103	190	8	complete	complete	ADJ
ap-6103	190	9	laurent	laurent	NOUN
ap-6103	190	10	series	series	NOUN
ap-6103	190	11	,	,	PUNCT
ap-6103	190	12	which	which	PRON
ap-6103	190	13	must	must	AUX
ap-6103	190	14	necessarily	necessarily	ADV
ap-6103	190	15	be	be	AUX
ap-6103	190	16	convergent	convergent	ADJ
ap-6103	190	17	in	in	ADP
ap-6103	190	18	an	an	DET
ap-6103	190	19	annulus	annulus	NOUN
ap-6103	190	20	centred	centre	VERB
ap-6103	190	21	on	on	ADP
ap-6103	190	22	the	the	DET
ap-6103	190	23	singularity.the	singularity.the	DET
ap-6103	190	24	kummerschwarz	kummerschwarz	PROPN
ap-6103	190	25	equation	equation	NOUN
ap-6103	190	26	and	and	CCONJ
ap-6103	190	27	the	the	DET
ap-6103	190	28	members	member	NOUN
ap-6103	190	29	of	of	ADP
ap-6103	190	30	the	the	DET
ap-6103	190	31	sequence	sequence	NOUN
ap-6103	190	32	generated	generate	VERB
ap-6103	190	33	from	from	ADP
ap-6103	190	34	it	it	PRON
ap-6103	190	35	by	by	ADP
ap-6103	190	36	the	the	DET
ap-6103	190	37	generator	generator	NOUN
ap-6103	190	38	(	(	PUNCT
ap-6103	190	39	12	12	NUM
ap-6103	190	40	)	)	PUNCT
ap-6103	190	41	can	can	AUX
ap-6103	190	42	be	be	AUX
ap-6103	190	43	easily	easily	ADV
ap-6103	190	44	integrated	integrate	VERB
ap-6103	190	45	.	.	PUNCT
ap-6103	191	1	what	what	PRON
ap-6103	191	2	we	we	PRON
ap-6103	191	3	have	have	AUX
ap-6103	191	4	done	do	VERB
ap-6103	191	5	here	here	ADV
ap-6103	191	6	is	be	AUX
ap-6103	191	7	to	to	PART
ap-6103	191	8	explore	explore	VERB
ap-6103	191	9	its	its	PRON
ap-6103	191	10	properties	property	NOUN
ap-6103	191	11	from	from	ADP
ap-6103	191	12	a	a	DET
ap-6103	191	13	wider	wide	ADJ
ap-6103	191	14	perspective	perspective	NOUN
ap-6103	191	15	so	so	SCONJ
ap-6103	191	16	that	that	SCONJ
ap-6103	191	17	a	a	DET
ap-6103	191	18	greater	great	ADJ
ap-6103	191	19	appreciation	appreciation	NOUN
ap-6103	191	20	of	of	ADP
ap-6103	191	21	its	its	PRON
ap-6103	191	22	properties	property	NOUN
ap-6103	191	23	can	can	AUX
ap-6103	191	24	be	be	AUX
ap-6103	191	25	gained	gain	VERB
ap-6103	191	26	.	.	PUNCT
ap-6103	192	1	the	the	DET
ap-6103	192	2	exploration	exploration	NOUN
ap-6103	192	3	of	of	ADP
ap-6103	192	4	different	different	ADJ
ap-6103	192	5	aspects	aspect	NOUN
ap-6103	192	6	of	of	ADP
ap-6103	192	7	such	such	ADJ
ap-6103	192	8	sequences	sequence	NOUN
ap-6103	192	9	adds	add	VERB
ap-6103	192	10	to	to	ADP
ap-6103	192	11	our	our	PRON
ap-6103	192	12	understanding	understanding	NOUN
ap-6103	192	13	of	of	ADP
ap-6103	192	14	them	they	PRON
ap-6103	192	15	.	.	PUNCT
ap-6103	193	1	acknowledgements	acknowledgement	NOUN
ap-6103	193	2	pgll	pgll	VERB
ap-6103	193	3	would	would	AUX
ap-6103	193	4	like	like	VERB
ap-6103	193	5	to	to	PART
ap-6103	193	6	thank	thank	VERB
ap-6103	193	7	the	the	DET
ap-6103	193	8	national	national	PROPN
ap-6103	193	9	research	research	PROPN
ap-6103	193	10	foundation	foundation	PROPN
ap-6103	193	11	of	of	ADP
ap-6103	193	12	the	the	DET
ap-6103	193	13	republic	republic	NOUN
ap-6103	193	14	of	of	ADP
ap-6103	193	15	south	south	PROPN
ap-6103	193	16	africa	africa	PROPN
ap-6103	193	17	,	,	PUNCT
ap-6103	193	18	university	university	PROPN
ap-6103	193	19	of	of	ADP
ap-6103	193	20	kwazulu	kwazulu	PROPN
ap-6103	193	21	-	-	PUNCT
ap-6103	193	22	natal	natal	ADJ
ap-6103	193	23	and	and	CCONJ
ap-6103	193	24	durban	durban	PROPN
ap-6103	193	25	university	university	PROPN
ap-6103	193	26	of	of	ADP
ap-6103	193	27	technology	technology	NOUN
ap-6103	193	28	for	for	ADP
ap-6103	193	29	their	their	PRON
ap-6103	193	30	continued	continue	VERB
ap-6103	193	31	support	support	NOUN
ap-6103	193	32	.	.	PUNCT
ap-6103	194	1	am	be	AUX
ap-6103	194	2	would	would	AUX
ap-6103	194	3	like	like	VERB
ap-6103	194	4	to	to	PART
ap-6103	194	5	thank	thank	VERB
ap-6103	194	6	the	the	DET
ap-6103	194	7	durban	durban	PROPN
ap-6103	194	8	university	university	PROPN
ap-6103	194	9	of	of	ADP
ap-6103	194	10	technology	technology	NOUN
ap-6103	194	11	for	for	ADP
ap-6103	194	12	their	their	PRON
ap-6103	194	13	continued	continue	VERB
ap-6103	194	14	support	support	NOUN
ap-6103	194	15	.	.	PUNCT
ap-6103	195	1	433	433	NUM
ap-6103	195	2	a.	a.	NOUN
ap-6103	195	3	maharaj	maharaj	PROPN
ap-6103	195	4	,	,	PUNCT
ap-6103	195	5	k.	k.	PROPN
ap-6103	195	6	andriopoulos	andriopoulos	PROPN
ap-6103	195	7	,	,	PUNCT
ap-6103	195	8	p.	p.	NOUN
ap-6103	195	9	leach	leach	NOUN
ap-6103	195	10	acta	acta	PROPN
ap-6103	195	11	polytechnica	polytechnica	PROPN
ap-6103	195	12	references	reference	NOUN
ap-6103	195	13	[	[	X
ap-6103	195	14	1	1	NUM
ap-6103	195	15	]	]	PUNCT
ap-6103	195	16	p.	p.	NOUN
ap-6103	195	17	j.	j.	PROPN
ap-6103	195	18	olver	olver	PROPN
ap-6103	195	19	.	.	PUNCT
ap-6103	196	1	evolution	evolution	NOUN
ap-6103	196	2	equations	equation	NOUN
ap-6103	196	3	possessing	possess	VERB
ap-6103	196	4	infinitely	infinitely	ADV
ap-6103	196	5	many	many	ADJ
ap-6103	196	6	symmetries	symmetry	NOUN
ap-6103	196	7	.	.	PUNCT
ap-6103	197	1	journal	journal	PROPN
ap-6103	197	2	of	of	ADP
ap-6103	197	3	mathematical	mathematical	ADJ
ap-6103	197	4	physics	physics	NOUN
ap-6103	197	5	18:1212	18:1212	NUM
ap-6103	197	6	–	–	PUNCT
ap-6103	197	7	1215	1215	NUM
ap-6103	197	8	,	,	PUNCT
ap-6103	197	9	1977	1977	NUM
ap-6103	197	10	.	.	PUNCT
ap-6103	198	1	doi:10.1063/1.523393	doi:10.1063/1.523393	PROPN
ap-6103	198	2	.	.	PUNCT
ap-6103	199	1	[	[	X
ap-6103	199	2	2	2	NUM
ap-6103	199	3	]	]	PUNCT
ap-6103	199	4	c.	c.	PROPN
ap-6103	199	5	s.	s.	PROPN
ap-6103	199	6	gardner	gardner	PROPN
ap-6103	199	7	.	.	PUNCT
ap-6103	200	1	korteweg	korteweg	PROPN
ap-6103	200	2	-	-	PUNCT
ap-6103	200	3	de	de	PROPN
ap-6103	200	4	vries	vries	PROPN
ap-6103	200	5	equation	equation	NOUN
ap-6103	200	6	and	and	CCONJ
ap-6103	200	7	generalisations	generalisation	NOUN
ap-6103	200	8	iv	iv	NUM
ap-6103	200	9	.	.	PUNCT
ap-6103	201	1	the	the	DET
ap-6103	201	2	korteweg	korteweg	PROPN
ap-6103	201	3	-	-	PUNCT
ap-6103	201	4	de	de	NOUN
ap-6103	201	5	vries	vries	PROPN
ap-6103	201	6	equation	equation	NOUN
ap-6103	201	7	as	as	ADP
ap-6103	201	8	a	a	DET
ap-6103	201	9	hamiltonian	hamiltonian	ADJ
ap-6103	201	10	system	system	NOUN
ap-6103	201	11	.	.	PUNCT
ap-6103	202	1	journal	journal	PROPN
ap-6103	202	2	of	of	ADP
ap-6103	202	3	mathematical	mathematical	ADJ
ap-6103	202	4	physics	physics	PROPN
ap-6103	202	5	12:1548	12:1548	NUM
ap-6103	202	6	–	–	PUNCT
ap-6103	202	7	1551	1551	NUM
ap-6103	202	8	,	,	PUNCT
ap-6103	202	9	1971	1971	NUM
ap-6103	202	10	.	.	PUNCT
ap-6103	203	1	doi:10.1063/1.1665772	doi:10.1063/1.1665772	PROPN
ap-6103	203	2	.	.	PUNCT
ap-6103	204	1	[	[	X
ap-6103	204	2	3	3	NUM
ap-6103	204	3	]	]	X
ap-6103	204	4	i.	i.	PROPN
ap-6103	204	5	m.	m.	PROPN
ap-6103	204	6	gelfand	gelfand	PROPN
ap-6103	204	7	,	,	PUNCT
ap-6103	204	8	l.	l.	PROPN
ap-6103	204	9	a.	a.	PROPN
ap-6103	204	10	dikii	dikii	PROPN
ap-6103	204	11	.	.	PUNCT
ap-6103	205	1	asymptotic	asymptotic	ADJ
ap-6103	205	2	behaviour	behaviour	NOUN
ap-6103	205	3	of	of	ADP
ap-6103	205	4	the	the	DET
ap-6103	205	5	resolvent	resolvent	NOUN
ap-6103	205	6	of	of	ADP
ap-6103	205	7	sturm	sturm	PROPN
ap-6103	205	8	-	-	PUNCT
ap-6103	205	9	liouville	liouville	NOUN
ap-6103	205	10	equations	equation	NOUN
ap-6103	205	11	and	and	CCONJ
ap-6103	205	12	the	the	DET
ap-6103	205	13	algebra	algebra	NOUN
ap-6103	205	14	of	of	ADP
ap-6103	205	15	the	the	DET
ap-6103	205	16	korteweg	korteweg	NOUN
ap-6103	205	17	-	-	PUNCT
ap-6103	205	18	de	de	NOUN
ap-6103	205	19	vries	vries	PROPN
ap-6103	205	20	equations	equation	NOUN
ap-6103	205	21	.	.	PUNCT
ap-6103	206	1	russian	russian	ADJ
ap-6103	206	2	mathematical	mathematical	ADJ
ap-6103	206	3	surveys	survey	NOUN
ap-6103	206	4	30:77	30:77	NUM
ap-6103	206	5	–	–	PUNCT
ap-6103	206	6	113	113	NUM
ap-6103	206	7	,	,	PUNCT
ap-6103	206	8	1975	1975	NUM
ap-6103	206	9	.	.	PUNCT
ap-6103	207	1	doi:10.1070	doi:10.1070	NOUN
ap-6103	207	2	/	/	SYM
ap-6103	207	3	rm1975v030n05aneh001522	rm1975v030n05aneh001522	NOUN
ap-6103	207	4	.	.	PUNCT
ap-6103	208	1	[	[	X
ap-6103	208	2	4	4	X
ap-6103	208	3	]	]	X
ap-6103	208	4	m.	m.	NOUN
ap-6103	208	5	euler	euler	PROPN
ap-6103	208	6	,	,	PUNCT
ap-6103	208	7	n.	n.	PROPN
ap-6103	208	8	euler	euler	PROPN
ap-6103	208	9	,	,	PUNCT
ap-6103	208	10	n.	n.	PROPN
ap-6103	208	11	petersson	petersson	PROPN
ap-6103	208	12	.	.	PUNCT
ap-6103	209	1	linearizable	linearizable	ADJ
ap-6103	209	2	hierarchies	hierarchy	NOUN
ap-6103	209	3	of	of	ADP
ap-6103	209	4	evolution	evolution	NOUN
ap-6103	209	5	equations	equation	NOUN
ap-6103	209	6	in	in	ADP
ap-6103	209	7	(	(	PUNCT
ap-6103	209	8	1	1	NUM
ap-6103	209	9	+	+	NUM
ap-6103	209	10	1	1	NUM
ap-6103	209	11	)	)	PUNCT
ap-6103	209	12	dimensions	dimension	NOUN
ap-6103	209	13	.	.	PUNCT
ap-6103	210	1	studies	study	NOUN
ap-6103	210	2	in	in	ADP
ap-6103	210	3	applied	applied	ADJ
ap-6103	210	4	mathematics	mathematic	NOUN
ap-6103	210	5	111:315	111:315	PROPN
ap-6103	210	6	–	–	PUNCT
ap-6103	210	7	337	337	NUM
ap-6103	210	8	,	,	PUNCT
ap-6103	210	9	2003	2003	NUM
ap-6103	210	10	.	.	PUNCT
ap-6103	211	1	doi:10.1111/1467	doi:10.1111/1467	ADJ
ap-6103	211	2	-	-	PUNCT
ap-6103	211	3	9590.t01	9590.t01	NUM
ap-6103	211	4	-	-	PUNCT
ap-6103	211	5	1	1	NUM
ap-6103	211	6	-	-	PUNCT
ap-6103	211	7	00236	00236	NUM
ap-6103	211	8	.	.	PUNCT
ap-6103	212	1	[	[	X
ap-6103	212	2	5	5	NUM
ap-6103	212	3	]	]	X
ap-6103	212	4	n.	n.	NOUN
ap-6103	212	5	petersson	petersson	PROPN
ap-6103	212	6	,	,	PUNCT
ap-6103	212	7	n.	n.	PROPN
ap-6103	212	8	euler	euler	PROPN
ap-6103	212	9	,	,	PUNCT
ap-6103	212	10	m.	m.	NOUN
ap-6103	212	11	euler	euler	PROPN
ap-6103	212	12	.	.	PUNCT
ap-6103	212	13	recursion	recursion	NOUN
ap-6103	212	14	operators	operator	NOUN
ap-6103	212	15	for	for	ADP
ap-6103	212	16	a	a	DET
ap-6103	212	17	class	class	NOUN
ap-6103	212	18	of	of	ADP
ap-6103	212	19	integrable	integrable	ADJ
ap-6103	212	20	third	third	ADJ
ap-6103	212	21	-	-	PUNCT
ap-6103	212	22	order	order	NOUN
ap-6103	212	23	evolution	evolution	NOUN
ap-6103	212	24	equations	equation	NOUN
ap-6103	212	25	.	.	PUNCT
ap-6103	213	1	journal	journal	PROPN
ap-6103	213	2	of	of	ADP
ap-6103	213	3	mathematical	mathematical	ADJ
ap-6103	213	4	physics	physics	NOUN
ap-6103	213	5	112:201	112:201	PROPN
ap-6103	213	6	–	–	PUNCT
ap-6103	213	7	225	225	NUM
ap-6103	213	8	,	,	PUNCT
ap-6103	213	9	2004	2004	NUM
ap-6103	213	10	.	.	PUNCT
ap-6103	214	1	doi:10.111	doi:10.111	NOUN
ap-6103	214	2	/	/	SYM
ap-6103	214	3	j.0022	j.0022	NOUN
ap-6103	214	4	-	-	PUNCT
ap-6103	214	5	2526.2004.02511.x	2526.2004.02511.x	NOUN
ap-6103	214	6	.	.	PUNCT
ap-6103	215	1	[	[	X
ap-6103	215	2	6	6	NUM
ap-6103	215	3	]	]	PUNCT
ap-6103	215	4	m.	m.	NOUN
ap-6103	215	5	euler	euler	PROPN
ap-6103	215	6	,	,	PUNCT
ap-6103	215	7	n.	n.	PROPN
ap-6103	215	8	euler	euler	PROPN
ap-6103	215	9	,	,	PUNCT
ap-6103	215	10	p.	p.	NOUN
ap-6103	215	11	g.	g.	PROPN
ap-6103	215	12	l.	l.	PROPN
ap-6103	215	13	leach	leach	NOUN
ap-6103	215	14	.	.	PUNCT
ap-6103	216	1	the	the	DET
ap-6103	216	2	riccati	riccati	PROPN
ap-6103	216	3	and	and	CCONJ
ap-6103	216	4	ermakov	ermakov	ADJ
ap-6103	216	5	-	-	PUNCT
ap-6103	216	6	pinney	pinney	NOUN
ap-6103	216	7	hierarchies	hierarchy	NOUN
ap-6103	216	8	.	.	PUNCT
ap-6103	217	1	journal	journal	PROPN
ap-6103	217	2	of	of	ADP
ap-6103	217	3	nonlinear	nonlinear	PROPN
ap-6103	217	4	mathematical	mathematical	ADJ
ap-6103	217	5	physics	physics	NOUN
ap-6103	217	6	14:290	14:290	NUM
ap-6103	217	7	–	–	PUNCT
ap-6103	217	8	310	310	NUM
ap-6103	217	9	,	,	PUNCT
ap-6103	217	10	2007	2007	NUM
ap-6103	217	11	.	.	PUNCT
ap-6103	218	1	doi:10.2991	doi:10.2991	PROPN
ap-6103	218	2	/	/	SYM
ap-6103	218	3	jnmp.2007.14.2.11	jnmp.2007.14.2.11	PROPN
ap-6103	218	4	.	.	PUNCT
ap-6103	219	1	[	[	X
ap-6103	219	2	7	7	X
ap-6103	219	3	]	]	X
ap-6103	219	4	k.	k.	PROPN
ap-6103	219	5	andriopoulos	andriopoulos	PROPN
ap-6103	219	6	,	,	PUNCT
ap-6103	219	7	p.	p.	NOUN
ap-6103	219	8	g.	g.	PROPN
ap-6103	219	9	l.	l.	PROPN
ap-6103	219	10	leach	leach	PROPN
ap-6103	219	11	,	,	PUNCT
ap-6103	219	12	a.	a.	NOUN
ap-6103	219	13	maharaj	maharaj	PROPN
ap-6103	219	14	.	.	PUNCT
ap-6103	220	1	on	on	ADP
ap-6103	220	2	differential	differential	ADJ
ap-6103	220	3	sequences	sequence	NOUN
ap-6103	220	4	.	.	PUNCT
ap-6103	221	1	applied	apply	VERB
ap-6103	221	2	mathematics	mathematic	NOUN
ap-6103	221	3	and	and	CCONJ
ap-6103	221	4	information	information	NOUN
ap-6103	221	5	sciences	science	NOUN
ap-6103	221	6	an	an	DET
ap-6103	221	7	international	international	ADJ
ap-6103	221	8	journal	journal	NOUN
ap-6103	221	9	5(3	5(3	NUM
ap-6103	221	10	)	)	PUNCT
ap-6103	221	11	,	,	PUNCT
ap-6103	221	12	2011	2011	NUM
ap-6103	221	13	.	.	PUNCT
ap-6103	222	1	[	[	X
ap-6103	222	2	8	8	NUM
ap-6103	222	3	]	]	X
ap-6103	222	4	n.	n.	PROPN
ap-6103	222	5	euler	euler	PROPN
ap-6103	222	6	,	,	PUNCT
ap-6103	222	7	p.	p.	NOUN
ap-6103	222	8	g.	g.	PROPN
ap-6103	222	9	l.	l.	PROPN
ap-6103	222	10	leach	leach	NOUN
ap-6103	222	11	.	.	PUNCT
ap-6103	223	1	aspects	aspect	NOUN
ap-6103	223	2	of	of	ADP
ap-6103	223	3	proper	proper	ADJ
ap-6103	223	4	differential	differential	ADJ
ap-6103	223	5	sequences	sequence	NOUN
ap-6103	223	6	of	of	ADP
ap-6103	223	7	ordinary	ordinary	ADJ
ap-6103	223	8	differential	differential	ADJ
ap-6103	223	9	equations	equation	NOUN
ap-6103	223	10	.	.	PUNCT
ap-6103	224	1	theoretical	theoretical	ADJ
ap-6103	224	2	and	and	CCONJ
ap-6103	224	3	mathematical	mathematical	ADJ
ap-6103	224	4	physics	physics	NOUN
ap-6103	224	5	159:473	159:473	NUM
ap-6103	224	6	–	–	PUNCT
ap-6103	224	7	486	486	NUM
ap-6103	224	8	,	,	PUNCT
ap-6103	224	9	2009	2009	NUM
ap-6103	224	10	.	.	PUNCT
ap-6103	225	1	doi:10.1007	doi:10.1007	VERB
ap-6103	225	2	/	/	SYM
ap-6103	225	3	s11232	s11232	NOUN
ap-6103	225	4	-	-	PUNCT
ap-6103	225	5	009	009	NUM
ap-6103	225	6	-	-	PUNCT
ap-6103	225	7	0038	0038	NUM
ap-6103	225	8	-	-	PUNCT
ap-6103	225	9	y.	y.	NOUN
ap-6103	226	1	[	[	X
ap-6103	226	2	9	9	NUM
ap-6103	226	3	]	]	PUNCT
ap-6103	226	4	k.	k.	PROPN
ap-6103	226	5	andriopoulos	andriopoulos	PROPN
ap-6103	226	6	,	,	PUNCT
ap-6103	226	7	p.	p.	NOUN
ap-6103	226	8	g.	g.	PROPN
ap-6103	226	9	l.	l.	PROPN
ap-6103	226	10	leach	leach	PROPN
ap-6103	226	11	,	,	PUNCT
ap-6103	226	12	g.	g.	PROPN
ap-6103	226	13	p.	p.	PROPN
ap-6103	226	14	flessas	flessas	PROPN
ap-6103	226	15	.	.	PUNCT
ap-6103	227	1	complete	complete	ADJ
ap-6103	227	2	symmetry	symmetry	NOUN
ap-6103	227	3	groups	group	NOUN
ap-6103	227	4	of	of	ADP
ap-6103	227	5	ordinary	ordinary	ADJ
ap-6103	227	6	differential	differential	ADJ
ap-6103	227	7	equations	equation	NOUN
ap-6103	227	8	and	and	CCONJ
ap-6103	227	9	their	their	PRON
ap-6103	227	10	integrals	integral	NOUN
ap-6103	227	11	:	:	PUNCT
ap-6103	227	12	some	some	DET
ap-6103	227	13	basic	basic	ADJ
ap-6103	227	14	considerations	consideration	NOUN
ap-6103	227	15	.	.	PUNCT
ap-6103	228	1	journal	journal	NOUN
ap-6103	228	2	of	of	ADP
ap-6103	228	3	mathematical	mathematical	ADJ
ap-6103	228	4	analysis	analysis	NOUN
ap-6103	228	5	and	and	CCONJ
ap-6103	228	6	applications	application	NOUN
ap-6103	228	7	262:256	262:256	NUM
ap-6103	228	8	–	–	PUNCT
ap-6103	228	9	273	273	NUM
ap-6103	228	10	,	,	PUNCT
ap-6103	228	11	2001	2001	NUM
ap-6103	228	12	.	.	PUNCT
ap-6103	229	1	doi:10.1006	doi:10.1006	X
ap-6103	229	2	/	/	SYM
ap-6103	229	3	jmaa.2001.7570	jmaa.2001.7570	ADJ
ap-6103	229	4	.	.	PUNCT
ap-6103	230	1	[	[	X
ap-6103	230	2	10	10	NUM
ap-6103	230	3	]	]	X
ap-6103	230	4	k.	k.	PROPN
ap-6103	230	5	andriopoulos	andriopoulos	PROPN
ap-6103	230	6	,	,	PUNCT
ap-6103	230	7	p.	p.	NOUN
ap-6103	230	8	g.	g.	PROPN
ap-6103	230	9	l.	l.	PROPN
ap-6103	230	10	leach	leach	NOUN
ap-6103	230	11	.	.	PUNCT
ap-6103	231	1	the	the	DET
ap-6103	231	2	economy	economy	NOUN
ap-6103	231	3	of	of	ADP
ap-6103	231	4	complete	complete	ADJ
ap-6103	231	5	symmetry	symmetry	NOUN
ap-6103	231	6	groups	group	NOUN
ap-6103	231	7	for	for	ADP
ap-6103	231	8	linear	linear	ADJ
ap-6103	231	9	higher	high	ADJ
ap-6103	231	10	dimensional	dimensional	ADJ
ap-6103	231	11	systems	system	NOUN
ap-6103	231	12	.	.	PUNCT
ap-6103	232	1	journal	journal	PROPN
ap-6103	232	2	of	of	ADP
ap-6103	232	3	nonlinear	nonlinear	PROPN
ap-6103	232	4	mathematical	mathematical	ADJ
ap-6103	232	5	physics	physics	NOUN
ap-6103	232	6	9(s-2	9(s-2	NUM
ap-6103	232	7	)	)	PUNCT
ap-6103	232	8	,	,	PUNCT
ap-6103	232	9	2002	2002	NUM
ap-6103	232	10	.	.	PUNCT
ap-6103	233	1	434	434	NUM
ap-6103	233	2	http://dx.doi.org/10.1063/1.523393	http://dx.doi.org/10.1063/1.523393	NOUN
ap-6103	233	3	http://dx.doi.org/10.1063/1.1665772	http://dx.doi.org/10.1063/1.1665772	NOUN
ap-6103	233	4	http://dx.doi.org/10.1070/rm1975v030n05aneh001522	http://dx.doi.org/10.1070/rm1975v030n05aneh001522	PRON
ap-6103	233	5	http://dx.doi.org/10.1111/1467-9590.t01-1-00236	http://dx.doi.org/10.1111/1467-9590.t01-1-00236	VERB
ap-6103	233	6	http://dx.doi.org/10.111/j.0022-2526.2004.02511.x	http://dx.doi.org/10.111/j.0022-2526.2004.02511.x	NOUN
ap-6103	233	7	http://dx.doi.org/10.2991/jnmp.2007.14.2.11	http://dx.doi.org/10.2991/jnmp.2007.14.2.11	ADJ
ap-6103	233	8	http://dx.doi.org/10.1007/s11232-009-0038-y	http://dx.doi.org/10.1007/s11232-009-0038-y	NOUN
ap-6103	233	9	http://dx.doi.org/10.1006/jmaa.2001.7570	http://dx.doi.org/10.1006/jmaa.2001.7570	PROPN
ap-6103	233	10	acta	acta	PROPN
ap-6103	233	11	polytechnica	polytechnica	PROPN
ap-6103	233	12	60(5):428–434	60(5):428–434	PROPN
ap-6103	233	13	,	,	PUNCT
ap-6103	233	14	2020	2020	NUM
ap-6103	233	15	1	1	NUM
ap-6103	233	16	introduction	introduction	NOUN
ap-6103	233	17	2	2	NUM
ap-6103	233	18	the	the	DET
ap-6103	233	19	first	first	ADJ
ap-6103	233	20	-	-	PUNCT
ap-6103	233	21	order	order	NOUN
ap-6103	233	22	recursion	recursion	NOUN
ap-6103	233	23	operator	operator	NOUN
ap-6103	233	24	for	for	ADP
ap-6103	233	25	the	the	DET
ap-6103	233	26	kummer	kummer	NOUN
ap-6103	233	27	-	-	PUNCT
ap-6103	233	28	schwarz	schwarz	PROPN
ap-6103	233	29	equation	equation	NOUN
ap-6103	233	30	3	3	NUM
ap-6103	233	31	the	the	DET
ap-6103	233	32	early	early	ADJ
ap-6103	233	33	elements	element	NOUN
ap-6103	233	34	of	of	ADP
ap-6103	233	35	the	the	DET
ap-6103	233	36	new	new	ADJ
ap-6103	233	37	sequence	sequence	NOUN
ap-6103	233	38	4	4	NUM
ap-6103	233	39	singularity	singularity	NOUN
ap-6103	233	40	analysis	analysis	NOUN
ap-6103	233	41	5	5	NUM
ap-6103	233	42	complete	complete	ADJ
ap-6103	233	43	symmetry	symmetry	NOUN
ap-6103	233	44	group	group	NOUN
ap-6103	233	45	6	6	NUM
ap-6103	233	46	the	the	DET
ap-6103	233	47	alternate	alternate	ADJ
ap-6103	233	48	sequence	sequence	NOUN
ap-6103	233	49	7	7	NUM
ap-6103	233	50	conclusion	conclusion	NOUN
ap-6103	233	51	acknowledgements	acknowledgement	NOUN
ap-6103	233	52	references	reference	NOUN