id	sid	tid	token	lemma	pos
ap-3980	1	1	acta	acta	PROPN
ap-3980	1	2	polytechnica	polytechnica	PROPN
ap-3980	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3980	1	4	/	/	SYM
ap-3980	1	5	ap.2017.57.0467	ap.2017.57.0467	PROPN
ap-3980	1	6	acta	acta	PROPN
ap-3980	1	7	polytechnica	polytechnica	PROPN
ap-3980	1	8	57(6):467–469	57(6):467–469	PROPN
ap-3980	1	9	,	,	PUNCT
ap-3980	1	10	2017	2017	NUM
ap-3980	1	11	©	©	PROPN
ap-3980	1	12	czech	czech	PROPN
ap-3980	1	13	technical	technical	PROPN
ap-3980	1	14	university	university	PROPN
ap-3980	1	15	in	in	ADP
ap-3980	1	16	prague	prague	PROPN
ap-3980	1	17	,	,	PUNCT
ap-3980	1	18	2017	2017	NUM
ap-3980	1	19	available	available	ADJ
ap-3980	1	20	online	online	ADV
ap-3980	1	21	at	at	ADP
ap-3980	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3980	1	23	further	further	ADJ
ap-3980	1	24	generalisations	generalisation	NOUN
ap-3980	1	25	of	of	ADP
ap-3980	1	26	the	the	DET
ap-3980	1	27	kummer	kummer	NOUN
ap-3980	1	28	-	-	PUNCT
ap-3980	1	29	schwarz	schwarz	PROPN
ap-3980	1	30	equation	equation	NOUN
ap-3980	1	31	:	:	PUNCT
ap-3980	1	32	algebraic	algebraic	ADJ
ap-3980	1	33	and	and	CCONJ
ap-3980	1	34	singularity	singularity	NOUN
ap-3980	1	35	properties	property	NOUN
ap-3980	1	36	r.	r.	PROPN
ap-3980	1	37	sinuvasana	sinuvasana	PROPN
ap-3980	1	38	,	,	PUNCT
ap-3980	1	39	c,∗	c,∗	PROPN
ap-3980	1	40	,	,	PUNCT
ap-3980	1	41	k.	k.	PROPN
ap-3980	1	42	krishnakumara	krishnakumara	PROPN
ap-3980	1	43	,	,	PUNCT
ap-3980	1	44	k.	k.	PROPN
ap-3980	1	45	m.	m.	PROPN
ap-3980	1	46	tamizhmania	tamizhmania	PROPN
ap-3980	1	47	,	,	PUNCT
ap-3980	2	1	p.	p.	NOUN
ap-3980	2	2	g.	g.	PROPN
ap-3980	2	3	l.	l.	PROPN
ap-3980	2	4	leachb	leachb	PROPN
ap-3980	2	5	a	a	DET
ap-3980	2	6	department	department	NOUN
ap-3980	2	7	of	of	ADP
ap-3980	2	8	mathematics	mathematic	NOUN
ap-3980	2	9	,	,	PUNCT
ap-3980	2	10	pondicherry	pondicherry	PROPN
ap-3980	2	11	university	university	PROPN
ap-3980	2	12	,	,	PUNCT
ap-3980	2	13	kalapet	kalapet	PROPN
ap-3980	2	14	,	,	PUNCT
ap-3980	2	15	india	india	PROPN
ap-3980	2	16	605	605	NUM
ap-3980	2	17	014	014	NUM
ap-3980	2	18	b	b	NOUN
ap-3980	2	19	school	school	NOUN
ap-3980	2	20	of	of	ADP
ap-3980	2	21	mathematics	mathematic	NOUN
ap-3980	2	22	,	,	PUNCT
ap-3980	2	23	statistics	statistic	NOUN
ap-3980	2	24	and	and	CCONJ
ap-3980	2	25	computer	computer	NOUN
ap-3980	2	26	science	science	NOUN
ap-3980	2	27	,	,	PUNCT
ap-3980	2	28	university	university	NOUN
ap-3980	2	29	of	of	ADP
ap-3980	2	30	kwazulu	kwazulu	PROPN
ap-3980	2	31	-	-	PUNCT
ap-3980	2	32	natal	natal	ADJ
ap-3980	2	33	,	,	PUNCT
ap-3980	2	34	private	private	ADJ
ap-3980	2	35	bag	bag	NOUN
ap-3980	2	36	x54001	x54001	PROPN
ap-3980	2	37	,	,	PUNCT
ap-3980	2	38	durban	durban	PROPN
ap-3980	2	39	4000	4000	NUM
ap-3980	2	40	,	,	PUNCT
ap-3980	2	41	republic	republic	NOUN
ap-3980	2	42	of	of	ADP
ap-3980	2	43	south	south	PROPN
ap-3980	2	44	africa	africa	PROPN
ap-3980	2	45	and	and	CCONJ
ap-3980	2	46	institute	institute	PROPN
ap-3980	2	47	for	for	ADP
ap-3980	2	48	systems	system	NOUN
ap-3980	2	49	science	science	NOUN
ap-3980	2	50	,	,	PUNCT
ap-3980	2	51	department	department	NOUN
ap-3980	2	52	of	of	ADP
ap-3980	2	53	mathematics	mathematics	PROPN
ap-3980	2	54	,	,	PUNCT
ap-3980	2	55	durban	durban	PROPN
ap-3980	2	56	university	university	PROPN
ap-3980	2	57	of	of	ADP
ap-3980	2	58	technology	technology	NOUN
ap-3980	2	59	,	,	PUNCT
ap-3980	2	60	pob	pob	PROPN
ap-3980	2	61	1334	1334	NUM
ap-3980	2	62	,	,	PUNCT
ap-3980	2	63	durban	durban	PROPN
ap-3980	2	64	4000	4000	NUM
ap-3980	2	65	,	,	PUNCT
ap-3980	2	66	republic	republic	NOUN
ap-3980	2	67	of	of	ADP
ap-3980	2	68	south	south	PROPN
ap-3980	2	69	africa	africa	PROPN
ap-3980	2	70	c	c	PROPN
ap-3980	2	71	department	department	PROPN
ap-3980	2	72	of	of	ADP
ap-3980	2	73	mathematics	mathematics	PROPN
ap-3980	2	74	,	,	PUNCT
ap-3980	2	75	sastra	sastra	PROPN
ap-3980	2	76	deemed	deemed	PROPN
ap-3980	2	77	university	university	PROPN
ap-3980	2	78	,	,	PUNCT
ap-3980	2	79	thanjavur	thanjavur	PROPN
ap-3980	2	80	,	,	PUNCT
ap-3980	2	81	india	india	PROPN
ap-3980	2	82	613	613	NUM
ap-3980	2	83	401	401	NUM
ap-3980	2	84	∗	∗	NOUN
ap-3980	2	85	corresponding	correspond	VERB
ap-3980	2	86	author	author	NOUN
ap-3980	3	1	:	:	PUNCT
ap-3980	3	2	rsinuvasan@gmail.com	rsinuvasan@gmail.com	X
ap-3980	3	3	abstract	abstract	ADJ
ap-3980	3	4	.	.	PUNCT
ap-3980	4	1	the	the	DET
ap-3980	4	2	kummer	kummer	PROPN
ap-3980	4	3	–	–	PUNCT
ap-3980	4	4	schwarz	schwarz	NOUN
ap-3980	4	5	equation	equation	NOUN
ap-3980	4	6	,	,	PUNCT
ap-3980	4	7	2y′y′′′	2y′y′′′	NUM
ap-3980	4	8	−	−	NOUN
ap-3980	4	9	3(y′′)2	3(y′′)2	NUM
ap-3980	4	10	=	=	SYM
ap-3980	4	11	0	0	NUM
ap-3980	4	12	,	,	PUNCT
ap-3980	4	13	has	have	VERB
ap-3980	4	14	a	a	DET
ap-3980	4	15	generalisation	generalisation	NOUN
ap-3980	4	16	,	,	PUNCT
ap-3980	4	17	(	(	PUNCT
ap-3980	4	18	n	n	CCONJ
ap-3980	4	19	−	−	PROPN
ap-3980	4	20	1)y(n−2)y(n	1)y(n−2)y(n	NUM
ap-3980	4	21	)	)	PUNCT
ap-3980	4	22	−	−	NOUN
ap-3980	4	23	ny(n−1)2	ny(n−1)2	PRON
ap-3980	4	24	=	=	NOUN
ap-3980	4	25	0	0	NUM
ap-3980	4	26	,	,	PUNCT
ap-3980	4	27	which	which	PRON
ap-3980	4	28	shares	share	VERB
ap-3980	4	29	many	many	ADJ
ap-3980	4	30	properties	property	NOUN
ap-3980	4	31	with	with	ADP
ap-3980	4	32	the	the	DET
ap-3980	4	33	parent	parent	NOUN
ap-3980	4	34	form	form	NOUN
ap-3980	4	35	(	(	PUNCT
ap-3980	4	36	see	see	VERB
ap-3980	4	37	sinuvasan	sinuvasan	ADJ
ap-3980	4	38	r	r	NOUN
ap-3980	4	39	,	,	PUNCT
ap-3980	4	40	tamizhmani	tamizhmani	NOUN
ap-3980	4	41	k	k	PROPN
ap-3980	4	42	m	m	PROPN
ap-3980	4	43	&	&	CCONJ
ap-3980	4	44	leach	leach	NOUN
ap-3980	4	45	p	p	NOUN
ap-3980	4	46	g	g	PROPN
ap-3980	4	47	l	l	NOUN
ap-3980	4	48	,	,	PUNCT
ap-3980	4	49	algebraic	algebraic	ADJ
ap-3980	4	50	and	and	CCONJ
ap-3980	4	51	singularity	singularity	NOUN
ap-3980	4	52	properties	property	NOUN
ap-3980	4	53	of	of	ADP
ap-3980	4	54	a	a	DET
ap-3980	4	55	class	class	NOUN
ap-3980	4	56	of	of	ADP
ap-3980	4	57	generalisations	generalisation	NOUN
ap-3980	4	58	of	of	ADP
ap-3980	4	59	the	the	DET
ap-3980	4	60	kummer	kummer	NOUN
ap-3980	4	61	–	–	PUNCT
ap-3980	4	62	schwarz	schwarz	PROPN
ap-3980	4	63	equation	equation	NOUN
ap-3980	4	64	differ	differ	VERB
ap-3980	4	65	,	,	PUNCT
ap-3980	4	66	equ	equ	PROPN
ap-3980	4	67	dyn	dyn	PROPN
ap-3980	4	68	syst	syst	PROPN
ap-3980	4	69	(	(	PUNCT
ap-3980	4	70	2016	2016	NUM
ap-3980	4	71	)	)	PUNCT
ap-3980	4	72	,	,	PUNCT
ap-3980	4	73	doi:10.1007	doi:10.1007	VERB
ap-3980	4	74	/	/	SYM
ap-3980	4	75	s12591	s12591	NOUN
ap-3980	4	76	-	-	PUNCT
ap-3980	4	77	016	016	NUM
ap-3980	4	78	-	-	PUNCT
ap-3980	4	79	0327	0327	NUM
ap-3980	4	80	-	-	PUNCT
ap-3980	4	81	5	5	NUM
ap-3980	4	82	)	)	PUNCT
ap-3980	4	83	in	in	ADP
ap-3980	4	84	terms	term	NOUN
ap-3980	4	85	of	of	ADP
ap-3980	4	86	symmetry	symmetry	NOUN
ap-3980	4	87	and	and	CCONJ
ap-3980	4	88	singularity	singularity	NOUN
ap-3980	4	89	.	.	PUNCT
ap-3980	5	1	all	all	DET
ap-3980	5	2	equations	equation	NOUN
ap-3980	5	3	of	of	ADP
ap-3980	5	4	the	the	DET
ap-3980	5	5	class	class	NOUN
ap-3980	5	6	are	be	AUX
ap-3980	5	7	integrable	integrable	ADJ
ap-3980	5	8	in	in	ADP
ap-3980	5	9	closed	closed	ADJ
ap-3980	5	10	form	form	NOUN
ap-3980	5	11	.	.	PUNCT
ap-3980	6	1	here	here	ADV
ap-3980	6	2	we	we	PRON
ap-3980	6	3	introduce	introduce	VERB
ap-3980	6	4	a	a	DET
ap-3980	6	5	new	new	ADJ
ap-3980	6	6	class	class	NOUN
ap-3980	6	7	,	,	PUNCT
ap-3980	6	8	(	(	PUNCT
ap-3980	6	9	n+q−2)y(n−2)y(n)−	n+q−2)y(n−2)y(n)−	PROPN
ap-3980	6	10	(	(	PUNCT
ap-3980	6	11	n+q−1)y(n−1)2	n+q−1)y(n−1)2	PROPN
ap-3980	6	12	=	=	SYM
ap-3980	6	13	0	0	PROPN
ap-3980	6	14	,	,	PUNCT
ap-3980	6	15	which	which	PRON
ap-3980	6	16	has	have	VERB
ap-3980	6	17	different	different	ADJ
ap-3980	6	18	integrability	integrability	NOUN
ap-3980	6	19	and	and	CCONJ
ap-3980	6	20	singularity	singularity	NOUN
ap-3980	6	21	properties	property	NOUN
ap-3980	6	22	.	.	PUNCT
ap-3980	7	1	keywords	keyword	NOUN
ap-3980	7	2	:	:	PUNCT
ap-3980	7	3	kummer	kummer	NOUN
ap-3980	7	4	-	-	PUNCT
ap-3980	7	5	schwarz	schwarz	PROPN
ap-3980	7	6	;	;	PUNCT
ap-3980	7	7	symmetries	symmetry	NOUN
ap-3980	7	8	;	;	PUNCT
ap-3980	7	9	singularities	singularity	NOUN
ap-3980	7	10	;	;	PUNCT
ap-3980	7	11	integrability	integrability	NOUN
ap-3980	7	12	.	.	PUNCT
ap-3980	8	1	1	1	X
ap-3980	8	2	.	.	X
ap-3980	8	3	introduction	introduction	NOUN
ap-3980	8	4	in	in	ADP
ap-3980	8	5	[	[	X
ap-3980	8	6	12	12	NUM
ap-3980	8	7	]	]	X
ap-3980	8	8	we	we	PRON
ap-3980	8	9	delineated	delineate	VERB
ap-3980	8	10	the	the	DET
ap-3980	8	11	properties	property	NOUN
ap-3980	8	12	of	of	ADP
ap-3980	8	13	the	the	DET
ap-3980	8	14	class	class	NOUN
ap-3980	8	15	of	of	ADP
ap-3980	8	16	equations	equation	NOUN
ap-3980	8	17	(	(	PUNCT
ap-3980	8	18	n−1)y(n−2)y(n)−n(y(n−1))2	n−1)y(n−2)y(n)−n(y(n−1))2	NOUN
ap-3980	8	19	=	=	SYM
ap-3980	8	20	0	0	NUM
ap-3980	8	21	,	,	PUNCT
ap-3980	8	22	n	n	NOUN
ap-3980	8	23	=	=	SYM
ap-3980	8	24	2	2	NUM
ap-3980	8	25	,	,	PUNCT
ap-3980	8	26	3	3	NUM
ap-3980	8	27	,	,	PUNCT
ap-3980	8	28	.	.	PUNCT
ap-3980	8	29	.	.	PUNCT
ap-3980	8	30	.	.	PUNCT
ap-3980	9	1	(	(	PUNCT
ap-3980	9	2	1	1	X
ap-3980	9	3	)	)	PUNCT
ap-3980	9	4	in	in	ADP
ap-3980	9	5	terms	term	NOUN
ap-3980	9	6	of	of	ADP
ap-3980	9	7	symmetry	symmetry	NOUN
ap-3980	9	8	,	,	PUNCT
ap-3980	9	9	singularity	singularity	NOUN
ap-3980	9	10	and	and	CCONJ
ap-3980	9	11	integrability	integrability	NOUN
ap-3980	9	12	.	.	PUNCT
ap-3980	10	1	the	the	DET
ap-3980	10	2	class	class	NOUN
ap-3980	10	3	(	(	PUNCT
ap-3980	10	4	1	1	NUM
ap-3980	10	5	)	)	PUNCT
ap-3980	10	6	differed	differ	VERB
ap-3980	10	7	from	from	ADP
ap-3980	10	8	the	the	DET
ap-3980	10	9	class	class	NOUN
ap-3980	10	10	with	with	ADP
ap-3980	10	11	general	general	ADJ
ap-3980	10	12	numerical	numerical	ADJ
ap-3980	10	13	coefficients	coefficient	NOUN
ap-3980	10	14	in	in	ADP
ap-3980	10	15	that	that	SCONJ
ap-3980	10	16	the	the	DET
ap-3980	10	17	number	number	NOUN
ap-3980	10	18	of	of	ADP
ap-3980	10	19	lie	lie	NOUN
ap-3980	10	20	point	point	NOUN
ap-3980	10	21	symmetries	symmetry	NOUN
ap-3980	10	22	was	be	AUX
ap-3980	10	23	one	one	NUM
ap-3980	10	24	greater	great	ADJ
ap-3980	10	25	for	for	ADP
ap-3980	10	26	general	general	ADJ
ap-3980	10	27	values	value	NOUN
ap-3980	10	28	of	of	ADP
ap-3980	10	29	n	n	PROPN
ap-3980	10	30	(	(	PUNCT
ap-3980	10	31	with	with	ADP
ap-3980	10	32	n	n	NOUN
ap-3980	10	33	=	=	SYM
ap-3980	10	34	2	2	NUM
ap-3980	10	35	being	be	AUX
ap-3980	10	36	an	an	DET
ap-3980	10	37	exceptional	exceptional	ADJ
ap-3980	10	38	case	case	NOUN
ap-3980	10	39	)	)	PUNCT
ap-3980	10	40	.	.	PUNCT
ap-3980	11	1	in	in	ADP
ap-3980	11	2	the	the	DET
ap-3980	11	3	case	case	NOUN
ap-3980	11	4	of	of	ADP
ap-3980	11	5	the	the	DET
ap-3980	11	6	kummer	kummer	NOUN
ap-3980	11	7	–	–	PUNCT
ap-3980	11	8	schwarz	schwarz	NOUN
ap-3980	11	9	equation	equation	NOUN
ap-3980	11	10	[	[	X
ap-3980	11	11	4	4	X
ap-3980	11	12	]	]	PUNCT
ap-3980	11	13	it	it	PRON
ap-3980	11	14	was	be	AUX
ap-3980	11	15	two	two	NUM
ap-3980	11	16	greater	great	ADJ
ap-3980	11	17	,	,	PUNCT
ap-3980	11	18	being	be	AUX
ap-3980	11	19	the	the	DET
ap-3980	11	20	six	six	NUM
ap-3980	11	21	comprising	comprise	VERB
ap-3980	11	22	the	the	DET
ap-3980	11	23	direct	direct	ADJ
ap-3980	11	24	sum	sum	NOUN
ap-3980	11	25	of	of	ADP
ap-3980	11	26	two	two	NUM
ap-3980	11	27	sl(2	sl(2	PROPN
ap-3980	11	28	,	,	PUNCT
ap-3980	11	29	r	r	NOUN
ap-3980	11	30	)	)	PUNCT
ap-3980	11	31	subalgebras	subalgebra	NOUN
ap-3980	11	32	.	.	PUNCT
ap-3980	12	1	here	here	ADV
ap-3980	12	2	we	we	PRON
ap-3980	12	3	consider	consider	VERB
ap-3980	12	4	the	the	DET
ap-3980	12	5	generalisation	generalisation	NOUN
ap-3980	12	6	(	(	PUNCT
ap-3980	12	7	n+	n+	NUM
ap-3980	12	8	q−	q−	PROPN
ap-3980	12	9	2)y(n−2)y(n	2)y(n−2)y(n	PROPN
ap-3980	12	10	)	)	PUNCT
ap-3980	12	11	−	−	PROPN
ap-3980	13	1	(	(	PUNCT
ap-3980	13	2	n+	n+	NUM
ap-3980	13	3	q−	q−	PROPN
ap-3980	13	4	1)y(n−1)2	1)y(n−1)2	NUM
ap-3980	13	5	=	=	SYM
ap-3980	13	6	0	0	NUM
ap-3980	13	7	,	,	PUNCT
ap-3980	13	8	n	n	NOUN
ap-3980	13	9	=	=	SYM
ap-3980	13	10	2	2	NUM
ap-3980	13	11	,	,	PUNCT
ap-3980	13	12	3	3	NUM
ap-3980	13	13	,	,	PUNCT
ap-3980	13	14	.	.	PUNCT
ap-3980	13	15	.	.	PUNCT
ap-3980	13	16	.	.	PUNCT
ap-3980	14	1	,	,	PUNCT
ap-3980	14	2	(	(	PUNCT
ap-3980	14	3	2	2	X
ap-3980	14	4	)	)	PUNCT
ap-3980	14	5	where	where	SCONJ
ap-3980	14	6	q	q	NOUN
ap-3980	14	7	is	be	AUX
ap-3980	14	8	a	a	DET
ap-3980	14	9	real	real	ADJ
ap-3980	14	10	number	number	NOUN
ap-3980	14	11	,	,	PUNCT
ap-3980	14	12	subsequently	subsequently	ADV
ap-3980	14	13	to	to	PART
ap-3980	14	14	be	be	AUX
ap-3980	14	15	more	more	ADV
ap-3980	14	16	precisely	precisely	ADV
ap-3980	14	17	defined	define	VERB
ap-3980	14	18	.	.	PUNCT
ap-3980	15	1	we	we	PRON
ap-3980	15	2	examine	examine	VERB
ap-3980	15	3	(	(	PUNCT
ap-3980	15	4	2	2	NUM
ap-3980	15	5	)	)	PUNCT
ap-3980	15	6	in	in	ADP
ap-3980	15	7	terms	term	NOUN
ap-3980	15	8	of	of	ADP
ap-3980	15	9	its	its	PRON
ap-3980	15	10	singularity	singularity	NOUN
ap-3980	15	11	properties	property	NOUN
ap-3980	15	12	,	,	PUNCT
ap-3980	15	13	symmetry	symmetry	NOUN
ap-3980	15	14	properties	property	NOUN
ap-3980	15	15	and	and	CCONJ
ap-3980	15	16	general	general	ADJ
ap-3980	15	17	integrability	integrability	NOUN
ap-3980	15	18	.	.	PUNCT
ap-3980	16	1	we	we	PRON
ap-3980	16	2	commence	commence	VERB
ap-3980	16	3	with	with	ADP
ap-3980	16	4	the	the	DET
ap-3980	16	5	singularity	singularity	NOUN
ap-3980	16	6	properties	property	NOUN
ap-3980	16	7	of	of	ADP
ap-3980	16	8	(	(	PUNCT
ap-3980	16	9	2	2	NUM
ap-3980	16	10	)	)	PUNCT
ap-3980	16	11	and	and	CCONJ
ap-3980	16	12	see	see	VERB
ap-3980	16	13	that	that	SCONJ
ap-3980	16	14	a	a	DET
ap-3980	16	15	successful	successful	ADJ
ap-3980	16	16	satisfaction	satisfaction	NOUN
ap-3980	16	17	of	of	ADP
ap-3980	16	18	the	the	DET
ap-3980	16	19	requirements	requirement	NOUN
ap-3980	16	20	imposes	impose	VERB
ap-3980	16	21	a	a	DET
ap-3980	16	22	constraint	constraint	NOUN
ap-3980	16	23	on	on	ADP
ap-3980	16	24	the	the	DET
ap-3980	16	25	permissible	permissible	ADJ
ap-3980	16	26	values	value	NOUN
ap-3980	16	27	of	of	ADP
ap-3980	16	28	q	q	NOUN
ap-3980	16	29	for	for	SCONJ
ap-3980	16	30	the	the	DET
ap-3980	16	31	solution	solution	NOUN
ap-3980	16	32	to	to	PART
ap-3980	16	33	be	be	AUX
ap-3980	16	34	analytic	analytic	ADJ
ap-3980	16	35	.	.	PUNCT
ap-3980	17	1	we	we	PRON
ap-3980	17	2	turn	turn	VERB
ap-3980	17	3	to	to	ADP
ap-3980	17	4	the	the	DET
ap-3980	17	5	symmetry	symmetry	NOUN
ap-3980	17	6	properties	property	NOUN
ap-3980	17	7	of	of	ADP
ap-3980	17	8	(	(	PUNCT
ap-3980	17	9	2	2	NUM
ap-3980	17	10	)	)	PUNCT
ap-3980	17	11	and	and	CCONJ
ap-3980	17	12	find	find	VERB
ap-3980	17	13	some	some	DET
ap-3980	17	14	unexpected	unexpected	ADJ
ap-3980	17	15	results	result	NOUN
ap-3980	17	16	.	.	PUNCT
ap-3980	18	1	in	in	ADP
ap-3980	18	2	terms	term	NOUN
ap-3980	18	3	of	of	ADP
ap-3980	18	4	integrability	integrability	NOUN
ap-3980	18	5	there	there	PRON
ap-3980	18	6	are	be	VERB
ap-3980	18	7	no	no	DET
ap-3980	18	8	restrictions	restriction	NOUN
ap-3980	18	9	upon	upon	SCONJ
ap-3980	18	10	the	the	DET
ap-3980	18	11	value	value	NOUN
ap-3980	18	12	of	of	ADP
ap-3980	18	13	q	q	NOUN
ap-3980	18	14	in	in	ADP
ap-3980	18	15	a	a	DET
ap-3980	18	16	formal	formal	ADJ
ap-3980	18	17	sense	sense	NOUN
ap-3980	18	18	although	although	SCONJ
ap-3980	18	19	in	in	ADP
ap-3980	18	20	practice	practice	NOUN
ap-3980	18	21	there	there	PRON
ap-3980	18	22	may	may	AUX
ap-3980	18	23	be	be	AUX
ap-3980	18	24	restrictions	restriction	NOUN
ap-3980	18	25	.	.	PUNCT
ap-3980	19	1	2	2	X
ap-3980	19	2	.	.	X
ap-3980	19	3	singularity	singularity	NOUN
ap-3980	19	4	analysis	analysis	NOUN
ap-3980	19	5	we	we	PRON
ap-3980	19	6	examine	examine	VERB
ap-3980	19	7	the	the	DET
ap-3980	19	8	sequence	sequence	NOUN
ap-3980	19	9	of	of	ADP
ap-3980	19	10	equations	equation	NOUN
ap-3980	19	11	introduced	introduce	VERB
ap-3980	19	12	above	above	ADV
ap-3980	19	13	in	in	ADP
ap-3980	19	14	terms	term	NOUN
ap-3980	19	15	of	of	ADP
ap-3980	19	16	singularity	singularity	NOUN
ap-3980	19	17	analysis	analysis	NOUN
ap-3980	19	18	.	.	PUNCT
ap-3980	20	1	we	we	PRON
ap-3980	20	2	follow	follow	VERB
ap-3980	20	3	the	the	DET
ap-3980	20	4	general	general	ADJ
ap-3980	20	5	method	method	NOUN
ap-3980	20	6	as	as	SCONJ
ap-3980	20	7	outlined	outline	VERB
ap-3980	20	8	in	in	ADP
ap-3980	20	9	[	[	X
ap-3980	20	10	10	10	NUM
ap-3980	20	11	,	,	PUNCT
ap-3980	20	12	14	14	NUM
ap-3980	20	13	]	]	PUNCT
ap-3980	20	14	with	with	ADP
ap-3980	20	15	the	the	DET
ap-3980	20	16	modification	modification	NOUN
ap-3980	20	17	for	for	ADP
ap-3980	20	18	negative	negative	ADJ
ap-3980	20	19	nongeneric	nongeneric	ADJ
ap-3980	20	20	resonances	resonance	NOUN
ap-3980	20	21	introduced	introduce	VERB
ap-3980	20	22	by	by	ADP
ap-3980	20	23	andriopoulos	andriopoulos	PROPN
ap-3980	20	24	et	et	PROPN
ap-3980	20	25	al	al	PROPN
ap-3980	20	26	.	.	PUNCT
ap-3980	21	1	[	[	X
ap-3980	21	2	1	1	NUM
ap-3980	21	3	]	]	PUNCT
ap-3980	21	4	.	.	PUNCT
ap-3980	21	5	theorem	theorem	VERB
ap-3980	21	6	.	.	PUNCT
ap-3980	22	1	the	the	DET
ap-3980	22	2	exponent	exponent	NOUN
ap-3980	22	3	of	of	ADP
ap-3980	22	4	the	the	DET
ap-3980	22	5	leading	lead	VERB
ap-3980	22	6	-	-	PUNCT
ap-3980	22	7	order	order	NOUN
ap-3980	22	8	term	term	NOUN
ap-3980	22	9	and	and	CCONJ
ap-3980	22	10	the	the	DET
ap-3980	22	11	resonances	resonance	NOUN
ap-3980	22	12	of	of	ADP
ap-3980	22	13	the	the	DET
ap-3980	22	14	nth	nth	NOUN
ap-3980	22	15	member	member	NOUN
ap-3980	22	16	of	of	ADP
ap-3980	22	17	the	the	DET
ap-3980	22	18	sequence	sequence	NOUN
ap-3980	22	19	of	of	ADP
ap-3980	22	20	equations	equation	NOUN
ap-3980	22	21	,	,	PUNCT
ap-3980	22	22	(	(	PUNCT
ap-3980	22	23	n+	n+	NUM
ap-3980	22	24	q−	q−	PROPN
ap-3980	22	25	2)y(n−2)y(n	2)y(n−2)y(n	PROPN
ap-3980	22	26	)	)	PUNCT
ap-3980	22	27	−	−	PROPN
ap-3980	22	28	(	(	PUNCT
ap-3980	22	29	n+	n+	NUM
ap-3980	22	30	q−	q−	PROPN
ap-3980	22	31	1)(y(n−1))2	1)(y(n−1))2	NUM
ap-3980	23	1	=	=	SYM
ap-3980	23	2	0	0	NUM
ap-3980	23	3	,	,	PUNCT
ap-3980	23	4	n	n	PRON
ap-3980	23	5	∈	∈	PROPN
ap-3980	23	6	n	n	CCONJ
ap-3980	23	7	,	,	PUNCT
ap-3980	23	8	n	n	CCONJ
ap-3980	23	9	>	>	X
ap-3980	23	10	1	1	NUM
ap-3980	23	11	,	,	PUNCT
ap-3980	23	12	(	(	PUNCT
ap-3980	23	13	3	3	X
ap-3980	23	14	)	)	PUNCT
ap-3980	23	15	are	be	AUX
ap-3980	23	16	p	p	NOUN
ap-3980	23	17	=	=	NOUN
ap-3980	23	18	−q	−q	NOUN
ap-3980	23	19	and	and	CCONJ
ap-3980	23	20	s	s	NOUN
ap-3980	23	21	=	=	NOUN
ap-3980	23	22	−1	−1	NOUN
ap-3980	23	23	,	,	PUNCT
ap-3980	23	24	0	0	NUM
ap-3980	23	25	,	,	PUNCT
ap-3980	23	26	q	q	ADJ
ap-3980	23	27	,	,	PUNCT
ap-3980	23	28	1	1	NUM
ap-3980	23	29	+	+	CCONJ
ap-3980	23	30	q	q	ADJ
ap-3980	23	31	,	,	PUNCT
ap-3980	23	32	.	.	PUNCT
ap-3980	23	33	.	.	PUNCT
ap-3980	24	1	.	.	PUNCT
ap-3980	25	1	,	,	PUNCT
ap-3980	25	2	n−	n−	NOUN
ap-3980	25	3	3	3	NUM
ap-3980	25	4	+	+	CCONJ
ap-3980	25	5	q.	q.	NOUN
ap-3980	25	6	proof	proof	NOUN
ap-3980	25	7	.	.	PUNCT
ap-3980	26	1	we	we	PRON
ap-3980	26	2	substitute	substitute	VERB
ap-3980	26	3	y	y	PROPN
ap-3980	26	4	=	=	SYM
ap-3980	26	5	αχp	αχp	PROPN
ap-3980	26	6	,	,	PUNCT
ap-3980	26	7	where	where	SCONJ
ap-3980	26	8	χ	χ	X
ap-3980	26	9	=	=	PUNCT
ap-3980	26	10	x	x	SYM
ap-3980	26	11	−	−	NOUN
ap-3980	26	12	x0	x0	PROPN
ap-3980	26	13	and	and	CCONJ
ap-3980	26	14	x0	x0	PROPN
ap-3980	26	15	is	be	AUX
ap-3980	26	16	the	the	DET
ap-3980	26	17	location	location	NOUN
ap-3980	26	18	of	of	ADP
ap-3980	26	19	the	the	DET
ap-3980	26	20	putative	putative	ADJ
ap-3980	26	21	singularity	singularity	NOUN
ap-3980	26	22	.	.	PUNCT
ap-3980	27	1	we	we	PRON
ap-3980	27	2	remove	remove	VERB
ap-3980	27	3	a	a	DET
ap-3980	27	4	common	common	ADJ
ap-3980	27	5	factor	factor	NOUN
ap-3980	27	6	p2(p−1)2	p2(p−1)2	VERB
ap-3980	27	7	·	·	PUNCT
ap-3980	27	8	·	·	PUNCT
ap-3980	27	9	·	·	PUNCT
ap-3980	28	1	(	(	PUNCT
ap-3980	28	2	p−n+3)2(p−	p−n+3)2(p−	VERB
ap-3980	28	3	n+	n+	NOUN
ap-3980	28	4	2	2	NUM
ap-3980	28	5	)	)	PUNCT
ap-3980	28	6	.	.	PUNCT
ap-3980	29	1	the	the	DET
ap-3980	29	2	values	value	NOUN
ap-3980	29	3	of	of	ADP
ap-3980	29	4	p	p	NOUN
ap-3980	29	5	removed	remove	VERB
ap-3980	29	6	are	be	AUX
ap-3980	29	7	all	all	ADV
ap-3980	29	8	positive	positive	ADJ
ap-3980	29	9	and	and	CCONJ
ap-3980	29	10	so	so	ADV
ap-3980	29	11	of	of	ADP
ap-3980	29	12	no	no	DET
ap-3980	29	13	relevance	relevance	NOUN
ap-3980	29	14	to	to	ADP
ap-3980	29	15	the	the	DET
ap-3980	29	16	singularity	singularity	NOUN
ap-3980	29	17	analysis	analysis	NOUN
ap-3980	29	18	.	.	PUNCT
ap-3980	30	1	the	the	DET
ap-3980	30	2	remaining	remain	VERB
ap-3980	30	3	terms	term	NOUN
ap-3980	30	4	are	be	AUX
ap-3980	30	5	(	(	PUNCT
ap-3980	30	6	n+	n+	NUM
ap-3980	30	7	q−	q−	PROPN
ap-3980	30	8	2)(p−n+	2)(p−n+	NUM
ap-3980	30	9	1)−	1)−	NUM
ap-3980	30	10	(	(	PUNCT
ap-3980	30	11	n+	n+	NUM
ap-3980	30	12	q−	q−	PROPN
ap-3980	30	13	1)(p−n+	1)(p−n+	NUM
ap-3980	30	14	2	2	NUM
ap-3980	30	15	)	)	PUNCT
ap-3980	30	16	which	which	PRON
ap-3980	30	17	,	,	PUNCT
ap-3980	30	18	when	when	SCONJ
ap-3980	30	19	put	put	VERB
ap-3980	30	20	equal	equal	ADJ
ap-3980	30	21	to	to	ADP
ap-3980	30	22	zero	zero	NUM
ap-3980	30	23	,	,	PUNCT
ap-3980	30	24	give	give	VERB
ap-3980	30	25	the	the	DET
ap-3980	30	26	singularity	singularity	NOUN
ap-3980	30	27	to	to	PART
ap-3980	30	28	be	be	AUX
ap-3980	30	29	p	p	NOUN
ap-3980	30	30	=	=	NOUN
ap-3980	30	31	−q	−q	NOUN
ap-3980	30	32	.	.	PUNCT
ap-3980	31	1	we	we	PRON
ap-3980	31	2	write	write	VERB
ap-3980	31	3	y	y	NOUN
ap-3980	31	4	=	=	PUNCT
ap-3980	31	5	αχ−q	αχ−q	NOUN
ap-3980	31	6	+	+	CCONJ
ap-3980	31	7	µχ−q+s	µχ−q+s	PUNCT
ap-3980	31	8	and	and	CCONJ
ap-3980	31	9	substitute	substitute	VERB
ap-3980	31	10	into	into	ADP
ap-3980	31	11	(	(	PUNCT
ap-3980	31	12	3	3	NUM
ap-3980	31	13	)	)	PUNCT
ap-3980	31	14	.	.	PUNCT
ap-3980	32	1	we	we	PRON
ap-3980	32	2	remove	remove	VERB
ap-3980	32	3	the	the	DET
ap-3980	32	4	common	common	ADJ
ap-3980	32	5	factors	factor	NOUN
ap-3980	32	6	χ−2	χ−2	PROPN
ap-3980	32	7	and	and	CCONJ
ap-3980	32	8	obtain	obtain	VERB
ap-3980	32	9	(	(	PUNCT
ap-3980	32	10	−q)(−q−1	−q)(−q−1	X
ap-3980	32	11	)	)	PUNCT
ap-3980	32	12	·	·	PUNCT
ap-3980	32	13	·	·	PUNCT
ap-3980	32	14	·	·	PUNCT
ap-3980	32	15	(	(	PUNCT
ap-3980	32	16	−q−n+3)(−q+s)(−q+s−1	−q−n+3)(−q+s)(−q+s−1	NUM
ap-3980	32	17	)	)	PUNCT
ap-3980	32	18	·	·	PUNCT
ap-3980	32	19	·	·	PUNCT
ap-3980	32	20	·	·	PUNCT
ap-3980	32	21	·	·	PUNCT
ap-3980	32	22	·	·	PUNCT
ap-3980	32	23	·	·	PUNCT
ap-3980	32	24	(	(	PUNCT
ap-3980	32	25	−q+	−q+	NOUN
ap-3980	32	26	s−n+	s−n+	PROPN
ap-3980	32	27	3	3	NUM
ap-3980	32	28	)	)	PUNCT
ap-3980	32	29	this	this	PRON
ap-3980	32	30	immediately	immediately	ADV
ap-3980	32	31	gives	give	VERB
ap-3980	32	32	the	the	DET
ap-3980	32	33	resonances	resonance	NOUN
ap-3980	32	34	,	,	PUNCT
ap-3980	32	35	s	s	NOUN
ap-3980	32	36	=	=	NOUN
ap-3980	32	37	q	q	NOUN
ap-3980	32	38	,	,	PUNCT
ap-3980	32	39	q	q	PROPN
ap-3980	33	1	+	+	NUM
ap-3980	33	2	1	1	NUM
ap-3980	33	3	,	,	PUNCT
ap-3980	33	4	.	.	PUNCT
ap-3980	33	5	.	.	PUNCT
ap-3980	34	1	.	.	PUNCT
ap-3980	35	1	,	,	PUNCT
ap-3980	35	2	q	q	X
ap-3980	36	1	+	+	NUM
ap-3980	36	2	n−	n−	NOUN
ap-3980	36	3	3	3	NUM
ap-3980	36	4	,	,	PUNCT
ap-3980	36	5	which	which	PRON
ap-3980	36	6	are	be	AUX
ap-3980	36	7	all	all	ADV
ap-3980	36	8	positive	positive	ADJ
ap-3980	36	9	.	.	PUNCT
ap-3980	37	1	the	the	DET
ap-3980	37	2	remaining	remain	VERB
ap-3980	37	3	terms	term	NOUN
ap-3980	37	4	are	be	AUX
ap-3980	37	5	(	(	PUNCT
ap-3980	37	6	n+	n+	NUM
ap-3980	37	7	q−	q−	PROPN
ap-3980	37	8	2)(−q−n+	2)(−q−n+	NUM
ap-3980	37	9	2)(−q−n+	2)(−q−n+	NUM
ap-3980	37	10	1	1	NUM
ap-3980	37	11	)	)	PUNCT
ap-3980	38	1	+	+	CCONJ
ap-3980	38	2	(	(	PUNCT
ap-3980	38	3	n+	n+	NUM
ap-3980	38	4	q−	q−	PROPN
ap-3980	38	5	2)(−q+	2)(−q+	PROPN
ap-3980	39	1	s−n+	s−n+	PROPN
ap-3980	39	2	2)(−q+	2)(−q+	PROPN
ap-3980	39	3	s−n+	s−n+	PROPN
ap-3980	39	4	1	1	NUM
ap-3980	39	5	)	)	PUNCT
ap-3980	39	6	−	−	NOUN
ap-3980	40	1	2(n+	2(n+	NOUN
ap-3980	41	1	q−	q−	PROPN
ap-3980	41	2	1)(−q−n+	1)(−q−n+	NUM
ap-3980	41	3	2)(−q+	2)(−q+	NUM
ap-3980	41	4	s−n+	s−n+	PROPN
ap-3980	41	5	2	2	NUM
ap-3980	41	6	)	)	PUNCT
ap-3980	41	7	.	.	PUNCT
ap-3980	42	1	467	467	NUM
ap-3980	42	2	http://dx.doi.org/10.14311/ap.2017.57.0467	http://dx.doi.org/10.14311/ap.2017.57.0467	X
ap-3980	42	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3980	42	4	r.	r.	PROPN
ap-3980	42	5	sinuvasan	sinuvasan	PROPN
ap-3980	42	6	,	,	PUNCT
ap-3980	42	7	k.	k.	PROPN
ap-3980	42	8	krishnakumar	krishnakumar	PROPN
ap-3980	42	9	,	,	PUNCT
ap-3980	42	10	k.	k.	PROPN
ap-3980	42	11	m.	m.	PROPN
ap-3980	42	12	tamizhmani	tamizhmani	PROPN
ap-3980	42	13	,	,	PUNCT
ap-3980	42	14	p.	p.	NOUN
ap-3980	42	15	g.	g.	PROPN
ap-3980	42	16	l.	l.	PROPN
ap-3980	42	17	leach	leach	PROPN
ap-3980	42	18	acta	acta	PROPN
ap-3980	42	19	polytechnica	polytechnica	PROPN
ap-3980	42	20	when	when	SCONJ
ap-3980	42	21	this	this	PRON
ap-3980	42	22	equated	equate	VERB
ap-3980	42	23	to	to	ADP
ap-3980	42	24	zero	zero	NUM
ap-3980	42	25	,	,	PUNCT
ap-3980	42	26	we	we	PRON
ap-3980	42	27	obtain	obtain	VERB
ap-3980	42	28	the	the	DET
ap-3980	42	29	two	two	NUM
ap-3980	42	30	additional	additional	ADJ
ap-3980	42	31	resonances	resonance	NOUN
ap-3980	42	32	s	s	PART
ap-3980	42	33	=	=	X
ap-3980	42	34	−1	−1	NOUN
ap-3980	42	35	,	,	PUNCT
ap-3980	42	36	0	0	X
ap-3980	42	37	.	.	PUNCT
ap-3980	43	1	apart	apart	ADV
ap-3980	43	2	from	from	ADP
ap-3980	43	3	the	the	DET
ap-3980	43	4	generic	generic	ADJ
ap-3980	43	5	resonance	resonance	NOUN
ap-3980	43	6	of	of	ADP
ap-3980	43	7	−1	−1	NOUN
ap-3980	43	8	all	all	PRON
ap-3980	43	9	of	of	ADP
ap-3980	43	10	the	the	DET
ap-3980	43	11	resonances	resonance	NOUN
ap-3980	43	12	are	be	AUX
ap-3980	43	13	nonnegative	nonnegative	ADJ
ap-3980	43	14	numbers	number	NOUN
ap-3980	43	15	which	which	PRON
ap-3980	43	16	contain	contain	VERB
ap-3980	43	17	the	the	DET
ap-3980	43	18	positive	positive	ADJ
ap-3980	43	19	number	number	NOUN
ap-3980	43	20	q.	q.	NOUN
ap-3980	43	21	when	when	SCONJ
ap-3980	43	22	the	the	DET
ap-3980	43	23	resulting	result	VERB
ap-3980	43	24	expansion	expansion	NOUN
ap-3980	43	25	make	make	VERB
ap-3980	43	26	sense	sense	NOUN
ap-3980	43	27	,	,	PUNCT
ap-3980	43	28	the	the	DET
ap-3980	43	29	laurent	laurent	NOUN
ap-3980	43	30	expansion	expansion	NOUN
ap-3980	43	31	is	be	AUX
ap-3980	43	32	a	a	DET
ap-3980	43	33	right	right	ADJ
ap-3980	43	34	painlevé	painlevé	NOUN
ap-3980	43	35	series	series	NOUN
ap-3980	43	36	[	[	X
ap-3980	43	37	2	2	NUM
ap-3980	43	38	]	]	PUNCT
ap-3980	43	39	.	.	PUNCT
ap-3980	44	1	we	we	PRON
ap-3980	44	2	illustrate	illustrate	VERB
ap-3980	44	3	the	the	DET
ap-3980	44	4	method	method	NOUN
ap-3980	44	5	with	with	ADP
ap-3980	44	6	the	the	DET
ap-3980	44	7	fifth	fifth	ADJ
ap-3980	44	8	-	-	PUNCT
ap-3980	44	9	order	order	NOUN
ap-3980	44	10	equation	equation	NOUN
ap-3980	44	11	,	,	PUNCT
ap-3980	44	12	(	(	PUNCT
ap-3980	44	13	q+	q+	ADP
ap-3980	44	14	3)y′′′y(5	3)y′′′y(5	NUM
ap-3980	44	15	)	)	PUNCT
ap-3980	44	16	−	−	PROPN
ap-3980	45	1	(	(	PUNCT
ap-3980	45	2	q+	q+	ADP
ap-3980	45	3	4)(y(4))2	4)(y(4))2	NUM
ap-3980	45	4	=	=	SYM
ap-3980	45	5	0	0	X
ap-3980	45	6	.	.	PUNCT
ap-3980	46	1	(	(	PUNCT
ap-3980	46	2	4	4	NUM
ap-3980	46	3	)	)	PUNCT
ap-3980	46	4	to	to	PART
ap-3980	46	5	determine	determine	VERB
ap-3980	46	6	the	the	DET
ap-3980	46	7	leading	lead	VERB
ap-3980	46	8	-	-	PUNCT
ap-3980	46	9	order	order	NOUN
ap-3980	46	10	behaviour	behaviour	NOUN
ap-3980	46	11	we	we	PRON
ap-3980	46	12	set	set	VERB
ap-3980	46	13	y	y	PROPN
ap-3980	46	14	=	=	SYM
ap-3980	46	15	αχp	αχp	PROPN
ap-3980	46	16	,	,	PUNCT
ap-3980	46	17	where	where	SCONJ
ap-3980	46	18	χ	χ	ADJ
ap-3980	46	19	=	=	SYM
ap-3980	46	20	x−	x−	PROPN
ap-3980	46	21	x0	x0	PROPN
ap-3980	46	22	and	and	CCONJ
ap-3980	46	23	x0	x0	PROPN
ap-3980	46	24	is	be	AUX
ap-3980	46	25	the	the	DET
ap-3980	46	26	location	location	NOUN
ap-3980	46	27	of	of	ADP
ap-3980	46	28	the	the	DET
ap-3980	46	29	putative	putative	ADJ
ap-3980	46	30	singularity	singularity	NOUN
ap-3980	46	31	.	.	PUNCT
ap-3980	47	1	we	we	PRON
ap-3980	47	2	obtain	obtain	VERB
ap-3980	47	3	(	(	PUNCT
ap-3980	47	4	q+	q+	ADP
ap-3980	47	5	3)α2p2(p−	3)α2p2(p−	NUM
ap-3980	47	6	1)2(p−	1)2(p−	NUM
ap-3980	47	7	2)2(p−	2)2(p−	NUM
ap-3980	47	8	3)(p−	3)(p−	NUM
ap-3980	47	9	4)χ2p−8	4)χ2p−8	NOUN
ap-3980	47	10	−	−	PROPN
ap-3980	48	1	(	(	PUNCT
ap-3980	48	2	q+	q+	ADP
ap-3980	48	3	4)α2p2(p−	4)α2p2(p−	X
ap-3980	48	4	1)2(p−	1)2(p−	NUM
ap-3980	48	5	2)2(p−	2)2(p−	NUM
ap-3980	48	6	3)2χ2p−8	3)2χ2p−8	NOUN
ap-3980	48	7	which	which	PRON
ap-3980	48	8	is	be	AUX
ap-3980	48	9	zero	zero	NUM
ap-3980	48	10	if	if	SCONJ
ap-3980	48	11	(	(	PUNCT
ap-3980	48	12	q	q	X
ap-3980	48	13	+	+	NUM
ap-3980	48	14	3)(p−	3)(p−	NUM
ap-3980	48	15	4	4	NUM
ap-3980	48	16	)	)	PUNCT
ap-3980	48	17	=	=	SYM
ap-3980	48	18	(	(	PUNCT
ap-3980	48	19	q	q	PROPN
ap-3980	48	20	+	+	CCONJ
ap-3980	48	21	4)(p−	4)(p−	NUM
ap-3980	48	22	3	3	NUM
ap-3980	48	23	)	)	PUNCT
ap-3980	48	24	,	,	PUNCT
ap-3980	48	25	i.e.	i.e.	X
ap-3980	48	26	,	,	PUNCT
ap-3980	48	27	p	p	NOUN
ap-3980	48	28	=	=	NOUN
ap-3980	48	29	−q	−q	NOUN
ap-3980	48	30	.	.	PUNCT
ap-3980	49	1	note	note	VERB
ap-3980	49	2	that	that	SCONJ
ap-3980	49	3	the	the	DET
ap-3980	49	4	coefficient	coefficient	NOUN
ap-3980	49	5	of	of	ADP
ap-3980	49	6	the	the	DET
ap-3980	49	7	leading	lead	VERB
ap-3980	49	8	-	-	PUNCT
ap-3980	49	9	order	order	NOUN
ap-3980	49	10	term	term	NOUN
ap-3980	49	11	is	be	AUX
ap-3980	49	12	arbitrary	arbitrary	ADJ
ap-3980	49	13	.	.	PUNCT
ap-3980	50	1	to	to	PART
ap-3980	50	2	establish	establish	VERB
ap-3980	50	3	the	the	DET
ap-3980	50	4	terms	term	NOUN
ap-3980	50	5	at	at	ADP
ap-3980	50	6	which	which	PRON
ap-3980	50	7	the	the	DET
ap-3980	50	8	remaining	remain	VERB
ap-3980	50	9	constants	constant	NOUN
ap-3980	50	10	of	of	ADP
ap-3980	50	11	integration	integration	NOUN
ap-3980	50	12	occur	occur	VERB
ap-3980	50	13	in	in	ADP
ap-3980	50	14	the	the	DET
ap-3980	50	15	laurent	laurent	NOUN
ap-3980	50	16	expansion	expansion	NOUN
ap-3980	50	17	we	we	PRON
ap-3980	50	18	make	make	VERB
ap-3980	50	19	the	the	DET
ap-3980	50	20	substitution	substitution	NOUN
ap-3980	51	1	y	y	NOUN
ap-3980	51	2	=	=	PUNCT
ap-3980	51	3	αχ−q	αχ−q	NOUN
ap-3980	51	4	+	+	NOUN
ap-3980	51	5	mχ−q+s	mχ−q+	NOUN
ap-3980	51	6	.	.	PUNCT
ap-3980	52	1	the	the	DET
ap-3980	52	2	various	various	ADJ
ap-3980	52	3	values	value	NOUN
ap-3980	52	4	s	s	AUX
ap-3980	52	5	may	may	AUX
ap-3980	52	6	take	take	VERB
ap-3980	52	7	are	be	AUX
ap-3980	52	8	determined	determine	VERB
ap-3980	52	9	by	by	ADP
ap-3980	52	10	those	those	DET
ap-3980	52	11	values	value	NOUN
ap-3980	52	12	of	of	ADP
ap-3980	52	13	s	s	PRON
ap-3980	52	14	which	which	PRON
ap-3980	52	15	make	make	VERB
ap-3980	52	16	the	the	DET
ap-3980	52	17	coefficient	coefficient	NOUN
ap-3980	52	18	of	of	ADP
ap-3980	52	19	m	m	PRON
ap-3980	52	20	so	so	SCONJ
ap-3980	52	21	that	that	SCONJ
ap-3980	52	22	m	m	NOUN
ap-3980	52	23	is	be	AUX
ap-3980	52	24	arbitrary	arbitrary	ADJ
ap-3980	52	25	.	.	PUNCT
ap-3980	53	1	the	the	DET
ap-3980	53	2	coefficient	coefficient	NOUN
ap-3980	53	3	of	of	ADP
ap-3980	53	4	m	m	PROPN
ap-3980	53	5	is	be	AUX
ap-3980	53	6	a	a	DET
ap-3980	53	7	fifth	fifth	ADJ
ap-3980	53	8	-	-	PUNCT
ap-3980	53	9	order	order	NOUN
ap-3980	53	10	polynomial	polynomial	NOUN
ap-3980	53	11	the	the	DET
ap-3980	53	12	roots	root	NOUN
ap-3980	53	13	of	of	ADP
ap-3980	53	14	which	which	PRON
ap-3980	53	15	are	be	AUX
ap-3980	53	16	s	s	NOUN
ap-3980	53	17	=	=	NOUN
ap-3980	53	18	−1	−1	NOUN
ap-3980	53	19	,	,	PUNCT
ap-3980	53	20	0	0	NUM
ap-3980	53	21	,	,	PUNCT
ap-3980	53	22	q	q	ADJ
ap-3980	53	23	,	,	PUNCT
ap-3980	53	24	1	1	NUM
ap-3980	53	25	+	+	CCONJ
ap-3980	53	26	q	q	ADJ
ap-3980	53	27	,	,	PUNCT
ap-3980	53	28	2	2	NUM
ap-3980	53	29	+	+	CCONJ
ap-3980	53	30	q.	q.	PROPN
ap-3980	53	31	3	3	NUM
ap-3980	53	32	.	.	PUNCT
ap-3980	53	33	solution	solution	NOUN
ap-3980	53	34	of	of	ADP
ap-3980	53	35	the	the	DET
ap-3980	53	36	general	general	ADJ
ap-3980	53	37	equation	equation	NOUN
ap-3980	53	38	equation	equation	NOUN
ap-3980	53	39	(	(	PUNCT
ap-3980	53	40	2	2	NUM
ap-3980	53	41	)	)	PUNCT
ap-3980	53	42	,	,	PUNCT
ap-3980	53	43	up	up	ADP
ap-3980	53	44	to	to	ADP
ap-3980	53	45	a	a	DET
ap-3980	53	46	multiplicative	multiplicative	ADJ
ap-3980	53	47	constant	constant	NOUN
ap-3980	53	48	,	,	PUNCT
ap-3980	53	49	may	may	AUX
ap-3980	53	50	be	be	AUX
ap-3980	53	51	written	write	VERB
ap-3980	53	52	as	as	ADP
ap-3980	53	53	d2y(n−2)(x)−	d2y(n−2)(x)−	PROPN
ap-3980	53	54	1	1	NUM
ap-3980	53	55	n+q−2	n+q−2	PROPN
ap-3980	53	56	dx2	dx2	PROPN
ap-3980	53	57	=	=	PROPN
ap-3980	53	58	0	0	NUM
ap-3980	53	59	which	which	PRON
ap-3980	53	60	is	be	AUX
ap-3980	53	61	readily	readily	ADV
ap-3980	53	62	integrated	integrate	VERB
ap-3980	53	63	to	to	PART
ap-3980	53	64	give	give	VERB
ap-3980	53	65	the	the	DET
ap-3980	53	66	general	general	ADJ
ap-3980	53	67	solution	solution	NOUN
ap-3980	53	68	of	of	ADP
ap-3980	53	69	(	(	PUNCT
ap-3980	53	70	2	2	NUM
ap-3980	53	71	)	)	PUNCT
ap-3980	53	72	as	as	ADP
ap-3980	53	73	y	y	PROPN
ap-3980	53	74	=	=	SYM
ap-3980	53	75	(	(	PUNCT
ap-3980	53	76	−1)n	−1)n	X
ap-3980	53	77	(	(	PUNCT
ap-3980	53	78	ax+	ax+	VERB
ap-3980	53	79	b)−q	b)−q	X
ap-3980	53	80	an−2(q+n−	an−2(q+n−	VERB
ap-3980	53	81	3)(n−3	3)(n−3	NUM
ap-3980	53	82	)	)	PUNCT
ap-3980	54	1	+	+	CCONJ
ap-3980	54	2	n−3∑	n−3∑	PROPN
ap-3980	54	3	i=0	i=0	PROPN
ap-3980	54	4	cix	cix	PROPN
ap-3980	54	5	i	i	PRON
ap-3980	54	6	,	,	PUNCT
ap-3980	54	7	(	(	PUNCT
ap-3980	54	8	5	5	NUM
ap-3980	54	9	)	)	PUNCT
ap-3980	54	10	where	where	SCONJ
ap-3980	54	11	the	the	DET
ap-3980	54	12	notation	notation	NOUN
ap-3980	54	13	(	(	PUNCT
ap-3980	54	14	q+n−	q+n−	PROPN
ap-3980	54	15	3)(n−3	3)(n−3	NUM
ap-3980	54	16	)	)	PUNCT
ap-3980	54	17	denotes	denote	VERB
ap-3980	54	18	the	the	DET
ap-3980	54	19	rising	rise	VERB
ap-3980	54	20	pochhammer	pochhammer	NOUN
ap-3980	54	21	symbol	symbol	NOUN
ap-3980	54	22	and	and	CCONJ
ap-3980	54	23	means	mean	VERB
ap-3980	54	24	q(q+1	q(q+1	PROPN
ap-3980	54	25	)	)	PUNCT
ap-3980	54	26	·	·	PUNCT
ap-3980	54	27	·	·	PUNCT
ap-3980	54	28	·	·	PUNCT
ap-3980	54	29	(	(	PUNCT
ap-3980	54	30	q+n−3	q+n−3	NOUN
ap-3980	54	31	)	)	PUNCT
ap-3980	54	32	.	.	PUNCT
ap-3980	55	1	we	we	PRON
ap-3980	55	2	note	note	VERB
ap-3980	55	3	that	that	SCONJ
ap-3980	55	4	the	the	DET
ap-3980	55	5	solution	solution	NOUN
ap-3980	55	6	of	of	ADP
ap-3980	55	7	(	(	PUNCT
ap-3980	55	8	2	2	NUM
ap-3980	55	9	)	)	PUNCT
ap-3980	55	10	exists	exist	VERB
ap-3980	55	11	no	no	ADV
ap-3980	55	12	matter	matter	ADV
ap-3980	55	13	the	the	DET
ap-3980	55	14	value	value	NOUN
ap-3980	55	15	of	of	ADP
ap-3980	55	16	q.	q.	PROPN
ap-3980	55	17	naturally	naturally	ADV
ap-3980	55	18	the	the	DET
ap-3980	55	19	utility	utility	NOUN
ap-3980	55	20	of	of	ADP
ap-3980	55	21	the	the	DET
ap-3980	55	22	solution	solution	NOUN
ap-3980	55	23	depends	depend	VERB
ap-3980	55	24	upon	upon	SCONJ
ap-3980	55	25	the	the	DET
ap-3980	55	26	value	value	NOUN
ap-3980	55	27	of	of	ADP
ap-3980	55	28	q	q	NOUN
ap-3980	55	29	because	because	SCONJ
ap-3980	55	30	we	we	PRON
ap-3980	55	31	are	be	AUX
ap-3980	55	32	dealing	deal	VERB
ap-3980	55	33	with	with	ADP
ap-3980	55	34	values	value	NOUN
ap-3980	55	35	in	in	ADP
ap-3980	55	36	the	the	DET
ap-3980	55	37	complex	complex	ADJ
ap-3980	55	38	plane	plane	NOUN
ap-3980	55	39	.	.	PUNCT
ap-3980	56	1	4	4	X
ap-3980	56	2	.	.	X
ap-3980	56	3	symmetry	symmetry	NOUN
ap-3980	56	4	properties	property	NOUN
ap-3980	56	5	the	the	DET
ap-3980	56	6	symmetry	symmetry	NOUN
ap-3980	56	7	properties	property	NOUN
ap-3980	56	8	of	of	ADP
ap-3980	56	9	(	(	PUNCT
ap-3980	56	10	2	2	NUM
ap-3980	56	11	)	)	PUNCT
ap-3980	56	12	are	be	AUX
ap-3980	56	13	rather	rather	ADV
ap-3980	56	14	complex	complex	ADJ
ap-3980	56	15	and	and	CCONJ
ap-3980	56	16	to	to	PART
ap-3980	56	17	give	give	VERB
ap-3980	56	18	an	an	DET
ap-3980	56	19	indication	indication	NOUN
ap-3980	56	20	of	of	ADP
ap-3980	56	21	the	the	DET
ap-3980	56	22	complexity	complexity	NOUN
ap-3980	56	23	we	we	PRON
ap-3980	56	24	quote	quote	VERB
ap-3980	56	25	the	the	DET
ap-3980	56	26	results	result	NOUN
ap-3980	56	27	for	for	ADP
ap-3980	56	28	a	a	DET
ap-3980	56	29	small	small	ADJ
ap-3980	56	30	sample	sample	NOUN
ap-3980	56	31	of	of	ADP
ap-3980	56	32	equations	equation	NOUN
ap-3980	56	33	.	.	PUNCT
ap-3980	57	1	we	we	PRON
ap-3980	57	2	commence	commence	VERB
ap-3980	57	3	with	with	ADP
ap-3980	57	4	n	n	NOUN
ap-3980	57	5	=	=	SYM
ap-3980	57	6	2	2	NUM
ap-3980	57	7	for	for	ADP
ap-3980	57	8	which	which	PRON
ap-3980	57	9	we	we	PRON
ap-3980	57	10	obtain	obtain	VERB
ap-3980	57	11	the	the	DET
ap-3980	57	12	symmetries	symmetry	NOUN
ap-3980	57	13	,	,	PUNCT
ap-3980	57	14	{	{	PUNCT
ap-3980	57	15	∂	∂	NUM
ap-3980	57	16	∂x	∂x	PROPN
ap-3980	57	17	,	,	PUNCT
ap-3980	57	18	y	y	PROPN
ap-3980	57	19	∂	∂	ADV
ap-3980	57	20	∂y	∂y	NOUN
ap-3980	57	21	,	,	PUNCT
ap-3980	57	22	x	x	SYM
ap-3980	57	23	∂	∂	NUM
ap-3980	57	24	∂x	∂x	PROPN
ap-3980	57	25	,	,	PUNCT
ap-3980	57	26	y	y	PROPN
ap-3980	57	27	1	1	NUM
ap-3980	57	28	q	q	NOUN
ap-3980	57	29	+1	+1	PROPN
ap-3980	57	30	∂	∂	X
ap-3980	57	31	∂y	∂y	NOUN
ap-3980	57	32	,	,	PUNCT
ap-3980	57	33	xy	xy	PROPN
ap-3980	57	34	1	1	NUM
ap-3980	57	35	q	q	NOUN
ap-3980	57	36	+1	+1	PROPN
ap-3980	57	37	∂	∂	X
ap-3980	57	38	∂y	∂y	NOUN
ap-3980	57	39	,	,	PUNCT
ap-3980	57	40	qy−1	qy−1	PROPN
ap-3980	57	41	/	/	SYM
ap-3980	57	42	q	q	NOUN
ap-3980	57	43	∂	∂	NUM
ap-3980	57	44	∂x	∂x	PROPN
ap-3980	57	45	,	,	PUNCT
ap-3980	57	46	xy	xy	PROPN
ap-3980	57	47	∂	∂	NOUN
ap-3980	58	1	∂y	∂y	NOUN
ap-3980	58	2	−	−	NOUN
ap-3980	59	1	x2	x2	PROPN
ap-3980	59	2	q	q	PROPN
ap-3980	59	3	∂	∂	NUM
ap-3980	59	4	∂x	∂x	PROPN
ap-3980	59	5	,	,	PUNCT
ap-3980	59	6	y1−	y1−	PROPN
ap-3980	59	7	1	1	NUM
ap-3980	59	8	q	q	NOUN
ap-3980	59	9	∂	∂	NOUN
ap-3980	59	10	∂y	∂y	NOUN
ap-3980	59	11	−	−	NOUN
ap-3980	59	12	1	1	NUM
ap-3980	59	13	q	q	NOUN
ap-3980	59	14	(	(	PUNCT
ap-3980	59	15	xy−1	xy−1	PROPN
ap-3980	59	16	/	/	SYM
ap-3980	59	17	q	q	NOUN
ap-3980	59	18	)	)	PUNCT
ap-3980	59	19	∂	∂	NOUN
ap-3980	59	20	∂x	∂x	PROPN
ap-3980	59	21	}	}	PUNCT
ap-3980	59	22	,	,	PUNCT
ap-3980	59	23	with	with	ADP
ap-3980	59	24	the	the	DET
ap-3980	59	25	algebra	algebra	PROPN
ap-3980	59	26	sl(3	sl(3	PROPN
ap-3980	59	27	,	,	PUNCT
ap-3980	59	28	r	r	NOUN
ap-3980	59	29	)	)	PUNCT
ap-3980	59	30	.	.	PUNCT
ap-3980	60	1	the	the	DET
ap-3980	60	2	transformation	transformation	NOUN
ap-3980	60	3	to	to	ADP
ap-3980	60	4	the	the	DET
ap-3980	60	5	archetypal	archetypal	ADJ
ap-3980	60	6	second	second	ADJ
ap-3980	60	7	-	-	PUNCT
ap-3980	60	8	order	order	NOUN
ap-3980	60	9	equation	equation	NOUN
ap-3980	60	10	(	(	PUNCT
ap-3980	60	11	up	up	ADP
ap-3980	60	12	to	to	ADP
ap-3980	60	13	a	a	DET
ap-3980	60	14	multiplicative	multiplicative	ADJ
ap-3980	60	15	factor	factor	NOUN
ap-3980	60	16	)	)	PUNCT
ap-3980	60	17	is	be	AUX
ap-3980	60	18	y(x	y(x	NOUN
ap-3980	60	19	)	)	PUNCT
ap-3980	60	20	→	→	SYM
ap-3980	60	21	w(x)−q	w(x)−q	PROPN
ap-3980	60	22	.	.	PUNCT
ap-3980	61	1	the	the	DET
ap-3980	61	2	transformation	transformation	NOUN
ap-3980	61	3	follows	follow	VERB
ap-3980	61	4	from	from	ADP
ap-3980	61	5	inspection	inspection	NOUN
ap-3980	61	6	of	of	ADP
ap-3980	61	7	the	the	DET
ap-3980	61	8	structures	structure	NOUN
ap-3980	61	9	of	of	ADP
ap-3980	61	10	the	the	DET
ap-3980	61	11	symmetries	symmetry	NOUN
ap-3980	61	12	above	above	ADV
ap-3980	61	13	.	.	PUNCT
ap-3980	62	1	in	in	ADP
ap-3980	62	2	the	the	DET
ap-3980	62	3	case	case	NOUN
ap-3980	62	4	of	of	ADP
ap-3980	62	5	the	the	DET
ap-3980	62	6	third	third	ADJ
ap-3980	62	7	-	-	PUNCT
ap-3980	62	8	order	order	NOUN
ap-3980	62	9	equation	equation	NOUN
ap-3980	62	10	,	,	PUNCT
ap-3980	62	11	i.e.	i.e.	X
ap-3980	62	12	,	,	PUNCT
ap-3980	62	13	n	n	PROPN
ap-3980	62	14	=	=	SYM
ap-3980	62	15	3	3	NUM
ap-3980	62	16	,	,	PUNCT
ap-3980	62	17	we	we	PRON
ap-3980	62	18	obtain	obtain	VERB
ap-3980	62	19	four	four	NUM
ap-3980	62	20	possible	possible	ADJ
ap-3980	62	21	algebraic	algebraic	ADJ
ap-3980	62	22	structures	structure	NOUN
ap-3980	62	23	.	.	PUNCT
ap-3980	63	1	these	these	PRON
ap-3980	63	2	are	be	AUX
ap-3980	63	3	{	{	PUNCT
ap-3980	63	4	∂	∂	NUM
ap-3980	63	5	∂y	∂y	NOUN
ap-3980	63	6	,	,	PUNCT
ap-3980	63	7	∂	∂	NUM
ap-3980	63	8	∂x	∂x	PROPN
ap-3980	63	9	,	,	PUNCT
ap-3980	63	10	y	y	PROPN
ap-3980	63	11	∂	∂	ADV
ap-3980	63	12	∂y	∂y	NOUN
ap-3980	63	13	,	,	PUNCT
ap-3980	63	14	x	x	SYM
ap-3980	63	15	∂	∂	NUM
ap-3980	63	16	∂x	∂x	PROPN
ap-3980	63	17	}	}	PUNCT
ap-3980	63	18	,	,	PUNCT
ap-3980	63	19	{	{	PUNCT
ap-3980	63	20	∂	∂	NUM
ap-3980	63	21	∂y	∂y	NOUN
ap-3980	63	22	,	,	PUNCT
ap-3980	63	23	∂	∂	NUM
ap-3980	63	24	∂x	∂x	PROPN
ap-3980	63	25	,	,	PUNCT
ap-3980	63	26	y	y	PROPN
ap-3980	63	27	∂	∂	ADV
ap-3980	63	28	∂y	∂y	NOUN
ap-3980	63	29	,	,	PUNCT
ap-3980	63	30	x	x	SYM
ap-3980	63	31	∂	∂	NUM
ap-3980	63	32	∂x	∂x	PROPN
ap-3980	63	33	,	,	PUNCT
ap-3980	64	1	y2	y2	PROPN
ap-3980	64	2	∂	∂	NUM
ap-3980	64	3	∂y	∂y	PROPN
ap-3980	64	4	,	,	PUNCT
ap-3980	64	5	x2	x2	PROPN
ap-3980	64	6	∂	∂	NUM
ap-3980	64	7	∂x	∂x	PROPN
ap-3980	64	8	}	}	PUNCT
ap-3980	64	9	,	,	PUNCT
ap-3980	64	10	{	{	PUNCT
ap-3980	64	11	∂	∂	NUM
ap-3980	64	12	∂y	∂y	NOUN
ap-3980	64	13	,	,	PUNCT
ap-3980	64	14	∂	∂	NUM
ap-3980	64	15	∂x	∂x	PROPN
ap-3980	64	16	,	,	PUNCT
ap-3980	64	17	y	y	PROPN
ap-3980	64	18	∂	∂	ADV
ap-3980	64	19	∂y	∂y	NOUN
ap-3980	64	20	,	,	PUNCT
ap-3980	64	21	x	x	PROPN
ap-3980	64	22	∂	∂	NUM
ap-3980	64	23	∂y	∂y	NOUN
ap-3980	64	24	,	,	PUNCT
ap-3980	64	25	x	x	SYM
ap-3980	64	26	∂	∂	NUM
ap-3980	64	27	∂x	∂x	PROPN
ap-3980	64	28	,	,	PUNCT
ap-3980	64	29	x2	x2	PROPN
ap-3980	64	30	∂	∂	ADV
ap-3980	64	31	∂y	∂y	NOUN
ap-3980	64	32	,	,	PUNCT
ap-3980	64	33	x2	x2	PROPN
ap-3980	64	34	∂	∂	NUM
ap-3980	64	35	∂x	∂x	PROPN
ap-3980	64	36	+	+	CCONJ
ap-3980	64	37	2xy	2xy	ADJ
ap-3980	64	38	∂	∂	X
ap-3980	64	39	∂y	∂y	NOUN
ap-3980	64	40	}	}	PUNCT
ap-3980	64	41	,	,	PUNCT
ap-3980	64	42	{	{	PUNCT
ap-3980	64	43	∂	∂	NUM
ap-3980	64	44	∂y	∂y	NOUN
ap-3980	64	45	,	,	PUNCT
ap-3980	64	46	∂	∂	NUM
ap-3980	64	47	∂x	∂x	PROPN
ap-3980	64	48	,	,	PUNCT
ap-3980	64	49	y	y	PROPN
ap-3980	64	50	∂	∂	ADV
ap-3980	64	51	∂y	∂y	PROPN
ap-3980	64	52	,	,	PUNCT
ap-3980	64	53	y	y	PROPN
ap-3980	64	54	∂	∂	NOUN
ap-3980	64	55	∂x	∂x	PROPN
ap-3980	64	56	,	,	PUNCT
ap-3980	64	57	x	x	SYM
ap-3980	64	58	∂	∂	NUM
ap-3980	64	59	∂x	∂x	PROPN
ap-3980	64	60	,	,	PUNCT
ap-3980	64	61	y2	y2	PROPN
ap-3980	64	62	∂	∂	NOUN
ap-3980	64	63	∂x	∂x	PROPN
ap-3980	64	64	,	,	PUNCT
ap-3980	64	65	2xy	2xy	ADJ
ap-3980	64	66	∂	∂	NOUN
ap-3980	65	1	∂x	∂x	PROPN
ap-3980	65	2	+	+	CCONJ
ap-3980	65	3	y2	y2	PROPN
ap-3980	65	4	∂	∂	NOUN
ap-3980	65	5	∂y	∂y	NOUN
ap-3980	65	6	}	}	PUNCT
ap-3980	65	7	corresponding	correspond	VERB
ap-3980	65	8	to	to	ADP
ap-3980	65	9	general	general	ADJ
ap-3980	65	10	q	q	NOUN
ap-3980	65	11	,	,	PUNCT
ap-3980	65	12	q	q	NOUN
ap-3980	65	13	=	=	NOUN
ap-3980	65	14	1	1	NUM
ap-3980	65	15	,	,	PUNCT
ap-3980	65	16	q	q	NOUN
ap-3980	65	17	=	=	PUNCT
ap-3980	65	18	−2	−2	NOUN
ap-3980	65	19	and	and	CCONJ
ap-3980	65	20	q	q	NOUN
ap-3980	66	1	=	=	SYM
ap-3980	66	2	−	−	PROPN
ap-3980	66	3	1	1	NUM
ap-3980	66	4	2	2	NUM
ap-3980	66	5	.	.	PUNCT
ap-3980	67	1	clearly	clearly	ADV
ap-3980	67	2	the	the	DET
ap-3980	67	3	latter	latter	ADJ
ap-3980	67	4	two	two	NUM
ap-3980	67	5	cases	case	NOUN
ap-3980	67	6	did	do	AUX
ap-3980	67	7	not	not	PART
ap-3980	67	8	come	come	VERB
ap-3980	67	9	within	within	ADP
ap-3980	67	10	the	the	DET
ap-3980	67	11	purview	purview	NOUN
ap-3980	67	12	of	of	ADP
ap-3980	67	13	the	the	DET
ap-3980	67	14	singularity	singularity	NOUN
ap-3980	67	15	analysis	analysis	NOUN
ap-3980	67	16	discussed	discuss	VERB
ap-3980	67	17	above	above	ADV
ap-3980	67	18	.	.	PUNCT
ap-3980	68	1	for	for	ADP
ap-3980	68	2	general	general	ADJ
ap-3980	68	3	q	q	PUNCT
ap-3980	68	4	the	the	DET
ap-3980	68	5	algebra	algebra	NOUN
ap-3980	68	6	is	be	AUX
ap-3980	68	7	a2	a2	PROPN
ap-3980	68	8	⊕	⊕	PROPN
ap-3980	68	9	a2	a2	PROPN
ap-3980	68	10	which	which	PRON
ap-3980	68	11	can	can	AUX
ap-3980	68	12	also	also	ADV
ap-3980	68	13	be	be	AUX
ap-3980	68	14	written	write	VERB
ap-3980	68	15	as	as	ADP
ap-3980	68	16	2a2	2a2	NUM
ap-3980	68	17	.	.	PUNCT
ap-3980	69	1	(	(	PUNCT
ap-3980	69	2	we	we	PRON
ap-3980	69	3	make	make	VERB
ap-3980	69	4	use	use	NOUN
ap-3980	69	5	of	of	ADP
ap-3980	69	6	the	the	DET
ap-3980	69	7	mubarakzyanov	mubarakzyanov	NOUN
ap-3980	69	8	classification	classification	NOUN
ap-3980	69	9	scheme	scheme	NOUN
ap-3980	69	10	[	[	X
ap-3980	69	11	5–8	5–8	NOUN
ap-3980	69	12	]	]	X
ap-3980	69	13	(	(	PUNCT
ap-3980	69	14	see	see	VERB
ap-3980	69	15	also	also	ADV
ap-3980	69	16	[	[	X
ap-3980	69	17	9	9	NUM
ap-3980	69	18	,	,	PUNCT
ap-3980	69	19	11	11	NUM
ap-3980	69	20	,	,	PUNCT
ap-3980	69	21	13	13	NUM
ap-3980	69	22	]	]	PUNCT
ap-3980	69	23	)	)	PUNCT
ap-3980	69	24	throughout	throughout	ADP
ap-3980	69	25	this	this	DET
ap-3980	69	26	paper	paper	NOUN
ap-3980	69	27	.	.	PUNCT
ap-3980	69	28	)	)	PUNCT
ap-3980	70	1	in	in	ADP
ap-3980	70	2	the	the	DET
ap-3980	70	3	case	case	NOUN
ap-3980	70	4	of	of	ADP
ap-3980	70	5	q	q	NOUN
ap-3980	70	6	=	=	SYM
ap-3980	70	7	1	1	NUM
ap-3980	70	8	we	we	PRON
ap-3980	70	9	have	have	VERB
ap-3980	70	10	the	the	DET
ap-3980	70	11	well	well	ADV
ap-3980	70	12	-	-	PUNCT
ap-3980	70	13	known	know	VERB
ap-3980	70	14	kummer	kummer	NOUN
ap-3980	70	15	-	-	PUNCT
ap-3980	70	16	schwarz	schwarz	PROPN
ap-3980	70	17	equation	equation	NOUN
ap-3980	70	18	with	with	ADP
ap-3980	70	19	the	the	DET
ap-3980	70	20	algebra	algebra	NOUN
ap-3980	70	21	2sl(2	2sl(2	NUM
ap-3980	70	22	,	,	PUNCT
ap-3980	70	23	r	r	NOUN
ap-3980	70	24	)	)	PUNCT
ap-3980	70	25	or	or	CCONJ
ap-3980	70	26	2a3,8	2a3,8	NUM
ap-3980	70	27	.	.	PUNCT
ap-3980	71	1	for	for	ADP
ap-3980	71	2	the	the	DET
ap-3980	71	3	values	value	NOUN
ap-3980	71	4	of	of	ADP
ap-3980	71	5	q	q	DET
ap-3980	71	6	−2	−2	NOUN
ap-3980	71	7	and	and	CCONJ
ap-3980	71	8	−	−	PROPN
ap-3980	71	9	1	1	NUM
ap-3980	71	10	2	2	NUM
ap-3980	71	11	the	the	DET
ap-3980	71	12	algebra	algebra	NOUN
ap-3980	71	13	is	be	AUX
ap-3980	71	14	the	the	DET
ap-3980	71	15	same	same	ADJ
ap-3980	71	16	and	and	CCONJ
ap-3980	71	17	is	be	AUX
ap-3980	71	18	the	the	DET
ap-3980	71	19	maximal	maximal	ADJ
ap-3980	71	20	algebra	algebra	NOUN
ap-3980	71	21	for	for	ADP
ap-3980	71	22	a	a	DET
ap-3980	71	23	third	third	ADJ
ap-3980	71	24	-	-	PUNCT
ap-3980	71	25	order	order	NOUN
ap-3980	71	26	equation	equation	NOUN
ap-3980	71	27	.	.	PUNCT
ap-3980	72	1	for	for	ADP
ap-3980	72	2	q	q	NOUN
ap-3980	72	3	=	=	PUNCT
ap-3980	72	4	−2	−2	NOUN
ap-3980	72	5	the	the	DET
ap-3980	72	6	representation	representation	NOUN
ap-3980	72	7	is	be	AUX
ap-3980	72	8	the	the	DET
ap-3980	72	9	standard	standard	ADJ
ap-3980	72	10	representation	representation	NOUN
ap-3980	72	11	for	for	ADP
ap-3980	72	12	y′′′	y′′′	PROPN
ap-3980	72	13	=	=	SYM
ap-3980	72	14	0	0	PROPN
ap-3980	72	15	.	.	PUNCT
ap-3980	73	1	the	the	DET
ap-3980	73	2	representation	representation	NOUN
ap-3980	73	3	for	for	ADP
ap-3980	73	4	q	q	NOUN
ap-3980	73	5	=	=	SYM
ap-3980	73	6	−	−	NUM
ap-3980	73	7	1	1	NUM
ap-3980	73	8	2	2	NUM
ap-3980	73	9	has	have	AUX
ap-3980	73	10	not	not	PART
ap-3980	73	11	been	be	AUX
ap-3980	73	12	reported	report	VERB
ap-3980	73	13	before	before	ADV
ap-3980	73	14	.	.	PUNCT
ap-3980	74	1	however	however	ADV
ap-3980	74	2	,	,	PUNCT
ap-3980	74	3	the	the	DET
ap-3980	74	4	latter	latter	ADJ
ap-3980	74	5	result	result	NOUN
ap-3980	74	6	follows	follow	VERB
ap-3980	74	7	from	from	ADP
ap-3980	74	8	an	an	DET
ap-3980	74	9	interchange	interchange	NOUN
ap-3980	74	10	of	of	ADP
ap-3980	74	11	x	x	PUNCT
ap-3980	74	12	and	and	CCONJ
ap-3980	74	13	y.	y.	NOUN
ap-3980	74	14	the	the	DET
ap-3980	74	15	fourth	fourth	ADJ
ap-3980	74	16	-	-	PUNCT
ap-3980	74	17	order	order	NOUN
ap-3980	74	18	equation	equation	NOUN
ap-3980	74	19	is	be	AUX
ap-3980	74	20	the	the	DET
ap-3980	74	21	prototype	prototype	NOUN
ap-3980	74	22	for	for	ADP
ap-3980	74	23	subsequent	subsequent	ADJ
ap-3980	74	24	equations	equation	NOUN
ap-3980	74	25	and	and	CCONJ
ap-3980	74	26	we	we	PRON
ap-3980	74	27	find	find	VERB
ap-3980	74	28	the	the	DET
ap-3980	74	29	symmetries	symmetry	NOUN
ap-3980	74	30	{	{	PUNCT
ap-3980	74	31	∂	∂	NUM
ap-3980	74	32	∂y	∂y	NOUN
ap-3980	74	33	,	,	PUNCT
ap-3980	74	34	x	x	PROPN
ap-3980	74	35	∂	∂	NUM
ap-3980	74	36	∂y	∂y	NOUN
ap-3980	74	37	,	,	PUNCT
ap-3980	74	38	y	y	PROPN
ap-3980	74	39	∂	∂	NOUN
ap-3980	74	40	∂y	∂y	PROPN
ap-3980	74	41	,	,	PUNCT
ap-3980	74	42	∂	∂	NUM
ap-3980	74	43	∂x	∂x	PROPN
ap-3980	74	44	,	,	PUNCT
ap-3980	74	45	x	x	SYM
ap-3980	74	46	∂	∂	NUM
ap-3980	74	47	∂x	∂x	PROPN
ap-3980	74	48	}	}	PUNCT
ap-3980	74	49	,	,	PUNCT
ap-3980	74	50	{	{	PUNCT
ap-3980	74	51	∂	∂	NUM
ap-3980	74	52	∂y	∂y	NOUN
ap-3980	74	53	,	,	PUNCT
ap-3980	74	54	x	x	PROPN
ap-3980	74	55	∂	∂	NUM
ap-3980	74	56	∂y	∂y	NOUN
ap-3980	74	57	,	,	PUNCT
ap-3980	74	58	y	y	PROPN
ap-3980	74	59	∂	∂	NOUN
ap-3980	74	60	∂y	∂y	PROPN
ap-3980	74	61	,	,	PUNCT
ap-3980	74	62	∂	∂	NUM
ap-3980	74	63	∂x	∂x	PROPN
ap-3980	74	64	,	,	PUNCT
ap-3980	74	65	x	x	SYM
ap-3980	74	66	∂	∂	NUM
ap-3980	75	1	∂x	∂x	NOUN
ap-3980	75	2	+	+	CCONJ
ap-3980	75	3	1	1	NUM
ap-3980	75	4	2y	2y	NUM
ap-3980	75	5	∂	∂	NOUN
ap-3980	75	6	∂y	∂y	NOUN
ap-3980	75	7	,	,	PUNCT
ap-3980	75	8	x2	x2	PROPN
ap-3980	75	9	∂	∂	NUM
ap-3980	75	10	∂x	∂x	PROPN
ap-3980	76	1	+	+	CCONJ
ap-3980	76	2	xy	xy	PROPN
ap-3980	76	3	∂	∂	NOUN
ap-3980	76	4	∂y	∂y	NOUN
ap-3980	76	5	}	}	PUNCT
ap-3980	76	6	,	,	PUNCT
ap-3980	76	7	{	{	PUNCT
ap-3980	76	8	∂	∂	NUM
ap-3980	76	9	∂y	∂y	NOUN
ap-3980	76	10	,	,	PUNCT
ap-3980	76	11	x	x	PROPN
ap-3980	76	12	∂	∂	NUM
ap-3980	76	13	∂y	∂y	NOUN
ap-3980	76	14	,	,	PUNCT
ap-3980	76	15	x2	x2	PROPN
ap-3980	76	16	∂	∂	ADV
ap-3980	76	17	∂y	∂y	NOUN
ap-3980	76	18	,	,	PUNCT
ap-3980	76	19	x3	x3	PROPN
ap-3980	76	20	∂	∂	ADV
ap-3980	76	21	∂y	∂y	NOUN
ap-3980	76	22	,	,	PUNCT
ap-3980	76	23	y	y	PROPN
ap-3980	76	24	∂	∂	NOUN
ap-3980	76	25	∂y	∂y	PROPN
ap-3980	76	26	,	,	PUNCT
ap-3980	76	27	∂	∂	NUM
ap-3980	76	28	∂x	∂x	PROPN
ap-3980	76	29	,	,	PUNCT
ap-3980	76	30	x	x	SYM
ap-3980	76	31	∂	∂	NUM
ap-3980	76	32	∂x	∂x	NOUN
ap-3980	77	1	+	+	CCONJ
ap-3980	77	2	3	3	NUM
ap-3980	77	3	2y	2y	NUM
ap-3980	77	4	∂	∂	NOUN
ap-3980	77	5	∂y	∂y	NOUN
ap-3980	77	6	,	,	PUNCT
ap-3980	77	7	x2	x2	PROPN
ap-3980	77	8	∂	∂	NUM
ap-3980	78	1	∂x	∂x	PROPN
ap-3980	78	2	+	+	CCONJ
ap-3980	78	3	3xy	3xy	NOUN
ap-3980	78	4	∂	∂	X
ap-3980	78	5	∂y	∂y	NOUN
ap-3980	78	6	}	}	PUNCT
ap-3980	78	7	.	.	PUNCT
ap-3980	79	1	the	the	DET
ap-3980	79	2	five	five	NUM
ap-3980	79	3	-	-	PUNCT
ap-3980	79	4	dimensional	dimensional	ADJ
ap-3980	79	5	algebra	algebra	NOUN
ap-3980	79	6	is	be	AUX
ap-3980	79	7	a2⊕sa3,3	a2⊕sa3,3	VERB
ap-3980	79	8	.	.	PUNCT
ap-3980	80	1	the	the	DET
ap-3980	80	2	latter	latter	ADJ
ap-3980	80	3	subalgebra	subalgebra	NOUN
ap-3980	80	4	is	be	AUX
ap-3980	80	5	also	also	ADV
ap-3980	80	6	known	know	VERB
ap-3980	80	7	as	as	ADP
ap-3980	80	8	d⊕s	d⊕s	NOUN
ap-3980	80	9	t2	t2	NOUN
ap-3980	80	10	,	,	PUNCT
ap-3980	80	11	i.e.	i.e.	X
ap-3980	80	12	,	,	PUNCT
ap-3980	80	13	dilations	dilation	NOUN
ap-3980	80	14	and	and	CCONJ
ap-3980	80	15	translations	translation	NOUN
ap-3980	80	16	in	in	ADP
ap-3980	80	17	the	the	DET
ap-3980	80	18	plane	plane	NOUN
ap-3980	80	19	.	.	PUNCT
ap-3980	81	1	the	the	DET
ap-3980	81	2	six	six	NUM
ap-3980	81	3	-	-	PUNCT
ap-3980	81	4	dimensional	dimensional	ADJ
ap-3980	81	5	algebra	algebra	NOUN
ap-3980	81	6	is	be	AUX
ap-3980	81	7	a3,3	a3,3	ADV
ap-3980	81	8	⊕s	⊕s	NOUN
ap-3980	81	9	sl(2	sl(2	PROPN
ap-3980	81	10	,	,	PUNCT
ap-3980	81	11	r	r	NOUN
ap-3980	81	12	)	)	PUNCT
ap-3980	81	13	.	.	PUNCT
ap-3980	82	1	we	we	PRON
ap-3980	82	2	note	note	VERB
ap-3980	82	3	that	that	SCONJ
ap-3980	82	4	these	these	DET
ap-3980	82	5	symmetries	symmetry	NOUN
ap-3980	82	6	are	be	AUX
ap-3980	82	7	the	the	DET
ap-3980	82	8	same	same	ADJ
ap-3980	82	9	as	as	ADP
ap-3980	82	10	those	those	PRON
ap-3980	82	11	of	of	ADP
ap-3980	82	12	y′′	y′′	NOUN
ap-3980	82	13	=	=	SYM
ap-3980	82	14	0	0	PUNCT
ap-3980	83	1	apart	apart	ADV
ap-3980	83	2	from	from	ADP
ap-3980	83	3	the	the	DET
ap-3980	83	4	two	two	NUM
ap-3980	83	5	noncartan	noncartan	ADJ
ap-3980	83	6	symmetries	symmetry	NOUN
ap-3980	83	7	typical	typical	ADJ
ap-3980	83	8	of	of	ADP
ap-3980	83	9	a	a	DET
ap-3980	83	10	linear	linear	ADJ
ap-3980	83	11	second	second	ADJ
ap-3980	83	12	-	-	PUNCT
ap-3980	83	13	order	order	NOUN
ap-3980	83	14	equation	equation	NOUN
ap-3980	83	15	[	[	X
ap-3980	83	16	3	3	NUM
ap-3980	83	17	]	]	PUNCT
ap-3980	83	18	.	.	PUNCT
ap-3980	84	1	468	468	NUM
ap-3980	84	2	vol	vol	NOUN
ap-3980	84	3	.	.	PUNCT
ap-3980	84	4	57	57	NUM
ap-3980	84	5	no	no	NOUN
ap-3980	84	6	.	.	PUNCT
ap-3980	85	1	6/2017	6/2017	NUM
ap-3980	85	2	further	further	ADJ
ap-3980	85	3	generalisations	generalisation	NOUN
ap-3980	85	4	of	of	ADP
ap-3980	85	5	the	the	DET
ap-3980	85	6	kummer	kummer	NOUN
ap-3980	85	7	-	-	PUNCT
ap-3980	85	8	schwarz	schwarz	PROPN
ap-3980	85	9	equation	equation	NOUN
ap-3980	85	10	the	the	DET
ap-3980	85	11	eight	eight	NUM
ap-3980	85	12	-	-	PUNCT
ap-3980	85	13	dimensional	dimensional	ADJ
ap-3980	85	14	algebra	algebra	NOUN
ap-3980	85	15	is	be	AUX
ap-3980	85	16	the	the	DET
ap-3980	85	17	maximal	maximal	ADJ
ap-3980	85	18	algebra	algebra	NOUN
ap-3980	85	19	for	for	ADP
ap-3980	85	20	a	a	DET
ap-3980	85	21	forth	forth	ADJ
ap-3980	85	22	-	-	PUNCT
ap-3980	85	23	order	order	NOUN
ap-3980	85	24	scalar	scalar	ADJ
ap-3980	85	25	equation	equation	NOUN
ap-3980	85	26	.	.	PUNCT
ap-3980	86	1	this	this	PRON
ap-3980	86	2	occurs	occur	VERB
ap-3980	86	3	for	for	ADP
ap-3980	86	4	q	q	NOUN
ap-3980	86	5	=	=	PUNCT
ap-3980	87	1	−3	−3	PROPN
ap-3980	87	2	.	.	PUNCT
ap-3980	88	1	then	then	ADV
ap-3980	88	2	(	(	PUNCT
ap-3980	88	3	2	2	X
ap-3980	88	4	)	)	PUNCT
ap-3980	88	5	is	be	AUX
ap-3980	88	6	simply	simply	ADV
ap-3980	88	7	y(4	y(4	PROPN
ap-3980	88	8	)	)	PUNCT
ap-3980	88	9	=	=	PUNCT
ap-3980	88	10	0	0	NUM
ap-3980	88	11	up	up	ADP
ap-3980	88	12	to	to	ADP
ap-3980	88	13	a	a	DET
ap-3980	88	14	multiplier	multipli	ADJ
ap-3980	88	15	.	.	PUNCT
ap-3980	89	1	unlike	unlike	ADP
ap-3980	89	2	in	in	ADP
ap-3980	89	3	the	the	DET
ap-3980	89	4	case	case	NOUN
ap-3980	89	5	of	of	ADP
ap-3980	89	6	the	the	DET
ap-3980	89	7	third	third	ADJ
ap-3980	89	8	-	-	PUNCT
ap-3980	89	9	order	order	NOUN
ap-3980	89	10	equation	equation	NOUN
ap-3980	89	11	there	there	PRON
ap-3980	89	12	is	be	VERB
ap-3980	89	13	no	no	DET
ap-3980	89	14	existence	existence	NOUN
ap-3980	89	15	of	of	ADP
ap-3980	89	16	an	an	DET
ap-3980	89	17	n+	n+	ADJ
ap-3980	89	18	3	3	NUM
ap-3980	89	19	-	-	PUNCT
ap-3980	89	20	dimensional	dimensional	ADJ
ap-3980	89	21	algebra	algebra	NOUN
ap-3980	89	22	.	.	PUNCT
ap-3980	90	1	this	this	DET
ap-3980	90	2	pattern	pattern	NOUN
ap-3980	90	3	of	of	ADP
ap-3980	90	4	behaviour	behaviour	NOUN
ap-3980	90	5	persists	persist	VERB
ap-3980	90	6	mutatis	mutatis	NOUN
ap-3980	90	7	mutandis	mutandi	NOUN
ap-3980	90	8	for	for	ADP
ap-3980	90	9	higher	high	ADJ
ap-3980	90	10	-	-	PUNCT
ap-3980	90	11	order	order	NOUN
ap-3980	90	12	equations	equation	NOUN
ap-3980	90	13	.	.	PUNCT
ap-3980	91	1	the	the	DET
ap-3980	91	2	general	general	ADJ
ap-3980	91	3	nth	nth	NOUN
ap-3980	91	4	-	-	PUNCT
ap-3980	91	5	order	order	NOUN
ap-3980	91	6	equation	equation	NOUN
ap-3980	91	7	has	have	VERB
ap-3980	91	8	three	three	NUM
ap-3980	91	9	possible	possible	ADJ
ap-3980	91	10	numbers	number	NOUN
ap-3980	91	11	of	of	ADP
ap-3980	91	12	symmetries	symmetry	NOUN
ap-3980	91	13	,	,	PUNCT
ap-3980	91	14	namely	namely	ADV
ap-3980	91	15	n	n	CCONJ
ap-3980	91	16	+	+	NUM
ap-3980	91	17	1	1	NUM
ap-3980	91	18	,	,	PUNCT
ap-3980	91	19	n	n	PROPN
ap-3980	91	20	+	+	CCONJ
ap-3980	91	21	2	2	NUM
ap-3980	91	22	and	and	CCONJ
ap-3980	91	23	n	n	PRON
ap-3980	91	24	+	+	NOUN
ap-3980	91	25	4	4	X
ap-3980	91	26	.	.	PUNCT
ap-3980	92	1	the	the	DET
ap-3980	92	2	algebras	algebra	NOUN
ap-3980	92	3	are	be	AUX
ap-3980	92	4	as	as	ADV
ap-3980	92	5	delineated	delineated	ADJ
ap-3980	92	6	above	above	ADV
ap-3980	92	7	.	.	PUNCT
ap-3980	93	1	we	we	PRON
ap-3980	93	2	note	note	VERB
ap-3980	93	3	that	that	SCONJ
ap-3980	93	4	the	the	DET
ap-3980	93	5	exceptional	exceptional	ADJ
ap-3980	93	6	property	property	NOUN
ap-3980	93	7	of	of	ADP
ap-3980	93	8	the	the	DET
ap-3980	93	9	third	third	ADJ
ap-3980	93	10	-	-	PUNCT
ap-3980	93	11	order	order	NOUN
ap-3980	93	12	equation	equation	NOUN
ap-3980	93	13	,	,	PUNCT
ap-3980	93	14	the	the	DET
ap-3980	93	15	possession	possession	NOUN
ap-3980	93	16	of	of	ADP
ap-3980	93	17	a	a	DET
ap-3980	93	18	double	double	ADJ
ap-3980	93	19	sl(2	sl(2	PROPN
ap-3980	93	20	,	,	PUNCT
ap-3980	93	21	r	r	NOUN
ap-3980	93	22	)	)	PUNCT
ap-3980	93	23	algebras	algebra	NOUN
ap-3980	93	24	,	,	PUNCT
ap-3980	93	25	is	be	AUX
ap-3980	93	26	indeed	indeed	ADV
ap-3980	93	27	exceptional	exceptional	ADJ
ap-3980	93	28	.	.	PUNCT
ap-3980	94	1	5	5	X
ap-3980	94	2	.	.	X
ap-3980	94	3	conclusion	conclusion	NOUN
ap-3980	94	4	in	in	ADP
ap-3980	94	5	[	[	X
ap-3980	94	6	12	12	NUM
ap-3980	94	7	]	]	PUNCT
ap-3980	94	8	we	we	PRON
ap-3980	94	9	considered	consider	VERB
ap-3980	94	10	a	a	DET
ap-3980	94	11	family	family	NOUN
ap-3980	94	12	of	of	ADP
ap-3980	94	13	ordinary	ordinary	ADJ
ap-3980	94	14	differential	differential	ADJ
ap-3980	94	15	equations	equation	NOUN
ap-3980	94	16	(	(	PUNCT
ap-3980	94	17	n−	n−	NOUN
ap-3980	94	18	1)y(n−2)y(n	1)y(n−2)y(n	NOUN
ap-3980	94	19	)	)	PUNCT
ap-3980	94	20	−	−	NOUN
ap-3980	94	21	n(y(n−1))2	n(y(n−1))2	NOUN
ap-3980	94	22	=	=	NOUN
ap-3980	94	23	0	0	NUM
ap-3980	94	24	as	as	ADP
ap-3980	94	25	a	a	DET
ap-3980	94	26	natural	natural	ADJ
ap-3980	94	27	generalisation	generalisation	NOUN
ap-3980	94	28	of	of	ADP
ap-3980	94	29	the	the	DET
ap-3980	94	30	well	well	ADV
ap-3980	94	31	-	-	PUNCT
ap-3980	94	32	known	know	VERB
ap-3980	94	33	kummerschwarz	kummerschwarz	NOUN
ap-3980	94	34	equation	equation	NOUN
ap-3980	94	35	2y′y′′′	2y′y′′′	NUM
ap-3980	94	36	−	−	NOUN
ap-3980	94	37	3(y′′)2	3(y′′)2	NUM
ap-3980	94	38	=	=	SYM
ap-3980	94	39	0	0	X
ap-3980	94	40	.	.	PUNCT
ap-3980	95	1	we	we	PRON
ap-3980	95	2	reported	report	VERB
ap-3980	95	3	the	the	DET
ap-3980	95	4	symmetries	symmetry	NOUN
ap-3980	95	5	,	,	PUNCT
ap-3980	95	6	singularity	singularity	NOUN
ap-3980	95	7	properties	property	NOUN
ap-3980	95	8	and	and	CCONJ
ap-3980	95	9	solutions	solution	NOUN
ap-3980	95	10	for	for	ADP
ap-3980	95	11	the	the	DET
ap-3980	95	12	members	member	NOUN
ap-3980	95	13	of	of	ADP
ap-3980	95	14	the	the	DET
ap-3980	95	15	family	family	NOUN
ap-3980	95	16	.	.	PUNCT
ap-3980	96	1	these	these	DET
ap-3980	96	2	properties	property	NOUN
ap-3980	96	3	were	be	AUX
ap-3980	96	4	remarkably	remarkably	ADV
ap-3980	96	5	robust	robust	ADJ
ap-3980	96	6	throughout	throughout	ADP
ap-3980	96	7	the	the	DET
ap-3980	96	8	whole	whole	ADJ
ap-3980	96	9	family	family	NOUN
ap-3980	96	10	except	except	SCONJ
ap-3980	96	11	for	for	ADP
ap-3980	96	12	the	the	DET
ap-3980	96	13	kummer	kummer	NOUN
ap-3980	96	14	-	-	PUNCT
ap-3980	96	15	schwarz	schwarz	PROPN
ap-3980	96	16	equation	equation	NOUN
ap-3980	96	17	itself	itself	PRON
ap-3980	96	18	which	which	PRON
ap-3980	96	19	had	have	VERB
ap-3980	96	20	the	the	DET
ap-3980	96	21	additional	additional	ADJ
ap-3980	96	22	property	property	NOUN
ap-3980	96	23	of	of	ADP
ap-3980	96	24	six	six	NUM
ap-3980	96	25	lie	lie	NOUN
ap-3980	96	26	point	point	NOUN
ap-3980	96	27	symmetries	symmetry	NOUN
ap-3980	96	28	that	that	PRON
ap-3980	96	29	makes	make	VERB
ap-3980	96	30	it	it	PRON
ap-3980	96	31	exceptional	exceptional	ADJ
ap-3980	96	32	in	in	ADP
ap-3980	96	33	the	the	DET
ap-3980	96	34	class	class	NOUN
ap-3980	96	35	of	of	ADP
ap-3980	96	36	third	third	ADJ
ap-3980	96	37	-	-	PUNCT
ap-3980	96	38	order	order	NOUN
ap-3980	96	39	equations	equation	NOUN
ap-3980	96	40	.	.	PUNCT
ap-3980	97	1	in	in	ADP
ap-3980	97	2	this	this	DET
ap-3980	97	3	paper	paper	NOUN
ap-3980	97	4	we	we	PRON
ap-3980	97	5	have	have	AUX
ap-3980	97	6	considered	consider	VERB
ap-3980	97	7	a	a	DET
ap-3980	97	8	variation	variation	NOUN
ap-3980	97	9	on	on	ADP
ap-3980	97	10	the	the	DET
ap-3980	97	11	kummer	kummer	NOUN
ap-3980	97	12	-	-	PUNCT
ap-3980	97	13	schwarz	schwarz	PROPN
ap-3980	97	14	equation	equation	NOUN
ap-3980	97	15	and	and	CCONJ
ap-3980	97	16	its	its	PRON
ap-3980	97	17	natural	natural	ADJ
ap-3980	97	18	generalisation	generalisation	NOUN
ap-3980	97	19	to	to	ADP
ap-3980	97	20	higher	high	ADJ
ap-3980	97	21	-	-	PUNCT
ap-3980	97	22	order	order	NOUN
ap-3980	97	23	equations	equation	NOUN
ap-3980	97	24	by	by	ADP
ap-3980	97	25	the	the	DET
ap-3980	97	26	inclusion	inclusion	NOUN
ap-3980	97	27	of	of	ADP
ap-3980	97	28	a	a	DET
ap-3980	97	29	parameter	parameter	NOUN
ap-3980	97	30	q	q	PUNCT
ap-3980	97	31	to	to	PART
ap-3980	97	32	give	give	VERB
ap-3980	97	33	the	the	DET
ap-3980	97	34	nonlinear	nonlinear	ADJ
ap-3980	97	35	family	family	NOUN
ap-3980	97	36	(	(	PUNCT
ap-3980	97	37	n+	n+	NUM
ap-3980	97	38	q−	q−	PROPN
ap-3980	97	39	2)y(n−2)y(n	2)y(n−2)y(n	PROPN
ap-3980	97	40	)	)	PUNCT
ap-3980	97	41	−	−	PROPN
ap-3980	98	1	(	(	PUNCT
ap-3980	98	2	n+	n+	NUM
ap-3980	98	3	q−	q−	PROPN
ap-3980	98	4	1)(y(n−1))2	1)(y(n−1))2	NUM
ap-3980	99	1	=	=	SYM
ap-3980	99	2	0	0	X
ap-3980	99	3	.	.	PUNCT
ap-3980	100	1	there	there	PRON
ap-3980	100	2	is	be	VERB
ap-3980	100	3	no	no	DET
ap-3980	100	4	a	a	DET
ap-3980	100	5	priori	priori	ADJ
ap-3980	100	6	constraint	constraint	NOUN
ap-3980	100	7	upon	upon	SCONJ
ap-3980	100	8	the	the	DET
ap-3980	100	9	value	value	NOUN
ap-3980	100	10	of	of	ADP
ap-3980	100	11	q.	q.	PROPN
ap-3980	100	12	apart	apart	ADV
ap-3980	100	13	from	from	ADP
ap-3980	100	14	some	some	DET
ap-3980	100	15	special	special	ADJ
ap-3980	100	16	values	value	NOUN
ap-3980	100	17	noted	note	VERB
ap-3980	100	18	in	in	ADP
ap-3980	100	19	§	§	PROPN
ap-3980	100	20	3	3	NUM
ap-3980	100	21	the	the	DET
ap-3980	100	22	value	value	NOUN
ap-3980	100	23	of	of	ADP
ap-3980	100	24	q	q	NOUN
ap-3980	100	25	does	do	AUX
ap-3980	100	26	not	not	PART
ap-3980	100	27	influence	influence	VERB
ap-3980	100	28	the	the	DET
ap-3980	100	29	symmetry	symmetry	NOUN
ap-3980	100	30	properties	property	NOUN
ap-3980	100	31	,	,	PUNCT
ap-3980	100	32	i.e.	i.e.	X
ap-3980	100	33	,	,	PUNCT
ap-3980	100	34	in	in	ADP
ap-3980	100	35	general	general	ADJ
ap-3980	100	36	the	the	DET
ap-3980	100	37	number	number	NOUN
ap-3980	100	38	of	of	ADP
ap-3980	100	39	symmetries	symmetry	NOUN
ap-3980	100	40	is	be	AUX
ap-3980	100	41	the	the	DET
ap-3980	100	42	same	same	ADJ
ap-3980	100	43	independently	independently	ADV
ap-3980	100	44	of	of	ADP
ap-3980	100	45	the	the	DET
ap-3980	100	46	value	value	NOUN
ap-3980	100	47	of	of	ADP
ap-3980	100	48	q.	q.	PROPN
ap-3980	100	49	however	however	ADV
ap-3980	100	50	,	,	PUNCT
ap-3980	100	51	when	when	SCONJ
ap-3980	100	52	one	one	PRON
ap-3980	100	53	considers	consider	VERB
ap-3980	100	54	the	the	DET
ap-3980	100	55	singularity	singularity	NOUN
ap-3980	100	56	analysis	analysis	NOUN
ap-3980	100	57	,	,	PUNCT
ap-3980	100	58	q	q	NOUN
ap-3980	100	59	must	must	AUX
ap-3980	100	60	necessarily	necessarily	ADV
ap-3980	100	61	be	be	AUX
ap-3980	100	62	positive	positive	ADJ
ap-3980	100	63	to	to	PART
ap-3980	100	64	enable	enable	VERB
ap-3980	100	65	the	the	DET
ap-3980	100	66	existence	existence	NOUN
ap-3980	100	67	of	of	ADP
ap-3980	100	68	a	a	DET
ap-3980	100	69	singularity	singularity	NOUN
ap-3980	100	70	,	,	PUNCT
ap-3980	100	71	indeed	indeed	ADV
ap-3980	100	72	a	a	DET
ap-3980	100	73	positive	positive	ADJ
ap-3980	100	74	integer	integer	NOUN
ap-3980	100	75	for	for	ADP
ap-3980	100	76	the	the	DET
ap-3980	100	77	usual	usual	ADJ
ap-3980	100	78	analysis	analysis	NOUN
ap-3980	100	79	to	to	PART
ap-3980	100	80	apply	apply	VERB
ap-3980	100	81	.	.	PUNCT
ap-3980	101	1	the	the	DET
ap-3980	101	2	value	value	NOUN
ap-3980	101	3	of	of	ADP
ap-3980	101	4	q	q	NOUN
ap-3980	101	5	affects	affect	VERB
ap-3980	101	6	only	only	ADV
ap-3980	101	7	the	the	DET
ap-3980	101	8	leading	lead	VERB
ap-3980	101	9	-	-	PUNCT
ap-3980	101	10	order	order	NOUN
ap-3980	101	11	term	term	NOUN
ap-3980	101	12	.	.	PUNCT
ap-3980	102	1	independently	independently	ADV
ap-3980	102	2	of	of	ADP
ap-3980	102	3	the	the	DET
ap-3980	102	4	value	value	NOUN
ap-3980	102	5	of	of	ADP
ap-3980	102	6	q	q	DET
ap-3980	102	7	the	the	DET
ap-3980	102	8	resonances	resonance	NOUN
ap-3980	102	9	take	take	VERB
ap-3980	102	10	the	the	DET
ap-3980	102	11	values	value	NOUN
ap-3980	102	12	−1	−1	NOUN
ap-3980	102	13	and	and	CCONJ
ap-3980	102	14	0	0	NUM
ap-3980	102	15	.	.	PUNCT
ap-3980	103	1	thereafter	thereafter	ADV
ap-3980	103	2	the	the	DET
ap-3980	103	3	value	value	NOUN
ap-3980	103	4	of	of	ADP
ap-3980	103	5	q	q	NOUN
ap-3980	103	6	enters	enter	NOUN
ap-3980	103	7	into	into	ADP
ap-3980	103	8	the	the	DET
ap-3980	103	9	values	value	NOUN
ap-3980	103	10	of	of	ADP
ap-3980	103	11	the	the	DET
ap-3980	103	12	resonances	resonance	NOUN
ap-3980	103	13	.	.	PUNCT
ap-3980	104	1	acknowledgements	acknowledgement	NOUN
ap-3980	104	2	r	r	NOUN
ap-3980	104	3	sinuvasan	sinuvasan	VERB
ap-3980	104	4	thanks	thank	NOUN
ap-3980	104	5	the	the	DET
ap-3980	104	6	university	university	NOUN
ap-3980	104	7	grants	grant	NOUN
ap-3980	104	8	commission	commission	PROPN
ap-3980	104	9	for	for	ADP
ap-3980	104	10	its	its	PRON
ap-3980	104	11	support	support	NOUN
ap-3980	104	12	.	.	PUNCT
ap-3980	105	1	pgll	pgll	PROPN
ap-3980	105	2	thanks	thanks	PROPN
ap-3980	105	3	professor	professor	NOUN
ap-3980	105	4	km	km	PROPN
ap-3980	105	5	tamizhmani	tamizhmani	NOUN
ap-3980	105	6	and	and	CCONJ
ap-3980	105	7	the	the	DET
ap-3980	105	8	department	department	NOUN
ap-3980	105	9	of	of	ADP
ap-3980	105	10	mathematics	mathematics	PROPN
ap-3980	105	11	,	,	PUNCT
ap-3980	105	12	university	university	NOUN
ap-3980	105	13	of	of	ADP
ap-3980	105	14	pondicherry	pondicherry	PROPN
ap-3980	105	15	,	,	PUNCT
ap-3980	105	16	for	for	ADP
ap-3980	105	17	the	the	DET
ap-3980	105	18	provision	provision	NOUN
ap-3980	105	19	of	of	ADP
ap-3980	105	20	facilities	facility	NOUN
ap-3980	105	21	whilst	whilst	SCONJ
ap-3980	105	22	this	this	DET
ap-3980	105	23	work	work	NOUN
ap-3980	105	24	was	be	AUX
ap-3980	105	25	undertaken	undertake	VERB
ap-3980	105	26	.	.	PUNCT
ap-3980	106	1	pgll	pgll	PROPN
ap-3980	106	2	also	also	ADV
ap-3980	106	3	thanks	thank	NOUN
ap-3980	106	4	the	the	DET
ap-3980	106	5	university	university	PROPN
ap-3980	106	6	of	of	ADP
ap-3980	106	7	kwazulu	kwazulu	PROPN
ap-3980	106	8	-	-	PUNCT
ap-3980	106	9	natal	natal	NOUN
ap-3980	106	10	and	and	CCONJ
ap-3980	106	11	the	the	DET
ap-3980	106	12	national	national	PROPN
ap-3980	106	13	research	research	PROPN
ap-3980	106	14	foundation	foundation	PROPN
ap-3980	106	15	of	of	ADP
ap-3980	106	16	the	the	DET
ap-3980	106	17	republic	republic	NOUN
ap-3980	106	18	of	of	ADP
ap-3980	106	19	south	south	PROPN
ap-3980	106	20	africa	africa	PROPN
ap-3980	106	21	for	for	ADP
ap-3980	106	22	their	their	PRON
ap-3980	106	23	continued	continue	VERB
ap-3980	106	24	support	support	NOUN
ap-3980	106	25	.	.	PUNCT
ap-3980	107	1	any	any	DET
ap-3980	107	2	views	view	NOUN
ap-3980	107	3	expressed	express	VERB
ap-3980	107	4	in	in	ADP
ap-3980	107	5	this	this	DET
ap-3980	107	6	paper	paper	NOUN
ap-3980	107	7	are	be	AUX
ap-3980	107	8	not	not	PART
ap-3980	107	9	necessarily	necessarily	ADV
ap-3980	107	10	those	those	PRON
ap-3980	107	11	of	of	ADP
ap-3980	107	12	the	the	DET
ap-3980	107	13	two	two	NUM
ap-3980	107	14	institutions	institution	NOUN
ap-3980	107	15	.	.	PUNCT
ap-3980	108	1	references	reference	NOUN
ap-3980	108	2	[	[	X
ap-3980	108	3	1	1	NUM
ap-3980	108	4	]	]	X
ap-3980	108	5	andriopoulos	andriopoulo	NOUN
ap-3980	108	6	,	,	PUNCT
ap-3980	108	7	k.	k.	NOUN
ap-3980	108	8	,	,	PUNCT
ap-3980	108	9	leach	leach	NOUN
ap-3980	108	10	,	,	PUNCT
ap-3980	108	11	p.	p.	NOUN
ap-3980	108	12	g.	g.	PROPN
ap-3980	108	13	l.	l.	PROPN
ap-3980	108	14	:	:	PUNCT
ap-3980	108	15	an	an	DET
ap-3980	108	16	interpretation	interpretation	NOUN
ap-3980	108	17	of	of	ADP
ap-3980	108	18	the	the	DET
ap-3980	108	19	presence	presence	NOUN
ap-3980	108	20	of	of	ADP
ap-3980	108	21	both	both	CCONJ
ap-3980	108	22	positive	positive	ADJ
ap-3980	108	23	and	and	CCONJ
ap-3980	108	24	negative	negative	ADJ
ap-3980	108	25	nongeneric	nongeneric	ADJ
ap-3980	108	26	resonances	resonance	NOUN
ap-3980	108	27	in	in	ADP
ap-3980	108	28	the	the	DET
ap-3980	108	29	singularity	singularity	NOUN
ap-3980	108	30	analysis	analysis	NOUN
ap-3980	108	31	.	.	PUNCT
ap-3980	109	1	physics	physics	NOUN
ap-3980	109	2	letters	letter	NOUN
ap-3980	109	3	a	a	PRON
ap-3980	109	4	,	,	PUNCT
ap-3980	109	5	359	359	NUM
ap-3980	109	6	,	,	PUNCT
ap-3980	109	7	2006	2006	NUM
ap-3980	109	8	,	,	PUNCT
ap-3980	109	9	p.	p.	NOUN
ap-3980	109	10	199	199	NUM
ap-3980	109	11	-	-	SYM
ap-3980	109	12	203	203	NUM
ap-3980	109	13	.	.	PUNCT
ap-3980	110	1	(	(	PUNCT
ap-3980	110	2	doi.org/10.1016/j.physleta	doi.org/10.1016/j.physleta	PROPN
ap-3980	110	3	2006.06.026	2006.06.026	NOUN
ap-3980	110	4	)	)	PUNCT
ap-3980	111	1	[	[	X
ap-3980	111	2	2	2	NUM
ap-3980	111	3	]	]	X
ap-3980	111	4	feix	feix	PROPN
ap-3980	111	5	,	,	PUNCT
ap-3980	111	6	m.	m.	PROPN
ap-3980	111	7	r.	r.	PROPN
ap-3980	111	8	,	,	PUNCT
ap-3980	111	9	geronimi	geronimi	PROPN
ap-3980	111	10	,	,	PUNCT
ap-3980	111	11	c.	c.	NOUN
ap-3980	111	12	,	,	PUNCT
ap-3980	111	13	leach	leach	NOUN
ap-3980	111	14	,	,	PUNCT
ap-3980	111	15	p.	p.	NOUN
ap-3980	111	16	g.	g.	PROPN
ap-3980	111	17	l.	l.	PROPN
ap-3980	111	18	,	,	PUNCT
ap-3980	111	19	lemmer	lemmer	PROPN
ap-3980	111	20	,	,	PUNCT
ap-3980	111	21	r.	r.	PROPN
ap-3980	111	22	l.	l.	PROPN
ap-3980	111	23	,	,	PUNCT
ap-3980	111	24	bouquet	bouquet	PROPN
ap-3980	111	25	,	,	PUNCT
ap-3980	111	26	s.	s.	PROPN
ap-3980	111	27	:	:	PUNCT
ap-3980	111	28	on	on	ADP
ap-3980	111	29	the	the	DET
ap-3980	111	30	singularity	singularity	NOUN
ap-3980	111	31	analysis	analysis	NOUN
ap-3980	111	32	of	of	ADP
ap-3980	111	33	ordinary	ordinary	ADJ
ap-3980	111	34	differential	differential	ADJ
ap-3980	111	35	equations	equation	NOUN
ap-3980	111	36	invariant	invariant	VERB
ap-3980	111	37	under	under	ADP
ap-3980	111	38	time	time	NOUN
ap-3980	111	39	translation	translation	NOUN
ap-3980	111	40	and	and	CCONJ
ap-3980	111	41	rescaling	rescaling	NOUN
ap-3980	111	42	.	.	PUNCT
ap-3980	112	1	journal	journal	PROPN
ap-3980	112	2	of	of	ADP
ap-3980	112	3	physics	physics	PROPN
ap-3980	112	4	a	a	PRON
ap-3980	112	5	:	:	PUNCT
ap-3980	112	6	mathematical	mathematical	ADJ
ap-3980	112	7	and	and	CCONJ
ap-3980	112	8	general	general	ADJ
ap-3980	112	9	,	,	PUNCT
ap-3980	112	10	30(21	30(21	PROPN
ap-3980	112	11	)	)	PUNCT
ap-3980	112	12	,	,	PUNCT
ap-3980	112	13	1997	1997	NUM
ap-3980	112	14	,	,	PUNCT
ap-3980	112	15	p.	p.	NOUN
ap-3980	112	16	7437	7437	NUM
ap-3980	112	17	-	-	SYM
ap-3980	112	18	7461	7461	NUM
ap-3980	112	19	.	.	PUNCT
ap-3980	113	1	(	(	PUNCT
ap-3980	113	2	doi.org/10.1088/0305-4470/30/21/017	doi.org/10.1088/0305-4470/30/21/017	NOUN
ap-3980	113	3	)	)	PUNCT
ap-3980	114	1	[	[	X
ap-3980	114	2	3	3	NUM
ap-3980	114	3	]	]	X
ap-3980	114	4	hsu	hsu	PROPN
ap-3980	114	5	,	,	PUNCT
ap-3980	114	6	l.	l.	PROPN
ap-3980	114	7	,	,	PUNCT
ap-3980	114	8	kamran	kamran	PROPN
ap-3980	114	9	,	,	PUNCT
ap-3980	114	10	n.	n.	NOUN
ap-3980	114	11	:	:	PUNCT
ap-3980	114	12	classification	classification	NOUN
ap-3980	114	13	of	of	ADP
ap-3980	114	14	second	second	ADJ
ap-3980	114	15	-	-	PUNCT
ap-3980	114	16	order	order	NOUN
ap-3980	114	17	ordinary	ordinary	ADJ
ap-3980	114	18	differential	differential	ADJ
ap-3980	114	19	equations	equation	NOUN
ap-3980	114	20	admitting	admit	VERB
ap-3980	114	21	lie	lie	NOUN
ap-3980	114	22	groups	group	NOUN
ap-3980	114	23	of	of	ADP
ap-3980	114	24	fibre	fibre	NOUN
ap-3980	114	25	-	-	PUNCT
ap-3980	114	26	preserving	preserve	VERB
ap-3980	114	27	point	point	NOUN
ap-3980	114	28	symmetries	symmetry	NOUN
ap-3980	114	29	.	.	PUNCT
ap-3980	115	1	proceedings	proceeding	NOUN
ap-3980	115	2	of	of	ADP
ap-3980	115	3	the	the	DET
ap-3980	115	4	london	london	PROPN
ap-3980	115	5	mathematical	mathematical	ADJ
ap-3980	115	6	society	society	NOUN
ap-3980	115	7	,	,	PUNCT
ap-3980	115	8	58	58	NUM
ap-3980	115	9	,	,	PUNCT
ap-3980	115	10	1989	1989	NUM
ap-3980	115	11	,	,	PUNCT
ap-3980	115	12	p.	p.	NOUN
ap-3980	115	13	387	387	NUM
ap-3980	115	14	-	-	SYM
ap-3980	115	15	416	416	NUM
ap-3980	115	16	.	.	PUNCT
ap-3980	116	1	(	(	PUNCT
ap-3980	116	2	doi.org/10.1112/plms/s3-58.2.387	doi.org/10.1112/plms/s3-58.2.387	X
ap-3980	116	3	)	)	PUNCT
ap-3980	117	1	[	[	X
ap-3980	117	2	4	4	NUM
ap-3980	117	3	]	]	X
ap-3980	117	4	kummer	kummer	NOUN
ap-3980	117	5	,	,	PUNCT
ap-3980	117	6	e.	e.	PROPN
ap-3980	117	7	e.	e.	PROPN
ap-3980	117	8	:	:	PUNCT
ap-3980	117	9	de	de	PROPN
ap-3980	117	10	generali	generali	PROPN
ap-3980	117	11	quadam	quadam	PROPN
ap-3980	117	12	æquatione	æquatione	PROPN
ap-3980	117	13	differentiali	differentiali	PROPN
ap-3980	117	14	tertii	tertii	NOUN
ap-3980	117	15	ordinis	ordinis	X
ap-3980	117	16	.	.	PUNCT
ap-3980	118	1	journal	journal	PROPN
ap-3980	118	2	der	der	PROPN
ap-3980	118	3	reine	reine	PROPN
ap-3980	118	4	und	und	PROPN
ap-3980	118	5	angewandte	angewandte	PROPN
ap-3980	118	6	mathematik	mathematik	PROPN
ap-3980	118	7	,	,	PUNCT
ap-3980	118	8	100	100	NUM
ap-3980	118	9	,	,	PUNCT
ap-3980	118	10	1887	1887	NUM
ap-3980	118	11	,	,	PUNCT
ap-3980	118	12	p.	p.	NOUN
ap-3980	118	13	1	1	NUM
ap-3980	118	14	-	-	SYM
ap-3980	118	15	9	9	NUM
ap-3980	118	16	.	.	PUNCT
ap-3980	119	1	(	(	PUNCT
ap-3980	119	2	reprinted	reprint	VERB
ap-3980	119	3	from	from	ADP
ap-3980	119	4	the	the	DET
ap-3980	119	5	programm	programm	PROPN
ap-3980	119	6	des	des	PROPN
ap-3980	119	7	evangelischen	evangelischen	PROPN
ap-3980	119	8	königl	königl	PROPN
ap-3980	119	9	und	und	PROPN
ap-3980	119	10	stadtgymnasiums	stadtgymnasium	NOUN
ap-3980	119	11	in	in	ADP
ap-3980	119	12	liegnitz	liegnitz	NOUN
ap-3980	119	13	for	for	ADP
ap-3980	119	14	the	the	DET
ap-3980	119	15	year	year	NOUN
ap-3980	119	16	1834	1834	NUM
ap-3980	119	17	)	)	PUNCT
ap-3980	120	1	(	(	PUNCT
ap-3980	120	2	doi.org/10.1515/crll.1887.100.1	doi.org/10.1515/crll.1887.100.1	X
ap-3980	120	3	)	)	PUNCT
ap-3980	121	1	[	[	X
ap-3980	121	2	5	5	NUM
ap-3980	121	3	]	]	X
ap-3980	121	4	morozov	morozov	NOUN
ap-3980	121	5	,	,	PUNCT
ap-3980	121	6	v.	v.	ADP
ap-3980	121	7	v.	v.	ADP
ap-3980	121	8	,	,	PUNCT
ap-3980	121	9	classification	classification	NOUN
ap-3980	121	10	of	of	ADP
ap-3980	121	11	six	six	NUM
ap-3980	121	12	-	-	PUNCT
ap-3980	121	13	dimensional	dimensional	ADJ
ap-3980	121	14	nilpotent	nilpotent	ADJ
ap-3980	121	15	lie	lie	NOUN
ap-3980	121	16	algebras	algebra	NOUN
ap-3980	121	17	.	.	PUNCT
ap-3980	122	1	izvestia	izvestia	PROPN
ap-3980	122	2	vysshikh	vysshikh	PROPN
ap-3980	122	3	uchebn	uchebn	NOUN
ap-3980	122	4	zavendenĭı	zavendenĭı	PROPN
ap-3980	122	5	matematika	matematika	NOUN
ap-3980	122	6	,	,	PUNCT
ap-3980	122	7	5	5	NUM
ap-3980	122	8	,	,	PUNCT
ap-3980	122	9	1958	1958	NUM
ap-3980	122	10	,	,	PUNCT
ap-3980	122	11	p.	p.	NOUN
ap-3980	122	12	161	161	NUM
ap-3980	122	13	-	-	SYM
ap-3980	122	14	171	171	NUM
ap-3980	122	15	.	.	PUNCT
ap-3980	123	1	[	[	X
ap-3980	123	2	6	6	NUM
ap-3980	123	3	]	]	X
ap-3980	123	4	mubarakzyanov	mubarakzyanov	NOUN
ap-3980	123	5	,	,	PUNCT
ap-3980	123	6	g.	g.	PROPN
ap-3980	123	7	m.	m.	PROPN
ap-3980	123	8	:	:	PUNCT
ap-3980	123	9	on	on	ADP
ap-3980	123	10	solvable	solvable	ADJ
ap-3980	123	11	lie	lie	NOUN
ap-3980	123	12	algebras	algebras	PROPN
ap-3980	123	13	.	.	PUNCT
ap-3980	124	1	izvestia	izvestia	PROPN
ap-3980	124	2	vysshikh	vysshikh	PROPN
ap-3980	124	3	uchebn	uchebn	NOUN
ap-3980	124	4	zavendenĭı	zavendenĭı	PROPN
ap-3980	124	5	matematika	matematika	NOUN
ap-3980	124	6	,	,	PUNCT
ap-3980	124	7	32	32	NUM
ap-3980	124	8	,	,	PUNCT
ap-3980	124	9	p.	p.	NOUN
ap-3980	124	10	114	114	NUM
ap-3980	124	11	-	-	SYM
ap-3980	124	12	123	123	NUM
ap-3980	124	13	.	.	PUNCT
ap-3980	125	1	[	[	X
ap-3980	125	2	7	7	NUM
ap-3980	125	3	]	]	X
ap-3980	125	4	mubarakzyanov	mubarakzyanov	NOUN
ap-3980	125	5	,	,	PUNCT
ap-3980	125	6	g.	g.	PROPN
ap-3980	125	7	m.	m.	NOUN
ap-3980	125	8	:	:	PUNCT
ap-3980	125	9	classification	classification	NOUN
ap-3980	125	10	of	of	ADP
ap-3980	125	11	real	real	ADJ
ap-3980	125	12	structures	structure	NOUN
ap-3980	125	13	of	of	ADP
ap-3980	125	14	five	five	NUM
ap-3980	125	15	-	-	PUNCT
ap-3980	125	16	dimensional	dimensional	ADJ
ap-3980	125	17	lie	lie	NOUN
ap-3980	125	18	algebras	algebra	NOUN
ap-3980	125	19	.	.	PUNCT
ap-3980	126	1	izvestia	izvestia	PROPN
ap-3980	126	2	vysshikh	vysshikh	PROPN
ap-3980	126	3	uchebn	uchebn	NOUN
ap-3980	126	4	zavendenĭı	zavendenĭı	PROPN
ap-3980	126	5	matematika	matematika	NOUN
ap-3980	126	6	,	,	PUNCT
ap-3980	126	7	34	34	NUM
ap-3980	126	8	,	,	PUNCT
ap-3980	126	9	1963	1963	NUM
ap-3980	126	10	,	,	PUNCT
ap-3980	126	11	p.	p.	NOUN
ap-3980	126	12	99	99	NUM
ap-3980	126	13	-	-	SYM
ap-3980	126	14	106	106	NUM
ap-3980	126	15	.	.	PUNCT
ap-3980	127	1	[	[	X
ap-3980	127	2	8	8	NUM
ap-3980	127	3	]	]	X
ap-3980	127	4	mubarakzyanov	mubarakzyanov	NOUN
ap-3980	127	5	,	,	PUNCT
ap-3980	127	6	g.	g.	PROPN
ap-3980	127	7	m.	m.	NOUN
ap-3980	127	8	:	:	PUNCT
ap-3980	127	9	classification	classification	NOUN
ap-3980	127	10	of	of	ADP
ap-3980	127	11	solvable	solvable	ADJ
ap-3980	127	12	six	six	NUM
ap-3980	127	13	-	-	PUNCT
ap-3980	127	14	dimensional	dimensional	ADJ
ap-3980	127	15	lie	lie	NOUN
ap-3980	127	16	algebras	algebra	NOUN
ap-3980	127	17	with	with	ADP
ap-3980	127	18	one	one	NUM
ap-3980	127	19	nilpotent	nilpotent	ADJ
ap-3980	127	20	base	base	NOUN
ap-3980	127	21	element	element	NOUN
ap-3980	127	22	.	.	PUNCT
ap-3980	128	1	izvestia	izvestia	PROPN
ap-3980	128	2	vysshikh	vysshikh	NOUN
ap-3980	128	3	uchebn	uchebn	NOUN
ap-3980	128	4	zavendenĭı	zavendenĭı	PROPN
ap-3980	128	5	matematika	matematika	NOUN
ap-3980	128	6	,	,	PUNCT
ap-3980	128	7	35	35	NUM
ap-3980	128	8	,	,	PUNCT
ap-3980	128	9	1963	1963	NUM
ap-3980	128	10	,	,	PUNCT
ap-3980	128	11	p.	p.	NOUN
ap-3980	128	12	104	104	NUM
ap-3980	128	13	-	-	SYM
ap-3980	128	14	116	116	NUM
ap-3980	128	15	.	.	PUNCT
ap-3980	129	1	[	[	X
ap-3980	129	2	9	9	NUM
ap-3980	129	3	]	]	PUNCT
ap-3980	129	4	patera	patera	NOUN
ap-3980	129	5	,	,	PUNCT
ap-3980	129	6	j.	j.	PROPN
ap-3980	129	7	,	,	PUNCT
ap-3980	129	8	sharp	sharp	PROPN
ap-3980	129	9	,	,	PUNCT
ap-3980	129	10	r.	r.	PROPN
ap-3980	129	11	t.	t.	PROPN
ap-3980	129	12	,	,	PUNCT
ap-3980	129	13	winternitz	winternitz	PROPN
ap-3980	129	14	,	,	PUNCT
ap-3980	129	15	p.	p.	NOUN
ap-3980	129	16	,	,	PUNCT
ap-3980	129	17	zassenhaus	zassenhaus	PROPN
ap-3980	129	18	,	,	PUNCT
ap-3980	129	19	h.	h.	NOUN
ap-3980	129	20	:	:	PUNCT
ap-3980	129	21	invariants	invariant	NOUN
ap-3980	129	22	of	of	ADP
ap-3980	129	23	real	real	ADJ
ap-3980	129	24	low	low	ADJ
ap-3980	129	25	dimension	dimension	NOUN
ap-3980	129	26	lie	lie	NOUN
ap-3980	129	27	algebras	algebras	PROPN
ap-3980	129	28	.	.	PUNCT
ap-3980	129	29	journal	journal	PROPN
ap-3980	129	30	of	of	ADP
ap-3980	129	31	mathematical	mathematical	ADJ
ap-3980	129	32	physics	physics	NOUN
ap-3980	129	33	,	,	PUNCT
ap-3980	129	34	17(6	17(6	NUM
ap-3980	129	35	)	)	PUNCT
ap-3980	129	36	,	,	PUNCT
ap-3980	129	37	1976	1976	NUM
ap-3980	129	38	,	,	PUNCT
ap-3980	129	39	986	986	NUM
ap-3980	129	40	-	-	SYM
ap-3980	129	41	994	994	NUM
ap-3980	129	42	.	.	PUNCT
ap-3980	129	43	(	(	PUNCT
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ap-3980	129	45	)	)	PUNCT
ap-3980	129	46	[	[	X
ap-3980	129	47	10	10	NUM
ap-3980	129	48	]	]	X
ap-3980	129	49	ramani	ramani	PROPN
ap-3980	129	50	,	,	PUNCT
ap-3980	129	51	a.	a.	PROPN
ap-3980	129	52	,	,	PUNCT
ap-3980	129	53	grammaticos	grammaticos	PROPN
ap-3980	129	54	,	,	PUNCT
ap-3980	129	55	b.	b.	PROPN
ap-3980	129	56	,	,	PUNCT
ap-3980	129	57	bountis	bountis	PROPN
ap-3980	129	58	,	,	PUNCT
ap-3980	129	59	t.	t.	PROPN
ap-3980	129	60	:	:	PUNCT
ap-3980	129	61	the	the	DET
ap-3980	129	62	painlevé	painlevé	NOUN
ap-3980	129	63	property	property	NOUN
ap-3980	129	64	and	and	CCONJ
ap-3980	129	65	singularity	singularity	NOUN
ap-3980	129	66	analysis	analysis	NOUN
ap-3980	129	67	of	of	ADP
ap-3980	129	68	integrable	integrable	ADJ
ap-3980	129	69	and	and	CCONJ
ap-3980	129	70	nonintegrable	nonintegrable	ADJ
ap-3980	129	71	systems	system	NOUN
ap-3980	129	72	.	.	PUNCT
ap-3980	130	1	physics	physics	NOUN
ap-3980	130	2	reports	report	NOUN
ap-3980	130	3	,	,	PUNCT
ap-3980	130	4	180	180	NUM
ap-3980	130	5	,	,	PUNCT
ap-3980	130	6	1989	1989	NUM
ap-3980	130	7	,	,	PUNCT
ap-3980	130	8	p.	p.	NOUN
ap-3980	130	9	159	159	NUM
ap-3980	130	10	-	-	SYM
ap-3980	130	11	245	245	NUM
ap-3980	130	12	.	.	PUNCT
ap-3980	131	1	(	(	PUNCT
ap-3980	131	2	doi.org/10.1016/0370-1573(89)90024-0	doi.org/10.1016/0370-1573(89)90024-0	PROPN
ap-3980	131	3	)	)	PUNCT
ap-3980	132	1	[	[	X
ap-3980	132	2	11	11	NUM
ap-3980	132	3	]	]	X
ap-3980	132	4	shabanskaya	shabanskaya	PROPN
ap-3980	132	5	,	,	PUNCT
ap-3980	132	6	a.	a.	PROPN
ap-3980	132	7	,	,	PUNCT
ap-3980	132	8	thompson	thompson	PROPN
ap-3980	132	9	,	,	PUNCT
ap-3980	132	10	g.	g.	NOUN
ap-3980	132	11	:	:	PUNCT
ap-3980	132	12	six	six	NUM
ap-3980	132	13	-	-	PUNCT
ap-3980	132	14	dimensional	dimensional	ADJ
ap-3980	132	15	lie	lie	NOUN
ap-3980	132	16	algebras	algebra	NOUN
ap-3980	132	17	with	with	ADP
ap-3980	132	18	a	a	DET
ap-3980	132	19	five	five	NUM
ap-3980	132	20	-	-	PUNCT
ap-3980	132	21	dimensional	dimensional	ADJ
ap-3980	132	22	nilradical	nilradical	ADJ
ap-3980	132	23	.	.	PUNCT
ap-3980	133	1	journal	journal	PROPN
ap-3980	133	2	of	of	ADP
ap-3980	133	3	lie	lie	NOUN
ap-3980	133	4	theory	theory	NOUN
ap-3980	133	5	,	,	PUNCT
ap-3980	133	6	23(2	23(2	NOUN
ap-3980	133	7	)	)	PUNCT
ap-3980	133	8	,	,	PUNCT
ap-3980	133	9	2013	2013	NUM
ap-3980	133	10	,	,	PUNCT
ap-3980	133	11	p.	p.	NOUN
ap-3980	133	12	313	313	NUM
ap-3980	133	13	-	-	SYM
ap-3980	133	14	355	355	NUM
ap-3980	133	15	.	.	PUNCT
ap-3980	134	1	[	[	X
ap-3980	134	2	12	12	NUM
ap-3980	134	3	]	]	X
ap-3980	134	4	sinuvasan	sinuvasan	PROPN
ap-3980	134	5	,	,	PUNCT
ap-3980	134	6	r.	r.	PROPN
ap-3980	134	7	,	,	PUNCT
ap-3980	134	8	tamizhmani	tamizhmani	PROPN
ap-3980	134	9	,	,	PUNCT
ap-3980	134	10	k.	k.	PROPN
ap-3980	134	11	m.	m.	PROPN
ap-3980	134	12	,	,	PUNCT
ap-3980	134	13	leach	leach	NOUN
ap-3980	134	14	,	,	PUNCT
ap-3980	134	15	p.	p.	NOUN
ap-3980	134	16	g.	g.	PROPN
ap-3980	134	17	l.	l.	PROPN
ap-3980	134	18	:	:	PUNCT
ap-3980	135	1	algebraic	algebraic	ADJ
ap-3980	135	2	and	and	CCONJ
ap-3980	135	3	singularity	singularity	NOUN
ap-3980	135	4	properties	property	NOUN
ap-3980	135	5	of	of	ADP
ap-3980	135	6	a	a	DET
ap-3980	135	7	class	class	NOUN
ap-3980	135	8	of	of	ADP
ap-3980	135	9	generalisations	generalisation	NOUN
ap-3980	135	10	of	of	ADP
ap-3980	135	11	the	the	DET
ap-3980	135	12	kummer	kummer	NOUN
ap-3980	135	13	-	-	PUNCT
ap-3980	135	14	schwarz	schwarz	PROPN
ap-3980	135	15	equation	equation	NOUN
ap-3980	135	16	.	.	PUNCT
ap-3980	136	1	differential	differential	ADJ
ap-3980	136	2	equations	equation	NOUN
ap-3980	136	3	and	and	CCONJ
ap-3980	136	4	dynamical	dynamical	ADJ
ap-3980	136	5	systems	system	NOUN
ap-3980	136	6	,	,	PUNCT
ap-3980	136	7	2016	2016	NUM
ap-3980	136	8	,	,	PUNCT
ap-3980	136	9	doi:10.1007	doi:10.1007	NOUN
ap-3980	136	10	/	/	PUNCT
ap-3980	136	11	s12591	s12591	NOUN
ap-3980	136	12	-	-	PUNCT
ap-3980	136	13	016	016	NUM
ap-3980	136	14	-	-	PUNCT
ap-3980	136	15	0327	0327	NUM
ap-3980	136	16	-	-	PUNCT
ap-3980	136	17	5	5	NUM
ap-3980	136	18	.	.	PUNCT
ap-3980	137	1	[	[	X
ap-3980	137	2	13	13	NUM
ap-3980	137	3	]	]	SYM
ap-3980	137	4	ŝnobl	ŝnobl	NOUN
ap-3980	137	5	,	,	PUNCT
ap-3980	137	6	l.	l.	PROPN
ap-3980	137	7	,	,	PUNCT
ap-3980	137	8	winternitz	winternitz	PROPN
ap-3980	137	9	,	,	PUNCT
ap-3980	137	10	p.	p.	NOUN
ap-3980	137	11	:	:	PUNCT
ap-3980	137	12	classification	classification	NOUN
ap-3980	137	13	and	and	CCONJ
ap-3980	137	14	identification	identification	NOUN
ap-3980	137	15	of	of	ADP
ap-3980	137	16	lie	lie	NOUN
ap-3980	137	17	algebras	algebras	PROPN
ap-3980	137	18	33	33	NUM
ap-3980	137	19	.	.	PUNCT
ap-3980	138	1	american	american	PROPN
ap-3980	138	2	mathematical	mathematical	PROPN
ap-3980	138	3	society	society	NOUN
ap-3980	138	4	.	.	PUNCT
ap-3980	139	1	providence	providence	NOUN
ap-3980	139	2	,	,	PUNCT
ap-3980	139	3	r.i	r.i	PROPN
ap-3980	139	4	.	.	PROPN
ap-3980	139	5	2014	2014	NUM
ap-3980	139	6	.	.	PUNCT
ap-3980	140	1	[	[	X
ap-3980	140	2	14	14	NUM
ap-3980	140	3	]	]	X
ap-3980	140	4	tabor	tabor	NOUN
ap-3980	140	5	,	,	PUNCT
ap-3980	140	6	m.	m.	NOUN
ap-3980	140	7	:	:	PUNCT
ap-3980	140	8	chaos	chaos	NOUN
ap-3980	140	9	and	and	CCONJ
ap-3980	140	10	integrability	integrability	NOUN
ap-3980	140	11	in	in	ADP
ap-3980	140	12	nonlinear	nonlinear	ADJ
ap-3980	140	13	dynamics	dynamic	NOUN
ap-3980	140	14	.	.	PUNCT
ap-3980	141	1	new	new	PROPN
ap-3980	141	2	york	york	PROPN
ap-3980	141	3	:	:	PUNCT
ap-3980	142	1	john	john	PROPN
ap-3980	142	2	wiley	wiley	PROPN
ap-3980	142	3	,	,	PUNCT
ap-3980	142	4	1989	1989	NUM
ap-3980	142	5	.	.	PUNCT
ap-3980	143	1	(	(	PUNCT
ap-3980	143	2	isbn:978	isbn:978	NOUN
ap-3980	143	3	-	-	SYM
ap-3980	143	4	0	0	NUM
ap-3980	143	5	-	-	PUNCT
ap-3980	143	6	471	471	NUM
ap-3980	143	7	-	-	PUNCT
ap-3980	143	8	82728	82728	NUM
ap-3980	143	9	-	-	PUNCT
ap-3980	143	10	3	3	NUM
ap-3980	143	11	)	)	PUNCT
ap-3980	143	12	469	469	NUM
ap-3980	143	13	acta	acta	PROPN
ap-3980	143	14	polytechnica	polytechnica	PROPN
ap-3980	143	15	57(6):467–469	57(6):467–469	PROPN
ap-3980	143	16	,	,	PUNCT
ap-3980	143	17	2017	2017	NUM
ap-3980	143	18	1	1	NUM
ap-3980	143	19	introduction	introduction	NOUN
ap-3980	143	20	2	2	NUM
ap-3980	143	21	singularity	singularity	NOUN
ap-3980	143	22	analysis	analysis	NOUN
ap-3980	143	23	3	3	NUM
ap-3980	143	24	solution	solution	NOUN
ap-3980	143	25	of	of	ADP
ap-3980	143	26	the	the	DET
ap-3980	143	27	general	general	ADJ
ap-3980	143	28	equation	equation	NOUN
ap-3980	143	29	4	4	NUM
ap-3980	143	30	symmetry	symmetry	NOUN
ap-3980	143	31	properties	property	NOUN
ap-3980	143	32	5	5	NUM
ap-3980	143	33	conclusion	conclusion	NOUN
ap-3980	143	34	acknowledgements	acknowledgement	NOUN
ap-3980	143	35	references	reference	NOUN