id	sid	tid	token	lemma	pos
ap-1811	1	1	acta	acta	PROPN
ap-1811	1	2	polytechnica	polytechnica	PROPN
ap-1811	1	3	acta	acta	PROPN
ap-1811	1	4	polytechnica	polytechnica	PROPN
ap-1811	1	5	53(3):302–305	53(3):302–305	PROPN
ap-1811	1	6	,	,	PUNCT
ap-1811	1	7	2013	2013	NUM
ap-1811	1	8	©	©	PROPN
ap-1811	1	9	czech	czech	PROPN
ap-1811	1	10	technical	technical	PROPN
ap-1811	1	11	university	university	PROPN
ap-1811	1	12	in	in	ADP
ap-1811	1	13	prague	prague	PROPN
ap-1811	1	14	,	,	PUNCT
ap-1811	1	15	2013	2013	NUM
ap-1811	1	16	available	available	ADJ
ap-1811	1	17	online	online	ADV
ap-1811	1	18	at	at	ADP
ap-1811	1	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1811	1	20	emmy	emmy	ADJ
ap-1811	1	21	noether	noether	ADJ
ap-1811	1	22	and	and	CCONJ
ap-1811	1	23	linear	linear	ADJ
ap-1811	1	24	evolution	evolution	NOUN
ap-1811	1	25	equations	equation	NOUN
ap-1811	1	26	p.	p.	PROPN
ap-1811	1	27	g.	g.	PROPN
ap-1811	1	28	l.	l.	PROPN
ap-1811	1	29	leacha	leacha	PROPN
ap-1811	1	30	,	,	PUNCT
ap-1811	1	31	b,∗	b,∗	VERB
ap-1811	1	32	a	a	DET
ap-1811	1	33	school	school	NOUN
ap-1811	1	34	of	of	ADP
ap-1811	1	35	mathematical	mathematical	ADJ
ap-1811	1	36	sciences	sciences	PROPN
ap-1811	1	37	,	,	PUNCT
ap-1811	1	38	university	university	NOUN
ap-1811	1	39	of	of	ADP
ap-1811	1	40	kwazulu	kwazulu	PROPN
ap-1811	1	41	-	-	PUNCT
ap-1811	1	42	natal	natal	ADJ
ap-1811	1	43	,	,	PUNCT
ap-1811	1	44	private	private	ADJ
ap-1811	1	45	bag	bag	NOUN
ap-1811	1	46	x54001	x54001	PROPN
ap-1811	1	47	,	,	PUNCT
ap-1811	1	48	durban	durban	PROPN
ap-1811	1	49	4000	4000	NUM
ap-1811	1	50	,	,	PUNCT
ap-1811	1	51	republic	republic	NOUN
ap-1811	1	52	of	of	ADP
ap-1811	1	53	south	south	PROPN
ap-1811	1	54	africa	africa	PROPN
ap-1811	2	1	b	b	PROPN
ap-1811	2	2	department	department	PROPN
ap-1811	2	3	of	of	ADP
ap-1811	2	4	mathematics	mathematics	PROPN
ap-1811	2	5	and	and	CCONJ
ap-1811	2	6	statistics	statistic	NOUN
ap-1811	2	7	,	,	PUNCT
ap-1811	2	8	university	university	PROPN
ap-1811	2	9	of	of	ADP
ap-1811	2	10	cyprus	cyprus	PROPN
ap-1811	2	11	,	,	PUNCT
ap-1811	2	12	lefkosia	lefkosia	PROPN
ap-1811	2	13	,	,	PUNCT
ap-1811	2	14	republic	republic	NOUN
ap-1811	2	15	of	of	ADP
ap-1811	2	16	cyprus	cyprus	PROPN
ap-1811	2	17	∗	∗	PROPN
ap-1811	2	18	corresponding	correspond	VERB
ap-1811	2	19	author	author	NOUN
ap-1811	2	20	:	:	PUNCT
ap-1811	2	21	leachp@ukzn.ac.za	leachp@ukzn.ac.za	ADJ
ap-1811	2	22	abstract	abstract	NOUN
ap-1811	2	23	.	.	PUNCT
ap-1811	3	1	noether	noether	PROPN
ap-1811	3	2	’s	’s	PART
ap-1811	3	3	theorem	theorem	PROPN
ap-1811	3	4	relates	relate	VERB
ap-1811	3	5	the	the	DET
ap-1811	3	6	action	action	NOUN
ap-1811	3	7	integral	integral	ADJ
ap-1811	3	8	of	of	ADP
ap-1811	3	9	a	a	DET
ap-1811	3	10	lagrangian	lagrangian	NOUN
ap-1811	3	11	with	with	ADP
ap-1811	3	12	symmetries	symmetry	NOUN
ap-1811	3	13	which	which	PRON
ap-1811	3	14	leave	leave	VERB
ap-1811	3	15	it	it	PRON
ap-1811	3	16	invariant	invariant	ADJ
ap-1811	3	17	and	and	CCONJ
ap-1811	3	18	the	the	DET
ap-1811	3	19	first	first	ADJ
ap-1811	3	20	integrals	integral	NOUN
ap-1811	3	21	consequent	consequent	ADJ
ap-1811	3	22	upon	upon	SCONJ
ap-1811	3	23	the	the	DET
ap-1811	3	24	variational	variational	ADJ
ap-1811	3	25	principle	principle	NOUN
ap-1811	3	26	and	and	CCONJ
ap-1811	3	27	the	the	DET
ap-1811	3	28	existence	existence	NOUN
ap-1811	3	29	of	of	ADP
ap-1811	3	30	the	the	DET
ap-1811	3	31	symmetries	symmetry	NOUN
ap-1811	3	32	.	.	PUNCT
ap-1811	4	1	these	these	DET
ap-1811	4	2	each	each	PRON
ap-1811	4	3	have	have	VERB
ap-1811	4	4	an	an	DET
ap-1811	4	5	equivalent	equivalent	NOUN
ap-1811	4	6	in	in	ADP
ap-1811	4	7	the	the	DET
ap-1811	4	8	schrödinger	schrödinger	ADJ
ap-1811	4	9	equation	equation	NOUN
ap-1811	4	10	corresponding	correspond	VERB
ap-1811	4	11	to	to	ADP
ap-1811	4	12	the	the	DET
ap-1811	4	13	lagrangian	lagrangian	ADJ
ap-1811	4	14	and	and	CCONJ
ap-1811	4	15	by	by	ADP
ap-1811	4	16	extension	extension	NOUN
ap-1811	4	17	to	to	PART
ap-1811	4	18	linear	linear	VERB
ap-1811	4	19	evolution	evolution	NOUN
ap-1811	4	20	equations	equation	NOUN
ap-1811	4	21	in	in	ADP
ap-1811	4	22	general	general	ADJ
ap-1811	4	23	.	.	PUNCT
ap-1811	5	1	the	the	DET
ap-1811	5	2	implications	implication	NOUN
ap-1811	5	3	of	of	ADP
ap-1811	5	4	these	these	DET
ap-1811	5	5	connections	connection	NOUN
ap-1811	5	6	are	be	AUX
ap-1811	5	7	investigated	investigate	VERB
ap-1811	5	8	.	.	PUNCT
ap-1811	6	1	keywords	keyword	NOUN
ap-1811	6	2	:	:	PUNCT
ap-1811	6	3	lagrangian	lagrangian	ADJ
ap-1811	6	4	,	,	PUNCT
ap-1811	6	5	hamitonian	hamitonian	ADJ
ap-1811	6	6	,	,	PUNCT
ap-1811	6	7	schrödinger	schrödinger	ADJ
ap-1811	6	8	,	,	PUNCT
ap-1811	6	9	black	black	ADJ
ap-1811	6	10	-	-	PUNCT
ap-1811	6	11	scholes	schole	NOUN
ap-1811	6	12	-	-	PUNCT
ap-1811	6	13	merton	merton	NOUN
ap-1811	6	14	.	.	PUNCT
ap-1811	7	1	1	1	NUM
ap-1811	7	2	.	.	X
ap-1811	8	1	noether	noether	PROPN
ap-1811	8	2	’s	’s	PART
ap-1811	8	3	theorem	theorem	NOUN
ap-1811	8	4	in	in	ADP
ap-1811	8	5	1918	1918	NUM
ap-1811	8	6	emmy	emmy	ADJ
ap-1811	8	7	noether	noether	ADJ
ap-1811	9	1	[	[	X
ap-1811	9	2	13	13	NUM
ap-1811	9	3	]	]	PUNCT
ap-1811	9	4	presented	present	VERB
ap-1811	9	5	a	a	DET
ap-1811	9	6	theorem	theorem	NOUN
ap-1811	9	7	in	in	ADP
ap-1811	9	8	the	the	DET
ap-1811	9	9	festschrift	festschrift	NOUN
ap-1811	9	10	to	to	PART
ap-1811	9	11	mark	mark	VERB
ap-1811	9	12	the	the	DET
ap-1811	9	13	diamond	diamond	NOUN
ap-1811	9	14	jubilee	jubilee	NOUN
ap-1811	9	15	of	of	ADP
ap-1811	9	16	the	the	DET
ap-1811	9	17	thesis	thesis	NOUN
ap-1811	9	18	of	of	ADP
ap-1811	9	19	felix	felix	PROPN
ap-1811	9	20	klein	klein	PROPN
ap-1811	9	21	.	.	PUNCT
ap-1811	10	1	her	her	PRON
ap-1811	10	2	presentation	presentation	NOUN
ap-1811	10	3	dealt	deal	VERB
ap-1811	10	4	with	with	ADP
ap-1811	10	5	a	a	DET
ap-1811	10	6	functional	functional	NOUN
ap-1811	10	7	of	of	ADP
ap-1811	10	8	several	several	ADJ
ap-1811	10	9	independent	independent	ADJ
ap-1811	10	10	variables	variable	NOUN
ap-1811	10	11	.	.	PUNCT
ap-1811	11	1	given	give	VERB
ap-1811	11	2	our	our	PRON
ap-1811	11	3	present	present	ADJ
ap-1811	11	4	interest	interest	NOUN
ap-1811	11	5	we	we	PRON
ap-1811	11	6	quote	quote	VERB
ap-1811	11	7	the	the	DET
ap-1811	11	8	theorem	theorem	NOUN
ap-1811	11	9	for	for	ADP
ap-1811	11	10	one	one	NUM
ap-1811	11	11	independent	independent	ADJ
ap-1811	11	12	variable	variable	NOUN
ap-1811	11	13	,	,	PUNCT
ap-1811	11	14	one	one	NUM
ap-1811	11	15	dependent	dependent	ADJ
ap-1811	11	16	variable	variable	NOUN
ap-1811	11	17	and	and	CCONJ
ap-1811	11	18	a	a	DET
ap-1811	11	19	first	first	ADJ
ap-1811	11	20	-	-	PUNCT
ap-1811	11	21	order	order	NOUN
ap-1811	11	22	lagrangian	lagrangian	NOUN
ap-1811	11	23	.	.	PUNCT
ap-1811	12	1	if	if	SCONJ
ap-1811	12	2	the	the	DET
ap-1811	12	3	action	action	NOUN
ap-1811	12	4	integral	integral	VERB
ap-1811	12	5	a	a	DET
ap-1811	12	6	=	=	SYM
ap-1811	12	7	∫	∫	PROPN
ap-1811	12	8	t1	t1	PROPN
ap-1811	12	9	t0	t0	PROPN
ap-1811	12	10	l	l	PROPN
ap-1811	12	11	(	(	PUNCT
ap-1811	12	12	t	t	PROPN
ap-1811	12	13	,	,	PUNCT
ap-1811	12	14	x	x	PRON
ap-1811	12	15	,	,	PUNCT
ap-1811	12	16	ẋ)dt	ẋ)dt	PROPN
ap-1811	12	17	is	be	AUX
ap-1811	12	18	invariant	invariant	ADJ
ap-1811	12	19	under	under	ADP
ap-1811	12	20	the	the	DET
ap-1811	12	21	infinitesimal	infinitesimal	ADJ
ap-1811	12	22	transformation	transformation	NOUN
ap-1811	12	23	generated	generate	VERB
ap-1811	12	24	by	by	ADP
ap-1811	12	25	γ	γ	X
ap-1811	12	26	=	=	SYM
ap-1811	12	27	τ∂t	τ∂t	NOUN
ap-1811	12	28	+	+	CCONJ
ap-1811	12	29	η∂x	η∂x	VERB
ap-1811	12	30	,	,	PUNCT
ap-1811	12	31	then	then	ADV
ap-1811	12	32	there	there	PRON
ap-1811	12	33	exists	exist	VERB
ap-1811	12	34	a	a	DET
ap-1811	12	35	function	function	NOUN
ap-1811	12	36	f(t	f(t	NOUN
ap-1811	12	37	,	,	PUNCT
ap-1811	12	38	x	x	NOUN
ap-1811	12	39	)	)	PUNCT
ap-1811	13	1	such	such	ADJ
ap-1811	13	2	that	that	SCONJ
ap-1811	13	3	ḟ	ḟ	PROPN
ap-1811	13	4	=	=	SYM
ap-1811	13	5	τ	τ	X
ap-1811	13	6	∂l	∂l	PROPN
ap-1811	14	1	∂t	∂t	PROPN
ap-1811	14	2	+	+	CCONJ
ap-1811	14	3	η	η	PROPN
ap-1811	14	4	∂l	∂l	PROPN
ap-1811	14	5	∂x	∂x	PROPN
ap-1811	14	6	+	+	CCONJ
ap-1811	14	7	(	(	PUNCT
ap-1811	14	8	η̇	η̇	PROPN
ap-1811	14	9	−	−	PROPN
ap-1811	14	10	ẋτ̇	ẋτ̇	NOUN
ap-1811	14	11	)	)	PUNCT
ap-1811	15	1	∂l	∂l	PROPN
ap-1811	16	1	∂ẋ	∂ẋ	ADJ
ap-1811	16	2	+	+	CCONJ
ap-1811	16	3	τ̇l	τ̇l	PROPN
ap-1811	16	4	.	.	PUNCT
ap-1811	17	1	in	in	ADP
ap-1811	17	2	the	the	DET
ap-1811	17	3	present	present	ADJ
ap-1811	17	4	context	context	NOUN
ap-1811	17	5	of	of	ADP
ap-1811	17	6	the	the	DET
ap-1811	17	7	functions	function	NOUN
ap-1811	17	8	τ	τ	PROPN
ap-1811	17	9	and	and	CCONJ
ap-1811	17	10	η	η	PROPN
ap-1811	17	11	are	be	AUX
ap-1811	17	12	to	to	PART
ap-1811	17	13	be	be	AUX
ap-1811	17	14	considered	consider	VERB
ap-1811	17	15	as	as	ADP
ap-1811	17	16	depending	depend	VERB
ap-1811	17	17	upon	upon	SCONJ
ap-1811	17	18	t	t	NOUN
ap-1811	17	19	and	and	CCONJ
ap-1811	17	20	x	x	X
ap-1811	17	21	only	only	ADV
ap-1811	17	22	,	,	PUNCT
ap-1811	17	23	but	but	CCONJ
ap-1811	17	24	in	in	ADP
ap-1811	17	25	a	a	DET
ap-1811	17	26	more	more	ADV
ap-1811	17	27	general	general	ADJ
ap-1811	17	28	context	context	NOUN
ap-1811	17	29	they	they	PRON
ap-1811	17	30	can	can	AUX
ap-1811	17	31	also	also	ADV
ap-1811	17	32	depend	depend	VERB
ap-1811	17	33	upon	upon	SCONJ
ap-1811	17	34	ẋ.	ẋ.	PROPN
ap-1811	17	35	the	the	DET
ap-1811	17	36	function	function	NOUN
ap-1811	17	37	,	,	PUNCT
ap-1811	17	38	f(t	f(t	PROPN
ap-1811	17	39	,	,	PUNCT
ap-1811	17	40	x	x	NOUN
ap-1811	17	41	)	)	PUNCT
ap-1811	17	42	,	,	PUNCT
ap-1811	17	43	is	be	AUX
ap-1811	17	44	the	the	DET
ap-1811	17	45	variation	variation	NOUN
ap-1811	17	46	induced	induce	VERB
ap-1811	17	47	in	in	ADP
ap-1811	17	48	a	a	PRON
ap-1811	17	49	by	by	ADP
ap-1811	17	50	the	the	DET
ap-1811	17	51	variation	variation	NOUN
ap-1811	17	52	in	in	ADP
ap-1811	17	53	the	the	DET
ap-1811	17	54	limits	limit	NOUN
ap-1811	17	55	in	in	ADP
ap-1811	17	56	the	the	DET
ap-1811	17	57	action	action	NOUN
ap-1811	17	58	integral	integral	ADJ
ap-1811	17	59	.	.	PUNCT
ap-1811	18	1	thus	thus	ADV
ap-1811	18	2	it	it	PRON
ap-1811	18	3	is	be	AUX
ap-1811	18	4	called	call	VERB
ap-1811	18	5	a	a	DET
ap-1811	18	6	boundary	boundary	ADJ
ap-1811	18	7	term	term	NOUN
ap-1811	18	8	despite	despite	SCONJ
ap-1811	18	9	the	the	DET
ap-1811	18	10	earnest	earnest	ADJ
ap-1811	18	11	efforts	effort	NOUN
ap-1811	18	12	of	of	ADP
ap-1811	18	13	successors	successor	NOUN
ap-1811	18	14	to	to	PART
ap-1811	18	15	describe	describe	VERB
ap-1811	18	16	it	it	PRON
ap-1811	18	17	as	as	ADP
ap-1811	18	18	a	a	DET
ap-1811	18	19	gauge	gauge	NOUN
ap-1811	18	20	function	function	NOUN
ap-1811	18	21	.	.	PUNCT
ap-1811	19	1	when	when	SCONJ
ap-1811	19	2	the	the	DET
ap-1811	19	3	variational	variational	ADJ
ap-1811	19	4	principle	principle	NOUN
ap-1811	19	5	is	be	AUX
ap-1811	19	6	invoked	invoke	VERB
ap-1811	19	7	,	,	PUNCT
ap-1811	19	8	it	it	PRON
ap-1811	19	9	follows	follow	VERB
ap-1811	19	10	that	that	SCONJ
ap-1811	19	11	there	there	PRON
ap-1811	19	12	is	be	VERB
ap-1811	19	13	a	a	DET
ap-1811	19	14	first	first	ADJ
ap-1811	19	15	integral	integral	ADJ
ap-1811	19	16	given	give	VERB
ap-1811	19	17	by	by	ADP
ap-1811	19	18	i	i	PROPN
ap-1811	20	1	=	=	PROPN
ap-1811	20	2	f	f	PROPN
ap-1811	21	1	−	−	PROPN
ap-1811	21	2	(	(	PUNCT
ap-1811	21	3	τl+	τl+	PROPN
ap-1811	21	4	(	(	PUNCT
ap-1811	21	5	η	η	PROPN
ap-1811	21	6	−	−	PROPN
ap-1811	21	7	ẋτ	ẋτ	PROPN
ap-1811	21	8	)	)	PUNCT
ap-1811	22	1	∂l	∂l	PROPN
ap-1811	22	2	∂ẋ	∂ẋ	ADJ
ap-1811	22	3	)	)	PUNCT
ap-1811	22	4	.	.	PUNCT
ap-1811	23	1	over	over	ADP
ap-1811	23	2	the	the	DET
ap-1811	23	3	approximately	approximately	ADV
ap-1811	23	4	90	90	NUM
ap-1811	23	5	years	year	NOUN
ap-1811	23	6	since	since	SCONJ
ap-1811	23	7	noether	noether	PROPN
ap-1811	23	8	presented	present	VERB
ap-1811	23	9	her	her	PRON
ap-1811	23	10	theorem	theorem	NOUN
ap-1811	23	11	there	there	PRON
ap-1811	23	12	have	have	AUX
ap-1811	23	13	been	be	AUX
ap-1811	23	14	many	many	ADJ
ap-1811	23	15	efforts	effort	NOUN
ap-1811	23	16	to	to	PART
ap-1811	23	17	misquote	misquote	VERB
ap-1811	23	18	it	it	PRON
ap-1811	23	19	.	.	PUNCT
ap-1811	24	1	as	as	ADP
ap-1811	24	2	a	a	DET
ap-1811	24	3	consequence	consequence	NOUN
ap-1811	24	4	of	of	ADP
ap-1811	24	5	these	these	DET
ap-1811	24	6	various	various	ADJ
ap-1811	24	7	failures	failure	NOUN
ap-1811	24	8	to	to	PART
ap-1811	24	9	understand	understand	VERB
ap-1811	24	10	the	the	DET
ap-1811	24	11	quite	quite	ADV
ap-1811	24	12	clear	clear	ADJ
ap-1811	24	13	exposition	exposition	NOUN
ap-1811	24	14	in	in	ADP
ap-1811	24	15	noether	noether	PROPN
ap-1811	24	16	’s	’s	PART
ap-1811	24	17	paper	paper	NOUN
ap-1811	24	18	various	various	ADJ
ap-1811	24	19	stratagems	stratagem	NOUN
ap-1811	24	20	have	have	AUX
ap-1811	24	21	been	be	AUX
ap-1811	24	22	advanced	advanced	ADJ
ap-1811	24	23	to	to	PART
ap-1811	24	24	remedy	remedy	VERB
ap-1811	24	25	the	the	DET
ap-1811	24	26	perceived	perceive	VERB
ap-1811	24	27	deficiencies	deficiency	NOUN
ap-1811	24	28	of	of	ADP
ap-1811	24	29	the	the	DET
ap-1811	24	30	theorem	theorem	NOUN
ap-1811	24	31	.	.	PUNCT
ap-1811	25	1	generally	generally	ADV
ap-1811	25	2	speaking	speak	VERB
ap-1811	25	3	these	these	DET
ap-1811	25	4	advances	advance	NOUN
ap-1811	25	5	were	be	AUX
ap-1811	25	6	not	not	PART
ap-1811	25	7	necessary	necessary	ADJ
ap-1811	25	8	.	.	PUNCT
ap-1811	26	1	2	2	X
ap-1811	26	2	.	.	X
ap-1811	26	3	quantisation	quantisation	NOUN
ap-1811	26	4	around	around	ADP
ap-1811	26	5	1835	1835	NUM
ap-1811	26	6	hamilton	hamilton	PROPN
ap-1811	26	7	essentially	essentially	ADV
ap-1811	26	8	reduced	reduce	VERB
ap-1811	26	9	the	the	DET
ap-1811	26	10	study	study	NOUN
ap-1811	26	11	of	of	ADP
ap-1811	26	12	second	second	ADJ
ap-1811	26	13	-	-	PUNCT
ap-1811	26	14	order	order	NOUN
ap-1811	26	15	equations	equation	NOUN
ap-1811	26	16	to	to	ADP
ap-1811	26	17	first	first	ADJ
ap-1811	26	18	-	-	PUNCT
ap-1811	26	19	order	order	NOUN
ap-1811	26	20	equations	equation	NOUN
ap-1811	26	21	by	by	ADP
ap-1811	26	22	the	the	DET
ap-1811	26	23	introduction	introduction	NOUN
ap-1811	26	24	–	–	PUNCT
ap-1811	26	25	indeed	indeed	ADV
ap-1811	26	26	in	in	ADP
ap-1811	26	27	light	light	NOUN
ap-1811	26	28	of	of	ADP
ap-1811	26	29	newton	newton	PROPN
ap-1811	26	30	’s	’s	PART
ap-1811	26	31	second	second	ADJ
ap-1811	26	32	law	law	NOUN
ap-1811	26	33	,	,	PUNCT
ap-1811	26	34	reintroduction	reintroduction	NOUN
ap-1811	26	35	–	–	PUNCT
ap-1811	26	36	of	of	ADP
ap-1811	26	37	momentum	momentum	NOUN
ap-1811	26	38	as	as	ADP
ap-1811	26	39	a	a	DET
ap-1811	26	40	variable	variable	ADJ
ap-1811	26	41	conjugate	conjugate	NOUN
ap-1811	26	42	to	to	ADP
ap-1811	26	43	position	position	NOUN
ap-1811	26	44	.	.	PUNCT
ap-1811	27	1	the	the	DET
ap-1811	27	2	momentum	momentum	NOUN
ap-1811	27	3	was	be	AUX
ap-1811	27	4	defined	define	VERB
ap-1811	27	5	according	accord	VERB
ap-1811	27	6	to	to	ADP
ap-1811	27	7	p	p	NOUN
ap-1811	27	8	=	=	PUNCT
ap-1811	27	9	∂l	∂l	PROPN
ap-1811	27	10	∂ẋ	∂ẋ	ADJ
ap-1811	27	11	and	and	CCONJ
ap-1811	27	12	a	a	DET
ap-1811	27	13	new	new	ADJ
ap-1811	27	14	function	function	NOUN
ap-1811	27	15	,	,	PUNCT
ap-1811	27	16	nowadays	nowadays	ADV
ap-1811	27	17	called	call	VERB
ap-1811	27	18	the	the	DET
ap-1811	27	19	hamiltonian	hamiltonian	NOUN
ap-1811	27	20	,	,	PUNCT
ap-1811	27	21	was	be	AUX
ap-1811	27	22	introduced	introduce	VERB
ap-1811	27	23	according	accord	VERB
ap-1811	27	24	to	to	ADP
ap-1811	27	25	the	the	DET
ap-1811	27	26	formula	formula	NOUN
ap-1811	27	27	h	h	NOUN
ap-1811	27	28	=	=	PUNCT
ap-1811	27	29	pẋ−	pẋ−	PROPN
ap-1811	27	30	l.	l.	PROPN
ap-1811	27	31	quite	quite	DET
ap-1811	27	32	a	a	DET
ap-1811	27	33	deal	deal	NOUN
ap-1811	27	34	of	of	ADP
ap-1811	27	35	interesting	interesting	ADJ
ap-1811	27	36	theory	theory	NOUN
ap-1811	27	37	was	be	AUX
ap-1811	27	38	developed	develop	VERB
ap-1811	27	39	and	and	CCONJ
ap-1811	27	40	became	become	VERB
ap-1811	27	41	the	the	DET
ap-1811	27	42	substance	substance	NOUN
ap-1811	27	43	of	of	ADP
ap-1811	27	44	hamiltonian	hamiltonian	ADJ
ap-1811	27	45	mechanics	mechanic	NOUN
ap-1811	27	46	.	.	PUNCT
ap-1811	28	1	however	however	ADV
ap-1811	28	2	,	,	PUNCT
ap-1811	28	3	our	our	PRON
ap-1811	28	4	present	present	ADJ
ap-1811	28	5	interest	interest	NOUN
ap-1811	28	6	is	be	AUX
ap-1811	28	7	the	the	DET
ap-1811	28	8	observation	observation	NOUN
ap-1811	28	9	by	by	ADP
ap-1811	28	10	dirac	dirac	NOUN
ap-1811	28	11	in	in	ADP
ap-1811	28	12	1926	1926	NUM
ap-1811	28	13	of	of	ADP
ap-1811	28	14	the	the	DET
ap-1811	28	15	resemblance	resemblance	NOUN
ap-1811	28	16	of	of	ADP
ap-1811	28	17	the	the	DET
ap-1811	28	18	operators	operator	NOUN
ap-1811	28	19	needed	need	VERB
ap-1811	28	20	for	for	ADP
ap-1811	28	21	quantum	quantum	ADJ
ap-1811	28	22	mechanics	mechanic	NOUN
ap-1811	28	23	and	and	CCONJ
ap-1811	28	24	the	the	DET
ap-1811	28	25	canonical	canonical	ADJ
ap-1811	28	26	variables	variable	NOUN
ap-1811	28	27	of	of	ADP
ap-1811	28	28	hamiltonian	hamiltonian	ADJ
ap-1811	28	29	mechanics	mechanic	NOUN
ap-1811	28	30	and	and	CCONJ
ap-1811	28	31	their	their	PRON
ap-1811	28	32	poisson	poisson	NOUN
ap-1811	28	33	brackets	bracket	NOUN
ap-1811	28	34	.	.	PUNCT
ap-1811	29	1	thus	thus	ADV
ap-1811	29	2	the	the	DET
ap-1811	29	3	schrödinger	schrödinger	ADJ
ap-1811	29	4	equation	equation	NOUN
ap-1811	29	5	could	could	AUX
ap-1811	29	6	be	be	AUX
ap-1811	29	7	written	write	VERB
ap-1811	29	8	as	as	ADP
ap-1811	29	9	i~	i~	PROPN
ap-1811	29	10	∂u	∂u	PROPN
ap-1811	29	11	∂t	∂t	PROPN
ap-1811	29	12	=	=	SYM
ap-1811	29	13	ĥu	ĥu	PROPN
ap-1811	29	14	,	,	PUNCT
ap-1811	29	15	where	where	SCONJ
ap-1811	29	16	ĥ	ĥ	PROPN
ap-1811	29	17	is	be	AUX
ap-1811	29	18	the	the	DET
ap-1811	29	19	operator	operator	NOUN
ap-1811	29	20	obtained	obtain	VERB
ap-1811	29	21	by	by	ADP
ap-1811	29	22	replacing	replace	VERB
ap-1811	29	23	the	the	DET
ap-1811	29	24	variables	variable	NOUN
ap-1811	29	25	x	x	PUNCT
ap-1811	29	26	and	and	CCONJ
ap-1811	29	27	p	p	NOUN
ap-1811	29	28	by	by	ADP
ap-1811	29	29	the	the	DET
ap-1811	29	30	operators	operator	NOUN
ap-1811	29	31	x̂	x̂	PUNCT
ap-1811	29	32	and	and	CCONJ
ap-1811	29	33	p̂.	p̂.	NOUN
ap-1811	29	34	a	a	DET
ap-1811	29	35	matter	matter	NOUN
ap-1811	29	36	which	which	PRON
ap-1811	29	37	should	should	AUX
ap-1811	29	38	be	be	AUX
ap-1811	29	39	of	of	ADP
ap-1811	29	40	some	some	DET
ap-1811	29	41	interest	interest	NOUN
ap-1811	29	42	is	be	AUX
ap-1811	29	43	the	the	DET
ap-1811	29	44	nature	nature	NOUN
ap-1811	29	45	of	of	ADP
ap-1811	29	46	the	the	DET
ap-1811	29	47	function	function	NOUN
ap-1811	29	48	h	h	NOUN
ap-1811	29	49	,	,	PUNCT
ap-1811	29	50	which	which	PRON
ap-1811	29	51	can	can	AUX
ap-1811	29	52	be	be	AUX
ap-1811	29	53	used	use	VERB
ap-1811	29	54	as	as	ADP
ap-1811	29	55	an	an	DET
ap-1811	29	56	operator	operator	NOUN
ap-1811	29	57	in	in	ADP
ap-1811	29	58	the	the	DET
ap-1811	29	59	schrödinger	schrödinger	ADJ
ap-1811	29	60	equation	equation	NOUN
ap-1811	29	61	.	.	PUNCT
ap-1811	30	1	this	this	PRON
ap-1811	30	2	is	be	AUX
ap-1811	30	3	not	not	PART
ap-1811	30	4	a	a	DET
ap-1811	30	5	trivial	trivial	ADJ
ap-1811	30	6	question	question	NOUN
ap-1811	30	7	for	for	SCONJ
ap-1811	30	8	it	it	PRON
ap-1811	30	9	must	must	AUX
ap-1811	30	10	be	be	AUX
ap-1811	30	11	borne	bear	VERB
ap-1811	30	12	in	in	ADP
ap-1811	30	13	mind	mind	NOUN
ap-1811	30	14	that	that	SCONJ
ap-1811	30	15	hamiltonian	hamiltonian	ADJ
ap-1811	30	16	mechanics	mechanic	NOUN
ap-1811	30	17	is	be	AUX
ap-1811	30	18	a	a	DET
ap-1811	30	19	reformulation	reformulation	NOUN
ap-1811	30	20	of	of	ADP
ap-1811	30	21	lagrangian	lagrangian	ADJ
ap-1811	30	22	mechanics	mechanic	NOUN
ap-1811	30	23	,	,	PUNCT
ap-1811	30	24	which	which	PRON
ap-1811	30	25	is	be	AUX
ap-1811	30	26	based	base	VERB
ap-1811	30	27	upon	upon	SCONJ
ap-1811	30	28	newtonian	newtonian	ADJ
ap-1811	30	29	mechanics	mechanic	NOUN
ap-1811	30	30	,	,	PUNCT
ap-1811	30	31	and	and	CCONJ
ap-1811	30	32	the	the	DET
ap-1811	30	33	fundamental	fundamental	ADJ
ap-1811	30	34	object	object	NOUN
ap-1811	30	35	of	of	ADP
ap-1811	30	36	the	the	DET
ap-1811	30	37	last	last	ADJ
ap-1811	30	38	is	be	AUX
ap-1811	30	39	newton	newton	PROPN
ap-1811	30	40	’s	’s	PART
ap-1811	30	41	equation	equation	NOUN
ap-1811	30	42	of	of	ADP
ap-1811	30	43	motion	motion	NOUN
ap-1811	30	44	.	.	PUNCT
ap-1811	31	1	whether	whether	SCONJ
ap-1811	31	2	one	one	NUM
ap-1811	31	3	applies	apply	VERB
ap-1811	31	4	hamilton	hamilton	PROPN
ap-1811	31	5	’s	’s	PART
ap-1811	31	6	equations	equation	NOUN
ap-1811	31	7	or	or	CCONJ
ap-1811	31	8	the	the	DET
ap-1811	31	9	euler	euler	PROPN
ap-1811	31	10	–	–	PUNCT
ap-1811	31	11	lagrange	lagrange	NOUN
ap-1811	31	12	equation	equation	NOUN
ap-1811	31	13	,	,	PUNCT
ap-1811	31	14	the	the	DET
ap-1811	31	15	end	end	NOUN
ap-1811	31	16	result	result	NOUN
ap-1811	31	17	should	should	AUX
ap-1811	31	18	be	be	AUX
ap-1811	31	19	newton	newton	PROPN
ap-1811	31	20	’s	’s	PART
ap-1811	31	21	equation	equation	NOUN
ap-1811	31	22	.	.	PUNCT
ap-1811	32	1	it	it	PRON
ap-1811	32	2	is	be	AUX
ap-1811	32	3	evident	evident	ADJ
ap-1811	32	4	from	from	ADP
ap-1811	32	5	dirac	dirac	NOUN
ap-1811	32	6	’s	’s	PART
ap-1811	32	7	book	book	NOUN
ap-1811	33	1	[	[	X
ap-1811	33	2	4	4	X
ap-1811	33	3	]	]	PUNCT
ap-1811	33	4	that	that	SCONJ
ap-1811	33	5	he	he	PRON
ap-1811	33	6	considered	consider	VERB
ap-1811	33	7	the	the	DET
ap-1811	33	8	appropriate	appropriate	ADJ
ap-1811	33	9	hamiltonian	hamiltonian	NOUN
ap-1811	33	10	to	to	PART
ap-1811	33	11	be	be	AUX
ap-1811	33	12	the	the	DET
ap-1811	33	13	energy	energy	NOUN
ap-1811	33	14	,	,	PUNCT
ap-1811	33	15	and	and	CCONJ
ap-1811	33	16	a	a	DET
ap-1811	33	17	302	302	NUM
ap-1811	33	18	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	ADJ
ap-1811	33	19	vol	vol	NOUN
ap-1811	33	20	.	.	PUNCT
ap-1811	34	1	53	53	NUM
ap-1811	34	2	no	no	NOUN
ap-1811	34	3	.	.	PUNCT
ap-1811	35	1	3/2013	3/2013	PROPN
ap-1811	35	2	emmy	emmy	ADJ
ap-1811	35	3	noether	noether	PROPN
ap-1811	35	4	and	and	CCONJ
ap-1811	35	5	linear	linear	ADJ
ap-1811	35	6	evolution	evolution	NOUN
ap-1811	35	7	equations	equation	NOUN
ap-1811	35	8	symmetry	symmetry	VERB
ap-1811	35	9	boundary	boundary	ADJ
ap-1811	35	10	term	term	NOUN
ap-1811	35	11	σ1	σ1	PROPN
ap-1811	35	12	=	=	SYM
ap-1811	35	13	∂t	∂t	PROPN
ap-1811	35	14	f1	f1	PROPN
ap-1811	35	15	=	=	SYM
ap-1811	35	16	0	0	NUM
ap-1811	35	17	σ2	σ2	NOUN
ap-1811	35	18	=	=	PUNCT
ap-1811	35	19	t∂t	t∂t	NOUN
ap-1811	35	20	+	+	SYM
ap-1811	35	21	1	1	NUM
ap-1811	35	22	2x∂x	2x∂x	NUM
ap-1811	35	23	f2	f2	ADJ
ap-1811	35	24	=	=	SYM
ap-1811	35	25	0	0	NUM
ap-1811	35	26	σ3	σ3	NOUN
ap-1811	35	27	=	=	PUNCT
ap-1811	35	28	t2∂t	t2∂t	PROPN
ap-1811	35	29	+	+	CCONJ
ap-1811	35	30	tx∂x	tx∂x	NOUN
ap-1811	35	31	f3	f3	NOUN
ap-1811	35	32	=	=	SYM
ap-1811	35	33	1	1	NUM
ap-1811	35	34	2x	2x	NUM
ap-1811	35	35	2	2	NUM
ap-1811	35	36	σ4	σ4	NOUN
ap-1811	35	37	=	=	NOUN
ap-1811	35	38	∂x	∂x	PROPN
ap-1811	35	39	f4	f4	PROPN
ap-1811	35	40	=	=	SYM
ap-1811	35	41	0	0	NUM
ap-1811	35	42	σ5	σ5	PROPN
ap-1811	35	43	=	=	SYM
ap-1811	35	44	x∂x	x∂x	PUNCT
ap-1811	35	45	f5	f5	VERB
ap-1811	35	46	=	=	PUNCT
ap-1811	35	47	x	x	SYM
ap-1811	35	48	f6	f6	PROPN
ap-1811	35	49	=	=	SYM
ap-1811	35	50	1	1	NUM
ap-1811	35	51	table	table	NOUN
ap-1811	35	52	1	1	NUM
ap-1811	35	53	.	.	PUNCT
ap-1811	36	1	noether	noether	ADJ
ap-1811	36	2	point	point	NOUN
ap-1811	36	3	symmetries	symmetry	NOUN
ap-1811	36	4	.	.	PUNCT
ap-1811	37	1	conserved	conserve	VERB
ap-1811	37	2	energy	energy	NOUN
ap-1811	37	3	at	at	ADP
ap-1811	37	4	that	that	PRON
ap-1811	37	5	.	.	PUNCT
ap-1811	38	1	this	this	PRON
ap-1811	38	2	marks	mark	VERB
ap-1811	38	3	a	a	DET
ap-1811	38	4	strong	strong	ADJ
ap-1811	38	5	constraint	constraint	NOUN
ap-1811	38	6	upon	upon	SCONJ
ap-1811	38	7	the	the	DET
ap-1811	38	8	nature	nature	NOUN
ap-1811	38	9	of	of	ADP
ap-1811	38	10	the	the	DET
ap-1811	38	11	hamiltonian	hamiltonian	NOUN
ap-1811	38	12	and	and	CCONJ
ap-1811	38	13	hence	hence	ADV
ap-1811	38	14	the	the	DET
ap-1811	38	15	lagrangian	lagrangian	ADJ
ap-1811	38	16	.	.	PUNCT
ap-1811	39	1	as	as	ADP
ap-1811	39	2	a	a	DET
ap-1811	39	3	simple	simple	ADJ
ap-1811	39	4	example	example	NOUN
ap-1811	39	5	consider	consider	VERB
ap-1811	39	6	the	the	DET
ap-1811	39	7	two	two	NUM
ap-1811	39	8	lagrangians	lagrangian	NOUN
ap-1811	39	9	for	for	ADP
ap-1811	39	10	the	the	DET
ap-1811	39	11	free	free	ADJ
ap-1811	39	12	particle	particle	NOUN
ap-1811	39	13	given	give	VERB
ap-1811	39	14	by	by	ADP
ap-1811	39	15	l1	l1	PROPN
ap-1811	39	16	=	=	PROPN
ap-1811	39	17	1	1	NUM
ap-1811	39	18	2	2	NUM
ap-1811	39	19	ẋ	ẋ	NUM
ap-1811	39	20	2	2	NUM
ap-1811	39	21	and	and	CCONJ
ap-1811	39	22	l2	l2	NOUN
ap-1811	39	23	=	=	SYM
ap-1811	39	24	1	1	NUM
ap-1811	39	25	ẋ	ẋ	PROPN
ap-1811	39	26	.	.	PUNCT
ap-1811	40	1	both	both	PRON
ap-1811	40	2	give	give	VERB
ap-1811	40	3	rise	rise	NOUN
ap-1811	40	4	to	to	ADP
ap-1811	40	5	the	the	DET
ap-1811	40	6	newtonian	newtonian	ADJ
ap-1811	40	7	equation	equation	NOUN
ap-1811	40	8	ẍ	ẍ	PUNCT
ap-1811	41	1	=	=	PUNCT
ap-1811	41	2	0	0	PROPN
ap-1811	41	3	.	.	PUNCT
ap-1811	42	1	both	both	PRON
ap-1811	42	2	have	have	VERB
ap-1811	42	3	the	the	DET
ap-1811	42	4	maximal	maximal	ADJ
ap-1811	42	5	number	number	NOUN
ap-1811	42	6	of	of	ADP
ap-1811	42	7	noether	noether	ADJ
ap-1811	42	8	symmetries	symmetry	NOUN
ap-1811	42	9	,	,	PUNCT
ap-1811	42	10	five	five	NUM
ap-1811	42	11	,	,	PUNCT
ap-1811	42	12	for	for	ADP
ap-1811	42	13	the	the	DET
ap-1811	42	14	lagrangian	lagrangian	NOUN
ap-1811	42	15	of	of	ADP
ap-1811	42	16	a	a	DET
ap-1811	42	17	one	one	NUM
ap-1811	42	18	-	-	PUNCT
ap-1811	42	19	degree	degree	NOUN
ap-1811	42	20	-	-	PUNCT
ap-1811	42	21	offreedom	offreedom	ADJ
ap-1811	42	22	system	system	NOUN
ap-1811	42	23	.	.	PUNCT
ap-1811	43	1	the	the	DET
ap-1811	43	2	former	former	ADJ
ap-1811	43	3	represents	represent	VERB
ap-1811	43	4	the	the	DET
ap-1811	43	5	energy	energy	NOUN
ap-1811	43	6	.	.	PUNCT
ap-1811	44	1	why	why	SCONJ
ap-1811	44	2	choose	choose	VERB
ap-1811	44	3	one	one	NUM
ap-1811	44	4	above	above	ADP
ap-1811	44	5	the	the	DET
ap-1811	44	6	other	other	ADJ
ap-1811	44	7	?	?	PUNCT
ap-1811	45	1	if	if	SCONJ
ap-1811	45	2	we	we	PRON
ap-1811	45	3	do	do	VERB
ap-1811	45	4	the	the	DET
ap-1811	45	5	usual	usual	ADJ
ap-1811	45	6	trick	trick	NOUN
ap-1811	45	7	of	of	ADP
ap-1811	45	8	setting	set	VERB
ap-1811	45	9	plank	plank	NOUN
ap-1811	45	10	’s	’s	PART
ap-1811	45	11	constant	constant	ADJ
ap-1811	45	12	to	to	ADP
ap-1811	45	13	unity	unity	NOUN
ap-1811	45	14	in	in	ADP
ap-1811	45	15	the	the	DET
ap-1811	45	16	schrödinger	schrödinger	ADJ
ap-1811	45	17	equation	equation	NOUN
ap-1811	45	18	for	for	ADP
ap-1811	45	19	the	the	DET
ap-1811	45	20	free	free	ADJ
ap-1811	45	21	particle	particle	NOUN
ap-1811	45	22	obtained	obtain	VERB
ap-1811	45	23	by	by	ADP
ap-1811	45	24	using	use	VERB
ap-1811	45	25	the	the	DET
ap-1811	45	26	hamiltonian	hamiltonian	ADJ
ap-1811	45	27	operator	operator	NOUN
ap-1811	45	28	representing	represent	VERB
ap-1811	45	29	the	the	DET
ap-1811	45	30	energy	energy	NOUN
ap-1811	45	31	,	,	PUNCT
ap-1811	45	32	the	the	DET
ap-1811	45	33	equation	equation	NOUN
ap-1811	45	34	is	be	AUX
ap-1811	45	35	2i∂u	2i∂u	NUM
ap-1811	45	36	∂t	∂t	PROPN
ap-1811	45	37	+	+	CCONJ
ap-1811	45	38	∂2u	∂2u	ADJ
ap-1811	45	39	∂x2	∂x2	PROPN
ap-1811	45	40	=	=	SYM
ap-1811	45	41	0	0	X
ap-1811	45	42	.	.	PUNCT
ap-1811	46	1	a	a	DET
ap-1811	46	2	calculation	calculation	NOUN
ap-1811	46	3	of	of	ADP
ap-1811	46	4	the	the	DET
ap-1811	46	5	lie	lie	NOUN
ap-1811	46	6	point	point	NOUN
ap-1811	46	7	symmetries	symmetry	NOUN
ap-1811	46	8	results	result	VERB
ap-1811	46	9	in	in	ADP
ap-1811	46	10	γ1	γ1	PROPN
ap-1811	46	11	=	=	SYM
ap-1811	46	12	∂t	∂t	PROPN
ap-1811	46	13	,	,	PUNCT
ap-1811	46	14	γ2	γ2	PROPN
ap-1811	46	15	=	=	SYM
ap-1811	46	16	2t∂t	2t∂t	PROPN
ap-1811	47	1	+	+	CCONJ
ap-1811	47	2	x∂x	x∂x	NOUN
ap-1811	47	3	,	,	PUNCT
ap-1811	47	4	γ3	γ3	NOUN
ap-1811	47	5	=	=	PUNCT
ap-1811	47	6	2t2∂t	2t2∂t	NOUN
ap-1811	48	1	+	+	NUM
ap-1811	48	2	2tx∂x	2tx∂x	NUM
ap-1811	48	3	+	+	CCONJ
ap-1811	48	4	(	(	PUNCT
ap-1811	48	5	ix2	ix2	PROPN
ap-1811	48	6	−	−	PROPN
ap-1811	48	7	t	t	PROPN
ap-1811	48	8	)	)	PUNCT
ap-1811	48	9	u∂u	u∂u	NOUN
ap-1811	48	10	,	,	PUNCT
ap-1811	48	11	γ4	γ4	NOUN
ap-1811	48	12	=	=	SYM
ap-1811	48	13	∂x	∂x	PROPN
ap-1811	48	14	,	,	PUNCT
ap-1811	48	15	γ5	γ5	NOUN
ap-1811	48	16	=	=	PUNCT
ap-1811	48	17	t∂x	t∂x	PROPN
ap-1811	48	18	+	+	CCONJ
ap-1811	48	19	ixu∂u	ixu∂u	PROPN
ap-1811	48	20	,	,	PUNCT
ap-1811	48	21	γ6	γ6	PROPN
ap-1811	48	22	=	=	SYM
ap-1811	48	23	u∂u	u∂u	NOUN
ap-1811	48	24	,	,	PUNCT
ap-1811	48	25	γ∞	γ∞	VERB
ap-1811	48	26	=	=	PUNCT
ap-1811	48	27	f(t	f(t	NOUN
ap-1811	48	28	,	,	PUNCT
ap-1811	48	29	x)∂u	x)∂u	PROPN
ap-1811	48	30	,	,	PUNCT
ap-1811	48	31	where	where	SCONJ
ap-1811	48	32	the	the	DET
ap-1811	48	33	coefficient	coefficient	NOUN
ap-1811	48	34	function	function	NOUN
ap-1811	48	35	in	in	ADP
ap-1811	48	36	γ∞	γ∞	NOUN
ap-1811	48	37	represents	represent	VERB
ap-1811	48	38	a	a	DET
ap-1811	48	39	solution	solution	NOUN
ap-1811	48	40	of	of	ADP
ap-1811	48	41	the	the	DET
ap-1811	48	42	original	original	ADJ
ap-1811	48	43	equation	equation	NOUN
ap-1811	48	44	and	and	CCONJ
ap-1811	48	45	shall	shall	AUX
ap-1811	48	46	not	not	PART
ap-1811	48	47	be	be	AUX
ap-1811	48	48	of	of	ADP
ap-1811	48	49	further	further	ADJ
ap-1811	48	50	interest	interest	NOUN
ap-1811	48	51	here	here	ADV
ap-1811	48	52	.	.	PUNCT
ap-1811	49	1	the	the	DET
ap-1811	49	2	symmetry	symmetry	NOUN
ap-1811	49	3	,	,	PUNCT
ap-1811	49	4	γ6	γ6	PROPN
ap-1811	49	5	is	be	AUX
ap-1811	49	6	a	a	DET
ap-1811	49	7	consequence	consequence	NOUN
ap-1811	49	8	of	of	ADP
ap-1811	49	9	the	the	DET
ap-1811	49	10	homogeneity	homogeneity	NOUN
ap-1811	49	11	in	in	ADP
ap-1811	49	12	u	u	NOUN
ap-1811	49	13	of	of	ADP
ap-1811	49	14	the	the	DET
ap-1811	49	15	equation	equation	NOUN
ap-1811	49	16	.	.	PUNCT
ap-1811	50	1	the	the	DET
ap-1811	50	2	remaining	remain	VERB
ap-1811	50	3	five	five	NUM
ap-1811	50	4	symmetries	symmetry	NOUN
ap-1811	50	5	are	be	AUX
ap-1811	50	6	closely	closely	ADV
ap-1811	50	7	related	relate	VERB
ap-1811	50	8	to	to	ADP
ap-1811	50	9	the	the	DET
ap-1811	50	10	five	five	NUM
ap-1811	50	11	noether	noether	ADJ
ap-1811	50	12	point	point	NOUN
ap-1811	50	13	symmetries	symmetry	NOUN
ap-1811	50	14	of	of	ADP
ap-1811	50	15	the	the	DET
ap-1811	50	16	lagrangian	lagrangian	ADJ
ap-1811	50	17	l	l	NOUN
ap-1811	50	18	=	=	SYM
ap-1811	50	19	1	1	NUM
ap-1811	50	20	2	2	NUM
ap-1811	50	21	ẋ	ẋ	NOUN
ap-1811	50	22	2	2	NUM
ap-1811	50	23	.	.	PUNCT
ap-1811	51	1	the	the	DET
ap-1811	51	2	latter	latter	ADJ
ap-1811	51	3	with	with	ADP
ap-1811	51	4	the	the	DET
ap-1811	51	5	boundary	boundary	ADJ
ap-1811	51	6	term	term	NOUN
ap-1811	51	7	are	be	AUX
ap-1811	51	8	in	in	ADP
ap-1811	51	9	table	table	NOUN
ap-1811	51	10	1	1	NUM
ap-1811	51	11	which	which	PRON
ap-1811	51	12	are	be	AUX
ap-1811	51	13	not	not	PART
ap-1811	51	14	quite	quite	DET
ap-1811	51	15	the	the	DET
ap-1811	51	16	same	same	ADJ
ap-1811	51	17	in	in	ADP
ap-1811	51	18	that	that	SCONJ
ap-1811	51	19	the	the	DET
ap-1811	51	20	boundary	boundary	ADJ
ap-1811	51	21	terms	term	NOUN
ap-1811	51	22	and	and	CCONJ
ap-1811	51	23	the	the	DET
ap-1811	51	24	coefficient	coefficient	NOUN
ap-1811	51	25	of	of	ADP
ap-1811	51	26	u∂u	u∂u	NOUN
ap-1811	51	27	are	be	AUX
ap-1811	51	28	not	not	PART
ap-1811	51	29	identical	identical	ADJ
ap-1811	51	30	,	,	PUNCT
ap-1811	51	31	but	but	CCONJ
ap-1811	51	32	are	be	AUX
ap-1811	51	33	suggestive	suggestive	ADJ
ap-1811	51	34	of	of	ADP
ap-1811	51	35	some	some	DET
ap-1811	51	36	connection	connection	NOUN
ap-1811	51	37	.	.	PUNCT
ap-1811	52	1	this	this	DET
ap-1811	52	2	connection	connection	NOUN
ap-1811	52	3	is	be	AUX
ap-1811	52	4	made	make	VERB
ap-1811	52	5	clearer	clear	ADJ
ap-1811	52	6	when	when	SCONJ
ap-1811	52	7	one	one	PRON
ap-1811	52	8	writes	write	VERB
ap-1811	52	9	γ	γ	X
ap-1811	52	10	=	=	SYM
ap-1811	52	11	a(t)∂t	a(t)∂t	PROPN
ap-1811	53	1	+	+	CCONJ
ap-1811	53	2	(	(	PUNCT
ap-1811	53	3	1	1	NUM
ap-1811	53	4	2	2	NUM
ap-1811	53	5	ȧ(t	ȧ(t	NOUN
ap-1811	53	6	)	)	PUNCT
ap-1811	53	7	+	+	NUM
ap-1811	53	8	b(t	b(t	NOUN
ap-1811	53	9	)	)	PUNCT
ap-1811	53	10	)	)	PUNCT
ap-1811	54	1	∂x	∂x	PROPN
ap-1811	54	2	+	+	CCONJ
ap-1811	54	3	(	(	PUNCT
ap-1811	54	4	1	1	NUM
ap-1811	54	5	4	4	NUM
ap-1811	54	6	iä(t)x2	iä(t)x2	NOUN
ap-1811	54	7	+	+	NOUN
ap-1811	54	8	iḃ(t)x+	iḃ(t)x+	NOUN
ap-1811	54	9	c(t	c(t	PROPN
ap-1811	54	10	)	)	PUNCT
ap-1811	54	11	)	)	PUNCT
ap-1811	54	12	u∂u	u∂u	NUM
ap-1811	54	13	and	and	CCONJ
ap-1811	54	14	σ	σ	NOUN
ap-1811	54	15	=	=	SYM
ap-1811	54	16	a(t)∂t	a(t)∂t	PROPN
ap-1811	55	1	+	+	CCONJ
ap-1811	55	2	(	(	PUNCT
ap-1811	55	3	1	1	NUM
ap-1811	55	4	2	2	NUM
ap-1811	55	5	ȧ(t	ȧ(t	NOUN
ap-1811	55	6	)	)	PUNCT
ap-1811	55	7	+	+	NUM
ap-1811	55	8	b(t	b(t	NOUN
ap-1811	55	9	)	)	PUNCT
ap-1811	55	10	)	)	PUNCT
ap-1811	56	1	∂x	∂x	PROPN
ap-1811	56	2	with	with	ADP
ap-1811	56	3	f(t	f(t	NOUN
ap-1811	56	4	,	,	PUNCT
ap-1811	56	5	x	x	X
ap-1811	56	6	)	)	PUNCT
ap-1811	56	7	=	=	SYM
ap-1811	56	8	1	1	NUM
ap-1811	56	9	4	4	NUM
ap-1811	56	10	ä(t)x2	ä(t)x2	PROPN
ap-1811	56	11	+	+	CCONJ
ap-1811	56	12	ḃ(t)x+	ḃ(t)x+	PROPN
ap-1811	56	13	c(t	c(t	PROPN
ap-1811	56	14	)	)	PUNCT
ap-1811	56	15	,	,	PUNCT
ap-1811	56	16	where	where	SCONJ
ap-1811	56	17	in	in	ADP
ap-1811	56	18	the	the	DET
ap-1811	56	19	latter	latter	ADJ
ap-1811	56	20	case	case	NOUN
ap-1811	56	21	c(t	c(t	PROPN
ap-1811	56	22	)	)	PUNCT
ap-1811	56	23	=	=	SYM
ap-1811	56	24	c0	c0	NOUN
ap-1811	56	25	and	and	CCONJ
ap-1811	56	26	in	in	ADP
ap-1811	56	27	the	the	DET
ap-1811	56	28	former	former	ADJ
ap-1811	56	29	case	case	NOUN
ap-1811	56	30	c(t	c(t	PROPN
ap-1811	56	31	)	)	PUNCT
ap-1811	57	1	=	=	SYM
ap-1811	57	2	c0	c0	NOUN
ap-1811	57	3	−	−	PROPN
ap-1811	57	4	1	1	NUM
ap-1811	57	5	4	4	NUM
ap-1811	57	6	ȧ(t	ȧ(t	NUM
ap-1811	57	7	)	)	PUNCT
ap-1811	57	8	.	.	PUNCT
ap-1811	58	1	there	there	PRON
ap-1811	58	2	is	be	VERB
ap-1811	58	3	a	a	DET
ap-1811	58	4	precise	precise	ADJ
ap-1811	58	5	connection	connection	NOUN
ap-1811	58	6	.	.	PUNCT
ap-1811	59	1	3	3	X
ap-1811	59	2	.	.	X
ap-1811	59	3	the	the	DET
ap-1811	59	4	heat	heat	NOUN
ap-1811	59	5	equation	equation	NOUN
ap-1811	59	6	the	the	DET
ap-1811	59	7	schrödinger	schrödinger	ADJ
ap-1811	59	8	equation	equation	NOUN
ap-1811	59	9	for	for	ADP
ap-1811	59	10	the	the	DET
ap-1811	59	11	free	free	ADJ
ap-1811	59	12	particle	particle	NOUN
ap-1811	59	13	,	,	PUNCT
ap-1811	59	14	2i∂u	2i∂u	PROPN
ap-1811	59	15	∂t	∂t	PROPN
ap-1811	59	16	+	+	CCONJ
ap-1811	59	17	∂2u	∂2u	ADJ
ap-1811	59	18	∂x2	∂x2	PROPN
ap-1811	59	19	=	=	SYM
ap-1811	59	20	0	0	NUM
ap-1811	59	21	,	,	PUNCT
ap-1811	59	22	may	may	AUX
ap-1811	59	23	be	be	AUX
ap-1811	59	24	rewritten	rewrite	VERB
ap-1811	59	25	as	as	ADP
ap-1811	59	26	∂u	∂u	PROPN
ap-1811	59	27	∂it/2	∂it/2	PROPN
ap-1811	59	28	−	−	PROPN
ap-1811	59	29	∂2u	∂2u	ADJ
ap-1811	59	30	∂x2	∂x2	NOUN
ap-1811	59	31	=	=	SYM
ap-1811	59	32	0	0	PUNCT
ap-1811	60	1	so	so	SCONJ
ap-1811	60	2	that	that	SCONJ
ap-1811	60	3	the	the	DET
ap-1811	60	4	change	change	NOUN
ap-1811	60	5	of	of	ADP
ap-1811	60	6	variable	variable	NOUN
ap-1811	60	7	,	,	PUNCT
ap-1811	60	8	it/2	it/2	ADV
ap-1811	60	9	−→	−→	ADJ
ap-1811	60	10	t̃	t̃	PROPN
ap-1811	60	11	,	,	PUNCT
ap-1811	60	12	gives	give	VERB
ap-1811	60	13	the	the	DET
ap-1811	60	14	classical	classical	ADJ
ap-1811	60	15	heat	heat	NOUN
ap-1811	60	16	equation	equation	NOUN
ap-1811	60	17	∂u	∂u	NOUN
ap-1811	60	18	∂t̃	∂t̃	NOUN
ap-1811	60	19	−	−	NOUN
ap-1811	60	20	∂2u	∂2u	ADJ
ap-1811	60	21	∂x2	∂x2	NOUN
ap-1811	60	22	=	=	NOUN
ap-1811	60	23	0	0	X
ap-1811	60	24	.	.	PUNCT
ap-1811	61	1	since	since	SCONJ
ap-1811	61	2	the	the	DET
ap-1811	61	3	transformation	transformation	NOUN
ap-1811	61	4	is	be	AUX
ap-1811	61	5	a	a	DET
ap-1811	61	6	point	point	NOUN
ap-1811	61	7	transformation	transformation	NOUN
ap-1811	61	8	,	,	PUNCT
ap-1811	61	9	the	the	DET
ap-1811	61	10	number	number	NOUN
ap-1811	61	11	of	of	ADP
ap-1811	61	12	lie	lie	NOUN
ap-1811	61	13	point	point	NOUN
ap-1811	61	14	symmetries	symmetry	NOUN
ap-1811	61	15	is	be	AUX
ap-1811	61	16	unchanged	unchanged	ADJ
ap-1811	61	17	.	.	PUNCT
ap-1811	62	1	specifically	specifically	ADV
ap-1811	62	2	they	they	PRON
ap-1811	62	3	are	be	AUX
ap-1811	62	4	∆1	∆1	PROPN
ap-1811	62	5	=	=	SYM
ap-1811	62	6	∂t	∂t	PROPN
ap-1811	62	7	,	,	PUNCT
ap-1811	62	8	∆2	∆2	X
ap-1811	62	9	=	=	SYM
ap-1811	62	10	2t∂t	2t∂t	PROPN
ap-1811	63	1	+	+	CCONJ
ap-1811	63	2	x∂x	x∂x	NUM
ap-1811	63	3	,	,	PUNCT
ap-1811	63	4	∆3	∆3	NOUN
ap-1811	63	5	=	=	PUNCT
ap-1811	63	6	4t2∂t	4t2∂t	PROPN
ap-1811	64	1	+	+	NUM
ap-1811	65	1	4tx∂x	4tx∂x	NUM
ap-1811	65	2	−	−	PROPN
ap-1811	65	3	(	(	PUNCT
ap-1811	65	4	2t+	2t+	NUM
ap-1811	65	5	x2)u∂u	x2)u∂u	PROPN
ap-1811	65	6	,	,	PUNCT
ap-1811	65	7	∆4	∆4	NOUN
ap-1811	65	8	=	=	SYM
ap-1811	65	9	∂x	∂x	PROPN
ap-1811	65	10	,	,	PUNCT
ap-1811	65	11	∆5	∆5	VERB
ap-1811	65	12	=	=	SYM
ap-1811	65	13	2t∂x	2t∂x	PROPN
ap-1811	65	14	−	−	PROPN
ap-1811	65	15	xu∂u	xu∂u	PROPN
ap-1811	65	16	,	,	PUNCT
ap-1811	65	17	∆6	∆6	NUM
ap-1811	65	18	=	=	SYM
ap-1811	65	19	u∂u	u∂u	NOUN
ap-1811	65	20	,	,	PUNCT
ap-1811	65	21	∆∞	∆∞	NOUN
ap-1811	65	22	=	=	SYM
ap-1811	65	23	f(t	f(t	NOUN
ap-1811	65	24	,	,	PUNCT
ap-1811	65	25	x)∂u	x)∂u	PROPN
ap-1811	65	26	,	,	PUNCT
ap-1811	65	27	where	where	SCONJ
ap-1811	65	28	,	,	PUNCT
ap-1811	65	29	as	as	SCONJ
ap-1811	65	30	has	have	AUX
ap-1811	65	31	been	be	AUX
ap-1811	65	32	the	the	DET
ap-1811	65	33	case	case	NOUN
ap-1811	65	34	above	above	ADV
ap-1811	65	35	,	,	PUNCT
ap-1811	65	36	f(t	f(t	PROPN
ap-1811	65	37	,	,	PUNCT
ap-1811	65	38	x	x	X
ap-1811	65	39	)	)	PUNCT
ap-1811	65	40	is	be	AUX
ap-1811	65	41	any	any	DET
ap-1811	65	42	solution	solution	NOUN
ap-1811	65	43	of	of	ADP
ap-1811	65	44	the	the	DET
ap-1811	65	45	heat	heat	NOUN
ap-1811	65	46	equation	equation	NOUN
ap-1811	65	47	.	.	PUNCT
ap-1811	66	1	the	the	DET
ap-1811	66	2	lie	lie	NOUN
ap-1811	66	3	algebra	algebra	NOUN
ap-1811	66	4	of	of	ADP
ap-1811	66	5	the	the	DET
ap-1811	66	6	symmetries	symmetry	NOUN
ap-1811	66	7	is	be	AUX
ap-1811	66	8	{	{	PUNCT
ap-1811	66	9	sl(2	sl(2	PROPN
ap-1811	66	10	,	,	PUNCT
ap-1811	66	11	r)⊕s	r)⊕s	NUM
ap-1811	66	12	w3	w3	PROPN
ap-1811	66	13	}	}	PUNCT
ap-1811	66	14	⊕s	⊕s	PROPN
ap-1811	66	15	∞a1	∞a1	NUM
ap-1811	66	16	.	.	PUNCT
ap-1811	67	1	the	the	DET
ap-1811	67	2	symmetries	symmetry	NOUN
ap-1811	67	3	,	,	PUNCT
ap-1811	67	4	∆1	∆1	PROPN
ap-1811	67	5	and	and	CCONJ
ap-1811	67	6	∆2	∆2	PROPN
ap-1811	67	7	,	,	PUNCT
ap-1811	67	8	play	play	VERB
ap-1811	67	9	a	a	DET
ap-1811	67	10	similar	similar	ADJ
ap-1811	67	11	role	role	NOUN
ap-1811	67	12	to	to	ADP
ap-1811	67	13	those	those	PRON
ap-1811	67	14	of	of	ADP
ap-1811	67	15	the	the	DET
ap-1811	67	16	quantal	quantal	ADJ
ap-1811	67	17	simple	simple	ADJ
ap-1811	67	18	harmonic	harmonic	ADJ
ap-1811	67	19	oscillator	oscillator	NOUN
ap-1811	67	20	as	as	ADP
ap-1811	67	21	creation	creation	NOUN
ap-1811	67	22	and	and	CCONJ
ap-1811	67	23	annihilation	annihilation	NOUN
ap-1811	67	24	operators	operator	NOUN
ap-1811	67	25	.	.	PUNCT
ap-1811	68	1	they	they	PRON
ap-1811	68	2	have	have	AUX
ap-1811	68	3	been	be	AUX
ap-1811	68	4	used	use	VERB
ap-1811	68	5	to	to	PART
ap-1811	68	6	generate	generate	VERB
ap-1811	68	7	heat	heat	NOUN
ap-1811	68	8	polynomials	polynomial	NOUN
ap-1811	68	9	[	[	X
ap-1811	68	10	8	8	NUM
ap-1811	68	11	]	]	PUNCT
ap-1811	68	12	.	.	PUNCT
ap-1811	69	1	4	4	X
ap-1811	69	2	.	.	X
ap-1811	69	3	the	the	DET
ap-1811	69	4	wonderful	wonderful	ADJ
ap-1811	69	5	world	world	NOUN
ap-1811	69	6	of	of	ADP
ap-1811	69	7	finance	finance	NOUN
ap-1811	69	8	approximately	approximately	ADV
ap-1811	69	9	40	40	NUM
ap-1811	69	10	years	year	NOUN
ap-1811	69	11	ago	ago	ADV
ap-1811	69	12	black	black	ADJ
ap-1811	69	13	and	and	CCONJ
ap-1811	69	14	scholes	schole	VERB
ap-1811	70	1	[	[	X
ap-1811	70	2	1	1	NUM
ap-1811	70	3	,	,	PUNCT
ap-1811	70	4	2	2	NUM
ap-1811	70	5	]	]	PUNCT
ap-1811	70	6	and	and	CCONJ
ap-1811	70	7	,	,	PUNCT
ap-1811	70	8	independently	independently	ADV
ap-1811	70	9	,	,	PUNCT
ap-1811	70	10	merton	merton	PROPN
ap-1811	71	1	[	[	X
ap-1811	71	2	9–12	9–12	X
ap-1811	71	3	]	]	PUNCT
ap-1811	71	4	developed	develop	VERB
ap-1811	71	5	a	a	DET
ap-1811	71	6	model	model	NOUN
ap-1811	71	7	for	for	ADP
ap-1811	71	8	the	the	DET
ap-1811	71	9	pricing	pricing	NOUN
ap-1811	71	10	of	of	ADP
ap-1811	71	11	options	option	NOUN
ap-1811	71	12	.	.	PUNCT
ap-1811	72	1	at	at	ADP
ap-1811	72	2	the	the	DET
ap-1811	72	3	time	time	NOUN
ap-1811	72	4	it	it	PRON
ap-1811	72	5	was	be	AUX
ap-1811	72	6	remarked	remark	VERB
ap-1811	72	7	that	that	SCONJ
ap-1811	72	8	the	the	DET
ap-1811	72	9	subject	subject	NOUN
ap-1811	72	10	under	under	ADP
ap-1811	72	11	investigation	investigation	NOUN
ap-1811	72	12	was	be	AUX
ap-1811	72	13	of	of	ADP
ap-1811	72	14	no	no	DET
ap-1811	72	15	great	great	ADJ
ap-1811	72	16	importance	importance	NOUN
ap-1811	72	17	since	since	SCONJ
ap-1811	72	18	trading	trade	VERB
ap-1811	72	19	in	in	ADP
ap-1811	72	20	options	option	NOUN
ap-1811	72	21	was	be	AUX
ap-1811	72	22	a	a	DET
ap-1811	72	23	minor	minor	ADJ
ap-1811	72	24	feature	feature	NOUN
ap-1811	72	25	of	of	ADP
ap-1811	72	26	the	the	DET
ap-1811	72	27	financial	financial	ADJ
ap-1811	72	28	markets	market	NOUN
ap-1811	72	29	.	.	PUNCT
ap-1811	73	1	a	a	DET
ap-1811	73	2	later	later	ADJ
ap-1811	73	3	observation	observation	NOUN
ap-1811	73	4	about	about	ADP
ap-1811	73	5	the	the	DET
ap-1811	73	6	applicability	applicability	NOUN
ap-1811	73	7	of	of	ADP
ap-1811	73	8	the	the	DET
ap-1811	73	9	model	model	NOUN
ap-1811	73	10	to	to	ADP
ap-1811	73	11	any	any	DET
ap-1811	73	12	financial	financial	ADJ
ap-1811	73	13	instrument	instrument	NOUN
ap-1811	73	14	the	the	DET
ap-1811	73	15	future	future	NOUN
ap-1811	73	16	of	of	ADP
ap-1811	73	17	which	which	PRON
ap-1811	73	18	was	be	AUX
ap-1811	73	19	uncertain	uncertain	ADJ
ap-1811	73	20	at	at	ADP
ap-1811	73	21	the	the	DET
ap-1811	73	22	present	present	ADJ
ap-1811	73	23	time	time	NOUN
ap-1811	73	24	certainly	certainly	ADV
ap-1811	73	25	extended	extend	VERB
ap-1811	73	26	the	the	DET
ap-1811	73	27	relevance	relevance	NOUN
ap-1811	73	28	of	of	ADP
ap-1811	73	29	the	the	DET
ap-1811	73	30	equation	equation	NOUN
ap-1811	73	31	proposed	propose	VERB
ap-1811	73	32	.	.	PUNCT
ap-1811	74	1	the	the	DET
ap-1811	74	2	black	black	ADJ
ap-1811	74	3	-	-	PUNCT
ap-1811	74	4	scholes	schole	NOUN
ap-1811	74	5	-	-	PUNCT
ap-1811	74	6	merton	merton	NOUN
ap-1811	74	7	equation	equation	NOUN
ap-1811	74	8	,	,	PUNCT
ap-1811	74	9	ut	ut	PROPN
ap-1811	74	10	+	+	CCONJ
ap-1811	74	11	1	1	NUM
ap-1811	74	12	2σ	2σ	X
ap-1811	74	13	2x2uxx	2x2uxx	NUM
ap-1811	74	14	+	+	CCONJ
ap-1811	74	15	rxux	rxux	ADJ
ap-1811	74	16	−	−	PROPN
ap-1811	74	17	ru	ru	NOUN
ap-1811	74	18	=	=	NOUN
ap-1811	74	19	0	0	PROPN
ap-1811	74	20	,	,	PUNCT
ap-1811	74	21	(	(	PUNCT
ap-1811	74	22	∗	∗	NOUN
ap-1811	74	23	)	)	PUNCT
ap-1811	74	24	was	be	AUX
ap-1811	74	25	originally	originally	ADV
ap-1811	74	26	presented	present	VERB
ap-1811	74	27	by	by	ADP
ap-1811	74	28	black	black	ADJ
ap-1811	74	29	and	and	CCONJ
ap-1811	74	30	scholes	schole	NOUN
ap-1811	74	31	,	,	PUNCT
ap-1811	74	32	but	but	CCONJ
ap-1811	74	33	merton	merton	PROPN
ap-1811	74	34	’s	’s	PART
ap-1811	74	35	name	name	NOUN
ap-1811	74	36	is	be	AUX
ap-1811	74	37	usually	usually	ADV
ap-1811	74	38	added	add	VERB
ap-1811	74	39	to	to	PART
ap-1811	74	40	indicate	indicate	VERB
ap-1811	74	41	his	his	PRON
ap-1811	74	42	contribution	contribution	NOUN
ap-1811	74	43	to	to	ADP
ap-1811	74	44	the	the	DET
ap-1811	74	45	development	development	NOUN
ap-1811	74	46	of	of	ADP
ap-1811	74	47	this	this	DET
ap-1811	74	48	part	part	NOUN
ap-1811	74	49	of	of	ADP
ap-1811	74	50	the	the	DET
ap-1811	74	51	theory	theory	NOUN
ap-1811	74	52	of	of	ADP
ap-1811	74	53	financial	financial	ADJ
ap-1811	74	54	mathematics	mathematic	NOUN
ap-1811	74	55	.	.	PUNCT
ap-1811	75	1	this	this	DET
ap-1811	75	2	model	model	NOUN
ap-1811	75	3	is	be	AUX
ap-1811	75	4	the	the	DET
ap-1811	75	5	precursor	precursor	NOUN
ap-1811	75	6	of	of	ADP
ap-1811	75	7	the	the	DET
ap-1811	75	8	many	many	ADJ
ap-1811	75	9	evolution	evolution	NOUN
ap-1811	75	10	of	of	ADP
ap-1811	75	11	partial	partial	ADJ
ap-1811	75	12	differential	differential	ADJ
ap-1811	75	13	equations	equation	NOUN
ap-1811	75	14	which	which	PRON
ap-1811	75	15	have	have	AUX
ap-1811	75	16	been	be	AUX
ap-1811	75	17	derived	derive	VERB
ap-1811	75	18	in	in	ADP
ap-1811	75	19	the	the	DET
ap-1811	75	20	modelling	modelling	NOUN
ap-1811	75	21	of	of	ADP
ap-1811	75	22	various	various	ADJ
ap-1811	75	23	303	303	NUM
ap-1811	75	24	p.	p.	NOUN
ap-1811	75	25	g.	g.	PROPN
ap-1811	75	26	l.	l.	PROPN
ap-1811	75	27	leach	leach	PROPN
ap-1811	75	28	acta	acta	PROPN
ap-1811	75	29	polytechnica	polytechnica	PROPN
ap-1811	75	30	financial	financial	ADJ
ap-1811	75	31	processes	process	NOUN
ap-1811	75	32	.	.	PUNCT
ap-1811	76	1	basically	basically	ADV
ap-1811	76	2	it	it	PRON
ap-1811	76	3	has	have	VERB
ap-1811	76	4	to	to	PART
ap-1811	76	5	do	do	VERB
ap-1811	76	6	with	with	ADP
ap-1811	76	7	the	the	DET
ap-1811	76	8	pricing	pricing	NOUN
ap-1811	76	9	of	of	ADP
ap-1811	76	10	options	option	NOUN
ap-1811	76	11	,	,	PUNCT
ap-1811	76	12	but	but	CCONJ
ap-1811	76	13	anything	anything	PRON
ap-1811	76	14	vaguely	vaguely	ADV
ap-1811	76	15	connected	connect	VERB
ap-1811	76	16	such	such	ADJ
ap-1811	76	17	as	as	ADP
ap-1811	76	18	corporate	corporate	ADJ
ap-1811	76	19	debt	debt	NOUN
ap-1811	76	20	is	be	AUX
ap-1811	76	21	equally	equally	ADV
ap-1811	76	22	grist	grist	NOUN
ap-1811	76	23	for	for	ADP
ap-1811	76	24	its	its	PRON
ap-1811	76	25	mill	mill	NOUN
ap-1811	76	26	.	.	PUNCT
ap-1811	77	1	the	the	DET
ap-1811	77	2	symmetry	symmetry	NOUN
ap-1811	77	3	analysis	analysis	NOUN
ap-1811	77	4	of	of	ADP
ap-1811	77	5	(	(	PUNCT
ap-1811	77	6	∗	∗	NOUN
ap-1811	77	7	)	)	PUNCT
ap-1811	77	8	was	be	AUX
ap-1811	77	9	firstly	firstly	ADV
ap-1811	77	10	undertaken	undertake	VERB
ap-1811	77	11	by	by	ADP
ap-1811	77	12	gasizov	gasizov	NOUN
ap-1811	77	13	and	and	CCONJ
ap-1811	77	14	ibragimov	ibragimov	ADJ
ap-1811	77	15	[	[	X
ap-1811	77	16	5	5	NUM
ap-1811	77	17	]	]	PUNCT
ap-1811	77	18	.	.	PUNCT
ap-1811	78	1	after	after	ADP
ap-1811	78	2	determining	determine	VERB
ap-1811	78	3	the	the	DET
ap-1811	78	4	symmetries	symmetry	NOUN
ap-1811	78	5	they	they	PRON
ap-1811	78	6	obtained	obtain	VERB
ap-1811	78	7	from	from	ADP
ap-1811	78	8	the	the	DET
ap-1811	78	9	solution	solution	NOUN
ap-1811	78	10	for	for	ADP
ap-1811	78	11	the	the	DET
ap-1811	78	12	initial	initial	ADJ
ap-1811	78	13	condition	condition	NOUN
ap-1811	78	14	being	be	AUX
ap-1811	78	15	a	a	DET
ap-1811	78	16	delta	delta	NOUN
ap-1811	78	17	function	function	NOUN
ap-1811	78	18	which	which	PRON
ap-1811	78	19	is	be	AUX
ap-1811	78	20	a	a	DET
ap-1811	78	21	typical	typical	ADJ
ap-1811	78	22	initial	initial	ADJ
ap-1811	78	23	condition	condition	NOUN
ap-1811	78	24	for	for	ADP
ap-1811	78	25	the	the	DET
ap-1811	78	26	heat	heat	NOUN
ap-1811	78	27	equation.1	equation.1	ADP
ap-1811	78	28	a	a	DET
ap-1811	78	29	more	more	ADV
ap-1811	78	30	typical	typical	ADJ
ap-1811	78	31	problem	problem	NOUN
ap-1811	78	32	is	be	AUX
ap-1811	78	33	the	the	DET
ap-1811	78	34	solution	solution	NOUN
ap-1811	78	35	of	of	ADP
ap-1811	78	36	(	(	PUNCT
ap-1811	78	37	∗	∗	NOUN
ap-1811	78	38	)	)	PUNCT
ap-1811	78	39	,	,	PUNCT
ap-1811	78	40	the	the	DET
ap-1811	78	41	subject	subject	NOUN
ap-1811	78	42	of	of	ADP
ap-1811	78	43	which	which	PRON
ap-1811	78	44	is	be	AUX
ap-1811	78	45	known	know	VERB
ap-1811	78	46	as	as	ADP
ap-1811	78	47	a	a	DET
ap-1811	78	48	terminal	terminal	ADJ
ap-1811	78	49	condition	condition	NOUN
ap-1811	78	50	,	,	PUNCT
ap-1811	78	51	ie	ie	X
ap-1811	78	52	u(t	u(t	NOUN
ap-1811	78	53	,	,	PUNCT
ap-1811	78	54	x	x	X
ap-1811	78	55	)	)	PUNCT
ap-1811	78	56	=	=	SYM
ap-1811	78	57	u	u	NOUN
ap-1811	78	58	when	when	SCONJ
ap-1811	78	59	t	t	PROPN
ap-1811	78	60	=	=	SYM
ap-1811	78	61	t	t	PROPN
ap-1811	78	62	.	.	PUNCT
ap-1811	79	1	the	the	DET
ap-1811	79	2	lie	lie	NOUN
ap-1811	79	3	point	point	NOUN
ap-1811	79	4	symmetries	symmetry	NOUN
ap-1811	79	5	of	of	ADP
ap-1811	79	6	(	(	PUNCT
ap-1811	79	7	∗	∗	NOUN
ap-1811	79	8	)	)	PUNCT
ap-1811	79	9	are	be	AUX
ap-1811	79	10	γ1	γ1	NOUN
ap-1811	79	11	=	=	SYM
ap-1811	79	12	x∂x	x∂x	PUNCT
ap-1811	80	1	γ2	γ2	PROPN
ap-1811	80	2	=	=	PUNCT
ap-1811	80	3	2tx∂x	2tx∂x	NUM
ap-1811	81	1	+	+	CCONJ
ap-1811	81	2	{	{	PUNCT
ap-1811	81	3	t−	t−	PROPN
ap-1811	81	4	2	2	NUM
ap-1811	81	5	σ2	σ2	PROPN
ap-1811	81	6	(	(	PUNCT
ap-1811	81	7	rt−	rt−	NUM
ap-1811	81	8	log	log	PROPN
ap-1811	81	9	x	x	NOUN
ap-1811	81	10	)	)	PUNCT
ap-1811	81	11	}	}	PUNCT
ap-1811	81	12	u∂u	u∂u	NUM
ap-1811	81	13	γ3	γ3	NOUN
ap-1811	81	14	=	=	SYM
ap-1811	81	15	u∂u	u∂u	NOUN
ap-1811	81	16	γ4	γ4	NOUN
ap-1811	81	17	=	=	SYM
ap-1811	81	18	∂t	∂t	PROPN
ap-1811	81	19	γ5	γ5	NOUN
ap-1811	81	20	=	=	PUNCT
ap-1811	81	21	8t∂t	8t∂t	PROPN
ap-1811	82	1	+	+	CCONJ
ap-1811	82	2	4x	4x	NUM
ap-1811	82	3	log	log	NOUN
ap-1811	82	4	x∂x	x∂x	X
ap-1811	83	1	+	+	CCONJ
ap-1811	83	2	{	{	PUNCT
ap-1811	83	3	4tr	4tr	ADJ
ap-1811	83	4	+	+	PUNCT
ap-1811	83	5	σ2t+	σ2t+	NUM
ap-1811	83	6	2	2	NUM
ap-1811	83	7	log	log	NOUN
ap-1811	83	8	x+	x+	SYM
ap-1811	83	9	4r	4r	PROPN
ap-1811	83	10	σ2	σ2	PROPN
ap-1811	83	11	(	(	PUNCT
ap-1811	83	12	rt−	rt−	NUM
ap-1811	83	13	log	log	PROPN
ap-1811	83	14	x	x	NOUN
ap-1811	83	15	)	)	PUNCT
ap-1811	83	16	}	}	PUNCT
ap-1811	83	17	u∂u	u∂u	NUM
ap-1811	83	18	γ6	γ6	NOUN
ap-1811	83	19	=	=	PUNCT
ap-1811	83	20	8t2∂t	8t2∂t	PROPN
ap-1811	83	21	+	+	CCONJ
ap-1811	83	22	8tx	8tx	ADJ
ap-1811	83	23	log	log	NOUN
ap-1811	83	24	x∂x	x∂x	X
ap-1811	84	1	+	+	CCONJ
ap-1811	84	2	{	{	PUNCT
ap-1811	84	3	−4t+	−4t+	PRON
ap-1811	84	4	4t2r	4t2r	NOUN
ap-1811	85	1	+	+	CCONJ
ap-1811	85	2	σ2t2	σ2t2	NUM
ap-1811	85	3	+	+	SYM
ap-1811	85	4	4	4	NUM
ap-1811	85	5	t	t	NOUN
ap-1811	85	6	log	log	NOUN
ap-1811	85	7	x+	x+	NUM
ap-1811	85	8	4	4	NUM
ap-1811	85	9	σ2	σ2	PROPN
ap-1811	85	10	(	(	PUNCT
ap-1811	85	11	rt−	rt−	NUM
ap-1811	85	12	log	log	NOUN
ap-1811	85	13	x)2	x)2	X
ap-1811	85	14	}	}	PUNCT
ap-1811	85	15	u∂u	u∂u	PART
ap-1811	85	16	γ∞	γ∞	NOUN
ap-1811	85	17	=	=	PUNCT
ap-1811	85	18	f(t	f(t	NOUN
ap-1811	85	19	,	,	PUNCT
ap-1811	85	20	x)∂u	x)∂u	PROPN
ap-1811	85	21	,	,	PUNCT
ap-1811	85	22	where	where	SCONJ
ap-1811	85	23	γ∞	γ∞	NOUN
ap-1811	85	24	is	be	AUX
ap-1811	85	25	the	the	DET
ap-1811	85	26	infinite	infinite	ADJ
ap-1811	85	27	subset	subset	NOUN
ap-1811	85	28	of	of	ADP
ap-1811	85	29	solutions	solution	NOUN
ap-1811	85	30	to	to	ADP
ap-1811	85	31	(	(	PUNCT
ap-1811	85	32	∗	∗	NOUN
ap-1811	85	33	)	)	PUNCT
ap-1811	85	34	.	.	PUNCT
ap-1811	86	1	the	the	DET
ap-1811	86	2	algebra	algebra	NOUN
ap-1811	86	3	of	of	ADP
ap-1811	86	4	the	the	DET
ap-1811	86	5	finite	finite	NOUN
ap-1811	86	6	subset	subset	NOUN
ap-1811	86	7	is	be	AUX
ap-1811	86	8	sl(2	sl(2	PROPN
ap-1811	86	9	,	,	PUNCT
ap-1811	86	10	r	r	NOUN
ap-1811	86	11	)	)	PUNCT
ap-1811	86	12	⊕s	⊕s	NOUN
ap-1811	86	13	w3	w3	PROPN
ap-1811	86	14	,	,	PUNCT
ap-1811	86	15	where	where	SCONJ
ap-1811	86	16	w3	w3	PROPN
ap-1811	86	17	is	be	AUX
ap-1811	86	18	the	the	DET
ap-1811	86	19	three	three	NUM
ap-1811	86	20	-	-	PUNCT
ap-1811	86	21	dimensional	dimensional	ADJ
ap-1811	86	22	heisenberg	heisenberg	PROPN
ap-1811	86	23	-	-	PUNCT
ap-1811	86	24	weyl	weyl	VERB
ap-1811	86	25	algebra	algebra	NOUN
ap-1811	86	26	.	.	PUNCT
ap-1811	87	1	the	the	DET
ap-1811	87	2	important	important	ADJ
ap-1811	87	3	thing	thing	NOUN
ap-1811	87	4	to	to	PART
ap-1811	87	5	note	note	VERB
ap-1811	87	6	is	be	AUX
ap-1811	87	7	that	that	SCONJ
ap-1811	87	8	the	the	DET
ap-1811	87	9	algebra	algebra	NOUN
ap-1811	87	10	of	of	ADP
ap-1811	87	11	the	the	DET
ap-1811	87	12	symmetries	symmetry	NOUN
ap-1811	87	13	presented	present	VERB
ap-1811	87	14	above	above	ADV
ap-1811	87	15	is	be	AUX
ap-1811	87	16	just	just	ADV
ap-1811	87	17	that	that	PRON
ap-1811	87	18	of	of	ADP
ap-1811	87	19	the	the	DET
ap-1811	87	20	classical	classical	ADJ
ap-1811	87	21	equation	equation	NOUN
ap-1811	87	22	which	which	PRON
ap-1811	87	23	we	we	PRON
ap-1811	87	24	have	have	AUX
ap-1811	87	25	seen	see	VERB
ap-1811	87	26	is	be	AUX
ap-1811	87	27	related	relate	VERB
ap-1811	87	28	to	to	ADP
ap-1811	87	29	the	the	DET
ap-1811	87	30	schrödinger	schrödinger	ADJ
ap-1811	87	31	equation	equation	NOUN
ap-1811	87	32	for	for	ADP
ap-1811	87	33	the	the	DET
ap-1811	87	34	free	free	ADJ
ap-1811	87	35	particle	particle	NOUN
ap-1811	87	36	and	and	CCONJ
ap-1811	87	37	so	so	ADV
ap-1811	87	38	to	to	ADP
ap-1811	87	39	the	the	DET
ap-1811	87	40	noether	noether	ADJ
ap-1811	87	41	point	point	NOUN
ap-1811	87	42	symmetries	symmetry	NOUN
ap-1811	87	43	of	of	ADP
ap-1811	87	44	a	a	DET
ap-1811	87	45	classical	classical	ADJ
ap-1811	87	46	lagrangian	lagrangian	NOUN
ap-1811	87	47	.	.	PUNCT
ap-1811	88	1	a	a	DET
ap-1811	88	2	question	question	NOUN
ap-1811	88	3	of	of	ADP
ap-1811	88	4	course	course	NOUN
ap-1811	88	5	could	could	AUX
ap-1811	88	6	be	be	AUX
ap-1811	88	7	posed	pose	VERB
ap-1811	88	8	as	as	ADP
ap-1811	88	9	to	to	ADP
ap-1811	88	10	the	the	DET
ap-1811	88	11	identity	identity	NOUN
ap-1811	88	12	of	of	ADP
ap-1811	88	13	the	the	DET
ap-1811	88	14	classical	classical	ADJ
ap-1811	88	15	lagrangian	lagrangian	NOUN
ap-1811	88	16	.	.	PUNCT
ap-1811	89	1	equation	equation	NOUN
ap-1811	89	2	(	(	PUNCT
ap-1811	89	3	∗	∗	NOUN
ap-1811	89	4	)	)	PUNCT
ap-1811	89	5	is	be	AUX
ap-1811	89	6	not	not	PART
ap-1811	89	7	quite	quite	ADV
ap-1811	89	8	in	in	ADP
ap-1811	89	9	the	the	DET
ap-1811	89	10	form	form	NOUN
ap-1811	89	11	of	of	ADP
ap-1811	89	12	the	the	DET
ap-1811	89	13	classical	classical	ADJ
ap-1811	89	14	heat	heat	NOUN
ap-1811	89	15	equation	equation	NOUN
ap-1811	89	16	,	,	PUNCT
ap-1811	89	17	for	for	ADP
ap-1811	89	18	which	which	PRON
ap-1811	89	19	we	we	PRON
ap-1811	89	20	could	could	AUX
ap-1811	89	21	easily	easily	ADV
ap-1811	89	22	make	make	VERB
ap-1811	89	23	a	a	DET
ap-1811	89	24	definite	definite	ADJ
ap-1811	89	25	identification	identification	NOUN
ap-1811	89	26	of	of	ADP
ap-1811	89	27	the	the	DET
ap-1811	89	28	corresponding	corresponding	ADJ
ap-1811	89	29	lagrangian	lagrangian	NOUN
ap-1811	89	30	.	.	PUNCT
ap-1811	90	1	under	under	ADP
ap-1811	90	2	the	the	DET
ap-1811	90	3	transformations	transformation	NOUN
ap-1811	90	4	x	x	X
ap-1811	90	5	7→	7→	NUM
ap-1811	90	6	exp[σy	exp[σy	ADJ
ap-1811	90	7	]	]	PUNCT
ap-1811	90	8	,	,	PUNCT
ap-1811	90	9	u(t	u(t	NOUN
ap-1811	90	10	,	,	PUNCT
ap-1811	90	11	x	x	NOUN
ap-1811	90	12	)	)	PUNCT
ap-1811	90	13	7→	7→	NUM
ap-1811	90	14	w(t	w(t	PROPN
ap-1811	90	15	,	,	PUNCT
ap-1811	90	16	y	y	NOUN
ap-1811	90	17	)	)	PUNCT
ap-1811	90	18	exp	exp	NOUN
ap-1811	90	19	[	[	PUNCT
ap-1811	90	20	1	1	NUM
ap-1811	90	21	2	2	NUM
ap-1811	90	22	(	(	PUNCT
ap-1811	90	23	1−	1−	NUM
ap-1811	90	24	2r	2r	NUM
ap-1811	90	25	σ2	σ2	PROPN
ap-1811	90	26	)	)	PUNCT
ap-1811	90	27	y	y	PROPN
ap-1811	91	1	+	+	NOUN
ap-1811	91	2	1	1	NUM
ap-1811	91	3	8σ2	8σ2	NUM
ap-1811	91	4	(	(	PUNCT
ap-1811	91	5	σ2	σ2	PROPN
ap-1811	91	6	+	+	PROPN
ap-1811	91	7	2r	2r	NUM
ap-1811	91	8	)	)	PUNCT
ap-1811	91	9	2	2	NUM
ap-1811	91	10	]	]	PUNCT
ap-1811	91	11	we	we	PRON
ap-1811	91	12	obtain	obtain	VERB
ap-1811	91	13	2wt	2wt	NOUN
ap-1811	92	1	+	+	CCONJ
ap-1811	92	2	wyy	wyy	NOUN
ap-1811	92	3	=	=	SYM
ap-1811	92	4	0	0	X
ap-1811	92	5	.	.	PUNCT
ap-1811	93	1	one	one	PRON
ap-1811	93	2	can	can	AUX
ap-1811	93	3	detect	detect	VERB
ap-1811	93	4	a	a	DET
ap-1811	93	5	certain	certain	ADJ
ap-1811	93	6	degree	degree	NOUN
ap-1811	93	7	of	of	ADP
ap-1811	93	8	irony	irony	NOUN
ap-1811	93	9	in	in	ADP
ap-1811	93	10	the	the	DET
ap-1811	93	11	identification	identification	NOUN
ap-1811	93	12	of	of	ADP
ap-1811	93	13	the	the	DET
ap-1811	93	14	most	most	ADV
ap-1811	93	15	famous	famous	ADJ
ap-1811	93	16	equation	equation	NOUN
ap-1811	93	17	of	of	ADP
ap-1811	93	18	financial	financial	ADJ
ap-1811	93	19	mathematics	mathematic	NOUN
ap-1811	93	20	with	with	ADP
ap-1811	93	21	the	the	DET
ap-1811	93	22	free	free	ADJ
ap-1811	93	23	particle	particle	NOUN
ap-1811	93	24	.	.	PUNCT
ap-1811	94	1	the	the	DET
ap-1811	94	2	black	black	ADJ
ap-1811	94	3	-	-	PUNCT
ap-1811	94	4	scholes	schole	NOUN
ap-1811	94	5	-	-	PUNCT
ap-1811	94	6	merton	merton	NOUN
ap-1811	94	7	equation	equation	NOUN
ap-1811	94	8	is	be	AUX
ap-1811	94	9	but	but	CCONJ
ap-1811	94	10	one	one	NUM
ap-1811	94	11	of	of	ADP
ap-1811	94	12	a	a	DET
ap-1811	94	13	number	number	NOUN
ap-1811	94	14	of	of	ADP
ap-1811	94	15	evolution	evolution	NOUN
ap-1811	94	16	equations	equation	NOUN
ap-1811	94	17	to	to	PART
ap-1811	94	18	be	be	AUX
ap-1811	94	19	found	find	VERB
ap-1811	94	20	in	in	ADP
ap-1811	94	21	financial	financial	ADJ
ap-1811	94	22	1one	1one	PROPN
ap-1811	94	23	would	would	AUX
ap-1811	94	24	hope	hope	VERB
ap-1811	94	25	that	that	SCONJ
ap-1811	94	26	this	this	DET
ap-1811	94	27	initial	initial	ADJ
ap-1811	94	28	condition	condition	NOUN
ap-1811	94	29	would	would	AUX
ap-1811	94	30	not	not	PART
ap-1811	94	31	apply	apply	VERB
ap-1811	94	32	in	in	ADP
ap-1811	94	33	financial	financial	ADJ
ap-1811	94	34	matters	matter	NOUN
ap-1811	94	35	!	!	PUNCT
ap-1811	95	1	unfortunately	unfortunately	ADV
ap-1811	95	2	there	there	PRON
ap-1811	95	3	are	be	VERB
ap-1811	95	4	some	some	DET
ap-1811	95	5	instances	instance	NOUN
ap-1811	95	6	of	of	ADP
ap-1811	95	7	financial	financial	ADJ
ap-1811	95	8	instability	instability	NOUN
ap-1811	95	9	in	in	ADP
ap-1811	95	10	which	which	PRON
ap-1811	95	11	such	such	DET
ap-1811	95	12	an	an	DET
ap-1811	95	13	initial	initial	ADJ
ap-1811	95	14	condition	condition	NOUN
ap-1811	95	15	is	be	AUX
ap-1811	95	16	far	far	ADV
ap-1811	95	17	too	too	ADV
ap-1811	95	18	accurate	accurate	ADJ
ap-1811	95	19	a	a	DET
ap-1811	95	20	model	model	NOUN
ap-1811	95	21	.	.	PUNCT
ap-1811	96	1	note	note	VERB
ap-1811	96	2	that	that	SCONJ
ap-1811	96	3	the	the	DET
ap-1811	96	4	paper	paper	NOUN
ap-1811	96	5	[	[	X
ap-1811	96	6	7	7	X
ap-1811	96	7	]	]	PUNCT
ap-1811	96	8	with	with	ADP
ap-1811	96	9	more	more	ADV
ap-1811	96	10	realistic	realistic	ADJ
ap-1811	96	11	conditions	condition	NOUN
ap-1811	96	12	appeared	appear	VERB
ap-1811	96	13	earlier	early	ADV
ap-1811	96	14	,	,	PUNCT
ap-1811	96	15	but	but	CCONJ
ap-1811	96	16	the	the	DET
ap-1811	96	17	content	content	NOUN
ap-1811	96	18	of	of	ADP
ap-1811	96	19	[	[	X
ap-1811	96	20	5	5	NUM
ap-1811	96	21	]	]	PUNCT
ap-1811	96	22	had	have	AUX
ap-1811	96	23	already	already	ADV
ap-1811	96	24	been	be	AUX
ap-1811	96	25	presented	present	VERB
ap-1811	96	26	at	at	ADP
ap-1811	96	27	a	a	DET
ap-1811	96	28	seminar	seminar	NOUN
ap-1811	96	29	in	in	ADP
ap-1811	96	30	the	the	DET
ap-1811	96	31	department	department	NOUN
ap-1811	96	32	of	of	ADP
ap-1811	96	33	physics	physics	PROPN
ap-1811	96	34	,	,	PUNCT
ap-1811	96	35	the	the	DET
ap-1811	96	36	university	university	NOUN
ap-1811	96	37	of	of	ADP
ap-1811	96	38	the	the	DET
ap-1811	96	39	witwatersrand	witwatersrand	NOUN
ap-1811	96	40	,	,	PUNCT
ap-1811	96	41	johannesburg	johannesburg	PROPN
ap-1811	96	42	,	,	PUNCT
ap-1811	96	43	in	in	ADP
ap-1811	96	44	1996	1996	NUM
ap-1811	96	45	.	.	PUNCT
ap-1811	97	1	mathematics	mathematic	NOUN
ap-1811	97	2	which	which	PRON
ap-1811	97	3	are	be	AUX
ap-1811	97	4	rather	rather	ADV
ap-1811	97	5	blessed	bless	VERB
ap-1811	97	6	with	with	ADP
ap-1811	97	7	an	an	DET
ap-1811	97	8	abundance	abundance	NOUN
ap-1811	97	9	of	of	ADP
ap-1811	97	10	symmetry	symmetry	NOUN
ap-1811	97	11	.	.	PUNCT
ap-1811	98	1	admittedly	admittedly	ADV
ap-1811	98	2	not	not	PART
ap-1811	98	3	all	all	PRON
ap-1811	98	4	of	of	ADP
ap-1811	98	5	them	they	PRON
ap-1811	98	6	possess	possess	VERB
ap-1811	98	7	the	the	DET
ap-1811	98	8	richness	richness	NOUN
ap-1811	98	9	of	of	ADP
ap-1811	98	10	the	the	DET
ap-1811	98	11	algebra	algebra	NOUN
ap-1811	98	12	{	{	PUNCT
ap-1811	98	13	sl(2	sl(2	PROPN
ap-1811	98	14	,	,	PUNCT
ap-1811	98	15	r)⊕s	r)⊕s	NUM
ap-1811	98	16	w3	w3	PROPN
ap-1811	98	17	}	}	PUNCT
ap-1811	98	18	⊕s∞a1	⊕s∞a1	NOUN
ap-1811	98	19	,	,	PUNCT
ap-1811	98	20	but	but	CCONJ
ap-1811	98	21	one	one	PRON
ap-1811	98	22	can	can	AUX
ap-1811	98	23	be	be	AUX
ap-1811	98	24	successful	successful	ADJ
ap-1811	98	25	in	in	ADP
ap-1811	98	26	the	the	DET
ap-1811	98	27	resolution	resolution	NOUN
ap-1811	98	28	of	of	ADP
ap-1811	98	29	the	the	DET
ap-1811	98	30	equation	equation	NOUN
ap-1811	98	31	with	with	ADP
ap-1811	98	32	fewer	few	ADJ
ap-1811	98	33	symmetries	symmetry	NOUN
ap-1811	98	34	.	.	PUNCT
ap-1811	99	1	these	these	DET
ap-1811	99	2	algebraic	algebraic	ADJ
ap-1811	99	3	properties	property	NOUN
ap-1811	99	4	are	be	AUX
ap-1811	99	5	not	not	PART
ap-1811	99	6	confined	confine	VERB
ap-1811	99	7	to	to	ADP
ap-1811	99	8	1	1	NUM
ap-1811	99	9	+	+	SYM
ap-1811	99	10	1	1	NUM
ap-1811	99	11	evolution	evolution	NOUN
ap-1811	99	12	equations	equation	NOUN
ap-1811	99	13	.	.	PUNCT
ap-1811	100	1	an	an	DET
ap-1811	100	2	interesting	interesting	ADJ
ap-1811	100	3	example	example	NOUN
ap-1811	100	4	is	be	AUX
ap-1811	100	5	to	to	PART
ap-1811	100	6	be	be	AUX
ap-1811	100	7	found	find	VERB
ap-1811	100	8	in	in	ADP
ap-1811	100	9	the	the	DET
ap-1811	100	10	model	model	NOUN
ap-1811	100	11	of	of	ADP
ap-1811	100	12	the	the	DET
ap-1811	100	13	pricing	pricing	NOUN
ap-1811	100	14	of	of	ADP
ap-1811	100	15	commodities	commodity	NOUN
ap-1811	100	16	developed	develop	VERB
ap-1811	100	17	by	by	ADP
ap-1811	100	18	eduardo	eduardo	PROPN
ap-1811	100	19	schwartz	schwartz	PROPN
ap-1811	101	1	[	[	X
ap-1811	101	2	3	3	NUM
ap-1811	101	3	,	,	PUNCT
ap-1811	101	4	6	6	NUM
ap-1811	101	5	,	,	PUNCT
ap-1811	101	6	14	14	NUM
ap-1811	101	7	]	]	PUNCT
ap-1811	101	8	,	,	PUNCT
ap-1811	101	9	which	which	PRON
ap-1811	101	10	was	be	AUX
ap-1811	101	11	examined	examine	VERB
ap-1811	101	12	from	from	ADP
ap-1811	101	13	the	the	DET
ap-1811	101	14	viewpoint	viewpoint	NOUN
ap-1811	101	15	of	of	ADP
ap-1811	101	16	symmetry	symmetry	NOUN
ap-1811	101	17	in	in	ADP
ap-1811	101	18	[	[	X
ap-1811	101	19	15	15	NUM
ap-1811	101	20	]	]	PUNCT
ap-1811	101	21	.	.	PUNCT
ap-1811	102	1	schwartz	schwartz	PROPN
ap-1811	102	2	considered	consider	VERB
ap-1811	102	3	models	model	NOUN
ap-1811	102	4	with	with	ADP
ap-1811	102	5	one	one	NUM
ap-1811	102	6	,	,	PUNCT
ap-1811	102	7	two	two	NUM
ap-1811	102	8	and	and	CCONJ
ap-1811	102	9	three	three	NUM
ap-1811	102	10	‘	'	PUNCT
ap-1811	102	11	spatial	spatial	ADJ
ap-1811	102	12	’	'	PUNCT
ap-1811	102	13	variables	variable	NOUN
ap-1811	102	14	.	.	PUNCT
ap-1811	103	1	in	in	ADP
ap-1811	103	2	terms	term	NOUN
ap-1811	103	3	of	of	ADP
ap-1811	103	4	the	the	DET
ap-1811	103	5	type	type	NOUN
ap-1811	103	6	of	of	ADP
ap-1811	103	7	model	model	NOUN
ap-1811	103	8	that	that	PRON
ap-1811	103	9	he	he	PRON
ap-1811	103	10	proposed	propose	VERB
ap-1811	103	11	,	,	PUNCT
ap-1811	103	12	the	the	DET
ap-1811	103	13	number	number	NOUN
ap-1811	103	14	of	of	ADP
ap-1811	103	15	dimensions	dimension	NOUN
ap-1811	103	16	becomes	become	VERB
ap-1811	103	17	irrelevant	irrelevant	ADJ
ap-1811	103	18	since	since	SCONJ
ap-1811	103	19	there	there	PRON
ap-1811	103	20	is	be	VERB
ap-1811	103	21	sufficient	sufficient	ADJ
ap-1811	103	22	increase	increase	NOUN
ap-1811	103	23	in	in	ADP
ap-1811	103	24	symmetry	symmetry	NOUN
ap-1811	103	25	with	with	ADP
ap-1811	103	26	the	the	DET
ap-1811	103	27	increase	increase	NOUN
ap-1811	103	28	in	in	ADP
ap-1811	103	29	the	the	DET
ap-1811	103	30	number	number	NOUN
ap-1811	103	31	of	of	ADP
ap-1811	103	32	dimensions	dimension	NOUN
ap-1811	103	33	.	.	PUNCT
ap-1811	104	1	it	it	PRON
ap-1811	104	2	is	be	AUX
ap-1811	104	3	rather	rather	ADV
ap-1811	104	4	intriguing	intriguing	ADJ
ap-1811	104	5	that	that	SCONJ
ap-1811	104	6	so	so	ADV
ap-1811	104	7	many	many	ADJ
ap-1811	104	8	of	of	ADP
ap-1811	104	9	the	the	DET
ap-1811	104	10	equations	equation	NOUN
ap-1811	104	11	which	which	PRON
ap-1811	104	12	arise	arise	VERB
ap-1811	104	13	in	in	ADP
ap-1811	104	14	the	the	DET
ap-1811	104	15	mathematics	mathematic	NOUN
ap-1811	104	16	of	of	ADP
ap-1811	104	17	finance	finance	NOUN
ap-1811	104	18	should	should	AUX
ap-1811	104	19	be	be	AUX
ap-1811	104	20	so	so	ADV
ap-1811	104	21	richly	richly	ADV
ap-1811	104	22	endowed	endow	VERB
ap-1811	104	23	with	with	ADP
ap-1811	104	24	symmetry	symmetry	NOUN
ap-1811	104	25	.	.	PUNCT
ap-1811	105	1	naturally	naturally	ADV
ap-1811	105	2	the	the	DET
ap-1811	105	3	possession	possession	NOUN
ap-1811	105	4	of	of	ADP
ap-1811	105	5	symmetry	symmetry	NOUN
ap-1811	105	6	is	be	AUX
ap-1811	105	7	an	an	DET
ap-1811	105	8	indispensable	indispensable	ADJ
ap-1811	105	9	aid	aid	NOUN
ap-1811	105	10	to	to	ADP
ap-1811	105	11	a	a	DET
ap-1811	105	12	ready	ready	ADJ
ap-1811	105	13	resolution	resolution	NOUN
ap-1811	105	14	of	of	ADP
ap-1811	105	15	a	a	DET
ap-1811	105	16	differential	differential	ADJ
ap-1811	105	17	equation	equation	NOUN
ap-1811	105	18	which	which	PRON
ap-1811	105	19	may	may	AUX
ap-1811	105	20	explain	explain	VERB
ap-1811	105	21	the	the	DET
ap-1811	105	22	comment	comment	NOUN
ap-1811	105	23	of	of	ADP
ap-1811	105	24	a	a	DET
ap-1811	105	25	learned	learn	VERB
ap-1811	105	26	referee	referee	NOUN
ap-1811	105	27	that	that	SCONJ
ap-1811	105	28	any	any	DET
ap-1811	105	29	competent	competent	ADJ
ap-1811	105	30	applied	apply	VERB
ap-1811	105	31	mathematician	mathematician	NOUN
ap-1811	105	32	can	can	AUX
ap-1811	105	33	solve	solve	VERB
ap-1811	105	34	these	these	DET
ap-1811	105	35	equations	equation	NOUN
ap-1811	105	36	without	without	ADP
ap-1811	105	37	recourse	recourse	NOUN
ap-1811	105	38	to	to	ADP
ap-1811	105	39	the	the	DET
ap-1811	105	40	arcane	arcane	ADJ
ap-1811	105	41	methods	method	NOUN
ap-1811	105	42	of	of	ADP
ap-1811	105	43	a	a	DET
ap-1811	105	44	norwegian	norwegian	ADJ
ap-1811	105	45	mathematician	mathematician	NOUN
ap-1811	105	46	.	.	PUNCT
ap-1811	106	1	5	5	X
ap-1811	106	2	.	.	X
ap-1811	106	3	initial	initial	ADJ
ap-1811	106	4	/	/	SYM
ap-1811	106	5	boundary	boundary	ADJ
ap-1811	106	6	conditions	condition	NOUN
ap-1811	106	7	thus	thus	ADV
ap-1811	106	8	far	far	ADV
ap-1811	106	9	we	we	PRON
ap-1811	106	10	have	have	AUX
ap-1811	106	11	considered	consider	VERB
ap-1811	106	12	only	only	ADV
ap-1811	106	13	the	the	DET
ap-1811	106	14	differential	differential	ADJ
ap-1811	106	15	equations	equation	NOUN
ap-1811	106	16	and	and	CCONJ
ap-1811	106	17	not	not	PART
ap-1811	106	18	those	those	DET
ap-1811	106	19	pesky	pesky	ADJ
ap-1811	106	20	little	little	ADJ
ap-1811	106	21	things	thing	NOUN
ap-1811	106	22	which	which	PRON
ap-1811	106	23	accompany	accompany	VERB
ap-1811	106	24	them	they	PRON
ap-1811	106	25	when	when	SCONJ
ap-1811	106	26	one	one	PRON
ap-1811	106	27	wants	want	VERB
ap-1811	106	28	to	to	PART
ap-1811	106	29	state	state	VERB
ap-1811	106	30	the	the	DET
ap-1811	106	31	equation	equation	NOUN
ap-1811	106	32	correctly	correctly	ADV
ap-1811	106	33	,	,	PUNCT
ap-1811	106	34	i.e.	i.e.	X
ap-1811	106	35	the	the	DET
ap-1811	106	36	initial	initial	ADJ
ap-1811	106	37	and/or	and/or	CCONJ
ap-1811	106	38	boundary	boundary	ADJ
ap-1811	106	39	conditions	condition	NOUN
ap-1811	106	40	.	.	PUNCT
ap-1811	107	1	in	in	ADP
ap-1811	107	2	the	the	DET
ap-1811	107	3	case	case	NOUN
ap-1811	107	4	of	of	ADP
ap-1811	107	5	classical	classical	ADJ
ap-1811	107	6	mechanics	mechanic	NOUN
ap-1811	107	7	with	with	ADP
ap-1811	107	8	a	a	DET
ap-1811	107	9	single	single	ADJ
ap-1811	107	10	independent	independent	ADJ
ap-1811	107	11	variable	variable	NOUN
ap-1811	107	12	,	,	PUNCT
ap-1811	107	13	the	the	DET
ap-1811	107	14	situation	situation	NOUN
ap-1811	107	15	is	be	AUX
ap-1811	107	16	quite	quite	ADV
ap-1811	107	17	simple	simple	ADJ
ap-1811	107	18	.	.	PUNCT
ap-1811	108	1	one	one	NUM
ap-1811	108	2	solves	solve	VERB
ap-1811	108	3	the	the	DET
ap-1811	108	4	equation	equation	NOUN
ap-1811	108	5	by	by	ADP
ap-1811	108	6	one	one	NUM
ap-1811	108	7	means	mean	NOUN
ap-1811	108	8	or	or	CCONJ
ap-1811	108	9	another	another	PRON
ap-1811	108	10	and	and	CCONJ
ap-1811	108	11	then	then	ADV
ap-1811	108	12	evaluates	evaluate	VERB
ap-1811	108	13	the	the	DET
ap-1811	108	14	constants	constant	NOUN
ap-1811	108	15	of	of	ADP
ap-1811	108	16	integration	integration	NOUN
ap-1811	108	17	using	use	VERB
ap-1811	108	18	the	the	DET
ap-1811	108	19	initial	initial	ADJ
ap-1811	108	20	conditions	condition	NOUN
ap-1811	108	21	.	.	PUNCT
ap-1811	109	1	to	to	PART
ap-1811	109	2	be	be	AUX
ap-1811	109	3	quite	quite	ADV
ap-1811	109	4	honest	honest	ADJ
ap-1811	109	5	,	,	PUNCT
ap-1811	109	6	i	i	PRON
ap-1811	109	7	have	have	AUX
ap-1811	109	8	never	never	ADV
ap-1811	109	9	thought	think	VERB
ap-1811	109	10	of	of	ADP
ap-1811	109	11	applying	apply	VERB
ap-1811	109	12	the	the	DET
ap-1811	109	13	methodology	methodology	NOUN
ap-1811	109	14	to	to	PART
ap-1811	109	15	be	be	AUX
ap-1811	109	16	discussed	discuss	VERB
ap-1811	109	17	below	below	ADP
ap-1811	109	18	to	to	ADP
ap-1811	109	19	an	an	DET
ap-1811	109	20	initial	initial	ADJ
ap-1811	109	21	value	value	NOUN
ap-1811	109	22	problem	problem	NOUN
ap-1811	109	23	in	in	ADP
ap-1811	109	24	classical	classical	ADJ
ap-1811	109	25	mechanics	mechanic	NOUN
ap-1811	109	26	!	!	PUNCT
ap-1811	110	1	when	when	SCONJ
ap-1811	110	2	it	it	PRON
ap-1811	110	3	comes	come	VERB
ap-1811	110	4	to	to	ADP
ap-1811	110	5	partial	partial	ADJ
ap-1811	110	6	differential	differential	NOUN
ap-1811	110	7	equations	equation	NOUN
ap-1811	110	8	,	,	PUNCT
ap-1811	110	9	the	the	DET
ap-1811	110	10	situation	situation	NOUN
ap-1811	110	11	is	be	AUX
ap-1811	110	12	not	not	PART
ap-1811	110	13	so	so	ADV
ap-1811	110	14	simple	simple	ADJ
ap-1811	110	15	,	,	PUNCT
ap-1811	110	16	for	for	SCONJ
ap-1811	110	17	one	one	PRON
ap-1811	110	18	can	can	AUX
ap-1811	110	19	have	have	VERB
ap-1811	110	20	both	both	PRON
ap-1811	110	21	boundary	boundary	ADJ
ap-1811	110	22	conditions	condition	NOUN
ap-1811	110	23	and	and	CCONJ
ap-1811	110	24	initial	initial	ADJ
ap-1811	110	25	conditions	condition	NOUN
ap-1811	110	26	.	.	PUNCT
ap-1811	111	1	actually	actually	ADV
ap-1811	111	2	in	in	ADP
ap-1811	111	3	the	the	DET
ap-1811	111	4	case	case	NOUN
ap-1811	111	5	of	of	ADP
ap-1811	111	6	financial	financial	ADJ
ap-1811	111	7	problems	problem	NOUN
ap-1811	111	8	it	it	PRON
ap-1811	111	9	is	be	AUX
ap-1811	111	10	usually	usually	ADV
ap-1811	111	11	a	a	DET
ap-1811	111	12	terminal	terminal	ADJ
ap-1811	111	13	condition	condition	NOUN
ap-1811	111	14	rather	rather	ADV
ap-1811	111	15	than	than	ADP
ap-1811	111	16	an	an	DET
ap-1811	111	17	initial	initial	ADJ
ap-1811	111	18	condition	condition	NOUN
ap-1811	111	19	,	,	PUNCT
ap-1811	111	20	but	but	CCONJ
ap-1811	111	21	that	that	PRON
ap-1811	111	22	is	be	AUX
ap-1811	111	23	merely	merely	ADV
ap-1811	111	24	a	a	DET
ap-1811	111	25	matter	matter	NOUN
ap-1811	111	26	of	of	ADP
ap-1811	111	27	one	one	NUM
ap-1811	111	28	’s	’s	PART
ap-1811	111	29	attitude	attitude	NOUN
ap-1811	111	30	to	to	ADP
ap-1811	111	31	the	the	DET
ap-1811	111	32	arrow	arrow	NOUN
ap-1811	111	33	of	of	ADP
ap-1811	111	34	time	time	NOUN
ap-1811	111	35	.	.	PUNCT
ap-1811	112	1	typically	typically	ADV
ap-1811	112	2	the	the	DET
ap-1811	112	3	problem	problem	NOUN
ap-1811	112	4	with	with	ADP
ap-1811	112	5	options	option	NOUN
ap-1811	112	6	is	be	AUX
ap-1811	112	7	to	to	PART
ap-1811	112	8	determine	determine	VERB
ap-1811	112	9	the	the	DET
ap-1811	112	10	price	price	NOUN
ap-1811	112	11	which	which	PRON
ap-1811	112	12	one	one	PRON
ap-1811	112	13	should	should	AUX
ap-1811	112	14	pay	pay	VERB
ap-1811	112	15	now	now	ADV
ap-1811	112	16	,	,	PUNCT
ap-1811	112	17	say	say	INTJ
ap-1811	112	18	,	,	PUNCT
ap-1811	112	19	to	to	PART
ap-1811	112	20	purchase	purchase	VERB
ap-1811	112	21	some	some	DET
ap-1811	112	22	stock	stock	NOUN
ap-1811	112	23	in	in	ADP
ap-1811	112	24	the	the	DET
ap-1811	112	25	future	future	NOUN
ap-1811	112	26	at	at	ADP
ap-1811	112	27	a	a	DET
ap-1811	112	28	now	now	ADV
ap-1811	112	29	-	-	PUNCT
ap-1811	112	30	determined	determine	VERB
ap-1811	112	31	price	price	NOUN
ap-1811	112	32	.	.	PUNCT
ap-1811	113	1	i	i	PRON
ap-1811	113	2	suspect	suspect	VERB
ap-1811	113	3	that	that	SCONJ
ap-1811	113	4	we	we	PRON
ap-1811	113	5	all	all	PRON
ap-1811	113	6	have	have	VERB
ap-1811	113	7	our	our	PRON
ap-1811	113	8	favourites	favourite	NOUN
ap-1811	113	9	ways	way	NOUN
ap-1811	113	10	to	to	PART
ap-1811	113	11	write	write	VERB
ap-1811	113	12	the	the	DET
ap-1811	113	13	one	one	NUM
ap-1811	113	14	-	-	PUNCT
ap-1811	113	15	parameter	parameter	NOUN
ap-1811	113	16	elements	element	NOUN
ap-1811	113	17	of	of	ADP
ap-1811	113	18	the	the	DET
ap-1811	113	19	lie	lie	NOUN
ap-1811	113	20	symmetries	symmetry	NOUN
ap-1811	113	21	of	of	ADP
ap-1811	113	22	a	a	DET
ap-1811	113	23	differential	differential	ADJ
ap-1811	113	24	equation	equation	NOUN
ap-1811	113	25	.	.	PUNCT
ap-1811	114	1	nevertheless	nevertheless	ADV
ap-1811	114	2	it	it	PRON
ap-1811	114	3	is	be	AUX
ap-1811	114	4	well	well	ADV
ap-1811	114	5	that	that	SCONJ
ap-1811	114	6	from	from	ADP
ap-1811	114	7	time	time	NOUN
ap-1811	114	8	to	to	ADP
ap-1811	114	9	time	time	NOUN
ap-1811	114	10	we	we	PRON
ap-1811	114	11	should	should	AUX
ap-1811	114	12	be	be	AUX
ap-1811	114	13	reminded	remind	VERB
ap-1811	114	14	that	that	SCONJ
ap-1811	114	15	the	the	DET
ap-1811	114	16	differential	differential	ADJ
ap-1811	114	17	equation	equation	NOUN
ap-1811	114	18	admits	admit	VERB
ap-1811	114	19	a	a	DET
ap-1811	114	20	single	single	ADJ
ap-1811	114	21	symmetry	symmetry	NOUN
ap-1811	114	22	.	.	PUNCT
ap-1811	115	1	if	if	SCONJ
ap-1811	115	2	we	we	PRON
ap-1811	115	3	are	be	AUX
ap-1811	115	4	fortunate	fortunate	ADJ
ap-1811	115	5	,	,	PUNCT
ap-1811	115	6	the	the	DET
ap-1811	115	7	single	single	ADJ
ap-1811	115	8	symmetry	symmetry	NOUN
ap-1811	115	9	will	will	AUX
ap-1811	115	10	be	be	AUX
ap-1811	115	11	a	a	DET
ap-1811	115	12	multiparameter	multiparameter	NOUN
ap-1811	115	13	symmetry	symmetry	NOUN
ap-1811	115	14	which	which	PRON
ap-1811	115	15	gives	give	VERB
ap-1811	115	16	some	some	DET
ap-1811	115	17	freedom	freedom	NOUN
ap-1811	115	18	when	when	SCONJ
ap-1811	115	19	it	it	PRON
ap-1811	115	20	comes	come	VERB
ap-1811	115	21	to	to	ADP
ap-1811	115	22	dealing	deal	VERB
ap-1811	115	23	with	with	ADP
ap-1811	115	24	the	the	DET
ap-1811	115	25	dreaded	dread	VERB
ap-1811	115	26	boundary	boundary	ADJ
ap-1811	115	27	/	/	SYM
ap-1811	115	28	initial	initial	ADJ
ap-1811	115	29	conditions	condition	NOUN
ap-1811	115	30	.	.	PUNCT
ap-1811	116	1	consider	consider	VERB
ap-1811	116	2	the	the	DET
ap-1811	116	3	case	case	NOUN
ap-1811	116	4	of	of	ADP
ap-1811	116	5	the	the	DET
ap-1811	116	6	black	black	ADJ
ap-1811	116	7	-	-	PUNCT
ap-1811	116	8	scholesmerton	scholesmerton	NOUN
ap-1811	116	9	equation	equation	NOUN
ap-1811	116	10	,	,	PUNCT
ap-1811	116	11	(	(	PUNCT
ap-1811	116	12	∗	∗	NOUN
ap-1811	116	13	)	)	PUNCT
ap-1811	116	14	,	,	PUNCT
ap-1811	116	15	and	and	CCONJ
ap-1811	116	16	the	the	DET
ap-1811	116	17	terminal	terminal	ADJ
ap-1811	116	18	condition	condition	NOUN
ap-1811	116	19	u(t	u(t	NOUN
ap-1811	116	20	,	,	PUNCT
ap-1811	116	21	x	x	X
ap-1811	116	22	)	)	PUNCT
ap-1811	116	23	=	=	SYM
ap-1811	116	24	u	u	NOUN
ap-1811	116	25	when	when	SCONJ
ap-1811	116	26	t	t	PROPN
ap-1811	116	27	=	=	SYM
ap-1811	116	28	t	t	PROPN
ap-1811	116	29	.	.	PUNCT
ap-1811	117	1	we	we	PRON
ap-1811	117	2	need	need	VERB
ap-1811	117	3	a	a	DET
ap-1811	117	4	symmetry	symmetry	NOUN
ap-1811	117	5	which	which	DET
ap-1811	117	6	304	304	NUM
ap-1811	117	7	vol	vol	NOUN
ap-1811	117	8	.	.	PUNCT
ap-1811	118	1	53	53	NUM
ap-1811	118	2	no	no	NOUN
ap-1811	118	3	.	.	PUNCT
ap-1811	119	1	3/2013	3/2013	PROPN
ap-1811	119	2	emmy	emmy	ADJ
ap-1811	119	3	noether	noether	PROPN
ap-1811	119	4	and	and	CCONJ
ap-1811	119	5	linear	linear	ADJ
ap-1811	119	6	evolution	evolution	NOUN
ap-1811	119	7	equations	equation	NOUN
ap-1811	119	8	is	be	AUX
ap-1811	119	9	compatible	compatible	ADJ
ap-1811	119	10	with	with	ADP
ap-1811	119	11	these	these	DET
ap-1811	119	12	conditions	condition	NOUN
ap-1811	119	13	.	.	PUNCT
ap-1811	120	1	we	we	PRON
ap-1811	120	2	write	write	VERB
ap-1811	120	3	the	the	DET
ap-1811	120	4	symmetry	symmetry	NOUN
ap-1811	120	5	of	of	ADP
ap-1811	120	6	(	(	PUNCT
ap-1811	120	7	∗	∗	NOUN
ap-1811	120	8	)	)	PUNCT
ap-1811	120	9	as	as	ADP
ap-1811	120	10	γ	γ	PROPN
ap-1811	120	11	=	=	SYM
ap-1811	120	12	σi=6	σi=6	PROPN
ap-1811	120	13	i=1αiγi	i=1αiγi	NOUN
ap-1811	120	14	and	and	CCONJ
ap-1811	120	15	apply	apply	VERB
ap-1811	120	16	this	this	DET
ap-1811	120	17	general	general	ADJ
ap-1811	120	18	symmetry	symmetry	NOUN
ap-1811	120	19	to	to	ADP
ap-1811	120	20	the	the	DET
ap-1811	120	21	dual	dual	ADJ
ap-1811	120	22	terminal	terminal	ADJ
ap-1811	120	23	conditions	condition	NOUN
ap-1811	120	24	.	.	PUNCT
ap-1811	121	1	note	note	VERB
ap-1811	121	2	that	that	SCONJ
ap-1811	121	3	the	the	DET
ap-1811	121	4	solution	solution	NOUN
ap-1811	121	5	symmetries	symmetry	NOUN
ap-1811	121	6	,	,	PUNCT
ap-1811	121	7	the	the	DET
ap-1811	121	8	components	component	NOUN
ap-1811	121	9	of	of	ADP
ap-1811	121	10	the	the	DET
ap-1811	121	11	subalgebra	subalgebra	NOUN
ap-1811	121	12	∞a1	∞a1	NUM
ap-1811	121	13	,	,	PUNCT
ap-1811	121	14	do	do	AUX
ap-1811	121	15	not	not	PART
ap-1811	121	16	enter	enter	VERB
ap-1811	121	17	into	into	ADP
ap-1811	121	18	the	the	DET
ap-1811	121	19	discussion	discussion	NOUN
ap-1811	121	20	.	.	PUNCT
ap-1811	122	1	the	the	DET
ap-1811	122	2	details	detail	NOUN
ap-1811	122	3	of	of	ADP
ap-1811	122	4	the	the	DET
ap-1811	122	5	calculation	calculation	NOUN
ap-1811	122	6	are	be	AUX
ap-1811	122	7	irrelevant	irrelevant	ADJ
ap-1811	122	8	for	for	ADP
ap-1811	122	9	our	our	PRON
ap-1811	122	10	present	present	ADJ
ap-1811	122	11	purpose	purpose	NOUN
ap-1811	122	12	.	.	PUNCT
ap-1811	123	1	suffice	suffice	VERB
ap-1811	123	2	it	it	PRON
ap-1811	123	3	to	to	PART
ap-1811	123	4	say	say	VERB
ap-1811	123	5	that	that	SCONJ
ap-1811	123	6	the	the	DET
ap-1811	123	7	six	six	NUM
ap-1811	123	8	constants	constant	NOUN
ap-1811	123	9	in	in	ADP
ap-1811	123	10	the	the	DET
ap-1811	123	11	general	general	ADJ
ap-1811	123	12	form	form	NOUN
ap-1811	123	13	of	of	ADP
ap-1811	123	14	γ	γ	NOUN
ap-1811	123	15	are	be	AUX
ap-1811	123	16	constrained	constrain	VERB
ap-1811	123	17	to	to	PART
ap-1811	123	18	give	give	VERB
ap-1811	123	19	two	two	NUM
ap-1811	123	20	oneparameter	oneparameter	ADJ
ap-1811	123	21	symmetries	symmetry	NOUN
ap-1811	123	22	.	.	PUNCT
ap-1811	124	1	in	in	ADP
ap-1811	124	2	general	general	ADJ
ap-1811	124	3	the	the	DET
ap-1811	124	4	algebra	algebra	NOUN
ap-1811	124	5	of	of	ADP
ap-1811	124	6	these	these	DET
ap-1811	124	7	symmetries	symmetry	NOUN
ap-1811	124	8	is	be	AUX
ap-1811	124	9	non	non	ADJ
ap-1811	124	10	-	-	ADJ
ap-1811	124	11	abelian	abelian	ADJ
ap-1811	124	12	.	.	PUNCT
ap-1811	125	1	fortunately	fortunately	ADV
ap-1811	125	2	there	there	PRON
ap-1811	125	3	is	be	VERB
ap-1811	125	4	a	a	DET
ap-1811	125	5	very	very	ADV
ap-1811	125	6	useful	useful	ADJ
ap-1811	125	7	theorem	theorem	NOUN
ap-1811	125	8	which	which	PRON
ap-1811	125	9	guarantees	guarantee	VERB
ap-1811	125	10	the	the	DET
ap-1811	125	11	uniqueness	uniqueness	NOUN
ap-1811	125	12	of	of	ADP
ap-1811	125	13	the	the	DET
ap-1811	125	14	solution	solution	NOUN
ap-1811	125	15	of	of	ADP
ap-1811	125	16	the	the	DET
ap-1811	125	17	equation	equation	NOUN
ap-1811	125	18	under	under	ADP
ap-1811	125	19	these	these	DET
ap-1811	125	20	circumstances	circumstance	NOUN
ap-1811	125	21	.	.	PUNCT
ap-1811	126	1	consequently	consequently	ADV
ap-1811	126	2	one	one	NUM
ap-1811	126	3	chooses	choose	VERB
ap-1811	126	4	the	the	DET
ap-1811	126	5	simpler	simple	ADJ
ap-1811	126	6	symmetry	symmetry	NOUN
ap-1811	126	7	for	for	ADP
ap-1811	126	8	further	further	ADJ
ap-1811	126	9	calculation	calculation	NOUN
ap-1811	126	10	.	.	PUNCT
ap-1811	127	1	6	6	X
ap-1811	127	2	.	.	X
ap-1811	127	3	tantum	tantum	PROPN
ap-1811	127	4	adesse	adesse	PROPN
ap-1811	128	1	i	i	PRON
ap-1811	128	2	have	have	AUX
ap-1811	128	3	concentrated	concentrate	VERB
ap-1811	128	4	in	in	ADP
ap-1811	128	5	the	the	DET
ap-1811	128	6	end	end	NOUN
ap-1811	128	7	on	on	ADP
ap-1811	128	8	the	the	DET
ap-1811	128	9	applications	application	NOUN
ap-1811	128	10	of	of	ADP
ap-1811	128	11	symmetry	symmetry	NOUN
ap-1811	128	12	to	to	ADP
ap-1811	128	13	the	the	DET
ap-1811	128	14	equations	equation	NOUN
ap-1811	128	15	of	of	ADP
ap-1811	128	16	financial	financial	ADJ
ap-1811	128	17	mathematics	mathematic	NOUN
ap-1811	128	18	,	,	PUNCT
ap-1811	128	19	but	but	CCONJ
ap-1811	128	20	it	it	PRON
ap-1811	128	21	is	be	AUX
ap-1811	128	22	quite	quite	ADV
ap-1811	128	23	evident	evident	ADJ
ap-1811	128	24	that	that	SCONJ
ap-1811	128	25	these	these	DET
ap-1811	128	26	considerations	consideration	NOUN
ap-1811	128	27	apply	apply	VERB
ap-1811	128	28	to	to	ADP
ap-1811	128	29	evolution	evolution	NOUN
ap-1811	128	30	equations	equation	NOUN
ap-1811	128	31	wherever	wherever	SCONJ
ap-1811	128	32	they	they	PRON
ap-1811	128	33	arise	arise	VERB
ap-1811	128	34	.	.	PUNCT
ap-1811	129	1	the	the	DET
ap-1811	129	2	connection	connection	NOUN
ap-1811	129	3	between	between	ADP
ap-1811	129	4	the	the	DET
ap-1811	129	5	lie	lie	NOUN
ap-1811	129	6	point	point	NOUN
ap-1811	129	7	symmetries	symmetry	NOUN
ap-1811	129	8	of	of	ADP
ap-1811	129	9	these	these	DET
ap-1811	129	10	evolution	evolution	NOUN
ap-1811	129	11	partial	partial	ADJ
ap-1811	129	12	differential	differential	NOUN
ap-1811	129	13	equations	equation	NOUN
ap-1811	129	14	and	and	CCONJ
ap-1811	129	15	the	the	DET
ap-1811	129	16	noether	noether	ADJ
ap-1811	129	17	point	point	NOUN
ap-1811	129	18	symmetries	symmetry	NOUN
ap-1811	129	19	classical	classical	ADJ
ap-1811	129	20	lagrangians	lagrangian	NOUN
ap-1811	129	21	has	have	AUX
ap-1811	129	22	not	not	PART
ap-1811	129	23	been	be	AUX
ap-1811	129	24	exploited	exploit	VERB
ap-1811	129	25	.	.	PUNCT
ap-1811	130	1	it	it	PRON
ap-1811	130	2	may	may	AUX
ap-1811	130	3	well	well	ADV
ap-1811	130	4	be	be	AUX
ap-1811	130	5	that	that	PRON
ap-1811	130	6	for	for	ADP
ap-1811	130	7	1	1	NUM
ap-1811	130	8	+	+	SYM
ap-1811	130	9	1	1	NUM
ap-1811	130	10	evolution	evolution	NOUN
ap-1811	130	11	equations	equation	NOUN
ap-1811	130	12	the	the	DET
ap-1811	130	13	degree	degree	NOUN
ap-1811	130	14	of	of	ADP
ap-1811	130	15	exploitation	exploitation	NOUN
ap-1811	130	16	may	may	AUX
ap-1811	130	17	be	be	AUX
ap-1811	130	18	limited	limit	VERB
ap-1811	130	19	.	.	PUNCT
ap-1811	131	1	however	however	ADV
ap-1811	131	2	,	,	PUNCT
ap-1811	131	3	when	when	SCONJ
ap-1811	131	4	it	it	PRON
ap-1811	131	5	comes	come	VERB
ap-1811	131	6	to	to	ADP
ap-1811	131	7	more	more	ADJ
ap-1811	131	8	degrees	degree	NOUN
ap-1811	131	9	of	of	ADP
ap-1811	131	10	freedom	freedom	NOUN
ap-1811	131	11	–	–	PUNCT
ap-1811	131	12	as	as	ADP
ap-1811	131	13	in	in	ADP
ap-1811	131	14	the	the	DET
ap-1811	131	15	commodities	commodity	NOUN
ap-1811	131	16	model	model	NOUN
ap-1811	131	17	of	of	ADP
ap-1811	131	18	schwartz	schwartz	PROPN
ap-1811	131	19	–	–	PUNCT
ap-1811	131	20	there	there	PRON
ap-1811	131	21	may	may	AUX
ap-1811	131	22	be	be	AUX
ap-1811	131	23	some	some	DET
ap-1811	131	24	benefit	benefit	NOUN
ap-1811	131	25	in	in	ADP
ap-1811	131	26	the	the	DET
ap-1811	131	27	investigation	investigation	NOUN
ap-1811	131	28	of	of	ADP
ap-1811	131	29	the	the	DET
ap-1811	131	30	properties	property	NOUN
ap-1811	131	31	that	that	PRON
ap-1811	131	32	the	the	DET
ap-1811	131	33	classically	classically	ADV
ap-1811	131	34	conserved	conserve	VERB
ap-1811	131	35	quantities	quantity	NOUN
ap-1811	131	36	may	may	AUX
ap-1811	131	37	have	have	VERB
ap-1811	131	38	for	for	ADP
ap-1811	131	39	these	these	DET
ap-1811	131	40	evolution	evolution	NOUN
ap-1811	131	41	equations	equation	NOUN
ap-1811	131	42	.	.	PUNCT
ap-1811	132	1	finally	finally	ADV
ap-1811	132	2	there	there	PRON
ap-1811	132	3	are	be	VERB
ap-1811	132	4	the	the	DET
ap-1811	132	5	questions	question	NOUN
ap-1811	132	6	of	of	ADP
ap-1811	132	7	alternate	alternate	ADJ
ap-1811	132	8	lagrangians	lagrangian	NOUN
ap-1811	132	9	and	and	CCONJ
ap-1811	132	10	of	of	ADP
ap-1811	132	11	evolution	evolution	NOUN
ap-1811	132	12	equations	equation	NOUN
ap-1811	132	13	which	which	PRON
ap-1811	132	14	are	be	AUX
ap-1811	132	15	not	not	PART
ap-1811	132	16	presumed	presume	VERB
ap-1811	132	17	to	to	PART
ap-1811	132	18	be	be	AUX
ap-1811	132	19	linear	linear	ADJ
ap-1811	132	20	.	.	PUNCT
ap-1811	133	1	acknowledgements	acknowledgement	NOUN
ap-1811	133	2	this	this	DET
ap-1811	133	3	contribution	contribution	NOUN
ap-1811	133	4	was	be	AUX
ap-1811	133	5	prepared	prepare	VERB
ap-1811	133	6	while	while	SCONJ
ap-1811	133	7	pgll	pgll	NOUN
ap-1811	133	8	was	be	AUX
ap-1811	133	9	enjoying	enjoy	VERB
ap-1811	133	10	the	the	DET
ap-1811	133	11	hospitality	hospitality	NOUN
ap-1811	133	12	of	of	ADP
ap-1811	133	13	professor	professor	NOUN
ap-1811	133	14	mc	mc	PROPN
ap-1811	133	15	nucci	nucci	ADV
ap-1811	133	16	and	and	CCONJ
ap-1811	133	17	the	the	DET
ap-1811	133	18	dipartimento	dipartimento	NOUN
ap-1811	133	19	di	di	X
ap-1811	133	20	matematica	matematica	PROPN
ap-1811	133	21	e	e	PROPN
ap-1811	133	22	informatica	informatica	PROPN
ap-1811	133	23	,	,	PUNCT
ap-1811	133	24	università	università	PROPN
ap-1811	133	25	di	di	PROPN
ap-1811	133	26	perugia	perugia	PROPN
ap-1811	133	27	.	.	PUNCT
ap-1811	134	1	the	the	DET
ap-1811	134	2	continuing	continue	VERB
ap-1811	134	3	support	support	NOUN
ap-1811	134	4	of	of	ADP
ap-1811	134	5	the	the	DET
ap-1811	134	6	university	university	NOUN
ap-1811	134	7	of	of	ADP
ap-1811	134	8	kwazulunatal	kwazulunatal	NOUN
ap-1811	134	9	and	and	CCONJ
ap-1811	134	10	the	the	DET
ap-1811	134	11	national	national	PROPN
ap-1811	134	12	research	research	PROPN
ap-1811	134	13	foundation	foundation	PROPN
ap-1811	134	14	of	of	ADP
ap-1811	134	15	south	south	PROPN
ap-1811	134	16	africa	africa	PROPN
ap-1811	134	17	is	be	AUX
ap-1811	134	18	gratefully	gratefully	ADV
ap-1811	134	19	acknowledged	acknowledge	VERB
ap-1811	134	20	.	.	PUNCT
ap-1811	135	1	any	any	DET
ap-1811	135	2	opinions	opinion	NOUN
ap-1811	135	3	expressed	express	VERB
ap-1811	135	4	in	in	ADP
ap-1811	135	5	this	this	DET
ap-1811	135	6	talk	talk	NOUN
ap-1811	135	7	should	should	AUX
ap-1811	135	8	not	not	PART
ap-1811	135	9	be	be	AUX
ap-1811	135	10	construed	construe	VERB
ap-1811	135	11	as	as	ADP
ap-1811	135	12	being	be	AUX
ap-1811	135	13	those	those	PRON
ap-1811	135	14	of	of	ADP
ap-1811	135	15	the	the	DET
ap-1811	135	16	latter	latter	ADJ
ap-1811	135	17	two	two	NUM
ap-1811	135	18	institutions	institution	NOUN
ap-1811	135	19	.	.	PUNCT
ap-1811	136	1	references	reference	NOUN
ap-1811	136	2	[	[	X
ap-1811	136	3	1	1	NUM
ap-1811	136	4	]	]	X
ap-1811	136	5	black	black	ADJ
ap-1811	136	6	fischer	fischer	PROPN
ap-1811	136	7	&	&	CCONJ
ap-1811	136	8	scholes	scholes	PROPN
ap-1811	136	9	myron	myron	PROPN
ap-1811	136	10	(	(	PUNCT
ap-1811	136	11	1972	1972	NUM
ap-1811	136	12	)	)	PUNCT
ap-1811	136	13	the	the	DET
ap-1811	136	14	valuation	valuation	NOUN
ap-1811	136	15	of	of	ADP
ap-1811	136	16	option	option	NOUN
ap-1811	136	17	contracts	contract	NOUN
ap-1811	136	18	and	and	CCONJ
ap-1811	136	19	a	a	DET
ap-1811	136	20	test	test	NOUN
ap-1811	136	21	of	of	ADP
ap-1811	136	22	market	market	NOUN
ap-1811	136	23	efficiency	efficiency	NOUN
ap-1811	136	24	journal	journal	NOUN
ap-1811	136	25	of	of	ADP
ap-1811	136	26	finance	finance	NOUN
ap-1811	136	27	27	27	NUM
ap-1811	136	28	399–417	399–417	NUM
ap-1811	136	29	.	.	PUNCT
ap-1811	137	1	[	[	X
ap-1811	137	2	2	2	NUM
ap-1811	137	3	]	]	X
ap-1811	137	4	black	black	ADJ
ap-1811	137	5	fischer	fischer	PROPN
ap-1811	137	6	&	&	CCONJ
ap-1811	137	7	scholes	scholes	PROPN
ap-1811	137	8	myron	myron	PROPN
ap-1811	137	9	(	(	PUNCT
ap-1811	137	10	1973	1973	NUM
ap-1811	137	11	)	)	PUNCT
ap-1811	137	12	the	the	DET
ap-1811	137	13	pricing	pricing	NOUN
ap-1811	137	14	of	of	ADP
ap-1811	137	15	options	option	NOUN
ap-1811	137	16	and	and	CCONJ
ap-1811	137	17	corporate	corporate	ADJ
ap-1811	137	18	liabilities	liability	NOUN
ap-1811	137	19	journal	journal	NOUN
ap-1811	137	20	of	of	ADP
ap-1811	137	21	political	political	ADJ
ap-1811	137	22	economy	economy	NOUN
ap-1811	137	23	81	81	NUM
ap-1811	137	24	637–659	637–659	NUM
ap-1811	137	25	.	.	PUNCT
ap-1811	138	1	[	[	X
ap-1811	138	2	3	3	X
ap-1811	138	3	]	]	X
ap-1811	138	4	brennan	brennan	PROPN
ap-1811	138	5	mj	mj	PROPN
ap-1811	138	6	&	&	CCONJ
ap-1811	138	7	schwartz	schwartz	PROPN
ap-1811	138	8	es	es	PROPN
ap-1811	138	9	(	(	PUNCT
ap-1811	138	10	1985	1985	NUM
ap-1811	138	11	)	)	PUNCT
ap-1811	138	12	evaluating	evaluate	VERB
ap-1811	138	13	natural	natural	ADJ
ap-1811	138	14	resource	resource	NOUN
ap-1811	138	15	investments	investment	NOUN
ap-1811	138	16	journal	journal	NOUN
ap-1811	138	17	of	of	ADP
ap-1811	138	18	business	business	NOUN
ap-1811	138	19	58	58	NUM
ap-1811	138	20	133–155	133–155	NUM
ap-1811	138	21	.	.	PUNCT
ap-1811	139	1	[	[	X
ap-1811	139	2	4	4	NUM
ap-1811	139	3	]	]	X
ap-1811	139	4	dirac	dirac	NOUN
ap-1811	139	5	pam	pam	NOUN
ap-1811	139	6	(	(	PUNCT
ap-1811	139	7	1932	1932	NUM
ap-1811	139	8	)	)	PUNCT
ap-1811	139	9	the	the	DET
ap-1811	139	10	principles	principle	NOUN
ap-1811	139	11	of	of	ADP
ap-1811	139	12	quantum	quantum	ADJ
ap-1811	139	13	mechanics	mechanic	NOUN
ap-1811	139	14	(	(	PUNCT
ap-1811	139	15	cambridge	cambridge	PROPN
ap-1811	139	16	,	,	PUNCT
ap-1811	139	17	at	at	ADP
ap-1811	139	18	the	the	DET
ap-1811	139	19	clarendon	clarendon	PROPN
ap-1811	139	20	press	press	NOUN
ap-1811	139	21	)	)	PUNCT
ap-1811	139	22	.	.	PUNCT
ap-1811	140	1	[	[	X
ap-1811	140	2	5	5	NUM
ap-1811	140	3	]	]	PUNCT
ap-1811	140	4	gasizov	gasizov	NOUN
ap-1811	140	5	r	r	NOUN
ap-1811	140	6	&	&	CCONJ
ap-1811	140	7	ibragimov	ibragimov	ADJ
ap-1811	140	8	nh	nh	PROPN
ap-1811	140	9	(	(	PUNCT
ap-1811	140	10	1998	1998	NUM
ap-1811	140	11	)	)	PUNCT
ap-1811	140	12	lie	lie	NOUN
ap-1811	140	13	symmetry	symmetry	NOUN
ap-1811	140	14	analysis	analysis	NOUN
ap-1811	140	15	of	of	ADP
ap-1811	140	16	differential	differential	ADJ
ap-1811	140	17	equations	equation	NOUN
ap-1811	140	18	in	in	ADP
ap-1811	140	19	finance	finance	NOUN
ap-1811	140	20	nonlinear	nonlinear	ADJ
ap-1811	140	21	dynamics	dynamic	NOUN
ap-1811	140	22	17	17	NUM
ap-1811	140	23	387–407	387–407	NUM
ap-1811	140	24	.	.	PUNCT
ap-1811	141	1	[	[	X
ap-1811	141	2	6	6	NUM
ap-1811	141	3	]	]	PUNCT
ap-1811	141	4	gibson	gibson	PROPN
ap-1811	141	5	r	r	PROPN
ap-1811	141	6	&	&	CCONJ
ap-1811	141	7	schwartz	schwartz	PROPN
ap-1811	141	8	es	es	PROPN
ap-1811	141	9	(	(	PUNCT
ap-1811	141	10	1990	1990	NUM
ap-1811	141	11	)	)	PUNCT
ap-1811	141	12	stochastic	stochastic	ADJ
ap-1811	141	13	convenience	convenience	NOUN
ap-1811	141	14	yield	yield	NOUN
ap-1811	141	15	and	and	CCONJ
ap-1811	141	16	the	the	DET
ap-1811	141	17	pricing	pricing	NOUN
ap-1811	141	18	of	of	ADP
ap-1811	141	19	oil	oil	NOUN
ap-1811	141	20	contingent	contingent	NOUN
ap-1811	141	21	claims	claim	NOUN
ap-1811	141	22	journal	journal	NOUN
ap-1811	141	23	of	of	ADP
ap-1811	141	24	finance	finance	NOUN
ap-1811	141	25	45	45	NUM
ap-1811	141	26	959–976	959–976	NUM
ap-1811	141	27	.	.	PUNCT
ap-1811	142	1	[	[	X
ap-1811	142	2	7	7	NUM
ap-1811	142	3	]	]	X
ap-1811	142	4	ibragimov	ibragimov	ADJ
ap-1811	142	5	nh	nh	PROPN
ap-1811	142	6	&	&	CCONJ
ap-1811	142	7	wafo	wafo	PROPN
ap-1811	142	8	soh	soh	PROPN
ap-1811	142	9	c	c	PROPN
ap-1811	142	10	(	(	PUNCT
ap-1811	142	11	1997	1997	NUM
ap-1811	142	12	)	)	PUNCT
ap-1811	142	13	solution	solution	NOUN
ap-1811	142	14	of	of	ADP
ap-1811	142	15	the	the	DET
ap-1811	142	16	cauchy	cauchy	ADJ
ap-1811	142	17	problem	problem	NOUN
ap-1811	142	18	for	for	ADP
ap-1811	142	19	the	the	DET
ap-1811	142	20	black	black	ADJ
ap-1811	142	21	-	-	PUNCT
ap-1811	142	22	scholes	schole	NOUN
ap-1811	142	23	equation	equation	NOUN
ap-1811	142	24	using	use	VERB
ap-1811	142	25	its	its	PRON
ap-1811	142	26	symmetries	symmetry	NOUN
ap-1811	142	27	modern	modern	ADJ
ap-1811	142	28	group	group	NOUN
ap-1811	142	29	analysis	analysis	NOUN
ap-1811	142	30	,	,	PUNCT
ap-1811	142	31	international	international	ADJ
ap-1811	142	32	conference	conference	NOUN
ap-1811	142	33	at	at	ADP
ap-1811	142	34	the	the	DET
ap-1811	142	35	sophus	sophus	PROPN
ap-1811	142	36	lie	lie	NOUN
ap-1811	142	37	conference	conference	NOUN
ap-1811	142	38	centre	centre	PROPN
ap-1811	142	39	ibragimov	ibragimov	PROPN
ap-1811	142	40	nh	nh	PROPN
ap-1811	142	41	,	,	PUNCT
ap-1811	142	42	naqvi	naqvi	PROPN
ap-1811	142	43	kr	kr	PROPN
ap-1811	142	44	&	&	CCONJ
ap-1811	142	45	straume	straume	PROPN
ap-1811	142	46	e	e	PROPN
ap-1811	142	47	edd	edd	PROPN
ap-1811	142	48	(	(	PUNCT
ap-1811	142	49	mars	mar	NOUN
ap-1811	142	50	publishers	publisher	NOUN
ap-1811	142	51	,	,	PUNCT
ap-1811	142	52	norway	norway	PROPN
ap-1811	142	53	)	)	PUNCT
ap-1811	142	54	.	.	PUNCT
ap-1811	143	1	[	[	X
ap-1811	143	2	8	8	NUM
ap-1811	143	3	]	]	PUNCT
ap-1811	143	4	leach	leach	NOUN
ap-1811	143	5	pgl	pgl	NOUN
ap-1811	143	6	(	(	PUNCT
ap-1811	143	7	2006	2006	NUM
ap-1811	143	8	)	)	PUNCT
ap-1811	143	9	heat	heat	NOUN
ap-1811	143	10	polynomials	polynomial	NOUN
ap-1811	143	11	and	and	CCONJ
ap-1811	143	12	lie	lie	NOUN
ap-1811	143	13	point	point	NOUN
ap-1811	143	14	symmetries	symmetries	PROPN
ap-1811	143	15	journal	journal	PROPN
ap-1811	143	16	of	of	ADP
ap-1811	143	17	mathematical	mathematical	ADJ
ap-1811	143	18	analysis	analysis	NOUN
ap-1811	143	19	and	and	CCONJ
ap-1811	143	20	applications	application	NOUN
ap-1811	143	21	322	322	NUM
ap-1811	143	22	288–297	288–297	NUM
ap-1811	143	23	.	.	PUNCT
ap-1811	144	1	[	[	X
ap-1811	144	2	9	9	NUM
ap-1811	144	3	]	]	SYM
ap-1811	144	4	merton	merton	PROPN
ap-1811	144	5	rc	rc	PROPN
ap-1811	144	6	(	(	PUNCT
ap-1811	144	7	1969	1969	NUM
ap-1811	144	8	)	)	PUNCT
ap-1811	144	9	lifetime	lifetime	NOUN
ap-1811	144	10	portfolio	portfolio	NOUN
ap-1811	144	11	selection	selection	NOUN
ap-1811	144	12	under	under	ADP
ap-1811	144	13	uncertainty	uncertainty	NOUN
ap-1811	144	14	:	:	PUNCT
ap-1811	144	15	the	the	DET
ap-1811	144	16	continuous	continuous	ADJ
ap-1811	144	17	-	-	PUNCT
ap-1811	144	18	time	time	NOUN
ap-1811	144	19	case	case	NOUN
ap-1811	144	20	review	review	NOUN
ap-1811	144	21	of	of	ADP
ap-1811	144	22	economics	economic	NOUN
ap-1811	144	23	and	and	CCONJ
ap-1811	144	24	statistics	statistic	NOUN
ap-1811	144	25	51	51	NUM
ap-1811	144	26	247–257	247–257	NUM
ap-1811	144	27	.	.	PUNCT
ap-1811	145	1	[	[	X
ap-1811	145	2	10	10	NUM
ap-1811	145	3	]	]	SYM
ap-1811	145	4	merton	merton	PROPN
ap-1811	145	5	rc	rc	PROPN
ap-1811	145	6	(	(	PUNCT
ap-1811	145	7	1971	1971	NUM
ap-1811	145	8	)	)	PUNCT
ap-1811	145	9	consumption	consumption	NOUN
ap-1811	145	10	and	and	CCONJ
ap-1811	145	11	portfolio	portfolio	NOUN
ap-1811	145	12	rules	rule	NOUN
ap-1811	145	13	in	in	ADP
ap-1811	145	14	a	a	DET
ap-1811	145	15	continuous	continuous	ADJ
ap-1811	145	16	time	time	NOUN
ap-1811	145	17	model	model	PROPN
ap-1811	145	18	journal	journal	PROPN
ap-1811	145	19	of	of	ADP
ap-1811	145	20	economic	economic	ADJ
ap-1811	145	21	theory	theory	NOUN
ap-1811	145	22	3,4	3,4	NUM
ap-1811	145	23	373–413	373–413	NUM
ap-1811	145	24	.	.	PUNCT
ap-1811	146	1	[	[	X
ap-1811	146	2	11	11	NUM
ap-1811	146	3	]	]	SYM
ap-1811	146	4	merton	merton	PROPN
ap-1811	146	5	robert	robert	PROPN
ap-1811	146	6	c	c	PROPN
ap-1811	146	7	(	(	PUNCT
ap-1811	146	8	1973	1973	NUM
ap-1811	146	9	)	)	PUNCT
ap-1811	146	10	theory	theory	NOUN
ap-1811	146	11	of	of	ADP
ap-1811	146	12	rational	rational	ADJ
ap-1811	146	13	option	option	NOUN
ap-1811	146	14	pricing	pricing	NOUN
ap-1811	146	15	bell	bell	PROPN
ap-1811	146	16	journal	journal	PROPN
ap-1811	146	17	of	of	ADP
ap-1811	146	18	economics	economic	NOUN
ap-1811	146	19	and	and	CCONJ
ap-1811	146	20	management	management	NOUN
ap-1811	146	21	science	science	NOUN
ap-1811	146	22	4	4	NUM
ap-1811	146	23	141–183	141–183	NUM
ap-1811	146	24	.	.	PUNCT
ap-1811	147	1	[	[	X
ap-1811	147	2	12	12	NUM
ap-1811	147	3	]	]	SYM
ap-1811	147	4	merton	merton	PROPN
ap-1811	147	5	rc	rc	PROPN
ap-1811	147	6	(	(	PUNCT
ap-1811	147	7	1974	1974	NUM
ap-1811	147	8	)	)	PUNCT
ap-1811	147	9	on	on	ADP
ap-1811	147	10	the	the	DET
ap-1811	147	11	pricing	pricing	NOUN
ap-1811	147	12	of	of	ADP
ap-1811	147	13	corporate	corporate	ADJ
ap-1811	147	14	data	datum	NOUN
ap-1811	147	15	:	:	PUNCT
ap-1811	147	16	the	the	DET
ap-1811	147	17	risk	risk	NOUN
ap-1811	147	18	structure	structure	NOUN
ap-1811	147	19	of	of	ADP
ap-1811	147	20	interest	interest	NOUN
ap-1811	147	21	rates	rate	NOUN
ap-1811	147	22	journal	journal	NOUN
ap-1811	147	23	of	of	ADP
ap-1811	147	24	finance	finance	NOUN
ap-1811	147	25	29	29	NUM
ap-1811	147	26	449–470	449–470	NUM
ap-1811	147	27	.	.	PUNCT
ap-1811	148	1	[	[	X
ap-1811	148	2	13	13	NUM
ap-1811	148	3	]	]	X
ap-1811	148	4	noether	noether	ADJ
ap-1811	148	5	emmy	emmy	PROPN
ap-1811	148	6	(	(	PUNCT
ap-1811	148	7	1918	1918	NUM
ap-1811	148	8	)	)	PUNCT
ap-1811	148	9	invariante	invariante	PROPN
ap-1811	148	10	variationsprobleme	variationsprobleme	PROPN
ap-1811	148	11	königlich	königlich	PROPN
ap-1811	148	12	gesellschaft	gesellschaft	PROPN
ap-1811	148	13	der	der	NOUN
ap-1811	148	14	wissenschaften	wissenschaften	VERB
ap-1811	148	15	göttingen	göttingen	PROPN
ap-1811	148	16	nachrichten	nachrichten	PROPN
ap-1811	148	17	mathematik	mathematik	PROPN
ap-1811	148	18	-	-	PUNCT
ap-1811	148	19	physik	physik	PROPN
ap-1811	148	20	klasse	klasse	NOUN
ap-1811	148	21	2	2	NUM
ap-1811	148	22	235–267	235–267	NUM
ap-1811	148	23	.	.	PUNCT
ap-1811	149	1	[	[	X
ap-1811	149	2	14	14	NUM
ap-1811	149	3	]	]	X
ap-1811	149	4	schwartz	schwartz	PROPN
ap-1811	149	5	es	es	PROPN
ap-1811	149	6	(	(	PUNCT
ap-1811	149	7	1997	1997	NUM
ap-1811	149	8	)	)	PUNCT
ap-1811	149	9	the	the	DET
ap-1811	149	10	stochastic	stochastic	ADJ
ap-1811	149	11	behaviour	behaviour	NOUN
ap-1811	149	12	of	of	ADP
ap-1811	149	13	commodity	commodity	NOUN
ap-1811	149	14	prices	price	NOUN
ap-1811	149	15	:	:	PUNCT
ap-1811	149	16	implications	implication	NOUN
ap-1811	149	17	for	for	ADP
ap-1811	149	18	valuation	valuation	NOUN
ap-1811	149	19	and	and	CCONJ
ap-1811	149	20	hedging	hedge	VERB
ap-1811	149	21	the	the	DET
ap-1811	149	22	journal	journal	NOUN
ap-1811	149	23	of	of	ADP
ap-1811	149	24	finance	finance	NOUN
ap-1811	149	25	52	52	NUM
ap-1811	149	26	923–973	923–973	NUM
ap-1811	149	27	.	.	PUNCT
ap-1811	150	1	[	[	X
ap-1811	150	2	15	15	NUM
ap-1811	150	3	]	]	X
ap-1811	150	4	sophocleous	sophocleous	PROPN
ap-1811	150	5	c	c	NOUN
ap-1811	150	6	,	,	PUNCT
ap-1811	150	7	leach	leach	NOUN
ap-1811	150	8	pgl	pgl	NOUN
ap-1811	150	9	&	&	CCONJ
ap-1811	150	10	andriopoulos	andriopoulos	PROPN
ap-1811	150	11	k	k	PROPN
ap-1811	150	12	(	(	PUNCT
ap-1811	150	13	2008	2008	NUM
ap-1811	150	14	)	)	PUNCT
ap-1811	150	15	algebraic	algebraic	ADJ
ap-1811	150	16	properties	property	NOUN
ap-1811	150	17	of	of	ADP
ap-1811	150	18	evolution	evolution	NOUN
ap-1811	150	19	partial	partial	ADJ
ap-1811	150	20	differential	differential	NOUN
ap-1811	150	21	equations	equation	NOUN
ap-1811	150	22	modelling	model	VERB
ap-1811	150	23	prices	price	NOUN
ap-1811	150	24	of	of	ADP
ap-1811	150	25	commodities	commodity	NOUN
ap-1811	150	26	mathematical	mathematical	ADJ
ap-1811	150	27	methods	method	NOUN
ap-1811	150	28	in	in	ADP
ap-1811	150	29	the	the	DET
ap-1811	150	30	applied	apply	VERB
ap-1811	150	31	sciences	science	NOUN
ap-1811	150	32	31	31	NUM
ap-1811	150	33	679–694	679–694	NUM
ap-1811	150	34	.	.	PUNCT
ap-1811	151	1	305	305	NUM
ap-1811	151	2	acta	acta	PROPN
ap-1811	151	3	polytechnica	polytechnica	PROPN
ap-1811	151	4	53(3):302–305	53(3):302–305	PROPN
ap-1811	151	5	,	,	PUNCT
ap-1811	151	6	2013	2013	NUM
ap-1811	151	7	1	1	NUM
ap-1811	151	8	noether	noether	PROPN
ap-1811	151	9	's	's	PART
ap-1811	151	10	theorem	theorem	ADJ
ap-1811	151	11	2	2	NUM
ap-1811	151	12	quantisation	quantisation	NOUN
ap-1811	151	13	3	3	NUM
ap-1811	151	14	the	the	DET
ap-1811	151	15	heat	heat	NOUN
ap-1811	151	16	equation	equation	NOUN
ap-1811	151	17	4	4	NUM
ap-1811	151	18	the	the	DET
ap-1811	151	19	wonderful	wonderful	ADJ
ap-1811	151	20	world	world	NOUN
ap-1811	151	21	of	of	ADP
ap-1811	151	22	finance	finance	NOUN
ap-1811	151	23	5	5	NUM
ap-1811	151	24	initial	initial	ADJ
ap-1811	151	25	/	/	SYM
ap-1811	151	26	boundary	boundary	ADJ
ap-1811	151	27	conditions	condition	NOUN
ap-1811	151	28	6	6	NUM
ap-1811	151	29	tantum	tantum	PROPN
ap-1811	151	30	adesse	adesse	NOUN
ap-1811	151	31	acknowledgements	acknowledgement	NOUN
ap-1811	151	32	references	reference	NOUN