id	sid	tid	token	lemma	pos
ejpam-3868	1	1	european	european	PROPN
ejpam-3868	1	2	journal	journal	PROPN
ejpam-3868	1	3	of	of	ADP
ejpam-3868	1	4	pure	pure	ADJ
ejpam-3868	1	5	and	and	CCONJ
ejpam-3868	1	6	applied	apply	VERB
ejpam-3868	1	7	mathematics	mathematic	NOUN
ejpam-3868	1	8	vol	vol	NOUN
ejpam-3868	1	9	.	.	PROPN
ejpam-3868	2	1	13	13	NUM
ejpam-3868	2	2	,	,	PUNCT
ejpam-3868	2	3	no	no	INTJ
ejpam-3868	2	4	.	.	NOUN
ejpam-3868	2	5	4	4	NUM
ejpam-3868	2	6	,	,	PUNCT
ejpam-3868	2	7	2020	2020	NUM
ejpam-3868	2	8	,	,	PUNCT
ejpam-3868	2	9	1016	1016	NUM
ejpam-3868	2	10	-	-	SYM
ejpam-3868	2	11	1034	1034	NUM
ejpam-3868	2	12	issn	issn	PROPN
ejpam-3868	2	13	1307	1307	NUM
ejpam-3868	2	14	-	-	SYM
ejpam-3868	2	15	5543	5543	NUM
ejpam-3868	2	16	–	–	PUNCT
ejpam-3868	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3868	2	18	published	publish	VERB
ejpam-3868	2	19	by	by	ADP
ejpam-3868	2	20	new	new	PROPN
ejpam-3868	2	21	york	york	PROPN
ejpam-3868	2	22	business	business	PROPN
ejpam-3868	2	23	global	global	PROPN
ejpam-3868	2	24	cartan	cartan	PROPN
ejpam-3868	2	25	’s	’s	PART
ejpam-3868	2	26	approach	approach	NOUN
ejpam-3868	2	27	to	to	ADP
ejpam-3868	2	28	second	second	ADJ
ejpam-3868	2	29	order	order	NOUN
ejpam-3868	2	30	ordinary	ordinary	ADJ
ejpam-3868	2	31	differential	differential	ADJ
ejpam-3868	2	32	equations	equation	NOUN
ejpam-3868	2	33	paul	paul	PROPN
ejpam-3868	2	34	bracken	bracken	PROPN
ejpam-3868	2	35	department	department	PROPN
ejpam-3868	2	36	of	of	ADP
ejpam-3868	2	37	mathematics	mathematics	PROPN
ejpam-3868	2	38	,	,	PUNCT
ejpam-3868	2	39	university	university	PROPN
ejpam-3868	2	40	of	of	ADP
ejpam-3868	2	41	texas	texas	PROPN
ejpam-3868	2	42	,	,	PUNCT
ejpam-3868	2	43	edinburg	edinburg	PROPN
ejpam-3868	2	44	,	,	PUNCT
ejpam-3868	2	45	tx	tx	PROPN
ejpam-3868	2	46	,	,	PUNCT
ejpam-3868	2	47	78540	78540	NUM
ejpam-3868	2	48	-	-	SYM
ejpam-3868	2	49	2999	2999	NUM
ejpam-3868	2	50	,	,	PUNCT
ejpam-3868	2	51	usa	usa	PROPN
ejpam-3868	2	52	abstract	abstract	NOUN
ejpam-3868	2	53	.	.	PUNCT
ejpam-3868	3	1	in	in	ADP
ejpam-3868	3	2	his	his	PRON
ejpam-3868	3	3	work	work	NOUN
ejpam-3868	3	4	on	on	ADP
ejpam-3868	3	5	projective	projective	ADJ
ejpam-3868	3	6	connections	connection	NOUN
ejpam-3868	3	7	,	,	PUNCT
ejpam-3868	3	8	cartan	cartan	PROPN
ejpam-3868	3	9	discusses	discuss	VERB
ejpam-3868	3	10	his	his	PRON
ejpam-3868	3	11	theory	theory	NOUN
ejpam-3868	3	12	of	of	ADP
ejpam-3868	3	13	second	second	ADJ
ejpam-3868	3	14	order	order	NOUN
ejpam-3868	3	15	differential	differential	NOUN
ejpam-3868	3	16	equations	equation	NOUN
ejpam-3868	3	17	.	.	PUNCT
ejpam-3868	4	1	it	it	PRON
ejpam-3868	4	2	is	be	AUX
ejpam-3868	4	3	the	the	DET
ejpam-3868	4	4	aim	aim	NOUN
ejpam-3868	4	5	here	here	ADV
ejpam-3868	4	6	to	to	PART
ejpam-3868	4	7	look	look	VERB
ejpam-3868	4	8	at	at	ADP
ejpam-3868	4	9	how	how	SCONJ
ejpam-3868	4	10	a	a	DET
ejpam-3868	4	11	normal	normal	ADJ
ejpam-3868	4	12	projective	projective	ADJ
ejpam-3868	4	13	connection	connection	NOUN
ejpam-3868	4	14	can	can	AUX
ejpam-3868	4	15	be	be	AUX
ejpam-3868	4	16	constructed	construct	VERB
ejpam-3868	4	17	and	and	CCONJ
ejpam-3868	4	18	how	how	SCONJ
ejpam-3868	4	19	it	it	PRON
ejpam-3868	4	20	relates	relate	VERB
ejpam-3868	4	21	to	to	ADP
ejpam-3868	4	22	the	the	DET
ejpam-3868	4	23	geometry	geometry	NOUN
ejpam-3868	4	24	of	of	ADP
ejpam-3868	4	25	a	a	DET
ejpam-3868	4	26	single	single	ADJ
ejpam-3868	4	27	second	second	ADJ
ejpam-3868	4	28	order	order	NOUN
ejpam-3868	4	29	differential	differential	ADJ
ejpam-3868	4	30	equation	equation	NOUN
ejpam-3868	4	31	.	.	PUNCT
ejpam-3868	5	1	the	the	DET
ejpam-3868	5	2	calculations	calculation	NOUN
ejpam-3868	5	3	are	be	AUX
ejpam-3868	5	4	presented	present	VERB
ejpam-3868	5	5	in	in	ADP
ejpam-3868	5	6	some	some	DET
ejpam-3868	5	7	detail	detail	NOUN
ejpam-3868	5	8	in	in	ADP
ejpam-3868	5	9	order	order	NOUN
ejpam-3868	5	10	to	to	PART
ejpam-3868	5	11	highlight	highlight	VERB
ejpam-3868	5	12	the	the	DET
ejpam-3868	5	13	use	use	NOUN
ejpam-3868	5	14	of	of	ADP
ejpam-3868	5	15	gauge	gauge	ADJ
ejpam-3868	5	16	conditions	condition	NOUN
ejpam-3868	5	17	.	.	PUNCT
ejpam-3868	6	1	2020	2020	NUM
ejpam-3868	6	2	mathematics	mathematic	NOUN
ejpam-3868	6	3	subject	subject	NOUN
ejpam-3868	6	4	classifications	classification	NOUN
ejpam-3868	6	5	:	:	PUNCT
ejpam-3868	6	6	34g10	34g10	NUM
ejpam-3868	6	7	,	,	PUNCT
ejpam-3868	6	8	34a30	34a30	NUM
ejpam-3868	6	9	,	,	PUNCT
ejpam-3868	6	10	34a26	34a26	NUM
ejpam-3868	6	11	,	,	PUNCT
ejpam-3868	6	12	53b10	53b10	NUM
ejpam-3868	6	13	key	key	ADJ
ejpam-3868	6	14	words	word	NOUN
ejpam-3868	6	15	and	and	CCONJ
ejpam-3868	6	16	phrases	phrase	NOUN
ejpam-3868	6	17	:	:	PUNCT
ejpam-3868	6	18	differential	differential	ADJ
ejpam-3868	6	19	equation	equation	NOUN
ejpam-3868	6	20	,	,	PUNCT
ejpam-3868	6	21	geometry	geometry	NOUN
ejpam-3868	6	22	,	,	PUNCT
ejpam-3868	6	23	gauge	gauge	NOUN
ejpam-3868	6	24	,	,	PUNCT
ejpam-3868	6	25	differential	differential	ADJ
ejpam-3868	6	26	form	form	NOUN
ejpam-3868	6	27	,	,	PUNCT
ejpam-3868	6	28	duality	duality	NOUN
ejpam-3868	6	29	1	1	NUM
ejpam-3868	6	30	.	.	PUNCT
ejpam-3868	6	31	introduction	introduction	NOUN
ejpam-3868	6	32	two	two	NUM
ejpam-3868	6	33	problems	problem	NOUN
ejpam-3868	6	34	which	which	PRON
ejpam-3868	6	35	have	have	AUX
ejpam-3868	6	36	seen	see	VERB
ejpam-3868	6	37	a	a	DET
ejpam-3868	6	38	resurgence	resurgence	NOUN
ejpam-3868	6	39	of	of	ADP
ejpam-3868	6	40	interest	interest	NOUN
ejpam-3868	6	41	recently	recently	ADV
ejpam-3868	6	42	are	be	AUX
ejpam-3868	6	43	two	two	NUM
ejpam-3868	6	44	classical	classical	ADJ
ejpam-3868	6	45	subjects	subject	NOUN
ejpam-3868	6	46	,	,	PUNCT
ejpam-3868	6	47	namely	namely	ADV
ejpam-3868	6	48	,	,	PUNCT
ejpam-3868	6	49	the	the	DET
ejpam-3868	6	50	equivalence	equivalence	NOUN
ejpam-3868	6	51	problem	problem	NOUN
ejpam-3868	6	52	under	under	ADP
ejpam-3868	6	53	different	different	ADJ
ejpam-3868	6	54	kinds	kind	NOUN
ejpam-3868	6	55	of	of	ADP
ejpam-3868	6	56	tranformations	tranformation	NOUN
ejpam-3868	6	57	and	and	CCONJ
ejpam-3868	6	58	study	study	NOUN
ejpam-3868	6	59	of	of	ADP
ejpam-3868	6	60	the	the	DET
ejpam-3868	6	61	natural	natural	ADJ
ejpam-3868	6	62	geometric	geometric	ADJ
ejpam-3868	6	63	structures	structure	NOUN
ejpam-3868	6	64	induced	induce	VERB
ejpam-3868	6	65	on	on	ADP
ejpam-3868	6	66	their	their	PRON
ejpam-3868	6	67	solution	solution	NOUN
ejpam-3868	6	68	spaces	space	VERB
ejpam-3868	6	69	.	.	PUNCT
ejpam-3868	7	1	in	in	ADP
ejpam-3868	7	2	the	the	DET
ejpam-3868	7	3	early	early	ADJ
ejpam-3868	7	4	part	part	NOUN
ejpam-3868	7	5	of	of	ADP
ejpam-3868	7	6	the	the	DET
ejpam-3868	7	7	twentieth	twentieth	ADJ
ejpam-3868	7	8	century	century	NOUN
ejpam-3868	7	9	,	,	PUNCT
ejpam-3868	7	10	cartan	cartan	PROPN
ejpam-3868	7	11	proposed	propose	VERB
ejpam-3868	7	12	a	a	DET
ejpam-3868	7	13	theory	theory	NOUN
ejpam-3868	7	14	of	of	ADP
ejpam-3868	7	15	the	the	DET
ejpam-3868	7	16	second	second	ADJ
ejpam-3868	7	17	-	-	PUNCT
ejpam-3868	7	18	order	order	NOUN
ejpam-3868	7	19	ordinary	ordinary	ADJ
ejpam-3868	7	20	differential	differential	ADJ
ejpam-3868	7	21	equation	equation	NOUN
ejpam-3868	7	22	which	which	PRON
ejpam-3868	7	23	came	come	VERB
ejpam-3868	7	24	out	out	ADP
ejpam-3868	7	25	of	of	ADP
ejpam-3868	7	26	his	his	PRON
ejpam-3868	7	27	theory	theory	NOUN
ejpam-3868	7	28	of	of	ADP
ejpam-3868	7	29	projective	projective	ADJ
ejpam-3868	7	30	connections	connection	NOUN
ejpam-3868	7	31	[	[	X
ejpam-3868	7	32	3	3	NUM
ejpam-3868	7	33	]	]	PUNCT
ejpam-3868	7	34	.	.	PUNCT
ejpam-3868	8	1	the	the	DET
ejpam-3868	8	2	point	point	NOUN
ejpam-3868	8	3	of	of	ADP
ejpam-3868	8	4	interest	interest	NOUN
ejpam-3868	8	5	here	here	ADV
ejpam-3868	8	6	is	be	AUX
ejpam-3868	8	7	that	that	SCONJ
ejpam-3868	8	8	it	it	PRON
ejpam-3868	8	9	is	be	AUX
ejpam-3868	8	10	possible	possible	ADJ
ejpam-3868	8	11	to	to	PART
ejpam-3868	8	12	construct	construct	VERB
ejpam-3868	8	13	certain	certain	ADJ
ejpam-3868	8	14	kinds	kind	NOUN
ejpam-3868	8	15	of	of	ADP
ejpam-3868	8	16	geometric	geometric	ADJ
ejpam-3868	8	17	structures	structure	NOUN
ejpam-3868	8	18	on	on	ADP
ejpam-3868	8	19	the	the	DET
ejpam-3868	8	20	spaces	space	NOUN
ejpam-3868	8	21	of	of	ADP
ejpam-3868	8	22	particular	particular	ADJ
ejpam-3868	8	23	types	type	NOUN
ejpam-3868	8	24	of	of	ADP
ejpam-3868	8	25	differential	differential	ADJ
ejpam-3868	8	26	equations	equation	NOUN
ejpam-3868	8	27	.	.	PUNCT
ejpam-3868	9	1	in	in	ADP
ejpam-3868	9	2	the	the	DET
ejpam-3868	9	3	case	case	NOUN
ejpam-3868	9	4	of	of	ADP
ejpam-3868	9	5	the	the	DET
ejpam-3868	9	6	third	third	ADJ
ejpam-3868	9	7	order	order	NOUN
ejpam-3868	9	8	differential	differential	NOUN
ejpam-3868	9	9	equation	equation	NOUN
ejpam-3868	9	10	,	,	PUNCT
ejpam-3868	9	11	it	it	PRON
ejpam-3868	9	12	is	be	AUX
ejpam-3868	9	13	possible	possible	ADJ
ejpam-3868	9	14	to	to	PART
ejpam-3868	9	15	create	create	VERB
ejpam-3868	9	16	from	from	ADP
ejpam-3868	9	17	the	the	DET
ejpam-3868	9	18	equation	equation	NOUN
ejpam-3868	9	19	a	a	DET
ejpam-3868	9	20	conformal	conformal	ADJ
ejpam-3868	9	21	class	class	NOUN
ejpam-3868	9	22	of	of	ADP
ejpam-3868	9	23	lorentzian	lorentzian	ADJ
ejpam-3868	9	24	metrics	metric	NOUN
ejpam-3868	9	25	on	on	ADP
ejpam-3868	9	26	the	the	DET
ejpam-3868	9	27	solution	solution	NOUN
ejpam-3868	9	28	space	space	NOUN
ejpam-3868	9	29	,	,	PUNCT
ejpam-3868	9	30	provided	provide	VERB
ejpam-3868	9	31	a	a	DET
ejpam-3868	9	32	function	function	NOUN
ejpam-3868	9	33	associated	associate	VERB
ejpam-3868	9	34	with	with	ADP
ejpam-3868	9	35	the	the	DET
ejpam-3868	9	36	equation	equation	NOUN
ejpam-3868	9	37	vanishes	vanish	VERB
ejpam-3868	9	38	[	[	X
ejpam-3868	9	39	6	6	NUM
ejpam-3868	9	40	,	,	PUNCT
ejpam-3868	9	41	12	12	NUM
ejpam-3868	9	42	,	,	PUNCT
ejpam-3868	9	43	13	13	NUM
ejpam-3868	9	44	]	]	PUNCT
ejpam-3868	9	45	this	this	DET
ejpam-3868	9	46	function	function	NOUN
ejpam-3868	9	47	is	be	AUX
ejpam-3868	9	48	a	a	DET
ejpam-3868	9	49	relative	relative	ADJ
ejpam-3868	9	50	invariant	invariant	NOUN
ejpam-3868	9	51	of	of	ADP
ejpam-3868	9	52	the	the	DET
ejpam-3868	9	53	equation	equation	NOUN
ejpam-3868	9	54	under	under	ADP
ejpam-3868	9	55	contact	contact	NOUN
ejpam-3868	9	56	transformations	transformation	NOUN
ejpam-3868	9	57	.	.	PUNCT
ejpam-3868	10	1	these	these	DET
ejpam-3868	10	2	kinds	kind	NOUN
ejpam-3868	10	3	of	of	ADP
ejpam-3868	10	4	constructions	construction	NOUN
ejpam-3868	10	5	turn	turn	VERB
ejpam-3868	10	6	out	out	ADP
ejpam-3868	10	7	to	to	PART
ejpam-3868	10	8	be	be	AUX
ejpam-3868	10	9	both	both	CCONJ
ejpam-3868	10	10	useful	useful	ADJ
ejpam-3868	10	11	and	and	CCONJ
ejpam-3868	10	12	mathematically	mathematically	ADV
ejpam-3868	10	13	interesting	interesting	ADJ
ejpam-3868	10	14	.	.	PUNCT
ejpam-3868	11	1	there	there	PRON
ejpam-3868	11	2	are	be	VERB
ejpam-3868	11	3	numerous	numerous	ADJ
ejpam-3868	11	4	applications	application	NOUN
ejpam-3868	11	5	of	of	ADP
ejpam-3868	11	6	this	this	DET
ejpam-3868	11	7	kind	kind	NOUN
ejpam-3868	11	8	of	of	ADP
ejpam-3868	11	9	work	work	NOUN
ejpam-3868	11	10	,	,	PUNCT
ejpam-3868	11	11	for	for	ADP
ejpam-3868	11	12	example	example	NOUN
ejpam-3868	11	13	,	,	PUNCT
ejpam-3868	11	14	in	in	ADP
ejpam-3868	11	15	the	the	DET
ejpam-3868	11	16	study	study	NOUN
ejpam-3868	11	17	of	of	ADP
ejpam-3868	11	18	general	general	ADJ
ejpam-3868	11	19	relativity	relativity	NOUN
ejpam-3868	11	20	[	[	X
ejpam-3868	11	21	10	10	NUM
ejpam-3868	11	22	]	]	PUNCT
ejpam-3868	11	23	.	.	PUNCT
ejpam-3868	12	1	the	the	DET
ejpam-3868	12	2	simplest	simple	ADJ
ejpam-3868	12	3	one	one	NOUN
ejpam-3868	12	4	to	to	PART
ejpam-3868	12	5	begin	begin	VERB
ejpam-3868	12	6	with	with	ADP
ejpam-3868	12	7	is	be	AUX
ejpam-3868	12	8	the	the	DET
ejpam-3868	12	9	second	second	ADJ
ejpam-3868	12	10	order	order	NOUN
ejpam-3868	12	11	ordinary	ordinary	ADJ
ejpam-3868	12	12	differential	differential	ADJ
ejpam-3868	12	13	equation	equation	NOUN
ejpam-3868	12	14	.	.	PUNCT
ejpam-3868	13	1	a	a	DET
ejpam-3868	13	2	geometric	geometric	ADJ
ejpam-3868	13	3	structure	structure	NOUN
ejpam-3868	13	4	can	can	AUX
ejpam-3868	13	5	be	be	AUX
ejpam-3868	13	6	constructed	construct	VERB
ejpam-3868	13	7	on	on	ADP
ejpam-3868	13	8	the	the	DET
ejpam-3868	13	9	solution	solution	NOUN
ejpam-3868	13	10	space	space	NOUN
ejpam-3868	13	11	of	of	ADP
ejpam-3868	13	12	such	such	DET
ejpam-3868	13	13	an	an	DET
ejpam-3868	13	14	equation	equation	NOUN
ejpam-3868	13	15	and	and	CCONJ
ejpam-3868	13	16	a	a	DET
ejpam-3868	13	17	function	function	NOUN
ejpam-3868	13	18	which	which	PRON
ejpam-3868	13	19	is	be	AUX
ejpam-3868	13	20	a	a	DET
ejpam-3868	13	21	relative	relative	ADJ
ejpam-3868	13	22	invariant	invariant	NOUN
ejpam-3868	13	23	of	of	ADP
ejpam-3868	13	24	the	the	DET
ejpam-3868	13	25	equation	equation	NOUN
ejpam-3868	13	26	can	can	AUX
ejpam-3868	13	27	be	be	AUX
ejpam-3868	13	28	identified	identify	VERB
ejpam-3868	13	29	.	.	PUNCT
ejpam-3868	14	1	the	the	DET
ejpam-3868	14	2	concept	concept	NOUN
ejpam-3868	14	3	of	of	ADP
ejpam-3868	14	4	duality	duality	NOUN
ejpam-3868	14	5	was	be	AUX
ejpam-3868	14	6	also	also	ADV
ejpam-3868	14	7	studied	study	VERB
ejpam-3868	14	8	by	by	ADP
ejpam-3868	14	9	cartan	cartan	PROPN
ejpam-3868	14	10	.	.	PUNCT
ejpam-3868	15	1	considerable	considerable	ADJ
ejpam-3868	15	2	work	work	NOUN
ejpam-3868	15	3	has	have	AUX
ejpam-3868	15	4	been	be	AUX
ejpam-3868	15	5	done	do	VERB
ejpam-3868	15	6	on	on	ADP
ejpam-3868	15	7	the	the	DET
ejpam-3868	15	8	construction	construction	NOUN
ejpam-3868	15	9	of	of	ADP
ejpam-3868	15	10	a	a	DET
ejpam-3868	15	11	geometric	geometric	ADJ
ejpam-3868	15	12	structure	structure	NOUN
ejpam-3868	15	13	on	on	ADP
ejpam-3868	15	14	the	the	DET
ejpam-3868	15	15	solution	solution	NOUN
ejpam-3868	15	16	space	space	NOUN
ejpam-3868	15	17	of	of	ADP
ejpam-3868	15	18	a	a	DET
ejpam-3868	15	19	second	second	ADJ
ejpam-3868	15	20	order	order	NOUN
ejpam-3868	15	21	differential	differential	ADJ
ejpam-3868	15	22	equation	equation	NOUN
ejpam-3868	15	23	.	.	PUNCT
ejpam-3868	16	1	the	the	DET
ejpam-3868	16	2	intention	intention	NOUN
ejpam-3868	16	3	here	here	ADV
ejpam-3868	16	4	is	be	AUX
ejpam-3868	16	5	to	to	PART
ejpam-3868	16	6	discuss	discuss	VERB
ejpam-3868	16	7	the	the	DET
ejpam-3868	16	8	theory	theory	NOUN
ejpam-3868	16	9	of	of	ADP
ejpam-3868	16	10	the	the	DET
ejpam-3868	16	11	second	second	ADJ
ejpam-3868	16	12	order	order	NOUN
ejpam-3868	16	13	ordinary	ordinary	ADJ
ejpam-3868	16	14	differential	differential	ADJ
ejpam-3868	16	15	equation	equation	NOUN
ejpam-3868	16	16	doi	doi	NOUN
ejpam-3868	16	17	:	:	PUNCT
ejpam-3868	16	18	https://doi.org/10.29020/nybg.ejpam.v13i4.3831	https://doi.org/10.29020/nybg.ejpam.v13i4.3831	PROPN
ejpam-3868	16	19	email	email	NOUN
ejpam-3868	16	20	addresses	address	NOUN
ejpam-3868	16	21	:	:	PUNCT
ejpam-3868	16	22	paul.bracken@utrgv.edu	paul.bracken@utrgv.edu	PROPN
ejpam-3868	16	23	(	(	PUNCT
ejpam-3868	16	24	p.	p.	NOUN
ejpam-3868	16	25	bracken	bracken	NOUN
ejpam-3868	16	26	)	)	PUNCT
ejpam-3868	16	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3868	16	28	1016	1016	NUM
ejpam-3868	17	1	c	c	NOUN
ejpam-3868	17	2	©	©	PROPN
ejpam-3868	17	3	2020	2020	NUM
ejpam-3868	17	4	ejpam	ejpam	VERB
ejpam-3868	17	5	all	all	DET
ejpam-3868	17	6	rights	right	NOUN
ejpam-3868	17	7	reserved	reserve	VERB
ejpam-3868	17	8	.	.	PUNCT
ejpam-3868	18	1	p.	p.	NOUN
ejpam-3868	18	2	bracken	bracken	NOUN
ejpam-3868	18	3	/	/	SYM
ejpam-3868	18	4	eur	eur	PROPN
ejpam-3868	18	5	.	.	PUNCT
ejpam-3868	19	1	j.	j.	PROPN
ejpam-3868	19	2	pure	pure	PROPN
ejpam-3868	19	3	appl	appl	PROPN
ejpam-3868	19	4	.	.	PROPN
ejpam-3868	19	5	math	math	PROPN
ejpam-3868	19	6	,	,	PUNCT
ejpam-3868	19	7	13	13	NUM
ejpam-3868	19	8	(	(	PUNCT
ejpam-3868	19	9	4	4	NUM
ejpam-3868	19	10	)	)	PUNCT
ejpam-3868	19	11	(	(	PUNCT
ejpam-3868	19	12	2020	2020	NUM
ejpam-3868	19	13	)	)	PUNCT
ejpam-3868	19	14	,	,	PUNCT
ejpam-3868	19	15	1016	1016	NUM
ejpam-3868	19	16	-	-	SYM
ejpam-3868	19	17	1034	1034	NUM
ejpam-3868	19	18	1017	1017	NUM
ejpam-3868	19	19	which	which	PRON
ejpam-3868	19	20	cartan	cartan	PROPN
ejpam-3868	19	21	began	begin	VERB
ejpam-3868	19	22	and	and	CCONJ
ejpam-3868	19	23	to	to	PART
ejpam-3868	19	24	study	study	VERB
ejpam-3868	19	25	in	in	ADP
ejpam-3868	19	26	particular	particular	ADJ
ejpam-3868	19	27	cartan	cartan	PROPN
ejpam-3868	19	28	’s	’s	PART
ejpam-3868	19	29	notion	notion	NOUN
ejpam-3868	19	30	of	of	ADP
ejpam-3868	19	31	duality	duality	NOUN
ejpam-3868	19	32	between	between	ADP
ejpam-3868	19	33	such	such	ADJ
ejpam-3868	19	34	types	type	NOUN
ejpam-3868	19	35	of	of	ADP
ejpam-3868	19	36	equations	equation	NOUN
ejpam-3868	19	37	[	[	X
ejpam-3868	19	38	9	9	NUM
ejpam-3868	19	39	]	]	PUNCT
ejpam-3868	19	40	.	.	PUNCT
ejpam-3868	20	1	the	the	DET
ejpam-3868	20	2	idea	idea	NOUN
ejpam-3868	20	3	of	of	ADP
ejpam-3868	20	4	what	what	PRON
ejpam-3868	20	5	cartan	cartan	PROPN
ejpam-3868	20	6	referred	refer	VERB
ejpam-3868	20	7	to	to	ADP
ejpam-3868	20	8	as	as	ADP
ejpam-3868	20	9	a	a	DET
ejpam-3868	20	10	manifold	manifold	NOUN
ejpam-3868	20	11	of	of	ADP
ejpam-3868	20	12	elements	element	NOUN
ejpam-3868	20	13	with	with	ADP
ejpam-3868	20	14	projective	projective	ADJ
ejpam-3868	20	15	connection	connection	NOUN
ejpam-3868	20	16	in	in	ADP
ejpam-3868	20	17	the	the	DET
ejpam-3868	20	18	two	two	NUM
ejpam-3868	20	19	-	-	PUNCT
ejpam-3868	20	20	dimensional	dimensional	ADJ
ejpam-3868	20	21	case	case	NOUN
ejpam-3868	20	22	is	be	AUX
ejpam-3868	20	23	of	of	ADP
ejpam-3868	20	24	great	great	ADJ
ejpam-3868	20	25	interest	interest	NOUN
ejpam-3868	20	26	[	[	X
ejpam-3868	20	27	2	2	NUM
ejpam-3868	20	28	,	,	PUNCT
ejpam-3868	20	29	4	4	NUM
ejpam-3868	20	30	,	,	PUNCT
ejpam-3868	20	31	5	5	NUM
ejpam-3868	20	32	,	,	PUNCT
ejpam-3868	20	33	8	8	NUM
ejpam-3868	20	34	]	]	PUNCT
ejpam-3868	20	35	.	.	PUNCT
ejpam-3868	21	1	by	by	ADP
ejpam-3868	21	2	way	way	NOUN
ejpam-3868	21	3	of	of	ADP
ejpam-3868	21	4	introduction	introduction	NOUN
ejpam-3868	21	5	,	,	PUNCT
ejpam-3868	21	6	some	some	DET
ejpam-3868	21	7	definitions	definition	NOUN
ejpam-3868	21	8	of	of	ADP
ejpam-3868	21	9	basic	basic	ADJ
ejpam-3868	21	10	concepts	concept	NOUN
ejpam-3868	21	11	is	be	AUX
ejpam-3868	21	12	introduced	introduce	VERB
ejpam-3868	21	13	.	.	PUNCT
ejpam-3868	22	1	an	an	DET
ejpam-3868	22	2	element	element	NOUN
ejpam-3868	22	3	is	be	AUX
ejpam-3868	22	4	a	a	DET
ejpam-3868	22	5	pair	pair	NOUN
ejpam-3868	22	6	consisting	consist	VERB
ejpam-3868	22	7	of	of	ADP
ejpam-3868	22	8	a	a	DET
ejpam-3868	22	9	point	point	NOUN
ejpam-3868	22	10	of	of	ADP
ejpam-3868	22	11	a	a	DET
ejpam-3868	22	12	differentiable	differentiable	ADJ
ejpam-3868	22	13	manifold	manifold	ADJ
ejpam-3868	22	14	m	m	NOUN
ejpam-3868	22	15	and	and	CCONJ
ejpam-3868	22	16	a	a	DET
ejpam-3868	22	17	one	one	NUM
ejpam-3868	22	18	-	-	PUNCT
ejpam-3868	22	19	dimensional	dimensional	ADJ
ejpam-3868	22	20	subspace	subspace	NOUN
ejpam-3868	22	21	of	of	ADP
ejpam-3868	22	22	the	the	DET
ejpam-3868	22	23	tangent	tangent	ADJ
ejpam-3868	22	24	space	space	NOUN
ejpam-3868	22	25	to	to	ADP
ejpam-3868	22	26	m	m	VERB
ejpam-3868	22	27	at	at	ADP
ejpam-3868	22	28	that	that	DET
ejpam-3868	22	29	point	point	NOUN
ejpam-3868	22	30	.	.	PUNCT
ejpam-3868	23	1	a	a	DET
ejpam-3868	23	2	manifold	manifold	NOUN
ejpam-3868	23	3	of	of	ADP
ejpam-3868	23	4	elements	element	NOUN
ejpam-3868	23	5	is	be	AUX
ejpam-3868	23	6	the	the	DET
ejpam-3868	23	7	projective	projective	ADJ
ejpam-3868	23	8	tangent	tangent	PROPN
ejpam-3868	23	9	bundle	bundle	PROPN
ejpam-3868	23	10	ptm	ptm	PROPN
ejpam-3868	23	11	of	of	ADP
ejpam-3868	23	12	a	a	DET
ejpam-3868	23	13	twodimensional	twodimensional	ADJ
ejpam-3868	23	14	manifold	manifold	ADJ
ejpam-3868	23	15	m	m	NOUN
ejpam-3868	23	16	.	.	PUNCT
ejpam-3868	24	1	let	let	VERB
ejpam-3868	24	2	p	p	NOUN
ejpam-3868	24	3	2	2	NUM
ejpam-3868	24	4	denote	denote	VERB
ejpam-3868	24	5	real	real	ADJ
ejpam-3868	24	6	projective	projective	ADJ
ejpam-3868	24	7	space	space	NOUN
ejpam-3868	24	8	with	with	ADP
ejpam-3868	24	9	two	two	NUM
ejpam-3868	24	10	-	-	PUNCT
ejpam-3868	24	11	dimensions	dimension	NOUN
ejpam-3868	24	12	.	.	PUNCT
ejpam-3868	25	1	its	its	PRON
ejpam-3868	25	2	projective	projective	ADJ
ejpam-3868	25	3	tangent	tangent	NOUN
ejpam-3868	25	4	bundle	bundle	PROPN
ejpam-3868	25	5	ptp	ptp	PROPN
ejpam-3868	25	6	2	2	PROPN
ejpam-3868	25	7	can	can	AUX
ejpam-3868	25	8	be	be	AUX
ejpam-3868	25	9	expressed	express	VERB
ejpam-3868	25	10	as	as	ADP
ejpam-3868	25	11	the	the	DET
ejpam-3868	25	12	homogeneous	homogeneous	ADJ
ejpam-3868	25	13	space	space	NOUN
ejpam-3868	25	14	g	g	NOUN
ejpam-3868	25	15	/	/	SYM
ejpam-3868	25	16	h	h	NOUN
ejpam-3868	25	17	where	where	SCONJ
ejpam-3868	25	18	g	g	NOUN
ejpam-3868	25	19	=	=	SYM
ejpam-3868	25	20	sl(2,r	sl(2,r	PROPN
ejpam-3868	25	21	)	)	PUNCT
ejpam-3868	25	22	and	and	CCONJ
ejpam-3868	25	23	h	h	NOUN
ejpam-3868	25	24	is	be	AUX
ejpam-3868	25	25	the	the	DET
ejpam-3868	25	26	subgroup	subgroup	NOUN
ejpam-3868	25	27	of	of	ADP
ejpam-3868	25	28	g	g	PROPN
ejpam-3868	25	29	consisting	consist	VERB
ejpam-3868	25	30	of	of	ADP
ejpam-3868	25	31	all	all	DET
ejpam-3868	25	32	upper	upper	ADJ
ejpam-3868	25	33	triangular	triangular	NOUN
ejpam-3868	25	34	elements	element	NOUN
ejpam-3868	25	35	.	.	PUNCT
ejpam-3868	26	1	a	a	DET
ejpam-3868	26	2	manifold	manifold	NOUN
ejpam-3868	26	3	of	of	ADP
ejpam-3868	26	4	elements	element	NOUN
ejpam-3868	26	5	with	with	ADP
ejpam-3868	26	6	projective	projective	ADJ
ejpam-3868	26	7	connection	connection	NOUN
ejpam-3868	26	8	is	be	AUX
ejpam-3868	26	9	a	a	DET
ejpam-3868	26	10	cartan	cartan	ADJ
ejpam-3868	26	11	geometry	geometry	NOUN
ejpam-3868	26	12	ptm	ptm	PROPN
ejpam-3868	26	13	modeled	model	VERB
ejpam-3868	26	14	on	on	ADP
ejpam-3868	26	15	ptp	ptp	PROPN
ejpam-3868	26	16	2	2	NUM
ejpam-3868	26	17	in	in	ADP
ejpam-3868	26	18	which	which	PRON
ejpam-3868	26	19	certain	certain	ADJ
ejpam-3868	26	20	conditions	condition	NOUN
ejpam-3868	26	21	regarding	regard	VERB
ejpam-3868	26	22	the	the	DET
ejpam-3868	26	23	development	development	NOUN
ejpam-3868	26	24	of	of	ADP
ejpam-3868	26	25	curves	curve	NOUN
ejpam-3868	26	26	which	which	PRON
ejpam-3868	26	27	arise	arise	VERB
ejpam-3868	26	28	out	out	ADP
ejpam-3868	26	29	of	of	ADP
ejpam-3868	26	30	the	the	DET
ejpam-3868	26	31	projective	projective	ADJ
ejpam-3868	26	32	tangent	tangent	NOUN
ejpam-3868	26	33	structures	structure	NOUN
ejpam-3868	26	34	of	of	ADP
ejpam-3868	26	35	the	the	DET
ejpam-3868	26	36	underlying	underlie	VERB
ejpam-3868	26	37	manifold	manifold	ADJ
ejpam-3868	26	38	and	and	CCONJ
ejpam-3868	26	39	model	model	NOUN
ejpam-3868	26	40	geometry	geometry	NOUN
ejpam-3868	26	41	are	be	AUX
ejpam-3868	26	42	satisfied	satisfied	ADJ
ejpam-3868	26	43	[	[	X
ejpam-3868	26	44	1	1	NUM
ejpam-3868	26	45	,	,	PUNCT
ejpam-3868	26	46	14	14	NUM
ejpam-3868	26	47	,	,	PUNCT
ejpam-3868	26	48	16	16	NUM
ejpam-3868	26	49	]	]	PUNCT
ejpam-3868	26	50	.	.	PUNCT
ejpam-3868	27	1	it	it	PRON
ejpam-3868	27	2	should	should	AUX
ejpam-3868	27	3	also	also	ADV
ejpam-3868	27	4	be	be	AUX
ejpam-3868	27	5	stressed	stress	VERB
ejpam-3868	27	6	that	that	SCONJ
ejpam-3868	27	7	there	there	PRON
ejpam-3868	27	8	are	be	VERB
ejpam-3868	27	9	many	many	ADJ
ejpam-3868	27	10	physical	physical	ADJ
ejpam-3868	27	11	applications	application	NOUN
ejpam-3868	27	12	of	of	ADP
ejpam-3868	27	13	this	this	DET
ejpam-3868	27	14	work	work	NOUN
ejpam-3868	27	15	especially	especially	ADV
ejpam-3868	27	16	in	in	ADP
ejpam-3868	27	17	relativity	relativity	NOUN
ejpam-3868	27	18	[	[	X
ejpam-3868	27	19	7	7	NUM
ejpam-3868	27	20	,	,	PUNCT
ejpam-3868	27	21	11	11	NUM
ejpam-3868	27	22	,	,	PUNCT
ejpam-3868	27	23	15	15	NUM
ejpam-3868	27	24	]	]	PUNCT
ejpam-3868	27	25	.	.	PUNCT
ejpam-3868	28	1	2	2	X
ejpam-3868	28	2	.	.	X
ejpam-3868	28	3	manifolds	manifold	NOUN
ejpam-3868	28	4	with	with	ADP
ejpam-3868	28	5	projective	projective	ADJ
ejpam-3868	28	6	connections	connection	NOUN
ejpam-3868	28	7	local	local	ADJ
ejpam-3868	28	8	coordinates	coordinate	NOUN
ejpam-3868	28	9	can	can	AUX
ejpam-3868	28	10	be	be	AUX
ejpam-3868	28	11	introduced	introduce	VERB
ejpam-3868	28	12	on	on	ADP
ejpam-3868	28	13	ptm	ptm	PROPN
ejpam-3868	28	14	by	by	ADP
ejpam-3868	28	15	taking	take	VERB
ejpam-3868	28	16	local	local	ADJ
ejpam-3868	28	17	coordinates	coordinate	NOUN
ejpam-3868	28	18	(	(	PUNCT
ejpam-3868	28	19	x	x	X
ejpam-3868	28	20	,	,	PUNCT
ejpam-3868	28	21	y	y	NOUN
ejpam-3868	28	22	)	)	PUNCT
ejpam-3868	28	23	on	on	ADP
ejpam-3868	28	24	m	m	NOUN
ejpam-3868	28	25	and	and	CCONJ
ejpam-3868	28	26	noting	note	VERB
ejpam-3868	28	27	that	that	SCONJ
ejpam-3868	28	28	every	every	DET
ejpam-3868	28	29	equivalence	equivalence	NOUN
ejpam-3868	28	30	class	class	NOUN
ejpam-3868	28	31	of	of	ADP
ejpam-3868	28	32	tangent	tangent	NOUN
ejpam-3868	28	33	vectors	vector	NOUN
ejpam-3868	28	34	u	u	NOUN
ejpam-3868	28	35	∂x	∂x	PROPN
ejpam-3868	28	36	+	+	CCONJ
ejpam-3868	28	37	v∂y	v∂y	NOUN
ejpam-3868	28	38	for	for	ADP
ejpam-3868	28	39	which	which	PRON
ejpam-3868	28	40	u	u	PROPN
ejpam-3868	28	41	6=	6=	ADP
ejpam-3868	28	42	0	0	NUM
ejpam-3868	28	43	has	have	VERB
ejpam-3868	28	44	a	a	DET
ejpam-3868	28	45	unique	unique	ADJ
ejpam-3868	28	46	representative	representative	NOUN
ejpam-3868	28	47	of	of	ADP
ejpam-3868	28	48	the	the	DET
ejpam-3868	28	49	form	form	NOUN
ejpam-3868	28	50	∂x	∂x	PROPN
ejpam-3868	28	51	+	+	CCONJ
ejpam-3868	28	52	y′	y′	NOUN
ejpam-3868	28	53	∂y	∂y	NOUN
ejpam-3868	28	54	,	,	PUNCT
ejpam-3868	28	55	then	then	ADV
ejpam-3868	28	56	(	(	PUNCT
ejpam-3868	28	57	x	x	X
ejpam-3868	28	58	,	,	PUNCT
ejpam-3868	28	59	y	y	PROPN
ejpam-3868	28	60	,	,	PUNCT
ejpam-3868	28	61	y′	y′	NUM
ejpam-3868	28	62	)	)	PUNCT
ejpam-3868	28	63	are	be	AUX
ejpam-3868	28	64	local	local	ADJ
ejpam-3868	28	65	coordinates	coordinate	NOUN
ejpam-3868	28	66	on	on	ADP
ejpam-3868	28	67	ptm	ptm	PROPN
ejpam-3868	28	68	which	which	PRON
ejpam-3868	28	69	we	we	PRON
ejpam-3868	28	70	work	work	VERB
ejpam-3868	28	71	with	with	ADP
ejpam-3868	28	72	in	in	ADP
ejpam-3868	28	73	noting	note	VERB
ejpam-3868	28	74	they	they	PRON
ejpam-3868	28	75	do	do	AUX
ejpam-3868	28	76	not	not	PART
ejpam-3868	28	77	cover	cover	VERB
ejpam-3868	28	78	those	those	DET
ejpam-3868	28	79	equivalence	equivalence	NOUN
ejpam-3868	28	80	classes	class	NOUN
ejpam-3868	28	81	of	of	ADP
ejpam-3868	28	82	tangent	tangent	ADJ
ejpam-3868	28	83	vectors	vector	NOUN
ejpam-3868	28	84	for	for	ADP
ejpam-3868	28	85	which	which	PRON
ejpam-3868	28	86	u	u	NOUN
ejpam-3868	28	87	=	=	NOUN
ejpam-3868	28	88	0	0	PROPN
ejpam-3868	28	89	.	.	PUNCT
ejpam-3868	29	1	a	a	DET
ejpam-3868	29	2	klein	klein	PROPN
ejpam-3868	29	3	geometry	geometry	NOUN
ejpam-3868	29	4	is	be	AUX
ejpam-3868	29	5	a	a	DET
ejpam-3868	29	6	homogeneous	homogeneous	ADJ
ejpam-3868	29	7	space	space	NOUN
ejpam-3868	29	8	g	g	NOUN
ejpam-3868	29	9	so	so	SCONJ
ejpam-3868	29	10	that	that	SCONJ
ejpam-3868	29	11	it	it	PRON
ejpam-3868	29	12	is	be	AUX
ejpam-3868	29	13	a	a	DET
ejpam-3868	29	14	manifold	manifold	ADJ
ejpam-3868	29	15	m	m	NOUN
ejpam-3868	29	16	with	with	ADP
ejpam-3868	29	17	a	a	DET
ejpam-3868	29	18	transitive	transitive	ADJ
ejpam-3868	29	19	action	action	NOUN
ejpam-3868	29	20	of	of	ADP
ejpam-3868	29	21	g.	g.	PROPN
ejpam-3868	29	22	take	take	VERB
ejpam-3868	29	23	a	a	DET
ejpam-3868	29	24	point	point	NOUN
ejpam-3868	30	1	x0	x0	PROPN
ejpam-3868	30	2	∈	∈	PROPN
ejpam-3868	30	3	m	m	PROPN
ejpam-3868	31	1	and	and	CCONJ
ejpam-3868	31	2	let	let	VERB
ejpam-3868	31	3	h	h	NOUN
ejpam-3868	31	4	be	be	AUX
ejpam-3868	31	5	the	the	DET
ejpam-3868	31	6	stabilizer	stabilizer	NOUN
ejpam-3868	31	7	of	of	ADP
ejpam-3868	31	8	x0	x0	PROPN
ejpam-3868	31	9	.	.	PUNCT
ejpam-3868	32	1	then	then	ADV
ejpam-3868	32	2	m	m	VERB
ejpam-3868	32	3	can	can	AUX
ejpam-3868	32	4	be	be	AUX
ejpam-3868	32	5	identified	identify	VERB
ejpam-3868	32	6	with	with	ADP
ejpam-3868	32	7	the	the	DET
ejpam-3868	32	8	coset	coset	NOUN
ejpam-3868	32	9	space	space	NOUN
ejpam-3868	32	10	g	g	PROPN
ejpam-3868	32	11	/	/	SYM
ejpam-3868	32	12	h.	h.	PROPN
ejpam-3868	33	1	then	then	ADV
ejpam-3868	33	2	g	g	PROPN
ejpam-3868	33	3	becomes	become	VERB
ejpam-3868	33	4	a	a	DET
ejpam-3868	33	5	right	right	ADJ
ejpam-3868	33	6	principle	principle	ADJ
ejpam-3868	33	7	h	h	NOUN
ejpam-3868	33	8	-	-	PUNCT
ejpam-3868	33	9	bundle	bundle	NOUN
ejpam-3868	33	10	over	over	ADP
ejpam-3868	33	11	m	m	PROPN
ejpam-3868	33	12	with	with	ADP
ejpam-3868	33	13	projection	projection	NOUN
ejpam-3868	33	14	g	g	PROPN
ejpam-3868	33	15	→	→	SYM
ejpam-3868	33	16	gx0	gx0	NOUN
ejpam-3868	33	17	.	.	PUNCT
ejpam-3868	34	1	the	the	DET
ejpam-3868	34	2	space	space	NOUN
ejpam-3868	34	3	(	(	PUNCT
ejpam-3868	34	4	g	g	NOUN
ejpam-3868	34	5	,	,	PUNCT
ejpam-3868	34	6	h	h	NOUN
ejpam-3868	34	7	)	)	PUNCT
ejpam-3868	34	8	may	may	AUX
ejpam-3868	34	9	be	be	AUX
ejpam-3868	34	10	referred	refer	VERB
ejpam-3868	34	11	to	to	ADP
ejpam-3868	34	12	as	as	ADP
ejpam-3868	34	13	the	the	DET
ejpam-3868	34	14	klein	klein	PROPN
ejpam-3868	34	15	geometry	geometry	PROPN
ejpam-3868	34	16	.	.	PUNCT
ejpam-3868	35	1	gauge	gauge	NOUN
ejpam-3868	35	2	changes	change	NOUN
ejpam-3868	35	3	may	may	AUX
ejpam-3868	35	4	be	be	AUX
ejpam-3868	35	5	made	make	VERB
ejpam-3868	35	6	on	on	ADP
ejpam-3868	35	7	a	a	DET
ejpam-3868	35	8	projective	projective	ADJ
ejpam-3868	35	9	connection	connection	NOUN
ejpam-3868	35	10	on	on	ADP
ejpam-3868	35	11	such	such	DET
ejpam-3868	35	12	a	a	DET
ejpam-3868	35	13	manifold	manifold	NOUN
ejpam-3868	35	14	.	.	PUNCT
ejpam-3868	36	1	if	if	SCONJ
ejpam-3868	36	2	ω	ω	PROPN
ejpam-3868	36	3	is	be	AUX
ejpam-3868	36	4	a	a	DET
ejpam-3868	36	5	connection	connection	NOUN
ejpam-3868	36	6	form	form	NOUN
ejpam-3868	36	7	that	that	PRON
ejpam-3868	36	8	is	be	AUX
ejpam-3868	36	9	a	a	DET
ejpam-3868	36	10	trace	trace	NOUN
ejpam-3868	36	11	-	-	PUNCT
ejpam-3868	36	12	free	free	ADJ
ejpam-3868	36	13	3×	3×	NUM
ejpam-3868	36	14	3	3	NUM
ejpam-3868	36	15	matrix	matrix	NOUN
ejpam-3868	36	16	of	of	ADP
ejpam-3868	36	17	local	local	ADJ
ejpam-3868	36	18	one	one	NUM
ejpam-3868	36	19	forms	form	NOUN
ejpam-3868	36	20	on	on	ADP
ejpam-3868	36	21	ptm	ptm	PROPN
ejpam-3868	36	22	,	,	PUNCT
ejpam-3868	36	23	and	and	CCONJ
ejpam-3868	36	24	h	h	NOUN
ejpam-3868	36	25	is	be	AUX
ejpam-3868	36	26	an	an	DET
ejpam-3868	36	27	h	h	NOUN
ejpam-3868	36	28	-	-	PUNCT
ejpam-3868	36	29	valued	value	VERB
ejpam-3868	36	30	function	function	NOUN
ejpam-3868	36	31	,	,	PUNCT
ejpam-3868	36	32	then	then	ADV
ejpam-3868	36	33	the	the	DET
ejpam-3868	36	34	gauged	gauge	VERB
ejpam-3868	36	35	connection	connection	NOUN
ejpam-3868	36	36	form	form	NOUN
ejpam-3868	36	37	is	be	AUX
ejpam-3868	36	38	h−1	h−1	PROPN
ejpam-3868	36	39	ω	ω	NUM
ejpam-3868	36	40	h+	h+	PROPN
ejpam-3868	37	1	h−1	h−1	PROPN
ejpam-3868	37	2	dh	dh	NOUN
ejpam-3868	37	3	.	.	PUNCT
ejpam-3868	38	1	(	(	PUNCT
ejpam-3868	38	2	1	1	X
ejpam-3868	38	3	)	)	PUNCT
ejpam-3868	38	4	if	if	SCONJ
ejpam-3868	38	5	ω	ω	PROPN
ejpam-3868	38	6	is	be	AUX
ejpam-3868	38	7	a	a	DET
ejpam-3868	38	8	curvature	curvature	NOUN
ejpam-3868	38	9	two	two	NUM
ejpam-3868	38	10	-	-	PUNCT
ejpam-3868	38	11	form	form	NOUN
ejpam-3868	38	12	corresponding	correspond	VERB
ejpam-3868	38	13	to	to	ADP
ejpam-3868	38	14	ω	ω	NUM
ejpam-3868	38	15	,	,	PUNCT
ejpam-3868	38	16	the	the	DET
ejpam-3868	38	17	regauged	regauge	VERB
ejpam-3868	38	18	curvature	curvature	NOUN
ejpam-3868	38	19	is	be	AUX
ejpam-3868	38	20	h−1ωh	h−1ωh	VERB
ejpam-3868	38	21	.	.	PUNCT
ejpam-3868	39	1	introducing	introduce	VERB
ejpam-3868	39	2	h	h	NOUN
ejpam-3868	39	3	=	=	PUNCT
ejpam-3868	40	1	a	a	NOUN
ejpam-3868	40	2	d	d	PROPN
ejpam-3868	40	3	f	f	PROPN
ejpam-3868	40	4	0	0	PROPN
ejpam-3868	40	5	b	b	PROPN
ejpam-3868	40	6	e	e	X
ejpam-3868	40	7	0	0	NUM
ejpam-3868	40	8	0	0	NUM
ejpam-3868	40	9	c	c	NOUN
ejpam-3868	40	10			PROPN
ejpam-3868	40	11	(	(	PUNCT
ejpam-3868	40	12	2	2	NUM
ejpam-3868	40	13	)	)	PUNCT
ejpam-3868	40	14	p.	p.	NOUN
ejpam-3868	40	15	bracken	bracken	NOUN
ejpam-3868	40	16	/	/	SYM
ejpam-3868	40	17	eur	eur	PROPN
ejpam-3868	40	18	.	.	PUNCT
ejpam-3868	41	1	j.	j.	PROPN
ejpam-3868	41	2	pure	pure	PROPN
ejpam-3868	41	3	appl	appl	PROPN
ejpam-3868	41	4	.	.	PROPN
ejpam-3868	41	5	math	math	PROPN
ejpam-3868	41	6	,	,	PUNCT
ejpam-3868	41	7	13	13	NUM
ejpam-3868	41	8	(	(	PUNCT
ejpam-3868	41	9	4	4	NUM
ejpam-3868	41	10	)	)	PUNCT
ejpam-3868	41	11	(	(	PUNCT
ejpam-3868	41	12	2020	2020	NUM
ejpam-3868	41	13	)	)	PUNCT
ejpam-3868	41	14	,	,	PUNCT
ejpam-3868	41	15	1016	1016	NUM
ejpam-3868	41	16	-	-	SYM
ejpam-3868	41	17	1034	1034	NUM
ejpam-3868	41	18	1018	1018	NUM
ejpam-3868	42	1	where	where	SCONJ
ejpam-3868	42	2	abc	abc	PROPN
ejpam-3868	42	3	=	=	SYM
ejpam-3868	42	4	1	1	NUM
ejpam-3868	42	5	and	and	CCONJ
ejpam-3868	42	6	the	the	DET
ejpam-3868	42	7	inverse	inverse	NOUN
ejpam-3868	42	8	element	element	NOUN
ejpam-3868	42	9	is	be	AUX
ejpam-3868	42	10	calculated	calculate	VERB
ejpam-3868	42	11	to	to	PART
ejpam-3868	42	12	be	be	AUX
ejpam-3868	42	13	h−1	h−1	PROPN
ejpam-3868	42	14	=	=	SYM
ejpam-3868	42	15	a−1	a−1	NUM
ejpam-3868	42	16	−cd	−cd	PROPN
ejpam-3868	42	17	de	de	X
ejpam-3868	42	18	−bf	−bf	NOUN
ejpam-3868	42	19	0	0	NUM
ejpam-3868	43	1	b−1	b−1	PROPN
ejpam-3868	44	1	−ae	−ae	PROPN
ejpam-3868	44	2	0	0	NUM
ejpam-3868	44	3	0	0	NUM
ejpam-3868	44	4	0	0	NUM
ejpam-3868	44	5			PROPN
ejpam-3868	44	6	(	(	PUNCT
ejpam-3868	44	7	3	3	NUM
ejpam-3868	44	8	)	)	PUNCT
ejpam-3868	44	9	the	the	DET
ejpam-3868	44	10	effect	effect	NOUN
ejpam-3868	44	11	of	of	ADP
ejpam-3868	44	12	a	a	DET
ejpam-3868	44	13	change	change	NOUN
ejpam-3868	44	14	of	of	ADP
ejpam-3868	44	15	gauge	gauge	NOUN
ejpam-3868	44	16	on	on	ADP
ejpam-3868	44	17	the	the	DET
ejpam-3868	44	18	lower	low	ADJ
ejpam-3868	44	19	triangular	triangular	NOUN
ejpam-3868	44	20	terms	term	NOUN
ejpam-3868	44	21	is	be	AUX
ejpam-3868	44	22	of	of	ADP
ejpam-3868	44	23	most	most	ADJ
ejpam-3868	44	24	interest	interest	NOUN
ejpam-3868	44	25	.	.	PUNCT
ejpam-3868	45	1	since	since	SCONJ
ejpam-3868	45	2	h−1	h−1	PROPN
ejpam-3868	45	3	dh	dh	PROPN
ejpam-3868	45	4	is	be	AUX
ejpam-3868	45	5	upper	upper	ADJ
ejpam-3868	45	6	triangular	triangular	NOUN
ejpam-3868	45	7	,	,	PUNCT
ejpam-3868	45	8	it	it	PRON
ejpam-3868	45	9	has	have	VERB
ejpam-3868	45	10	no	no	DET
ejpam-3868	45	11	effect	effect	NOUN
ejpam-3868	45	12	on	on	ADP
ejpam-3868	45	13	these	these	DET
ejpam-3868	45	14	terms	term	NOUN
ejpam-3868	45	15	.	.	PUNCT
ejpam-3868	46	1	in	in	ADP
ejpam-3868	46	2	any	any	DET
ejpam-3868	46	3	event	event	NOUN
ejpam-3868	46	4	,	,	PUNCT
ejpam-3868	46	5	the	the	DET
ejpam-3868	46	6	entire	entire	ADJ
ejpam-3868	46	7	matrix	matrix	NOUN
ejpam-3868	46	8	can	can	AUX
ejpam-3868	46	9	be	be	AUX
ejpam-3868	46	10	computed	compute	VERB
ejpam-3868	46	11	.	.	PUNCT
ejpam-3868	47	1	suppose	suppose	VERB
ejpam-3868	47	2	ω	ω	NOUN
ejpam-3868	47	3	is	be	AUX
ejpam-3868	47	4	given	give	VERB
ejpam-3868	47	5	as	as	ADP
ejpam-3868	47	6	ω	ω	NOUN
ejpam-3868	47	7	=	=	SYM
ejpam-3868	47	8			PROPN
ejpam-3868	47	9	0	0	NUM
ejpam-3868	47	10	ω1	ω1	PROPN
ejpam-3868	47	11	2	2	NUM
ejpam-3868	47	12	ω1	ω1	PROPN
ejpam-3868	47	13	3	3	NUM
ejpam-3868	47	14	−ω1	−ω1	ADP
ejpam-3868	47	15	2	2	NUM
ejpam-3868	47	16	0	0	NUM
ejpam-3868	47	17	ω2	ω2	ADJ
ejpam-3868	47	18	3	3	NUM
ejpam-3868	47	19	−ω1	−ω1	NOUN
ejpam-3868	47	20	3	3	NUM
ejpam-3868	47	21	−ω2	−ω2	NOUN
ejpam-3868	47	22	3	3	NUM
ejpam-3868	47	23	0	0	NUM
ejpam-3868	47	24			PROPN
ejpam-3868	47	25	,	,	PUNCT
ejpam-3868	47	26	ωt	ωt	NOUN
ejpam-3868	47	27	=	=	PUNCT
ejpam-3868	47	28	−ω	−ω	NOUN
ejpam-3868	47	29	.	.	PUNCT
ejpam-3868	48	1	(	(	PUNCT
ejpam-3868	48	2	4	4	X
ejpam-3868	48	3	)	)	PUNCT
ejpam-3868	48	4	using	use	VERB
ejpam-3868	48	5	(	(	PUNCT
ejpam-3868	48	6	2	2	NUM
ejpam-3868	48	7	)	)	PUNCT
ejpam-3868	48	8	and	and	CCONJ
ejpam-3868	48	9	(	(	PUNCT
ejpam-3868	48	10	3	3	NUM
ejpam-3868	48	11	)	)	PUNCT
ejpam-3868	48	12	,	,	PUNCT
ejpam-3868	48	13	we	we	PRON
ejpam-3868	48	14	calculate	calculate	VERB
ejpam-3868	48	15	h−1	h−1	PROPN
ejpam-3868	48	16	ω	ω	NUM
ejpam-3868	48	17	h	h	NOUN
ejpam-3868	49	1	=	=	NOUN
ejpam-3868	49	2			NOUN
ejpam-3868	49	3	acdω1	acdω1	X
ejpam-3868	49	4	2	2	NUM
ejpam-3868	49	5	−a(de	−a(de	NOUN
ejpam-3868	49	6	−bf	−bf	PROPN
ejpam-3868	49	7	)	)	PUNCT
ejpam-3868	49	8	ω1	ω1	PROPN
ejpam-3868	49	9	3	3	NUM
ejpam-3868	49	10	a−1bω1	a−1bω1	NOUN
ejpam-3868	49	11	2	2	NUM
ejpam-3868	49	12	+	+	CCONJ
ejpam-3868	49	13	cd2ω1	cd2ω1	PROPN
ejpam-3868	49	14	2	2	NUM
ejpam-3868	49	15	a−1(eω1	a−1(eω1	NOUN
ejpam-3868	49	16	2	2	NUM
ejpam-3868	49	17	+	+	CCONJ
ejpam-3868	49	18	cω1	cω1	NOUN
ejpam-3868	49	19	3	3	NUM
ejpam-3868	49	20	)	)	PUNCT
ejpam-3868	49	21	+	+	NUM
ejpam-3868	49	22	cd(eω1	cd(eω1	AUX
ejpam-3868	49	23	2	2	NUM
ejpam-3868	49	24	−	−	NOUN
ejpam-3868	49	25	cω2	cω2	NOUN
ejpam-3868	49	26	3	3	X
ejpam-3868	49	27	)	)	PUNCT
ejpam-3868	49	28	−(de	−(de	PROPN
ejpam-3868	49	29	−bf	−bf	NOUN
ejpam-3868	49	30	)	)	PUNCT
ejpam-3868	49	31	(	(	PUNCT
ejpam-3868	49	32	dω1	dω1	X
ejpam-3868	49	33	3	3	NUM
ejpam-3868	49	34	−bω2	−bω2	NUM
ejpam-3868	49	35	3	3	NUM
ejpam-3868	49	36	)	)	PUNCT
ejpam-3868	49	37	−(de	−(de	PROPN
ejpam-3868	49	38	−bf	−bf	NOUN
ejpam-3868	49	39	)	)	PUNCT
ejpam-3868	49	40	(	(	PUNCT
ejpam-3868	49	41	fω1	fω1	NOUN
ejpam-3868	49	42	3	3	NUM
ejpam-3868	50	1	+	+	CCONJ
ejpam-3868	50	2	eω2	eω2	PROPN
ejpam-3868	50	3	3	3	NUM
ejpam-3868	50	4	)	)	PUNCT
ejpam-3868	50	5	−ab−1ω1	−ab−1ω1	NOUN
ejpam-3868	50	6	2	2	NUM
ejpam-3868	51	1	+	+	NOUN
ejpam-3868	51	2	a2eω1	a2eω1	NOUN
ejpam-3868	51	3	3	3	NUM
ejpam-3868	51	4	−b−1dω1	−b−1dω1	ADP
ejpam-3868	51	5	2	2	NUM
ejpam-3868	52	1	+	+	SYM
ejpam-3868	52	2	ae(dω1	ae(dω1	X
ejpam-3868	52	3	3	3	NUM
ejpam-3868	52	4	+	+	NOUN
ejpam-3868	52	5	bω2	bω2	NOUN
ejpam-3868	52	6	3	3	NUM
ejpam-3868	52	7	)	)	PUNCT
ejpam-3868	52	8	b−1(−fω1	b−1(−fω1	PROPN
ejpam-3868	52	9	2	2	NUM
ejpam-3868	52	10	+	+	CCONJ
ejpam-3868	52	11	cω2	cω2	NOUN
ejpam-3868	52	12	3	3	NUM
ejpam-3868	52	13	)	)	PUNCT
ejpam-3868	52	14	+	+	NOUN
ejpam-3868	52	15	ae(fω1	ae(fω1	X
ejpam-3868	52	16	3	3	NUM
ejpam-3868	52	17	+	+	CCONJ
ejpam-3868	52	18	eω2	eω2	PROPN
ejpam-3868	52	19	3	3	NUM
ejpam-3868	52	20	)	)	PUNCT
ejpam-3868	52	21	−c−1aω1	−c−1aω1	NUM
ejpam-3868	52	22	3	3	NUM
ejpam-3868	52	23	−c−1(dω1	−c−1(dω1	ADP
ejpam-3868	52	24	3	3	NUM
ejpam-3868	52	25	+	+	NOUN
ejpam-3868	52	26	bω2	bω2	NOUN
ejpam-3868	52	27	3	3	NUM
ejpam-3868	52	28	)	)	PUNCT
ejpam-3868	52	29	−c−1(fω1	−c−1(fω1	NOUN
ejpam-3868	52	30	3	3	NUM
ejpam-3868	53	1	+	+	CCONJ
ejpam-3868	53	2	eω2	eω2	PROPN
ejpam-3868	53	3	3	3	NUM
ejpam-3868	53	4	)	)	PUNCT
ejpam-3868	53	5			NOUN
ejpam-3868	53	6	(	(	PUNCT
ejpam-3868	53	7	5	5	X
ejpam-3868	53	8	)	)	PUNCT
ejpam-3868	53	9	let	let	VERB
ejpam-3868	53	10	ω	ω	NOUN
ejpam-3868	53	11	be	be	AUX
ejpam-3868	53	12	the	the	DET
ejpam-3868	53	13	curvature	curvature	NOUN
ejpam-3868	53	14	form	form	NOUN
ejpam-3868	53	15	given	give	VERB
ejpam-3868	53	16	by	by	ADP
ejpam-3868	53	17	ω	ω	PROPN
ejpam-3868	53	18	=	=	PUNCT
ejpam-3868	53	19	0	0	SCONJ
ejpam-3868	53	20	ω12	ω12	NOUN
ejpam-3868	53	21	ω13	ω13	VERB
ejpam-3868	53	22	0	0	NUM
ejpam-3868	53	23	0	0	NUM
ejpam-3868	53	24	ω23	ω23	NUM
ejpam-3868	53	25	0	0	NUM
ejpam-3868	53	26	0	0	NUM
ejpam-3868	53	27	0	0	NUM
ejpam-3868	54	1			PROPN
ejpam-3868	54	2	(	(	PUNCT
ejpam-3868	54	3	6	6	NUM
ejpam-3868	54	4	)	)	PUNCT
ejpam-3868	54	5	the	the	DET
ejpam-3868	54	6	effect	effect	NOUN
ejpam-3868	54	7	of	of	ADP
ejpam-3868	54	8	a	a	DET
ejpam-3868	54	9	change	change	NOUN
ejpam-3868	54	10	of	of	ADP
ejpam-3868	54	11	gauge	gauge	NOUN
ejpam-3868	54	12	on	on	ADP
ejpam-3868	54	13	(	(	PUNCT
ejpam-3868	54	14	6	6	NUM
ejpam-3868	54	15	)	)	PUNCT
ejpam-3868	54	16	using	use	VERB
ejpam-3868	54	17	(	(	PUNCT
ejpam-3868	54	18	3	3	NUM
ejpam-3868	54	19	)	)	PUNCT
ejpam-3868	54	20	is	be	AUX
ejpam-3868	54	21	found	find	VERB
ejpam-3868	54	22	to	to	PART
ejpam-3868	54	23	be	be	AUX
ejpam-3868	54	24	h−1	h−1	PROPN
ejpam-3868	54	25	ωh	ωh	ADP
ejpam-3868	54	26	=	=	PUNCT
ejpam-3868	54	27	0	0	ADV
ejpam-3868	54	28	a−1bω12	a−1bω12	PUNCT
ejpam-3868	54	29	a−1(e	a−1(e	VERB
ejpam-3868	54	30	+	+	CCONJ
ejpam-3868	54	31	c)ω13	c)ω13	NOUN
ejpam-3868	55	1	−	−	NOUN
ejpam-3868	56	1	c2dω23	c2dω23	NOUN
ejpam-3868	56	2	0	0	NUM
ejpam-3868	56	3	0	0	NUM
ejpam-3868	57	1	b−1cω23	b−1cω23	NOUN
ejpam-3868	57	2	0	0	NUM
ejpam-3868	57	3	0	0	NUM
ejpam-3868	57	4	0	0	NUM
ejpam-3868	58	1			PROPN
ejpam-3868	58	2	(	(	PUNCT
ejpam-3868	58	3	7	7	NUM
ejpam-3868	58	4	)	)	PUNCT
ejpam-3868	58	5	the	the	DET
ejpam-3868	58	6	equation	equation	NOUN
ejpam-3868	58	7	for	for	ADP
ejpam-3868	58	8	the	the	DET
ejpam-3868	58	9	development	development	NOUN
ejpam-3868	58	10	of	of	ADP
ejpam-3868	58	11	a	a	DET
ejpam-3868	58	12	curve	curve	NOUN
ejpam-3868	58	13	will	will	AUX
ejpam-3868	58	14	be	be	AUX
ejpam-3868	58	15	required	require	VERB
ejpam-3868	58	16	so	so	ADV
ejpam-3868	58	17	to	to	ADP
ejpam-3868	58	18	this	this	DET
ejpam-3868	58	19	end	end	NOUN
ejpam-3868	58	20	,	,	PUNCT
ejpam-3868	58	21	the	the	DET
ejpam-3868	58	22	following	follow	VERB
ejpam-3868	58	23	mapping	mapping	NOUN
ejpam-3868	58	24	is	be	AUX
ejpam-3868	58	25	proposed	propose	VERB
ejpam-3868	58	26	(	(	PUNCT
ejpam-3868	58	27	ξ	ξ	PROPN
ejpam-3868	58	28	,	,	PUNCT
ejpam-3868	58	29	η	η	PROPN
ejpam-3868	58	30	,	,	PUNCT
ejpam-3868	58	31	η′)→	η′)→	NOUN
ejpam-3868	58	32	1	1	X
ejpam-3868	58	33	0	0	NUM
ejpam-3868	58	34	0	0	SYM
ejpam-3868	58	35	ξ	ξ	SYM
ejpam-3868	58	36	1	1	NUM
ejpam-3868	58	37	0	0	NUM
ejpam-3868	58	38	η	η	PROPN
ejpam-3868	58	39	η′	η′	PROPN
ejpam-3868	58	40	1	1	NUM
ejpam-3868	58	41			PROPN
ejpam-3868	58	42	(	(	PUNCT
ejpam-3868	58	43	8)	8)	NUM
ejpam-3868	58	44	this	this	PRON
ejpam-3868	58	45	is	be	AUX
ejpam-3868	58	46	a	a	DET
ejpam-3868	58	47	local	local	ADJ
ejpam-3868	58	48	section	section	NOUN
ejpam-3868	58	49	of	of	ADP
ejpam-3868	58	50	sl(3,r	sl(3,r	ADJ
ejpam-3868	58	51	)	)	PUNCT
ejpam-3868	58	52	→	→	SYM
ejpam-3868	58	53	ptp	ptp	PROPN
ejpam-3868	58	54	2	2	NUM
ejpam-3868	58	55	.	.	PUNCT
ejpam-3868	59	1	the	the	DET
ejpam-3868	59	2	corresponding	correspond	VERB
ejpam-3868	59	3	maurer	maurer	PROPN
ejpam-3868	59	4	-	-	PUNCT
ejpam-3868	59	5	cartan	cartan	ADJ
ejpam-3868	59	6	form	form	NOUN
ejpam-3868	59	7	is	be	AUX
ejpam-3868	59	8	obtained	obtain	VERB
ejpam-3868	59	9	by	by	ADP
ejpam-3868	59	10	working	work	VERB
ejpam-3868	59	11	out	out	ADP
ejpam-3868	59	12	the	the	DET
ejpam-3868	59	13	exterior	exterior	ADJ
ejpam-3868	59	14	derivative	derivative	NOUN
ejpam-3868	59	15	of	of	ADP
ejpam-3868	59	16	(	(	PUNCT
ejpam-3868	59	17	8)	8)	NUM
ejpam-3868	59	18	,	,	PUNCT
ejpam-3868	59	19	at	at	ADP
ejpam-3868	59	20	this	this	DET
ejpam-3868	59	21	point	point	NOUN
ejpam-3868	59	22	,	,	PUNCT
ejpam-3868	59	23	the	the	DET
ejpam-3868	59	24	connection	connection	NOUN
ejpam-3868	59	25	form	form	NOUN
ejpam-3868	59	26	needed	need	VERB
ejpam-3868	59	27	to	to	PART
ejpam-3868	59	28	calculate	calculate	VERB
ejpam-3868	59	29	the	the	DET
ejpam-3868	59	30	development	development	NOUN
ejpam-3868	59	31	equations	equation	NOUN
ejpam-3868	59	32	later	later	ADV
ejpam-3868	59	33	is	be	AUX
ejpam-3868	59	34	given	give	VERB
ejpam-3868	59	35	,	,	PUNCT
ejpam-3868	59	36	ω	ω	X
ejpam-3868	59	37	=	=	X
ejpam-3868	59	38	ω0	ω0	NOUN
ejpam-3868	59	39	0	0	NUM
ejpam-3868	59	40	ω0	ω0	ADP
ejpam-3868	59	41	1	1	NUM
ejpam-3868	59	42	ω0	ω0	ADP
ejpam-3868	59	43	2	2	NUM
ejpam-3868	59	44	ω1	ω1	PROPN
ejpam-3868	59	45	0	0	NUM
ejpam-3868	59	46	ω1	ω1	PROPN
ejpam-3868	59	47	1	1	NUM
ejpam-3868	59	48	ω1	ω1	PROPN
ejpam-3868	59	49	2	2	NUM
ejpam-3868	59	50	ω2	ω2	NOUN
ejpam-3868	59	51	0	0	NUM
ejpam-3868	60	1	ω2	ω2	ADJ
ejpam-3868	60	2	1	1	NUM
ejpam-3868	60	3	ω2	ω2	ADJ
ejpam-3868	60	4	2	2	NUM
ejpam-3868	60	5			PROPN
ejpam-3868	60	6	(	(	PUNCT
ejpam-3868	60	7	9	9	NUM
ejpam-3868	60	8	)	)	PUNCT
ejpam-3868	60	9	p.	p.	NOUN
ejpam-3868	60	10	bracken	bracken	NOUN
ejpam-3868	60	11	/	/	SYM
ejpam-3868	60	12	eur	eur	PROPN
ejpam-3868	60	13	.	.	PUNCT
ejpam-3868	61	1	j.	j.	PROPN
ejpam-3868	61	2	pure	pure	PROPN
ejpam-3868	61	3	appl	appl	PROPN
ejpam-3868	61	4	.	.	PROPN
ejpam-3868	61	5	math	math	PROPN
ejpam-3868	61	6	,	,	PUNCT
ejpam-3868	61	7	13	13	NUM
ejpam-3868	61	8	(	(	PUNCT
ejpam-3868	61	9	4	4	NUM
ejpam-3868	61	10	)	)	PUNCT
ejpam-3868	61	11	(	(	PUNCT
ejpam-3868	61	12	2020	2020	NUM
ejpam-3868	61	13	)	)	PUNCT
ejpam-3868	61	14	,	,	PUNCT
ejpam-3868	61	15	1016	1016	NUM
ejpam-3868	61	16	-	-	SYM
ejpam-3868	61	17	1034	1034	NUM
ejpam-3868	61	18	1019	1019	NUM
ejpam-3868	61	19	the	the	DET
ejpam-3868	61	20	development	development	NOUN
ejpam-3868	61	21	equation	equation	NOUN
ejpam-3868	61	22	for	for	ADP
ejpam-3868	61	23	a	a	DET
ejpam-3868	61	24	curve	curve	NOUN
ejpam-3868	61	25	γ	γ	NOUN
ejpam-3868	61	26	in	in	ADP
ejpam-3868	61	27	ptm	ptm	PROPN
ejpam-3868	61	28	gives	give	VERB
ejpam-3868	61	29	aξ̇	aξ̇	PROPN
ejpam-3868	61	30	−	−	ADP
ejpam-3868	61	31	b(η̇	b(η̇	NOUN
ejpam-3868	61	32	−	−	PROPN
ejpam-3868	61	33	η′ξ̇	η′ξ̇	PROPN
ejpam-3868	61	34	)	)	PUNCT
ejpam-3868	61	35	=	=	PUNCT
ejpam-3868	62	1	〈	〈	PROPN
ejpam-3868	62	2	γ̇	γ̇	NOUN
ejpam-3868	62	3	,	,	PUNCT
ejpam-3868	62	4	ω1	ω1	PROPN
ejpam-3868	62	5	0	0	NUM
ejpam-3868	62	6	〉	〉	PROPN
ejpam-3868	62	7	,	,	PUNCT
ejpam-3868	62	8	c(η̇	c(η̇	ADP
ejpam-3868	62	9	−	−	PROPN
ejpam-3868	62	10	η′ξ̇	η′ξ̇	PROPN
ejpam-3868	62	11	)	)	PUNCT
ejpam-3868	62	12	=	=	PUNCT
ejpam-3868	63	1	〈	〈	PROPN
ejpam-3868	63	2	γ̇	γ̇	NOUN
ejpam-3868	63	3	,	,	PUNCT
ejpam-3868	63	4	ω2	ω2	PROPN
ejpam-3868	63	5	0	0	NUM
ejpam-3868	63	6	〉	〉	NUM
ejpam-3868	63	7	,	,	PUNCT
ejpam-3868	63	8	(	(	PUNCT
ejpam-3868	63	9	10	10	NUM
ejpam-3868	63	10	)	)	PUNCT
ejpam-3868	63	11	for	for	ADP
ejpam-3868	63	12	some	some	DET
ejpam-3868	63	13	functions	function	NOUN
ejpam-3868	63	14	a(t	a(t	NOUN
ejpam-3868	63	15	)	)	PUNCT
ejpam-3868	63	16	,	,	PUNCT
ejpam-3868	63	17	b(t	b(t	PROPN
ejpam-3868	63	18	)	)	PUNCT
ejpam-3868	63	19	,	,	PUNCT
ejpam-3868	63	20	c(t	c(t	PROPN
ejpam-3868	63	21	)	)	PUNCT
ejpam-3868	63	22	.	.	PUNCT
ejpam-3868	64	1	knowing	know	VERB
ejpam-3868	64	2	these	these	DET
ejpam-3868	64	3	formulas	formula	NOUN
ejpam-3868	64	4	,	,	PUNCT
ejpam-3868	64	5	the	the	DET
ejpam-3868	64	6	conditions	condition	NOUN
ejpam-3868	64	7	to	to	PART
ejpam-3868	64	8	be	be	AUX
ejpam-3868	64	9	imposed	impose	VERB
ejpam-3868	64	10	on	on	ADP
ejpam-3868	64	11	the	the	DET
ejpam-3868	64	12	development	development	NOUN
ejpam-3868	64	13	of	of	ADP
ejpam-3868	64	14	a	a	DET
ejpam-3868	64	15	curve	curve	NOUN
ejpam-3868	64	16	should	should	AUX
ejpam-3868	64	17	be	be	AUX
ejpam-3868	64	18	considered	consider	VERB
ejpam-3868	64	19	further	far	ADV
ejpam-3868	64	20	.	.	PUNCT
ejpam-3868	65	1	there	there	PRON
ejpam-3868	65	2	are	be	VERB
ejpam-3868	65	3	two	two	NUM
ejpam-3868	65	4	kinds	kind	NOUN
ejpam-3868	65	5	of	of	ADP
ejpam-3868	65	6	curve	curve	NOUN
ejpam-3868	65	7	on	on	ADP
ejpam-3868	65	8	ptm	ptm	PROPN
ejpam-3868	65	9	.	.	PUNCT
ejpam-3868	66	1	there	there	PRON
ejpam-3868	66	2	are	be	VERB
ejpam-3868	66	3	vertical	vertical	ADJ
ejpam-3868	66	4	curves	curve	NOUN
ejpam-3868	66	5	and	and	CCONJ
ejpam-3868	66	6	there	there	PRON
ejpam-3868	66	7	are	be	VERB
ejpam-3868	66	8	natural	natural	ADJ
ejpam-3868	66	9	lifts	lift	NOUN
ejpam-3868	66	10	.	.	PUNCT
ejpam-3868	67	1	with	with	ADP
ejpam-3868	67	2	respect	respect	NOUN
ejpam-3868	67	3	to	to	ADP
ejpam-3868	67	4	the	the	DET
ejpam-3868	67	5	coordinates	coordinate	NOUN
ejpam-3868	67	6	(	(	PUNCT
ejpam-3868	67	7	x	x	X
ejpam-3868	67	8	,	,	PUNCT
ejpam-3868	67	9	y	y	PROPN
ejpam-3868	67	10	,	,	PUNCT
ejpam-3868	67	11	y′	y′	NUM
ejpam-3868	67	12	)	)	PUNCT
ejpam-3868	67	13	introduced	introduce	VERB
ejpam-3868	67	14	above	above	ADV
ejpam-3868	67	15	,	,	PUNCT
ejpam-3868	67	16	a	a	DET
ejpam-3868	67	17	curve	curve	NOUN
ejpam-3868	67	18	in	in	ADP
ejpam-3868	67	19	ptm	ptm	PROPN
ejpam-3868	67	20	is	be	AUX
ejpam-3868	67	21	a	a	DET
ejpam-3868	67	22	natural	natural	ADJ
ejpam-3868	67	23	lift	lift	NOUN
ejpam-3868	67	24	if	if	SCONJ
ejpam-3868	67	25	its	its	PRON
ejpam-3868	67	26	tangent	tangent	NOUN
ejpam-3868	67	27	vector	vector	NOUN
ejpam-3868	67	28	is	be	AUX
ejpam-3868	67	29	annihilated	annihilate	VERB
ejpam-3868	67	30	by	by	ADP
ejpam-3868	67	31	the	the	DET
ejpam-3868	67	32	contact	contact	NOUN
ejpam-3868	67	33	form	form	NOUN
ejpam-3868	67	34	dy−y′dx	dy−y′dx	PROPN
ejpam-3868	67	35	.	.	PUNCT
ejpam-3868	68	1	the	the	DET
ejpam-3868	68	2	conditions	condition	NOUN
ejpam-3868	68	3	are	be	AUX
ejpam-3868	68	4	then	then	ADV
ejpam-3868	68	5	(	(	PUNCT
ejpam-3868	68	6	i	i	NOUN
ejpam-3868	68	7	)	)	PUNCT
ejpam-3868	68	8	the	the	DET
ejpam-3868	68	9	development	development	NOUN
ejpam-3868	68	10	into	into	ADP
ejpam-3868	68	11	ptp	ptp	PROPN
ejpam-3868	68	12	2	2	NUM
ejpam-3868	68	13	of	of	ADP
ejpam-3868	68	14	a	a	DET
ejpam-3868	68	15	natural	natural	ADJ
ejpam-3868	68	16	curve	curve	NOUN
ejpam-3868	68	17	in	in	ADP
ejpam-3868	68	18	ptm	ptm	PROPN
ejpam-3868	68	19	is	be	AUX
ejpam-3868	68	20	vertical	vertical	ADJ
ejpam-3868	68	21	(	(	PUNCT
ejpam-3868	68	22	ii	ii	NOUN
ejpam-3868	68	23	)	)	PUNCT
ejpam-3868	68	24	the	the	DET
ejpam-3868	68	25	development	development	NOUN
ejpam-3868	68	26	into	into	ADP
ejpam-3868	68	27	ptp	ptp	PROPN
ejpam-3868	68	28	2	2	NUM
ejpam-3868	68	29	of	of	ADP
ejpam-3868	68	30	a	a	DET
ejpam-3868	68	31	natural	natural	ADJ
ejpam-3868	68	32	lift	lift	NOUN
ejpam-3868	68	33	in	in	ADP
ejpam-3868	68	34	ptm	ptm	PROPN
ejpam-3868	68	35	is	be	AUX
ejpam-3868	68	36	a	a	DET
ejpam-3868	68	37	natural	natural	ADJ
ejpam-3868	68	38	lift	lift	NOUN
ejpam-3868	68	39	.	.	PUNCT
ejpam-3868	69	1	these	these	DET
ejpam-3868	69	2	conditions	condition	NOUN
ejpam-3868	69	3	require	require	VERB
ejpam-3868	69	4	that	that	SCONJ
ejpam-3868	69	5	if	if	SCONJ
ejpam-3868	69	6	γ	γ	NOUN
ejpam-3868	69	7	is	be	AUX
ejpam-3868	69	8	vertical	vertical	ADJ
ejpam-3868	69	9	then	then	ADV
ejpam-3868	69	10	〈	〈	PROPN
ejpam-3868	69	11	γ	γ	X
ejpam-3868	69	12	,	,	PUNCT
ejpam-3868	69	13	ω1	ω1	PROPN
ejpam-3868	69	14	0	0	NUM
ejpam-3868	69	15	〉	〉	PROPN
ejpam-3868	69	16	=	=	SYM
ejpam-3868	69	17	〈	〈	PROPN
ejpam-3868	69	18	γ	γ	X
ejpam-3868	69	19	,	,	PUNCT
ejpam-3868	69	20	ω2	ω2	ADJ
ejpam-3868	69	21	0	0	NUM
ejpam-3868	69	22	〉	〉	NUM
ejpam-3868	69	23	=	=	SYM
ejpam-3868	69	24	0	0	NUM
ejpam-3868	69	25	,	,	PUNCT
ejpam-3868	69	26	while	while	SCONJ
ejpam-3868	69	27	if	if	SCONJ
ejpam-3868	69	28	γ	γ	NOUN
ejpam-3868	69	29	is	be	AUX
ejpam-3868	69	30	a	a	DET
ejpam-3868	69	31	natural	natural	ADJ
ejpam-3868	69	32	lift	lift	NOUN
ejpam-3868	69	33	,	,	PUNCT
ejpam-3868	69	34	then	then	ADV
ejpam-3868	69	35	〈	〈	PROPN
ejpam-3868	69	36	γ	γ	X
ejpam-3868	69	37	,	,	PUNCT
ejpam-3868	69	38	ω2	ω2	ADJ
ejpam-3868	69	39	0	0	NUM
ejpam-3868	69	40	〉	〉	NUM
ejpam-3868	69	41	=	=	SYM
ejpam-3868	69	42	0	0	X
ejpam-3868	69	43	.	.	PUNCT
ejpam-3868	70	1	it	it	PRON
ejpam-3868	70	2	follows	follow	VERB
ejpam-3868	70	3	that	that	SCONJ
ejpam-3868	70	4	ω1	ω1	PROPN
ejpam-3868	70	5	0	0	PUNCT
ejpam-3868	70	6	=	=	SYM
ejpam-3868	70	7	λ	λ	PROPN
ejpam-3868	70	8	dx+	dx+	NOUN
ejpam-3868	70	9	µdy	µdy	NOUN
ejpam-3868	70	10	,	,	PUNCT
ejpam-3868	70	11	ω2	ω2	NOUN
ejpam-3868	70	12	0	0	X
ejpam-3868	70	13	=	=	SYM
ejpam-3868	70	14	ν(dy	ν(dy	NUM
ejpam-3868	70	15	−	−	NUM
ejpam-3868	70	16	y′	y′	NOUN
ejpam-3868	70	17	dx	dx	PROPN
ejpam-3868	70	18	)	)	PUNCT
ejpam-3868	70	19	.	.	PUNCT
ejpam-3868	71	1	(	(	PUNCT
ejpam-3868	71	2	11	11	NUM
ejpam-3868	71	3	)	)	PUNCT
ejpam-3868	71	4	for	for	ADP
ejpam-3868	71	5	some	some	DET
ejpam-3868	71	6	functions	function	NOUN
ejpam-3868	71	7	λ	λ	PROPN
ejpam-3868	71	8	,	,	PUNCT
ejpam-3868	71	9	µ	µ	NOUN
ejpam-3868	71	10	,	,	PUNCT
ejpam-3868	71	11	ν	ν	NOUN
ejpam-3868	71	12	on	on	ADP
ejpam-3868	71	13	ptm	ptm	PROPN
ejpam-3868	71	14	.	.	PUNCT
ejpam-3868	72	1	the	the	DET
ejpam-3868	72	2	connection	connection	NOUN
ejpam-3868	72	3	matrix	matrix	NOUN
ejpam-3868	72	4	ω	ω	NOUN
ejpam-3868	72	5	can	can	AUX
ejpam-3868	72	6	now	now	ADV
ejpam-3868	72	7	be	be	AUX
ejpam-3868	72	8	simplified	simplify	VERB
ejpam-3868	72	9	by	by	ADP
ejpam-3868	72	10	introducing	introduce	VERB
ejpam-3868	72	11	a	a	DET
ejpam-3868	72	12	change	change	NOUN
ejpam-3868	72	13	of	of	ADP
ejpam-3868	72	14	gauge	gauge	NOUN
ejpam-3868	72	15	,	,	PUNCT
ejpam-3868	72	16	so	so	ADV
ejpam-3868	72	17	setting	set	VERB
ejpam-3868	72	18	a	a	PRON
ejpam-3868	72	19	=	=	X
ejpam-3868	72	20	(	(	PUNCT
ejpam-3868	72	21	(	(	PUNCT
ejpam-3868	72	22	λ+	λ+	VERB
ejpam-3868	72	23	µy′)ν)−1/3	µy′)ν)−1/3	NOUN
ejpam-3868	72	24	,	,	PUNCT
ejpam-3868	72	25	b	b	NOUN
ejpam-3868	72	26	=	=	PUNCT
ejpam-3868	72	27	(	(	PUNCT
ejpam-3868	72	28	λ+	λ+	X
ejpam-3868	72	29	µy′)a	µy′)a	NUM
ejpam-3868	72	30	,	,	PUNCT
ejpam-3868	72	31	c	c	NOUN
ejpam-3868	72	32	=	=	SYM
ejpam-3868	72	33	νa	νa	NOUN
ejpam-3868	72	34	,	,	PUNCT
ejpam-3868	72	35	e	e	NOUN
ejpam-3868	72	36	=	=	SYM
ejpam-3868	72	37	µa	µa	PROPN
ejpam-3868	72	38	,	,	PUNCT
ejpam-3868	72	39	(	(	PUNCT
ejpam-3868	72	40	12	12	NUM
ejpam-3868	72	41	)	)	PUNCT
ejpam-3868	72	42	it	it	PRON
ejpam-3868	72	43	can	can	AUX
ejpam-3868	72	44	be	be	AUX
ejpam-3868	72	45	ensured	ensure	VERB
ejpam-3868	72	46	that	that	SCONJ
ejpam-3868	72	47	ω1	ω1	PROPN
ejpam-3868	72	48	0	0	PROPN
ejpam-3868	72	49	=	=	SYM
ejpam-3868	72	50	dx	dx	PROPN
ejpam-3868	72	51	and	and	CCONJ
ejpam-3868	72	52	ω2	ω2	NOUN
ejpam-3868	72	53	0	0	X
ejpam-3868	73	1	=	=	SYM
ejpam-3868	73	2	dy	dy	NOUN
ejpam-3868	73	3	−	−	NOUN
ejpam-3868	73	4	y′	y′	NOUN
ejpam-3868	73	5	dx	dx	PROPN
ejpam-3868	74	1	=	=	PUNCT
ejpam-3868	74	2	ϑ.	ϑ.	VERB
ejpam-3868	74	3	it	it	PRON
ejpam-3868	74	4	is	be	AUX
ejpam-3868	74	5	possible	possible	ADJ
ejpam-3868	74	6	to	to	PART
ejpam-3868	74	7	write	write	VERB
ejpam-3868	74	8	the	the	DET
ejpam-3868	74	9	form	form	NOUN
ejpam-3868	74	10	ω2	ω2	CCONJ
ejpam-3868	74	11	1	1	NUM
ejpam-3868	74	12	as	as	ADP
ejpam-3868	74	13	ω2	ω2	ADJ
ejpam-3868	74	14	1	1	NUM
ejpam-3868	74	15	=	=	SYM
ejpam-3868	74	16	k(dy′	k(dy′	ADP
ejpam-3868	74	17	−	−	PROPN
ejpam-3868	74	18	tdx	tdx	PROPN
ejpam-3868	74	19	)	)	PUNCT
ejpam-3868	75	1	+	+	NOUN
ejpam-3868	75	2	mdϑ	mdϑ	NOUN
ejpam-3868	75	3	for	for	ADP
ejpam-3868	75	4	some	some	DET
ejpam-3868	75	5	functions	function	NOUN
ejpam-3868	76	1	f	f	NOUN
ejpam-3868	76	2	,	,	PUNCT
ejpam-3868	76	3	k	k	PROPN
ejpam-3868	76	4	and	and	CCONJ
ejpam-3868	76	5	m	m	VERB
ejpam-3868	76	6	on	on	ADP
ejpam-3868	76	7	ptm	ptm	PROPN
ejpam-3868	76	8	.	.	PUNCT
ejpam-3868	77	1	the	the	DET
ejpam-3868	77	2	function	function	NOUN
ejpam-3868	77	3	k	k	PROPN
ejpam-3868	77	4	must	must	AUX
ejpam-3868	77	5	be	be	AUX
ejpam-3868	77	6	nonzero	nonzero	NOUN
ejpam-3868	77	7	because	because	SCONJ
ejpam-3868	77	8	the	the	DET
ejpam-3868	77	9	forms	form	NOUN
ejpam-3868	77	10	ω1	ω1	PROPN
ejpam-3868	77	11	0	0	NUM
ejpam-3868	77	12	,	,	PUNCT
ejpam-3868	77	13	ω2	ω2	NOUN
ejpam-3868	77	14	0	0	NUM
ejpam-3868	77	15	and	and	CCONJ
ejpam-3868	77	16	ω2	ω2	ADJ
ejpam-3868	77	17	1	1	NUM
ejpam-3868	77	18	have	have	VERB
ejpam-3868	77	19	to	to	PART
ejpam-3868	77	20	be	be	AUX
ejpam-3868	77	21	linearly	linearly	ADV
ejpam-3868	77	22	independent	independent	ADJ
ejpam-3868	77	23	.	.	PUNCT
ejpam-3868	78	1	upon	upon	SCONJ
ejpam-3868	78	2	setting	set	VERB
ejpam-3868	78	3	dy′	dy′	NOUN
ejpam-3868	78	4	−	−	PROPN
ejpam-3868	78	5	f	f	NOUN
ejpam-3868	78	6	dx	dx	PROPN
ejpam-3868	78	7	=	=	SYM
ejpam-3868	78	8	ϕ	ϕ	PROPN
ejpam-3868	78	9	,	,	PUNCT
ejpam-3868	78	10	the	the	DET
ejpam-3868	78	11	set	set	NOUN
ejpam-3868	78	12	of	of	ADP
ejpam-3868	78	13	forms	form	NOUN
ejpam-3868	78	14	dx	dx	PROPN
ejpam-3868	78	15	,	,	PUNCT
ejpam-3868	78	16	ϑ	ϑ	X
ejpam-3868	78	17	and	and	CCONJ
ejpam-3868	78	18	ϕ	ϕ	NOUN
ejpam-3868	78	19	constitute	constitute	VERB
ejpam-3868	78	20	a	a	DET
ejpam-3868	78	21	local	local	ADJ
ejpam-3868	78	22	basis	basis	NOUN
ejpam-3868	78	23	of	of	ADP
ejpam-3868	78	24	one	one	NUM
ejpam-3868	78	25	-	-	PUNCT
ejpam-3868	78	26	forms	form	NOUN
ejpam-3868	78	27	.	.	PUNCT
ejpam-3868	79	1	it	it	PRON
ejpam-3868	79	2	can	can	AUX
ejpam-3868	79	3	be	be	AUX
ejpam-3868	79	4	summarized	summarize	VERB
ejpam-3868	79	5	by	by	ADP
ejpam-3868	79	6	saying	say	VERB
ejpam-3868	79	7	that	that	SCONJ
ejpam-3868	79	8	a	a	DET
ejpam-3868	79	9	gauge	gauge	NOUN
ejpam-3868	79	10	has	have	AUX
ejpam-3868	79	11	been	be	AUX
ejpam-3868	79	12	chosen	choose	VERB
ejpam-3868	79	13	such	such	ADJ
ejpam-3868	79	14	that	that	SCONJ
ejpam-3868	79	15	ω	ω	PROPN
ejpam-3868	79	16	=	=	X
ejpam-3868	80	1	ω2	ω2	NOUN
ejpam-3868	80	2	0	0	NUM
ejpam-3868	80	3	ω0	ω0	PROPN
ejpam-3868	80	4	1	1	NUM
ejpam-3868	80	5	ω0	ω0	NUM
ejpam-3868	80	6	2	2	NUM
ejpam-3868	80	7	dx	dx	NOUN
ejpam-3868	80	8	ω1	ω1	PROPN
ejpam-3868	80	9	1	1	NUM
ejpam-3868	80	10	ω1	ω1	PROPN
ejpam-3868	80	11	2	2	NUM
ejpam-3868	80	12	ϑ	ϑ	NOUN
ejpam-3868	80	13	kϕ+mϑ	kϕ+mϑ	NOUN
ejpam-3868	80	14	ω2	ω2	PROPN
ejpam-3868	80	15	2	2	NUM
ejpam-3868	80	16			PROPN
ejpam-3868	80	17	(	(	PUNCT
ejpam-3868	80	18	13	13	NUM
ejpam-3868	80	19	)	)	PUNCT
ejpam-3868	80	20	the	the	DET
ejpam-3868	80	21	remaining	remain	VERB
ejpam-3868	80	22	gauge	gauge	NOUN
ejpam-3868	80	23	freedom	freedom	NOUN
ejpam-3868	80	24	involves	involve	VERB
ejpam-3868	80	25	the	the	DET
ejpam-3868	80	26	functions	function	NOUN
ejpam-3868	80	27	d	d	NOUN
ejpam-3868	80	28	and	and	CCONJ
ejpam-3868	80	29	f	f	PROPN
ejpam-3868	80	30	.	.	PUNCT
ejpam-3868	81	1	consider	consider	VERB
ejpam-3868	81	2	a	a	DET
ejpam-3868	81	3	further	further	ADJ
ejpam-3868	81	4	gauge	gauge	NOUN
ejpam-3868	81	5	change	change	NOUN
ejpam-3868	81	6	which	which	PRON
ejpam-3868	81	7	is	be	AUX
ejpam-3868	81	8	specified	specify	VERB
ejpam-3868	81	9	by	by	ADP
ejpam-3868	81	10	taking	take	VERB
ejpam-3868	81	11	h	h	NOUN
ejpam-3868	82	1	=	=	PUNCT
ejpam-3868	82	2	1	1	PROPN
ejpam-3868	82	3	d	d	X
ejpam-3868	82	4	f	f	PROPN
ejpam-3868	82	5	0	0	NUM
ejpam-3868	82	6	1	1	NUM
ejpam-3868	82	7	0	0	NUM
ejpam-3868	82	8	0	0	NUM
ejpam-3868	82	9	0	0	NUM
ejpam-3868	82	10	1	1	NUM
ejpam-3868	82	11			PROPN
ejpam-3868	82	12	,	,	PUNCT
ejpam-3868	83	1	h−1	h−1	PROPN
ejpam-3868	83	2	=	=	PUNCT
ejpam-3868	83	3	1	1	PROPN
ejpam-3868	83	4	−d	−d	VERB
ejpam-3868	83	5	−f	−f	NOUN
ejpam-3868	83	6	0	0	NUM
ejpam-3868	83	7	1	1	NUM
ejpam-3868	83	8	0	0	NUM
ejpam-3868	83	9	0	0	NUM
ejpam-3868	83	10	0	0	NUM
ejpam-3868	83	11	1	1	NUM
ejpam-3868	83	12			PROPN
ejpam-3868	83	13	(	(	PUNCT
ejpam-3868	83	14	14	14	NUM
ejpam-3868	83	15	)	)	PUNCT
ejpam-3868	83	16	by	by	ADP
ejpam-3868	83	17	using	use	VERB
ejpam-3868	83	18	(	(	PUNCT
ejpam-3868	83	19	13	13	NUM
ejpam-3868	83	20	)	)	PUNCT
ejpam-3868	83	21	and	and	CCONJ
ejpam-3868	83	22	(	(	PUNCT
ejpam-3868	83	23	14	14	NUM
ejpam-3868	83	24	)	)	PUNCT
ejpam-3868	83	25	,	,	PUNCT
ejpam-3868	83	26	we	we	PRON
ejpam-3868	83	27	find	find	VERB
ejpam-3868	83	28	that	that	SCONJ
ejpam-3868	83	29	h−1	h−1	PROPN
ejpam-3868	83	30	ω	ω	PROPN
ejpam-3868	83	31	h+	h+	PROPN
ejpam-3868	83	32	h−1	h−1	PROPN
ejpam-3868	83	33	dh	dh	NOUN
ejpam-3868	84	1	=	=	NOUN
ejpam-3868	84	2	ω0	ω0	NOUN
ejpam-3868	84	3	0	0	PUNCT
ejpam-3868	85	1	−ddx−	−ddx−	PROPN
ejpam-3868	85	2	fϑ	fϑ	PROPN
ejpam-3868	85	3	ω0	ω0	PROPN
ejpam-3868	85	4	1	1	NUM
ejpam-3868	85	5	−dω1	−dω1	ADP
ejpam-3868	85	6	1	1	NUM
ejpam-3868	85	7	−	−	NOUN
ejpam-3868	85	8	fω2	fω2	NOUN
ejpam-3868	85	9	1	1	NUM
ejpam-3868	85	10	+	+	NUM
ejpam-3868	85	11	dd	dd	NOUN
ejpam-3868	85	12	ω0	ω0	NOUN
ejpam-3868	85	13	2	2	NUM
ejpam-3868	85	14	−dω1	−dω1	ADP
ejpam-3868	85	15	2	2	NUM
ejpam-3868	85	16	−	−	NOUN
ejpam-3868	85	17	fω2	fω2	NOUN
ejpam-3868	85	18	2	2	NUM
ejpam-3868	85	19	+	+	NUM
ejpam-3868	85	20	df	df	PROPN
ejpam-3868	85	21	dx	dx	PROPN
ejpam-3868	85	22	ω1	ω1	PROPN
ejpam-3868	85	23	1	1	NUM
ejpam-3868	85	24	ω1	ω1	PROPN
ejpam-3868	85	25	2	2	NUM
ejpam-3868	85	26	ϑ	ϑ	X
ejpam-3868	85	27	ω2	ω2	ADJ
ejpam-3868	85	28	1	1	NUM
ejpam-3868	85	29	ω2	ω2	PROPN
ejpam-3868	85	30	2	2	NUM
ejpam-3868	85	31			PROPN
ejpam-3868	85	32	(	(	PUNCT
ejpam-3868	85	33	15	15	NUM
ejpam-3868	85	34	)	)	PUNCT
ejpam-3868	85	35	p.	p.	NOUN
ejpam-3868	85	36	bracken	bracken	NOUN
ejpam-3868	85	37	/	/	SYM
ejpam-3868	85	38	eur	eur	PROPN
ejpam-3868	85	39	.	.	PUNCT
ejpam-3868	86	1	j.	j.	PROPN
ejpam-3868	86	2	pure	pure	PROPN
ejpam-3868	86	3	appl	appl	PROPN
ejpam-3868	86	4	.	.	PROPN
ejpam-3868	86	5	math	math	PROPN
ejpam-3868	86	6	,	,	PUNCT
ejpam-3868	86	7	13	13	NUM
ejpam-3868	86	8	(	(	PUNCT
ejpam-3868	86	9	4	4	NUM
ejpam-3868	86	10	)	)	PUNCT
ejpam-3868	86	11	(	(	PUNCT
ejpam-3868	86	12	2020	2020	NUM
ejpam-3868	86	13	)	)	PUNCT
ejpam-3868	86	14	,	,	PUNCT
ejpam-3868	86	15	1016	1016	NUM
ejpam-3868	86	16	-	-	SYM
ejpam-3868	86	17	1034	1034	NUM
ejpam-3868	86	18	1020	1020	NUM
ejpam-3868	86	19	therefore	therefore	ADV
ejpam-3868	86	20	,	,	PUNCT
ejpam-3868	86	21	a	a	DET
ejpam-3868	86	22	gauge	gauge	NOUN
ejpam-3868	86	23	can	can	AUX
ejpam-3868	86	24	be	be	AUX
ejpam-3868	86	25	chosen	choose	VERB
ejpam-3868	86	26	for	for	ADP
ejpam-3868	86	27	any	any	DET
ejpam-3868	86	28	projective	projective	NOUN
ejpam-3868	86	29	connectionof	connectionof	NOUN
ejpam-3868	86	30	a	a	DET
ejpam-3868	86	31	manifold	manifold	NOUN
ejpam-3868	86	32	of	of	ADP
ejpam-3868	86	33	elements	element	NOUN
ejpam-3868	86	34	such	such	ADJ
ejpam-3868	86	35	that	that	DET
ejpam-3868	86	36	ω1	ω1	PROPN
ejpam-3868	86	37	0	0	NUM
ejpam-3868	86	38	=	=	SYM
ejpam-3868	86	39	dx	dx	PROPN
ejpam-3868	86	40	,	,	PUNCT
ejpam-3868	86	41	ω2	ω2	NOUN
ejpam-3868	86	42	0	0	NUM
ejpam-3868	87	1	=	=	SYM
ejpam-3868	87	2	ϑ	ϑ	X
ejpam-3868	87	3	,	,	PUNCT
ejpam-3868	87	4	ω0	ω0	PROPN
ejpam-3868	87	5	0	0	NUM
ejpam-3868	87	6	=	=	SYM
ejpam-3868	87	7	κϕ	κϕ	NOUN
ejpam-3868	87	8	,	,	PUNCT
ejpam-3868	87	9	(	(	PUNCT
ejpam-3868	87	10	16	16	NUM
ejpam-3868	87	11	)	)	PUNCT
ejpam-3868	87	12	for	for	ADP
ejpam-3868	87	13	some	some	DET
ejpam-3868	87	14	function	function	NOUN
ejpam-3868	87	15	κ	κ	NOUN
ejpam-3868	87	16	.	.	PUNCT
ejpam-3868	88	1	this	this	PRON
ejpam-3868	88	2	is	be	AUX
ejpam-3868	88	3	referred	refer	VERB
ejpam-3868	88	4	to	to	ADP
ejpam-3868	88	5	as	as	ADP
ejpam-3868	88	6	the	the	DET
ejpam-3868	88	7	standard	standard	ADJ
ejpam-3868	88	8	gauge	gauge	NOUN
ejpam-3868	88	9	for	for	ADP
ejpam-3868	88	10	the	the	DET
ejpam-3868	88	11	projective	projective	ADJ
ejpam-3868	88	12	connection	connection	NOUN
ejpam-3868	88	13	.	.	PUNCT
ejpam-3868	89	1	a	a	DET
ejpam-3868	89	2	geodesic	geodesic	NOUN
ejpam-3868	89	3	of	of	ADP
ejpam-3868	89	4	this	this	DET
ejpam-3868	89	5	projective	projective	ADJ
ejpam-3868	89	6	connection	connection	NOUN
ejpam-3868	89	7	is	be	AUX
ejpam-3868	89	8	a	a	DET
ejpam-3868	89	9	curve	curve	NOUN
ejpam-3868	89	10	whose	whose	DET
ejpam-3868	89	11	development	development	NOUN
ejpam-3868	89	12	satisfies	satisfy	VERB
ejpam-3868	89	13	the	the	DET
ejpam-3868	89	14	equations	equation	NOUN
ejpam-3868	89	15	η̇	η̇	PROPN
ejpam-3868	89	16	−	−	PROPN
ejpam-3868	89	17	η′ξ	η′ξ	VERB
ejpam-3868	89	18	=	=	NOUN
ejpam-3868	89	19	0	0	NUM
ejpam-3868	89	20	and	and	CCONJ
ejpam-3868	89	21	η̇′	η̇′	NOUN
ejpam-3868	89	22	=	=	SYM
ejpam-3868	90	1	0	0	X
ejpam-3868	90	2	.	.	PUNCT
ejpam-3868	90	3	put	put	VERB
ejpam-3868	90	4	another	another	DET
ejpam-3868	90	5	way	way	NOUN
ejpam-3868	90	6	,	,	PUNCT
ejpam-3868	90	7	a	a	DET
ejpam-3868	90	8	geodesic	geodesic	NOUN
ejpam-3868	90	9	is	be	AUX
ejpam-3868	90	10	a	a	DET
ejpam-3868	90	11	curve	curve	NOUN
ejpam-3868	90	12	whose	whose	DET
ejpam-3868	90	13	tangents	tangent	NOUN
ejpam-3868	90	14	are	be	AUX
ejpam-3868	90	15	annihilated	annihilate	VERB
ejpam-3868	90	16	by	by	ADP
ejpam-3868	90	17	ϑ	ϑ	PROPN
ejpam-3868	90	18	and	and	CCONJ
ejpam-3868	90	19	ϕ	ϕ	NOUN
ejpam-3868	90	20	,	,	PUNCT
ejpam-3868	90	21	and	and	CCONJ
ejpam-3868	90	22	therefore	therefore	ADV
ejpam-3868	90	23	is	be	AUX
ejpam-3868	90	24	a	a	DET
ejpam-3868	90	25	solution	solution	NOUN
ejpam-3868	90	26	of	of	ADP
ejpam-3868	90	27	the	the	DET
ejpam-3868	90	28	second	second	ADJ
ejpam-3868	90	29	-	-	PUNCT
ejpam-3868	90	30	order	order	NOUN
ejpam-3868	90	31	equation	equation	NOUN
ejpam-3868	90	32	d2y	d2y	NOUN
ejpam-3868	90	33	dx2	dx2	PROPN
ejpam-3868	90	34	=	=	SYM
ejpam-3868	90	35	f(x	f(x	PROPN
ejpam-3868	90	36	,	,	PUNCT
ejpam-3868	90	37	y	y	PROPN
ejpam-3868	90	38	,	,	PUNCT
ejpam-3868	90	39	dy	dy	PROPN
ejpam-3868	90	40	dx	dx	PROPN
ejpam-3868	90	41	)	)	PUNCT
ejpam-3868	90	42	.	.	PUNCT
ejpam-3868	91	1	(	(	PUNCT
ejpam-3868	91	2	17	17	NUM
ejpam-3868	91	3	)	)	PUNCT
ejpam-3868	91	4	geodesics	geodesic	NOUN
ejpam-3868	91	5	are	be	AUX
ejpam-3868	91	6	the	the	DET
ejpam-3868	91	7	base	base	ADJ
ejpam-3868	91	8	integral	integral	ADJ
ejpam-3868	91	9	curves	curve	NOUN
ejpam-3868	91	10	of	of	ADP
ejpam-3868	91	11	the	the	DET
ejpam-3868	91	12	following	follow	VERB
ejpam-3868	91	13	vector	vector	NOUN
ejpam-3868	91	14	field	field	NOUN
ejpam-3868	91	15	on	on	ADP
ejpam-3868	91	16	ptm	ptm	PROPN
ejpam-3868	91	17	,	,	PUNCT
ejpam-3868	91	18	γ	γ	NOUN
ejpam-3868	91	19	=	=	SYM
ejpam-3868	91	20	∂	∂	NOUN
ejpam-3868	91	21	∂x	∂x	PROPN
ejpam-3868	92	1	+	+	CCONJ
ejpam-3868	92	2	y′	y′	NOUN
ejpam-3868	92	3	∂	∂	X
ejpam-3868	92	4	∂y	∂y	NOUN
ejpam-3868	93	1	+	+	CCONJ
ejpam-3868	93	2	f	f	PROPN
ejpam-3868	93	3	∂	∂	PROPN
ejpam-3868	93	4	∂y′	∂y′	PROPN
ejpam-3868	93	5	.	.	PUNCT
ejpam-3868	94	1	(	(	PUNCT
ejpam-3868	94	2	18	18	NUM
ejpam-3868	94	3	)	)	PUNCT
ejpam-3868	94	4	this	this	PRON
ejpam-3868	94	5	can	can	AUX
ejpam-3868	94	6	be	be	AUX
ejpam-3868	94	7	referred	refer	VERB
ejpam-3868	94	8	to	to	ADP
ejpam-3868	94	9	as	as	ADP
ejpam-3868	94	10	the	the	DET
ejpam-3868	94	11	second	second	ADJ
ejpam-3868	94	12	-	-	PUNCT
ejpam-3868	94	13	order	order	NOUN
ejpam-3868	94	14	differential	differential	ADJ
ejpam-3868	94	15	equation	equation	NOUN
ejpam-3868	94	16	field	field	NOUN
ejpam-3868	94	17	corresponding	correspond	VERB
ejpam-3868	94	18	to	to	ADP
ejpam-3868	94	19	the	the	DET
ejpam-3868	94	20	projective	projective	ADJ
ejpam-3868	94	21	connection	connection	NOUN
ejpam-3868	94	22	.	.	PUNCT
ejpam-3868	95	1	note	note	VERB
ejpam-3868	95	2	that	that	SCONJ
ejpam-3868	95	3	γ	γ	PROPN
ejpam-3868	95	4	is	be	AUX
ejpam-3868	95	5	determined	determine	VERB
ejpam-3868	95	6	by	by	ADP
ejpam-3868	95	7	the	the	DET
ejpam-3868	95	8	conditions	condition	NOUN
ejpam-3868	95	9	〈	〈	PROPN
ejpam-3868	95	10	γ	γ	X
ejpam-3868	95	11	,	,	PUNCT
ejpam-3868	95	12	dx	dx	PROPN
ejpam-3868	95	13	〉	〉	NOUN
ejpam-3868	95	14	=	=	SYM
ejpam-3868	95	15	1	1	NUM
ejpam-3868	95	16	,	,	PUNCT
ejpam-3868	95	17	〈	〈	PROPN
ejpam-3868	95	18	γ	γ	X
ejpam-3868	95	19	,	,	PUNCT
ejpam-3868	95	20	ϑ	ϑ	NOUN
ejpam-3868	95	21	〉	〉	NOUN
ejpam-3868	95	22	=	=	SYM
ejpam-3868	95	23	〈	〈	PROPN
ejpam-3868	95	24	γ	γ	X
ejpam-3868	95	25	,	,	PUNCT
ejpam-3868	95	26	ϕ	ϕ	PROPN
ejpam-3868	95	27	〉	〉	NOUN
ejpam-3868	95	28	=	=	SYM
ejpam-3868	95	29	0	0	PROPN
ejpam-3868	95	30	.	.	PUNCT
ejpam-3868	96	1	(	(	PUNCT
ejpam-3868	96	2	19	19	NUM
ejpam-3868	96	3	)	)	PUNCT
ejpam-3868	96	4	under	under	ADP
ejpam-3868	96	5	a	a	DET
ejpam-3868	96	6	change	change	NOUN
ejpam-3868	96	7	of	of	ADP
ejpam-3868	96	8	coordinates	coordinate	NOUN
ejpam-3868	96	9	on	on	ADP
ejpam-3868	96	10	the	the	DET
ejpam-3868	96	11	base	base	NOUN
ejpam-3868	96	12	manifold	manifold	ADJ
ejpam-3868	96	13	m	m	NOUN
ejpam-3868	96	14	,	,	PUNCT
ejpam-3868	96	15	with	with	ADP
ejpam-3868	96	16	induced	induced	ADJ
ejpam-3868	96	17	change	change	NOUN
ejpam-3868	96	18	on	on	ADP
ejpam-3868	96	19	ptm	ptm	PROPN
ejpam-3868	96	20	,	,	PUNCT
ejpam-3868	96	21	the	the	DET
ejpam-3868	96	22	field	field	NOUN
ejpam-3868	96	23	γ	γ	PROPN
ejpam-3868	96	24	will	will	AUX
ejpam-3868	96	25	acquire	acquire	VERB
ejpam-3868	96	26	an	an	DET
ejpam-3868	96	27	overall	overall	ADJ
ejpam-3868	96	28	factor	factor	NOUN
ejpam-3868	96	29	which	which	PRON
ejpam-3868	96	30	depends	depend	VERB
ejpam-3868	96	31	on	on	ADP
ejpam-3868	96	32	the	the	DET
ejpam-3868	96	33	coordinate	coordinate	NOUN
ejpam-3868	96	34	transformation	transformation	NOUN
ejpam-3868	96	35	functions	function	NOUN
ejpam-3868	96	36	.	.	PUNCT
ejpam-3868	97	1	it	it	PRON
ejpam-3868	97	2	may	may	AUX
ejpam-3868	97	3	be	be	AUX
ejpam-3868	97	4	said	say	VERB
ejpam-3868	97	5	that	that	SCONJ
ejpam-3868	97	6	we	we	PRON
ejpam-3868	97	7	are	be	AUX
ejpam-3868	97	8	really	really	ADV
ejpam-3868	97	9	working	work	VERB
ejpam-3868	97	10	not	not	PART
ejpam-3868	97	11	with	with	ADP
ejpam-3868	97	12	a	a	DET
ejpam-3868	97	13	vector	vector	NOUN
ejpam-3868	97	14	field	field	NOUN
ejpam-3868	97	15	γ	γ	NOUN
ejpam-3868	97	16	,	,	PUNCT
ejpam-3868	97	17	but	but	CCONJ
ejpam-3868	97	18	with	with	ADP
ejpam-3868	97	19	a	a	DET
ejpam-3868	97	20	line	line	NOUN
ejpam-3868	97	21	element	element	NOUN
ejpam-3868	97	22	field	field	NOUN
ejpam-3868	97	23	.	.	PUNCT
ejpam-3868	98	1	having	having	AUX
ejpam-3868	98	2	fixed	fix	VERB
ejpam-3868	98	3	the	the	DET
ejpam-3868	98	4	gauge	gauge	NOUN
ejpam-3868	98	5	,	,	PUNCT
ejpam-3868	98	6	the	the	DET
ejpam-3868	98	7	next	next	ADJ
ejpam-3868	98	8	step	step	NOUN
ejpam-3868	98	9	is	be	AUX
ejpam-3868	98	10	to	to	PART
ejpam-3868	98	11	impose	impose	VERB
ejpam-3868	98	12	gauge	gauge	ADJ
ejpam-3868	98	13	-	-	PUNCT
ejpam-3868	98	14	invariant	invariant	ADJ
ejpam-3868	98	15	conditions	condition	NOUN
ejpam-3868	98	16	on	on	ADP
ejpam-3868	98	17	the	the	DET
ejpam-3868	98	18	curvature	curvature	NOUN
ejpam-3868	98	19	in	in	ADP
ejpam-3868	98	20	order	order	NOUN
ejpam-3868	98	21	to	to	PART
ejpam-3868	98	22	single	single	VERB
ejpam-3868	98	23	out	out	ADP
ejpam-3868	98	24	a	a	DET
ejpam-3868	98	25	particular	particular	ADJ
ejpam-3868	98	26	connection	connection	NOUN
ejpam-3868	98	27	form	form	NOUN
ejpam-3868	98	28	out	out	ADP
ejpam-3868	98	29	of	of	ADP
ejpam-3868	98	30	the	the	DET
ejpam-3868	98	31	class	class	NOUN
ejpam-3868	98	32	of	of	ADP
ejpam-3868	98	33	connections	connection	NOUN
ejpam-3868	98	34	under	under	ADP
ejpam-3868	98	35	consideration	consideration	NOUN
ejpam-3868	98	36	.	.	PUNCT
ejpam-3868	99	1	in	in	ADP
ejpam-3868	99	2	fact	fact	NOUN
ejpam-3868	99	3	,	,	PUNCT
ejpam-3868	99	4	cartan	cartan	PROPN
ejpam-3868	99	5	showed	show	VERB
ejpam-3868	99	6	in	in	ADP
ejpam-3868	99	7	effect	effect	NOUN
ejpam-3868	99	8	that	that	SCONJ
ejpam-3868	99	9	there	there	PRON
ejpam-3868	99	10	is	be	VERB
ejpam-3868	99	11	a	a	DET
ejpam-3868	99	12	unique	unique	ADJ
ejpam-3868	99	13	choice	choice	NOUN
ejpam-3868	99	14	of	of	ADP
ejpam-3868	99	15	the	the	DET
ejpam-3868	99	16	remaining	remain	VERB
ejpam-3868	99	17	connection	connection	NOUN
ejpam-3868	99	18	forms	form	NOUN
ejpam-3868	99	19	so	so	SCONJ
ejpam-3868	99	20	that	that	SCONJ
ejpam-3868	99	21	the	the	DET
ejpam-3868	99	22	curvature	curvature	NOUN
ejpam-3868	99	23	ω	ω	PROPN
ejpam-3868	99	24	is	be	AUX
ejpam-3868	99	25	upper	upper	ADJ
ejpam-3868	99	26	triangular	triangular	NOUN
ejpam-3868	99	27	,	,	PUNCT
ejpam-3868	99	28	with	with	ADP
ejpam-3868	99	29	ω0	ω0	PROPN
ejpam-3868	99	30	1	1	NUM
ejpam-3868	99	31	a	a	DET
ejpam-3868	99	32	multiple	multiple	NOUN
ejpam-3868	99	33	of	of	ADP
ejpam-3868	99	34	dx	dx	PROPN
ejpam-3868	99	35	∧	∧	PROPN
ejpam-3868	99	36	ϑ.	ϑ.	VERB
ejpam-3868	99	37	the	the	DET
ejpam-3868	99	38	unique	unique	ADJ
ejpam-3868	99	39	connection	connection	NOUN
ejpam-3868	99	40	obtained	obtain	VERB
ejpam-3868	99	41	this	this	DET
ejpam-3868	99	42	way	way	NOUN
ejpam-3868	99	43	is	be	AUX
ejpam-3868	99	44	usually	usually	ADV
ejpam-3868	99	45	referred	refer	VERB
ejpam-3868	99	46	to	to	ADP
ejpam-3868	99	47	as	as	ADP
ejpam-3868	99	48	the	the	DET
ejpam-3868	99	49	normal	normal	ADJ
ejpam-3868	99	50	projective	projective	ADJ
ejpam-3868	99	51	connection	connection	NOUN
ejpam-3868	99	52	on	on	ADP
ejpam-3868	99	53	the	the	DET
ejpam-3868	99	54	manifold	manifold	NOUN
ejpam-3868	99	55	of	of	ADP
ejpam-3868	99	56	elements	element	NOUN
ejpam-3868	99	57	associated	associate	VERB
ejpam-3868	99	58	with	with	ADP
ejpam-3868	99	59	the	the	DET
ejpam-3868	99	60	second	second	ADJ
ejpam-3868	99	61	order	order	NOUN
ejpam-3868	99	62	differential	differential	NOUN
ejpam-3868	99	63	equation	equation	NOUN
ejpam-3868	99	64	.	.	PUNCT
ejpam-3868	100	1	3	3	X
ejpam-3868	100	2	.	.	PUNCT
ejpam-3868	100	3	model	model	NOUN
ejpam-3868	100	4	geometry	geometry	NOUN
ejpam-3868	100	5	and	and	CCONJ
ejpam-3868	100	6	duality	duality	NOUN
ejpam-3868	100	7	of	of	ADP
ejpam-3868	100	8	points	point	NOUN
ejpam-3868	100	9	and	and	CCONJ
ejpam-3868	100	10	lines	line	NOUN
ejpam-3868	100	11	in	in	ADP
ejpam-3868	100	12	projective	projective	ADJ
ejpam-3868	100	13	geometry	geometry	NOUN
ejpam-3868	100	14	let	let	VERB
ejpam-3868	100	15	m	m	PRON
ejpam-3868	100	16	and	and	CCONJ
ejpam-3868	100	17	m̄	m̄	VERB
ejpam-3868	100	18	be	be	AUX
ejpam-3868	100	19	two	two	NUM
ejpam-3868	100	20	-	-	PUNCT
ejpam-3868	100	21	dimensional	dimensional	ADJ
ejpam-3868	100	22	manifolds	manifold	NOUN
ejpam-3868	100	23	,	,	PUNCT
ejpam-3868	100	24	and	and	CCONJ
ejpam-3868	100	25	s	s	VERB
ejpam-3868	100	26	a	a	DET
ejpam-3868	100	27	co	co	NOUN
ejpam-3868	100	28	-	-	NOUN
ejpam-3868	100	29	dimension	dimension	ADJ
ejpam-3868	100	30	one	one	NUM
ejpam-3868	100	31	submanifold	submanifold	NOUN
ejpam-3868	100	32	of	of	ADP
ejpam-3868	100	33	m	m	PROPN
ejpam-3868	100	34	×	×	PROPN
ejpam-3868	100	35	m̄	m̄	NOUN
ejpam-3868	100	36	,	,	PUNCT
ejpam-3868	100	37	which	which	PRON
ejpam-3868	100	38	is	be	AUX
ejpam-3868	100	39	fibered	fibere	VERB
ejpam-3868	100	40	over	over	ADP
ejpam-3868	100	41	both	both	DET
ejpam-3868	100	42	m	m	PROPN
ejpam-3868	100	43	and	and	CCONJ
ejpam-3868	100	44	m̄	m̄	VERB
ejpam-3868	100	45	.	.	PUNCT
ejpam-3868	101	1	for	for	ADP
ejpam-3868	101	2	any	any	DET
ejpam-3868	101	3	p̄	p̄	PROPN
ejpam-3868	101	4	∈	∈	PROPN
ejpam-3868	101	5	m̄	m̄	NOUN
ejpam-3868	101	6	the	the	DET
ejpam-3868	101	7	set	set	NOUN
ejpam-3868	101	8	{	{	PUNCT
ejpam-3868	101	9	p	p	NOUN
ejpam-3868	101	10	∈m	∈m	NOUN
ejpam-3868	101	11	|(p	|(p	ADV
ejpam-3868	101	12	,	,	PUNCT
ejpam-3868	101	13	p̄	p̄	NOUN
ejpam-3868	101	14	)	)	PUNCT
ejpam-3868	101	15	∈	∈	PROPN
ejpam-3868	101	16	s	s	PART
ejpam-3868	101	17	}	}	PUNCT
ejpam-3868	101	18	is	be	AUX
ejpam-3868	101	19	a	a	DET
ejpam-3868	101	20	path	path	NOUN
ejpam-3868	101	21	in	in	ADP
ejpam-3868	101	22	m	m	PROPN
ejpam-3868	101	23	,	,	PUNCT
ejpam-3868	101	24	call	call	VERB
ejpam-3868	101	25	it	it	PRON
ejpam-3868	101	26	σp̄.	σp̄.	VERB
ejpam-3868	101	27	for	for	ADP
ejpam-3868	101	28	p	p	PROPN
ejpam-3868	101	29	∈	∈	PROPN
ejpam-3868	101	30	m	m	NOUN
ejpam-3868	101	31	,	,	PUNCT
ejpam-3868	101	32	{	{	PUNCT
ejpam-3868	101	33	p̄	p̄	PROPN
ejpam-3868	101	34	∈	∈	PROPN
ejpam-3868	101	35	m̄	m̄	PROPN
ejpam-3868	101	36	|(p	|(p	PROPN
ejpam-3868	101	37	,	,	PUNCT
ejpam-3868	101	38	p̄	p̄	NOUN
ejpam-3868	101	39	)	)	PUNCT
ejpam-3868	101	40	∈	∈	PROPN
ejpam-3868	101	41	s	s	PART
ejpam-3868	101	42	}	}	PUNCT
ejpam-3868	101	43	determines	determine	VERB
ejpam-3868	101	44	a	a	DET
ejpam-3868	101	45	one	one	NUM
ejpam-3868	101	46	-	-	PUNCT
ejpam-3868	101	47	parameter	parameter	NOUN
ejpam-3868	101	48	family	family	NOUN
ejpam-3868	101	49	of	of	ADP
ejpam-3868	101	50	paths	path	NOUN
ejpam-3868	101	51	σp̄	σp̄	ADP
ejpam-3868	101	52	⊂	⊂	PROPN
ejpam-3868	101	53	m	m	VERB
ejpam-3868	101	54	such	such	ADJ
ejpam-3868	101	55	that	that	SCONJ
ejpam-3868	101	56	p	p	PROPN
ejpam-3868	101	57	∈	∈	PROPN
ejpam-3868	101	58	σp̄	σp̄	NOUN
ejpam-3868	101	59	for	for	ADP
ejpam-3868	101	60	all	all	DET
ejpam-3868	101	61	such	such	ADJ
ejpam-3868	101	62	p̄.	p̄.	VERB
ejpam-3868	101	63	require	require	VERB
ejpam-3868	101	64	that	that	SCONJ
ejpam-3868	101	65	this	this	DET
ejpam-3868	101	66	construction	construction	NOUN
ejpam-3868	101	67	define	define	VERB
ejpam-3868	101	68	a	a	DET
ejpam-3868	101	69	path	path	NOUN
ejpam-3868	101	70	space	space	NOUN
ejpam-3868	101	71	on	on	ADP
ejpam-3868	101	72	m	m	PROPN
ejpam-3868	101	73	.	.	PUNCT
ejpam-3868	102	1	for	for	ADP
ejpam-3868	102	2	every	every	DET
ejpam-3868	102	3	p	p	PROPN
ejpam-3868	102	4	∈	∈	PROPN
ejpam-3868	102	5	m	m	NOUN
ejpam-3868	102	6	and	and	CCONJ
ejpam-3868	102	7	[	[	X
ejpam-3868	102	8	u	u	X
ejpam-3868	102	9	]	]	X
ejpam-3868	102	10	∈	∈	PROPN
ejpam-3868	102	11	ptpm	ptpm	NOUN
ejpam-3868	102	12	,	,	PUNCT
ejpam-3868	102	13	there	there	PRON
ejpam-3868	102	14	is	be	VERB
ejpam-3868	102	15	a	a	DET
ejpam-3868	102	16	unique	unique	ADJ
ejpam-3868	102	17	p̄	p̄	NOUN
ejpam-3868	102	18	∈	∈	PROPN
ejpam-3868	102	19	m̄	m̄	NOUN
ejpam-3868	102	20	with	with	ADP
ejpam-3868	102	21	(	(	PUNCT
ejpam-3868	102	22	p	p	X
ejpam-3868	102	23	,	,	PUNCT
ejpam-3868	102	24	p̄	p̄	NOUN
ejpam-3868	102	25	)	)	PUNCT
ejpam-3868	102	26	∈	∈	PROPN
ejpam-3868	102	27	s	s	VERB
ejpam-3868	102	28	the	the	DET
ejpam-3868	102	29	direction	direction	NOUN
ejpam-3868	102	30	of	of	ADP
ejpam-3868	102	31	the	the	DET
ejpam-3868	102	32	tangent	tangent	NOUN
ejpam-3868	102	33	to	to	PART
ejpam-3868	102	34	σp̄	σp̄	VERB
ejpam-3868	102	35	at	at	ADP
ejpam-3868	102	36	x	x	PROPN
ejpam-3868	102	37	is	be	AUX
ejpam-3868	102	38	[	[	X
ejpam-3868	102	39	u	u	NOUN
ejpam-3868	102	40	]	]	X
ejpam-3868	102	41	.	.	PUNCT
ejpam-3868	103	1	let	let	VERB
ejpam-3868	103	2	(	(	PUNCT
ejpam-3868	103	3	x	x	NOUN
ejpam-3868	103	4	,	,	PUNCT
ejpam-3868	103	5	y	y	NOUN
ejpam-3868	103	6	)	)	PUNCT
ejpam-3868	103	7	be	be	VERB
ejpam-3868	103	8	coordinates	coordinate	NOUN
ejpam-3868	103	9	on	on	ADP
ejpam-3868	103	10	m	m	PRON
ejpam-3868	103	11	and	and	CCONJ
ejpam-3868	103	12	(	(	PUNCT
ejpam-3868	103	13	x̄	x̄	PROPN
ejpam-3868	103	14	,	,	PUNCT
ejpam-3868	103	15	ȳ	ȳ	PROPN
ejpam-3868	103	16	)	)	PUNCT
ejpam-3868	103	17	those	those	PRON
ejpam-3868	103	18	on	on	ADP
ejpam-3868	103	19	m̄	m̄	NOUN
ejpam-3868	103	20	,	,	PUNCT
ejpam-3868	103	21	and	and	CCONJ
ejpam-3868	103	22	suppose	suppose	VERB
ejpam-3868	103	23	the	the	DET
ejpam-3868	103	24	submanifold	submanifold	NOUN
ejpam-3868	103	25	s	s	X
ejpam-3868	103	26	of	of	ADP
ejpam-3868	103	27	m	m	PROPN
ejpam-3868	103	28	×	×	PROPN
ejpam-3868	103	29	m̄	m̄	NOUN
ejpam-3868	103	30	is	be	AUX
ejpam-3868	103	31	given	give	VERB
ejpam-3868	103	32	by	by	ADP
ejpam-3868	103	33	φ(x	φ(x	PROPN
ejpam-3868	103	34	,	,	PUNCT
ejpam-3868	103	35	y	y	PROPN
ejpam-3868	103	36	,	,	PUNCT
ejpam-3868	103	37	x̄	x̄	PROPN
ejpam-3868	103	38	,	,	PUNCT
ejpam-3868	103	39	ȳ	ȳ	PROPN
ejpam-3868	103	40	)	)	PUNCT
ejpam-3868	103	41	=	=	SYM
ejpam-3868	104	1	0	0	X
ejpam-3868	104	2	.	.	PUNCT
ejpam-3868	105	1	then	then	ADV
ejpam-3868	105	2	σ(x̄0	σ(x̄0	NOUN
ejpam-3868	105	3	,	,	PUNCT
ejpam-3868	105	4	ȳ0	ȳ0	NUM
ejpam-3868	105	5	)	)	PUNCT
ejpam-3868	105	6	is	be	AUX
ejpam-3868	105	7	φ(x	φ(x	PROPN
ejpam-3868	105	8	,	,	PUNCT
ejpam-3868	105	9	y	y	PROPN
ejpam-3868	105	10	,	,	PUNCT
ejpam-3868	105	11	x̄0	x̄0	PROPN
ejpam-3868	105	12	,	,	PUNCT
ejpam-3868	105	13	ȳ0	ȳ0	NUM
ejpam-3868	105	14	)	)	PUNCT
ejpam-3868	105	15	=	=	SYM
ejpam-3868	105	16	0	0	NUM
ejpam-3868	105	17	and	and	CCONJ
ejpam-3868	105	18	vector	vector	NOUN
ejpam-3868	105	19	(	(	PUNCT
ejpam-3868	105	20	∂	∂	NOUN
ejpam-3868	105	21	∂x	∂x	PROPN
ejpam-3868	105	22	+	+	CCONJ
ejpam-3868	105	23	y′	y′	NOUN
ejpam-3868	105	24	∂	∂	X
ejpam-3868	105	25	∂y	∂y	NOUN
ejpam-3868	105	26	)	)	PUNCT
ejpam-3868	105	27	(	(	PUNCT
ejpam-3868	105	28	x̄0,ȳ0	x̄0,ȳ0	PROPN
ejpam-3868	105	29	)	)	PUNCT
ejpam-3868	105	30	(	(	PUNCT
ejpam-3868	105	31	20	20	NUM
ejpam-3868	105	32	)	)	PUNCT
ejpam-3868	106	1	p.	p.	NOUN
ejpam-3868	106	2	bracken	bracken	NOUN
ejpam-3868	106	3	/	/	SYM
ejpam-3868	106	4	eur	eur	PROPN
ejpam-3868	106	5	.	.	PUNCT
ejpam-3868	107	1	j.	j.	PROPN
ejpam-3868	107	2	pure	pure	PROPN
ejpam-3868	107	3	appl	appl	PROPN
ejpam-3868	107	4	.	.	PROPN
ejpam-3868	107	5	math	math	PROPN
ejpam-3868	107	6	,	,	PUNCT
ejpam-3868	107	7	13	13	NUM
ejpam-3868	107	8	(	(	PUNCT
ejpam-3868	107	9	4	4	NUM
ejpam-3868	107	10	)	)	PUNCT
ejpam-3868	107	11	(	(	PUNCT
ejpam-3868	107	12	2020	2020	NUM
ejpam-3868	107	13	)	)	PUNCT
ejpam-3868	107	14	,	,	PUNCT
ejpam-3868	107	15	1016	1016	NUM
ejpam-3868	107	16	-	-	SYM
ejpam-3868	107	17	1034	1034	NUM
ejpam-3868	107	18	1021	1021	NUM
ejpam-3868	107	19	is	be	AUX
ejpam-3868	107	20	a	a	DET
ejpam-3868	107	21	representative	representative	NOUN
ejpam-3868	107	22	of	of	ADP
ejpam-3868	107	23	some	some	DET
ejpam-3868	107	24	tangent	tangent	ADJ
ejpam-3868	107	25	vector	vector	NOUN
ejpam-3868	107	26	with	with	ADP
ejpam-3868	107	27	u	u	PROPN
ejpam-3868	107	28	6=	6=	ADP
ejpam-3868	107	29	0	0	NUM
ejpam-3868	107	30	and	and	CCONJ
ejpam-3868	107	31	is	be	AUX
ejpam-3868	107	32	tangent	tangent	ADJ
ejpam-3868	107	33	to	to	ADP
ejpam-3868	107	34	this	this	DET
ejpam-3868	107	35	path	path	NOUN
ejpam-3868	107	36	provided	provide	VERB
ejpam-3868	107	37	φx(x0	φx(x0	PROPN
ejpam-3868	107	38	,	,	PUNCT
ejpam-3868	107	39	y0	y0	PROPN
ejpam-3868	107	40	,	,	PUNCT
ejpam-3868	107	41	x̄0	x̄0	PROPN
ejpam-3868	107	42	,	,	PUNCT
ejpam-3868	107	43	ȳ0	ȳ0	NUM
ejpam-3868	107	44	)	)	PUNCT
ejpam-3868	108	1	+	+	CCONJ
ejpam-3868	108	2	y′φy(x0	y′φy(x0	PROPN
ejpam-3868	108	3	,	,	PUNCT
ejpam-3868	108	4	y0	y0	PROPN
ejpam-3868	108	5	,	,	PUNCT
ejpam-3868	108	6	x̄0	x̄0	PROPN
ejpam-3868	108	7	,	,	PUNCT
ejpam-3868	108	8	ȳ0	ȳ0	NUM
ejpam-3868	108	9	)	)	PUNCT
ejpam-3868	108	10	=	=	SYM
ejpam-3868	108	11	0	0	NUM
ejpam-3868	108	12	,	,	PUNCT
ejpam-3868	108	13	(	(	PUNCT
ejpam-3868	108	14	21	21	NUM
ejpam-3868	108	15	)	)	PUNCT
ejpam-3868	108	16	where	where	SCONJ
ejpam-3868	108	17	φ(x0	φ(x0	NOUN
ejpam-3868	108	18	,	,	PUNCT
ejpam-3868	108	19	y0	y0	PROPN
ejpam-3868	108	20	,	,	PUNCT
ejpam-3868	108	21	x̄0	x̄0	PROPN
ejpam-3868	108	22	,	,	PUNCT
ejpam-3868	108	23	ȳ0	ȳ0	NUM
ejpam-3868	108	24	)	)	PUNCT
ejpam-3868	108	25	=	=	SYM
ejpam-3868	109	1	0	0	X
ejpam-3868	109	2	.	.	PUNCT
ejpam-3868	110	1	therefore	therefore	ADV
ejpam-3868	110	2	,	,	PUNCT
ejpam-3868	110	3	the	the	DET
ejpam-3868	110	4	map	map	NOUN
ejpam-3868	110	5	s	s	PART
ejpam-3868	110	6	→	→	SYM
ejpam-3868	110	7	ptm	ptm	PROPN
ejpam-3868	110	8	is	be	AUX
ejpam-3868	110	9	given	give	VERB
ejpam-3868	110	10	by	by	ADP
ejpam-3868	110	11	(	(	PUNCT
ejpam-3868	110	12	x	x	PROPN
ejpam-3868	110	13	,	,	PUNCT
ejpam-3868	110	14	y	y	PROPN
ejpam-3868	110	15	,	,	PUNCT
ejpam-3868	110	16	x̄	x̄	PROPN
ejpam-3868	110	17	,	,	PUNCT
ejpam-3868	110	18	ȳ	ȳ	PROPN
ejpam-3868	110	19	)	)	PUNCT
ejpam-3868	110	20	→	→	SYM
ejpam-3868	110	21	(	(	PUNCT
ejpam-3868	110	22	x	x	X
ejpam-3868	110	23	,	,	PUNCT
ejpam-3868	110	24	y	y	PROPN
ejpam-3868	110	25	,	,	PUNCT
ejpam-3868	110	26	y′	y′	NUM
ejpam-3868	110	27	)	)	PUNCT
ejpam-3868	110	28	such	such	ADJ
ejpam-3868	110	29	that	that	SCONJ
ejpam-3868	110	30	φ(x	φ(x	PROPN
ejpam-3868	110	31	,	,	PUNCT
ejpam-3868	110	32	y	y	PROPN
ejpam-3868	110	33	,	,	PUNCT
ejpam-3868	110	34	x̄	x̄	PROPN
ejpam-3868	110	35	,	,	PUNCT
ejpam-3868	110	36	ȳ	ȳ	PROPN
ejpam-3868	110	37	)	)	PUNCT
ejpam-3868	110	38	=	=	SYM
ejpam-3868	110	39	0	0	NUM
ejpam-3868	110	40	,	,	PUNCT
ejpam-3868	110	41	φx(x	φx(x	NUM
ejpam-3868	110	42	,	,	PUNCT
ejpam-3868	110	43	y	y	PROPN
ejpam-3868	110	44	,	,	PUNCT
ejpam-3868	110	45	x̄	x̄	PROPN
ejpam-3868	110	46	,	,	PUNCT
ejpam-3868	110	47	ȳ	ȳ	PROPN
ejpam-3868	110	48	)	)	PUNCT
ejpam-3868	110	49	+	+	NUM
ejpam-3868	110	50	y′φy(x	y′φy(x	PROPN
ejpam-3868	110	51	,	,	PUNCT
ejpam-3868	110	52	y	y	PROPN
ejpam-3868	110	53	,	,	PUNCT
ejpam-3868	110	54	x̄	x̄	PROPN
ejpam-3868	110	55	,	,	PUNCT
ejpam-3868	110	56	ȳ	ȳ	PROPN
ejpam-3868	110	57	)	)	PUNCT
ejpam-3868	110	58	=	=	SYM
ejpam-3868	111	1	0	0	X
ejpam-3868	111	2	.	.	PUNCT
ejpam-3868	112	1	(	(	PUNCT
ejpam-3868	112	2	22	22	NUM
ejpam-3868	112	3	)	)	PUNCT
ejpam-3868	112	4	it	it	PRON
ejpam-3868	112	5	is	be	AUX
ejpam-3868	112	6	required	require	VERB
ejpam-3868	112	7	that	that	SCONJ
ejpam-3868	112	8	φx	φx	PROPN
ejpam-3868	112	9	and	and	CCONJ
ejpam-3868	112	10	φy	φy	INTJ
ejpam-3868	112	11	do	do	AUX
ejpam-3868	112	12	not	not	PART
ejpam-3868	112	13	vanish	vanish	VERB
ejpam-3868	112	14	simultaneously	simultaneously	ADV
ejpam-3868	112	15	.	.	PUNCT
ejpam-3868	113	1	in	in	ADP
ejpam-3868	113	2	a	a	DET
ejpam-3868	113	3	similar	similar	ADJ
ejpam-3868	113	4	way	way	NOUN
ejpam-3868	113	5	,	,	PUNCT
ejpam-3868	113	6	the	the	DET
ejpam-3868	113	7	map	map	NOUN
ejpam-3868	113	8	s	s	PART
ejpam-3868	113	9	→	→	SYM
ejpam-3868	113	10	ptm̄	ptm̄	NUM
ejpam-3868	113	11	is	be	AUX
ejpam-3868	113	12	given	give	VERB
ejpam-3868	113	13	by	by	ADP
ejpam-3868	113	14	(	(	PUNCT
ejpam-3868	113	15	x	x	PROPN
ejpam-3868	113	16	,	,	PUNCT
ejpam-3868	113	17	y	y	PROPN
ejpam-3868	113	18	,	,	PUNCT
ejpam-3868	113	19	x̄	x̄	PROPN
ejpam-3868	113	20	,	,	PUNCT
ejpam-3868	113	21	ȳ)→	ȳ)→	PROPN
ejpam-3868	113	22	(	(	PUNCT
ejpam-3868	113	23	x̄	x̄	PROPN
ejpam-3868	113	24	,	,	PUNCT
ejpam-3868	113	25	ȳ	ȳ	PROPN
ejpam-3868	113	26	,	,	PUNCT
ejpam-3868	113	27	ȳ′	ȳ′	PROPN
ejpam-3868	113	28	)	)	PUNCT
ejpam-3868	114	1	where	where	SCONJ
ejpam-3868	114	2	φ(x	φ(x	PROPN
ejpam-3868	114	3	,	,	PUNCT
ejpam-3868	114	4	y	y	PROPN
ejpam-3868	114	5	,	,	PUNCT
ejpam-3868	114	6	x̄	x̄	PROPN
ejpam-3868	114	7	,	,	PUNCT
ejpam-3868	114	8	ȳ	ȳ	PROPN
ejpam-3868	114	9	)	)	PUNCT
ejpam-3868	114	10	=	=	SYM
ejpam-3868	114	11	0	0	NUM
ejpam-3868	114	12	,	,	PUNCT
ejpam-3868	114	13	φx̄(x	φx̄(x	PROPN
ejpam-3868	114	14	,	,	PUNCT
ejpam-3868	114	15	y	y	PROPN
ejpam-3868	114	16	,	,	PUNCT
ejpam-3868	114	17	x̄	x̄	PROPN
ejpam-3868	114	18	,	,	PUNCT
ejpam-3868	114	19	ȳ	ȳ	PROPN
ejpam-3868	114	20	)	)	PUNCT
ejpam-3868	114	21	+	+	NUM
ejpam-3868	114	22	ȳ′φȳ(x	ȳ′φȳ(x	NOUN
ejpam-3868	114	23	,	,	PUNCT
ejpam-3868	114	24	y	y	PROPN
ejpam-3868	114	25	,	,	PUNCT
ejpam-3868	114	26	x̄	x̄	PROPN
ejpam-3868	114	27	,	,	PUNCT
ejpam-3868	114	28	ȳ	ȳ	PROPN
ejpam-3868	114	29	)	)	PUNCT
ejpam-3868	114	30	=	=	SYM
ejpam-3868	114	31	0	0	NUM
ejpam-3868	114	32	,	,	PUNCT
ejpam-3868	114	33	and	and	CCONJ
ejpam-3868	114	34	φx̄	φx̄	PROPN
ejpam-3868	114	35	,	,	PUNCT
ejpam-3868	114	36	φȳ	φȳ	PROPN
ejpam-3868	114	37	must	must	AUX
ejpam-3868	114	38	not	not	PART
ejpam-3868	114	39	vanish	vanish	VERB
ejpam-3868	114	40	at	at	ADP
ejpam-3868	114	41	the	the	DET
ejpam-3868	114	42	same	same	ADJ
ejpam-3868	114	43	time	time	NOUN
ejpam-3868	114	44	.	.	PUNCT
ejpam-3868	115	1	the	the	DET
ejpam-3868	115	2	condition	condition	NOUN
ejpam-3868	115	3	that	that	SCONJ
ejpam-3868	115	4	the	the	DET
ejpam-3868	115	5	first	first	ADJ
ejpam-3868	115	6	pair	pair	NOUN
ejpam-3868	115	7	of	of	ADP
ejpam-3868	115	8	equations	equation	NOUN
ejpam-3868	115	9	determines	determine	VERB
ejpam-3868	115	10	x̄	x̄	NOUN
ejpam-3868	115	11	and	and	CCONJ
ejpam-3868	115	12	ȳ	ȳ	NUM
ejpam-3868	115	13	in	in	ADP
ejpam-3868	115	14	terms	term	NOUN
ejpam-3868	115	15	of	of	ADP
ejpam-3868	115	16	x	x	X
ejpam-3868	115	17	,	,	PUNCT
ejpam-3868	115	18	y	y	PROPN
ejpam-3868	115	19	and	and	CCONJ
ejpam-3868	115	20	y′	y′	NOUN
ejpam-3868	115	21	is	be	AUX
ejpam-3868	115	22	that	that	SCONJ
ejpam-3868	115	23	the	the	DET
ejpam-3868	115	24	following	follow	VERB
ejpam-3868	115	25	matrix	matrix	NOUN
ejpam-3868	115	26	be	be	AUX
ejpam-3868	115	27	nonsingular,	nonsingular,	NOUN
ejpam-3868	115	28	0	0	NUM
ejpam-3868	115	29	φx	φx	PROPN
ejpam-3868	115	30	φy	φy	PROPN
ejpam-3868	115	31	φx̄	φx̄	NOUN
ejpam-3868	115	32	φxx̄	φxx̄	ADP
ejpam-3868	115	33	φyx̄	φyx̄	PROPN
ejpam-3868	115	34	φȳ	φȳ	PROPN
ejpam-3868	115	35	φxȳ	φxȳ	NOUN
ejpam-3868	115	36	φyȳ	φyȳ	VERB
ejpam-3868	115	37			PROPN
ejpam-3868	115	38	(	(	PUNCT
ejpam-3868	115	39	23	23	NUM
ejpam-3868	115	40	)	)	PUNCT
ejpam-3868	115	41	the	the	DET
ejpam-3868	115	42	same	same	ADJ
ejpam-3868	115	43	condition	condition	NOUN
ejpam-3868	115	44	ensures	ensure	VERB
ejpam-3868	115	45	that	that	SCONJ
ejpam-3868	115	46	the	the	DET
ejpam-3868	115	47	second	second	ADJ
ejpam-3868	115	48	pair	pair	NOUN
ejpam-3868	115	49	of	of	ADP
ejpam-3868	115	50	equations	equation	NOUN
ejpam-3868	115	51	can	can	AUX
ejpam-3868	115	52	be	be	AUX
ejpam-3868	115	53	solved	solve	VERB
ejpam-3868	115	54	for	for	ADP
ejpam-3868	115	55	x	x	PUNCT
ejpam-3868	115	56	and	and	CCONJ
ejpam-3868	115	57	y	y	PROPN
ejpam-3868	115	58	in	in	ADP
ejpam-3868	115	59	terms	term	NOUN
ejpam-3868	115	60	of	of	ADP
ejpam-3868	115	61	bared	bared	ADJ
ejpam-3868	115	62	variables	variable	NOUN
ejpam-3868	115	63	with	with	ADP
ejpam-3868	115	64	bars	bar	NOUN
ejpam-3868	115	65	.	.	PUNCT
ejpam-3868	116	1	this	this	PRON
ejpam-3868	116	2	assumes	assume	VERB
ejpam-3868	116	3	that	that	SCONJ
ejpam-3868	116	4	φx	φx	ADV
ejpam-3868	116	5	,	,	PUNCT
ejpam-3868	116	6	φy	φy	NOUN
ejpam-3868	116	7	do	do	AUX
ejpam-3868	116	8	not	not	PART
ejpam-3868	116	9	both	both	PRON
ejpam-3868	116	10	vanish	vanish	VERB
ejpam-3868	116	11	simultaneously	simultaneously	ADV
ejpam-3868	116	12	and	and	CCONJ
ejpam-3868	116	13	the	the	DET
ejpam-3868	116	14	same	same	ADJ
ejpam-3868	116	15	for	for	ADP
ejpam-3868	116	16	φx̄	φx̄	NOUN
ejpam-3868	116	17	φȳ	φȳ	PROPN
ejpam-3868	116	18	as	as	ADV
ejpam-3868	116	19	well	well	ADV
ejpam-3868	116	20	.	.	PUNCT
ejpam-3868	117	1	assume	assume	VERB
ejpam-3868	117	2	that	that	SCONJ
ejpam-3868	117	3	this	this	DET
ejpam-3868	117	4	condition	condition	NOUN
ejpam-3868	117	5	holds	hold	VERB
ejpam-3868	117	6	on	on	ADP
ejpam-3868	117	7	s.	s.	PROPN
ejpam-3868	117	8	it	it	PRON
ejpam-3868	117	9	can	can	AUX
ejpam-3868	117	10	be	be	AUX
ejpam-3868	117	11	stated	state	VERB
ejpam-3868	117	12	in	in	ADP
ejpam-3868	117	13	the	the	DET
ejpam-3868	117	14	form	form	NOUN
ejpam-3868	117	15	∆	∆	X
ejpam-3868	117	16	6=	6=	ADP
ejpam-3868	117	17	0	0	NUM
ejpam-3868	117	18	,	,	PUNCT
ejpam-3868	117	19	where	where	SCONJ
ejpam-3868	117	20	∆	∆	PROPN
ejpam-3868	117	21	is	be	AUX
ejpam-3868	117	22	the	the	DET
ejpam-3868	117	23	determinant	determinant	ADJ
ejpam-3868	117	24	∆	∆	NOUN
ejpam-3868	117	25	=	=	PUNCT
ejpam-3868	118	1	−φyφȳ(φxx̄	−φyφȳ(φxx̄	PROPN
ejpam-3868	118	2	+	+	NUM
ejpam-3868	118	3	y′φyx̄	y′φyx̄	NOUN
ejpam-3868	118	4	+	+	CCONJ
ejpam-3868	118	5	ȳφxȳ	ȳφxȳ	X
ejpam-3868	118	6	+	+	CCONJ
ejpam-3868	118	7	y′ȳ′φyȳ	y′ȳ′φyȳ	NOUN
ejpam-3868	118	8	)	)	PUNCT
ejpam-3868	118	9	,	,	PUNCT
ejpam-3868	118	10	φyφy′	φyφy′	PROPN
ejpam-3868	118	11	6=	6=	ADP
ejpam-3868	118	12	0	0	NUM
ejpam-3868	118	13	.	.	PUNCT
ejpam-3868	119	1	(	(	PUNCT
ejpam-3868	119	2	24	24	NUM
ejpam-3868	119	3	)	)	PUNCT
ejpam-3868	119	4	take	take	VERB
ejpam-3868	119	5	some	some	DET
ejpam-3868	119	6	fixed	fix	VERB
ejpam-3868	119	7	point	point	NOUN
ejpam-3868	119	8	(	(	PUNCT
ejpam-3868	119	9	x̄	x̄	PROPN
ejpam-3868	119	10	,	,	PUNCT
ejpam-3868	119	11	ȳ	ȳ	PROPN
ejpam-3868	119	12	)	)	PUNCT
ejpam-3868	119	13	∈	∈	PROPN
ejpam-3868	119	14	m̄	m̄	NOUN
ejpam-3868	119	15	such	such	ADJ
ejpam-3868	119	16	that	that	SCONJ
ejpam-3868	119	17	the	the	DET
ejpam-3868	119	18	path	path	NOUN
ejpam-3868	119	19	it	it	PRON
ejpam-3868	119	20	takes	take	VERB
ejpam-3868	119	21	in	in	ADP
ejpam-3868	119	22	m	m	PROPN
ejpam-3868	119	23	can	can	AUX
ejpam-3868	119	24	be	be	AUX
ejpam-3868	119	25	parametrized	parametrize	VERB
ejpam-3868	119	26	by	by	ADP
ejpam-3868	119	27	x.	x.	NOUN
ejpam-3868	120	1	then	then	ADV
ejpam-3868	120	2	y′	y′	PROPN
ejpam-3868	120	3	and	and	CCONJ
ejpam-3868	120	4	y′′	y′′	PROPN
ejpam-3868	120	5	satisfy	satisfy	NOUN
ejpam-3868	120	6	φxx	φxx	PROPN
ejpam-3868	120	7	+	+	CCONJ
ejpam-3868	120	8	2	2	NUM
ejpam-3868	120	9	dy	dy	NOUN
ejpam-3868	120	10	dx	dx	PROPN
ejpam-3868	120	11	φxy	φxy	PROPN
ejpam-3868	120	12	+	+	CCONJ
ejpam-3868	120	13	(	(	PUNCT
ejpam-3868	120	14	dy	dy	X
ejpam-3868	120	15	dx	dx	PROPN
ejpam-3868	120	16	)	)	PUNCT
ejpam-3868	121	1	2φyy	2φyy	PROPN
ejpam-3868	121	2	+	+	CCONJ
ejpam-3868	121	3	(	(	PUNCT
ejpam-3868	121	4	d2y	d2y	ADJ
ejpam-3868	121	5	dx2	dx2	NOUN
ejpam-3868	121	6	)	)	PUNCT
ejpam-3868	121	7	φy	φy	PROPN
ejpam-3868	121	8	=	=	NOUN
ejpam-3868	121	9	0	0	PROPN
ejpam-3868	121	10	.	.	PUNCT
ejpam-3868	122	1	(	(	PUNCT
ejpam-3868	122	2	25	25	NUM
ejpam-3868	122	3	)	)	PUNCT
ejpam-3868	122	4	the	the	DET
ejpam-3868	122	5	path	path	NOUN
ejpam-3868	122	6	then	then	ADV
ejpam-3868	122	7	is	be	AUX
ejpam-3868	122	8	a	a	DET
ejpam-3868	122	9	solution	solution	NOUN
ejpam-3868	122	10	to	to	ADP
ejpam-3868	122	11	the	the	DET
ejpam-3868	122	12	second	second	ADJ
ejpam-3868	122	13	order	order	NOUN
ejpam-3868	122	14	equation	equation	NOUN
ejpam-3868	122	15	d2y	d2y	NOUN
ejpam-3868	122	16	dx2	dx2	PROPN
ejpam-3868	122	17	=	=	SYM
ejpam-3868	122	18	f(x	f(x	PROPN
ejpam-3868	122	19	,	,	PUNCT
ejpam-3868	122	20	y	y	PROPN
ejpam-3868	122	21	,	,	PUNCT
ejpam-3868	122	22	y′	y′	NUM
ejpam-3868	122	23	)	)	PUNCT
ejpam-3868	122	24	,	,	PUNCT
ejpam-3868	122	25	(	(	PUNCT
ejpam-3868	122	26	26	26	NUM
ejpam-3868	122	27	)	)	PUNCT
ejpam-3868	122	28	where	where	SCONJ
ejpam-3868	122	29	f(x	f(x	PROPN
ejpam-3868	122	30	,	,	PUNCT
ejpam-3868	122	31	y	y	PROPN
ejpam-3868	122	32	,	,	PUNCT
ejpam-3868	122	33	y′	y′	NUM
ejpam-3868	122	34	)	)	PUNCT
ejpam-3868	122	35	is	be	AUX
ejpam-3868	122	36	obtained	obtain	VERB
ejpam-3868	122	37	by	by	ADP
ejpam-3868	122	38	eliminating	eliminate	VERB
ejpam-3868	122	39	x̄	x̄	NOUN
ejpam-3868	122	40	and	and	CCONJ
ejpam-3868	122	41	ȳ	ȳ	NOUN
ejpam-3868	122	42	between	between	ADP
ejpam-3868	122	43	the	the	DET
ejpam-3868	122	44	equations	equation	NOUN
ejpam-3868	122	45	φ	φ	X
ejpam-3868	122	46	=	=	SYM
ejpam-3868	122	47	0	0	NUM
ejpam-3868	122	48	,	,	PUNCT
ejpam-3868	122	49	φx	φx	ADV
ejpam-3868	122	50	+	+	CCONJ
ejpam-3868	122	51	y′φy	y′φy	ADJ
ejpam-3868	122	52	=	=	SYM
ejpam-3868	122	53	0	0	NUM
ejpam-3868	122	54	,	,	PUNCT
ejpam-3868	122	55	φxx	φxx	X
ejpam-3868	122	56	+	+	NUM
ejpam-3868	122	57	2y′φxy	2y′φxy	NOUN
ejpam-3868	122	58	+	+	CCONJ
ejpam-3868	122	59	(	(	PUNCT
ejpam-3868	122	60	y′)2φyy	y′)2φyy	NOUN
ejpam-3868	122	61	+	+	CCONJ
ejpam-3868	122	62	f	f	PROPN
ejpam-3868	122	63	φy	φy	NOUN
ejpam-3868	122	64	=	=	NOUN
ejpam-3868	122	65	0	0	PROPN
ejpam-3868	122	66	.	.	PUNCT
ejpam-3868	123	1	(	(	PUNCT
ejpam-3868	123	2	27	27	NUM
ejpam-3868	123	3	)	)	PUNCT
ejpam-3868	123	4	the	the	DET
ejpam-3868	123	5	right	right	ADJ
ejpam-3868	123	6	-	-	PUNCT
ejpam-3868	123	7	hand	hand	NOUN
ejpam-3868	123	8	side	side	NOUN
ejpam-3868	123	9	f̄(x̄	f̄(x̄	PROPN
ejpam-3868	123	10	,	,	PUNCT
ejpam-3868	123	11	ȳ	ȳ	PROPN
ejpam-3868	123	12	,	,	PUNCT
ejpam-3868	123	13	ȳ′	ȳ′	PROPN
ejpam-3868	123	14	)	)	PUNCT
ejpam-3868	123	15	of	of	ADP
ejpam-3868	123	16	the	the	DET
ejpam-3868	123	17	equation	equation	NOUN
ejpam-3868	123	18	giving	give	VERB
ejpam-3868	123	19	the	the	DET
ejpam-3868	123	20	dual	dual	ADJ
ejpam-3868	123	21	path	path	NOUN
ejpam-3868	123	22	is	be	AUX
ejpam-3868	123	23	obtained	obtain	VERB
ejpam-3868	123	24	by	by	ADP
ejpam-3868	123	25	eliminating	eliminate	VERB
ejpam-3868	123	26	x	x	PUNCT
ejpam-3868	123	27	and	and	CCONJ
ejpam-3868	123	28	y	y	PROPN
ejpam-3868	123	29	between	between	ADP
ejpam-3868	123	30	the	the	DET
ejpam-3868	123	31	equations	equation	NOUN
ejpam-3868	123	32	φ	φ	X
ejpam-3868	123	33	=	=	SYM
ejpam-3868	123	34	0	0	NUM
ejpam-3868	123	35	,	,	PUNCT
ejpam-3868	123	36	φx̄	φx̄	NOUN
ejpam-3868	124	1	+	+	CCONJ
ejpam-3868	124	2	ȳ′φȳ	ȳ′φȳ	PROPN
ejpam-3868	124	3	=	=	SYM
ejpam-3868	124	4	0	0	PROPN
ejpam-3868	124	5	,	,	PUNCT
ejpam-3868	124	6	φx̄x̄	φx̄x̄	VERB
ejpam-3868	124	7	+	+	CCONJ
ejpam-3868	124	8	2ȳ′φx̄ȳ	2ȳ′φx̄ȳ	NUM
ejpam-3868	125	1	+	+	CCONJ
ejpam-3868	125	2	(	(	PUNCT
ejpam-3868	125	3	ȳ′)2φȳȳ	ȳ′)2φȳȳ	NUM
ejpam-3868	126	1	+	+	NUM
ejpam-3868	126	2	f̄φȳ	f̄φȳ	ADJ
ejpam-3868	126	3	=	=	SYM
ejpam-3868	126	4	0	0	X
ejpam-3868	126	5	.	.	PUNCT
ejpam-3868	127	1	(	(	PUNCT
ejpam-3868	127	2	28	28	NUM
ejpam-3868	127	3	)	)	PUNCT
ejpam-3868	127	4	p.	p.	NOUN
ejpam-3868	127	5	bracken	bracken	NOUN
ejpam-3868	127	6	/	/	SYM
ejpam-3868	127	7	eur	eur	PROPN
ejpam-3868	127	8	.	.	PUNCT
ejpam-3868	128	1	j.	j.	PROPN
ejpam-3868	128	2	pure	pure	PROPN
ejpam-3868	128	3	appl	appl	PROPN
ejpam-3868	128	4	.	.	PROPN
ejpam-3868	128	5	math	math	PROPN
ejpam-3868	128	6	,	,	PUNCT
ejpam-3868	128	7	13	13	NUM
ejpam-3868	128	8	(	(	PUNCT
ejpam-3868	128	9	4	4	NUM
ejpam-3868	128	10	)	)	PUNCT
ejpam-3868	128	11	(	(	PUNCT
ejpam-3868	128	12	2020	2020	NUM
ejpam-3868	128	13	)	)	PUNCT
ejpam-3868	128	14	,	,	PUNCT
ejpam-3868	128	15	1016	1016	NUM
ejpam-3868	128	16	-	-	SYM
ejpam-3868	128	17	1034	1034	NUM
ejpam-3868	128	18	1022	1022	NUM
ejpam-3868	128	19	there	there	PRON
ejpam-3868	128	20	are	be	VERB
ejpam-3868	128	21	two	two	NUM
ejpam-3868	128	22	cartan	cartan	ADJ
ejpam-3868	128	23	normal	normal	ADJ
ejpam-3868	128	24	projective	projective	ADJ
ejpam-3868	128	25	connection	connection	NOUN
ejpam-3868	128	26	forms	form	NOUN
ejpam-3868	128	27	associated	associate	VERB
ejpam-3868	128	28	with	with	ADP
ejpam-3868	128	29	this	this	DET
ejpam-3868	128	30	structure	structure	NOUN
ejpam-3868	128	31	.	.	PUNCT
ejpam-3868	129	1	there	there	PRON
ejpam-3868	129	2	is	be	VERB
ejpam-3868	129	3	one	one	NUM
ejpam-3868	129	4	corresponding	correspond	VERB
ejpam-3868	129	5	to	to	ADP
ejpam-3868	129	6	d2y	d2y	VERB
ejpam-3868	129	7	/	/	SYM
ejpam-3868	129	8	dx2	dx2	NOUN
ejpam-3868	129	9	=	=	SYM
ejpam-3868	129	10	f	f	PROPN
ejpam-3868	129	11	and	and	CCONJ
ejpam-3868	129	12	the	the	DET
ejpam-3868	129	13	other	other	ADJ
ejpam-3868	129	14	to	to	PART
ejpam-3868	129	15	d2ȳ/dx̄2	d2ȳ/dx̄2	VERB
ejpam-3868	129	16	=	=	PUNCT
ejpam-3868	129	17	f̄	f̄	PROPN
ejpam-3868	129	18	.	.	PUNCT
ejpam-3868	130	1	each	each	PRON
ejpam-3868	130	2	can	can	AUX
ejpam-3868	130	3	be	be	AUX
ejpam-3868	130	4	represented	represent	VERB
ejpam-3868	130	5	by	by	ADP
ejpam-3868	130	6	a	a	DET
ejpam-3868	130	7	connection	connection	NOUN
ejpam-3868	130	8	form	form	NOUN
ejpam-3868	130	9	on	on	ADP
ejpam-3868	130	10	s.	s.	PROPN
ejpam-3868	130	11	the	the	DET
ejpam-3868	130	12	connection	connection	NOUN
ejpam-3868	130	13	form	form	NOUN
ejpam-3868	130	14	associated	associate	VERB
ejpam-3868	130	15	with	with	ADP
ejpam-3868	130	16	the	the	DET
ejpam-3868	130	17	bar	bar	NOUN
ejpam-3868	130	18	equation	equation	NOUN
ejpam-3868	130	19	takes	take	VERB
ejpam-3868	130	20	a	a	DET
ejpam-3868	130	21	lower	low	ADJ
ejpam-3868	130	22	triangular	triangular	NOUN
ejpam-3868	130	23	form	form	NOUN
ejpam-3868	130	24	ω̄	ω̄	NOUN
ejpam-3868	131	1	=	=	SYM
ejpam-3868	131	2	dx̄	dx̄	NOUN
ejpam-3868	131	3	ϑ̄	ϑ̄	ADJ
ejpam-3868	131	4	ϕ̄−	ϕ̄−	PROPN
ejpam-3868	131	5	1	1	NUM
ejpam-3868	131	6	3	3	NUM
ejpam-3868	131	7	f̄ȳϑ̄	f̄ȳϑ̄	NUM
ejpam-3868	131	8			PROPN
ejpam-3868	131	9	,	,	PUNCT
ejpam-3868	131	10	ϑ̄	ϑ̄	ADJ
ejpam-3868	131	11	=	=	SYM
ejpam-3868	131	12	dȳ	dȳ	NOUN
ejpam-3868	131	13	−	−	PROPN
ejpam-3868	131	14	ȳ′	ȳ′	PROPN
ejpam-3868	131	15	dx̄	dx̄	PROPN
ejpam-3868	131	16	,	,	PUNCT
ejpam-3868	131	17	ϕ̄	ϕ̄	PROPN
ejpam-3868	131	18	=	=	PROPN
ejpam-3868	131	19	dȳ′	dȳ′	VERB
ejpam-3868	131	20	−	−	PROPN
ejpam-3868	131	21	f̄	f̄	PROPN
ejpam-3868	131	22	dx̄.	dx̄.	X
ejpam-3868	131	23	(	(	PUNCT
ejpam-3868	131	24	29	29	NUM
ejpam-3868	131	25	)	)	PUNCT
ejpam-3868	131	26	now	now	ADV
ejpam-3868	131	27	(	(	PUNCT
ejpam-3868	131	28	x	x	X
ejpam-3868	131	29	,	,	PUNCT
ejpam-3868	131	30	y	y	PROPN
ejpam-3868	131	31	,	,	PUNCT
ejpam-3868	131	32	y′	y′	NUM
ejpam-3868	131	33	)	)	PUNCT
ejpam-3868	131	34	and	and	CCONJ
ejpam-3868	131	35	(	(	PUNCT
ejpam-3868	131	36	x̄	x̄	PROPN
ejpam-3868	131	37	,	,	PUNCT
ejpam-3868	131	38	ȳ	ȳ	PROPN
ejpam-3868	131	39	,	,	PUNCT
ejpam-3868	131	40	ȳ′	ȳ′	PROPN
ejpam-3868	131	41	)	)	PUNCT
ejpam-3868	131	42	can	can	AUX
ejpam-3868	131	43	be	be	AUX
ejpam-3868	131	44	regarded	regard	VERB
ejpam-3868	131	45	as	as	ADP
ejpam-3868	131	46	alternative	alternative	ADJ
ejpam-3868	131	47	coordinates	coordinate	NOUN
ejpam-3868	131	48	on	on	ADP
ejpam-3868	131	49	s	s	PRON
ejpam-3868	131	50	with	with	ADP
ejpam-3868	131	51	transformation	transformation	NOUN
ejpam-3868	131	52	given	give	VERB
ejpam-3868	131	53	by	by	ADP
ejpam-3868	131	54	φ(x	φ(x	PROPN
ejpam-3868	131	55	,	,	PUNCT
ejpam-3868	131	56	y	y	PROPN
ejpam-3868	131	57	,	,	PUNCT
ejpam-3868	131	58	x̄	x̄	PROPN
ejpam-3868	131	59	,	,	PUNCT
ejpam-3868	131	60	ȳ	ȳ	PROPN
ejpam-3868	131	61	)	)	PUNCT
ejpam-3868	131	62	=	=	SYM
ejpam-3868	131	63	0	0	NUM
ejpam-3868	131	64	,	,	PUNCT
ejpam-3868	131	65	φx(x	φx(x	NUM
ejpam-3868	131	66	,	,	PUNCT
ejpam-3868	131	67	y	y	PROPN
ejpam-3868	131	68	,	,	PUNCT
ejpam-3868	131	69	x̄	x̄	PROPN
ejpam-3868	131	70	,	,	PUNCT
ejpam-3868	131	71	ȳ)+y′φy(x	ȳ)+y′φy(x	PROPN
ejpam-3868	131	72	,	,	PUNCT
ejpam-3868	131	73	y	y	PROPN
ejpam-3868	131	74	,	,	PUNCT
ejpam-3868	131	75	x̄	x̄	PROPN
ejpam-3868	131	76	,	,	PUNCT
ejpam-3868	131	77	ȳ	ȳ	PROPN
ejpam-3868	131	78	)	)	PUNCT
ejpam-3868	131	79	=	=	SYM
ejpam-3868	131	80	0	0	NUM
ejpam-3868	131	81	,	,	PUNCT
ejpam-3868	131	82	φx̄(x	φx̄(x	PROPN
ejpam-3868	131	83	,	,	PUNCT
ejpam-3868	131	84	y	y	PROPN
ejpam-3868	131	85	,	,	PUNCT
ejpam-3868	131	86	x̄	x̄	PROPN
ejpam-3868	131	87	,	,	PUNCT
ejpam-3868	131	88	ȳ)+ȳ′φȳ(x	ȳ)+ȳ′φȳ(x	PROPN
ejpam-3868	131	89	,	,	PUNCT
ejpam-3868	131	90	y	y	PROPN
ejpam-3868	131	91	,	,	PUNCT
ejpam-3868	131	92	x̄	x̄	PROPN
ejpam-3868	131	93	,	,	PUNCT
ejpam-3868	131	94	ȳ	ȳ	PROPN
ejpam-3868	131	95	)	)	PUNCT
ejpam-3868	131	96	=	=	SYM
ejpam-3868	132	1	0	0	X
ejpam-3868	132	2	.	.	PUNCT
ejpam-3868	132	3	(	(	PUNCT
ejpam-3868	132	4	30	30	NUM
ejpam-3868	132	5	)	)	PUNCT
ejpam-3868	132	6	it	it	PRON
ejpam-3868	132	7	can	can	AUX
ejpam-3868	132	8	be	be	AUX
ejpam-3868	132	9	shown	show	VERB
ejpam-3868	132	10	that	that	SCONJ
ejpam-3868	132	11	the	the	DET
ejpam-3868	132	12	jacobian	jacobian	ADJ
ejpam-3868	132	13	matrix	matrix	NOUN
ejpam-3868	132	14	of	of	ADP
ejpam-3868	132	15	(	(	PUNCT
ejpam-3868	132	16	x̄	x̄	PROPN
ejpam-3868	132	17	,	,	PUNCT
ejpam-3868	132	18	ȳ	ȳ	PROPN
ejpam-3868	132	19	,	,	PUNCT
ejpam-3868	132	20	ȳ′	ȳ′	PROPN
ejpam-3868	132	21	)	)	PUNCT
ejpam-3868	132	22	with	with	ADP
ejpam-3868	132	23	respect	respect	NOUN
ejpam-3868	132	24	to	to	ADP
ejpam-3868	132	25	(	(	PUNCT
ejpam-3868	132	26	x	x	X
ejpam-3868	132	27	,	,	PUNCT
ejpam-3868	132	28	y	y	PROPN
ejpam-3868	132	29	,	,	PUNCT
ejpam-3868	132	30	y′	y′	NUM
ejpam-3868	132	31	)	)	PUNCT
ejpam-3868	132	32	is	be	AUX
ejpam-3868	132	33	nonsingular	nonsingular	ADJ
ejpam-3868	132	34	since	since	SCONJ
ejpam-3868	132	35	it	it	PRON
ejpam-3868	132	36	is	be	AUX
ejpam-3868	132	37	assumed	assume	VERB
ejpam-3868	132	38	that	that	SCONJ
ejpam-3868	132	39	∆	∆	PROPN
ejpam-3868	132	40	6=	6=	ADP
ejpam-3868	132	41	0	0	NUM
ejpam-3868	132	42	and	and	CCONJ
ejpam-3868	132	43	moreover	moreover	ADV
ejpam-3868	132	44	φxx	φxx	X
ejpam-3868	132	45	+	+	NUM
ejpam-3868	132	46	2y′φxy	2y′φxy	NOUN
ejpam-3868	132	47	+	+	CCONJ
ejpam-3868	132	48	(	(	PUNCT
ejpam-3868	132	49	y′)2φyy	y′)2φyy	NOUN
ejpam-3868	132	50	+	+	CCONJ
ejpam-3868	132	51	fφy	fφy	NOUN
ejpam-3868	132	52	=	=	NOUN
ejpam-3868	132	53	0	0	X
ejpam-3868	132	54	.	.	PUNCT
ejpam-3868	133	1	there	there	PRON
ejpam-3868	133	2	is	be	VERB
ejpam-3868	133	3	a	a	DET
ejpam-3868	133	4	similar	similar	ADJ
ejpam-3868	133	5	equation	equation	NOUN
ejpam-3868	133	6	in	in	ADP
ejpam-3868	133	7	f̄	f̄	NOUN
ejpam-3868	133	8	of	of	ADP
ejpam-3868	133	9	course	course	NOUN
ejpam-3868	133	10	.	.	PUNCT
ejpam-3868	134	1	consider	consider	VERB
ejpam-3868	134	2	now	now	ADV
ejpam-3868	134	3	everything	everything	PRON
ejpam-3868	134	4	expressed	express	VERB
ejpam-3868	134	5	in	in	ADP
ejpam-3868	134	6	terms	term	NOUN
ejpam-3868	134	7	of	of	ADP
ejpam-3868	134	8	the	the	DET
ejpam-3868	134	9	unbarred	unbarred	ADJ
ejpam-3868	134	10	coordinates	coordinate	NOUN
ejpam-3868	134	11	.	.	PUNCT
ejpam-3868	135	1	by	by	ADP
ejpam-3868	135	2	taking	take	VERB
ejpam-3868	135	3	the	the	DET
ejpam-3868	135	4	exterior	exterior	ADJ
ejpam-3868	135	5	derivative	derivative	NOUN
ejpam-3868	135	6	of	of	ADP
ejpam-3868	135	7	the	the	DET
ejpam-3868	135	8	equation	equation	NOUN
ejpam-3868	135	9	φ	φ	NOUN
ejpam-3868	135	10	=	=	SYM
ejpam-3868	135	11	0	0	PUNCT
ejpam-3868	135	12	and	and	CCONJ
ejpam-3868	135	13	expressing	express	VERB
ejpam-3868	135	14	dy	dy	NOUN
ejpam-3868	135	15	and	and	CCONJ
ejpam-3868	135	16	dȳ	dȳ	NOUN
ejpam-3868	135	17	in	in	ADP
ejpam-3868	135	18	terms	term	NOUN
ejpam-3868	135	19	of	of	ADP
ejpam-3868	135	20	ϑ	ϑ	PROPN
ejpam-3868	135	21	and	and	CCONJ
ejpam-3868	135	22	ϑ̄	ϑ̄	ADJ
ejpam-3868	135	23	,	,	PUNCT
ejpam-3868	135	24	dx	dx	PROPN
ejpam-3868	135	25	and	and	CCONJ
ejpam-3868	135	26	dx̄	dx̄	PROPN
ejpam-3868	135	27	,	,	PUNCT
ejpam-3868	135	28	we	we	PRON
ejpam-3868	135	29	obtain	obtain	VERB
ejpam-3868	135	30	that	that	DET
ejpam-3868	135	31	(	(	PUNCT
ejpam-3868	135	32	φx	φx	PROPN
ejpam-3868	135	33	+	+	SYM
ejpam-3868	135	34	y′φy	y′φy	NOUN
ejpam-3868	135	35	)	)	PUNCT
ejpam-3868	135	36	dx+	dx+	NOUN
ejpam-3868	136	1	φyϑ+	φyϑ+	PROPN
ejpam-3868	136	2	(	(	PUNCT
ejpam-3868	136	3	φx̄	φx̄	NOUN
ejpam-3868	136	4	+	+	CCONJ
ejpam-3868	136	5	ȳ′φȳ	ȳ′φȳ	X
ejpam-3868	136	6	)	)	PUNCT
ejpam-3868	136	7	dx̄+	dx̄+	NOUN
ejpam-3868	136	8	φȳϑ̄	φȳϑ̄	NOUN
ejpam-3868	136	9	=	=	SYM
ejpam-3868	136	10	0	0	NUM
ejpam-3868	136	11	,	,	PUNCT
ejpam-3868	136	12	(	(	PUNCT
ejpam-3868	136	13	31	31	NUM
ejpam-3868	136	14	)	)	PUNCT
ejpam-3868	136	15	so	so	ADV
ejpam-3868	136	16	there	there	PRON
ejpam-3868	136	17	is	be	VERB
ejpam-3868	136	18	the	the	DET
ejpam-3868	136	19	relation	relation	NOUN
ejpam-3868	136	20	ϑ̄	ϑ̄	VERB
ejpam-3868	136	21	=	=	SYM
ejpam-3868	136	22	−φy	−φy	NOUN
ejpam-3868	136	23	φȳ	φȳ	ADV
ejpam-3868	136	24	ϑ.	ϑ.	NOUN
ejpam-3868	136	25	(	(	PUNCT
ejpam-3868	136	26	32	32	NUM
ejpam-3868	136	27	)	)	PUNCT
ejpam-3868	136	28	in	in	ADP
ejpam-3868	136	29	a	a	DET
ejpam-3868	136	30	similar	similar	ADJ
ejpam-3868	136	31	way	way	NOUN
ejpam-3868	136	32	,	,	PUNCT
ejpam-3868	136	33	the	the	DET
ejpam-3868	136	34	exterior	exterior	ADJ
ejpam-3868	136	35	derivative	derivative	NOUN
ejpam-3868	136	36	of	of	ADP
ejpam-3868	136	37	φx	φx	PROPN
ejpam-3868	136	38	+	+	NOUN
ejpam-3868	136	39	y′φ	y′φ	NOUN
ejpam-3868	136	40	=	=	SYM
ejpam-3868	136	41	0	0	NUM
ejpam-3868	136	42	is	be	AUX
ejpam-3868	136	43	worked	work	VERB
ejpam-3868	136	44	out	out	ADP
ejpam-3868	136	45	and	and	CCONJ
ejpam-3868	136	46	the	the	DET
ejpam-3868	136	47	differentials	differential	NOUN
ejpam-3868	136	48	dy	dy	NOUN
ejpam-3868	136	49	,	,	PUNCT
ejpam-3868	136	50	dȳ	dȳ	NOUN
ejpam-3868	136	51	are	be	AUX
ejpam-3868	136	52	replaced	replace	VERB
ejpam-3868	136	53	yielding	yield	VERB
ejpam-3868	136	54	an	an	DET
ejpam-3868	136	55	expression	expression	NOUN
ejpam-3868	136	56	in	in	ADP
ejpam-3868	136	57	terms	term	NOUN
ejpam-3868	136	58	of	of	ADP
ejpam-3868	136	59	dx	dx	PROPN
ejpam-3868	136	60	,	,	PUNCT
ejpam-3868	136	61	dx̄	dx̄	ADV
ejpam-3868	136	62	,	,	PUNCT
ejpam-3868	136	63	ϑ	ϑ	NOUN
ejpam-3868	136	64	,	,	PUNCT
ejpam-3868	136	65	ϑ̄	ϑ̄	ADJ
ejpam-3868	136	66	and	and	CCONJ
ejpam-3868	136	67	ϕ	ϕ	NOUN
ejpam-3868	136	68	,	,	PUNCT
ejpam-3868	136	69	d(φx+y′φy	d(φx+y′φy	NUM
ejpam-3868	136	70	)	)	PUNCT
ejpam-3868	137	1	=	=	PRON
ejpam-3868	138	1	φxx	φxx	ADJ
ejpam-3868	138	2	dx+φxy	dx+φxy	NOUN
ejpam-3868	138	3	dy+φx̄x	dy+φx̄x	PROPN
ejpam-3868	138	4	dx̄+φȳx	dx̄+φȳx	PROPN
ejpam-3868	139	1	dȳ+dy′φy+y′(φxy	dȳ+dy′φy+y′(φxy	PRON
ejpam-3868	139	2	dx+φyy	dx+φyy	VERB
ejpam-3868	139	3	dy+φx̄y	dy+φx̄y	PROPN
ejpam-3868	139	4	dx̄+φȳy	dx̄+φȳy	NOUN
ejpam-3868	139	5	)	)	PUNCT
ejpam-3868	139	6	=	=	SYM
ejpam-3868	140	1	(	(	PUNCT
ejpam-3868	140	2	φxx	φxx	X
ejpam-3868	140	3	+	+	NUM
ejpam-3868	140	4	2y′φxy	2y′φxy	NOUN
ejpam-3868	140	5	+	+	CCONJ
ejpam-3868	140	6	(	(	PUNCT
ejpam-3868	140	7	y′)2φyy	y′)2φyy	NOUN
ejpam-3868	140	8	+	+	CCONJ
ejpam-3868	140	9	fφy	fφy	NOUN
ejpam-3868	140	10	)	)	PUNCT
ejpam-3868	140	11	dx+	dx+	NOUN
ejpam-3868	140	12	(	(	PUNCT
ejpam-3868	140	13	φxx̄	φxx̄	ADJ
ejpam-3868	140	14	+	+	CCONJ
ejpam-3868	140	15	y′φyx̄	y′φyx̄	PROPN
ejpam-3868	140	16	+	+	CCONJ
ejpam-3868	140	17	y′φxȳ	y′φxȳ	PROPN
ejpam-3868	140	18	+	+	CCONJ
ejpam-3868	140	19	y′ȳ′φyȳ	y′ȳ′φyȳ	NOUN
ejpam-3868	140	20	)	)	PUNCT
ejpam-3868	140	21	dx̄	dx̄	NOUN
ejpam-3868	140	22	(	(	PUNCT
ejpam-3868	140	23	33	33	NUM
ejpam-3868	140	24	)	)	PUNCT
ejpam-3868	141	1	+	+	PROPN
ejpam-3868	141	2	(	(	PUNCT
ejpam-3868	141	3	φxy	φxy	NOUN
ejpam-3868	141	4	+	+	CCONJ
ejpam-3868	141	5	y′φyy)ϑ+	y′φyy)ϑ+	X
ejpam-3868	141	6	(	(	PUNCT
ejpam-3868	141	7	φxȳ	φxȳ	NUM
ejpam-3868	141	8	+	+	SYM
ejpam-3868	141	9	y′φyȳ)ϑ̄+	y′φyȳ)ϑ̄+	NUM
ejpam-3868	141	10	φyϕ	φyϕ	NOUN
ejpam-3868	141	11	=	=	SYM
ejpam-3868	141	12	0	0	NUM
ejpam-3868	141	13	.	.	PUNCT
ejpam-3868	142	1	thus	thus	ADV
ejpam-3868	142	2	,	,	PUNCT
ejpam-3868	142	3	dx̄	dx̄	ADV
ejpam-3868	142	4	=	=	SYM
ejpam-3868	142	5	(	(	PUNCT
ejpam-3868	142	6	φ2	φ2	PROPN
ejpam-3868	142	7	yφȳ	yφȳ	VERB
ejpam-3868	142	8	∆	∆	PROPN
ejpam-3868	142	9	)	)	PUNCT
ejpam-3868	142	10	ϕ	ϕ	PROPN
ejpam-3868	142	11	,	,	PUNCT
ejpam-3868	142	12	mod	mod	ADJ
ejpam-3868	142	13	ϑ.	ϑ.	NOUN
ejpam-3868	142	14	as	as	SCONJ
ejpam-3868	142	15	∆	∆	PROPN
ejpam-3868	142	16	is	be	AUX
ejpam-3868	142	17	unchanged	unchanged	ADJ
ejpam-3868	142	18	when	when	SCONJ
ejpam-3868	142	19	barred	bar	VERB
ejpam-3868	142	20	and	and	CCONJ
ejpam-3868	142	21	unbarred	unbarred	ADJ
ejpam-3868	142	22	quantities	quantity	NOUN
ejpam-3868	142	23	are	be	AUX
ejpam-3868	142	24	interchanged	interchange	VERB
ejpam-3868	142	25	,	,	PUNCT
ejpam-3868	142	26	dx	dx	PROPN
ejpam-3868	142	27	can	can	AUX
ejpam-3868	142	28	be	be	AUX
ejpam-3868	142	29	expressed	express	VERB
ejpam-3868	142	30	in	in	ADP
ejpam-3868	142	31	a	a	DET
ejpam-3868	142	32	similar	similar	ADJ
ejpam-3868	142	33	way	way	NOUN
ejpam-3868	142	34	,	,	PUNCT
ejpam-3868	142	35	dx	dx	PROPN
ejpam-3868	142	36	=	=	SYM
ejpam-3868	143	1	φyφ̄2	φyφ̄2	NOUN
ejpam-3868	143	2	ȳ	ȳ	NUM
ejpam-3868	143	3	∆	∆	PROPN
ejpam-3868	143	4	ϕ̄.	ϕ̄.	PUNCT
ejpam-3868	143	5	thus	thus	ADV
ejpam-3868	143	6	to	to	PART
ejpam-3868	143	7	briefly	briefly	ADV
ejpam-3868	143	8	summarize	summarize	VERB
ejpam-3868	143	9	,	,	PUNCT
ejpam-3868	143	10	dx̄	dx̄	ADJ
ejpam-3868	143	11	=	=	SYM
ejpam-3868	143	12	φ2	φ2	PROPN
ejpam-3868	143	13	yφȳ	yφȳ	NOUN
ejpam-3868	144	1	∆	∆	PROPN
ejpam-3868	144	2	ϕ	ϕ	PROPN
ejpam-3868	144	3	,	,	PUNCT
ejpam-3868	144	4	ϑ̄	ϑ̄	ADJ
ejpam-3868	144	5	=	=	SYM
ejpam-3868	144	6	−φy	−φy	NOUN
ejpam-3868	144	7	φȳ	φȳ	X
ejpam-3868	144	8	ϑ	ϑ	X
ejpam-3868	144	9	,	,	PUNCT
ejpam-3868	144	10	ϑ̄	ϑ̄	ADJ
ejpam-3868	144	11	=	=	PUNCT
ejpam-3868	144	12	∆	∆	X
ejpam-3868	144	13	φyφȳ	φyφȳ	PROPN
ejpam-3868	144	14	dx	dx	PROPN
ejpam-3868	144	15	mod	mod	PROPN
ejpam-3868	144	16	ϑ.	ϑ.	PROPN
ejpam-3868	144	17	(	(	PUNCT
ejpam-3868	144	18	34	34	NUM
ejpam-3868	144	19	)	)	PUNCT
ejpam-3868	144	20	p.	p.	NOUN
ejpam-3868	144	21	bracken	bracken	NOUN
ejpam-3868	144	22	/	/	SYM
ejpam-3868	144	23	eur	eur	PROPN
ejpam-3868	144	24	.	.	PUNCT
ejpam-3868	145	1	j.	j.	PROPN
ejpam-3868	145	2	pure	pure	PROPN
ejpam-3868	145	3	appl	appl	PROPN
ejpam-3868	145	4	.	.	PROPN
ejpam-3868	145	5	math	math	PROPN
ejpam-3868	145	6	,	,	PUNCT
ejpam-3868	145	7	13	13	NUM
ejpam-3868	145	8	(	(	PUNCT
ejpam-3868	145	9	4	4	NUM
ejpam-3868	145	10	)	)	PUNCT
ejpam-3868	145	11	(	(	PUNCT
ejpam-3868	145	12	2020	2020	NUM
ejpam-3868	145	13	)	)	PUNCT
ejpam-3868	145	14	,	,	PUNCT
ejpam-3868	145	15	1016	1016	NUM
ejpam-3868	145	16	-	-	SYM
ejpam-3868	145	17	1034	1034	NUM
ejpam-3868	145	18	1023	1023	NUM
ejpam-3868	145	19	it	it	PRON
ejpam-3868	145	20	is	be	AUX
ejpam-3868	145	21	desired	desire	VERB
ejpam-3868	145	22	to	to	PART
ejpam-3868	145	23	reduce	reduce	VERB
ejpam-3868	145	24	ω̄	ω̄	ADV
ejpam-3868	145	25	to	to	ADP
ejpam-3868	145	26	a	a	DET
ejpam-3868	145	27	form	form	NOUN
ejpam-3868	145	28	as	as	ADV
ejpam-3868	145	29	close	close	ADJ
ejpam-3868	145	30	as	as	ADP
ejpam-3868	145	31	possible	possible	ADJ
ejpam-3868	145	32	to	to	ADP
ejpam-3868	145	33	the	the	DET
ejpam-3868	145	34	standard	standard	ADJ
ejpam-3868	145	35	one	one	NUM
ejpam-3868	145	36	for	for	ADP
ejpam-3868	145	37	a	a	DET
ejpam-3868	145	38	projective	projective	ADJ
ejpam-3868	145	39	connection	connection	NOUN
ejpam-3868	145	40	by	by	ADP
ejpam-3868	145	41	means	mean	NOUN
ejpam-3868	145	42	of	of	ADP
ejpam-3868	145	43	a	a	DET
ejpam-3868	145	44	gauge	gauge	ADJ
ejpam-3868	145	45	transformation	transformation	NOUN
ejpam-3868	145	46	.	.	PUNCT
ejpam-3868	146	1	this	this	PRON
ejpam-3868	146	2	should	should	AUX
ejpam-3868	146	3	involve	involve	VERB
ejpam-3868	146	4	the	the	DET
ejpam-3868	146	5	interchange	interchange	NOUN
ejpam-3868	146	6	of	of	ADP
ejpam-3868	146	7	the	the	DET
ejpam-3868	146	8	positions	position	NOUN
ejpam-3868	146	9	of	of	ADP
ejpam-3868	146	10	the	the	DET
ejpam-3868	146	11	dx	dx	PROPN
ejpam-3868	146	12	and	and	CCONJ
ejpam-3868	146	13	kϕ	kϕ	PROPN
ejpam-3868	147	1	+	+	CCONJ
ejpam-3868	148	1	mϑ	mϑ	PROPN
ejpam-3868	148	2	terms	term	NOUN
ejpam-3868	148	3	in	in	ADP
ejpam-3868	148	4	a	a	DET
ejpam-3868	148	5	matrix	matrix	NOUN
ejpam-3868	148	6	of	of	ADP
ejpam-3868	148	7	the	the	DET
ejpam-3868	148	8	form	form	NOUN
ejpam-3868	148	9	(	(	PUNCT
ejpam-3868	148	10	13	13	NUM
ejpam-3868	148	11	)	)	PUNCT
ejpam-3868	148	12	.	.	PUNCT
ejpam-3868	149	1	however	however	ADV
ejpam-3868	149	2	,	,	PUNCT
ejpam-3868	149	3	for	for	ADP
ejpam-3868	149	4	normal	normal	ADJ
ejpam-3868	149	5	projective	projective	ADJ
ejpam-3868	149	6	connections	connection	NOUN
ejpam-3868	149	7	we	we	PRON
ejpam-3868	149	8	have	have	VERB
ejpam-3868	149	9	k	k	NOUN
ejpam-3868	149	10	=	=	SYM
ejpam-3868	149	11	1	1	X
ejpam-3868	149	12	.	.	PUNCT
ejpam-3868	149	13	from	from	ADP
ejpam-3868	149	14	the	the	DET
ejpam-3868	149	15	formulas	formula	NOUN
ejpam-3868	149	16	of	of	ADP
ejpam-3868	149	17	a	a	DET
ejpam-3868	149	18	gauge	gauge	ADJ
ejpam-3868	149	19	transformation	transformation	NOUN
ejpam-3868	149	20	derived	derive	VERB
ejpam-3868	149	21	before	before	ADV
ejpam-3868	149	22	,	,	PUNCT
ejpam-3868	149	23	this	this	PRON
ejpam-3868	149	24	is	be	AUX
ejpam-3868	149	25	impossible	impossible	ADJ
ejpam-3868	149	26	as	as	SCONJ
ejpam-3868	149	27	it	it	PRON
ejpam-3868	149	28	would	would	AUX
ejpam-3868	149	29	require	require	VERB
ejpam-3868	149	30	taking	take	VERB
ejpam-3868	149	31	a	a	DET
ejpam-3868	149	32	,	,	PUNCT
ejpam-3868	149	33	b	b	NOUN
ejpam-3868	149	34	and	and	CCONJ
ejpam-3868	149	35	c	c	X
ejpam-3868	149	36	the	the	DET
ejpam-3868	149	37	diagonal	diagonal	ADJ
ejpam-3868	149	38	entries	entry	NOUN
ejpam-3868	149	39	in	in	ADP
ejpam-3868	149	40	the	the	DET
ejpam-3868	149	41	gauge	gauge	ADJ
ejpam-3868	149	42	transformation	transformation	NOUN
ejpam-3868	149	43	matrix	matrix	NOUN
ejpam-3868	149	44	to	to	PART
ejpam-3868	149	45	satisfy	satisfy	VERB
ejpam-3868	149	46	inconsistent	inconsistent	ADJ
ejpam-3868	149	47	equations	equation	NOUN
ejpam-3868	149	48	.	.	PUNCT
ejpam-3868	150	1	for	for	ADP
ejpam-3868	150	2	definiteness	definiteness	NOUN
ejpam-3868	150	3	we	we	PRON
ejpam-3868	150	4	suppose	suppose	VERB
ejpam-3868	150	5	that	that	SCONJ
ejpam-3868	150	6	a	a	DET
ejpam-3868	150	7	c	c	NOUN
ejpam-3868	150	8	=	=	PRON
ejpam-3868	150	9	φȳ	φȳ	X
ejpam-3868	150	10	φy	φy	INTJ
ejpam-3868	150	11	,	,	PUNCT
ejpam-3868	150	12	a	a	DET
ejpam-3868	150	13	b	b	NOUN
ejpam-3868	150	14	=	=	SYM
ejpam-3868	150	15	∆	∆	PROPN
ejpam-3868	150	16	φ2	φ2	PROPN
ejpam-3868	150	17	yφȳ	yφȳ	PROPN
ejpam-3868	150	18	,	,	PUNCT
ejpam-3868	150	19	b	b	X
ejpam-3868	150	20	c	c	NOUN
ejpam-3868	150	21	=	=	SYM
ejpam-3868	150	22	φyφ2	φyφ2	PROPN
ejpam-3868	150	23	ȳ	ȳ	PROPN
ejpam-3868	150	24	∆	∆	PROPN
ejpam-3868	150	25	.	.	PUNCT
ejpam-3868	151	1	(	(	PUNCT
ejpam-3868	151	2	35	35	NUM
ejpam-3868	151	3	)	)	PUNCT
ejpam-3868	151	4	the	the	DET
ejpam-3868	151	5	other	other	ADJ
ejpam-3868	151	6	coefficients	coefficient	NOUN
ejpam-3868	151	7	of	of	ADP
ejpam-3868	151	8	the	the	DET
ejpam-3868	151	9	gauge	gauge	ADJ
ejpam-3868	151	10	transformation	transformation	NOUN
ejpam-3868	151	11	are	be	AUX
ejpam-3868	151	12	chosen	choose	VERB
ejpam-3868	151	13	so	so	SCONJ
ejpam-3868	151	14	that	that	SCONJ
ejpam-3868	151	15	the	the	DET
ejpam-3868	151	16	ϑ	ϑ	PROPN
ejpam-3868	151	17	component	component	NOUN
ejpam-3868	151	18	of	of	ADP
ejpam-3868	151	19	ω̄1	ω̄1	NUM
ejpam-3868	151	20	2	2	NUM
ejpam-3868	151	21	is	be	AUX
ejpam-3868	151	22	eliminated	eliminate	VERB
ejpam-3868	151	23	as	as	ADV
ejpam-3868	151	24	well	well	ADV
ejpam-3868	151	25	as	as	ADP
ejpam-3868	151	26	the	the	DET
ejpam-3868	151	27	dx	dx	PROPN
ejpam-3868	151	28	and	and	CCONJ
ejpam-3868	151	29	ϑ	ϑ	PRON
ejpam-3868	151	30	components	component	NOUN
ejpam-3868	151	31	of	of	ADP
ejpam-3868	151	32	ω̄2	ω̄2	NUM
ejpam-3868	151	33	2	2	NUM
ejpam-3868	151	34	.	.	X
ejpam-3868	152	1	there	there	PRON
ejpam-3868	152	2	is	be	VERB
ejpam-3868	152	3	then	then	ADV
ejpam-3868	152	4	a	a	DET
ejpam-3868	152	5	unique	unique	ADJ
ejpam-3868	152	6	gauge	gauge	NOUN
ejpam-3868	152	7	transformation	transformation	NOUN
ejpam-3868	152	8	matrix	matrix	NOUN
ejpam-3868	152	9	h	h	NOUN
ejpam-3868	152	10	such	such	ADJ
ejpam-3868	152	11	that	that	SCONJ
ejpam-3868	152	12	it	it	PRON
ejpam-3868	152	13	has	have	AUX
ejpam-3868	152	14	a	a	DET
ejpam-3868	152	15	lower	low	ADJ
ejpam-3868	152	16	triangular	triangular	NOUN
ejpam-3868	152	17	form	form	NOUN
ejpam-3868	152	18	,	,	PUNCT
ejpam-3868	152	19	h−1ω̄h+	h−1ω̄h+	VERB
ejpam-3868	152	20	h−1	h−1	PROPN
ejpam-3868	152	21	dh	dh	NOUN
ejpam-3868	152	22	=	=	SYM
ejpam-3868	152	23	ϕ+mϑ	ϕ+mϑ	PROPN
ejpam-3868	152	24	ϑ	ϑ	X
ejpam-3868	152	25	dx	dx	PROPN
ejpam-3868	152	26	κϕ	κϕ	ADP
ejpam-3868	152	27			PROPN
ejpam-3868	152	28	(	(	PUNCT
ejpam-3868	152	29	36	36	NUM
ejpam-3868	152	30	)	)	PUNCT
ejpam-3868	152	31	given	give	VERB
ejpam-3868	152	32	a	a	DET
ejpam-3868	152	33	trace	trace	NOUN
ejpam-3868	152	34	-	-	PUNCT
ejpam-3868	152	35	free	free	ADJ
ejpam-3868	152	36	matrix	matrix	NOUN
ejpam-3868	152	37	valued	value	VERB
ejpam-3868	152	38	one	one	NUM
ejpam-3868	152	39	-	-	PUNCT
ejpam-3868	152	40	form	form	NOUN
ejpam-3868	152	41	$	$	SYM
ejpam-3868	152	42	with	with	ADP
ejpam-3868	152	43	$	$	SYM
ejpam-3868	152	44	2	2	NUM
ejpam-3868	152	45	=	=	SYM
ejpam-3868	152	46	−ϑ	−ϑ	NOUN
ejpam-3868	152	47	$	$	SYM
ejpam-3868	152	48	2	2	NUM
ejpam-3868	152	49	1	1	NUM
ejpam-3868	152	50	=	=	SYM
ejpam-3868	152	51	dx	dx	PROPN
ejpam-3868	152	52	and	and	CCONJ
ejpam-3868	152	53	$	$	SYM
ejpam-3868	152	54	a	a	DET
ejpam-3868	152	55	multiple	multiple	NOUN
ejpam-3868	152	56	of	of	ADP
ejpam-3868	152	57	ϕ	ϕ	NOUN
ejpam-3868	152	58	,	,	PUNCT
ejpam-3868	152	59	the	the	DET
ejpam-3868	152	60	remaining	remain	VERB
ejpam-3868	152	61	elements	element	NOUN
ejpam-3868	152	62	of	of	ADP
ejpam-3868	152	63	$	$	SYM
ejpam-3868	152	64	are	be	AUX
ejpam-3868	152	65	uniquely	uniquely	ADV
ejpam-3868	152	66	determined	determine	VERB
ejpam-3868	152	67	by	by	ADP
ejpam-3868	152	68	the	the	DET
ejpam-3868	152	69	following	follow	VERB
ejpam-3868	152	70	conditions	condition	NOUN
ejpam-3868	152	71	on	on	ADP
ejpam-3868	152	72	its	its	PRON
ejpam-3868	152	73	curvature	curvature	NOUN
ejpam-3868	152	74	form	form	NOUN
ejpam-3868	152	75	π	π	NOUN
ejpam-3868	152	76	:	:	PUNCT
ejpam-3868	152	77	it	it	PRON
ejpam-3868	152	78	must	must	AUX
ejpam-3868	152	79	be	be	AUX
ejpam-3868	152	80	strictly	strictly	ADV
ejpam-3868	152	81	upper	upper	ADJ
ejpam-3868	152	82	-	-	PUNCT
ejpam-3868	152	83	triangular	triangular	NOUN
ejpam-3868	152	84	and	and	CCONJ
ejpam-3868	152	85	π1	π1	NOUN
ejpam-3868	152	86	2	2	NUM
ejpam-3868	152	87	is	be	AUX
ejpam-3868	152	88	a	a	DET
ejpam-3868	152	89	multiple	multiple	NOUN
ejpam-3868	152	90	of	of	ADP
ejpam-3868	152	91	dx	dx	PROPN
ejpam-3868	152	92	∧	∧	PROPN
ejpam-3868	152	93	ϑ.	ϑ.	VERB
ejpam-3868	152	94	the	the	DET
ejpam-3868	152	95	strategy	strategy	NOUN
ejpam-3868	152	96	is	be	AUX
ejpam-3868	152	97	to	to	PART
ejpam-3868	152	98	compute	compute	VERB
ejpam-3868	152	99	the	the	DET
ejpam-3868	152	100	componets	componet	NOUN
ejpam-3868	152	101	of	of	ADP
ejpam-3868	152	102	π	π	PROPN
ejpam-3868	152	103	and	and	CCONJ
ejpam-3868	152	104	look	look	VERB
ejpam-3868	152	105	at	at	ADP
ejpam-3868	152	106	the	the	DET
ejpam-3868	152	107	consequences	consequence	NOUN
ejpam-3868	152	108	of	of	ADP
ejpam-3868	152	109	taking	take	VERB
ejpam-3868	152	110	them	they	PRON
ejpam-3868	152	111	to	to	PART
ejpam-3868	152	112	be	be	AUX
ejpam-3868	152	113	zero	zero	NUM
ejpam-3868	152	114	.	.	PUNCT
ejpam-3868	153	1	to	to	PART
ejpam-3868	153	2	calculate	calculate	VERB
ejpam-3868	153	3	π	π	PROPN
ejpam-3868	153	4	,	,	PUNCT
ejpam-3868	153	5	we	we	PRON
ejpam-3868	153	6	have	have	VERB
ejpam-3868	153	7	to	to	ADP
ejpam-3868	153	8	calculateω̃0	calculateω̃0	NOUN
ejpam-3868	153	9	0	0	NUM
ejpam-3868	153	10	ω̃0	ω̃0	NUM
ejpam-3868	153	11	1	1	NUM
ejpam-3868	153	12	ω̃0	ω̃0	NUM
ejpam-3868	153	13	2	2	NUM
ejpam-3868	153	14	ω̃1	ω̃1	NOUN
ejpam-3868	153	15	0	0	NUM
ejpam-3868	153	16	ω̃1	ω̃1	PROPN
ejpam-3868	153	17	1	1	NUM
ejpam-3868	153	18	ω̃1	ω̃1	PROPN
ejpam-3868	153	19	2	2	NUM
ejpam-3868	153	20	ω̃2	ω̃2	PROPN
ejpam-3868	153	21	0	0	NUM
ejpam-3868	153	22	ω̃2	ω̃2	PROPN
ejpam-3868	153	23	1	1	NUM
ejpam-3868	153	24	ω̃2	ω̃2	PROPN
ejpam-3868	153	25	2	2	NUM
ejpam-3868	153	26			PROPN
ejpam-3868	153	27	∧	∧	PROPN
ejpam-3868	153	28	ω̃0	ω̃0	NOUN
ejpam-3868	153	29	0	0	NUM
ejpam-3868	153	30	ω̃0	ω̃0	NUM
ejpam-3868	153	31	1	1	NUM
ejpam-3868	153	32	ω̃0	ω̃0	NUM
ejpam-3868	153	33	2	2	NUM
ejpam-3868	153	34	ω̃1	ω̃1	NOUN
ejpam-3868	153	35	0	0	NUM
ejpam-3868	153	36	ω̃1	ω̃1	PROPN
ejpam-3868	153	37	1	1	NUM
ejpam-3868	153	38	ω̃1	ω̃1	PROPN
ejpam-3868	153	39	2	2	NUM
ejpam-3868	153	40	ω̃2	ω̃2	PROPN
ejpam-3868	153	41	0	0	NUM
ejpam-3868	153	42	ω̃2	ω̃2	PROPN
ejpam-3868	153	43	1	1	NUM
ejpam-3868	153	44	ω̃2	ω̃2	PROPN
ejpam-3868	153	45	2	2	NUM
ejpam-3868	153	46			PROPN
ejpam-3868	153	47	suppose	suppose	VERB
ejpam-3868	153	48	µ	µ	PRON
ejpam-3868	153	49	,	,	PUNCT
ejpam-3868	153	50	λ	λ	PROPN
ejpam-3868	153	51	,	,	PUNCT
ejpam-3868	153	52	ν	ν	NOUN
ejpam-3868	153	53	are	be	AUX
ejpam-3868	153	54	functions	function	NOUN
ejpam-3868	153	55	,	,	PUNCT
ejpam-3868	153	56	then	then	ADV
ejpam-3868	153	57	we	we	PRON
ejpam-3868	153	58	note	note	VERB
ejpam-3868	153	59	that	that	SCONJ
ejpam-3868	153	60	dν	dν	PROPN
ejpam-3868	153	61	=	=	SYM
ejpam-3868	153	62	γ(ν	γ(ν	NOUN
ejpam-3868	153	63	)	)	PUNCT
ejpam-3868	153	64	dx+	dx+	NOUN
ejpam-3868	153	65	νyϑ+	νyϑ+	PROPN
ejpam-3868	153	66	νy′	νy′	NOUN
ejpam-3868	153	67	ϕ	ϕ	NOUN
ejpam-3868	153	68	,	,	PUNCT
ejpam-3868	153	69	(	(	PUNCT
ejpam-3868	153	70	37	37	NUM
ejpam-3868	153	71	)	)	PUNCT
ejpam-3868	153	72	and	and	CCONJ
ejpam-3868	153	73	moreover	moreover	ADV
ejpam-3868	153	74	,	,	PUNCT
ejpam-3868	153	75	dϑ	dϑ	NOUN
ejpam-3868	153	76	=	=	SYM
ejpam-3868	153	77	−ϕ	−ϕ	ADJ
ejpam-3868	153	78	∧	∧	PROPN
ejpam-3868	153	79	dx	dx	PROPN
ejpam-3868	153	80	,	,	PUNCT
ejpam-3868	153	81	dϕ	dϕ	PROPN
ejpam-3868	153	82	=	=	PUNCT
ejpam-3868	153	83	−df	−df	PROPN
ejpam-3868	153	84	∧	∧	PROPN
ejpam-3868	153	85	dx	dx	PROPN
ejpam-3868	153	86	=	=	PROPN
ejpam-3868	153	87	−(fyϑ+	−(fyϑ+	PROPN
ejpam-3868	153	88	fy′ϕ	fy′ϕ	PROPN
ejpam-3868	153	89	)	)	PUNCT
ejpam-3868	153	90	∧	∧	PROPN
ejpam-3868	153	91	dx	dx	PROPN
ejpam-3868	153	92	.	.	PUNCT
ejpam-3868	154	1	(	(	PUNCT
ejpam-3868	154	2	38	38	NUM
ejpam-3868	154	3	)	)	PUNCT
ejpam-3868	154	4	the	the	DET
ejpam-3868	154	5	notation	notation	NOUN
ejpam-3868	154	6	for	for	ADP
ejpam-3868	154	7	the	the	DET
ejpam-3868	154	8	components	component	NOUN
ejpam-3868	154	9	of	of	ADP
ejpam-3868	154	10	$	$	SYM
ejpam-3868	154	11	and	and	CCONJ
ejpam-3868	154	12	π	π	PROPN
ejpam-3868	154	13	follows	follow	VERB
ejpam-3868	154	14	the	the	DET
ejpam-3868	154	15	same	same	ADJ
ejpam-3868	154	16	system	system	NOUN
ejpam-3868	154	17	as	as	ADP
ejpam-3868	154	18	for	for	ADP
ejpam-3868	154	19	ω	ω	PROPN
ejpam-3868	154	20	.	.	PUNCT
ejpam-3868	155	1	first	first	ADV
ejpam-3868	155	2	we	we	PRON
ejpam-3868	155	3	have	have	VERB
ejpam-3868	155	4	π2	π2	NOUN
ejpam-3868	155	5	1	1	NUM
ejpam-3868	155	6	=	=	SYM
ejpam-3868	155	7	d$2	d$2	NOUN
ejpam-3868	155	8	1	1	NUM
ejpam-3868	156	1	+	+	NOUN
ejpam-3868	156	2	$	$	SYM
ejpam-3868	156	3	2	2	NUM
ejpam-3868	156	4	∧$0	∧$0	NOUN
ejpam-3868	156	5	1	1	NUM
ejpam-3868	156	6	+	+	SYM
ejpam-3868	156	7	$	$	SYM
ejpam-3868	156	8	2	2	NUM
ejpam-3868	156	9	1	1	NUM
ejpam-3868	156	10	∧$1	∧$1	NOUN
ejpam-3868	156	11	1	1	NUM
ejpam-3868	156	12	+	+	NOUN
ejpam-3868	156	13	$	$	SYM
ejpam-3868	156	14	2	2	NUM
ejpam-3868	156	15	2	2	NUM
ejpam-3868	156	16	∧$2	∧$2	NUM
ejpam-3868	156	17	1	1	NUM
ejpam-3868	156	18	=	=	SYM
ejpam-3868	156	19	−ϑ	−ϑ	NOUN
ejpam-3868	156	20	∧$0	∧$0	NOUN
ejpam-3868	156	21	1	1	NUM
ejpam-3868	156	22	+	+	NUM
ejpam-3868	156	23	dx	dx	PROPN
ejpam-3868	156	24	∧	∧	PROPN
ejpam-3868	156	25	(	(	PUNCT
ejpam-3868	156	26	$	$	SYM
ejpam-3868	156	27	1	1	NUM
ejpam-3868	156	28	1	1	NUM
ejpam-3868	156	29	∧$2	∧$2	NOUN
ejpam-3868	156	30	2	2	NUM
ejpam-3868	156	31	)	)	PUNCT
ejpam-3868	156	32	.	.	PUNCT
ejpam-3868	157	1	(	(	PUNCT
ejpam-3868	157	2	39	39	NUM
ejpam-3868	157	3	)	)	PUNCT
ejpam-3868	157	4	this	this	PRON
ejpam-3868	157	5	will	will	AUX
ejpam-3868	157	6	vanish	vanish	VERB
ejpam-3868	157	7	provided	provide	VERB
ejpam-3868	157	8	that	that	SCONJ
ejpam-3868	157	9	,	,	PUNCT
ejpam-3868	157	10	$	$	SYM
ejpam-3868	157	11	0	0	NUM
ejpam-3868	157	12	1	1	NUM
ejpam-3868	157	13	=	=	SYM
ejpam-3868	157	14	λ	λ	PROPN
ejpam-3868	157	15	∧	∧	PROPN
ejpam-3868	157	16	dx	dx	PROPN
ejpam-3868	157	17	,	,	PUNCT
ejpam-3868	157	18	$	$	SYM
ejpam-3868	157	19	1	1	NUM
ejpam-3868	157	20	1	1	NUM
ejpam-3868	157	21	=	=	SYM
ejpam-3868	157	22	$	$	SYM
ejpam-3868	157	23	2	2	NUM
ejpam-3868	157	24	2	2	NUM
ejpam-3868	157	25	+	+	NOUN
ejpam-3868	157	26	λ0	λ0	NOUN
ejpam-3868	157	27	dx−	dx−	NUM
ejpam-3868	157	28	λϑ.	λϑ.	NOUN
ejpam-3868	157	29	(	(	PUNCT
ejpam-3868	157	30	40	40	NUM
ejpam-3868	157	31	)	)	PUNCT
ejpam-3868	157	32	as	as	ADP
ejpam-3868	157	33	noted	note	VERB
ejpam-3868	157	34	λ	λ	NOUN
ejpam-3868	157	35	and	and	CCONJ
ejpam-3868	157	36	µ	µ	PROPN
ejpam-3868	157	37	are	be	AUX
ejpam-3868	157	38	functions	function	NOUN
ejpam-3868	157	39	which	which	PRON
ejpam-3868	157	40	are	be	AUX
ejpam-3868	157	41	arbitrary	arbitrary	ADJ
ejpam-3868	157	42	at	at	ADP
ejpam-3868	157	43	first	first	ADV
ejpam-3868	157	44	.	.	PUNCT
ejpam-3868	158	1	the	the	DET
ejpam-3868	158	2	next	next	ADJ
ejpam-3868	158	3	component	component	NOUN
ejpam-3868	158	4	is	be	AUX
ejpam-3868	158	5	π2	π2	NOUN
ejpam-3868	158	6	=	=	PUNCT
ejpam-3868	158	7	d$2	d$2	PROPN
ejpam-3868	159	1	+	+	NOUN
ejpam-3868	159	2	$	$	SYM
ejpam-3868	159	3	2	2	NUM
ejpam-3868	159	4	∧$0	∧$0	NOUN
ejpam-3868	159	5	0	0	NUM
ejpam-3868	160	1	+	+	NOUN
ejpam-3868	160	2	$	$	SYM
ejpam-3868	160	3	2	2	NUM
ejpam-3868	160	4	1	1	NUM
ejpam-3868	160	5	∧$1	∧$1	NOUN
ejpam-3868	160	6	+	+	NOUN
ejpam-3868	160	7	$	$	SYM
ejpam-3868	160	8	2	2	NUM
ejpam-3868	160	9	2	2	NUM
ejpam-3868	160	10	∧$2	∧$2	NOUN
ejpam-3868	160	11	=	=	PUNCT
ejpam-3868	160	12	(	(	PUNCT
ejpam-3868	160	13	ϕ−$1	ϕ−$1	ADJ
ejpam-3868	160	14	)	)	PUNCT
ejpam-3868	160	15	∧	∧	PROPN
ejpam-3868	160	16	dx−	dx−	NUM
ejpam-3868	160	17	ϑ	ϑ	PROPN
ejpam-3868	160	18	∧	∧	PROPN
ejpam-3868	160	19	(	(	PUNCT
ejpam-3868	160	20	$	$	SYM
ejpam-3868	160	21	0	0	NUM
ejpam-3868	160	22	0	0	NUM
ejpam-3868	160	23	−$2	−$2	PROPN
ejpam-3868	160	24	2	2	NUM
ejpam-3868	160	25	)	)	PUNCT
ejpam-3868	160	26	.	.	PUNCT
ejpam-3868	161	1	(	(	PUNCT
ejpam-3868	161	2	41	41	NUM
ejpam-3868	161	3	)	)	PUNCT
ejpam-3868	161	4	p.	p.	NOUN
ejpam-3868	161	5	bracken	bracken	NOUN
ejpam-3868	161	6	/	/	SYM
ejpam-3868	161	7	eur	eur	PROPN
ejpam-3868	161	8	.	.	PUNCT
ejpam-3868	162	1	j.	j.	PROPN
ejpam-3868	162	2	pure	pure	PROPN
ejpam-3868	162	3	appl	appl	PROPN
ejpam-3868	162	4	.	.	PROPN
ejpam-3868	162	5	math	math	PROPN
ejpam-3868	162	6	,	,	PUNCT
ejpam-3868	162	7	13	13	NUM
ejpam-3868	162	8	(	(	PUNCT
ejpam-3868	162	9	4	4	NUM
ejpam-3868	162	10	)	)	PUNCT
ejpam-3868	162	11	(	(	PUNCT
ejpam-3868	162	12	2020	2020	NUM
ejpam-3868	162	13	)	)	PUNCT
ejpam-3868	162	14	,	,	PUNCT
ejpam-3868	162	15	1016	1016	NUM
ejpam-3868	162	16	-	-	SYM
ejpam-3868	162	17	1034	1034	NUM
ejpam-3868	162	18	1024	1024	NUM
ejpam-3868	162	19	this	this	PRON
ejpam-3868	162	20	is	be	AUX
ejpam-3868	162	21	zero	zero	NUM
ejpam-3868	162	22	if	if	SCONJ
ejpam-3868	162	23	and	and	CCONJ
ejpam-3868	162	24	only	only	ADV
ejpam-3868	162	25	if	if	SCONJ
ejpam-3868	162	26	the	the	DET
ejpam-3868	162	27	coefficient	coefficient	NOUN
ejpam-3868	162	28	of	of	ADP
ejpam-3868	162	29	ϕ	ϕ	NOUN
ejpam-3868	162	30	in	in	ADP
ejpam-3868	162	31	$	$	SYM
ejpam-3868	162	32	1	1	NUM
ejpam-3868	162	33	is	be	AUX
ejpam-3868	162	34	one	one	NUM
ejpam-3868	162	35	and	and	CCONJ
ejpam-3868	162	36	also	also	ADV
ejpam-3868	162	37	$	$	SYM
ejpam-3868	162	38	0	0	NUM
ejpam-3868	162	39	0	0	NUM
ejpam-3868	162	40	=	=	SYM
ejpam-3868	162	41	$	$	SYM
ejpam-3868	162	42	2	2	NUM
ejpam-3868	162	43	2	2	NUM
ejpam-3868	162	44	−	−	PROPN
ejpam-3868	162	45	µdx+	µdx+	PROPN
ejpam-3868	162	46	νϑ	νϑ	NOUN
ejpam-3868	162	47	,	,	PUNCT
ejpam-3868	162	48	$	$	SYM
ejpam-3868	162	49	1	1	NUM
ejpam-3868	162	50	=	=	SYM
ejpam-3868	162	51	$	$	SYM
ejpam-3868	162	52	+	+	X
ejpam-3868	162	53	µϑ.	µϑ.	X
ejpam-3868	162	54	(	(	PUNCT
ejpam-3868	162	55	42	42	NUM
ejpam-3868	162	56	)	)	PUNCT
ejpam-3868	162	57	the	the	DET
ejpam-3868	162	58	trace	trace	NOUN
ejpam-3868	162	59	of	of	ADP
ejpam-3868	162	60	the	the	DET
ejpam-3868	162	61	matrix	matrix	NOUN
ejpam-3868	162	62	of	of	ADP
ejpam-3868	162	63	forms	form	NOUN
ejpam-3868	162	64	$	$	SYM
ejpam-3868	162	65	is	be	AUX
ejpam-3868	162	66	to	to	PART
ejpam-3868	162	67	be	be	AUX
ejpam-3868	162	68	zero	zero	NUM
ejpam-3868	162	69	.	.	PUNCT
ejpam-3868	163	1	this	this	DET
ejpam-3868	163	2	constraint	constraint	NOUN
ejpam-3868	163	3	implies	imply	VERB
ejpam-3868	163	4	that	that	SCONJ
ejpam-3868	163	5	$	$	SYM
ejpam-3868	163	6	0	0	NUM
ejpam-3868	163	7	0	0	NUM
ejpam-3868	163	8	+	+	NOUN
ejpam-3868	163	9	$	$	SYM
ejpam-3868	163	10	1	1	NUM
ejpam-3868	163	11	1	1	NUM
ejpam-3868	163	12	+	+	ADV
ejpam-3868	163	13	$	$	SYM
ejpam-3868	163	14	2	2	NUM
ejpam-3868	163	15	2	2	NUM
ejpam-3868	163	16	=	=	SYM
ejpam-3868	163	17	$	$	SYM
ejpam-3868	163	18	2	2	NUM
ejpam-3868	163	19	2	2	NUM
ejpam-3868	163	20	−	−	NOUN
ejpam-3868	163	21	µdx+	µdx+	PROPN
ejpam-3868	163	22	νϑ+$2	νϑ+$2	ADJ
ejpam-3868	163	23	2	2	NUM
ejpam-3868	163	24	+	+	NOUN
ejpam-3868	163	25	λ0	λ0	NOUN
ejpam-3868	163	26	dx−	dx−	PRON
ejpam-3868	163	27	λϑ+$2	λϑ+$2	PROPN
ejpam-3868	163	28	2	2	NUM
ejpam-3868	163	29	=	=	SYM
ejpam-3868	163	30	(	(	PUNCT
ejpam-3868	163	31	λ−	λ−	PROPN
ejpam-3868	163	32	µ	µ	X
ejpam-3868	163	33	)	)	PUNCT
ejpam-3868	163	34	dx+	dx+	NOUN
ejpam-3868	163	35	(	(	PUNCT
ejpam-3868	163	36	ν	ν	X
ejpam-3868	163	37	−	−	PROPN
ejpam-3868	163	38	λ)ϑ+	λ)ϑ+	X
ejpam-3868	163	39	3$2	3$2	NUM
ejpam-3868	163	40	2	2	NUM
ejpam-3868	163	41	=	=	SYM
ejpam-3868	163	42	(	(	PUNCT
ejpam-3868	163	43	λ0	λ0	NOUN
ejpam-3868	163	44	−	−	PROPN
ejpam-3868	163	45	µ	µ	NOUN
ejpam-3868	163	46	)	)	PUNCT
ejpam-3868	163	47	dx+	dx+	NOUN
ejpam-3868	163	48	(	(	PUNCT
ejpam-3868	163	49	ν	ν	X
ejpam-3868	163	50	−	−	PROPN
ejpam-3868	163	51	λ)ϑ+	λ)ϑ+	X
ejpam-3868	163	52	3κϕ.	3κϕ.	NUM
ejpam-3868	163	53	(	(	PUNCT
ejpam-3868	163	54	43	43	NUM
ejpam-3868	163	55	)	)	PUNCT
ejpam-3868	163	56	since	since	SCONJ
ejpam-3868	163	57	dx	dx	PROPN
ejpam-3868	163	58	,	,	PUNCT
ejpam-3868	163	59	ϑ	ϑ	X
ejpam-3868	163	60	,	,	PUNCT
ejpam-3868	163	61	and	and	CCONJ
ejpam-3868	163	62	ϕ	ϕ	NOUN
ejpam-3868	163	63	are	be	AUX
ejpam-3868	163	64	independent	independent	ADJ
ejpam-3868	163	65	it	it	PRON
ejpam-3868	163	66	follows	follow	VERB
ejpam-3868	163	67	that	that	PRON
ejpam-3868	163	68	κ	κ	PROPN
ejpam-3868	163	69	=	=	SYM
ejpam-3868	163	70	0	0	NUM
ejpam-3868	163	71	,	,	PUNCT
ejpam-3868	163	72	λ0	λ0	NOUN
ejpam-3868	163	73	=	=	SYM
ejpam-3868	163	74	µ	µ	X
ejpam-3868	163	75	,	,	PUNCT
ejpam-3868	163	76	λ	λ	X
ejpam-3868	163	77	=	=	SYM
ejpam-3868	163	78	ν	ν	NOUN
ejpam-3868	163	79	,	,	PUNCT
ejpam-3868	163	80	$	$	SYM
ejpam-3868	163	81	2	2	NUM
ejpam-3868	163	82	2	2	NUM
ejpam-3868	163	83	=	=	SYM
ejpam-3868	163	84	0	0	NUM
ejpam-3868	163	85	,	,	PUNCT
ejpam-3868	163	86	$	$	SYM
ejpam-3868	163	87	0	0	NUM
ejpam-3868	163	88	0	0	NUM
ejpam-3868	163	89	=	=	SYM
ejpam-3868	163	90	−$1	−$1	VERB
ejpam-3868	164	1	1	1	NUM
ejpam-3868	164	2	=	=	SYM
ejpam-3868	164	3	−µdx+	−µdx+	ADJ
ejpam-3868	164	4	νϑ.	νϑ.	NOUN
ejpam-3868	164	5	(	(	PUNCT
ejpam-3868	164	6	44	44	NUM
ejpam-3868	164	7	)	)	PUNCT
ejpam-3868	164	8	the	the	DET
ejpam-3868	164	9	next	next	ADJ
ejpam-3868	164	10	component	component	NOUN
ejpam-3868	164	11	of	of	ADP
ejpam-3868	164	12	π	π	PROPN
ejpam-3868	164	13	to	to	PART
ejpam-3868	164	14	consider	consider	VERB
ejpam-3868	164	15	is	be	AUX
ejpam-3868	164	16	π1	π1	ADJ
ejpam-3868	164	17	=	=	PUNCT
ejpam-3868	164	18	d$1	d$1	NOUN
ejpam-3868	164	19	+	+	ADV
ejpam-3868	164	20	$	$	SYM
ejpam-3868	164	21	1	1	NUM
ejpam-3868	164	22	∧$2	∧$2	NOUN
ejpam-3868	164	23	0	0	NUM
ejpam-3868	165	1	+	+	NOUN
ejpam-3868	165	2	$	$	SYM
ejpam-3868	165	3	1	1	NUM
ejpam-3868	165	4	1	1	NUM
ejpam-3868	165	5	∧$1	∧$1	NOUN
ejpam-3868	165	6	+	+	NOUN
ejpam-3868	165	7	$	$	SYM
ejpam-3868	165	8	1	1	NUM
ejpam-3868	165	9	2	2	NUM
ejpam-3868	165	10	∧$2	∧$2	NOUN
ejpam-3868	165	11	=	=	SYM
ejpam-3868	165	12	d(ϕ+µϑ)+$1∧($0	d(ϕ+µϑ)+$1∧($0	PROPN
ejpam-3868	166	1	0−$1	0−$1	PROPN
ejpam-3868	166	2	1)+$1	1)+$1	NUM
ejpam-3868	167	1	2∧$2	2∧$2	NUM
ejpam-3868	167	2	=	=	SYM
ejpam-3868	167	3	dϕ+dµ∧ϑ+µdϑ+2(ϕ+µϑ)∧(−µdx+νϑ)−$1	dϕ+dµ∧ϑ+µdϑ+2(ϕ+µϑ)∧(−µdx+νϑ)−$1	NOUN
ejpam-3868	167	4	2	2	NUM
ejpam-3868	167	5	∧ϑ	∧ϑ	NOUN
ejpam-3868	167	6	(	(	PUNCT
ejpam-3868	167	7	45	45	NUM
ejpam-3868	167	8	)	)	PUNCT
ejpam-3868	167	9	=	=	VERB
ejpam-3868	167	10	dϕ+	dϕ+	PROPN
ejpam-3868	167	11	dµ	dµ	PROPN
ejpam-3868	167	12	∧	∧	PROPN
ejpam-3868	167	13	ϑ−	ϑ−	PROPN
ejpam-3868	167	14	µϕ	µϕ	ADP
ejpam-3868	167	15	∧	∧	PROPN
ejpam-3868	167	16	dx+	dx+	NOUN
ejpam-3868	167	17	2(ϕ+	2(ϕ+	NUM
ejpam-3868	167	18	µϑ	µϑ	NOUN
ejpam-3868	167	19	)	)	PUNCT
ejpam-3868	167	20	∧	∧	NOUN
ejpam-3868	167	21	(	(	PUNCT
ejpam-3868	167	22	−µdx+	−µdx+	ADJ
ejpam-3868	167	23	νϑ)−$1	νϑ)−$1	PROPN
ejpam-3868	167	24	2	2	NUM
ejpam-3868	167	25	∧	∧	PROPN
ejpam-3868	167	26	ϑ.	ϑ.	VERB
ejpam-3868	167	27	the	the	DET
ejpam-3868	167	28	differentials	differential	NOUN
ejpam-3868	167	29	dµ	dµ	VERB
ejpam-3868	167	30	and	and	CCONJ
ejpam-3868	167	31	df	df	PROPN
ejpam-3868	167	32	are	be	AUX
ejpam-3868	167	33	given	give	VERB
ejpam-3868	167	34	by	by	ADP
ejpam-3868	167	35	dµ	dµ	ADJ
ejpam-3868	167	36	=	=	SYM
ejpam-3868	167	37	γ(µ	γ(µ	PROPN
ejpam-3868	167	38	)	)	PUNCT
ejpam-3868	167	39	dx+	dx+	NOUN
ejpam-3868	168	1	µyϑ+	µyϑ+	PROPN
ejpam-3868	168	2	µy′	µy′	PROPN
ejpam-3868	168	3	ϕ	ϕ	NOUN
ejpam-3868	168	4	,	,	PUNCT
ejpam-3868	168	5	df	df	PROPN
ejpam-3868	168	6	=	=	SYM
ejpam-3868	168	7	fx	fx	PROPN
ejpam-3868	168	8	dx+	dx+	NOUN
ejpam-3868	168	9	fy(ϑ+	fy(ϑ+	PROPN
ejpam-3868	168	10	y′	y′	NOUN
ejpam-3868	168	11	dx	dx	PROPN
ejpam-3868	168	12	)	)	PUNCT
ejpam-3868	168	13	+	+	CCONJ
ejpam-3868	168	14	fy′(ϕ+	fy′(ϕ+	NOUN
ejpam-3868	168	15	f	f	PROPN
ejpam-3868	168	16	dx	dx	PROPN
ejpam-3868	168	17	)	)	PUNCT
ejpam-3868	168	18	.	.	PUNCT
ejpam-3868	169	1	(	(	PUNCT
ejpam-3868	169	2	46	46	NUM
ejpam-3868	169	3	)	)	PUNCT
ejpam-3868	169	4	consequently	consequently	ADV
ejpam-3868	169	5	,	,	PUNCT
ejpam-3868	169	6	π1	π1	NOUN
ejpam-3868	169	7	is	be	AUX
ejpam-3868	169	8	π1	π1	NOUN
ejpam-3868	169	9	=	=	SYM
ejpam-3868	169	10	−(fy(ϑ+	−(fy(ϑ+	PROPN
ejpam-3868	169	11	y′	y′	PUNCT
ejpam-3868	169	12	dx	dx	PROPN
ejpam-3868	169	13	)	)	PUNCT
ejpam-3868	170	1	+	+	CCONJ
ejpam-3868	170	2	fy′(ϕ+	fy′(ϕ+	NOUN
ejpam-3868	170	3	f	f	PROPN
ejpam-3868	170	4	dx	dx	PROPN
ejpam-3868	170	5	)	)	PUNCT
ejpam-3868	170	6	)	)	PUNCT
ejpam-3868	170	7	∧	∧	NOUN
ejpam-3868	170	8	dx+	dx+	NOUN
ejpam-3868	170	9	(	(	PUNCT
ejpam-3868	170	10	γ(µ)dx+	γ(µ)dx+	ADV
ejpam-3868	170	11	µyϑ+	µyϑ+	ADV
ejpam-3868	170	12	µy′ϕ	µy′ϕ	ADJ
ejpam-3868	170	13	)	)	PUNCT
ejpam-3868	170	14	∧	∧	PROPN
ejpam-3868	170	15	ϑ	ϑ	X
ejpam-3868	170	16	−µϕ	−µϕ	NOUN
ejpam-3868	170	17	∧	∧	NOUN
ejpam-3868	170	18	dx−	dx−	NUM
ejpam-3868	170	19	2µϕ	2µϕ	NOUN
ejpam-3868	170	20	∧	∧	NOUN
ejpam-3868	170	21	dx+	dx+	NOUN
ejpam-3868	170	22	2νϕ	2νϕ	ADJ
ejpam-3868	170	23	∧	∧	PROPN
ejpam-3868	170	24	ϑ−	ϑ−	PROPN
ejpam-3868	170	25	2µ2ϑ	2µ2ϑ	NUM
ejpam-3868	170	26	∧	∧	NOUN
ejpam-3868	170	27	dx−$1	dx−$1	ADP
ejpam-3868	170	28	2	2	NUM
ejpam-3868	170	29	∧	∧	PROPN
ejpam-3868	170	30	ϑ	ϑ	X
ejpam-3868	170	31	(	(	PUNCT
ejpam-3868	170	32	47	47	NUM
ejpam-3868	170	33	)	)	PUNCT
ejpam-3868	170	34	=	=	SYM
ejpam-3868	170	35	(	(	PUNCT
ejpam-3868	170	36	fy′	fy′	PRON
ejpam-3868	170	37	+	+	NUM
ejpam-3868	170	38	3µ	3µ	NUM
ejpam-3868	170	39	)	)	PUNCT
ejpam-3868	170	40	dx	dx	PROPN
ejpam-3868	170	41	∧	∧	PROPN
ejpam-3868	170	42	ϕ+	ϕ+	INTJ
ejpam-3868	170	43	(	(	PUNCT
ejpam-3868	170	44	fy	fy	PROPN
ejpam-3868	170	45	+	+	PROPN
ejpam-3868	170	46	γ(µ	γ(µ	PROPN
ejpam-3868	170	47	)	)	PUNCT
ejpam-3868	171	1	+	+	CCONJ
ejpam-3868	171	2	2µ2	2µ2	NUM
ejpam-3868	171	3	)	)	PUNCT
ejpam-3868	171	4	dx	dx	PROPN
ejpam-3868	171	5	∧	∧	PROPN
ejpam-3868	171	6	ϑ+	ϑ+	X
ejpam-3868	171	7	(	(	PUNCT
ejpam-3868	171	8	µy′	µy′	PROPN
ejpam-3868	171	9	+	+	SYM
ejpam-3868	171	10	2ν)ϕ	2ν)ϕ	NUM
ejpam-3868	171	11	∧	∧	NOUN
ejpam-3868	171	12	ϑ−$1	ϑ−$1	NOUN
ejpam-3868	171	13	2	2	NUM
ejpam-3868	171	14	∧	∧	PROPN
ejpam-3868	171	15	ϑ.	ϑ.	NOUN
ejpam-3868	171	16	necessary	necessary	ADJ
ejpam-3868	171	17	and	and	CCONJ
ejpam-3868	171	18	sufficient	sufficient	ADJ
ejpam-3868	171	19	conditions	condition	NOUN
ejpam-3868	171	20	for	for	ADP
ejpam-3868	171	21	π1	π1	NOUN
ejpam-3868	171	22	to	to	PART
ejpam-3868	171	23	be	be	AUX
ejpam-3868	171	24	zero	zero	NUM
ejpam-3868	171	25	are	be	AUX
ejpam-3868	171	26	the	the	DET
ejpam-3868	171	27	following	follow	VERB
ejpam-3868	171	28	µ	µ	X
ejpam-3868	171	29	=	=	SYM
ejpam-3868	171	30	−1	−1	NOUN
ejpam-3868	171	31	3	3	NUM
ejpam-3868	171	32	fy′	fy′	ADV
ejpam-3868	171	33	,	,	PUNCT
ejpam-3868	171	34	$	$	SYM
ejpam-3868	171	35	1	1	NUM
ejpam-3868	171	36	2	2	NUM
ejpam-3868	171	37	=	=	SYM
ejpam-3868	171	38	(	(	PUNCT
ejpam-3868	171	39	fy	fy	PROPN
ejpam-3868	171	40	+	+	CCONJ
ejpam-3868	171	41	2	2	NUM
ejpam-3868	171	42	9	9	NUM
ejpam-3868	171	43	f2	f2	ADV
ejpam-3868	171	44	y′	y′	NOUN
ejpam-3868	171	45	−	−	PROPN
ejpam-3868	171	46	1	1	NUM
ejpam-3868	171	47	3	3	NUM
ejpam-3868	171	48	γ(fy′	γ(fy′	NOUN
ejpam-3868	171	49	)	)	PUNCT
ejpam-3868	171	50	)	)	PUNCT
ejpam-3868	172	1	dx+	dx+	NOUN
ejpam-3868	172	2	(	(	PUNCT
ejpam-3868	172	3	2ν	2ν	NOUN
ejpam-3868	172	4	−	−	NOUN
ejpam-3868	172	5	1	1	NUM
ejpam-3868	172	6	3	3	NUM
ejpam-3868	172	7	fy′y′)ϕ+	fy′y′)ϕ+	NOUN
ejpam-3868	172	8	ρϑ.	ρϑ.	NOUN
ejpam-3868	172	9	(	(	PUNCT
ejpam-3868	172	10	48	48	NUM
ejpam-3868	172	11	)	)	PUNCT
ejpam-3868	172	12	the	the	DET
ejpam-3868	172	13	second	second	ADJ
ejpam-3868	172	14	diagonal	diagonal	ADJ
ejpam-3868	172	15	element	element	NOUN
ejpam-3868	172	16	of	of	ADP
ejpam-3868	172	17	π	π	PROPN
ejpam-3868	172	18	is	be	AUX
ejpam-3868	172	19	π2	π2	ADV
ejpam-3868	172	20	2	2	NUM
ejpam-3868	172	21	=	=	SYM
ejpam-3868	172	22	$	$	SYM
ejpam-3868	172	23	2∧$0	2∧$0	NUM
ejpam-3868	172	24	2	2	NUM
ejpam-3868	172	25	+	+	ADV
ejpam-3868	172	26	$	$	SYM
ejpam-3868	172	27	2	2	NUM
ejpam-3868	172	28	1∧$1	1∧$1	NUM
ejpam-3868	172	29	2	2	NUM
ejpam-3868	172	30	=	=	NOUN
ejpam-3868	172	31	−ϑ∧$0	−ϑ∧$0	NOUN
ejpam-3868	172	32	2	2	NUM
ejpam-3868	173	1	+	+	NOUN
ejpam-3868	173	2	dx∧$1	dx∧$1	PROPN
ejpam-3868	173	3	2	2	NUM
ejpam-3868	173	4	=	=	SYM
ejpam-3868	173	5	(	(	PUNCT
ejpam-3868	173	6	$	$	SYM
ejpam-3868	173	7	0	0	NUM
ejpam-3868	173	8	2	2	NUM
ejpam-3868	173	9	+	+	NOUN
ejpam-3868	173	10	ρ	ρ	NOUN
ejpam-3868	173	11	dx)∧ϑ+(2ν−	dx)∧ϑ+(2ν−	ADJ
ejpam-3868	173	12	1	1	NUM
ejpam-3868	173	13	3	3	NUM
ejpam-3868	173	14	fy′y′)dx∧ϕ.	fy′y′)dx∧ϕ.	NOUN
ejpam-3868	173	15	(	(	PUNCT
ejpam-3868	173	16	49	49	NUM
ejpam-3868	173	17	)	)	PUNCT
ejpam-3868	173	18	the	the	DET
ejpam-3868	173	19	component	component	NOUN
ejpam-3868	173	20	π2	π2	NOUN
ejpam-3868	173	21	2	2	NUM
ejpam-3868	173	22	vanishes	vanish	VERB
ejpam-3868	173	23	if	if	SCONJ
ejpam-3868	173	24	and	and	CCONJ
ejpam-3868	173	25	only	only	ADV
ejpam-3868	173	26	if	if	SCONJ
ejpam-3868	173	27	$	$	SYM
ejpam-3868	173	28	0	0	NUM
ejpam-3868	173	29	2	2	NUM
ejpam-3868	173	30	=	=	NOUN
ejpam-3868	173	31	−ρ	−ρ	NOUN
ejpam-3868	173	32	dx+	dx+	NOUN
ejpam-3868	173	33	σϑ	σϑ	PROPN
ejpam-3868	173	34	,	,	PUNCT
ejpam-3868	173	35	ν	ν	X
ejpam-3868	173	36	=	=	SYM
ejpam-3868	173	37	1	1	NUM
ejpam-3868	173	38	6	6	NUM
ejpam-3868	173	39	fy′y′	fy′y′	VERB
ejpam-3868	173	40	.	.	PUNCT
ejpam-3868	174	1	(	(	PUNCT
ejpam-3868	174	2	50	50	NUM
ejpam-3868	174	3	)	)	PUNCT
ejpam-3868	174	4	notice	notice	VERB
ejpam-3868	174	5	that	that	SCONJ
ejpam-3868	174	6	the	the	DET
ejpam-3868	174	7	latter	latter	ADJ
ejpam-3868	174	8	condition	condition	NOUN
ejpam-3868	174	9	makes	make	VERB
ejpam-3868	174	10	the	the	DET
ejpam-3868	174	11	ϕ	ϕ	PROPN
ejpam-3868	174	12	component	component	NOUN
ejpam-3868	174	13	vanish	vanish	VERB
ejpam-3868	174	14	in	in	ADP
ejpam-3868	174	15	$	$	SYM
ejpam-3868	174	16	1	1	NUM
ejpam-3868	174	17	2	2	NUM
ejpam-3868	174	18	.	.	PUNCT
ejpam-3868	175	1	p.	p.	NOUN
ejpam-3868	175	2	bracken	bracken	NOUN
ejpam-3868	175	3	/	/	SYM
ejpam-3868	175	4	eur	eur	PROPN
ejpam-3868	175	5	.	.	PUNCT
ejpam-3868	176	1	j.	j.	PROPN
ejpam-3868	176	2	pure	pure	PROPN
ejpam-3868	176	3	appl	appl	PROPN
ejpam-3868	176	4	.	.	PROPN
ejpam-3868	176	5	math	math	PROPN
ejpam-3868	176	6	,	,	PUNCT
ejpam-3868	176	7	13	13	NUM
ejpam-3868	176	8	(	(	PUNCT
ejpam-3868	176	9	4	4	NUM
ejpam-3868	176	10	)	)	PUNCT
ejpam-3868	176	11	(	(	PUNCT
ejpam-3868	176	12	2020	2020	NUM
ejpam-3868	176	13	)	)	PUNCT
ejpam-3868	176	14	,	,	PUNCT
ejpam-3868	176	15	1016	1016	NUM
ejpam-3868	176	16	-	-	SYM
ejpam-3868	176	17	1034	1034	NUM
ejpam-3868	176	18	1025	1025	NUM
ejpam-3868	176	19	the	the	DET
ejpam-3868	176	20	next	next	ADJ
ejpam-3868	176	21	component	component	NOUN
ejpam-3868	176	22	to	to	PART
ejpam-3868	176	23	consider	consider	VERB
ejpam-3868	176	24	is	be	AUX
ejpam-3868	176	25	π0	π0	NOUN
ejpam-3868	176	26	0	0	NUM
ejpam-3868	176	27	which	which	PRON
ejpam-3868	176	28	is	be	AUX
ejpam-3868	176	29	given	give	VERB
ejpam-3868	176	30	by	by	ADP
ejpam-3868	176	31	π0	π0	NOUN
ejpam-3868	176	32	0	0	PUNCT
ejpam-3868	177	1	=	=	SYM
ejpam-3868	177	2	d$0	d$0	NOUN
ejpam-3868	177	3	0	0	PUNCT
ejpam-3868	178	1	+	+	NOUN
ejpam-3868	178	2	$	$	SYM
ejpam-3868	178	3	0	0	NUM
ejpam-3868	178	4	1	1	NUM
ejpam-3868	178	5	∧$1	∧$1	NOUN
ejpam-3868	178	6	+	+	NOUN
ejpam-3868	178	7	$	$	SYM
ejpam-3868	178	8	0	0	NUM
ejpam-3868	178	9	2	2	NUM
ejpam-3868	179	1	∧$2	∧$2	NOUN
ejpam-3868	179	2	=	=	SYM
ejpam-3868	179	3	d$0	d$0	NOUN
ejpam-3868	179	4	0	0	PUNCT
ejpam-3868	180	1	+	+	NOUN
ejpam-3868	180	2	$	$	SYM
ejpam-3868	180	3	0	0	NUM
ejpam-3868	180	4	1	1	NUM
ejpam-3868	180	5	∧$1	∧$1	NOUN
ejpam-3868	180	6	+	+	NOUN
ejpam-3868	180	7	$	$	SYM
ejpam-3868	180	8	0	0	NUM
ejpam-3868	180	9	2	2	NUM
ejpam-3868	180	10	∧	∧	NOUN
ejpam-3868	180	11	ϑ.	ϑ.	NOUN
ejpam-3868	180	12	(	(	PUNCT
ejpam-3868	180	13	51	51	NUM
ejpam-3868	180	14	)	)	PUNCT
ejpam-3868	180	15	using	use	VERB
ejpam-3868	180	16	the	the	DET
ejpam-3868	180	17	fact	fact	NOUN
ejpam-3868	180	18	that	that	SCONJ
ejpam-3868	180	19	dfy′y′	dfy′y′	X
ejpam-3868	180	20	=	=	SYM
ejpam-3868	180	21	γ(fy′y′	γ(fy′y′	PROPN
ejpam-3868	180	22	)	)	PUNCT
ejpam-3868	180	23	dx+	dx+	NOUN
ejpam-3868	180	24	fy′y′y	fy′y′y	NOUN
ejpam-3868	180	25	ϑ+	ϑ+	ADJ
ejpam-3868	180	26	fy′y′y′	fy′y′y′	PROPN
ejpam-3868	180	27	ϕ	ϕ	PROPN
ejpam-3868	180	28	,	,	PUNCT
ejpam-3868	180	29	(	(	PUNCT
ejpam-3868	180	30	52	52	NUM
ejpam-3868	180	31	)	)	PUNCT
ejpam-3868	180	32	the	the	DET
ejpam-3868	180	33	element	element	NOUN
ejpam-3868	180	34	π0	π0	NOUN
ejpam-3868	180	35	0	0	PUNCT
ejpam-3868	180	36	is	be	AUX
ejpam-3868	180	37	explicitly	explicitly	ADV
ejpam-3868	180	38	calculated	calculate	VERB
ejpam-3868	180	39	to	to	PART
ejpam-3868	180	40	be	be	AUX
ejpam-3868	180	41	π0	π0	NOUN
ejpam-3868	180	42	0	0	PUNCT
ejpam-3868	181	1	=	=	SYM
ejpam-3868	181	2	d	d	NOUN
ejpam-3868	181	3	(	(	PUNCT
ejpam-3868	181	4	1	1	NUM
ejpam-3868	181	5	3	3	NUM
ejpam-3868	181	6	fy′	fy′	DET
ejpam-3868	181	7	dx+	dx+	NOUN
ejpam-3868	181	8	1	1	NUM
ejpam-3868	181	9	6	6	NUM
ejpam-3868	181	10	fy′y′	fy′y′	NOUN
ejpam-3868	181	11	ϑ	ϑ	NOUN
ejpam-3868	181	12	)	)	PUNCT
ejpam-3868	181	13	+	+	CCONJ
ejpam-3868	181	14	(	(	PUNCT
ejpam-3868	181	15	1	1	NUM
ejpam-3868	181	16	6	6	NUM
ejpam-3868	181	17	fy′y′	fy′y′	VERB
ejpam-3868	181	18	dx+	dx+	NOUN
ejpam-3868	181	19	λ′ϑ	λ′ϑ	NOUN
ejpam-3868	181	20	)	)	PUNCT
ejpam-3868	181	21	∧	∧	NOUN
ejpam-3868	181	22	(	(	PUNCT
ejpam-3868	181	23	ϕ−	ϕ−	PROPN
ejpam-3868	181	24	1	1	NUM
ejpam-3868	181	25	3	3	NUM
ejpam-3868	181	26	fy′ϑ	fy′ϑ	NOUN
ejpam-3868	181	27	)	)	PUNCT
ejpam-3868	181	28	+	+	NUM
ejpam-3868	181	29	ρ	ρ	NUM
ejpam-3868	181	30	dx	dx	PROPN
ejpam-3868	181	31	∧	∧	PROPN
ejpam-3868	181	32	ϑ	ϑ	X
ejpam-3868	181	33	=	=	SYM
ejpam-3868	181	34	1	1	NUM
ejpam-3868	181	35	3	3	NUM
ejpam-3868	181	36	(	(	PUNCT
ejpam-3868	181	37	fyy′ϑ+	fyy′ϑ+	PROPN
ejpam-3868	181	38	fy′y′	fy′y′	VERB
ejpam-3868	181	39	ϕ)∧	ϕ)∧	PROPN
ejpam-3868	181	40	dx+	dx+	NOUN
ejpam-3868	181	41	1	1	NUM
ejpam-3868	181	42	6	6	NUM
ejpam-3868	181	43	(	(	PUNCT
ejpam-3868	181	44	γ(fy′y′)dx+	γ(fy′y′)dx+	ADJ
ejpam-3868	181	45	fy′y′yϑ+	fy′y′yϑ+	PROPN
ejpam-3868	181	46	fy′y′y′ϕ)∧	fy′y′y′ϕ)∧	NUM
ejpam-3868	181	47	ϑ−	ϑ−	PROPN
ejpam-3868	181	48	1	1	NUM
ejpam-3868	181	49	6	6	NUM
ejpam-3868	181	50	fy′y′	fy′y′	VERB
ejpam-3868	181	51	ϕ+	ϕ+	PUNCT
ejpam-3868	181	52	1	1	NUM
ejpam-3868	181	53	6	6	NUM
ejpam-3868	181	54	fy′y′	fy′y′	NOUN
ejpam-3868	181	55	dx∧ϕ	dx∧ϕ	NOUN
ejpam-3868	181	56	−	−	NUM
ejpam-3868	181	57	1	1	NUM
ejpam-3868	181	58	18	18	NUM
ejpam-3868	181	59	fy′fy′y′	fy′fy′y′	PROPN
ejpam-3868	181	60	dx	dx	PROPN
ejpam-3868	181	61	∧	∧	PROPN
ejpam-3868	181	62	ϑ+	ϑ+	PUNCT
ejpam-3868	181	63	λ′ϑ	λ′ϑ	PROPN
ejpam-3868	181	64	∧	∧	PROPN
ejpam-3868	181	65	ϕ+	ϕ+	PROPN
ejpam-3868	181	66	ρ	ρ	PROPN
ejpam-3868	181	67	dx	dx	PROPN
ejpam-3868	181	68	∧	∧	PROPN
ejpam-3868	181	69	ϑ	ϑ	X
ejpam-3868	181	70	(	(	PUNCT
ejpam-3868	181	71	53	53	NUM
ejpam-3868	181	72	)	)	PUNCT
ejpam-3868	181	73	=	=	PRON
ejpam-3868	181	74	(	(	PUNCT
ejpam-3868	181	75	ρ−	ρ−	NOUN
ejpam-3868	181	76	1	1	NUM
ejpam-3868	181	77	3	3	NUM
ejpam-3868	181	78	fy′y	fy′y	NOUN
ejpam-3868	181	79	−	−	NOUN
ejpam-3868	181	80	1	1	NUM
ejpam-3868	181	81	18	18	NUM
ejpam-3868	181	82	fy′fy′y′	fy′fy′y′	ADJ
ejpam-3868	181	83	+	+	CCONJ
ejpam-3868	181	84	1	1	NUM
ejpam-3868	181	85	6	6	NUM
ejpam-3868	181	86	γ(fy′y′	γ(fy′y′	NUM
ejpam-3868	181	87	)	)	PUNCT
ejpam-3868	181	88	)	)	PUNCT
ejpam-3868	182	1	dx	dx	PROPN
ejpam-3868	182	2	∧	∧	PROPN
ejpam-3868	182	3	ϑ+	ϑ+	X
ejpam-3868	182	4	(	(	PUNCT
ejpam-3868	182	5	λ′	λ′	X
ejpam-3868	182	6	−	−	NOUN
ejpam-3868	182	7	1	1	NUM
ejpam-3868	182	8	6	6	NUM
ejpam-3868	182	9	fy′y′y′)ϑ	fy′y′y′)ϑ	ADP
ejpam-3868	182	10	∧	∧	PROPN
ejpam-3868	182	11	ϕ.	ϕ.	NOUN
ejpam-3868	182	12	for	for	ADP
ejpam-3868	182	13	π0	π0	NOUN
ejpam-3868	182	14	0	0	NUM
ejpam-3868	182	15	to	to	PART
ejpam-3868	182	16	vanish	vanish	VERB
ejpam-3868	182	17	,	,	PUNCT
ejpam-3868	182	18	it	it	PRON
ejpam-3868	182	19	is	be	AUX
ejpam-3868	182	20	required	require	VERB
ejpam-3868	182	21	that	that	SCONJ
ejpam-3868	182	22	ρ	ρ	NOUN
ejpam-3868	182	23	=	=	SYM
ejpam-3868	182	24	1	1	NUM
ejpam-3868	182	25	3	3	NUM
ejpam-3868	182	26	fyy′	fyy′	ADJ
ejpam-3868	182	27	+	+	NUM
ejpam-3868	182	28	1	1	NUM
ejpam-3868	182	29	18	18	NUM
ejpam-3868	182	30	fy′fy′y′	fy′fy′y′	ADJ
ejpam-3868	182	31	−	−	PROPN
ejpam-3868	182	32	1	1	NUM
ejpam-3868	182	33	6	6	NUM
ejpam-3868	182	34	γ(fy′y′	γ(fy′y′	NUM
ejpam-3868	182	35	)	)	PUNCT
ejpam-3868	182	36	)	)	PUNCT
ejpam-3868	182	37	λ′	λ′	X
ejpam-3868	183	1	=	=	NOUN
ejpam-3868	183	2	1	1	NUM
ejpam-3868	183	3	6	6	NUM
ejpam-3868	183	4	fy′y′y′	fy′y′y′	ADJ
ejpam-3868	183	5	.	.	PUNCT
ejpam-3868	184	1	(	(	PUNCT
ejpam-3868	184	2	54	54	NUM
ejpam-3868	184	3	)	)	PUNCT
ejpam-3868	184	4	when	when	SCONJ
ejpam-3868	184	5	these	these	DET
ejpam-3868	184	6	conditions	condition	NOUN
ejpam-3868	184	7	hold	hold	VERB
ejpam-3868	184	8	,	,	PUNCT
ejpam-3868	184	9	the	the	DET
ejpam-3868	184	10	component	component	NOUN
ejpam-3868	184	11	π1	π1	NOUN
ejpam-3868	184	12	1	1	NUM
ejpam-3868	184	13	will	will	AUX
ejpam-3868	184	14	also	also	ADV
ejpam-3868	184	15	be	be	AUX
ejpam-3868	184	16	zero	zero	NUM
ejpam-3868	184	17	since	since	SCONJ
ejpam-3868	184	18	it	it	PRON
ejpam-3868	184	19	is	be	AUX
ejpam-3868	184	20	required	require	VERB
ejpam-3868	184	21	that	that	SCONJ
ejpam-3868	184	22	the	the	DET
ejpam-3868	184	23	trace	trace	NOUN
ejpam-3868	184	24	of	of	ADP
ejpam-3868	184	25	π	π	PROPN
ejpam-3868	184	26	vanish	vanish	VERB
ejpam-3868	184	27	.	.	PUNCT
ejpam-3868	185	1	all	all	PRON
ejpam-3868	185	2	of	of	ADP
ejpam-3868	185	3	$	$	SYM
ejpam-3868	185	4	has	have	AUX
ejpam-3868	185	5	been	be	AUX
ejpam-3868	185	6	fixed	fix	VERB
ejpam-3868	185	7	,	,	PUNCT
ejpam-3868	185	8	but	but	CCONJ
ejpam-3868	185	9	with	with	ADP
ejpam-3868	185	10	the	the	DET
ejpam-3868	185	11	exception	exception	NOUN
ejpam-3868	185	12	of	of	ADP
ejpam-3868	185	13	the	the	DET
ejpam-3868	185	14	coefficient	coefficient	NOUN
ejpam-3868	185	15	σ	σ	PROPN
ejpam-3868	185	16	in	in	ADP
ejpam-3868	185	17	$	$	SYM
ejpam-3868	185	18	0	0	NUM
ejpam-3868	185	19	2	2	NUM
ejpam-3868	185	20	.	.	PUNCT
ejpam-3868	186	1	this	this	PRON
ejpam-3868	186	2	is	be	AUX
ejpam-3868	186	3	determined	determine	VERB
ejpam-3868	186	4	by	by	ADP
ejpam-3868	186	5	imposing	impose	VERB
ejpam-3868	186	6	that	that	DET
ejpam-3868	186	7	π1	π1	NOUN
ejpam-3868	186	8	2	2	NUM
ejpam-3868	186	9	be	be	AUX
ejpam-3868	186	10	a	a	DET
ejpam-3868	186	11	multiple	multiple	NOUN
ejpam-3868	186	12	of	of	ADP
ejpam-3868	186	13	dx	dx	PROPN
ejpam-3868	186	14	∧	∧	PROPN
ejpam-3868	186	15	ϑ	ϑ	PROPN
ejpam-3868	186	16	hence	hence	ADV
ejpam-3868	186	17	semi	semi	ADJ
ejpam-3868	186	18	-	-	ADJ
ejpam-3868	186	19	basic	basic	ADJ
ejpam-3868	186	20	.	.	PUNCT
ejpam-3868	187	1	since	since	SCONJ
ejpam-3868	187	2	∂	∂	NOUN
ejpam-3868	187	3	∂y′	∂y′	PROPN
ejpam-3868	187	4	(	(	PUNCT
ejpam-3868	187	5	fy	fy	PROPN
ejpam-3868	188	1	+	+	CCONJ
ejpam-3868	188	2	2	2	NUM
ejpam-3868	188	3	9	9	NUM
ejpam-3868	188	4	f2	f2	PRON
ejpam-3868	188	5	y′−	y′−	NOUN
ejpam-3868	188	6	1	1	NUM
ejpam-3868	188	7	3	3	NUM
ejpam-3868	188	8	(	(	PUNCT
ejpam-3868	188	9	∂fy′	∂fy′	NOUN
ejpam-3868	188	10	∂x	∂x	PROPN
ejpam-3868	188	11	+	+	NOUN
ejpam-3868	188	12	y′	y′	NOUN
ejpam-3868	188	13	∂fy′	∂fy′	NOUN
ejpam-3868	188	14	∂y	∂y	X
ejpam-3868	189	1	+	+	NOUN
ejpam-3868	189	2	f	f	PROPN
ejpam-3868	189	3	∂fy′	∂fy′	PRON
ejpam-3868	189	4	∂y′	∂y′	PROPN
ejpam-3868	189	5	)	)	PUNCT
ejpam-3868	189	6	)	)	PUNCT
ejpam-3868	190	1	=	=	PUNCT
ejpam-3868	191	1	fyy′	fyy′	ADJ
ejpam-3868	191	2	+	+	CCONJ
ejpam-3868	191	3	4	4	NUM
ejpam-3868	191	4	9	9	NUM
ejpam-3868	191	5	fy′fy′y−	fy′fy′y−	VERB
ejpam-3868	191	6	1	1	NUM
ejpam-3868	191	7	3	3	NUM
ejpam-3868	191	8	γ(fy′y′)−	γ(fy′y′)−	ADP
ejpam-3868	191	9	1	1	NUM
ejpam-3868	191	10	3	3	NUM
ejpam-3868	191	11	fyy′−	fyy′−	PROPN
ejpam-3868	191	12	1	1	NUM
ejpam-3868	191	13	3	3	NUM
ejpam-3868	191	14	fy′fy′y′	fy′fy′y′	NOUN
ejpam-3868	191	15	=	=	SYM
ejpam-3868	191	16	2	2	NUM
ejpam-3868	191	17	3	3	NUM
ejpam-3868	191	18	fyy	fyy	NOUN
ejpam-3868	191	19	+	+	NOUN
ejpam-3868	191	20	1	1	NUM
ejpam-3868	191	21	9	9	NUM
ejpam-3868	191	22	fy′fy′y′	fy′fy′y′	ADJ
ejpam-3868	191	23	−	−	PROPN
ejpam-3868	191	24	1	1	NUM
ejpam-3868	191	25	3	3	NUM
ejpam-3868	191	26	γ(fy′y′	γ(fy′y′	PROPN
ejpam-3868	191	27	)	)	PUNCT
ejpam-3868	191	28	=	=	NOUN
ejpam-3868	191	29	2ρ	2ρ	NOUN
ejpam-3868	191	30	.	.	PUNCT
ejpam-3868	192	1	(	(	PUNCT
ejpam-3868	192	2	55	55	NUM
ejpam-3868	192	3	)	)	PUNCT
ejpam-3868	192	4	using	use	VERB
ejpam-3868	192	5	this	this	PRON
ejpam-3868	192	6	,	,	PUNCT
ejpam-3868	192	7	we	we	PRON
ejpam-3868	192	8	find	find	VERB
ejpam-3868	192	9	that	that	SCONJ
ejpam-3868	192	10	∂/∂y′cπ1	∂/∂y′cπ1	ADJ
ejpam-3868	192	11	2	2	NUM
ejpam-3868	192	12	=	=	SYM
ejpam-3868	192	13	(	(	PUNCT
ejpam-3868	192	14	ρy′	ρy′	NOUN
ejpam-3868	192	15	+	+	ADV
ejpam-3868	192	16	σ)ϑ	σ)ϑ	PRON
ejpam-3868	192	17	,	,	PUNCT
ejpam-3868	192	18	so	so	SCONJ
ejpam-3868	192	19	π1	π1	ADJ
ejpam-3868	192	20	2	2	NUM
ejpam-3868	192	21	is	be	AUX
ejpam-3868	192	22	semi	semi	ADJ
ejpam-3868	192	23	-	-	ADJ
ejpam-3868	192	24	basic	basic	ADJ
ejpam-3868	192	25	if	if	SCONJ
ejpam-3868	193	1	and	and	CCONJ
ejpam-3868	193	2	only	only	ADV
ejpam-3868	193	3	if	if	SCONJ
ejpam-3868	193	4	σ	σ	PROPN
ejpam-3868	193	5	=	=	SYM
ejpam-3868	193	6	−ρy′	−ρy′	PROPN
ejpam-3868	193	7	.	.	PUNCT
ejpam-3868	194	1	this	this	PRON
ejpam-3868	194	2	completes	complete	VERB
ejpam-3868	194	3	the	the	DET
ejpam-3868	194	4	determination	determination	NOUN
ejpam-3868	194	5	of	of	ADP
ejpam-3868	194	6	$	$	SYM
ejpam-3868	194	7	.	.	PUNCT
ejpam-3868	195	1	in	in	ADP
ejpam-3868	195	2	fact	fact	NOUN
ejpam-3868	195	3	,	,	PUNCT
ejpam-3868	195	4	$	$	SYM
ejpam-3868	195	5	is	be	AUX
ejpam-3868	195	6	given	give	VERB
ejpam-3868	195	7	in	in	ADP
ejpam-3868	195	8	terms	term	NOUN
ejpam-3868	195	9	of	of	ADP
ejpam-3868	195	10	the	the	DET
ejpam-3868	195	11	first	first	ADJ
ejpam-3868	195	12	normal	normal	ADJ
ejpam-3868	195	13	projective	projective	ADJ
ejpam-3868	195	14	connection	connection	NOUN
ejpam-3868	195	15	by	by	ADP
ejpam-3868	195	16	$	$	SYM
ejpam-3868	195	17	0	0	NUM
ejpam-3868	195	18	1	1	NUM
ejpam-3868	195	19	=	=	NOUN
ejpam-3868	195	20	−ω2	−ω2	ADP
ejpam-3868	195	21	2	2	NUM
ejpam-3868	195	22	,	,	PUNCT
ejpam-3868	195	23	$	$	SYM
ejpam-3868	195	24	0	0	NUM
ejpam-3868	195	25	1	1	NUM
ejpam-3868	195	26	=	=	SYM
ejpam-3868	195	27	ω1	ω1	X
ejpam-3868	195	28	2	2	NUM
ejpam-3868	195	29	$	$	SYM
ejpam-3868	195	30	0	0	NUM
ejpam-3868	195	31	2	2	NUM
ejpam-3868	195	32	=	=	SYM
ejpam-3868	195	33	−ω0	−ω0	NOUN
ejpam-3868	195	34	0	0	NUM
ejpam-3868	195	35	$	$	SYM
ejpam-3868	195	36	1	1	NUM
ejpam-3868	195	37	=	=	SYM
ejpam-3868	195	38	ω2	ω2	ADJ
ejpam-3868	195	39	1	1	NUM
ejpam-3868	195	40	$	$	SYM
ejpam-3868	195	41	1	1	NUM
ejpam-3868	195	42	1	1	NUM
ejpam-3868	195	43	=	=	SYM
ejpam-3868	195	44	−ω1	−ω1	ADP
ejpam-3868	195	45	1	1	NUM
ejpam-3868	195	46	$	$	SYM
ejpam-3868	195	47	1	1	NUM
ejpam-3868	195	48	2	2	NUM
ejpam-3868	195	49	=	=	PUNCT
ejpam-3868	195	50	ω0	ω0	ADP
ejpam-3868	195	51	1	1	NUM
ejpam-3868	195	52	,	,	PUNCT
ejpam-3868	195	53	$	$	SYM
ejpam-3868	195	54	2	2	NUM
ejpam-3868	195	55	=	=	NOUN
ejpam-3868	195	56	−ω2	−ω2	ADP
ejpam-3868	195	57	$	$	SYM
ejpam-3868	195	58	2	2	NUM
ejpam-3868	195	59	1	1	NUM
ejpam-3868	195	60	=	=	SYM
ejpam-3868	195	61	ω1	ω1	X
ejpam-3868	195	62	$	$	SYM
ejpam-3868	195	63	2	2	NUM
ejpam-3868	195	64	2	2	NUM
ejpam-3868	195	65	=	=	SYM
ejpam-3868	195	66	−ω0	−ω0	NOUN
ejpam-3868	195	67	0	0	NUM
ejpam-3868	195	68	.	.	PUNCT
ejpam-3868	196	1	(	(	PUNCT
ejpam-3868	196	2	56	56	NUM
ejpam-3868	196	3	)	)	PUNCT
ejpam-3868	196	4	this	this	PRON
ejpam-3868	196	5	can	can	AUX
ejpam-3868	196	6	be	be	AUX
ejpam-3868	196	7	summarized	summarize	VERB
ejpam-3868	196	8	concisely	concisely	ADV
ejpam-3868	196	9	in	in	ADP
ejpam-3868	196	10	matrix	matrix	NOUN
ejpam-3868	196	11	form	form	NOUN
ejpam-3868	196	12	as	as	SCONJ
ejpam-3868	196	13	follows	follow	VERB
ejpam-3868	196	14	$	$	SYM
ejpam-3868	196	15	=	=	SYM
ejpam-3868	196	16	−kωtk	−kωtk	NOUN
ejpam-3868	196	17	,	,	PUNCT
ejpam-3868	196	18	(	(	PUNCT
ejpam-3868	196	19	57	57	NUM
ejpam-3868	196	20	)	)	PUNCT
ejpam-3868	196	21	where	where	SCONJ
ejpam-3868	196	22	ωt	ωt	PROPN
ejpam-3868	196	23	is	be	AUX
ejpam-3868	196	24	the	the	DET
ejpam-3868	196	25	transpose	transpose	NOUN
ejpam-3868	196	26	of	of	ADP
ejpam-3868	196	27	ω	ω	NUM
ejpam-3868	196	28	and	and	CCONJ
ejpam-3868	196	29	matrix	matrix	NOUN
ejpam-3868	196	30	k	k	NOUN
ejpam-3868	196	31	is	be	AUX
ejpam-3868	196	32	defined	define	VERB
ejpam-3868	196	33	to	to	PART
ejpam-3868	196	34	be	be	AUX
ejpam-3868	196	35	k	k	X
ejpam-3868	197	1	=	=	PUNCT
ejpam-3868	197	2			PROPN
ejpam-3868	197	3	0	0	NUM
ejpam-3868	197	4	0	0	NUM
ejpam-3868	197	5	−1	−1	NOUN
ejpam-3868	197	6	0	0	NUM
ejpam-3868	197	7	1	1	NUM
ejpam-3868	197	8	0	0	NUM
ejpam-3868	197	9	−1	−1	NOUN
ejpam-3868	197	10	0	0	NUM
ejpam-3868	197	11	0	0	NUM
ejpam-3868	197	12			PROPN
ejpam-3868	197	13	(	(	PUNCT
ejpam-3868	197	14	58	58	NUM
ejpam-3868	197	15	)	)	PUNCT
ejpam-3868	197	16	p.	p.	NOUN
ejpam-3868	197	17	bracken	bracken	NOUN
ejpam-3868	197	18	/	/	SYM
ejpam-3868	197	19	eur	eur	PROPN
ejpam-3868	197	20	.	.	PUNCT
ejpam-3868	198	1	j.	j.	PROPN
ejpam-3868	198	2	pure	pure	PROPN
ejpam-3868	198	3	appl	appl	PROPN
ejpam-3868	198	4	.	.	PROPN
ejpam-3868	198	5	math	math	PROPN
ejpam-3868	198	6	,	,	PUNCT
ejpam-3868	198	7	13	13	NUM
ejpam-3868	198	8	(	(	PUNCT
ejpam-3868	198	9	4	4	NUM
ejpam-3868	198	10	)	)	PUNCT
ejpam-3868	198	11	(	(	PUNCT
ejpam-3868	198	12	2020	2020	NUM
ejpam-3868	198	13	)	)	PUNCT
ejpam-3868	198	14	,	,	PUNCT
ejpam-3868	198	15	1016	1016	NUM
ejpam-3868	198	16	-	-	SYM
ejpam-3868	198	17	1034	1034	NUM
ejpam-3868	198	18	1026	1026	NUM
ejpam-3868	198	19	it	it	PRON
ejpam-3868	198	20	may	may	AUX
ejpam-3868	198	21	be	be	AUX
ejpam-3868	198	22	verified	verify	VERB
ejpam-3868	198	23	that	that	SCONJ
ejpam-3868	198	24	when	when	SCONJ
ejpam-3868	198	25	$	$	PRON
ejpam-3868	198	26	and	and	CCONJ
ejpam-3868	198	27	ω	ω	NUM
ejpam-3868	198	28	are	be	AUX
ejpam-3868	198	29	related	relate	VERB
ejpam-3868	198	30	as	as	ADP
ejpam-3868	198	31	in	in	ADP
ejpam-3868	198	32	(	(	PUNCT
ejpam-3868	198	33	57	57	NUM
ejpam-3868	198	34	)	)	PUNCT
ejpam-3868	198	35	,	,	PUNCT
ejpam-3868	198	36	their	their	PRON
ejpam-3868	198	37	curvatures	curvature	NOUN
ejpam-3868	198	38	π	π	NOUN
ejpam-3868	198	39	and	and	CCONJ
ejpam-3868	198	40	ω	ω	PROPN
ejpam-3868	198	41	are	be	AUX
ejpam-3868	198	42	related	relate	VERB
ejpam-3868	198	43	in	in	ADP
ejpam-3868	198	44	the	the	DET
ejpam-3868	198	45	same	same	ADJ
ejpam-3868	198	46	way	way	NOUN
ejpam-3868	198	47	.	.	PUNCT
ejpam-3868	199	1	the	the	DET
ejpam-3868	199	2	minus	minus	ADJ
ejpam-3868	199	3	signs	sign	NOUN
ejpam-3868	199	4	are	be	AUX
ejpam-3868	199	5	important	important	ADJ
ejpam-3868	199	6	for	for	SCONJ
ejpam-3868	199	7	this	this	PRON
ejpam-3868	199	8	to	to	PART
ejpam-3868	199	9	hold	hold	VERB
ejpam-3868	199	10	.	.	PUNCT
ejpam-3868	200	1	there	there	PRON
ejpam-3868	200	2	would	would	AUX
ejpam-3868	200	3	be	be	AUX
ejpam-3868	200	4	no	no	DET
ejpam-3868	200	5	obvious	obvious	ADJ
ejpam-3868	200	6	relation	relation	NOUN
ejpam-3868	200	7	between	between	ADP
ejpam-3868	200	8	the	the	DET
ejpam-3868	200	9	components	component	NOUN
ejpam-3868	200	10	if	if	SCONJ
ejpam-3868	200	11	that	that	PRON
ejpam-3868	200	12	were	be	AUX
ejpam-3868	200	13	the	the	DET
ejpam-3868	200	14	case	case	NOUN
ejpam-3868	200	15	.	.	PUNCT
ejpam-3868	201	1	the	the	DET
ejpam-3868	201	2	crucial	crucial	ADJ
ejpam-3868	201	3	point	point	NOUN
ejpam-3868	201	4	is	be	AUX
ejpam-3868	201	5	that	that	SCONJ
ejpam-3868	201	6	the	the	DET
ejpam-3868	201	7	mapping	mapping	NOUN
ejpam-3868	201	8	m	m	NOUN
ejpam-3868	201	9	→	→	SYM
ejpam-3868	201	10	−kmtk	−kmtk	NOUN
ejpam-3868	202	1	=	=	NOUN
ejpam-3868	202	2	m	m	VERB
ejpam-3868	202	3	′	′	VERB
ejpam-3868	202	4	is	be	AUX
ejpam-3868	202	5	a	a	DET
ejpam-3868	202	6	homomorphism	homomorphism	NOUN
ejpam-3868	202	7	of	of	ADP
ejpam-3868	202	8	the	the	DET
ejpam-3868	202	9	matrix	matrix	NOUN
ejpam-3868	202	10	lie	lie	NOUN
ejpam-3868	202	11	algebra	algebra	NOUN
ejpam-3868	202	12	so	so	ADV
ejpam-3868	202	13	in	in	ADP
ejpam-3868	202	14	fact	fact	NOUN
ejpam-3868	202	15	[	[	X
ejpam-3868	202	16	m	m	NOUN
ejpam-3868	202	17	′1,m	′1,m	ADJ
ejpam-3868	202	18	′	′	NUM
ejpam-3868	202	19	2	2	NUM
ejpam-3868	202	20	]	]	PUNCT
ejpam-3868	203	1	=	=	SYM
ejpam-3868	203	2	k[mt	k[mt	NOUN
ejpam-3868	203	3	1	1	NUM
ejpam-3868	203	4	,	,	PUNCT
ejpam-3868	203	5	m	m	VERB
ejpam-3868	203	6	t	t	NOUN
ejpam-3868	203	7	2	2	NUM
ejpam-3868	203	8	]	]	X
ejpam-3868	203	9	k	k	X
ejpam-3868	203	10	=	=	PUNCT
ejpam-3868	203	11	−k[m1,m2]tk	−k[m1,m2]tk	X
ejpam-3868	203	12	=	=	PUNCT
ejpam-3868	204	1	[	[	X
ejpam-3868	204	2	m1,m2]′.	m1,m2]′.	X
ejpam-3868	204	3	(	(	PUNCT
ejpam-3868	204	4	59	59	NUM
ejpam-3868	204	5	)	)	PUNCT
ejpam-3868	204	6	this	this	PRON
ejpam-3868	204	7	holds	hold	VERB
ejpam-3868	204	8	for	for	ADP
ejpam-3868	204	9	any	any	DET
ejpam-3868	204	10	k	k	PROPN
ejpam-3868	204	11	such	such	ADJ
ejpam-3868	204	12	that	that	SCONJ
ejpam-3868	204	13	k2	k2	PROPN
ejpam-3868	204	14	is	be	AUX
ejpam-3868	204	15	the	the	DET
ejpam-3868	204	16	identity	identity	NOUN
ejpam-3868	204	17	.	.	PUNCT
ejpam-3868	205	1	without	without	ADP
ejpam-3868	205	2	the	the	DET
ejpam-3868	205	3	minus	minus	NOUN
ejpam-3868	205	4	sign	sign	VERB
ejpam-3868	205	5	an	an	DET
ejpam-3868	205	6	antihomomorphism	antihomomorphism	NOUN
ejpam-3868	205	7	results	result	NOUN
ejpam-3868	205	8	instead	instead	ADV
ejpam-3868	205	9	and	and	CCONJ
ejpam-3868	205	10	then	then	ADV
ejpam-3868	205	11	dω′	dω′	VERB
ejpam-3868	206	1	+	+	CCONJ
ejpam-3868	206	2	1	1	NUM
ejpam-3868	206	3	2	2	NUM
ejpam-3868	206	4	[	[	X
ejpam-3868	206	5	ω′	ω′	X
ejpam-3868	206	6	∧	∧	PROPN
ejpam-3868	206	7	ω′	ω′	X
ejpam-3868	206	8	]	]	PUNCT
ejpam-3868	207	1	=	=	PUNCT
ejpam-3868	207	2	dω′	dω′	X
ejpam-3868	208	1	+	+	CCONJ
ejpam-3868	208	2	1	1	NUM
ejpam-3868	208	3	2	2	NUM
ejpam-3868	208	4	[	[	X
ejpam-3868	208	5	ω	ω	NUM
ejpam-3868	208	6	∧	∧	PROPN
ejpam-3868	208	7	ω]′.	ω]′.	NOUN
ejpam-3868	208	8	(	(	PUNCT
ejpam-3868	208	9	60	60	NUM
ejpam-3868	208	10	)	)	PUNCT
ejpam-3868	208	11	if	if	SCONJ
ejpam-3868	208	12	ω	ω	PROPN
ejpam-3868	208	13	has	have	VERB
ejpam-3868	208	14	the	the	DET
ejpam-3868	208	15	upper	upper	ADJ
ejpam-3868	208	16	triangular	triangular	NOUN
ejpam-3868	208	17	form,0	form,0	PROPN
ejpam-3868	208	18	b	b	PROPN
ejpam-3868	208	19	dx	dx	PROPN
ejpam-3868	208	20	∧	∧	PROPN
ejpam-3868	208	21	ϑ	ϑ	PROPN
ejpam-3868	208	22	ω0	ω0	ADV
ejpam-3868	208	23	2	2	NUM
ejpam-3868	208	24	0	0	NUM
ejpam-3868	208	25	0	0	NUM
ejpam-3868	208	26	aϑ	aϑ	ADP
ejpam-3868	208	27	∧	∧	PROPN
ejpam-3868	208	28	ϕ	ϕ	PROPN
ejpam-3868	208	29	0	0	NUM
ejpam-3868	208	30	0	0	NUM
ejpam-3868	208	31	0	0	NUM
ejpam-3868	208	32			PROPN
ejpam-3868	208	33	(	(	PUNCT
ejpam-3868	208	34	61	61	NUM
ejpam-3868	208	35	)	)	PUNCT
ejpam-3868	208	36	then	then	ADV
ejpam-3868	208	37	the	the	DET
ejpam-3868	208	38	fact	fact	NOUN
ejpam-3868	208	39	that	that	SCONJ
ejpam-3868	208	40	π	π	PROPN
ejpam-3868	208	41	=	=	SYM
ejpam-3868	208	42	−kωtk	−kωtk	PROPN
ejpam-3868	208	43	implies	imply	VERB
ejpam-3868	208	44	that	that	SCONJ
ejpam-3868	208	45	π	π	PROPN
ejpam-3868	208	46	is	be	AUX
ejpam-3868	208	47	given	give	VERB
ejpam-3868	208	48	as	as	ADP
ejpam-3868	208	49	π	π	PROPN
ejpam-3868	208	50	=	=	SYM
ejpam-3868	208	51	−kωtk	−kωtk	PROPN
ejpam-3868	208	52	=	=	PUNCT
ejpam-3868	208	53	0	0	ADP
ejpam-3868	208	54	ϑ	ϑ	X
ejpam-3868	208	55	∧	∧	PROPN
ejpam-3868	208	56	ϕ	ϕ	PROPN
ejpam-3868	208	57	−ω0	−ω0	PROPN
ejpam-3868	208	58	2	2	NUM
ejpam-3868	208	59	0	0	NUM
ejpam-3868	208	60	0	0	NUM
ejpam-3868	208	61	b	b	NOUN
ejpam-3868	208	62	dx	dx	PROPN
ejpam-3868	208	63	∧	∧	PROPN
ejpam-3868	208	64	ϑ	ϑ	PROPN
ejpam-3868	208	65	0	0	NUM
ejpam-3868	208	66	0	0	NUM
ejpam-3868	208	67	0	0	NUM
ejpam-3868	209	1			PROPN
ejpam-3868	209	2	.	.	PUNCT
ejpam-3868	210	1	(	(	PUNCT
ejpam-3868	210	2	62	62	NUM
ejpam-3868	210	3	)	)	PUNCT
ejpam-3868	210	4	the	the	DET
ejpam-3868	210	5	gauged	gauge	VERB
ejpam-3868	210	6	version	version	NOUN
ejpam-3868	210	7	of	of	ADP
ejpam-3868	210	8	the	the	DET
ejpam-3868	210	9	second	second	ADJ
ejpam-3868	210	10	normal	normal	ADJ
ejpam-3868	210	11	projective	projective	ADJ
ejpam-3868	210	12	connection	connection	NOUN
ejpam-3868	210	13	h−1ω̄h	h−1ω̄h	PROPN
ejpam-3868	210	14	+	+	CCONJ
ejpam-3868	210	15	h−1	h−1	PROPN
ejpam-3868	210	16	dh	dh	NOUN
ejpam-3868	210	17	can	can	AUX
ejpam-3868	210	18	be	be	AUX
ejpam-3868	210	19	reconsidered	reconsider	VERB
ejpam-3868	210	20	.	.	PUNCT
ejpam-3868	211	1	by	by	ADP
ejpam-3868	211	2	calculation	calculation	NOUN
ejpam-3868	211	3	,	,	PUNCT
ejpam-3868	211	4	h−1ω̄h	h−1ω̄h	PROPN
ejpam-3868	211	5	=	=	PUNCT
ejpam-3868	211	6	0	0	ADP
ejpam-3868	211	7	a−1bb̄	a−1bb̄	ADJ
ejpam-3868	211	8	dx̄	dx̄	PROPN
ejpam-3868	211	9	∧	∧	PROPN
ejpam-3868	211	10	ϑ̄	ϑ̄	ADJ
ejpam-3868	211	11	a−1eb̄dx̄	a−1eb̄dx̄	X
ejpam-3868	211	12	∧	∧	PROPN
ejpam-3868	211	13	ϑ̄+a−1cω̄0	ϑ̄+a−1cω̄0	NOUN
ejpam-3868	211	14	2	2	NUM
ejpam-3868	211	15	+	+	CCONJ
ejpam-3868	211	16	(	(	PUNCT
ejpam-3868	211	17	de	de	X
ejpam-3868	211	18	−bf	−bf	NOUN
ejpam-3868	211	19	)	)	PUNCT
ejpam-3868	211	20	cāϑ̄	cāϑ̄	PROPN
ejpam-3868	211	21	∧	∧	PROPN
ejpam-3868	211	22	ϕ̄	ϕ̄	PROPN
ejpam-3868	211	23	0	0	NUM
ejpam-3868	211	24	0	0	NUM
ejpam-3868	211	25	b−1cāϑ̄	b−1cāϑ̄	NUM
ejpam-3868	211	26	∧	∧	PROPN
ejpam-3868	211	27	ϕ̄	ϕ̄	PROPN
ejpam-3868	211	28	0	0	NUM
ejpam-3868	211	29	0	0	NUM
ejpam-3868	211	30	0	0	NUM
ejpam-3868	211	31			PROPN
ejpam-3868	211	32	(	(	PUNCT
ejpam-3868	211	33	63	63	NUM
ejpam-3868	211	34	)	)	PUNCT
ejpam-3868	211	35	thus	thus	ADV
ejpam-3868	211	36	the	the	DET
ejpam-3868	211	37	gauge	gauge	NOUN
ejpam-3868	211	38	transformed	transform	VERB
ejpam-3868	211	39	version	version	NOUN
ejpam-3868	212	1	h−1ω̄h+h−1	h−1ω̄h+h−1	NOUN
ejpam-3868	212	2	dh	dh	NOUN
ejpam-3868	212	3	satisfies	satisfy	VERB
ejpam-3868	212	4	the	the	DET
ejpam-3868	212	5	conditions	condition	NOUN
ejpam-3868	212	6	that	that	PRON
ejpam-3868	212	7	uniquely	uniquely	ADV
ejpam-3868	212	8	determine	determine	VERB
ejpam-3868	212	9	$	$	NUM
ejpam-3868	212	10	and	and	CCONJ
ejpam-3868	212	11	therefore	therefore	ADV
ejpam-3868	212	12	must	must	AUX
ejpam-3868	212	13	be	be	AUX
ejpam-3868	212	14	$	$	SYM
ejpam-3868	212	15	=	=	PUNCT
ejpam-3868	212	16	h−1ω̄h+	h−1ω̄h+	PROPN
ejpam-3868	212	17	h−1	h−1	PROPN
ejpam-3868	212	18	dh	dh	NOUN
ejpam-3868	212	19	.	.	PROPN
ejpam-3868	213	1	4	4	X
ejpam-3868	213	2	.	.	X
ejpam-3868	213	3	duality	duality	NOUN
ejpam-3868	213	4	the	the	DET
ejpam-3868	213	5	condition	condition	NOUN
ejpam-3868	213	6	∆	∆	X
ejpam-3868	213	7	6=	6=	PRON
ejpam-3868	213	8	0	0	NUM
ejpam-3868	213	9	inposed	inpose	VERB
ejpam-3868	213	10	previously	previously	ADV
ejpam-3868	213	11	may	may	AUX
ejpam-3868	213	12	be	be	AUX
ejpam-3868	213	13	thought	think	VERB
ejpam-3868	213	14	of	of	ADP
ejpam-3868	213	15	in	in	ADP
ejpam-3868	213	16	another	another	DET
ejpam-3868	213	17	way	way	NOUN
ejpam-3868	213	18	.	.	PUNCT
ejpam-3868	214	1	it	it	PRON
ejpam-3868	214	2	states	state	VERB
ejpam-3868	214	3	that	that	SCONJ
ejpam-3868	214	4	the	the	DET
ejpam-3868	214	5	one	one	NUM
ejpam-3868	214	6	-	-	PUNCT
ejpam-3868	214	7	form	form	NOUN
ejpam-3868	214	8	θ	θ	NOUN
ejpam-3868	214	9	=	=	PUNCT
ejpam-3868	214	10	φx	φx	VERB
ejpam-3868	214	11	dx+	dx+	NOUN
ejpam-3868	214	12	φy	φy	ADP
ejpam-3868	214	13	dy	dy	NOUN
ejpam-3868	214	14	=	=	NOUN
ejpam-3868	214	15	−(φx̄	−(φx̄	NOUN
ejpam-3868	214	16	dx̄+	dx̄+	PROPN
ejpam-3868	214	17	φȳ	φȳ	NOUN
ejpam-3868	214	18	dȳ	dȳ	NOUN
ejpam-3868	214	19	)	)	PUNCT
ejpam-3868	214	20	satisfies	satisfy	VERB
ejpam-3868	214	21	the	the	DET
ejpam-3868	214	22	condition	condition	NOUN
ejpam-3868	214	23	θ	θ	PROPN
ejpam-3868	214	24	∧	∧	PROPN
ejpam-3868	214	25	dθ	dθ	PROPN
ejpam-3868	214	26	on	on	ADP
ejpam-3868	214	27	s.	s.	PROPN
ejpam-3868	214	28	it	it	PRON
ejpam-3868	214	29	may	may	AUX
ejpam-3868	214	30	be	be	AUX
ejpam-3868	214	31	said	say	VERB
ejpam-3868	214	32	it	it	PRON
ejpam-3868	214	33	defines	define	VERB
ejpam-3868	214	34	a	a	DET
ejpam-3868	214	35	contact	contact	NOUN
ejpam-3868	214	36	structure	structure	NOUN
ejpam-3868	214	37	on	on	ADP
ejpam-3868	214	38	this	this	DET
ejpam-3868	214	39	three	three	NUM
ejpam-3868	214	40	-	-	PUNCT
ejpam-3868	214	41	dimensional	dimensional	ADJ
ejpam-3868	214	42	manifold	manifold	NOUN
ejpam-3868	214	43	.	.	PUNCT
ejpam-3868	215	1	let	let	VERB
ejpam-3868	215	2	s	s	PRON
ejpam-3868	215	3	be	be	AUX
ejpam-3868	215	4	a	a	DET
ejpam-3868	215	5	three	three	NUM
ejpam-3868	215	6	-	-	PUNCT
ejpam-3868	215	7	dimensional	dimensional	ADJ
ejpam-3868	215	8	manifold	manifold	NOUN
ejpam-3868	215	9	endowed	endow	VERB
ejpam-3868	215	10	with	with	ADP
ejpam-3868	215	11	a	a	DET
ejpam-3868	215	12	contact	contact	NOUN
ejpam-3868	215	13	structure	structure	NOUN
ejpam-3868	215	14	which	which	PRON
ejpam-3868	215	15	it	it	PRON
ejpam-3868	215	16	may	may	AUX
ejpam-3868	215	17	be	be	AUX
ejpam-3868	215	18	convenient	convenient	ADJ
ejpam-3868	215	19	to	to	PART
ejpam-3868	215	20	think	think	VERB
ejpam-3868	215	21	of	of	ADP
ejpam-3868	215	22	as	as	ADP
ejpam-3868	215	23	a	a	DET
ejpam-3868	215	24	two	two	NUM
ejpam-3868	215	25	-	-	PUNCT
ejpam-3868	215	26	dimensional	dimensional	ADJ
ejpam-3868	215	27	distribution	distribution	NOUN
ejpam-3868	215	28	d	d	NOUN
ejpam-3868	215	29	which	which	PRON
ejpam-3868	215	30	is	be	AUX
ejpam-3868	215	31	nonintegrable	nonintegrable	ADJ
ejpam-3868	215	32	in	in	ADP
ejpam-3868	215	33	the	the	DET
ejpam-3868	215	34	following	follow	VERB
ejpam-3868	215	35	sense	sense	NOUN
ejpam-3868	215	36	.	.	PUNCT
ejpam-3868	216	1	for	for	ADP
ejpam-3868	216	2	any	any	DET
ejpam-3868	216	3	pair	pair	NOUN
ejpam-3868	216	4	of	of	ADP
ejpam-3868	216	5	linearly	linearly	ADV
ejpam-3868	216	6	independent	independent	ADJ
ejpam-3868	216	7	vector	vector	NOUN
ejpam-3868	216	8	fields	field	NOUN
ejpam-3868	216	9	x	x	X
ejpam-3868	216	10	,	,	PUNCT
ejpam-3868	216	11	y	y	PROPN
ejpam-3868	216	12	∈	∈	PROPN
ejpam-3868	216	13	d	d	NOUN
ejpam-3868	216	14	,	,	PUNCT
ejpam-3868	216	15	[	[	X
ejpam-3868	216	16	x	x	X
ejpam-3868	216	17	,	,	PUNCT
ejpam-3868	216	18	y	y	PROPN
ejpam-3868	216	19	]	]	PUNCT
ejpam-3868	216	20	/∈	/∈	PUNCT
ejpam-3868	217	1	d.	d.	PROPN
ejpam-3868	218	1	any	any	DET
ejpam-3868	218	2	one	one	NUM
ejpam-3868	218	3	-	-	PUNCT
ejpam-3868	218	4	form	form	NOUN
ejpam-3868	218	5	θ	θ	NOUN
ejpam-3868	218	6	on	on	ADP
ejpam-3868	218	7	s	s	ADP
ejpam-3868	218	8	which	which	PRON
ejpam-3868	218	9	is	be	AUX
ejpam-3868	218	10	an	an	DET
ejpam-3868	218	11	annihilator	annihilator	NOUN
ejpam-3868	218	12	of	of	ADP
ejpam-3868	218	13	d	d	PROPN
ejpam-3868	218	14	satisfies	satisfy	VERB
ejpam-3868	218	15	the	the	DET
ejpam-3868	218	16	condition	condition	NOUN
ejpam-3868	218	17	θ	θ	PROPN
ejpam-3868	218	18	∧	∧	PROPN
ejpam-3868	218	19	dθ	dθ	PROPN
ejpam-3868	218	20	6=	6=	PROPN
ejpam-3868	218	21	0	0	NUM
ejpam-3868	218	22	.	.	PUNCT
ejpam-3868	219	1	suppose	suppose	VERB
ejpam-3868	219	2	a	a	DET
ejpam-3868	219	3	basis	basis	NOUN
ejpam-3868	219	4	has	have	AUX
ejpam-3868	219	5	been	be	AUX
ejpam-3868	219	6	given	give	VERB
ejpam-3868	219	7	for	for	ADP
ejpam-3868	219	8	d	d	NOUN
ejpam-3868	219	9	,	,	PUNCT
ejpam-3868	219	10	and	and	CCONJ
ejpam-3868	219	11	these	these	DET
ejpam-3868	219	12	basis	basis	NOUN
ejpam-3868	219	13	vectors	vector	NOUN
ejpam-3868	219	14	are	be	AUX
ejpam-3868	219	15	denoted	denote	VERB
ejpam-3868	219	16	as	as	ADP
ejpam-3868	219	17	x	x	X
ejpam-3868	219	18	,	,	PUNCT
ejpam-3868	219	19	x̄.	x̄.	PUNCT
ejpam-3868	219	20	this	this	PRON
ejpam-3868	219	21	means	mean	VERB
ejpam-3868	219	22	that	that	SCONJ
ejpam-3868	219	23	the	the	DET
ejpam-3868	219	24	set	set	NOUN
ejpam-3868	219	25	{	{	PUNCT
ejpam-3868	219	26	x	x	NOUN
ejpam-3868	219	27	,	,	PUNCT
ejpam-3868	219	28	x̄	x̄	PROPN
ejpam-3868	219	29	,	,	PUNCT
ejpam-3868	219	30	[	[	X
ejpam-3868	219	31	x	x	X
ejpam-3868	219	32	,	,	PUNCT
ejpam-3868	219	33	x̄	x̄	PROPN
ejpam-3868	219	34	]	]	PUNCT
ejpam-3868	219	35	}	}	PUNCT
ejpam-3868	219	36	is	be	AUX
ejpam-3868	219	37	a	a	DET
ejpam-3868	219	38	basis	basis	NOUN
ejpam-3868	219	39	for	for	ADP
ejpam-3868	219	40	vector	vector	NOUN
ejpam-3868	219	41	fields	field	NOUN
ejpam-3868	219	42	on	on	ADP
ejpam-3868	219	43	s.	s.	PROPN
ejpam-3868	219	44	let	let	VERB
ejpam-3868	219	45	the	the	DET
ejpam-3868	219	46	set	set	NOUN
ejpam-3868	219	47	{	{	PUNCT
ejpam-3868	219	48	φ	φ	PROPN
ejpam-3868	219	49	,	,	PUNCT
ejpam-3868	219	50	φ̄	φ̄	PROPN
ejpam-3868	219	51	,	,	PUNCT
ejpam-3868	219	52	θ	θ	PROPN
ejpam-3868	219	53	}	}	PUNCT
ejpam-3868	219	54	be	be	AUX
ejpam-3868	219	55	the	the	DET
ejpam-3868	219	56	dual	dual	ADJ
ejpam-3868	219	57	basis	basis	NOUN
ejpam-3868	219	58	of	of	ADP
ejpam-3868	219	59	one	one	NUM
ejpam-3868	219	60	-	-	PUNCT
ejpam-3868	219	61	forms	form	NOUN
ejpam-3868	219	62	.	.	PUNCT
ejpam-3868	220	1	p.	p.	NOUN
ejpam-3868	220	2	bracken	bracken	NOUN
ejpam-3868	220	3	/	/	SYM
ejpam-3868	220	4	eur	eur	PROPN
ejpam-3868	220	5	.	.	PUNCT
ejpam-3868	221	1	j.	j.	PROPN
ejpam-3868	221	2	pure	pure	PROPN
ejpam-3868	221	3	appl	appl	PROPN
ejpam-3868	221	4	.	.	PROPN
ejpam-3868	221	5	math	math	PROPN
ejpam-3868	221	6	,	,	PUNCT
ejpam-3868	221	7	13	13	NUM
ejpam-3868	221	8	(	(	PUNCT
ejpam-3868	221	9	4	4	NUM
ejpam-3868	221	10	)	)	PUNCT
ejpam-3868	221	11	(	(	PUNCT
ejpam-3868	221	12	2020	2020	NUM
ejpam-3868	221	13	)	)	PUNCT
ejpam-3868	221	14	,	,	PUNCT
ejpam-3868	221	15	1016	1016	NUM
ejpam-3868	221	16	-	-	SYM
ejpam-3868	221	17	1034	1034	NUM
ejpam-3868	221	18	1027	1027	NUM
ejpam-3868	221	19	in	in	ADP
ejpam-3868	221	20	this	this	DET
ejpam-3868	221	21	case	case	NOUN
ejpam-3868	221	22	,	,	PUNCT
ejpam-3868	221	23	we	we	PRON
ejpam-3868	221	24	would	would	AUX
ejpam-3868	221	25	take	take	VERB
ejpam-3868	221	26	x	x	INTJ
ejpam-3868	221	27	to	to	PART
ejpam-3868	221	28	be	be	AUX
ejpam-3868	221	29	tangent	tangent	ADJ
ejpam-3868	221	30	to	to	ADP
ejpam-3868	221	31	one	one	NUM
ejpam-3868	221	32	of	of	ADP
ejpam-3868	221	33	the	the	DET
ejpam-3868	221	34	fibers	fiber	NOUN
ejpam-3868	221	35	of	of	ADP
ejpam-3868	221	36	the	the	DET
ejpam-3868	221	37	double	double	ADJ
ejpam-3868	221	38	fibration	fibration	NOUN
ejpam-3868	221	39	of	of	ADP
ejpam-3868	221	40	s	s	PRON
ejpam-3868	221	41	and	and	CCONJ
ejpam-3868	221	42	x̄	x̄	NOUN
ejpam-3868	221	43	to	to	ADP
ejpam-3868	221	44	the	the	DET
ejpam-3868	221	45	other	other	ADJ
ejpam-3868	221	46	.	.	PUNCT
ejpam-3868	222	1	then	then	ADV
ejpam-3868	222	2	d	d	X
ejpam-3868	222	3	would	would	AUX
ejpam-3868	222	4	be	be	AUX
ejpam-3868	222	5	the	the	DET
ejpam-3868	222	6	distribution	distribution	NOUN
ejpam-3868	222	7	spanned	span	VERB
ejpam-3868	222	8	by	by	ADP
ejpam-3868	222	9	x	x	X
ejpam-3868	222	10	,	,	PUNCT
ejpam-3868	222	11	x̄	x̄	NOUN
ejpam-3868	222	12	and	and	CCONJ
ejpam-3868	222	13	θ	θ	PROPN
ejpam-3868	222	14	would	would	AUX
ejpam-3868	222	15	be	be	AUX
ejpam-3868	222	16	a	a	DET
ejpam-3868	222	17	scalar	scalar	ADJ
ejpam-3868	222	18	multiple	multiple	NOUN
ejpam-3868	222	19	of	of	ADP
ejpam-3868	222	20	φx	φx	ADJ
ejpam-3868	222	21	dx+	dx+	NOUN
ejpam-3868	223	1	φy	φy	ADP
ejpam-3868	223	2	dy	dy	NOUN
ejpam-3868	223	3	.	.	PUNCT
ejpam-3868	224	1	the	the	DET
ejpam-3868	224	2	purpose	purpose	NOUN
ejpam-3868	224	3	of	of	ADP
ejpam-3868	224	4	this	this	DET
ejpam-3868	224	5	discussion	discussion	NOUN
ejpam-3868	224	6	is	be	AUX
ejpam-3868	224	7	to	to	PART
ejpam-3868	224	8	reexamine	reexamine	VERB
ejpam-3868	224	9	the	the	DET
ejpam-3868	224	10	the	the	DET
ejpam-3868	224	11	effect	effect	NOUN
ejpam-3868	224	12	of	of	ADP
ejpam-3868	224	13	the	the	DET
ejpam-3868	224	14	cartan	cartan	ADJ
ejpam-3868	224	15	connection	connection	NOUN
ejpam-3868	224	16	form	form	NOUN
ejpam-3868	224	17	of	of	ADP
ejpam-3868	224	18	interchanging	interchange	VERB
ejpam-3868	224	19	the	the	DET
ejpam-3868	224	20	roles	role	NOUN
ejpam-3868	224	21	of	of	ADP
ejpam-3868	224	22	the	the	DET
ejpam-3868	224	23	fibrations	fibration	NOUN
ejpam-3868	224	24	while	while	SCONJ
ejpam-3868	224	25	treating	treat	VERB
ejpam-3868	224	26	them	they	PRON
ejpam-3868	224	27	on	on	ADP
ejpam-3868	224	28	an	an	DET
ejpam-3868	224	29	equal	equal	ADJ
ejpam-3868	224	30	footing	footing	NOUN
ejpam-3868	224	31	.	.	PUNCT
ejpam-3868	225	1	this	this	PRON
ejpam-3868	225	2	is	be	AUX
ejpam-3868	225	3	accomplished	accomplish	VERB
ejpam-3868	225	4	by	by	ADP
ejpam-3868	225	5	working	work	VERB
ejpam-3868	225	6	in	in	ADP
ejpam-3868	225	7	terms	term	NOUN
ejpam-3868	225	8	of	of	ADP
ejpam-3868	225	9	the	the	DET
ejpam-3868	225	10	dual	dual	ADJ
ejpam-3868	225	11	basis	basis	NOUN
ejpam-3868	225	12	just	just	ADV
ejpam-3868	225	13	proposed	propose	VERB
ejpam-3868	225	14	.	.	PUNCT
ejpam-3868	226	1	when	when	SCONJ
ejpam-3868	226	2	x	x	PRON
ejpam-3868	226	3	and	and	CCONJ
ejpam-3868	226	4	x̄	x̄	NOUN
ejpam-3868	226	5	are	be	AUX
ejpam-3868	226	6	interchanged	interchange	VERB
ejpam-3868	226	7	,	,	PUNCT
ejpam-3868	226	8	the	the	DET
ejpam-3868	226	9	new	new	ADJ
ejpam-3868	226	10	basis	basis	NOUN
ejpam-3868	226	11	of	of	ADP
ejpam-3868	226	12	one	one	NUM
ejpam-3868	226	13	-	-	PUNCT
ejpam-3868	226	14	forms	form	NOUN
ejpam-3868	226	15	becomes	become	VERB
ejpam-3868	226	16	{	{	PUNCT
ejpam-3868	226	17	φ̄	φ̄	NOUN
ejpam-3868	226	18	,	,	PUNCT
ejpam-3868	226	19	φ,−θ	φ,−θ	NOUN
ejpam-3868	226	20	}	}	PUNCT
ejpam-3868	226	21	.	.	PUNCT
ejpam-3868	227	1	for	for	ADP
ejpam-3868	227	2	the	the	DET
ejpam-3868	227	3	normal	normal	ADJ
ejpam-3868	227	4	cartan	cartan	PROPN
ejpam-3868	227	5	projective	projective	PROPN
ejpam-3868	227	6	connection	connection	NOUN
ejpam-3868	227	7	already	already	ADV
ejpam-3868	227	8	described	describe	VERB
ejpam-3868	227	9	,	,	PUNCT
ejpam-3868	227	10	x	x	X
ejpam-3868	227	11	=	=	SYM
ejpam-3868	227	12	γ	γ	X
ejpam-3868	227	13	,	,	PUNCT
ejpam-3868	227	14	x̄	x̄	NOUN
ejpam-3868	227	15	=	=	SYM
ejpam-3868	227	16	∂	∂	NUM
ejpam-3868	227	17	∂y	∂y	NOUN
ejpam-3868	227	18	.	.	PUNCT
ejpam-3868	228	1	(	(	PUNCT
ejpam-3868	228	2	64	64	NUM
ejpam-3868	228	3	)	)	PUNCT
ejpam-3868	228	4	it	it	PRON
ejpam-3868	228	5	is	be	AUX
ejpam-3868	228	6	then	then	ADV
ejpam-3868	228	7	possible	possible	ADJ
ejpam-3868	228	8	to	to	PART
ejpam-3868	228	9	calculate	calculate	VERB
ejpam-3868	228	10	the	the	DET
ejpam-3868	228	11	following	follow	VERB
ejpam-3868	228	12	bracket	bracket	NOUN
ejpam-3868	228	13	,	,	PUNCT
ejpam-3868	228	14	[	[	X
ejpam-3868	228	15	x	x	X
ejpam-3868	228	16	,	,	PUNCT
ejpam-3868	228	17	x̄	x̄	X
ejpam-3868	228	18	]	]	X
ejpam-3868	229	1	=	=	PUNCT
ejpam-3868	229	2	−	−	PROPN
ejpam-3868	229	3	∂	∂	NOUN
ejpam-3868	229	4	∂y	∂y	NOUN
ejpam-3868	229	5	−	−	PROPN
ejpam-3868	229	6	fy′	fy′	PROPN
ejpam-3868	229	7	∂	∂	NUM
ejpam-3868	229	8	∂y′	∂y′	PROPN
ejpam-3868	229	9	.	.	PUNCT
ejpam-3868	230	1	(	(	PUNCT
ejpam-3868	230	2	65	65	NUM
ejpam-3868	230	3	)	)	PUNCT
ejpam-3868	230	4	the	the	DET
ejpam-3868	230	5	one	one	NUM
ejpam-3868	230	6	-	-	PUNCT
ejpam-3868	230	7	forms	form	NOUN
ejpam-3868	230	8	which	which	PRON
ejpam-3868	230	9	reside	reside	VERB
ejpam-3868	230	10	in	in	ADP
ejpam-3868	230	11	the	the	DET
ejpam-3868	230	12	lower	low	ADJ
ejpam-3868	230	13	triangular	triangular	NOUN
ejpam-3868	230	14	portion	portion	NOUN
ejpam-3868	230	15	of	of	ADP
ejpam-3868	230	16	the	the	DET
ejpam-3868	230	17	connection	connection	NOUN
ejpam-3868	230	18	matrix	matrix	NOUN
ejpam-3868	230	19	dx	dx	PROPN
ejpam-3868	230	20	,	,	PUNCT
ejpam-3868	230	21	φ	φ	PROPN
ejpam-3868	230	22	−	−	PROPN
ejpam-3868	230	23	1	1	NUM
ejpam-3868	230	24	3fy′θ	3fy′θ	NUM
ejpam-3868	230	25	and	and	CCONJ
ejpam-3868	230	26	θ	θ	PROPN
ejpam-3868	230	27	are	be	AUX
ejpam-3868	230	28	not	not	PART
ejpam-3868	230	29	dual	dual	ADJ
ejpam-3868	230	30	to	to	ADP
ejpam-3868	230	31	the	the	DET
ejpam-3868	230	32	basis	basis	NOUN
ejpam-3868	230	33	of	of	ADP
ejpam-3868	230	34	vector	vector	NOUN
ejpam-3868	230	35	fields	field	NOUN
ejpam-3868	230	36	.	.	PUNCT
ejpam-3868	231	1	this	this	PRON
ejpam-3868	231	2	is	be	AUX
ejpam-3868	231	3	the	the	DET
ejpam-3868	231	4	main	main	ADJ
ejpam-3868	231	5	difference	difference	NOUN
ejpam-3868	231	6	between	between	ADP
ejpam-3868	231	7	what	what	PRON
ejpam-3868	231	8	has	have	AUX
ejpam-3868	231	9	been	be	AUX
ejpam-3868	231	10	discussed	discuss	VERB
ejpam-3868	231	11	and	and	CCONJ
ejpam-3868	231	12	what	what	PRON
ejpam-3868	231	13	comes	come	VERB
ejpam-3868	231	14	next	next	ADV
ejpam-3868	231	15	.	.	PUNCT
ejpam-3868	232	1	the	the	DET
ejpam-3868	232	2	dual	dual	ADJ
ejpam-3868	232	3	one	one	NUM
ejpam-3868	232	4	-	-	PUNCT
ejpam-3868	232	5	form	form	NOUN
ejpam-3868	232	6	basis	basis	NOUN
ejpam-3868	232	7	is	be	AUX
ejpam-3868	232	8	actually	actually	ADV
ejpam-3868	232	9	given	give	VERB
ejpam-3868	232	10	as	as	SCONJ
ejpam-3868	232	11	{	{	PUNCT
ejpam-3868	232	12	dx	dx	PROPN
ejpam-3868	232	13	,	,	PUNCT
ejpam-3868	232	14	φ−	φ−	PROPN
ejpam-3868	232	15	fydθ,−θ	fydθ,−θ	PROPN
ejpam-3868	232	16	}	}	PUNCT
ejpam-3868	232	17	the	the	DET
ejpam-3868	232	18	new	new	ADJ
ejpam-3868	232	19	approach	approach	NOUN
ejpam-3868	232	20	requires	require	VERB
ejpam-3868	232	21	us	we	PRON
ejpam-3868	232	22	to	to	PART
ejpam-3868	232	23	take	take	VERB
ejpam-3868	232	24	the	the	DET
ejpam-3868	232	25	cartan	cartan	ADJ
ejpam-3868	232	26	connection	connection	NOUN
ejpam-3868	232	27	form	form	NOUN
ejpam-3868	232	28	in	in	ADP
ejpam-3868	232	29	the	the	DET
ejpam-3868	232	30	lower	low	ADJ
ejpam-3868	232	31	triangular	triangular	NOUN
ejpam-3868	232	32	part	part	NOUN
ejpam-3868	232	33	of	of	ADP
ejpam-3868	232	34	the	the	DET
ejpam-3868	232	35	connection	connection	NOUN
ejpam-3868	232	36	form	form	NOUN
ejpam-3868	232	37	matrix	matrix	NOUN
ejpam-3868	232	38	as	as	ADP
ejpam-3868	232	39			PROPN
ejpam-3868	232	40	φ	φ	PROPN
ejpam-3868	232	41	−θ	−θ	PROPN
ejpam-3868	232	42	φ̄	φ̄	PROPN
ejpam-3868	232	43			PROPN
ejpam-3868	232	44	(	(	PUNCT
ejpam-3868	232	45	66	66	NUM
ejpam-3868	232	46	)	)	PUNCT
ejpam-3868	232	47	in	in	ADP
ejpam-3868	232	48	the	the	DET
ejpam-3868	232	49	case	case	NOUN
ejpam-3868	232	50	just	just	ADV
ejpam-3868	232	51	discussed	discuss	VERB
ejpam-3868	232	52	,	,	PUNCT
ejpam-3868	232	53	this	this	PRON
ejpam-3868	232	54	would	would	AUX
ejpam-3868	232	55	be	be	AUX
ejpam-3868	232	56	gauge	gauge	NOUN
ejpam-3868	232	57	-	-	PUNCT
ejpam-3868	232	58	equivalent	equivalent	ADJ
ejpam-3868	232	59	to	to	ADP
ejpam-3868	232	60	the	the	DET
ejpam-3868	232	61	version	version	NOUN
ejpam-3868	232	62	used	use	VERB
ejpam-3868	232	63	previously	previously	ADV
ejpam-3868	232	64	.	.	PUNCT
ejpam-3868	233	1	it	it	PRON
ejpam-3868	233	2	is	be	AUX
ejpam-3868	233	3	to	to	PART
ejpam-3868	233	4	be	be	AUX
ejpam-3868	233	5	emphasized	emphasize	VERB
ejpam-3868	233	6	that	that	SCONJ
ejpam-3868	233	7	now	now	ADV
ejpam-3868	233	8	x	x	PRON
ejpam-3868	233	9	may	may	AUX
ejpam-3868	233	10	be	be	AUX
ejpam-3868	233	11	any	any	DET
ejpam-3868	233	12	vector	vector	NOUN
ejpam-3868	233	13	field	field	NOUN
ejpam-3868	233	14	tangent	tangent	NOUN
ejpam-3868	233	15	to	to	ADP
ejpam-3868	233	16	the	the	DET
ejpam-3868	233	17	first	first	ADJ
ejpam-3868	233	18	fibration	fibration	NOUN
ejpam-3868	233	19	and	and	CCONJ
ejpam-3868	233	20	x̄	x̄	NOUN
ejpam-3868	233	21	any	any	DET
ejpam-3868	233	22	vector	vector	NOUN
ejpam-3868	233	23	field	field	NOUN
ejpam-3868	233	24	tangent	tangent	NOUN
ejpam-3868	233	25	to	to	ADP
ejpam-3868	233	26	the	the	DET
ejpam-3868	233	27	second	second	NOUN
ejpam-3868	233	28	.	.	PUNCT
ejpam-3868	234	1	thus	thus	ADV
ejpam-3868	234	2	in	in	ADP
ejpam-3868	234	3	the	the	DET
ejpam-3868	234	4	present	present	ADJ
ejpam-3868	234	5	version	version	NOUN
ejpam-3868	234	6	of	of	ADP
ejpam-3868	234	7	the	the	DET
ejpam-3868	234	8	theory	theory	NOUN
ejpam-3868	234	9	,	,	PUNCT
ejpam-3868	234	10	transformations	transformation	NOUN
ejpam-3868	234	11	of	of	ADP
ejpam-3868	234	12	the	the	DET
ejpam-3868	234	13	form	form	NOUN
ejpam-3868	234	14	x	x	PUNCT
ejpam-3868	234	15	→	→	SYM
ejpam-3868	234	16	λx	λx	PROPN
ejpam-3868	234	17	and	and	CCONJ
ejpam-3868	234	18	x̄	x̄	NOUN
ejpam-3868	234	19	→	→	PUNCT
ejpam-3868	234	20	λ̄x̄	λ̄x̄	PROPN
ejpam-3868	234	21	for	for	ADP
ejpam-3868	234	22	any	any	DET
ejpam-3868	234	23	nonvanishing	nonvanishing	NOUN
ejpam-3868	234	24	functions	function	NOUN
ejpam-3868	234	25	λ	λ	NOUN
ejpam-3868	234	26	,	,	PUNCT
ejpam-3868	234	27	λ̄	λ̄	VERB
ejpam-3868	234	28	,	,	PUNCT
ejpam-3868	234	29	will	will	AUX
ejpam-3868	234	30	be	be	AUX
ejpam-3868	234	31	allowed	allow	VERB
ejpam-3868	234	32	:	:	PUNCT
ejpam-3868	234	33	such	such	ADJ
ejpam-3868	234	34	transformations	transformation	NOUN
ejpam-3868	234	35	induce	induce	VERB
ejpam-3868	234	36	gauge	gauge	ADJ
ejpam-3868	234	37	transformations	transformation	NOUN
ejpam-3868	234	38	of	of	ADP
ejpam-3868	234	39	the	the	DET
ejpam-3868	234	40	kind	kind	NOUN
ejpam-3868	234	41	discussed	discuss	VERB
ejpam-3868	234	42	previously	previously	ADV
ejpam-3868	234	43	,	,	PUNCT
ejpam-3868	234	44	with	with	ADP
ejpam-3868	234	45	coefficients	coefficient	NOUN
ejpam-3868	234	46	given	give	VERB
ejpam-3868	234	47	in	in	ADP
ejpam-3868	234	48	terms	term	NOUN
ejpam-3868	234	49	of	of	ADP
ejpam-3868	234	50	λ	λ	NOUN
ejpam-3868	234	51	,	,	PUNCT
ejpam-3868	234	52	λ̄	λ̄	X
ejpam-3868	234	53	and	and	CCONJ
ejpam-3868	234	54	their	their	PRON
ejpam-3868	234	55	derivatives	derivative	NOUN
ejpam-3868	234	56	.	.	PUNCT
ejpam-3868	235	1	it	it	PRON
ejpam-3868	235	2	is	be	AUX
ejpam-3868	235	3	a	a	DET
ejpam-3868	235	4	consequence	consequence	NOUN
ejpam-3868	235	5	of	of	ADP
ejpam-3868	235	6	these	these	DET
ejpam-3868	235	7	definitions	definition	NOUN
ejpam-3868	235	8	that	that	SCONJ
ejpam-3868	235	9	the	the	DET
ejpam-3868	235	10	exterior	exterior	ADJ
ejpam-3868	235	11	derivatives	derivative	NOUN
ejpam-3868	235	12	of	of	ADP
ejpam-3868	235	13	the	the	DET
ejpam-3868	235	14	basis	basis	NOUN
ejpam-3868	235	15	oneforms	oneform	NOUN
ejpam-3868	235	16	can	can	AUX
ejpam-3868	235	17	be	be	AUX
ejpam-3868	235	18	written	write	VERB
ejpam-3868	235	19	as	as	ADP
ejpam-3868	235	20	dφ	dφ	ADP
ejpam-3868	235	21	=	=	SYM
ejpam-3868	235	22	ψ	ψ	NOUN
ejpam-3868	235	23	∧	∧	PROPN
ejpam-3868	235	24	θ	θ	PROPN
ejpam-3868	235	25	,	,	PUNCT
ejpam-3868	235	26	dφ̄	dφ̄	NOUN
ejpam-3868	235	27	=	=	SYM
ejpam-3868	235	28	−ψ̄	−ψ̄	NOUN
ejpam-3868	235	29	∧	∧	PROPN
ejpam-3868	235	30	θ	θ	PROPN
ejpam-3868	235	31	,	,	PUNCT
ejpam-3868	235	32	dθ	dθ	PROPN
ejpam-3868	235	33	=	=	PROPN
ejpam-3868	235	34	−φ	−φ	NOUN
ejpam-3868	235	35	∧	∧	PROPN
ejpam-3868	235	36	φ̄+	φ̄+	PUNCT
ejpam-3868	235	37	χ	χ	PROPN
ejpam-3868	235	38	∧	∧	PROPN
ejpam-3868	235	39	θ̄	θ̄	ADJ
ejpam-3868	235	40	,	,	PUNCT
ejpam-3868	235	41	(	(	PUNCT
ejpam-3868	235	42	67	67	NUM
ejpam-3868	235	43	)	)	PUNCT
ejpam-3868	235	44	where	where	SCONJ
ejpam-3868	235	45	ψ	ψ	VERB
ejpam-3868	235	46	,	,	PUNCT
ejpam-3868	235	47	ψ̄	ψ̄	PUNCT
ejpam-3868	235	48	and	and	CCONJ
ejpam-3868	235	49	χ	χ	NOUN
ejpam-3868	235	50	are	be	AUX
ejpam-3868	235	51	certain	certain	ADJ
ejpam-3868	235	52	one	one	NUM
ejpam-3868	235	53	-	-	PUNCT
ejpam-3868	235	54	forms	form	NOUN
ejpam-3868	235	55	which	which	PRON
ejpam-3868	235	56	are	be	AUX
ejpam-3868	235	57	linear	linear	ADJ
ejpam-3868	235	58	combinations	combination	NOUN
ejpam-3868	235	59	of	of	ADP
ejpam-3868	235	60	φ	φ	PROPN
ejpam-3868	235	61	and	and	CCONJ
ejpam-3868	235	62	φ̄.	φ̄.	NOUN
ejpam-3868	235	63	changing	change	VERB
ejpam-3868	235	64	the	the	DET
ejpam-3868	235	65	notation	notation	NOUN
ejpam-3868	235	66	proves	prove	VERB
ejpam-3868	235	67	to	to	PART
ejpam-3868	235	68	be	be	AUX
ejpam-3868	235	69	useful	useful	ADJ
ejpam-3868	235	70	,	,	PUNCT
ejpam-3868	235	71	so	so	CCONJ
ejpam-3868	235	72	the	the	DET
ejpam-3868	235	73	connection	connection	NOUN
ejpam-3868	235	74	form	form	NOUN
ejpam-3868	235	75	has	have	VERB
ejpam-3868	235	76	the	the	DET
ejpam-3868	235	77	structure	structure	NOUN
ejpam-3868	235	78	,	,	PUNCT
ejpam-3868	235	79	ω	ω	NOUN
ejpam-3868	235	80	=	=	PUNCT
ejpam-3868	235	81			PROPN
ejpam-3868	235	82	α	α	X
ejpam-3868	235	83	β	β	X
ejpam-3868	235	84	γ	γ	PROPN
ejpam-3868	235	85	φ	φ	PROPN
ejpam-3868	235	86	−α−	−α−	VERB
ejpam-3868	235	87	α′	α′	NUM
ejpam-3868	235	88	β′	β′	PUNCT
ejpam-3868	236	1	−θ	−θ	ADV
ejpam-3868	236	2	φ̄	φ̄	PROPN
ejpam-3868	237	1	α′	α′	NUM
ejpam-3868	237	2			PROPN
ejpam-3868	237	3	(	(	PUNCT
ejpam-3868	237	4	68	68	NUM
ejpam-3868	237	5	)	)	PUNCT
ejpam-3868	237	6	it	it	PRON
ejpam-3868	237	7	is	be	AUX
ejpam-3868	237	8	assumed	assume	VERB
ejpam-3868	237	9	that	that	SCONJ
ejpam-3868	237	10	x	x	PROPN
ejpam-3868	237	11	and	and	CCONJ
ejpam-3868	237	12	x̄	x̄	NOUN
ejpam-3868	237	13	and	and	CCONJ
ejpam-3868	237	14	hence	hence	ADV
ejpam-3868	237	15	φ	φ	NUM
ejpam-3868	237	16	,	,	PUNCT
ejpam-3868	237	17	φ̄	φ̄	PROPN
ejpam-3868	237	18	and	and	CCONJ
ejpam-3868	237	19	θ	θ	PROPN
ejpam-3868	237	20	have	have	AUX
ejpam-3868	237	21	been	be	AUX
ejpam-3868	237	22	fixed	fix	VERB
ejpam-3868	237	23	.	.	PUNCT
ejpam-3868	238	1	therefore	therefore	ADV
ejpam-3868	238	2	,	,	PUNCT
ejpam-3868	238	3	the	the	DET
ejpam-3868	238	4	only	only	ADJ
ejpam-3868	238	5	remaining	remaining	ADJ
ejpam-3868	238	6	gauge	gauge	NOUN
ejpam-3868	238	7	freedom	freedom	NOUN
ejpam-3868	238	8	is	be	AUX
ejpam-3868	238	9	the	the	DET
ejpam-3868	238	10	one	one	NUM
ejpam-3868	238	11	coming	come	VERB
ejpam-3868	238	12	from	from	ADP
ejpam-3868	238	13	a	a	DET
ejpam-3868	238	14	gauge	gauge	ADJ
ejpam-3868	238	15	transformation	transformation	NOUN
ejpam-3868	238	16	of	of	ADP
ejpam-3868	238	17	the	the	DET
ejpam-3868	238	18	form	form	NOUN
ejpam-3868	238	19	h	h	NOUN
ejpam-3868	238	20	=	=	PUNCT
ejpam-3868	238	21	1	1	PROPN
ejpam-3868	238	22	0	0	NUM
ejpam-3868	239	1	f	f	NOUN
ejpam-3868	239	2	0	0	NUM
ejpam-3868	239	3	1	1	NUM
ejpam-3868	239	4	0	0	NUM
ejpam-3868	239	5	0	0	NUM
ejpam-3868	239	6	0	0	NUM
ejpam-3868	239	7	1	1	NUM
ejpam-3868	239	8			PROPN
ejpam-3868	239	9	,	,	PUNCT
ejpam-3868	239	10	h−1	h−1	PROPN
ejpam-3868	239	11	=	=	PUNCT
ejpam-3868	239	12	1	1	PROPN
ejpam-3868	239	13	0	0	NUM
ejpam-3868	240	1	−f	−f	NOUN
ejpam-3868	240	2	0	0	NUM
ejpam-3868	240	3	1	1	NUM
ejpam-3868	240	4	0	0	NUM
ejpam-3868	240	5	0	0	NUM
ejpam-3868	240	6	0	0	NUM
ejpam-3868	240	7	1	1	NUM
ejpam-3868	240	8			PROPN
ejpam-3868	240	9	(	(	PUNCT
ejpam-3868	240	10	69	69	NUM
ejpam-3868	240	11	)	)	PUNCT
ejpam-3868	240	12	p.	p.	NOUN
ejpam-3868	240	13	bracken	bracken	NOUN
ejpam-3868	240	14	/	/	SYM
ejpam-3868	240	15	eur	eur	PROPN
ejpam-3868	240	16	.	.	PUNCT
ejpam-3868	241	1	j.	j.	PROPN
ejpam-3868	241	2	pure	pure	PROPN
ejpam-3868	241	3	appl	appl	PROPN
ejpam-3868	241	4	.	.	PROPN
ejpam-3868	241	5	math	math	PROPN
ejpam-3868	241	6	,	,	PUNCT
ejpam-3868	241	7	13	13	NUM
ejpam-3868	241	8	(	(	PUNCT
ejpam-3868	241	9	4	4	NUM
ejpam-3868	241	10	)	)	PUNCT
ejpam-3868	241	11	(	(	PUNCT
ejpam-3868	241	12	2020	2020	NUM
ejpam-3868	241	13	)	)	PUNCT
ejpam-3868	241	14	,	,	PUNCT
ejpam-3868	241	15	1016	1016	NUM
ejpam-3868	241	16	-	-	SYM
ejpam-3868	241	17	1034	1034	NUM
ejpam-3868	241	18	1028	1028	NUM
ejpam-3868	241	19	for	for	ADP
ejpam-3868	241	20	such	such	DET
ejpam-3868	241	21	a	a	DET
ejpam-3868	241	22	choice	choice	NOUN
ejpam-3868	241	23	of	of	ADP
ejpam-3868	241	24	h	h	NOUN
ejpam-3868	241	25	,	,	PUNCT
ejpam-3868	241	26	it	it	PRON
ejpam-3868	241	27	is	be	AUX
ejpam-3868	241	28	determined	determined	ADJ
ejpam-3868	241	29	that	that	SCONJ
ejpam-3868	241	30	h−1ωh+	h−1ωh+	VERB
ejpam-3868	242	1	h−1	h−1	INTJ
ejpam-3868	242	2	dh	dh	NOUN
ejpam-3868	243	1	=	=	PUNCT
ejpam-3868	243	2	α−	α−	PROPN
ejpam-3868	243	3	fθ	fθ	PROPN
ejpam-3868	243	4	β	β	X
ejpam-3868	243	5	−	−	NOUN
ejpam-3868	243	6	fφ̄	fφ̄	PROPN
ejpam-3868	243	7	f	f	X
ejpam-3868	243	8	(	(	PUNCT
ejpam-3868	243	9	α−	α−	ADP
ejpam-3868	243	10	fθ	fθ	VERB
ejpam-3868	243	11	)	)	PUNCT
ejpam-3868	243	12	φ	φ	PROPN
ejpam-3868	243	13	−α−	−α−	VERB
ejpam-3868	243	14	α′	α′	NUM
ejpam-3868	243	15	fφ−	fφ−	PUNCT
ejpam-3868	243	16	β′	β′	NUM
ejpam-3868	243	17	θ	θ	X
ejpam-3868	243	18	φ̄	φ̄	NOUN
ejpam-3868	244	1	fθ	fθ	ADJ
ejpam-3868	244	2	+	+	NUM
ejpam-3868	244	3	α′	α′	NUM
ejpam-3868	244	4			PROPN
ejpam-3868	244	5	(	(	PUNCT
ejpam-3868	244	6	70	70	NUM
ejpam-3868	244	7	)	)	PUNCT
ejpam-3868	244	8	by	by	ADP
ejpam-3868	244	9	pursuing	pursue	VERB
ejpam-3868	244	10	an	an	DET
ejpam-3868	244	11	argument	argument	NOUN
ejpam-3868	244	12	similar	similar	ADJ
ejpam-3868	244	13	to	to	ADP
ejpam-3868	244	14	the	the	DET
ejpam-3868	244	15	one	one	NOUN
ejpam-3868	244	16	used	use	VERB
ejpam-3868	244	17	before	before	ADV
ejpam-3868	244	18	,	,	PUNCT
ejpam-3868	244	19	that	that	SCONJ
ejpam-3868	244	20	α	α	NOUN
ejpam-3868	244	21	,	,	PUNCT
ejpam-3868	244	22	α′	α′	NUM
ejpam-3868	244	23	,	,	PUNCT
ejpam-3868	244	24	β	β	X
ejpam-3868	244	25	,	,	PUNCT
ejpam-3868	244	26	β′	β′	NUM
ejpam-3868	244	27	and	and	CCONJ
ejpam-3868	244	28	γ	γ	NOUN
ejpam-3868	244	29	are	be	AUX
ejpam-3868	244	30	uniquely	uniquely	ADV
ejpam-3868	244	31	determined	determined	ADJ
ejpam-3868	244	32	in	in	ADP
ejpam-3868	244	33	terms	term	NOUN
ejpam-3868	244	34	of	of	ADP
ejpam-3868	244	35	ψ	ψ	NOUN
ejpam-3868	244	36	,	,	PUNCT
ejpam-3868	244	37	ψ̄	ψ̄	PUNCT
ejpam-3868	244	38	and	and	CCONJ
ejpam-3868	244	39	χ	χ	NOUN
ejpam-3868	244	40	and	and	CCONJ
ejpam-3868	244	41	their	their	PRON
ejpam-3868	244	42	derivatives	derivative	NOUN
ejpam-3868	244	43	by	by	ADP
ejpam-3868	244	44	the	the	DET
ejpam-3868	244	45	requirement	requirement	NOUN
ejpam-3868	244	46	that	that	SCONJ
ejpam-3868	244	47	the	the	DET
ejpam-3868	244	48	curvature	curvature	NOUN
ejpam-3868	244	49	ω	ω	PROPN
ejpam-3868	244	50	of	of	ADP
ejpam-3868	244	51	ω	ω	PROPN
ejpam-3868	244	52	takes	take	VERB
ejpam-3868	244	53	the	the	DET
ejpam-3868	244	54	form	form	NOUN
ejpam-3868	244	55	,	,	PUNCT
ejpam-3868	244	56	ω	ω	NOUN
ejpam-3868	244	57	=	=	PUNCT
ejpam-3868	244	58	0	0	ADP
ejpam-3868	244	59	b	b	X
ejpam-3868	244	60	0	0	NUM
ejpam-3868	244	61	0	0	NUM
ejpam-3868	244	62	0	0	NUM
ejpam-3868	244	63	b′	b′	NUM
ejpam-3868	245	1	0	0	NUM
ejpam-3868	245	2	0	0	SYM
ejpam-3868	245	3	0	0	NUM
ejpam-3868	245	4			PROPN
ejpam-3868	245	5	(	(	PUNCT
ejpam-3868	245	6	71	71	NUM
ejpam-3868	245	7	)	)	PUNCT
ejpam-3868	245	8	with	with	ADP
ejpam-3868	245	9	b	b	PROPN
ejpam-3868	245	10	a	a	DET
ejpam-3868	245	11	multiple	multiple	NOUN
ejpam-3868	245	12	of	of	ADP
ejpam-3868	245	13	φ	φ	PROPN
ejpam-3868	245	14	∧	∧	PROPN
ejpam-3868	245	15	θ	θ	PROPN
ejpam-3868	245	16	.	.	PUNCT
ejpam-3868	246	1	the	the	DET
ejpam-3868	246	2	constraints	constraint	NOUN
ejpam-3868	246	3	that	that	PRON
ejpam-3868	246	4	require	require	VERB
ejpam-3868	246	5	the	the	DET
ejpam-3868	246	6	torsion	torsion	NOUN
ejpam-3868	246	7	to	to	PART
ejpam-3868	246	8	vanish	vanish	VERB
ejpam-3868	246	9	amount	amount	NOUN
ejpam-3868	246	10	to	to	ADP
ejpam-3868	246	11	the	the	DET
ejpam-3868	246	12	following	follow	VERB
ejpam-3868	246	13	system	system	NOUN
ejpam-3868	246	14	:	:	PUNCT
ejpam-3868	246	15	dφ−(2α+α′)∧φ−β′∧θ	dφ−(2α+α′)∧φ−β′∧θ	NOUN
ejpam-3868	246	16	=	=	SYM
ejpam-3868	246	17	0	0	NUM
ejpam-3868	246	18	,	,	PUNCT
ejpam-3868	246	19	dφ̄+(α+2α′)∧γ̄+β∧θ	dφ̄+(α+2α′)∧γ̄+β∧θ	X
ejpam-3868	246	20	=	=	SYM
ejpam-3868	246	21	0	0	NUM
ejpam-3868	246	22	,	,	PUNCT
ejpam-3868	246	23	dθ−(α−α′)∧θ+φ∧φ̄	dθ−(α−α′)∧θ+φ∧φ̄	NOUN
ejpam-3868	246	24	=	=	SYM
ejpam-3868	246	25	0	0	X
ejpam-3868	246	26	.	.	PUNCT
ejpam-3868	247	1	(	(	PUNCT
ejpam-3868	247	2	72	72	NUM
ejpam-3868	247	3	)	)	PUNCT
ejpam-3868	247	4	it	it	PRON
ejpam-3868	247	5	follows	follow	VERB
ejpam-3868	247	6	from	from	ADP
ejpam-3868	247	7	the	the	DET
ejpam-3868	247	8	last	last	NOUN
ejpam-3868	247	9	of	of	ADP
ejpam-3868	247	10	these	these	PRON
ejpam-3868	247	11	together	together	ADV
ejpam-3868	247	12	with	with	ADP
ejpam-3868	247	13	the	the	DET
ejpam-3868	247	14	gauge	gauge	NOUN
ejpam-3868	247	15	-	-	PUNCT
ejpam-3868	247	16	fixing	fix	VERB
ejpam-3868	247	17	assumption	assumption	NOUN
ejpam-3868	247	18	that	that	SCONJ
ejpam-3868	247	19	α−α′	α−α′	NUM
ejpam-3868	247	20	=	=	SYM
ejpam-3868	247	21	χ	χ	X
ejpam-3868	247	22	.	.	PUNCT
ejpam-3868	248	1	the	the	DET
ejpam-3868	248	2	first	first	ADJ
ejpam-3868	248	3	two	two	NUM
ejpam-3868	248	4	equations	equation	NOUN
ejpam-3868	248	5	in	in	ADP
ejpam-3868	248	6	(	(	PUNCT
ejpam-3868	248	7	72	72	NUM
ejpam-3868	248	8	)	)	PUNCT
ejpam-3868	248	9	determine	determine	VERB
ejpam-3868	248	10	the	the	DET
ejpam-3868	248	11	φ	φ	NOUN
ejpam-3868	248	12	and	and	CCONJ
ejpam-3868	248	13	φ̄	φ̄	ADJ
ejpam-3868	248	14	components	component	NOUN
ejpam-3868	248	15	of	of	ADP
ejpam-3868	248	16	α	α	PROPN
ejpam-3868	248	17	.	.	PUNCT
ejpam-3868	249	1	therefore	therefore	ADV
ejpam-3868	249	2	α′	α′	PROPN
ejpam-3868	249	3	is	be	AUX
ejpam-3868	249	4	in	in	ADP
ejpam-3868	249	5	terms	term	NOUN
ejpam-3868	249	6	of	of	ADP
ejpam-3868	249	7	ψ	ψ	NOUN
ejpam-3868	249	8	,	,	PUNCT
ejpam-3868	249	9	ψ̄	ψ̄	PUNCT
ejpam-3868	249	10	and	and	CCONJ
ejpam-3868	249	11	χ	χ	X
ejpam-3868	249	12	with	with	ADP
ejpam-3868	249	13	the	the	DET
ejpam-3868	249	14	φ	φ	PROPN
ejpam-3868	249	15	,	,	PUNCT
ejpam-3868	249	16	φ̄	φ̄	ADJ
ejpam-3868	249	17	components	component	NOUN
ejpam-3868	249	18	of	of	ADP
ejpam-3868	249	19	β	β	PROPN
ejpam-3868	249	20	and	and	CCONJ
ejpam-3868	249	21	β′	β′	NUM
ejpam-3868	249	22	in	in	ADP
ejpam-3868	249	23	terms	term	NOUN
ejpam-3868	249	24	of	of	ADP
ejpam-3868	249	25	α	α	NOUN
ejpam-3868	249	26	and	and	CCONJ
ejpam-3868	249	27	α′.	α′.	NOUN
ejpam-3868	249	28	the	the	DET
ejpam-3868	249	29	conditions	condition	NOUN
ejpam-3868	249	30	that	that	PRON
ejpam-3868	249	31	the	the	DET
ejpam-3868	249	32	diagonal	diagonal	ADJ
ejpam-3868	249	33	elements	element	NOUN
ejpam-3868	249	34	of	of	ADP
ejpam-3868	249	35	ω	ω	PROPN
ejpam-3868	249	36	must	must	AUX
ejpam-3868	249	37	vanish	vanish	VERB
ejpam-3868	249	38	results	result	NOUN
ejpam-3868	249	39	in	in	ADP
ejpam-3868	249	40	the	the	DET
ejpam-3868	249	41	pair	pair	NOUN
ejpam-3868	249	42	dα+	dα+	NOUN
ejpam-3868	249	43	β	β	X
ejpam-3868	249	44	∧	∧	PROPN
ejpam-3868	249	45	φ+	φ+	PUNCT
ejpam-3868	249	46	γ	γ	X
ejpam-3868	249	47	∧	∧	PROPN
ejpam-3868	249	48	θ	θ	PROPN
ejpam-3868	249	49	=	=	SYM
ejpam-3868	249	50	0	0	NUM
ejpam-3868	249	51	,	,	PUNCT
ejpam-3868	249	52	dα′	dα′	NOUN
ejpam-3868	249	53	−	−	NOUN
ejpam-3868	249	54	β′	β′	PUNCT
ejpam-3868	250	1	∧	∧	NOUN
ejpam-3868	250	2	φ̄+	φ̄+	PUNCT
ejpam-3868	250	3	γ	γ	X
ejpam-3868	250	4	∧	∧	NOUN
ejpam-3868	250	5	θ	θ	NOUN
ejpam-3868	250	6	=	=	SYM
ejpam-3868	250	7	0	0	NUM
ejpam-3868	250	8	.	.	PUNCT
ejpam-3868	251	1	(	(	PUNCT
ejpam-3868	251	2	73	73	NUM
ejpam-3868	251	3	)	)	PUNCT
ejpam-3868	251	4	this	this	PRON
ejpam-3868	251	5	are	be	AUX
ejpam-3868	251	6	equivalent	equivalent	ADJ
ejpam-3868	251	7	under	under	ADP
ejpam-3868	251	8	linear	linear	ADJ
ejpam-3868	251	9	combinations	combination	NOUN
ejpam-3868	251	10	to	to	ADP
ejpam-3868	251	11	the	the	DET
ejpam-3868	251	12	following	following	NOUN
ejpam-3868	251	13	,	,	PUNCT
ejpam-3868	251	14	d(α+	d(α+	NOUN
ejpam-3868	251	15	α′	α′	NUM
ejpam-3868	251	16	)	)	PUNCT
ejpam-3868	252	1	+	+	CCONJ
ejpam-3868	252	2	β	β	X
ejpam-3868	252	3	∧	∧	PROPN
ejpam-3868	252	4	φ−	φ−	PROPN
ejpam-3868	252	5	β′	β′	NUM
ejpam-3868	252	6	∧	∧	PROPN
ejpam-3868	252	7	φ̄	φ̄	NOUN
ejpam-3868	253	1	=	=	SYM
ejpam-3868	254	1	0	0	NUM
ejpam-3868	254	2	,	,	PUNCT
ejpam-3868	254	3	d(α−	d(α−	VERB
ejpam-3868	254	4	α′	α′	NUM
ejpam-3868	254	5	)	)	PUNCT
ejpam-3868	255	1	+	+	CCONJ
ejpam-3868	255	2	β	β	X
ejpam-3868	255	3	∧	∧	NOUN
ejpam-3868	255	4	φ+	φ+	PUNCT
ejpam-3868	255	5	β′	β′	NUM
ejpam-3868	255	6	∧	∧	PROPN
ejpam-3868	255	7	φ̄	φ̄	NOUN
ejpam-3868	255	8	=	=	SYM
ejpam-3868	255	9	2γ	2γ	NUM
ejpam-3868	255	10	∧	∧	PROPN
ejpam-3868	255	11	θ	θ	PROPN
ejpam-3868	255	12	.	.	PUNCT
ejpam-3868	256	1	(	(	PUNCT
ejpam-3868	256	2	74	74	NUM
ejpam-3868	256	3	)	)	PUNCT
ejpam-3868	256	4	the	the	DET
ejpam-3868	256	5	φ	φ	PROPN
ejpam-3868	256	6	∧	∧	PROPN
ejpam-3868	256	7	φ̄	φ̄	PROPN
ejpam-3868	256	8	component	component	NOUN
ejpam-3868	256	9	of	of	ADP
ejpam-3868	256	10	these	these	PRON
ejpam-3868	256	11	determines	determine	VERB
ejpam-3868	256	12	the	the	DET
ejpam-3868	256	13	θ	θ	PROPN
ejpam-3868	256	14	component	component	NOUN
ejpam-3868	256	15	of	of	ADP
ejpam-3868	256	16	α	α	NOUN
ejpam-3868	256	17	+	+	X
ejpam-3868	256	18	α′	α′	NUM
ejpam-3868	256	19	and	and	CCONJ
ejpam-3868	256	20	therefore	therefore	ADV
ejpam-3868	256	21	of	of	ADP
ejpam-3868	256	22	α	α	NOUN
ejpam-3868	256	23	and	and	CCONJ
ejpam-3868	256	24	α′	α′	PROPN
ejpam-3868	256	25	since	since	SCONJ
ejpam-3868	256	26	they	they	PRON
ejpam-3868	256	27	have	have	VERB
ejpam-3868	256	28	the	the	DET
ejpam-3868	256	29	same	same	ADJ
ejpam-3868	256	30	θ	θ	PROPN
ejpam-3868	256	31	component	component	NOUN
ejpam-3868	256	32	.	.	PUNCT
ejpam-3868	257	1	the	the	DET
ejpam-3868	257	2	remaining	remain	VERB
ejpam-3868	257	3	components	component	NOUN
ejpam-3868	257	4	determine	determine	VERB
ejpam-3868	257	5	the	the	DET
ejpam-3868	257	6	θ	θ	PROPN
ejpam-3868	257	7	components	component	NOUN
ejpam-3868	257	8	of	of	ADP
ejpam-3868	257	9	β	β	PROPN
ejpam-3868	257	10	and	and	CCONJ
ejpam-3868	257	11	β′.	β′.	PROPN
ejpam-3868	257	12	the	the	DET
ejpam-3868	257	13	φ	φ	PROPN
ejpam-3868	257	14	∧	∧	PROPN
ejpam-3868	257	15	φ̄	φ̄	PROPN
ejpam-3868	257	16	component	component	NOUN
ejpam-3868	257	17	of	of	ADP
ejpam-3868	257	18	the	the	DET
ejpam-3868	257	19	second	second	ADJ
ejpam-3868	257	20	equation	equation	NOUN
ejpam-3868	257	21	is	be	AUX
ejpam-3868	257	22	satisfied	satisfied	ADJ
ejpam-3868	257	23	identically	identically	ADV
ejpam-3868	257	24	,	,	PUNCT
ejpam-3868	257	25	and	and	CCONJ
ejpam-3868	257	26	the	the	DET
ejpam-3868	257	27	other	other	ADJ
ejpam-3868	257	28	two	two	NUM
ejpam-3868	257	29	components	component	NOUN
ejpam-3868	257	30	yield	yield	VERB
ejpam-3868	257	31	the	the	DET
ejpam-3868	257	32	φ	φ	NOUN
ejpam-3868	257	33	and	and	CCONJ
ejpam-3868	257	34	φ̄	φ̄	ADJ
ejpam-3868	257	35	components	component	NOUN
ejpam-3868	257	36	of	of	ADP
ejpam-3868	257	37	γ	γ	PROPN
ejpam-3868	257	38	.	.	PUNCT
ejpam-3868	257	39	given	give	VERB
ejpam-3868	257	40	that	that	SCONJ
ejpam-3868	257	41	ω	ω	PROPN
ejpam-3868	257	42	has	have	AUX
ejpam-3868	257	43	the	the	DET
ejpam-3868	257	44	form	form	NOUN
ejpam-3868	257	45	(	(	PUNCT
ejpam-3868	257	46	68	68	NUM
ejpam-3868	257	47	)	)	PUNCT
ejpam-3868	257	48	the	the	DET
ejpam-3868	257	49	curvature	curvature	NOUN
ejpam-3868	257	50	form	form	NOUN
ejpam-3868	257	51	ω	ω	PROPN
ejpam-3868	257	52	is	be	AUX
ejpam-3868	257	53	given	give	VERB
ejpam-3868	257	54	by	by	ADJ
ejpam-3868	257	55	dα	dα	NOUN
ejpam-3868	257	56	dβ	dβ	ADP
ejpam-3868	257	57	dγ	dγ	PROPN
ejpam-3868	257	58	dφ	dφ	ADP
ejpam-3868	257	59	−d(α+	−d(α+	NOUN
ejpam-3868	257	60	α′	α′	NUM
ejpam-3868	257	61	)	)	PUNCT
ejpam-3868	257	62	dβ′	dβ′	NOUN
ejpam-3868	257	63	−dθ	−dθ	NUM
ejpam-3868	257	64	dφ̄	dφ̄	NOUN
ejpam-3868	257	65	dα′	dα′	X
ejpam-3868	257	66			PROPN
ejpam-3868	257	67	+	+	CCONJ
ejpam-3868	257	68			PROPN
ejpam-3868	257	69	β	β	X
ejpam-3868	257	70	∧	∧	PROPN
ejpam-3868	257	71	φ−	φ−	PROPN
ejpam-3868	257	72	γ	γ	X
ejpam-3868	257	73	∧	∧	PROPN
ejpam-3868	257	74	θ	θ	PROPN
ejpam-3868	257	75	α	α	NOUN
ejpam-3868	257	76	∧	∧	PROPN
ejpam-3868	257	77	β	β	X
ejpam-3868	257	78	−	−	NOUN
ejpam-3868	257	79	β	β	X
ejpam-3868	257	80	∧	∧	PROPN
ejpam-3868	257	81	(	(	PUNCT
ejpam-3868	257	82	α+	α+	X
ejpam-3868	257	83	α′	α′	NUM
ejpam-3868	257	84	)	)	PUNCT
ejpam-3868	257	85	+	+	CCONJ
ejpam-3868	257	86	γ	γ	PROPN
ejpam-3868	257	87	∧	∧	PROPN
ejpam-3868	257	88	φ̄	φ̄	PROPN
ejpam-3868	257	89	α	α	PROPN
ejpam-3868	257	90	∧	∧	PROPN
ejpam-3868	257	91	γ	γ	X
ejpam-3868	257	92	+	+	X
ejpam-3868	257	93	β	β	X
ejpam-3868	257	94	∧	∧	NOUN
ejpam-3868	257	95	β′	β′	PUNCT
ejpam-3868	258	1	+	+	CCONJ
ejpam-3868	258	2	γ	γ	PROPN
ejpam-3868	258	3	∧	∧	PROPN
ejpam-3868	258	4	α′	α′	NUM
ejpam-3868	258	5	φ	φ	NUM
ejpam-3868	258	6	∧	∧	PROPN
ejpam-3868	258	7	α−	α−	ADP
ejpam-3868	258	8	(	(	PUNCT
ejpam-3868	258	9	α+	α+	X
ejpam-3868	258	10	α′	α′	NUM
ejpam-3868	258	11	)	)	PUNCT
ejpam-3868	258	12	∧	∧	PROPN
ejpam-3868	258	13	φ−	φ−	PROPN
ejpam-3868	258	14	β′	β′	NUM
ejpam-3868	258	15	∧	∧	PROPN
ejpam-3868	258	16	θ	θ	PROPN
ejpam-3868	258	17	φ	φ	NUM
ejpam-3868	258	18	∧	∧	PROPN
ejpam-3868	258	19	β	β	X
ejpam-3868	259	1	+	+	CCONJ
ejpam-3868	259	2	β′	β′	NUM
ejpam-3868	259	3	∧	∧	PROPN
ejpam-3868	259	4	φ̄	φ̄	PROPN
ejpam-3868	259	5	φ	φ	PROPN
ejpam-3868	259	6	∧	∧	PROPN
ejpam-3868	259	7	γ	γ	X
ejpam-3868	259	8	−	−	PROPN
ejpam-3868	259	9	(	(	PUNCT
ejpam-3868	259	10	α+	α+	X
ejpam-3868	259	11	α′	α′	NUM
ejpam-3868	259	12	)	)	PUNCT
ejpam-3868	259	13	∧	∧	NOUN
ejpam-3868	259	14	β′	β′	NUM
ejpam-3868	260	1	+	+	CCONJ
ejpam-3868	260	2	β′	β′	NUM
ejpam-3868	260	3	∧	∧	PROPN
ejpam-3868	260	4	α′	α′	VERB
ejpam-3868	260	5	−θ	−θ	ADJ
ejpam-3868	260	6	∧	∧	PROPN
ejpam-3868	260	7	α+	α+	PRON
ejpam-3868	260	8	φ̄	φ̄	NOUN
ejpam-3868	260	9	∧	∧	PROPN
ejpam-3868	260	10	φ−	φ−	PROPN
ejpam-3868	260	11	α′	α′	NUM
ejpam-3868	260	12	∧	∧	PROPN
ejpam-3868	260	13	θ	θ	PROPN
ejpam-3868	260	14	−θ	−θ	NOUN
ejpam-3868	260	15	∧	∧	PROPN
ejpam-3868	260	16	β	β	X
ejpam-3868	260	17	−	−	NOUN
ejpam-3868	260	18	φ̄	φ̄	NOUN
ejpam-3868	260	19	∧	∧	PROPN
ejpam-3868	260	20	(	(	PUNCT
ejpam-3868	260	21	α+	α+	X
ejpam-3868	260	22	α′	α′	NUM
ejpam-3868	260	23	)	)	PUNCT
ejpam-3868	261	1	+	+	CCONJ
ejpam-3868	261	2	α′	α′	NUM
ejpam-3868	261	3	∧	∧	PROPN
ejpam-3868	261	4	φ	φ	NUM
ejpam-3868	261	5	−θ	−θ	PROPN
ejpam-3868	261	6	∧	∧	PROPN
ejpam-3868	261	7	β	β	X
ejpam-3868	261	8	−	−	NOUN
ejpam-3868	261	9	φ̄	φ̄	NOUN
ejpam-3868	261	10	∧	∧	PROPN
ejpam-3868	261	11	(	(	PUNCT
ejpam-3868	261	12	α+	α+	X
ejpam-3868	261	13	α′	α′	NUM
ejpam-3868	261	14	)	)	PUNCT
ejpam-3868	262	1	+	+	CCONJ
ejpam-3868	262	2	α′	α′	NUM
ejpam-3868	262	3	∧	∧	PROPN
ejpam-3868	262	4	φ	φ	PRON
ejpam-3868	262	5			PROPN
ejpam-3868	262	6	(	(	PUNCT
ejpam-3868	262	7	75	75	NUM
ejpam-3868	262	8	)	)	PUNCT
ejpam-3868	262	9	p.	p.	NOUN
ejpam-3868	262	10	bracken	bracken	NOUN
ejpam-3868	262	11	/	/	SYM
ejpam-3868	262	12	eur	eur	PROPN
ejpam-3868	262	13	.	.	PUNCT
ejpam-3868	263	1	j.	j.	PROPN
ejpam-3868	263	2	pure	pure	PROPN
ejpam-3868	263	3	appl	appl	PROPN
ejpam-3868	263	4	.	.	PROPN
ejpam-3868	263	5	math	math	PROPN
ejpam-3868	263	6	,	,	PUNCT
ejpam-3868	263	7	13	13	NUM
ejpam-3868	263	8	(	(	PUNCT
ejpam-3868	263	9	4	4	NUM
ejpam-3868	263	10	)	)	PUNCT
ejpam-3868	263	11	(	(	PUNCT
ejpam-3868	263	12	2020	2020	NUM
ejpam-3868	263	13	)	)	PUNCT
ejpam-3868	263	14	,	,	PUNCT
ejpam-3868	263	15	1016	1016	NUM
ejpam-3868	263	16	-	-	SYM
ejpam-3868	263	17	1034	1034	NUM
ejpam-3868	263	18	1029	1029	NUM
ejpam-3868	263	19	it	it	PRON
ejpam-3868	263	20	is	be	AUX
ejpam-3868	263	21	required	require	VERB
ejpam-3868	263	22	that	that	SCONJ
ejpam-3868	263	23	the	the	DET
ejpam-3868	263	24	curvature	curvature	NOUN
ejpam-3868	263	25	have	have	VERB
ejpam-3868	263	26	the	the	DET
ejpam-3868	263	27	following	follow	VERB
ejpam-3868	263	28	structure	structure	NOUN
ejpam-3868	263	29	ω	ω	NOUN
ejpam-3868	263	30	=	=	PUNCT
ejpam-3868	263	31	0	0	ADP
ejpam-3868	263	32	b	b	X
ejpam-3868	263	33	0	0	NUM
ejpam-3868	263	34	0	0	NUM
ejpam-3868	263	35	0	0	NUM
ejpam-3868	263	36	b′	b′	NUM
ejpam-3868	264	1	0	0	NUM
ejpam-3868	264	2	0	0	SYM
ejpam-3868	264	3	0	0	NUM
ejpam-3868	264	4			PROPN
ejpam-3868	264	5	(	(	PUNCT
ejpam-3868	264	6	76	76	NUM
ejpam-3868	264	7	)	)	PUNCT
ejpam-3868	264	8	the	the	DET
ejpam-3868	264	9	requirement	requirement	NOUN
ejpam-3868	264	10	that	that	SCONJ
ejpam-3868	264	11	the	the	DET
ejpam-3868	264	12	lower	low	ADJ
ejpam-3868	264	13	left	left	ADJ
ejpam-3868	264	14	entries	entry	NOUN
ejpam-3868	264	15	vanish	vanish	VERB
ejpam-3868	264	16	gives	give	VERB
ejpam-3868	264	17	rise	rise	NOUN
ejpam-3868	264	18	to	to	ADP
ejpam-3868	264	19	the	the	DET
ejpam-3868	264	20	following	follow	VERB
ejpam-3868	264	21	three	three	NUM
ejpam-3868	264	22	equations	equation	NOUN
ejpam-3868	264	23	dφ+φ∧(2α∧α′)−β′∧θ	dφ+φ∧(2α∧α′)−β′∧θ	NOUN
ejpam-3868	264	24	=	=	NOUN
ejpam-3868	264	25	0	0	NUM
ejpam-3868	264	26	,	,	PUNCT
ejpam-3868	264	27	dφ̄+(α+2α′)∧φ̄+β∧θ	dφ̄+(α+2α′)∧φ̄+β∧θ	ADV
ejpam-3868	264	28	=	=	SYM
ejpam-3868	264	29	0	0	NUM
ejpam-3868	264	30	,	,	PUNCT
ejpam-3868	264	31	dθ−(α−α′)∧θ+φ∧φ̄	dθ−(α−α′)∧θ+φ∧φ̄	NOUN
ejpam-3868	264	32	=	=	SYM
ejpam-3868	264	33	0	0	X
ejpam-3868	264	34	.	.	PUNCT
ejpam-3868	265	1	(	(	PUNCT
ejpam-3868	265	2	77	77	X
ejpam-3868	265	3	)	)	PUNCT
ejpam-3868	265	4	these	these	PRON
ejpam-3868	265	5	may	may	AUX
ejpam-3868	265	6	be	be	AUX
ejpam-3868	265	7	referred	refer	VERB
ejpam-3868	265	8	to	to	ADP
ejpam-3868	265	9	as	as	ADP
ejpam-3868	265	10	the	the	DET
ejpam-3868	265	11	torsion	torsion	NOUN
ejpam-3868	265	12	equations	equation	NOUN
ejpam-3868	265	13	.	.	PUNCT
ejpam-3868	266	1	the	the	DET
ejpam-3868	266	2	diagonal	diagonal	ADJ
ejpam-3868	266	3	elements	element	NOUN
ejpam-3868	266	4	of	of	ADP
ejpam-3868	266	5	the	the	DET
ejpam-3868	266	6	curvature	curvature	NOUN
ejpam-3868	266	7	ω	ω	PROPN
ejpam-3868	266	8	yield	yield	NOUN
ejpam-3868	266	9	the	the	DET
ejpam-3868	266	10	constraints	constraint	NOUN
ejpam-3868	266	11	dφ+	dφ+	NOUN
ejpam-3868	266	12	β	β	X
ejpam-3868	266	13	∧φ−	∧φ−	VERB
ejpam-3868	266	14	γ	γ	PROPN
ejpam-3868	266	15	∧	∧	PROPN
ejpam-3868	266	16	θ	θ	PROPN
ejpam-3868	266	17	=	=	SYM
ejpam-3868	266	18	0	0	NUM
ejpam-3868	266	19	,	,	PUNCT
ejpam-3868	266	20	dα′−	dα′−	VERB
ejpam-3868	266	21	θ∧	θ∧	PROPN
ejpam-3868	266	22	γ+	γ+	PUNCT
ejpam-3868	266	23	φ̄∧	φ̄∧	PROPN
ejpam-3868	266	24	β′	β′	NUM
ejpam-3868	267	1	=	=	SYM
ejpam-3868	267	2	0	0	NUM
ejpam-3868	267	3	,	,	PUNCT
ejpam-3868	267	4	−d(α+α′	−d(α+α′	NOUN
ejpam-3868	267	5	)	)	PUNCT
ejpam-3868	268	1	+	+	NOUN
ejpam-3868	268	2	φ∧	φ∧	NOUN
ejpam-3868	268	3	β+	β+	PUNCT
ejpam-3868	268	4	β′	β′	NUM
ejpam-3868	268	5	∧φ	∧φ	PROPN
ejpam-3868	268	6	=	=	SYM
ejpam-3868	268	7	0	0	NUM
ejpam-3868	268	8	,	,	PUNCT
ejpam-3868	268	9	(	(	PUNCT
ejpam-3868	268	10	78	78	X
ejpam-3868	268	11	)	)	PUNCT
ejpam-3868	268	12	adding	add	VERB
ejpam-3868	268	13	together	together	ADV
ejpam-3868	268	14	the	the	DET
ejpam-3868	268	15	first	first	ADJ
ejpam-3868	268	16	two	two	NUM
ejpam-3868	268	17	in	in	ADP
ejpam-3868	268	18	(	(	PUNCT
ejpam-3868	268	19	78	78	NUM
ejpam-3868	268	20	)	)	PUNCT
ejpam-3868	268	21	the	the	DET
ejpam-3868	268	22	negative	negative	NOUN
ejpam-3868	268	23	of	of	ADP
ejpam-3868	268	24	the	the	DET
ejpam-3868	268	25	third	third	ADJ
ejpam-3868	268	26	one	one	NUM
ejpam-3868	268	27	results	result	NOUN
ejpam-3868	268	28	and	and	CCONJ
ejpam-3868	268	29	everything	everything	PRON
ejpam-3868	268	30	is	be	AUX
ejpam-3868	268	31	consistent	consistent	ADJ
ejpam-3868	268	32	.	.	PUNCT
ejpam-3868	269	1	as	as	ADV
ejpam-3868	269	2	well	well	ADV
ejpam-3868	269	3	,	,	PUNCT
ejpam-3868	269	4	d(α−	d(α−	VERB
ejpam-3868	269	5	α′	α′	NUM
ejpam-3868	269	6	)	)	PUNCT
ejpam-3868	270	1	+	+	CCONJ
ejpam-3868	270	2	β	β	X
ejpam-3868	270	3	∧	∧	PROPN
ejpam-3868	270	4	φ−	φ−	PROPN
ejpam-3868	270	5	φ̄	φ̄	PROPN
ejpam-3868	270	6	∧	∧	PROPN
ejpam-3868	270	7	β′	β′	NUM
ejpam-3868	271	1	=	=	NOUN
ejpam-3868	271	2	2γ	2γ	NUM
ejpam-3868	271	3	∧	∧	PROPN
ejpam-3868	271	4	θ	θ	PROPN
ejpam-3868	271	5	.	.	PUNCT
ejpam-3868	272	1	(	(	PUNCT
ejpam-3868	272	2	79	79	NUM
ejpam-3868	272	3	)	)	PUNCT
ejpam-3868	272	4	it	it	PRON
ejpam-3868	272	5	follows	follow	VERB
ejpam-3868	272	6	from	from	ADP
ejpam-3868	272	7	their	their	PRON
ejpam-3868	272	8	basic	basic	ADJ
ejpam-3868	272	9	definitions	definition	NOUN
ejpam-3868	272	10	that	that	SCONJ
ejpam-3868	272	11	the	the	DET
ejpam-3868	272	12	exterior	exterior	ADJ
ejpam-3868	272	13	derivatives	derivative	NOUN
ejpam-3868	272	14	of	of	ADP
ejpam-3868	272	15	the	the	DET
ejpam-3868	272	16	basic	basic	ADJ
ejpam-3868	272	17	one	one	NUM
ejpam-3868	272	18	-	-	PUNCT
ejpam-3868	272	19	forms	form	NOUN
ejpam-3868	272	20	can	can	AUX
ejpam-3868	272	21	be	be	AUX
ejpam-3868	272	22	expressed	express	VERB
ejpam-3868	272	23	as	as	ADP
ejpam-3868	272	24	dφ	dφ	ADP
ejpam-3868	272	25	=	=	SYM
ejpam-3868	272	26	ψ	ψ	NOUN
ejpam-3868	272	27	∧	∧	PROPN
ejpam-3868	272	28	θ	θ	PROPN
ejpam-3868	272	29	,	,	PUNCT
ejpam-3868	272	30	dφ̄	dφ̄	NOUN
ejpam-3868	272	31	=	=	SYM
ejpam-3868	272	32	−ψ̄	−ψ̄	NOUN
ejpam-3868	272	33	∧	∧	PROPN
ejpam-3868	272	34	θ	θ	PROPN
ejpam-3868	272	35	,	,	PUNCT
ejpam-3868	272	36	dθ	dθ	PROPN
ejpam-3868	272	37	=	=	PROPN
ejpam-3868	272	38	−φ	−φ	NOUN
ejpam-3868	272	39	∧	∧	PROPN
ejpam-3868	272	40	φ̄+	φ̄+	PUNCT
ejpam-3868	272	41	χ	χ	PROPN
ejpam-3868	272	42	∧	∧	PROPN
ejpam-3868	272	43	θ	θ	PROPN
ejpam-3868	272	44	.	.	PUNCT
ejpam-3868	273	1	(	(	PUNCT
ejpam-3868	273	2	80	80	NUM
ejpam-3868	273	3	)	)	PUNCT
ejpam-3868	273	4	the	the	DET
ejpam-3868	273	5	one	one	NUM
ejpam-3868	273	6	-	-	PUNCT
ejpam-3868	273	7	forms	form	NOUN
ejpam-3868	273	8	ψ	ψ	NOUN
ejpam-3868	273	9	,	,	PUNCT
ejpam-3868	273	10	ψ̄	ψ̄	PUNCT
ejpam-3868	273	11	and	and	CCONJ
ejpam-3868	273	12	χ	χ	NOUN
ejpam-3868	273	13	are	be	AUX
ejpam-3868	273	14	linear	linear	ADJ
ejpam-3868	273	15	combinations	combination	NOUN
ejpam-3868	273	16	of	of	ADP
ejpam-3868	273	17	φ	φ	PROPN
ejpam-3868	273	18	and	and	CCONJ
ejpam-3868	273	19	φ̄.	φ̄.	NOUN
ejpam-3868	273	20	substituting	substitute	VERB
ejpam-3868	273	21	these	these	DET
ejpam-3868	273	22	derivatives	derivative	NOUN
ejpam-3868	273	23	into	into	ADP
ejpam-3868	273	24	the	the	DET
ejpam-3868	273	25	torsion	torsion	NOUN
ejpam-3868	273	26	equations	equation	NOUN
ejpam-3868	273	27	,	,	PUNCT
ejpam-3868	273	28	the	the	DET
ejpam-3868	273	29	following	follow	VERB
ejpam-3868	273	30	are	be	AUX
ejpam-3868	273	31	obtained	obtain	VERB
ejpam-3868	273	32	(	(	PUNCT
ejpam-3868	273	33	2α+α′)∧φ+(β′−ψ)∧θ	2α+α′)∧φ+(β′−ψ)∧θ	NUM
ejpam-3868	273	34	=	=	SYM
ejpam-3868	273	35	0	0	NUM
ejpam-3868	273	36	,	,	PUNCT
ejpam-3868	273	37	(	(	PUNCT
ejpam-3868	273	38	α+2α′)∧	α+2α′)∧	NUM
ejpam-3868	273	39	φ̄+(β−	φ̄+(β−	VERB
ejpam-3868	273	40	φ̄)∧θ	φ̄)∧θ	NOUN
ejpam-3868	273	41	=	=	SYM
ejpam-3868	273	42	0	0	PROPN
ejpam-3868	273	43	,	,	PUNCT
ejpam-3868	273	44	(	(	PUNCT
ejpam-3868	273	45	χ−(α−α′))∧θ	χ−(α−α′))∧θ	X
ejpam-3868	273	46	=	=	NOUN
ejpam-3868	273	47	0	0	X
ejpam-3868	273	48	.	.	PUNCT
ejpam-3868	274	1	(	(	PUNCT
ejpam-3868	274	2	81	81	NUM
ejpam-3868	274	3	)	)	PUNCT
ejpam-3868	274	4	from	from	ADP
ejpam-3868	274	5	the	the	DET
ejpam-3868	274	6	first	first	ADJ
ejpam-3868	274	7	two	two	NUM
ejpam-3868	274	8	of	of	ADP
ejpam-3868	274	9	these	these	PRON
ejpam-3868	274	10	,	,	PUNCT
ejpam-3868	274	11	2α	2α	NOUN
ejpam-3868	274	12	+	+	CCONJ
ejpam-3868	274	13	α′	α′	NUM
ejpam-3868	274	14	can	can	AUX
ejpam-3868	274	15	be	be	AUX
ejpam-3868	274	16	taken	take	VERB
ejpam-3868	274	17	proportional	proportional	ADJ
ejpam-3868	274	18	to	to	ADP
ejpam-3868	274	19	φ	φ	NUM
ejpam-3868	274	20	,	,	PUNCT
ejpam-3868	274	21	β′	β′	NUM
ejpam-3868	274	22	−	−	PROPN
ejpam-3868	274	23	ψ	ψ	ADP
ejpam-3868	274	24	proportional	proportional	ADJ
ejpam-3868	274	25	to	to	ADP
ejpam-3868	274	26	θ	θ	PROPN
ejpam-3868	274	27	,	,	PUNCT
ejpam-3868	274	28	α+	α+	PRON
ejpam-3868	274	29	2α′	2α′	NUM
ejpam-3868	274	30	proportional	proportional	NOUN
ejpam-3868	274	31	to	to	ADP
ejpam-3868	274	32	φ̄	φ̄	PROPN
ejpam-3868	274	33	and	and	CCONJ
ejpam-3868	274	34	β	β	ADJ
ejpam-3868	274	35	−	−	PROPN
ejpam-3868	274	36	ψ̄	ψ̄	NOUN
ejpam-3868	274	37	proportional	proportional	ADJ
ejpam-3868	274	38	to	to	ADP
ejpam-3868	274	39	θ	θ	PROPN
ejpam-3868	274	40	,	,	PUNCT
ejpam-3868	274	41	hence	hence	ADV
ejpam-3868	274	42	2α+	2α+	NUM
ejpam-3868	274	43	α′	α′	NUM
ejpam-3868	274	44	=	=	PUNCT
ejpam-3868	274	45	c1φ	c1φ	PROPN
ejpam-3868	274	46	,	,	PUNCT
ejpam-3868	274	47	α+	α+	PRON
ejpam-3868	274	48	2α′	2α′	NUM
ejpam-3868	274	49	=	=	SYM
ejpam-3868	274	50	c2φ̄.	c2φ̄.	PROPN
ejpam-3868	274	51	(	(	PUNCT
ejpam-3868	274	52	82	82	NUM
ejpam-3868	274	53	)	)	PUNCT
ejpam-3868	274	54	taking	take	VERB
ejpam-3868	274	55	the	the	DET
ejpam-3868	274	56	constants	constant	NOUN
ejpam-3868	274	57	c1	c1	NOUN
ejpam-3868	274	58	=	=	PROPN
ejpam-3868	274	59	c2	c2	PROPN
ejpam-3868	274	60	=	=	SYM
ejpam-3868	274	61	1	1	NUM
ejpam-3868	274	62	,	,	PUNCT
ejpam-3868	274	63	these	these	PRON
ejpam-3868	274	64	imply	imply	VERB
ejpam-3868	274	65	that	that	SCONJ
ejpam-3868	274	66	α	α	PRON
ejpam-3868	274	67	=	=	NOUN
ejpam-3868	274	68	2	2	NUM
ejpam-3868	274	69	3	3	NUM
ejpam-3868	274	70	φ−	φ−	PROPN
ejpam-3868	274	71	1	1	NUM
ejpam-3868	274	72	3	3	NUM
ejpam-3868	274	73	φ̄	φ̄	NOUN
ejpam-3868	274	74	,	,	PUNCT
ejpam-3868	274	75	α′	α′	ADJ
ejpam-3868	274	76	=	=	SYM
ejpam-3868	274	77	−1	−1	NOUN
ejpam-3868	274	78	3	3	NUM
ejpam-3868	274	79	φ+	φ+	NOUN
ejpam-3868	274	80	2	2	NUM
ejpam-3868	274	81	3	3	NUM
ejpam-3868	274	82	φ̄.	φ̄.	NUM
ejpam-3868	274	83	(	(	PUNCT
ejpam-3868	274	84	83	83	NUM
ejpam-3868	274	85	)	)	PUNCT
ejpam-3868	274	86	the	the	DET
ejpam-3868	274	87	third	third	ADJ
ejpam-3868	274	88	constraint	constraint	NOUN
ejpam-3868	274	89	in	in	ADP
ejpam-3868	274	90	(	(	PUNCT
ejpam-3868	274	91	81	81	NUM
ejpam-3868	274	92	)	)	PUNCT
ejpam-3868	274	93	can	can	AUX
ejpam-3868	274	94	be	be	AUX
ejpam-3868	274	95	satisfied	satisfy	VERB
ejpam-3868	274	96	by	by	ADP
ejpam-3868	274	97	taking	take	VERB
ejpam-3868	274	98	χ−	χ−	PROPN
ejpam-3868	274	99	(	(	PUNCT
ejpam-3868	274	100	α−	α−	ADP
ejpam-3868	274	101	α′	α′	NUM
ejpam-3868	274	102	)	)	PUNCT
ejpam-3868	275	1	=	=	SYM
ejpam-3868	275	2	0	0	NUM
ejpam-3868	275	3	independent	independent	NOUN
ejpam-3868	275	4	of	of	ADP
ejpam-3868	275	5	θ	θ	PROPN
ejpam-3868	275	6	as	as	ADP
ejpam-3868	275	7	a	a	DET
ejpam-3868	275	8	gauge	gauge	ADJ
ejpam-3868	275	9	condition	condition	NOUN
ejpam-3868	275	10	so	so	SCONJ
ejpam-3868	275	11	χ	χ	PROPN
ejpam-3868	275	12	=	=	X
ejpam-3868	276	1	α−	α−	ADP
ejpam-3868	276	2	α′	α′	NUM
ejpam-3868	276	3	=	=	SYM
ejpam-3868	276	4	φ−	φ−	PROPN
ejpam-3868	276	5	φ̄.	φ̄.	NUM
ejpam-3868	276	6	(	(	PUNCT
ejpam-3868	276	7	84	84	NUM
ejpam-3868	276	8	)	)	PUNCT
ejpam-3868	276	9	using	use	VERB
ejpam-3868	276	10	(	(	PUNCT
ejpam-3868	276	11	80	80	NUM
ejpam-3868	276	12	)	)	PUNCT
ejpam-3868	276	13	,	,	PUNCT
ejpam-3868	276	14	it	it	PRON
ejpam-3868	276	15	is	be	AUX
ejpam-3868	276	16	found	find	VERB
ejpam-3868	276	17	that	that	SCONJ
ejpam-3868	276	18	this	this	PRON
ejpam-3868	276	19	implies	imply	VERB
ejpam-3868	276	20	that	that	SCONJ
ejpam-3868	276	21	dχ	dχ	NOUN
ejpam-3868	276	22	=	=	PUNCT
ejpam-3868	276	23	d(α−	d(α−	NOUN
ejpam-3868	276	24	α′	α′	NUM
ejpam-3868	276	25	)	)	PUNCT
ejpam-3868	276	26	=	=	PUNCT
ejpam-3868	276	27	dφ−	dφ−	PROPN
ejpam-3868	276	28	dφ̄	dφ̄	NOUN
ejpam-3868	276	29	=	=	SYM
ejpam-3868	276	30	(	(	PUNCT
ejpam-3868	276	31	ψ	ψ	X
ejpam-3868	276	32	−	−	NOUN
ejpam-3868	276	33	ψ̄	ψ̄	NOUN
ejpam-3868	276	34	)	)	PUNCT
ejpam-3868	276	35	∧	∧	PROPN
ejpam-3868	276	36	θ	θ	PROPN
ejpam-3868	276	37	.	.	PUNCT
ejpam-3868	276	38	(	(	PUNCT
ejpam-3868	276	39	85	85	NUM
ejpam-3868	276	40	)	)	PUNCT
ejpam-3868	276	41	it	it	PRON
ejpam-3868	276	42	makes	make	VERB
ejpam-3868	276	43	sense	sense	NOUN
ejpam-3868	276	44	to	to	PART
ejpam-3868	276	45	take	take	VERB
ejpam-3868	276	46	β′	β′	NOUN
ejpam-3868	276	47	=	=	SYM
ejpam-3868	276	48	ψ	ψ	PROPN
ejpam-3868	276	49	and	and	CCONJ
ejpam-3868	276	50	β	β	X
ejpam-3868	276	51	=	=	NOUN
ejpam-3868	276	52	ψ̄	ψ̄	NOUN
ejpam-3868	276	53	in	in	ADP
ejpam-3868	276	54	which	which	DET
ejpam-3868	276	55	case	case	NOUN
ejpam-3868	276	56	,	,	PUNCT
ejpam-3868	276	57	the	the	DET
ejpam-3868	276	58	other	other	ADJ
ejpam-3868	276	59	two	two	NUM
ejpam-3868	276	60	constraints	constraint	NOUN
ejpam-3868	276	61	are	be	AUX
ejpam-3868	276	62	satisfied	satisfied	ADJ
ejpam-3868	276	63	.	.	PUNCT
ejpam-3868	277	1	p.	p.	NOUN
ejpam-3868	277	2	bracken	bracken	NOUN
ejpam-3868	277	3	/	/	SYM
ejpam-3868	277	4	eur	eur	PROPN
ejpam-3868	277	5	.	.	PUNCT
ejpam-3868	278	1	j.	j.	PROPN
ejpam-3868	278	2	pure	pure	PROPN
ejpam-3868	278	3	appl	appl	PROPN
ejpam-3868	278	4	.	.	PROPN
ejpam-3868	278	5	math	math	PROPN
ejpam-3868	278	6	,	,	PUNCT
ejpam-3868	278	7	13	13	NUM
ejpam-3868	278	8	(	(	PUNCT
ejpam-3868	278	9	4	4	NUM
ejpam-3868	278	10	)	)	PUNCT
ejpam-3868	278	11	(	(	PUNCT
ejpam-3868	278	12	2020	2020	NUM
ejpam-3868	278	13	)	)	PUNCT
ejpam-3868	278	14	,	,	PUNCT
ejpam-3868	278	15	1016	1016	NUM
ejpam-3868	278	16	-	-	SYM
ejpam-3868	278	17	1034	1034	NUM
ejpam-3868	278	18	1030	1030	NUM
ejpam-3868	278	19	returning	return	VERB
ejpam-3868	278	20	to	to	ADP
ejpam-3868	278	21	ω	ω	PROPN
ejpam-3868	278	22	in	in	ADP
ejpam-3868	278	23	(	(	PUNCT
ejpam-3868	278	24	74	74	NUM
ejpam-3868	278	25	)	)	PUNCT
ejpam-3868	278	26	the	the	DET
ejpam-3868	278	27	components	component	NOUN
ejpam-3868	278	28	b	b	PROPN
ejpam-3868	278	29	and	and	CCONJ
ejpam-3868	278	30	b′	b′	NUM
ejpam-3868	278	31	are	be	AUX
ejpam-3868	278	32	given	give	VERB
ejpam-3868	278	33	as	as	ADP
ejpam-3868	278	34	b	b	NOUN
ejpam-3868	278	35	=	=	NOUN
ejpam-3868	278	36	dβ	dβ	PROPN
ejpam-3868	278	37	+	+	CCONJ
ejpam-3868	278	38	(	(	PUNCT
ejpam-3868	278	39	2α+	2α+	NUM
ejpam-3868	278	40	α′	α′	NUM
ejpam-3868	278	41	)	)	PUNCT
ejpam-3868	278	42	∧	∧	PROPN
ejpam-3868	278	43	β	β	X
ejpam-3868	278	44	+	+	CCONJ
ejpam-3868	278	45	γ	γ	PROPN
ejpam-3868	278	46	∧	∧	PROPN
ejpam-3868	278	47	φ̄	φ̄	PROPN
ejpam-3868	278	48	,	,	PUNCT
ejpam-3868	278	49	b′	b′	NOUN
ejpam-3868	278	50	=	=	SYM
ejpam-3868	278	51	dβ′	dβ′	NOUN
ejpam-3868	278	52	−	−	PROPN
ejpam-3868	279	1	(	(	PUNCT
ejpam-3868	279	2	α−	α−	ADP
ejpam-3868	279	3	2α′	2α′	NUM
ejpam-3868	279	4	)	)	PUNCT
ejpam-3868	279	5	∧	∧	NOUN
ejpam-3868	279	6	β′	β′	NUM
ejpam-3868	280	1	+	+	CCONJ
ejpam-3868	280	2	φ	φ	PROPN
ejpam-3868	280	3	∧	∧	PROPN
ejpam-3868	280	4	γ	γ	X
ejpam-3868	280	5	.	.	PROPN
ejpam-3868	280	6	(	(	PUNCT
ejpam-3868	280	7	86	86	NUM
ejpam-3868	280	8	)	)	PUNCT
ejpam-3868	280	9	upon	upon	SCONJ
ejpam-3868	280	10	differentiating	differentiate	VERB
ejpam-3868	280	11	the	the	DET
ejpam-3868	280	12	equation	equation	NOUN
ejpam-3868	280	13	dφ̄+	dφ̄+	NOUN
ejpam-3868	280	14	(	(	PUNCT
ejpam-3868	280	15	α+	α+	X
ejpam-3868	280	16	2α′	2α′	NUM
ejpam-3868	280	17	)	)	PUNCT
ejpam-3868	280	18	∧	∧	NOUN
ejpam-3868	280	19	φ̄+	φ̄+	PUNCT
ejpam-3868	280	20	β	β	X
ejpam-3868	280	21	∧	∧	NOUN
ejpam-3868	280	22	θ	θ	NOUN
ejpam-3868	280	23	=	=	SYM
ejpam-3868	280	24	0	0	NUM
ejpam-3868	280	25	it	it	PRON
ejpam-3868	280	26	follows	follow	VERB
ejpam-3868	280	27	that	that	SCONJ
ejpam-3868	280	28	d(β	d(β	PROPN
ejpam-3868	280	29	∧	∧	PROPN
ejpam-3868	280	30	θ	θ	PROPN
ejpam-3868	280	31	)	)	PUNCT
ejpam-3868	280	32	+	+	CCONJ
ejpam-3868	280	33	d((α+	d((α+	DET
ejpam-3868	280	34	2α′	2α′	NUM
ejpam-3868	280	35	)	)	PUNCT
ejpam-3868	280	36	∧	∧	PROPN
ejpam-3868	280	37	φ̄	φ̄	NOUN
ejpam-3868	280	38	)	)	PUNCT
ejpam-3868	280	39	=	=	SYM
ejpam-3868	280	40	0	0	NUM
ejpam-3868	280	41	,	,	PUNCT
ejpam-3868	280	42	dβ	dβ	ADJ
ejpam-3868	280	43	∧	∧	PROPN
ejpam-3868	280	44	θ	θ	PROPN
ejpam-3868	280	45	−	−	NOUN
ejpam-3868	280	46	β	β	X
ejpam-3868	280	47	∧	∧	PROPN
ejpam-3868	280	48	dθ	dθ	NOUN
ejpam-3868	280	49	+	+	CCONJ
ejpam-3868	280	50	d(α+	d(α+	NOUN
ejpam-3868	280	51	2α′	2α′	NUM
ejpam-3868	280	52	)	)	PUNCT
ejpam-3868	280	53	∧	∧	NOUN
ejpam-3868	280	54	φ̄−	φ̄−	ADV
ejpam-3868	280	55	(	(	PUNCT
ejpam-3868	280	56	α−	α−	ADP
ejpam-3868	280	57	2α′	2α′	NUM
ejpam-3868	280	58	)	)	PUNCT
ejpam-3868	280	59	∧	∧	NOUN
ejpam-3868	280	60	dφ̄	dφ̄	NOUN
ejpam-3868	280	61	=	=	SYM
ejpam-3868	280	62	0	0	NUM
ejpam-3868	280	63	,	,	PUNCT
ejpam-3868	280	64	dβ	dβ	ADJ
ejpam-3868	280	65	∧	∧	PROPN
ejpam-3868	280	66	θ	θ	PROPN
ejpam-3868	280	67	−	−	NOUN
ejpam-3868	280	68	β	β	X
ejpam-3868	280	69	∧	∧	PROPN
ejpam-3868	280	70	dθ	dθ	PROPN
ejpam-3868	280	71	+	+	X
ejpam-3868	280	72	(	(	PUNCT
ejpam-3868	280	73	−β	−β	PROPN
ejpam-3868	280	74	∧	∧	PROPN
ejpam-3868	280	75	φ+	φ+	PUNCT
ejpam-3868	280	76	γ	γ	X
ejpam-3868	280	77	∧	∧	PROPN
ejpam-3868	280	78	θ	θ	PROPN
ejpam-3868	280	79	+	+	CCONJ
ejpam-3868	280	80	2β′	2β′	NUM
ejpam-3868	280	81	∧	∧	NOUN
ejpam-3868	280	82	φ̄−	φ̄−	ADV
ejpam-3868	280	83	2γ	2γ	X
ejpam-3868	280	84	∧	∧	PROPN
ejpam-3868	280	85	θ	θ	NOUN
ejpam-3868	280	86	)	)	PUNCT
ejpam-3868	280	87	∧	∧	NOUN
ejpam-3868	280	88	φ̄−	φ̄−	ADV
ejpam-3868	280	89	(	(	PUNCT
ejpam-3868	280	90	α+	α+	X
ejpam-3868	280	91	2α′	2α′	NUM
ejpam-3868	280	92	)	)	PUNCT
ejpam-3868	280	93	∧	∧	NOUN
ejpam-3868	280	94	dφ̄	dφ̄	NOUN
ejpam-3868	280	95	=	=	SYM
ejpam-3868	280	96	0	0	NUM
ejpam-3868	280	97	,	,	PUNCT
ejpam-3868	280	98	dβ	dβ	ADJ
ejpam-3868	280	99	∧	∧	PROPN
ejpam-3868	280	100	θ	θ	PROPN
ejpam-3868	280	101	−	−	NOUN
ejpam-3868	280	102	β	β	X
ejpam-3868	280	103	∧	∧	PROPN
ejpam-3868	280	104	dθ	dθ	PROPN
ejpam-3868	280	105	−	−	PROPN
ejpam-3868	280	106	β	β	X
ejpam-3868	280	107	∧	∧	PROPN
ejpam-3868	280	108	φ	φ	NUM
ejpam-3868	280	109	∧	∧	PROPN
ejpam-3868	280	110	φ̄−	φ̄−	ADV
ejpam-3868	280	111	γ	γ	X
ejpam-3868	280	112	∧	∧	PROPN
ejpam-3868	280	113	θ	θ	PROPN
ejpam-3868	280	114	∧	∧	NOUN
ejpam-3868	280	115	φ̄−	φ̄−	ADV
ejpam-3868	280	116	(	(	PUNCT
ejpam-3868	280	117	α+	α+	X
ejpam-3868	280	118	2α′	2α′	NUM
ejpam-3868	280	119	)	)	PUNCT
ejpam-3868	280	120	∧	∧	NOUN
ejpam-3868	280	121	dφ̄	dφ̄	NOUN
ejpam-3868	280	122	=	=	SYM
ejpam-3868	280	123	0	0	NUM
ejpam-3868	280	124	,	,	PUNCT
ejpam-3868	280	125	(	(	PUNCT
ejpam-3868	280	126	87	87	NUM
ejpam-3868	280	127	)	)	PUNCT
ejpam-3868	280	128	(	(	PUNCT
ejpam-3868	280	129	dβ	dβ	ADP
ejpam-3868	280	130	+	+	CCONJ
ejpam-3868	280	131	(	(	PUNCT
ejpam-3868	280	132	2α+	2α+	NUM
ejpam-3868	280	133	α′	α′	NUM
ejpam-3868	280	134	)	)	PUNCT
ejpam-3868	280	135	∧	∧	PROPN
ejpam-3868	280	136	β	β	X
ejpam-3868	280	137	+	+	CCONJ
ejpam-3868	280	138	γ	γ	PROPN
ejpam-3868	280	139	∧	∧	PROPN
ejpam-3868	280	140	φ̄	φ̄	PROPN
ejpam-3868	280	141	)	)	PUNCT
ejpam-3868	280	142	∧	∧	PROPN
ejpam-3868	280	143	θ	θ	NOUN
ejpam-3868	280	144	=	=	SYM
ejpam-3868	280	145	0	0	X
ejpam-3868	280	146	.	.	PUNCT
ejpam-3868	281	1	the	the	DET
ejpam-3868	281	2	expression	expression	NOUN
ejpam-3868	281	3	which	which	PRON
ejpam-3868	281	4	remains	remain	VERB
ejpam-3868	281	5	inside	inside	ADP
ejpam-3868	281	6	the	the	DET
ejpam-3868	281	7	brackets	bracket	NOUN
ejpam-3868	281	8	is	be	AUX
ejpam-3868	281	9	exactly	exactly	ADV
ejpam-3868	281	10	b	b	NUM
ejpam-3868	281	11	,	,	PUNCT
ejpam-3868	281	12	so	so	SCONJ
ejpam-3868	281	13	this	this	DET
ejpam-3868	281	14	result	result	NOUN
ejpam-3868	281	15	can	can	AUX
ejpam-3868	281	16	be	be	AUX
ejpam-3868	281	17	written	write	VERB
ejpam-3868	281	18	more	more	ADV
ejpam-3868	281	19	concisely	concisely	ADV
ejpam-3868	281	20	as	as	ADP
ejpam-3868	281	21	b	b	PROPN
ejpam-3868	281	22	∧	∧	PROPN
ejpam-3868	281	23	θ	θ	NOUN
ejpam-3868	281	24	=	=	SYM
ejpam-3868	282	1	0	0	PROPN
ejpam-3868	282	2	.	.	PUNCT
ejpam-3868	283	1	(	(	PUNCT
ejpam-3868	283	2	88	88	NUM
ejpam-3868	283	3	)	)	PUNCT
ejpam-3868	283	4	differentiate	differentiate	VERB
ejpam-3868	283	5	exteriorly	exteriorly	ADV
ejpam-3868	283	6	dφ	dφ	ADP
ejpam-3868	283	7	=	=	PUNCT
ejpam-3868	283	8	β′	β′	NUM
ejpam-3868	283	9	∧	∧	PROPN
ejpam-3868	283	10	θ	θ	PROPN
ejpam-3868	284	1	−	−	PROPN
ejpam-3868	285	1	φ	φ	PROPN
ejpam-3868	285	2	∧	∧	PROPN
ejpam-3868	285	3	(	(	PUNCT
ejpam-3868	285	4	2α+	2α+	NUM
ejpam-3868	285	5	α	α	NOUN
ejpam-3868	285	6	)	)	PUNCT
ejpam-3868	285	7	to	to	PART
ejpam-3868	285	8	obtain	obtain	VERB
ejpam-3868	285	9	dβ′	dβ′	ADJ
ejpam-3868	285	10	∧	∧	PROPN
ejpam-3868	285	11	θ	θ	PROPN
ejpam-3868	285	12	−	−	PROPN
ejpam-3868	285	13	β′	β′	NUM
ejpam-3868	286	1	∧	∧	PROPN
ejpam-3868	286	2	θ	θ	NOUN
ejpam-3868	286	3	−	−	PROPN
ejpam-3868	286	4	dφ	dφ	ADP
ejpam-3868	286	5	∧	∧	PROPN
ejpam-3868	286	6	(	(	PUNCT
ejpam-3868	286	7	2α+	2α+	NUM
ejpam-3868	286	8	α′	α′	NUM
ejpam-3868	286	9	)	)	PUNCT
ejpam-3868	287	1	+	+	CCONJ
ejpam-3868	287	2	φ	φ	PROPN
ejpam-3868	287	3	∧	∧	PROPN
ejpam-3868	287	4	(	(	PUNCT
ejpam-3868	287	5	−2β	−2β	PROPN
ejpam-3868	287	6	∧	∧	PROPN
ejpam-3868	287	7	φ+	φ+	PUNCT
ejpam-3868	287	8	2γ	2γ	X
ejpam-3868	287	9	∧	∧	PROPN
ejpam-3868	287	10	θ	θ	PROPN
ejpam-3868	287	11	+	+	CCONJ
ejpam-3868	287	12	θ	θ	PROPN
ejpam-3868	287	13	∧	∧	NOUN
ejpam-3868	287	14	γ	γ	NOUN
ejpam-3868	287	15	−	−	NOUN
ejpam-3868	287	16	φ̄	φ̄	NOUN
ejpam-3868	287	17	∧	∧	PROPN
ejpam-3868	287	18	β′	β′	NUM
ejpam-3868	287	19	)	)	PUNCT
ejpam-3868	287	20	=	=	SYM
ejpam-3868	288	1	0	0	X
ejpam-3868	288	2	.	.	X
ejpam-3868	288	3	dβ′	dβ′	VERB
ejpam-3868	288	4	∧	∧	NOUN
ejpam-3868	288	5	θ	θ	PROPN
ejpam-3868	288	6	−	−	PROPN
ejpam-3868	288	7	β′	β′	PUNCT
ejpam-3868	289	1	∧	∧	PROPN
ejpam-3868	289	2	(	(	PUNCT
ejpam-3868	289	3	dθ	dθ	PROPN
ejpam-3868	289	4	+	+	PROPN
ejpam-3868	289	5	θ	θ	PROPN
ejpam-3868	289	6	∧	∧	NOUN
ejpam-3868	289	7	(	(	PUNCT
ejpam-3868	289	8	2α+	2α+	NUM
ejpam-3868	289	9	α′	α′	NUM
ejpam-3868	289	10	)	)	PUNCT
ejpam-3868	290	1	+	+	CCONJ
ejpam-3868	290	2	φ	φ	PROPN
ejpam-3868	290	3	∧	∧	PROPN
ejpam-3868	290	4	φ̄	φ̄	PROPN
ejpam-3868	290	5	)	)	PUNCT
ejpam-3868	290	6	+	+	CCONJ
ejpam-3868	290	7	φ	φ	PROPN
ejpam-3868	290	8	∧	∧	PROPN
ejpam-3868	290	9	γ	γ	X
ejpam-3868	290	10	∧	∧	PROPN
ejpam-3868	290	11	θ	θ	NOUN
ejpam-3868	290	12	=	=	SYM
ejpam-3868	290	13	0	0	X
ejpam-3868	290	14	.	.	PUNCT
ejpam-3868	291	1	finally	finally	ADV
ejpam-3868	291	2	after	after	ADP
ejpam-3868	291	3	simplifying	simplify	VERB
ejpam-3868	291	4	,	,	PUNCT
ejpam-3868	291	5	we	we	PRON
ejpam-3868	291	6	have	have	AUX
ejpam-3868	291	7	,	,	PUNCT
ejpam-3868	291	8	(	(	PUNCT
ejpam-3868	291	9	dβ′	dβ′	ADJ
ejpam-3868	291	10	+	+	PUNCT
ejpam-3868	291	11	β′	β′	NUM
ejpam-3868	291	12	∧	∧	NOUN
ejpam-3868	291	13	(	(	PUNCT
ejpam-3868	291	14	α+	α+	X
ejpam-3868	291	15	2α′	2α′	NUM
ejpam-3868	291	16	)	)	PUNCT
ejpam-3868	292	1	+	+	CCONJ
ejpam-3868	292	2	φ	φ	PROPN
ejpam-3868	292	3	∧	∧	PROPN
ejpam-3868	292	4	γ	γ	PROPN
ejpam-3868	292	5	)	)	PUNCT
ejpam-3868	292	6	∧	∧	PROPN
ejpam-3868	292	7	θ	θ	NOUN
ejpam-3868	292	8	=	=	SYM
ejpam-3868	292	9	0	0	PROPN
ejpam-3868	292	10	.	.	PUNCT
ejpam-3868	293	1	(	(	PUNCT
ejpam-3868	293	2	89	89	NUM
ejpam-3868	293	3	)	)	PUNCT
ejpam-3868	293	4	the	the	DET
ejpam-3868	293	5	form	form	NOUN
ejpam-3868	293	6	inside	inside	ADP
ejpam-3868	293	7	the	the	DET
ejpam-3868	293	8	bracket	bracket	NOUN
ejpam-3868	293	9	is	be	AUX
ejpam-3868	293	10	exactly	exactly	ADV
ejpam-3868	293	11	b′	b′	ADJ
ejpam-3868	293	12	,	,	PUNCT
ejpam-3868	293	13	so	so	CCONJ
ejpam-3868	293	14	(	(	PUNCT
ejpam-3868	293	15	89	89	NUM
ejpam-3868	293	16	)	)	PUNCT
ejpam-3868	293	17	is	be	AUX
ejpam-3868	293	18	just	just	ADV
ejpam-3868	293	19	the	the	DET
ejpam-3868	293	20	equation	equation	NOUN
ejpam-3868	294	1	b′	b′	NUM
ejpam-3868	295	1	∧	∧	PROPN
ejpam-3868	295	2	θ	θ	NOUN
ejpam-3868	295	3	=	=	SYM
ejpam-3868	295	4	0	0	PROPN
ejpam-3868	295	5	.	.	PUNCT
ejpam-3868	296	1	(	(	PUNCT
ejpam-3868	296	2	90	90	NUM
ejpam-3868	296	3	)	)	PUNCT
ejpam-3868	296	4	suppose	suppose	VERB
ejpam-3868	296	5	b	b	NOUN
ejpam-3868	296	6	is	be	AUX
ejpam-3868	296	7	a	a	DET
ejpam-3868	296	8	scalar	scalar	ADJ
ejpam-3868	296	9	multiple	multiple	NOUN
ejpam-3868	296	10	of	of	ADP
ejpam-3868	296	11	φ	φ	PROPN
ejpam-3868	296	12	∧	∧	PROPN
ejpam-3868	296	13	θ	θ	PROPN
ejpam-3868	297	1	so	so	ADV
ejpam-3868	297	2	b	b	X
ejpam-3868	297	3	=	=	SYM
ejpam-3868	297	4	c	c	PROPN
ejpam-3868	297	5	φ	φ	NUM
ejpam-3868	297	6	∧	∧	PROPN
ejpam-3868	297	7	θ	θ	PROPN
ejpam-3868	298	1	=	=	PUNCT
ejpam-3868	298	2	dβ	dβ	ADP
ejpam-3868	298	3	+	+	CCONJ
ejpam-3868	298	4	(	(	PUNCT
ejpam-3868	298	5	2α+	2α+	NUM
ejpam-3868	298	6	α′	α′	NUM
ejpam-3868	298	7	)	)	PUNCT
ejpam-3868	299	1	∧	∧	PROPN
ejpam-3868	299	2	β	β	X
ejpam-3868	299	3	+	+	CCONJ
ejpam-3868	299	4	γ	γ	X
ejpam-3868	299	5	∧	∧	PROPN
ejpam-3868	299	6	φ̄.	φ̄.	NUM
ejpam-3868	299	7	(	(	PUNCT
ejpam-3868	299	8	91	91	NUM
ejpam-3868	299	9	)	)	PUNCT
ejpam-3868	299	10	this	this	PRON
ejpam-3868	299	11	holds	hold	VERB
ejpam-3868	299	12	if	if	SCONJ
ejpam-3868	299	13	and	and	CCONJ
ejpam-3868	299	14	only	only	ADV
ejpam-3868	299	15	if	if	SCONJ
ejpam-3868	299	16	dβ	dβ	ADP
ejpam-3868	299	17	∧	∧	NOUN
ejpam-3868	299	18	φ+	φ+	X
ejpam-3868	299	19	(	(	PUNCT
ejpam-3868	299	20	2α+	2α+	NUM
ejpam-3868	299	21	α′	α′	NUM
ejpam-3868	299	22	)	)	PUNCT
ejpam-3868	299	23	∧	∧	PROPN
ejpam-3868	299	24	β	β	X
ejpam-3868	299	25	∧	∧	PROPN
ejpam-3868	299	26	φ	φ	NOUN
ejpam-3868	299	27	=	=	PROPN
ejpam-3868	299	28	γ	γ	PROPN
ejpam-3868	299	29	∧	∧	PROPN
ejpam-3868	299	30	φ	φ	PROPN
ejpam-3868	299	31	∧	∧	PROPN
ejpam-3868	299	32	φ̄.	φ̄.	NUM
ejpam-3868	299	33	(	(	PUNCT
ejpam-3868	299	34	92	92	NUM
ejpam-3868	299	35	)	)	PUNCT
ejpam-3868	299	36	however	however	ADV
ejpam-3868	299	37	,	,	PUNCT
ejpam-3868	299	38	dβ	dβ	ADP
ejpam-3868	299	39	∧	∧	PROPN
ejpam-3868	299	40	φ	φ	PROPN
ejpam-3868	299	41	=	=	PROPN
ejpam-3868	299	42	β	β	X
ejpam-3868	299	43	∧	∧	PROPN
ejpam-3868	299	44	dφ+	dφ+	NOUN
ejpam-3868	299	45	d(γ	d(γ	PROPN
ejpam-3868	299	46	∧	∧	PROPN
ejpam-3868	299	47	θ	θ	PROPN
ejpam-3868	299	48	)	)	PUNCT
ejpam-3868	299	49	and	and	CCONJ
ejpam-3868	299	50	so	so	ADV
ejpam-3868	299	51	consequently	consequently	ADV
ejpam-3868	299	52	,	,	PUNCT
ejpam-3868	299	53	dβ∧φ+(2α+α′)∧β∧φ	dβ∧φ+(2α+α′)∧β∧φ	PROPN
ejpam-3868	299	54	=	=	SYM
ejpam-3868	299	55	β∧dφ+d(γ∧θ)+(2α+α′)∧β∧φ	β∧dφ+d(γ∧θ)+(2α+α′)∧β∧φ	X
ejpam-3868	299	56	=	=	SYM
ejpam-3868	299	57	β∧β′∧θ+d(γ∧θ	β∧β′∧θ+d(γ∧θ	NOUN
ejpam-3868	299	58	)	)	PUNCT
ejpam-3868	299	59	.	.	PUNCT
ejpam-3868	300	1	(	(	PUNCT
ejpam-3868	300	2	93	93	NUM
ejpam-3868	300	3	)	)	PUNCT
ejpam-3868	300	4	since	since	SCONJ
ejpam-3868	300	5	b′	b′	NUM
ejpam-3868	300	6	is	be	AUX
ejpam-3868	300	7	a	a	DET
ejpam-3868	300	8	multiple	multiple	NOUN
ejpam-3868	300	9	of	of	ADP
ejpam-3868	300	10	φ̄	φ̄	ADJ
ejpam-3868	300	11	∧	∧	PROPN
ejpam-3868	300	12	θ	θ	PROPN
ejpam-3868	300	13	,	,	PUNCT
ejpam-3868	300	14	or	or	CCONJ
ejpam-3868	300	15	explicitly	explicitly	ADV
ejpam-3868	300	16	,	,	PUNCT
ejpam-3868	300	17	b′	b′	ADJ
ejpam-3868	300	18	=	=	SYM
ejpam-3868	300	19	c̃	c̃	PROPN
ejpam-3868	300	20	φ̄	φ̄	NOUN
ejpam-3868	300	21	∧	∧	PROPN
ejpam-3868	300	22	θ	θ	PROPN
ejpam-3868	300	23	=	=	SYM
ejpam-3868	300	24	dβ′	dβ′	PROPN
ejpam-3868	300	25	−	−	NOUN
ejpam-3868	300	26	(	(	PUNCT
ejpam-3868	300	27	α+	α+	X
ejpam-3868	300	28	2α′	2α′	NUM
ejpam-3868	300	29	)	)	PUNCT
ejpam-3868	300	30	∧	∧	PROPN
ejpam-3868	300	31	β′	β′	NUM
ejpam-3868	300	32	−	−	PROPN
ejpam-3868	300	33	γ	γ	PROPN
ejpam-3868	300	34	∧	∧	PROPN
ejpam-3868	300	35	φ	φ	PROPN
ejpam-3868	300	36	.	.	PUNCT
ejpam-3868	301	1	(	(	PUNCT
ejpam-3868	301	2	94	94	X
ejpam-3868	301	3	)	)	PUNCT
ejpam-3868	301	4	p.	p.	NOUN
ejpam-3868	301	5	bracken	bracken	NOUN
ejpam-3868	301	6	/	/	SYM
ejpam-3868	301	7	eur	eur	PROPN
ejpam-3868	301	8	.	.	PUNCT
ejpam-3868	302	1	j.	j.	PROPN
ejpam-3868	302	2	pure	pure	PROPN
ejpam-3868	302	3	appl	appl	PROPN
ejpam-3868	302	4	.	.	PROPN
ejpam-3868	302	5	math	math	PROPN
ejpam-3868	302	6	,	,	PUNCT
ejpam-3868	302	7	13	13	NUM
ejpam-3868	302	8	(	(	PUNCT
ejpam-3868	302	9	4	4	NUM
ejpam-3868	302	10	)	)	PUNCT
ejpam-3868	302	11	(	(	PUNCT
ejpam-3868	302	12	2020	2020	NUM
ejpam-3868	302	13	)	)	PUNCT
ejpam-3868	302	14	,	,	PUNCT
ejpam-3868	302	15	1016	1016	NUM
ejpam-3868	302	16	-	-	SYM
ejpam-3868	302	17	1034	1034	NUM
ejpam-3868	302	18	1031	1031	NUM
ejpam-3868	302	19	this	this	PRON
ejpam-3868	302	20	occurs	occur	VERB
ejpam-3868	302	21	if	if	SCONJ
ejpam-3868	302	22	and	and	CCONJ
ejpam-3868	302	23	only	only	ADV
ejpam-3868	302	24	if	if	SCONJ
ejpam-3868	302	25	(	(	PUNCT
ejpam-3868	302	26	dβ′	dβ′	ADJ
ejpam-3868	302	27	−	−	NOUN
ejpam-3868	302	28	(	(	PUNCT
ejpam-3868	302	29	α+	α+	X
ejpam-3868	302	30	2α′	2α′	NUM
ejpam-3868	302	31	)	)	PUNCT
ejpam-3868	302	32	∧	∧	NOUN
ejpam-3868	302	33	β′	β′	NOUN
ejpam-3868	302	34	)	)	PUNCT
ejpam-3868	302	35	∧	∧	NOUN
ejpam-3868	302	36	φ̄	φ̄	NOUN
ejpam-3868	302	37	=	=	SYM
ejpam-3868	302	38	γ	γ	PROPN
ejpam-3868	302	39	∧	∧	PROPN
ejpam-3868	302	40	φ	φ	PROPN
ejpam-3868	302	41	∧	∧	PROPN
ejpam-3868	302	42	φ̄.	φ̄.	PUNCT
ejpam-3868	302	43	(	(	PUNCT
ejpam-3868	302	44	95	95	NUM
ejpam-3868	302	45	)	)	PUNCT
ejpam-3868	302	46	since	since	SCONJ
ejpam-3868	302	47	dβ′	dβ′	VERB
ejpam-3868	302	48	∧	∧	NOUN
ejpam-3868	302	49	φ̄	φ̄	NOUN
ejpam-3868	302	50	=	=	SYM
ejpam-3868	302	51	β′	β′	NUM
ejpam-3868	303	1	∧	∧	PROPN
ejpam-3868	303	2	dφ̄+	dφ̄+	PROPN
ejpam-3868	303	3	d(γ	d(γ	PROPN
ejpam-3868	303	4	∧	∧	PROPN
ejpam-3868	303	5	θ	θ	PROPN
ejpam-3868	303	6	)	)	PUNCT
ejpam-3868	303	7	we	we	PRON
ejpam-3868	303	8	have	have	VERB
ejpam-3868	303	9	β′	β′	NUM
ejpam-3868	303	10	∧	∧	PROPN
ejpam-3868	303	11	dφ̄+	dφ̄+	PROPN
ejpam-3868	303	12	d(γ	d(γ	PROPN
ejpam-3868	303	13	∧	∧	PROPN
ejpam-3868	303	14	θ)−	θ)−	PROPN
ejpam-3868	303	15	(	(	PUNCT
ejpam-3868	303	16	α+	α+	X
ejpam-3868	303	17	2α′	2α′	NUM
ejpam-3868	303	18	)	)	PUNCT
ejpam-3868	303	19	∧	∧	NOUN
ejpam-3868	303	20	β′	β′	NUM
ejpam-3868	303	21	∧	∧	PROPN
ejpam-3868	303	22	φ̄	φ̄	NOUN
ejpam-3868	303	23	=	=	SYM
ejpam-3868	303	24	γ	γ	PROPN
ejpam-3868	303	25	∧	∧	PROPN
ejpam-3868	303	26	φ	φ	PROPN
ejpam-3868	303	27	∧	∧	PROPN
ejpam-3868	303	28	φ̄.	φ̄.	PUNCT
ejpam-3868	303	29	(	(	PUNCT
ejpam-3868	303	30	96	96	NUM
ejpam-3868	303	31	)	)	PUNCT
ejpam-3868	303	32	therefore	therefore	ADV
ejpam-3868	303	33	,	,	PUNCT
ejpam-3868	303	34	it	it	PRON
ejpam-3868	303	35	follows	follow	VERB
ejpam-3868	303	36	that	that	SCONJ
ejpam-3868	303	37	dβ′	dβ′	PROPN
ejpam-3868	303	38	∧φ−	∧φ−	NOUN
ejpam-3868	303	39	(	(	PUNCT
ejpam-3868	303	40	α+	α+	PROPN
ejpam-3868	303	41	2α′)∧	2α′)∧	NUM
ejpam-3868	303	42	β	β	X
ejpam-3868	303	43	∧	∧	PROPN
ejpam-3868	303	44	φ̄	φ̄	NOUN
ejpam-3868	303	45	=	=	SYM
ejpam-3868	303	46	−β′	−β′	PROPN
ejpam-3868	303	47	∧	∧	PROPN
ejpam-3868	303	48	(	(	PUNCT
ejpam-3868	303	49	α+	α+	PROPN
ejpam-3868	303	50	2α′)∧	2α′)∧	NUM
ejpam-3868	303	51	φ̄−	φ̄−	ADV
ejpam-3868	303	52	β′	β′	NUM
ejpam-3868	303	53	∧	∧	NOUN
ejpam-3868	303	54	β	β	X
ejpam-3868	303	55	∧	∧	PROPN
ejpam-3868	303	56	θ+	θ+	PUNCT
ejpam-3868	303	57	d(γ	d(γ	PROPN
ejpam-3868	303	58	∧	∧	PROPN
ejpam-3868	303	59	θ)−	θ)−	PROPN
ejpam-3868	303	60	(	(	PUNCT
ejpam-3868	303	61	α+	α+	PROPN
ejpam-3868	303	62	2α′)∧	2α′)∧	NUM
ejpam-3868	303	63	β′	β′	NUM
ejpam-3868	303	64	∧	∧	PROPN
ejpam-3868	303	65	φ̄	φ̄	NOUN
ejpam-3868	303	66	=	=	SYM
ejpam-3868	303	67	−β′	−β′	PROPN
ejpam-3868	303	68	∧	∧	PROPN
ejpam-3868	303	69	β	β	X
ejpam-3868	303	70	∧	∧	PROPN
ejpam-3868	303	71	θ	θ	PROPN
ejpam-3868	303	72	+	+	CCONJ
ejpam-3868	303	73	d(γ	d(γ	PROPN
ejpam-3868	303	74	∧	∧	PROPN
ejpam-3868	303	75	θ	θ	PROPN
ejpam-3868	303	76	)	)	PUNCT
ejpam-3868	303	77	.	.	PUNCT
ejpam-3868	304	1	(	(	PUNCT
ejpam-3868	304	2	97	97	NUM
ejpam-3868	304	3	)	)	PUNCT
ejpam-3868	304	4	the	the	DET
ejpam-3868	304	5	same	same	ADJ
ejpam-3868	304	6	condition	condition	NOUN
ejpam-3868	304	7	arises	arise	VERB
ejpam-3868	304	8	both	both	DET
ejpam-3868	304	9	ways	way	NOUN
ejpam-3868	304	10	β	β	X
ejpam-3868	304	11	∧	∧	NOUN
ejpam-3868	304	12	β′	β′	NUM
ejpam-3868	305	1	∧	∧	PROPN
ejpam-3868	305	2	θ	θ	PROPN
ejpam-3868	305	3	+	+	CCONJ
ejpam-3868	305	4	d(γ	d(γ	PROPN
ejpam-3868	305	5	∧	∧	PROPN
ejpam-3868	305	6	θ	θ	PROPN
ejpam-3868	305	7	)	)	PUNCT
ejpam-3868	305	8	=	=	SYM
ejpam-3868	305	9	γ	γ	PROPN
ejpam-3868	305	10	∧	∧	PROPN
ejpam-3868	305	11	φ	φ	PROPN
ejpam-3868	305	12	∧	∧	PROPN
ejpam-3868	305	13	φ̄.	φ̄.	PUNCT
ejpam-3868	305	14	(	(	PUNCT
ejpam-3868	305	15	98	98	NUM
ejpam-3868	305	16	)	)	PUNCT
ejpam-3868	305	17	therefore	therefore	ADV
ejpam-3868	305	18	,	,	PUNCT
ejpam-3868	305	19	it	it	PRON
ejpam-3868	305	20	holds	hold	VERB
ejpam-3868	305	21	that	that	PRON
ejpam-3868	305	22	b	b	PROPN
ejpam-3868	305	23	∧	∧	PROPN
ejpam-3868	305	24	φ	φ	PROPN
ejpam-3868	305	25	=	=	SYM
ejpam-3868	305	26	0	0	PUNCT
ejpam-3868	306	1	if	if	SCONJ
ejpam-3868	306	2	and	and	CCONJ
ejpam-3868	306	3	only	only	ADV
ejpam-3868	306	4	if	if	SCONJ
ejpam-3868	306	5	b′	b′	NUM
ejpam-3868	306	6	∧	∧	NOUN
ejpam-3868	306	7	φ̄	φ̄	NOUN
ejpam-3868	306	8	=	=	SYM
ejpam-3868	306	9	0	0	NUM
ejpam-3868	306	10	,	,	PUNCT
ejpam-3868	306	11	so	so	ADV
ejpam-3868	306	12	the	the	DET
ejpam-3868	306	13	condition	condition	NOUN
ejpam-3868	306	14	that	that	SCONJ
ejpam-3868	306	15	b	b	X
ejpam-3868	306	16	be	be	AUX
ejpam-3868	306	17	a	a	DET
ejpam-3868	306	18	multiple	multiple	NOUN
ejpam-3868	306	19	of	of	ADP
ejpam-3868	306	20	φ	φ	PROPN
ejpam-3868	306	21	∧	∧	PROPN
ejpam-3868	306	22	θ	θ	PROPN
ejpam-3868	306	23	and	and	CCONJ
ejpam-3868	306	24	b′	b′	NUM
ejpam-3868	306	25	a	a	DET
ejpam-3868	306	26	multiple	multiple	NOUN
ejpam-3868	306	27	of	of	ADP
ejpam-3868	306	28	φ̄	φ̄	X
ejpam-3868	306	29	∧	∧	PROPN
ejpam-3868	306	30	θ	θ	PROPN
ejpam-3868	306	31	are	be	AUX
ejpam-3868	306	32	the	the	DET
ejpam-3868	306	33	same	same	ADJ
ejpam-3868	306	34	.	.	PUNCT
ejpam-3868	307	1	finally	finally	ADV
ejpam-3868	307	2	,	,	PUNCT
ejpam-3868	307	3	let	let	VERB
ejpam-3868	307	4	us	we	PRON
ejpam-3868	307	5	discuss	discuss	VERB
ejpam-3868	307	6	the	the	DET
ejpam-3868	307	7	effects	effect	NOUN
ejpam-3868	307	8	of	of	ADP
ejpam-3868	307	9	the	the	DET
ejpam-3868	307	10	duality	duality	NOUN
ejpam-3868	307	11	transformation	transformation	NOUN
ejpam-3868	307	12	x	x	PRON
ejpam-3868	307	13	→	→	PUNCT
ejpam-3868	307	14	x̄	x̄	NOUN
ejpam-3868	307	15	and	and	CCONJ
ejpam-3868	307	16	x̄	x̄	NOUN
ejpam-3868	307	17	→	→	PUNCT
ejpam-3868	307	18	x.	x.	NOUN
ejpam-3868	307	19	this	this	PRON
ejpam-3868	307	20	is	be	AUX
ejpam-3868	307	21	supposed	suppose	VERB
ejpam-3868	307	22	to	to	PART
ejpam-3868	307	23	suggest	suggest	VERB
ejpam-3868	307	24	the	the	DET
ejpam-3868	307	25	idea	idea	NOUN
ejpam-3868	307	26	that	that	SCONJ
ejpam-3868	307	27	this	this	DET
ejpam-3868	307	28	action	action	NOUN
ejpam-3868	307	29	look	look	VERB
ejpam-3868	307	30	like	like	ADP
ejpam-3868	307	31	complex	complex	ADJ
ejpam-3868	307	32	conjugation	conjugation	NOUN
ejpam-3868	307	33	so	so	SCONJ
ejpam-3868	307	34	θ	θ	PROPN
ejpam-3868	307	35	can	can	AUX
ejpam-3868	307	36	be	be	AUX
ejpam-3868	307	37	thought	think	VERB
ejpam-3868	307	38	of	of	ADP
ejpam-3868	307	39	as	as	ADV
ejpam-3868	307	40	purely	purely	ADV
ejpam-3868	307	41	imaginary	imaginary	ADJ
ejpam-3868	307	42	and	and	CCONJ
ejpam-3868	307	43	χ	χ	NOUN
ejpam-3868	307	44	as	as	ADV
ejpam-3868	307	45	real	real	ADJ
ejpam-3868	307	46	.	.	PUNCT
ejpam-3868	308	1	the	the	DET
ejpam-3868	308	2	dual	dual	ADJ
ejpam-3868	308	3	connection	connection	NOUN
ejpam-3868	308	4	form	form	NOUN
ejpam-3868	308	5	is	be	AUX
ejpam-3868	308	6	ω̄	ω̄	ADJ
ejpam-3868	308	7	and	and	CCONJ
ejpam-3868	308	8	takes	take	VERB
ejpam-3868	308	9	the	the	DET
ejpam-3868	308	10	form	form	NOUN
ejpam-3868	308	11	ω̄	ω̄	ADP
ejpam-3868	309	1	=	=	PUNCT
ejpam-3868	309	2	ᾱ	ᾱ	PROPN
ejpam-3868	309	3	β̄	β̄	PROPN
ejpam-3868	309	4	γ̄	γ̄	PROPN
ejpam-3868	309	5	φ̄	φ̄	PROPN
ejpam-3868	310	1	−ᾱ−	−ᾱ−	PROPN
ejpam-3868	310	2	ᾱ′	ᾱ′	NOUN
ejpam-3868	310	3	β̄′	β̄′	NOUN
ejpam-3868	311	1	θ	θ	PROPN
ejpam-3868	311	2	φ	φ	PROPN
ejpam-3868	311	3	ᾱ′	ᾱ′	NOUN
ejpam-3868	312	1			PROPN
ejpam-3868	312	2	(	(	PUNCT
ejpam-3868	312	3	99	99	NUM
ejpam-3868	312	4	)	)	PUNCT
ejpam-3868	312	5	it	it	PRON
ejpam-3868	312	6	is	be	AUX
ejpam-3868	312	7	assumed	assume	VERB
ejpam-3868	312	8	to	to	PART
ejpam-3868	312	9	be	be	AUX
ejpam-3868	312	10	gauged	gauge	VERB
ejpam-3868	312	11	so	so	SCONJ
ejpam-3868	312	12	that	that	SCONJ
ejpam-3868	312	13	ᾱ	ᾱ	NOUN
ejpam-3868	312	14	−	−	PROPN
ejpam-3868	312	15	ᾱ′	ᾱ′	NOUN
ejpam-3868	312	16	is	be	AUX
ejpam-3868	312	17	independent	independent	ADJ
ejpam-3868	312	18	of	of	ADP
ejpam-3868	312	19	θ	θ	PROPN
ejpam-3868	312	20	as	as	ADP
ejpam-3868	312	21	before	before	ADV
ejpam-3868	312	22	.	.	PUNCT
ejpam-3868	313	1	using	use	VERB
ejpam-3868	313	2	(	(	PUNCT
ejpam-3868	313	3	99	99	NUM
ejpam-3868	313	4	)	)	PUNCT
ejpam-3868	313	5	the	the	DET
ejpam-3868	313	6	curvature	curvature	NOUN
ejpam-3868	313	7	form	form	NOUN
ejpam-3868	313	8	is	be	AUX
ejpam-3868	313	9	found	find	VERB
ejpam-3868	313	10	to	to	PART
ejpam-3868	313	11	be	be	AUX
ejpam-3868	313	12	dᾱ	dᾱ	NUM
ejpam-3868	314	1	dβ̄	dβ̄	PROPN
ejpam-3868	314	2	dγ̄	dγ̄	PROPN
ejpam-3868	314	3	dφ̄	dφ̄	PROPN
ejpam-3868	314	4	−d(ᾱ+	−d(ᾱ+	NOUN
ejpam-3868	314	5	ᾱ′	ᾱ′	PROPN
ejpam-3868	314	6	)	)	PUNCT
ejpam-3868	314	7	dβ̄′	dβ̄′	PROPN
ejpam-3868	314	8	dθ	dθ	PROPN
ejpam-3868	314	9	dφ	dφ	ADP
ejpam-3868	314	10	dᾱ′	dᾱ′	VERB
ejpam-3868	314	11			PROPN
ejpam-3868	314	12	+	+	CCONJ
ejpam-3868	314	13			PROPN
ejpam-3868	314	14	β̄	β̄	ADJ
ejpam-3868	314	15	∧	∧	PROPN
ejpam-3868	314	16	φ̄+	φ̄+	PUNCT
ejpam-3868	314	17	γ̄	γ̄	PROPN
ejpam-3868	314	18	∧	∧	PROPN
ejpam-3868	314	19	θ	θ	PROPN
ejpam-3868	314	20	ᾱ	ᾱ	NOUN
ejpam-3868	314	21	∧	∧	PROPN
ejpam-3868	314	22	β̄	β̄	NOUN
ejpam-3868	315	1	−	−	NOUN
ejpam-3868	315	2	β̄	β̄	NOUN
ejpam-3868	315	3	−	−	NOUN
ejpam-3868	315	4	β̄	β̄	ADJ
ejpam-3868	315	5	∧	∧	PROPN
ejpam-3868	315	6	(	(	PUNCT
ejpam-3868	315	7	ᾱ+	ᾱ+	NUM
ejpam-3868	315	8	ᾱ′	ᾱ′	NOUN
ejpam-3868	315	9	)	)	PUNCT
ejpam-3868	316	1	+	+	CCONJ
ejpam-3868	316	2	γ̄	γ̄	PROPN
ejpam-3868	316	3	∧	∧	PROPN
ejpam-3868	316	4	φ	φ	PROPN
ejpam-3868	316	5	ᾱ	ᾱ	PROPN
ejpam-3868	316	6	∧	∧	PROPN
ejpam-3868	316	7	γ̄	γ̄	PROPN
ejpam-3868	317	1	+	+	CCONJ
ejpam-3868	317	2	β̄	β̄	ADJ
ejpam-3868	317	3	∧	∧	PROPN
ejpam-3868	317	4	β̄′	β̄′	NOUN
ejpam-3868	317	5	+	+	CCONJ
ejpam-3868	317	6	γ̄′	γ̄′	NOUN
ejpam-3868	317	7	∧	∧	PROPN
ejpam-3868	317	8	ᾱ′	ᾱ′	PROPN
ejpam-3868	317	9	φ̄	φ̄	PROPN
ejpam-3868	318	1	∧	∧	PROPN
ejpam-3868	318	2	ᾱ−	ᾱ−	PROPN
ejpam-3868	318	3	(	(	PUNCT
ejpam-3868	318	4	ᾱ+	ᾱ+	NUM
ejpam-3868	318	5	ᾱ′	ᾱ′	NOUN
ejpam-3868	318	6	)	)	PUNCT
ejpam-3868	318	7	∧	∧	PROPN
ejpam-3868	318	8	φ+	φ+	X
ejpam-3868	318	9	β̄′	β̄′	X
ejpam-3868	318	10	∧	∧	PROPN
ejpam-3868	318	11	θ	θ	PROPN
ejpam-3868	318	12	φ̄	φ̄	NOUN
ejpam-3868	318	13	∧	∧	PROPN
ejpam-3868	318	14	β̄	β̄	PROPN
ejpam-3868	318	15	+	+	CCONJ
ejpam-3868	318	16	β̄′	β̄′	PROPN
ejpam-3868	318	17	∧	∧	PROPN
ejpam-3868	318	18	φ	φ	X
ejpam-3868	318	19	φ̄	φ̄	PROPN
ejpam-3868	318	20	∧	∧	PROPN
ejpam-3868	318	21	γ̄	γ̄	PROPN
ejpam-3868	318	22	−	−	PROPN
ejpam-3868	318	23	(	(	PUNCT
ejpam-3868	318	24	ᾱ+	ᾱ+	NUM
ejpam-3868	318	25	ᾱ′	ᾱ′	NOUN
ejpam-3868	318	26	)	)	PUNCT
ejpam-3868	319	1	∧	∧	PROPN
ejpam-3868	319	2	β	β	X
ejpam-3868	319	3	+	+	ADJ
ejpam-3868	319	4	β̄′	β̄′	PROPN
ejpam-3868	319	5	∧	∧	PROPN
ejpam-3868	319	6	ᾱ′	ᾱ′	NOUN
ejpam-3868	319	7	θ	θ	PROPN
ejpam-3868	319	8	∧	∧	PROPN
ejpam-3868	319	9	ᾱ+	ᾱ+	NUM
ejpam-3868	319	10	φ	φ	NUM
ejpam-3868	319	11	∧	∧	PROPN
ejpam-3868	319	12	φ̄+	φ̄+	PUNCT
ejpam-3868	319	13	ᾱ′	ᾱ′	NOUN
ejpam-3868	319	14	∧	∧	PROPN
ejpam-3868	319	15	θ	θ	PROPN
ejpam-3868	319	16	θ	θ	X
ejpam-3868	319	17	∧	∧	PROPN
ejpam-3868	319	18	β̄	β̄	PROPN
ejpam-3868	319	19	−	−	PROPN
ejpam-3868	319	20	φ	φ	PROPN
ejpam-3868	319	21	∧	∧	PROPN
ejpam-3868	319	22	(	(	PUNCT
ejpam-3868	319	23	ᾱ+	ᾱ+	NUM
ejpam-3868	319	24	ᾱ′	ᾱ′	NOUN
ejpam-3868	319	25	)	)	PUNCT
ejpam-3868	320	1	+	+	CCONJ
ejpam-3868	321	1	ᾱ′	ᾱ′	NOUN
ejpam-3868	321	2	∧	∧	PROPN
ejpam-3868	321	3	φ	φ	NUM
ejpam-3868	321	4	θ	θ	PROPN
ejpam-3868	321	5	∧	∧	PROPN
ejpam-3868	321	6	γ̄	γ̄	PROPN
ejpam-3868	321	7	+	+	CCONJ
ejpam-3868	321	8	φ	φ	PROPN
ejpam-3868	321	9	∧	∧	PROPN
ejpam-3868	321	10	β̄′	β̄′	ADV
ejpam-3868	322	1			PROPN
ejpam-3868	322	2	(	(	PUNCT
ejpam-3868	322	3	100	100	NUM
ejpam-3868	322	4	)	)	PUNCT
ejpam-3868	322	5	the	the	DET
ejpam-3868	322	6	connection	connection	NOUN
ejpam-3868	322	7	is	be	AUX
ejpam-3868	322	8	then	then	ADV
ejpam-3868	322	9	uniquely	uniquely	ADV
ejpam-3868	322	10	determined	determine	VERB
ejpam-3868	322	11	by	by	ADP
ejpam-3868	322	12	the	the	DET
ejpam-3868	322	13	conditions	condition	NOUN
ejpam-3868	322	14	for	for	SCONJ
ejpam-3868	322	15	the	the	DET
ejpam-3868	322	16	torsion	torsion	NOUN
ejpam-3868	322	17	to	to	PART
ejpam-3868	322	18	vanish	vanish	VERB
ejpam-3868	322	19	dφ̄+φ̄∧ᾱ∧φ̄+β̄′∧θ	dφ̄+φ̄∧ᾱ∧φ̄+β̄′∧θ	NOUN
ejpam-3868	322	20	=	=	SYM
ejpam-3868	322	21	0	0	NUM
ejpam-3868	322	22	,	,	PUNCT
ejpam-3868	322	23	dφ+θ∧β̄−φ∧(ᾱ+2ᾱ′	dφ+θ∧β̄−φ∧(ᾱ+2ᾱ′	PUNCT
ejpam-3868	322	24	)	)	PUNCT
ejpam-3868	322	25	=	=	SYM
ejpam-3868	322	26	0	0	NUM
ejpam-3868	322	27	,	,	PUNCT
ejpam-3868	322	28	dθ+θ∧ᾱ+φ∧φ̄+ᾱ′∧θ	dθ+θ∧ᾱ+φ∧φ̄+ᾱ′∧θ	NOUN
ejpam-3868	322	29	=	=	NOUN
ejpam-3868	322	30	0	0	X
ejpam-3868	322	31	.	.	PUNCT
ejpam-3868	323	1	(	(	PUNCT
ejpam-3868	323	2	101	101	NUM
ejpam-3868	323	3	)	)	PUNCT
ejpam-3868	323	4	vanishing	vanishing	NOUN
ejpam-3868	323	5	of	of	ADP
ejpam-3868	323	6	the	the	DET
ejpam-3868	323	7	diagonal	diagonal	ADJ
ejpam-3868	323	8	elements	element	NOUN
ejpam-3868	323	9	of	of	ADP
ejpam-3868	323	10	ω̄	ω̄	ADP
ejpam-3868	323	11	gives	give	VERB
ejpam-3868	323	12	dᾱ+	dᾱ+	PROPN
ejpam-3868	323	13	β̄	β̄	PUNCT
ejpam-3868	323	14	∧	∧	PROPN
ejpam-3868	323	15	φ̄+	φ̄+	PUNCT
ejpam-3868	323	16	γ̄	γ̄	NOUN
ejpam-3868	323	17	∧	∧	PROPN
ejpam-3868	323	18	θ	θ	PROPN
ejpam-3868	323	19	=	=	SYM
ejpam-3868	323	20	0	0	NUM
ejpam-3868	323	21	,	,	PUNCT
ejpam-3868	323	22	dα′	dα′	NOUN
ejpam-3868	323	23	−	−	NOUN
ejpam-3868	323	24	β′	β′	PUNCT
ejpam-3868	324	1	∧	∧	PROPN
ejpam-3868	324	2	φ−	φ−	PROPN
ejpam-3868	324	3	γ	γ	X
ejpam-3868	324	4	∧	∧	PROPN
ejpam-3868	324	5	θ	θ	PROPN
ejpam-3868	324	6	=	=	SYM
ejpam-3868	324	7	0	0	NUM
ejpam-3868	324	8	.	.	PUNCT
ejpam-3868	325	1	(	(	PUNCT
ejpam-3868	325	2	102	102	NUM
ejpam-3868	325	3	)	)	PUNCT
ejpam-3868	325	4	p.	p.	NOUN
ejpam-3868	325	5	bracken	bracken	NOUN
ejpam-3868	325	6	/	/	SYM
ejpam-3868	325	7	eur	eur	PROPN
ejpam-3868	325	8	.	.	PUNCT
ejpam-3868	326	1	j.	j.	PROPN
ejpam-3868	326	2	pure	pure	PROPN
ejpam-3868	326	3	appl	appl	PROPN
ejpam-3868	326	4	.	.	PROPN
ejpam-3868	326	5	math	math	PROPN
ejpam-3868	326	6	,	,	PUNCT
ejpam-3868	326	7	13	13	NUM
ejpam-3868	326	8	(	(	PUNCT
ejpam-3868	326	9	4	4	NUM
ejpam-3868	326	10	)	)	PUNCT
ejpam-3868	326	11	(	(	PUNCT
ejpam-3868	326	12	2020	2020	NUM
ejpam-3868	326	13	)	)	PUNCT
ejpam-3868	326	14	,	,	PUNCT
ejpam-3868	326	15	1016	1016	NUM
ejpam-3868	326	16	-	-	SYM
ejpam-3868	326	17	1034	1034	NUM
ejpam-3868	326	18	1032	1032	NUM
ejpam-3868	326	19	at	at	ADP
ejpam-3868	326	20	last	last	ADV
ejpam-3868	326	21	,	,	PUNCT
ejpam-3868	326	22	we	we	PRON
ejpam-3868	326	23	have	have	VERB
ejpam-3868	326	24	γ̄	γ̄	PROPN
ejpam-3868	326	25	∧	∧	PROPN
ejpam-3868	326	26	φ	φ	PROPN
ejpam-3868	326	27	∧	∧	PROPN
ejpam-3868	326	28	φ̄	φ̄	NOUN
ejpam-3868	327	1	=	=	PRON
ejpam-3868	328	1	−(dβ̄	−(dβ̄	NOUN
ejpam-3868	329	1	+	+	CCONJ
ejpam-3868	330	1	(	(	PUNCT
ejpam-3868	330	2	2ᾱ+	2ᾱ+	PROPN
ejpam-3868	330	3	ᾱ′	ᾱ′	NOUN
ejpam-3868	330	4	)	)	PUNCT
ejpam-3868	331	1	∧	∧	NOUN
ejpam-3868	331	2	φ̄	φ̄	NOUN
ejpam-3868	331	3	=	=	NOUN
ejpam-3868	331	4	−(dβ̄′	−(dβ̄′	NOUN
ejpam-3868	331	5	−	−	PROPN
ejpam-3868	331	6	(	(	PUNCT
ejpam-3868	331	7	ᾱ+	ᾱ+	NUM
ejpam-3868	331	8	2ᾱ′	2ᾱ′	NUM
ejpam-3868	331	9	)	)	PUNCT
ejpam-3868	331	10	∧	∧	NOUN
ejpam-3868	331	11	β′	β′	NUM
ejpam-3868	331	12	)	)	PUNCT
ejpam-3868	332	1	∧	∧	PROPN
ejpam-3868	332	2	φ	φ	X
ejpam-3868	332	3	.	.	PUNCT
ejpam-3868	333	1	(	(	PUNCT
ejpam-3868	333	2	103	103	NUM
ejpam-3868	333	3	)	)	PUNCT
ejpam-3868	333	4	this	this	PRON
ejpam-3868	333	5	is	be	AUX
ejpam-3868	333	6	just	just	ADV
ejpam-3868	333	7	b̄	b̄	VERB
ejpam-3868	333	8	∧	∧	NOUN
ejpam-3868	333	9	φ̄	φ̄	NOUN
ejpam-3868	333	10	=	=	SYM
ejpam-3868	333	11	0	0	NUM
ejpam-3868	333	12	or	or	CCONJ
ejpam-3868	333	13	equivalently	equivalently	ADV
ejpam-3868	333	14	,	,	PUNCT
ejpam-3868	333	15	b̄′	b̄′	NOUN
ejpam-3868	333	16	∧	∧	PROPN
ejpam-3868	333	17	φ	φ	PROPN
ejpam-3868	333	18	=	=	SYM
ejpam-3868	333	19	0	0	PROPN
ejpam-3868	333	20	.	.	PUNCT
ejpam-3868	334	1	subtracting	subtract	VERB
ejpam-3868	334	2	the	the	DET
ejpam-3868	334	3	two	two	NUM
ejpam-3868	334	4	expressions	expression	NOUN
ejpam-3868	334	5	dθ−(α−α′)∧θ+φ∧φ̄	dθ−(α−α′)∧θ+φ∧φ̄	NOUN
ejpam-3868	334	6	=	=	SYM
ejpam-3868	334	7	0	0	NUM
ejpam-3868	334	8	and	and	CCONJ
ejpam-3868	334	9	dθ−(ᾱ−ᾱ′)∧θ+φ∧φ̄	dθ−(ᾱ−ᾱ′)∧θ+φ∧φ̄	PROPN
ejpam-3868	335	1	=	=	SYM
ejpam-3868	335	2	0	0	NUM
ejpam-3868	335	3	,	,	PUNCT
ejpam-3868	335	4	it	it	PRON
ejpam-3868	335	5	is	be	AUX
ejpam-3868	335	6	found	find	VERB
ejpam-3868	335	7	that	that	SCONJ
ejpam-3868	335	8	(	(	PUNCT
ejpam-3868	335	9	α−	α−	ADP
ejpam-3868	335	10	α′	α′	NUM
ejpam-3868	335	11	)	)	PUNCT
ejpam-3868	335	12	∧	∧	NOUN
ejpam-3868	335	13	θ	θ	NOUN
ejpam-3868	335	14	=	=	SYM
ejpam-3868	335	15	(	(	PUNCT
ejpam-3868	335	16	ᾱ−	ᾱ−	PROPN
ejpam-3868	335	17	ᾱ′	ᾱ′	PROPN
ejpam-3868	335	18	)	)	PUNCT
ejpam-3868	335	19	∧	∧	PROPN
ejpam-3868	335	20	θ	θ	PROPN
ejpam-3868	335	21	.	.	PUNCT
ejpam-3868	336	1	(	(	PUNCT
ejpam-3868	336	2	104	104	NUM
ejpam-3868	336	3	)	)	PUNCT
ejpam-3868	336	4	this	this	PRON
ejpam-3868	336	5	implies	imply	VERB
ejpam-3868	336	6	that	that	SCONJ
ejpam-3868	336	7	α−	α−	ADP
ejpam-3868	336	8	α′	α′	NUM
ejpam-3868	336	9	=	=	SYM
ejpam-3868	336	10	ᾱ−	ᾱ−	NOUN
ejpam-3868	336	11	ᾱ′	ᾱ′	NOUN
ejpam-3868	336	12	which	which	PRON
ejpam-3868	336	13	is	be	AUX
ejpam-3868	336	14	equivalent	equivalent	ADJ
ejpam-3868	336	15	to	to	ADP
ejpam-3868	336	16	α+	α+	PRON
ejpam-3868	336	17	ᾱ′	ᾱ′	NOUN
ejpam-3868	336	18	=	=	PUNCT
ejpam-3868	337	1	ᾱ+	ᾱ+	NUM
ejpam-3868	337	2	α′.	α′.	NOUN
ejpam-3868	337	3	grouping	group	VERB
ejpam-3868	337	4	from	from	ADP
ejpam-3868	337	5	both	both	DET
ejpam-3868	337	6	sets	set	NOUN
ejpam-3868	337	7	,	,	PUNCT
ejpam-3868	337	8	there	there	PRON
ejpam-3868	337	9	are	be	VERB
ejpam-3868	337	10	four	four	NUM
ejpam-3868	337	11	torsion	torsion	NOUN
ejpam-3868	337	12	equations	equation	NOUN
ejpam-3868	337	13	which	which	PRON
ejpam-3868	337	14	remain	remain	VERB
ejpam-3868	337	15	,	,	PUNCT
ejpam-3868	337	16	and	and	CCONJ
ejpam-3868	337	17	these	these	PRON
ejpam-3868	337	18	are	be	AUX
ejpam-3868	337	19	dφ−	dφ−	PROPN
ejpam-3868	337	20	(	(	PUNCT
ejpam-3868	337	21	2α+	2α+	NUM
ejpam-3868	337	22	α′	α′	NUM
ejpam-3868	337	23	)	)	PUNCT
ejpam-3868	338	1	∧	∧	PROPN
ejpam-3868	338	2	φ−	φ−	PROPN
ejpam-3868	338	3	β′	β′	NUM
ejpam-3868	338	4	∧	∧	NOUN
ejpam-3868	338	5	θ	θ	NOUN
ejpam-3868	338	6	=	=	SYM
ejpam-3868	338	7	0	0	NUM
ejpam-3868	338	8	dφ̄+	dφ̄+	NOUN
ejpam-3868	338	9	(	(	PUNCT
ejpam-3868	338	10	α+	α+	NOUN
ejpam-3868	338	11	2α′	2α′	NUM
ejpam-3868	338	12	)	)	PUNCT
ejpam-3868	338	13	∧	∧	NOUN
ejpam-3868	338	14	φ̄+	φ̄+	PUNCT
ejpam-3868	338	15	β	β	X
ejpam-3868	338	16	∧	∧	NOUN
ejpam-3868	338	17	θ	θ	NOUN
ejpam-3868	338	18	=	=	SYM
ejpam-3868	338	19	0	0	NUM
ejpam-3868	338	20	dφ+	dφ+	NOUN
ejpam-3868	338	21	(	(	PUNCT
ejpam-3868	338	22	ᾱ+	ᾱ+	NUM
ejpam-3868	338	23	2ᾱ′	2ᾱ′	NUM
ejpam-3868	338	24	)	)	PUNCT
ejpam-3868	338	25	∧	∧	NOUN
ejpam-3868	338	26	φ−	φ−	PROPN
ejpam-3868	338	27	β̄	β̄	NOUN
ejpam-3868	338	28	∧	∧	NOUN
ejpam-3868	338	29	θ	θ	NOUN
ejpam-3868	338	30	=	=	SYM
ejpam-3868	338	31	0	0	PUNCT
ejpam-3868	339	1	dφ̄−	dφ̄−	NUM
ejpam-3868	339	2	(	(	PUNCT
ejpam-3868	339	3	2ᾱ+	2ᾱ+	NUM
ejpam-3868	339	4	ᾱ′	ᾱ′	NOUN
ejpam-3868	339	5	)	)	PUNCT
ejpam-3868	340	1	∧	∧	PROPN
ejpam-3868	340	2	φ̄+	φ̄+	X
ejpam-3868	340	3	β̄′	β̄′	NOUN
ejpam-3868	340	4	∧	∧	PROPN
ejpam-3868	340	5	θ	θ	NOUN
ejpam-3868	340	6	=	=	SYM
ejpam-3868	340	7	0	0	NUM
ejpam-3868	340	8	.	.	PUNCT
ejpam-3868	341	1	(	(	PUNCT
ejpam-3868	341	2	105	105	NUM
ejpam-3868	341	3	)	)	PUNCT
ejpam-3868	341	4	subtracting	subtract	VERB
ejpam-3868	341	5	the	the	DET
ejpam-3868	341	6	equations	equation	NOUN
ejpam-3868	341	7	in	in	ADP
ejpam-3868	341	8	(	(	PUNCT
ejpam-3868	341	9	105	105	NUM
ejpam-3868	341	10	)	)	PUNCT
ejpam-3868	341	11	pairwise	pairwise	NOUN
ejpam-3868	341	12	,	,	PUNCT
ejpam-3868	341	13	the	the	DET
ejpam-3868	341	14	following	follow	VERB
ejpam-3868	341	15	linear	linear	PROPN
ejpam-3868	341	16	combinations	combination	NOUN
ejpam-3868	341	17	are	be	AUX
ejpam-3868	341	18	produced	produce	VERB
ejpam-3868	341	19	,	,	PUNCT
ejpam-3868	341	20	(	(	PUNCT
ejpam-3868	341	21	2(α+ᾱ′)+α′+ᾱ)∧φ+(β′−β̄)∧θ	2(α+ᾱ′)+α′+ᾱ)∧φ+(β′−β̄)∧θ	NUM
ejpam-3868	341	22	=	=	SYM
ejpam-3868	341	23	0	0	NUM
ejpam-3868	341	24	,	,	PUNCT
ejpam-3868	341	25	(	(	PUNCT
ejpam-3868	341	26	α+ᾱ′+2(α′+ᾱ))∧φ̄+(β+β̄′)∧θ	α+ᾱ′+2(α′+ᾱ))∧φ̄+(β+β̄′)∧θ	NUM
ejpam-3868	341	27	=	=	SYM
ejpam-3868	341	28	0	0	PROPN
ejpam-3868	341	29	.	.	PUNCT
ejpam-3868	342	1	(	(	PUNCT
ejpam-3868	342	2	106	106	NUM
ejpam-3868	342	3	)	)	PUNCT
ejpam-3868	342	4	forming	form	VERB
ejpam-3868	342	5	the	the	DET
ejpam-3868	342	6	wedge	wedge	NOUN
ejpam-3868	342	7	product	product	NOUN
ejpam-3868	342	8	with	with	ADP
ejpam-3868	342	9	θ	θ	PROPN
ejpam-3868	342	10	,	,	PUNCT
ejpam-3868	342	11	the	the	DET
ejpam-3868	342	12	results	result	NOUN
ejpam-3868	342	13	in	in	ADP
ejpam-3868	342	14	(	(	PUNCT
ejpam-3868	342	15	106	106	NUM
ejpam-3868	342	16	)	)	PUNCT
ejpam-3868	342	17	imply	imply	VERB
ejpam-3868	342	18	that	that	SCONJ
ejpam-3868	342	19	(	(	PUNCT
ejpam-3868	342	20	2(α+	2(α+	NUM
ejpam-3868	342	21	ᾱ′	ᾱ′	NOUN
ejpam-3868	342	22	)	)	PUNCT
ejpam-3868	343	1	+	+	CCONJ
ejpam-3868	343	2	α′	α′	NUM
ejpam-3868	343	3	+	+	CCONJ
ejpam-3868	343	4	ᾱ	ᾱ	NOUN
ejpam-3868	343	5	)	)	PUNCT
ejpam-3868	343	6	∧	∧	NOUN
ejpam-3868	343	7	φ	φ	NUM
ejpam-3868	343	8	∧	∧	PROPN
ejpam-3868	343	9	θ	θ	PROPN
ejpam-3868	343	10	=	=	SYM
ejpam-3868	343	11	0	0	NUM
ejpam-3868	343	12	,	,	PUNCT
ejpam-3868	343	13	(	(	PUNCT
ejpam-3868	343	14	α+	α+	NOUN
ejpam-3868	343	15	ᾱ′	ᾱ′	NOUN
ejpam-3868	343	16	+	+	CCONJ
ejpam-3868	343	17	2(α′	2(α′	NOUN
ejpam-3868	343	18	+	+	CCONJ
ejpam-3868	343	19	ᾱ	ᾱ	NOUN
ejpam-3868	343	20	)	)	PUNCT
ejpam-3868	343	21	)	)	PUNCT
ejpam-3868	344	1	∧	∧	NOUN
ejpam-3868	344	2	φ̄	φ̄	NOUN
ejpam-3868	344	3	∧	∧	PROPN
ejpam-3868	344	4	θ	θ	PROPN
ejpam-3868	344	5	=	=	SYM
ejpam-3868	344	6	0	0	PROPN
ejpam-3868	344	7	.	.	PUNCT
ejpam-3868	345	1	(	(	PUNCT
ejpam-3868	345	2	107	107	NUM
ejpam-3868	345	3	)	)	PUNCT
ejpam-3868	345	4	based	base	VERB
ejpam-3868	345	5	on	on	ADP
ejpam-3868	345	6	the	the	DET
ejpam-3868	345	7	fact	fact	NOUN
ejpam-3868	345	8	that	that	SCONJ
ejpam-3868	345	9	α+	α+	PRON
ejpam-3868	345	10	α′	α′	NOUN
ejpam-3868	345	11	is	be	AUX
ejpam-3868	345	12	a	a	DET
ejpam-3868	345	13	multiple	multiple	NOUN
ejpam-3868	345	14	of	of	ADP
ejpam-3868	345	15	θ	θ	NOUN
ejpam-3868	345	16	we	we	PRON
ejpam-3868	345	17	can	can	AUX
ejpam-3868	345	18	write	write	VERB
ejpam-3868	345	19	this	this	PRON
ejpam-3868	345	20	as	as	ADP
ejpam-3868	345	21	κ	κ	PROPN
ejpam-3868	345	22	θ	θ	PROPN
ejpam-3868	345	23	,	,	PUNCT
ejpam-3868	345	24	κ	κ	ADP
ejpam-3868	345	25	a	a	DET
ejpam-3868	345	26	scalar	scalar	NOUN
ejpam-3868	345	27	.	.	PUNCT
ejpam-3868	346	1	also	also	ADV
ejpam-3868	346	2	reasoning	reason	VERB
ejpam-3868	346	3	in	in	ADP
ejpam-3868	346	4	a	a	DET
ejpam-3868	346	5	similar	similar	ADJ
ejpam-3868	346	6	way	way	NOUN
ejpam-3868	346	7	,	,	PUNCT
ejpam-3868	346	8	α	α	NOUN
ejpam-3868	346	9	+	+	CCONJ
ejpam-3868	346	10	ᾱ′	ᾱ′	NOUN
ejpam-3868	346	11	=	=	PUNCT
ejpam-3868	347	1	κθ	κθ	X
ejpam-3868	347	2	.	.	PUNCT
ejpam-3868	347	3	applying	apply	VERB
ejpam-3868	347	4	these	these	DET
ejpam-3868	347	5	new	new	ADJ
ejpam-3868	347	6	results	result	NOUN
ejpam-3868	347	7	in	in	ADP
ejpam-3868	347	8	(	(	PUNCT
ejpam-3868	347	9	106	106	NUM
ejpam-3868	347	10	)	)	PUNCT
ejpam-3868	347	11	,	,	PUNCT
ejpam-3868	347	12	it	it	PRON
ejpam-3868	347	13	is	be	AUX
ejpam-3868	347	14	found	find	VERB
ejpam-3868	347	15	that	that	SCONJ
ejpam-3868	347	16	(	(	PUNCT
ejpam-3868	347	17	β′	β′	NUM
ejpam-3868	347	18	−	−	NOUN
ejpam-3868	347	19	β	β	X
ejpam-3868	347	20	)	)	PUNCT
ejpam-3868	347	21	∧	∧	PROPN
ejpam-3868	347	22	θ	θ	NOUN
ejpam-3868	347	23	=	=	SYM
ejpam-3868	347	24	−3κθ	−3κθ	PUNCT
ejpam-3868	347	25	∧	∧	PROPN
ejpam-3868	347	26	φ	φ	X
ejpam-3868	347	27	.	.	PUNCT
ejpam-3868	348	1	(	(	PUNCT
ejpam-3868	348	2	108	108	NUM
ejpam-3868	348	3	)	)	PUNCT
ejpam-3868	348	4	on	on	ADP
ejpam-3868	348	5	the	the	DET
ejpam-3868	348	6	other	other	ADJ
ejpam-3868	348	7	hand	hand	NOUN
ejpam-3868	348	8	,	,	PUNCT
ejpam-3868	348	9	it	it	PRON
ejpam-3868	348	10	follows	follow	VERB
ejpam-3868	348	11	that	that	SCONJ
ejpam-3868	348	12	d(α′	d(α′	NOUN
ejpam-3868	348	13	+	+	CCONJ
ejpam-3868	348	14	ᾱ	ᾱ	NOUN
ejpam-3868	348	15	)	)	PUNCT
ejpam-3868	348	16	=	=	SYM
ejpam-3868	348	17	dκ	dκ	ADP
ejpam-3868	348	18	∧	∧	PROPN
ejpam-3868	348	19	θ	θ	PROPN
ejpam-3868	348	20	+	+	CCONJ
ejpam-3868	348	21	κ(φ	κ(φ	PROPN
ejpam-3868	348	22	∧	∧	PROPN
ejpam-3868	348	23	φ̄−	φ̄−	ADV
ejpam-3868	348	24	χ	χ	DET
ejpam-3868	348	25	∧	∧	PROPN
ejpam-3868	348	26	θ	θ	PROPN
ejpam-3868	348	27	)	)	PUNCT
ejpam-3868	348	28	=	=	SYM
ejpam-3868	348	29	(	(	PUNCT
ejpam-3868	348	30	β′	β′	NUM
ejpam-3868	348	31	−	−	NOUN
ejpam-3868	348	32	β	β	X
ejpam-3868	348	33	)	)	PUNCT
ejpam-3868	348	34	∧	∧	NOUN
ejpam-3868	348	35	φ̄−	φ̄−	ADV
ejpam-3868	348	36	(	(	PUNCT
ejpam-3868	348	37	γ	γ	PROPN
ejpam-3868	348	38	+	+	SYM
ejpam-3868	348	39	γ̄	γ̄	NOUN
ejpam-3868	348	40	)	)	PUNCT
ejpam-3868	348	41	∧	∧	PROPN
ejpam-3868	348	42	θ	θ	PROPN
ejpam-3868	348	43	.	.	PUNCT
ejpam-3868	348	44	(	(	PUNCT
ejpam-3868	348	45	109	109	NUM
ejpam-3868	348	46	)	)	PUNCT
ejpam-3868	348	47	taking	take	VERB
ejpam-3868	348	48	the	the	DET
ejpam-3868	348	49	exterior	exterior	ADJ
ejpam-3868	348	50	product	product	NOUN
ejpam-3868	348	51	of	of	ADP
ejpam-3868	348	52	this	this	PRON
ejpam-3868	348	53	with	with	ADP
ejpam-3868	348	54	θ	θ	PROPN
ejpam-3868	348	55	we	we	PRON
ejpam-3868	348	56	obtain	obtain	VERB
ejpam-3868	348	57	κφ∧	κφ∧	NOUN
ejpam-3868	348	58	φ̄∧	φ̄∧	PROPN
ejpam-3868	348	59	θ	θ	NOUN
ejpam-3868	348	60	=	=	SYM
ejpam-3868	348	61	0	0	NUM
ejpam-3868	348	62	which	which	PRON
ejpam-3868	348	63	leads	lead	VERB
ejpam-3868	348	64	to	to	ADP
ejpam-3868	348	65	κ	κ	NOUN
ejpam-3868	348	66	=	=	SYM
ejpam-3868	348	67	0	0	PROPN
ejpam-3868	348	68	.	.	PUNCT
ejpam-3868	349	1	therefore	therefore	ADV
ejpam-3868	349	2	,	,	PUNCT
ejpam-3868	349	3	it	it	PRON
ejpam-3868	349	4	is	be	AUX
ejpam-3868	349	5	concluded	conclude	VERB
ejpam-3868	349	6	that	that	SCONJ
ejpam-3868	349	7	α′	α′	NUM
ejpam-3868	349	8	=	=	SYM
ejpam-3868	349	9	−ᾱ	−ᾱ	NOUN
ejpam-3868	349	10	,	,	PUNCT
ejpam-3868	349	11	ᾱ′	ᾱ′	NOUN
ejpam-3868	349	12	=	=	PUNCT
ejpam-3868	349	13	−α	−α	PROPN
ejpam-3868	349	14	.	.	PUNCT
ejpam-3868	350	1	(	(	PUNCT
ejpam-3868	350	2	110	110	NUM
ejpam-3868	350	3	)	)	PUNCT
ejpam-3868	350	4	thus	thus	ADV
ejpam-3868	350	5	β′	β′	NUM
ejpam-3868	351	1	−	−	NUM
ejpam-3868	351	2	β̄	β̄	NOUN
ejpam-3868	351	3	is	be	AUX
ejpam-3868	351	4	in	in	ADP
ejpam-3868	351	5	fact	fact	NOUN
ejpam-3868	351	6	a	a	DET
ejpam-3868	351	7	scalar	scalar	ADJ
ejpam-3868	351	8	multiple	multiple	NOUN
ejpam-3868	351	9	of	of	ADP
ejpam-3868	351	10	θ	θ	PROPN
ejpam-3868	351	11	,	,	PUNCT
ejpam-3868	351	12	and	and	CCONJ
ejpam-3868	351	13	similarly	similarly	ADV
ejpam-3868	351	14	as	as	ADV
ejpam-3868	351	15	well	well	ADV
ejpam-3868	351	16	,	,	PUNCT
ejpam-3868	351	17	so	so	ADV
ejpam-3868	351	18	is	be	AUX
ejpam-3868	351	19	β	β	NOUN
ejpam-3868	351	20	−	−	NOUN
ejpam-3868	351	21	β̄′.	β̄′.	PUNCT
ejpam-3868	351	22	since	since	SCONJ
ejpam-3868	351	23	α′	α′	NUM
ejpam-3868	351	24	+	+	CCONJ
ejpam-3868	351	25	ᾱ	ᾱ	NOUN
ejpam-3868	351	26	=	=	SYM
ejpam-3868	351	27	0	0	NUM
ejpam-3868	351	28	,	,	PUNCT
ejpam-3868	351	29	it	it	PRON
ejpam-3868	351	30	is	be	AUX
ejpam-3868	351	31	concluded	conclude	VERB
ejpam-3868	351	32	that	that	SCONJ
ejpam-3868	351	33	(	(	PUNCT
ejpam-3868	351	34	β′	β′	NUM
ejpam-3868	351	35	−	−	NOUN
ejpam-3868	351	36	β̄	β̄	INTJ
ejpam-3868	351	37	)	)	PUNCT
ejpam-3868	351	38	∧	∧	NOUN
ejpam-3868	351	39	φ̄	φ̄	NOUN
ejpam-3868	351	40	=	=	SYM
ejpam-3868	351	41	(	(	PUNCT
ejpam-3868	351	42	γ	γ	X
ejpam-3868	351	43	+	+	SYM
ejpam-3868	351	44	γ̄	γ̄	NOUN
ejpam-3868	351	45	)	)	PUNCT
ejpam-3868	351	46	∧	∧	NOUN
ejpam-3868	351	47	θ	θ	NOUN
ejpam-3868	351	48	=	=	SYM
ejpam-3868	351	49	(	(	PUNCT
ejpam-3868	351	50	β	β	X
ejpam-3868	351	51	−	−	NOUN
ejpam-3868	351	52	β̄′	β̄′	ADV
ejpam-3868	351	53	)	)	PUNCT
ejpam-3868	351	54	∧	∧	PROPN
ejpam-3868	351	55	φ	φ	X
ejpam-3868	351	56	.	.	PUNCT
ejpam-3868	352	1	(	(	PUNCT
ejpam-3868	352	2	111	111	NUM
ejpam-3868	352	3	)	)	PUNCT
ejpam-3868	352	4	it	it	PRON
ejpam-3868	352	5	follows	follow	VERB
ejpam-3868	352	6	that	that	SCONJ
ejpam-3868	352	7	β′	β′	NUM
ejpam-3868	353	1	=	=	SYM
ejpam-3868	353	2	β̄	β̄	ADJ
ejpam-3868	353	3	and	and	CCONJ
ejpam-3868	353	4	β̄′	β̄′	NOUN
ejpam-3868	353	5	=	=	SYM
ejpam-3868	353	6	β	β	X
ejpam-3868	353	7	with	with	ADP
ejpam-3868	353	8	γ	γ	X
ejpam-3868	353	9	∧	∧	PROPN
ejpam-3868	353	10	θ	θ	NOUN
ejpam-3868	353	11	=	=	SYM
ejpam-3868	353	12	−γ̄	−γ̄	ADJ
ejpam-3868	353	13	∧	∧	PROPN
ejpam-3868	353	14	θ	θ	PROPN
ejpam-3868	353	15	.	.	PUNCT
ejpam-3868	354	1	the	the	DET
ejpam-3868	354	2	conditions	condition	NOUN
ejpam-3868	354	3	on	on	ADP
ejpam-3868	354	4	b	b	NOUN
ejpam-3868	354	5	and	and	CCONJ
ejpam-3868	354	6	b′	b′	NUM
ejpam-3868	354	7	yield	yield	VERB
ejpam-3868	354	8	the	the	DET
ejpam-3868	354	9	final	final	ADJ
ejpam-3868	354	10	conclusion	conclusion	NOUN
ejpam-3868	354	11	,	,	PUNCT
ejpam-3868	354	12	γ̄	γ̄	PROPN
ejpam-3868	354	13	∧	∧	PROPN
ejpam-3868	354	14	φ	φ	PROPN
ejpam-3868	354	15	∧	∧	PROPN
ejpam-3868	354	16	φ̄	φ̄	NOUN
ejpam-3868	355	1	=	=	SYM
ejpam-3868	356	1	−(dβ	−(dβ	NOUN
ejpam-3868	356	2	+	+	NUM
ejpam-3868	356	3	α′	α′	NUM
ejpam-3868	356	4	+	+	CCONJ
ejpam-3868	356	5	2α	2α	NOUN
ejpam-3868	356	6	)	)	PUNCT
ejpam-3868	356	7	∧	∧	NOUN
ejpam-3868	356	8	β	β	NOUN
ejpam-3868	356	9	)	)	PUNCT
ejpam-3868	356	10	∧	∧	PROPN
ejpam-3868	356	11	φ	φ	NOUN
ejpam-3868	356	12	=	=	SYM
ejpam-3868	356	13	−γ	−γ	PROPN
ejpam-3868	356	14	∧	∧	PROPN
ejpam-3868	356	15	φ	φ	PROPN
ejpam-3868	356	16	∧	∧	PROPN
ejpam-3868	356	17	φ̄.	φ̄.	PUNCT
ejpam-3868	356	18	(	(	PUNCT
ejpam-3868	356	19	112	112	NUM
ejpam-3868	356	20	)	)	PUNCT
ejpam-3868	356	21	references	reference	NOUN
ejpam-3868	356	22	1033	1033	NUM
ejpam-3868	356	23	this	this	PRON
ejpam-3868	356	24	implies	imply	VERB
ejpam-3868	356	25	that	that	SCONJ
ejpam-3868	356	26	γ̄	γ̄	PROPN
ejpam-3868	356	27	=	=	SYM
ejpam-3868	356	28	−γ	−γ	NOUN
ejpam-3868	356	29	.	.	PUNCT
ejpam-3868	357	1	finally	finally	ADV
ejpam-3868	357	2	,	,	PUNCT
ejpam-3868	357	3	it	it	PRON
ejpam-3868	357	4	follows	follow	VERB
ejpam-3868	357	5	that	that	SCONJ
ejpam-3868	357	6	the	the	DET
ejpam-3868	357	7	form	form	NOUN
ejpam-3868	357	8	ω	ω	NOUN
ejpam-3868	357	9	can	can	AUX
ejpam-3868	357	10	be	be	AUX
ejpam-3868	357	11	summarized	summarize	VERB
ejpam-3868	357	12	in	in	ADP
ejpam-3868	357	13	matrix	matrix	NOUN
ejpam-3868	357	14	form	form	NOUN
ejpam-3868	357	15	,	,	PUNCT
ejpam-3868	357	16	ω	ω	NOUN
ejpam-3868	357	17	=	=	PUNCT
ejpam-3868	357	18			PROPN
ejpam-3868	357	19	α	α	X
ejpam-3868	357	20	β	β	X
ejpam-3868	357	21	γ	γ	PROPN
ejpam-3868	357	22	φ	φ	PROPN
ejpam-3868	357	23	−(α−	−(α−	PROPN
ejpam-3868	357	24	ᾱ	ᾱ	NOUN
ejpam-3868	357	25	)	)	PUNCT
ejpam-3868	357	26	β̄	β̄	PROPN
ejpam-3868	358	1	−θ	−θ	PROPN
ejpam-3868	358	2	φ̄	φ̄	PROPN
ejpam-3868	358	3	−ᾱ	−ᾱ	PROPN
ejpam-3868	358	4			PROPN
ejpam-3868	358	5	(	(	PUNCT
ejpam-3868	358	6	113	113	NUM
ejpam-3868	358	7	)	)	PUNCT
ejpam-3868	358	8	where	where	SCONJ
ejpam-3868	358	9	γ̄	γ̄	PROPN
ejpam-3868	358	10	=	=	X
ejpam-3868	358	11	−γ	−γ	NOUN
ejpam-3868	358	12	and	and	CCONJ
ejpam-3868	358	13	ω̄	ω̄	NOUN
ejpam-3868	358	14	is	be	AUX
ejpam-3868	358	15	calculated	calculate	VERB
ejpam-3868	358	16	from	from	ADP
ejpam-3868	358	17	ω	ω	NUM
ejpam-3868	358	18	through	through	ADP
ejpam-3868	358	19	ω̄	ω̄	ADJ
ejpam-3868	358	20	=	=	PUNCT
ejpam-3868	358	21	−kωt	−kωt	NOUN
ejpam-3868	358	22	k.	k.	PROPN
ejpam-3868	359	1	(	(	PUNCT
ejpam-3868	359	2	114	114	NUM
ejpam-3868	359	3	)	)	PUNCT
ejpam-3868	359	4	it	it	PRON
ejpam-3868	359	5	may	may	AUX
ejpam-3868	359	6	be	be	AUX
ejpam-3868	359	7	concluded	conclude	VERB
ejpam-3868	359	8	that	that	SCONJ
ejpam-3868	359	9	ω	ω	NOUN
ejpam-3868	359	10	=	=	X
ejpam-3868	359	11	−k	−k	PROPN
ejpam-3868	359	12	ωt	ωt	ADP
ejpam-3868	359	13	k	k	NOUN
ejpam-3868	359	14	,	,	PUNCT
ejpam-3868	359	15	and	and	CCONJ
ejpam-3868	359	16	it	it	PRON
ejpam-3868	359	17	follows	follow	VERB
ejpam-3868	359	18	that	that	SCONJ
ejpam-3868	359	19	b′	b′	NOUN
ejpam-3868	359	20	=	=	PUNCT
ejpam-3868	359	21	b̄	b̄	NOUN
ejpam-3868	359	22	and	and	CCONJ
ejpam-3868	359	23	b̄′	b̄′	NOUN
ejpam-3868	360	1	=	=	SYM
ejpam-3868	360	2	b	b	X
ejpam-3868	360	3	hold	hold	NOUN
ejpam-3868	360	4	.	.	PUNCT
ejpam-3868	361	1	references	reference	NOUN
ejpam-3868	361	2	[	[	X
ejpam-3868	361	3	1	1	NUM
ejpam-3868	361	4	]	]	PUNCT
ejpam-3868	361	5	schouten	schouten	PROPN
ejpam-3868	361	6	j.	j.	PROPN
ejpam-3868	361	7	a.	a.	PROPN
ejpam-3868	361	8	ricci	ricci	PROPN
ejpam-3868	361	9	calculus	calculus	PROPN
ejpam-3868	361	10	.	.	PUNCT
ejpam-3868	362	1	springer	springer	NOUN
ejpam-3868	362	2	-	-	PUNCT
ejpam-3868	362	3	verlag	verlag	PROPN
ejpam-3868	362	4	,	,	PUNCT
ejpam-3868	362	5	berlin	berlin	PROPN
ejpam-3868	362	6	,	,	PUNCT
ejpam-3868	362	7	1954	1954	NUM
ejpam-3868	362	8	.	.	PUNCT
ejpam-3868	363	1	[	[	X
ejpam-3868	363	2	2	2	X
ejpam-3868	363	3	]	]	PUNCT
ejpam-3868	363	4	tressé	tressé	VERB
ejpam-3868	363	5	a.	a.	PROPN
ejpam-3868	363	6	sur	sur	PROPN
ejpam-3868	363	7	les	les	PROPN
ejpam-3868	363	8	invariant	invariant	PROPN
ejpam-3868	363	9	différential	différential	PROPN
ejpam-3868	363	10	des	des	X
ejpam-3868	363	11	groupes	groupes	X
ejpam-3868	363	12	continus	continus	X
ejpam-3868	363	13	de	de	X
ejpam-3868	363	14	transformations	transformation	NOUN
ejpam-3868	363	15	.	.	PUNCT
ejpam-3868	364	1	acta	acta	PROPN
ejpam-3868	364	2	.	.	PUNCT
ejpam-3868	365	1	math	math	NOUN
ejpam-3868	365	2	.	.	PUNCT
ejpam-3868	366	1	18	18	NUM
ejpam-3868	366	2	,	,	PUNCT
ejpam-3868	366	3	1894	1894	NUM
ejpam-3868	366	4	.	.	PUNCT
ejpam-3868	367	1	[	[	X
ejpam-3868	367	2	3	3	X
ejpam-3868	367	3	]	]	X
ejpam-3868	367	4	cartan	cartan	PROPN
ejpam-3868	367	5	é.	é.	PROPN
ejpam-3868	367	6	sur	sur	PROPN
ejpam-3868	367	7	les	les	PROPN
ejpam-3868	367	8	variétés	variétés	PROPN
ejpam-3868	367	9	à	à	PROPN
ejpam-3868	367	10	connexion	connexion	PROPN
ejpam-3868	367	11	projective	projective	NOUN
ejpam-3868	367	12	.	.	PUNCT
ejpam-3868	368	1	bull	bull	NOUN
ejpam-3868	368	2	.	.	PUNCT
ejpam-3868	369	1	soc	soc	PROPN
ejpam-3868	369	2	.	.	PUNCT
ejpam-3868	370	1	math	math	PROPN
ejpam-3868	370	2	.	.	PUNCT
ejpam-3868	371	1	france	france	PROPN
ejpam-3868	371	2	,	,	PUNCT
ejpam-3868	371	3	52	52	NUM
ejpam-3868	371	4	,	,	PUNCT
ejpam-3868	371	5	1924	1924	NUM
ejpam-3868	371	6	.	.	PUNCT
ejpam-3868	372	1	[	[	X
ejpam-3868	372	2	4	4	NUM
ejpam-3868	372	3	]	]	X
ejpam-3868	372	4	c.	c.	PROPN
ejpam-3868	372	5	grissom	grissom	PROPN
ejpam-3868	372	6	,	,	PUNCT
ejpam-3868	372	7	g.	g.	PROPN
ejpam-3868	372	8	thompson	thompson	PROPN
ejpam-3868	372	9	,	,	PUNCT
ejpam-3868	372	10	and	and	CCONJ
ejpam-3868	372	11	g.	g.	PROPN
ejpam-3868	372	12	wilkens	wilkens	PROPN
ejpam-3868	372	13	.	.	PUNCT
ejpam-3868	373	1	linearization	linearization	NOUN
ejpam-3868	373	2	of	of	ADP
ejpam-3868	373	3	second	second	ADJ
ejpam-3868	373	4	order	order	NOUN
ejpam-3868	373	5	ordinary	ordinary	ADJ
ejpam-3868	373	6	differential	differential	ADJ
ejpam-3868	373	7	equations	equation	NOUN
ejpam-3868	373	8	via	via	ADP
ejpam-3868	373	9	cartan	cartan	PROPN
ejpam-3868	373	10	’s	’s	PART
ejpam-3868	373	11	equivalence	equivalence	NOUN
ejpam-3868	373	12	method	method	NOUN
ejpam-3868	373	13	,	,	PUNCT
ejpam-3868	373	14	journal	journal	NOUN
ejpam-3868	373	15	of	of	ADP
ejpam-3868	373	16	differential	differential	ADJ
ejpam-3868	373	17	equations	equation	NOUN
ejpam-3868	373	18	,	,	PUNCT
ejpam-3868	373	19	77	77	NUM
ejpam-3868	373	20	.	.	NOUN
ejpam-3868	373	21	1	1	NUM
ejpam-3868	373	22	,	,	PUNCT
ejpam-3868	373	23	1989	1989	NUM
ejpam-3868	373	24	.	.	PUNCT
ejpam-3868	374	1	[	[	X
ejpam-3868	374	2	5	5	NUM
ejpam-3868	374	3	]	]	X
ejpam-3868	374	4	n.	n.	PROPN
ejpam-3868	374	5	h.	h.	PROPN
ejpam-3868	374	6	ibragimov	ibragimov	PROPN
ejpam-3868	374	7	and	and	CCONJ
ejpam-3868	374	8	franco	franco	NOUN
ejpam-3868	374	9	magri	magri	NOUN
ejpam-3868	374	10	.	.	PUNCT
ejpam-3868	375	1	geometric	geometric	ADJ
ejpam-3868	375	2	proof	proof	NOUN
ejpam-3868	375	3	of	of	ADP
ejpam-3868	375	4	lie	lie	NOUN
ejpam-3868	375	5	’s	’s	PART
ejpam-3868	375	6	linearization	linearization	NOUN
ejpam-3868	375	7	theorem	theorem	VERB
ejpam-3868	375	8	.	.	PUNCT
ejpam-3868	376	1	non	non	PROPN
ejpam-3868	376	2	.	.	PROPN
ejpam-3868	376	3	dynamics	dynamic	NOUN
ejpam-3868	376	4	,	,	PUNCT
ejpam-3868	376	5	36	36	NUM
ejpam-3868	376	6	,	,	PUNCT
ejpam-3868	376	7	2004	2004	NUM
ejpam-3868	376	8	.	.	PUNCT
ejpam-3868	377	1	[	[	X
ejpam-3868	377	2	6	6	X
ejpam-3868	377	3	]	]	X
ejpam-3868	377	4	douglas	douglas	PROPN
ejpam-3868	377	5	j.	j.	PROPN
ejpam-3868	377	6	the	the	DET
ejpam-3868	377	7	general	general	ADJ
ejpam-3868	377	8	geometry	geometry	NOUN
ejpam-3868	377	9	of	of	ADP
ejpam-3868	377	10	paths	path	NOUN
ejpam-3868	377	11	.	.	PUNCT
ejpam-3868	378	1	ann	ann	PROPN
ejpam-3868	378	2	.	.	PUNCT
ejpam-3868	378	3	math	math	PROPN
ejpam-3868	378	4	.	.	PUNCT
ejpam-3868	379	1	29	29	NUM
ejpam-3868	379	2	,	,	PUNCT
ejpam-3868	379	3	1927	1927	NUM
ejpam-3868	379	4	.	.	PUNCT
ejpam-3868	380	1	[	[	X
ejpam-3868	380	2	7	7	X
ejpam-3868	380	3	]	]	X
ejpam-3868	380	4	olver	olver	NOUN
ejpam-3868	380	5	p.	p.	PROPN
ejpam-3868	380	6	j.	j.	PROPN
ejpam-3868	380	7	equivalent	equivalent	ADJ
ejpam-3868	380	8	invariants	invariant	NOUN
ejpam-3868	380	9	and	and	CCONJ
ejpam-3868	380	10	symmetry	symmetry	NOUN
ejpam-3868	380	11	.	.	PUNCT
ejpam-3868	381	1	cambridge	cambridge	PROPN
ejpam-3868	381	2	university	university	PROPN
ejpam-3868	381	3	press	press	NOUN
ejpam-3868	381	4	,	,	PUNCT
ejpam-3868	381	5	1996	1996	NUM
ejpam-3868	381	6	.	.	PUNCT
ejpam-3868	382	1	[	[	X
ejpam-3868	382	2	8	8	NUM
ejpam-3868	382	3	]	]	X
ejpam-3868	382	4	bryant	bryant	PROPN
ejpam-3868	382	5	r	r	PROPN
ejpam-3868	382	6	l.	l.	PROPN
ejpam-3868	382	7	élie	élie	PROPN
ejpam-3868	382	8	cartan	cartan	ADJ
ejpam-3868	382	9	and	and	CCONJ
ejpam-3868	382	10	geometric	geometric	ADJ
ejpam-3868	382	11	duality	duality	NOUN
ejpam-3868	382	12	.	.	PUNCT
ejpam-3868	383	1	journées	journée	NOUN
ejpam-3868	383	2	élie	élie	VERB
ejpam-3868	383	3	cartan	cartan	ADJ
ejpam-3868	383	4	1998/1999	1998/1999	NUM
ejpam-3868	383	5	,	,	PUNCT
ejpam-3868	383	6	inst	inst	PROPN
ejpam-3868	383	7	.	.	PUNCT
ejpam-3868	384	1	é.	é.	PROPN
ejpam-3868	384	2	cartan	cartan	PROPN
ejpam-3868	384	3	16	16	NUM
ejpam-3868	384	4	,	,	PUNCT
ejpam-3868	384	5	2000	2000	NUM
ejpam-3868	384	6	.	.	PUNCT
ejpam-3868	385	1	[	[	X
ejpam-3868	385	2	9	9	NUM
ejpam-3868	385	3	]	]	X
ejpam-3868	385	4	crampin	crampin	NOUN
ejpam-3868	385	5	m	m	PROPN
ejpam-3868	385	6	and	and	CCONJ
ejpam-3868	385	7	saunders	saunders	PROPN
ejpam-3868	385	8	d.	d.	PROPN
ejpam-3868	385	9	cartan	cartan	PROPN
ejpam-3868	385	10	’s	’s	PART
ejpam-3868	385	11	concept	concept	NOUN
ejpam-3868	385	12	of	of	ADP
ejpam-3868	385	13	duality	duality	NOUN
ejpam-3868	385	14	for	for	ADP
ejpam-3868	385	15	second	second	ADJ
ejpam-3868	385	16	order	order	NOUN
ejpam-3868	385	17	ordinary	ordinary	ADJ
ejpam-3868	385	18	differential	differential	ADJ
ejpam-3868	385	19	equations	equation	NOUN
ejpam-3868	385	20	.	.	PUNCT
ejpam-3868	386	1	j.	j.	PROPN
ejpam-3868	386	2	geom	geom	PROPN
ejpam-3868	386	3	.	.	PUNCT
ejpam-3868	387	1	phys	phy	NOUN
ejpam-3868	387	2	.	.	PUNCT
ejpam-3868	388	1	54	54	NUM
ejpam-3868	388	2	,	,	PUNCT
ejpam-3868	388	3	2005	2005	NUM
ejpam-3868	388	4	.	.	PUNCT
ejpam-3868	389	1	[	[	X
ejpam-3868	389	2	10	10	NUM
ejpam-3868	389	3	]	]	PUNCT
ejpam-3868	389	4	tod	tod	X
ejpam-3868	389	5	k	k	PROPN
ejpam-3868	389	6	p	p	PROPN
ejpam-3868	389	7	,	,	PUNCT
ejpam-3868	389	8	einstein	einstein	NOUN
ejpam-3868	389	9	-	-	PUNCT
ejpam-3868	389	10	weyl	weyl	VERB
ejpam-3868	389	11	spaces	space	NOUN
ejpam-3868	389	12	,	,	PUNCT
ejpam-3868	389	13	and	and	CCONJ
ejpam-3868	389	14	third	third	ADJ
ejpam-3868	389	15	-	-	PUNCT
ejpam-3868	389	16	order	order	NOUN
ejpam-3868	389	17	differential	differential	ADJ
ejpam-3868	389	18	equations	equation	NOUN
ejpam-3868	389	19	.	.	PUNCT
ejpam-3868	390	1	j.	j.	PROPN
ejpam-3868	390	2	math	math	PROPN
ejpam-3868	390	3	.	.	PUNCT
ejpam-3868	391	1	phys	phy	NOUN
ejpam-3868	391	2	.	.	PUNCT
ejpam-3868	392	1	41	41	NUM
ejpam-3868	392	2	,	,	PUNCT
ejpam-3868	392	3	5572	5572	NUM
ejpam-3868	392	4	,	,	PUNCT
ejpam-3868	392	5	2000	2000	NUM
ejpam-3868	392	6	.	.	PUNCT
ejpam-3868	393	1	[	[	X
ejpam-3868	393	2	11	11	NUM
ejpam-3868	393	3	]	]	PUNCT
ejpam-3868	393	4	r.	r.	PROPN
ejpam-3868	393	5	penrose	penrose	PROPN
ejpam-3868	393	6	.	.	PUNCT
ejpam-3868	394	1	a	a	DET
ejpam-3868	394	2	spinor	spinor	NOUN
ejpam-3868	394	3	approach	approach	NOUN
ejpam-3868	394	4	to	to	ADP
ejpam-3868	394	5	general	general	ADJ
ejpam-3868	394	6	relativity	relativity	NOUN
ejpam-3868	394	7	,	,	PUNCT
ejpam-3868	394	8	ann	ann	PROPN
ejpam-3868	394	9	.	.	PUNCT
ejpam-3868	395	1	phys	phys	PROPN
ejpam-3868	395	2	.	.	PUNCT
ejpam-3868	395	3	,	,	PUNCT
ejpam-3868	395	4	10:171201	10:171201	NUM
ejpam-3868	395	5	,	,	PUNCT
ejpam-3868	395	6	,	,	PUNCT
ejpam-3868	395	7	1960	1960	NUM
ejpam-3868	395	8	.	.	PUNCT
ejpam-3868	396	1	[	[	X
ejpam-3868	396	2	12	12	NUM
ejpam-3868	396	3	]	]	X
ejpam-3868	396	4	chern	chern	PROPN
ejpam-3868	396	5	s.	s.	PROPN
ejpam-3868	396	6	s.	s.	PROPN
ejpam-3868	396	7	the	the	DET
ejpam-3868	396	8	geometry	geometry	NOUN
ejpam-3868	396	9	of	of	ADP
ejpam-3868	396	10	the	the	DET
ejpam-3868	396	11	differential	differential	ADJ
ejpam-3868	396	12	equation	equation	NOUN
ejpam-3868	396	13	y′′′	y′′′	PROPN
ejpam-3868	396	14	=	=	SYM
ejpam-3868	396	15	f	f	PROPN
ejpam-3868	396	16	(	(	PUNCT
ejpam-3868	396	17	x.y	x.y	PROPN
ejpam-3868	396	18	,	,	PUNCT
ejpam-3868	396	19	y′	y′	NUM
ejpam-3868	396	20	,	,	PUNCT
ejpam-3868	396	21	y′′	y′′	PROPN
ejpam-3868	396	22	)	)	PUNCT
ejpam-3868	396	23	,	,	PUNCT
ejpam-3868	396	24	1978	1978	NUM
ejpam-3868	396	25	.	.	PUNCT
ejpam-3868	397	1	[	[	X
ejpam-3868	397	2	13	13	NUM
ejpam-3868	397	3	]	]	X
ejpam-3868	397	4	fritelli	fritelli	PROPN
ejpam-3868	397	5	s	s	PROPN
ejpam-3868	397	6	,	,	PUNCT
ejpam-3868	397	7	kozameh	kozameh	PROPN
ejpam-3868	397	8	c	c	NOUN
ejpam-3868	397	9	,	,	PUNCT
ejpam-3868	397	10	and	and	CCONJ
ejpam-3868	397	11	newman	newman	PROPN
ejpam-3868	397	12	e.	e.	PROPN
ejpam-3868	397	13	differential	differential	PROPN
ejpam-3868	397	14	geometry	geometry	NOUN
ejpam-3868	397	15	from	from	ADP
ejpam-3868	397	16	differential	differential	ADJ
ejpam-3868	397	17	equations	equation	NOUN
ejpam-3868	397	18	.	.	PUNCT
ejpam-3868	398	1	commun	commun	PROPN
ejpam-3868	398	2	.	.	PUNCT
ejpam-3868	399	1	math	math	NOUN
ejpam-3868	399	2	.	.	PUNCT
ejpam-3868	400	1	phys	phy	NOUN
ejpam-3868	400	2	.	.	PUNCT
ejpam-3868	400	3	223	223	NUM
ejpam-3868	400	4	,	,	PUNCT
ejpam-3868	400	5	2001	2001	NUM
ejpam-3868	400	6	.	.	PUNCT
ejpam-3868	401	1	references	reference	NOUN
ejpam-3868	401	2	1034	1034	NUM
ejpam-3868	401	3	[	[	X
ejpam-3868	401	4	14	14	NUM
ejpam-3868	401	5	]	]	PUNCT
ejpam-3868	401	6	z.	z.	PROPN
ejpam-3868	401	7	shen	shen	PROPN
ejpam-3868	401	8	.	.	PUNCT
ejpam-3868	402	1	differential	differential	ADJ
ejpam-3868	402	2	geometry	geometry	NOUN
ejpam-3868	402	3	of	of	ADP
ejpam-3868	402	4	spray	spray	NOUN
ejpam-3868	402	5	and	and	CCONJ
ejpam-3868	402	6	finsler	finsler	NOUN
ejpam-3868	402	7	spaces	space	NOUN
ejpam-3868	402	8	.	.	PUNCT
ejpam-3868	403	1	klewer	klewer	PROPN
ejpam-3868	403	2	,	,	PUNCT
ejpam-3868	403	3	dordrecht	dordrecht	PROPN
ejpam-3868	403	4	,	,	PUNCT
ejpam-3868	403	5	2001	2001	NUM
ejpam-3868	403	6	.	.	PUNCT
ejpam-3868	404	1	[	[	X
ejpam-3868	404	2	15	15	NUM
ejpam-3868	404	3	]	]	PUNCT
ejpam-3868	404	4	a.	a.	NOUN
ejpam-3868	404	5	trautman	trautman	NOUN
ejpam-3868	404	6	.	.	PUNCT
ejpam-3868	405	1	deformations	deformation	NOUN
ejpam-3868	405	2	of	of	ADP
ejpam-3868	405	3	the	the	DET
ejpam-3868	405	4	hodge	hodge	PROPN
ejpam-3868	405	5	map	map	NOUN
ejpam-3868	405	6	and	and	CCONJ
ejpam-3868	405	7	optical	optical	ADJ
ejpam-3868	405	8	geometry	geometry	NOUN
ejpam-3868	405	9	.	.	PUNCT
ejpam-3868	406	1	j.	j.	PROPN
ejpam-3868	406	2	geom	geom	PROPN
ejpam-3868	406	3	.	.	PUNCT
ejpam-3868	407	1	phys	phy	NOUN
ejpam-3868	407	2	.	.	PUNCT
ejpam-3868	407	3	,	,	PUNCT
ejpam-3868	407	4	1:8595	1:8595	NUM
ejpam-3868	407	5	,	,	PUNCT
ejpam-3868	407	6	,	,	PUNCT
ejpam-3868	407	7	1984	1984	NUM
ejpam-3868	407	8	.	.	PUNCT
ejpam-3868	408	1	[	[	X
ejpam-3868	408	2	16	16	NUM
ejpam-3868	408	3	]	]	X
ejpam-3868	408	4	sharpe	sharpe	PROPN
ejpam-3868	408	5	r.	r.	PROPN
ejpam-3868	408	6	w.	w.	PROPN
ejpam-3868	408	7	differential	differential	PROPN
ejpam-3868	408	8	geometry	geometry	NOUN
ejpam-3868	408	9	.	.	PUNCT
ejpam-3868	409	1	springer	springer	NOUN
ejpam-3868	409	2	-	-	PUNCT
ejpam-3868	409	3	verlag	verlag	PROPN
ejpam-3868	409	4	,	,	PUNCT
ejpam-3868	409	5	berlin	berlin	PROPN
ejpam-3868	409	6	,	,	PUNCT
ejpam-3868	409	7	1997	1997	NUM
ejpam-3868	409	8	.	.	PUNCT