id	sid	tid	token	lemma	pos
ma-310	1	1	2025	2025	NUM
ma-310	1	2	ada	ada	PROPN
ma-310	1	3	academica	academica	PROPN
ma-310	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-310	1	5	.	.	PUNCT
ma-310	2	1	j.	j.	PROPN
ma-310	2	2	math	math	PROPN
ma-310	2	3	.	.	PUNCT
ma-310	3	1	anal	anal	ADJ
ma-310	3	2	.	.	PUNCT
ma-310	4	1	5	5	NUM
ma-310	4	2	(	(	PUNCT
ma-310	4	3	2025	2025	NUM
ma-310	4	4	)	)	PUNCT
ma-310	4	5	10doi	10doi	NUM
ma-310	4	6	:	:	PUNCT
ma-310	4	7	10.28924	10.28924	NUM
ma-310	4	8	/	/	SYM
ma-310	4	9	ada	ada	PROPN
ma-310	4	10	/	/	SYM
ma-310	4	11	ma.5.10	ma.5.10	PROPN
ma-310	4	12	neumann	neumann	PROPN
ma-310	4	13	and	and	CCONJ
ma-310	4	14	dirichlet	dirichlet	PROPN
ma-310	4	15	problems	problem	NOUN
ma-310	4	16	for	for	ADP
ma-310	4	17	the	the	DET
ma-310	4	18	cauchy	cauchy	PROPN
ma-310	4	19	–	–	PUNCT
ma-310	4	20	riemann	riemann	PROPN
ma-310	4	21	and	and	CCONJ
ma-310	4	22	the	the	DET
ma-310	4	23	poisson	poisson	PROPN
ma-310	4	24	equations	equation	NOUN
ma-310	4	25	in	in	ADP
ma-310	4	26	the	the	DET
ma-310	4	27	partial	partial	ADJ
ma-310	4	28	eclipse	eclipse	NOUN
ma-310	4	29	domain	domain	NOUN
ma-310	4	30	ali	ali	PROPN
ma-310	4	31	darya∗	darya∗	PROPN
ma-310	4	32	,	,	PUNCT
ma-310	4	33	nasir	nasir	PROPN
ma-310	4	34	taghizadeh	taghizadeh	PROPN
ma-310	4	35	faculty	faculty	NOUN
ma-310	4	36	of	of	ADP
ma-310	4	37	mathematics	mathematics	PROPN
ma-310	4	38	sciences	sciences	PROPN
ma-310	4	39	,	,	PUNCT
ma-310	4	40	university	university	NOUN
ma-310	4	41	of	of	ADP
ma-310	4	42	guilan	guilan	PROPN
ma-310	4	43	,	,	PUNCT
ma-310	4	44	rasht	rasht	NOUN
ma-310	4	45	,	,	PUNCT
ma-310	4	46	19141	19141	NUM
ma-310	4	47	,	,	PUNCT
ma-310	4	48	iran	iran	PROPN
ma-310	4	49	alidarya@phd.guilan.ac.ir	alidarya@phd.guilan.ac.ir	VERB
ma-310	4	50	,	,	PUNCT
ma-310	4	51	taghizadeh@guilan.ac.ir	taghizadeh@guilan.ac.ir	ADJ
ma-310	4	52	∗correspondence	∗correspondence	NOUN
ma-310	4	53	:	:	PUNCT
ma-310	4	54	alidarya@phd.guilan.ac.ir	alidarya@phd.guilan.ac.ir	PROPN
ma-310	4	55	abstract	abstract	ADJ
ma-310	4	56	.	.	PUNCT
ma-310	5	1	in	in	ADP
ma-310	5	2	this	this	DET
ma-310	5	3	paper	paper	NOUN
ma-310	5	4	,	,	PUNCT
ma-310	5	5	we	we	PRON
ma-310	5	6	consider	consider	VERB
ma-310	5	7	the	the	DET
ma-310	5	8	neumann	neumann	PROPN
ma-310	5	9	boundary	boundary	PROPN
ma-310	5	10	value	value	NOUN
ma-310	5	11	problem	problem	NOUN
ma-310	5	12	and	and	CCONJ
ma-310	5	13	the	the	DET
ma-310	5	14	dirichlet	dirichlet	PROPN
ma-310	5	15	boundaryvalue	boundaryvalue	PROPN
ma-310	5	16	problem	problem	NOUN
ma-310	5	17	for	for	ADP
ma-310	5	18	complex	complex	ADJ
ma-310	5	19	partial	partial	ADJ
ma-310	5	20	differential	differential	NOUN
ma-310	5	21	equations	equation	NOUN
ma-310	5	22	in	in	ADP
ma-310	5	23	the	the	DET
ma-310	5	24	partial	partial	ADJ
ma-310	5	25	eclipse	eclipse	NOUN
ma-310	5	26	domain	domain	NOUN
ma-310	5	27	.	.	PUNCT
ma-310	6	1	first	first	ADV
ma-310	6	2	,	,	PUNCT
ma-310	6	3	by	by	ADP
ma-310	6	4	theparqueting	theparquete	VERB
ma-310	6	5	–	–	PUNCT
ma-310	6	6	reflection	reflection	NOUN
ma-310	6	7	principle	principle	NOUN
ma-310	6	8	and	and	CCONJ
ma-310	6	9	the	the	DET
ma-310	6	10	cauchy	cauchy	PROPN
ma-310	6	11	–	–	PUNCT
ma-310	6	12	pompeiu	pompeiu	NOUN
ma-310	6	13	formula	formula	NOUN
ma-310	6	14	,	,	PUNCT
ma-310	6	15	a	a	DET
ma-310	6	16	modified	modify	VERB
ma-310	6	17	integral	integral	ADJ
ma-310	6	18	representationformula	representationformula	NOUN
ma-310	6	19	in	in	ADP
ma-310	6	20	the	the	DET
ma-310	6	21	partial	partial	ADJ
ma-310	6	22	eclipse	eclipse	NOUN
ma-310	6	23	domain	domain	NOUN
ma-310	6	24	is	be	AUX
ma-310	6	25	constructed	construct	VERB
ma-310	6	26	.	.	PUNCT
ma-310	7	1	then	then	ADV
ma-310	7	2	,	,	PUNCT
ma-310	7	3	we	we	PRON
ma-310	7	4	explicitly	explicitly	ADV
ma-310	7	5	solve	solve	VERB
ma-310	7	6	the	the	DET
ma-310	7	7	neumann	neumann	PROPN
ma-310	7	8	problemfor	problemfor	ADP
ma-310	7	9	the	the	DET
ma-310	7	10	homogeneous	homogeneous	ADJ
ma-310	7	11	equation	equation	NOUN
ma-310	7	12	and	and	CCONJ
ma-310	7	13	discuss	discuss	VERB
ma-310	7	14	the	the	DET
ma-310	7	15	solvability	solvability	NOUN
ma-310	7	16	conditions	condition	NOUN
ma-310	7	17	.	.	PUNCT
ma-310	8	1	moreover	moreover	ADV
ma-310	8	2	,	,	PUNCT
ma-310	8	3	we	we	PRON
ma-310	8	4	investigate	investigate	VERB
ma-310	8	5	thedirichlet	thedirichlet	ADJ
ma-310	8	6	problem	problem	NOUN
ma-310	8	7	for	for	ADP
ma-310	8	8	the	the	DET
ma-310	8	9	poisson	poisson	NOUN
ma-310	8	10	equation	equation	NOUN
ma-310	8	11	in	in	ADP
ma-310	8	12	the	the	DET
ma-310	8	13	partial	partial	ADJ
ma-310	8	14	eclipse	eclipse	NOUN
ma-310	8	15	domain	domain	NOUN
ma-310	8	16	.	.	PUNCT
ma-310	9	1	in	in	ADP
ma-310	9	2	other	other	ADJ
ma-310	9	3	words	word	NOUN
ma-310	9	4	,	,	PUNCT
ma-310	9	5	with	with	ADP
ma-310	9	6	thehelp	thehelp	NOUN
ma-310	9	7	of	of	ADP
ma-310	9	8	the	the	DET
ma-310	9	9	green	green	PROPN
ma-310	9	10	’s	’s	PART
ma-310	9	11	function	function	NOUN
ma-310	9	12	,	,	PUNCT
ma-310	9	13	we	we	PRON
ma-310	9	14	provide	provide	VERB
ma-310	9	15	a	a	DET
ma-310	9	16	unique	unique	ADJ
ma-310	9	17	solution	solution	NOUN
ma-310	9	18	for	for	ADP
ma-310	9	19	the	the	DET
ma-310	9	20	dirichlet	dirichlet	PROPN
ma-310	9	21	boundary	boundary	ADJ
ma-310	9	22	value	value	NOUN
ma-310	9	23	problemfor	problemfor	ADP
ma-310	9	24	the	the	DET
ma-310	9	25	poisson	poisson	NOUN
ma-310	9	26	equation	equation	NOUN
ma-310	9	27	and	and	CCONJ
ma-310	9	28	consider	consider	VERB
ma-310	9	29	boundary	boundary	ADJ
ma-310	9	30	behavior	behavior	NOUN
ma-310	9	31	.	.	PUNCT
ma-310	10	1	1	1	X
ma-310	10	2	.	.	X
ma-310	10	3	introduction	introduction	NOUN
ma-310	10	4	mathematical	mathematical	ADJ
ma-310	10	5	analysis	analysis	NOUN
ma-310	10	6	is	be	AUX
ma-310	10	7	an	an	DET
ma-310	10	8	active	active	ADJ
ma-310	10	9	branch	branch	NOUN
ma-310	10	10	in	in	ADP
ma-310	10	11	mathematics	mathematic	NOUN
ma-310	10	12	which	which	PRON
ma-310	10	13	has	have	AUX
ma-310	10	14	grown	grow	VERB
ma-310	10	15	significantly	significantly	ADV
ma-310	10	16	.	.	PUNCT
ma-310	11	1	it	it	PRON
ma-310	11	2	hasindeed	hasindee	VERB
ma-310	11	3	flourished	flourish	VERB
ma-310	11	4	,	,	PUNCT
ma-310	11	5	playing	play	VERB
ma-310	11	6	a	a	DET
ma-310	11	7	pivotal	pivotal	ADJ
ma-310	11	8	role	role	NOUN
ma-310	11	9	in	in	ADP
ma-310	11	10	advancement	advancement	NOUN
ma-310	11	11	of	of	ADP
ma-310	11	12	both	both	CCONJ
ma-310	11	13	pure	pure	ADJ
ma-310	11	14	and	and	CCONJ
ma-310	11	15	applied	apply	VERB
ma-310	11	16	mathematics.its	mathematics.its	X
ma-310	11	17	growth	growth	NOUN
ma-310	11	18	can	can	AUX
ma-310	11	19	be	be	AUX
ma-310	11	20	seen	see	VERB
ma-310	11	21	in	in	ADP
ma-310	11	22	the	the	DET
ma-310	11	23	development	development	NOUN
ma-310	11	24	of	of	ADP
ma-310	11	25	new	new	ADJ
ma-310	11	26	techniques	technique	NOUN
ma-310	11	27	for	for	ADP
ma-310	11	28	solving	solve	VERB
ma-310	11	29	differential	differential	ADJ
ma-310	11	30	equations	equation	NOUN
ma-310	11	31	,	,	PUNCT
ma-310	11	32	advancements	advancement	NOUN
ma-310	11	33	in	in	ADP
ma-310	11	34	complex	complex	ADJ
ma-310	11	35	analysis	analysis	NOUN
ma-310	11	36	,	,	PUNCT
ma-310	11	37	and	and	CCONJ
ma-310	11	38	profound	profound	ADJ
ma-310	11	39	contributions	contribution	NOUN
ma-310	11	40	to	to	ADP
ma-310	11	41	functional	functional	ADJ
ma-310	11	42	analysis	analysis	NOUN
ma-310	11	43	.	.	PUNCT
ma-310	12	1	this	this	DET
ma-310	12	2	expan	expan	PROPN
ma-310	12	3	-	-	PUNCT
ma-310	12	4	sion	sion	PROPN
ma-310	12	5	has	have	AUX
ma-310	12	6	not	not	PART
ma-310	12	7	only	only	ADV
ma-310	12	8	deepened	deepen	VERB
ma-310	12	9	our	our	PRON
ma-310	12	10	theoretical	theoretical	ADJ
ma-310	12	11	understanding	understanding	NOUN
ma-310	12	12	but	but	CCONJ
ma-310	12	13	has	have	AUX
ma-310	12	14	also	also	ADV
ma-310	12	15	paved	pave	VERB
ma-310	12	16	the	the	DET
ma-310	12	17	way	way	NOUN
ma-310	12	18	for	for	ADP
ma-310	12	19	practicalapplications	practicalapplication	NOUN
ma-310	12	20	in	in	ADP
ma-310	12	21	fields	field	NOUN
ma-310	12	22	like	like	ADP
ma-310	12	23	mathematical	mathematical	ADJ
ma-310	12	24	physics	physics	NOUN
ma-310	12	25	,	,	PUNCT
ma-310	12	26	fluid	fluid	ADJ
ma-310	12	27	dynamics	dynamic	NOUN
ma-310	12	28	,	,	PUNCT
ma-310	12	29	engineering	engineering	NOUN
ma-310	12	30	,	,	PUNCT
ma-310	12	31	etc	etc	X
ma-310	13	1	[	[	X
ma-310	13	2	1	1	NUM
ma-310	13	3	,	,	PUNCT
ma-310	13	4	3	3	NUM
ma-310	13	5	,	,	PUNCT
ma-310	13	6	6	6	NUM
ma-310	13	7	,	,	PUNCT
ma-310	13	8	9].the	9].the	DET
ma-310	13	9	theory	theory	NOUN
ma-310	13	10	of	of	ADP
ma-310	13	11	boundary	boundary	ADJ
ma-310	13	12	value	value	NOUN
ma-310	13	13	problems	problem	NOUN
ma-310	13	14	for	for	ADP
ma-310	13	15	partial	partial	ADJ
ma-310	13	16	differential	differential	ADJ
ma-310	13	17	equations	equation	NOUN
ma-310	13	18	is	be	AUX
ma-310	13	19	a	a	DET
ma-310	13	20	key	key	ADJ
ma-310	13	21	area	area	NOUN
ma-310	13	22	in	in	ADP
ma-310	13	23	math	math	NOUN
ma-310	13	24	-	-	PUNCT
ma-310	13	25	ematical	ematical	ADJ
ma-310	13	26	analysis	analysis	NOUN
ma-310	13	27	and	and	CCONJ
ma-310	13	28	mathematical	mathematical	ADJ
ma-310	13	29	physics	physics	NOUN
ma-310	13	30	.	.	PUNCT
ma-310	14	1	the	the	DET
ma-310	14	2	theory	theory	NOUN
ma-310	14	3	often	often	ADV
ma-310	14	4	focuses	focus	VERB
ma-310	14	5	on	on	ADP
ma-310	14	6	conditions	condition	NOUN
ma-310	14	7	under	under	ADP
ma-310	14	8	whichsolutions	whichsolution	NOUN
ma-310	14	9	exist	exist	VERB
ma-310	14	10	and	and	CCONJ
ma-310	14	11	are	be	AUX
ma-310	14	12	unique	unique	ADJ
ma-310	14	13	.	.	PUNCT
ma-310	15	1	these	these	DET
ma-310	15	2	conditions	condition	NOUN
ma-310	15	3	can	can	AUX
ma-310	15	4	depend	depend	VERB
ma-310	15	5	on	on	ADP
ma-310	15	6	the	the	DET
ma-310	15	7	properties	property	NOUN
ma-310	15	8	of	of	ADP
ma-310	15	9	the	the	DET
ma-310	15	10	differential	differential	ADJ
ma-310	15	11	op	op	NOUN
ma-310	15	12	-	-	PUNCT
ma-310	15	13	erator	erator	NOUN
ma-310	15	14	,	,	PUNCT
ma-310	15	15	the	the	DET
ma-310	15	16	domain	domain	NOUN
ma-310	15	17	,	,	PUNCT
ma-310	15	18	and	and	CCONJ
ma-310	15	19	the	the	DET
ma-310	15	20	boundary	boundary	ADJ
ma-310	15	21	conditions	condition	NOUN
ma-310	15	22	.	.	PUNCT
ma-310	16	1	boundary	boundary	ADJ
ma-310	16	2	value	value	NOUN
ma-310	16	3	problems	problem	NOUN
ma-310	16	4	are	be	AUX
ma-310	16	5	critical	critical	ADJ
ma-310	16	6	in	in	ADP
ma-310	16	7	the	the	DET
ma-310	16	8	studyof	studyof	ADJ
ma-310	16	9	partial	partial	ADJ
ma-310	16	10	differential	differential	NOUN
ma-310	16	11	equations	equation	NOUN
ma-310	16	12	,	,	PUNCT
ma-310	16	13	as	as	SCONJ
ma-310	16	14	they	they	PRON
ma-310	16	15	involve	involve	VERB
ma-310	16	16	finding	find	VERB
ma-310	16	17	a	a	DET
ma-310	16	18	solution	solution	NOUN
ma-310	16	19	to	to	ADP
ma-310	16	20	a	a	DET
ma-310	16	21	partial	partial	ADJ
ma-310	16	22	differential	differential	NOUN
ma-310	16	23	equationthat	equationthat	PROPN
ma-310	16	24	satisfies	satisfy	VERB
ma-310	16	25	certain	certain	ADJ
ma-310	16	26	conditions	condition	NOUN
ma-310	16	27	at	at	ADP
ma-310	16	28	the	the	DET
ma-310	16	29	boundaries	boundary	NOUN
ma-310	16	30	of	of	ADP
ma-310	16	31	the	the	DET
ma-310	16	32	domain	domain	NOUN
ma-310	16	33	.	.	PUNCT
ma-310	17	1	the	the	DET
ma-310	17	2	most	most	ADV
ma-310	17	3	common	common	ADJ
ma-310	17	4	boundary	boundary	ADJ
ma-310	17	5	valueproblems	valueproblem	NOUN
ma-310	17	6	are	be	AUX
ma-310	17	7	the	the	DET
ma-310	17	8	dirichlet	dirichlet	PROPN
ma-310	17	9	,	,	PUNCT
ma-310	17	10	the	the	DET
ma-310	17	11	neumann	neumann	PROPN
ma-310	17	12	and	and	CCONJ
ma-310	17	13	the	the	DET
ma-310	17	14	schwarz	schwarz	PROPN
ma-310	17	15	problems	problem	NOUN
ma-310	17	16	.	.	PUNCT
ma-310	18	1	in	in	ADP
ma-310	18	2	particular	particular	ADJ
ma-310	18	3	,	,	PUNCT
ma-310	18	4	the	the	DET
ma-310	18	5	dirichlet	dirichlet	NOUN
ma-310	18	6	received	receive	VERB
ma-310	18	7	:	:	PUNCT
ma-310	18	8	2	2	NUM
ma-310	18	9	dec	dec	PROPN
ma-310	18	10	2024	2024	NUM
ma-310	18	11	.	.	PUNCT
ma-310	19	1	key	key	ADJ
ma-310	19	2	words	word	NOUN
ma-310	19	3	and	and	CCONJ
ma-310	19	4	phrases	phrase	NOUN
ma-310	19	5	.	.	PUNCT
ma-310	20	1	boundary	boundary	ADJ
ma-310	20	2	value	value	NOUN
ma-310	20	3	problem	problem	NOUN
ma-310	20	4	;	;	PUNCT
ma-310	20	5	neumann	neumann	PROPN
ma-310	20	6	problem	problem	NOUN
ma-310	20	7	;	;	PUNCT
ma-310	20	8	dirichlet	dirichlet	PROPN
ma-310	20	9	problem	problem	NOUN
ma-310	20	10	;	;	PUNCT
ma-310	20	11	partial	partial	ADJ
ma-310	20	12	eclipse	eclipse	NOUN
ma-310	20	13	domain.1	domain.1	PROPN
ma-310	20	14	https://adac.ee	https://adac.ee	PROPN
ma-310	20	15	https://doi.org/10.28924/ada/ma.5.10	https://doi.org/10.28924/ada/ma.5.10	PROPN
ma-310	20	16	eur	eur	PROPN
ma-310	20	17	.	.	PUNCT
ma-310	21	1	j.	j.	PROPN
ma-310	21	2	math	math	PROPN
ma-310	21	3	.	.	PUNCT
ma-310	22	1	anal	anal	PROPN
ma-310	22	2	.	.	PUNCT
ma-310	23	1	10.28924	10.28924	NUM
ma-310	23	2	/	/	SYM
ma-310	23	3	ada	ada	NOUN
ma-310	23	4	/	/	SYM
ma-310	23	5	ma.5.10	ma.5.10	NOUN
ma-310	23	6	2problem	2problem	PROPN
ma-310	23	7	specifies	specify	VERB
ma-310	23	8	the	the	DET
ma-310	23	9	value	value	NOUN
ma-310	23	10	of	of	ADP
ma-310	23	11	the	the	DET
ma-310	23	12	function	function	NOUN
ma-310	23	13	on	on	ADP
ma-310	23	14	the	the	DET
ma-310	23	15	boundary	boundary	NOUN
ma-310	23	16	and	and	CCONJ
ma-310	23	17	the	the	DET
ma-310	23	18	neumann	neumann	PROPN
ma-310	23	19	problem	problem	NOUN
ma-310	23	20	specifiesthe	specifiesthe	DET
ma-310	23	21	values	value	NOUN
ma-310	23	22	of	of	ADP
ma-310	23	23	the	the	DET
ma-310	23	24	derivative	derivative	NOUN
ma-310	23	25	(	(	PUNCT
ma-310	23	26	normal	normal	ADJ
ma-310	23	27	to	to	ADP
ma-310	23	28	the	the	DET
ma-310	23	29	boundary).several	boundary).several	ADJ
ma-310	23	30	analytical	analytical	ADJ
ma-310	23	31	and	and	CCONJ
ma-310	23	32	computational	computational	ADJ
ma-310	23	33	methods	method	NOUN
ma-310	23	34	are	be	AUX
ma-310	23	35	used	use	VERB
ma-310	23	36	to	to	PART
ma-310	23	37	solve	solve	VERB
ma-310	23	38	boundary	boundary	ADJ
ma-310	23	39	value	value	NOUN
ma-310	23	40	problems	problem	NOUN
ma-310	23	41	,	,	PUNCT
ma-310	23	42	includ	includ	NOUN
ma-310	23	43	-	-	ADJ
ma-310	23	44	ing	ing	ADJ
ma-310	23	45	integral	integral	ADJ
ma-310	23	46	representation	representation	NOUN
ma-310	23	47	formulas	formula	NOUN
ma-310	23	48	,	,	PUNCT
ma-310	23	49	the	the	DET
ma-310	23	50	green	green	PROPN
ma-310	23	51	’s	’s	PART
ma-310	23	52	functions	function	NOUN
ma-310	23	53	,	,	PUNCT
ma-310	23	54	etc	etc	X
ma-310	23	55	.	.	X
ma-310	23	56	integral	integral	ADJ
ma-310	23	57	representation	representation	NOUN
ma-310	23	58	formulasare	formulasare	NOUN
ma-310	23	59	crucial	crucial	ADJ
ma-310	23	60	tools	tool	NOUN
ma-310	23	61	in	in	ADP
ma-310	23	62	solving	solve	VERB
ma-310	23	63	complex	complex	ADJ
ma-310	23	64	boundary	boundary	ADJ
ma-310	23	65	value	value	NOUN
ma-310	23	66	problems	problem	NOUN
ma-310	23	67	,	,	PUNCT
ma-310	23	68	especially	especially	ADV
ma-310	23	69	for	for	ADP
ma-310	23	70	analytic	analytic	ADJ
ma-310	23	71	and	and	CCONJ
ma-310	23	72	harmonicfunctions	harmonicfunction	NOUN
ma-310	23	73	.	.	PUNCT
ma-310	24	1	the	the	DET
ma-310	24	2	green	green	PROPN
ma-310	24	3	’s	’s	PART
ma-310	24	4	functions	function	NOUN
ma-310	24	5	are	be	AUX
ma-310	24	6	used	use	VERB
ma-310	24	7	to	to	PART
ma-310	24	8	construct	construct	VERB
ma-310	24	9	solutions	solution	NOUN
ma-310	24	10	for	for	ADP
ma-310	24	11	complex	complex	ADJ
ma-310	24	12	partial	partial	ADJ
ma-310	24	13	equation	equation	NOUN
ma-310	24	14	withboundary	withboundary	ADJ
ma-310	24	15	conditions	condition	NOUN
ma-310	24	16	.	.	PUNCT
ma-310	25	1	for	for	ADP
ma-310	25	2	the	the	DET
ma-310	25	3	dirichlet	dirichlet	PROPN
ma-310	25	4	problem	problem	NOUN
ma-310	25	5	,	,	PUNCT
ma-310	25	6	the	the	DET
ma-310	25	7	green	green	NOUN
ma-310	25	8	’s	’s	PART
ma-310	25	9	function	function	NOUN
ma-310	25	10	represents	represent	VERB
ma-310	25	11	the	the	DET
ma-310	25	12	influence	influence	NOUN
ma-310	25	13	of	of	ADP
ma-310	25	14	apoint	apoint	NOUN
ma-310	25	15	source	source	NOUN
ma-310	25	16	on	on	ADP
ma-310	25	17	the	the	DET
ma-310	25	18	boundary	boundary	NOUN
ma-310	25	19	and	and	CCONJ
ma-310	25	20	is	be	AUX
ma-310	25	21	used	use	VERB
ma-310	25	22	to	to	PART
ma-310	25	23	build	build	VERB
ma-310	25	24	the	the	DET
ma-310	25	25	solution	solution	NOUN
ma-310	25	26	,	,	PUNCT
ma-310	25	27	see	see	VERB
ma-310	25	28	[	[	X
ma-310	25	29	1–9,16].in	1–9,16].in	NUM
ma-310	25	30	recent	recent	ADJ
ma-310	25	31	years	year	NOUN
ma-310	25	32	,	,	PUNCT
ma-310	25	33	many	many	ADJ
ma-310	25	34	mathematician	mathematician	NOUN
ma-310	25	35	have	have	AUX
ma-310	25	36	studied	study	VERB
ma-310	25	37	boundary	boundary	ADJ
ma-310	25	38	value	value	NOUN
ma-310	25	39	problems	problem	NOUN
ma-310	25	40	for	for	ADP
ma-310	25	41	complex	complex	ADJ
ma-310	25	42	partialdifferential	partialdifferential	ADJ
ma-310	25	43	equations	equation	NOUN
ma-310	25	44	and	and	CCONJ
ma-310	25	45	numerous	numerous	ADJ
ma-310	25	46	results	result	NOUN
ma-310	25	47	have	have	AUX
ma-310	25	48	been	be	AUX
ma-310	25	49	obtained	obtain	VERB
ma-310	25	50	,	,	PUNCT
ma-310	25	51	can	can	AUX
ma-310	25	52	be	be	AUX
ma-310	25	53	referenced	reference	VERB
ma-310	25	54	in	in	ADP
ma-310	25	55	[	[	X
ma-310	25	56	1–16	1–16	NOUN
ma-310	25	57	]	]	PUNCT
ma-310	25	58	.	.	PUNCT
ma-310	26	1	in2024	in2024	VERB
ma-310	26	2	,	,	PUNCT
ma-310	26	3	we	we	PRON
ma-310	26	4	introduced	introduce	VERB
ma-310	26	5	a	a	DET
ma-310	26	6	new	new	ADJ
ma-310	26	7	domain	domain	NOUN
ma-310	26	8	called	call	VERB
ma-310	26	9	partial	partial	ADJ
ma-310	26	10	eclipse	eclipse	NOUN
ma-310	26	11	and	and	CCONJ
ma-310	26	12	also	also	ADV
ma-310	26	13	investigated	investigate	VERB
ma-310	26	14	the	the	DET
ma-310	26	15	schwarz	schwarz	PROPN
ma-310	26	16	andthe	andthe	PROPN
ma-310	26	17	dirichlet	dirichlet	PROPN
ma-310	26	18	boundary	boundary	PROPN
ma-310	26	19	value	value	NOUN
ma-310	26	20	problem	problem	NOUN
ma-310	26	21	for	for	ADP
ma-310	26	22	cauchy	cauchy	PROPN
ma-310	26	23	–	–	PUNCT
ma-310	26	24	riemann	riemann	PROPN
ma-310	26	25	equations	equation	NOUN
ma-310	26	26	in	in	ADP
ma-310	26	27	the	the	DET
ma-310	26	28	partial	partial	ADJ
ma-310	26	29	eclipse	eclipse	NOUN
ma-310	26	30	domain	domain	NOUN
ma-310	26	31	,	,	PUNCT
ma-310	26	32	(	(	PUNCT
ma-310	26	33	ali	ali	PROPN
ma-310	26	34	darya	darya	PROPN
ma-310	26	35	and	and	CCONJ
ma-310	26	36	nasir	nasir	PROPN
ma-310	26	37	taghizadeh	taghizadeh	PROPN
ma-310	26	38	,	,	PUNCT
ma-310	26	39	“	"	PUNCT
ma-310	26	40	schwarz	schwarz	NOUN
ma-310	26	41	and	and	CCONJ
ma-310	26	42	dirichlet	dirichlet	PROPN
ma-310	26	43	problems	problem	NOUN
ma-310	26	44	for	for	ADP
ma-310	26	45	complex	complex	ADJ
ma-310	26	46	partial	partial	ADJ
ma-310	26	47	differentialequations	differentialequation	NOUN
ma-310	26	48	in	in	ADP
ma-310	26	49	the	the	DET
ma-310	26	50	eclipse	eclipse	NOUN
ma-310	26	51	domain	domain	NOUN
ma-310	26	52	,	,	PUNCT
ma-310	26	53	”	"	PUNCT
ma-310	26	54	j	j	PROPN
ma-310	26	55	math	math	PROPN
ma-310	26	56	sci	sci	PROPN
ma-310	26	57	)	)	PUNCT
ma-310	26	58	see	see	VERB
ma-310	27	1	[	[	X
ma-310	27	2	1].in	1].in	NUM
ma-310	27	3	the	the	DET
ma-310	27	4	present	present	ADJ
ma-310	27	5	paper	paper	NOUN
ma-310	27	6	,	,	PUNCT
ma-310	27	7	we	we	PRON
ma-310	27	8	consider	consider	VERB
ma-310	27	9	the	the	DET
ma-310	27	10	neumann	neumann	PROPN
ma-310	27	11	problem	problem	NOUN
ma-310	27	12	for	for	ADP
ma-310	27	13	first	first	ADJ
ma-310	27	14	-	-	PUNCT
ma-310	27	15	order	order	NOUN
ma-310	27	16	partial	partial	ADJ
ma-310	27	17	differential	differential	ADJ
ma-310	27	18	equa	equa	NOUN
ma-310	27	19	-	-	PUNCT
ma-310	27	20	tion	tion	NOUN
ma-310	27	21	and	and	CCONJ
ma-310	27	22	the	the	DET
ma-310	27	23	dirichlet	dirichlet	PROPN
ma-310	27	24	problem	problem	NOUN
ma-310	27	25	for	for	ADP
ma-310	27	26	second	second	ADJ
ma-310	27	27	-	-	PUNCT
ma-310	27	28	order	order	NOUN
ma-310	27	29	partial	partial	ADJ
ma-310	27	30	differential	differential	NOUN
ma-310	27	31	equation	equation	NOUN
ma-310	27	32	in	in	ADP
ma-310	27	33	the	the	DET
ma-310	27	34	partial	partial	ADJ
ma-310	27	35	eclipsedomain	eclipsedomain	NOUN
ma-310	27	36	.	.	PUNCT
ma-310	28	1	in	in	ADP
ma-310	28	2	other	other	ADJ
ma-310	28	3	words	word	NOUN
ma-310	28	4	,	,	PUNCT
ma-310	28	5	we	we	PRON
ma-310	28	6	first	first	ADV
ma-310	28	7	solve	solve	VERB
ma-310	28	8	the	the	DET
ma-310	28	9	neumann	neumann	PROPN
ma-310	28	10	problem	problem	VERB
ma-310	28	11	the	the	DET
ma-310	28	12	homogeneous	homogeneous	ADJ
ma-310	28	13	cauchy	cauchy	NOUN
ma-310	28	14	–	–	PUNCT
ma-310	28	15	riemannequation	riemannequation	NOUN
ma-310	28	16	and	and	CCONJ
ma-310	28	17	discuss	discuss	VERB
ma-310	28	18	the	the	DET
ma-310	28	19	solvability	solvability	NOUN
ma-310	28	20	conditions	condition	NOUN
ma-310	28	21	.	.	PUNCT
ma-310	29	1	in	in	ADP
ma-310	29	2	the	the	DET
ma-310	29	3	next	next	ADJ
ma-310	29	4	step	step	NOUN
ma-310	29	5	,	,	PUNCT
ma-310	29	6	with	with	ADP
ma-310	29	7	the	the	DET
ma-310	29	8	help	help	NOUN
ma-310	29	9	of	of	ADP
ma-310	29	10	the	the	DET
ma-310	29	11	green	green	PROPN
ma-310	29	12	’s	’s	PART
ma-310	29	13	func	func	NOUN
ma-310	29	14	-	-	PUNCT
ma-310	29	15	tion	tion	NOUN
ma-310	29	16	,	,	PUNCT
ma-310	29	17	we	we	PRON
ma-310	29	18	construct	construct	VERB
ma-310	29	19	a	a	DET
ma-310	29	20	unique	unique	ADJ
ma-310	29	21	solution	solution	NOUN
ma-310	29	22	for	for	ADP
ma-310	29	23	the	the	DET
ma-310	29	24	dirichlet	dirichlet	PROPN
ma-310	29	25	problem	problem	NOUN
ma-310	29	26	for	for	ADP
ma-310	29	27	the	the	DET
ma-310	29	28	poisson	poisson	NOUN
ma-310	29	29	equation	equation	NOUN
ma-310	29	30	in	in	ADP
ma-310	29	31	the	the	DET
ma-310	29	32	partialeclipse	partialeclipse	NOUN
ma-310	29	33	domain	domain	NOUN
ma-310	29	34	and	and	CCONJ
ma-310	29	35	investigate	investigate	VERB
ma-310	29	36	the	the	DET
ma-310	29	37	dirichlet	dirichlet	PROPN
ma-310	29	38	problem	problem	NOUN
ma-310	29	39	.	.	PUNCT
ma-310	30	1	in	in	ADP
ma-310	30	2	particular	particular	ADJ
ma-310	30	3	,	,	PUNCT
ma-310	30	4	we	we	PRON
ma-310	30	5	study	study	VERB
ma-310	30	6	the	the	DET
ma-310	30	7	boundary	boundary	ADJ
ma-310	30	8	behavior	behavior	NOUN
ma-310	30	9	.	.	PUNCT
ma-310	31	1	let	let	VERB
ma-310	31	2	m	m	PRON
ma-310	31	3	be	be	AUX
ma-310	31	4	the	the	DET
ma-310	31	5	partial	partial	ADJ
ma-310	31	6	eclipse	eclipse	NOUN
ma-310	31	7	domain	domain	NOUN
ma-310	31	8	in	in	ADP
ma-310	31	9	the	the	DET
ma-310	31	10	complex	complex	ADJ
ma-310	31	11	plane	plane	NOUN
ma-310	31	12	c	c	NOUN
ma-310	31	13	defined	define	VERB
ma-310	31	14	by	by	ADP
ma-310	31	15	[	[	X
ma-310	31	16	1	1	NUM
ma-310	31	17	]	]	X
ma-310	31	18	m	m	VERB
ma-310	31	19	=	=	PUNCT
ma-310	31	20	{	{	PUNCT
ma-310	31	21	z	z	NOUN
ma-310	31	22	∈	∈	PROPN
ma-310	31	23	c	c	NOUN
ma-310	31	24	:	:	PUNCT
ma-310	32	1	|z	|z	PROPN
ma-310	32	2	−	−	PROPN
ma-310	32	3	ai	ai	VERB
ma-310	32	4	|	|	ADV
ma-310	32	5	<	<	X
ma-310	32	6	√	√	NOUN
ma-310	32	7	2a	2a	NUM
ma-310	32	8	,	,	PUNCT
ma-310	32	9	|z	|z	PROPN
ma-310	33	1	+	+	CCONJ
ma-310	33	2	ai	ai	VERB
ma-310	33	3	|	|	ADV
ma-310	33	4	>	>	X
ma-310	33	5	√	√	PROPN
ma-310	33	6	2a	2a	NUM
ma-310	33	7	}	}	PUNCT
ma-310	33	8	where	where	SCONJ
ma-310	33	9	c1	c1	PROPN
ma-310	33	10	=	=	PUNCT
ma-310	33	11	{	{	PUNCT
ma-310	33	12	z	z	NOUN
ma-310	33	13	:	:	PUNCT
ma-310	33	14	|z	|z	PROPN
ma-310	34	1	−	−	PROPN
ma-310	34	2	ai	ai	VERB
ma-310	34	3	|	|	ADV
ma-310	34	4	=	=	NOUN
ma-310	34	5	√	√	PROPN
ma-310	35	1	2a	2a	NUM
ma-310	36	1	}	}	PUNCT
ma-310	37	1	and	and	CCONJ
ma-310	37	2	c2	c2	PROPN
ma-310	37	3	=	=	PUNCT
ma-310	37	4	{	{	PUNCT
ma-310	37	5	z	z	NOUN
ma-310	37	6	:	:	PUNCT
ma-310	37	7	|z	|z	PROPN
ma-310	38	1	+	+	CCONJ
ma-310	38	2	ai	ai	VERB
ma-310	38	3	|	|	ADV
ma-310	38	4	=	=	NOUN
ma-310	38	5	√	√	PROPN
ma-310	38	6	2a	2a	NUM
ma-310	38	7	}	}	PUNCT
ma-310	38	8	are	be	AUX
ma-310	38	9	two	two	NUM
ma-310	38	10	circles	circle	NOUN
ma-310	38	11	with	with	ADP
ma-310	38	12	the	the	DET
ma-310	38	13	sameradius	sameradius	NOUN
ma-310	38	14	and	and	CCONJ
ma-310	38	15	the	the	DET
ma-310	38	16	boundary	boundary	NOUN
ma-310	38	17	of	of	ADP
ma-310	38	18	m	m	PROPN
ma-310	38	19	is	be	AUX
ma-310	38	20	denoted	denote	VERB
ma-310	38	21	by	by	ADP
ma-310	38	22	∂m	∂m	PROPN
ma-310	38	23	.	.	PUNCT
ma-310	39	1	due	due	ADP
ma-310	39	2	to	to	ADP
ma-310	39	3	the	the	DET
ma-310	39	4	fact	fact	NOUN
ma-310	39	5	that	that	SCONJ
ma-310	39	6	the	the	DET
ma-310	39	7	real	real	ADJ
ma-310	39	8	number	number	NOUN
ma-310	39	9	a	a	PRON
ma-310	39	10	has	have	AUX
ma-310	39	11	apositive	apositive	ADJ
ma-310	39	12	arbitrary	arbitrary	ADJ
ma-310	39	13	amount	amount	NOUN
ma-310	39	14	,	,	PUNCT
ma-310	39	15	the	the	DET
ma-310	39	16	desired	desire	VERB
ma-310	39	17	partial	partial	ADJ
ma-310	39	18	eclipse	eclipse	NOUN
ma-310	39	19	can	can	AUX
ma-310	39	20	be	be	AUX
ma-310	39	21	created	create	VERB
ma-310	39	22	by	by	ADP
ma-310	39	23	choosing	choose	VERB
ma-310	39	24	a.	a.	NOUN
ma-310	40	1	so	so	SCONJ
ma-310	40	2	the	the	DET
ma-310	40	3	lengthof	lengthof	NOUN
ma-310	40	4	the	the	DET
ma-310	40	5	borders	border	NOUN
ma-310	40	6	of	of	ADP
ma-310	40	7	the	the	DET
ma-310	40	8	partial	partial	ADJ
ma-310	40	9	eclipse	eclipse	NOUN
ma-310	40	10	changes	change	NOUN
ma-310	40	11	according	accord	VERB
ma-310	40	12	to	to	ADP
ma-310	40	13	the	the	DET
ma-310	40	14	number	number	NOUN
ma-310	40	15	.	.	PUNCT
ma-310	41	1	the	the	DET
ma-310	41	2	parqueting	parqueting	ADJ
ma-310	41	3	–	–	PUNCT
ma-310	41	4	reflection	reflection	NOUN
ma-310	41	5	principle	principle	NOUN
ma-310	41	6	is	be	AUX
ma-310	41	7	a	a	DET
ma-310	41	8	technique	technique	NOUN
ma-310	41	9	used	use	VERB
ma-310	41	10	to	to	PART
ma-310	41	11	solve	solve	VERB
ma-310	41	12	boundary	boundary	ADJ
ma-310	41	13	value	value	NOUN
ma-310	41	14	problems	problem	NOUN
ma-310	41	15	for	for	ADP
ma-310	41	16	com	com	NOUN
ma-310	41	17	-	-	PUNCT
ma-310	41	18	plex	plex	ADJ
ma-310	41	19	partial	partial	ADJ
ma-310	41	20	differential	differential	NOUN
ma-310	41	21	equations	equation	NOUN
ma-310	41	22	,	,	PUNCT
ma-310	41	23	particularly	particularly	ADV
ma-310	41	24	for	for	ADP
ma-310	41	25	domains	domain	NOUN
ma-310	41	26	with	with	ADP
ma-310	41	27	complex	complex	ADJ
ma-310	41	28	geometries	geometry	NOUN
ma-310	41	29	.	.	PUNCT
ma-310	42	1	the	the	DET
ma-310	42	2	methodinvolves	methodinvolve	NOUN
ma-310	42	3	reflecting	reflect	VERB
ma-310	42	4	the	the	DET
ma-310	42	5	domain	domain	NOUN
ma-310	42	6	across	across	ADP
ma-310	42	7	its	its	PRON
ma-310	42	8	boundaries	boundary	NOUN
ma-310	42	9	to	to	PART
ma-310	42	10	simplify	simplify	VERB
ma-310	42	11	the	the	DET
ma-310	42	12	problem	problem	NOUN
ma-310	42	13	.	.	PUNCT
ma-310	43	1	by	by	ADP
ma-310	43	2	doing	do	VERB
ma-310	43	3	so	so	ADV
ma-310	43	4	,	,	PUNCT
ma-310	43	5	theboundary	theboundary	ADJ
ma-310	43	6	conditions	condition	NOUN
ma-310	43	7	can	can	AUX
ma-310	43	8	be	be	AUX
ma-310	43	9	transformed	transform	VERB
ma-310	43	10	into	into	ADP
ma-310	43	11	simpler	simple	ADJ
ma-310	43	12	forms	form	NOUN
ma-310	43	13	,	,	PUNCT
ma-310	43	14	making	make	VERB
ma-310	43	15	it	it	PRON
ma-310	43	16	easier	easy	ADJ
ma-310	43	17	to	to	PART
ma-310	43	18	find	find	VERB
ma-310	43	19	solutions	solution	NOUN
ma-310	43	20	.	.	PUNCT
ma-310	44	1	byusing	byuse	VERB
ma-310	44	2	the	the	DET
ma-310	44	3	reflections	reflection	NOUN
ma-310	44	4	,	,	PUNCT
ma-310	44	5	one	one	PRON
ma-310	44	6	can	can	AUX
ma-310	44	7	construct	construct	VERB
ma-310	44	8	solutions	solution	NOUN
ma-310	44	9	for	for	ADP
ma-310	44	10	complex	complex	ADJ
ma-310	44	11	boundary	boundary	ADJ
ma-310	44	12	value	value	NOUN
ma-310	44	13	problems	problem	NOUN
ma-310	44	14	such	such	ADJ
ma-310	44	15	as	as	ADP
ma-310	44	16	theschwarz	theschwarz	NOUN
ma-310	44	17	,	,	PUNCT
ma-310	44	18	the	the	DET
ma-310	44	19	dirichlet	dirichlet	PROPN
ma-310	44	20	and	and	CCONJ
ma-310	44	21	neumann	neumann	PROPN
ma-310	44	22	problems	problem	NOUN
ma-310	44	23	.	.	PUNCT
ma-310	45	1	this	this	PRON
ma-310	45	2	is	be	AUX
ma-310	45	3	particularly	particularly	ADV
ma-310	45	4	useful	useful	ADJ
ma-310	45	5	for	for	ADP
ma-310	45	6	domains	domain	NOUN
ma-310	45	7	composedof	composedof	ADJ
ma-310	45	8	circular	circular	ADJ
ma-310	45	9	arcs	arc	NOUN
ma-310	45	10	and	and	CCONJ
ma-310	45	11	straight	straight	ADJ
ma-310	45	12	lines	line	NOUN
ma-310	45	13	[	[	X
ma-310	45	14	1–4,6	1–4,6	NOUN
ma-310	45	15	,	,	PUNCT
ma-310	45	16	8–10	8–10	NOUN
ma-310	45	17	]	]	PUNCT
ma-310	45	18	.	.	PUNCT
ma-310	46	1	https://doi.org/10.28924/ada/ma.5.10	https://doi.org/10.28924/ada/ma.5.10	PROPN
ma-310	46	2	eur	eur	PROPN
ma-310	46	3	.	.	PUNCT
ma-310	47	1	j.	j.	PROPN
ma-310	47	2	math	math	PROPN
ma-310	47	3	.	.	PUNCT
ma-310	48	1	anal	anal	PROPN
ma-310	48	2	.	.	PUNCT
ma-310	49	1	10.28924	10.28924	NUM
ma-310	49	2	/	/	SYM
ma-310	49	3	ada	ada	PROPN
ma-310	49	4	/	/	SYM
ma-310	49	5	ma.5.10	ma.5.10	NOUN
ma-310	49	6	3	3	NUM
ma-310	49	7	in	in	ADP
ma-310	49	8	this	this	DET
ma-310	49	9	section	section	NOUN
ma-310	49	10	,	,	PUNCT
ma-310	49	11	using	use	VERB
ma-310	49	12	the	the	DET
ma-310	49	13	parqueting	parqueting	ADJ
ma-310	49	14	–	–	PUNCT
ma-310	49	15	reflection	reflection	NOUN
ma-310	49	16	method	method	NOUN
ma-310	49	17	for	for	ADP
ma-310	49	18	the	the	DET
ma-310	49	19	introduced	introduce	VERB
ma-310	49	20	domain	domain	NOUN
ma-310	49	21	m	m	NOUN
ma-310	49	22	,	,	PUNCT
ma-310	49	23	we	we	PRON
ma-310	49	24	achievecoverage	achievecoverage	VERB
ma-310	49	25	for	for	ADP
ma-310	49	26	the	the	DET
ma-310	49	27	entire	entire	ADJ
ma-310	49	28	complex	complex	ADJ
ma-310	49	29	plane	plane	NOUN
ma-310	49	30	c.	c.	NOUN
ma-310	49	31	this	this	DET
ma-310	49	32	coverage	coverage	NOUN
ma-310	49	33	is	be	AUX
ma-310	49	34	obtained	obtain	VERB
ma-310	49	35	from	from	ADP
ma-310	49	36	reflections	reflection	NOUN
ma-310	49	37	with	with	ADP
ma-310	49	38	threerepetitions.the	threerepetitions.the	DET
ma-310	49	39	reflection	reflection	NOUN
ma-310	49	40	of	of	ADP
ma-310	49	41	z	z	PROPN
ma-310	49	42	∈	∈	PROPN
ma-310	49	43	m	m	VERB
ma-310	49	44	at	at	ADP
ma-310	49	45	c1	c1	NOUN
ma-310	49	46	,	,	PUNCT
ma-310	49	47	is	be	AUX
ma-310	49	48	|z	|z	PROPN
ma-310	49	49	−	−	PROPN
ma-310	49	50	ai	ai	VERB
ma-310	49	51	|	|	ADV
ma-310	49	52	=	=	NOUN
ma-310	49	53	√	√	NUM
ma-310	49	54	2a⇒	2a⇒	NUM
ma-310	49	55	(	(	PUNCT
ma-310	49	56	z	z	NOUN
ma-310	49	57	−	−	NOUN
ma-310	49	58	ai	ai	NOUN
ma-310	49	59	)	)	PUNCT
ma-310	49	60	(	(	PUNCT
ma-310	49	61	z̄	z̄	X
ma-310	49	62	+	+	CCONJ
ma-310	49	63	ai	ai	NOUN
ma-310	49	64	)	)	PUNCT
ma-310	49	65	=	=	SYM
ma-310	49	66	2a2	2a2	NUM
ma-310	49	67	⇒	⇒	NOUN
ma-310	49	68	z∗1	z∗1	NOUN
ma-310	49	69	=	=	SYM
ma-310	49	70	ai	ai	VERB
ma-310	49	71	z̄	z̄	INTJ
ma-310	49	72	−	−	PROPN
ma-310	49	73	a2	a2	PROPN
ma-310	49	74	+	+	CCONJ
ma-310	49	75	2a2	2a2	NUM
ma-310	49	76	z̄	z̄	NOUN
ma-310	49	77	+	+	CCONJ
ma-310	49	78	ai	ai	VERB
ma-310	49	79	⇒	⇒	NOUN
ma-310	49	80	z∗1	z∗1	NOUN
ma-310	49	81	=	=	PUNCT
ma-310	49	82	ai	ai	VERB
ma-310	49	83	z̄	z̄	PROPN
ma-310	49	84	+	+	NUM
ma-310	49	85	a2	a2	PROPN
ma-310	49	86	z̄	z̄	PROPN
ma-310	49	87	+	+	CCONJ
ma-310	49	88	ai	ai	VERB
ma-310	49	89	.	.	PUNCT
ma-310	50	1	similarly	similarly	ADV
ma-310	50	2	,	,	PUNCT
ma-310	50	3	the	the	DET
ma-310	50	4	reflections	reflection	NOUN
ma-310	50	5	of	of	ADP
ma-310	50	6	z∗1	z∗1	NOUN
ma-310	50	7	and	and	CCONJ
ma-310	50	8	z	z	NOUN
ma-310	50	9	at	at	ADP
ma-310	50	10	c2	c2	PROPN
ma-310	50	11	,	,	PUNCT
ma-310	50	12	are	be	AUX
ma-310	50	13	the	the	DET
ma-310	50	14	points	point	NOUN
ma-310	50	15	,	,	PUNCT
ma-310	50	16	z∗2	z∗2	NOUN
ma-310	50	17	=	=	SYM
ma-310	50	18	a2	a2	PROPN
ma-310	50	19	z	z	PROPN
ma-310	50	20	,	,	PUNCT
ma-310	50	21	z∗3	z∗3	NOUN
ma-310	50	22	=	=	PUNCT
ma-310	50	23	−ai	−ai	PROPN
ma-310	50	24	z̄	z̄	PROPN
ma-310	50	25	+	+	CCONJ
ma-310	50	26	a2	a2	PROPN
ma-310	50	27	z̄	z̄	PROPN
ma-310	50	28	−	−	NOUN
ma-310	50	29	ai	ai	VERB
ma-310	50	30	.	.	PUNCT
ma-310	51	1	those	those	DET
ma-310	51	2	reflections	reflection	NOUN
ma-310	51	3	produce	produce	VERB
ma-310	51	4	a	a	DET
ma-310	51	5	parqueting	parqueting	NOUN
ma-310	51	6	of	of	ADP
ma-310	51	7	the	the	DET
ma-310	51	8	entire	entire	ADJ
ma-310	51	9	complex	complex	ADJ
ma-310	51	10	plane	plane	NOUN
ma-310	51	11	and	and	CCONJ
ma-310	51	12	those	those	DET
ma-310	51	13	points	point	NOUN
ma-310	51	14	will	will	AUX
ma-310	51	15	alsobe	alsobe	ADV
ma-310	51	16	needed	need	VERB
ma-310	51	17	for	for	ADP
ma-310	51	18	constructing	construct	VERB
ma-310	51	19	the	the	DET
ma-310	51	20	integral	integral	ADJ
ma-310	51	21	representation	representation	NOUN
ma-310	51	22	formula	formula	NOUN
ma-310	51	23	for	for	ADP
ma-310	51	24	m	m	PROPN
ma-310	51	25	.	.	PUNCT
ma-310	52	1	to	to	PART
ma-310	52	2	solve	solve	VERB
ma-310	52	3	boundary	boundary	ADJ
ma-310	52	4	valueproblems	valueproblem	NOUN
ma-310	52	5	for	for	ADP
ma-310	52	6	partial	partial	ADJ
ma-310	52	7	differential	differential	ADJ
ma-310	52	8	equations	equation	NOUN
ma-310	52	9	,	,	PUNCT
ma-310	52	10	the	the	DET
ma-310	52	11	integral	integral	ADJ
ma-310	52	12	formula	formula	NOUN
ma-310	52	13	should	should	AUX
ma-310	52	14	be	be	AUX
ma-310	52	15	appropriately	appropriately	ADV
ma-310	52	16	modifiedaccording	modifiedaccorde	VERB
ma-310	52	17	to	to	ADP
ma-310	52	18	the	the	DET
ma-310	52	19	type	type	NOUN
ma-310	52	20	of	of	ADP
ma-310	52	21	problem	problem	NOUN
ma-310	52	22	and	and	CCONJ
ma-310	52	23	partial	partial	ADJ
ma-310	52	24	differential	differential	NOUN
ma-310	52	25	equation	equation	NOUN
ma-310	52	26	,	,	PUNCT
ma-310	53	1	[	[	X
ma-310	53	2	1–4,7	1–4,7	NOUN
ma-310	53	3	,	,	PUNCT
ma-310	53	4	8	8	NUM
ma-310	53	5	,	,	PUNCT
ma-310	53	6	10].the	10].the	PROPN
ma-310	53	7	neumann	neumann	PROPN
ma-310	53	8	boundary	boundary	ADJ
ma-310	53	9	value	value	NOUN
ma-310	53	10	problem	problem	NOUN
ma-310	53	11	is	be	AUX
ma-310	53	12	a	a	DET
ma-310	53	13	classical	classical	NOUN
ma-310	53	14	in	in	ADP
ma-310	53	15	the	the	DET
ma-310	53	16	field	field	NOUN
ma-310	53	17	of	of	ADP
ma-310	53	18	complex	complex	ADJ
ma-310	53	19	analysis	analysis	NOUN
ma-310	53	20	and	and	CCONJ
ma-310	53	21	partialdifferential	partialdifferential	ADJ
ma-310	53	22	equations	equation	NOUN
ma-310	53	23	.	.	PUNCT
ma-310	54	1	it	it	PRON
ma-310	54	2	involves	involve	VERB
ma-310	54	3	finding	find	VERB
ma-310	54	4	a	a	DET
ma-310	54	5	function	function	NOUN
ma-310	54	6	that	that	PRON
ma-310	54	7	satisfies	satisfy	VERB
ma-310	54	8	complex	complex	ADJ
ma-310	54	9	partial	partial	ADJ
ma-310	54	10	differential	differential	ADJ
ma-310	54	11	equa	equa	NOUN
ma-310	54	12	-	-	PUNCT
ma-310	54	13	tions	tion	NOUN
ma-310	54	14	within	within	ADP
ma-310	54	15	a	a	DET
ma-310	54	16	given	give	VERB
ma-310	54	17	domain	domain	NOUN
ma-310	54	18	and	and	CCONJ
ma-310	54	19	whose	whose	DET
ma-310	54	20	normal	normal	ADJ
ma-310	54	21	derivative	derivative	NOUN
ma-310	54	22	on	on	ADP
ma-310	54	23	the	the	DET
ma-310	54	24	boundary	boundary	NOUN
ma-310	54	25	of	of	ADP
ma-310	54	26	the	the	DET
ma-310	54	27	domain	domain	NOUN
ma-310	54	28	matchesa	matchesa	NOUN
ma-310	54	29	specified	specify	VERB
ma-310	54	30	function	function	NOUN
ma-310	54	31	.	.	PUNCT
ma-310	55	1	the	the	DET
ma-310	55	2	neumann	neumann	PROPN
ma-310	55	3	boundary	boundary	PROPN
ma-310	55	4	value	value	NOUN
ma-310	55	5	problem	problem	NOUN
ma-310	55	6	is	be	AUX
ma-310	55	7	significant	significant	ADJ
ma-310	55	8	,	,	PUNCT
ma-310	55	9	because	because	SCONJ
ma-310	55	10	it	it	PRON
ma-310	55	11	is	be	AUX
ma-310	55	12	a	a	DET
ma-310	55	13	gatewayto	gatewayto	NOUN
ma-310	55	14	understanding	understand	VERB
ma-310	55	15	the	the	DET
ma-310	55	16	deeper	deep	ADJ
ma-310	55	17	intricacies	intricacy	NOUN
ma-310	55	18	of	of	ADP
ma-310	55	19	complex	complex	ADJ
ma-310	55	20	functions	function	NOUN
ma-310	55	21	and	and	CCONJ
ma-310	55	22	broader	broad	ADJ
ma-310	55	23	field	field	NOUN
ma-310	55	24	of	of	ADP
ma-310	55	25	complex	complex	ADJ
ma-310	55	26	analysis.the	analysis.the	DET
ma-310	55	27	insights	insight	NOUN
ma-310	55	28	gained	gain	VERB
ma-310	55	29	from	from	ADP
ma-310	55	30	solving	solve	VERB
ma-310	55	31	these	these	DET
ma-310	55	32	problems	problem	NOUN
ma-310	55	33	can	can	AUX
ma-310	55	34	lead	lead	VERB
ma-310	55	35	to	to	PART
ma-310	55	36	advancement	advancement	VERB
ma-310	55	37	in	in	ADP
ma-310	55	38	both	both	DET
ma-310	55	39	mathematicaltheory	mathematicaltheory	ADJ
ma-310	55	40	and	and	CCONJ
ma-310	55	41	practical	practical	ADJ
ma-310	55	42	applications	application	NOUN
ma-310	55	43	,	,	PUNCT
ma-310	55	44	see	see	VERB
ma-310	55	45	[	[	X
ma-310	55	46	2	2	NUM
ma-310	55	47	,	,	PUNCT
ma-310	55	48	6	6	NUM
ma-310	55	49	,	,	PUNCT
ma-310	55	50	7	7	NUM
ma-310	55	51	,	,	PUNCT
ma-310	55	52	9	9	NUM
ma-310	55	53	,	,	PUNCT
ma-310	55	54	11].in	11].in	NUM
ma-310	55	55	this	this	DET
ma-310	55	56	section	section	NOUN
ma-310	55	57	,	,	PUNCT
ma-310	55	58	we	we	PRON
ma-310	55	59	investigate	investigate	VERB
ma-310	55	60	the	the	DET
ma-310	55	61	neumann	neumann	PROPN
ma-310	55	62	boundary	boundary	PROPN
ma-310	55	63	value	value	NOUN
ma-310	55	64	problem	problem	NOUN
ma-310	55	65	for	for	ADP
ma-310	55	66	the	the	DET
ma-310	55	67	homogeneouscauchy	homogeneouscauchy	ADJ
ma-310	55	68	–	–	PUNCT
ma-310	55	69	riemann	riemann	PROPN
ma-310	55	70	equation	equation	NOUN
ma-310	55	71	.	.	PUNCT
ma-310	56	1	the	the	DET
ma-310	56	2	fundamental	fundamental	ADJ
ma-310	56	3	tool	tool	NOUN
ma-310	56	4	for	for	ADP
ma-310	56	5	complex	complex	ADJ
ma-310	56	6	boundary	boundary	ADJ
ma-310	56	7	value	value	NOUN
ma-310	56	8	problems	problem	NOUN
ma-310	56	9	is	be	AUX
ma-310	56	10	theintegral	theintegral	ADJ
ma-310	56	11	representation	representation	NOUN
ma-310	56	12	formula	formula	NOUN
ma-310	56	13	which	which	PRON
ma-310	56	14	just	just	ADV
ma-310	56	15	has	have	VERB
ma-310	56	16	to	to	PART
ma-310	56	17	be	be	AUX
ma-310	56	18	properly	properly	ADV
ma-310	56	19	modified	modify	VERB
ma-310	56	20	.	.	PUNCT
ma-310	57	1	theorem	theorem	VERB
ma-310	57	2	1.1	1.1	NUM
ma-310	57	3	.	.	PUNCT
ma-310	58	1	any	any	DET
ma-310	58	2	ω	ω	PROPN
ma-310	58	3	∈	∈	PROPN
ma-310	58	4	c1(m;c	c1(m;c	NOUN
ma-310	58	5	)	)	PUNCT
ma-310	58	6	⋂	⋂	PROPN
ma-310	58	7	c(m;c	c(m;c	NOUN
ma-310	58	8	)	)	PUNCT
ma-310	58	9	can	can	AUX
ma-310	58	10	be	be	AUX
ma-310	58	11	represented	represent	VERB
ma-310	58	12	as	as	ADP
ma-310	58	13	ω(z	ω(z	PROPN
ma-310	58	14	)	)	PUNCT
ma-310	58	15	=	=	SYM
ma-310	58	16	1	1	NUM
ma-310	58	17	2πi	2πi	NOUN
ma-310	58	18	∫	∫	PROPN
ma-310	58	19	∂m	∂m	PROPN
ma-310	58	20	ω(ζ	ω(ζ	NOUN
ma-310	58	21	)	)	PUNCT
ma-310	58	22	[	[	PUNCT
ma-310	58	23	1	1	NUM
ma-310	58	24	ζ	ζ	NOUN
ma-310	58	25	−	−	PROPN
ma-310	58	26	z	z	NOUN
ma-310	59	1	+	+	NUM
ma-310	59	2	z	z	NOUN
ma-310	59	3	ζz	ζz	ADP
ma-310	59	4	−	−	PROPN
ma-310	59	5	a2	a2	PROPN
ma-310	59	6	]	]	PUNCT
ma-310	59	7	dζ	dζ	PROPN
ma-310	59	8	−	−	PROPN
ma-310	59	9	1	1	NUM
ma-310	59	10	π	π	PROPN
ma-310	59	11	∫	∫	PROPN
ma-310	59	12	m	m	PROPN
ma-310	59	13	ωζ̄(ζ	ωζ̄(ζ	NOUN
ma-310	59	14	)	)	PUNCT
ma-310	59	15	[	[	PUNCT
ma-310	59	16	1	1	NUM
ma-310	59	17	ζ	ζ	NOUN
ma-310	59	18	−	−	PROPN
ma-310	59	19	z	z	NOUN
ma-310	60	1	+	+	NUM
ma-310	60	2	z	z	AUX
ma-310	60	3	ζz	ζz	ADP
ma-310	60	4	−	−	PROPN
ma-310	60	5	a2	a2	PROPN
ma-310	60	6	]	]	PUNCT
ma-310	60	7	dξdη	dξdη	PROPN
ma-310	60	8	,	,	PUNCT
ma-310	60	9	(	(	PUNCT
ma-310	60	10	1.1	1.1	NUM
ma-310	60	11	)	)	PUNCT
ma-310	61	1	where	where	SCONJ
ma-310	61	2	ζ	ζ	NOUN
ma-310	61	3	=	=	SYM
ma-310	61	4	ξ	ξ	PROPN
ma-310	61	5	+	+	NUM
ma-310	61	6	iη	iη	NOUN
ma-310	61	7	.	.	PUNCT
ma-310	62	1	proof	proof	NOUN
ma-310	62	2	.	.	PUNCT
ma-310	63	1	the	the	DET
ma-310	63	2	cauchy	cauchy	PROPN
ma-310	63	3	–	–	PUNCT
ma-310	63	4	pompieu	pompieu	NOUN
ma-310	63	5	formula	formula	NOUN
ma-310	63	6	1	1	NUM
ma-310	63	7	2πi	2πi	NOUN
ma-310	63	8	∫	∫	PROPN
ma-310	63	9	∂m	∂m	PROPN
ma-310	63	10	ω(ζ	ω(ζ	PROPN
ma-310	63	11	)	)	PUNCT
ma-310	63	12	dζ	dζ	PROPN
ma-310	63	13	ζ	ζ	NOUN
ma-310	63	14	−	−	PROPN
ma-310	63	15	z	z	NOUN
ma-310	63	16	−	−	NOUN
ma-310	63	17	1	1	NUM
ma-310	63	18	π	π	PROPN
ma-310	63	19	∫	∫	PROPN
ma-310	63	20	m	m	PROPN
ma-310	63	21	ωζ̄(ζ	ωζ̄(ζ	NOUN
ma-310	63	22	)	)	PUNCT
ma-310	63	23	dξdη	dξdη	NOUN
ma-310	63	24	ζ	ζ	NOUN
ma-310	63	25	−	−	NOUN
ma-310	63	26	z	z	NOUN
ma-310	63	27	=	=	PRON
ma-310	63	28	{	{	PUNCT
ma-310	63	29	ω(z	ω(z	PROPN
ma-310	63	30	)	)	PUNCT
ma-310	63	31	z	z	NOUN
ma-310	63	32	∈	∈	PROPN
ma-310	63	33	m	m	PROPN
ma-310	63	34	,	,	PUNCT
ma-310	63	35	0	0	PROPN
ma-310	63	36	z	z	NOUN
ma-310	63	37	/∈	/∈	PUNCT
ma-310	64	1	m	m	VERB
ma-310	64	2	,	,	PUNCT
ma-310	64	3	applied	apply	VERB
ma-310	64	4	to	to	ADP
ma-310	64	5	z	z	PROPN
ma-310	64	6	∈	∈	PROPN
ma-310	64	7	m	m	NOUN
ma-310	64	8	and	and	CCONJ
ma-310	64	9	z∗2	z∗2	PROPN
ma-310	64	10	/∈	/∈	PUNCT
ma-310	65	1	m	m	NOUN
ma-310	65	2	,	,	PUNCT
ma-310	65	3	respectively	respectively	ADV
ma-310	65	4	,	,	PUNCT
ma-310	65	5	gives	give	VERB
ma-310	65	6	the	the	DET
ma-310	65	7	following	follow	VERB
ma-310	65	8	equalities	equality	NOUN
ma-310	65	9	:	:	PUNCT
ma-310	65	10	ω(z	ω(z	NUM
ma-310	65	11	)	)	PUNCT
ma-310	65	12	=	=	SYM
ma-310	66	1	1	1	NUM
ma-310	66	2	2πi	2πi	NOUN
ma-310	66	3	∫	∫	PROPN
ma-310	66	4	∂m	∂m	PROPN
ma-310	66	5	ω(ζ	ω(ζ	PROPN
ma-310	66	6	)	)	PUNCT
ma-310	66	7	dζ	dζ	PROPN
ma-310	66	8	ζ	ζ	NOUN
ma-310	66	9	−	−	PROPN
ma-310	66	10	z	z	NOUN
ma-310	66	11	−	−	NOUN
ma-310	66	12	1	1	NUM
ma-310	66	13	π	π	PROPN
ma-310	66	14	∫	∫	PROPN
ma-310	66	15	m	m	PROPN
ma-310	66	16	ωζ̄(ζ	ωζ̄(ζ	NOUN
ma-310	66	17	)	)	PUNCT
ma-310	66	18	dξdη	dξdη	NOUN
ma-310	66	19	ζ	ζ	NOUN
ma-310	66	20	−	−	PROPN
ma-310	66	21	z	z	NOUN
ma-310	66	22	,	,	PUNCT
ma-310	66	23	(	(	PUNCT
ma-310	66	24	1.2	1.2	NUM
ma-310	66	25	)	)	PUNCT
ma-310	66	26	https://doi.org/10.28924/ada/ma.5.10	https://doi.org/10.28924/ada/ma.5.10	PROPN
ma-310	66	27	eur	eur	PROPN
ma-310	66	28	.	.	PUNCT
ma-310	67	1	j.	j.	PROPN
ma-310	67	2	math	math	PROPN
ma-310	67	3	.	.	PUNCT
ma-310	68	1	anal	anal	PROPN
ma-310	68	2	.	.	PUNCT
ma-310	69	1	10.28924	10.28924	NUM
ma-310	69	2	/	/	SYM
ma-310	69	3	ada	ada	PROPN
ma-310	69	4	/	/	SYM
ma-310	69	5	ma.5.10	ma.5.10	NOUN
ma-310	69	6	4	4	NUM
ma-310	69	7	0	0	NUM
ma-310	69	8	=	=	SYM
ma-310	69	9	1	1	NUM
ma-310	69	10	2πi	2πi	NOUN
ma-310	69	11	∫	∫	PROPN
ma-310	69	12	∂m	∂m	PROPN
ma-310	69	13	ω(ζ	ω(ζ	NOUN
ma-310	69	14	)	)	PUNCT
ma-310	69	15	zdζ	zdζ	NOUN
ma-310	69	16	ζz	ζz	ADP
ma-310	69	17	−	−	PROPN
ma-310	69	18	a2	a2	PROPN
ma-310	69	19	−	−	PROPN
ma-310	70	1	1	1	NUM
ma-310	70	2	π	π	PROPN
ma-310	70	3	∫	∫	PROPN
ma-310	70	4	m	m	PROPN
ma-310	70	5	ωζ̄(ζ	ωζ̄(ζ	NOUN
ma-310	70	6	)	)	PUNCT
ma-310	70	7	zdξdη	zdξdη	NOUN
ma-310	70	8	ζz	ζz	ADP
ma-310	70	9	−	−	PROPN
ma-310	70	10	a2	a2	PROPN
ma-310	70	11	,	,	PUNCT
ma-310	70	12	(	(	PUNCT
ma-310	70	13	1.3	1.3	NUM
ma-310	70	14	)	)	PUNCT
ma-310	70	15	adding	add	VERB
ma-310	70	16	the	the	DET
ma-310	70	17	resulting	result	VERB
ma-310	70	18	above	above	ADP
ma-310	70	19	relations	relation	NOUN
ma-310	70	20	,	,	PUNCT
ma-310	70	21	leads	lead	VERB
ma-310	70	22	to	to	PART
ma-310	70	23	claimed	claim	VERB
ma-310	70	24	the	the	DET
ma-310	70	25	integral	integral	ADJ
ma-310	70	26	representation	representation	NOUN
ma-310	70	27	formula	formula	NOUN
ma-310	70	28	.	.	PUNCT
ma-310	71	1	�	�	PROPN
ma-310	71	2	next	next	ADV
ma-310	71	3	,	,	PUNCT
ma-310	71	4	we	we	PRON
ma-310	71	5	state	state	VERB
ma-310	71	6	the	the	DET
ma-310	71	7	neumann	neumann	PROPN
ma-310	71	8	boundary	boundary	PROPN
ma-310	71	9	value	value	NOUN
ma-310	71	10	problem	problem	NOUN
ma-310	71	11	for	for	ADP
ma-310	71	12	cauchy	cauchy	PROPN
ma-310	71	13	–	–	PUNCT
ma-310	71	14	riemann	riemann	PROPN
ma-310	71	15	equation	equation	NOUN
ma-310	71	16	in	in	ADP
ma-310	71	17	the	the	DET
ma-310	71	18	par	par	ADJ
ma-310	71	19	-	-	PUNCT
ma-310	71	20	tial	tial	ADJ
ma-310	71	21	eclipse	eclipse	NOUN
ma-310	71	22	domain	domain	NOUN
ma-310	71	23	as	as	SCONJ
ma-310	71	24	follows	follow	VERB
ma-310	71	25	.	.	PUNCT
ma-310	72	1	neumann	neumann	PROPN
ma-310	72	2	boundary	boundary	PROPN
ma-310	72	3	value	value	NOUN
ma-310	72	4	problem	problem	NOUN
ma-310	72	5	:	:	PUNCT
ma-310	72	6	find	find	VERB
ma-310	72	7	an	an	DET
ma-310	72	8	analytic	analytic	ADJ
ma-310	72	9	function	function	NOUN
ma-310	72	10	in	in	ADP
ma-310	72	11	the	the	DET
ma-310	72	12	partial	partial	ADJ
ma-310	72	13	eclipse	eclipse	NOUN
ma-310	72	14	domain	domain	NOUN
ma-310	72	15	,	,	PUNCT
ma-310	72	16	i.e.	i.e.	X
ma-310	72	17	asolution	asolution	NOUN
ma-310	72	18	to	to	ADP
ma-310	72	19	cauchy	cauchy	PROPN
ma-310	72	20	–	–	PUNCT
ma-310	72	21	riemann	riemann	PROPN
ma-310	72	22	equation	equation	NOUN
ma-310	72	23	,	,	PUNCT
ma-310	72	24	satisfying	satisfy	VERB
ma-310	72	25	,	,	PUNCT
ma-310	72	26	∂vzω	∂vzω	ADV
ma-310	72	27	=	=	SYM
ma-310	72	28	γ	γ	NOUN
ma-310	72	29	,	,	PUNCT
ma-310	72	30	on	on	ADP
ma-310	72	31	∂m	∂m	PROPN
ma-310	72	32	,	,	PUNCT
ma-310	72	33	γ	γ	PROPN
ma-310	72	34	∈	∈	PROPN
ma-310	72	35	c(∂m;c	c(∂m;c	NOUN
ma-310	72	36	)	)	PUNCT
ma-310	72	37	.	.	PUNCT
ma-310	73	1	the	the	DET
ma-310	73	2	classical	classical	ADJ
ma-310	73	3	neumann	neumann	PROPN
ma-310	73	4	problem	problem	NOUN
ma-310	73	5	involves	involve	VERB
ma-310	73	6	finding	find	VERB
ma-310	73	7	a	a	DET
ma-310	73	8	function	function	NOUN
ma-310	73	9	that	that	PRON
ma-310	73	10	satisfies	satisfy	VERB
ma-310	73	11	cauchy	cauchy	PROPN
ma-310	73	12	–	–	PUNCT
ma-310	73	13	riemann	riemann	PROPN
ma-310	73	14	equa	equa	NOUN
ma-310	73	15	-	-	PUNCT
ma-310	73	16	tion	tion	NOUN
ma-310	73	17	in	in	ADP
ma-310	73	18	a	a	DET
ma-310	73	19	domain	domain	NOUN
ma-310	73	20	,	,	PUNCT
ma-310	73	21	along	along	ADP
ma-310	73	22	with	with	ADP
ma-310	73	23	prescribed	prescribed	ADJ
ma-310	73	24	values	value	NOUN
ma-310	73	25	of	of	ADP
ma-310	73	26	its	its	PRON
ma-310	73	27	normal	normal	ADJ
ma-310	73	28	derivative	derivative	NOUN
ma-310	73	29	on	on	ADP
ma-310	73	30	the	the	DET
ma-310	73	31	boundary	boundary	NOUN
ma-310	73	32	.	.	PUNCT
ma-310	74	1	when	when	SCONJ
ma-310	74	2	ad	ad	NOUN
ma-310	74	3	-	-	PUNCT
ma-310	74	4	justed	juste	VERB
ma-310	74	5	for	for	ADP
ma-310	74	6	analytic	analytic	ADJ
ma-310	74	7	functions	function	NOUN
ma-310	74	8	,	,	PUNCT
ma-310	74	9	the	the	DET
ma-310	74	10	neumann	neumann	PROPN
ma-310	74	11	condition	condition	NOUN
ma-310	74	12	is	be	AUX
ma-310	74	13	often	often	ADV
ma-310	74	14	reformulated	reformulate	VERB
ma-310	74	15	to	to	PART
ma-310	74	16	align	align	VERB
ma-310	74	17	with	with	ADP
ma-310	74	18	the	the	DET
ma-310	74	19	conceptof	conceptof	NOUN
ma-310	74	20	analyticity	analyticity	NOUN
ma-310	74	21	,	,	PUNCT
ma-310	74	22	ensuring	ensure	VERB
ma-310	74	23	the	the	DET
ma-310	74	24	function	function	NOUN
ma-310	74	25	meets	meet	VERB
ma-310	74	26	the	the	DET
ma-310	74	27	criteria	criterion	NOUN
ma-310	74	28	for	for	ADP
ma-310	74	29	complex	complex	ADJ
ma-310	74	30	differentiability	differentiability	NOUN
ma-310	75	1	[	[	X
ma-310	75	2	2,6,7,9,11,16].to	2,6,7,9,11,16].to	NUM
ma-310	75	3	formulate	formulate	VERB
ma-310	75	4	the	the	DET
ma-310	75	5	neumann	neumann	PROPN
ma-310	75	6	boundary	boundary	PROPN
ma-310	75	7	value	value	NOUN
ma-310	75	8	problem	problem	NOUN
ma-310	75	9	,	,	PUNCT
ma-310	75	10	we	we	PRON
ma-310	75	11	need	need	VERB
ma-310	75	12	to	to	PART
ma-310	75	13	define	define	VERB
ma-310	75	14	the	the	DET
ma-310	75	15	outward	outward	ADJ
ma-310	75	16	normalderivative	normalderivative	NOUN
ma-310	75	17	at	at	ADP
ma-310	75	18	the	the	DET
ma-310	75	19	boundary	boundary	NOUN
ma-310	75	20	of	of	ADP
ma-310	75	21	m.	m.	NOUN
ma-310	75	22	the	the	DET
ma-310	75	23	normal	normal	ADJ
ma-310	75	24	derivative	derivative	NOUN
ma-310	75	25	on	on	ADP
ma-310	75	26	the	the	DET
ma-310	75	27	boundary	boundary	NOUN
ma-310	75	28	of	of	ADP
ma-310	75	29	is	be	AUX
ma-310	75	30	given	give	VERB
ma-310	75	31	by	by	ADP
ma-310	75	32	the	the	DET
ma-310	75	33	formulas	formula	NOUN
ma-310	75	34	,	,	PUNCT
ma-310	75	35	∂vzω	∂vzω	X
ma-310	75	36	=	=	SYM
ma-310	75	37			PUNCT
ma-310	75	38	(	(	PUNCT
ma-310	75	39	z−ai√	z−ai√	NUM
ma-310	75	40	2a	2a	NUM
ma-310	75	41	)	)	PUNCT
ma-310	75	42	ωz	ωz	X
ma-310	75	43	,	,	PUNCT
ma-310	75	44	on	on	ADP
ma-310	75	45	c1	c1	PROPN
ma-310	75	46	,	,	PUNCT
ma-310	75	47	(	(	PUNCT
ma-310	75	48	z+ai√	z+ai√	NOUN
ma-310	75	49	2a	2a	NUM
ma-310	75	50	)	)	PUNCT
ma-310	75	51	ωz	ωz	X
ma-310	75	52	,	,	PUNCT
ma-310	75	53	on	on	ADP
ma-310	75	54	c2	c2	PROPN
ma-310	75	55	.	.	PUNCT
ma-310	76	1	now	now	ADV
ma-310	76	2	,	,	PUNCT
ma-310	76	3	according	accord	VERB
ma-310	76	4	to	to	ADP
ma-310	76	5	the	the	DET
ma-310	76	6	above	above	ADJ
ma-310	76	7	definition	definition	NOUN
ma-310	76	8	,	,	PUNCT
ma-310	76	9	we	we	PRON
ma-310	76	10	state	state	VERB
ma-310	76	11	and	and	CCONJ
ma-310	76	12	prove	prove	VERB
ma-310	76	13	the	the	DET
ma-310	76	14	following	follow	VERB
ma-310	76	15	theorem	theorem	VERB
ma-310	76	16	.	.	PUNCT
ma-310	76	17	theorem	theorem	VERB
ma-310	76	18	1.2	1.2	NUM
ma-310	76	19	.	.	PUNCT
ma-310	77	1	the	the	DET
ma-310	77	2	neumann	neumann	PROPN
ma-310	77	3	boundary	boundary	PROPN
ma-310	77	4	value	value	NOUN
ma-310	77	5	problem	problem	NOUN
ma-310	77	6	ωz̄	ωz̄	NOUN
ma-310	78	1	=	=	PUNCT
ma-310	78	2	0	0	NUM
ma-310	78	3	,	,	PUNCT
ma-310	78	4	z	z	PROPN
ma-310	78	5	∈	∈	PROPN
ma-310	78	6	m	m	NOUN
ma-310	78	7	,	,	PUNCT
ma-310	78	8	∂vzω	∂vzω	ADV
ma-310	78	9	=	=	SYM
ma-310	78	10	γ	γ	X
ma-310	78	11	,	,	PUNCT
ma-310	78	12	z	z	PROPN
ma-310	78	13	∈	∈	PROPN
ma-310	79	1	∂m	∂m	PROPN
ma-310	79	2	,	,	PUNCT
ma-310	79	3	(	(	PUNCT
ma-310	79	4	1.4	1.4	NUM
ma-310	79	5	)	)	PUNCT
ma-310	79	6	ω(t	ω(t	NOUN
ma-310	79	7	)	)	PUNCT
ma-310	79	8	=	=	SYM
ma-310	80	1	c	c	X
ma-310	80	2	,	,	PUNCT
ma-310	80	3	where	where	SCONJ
ma-310	80	4	t	t	PROPN
ma-310	80	5	∈	∈	PROPN
ma-310	80	6	m	m	PROPN
ma-310	80	7	,	,	PUNCT
ma-310	80	8	c	c	PROPN
ma-310	80	9	∈	∈	PROPN
ma-310	80	10	c	c	NOUN
ma-310	80	11	and	and	CCONJ
ma-310	80	12	∂vzω	∂vzω	NUM
ma-310	80	13	=	=	PUNCT
ma-310	80	14			PUNCT
ma-310	80	15	(	(	PUNCT
ma-310	80	16	z−ai√	z−ai√	NUM
ma-310	80	17	2a	2a	NUM
ma-310	80	18	)	)	PUNCT
ma-310	80	19	ωz	ωz	X
ma-310	80	20	,	,	PUNCT
ma-310	80	21	on	on	ADP
ma-310	80	22	c1	c1	PROPN
ma-310	80	23	,	,	PUNCT
ma-310	80	24	(	(	PUNCT
ma-310	80	25	z+ai√	z+ai√	NOUN
ma-310	80	26	2a	2a	NUM
ma-310	80	27	)	)	PUNCT
ma-310	80	28	ωz	ωz	X
ma-310	80	29	,	,	PUNCT
ma-310	80	30	on	on	ADP
ma-310	80	31	c2	c2	PROPN
ma-310	80	32	,	,	PUNCT
ma-310	80	33	is	be	AUX
ma-310	80	34	solvable	solvable	ADJ
ma-310	80	35	,	,	PUNCT
ma-310	80	36	if	if	SCONJ
ma-310	80	37	and	and	CCONJ
ma-310	80	38	only	only	ADV
ma-310	80	39	if	if	SCONJ
ma-310	80	40	,	,	PUNCT
ma-310	80	41	for	for	ADP
ma-310	80	42	z	z	PROPN
ma-310	80	43	∈	∈	PROPN
ma-310	80	44	m	m	PROPN
ma-310	80	45	,	,	PUNCT
ma-310	80	46	1	1	NUM
ma-310	80	47	2πi	2πi	NOUN
ma-310	80	48	∫	∫	PROPN
ma-310	80	49	∂m	∂m	PROPN
ma-310	80	50	γ(ζ	γ(ζ	PROPN
ma-310	80	51	)	)	PUNCT
ma-310	80	52	[	[	PUNCT
ma-310	80	53	z̄	z̄	INTJ
ma-310	80	54	−	−	ADP
ma-310	80	55	ai	ai	VERB
ma-310	80	56	ζ(z̄	ζ(z̄	PUNCT
ma-310	80	57	−	−	PRON
ma-310	80	58	ai	ai	VERB
ma-310	80	59	)	)	PUNCT
ma-310	80	60	+	+	CCONJ
ma-310	80	61	ai	ai	PROPN
ma-310	80	62	z̄	z̄	INTJ
ma-310	80	63	−	−	PROPN
ma-310	80	64	a2	a2	PROPN
ma-310	80	65	+	+	CCONJ
ma-310	80	66	z̄	z̄	PROPN
ma-310	80	67	+	+	CCONJ
ma-310	80	68	ai	ai	PROPN
ma-310	80	69	ζ(z̄	ζ(z̄	ADJ
ma-310	80	70	+	+	NUM
ma-310	80	71	ai)−	ai)−	NOUN
ma-310	80	72	ai	ai	VERB
ma-310	80	73	z̄	z̄	NOUN
ma-310	80	74	−	−	PROPN
ma-310	80	75	a2	a2	PROPN
ma-310	80	76	]	]	PUNCT
ma-310	80	77	dζ	dζ	PROPN
ma-310	80	78	=	=	SYM
ma-310	80	79	0	0	NUM
ma-310	80	80	,	,	PUNCT
ma-310	80	81	and	and	CCONJ
ma-310	80	82	its	its	PRON
ma-310	80	83	solution	solution	NOUN
ma-310	80	84	is	be	AUX
ma-310	80	85	ω(z	ω(z	PROPN
ma-310	80	86	)	)	PUNCT
ma-310	80	87	=	=	SYM
ma-310	80	88	1	1	NUM
ma-310	80	89	2πi	2πi	NOUN
ma-310	80	90	∫	∫	PROPN
ma-310	80	91	∂m	∂m	PROPN
ma-310	80	92	γ(ζ	γ(ζ	PROPN
ma-310	80	93	)	)	PUNCT
ma-310	81	1	[	[	PUNCT
ma-310	81	2	z	z	NOUN
ma-310	81	3	−	−	PROPN
ma-310	81	4	t	t	NOUN
ma-310	81	5	ζ	ζ	NOUN
ma-310	81	6	−	−	PROPN
ma-310	81	7	log	log	NOUN
ma-310	81	8	(	(	PUNCT
ma-310	81	9	ζ	ζ	NOUN
ma-310	81	10	−	−	PROPN
ma-310	81	11	z	z	NOUN
ma-310	81	12	ζ	ζ	NOUN
ma-310	81	13	−	−	PROPN
ma-310	81	14	t	t	NOUN
ma-310	81	15	)	)	PUNCT
ma-310	82	1	+	+	NUM
ma-310	82	2	a2	a2	PROPN
ma-310	82	3	ζ2	ζ2	NOUN
ma-310	82	4	log	log	NOUN
ma-310	82	5	(	(	PUNCT
ma-310	82	6	ζz	ζz	ADP
ma-310	82	7	−	−	PROPN
ma-310	82	8	a2	a2	PROPN
ma-310	82	9	ζt	ζt	PROPN
ma-310	82	10	−	−	PROPN
ma-310	82	11	a2	a2	PROPN
ma-310	82	12	)	)	PUNCT
ma-310	82	13	]	]	PUNCT
ma-310	83	1	dζ	dζ	PROPN
ma-310	83	2	,	,	PUNCT
ma-310	83	3	where	where	SCONJ
ma-310	83	4	ζ	ζ	NOUN
ma-310	83	5	=	=	SYM
ma-310	83	6	ξ	ξ	PROPN
ma-310	83	7	+	+	NUM
ma-310	83	8	iη	iη	NOUN
ma-310	83	9	.	.	PUNCT
ma-310	83	10	https://doi.org/10.28924/ada/ma.5.10	https://doi.org/10.28924/ada/ma.5.10	PROPN
ma-310	83	11	eur	eur	PROPN
ma-310	83	12	.	.	PUNCT
ma-310	84	1	j.	j.	PROPN
ma-310	84	2	math	math	PROPN
ma-310	84	3	.	.	PUNCT
ma-310	85	1	anal	anal	PROPN
ma-310	85	2	.	.	PUNCT
ma-310	86	1	10.28924	10.28924	NUM
ma-310	86	2	/	/	SYM
ma-310	86	3	ada	ada	PROPN
ma-310	86	4	/	/	SYM
ma-310	86	5	ma.5.10	ma.5.10	ADJ
ma-310	86	6	5	5	NUM
ma-310	86	7	proof	proof	NOUN
ma-310	86	8	.	.	PUNCT
ma-310	87	1	suppose	suppose	VERB
ma-310	87	2	ω	ω	NOUN
ma-310	87	3	is	be	AUX
ma-310	87	4	a	a	DET
ma-310	87	5	solution	solution	NOUN
ma-310	87	6	to	to	ADP
ma-310	87	7	the	the	DET
ma-310	87	8	neumann	neumann	PROPN
ma-310	87	9	problem	problem	NOUN
ma-310	87	10	.	.	PUNCT
ma-310	88	1	introducing	introduce	VERB
ma-310	88	2	a	a	DET
ma-310	88	3	new	new	ADJ
ma-310	88	4	function	function	NOUN
ma-310	88	5	φ	φ	NOUN
ma-310	88	6	=	=	SYM
ma-310	88	7	ωz	ωz	PROPN
ma-310	88	8	,	,	PUNCT
ma-310	88	9	since	since	SCONJ
ma-310	88	10	φ	φ	PROPN
ma-310	88	11	is	be	AUX
ma-310	88	12	an	an	DET
ma-310	88	13	analytic	analytic	ADJ
ma-310	88	14	function	function	NOUN
ma-310	88	15	,	,	PUNCT
ma-310	88	16	φ	φ	PROPN
ma-310	88	17	=	=	PUNCT
ma-310	88	18	ωz	ωz	PROPN
ma-310	88	19	is	be	AUX
ma-310	88	20	a	a	DET
ma-310	88	21	solution	solution	NOUN
ma-310	88	22	to	to	ADP
ma-310	88	23	the	the	DET
ma-310	88	24	following	following	ADJ
ma-310	88	25	problem	problem	NOUN
ma-310	88	26	,	,	PUNCT
ma-310	88	27	φz̄	φz̄	NOUN
ma-310	88	28	=	=	NOUN
ma-310	88	29	0	0	NUM
ma-310	88	30	,	,	PUNCT
ma-310	88	31	in	in	ADP
ma-310	88	32	m	m	PROPN
ma-310	88	33	,	,	PUNCT
ma-310	88	34	φ	φ	PROPN
ma-310	88	35	=	=	SYM
ma-310	88	36	ωz	ωz	PROPN
ma-310	88	37	,	,	PUNCT
ma-310	88	38	on	on	ADP
ma-310	88	39	∂m	∂m	PROPN
ma-310	88	40	,	,	PUNCT
ma-310	88	41	(	(	PUNCT
ma-310	88	42	1.5)where	1.5)where	NUM
ma-310	88	43	ωz	ωz	NOUN
ma-310	88	44	on	on	ADP
ma-310	88	45	∂m	∂m	PROPN
ma-310	88	46	is	be	AUX
ma-310	88	47	represented	represent	VERB
ma-310	88	48	by	by	ADP
ma-310	88	49	,	,	PUNCT
ma-310	88	50	ωz(z	ωz(z	NUM
ma-310	88	51	)	)	PUNCT
ma-310	88	52	=	=	PUNCT
ma-310	89	1			PUNCT
ma-310	89	2	(	(	PUNCT
ma-310	89	3	z̄−ai√	z̄−ai√	NUM
ma-310	89	4	2a	2a	NUM
ma-310	89	5	)	)	PUNCT
ma-310	90	1	γ	γ	X
ma-310	90	2	,	,	PUNCT
ma-310	90	3	on	on	ADP
ma-310	90	4	c1	c1	PROPN
ma-310	90	5	,	,	PUNCT
ma-310	90	6	(	(	PUNCT
ma-310	90	7	z̄+ai√	z̄+ai√	PROPN
ma-310	90	8	2a	2a	NUM
ma-310	90	9	)	)	PUNCT
ma-310	90	10	γ	γ	X
ma-310	90	11	,	,	PUNCT
ma-310	90	12	on	on	ADP
ma-310	90	13	c2.equation	c2.equation	NOUN
ma-310	90	14	(	(	PUNCT
ma-310	90	15	5	5	NUM
ma-310	90	16	)	)	PUNCT
ma-310	90	17	is	be	AUX
ma-310	90	18	equivalent	equivalent	ADJ
ma-310	90	19	to	to	ADP
ma-310	90	20	the	the	DET
ma-310	90	21	dirichlet	dirichlet	PROPN
ma-310	90	22	boundary	boundary	PROPN
ma-310	90	23	value	value	NOUN
ma-310	90	24	problem	problem	NOUN
ma-310	90	25	for	for	ADP
ma-310	90	26	the	the	DET
ma-310	90	27	homogeneous	homogeneous	ADJ
ma-310	90	28	cauchy	cauchy	PROPN
ma-310	90	29	–	–	PUNCT
ma-310	90	30	riemann	riemann	PROPN
ma-310	90	31	equation	equation	NOUN
ma-310	90	32	.	.	PUNCT
ma-310	91	1	by	by	ADP
ma-310	91	2	theorem	theorem	NOUN
ma-310	91	3	3.2	3.2	NUM
ma-310	91	4	in	in	ADP
ma-310	91	5	[	[	X
ma-310	91	6	1	1	NUM
ma-310	91	7	]	]	PUNCT
ma-310	91	8	,	,	PUNCT
ma-310	91	9	the	the	DET
ma-310	91	10	above	above	ADJ
ma-310	91	11	dirichlet	dirichlet	PROPN
ma-310	91	12	problem	problem	NOUN
ma-310	91	13	is	be	AUX
ma-310	91	14	solvable	solvable	ADJ
ma-310	91	15	if	if	SCONJ
ma-310	91	16	and	and	CCONJ
ma-310	91	17	only	only	ADV
ma-310	91	18	if	if	SCONJ
ma-310	91	19	1	1	NUM
ma-310	91	20	2πi	2πi	NOUN
ma-310	91	21	∫	∫	PROPN
ma-310	91	22	∂m	∂m	PROPN
ma-310	91	23	γ(ζ	γ(ζ	PROPN
ma-310	91	24	)	)	PUNCT
ma-310	91	25	[	[	PUNCT
ma-310	91	26	z̄	z̄	INTJ
ma-310	91	27	−	−	ADP
ma-310	91	28	ai	ai	VERB
ma-310	91	29	ζ(z̄	ζ(z̄	PUNCT
ma-310	91	30	−	−	PRON
ma-310	91	31	ai	ai	VERB
ma-310	91	32	)	)	PUNCT
ma-310	91	33	+	+	CCONJ
ma-310	91	34	ai	ai	PROPN
ma-310	91	35	z̄	z̄	INTJ
ma-310	91	36	−	−	PROPN
ma-310	91	37	a2	a2	PROPN
ma-310	91	38	+	+	CCONJ
ma-310	91	39	z̄	z̄	PROPN
ma-310	91	40	+	+	CCONJ
ma-310	91	41	ai	ai	PROPN
ma-310	91	42	ζ(z̄	ζ(z̄	ADJ
ma-310	91	43	+	+	NUM
ma-310	91	44	ai)−	ai)−	NOUN
ma-310	91	45	ai	ai	VERB
ma-310	91	46	z̄	z̄	NOUN
ma-310	91	47	−	−	PROPN
ma-310	91	48	a2	a2	PROPN
ma-310	91	49	]	]	PUNCT
ma-310	91	50	dζ	dζ	PROPN
ma-310	91	51	=	=	SYM
ma-310	91	52	0	0	PROPN
ma-310	91	53	,	,	PUNCT
ma-310	91	54	then	then	ADV
ma-310	91	55	,	,	PUNCT
ma-310	91	56	the	the	DET
ma-310	91	57	unique	unique	ADJ
ma-310	91	58	solution	solution	NOUN
ma-310	91	59	is	be	AUX
ma-310	91	60	given	give	VERB
ma-310	91	61	by	by	ADP
ma-310	91	62	,	,	PUNCT
ma-310	91	63	ωz(z	ωz(z	NUM
ma-310	91	64	)	)	PUNCT
ma-310	91	65	=	=	SYM
ma-310	91	66	1	1	NUM
ma-310	91	67	2πi	2πi	NOUN
ma-310	91	68	∫	∫	PROPN
ma-310	91	69	∂m	∂m	PROPN
ma-310	91	70	γ(ζ	γ(ζ	PROPN
ma-310	91	71	)	)	PUNCT
ma-310	91	72	[	[	PUNCT
ma-310	91	73	1	1	NUM
ma-310	91	74	ζ	ζ	NOUN
ma-310	91	75	−	−	PROPN
ma-310	91	76	z	z	NOUN
ma-310	92	1	+	+	NUM
ma-310	92	2	z	z	NOUN
ma-310	92	3	ζz	ζz	ADP
ma-310	92	4	−	−	PROPN
ma-310	92	5	a2	a2	PROPN
ma-310	92	6	]	]	PUNCT
ma-310	92	7	dζ	dζ	PROPN
ma-310	92	8	.	.	PROPN
ma-310	93	1	(	(	PUNCT
ma-310	93	2	1.6	1.6	NUM
ma-310	93	3	)	)	PUNCT
ma-310	93	4	the	the	DET
ma-310	93	5	primitive	primitive	NOUN
ma-310	93	6	of	of	ADP
ma-310	93	7	the	the	DET
ma-310	93	8	function	function	NOUN
ma-310	93	9	in	in	ADP
ma-310	93	10	(	(	PUNCT
ma-310	93	11	6	6	NUM
ma-310	93	12	)	)	PUNCT
ma-310	93	13	is	be	AUX
ma-310	93	14	ω(z	ω(z	PROPN
ma-310	93	15	)	)	PUNCT
ma-310	93	16	=	=	SYM
ma-310	93	17	1	1	NUM
ma-310	93	18	2πi	2πi	NOUN
ma-310	93	19	∫	∫	PROPN
ma-310	93	20	∂m	∂m	PROPN
ma-310	93	21	γ(ζ	γ(ζ	PROPN
ma-310	93	22	)	)	PUNCT
ma-310	94	1	[	[	PUNCT
ma-310	94	2	z	z	NOUN
ma-310	94	3	ζ	ζ	NOUN
ma-310	94	4	−	−	PROPN
ma-310	94	5	log(ζ	log(ζ	PROPN
ma-310	94	6	−	−	PROPN
ma-310	94	7	z	z	NOUN
ma-310	94	8	)	)	PUNCT
ma-310	95	1	+	+	NUM
ma-310	95	2	a2	a2	PROPN
ma-310	95	3	ζ2	ζ2	NOUN
ma-310	95	4	log(ζz	log(ζz	NOUN
ma-310	95	5	−	−	PROPN
ma-310	95	6	a2	a2	PROPN
ma-310	95	7	)	)	PUNCT
ma-310	95	8	]	]	PUNCT
ma-310	96	1	dζ	dζ	PROPN
ma-310	96	2	+	+	CCONJ
ma-310	96	3	c.	c.	NOUN
ma-310	96	4	define	define	VERB
ma-310	96	5	c	c	PROPN
ma-310	96	6	as	as	ADP
ma-310	96	7	c	c	PROPN
ma-310	96	8	=	=	SYM
ma-310	96	9	−	−	PROPN
ma-310	96	10	1	1	NUM
ma-310	96	11	2πi	2πi	NOUN
ma-310	96	12	∫	∫	PROPN
ma-310	96	13	∂m	∂m	PROPN
ma-310	96	14	γ(ζ	γ(ζ	PROPN
ma-310	96	15	)	)	PUNCT
ma-310	96	16	[	[	PUNCT
ma-310	96	17	t	t	NOUN
ma-310	96	18	ζ	ζ	NOUN
ma-310	96	19	−	−	PROPN
ma-310	96	20	log(ζ	log(ζ	PROPN
ma-310	96	21	−	−	PROPN
ma-310	96	22	t	t	PROPN
ma-310	96	23	)	)	PUNCT
ma-310	96	24	+	+	NUM
ma-310	96	25	a2	a2	PROPN
ma-310	96	26	ζ2	ζ2	PROPN
ma-310	96	27	log(ζt	log(ζt	PROPN
ma-310	96	28	−	−	PROPN
ma-310	96	29	a2	a2	PROPN
ma-310	96	30	)	)	PUNCT
ma-310	96	31	]	]	PUNCT
ma-310	97	1	dζ	dζ	PROPN
ma-310	97	2	.	.	PROPN
ma-310	98	1	this	this	PRON
ma-310	98	2	completes	complete	VERB
ma-310	98	3	the	the	DET
ma-310	98	4	proof	proof	NOUN
ma-310	98	5	.	.	PUNCT
ma-310	99	1	�	�	PROPN
ma-310	99	2	2	2	NUM
ma-310	99	3	.	.	PUNCT
ma-310	100	1	the	the	DET
ma-310	100	2	dirichlet	dirichlet	PROPN
ma-310	100	3	problem	problem	NOUN
ma-310	100	4	for	for	ADP
ma-310	100	5	m	m	PROPN
ma-310	100	6	in	in	ADP
ma-310	100	7	this	this	DET
ma-310	100	8	section	section	NOUN
ma-310	100	9	,	,	PUNCT
ma-310	100	10	we	we	PRON
ma-310	100	11	consider	consider	VERB
ma-310	100	12	the	the	DET
ma-310	100	13	dirichlet	dirichlet	PROPN
ma-310	100	14	problem	problem	NOUN
ma-310	100	15	for	for	ADP
ma-310	100	16	the	the	DET
ma-310	100	17	poisson	poisson	NOUN
ma-310	100	18	equation	equation	NOUN
ma-310	100	19	in	in	ADP
ma-310	100	20	the	the	DET
ma-310	100	21	partial	partial	ADJ
ma-310	100	22	eclipsedomain	eclipsedomain	NOUN
ma-310	100	23	.	.	PUNCT
ma-310	101	1	in	in	ADP
ma-310	101	2	order	order	NOUN
ma-310	101	3	to	to	PART
ma-310	101	4	treat	treat	VERB
ma-310	101	5	the	the	DET
ma-310	101	6	dirichlet	dirichlet	PROPN
ma-310	101	7	boundary	boundary	PROPN
ma-310	101	8	value	value	NOUN
ma-310	101	9	problem	problem	NOUN
ma-310	101	10	for	for	ADP
ma-310	101	11	second	second	ADJ
ma-310	101	12	order	order	NOUN
ma-310	101	13	complex	complex	ADJ
ma-310	101	14	partialdifferential	partialdifferential	ADJ
ma-310	101	15	equations	equation	NOUN
ma-310	101	16	some	some	DET
ma-310	101	17	special	special	ADJ
ma-310	101	18	kernel	kernel	NOUN
ma-310	101	19	functions	function	NOUN
ma-310	101	20	,	,	PUNCT
ma-310	101	21	the	the	DET
ma-310	101	22	green	green	ADJ
ma-310	101	23	functions	function	NOUN
ma-310	101	24	,	,	PUNCT
ma-310	101	25	have	have	VERB
ma-310	101	26	to	to	PART
ma-310	101	27	be	be	AUX
ma-310	101	28	constructed.it	constructed.it	NOUN
ma-310	101	29	is	be	AUX
ma-310	101	30	essential	essential	ADJ
ma-310	101	31	to	to	PART
ma-310	101	32	construct	construct	VERB
ma-310	101	33	the	the	DET
ma-310	101	34	green	green	PROPN
ma-310	101	35	’s	’s	PART
ma-310	101	36	functions	function	NOUN
ma-310	101	37	tailored	tailor	VERB
ma-310	101	38	to	to	ADP
ma-310	101	39	the	the	DET
ma-310	101	40	specific	specific	ADJ
ma-310	101	41	domain	domain	NOUN
ma-310	101	42	.	.	PUNCT
ma-310	102	1	these	these	DET
ma-310	102	2	green’sfunctions	green’sfunction	NOUN
ma-310	102	3	serve	serve	VERB
ma-310	102	4	as	as	ADP
ma-310	102	5	fundamental	fundamental	ADJ
ma-310	102	6	tools	tool	NOUN
ma-310	102	7	,	,	PUNCT
ma-310	102	8	transforming	transform	VERB
ma-310	102	9	the	the	DET
ma-310	102	10	differential	differential	ADJ
ma-310	102	11	equation	equation	NOUN
ma-310	102	12	into	into	ADP
ma-310	102	13	an	an	DET
ma-310	102	14	integral	integral	ADJ
ma-310	102	15	formthat	formthat	NOUN
ma-310	102	16	can	can	AUX
ma-310	102	17	be	be	AUX
ma-310	102	18	more	more	ADV
ma-310	102	19	easily	easily	ADV
ma-310	102	20	analyzed	analyze	VERB
ma-310	102	21	and	and	CCONJ
ma-310	102	22	solved	solve	VERB
ma-310	102	23	,	,	PUNCT
ma-310	102	24	see	see	VERB
ma-310	102	25	[	[	X
ma-310	102	26	5–9	5–9	X
ma-310	102	27	]	]	PUNCT
ma-310	102	28	.	.	PUNCT
ma-310	103	1	the	the	DET
ma-310	103	2	harmonic	harmonic	ADJ
ma-310	103	3	green	green	ADJ
ma-310	103	4	function	function	NOUN
ma-310	103	5	for	for	ADP
ma-310	103	6	the	the	DET
ma-310	103	7	partialeclipse	partialeclipse	NOUN
ma-310	103	8	domain	domain	NOUN
ma-310	103	9	m	m	NOUN
ma-310	103	10	is	be	AUX
ma-310	103	11	g1(z	g1(z	PROPN
ma-310	103	12	,	,	PUNCT
ma-310	103	13	ζ	ζ	NOUN
ma-310	103	14	)	)	PUNCT
ma-310	103	15	=	=	PUNCT
ma-310	103	16	log	log	PROPN
ma-310	103	17	∣∣∣∣	∣∣∣∣	PROPN
ma-310	103	18	ζ̄(z	ζ̄(z	PROPN
ma-310	103	19	+	+	CCONJ
ma-310	103	20	ai)−	ai)−	NOUN
ma-310	103	21	aiz	aiz	X
ma-310	103	22	−	−	PROPN
ma-310	103	23	a2	a2	PROPN
ma-310	103	24	ζ	ζ	NOUN
ma-310	103	25	−	−	PROPN
ma-310	103	26	z	z	PROPN
ma-310	103	27	ζ̄(z	ζ̄(z	PROPN
ma-310	103	28	−	−	NOUN
ma-310	103	29	aiz	aiz	X
ma-310	103	30	)	)	PUNCT
ma-310	104	1	+	+	CCONJ
ma-310	104	2	aiz	aiz	X
ma-310	104	3	−	−	PROPN
ma-310	104	4	a2	a2	PROPN
ma-310	104	5	ζz	ζz	ADP
ma-310	104	6	−	−	PROPN
ma-310	104	7	a2	a2	PROPN
ma-310	104	8	∣∣∣∣2	∣∣∣∣2	NOUN
ma-310	104	9	.	.	PUNCT
ma-310	105	1	https://doi.org/10.28924/ada/ma.5.10	https://doi.org/10.28924/ada/ma.5.10	PROPN
ma-310	105	2	eur	eur	PROPN
ma-310	105	3	.	.	PUNCT
ma-310	106	1	j.	j.	PROPN
ma-310	106	2	math	math	PROPN
ma-310	106	3	.	.	PUNCT
ma-310	107	1	anal	anal	PROPN
ma-310	107	2	.	.	PUNCT
ma-310	108	1	10.28924	10.28924	NUM
ma-310	108	2	/	/	SYM
ma-310	108	3	ada	ada	PROPN
ma-310	108	4	/	/	SYM
ma-310	108	5	ma.5.10	ma.5.10	NOUN
ma-310	108	6	6the	6the	PROPN
ma-310	108	7	outward	outward	VERB
ma-310	108	8	normal	normal	ADJ
ma-310	108	9	derivative	derivative	NOUN
ma-310	108	10	of	of	ADP
ma-310	108	11	the	the	DET
ma-310	108	12	boundary	boundary	NOUN
ma-310	108	13	∂m	∂m	PROPN
ma-310	108	14	is	be	AUX
ma-310	108	15	given	give	VERB
ma-310	108	16	by	by	ADP
ma-310	108	17	for	for	ADP
ma-310	108	18	z	z	PROPN
ma-310	108	19	∈	∈	PROPN
ma-310	108	20	∂m	∂m	PROPN
ma-310	108	21	∩	∩	ADJ
ma-310	108	22	c1	c1	PROPN
ma-310	108	23	,	,	PUNCT
ma-310	108	24	that	that	ADV
ma-310	108	25	is	is	ADV
ma-310	108	26	,	,	PUNCT
ma-310	108	27	|z	|z	PROPN
ma-310	109	1	−	−	PROPN
ma-310	109	2	ai	ai	VERB
ma-310	109	3	|	|	ADV
ma-310	109	4	=	=	NOUN
ma-310	109	5	√	√	NUM
ma-310	109	6	2a	2a	NUM
ma-310	109	7	,	,	PUNCT
ma-310	109	8	we	we	PRON
ma-310	109	9	have	have	VERB
ma-310	109	10	∂vzg1(z	∂vzg1(z	NOUN
ma-310	109	11	,	,	PUNCT
ma-310	109	12	ζ	ζ	NOUN
ma-310	109	13	)	)	PUNCT
ma-310	109	14	=	=	SYM
ma-310	109	15	(	(	PUNCT
ma-310	109	16	(	(	PUNCT
ma-310	109	17	z	z	NOUN
ma-310	109	18	−	−	NOUN
ma-310	109	19	ai√	ai√	PUNCT
ma-310	109	20	2a	2a	NUM
ma-310	109	21	)	)	PUNCT
ma-310	110	1	∂z	∂z	PROPN
ma-310	110	2	+	+	CCONJ
ma-310	110	3	(	(	PUNCT
ma-310	110	4	z̄	z̄	X
ma-310	110	5	+	+	NUM
ma-310	110	6	ai√	ai√	NOUN
ma-310	110	7	2a	2a	NUM
ma-310	110	8	)	)	PUNCT
ma-310	111	1	∂z̄	∂z̄	PROPN
ma-310	111	2	)	)	PUNCT
ma-310	112	1	g1(z	g1(z	PROPN
ma-310	112	2	,	,	PUNCT
ma-310	112	3	ζ	ζ	NOUN
ma-310	112	4	)	)	PUNCT
ma-310	112	5	,	,	PUNCT
ma-310	112	6	and	and	CCONJ
ma-310	112	7	for	for	ADP
ma-310	112	8	z	z	PROPN
ma-310	112	9	∈	∈	PROPN
ma-310	112	10	∂m	∂m	PROPN
ma-310	112	11	∩	∩	PROPN
ma-310	112	12	c2	c2	PROPN
ma-310	112	13	,	,	PUNCT
ma-310	112	14	that	that	ADV
ma-310	112	15	is	is	ADV
ma-310	112	16	,	,	PUNCT
ma-310	112	17	|z	|z	PROPN
ma-310	113	1	+	+	CCONJ
ma-310	113	2	ai	ai	VERB
ma-310	113	3	|	|	ADV
ma-310	113	4	=	=	NOUN
ma-310	113	5	√	√	NUM
ma-310	113	6	2a	2a	NUM
ma-310	113	7	,	,	PUNCT
ma-310	113	8	we	we	PRON
ma-310	113	9	have	have	VERB
ma-310	113	10	∂vzg1(z	∂vzg1(z	NOUN
ma-310	113	11	,	,	PUNCT
ma-310	113	12	ζ	ζ	NOUN
ma-310	113	13	)	)	PUNCT
ma-310	113	14	=	=	SYM
ma-310	113	15	(	(	PUNCT
ma-310	113	16	(	(	PUNCT
ma-310	113	17	z	z	NOUN
ma-310	113	18	+	+	NUM
ma-310	113	19	ai√	ai√	NOUN
ma-310	113	20	2a	2a	NUM
ma-310	113	21	)	)	PUNCT
ma-310	114	1	∂z	∂z	PROPN
ma-310	114	2	+	+	CCONJ
ma-310	114	3	(	(	PUNCT
ma-310	114	4	z̄	z̄	INTJ
ma-310	114	5	−	−	NOUN
ma-310	114	6	ai√	ai√	NOUN
ma-310	114	7	2a	2a	NUM
ma-310	114	8	)	)	PUNCT
ma-310	115	1	∂z̄	∂z̄	PROPN
ma-310	115	2	)	)	PUNCT
ma-310	116	1	g1(z	g1(z	PROPN
ma-310	116	2	,	,	PUNCT
ma-310	116	3	ζ	ζ	NOUN
ma-310	116	4	)	)	PUNCT
ma-310	116	5	.	.	PUNCT
ma-310	117	1	the	the	DET
ma-310	117	2	harmonic	harmonic	ADJ
ma-310	117	3	green	green	ADJ
ma-310	117	4	functions	function	NOUN
ma-310	117	5	play	play	VERB
ma-310	117	6	an	an	DET
ma-310	117	7	essential	essential	ADJ
ma-310	117	8	role	role	NOUN
ma-310	117	9	in	in	ADP
ma-310	117	10	solving	solve	VERB
ma-310	117	11	the	the	DET
ma-310	117	12	dirichlet	dirichlet	PROPN
ma-310	117	13	boundary	boundary	ADJ
ma-310	117	14	valueproblem	valueproblem	NOUN
ma-310	117	15	for	for	ADP
ma-310	117	16	second	second	ADJ
ma-310	117	17	order	order	NOUN
ma-310	117	18	complex	complex	ADJ
ma-310	117	19	partial	partial	ADJ
ma-310	117	20	differential	differential	NOUN
ma-310	117	21	equations	equation	NOUN
ma-310	117	22	.	.	PUNCT
ma-310	118	1	the	the	DET
ma-310	118	2	next	next	ADJ
ma-310	118	3	theorem	theorem	NOUN
ma-310	118	4	contains	contain	VERB
ma-310	118	5	arepresentation	arepresentation	NOUN
ma-310	118	6	formula	formula	NOUN
ma-310	118	7	for	for	ADP
ma-310	118	8	a	a	DET
ma-310	118	9	class	class	NOUN
ma-310	118	10	of	of	ADP
ma-310	118	11	functions	function	NOUN
ma-310	118	12	via	via	ADP
ma-310	118	13	the	the	DET
ma-310	118	14	green	green	ADJ
ma-310	118	15	function	function	NOUN
ma-310	118	16	,	,	PUNCT
ma-310	118	17	which	which	PRON
ma-310	118	18	is	be	AUX
ma-310	118	19	used	use	VERB
ma-310	118	20	to	to	PART
ma-310	118	21	solve	solve	VERB
ma-310	118	22	thedirichlet	thedirichlet	ADJ
ma-310	118	23	problem	problem	NOUN
ma-310	118	24	for	for	ADP
ma-310	118	25	poisson	poisson	NOUN
ma-310	118	26	equation	equation	NOUN
ma-310	118	27	(	(	PUNCT
ma-310	118	28	see	see	VERB
ma-310	118	29	[	[	X
ma-310	118	30	5	5	NUM
ma-310	118	31	,	,	PUNCT
ma-310	118	32	7	7	NUM
ma-310	118	33	,	,	PUNCT
ma-310	118	34	9	9	NUM
ma-310	118	35	]	]	NUM
ma-310	118	36	)	)	PUNCT
ma-310	118	37	.	.	PUNCT
ma-310	119	1	theorem	theorem	VERB
ma-310	119	2	2.1	2.1	NUM
ma-310	119	3	.	.	PUNCT
ma-310	120	1	let	let	VERB
ma-310	120	2	ω	ω	PROPN
ma-310	120	3	⊂	⊂	PROPN
ma-310	120	4	c	c	AUX
ma-310	120	5	be	be	AUX
ma-310	120	6	a	a	DET
ma-310	120	7	regular	regular	ADJ
ma-310	120	8	domain	domain	NOUN
ma-310	120	9	,	,	PUNCT
ma-310	120	10	and	and	CCONJ
ma-310	120	11	let	let	VERB
ma-310	120	12	g1	g1	PROPN
ma-310	120	13	be	be	AUX
ma-310	120	14	the	the	DET
ma-310	120	15	harmonic	harmonic	ADJ
ma-310	120	16	green	green	ADJ
ma-310	120	17	function	function	NOUN
ma-310	120	18	for	for	ADP
ma-310	120	19	ω	ω	PROPN
ma-310	120	20	then	then	ADV
ma-310	120	21	any	any	DET
ma-310	120	22	ω	ω	PROPN
ma-310	120	23	∈	∈	PROPN
ma-310	120	24	c2(ω;c	c2(ω;c	NOUN
ma-310	120	25	)	)	PUNCT
ma-310	120	26	∩	∩	NOUN
ma-310	120	27	c1(ω;c	c1(ω;c	NOUN
ma-310	120	28	)	)	PUNCT
ma-310	120	29	can	can	AUX
ma-310	120	30	be	be	AUX
ma-310	120	31	represented	represent	VERB
ma-310	120	32	as	as	SCONJ
ma-310	120	33	follows	follow	VERB
ma-310	120	34	:	:	PUNCT
ma-310	120	35	ω(z	ω(z	NUM
ma-310	120	36	)	)	PUNCT
ma-310	121	1	=	=	SYM
ma-310	121	2	−	−	PROPN
ma-310	122	1	1	1	NUM
ma-310	123	1	4π	4π	NUM
ma-310	123	2	∫	∫	PROPN
ma-310	123	3	∂ω	∂ω	PROPN
ma-310	123	4	ω(ζ)∂vζg1(z	ω(ζ)∂vζg1(z	PROPN
ma-310	123	5	,	,	PUNCT
ma-310	123	6	ζ)dtζ	ζ)dtζ	PROPN
ma-310	123	7	−	−	NOUN
ma-310	123	8	1	1	NUM
ma-310	123	9	π	π	PROPN
ma-310	123	10	∫	∫	PROPN
ma-310	123	11	ω	ω	PROPN
ma-310	123	12	ωζζ̄(ζ)g1(z	ωζζ̄(ζ)g1(z	PROPN
ma-310	123	13	,	,	PUNCT
ma-310	123	14	ζ)dξdη	ζ)dξdη	PROPN
ma-310	123	15	,	,	PUNCT
ma-310	123	16	where	where	SCONJ
ma-310	123	17	v	v	NOUN
ma-310	123	18	is	be	AUX
ma-310	123	19	the	the	DET
ma-310	123	20	outward	outward	ADJ
ma-310	123	21	normal	normal	ADJ
ma-310	123	22	derivative	derivative	NOUN
ma-310	123	23	on	on	ADP
ma-310	123	24	∂ω	∂ω	PROPN
ma-310	123	25	and	and	CCONJ
ma-310	123	26	t	t	PROPN
ma-310	123	27	is	be	AUX
ma-310	123	28	the	the	DET
ma-310	123	29	arc	arc	NOUN
ma-310	123	30	length	length	NOUN
ma-310	123	31	parameter	parameter	NOUN
ma-310	124	1	[	[	X
ma-310	124	2	5	5	NUM
ma-310	124	3	,	,	PUNCT
ma-310	124	4	7	7	NUM
ma-310	124	5	,	,	PUNCT
ma-310	124	6	9	9	NUM
ma-310	124	7	]	]	PUNCT
ma-310	124	8	.	.	PUNCT
ma-310	125	1	therefore	therefore	ADV
ma-310	125	2	,	,	PUNCT
ma-310	125	3	based	base	VERB
ma-310	125	4	on	on	ADP
ma-310	125	5	theorem	theorem	NOUN
ma-310	125	6	3	3	NUM
ma-310	125	7	,	,	PUNCT
ma-310	125	8	the	the	DET
ma-310	125	9	explicit	explicit	ADJ
ma-310	125	10	form	form	NOUN
ma-310	125	11	of	of	ADP
ma-310	125	12	the	the	DET
ma-310	125	13	green	green	ADJ
ma-310	125	14	representation	representation	NOUN
ma-310	125	15	formula	formula	NOUN
ma-310	125	16	for	for	ADP
ma-310	125	17	thepartial	thepartial	ADJ
ma-310	125	18	eclipse	eclipse	NOUN
ma-310	125	19	domain	domain	NOUN
ma-310	125	20	is	be	AUX
ma-310	125	21	as	as	SCONJ
ma-310	125	22	following	follow	VERB
ma-310	125	23	:	:	PUNCT
ma-310	125	24	ω(z	ω(z	NUM
ma-310	125	25	)	)	PUNCT
ma-310	125	26	=	=	SYM
ma-310	125	27	1	1	NUM
ma-310	125	28	2πi	2πi	NOUN
ma-310	125	29	∫	∫	PROPN
ma-310	125	30	∂m	∂m	PROPN
ma-310	125	31	⋂	⋂	PROPN
ma-310	125	32	c1	c1	PROPN
ma-310	125	33	ω(ζ	ω(ζ	NOUN
ma-310	125	34	)	)	PUNCT
ma-310	125	35	(	(	PUNCT
ma-310	125	36	ζ	ζ	NOUN
ma-310	125	37	+	+	CCONJ
ma-310	125	38	ai	ai	VERB
ma-310	125	39	ζ	ζ	NOUN
ma-310	125	40	−	−	PROPN
ma-310	125	41	z	z	NOUN
ma-310	125	42	+	+	NOUN
ma-310	125	43	ζ̄	ζ̄	VERB
ma-310	125	44	−	−	NOUN
ma-310	125	45	ai	ai	VERB
ma-310	125	46	ζ̄	ζ̄	ADV
ma-310	126	1	−	−	PROPN
ma-310	126	2	z̄	z̄	NOUN
ma-310	126	3	−	−	ADP
ma-310	126	4	1	1	NUM
ma-310	126	5	+	+	NUM
ma-310	126	6	z(ζ	z(ζ	NOUN
ma-310	126	7	−	−	NOUN
ma-310	126	8	ai	ai	NOUN
ma-310	126	9	)	)	PUNCT
ma-310	126	10	ζz	ζz	ADP
ma-310	126	11	−	−	PROPN
ma-310	126	12	a2	a2	PROPN
ma-310	126	13	+	+	CCONJ
ma-310	126	14	z̄(ζ̄	z̄(ζ̄	PROPN
ma-310	126	15	+	+	CCONJ
ma-310	126	16	ai	ai	ADJ
ma-310	126	17	)	)	PUNCT
ma-310	126	18	ζ̄z̄	ζ̄z̄	NOUN
ma-310	126	19	−	−	PROPN
ma-310	126	20	a2	a2	PROPN
ma-310	126	21	−	−	PROPN
ma-310	126	22	1	1	NUM
ma-310	126	23	)	)	PUNCT
ma-310	126	24	dζ	dζ	PROPN
ma-310	126	25	ζ	ζ	NOUN
ma-310	126	26	−	−	NOUN
ma-310	127	1	ai	ai	NOUN
ma-310	127	2	+	+	PROPN
ma-310	127	3	1	1	NUM
ma-310	127	4	2πi	2πi	NOUN
ma-310	127	5	∫	∫	PROPN
ma-310	128	1	∂m	∂m	PROPN
ma-310	128	2	⋂	⋂	PROPN
ma-310	128	3	c2	c2	PROPN
ma-310	128	4	ω(ζ	ω(ζ	NOUN
ma-310	128	5	)	)	PUNCT
ma-310	128	6	(	(	PUNCT
ma-310	128	7	ζ	ζ	NOUN
ma-310	128	8	+	+	CCONJ
ma-310	128	9	ai	ai	VERB
ma-310	128	10	ζ	ζ	NOUN
ma-310	128	11	−	−	PROPN
ma-310	128	12	z	z	NOUN
ma-310	129	1	+	+	NOUN
ma-310	129	2	ζ̄	ζ̄	VERB
ma-310	129	3	−	−	NOUN
ma-310	129	4	ai	ai	VERB
ma-310	129	5	ζ̄	ζ̄	ADV
ma-310	129	6	−	−	PROPN
ma-310	129	7	z̄	z̄	NOUN
ma-310	129	8	−	−	ADP
ma-310	129	9	1	1	NUM
ma-310	130	1	+	+	NUM
ma-310	130	2	z(ζ	z(ζ	NOUN
ma-310	130	3	+	+	CCONJ
ma-310	130	4	ai	ai	NOUN
ma-310	130	5	)	)	PUNCT
ma-310	130	6	ζz	ζz	ADP
ma-310	130	7	−	−	PROPN
ma-310	130	8	a2	a2	PROPN
ma-310	130	9	+	+	CCONJ
ma-310	130	10	z̄(ζ̄	z̄(ζ̄	PROPN
ma-310	130	11	−	−	NOUN
ma-310	130	12	ai	ai	NOUN
ma-310	130	13	)	)	PUNCT
ma-310	130	14	ζ̄z̄	ζ̄z̄	NOUN
ma-310	130	15	−	−	PROPN
ma-310	130	16	a2	a2	PROPN
ma-310	130	17	−	−	PROPN
ma-310	130	18	1	1	NUM
ma-310	130	19	)	)	PUNCT
ma-310	130	20	dζ	dζ	PROPN
ma-310	130	21	ζ	ζ	PROPN
ma-310	130	22	+	+	CCONJ
ma-310	130	23	ai	ai	PROPN
ma-310	130	24	−	−	PROPN
ma-310	130	25	1	1	NUM
ma-310	130	26	π	π	PROPN
ma-310	130	27	∫	∫	PROPN
ma-310	130	28	m	m	VERB
ma-310	130	29	ωζζ̄(ζ)g1(z	ωζζ̄(ζ)g1(z	NOUN
ma-310	130	30	,	,	PUNCT
ma-310	130	31	ζ)dξdη	ζ)dξdη	NUM
ma-310	130	32	.	.	PUNCT
ma-310	131	1	(	(	PUNCT
ma-310	131	2	2.1	2.1	NUM
ma-310	131	3	)	)	PUNCT
ma-310	131	4	in	in	ADP
ma-310	131	5	fact	fact	NOUN
ma-310	131	6	formula	formula	NOUN
ma-310	131	7	(	(	PUNCT
ma-310	131	8	7	7	X
ma-310	131	9	)	)	PUNCT
ma-310	131	10	provides	provide	VERB
ma-310	131	11	a	a	DET
ma-310	131	12	solution	solution	NOUN
ma-310	131	13	to	to	ADP
ma-310	131	14	the	the	DET
ma-310	131	15	dirichlet	dirichlet	PROPN
ma-310	131	16	problem	problem	NOUN
ma-310	131	17	for	for	ADP
ma-310	131	18	the	the	DET
ma-310	131	19	poisson	poisson	NOUN
ma-310	131	20	equation	equation	NOUN
ma-310	131	21	in	in	ADP
ma-310	131	22	m	m	PROPN
ma-310	131	23	.	.	PUNCT
ma-310	132	1	theorem	theorem	ADJ
ma-310	132	2	2.2	2.2	NUM
ma-310	132	3	.	.	PUNCT
ma-310	133	1	the	the	DET
ma-310	133	2	dirichlet	dirichlet	PROPN
ma-310	133	3	problem	problem	NOUN
ma-310	133	4	for	for	ADP
ma-310	133	5	the	the	DET
ma-310	133	6	poisson	poisson	NOUN
ma-310	133	7	equation	equation	NOUN
ma-310	133	8	in	in	ADP
ma-310	133	9	m	m	NOUN
ma-310	133	10	ωzz̄	ωzz̄	NOUN
ma-310	134	1	=	=	SYM
ma-310	134	2	f	f	PROPN
ma-310	134	3	,	,	PUNCT
ma-310	134	4	z	z	PROPN
ma-310	134	5	∈	∈	PROPN
ma-310	134	6	m	m	PROPN
ma-310	134	7	,	,	PUNCT
ma-310	134	8	f	f	PROPN
ma-310	134	9	∈	∈	PROPN
ma-310	134	10	c(m;c	c(m;c	NOUN
ma-310	134	11	)	)	PUNCT
ma-310	134	12	,	,	PUNCT
ma-310	134	13	ω	ω	X
ma-310	134	14	=	=	SYM
ma-310	134	15	γ	γ	PROPN
ma-310	134	16	,	,	PUNCT
ma-310	134	17	on	on	ADP
ma-310	134	18	∂m	∂m	PROPN
ma-310	134	19	,	,	PUNCT
ma-310	134	20	γ	γ	PROPN
ma-310	134	21	∈	∈	PROPN
ma-310	134	22	c(∂m;c	c(∂m;c	NOUN
ma-310	134	23	)	)	PUNCT
ma-310	134	24	,	,	PUNCT
ma-310	134	25	(	(	PUNCT
ma-310	134	26	2.2	2.2	NUM
ma-310	134	27	)	)	PUNCT
ma-310	134	28	https://doi.org/10.28924/ada/ma.5.10	https://doi.org/10.28924/ada/ma.5.10	PROPN
ma-310	134	29	eur	eur	PROPN
ma-310	134	30	.	.	PUNCT
ma-310	135	1	j.	j.	PROPN
ma-310	135	2	math	math	PROPN
ma-310	135	3	.	.	PUNCT
ma-310	136	1	anal	anal	PROPN
ma-310	136	2	.	.	PUNCT
ma-310	137	1	10.28924	10.28924	NUM
ma-310	137	2	/	/	SYM
ma-310	137	3	ada	ada	NOUN
ma-310	137	4	/	/	SYM
ma-310	137	5	ma.5.10	ma.5.10	NOUN
ma-310	137	6	7	7	NUM
ma-310	137	7	is	be	AUX
ma-310	137	8	uniquely	uniquely	ADV
ma-310	137	9	solvable	solvable	ADJ
ma-310	137	10	and	and	CCONJ
ma-310	137	11	the	the	DET
ma-310	137	12	solution	solution	NOUN
ma-310	137	13	is	be	AUX
ma-310	137	14	given	give	VERB
ma-310	137	15	by	by	ADP
ma-310	137	16	ω(z	ω(z	PROPN
ma-310	137	17	)	)	PUNCT
ma-310	137	18	=	=	SYM
ma-310	137	19	1	1	NUM
ma-310	137	20	2πi	2πi	NOUN
ma-310	137	21	∫	∫	PROPN
ma-310	137	22	∂m	∂m	PROPN
ma-310	137	23	⋂	⋂	PROPN
ma-310	137	24	c1	c1	PROPN
ma-310	137	25	γ(ζ	γ(ζ	PROPN
ma-310	137	26	)	)	PUNCT
ma-310	137	27	(	(	PUNCT
ma-310	137	28	ζ	ζ	NOUN
ma-310	137	29	−	−	NOUN
ma-310	137	30	ai	ai	VERB
ma-310	137	31	ζ	ζ	NOUN
ma-310	137	32	−	−	PROPN
ma-310	137	33	z	z	NOUN
ma-310	137	34	+	+	NOUN
ma-310	137	35	ζ̄	ζ̄	X
ma-310	137	36	+	+	CCONJ
ma-310	137	37	ai	ai	VERB
ma-310	137	38	ζ̄	ζ̄	ADV
ma-310	138	1	−	−	PROPN
ma-310	138	2	z̄	z̄	NOUN
ma-310	138	3	−	−	ADP
ma-310	138	4	1	1	NUM
ma-310	138	5	+	+	NUM
ma-310	138	6	z(ζ	z(ζ	NOUN
ma-310	138	7	−	−	NOUN
ma-310	138	8	ai	ai	NOUN
ma-310	138	9	)	)	PUNCT
ma-310	138	10	ζz	ζz	ADP
ma-310	138	11	−	−	PROPN
ma-310	138	12	a2	a2	PROPN
ma-310	138	13	+	+	CCONJ
ma-310	138	14	z̄(ζ̄	z̄(ζ̄	PROPN
ma-310	138	15	+	+	CCONJ
ma-310	138	16	ai	ai	ADJ
ma-310	138	17	)	)	PUNCT
ma-310	138	18	ζ̄z̄	ζ̄z̄	NOUN
ma-310	138	19	−	−	PROPN
ma-310	138	20	a2	a2	PROPN
ma-310	138	21	−	−	PROPN
ma-310	138	22	1	1	NUM
ma-310	138	23	)	)	PUNCT
ma-310	138	24	dζ	dζ	PROPN
ma-310	138	25	ζ	ζ	NOUN
ma-310	138	26	−	−	NOUN
ma-310	139	1	ai	ai	NOUN
ma-310	139	2	+	+	PROPN
ma-310	139	3	1	1	NUM
ma-310	139	4	2πi	2πi	NOUN
ma-310	139	5	∫	∫	PROPN
ma-310	140	1	∂m	∂m	PROPN
ma-310	140	2	⋂	⋂	PROPN
ma-310	140	3	c2	c2	PROPN
ma-310	140	4	γ(ζ	γ(ζ	PROPN
ma-310	140	5	)	)	PUNCT
ma-310	140	6	(	(	PUNCT
ma-310	140	7	ζ	ζ	NOUN
ma-310	141	1	+	+	CCONJ
ma-310	141	2	ai	ai	VERB
ma-310	141	3	ζ	ζ	NOUN
ma-310	141	4	−	−	PROPN
ma-310	141	5	z	z	NOUN
ma-310	141	6	+	+	NOUN
ma-310	141	7	ζ̄	ζ̄	VERB
ma-310	141	8	−	−	NOUN
ma-310	141	9	ai	ai	VERB
ma-310	141	10	ζ̄	ζ̄	ADV
ma-310	141	11	−	−	PROPN
ma-310	141	12	z̄	z̄	NOUN
ma-310	141	13	−	−	ADP
ma-310	141	14	1	1	NUM
ma-310	141	15	+	+	NUM
ma-310	141	16	z(ζ	z(ζ	NOUN
ma-310	141	17	+	+	CCONJ
ma-310	141	18	ai	ai	NOUN
ma-310	141	19	)	)	PUNCT
ma-310	141	20	ζz	ζz	ADP
ma-310	141	21	−	−	PROPN
ma-310	141	22	a2	a2	PROPN
ma-310	141	23	+	+	CCONJ
ma-310	141	24	z̄(ζ̄	z̄(ζ̄	PROPN
ma-310	141	25	−	−	NOUN
ma-310	141	26	ai	ai	NOUN
ma-310	141	27	)	)	PUNCT
ma-310	141	28	ζ̄z̄	ζ̄z̄	NOUN
ma-310	141	29	−	−	PROPN
ma-310	141	30	a2	a2	PROPN
ma-310	141	31	−	−	PROPN
ma-310	141	32	1	1	NUM
ma-310	141	33	)	)	PUNCT
ma-310	141	34	dζ	dζ	PROPN
ma-310	141	35	ζ	ζ	PROPN
ma-310	142	1	+	+	CCONJ
ma-310	142	2	ai	ai	PROPN
ma-310	142	3	−	−	PROPN
ma-310	142	4	1	1	NUM
ma-310	142	5	π	π	PROPN
ma-310	142	6	∫	∫	PROPN
ma-310	142	7	m	m	PROPN
ma-310	142	8	f	f	PROPN
ma-310	142	9	(	(	PUNCT
ma-310	142	10	ζ)g1(z	ζ)g1(z	PROPN
ma-310	142	11	,	,	PUNCT
ma-310	142	12	ζ)dξdη	ζ)dξdη	NUM
ma-310	142	13	.	.	PUNCT
ma-310	143	1	(	(	PUNCT
ma-310	143	2	2.3	2.3	NUM
ma-310	143	3	)	)	PUNCT
ma-310	143	4	where	where	SCONJ
ma-310	143	5	ζ	ζ	NOUN
ma-310	143	6	=	=	SYM
ma-310	143	7	ξ	ξ	PROPN
ma-310	143	8	+	+	NUM
ma-310	143	9	iη	iη	NOUN
ma-310	143	10	.	.	PUNCT
ma-310	144	1	proof	proof	NOUN
ma-310	144	2	.	.	PUNCT
ma-310	145	1	by	by	ADP
ma-310	145	2	the	the	DET
ma-310	145	3	properties	property	NOUN
ma-310	145	4	of	of	ADP
ma-310	145	5	the	the	DET
ma-310	145	6	green	green	ADJ
ma-310	145	7	function	function	NOUN
ma-310	145	8	and	and	CCONJ
ma-310	145	9	the	the	DET
ma-310	145	10	harmonicity	harmonicity	NOUN
ma-310	145	11	of	of	ADP
ma-310	145	12	the	the	DET
ma-310	145	13	boundary	boundary	ADJ
ma-310	145	14	integrals	integral	NOUN
ma-310	145	15	ωis	ωis	PROPN
ma-310	145	16	seen	see	VERB
ma-310	145	17	to	to	PART
ma-310	145	18	be	be	AUX
ma-310	145	19	a	a	DET
ma-310	145	20	solution	solution	NOUN
ma-310	145	21	to	to	ADP
ma-310	145	22	the	the	DET
ma-310	145	23	poisson	poisson	NOUN
ma-310	145	24	equation	equation	NOUN
ma-310	145	25	(	(	PUNCT
ma-310	145	26	see	see	VERB
ma-310	145	27	[	[	X
ma-310	145	28	7	7	NUM
ma-310	145	29	]	]	NUM
ma-310	145	30	)	)	PUNCT
ma-310	145	31	.	.	PUNCT
ma-310	146	1	so	so	ADV
ma-310	146	2	,	,	PUNCT
ma-310	146	3	it	it	PRON
ma-310	146	4	remain	remain	VERB
ma-310	146	5	remains	remain	VERB
ma-310	146	6	to	to	PART
ma-310	146	7	check	check	VERB
ma-310	146	8	theboundary	theboundary	ADJ
ma-310	146	9	relation	relation	NOUN
ma-310	146	10	.	.	PUNCT
ma-310	147	1	the	the	DET
ma-310	147	2	study	study	NOUN
ma-310	147	3	of	of	ADP
ma-310	147	4	integral	integral	ADJ
ma-310	147	5	boundary	boundary	ADJ
ma-310	147	6	behavior	behavior	NOUN
ma-310	147	7	requires	require	VERB
ma-310	147	8	calculations	calculation	NOUN
ma-310	147	9	in	in	ADP
ma-310	147	10	different	different	ADJ
ma-310	147	11	partsof	partsof	NOUN
ma-310	147	12	the	the	DET
ma-310	147	13	boundary	boundary	NOUN
ma-310	147	14	.	.	PUNCT
ma-310	148	1	since	since	SCONJ
ma-310	148	2	,	,	PUNCT
ma-310	148	3	for	for	ADP
ma-310	148	4	z	z	PROPN
ma-310	148	5	∈	∈	PROPN
ma-310	148	6	∂m⋂c1	∂m⋂c1	PROPN
ma-310	148	7	,	,	PUNCT
ma-310	148	8	case1	case1	PROPN
ma-310	148	9	:	:	PUNCT
ma-310	148	10	ζ	ζ	PROPN
ma-310	148	11	∈	∈	PROPN
ma-310	148	12	c1	c1	NOUN
ma-310	148	13	,	,	PUNCT
ma-310	148	14	z̄(ζ̄	z̄(ζ̄	X
ma-310	148	15	+	+	CCONJ
ma-310	148	16	ai	ai	ADJ
ma-310	148	17	)	)	PUNCT
ma-310	148	18	ζ̄z̄	ζ̄z̄	NOUN
ma-310	148	19	−	−	PROPN
ma-310	148	20	a2	a2	PROPN
ma-310	148	21	=	=	PUNCT
ma-310	148	22	aiz−a2	aiz−a2	PROPN
ma-310	148	23	ζz	ζz	ADP
ma-310	148	24	−	−	PROPN
ma-310	148	25	a2	a2	PROPN
ma-310	148	26	.	.	PUNCT
ma-310	149	1	case2	case2	PROPN
ma-310	149	2	:	:	PUNCT
ma-310	149	3	ζ	ζ	PROPN
ma-310	149	4	∈	∈	PROPN
ma-310	149	5	c2	c2	PROPN
ma-310	149	6	,	,	PUNCT
ma-310	149	7	ζ̄	ζ̄	ADV
ma-310	149	8	−	−	PROPN
ma-310	149	9	ai	ai	VERB
ma-310	149	10	ζ̄	ζ̄	ADV
ma-310	149	11	−	−	NOUN
ma-310	149	12	z̄	z̄	NOUN
ma-310	149	13	=	=	SYM
ma-310	149	14	−aiz	−aiz	NOUN
ma-310	149	15	−	−	PROPN
ma-310	149	16	a2	a2	PROPN
ma-310	149	17	ζz	ζz	ADP
ma-310	149	18	−	−	PROPN
ma-310	149	19	a2	a2	PROPN
ma-310	149	20	,	,	PUNCT
ma-310	149	21	z̄(ζ̄	z̄(ζ̄	AUX
ma-310	149	22	−	−	NOUN
ma-310	149	23	ai	ai	NOUN
ma-310	149	24	)	)	PUNCT
ma-310	149	25	ζ̄z̄	ζ̄z̄	NOUN
ma-310	149	26	−	−	PROPN
ma-310	149	27	a2	a2	PROPN
ma-310	149	28	=	=	PROPN
ma-310	150	1	−z	−z	NOUN
ma-310	150	2	−	−	PROPN
ma-310	150	3	ai	ai	VERB
ma-310	150	4	ζ	ζ	NOUN
ma-310	150	5	−	−	PROPN
ma-310	150	6	z	z	NOUN
ma-310	150	7	.	.	PUNCT
ma-310	151	1	thus	thus	ADV
ma-310	151	2	,	,	PUNCT
ma-310	151	3	on	on	ADP
ma-310	151	4	∂m⋂c1	∂m⋂c1	PROPN
ma-310	151	5	,	,	PUNCT
ma-310	151	6	lim	lim	PROPN
ma-310	151	7	z→ζ	z→ζ	NUM
ma-310	151	8	ω(z	ω(z	NUM
ma-310	151	9	)	)	PUNCT
ma-310	151	10	=	=	SYM
ma-310	151	11	lim	lim	PROPN
ma-310	151	12	z→ζ	z→ζ	NUM
ma-310	151	13	1	1	NUM
ma-310	151	14	2πi	2πi	NOUN
ma-310	151	15	∫	∫	PROPN
ma-310	151	16	∂m	∂m	PROPN
ma-310	151	17	⋂	⋂	PROPN
ma-310	151	18	c1	c1	PROPN
ma-310	151	19	γ(ζ	γ(ζ	PROPN
ma-310	151	20	)	)	PUNCT
ma-310	151	21	[	[	PUNCT
ma-310	151	22	ζ	ζ	NOUN
ma-310	151	23	−	−	NOUN
ma-310	151	24	ai	ai	VERB
ma-310	151	25	ζ	ζ	NOUN
ma-310	151	26	−	−	PROPN
ma-310	151	27	z	z	NOUN
ma-310	151	28	+	+	NOUN
ma-310	151	29	ζ̄	ζ̄	X
ma-310	151	30	+	+	CCONJ
ma-310	151	31	ai	ai	VERB
ma-310	151	32	ζ̄	ζ̄	ADV
ma-310	151	33	−	−	PROPN
ma-310	151	34	z̄	z̄	NOUN
ma-310	151	35	−	−	ADP
ma-310	151	36	1	1	NUM
ma-310	151	37	]	]	PUNCT
ma-310	151	38	dζ	dζ	PROPN
ma-310	151	39	ζ	ζ	NOUN
ma-310	151	40	−	−	PROPN
ma-310	151	41	ai	ai	PROPN
ma-310	151	42	=	=	PROPN
ma-310	151	43	lim	lim	PROPN
ma-310	151	44	z→ζ	z→ζ	NUM
ma-310	151	45	1	1	NUM
ma-310	151	46	2πi	2πi	ADJ
ma-310	151	47	∫	∫	PROPN
ma-310	151	48	c1	c1	PROPN
ma-310	151	49	υ(ζ	υ(ζ	PROPN
ma-310	151	50	)	)	PUNCT
ma-310	151	51	[	[	PUNCT
ma-310	151	52	ζ	ζ	NOUN
ma-310	151	53	−	−	NOUN
ma-310	151	54	ai	ai	VERB
ma-310	151	55	ζ	ζ	NOUN
ma-310	151	56	−	−	PROPN
ma-310	151	57	z	z	NOUN
ma-310	151	58	+	+	NOUN
ma-310	151	59	ζ̄	ζ̄	X
ma-310	151	60	+	+	CCONJ
ma-310	151	61	ai	ai	VERB
ma-310	151	62	ζ̄	ζ̄	ADV
ma-310	151	63	−	−	PROPN
ma-310	151	64	z̄	z̄	NOUN
ma-310	151	65	−	−	ADP
ma-310	151	66	1	1	NUM
ma-310	151	67	]	]	PUNCT
ma-310	151	68	dζ	dζ	PROPN
ma-310	151	69	ζ	ζ	NOUN
ma-310	151	70	−	−	NOUN
ma-310	151	71	ai	ai	INTJ
ma-310	151	72	,	,	PUNCT
ma-310	151	73	where	where	SCONJ
ma-310	151	74	υ(ζ	υ(ζ	NOUN
ma-310	151	75	)	)	PUNCT
ma-310	152	1	=	=	PRON
ma-310	152	2	{	{	PUNCT
ma-310	152	3	γ(ζ	γ(ζ	PROPN
ma-310	152	4	)	)	PUNCT
ma-310	152	5	ζ	ζ	NOUN
ma-310	152	6	∈	∈	PROPN
ma-310	152	7	∂m	∂m	PROPN
ma-310	152	8	⋂	⋂	PROPN
ma-310	152	9	c1	c1	PROPN
ma-310	152	10	,	,	PUNCT
ma-310	152	11	0	0	NUM
ma-310	152	12	ζ	ζ	NOUN
ma-310	152	13	∈	∈	PROPN
ma-310	152	14	c1\(∂m).so	c1\(∂m).so	PROPN
ma-310	152	15	based	base	VERB
ma-310	152	16	on	on	ADP
ma-310	152	17	the	the	DET
ma-310	152	18	properties	property	NOUN
ma-310	152	19	of	of	ADP
ma-310	152	20	the	the	DET
ma-310	152	21	poisson	poisson	NOUN
ma-310	152	22	kernel	kernel	PROPN
ma-310	152	23	for	for	ADP
ma-310	152	24	c1	c1	PROPN
ma-310	152	25	,	,	PUNCT
ma-310	152	26	[	[	X
ma-310	152	27	6	6	NUM
ma-310	152	28	]	]	X
ma-310	152	29	lim	lim	PROPN
ma-310	152	30	z→ζ	z→ζ	NUM
ma-310	152	31	ω(z	ω(z	NUM
ma-310	152	32	)	)	PUNCT
ma-310	152	33	=	=	SYM
ma-310	152	34	γ(ζ	γ(ζ	PROPN
ma-310	152	35	)	)	PUNCT
ma-310	152	36	,	,	PUNCT
ma-310	152	37	https://doi.org/10.28924/ada/ma.5.10	https://doi.org/10.28924/ada/ma.5.10	PROPN
ma-310	152	38	eur	eur	PROPN
ma-310	152	39	.	.	PUNCT
ma-310	153	1	j.	j.	PROPN
ma-310	153	2	math	math	PROPN
ma-310	153	3	.	.	PUNCT
ma-310	154	1	anal	anal	PROPN
ma-310	154	2	.	.	PUNCT
ma-310	155	1	10.28924	10.28924	NUM
ma-310	155	2	/	/	SYM
ma-310	155	3	ada	ada	NOUN
ma-310	155	4	/	/	SYM
ma-310	155	5	ma.5.10	ma.5.10	NOUN
ma-310	155	6	8follows	8follow	VERB
ma-310	155	7	for	for	ADP
ma-310	155	8	ζ	ζ	PROPN
ma-310	155	9	∈	∈	PROPN
ma-310	155	10	∂m⋂c1	∂m⋂c1	PROPN
ma-310	155	11	up	up	ADP
ma-310	155	12	to	to	ADP
ma-310	155	13	the	the	DET
ma-310	155	14	corner	corner	NOUN
ma-310	155	15	points	point	VERB
ma-310	156	1	±a	±a	PROPN
ma-310	156	2	of	of	ADP
ma-310	156	3	the	the	DET
ma-310	156	4	domain	domain	NOUN
ma-310	156	5	m	m	NOUN
ma-310	156	6	,	,	PUNCT
ma-310	156	7	because	because	SCONJ
ma-310	156	8	υ	υ	PROPN
ma-310	156	9	fails	fail	VERB
ma-310	156	10	to	to	PART
ma-310	156	11	be	be	AUX
ma-310	156	12	con	con	NOUN
ma-310	156	13	-	-	PUNCT
ma-310	156	14	tinuous	tinuous	NOUN
ma-310	156	15	there	there	ADV
ma-310	156	16	if	if	SCONJ
ma-310	156	17	γ	γ	NOUN
ma-310	156	18	not	not	PART
ma-310	156	19	accidentally	accidentally	ADV
ma-310	156	20	vanishes	vanish	VERB
ma-310	156	21	at	at	ADP
ma-310	156	22	these	these	DET
ma-310	156	23	points.by	points.by	PROPN
ma-310	156	24	the	the	DET
ma-310	156	25	same	same	ADJ
ma-310	156	26	way	way	NOUN
ma-310	156	27	,	,	PUNCT
ma-310	156	28	for	for	ADP
ma-310	156	29	z	z	PROPN
ma-310	156	30	∈	∈	PROPN
ma-310	156	31	∂m⋂c2	∂m⋂c2	PROPN
ma-310	156	32	,	,	PUNCT
ma-310	156	33	case	case	NOUN
ma-310	156	34	1	1	NUM
ma-310	156	35	:	:	PUNCT
ma-310	156	36	ζ	ζ	NOUN
ma-310	156	37	∈c1	∈c1	NOUN
ma-310	156	38	,	,	PUNCT
ma-310	156	39	ζ̄	ζ̄	VERB
ma-310	156	40	+	+	CCONJ
ma-310	156	41	ai	ai	VERB
ma-310	156	42	ζ̄	ζ̄	ADV
ma-310	156	43	−	−	NOUN
ma-310	156	44	z̄	z̄	X
ma-310	156	45	=	=	SYM
ma-310	156	46	aiz	aiz	X
ma-310	156	47	−	−	PROPN
ma-310	156	48	a2	a2	PROPN
ma-310	156	49	ζz	ζz	ADP
ma-310	156	50	−	−	PROPN
ma-310	156	51	a2	a2	PROPN
ma-310	156	52	,	,	PUNCT
ma-310	156	53	z̄(ζ̄	z̄(ζ̄	PROPN
ma-310	156	54	+	+	CCONJ
ma-310	156	55	ai	ai	ADJ
ma-310	156	56	)	)	PUNCT
ma-310	156	57	ζ̄z̄	ζ̄z̄	NOUN
ma-310	156	58	−	−	PROPN
ma-310	156	59	a2	a2	PROPN
ma-310	156	60	=	=	PROPN
ma-310	156	61	−z	−z	PROPN
ma-310	157	1	+	+	CCONJ
ma-310	157	2	ai	ai	VERB
ma-310	157	3	ζ	ζ	NOUN
ma-310	157	4	−	−	PROPN
ma-310	157	5	z	z	NOUN
ma-310	157	6	.	.	PUNCT
ma-310	158	1	case	case	NOUN
ma-310	158	2	2	2	NUM
ma-310	158	3	:	:	PUNCT
ma-310	158	4	ζ	ζ	PROPN
ma-310	158	5	∈	∈	PROPN
ma-310	158	6	c2	c2	PROPN
ma-310	158	7	,	,	PUNCT
ma-310	158	8	z̄(ζ̄	z̄(ζ̄	AUX
ma-310	158	9	+	+	CCONJ
ma-310	158	10	a	a	X
ma-310	158	11	)	)	PUNCT
ma-310	158	12	ζ̄z̄	ζ̄z̄	NOUN
ma-310	158	13	−	−	PROPN
ma-310	158	14	a2	a2	PROPN
ma-310	158	15	=	=	PUNCT
ma-310	158	16	−aiz	−aiz	NOUN
ma-310	158	17	−	−	PROPN
ma-310	158	18	a2	a2	PROPN
ma-310	158	19	ζz	ζz	ADP
ma-310	158	20	−	−	PROPN
ma-310	158	21	a2	a2	PROPN
ma-310	158	22	.	.	PUNCT
ma-310	159	1	thus	thus	ADV
ma-310	159	2	,	,	PUNCT
ma-310	159	3	on	on	ADP
ma-310	159	4	∂m⋂c2	∂m⋂c2	PROPN
ma-310	159	5	,	,	PUNCT
ma-310	159	6	lim	lim	PROPN
ma-310	159	7	z→ζ	z→ζ	NUM
ma-310	159	8	ω(z	ω(z	NUM
ma-310	159	9	)	)	PUNCT
ma-310	159	10	=	=	SYM
ma-310	159	11	lim	lim	PROPN
ma-310	159	12	z→ζ	z→ζ	NUM
ma-310	159	13	1	1	NUM
ma-310	159	14	2πi	2πi	NOUN
ma-310	159	15	∫	∫	PROPN
ma-310	159	16	∂m	∂m	PROPN
ma-310	159	17	⋂	⋂	PROPN
ma-310	159	18	c2	c2	PROPN
ma-310	159	19	γ(ζ	γ(ζ	PROPN
ma-310	159	20	)	)	PUNCT
ma-310	159	21	[	[	PUNCT
ma-310	159	22	ζ	ζ	NOUN
ma-310	159	23	+	+	CCONJ
ma-310	159	24	ai	ai	VERB
ma-310	159	25	ζ	ζ	NOUN
ma-310	159	26	−	−	PROPN
ma-310	159	27	z	z	NOUN
ma-310	159	28	+	+	NOUN
ma-310	159	29	ζ̄	ζ̄	VERB
ma-310	159	30	−	−	NOUN
ma-310	159	31	ai	ai	VERB
ma-310	159	32	ζ̄	ζ̄	ADV
ma-310	159	33	−	−	PROPN
ma-310	159	34	z̄	z̄	NOUN
ma-310	159	35	−	−	ADP
ma-310	159	36	1	1	NUM
ma-310	159	37	]	]	PUNCT
ma-310	159	38	dζ	dζ	PROPN
ma-310	159	39	ζ	ζ	PROPN
ma-310	159	40	+	+	CCONJ
ma-310	159	41	ai	ai	PROPN
ma-310	159	42	=	=	PROPN
ma-310	159	43	lim	lim	PROPN
ma-310	159	44	z→ζ	z→ζ	NUM
ma-310	159	45	1	1	NUM
ma-310	159	46	2πi	2πi	ADJ
ma-310	159	47	∫	∫	PROPN
ma-310	159	48	c2	c2	PROPN
ma-310	159	49	υ(ζ	υ(ζ	PROPN
ma-310	159	50	)	)	PUNCT
ma-310	159	51	[	[	PUNCT
ma-310	159	52	ζ	ζ	NOUN
ma-310	159	53	+	+	CCONJ
ma-310	159	54	ai	ai	VERB
ma-310	159	55	ζ	ζ	NOUN
ma-310	159	56	−	−	PROPN
ma-310	159	57	z	z	NOUN
ma-310	159	58	+	+	NOUN
ma-310	159	59	ζ̄	ζ̄	VERB
ma-310	159	60	−	−	NOUN
ma-310	159	61	ai	ai	VERB
ma-310	159	62	ζ̄	ζ̄	ADV
ma-310	159	63	−	−	PROPN
ma-310	159	64	z̄	z̄	NOUN
ma-310	159	65	−	−	ADP
ma-310	159	66	1	1	NUM
ma-310	159	67	]	]	PUNCT
ma-310	159	68	dζ	dζ	PROPN
ma-310	159	69	ζ	ζ	PROPN
ma-310	159	70	+	+	X
ma-310	159	71	ai	ai	INTJ
ma-310	159	72	,	,	PUNCT
ma-310	159	73	where	where	SCONJ
ma-310	159	74	υ(ζ	υ(ζ	NOUN
ma-310	159	75	)	)	PUNCT
ma-310	159	76	=	=	PRON
ma-310	159	77	{	{	PUNCT
ma-310	159	78	γ(ζ	γ(ζ	PROPN
ma-310	159	79	)	)	PUNCT
ma-310	159	80	ζ	ζ	NOUN
ma-310	159	81	∈	∈	PROPN
ma-310	159	82	∂m	∂m	PROPN
ma-310	159	83	⋂	⋂	PROPN
ma-310	159	84	c2	c2	PROPN
ma-310	159	85	,	,	PUNCT
ma-310	159	86	0	0	NUM
ma-310	159	87	ζ	ζ	PROPN
ma-310	159	88	∈	∈	NOUN
ma-310	159	89	c2\(∂m).so	c2\(∂m).so	PROPN
ma-310	159	90	based	base	VERB
ma-310	159	91	on	on	ADP
ma-310	159	92	the	the	DET
ma-310	159	93	properties	property	NOUN
ma-310	159	94	of	of	ADP
ma-310	159	95	the	the	DET
ma-310	159	96	poisson	poisson	NOUN
ma-310	159	97	kernel	kernel	PROPN
ma-310	159	98	for	for	ADP
ma-310	159	99	c2	c2	PROPN
ma-310	159	100	,	,	PUNCT
ma-310	159	101	lim	lim	PROPN
ma-310	159	102	z→ζ	z→ζ	NUM
ma-310	159	103	ω(z	ω(z	NUM
ma-310	159	104	)	)	PUNCT
ma-310	159	105	=	=	SYM
ma-310	159	106	γ(ζ	γ(ζ	PROPN
ma-310	159	107	)	)	PUNCT
ma-310	159	108	,	,	PUNCT
ma-310	159	109	follows	follow	VERB
ma-310	159	110	for	for	ADP
ma-310	159	111	ζ	ζ	NOUN
ma-310	159	112	∈	∈	PROPN
ma-310	159	113	∂m⋂c2	∂m⋂c2	PROPN
ma-310	159	114	up	up	ADP
ma-310	159	115	to	to	ADP
ma-310	159	116	the	the	DET
ma-310	159	117	corner	corner	NOUN
ma-310	159	118	points	point	VERB
ma-310	159	119	±a	±a	PROPN
ma-310	159	120	of	of	ADP
ma-310	159	121	the	the	DET
ma-310	159	122	domain	domain	NOUN
ma-310	159	123	m	m	NOUN
ma-310	159	124	,	,	PUNCT
ma-310	159	125	because	because	SCONJ
ma-310	159	126	υ	υ	PROPN
ma-310	159	127	fails	fail	VERB
ma-310	159	128	to	to	PART
ma-310	159	129	be	be	AUX
ma-310	159	130	con	con	NOUN
ma-310	159	131	-	-	PUNCT
ma-310	159	132	tinuous	tinuous	NOUN
ma-310	159	133	there	there	ADV
ma-310	159	134	if	if	SCONJ
ma-310	159	135	γ	γ	NOUN
ma-310	159	136	not	not	PART
ma-310	159	137	accidentally	accidentally	ADV
ma-310	159	138	vanishes	vanish	VERB
ma-310	159	139	at	at	ADP
ma-310	159	140	these	these	DET
ma-310	159	141	points	point	NOUN
ma-310	159	142	.	.	PUNCT
ma-310	160	1	now	now	ADV
ma-310	160	2	,	,	PUNCT
ma-310	160	3	we	we	PRON
ma-310	160	4	consider	consider	VERB
ma-310	160	5	the	the	DET
ma-310	160	6	boundary	boundary	ADJ
ma-310	160	7	behaviors	behavior	NOUN
ma-310	160	8	at	at	ADP
ma-310	160	9	the	the	DET
ma-310	160	10	tips	tip	NOUN
ma-310	160	11	±a	±a	PROPN
ma-310	160	12	.	.	PUNCT
ma-310	161	1	we	we	PRON
ma-310	161	2	represent	represent	VERB
ma-310	161	3	the	the	DET
ma-310	161	4	constant	constant	ADJ
ma-310	161	5	function1	function1	NOUN
ma-310	161	6	as	as	SCONJ
ma-310	161	7	1	1	NUM
ma-310	161	8	=	=	SYM
ma-310	161	9	1	1	NUM
ma-310	161	10	2πi	2πi	NOUN
ma-310	161	11	∫	∫	PROPN
ma-310	161	12	∂m	∂m	PROPN
ma-310	161	13	⋂	⋂	PROPN
ma-310	161	14	c1	c1	PROPN
ma-310	161	15	[	[	PUNCT
ma-310	161	16	ζ	ζ	NOUN
ma-310	161	17	−	−	PROPN
ma-310	161	18	ai	ai	VERB
ma-310	161	19	ζ	ζ	NOUN
ma-310	161	20	−	−	PROPN
ma-310	161	21	z	z	NOUN
ma-310	161	22	+	+	NOUN
ma-310	161	23	ζ̄	ζ̄	X
ma-310	161	24	+	+	CCONJ
ma-310	161	25	ai	ai	VERB
ma-310	161	26	ζ̄	ζ̄	ADV
ma-310	161	27	−	−	PROPN
ma-310	161	28	z̄	z̄	NOUN
ma-310	161	29	−	−	ADP
ma-310	161	30	1	1	NUM
ma-310	161	31	+	+	NUM
ma-310	161	32	z(ζ	z(ζ	NOUN
ma-310	161	33	−	−	NOUN
ma-310	161	34	ai	ai	NOUN
ma-310	161	35	)	)	PUNCT
ma-310	161	36	ζz	ζz	ADP
ma-310	161	37	−	−	PROPN
ma-310	161	38	a2	a2	PROPN
ma-310	161	39	+	+	CCONJ
ma-310	161	40	z̄(ζ̄	z̄(ζ̄	PROPN
ma-310	161	41	+	+	CCONJ
ma-310	161	42	ai	ai	ADJ
ma-310	161	43	)	)	PUNCT
ma-310	161	44	ζ̄z̄	ζ̄z̄	NOUN
ma-310	161	45	−	−	PROPN
ma-310	161	46	a2	a2	PROPN
ma-310	161	47	−	−	PROPN
ma-310	161	48	1	1	NUM
ma-310	161	49	]	]	PUNCT
ma-310	161	50	dζ	dζ	PROPN
ma-310	161	51	ζ	ζ	NOUN
ma-310	161	52	−	−	NOUN
ma-310	161	53	ai	ai	NOUN
ma-310	161	54	+	+	PROPN
ma-310	161	55	1	1	NUM
ma-310	161	56	2πi	2πi	NOUN
ma-310	161	57	∫	∫	PROPN
ma-310	161	58	∂m	∂m	PROPN
ma-310	161	59	⋂	⋂	PROPN
ma-310	161	60	c2	c2	PROPN
ma-310	161	61	[	[	PUNCT
ma-310	161	62	ζ	ζ	PROPN
ma-310	161	63	+	+	CCONJ
ma-310	161	64	ai	ai	VERB
ma-310	161	65	ζ	ζ	NOUN
ma-310	161	66	−	−	PROPN
ma-310	161	67	z	z	NOUN
ma-310	161	68	+	+	NOUN
ma-310	161	69	ζ̄	ζ̄	VERB
ma-310	161	70	−	−	NOUN
ma-310	161	71	ai	ai	VERB
ma-310	161	72	ζ̄	ζ̄	ADV
ma-310	161	73	−	−	PROPN
ma-310	161	74	z̄	z̄	NOUN
ma-310	161	75	−	−	ADP
ma-310	161	76	1	1	NUM
ma-310	161	77	+	+	NUM
ma-310	161	78	z(ζ	z(ζ	NOUN
ma-310	161	79	+	+	CCONJ
ma-310	161	80	ai	ai	NOUN
ma-310	161	81	)	)	PUNCT
ma-310	161	82	ζz	ζz	ADP
ma-310	161	83	−	−	PROPN
ma-310	161	84	a2	a2	PROPN
ma-310	161	85	+	+	CCONJ
ma-310	161	86	z̄(ζ̄	z̄(ζ̄	PROPN
ma-310	161	87	−	−	NOUN
ma-310	161	88	ai	ai	NOUN
ma-310	161	89	)	)	PUNCT
ma-310	161	90	ζ̄z̄	ζ̄z̄	NOUN
ma-310	161	91	−	−	PROPN
ma-310	161	92	a2	a2	PROPN
ma-310	161	93	−	−	PROPN
ma-310	161	94	1	1	NUM
ma-310	161	95	]	]	PUNCT
ma-310	161	96	dζ	dζ	PROPN
ma-310	161	97	ζ	ζ	PROPN
ma-310	161	98	+	+	X
ma-310	161	99	ai	ai	VERB
ma-310	161	100	.	.	PUNCT
ma-310	162	1	multiplying	multiply	VERB
ma-310	162	2	this	this	DET
ma-310	162	3	relation	relation	NOUN
ma-310	162	4	with	with	ADP
ma-310	162	5	γ(±a	γ(±a	NOUN
ma-310	162	6	)	)	PUNCT
ma-310	162	7	and	and	CCONJ
ma-310	162	8	subtracting	subtract	VERB
ma-310	162	9	the	the	DET
ma-310	162	10	resulting	result	VERB
ma-310	162	11	equation	equation	NOUN
ma-310	162	12	from	from	ADP
ma-310	162	13	ω(z	ω(z	PROPN
ma-310	162	14	)	)	PUNCT
ma-310	162	15	shows	show	VERB
ma-310	162	16	for	for	ADP
ma-310	162	17	z	z	PROPN
ma-310	162	18	∈	∈	PROPN
ma-310	162	19	∂m	∂m	PROPN
ma-310	162	20	⋂	⋂	PROPN
ma-310	162	21	c1	c1	PROPN
ma-310	162	22	,	,	PUNCT
ma-310	162	23	lim	lim	PROPN
ma-310	162	24	z→ζ	z→ζ	NUM
ma-310	162	25	(	(	PUNCT
ma-310	162	26	ω(z)−	ω(z)−	PROPN
ma-310	162	27	γ(±a	γ(±a	ADJ
ma-310	162	28	)	)	PUNCT
ma-310	162	29	)	)	PUNCT
ma-310	163	1	=	=	SYM
ma-310	163	2	lim	lim	PROPN
ma-310	163	3	z→ζ	z→ζ	NUM
ma-310	163	4	1	1	NUM
ma-310	163	5	2πi	2πi	NOUN
ma-310	163	6	∫	∫	PROPN
ma-310	163	7	∂m	∂m	PROPN
ma-310	163	8	⋂	⋂	PROPN
ma-310	163	9	c1	c1	PROPN
ma-310	163	10	γ̃(ζ	γ̃(ζ	PROPN
ma-310	163	11	)	)	PUNCT
ma-310	163	12	[	[	PUNCT
ma-310	163	13	ζ	ζ	NOUN
ma-310	163	14	−	−	NOUN
ma-310	163	15	ai	ai	VERB
ma-310	163	16	ζ	ζ	NOUN
ma-310	163	17	−	−	PROPN
ma-310	163	18	z	z	NOUN
ma-310	163	19	+	+	NOUN
ma-310	163	20	ζ̄	ζ̄	X
ma-310	163	21	+	+	CCONJ
ma-310	163	22	ai	ai	VERB
ma-310	163	23	ζ̄	ζ̄	ADV
ma-310	163	24	−	−	PROPN
ma-310	163	25	z̄	z̄	NOUN
ma-310	163	26	−	−	ADP
ma-310	163	27	1	1	NUM
ma-310	163	28	]	]	PUNCT
ma-310	163	29	dζ	dζ	PROPN
ma-310	163	30	ζ	ζ	NOUN
ma-310	163	31	−	−	PROPN
ma-310	163	32	ai	ai	VERB
ma-310	163	33	,	,	PUNCT
ma-310	163	34	https://doi.org/10.28924/ada/ma.5.10	https://doi.org/10.28924/ada/ma.5.10	PROPN
ma-310	163	35	eur	eur	PROPN
ma-310	163	36	.	.	PUNCT
ma-310	164	1	j.	j.	PROPN
ma-310	164	2	math	math	PROPN
ma-310	164	3	.	.	PUNCT
ma-310	165	1	anal	anal	PROPN
ma-310	165	2	.	.	PUNCT
ma-310	166	1	10.28924	10.28924	NUM
ma-310	166	2	/	/	SYM
ma-310	166	3	ada	ada	PROPN
ma-310	166	4	/	/	SYM
ma-310	166	5	ma.5.10	ma.5.10	NOUN
ma-310	166	6	9	9	NUM
ma-310	166	7	where	where	SCONJ
ma-310	166	8	γ̃(ζ	γ̃(ζ	NOUN
ma-310	166	9	)	)	PUNCT
ma-310	167	1	=	=	SYM
ma-310	167	2	γ(ζ)−	γ(ζ)−	NOUN
ma-310	167	3	γ(±a	γ(±a	ADV
ma-310	167	4	)	)	PUNCT
ma-310	167	5	and	and	CCONJ
ma-310	167	6	γ̃(±a	γ̃(±a	ADJ
ma-310	167	7	)	)	PUNCT
ma-310	167	8	=	=	SYM
ma-310	167	9	0	0	PROPN
ma-310	167	10	,	,	PUNCT
ma-310	167	11	lim	lim	PROPN
ma-310	167	12	z→±a	z→±a	PROPN
ma-310	167	13	ω(z	ω(z	PROPN
ma-310	167	14	)	)	PUNCT
ma-310	167	15	=	=	PUNCT
ma-310	167	16	γ(±a	γ(±a	NOUN
ma-310	167	17	)	)	PUNCT
ma-310	167	18	.	.	PUNCT
ma-310	168	1	similarly	similarly	ADV
ma-310	168	2	,	,	PUNCT
ma-310	168	3	for	for	ADP
ma-310	168	4	z	z	PROPN
ma-310	168	5	∈	∈	PROPN
ma-310	168	6	∂m⋂c2	∂m⋂c2	PROPN
ma-310	168	7	,	,	PUNCT
ma-310	168	8	lim	lim	PROPN
ma-310	168	9	z→ζ	z→ζ	NUM
ma-310	168	10	(	(	PUNCT
ma-310	168	11	ω(z)−	ω(z)−	PROPN
ma-310	168	12	γ(±a	γ(±a	ADJ
ma-310	168	13	)	)	PUNCT
ma-310	168	14	)	)	PUNCT
ma-310	169	1	=	=	SYM
ma-310	169	2	lim	lim	PROPN
ma-310	169	3	z→ζ	z→ζ	NUM
ma-310	169	4	1	1	NUM
ma-310	169	5	2πi	2πi	NOUN
ma-310	169	6	∫	∫	PROPN
ma-310	170	1	∂m	∂m	PROPN
ma-310	170	2	⋂	⋂	PROPN
ma-310	170	3	c2	c2	PROPN
ma-310	170	4	γ̂(ζ	γ̂(ζ	PRON
ma-310	170	5	)	)	PUNCT
ma-310	170	6	[	[	PUNCT
ma-310	170	7	ζ	ζ	NOUN
ma-310	170	8	+	+	CCONJ
ma-310	170	9	ai	ai	VERB
ma-310	170	10	ζ	ζ	NOUN
ma-310	170	11	−	−	PROPN
ma-310	170	12	z	z	NOUN
ma-310	170	13	+	+	NOUN
ma-310	170	14	ζ̄	ζ̄	VERB
ma-310	170	15	−	−	NOUN
ma-310	170	16	ai	ai	VERB
ma-310	170	17	ζ̄	ζ̄	ADV
ma-310	170	18	−	−	PROPN
ma-310	170	19	z̄	z̄	NOUN
ma-310	170	20	−	−	ADP
ma-310	170	21	1	1	NUM
ma-310	170	22	]	]	PUNCT
ma-310	170	23	dζ	dζ	PROPN
ma-310	170	24	ζ	ζ	PROPN
ma-310	170	25	+	+	X
ma-310	170	26	ai	ai	INTJ
ma-310	170	27	,	,	PUNCT
ma-310	170	28	where	where	SCONJ
ma-310	170	29	γ̂(ζ	γ̂(ζ	NOUN
ma-310	170	30	)	)	PUNCT
ma-310	170	31	=	=	SYM
ma-310	170	32	γ(ζ)−	γ(ζ)−	NOUN
ma-310	170	33	γ(±a	γ(±a	ADJ
ma-310	170	34	)	)	PUNCT
ma-310	170	35	and	and	CCONJ
ma-310	170	36	γ̂(±a	γ̂(±a	NOUN
ma-310	170	37	)	)	PUNCT
ma-310	170	38	=	=	SYM
ma-310	170	39	0,therefore	0,therefore	NOUN
ma-310	170	40	,	,	PUNCT
ma-310	170	41	lim	lim	PROPN
ma-310	170	42	z→±a	z→±a	PROPN
ma-310	170	43	ω(z	ω(z	PROPN
ma-310	170	44	)	)	PUNCT
ma-310	170	45	=	=	PUNCT
ma-310	170	46	γ(±a	γ(±a	NOUN
ma-310	170	47	)	)	PUNCT
ma-310	170	48	.	.	PUNCT
ma-310	171	1	therefore	therefore	ADV
ma-310	171	2	,	,	PUNCT
ma-310	171	3	the	the	DET
ma-310	171	4	proof	proof	NOUN
ma-310	171	5	is	be	AUX
ma-310	171	6	finished	finish	VERB
ma-310	171	7	.	.	PUNCT
ma-310	172	1	�	�	PROPN
ma-310	172	2	references	reference	NOUN
ma-310	172	3	[	[	X
ma-310	172	4	1	1	NUM
ma-310	172	5	]	]	PUNCT
ma-310	172	6	a.	a.	NOUN
ma-310	172	7	darya	darya	PROPN
ma-310	172	8	,	,	PUNCT
ma-310	172	9	n.	n.	PROPN
ma-310	172	10	taghizadeh	taghizadeh	PROPN
ma-310	172	11	,	,	PUNCT
ma-310	172	12	schwarz	schwarz	NOUN
ma-310	172	13	and	and	CCONJ
ma-310	172	14	dirichlet	dirichlet	PROPN
ma-310	172	15	problems	problem	NOUN
ma-310	172	16	for	for	ADP
ma-310	172	17	complex	complex	ADJ
ma-310	172	18	partial	partial	ADJ
ma-310	172	19	differential	differential	NOUN
ma-310	172	20	equations	equation	NOUN
ma-310	172	21	in	in	ADP
ma-310	172	22	the	the	DET
ma-310	172	23	partialeclipse	partialeclipse	NOUN
ma-310	172	24	domain	domain	NOUN
ma-310	172	25	,	,	PUNCT
ma-310	172	26	j.	j.	PROPN
ma-310	172	27	math	math	PROPN
ma-310	172	28	.	.	PUNCT
ma-310	173	1	sci	sci	PROPN
ma-310	173	2	.	.	PUNCT
ma-310	174	1	(	(	PUNCT
ma-310	174	2	2024	2024	NUM
ma-310	174	3	)	)	PUNCT
ma-310	174	4	.	.	PUNCT
ma-310	175	1	https://doi.org/10.1007/s10958-024-07337-0.[2	https://doi.org/10.1007/s10958-024-07337-0.[2	PROPN
ma-310	175	2	]	]	X
ma-310	175	3	a.	a.	NOUN
ma-310	175	4	darya	darya	PROPN
ma-310	175	5	,	,	PUNCT
ma-310	175	6	n.	n.	PROPN
ma-310	175	7	taghizadeh	taghizadeh	PROPN
ma-310	175	8	,	,	PUNCT
ma-310	175	9	three	three	NUM
ma-310	175	10	boundary	boundary	ADJ
ma-310	175	11	value	value	NOUN
ma-310	175	12	problems	problem	NOUN
ma-310	175	13	for	for	ADP
ma-310	175	14	complex	complex	ADJ
ma-310	175	15	partial	partial	ADJ
ma-310	175	16	differential	differential	NOUN
ma-310	175	17	equations	equation	NOUN
ma-310	175	18	in	in	ADP
ma-310	175	19	the	the	DET
ma-310	175	20	lensdomain	lensdomain	NOUN
ma-310	175	21	,	,	PUNCT
ma-310	175	22	comput	comput	NOUN
ma-310	175	23	.	.	PUNCT
ma-310	176	1	math	math	NOUN
ma-310	176	2	.	.	PUNCT
ma-310	177	1	math	math	NOUN
ma-310	177	2	.	.	PUNCT
ma-310	178	1	phys	phy	NOUN
ma-310	178	2	.	.	PUNCT
ma-310	179	1	64	64	NUM
ma-310	179	2	(	(	PUNCT
ma-310	179	3	2024	2024	NUM
ma-310	179	4	)	)	PUNCT
ma-310	179	5	,	,	PUNCT
ma-310	179	6	1295–1305	1295–1305	NUM
ma-310	179	7	.	.	PUNCT
ma-310	180	1	https://doi.org/10.1134/s0965542524700520.[3	https://doi.org/10.1134/s0965542524700520.[3	PROPN
ma-310	180	2	]	]	PUNCT
ma-310	180	3	a.	a.	NOUN
ma-310	180	4	darya	darya	PROPN
ma-310	180	5	,	,	PUNCT
ma-310	180	6	n.	n.	PROPN
ma-310	180	7	tagizadeh	tagizadeh	PROPN
ma-310	180	8	,	,	PUNCT
ma-310	180	9	on	on	ADP
ma-310	180	10	the	the	DET
ma-310	180	11	dirichlet	dirichlet	PROPN
ma-310	180	12	boundary	boundary	PROPN
ma-310	180	13	value	value	NOUN
ma-310	180	14	problem	problem	NOUN
ma-310	180	15	for	for	ADP
ma-310	180	16	the	the	DET
ma-310	180	17	cauchy	cauchy	PROPN
ma-310	180	18	-	-	PUNCT
ma-310	180	19	riemann	riemann	PROPN
ma-310	180	20	equations	equation	NOUN
ma-310	180	21	in	in	ADP
ma-310	180	22	the	the	DET
ma-310	180	23	halfdisc	halfdisc	NOUN
ma-310	180	24	,	,	PUNCT
ma-310	180	25	eur	eur	PROPN
ma-310	180	26	.	.	PUNCT
ma-310	181	1	j.	j.	PROPN
ma-310	181	2	math	math	PROPN
ma-310	181	3	.	.	PUNCT
ma-310	182	1	anal	anal	ADJ
ma-310	182	2	.	.	PUNCT
ma-310	183	1	4	4	NUM
ma-310	183	2	(	(	PUNCT
ma-310	183	3	2024	2024	NUM
ma-310	183	4	)	)	PUNCT
ma-310	183	5	,	,	PUNCT
ma-310	183	6	15	15	NUM
ma-310	183	7	.	.	PUNCT
ma-310	184	1	https://doi.org/10.28924/ada/ma.4.15.[4	https://doi.org/10.28924/ada/ma.4.15.[4	PUNCT
ma-310	184	2	]	]	X
ma-310	184	3	a.	a.	NOUN
ma-310	184	4	darya	darya	PROPN
ma-310	184	5	,	,	PUNCT
ma-310	184	6	n.	n.	PROPN
ma-310	184	7	taghizadeh	taghizadeh	PROPN
ma-310	184	8	,	,	PUNCT
ma-310	184	9	schwarz	schwarz	NOUN
ma-310	184	10	and	and	CCONJ
ma-310	184	11	dirichlet	dirichlet	PROPN
ma-310	184	12	problems	problem	NOUN
ma-310	184	13	for	for	ADP
ma-310	184	14	∂̄-equation	∂̄-equation	NOUN
ma-310	184	15	in	in	ADP
ma-310	184	16	a	a	DET
ma-310	184	17	triangular	triangular	NOUN
ma-310	184	18	domain	domain	NOUN
ma-310	184	19	,	,	PUNCT
ma-310	184	20	russ	russ	PROPN
ma-310	184	21	.	.	PROPN
ma-310	184	22	math	math	PROPN
ma-310	184	23	.	.	PUNCT
ma-310	185	1	68(2024	68(2024	NUM
ma-310	185	2	)	)	PUNCT
ma-310	185	3	,	,	PUNCT
ma-310	185	4	9–17	9–17	PROPN
ma-310	185	5	.	.	PUNCT
ma-310	186	1	https://doi.org/10.3103/s1066369x24700853.[5	https://doi.org/10.3103/s1066369x24700853.[5	PRON
ma-310	186	2	]	]	X
ma-310	186	3	a.	a.	NOUN
ma-310	186	4	darya	darya	PROPN
ma-310	186	5	,	,	PUNCT
ma-310	186	6	n.	n.	NOUN
ma-310	186	7	taghizadeh	taghizadeh	PROPN
ma-310	186	8	,	,	PUNCT
ma-310	186	9	on	on	ADP
ma-310	186	10	a	a	DET
ma-310	186	11	boundary	boundary	ADJ
ma-310	186	12	-	-	PUNCT
ma-310	186	13	value	value	NOUN
ma-310	186	14	problem	problem	NOUN
ma-310	186	15	for	for	ADP
ma-310	186	16	the	the	DET
ma-310	186	17	poisson	poisson	NOUN
ma-310	186	18	equation	equation	NOUN
ma-310	186	19	and	and	CCONJ
ma-310	186	20	the	the	DET
ma-310	186	21	cauchy	cauchy	PROPN
ma-310	186	22	-	-	PUNCT
ma-310	186	23	riemann	riemann	PROPN
ma-310	186	24	equa	equa	NOUN
ma-310	186	25	-	-	PUNCT
ma-310	186	26	tion	tion	NOUN
ma-310	186	27	in	in	ADP
ma-310	186	28	a	a	DET
ma-310	186	29	lens	len	NOUN
ma-310	186	30	,	,	PUNCT
ma-310	186	31	iss	iss	PROPN
ma-310	186	32	.	.	PROPN
ma-310	186	33	anal	anal	PROPN
ma-310	186	34	.	.	PUNCT
ma-310	187	1	32	32	NUM
ma-310	187	2	(	(	PUNCT
ma-310	187	3	2025	2025	NUM
ma-310	187	4	)	)	PUNCT
ma-310	187	5	,	,	PUNCT
ma-310	187	6	77–87	77–87	NUM
ma-310	187	7	.	.	PUNCT
ma-310	188	1	https://doi.org/10.15393/j3.art.2025.16810.[6	https://doi.org/10.15393/j3.art.2025.16810.[6	PROPN
ma-310	188	2	]	]	PUNCT
ma-310	188	3	h.	h.	PROPN
ma-310	188	4	begehr	begehr	PROPN
ma-310	188	5	,	,	PUNCT
ma-310	188	6	boundary	boundary	ADJ
ma-310	188	7	value	value	NOUN
ma-310	188	8	problems	problem	NOUN
ma-310	188	9	in	in	ADP
ma-310	188	10	complex	complex	ADJ
ma-310	188	11	analysis	analysis	NOUN
ma-310	188	12	i	i	PRON
ma-310	188	13	,	,	PUNCT
ma-310	188	14	bol	bol	NOUN
ma-310	188	15	.	.	PUNCT
ma-310	189	1	aosc	aosc	PROPN
ma-310	189	2	.	.	PUNCT
ma-310	190	1	math	math	NOUN
ma-310	190	2	.	.	PUNCT
ma-310	191	1	venezolana	venezolana	PROPN
ma-310	191	2	,	,	PUNCT
ma-310	191	3	12	12	NUM
ma-310	191	4	(	(	PUNCT
ma-310	191	5	2005	2005	NUM
ma-310	191	6	)	)	PUNCT
ma-310	191	7	,	,	PUNCT
ma-310	191	8	65	65	NUM
ma-310	191	9	-	-	SYM
ma-310	191	10	85.[7	85.[7	NUM
ma-310	191	11	]	]	X
ma-310	191	12	h.	h.	PROPN
ma-310	191	13	begehr	begehr	PROPN
ma-310	191	14	,	,	PUNCT
ma-310	191	15	t.	t.	PROPN
ma-310	191	16	vaitekhovich	vaitekhovich	PROPN
ma-310	191	17	,	,	PUNCT
ma-310	191	18	harmonic	harmonic	ADJ
ma-310	191	19	boundary	boundary	ADJ
ma-310	191	20	value	value	NOUN
ma-310	191	21	problems	problem	NOUN
ma-310	191	22	in	in	ADP
ma-310	191	23	half	half	ADJ
ma-310	191	24	disc	disc	NOUN
ma-310	191	25	and	and	CCONJ
ma-310	191	26	half	half	NOUN
ma-310	191	27	ring	ring	NOUN
ma-310	191	28	,	,	PUNCT
ma-310	191	29	funct	funct	NOUN
ma-310	191	30	.	.	PUNCT
ma-310	192	1	approx	approx	PROPN
ma-310	192	2	.	.	PUNCT
ma-310	193	1	comment.math	comment.math	NOUN
ma-310	193	2	.	.	PROPN
ma-310	194	1	40	40	NUM
ma-310	194	2	(	(	PUNCT
ma-310	194	3	2009	2009	NUM
ma-310	194	4	)	)	PUNCT
ma-310	194	5	,	,	PUNCT
ma-310	194	6	251–282	251–282	NUM
ma-310	194	7	.	.	PUNCT
ma-310	195	1	https://doi.org/10.7169/facm/1246454030.[8	https://doi.org/10.7169/facm/1246454030.[8	PROPN
ma-310	195	2	]	]	PUNCT
ma-310	195	3	h.	h.	PROPN
ma-310	195	4	begehr	begehr	PROPN
ma-310	195	5	,	,	PUNCT
ma-310	195	6	t.	t.	PROPN
ma-310	195	7	vaitekhovich	vaitekhovich	PROPN
ma-310	195	8	,	,	PUNCT
ma-310	195	9	the	the	DET
ma-310	195	10	parqueting	parqueting	ADJ
ma-310	195	11	–	–	PUNCT
ma-310	195	12	reflection	reflection	NOUN
ma-310	195	13	principle	principle	NOUN
ma-310	195	14	for	for	ADP
ma-310	195	15	constructing	construct	VERB
ma-310	195	16	green	green	ADJ
ma-310	195	17	function	function	NOUN
ma-310	195	18	,	,	PUNCT
ma-310	195	19	in	in	ADP
ma-310	195	20	:	:	PUNCT
ma-310	195	21	conference	conference	NOUN
ma-310	195	22	:	:	PUNCT
ma-310	195	23	analytic	analytic	ADJ
ma-310	195	24	methods	method	NOUN
ma-310	195	25	of	of	ADP
ma-310	195	26	analysis	analysis	NOUN
ma-310	195	27	and	and	CCONJ
ma-310	195	28	differential	differential	ADJ
ma-310	195	29	equations	equation	NOUN
ma-310	195	30	,	,	PUNCT
ma-310	195	31	2012.[9	2012.[9	NUM
ma-310	195	32	]	]	X
ma-310	195	33	y.	y.	PROPN
ma-310	195	34	wang	wang	PROPN
ma-310	195	35	,	,	PUNCT
ma-310	195	36	boundary	boundary	ADJ
ma-310	195	37	value	value	NOUN
ma-310	195	38	problems	problem	NOUN
ma-310	195	39	for	for	ADP
ma-310	195	40	complex	complex	ADJ
ma-310	195	41	partial	partial	ADJ
ma-310	195	42	differential	differential	NOUN
ma-310	195	43	equations	equation	NOUN
ma-310	195	44	in	in	ADP
ma-310	195	45	the	the	DET
ma-310	195	46	fan	fan	NOUN
ma-310	195	47	–	–	PUNCT
ma-310	195	48	shaped	shaped	ADJ
ma-310	195	49	domain	domain	NOUN
ma-310	195	50	,	,	PUNCT
ma-310	195	51	ph.d.thesis	ph.d.thesis	NOUN
ma-310	195	52	,	,	PUNCT
ma-310	195	53	fu	fu	PROPN
ma-310	195	54	berlin	berlin	PROPN
ma-310	195	55	,	,	PUNCT
ma-310	195	56	2011.[10	2011.[10	NUM
ma-310	195	57	]	]	PUNCT
ma-310	195	58	h.	h.	PROPN
ma-310	195	59	begehr	begehr	PROPN
ma-310	195	60	,	,	PUNCT
ma-310	195	61	t.	t.	PROPN
ma-310	195	62	vaitekhovich	vaitekhovich	PROPN
ma-310	195	63	,	,	PUNCT
ma-310	195	64	schwarz	schwarz	PROPN
ma-310	195	65	problem	problem	NOUN
ma-310	195	66	in	in	ADP
ma-310	195	67	lens	lens	NOUN
ma-310	195	68	and	and	CCONJ
ma-310	195	69	lune	lune	PROPN
ma-310	195	70	,	,	PUNCT
ma-310	195	71	complex	complex	ADJ
ma-310	195	72	var	var	NOUN
ma-310	195	73	.	.	PUNCT
ma-310	196	1	elliptic	elliptic	PROPN
ma-310	196	2	equ	equ	PROPN
ma-310	196	3	.	.	PROPN
ma-310	196	4	59	59	NUM
ma-310	196	5	(	(	PUNCT
ma-310	196	6	2014	2014	NUM
ma-310	196	7	)	)	PUNCT
ma-310	196	8	,	,	PUNCT
ma-310	196	9	76–84	76–84	NOUN
ma-310	196	10	.	.	PUNCT
ma-310	197	1	https://doi.org/10.1080/17476933.2013.799152.[11	https://doi.org/10.1080/17476933.2013.799152.[11	PROPN
ma-310	197	2	]	]	PUNCT
ma-310	197	3	i̇.	i̇.	PROPN
ma-310	197	4	gençtürk	gençtürk	PROPN
ma-310	197	5	,	,	PUNCT
ma-310	197	6	k.	k.	PROPN
ma-310	197	7	koca	koca	PROPN
ma-310	197	8	,	,	PUNCT
ma-310	197	9	neumann	neumann	PROPN
ma-310	197	10	boundary	boundary	PROPN
ma-310	197	11	value	value	NOUN
ma-310	197	12	problem	problem	NOUN
ma-310	197	13	for	for	ADP
ma-310	197	14	bitsadze	bitsadze	NOUN
ma-310	197	15	equation	equation	NOUN
ma-310	197	16	in	in	ADP
ma-310	197	17	a	a	DET
ma-310	197	18	ring	ring	NOUN
ma-310	197	19	domain	domain	NOUN
ma-310	197	20	,	,	PUNCT
ma-310	197	21	j.	j.	PROPN
ma-310	197	22	anal	anal	PROPN
ma-310	197	23	.	.	PUNCT
ma-310	198	1	28	28	NUM
ma-310	199	1	(	(	PUNCT
ma-310	199	2	2020),799–815	2020),799–815	NOUN
ma-310	199	3	.	.	PUNCT
ma-310	199	4	https://doi.org/10.1007/s41478-019-00202-3.[12	https://doi.org/10.1007/s41478-019-00202-3.[12	X
ma-310	199	5	]	]	X
ma-310	199	6	p.n	p.n	PROPN
ma-310	199	7	.	.	PROPN
ma-310	199	8	ivanshin	ivanshin	PROPN
ma-310	199	9	,	,	PUNCT
ma-310	199	10	e.a	e.a	PROPN
ma-310	199	11	.	.	PROPN
ma-310	199	12	shirokova	shirokova	PROPN
ma-310	199	13	,	,	PUNCT
ma-310	199	14	the	the	DET
ma-310	199	15	solution	solution	NOUN
ma-310	199	16	of	of	ADP
ma-310	199	17	a	a	DET
ma-310	199	18	mixed	mixed	ADJ
ma-310	199	19	boundary	boundary	ADJ
ma-310	199	20	value	value	NOUN
ma-310	199	21	problem	problem	NOUN
ma-310	199	22	for	for	ADP
ma-310	199	23	the	the	DET
ma-310	199	24	laplace	laplace	NOUN
ma-310	199	25	equation	equation	NOUN
ma-310	199	26	in	in	ADP
ma-310	199	27	amultiply	amultiply	NOUN
ma-310	199	28	connected	connect	VERB
ma-310	199	29	domain	domain	NOUN
ma-310	199	30	,	,	PUNCT
ma-310	199	31	iss	iss	PROPN
ma-310	199	32	.	.	PROPN
ma-310	200	1	anal	anal	PROPN
ma-310	200	2	.	.	PUNCT
ma-310	201	1	26	26	NUM
ma-310	201	2	(	(	PUNCT
ma-310	201	3	2019	2019	NUM
ma-310	201	4	)	)	PUNCT
ma-310	201	5	,	,	PUNCT
ma-310	201	6	51–66	51–66	NUM
ma-310	201	7	.	.	PUNCT
ma-310	202	1	https://doi.org/10.15393/j3.art.2019.5570.[13	https://doi.org/10.15393/j3.art.2019.5570.[13	NOUN
ma-310	202	2	]	]	X
ma-310	202	3	s.g	s.g	PROPN
ma-310	202	4	.	.	PROPN
ma-310	202	5	pyatkov	pyatkov	PROPN
ma-310	202	6	,	,	PUNCT
ma-310	202	7	boundary	boundary	ADJ
ma-310	202	8	value	value	NOUN
ma-310	202	9	and	and	CCONJ
ma-310	202	10	inverse	inverse	NOUN
ma-310	202	11	problems	problem	NOUN
ma-310	202	12	for	for	ADP
ma-310	202	13	some	some	DET
ma-310	202	14	classes	class	NOUN
ma-310	202	15	of	of	ADP
ma-310	202	16	nonclassical	nonclassical	ADJ
ma-310	202	17	operator	operator	NOUN
ma-310	202	18	-	-	PUNCT
ma-310	202	19	differential	differential	NOUN
ma-310	202	20	equa	equa	NOUN
ma-310	202	21	-	-	PUNCT
ma-310	202	22	tions	tion	NOUN
ma-310	202	23	,	,	PUNCT
ma-310	202	24	sib	sib	PROPN
ma-310	202	25	.	.	PROPN
ma-310	202	26	math	math	PROPN
ma-310	202	27	.	.	PUNCT
ma-310	203	1	j.	j.	PROPN
ma-310	203	2	62	62	NUM
ma-310	203	3	(	(	PUNCT
ma-310	203	4	2021	2021	NUM
ma-310	203	5	)	)	PUNCT
ma-310	203	6	,	,	PUNCT
ma-310	203	7	489–502	489–502	NUM
ma-310	203	8	.	.	PUNCT
ma-310	204	1	https://doi.org/10.1134/s0037446621030125.[14	https://doi.org/10.1134/s0037446621030125.[14	PUNCT
ma-310	204	2	]	]	X
ma-310	204	3	k.b	k.b	PROPN
ma-310	204	4	.	.	PROPN
ma-310	204	5	sabitov	sabitov	PROPN
ma-310	204	6	,	,	PUNCT
ma-310	204	7	dirichlet	dirichlet	PROPN
ma-310	204	8	problems	problem	NOUN
ma-310	204	9	for	for	ADP
ma-310	204	10	mixed	mixed	ADJ
ma-310	204	11	-	-	PUNCT
ma-310	204	12	type	type	NOUN
ma-310	204	13	equations	equation	NOUN
ma-310	204	14	with	with	ADP
ma-310	204	15	fractional	fractional	ADJ
ma-310	204	16	derivatives	derivative	NOUN
ma-310	204	17	,	,	PUNCT
ma-310	204	18	russ	russ	PROPN
ma-310	204	19	.	.	PUNCT
ma-310	204	20	math	math	NOUN
ma-310	204	21	.	.	PUNCT
ma-310	205	1	66	66	NUM
ma-310	205	2	(	(	PUNCT
ma-310	205	3	2022),71–81	2022),71–81	NUM
ma-310	205	4	.	.	PUNCT
ma-310	205	5	https://doi.org/10.3103/s1066369x22090080	https://doi.org/10.3103/s1066369x22090080	PROPN
ma-310	205	6	.	.	PUNCT
ma-310	206	1	https://doi.org/10.28924/ada/ma.5.10	https://doi.org/10.28924/ada/ma.5.10	PROPN
ma-310	206	2	https://doi.org/10.1007/s10958-024-07337-0	https://doi.org/10.1007/s10958-024-07337-0	NUM
ma-310	206	3	https://doi.org/10.1134/s0965542524700520	https://doi.org/10.1134/s0965542524700520	NUM
ma-310	206	4	https://doi.org/10.28924/ada/ma.4.15	https://doi.org/10.28924/ada/ma.4.15	NOUN
ma-310	206	5	https://doi.org/10.3103/s1066369x24700853	https://doi.org/10.3103/s1066369x24700853	ADV
ma-310	206	6	https://doi.org/10.15393/j3.art.2025.16810	https://doi.org/10.15393/j3.art.2025.16810	PRON
ma-310	206	7	https://doi.org/10.7169/facm/1246454030	https://doi.org/10.7169/facm/1246454030	PROPN
ma-310	206	8	https://doi.org/10.1080/17476933.2013.799152	https://doi.org/10.1080/17476933.2013.799152	PROPN
ma-310	206	9	https://doi.org/10.1007/s41478-019-00202-3	https://doi.org/10.1007/s41478-019-00202-3	NUM
ma-310	206	10	https://doi.org/10.15393/j3.art.2019.5570	https://doi.org/10.15393/j3.art.2019.5570	NOUN
ma-310	206	11	https://doi.org/10.1134/s0037446621030125	https://doi.org/10.1134/s0037446621030125	PROPN
ma-310	206	12	https://doi.org/10.3103/s1066369x22090080	https://doi.org/10.3103/s1066369x22090080	NOUN
ma-310	206	13	eur	eur	PROPN
ma-310	206	14	.	.	PUNCT
ma-310	207	1	j.	j.	PROPN
ma-310	207	2	math	math	PROPN
ma-310	207	3	.	.	PUNCT
ma-310	208	1	anal	anal	PROPN
ma-310	208	2	.	.	PUNCT
ma-310	209	1	10.28924	10.28924	NUM
ma-310	209	2	/	/	SYM
ma-310	209	3	ada	ada	PROPN
ma-310	209	4	/	/	SYM
ma-310	209	5	ma.5.10	ma.5.10	NOUN
ma-310	209	6	10	10	NUM
ma-310	210	1	[	[	SYM
ma-310	210	2	15	15	NUM
ma-310	210	3	]	]	PUNCT
ma-310	210	4	k.	k.	PROPN
ma-310	210	5	ravikumar	ravikumar	PROPN
ma-310	210	6	,	,	PUNCT
ma-310	210	7	k.	k.	PROPN
ma-310	210	8	ramkumar	ramkumar	PROPN
ma-310	210	9	,	,	PUNCT
ma-310	210	10	d.	d.	PROPN
ma-310	210	11	chalishajar	chalishajar	PROPN
ma-310	210	12	,	,	PUNCT
ma-310	210	13	existence	existence	NOUN
ma-310	210	14	and	and	CCONJ
ma-310	210	15	stability	stability	NOUN
ma-310	210	16	results	result	NOUN
ma-310	210	17	for	for	ADP
ma-310	210	18	second	second	ADJ
ma-310	210	19	-	-	PUNCT
ma-310	210	20	order	order	NOUN
ma-310	210	21	neutral	neutral	ADJ
ma-310	210	22	stochasticdifferential	stochasticdifferential	ADJ
ma-310	210	23	equations	equation	NOUN
ma-310	210	24	with	with	ADP
ma-310	210	25	random	random	ADJ
ma-310	210	26	impulses	impulse	NOUN
ma-310	210	27	and	and	CCONJ
ma-310	210	28	poisson	poisson	NOUN
ma-310	210	29	jumps	jump	VERB
ma-310	210	30	,	,	PUNCT
ma-310	210	31	eur	eur	PROPN
ma-310	210	32	.	.	PUNCT
ma-310	211	1	j.	j.	PROPN
ma-310	211	2	math	math	PROPN
ma-310	211	3	.	.	PUNCT
ma-310	212	1	anal	anal	ADJ
ma-310	212	2	.	.	PUNCT
ma-310	213	1	1	1	NUM
ma-310	213	2	(	(	PUNCT
ma-310	213	3	2021	2021	NUM
ma-310	213	4	)	)	PUNCT
ma-310	213	5	,	,	PUNCT
ma-310	214	1	1–18	1–18	NUM
ma-310	214	2	.	.	PUNCT
ma-310	214	3	https	https	NOUN
ma-310	214	4	:	:	PUNCT
ma-310	214	5	//doi.org/10.28924	//doi.org/10.28924	X
ma-310	214	6	/	/	SYM
ma-310	214	7	ada	ada	PROPN
ma-310	214	8	/	/	SYM
ma-310	214	9	ma.1.1.[16	ma.1.1.[16	PROPN
ma-310	214	10	]	]	X
ma-310	214	11	i.n	i.n	PROPN
ma-310	214	12	.	.	PROPN
ma-310	214	13	vekua	vekua	NOUN
ma-310	214	14	,	,	PUNCT
ma-310	214	15	generalized	generalized	ADJ
ma-310	214	16	analytic	analytic	ADJ
ma-310	214	17	functions	function	NOUN
ma-310	214	18	,	,	PUNCT
ma-310	214	19	pergamon	pergamon	PROPN
ma-310	214	20	press	press	PROPN
ma-310	214	21	,	,	PUNCT
ma-310	214	22	oxford	oxford	PROPN
ma-310	214	23	,	,	PUNCT
ma-310	214	24	1962	1962	NUM
ma-310	214	25	.	.	PUNCT
ma-310	215	1	https://doi.org/10.28924/ada/ma.5.10	https://doi.org/10.28924/ada/ma.5.10	PROPN
ma-310	215	2	https://doi.org/10.28924/ada/ma.1.1	https://doi.org/10.28924/ada/ma.1.1	PROPN
ma-310	215	3	https://doi.org/10.28924/ada/ma.1.1	https://doi.org/10.28924/ada/ma.1.1	PROPN
ma-310	215	4	1	1	NUM
ma-310	215	5	.	.	PUNCT
ma-310	216	1	introduction	introduction	NOUN
ma-310	216	2	2	2	NUM
ma-310	216	3	.	.	PUNCT
ma-310	217	1	the	the	DET
ma-310	217	2	dirichlet	dirichlet	PROPN
ma-310	217	3	problem	problem	NOUN
ma-310	217	4	for	for	ADP
ma-310	217	5	m	m	PROPN
ma-310	217	6	references	reference	NOUN