id	sid	tid	token	lemma	pos
iajs-1807	1	1	microsoft	microsoft	PROPN
iajs-1807	1	2	word	word	NOUN
iajs-1807	1	3	344	344	NUM
iajs-1807	1	4	-	-	SYM
iajs-1807	1	5	352	352	NUM
iajs-1807	1	6	ihsciconf	ihsciconf	NOUN
iajs-1807	1	7	2017	2017	NUM
iajs-1807	1	8	special	special	ADJ
iajs-1807	1	9	issue	issue	NOUN
iajs-1807	1	10	ibn	ibn	PROPN
iajs-1807	1	11	al	al	PROPN
iajs-1807	1	12	-	-	PUNCT
iajs-1807	1	13	haitham	haitham	PROPN
iajs-1807	1	14	journal	journal	PROPN
iajs-1807	1	15	for	for	ADP
iajs-1807	1	16	pure	pure	ADJ
iajs-1807	1	17	and	and	CCONJ
iajs-1807	1	18	applied	apply	VERB
iajs-1807	1	19	science	science	NOUN
iajs-1807	1	20	https://doi.org/	https://doi.org/	NOUN
iajs-1807	1	21	10.30526/2017.ihsciconf.1807	10.30526/2017.ihsciconf.1807	ADJ
iajs-1807	1	22	for	for	ADP
iajs-1807	1	23	more	more	ADJ
iajs-1807	1	24	information	information	NOUN
iajs-1807	1	25	about	about	ADP
iajs-1807	1	26	the	the	DET
iajs-1807	1	27	conference	conference	NOUN
iajs-1807	1	28	please	please	INTJ
iajs-1807	1	29	visit	visit	VERB
iajs-1807	1	30	the	the	DET
iajs-1807	1	31	websites	website	NOUN
iajs-1807	1	32	:	:	PUNCT
iajs-1807	1	33	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1807	1	34	  	  	SPACE
iajs-1807	1	35	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1807	1	36	   	   	SPACE
iajs-1807	1	37	mathematics	mathematic	NOUN
iajs-1807	1	38	|344	|344	NOUN
iajs-1807	1	39	    	    	SPACE
iajs-1807	1	40	finite	finite	PROPN
iajs-1807	1	41	element	element	NOUN
iajs-1807	1	42	method	method	NOUN
iajs-1807	1	43	with	with	ADP
iajs-1807	1	44	linear	linear	PROPN
iajs-1807	1	45	rectangular	rectangular	ADJ
iajs-1807	1	46	element	element	NOUN
iajs-1807	1	47	for	for	ADP
iajs-1807	1	48	solving	solve	VERB
iajs-1807	1	49	nanoscale	nanoscale	NOUN
iajs-1807	1	50	𝑰𝒏𝑨𝒔	𝑰𝒏𝑨𝒔	PROPN
iajs-1807	1	51	𝑮𝒂𝑨𝒔⁄	𝑮𝒂𝑨𝒔⁄	VERB
iajs-1807	1	52	quantum	quantum	NOUN
iajs-1807	1	53	ring	ring	NOUN
iajs-1807	1	54	structures	structure	NOUN
iajs-1807	1	55	eman	eman	PROPN
iajs-1807	1	56	ali	ali	PROPN
iajs-1807	1	57	hussain	hussain	PROPN
iajs-1807	1	58	dreman@uomustansiriyah.edu.iq	dreman@uomustansiriyah.edu.iq	PROPN
iajs-1807	1	59	dept	dept	PROPN
iajs-1807	1	60	.	.	PROPN
iajs-1807	2	1	of	of	ADP
iajs-1807	2	2	mathematics/	mathematics/	NUM
iajs-1807	2	3	college	college	NOUN
iajs-1807	2	4	of	of	ADP
iajs-1807	2	5	science/	science/	NUM
iajs-1807	2	6	university	university	PROPN
iajs-1807	2	7	of	of	ADP
iajs-1807	2	8	mustansiriyah	mustansiriyah	PROPN
iajs-1807	2	9	jamil	jamil	PROPN
iajs-1807	2	10	a.	a.	PROPN
iajs-1807	2	11	al	al	PROPN
iajs-1807	2	12	-	-	PUNCT
iajs-1807	2	13	hawasy	hawasy	PROPN
iajs-1807	2	14	jhawassya@uomustansiriyah.edu.iq	jhawassya@uomustansiriyah.edu.iq	PROPN
iajs-1807	2	15	dept	dept	PROPN
iajs-1807	2	16	.	.	PROPN
iajs-1807	3	1	of	of	ADP
iajs-1807	3	2	mathematics/	mathematics/	NUM
iajs-1807	3	3	college	college	NOUN
iajs-1807	3	4	of	of	ADP
iajs-1807	3	5	science/	science/	NUM
iajs-1807	3	6	university	university	PROPN
iajs-1807	3	7	of	of	ADP
iajs-1807	3	8	mustansiriyah	mustansiriyah	PROPN
iajs-1807	3	9	lamyaa	lamyaa	PROPN
iajs-1807	3	10	h.	h.	PROPN
iajs-1807	3	11	ali	ali	PROPN
iajs-1807	3	12	lamya_h2@uomustansiriyah.edu.iq	lamya_h2@uomustansiriyah.edu.iq	PROPN
iajs-1807	3	13	dept	dept	PROPN
iajs-1807	3	14	.	.	PROPN
iajs-1807	4	1	of	of	ADP
iajs-1807	4	2	mathematics/	mathematics/	NUM
iajs-1807	4	3	college	college	NOUN
iajs-1807	4	4	of	of	ADP
iajs-1807	4	5	science/	science/	NUM
iajs-1807	4	6	university	university	PROPN
iajs-1807	4	7	of	of	ADP
iajs-1807	4	8	mustansiriyah	mustansiriyah	NOUN
iajs-1807	4	9	abstract	abstract	ADV
iajs-1807	4	10	this	this	DET
iajs-1807	4	11	paper	paper	NOUN
iajs-1807	4	12	is	be	AUX
iajs-1807	4	13	concerned	concern	VERB
iajs-1807	4	14	with	with	ADP
iajs-1807	4	15	the	the	DET
iajs-1807	4	16	solution	solution	NOUN
iajs-1807	4	17	of	of	ADP
iajs-1807	4	18	the	the	DET
iajs-1807	4	19	nanoscale	nanoscale	NOUN
iajs-1807	4	20	structures	structure	NOUN
iajs-1807	4	21	consisting	consist	VERB
iajs-1807	4	22	of	of	ADP
iajs-1807	4	23	the	the	DET
iajs-1807	4	24	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	4	25	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	NOUN
iajs-1807	4	26	with	with	ADP
iajs-1807	4	27	an	an	DET
iajs-1807	4	28	effective	effective	ADJ
iajs-1807	4	29	mass	mass	NOUN
iajs-1807	4	30	envelope	envelope	NOUN
iajs-1807	4	31	function	function	NOUN
iajs-1807	4	32	theory	theory	NOUN
iajs-1807	4	33	,	,	PUNCT
iajs-1807	4	34	the	the	DET
iajs-1807	4	35	electronic	electronic	ADJ
iajs-1807	4	36	states	state	NOUN
iajs-1807	4	37	of	of	ADP
iajs-1807	4	38	the	the	DET
iajs-1807	4	39	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	4	40	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	ADJ
iajs-1807	4	41	quantum	quantum	NOUN
iajs-1807	4	42	ring	ring	NOUN
iajs-1807	4	43	are	be	AUX
iajs-1807	4	44	studied	study	VERB
iajs-1807	4	45	.	.	PUNCT
iajs-1807	5	1	in	in	ADP
iajs-1807	5	2	calculations	calculation	NOUN
iajs-1807	5	3	,	,	PUNCT
iajs-1807	5	4	the	the	DET
iajs-1807	5	5	effects	effect	NOUN
iajs-1807	5	6	due	due	ADJ
iajs-1807	5	7	to	to	ADP
iajs-1807	5	8	the	the	DET
iajs-1807	5	9	different	different	ADJ
iajs-1807	5	10	effective	effective	ADJ
iajs-1807	5	11	masses	masse	NOUN
iajs-1807	5	12	of	of	ADP
iajs-1807	5	13	electrons	electron	NOUN
iajs-1807	5	14	in	in	ADP
iajs-1807	5	15	and	and	CCONJ
iajs-1807	5	16	out	out	ADP
iajs-1807	5	17	the	the	DET
iajs-1807	5	18	rings	ring	NOUN
iajs-1807	5	19	are	be	AUX
iajs-1807	5	20	included	include	VERB
iajs-1807	5	21	.	.	PUNCT
iajs-1807	6	1	the	the	DET
iajs-1807	6	2	energy	energy	NOUN
iajs-1807	6	3	levels	level	NOUN
iajs-1807	6	4	of	of	ADP
iajs-1807	6	5	the	the	DET
iajs-1807	6	6	electron	electron	NOUN
iajs-1807	6	7	are	be	AUX
iajs-1807	6	8	calculated	calculate	VERB
iajs-1807	6	9	in	in	ADP
iajs-1807	6	10	the	the	DET
iajs-1807	6	11	different	different	ADJ
iajs-1807	6	12	shapes	shape	NOUN
iajs-1807	6	13	of	of	ADP
iajs-1807	6	14	rings	ring	NOUN
iajs-1807	6	15	,	,	PUNCT
iajs-1807	6	16	i.e.	i.e.	X
iajs-1807	6	17	,	,	PUNCT
iajs-1807	6	18	that	that	SCONJ
iajs-1807	6	19	the	the	DET
iajs-1807	6	20	inner	inner	ADJ
iajs-1807	6	21	radius	radius	NOUN
iajs-1807	6	22	of	of	ADP
iajs-1807	6	23	rings	ring	NOUN
iajs-1807	6	24	sensitively	sensitively	ADV
iajs-1807	6	25	change	change	VERB
iajs-1807	6	26	the	the	DET
iajs-1807	6	27	electronic	electronic	ADJ
iajs-1807	6	28	states	state	NOUN
iajs-1807	6	29	.	.	PUNCT
iajs-1807	7	1	the	the	DET
iajs-1807	7	2	energy	energy	NOUN
iajs-1807	7	3	levels	level	NOUN
iajs-1807	7	4	of	of	ADP
iajs-1807	7	5	the	the	DET
iajs-1807	7	6	electron	electron	NOUN
iajs-1807	7	7	are	be	AUX
iajs-1807	7	8	not	not	PART
iajs-1807	7	9	sensitively	sensitively	ADV
iajs-1807	7	10	dependent	dependent	ADJ
iajs-1807	7	11	on	on	ADP
iajs-1807	7	12	the	the	DET
iajs-1807	7	13	outer	outer	ADJ
iajs-1807	7	14	radius	radius	NOUN
iajs-1807	7	15	for	for	ADP
iajs-1807	7	16	large	large	ADJ
iajs-1807	7	17	rings	ring	NOUN
iajs-1807	7	18	.	.	PUNCT
iajs-1807	8	1	the	the	DET
iajs-1807	8	2	structures	structure	NOUN
iajs-1807	8	3	of	of	ADP
iajs-1807	8	4	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	8	5	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	ADJ
iajs-1807	8	6	quantum	quantum	NOUN
iajs-1807	8	7	rings	ring	NOUN
iajs-1807	8	8	are	be	AUX
iajs-1807	8	9	studied	study	VERB
iajs-1807	8	10	by	by	ADP
iajs-1807	8	11	the	the	DET
iajs-1807	8	12	one	one	NUM
iajs-1807	8	13	electronic	electronic	ADJ
iajs-1807	8	14	band	band	NOUN
iajs-1807	8	15	hamiltonian	hamiltonian	ADJ
iajs-1807	8	16	effective	effective	ADJ
iajs-1807	8	17	mass	mass	NOUN
iajs-1807	8	18	approximation	approximation	NOUN
iajs-1807	8	19	,	,	PUNCT
iajs-1807	8	20	the	the	DET
iajs-1807	8	21	energyand	energyand	ADJ
iajs-1807	8	22	position	position	NOUN
iajs-1807	8	23	-	-	PUNCT
iajs-1807	8	24	dependent	dependent	ADJ
iajs-1807	8	25	on	on	ADP
iajs-1807	8	26	electron	electron	NOUN
iajs-1807	8	27	effective	effective	ADJ
iajs-1807	8	28	mass	mass	NOUN
iajs-1807	8	29	approximation	approximation	NOUN
iajs-1807	8	30	,	,	PUNCT
iajs-1807	8	31	and	and	CCONJ
iajs-1807	8	32	the	the	DET
iajs-1807	8	33	spindependent	spindependent	NOUN
iajs-1807	8	34	on	on	ADP
iajs-1807	8	35	the	the	DET
iajs-1807	8	36	ben	ben	PROPN
iajs-1807	8	37	daniel	daniel	PROPN
iajs-1807	8	38	-	-	PUNCT
iajs-1807	8	39	duke	duke	PROPN
iajs-1807	8	40	boundary	boundary	ADJ
iajs-1807	8	41	conditions	condition	NOUN
iajs-1807	8	42	.	.	PUNCT
iajs-1807	9	1	in	in	ADP
iajs-1807	9	2	the	the	DET
iajs-1807	9	3	description	description	NOUN
iajs-1807	9	4	of	of	ADP
iajs-1807	9	5	the	the	DET
iajs-1807	9	6	hamiltonian	hamiltonian	ADJ
iajs-1807	9	7	matrix	matrix	NOUN
iajs-1807	9	8	elements	element	NOUN
iajs-1807	9	9	,	,	PUNCT
iajs-1807	9	10	the	the	DET
iajs-1807	9	11	finite	finite	ADJ
iajs-1807	9	12	elements	element	NOUN
iajs-1807	9	13	method	method	VERB
iajs-1807	9	14	with	with	ADP
iajs-1807	9	15	different	different	ADJ
iajs-1807	9	16	base	base	NOUN
iajs-1807	9	17	piecewise	piecewise	NOUN
iajs-1807	9	18	linear	linear	NOUN
iajs-1807	9	19	function	function	NOUN
iajs-1807	9	20	is	be	AUX
iajs-1807	9	21	adopted	adopt	VERB
iajs-1807	9	22	.	.	PUNCT
iajs-1807	10	1	the	the	DET
iajs-1807	10	2	non	non	ADJ
iajs-1807	10	3	-	-	ADJ
iajs-1807	10	4	linear	linear	ADJ
iajs-1807	10	5	energy	energy	NOUN
iajs-1807	10	6	confinement	confinement	NOUN
iajs-1807	10	7	problem	problem	NOUN
iajs-1807	10	8	is	be	AUX
iajs-1807	10	9	solved	solve	VERB
iajs-1807	10	10	approximately	approximately	ADV
iajs-1807	10	11	by	by	ADP
iajs-1807	10	12	using	use	VERB
iajs-1807	10	13	the	the	DET
iajs-1807	10	14	finite	finite	ADJ
iajs-1807	10	15	elements	element	NOUN
iajs-1807	10	16	method	method	VERB
iajs-1807	10	17	with	with	ADP
iajs-1807	10	18	piecewise	piecewise	NOUN
iajs-1807	10	19	linear	linear	NOUN
iajs-1807	10	20	function	function	NOUN
iajs-1807	10	21	,	,	PUNCT
iajs-1807	10	22	to	to	PART
iajs-1807	10	23	calculate	calculate	VERB
iajs-1807	10	24	the	the	DET
iajs-1807	10	25	energy	energy	NOUN
iajs-1807	10	26	of	of	ADP
iajs-1807	10	27	the	the	DET
iajs-1807	10	28	one	one	NUM
iajs-1807	10	29	electron	electron	NOUN
iajs-1807	10	30	states	state	NOUN
iajs-1807	10	31	for	for	ADP
iajs-1807	10	32	the	the	DET
iajs-1807	10	33	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	10	34	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	ADJ
iajs-1807	10	35	quantum	quantum	NOUN
iajs-1807	10	36	ring	ring	NOUN
iajs-1807	10	37	.	.	PUNCT
iajs-1807	11	1	the	the	DET
iajs-1807	11	2	results	result	NOUN
iajs-1807	11	3	of	of	ADP
iajs-1807	11	4	numerical	numerical	ADJ
iajs-1807	11	5	example	example	NOUN
iajs-1807	11	6	are	be	AUX
iajs-1807	11	7	compared	compare	VERB
iajs-1807	11	8	for	for	ADP
iajs-1807	11	9	accuracy	accuracy	NOUN
iajs-1807	11	10	and	and	CCONJ
iajs-1807	11	11	efficiency	efficiency	NOUN
iajs-1807	11	12	with	with	ADP
iajs-1807	11	13	the	the	DET
iajs-1807	11	14	finite	finite	ADJ
iajs-1807	11	15	element	element	NOUN
iajs-1807	11	16	method	method	NOUN
iajs-1807	11	17	of	of	ADP
iajs-1807	11	18	linear	linear	PROPN
iajs-1807	11	19	triangular	triangular	NOUN
iajs-1807	11	20	element	element	NOUN
iajs-1807	11	21	.	.	PUNCT
iajs-1807	12	1	this	this	DET
iajs-1807	12	2	comparison	comparison	NOUN
iajs-1807	12	3	shows	show	VERB
iajs-1807	12	4	that	that	SCONJ
iajs-1807	12	5	good	good	ADJ
iajs-1807	12	6	results	result	NOUN
iajs-1807	12	7	of	of	ADP
iajs-1807	12	8	numerical	numerical	ADJ
iajs-1807	12	9	example	example	NOUN
iajs-1807	12	10	.	.	PUNCT
iajs-1807	13	1	keywords	keyword	NOUN
iajs-1807	13	2	:	:	PUNCT
iajs-1807	13	3	nanoscale	nanoscale	NOUN
iajs-1807	13	4	,	,	PUNCT
iajs-1807	13	5	finite	finite	ADJ
iajs-1807	13	6	elements	element	NOUN
iajs-1807	13	7	method	method	NOUN
iajs-1807	13	8	,	,	PUNCT
iajs-1807	13	9	ben	ben	PROPN
iajs-1807	13	10	daniel	daniel	PROPN
iajs-1807	13	11	-	-	PUNCT
iajs-1807	13	12	duke	duke	PROPN
iajs-1807	13	13	boundary	boundary	ADJ
iajs-1807	13	14	conditions	condition	NOUN
iajs-1807	13	15	,	,	PUNCT
iajs-1807	13	16	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	13	17	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	ADJ
iajs-1807	13	18	quantum	quantum	NOUN
iajs-1807	13	19	rings	ring	NOUN
iajs-1807	13	20	.	.	PUNCT
iajs-1807	14	1	ihsciconf	ihsciconf	PROPN
iajs-1807	14	2	2017	2017	NUM
iajs-1807	14	3	special	special	ADJ
iajs-1807	14	4	issue	issue	NOUN
iajs-1807	14	5	ibn	ibn	PROPN
iajs-1807	14	6	al	al	PROPN
iajs-1807	14	7	-	-	PUNCT
iajs-1807	14	8	haitham	haitham	PROPN
iajs-1807	14	9	journal	journal	PROPN
iajs-1807	14	10	for	for	ADP
iajs-1807	14	11	pure	pure	ADJ
iajs-1807	14	12	and	and	CCONJ
iajs-1807	14	13	applied	apply	VERB
iajs-1807	14	14	science	science	NOUN
iajs-1807	14	15	https://doi.org/	https://doi.org/	NOUN
iajs-1807	14	16	10.30526/2017.ihsciconf.1807	10.30526/2017.ihsciconf.1807	ADJ
iajs-1807	14	17	for	for	ADP
iajs-1807	14	18	more	more	ADJ
iajs-1807	14	19	information	information	NOUN
iajs-1807	14	20	about	about	ADP
iajs-1807	14	21	the	the	DET
iajs-1807	14	22	conference	conference	NOUN
iajs-1807	14	23	please	please	INTJ
iajs-1807	14	24	visit	visit	VERB
iajs-1807	14	25	the	the	DET
iajs-1807	14	26	websites	website	NOUN
iajs-1807	14	27	:	:	PUNCT
iajs-1807	14	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1807	14	29	  	  	SPACE
iajs-1807	14	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1807	14	31	   	   	SPACE
iajs-1807	14	32	mathematics	mathematic	NOUN
iajs-1807	14	33	|345	|345	PROPN
iajs-1807	14	34	    	    	SPACE
iajs-1807	14	35	1	1	NUM
iajs-1807	14	36	.	.	PUNCT
iajs-1807	14	37	introduction	introduction	NOUN
iajs-1807	14	38	the	the	DET
iajs-1807	14	39	modeling	modeling	NOUN
iajs-1807	14	40	of	of	ADP
iajs-1807	14	41	the	the	DET
iajs-1807	14	42	electron	electron	NOUN
iajs-1807	14	43	states	state	NOUN
iajs-1807	14	44	in	in	ADP
iajs-1807	14	45	semiconductor	semiconductor	NOUN
iajs-1807	14	46	nanostructures	nanostructure	NOUN
iajs-1807	14	47	remains	remain	VERB
iajs-1807	14	48	a	a	DET
iajs-1807	14	49	difficult	difficult	ADJ
iajs-1807	14	50	computational	computational	ADJ
iajs-1807	14	51	task	task	NOUN
iajs-1807	14	52	.	.	PUNCT
iajs-1807	15	1	the	the	DET
iajs-1807	15	2	one	one	NUM
iajs-1807	15	3	electron	electron	NOUN
iajs-1807	15	4	states	state	NOUN
iajs-1807	15	5	are	be	AUX
iajs-1807	15	6	helpful	helpful	ADJ
iajs-1807	15	7	for	for	ADP
iajs-1807	15	8	studying	study	VERB
iajs-1807	15	9	the	the	DET
iajs-1807	15	10	electron	electron	NOUN
iajs-1807	15	11	correlations	correlation	NOUN
iajs-1807	15	12	and	and	CCONJ
iajs-1807	15	13	,	,	PUNCT
iajs-1807	15	14	the	the	DET
iajs-1807	15	15	effects	effect	NOUN
iajs-1807	15	16	of	of	ADP
iajs-1807	15	17	magnetic	magnetic	ADJ
iajs-1807	15	18	fields	field	NOUN
iajs-1807	15	19	in	in	ADP
iajs-1807	15	20	quantum	quantum	NOUN
iajs-1807	15	21	rings	ring	NOUN
iajs-1807	15	22	and	and	CCONJ
iajs-1807	15	23	useful	useful	ADJ
iajs-1807	15	24	for	for	ADP
iajs-1807	15	25	designing	design	VERB
iajs-1807	15	26	and	and	CCONJ
iajs-1807	15	27	fabricating	fabricate	VERB
iajs-1807	15	28	the	the	DET
iajs-1807	15	29	double	double	ADJ
iajs-1807	15	30	colors	color	NOUN
iajs-1807	15	31	detector	detector	NOUN
iajs-1807	15	32	by	by	ADP
iajs-1807	15	33	intra	intra	ADJ
iajs-1807	15	34	band	band	NOUN
iajs-1807	15	35	and	and	CCONJ
iajs-1807	15	36	inter	inter	ADJ
iajs-1807	15	37	band	band	NOUN
iajs-1807	15	38	translations	translation	NOUN
iajs-1807	15	39	.	.	PUNCT
iajs-1807	16	1	in	in	ADP
iajs-1807	16	2	1990	1990	NUM
iajs-1807	16	3	,	,	PUNCT
iajs-1807	16	4	paasch	paasch	PROPN
iajs-1807	16	5	et	et	PROPN
iajs-1807	16	6	.	.	PUNCT
iajs-1807	17	1	al	al	PROPN
iajs-1807	17	2	.	.	PROPN
iajs-1807	17	3	,	,	PUNCT
iajs-1807	18	1	[	[	X
iajs-1807	18	2	3	3	X
iajs-1807	18	3	]	]	PUNCT
iajs-1807	18	4	used	use	VERB
iajs-1807	18	5	envelope	envelope	NOUN
iajs-1807	18	6	equation	equation	NOUN
iajs-1807	18	7	and	and	CCONJ
iajs-1807	18	8	wave	wave	NOUN
iajs-1807	18	9	function	function	NOUN
iajs-1807	18	10	matching	match	VERB
iajs-1807	18	11	for	for	ADP
iajs-1807	18	12	narrowgap	narrowgap	ADJ
iajs-1807	18	13	semiconductors	semiconductor	NOUN
iajs-1807	18	14	.	.	PUNCT
iajs-1807	19	1	in	in	ADP
iajs-1807	19	2	1995	1995	NUM
iajs-1807	19	3	,	,	PUNCT
iajs-1807	19	4	mathine	mathine	PROPN
iajs-1807	19	5	et	et	PROPN
iajs-1807	19	6	.	.	PUNCT
iajs-1807	20	1	al	al	PROPN
iajs-1807	20	2	.	.	PROPN
iajs-1807	20	3	,	,	PUNCT
iajs-1807	21	1	[	[	X
iajs-1807	21	2	4	4	NUM
iajs-1807	21	3	]	]	PUNCT
iajs-1807	21	4	applied	apply	VERB
iajs-1807	21	5	computational	computational	ADJ
iajs-1807	21	6	fourier	fourier	NOUN
iajs-1807	21	7	series	series	NOUN
iajs-1807	21	8	solution	solution	NOUN
iajs-1807	21	9	of	of	ADP
iajs-1807	21	10	the	the	DET
iajs-1807	21	11	bendaniel	bendaniel	NOUN
iajs-1807	21	12	-	-	PUNCT
iajs-1807	21	13	duke	duke	NOUN
iajs-1807	21	14	hamiltonian	hamiltonian	NOUN
iajs-1807	21	15	for	for	ADP
iajs-1807	21	16	arbitrary	arbitrary	ADJ
iajs-1807	21	17	shaped	shaped	ADJ
iajs-1807	21	18	quantum	quantum	ADJ
iajs-1807	21	19	wells	well	NOUN
iajs-1807	21	20	.	.	PUNCT
iajs-1807	22	1	in	in	ADP
iajs-1807	22	2	2001	2001	NUM
iajs-1807	22	3	,	,	PUNCT
iajs-1807	22	4	yiming	yiming	PROPN
iajs-1807	22	5	li	li	PROPN
iajs-1807	22	6	et	et	PROPN
iajs-1807	22	7	al	al	PROPN
iajs-1807	22	8	,	,	PUNCT
iajs-1807	22	9	[	[	X
iajs-1807	22	10	1	1	X
iajs-1807	22	11	]	]	PUNCT
iajs-1807	22	12	used	use	VERB
iajs-1807	22	13	computer	computer	NOUN
iajs-1807	22	14	simulation	simulation	NOUN
iajs-1807	22	15	of	of	ADP
iajs-1807	22	16	electron	electron	NOUN
iajs-1807	22	17	energy	energy	NOUN
iajs-1807	22	18	levels	level	NOUN
iajs-1807	22	19	for	for	ADP
iajs-1807	22	20	different	different	ADJ
iajs-1807	22	21	shape	shape	NOUN
iajs-1807	22	22	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	22	23	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	ADJ
iajs-1807	22	24	semiconductor	semiconductor	NOUN
iajs-1807	22	25	quantum	quantum	NOUN
iajs-1807	22	26	dots	dot	NOUN
iajs-1807	22	27	.	.	PUNCT
iajs-1807	23	1	in	in	ADP
iajs-1807	23	2	2002	2002	NUM
iajs-1807	23	3	,	,	PUNCT
iajs-1807	23	4	yiming	yiming	PROPN
iajs-1807	23	5	li	li	PROPN
iajs-1807	23	6	et	et	PROPN
iajs-1807	23	7	al	al	PROPN
iajs-1807	23	8	,	,	PUNCT
iajs-1807	23	9	[	[	X
iajs-1807	23	10	2	2	X
iajs-1807	23	11	]	]	PUNCT
iajs-1807	23	12	used	use	VERB
iajs-1807	23	13	electron	electron	NOUN
iajs-1807	23	14	energy	energy	NOUN
iajs-1807	23	15	state	state	NOUN
iajs-1807	23	16	spin	spin	NOUN
iajs-1807	23	17	-	-	PUNCT
iajs-1807	23	18	splitting	splitting	NOUN
iajs-1807	23	19	in	in	ADP
iajs-1807	23	20	3d	3d	NUM
iajs-1807	23	21	cylindrical	cylindrical	ADJ
iajs-1807	23	22	semiconductor	semiconductor	NOUN
iajs-1807	23	23	quantum	quantum	NOUN
iajs-1807	23	24	dots	dot	NOUN
iajs-1807	23	25	.	.	PUNCT
iajs-1807	24	1	in	in	ADP
iajs-1807	24	2	2003	2003	NUM
iajs-1807	24	3	,	,	PUNCT
iajs-1807	24	4	melnik	melnik	X
iajs-1807	24	5	et	et	PROPN
iajs-1807	24	6	al	al	PROPN
iajs-1807	24	7	,	,	PUNCT
iajs-1807	24	8	[	[	X
iajs-1807	24	9	5	5	NUM
iajs-1807	24	10	]	]	PUNCT
iajs-1807	24	11	applied	apply	VERB
iajs-1807	24	12	finite	finite	ADJ
iajs-1807	24	13	element	element	NOUN
iajs-1807	24	14	analysis	analysis	NOUN
iajs-1807	24	15	of	of	ADP
iajs-1807	24	16	nanowire	nanowire	ADJ
iajs-1807	24	17	superlattice	superlattice	NOUN
iajs-1807	24	18	structures	structure	NOUN
iajs-1807	24	19	.	.	PUNCT
iajs-1807	25	1	whereas	whereas	SCONJ
iajs-1807	25	2	2005	2005	NUM
iajs-1807	25	3	,	,	PUNCT
iajs-1807	25	4	yiming	yiming	ADJ
iajs-1807	25	5	li	li	PROPN
iajs-1807	25	6	,	,	PUNCT
iajs-1807	26	1	[	[	X
iajs-1807	26	2	6	6	NUM
iajs-1807	26	3	]	]	PUNCT
iajs-1807	26	4	using	use	VERB
iajs-1807	26	5	an	an	DET
iajs-1807	26	6	iterative	iterative	NOUN
iajs-1807	26	7	method	method	NOUN
iajs-1807	26	8	for	for	ADP
iajs-1807	26	9	single	single	ADJ
iajs-1807	26	10	and	and	CCONJ
iajs-1807	26	11	vertically	vertically	ADV
iajs-1807	26	12	stacked	stack	VERB
iajs-1807	26	13	semiconductor	semiconductor	NOUN
iajs-1807	26	14	quantum	quantum	NOUN
iajs-1807	26	15	dots	dot	NOUN
iajs-1807	26	16	simulation	simulation	NOUN
iajs-1807	26	17	.	.	PUNCT
iajs-1807	27	1	in	in	ADP
iajs-1807	27	2	2016	2016	NUM
iajs-1807	27	3	,	,	PUNCT
iajs-1807	27	4	deyasi	deyasi	NOUN
iajs-1807	27	5	et	et	PROPN
iajs-1807	27	6	.	.	PUNCT
iajs-1807	28	1	al	al	PROPN
iajs-1807	28	2	.	.	PROPN
iajs-1807	28	3	,	,	PUNCT
iajs-1807	29	1	[	[	X
iajs-1807	29	2	7	7	X
iajs-1807	29	3	]	]	PUNCT
iajs-1807	29	4	applied	apply	VERB
iajs-1807	29	5	numerically	numerically	ADV
iajs-1807	29	6	computed	compute	VERB
iajs-1807	29	7	in	in	ADP
iajs-1807	29	8	presence	presence	NOUN
iajs-1807	29	9	of	of	ADP
iajs-1807	29	10	electric	electric	ADJ
iajs-1807	29	11	field	field	NOUN
iajs-1807	29	12	using	use	VERB
iajs-1807	29	13	propagation	propagation	NOUN
iajs-1807	29	14	matrix	matrix	NOUN
iajs-1807	29	15	method	method	NOUN
iajs-1807	29	16	.	.	PUNCT
iajs-1807	30	1	in	in	ADP
iajs-1807	30	2	2017	2017	NUM
iajs-1807	30	3	,	,	PUNCT
iajs-1807	30	4	eman	eman	PROPN
iajs-1807	30	5	et	et	PROPN
iajs-1807	30	6	.	.	PUNCT
iajs-1807	31	1	al	al	PROPN
iajs-1807	31	2	.	.	PROPN
iajs-1807	31	3	,	,	PUNCT
iajs-1807	32	1	[	[	X
iajs-1807	32	2	8	8	NUM
iajs-1807	32	3	]	]	PUNCT
iajs-1807	32	4	using	use	VERB
iajs-1807	32	5	finite	finite	ADJ
iajs-1807	32	6	element	element	NOUN
iajs-1807	32	7	method	method	NOUN
iajs-1807	32	8	with	with	ADP
iajs-1807	32	9	linear	linear	ADJ
iajs-1807	32	10	triangular	triangular	NOUN
iajs-1807	32	11	element	element	NOUN
iajs-1807	32	12	for	for	ADP
iajs-1807	32	13	solving	solve	VERB
iajs-1807	32	14	finite	finite	ADJ
iajs-1807	32	15	nanowire	nanowire	ADJ
iajs-1807	32	16	superlattice	superlattice	NOUN
iajs-1807	32	17	quantum	quantum	NOUN
iajs-1807	32	18	dot	dot	NOUN
iajs-1807	32	19	structures	structure	NOUN
iajs-1807	32	20	𝐺𝑎𝐴𝑠	𝐺𝑎𝐴𝑠	PROPN
iajs-1807	32	21	𝐴𝑙𝐺𝑎𝐴𝑠⁄	𝐴𝑙𝐺𝑎𝐴𝑠⁄	PROPN
iajs-1807	32	22	.	.	PUNCT
iajs-1807	33	1	in	in	ADP
iajs-1807	33	2	2017	2017	NUM
iajs-1807	33	3	,	,	PUNCT
iajs-1807	33	4	eman	eman	PROPN
iajs-1807	33	5	et	et	PROPN
iajs-1807	33	6	.	.	PUNCT
iajs-1807	34	1	al	al	PROPN
iajs-1807	34	2	.	.	PROPN
iajs-1807	34	3	,	,	PUNCT
iajs-1807	35	1	[	[	X
iajs-1807	35	2	9	9	NUM
iajs-1807	35	3	]	]	PUNCT
iajs-1807	35	4	using	use	VERB
iajs-1807	35	5	finite	finite	PROPN
iajs-1807	35	6	element	element	NOUN
iajs-1807	35	7	method	method	NOUN
iajs-1807	35	8	with	with	ADP
iajs-1807	35	9	linear	linear	PROPN
iajs-1807	35	10	rectangular	rectangular	ADJ
iajs-1807	35	11	element	element	NOUN
iajs-1807	35	12	for	for	ADP
iajs-1807	35	13	solving	solve	VERB
iajs-1807	35	14	finite	finite	ADJ
iajs-1807	35	15	nanowire	nanowire	ADJ
iajs-1807	35	16	superlattice	superlattice	NOUN
iajs-1807	35	17	quantum	quantum	NOUN
iajs-1807	35	18	dot	dot	NOUN
iajs-1807	35	19	structures	structure	NOUN
iajs-1807	35	20	𝐺𝑎𝐴𝑠	𝐺𝑎𝐴𝑠	PROPN
iajs-1807	35	21	𝐴𝑙𝐺𝑎𝐴𝑠⁄	𝐴𝑙𝐺𝑎𝐴𝑠⁄	PROPN
iajs-1807	35	22	results	result	VERB
iajs-1807	35	23	.	.	PUNCT
iajs-1807	36	1	modeling	model	VERB
iajs-1807	36	2	energy	energy	NOUN
iajs-1807	36	3	stat	stat	NOUN
iajs-1807	36	4	with	with	ADP
iajs-1807	36	5	spin	spin	NOUN
iajs-1807	36	6	-	-	PUNCT
iajs-1807	36	7	dependent	dependent	ADJ
iajs-1807	36	8	boundary	boundary	ADJ
iajs-1807	36	9	conditions	condition	NOUN
iajs-1807	36	10	[	[	X
iajs-1807	36	11	5	5	NUM
iajs-1807	36	12	&	&	CCONJ
iajs-1807	36	13	6	6	NUM
iajs-1807	36	14	]	]	X
iajs-1807	36	15	we	we	PRON
iajs-1807	36	16	consider	consider	VERB
iajs-1807	36	17	the	the	DET
iajs-1807	36	18	problem	problem	NOUN
iajs-1807	36	19	to	to	PART
iajs-1807	36	20	compute	compute	VERB
iajs-1807	36	21	relevant	relevant	ADJ
iajs-1807	36	22	energy	energy	NOUN
iajs-1807	36	23	states	state	NOUN
iajs-1807	36	24	and	and	CCONJ
iajs-1807	36	25	corresponding	corresponding	ADJ
iajs-1807	36	26	wave	wave	NOUN
iajs-1807	36	27	functions	function	NOUN
iajs-1807	36	28	of	of	ADP
iajs-1807	36	29	a	a	DET
iajs-1807	36	30	three	three	NUM
iajs-1807	36	31	dimensional	dimensional	ADJ
iajs-1807	36	32	semiconductor	semiconductor	NOUN
iajs-1807	36	33	quantum	quantum	NOUN
iajs-1807	36	34	ring	ring	NOUN
iajs-1807	36	35	.	.	PUNCT
iajs-1807	37	1	consider	consider	VERB
iajs-1807	37	2	the	the	DET
iajs-1807	37	3	one	one	NUM
iajs-1807	37	4	electrons	electron	NOUN
iajs-1807	37	5	is	be	AUX
iajs-1807	37	6	confined	confine	VERB
iajs-1807	37	7	in	in	ADP
iajs-1807	37	8	system	system	NOUN
iajs-1807	37	9	of	of	ADP
iajs-1807	37	10	the	the	DET
iajs-1807	37	11	three	three	NUM
iajs-1807	37	12	-	-	PUNCT
iajs-1807	37	13	dimensional	dimensional	ADJ
iajs-1807	37	14	quantum	quantum	NOUN
iajs-1807	37	15	ring	ring	NOUN
iajs-1807	37	16	structures	structure	NOUN
iajs-1807	37	17	and	and	CCONJ
iajs-1807	37	18	apply	apply	VERB
iajs-1807	37	19	an	an	DET
iajs-1807	37	20	effective	effective	ADJ
iajs-1807	37	21	one	one	NUM
iajs-1807	37	22	electronic	electronic	ADJ
iajs-1807	37	23	band	band	NOUN
iajs-1807	37	24	hamiltonian	hamiltonian	NOUN
iajs-1807	37	25	,	,	PUNCT
iajs-1807	37	26	is	be	AUX
iajs-1807	37	27	given	give	VERB
iajs-1807	37	28	by	by	ADP
iajs-1807	37	29	:	:	PUNCT
iajs-1807	37	30	𝐻	𝐻	PROPN
iajs-1807	37	31	𝐻	𝐻	PROPN
iajs-1807	37	32	𝑉	𝑉	PROPN
iajs-1807	37	33	𝑟	𝑟	NOUN
iajs-1807	37	34	,	,	PUNCT
iajs-1807	37	35	1	1	NUM
iajs-1807	37	36	where	where	SCONJ
iajs-1807	37	37	𝐻	𝐻	PROPN
iajs-1807	37	38	is	be	AUX
iajs-1807	37	39	the	the	DET
iajs-1807	37	40	hamiltonian	hamiltonian	NOUN
iajs-1807	37	41	of	of	ADP
iajs-1807	37	42	the	the	DET
iajs-1807	37	43	system	system	NOUN
iajs-1807	37	44	without	without	ADP
iajs-1807	37	45	spin	spin	NOUN
iajs-1807	37	46	-	-	PUNCT
iajs-1807	37	47	orbit	orbit	NOUN
iajs-1807	37	48	interaction	interaction	NOUN
iajs-1807	37	49	,	,	PUNCT
iajs-1807	37	50	𝑉	𝑉	PROPN
iajs-1807	37	51	𝑟	𝑟	NOUN
iajs-1807	37	52	is	be	AUX
iajs-1807	37	53	the	the	DET
iajs-1807	37	54	spinorbit	spinorbit	NOUN
iajs-1807	37	55	interaction	interaction	NOUN
iajs-1807	37	56	for	for	ADP
iajs-1807	37	57	the	the	DET
iajs-1807	37	58	conduction	conduction	NOUN
iajs-1807	37	59	band	band	NOUN
iajs-1807	37	60	electrons	electron	NOUN
iajs-1807	37	61	,	,	PUNCT
iajs-1807	37	62	and	and	CCONJ
iajs-1807	37	63	the	the	DET
iajs-1807	37	64	expression	expression	NOUN
iajs-1807	37	65	for	for	ADP
iajs-1807	37	66	𝐻	𝐻	PROPN
iajs-1807	37	67	is	be	AUX
iajs-1807	37	68	as	as	SCONJ
iajs-1807	37	69	follows	follow	VERB
iajs-1807	37	70	:	:	PUNCT
iajs-1807	38	1	𝐻	𝐻	PROPN
iajs-1807	38	2	ℏ	ℏ	NOUN
iajs-1807	38	3	2	2	NUM
iajs-1807	38	4	∇	∇	X
iajs-1807	38	5	1	1	NUM
iajs-1807	38	6	𝑚	𝑚	PROPN
iajs-1807	38	7	𝐸	𝐸	PROPN
iajs-1807	38	8	,	,	PUNCT
iajs-1807	38	9	𝑟	𝑟	X
iajs-1807	38	10	∇	∇	VERB
iajs-1807	38	11	𝑉	𝑉	X
iajs-1807	38	12	𝑟	𝑟	NOUN
iajs-1807	38	13	2	2	NUM
iajs-1807	38	14	where	where	SCONJ
iajs-1807	38	15	∇	∇	PROPN
iajs-1807	38	16	is	be	AUX
iajs-1807	38	17	the	the	DET
iajs-1807	38	18	spatial	spatial	ADJ
iajs-1807	38	19	gradient	gradient	NOUN
iajs-1807	38	20	,	,	PUNCT
iajs-1807	38	21	𝑚	𝑚	PROPN
iajs-1807	38	22	𝐸	𝐸	PROPN
iajs-1807	38	23	,	,	PUNCT
iajs-1807	38	24	𝑟	𝑟	PRON
iajs-1807	38	25	is	be	AUX
iajs-1807	38	26	the	the	DET
iajs-1807	38	27	energy	energy	NOUN
iajs-1807	38	28	dependent	dependent	ADJ
iajs-1807	38	29	electron	electron	NOUN
iajs-1807	38	30	effective	effective	ADJ
iajs-1807	38	31	mass	mass	NOUN
iajs-1807	38	32	,	,	PUNCT
iajs-1807	38	33	and	and	CCONJ
iajs-1807	38	34	𝑉	𝑉	PROPN
iajs-1807	38	35	𝑟	𝑟	NOUN
iajs-1807	38	36	is	be	AUX
iajs-1807	38	37	the	the	DET
iajs-1807	38	38	confinement	confinement	ADJ
iajs-1807	38	39	potential	potential	NOUN
iajs-1807	38	40	.	.	PUNCT
iajs-1807	39	1	1	1	NUM
iajs-1807	39	2	𝑚	𝑚	X
iajs-1807	39	3	𝐸	𝐸	PROPN
iajs-1807	39	4	,	,	PUNCT
iajs-1807	39	5	𝑟	𝑟	PRON
iajs-1807	39	6	𝑃	𝑃	VERB
iajs-1807	39	7	ℏ	ℏ	PROPN
iajs-1807	39	8	2	2	NUM
iajs-1807	39	9	𝐸	𝐸	NOUN
iajs-1807	39	10	𝐸	𝐸	PROPN
iajs-1807	39	11	𝑟	𝑟	NOUN
iajs-1807	39	12	𝑉	𝑉	NOUN
iajs-1807	39	13	𝑟	𝑟	NOUN
iajs-1807	39	14	1	1	NUM
iajs-1807	39	15	𝐸	𝐸	PROPN
iajs-1807	39	16	𝐸	𝐸	PROPN
iajs-1807	39	17	𝑟	𝑟	NOUN
iajs-1807	39	18	∆	∆	PRON
iajs-1807	39	19	𝑟	𝑟	X
iajs-1807	39	20	𝑉	𝑉	VERB
iajs-1807	39	21	𝑟	𝑟	NOUN
iajs-1807	39	22	3	3	NUM
iajs-1807	39	23	where	where	SCONJ
iajs-1807	39	24	𝐸	𝐸	PROPN
iajs-1807	39	25	𝑟	𝑟	NOUN
iajs-1807	39	26	and	and	CCONJ
iajs-1807	39	27	∆	∆	PROPN
iajs-1807	39	28	𝑟	𝑟	PRON
iajs-1807	39	29	stand	stand	VERB
iajs-1807	39	30	for	for	ADP
iajs-1807	39	31	the	the	DET
iajs-1807	39	32	position	position	NOUN
iajs-1807	39	33	dependent	dependent	ADJ
iajs-1807	39	34	band	band	NOUN
iajs-1807	39	35	gap	gap	NOUN
iajs-1807	39	36	and	and	CCONJ
iajs-1807	39	37	the	the	DET
iajs-1807	39	38	spin	spin	NOUN
iajs-1807	39	39	-	-	PUNCT
iajs-1807	39	40	orbit	orbit	NOUN
iajs-1807	39	41	splitting	splitting	NOUN
iajs-1807	39	42	in	in	ADP
iajs-1807	39	43	the	the	DET
iajs-1807	39	44	valence	valence	NOUN
iajs-1807	39	45	band	band	NOUN
iajs-1807	39	46	,	,	PUNCT
iajs-1807	39	47	respectively	respectively	ADV
iajs-1807	39	48	and	and	CCONJ
iajs-1807	39	49	,	,	PUNCT
iajs-1807	39	50	𝑃	𝑃	PROPN
iajs-1807	39	51	is	be	AUX
iajs-1807	39	52	the	the	DET
iajs-1807	39	53	momentum	momentum	NOUN
iajs-1807	39	54	matrix	matrix	NOUN
iajs-1807	39	55	element	element	NOUN
iajs-1807	39	56	..	..	PUNCT
iajs-1807	40	1	the	the	DET
iajs-1807	40	2	spin	spin	NOUN
iajs-1807	40	3	-	-	PUNCT
iajs-1807	40	4	orbit	orbit	NOUN
iajs-1807	40	5	interaction	interaction	NOUN
iajs-1807	40	6	for	for	ADP
iajs-1807	40	7	the	the	DET
iajs-1807	40	8	conduction	conduction	NOUN
iajs-1807	40	9	band	band	NOUN
iajs-1807	40	10	electrons	electron	NOUN
iajs-1807	40	11	𝑉	𝑉	PROPN
iajs-1807	40	12	𝑟	𝑟	NOUN
iajs-1807	40	13	is	be	AUX
iajs-1807	40	14	given	give	VERB
iajs-1807	40	15	by	by	ADP
iajs-1807	40	16	ihsciconf	ihsciconf	PROPN
iajs-1807	40	17	2017	2017	NUM
iajs-1807	40	18	special	special	ADJ
iajs-1807	40	19	issue	issue	NOUN
iajs-1807	40	20	ibn	ibn	PROPN
iajs-1807	40	21	al	al	PROPN
iajs-1807	40	22	-	-	PUNCT
iajs-1807	40	23	haitham	haitham	PROPN
iajs-1807	40	24	journal	journal	PROPN
iajs-1807	40	25	for	for	ADP
iajs-1807	40	26	pure	pure	ADJ
iajs-1807	40	27	and	and	CCONJ
iajs-1807	40	28	applied	apply	VERB
iajs-1807	40	29	science	science	NOUN
iajs-1807	40	30	https://doi.org/	https://doi.org/	NOUN
iajs-1807	40	31	10.30526/2017.ihsciconf.1807	10.30526/2017.ihsciconf.1807	ADJ
iajs-1807	40	32	for	for	ADP
iajs-1807	40	33	more	more	ADJ
iajs-1807	40	34	information	information	NOUN
iajs-1807	40	35	about	about	ADP
iajs-1807	40	36	the	the	DET
iajs-1807	40	37	conference	conference	NOUN
iajs-1807	40	38	please	please	INTJ
iajs-1807	40	39	visit	visit	VERB
iajs-1807	40	40	the	the	DET
iajs-1807	40	41	websites	website	NOUN
iajs-1807	40	42	:	:	PUNCT
iajs-1807	40	43	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1807	40	44	  	  	SPACE
iajs-1807	40	45	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1807	40	46	   	   	SPACE
iajs-1807	40	47	mathematics	mathematic	NOUN
iajs-1807	40	48	|346	|346	VERB
iajs-1807	40	49	    	    	SPACE
iajs-1807	40	50	𝑉	𝑉	PROPN
iajs-1807	40	51	𝑟	𝑟	NOUN
iajs-1807	40	52	𝑖∇𝛽	𝑖∇𝛽	PROPN
iajs-1807	40	53	𝐸	𝐸	PROPN
iajs-1807	40	54	,	,	PUNCT
iajs-1807	40	55	𝑟	𝑟	X
iajs-1807	40	56	∙	∙	PROPN
iajs-1807	40	57	𝜎	𝜎	PROPN
iajs-1807	40	58	∇	∇	X
iajs-1807	40	59	4	4	NUM
iajs-1807	40	60	where	where	SCONJ
iajs-1807	40	61	𝛽	𝛽	PROPN
iajs-1807	40	62	𝐸	𝐸	PROPN
iajs-1807	40	63	,	,	PUNCT
iajs-1807	40	64	𝑟	𝑟	PRON
iajs-1807	40	65	is	be	AUX
iajs-1807	40	66	the	the	DET
iajs-1807	40	67	spin	spin	NOUN
iajs-1807	40	68	-	-	PUNCT
iajs-1807	40	69	orbit	orbit	NOUN
iajs-1807	40	70	coupling	coupling	NOUN
iajs-1807	40	71	parameter	parameter	NOUN
iajs-1807	40	72	and	and	CCONJ
iajs-1807	40	73	𝜎	𝜎	PROPN
iajs-1807	40	74	𝜎	𝜎	PROPN
iajs-1807	40	75	,	,	PUNCT
iajs-1807	40	76	𝜎	𝜎	PROPN
iajs-1807	40	77	,	,	PUNCT
iajs-1807	40	78	𝜎	𝜎	PROPN
iajs-1807	40	79	is	be	AUX
iajs-1807	40	80	the	the	DET
iajs-1807	40	81	vector	vector	NOUN
iajs-1807	40	82	of	of	ADP
iajs-1807	40	83	the	the	DET
iajs-1807	40	84	pauli	pauli	PROPN
iajs-1807	40	85	matrices	matrix	NOUN
iajs-1807	40	86	.	.	PUNCT
iajs-1807	41	1	the	the	DET
iajs-1807	41	2	energy	energy	NOUN
iajs-1807	41	3	and	and	CCONJ
iajs-1807	41	4	position	position	NOUN
iajs-1807	41	5	dependent	dependent	ADJ
iajs-1807	41	6	𝛽	𝛽	PROPN
iajs-1807	41	7	𝐸	𝐸	PROPN
iajs-1807	41	8	,	,	PUNCT
iajs-1807	41	9	𝑟	𝑟	NOUN
iajs-1807	41	10	has	have	VERB
iajs-1807	41	11	the	the	DET
iajs-1807	41	12	form	form	NOUN
iajs-1807	41	13	𝛽	𝛽	PROPN
iajs-1807	41	14	𝐸	𝐸	PROPN
iajs-1807	41	15	,	,	PUNCT
iajs-1807	41	16	𝑟	𝑟	PRON
iajs-1807	41	17	𝑃	𝑃	VERB
iajs-1807	41	18	2	2	NUM
iajs-1807	41	19	1	1	NUM
iajs-1807	41	20	𝐸	𝐸	PROPN
iajs-1807	41	21	𝐸	𝐸	PROPN
iajs-1807	41	22	𝑟	𝑟	NOUN
iajs-1807	41	23	𝑉	𝑉	NOUN
iajs-1807	41	24	𝑟	𝑟	NOUN
iajs-1807	41	25	1	1	NUM
iajs-1807	41	26	𝐸	𝐸	PROPN
iajs-1807	41	27	𝐸	𝐸	PROPN
iajs-1807	41	28	𝑟	𝑟	NOUN
iajs-1807	41	29	∆	∆	PRON
iajs-1807	41	30	𝑟	𝑟	X
iajs-1807	41	31	𝑉	𝑉	NOUN
iajs-1807	41	32	𝑟	𝑟	NOUN
iajs-1807	41	33	5	5	NUM
iajs-1807	41	34	for	for	ADP
iajs-1807	41	35	those	those	DET
iajs-1807	41	36	quantum	quantum	NOUN
iajs-1807	41	37	ring	ring	NOUN
iajs-1807	41	38	systems	system	NOUN
iajs-1807	41	39	that	that	PRON
iajs-1807	41	40	have	have	VERB
iajs-1807	41	41	sharp	sharp	ADJ
iajs-1807	41	42	discontinuity	discontinuity	NOUN
iajs-1807	41	43	on	on	ADP
iajs-1807	41	44	the	the	DET
iajs-1807	41	45	conduction	conduction	NOUN
iajs-1807	41	46	band	band	NOUN
iajs-1807	41	47	interfaces	interface	NOUN
iajs-1807	41	48	between	between	ADP
iajs-1807	41	49	the	the	DET
iajs-1807	41	50	quantum	quantum	NOUN
iajs-1807	41	51	ring	ring	NOUN
iajs-1807	41	52	(	(	PUNCT
iajs-1807	41	53	"	"	PUNCT
iajs-1807	41	54	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	ADJ
iajs-1807	41	55	"	"	PUNCT
iajs-1807	41	56	material	material	NOUN
iajs-1807	41	57	1	1	NUM
iajs-1807	41	58	)	)	PUNCT
iajs-1807	41	59	and	and	CCONJ
iajs-1807	41	60	semiconductor	semiconductor	NOUN
iajs-1807	41	61	matrix	matrix	NOUN
iajs-1807	41	62	(	(	PUNCT
iajs-1807	41	63	"	"	PUNCT
iajs-1807	41	64	𝐺𝑎𝐴𝑠	𝐺𝑎𝐴𝑠	PROPN
iajs-1807	41	65	"	"	PUNCT
iajs-1807	41	66	material	material	NOUN
iajs-1807	41	67	2	2	NUM
iajs-1807	41	68	)	)	PUNCT
iajs-1807	41	69	,	,	PUNCT
iajs-1807	41	70	the	the	DET
iajs-1807	41	71	hard	hard	ADJ
iajs-1807	41	72	-	-	PUNCT
iajs-1807	41	73	wall	wall	NOUN
iajs-1807	41	74	confinement	confinement	PROPN
iajs-1807	41	75	potential	potential	NOUN
iajs-1807	41	76	is	be	AUX
iajs-1807	41	77	𝑉	𝑉	PROPN
iajs-1807	41	78	𝑟	𝑟	NOUN
iajs-1807	41	79	0	0	NUM
iajs-1807	41	80	,	,	PUNCT
iajs-1807	41	81	𝑟	𝑟	PRON
iajs-1807	41	82	∈	∈	NOUN
iajs-1807	41	83	material	material	NOUN
iajs-1807	41	84	1	1	NUM
iajs-1807	41	85	𝑉	𝑉	PROPN
iajs-1807	41	86	,	,	PUNCT
iajs-1807	41	87	𝑟	𝑟	X
iajs-1807	41	88	∈	∈	NOUN
iajs-1807	41	89	material	material	NOUN
iajs-1807	41	90	2	2	NUM
iajs-1807	41	91	,	,	PUNCT
iajs-1807	41	92	6	6	NUM
iajs-1807	41	93	where	where	SCONJ
iajs-1807	41	94	𝑉	𝑉	PROPN
iajs-1807	41	95	is	be	AUX
iajs-1807	41	96	the	the	DET
iajs-1807	41	97	structure	structure	NOUN
iajs-1807	41	98	band	band	NOUN
iajs-1807	41	99	offset	offset	VERB
iajs-1807	41	100	.	.	PUNCT
iajs-1807	42	1	combining	combine	VERB
iajs-1807	42	2	the	the	DET
iajs-1807	42	3	hamiltonian	hamiltonian	NOUN
iajs-1807	42	4	in	in	ADP
iajs-1807	42	5	equations	equation	NOUN
iajs-1807	42	6	(	(	PUNCT
iajs-1807	42	7	1	1	NUM
iajs-1807	42	8	)	)	PUNCT
iajs-1807	42	9	,	,	PUNCT
iajs-1807	42	10	(	(	PUNCT
iajs-1807	42	11	2	2	NUM
iajs-1807	42	12	)	)	PUNCT
iajs-1807	42	13	,	,	PUNCT
iajs-1807	42	14	and	and	CCONJ
iajs-1807	42	15	(	(	PUNCT
iajs-1807	42	16	4	4	NUM
iajs-1807	42	17	)	)	PUNCT
iajs-1807	42	18	,	,	PUNCT
iajs-1807	42	19	the	the	DET
iajs-1807	42	20	spin	spin	NOUN
iajs-1807	42	21	dependent	dependent	ADJ
iajs-1807	42	22	ben	ben	PROPN
iajs-1807	42	23	daniel	daniel	PROPN
iajs-1807	42	24	-	-	PUNCT
iajs-1807	42	25	duke	duke	PROPN
iajs-1807	42	26	boundary	boundary	ADJ
iajs-1807	42	27	conditions	condition	NOUN
iajs-1807	42	28	for	for	ADP
iajs-1807	42	29	the	the	DET
iajs-1807	42	30	electron	electron	NOUN
iajs-1807	42	31	wave	wave	NOUN
iajs-1807	42	32	function	function	NOUN
iajs-1807	42	33	ψ	ψ	ADP
iajs-1807	42	34	𝑟	𝑟	NOUN
iajs-1807	42	35	is	be	AUX
iajs-1807	42	36	written	write	VERB
iajs-1807	42	37	as	as	SCONJ
iajs-1807	42	38	follows	follow	VERB
iajs-1807	42	39	:	:	PUNCT
iajs-1807	42	40	ψ	ψ	X
iajs-1807	42	41	𝑟	𝑟	X
iajs-1807	42	42	ψ	ψ	X
iajs-1807	42	43	𝑟	𝑟	X
iajs-1807	42	44	ℏ	ℏ	PRON
iajs-1807	42	45	2𝑚	2𝑚	PROPN
iajs-1807	42	46	𝐸	𝐸	PROPN
iajs-1807	42	47	,	,	PUNCT
iajs-1807	42	48	𝑟	𝑟	X
iajs-1807	42	49	∇	∇	VERB
iajs-1807	42	50	𝑖∇𝛽	𝑖∇𝛽	PROPN
iajs-1807	42	51	𝐸	𝐸	PROPN
iajs-1807	42	52	,	,	PUNCT
iajs-1807	42	53	𝑟	𝑟	X
iajs-1807	42	54	𝜎	𝜎	X
iajs-1807	42	55	∇	∇	X
iajs-1807	42	56	ψ	ψ	X
iajs-1807	42	57	𝑟	𝑟	SYM
iajs-1807	42	58	c	c	PROPN
iajs-1807	42	59	7	7	NUM
iajs-1807	42	60	where	where	SCONJ
iajs-1807	42	61	𝑉	𝑉	PROPN
iajs-1807	42	62	is	be	AUX
iajs-1807	42	63	the	the	DET
iajs-1807	42	64	some	some	ADV
iajs-1807	42	65	constant	constant	ADJ
iajs-1807	42	66	,	,	PUNCT
iajs-1807	42	67	𝑟	𝑟	PRON
iajs-1807	42	68	denotes	denote	VERB
iajs-1807	42	69	the	the	DET
iajs-1807	42	70	position	position	NOUN
iajs-1807	42	71	of	of	ADP
iajs-1807	42	72	the	the	DET
iajs-1807	42	73	system	system	NOUN
iajs-1807	42	74	interface	interface	NOUN
iajs-1807	42	75	.	.	PUNCT
iajs-1807	43	1	note	note	NOUN
iajs-1807	43	2	(	(	PUNCT
iajs-1807	43	3	1	1	NUM
iajs-1807	43	4	):	):	PUNCT
iajs-1807	43	5	we	we	PRON
iajs-1807	43	6	note	note	VERB
iajs-1807	43	7	that	that	SCONJ
iajs-1807	43	8	the	the	DET
iajs-1807	43	9	expressions	expression	NOUN
iajs-1807	43	10	of	of	ADP
iajs-1807	43	11	electron	electron	NOUN
iajs-1807	43	12	effective	effective	ADJ
iajs-1807	43	13	mass	mass	NOUN
iajs-1807	43	14	in	in	ADP
iajs-1807	43	15	equation	equation	NOUN
iajs-1807	43	16	(	(	PUNCT
iajs-1807	43	17	3	3	NUM
iajs-1807	43	18	)	)	PUNCT
iajs-1807	43	19	,	,	PUNCT
iajs-1807	43	20	spin	spin	NOUN
iajs-1807	43	21	-	-	PUNCT
iajs-1807	43	22	orbit	orbit	NOUN
iajs-1807	43	23	coupling	coupling	NOUN
iajs-1807	43	24	parameter	parameter	NOUN
iajs-1807	43	25	in	in	ADP
iajs-1807	43	26	equation	equation	NOUN
iajs-1807	43	27	(	(	PUNCT
iajs-1807	43	28	5	5	NUM
iajs-1807	43	29	)	)	PUNCT
iajs-1807	43	30	,	,	PUNCT
iajs-1807	43	31	and	and	CCONJ
iajs-1807	43	32	the	the	DET
iajs-1807	43	33	equations	equation	NOUN
iajs-1807	43	34	of	of	ADP
iajs-1807	43	35	ben	ben	PROPN
iajs-1807	43	36	daniel	daniel	PROPN
iajs-1807	43	37	-	-	PUNCT
iajs-1807	43	38	duke	duke	PROPN
iajs-1807	43	39	boundary	boundary	ADJ
iajs-1807	43	40	condition	condition	NOUN
iajs-1807	43	41	in	in	ADP
iajs-1807	43	42	equation	equation	NOUN
iajs-1807	43	43	(	(	PUNCT
iajs-1807	43	44	7	7	X
iajs-1807	43	45	)	)	PUNCT
iajs-1807	43	46	are	be	AUX
iajs-1807	43	47	all	all	PRON
iajs-1807	43	48	energy	energy	NOUN
iajs-1807	43	49	and	and	CCONJ
iajs-1807	43	50	position	position	VERB
iajs-1807	43	51	dependent	dependent	ADJ
iajs-1807	43	52	relationships	relationship	NOUN
iajs-1807	43	53	in	in	ADP
iajs-1807	43	54	this	this	DET
iajs-1807	43	55	study	study	NOUN
iajs-1807	43	56	.	.	PUNCT
iajs-1807	44	1	2	2	X
iajs-1807	44	2	.	.	X
iajs-1807	44	3	finite	finite	PROPN
iajs-1807	44	4	element	element	PROPN
iajs-1807	44	5	method	method	NOUN
iajs-1807	44	6	dependence	dependence	NOUN
iajs-1807	44	7	of	of	ADP
iajs-1807	44	8	the	the	DET
iajs-1807	44	9	electron	electron	NOUN
iajs-1807	44	10	effective	effective	ADJ
iajs-1807	44	11	mass	mass	NOUN
iajs-1807	44	12	and	and	CCONJ
iajs-1807	44	13	spin	spin	NOUN
iajs-1807	44	14	–	–	PUNCT
iajs-1807	44	15	orbit	orbit	NOUN
iajs-1807	44	16	coupling	couple	VERB
iajs-1807	44	17	parameter	parameter	NOUN
iajs-1807	44	18	on	on	ADP
iajs-1807	44	19	each	each	DET
iajs-1807	44	20	energy	energy	NOUN
iajs-1807	44	21	state	state	NOUN
iajs-1807	44	22	results	result	NOUN
iajs-1807	44	23	in	in	ADP
iajs-1807	44	24	a	a	DET
iajs-1807	44	25	nonlinear	nonlinear	ADJ
iajs-1807	44	26	equation	equation	NOUN
iajs-1807	44	27	(	(	PUNCT
iajs-1807	44	28	9	9	NUM
iajs-1807	44	29	)	)	PUNCT
iajs-1807	44	30	and	and	CCONJ
iajs-1807	44	31	(	(	PUNCT
iajs-1807	44	32	10	10	NUM
iajs-1807	44	33	)	)	PUNCT
iajs-1807	44	34	.	.	PUNCT
iajs-1807	45	1	the	the	DET
iajs-1807	45	2	nonlinear	nonlinear	ADJ
iajs-1807	45	3	equations	equation	NOUN
iajs-1807	45	4	complicate	complicate	VERB
iajs-1807	45	5	the	the	DET
iajs-1807	45	6	process	process	NOUN
iajs-1807	45	7	of	of	ADP
iajs-1807	45	8	analytical	analytical	ADJ
iajs-1807	45	9	solution	solution	NOUN
iajs-1807	45	10	in	in	ADP
iajs-1807	45	11	the	the	DET
iajs-1807	45	12	explored	explore	VERB
iajs-1807	45	13	quantum	quantum	NOUN
iajs-1807	45	14	ring	ring	NOUN
iajs-1807	45	15	.	.	PUNCT
iajs-1807	46	1	therefore	therefore	ADV
iajs-1807	46	2	,	,	PUNCT
iajs-1807	46	3	the	the	DET
iajs-1807	46	4	numerical	numerical	ADJ
iajs-1807	46	5	approach	approach	NOUN
iajs-1807	46	6	to	to	ADP
iajs-1807	46	7	the	the	DET
iajs-1807	46	8	solution	solution	NOUN
iajs-1807	46	9	of	of	ADP
iajs-1807	46	10	the	the	DET
iajs-1807	46	11	nonlinear	nonlinear	ADJ
iajs-1807	46	12	equations	equation	NOUN
iajs-1807	46	13	is	be	AUX
iajs-1807	46	14	advanced	advance	VERB
iajs-1807	46	15	in	in	ADP
iajs-1807	46	16	the	the	DET
iajs-1807	46	17	calculation	calculation	NOUN
iajs-1807	46	18	of	of	ADP
iajs-1807	46	19	the	the	DET
iajs-1807	46	20	electronic	electronic	ADJ
iajs-1807	46	21	structure	structure	NOUN
iajs-1807	46	22	of	of	ADP
iajs-1807	46	23	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	46	24	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	ADJ
iajs-1807	46	25	quantum	quantum	NOUN
iajs-1807	46	26	rings	ring	NOUN
iajs-1807	46	27	.	.	PUNCT
iajs-1807	47	1	the	the	DET
iajs-1807	47	2	finite	finite	PROPN
iajs-1807	47	3	element	element	NOUN
iajs-1807	47	4	method	method	NOUN
iajs-1807	47	5	is	be	AUX
iajs-1807	47	6	applied	apply	VERB
iajs-1807	47	7	to	to	PART
iajs-1807	47	8	solve	solve	VERB
iajs-1807	47	9	the	the	DET
iajs-1807	47	10	above	above	ADJ
iajs-1807	47	11	problem	problem	NOUN
iajs-1807	47	12	for	for	ADP
iajs-1807	47	13	the	the	DET
iajs-1807	47	14	nanoscale	nanoscale	ADJ
iajs-1807	47	15	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	47	16	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	ADJ
iajs-1807	47	17	quantum	quantum	NOUN
iajs-1807	47	18	rings	ring	NOUN
iajs-1807	47	19	.	.	PUNCT
iajs-1807	48	1	energy	energy	NOUN
iajs-1807	48	2	states	state	NOUN
iajs-1807	48	3	and	and	CCONJ
iajs-1807	48	4	spin	spin	NOUN
iajs-1807	48	5	-	-	PUNCT
iajs-1807	48	6	splitting	splitting	NOUN
iajs-1807	48	7	are	be	AUX
iajs-1807	48	8	numerically	numerically	ADV
iajs-1807	48	9	calculated	calculate	VERB
iajs-1807	48	10	without	without	ADP
iajs-1807	48	11	any	any	DET
iajs-1807	48	12	fitting	fitting	ADJ
iajs-1807	48	13	parameters	parameter	NOUN
iajs-1807	48	14	.	.	PUNCT
iajs-1807	49	1	starting	start	VERB
iajs-1807	49	2	from	from	ADP
iajs-1807	49	3	a	a	DET
iajs-1807	49	4	given	give	VERB
iajs-1807	49	5	initial	initial	ADJ
iajs-1807	49	6	energy	energy	NOUN
iajs-1807	49	7	,	,	PUNCT
iajs-1807	49	8	the	the	DET
iajs-1807	49	9	finite	finite	PROPN
iajs-1807	49	10	element	element	NOUN
iajs-1807	49	11	method	method	NOUN
iajs-1807	49	12	globally	globally	ADV
iajs-1807	49	13	calculates	calculate	VERB
iajs-1807	49	14	all	all	DET
iajs-1807	49	15	bounded	bound	VERB
iajs-1807	49	16	energies	energy	NOUN
iajs-1807	49	17	for	for	ADP
iajs-1807	49	18	the	the	DET
iajs-1807	49	19	corresponding	corresponding	ADJ
iajs-1807	49	20	nonlinear	nonlinear	ADJ
iajs-1807	49	21	algebraic	algebraic	PROPN
iajs-1807	49	22	eigenvalue	eigenvalue	PROPN
iajs-1807	49	23	problem	problem	NOUN
iajs-1807	49	24	.	.	PUNCT
iajs-1807	50	1	a	a	DET
iajs-1807	50	2	computational	computational	ADJ
iajs-1807	50	3	procedure	procedure	NOUN
iajs-1807	50	4	of	of	ADP
iajs-1807	50	5	the	the	DET
iajs-1807	50	6	finite	finite	PROPN
iajs-1807	50	7	element	element	NOUN
iajs-1807	50	8	method	method	NOUN
iajs-1807	50	9	is	be	AUX
iajs-1807	50	10	shown	show	VERB
iajs-1807	50	11	below	below	ADP
iajs-1807	50	12	:	:	PUNCT
iajs-1807	50	13	ℏ	ℏ	PROPN
iajs-1807	50	14	2𝑚	2𝑚	NOUN
iajs-1807	50	15	𝐸	𝐸	PROPN
iajs-1807	50	16	𝜕	𝜕	PROPN
iajs-1807	50	17	𝜕𝑅	𝜕𝑅	PROPN
iajs-1807	50	18	𝜕	𝜕	PROPN
iajs-1807	50	19	𝑅𝜕𝑅	𝑅𝜕𝑅	PROPN
iajs-1807	50	20	𝜕	𝜕	PROPN
iajs-1807	50	21	𝜕𝑍	𝜕𝑍	PROPN
iajs-1807	50	22	𝑙	𝑙	PROPN
iajs-1807	50	23	𝑅	𝑅	PROPN
iajs-1807	50	24	𝜙	𝜙	PROPN
iajs-1807	50	25	𝑅	𝑅	PROPN
iajs-1807	50	26	,	,	PUNCT
iajs-1807	50	27	𝑍	𝑍	PROPN
iajs-1807	50	28	𝑉	𝑉	PROPN
iajs-1807	50	29	𝜙	𝜙	PROPN
iajs-1807	50	30	𝑅	𝑅	PROPN
iajs-1807	50	31	,	,	PUNCT
iajs-1807	50	32	𝑍	𝑍	PROPN
iajs-1807	50	33	𝐸𝜙	𝐸𝜙	PROPN
iajs-1807	50	34	𝑅	𝑅	PROPN
iajs-1807	50	35	,	,	PUNCT
iajs-1807	50	36	𝑍	𝑍	NOUN
iajs-1807	50	37	,	,	PUNCT
iajs-1807	50	38	∀	∀	X
iajs-1807	50	39	𝑅	𝑅	NOUN
iajs-1807	50	40	,	,	PUNCT
iajs-1807	50	41	𝑍	𝑍	PROPN
iajs-1807	50	42	∈	∈	NOUN
iajs-1807	50	43	𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙	𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙	ADJ
iajs-1807	50	44	𝑖	𝑖	ADP
iajs-1807	50	45	12	12	NUM
iajs-1807	50	46	where	where	SCONJ
iajs-1807	50	47	𝑖	𝑖	ADP
iajs-1807	50	48	1,2	1,2	NUM
iajs-1807	50	49	since	since	SCONJ
iajs-1807	50	50	the	the	DET
iajs-1807	50	51	cylindrical	cylindrical	NOUN
iajs-1807	50	52	is	be	AUX
iajs-1807	50	53	symmetry	symmetry	NOUN
iajs-1807	50	54	,	,	PUNCT
iajs-1807	50	55	𝑉	𝑉	PROPN
iajs-1807	50	56	𝑉	𝑉	PROPN
iajs-1807	50	57	𝑅	𝑅	PROPN
iajs-1807	50	58	,	,	PUNCT
iajs-1807	50	59	𝑍	𝑍	PROPN
iajs-1807	50	60	,	,	PUNCT
iajs-1807	50	61	and	and	CCONJ
iajs-1807	50	62	𝜙	𝜙	PRON
iajs-1807	50	63	𝑢	𝑢	PROPN
iajs-1807	50	64	𝑅	𝑅	PROPN
iajs-1807	50	65	,	,	PUNCT
iajs-1807	50	66	𝑍	𝑍	VERB
iajs-1807	50	67	𝑒	𝑒	PROPN
iajs-1807	50	68	,	,	PUNCT
iajs-1807	50	69	where	where	SCONJ
iajs-1807	50	70	𝑙	𝑙	PROPN
iajs-1807	50	71	is	be	AUX
iajs-1807	50	72	an	an	DET
iajs-1807	50	73	integer	integer	NOUN
iajs-1807	50	74	.	.	PUNCT
iajs-1807	51	1	equation	equation	NOUN
iajs-1807	51	2	(	(	PUNCT
iajs-1807	51	3	12	12	NUM
iajs-1807	51	4	)	)	PUNCT
iajs-1807	51	5	becomes	become	VERB
iajs-1807	51	6	ihsciconf	ihsciconf	ADJ
iajs-1807	51	7	2017	2017	NUM
iajs-1807	51	8	special	special	ADJ
iajs-1807	51	9	issue	issue	NOUN
iajs-1807	51	10	ibn	ibn	PROPN
iajs-1807	51	11	al	al	PROPN
iajs-1807	51	12	-	-	PUNCT
iajs-1807	51	13	haitham	haitham	PROPN
iajs-1807	51	14	journal	journal	PROPN
iajs-1807	51	15	for	for	ADP
iajs-1807	51	16	pure	pure	ADJ
iajs-1807	51	17	and	and	CCONJ
iajs-1807	51	18	applied	apply	VERB
iajs-1807	51	19	science	science	NOUN
iajs-1807	51	20	https://doi.org/	https://doi.org/	NOUN
iajs-1807	51	21	10.30526/2017.ihsciconf.1807	10.30526/2017.ihsciconf.1807	ADJ
iajs-1807	51	22	for	for	ADP
iajs-1807	51	23	more	more	ADJ
iajs-1807	51	24	information	information	NOUN
iajs-1807	51	25	about	about	ADP
iajs-1807	51	26	the	the	DET
iajs-1807	51	27	conference	conference	NOUN
iajs-1807	51	28	please	please	INTJ
iajs-1807	51	29	visit	visit	VERB
iajs-1807	51	30	the	the	DET
iajs-1807	51	31	websites	website	NOUN
iajs-1807	51	32	:	:	PUNCT
iajs-1807	51	33	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1807	51	34	  	  	SPACE
iajs-1807	51	35	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1807	51	36	   	   	SPACE
iajs-1807	51	37	mathematics	mathematic	NOUN
iajs-1807	51	38	|347	|347	NOUN
iajs-1807	51	39	    	    	SPACE
iajs-1807	51	40	ℏ	ℏ	PROPN
iajs-1807	51	41	2𝑚	2𝑚	NOUN
iajs-1807	51	42	𝐸	𝐸	NOUN
iajs-1807	51	43	1	1	NUM
iajs-1807	51	44	𝑅	𝑅	PROPN
iajs-1807	51	45	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	51	46	𝜕𝑅	𝜕𝑅	PROPN
iajs-1807	51	47	𝜕	𝜕	NOUN
iajs-1807	51	48	𝜕𝑅	𝜕𝑅	PROPN
iajs-1807	51	49	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	51	50	𝜕𝑅	𝜕𝑅	NOUN
iajs-1807	51	51	𝑙	𝑙	X
iajs-1807	51	52	𝑅	𝑅	PROPN
iajs-1807	51	53	𝑢	𝑢	PROPN
iajs-1807	51	54	𝜕	𝜕	PROPN
iajs-1807	51	55	𝜕𝑍	𝜕𝑍	PROPN
iajs-1807	51	56	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	51	57	𝜕𝑍	𝜕𝑍	NOUN
iajs-1807	51	58	𝑉𝑢	𝑉𝑢	PROPN
iajs-1807	51	59	𝐸𝑢	𝐸𝑢	PROPN
iajs-1807	51	60	13	13	NUM
iajs-1807	51	61	the	the	DET
iajs-1807	51	62	electron	electron	NOUN
iajs-1807	51	63	energy	energy	NOUN
iajs-1807	51	64	spectra	spectra	NOUN
iajs-1807	51	65	for	for	ADP
iajs-1807	51	66	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	51	67	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	ADJ
iajs-1807	51	68	quantum	quantum	NOUN
iajs-1807	51	69	rings	ring	NOUN
iajs-1807	51	70	the	the	DET
iajs-1807	51	71	semiconductor	semiconductor	NOUN
iajs-1807	51	72	band	band	NOUN
iajs-1807	51	73	structure	structure	NOUN
iajs-1807	51	74	governing	govern	VERB
iajs-1807	51	75	physical	physical	ADJ
iajs-1807	51	76	process	process	NOUN
iajs-1807	51	77	in	in	ADP
iajs-1807	51	78	a	a	DET
iajs-1807	51	79	ring	ring	NOUN
iajs-1807	51	80	nanoscale	nanoscale	NOUN
iajs-1807	51	81	are	be	AUX
iajs-1807	51	82	described	describe	VERB
iajs-1807	51	83	in	in	ADP
iajs-1807	51	84	terms	term	NOUN
iajs-1807	51	85	of	of	ADP
iajs-1807	51	86	cylindrical	cylindrical	ADJ
iajs-1807	51	87	coordinates	coordinate	NOUN
iajs-1807	51	88	.	.	PUNCT
iajs-1807	52	1	when	when	SCONJ
iajs-1807	52	2	the	the	DET
iajs-1807	52	3	geometry	geometry	NOUN
iajs-1807	52	4	,	,	PUNCT
iajs-1807	52	5	loading	loading	NOUN
iajs-1807	52	6	,	,	PUNCT
iajs-1807	52	7	and	and	CCONJ
iajs-1807	52	8	boundary	boundary	ADJ
iajs-1807	52	9	conditions	condition	NOUN
iajs-1807	52	10	are	be	AUX
iajs-1807	52	11	independent	independent	ADJ
iajs-1807	52	12	of	of	ADP
iajs-1807	52	13	the	the	DET
iajs-1807	52	14	circumferential	circumferential	ADJ
iajs-1807	52	15	direction	direction	NOUN
iajs-1807	52	16	(	(	PUNCT
iajs-1807	52	17	𝜙	𝜙	NOUN
iajs-1807	52	18	-coordinate	-coordinate	NOUN
iajs-1807	52	19	)	)	PUNCT
iajs-1807	52	20	,	,	PUNCT
iajs-1807	52	21	the	the	DET
iajs-1807	52	22	electron	electron	NOUN
iajs-1807	52	23	energy	energy	NOUN
iajs-1807	52	24	spectra	spectra	NOUN
iajs-1807	52	25	for	for	ADP
iajs-1807	52	26	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	52	27	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	ADJ
iajs-1807	52	28	quantum	quantum	NOUN
iajs-1807	52	29	rings	ring	NOUN
iajs-1807	52	30	of	of	ADP
iajs-1807	52	31	the	the	DET
iajs-1807	52	32	semiconductor	semiconductor	NOUN
iajs-1807	52	33	band	band	NOUN
iajs-1807	52	34	structure	structure	NOUN
iajs-1807	52	35	equation	equation	NOUN
iajs-1807	52	36	become	become	VERB
iajs-1807	52	37	twodimensional	twodimensional	ADJ
iajs-1807	52	38	in	in	ADP
iajs-1807	52	39	terms	term	NOUN
iajs-1807	52	40	of	of	ADP
iajs-1807	52	41	𝑅	𝑅	PROPN
iajs-1807	52	42	and	and	CCONJ
iajs-1807	52	43	𝑍.	𝑍.	PROPN
iajs-1807	52	44	2.1	2.1	NUM
iajs-1807	52	45	weak	weak	ADJ
iajs-1807	52	46	form	form	NOUN
iajs-1807	52	47	assume	assume	VERB
iajs-1807	52	48	that	that	SCONJ
iajs-1807	52	49	ω	ω	PROPN
iajs-1807	52	50	is	be	AUX
iajs-1807	52	51	a	a	DET
iajs-1807	52	52	typical	typical	ADJ
iajs-1807	52	53	element	element	NOUN
iajs-1807	52	54	the	the	DET
iajs-1807	52	55	piecewise	piecewise	NOUN
iajs-1807	52	56	linear	linear	NOUN
iajs-1807	52	57	function	function	NOUN
iajs-1807	52	58	of	of	ADP
iajs-1807	52	59	the	the	DET
iajs-1807	52	60	finite	finite	PROPN
iajs-1807	52	61	element	element	NOUN
iajs-1807	52	62	mesh	mesh	NOUN
iajs-1807	52	63	,	,	PUNCT
iajs-1807	52	64	and	and	CCONJ
iajs-1807	52	65	we	we	PRON
iajs-1807	52	66	develop	develop	VERB
iajs-1807	52	67	the	the	DET
iajs-1807	52	68	finite	finite	PROPN
iajs-1807	52	69	element	element	NOUN
iajs-1807	52	70	model	model	NOUN
iajs-1807	52	71	of	of	ADP
iajs-1807	52	72	equation	equation	NOUN
iajs-1807	52	73	(	(	PUNCT
iajs-1807	52	74	13	13	NUM
iajs-1807	52	75	)	)	PUNCT
iajs-1807	52	76	over	over	ADP
iajs-1807	52	77	ω	ω	PROPN
iajs-1807	52	78	.	.	PUNCT
iajs-1807	53	1	various	various	ADJ
iajs-1807	53	2	twodimensional	twodimensional	ADJ
iajs-1807	53	3	elements	element	NOUN
iajs-1807	53	4	will	will	AUX
iajs-1807	53	5	be	be	AUX
iajs-1807	53	6	discussed	discuss	VERB
iajs-1807	53	7	in	in	ADP
iajs-1807	53	8	the	the	DET
iajs-1807	53	9	sequel	sequel	NOUN
iajs-1807	53	10	.	.	PUNCT
iajs-1807	54	1	there	there	PRON
iajs-1807	54	2	are	be	VERB
iajs-1807	54	3	three	three	NUM
iajs-1807	54	4	steps	step	NOUN
iajs-1807	54	5	in	in	ADP
iajs-1807	54	6	the	the	DET
iajs-1807	54	7	development	development	NOUN
iajs-1807	54	8	of	of	ADP
iajs-1807	54	9	the	the	DET
iajs-1807	54	10	weak	weak	ADJ
iajs-1807	54	11	form	form	NOUN
iajs-1807	54	12	of	of	ADP
iajs-1807	54	13	equation	equation	NOUN
iajs-1807	54	14	(	(	PUNCT
iajs-1807	54	15	13	13	NUM
iajs-1807	54	16	)	)	PUNCT
iajs-1807	54	17	over	over	ADP
iajs-1807	54	18	the	the	DET
iajs-1807	54	19	typical	typical	ADJ
iajs-1807	54	20	element	element	PROPN
iajs-1807	54	21	ω	ω	PROPN
iajs-1807	54	22	.	.	PUNCT
iajs-1807	55	1	the	the	DET
iajs-1807	55	2	first	first	ADJ
iajs-1807	55	3	step	step	NOUN
iajs-1807	55	4	is	be	AUX
iajs-1807	55	5	formulated	formulate	VERB
iajs-1807	55	6	equation	equation	NOUN
iajs-1807	55	7	(	(	PUNCT
iajs-1807	55	8	13	13	NUM
iajs-1807	55	9	)	)	PUNCT
iajs-1807	55	10	by	by	ADP
iajs-1807	55	11	the	the	DET
iajs-1807	55	12	following	follow	VERB
iajs-1807	55	13	weak	weak	ADJ
iajs-1807	55	14	form	form	NOUN
iajs-1807	55	15	.	.	PUNCT
iajs-1807	55	16	0	0	NUM
iajs-1807	56	1	ℏ	ℏ	PROPN
iajs-1807	56	2	2	2	NUM
iajs-1807	56	3	𝑤	𝑤	ADP
iajs-1807	56	4	1	1	NUM
iajs-1807	56	5	𝑚	𝑚	DET
iajs-1807	56	6	𝐸	𝐸	PROPN
iajs-1807	56	7	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	56	8	𝜕𝑅	𝜕𝑅	VERB
iajs-1807	56	9	𝑤𝑅	𝑤𝑅	VERB
iajs-1807	56	10	𝜕𝐹	𝜕𝐹	NOUN
iajs-1807	56	11	𝜕𝑅	𝜕𝑅	X
iajs-1807	56	12	𝑙	𝑙	X
iajs-1807	56	13	𝑚	𝑚	ADP
iajs-1807	56	14	𝐸	𝐸	PROPN
iajs-1807	56	15	𝑅	𝑅	PROPN
iajs-1807	56	16	𝑤𝑢	𝑤𝑢	X
iajs-1807	56	17	𝑤𝑅	𝑤𝑅	X
iajs-1807	56	18	𝜕𝐹	𝜕𝐹	PRON
iajs-1807	56	19	𝜕𝑍	𝜕𝑍	PROPN
iajs-1807	56	20	𝑉𝑤𝑅𝑢	𝑉𝑤𝑅𝑢	PROPN
iajs-1807	56	21	ω	ω	PROPN
iajs-1807	56	22	𝐸𝑤𝑅𝑢	𝐸𝑤𝑅𝑢	PROPN
iajs-1807	56	23	𝑑𝑅𝑑𝑍	𝑑𝑅𝑑𝑍	VERB
iajs-1807	56	24	12	12	NUM
iajs-1807	56	25	where	where	SCONJ
iajs-1807	56	26	𝐹	𝐹	PROPN
iajs-1807	56	27	1	1	NUM
iajs-1807	56	28	𝑚	𝑚	PRON
iajs-1807	56	29	𝐸	𝐸	PROPN
iajs-1807	56	30	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	57	1	𝜕𝑅	𝜕𝑅	PROPN
iajs-1807	58	1	and	and	CCONJ
iajs-1807	58	2	𝐹	𝐹	PROPN
iajs-1807	58	3	1	1	NUM
iajs-1807	58	4	𝑚	𝑚	PRON
iajs-1807	58	5	𝐸	𝐸	PROPN
iajs-1807	58	6	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	58	7	𝜕𝑍	𝜕𝑍	NOUN
iajs-1807	58	8	in	in	ADP
iajs-1807	58	9	the	the	DET
iajs-1807	58	10	second	second	ADJ
iajs-1807	58	11	step	step	NOUN
iajs-1807	58	12	,	,	PUNCT
iajs-1807	58	13	we	we	PRON
iajs-1807	58	14	note	note	VERB
iajs-1807	58	15	the	the	DET
iajs-1807	58	16	identities	identity	NOUN
iajs-1807	58	17	𝑤𝑅	𝑤𝑅	VERB
iajs-1807	58	18	𝜕𝐹	𝜕𝐹	NOUN
iajs-1807	58	19	𝜕𝑅	𝜕𝑅	X
iajs-1807	58	20	𝑅	𝑅	NOUN
iajs-1807	58	21	𝜕𝑤	𝜕𝑤	VERB
iajs-1807	58	22	𝜕𝑅	𝜕𝑅	PROPN
iajs-1807	58	23	𝐹	𝐹	PROPN
iajs-1807	58	24	𝑅	𝑅	PROPN
iajs-1807	58	25	𝜕	𝜕	PROPN
iajs-1807	58	26	𝜕𝑅	𝜕𝑅	PROPN
iajs-1807	58	27	𝑤𝐹	𝑤𝐹	NOUN
iajs-1807	58	28	15a	15a	NOUN
iajs-1807	58	29	𝑤𝑅	𝑤𝑅	VERB
iajs-1807	58	30	𝜕𝐹	𝜕𝐹	VERB
iajs-1807	58	31	𝜕𝑍	𝜕𝑍	NOUN
iajs-1807	58	32	𝑅	𝑅	PROPN
iajs-1807	58	33	𝜕𝑤	𝜕𝑤	VERB
iajs-1807	58	34	𝜕𝑍	𝜕𝑍	NOUN
iajs-1807	58	35	𝐹	𝐹	PROPN
iajs-1807	58	36	𝑅	𝑅	PROPN
iajs-1807	58	37	𝜕	𝜕	PROPN
iajs-1807	58	38	𝜕𝑍	𝜕𝑍	PROPN
iajs-1807	58	39	𝑤𝐹	𝑤𝐹	NOUN
iajs-1807	58	40	15b	15b	NOUN
iajs-1807	58	41	next	next	ADV
iajs-1807	58	42	,	,	PUNCT
iajs-1807	58	43	using	use	VERB
iajs-1807	58	44	equation	equation	NOUN
iajs-1807	58	45	(	(	PUNCT
iajs-1807	58	46	15a	15a	NOUN
iajs-1807	58	47	)	)	PUNCT
iajs-1807	58	48	and	and	CCONJ
iajs-1807	58	49	equation	equation	NOUN
iajs-1807	58	50	(	(	PUNCT
iajs-1807	58	51	15b	15b	NOUN
iajs-1807	58	52	)	)	PUNCT
iajs-1807	58	53	in	in	ADP
iajs-1807	58	54	the	the	DET
iajs-1807	58	55	equation	equation	NOUN
iajs-1807	58	56	(	(	PUNCT
iajs-1807	58	57	14	14	NUM
iajs-1807	58	58	)	)	PUNCT
iajs-1807	58	59	then	then	ADV
iajs-1807	58	60	applying	apply	VERB
iajs-1807	58	61	the	the	DET
iajs-1807	58	62	divergence	divergence	NOUN
iajs-1807	58	63	theorem	theorem	NOUN
iajs-1807	58	64	,	,	PUNCT
iajs-1807	58	65	we	we	PRON
iajs-1807	58	66	obtain	obtain	VERB
iajs-1807	58	67	ihsciconf	ihsciconf	NOUN
iajs-1807	58	68	2017	2017	NUM
iajs-1807	58	69	special	special	ADJ
iajs-1807	58	70	issue	issue	NOUN
iajs-1807	58	71	ibn	ibn	PROPN
iajs-1807	58	72	al	al	PROPN
iajs-1807	58	73	-	-	PUNCT
iajs-1807	58	74	haitham	haitham	PROPN
iajs-1807	58	75	journal	journal	PROPN
iajs-1807	58	76	for	for	ADP
iajs-1807	58	77	pure	pure	ADJ
iajs-1807	58	78	and	and	CCONJ
iajs-1807	58	79	applied	apply	VERB
iajs-1807	58	80	science	science	NOUN
iajs-1807	58	81	https://doi.org/	https://doi.org/	NOUN
iajs-1807	58	82	10.30526/2017.ihsciconf.1807	10.30526/2017.ihsciconf.1807	ADJ
iajs-1807	58	83	for	for	ADP
iajs-1807	58	84	more	more	ADJ
iajs-1807	58	85	information	information	NOUN
iajs-1807	58	86	about	about	ADP
iajs-1807	58	87	the	the	DET
iajs-1807	58	88	conference	conference	NOUN
iajs-1807	58	89	please	please	INTJ
iajs-1807	58	90	visit	visit	VERB
iajs-1807	58	91	the	the	DET
iajs-1807	58	92	websites	website	NOUN
iajs-1807	58	93	:	:	PUNCT
iajs-1807	58	94	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1807	58	95	  	  	SPACE
iajs-1807	58	96	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1807	58	97	   	   	SPACE
iajs-1807	58	98	mathematics	mathematic	NOUN
iajs-1807	58	99	|348	|348	ADP
iajs-1807	58	100	    	    	SPACE
iajs-1807	58	101	0	0	NUM
iajs-1807	59	1	ℏ	ℏ	PROPN
iajs-1807	59	2	2𝑚	2𝑚	NOUN
iajs-1807	59	3	𝑤	𝑤	ADP
iajs-1807	59	4	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	59	5	𝜕𝑅	𝜕𝑅	NOUN
iajs-1807	59	6	ℏ	ℏ	NOUN
iajs-1807	59	7	2	2	NUM
iajs-1807	59	8	𝑅	𝑅	PROPN
iajs-1807	59	9	𝜕𝑤	𝜕𝑤	NOUN
iajs-1807	59	10	𝜕𝑅	𝜕𝑅	NOUN
iajs-1807	59	11	1	1	NUM
iajs-1807	59	12	𝑚	𝑚	ADP
iajs-1807	59	13	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	59	14	𝜕𝑅	𝜕𝑅	X
iajs-1807	59	15	ℏ	ℏ	NOUN
iajs-1807	59	16	𝐿	𝐿	NOUN
iajs-1807	59	17	2𝑚	2𝑚	NOUN
iajs-1807	59	18	𝑅	𝑅	PROPN
iajs-1807	59	19	𝑤𝑢	𝑤𝑢	NOUN
iajs-1807	59	20	ℏ	ℏ	PROPN
iajs-1807	59	21	2	2	NUM
iajs-1807	59	22	𝑅	𝑅	NOUN
iajs-1807	59	23	𝜕𝑤	𝜕𝑤	NOUN
iajs-1807	59	24	𝜕𝓏	𝜕𝓏	NOUN
iajs-1807	59	25	1	1	NUM
iajs-1807	59	26	𝑚	𝑚	PART
iajs-1807	59	27	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	59	28	𝜕𝑍	𝜕𝑍	NOUN
iajs-1807	59	29	𝑤𝑅𝑉𝑢	𝑤𝑅𝑉𝑢	CCONJ
iajs-1807	59	30	ω	ω	NOUN
iajs-1807	59	31	𝑤𝑅𝐸𝑢	𝑤𝑅𝐸𝑢	CCONJ
iajs-1807	59	32	𝑑𝑅𝑑𝑍	𝑑𝑅𝑑𝑍	NOUN
iajs-1807	59	33	𝑤	𝑤	ADP
iajs-1807	59	34	𝑛	𝑛	DET
iajs-1807	59	35	1	1	NUM
iajs-1807	59	36	𝑚	𝑚	NOUN
iajs-1807	59	37	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	59	38	𝜕𝑍	𝜕𝑍	NOUN
iajs-1807	59	39	𝑛	𝑛	PRON
iajs-1807	59	40	𝑅	𝑅	PROPN
iajs-1807	59	41	𝑚	𝑚	PROPN
iajs-1807	59	42	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	59	43	𝜕𝑅	𝜕𝑅	NOUN
iajs-1807	59	44	𝑑𝑠	𝑑𝑠	NOUN
iajs-1807	59	45	16	16	NUM
iajs-1807	59	46	where	where	SCONJ
iajs-1807	59	47	𝑛	𝑛	DET
iajs-1807	59	48	𝑛	𝑛	PROPN
iajs-1807	59	49	,	,	PUNCT
iajs-1807	59	50	𝑛	𝑛	PROPN
iajs-1807	59	51	is	be	AUX
iajs-1807	59	52	an	an	DET
iajs-1807	59	53	outer	outer	ADJ
iajs-1807	59	54	unite	unite	VERB
iajs-1807	59	55	vector	vector	NOUN
iajs-1807	59	56	normal	normal	ADJ
iajs-1807	59	57	on	on	ADP
iajs-1807	59	58	γ	γ	NOUN
iajs-1807	59	59	and	and	CCONJ
iajs-1807	59	60	𝑑𝑠	𝑑𝑠	NOUN
iajs-1807	59	61	is	be	AUX
iajs-1807	59	62	the	the	DET
iajs-1807	59	63	length	length	NOUN
iajs-1807	59	64	of	of	ADP
iajs-1807	59	65	an	an	DET
iajs-1807	59	66	infinitesimal	infinitesimal	ADJ
iajs-1807	59	67	line	line	NOUN
iajs-1807	59	68	element	element	NOUN
iajs-1807	59	69	along	along	ADP
iajs-1807	59	70	the	the	DET
iajs-1807	59	71	boundary	boundary	NOUN
iajs-1807	59	72	.	.	PUNCT
iajs-1807	60	1	from	from	ADP
iajs-1807	60	2	an	an	DET
iajs-1807	60	3	inspection	inspection	NOUN
iajs-1807	60	4	of	of	ADP
iajs-1807	60	5	the	the	DET
iajs-1807	60	6	boundary	boundary	ADJ
iajs-1807	60	7	integral	integral	NOUN
iajs-1807	60	8	in	in	ADP
iajs-1807	60	9	(	(	PUNCT
iajs-1807	60	10	16	16	NUM
iajs-1807	60	11	)	)	PUNCT
iajs-1807	60	12	,	,	PUNCT
iajs-1807	60	13	we	we	PRON
iajs-1807	60	14	note	note	VERB
iajs-1807	60	15	that	that	SCONJ
iajs-1807	60	16	the	the	DET
iajs-1807	60	17	specification	specification	NOUN
iajs-1807	60	18	of	of	ADP
iajs-1807	60	19	𝑢	𝑢	PRON
iajs-1807	60	20	constitutes	constitute	VERB
iajs-1807	60	21	the	the	DET
iajs-1807	60	22	essential	essential	ADJ
iajs-1807	60	23	boundary	boundary	ADJ
iajs-1807	60	24	condition	condition	NOUN
iajs-1807	60	25	,	,	PUNCT
iajs-1807	60	26	and	and	CCONJ
iajs-1807	60	27	hence	hence	ADV
iajs-1807	60	28	𝑢	𝑢	PRON
iajs-1807	60	29	is	be	AUX
iajs-1807	60	30	the	the	DET
iajs-1807	60	31	primary	primary	ADJ
iajs-1807	60	32	variable	variable	NOUN
iajs-1807	60	33	.	.	PUNCT
iajs-1807	61	1	the	the	DET
iajs-1807	61	2	specification	specification	NOUN
iajs-1807	61	3	of	of	ADP
iajs-1807	61	4	the	the	DET
iajs-1807	61	5	coefficient	coefficient	NOUN
iajs-1807	61	6	of	of	ADP
iajs-1807	61	7	the	the	DET
iajs-1807	61	8	weight	weight	NOUN
iajs-1807	61	9	function	function	NOUN
iajs-1807	61	10	in	in	ADP
iajs-1807	61	11	the	the	DET
iajs-1807	61	12	boundary	boundary	ADJ
iajs-1807	61	13	expression	expression	NOUN
iajs-1807	61	14	,	,	PUNCT
iajs-1807	61	15	i.e.	i.e.	X
iajs-1807	61	16	we	we	PRON
iajs-1807	61	17	can	can	AUX
iajs-1807	61	18	let	let	VERB
iajs-1807	61	19	𝑑	𝑑	PROPN
iajs-1807	61	20	≡	≡	PROPN
iajs-1807	61	21	𝑛	𝑛	ADP
iajs-1807	61	22	1	1	NUM
iajs-1807	61	23	𝑚	𝑚	X
iajs-1807	61	24	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	61	25	𝜕𝑍	𝜕𝑍	NOUN
iajs-1807	61	26	𝑛	𝑛	PRON
iajs-1807	61	27	𝑅	𝑅	PROPN
iajs-1807	61	28	𝑚	𝑚	PROPN
iajs-1807	61	29	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	61	30	𝜕𝑅	𝜕𝑅	PROPN
iajs-1807	61	31	17	17	NUM
iajs-1807	61	32	the	the	DET
iajs-1807	61	33	third	third	ADJ
iajs-1807	61	34	and	and	CCONJ
iajs-1807	61	35	last	last	ADJ
iajs-1807	61	36	step	step	NOUN
iajs-1807	61	37	of	of	ADP
iajs-1807	61	38	the	the	DET
iajs-1807	61	39	formulation	formulation	NOUN
iajs-1807	61	40	is	be	AUX
iajs-1807	61	41	to	to	PART
iajs-1807	61	42	substitute	substitute	VERB
iajs-1807	61	43	the	the	DET
iajs-1807	61	44	definition	definition	NOUN
iajs-1807	61	45	(	(	PUNCT
iajs-1807	61	46	17	17	NUM
iajs-1807	61	47	)	)	PUNCT
iajs-1807	61	48	in	in	ADP
iajs-1807	61	49	(	(	PUNCT
iajs-1807	61	50	16	16	NUM
iajs-1807	61	51	)	)	PUNCT
iajs-1807	61	52	and	and	CCONJ
iajs-1807	61	53	write	write	VERB
iajs-1807	61	54	the	the	DET
iajs-1807	61	55	weak	weak	ADJ
iajs-1807	61	56	form	form	NOUN
iajs-1807	61	57	of	of	ADP
iajs-1807	61	58	(	(	PUNCT
iajs-1807	61	59	13	13	NUM
iajs-1807	61	60	)	)	PUNCT
iajs-1807	61	61	as	as	ADP
iajs-1807	61	62	0	0	NUM
iajs-1807	61	63	ℏ	ℏ	PROPN
iajs-1807	61	64	2𝑚	2𝑚	NOUN
iajs-1807	62	1	𝑤	𝑤	ADP
iajs-1807	62	2	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	62	3	𝜕𝑅	𝜕𝑅	NOUN
iajs-1807	62	4	ℏ	ℏ	NOUN
iajs-1807	62	5	2	2	NUM
iajs-1807	62	6	𝑅	𝑅	PROPN
iajs-1807	62	7	𝜕𝑤	𝜕𝑤	NOUN
iajs-1807	62	8	𝜕𝑅	𝜕𝑅	NOUN
iajs-1807	62	9	1	1	NUM
iajs-1807	62	10	𝑚	𝑚	ADP
iajs-1807	62	11	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	62	12	𝜕𝑅	𝜕𝑅	X
iajs-1807	62	13	ℏ	ℏ	NOUN
iajs-1807	62	14	𝐿	𝐿	NOUN
iajs-1807	62	15	2𝑚	2𝑚	NOUN
iajs-1807	62	16	𝑅	𝑅	PROPN
iajs-1807	62	17	𝑤𝑢	𝑤𝑢	NOUN
iajs-1807	62	18	ℏ	ℏ	PROPN
iajs-1807	62	19	2	2	NUM
iajs-1807	62	20	𝑟	𝑟	NOUN
iajs-1807	62	21	𝜕𝑤	𝜕𝑤	VERB
iajs-1807	62	22	𝜕𝑍	𝜕𝑍	NOUN
iajs-1807	62	23	1	1	NUM
iajs-1807	62	24	𝑚	𝑚	PRON
iajs-1807	62	25	𝜕𝑢	𝜕𝑢	NOUN
iajs-1807	62	26	𝜕𝑍	𝜕𝑍	NOUN
iajs-1807	62	27	𝑤𝑟𝑉𝑢	𝑤𝑟𝑉𝑢	PROPN
iajs-1807	62	28	ω	ω	NOUN
iajs-1807	62	29	𝑤𝑟𝐸𝑢	𝑤𝑟𝐸𝑢	PRON
iajs-1807	62	30	𝑑𝑅𝑑𝑍	𝑑𝑅𝑑𝑍	VERB
iajs-1807	62	31	𝑤𝑑	𝑤𝑑	ADP
iajs-1807	62	32	𝑑𝑠	𝑑𝑠	ADP
iajs-1807	62	33	18	18	NUM
iajs-1807	62	34	now	now	ADV
iajs-1807	62	35	,	,	PUNCT
iajs-1807	62	36	𝑢	𝑢	PROPN
iajs-1807	62	37	𝑅	𝑅	PROPN
iajs-1807	62	38	,	,	PUNCT
iajs-1807	62	39	𝑍	𝑍	PROPN
iajs-1807	62	40	is	be	AUX
iajs-1807	62	41	approximated	approximate	VERB
iajs-1807	62	42	over	over	ADP
iajs-1807	62	43	a	a	DET
iajs-1807	62	44	typical	typical	ADJ
iajs-1807	62	45	finite	finite	PROPN
iajs-1807	62	46	element	element	PROPN
iajs-1807	62	47	ω	ω	PROPN
iajs-1807	62	48	by	by	ADP
iajs-1807	62	49	the	the	DET
iajs-1807	62	50	expression	expression	NOUN
iajs-1807	62	51	𝑢	𝑢	PROPN
iajs-1807	62	52	𝑅	𝑅	PROPN
iajs-1807	62	53	,	,	PUNCT
iajs-1807	62	54	𝑍	𝑍	VERB
iajs-1807	62	55	𝑢	𝑢	PROPN
iajs-1807	62	56	𝑅	𝑅	PROPN
iajs-1807	62	57	,	,	PUNCT
iajs-1807	62	58	𝑍	𝑍	VERB
iajs-1807	62	59	𝑢	𝑢	PROPN
iajs-1807	62	60	𝜓	𝜓	PROPN
iajs-1807	62	61	𝑅	𝑅	PROPN
iajs-1807	62	62	,	,	PUNCT
iajs-1807	62	63	𝑍	𝑍	PROPN
iajs-1807	62	64	19	19	NUM
iajs-1807	62	65	where	where	SCONJ
iajs-1807	62	66	𝑢	𝑢	PROPN
iajs-1807	62	67	𝑅	𝑅	PROPN
iajs-1807	62	68	,	,	PUNCT
iajs-1807	62	69	𝑍	𝑍	PROPN
iajs-1807	62	70	is	be	AUX
iajs-1807	62	71	the	the	DET
iajs-1807	62	72	value	value	NOUN
iajs-1807	62	73	of	of	ADP
iajs-1807	62	74	𝑢	𝑢	PROPN
iajs-1807	62	75	𝑅	𝑅	PROPN
iajs-1807	62	76	,	,	PUNCT
iajs-1807	62	77	𝑍	𝑍	PROPN
iajs-1807	62	78	at	at	ADP
iajs-1807	62	79	the	the	DET
iajs-1807	62	80	𝑗	𝑗	PROPN
iajs-1807	62	81	node	node	PROPN
iajs-1807	62	82	𝑅	𝑅	PROPN
iajs-1807	62	83	,	,	PUNCT
iajs-1807	62	84	𝑍	𝑍	PROPN
iajs-1807	62	85	of	of	ADP
iajs-1807	62	86	the	the	DET
iajs-1807	62	87	element	element	NOUN
iajs-1807	62	88	.	.	PUNCT
iajs-1807	63	1	substituting	substitute	VERB
iajs-1807	63	2	the	the	DET
iajs-1807	63	3	finite	finite	ADJ
iajs-1807	63	4	element	element	NOUN
iajs-1807	63	5	approximation	approximation	NOUN
iajs-1807	63	6	(	(	PUNCT
iajs-1807	63	7	19	19	NUM
iajs-1807	63	8	)	)	PUNCT
iajs-1807	63	9	for	for	ADP
iajs-1807	63	10	𝑢	𝑢	NOUN
iajs-1807	63	11	into	into	ADP
iajs-1807	63	12	the	the	DET
iajs-1807	63	13	weak	weak	ADJ
iajs-1807	63	14	form	form	NOUN
iajs-1807	63	15	(	(	PUNCT
iajs-1807	63	16	18	18	NUM
iajs-1807	63	17	)	)	PUNCT
iajs-1807	63	18	,	,	PUNCT
iajs-1807	63	19	we	we	PRON
iajs-1807	63	20	get	get	VERB
iajs-1807	63	21	ihsciconf	ihsciconf	NOUN
iajs-1807	63	22	2017	2017	NUM
iajs-1807	63	23	special	special	ADJ
iajs-1807	63	24	issue	issue	NOUN
iajs-1807	63	25	ibn	ibn	PROPN
iajs-1807	63	26	al	al	PROPN
iajs-1807	63	27	-	-	PUNCT
iajs-1807	63	28	haitham	haitham	PROPN
iajs-1807	63	29	journal	journal	PROPN
iajs-1807	63	30	for	for	ADP
iajs-1807	63	31	pure	pure	ADJ
iajs-1807	63	32	and	and	CCONJ
iajs-1807	63	33	applied	apply	VERB
iajs-1807	63	34	science	science	NOUN
iajs-1807	63	35	https://doi.org/	https://doi.org/	NOUN
iajs-1807	63	36	10.30526/2017.ihsciconf.1807	10.30526/2017.ihsciconf.1807	ADJ
iajs-1807	63	37	for	for	ADP
iajs-1807	63	38	more	more	ADJ
iajs-1807	63	39	information	information	NOUN
iajs-1807	63	40	about	about	ADP
iajs-1807	63	41	the	the	DET
iajs-1807	63	42	conference	conference	NOUN
iajs-1807	63	43	please	please	INTJ
iajs-1807	63	44	visit	visit	VERB
iajs-1807	63	45	the	the	DET
iajs-1807	63	46	websites	website	NOUN
iajs-1807	63	47	:	:	PUNCT
iajs-1807	63	48	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1807	63	49	  	  	SPACE
iajs-1807	63	50	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1807	63	51	   	   	SPACE
iajs-1807	63	52	mathematics	mathematic	NOUN
iajs-1807	63	53	|349	|349	NOUN
iajs-1807	63	54	    	    	SPACE
iajs-1807	63	55	0	0	NUM
iajs-1807	64	1	ℏ	ℏ	PROPN
iajs-1807	64	2	2𝑚	2𝑚	NOUN
iajs-1807	64	3	𝑤	𝑤	ADP
iajs-1807	64	4	𝑢	𝑢	PROPN
iajs-1807	64	5	𝜕𝜓	𝜕𝜓	PROPN
iajs-1807	64	6	𝜕𝑅	𝜕𝑅	PROPN
iajs-1807	64	7	ℏ	ℏ	NOUN
iajs-1807	64	8	2	2	NUM
iajs-1807	64	9	𝑅	𝑅	PROPN
iajs-1807	64	10	𝜕𝑤	𝜕𝑤	NOUN
iajs-1807	64	11	𝜕𝑅	𝜕𝑅	NOUN
iajs-1807	64	12	1	1	NUM
iajs-1807	64	13	𝑚	𝑚	PROPN
iajs-1807	64	14	𝑢	𝑢	PROPN
iajs-1807	64	15	𝜕𝜓	𝜕𝜓	PROPN
iajs-1807	64	16	𝜕𝑅	𝜕𝑅	X
iajs-1807	64	17	ℏ	ℏ	NOUN
iajs-1807	64	18	𝑙	𝑙	PRON
iajs-1807	64	19	2𝑚	2𝑚	NOUN
iajs-1807	64	20	𝑅	𝑅	PROPN
iajs-1807	64	21	𝑤	𝑤	ADP
iajs-1807	64	22	𝑢	𝑢	PROPN
iajs-1807	64	23	𝜓	𝜓	PROPN
iajs-1807	64	24	ω	ω	NUM
iajs-1807	64	25	ℏ	ℏ	PROPN
iajs-1807	64	26	2	2	NUM
iajs-1807	64	27	𝑅	𝑅	PROPN
iajs-1807	64	28	𝜕𝑤	𝜕𝑤	ADJ
iajs-1807	64	29	𝜕𝑍	𝜕𝑍	NOUN
iajs-1807	64	30	1	1	NUM
iajs-1807	64	31	𝑚	𝑚	NOUN
iajs-1807	64	32	𝑢	𝑢	PROPN
iajs-1807	64	33	𝜕𝜓	𝜕𝜓	PROPN
iajs-1807	64	34	𝜕𝑍	𝜕𝑍	PROPN
iajs-1807	64	35	𝑤𝑅𝑉	𝑤𝑅𝑉	NOUN
iajs-1807	64	36	𝑢	𝑢	X
iajs-1807	64	37	𝜓	𝜓	PROPN
iajs-1807	64	38	𝑤𝑅𝐸	𝑤𝑅𝐸	NUM
iajs-1807	64	39	𝑢	𝑢	PROPN
iajs-1807	64	40	𝜓	𝜓	NOUN
iajs-1807	64	41	𝑑𝑅𝑑𝑍	𝑑𝑅𝑑𝑍	VERB
iajs-1807	64	42	𝑤𝑑	𝑤𝑑	ADP
iajs-1807	64	43	𝑑𝑠	𝑑𝑠	ADP
iajs-1807	64	44	20	20	NUM
iajs-1807	64	45	this	this	DET
iajs-1807	64	46	equation	equation	NOUN
iajs-1807	64	47	must	must	AUX
iajs-1807	64	48	hold	hold	VERB
iajs-1807	64	49	for	for	ADP
iajs-1807	64	50	every	every	DET
iajs-1807	64	51	admissible	admissible	ADJ
iajs-1807	64	52	choice	choice	NOUN
iajs-1807	64	53	of	of	ADP
iajs-1807	64	54	weight	weight	NOUN
iajs-1807	64	55	function	function	NOUN
iajs-1807	64	56	𝑤.	𝑤.	NOUN
iajs-1807	64	57	since	since	SCONJ
iajs-1807	64	58	we	we	PRON
iajs-1807	64	59	need	need	VERB
iajs-1807	64	60	𝑛	𝑛	DET
iajs-1807	64	61	independent	independent	ADJ
iajs-1807	64	62	algebraic	algebraic	ADJ
iajs-1807	64	63	equations	equation	NOUN
iajs-1807	64	64	to	to	PART
iajs-1807	64	65	solve	solve	VERB
iajs-1807	64	66	for	for	ADP
iajs-1807	64	67	the	the	DET
iajs-1807	64	68	𝑛	𝑛	PROPN
iajs-1807	64	69	unknowns	unknown	NOUN
iajs-1807	64	70	,	,	PUNCT
iajs-1807	64	71	𝑢	𝑢	PRON
iajs-1807	64	72	,	,	PUNCT
iajs-1807	64	73	𝑢	𝑢	X
iajs-1807	64	74	,	,	PUNCT
iajs-1807	64	75	…	…	PUNCT
iajs-1807	64	76	,	,	PUNCT
iajs-1807	64	77	𝑢	𝑢	X
iajs-1807	64	78	,	,	PUNCT
iajs-1807	64	79	we	we	PRON
iajs-1807	64	80	choose	choose	VERB
iajs-1807	64	81	𝑛	𝑛	DET
iajs-1807	64	82	linearly	linearly	ADV
iajs-1807	64	83	independent	independent	ADJ
iajs-1807	64	84	functions	function	NOUN
iajs-1807	64	85	for	for	ADP
iajs-1807	64	86	𝑤	𝑤	ADP
iajs-1807	64	87	:	:	PUNCT
iajs-1807	64	88	𝑤	𝑤	PART
iajs-1807	64	89	𝜓	𝜓	PROPN
iajs-1807	64	90	,	,	PUNCT
iajs-1807	64	91	𝜓	𝜓	PROPN
iajs-1807	64	92	,	,	PUNCT
iajs-1807	64	93	…	…	PUNCT
iajs-1807	64	94	,	,	PUNCT
iajs-1807	64	95	𝜓	𝜓	PROPN
iajs-1807	64	96	.	.	PUNCT
iajs-1807	65	1	for	for	ADP
iajs-1807	65	2	each	each	DET
iajs-1807	65	3	choice	choice	NOUN
iajs-1807	65	4	of	of	ADP
iajs-1807	65	5	𝑤	𝑤	ADP
iajs-1807	65	6	we	we	PRON
iajs-1807	65	7	obtain	obtain	VERB
iajs-1807	65	8	an	an	DET
iajs-1807	65	9	algebraic	algebraic	ADJ
iajs-1807	65	10	relation	relation	NOUN
iajs-1807	65	11	among	among	ADP
iajs-1807	65	12	𝑢	𝑢	PRON
iajs-1807	65	13	,	,	PUNCT
iajs-1807	65	14	𝑢	𝑢	X
iajs-1807	65	15	,	,	PUNCT
iajs-1807	65	16	…	…	PUNCT
iajs-1807	65	17	,	,	PUNCT
iajs-1807	65	18	𝑢	𝑢	X
iajs-1807	65	19	.	.	PUNCT
iajs-1807	66	1	we	we	PRON
iajs-1807	66	2	label	label	VERB
iajs-1807	66	3	the	the	DET
iajs-1807	66	4	algebraic	algebraic	ADJ
iajs-1807	66	5	equation	equation	NOUN
iajs-1807	66	6	resulting	result	VERB
iajs-1807	66	7	from	from	ADP
iajs-1807	66	8	substitution	substitution	NOUN
iajs-1807	66	9	of	of	ADP
iajs-1807	66	10	𝑤	𝑤	ADP
iajs-1807	66	11	𝜓	𝜓	NOUN
iajs-1807	66	12	into	into	ADP
iajs-1807	66	13	(	(	PUNCT
iajs-1807	66	14	20	20	NUM
iajs-1807	66	15	):	):	SYM
iajs-1807	66	16	0	0	NUM
iajs-1807	66	17	ℏ	ℏ	NOUN
iajs-1807	66	18	2𝑚	2𝑚	NOUN
iajs-1807	66	19	𝜓	𝜓	PROPN
iajs-1807	66	20	𝜕𝜓	𝜕𝜓	PROPN
iajs-1807	66	21	𝜕𝑅	𝜕𝑅	PROPN
iajs-1807	66	22	ℏ	ℏ	NOUN
iajs-1807	66	23	2	2	NUM
iajs-1807	66	24	𝑅	𝑅	PROPN
iajs-1807	66	25	𝜕𝜓	𝜕𝜓	NOUN
iajs-1807	66	26	𝜕𝑅	𝜕𝑅	PROPN
iajs-1807	66	27	1	1	NUM
iajs-1807	66	28	𝑚	𝑚	PROPN
iajs-1807	66	29	𝜕𝜓	𝜕𝜓	PROPN
iajs-1807	66	30	𝜕𝑅	𝜕𝑅	X
iajs-1807	66	31	ℏ	ℏ	NOUN
iajs-1807	66	32	𝐿	𝐿	NOUN
iajs-1807	66	33	2𝑚	2𝑚	NOUN
iajs-1807	66	34	𝑅	𝑅	PROPN
iajs-1807	66	35	𝜓	𝜓	PROPN
iajs-1807	66	36	𝜓	𝜓	ADP
iajs-1807	66	37	ℏ	ℏ	PROPN
iajs-1807	66	38	2	2	NUM
iajs-1807	66	39	𝑅	𝑅	PROPN
iajs-1807	66	40	𝜕𝜓	𝜕𝜓	NOUN
iajs-1807	66	41	𝜕𝓏	𝜕𝓏	NOUN
iajs-1807	66	42	1	1	NUM
iajs-1807	66	43	𝑚	𝑚	PROPN
iajs-1807	66	44	𝜕𝜓	𝜕𝜓	NOUN
iajs-1807	66	45	𝜕𝑍	𝜕𝑍	PROPN
iajs-1807	66	46	ω	ω	PROPN
iajs-1807	66	47	𝑅𝑉𝜓	𝑅𝑉𝜓	NOUN
iajs-1807	66	48	𝜓	𝜓	PROPN
iajs-1807	66	49	𝑅𝐸𝜓	𝑅𝐸𝜓	NOUN
iajs-1807	66	50	𝜓	𝜓	VERB
iajs-1807	66	51	𝑑𝑅𝑑𝑍	𝑑𝑅𝑑𝑍	VERB
iajs-1807	66	52	𝑢	𝑢	NOUN
iajs-1807	66	53	𝑤𝑑	𝑤𝑑	ADP
iajs-1807	66	54	𝑑𝑠	𝑑𝑠	ADP
iajs-1807	66	55	;	;	PUNCT
iajs-1807	66	56	𝑖	𝑖	SYM
iajs-1807	66	57	,	,	PUNCT
iajs-1807	66	58	𝑗	𝑗	PROPN
iajs-1807	66	59	1,2	1,2	NUM
iajs-1807	66	60	,	,	PUNCT
iajs-1807	66	61	…	…	PUNCT
iajs-1807	66	62	,	,	PUNCT
iajs-1807	66	63	𝑛	𝑛	DET
iajs-1807	66	64	21	21	NUM
iajs-1807	66	65	2.2	2.2	NUM
iajs-1807	66	66	finite	finite	ADJ
iajs-1807	66	67	element	element	NOUN
iajs-1807	66	68	method	method	NOUN
iajs-1807	66	69	for	for	ADP
iajs-1807	66	70	the	the	DET
iajs-1807	66	71	model	model	NOUN
iajs-1807	66	72	with	with	ADP
iajs-1807	66	73	piecewise	piecewise	NOUN
iajs-1807	66	74	linear	linear	NOUN
iajs-1807	66	75	functions	function	NOUN
iajs-1807	66	76	in	in	ADP
iajs-1807	66	77	this	this	DET
iajs-1807	66	78	section	section	NOUN
iajs-1807	66	79	,	,	PUNCT
iajs-1807	66	80	the	the	DET
iajs-1807	66	81	solution	solution	NOUN
iajs-1807	66	82	u	u	NOUN
iajs-1807	66	83	of	of	ADP
iajs-1807	66	84	equation	equation	NOUN
iajs-1807	66	85	(	(	PUNCT
iajs-1807	66	86	18	18	NUM
iajs-1807	66	87	)	)	PUNCT
iajs-1807	66	88	is	be	AUX
iajs-1807	66	89	approximated	approximate	VERB
iajs-1807	66	90	by	by	ADP
iajs-1807	66	91	a	a	DET
iajs-1807	66	92	fem	fem	NOUN
iajs-1807	66	93	for	for	ADP
iajs-1807	66	94	the	the	DET
iajs-1807	66	95	model	model	NOUN
iajs-1807	66	96	with	with	ADP
iajs-1807	66	97	piecewise	piecewise	PROPN
iajs-1807	66	98	linear	linear	NOUN
iajs-1807	66	99	function	function	NOUN
iajs-1807	66	100	.	.	PUNCT
iajs-1807	67	1	we	we	PRON
iajs-1807	67	2	now	now	ADV
iajs-1807	67	3	define	define	VERB
iajs-1807	67	4	𝑉	𝑉	PROPN
iajs-1807	67	5	as	as	SCONJ
iajs-1807	67	6	follows	follow	VERB
iajs-1807	67	7	:	:	PUNCT
iajs-1807	67	8	𝑉	𝑉	PROPN
iajs-1807	67	9	𝑣	𝑣	NOUN
iajs-1807	67	10	:	:	PUNCT
iajs-1807	67	11	𝑣	𝑣	X
iajs-1807	67	12	𝑖𝑠	𝑖𝑠	ADV
iajs-1807	67	13	𝑐𝑜𝑡𝑖𝑛𝑢𝑜𝑢𝑠	𝑐𝑜𝑡𝑖𝑛𝑢𝑜𝑢𝑠	NOUN
iajs-1807	67	14	𝑜𝑛	𝑜𝑛	PROPN
iajs-1807	67	15	ω	ω	PROPN
iajs-1807	67	16	,	,	PUNCT
iajs-1807	67	17	𝑣	𝑣	PROPN
iajs-1807	67	18	0	0	NUM
iajs-1807	67	19	𝑜𝑛	𝑜𝑛	PROPN
iajs-1807	67	20	γ	γ	X
iajs-1807	67	21	.	.	PUNCT
iajs-1807	68	1	the	the	DET
iajs-1807	68	2	space	space	NOUN
iajs-1807	68	3	𝑉	𝑉	PROPN
iajs-1807	68	4	consists	consist	VERB
iajs-1807	68	5	of	of	ADP
iajs-1807	68	6	all	all	DET
iajs-1807	68	7	continuous	continuous	ADJ
iajs-1807	68	8	function	function	NOUN
iajs-1807	68	9	that	that	PRON
iajs-1807	68	10	are	be	AUX
iajs-1807	68	11	linear	linear	ADJ
iajs-1807	68	12	on	on	ADP
iajs-1807	68	13	each	each	DET
iajs-1807	68	14	triangle	triangle	NOUN
iajs-1807	68	15	𝐾	𝐾	PROPN
iajs-1807	68	16	and	and	CCONJ
iajs-1807	68	17	vanish	vanish	VERB
iajs-1807	68	18	on	on	ADP
iajs-1807	68	19	γ	γ	PROPN
iajs-1807	68	20	.	.	PUNCT
iajs-1807	69	1	we	we	PRON
iajs-1807	69	2	notice	notice	VERB
iajs-1807	69	3	that	that	SCONJ
iajs-1807	69	4	𝑉	𝑉	PROPN
iajs-1807	69	5	⊂	⊂	PROPN
iajs-1807	69	6	𝑉.	𝑉.	PROPN
iajs-1807	69	7	as	as	SCONJ
iajs-1807	69	8	parameters	parameter	NOUN
iajs-1807	69	9	to	to	PART
iajs-1807	69	10	describe	describe	VERB
iajs-1807	69	11	a	a	DET
iajs-1807	69	12	function	function	NOUN
iajs-1807	69	13	𝑣	𝑣	ADP
iajs-1807	69	14	∈	∈	PROPN
iajs-1807	69	15	𝑉	𝑉	PROPN
iajs-1807	69	16	we	we	PRON
iajs-1807	69	17	choose	choose	VERB
iajs-1807	69	18	the	the	DET
iajs-1807	69	19	values	value	NOUN
iajs-1807	69	20	𝑣	𝑣	ADP
iajs-1807	69	21	𝑁	𝑁	PROPN
iajs-1807	69	22	of	of	ADP
iajs-1807	69	23	𝑣	𝑣	PRON
iajs-1807	69	24	at	at	ADP
iajs-1807	69	25	the	the	DET
iajs-1807	69	26	nodes	node	NOUN
iajs-1807	69	27	𝑁	𝑁	PROPN
iajs-1807	69	28	,	,	PUNCT
iajs-1807	69	29	𝑖	𝑖	NOUN
iajs-1807	69	30	1	1	NUM
iajs-1807	69	31	,	,	PUNCT
iajs-1807	69	32	…	…	PUNCT
iajs-1807	69	33	,	,	PUNCT
iajs-1807	69	34	𝑁	𝑁	PROPN
iajs-1807	69	35	,	,	PUNCT
iajs-1807	69	36	of	of	ADP
iajs-1807	69	37	𝑇	𝑇	NOUN
iajs-1807	69	38	but	but	CCONJ
iajs-1807	69	39	exclude	exclude	VERB
iajs-1807	69	40	the	the	DET
iajs-1807	69	41	nodes	node	NOUN
iajs-1807	69	42	on	on	ADP
iajs-1807	69	43	the	the	DET
iajs-1807	69	44	boundary	boundary	NOUN
iajs-1807	69	45	since	since	SCONJ
iajs-1807	69	46	𝑣	𝑣	ADP
iajs-1807	69	47	0	0	NUM
iajs-1807	69	48	on	on	ADP
iajs-1807	69	49	γ	γ	PROPN
iajs-1807	69	50	.	.	PUNCT
iajs-1807	70	1	the	the	DET
iajs-1807	70	2	corresponding	corresponding	ADJ
iajs-1807	70	3	basis	basis	NOUN
iajs-1807	70	4	function	function	NOUN
iajs-1807	70	5	φ	φ	PROPN
iajs-1807	70	6	∈	∈	PROPN
iajs-1807	70	7	𝑉	𝑉	PROPN
iajs-1807	70	8	,	,	PUNCT
iajs-1807	70	9	𝑗	𝑗	PROPN
iajs-1807	70	10	1	1	NUM
iajs-1807	70	11	,	,	PUNCT
iajs-1807	70	12	…	…	PUNCT
iajs-1807	70	13	,	,	PUNCT
iajs-1807	70	14	𝑁	𝑁	PROPN
iajs-1807	70	15	,	,	PUNCT
iajs-1807	70	16	are	be	AUX
iajs-1807	70	17	then	then	ADV
iajs-1807	70	18	defined	define	VERB
iajs-1807	70	19	by	by	ADP
iajs-1807	70	20	(	(	PUNCT
iajs-1807	70	21	see	see	VERB
iajs-1807	70	22	figure(2	figure(2	NOUN
iajs-1807	70	23	)	)	PUNCT
iajs-1807	70	24	)	)	PUNCT
iajs-1807	71	1	φ	φ	PROPN
iajs-1807	72	1	𝑁	𝑁	PROPN
iajs-1807	72	2	𝛿	𝛿	PRON
iajs-1807	72	3	≡	≡	PROPN
iajs-1807	72	4	1	1	NUM
iajs-1807	72	5	𝑖𝑓	𝑖𝑓	ADP
iajs-1807	72	6	𝑖	𝑖	SYM
iajs-1807	72	7	𝑗	𝑗	NOUN
iajs-1807	72	8	0	0	NUM
iajs-1807	73	1	𝑖𝑓	𝑖𝑓	NOUN
iajs-1807	73	2	𝑖	𝑖	PUNCT
iajs-1807	73	3	𝑗	𝑗	PROPN
iajs-1807	73	4	𝑖	𝑖	SYM
iajs-1807	73	5	,	,	PUNCT
iajs-1807	73	6	𝑗	𝑗	PROPN
iajs-1807	73	7	1	1	NUM
iajs-1807	73	8	,	,	PUNCT
iajs-1807	73	9	…	…	PUNCT
iajs-1807	73	10	,	,	PUNCT
iajs-1807	73	11	𝑀.	𝑀.	PROPN
iajs-1807	73	12	the	the	DET
iajs-1807	73	13	finite	finite	PROPN
iajs-1807	73	14	element	element	NOUN
iajs-1807	73	15	method	method	NOUN
iajs-1807	73	16	was	be	AUX
iajs-1807	73	17	applied	apply	VERB
iajs-1807	73	18	to	to	PART
iajs-1807	73	19	project	project	VERB
iajs-1807	73	20	the	the	DET
iajs-1807	73	21	variational	variational	ADJ
iajs-1807	73	22	form	form	NOUN
iajs-1807	73	23	of	of	ADP
iajs-1807	73	24	the	the	DET
iajs-1807	73	25	problem	problem	NOUN
iajs-1807	73	26	onto	onto	ADP
iajs-1807	73	27	a	a	DET
iajs-1807	73	28	finite	finite	ADJ
iajs-1807	73	29	dimensional	dimensional	ADJ
iajs-1807	73	30	space	space	NOUN
iajs-1807	73	31	.	.	PUNCT
iajs-1807	74	1	as	as	ADP
iajs-1807	74	2	a	a	DET
iajs-1807	74	3	result	result	NOUN
iajs-1807	74	4	,	,	PUNCT
iajs-1807	74	5	the	the	DET
iajs-1807	74	6	problem	problem	NOUN
iajs-1807	74	7	was	be	AUX
iajs-1807	74	8	reduced	reduce	VERB
iajs-1807	74	9	to	to	ADP
iajs-1807	74	10	the	the	DET
iajs-1807	74	11	following	follow	VERB
iajs-1807	74	12	generalized	generalized	ADJ
iajs-1807	74	13	eigenvalue	eigenvalue	NOUN
iajs-1807	74	14	problem	problem	NOUN
iajs-1807	74	15	:	:	PUNCT
iajs-1807	75	1	𝐴𝑢	𝐴𝑢	ADP
iajs-1807	75	2	𝜆𝐵	𝜆𝐵	PROPN
iajs-1807	75	3	22	22	NUM
iajs-1807	75	4	where	where	SCONJ
iajs-1807	75	5	a	a	PRON
iajs-1807	75	6	and	and	CCONJ
iajs-1807	75	7	b	b	NOUN
iajs-1807	75	8	are	be	AUX
iajs-1807	75	9	𝑁	𝑁	ADJ
iajs-1807	75	10	𝑁	𝑁	PROPN
iajs-1807	75	11	matrices	matrix	NOUN
iajs-1807	75	12	,	,	PUNCT
iajs-1807	75	13	𝑢	𝑢	PRON
iajs-1807	75	14	the	the	DET
iajs-1807	75	15	vector	vector	NOUN
iajs-1807	75	16	of	of	ADP
iajs-1807	75	17	unknowns	unknown	NOUN
iajs-1807	75	18	of	of	ADP
iajs-1807	75	19	dimensionality	dimensionality	NOUN
iajs-1807	75	20	𝑁	𝑁	PROPN
iajs-1807	75	21	,	,	PUNCT
iajs-1807	75	22	and	and	CCONJ
iajs-1807	75	23	𝑁	𝑁	ADP
iajs-1807	75	24	the	the	DET
iajs-1807	75	25	number	number	NOUN
iajs-1807	75	26	of	of	ADP
iajs-1807	75	27	nodes	node	NOUN
iajs-1807	75	28	in	in	ADP
iajs-1807	75	29	which	which	PRON
iajs-1807	75	30	the	the	DET
iajs-1807	75	31	solution	solution	NOUN
iajs-1807	75	32	to	to	ADP
iajs-1807	75	33	the	the	DET
iajs-1807	75	34	problem	problem	NOUN
iajs-1807	75	35	(	(	PUNCT
iajs-1807	75	36	13	13	NUM
iajs-1807	75	37	)	)	PUNCT
iajs-1807	75	38	is	be	AUX
iajs-1807	75	39	being	be	AUX
iajs-1807	75	40	sought	seek	VERB
iajs-1807	75	41	.	.	PUNCT
iajs-1807	76	1	computational	computational	ADJ
iajs-1807	76	2	domains	domain	NOUN
iajs-1807	76	3	of	of	ADP
iajs-1807	76	4	interest	interest	NOUN
iajs-1807	76	5	are	be	AUX
iajs-1807	76	6	symmetric	symmetric	ADJ
iajs-1807	76	7	with	with	ADP
iajs-1807	76	8	respect	respect	NOUN
iajs-1807	76	9	to	to	ADP
iajs-1807	76	10	the	the	DET
iajs-1807	76	11	z	z	NOUN
iajs-1807	76	12	-	-	PUNCT
iajs-1807	76	13	axis	axis	ADJ
iajs-1807	76	14	,	,	PUNCT
iajs-1807	76	15	where	where	SCONJ
iajs-1807	76	16	we	we	PRON
iajs-1807	76	17	imposed	impose	VERB
iajs-1807	76	18	neumann	neumann	PROPN
iajs-1807	76	19	's	's	PART
iajs-1807	76	20	boundary	boundary	ADJ
iajs-1807	76	21	conditions	condition	NOUN
iajs-1807	76	22	if	if	SCONJ
iajs-1807	76	23	𝐿	𝐿	PROPN
iajs-1807	76	24	0	0	NUM
iajs-1807	76	25	.	.	PUNCT
iajs-1807	77	1	the	the	DET
iajs-1807	77	2	solution	solution	NOUN
iajs-1807	77	3	to	to	ADP
iajs-1807	77	4	equation	equation	NOUN
iajs-1807	77	5	(	(	PUNCT
iajs-1807	77	6	22	22	NUM
iajs-1807	77	7	)	)	PUNCT
iajs-1807	77	8	was	be	AUX
iajs-1807	77	9	found	find	VERB
iajs-1807	77	10	in	in	ADP
iajs-1807	77	11	matlab	matlab	PROPN
iajs-1807	77	12	.	.	PUNCT
iajs-1807	78	1	ihsciconf	ihsciconf	PROPN
iajs-1807	78	2	2017	2017	NUM
iajs-1807	78	3	special	special	ADJ
iajs-1807	78	4	issue	issue	NOUN
iajs-1807	78	5	ibn	ibn	PROPN
iajs-1807	78	6	al	al	PROPN
iajs-1807	78	7	-	-	PUNCT
iajs-1807	78	8	haitham	haitham	PROPN
iajs-1807	78	9	journal	journal	PROPN
iajs-1807	78	10	for	for	ADP
iajs-1807	78	11	pure	pure	ADJ
iajs-1807	78	12	and	and	CCONJ
iajs-1807	78	13	applied	apply	VERB
iajs-1807	78	14	science	science	NOUN
iajs-1807	78	15	https://doi.org/	https://doi.org/	NOUN
iajs-1807	78	16	10.30526/2017.ihsciconf.1807	10.30526/2017.ihsciconf.1807	ADJ
iajs-1807	78	17	for	for	ADP
iajs-1807	78	18	more	more	ADJ
iajs-1807	78	19	information	information	NOUN
iajs-1807	78	20	about	about	ADP
iajs-1807	78	21	the	the	DET
iajs-1807	78	22	conference	conference	NOUN
iajs-1807	78	23	please	please	INTJ
iajs-1807	78	24	visit	visit	VERB
iajs-1807	78	25	the	the	DET
iajs-1807	78	26	websites	website	NOUN
iajs-1807	78	27	:	:	PUNCT
iajs-1807	78	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1807	78	29	  	  	SPACE
iajs-1807	78	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1807	78	31	   	   	SPACE
iajs-1807	78	32	mathematics	mathematic	NOUN
iajs-1807	78	33	|350	|350	PROPN
iajs-1807	78	34	    	    	SPACE
iajs-1807	78	35	we	we	PRON
iajs-1807	78	36	employed	employ	VERB
iajs-1807	78	37	the	the	DET
iajs-1807	78	38	finite	finite	ADJ
iajs-1807	78	39	element	element	NOUN
iajs-1807	78	40	method	method	NOUN
iajs-1807	78	41	so	so	SCONJ
iajs-1807	78	42	as	as	SCONJ
iajs-1807	78	43	to	to	PART
iajs-1807	78	44	calculate	calculate	VERB
iajs-1807	78	45	electron	electron	NOUN
iajs-1807	78	46	eigenvalues	eigenvalue	NOUN
iajs-1807	78	47	and	and	CCONJ
iajs-1807	78	48	eigenstates	eigenstate	NOUN
iajs-1807	78	49	for	for	ADP
iajs-1807	78	50	a	a	DET
iajs-1807	78	51	series	series	NOUN
iajs-1807	78	52	of	of	ADP
iajs-1807	78	53	finite	finite	PROPN
iajs-1807	78	54	nwsl	nwsl	ADJ
iajs-1807	78	55	structures	structure	NOUN
iajs-1807	78	56	with	with	ADP
iajs-1807	78	57	a	a	DET
iajs-1807	78	58	cylindrical	cylindrical	ADJ
iajs-1807	78	59	cross	cross	NOUN
iajs-1807	78	60	-	-	NOUN
iajs-1807	78	61	section	section	NOUN
iajs-1807	78	62	.	.	PUNCT
iajs-1807	79	1	in	in	ADP
iajs-1807	79	2	this	this	DET
iajs-1807	79	3	case	case	NOUN
iajs-1807	79	4	the	the	DET
iajs-1807	79	5	matrices	matrix	NOUN
iajs-1807	79	6	in	in	ADP
iajs-1807	79	7	equation	equation	NOUN
iajs-1807	79	8	(	(	PUNCT
iajs-1807	79	9	22	22	NUM
iajs-1807	79	10	)	)	PUNCT
iajs-1807	79	11	has	have	VERB
iajs-1807	79	12	the	the	DET
iajs-1807	79	13	following	follow	VERB
iajs-1807	79	14	form	form	NOUN
iajs-1807	79	15	where	where	SCONJ
iajs-1807	79	16	𝐴	𝐴	PROPN
iajs-1807	79	17	𝐴	𝐴	PROPN
iajs-1807	79	18	and	and	CCONJ
iajs-1807	79	19	𝐵	𝐵	PROPN
iajs-1807	79	20	𝐵	𝐵	NOUN
iajs-1807	79	21	,	,	PUNCT
iajs-1807	79	22	𝑖	𝑖	NOUN
iajs-1807	79	23	1,2	1,2	NUM
iajs-1807	79	24	,	,	PUNCT
iajs-1807	79	25	…	…	PUNCT
iajs-1807	79	26	,	,	PUNCT
iajs-1807	79	27	𝑁	𝑁	PROPN
iajs-1807	79	28	,	,	PUNCT
iajs-1807	79	29	𝑗	𝑗	PROPN
iajs-1807	79	30	1,2	1,2	NUM
iajs-1807	79	31	,	,	PUNCT
iajs-1807	79	32	…	…	PUNCT
iajs-1807	79	33	,	,	PUNCT
iajs-1807	79	34	𝑁.	𝑁.	PROPN
iajs-1807	79	35	𝐴	𝐴	PROPN
iajs-1807	79	36	ℏ	ℏ	PROPN
iajs-1807	79	37	2𝑚	2𝑚	NOUN
iajs-1807	79	38	𝜓	𝜓	PROPN
iajs-1807	79	39	𝜕𝜓	𝜕𝜓	NOUN
iajs-1807	79	40	𝜕𝑟	𝜕𝑟	NOUN
iajs-1807	79	41	ℏ	ℏ	ADP
iajs-1807	79	42	2	2	NUM
iajs-1807	79	43	𝑟	𝑟	NOUN
iajs-1807	79	44	𝜕𝜓	𝜕𝜓	NOUN
iajs-1807	79	45	𝜕𝑟	𝜕𝑟	NOUN
iajs-1807	79	46	1	1	NUM
iajs-1807	79	47	𝑚	𝑚	PROPN
iajs-1807	79	48	𝜕𝜓	𝜕𝜓	NOUN
iajs-1807	79	49	𝜕𝑟	𝜕𝑟	NOUN
iajs-1807	79	50	ℏ	ℏ	NOUN
iajs-1807	79	51	l	l	NOUN
iajs-1807	79	52	2mr	2mr	NOUN
iajs-1807	79	53	𝜓	𝜓	SCONJ
iajs-1807	79	54	𝜓	𝜓	ADP
iajs-1807	79	55	ℏ	ℏ	PROPN
iajs-1807	79	56	2	2	NUM
iajs-1807	79	57	𝑟	𝑟	NOUN
iajs-1807	79	58	𝜕𝜓	𝜕𝜓	NOUN
iajs-1807	79	59	𝜕𝓏	𝜕𝓏	NOUN
iajs-1807	79	60	1	1	NUM
iajs-1807	79	61	𝑚	𝑚	NOUN
iajs-1807	79	62	𝜕𝜓	𝜕𝜓	NOUN
iajs-1807	79	63	𝜕𝓏	𝜕𝓏	NOUN
iajs-1807	79	64	𝑑𝑟𝑑𝓏	𝑑𝑟𝑑𝓏	VERB
iajs-1807	79	65	23	23	NUM
iajs-1807	79	66	𝐵	𝐵	PROPN
iajs-1807	79	67	𝑉	𝑉	PROPN
iajs-1807	79	68	𝐸	𝐸	PROPN
iajs-1807	79	69	𝑟𝜓	𝑟𝜓	ADP
iajs-1807	79	70	𝜓	𝜓	PROPN
iajs-1807	79	71	𝑑𝑟𝑑𝓏	𝑑𝑟𝑑𝓏	PROPN
iajs-1807	79	72	ω	ω	NUM
iajs-1807	79	73	24	24	NUM
iajs-1807	79	74	as	as	ADP
iajs-1807	79	75	a	a	DET
iajs-1807	79	76	first	first	ADJ
iajs-1807	79	77	choice	choice	NOUN
iajs-1807	79	78	the	the	DET
iajs-1807	79	79	uniform	uniform	ADJ
iajs-1807	79	80	mesh	mesh	NOUN
iajs-1807	79	81	are	be	AUX
iajs-1807	79	82	used	use	VERB
iajs-1807	79	83	by	by	ADP
iajs-1807	79	84	the	the	DET
iajs-1807	79	85	piecewise	piecewise	NOUN
iajs-1807	79	86	linear	linear	NOUN
iajs-1807	79	87	function	function	VERB
iajs-1807	79	88	three	three	NUM
iajs-1807	79	89	element	element	NOUN
iajs-1807	79	90	,	,	PUNCT
iajs-1807	79	91	as	as	SCONJ
iajs-1807	79	92	shown	show	VERB
iajs-1807	79	93	in	in	ADP
iajs-1807	79	94	figure	figure	NOUN
iajs-1807	79	95	(	(	PUNCT
iajs-1807	79	96	3	3	NUM
iajs-1807	79	97	)	)	PUNCT
iajs-1807	79	98	to	to	PART
iajs-1807	79	99	represent	represent	VERB
iajs-1807	79	100	the	the	DET
iajs-1807	79	101	domain	domain	NOUN
iajs-1807	79	102	,	,	PUNCT
iajs-1807	79	103	to	to	PART
iajs-1807	79	104	determine	determine	VERB
iajs-1807	79	105	the	the	DET
iajs-1807	79	106	element	element	ADJ
iajs-1807	79	107	coefficient	coefficient	NOUN
iajs-1807	79	108	matrices	matrix	NOUN
iajs-1807	79	109	𝐴	𝐴	PROPN
iajs-1807	79	110	and	and	CCONJ
iajs-1807	79	111	𝐵	𝐵	NOUN
iajs-1807	79	112	of	of	ADP
iajs-1807	79	113	eq	eq	PROPN
iajs-1807	79	114	.	.	PUNCT
iajs-1807	80	1	(	(	PUNCT
iajs-1807	80	2	22	22	NUM
iajs-1807	80	3	)	)	PUNCT
iajs-1807	80	4	.	.	PUNCT
iajs-1807	81	1	to	to	ADP
iajs-1807	81	2	evaluation	evaluation	NOUN
iajs-1807	81	3	of	of	ADP
iajs-1807	81	4	the	the	DET
iajs-1807	81	5	integral	integral	NOUN
iajs-1807	81	6	in	in	ADP
iajs-1807	81	7	eq	eq	ADP
iajs-1807	81	8	.	.	PUNCT
iajs-1807	82	1	(	(	PUNCT
iajs-1807	82	2	23	23	NUM
iajs-1807	82	3	)	)	PUNCT
iajs-1807	82	4	and	and	CCONJ
iajs-1807	82	5	eq	eq	NOUN
iajs-1807	82	6	.	.	PUNCT
iajs-1807	83	1	(	(	PUNCT
iajs-1807	83	2	24	24	NUM
iajs-1807	83	3	)	)	PUNCT
iajs-1807	83	4	,	,	PUNCT
iajs-1807	83	5	it	it	PRON
iajs-1807	83	6	is	be	AUX
iajs-1807	83	7	possible	possible	ADJ
iajs-1807	83	8	to	to	PART
iajs-1807	83	9	obtain	obtain	VERB
iajs-1807	83	10	the	the	DET
iajs-1807	83	11	closed	closed	ADJ
iajs-1807	83	12	form	form	NOUN
iajs-1807	83	13	for	for	ADP
iajs-1807	83	14	the	the	DET
iajs-1807	83	15	𝐴	𝐴	PROPN
iajs-1807	83	16	and	and	CCONJ
iajs-1807	83	17	𝐵	𝐵	NOUN
iajs-1807	83	18	matrices	matrix	NOUN
iajs-1807	83	19	by	by	ADP
iajs-1807	83	20	carrying	carry	VERB
iajs-1807	83	21	out	out	ADP
iajs-1807	83	22	the	the	DET
iajs-1807	83	23	integrals	integral	NOUN
iajs-1807	83	24	in	in	ADP
iajs-1807	83	25	eq	eq	ADP
iajs-1807	83	26	.	.	PUNCT
iajs-1807	84	1	(	(	PUNCT
iajs-1807	84	2	23	23	NUM
iajs-1807	84	3	)	)	PUNCT
iajs-1807	84	4	and	and	CCONJ
iajs-1807	84	5	eq	eq	NOUN
iajs-1807	84	6	.	.	PUNCT
iajs-1807	85	1	(	(	PUNCT
iajs-1807	85	2	24	24	NUM
iajs-1807	85	3	)	)	PUNCT
iajs-1807	85	4	exactly	exactly	ADV
iajs-1807	85	5	respectively	respectively	ADV
iajs-1807	85	6	.	.	PUNCT
iajs-1807	86	1	we	we	PRON
iajs-1807	86	2	consider	consider	VERB
iajs-1807	86	3	element	element	NOUN
iajs-1807	86	4	1	1	NUM
iajs-1807	86	5	as	as	ADP
iajs-1807	86	6	the	the	DET
iajs-1807	86	7	typical	typical	ADJ
iajs-1807	86	8	element	element	NOUN
iajs-1807	86	9	.	.	PUNCT
iajs-1807	87	1	hence	hence	ADV
iajs-1807	87	2	,	,	PUNCT
iajs-1807	87	3	the	the	DET
iajs-1807	87	4	element	element	NOUN
iajs-1807	87	5	coefficient	coefficient	NOUN
iajs-1807	87	6	𝐴	𝐴	PROPN
iajs-1807	87	7	and	and	CCONJ
iajs-1807	87	8	𝐵	𝐵	NOUN
iajs-1807	87	9	matrices	matrix	NOUN
iajs-1807	87	10	are	be	AUX
iajs-1807	87	11	notes	note	NOUN
iajs-1807	87	12	(	(	PUNCT
iajs-1807	87	13	1	1	NUM
iajs-1807	87	14	):	):	PUNCT
iajs-1807	87	15	in	in	ADP
iajs-1807	87	16	the	the	DET
iajs-1807	87	17	following	follow	VERB
iajs-1807	87	18	example	example	NOUN
iajs-1807	87	19	,	,	PUNCT
iajs-1807	87	20	the	the	DET
iajs-1807	87	21	representative	representative	NOUN
iajs-1807	87	22	set	set	NOUN
iajs-1807	87	23	of	of	ADP
iajs-1807	87	24	parameters	parameter	NOUN
iajs-1807	87	25	were	be	AUX
iajs-1807	87	26	used	use	VERB
iajs-1807	87	27	for	for	ADP
iajs-1807	87	28	the	the	DET
iajs-1807	87	29	calculations	calculation	NOUN
iajs-1807	87	30	as	as	ADP
iajs-1807	87	31	:	:	PUNCT
iajs-1807	87	32	for	for	ADP
iajs-1807	87	33	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	87	34	,	,	PUNCT
iajs-1807	87	35	the	the	DET
iajs-1807	87	36	energy	energy	NOUN
iajs-1807	87	37	gap	gap	NOUN
iajs-1807	87	38	𝐸	𝐸	PROPN
iajs-1807	87	39	0.42	0.42	NUM
iajs-1807	87	40	ev	ev	NOUN
iajs-1807	87	41	,	,	PUNCT
iajs-1807	87	42	∆	∆	PROPN
iajs-1807	87	43	0.38	0.38	NUM
iajs-1807	87	44	𝑒𝑉	𝑒𝑉	NOUN
iajs-1807	87	45	,	,	PUNCT
iajs-1807	87	46	𝑚	𝑚	PROPN
iajs-1807	87	47	0	0	NUM
iajs-1807	87	48	0.024	0.024	NUM
iajs-1807	87	49	𝑚	𝑚	NOUN
iajs-1807	87	50	.	.	PUNCT
iajs-1807	88	1	for	for	ADP
iajs-1807	88	2	𝐺𝑎𝐴𝑠	𝐺𝑎𝐴𝑠	PROPN
iajs-1807	88	3	,	,	PUNCT
iajs-1807	88	4	the	the	DET
iajs-1807	88	5	energy	energy	NOUN
iajs-1807	88	6	gap	gap	NOUN
iajs-1807	88	7	𝐸	𝐸	PROPN
iajs-1807	88	8	1.52	1.52	NUM
iajs-1807	88	9	ev	ev	NOUN
iajs-1807	88	10	,	,	PUNCT
iajs-1807	88	11	∆	∆	PROPN
iajs-1807	88	12	0.34	0.34	NUM
iajs-1807	88	13	𝑒𝑉	𝑒𝑉	NOUN
iajs-1807	88	14	,	,	PUNCT
iajs-1807	88	15	𝑚	𝑚	PROPN
iajs-1807	88	16	0	0	NUM
iajs-1807	88	17	0.067	0.067	NUM
iajs-1807	88	18	𝑚	𝑚	NOUN
iajs-1807	88	19	.	.	PUNCT
iajs-1807	89	1	the	the	DET
iajs-1807	89	2	band	band	NOUN
iajs-1807	89	3	offset	offset	NOUN
iajs-1807	89	4	parameter	parameter	NOUN
iajs-1807	89	5	is	be	AUX
iajs-1807	89	6	taken	take	VERB
iajs-1807	89	7	as	as	ADP
iajs-1807	89	8	𝑉	𝑉	PROPN
iajs-1807	89	9	0.55	0.55	NUM
iajs-1807	89	10	ev	ev	PROPN
iajs-1807	89	11	.	.	PROPN
iajs-1807	89	12	example	example	NOUN
iajs-1807	89	13	(	(	PUNCT
iajs-1807	89	14	1	1	NUM
iajs-1807	89	15	):	):	PUNCT
iajs-1807	89	16	consider	consider	VERB
iajs-1807	89	17	the	the	DET
iajs-1807	89	18	nanoscal	nanoscal	ADJ
iajs-1807	89	19	𝐼𝑛𝐴𝑠/𝐺𝑎𝐴𝑠	𝐼𝑛𝐴𝑠/𝐺𝑎𝐴𝑠	NOUN
iajs-1807	89	20	,	,	PUNCT
iajs-1807	89	21	quantum	quantum	NOUN
iajs-1807	89	22	ring	ring	NOUN
iajs-1807	89	23	model	model	NOUN
iajs-1807	89	24	,	,	PUNCT
iajs-1807	89	25	with	with	ADP
iajs-1807	89	26	using	use	VERB
iajs-1807	89	27	the	the	DET
iajs-1807	89	28	above	above	ADJ
iajs-1807	89	29	date	date	NOUN
iajs-1807	89	30	to	to	PART
iajs-1807	89	31	solve	solve	VERB
iajs-1807	89	32	𝐼𝑛𝐴𝑠/𝐺𝑎𝐴𝑠	𝐼𝑛𝐴𝑠/𝐺𝑎𝐴𝑠	NOUN
iajs-1807	89	33	,	,	PUNCT
iajs-1807	89	34	nanostructures	nanostructure	NOUN
iajs-1807	89	35	quantum	quantum	NOUN
iajs-1807	89	36	ring	ring	NOUN
iajs-1807	89	37	.	.	PUNCT
iajs-1807	90	1	in	in	ADP
iajs-1807	90	2	this	this	DET
iajs-1807	90	3	example	example	NOUN
iajs-1807	90	4	the	the	DET
iajs-1807	90	5	fem	fem	NOUN
iajs-1807	90	6	with	with	ADP
iajs-1807	90	7	piecewise	piecewise	NOUN
iajs-1807	90	8	linear	linear	NOUN
iajs-1807	90	9	function	function	NOUN
iajs-1807	90	10	we	we	PRON
iajs-1807	90	11	used	use	VERB
iajs-1807	90	12	to	to	PART
iajs-1807	90	13	solve	solve	VERB
iajs-1807	90	14	equation	equation	NOUN
iajs-1807	90	15	(	(	PUNCT
iajs-1807	90	16	13	13	NUM
iajs-1807	90	17	)	)	PUNCT
iajs-1807	90	18	.	.	PUNCT
iajs-1807	91	1	equation	equation	NOUN
iajs-1807	91	2	(	(	PUNCT
iajs-1807	91	3	13	13	NUM
iajs-1807	91	4	)	)	PUNCT
iajs-1807	91	5	is	be	AUX
iajs-1807	91	6	solved	solve	VERB
iajs-1807	91	7	using	use	VERB
iajs-1807	91	8	matlab	matlab	PROPN
iajs-1807	91	9	program	program	NOUN
iajs-1807	91	10	at	at	ADP
iajs-1807	91	11	𝑛	𝑛	PROPN
iajs-1807	91	12	1296	1296	NUM
iajs-1807	91	13	.	.	PUNCT
iajs-1807	92	1	the	the	DET
iajs-1807	92	2	results	result	NOUN
iajs-1807	92	3	of	of	ADP
iajs-1807	92	4	numerical	numerical	ADJ
iajs-1807	92	5	example	example	NOUN
iajs-1807	92	6	give	give	VERB
iajs-1807	92	7	a	a	DET
iajs-1807	92	8	good	good	ADJ
iajs-1807	92	9	accuracy	accuracy	NOUN
iajs-1807	92	10	and	and	CCONJ
iajs-1807	92	11	efficiency	efficiency	NOUN
iajs-1807	92	12	of	of	ADP
iajs-1807	92	13	this	this	DET
iajs-1807	92	14	method	method	NOUN
iajs-1807	92	15	comparing	compare	VERB
iajs-1807	92	16	with	with	ADP
iajs-1807	92	17	the	the	DET
iajs-1807	92	18	results	result	NOUN
iajs-1807	92	19	with	with	ADP
iajs-1807	92	20	fem	fem	NOUN
iajs-1807	92	21	of	of	ADP
iajs-1807	92	22	linear	linear	PROPN
iajs-1807	92	23	triangular	triangular	NOUN
iajs-1807	92	24	element	element	NOUN
iajs-1807	92	25	and	and	CCONJ
iajs-1807	92	26	the	the	DET
iajs-1807	92	27	maximum	maximum	ADJ
iajs-1807	92	28	absolute	absolute	ADJ
iajs-1807	92	29	error	error	NOUN
iajs-1807	92	30	is	be	AUX
iajs-1807	92	31	less	less	ADJ
iajs-1807	92	32	than	than	ADP
iajs-1807	92	33	10	10	NUM
iajs-1807	92	34	ev	ev	NOUN
iajs-1807	92	35	(	(	PUNCT
iajs-1807	92	36	as	as	SCONJ
iajs-1807	92	37	shown	show	VERB
iajs-1807	92	38	in	in	ADP
iajs-1807	92	39	figure	figure	NOUN
iajs-1807	92	40	(	(	PUNCT
iajs-1807	92	41	4	4	NUM
iajs-1807	92	42	)	)	PUNCT
iajs-1807	92	43	)	)	PUNCT
iajs-1807	92	44	.	.	PUNCT
iajs-1807	93	1	ihsciconf	ihsciconf	PROPN
iajs-1807	93	2	2017	2017	NUM
iajs-1807	93	3	special	special	ADJ
iajs-1807	93	4	issue	issue	NOUN
iajs-1807	93	5	ibn	ibn	PROPN
iajs-1807	93	6	al	al	PROPN
iajs-1807	93	7	-	-	PUNCT
iajs-1807	93	8	haitham	haitham	PROPN
iajs-1807	93	9	journal	journal	PROPN
iajs-1807	93	10	for	for	ADP
iajs-1807	93	11	pure	pure	ADJ
iajs-1807	93	12	and	and	CCONJ
iajs-1807	93	13	applied	apply	VERB
iajs-1807	93	14	science	science	NOUN
iajs-1807	93	15	https://doi.org/	https://doi.org/	NOUN
iajs-1807	93	16	10.30526/2017.ihsciconf.1807	10.30526/2017.ihsciconf.1807	ADJ
iajs-1807	93	17	for	for	ADP
iajs-1807	93	18	more	more	ADJ
iajs-1807	93	19	information	information	NOUN
iajs-1807	93	20	about	about	ADP
iajs-1807	93	21	the	the	DET
iajs-1807	93	22	conference	conference	NOUN
iajs-1807	93	23	please	please	INTJ
iajs-1807	93	24	visit	visit	VERB
iajs-1807	93	25	the	the	DET
iajs-1807	93	26	websites	website	NOUN
iajs-1807	93	27	:	:	PUNCT
iajs-1807	93	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1807	93	29	  	  	SPACE
iajs-1807	93	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1807	93	31	   	   	SPACE
iajs-1807	93	32	mathematics	mathematics	PROPN
iajs-1807	93	33	|351	|351	NOUN
iajs-1807	93	34	    	    	SPACE
iajs-1807	93	35	figure	figure	NOUN
iajs-1807	93	36	(	(	PUNCT
iajs-1807	93	37	1	1	NUM
iajs-1807	93	38	):	):	PUNCT
iajs-1807	93	39	a	a	DET
iajs-1807	93	40	three	three	NUM
iajs-1807	93	41	-	-	PUNCT
iajs-1807	93	42	dimensional	dimensional	ADJ
iajs-1807	93	43	plot	plot	NOUN
iajs-1807	93	44	of	of	ADP
iajs-1807	93	45	the	the	DET
iajs-1807	93	46	disk	disk	NOUN
iajs-1807	93	47	shaped	shape	VERB
iajs-1807	93	48	semiconductor	semiconductor	NOUN
iajs-1807	93	49	quantum	quantum	NOUN
iajs-1807	93	50	ring	ring	NOUN
iajs-1807	93	51	.	.	PUNCT
iajs-1807	94	1	figure	figure	NOUN
iajs-1807	94	2	(	(	PUNCT
iajs-1807	94	3	2	2	NUM
iajs-1807	94	4	):	):	PUNCT
iajs-1807	94	5	the	the	DET
iajs-1807	94	6	basis	basis	NOUN
iajs-1807	94	7	function	function	NOUN
iajs-1807	94	8	φ	φ	PROPN
iajs-1807	94	9	.	.	PUNCT
iajs-1807	95	1	figure	figure	NOUN
iajs-1807	95	2	(	(	PUNCT
iajs-1807	95	3	3	3	NUM
iajs-1807	95	4	):	):	PUNCT
iajs-1807	95	5	the	the	DET
iajs-1807	95	6	uniform	uniform	ADJ
iajs-1807	95	7	mesh	mesh	NOUN
iajs-1807	95	8	piecewise	piecewise	PROPN
iajs-1807	95	9	linear	linear	NOUN
iajs-1807	95	10	function	function	NOUN
iajs-1807	95	11	three	three	NUM
iajs-1807	95	12	ele	ele	NOUN
iajs-1807	95	13	ihsciconf	ihsciconf	PROPN
iajs-1807	95	14	2017	2017	NUM
iajs-1807	95	15	special	special	ADJ
iajs-1807	95	16	issue	issue	NOUN
iajs-1807	95	17	ibn	ibn	PROPN
iajs-1807	95	18	al	al	PROPN
iajs-1807	95	19	-	-	PUNCT
iajs-1807	95	20	haitham	haitham	PROPN
iajs-1807	95	21	journal	journal	PROPN
iajs-1807	95	22	for	for	ADP
iajs-1807	95	23	pure	pure	ADJ
iajs-1807	95	24	and	and	CCONJ
iajs-1807	95	25	applied	apply	VERB
iajs-1807	95	26	science	science	NOUN
iajs-1807	95	27	https://doi.org/	https://doi.org/	NOUN
iajs-1807	95	28	10.30526/2017.ihsciconf.1807	10.30526/2017.ihsciconf.1807	ADJ
iajs-1807	95	29	for	for	ADP
iajs-1807	95	30	more	more	ADJ
iajs-1807	95	31	information	information	NOUN
iajs-1807	95	32	about	about	ADP
iajs-1807	95	33	the	the	DET
iajs-1807	95	34	conference	conference	NOUN
iajs-1807	95	35	please	please	INTJ
iajs-1807	95	36	visit	visit	VERB
iajs-1807	95	37	the	the	DET
iajs-1807	95	38	websites	website	NOUN
iajs-1807	95	39	:	:	PUNCT
iajs-1807	95	40	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1807	95	41	  	  	SPACE
iajs-1807	95	42	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1807	95	43	   	   	SPACE
iajs-1807	95	44	mathematics	mathematic	NOUN
iajs-1807	95	45	|352	|352	ADJ
iajs-1807	95	46	    	    	SPACE
iajs-1807	95	47	figure	figure	NOUN
iajs-1807	95	48	(	(	PUNCT
iajs-1807	95	49	4	4	NUM
iajs-1807	95	50	):	):	PUNCT
iajs-1807	95	51	(	(	PUNCT
iajs-1807	95	52	a	a	X
iajs-1807	95	53	)	)	PUNCT
iajs-1807	95	54	the	the	DET
iajs-1807	95	55	calculators	calculator	NOUN
iajs-1807	95	56	of	of	ADP
iajs-1807	95	57	equation	equation	NOUN
iajs-1807	95	58	(	(	PUNCT
iajs-1807	95	59	13	13	NUM
iajs-1807	95	60	)	)	PUNCT
iajs-1807	95	61	,	,	PUNCT
iajs-1807	95	62	calculated	calculate	VERB
iajs-1807	95	63	with	with	ADP
iajs-1807	95	64	the	the	DET
iajs-1807	95	65	fem	fem	NOUN
iajs-1807	95	66	piecewise	piecewise	PROPN
iajs-1807	95	67	linear	linear	PROPN
iajs-1807	95	68	function	function	NOUN
iajs-1807	95	69	.	.	PUNCT
iajs-1807	96	1	figure	figure	NOUN
iajs-1807	96	2	(	(	PUNCT
iajs-1807	96	3	5	5	NUM
iajs-1807	96	4	):	):	PUNCT
iajs-1807	96	5	(	(	PUNCT
iajs-1807	96	6	b	b	X
iajs-1807	96	7	)	)	PUNCT
iajs-1807	96	8	the	the	DET
iajs-1807	96	9	calculators	calculator	NOUN
iajs-1807	96	10	of	of	ADP
iajs-1807	96	11	equation	equation	NOUN
iajs-1807	96	12	(	(	PUNCT
iajs-1807	96	13	13	13	NUM
iajs-1807	96	14	)	)	PUNCT
iajs-1807	96	15	,	,	PUNCT
iajs-1807	96	16	calculated	calculate	VERB
iajs-1807	96	17	with	with	ADP
iajs-1807	96	18	the	the	DET
iajs-1807	96	19	fem	fem	NOUN
iajs-1807	96	20	of	of	ADP
iajs-1807	96	21	linear	linear	PROPN
iajs-1807	96	22	triangular	triangular	NOUN
iajs-1807	96	23	element	element	NOUN
iajs-1807	96	24	.	.	PUNCT
iajs-1807	97	1	3	3	X
iajs-1807	97	2	.	.	X
iajs-1807	97	3	conclusions	conclusion	NOUN
iajs-1807	97	4	the	the	DET
iajs-1807	97	5	finite	finite	PROPN
iajs-1807	97	6	element	element	NOUN
iajs-1807	97	7	method	method	NOUN
iajs-1807	97	8	with	with	ADP
iajs-1807	97	9	using	use	VERB
iajs-1807	97	10	different	different	ADJ
iajs-1807	97	11	base	base	NOUN
iajs-1807	97	12	piecewise	piecewise	NOUN
iajs-1807	97	13	linear	linear	NOUN
iajs-1807	97	14	function	function	NOUN
iajs-1807	97	15	are	be	AUX
iajs-1807	97	16	used	use	VERB
iajs-1807	97	17	for	for	ADP
iajs-1807	97	18	solving	solve	VERB
iajs-1807	97	19	the	the	DET
iajs-1807	97	20	nanoscale	nanoscale	NOUN
iajs-1807	97	21	structures	structure	NOUN
iajs-1807	97	22	consisting	consist	VERB
iajs-1807	97	23	of	of	ADP
iajs-1807	97	24	the	the	DET
iajs-1807	97	25	𝐼𝑛𝐴𝑠	𝐼𝑛𝐴𝑠	PROPN
iajs-1807	97	26	𝐺𝑎𝐴𝑠⁄	𝐺𝑎𝐴𝑠⁄	ADJ
iajs-1807	97	27	quantum	quantum	NOUN
iajs-1807	97	28	ring	ring	NOUN
iajs-1807	97	29	,	,	PUNCT
iajs-1807	97	30	and	and	CCONJ
iajs-1807	97	31	the	the	DET
iajs-1807	97	32	spin	spin	NOUN
iajs-1807	97	33	-	-	PUNCT
iajs-1807	97	34	dependent	dependent	ADJ
iajs-1807	97	35	on	on	ADP
iajs-1807	97	36	the	the	DET
iajs-1807	97	37	ben	ben	PROPN
iajs-1807	97	38	daniel	daniel	PROPN
iajs-1807	97	39	-	-	PUNCT
iajs-1807	97	40	duke	duke	PROPN
iajs-1807	97	41	boundary	boundary	ADJ
iajs-1807	97	42	conditions	condition	NOUN
iajs-1807	97	43	.	.	PUNCT
iajs-1807	98	1	the	the	DET
iajs-1807	98	2	results	result	NOUN
iajs-1807	98	3	of	of	ADP
iajs-1807	98	4	numerical	numerical	ADJ
iajs-1807	98	5	example	example	NOUN
iajs-1807	98	6	give	give	VERB
iajs-1807	98	7	a	a	DET
iajs-1807	98	8	perfect	perfect	ADJ
iajs-1807	98	9	accuracy	accuracy	NOUN
iajs-1807	98	10	and	and	CCONJ
iajs-1807	98	11	efficiency	efficiency	NOUN
iajs-1807	98	12	of	of	ADP
iajs-1807	98	13	this	this	DET
iajs-1807	98	14	approach	approach	NOUN
iajs-1807	98	15	.	.	PUNCT
iajs-1807	99	1	the	the	DET
iajs-1807	99	2	results	result	NOUN
iajs-1807	99	3	of	of	ADP
iajs-1807	99	4	numerical	numerical	ADJ
iajs-1807	99	5	example	example	NOUN
iajs-1807	99	6	give	give	VERB
iajs-1807	99	7	a	a	DET
iajs-1807	99	8	good	good	ADJ
iajs-1807	99	9	accuracy	accuracy	NOUN
iajs-1807	99	10	and	and	CCONJ
iajs-1807	99	11	efficiency	efficiency	NOUN
iajs-1807	99	12	of	of	ADP
iajs-1807	99	13	this	this	DET
iajs-1807	99	14	method	method	NOUN
iajs-1807	99	15	in	in	ADP
iajs-1807	99	16	comparison	comparison	NOUN
iajs-1807	99	17	with	with	ADP
iajs-1807	99	18	the	the	DET
iajs-1807	99	19	results	result	NOUN
iajs-1807	99	20	with	with	ADP
iajs-1807	99	21	fem	fem	NOUN
iajs-1807	99	22	of	of	ADP
iajs-1807	99	23	linear	linear	PROPN
iajs-1807	99	24	triangular	triangular	NOUN
iajs-1807	99	25	element	element	NOUN
iajs-1807	99	26	references	reference	NOUN
iajs-1807	99	27	[	[	X
iajs-1807	99	28	1	1	NUM
iajs-1807	99	29	]	]	X
iajs-1807	99	30	yiming	yiming	PROPN
iajs-1807	99	31	li;o	li;o	PROPN
iajs-1807	99	32	.	.	PUNCT
iajs-1807	100	1	voskoboynikov	voskoboynikov	PROPN
iajs-1807	100	2	;	;	PUNCT
iajs-1807	101	1	c.p	c.p	PROPN
iajs-1807	101	2	.	.	PROPN
iajs-1807	101	3	lee	lee	PROPN
iajs-1807	101	4	;	;	PUNCT
iajs-1807	101	5	s.m	s.m	PROPN
iajs-1807	101	6	.	.	PROPN
iajs-1807	101	7	sze	sze	PROPN
iajs-1807	101	8	‘	'	PUNCT
iajs-1807	101	9	‘	'	PUNCT
iajs-1807	101	10	computer	computer	NOUN
iajs-1807	101	11	simulation	simulation	NOUN
iajs-1807	101	12	of	of	ADP
iajs-1807	101	13	electron	electron	NOUN
iajs-1807	101	14	energy	energy	NOUN
iajs-1807	101	15	levels	level	NOUN
iajs-1807	101	16	for	for	ADP
iajs-1807	101	17	different	different	ADJ
iajs-1807	101	18	shape	shape	NOUN
iajs-1807	101	19	𝐼𝑛𝐴𝑠/𝐺𝑎𝐴𝑠	𝐼𝑛𝐴𝑠/𝐺𝑎𝐴𝑠	NOUN
iajs-1807	101	20	semiconductor	semiconductor	NOUN
iajs-1807	101	21	quantum	quantum	NOUN
iajs-1807	101	22	dots	dot	NOUN
iajs-1807	101	23	’’	’'	PUNCT
iajs-1807	101	24	computer	computer	NOUN
iajs-1807	101	25	physics	physics	NOUN
iajs-1807	101	26	communications	communication	NOUN
iajs-1807	101	27	,	,	PUNCT
iajs-1807	101	28	(	(	PUNCT
iajs-1807	101	29	141	141	NUM
iajs-1807	101	30	)	)	PUNCT
iajs-1807	101	31	,	,	PUNCT
iajs-1807	101	32	66	66	NUM
iajs-1807	101	33	-	-	SYM
iajs-1807	101	34	72	72	NUM
iajs-1807	101	35	.	.	PUNCT
iajs-1807	101	36	2001	2001	NUM
iajs-1807	101	37	.	.	PUNCT
iajs-1807	102	1	[	[	X
iajs-1807	102	2	2	2	NUM
iajs-1807	102	3	]	]	X
iajs-1807	102	4	yiming	yiming	PROPN
iajs-1807	102	5	li;o	li;o	PROPN
iajs-1807	102	6	.	.	PUNCT
iajs-1807	102	7	voskoboynikov	voskoboynikov	PROPN
iajs-1807	102	8	;	;	PUNCT
iajs-1807	103	1	c.p	c.p	PROPN
iajs-1807	103	2	.	.	PROPN
iajs-1807	103	3	lee	lee	PROPN
iajs-1807	103	4	;	;	PUNCT
iajs-1807	103	5	s.m	s.m	PROPN
iajs-1807	103	6	.	.	PROPN
iajs-1807	103	7	sze	sze	PROPN
iajs-1807	103	8	o.	o.	PROPN
iajs-1807	103	9	tretyak	tretyak	PROPN
iajs-1807	103	10	‘	'	PUNCT
iajs-1807	103	11	‘	'	PUNCT
iajs-1807	103	12	electron	electron	NOUN
iajs-1807	103	13	energy	energy	NOUN
iajs-1807	103	14	state	state	NOUN
iajs-1807	103	15	spin	spin	NOUN
iajs-1807	103	16	-	-	PUNCT
iajs-1807	103	17	splitting	splitting	NOUN
iajs-1807	103	18	in	in	ADP
iajs-1807	103	19	3d	3d	NUM
iajs-1807	103	20	cylindrical	cylindrical	ADJ
iajs-1807	103	21	semiconductor	semiconductor	NOUN
iajs-1807	103	22	quantum	quantum	NOUN
iajs-1807	103	23	dots	dot	NOUN
iajs-1807	103	24	’’	’'	PUNCT
iajs-1807	103	25	the	the	DET
iajs-1807	103	26	european	european	PROPN
iajs-1807	103	27	physical	physical	PROPN
iajs-1807	103	28	journal	journal	PROPN
iajs-1807	103	29	b	b	PROPN
iajs-1807	103	30	,	,	PUNCT
iajs-1807	103	31	.	.	PUNCT
iajs-1807	104	1	(	(	PUNCT
iajs-1807	104	2	28	28	NUM
iajs-1807	104	3	)	)	PUNCT
iajs-1807	104	4	,	,	PUNCT
iajs-1807	104	5	(	(	PUNCT
iajs-1807	104	6	8)	8)	NUM
iajs-1807	104	7	,	,	PUNCT
iajs-1807	104	8	475–481	475–481	NUM
iajs-1807	104	9	.	.	PUNCT
iajs-1807	104	10	2002	2002	NUM
iajs-1807	104	11	.	.	PUNCT
iajs-1807	105	1	[	[	X
iajs-1807	105	2	3	3	X
iajs-1807	105	3	]	]	X
iajs-1807	105	4	g.	g.	PROPN
iajs-1807	105	5	paasch	paasch	PROPN
iajs-1807	105	6	;	;	PUNCT
iajs-1807	106	1	p.	p.	PROPN
iajs-1807	106	2	h.	h.	PROPN
iajs-1807	106	3	nguyen	nguyen	PROPN
iajs-1807	106	4	and	and	CCONJ
iajs-1807	106	5	g.	g.	PROPN
iajs-1807	106	6	gobsch	gobsch	PROPN
iajs-1807	106	7	‘	'	PUNCT
iajs-1807	106	8	‘	'	PUNCT
iajs-1807	106	9	envelope	envelope	NOUN
iajs-1807	106	10	equation	equation	NOUN
iajs-1807	106	11	and	and	CCONJ
iajs-1807	106	12	wave	wave	NOUN
iajs-1807	106	13	function	function	NOUN
iajs-1807	106	14	matching	match	VERB
iajs-1807	106	15	for	for	ADP
iajs-1807	106	16	narrow	narrow	ADJ
iajs-1807	106	17	-	-	PUNCT
iajs-1807	106	18	gap	gap	NOUN
iajs-1807	106	19	semiconductors	semiconductor	NOUN
iajs-1807	106	20	’’	’'	PUNCT
iajs-1807	106	21	physica	physica	NOUN
iajs-1807	106	22	status	status	NOUN
iajs-1807	106	23	solidi	solidi	NOUN
iajs-1807	106	24	(	(	PUNCT
iajs-1807	106	25	b	b	NOUN
iajs-1807	106	26	)	)	PUNCT
iajs-1807	106	27	,	,	PUNCT
iajs-1807	106	28	(	(	PUNCT
iajs-1807	106	29	162	162	NUM
iajs-1807	106	30	)	)	PUNCT
iajs-1807	106	31	,	,	PUNCT
iajs-1807	106	32	(	(	PUNCT
iajs-1807	106	33	1	1	NUM
iajs-1807	106	34	)	)	PUNCT
iajs-1807	106	35	,	,	PUNCT
iajs-1807	106	36	155–163	155–163	NUM
iajs-1807	106	37	.	.	PUNCT
iajs-1807	106	38	1990	1990	NUM
iajs-1807	106	39	[	[	X
iajs-1807	106	40	4	4	X
iajs-1807	106	41	]	]	X
iajs-1807	106	42	d.	d.	PROPN
iajs-1807	106	43	l.	l.	PROPN
iajs-1807	106	44	mathine;s	mathine;s	PROPN
iajs-1807	106	45	.	.	PUNCT
iajs-1807	107	1	k.	k.	PROPN
iajs-1807	107	2	myjak	myjak	PROPN
iajs-1807	107	3	and	and	CCONJ
iajs-1807	107	4	g.	g.	PROPN
iajs-1807	107	5	n.	n.	PROPN
iajs-1807	107	6	maracas	maraca	NOUN
iajs-1807	107	7	‘	'	PUNCT
iajs-1807	107	8	‘	'	PUNCT
iajs-1807	107	9	a	a	DET
iajs-1807	107	10	computational	computational	ADJ
iajs-1807	107	11	fourier	fourier	NOUN
iajs-1807	107	12	series	series	NOUN
iajs-1807	107	13	solutin	solutin	ADJ
iajs-1807	107	14	of	of	ADP
iajs-1807	107	15	the	the	DET
iajs-1807	107	16	bendaniel	bendaniel	NOUN
iajs-1807	107	17	-	-	PUNCT
iajs-1807	107	18	duke	duke	NOUN
iajs-1807	107	19	hamiltonian	hamiltonian	NOUN
iajs-1807	107	20	for	for	ADP
iajs-1807	107	21	arbitrary	arbitrary	ADJ
iajs-1807	107	22	shaped	shaped	ADJ
iajs-1807	107	23	quantum	quantum	ADJ
iajs-1807	107	24	wells	well	NOUN
iajs-1807	107	25	’’	’'	PUNCT
iajs-1807	107	26	ieee	ieee	NOUN
iajs-1807	107	27	journal	journal	NOUN
iajs-1807	107	28	of	of	ADP
iajs-1807	107	29	quantum	quantum	ADJ
iajs-1807	107	30	electronics	electronic	NOUN
iajs-1807	107	31	,	,	PUNCT
iajs-1807	107	32	.	.	PUNCT
iajs-1807	108	1	(	(	PUNCT
iajs-1807	108	2	31	31	NUM
iajs-1807	108	3	)	)	PUNCT
iajs-1807	108	4	,	,	PUNCT
iajs-1807	108	5	1216‑1222	1216‑1222	NUM
iajs-1807	108	6	.	.	NOUN
iajs-1807	108	7	1995	1995	NUM
iajs-1807	109	1	[	[	X
iajs-1807	109	2	5	5	NUM
iajs-1807	109	3	]	]	PUNCT
iajs-1807	109	4	m.	m.	NOUN
iajs-1807	109	5	willatzence	willatzence	NOUN
iajs-1807	109	6	;	;	PUNCT
iajs-1807	109	7	r.	r.	PROPN
iajs-1807	109	8	melnik	melnik	X
iajs-1807	109	9	;	;	PUNCT
iajs-1807	109	10	c.	c.	PROPN
iajs-1807	109	11	galeriu	galeriu	PROPN
iajs-1807	109	12	and	and	CCONJ
iajs-1807	109	13	l.	l.	PROPN
iajs-1807	109	14	c.	c.	PROPN
iajs-1807	109	15	lew	lew	PROPN
iajs-1807	109	16	yan	yan	PROPN
iajs-1807	109	17	voon	voon	PROPN
iajs-1807	109	18	‘	'	PUNCT
iajs-1807	109	19	‘	'	PUNCT
iajs-1807	109	20	finite	finite	ADJ
iajs-1807	109	21	element	element	NOUN
iajs-1807	109	22	analysis	analysis	NOUN
iajs-1807	109	23	of	of	ADP
iajs-1807	109	24	nanowire	nanowire	ADJ
iajs-1807	109	25	superlattice	superlattice	NOUN
iajs-1807	109	26	structures	structure	NOUN
iajs-1807	109	27	’’	’'	PUNCT
iajs-1807	109	28	springer	springer	NOUN
iajs-1807	109	29	,	,	PUNCT
iajs-1807	109	30	(	(	PUNCT
iajs-1807	109	31	31	31	NUM
iajs-1807	109	32	)	)	PUNCT
iajs-1807	109	33	,	,	PUNCT
iajs-1807	109	34	755‑763	755‑763	NUM
iajs-1807	109	35	.	.	PUNCT
iajs-1807	109	36	2003	2003	NUM
iajs-1807	110	1	[	[	X
iajs-1807	110	2	6	6	NUM
iajs-1807	110	3	]	]	X
iajs-1807	110	4	yiming	yiming	PROPN
iajs-1807	110	5	li	li	PROPN
iajs-1807	110	6	,	,	PUNCT
iajs-1807	110	7	‘	'	PUNCT
iajs-1807	110	8	‘	'	PUNCT
iajs-1807	110	9	an	an	DET
iajs-1807	110	10	iterative	iterative	NOUN
iajs-1807	110	11	method	method	NOUN
iajs-1807	110	12	for	for	ADP
iajs-1807	110	13	single	single	ADJ
iajs-1807	110	14	and	and	CCONJ
iajs-1807	110	15	vertically	vertically	ADV
iajs-1807	110	16	stacked	stack	VERB
iajs-1807	110	17	semiconductor	semiconductor	NOUN
iajs-1807	110	18	quantum	quantum	NOUN
iajs-1807	110	19	dots	dot	NOUN
iajs-1807	110	20	simulation	simulation	NOUN
iajs-1807	110	21	’’	’'	PUNCT
iajs-1807	110	22	mathematical	mathematical	ADJ
iajs-1807	110	23	and	and	CCONJ
iajs-1807	110	24	computer	computer	NOUN
iajs-1807	110	25	modelling	modelling	NOUN
iajs-1807	110	26	,	,	PUNCT
iajs-1807	110	27	(	(	PUNCT
iajs-1807	110	28	42	42	NUM
iajs-1807	110	29	)	)	PUNCT
iajs-1807	110	30	,	,	PUNCT
iajs-1807	110	31	711‑718	711‑718	X
iajs-1807	110	32	.	.	PUNCT
iajs-1807	110	33	2005	2005	NUM
iajs-1807	111	1	[	[	X
iajs-1807	111	2	7	7	X
iajs-1807	111	3	]	]	X
iajs-1807	111	4	d.	d.	PROPN
iajs-1807	111	5	sarkara	sarkara	PROPN
iajs-1807	111	6	;	;	PUNCT
iajs-1807	111	7	a.	a.	NOUN
iajs-1807	111	8	deyasib	deyasib	NOUN
iajs-1807	111	9	‘	'	PUNCT
iajs-1807	111	10	‘	'	PUNCT
iajs-1807	111	11	field	field	NOUN
iajs-1807	111	12	induced	induce	VERB
iajs-1807	111	13	tuning	tuning	NOUN
iajs-1807	111	14	of	of	ADP
iajs-1807	111	15	dos	do	NOUN
iajs-1807	111	16	and	and	CCONJ
iajs-1807	111	17	eigenstates	eigenstate	NOUN
iajs-1807	111	18	in	in	ADP
iajs-1807	111	19	double	double	ADJ
iajs-1807	111	20	quantum	quantum	NOUN
iajs-1807	111	21	well	well	NOUN
iajs-1807	111	22	structure	structure	NOUN
iajs-1807	111	23	having	have	VERB
iajs-1807	111	24	gaussian	gaussian	ADJ
iajs-1807	111	25	geometry	geometry	NOUN
iajs-1807	111	26	’’	’'	PUNCT
iajs-1807	111	27	american	american	ADJ
iajs-1807	111	28	scientific	scientific	ADJ
iajs-1807	111	29	publishers	publisher	NOUN
iajs-1807	111	30	,	,	PUNCT
iajs-1807	111	31	(	(	PUNCT
iajs-1807	111	32	5	5	NUM
iajs-1807	111	33	)	)	PUNCT
iajs-1807	111	34	,	,	PUNCT
iajs-1807	111	35	(	(	PUNCT
iajs-1807	111	36	1	1	NUM
iajs-1807	111	37	)	)	PUNCT
iajs-1807	111	38	,	,	PUNCT
iajs-1807	111	39	138‑143	138‑143	NUM
iajs-1807	111	40	.	.	NOUN
iajs-1807	111	41	2016	2016	NUM
iajs-1807	112	1	[	[	X
iajs-1807	112	2	8	8	NUM
iajs-1807	112	3	]	]	X
iajs-1807	112	4	eman	eman	PROPN
iajs-1807	112	5	a.	a.	PROPN
iajs-1807	112	6	hussain	hussain	PROPN
iajs-1807	112	7	,	,	PUNCT
iajs-1807	113	1	jamil	jamil	PROPN
iajs-1807	113	2	a.	a.	PROPN
iajs-1807	113	3	a.	a.	PROPN
iajs-1807	113	4	al	al	PROPN
iajs-1807	113	5	-	-	PUNCT
iajs-1807	113	6	hawasy	hawasy	PROPN
iajs-1807	113	7	,	,	PUNCT
iajs-1807	113	8	lamyaa	lamyaa	PROPN
iajs-1807	113	9	h.	h.	PROPN
iajs-1807	113	10	ali	ali	PROPN
iajs-1807	113	11	,	,	PUNCT
iajs-1807	113	12	‘	'	PUNCT
iajs-1807	113	13	‘	'	PUNCT
iajs-1807	113	14	finite	finite	ADJ
iajs-1807	113	15	element	element	NOUN
iajs-1807	113	16	method	method	NOUN
iajs-1807	113	17	linear	linear	PROPN
iajs-1807	113	18	triangular	triangular	NOUN
iajs-1807	113	19	element	element	NOUN
iajs-1807	113	20	for	for	ADP
iajs-1807	113	21	solving	solve	VERB
iajs-1807	113	22	finite	finite	ADJ
iajs-1807	113	23	nanowire	nanowire	ADJ
iajs-1807	113	24	superlattice	superlattice	NOUN
iajs-1807	113	25	quantum	quantum	NOUN
iajs-1807	113	26	dot	dot	NOUN
iajs-1807	113	27	structures	structure	NOUN
iajs-1807	113	28	𝐺𝑎𝐴𝑠	𝐺𝑎𝐴𝑠	PROPN
iajs-1807	113	29	𝐴𝑙𝐺𝑎𝐴𝑠⁄	𝐴𝑙𝐺𝑎𝐴𝑠⁄	PROPN
iajs-1807	113	30	’’	’'	PUNCT
iajs-1807	113	31	journal	journal	NOUN
iajs-1807	113	32	of	of	ADP
iajs-1807	113	33	computer	computer	NOUN
iajs-1807	113	34	and	and	CCONJ
iajs-1807	113	35	mathematical	mathematical	ADJ
iajs-1807	113	36	sciences	science	NOUN
iajs-1807	113	37	,	,	PUNCT
iajs-1807	113	38	(	(	PUNCT
iajs-1807	113	39	2017	2017	NUM
iajs-1807	113	40	)	)	PUNCT
iajs-1807	113	41	,	,	PUNCT
iajs-1807	113	42	vol	vol	NOUN
iajs-1807	113	43	.	.	PUNCT
iajs-1807	113	44	8(3	8(3	NUM
iajs-1807	113	45	)	)	PUNCT
iajs-1807	113	46	,	,	PUNCT
iajs-1807	113	47	pp	pp	ADP
iajs-1807	113	48	.	.	PUNCT
iajs-1807	114	1	96	96	NUM
iajs-1807	114	2	-	-	SYM
iajs-1807	114	3	105	105	NUM
iajs-1807	114	4	.	.	PUNCT
iajs-1807	115	1	[	[	X
iajs-1807	115	2	9	9	NUM
iajs-1807	115	3	]	]	PUNCT
iajs-1807	115	4	eman	eman	PROPN
iajs-1807	115	5	a.	a.	PROPN
iajs-1807	115	6	hussain	hussain	PROPN
iajs-1807	115	7	,	,	PUNCT
iajs-1807	115	8	jamil	jamil	PROPN
iajs-1807	115	9	a.	a.	PROPN
iajs-1807	115	10	a.	a.	PROPN
iajs-1807	115	11	al	al	PROPN
iajs-1807	115	12	-	-	PUNCT
iajs-1807	115	13	hawasy	hawasy	PROPN
iajs-1807	115	14	,	,	PUNCT
iajs-1807	115	15	lamyaa	lamyaa	PROPN
iajs-1807	115	16	h.	h.	PROPN
iajs-1807	115	17	ali	ali	PROPN
iajs-1807	115	18	,	,	PUNCT
iajs-1807	115	19	‘	'	PUNCT
iajs-1807	115	20	‘	'	PUNCT
iajs-1807	115	21	finite	finite	ADJ
iajs-1807	115	22	element	element	NOUN
iajs-1807	115	23	method	method	NOUN
iajs-1807	115	24	linear	linear	PROPN
iajs-1807	115	25	rectangular	rectangular	ADJ
iajs-1807	115	26	element	element	NOUN
iajs-1807	115	27	for	for	ADP
iajs-1807	115	28	solving	solve	VERB
iajs-1807	115	29	finite	finite	ADJ
iajs-1807	115	30	nanowire	nanowire	ADJ
iajs-1807	115	31	superlattice	superlattice	NOUN
iajs-1807	115	32	quantum	quantum	NOUN
iajs-1807	115	33	dot	dot	NOUN
iajs-1807	115	34	structures	structure	NOUN
iajs-1807	115	35	𝐺𝑎𝐴𝑠	𝐺𝑎𝐴𝑠	PROPN
iajs-1807	115	36	𝐴𝑙𝐺𝑎𝐴𝑠⁄	𝐴𝑙𝐺𝑎𝐴𝑠⁄	PROPN
iajs-1807	115	37	’’	’'	PUNCT
iajs-1807	115	38	the	the	DET
iajs-1807	115	39	international	international	ADJ
iajs-1807	115	40	journal	journal	NOUN
iajs-1807	115	41	of	of	ADP
iajs-1807	115	42	engineering	engineering	NOUN
iajs-1807	115	43	and	and	CCONJ
iajs-1807	115	44	science	science	NOUN
iajs-1807	115	45	(	(	PUNCT
iajs-1807	115	46	ijes	ijes	PROPN
iajs-1807	115	47	)	)	PUNCT
iajs-1807	115	48	,	,	PUNCT
iajs-1807	115	49	6(4	6(4	NUM
iajs-1807	115	50	)	)	PUNCT
iajs-1807	115	51	,	,	PUNCT
iajs-1807	115	52	01	01	NUM
iajs-1807	115	53	-	-	SYM
iajs-1807	115	54	07	07	NUM
iajs-1807	115	55	.	.	PUNCT
iajs-1807	115	56	2017	2017	NUM
iajs-1807	115	57	.	.	PUNCT
iajs-1807	115	58	  	  	SPACE