id	sid	tid	token	lemma	pos
american_scientific_journal-2140	1	1	1	1	X
american_scientific_journal-2140	1	2	.	.	SYM
american_scientific_journal-2140	1	3	302	302	NUM
american_scientific_journal-2140	1	4	american	american	ADJ
american_scientific_journal-2140	1	5	scientific	scientific	ADJ
american_scientific_journal-2140	1	6	research	research	NOUN
american_scientific_journal-2140	1	7	journal	journal	NOUN
american_scientific_journal-2140	1	8	for	for	ADP
american_scientific_journal-2140	1	9	engineering	engineering	NOUN
american_scientific_journal-2140	1	10	,	,	PUNCT
american_scientific_journal-2140	1	11	technology	technology	NOUN
american_scientific_journal-2140	1	12	,	,	PUNCT
american_scientific_journal-2140	1	13	and	and	CCONJ
american_scientific_journal-2140	1	14	sciences	science	NOUN
american_scientific_journal-2140	1	15	(	(	PUNCT
american_scientific_journal-2140	1	16	asrjets	asrjet	NOUN
american_scientific_journal-2140	1	17	)	)	PUNCT
american_scientific_journal-2140	1	18	issn	issn	PROPN
american_scientific_journal-2140	1	19	(	(	PUNCT
american_scientific_journal-2140	1	20	print	print	NOUN
american_scientific_journal-2140	1	21	)	)	PUNCT
american_scientific_journal-2140	1	22	2313	2313	NUM
american_scientific_journal-2140	1	23	-	-	SYM
american_scientific_journal-2140	1	24	4410	4410	NUM
american_scientific_journal-2140	1	25	,	,	PUNCT
american_scientific_journal-2140	1	26	issn	issn	PROPN
american_scientific_journal-2140	1	27	(	(	PUNCT
american_scientific_journal-2140	1	28	online	online	ADJ
american_scientific_journal-2140	1	29	)	)	PUNCT
american_scientific_journal-2140	1	30	2313	2313	NUM
american_scientific_journal-2140	1	31	-	-	SYM
american_scientific_journal-2140	1	32	4402	4402	NUM
american_scientific_journal-2140	1	33	©	©	PROPN
american_scientific_journal-2140	1	34	global	global	ADJ
american_scientific_journal-2140	1	35	society	society	NOUN
american_scientific_journal-2140	1	36	of	of	ADP
american_scientific_journal-2140	1	37	scientific	scientific	ADJ
american_scientific_journal-2140	1	38	research	research	NOUN
american_scientific_journal-2140	1	39	and	and	CCONJ
american_scientific_journal-2140	1	40	researchers	researcher	NOUN
american_scientific_journal-2140	1	41	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-2140	1	42	on	on	ADP
american_scientific_journal-2140	1	43	extensions	extension	NOUN
american_scientific_journal-2140	1	44	of	of	ADP
american_scientific_journal-2140	1	45	the	the	DET
american_scientific_journal-2140	1	46	optical	optical	ADJ
american_scientific_journal-2140	1	47	optimization	optimization	NOUN
american_scientific_journal-2140	1	48	b.	b.	PROPN
american_scientific_journal-2140	1	49	n.	n.	PROPN
american_scientific_journal-2140	1	50	tiwari	tiwari	PROPN
american_scientific_journal-2140	2	1	a	a	DET
american_scientific_journal-2140	2	2	,	,	PUNCT
american_scientific_journal-2140	2	3	c	c	X
american_scientific_journal-2140	2	4	*	*	PUNCT
american_scientific_journal-2140	2	5	,	,	PUNCT
american_scientific_journal-2140	2	6	j.	j.	PROPN
american_scientific_journal-2140	2	7	k.	k.	PROPN
american_scientific_journal-2140	3	1	kuipo	kuipo	PROPN
american_scientific_journal-2140	3	2	b	b	PROPN
american_scientific_journal-2140	3	3	,	,	PUNCT
american_scientific_journal-2140	3	4	s.	s.	PROPN
american_scientific_journal-2140	3	5	bellucci	bellucci	PROPN
american_scientific_journal-2140	3	6	c	c	PROPN
american_scientific_journal-2140	3	7	,	,	PUNCT
american_scientific_journal-2140	3	8	n.	n.	PROPN
american_scientific_journal-2140	3	9	marina	marina	PROPN
american_scientific_journal-2140	4	1	d	d	X
american_scientific_journal-2140	4	2	a	a	PROPN
american_scientific_journal-2140	4	3	,	,	PUNCT
american_scientific_journal-2140	4	4	b	b	NOUN
american_scientific_journal-2140	4	5	,	,	PUNCT
american_scientific_journal-2140	4	6	d	d	PROPN
american_scientific_journal-2140	4	7	university	university	NOUN
american_scientific_journal-2140	4	8	of	of	ADP
american_scientific_journal-2140	4	9	information	information	NOUN
american_scientific_journal-2140	4	10	science	science	NOUN
american_scientific_journal-2140	4	11	and	and	CCONJ
american_scientific_journal-2140	4	12	technology	technology	NOUN
american_scientific_journal-2140	4	13	,	,	PUNCT
american_scientific_journal-2140	4	14	st	st	PROPN
american_scientific_journal-2140	4	15	.	.	PROPN
american_scientific_journal-2140	4	16	paul	paul	PROPN
american_scientific_journal-2140	4	17	the	the	DET
american_scientific_journal-2140	4	18	apostle	apostle	PROPN
american_scientific_journal-2140	4	19	,	,	PUNCT
american_scientific_journal-2140	4	20	partizanska	partizanska	NOUN
american_scientific_journal-2140	4	21	bb	bb	PROPN
american_scientific_journal-2140	4	22	,	,	PUNCT
american_scientific_journal-2140	4	23	6000	6000	NUM
american_scientific_journal-2140	4	24	ohrid	ohrid	PROPN
american_scientific_journal-2140	4	25	,	,	PUNCT
american_scientific_journal-2140	4	26	republic	republic	NOUN
american_scientific_journal-2140	4	27	of	of	ADP
american_scientific_journal-2140	4	28	macedonia	macedonia	PROPN
american_scientific_journal-2140	4	29	c	c	PROPN
american_scientific_journal-2140	4	30	infn	infn	PROPN
american_scientific_journal-2140	4	31	-	-	PUNCT
american_scientific_journal-2140	4	32	laboratori	laboratori	PROPN
american_scientific_journal-2140	4	33	nazionali	nazionali	PROPN
american_scientific_journal-2140	4	34	di	di	PROPN
american_scientific_journal-2140	4	35	frascati	frascati	PROPN
american_scientific_journal-2140	4	36	,	,	PUNCT
american_scientific_journal-2140	4	37	via	via	ADP
american_scientific_journal-2140	4	38	e.	e.	PROPN
american_scientific_journal-2140	4	39	fermi	fermi	PROPN
american_scientific_journal-2140	4	40	,	,	PUNCT
american_scientific_journal-2140	4	41	40	40	NUM
american_scientific_journal-2140	4	42	-i-00044	-i-00044	NUM
american_scientific_journal-2140	4	43	frascati	frascati	PROPN
american_scientific_journal-2140	4	44	,	,	PUNCT
american_scientific_journal-2140	4	45	rome	rome	PROPN
american_scientific_journal-2140	4	46	,	,	PUNCT
american_scientific_journal-2140	4	47	italy	italy	PROPN
american_scientific_journal-2140	4	48	a	a	DET
american_scientific_journal-2140	4	49	email	email	NOUN
american_scientific_journal-2140	4	50	:	:	PUNCT
american_scientific_journal-2140	4	51	bhupendra.tiwari@uist.edu.mk	bhupendra.tiwari@uist.edu.mk	PROPN
american_scientific_journal-2140	4	52	b	b	PROPN
american_scientific_journal-2140	4	53	email	email	NOUN
american_scientific_journal-2140	4	54	:	:	PUNCT
american_scientific_journal-2140	4	55	kuipo.kibinde.jude@cns.uist.edu.mk	kuipo.kibinde.jude@cns.uist.edu.mk	PROPN
american_scientific_journal-2140	4	56	c	c	NOUN
american_scientific_journal-2140	4	57	email	email	NOUN
american_scientific_journal-2140	4	58	:	:	PUNCT
american_scientific_journal-2140	4	59	stefano.bellucci@lnf.infn.it	stefano.bellucci@lnf.infn.it	NUM
american_scientific_journal-2140	4	60	d	d	NOUN
american_scientific_journal-2140	4	61	email	email	NOUN
american_scientific_journal-2140	4	62	:	:	PUNCT
american_scientific_journal-2140	4	63	rector@uist.edu.mk	rector@uist.edu.mk	NOUN
american_scientific_journal-2140	4	64	abstract	abstract	NOUN
american_scientific_journal-2140	4	65	we	we	PRON
american_scientific_journal-2140	4	66	offer	offer	VERB
american_scientific_journal-2140	4	67	an	an	DET
american_scientific_journal-2140	4	68	optimized	optimize	VERB
american_scientific_journal-2140	4	69	image	image	NOUN
american_scientific_journal-2140	4	70	formation	formation	NOUN
american_scientific_journal-2140	4	71	by	by	ADP
american_scientific_journal-2140	4	72	considering	consider	VERB
american_scientific_journal-2140	4	73	the	the	DET
american_scientific_journal-2140	4	74	focal	focal	ADJ
american_scientific_journal-2140	4	75	length	length	NOUN
american_scientific_journal-2140	4	76	of	of	ADP
american_scientific_journal-2140	4	77	a	a	DET
american_scientific_journal-2140	4	78	lens/	lens/	NUM
american_scientific_journal-2140	4	79	mirror	mirror	NOUN
american_scientific_journal-2140	4	80	or	or	CCONJ
american_scientific_journal-2140	4	81	their	their	PRON
american_scientific_journal-2140	4	82	combination	combination	NOUN
american_scientific_journal-2140	4	83	as	as	ADP
american_scientific_journal-2140	4	84	the	the	DET
american_scientific_journal-2140	4	85	objective	objective	ADJ
american_scientific_journal-2140	4	86	function	function	NOUN
american_scientific_journal-2140	4	87	.	.	PUNCT
american_scientific_journal-2140	5	1	we	we	PRON
american_scientific_journal-2140	5	2	characterize	characterize	VERB
american_scientific_journal-2140	5	3	the	the	DET
american_scientific_journal-2140	5	4	stability	stability	NOUN
american_scientific_journal-2140	5	5	and	and	CCONJ
american_scientific_journal-2140	5	6	correlation	correlation	NOUN
american_scientific_journal-2140	5	7	properties	property	NOUN
american_scientific_journal-2140	5	8	of	of	ADP
american_scientific_journal-2140	5	9	an	an	DET
american_scientific_journal-2140	5	10	image	image	NOUN
american_scientific_journal-2140	5	11	under	under	ADP
american_scientific_journal-2140	5	12	fluctuations	fluctuation	NOUN
american_scientific_journal-2140	5	13	of	of	ADP
american_scientific_journal-2140	5	14	the	the	DET
american_scientific_journal-2140	5	15	lateral	lateral	ADJ
american_scientific_journal-2140	5	16	magnification	magnification	NOUN
american_scientific_journal-2140	5	17	and	and	CCONJ
american_scientific_journal-2140	5	18	object	object	VERB
american_scientific_journal-2140	5	19	distance	distance	NOUN
american_scientific_journal-2140	5	20	.	.	PUNCT
american_scientific_journal-2140	6	1	the	the	DET
american_scientific_journal-2140	6	2	local	local	ADJ
american_scientific_journal-2140	6	3	stability	stability	NOUN
american_scientific_journal-2140	6	4	of	of	ADP
american_scientific_journal-2140	6	5	an	an	DET
american_scientific_journal-2140	6	6	image	image	NOUN
american_scientific_journal-2140	6	7	thus	thus	ADV
american_scientific_journal-2140	6	8	formed	form	VERB
american_scientific_journal-2140	6	9	is	be	AUX
american_scientific_journal-2140	6	10	determined	determine	VERB
american_scientific_journal-2140	6	11	by	by	ADP
american_scientific_journal-2140	6	12	the	the	DET
american_scientific_journal-2140	6	13	positivity	positivity	NOUN
american_scientific_journal-2140	6	14	of	of	ADP
american_scientific_journal-2140	6	15	the	the	DET
american_scientific_journal-2140	6	16	pure	pure	ADJ
american_scientific_journal-2140	6	17	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	6	18	components	component	NOUN
american_scientific_journal-2140	6	19	,	,	PUNCT
american_scientific_journal-2140	6	20	while	while	SCONJ
american_scientific_journal-2140	6	21	its	its	PRON
american_scientific_journal-2140	6	22	global	global	ADJ
american_scientific_journal-2140	6	23	counterpart	counterpart	NOUN
american_scientific_journal-2140	6	24	as	as	ADP
american_scientific_journal-2140	6	25	that	that	PRON
american_scientific_journal-2140	6	26	of	of	ADP
american_scientific_journal-2140	6	27	the	the	DET
american_scientific_journal-2140	6	28	determinant	determinant	NOUN
american_scientific_journal-2140	6	29	of	of	ADP
american_scientific_journal-2140	6	30	the	the	DET
american_scientific_journal-2140	6	31	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	6	32	matrix	matrix	NOUN
american_scientific_journal-2140	6	33	.	.	PUNCT
american_scientific_journal-2140	7	1	we	we	PRON
american_scientific_journal-2140	7	2	find	find	VERB
american_scientific_journal-2140	7	3	that	that	SCONJ
american_scientific_journal-2140	7	4	the	the	DET
american_scientific_journal-2140	7	5	concave	concave	ADJ
american_scientific_journal-2140	7	6	and	and	CCONJ
american_scientific_journal-2140	7	7	convex	convex	PROPN
american_scientific_journal-2140	7	8	systems	system	NOUN
american_scientific_journal-2140	7	9	render	render	VERB
american_scientific_journal-2140	7	10	disjoint	disjoint	NOUN
american_scientific_journal-2140	7	11	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	7	12	surfaces	surface	NOUN
american_scientific_journal-2140	7	13	about	about	ADP
american_scientific_journal-2140	7	14	the	the	DET
american_scientific_journal-2140	7	15	line	line	NOUN
american_scientific_journal-2140	7	16	of	of	ADP
american_scientific_journal-2140	7	17	the	the	DET
american_scientific_journal-2140	7	18	unit	unit	NOUN
american_scientific_journal-2140	7	19	lateral	lateral	ADJ
american_scientific_journal-2140	7	20	magnification	magnification	NOUN
american_scientific_journal-2140	7	21	.	.	PUNCT
american_scientific_journal-2140	8	1	extended	extend	VERB
american_scientific_journal-2140	8	2	objective	objective	ADJ
american_scientific_journal-2140	8	3	functions	function	NOUN
american_scientific_journal-2140	8	4	are	be	AUX
american_scientific_journal-2140	8	5	constructed	construct	VERB
american_scientific_journal-2140	8	6	for	for	ADP
american_scientific_journal-2140	8	7	optical	optical	ADJ
american_scientific_journal-2140	8	8	systems	system	NOUN
american_scientific_journal-2140	8	9	with	with	ADP
american_scientific_journal-2140	8	10	finitely	finitely	ADV
american_scientific_journal-2140	8	11	many	many	ADJ
american_scientific_journal-2140	8	12	constrained	constrain	VERB
american_scientific_journal-2140	8	13	and	and	CCONJ
american_scientific_journal-2140	8	14	unconstrained	unconstrained	ADJ
american_scientific_journal-2140	8	15	components	component	NOUN
american_scientific_journal-2140	8	16	.	.	PUNCT
american_scientific_journal-2140	9	1	keywords	keyword	NOUN
american_scientific_journal-2140	9	2	:	:	PUNCT
american_scientific_journal-2140	9	3	optics	optic	NOUN
american_scientific_journal-2140	9	4	;	;	PUNCT
american_scientific_journal-2140	9	5	optimization	optimization	NOUN
american_scientific_journal-2140	9	6	;	;	PUNCT
american_scientific_journal-2140	9	7	instrument	instrument	NOUN
american_scientific_journal-2140	9	8	designing	designing	NOUN
american_scientific_journal-2140	9	9	;	;	PUNCT
american_scientific_journal-2140	9	10	stability	stability	NOUN
american_scientific_journal-2140	9	11	analysis	analysis	NOUN
american_scientific_journal-2140	9	12	;	;	PUNCT
american_scientific_journal-2140	9	13	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	9	14	model	model	NOUN
american_scientific_journal-2140	9	15	.	.	PUNCT
american_scientific_journal-2140	10	1	1	1	X
american_scientific_journal-2140	10	2	.	.	X
american_scientific_journal-2140	10	3	introduction	introduction	NOUN
american_scientific_journal-2140	10	4	geometrical	geometrical	ADJ
american_scientific_journal-2140	10	5	and	and	CCONJ
american_scientific_journal-2140	10	6	physical	physical	ADJ
american_scientific_journal-2140	10	7	optics	optic	NOUN
american_scientific_journal-2140	10	8	are	be	AUX
american_scientific_journal-2140	10	9	two	two	NUM
american_scientific_journal-2140	10	10	rubrics	rubric	NOUN
american_scientific_journal-2140	10	11	of	of	ADP
american_scientific_journal-2140	10	12	photonics	photonic	NOUN
american_scientific_journal-2140	10	13	under	under	ADP
american_scientific_journal-2140	10	14	which	which	PRON
american_scientific_journal-2140	10	15	the	the	DET
american_scientific_journal-2140	10	16	study	study	NOUN
american_scientific_journal-2140	10	17	of	of	ADP
american_scientific_journal-2140	10	18	light	light	NOUN
american_scientific_journal-2140	10	19	is	be	AUX
american_scientific_journal-2140	10	20	manifested	manifest	VERB
american_scientific_journal-2140	10	21	[	[	PUNCT
american_scientific_journal-2140	10	22	13	13	NUM
american_scientific_journal-2140	10	23	]	]	PUNCT
american_scientific_journal-2140	10	24	towards	towards	ADP
american_scientific_journal-2140	10	25	the	the	DET
american_scientific_journal-2140	10	26	formation	formation	NOUN
american_scientific_journal-2140	10	27	of	of	ADP
american_scientific_journal-2140	10	28	the	the	DET
american_scientific_journal-2140	10	29	image	image	NOUN
american_scientific_journal-2140	10	30	of	of	ADP
american_scientific_journal-2140	10	31	an	an	DET
american_scientific_journal-2140	10	32	object	object	NOUN
american_scientific_journal-2140	10	33	.	.	PUNCT
american_scientific_journal-2140	11	1	the	the	DET
american_scientific_journal-2140	11	2	complex	complex	ADJ
american_scientific_journal-2140	11	3	behavior	behavior	NOUN
american_scientific_journal-2140	11	4	of	of	ADP
american_scientific_journal-2140	11	5	light	light	ADJ
american_scientific_journal-2140	11	6	results	result	NOUN
american_scientific_journal-2140	11	7	in	in	ADP
american_scientific_journal-2140	11	8	the	the	DET
american_scientific_journal-2140	11	9	image	image	NOUN
american_scientific_journal-2140	11	10	formation	formation	NOUN
american_scientific_journal-2140	11	11	of	of	ADP
american_scientific_journal-2140	11	12	an	an	DET
american_scientific_journal-2140	11	13	object	object	NOUN
american_scientific_journal-2140	11	14	via	via	ADP
american_scientific_journal-2140	11	15	lens/	lens/	NUM
american_scientific_journal-2140	11	16	mirror	mirror	NOUN
american_scientific_journal-2140	11	17	or	or	CCONJ
american_scientific_journal-2140	11	18	their	their	PRON
american_scientific_journal-2140	11	19	finite	finite	ADJ
american_scientific_journal-2140	11	20	combination	combination	NOUN
american_scientific_journal-2140	11	21	as	as	ADP
american_scientific_journal-2140	11	22	a	a	DET
american_scientific_journal-2140	11	23	consequence	consequence	NOUN
american_scientific_journal-2140	11	24	of	of	ADP
american_scientific_journal-2140	11	25	the	the	DET
american_scientific_journal-2140	11	26	ray	ray	NOUN
american_scientific_journal-2140	11	27	model	model	NOUN
american_scientific_journal-2140	11	28	of	of	ADP
american_scientific_journal-2140	11	29	the	the	DET
american_scientific_journal-2140	11	30	light	light	NOUN
american_scientific_journal-2140	11	31	[	[	X
american_scientific_journal-2140	11	32	4	4	NUM
american_scientific_journal-2140	11	33	]	]	PUNCT
american_scientific_journal-2140	11	34	.	.	PUNCT
american_scientific_journal-2140	12	1	this	this	DET
american_scientific_journal-2140	12	2	model	model	NOUN
american_scientific_journal-2140	12	3	is	be	AUX
american_scientific_journal-2140	12	4	termed	term	VERB
american_scientific_journal-2140	12	5	as	as	ADP
american_scientific_journal-2140	12	6	the	the	DET
american_scientific_journal-2140	12	7	geometrical	geometrical	ADJ
american_scientific_journal-2140	12	8	optics	optic	NOUN
american_scientific_journal-2140	12	9	or	or	CCONJ
american_scientific_journal-2140	12	10	ray	ray	NOUN
american_scientific_journal-2140	12	11	optics	optic	NOUN
american_scientific_journal-2140	12	12	because	because	SCONJ
american_scientific_journal-2140	12	13	of	of	ADP
american_scientific_journal-2140	12	14	the	the	DET
american_scientific_journal-2140	12	15	fact	fact	NOUN
american_scientific_journal-2140	12	16	that	that	SCONJ
american_scientific_journal-2140	12	17	the	the	DET
american_scientific_journal-2140	12	18	image	image	NOUN
american_scientific_journal-2140	12	19	is	be	AUX
american_scientific_journal-2140	12	20	formed	form	VERB
american_scientific_journal-2140	12	21	as	as	ADP
american_scientific_journal-2140	12	22	an	an	DET
american_scientific_journal-2140	12	23	outcome	outcome	NOUN
american_scientific_journal-2140	12	24	of	of	ADP
american_scientific_journal-2140	12	25	the	the	DET
american_scientific_journal-2140	12	26	beam	beam	NOUN
american_scientific_journal-2140	12	27	or	or	CCONJ
american_scientific_journal-2140	12	28	a	a	DET
american_scientific_journal-2140	12	29	collection	collection	NOUN
american_scientific_journal-2140	12	30	of	of	ADP
american_scientific_journal-2140	12	31	light	light	ADJ
american_scientific_journal-2140	12	32	rays	ray	NOUN
american_scientific_journal-2140	12	33	propagating	propagate	VERB
american_scientific_journal-2140	12	34	linearly	linearly	ADV
american_scientific_journal-2140	12	35	[	[	X
american_scientific_journal-2140	12	36	3	3	NUM
american_scientific_journal-2140	12	37	]	]	PUNCT
american_scientific_journal-2140	12	38	.	.	PUNCT
american_scientific_journal-2140	13	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-2140	14	1	*	*	PUNCT
american_scientific_journal-2140	14	2	corresponding	correspond	VERB
american_scientific_journal-2140	14	3	author	author	NOUN
american_scientific_journal-2140	14	4	.	.	PUNCT
american_scientific_journal-2140	15	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-2140	15	2	american	american	PROPN
american_scientific_journal-2140	15	3	scientific	scientific	PROPN
american_scientific_journal-2140	15	4	research	research	NOUN
american_scientific_journal-2140	15	5	journal	journal	NOUN
american_scientific_journal-2140	15	6	for	for	ADP
american_scientific_journal-2140	15	7	engineering	engineering	NOUN
american_scientific_journal-2140	15	8	,	,	PUNCT
american_scientific_journal-2140	15	9	technology	technology	NOUN
american_scientific_journal-2140	15	10	,	,	PUNCT
american_scientific_journal-2140	15	11	and	and	CCONJ
american_scientific_journal-2140	15	12	sciences	science	NOUN
american_scientific_journal-2140	15	13	(	(	PUNCT
american_scientific_journal-2140	15	14	asrjets	asrjet	NOUN
american_scientific_journal-2140	15	15	)	)	PUNCT
american_scientific_journal-2140	15	16	(	(	PUNCT
american_scientific_journal-2140	15	17	2016	2016	NUM
american_scientific_journal-2140	15	18	)	)	PUNCT
american_scientific_journal-2140	15	19	volume	volume	NOUN
american_scientific_journal-2140	15	20	26	26	NUM
american_scientific_journal-2140	15	21	,	,	PUNCT
american_scientific_journal-2140	15	22	no	no	DET
american_scientific_journal-2140	15	23	1	1	NUM
american_scientific_journal-2140	15	24	,	,	PUNCT
american_scientific_journal-2140	15	25	pp	pp	ADV
american_scientific_journal-2140	15	26	302	302	NUM
american_scientific_journal-2140	15	27	-	-	SYM
american_scientific_journal-2140	15	28	313	313	NUM
american_scientific_journal-2140	15	29	303	303	NUM
american_scientific_journal-2140	15	30	it	it	PRON
american_scientific_journal-2140	15	31	is	be	AUX
american_scientific_journal-2140	15	32	worth	worth	ADJ
american_scientific_journal-2140	15	33	mentioning	mention	VERB
american_scientific_journal-2140	15	34	that	that	SCONJ
american_scientific_journal-2140	15	35	physical	physical	ADJ
american_scientific_journal-2140	15	36	processes	process	NOUN
american_scientific_journal-2140	15	37	with	with	ADP
american_scientific_journal-2140	15	38	phase	phase	NOUN
american_scientific_journal-2140	15	39	discontinuities	discontinuity	NOUN
american_scientific_journal-2140	15	40	which	which	PRON
american_scientific_journal-2140	15	41	arise	arise	VERB
american_scientific_journal-2140	15	42	in	in	ADP
american_scientific_journal-2140	15	43	realism	realism	NOUN
american_scientific_journal-2140	15	44	of	of	ADP
american_scientific_journal-2140	15	45	the	the	DET
american_scientific_journal-2140	15	46	geometrical	geometrical	ADJ
american_scientific_journal-2140	15	47	optics	optic	NOUN
american_scientific_journal-2140	15	48	are	be	AUX
american_scientific_journal-2140	15	49	modelled	model	VERB
american_scientific_journal-2140	15	50	by	by	ADP
american_scientific_journal-2140	15	51	generalized	generalized	ADJ
american_scientific_journal-2140	15	52	principles	principle	NOUN
american_scientific_journal-2140	15	53	of	of	ADP
american_scientific_journal-2140	15	54	the	the	DET
american_scientific_journal-2140	15	55	reflection	reflection	NOUN
american_scientific_journal-2140	15	56	and	and	CCONJ
american_scientific_journal-2140	15	57	refraction	refraction	NOUN
american_scientific_journal-2140	15	58	[	[	X
american_scientific_journal-2140	15	59	5	5	NUM
american_scientific_journal-2140	15	60	]	]	PUNCT
american_scientific_journal-2140	15	61	.	.	PUNCT
american_scientific_journal-2140	16	1	further	far	ADV
american_scientific_journal-2140	16	2	,	,	PUNCT
american_scientific_journal-2140	16	3	metamaterial	metamaterial	ADJ
american_scientific_journal-2140	16	4	based	base	VERB
american_scientific_journal-2140	16	5	generalizations	generalization	NOUN
american_scientific_journal-2140	16	6	,	,	PUNCT
american_scientific_journal-2140	16	7	viz	viz	NOUN
american_scientific_journal-2140	16	8	.	.	PUNCT
american_scientific_journal-2140	17	1	optical	optical	ADJ
american_scientific_journal-2140	17	2	cavities	cavity	NOUN
american_scientific_journal-2140	17	3	[	[	X
american_scientific_journal-2140	17	4	6	6	NUM
american_scientific_journal-2140	17	5	]	]	PUNCT
american_scientific_journal-2140	17	6	offer	offer	NOUN
american_scientific_journal-2140	17	7	perspective	perspective	NOUN
american_scientific_journal-2140	17	8	component	component	NOUN
american_scientific_journal-2140	17	9	designing	design	VERB
american_scientific_journal-2140	17	10	by	by	ADP
american_scientific_journal-2140	17	11	strongly	strongly	ADV
american_scientific_journal-2140	17	12	modifying	modify	VERB
american_scientific_journal-2140	17	13	the	the	DET
american_scientific_journal-2140	17	14	spectrum	spectrum	NOUN
american_scientific_journal-2140	17	15	of	of	ADP
american_scientific_journal-2140	17	16	the	the	DET
american_scientific_journal-2140	17	17	light	light	NOUN
american_scientific_journal-2140	17	18	.	.	PUNCT
american_scientific_journal-2140	18	1	in	in	ADP
american_scientific_journal-2140	18	2	this	this	DET
american_scientific_journal-2140	18	3	concern	concern	NOUN
american_scientific_journal-2140	18	4	,	,	PUNCT
american_scientific_journal-2140	18	5	the	the	DET
american_scientific_journal-2140	18	6	ray	ray	NOUN
american_scientific_journal-2140	18	7	model	model	NOUN
american_scientific_journal-2140	18	8	characterizes	characterize	VERB
american_scientific_journal-2140	18	9	solitonic	solitonic	ADJ
american_scientific_journal-2140	18	10	features	feature	NOUN
american_scientific_journal-2140	18	11	of	of	ADP
american_scientific_journal-2140	18	12	light	light	NOUN
american_scientific_journal-2140	18	13	towards	towards	ADP
american_scientific_journal-2140	18	14	its	its	PRON
american_scientific_journal-2140	18	15	pulse	pulse	NOUN
american_scientific_journal-2140	18	16	narrowing	narrow	VERB
american_scientific_journal-2140	18	17	applications	application	NOUN
american_scientific_journal-2140	18	18	in	in	ADP
american_scientific_journal-2140	18	19	optical	optical	ADJ
american_scientific_journal-2140	18	20	instrumentations	instrumentation	NOUN
american_scientific_journal-2140	18	21	involving	involve	VERB
american_scientific_journal-2140	18	22	lenses	lense	NOUN
american_scientific_journal-2140	18	23	,	,	PUNCT
american_scientific_journal-2140	18	24	mirrors	mirror	NOUN
american_scientific_journal-2140	18	25	,	,	PUNCT
american_scientific_journal-2140	18	26	optical	optical	ADJ
american_scientific_journal-2140	18	27	fibers	fiber	NOUN
american_scientific_journal-2140	18	28	and	and	CCONJ
american_scientific_journal-2140	18	29	prisms	prism	NOUN
american_scientific_journal-2140	18	30	[	[	X
american_scientific_journal-2140	18	31	7	7	NUM
american_scientific_journal-2140	18	32	]	]	PUNCT
american_scientific_journal-2140	18	33	.	.	PUNCT
american_scientific_journal-2140	19	1	as	as	ADP
american_scientific_journal-2140	19	2	per	per	ADP
american_scientific_journal-2140	19	3	this	this	DET
american_scientific_journal-2140	19	4	consideration	consideration	NOUN
american_scientific_journal-2140	19	5	,	,	PUNCT
american_scientific_journal-2140	19	6	the	the	DET
american_scientific_journal-2140	19	7	image	image	NOUN
american_scientific_journal-2140	19	8	is	be	AUX
american_scientific_journal-2140	19	9	exhibited	exhibit	VERB
american_scientific_journal-2140	19	10	as	as	ADP
american_scientific_journal-2140	19	11	an	an	DET
american_scientific_journal-2140	19	12	electromagnetic	electromagnetic	ADJ
american_scientific_journal-2140	19	13	phenomenon	phenomenon	NOUN
american_scientific_journal-2140	19	14	of	of	ADP
american_scientific_journal-2140	19	15	incoming	incoming	ADJ
american_scientific_journal-2140	19	16	light	light	ADJ
american_scientific_journal-2140	19	17	rays	ray	NOUN
american_scientific_journal-2140	19	18	falling	fall	VERB
american_scientific_journal-2140	19	19	on	on	ADP
american_scientific_journal-2140	19	20	the	the	DET
american_scientific_journal-2140	19	21	instrument	instrument	NOUN
american_scientific_journal-2140	19	22	.	.	PUNCT
american_scientific_journal-2140	20	1	hereby	hereby	ADV
american_scientific_journal-2140	20	2	,	,	PUNCT
american_scientific_journal-2140	20	3	we	we	PRON
american_scientific_journal-2140	20	4	find	find	VERB
american_scientific_journal-2140	20	5	that	that	SCONJ
american_scientific_journal-2140	20	6	lenses	lense	NOUN
american_scientific_journal-2140	20	7	,	,	PUNCT
american_scientific_journal-2140	20	8	mirrors	mirror	NOUN
american_scientific_journal-2140	20	9	and	and	CCONJ
american_scientific_journal-2140	20	10	their	their	PRON
american_scientific_journal-2140	20	11	combinations	combination	NOUN
american_scientific_journal-2140	20	12	arise	arise	VERB
american_scientific_journal-2140	20	13	as	as	ADP
american_scientific_journal-2140	20	14	the	the	DET
american_scientific_journal-2140	20	15	central	central	ADJ
american_scientific_journal-2140	20	16	interest	interest	NOUN
american_scientific_journal-2140	20	17	in	in	ADP
american_scientific_journal-2140	20	18	optical	optical	ADJ
american_scientific_journal-2140	20	19	designing	designing	NOUN
american_scientific_journal-2140	20	20	and	and	CCONJ
american_scientific_journal-2140	20	21	instrumentation	instrumentation	NOUN
american_scientific_journal-2140	20	22	engineering	engineering	NOUN
american_scientific_journal-2140	20	23	.	.	PUNCT
american_scientific_journal-2140	21	1	this	this	PRON
american_scientific_journal-2140	21	2	is	be	AUX
american_scientific_journal-2140	21	3	characterized	characterize	VERB
american_scientific_journal-2140	21	4	in	in	ADP
american_scientific_journal-2140	21	5	two	two	NUM
american_scientific_journal-2140	21	6	types	type	NOUN
american_scientific_journal-2140	21	7	.	.	PUNCT
american_scientific_journal-2140	22	1	namely	namely	ADV
american_scientific_journal-2140	22	2	,	,	PUNCT
american_scientific_journal-2140	22	3	a	a	DET
american_scientific_journal-2140	22	4	convex	convex	ADJ
american_scientific_journal-2140	22	5	lens	lens	NOUN
american_scientific_journal-2140	22	6	brings	bring	VERB
american_scientific_journal-2140	22	7	all	all	DET
american_scientific_journal-2140	22	8	light	light	ADJ
american_scientific_journal-2140	22	9	rays	ray	NOUN
american_scientific_journal-2140	22	10	incident	incident	NOUN
american_scientific_journal-2140	22	11	on	on	ADP
american_scientific_journal-2140	22	12	it	it	PRON
american_scientific_journal-2140	22	13	to	to	PART
american_scientific_journal-2140	22	14	converge	converge	VERB
american_scientific_journal-2140	22	15	at	at	ADP
american_scientific_journal-2140	22	16	its	its	PRON
american_scientific_journal-2140	22	17	focal	focal	ADJ
american_scientific_journal-2140	22	18	point	point	NOUN
american_scientific_journal-2140	22	19	,	,	PUNCT
american_scientific_journal-2140	22	20	see	see	VERB
american_scientific_journal-2140	22	21	for	for	ADP
american_scientific_journal-2140	22	22	instance	instance	NOUN
american_scientific_journal-2140	22	23	[	[	X
american_scientific_journal-2140	22	24	4	4	NUM
american_scientific_journal-2140	22	25	]	]	PUNCT
american_scientific_journal-2140	22	26	.	.	PUNCT
american_scientific_journal-2140	23	1	from	from	ADP
american_scientific_journal-2140	23	2	this	this	DET
american_scientific_journal-2140	23	3	perspective	perspective	NOUN
american_scientific_journal-2140	23	4	,	,	PUNCT
american_scientific_journal-2140	23	5	the	the	DET
american_scientific_journal-2140	23	6	distance	distance	NOUN
american_scientific_journal-2140	23	7	between	between	ADP
american_scientific_journal-2140	23	8	the	the	DET
american_scientific_journal-2140	23	9	optical	optical	ADJ
american_scientific_journal-2140	23	10	center	center	NOUN
american_scientific_journal-2140	23	11	and	and	CCONJ
american_scientific_journal-2140	23	12	its	its	PRON
american_scientific_journal-2140	23	13	focal	focal	ADJ
american_scientific_journal-2140	23	14	point	point	NOUN
american_scientific_journal-2140	23	15	termed	term	VERB
american_scientific_journal-2140	23	16	as	as	SCONJ
american_scientific_journal-2140	23	17	the	the	DET
american_scientific_journal-2140	23	18	focal	focal	ADJ
american_scientific_journal-2140	23	19	length	length	NOUN
american_scientific_journal-2140	23	20	of	of	ADP
american_scientific_journal-2140	23	21	the	the	DET
american_scientific_journal-2140	23	22	instrument	instrument	NOUN
american_scientific_journal-2140	23	23	offers	offer	VERB
american_scientific_journal-2140	23	24	an	an	DET
american_scientific_journal-2140	23	25	optimization	optimization	NOUN
american_scientific_journal-2140	23	26	function	function	NOUN
american_scientific_journal-2140	23	27	towards	towards	ADP
american_scientific_journal-2140	23	28	the	the	DET
american_scientific_journal-2140	23	29	stability	stability	NOUN
american_scientific_journal-2140	23	30	and	and	CCONJ
american_scientific_journal-2140	23	31	correlation	correlation	NOUN
american_scientific_journal-2140	23	32	analysis	analysis	NOUN
american_scientific_journal-2140	23	33	undermining	undermine	VERB
american_scientific_journal-2140	23	34	the	the	DET
american_scientific_journal-2140	23	35	formation	formation	NOUN
american_scientific_journal-2140	23	36	of	of	ADP
american_scientific_journal-2140	23	37	an	an	DET
american_scientific_journal-2140	23	38	image	image	NOUN
american_scientific_journal-2140	23	39	[	[	X
american_scientific_journal-2140	23	40	8	8	NUM
american_scientific_journal-2140	23	41	]	]	PUNCT
american_scientific_journal-2140	23	42	.	.	PUNCT
american_scientific_journal-2140	24	1	moreover	moreover	ADV
american_scientific_journal-2140	24	2	,	,	PUNCT
american_scientific_journal-2140	24	3	a	a	DET
american_scientific_journal-2140	24	4	concave	concave	ADJ
american_scientific_journal-2140	24	5	lens	lens	NOUN
american_scientific_journal-2140	24	6	likewise	likewise	ADV
american_scientific_journal-2140	24	7	diverges	diverge	VERB
american_scientific_journal-2140	24	8	the	the	DET
american_scientific_journal-2140	24	9	light	light	ADJ
american_scientific_journal-2140	24	10	rays	ray	NOUN
american_scientific_journal-2140	24	11	passing	pass	VERB
american_scientific_journal-2140	24	12	through	through	ADP
american_scientific_journal-2140	24	13	its	its	PRON
american_scientific_journal-2140	24	14	boundary	boundary	NOUN
american_scientific_journal-2140	24	15	.	.	PUNCT
american_scientific_journal-2140	25	1	essentially	essentially	ADV
american_scientific_journal-2140	25	2	,	,	PUNCT
american_scientific_journal-2140	25	3	this	this	PRON
american_scientific_journal-2140	25	4	forms	form	VERB
american_scientific_journal-2140	25	5	a	a	DET
american_scientific_journal-2140	25	6	virtual	virtual	ADJ
american_scientific_journal-2140	25	7	image	image	NOUN
american_scientific_journal-2140	25	8	because	because	SCONJ
american_scientific_journal-2140	25	9	of	of	ADP
american_scientific_journal-2140	25	10	an	an	DET
american_scientific_journal-2140	25	11	apparent	apparent	ADJ
american_scientific_journal-2140	25	12	converging	converge	VERB
american_scientific_journal-2140	25	13	point	point	NOUN
american_scientific_journal-2140	25	14	of	of	ADP
american_scientific_journal-2140	25	15	the	the	DET
american_scientific_journal-2140	25	16	refracted	refract	VERB
american_scientific_journal-2140	25	17	light	light	ADJ
american_scientific_journal-2140	25	18	rays	ray	NOUN
american_scientific_journal-2140	25	19	from	from	ADP
american_scientific_journal-2140	25	20	the	the	DET
american_scientific_journal-2140	25	21	lens	len	NOUN
american_scientific_journal-2140	25	22	.	.	PUNCT
american_scientific_journal-2140	26	1	as	as	ADV
american_scientific_journal-2140	26	2	far	far	ADV
american_scientific_journal-2140	26	3	as	as	SCONJ
american_scientific_journal-2140	26	4	mirrors	mirror	NOUN
american_scientific_journal-2140	26	5	are	be	AUX
american_scientific_journal-2140	26	6	concerned	concern	VERB
american_scientific_journal-2140	26	7	,	,	PUNCT
american_scientific_journal-2140	26	8	a	a	DET
american_scientific_journal-2140	26	9	concave	concave	ADJ
american_scientific_journal-2140	26	10	type	type	NOUN
american_scientific_journal-2140	26	11	mirror	mirror	NOUN
american_scientific_journal-2140	26	12	converges	converge	VERB
american_scientific_journal-2140	26	13	the	the	DET
american_scientific_journal-2140	26	14	reflected	reflect	VERB
american_scientific_journal-2140	26	15	rays	ray	NOUN
american_scientific_journal-2140	26	16	to	to	ADP
american_scientific_journal-2140	26	17	its	its	PRON
american_scientific_journal-2140	26	18	single	single	ADJ
american_scientific_journal-2140	26	19	focal	focal	ADJ
american_scientific_journal-2140	26	20	point	point	NOUN
american_scientific_journal-2140	26	21	,	,	PUNCT
american_scientific_journal-2140	26	22	whereas	whereas	SCONJ
american_scientific_journal-2140	26	23	the	the	DET
american_scientific_journal-2140	26	24	convex	convex	NOUN
american_scientific_journal-2140	26	25	mirrors	mirror	NOUN
american_scientific_journal-2140	26	26	diverge	diverge	VERB
american_scientific_journal-2140	26	27	the	the	DET
american_scientific_journal-2140	26	28	light	light	ADJ
american_scientific_journal-2140	26	29	rays	ray	NOUN
american_scientific_journal-2140	26	30	falling	fall	VERB
american_scientific_journal-2140	26	31	across	across	ADP
american_scientific_journal-2140	26	32	its	its	PRON
american_scientific_journal-2140	26	33	boundary	boundary	NOUN
american_scientific_journal-2140	26	34	in	in	ADP
american_scientific_journal-2140	26	35	order	order	NOUN
american_scientific_journal-2140	26	36	to	to	PART
american_scientific_journal-2140	26	37	form	form	VERB
american_scientific_journal-2140	26	38	a	a	DET
american_scientific_journal-2140	26	39	virtual	virtual	ADJ
american_scientific_journal-2140	26	40	image	image	NOUN
american_scientific_journal-2140	26	41	.	.	PUNCT
american_scientific_journal-2140	27	1	such	such	ADJ
american_scientific_journal-2140	27	2	optical	optical	ADJ
american_scientific_journal-2140	27	3	events	event	NOUN
american_scientific_journal-2140	27	4	happen	happen	VERB
american_scientific_journal-2140	27	5	because	because	SCONJ
american_scientific_journal-2140	27	6	of	of	ADP
american_scientific_journal-2140	27	7	an	an	DET
american_scientific_journal-2140	27	8	apparent	apparent	ADJ
american_scientific_journal-2140	27	9	converging	converging	NOUN
american_scientific_journal-2140	27	10	of	of	ADP
american_scientific_journal-2140	27	11	the	the	DET
american_scientific_journal-2140	27	12	reflected	reflect	VERB
american_scientific_journal-2140	27	13	rays	ray	NOUN
american_scientific_journal-2140	27	14	from	from	ADP
american_scientific_journal-2140	27	15	the	the	DET
american_scientific_journal-2140	27	16	mirror	mirror	NOUN
american_scientific_journal-2140	27	17	[	[	X
american_scientific_journal-2140	27	18	4	4	NUM
american_scientific_journal-2140	27	19	]	]	PUNCT
american_scientific_journal-2140	27	20	,	,	PUNCT
american_scientific_journal-2140	27	21	whereby	whereby	SCONJ
american_scientific_journal-2140	27	22	an	an	DET
american_scientific_journal-2140	27	23	optimized	optimize	VERB
american_scientific_journal-2140	27	24	image	image	NOUN
american_scientific_journal-2140	27	25	is	be	AUX
american_scientific_journal-2140	27	26	obtained	obtain	VERB
american_scientific_journal-2140	27	27	by	by	ADP
american_scientific_journal-2140	27	28	considering	consider	VERB
american_scientific_journal-2140	27	29	its	its	PRON
american_scientific_journal-2140	27	30	focal	focal	ADJ
american_scientific_journal-2140	27	31	length	length	NOUN
american_scientific_journal-2140	27	32	as	as	ADP
american_scientific_journal-2140	27	33	the	the	DET
american_scientific_journal-2140	27	34	objective	objective	ADJ
american_scientific_journal-2140	27	35	function	function	NOUN
american_scientific_journal-2140	27	36	.	.	PUNCT
american_scientific_journal-2140	28	1	concerning	concern	VERB
american_scientific_journal-2140	28	2	the	the	DET
american_scientific_journal-2140	28	3	physical	physical	ADJ
american_scientific_journal-2140	28	4	dimensions	dimension	NOUN
american_scientific_journal-2140	28	5	of	of	ADP
american_scientific_journal-2140	28	6	an	an	DET
american_scientific_journal-2140	28	7	image	image	NOUN
american_scientific_journal-2140	28	8	,	,	PUNCT
american_scientific_journal-2140	28	9	it	it	PRON
american_scientific_journal-2140	28	10	is	be	AUX
american_scientific_journal-2140	28	11	worth	worth	ADJ
american_scientific_journal-2140	28	12	noticing	notice	VERB
american_scientific_journal-2140	28	13	that	that	SCONJ
american_scientific_journal-2140	28	14	an	an	DET
american_scientific_journal-2140	28	15	image	image	NOUN
american_scientific_journal-2140	28	16	can	can	AUX
american_scientific_journal-2140	28	17	both	both	PRON
american_scientific_journal-2140	28	18	be	be	AUX
american_scientific_journal-2140	28	19	upright	upright	ADJ
american_scientific_journal-2140	28	20	or	or	CCONJ
american_scientific_journal-2140	28	21	inverted	invert	VERB
american_scientific_journal-2140	28	22	,	,	PUNCT
american_scientific_journal-2140	28	23	and	and	CCONJ
american_scientific_journal-2140	28	24	minimized	minimize	VERB
american_scientific_journal-2140	28	25	or	or	CCONJ
american_scientific_journal-2140	28	26	maximized	maximize	VERB
american_scientific_journal-2140	28	27	than	than	ADP
american_scientific_journal-2140	28	28	the	the	DET
american_scientific_journal-2140	28	29	corresponding	corresponding	ADJ
american_scientific_journal-2140	28	30	dimensions	dimension	NOUN
american_scientific_journal-2140	28	31	of	of	ADP
american_scientific_journal-2140	28	32	the	the	DET
american_scientific_journal-2140	28	33	object	object	NOUN
american_scientific_journal-2140	28	34	[	[	X
american_scientific_journal-2140	28	35	9	9	NUM
american_scientific_journal-2140	28	36	]	]	PUNCT
american_scientific_journal-2140	28	37	.	.	PUNCT
american_scientific_journal-2140	29	1	optimized	optimize	VERB
american_scientific_journal-2140	29	2	properties	property	NOUN
american_scientific_journal-2140	29	3	of	of	ADP
american_scientific_journal-2140	29	4	an	an	DET
american_scientific_journal-2140	29	5	image	image	NOUN
american_scientific_journal-2140	29	6	essentially	essentially	ADV
american_scientific_journal-2140	29	7	depend	depend	VERB
american_scientific_journal-2140	29	8	on	on	ADP
american_scientific_journal-2140	29	9	a	a	DET
american_scientific_journal-2140	29	10	pair	pair	NOUN
american_scientific_journal-2140	29	11	of	of	ADP
american_scientific_journal-2140	29	12	physical	physical	ADJ
american_scientific_journal-2140	29	13	quantities	quantity	NOUN
american_scientific_journal-2140	29	14	undermining	undermine	VERB
american_scientific_journal-2140	29	15	the	the	DET
american_scientific_journal-2140	29	16	optical	optical	ADJ
american_scientific_journal-2140	29	17	configuration	configuration	NOUN
american_scientific_journal-2140	29	18	.	.	PUNCT
american_scientific_journal-2140	30	1	first	first	ADV
american_scientific_journal-2140	30	2	of	of	ADP
american_scientific_journal-2140	30	3	all	all	PRON
american_scientific_journal-2140	30	4	,	,	PUNCT
american_scientific_journal-2140	30	5	for	for	ADP
american_scientific_journal-2140	30	6	an	an	DET
american_scientific_journal-2140	30	7	object	object	NOUN
american_scientific_journal-2140	30	8	situated	situate	VERB
american_scientific_journal-2140	30	9	at	at	ADP
american_scientific_journal-2140	30	10	a	a	DET
american_scientific_journal-2140	30	11	finite	finite	ADJ
american_scientific_journal-2140	30	12	distance	distance	NOUN
american_scientific_journal-2140	30	13	from	from	ADP
american_scientific_journal-2140	30	14	the	the	DET
american_scientific_journal-2140	30	15	optical	optical	ADJ
american_scientific_journal-2140	30	16	center	center	NOUN
american_scientific_journal-2140	30	17	of	of	ADP
american_scientific_journal-2140	30	18	a	a	DET
american_scientific_journal-2140	30	19	lens/	lens/	NUM
american_scientific_journal-2140	30	20	mirror	mirror	NOUN
american_scientific_journal-2140	30	21	or	or	CCONJ
american_scientific_journal-2140	30	22	composite	composite	ADJ
american_scientific_journal-2140	30	23	system	system	NOUN
american_scientific_journal-2140	30	24	consisting	consist	VERB
american_scientific_journal-2140	30	25	of	of	ADP
american_scientific_journal-2140	30	26	multiple	multiple	ADJ
american_scientific_journal-2140	30	27	optical	optical	ADJ
american_scientific_journal-2140	30	28	elements	element	NOUN
american_scientific_journal-2140	30	29	,	,	PUNCT
american_scientific_journal-2140	30	30	the	the	DET
american_scientific_journal-2140	30	31	object	object	NOUN
american_scientific_journal-2140	30	32	distance	distance	NOUN
american_scientific_journal-2140	30	33	𝑢	𝑢	NOUN
american_scientific_journal-2140	30	34	arises	arise	VERB
american_scientific_journal-2140	30	35	as	as	ADP
american_scientific_journal-2140	30	36	an	an	DET
american_scientific_journal-2140	30	37	important	important	ADJ
american_scientific_journal-2140	30	38	factor	factor	NOUN
american_scientific_journal-2140	30	39	in	in	ADP
american_scientific_journal-2140	30	40	forming	form	VERB
american_scientific_journal-2140	30	41	the	the	DET
american_scientific_journal-2140	30	42	corresponding	correspond	VERB
american_scientific_journal-2140	30	43	image	image	NOUN
american_scientific_journal-2140	30	44	at	at	ADP
american_scientific_journal-2140	30	45	a	a	DET
american_scientific_journal-2140	30	46	distance	distance	NOUN
american_scientific_journal-2140	30	47	𝑣	𝑣	ADP
american_scientific_journal-2140	30	48	,	,	PUNCT
american_scientific_journal-2140	30	49	see	see	VERB
american_scientific_journal-2140	30	50	[	[	X
american_scientific_journal-2140	30	51	10	10	NUM
american_scientific_journal-2140	30	52	]	]	PUNCT
american_scientific_journal-2140	30	53	for	for	ADP
american_scientific_journal-2140	30	54	cold	cold	ADJ
american_scientific_journal-2140	30	55	neutron	neutron	NOUN
american_scientific_journal-2140	30	56	focusing	focus	VERB
american_scientific_journal-2140	30	57	with	with	ADP
american_scientific_journal-2140	30	58	multiple	multiple	ADJ
american_scientific_journal-2140	30	59	biconcave	biconcave	ADJ
american_scientific_journal-2140	30	60	lenses	lense	NOUN
american_scientific_journal-2140	30	61	.	.	PUNCT
american_scientific_journal-2140	31	1	our	our	PRON
american_scientific_journal-2140	31	2	consideration	consideration	NOUN
american_scientific_journal-2140	31	3	does	do	AUX
american_scientific_journal-2140	31	4	not	not	PART
american_scientific_journal-2140	31	5	stop	stop	VERB
american_scientific_journal-2140	31	6	here	here	ADV
american_scientific_journal-2140	31	7	,	,	PUNCT
american_scientific_journal-2140	31	8	but	but	CCONJ
american_scientific_journal-2140	31	9	it	it	PRON
american_scientific_journal-2140	31	10	continues	continue	VERB
american_scientific_journal-2140	31	11	finding	find	VERB
american_scientific_journal-2140	31	12	applications	application	NOUN
american_scientific_journal-2140	31	13	in	in	ADP
american_scientific_journal-2140	31	14	real	real	ADJ
american_scientific_journal-2140	31	15	image	image	NOUN
american_scientific_journal-2140	31	16	formations	formation	NOUN
american_scientific_journal-2140	31	17	by	by	ADP
american_scientific_journal-2140	31	18	a	a	DET
american_scientific_journal-2140	31	19	single	single	ADJ
american_scientific_journal-2140	31	20	converging	converge	VERB
american_scientific_journal-2140	31	21	lens	len	NOUN
american_scientific_journal-2140	31	22	and	and	CCONJ
american_scientific_journal-2140	31	23	concave	concave	NOUN
american_scientific_journal-2140	31	24	mirror	mirror	NOUN
american_scientific_journal-2140	31	25	[	[	X
american_scientific_journal-2140	31	26	9	9	NUM
american_scientific_journal-2140	31	27	]	]	PUNCT
american_scientific_journal-2140	31	28	,	,	PUNCT
american_scientific_journal-2140	31	29	and	and	CCONJ
american_scientific_journal-2140	31	30	their	their	PRON
american_scientific_journal-2140	31	31	confocal	confocal	ADJ
american_scientific_journal-2140	31	32	two	two	NUM
american_scientific_journal-2140	31	33	lens	lens	NOUN
american_scientific_journal-2140	31	34	extensions	extension	NOUN
american_scientific_journal-2140	31	35	towards	towards	ADP
american_scientific_journal-2140	31	36	an	an	DET
american_scientific_journal-2140	31	37	efficient	efficient	ADJ
american_scientific_journal-2140	31	38	designing	designing	NOUN
american_scientific_journal-2140	31	39	of	of	ADP
american_scientific_journal-2140	31	40	laser	laser	NOUN
american_scientific_journal-2140	31	41	diodes	diode	NOUN
american_scientific_journal-2140	31	42	as	as	ADP
american_scientific_journal-2140	31	43	a	a	DET
american_scientific_journal-2140	31	44	single	single	ADJ
american_scientific_journal-2140	31	45	-	-	PUNCT
american_scientific_journal-2140	31	46	mode	mode	NOUN
american_scientific_journal-2140	31	47	fiber	fiber	NOUN
american_scientific_journal-2140	31	48	[	[	X
american_scientific_journal-2140	31	49	8	8	NUM
american_scientific_journal-2140	31	50	]	]	PUNCT
american_scientific_journal-2140	31	51	.	.	PUNCT
american_scientific_journal-2140	32	1	secondly	secondly	ADV
american_scientific_journal-2140	32	2	,	,	PUNCT
american_scientific_journal-2140	32	3	concerning	concern	VERB
american_scientific_journal-2140	32	4	this	this	DET
american_scientific_journal-2140	32	5	proposition	proposition	NOUN
american_scientific_journal-2140	32	6	,	,	PUNCT
american_scientific_journal-2140	32	7	another	another	DET
american_scientific_journal-2140	32	8	notable	notable	ADJ
american_scientific_journal-2140	32	9	quantity	quantity	NOUN
american_scientific_journal-2140	32	10	in	in	ADP
american_scientific_journal-2140	32	11	rendering	render	VERB
american_scientific_journal-2140	32	12	an	an	DET
american_scientific_journal-2140	32	13	optimized	optimize	VERB
american_scientific_journal-2140	32	14	image	image	NOUN
american_scientific_journal-2140	32	15	is	be	AUX
american_scientific_journal-2140	32	16	the	the	DET
american_scientific_journal-2140	32	17	lateral	lateral	ADJ
american_scientific_journal-2140	32	18	magnification	magnification	NOUN
american_scientific_journal-2140	32	19	𝑚	𝑚	NOUN
american_scientific_journal-2140	32	20	,	,	PUNCT
american_scientific_journal-2140	32	21	which	which	PRON
american_scientific_journal-2140	32	22	we	we	PRON
american_scientific_journal-2140	32	23	consider	consider	VERB
american_scientific_journal-2140	32	24	as	as	ADP
american_scientific_journal-2140	32	25	the	the	DET
american_scientific_journal-2140	32	26	ratio	ratio	NOUN
american_scientific_journal-2140	32	27	of	of	ADP
american_scientific_journal-2140	32	28	the	the	DET
american_scientific_journal-2140	32	29	image	image	NOUN
american_scientific_journal-2140	32	30	distance	distance	NOUN
american_scientific_journal-2140	32	31	to	to	ADP
american_scientific_journal-2140	32	32	that	that	PRON
american_scientific_journal-2140	32	33	of	of	ADP
american_scientific_journal-2140	32	34	the	the	DET
american_scientific_journal-2140	32	35	object	object	NOUN
american_scientific_journal-2140	32	36	,	,	PUNCT
american_scientific_journal-2140	32	37	or	or	CCONJ
american_scientific_journal-2140	32	38	the	the	DET
american_scientific_journal-2140	32	39	image	image	NOUN
american_scientific_journal-2140	32	40	height	height	NOUN
american_scientific_journal-2140	32	41	to	to	ADP
american_scientific_journal-2140	32	42	that	that	PRON
american_scientific_journal-2140	32	43	of	of	ADP
american_scientific_journal-2140	32	44	the	the	DET
american_scientific_journal-2140	32	45	object	object	NOUN
american_scientific_journal-2140	32	46	[	[	X
american_scientific_journal-2140	32	47	1	1	NUM
american_scientific_journal-2140	32	48	]	]	PUNCT
american_scientific_journal-2140	32	49	.	.	PUNCT
american_scientific_journal-2140	33	1	in	in	ADP
american_scientific_journal-2140	33	2	this	this	DET
american_scientific_journal-2140	33	3	paper	paper	NOUN
american_scientific_journal-2140	33	4	,	,	PUNCT
american_scientific_journal-2140	33	5	we	we	PRON
american_scientific_journal-2140	33	6	focus	focus	VERB
american_scientific_journal-2140	33	7	on	on	ADP
american_scientific_journal-2140	33	8	the	the	DET
american_scientific_journal-2140	33	9	significance	significance	NOUN
american_scientific_journal-2140	33	10	and	and	CCONJ
american_scientific_journal-2140	33	11	extensions	extension	NOUN
american_scientific_journal-2140	33	12	of	of	ADP
american_scientific_journal-2140	33	13	the	the	DET
american_scientific_journal-2140	33	14	optical	optical	ADJ
american_scientific_journal-2140	33	15	optimization	optimization	NOUN
american_scientific_journal-2140	33	16	procedure	procedure	NOUN
american_scientific_journal-2140	33	17	in	in	ADP
american_scientific_journal-2140	33	18	order	order	NOUN
american_scientific_journal-2140	33	19	to	to	PART
american_scientific_journal-2140	33	20	examine	examine	VERB
american_scientific_journal-2140	33	21	the	the	DET
american_scientific_journal-2140	33	22	local	local	ADJ
american_scientific_journal-2140	33	23	and	and	CCONJ
american_scientific_journal-2140	33	24	global	global	ADJ
american_scientific_journal-2140	33	25	stability	stability	NOUN
american_scientific_journal-2140	33	26	criteria	criterion	NOUN
american_scientific_journal-2140	33	27	of	of	ADP
american_scientific_journal-2140	33	28	an	an	DET
american_scientific_journal-2140	33	29	image	image	NOUN
american_scientific_journal-2140	33	30	formed	form	VERB
american_scientific_journal-2140	33	31	by	by	ADP
american_scientific_journal-2140	33	32	lenses	lense	NOUN
american_scientific_journal-2140	33	33	,	,	PUNCT
american_scientific_journal-2140	33	34	mirrors	mirror	NOUN
american_scientific_journal-2140	33	35	and	and	CCONJ
american_scientific_journal-2140	33	36	their	their	PRON
american_scientific_journal-2140	33	37	combinations	combination	NOUN
american_scientific_journal-2140	33	38	both	both	CCONJ
american_scientific_journal-2140	33	39	in	in	ADP
american_scientific_journal-2140	33	40	constrained	constrained	ADJ
american_scientific_journal-2140	33	41	and	and	CCONJ
american_scientific_journal-2140	33	42	unconstrained	unconstrained	ADJ
american_scientific_journal-2140	33	43	environments	environment	NOUN
american_scientific_journal-2140	33	44	.	.	PUNCT
american_scientific_journal-2140	34	1	image	image	NOUN
american_scientific_journal-2140	34	2	formations	formation	NOUN
american_scientific_journal-2140	34	3	involving	involve	VERB
american_scientific_journal-2140	34	4	a	a	DET
american_scientific_journal-2140	34	5	single	single	ADJ
american_scientific_journal-2140	34	6	lens/	lens/	NUM
american_scientific_journal-2140	34	7	mirror	mirror	NOUN
american_scientific_journal-2140	34	8	or	or	CCONJ
american_scientific_journal-2140	34	9	optical	optical	ADJ
american_scientific_journal-2140	34	10	system	system	NOUN
american_scientific_journal-2140	34	11	consisting	consist	VERB
american_scientific_journal-2140	34	12	of	of	ADP
american_scientific_journal-2140	34	13	multiple	multiple	ADJ
american_scientific_journal-2140	34	14	elements	element	NOUN
american_scientific_journal-2140	34	15	comprising	comprise	VERB
american_scientific_journal-2140	34	16	either	either	CCONJ
american_scientific_journal-2140	34	17	converging	converge	VERB
american_scientific_journal-2140	34	18	and/	and/	NOUN
american_scientific_journal-2140	34	19	or	or	CCONJ
american_scientific_journal-2140	34	20	diverging	diverge	VERB
american_scientific_journal-2140	34	21	lenses/	lenses/	NUM
american_scientific_journal-2140	34	22	mirrors	mirror	NOUN
american_scientific_journal-2140	34	23	are	be	AUX
american_scientific_journal-2140	34	24	obtained	obtain	VERB
american_scientific_journal-2140	34	25	by	by	ADP
american_scientific_journal-2140	34	26	specific	specific	ADJ
american_scientific_journal-2140	34	27	ray	ray	NOUN
american_scientific_journal-2140	34	28	tracing	trace	VERB
american_scientific_journal-2140	34	29	model	model	NOUN
american_scientific_journal-2140	34	30	as	as	ADP
american_scientific_journal-2140	34	31	the	the	DET
american_scientific_journal-2140	34	32	laws	law	NOUN
american_scientific_journal-2140	34	33	of	of	ADP
american_scientific_journal-2140	34	34	reflection	reflection	NOUN
american_scientific_journal-2140	34	35	in	in	ADP
american_scientific_journal-2140	34	36	the	the	DET
american_scientific_journal-2140	34	37	case	case	NOUN
american_scientific_journal-2140	34	38	of	of	ADP
american_scientific_journal-2140	34	39	the	the	DET
american_scientific_journal-2140	34	40	mirrors	mirror	NOUN
american_scientific_journal-2140	34	41	and	and	CCONJ
american_scientific_journal-2140	34	42	that	that	PRON
american_scientific_journal-2140	34	43	of	of	ADP
american_scientific_journal-2140	34	44	the	the	DET
american_scientific_journal-2140	34	45	refraction	refraction	NOUN
american_scientific_journal-2140	34	46	in	in	ADP
american_scientific_journal-2140	34	47	the	the	DET
american_scientific_journal-2140	34	48	case	case	NOUN
american_scientific_journal-2140	34	49	of	of	ADP
american_scientific_journal-2140	34	50	the	the	DET
american_scientific_journal-2140	34	51	lenses	lense	NOUN
american_scientific_journal-2140	34	52	[	[	X
american_scientific_journal-2140	34	53	2	2	NUM
american_scientific_journal-2140	34	54	-	-	SYM
american_scientific_journal-2140	34	55	4	4	NUM
american_scientific_journal-2140	34	56	]	]	PUNCT
american_scientific_journal-2140	34	57	.	.	PUNCT
american_scientific_journal-2140	35	1	perspective	perspective	ADJ
american_scientific_journal-2140	35	2	generalizations	generalization	NOUN
american_scientific_journal-2140	35	3	with	with	ADP
american_scientific_journal-2140	35	4	phase	phase	NOUN
american_scientific_journal-2140	35	5	discontinuities	discontinuity	NOUN
american_scientific_journal-2140	35	6	[	[	X
american_scientific_journal-2140	35	7	5	5	NUM
american_scientific_journal-2140	35	8	]	]	PUNCT
american_scientific_journal-2140	35	9	are	be	AUX
american_scientific_journal-2140	35	10	left	leave	VERB
american_scientific_journal-2140	35	11	open	open	ADJ
american_scientific_journal-2140	35	12	for	for	ADP
american_scientific_journal-2140	35	13	a	a	DET
american_scientific_journal-2140	35	14	future	future	ADJ
american_scientific_journal-2140	35	15	research	research	NOUN
american_scientific_journal-2140	35	16	development	development	NOUN
american_scientific_journal-2140	35	17	.	.	PUNCT
american_scientific_journal-2140	36	1	american	american	ADJ
american_scientific_journal-2140	36	2	scientific	scientific	ADJ
american_scientific_journal-2140	36	3	research	research	PROPN
american_scientific_journal-2140	36	4	journal	journal	NOUN
american_scientific_journal-2140	36	5	for	for	ADP
american_scientific_journal-2140	36	6	engineering	engineering	NOUN
american_scientific_journal-2140	36	7	,	,	PUNCT
american_scientific_journal-2140	36	8	technology	technology	NOUN
american_scientific_journal-2140	36	9	,	,	PUNCT
american_scientific_journal-2140	36	10	and	and	CCONJ
american_scientific_journal-2140	36	11	sciences	science	NOUN
american_scientific_journal-2140	36	12	(	(	PUNCT
american_scientific_journal-2140	36	13	asrjets	asrjet	NOUN
american_scientific_journal-2140	36	14	)	)	PUNCT
american_scientific_journal-2140	36	15	(	(	PUNCT
american_scientific_journal-2140	36	16	2016	2016	NUM
american_scientific_journal-2140	36	17	)	)	PUNCT
american_scientific_journal-2140	36	18	volume	volume	NOUN
american_scientific_journal-2140	36	19	26	26	NUM
american_scientific_journal-2140	36	20	,	,	PUNCT
american_scientific_journal-2140	36	21	no	no	DET
american_scientific_journal-2140	36	22	1	1	NUM
american_scientific_journal-2140	36	23	,	,	PUNCT
american_scientific_journal-2140	36	24	pp	pp	ADV
american_scientific_journal-2140	36	25	302	302	NUM
american_scientific_journal-2140	36	26	-	-	SYM
american_scientific_journal-2140	36	27	313	313	NUM
american_scientific_journal-2140	36	28	304	304	NUM
american_scientific_journal-2140	36	29	the	the	DET
american_scientific_journal-2140	36	30	rest	rest	NOUN
american_scientific_journal-2140	36	31	of	of	ADP
american_scientific_journal-2140	36	32	the	the	DET
american_scientific_journal-2140	36	33	paper	paper	NOUN
american_scientific_journal-2140	36	34	is	be	AUX
american_scientific_journal-2140	36	35	organized	organize	VERB
american_scientific_journal-2140	36	36	as	as	SCONJ
american_scientific_journal-2140	36	37	follows	follow	VERB
american_scientific_journal-2140	36	38	.	.	PUNCT
american_scientific_journal-2140	37	1	in	in	ADP
american_scientific_journal-2140	37	2	section	section	NOUN
american_scientific_journal-2140	37	3	2	2	NUM
american_scientific_journal-2140	37	4	,	,	PUNCT
american_scientific_journal-2140	37	5	we	we	PRON
american_scientific_journal-2140	37	6	characterize	characterize	VERB
american_scientific_journal-2140	37	7	the	the	DET
american_scientific_journal-2140	37	8	optical	optical	ADJ
american_scientific_journal-2140	37	9	optimization	optimization	NOUN
american_scientific_journal-2140	37	10	problem	problem	NOUN
american_scientific_journal-2140	37	11	by	by	ADP
american_scientific_journal-2140	37	12	analyzing	analyze	VERB
american_scientific_journal-2140	37	13	the	the	DET
american_scientific_journal-2140	37	14	local	local	ADJ
american_scientific_journal-2140	37	15	and	and	CCONJ
american_scientific_journal-2140	37	16	global	global	ADJ
american_scientific_journal-2140	37	17	stabilities	stability	NOUN
american_scientific_journal-2140	37	18	and	and	CCONJ
american_scientific_journal-2140	37	19	correlations	correlation	NOUN
american_scientific_journal-2140	37	20	towards	towards	ADP
american_scientific_journal-2140	37	21	an	an	DET
american_scientific_journal-2140	37	22	image	image	NOUN
american_scientific_journal-2140	37	23	formation	formation	NOUN
american_scientific_journal-2140	37	24	of	of	ADP
american_scientific_journal-2140	37	25	a	a	DET
american_scientific_journal-2140	37	26	dynamical	dynamical	ADJ
american_scientific_journal-2140	37	27	object	object	NOUN
american_scientific_journal-2140	37	28	.	.	PUNCT
american_scientific_journal-2140	38	1	in	in	ADP
american_scientific_journal-2140	38	2	section	section	NOUN
american_scientific_journal-2140	38	3	3	3	NUM
american_scientific_journal-2140	38	4	,	,	PUNCT
american_scientific_journal-2140	38	5	we	we	PRON
american_scientific_journal-2140	38	6	offer	offer	VERB
american_scientific_journal-2140	38	7	physical	physical	ADJ
american_scientific_journal-2140	38	8	significances	significance	NOUN
american_scientific_journal-2140	38	9	undermining	undermine	VERB
american_scientific_journal-2140	38	10	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	38	11	analysis	analysis	NOUN
american_scientific_journal-2140	38	12	of	of	ADP
american_scientific_journal-2140	38	13	image	image	NOUN
american_scientific_journal-2140	38	14	formed	form	VERB
american_scientific_journal-2140	38	15	at	at	ADP
american_scientific_journal-2140	38	16	a	a	DET
american_scientific_journal-2140	38	17	fixed	fix	VERB
american_scientific_journal-2140	38	18	lateral	lateral	ADJ
american_scientific_journal-2140	38	19	magnification	magnification	NOUN
american_scientific_journal-2140	38	20	and	and	CCONJ
american_scientific_journal-2140	38	21	object	object	VERB
american_scientific_journal-2140	38	22	distance	distance	NOUN
american_scientific_journal-2140	38	23	.	.	PUNCT
american_scientific_journal-2140	39	1	in	in	ADP
american_scientific_journal-2140	39	2	section	section	NOUN
american_scientific_journal-2140	39	3	4	4	NUM
american_scientific_journal-2140	39	4	,	,	PUNCT
american_scientific_journal-2140	39	5	we	we	PRON
american_scientific_journal-2140	39	6	provide	provide	VERB
american_scientific_journal-2140	39	7	perspective	perspective	NOUN
american_scientific_journal-2140	39	8	extensions	extension	NOUN
american_scientific_journal-2140	39	9	for	for	ADP
american_scientific_journal-2140	39	10	constrained	constrain	VERB
american_scientific_journal-2140	39	11	and	and	CCONJ
american_scientific_journal-2140	39	12	unconstrained	unconstrained	ADJ
american_scientific_journal-2140	39	13	optical	optical	ADJ
american_scientific_journal-2140	39	14	systems	system	NOUN
american_scientific_journal-2140	39	15	with	with	ADP
american_scientific_journal-2140	39	16	finitely	finitely	ADV
american_scientific_journal-2140	39	17	many	many	ADJ
american_scientific_journal-2140	39	18	components	component	NOUN
american_scientific_journal-2140	39	19	.	.	PUNCT
american_scientific_journal-2140	40	1	in	in	ADP
american_scientific_journal-2140	40	2	section	section	NOUN
american_scientific_journal-2140	40	3	5	5	NUM
american_scientific_journal-2140	40	4	,	,	PUNCT
american_scientific_journal-2140	40	5	we	we	PRON
american_scientific_journal-2140	40	6	conclude	conclude	VERB
american_scientific_journal-2140	40	7	our	our	PRON
american_scientific_journal-2140	40	8	paper	paper	NOUN
american_scientific_journal-2140	40	9	with	with	ADP
american_scientific_journal-2140	40	10	future	future	ADJ
american_scientific_journal-2140	40	11	research	research	NOUN
american_scientific_journal-2140	40	12	directions	direction	NOUN
american_scientific_journal-2140	40	13	towards	towards	ADP
american_scientific_journal-2140	40	14	optoengineering	optoengineering	NOUN
american_scientific_journal-2140	40	15	and	and	CCONJ
american_scientific_journal-2140	40	16	instrument	instrument	NOUN
american_scientific_journal-2140	40	17	designing	designing	NOUN
american_scientific_journal-2140	40	18	.	.	PUNCT
american_scientific_journal-2140	41	1	2	2	X
american_scientific_journal-2140	41	2	.	.	X
american_scientific_journal-2140	41	3	optical	optical	ADJ
american_scientific_journal-2140	41	4	optimization	optimization	NOUN
american_scientific_journal-2140	41	5	in	in	ADP
american_scientific_journal-2140	41	6	this	this	DET
american_scientific_journal-2140	41	7	section	section	NOUN
american_scientific_journal-2140	41	8	,	,	PUNCT
american_scientific_journal-2140	41	9	we	we	PRON
american_scientific_journal-2140	41	10	present	present	VERB
american_scientific_journal-2140	41	11	the	the	DET
american_scientific_journal-2140	41	12	fundamentals	fundamental	NOUN
american_scientific_journal-2140	41	13	behind	behind	ADP
american_scientific_journal-2140	41	14	the	the	DET
american_scientific_journal-2140	41	15	optical	optical	ADJ
american_scientific_journal-2140	41	16	optimization	optimization	NOUN
american_scientific_journal-2140	41	17	.	.	PUNCT
american_scientific_journal-2140	42	1	in	in	ADP
american_scientific_journal-2140	42	2	the	the	DET
american_scientific_journal-2140	42	3	thin	thin	ADJ
american_scientific_journal-2140	42	4	approximation	approximation	NOUN
american_scientific_journal-2140	42	5	of	of	ADP
american_scientific_journal-2140	42	6	a	a	DET
american_scientific_journal-2140	42	7	given	give	VERB
american_scientific_journal-2140	42	8	lens/	lens/	NUM
american_scientific_journal-2140	42	9	mirror	mirror	NOUN
american_scientific_journal-2140	42	10	,	,	PUNCT
american_scientific_journal-2140	42	11	we	we	PRON
american_scientific_journal-2140	42	12	recall	recall	VERB
american_scientific_journal-2140	42	13	[	[	X
american_scientific_journal-2140	42	14	1	1	NUM
american_scientific_journal-2140	42	15	-	-	SYM
american_scientific_journal-2140	42	16	4	4	NUM
american_scientific_journal-2140	42	17	]	]	PUNCT
american_scientific_journal-2140	42	18	that	that	SCONJ
american_scientific_journal-2140	42	19	the	the	DET
american_scientific_journal-2140	42	20	expression	expression	NOUN
american_scientific_journal-2140	42	21	of	of	ADP
american_scientific_journal-2140	42	22	the	the	DET
american_scientific_journal-2140	42	23	focal	focal	ADJ
american_scientific_journal-2140	42	24	length	length	NOUN
american_scientific_journal-2140	42	25	𝑓	𝑓	DET
american_scientific_journal-2140	42	26	reads	read	NOUN
american_scientific_journal-2140	42	27	as	as	ADP
american_scientific_journal-2140	42	28	𝑓(𝑢	𝑓(𝑢	PROPN
american_scientific_journal-2140	42	29	,	,	PUNCT
american_scientific_journal-2140	42	30	𝑚	𝑚	NOUN
american_scientific_journal-2140	42	31	)	)	PUNCT
american_scientific_journal-2140	42	32	=	=	SYM
american_scientific_journal-2140	42	33	𝑢𝑚	𝑢𝑚	ADP
american_scientific_journal-2140	42	34	1−	1−	NUM
american_scientific_journal-2140	42	35	𝑚	𝑚	NOUN
american_scientific_journal-2140	42	36	,	,	PUNCT
american_scientific_journal-2140	42	37	(	(	PUNCT
american_scientific_journal-2140	42	38	1	1	X
american_scientific_journal-2140	42	39	)	)	PUNCT
american_scientific_journal-2140	42	40	where	where	SCONJ
american_scientific_journal-2140	42	41	𝑢	𝑢	PRON
american_scientific_journal-2140	42	42	denotes	denote	VERB
american_scientific_journal-2140	42	43	the	the	DET
american_scientific_journal-2140	42	44	object	object	NOUN
american_scientific_journal-2140	42	45	distance	distance	NOUN
american_scientific_journal-2140	42	46	and	and	CCONJ
american_scientific_journal-2140	42	47	𝑚	𝑚	X
american_scientific_journal-2140	42	48	the	the	DET
american_scientific_journal-2140	42	49	lateral	lateral	ADJ
american_scientific_journal-2140	42	50	magnification	magnification	NOUN
american_scientific_journal-2140	42	51	.	.	PUNCT
american_scientific_journal-2140	43	1	when	when	SCONJ
american_scientific_journal-2140	43	2	the	the	DET
american_scientific_journal-2140	43	3	optimization	optimization	NOUN
american_scientific_journal-2140	43	4	variables	variable	VERB
american_scientific_journal-2140	43	5	{	{	PUNCT
american_scientific_journal-2140	43	6	𝑢	𝑢	X
american_scientific_journal-2140	43	7	,	,	PUNCT
american_scientific_journal-2140	43	8	𝑚	𝑚	NOUN
american_scientific_journal-2140	43	9	}	}	PUNCT
american_scientific_journal-2140	43	10	are	be	AUX
american_scientific_journal-2140	43	11	varied	varied	ADJ
american_scientific_journal-2140	43	12	simultaneously	simultaneously	ADV
american_scientific_journal-2140	43	13	,	,	PUNCT
american_scientific_journal-2140	43	14	the	the	DET
american_scientific_journal-2140	43	15	stationary	stationary	ADJ
american_scientific_journal-2140	43	16	points	point	NOUN
american_scientific_journal-2140	43	17	as	as	SCONJ
american_scientific_journal-2140	43	18	the	the	DET
american_scientific_journal-2140	43	19	zeros	zero	NOUN
american_scientific_journal-2140	43	20	of	of	ADP
american_scientific_journal-2140	43	21	the	the	DET
american_scientific_journal-2140	43	22	first	first	ADJ
american_scientific_journal-2140	43	23	order	order	NOUN
american_scientific_journal-2140	43	24	partial	partial	ADJ
american_scientific_journal-2140	43	25	derivatives	derivative	NOUN
american_scientific_journal-2140	43	26	{	{	PUNCT
american_scientific_journal-2140	43	27	𝜕𝑓	𝜕𝑓	ADJ
american_scientific_journal-2140	43	28	𝜕𝑢	𝜕𝑢	NOUN
american_scientific_journal-2140	43	29	,	,	PUNCT
american_scientific_journal-2140	43	30	𝜕𝑓	𝜕𝑓	ADJ
american_scientific_journal-2140	43	31	𝜕𝑚	𝜕𝑚	NOUN
american_scientific_journal-2140	43	32	}	}	PUNCT
american_scientific_journal-2140	43	33	of	of	ADP
american_scientific_journal-2140	43	34	the	the	DET
american_scientific_journal-2140	43	35	objective	objective	ADJ
american_scientific_journal-2140	43	36	function	function	NOUN
american_scientific_journal-2140	43	37	𝑓	𝑓	PRON
american_scientific_journal-2140	43	38	,	,	PUNCT
american_scientific_journal-2140	43	39	it	it	PRON
american_scientific_journal-2140	43	40	follows	follow	VERB
american_scientific_journal-2140	43	41	that	that	SCONJ
american_scientific_journal-2140	43	42	the	the	DET
american_scientific_journal-2140	43	43	optical	optical	ADJ
american_scientific_journal-2140	43	44	center	center	NOUN
american_scientific_journal-2140	43	45	of	of	ADP
american_scientific_journal-2140	43	46	the	the	DET
american_scientific_journal-2140	43	47	optical	optical	ADJ
american_scientific_journal-2140	43	48	instrument	instrument	NOUN
american_scientific_journal-2140	43	49	,	,	PUNCT
american_scientific_journal-2140	43	50	viz	viz	PROPN
american_scientific_journal-2140	43	51	.	.	PUNCT
american_scientific_journal-2140	44	1	a	a	DET
american_scientific_journal-2140	44	2	lens	lens	NOUN
american_scientific_journal-2140	44	3	and	and	CCONJ
american_scientific_journal-2140	44	4	mirror	mirror	NOUN
american_scientific_journal-2140	44	5	is	be	AUX
american_scientific_journal-2140	44	6	the	the	DET
american_scientific_journal-2140	44	7	only	only	ADJ
american_scientific_journal-2140	44	8	stationary	stationary	ADJ
american_scientific_journal-2140	44	9	point	point	NOUN
american_scientific_journal-2140	44	10	.	.	PUNCT
american_scientific_journal-2140	45	1	this	this	PRON
american_scientific_journal-2140	45	2	is	be	AUX
american_scientific_journal-2140	45	3	because	because	SCONJ
american_scientific_journal-2140	45	4	of	of	ADP
american_scientific_journal-2140	45	5	the	the	DET
american_scientific_journal-2140	45	6	fact	fact	NOUN
american_scientific_journal-2140	45	7	that	that	SCONJ
american_scientific_journal-2140	45	8	𝑚	𝑚	PROPN
american_scientific_journal-2140	45	9	and	and	CCONJ
american_scientific_journal-2140	45	10	𝑢	𝑢	PROPN
american_scientific_journal-2140	45	11	vanish	vanish	VERB
american_scientific_journal-2140	45	12	identically	identically	ADV
american_scientific_journal-2140	45	13	as	as	ADP
american_scientific_journal-2140	45	14	the	the	DET
american_scientific_journal-2140	45	15	simultaneous	simultaneous	ADJ
american_scientific_journal-2140	45	16	root	root	NOUN
american_scientific_journal-2140	45	17	of	of	ADP
american_scientific_journal-2140	45	18	the	the	DET
american_scientific_journal-2140	45	19	flow	flow	NOUN
american_scientific_journal-2140	45	20	equations	equation	NOUN
american_scientific_journal-2140	45	21	𝜕𝑓	𝜕𝑓	ADP
american_scientific_journal-2140	45	22	𝜕𝑢	𝜕𝑢	NOUN
american_scientific_journal-2140	45	23	=	=	NOUN
american_scientific_journal-2140	45	24	0	0	NUM
american_scientific_journal-2140	45	25	and	and	CCONJ
american_scientific_journal-2140	45	26	𝜕𝑓	𝜕𝑓	ADJ
american_scientific_journal-2140	45	27	𝜕𝑚	𝜕𝑚	NOUN
american_scientific_journal-2140	45	28	=	=	SYM
american_scientific_journal-2140	45	29	0	0	X
american_scientific_journal-2140	45	30	.	.	PUNCT
american_scientific_journal-2140	46	1	furthermore	furthermore	ADV
american_scientific_journal-2140	46	2	,	,	PUNCT
american_scientific_journal-2140	46	3	by	by	ADP
american_scientific_journal-2140	46	4	invoking	invoke	VERB
american_scientific_journal-2140	46	5	the	the	DET
american_scientific_journal-2140	46	6	second	second	ADJ
american_scientific_journal-2140	46	7	order	order	NOUN
american_scientific_journal-2140	46	8	partial	partial	ADJ
american_scientific_journal-2140	46	9	derivatives	derivative	NOUN
american_scientific_journal-2140	46	10	,	,	PUNCT
american_scientific_journal-2140	46	11	we	we	PRON
american_scientific_journal-2140	46	12	determine	determine	VERB
american_scientific_journal-2140	46	13	the	the	DET
american_scientific_journal-2140	46	14	stability	stability	NOUN
american_scientific_journal-2140	46	15	characterization	characterization	NOUN
american_scientific_journal-2140	46	16	of	of	ADP
american_scientific_journal-2140	46	17	the	the	DET
american_scientific_journal-2140	46	18	optical	optical	ADJ
american_scientific_journal-2140	46	19	objective	objective	ADJ
american_scientific_journal-2140	46	20	function	function	NOUN
american_scientific_journal-2140	46	21	𝑓.	𝑓.	NOUN
american_scientific_journal-2140	46	22	namely	namely	ADV
american_scientific_journal-2140	46	23	,	,	PUNCT
american_scientific_journal-2140	46	24	via	via	ADP
american_scientific_journal-2140	46	25	the	the	DET
american_scientific_journal-2140	46	26	second	second	ADJ
american_scientific_journal-2140	46	27	order	order	NOUN
american_scientific_journal-2140	46	28	derivatives	derivative	NOUN
american_scientific_journal-2140	46	29	,	,	PUNCT
american_scientific_journal-2140	46	30	we	we	PRON
american_scientific_journal-2140	46	31	notice	notice	VERB
american_scientific_journal-2140	46	32	that	that	SCONJ
american_scientific_journal-2140	46	33	the	the	DET
american_scientific_journal-2140	46	34	pure	pure	ADJ
american_scientific_journal-2140	46	35	capacity	capacity	NOUN
american_scientific_journal-2140	46	36	𝜕2𝑓	𝜕2𝑓	ADJ
american_scientific_journal-2140	46	37	𝜕𝑢2	𝜕𝑢2	NOUN
american_scientific_journal-2140	46	38	vanishes	vanish	VERB
american_scientific_journal-2140	46	39	identically	identically	ADV
american_scientific_journal-2140	46	40	for	for	ADP
american_scientific_journal-2140	46	41	all	all	DET
american_scientific_journal-2140	46	42	values	value	NOUN
american_scientific_journal-2140	46	43	of	of	ADP
american_scientific_journal-2140	46	44	the	the	DET
american_scientific_journal-2140	46	45	optimization	optimization	NOUN
american_scientific_journal-2140	46	46	variables	variable	NOUN
american_scientific_journal-2140	46	47	{	{	PUNCT
american_scientific_journal-2140	46	48	𝑢	𝑢	X
american_scientific_journal-2140	46	49	,	,	PUNCT
american_scientific_journal-2140	46	50	𝑚	𝑚	NOUN
american_scientific_journal-2140	46	51	}	}	PUNCT
american_scientific_journal-2140	46	52	.	.	PUNCT
american_scientific_journal-2140	47	1	on	on	ADP
american_scientific_journal-2140	47	2	the	the	DET
american_scientific_journal-2140	47	3	other	other	ADJ
american_scientific_journal-2140	47	4	hand	hand	NOUN
american_scientific_journal-2140	47	5	,	,	PUNCT
american_scientific_journal-2140	47	6	it	it	PRON
american_scientific_journal-2140	47	7	follows	follow	VERB
american_scientific_journal-2140	47	8	from	from	ADP
american_scientific_journal-2140	47	9	eqn	eqn	NOUN
american_scientific_journal-2140	47	10	.	.	PUNCT
american_scientific_journal-2140	48	1	(	(	PUNCT
american_scientific_journal-2140	48	2	1	1	X
american_scientific_journal-2140	48	3	)	)	PUNCT
american_scientific_journal-2140	48	4	that	that	SCONJ
american_scientific_journal-2140	48	5	we	we	PRON
american_scientific_journal-2140	48	6	have	have	VERB
american_scientific_journal-2140	48	7	the	the	DET
american_scientific_journal-2140	48	8	following	follow	VERB
american_scientific_journal-2140	48	9	non	non	ADJ
american_scientific_journal-2140	48	10	-	-	ADJ
american_scientific_journal-2140	48	11	vanishing	vanishing	ADJ
american_scientific_journal-2140	48	12	pure	pure	ADJ
american_scientific_journal-2140	48	13	magnification	magnification	NOUN
american_scientific_journal-2140	48	14	capacity	capacity	NOUN
american_scientific_journal-2140	48	15	𝜕2𝑓	𝜕2𝑓	ADJ
american_scientific_journal-2140	48	16	𝜕𝑚2	𝜕𝑚2	NOUN
american_scientific_journal-2140	48	17	=	=	SYM
american_scientific_journal-2140	48	18	2𝑢	2𝑢	NUM
american_scientific_journal-2140	48	19	(	(	PUNCT
american_scientific_journal-2140	48	20	1−𝑚)3	1−𝑚)3	NUM
american_scientific_journal-2140	48	21	(	(	PUNCT
american_scientific_journal-2140	48	22	2	2	NUM
american_scientific_journal-2140	48	23	)	)	PUNCT
american_scientific_journal-2140	48	24	furthermore	furthermore	ADV
american_scientific_journal-2140	48	25	,	,	PUNCT
american_scientific_journal-2140	48	26	we	we	PRON
american_scientific_journal-2140	48	27	notice	notice	VERB
american_scientific_journal-2140	48	28	that	that	SCONJ
american_scientific_journal-2140	48	29	the	the	DET
american_scientific_journal-2140	48	30	cross	cross	NOUN
american_scientific_journal-2140	48	31	components	component	NOUN
american_scientific_journal-2140	48	32	𝜕2𝑓	𝜕2𝑓	ADJ
american_scientific_journal-2140	48	33	𝜕𝑢𝜕𝑚	𝜕𝑢𝜕𝑚	ADJ
american_scientific_journal-2140	48	34	and	and	CCONJ
american_scientific_journal-2140	48	35	𝜕2𝑓	𝜕2𝑓	PROPN
american_scientific_journal-2140	48	36	𝜕𝑚𝜕𝑢	𝜕𝑚𝜕𝑢	NOUN
american_scientific_journal-2140	48	37	remain	remain	VERB
american_scientific_journal-2140	48	38	identical	identical	ADJ
american_scientific_journal-2140	48	39	because	because	SCONJ
american_scientific_journal-2140	48	40	of	of	ADP
american_scientific_journal-2140	48	41	the	the	DET
american_scientific_journal-2140	48	42	smooth	smooth	ADJ
american_scientific_journal-2140	48	43	nature	nature	NOUN
american_scientific_journal-2140	48	44	of	of	ADP
american_scientific_journal-2140	48	45	the	the	DET
american_scientific_journal-2140	48	46	objective	objective	ADJ
american_scientific_journal-2140	48	47	function	function	NOUN
american_scientific_journal-2140	48	48	𝑓(𝑢	𝑓(𝑢	PROPN
american_scientific_journal-2140	48	49	,	,	PUNCT
american_scientific_journal-2140	48	50	𝑚	𝑚	NOUN
american_scientific_journal-2140	48	51	)	)	PUNCT
american_scientific_journal-2140	48	52	as	as	ADP
american_scientific_journal-2140	48	53	a	a	DET
american_scientific_journal-2140	48	54	real	real	ADJ
american_scientific_journal-2140	48	55	function	function	NOUN
american_scientific_journal-2140	48	56	of	of	ADP
american_scientific_journal-2140	48	57	{	{	PUNCT
american_scientific_journal-2140	48	58	𝑢	𝑢	X
american_scientific_journal-2140	48	59	,	,	PUNCT
american_scientific_journal-2140	48	60	𝑚	𝑚	NOUN
american_scientific_journal-2140	48	61	}	}	PUNCT
american_scientific_journal-2140	48	62	.	.	PUNCT
american_scientific_journal-2140	49	1	namely	namely	ADV
american_scientific_journal-2140	49	2	,	,	PUNCT
american_scientific_journal-2140	49	3	from	from	ADP
american_scientific_journal-2140	49	4	eqn	eqn	NOUN
american_scientific_journal-2140	49	5	.	.	PUNCT
american_scientific_journal-2140	50	1	(	(	PUNCT
american_scientific_journal-2140	50	2	1	1	NUM
american_scientific_journal-2140	50	3	)	)	PUNCT
american_scientific_journal-2140	50	4	,	,	PUNCT
american_scientific_journal-2140	50	5	it	it	PRON
american_scientific_journal-2140	50	6	follows	follow	VERB
american_scientific_journal-2140	50	7	that	that	SCONJ
american_scientific_journal-2140	50	8	we	we	PRON
american_scientific_journal-2140	50	9	have	have	VERB
american_scientific_journal-2140	50	10	the	the	DET
american_scientific_journal-2140	50	11	following	follow	VERB
american_scientific_journal-2140	50	12	absolutely	absolutely	ADV
american_scientific_journal-2140	50	13	positive	positive	ADJ
american_scientific_journal-2140	50	14	mixed	mixed	ADJ
american_scientific_journal-2140	50	15	capacity	capacity	NOUN
american_scientific_journal-2140	50	16	or	or	CCONJ
american_scientific_journal-2140	50	17	the	the	DET
american_scientific_journal-2140	50	18	optical	optical	ADJ
american_scientific_journal-2140	50	19	correlation	correlation	NOUN
american_scientific_journal-2140	50	20	𝜕2𝑓	𝜕2𝑓	ADJ
american_scientific_journal-2140	50	21	𝜕𝑢𝜕𝑚	𝜕𝑢𝜕𝑚	ADJ
american_scientific_journal-2140	50	22	=	=	PUNCT
american_scientific_journal-2140	50	23	𝜕2𝑓	𝜕2𝑓	ADJ
american_scientific_journal-2140	50	24	𝜕𝑚𝜕𝑢	𝜕𝑚𝜕𝑢	NOUN
american_scientific_journal-2140	50	25	=	=	SYM
american_scientific_journal-2140	50	26	1	1	NUM
american_scientific_journal-2140	50	27	(	(	PUNCT
american_scientific_journal-2140	50	28	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	50	29	(	(	PUNCT
american_scientific_journal-2140	50	30	3	3	NUM
american_scientific_journal-2140	50	31	)	)	PUNCT
american_scientific_journal-2140	50	32	for	for	ADP
american_scientific_journal-2140	50	33	all	all	DET
american_scientific_journal-2140	50	34	values	value	NOUN
american_scientific_journal-2140	50	35	of	of	ADP
american_scientific_journal-2140	50	36	the	the	DET
american_scientific_journal-2140	50	37	optimization	optimization	NOUN
american_scientific_journal-2140	50	38	variables	variable	NOUN
american_scientific_journal-2140	50	39	{	{	PUNCT
american_scientific_journal-2140	50	40	𝑢	𝑢	X
american_scientific_journal-2140	50	41	,	,	PUNCT
american_scientific_journal-2140	50	42	𝑚	𝑚	NOUN
american_scientific_journal-2140	50	43	}	}	PUNCT
american_scientific_journal-2140	50	44	.	.	PUNCT
american_scientific_journal-2140	51	1	thus	thus	ADV
american_scientific_journal-2140	51	2	,	,	PUNCT
american_scientific_journal-2140	51	3	by	by	ADP
american_scientific_journal-2140	51	4	substituting	substitute	VERB
american_scientific_journal-2140	51	5	the	the	DET
american_scientific_journal-2140	51	6	corresponding	corresponding	ADJ
american_scientific_journal-2140	51	7	pure	pure	ADJ
american_scientific_journal-2140	51	8	and	and	CCONJ
american_scientific_journal-2140	51	9	mixed	mixed	ADJ
american_scientific_journal-2140	51	10	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	51	11	components	component	NOUN
american_scientific_journal-2140	51	12	as	as	ADP
american_scientific_journal-2140	51	13	in	in	ADP
american_scientific_journal-2140	51	14	eqns	eqns	PROPN
american_scientific_journal-2140	51	15	.	.	PUNCT
american_scientific_journal-2140	52	1	(	(	PUNCT
american_scientific_journal-2140	52	2	2	2	NUM
american_scientific_journal-2140	52	3	,	,	PUNCT
american_scientific_journal-2140	52	4	3	3	NUM
american_scientific_journal-2140	52	5	)	)	PUNCT
american_scientific_journal-2140	52	6	and	and	CCONJ
american_scientific_journal-2140	52	7	the	the	DET
american_scientific_journal-2140	52	8	fact	fact	NOUN
american_scientific_journal-2140	52	9	that	that	SCONJ
american_scientific_journal-2140	52	10	𝜕2𝑓	𝜕2𝑓	ADJ
american_scientific_journal-2140	52	11	𝜕𝑢2	𝜕𝑢2	NOUN
american_scientific_journal-2140	52	12	vanishes	vanish	VERB
american_scientific_journal-2140	52	13	identically	identically	ADV
american_scientific_journal-2140	52	14	for	for	ADP
american_scientific_journal-2140	52	15	all	all	DET
american_scientific_journal-2140	52	16	values	value	NOUN
american_scientific_journal-2140	52	17	of	of	ADP
american_scientific_journal-2140	52	18	{	{	PUNCT
american_scientific_journal-2140	52	19	𝑢	𝑢	X
american_scientific_journal-2140	52	20	,	,	PUNCT
american_scientific_journal-2140	52	21	𝑚	𝑚	NOUN
american_scientific_journal-2140	52	22	}	}	PUNCT
american_scientific_journal-2140	52	23	,	,	PUNCT
american_scientific_journal-2140	52	24	we	we	PRON
american_scientific_journal-2140	52	25	find	find	VERB
american_scientific_journal-2140	52	26	from	from	ADP
american_scientific_journal-2140	52	27	the	the	DET
american_scientific_journal-2140	52	28	definition	definition	NOUN
american_scientific_journal-2140	52	29	of	of	ADP
american_scientific_journal-2140	52	30	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	52	31	theory	theory	NOUN
american_scientific_journal-2140	52	32	and	and	CCONJ
american_scientific_journal-2140	52	33	its	its	PRON
american_scientific_journal-2140	52	34	embedding	embed	VERB
american_scientific_journal-2140	52	35	perspectives	perspective	NOUN
american_scientific_journal-2140	52	36	[	[	X
american_scientific_journal-2140	52	37	11	11	NUM
american_scientific_journal-2140	52	38	,	,	PUNCT
american_scientific_journal-2140	52	39	12	12	NUM
american_scientific_journal-2140	52	40	]	]	PUNCT
american_scientific_journal-2140	52	41	that	that	SCONJ
american_scientific_journal-2140	52	42	the	the	DET
american_scientific_journal-2140	52	43	objective	objective	ADJ
american_scientific_journal-2140	52	44	function	function	NOUN
american_scientific_journal-2140	52	45	𝑓	𝑓	PRON
american_scientific_journal-2140	52	46	as	as	ADP
american_scientific_journal-2140	52	47	in	in	ADP
american_scientific_journal-2140	52	48	eqn	eqn	NOUN
american_scientific_journal-2140	52	49	.	.	PUNCT
american_scientific_journal-2140	53	1	(	(	PUNCT
american_scientific_journal-2140	53	2	1	1	X
american_scientific_journal-2140	53	3	)	)	PUNCT
american_scientific_journal-2140	53	4	yields	yield	VERB
american_scientific_journal-2140	53	5	the	the	DET
american_scientific_journal-2140	53	6	following	follow	VERB
american_scientific_journal-2140	53	7	hessian	hessian	ADJ
american_scientific_journal-2140	53	8	matrix	matrix	NOUN
american_scientific_journal-2140	53	9	𝐻	𝐻	NOUN
american_scientific_journal-2140	53	10	=	=	PUNCT
american_scientific_journal-2140	53	11	(	(	PUNCT
american_scientific_journal-2140	53	12	0	0	NUM
american_scientific_journal-2140	53	13	1	1	NUM
american_scientific_journal-2140	53	14	(	(	PUNCT
american_scientific_journal-2140	53	15	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	53	16	1	1	NUM
american_scientific_journal-2140	53	17	(	(	PUNCT
american_scientific_journal-2140	53	18	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	53	19	2𝑢	2𝑢	NUM
american_scientific_journal-2140	53	20	(	(	PUNCT
american_scientific_journal-2140	53	21	1−𝑚)3	1−𝑚)3	NUM
american_scientific_journal-2140	53	22	)	)	PUNCT
american_scientific_journal-2140	53	23	(	(	PUNCT
american_scientific_journal-2140	53	24	4	4	X
american_scientific_journal-2140	53	25	)	)	PUNCT
american_scientific_journal-2140	53	26	american	american	ADJ
american_scientific_journal-2140	53	27	scientific	scientific	ADJ
american_scientific_journal-2140	53	28	research	research	NOUN
american_scientific_journal-2140	53	29	journal	journal	NOUN
american_scientific_journal-2140	53	30	for	for	ADP
american_scientific_journal-2140	53	31	engineering	engineering	NOUN
american_scientific_journal-2140	53	32	,	,	PUNCT
american_scientific_journal-2140	53	33	technology	technology	NOUN
american_scientific_journal-2140	53	34	,	,	PUNCT
american_scientific_journal-2140	53	35	and	and	CCONJ
american_scientific_journal-2140	53	36	sciences	science	NOUN
american_scientific_journal-2140	53	37	(	(	PUNCT
american_scientific_journal-2140	53	38	asrjets	asrjet	NOUN
american_scientific_journal-2140	53	39	)	)	PUNCT
american_scientific_journal-2140	53	40	(	(	PUNCT
american_scientific_journal-2140	53	41	2016	2016	NUM
american_scientific_journal-2140	53	42	)	)	PUNCT
american_scientific_journal-2140	53	43	volume	volume	NOUN
american_scientific_journal-2140	53	44	26	26	NUM
american_scientific_journal-2140	53	45	,	,	PUNCT
american_scientific_journal-2140	53	46	no	no	DET
american_scientific_journal-2140	53	47	1	1	NUM
american_scientific_journal-2140	53	48	,	,	PUNCT
american_scientific_journal-2140	53	49	pp	pp	ADV
american_scientific_journal-2140	53	50	302	302	NUM
american_scientific_journal-2140	53	51	-	-	SYM
american_scientific_journal-2140	53	52	313	313	NUM
american_scientific_journal-2140	53	53	305	305	NUM
american_scientific_journal-2140	53	54	as	as	ADP
american_scientific_journal-2140	53	55	per	per	ADP
american_scientific_journal-2140	53	56	the	the	DET
american_scientific_journal-2140	53	57	above	above	ADJ
american_scientific_journal-2140	53	58	critical	critical	ADJ
american_scientific_journal-2140	53	59	point	point	NOUN
american_scientific_journal-2140	53	60	evaluation	evaluation	NOUN
american_scientific_journal-2140	53	61	,	,	PUNCT
american_scientific_journal-2140	53	62	the	the	DET
american_scientific_journal-2140	53	63	analysis	analysis	NOUN
american_scientific_journal-2140	53	64	of	of	ADP
american_scientific_journal-2140	53	65	the	the	DET
american_scientific_journal-2140	53	66	concave	concave	NOUN
american_scientific_journal-2140	53	67	and	and	CCONJ
american_scientific_journal-2140	53	68	convex	convex	VERB
american_scientific_journal-2140	53	69	nature	nature	NOUN
american_scientific_journal-2140	53	70	of	of	ADP
american_scientific_journal-2140	53	71	the	the	DET
american_scientific_journal-2140	53	72	lenses/	lenses/	NUM
american_scientific_journal-2140	53	73	mirrors	mirror	NOUN
american_scientific_journal-2140	53	74	with	with	ADP
american_scientific_journal-2140	53	75	the	the	DET
american_scientific_journal-2140	53	76	corresponding	correspond	VERB
american_scientific_journal-2140	53	77	objective	objective	ADJ
american_scientific_journal-2140	53	78	function	function	NOUN
american_scientific_journal-2140	53	79	𝑓	𝑓	PRON
american_scientific_journal-2140	53	80	at	at	ADP
american_scientific_journal-2140	53	81	its	its	PRON
american_scientific_journal-2140	53	82	stationary	stationary	ADJ
american_scientific_journal-2140	53	83	point	point	NOUN
american_scientific_journal-2140	53	84	(	(	PUNCT
american_scientific_journal-2140	53	85	0	0	NUM
american_scientific_journal-2140	53	86	,	,	PUNCT
american_scientific_journal-2140	53	87	0	0	NUM
american_scientific_journal-2140	53	88	)	)	PUNCT
american_scientific_journal-2140	53	89	is	be	AUX
american_scientific_journal-2140	53	90	performed	perform	VERB
american_scientific_journal-2140	53	91	by	by	ADP
american_scientific_journal-2140	53	92	computing	compute	VERB
american_scientific_journal-2140	53	93	the	the	DET
american_scientific_journal-2140	53	94	eigenvalues	eigenvalues	PROPN
american_scientific_journal-2140	53	95	𝜆	𝜆	PROPN
american_scientific_journal-2140	53	96	of	of	ADP
american_scientific_journal-2140	53	97	the	the	DET
american_scientific_journal-2140	53	98	hessian	hessian	ADJ
american_scientific_journal-2140	53	99	matrix	matrix	NOUN
american_scientific_journal-2140	53	100	𝐻.	𝐻.	PROPN
american_scientific_journal-2140	53	101	considering	consider	VERB
american_scientific_journal-2140	53	102	the	the	DET
american_scientific_journal-2140	53	103	hessian	hessian	ADJ
american_scientific_journal-2140	53	104	matrix	matrix	NOUN
american_scientific_journal-2140	53	105	𝐻	𝐻	PROPN
american_scientific_journal-2140	53	106	as	as	ADP
american_scientific_journal-2140	53	107	above	above	ADV
american_scientific_journal-2140	53	108	in	in	ADP
american_scientific_journal-2140	53	109	eqn	eqn	NOUN
american_scientific_journal-2140	53	110	.	.	PUNCT
american_scientific_journal-2140	54	1	(	(	PUNCT
american_scientific_journal-2140	54	2	4	4	X
american_scientific_journal-2140	54	3	)	)	PUNCT
american_scientific_journal-2140	54	4	having	have	VERB
american_scientific_journal-2140	54	5	a	a	DET
american_scientific_journal-2140	54	6	nonzero	nonzero	ADJ
american_scientific_journal-2140	54	7	column	column	NOUN
american_scientific_journal-2140	54	8	vector	vector	NOUN
american_scientific_journal-2140	54	9	𝑥	𝑥	PROPN
american_scientific_journal-2140	54	10	corresponding	correspond	VERB
american_scientific_journal-2140	54	11	to	to	ADP
american_scientific_journal-2140	54	12	a	a	DET
american_scientific_journal-2140	54	13	given	give	VERB
american_scientific_journal-2140	54	14	eigenvalue	eigenvalue	PROPN
american_scientific_journal-2140	54	15	𝜆	𝜆	ADP
american_scientific_journal-2140	54	16	,	,	PUNCT
american_scientific_journal-2140	54	17	the	the	DET
american_scientific_journal-2140	54	18	eigenvalue	eigenvalue	PROPN
american_scientific_journal-2140	54	19	equation	equation	NOUN
american_scientific_journal-2140	54	20	(	(	PUNCT
american_scientific_journal-2140	54	21	𝐻	𝐻	PROPN
american_scientific_journal-2140	54	22	−	−	NOUN
american_scientific_journal-2140	54	23	𝜆𝐼)𝑥	𝜆𝐼)𝑥	NOUN
american_scientific_journal-2140	54	24	=	=	SYM
american_scientific_journal-2140	54	25	0	0	PROPN
american_scientific_journal-2140	54	26	gives	give	VERB
american_scientific_journal-2140	54	27	a	a	DET
american_scientific_journal-2140	54	28	pair	pair	NOUN
american_scientific_journal-2140	54	29	of	of	ADP
american_scientific_journal-2140	54	30	eigenvalues	eigenvalue	NOUN
american_scientific_journal-2140	54	31	{	{	PUNCT
american_scientific_journal-2140	54	32	𝜆1	𝜆1	NOUN
american_scientific_journal-2140	54	33	,	,	PUNCT
american_scientific_journal-2140	54	34	𝜆2	𝜆2	PROPN
american_scientific_journal-2140	54	35	}	}	PUNCT
american_scientific_journal-2140	54	36	as	as	ADP
american_scientific_journal-2140	54	37	the	the	DET
american_scientific_journal-2140	54	38	solutions	solution	NOUN
american_scientific_journal-2140	54	39	to	to	ADP
american_scientific_journal-2140	54	40	the	the	DET
american_scientific_journal-2140	54	41	characteristic	characteristic	ADJ
american_scientific_journal-2140	54	42	equation	equation	NOUN
american_scientific_journal-2140	54	43	|𝐻	|𝐻	NOUN
american_scientific_journal-2140	55	1	−	−	PROPN
american_scientific_journal-2140	56	1	𝜆𝐼|	𝜆𝐼|	NOUN
american_scientific_journal-2140	57	1	=	=	SYM
american_scientific_journal-2140	58	1	0	0	PROPN
american_scientific_journal-2140	58	2	,	,	PUNCT
american_scientific_journal-2140	58	3	where	where	SCONJ
american_scientific_journal-2140	58	4	𝐼	𝐼	PROPN
american_scientific_journal-2140	58	5	is	be	AUX
american_scientific_journal-2140	58	6	a	a	DET
american_scientific_journal-2140	58	7	2×	2×	NUM
american_scientific_journal-2140	58	8	2	2	NUM
american_scientific_journal-2140	58	9	identity	identity	NOUN
american_scientific_journal-2140	58	10	matrix	matrix	NOUN
american_scientific_journal-2140	58	11	and	and	CCONJ
american_scientific_journal-2140	58	12	|𝐴|	|𝐴|	X
american_scientific_journal-2140	58	13	signifies	signify	VERB
american_scientific_journal-2140	58	14	the	the	DET
american_scientific_journal-2140	58	15	determinant	determinant	NOUN
american_scientific_journal-2140	58	16	of	of	ADP
american_scientific_journal-2140	58	17	the	the	DET
american_scientific_journal-2140	58	18	matrix	matrix	NOUN
american_scientific_journal-2140	58	19	𝐴	𝐴	NOUN
american_scientific_journal-2140	58	20	≔	≔	VERB
american_scientific_journal-2140	58	21	𝐻	𝐻	NOUN
american_scientific_journal-2140	58	22	−	−	NOUN
american_scientific_journal-2140	58	23	𝜆𝐼.	𝜆𝐼.	NOUN
american_scientific_journal-2140	58	24	herewith	herewith	NOUN
american_scientific_journal-2140	58	25	,	,	PUNCT
american_scientific_journal-2140	58	26	it	it	PRON
american_scientific_journal-2140	58	27	follows	follow	VERB
american_scientific_journal-2140	58	28	from	from	ADP
american_scientific_journal-2140	58	29	eqn	eqn	NOUN
american_scientific_journal-2140	58	30	.	.	PUNCT
american_scientific_journal-2140	59	1	(	(	PUNCT
american_scientific_journal-2140	59	2	4	4	NUM
american_scientific_journal-2140	59	3	)	)	PUNCT
american_scientific_journal-2140	59	4	that	that	PRON
american_scientific_journal-2140	59	5	we	we	PRON
american_scientific_journal-2140	59	6	have	have	VERB
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american_scientific_journal-2140	59	10	of	of	ADP
american_scientific_journal-2140	59	11	eigenvalues	eigenvalues	PROPN
american_scientific_journal-2140	59	12	𝜆1(𝑢	𝜆1(𝑢	PROPN
american_scientific_journal-2140	59	13	,	,	PUNCT
american_scientific_journal-2140	59	14	𝑚	𝑚	NOUN
american_scientific_journal-2140	59	15	)	)	PUNCT
american_scientific_journal-2140	59	16	=	=	NOUN
american_scientific_journal-2140	59	17	𝑢+	𝑢+	PUNCT
american_scientific_journal-2140	59	18	√𝑢2	√𝑢2	SYM
american_scientific_journal-2140	59	19	+	+	CCONJ
american_scientific_journal-2140	59	20	(	(	PUNCT
american_scientific_journal-2140	59	21	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	59	22	(	(	PUNCT
american_scientific_journal-2140	59	23	1−𝑚)3	1−𝑚)3	NUM
american_scientific_journal-2140	59	24	(	(	PUNCT
american_scientific_journal-2140	59	25	5	5	NUM
american_scientific_journal-2140	59	26	)	)	PUNCT
american_scientific_journal-2140	59	27	𝜆2(𝑢	𝜆2(𝑢	PROPN
american_scientific_journal-2140	59	28	,	,	PUNCT
american_scientific_journal-2140	59	29	𝑚	𝑚	NOUN
american_scientific_journal-2140	59	30	)	)	PUNCT
american_scientific_journal-2140	59	31	=	=	SYM
american_scientific_journal-2140	60	1	𝑢−	𝑢−	PROPN
american_scientific_journal-2140	60	2	√𝑢2	√𝑢2	PROPN
american_scientific_journal-2140	60	3	+	+	CCONJ
american_scientific_journal-2140	60	4	(	(	PUNCT
american_scientific_journal-2140	60	5	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	60	6	(	(	PUNCT
american_scientific_journal-2140	60	7	1−𝑚)3	1−𝑚)3	NUM
american_scientific_journal-2140	60	8	(	(	PUNCT
american_scientific_journal-2140	60	9	6	6	NUM
american_scientific_journal-2140	60	10	)	)	PUNCT
american_scientific_journal-2140	60	11	at	at	ADP
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american_scientific_journal-2140	60	13	stationary	stationary	ADJ
american_scientific_journal-2140	60	14	point	point	NOUN
american_scientific_journal-2140	60	15	(	(	PUNCT
american_scientific_journal-2140	60	16	0	0	NUM
american_scientific_journal-2140	60	17	,	,	PUNCT
american_scientific_journal-2140	60	18	0	0	NUM
american_scientific_journal-2140	60	19	)	)	PUNCT
american_scientific_journal-2140	60	20	,	,	PUNCT
american_scientific_journal-2140	60	21	we	we	PRON
american_scientific_journal-2140	60	22	observe	observe	VERB
american_scientific_journal-2140	60	23	that	that	SCONJ
american_scientific_journal-2140	60	24	𝜆1(0,0	𝜆1(0,0	NOUN
american_scientific_journal-2140	60	25	)	)	PUNCT
american_scientific_journal-2140	60	26	>	>	X
american_scientific_journal-2140	60	27	0	0	NUM
american_scientific_journal-2140	60	28	and	and	CCONJ
american_scientific_journal-2140	60	29	𝜆2(0,0	𝜆2(0,0	NOUN
american_scientific_journal-2140	60	30	)	)	PUNCT
american_scientific_journal-2140	60	31	<	<	X
american_scientific_journal-2140	60	32	0	0	X
american_scientific_journal-2140	60	33	.	.	PUNCT
american_scientific_journal-2140	61	1	from	from	ADP
american_scientific_journal-2140	61	2	an	an	DET
american_scientific_journal-2140	61	3	independent	independent	ADJ
american_scientific_journal-2140	61	4	signature	signature	NOUN
american_scientific_journal-2140	61	5	of	of	ADP
american_scientific_journal-2140	61	6	the	the	DET
american_scientific_journal-2140	61	7	eigenvalues	eigenvalue	NOUN
american_scientific_journal-2140	61	8	{	{	PUNCT
american_scientific_journal-2140	61	9	𝜆1	𝜆1	NOUN
american_scientific_journal-2140	61	10	,	,	PUNCT
american_scientific_journal-2140	61	11	𝜆2	𝜆2	PROPN
american_scientific_journal-2140	61	12	}	}	PUNCT
american_scientific_journal-2140	61	13	,	,	PUNCT
american_scientific_journal-2140	61	14	we	we	PRON
american_scientific_journal-2140	61	15	derive	derive	VERB
american_scientific_journal-2140	61	16	in	in	ADP
american_scientific_journal-2140	61	17	this	this	DET
american_scientific_journal-2140	61	18	case	case	NOUN
american_scientific_journal-2140	61	19	that	that	SCONJ
american_scientific_journal-2140	61	20	the	the	DET
american_scientific_journal-2140	61	21	determinant	determinant	ADJ
american_scientific_journal-2140	61	22	∆	∆	PROPN
american_scientific_journal-2140	61	23	of	of	ADP
american_scientific_journal-2140	61	24	the	the	DET
american_scientific_journal-2140	61	25	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	61	26	matrix	matrix	NOUN
american_scientific_journal-2140	61	27	𝐻	𝐻	NOUN
american_scientific_journal-2140	61	28	reads	read	VERB
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american_scientific_journal-2140	61	30	the	the	DET
american_scientific_journal-2140	61	31	product	product	NOUN
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american_scientific_journal-2140	61	33	the	the	DET
american_scientific_journal-2140	61	34	eigenvalues	eigenvalue	NOUN
american_scientific_journal-2140	61	35	𝜆1	𝜆1	PROPN
american_scientific_journal-2140	61	36	and	and	CCONJ
american_scientific_journal-2140	61	37	𝜆2	𝜆2	NOUN
american_scientific_journal-2140	61	38	,	,	PUNCT
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american_scientific_journal-2140	61	40	’s	’	VERB
american_scientific_journal-2140	61	41	we	we	PRON
american_scientific_journal-2140	61	42	have	have	VERB
american_scientific_journal-2140	61	43	∆=	∆=	ADJ
american_scientific_journal-2140	61	44	𝜆1𝜆2	𝜆1𝜆2	NOUN
american_scientific_journal-2140	61	45	.	.	PUNCT
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american_scientific_journal-2140	61	47	eqns	eqns	PROPN
american_scientific_journal-2140	61	48	.	.	PUNCT
american_scientific_journal-2140	62	1	(	(	PUNCT
american_scientific_journal-2140	62	2	5	5	NUM
american_scientific_journal-2140	62	3	,	,	PUNCT
american_scientific_journal-2140	62	4	6	6	NUM
american_scientific_journal-2140	62	5	)	)	PUNCT
american_scientific_journal-2140	62	6	,	,	PUNCT
american_scientific_journal-2140	62	7	it	it	PRON
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american_scientific_journal-2140	62	11	values	value	NOUN
american_scientific_journal-2140	62	12	of	of	ADP
american_scientific_journal-2140	62	13	{	{	PUNCT
american_scientific_journal-2140	62	14	𝑢	𝑢	X
american_scientific_journal-2140	62	15	,	,	PUNCT
american_scientific_journal-2140	62	16	𝑚	𝑚	NOUN
american_scientific_journal-2140	62	17	}	}	PUNCT
american_scientific_journal-2140	62	18	that	that	SCONJ
american_scientific_journal-2140	62	19	we	we	PRON
american_scientific_journal-2140	62	20	have	have	VERB
american_scientific_journal-2140	62	21	the	the	DET
american_scientific_journal-2140	62	22	following	follow	VERB
american_scientific_journal-2140	62	23	unconditionally	unconditionally	ADV
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american_scientific_journal-2140	62	25	determinant	determinant	ADJ
american_scientific_journal-2140	62	26	∆(𝑢	∆(𝑢	NOUN
american_scientific_journal-2140	62	27	,	,	PUNCT
american_scientific_journal-2140	62	28	𝑚	𝑚	NOUN
american_scientific_journal-2140	62	29	)	)	PUNCT
american_scientific_journal-2140	62	30	=	=	SYM
american_scientific_journal-2140	63	1	−	−	PROPN
american_scientific_journal-2140	63	2	1	1	NUM
american_scientific_journal-2140	63	3	(	(	PUNCT
american_scientific_journal-2140	63	4	1−𝑚)4	1−𝑚)4	NUM
american_scientific_journal-2140	63	5	(	(	PUNCT
american_scientific_journal-2140	63	6	7	7	X
american_scientific_journal-2140	63	7	)	)	PUNCT
american_scientific_journal-2140	63	8	this	this	PRON
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american_scientific_journal-2140	63	10	that	that	SCONJ
american_scientific_journal-2140	63	11	∆	∆	PROPN
american_scientific_journal-2140	63	12	remains	remain	VERB
american_scientific_journal-2140	63	13	negative	negative	ADJ
american_scientific_journal-2140	63	14	for	for	ADP
american_scientific_journal-2140	63	15	all	all	DET
american_scientific_journal-2140	63	16	values	value	NOUN
american_scientific_journal-2140	63	17	of	of	ADP
american_scientific_journal-2140	63	18	the	the	DET
american_scientific_journal-2140	63	19	lateral	lateral	ADJ
american_scientific_journal-2140	63	20	magnification	magnification	NOUN
american_scientific_journal-2140	63	21	𝑚	𝑚	NOUN
american_scientific_journal-2140	63	22	,	,	PUNCT
american_scientific_journal-2140	63	23	implying	imply	VERB
american_scientific_journal-2140	63	24	a	a	DET
american_scientific_journal-2140	63	25	universal	universal	ADJ
american_scientific_journal-2140	63	26	existence	existence	NOUN
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american_scientific_journal-2140	63	28	global	global	ADJ
american_scientific_journal-2140	63	29	instabilities	instability	NOUN
american_scientific_journal-2140	63	30	in	in	ADP
american_scientific_journal-2140	63	31	optical	optical	ADJ
american_scientific_journal-2140	63	32	image	image	NOUN
american_scientific_journal-2140	63	33	formation	formation	NOUN
american_scientific_journal-2140	63	34	.	.	PUNCT
american_scientific_journal-2140	64	1	for	for	ADP
american_scientific_journal-2140	64	2	a	a	DET
american_scientific_journal-2140	64	3	real	real	ADJ
american_scientific_journal-2140	64	4	image	image	NOUN
american_scientific_journal-2140	64	5	formation	formation	NOUN
american_scientific_journal-2140	64	6	,	,	PUNCT
american_scientific_journal-2140	64	7	we	we	PRON
american_scientific_journal-2140	64	8	require	require	VERB
american_scientific_journal-2140	64	9	a	a	DET
american_scientific_journal-2140	64	10	positive	positive	ADJ
american_scientific_journal-2140	64	11	determinant	determinant	ADJ
american_scientific_journal-2140	64	12	satisfying	satisfy	VERB
american_scientific_journal-2140	64	13	the	the	DET
american_scientific_journal-2140	64	14	local	local	ADJ
american_scientific_journal-2140	64	15	inequality	inequality	NOUN
american_scientific_journal-2140	64	16	𝑢2	𝑢2	PROPN
american_scientific_journal-2140	64	17	+	+	CCONJ
american_scientific_journal-2140	64	18	𝑚2	𝑚2	NOUN
american_scientific_journal-2140	64	19	+	+	CCONJ
american_scientific_journal-2140	64	20	1	1	NUM
american_scientific_journal-2140	64	21	>	>	DET
american_scientific_journal-2140	64	22	2𝑚	2𝑚	NOUN
american_scientific_journal-2140	64	23	in	in	ADP
american_scientific_journal-2140	64	24	optimization	optimization	NOUN
american_scientific_journal-2140	64	25	variables	variable	NOUN
american_scientific_journal-2140	64	26	{	{	PUNCT
american_scientific_journal-2140	64	27	𝑢	𝑢	X
american_scientific_journal-2140	64	28	,	,	PUNCT
american_scientific_journal-2140	64	29	𝑚	𝑚	NOUN
american_scientific_journal-2140	64	30	}	}	PUNCT
american_scientific_journal-2140	64	31	,	,	PUNCT
american_scientific_journal-2140	64	32	whereby	whereby	SCONJ
american_scientific_journal-2140	64	33	the	the	DET
american_scientific_journal-2140	64	34	image	image	NOUN
american_scientific_journal-2140	64	35	formed	form	VERB
american_scientific_journal-2140	64	36	by	by	ADP
american_scientific_journal-2140	64	37	the	the	DET
american_scientific_journal-2140	64	38	optical	optical	ADJ
american_scientific_journal-2140	64	39	system	system	NOUN
american_scientific_journal-2140	64	40	under	under	ADP
american_scientific_journal-2140	64	41	consideration	consideration	NOUN
american_scientific_journal-2140	64	42	remains	remain	VERB
american_scientific_journal-2140	64	43	globally	globally	ADV
american_scientific_journal-2140	64	44	unstable	unstable	ADJ
american_scientific_journal-2140	64	45	.	.	PUNCT
american_scientific_journal-2140	65	1	by	by	ADP
american_scientific_journal-2140	65	2	invoking	invoke	VERB
american_scientific_journal-2140	65	3	the	the	DET
american_scientific_journal-2140	65	4	eigenvalue	eigenvalue	ADJ
american_scientific_journal-2140	65	5	equation	equation	NOUN
american_scientific_journal-2140	65	6	𝐻𝑥	𝐻𝑥	NOUN
american_scientific_journal-2140	65	7	=	=	PUNCT
american_scientific_journal-2140	65	8	𝜆𝑥	𝜆𝑥	NOUN
american_scientific_journal-2140	65	9	with	with	ADP
american_scientific_journal-2140	65	10	𝑥	𝑥	DET
american_scientific_journal-2140	65	11	∈	∈	PROPN
american_scientific_journal-2140	65	12	ℝ2	ℝ2	VERB
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american_scientific_journal-2140	65	14	the	the	DET
american_scientific_journal-2140	65	15	real	real	ADV
american_scientific_journal-2140	65	16	valued	value	VERB
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american_scientific_journal-2140	65	18	vector	vector	NOUN
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american_scientific_journal-2140	65	23	as	as	ADP
american_scientific_journal-2140	65	24	the	the	DET
american_scientific_journal-2140	65	25	object	object	NOUN
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american_scientific_journal-2140	65	27	𝑢	𝑢	NOUN
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american_scientific_journal-2140	65	33	lateral	lateral	ADJ
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american_scientific_journal-2140	65	35	𝑚	𝑚	PROPN
american_scientific_journal-2140	65	36	as	as	ADP
american_scientific_journal-2140	65	37	the	the	DET
american_scientific_journal-2140	65	38	second	second	ADJ
american_scientific_journal-2140	65	39	,	,	PUNCT
american_scientific_journal-2140	65	40	it	it	PRON
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american_scientific_journal-2140	65	44	.	.	PUNCT
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american_scientific_journal-2140	66	2	5	5	NUM
american_scientific_journal-2140	66	3	,	,	PUNCT
american_scientific_journal-2140	66	4	6	6	NUM
american_scientific_journal-2140	66	5	)	)	PUNCT
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american_scientific_journal-2140	66	10	{	{	PUNCT
american_scientific_journal-2140	66	11	�	�	PROPN
american_scientific_journal-2140	66	12	̂	̂	VERB
american_scientific_journal-2140	66	13	�	�	NOUN
american_scientific_journal-2140	66	14	1	1	NUM
american_scientific_journal-2140	66	15	,	,	PUNCT
american_scientific_journal-2140	66	16	�	�	NOUN
american_scientific_journal-2140	66	17	̂	̂	VERB
american_scientific_journal-2140	66	18	�	�	NOUN
american_scientific_journal-2140	66	19	2	2	NUM
american_scientific_journal-2140	66	20	}	}	PUNCT
american_scientific_journal-2140	66	21	corresponding	correspond	VERB
american_scientific_journal-2140	66	22	to	to	ADP
american_scientific_journal-2140	66	23	𝜆	𝜆	DET
american_scientific_journal-2140	66	24	=	=	X
american_scientific_journal-2140	66	25	𝜆1	𝜆1	NOUN
american_scientific_journal-2140	66	26	and	and	CCONJ
american_scientific_journal-2140	66	27	𝜆	𝜆	PRON
american_scientific_journal-2140	66	28	=	=	SYM
american_scientific_journal-2140	66	29	𝜆2	𝜆2	PROPN
american_scientific_journal-2140	66	30	read	read	NOUN
american_scientific_journal-2140	66	31	as	as	ADP
american_scientific_journal-2140	66	32	�	�	PROPN
american_scientific_journal-2140	66	33	̂	̂	X
american_scientific_journal-2140	66	34	�	�	NOUN
american_scientific_journal-2140	66	35	1(𝑢	1(𝑢	NUM
american_scientific_journal-2140	66	36	,	,	PUNCT
american_scientific_journal-2140	66	37	𝑚	𝑚	NOUN
american_scientific_journal-2140	66	38	)	)	PUNCT
american_scientific_journal-2140	66	39	=	=	SYM
american_scientific_journal-2140	67	1	1	1	NUM
american_scientific_journal-2140	67	2	√1	√1	PROPN
american_scientific_journal-2140	67	3	+	+	CCONJ
american_scientific_journal-2140	67	4	(	(	PUNCT
american_scientific_journal-2140	67	5	1	1	NUM
american_scientific_journal-2140	67	6	(	(	PUNCT
american_scientific_journal-2140	67	7	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	67	8	𝜆1	𝜆1	NOUN
american_scientific_journal-2140	67	9	)	)	PUNCT
american_scientific_journal-2140	67	10	2	2	NUM
american_scientific_journal-2140	67	11	(	(	PUNCT
american_scientific_journal-2140	67	12	1	1	NUM
american_scientific_journal-2140	67	13	(	(	PUNCT
american_scientific_journal-2140	67	14	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	67	15	𝜆1	𝜆1	NOUN
american_scientific_journal-2140	67	16	1	1	NUM
american_scientific_journal-2140	67	17	)	)	PUNCT
american_scientific_journal-2140	67	18	(	(	PUNCT
american_scientific_journal-2140	67	19	8)	8)	NUM
american_scientific_journal-2140	67	20	�	�	NOUN
american_scientific_journal-2140	67	21	̂	̂	NOUN
american_scientific_journal-2140	67	22	�	�	NOUN
american_scientific_journal-2140	67	23	2(𝑢	2(𝑢	NUM
american_scientific_journal-2140	67	24	,	,	PUNCT
american_scientific_journal-2140	67	25	𝑚	𝑚	NOUN
american_scientific_journal-2140	67	26	)	)	PUNCT
american_scientific_journal-2140	67	27	=	=	SYM
american_scientific_journal-2140	67	28	1	1	NUM
american_scientific_journal-2140	67	29	√1	√1	PROPN
american_scientific_journal-2140	67	30	+	+	CCONJ
american_scientific_journal-2140	67	31	(	(	PUNCT
american_scientific_journal-2140	67	32	1	1	NUM
american_scientific_journal-2140	67	33	(	(	PUNCT
american_scientific_journal-2140	67	34	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	67	35	𝜆2	𝜆2	NOUN
american_scientific_journal-2140	67	36	)	)	PUNCT
american_scientific_journal-2140	67	37	2	2	NUM
american_scientific_journal-2140	67	38	(	(	PUNCT
american_scientific_journal-2140	67	39	1	1	NUM
american_scientific_journal-2140	67	40	(	(	PUNCT
american_scientific_journal-2140	67	41	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	67	42	𝜆2	𝜆2	NOUN
american_scientific_journal-2140	67	43	1	1	NUM
american_scientific_journal-2140	67	44	)	)	PUNCT
american_scientific_journal-2140	67	45	(	(	PUNCT
american_scientific_journal-2140	67	46	9	9	X
american_scientific_journal-2140	67	47	)	)	PUNCT
american_scientific_journal-2140	67	48	herewith	herewith	NOUN
american_scientific_journal-2140	67	49	,	,	PUNCT
american_scientific_journal-2140	67	50	the	the	DET
american_scientific_journal-2140	67	51	physical	physical	ADJ
american_scientific_journal-2140	67	52	implication	implication	NOUN
american_scientific_journal-2140	67	53	of	of	ADP
american_scientific_journal-2140	67	54	the	the	DET
american_scientific_journal-2140	67	55	above	above	ADJ
american_scientific_journal-2140	67	56	eigenvectors	eigenvector	NOUN
american_scientific_journal-2140	67	57	as	as	ADP
american_scientific_journal-2140	67	58	in	in	ADP
american_scientific_journal-2140	67	59	eqns	eqns	PROPN
american_scientific_journal-2140	67	60	.	.	PUNCT
american_scientific_journal-2140	68	1	(	(	PUNCT
american_scientific_journal-2140	68	2	8	8	NUM
american_scientific_journal-2140	68	3	,	,	PUNCT
american_scientific_journal-2140	68	4	9	9	NUM
american_scientific_journal-2140	68	5	)	)	PUNCT
american_scientific_journal-2140	68	6	illustrates	illustrate	VERB
american_scientific_journal-2140	68	7	an	an	DET
american_scientific_journal-2140	68	8	undermining	undermine	VERB
american_scientific_journal-2140	68	9	optimal	optimal	ADJ
american_scientific_journal-2140	68	10	zooming	zooming	NOUN
american_scientific_journal-2140	68	11	qualification	qualification	NOUN
american_scientific_journal-2140	68	12	in	in	ADP
american_scientific_journal-2140	68	13	the	the	DET
american_scientific_journal-2140	68	14	two	two	NUM
american_scientific_journal-2140	68	15	dimensional	dimensional	ADJ
american_scientific_journal-2140	68	16	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	68	17	space	space	NOUN
american_scientific_journal-2140	68	18	of	of	ADP
american_scientific_journal-2140	68	19	optical	optical	ADJ
american_scientific_journal-2140	68	20	optimization	optimization	NOUN
american_scientific_journal-2140	68	21	variables	variable	NOUN
american_scientific_journal-2140	68	22	{	{	PUNCT
american_scientific_journal-2140	68	23	𝑢	𝑢	X
american_scientific_journal-2140	68	24	,	,	PUNCT
american_scientific_journal-2140	68	25	𝑚	𝑚	NOUN
american_scientific_journal-2140	68	26	}	}	PUNCT
american_scientific_journal-2140	68	27	.	.	PUNCT
american_scientific_journal-2140	69	1	3	3	X
american_scientific_journal-2140	69	2	.	.	X
american_scientific_journal-2140	69	3	physical	physical	ADJ
american_scientific_journal-2140	69	4	implications	implication	NOUN
american_scientific_journal-2140	69	5	in	in	ADP
american_scientific_journal-2140	69	6	this	this	DET
american_scientific_journal-2140	69	7	section	section	NOUN
american_scientific_journal-2140	69	8	,	,	PUNCT
american_scientific_journal-2140	69	9	we	we	PRON
american_scientific_journal-2140	69	10	discuss	discuss	VERB
american_scientific_journal-2140	69	11	the	the	DET
american_scientific_journal-2140	69	12	stability	stability	NOUN
american_scientific_journal-2140	69	13	and	and	CCONJ
american_scientific_journal-2140	69	14	correlation	correlation	NOUN
american_scientific_journal-2140	69	15	structures	structure	NOUN
american_scientific_journal-2140	69	16	of	of	ADP
american_scientific_journal-2140	69	17	the	the	DET
american_scientific_journal-2140	69	18	image	image	NOUN
american_scientific_journal-2140	69	19	formed	form	VERB
american_scientific_journal-2140	69	20	by	by	ADP
american_scientific_journal-2140	69	21	a	a	DET
american_scientific_journal-2140	69	22	given	give	VERB
american_scientific_journal-2140	69	23	lens/	lens/	NUM
american_scientific_journal-2140	69	24	mirror	mirror	NOUN
american_scientific_journal-2140	69	25	american	american	ADJ
american_scientific_journal-2140	69	26	scientific	scientific	PROPN
american_scientific_journal-2140	69	27	research	research	NOUN
american_scientific_journal-2140	69	28	journal	journal	NOUN
american_scientific_journal-2140	69	29	for	for	ADP
american_scientific_journal-2140	69	30	engineering	engineering	NOUN
american_scientific_journal-2140	69	31	,	,	PUNCT
american_scientific_journal-2140	69	32	technology	technology	NOUN
american_scientific_journal-2140	69	33	,	,	PUNCT
american_scientific_journal-2140	69	34	and	and	CCONJ
american_scientific_journal-2140	69	35	sciences	science	NOUN
american_scientific_journal-2140	69	36	(	(	PUNCT
american_scientific_journal-2140	69	37	asrjets	asrjet	NOUN
american_scientific_journal-2140	69	38	)	)	PUNCT
american_scientific_journal-2140	69	39	(	(	PUNCT
american_scientific_journal-2140	69	40	2016	2016	NUM
american_scientific_journal-2140	69	41	)	)	PUNCT
american_scientific_journal-2140	69	42	volume	volume	NOUN
american_scientific_journal-2140	69	43	26	26	NUM
american_scientific_journal-2140	69	44	,	,	PUNCT
american_scientific_journal-2140	69	45	no	no	DET
american_scientific_journal-2140	69	46	1	1	NUM
american_scientific_journal-2140	69	47	,	,	PUNCT
american_scientific_journal-2140	69	48	pp	pp	ADV
american_scientific_journal-2140	69	49	302	302	NUM
american_scientific_journal-2140	69	50	-	-	SYM
american_scientific_journal-2140	69	51	313	313	NUM
american_scientific_journal-2140	69	52	306	306	NUM
american_scientific_journal-2140	69	53	under	under	ADP
american_scientific_journal-2140	69	54	specific	specific	ADJ
american_scientific_journal-2140	69	55	fluctuations	fluctuation	NOUN
american_scientific_journal-2140	69	56	of	of	ADP
american_scientific_journal-2140	69	57	the	the	DET
american_scientific_journal-2140	69	58	object	object	NOUN
american_scientific_journal-2140	69	59	distance	distance	NOUN
american_scientific_journal-2140	69	60	𝑢	𝑢	NOUN
american_scientific_journal-2140	69	61	and	and	CCONJ
american_scientific_journal-2140	69	62	lateral	lateral	ADJ
american_scientific_journal-2140	69	63	magnification	magnification	NOUN
american_scientific_journal-2140	69	64	𝑚.	𝑚.	ADV
american_scientific_journal-2140	69	65	in	in	ADP
american_scientific_journal-2140	69	66	the	the	DET
american_scientific_journal-2140	69	67	sequel	sequel	NOUN
american_scientific_journal-2140	69	68	,	,	PUNCT
american_scientific_journal-2140	69	69	in	in	ADP
american_scientific_journal-2140	69	70	the	the	DET
american_scientific_journal-2140	69	71	first	first	ADJ
american_scientific_journal-2140	69	72	part	part	NOUN
american_scientific_journal-2140	69	73	of	of	ADP
american_scientific_journal-2140	69	74	this	this	DET
american_scientific_journal-2140	69	75	section	section	NOUN
american_scientific_journal-2140	69	76	,	,	PUNCT
american_scientific_journal-2140	69	77	we	we	PRON
american_scientific_journal-2140	69	78	examine	examine	VERB
american_scientific_journal-2140	69	79	the	the	DET
american_scientific_journal-2140	69	80	stability	stability	NOUN
american_scientific_journal-2140	69	81	components	component	NOUN
american_scientific_journal-2140	69	82	of	of	ADP
american_scientific_journal-2140	69	83	an	an	DET
american_scientific_journal-2140	69	84	image	image	NOUN
american_scientific_journal-2140	69	85	formed	form	VERB
american_scientific_journal-2140	69	86	by	by	ADP
american_scientific_journal-2140	69	87	the	the	DET
american_scientific_journal-2140	69	88	optical	optical	ADJ
american_scientific_journal-2140	69	89	instrument	instrument	NOUN
american_scientific_journal-2140	69	90	at	at	ADP
american_scientific_journal-2140	69	91	a	a	DET
american_scientific_journal-2140	69	92	given	give	VERB
american_scientific_journal-2140	69	93	lateral	lateral	ADJ
american_scientific_journal-2140	69	94	magnification	magnification	NOUN
american_scientific_journal-2140	69	95	.	.	PUNCT
american_scientific_journal-2140	70	1	in	in	ADP
american_scientific_journal-2140	70	2	the	the	DET
american_scientific_journal-2140	70	3	second	second	ADJ
american_scientific_journal-2140	70	4	part	part	NOUN
american_scientific_journal-2140	70	5	of	of	ADP
american_scientific_journal-2140	70	6	this	this	DET
american_scientific_journal-2140	70	7	section	section	NOUN
american_scientific_journal-2140	70	8	,	,	PUNCT
american_scientific_journal-2140	70	9	we	we	PRON
american_scientific_journal-2140	70	10	focus	focus	VERB
american_scientific_journal-2140	70	11	on	on	ADP
american_scientific_journal-2140	70	12	the	the	DET
american_scientific_journal-2140	70	13	image	image	NOUN
american_scientific_journal-2140	70	14	stability	stability	NOUN
american_scientific_journal-2140	70	15	properties	property	NOUN
american_scientific_journal-2140	70	16	evaluated	evaluate	VERB
american_scientific_journal-2140	70	17	at	at	ADP
american_scientific_journal-2140	70	18	a	a	DET
american_scientific_journal-2140	70	19	given	give	VERB
american_scientific_journal-2140	70	20	object	object	NOUN
american_scientific_journal-2140	70	21	distance	distance	NOUN
american_scientific_journal-2140	70	22	in	in	ADP
american_scientific_journal-2140	70	23	the	the	DET
american_scientific_journal-2140	70	24	unit	unit	NOUN
american_scientific_journal-2140	70	25	of	of	ADP
american_scientific_journal-2140	70	26	the	the	DET
american_scientific_journal-2140	70	27	focal	focal	ADJ
american_scientific_journal-2140	70	28	length	length	NOUN
american_scientific_journal-2140	70	29	as	as	ADP
american_scientific_journal-2140	70	30	a	a	DET
american_scientific_journal-2140	70	31	characteristic	characteristic	ADJ
american_scientific_journal-2140	70	32	property	property	NOUN
american_scientific_journal-2140	70	33	of	of	ADP
american_scientific_journal-2140	70	34	the	the	DET
american_scientific_journal-2140	70	35	lens/	lens/	NUM
american_scientific_journal-2140	70	36	mirror	mirror	NOUN
american_scientific_journal-2140	70	37	.	.	PUNCT
american_scientific_journal-2140	71	1	3.1	3.1	NUM
american_scientific_journal-2140	71	2	.	.	PUNCT
american_scientific_journal-2140	72	1	fixed	fix	VERB
american_scientific_journal-2140	72	2	lateral	lateral	ADJ
american_scientific_journal-2140	72	3	magnification	magnification	NOUN
american_scientific_journal-2140	72	4	from	from	ADP
american_scientific_journal-2140	72	5	the	the	DET
american_scientific_journal-2140	72	6	perspective	perspective	NOUN
american_scientific_journal-2140	72	7	of	of	ADP
american_scientific_journal-2140	72	8	the	the	DET
american_scientific_journal-2140	72	9	stability	stability	NOUN
american_scientific_journal-2140	72	10	analysis	analysis	NOUN
american_scientific_journal-2140	72	11	as	as	SCONJ
american_scientific_journal-2140	72	12	introduced	introduce	VERB
american_scientific_journal-2140	72	13	in	in	ADP
american_scientific_journal-2140	72	14	section	section	NOUN
american_scientific_journal-2140	72	15	2	2	NUM
american_scientific_journal-2140	72	16	,	,	PUNCT
american_scientific_journal-2140	72	17	we	we	PRON
american_scientific_journal-2140	72	18	offer	offer	VERB
american_scientific_journal-2140	72	19	the	the	DET
american_scientific_journal-2140	72	20	functional	functional	ADJ
american_scientific_journal-2140	72	21	qualification	qualification	NOUN
american_scientific_journal-2140	72	22	of	of	ADP
american_scientific_journal-2140	72	23	the	the	DET
american_scientific_journal-2140	72	24	optical	optical	ADJ
american_scientific_journal-2140	72	25	designing	designing	NOUN
american_scientific_journal-2140	72	26	components	component	NOUN
american_scientific_journal-2140	72	27	,	,	PUNCT
american_scientific_journal-2140	72	28	viz	viz	PROPN
american_scientific_journal-2140	72	29	.	.	PUNCT
american_scientific_journal-2140	73	1	the	the	DET
american_scientific_journal-2140	73	2	focal	focal	ADJ
american_scientific_journal-2140	73	3	length	length	NOUN
american_scientific_journal-2140	73	4	𝑓	𝑓	X
american_scientific_journal-2140	73	5	,	,	PUNCT
american_scientific_journal-2140	73	6	flow	flow	NOUN
american_scientific_journal-2140	73	7	components	component	NOUN
american_scientific_journal-2140	73	8	{	{	PUNCT
american_scientific_journal-2140	73	9	𝑓𝑢	𝑓𝑢	PROPN
american_scientific_journal-2140	73	10	,	,	PUNCT
american_scientific_journal-2140	73	11	𝑓𝑚	𝑓𝑚	PROPN
american_scientific_journal-2140	73	12	}	}	PUNCT
american_scientific_journal-2140	73	13	,	,	PUNCT
american_scientific_journal-2140	73	14	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	73	15	capacities	capacity	NOUN
american_scientific_journal-2140	73	16	{	{	PUNCT
american_scientific_journal-2140	73	17	𝑓𝑚𝑚	𝑓𝑚𝑚	PROPN
american_scientific_journal-2140	73	18	,	,	PUNCT
american_scientific_journal-2140	73	19	𝑓𝑚𝑢	𝑓𝑚𝑢	NOUN
american_scientific_journal-2140	73	20	,	,	PUNCT
american_scientific_journal-2140	73	21	𝑓𝑢𝑢	𝑓𝑢𝑢	NOUN
american_scientific_journal-2140	73	22	}	}	PUNCT
american_scientific_journal-2140	73	23	and	and	CCONJ
american_scientific_journal-2140	73	24	eigenvalues	eigenvalue	VERB
american_scientific_journal-2140	73	25	{	{	PUNCT
american_scientific_journal-2140	73	26	𝜆1	𝜆1	NOUN
american_scientific_journal-2140	73	27	,	,	PUNCT
american_scientific_journal-2140	73	28	𝜆2	𝜆2	NOUN
american_scientific_journal-2140	73	29	}	}	PUNCT
american_scientific_journal-2140	73	30	at	at	ADP
american_scientific_journal-2140	73	31	a	a	DET
american_scientific_journal-2140	73	32	fixed	fix	VERB
american_scientific_journal-2140	73	33	lateral	lateral	ADJ
american_scientific_journal-2140	73	34	magnification	magnification	NOUN
american_scientific_journal-2140	73	35	𝑚	𝑚	PROPN
american_scientific_journal-2140	73	36	of	of	ADP
american_scientific_journal-2140	73	37	the	the	DET
american_scientific_journal-2140	73	38	system	system	NOUN
american_scientific_journal-2140	73	39	.	.	PUNCT
american_scientific_journal-2140	74	1	as	as	ADP
american_scientific_journal-2140	74	2	a	a	DET
american_scientific_journal-2140	74	3	function	function	NOUN
american_scientific_journal-2140	74	4	of	of	ADP
american_scientific_journal-2140	74	5	the	the	DET
american_scientific_journal-2140	74	6	object	object	NOUN
american_scientific_journal-2140	74	7	distance	distance	NOUN
american_scientific_journal-2140	74	8	𝑢	𝑢	NOUN
american_scientific_journal-2140	74	9	from	from	ADP
american_scientific_journal-2140	74	10	the	the	DET
american_scientific_journal-2140	74	11	optical	optical	ADJ
american_scientific_journal-2140	74	12	center	center	NOUN
american_scientific_journal-2140	74	13	of	of	ADP
american_scientific_journal-2140	74	14	an	an	DET
american_scientific_journal-2140	74	15	instrument	instrument	NOUN
american_scientific_journal-2140	74	16	,	,	PUNCT
american_scientific_journal-2140	74	17	the	the	DET
american_scientific_journal-2140	74	18	corresponding	corresponding	ADJ
american_scientific_journal-2140	74	19	expressions	expression	NOUN
american_scientific_journal-2140	74	20	are	be	AUX
american_scientific_journal-2140	74	21	hereby	hereby	ADV
american_scientific_journal-2140	74	22	enlisted	enlist	VERB
american_scientific_journal-2140	74	23	for	for	ADP
american_scientific_journal-2140	74	24	the	the	DET
american_scientific_journal-2140	74	25	lateral	lateral	ADJ
american_scientific_journal-2140	74	26	magnification	magnification	NOUN
american_scientific_journal-2140	74	27	𝑚	𝑚	ADP
american_scientific_journal-2140	74	28	∈	∈	PROPN
american_scientific_journal-2140	74	29	{	{	PUNCT
american_scientific_journal-2140	74	30	0	0	NUM
american_scientific_journal-2140	74	31	,	,	PUNCT
american_scientific_journal-2140	74	32	1	1	NUM
american_scientific_journal-2140	74	33	2⁄	2⁄	NUM
american_scientific_journal-2140	74	34	,	,	PUNCT
american_scientific_journal-2140	74	35	1	1	NUM
american_scientific_journal-2140	74	36	,	,	PUNCT
american_scientific_journal-2140	74	37	3	3	NUM
american_scientific_journal-2140	74	38	2⁄	2⁄	NUM
american_scientific_journal-2140	74	39	,	,	PUNCT
american_scientific_journal-2140	74	40	2	2	NUM
american_scientific_journal-2140	74	41	,	,	PUNCT
american_scientific_journal-2140	74	42	5/2	5/2	NUM
american_scientific_journal-2140	74	43	,	,	PUNCT
american_scientific_journal-2140	74	44	3	3	NUM
american_scientific_journal-2140	74	45	}	}	PUNCT
american_scientific_journal-2140	74	46	in	in	ADP
american_scientific_journal-2140	74	47	table	table	NOUN
american_scientific_journal-2140	74	48	1	1	NUM
american_scientific_journal-2140	74	49	below	below	ADV
american_scientific_journal-2140	74	50	.	.	PUNCT
american_scientific_journal-2140	75	1	table	table	NOUN
american_scientific_journal-2140	75	2	1	1	NUM
american_scientific_journal-2140	75	3	:	:	PUNCT
american_scientific_journal-2140	75	4	stability	stability	NOUN
american_scientific_journal-2140	75	5	components	component	NOUN
american_scientific_journal-2140	75	6	at	at	ADP
american_scientific_journal-2140	75	7	a	a	DET
american_scientific_journal-2140	75	8	fixed	fix	VERB
american_scientific_journal-2140	75	9	lateral	lateral	ADJ
american_scientific_journal-2140	75	10	magnification	magnification	NOUN
american_scientific_journal-2140	75	11	sn	sn	PROPN
american_scientific_journal-2140	75	12	𝑓	𝑓	ADJ
american_scientific_journal-2140	75	13	𝑓𝑢	𝑓𝑢	INTJ
american_scientific_journal-2140	75	14	𝑓𝑚	𝑓𝑚	PROPN
american_scientific_journal-2140	75	15	𝑓𝑚𝑚	𝑓𝑚𝑚	PROPN
american_scientific_journal-2140	75	16	𝑓𝑚𝑢	𝑓𝑚𝑢	PROPN
american_scientific_journal-2140	75	17	𝑓𝑢𝑢	𝑓𝑢𝑢	PROPN
american_scientific_journal-2140	75	18	𝜆1	𝜆1	PROPN
american_scientific_journal-2140	75	19	𝜆2	𝜆2	PROPN
american_scientific_journal-2140	75	20	𝑚	𝑚	ADP
american_scientific_journal-2140	75	21	0	0	NUM
american_scientific_journal-2140	75	22	0	0	NUM
american_scientific_journal-2140	75	23	0	0	NUM
american_scientific_journal-2140	76	1	𝑢	𝑢	NOUN
american_scientific_journal-2140	76	2	2𝑢	2𝑢	NUM
american_scientific_journal-2140	76	3	1	1	NUM
american_scientific_journal-2140	76	4	0	0	NUM
american_scientific_journal-2140	76	5	𝑢	𝑢	NOUN
american_scientific_journal-2140	76	6	+	+	X
american_scientific_journal-2140	76	7	√𝑢2	√𝑢2	PUNCT
american_scientific_journal-2140	77	1	+	+	CCONJ
american_scientific_journal-2140	77	2	1	1	NUM
american_scientific_journal-2140	77	3	𝑢	𝑢	PRON
american_scientific_journal-2140	77	4	−	−	NOUN
american_scientific_journal-2140	77	5	√𝑢2	√𝑢2	PUNCT
american_scientific_journal-2140	78	1	+	+	CCONJ
american_scientific_journal-2140	78	2	1	1	NUM
american_scientific_journal-2140	78	3	1	1	NUM
american_scientific_journal-2140	78	4	2	2	NUM
american_scientific_journal-2140	78	5	𝑢	𝑢	NUM
american_scientific_journal-2140	78	6	1	1	NUM
american_scientific_journal-2140	78	7	4𝑢	4𝑢	NUM
american_scientific_journal-2140	78	8	16𝑢	16𝑢	NOUN
american_scientific_journal-2140	78	9	4	4	NUM
american_scientific_journal-2140	78	10	0	0	NUM
american_scientific_journal-2140	78	11	8𝑢	8𝑢	NOUN
american_scientific_journal-2140	78	12	+	+	CCONJ
american_scientific_journal-2140	78	13	4√4𝑢2	4√4𝑢2	NUM
american_scientific_journal-2140	78	14	+	+	SYM
american_scientific_journal-2140	78	15	1	1	NUM
american_scientific_journal-2140	78	16	8𝑢	8𝑢	NUM
american_scientific_journal-2140	78	17	−	−	NOUN
american_scientific_journal-2140	78	18	4√4𝑢2	4√4𝑢2	NUM
american_scientific_journal-2140	79	1	+	+	CCONJ
american_scientific_journal-2140	79	2	1	1	NUM
american_scientific_journal-2140	79	3	1	1	NUM
american_scientific_journal-2140	79	4	∞	∞	NUM
american_scientific_journal-2140	79	5	∞	∞	NUM
american_scientific_journal-2140	79	6	∞	∞	NUM
american_scientific_journal-2140	79	7	∞	∞	NUM
american_scientific_journal-2140	79	8	∞	∞	NUM
american_scientific_journal-2140	79	9	0	0	NUM
american_scientific_journal-2140	80	1	∞	∞	NUM
american_scientific_journal-2140	80	2	∞	∞	NUM
american_scientific_journal-2140	80	3	3	3	NUM
american_scientific_journal-2140	80	4	2	2	NUM
american_scientific_journal-2140	80	5	−3𝑢	−3𝑢	PROPN
american_scientific_journal-2140	80	6	−3	−3	ADJ
american_scientific_journal-2140	80	7	4𝑢	4𝑢	NOUN
american_scientific_journal-2140	80	8	−16𝑢	−16𝑢	NOUN
american_scientific_journal-2140	80	9	4	4	NUM
american_scientific_journal-2140	80	10	0	0	NUM
american_scientific_journal-2140	81	1	−8𝑢	−8𝑢	DET
american_scientific_journal-2140	81	2	−	−	NOUN
american_scientific_journal-2140	81	3	4√4𝑢2	4√4𝑢2	NUM
american_scientific_journal-2140	81	4	+	+	NOUN
american_scientific_journal-2140	81	5	1	1	NUM
american_scientific_journal-2140	81	6	−8𝑢	−8𝑢	NOUN
american_scientific_journal-2140	81	7	+	+	NOUN
american_scientific_journal-2140	81	8	4√4𝑢2	4√4𝑢2	NUM
american_scientific_journal-2140	81	9	+	+	SYM
american_scientific_journal-2140	81	10	1	1	NUM
american_scientific_journal-2140	81	11	2	2	NUM
american_scientific_journal-2140	81	12	−2𝑢	−2𝑢	PROPN
american_scientific_journal-2140	81	13	−2	−2	NOUN
american_scientific_journal-2140	81	14	𝑢	𝑢	X
american_scientific_journal-2140	81	15	−2𝑢	−2𝑢	PROPN
american_scientific_journal-2140	81	16	1	1	NUM
american_scientific_journal-2140	81	17	0	0	NUM
american_scientific_journal-2140	81	18	−𝑢	−𝑢	NOUN
american_scientific_journal-2140	81	19	−	−	PROPN
american_scientific_journal-2140	82	1	√𝑢2	√𝑢2	PUNCT
american_scientific_journal-2140	83	1	+	+	PUNCT
american_scientific_journal-2140	83	2	1	1	NUM
american_scientific_journal-2140	83	3	−𝑢	−𝑢	NOUN
american_scientific_journal-2140	84	1	+	+	CCONJ
american_scientific_journal-2140	84	2	√𝑢2	√𝑢2	PUNCT
american_scientific_journal-2140	85	1	+	+	CCONJ
american_scientific_journal-2140	85	2	1	1	NUM
american_scientific_journal-2140	85	3	5	5	NUM
american_scientific_journal-2140	85	4	2	2	NUM
american_scientific_journal-2140	85	5	−	−	NUM
american_scientific_journal-2140	85	6	5	5	NUM
american_scientific_journal-2140	85	7	2	2	NUM
american_scientific_journal-2140	85	8	𝑢	𝑢	NOUN
american_scientific_journal-2140	85	9	−	−	PROPN
american_scientific_journal-2140	85	10	5	5	NUM
american_scientific_journal-2140	85	11	3	3	NUM
american_scientific_journal-2140	85	12	10	10	NUM
american_scientific_journal-2140	85	13	9	9	NUM
american_scientific_journal-2140	85	14	−	−	NUM
american_scientific_journal-2140	85	15	16	16	NUM
american_scientific_journal-2140	85	16	27	27	NUM
american_scientific_journal-2140	85	17	𝑢	𝑢	PRON
american_scientific_journal-2140	85	18	4	4	NUM
american_scientific_journal-2140	85	19	9	9	NUM
american_scientific_journal-2140	85	20	0	0	NUM
american_scientific_journal-2140	85	21	−8𝑢	−8𝑢	DET
american_scientific_journal-2140	85	22	−	−	NOUN
american_scientific_journal-2140	85	23	4√4𝑢2	4√4𝑢2	NUM
american_scientific_journal-2140	85	24	+	+	SYM
american_scientific_journal-2140	85	25	9	9	NUM
american_scientific_journal-2140	85	26	27	27	NUM
american_scientific_journal-2140	85	27	−8𝑢	−8𝑢	NOUN
american_scientific_journal-2140	85	28	+	+	NOUN
american_scientific_journal-2140	85	29	4√4𝑢2	4√4𝑢2	NUM
american_scientific_journal-2140	85	30	+	+	SYM
american_scientific_journal-2140	85	31	9	9	NUM
american_scientific_journal-2140	85	32	27	27	NUM
american_scientific_journal-2140	85	33	3	3	NUM
american_scientific_journal-2140	85	34	−	−	NOUN
american_scientific_journal-2140	85	35	3	3	NUM
american_scientific_journal-2140	85	36	2	2	NUM
american_scientific_journal-2140	85	37	𝑢	𝑢	NOUN
american_scientific_journal-2140	85	38	−	−	PROPN
american_scientific_journal-2140	85	39	3	3	NUM
american_scientific_journal-2140	85	40	2	2	NUM
american_scientific_journal-2140	85	41	4𝑢	4𝑢	NOUN
american_scientific_journal-2140	85	42	−	−	NOUN
american_scientific_journal-2140	85	43	1	1	NUM
american_scientific_journal-2140	85	44	4	4	NUM
american_scientific_journal-2140	85	45	𝑢	𝑢	PART
american_scientific_journal-2140	85	46	1	1	NUM
american_scientific_journal-2140	85	47	4	4	NUM
american_scientific_journal-2140	85	48	0	0	NUM
american_scientific_journal-2140	85	49	−𝑢	−𝑢	NOUN
american_scientific_journal-2140	85	50	−	−	PROPN
american_scientific_journal-2140	85	51	√𝑢2	√𝑢2	PUNCT
american_scientific_journal-2140	86	1	+	+	CCONJ
american_scientific_journal-2140	86	2	4	4	NUM
american_scientific_journal-2140	86	3	8	8	NUM
american_scientific_journal-2140	86	4	−𝑢	−𝑢	NOUN
american_scientific_journal-2140	87	1	+	+	CCONJ
american_scientific_journal-2140	87	2	√𝑢2	√𝑢2	PUNCT
american_scientific_journal-2140	88	1	+	+	CCONJ
american_scientific_journal-2140	88	2	4	4	NUM
american_scientific_journal-2140	88	3	8	8	NUM
american_scientific_journal-2140	88	4	for	for	ADP
american_scientific_journal-2140	88	5	a	a	DET
american_scientific_journal-2140	88	6	given	give	VERB
american_scientific_journal-2140	88	7	lateral	lateral	ADJ
american_scientific_journal-2140	88	8	magnification	magnification	NOUN
american_scientific_journal-2140	88	9	𝑚	𝑚	NOUN
american_scientific_journal-2140	88	10	,	,	PUNCT
american_scientific_journal-2140	88	11	namely	namely	ADV
american_scientific_journal-2140	88	12	,	,	PUNCT
american_scientific_journal-2140	88	13	at	at	ADP
american_scientific_journal-2140	88	14	its	its	PRON
american_scientific_journal-2140	88	15	discrete	discrete	ADJ
american_scientific_journal-2140	88	16	values	value	NOUN
american_scientific_journal-2140	88	17	𝑚	𝑚	X
american_scientific_journal-2140	88	18	∈	∈	PROPN
american_scientific_journal-2140	88	19	{	{	PUNCT
american_scientific_journal-2140	88	20	0	0	NUM
american_scientific_journal-2140	88	21	,	,	PUNCT
american_scientific_journal-2140	88	22	1	1	NUM
american_scientific_journal-2140	88	23	2⁄	2⁄	NUM
american_scientific_journal-2140	88	24	,	,	PUNCT
american_scientific_journal-2140	88	25	1	1	NUM
american_scientific_journal-2140	88	26	,	,	PUNCT
american_scientific_journal-2140	88	27	3	3	NUM
american_scientific_journal-2140	88	28	2⁄	2⁄	NUM
american_scientific_journal-2140	88	29	,	,	PUNCT
american_scientific_journal-2140	88	30	2	2	NUM
american_scientific_journal-2140	88	31	,	,	PUNCT
american_scientific_journal-2140	88	32	5/2	5/2	NUM
american_scientific_journal-2140	88	33	,	,	PUNCT
american_scientific_journal-2140	88	34	3	3	NUM
american_scientific_journal-2140	88	35	}	}	PUNCT
american_scientific_journal-2140	88	36	,	,	PUNCT
american_scientific_journal-2140	88	37	we	we	PRON
american_scientific_journal-2140	88	38	analyze	analyze	VERB
american_scientific_journal-2140	88	39	the	the	DET
american_scientific_journal-2140	88	40	nature	nature	NOUN
american_scientific_journal-2140	88	41	of	of	ADP
american_scientific_journal-2140	88	42	the	the	DET
american_scientific_journal-2140	88	43	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	88	44	quantities	quantity	NOUN
american_scientific_journal-2140	88	45	,	,	PUNCT
american_scientific_journal-2140	88	46	viz	viz	NOUN
american_scientific_journal-2140	88	47	.	.	PUNCT
american_scientific_journal-2140	89	1	the	the	DET
american_scientific_journal-2140	89	2	focal	focal	ADJ
american_scientific_journal-2140	89	3	length	length	NOUN
american_scientific_journal-2140	89	4	𝑓	𝑓	ADV
american_scientific_journal-2140	89	5	,	,	PUNCT
american_scientific_journal-2140	89	6	flow	flow	NOUN
american_scientific_journal-2140	89	7	components	component	NOUN
american_scientific_journal-2140	89	8	{	{	PUNCT
american_scientific_journal-2140	89	9	𝑓𝑢	𝑓𝑢	PROPN
american_scientific_journal-2140	89	10	,	,	PUNCT
american_scientific_journal-2140	89	11	𝑓𝑚	𝑓𝑚	PROPN
american_scientific_journal-2140	89	12	}	}	PUNCT
american_scientific_journal-2140	89	13	,	,	PUNCT
american_scientific_journal-2140	89	14	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	89	15	capacities	capacity	NOUN
american_scientific_journal-2140	89	16	{	{	PUNCT
american_scientific_journal-2140	89	17	𝑓𝑚𝑚	𝑓𝑚𝑚	PROPN
american_scientific_journal-2140	89	18	,	,	PUNCT
american_scientific_journal-2140	89	19	𝑓𝑚𝑢	𝑓𝑚𝑢	NOUN
american_scientific_journal-2140	89	20	,	,	PUNCT
american_scientific_journal-2140	89	21	𝑓𝑢𝑢	𝑓𝑢𝑢	NOUN
american_scientific_journal-2140	89	22	}	}	PUNCT
american_scientific_journal-2140	89	23	and	and	CCONJ
american_scientific_journal-2140	89	24	eigenvalues	eigenvalue	VERB
american_scientific_journal-2140	89	25	{	{	PUNCT
american_scientific_journal-2140	89	26	𝜆1	𝜆1	NOUN
american_scientific_journal-2140	89	27	,	,	PUNCT
american_scientific_journal-2140	89	28	𝜆2	𝜆2	NOUN
american_scientific_journal-2140	89	29	}	}	PUNCT
american_scientific_journal-2140	89	30	of	of	ADP
american_scientific_journal-2140	89	31	the	the	DET
american_scientific_journal-2140	89	32	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	89	33	matrix	matrix	NOUN
american_scientific_journal-2140	89	34	𝐻.	𝐻.	PROPN
american_scientific_journal-2140	89	35	from	from	ADP
american_scientific_journal-2140	89	36	the	the	DET
american_scientific_journal-2140	89	37	viewpoint	viewpoint	NOUN
american_scientific_journal-2140	89	38	of	of	ADP
american_scientific_journal-2140	89	39	the	the	DET
american_scientific_journal-2140	89	40	eigenvalue	eigenvalue	PROPN
american_scientific_journal-2140	89	41	𝜆1(𝑢	𝜆1(𝑢	PROPN
american_scientific_journal-2140	89	42	)	)	PUNCT
american_scientific_journal-2140	89	43	as	as	ADP
american_scientific_journal-2140	89	44	a	a	DET
american_scientific_journal-2140	89	45	function	function	NOUN
american_scientific_journal-2140	89	46	of	of	ADP
american_scientific_journal-2140	89	47	the	the	DET
american_scientific_journal-2140	89	48	object	object	NOUN
american_scientific_journal-2140	89	49	distance	distance	NOUN
american_scientific_journal-2140	89	50	𝑢	𝑢	PRON
american_scientific_journal-2140	89	51	considered	consider	VERB
american_scientific_journal-2140	89	52	at	at	ADP
american_scientific_journal-2140	89	53	a	a	DET
american_scientific_journal-2140	89	54	fixed	fix	VERB
american_scientific_journal-2140	89	55	lateral	lateral	ADJ
american_scientific_journal-2140	89	56	magnification	magnification	NOUN
american_scientific_journal-2140	89	57	𝑚	𝑚	ADP
american_scientific_journal-2140	89	58	∈	∈	PROPN
american_scientific_journal-2140	89	59	{	{	PUNCT
american_scientific_journal-2140	89	60	0	0	NUM
american_scientific_journal-2140	89	61	,	,	PUNCT
american_scientific_journal-2140	89	62	1/2	1/2	NUM
american_scientific_journal-2140	89	63	}	}	PUNCT
american_scientific_journal-2140	89	64	,	,	PUNCT
american_scientific_journal-2140	89	65	we	we	PRON
american_scientific_journal-2140	89	66	find	find	VERB
american_scientific_journal-2140	89	67	from	from	ADP
american_scientific_journal-2140	89	68	eqn	eqn	NOUN
american_scientific_journal-2140	89	69	.	.	PUNCT
american_scientific_journal-2140	90	1	(	(	PUNCT
american_scientific_journal-2140	90	2	5	5	NUM
american_scientific_journal-2140	90	3	)	)	PUNCT
american_scientific_journal-2140	90	4	that	that	SCONJ
american_scientific_journal-2140	90	5	the	the	DET
american_scientific_journal-2140	90	6	image	image	NOUN
american_scientific_journal-2140	90	7	stability	stability	NOUN
american_scientific_journal-2140	90	8	monotonically	monotonically	ADV
american_scientific_journal-2140	90	9	increases	increase	VERB
american_scientific_journal-2140	90	10	in	in	ADP
american_scientific_journal-2140	90	11	the	the	DET
american_scientific_journal-2140	90	12	interval	interval	NOUN
american_scientific_journal-2140	90	13	𝑢	𝑢	X
american_scientific_journal-2140	90	14	∈	∈	PROPN
american_scientific_journal-2140	90	15	(	(	PUNCT
american_scientific_journal-2140	90	16	0	0	NUM
american_scientific_journal-2140	90	17	,	,	PUNCT
american_scientific_journal-2140	90	18	2	2	NUM
american_scientific_journal-2140	90	19	)	)	PUNCT
american_scientific_journal-2140	90	20	.	.	PUNCT
american_scientific_journal-2140	91	1	namely	namely	ADV
american_scientific_journal-2140	91	2	,	,	PUNCT
american_scientific_journal-2140	91	3	the	the	DET
american_scientific_journal-2140	91	4	formation	formation	NOUN
american_scientific_journal-2140	91	5	of	of	ADP
american_scientific_journal-2140	91	6	an	an	DET
american_scientific_journal-2140	91	7	image	image	NOUN
american_scientific_journal-2140	91	8	locally	locally	ADV
american_scientific_journal-2140	91	9	exhibits	exhibit	VERB
american_scientific_journal-2140	91	10	a	a	DET
american_scientific_journal-2140	91	11	nonlinear	nonlinear	ADJ
american_scientific_journal-2140	91	12	behavior	behavior	NOUN
american_scientific_journal-2140	91	13	in	in	ADP
american_scientific_journal-2140	91	14	the	the	DET
american_scientific_journal-2140	91	15	vicinity	vicinity	NOUN
american_scientific_journal-2140	91	16	of	of	ADP
american_scientific_journal-2140	91	17	the	the	DET
american_scientific_journal-2140	91	18	optical	optical	ADJ
american_scientific_journal-2140	91	19	center	center	NOUN
american_scientific_journal-2140	91	20	of	of	ADP
american_scientific_journal-2140	91	21	the	the	DET
american_scientific_journal-2140	91	22	instrument	instrument	NOUN
american_scientific_journal-2140	91	23	.	.	PUNCT
american_scientific_journal-2140	92	1	however	however	ADV
american_scientific_journal-2140	92	2	,	,	PUNCT
american_scientific_journal-2140	92	3	we	we	PRON
american_scientific_journal-2140	92	4	find	find	VERB
american_scientific_journal-2140	92	5	that	that	SCONJ
american_scientific_journal-2140	92	6	it	it	PRON
american_scientific_journal-2140	92	7	fluctuates	fluctuate	VERB
american_scientific_journal-2140	92	8	approximately	approximately	ADV
american_scientific_journal-2140	92	9	linearly	linearly	ADV
american_scientific_journal-2140	92	10	for	for	ADP
american_scientific_journal-2140	92	11	a	a	DET
american_scientific_journal-2140	92	12	distant	distant	ADJ
american_scientific_journal-2140	92	13	object	object	NOUN
american_scientific_journal-2140	92	14	from	from	ADP
american_scientific_journal-2140	92	15	the	the	DET
american_scientific_journal-2140	92	16	optical	optical	ADJ
american_scientific_journal-2140	92	17	center	center	NOUN
american_scientific_journal-2140	92	18	of	of	ADP
american_scientific_journal-2140	92	19	the	the	DET
american_scientific_journal-2140	92	20	instrument	instrument	NOUN
american_scientific_journal-2140	92	21	.	.	PUNCT
american_scientific_journal-2140	93	1	moreover	moreover	ADV
american_scientific_journal-2140	93	2	,	,	PUNCT
american_scientific_journal-2140	93	3	for	for	ADP
american_scientific_journal-2140	93	4	a	a	DET
american_scientific_journal-2140	93	5	higher	high	ADJ
american_scientific_journal-2140	93	6	value	value	NOUN
american_scientific_journal-2140	93	7	of	of	ADP
american_scientific_journal-2140	93	8	the	the	DET
american_scientific_journal-2140	93	9	lateral	lateral	ADJ
american_scientific_journal-2140	93	10	magnification	magnification	NOUN
american_scientific_journal-2140	93	11	𝑚	𝑚	ADP
american_scientific_journal-2140	93	12	∈	∈	PROPN
american_scientific_journal-2140	93	13	{	{	PUNCT
american_scientific_journal-2140	93	14	3/2	3/2	NUM
american_scientific_journal-2140	93	15	,	,	PUNCT
american_scientific_journal-2140	93	16	2	2	NUM
american_scientific_journal-2140	93	17	,	,	PUNCT
american_scientific_journal-2140	93	18	5/2	5/2	NUM
american_scientific_journal-2140	93	19	,	,	PUNCT
american_scientific_journal-2140	93	20	3	3	NUM
american_scientific_journal-2140	93	21	}	}	PUNCT
american_scientific_journal-2140	93	22	,	,	PUNCT
american_scientific_journal-2140	93	23	we	we	PRON
american_scientific_journal-2140	93	24	notice	notice	VERB
american_scientific_journal-2140	93	25	that	that	SCONJ
american_scientific_journal-2140	93	26	𝜆1(𝑢	𝜆1(𝑢	VERB
american_scientific_journal-2140	93	27	)	)	PUNCT
american_scientific_journal-2140	93	28	decreases	decrease	VERB
american_scientific_journal-2140	93	29	continuously	continuously	ADV
american_scientific_journal-2140	93	30	with	with	ADP
american_scientific_journal-2140	93	31	same	same	ADJ
american_scientific_journal-2140	93	32	characterization	characterization	NOUN
american_scientific_journal-2140	93	33	as	as	ADP
american_scientific_journal-2140	93	34	the	the	DET
american_scientific_journal-2140	93	35	foregoing	forego	VERB
american_scientific_journal-2140	93	36	values	value	NOUN
american_scientific_journal-2140	93	37	of	of	ADP
american_scientific_journal-2140	93	38	the	the	DET
american_scientific_journal-2140	93	39	lateral	lateral	ADJ
american_scientific_journal-2140	93	40	magnification	magnification	NOUN
american_scientific_journal-2140	93	41	,	,	PUNCT
american_scientific_journal-2140	93	42	viz	viz	NOUN
american_scientific_journal-2140	93	43	.	.	PUNCT
american_scientific_journal-2140	94	1	𝑚	𝑚	PROPN
american_scientific_journal-2140	94	2	∈	∈	PROPN
american_scientific_journal-2140	94	3	{	{	PUNCT
american_scientific_journal-2140	94	4	0	0	NUM
american_scientific_journal-2140	94	5	,	,	PUNCT
american_scientific_journal-2140	94	6	1/2	1/2	NUM
american_scientific_journal-2140	94	7	}	}	PUNCT
american_scientific_journal-2140	94	8	.	.	PUNCT
american_scientific_journal-2140	95	1	furthermore	furthermore	ADV
american_scientific_journal-2140	95	2	,	,	PUNCT
american_scientific_journal-2140	95	3	it	it	PRON
american_scientific_journal-2140	95	4	is	be	AUX
american_scientific_journal-2140	95	5	worth	worth	ADJ
american_scientific_journal-2140	95	6	remarking	remark	VERB
american_scientific_journal-2140	95	7	that	that	SCONJ
american_scientific_journal-2140	95	8	the	the	DET
american_scientific_journal-2140	95	9	amplitude	amplitude	NOUN
american_scientific_journal-2140	95	10	american	american	ADJ
american_scientific_journal-2140	95	11	scientific	scientific	ADJ
american_scientific_journal-2140	95	12	research	research	NOUN
american_scientific_journal-2140	95	13	journal	journal	NOUN
american_scientific_journal-2140	95	14	for	for	ADP
american_scientific_journal-2140	95	15	engineering	engineering	NOUN
american_scientific_journal-2140	95	16	,	,	PUNCT
american_scientific_journal-2140	95	17	technology	technology	NOUN
american_scientific_journal-2140	95	18	,	,	PUNCT
american_scientific_journal-2140	95	19	and	and	CCONJ
american_scientific_journal-2140	95	20	sciences	science	NOUN
american_scientific_journal-2140	95	21	(	(	PUNCT
american_scientific_journal-2140	95	22	asrjets	asrjet	NOUN
american_scientific_journal-2140	95	23	)	)	PUNCT
american_scientific_journal-2140	95	24	(	(	PUNCT
american_scientific_journal-2140	95	25	2016	2016	NUM
american_scientific_journal-2140	95	26	)	)	PUNCT
american_scientific_journal-2140	95	27	volume	volume	NOUN
american_scientific_journal-2140	95	28	26	26	NUM
american_scientific_journal-2140	95	29	,	,	PUNCT
american_scientific_journal-2140	95	30	no	no	DET
american_scientific_journal-2140	95	31	1	1	NUM
american_scientific_journal-2140	95	32	,	,	PUNCT
american_scientific_journal-2140	95	33	pp	pp	ADV
american_scientific_journal-2140	95	34	302	302	NUM
american_scientific_journal-2140	95	35	-	-	SYM
american_scientific_journal-2140	95	36	313	313	NUM
american_scientific_journal-2140	95	37	307	307	NUM
american_scientific_journal-2140	95	38	variations	variation	NOUN
american_scientific_journal-2140	95	39	of	of	ADP
american_scientific_journal-2140	95	40	the	the	DET
american_scientific_journal-2140	95	41	above	above	ADV
american_scientific_journal-2140	95	42	mentioned	mention	VERB
american_scientific_journal-2140	95	43	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	95	44	capacities	capacity	NOUN
american_scientific_journal-2140	95	45	differ	differ	VERB
american_scientific_journal-2140	95	46	from	from	ADP
american_scientific_journal-2140	95	47	the	the	DET
american_scientific_journal-2140	95	48	one	one	NOUN
american_scientific_journal-2140	95	49	another	another	PRON
american_scientific_journal-2140	95	50	for	for	ADP
american_scientific_journal-2140	95	51	different	different	ADJ
american_scientific_journal-2140	95	52	values	value	NOUN
american_scientific_journal-2140	95	53	of	of	ADP
american_scientific_journal-2140	95	54	the	the	DET
american_scientific_journal-2140	95	55	lateral	lateral	ADJ
american_scientific_journal-2140	95	56	magnification	magnification	NOUN
american_scientific_journal-2140	95	57	of	of	ADP
american_scientific_journal-2140	95	58	the	the	DET
american_scientific_journal-2140	95	59	optical	optical	ADJ
american_scientific_journal-2140	95	60	instrument	instrument	NOUN
american_scientific_journal-2140	95	61	.	.	PUNCT
american_scientific_journal-2140	96	1	similarly	similarly	ADV
american_scientific_journal-2140	96	2	,	,	PUNCT
american_scientific_journal-2140	96	3	we	we	PRON
american_scientific_journal-2140	96	4	find	find	VERB
american_scientific_journal-2140	96	5	from	from	ADP
american_scientific_journal-2140	96	6	eqn	eqn	NOUN
american_scientific_journal-2140	96	7	.	.	PUNCT
american_scientific_journal-2140	97	1	(	(	PUNCT
american_scientific_journal-2140	97	2	6	6	NUM
american_scientific_journal-2140	97	3	)	)	PUNCT
american_scientific_journal-2140	97	4	that	that	SCONJ
american_scientific_journal-2140	97	5	the	the	DET
american_scientific_journal-2140	97	6	eigenvalue	eigenvalue	PROPN
american_scientific_journal-2140	97	7	𝜆2(𝑢	𝜆2(𝑢	NOUN
american_scientific_journal-2140	97	8	)	)	PUNCT
american_scientific_journal-2140	97	9	of	of	ADP
american_scientific_journal-2140	97	10	the	the	DET
american_scientific_journal-2140	97	11	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	97	12	matrix	matrix	NOUN
american_scientific_journal-2140	97	13	𝐻	𝐻	NOUN
american_scientific_journal-2140	97	14	at	at	ADP
american_scientific_journal-2140	97	15	the	the	DET
american_scientific_journal-2140	97	16	lateral	lateral	ADJ
american_scientific_journal-2140	97	17	magnification	magnification	NOUN
american_scientific_journal-2140	97	18	𝑚	𝑚	ADP
american_scientific_journal-2140	97	19	∈	∈	PROPN
american_scientific_journal-2140	97	20	{	{	PUNCT
american_scientific_journal-2140	97	21	0	0	NUM
american_scientific_journal-2140	97	22	,	,	PUNCT
american_scientific_journal-2140	97	23	1/2	1/2	NUM
american_scientific_journal-2140	97	24	}	}	PUNCT
american_scientific_journal-2140	97	25	produces	produce	VERB
american_scientific_journal-2140	97	26	an	an	DET
american_scientific_journal-2140	97	27	approximate	approximate	ADJ
american_scientific_journal-2140	97	28	semi	semi	NOUN
american_scientific_journal-2140	97	29	-	-	NOUN
american_scientific_journal-2140	97	30	parabola	parabola	ADJ
american_scientific_journal-2140	97	31	while	while	SCONJ
american_scientific_journal-2140	97	32	the	the	DET
american_scientific_journal-2140	97	33	object	object	NOUN
american_scientific_journal-2140	97	34	distance	distance	NOUN
american_scientific_journal-2140	97	35	𝑢	𝑢	PROPN
american_scientific_journal-2140	97	36	varies	vary	VERB
american_scientific_journal-2140	97	37	in	in	ADP
american_scientific_journal-2140	97	38	the	the	DET
american_scientific_journal-2140	97	39	interval	interval	NOUN
american_scientific_journal-2140	97	40	(	(	PUNCT
american_scientific_journal-2140	97	41	0	0	NUM
american_scientific_journal-2140	97	42	,	,	PUNCT
american_scientific_journal-2140	97	43	2	2	NUM
american_scientific_journal-2140	97	44	)	)	PUNCT
american_scientific_journal-2140	97	45	.	.	PUNCT
american_scientific_journal-2140	98	1	we	we	PRON
american_scientific_journal-2140	98	2	notice	notice	VERB
american_scientific_journal-2140	98	3	further	far	ADV
american_scientific_journal-2140	98	4	that	that	SCONJ
american_scientific_journal-2140	98	5	the	the	DET
american_scientific_journal-2140	98	6	parabola	parabola	PROPN
american_scientific_journal-2140	98	7	thus	thus	ADV
american_scientific_journal-2140	98	8	formed	form	VERB
american_scientific_journal-2140	98	9	has	have	VERB
american_scientific_journal-2140	98	10	its	its	PRON
american_scientific_journal-2140	98	11	vertex	vertex	NOUN
american_scientific_journal-2140	98	12	at	at	ADP
american_scientific_journal-2140	98	13	the	the	DET
american_scientific_journal-2140	98	14	optical	optical	ADJ
american_scientific_journal-2140	98	15	center	center	NOUN
american_scientific_journal-2140	98	16	of	of	ADP
american_scientific_journal-2140	98	17	the	the	DET
american_scientific_journal-2140	98	18	instrument	instrument	NOUN
american_scientific_journal-2140	98	19	.	.	PUNCT
american_scientific_journal-2140	99	1	on	on	ADP
american_scientific_journal-2140	99	2	the	the	DET
american_scientific_journal-2140	99	3	other	other	ADJ
american_scientific_journal-2140	99	4	hand	hand	NOUN
american_scientific_journal-2140	99	5	,	,	PUNCT
american_scientific_journal-2140	99	6	we	we	PRON
american_scientific_journal-2140	99	7	find	find	VERB
american_scientific_journal-2140	99	8	that	that	SCONJ
american_scientific_journal-2140	99	9	the	the	PRON
american_scientific_journal-2140	99	10	eigenvalue	eigenvalue	PROPN
american_scientific_journal-2140	99	11	𝜆2(𝑢	𝜆2(𝑢	X
american_scientific_journal-2140	99	12	)	)	PUNCT
american_scientific_journal-2140	99	13	at	at	ADP
american_scientific_journal-2140	99	14	the	the	DET
american_scientific_journal-2140	99	15	lateral	lateral	ADJ
american_scientific_journal-2140	99	16	magnifications	magnification	NOUN
american_scientific_journal-2140	99	17	𝑚	𝑚	ADP
american_scientific_journal-2140	99	18	∈	∈	PROPN
american_scientific_journal-2140	99	19	{	{	PUNCT
american_scientific_journal-2140	99	20	3/2	3/2	NUM
american_scientific_journal-2140	99	21	,	,	PUNCT
american_scientific_journal-2140	99	22	2	2	NUM
american_scientific_journal-2140	99	23	,	,	PUNCT
american_scientific_journal-2140	99	24	5/2	5/2	NUM
american_scientific_journal-2140	99	25	,	,	PUNCT
american_scientific_journal-2140	99	26	3	3	NUM
american_scientific_journal-2140	99	27	}	}	PUNCT
american_scientific_journal-2140	99	28	describes	describe	VERB
american_scientific_journal-2140	99	29	an	an	DET
american_scientific_journal-2140	99	30	inverse	inverse	ADJ
american_scientific_journal-2140	99	31	proportional	proportional	ADJ
american_scientific_journal-2140	99	32	decrease	decrease	NOUN
american_scientific_journal-2140	99	33	in	in	ADP
american_scientific_journal-2140	99	34	its	its	PRON
american_scientific_journal-2140	99	35	amplitude	amplitude	NOUN
american_scientific_journal-2140	99	36	as	as	SCONJ
american_scientific_journal-2140	99	37	the	the	DET
american_scientific_journal-2140	99	38	object	object	NOUN
american_scientific_journal-2140	99	39	moves	move	VERB
american_scientific_journal-2140	99	40	away	away	ADV
american_scientific_journal-2140	99	41	from	from	ADP
american_scientific_journal-2140	99	42	the	the	DET
american_scientific_journal-2140	99	43	optical	optical	ADJ
american_scientific_journal-2140	99	44	center	center	NOUN
american_scientific_journal-2140	99	45	of	of	ADP
american_scientific_journal-2140	99	46	the	the	DET
american_scientific_journal-2140	99	47	instrument	instrument	NOUN
american_scientific_journal-2140	99	48	.	.	PUNCT
american_scientific_journal-2140	100	1	hereby	hereby	ADV
american_scientific_journal-2140	100	2	,	,	PUNCT
american_scientific_journal-2140	100	3	we	we	PRON
american_scientific_journal-2140	100	4	notice	notice	VERB
american_scientific_journal-2140	100	5	from	from	ADP
american_scientific_journal-2140	100	6	eqn	eqn	PROPN
american_scientific_journal-2140	100	7	.	.	PUNCT
american_scientific_journal-2140	101	1	(	(	PUNCT
american_scientific_journal-2140	101	2	6	6	NUM
american_scientific_journal-2140	101	3	)	)	PUNCT
american_scientific_journal-2140	101	4	that	that	DET
american_scientific_journal-2140	101	5	𝜆2(𝑢	𝜆2(𝑢	X
american_scientific_journal-2140	101	6	)	)	PUNCT
american_scientific_journal-2140	101	7	has	have	VERB
american_scientific_journal-2140	101	8	a	a	DET
american_scientific_journal-2140	101	9	clear	clear	ADV
american_scientific_journal-2140	101	10	-	-	PUNCT
american_scientific_journal-2140	101	11	cut	cut	VERB
american_scientific_journal-2140	101	12	distinction	distinction	NOUN
american_scientific_journal-2140	101	13	in	in	ADP
american_scientific_journal-2140	101	14	its	its	PRON
american_scientific_journal-2140	101	15	amplitude	amplitude	NOUN
american_scientific_journal-2140	101	16	under	under	ADP
american_scientific_journal-2140	101	17	variations	variation	NOUN
american_scientific_journal-2140	101	18	of	of	ADP
american_scientific_journal-2140	101	19	the	the	DET
american_scientific_journal-2140	101	20	lateral	lateral	ADJ
american_scientific_journal-2140	101	21	magnification	magnification	NOUN
american_scientific_journal-2140	101	22	of	of	ADP
american_scientific_journal-2140	101	23	the	the	DET
american_scientific_journal-2140	101	24	lens/	lens/	NUM
american_scientific_journal-2140	101	25	mirror	mirror	NOUN
american_scientific_journal-2140	101	26	.	.	PUNCT
american_scientific_journal-2140	101	27	3.2	3.2	NUM
american_scientific_journal-2140	101	28	.	.	PUNCT
american_scientific_journal-2140	102	1	fixed	fix	VERB
american_scientific_journal-2140	102	2	object	object	NOUN
american_scientific_journal-2140	102	3	distance	distance	NOUN
american_scientific_journal-2140	102	4	when	when	SCONJ
american_scientific_journal-2140	102	5	the	the	DET
american_scientific_journal-2140	102	6	object	object	NOUN
american_scientific_journal-2140	102	7	distance	distance	NOUN
american_scientific_journal-2140	102	8	𝑢	𝑢	NOUN
american_scientific_journal-2140	102	9	is	be	AUX
american_scientific_journal-2140	102	10	measured	measure	VERB
american_scientific_journal-2140	102	11	in	in	ADP
american_scientific_journal-2140	102	12	the	the	DET
american_scientific_journal-2140	102	13	unit	unit	NOUN
american_scientific_journal-2140	102	14	of	of	ADP
american_scientific_journal-2140	102	15	the	the	DET
american_scientific_journal-2140	102	16	focal	focal	ADJ
american_scientific_journal-2140	102	17	length	length	NOUN
american_scientific_journal-2140	102	18	𝑓	𝑓	PRON
american_scientific_journal-2140	102	19	of	of	ADP
american_scientific_journal-2140	102	20	the	the	DET
american_scientific_journal-2140	102	21	instrument	instrument	NOUN
american_scientific_journal-2140	102	22	with	with	ADP
american_scientific_journal-2140	102	23	the	the	DET
american_scientific_journal-2140	102	24	scaling	scaling	ADJ
american_scientific_journal-2140	102	25	expression	expression	NOUN
american_scientific_journal-2140	102	26	𝑢	𝑢	PART
american_scientific_journal-2140	102	27	=	=	SYM
american_scientific_journal-2140	102	28	𝑘𝑓	𝑘𝑓	PROPN
american_scientific_journal-2140	102	29	,	,	PUNCT
american_scientific_journal-2140	102	30	we	we	PRON
american_scientific_journal-2140	102	31	find	find	VERB
american_scientific_journal-2140	102	32	from	from	ADP
american_scientific_journal-2140	102	33	eqn	eqn	NOUN
american_scientific_journal-2140	102	34	.	.	PUNCT
american_scientific_journal-2140	103	1	(	(	PUNCT
american_scientific_journal-2140	103	2	1	1	X
american_scientific_journal-2140	103	3	)	)	PUNCT
american_scientific_journal-2140	103	4	that	that	SCONJ
american_scientific_journal-2140	103	5	the	the	DET
american_scientific_journal-2140	103	6	objective	objective	ADJ
american_scientific_journal-2140	103	7	function	function	NOUN
american_scientific_journal-2140	103	8	𝑓	𝑓	PRON
american_scientific_journal-2140	103	9	leads	lead	VERB
american_scientific_journal-2140	103	10	to	to	ADP
american_scientific_journal-2140	103	11	the	the	DET
american_scientific_journal-2140	103	12	lateral	lateral	ADJ
american_scientific_journal-2140	103	13	magnification	magnification	NOUN
american_scientific_journal-2140	103	14	𝑚(𝑘	𝑚(𝑘	NUM
american_scientific_journal-2140	103	15	)	)	PUNCT
american_scientific_journal-2140	103	16	=	=	SYM
american_scientific_journal-2140	103	17	1	1	NUM
american_scientific_journal-2140	103	18	𝑘+1	𝑘+1	NUM
american_scientific_journal-2140	103	19	(	(	PUNCT
american_scientific_journal-2140	103	20	10	10	NUM
american_scientific_journal-2140	103	21	)	)	PUNCT
american_scientific_journal-2140	103	22	herewith	herewith	NOUN
american_scientific_journal-2140	103	23	,	,	PUNCT
american_scientific_journal-2140	103	24	we	we	PRON
american_scientific_journal-2140	103	25	provide	provide	VERB
american_scientific_journal-2140	103	26	specific	specific	ADJ
american_scientific_journal-2140	103	27	values	value	NOUN
american_scientific_journal-2140	103	28	of	of	ADP
american_scientific_journal-2140	103	29	the	the	DET
american_scientific_journal-2140	103	30	focal	focal	ADJ
american_scientific_journal-2140	103	31	length	length	NOUN
american_scientific_journal-2140	103	32	,	,	PUNCT
american_scientific_journal-2140	103	33	flow	flow	NOUN
american_scientific_journal-2140	103	34	components	component	NOUN
american_scientific_journal-2140	103	35	,	,	PUNCT
american_scientific_journal-2140	103	36	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	103	37	capacities	capacity	NOUN
american_scientific_journal-2140	103	38	and	and	CCONJ
american_scientific_journal-2140	103	39	eigenvalues	eigenvalue	VERB
american_scientific_journal-2140	103	40	for	for	ADP
american_scientific_journal-2140	103	41	varying	vary	VERB
american_scientific_journal-2140	103	42	values	value	NOUN
american_scientific_journal-2140	103	43	of	of	ADP
american_scientific_journal-2140	103	44	the	the	DET
american_scientific_journal-2140	103	45	object	object	NOUN
american_scientific_journal-2140	103	46	distance	distance	NOUN
american_scientific_journal-2140	103	47	in	in	ADP
american_scientific_journal-2140	103	48	table	table	NOUN
american_scientific_journal-2140	103	49	2	2	NUM
american_scientific_journal-2140	103	50	below	below	ADV
american_scientific_journal-2140	103	51	.	.	PUNCT
american_scientific_journal-2140	104	1	with	with	ADP
american_scientific_journal-2140	104	2	the	the	DET
american_scientific_journal-2140	104	3	scaling	scaling	NOUN
american_scientific_journal-2140	104	4	𝑢	𝑢	X
american_scientific_journal-2140	104	5	=	=	SYM
american_scientific_journal-2140	104	6	𝑘𝑓	𝑘𝑓	PROPN
american_scientific_journal-2140	104	7	,	,	PUNCT
american_scientific_journal-2140	104	8	it	it	PRON
american_scientific_journal-2140	104	9	follows	follow	VERB
american_scientific_journal-2140	104	10	from	from	ADP
american_scientific_journal-2140	104	11	eqn	eqn	NOUN
american_scientific_journal-2140	104	12	.	.	PUNCT
american_scientific_journal-2140	105	1	(	(	PUNCT
american_scientific_journal-2140	105	2	2	2	NUM
american_scientific_journal-2140	105	3	)	)	PUNCT
american_scientific_journal-2140	105	4	that	that	SCONJ
american_scientific_journal-2140	105	5	the	the	DET
american_scientific_journal-2140	105	6	correlation	correlation	NOUN
american_scientific_journal-2140	105	7	component	component	NOUN
american_scientific_journal-2140	105	8	𝑓𝑚𝑚	𝑓𝑚𝑚	NOUN
american_scientific_journal-2140	105	9	simplifies	simplifie	NOUN
american_scientific_journal-2140	105	10	as	as	ADP
american_scientific_journal-2140	105	11	𝑓𝑚𝑚	𝑓𝑚𝑚	NOUN
american_scientific_journal-2140	105	12	=	=	PUNCT
american_scientific_journal-2140	105	13	2𝑘𝑓	2𝑘𝑓	ADJ
american_scientific_journal-2140	105	14	(	(	PUNCT
american_scientific_journal-2140	105	15	1−𝑚)3	1−𝑚)3	NUM
american_scientific_journal-2140	105	16	(	(	PUNCT
american_scientific_journal-2140	105	17	11	11	NUM
american_scientific_journal-2140	105	18	)	)	PUNCT
american_scientific_journal-2140	105	19	in	in	ADP
american_scientific_journal-2140	105	20	general	general	ADJ
american_scientific_journal-2140	105	21	,	,	PUNCT
american_scientific_journal-2140	105	22	we	we	PRON
american_scientific_journal-2140	105	23	see	see	VERB
american_scientific_journal-2140	105	24	from	from	ADP
american_scientific_journal-2140	105	25	eqns	eqns	PROPN
american_scientific_journal-2140	105	26	.	.	PUNCT
american_scientific_journal-2140	106	1	(	(	PUNCT
american_scientific_journal-2140	106	2	5	5	NUM
american_scientific_journal-2140	106	3	,	,	PUNCT
american_scientific_journal-2140	106	4	6	6	NUM
american_scientific_journal-2140	106	5	)	)	PUNCT
american_scientific_journal-2140	106	6	that	that	PRON
american_scientific_journal-2140	106	7	𝜆1	𝜆1	NOUN
american_scientific_journal-2140	106	8	and	and	CCONJ
american_scientific_journal-2140	106	9	𝜆2	𝜆2	NOUN
american_scientific_journal-2140	106	10	reduce	reduce	VERB
american_scientific_journal-2140	106	11	as	as	ADP
american_scientific_journal-2140	106	12	per	per	ADP
american_scientific_journal-2140	106	13	the	the	DET
american_scientific_journal-2140	106	14	following	follow	VERB
american_scientific_journal-2140	106	15	expressions	expression	NOUN
american_scientific_journal-2140	106	16	𝜆1	𝜆1	NOUN
american_scientific_journal-2140	106	17	=	=	PUNCT
american_scientific_journal-2140	107	1	𝑘𝑓+√(𝑘𝑓)2	𝑘𝑓+√(𝑘𝑓)2	PROPN
american_scientific_journal-2140	107	2	+	+	CCONJ
american_scientific_journal-2140	107	3	(	(	PUNCT
american_scientific_journal-2140	107	4	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	107	5	(	(	PUNCT
american_scientific_journal-2140	107	6	1−𝑚)3	1−𝑚)3	NUM
american_scientific_journal-2140	107	7	(	(	PUNCT
american_scientific_journal-2140	107	8	12	12	NUM
american_scientific_journal-2140	107	9	)	)	PUNCT
american_scientific_journal-2140	107	10	𝜆2	𝜆2	NOUN
american_scientific_journal-2140	107	11	=	=	SYM
american_scientific_journal-2140	107	12	𝑘𝑓−√(𝑘𝑓)2	𝑘𝑓−√(𝑘𝑓)2	NUM
american_scientific_journal-2140	107	13	+	+	CCONJ
american_scientific_journal-2140	107	14	(	(	PUNCT
american_scientific_journal-2140	107	15	1−𝑚)2	1−𝑚)2	NUM
american_scientific_journal-2140	107	16	(	(	PUNCT
american_scientific_journal-2140	107	17	1−𝑚)3	1−𝑚)3	NUM
american_scientific_journal-2140	107	18	(	(	PUNCT
american_scientific_journal-2140	107	19	13	13	NUM
american_scientific_journal-2140	107	20	)	)	PUNCT
american_scientific_journal-2140	107	21	therefore	therefore	ADV
american_scientific_journal-2140	107	22	,	,	PUNCT
american_scientific_journal-2140	107	23	for	for	ADP
american_scientific_journal-2140	107	24	the	the	DET
american_scientific_journal-2140	107	25	scalar	scalar	ADJ
american_scientific_journal-2140	107	26	quantity	quantity	NOUN
american_scientific_journal-2140	107	27	𝑘	𝑘	PRON
american_scientific_journal-2140	107	28	∈	∈	NOUN
american_scientific_journal-2140	107	29	{	{	PUNCT
american_scientific_journal-2140	107	30	1	1	NUM
american_scientific_journal-2140	107	31	2⁄	2⁄	NUM
american_scientific_journal-2140	107	32	,	,	PUNCT
american_scientific_journal-2140	107	33	1	1	NUM
american_scientific_journal-2140	107	34	,	,	PUNCT
american_scientific_journal-2140	107	35	3	3	NUM
american_scientific_journal-2140	107	36	2⁄	2⁄	NUM
american_scientific_journal-2140	107	37	,	,	PUNCT
american_scientific_journal-2140	107	38	2	2	NUM
american_scientific_journal-2140	107	39	,	,	PUNCT
american_scientific_journal-2140	107	40	5/2	5/2	NUM
american_scientific_journal-2140	107	41	,	,	PUNCT
american_scientific_journal-2140	107	42	3	3	NUM
american_scientific_journal-2140	107	43	}	}	PUNCT
american_scientific_journal-2140	107	44	,	,	PUNCT
american_scientific_journal-2140	107	45	the	the	DET
american_scientific_journal-2140	107	46	corresponding	correspond	VERB
american_scientific_journal-2140	107	47	values	value	NOUN
american_scientific_journal-2140	107	48	of	of	ADP
american_scientific_journal-2140	107	49	the	the	DET
american_scientific_journal-2140	107	50	eigenvalues	eigenvalue	NOUN
american_scientific_journal-2140	107	51	{	{	PUNCT
american_scientific_journal-2140	107	52	𝜆1	𝜆1	NOUN
american_scientific_journal-2140	107	53	,	,	PUNCT
american_scientific_journal-2140	107	54	𝜆2	𝜆2	NOUN
american_scientific_journal-2140	107	55	}	}	PUNCT
american_scientific_journal-2140	107	56	are	be	AUX
american_scientific_journal-2140	107	57	enlisted	enlist	VERB
american_scientific_journal-2140	107	58	in	in	ADP
american_scientific_journal-2140	107	59	table	table	NOUN
american_scientific_journal-2140	107	60	2	2	NUM
american_scientific_journal-2140	107	61	.	.	PUNCT
american_scientific_journal-2140	108	1	it	it	PRON
american_scientific_journal-2140	108	2	is	be	AUX
american_scientific_journal-2140	108	3	worth	worth	ADJ
american_scientific_journal-2140	108	4	noticing	notice	VERB
american_scientific_journal-2140	108	5	that	that	SCONJ
american_scientific_journal-2140	108	6	the	the	DET
american_scientific_journal-2140	108	7	hessian	hessian	ADJ
american_scientific_journal-2140	108	8	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	108	9	components	component	NOUN
american_scientific_journal-2140	108	10	,	,	PUNCT
american_scientific_journal-2140	108	11	viz	viz	PROPN
american_scientific_journal-2140	108	12	.	.	PUNCT
american_scientific_journal-2140	108	13	𝑓𝑚𝑢	𝑓𝑚𝑢	PROPN
american_scientific_journal-2140	108	14	and	and	CCONJ
american_scientific_journal-2140	108	15	𝑓𝑢𝑢	𝑓𝑢𝑢	NOUN
american_scientific_journal-2140	108	16	as	as	SCONJ
american_scientific_journal-2140	108	17	mentioned	mention	VERB
american_scientific_journal-2140	108	18	before	before	ADV
american_scientific_journal-2140	108	19	remain	remain	VERB
american_scientific_journal-2140	108	20	independent	independent	ADJ
american_scientific_journal-2140	108	21	of	of	ADP
american_scientific_journal-2140	108	22	the	the	DET
american_scientific_journal-2140	108	23	object	object	NOUN
american_scientific_journal-2140	108	24	distance	distance	NOUN
american_scientific_journal-2140	108	25	𝑢.	𝑢.	NOUN
american_scientific_journal-2140	108	26	in	in	ADP
american_scientific_journal-2140	108	27	other	other	ADJ
american_scientific_journal-2140	108	28	words	word	NOUN
american_scientific_journal-2140	108	29	,	,	PUNCT
american_scientific_journal-2140	108	30	we	we	PRON
american_scientific_journal-2140	108	31	see	see	VERB
american_scientific_journal-2140	108	32	from	from	ADP
american_scientific_journal-2140	108	33	the	the	DET
american_scientific_journal-2140	108	34	table	table	NOUN
american_scientific_journal-2140	108	35	2	2	NUM
american_scientific_journal-2140	108	36	below	below	ADP
american_scientific_journal-2140	108	37	that	that	SCONJ
american_scientific_journal-2140	108	38	there	there	PRON
american_scientific_journal-2140	108	39	is	be	VERB
american_scientific_journal-2140	108	40	no	no	DET
american_scientific_journal-2140	108	41	change	change	NOUN
american_scientific_journal-2140	108	42	in	in	ADP
american_scientific_journal-2140	108	43	the	the	DET
american_scientific_journal-2140	108	44	behavior	behavior	NOUN
american_scientific_journal-2140	108	45	of	of	ADP
american_scientific_journal-2140	108	46	the	the	DET
american_scientific_journal-2140	108	47	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	108	48	components	component	NOUN
american_scientific_journal-2140	108	49	{	{	PUNCT
american_scientific_journal-2140	108	50	𝑓𝑚𝑢	𝑓𝑚𝑢	PROPN
american_scientific_journal-2140	108	51	,	,	PUNCT
american_scientific_journal-2140	108	52	𝑓𝑢𝑢	𝑓𝑢𝑢	NOUN
american_scientific_journal-2140	108	53	}	}	PUNCT
american_scientific_journal-2140	108	54	irrespective	irrespective	ADV
american_scientific_journal-2140	108	55	of	of	ADP
american_scientific_journal-2140	108	56	variations	variation	NOUN
american_scientific_journal-2140	108	57	of	of	ADP
american_scientific_journal-2140	108	58	the	the	DET
american_scientific_journal-2140	108	59	object	object	NOUN
american_scientific_journal-2140	108	60	distance	distance	NOUN
american_scientific_journal-2140	108	61	𝑢	𝑢	X
american_scientific_journal-2140	109	1	=	=	SYM
american_scientific_journal-2140	109	2	𝑘𝑓	𝑘𝑓	PROPN
american_scientific_journal-2140	109	3	from	from	ADP
american_scientific_journal-2140	109	4	the	the	DET
american_scientific_journal-2140	109	5	optical	optical	ADJ
american_scientific_journal-2140	109	6	center	center	NOUN
american_scientific_journal-2140	109	7	of	of	ADP
american_scientific_journal-2140	109	8	the	the	DET
american_scientific_journal-2140	109	9	instrument	instrument	NOUN
american_scientific_journal-2140	109	10	.	.	PUNCT
american_scientific_journal-2140	110	1	american	american	ADJ
american_scientific_journal-2140	110	2	scientific	scientific	ADJ
american_scientific_journal-2140	110	3	research	research	PROPN
american_scientific_journal-2140	110	4	journal	journal	NOUN
american_scientific_journal-2140	110	5	for	for	ADP
american_scientific_journal-2140	110	6	engineering	engineering	NOUN
american_scientific_journal-2140	110	7	,	,	PUNCT
american_scientific_journal-2140	110	8	technology	technology	NOUN
american_scientific_journal-2140	110	9	,	,	PUNCT
american_scientific_journal-2140	110	10	and	and	CCONJ
american_scientific_journal-2140	110	11	sciences	science	NOUN
american_scientific_journal-2140	110	12	(	(	PUNCT
american_scientific_journal-2140	110	13	asrjets	asrjet	NOUN
american_scientific_journal-2140	110	14	)	)	PUNCT
american_scientific_journal-2140	110	15	(	(	PUNCT
american_scientific_journal-2140	110	16	2016	2016	NUM
american_scientific_journal-2140	110	17	)	)	PUNCT
american_scientific_journal-2140	110	18	volume	volume	NOUN
american_scientific_journal-2140	110	19	26	26	NUM
american_scientific_journal-2140	110	20	,	,	PUNCT
american_scientific_journal-2140	110	21	no	no	DET
american_scientific_journal-2140	110	22	1	1	NUM
american_scientific_journal-2140	110	23	,	,	PUNCT
american_scientific_journal-2140	110	24	pp	pp	ADV
american_scientific_journal-2140	110	25	302	302	NUM
american_scientific_journal-2140	110	26	-	-	SYM
american_scientific_journal-2140	110	27	313	313	NUM
american_scientific_journal-2140	110	28	308	308	NUM
american_scientific_journal-2140	110	29	table	table	NOUN
american_scientific_journal-2140	110	30	2	2	NUM
american_scientific_journal-2140	110	31	:	:	PUNCT
american_scientific_journal-2140	110	32	stability	stability	NOUN
american_scientific_journal-2140	110	33	components	component	NOUN
american_scientific_journal-2140	110	34	as	as	ADP
american_scientific_journal-2140	110	35	a	a	DET
american_scientific_journal-2140	110	36	function	function	NOUN
american_scientific_journal-2140	110	37	of	of	ADP
american_scientific_journal-2140	110	38	the	the	DET
american_scientific_journal-2140	110	39	lateral	lateral	ADJ
american_scientific_journal-2140	110	40	magnification	magnification	NOUN
american_scientific_journal-2140	110	41	and	and	CCONJ
american_scientific_journal-2140	110	42	focal	focal	ADJ
american_scientific_journal-2140	110	43	length	length	NOUN
american_scientific_journal-2140	110	44	sn	sn	PROPN
american_scientific_journal-2140	111	1	𝑚	𝑚	PROPN
american_scientific_journal-2140	111	2	𝑓	𝑓	PRON
american_scientific_journal-2140	111	3	𝑓𝑢	𝑓𝑢	NOUN
american_scientific_journal-2140	111	4	𝑓𝑚	𝑓𝑚	PROPN
american_scientific_journal-2140	111	5	𝑓𝑚𝑚	𝑓𝑚𝑚	PROPN
american_scientific_journal-2140	111	6	𝑓𝑚𝑢	𝑓𝑚𝑢	PROPN
american_scientific_journal-2140	111	7	𝑓𝑢𝑢	𝑓𝑢𝑢	PROPN
american_scientific_journal-2140	111	8	𝜆1	𝜆1	PROPN
american_scientific_journal-2140	111	9	𝜆2	𝜆2	PROPN
american_scientific_journal-2140	111	10	𝑢	𝑢	X
american_scientific_journal-2140	111	11	=	=	X
american_scientific_journal-2140	111	12	𝑘𝑓	𝑘𝑓	INTJ
american_scientific_journal-2140	111	13	𝑓	𝑓	PRON
american_scientific_journal-2140	111	14	2	2	NUM
american_scientific_journal-2140	111	15	2	2	NUM
american_scientific_journal-2140	111	16	3	3	NUM
american_scientific_journal-2140	111	17	𝑓𝑚	𝑓𝑚	NOUN
american_scientific_journal-2140	111	18	2(1	2(1	NUM
american_scientific_journal-2140	111	19	−	−	ADP
american_scientific_journal-2140	111	20	𝑚	𝑚	NOUN
american_scientific_journal-2140	111	21	)	)	PUNCT
american_scientific_journal-2140	111	22	𝑚	𝑚	NOUN
american_scientific_journal-2140	111	23	(	(	PUNCT
american_scientific_journal-2140	111	24	1	1	NUM
american_scientific_journal-2140	111	25	−	−	NOUN
american_scientific_journal-2140	111	26	𝑚	𝑚	NOUN
american_scientific_journal-2140	111	27	)	)	PUNCT
american_scientific_journal-2140	111	28	𝑓	𝑓	DET
american_scientific_journal-2140	111	29	2(1	2(1	NUM
american_scientific_journal-2140	111	30	−	−	NOUN
american_scientific_journal-2140	111	31	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	111	32	𝑓	𝑓	X
american_scientific_journal-2140	111	33	(	(	PUNCT
american_scientific_journal-2140	111	34	1	1	NUM
american_scientific_journal-2140	111	35	−	−	NOUN
american_scientific_journal-2140	111	36	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	111	37	1	1	NUM
american_scientific_journal-2140	111	38	(	(	PUNCT
american_scientific_journal-2140	111	39	1	1	NUM
american_scientific_journal-2140	111	40	−	−	PROPN
american_scientific_journal-2140	111	41	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	111	42	0	0	NUM
american_scientific_journal-2140	111	43	𝑓	𝑓	DET
american_scientific_journal-2140	111	44	2	2	NUM
american_scientific_journal-2140	112	1	+	+	CCONJ
american_scientific_journal-2140	112	2	√𝑓2	√𝑓2	PROPN
american_scientific_journal-2140	112	3	4	4	NUM
american_scientific_journal-2140	112	4	+	+	CCONJ
american_scientific_journal-2140	112	5	(	(	PUNCT
american_scientific_journal-2140	112	6	1	1	NUM
american_scientific_journal-2140	112	7	−	−	NOUN
american_scientific_journal-2140	112	8	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	112	9	(	(	PUNCT
american_scientific_journal-2140	112	10	1	1	NUM
american_scientific_journal-2140	112	11	−	−	NOUN
american_scientific_journal-2140	112	12	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	112	13	𝑓	𝑓	DET
american_scientific_journal-2140	112	14	2	2	NUM
american_scientific_journal-2140	112	15	−	−	NOUN
american_scientific_journal-2140	112	16	√𝑓2	√𝑓2	PROPN
american_scientific_journal-2140	112	17	4	4	NUM
american_scientific_journal-2140	112	18	+	+	CCONJ
american_scientific_journal-2140	112	19	(	(	PUNCT
american_scientific_journal-2140	112	20	1	1	NUM
american_scientific_journal-2140	112	21	−	−	NOUN
american_scientific_journal-2140	112	22	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	112	23	(	(	PUNCT
american_scientific_journal-2140	112	24	1	1	NUM
american_scientific_journal-2140	112	25	−	−	NOUN
american_scientific_journal-2140	112	26	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	112	27	𝑓	𝑓	DET
american_scientific_journal-2140	112	28	1	1	NUM
american_scientific_journal-2140	112	29	2	2	NUM
american_scientific_journal-2140	112	30	𝑓𝑚	𝑓𝑚	NOUN
american_scientific_journal-2140	112	31	(	(	PUNCT
american_scientific_journal-2140	112	32	1	1	NUM
american_scientific_journal-2140	112	33	−	−	NOUN
american_scientific_journal-2140	112	34	𝑚	𝑚	NOUN
american_scientific_journal-2140	112	35	)	)	PUNCT
american_scientific_journal-2140	112	36	𝑚	𝑚	NOUN
american_scientific_journal-2140	112	37	(	(	PUNCT
american_scientific_journal-2140	112	38	1	1	NUM
american_scientific_journal-2140	112	39	−	−	NOUN
american_scientific_journal-2140	112	40	𝑚	𝑚	NOUN
american_scientific_journal-2140	112	41	)	)	PUNCT
american_scientific_journal-2140	112	42	𝑓	𝑓	PROPN
american_scientific_journal-2140	112	43	(	(	PUNCT
american_scientific_journal-2140	112	44	1	1	NUM
american_scientific_journal-2140	112	45	−	−	PROPN
american_scientific_journal-2140	112	46	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	112	47	2𝑓	2𝑓	NOUN
american_scientific_journal-2140	112	48	(	(	PUNCT
american_scientific_journal-2140	112	49	1	1	NUM
american_scientific_journal-2140	112	50	−	−	NOUN
american_scientific_journal-2140	112	51	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	112	52	1	1	NUM
american_scientific_journal-2140	112	53	(	(	PUNCT
american_scientific_journal-2140	112	54	1	1	NUM
american_scientific_journal-2140	112	55	−	−	PROPN
american_scientific_journal-2140	112	56	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	112	57	0	0	NUM
american_scientific_journal-2140	113	1	𝑓	𝑓	PRON
american_scientific_journal-2140	113	2	+	+	X
american_scientific_journal-2140	114	1	√𝑓2	√𝑓2	PROPN
american_scientific_journal-2140	114	2	+	+	CCONJ
american_scientific_journal-2140	114	3	(	(	PUNCT
american_scientific_journal-2140	114	4	1	1	NUM
american_scientific_journal-2140	114	5	−	−	PROPN
american_scientific_journal-2140	114	6	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	7	(	(	PUNCT
american_scientific_journal-2140	114	8	1	1	NUM
american_scientific_journal-2140	114	9	−	−	PROPN
american_scientific_journal-2140	114	10	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	11	𝑓	𝑓	DET
american_scientific_journal-2140	114	12	−	−	PUNCT
american_scientific_journal-2140	114	13	√𝑓2	√𝑓2	PROPN
american_scientific_journal-2140	114	14	+	+	CCONJ
american_scientific_journal-2140	114	15	(	(	PUNCT
american_scientific_journal-2140	114	16	1	1	NUM
american_scientific_journal-2140	114	17	−	−	PROPN
american_scientific_journal-2140	114	18	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	19	(	(	PUNCT
american_scientific_journal-2140	114	20	1	1	NUM
american_scientific_journal-2140	114	21	−	−	NOUN
american_scientific_journal-2140	114	22	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	23	3	3	NUM
american_scientific_journal-2140	114	24	2	2	NUM
american_scientific_journal-2140	114	25	𝑓	𝑓	PRON
american_scientific_journal-2140	114	26	2	2	NUM
american_scientific_journal-2140	114	27	5	5	NUM
american_scientific_journal-2140	114	28	3𝑓𝑚	3𝑓𝑚	NOUN
american_scientific_journal-2140	114	29	2(1	2(1	NUM
american_scientific_journal-2140	114	30	−	−	ADP
american_scientific_journal-2140	114	31	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	32	)	)	PUNCT
american_scientific_journal-2140	114	33	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	34	(	(	PUNCT
american_scientific_journal-2140	114	35	1	1	NUM
american_scientific_journal-2140	114	36	−	−	NOUN
american_scientific_journal-2140	114	37	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	38	)	)	PUNCT
american_scientific_journal-2140	114	39	3𝑓	3𝑓	NOUN
american_scientific_journal-2140	114	40	2(1	2(1	NUM
american_scientific_journal-2140	114	41	−	−	NOUN
american_scientific_journal-2140	114	42	𝑚)2	𝑚)2	NOUN
american_scientific_journal-2140	114	43	3𝑓	3𝑓	NOUN
american_scientific_journal-2140	114	44	(	(	PUNCT
american_scientific_journal-2140	114	45	1	1	NUM
american_scientific_journal-2140	114	46	−	−	NOUN
american_scientific_journal-2140	114	47	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	48	1	1	NUM
american_scientific_journal-2140	114	49	(	(	PUNCT
american_scientific_journal-2140	114	50	1	1	NUM
american_scientific_journal-2140	114	51	−	−	PROPN
american_scientific_journal-2140	114	52	𝑚)2	𝑚)2	NOUN
american_scientific_journal-2140	114	53	0	0	NUM
american_scientific_journal-2140	114	54	3𝑓	3𝑓	ADJ
american_scientific_journal-2140	114	55	2	2	NUM
american_scientific_journal-2140	114	56	+	+	SYM
american_scientific_journal-2140	114	57	√9𝑓2	√9𝑓2	NUM
american_scientific_journal-2140	114	58	4	4	NUM
american_scientific_journal-2140	114	59	+	+	CCONJ
american_scientific_journal-2140	114	60	(	(	PUNCT
american_scientific_journal-2140	114	61	1	1	NUM
american_scientific_journal-2140	114	62	−	−	NOUN
american_scientific_journal-2140	114	63	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	64	(	(	PUNCT
american_scientific_journal-2140	114	65	1	1	NUM
american_scientific_journal-2140	114	66	−	−	NOUN
american_scientific_journal-2140	114	67	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	68	3𝑓	3𝑓	ADJ
american_scientific_journal-2140	114	69	2	2	NUM
american_scientific_journal-2140	114	70	−	−	PROPN
american_scientific_journal-2140	114	71	√9𝑓2	√9𝑓2	NUM
american_scientific_journal-2140	114	72	4	4	NUM
american_scientific_journal-2140	114	73	+	+	CCONJ
american_scientific_journal-2140	114	74	(	(	PUNCT
american_scientific_journal-2140	114	75	1	1	NUM
american_scientific_journal-2140	114	76	−	−	NOUN
american_scientific_journal-2140	114	77	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	78	(	(	PUNCT
american_scientific_journal-2140	114	79	1	1	NUM
american_scientific_journal-2140	114	80	−	−	PROPN
american_scientific_journal-2140	114	81	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	82	2𝑓	2𝑓	NUM
american_scientific_journal-2140	114	83	1	1	NUM
american_scientific_journal-2140	114	84	3	3	NUM
american_scientific_journal-2140	114	85	2𝑓𝑚	2𝑓𝑚	NOUN
american_scientific_journal-2140	114	86	(	(	PUNCT
american_scientific_journal-2140	114	87	1	1	NUM
american_scientific_journal-2140	114	88	−	−	NOUN
american_scientific_journal-2140	114	89	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	90	)	)	PUNCT
american_scientific_journal-2140	114	91	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	92	(	(	PUNCT
american_scientific_journal-2140	114	93	1	1	NUM
american_scientific_journal-2140	114	94	−	−	NOUN
american_scientific_journal-2140	114	95	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	96	)	)	PUNCT
american_scientific_journal-2140	114	97	2𝑓	2𝑓	NOUN
american_scientific_journal-2140	114	98	(	(	PUNCT
american_scientific_journal-2140	114	99	1	1	NUM
american_scientific_journal-2140	114	100	−	−	PROPN
american_scientific_journal-2140	114	101	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	102	4𝑓	4𝑓	NUM
american_scientific_journal-2140	114	103	(	(	PUNCT
american_scientific_journal-2140	114	104	1	1	NUM
american_scientific_journal-2140	114	105	−	−	NOUN
american_scientific_journal-2140	114	106	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	107	1	1	NUM
american_scientific_journal-2140	114	108	(	(	PUNCT
american_scientific_journal-2140	114	109	1	1	NUM
american_scientific_journal-2140	114	110	−	−	PROPN
american_scientific_journal-2140	114	111	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	112	0	0	NUM
american_scientific_journal-2140	114	113	2𝑓	2𝑓	NOUN
american_scientific_journal-2140	114	114	+	+	CCONJ
american_scientific_journal-2140	114	115	√4𝑓2	√4𝑓2	X
american_scientific_journal-2140	114	116	+	+	CCONJ
american_scientific_journal-2140	114	117	(	(	PUNCT
american_scientific_journal-2140	114	118	1	1	NUM
american_scientific_journal-2140	114	119	−	−	NOUN
american_scientific_journal-2140	114	120	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	121	(	(	PUNCT
american_scientific_journal-2140	114	122	1	1	NUM
american_scientific_journal-2140	114	123	−	−	PROPN
american_scientific_journal-2140	114	124	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	125	2𝑓	2𝑓	NOUN
american_scientific_journal-2140	114	126	−	−	PROPN
american_scientific_journal-2140	114	127	√4𝑓2	√4𝑓2	X
american_scientific_journal-2140	114	128	+	+	CCONJ
american_scientific_journal-2140	114	129	(	(	PUNCT
american_scientific_journal-2140	114	130	1	1	NUM
american_scientific_journal-2140	114	131	−	−	NOUN
american_scientific_journal-2140	114	132	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	133	(	(	PUNCT
american_scientific_journal-2140	114	134	1	1	NUM
american_scientific_journal-2140	114	135	−	−	NOUN
american_scientific_journal-2140	114	136	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	137	5	5	NUM
american_scientific_journal-2140	114	138	2	2	NUM
american_scientific_journal-2140	114	139	𝑓	𝑓	DET
american_scientific_journal-2140	114	140	2	2	NUM
american_scientific_journal-2140	114	141	7	7	NUM
american_scientific_journal-2140	114	142	5𝑓𝑚	5𝑓𝑚	ADJ
american_scientific_journal-2140	114	143	2(1	2(1	NUM
american_scientific_journal-2140	114	144	−	−	ADP
american_scientific_journal-2140	114	145	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	146	)	)	PUNCT
american_scientific_journal-2140	114	147	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	148	(	(	PUNCT
american_scientific_journal-2140	114	149	1	1	NUM
american_scientific_journal-2140	114	150	−	−	NOUN
american_scientific_journal-2140	114	151	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	152	)	)	PUNCT
american_scientific_journal-2140	114	153	5𝑓	5𝑓	NOUN
american_scientific_journal-2140	114	154	2(1	2(1	NUM
american_scientific_journal-2140	114	155	−	−	NOUN
american_scientific_journal-2140	114	156	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	157	5𝑓	5𝑓	NOUN
american_scientific_journal-2140	114	158	(	(	PUNCT
american_scientific_journal-2140	114	159	1	1	NUM
american_scientific_journal-2140	114	160	−	−	NOUN
american_scientific_journal-2140	114	161	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	162	1	1	NUM
american_scientific_journal-2140	114	163	(	(	PUNCT
american_scientific_journal-2140	114	164	1	1	NUM
american_scientific_journal-2140	114	165	−	−	PROPN
american_scientific_journal-2140	114	166	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	167	0	0	NUM
american_scientific_journal-2140	114	168	5𝑓	5𝑓	NUM
american_scientific_journal-2140	114	169	2	2	NUM
american_scientific_journal-2140	114	170	+	+	CCONJ
american_scientific_journal-2140	114	171	√25𝑓2	√25𝑓2	PROPN
american_scientific_journal-2140	114	172	4	4	NUM
american_scientific_journal-2140	114	173	+	+	CCONJ
american_scientific_journal-2140	114	174	(	(	PUNCT
american_scientific_journal-2140	114	175	1	1	NUM
american_scientific_journal-2140	114	176	−	−	NOUN
american_scientific_journal-2140	114	177	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	178	(	(	PUNCT
american_scientific_journal-2140	114	179	1	1	NUM
american_scientific_journal-2140	114	180	−	−	NOUN
american_scientific_journal-2140	114	181	𝑚)3	𝑚)3	ADJ
american_scientific_journal-2140	114	182	5𝑓	5𝑓	NOUN
american_scientific_journal-2140	114	183	2	2	NUM
american_scientific_journal-2140	114	184	−	−	NOUN
american_scientific_journal-2140	114	185	√25𝑓2	√25𝑓2	NOUN
american_scientific_journal-2140	114	186	4	4	NUM
american_scientific_journal-2140	114	187	+	+	CCONJ
american_scientific_journal-2140	114	188	(	(	PUNCT
american_scientific_journal-2140	114	189	1	1	NUM
american_scientific_journal-2140	114	190	−	−	NOUN
american_scientific_journal-2140	114	191	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	192	(	(	PUNCT
american_scientific_journal-2140	114	193	1	1	NUM
american_scientific_journal-2140	114	194	−	−	NOUN
american_scientific_journal-2140	114	195	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	196	3𝑓	3𝑓	ADJ
american_scientific_journal-2140	114	197	1	1	NUM
american_scientific_journal-2140	114	198	4	4	NUM
american_scientific_journal-2140	114	199	3𝑓𝑚	3𝑓𝑚	NOUN
american_scientific_journal-2140	114	200	(	(	PUNCT
american_scientific_journal-2140	114	201	1	1	NUM
american_scientific_journal-2140	114	202	−	−	NOUN
american_scientific_journal-2140	114	203	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	204	)	)	PUNCT
american_scientific_journal-2140	114	205	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	206	(	(	PUNCT
american_scientific_journal-2140	114	207	1	1	NUM
american_scientific_journal-2140	114	208	−	−	NOUN
american_scientific_journal-2140	114	209	𝑚	𝑚	NOUN
american_scientific_journal-2140	114	210	)	)	PUNCT
american_scientific_journal-2140	114	211	3𝑓	3𝑓	NOUN
american_scientific_journal-2140	114	212	(	(	PUNCT
american_scientific_journal-2140	114	213	1	1	NUM
american_scientific_journal-2140	114	214	−	−	PROPN
american_scientific_journal-2140	114	215	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	114	216	6𝑓	6𝑓	NUM
american_scientific_journal-2140	114	217	(	(	PUNCT
american_scientific_journal-2140	114	218	1	1	NUM
american_scientific_journal-2140	114	219	−	−	NOUN
american_scientific_journal-2140	114	220	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	114	221	1	1	NUM
american_scientific_journal-2140	114	222	(	(	PUNCT
american_scientific_journal-2140	114	223	1	1	NUM
american_scientific_journal-2140	114	224	−	−	PROPN
american_scientific_journal-2140	114	225	𝑚)2	𝑚)2	NOUN
american_scientific_journal-2140	114	226	0	0	NUM
american_scientific_journal-2140	114	227	3𝑓	3𝑓	NOUN
american_scientific_journal-2140	114	228	+	+	X
american_scientific_journal-2140	114	229	√9𝑓2	√9𝑓2	NUM
american_scientific_journal-2140	115	1	+	+	CCONJ
american_scientific_journal-2140	116	1	(	(	PUNCT
american_scientific_journal-2140	116	2	1	1	NUM
american_scientific_journal-2140	116	3	−	−	NOUN
american_scientific_journal-2140	116	4	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	116	5	(	(	PUNCT
american_scientific_journal-2140	116	6	1	1	NUM
american_scientific_journal-2140	116	7	−	−	NOUN
american_scientific_journal-2140	116	8	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	116	9	3𝑓	3𝑓	NOUN
american_scientific_journal-2140	116	10	−	−	PROPN
american_scientific_journal-2140	116	11	√9𝑓2	√9𝑓2	PROPN
american_scientific_journal-2140	116	12	+	+	CCONJ
american_scientific_journal-2140	116	13	(	(	PUNCT
american_scientific_journal-2140	116	14	1	1	NUM
american_scientific_journal-2140	116	15	−	−	NOUN
american_scientific_journal-2140	116	16	𝑚)2	𝑚)2	PROPN
american_scientific_journal-2140	116	17	(	(	PUNCT
american_scientific_journal-2140	116	18	1	1	NUM
american_scientific_journal-2140	116	19	−	−	NOUN
american_scientific_journal-2140	116	20	𝑚)3	𝑚)3	NOUN
american_scientific_journal-2140	116	21	for	for	ADP
american_scientific_journal-2140	116	22	the	the	DET
american_scientific_journal-2140	116	23	above	above	ADJ
american_scientific_journal-2140	116	24	values	value	NOUN
american_scientific_journal-2140	116	25	of	of	ADP
american_scientific_journal-2140	116	26	the	the	DET
american_scientific_journal-2140	116	27	ratio	ratio	NOUN
american_scientific_journal-2140	116	28	𝑘	𝑘	NOUN
american_scientific_journal-2140	116	29	,	,	PUNCT
american_scientific_journal-2140	116	30	we	we	PRON
american_scientific_journal-2140	116	31	find	find	VERB
american_scientific_journal-2140	116	32	in	in	ADP
american_scientific_journal-2140	116	33	the	the	DET
american_scientific_journal-2140	116	34	magnification	magnification	NOUN
american_scientific_journal-2140	116	35	interval	interval	NOUN
american_scientific_journal-2140	116	36	(	(	PUNCT
american_scientific_journal-2140	116	37	0.9	0.9	NUM
american_scientific_journal-2140	116	38	,	,	PUNCT
american_scientific_journal-2140	116	39	1.1	1.1	NUM
american_scientific_journal-2140	116	40	)	)	PUNCT
american_scientific_journal-2140	116	41	that	that	SCONJ
american_scientific_journal-2140	116	42	the	the	DET
american_scientific_journal-2140	116	43	pure	pure	ADJ
american_scientific_journal-2140	116	44	component	component	NOUN
american_scientific_journal-2140	116	45	𝑓𝑚𝑚	𝑓𝑚𝑚	NOUN
american_scientific_journal-2140	116	46	as	as	ADP
american_scientific_journal-2140	116	47	in	in	ADP
american_scientific_journal-2140	116	48	eqn	eqn	NOUN
american_scientific_journal-2140	116	49	.	.	PUNCT
american_scientific_journal-2140	117	1	(	(	PUNCT
american_scientific_journal-2140	117	2	3	3	X
american_scientific_journal-2140	117	3	)	)	PUNCT
american_scientific_journal-2140	117	4	and	and	CCONJ
american_scientific_journal-2140	117	5	eigenvalue	eigenvalue	PROPN
american_scientific_journal-2140	117	6	𝜆1(𝑓	𝜆1(𝑓	PROPN
american_scientific_journal-2140	117	7	,	,	PUNCT
american_scientific_journal-2140	117	8	𝑚	𝑚	NOUN
american_scientific_journal-2140	117	9	)	)	PUNCT
american_scientific_journal-2140	117	10	as	as	ADP
american_scientific_journal-2140	117	11	in	in	ADP
american_scientific_journal-2140	117	12	eqn	eqn	NOUN
american_scientific_journal-2140	117	13	.	.	PUNCT
american_scientific_journal-2140	118	1	(	(	PUNCT
american_scientific_journal-2140	118	2	5	5	X
american_scientific_journal-2140	118	3	)	)	PUNCT
american_scientific_journal-2140	118	4	generate	generate	VERB
american_scientific_journal-2140	118	5	a	a	DET
american_scientific_journal-2140	118	6	separate	separate	ADJ
american_scientific_journal-2140	118	7	pair	pair	NOUN
american_scientific_journal-2140	118	8	of	of	ADP
american_scientific_journal-2140	118	9	negatively	negatively	ADV
american_scientific_journal-2140	118	10	and	and	CCONJ
american_scientific_journal-2140	118	11	positively	positively	ADV
american_scientific_journal-2140	118	12	curved	curve	VERB
american_scientific_journal-2140	118	13	surfaces	surface	NOUN
american_scientific_journal-2140	118	14	under	under	ADP
american_scientific_journal-2140	118	15	simultaneous	simultaneous	ADJ
american_scientific_journal-2140	118	16	fluctuations	fluctuation	NOUN
american_scientific_journal-2140	118	17	of	of	ADP
american_scientific_journal-2140	118	18	the	the	DET
american_scientific_journal-2140	118	19	focal	focal	ADJ
american_scientific_journal-2140	118	20	length	length	NOUN
american_scientific_journal-2140	118	21	𝑓	𝑓	PRON
american_scientific_journal-2140	118	22	and	and	CCONJ
american_scientific_journal-2140	118	23	lateral	lateral	ADJ
american_scientific_journal-2140	118	24	magnification	magnification	NOUN
american_scientific_journal-2140	118	25	𝑚.	𝑚.	ADJ
american_scientific_journal-2140	118	26	this	this	DET
american_scientific_journal-2140	118	27	pair	pair	NOUN
american_scientific_journal-2140	118	28	corresponds	correspond	VERB
american_scientific_journal-2140	118	29	to	to	ADP
american_scientific_journal-2140	118	30	the	the	DET
american_scientific_journal-2140	118	31	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	118	32	surfaces	surface	NOUN
american_scientific_journal-2140	118	33	of	of	ADP
american_scientific_journal-2140	118	34	concave	concave	NOUN
american_scientific_journal-2140	118	35	and	and	CCONJ
american_scientific_journal-2140	118	36	convex	convex	VERB
american_scientific_journal-2140	118	37	lenses/	lenses/	NUM
american_scientific_journal-2140	118	38	mirrors	mirror	NOUN
american_scientific_journal-2140	118	39	respectively	respectively	ADV
american_scientific_journal-2140	118	40	.	.	PUNCT
american_scientific_journal-2140	119	1	such	such	DET
american_scientific_journal-2140	119	2	a	a	DET
american_scientific_journal-2140	119	3	pair	pair	NOUN
american_scientific_journal-2140	119	4	of	of	ADP
american_scientific_journal-2140	119	5	surfaces	surface	NOUN
american_scientific_journal-2140	119	6	turns	turn	VERB
american_scientific_journal-2140	119	7	out	out	ADP
american_scientific_journal-2140	119	8	to	to	PART
american_scientific_journal-2140	119	9	be	be	AUX
american_scientific_journal-2140	119	10	asymptotically	asymptotically	ADV
american_scientific_journal-2140	119	11	disjoint	disjoint	VERB
american_scientific_journal-2140	119	12	about	about	ADP
american_scientific_journal-2140	119	13	the	the	DET
american_scientific_journal-2140	119	14	line	line	NOUN
american_scientific_journal-2140	119	15	of	of	ADP
american_scientific_journal-2140	119	16	the	the	DET
american_scientific_journal-2140	119	17	unit	unit	NOUN
american_scientific_journal-2140	119	18	lateral	lateral	ADJ
american_scientific_journal-2140	119	19	magnification	magnification	NOUN
american_scientific_journal-2140	119	20	𝑚	𝑚	NOUN
american_scientific_journal-2140	119	21	=	=	SYM
american_scientific_journal-2140	119	22	1	1	NUM
american_scientific_journal-2140	119	23	with	with	ADP
american_scientific_journal-2140	119	24	large	large	ADJ
american_scientific_journal-2140	119	25	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	119	26	amplitudes	amplitude	NOUN
american_scientific_journal-2140	119	27	of	of	ADP
american_scientific_journal-2140	119	28	the	the	DET
american_scientific_journal-2140	119	29	pure	pure	ADJ
american_scientific_journal-2140	119	30	magnification	magnification	NOUN
american_scientific_journal-2140	119	31	capacity	capacity	NOUN
american_scientific_journal-2140	119	32	𝑓𝑚𝑚.	𝑓𝑚𝑚.	NOUN
american_scientific_journal-2140	119	33	moreover	moreover	ADV
american_scientific_journal-2140	119	34	,	,	PUNCT
american_scientific_journal-2140	119	35	at	at	ADP
american_scientific_journal-2140	119	36	a	a	DET
american_scientific_journal-2140	119	37	given	give	VERB
american_scientific_journal-2140	119	38	object	object	NOUN
american_scientific_journal-2140	119	39	distance	distance	NOUN
american_scientific_journal-2140	119	40	𝑢	𝑢	NOUN
american_scientific_journal-2140	119	41	,	,	PUNCT
american_scientific_journal-2140	119	42	we	we	PRON
american_scientific_journal-2140	119	43	find	find	VERB
american_scientific_journal-2140	119	44	that	that	SCONJ
american_scientific_journal-2140	119	45	a	a	DET
american_scientific_journal-2140	119	46	finite	finite	ADJ
american_scientific_journal-2140	119	47	behavior	behavior	NOUN
american_scientific_journal-2140	119	48	of	of	ADP
american_scientific_journal-2140	119	49	𝑓𝑚𝑚	𝑓𝑚𝑚	NOUN
american_scientific_journal-2140	119	50	and	and	CCONJ
american_scientific_journal-2140	119	51	𝜆1	𝜆1	PROPN
american_scientific_journal-2140	119	52	as	as	SCONJ
american_scientific_journal-2140	119	53	observed	observe	VERB
american_scientific_journal-2140	119	54	in	in	ADP
american_scientific_journal-2140	119	55	their	their	PRON
american_scientific_journal-2140	119	56	amplitude	amplitude	NOUN
american_scientific_journal-2140	119	57	modulations	modulation	NOUN
american_scientific_journal-2140	119	58	under	under	ADP
american_scientific_journal-2140	119	59	the	the	DET
american_scientific_journal-2140	119	60	fluctuations	fluctuation	NOUN
american_scientific_journal-2140	119	61	of	of	ADP
american_scientific_journal-2140	119	62	the	the	DET
american_scientific_journal-2140	119	63	lateral	lateral	ADJ
american_scientific_journal-2140	119	64	magnification	magnification	NOUN
american_scientific_journal-2140	119	65	𝑚	𝑚	X
american_scientific_journal-2140	119	66	∊	∊	PROPN
american_scientific_journal-2140	119	67	(	(	PUNCT
american_scientific_journal-2140	119	68	0.9	0.9	NUM
american_scientific_journal-2140	119	69	,	,	PUNCT
american_scientific_journal-2140	119	70	1.1	1.1	NUM
american_scientific_journal-2140	119	71	)	)	PUNCT
american_scientific_journal-2140	119	72	offers	offer	VERB
american_scientific_journal-2140	119	73	an	an	DET
american_scientific_journal-2140	119	74	optical	optical	ADJ
american_scientific_journal-2140	119	75	fine	fine	NOUN
american_scientific_journal-2140	119	76	-	-	PUNCT
american_scientific_journal-2140	119	77	tuning	tuning	NOUN
american_scientific_journal-2140	119	78	towards	towards	ADP
american_scientific_journal-2140	119	79	lens	lens	NOUN
american_scientific_journal-2140	119	80	designing	design	VERB
american_scientific_journal-2140	119	81	.	.	PUNCT
american_scientific_journal-2140	120	1	under	under	ADP
american_scientific_journal-2140	120	2	the	the	DET
american_scientific_journal-2140	120	3	aforementioned	aforementioned	ADJ
american_scientific_journal-2140	120	4	values	value	NOUN
american_scientific_journal-2140	120	5	of	of	ADP
american_scientific_journal-2140	120	6	𝑘	𝑘	PRON
american_scientific_journal-2140	120	7	,	,	PUNCT
american_scientific_journal-2140	120	8	we	we	PRON
american_scientific_journal-2140	120	9	further	far	ADV
american_scientific_journal-2140	120	10	anticipate	anticipate	VERB
american_scientific_journal-2140	120	11	from	from	ADP
american_scientific_journal-2140	120	12	eqn	eqn	NOUN
american_scientific_journal-2140	120	13	.	.	PUNCT
american_scientific_journal-2140	121	1	(	(	PUNCT
american_scientific_journal-2140	121	2	6	6	NUM
american_scientific_journal-2140	121	3	)	)	PUNCT
american_scientific_journal-2140	121	4	that	that	SCONJ
american_scientific_journal-2140	121	5	the	the	DET
american_scientific_journal-2140	121	6	eigenvalue	eigenvalue	PROPN
american_scientific_journal-2140	121	7	𝜆2(𝑓	𝜆2(𝑓	PROPN
american_scientific_journal-2140	121	8	,	,	PUNCT
american_scientific_journal-2140	121	9	𝑚	𝑚	NOUN
american_scientific_journal-2140	121	10	)	)	PUNCT
american_scientific_journal-2140	121	11	of	of	ADP
american_scientific_journal-2140	121	12	the	the	DET
american_scientific_journal-2140	121	13	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	121	14	matrix	matrix	NOUN
american_scientific_journal-2140	121	15	𝐻	𝐻	NOUN
american_scientific_journal-2140	121	16	forms	form	VERB
american_scientific_journal-2140	121	17	a	a	DET
american_scientific_journal-2140	121	18	pair	pair	NOUN
american_scientific_journal-2140	121	19	of	of	ADP
american_scientific_journal-2140	121	20	positively	positively	ADV
american_scientific_journal-2140	121	21	and	and	CCONJ
american_scientific_journal-2140	121	22	negatively	negatively	ADV
american_scientific_journal-2140	121	23	curved	curve	VERB
american_scientific_journal-2140	121	24	surfaces	surface	NOUN
american_scientific_journal-2140	121	25	corresponding	correspond	VERB
american_scientific_journal-2140	121	26	to	to	ADP
american_scientific_journal-2140	121	27	the	the	DET
american_scientific_journal-2140	121	28	convex	convex	NOUN
american_scientific_journal-2140	121	29	and	and	CCONJ
american_scientific_journal-2140	121	30	concave	concave	VERB
american_scientific_journal-2140	121	31	lenses/	lenses/	NUM
american_scientific_journal-2140	121	32	mirrors	mirror	NOUN
american_scientific_journal-2140	121	33	,	,	PUNCT
american_scientific_journal-2140	121	34	as	as	ADV
american_scientific_journal-2140	121	35	well	well	ADV
american_scientific_journal-2140	121	36	.	.	PUNCT
american_scientific_journal-2140	122	1	moreover	moreover	ADV
american_scientific_journal-2140	122	2	,	,	PUNCT
american_scientific_journal-2140	122	3	it	it	PRON
american_scientific_journal-2140	122	4	follows	follow	VERB
american_scientific_journal-2140	122	5	that	that	SCONJ
american_scientific_journal-2140	122	6	the	the	DET
american_scientific_journal-2140	122	7	point	point	NOUN
american_scientific_journal-2140	122	8	of	of	ADP
american_scientific_journal-2140	122	9	discontinuity	discontinuity	NOUN
american_scientific_journal-2140	122	10	arises	arise	VERB
american_scientific_journal-2140	122	11	in	in	ADP
american_scientific_journal-2140	122	12	fluctuations	fluctuation	NOUN
american_scientific_journal-2140	122	13	of	of	ADP
american_scientific_journal-2140	122	14	the	the	DET
american_scientific_journal-2140	122	15	eigenvalue	eigenvalue	PROPN
american_scientific_journal-2140	122	16	𝜆2(𝑓	𝜆2(𝑓	PROPN
american_scientific_journal-2140	122	17	,	,	PUNCT
american_scientific_journal-2140	122	18	𝑚	𝑚	NOUN
american_scientific_journal-2140	122	19	)	)	PUNCT
american_scientific_journal-2140	122	20	as	as	ADP
american_scientific_journal-2140	122	21	above	above	ADV
american_scientific_journal-2140	122	22	in	in	ADP
american_scientific_journal-2140	122	23	eqn	eqn	NOUN
american_scientific_journal-2140	122	24	.	.	PUNCT
american_scientific_journal-2140	123	1	(	(	PUNCT
american_scientific_journal-2140	123	2	6	6	NUM
american_scientific_journal-2140	123	3	)	)	PUNCT
american_scientific_journal-2140	123	4	about	about	ADP
american_scientific_journal-2140	123	5	the	the	DET
american_scientific_journal-2140	123	6	line	line	NOUN
american_scientific_journal-2140	123	7	of	of	ADP
american_scientific_journal-2140	123	8	the	the	DET
american_scientific_journal-2140	123	9	unit	unit	NOUN
american_scientific_journal-2140	123	10	lateral	lateral	ADJ
american_scientific_journal-2140	123	11	magnification	magnification	NOUN
american_scientific_journal-2140	123	12	𝑚	𝑚	NOUN
american_scientific_journal-2140	123	13	=	=	SYM
american_scientific_journal-2140	123	14	1	1	X
american_scientific_journal-2140	123	15	.	.	X
american_scientific_journal-2140	123	16	herewith	herewith	NOUN
american_scientific_journal-2140	123	17	,	,	PUNCT
american_scientific_journal-2140	123	18	as	as	ADV
american_scientific_journal-2140	123	19	far	far	ADV
american_scientific_journal-2140	123	20	as	as	SCONJ
american_scientific_journal-2140	123	21	the	the	DET
american_scientific_journal-2140	123	22	stability	stability	NOUN
american_scientific_journal-2140	123	23	of	of	ADP
american_scientific_journal-2140	123	24	an	an	DET
american_scientific_journal-2140	123	25	image	image	NOUN
american_scientific_journal-2140	123	26	is	be	AUX
american_scientific_journal-2140	123	27	concerned	concern	VERB
american_scientific_journal-2140	123	28	,	,	PUNCT
american_scientific_journal-2140	123	29	we	we	PRON
american_scientific_journal-2140	123	30	find	find	VERB
american_scientific_journal-2140	123	31	that	that	SCONJ
american_scientific_journal-2140	123	32	similar	similar	ADJ
american_scientific_journal-2140	123	33	conclusions	conclusion	NOUN
american_scientific_journal-2140	123	34	hold	hold	VERB
american_scientific_journal-2140	123	35	for	for	ADP
american_scientific_journal-2140	123	36	higher	high	ADJ
american_scientific_journal-2140	123	37	values	value	NOUN
american_scientific_journal-2140	123	38	of	of	ADP
american_scientific_journal-2140	123	39	𝑘	𝑘	PRON
american_scientific_journal-2140	123	40	in	in	ADP
american_scientific_journal-2140	123	41	finetuning	finetune	VERB
american_scientific_journal-2140	123	42	the	the	DET
american_scientific_journal-2140	123	43	image	image	NOUN
american_scientific_journal-2140	123	44	for	for	ADP
american_scientific_journal-2140	123	45	a	a	DET
american_scientific_journal-2140	123	46	given	give	VERB
american_scientific_journal-2140	123	47	pair	pair	NOUN
american_scientific_journal-2140	123	48	of	of	ADP
american_scientific_journal-2140	123	49	varying	vary	VERB
american_scientific_journal-2140	123	50	lateral	lateral	ADJ
american_scientific_journal-2140	123	51	magnification	magnification	NOUN
american_scientific_journal-2140	123	52	and	and	CCONJ
american_scientific_journal-2140	123	53	focal	focal	ADJ
american_scientific_journal-2140	123	54	length	length	NOUN
american_scientific_journal-2140	123	55	of	of	ADP
american_scientific_journal-2140	123	56	the	the	DET
american_scientific_journal-2140	123	57	instrument	instrument	NOUN
american_scientific_journal-2140	123	58	.	.	PUNCT
american_scientific_journal-2140	124	1	american	american	ADJ
american_scientific_journal-2140	124	2	scientific	scientific	ADJ
american_scientific_journal-2140	124	3	research	research	PROPN
american_scientific_journal-2140	124	4	journal	journal	NOUN
american_scientific_journal-2140	124	5	for	for	ADP
american_scientific_journal-2140	124	6	engineering	engineering	NOUN
american_scientific_journal-2140	124	7	,	,	PUNCT
american_scientific_journal-2140	124	8	technology	technology	NOUN
american_scientific_journal-2140	124	9	,	,	PUNCT
american_scientific_journal-2140	124	10	and	and	CCONJ
american_scientific_journal-2140	124	11	sciences	science	NOUN
american_scientific_journal-2140	124	12	(	(	PUNCT
american_scientific_journal-2140	124	13	asrjets	asrjet	NOUN
american_scientific_journal-2140	124	14	)	)	PUNCT
american_scientific_journal-2140	124	15	(	(	PUNCT
american_scientific_journal-2140	124	16	2016	2016	NUM
american_scientific_journal-2140	124	17	)	)	PUNCT
american_scientific_journal-2140	124	18	volume	volume	NOUN
american_scientific_journal-2140	124	19	26	26	NUM
american_scientific_journal-2140	124	20	,	,	PUNCT
american_scientific_journal-2140	124	21	no	no	DET
american_scientific_journal-2140	124	22	1	1	NUM
american_scientific_journal-2140	124	23	,	,	PUNCT
american_scientific_journal-2140	124	24	pp	pp	ADV
american_scientific_journal-2140	124	25	302	302	NUM
american_scientific_journal-2140	124	26	-	-	SYM
american_scientific_journal-2140	124	27	313	313	NUM
american_scientific_journal-2140	124	28	309	309	NUM
american_scientific_journal-2140	124	29	4	4	NUM
american_scientific_journal-2140	124	30	.	.	PUNCT
american_scientific_journal-2140	124	31	extended	extend	VERB
american_scientific_journal-2140	124	32	optical	optical	ADJ
american_scientific_journal-2140	124	33	optimizations	optimization	NOUN
american_scientific_journal-2140	124	34	in	in	ADP
american_scientific_journal-2140	124	35	this	this	DET
american_scientific_journal-2140	124	36	section	section	NOUN
american_scientific_journal-2140	124	37	,	,	PUNCT
american_scientific_journal-2140	124	38	we	we	PRON
american_scientific_journal-2140	124	39	offer	offer	VERB
american_scientific_journal-2140	124	40	perspective	perspective	NOUN
american_scientific_journal-2140	124	41	directions	direction	NOUN
american_scientific_journal-2140	124	42	of	of	ADP
american_scientific_journal-2140	124	43	the	the	DET
american_scientific_journal-2140	124	44	foregoing	forego	VERB
american_scientific_journal-2140	124	45	optical	optical	ADJ
american_scientific_journal-2140	124	46	optimization	optimization	NOUN
american_scientific_journal-2140	124	47	model	model	NOUN
american_scientific_journal-2140	124	48	for	for	ADP
american_scientific_journal-2140	124	49	finite	finite	ADJ
american_scientific_journal-2140	124	50	combinations	combination	NOUN
american_scientific_journal-2140	124	51	of	of	ADP
american_scientific_journal-2140	124	52	lenses	lense	NOUN
american_scientific_journal-2140	124	53	and/	and/	VERB
american_scientific_journal-2140	124	54	or	or	CCONJ
american_scientific_journal-2140	124	55	mirrors	mirror	NOUN
american_scientific_journal-2140	124	56	with	with	ADP
american_scientific_journal-2140	124	57	and	and	CCONJ
american_scientific_journal-2140	124	58	without	without	ADP
american_scientific_journal-2140	124	59	their	their	PRON
american_scientific_journal-2140	124	60	extensions	extension	NOUN
american_scientific_journal-2140	124	61	to	to	ADP
american_scientific_journal-2140	124	62	constrained	constrained	ADJ
american_scientific_journal-2140	124	63	settings	setting	NOUN
american_scientific_journal-2140	124	64	.	.	PUNCT
american_scientific_journal-2140	125	1	with	with	ADP
american_scientific_journal-2140	125	2	reference	reference	NOUN
american_scientific_journal-2140	125	3	to	to	ADP
american_scientific_journal-2140	125	4	a	a	DET
american_scientific_journal-2140	125	5	constrained	constrain	VERB
american_scientific_journal-2140	125	6	optimization	optimization	NOUN
american_scientific_journal-2140	125	7	setting	setting	NOUN
american_scientific_journal-2140	125	8	,	,	PUNCT
american_scientific_journal-2140	125	9	we	we	PRON
american_scientific_journal-2140	125	10	formulate	formulate	VERB
american_scientific_journal-2140	125	11	an	an	DET
american_scientific_journal-2140	125	12	extended	extended	ADJ
american_scientific_journal-2140	125	13	model	model	NOUN
american_scientific_journal-2140	125	14	with	with	ADP
american_scientific_journal-2140	125	15	possible	possible	ADJ
american_scientific_journal-2140	125	16	involvements	involvement	NOUN
american_scientific_journal-2140	125	17	of	of	ADP
american_scientific_journal-2140	125	18	additional	additional	ADJ
american_scientific_journal-2140	125	19	optimization	optimization	NOUN
american_scientific_journal-2140	125	20	variables	variable	NOUN
american_scientific_journal-2140	125	21	,	,	PUNCT
american_scientific_journal-2140	125	22	apart	apart	ADV
american_scientific_journal-2140	125	23	from	from	ADP
american_scientific_journal-2140	125	24	the	the	DET
american_scientific_journal-2140	125	25	object	object	NOUN
american_scientific_journal-2140	125	26	distance	distance	NOUN
american_scientific_journal-2140	125	27	and	and	CCONJ
american_scientific_journal-2140	125	28	lateral	lateral	ADJ
american_scientific_journal-2140	125	29	magnification	magnification	NOUN
american_scientific_journal-2140	125	30	.	.	PUNCT
american_scientific_journal-2140	126	1	4.1	4.1	NUM
american_scientific_journal-2140	126	2	.	.	PUNCT
american_scientific_journal-2140	126	3	power	power	NOUN
american_scientific_journal-2140	126	4	optimization	optimization	NOUN
american_scientific_journal-2140	126	5	from	from	ADP
american_scientific_journal-2140	126	6	the	the	DET
american_scientific_journal-2140	126	7	perspective	perspective	NOUN
american_scientific_journal-2140	126	8	of	of	ADP
american_scientific_journal-2140	126	9	the	the	DET
american_scientific_journal-2140	126	10	thin	thin	ADJ
american_scientific_journal-2140	126	11	lens	lens	NOUN
american_scientific_journal-2140	126	12	approximation	approximation	NOUN
american_scientific_journal-2140	126	13	as	as	SCONJ
american_scientific_journal-2140	126	14	discussed	discuss	VERB
american_scientific_journal-2140	126	15	above	above	ADV
american_scientific_journal-2140	126	16	for	for	ADP
american_scientific_journal-2140	126	17	a	a	DET
american_scientific_journal-2140	126	18	given	give	VERB
american_scientific_journal-2140	126	19	single	single	ADJ
american_scientific_journal-2140	126	20	lens/	lens/	NUM
american_scientific_journal-2140	126	21	mirror	mirror	NOUN
american_scientific_journal-2140	126	22	or	or	CCONJ
american_scientific_journal-2140	126	23	an	an	DET
american_scientific_journal-2140	126	24	optical	optical	ADJ
american_scientific_journal-2140	126	25	instrument	instrument	NOUN
american_scientific_journal-2140	126	26	involving	involve	VERB
american_scientific_journal-2140	126	27	their	their	PRON
american_scientific_journal-2140	126	28	finite	finite	ADJ
american_scientific_journal-2140	126	29	combination	combination	NOUN
american_scientific_journal-2140	126	30	,	,	PUNCT
american_scientific_journal-2140	126	31	we	we	PRON
american_scientific_journal-2140	126	32	may	may	AUX
american_scientific_journal-2140	126	33	express	express	VERB
american_scientific_journal-2140	126	34	the	the	DET
american_scientific_journal-2140	126	35	net	net	ADJ
american_scientific_journal-2140	126	36	focal	focal	ADJ
american_scientific_journal-2140	126	37	length	length	NOUN
american_scientific_journal-2140	126	38	𝑓𝑛𝑒𝑡	𝑓𝑛𝑒𝑡	NOUN
american_scientific_journal-2140	126	39	of	of	ADP
american_scientific_journal-2140	126	40	the	the	DET
american_scientific_journal-2140	126	41	resulting	result	VERB
american_scientific_journal-2140	126	42	system	system	NOUN
american_scientific_journal-2140	126	43	[	[	X
american_scientific_journal-2140	126	44	1	1	NUM
american_scientific_journal-2140	126	45	-	-	SYM
american_scientific_journal-2140	126	46	4	4	NUM
american_scientific_journal-2140	126	47	]	]	PUNCT
american_scientific_journal-2140	126	48	as	as	ADP
american_scientific_journal-2140	126	49	1	1	NUM
american_scientific_journal-2140	126	50	𝑓𝑛𝑒𝑡	𝑓𝑛𝑒𝑡	NOUN
american_scientific_journal-2140	126	51	=	=	SYM
american_scientific_journal-2140	126	52	1	1	NUM
american_scientific_journal-2140	126	53	𝑓1(𝑢1,𝑣1	𝑓1(𝑢1,𝑣1	NOUN
american_scientific_journal-2140	126	54	)	)	PUNCT
american_scientific_journal-2140	126	55	+	+	CCONJ
american_scientific_journal-2140	126	56	1	1	NUM
american_scientific_journal-2140	126	57	𝑓2(𝑢2,𝑣2	𝑓2(𝑢2,𝑣2	NOUN
american_scientific_journal-2140	126	58	)	)	PUNCT
american_scientific_journal-2140	126	59	,	,	PUNCT
american_scientific_journal-2140	126	60	(	(	PUNCT
american_scientific_journal-2140	126	61	14	14	NUM
american_scientific_journal-2140	126	62	)	)	PUNCT
american_scientific_journal-2140	126	63	where	where	SCONJ
american_scientific_journal-2140	126	64	𝑓1	𝑓1	PROPN
american_scientific_journal-2140	126	65	as	as	ADP
american_scientific_journal-2140	126	66	the	the	DET
american_scientific_journal-2140	126	67	focal	focal	ADJ
american_scientific_journal-2140	126	68	length	length	NOUN
american_scientific_journal-2140	126	69	of	of	ADP
american_scientific_journal-2140	126	70	the	the	DET
american_scientific_journal-2140	126	71	first	first	ADJ
american_scientific_journal-2140	126	72	component	component	NOUN
american_scientific_journal-2140	126	73	emerges	emerge	VERB
american_scientific_journal-2140	126	74	as	as	ADP
american_scientific_journal-2140	126	75	a	a	DET
american_scientific_journal-2140	126	76	function	function	NOUN
american_scientific_journal-2140	126	77	of	of	ADP
american_scientific_journal-2140	126	78	the	the	DET
american_scientific_journal-2140	126	79	object	object	NOUN
american_scientific_journal-2140	126	80	distance	distance	NOUN
american_scientific_journal-2140	126	81	𝑢1	𝑢1	NOUN
american_scientific_journal-2140	126	82	and	and	CCONJ
american_scientific_journal-2140	126	83	image	image	NOUN
american_scientific_journal-2140	126	84	distance	distance	NOUN
american_scientific_journal-2140	126	85	𝑣1	𝑣1	NOUN
american_scientific_journal-2140	126	86	from	from	ADP
american_scientific_journal-2140	126	87	its	its	PRON
american_scientific_journal-2140	126	88	optical	optical	ADJ
american_scientific_journal-2140	126	89	center	center	NOUN
american_scientific_journal-2140	126	90	,	,	PUNCT
american_scientific_journal-2140	126	91	see	see	VERB
american_scientific_journal-2140	126	92	eqn	eqn	PRON
american_scientific_journal-2140	126	93	.	.	PUNCT
american_scientific_journal-2140	127	1	(	(	PUNCT
american_scientific_journal-2140	127	2	1	1	NUM
american_scientific_journal-2140	127	3	)	)	PUNCT
american_scientific_journal-2140	127	4	.	.	PUNCT
american_scientific_journal-2140	128	1	similarly	similarly	ADV
american_scientific_journal-2140	128	2	,	,	PUNCT
american_scientific_journal-2140	128	3	it	it	PRON
american_scientific_journal-2140	128	4	follows	follow	VERB
american_scientific_journal-2140	128	5	that	that	SCONJ
american_scientific_journal-2140	128	6	𝑓2	𝑓2	NOUN
american_scientific_journal-2140	128	7	is	be	AUX
american_scientific_journal-2140	128	8	solely	solely	ADV
american_scientific_journal-2140	128	9	a	a	DET
american_scientific_journal-2140	128	10	function	function	NOUN
american_scientific_journal-2140	128	11	of	of	ADP
american_scientific_journal-2140	128	12	the	the	DET
american_scientific_journal-2140	128	13	associated	associated	ADJ
american_scientific_journal-2140	128	14	object	object	NOUN
american_scientific_journal-2140	128	15	and	and	CCONJ
american_scientific_journal-2140	128	16	image	image	NOUN
american_scientific_journal-2140	128	17	distances	distance	NOUN
american_scientific_journal-2140	128	18	{	{	PUNCT
american_scientific_journal-2140	128	19	𝑢2	𝑢2	PROPN
american_scientific_journal-2140	128	20	,	,	PUNCT
american_scientific_journal-2140	128	21	𝑣2	𝑣2	PROPN
american_scientific_journal-2140	128	22	}	}	PUNCT
american_scientific_journal-2140	128	23	from	from	ADP
american_scientific_journal-2140	128	24	the	the	DET
american_scientific_journal-2140	128	25	optical	optical	ADJ
american_scientific_journal-2140	128	26	center	center	NOUN
american_scientific_journal-2140	128	27	of	of	ADP
american_scientific_journal-2140	128	28	the	the	DET
american_scientific_journal-2140	128	29	second	second	ADJ
american_scientific_journal-2140	128	30	component	component	NOUN
american_scientific_journal-2140	128	31	.	.	PUNCT
american_scientific_journal-2140	129	1	notice	notice	VERB
american_scientific_journal-2140	129	2	further	far	ADV
american_scientific_journal-2140	129	3	that	that	PRON
american_scientific_journal-2140	129	4	𝑓2	𝑓2	ADJ
american_scientific_journal-2140	129	5	satisfies	satisfie	NOUN
american_scientific_journal-2140	129	6	eqn	eqn	VERB
american_scientific_journal-2140	129	7	.	.	PUNCT
american_scientific_journal-2140	130	1	(	(	PUNCT
american_scientific_journal-2140	130	2	1	1	X
american_scientific_journal-2140	130	3	)	)	PUNCT
american_scientific_journal-2140	130	4	in	in	ADP
american_scientific_journal-2140	130	5	its	its	PRON
american_scientific_journal-2140	130	6	thin	thin	ADJ
american_scientific_journal-2140	130	7	lens	lens	NOUN
american_scientific_journal-2140	130	8	approximation	approximation	NOUN
american_scientific_journal-2140	130	9	,	,	PUNCT
american_scientific_journal-2140	130	10	as	as	ADV
american_scientific_journal-2140	130	11	well	well	ADV
american_scientific_journal-2140	130	12	.	.	PUNCT
american_scientific_journal-2140	131	1	thus	thus	ADV
american_scientific_journal-2140	131	2	,	,	PUNCT
american_scientific_journal-2140	131	3	the	the	DET
american_scientific_journal-2140	131	4	final	final	ADJ
american_scientific_journal-2140	131	5	object	object	NOUN
american_scientific_journal-2140	131	6	distance	distance	NOUN
american_scientific_journal-2140	131	7	𝑢	𝑢	NOUN
american_scientific_journal-2140	131	8	and	and	CCONJ
american_scientific_journal-2140	131	9	image	image	NOUN
american_scientific_journal-2140	131	10	distance	distance	NOUN
american_scientific_journal-2140	131	11	𝑣	𝑣	ADP
american_scientific_journal-2140	131	12	of	of	ADP
american_scientific_journal-2140	131	13	the	the	DET
american_scientific_journal-2140	131	14	combination	combination	NOUN
american_scientific_journal-2140	131	15	with	with	ADP
american_scientific_journal-2140	131	16	a	a	DET
american_scientific_journal-2140	131	17	common	common	ADJ
american_scientific_journal-2140	131	18	reference	reference	NOUN
american_scientific_journal-2140	131	19	point	point	NOUN
american_scientific_journal-2140	131	20	can	can	AUX
american_scientific_journal-2140	131	21	be	be	AUX
american_scientific_journal-2140	131	22	obtained	obtain	VERB
american_scientific_journal-2140	131	23	as	as	ADP
american_scientific_journal-2140	131	24	per	per	ADP
american_scientific_journal-2140	131	25	the	the	DET
american_scientific_journal-2140	131	26	transformations	transformation	NOUN
american_scientific_journal-2140	131	27	𝑢2	𝑢2	PROPN
american_scientific_journal-2140	131	28	→	→	SYM
american_scientific_journal-2140	131	29	𝑢2	𝑢2	PROPN
american_scientific_journal-2140	131	30	′	′	NUM
american_scientific_journal-2140	132	1	=	=	PUNCT
american_scientific_journal-2140	132	2	𝑢2	𝑢2	PROPN
american_scientific_journal-2140	132	3	+	+	CCONJ
american_scientific_journal-2140	132	4	𝑣1	𝑣1	PROPN
american_scientific_journal-2140	132	5	,	,	PUNCT
american_scientific_journal-2140	132	6	(	(	PUNCT
american_scientific_journal-2140	132	7	15	15	X
american_scientific_journal-2140	132	8	)	)	PUNCT
american_scientific_journal-2140	132	9	𝑣2	𝑣2	NOUN
american_scientific_journal-2140	132	10	→	→	PUNCT
american_scientific_journal-2140	132	11	𝑣2	𝑣2	X
american_scientific_journal-2140	132	12	′	′	NUM
american_scientific_journal-2140	132	13	=	=	PUNCT
american_scientific_journal-2140	132	14	𝑣2	𝑣2	PROPN
american_scientific_journal-2140	132	15	+	+	CCONJ
american_scientific_journal-2140	132	16	𝑣1	𝑣1	PROPN
american_scientific_journal-2140	132	17	+	+	CCONJ
american_scientific_journal-2140	132	18	𝑢1	𝑢1	PROPN
american_scientific_journal-2140	132	19	(	(	PUNCT
american_scientific_journal-2140	132	20	16	16	NUM
american_scientific_journal-2140	132	21	)	)	PUNCT
american_scientific_journal-2140	132	22	in	in	ADP
american_scientific_journal-2140	132	23	the	the	DET
american_scientific_journal-2140	132	24	presence	presence	NOUN
american_scientific_journal-2140	132	25	of	of	ADP
american_scientific_journal-2140	132	26	an	an	DET
american_scientific_journal-2140	132	27	interaction	interaction	NOUN
american_scientific_journal-2140	132	28	term	term	NOUN
american_scientific_journal-2140	132	29	𝑓i	𝑓i	ADP
american_scientific_journal-2140	132	30	which	which	PRON
american_scientific_journal-2140	132	31	arises	arise	VERB
american_scientific_journal-2140	132	32	by	by	ADP
american_scientific_journal-2140	132	33	going	go	VERB
american_scientific_journal-2140	132	34	beyond	beyond	ADP
american_scientific_journal-2140	132	35	the	the	DET
american_scientific_journal-2140	132	36	thin	thin	ADJ
american_scientific_journal-2140	132	37	lens	lens	NOUN
american_scientific_journal-2140	132	38	approximation	approximation	NOUN
american_scientific_journal-2140	132	39	[	[	X
american_scientific_journal-2140	132	40	1	1	NUM
american_scientific_journal-2140	132	41	-	-	SYM
american_scientific_journal-2140	132	42	4	4	NUM
american_scientific_journal-2140	132	43	]	]	PUNCT
american_scientific_journal-2140	132	44	,	,	PUNCT
american_scientific_journal-2140	132	45	the	the	DET
american_scientific_journal-2140	132	46	net	net	ADJ
american_scientific_journal-2140	132	47	focal	focal	ADJ
american_scientific_journal-2140	132	48	length	length	NOUN
american_scientific_journal-2140	132	49	𝑓𝑛𝑒𝑡	𝑓𝑛𝑒𝑡	NOUN
american_scientific_journal-2140	132	50	of	of	ADP
american_scientific_journal-2140	132	51	the	the	DET
american_scientific_journal-2140	132	52	combined	combine	VERB
american_scientific_journal-2140	132	53	optical	optical	ADJ
american_scientific_journal-2140	132	54	system	system	NOUN
american_scientific_journal-2140	132	55	can	can	AUX
american_scientific_journal-2140	132	56	be	be	AUX
american_scientific_journal-2140	132	57	represented	represent	VERB
american_scientific_journal-2140	132	58	as	as	ADP
american_scientific_journal-2140	132	59	1	1	NUM
american_scientific_journal-2140	132	60	𝑓𝑛𝑒𝑡(𝑢2	𝑓𝑛𝑒𝑡(𝑢2	NOUN
american_scientific_journal-2140	132	61	′	′	NUM
american_scientific_journal-2140	132	62	,	,	PUNCT
american_scientific_journal-2140	132	63	𝑣2	𝑣2	NOUN
american_scientific_journal-2140	132	64	′	′	NUM
american_scientific_journal-2140	132	65	)	)	PUNCT
american_scientific_journal-2140	133	1	=	=	SYM
american_scientific_journal-2140	133	2	1	1	NUM
american_scientific_journal-2140	133	3	𝑓1(𝑢1,𝑣1	𝑓1(𝑢1,𝑣1	NOUN
american_scientific_journal-2140	133	4	)	)	PUNCT
american_scientific_journal-2140	134	1	+	+	CCONJ
american_scientific_journal-2140	134	2	1	1	NUM
american_scientific_journal-2140	134	3	𝑓2(𝑢2,𝑣2	𝑓2(𝑢2,𝑣2	NOUN
american_scientific_journal-2140	134	4	)	)	PUNCT
american_scientific_journal-2140	134	5	−	−	PROPN
american_scientific_journal-2140	134	6	1	1	NUM
american_scientific_journal-2140	134	7	𝑓i(𝑢1	𝑓i(𝑢1	NOUN
american_scientific_journal-2140	134	8	,	,	PUNCT
american_scientific_journal-2140	134	9	𝑣1,𝑢2,𝑣2	𝑣1,𝑢2,𝑣2	NOUN
american_scientific_journal-2140	134	10	)	)	PUNCT
american_scientific_journal-2140	134	11	(	(	PUNCT
american_scientific_journal-2140	134	12	17	17	NUM
american_scientific_journal-2140	134	13	)	)	PUNCT
american_scientific_journal-2140	134	14	in	in	ADP
american_scientific_journal-2140	134	15	the	the	DET
american_scientific_journal-2140	134	16	light	light	NOUN
american_scientific_journal-2140	134	17	of	of	ADP
american_scientific_journal-2140	134	18	the	the	DET
american_scientific_journal-2140	134	19	above	above	ADJ
american_scientific_journal-2140	134	20	definition	definition	NOUN
american_scientific_journal-2140	134	21	,	,	PUNCT
american_scientific_journal-2140	134	22	we	we	PRON
american_scientific_journal-2140	134	23	find	find	VERB
american_scientific_journal-2140	134	24	that	that	SCONJ
american_scientific_journal-2140	134	25	the	the	DET
american_scientific_journal-2140	134	26	net	net	ADJ
american_scientific_journal-2140	134	27	optical	optical	ADJ
american_scientific_journal-2140	134	28	power	power	NOUN
american_scientific_journal-2140	134	29	𝐷	𝐷	PROPN
american_scientific_journal-2140	134	30	of	of	ADP
american_scientific_journal-2140	134	31	the	the	DET
american_scientific_journal-2140	134	32	combined	combine	VERB
american_scientific_journal-2140	134	33	optical	optical	ADJ
american_scientific_journal-2140	134	34	system	system	NOUN
american_scientific_journal-2140	134	35	arises	arise	VERB
american_scientific_journal-2140	134	36	as	as	ADP
american_scientific_journal-2140	134	37	the	the	DET
american_scientific_journal-2140	134	38	inverse	inverse	NOUN
american_scientific_journal-2140	134	39	of	of	ADP
american_scientific_journal-2140	134	40	the	the	DET
american_scientific_journal-2140	134	41	total	total	ADJ
american_scientific_journal-2140	134	42	focal	focal	ADJ
american_scientific_journal-2140	134	43	length	length	NOUN
american_scientific_journal-2140	134	44	𝑓	𝑓	PROPN
american_scientific_journal-2140	134	45	,	,	PUNCT
american_scientific_journal-2140	134	46	viz	viz	PROPN
american_scientific_journal-2140	134	47	.	.	PUNCT
american_scientific_journal-2140	135	1	we	we	PRON
american_scientific_journal-2140	135	2	have	have	VERB
american_scientific_journal-2140	135	3	𝐷	𝐷	NOUN
american_scientific_journal-2140	135	4	=	=	NOUN
american_scientific_journal-2140	135	5	1	1	NUM
american_scientific_journal-2140	135	6	𝑓𝑛𝑒𝑡⁄	𝑓𝑛𝑒𝑡⁄	PROPN
american_scientific_journal-2140	135	7	.	.	PUNCT
american_scientific_journal-2140	136	1	notice	notice	VERB
american_scientific_journal-2140	136	2	further	far	ADV
american_scientific_journal-2140	136	3	that	that	SCONJ
american_scientific_journal-2140	136	4	the	the	DET
american_scientific_journal-2140	136	5	optical	optical	ADJ
american_scientific_journal-2140	136	6	power	power	NOUN
american_scientific_journal-2140	136	7	of	of	ADP
american_scientific_journal-2140	136	8	an	an	DET
american_scientific_journal-2140	136	9	instrument	instrument	NOUN
american_scientific_journal-2140	136	10	is	be	AUX
american_scientific_journal-2140	136	11	measured	measure	VERB
american_scientific_journal-2140	136	12	in	in	ADP
american_scientific_journal-2140	136	13	the	the	DET
american_scientific_journal-2140	136	14	units	unit	NOUN
american_scientific_journal-2140	136	15	of	of	ADP
american_scientific_journal-2140	136	16	diopter	diopter	NOUN
american_scientific_journal-2140	137	1	[	[	X
american_scientific_journal-2140	137	2	1	1	NUM
american_scientific_journal-2140	137	3	]	]	PUNCT
american_scientific_journal-2140	137	4	.	.	PUNCT
american_scientific_journal-2140	138	1	similarly	similarly	ADV
american_scientific_journal-2140	138	2	,	,	PUNCT
american_scientific_journal-2140	138	3	we	we	PRON
american_scientific_journal-2140	138	4	may	may	AUX
american_scientific_journal-2140	138	5	define	define	VERB
american_scientific_journal-2140	138	6	the	the	DET
american_scientific_journal-2140	138	7	corresponding	corresponding	ADJ
american_scientific_journal-2140	138	8	component	component	NOUN
american_scientific_journal-2140	138	9	powers	power	NOUN
american_scientific_journal-2140	138	10	as	as	ADP
american_scientific_journal-2140	138	11	𝐷i	𝐷i	PROPN
american_scientific_journal-2140	138	12	=	=	PUNCT
american_scientific_journal-2140	138	13	1	1	NUM
american_scientific_journal-2140	138	14	𝑓⁄	𝑓⁄	NUM
american_scientific_journal-2140	138	15	i	i	PRON
american_scientific_journal-2140	138	16	,	,	PUNCT
american_scientific_journal-2140	138	17	i	i	PRON
american_scientific_journal-2140	138	18	=	=	NOUN
american_scientific_journal-2140	138	19	1	1	NUM
american_scientific_journal-2140	138	20	,	,	PUNCT
american_scientific_journal-2140	138	21	2	2	NUM
american_scientific_journal-2140	138	22	and	and	CCONJ
american_scientific_journal-2140	138	23	the	the	DET
american_scientific_journal-2140	138	24	combined	combine	VERB
american_scientific_journal-2140	138	25	interactive	interactive	ADJ
american_scientific_journal-2140	138	26	power	power	NOUN
american_scientific_journal-2140	138	27	of	of	ADP
american_scientific_journal-2140	138	28	the	the	DET
american_scientific_journal-2140	138	29	system	system	NOUN
american_scientific_journal-2140	138	30	as	as	ADP
american_scientific_journal-2140	138	31	𝑑({𝐷𝑖	𝑑({𝐷𝑖	NOUN
american_scientific_journal-2140	138	32	}	}	PUNCT
american_scientific_journal-2140	138	33	)	)	PUNCT
american_scientific_journal-2140	138	34	=	=	SYM
american_scientific_journal-2140	138	35	1	1	NUM
american_scientific_journal-2140	138	36	𝑓i⁄	𝑓i⁄	NOUN
american_scientific_journal-2140	138	37	.	.	PUNCT
american_scientific_journal-2140	139	1	therefore	therefore	ADV
american_scientific_journal-2140	139	2	,	,	PUNCT
american_scientific_journal-2140	139	3	under	under	ADP
american_scientific_journal-2140	139	4	small	small	ADJ
american_scientific_journal-2140	139	5	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	139	6	approximation	approximation	NOUN
american_scientific_journal-2140	139	7	,	,	PUNCT
american_scientific_journal-2140	139	8	it	it	PRON
american_scientific_journal-2140	139	9	follows	follow	VERB
american_scientific_journal-2140	139	10	that	that	SCONJ
american_scientific_journal-2140	139	11	the	the	DET
american_scientific_journal-2140	139	12	net	net	ADJ
american_scientific_journal-2140	139	13	optical	optical	ADJ
american_scientific_journal-2140	139	14	power	power	NOUN
american_scientific_journal-2140	139	15	𝐷({𝐷𝑖	𝐷({𝐷𝑖	NOUN
american_scientific_journal-2140	139	16	}	}	PUNCT
american_scientific_journal-2140	139	17	)	)	PUNCT
american_scientific_journal-2140	139	18	of	of	ADP
american_scientific_journal-2140	139	19	the	the	DET
american_scientific_journal-2140	139	20	combined	combine	VERB
american_scientific_journal-2140	139	21	system	system	NOUN
american_scientific_journal-2140	139	22	as	as	ADP
american_scientific_journal-2140	139	23	a	a	DET
american_scientific_journal-2140	139	24	function	function	NOUN
american_scientific_journal-2140	139	25	of	of	ADP
american_scientific_journal-2140	139	26	the	the	DET
american_scientific_journal-2140	139	27	component	component	NOUN
american_scientific_journal-2140	139	28	optical	optical	ADJ
american_scientific_journal-2140	139	29	powers	power	NOUN
american_scientific_journal-2140	139	30	{	{	PUNCT
american_scientific_journal-2140	139	31	𝐷𝑖	𝐷𝑖	ADV
american_scientific_journal-2140	139	32	|	|	ADV
american_scientific_journal-2140	139	33	𝑖	𝑖	NOUN
american_scientific_journal-2140	139	34	=	=	NOUN
american_scientific_journal-2140	139	35	1	1	NUM
american_scientific_journal-2140	139	36	,	,	PUNCT
american_scientific_journal-2140	139	37	2	2	NUM
american_scientific_journal-2140	139	38	}	}	PUNCT
american_scientific_journal-2140	139	39	can	can	AUX
american_scientific_journal-2140	139	40	be	be	AUX
american_scientific_journal-2140	139	41	expressed	express	VERB
american_scientific_journal-2140	139	42	as	as	ADP
american_scientific_journal-2140	139	43	𝐷({𝐷𝑖	𝐷({𝐷𝑖	NOUN
american_scientific_journal-2140	139	44	}	}	PUNCT
american_scientific_journal-2140	139	45	)	)	PUNCT
american_scientific_journal-2140	140	1	=	=	SYM
american_scientific_journal-2140	140	2	𝐷1	𝐷1	NOUN
american_scientific_journal-2140	140	3	+	+	NUM
american_scientific_journal-2140	140	4	𝐷2	𝐷2	PROPN
american_scientific_journal-2140	140	5	−	−	PROPN
american_scientific_journal-2140	140	6	𝑑({𝐷𝑖	𝑑({𝐷𝑖	PROPN
american_scientific_journal-2140	140	7	}	}	PUNCT
american_scientific_journal-2140	140	8	)	)	PUNCT
american_scientific_journal-2140	140	9	(	(	PUNCT
american_scientific_journal-2140	140	10	18	18	NUM
american_scientific_journal-2140	140	11	)	)	PUNCT
american_scientific_journal-2140	140	12	hereby	hereby	ADV
american_scientific_journal-2140	140	13	,	,	PUNCT
american_scientific_journal-2140	140	14	the	the	DET
american_scientific_journal-2140	140	15	interaction	interaction	NOUN
american_scientific_journal-2140	140	16	quantity	quantity	NOUN
american_scientific_journal-2140	140	17	𝑓i	𝑓i	ADP
american_scientific_journal-2140	140	18	of	of	ADP
american_scientific_journal-2140	140	19	the	the	DET
american_scientific_journal-2140	140	20	considered	consider	VERB
american_scientific_journal-2140	140	21	optical	optical	ADJ
american_scientific_journal-2140	140	22	components	component	NOUN
american_scientific_journal-2140	140	23	,	,	PUNCT
american_scientific_journal-2140	140	24	viz	viz	PROPN
american_scientific_journal-2140	140	25	.	.	PUNCT
american_scientific_journal-2140	141	1	the	the	DET
american_scientific_journal-2140	141	2	constituent	constituent	NOUN
american_scientific_journal-2140	141	3	lenses	lense	NOUN
american_scientific_journal-2140	141	4	and/	and/	PROPN
american_scientific_journal-2140	141	5	or	or	CCONJ
american_scientific_journal-2140	141	6	mirrors	mirror	NOUN
american_scientific_journal-2140	141	7	is	be	AUX
american_scientific_journal-2140	141	8	determined	determine	VERB
american_scientific_journal-2140	141	9	via	via	ADP
american_scientific_journal-2140	141	10	their	their	PRON
american_scientific_journal-2140	141	11	respective	respective	ADJ
american_scientific_journal-2140	141	12	curvatures	curvature	NOUN
american_scientific_journal-2140	141	13	.	.	PUNCT
american_scientific_journal-2140	142	1	with	with	ADP
american_scientific_journal-2140	142	2	the	the	DET
american_scientific_journal-2140	142	3	initial	initial	ADJ
american_scientific_journal-2140	142	4	conditions	condition	NOUN
american_scientific_journal-2140	142	5	𝐷(0,0	𝐷(0,0	NOUN
american_scientific_journal-2140	142	6	)	)	PUNCT
american_scientific_journal-2140	142	7	=	=	SYM
american_scientific_journal-2140	142	8	0	0	NUM
american_scientific_journal-2140	142	9	,	,	PUNCT
american_scientific_journal-2140	142	10	𝜕𝐷/𝜕𝐷1	𝜕𝐷/𝜕𝐷1	VERB
american_scientific_journal-2140	142	11	=	=	SYM
american_scientific_journal-2140	142	12	1	1	NUM
american_scientific_journal-2140	142	13	american	american	ADJ
american_scientific_journal-2140	142	14	scientific	scientific	ADJ
american_scientific_journal-2140	142	15	research	research	NOUN
american_scientific_journal-2140	142	16	journal	journal	NOUN
american_scientific_journal-2140	142	17	for	for	ADP
american_scientific_journal-2140	142	18	engineering	engineering	NOUN
american_scientific_journal-2140	142	19	,	,	PUNCT
american_scientific_journal-2140	142	20	technology	technology	NOUN
american_scientific_journal-2140	142	21	,	,	PUNCT
american_scientific_journal-2140	142	22	and	and	CCONJ
american_scientific_journal-2140	142	23	sciences	science	NOUN
american_scientific_journal-2140	142	24	(	(	PUNCT
american_scientific_journal-2140	142	25	asrjets	asrjet	NOUN
american_scientific_journal-2140	142	26	)	)	PUNCT
american_scientific_journal-2140	142	27	(	(	PUNCT
american_scientific_journal-2140	142	28	2016	2016	NUM
american_scientific_journal-2140	142	29	)	)	PUNCT
american_scientific_journal-2140	142	30	volume	volume	NOUN
american_scientific_journal-2140	142	31	26	26	NUM
american_scientific_journal-2140	142	32	,	,	PUNCT
american_scientific_journal-2140	142	33	no	no	DET
american_scientific_journal-2140	142	34	1	1	NUM
american_scientific_journal-2140	142	35	,	,	PUNCT
american_scientific_journal-2140	142	36	pp	pp	ADV
american_scientific_journal-2140	142	37	302	302	NUM
american_scientific_journal-2140	142	38	-	-	SYM
american_scientific_journal-2140	142	39	313	313	NUM
american_scientific_journal-2140	142	40	310	310	NUM
american_scientific_journal-2140	142	41	and	and	CCONJ
american_scientific_journal-2140	142	42	𝜕𝐷/𝜕𝐷2	𝜕𝐷/𝜕𝐷2	PROPN
american_scientific_journal-2140	142	43	=	=	SYM
american_scientific_journal-2140	142	44	1	1	NUM
american_scientific_journal-2140	142	45	,	,	PUNCT
american_scientific_journal-2140	142	46	in	in	ADP
american_scientific_journal-2140	142	47	the	the	DET
american_scientific_journal-2140	142	48	linear	linear	ADJ
american_scientific_journal-2140	142	49	approximation	approximation	NOUN
american_scientific_journal-2140	142	50	of	of	ADP
american_scientific_journal-2140	142	51	the	the	DET
american_scientific_journal-2140	142	52	taylor	taylor	PROPN
american_scientific_journal-2140	142	53	series	series	PROPN
american_scientific_journal-2140	142	54	expansion	expansion	NOUN
american_scientific_journal-2140	142	55	of	of	ADP
american_scientific_journal-2140	142	56	the	the	DET
american_scientific_journal-2140	142	57	net	net	ADJ
american_scientific_journal-2140	142	58	power	power	NOUN
american_scientific_journal-2140	142	59	𝐷({𝐷𝑖	𝐷({𝐷𝑖	NOUN
american_scientific_journal-2140	142	60	}	}	PUNCT
american_scientific_journal-2140	142	61	)	)	PUNCT
american_scientific_journal-2140	142	62	,	,	PUNCT
american_scientific_journal-2140	142	63	we	we	PRON
american_scientific_journal-2140	142	64	see	see	VERB
american_scientific_journal-2140	142	65	that	that	SCONJ
american_scientific_journal-2140	142	66	it	it	PRON
american_scientific_journal-2140	142	67	reads	read	VERB
american_scientific_journal-2140	142	68	as	as	ADP
american_scientific_journal-2140	142	69	per	per	ADP
american_scientific_journal-2140	142	70	the	the	DET
american_scientific_journal-2140	142	71	following	follow	VERB
american_scientific_journal-2140	142	72	summation	summation	NOUN
american_scientific_journal-2140	142	73	𝐷({𝐷𝑖	𝐷({𝐷𝑖	NOUN
american_scientific_journal-2140	142	74	}	}	PUNCT
american_scientific_journal-2140	142	75	)	)	PUNCT
american_scientific_journal-2140	143	1	⋍	⋍	ADJ
american_scientific_journal-2140	143	2	𝐷1	𝐷1	NOUN
american_scientific_journal-2140	143	3	+	+	CCONJ
american_scientific_journal-2140	143	4	𝐷2	𝐷2	PROPN
american_scientific_journal-2140	143	5	(	(	PUNCT
american_scientific_journal-2140	143	6	19	19	NUM
american_scientific_journal-2140	143	7	)	)	PUNCT
american_scientific_journal-2140	143	8	beyond	beyond	ADP
american_scientific_journal-2140	143	9	the	the	DET
american_scientific_journal-2140	143	10	thin	thin	ADJ
american_scientific_journal-2140	143	11	lens	lens	NOUN
american_scientific_journal-2140	143	12	approximation	approximation	NOUN
american_scientific_journal-2140	143	13	,	,	PUNCT
american_scientific_journal-2140	143	14	we	we	PRON
american_scientific_journal-2140	143	15	incorporate	incorporate	VERB
american_scientific_journal-2140	143	16	terms	term	NOUN
american_scientific_journal-2140	143	17	above	above	ADP
american_scientific_journal-2140	143	18	the	the	DET
american_scientific_journal-2140	143	19	linear	linear	ADJ
american_scientific_journal-2140	143	20	orders	order	NOUN
american_scientific_journal-2140	143	21	in	in	ADP
american_scientific_journal-2140	143	22	the	the	DET
american_scientific_journal-2140	143	23	series	series	NOUN
american_scientific_journal-2140	143	24	expansion	expansion	NOUN
american_scientific_journal-2140	143	25	of	of	ADP
american_scientific_journal-2140	143	26	𝐷({𝐷𝑖	𝐷({𝐷𝑖	NOUN
american_scientific_journal-2140	143	27	}	}	PUNCT
american_scientific_journal-2140	143	28	)	)	PUNCT
american_scientific_journal-2140	143	29	of	of	ADP
american_scientific_journal-2140	143	30	the	the	DET
american_scientific_journal-2140	143	31	combined	combined	ADJ
american_scientific_journal-2140	143	32	optical	optical	ADJ
american_scientific_journal-2140	143	33	system	system	NOUN
american_scientific_journal-2140	143	34	.	.	PUNCT
american_scientific_journal-2140	144	1	specifically	specifically	ADV
american_scientific_journal-2140	144	2	,	,	PUNCT
american_scientific_journal-2140	144	3	as	as	ADP
american_scientific_journal-2140	144	4	a	a	DET
american_scientific_journal-2140	144	5	function	function	NOUN
american_scientific_journal-2140	144	6	of	of	ADP
american_scientific_journal-2140	144	7	the	the	DET
american_scientific_journal-2140	144	8	component	component	NOUN
american_scientific_journal-2140	144	9	optical	optical	ADJ
american_scientific_journal-2140	144	10	powers	power	NOUN
american_scientific_journal-2140	144	11	{	{	PUNCT
american_scientific_journal-2140	144	12	𝐷𝑖|	𝐷𝑖|	NOUN
american_scientific_journal-2140	144	13	𝑖	𝑖	SYM
american_scientific_journal-2140	144	14	=	=	NOUN
american_scientific_journal-2140	144	15	1	1	NUM
american_scientific_journal-2140	144	16	,	,	PUNCT
american_scientific_journal-2140	144	17	2	2	NUM
american_scientific_journal-2140	144	18	}	}	PUNCT
american_scientific_journal-2140	144	19	forming	form	VERB
american_scientific_journal-2140	144	20	an	an	DET
american_scientific_journal-2140	144	21	optimization	optimization	NOUN
american_scientific_journal-2140	144	22	basis	basis	NOUN
american_scientific_journal-2140	144	23	,	,	PUNCT
american_scientific_journal-2140	144	24	the	the	DET
american_scientific_journal-2140	144	25	effective	effective	ADJ
american_scientific_journal-2140	144	26	optical	optical	ADJ
american_scientific_journal-2140	144	27	power	power	NOUN
american_scientific_journal-2140	144	28	𝐷({𝐷𝑖	𝐷({𝐷𝑖	NOUN
american_scientific_journal-2140	144	29	}	}	PUNCT
american_scientific_journal-2140	144	30	)	)	PUNCT
american_scientific_journal-2140	144	31	of	of	ADP
american_scientific_journal-2140	144	32	the	the	DET
american_scientific_journal-2140	144	33	combined	combine	VERB
american_scientific_journal-2140	144	34	system	system	NOUN
american_scientific_journal-2140	144	35	in	in	ADP
american_scientific_journal-2140	144	36	its	its	PRON
american_scientific_journal-2140	144	37	quadratic	quadratic	ADJ
american_scientific_journal-2140	144	38	approximation	approximation	NOUN
american_scientific_journal-2140	144	39	reads	read	NOUN
american_scientific_journal-2140	144	40	as	as	ADP
american_scientific_journal-2140	144	41	per	per	ADP
american_scientific_journal-2140	144	42	the	the	DET
american_scientific_journal-2140	144	43	expansion	expansion	NOUN
american_scientific_journal-2140	144	44	𝐷(𝐷1	𝐷(𝐷1	NOUN
american_scientific_journal-2140	144	45	,	,	PUNCT
american_scientific_journal-2140	144	46	𝐷2	𝐷2	NOUN
american_scientific_journal-2140	144	47	)	)	PUNCT
american_scientific_journal-2140	145	1	⋍	⋍	ADJ
american_scientific_journal-2140	145	2	∑	∑	PUNCT
american_scientific_journal-2140	146	1	𝐷𝑖𝑗	𝐷𝑖𝑗	PROPN
american_scientific_journal-2140	146	2	∆𝐷𝑖∆𝐷𝑗	∆𝐷𝑖∆𝐷𝑗	PROPN
american_scientific_journal-2140	146	3	2	2	NUM
american_scientific_journal-2140	146	4	𝑖,𝑗=0	𝑖,𝑗=0	NOUN
american_scientific_journal-2140	146	5	𝑖+𝑗=2	𝑖+𝑗=2	PROPN
american_scientific_journal-2140	146	6	,	,	PUNCT
american_scientific_journal-2140	146	7	(	(	PUNCT
american_scientific_journal-2140	146	8	20	20	NUM
american_scientific_journal-2140	146	9	)	)	PUNCT
american_scientific_journal-2140	146	10	where	where	SCONJ
american_scientific_journal-2140	146	11	𝐻	𝐻	PROPN
american_scientific_journal-2140	146	12	≔	≔	NOUN
american_scientific_journal-2140	146	13	(	(	PUNCT
american_scientific_journal-2140	146	14	𝐷𝑖𝑗	𝐷𝑖𝑗	PROPN
american_scientific_journal-2140	146	15	)	)	PUNCT
american_scientific_journal-2140	146	16	is	be	AUX
american_scientific_journal-2140	146	17	the	the	DET
american_scientific_journal-2140	146	18	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	146	19	matrix	matrix	NOUN
american_scientific_journal-2140	146	20	having	have	VERB
american_scientific_journal-2140	146	21	entries	entry	NOUN
american_scientific_journal-2140	146	22	as	as	SCONJ
american_scientific_journal-2140	146	23	the	the	DET
american_scientific_journal-2140	146	24	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	146	25	components	component	NOUN
american_scientific_journal-2140	146	26	𝐷𝑖𝑗	𝐷𝑖𝑗	PROPN
american_scientific_journal-2140	146	27	:	:	PUNCT
american_scientific_journal-2140	146	28	=	=	SYM
american_scientific_journal-2140	146	29	𝜕𝑖+𝑗𝐷	𝜕𝑖+𝑗𝐷	NUM
american_scientific_journal-2140	146	30	𝜕𝐷1	𝜕𝐷1	PROPN
american_scientific_journal-2140	146	31	𝑖	𝑖	VERB
american_scientific_journal-2140	146	32	𝜕𝐷2	𝜕𝐷2	VERB
american_scientific_journal-2140	146	33	𝑗	𝑗	INTJ
american_scientific_journal-2140	146	34	(	(	PUNCT
american_scientific_journal-2140	146	35	21	21	NUM
american_scientific_journal-2140	146	36	)	)	PUNCT
american_scientific_journal-2140	146	37	with	with	ADP
american_scientific_journal-2140	146	38	respect	respect	NOUN
american_scientific_journal-2140	146	39	to	to	ADP
american_scientific_journal-2140	146	40	the	the	DET
american_scientific_journal-2140	146	41	component	component	NOUN
american_scientific_journal-2140	146	42	optical	optical	ADJ
american_scientific_journal-2140	146	43	powers	power	NOUN
american_scientific_journal-2140	146	44	{	{	PUNCT
american_scientific_journal-2140	146	45	𝐷𝑖	𝐷𝑖	PROPN
american_scientific_journal-2140	146	46	|	|	ADV
american_scientific_journal-2140	146	47	𝑖	𝑖	ADP
american_scientific_journal-2140	146	48	,	,	PUNCT
american_scientific_journal-2140	146	49	𝑗	𝑗	NOUN
american_scientific_journal-2140	146	50	=	=	SYM
american_scientific_journal-2140	146	51	1	1	NUM
american_scientific_journal-2140	146	52	,	,	PUNCT
american_scientific_journal-2140	146	53	2	2	NUM
american_scientific_journal-2140	146	54	}	}	PUNCT
american_scientific_journal-2140	146	55	of	of	ADP
american_scientific_journal-2140	146	56	the	the	DET
american_scientific_journal-2140	146	57	combined	combined	ADJ
american_scientific_journal-2140	146	58	system	system	NOUN
american_scientific_journal-2140	146	59	.	.	PUNCT
american_scientific_journal-2140	147	1	4.2	4.2	NUM
american_scientific_journal-2140	147	2	constrained	constrain	VERB
american_scientific_journal-2140	147	3	optimization	optimization	NOUN
american_scientific_journal-2140	147	4	in	in	ADP
american_scientific_journal-2140	147	5	the	the	DET
american_scientific_journal-2140	147	6	presence	presence	NOUN
american_scientific_journal-2140	147	7	of	of	ADP
american_scientific_journal-2140	147	8	a	a	DET
american_scientific_journal-2140	147	9	constraint	constraint	NOUN
american_scientific_journal-2140	147	10	function	function	NOUN
american_scientific_journal-2140	147	11	𝑐(𝑢	𝑐(𝑢	PROPN
american_scientific_journal-2140	147	12	,	,	PUNCT
american_scientific_journal-2140	147	13	𝑚	𝑚	NOUN
american_scientific_journal-2140	147	14	)	)	PUNCT
american_scientific_journal-2140	147	15	acting	act	VERB
american_scientific_journal-2140	147	16	on	on	ADP
american_scientific_journal-2140	147	17	the	the	DET
american_scientific_journal-2140	147	18	optical	optical	ADJ
american_scientific_journal-2140	147	19	system	system	NOUN
american_scientific_journal-2140	147	20	,	,	PUNCT
american_scientific_journal-2140	147	21	the	the	DET
american_scientific_journal-2140	147	22	corresponding	corresponding	ADJ
american_scientific_journal-2140	147	23	objective	objective	ADJ
american_scientific_journal-2140	147	24	function	function	NOUN
american_scientific_journal-2140	147	25	𝑓𝑐	𝑓𝑐	ADP
american_scientific_journal-2140	147	26	of	of	ADP
american_scientific_journal-2140	147	27	the	the	DET
american_scientific_journal-2140	147	28	constrained	constrain	VERB
american_scientific_journal-2140	147	29	optimization	optimization	NOUN
american_scientific_journal-2140	147	30	system	system	NOUN
american_scientific_journal-2140	147	31	takes	take	VERB
american_scientific_journal-2140	147	32	the	the	DET
american_scientific_journal-2140	147	33	form	form	NOUN
american_scientific_journal-2140	147	34	𝑓𝑐(𝑢	𝑓𝑐(𝑢	NOUN
american_scientific_journal-2140	147	35	,	,	PUNCT
american_scientific_journal-2140	147	36	𝑚	𝑚	NOUN
american_scientific_journal-2140	147	37	)	)	PUNCT
american_scientific_journal-2140	147	38	=	=	SYM
american_scientific_journal-2140	147	39	𝑢𝑚	𝑢𝑚	ADP
american_scientific_journal-2140	147	40	1−	1−	NUM
american_scientific_journal-2140	147	41	𝑚	𝑚	NOUN
american_scientific_journal-2140	147	42	+	+	X
american_scientific_journal-2140	147	43	𝜆𝑐(𝑢	𝜆𝑐(𝑢	NUM
american_scientific_journal-2140	147	44	,	,	PUNCT
american_scientific_journal-2140	147	45	𝑚	𝑚	NOUN
american_scientific_journal-2140	147	46	)	)	PUNCT
american_scientific_journal-2140	147	47	,	,	PUNCT
american_scientific_journal-2140	147	48	(	(	PUNCT
american_scientific_journal-2140	147	49	22	22	NUM
american_scientific_journal-2140	147	50	)	)	PUNCT
american_scientific_journal-2140	147	51	where	where	SCONJ
american_scientific_journal-2140	147	52	𝜆	𝜆	NOUN
american_scientific_journal-2140	147	53	is	be	AUX
american_scientific_journal-2140	147	54	the	the	DET
american_scientific_journal-2140	147	55	lagrange	lagrange	NOUN
american_scientific_journal-2140	147	56	multiplier	multiplier	ADV
american_scientific_journal-2140	147	57	defining	define	VERB
american_scientific_journal-2140	147	58	the	the	DET
american_scientific_journal-2140	147	59	constraint	constraint	NOUN
american_scientific_journal-2140	147	60	optical	optical	ADJ
american_scientific_journal-2140	147	61	surface	surface	NOUN
american_scientific_journal-2140	147	62	𝑐(𝑢	𝑐(𝑢	PROPN
american_scientific_journal-2140	147	63	,	,	PUNCT
american_scientific_journal-2140	147	64	𝑚	𝑚	NOUN
american_scientific_journal-2140	147	65	)	)	PUNCT
american_scientific_journal-2140	147	66	=	=	SYM
american_scientific_journal-2140	148	1	0	0	X
american_scientific_journal-2140	148	2	.	.	PUNCT
american_scientific_journal-2140	149	1	under	under	ADP
american_scientific_journal-2140	149	2	fluctuations	fluctuation	NOUN
american_scientific_journal-2140	149	3	of	of	ADP
american_scientific_journal-2140	149	4	the	the	DET
american_scientific_journal-2140	149	5	optimization	optimization	NOUN
american_scientific_journal-2140	149	6	variables	variable	NOUN
american_scientific_journal-2140	149	7	{	{	PUNCT
american_scientific_journal-2140	149	8	𝑢	𝑢	X
american_scientific_journal-2140	149	9	,	,	PUNCT
american_scientific_journal-2140	149	10	𝑚	𝑚	NOUN
american_scientific_journal-2140	149	11	}	}	PUNCT
american_scientific_journal-2140	149	12	,	,	PUNCT
american_scientific_journal-2140	149	13	a	a	DET
american_scientific_journal-2140	149	14	constantly	constantly	ADV
american_scientific_journal-2140	149	15	constraint	constraint	NOUN
american_scientific_journal-2140	149	16	system	system	NOUN
american_scientific_journal-2140	149	17	is	be	AUX
american_scientific_journal-2140	149	18	defined	define	VERB
american_scientific_journal-2140	149	19	by	by	ADP
american_scientific_journal-2140	149	20	𝑐(𝑢	𝑐(𝑢	PROPN
american_scientific_journal-2140	149	21	,	,	PUNCT
american_scientific_journal-2140	149	22	𝑚	𝑚	NOUN
american_scientific_journal-2140	149	23	)	)	PUNCT
american_scientific_journal-2140	149	24	=	=	SYM
american_scientific_journal-2140	149	25	𝑐0	𝑐0	NOUN
american_scientific_journal-2140	149	26	,	,	PUNCT
american_scientific_journal-2140	149	27	where	where	SCONJ
american_scientific_journal-2140	149	28	𝑐0	𝑐0	NOUN
american_scientific_journal-2140	149	29	is	be	AUX
american_scientific_journal-2140	149	30	a	a	DET
american_scientific_journal-2140	149	31	fixed	fix	VERB
american_scientific_journal-2140	149	32	real	real	ADJ
american_scientific_journal-2140	149	33	constant	constant	ADJ
american_scientific_journal-2140	149	34	independent	independent	NOUN
american_scientific_journal-2140	149	35	of	of	ADP
american_scientific_journal-2140	149	36	the	the	DET
american_scientific_journal-2140	149	37	optimization	optimization	NOUN
american_scientific_journal-2140	149	38	variables	variable	NOUN
american_scientific_journal-2140	149	39	{	{	PUNCT
american_scientific_journal-2140	149	40	𝑢	𝑢	X
american_scientific_journal-2140	149	41	,	,	PUNCT
american_scientific_journal-2140	149	42	𝑚	𝑚	NOUN
american_scientific_journal-2140	149	43	}	}	PUNCT
american_scientific_journal-2140	149	44	.	.	PUNCT
american_scientific_journal-2140	150	1	in	in	ADP
american_scientific_journal-2140	150	2	this	this	DET
american_scientific_journal-2140	150	3	case	case	NOUN
american_scientific_journal-2140	150	4	,	,	PUNCT
american_scientific_journal-2140	150	5	we	we	PRON
american_scientific_journal-2140	150	6	find	find	VERB
american_scientific_journal-2140	150	7	hereby	hereby	ADV
american_scientific_journal-2140	150	8	that	that	SCONJ
american_scientific_journal-2140	150	9	the	the	DET
american_scientific_journal-2140	150	10	same	same	ADJ
american_scientific_journal-2140	150	11	optimization	optimization	NOUN
american_scientific_journal-2140	150	12	conclusions	conclusion	NOUN
american_scientific_journal-2140	150	13	hold	hold	VERB
american_scientific_journal-2140	150	14	as	as	SCONJ
american_scientific_journal-2140	150	15	given	give	VERB
american_scientific_journal-2140	150	16	in	in	ADP
american_scientific_journal-2140	150	17	section	section	NOUN
american_scientific_journal-2140	150	18	2	2	NUM
american_scientific_journal-2140	150	19	and	and	CCONJ
american_scientific_journal-2140	150	20	section	section	NOUN
american_scientific_journal-2140	150	21	3	3	NUM
american_scientific_journal-2140	150	22	for	for	ADP
american_scientific_journal-2140	150	23	the	the	DET
american_scientific_journal-2140	150	24	associated	associated	ADJ
american_scientific_journal-2140	150	25	unconstraint	unconstraint	ADJ
american_scientific_journal-2140	150	26	optical	optical	ADJ
american_scientific_journal-2140	150	27	system	system	NOUN
american_scientific_journal-2140	150	28	.	.	PUNCT
american_scientific_journal-2140	151	1	moreover	moreover	ADV
american_scientific_journal-2140	151	2	,	,	PUNCT
american_scientific_journal-2140	151	3	as	as	ADV
american_scientific_journal-2140	151	4	long	long	ADV
american_scientific_journal-2140	151	5	as	as	SCONJ
american_scientific_journal-2140	151	6	the	the	DET
american_scientific_journal-2140	151	7	partial	partial	ADJ
american_scientific_journal-2140	151	8	derivatives	derivative	NOUN
american_scientific_journal-2140	151	9	𝑐𝑢	𝑐𝑢	NOUN
american_scientific_journal-2140	151	10	and	and	CCONJ
american_scientific_journal-2140	151	11	𝑐𝑚	𝑐𝑚	X
american_scientific_journal-2140	151	12	of	of	ADP
american_scientific_journal-2140	151	13	𝑐(𝑢	𝑐(𝑢	PROPN
american_scientific_journal-2140	151	14	,	,	PUNCT
american_scientific_journal-2140	151	15	𝑚	𝑚	NOUN
american_scientific_journal-2140	151	16	)	)	PUNCT
american_scientific_journal-2140	151	17	with	with	ADP
american_scientific_journal-2140	151	18	respect	respect	NOUN
american_scientific_journal-2140	151	19	to	to	ADP
american_scientific_journal-2140	151	20	the	the	DET
american_scientific_journal-2140	151	21	variables	variable	NOUN
american_scientific_journal-2140	151	22	{	{	PUNCT
american_scientific_journal-2140	151	23	𝑢	𝑢	X
american_scientific_journal-2140	151	24	,	,	PUNCT
american_scientific_journal-2140	151	25	𝑚	𝑚	NOUN
american_scientific_journal-2140	151	26	}	}	PUNCT
american_scientific_journal-2140	151	27	exist	exist	VERB
american_scientific_journal-2140	151	28	,	,	PUNCT
american_scientific_journal-2140	151	29	it	it	PRON
american_scientific_journal-2140	151	30	follows	follow	VERB
american_scientific_journal-2140	151	31	that	that	SCONJ
american_scientific_journal-2140	151	32	the	the	DET
american_scientific_journal-2140	151	33	linear	linear	ADJ
american_scientific_journal-2140	151	34	truncation	truncation	NOUN
american_scientific_journal-2140	151	35	of	of	ADP
american_scientific_journal-2140	151	36	the	the	DET
american_scientific_journal-2140	151	37	constraint	constraint	NOUN
american_scientific_journal-2140	151	38	function	function	NOUN
american_scientific_journal-2140	151	39	𝑐(𝑢	𝑐(𝑢	PROPN
american_scientific_journal-2140	151	40	,	,	PUNCT
american_scientific_journal-2140	151	41	𝑚	𝑚	NOUN
american_scientific_journal-2140	151	42	)	)	PUNCT
american_scientific_journal-2140	151	43	redefines	redefine	VERB
american_scientific_journal-2140	151	44	the	the	DET
american_scientific_journal-2140	151	45	lens	lens	NOUN
american_scientific_journal-2140	151	46	designing	design	VERB
american_scientific_journal-2140	151	47	problem	problem	NOUN
american_scientific_journal-2140	151	48	as	as	ADP
american_scientific_journal-2140	151	49	the	the	DET
american_scientific_journal-2140	151	50	constrained	constrained	ADJ
american_scientific_journal-2140	151	51	optimization	optimization	NOUN
american_scientific_journal-2140	151	52	on	on	ADP
american_scientific_journal-2140	151	53	the	the	DET
american_scientific_journal-2140	151	54	surface	surface	NOUN
american_scientific_journal-2140	151	55	𝑐(𝑢	𝑐(𝑢	PROPN
american_scientific_journal-2140	151	56	,	,	PUNCT
american_scientific_journal-2140	151	57	𝑚	𝑚	NOUN
american_scientific_journal-2140	151	58	)	)	PUNCT
american_scientific_journal-2140	151	59	⋍	⋍	ADJ
american_scientific_journal-2140	151	60	𝑐0	𝑐0	NOUN
american_scientific_journal-2140	151	61	+	+	CCONJ
american_scientific_journal-2140	151	62	𝑐𝑢𝑢	𝑐𝑢𝑢	PROPN
american_scientific_journal-2140	151	63	+	+	CCONJ
american_scientific_journal-2140	151	64	𝑐𝑚𝑚	𝑐𝑚𝑚	NOUN
american_scientific_journal-2140	151	65	(	(	PUNCT
american_scientific_journal-2140	151	66	23	23	NUM
american_scientific_journal-2140	151	67	)	)	PUNCT
american_scientific_journal-2140	151	68	towards	towards	ADP
american_scientific_journal-2140	151	69	an	an	DET
american_scientific_journal-2140	151	70	extension	extension	NOUN
american_scientific_journal-2140	151	71	with	with	ADP
american_scientific_journal-2140	151	72	multiple	multiple	ADJ
american_scientific_journal-2140	151	73	constraints	constraint	NOUN
american_scientific_journal-2140	151	74	𝑐𝑖(𝑢	𝑐𝑖(𝑢	ADP
american_scientific_journal-2140	151	75	,	,	PUNCT
american_scientific_journal-2140	151	76	𝑚	𝑚	NOUN
american_scientific_journal-2140	151	77	)	)	PUNCT
american_scientific_journal-2140	151	78	to	to	ADP
american_scientific_journal-2140	151	79	the	the	DET
american_scientific_journal-2140	151	80	above	above	ADJ
american_scientific_journal-2140	151	81	optimization	optimization	NOUN
american_scientific_journal-2140	151	82	of	of	ADP
american_scientific_journal-2140	151	83	a	a	DET
american_scientific_journal-2140	151	84	single	single	ADJ
american_scientific_journal-2140	151	85	component	component	NOUN
american_scientific_journal-2140	151	86	as	as	ADP
american_scientific_journal-2140	151	87	in	in	ADP
american_scientific_journal-2140	151	88	eqn	eqn	NOUN
american_scientific_journal-2140	151	89	.	.	PUNCT
american_scientific_journal-2140	152	1	(	(	PUNCT
american_scientific_journal-2140	152	2	22	22	NUM
american_scientific_journal-2140	152	3	)	)	PUNCT
american_scientific_journal-2140	152	4	,	,	PUNCT
american_scientific_journal-2140	152	5	viz	viz	PROPN
american_scientific_journal-2140	152	6	.	.	PUNCT
american_scientific_journal-2140	152	7	lens/	lens/	NUM
american_scientific_journal-2140	152	8	mirror	mirror	NOUN
american_scientific_journal-2140	152	9	or	or	CCONJ
american_scientific_journal-2140	152	10	their	their	PRON
american_scientific_journal-2140	152	11	combinations	combination	NOUN
american_scientific_journal-2140	152	12	,	,	PUNCT
american_scientific_journal-2140	152	13	the	the	DET
american_scientific_journal-2140	152	14	corresponding	corresponding	ADJ
american_scientific_journal-2140	152	15	objective	objective	ADJ
american_scientific_journal-2140	152	16	function	function	NOUN
american_scientific_journal-2140	152	17	can	can	AUX
american_scientific_journal-2140	152	18	be	be	AUX
american_scientific_journal-2140	152	19	generalized	generalize	VERB
american_scientific_journal-2140	152	20	as	as	ADP
american_scientific_journal-2140	152	21	𝑓𝑐(𝑢	𝑓𝑐(𝑢	X
american_scientific_journal-2140	152	22	,	,	PUNCT
american_scientific_journal-2140	152	23	𝑚	𝑚	NOUN
american_scientific_journal-2140	152	24	)	)	PUNCT
american_scientific_journal-2140	152	25	=	=	SYM
american_scientific_journal-2140	152	26	𝑢𝑚	𝑢𝑚	ADP
american_scientific_journal-2140	152	27	1−𝑚	1−𝑚	NUM
american_scientific_journal-2140	153	1	+	+	CCONJ
american_scientific_journal-2140	153	2	∑	∑	PROPN
american_scientific_journal-2140	153	3	𝜆𝑖𝑐𝑖(𝑢	𝜆𝑖𝑐𝑖(𝑢	ADV
american_scientific_journal-2140	153	4	,	,	PUNCT
american_scientific_journal-2140	153	5	𝑚)𝑘	𝑚)𝑘	ADJ
american_scientific_journal-2140	153	6	𝑖=1	𝑖=1	PROPN
american_scientific_journal-2140	153	7	(	(	PUNCT
american_scientific_journal-2140	153	8	24	24	NUM
american_scientific_journal-2140	153	9	)	)	PUNCT
american_scientific_journal-2140	153	10	here	here	ADV
american_scientific_journal-2140	154	1	,	,	PUNCT
american_scientific_journal-2140	154	2	the	the	DET
american_scientific_journal-2140	154	3	parameters	parameter	NOUN
american_scientific_journal-2140	154	4	{	{	PUNCT
american_scientific_journal-2140	154	5	𝜆𝑖	𝜆𝑖	NOUN
american_scientific_journal-2140	154	6	|	|	NOUN
american_scientific_journal-2140	154	7	𝑖	𝑖	NOUN
american_scientific_journal-2140	154	8	=	=	NOUN
american_scientific_journal-2140	154	9	1	1	NUM
american_scientific_journal-2140	154	10	,	,	PUNCT
american_scientific_journal-2140	154	11	2	2	NUM
american_scientific_journal-2140	154	12	,	,	PUNCT
american_scientific_journal-2140	154	13	…	…	PUNCT
american_scientific_journal-2140	154	14	,	,	PUNCT
american_scientific_journal-2140	154	15	𝑘	𝑘	X
american_scientific_journal-2140	154	16	}	}	PUNCT
american_scientific_journal-2140	154	17	represent	represent	VERB
american_scientific_journal-2140	154	18	the	the	DET
american_scientific_journal-2140	154	19	lagrange	lagrange	NOUN
american_scientific_journal-2140	154	20	multipliers	multiplier	NOUN
american_scientific_journal-2140	154	21	of	of	ADP
american_scientific_journal-2140	154	22	the	the	DET
american_scientific_journal-2140	154	23	respective	respective	ADJ
american_scientific_journal-2140	154	24	constraining	constrain	VERB
american_scientific_journal-2140	154	25	american	american	ADJ
american_scientific_journal-2140	154	26	scientific	scientific	ADJ
american_scientific_journal-2140	154	27	research	research	NOUN
american_scientific_journal-2140	154	28	journal	journal	NOUN
american_scientific_journal-2140	154	29	for	for	ADP
american_scientific_journal-2140	154	30	engineering	engineering	NOUN
american_scientific_journal-2140	154	31	,	,	PUNCT
american_scientific_journal-2140	154	32	technology	technology	NOUN
american_scientific_journal-2140	154	33	,	,	PUNCT
american_scientific_journal-2140	154	34	and	and	CCONJ
american_scientific_journal-2140	154	35	sciences	science	NOUN
american_scientific_journal-2140	154	36	(	(	PUNCT
american_scientific_journal-2140	154	37	asrjets	asrjet	NOUN
american_scientific_journal-2140	154	38	)	)	PUNCT
american_scientific_journal-2140	154	39	(	(	PUNCT
american_scientific_journal-2140	154	40	2016	2016	NUM
american_scientific_journal-2140	154	41	)	)	PUNCT
american_scientific_journal-2140	154	42	volume	volume	NOUN
american_scientific_journal-2140	154	43	26	26	NUM
american_scientific_journal-2140	154	44	,	,	PUNCT
american_scientific_journal-2140	154	45	no	no	DET
american_scientific_journal-2140	154	46	1	1	NUM
american_scientific_journal-2140	154	47	,	,	PUNCT
american_scientific_journal-2140	154	48	pp	pp	ADV
american_scientific_journal-2140	154	49	302	302	NUM
american_scientific_journal-2140	154	50	-	-	SYM
american_scientific_journal-2140	154	51	313	313	NUM
american_scientific_journal-2140	154	52	311	311	NUM
american_scientific_journal-2140	154	53	surfaces	surface	NOUN
american_scientific_journal-2140	154	54	𝑐𝑖(𝑢	𝑐𝑖(𝑢	ADP
american_scientific_journal-2140	154	55	,	,	PUNCT
american_scientific_journal-2140	154	56	𝑚	𝑚	NOUN
american_scientific_journal-2140	154	57	)	)	PUNCT
american_scientific_journal-2140	154	58	=	=	SYM
american_scientific_journal-2140	154	59	0	0	PUNCT
american_scientific_journal-2140	155	1	acting	act	VERB
american_scientific_journal-2140	155	2	on	on	ADP
american_scientific_journal-2140	155	3	𝑖𝑡ℎ	𝑖𝑡ℎ	NOUN
american_scientific_journal-2140	155	4	component	component	NOUN
american_scientific_journal-2140	155	5	of	of	ADP
american_scientific_journal-2140	155	6	the	the	DET
american_scientific_journal-2140	155	7	optical	optical	ADJ
american_scientific_journal-2140	155	8	system	system	NOUN
american_scientific_journal-2140	155	9	,	,	PUNCT
american_scientific_journal-2140	155	10	where	where	SCONJ
american_scientific_journal-2140	155	11	𝑖	𝑖	ADP
american_scientific_journal-2140	155	12	=	=	SYM
american_scientific_journal-2140	155	13	1	1	NUM
american_scientific_journal-2140	155	14	,	,	PUNCT
american_scientific_journal-2140	155	15	2	2	NUM
american_scientific_journal-2140	155	16	,	,	PUNCT
american_scientific_journal-2140	155	17	…	…	PUNCT
american_scientific_journal-2140	155	18	,	,	PUNCT
american_scientific_journal-2140	155	19	𝑘	𝑘	INTJ
american_scientific_journal-2140	155	20	.	.	PUNCT
american_scientific_journal-2140	156	1	furthermore	furthermore	ADV
american_scientific_journal-2140	156	2	,	,	PUNCT
american_scientific_journal-2140	156	3	considering	consider	VERB
american_scientific_journal-2140	156	4	the	the	DET
american_scientific_journal-2140	156	5	foregoing	foregoing	NOUN
american_scientific_journal-2140	156	6	𝑘	𝑘	ADP
american_scientific_journal-2140	156	7	constraining	constrain	VERB
american_scientific_journal-2140	156	8	optical	optical	ADJ
american_scientific_journal-2140	156	9	surfaces	surface	NOUN
american_scientific_journal-2140	156	10	acting	act	VERB
american_scientific_journal-2140	156	11	on	on	ADP
american_scientific_journal-2140	156	12	a	a	DET
american_scientific_journal-2140	156	13	finite	finite	ADJ
american_scientific_journal-2140	156	14	combination	combination	NOUN
american_scientific_journal-2140	156	15	of	of	ADP
american_scientific_journal-2140	156	16	𝑛	𝑛	DET
american_scientific_journal-2140	156	17	optical	optical	ADJ
american_scientific_journal-2140	156	18	components	component	NOUN
american_scientific_journal-2140	156	19	,	,	PUNCT
american_scientific_journal-2140	156	20	we	we	PRON
american_scientific_journal-2140	156	21	find	find	VERB
american_scientific_journal-2140	156	22	from	from	ADP
american_scientific_journal-2140	156	23	eqn	eqn	NOUN
american_scientific_journal-2140	156	24	.	.	PUNCT
american_scientific_journal-2140	157	1	(	(	PUNCT
american_scientific_journal-2140	157	2	24	24	NUM
american_scientific_journal-2140	157	3	)	)	PUNCT
american_scientific_journal-2140	157	4	that	that	SCONJ
american_scientific_journal-2140	157	5	the	the	DET
american_scientific_journal-2140	157	6	net	net	ADJ
american_scientific_journal-2140	157	7	objective	objective	ADJ
american_scientific_journal-2140	157	8	function	function	NOUN
american_scientific_journal-2140	157	9	extends	extend	VERB
american_scientific_journal-2140	157	10	as	as	ADP
american_scientific_journal-2140	157	11	per	per	ADP
american_scientific_journal-2140	157	12	the	the	DET
american_scientific_journal-2140	157	13	following	follow	VERB
american_scientific_journal-2140	157	14	expression	expression	NOUN
american_scientific_journal-2140	157	15	𝑓𝑛𝑒𝑡({𝑢𝑖	𝑓𝑛𝑒𝑡({𝑢𝑖	NOUN
american_scientific_journal-2140	157	16	,	,	PUNCT
american_scientific_journal-2140	157	17	𝑚𝑖	𝑚𝑖	NOUN
american_scientific_journal-2140	157	18	}	}	PUNCT
american_scientific_journal-2140	157	19	)	)	PUNCT
american_scientific_journal-2140	157	20	=	=	PUNCT
american_scientific_journal-2140	158	1	∑	∑	PUNCT
american_scientific_journal-2140	158	2	(	(	PUNCT
american_scientific_journal-2140	158	3	𝑢𝑖	𝑢𝑖	NOUN
american_scientific_journal-2140	158	4	𝑚𝑖	𝑚𝑖	ADP
american_scientific_journal-2140	158	5	1−	1−	NUM
american_scientific_journal-2140	158	6	𝑚𝑖	𝑚𝑖	X
american_scientific_journal-2140	158	7	+	+	CCONJ
american_scientific_journal-2140	158	8	∑	∑	PUNCT
american_scientific_journal-2140	158	9	𝜆𝑖𝑗	𝜆𝑖𝑗	NOUN
american_scientific_journal-2140	158	10	𝑐𝑖𝑗	𝑐𝑖𝑗	VERB
american_scientific_journal-2140	158	11	𝑘	𝑘	PRON
american_scientific_journal-2140	158	12	𝑗=1	𝑗=1	PROPN
american_scientific_journal-2140	158	13	)	)	PUNCT
american_scientific_journal-2140	158	14	𝑛	𝑛	PRON
american_scientific_journal-2140	158	15	𝑖=1	𝑖=1	PROPN
american_scientific_journal-2140	158	16	,	,	PUNCT
american_scientific_journal-2140	158	17	(	(	PUNCT
american_scientific_journal-2140	158	18	25	25	NUM
american_scientific_journal-2140	158	19	)	)	PUNCT
american_scientific_journal-2140	158	20	where	where	SCONJ
american_scientific_journal-2140	158	21	the	the	DET
american_scientific_journal-2140	158	22	first	first	ADJ
american_scientific_journal-2140	158	23	term	term	NOUN
american_scientific_journal-2140	158	24	in	in	ADP
american_scientific_journal-2140	158	25	the	the	DET
american_scientific_journal-2140	158	26	summation	summation	NOUN
american_scientific_journal-2140	158	27	denotes	denote	NOUN
american_scientific_journal-2140	158	28	𝑖𝑡ℎ	𝑖𝑡ℎ	VERB
american_scientific_journal-2140	158	29	objective	objective	ADJ
american_scientific_journal-2140	158	30	function	function	NOUN
american_scientific_journal-2140	158	31	of	of	ADP
american_scientific_journal-2140	158	32	the	the	DET
american_scientific_journal-2140	158	33	free	free	ADJ
american_scientific_journal-2140	158	34	optical	optical	ADJ
american_scientific_journal-2140	158	35	component	component	NOUN
american_scientific_journal-2140	158	36	.	.	PUNCT
american_scientific_journal-2140	159	1	the	the	DET
american_scientific_journal-2140	159	2	second	second	ADJ
american_scientific_journal-2140	159	3	term	term	NOUN
american_scientific_journal-2140	159	4	sums	sum	NOUN
american_scientific_journal-2140	159	5	over	over	ADP
american_scientific_journal-2140	159	6	the	the	DET
american_scientific_journal-2140	159	7	respective	respective	ADJ
american_scientific_journal-2140	159	8	constraints	constraint	NOUN
american_scientific_journal-2140	159	9	given	give	VERB
american_scientific_journal-2140	159	10	by	by	ADP
american_scientific_journal-2140	159	11	the	the	DET
american_scientific_journal-2140	159	12	constraining	constrain	VERB
american_scientific_journal-2140	159	13	hypersurfaces	hypersurface	NOUN
american_scientific_journal-2140	159	14	𝑐𝑖𝑗({𝑢𝑖	𝑐𝑖𝑗({𝑢𝑖	NOUN
american_scientific_journal-2140	159	15	,	,	PUNCT
american_scientific_journal-2140	159	16	𝑚𝑖	𝑚𝑖	NOUN
american_scientific_journal-2140	159	17	}	}	PUNCT
american_scientific_journal-2140	159	18	)	)	PUNCT
american_scientific_journal-2140	159	19	=	=	SYM
american_scientific_journal-2140	160	1	0	0	NUM
american_scientific_journal-2140	160	2	,	,	PUNCT
american_scientific_journal-2140	160	3	where	where	SCONJ
american_scientific_journal-2140	160	4	we	we	PRON
american_scientific_journal-2140	160	5	have	have	VERB
american_scientific_journal-2140	160	6	𝑗	𝑗	NOUN
american_scientific_journal-2140	160	7	=	=	SYM
american_scientific_journal-2140	160	8	1	1	NUM
american_scientific_journal-2140	160	9	,	,	PUNCT
american_scientific_journal-2140	160	10	2	2	NUM
american_scientific_journal-2140	160	11	,	,	PUNCT
american_scientific_journal-2140	160	12	…	…	PUNCT
american_scientific_journal-2140	160	13	,	,	PUNCT
american_scientific_journal-2140	160	14	𝑘	𝑘	X
american_scientific_journal-2140	160	15	for	for	ADP
american_scientific_journal-2140	160	16	each	each	DET
american_scientific_journal-2140	160	17	component	component	NOUN
american_scientific_journal-2140	160	18	𝑖	𝑖	NOUN
american_scientific_journal-2140	160	19	=	=	SYM
american_scientific_journal-2140	160	20	1	1	NUM
american_scientific_journal-2140	160	21	,	,	PUNCT
american_scientific_journal-2140	160	22	2	2	NUM
american_scientific_journal-2140	160	23	,	,	PUNCT
american_scientific_journal-2140	160	24	…	…	PUNCT
american_scientific_journal-2140	160	25	,	,	PUNCT
american_scientific_journal-2140	160	26	𝑛	𝑛	PROPN
american_scientific_journal-2140	160	27	of	of	ADP
american_scientific_journal-2140	160	28	the	the	DET
american_scientific_journal-2140	160	29	optical	optical	ADJ
american_scientific_journal-2140	160	30	system	system	NOUN
american_scientific_journal-2140	160	31	.	.	PUNCT
american_scientific_journal-2140	161	1	herewith	herewith	NOUN
american_scientific_journal-2140	161	2	,	,	PUNCT
american_scientific_journal-2140	161	3	an	an	DET
american_scientific_journal-2140	161	4	optimization	optimization	NOUN
american_scientific_journal-2140	161	5	involving	involve	VERB
american_scientific_journal-2140	161	6	𝑘	𝑘	DET
american_scientific_journal-2140	161	7	number	number	NOUN
american_scientific_journal-2140	161	8	of	of	ADP
american_scientific_journal-2140	161	9	constraints	constraint	NOUN
american_scientific_journal-2140	161	10	to	to	ADP
american_scientific_journal-2140	161	11	the	the	DET
american_scientific_journal-2140	161	12	net	net	ADJ
american_scientific_journal-2140	161	13	objective	objective	ADJ
american_scientific_journal-2140	161	14	function	function	NOUN
american_scientific_journal-2140	161	15	𝑓𝑛𝑒𝑡({𝑢𝑖	𝑓𝑛𝑒𝑡({𝑢𝑖	NOUN
american_scientific_journal-2140	161	16	,	,	PUNCT
american_scientific_journal-2140	161	17	𝑚𝑖	𝑚𝑖	NOUN
american_scientific_journal-2140	161	18	}	}	PUNCT
american_scientific_journal-2140	161	19	)	)	PUNCT
american_scientific_journal-2140	161	20	as	as	ADP
american_scientific_journal-2140	161	21	in	in	ADP
american_scientific_journal-2140	161	22	eqn	eqn	NOUN
american_scientific_journal-2140	161	23	.	.	PUNCT
american_scientific_journal-2140	162	1	(	(	PUNCT
american_scientific_journal-2140	162	2	25	25	NUM
american_scientific_journal-2140	162	3	)	)	PUNCT
american_scientific_journal-2140	162	4	of	of	ADP
american_scientific_journal-2140	162	5	the	the	DET
american_scientific_journal-2140	162	6	combined	combine	VERB
american_scientific_journal-2140	162	7	optical	optical	ADJ
american_scientific_journal-2140	162	8	system	system	NOUN
american_scientific_journal-2140	162	9	is	be	AUX
american_scientific_journal-2140	162	10	anticipated	anticipate	VERB
american_scientific_journal-2140	162	11	to	to	PART
american_scientific_journal-2140	162	12	offer	offer	VERB
american_scientific_journal-2140	162	13	potential	potential	ADJ
american_scientific_journal-2140	162	14	industrial	industrial	ADJ
american_scientific_journal-2140	162	15	applications	application	NOUN
american_scientific_journal-2140	162	16	.	.	PUNCT
american_scientific_journal-2140	163	1	it	it	PRON
american_scientific_journal-2140	163	2	is	be	AUX
american_scientific_journal-2140	163	3	worth	worth	ADJ
american_scientific_journal-2140	163	4	remarking	remark	VERB
american_scientific_journal-2140	163	5	that	that	SCONJ
american_scientific_journal-2140	163	6	nonlinear	nonlinear	ADJ
american_scientific_journal-2140	163	7	extensions	extension	NOUN
american_scientific_journal-2140	163	8	of	of	ADP
american_scientific_journal-2140	163	9	an	an	DET
american_scientific_journal-2140	163	10	optical	optical	ADJ
american_scientific_journal-2140	163	11	system	system	NOUN
american_scientific_journal-2140	163	12	with	with	ADP
american_scientific_journal-2140	163	13	the	the	DET
american_scientific_journal-2140	163	14	constraining	constrain	VERB
american_scientific_journal-2140	163	15	hypersurfaces	hypersurface	NOUN
american_scientific_journal-2140	163	16	𝑐𝑖𝑗({𝑢𝑖	𝑐𝑖𝑗({𝑢𝑖	NOUN
american_scientific_journal-2140	163	17	,	,	PUNCT
american_scientific_journal-2140	163	18	𝑚𝑖	𝑚𝑖	NOUN
american_scientific_journal-2140	163	19	}	}	PUNCT
american_scientific_journal-2140	163	20	)	)	PUNCT
american_scientific_journal-2140	163	21	=	=	SYM
american_scientific_journal-2140	163	22	0	0	NUM
american_scientific_journal-2140	163	23	involve	involve	VERB
american_scientific_journal-2140	163	24	an	an	DET
american_scientific_journal-2140	163	25	optimization	optimization	NOUN
american_scientific_journal-2140	163	26	of	of	ADP
american_scientific_journal-2140	163	27	the	the	DET
american_scientific_journal-2140	163	28	net	net	ADJ
american_scientific_journal-2140	163	29	objective	objective	ADJ
american_scientific_journal-2140	163	30	function	function	NOUN
american_scientific_journal-2140	163	31	𝑓𝑛𝑒𝑡({𝑢𝑖	𝑓𝑛𝑒𝑡({𝑢𝑖	NOUN
american_scientific_journal-2140	163	32	,	,	PUNCT
american_scientific_journal-2140	163	33	𝑚𝑖	𝑚𝑖	NOUN
american_scientific_journal-2140	163	34	}	}	PUNCT
american_scientific_journal-2140	163	35	)	)	PUNCT
american_scientific_journal-2140	163	36	as	as	SCONJ
american_scientific_journal-2140	163	37	mentioned	mention	VERB
american_scientific_journal-2140	163	38	in	in	ADP
american_scientific_journal-2140	163	39	eqn	eqn	NOUN
american_scientific_journal-2140	163	40	.	.	PUNCT
american_scientific_journal-2140	164	1	(	(	PUNCT
american_scientific_journal-2140	164	2	25	25	NUM
american_scientific_journal-2140	164	3	)	)	PUNCT
american_scientific_journal-2140	164	4	in	in	ADP
american_scientific_journal-2140	164	5	order	order	NOUN
american_scientific_journal-2140	164	6	to	to	PART
american_scientific_journal-2140	164	7	form	form	VERB
american_scientific_journal-2140	164	8	a	a	DET
american_scientific_journal-2140	164	9	fine	fine	ADV
american_scientific_journal-2140	164	10	-	-	PUNCT
american_scientific_journal-2140	164	11	tuned	tune	VERB
american_scientific_journal-2140	164	12	image	image	NOUN
american_scientific_journal-2140	164	13	.	.	PUNCT
american_scientific_journal-2140	165	1	in	in	ADP
american_scientific_journal-2140	165	2	general	general	ADJ
american_scientific_journal-2140	165	3	,	,	PUNCT
american_scientific_journal-2140	165	4	such	such	DET
american_scientific_journal-2140	165	5	an	an	DET
american_scientific_journal-2140	165	6	optical	optical	ADJ
american_scientific_journal-2140	165	7	optimization	optimization	NOUN
american_scientific_journal-2140	165	8	may	may	AUX
american_scientific_journal-2140	165	9	have	have	VERB
american_scientific_journal-2140	165	10	different	different	ADJ
american_scientific_journal-2140	165	11	conclusions	conclusion	NOUN
american_scientific_journal-2140	165	12	than	than	ADP
american_scientific_journal-2140	165	13	its	its	PRON
american_scientific_journal-2140	165	14	unconstraint	unconstraint	ADJ
american_scientific_journal-2140	165	15	counterpart	counterpart	NOUN
american_scientific_journal-2140	165	16	as	as	SCONJ
american_scientific_journal-2140	165	17	outlined	outline	VERB
american_scientific_journal-2140	165	18	in	in	ADP
american_scientific_journal-2140	165	19	the	the	DET
american_scientific_journal-2140	165	20	foregoing	forego	VERB
american_scientific_journal-2140	165	21	sections	section	NOUN
american_scientific_journal-2140	165	22	(	(	PUNCT
american_scientific_journal-2140	165	23	2	2	NUM
american_scientific_journal-2140	165	24	,	,	PUNCT
american_scientific_journal-2140	165	25	3	3	NUM
american_scientific_journal-2140	165	26	)	)	PUNCT
american_scientific_journal-2140	165	27	.	.	PUNCT
american_scientific_journal-2140	166	1	hereby	hereby	ADV
american_scientific_journal-2140	166	2	,	,	PUNCT
american_scientific_journal-2140	166	3	we	we	PRON
american_scientific_journal-2140	166	4	find	find	VERB
american_scientific_journal-2140	166	5	that	that	SCONJ
american_scientific_journal-2140	166	6	similar	similar	ADJ
american_scientific_journal-2140	166	7	conclusions	conclusion	NOUN
american_scientific_journal-2140	166	8	hold	hold	VERB
american_scientific_journal-2140	166	9	for	for	ADP
american_scientific_journal-2140	166	10	both	both	CCONJ
american_scientific_journal-2140	166	11	the	the	DET
american_scientific_journal-2140	166	12	constantly	constantly	ADV
american_scientific_journal-2140	166	13	and	and	CCONJ
american_scientific_journal-2140	166	14	linearly	linearly	ADV
american_scientific_journal-2140	166	15	constraint	constraint	VERB
american_scientific_journal-2140	166	16	optical	optical	ADJ
american_scientific_journal-2140	166	17	systems	system	NOUN
american_scientific_journal-2140	166	18	as	as	ADP
american_scientific_journal-2140	166	19	an	an	DET
american_scientific_journal-2140	166	20	extension	extension	NOUN
american_scientific_journal-2140	166	21	of	of	ADP
american_scientific_journal-2140	166	22	the	the	DET
american_scientific_journal-2140	166	23	associated	associate	VERB
american_scientific_journal-2140	166	24	unconstrained	unconstrained	ADJ
american_scientific_journal-2140	166	25	system	system	NOUN
american_scientific_journal-2140	166	26	,	,	PUNCT
american_scientific_journal-2140	166	27	except	except	SCONJ
american_scientific_journal-2140	166	28	the	the	DET
american_scientific_journal-2140	166	29	fact	fact	NOUN
american_scientific_journal-2140	166	30	that	that	SCONJ
american_scientific_journal-2140	166	31	there	there	PRON
american_scientific_journal-2140	166	32	may	may	AUX
american_scientific_journal-2140	166	33	exist	exist	VERB
american_scientific_journal-2140	166	34	shifts	shift	NOUN
american_scientific_journal-2140	166	35	in	in	ADP
american_scientific_journal-2140	166	36	the	the	DET
american_scientific_journal-2140	166	37	fixed	fix	VERB
american_scientific_journal-2140	166	38	points	point	NOUN
american_scientific_journal-2140	166	39	for	for	ADP
american_scientific_journal-2140	166	40	the	the	DET
american_scientific_journal-2140	166	41	linearly	linearly	ADV
american_scientific_journal-2140	166	42	constrained	constrain	VERB
american_scientific_journal-2140	166	43	case	case	NOUN
american_scientific_journal-2140	166	44	.	.	PUNCT
american_scientific_journal-2140	167	1	beyond	beyond	ADP
american_scientific_journal-2140	167	2	the	the	DET
american_scientific_journal-2140	167	3	linear	linear	PROPN
american_scientific_journal-2140	167	4	approximation	approximation	NOUN
american_scientific_journal-2140	167	5	,	,	PUNCT
american_scientific_journal-2140	167	6	it	it	PRON
american_scientific_journal-2140	167	7	is	be	AUX
american_scientific_journal-2140	167	8	worth	worth	ADJ
american_scientific_journal-2140	167	9	mentioning	mention	VERB
american_scientific_journal-2140	167	10	that	that	SCONJ
american_scientific_journal-2140	167	11	the	the	DET
american_scientific_journal-2140	167	12	stability	stability	NOUN
american_scientific_journal-2140	167	13	analysis	analysis	NOUN
american_scientific_journal-2140	167	14	of	of	ADP
american_scientific_journal-2140	167	15	a	a	DET
american_scientific_journal-2140	167	16	constrained	constrain	VERB
american_scientific_journal-2140	167	17	optical	optical	ADJ
american_scientific_journal-2140	167	18	system	system	NOUN
american_scientific_journal-2140	167	19	with	with	ADP
american_scientific_journal-2140	167	20	finitely	finitely	ADV
american_scientific_journal-2140	167	21	many	many	ADJ
american_scientific_journal-2140	167	22	components	component	NOUN
american_scientific_journal-2140	167	23	could	could	AUX
american_scientific_journal-2140	167	24	depend	depend	VERB
american_scientific_journal-2140	167	25	in	in	ADP
american_scientific_journal-2140	167	26	principle	principle	NOUN
american_scientific_journal-2140	167	27	upon	upon	SCONJ
american_scientific_journal-2140	167	28	the	the	DET
american_scientific_journal-2140	167	29	nature	nature	NOUN
american_scientific_journal-2140	167	30	of	of	ADP
american_scientific_journal-2140	167	31	constraints	constraint	NOUN
american_scientific_journal-2140	167	32	concerning	concern	VERB
american_scientific_journal-2140	167	33	the	the	DET
american_scientific_journal-2140	167	34	experimental	experimental	ADJ
american_scientific_journal-2140	167	35	setup	setup	NOUN
american_scientific_journal-2140	167	36	,	,	PUNCT
american_scientific_journal-2140	167	37	as	as	ADV
american_scientific_journal-2140	167	38	well	well	ADV
american_scientific_journal-2140	167	39	.	.	PUNCT
american_scientific_journal-2140	168	1	such	such	ADJ
american_scientific_journal-2140	168	2	nonlinear	nonlinear	ADJ
american_scientific_journal-2140	168	3	extensions	extension	NOUN
american_scientific_journal-2140	168	4	are	be	AUX
american_scientific_journal-2140	168	5	the	the	DET
american_scientific_journal-2140	168	6	subject	subject	ADJ
american_scientific_journal-2140	168	7	matter	matter	NOUN
american_scientific_journal-2140	168	8	of	of	ADP
american_scientific_journal-2140	168	9	our	our	PRON
american_scientific_journal-2140	168	10	current	current	ADJ
american_scientific_journal-2140	168	11	research	research	NOUN
american_scientific_journal-2140	168	12	.	.	PUNCT
american_scientific_journal-2140	169	1	5	5	X
american_scientific_journal-2140	169	2	.	.	X
american_scientific_journal-2140	169	3	discussion	discussion	NOUN
american_scientific_journal-2140	169	4	and	and	CCONJ
american_scientific_journal-2140	169	5	conclusion	conclusion	NOUN
american_scientific_journal-2140	169	6	geometrical	geometrical	ADJ
american_scientific_journal-2140	169	7	optics	optic	NOUN
american_scientific_journal-2140	169	8	plays	play	VERB
american_scientific_journal-2140	169	9	a	a	DET
american_scientific_journal-2140	169	10	vital	vital	ADJ
american_scientific_journal-2140	169	11	role	role	NOUN
american_scientific_journal-2140	169	12	in	in	ADP
american_scientific_journal-2140	169	13	understanding	understand	VERB
american_scientific_journal-2140	169	14	image	image	NOUN
american_scientific_journal-2140	169	15	formation	formation	NOUN
american_scientific_journal-2140	169	16	via	via	ADP
american_scientific_journal-2140	169	17	optical	optical	ADJ
american_scientific_journal-2140	169	18	instruments	instrument	NOUN
american_scientific_journal-2140	169	19	,	,	PUNCT
american_scientific_journal-2140	169	20	viz	viz	PROPN
american_scientific_journal-2140	169	21	.	.	PUNCT
american_scientific_journal-2140	170	1	lenses	lense	NOUN
american_scientific_journal-2140	170	2	,	,	PUNCT
american_scientific_journal-2140	170	3	mirrors	mirror	NOUN
american_scientific_journal-2140	170	4	and	and	CCONJ
american_scientific_journal-2140	170	5	their	their	PRON
american_scientific_journal-2140	170	6	arbitrary	arbitrary	ADJ
american_scientific_journal-2140	170	7	combinations	combination	NOUN
american_scientific_journal-2140	170	8	.	.	PUNCT
american_scientific_journal-2140	171	1	an	an	DET
american_scientific_journal-2140	171	2	optimal	optimal	ADJ
american_scientific_journal-2140	171	3	optical	optical	ADJ
american_scientific_journal-2140	171	4	designing	designing	NOUN
american_scientific_journal-2140	171	5	is	be	AUX
american_scientific_journal-2140	171	6	likewise	likewise	ADV
american_scientific_journal-2140	171	7	reinforced	reinforce	VERB
american_scientific_journal-2140	171	8	under	under	ADP
american_scientific_journal-2140	171	9	motion	motion	NOUN
american_scientific_journal-2140	171	10	of	of	ADP
american_scientific_journal-2140	171	11	the	the	DET
american_scientific_journal-2140	171	12	object	object	NOUN
american_scientific_journal-2140	171	13	and	and	CCONJ
american_scientific_journal-2140	171	14	variations	variation	NOUN
american_scientific_journal-2140	171	15	over	over	ADP
american_scientific_journal-2140	171	16	the	the	DET
american_scientific_journal-2140	171	17	lateral	lateral	ADJ
american_scientific_journal-2140	171	18	magnification	magnification	NOUN
american_scientific_journal-2140	171	19	of	of	ADP
american_scientific_journal-2140	171	20	the	the	DET
american_scientific_journal-2140	171	21	instrument	instrument	NOUN
american_scientific_journal-2140	171	22	.	.	PUNCT
american_scientific_journal-2140	172	1	further	far	ADV
american_scientific_journal-2140	172	2	,	,	PUNCT
american_scientific_journal-2140	172	3	we	we	PRON
american_scientific_journal-2140	172	4	discuss	discuss	VERB
american_scientific_journal-2140	172	5	possible	possible	ADJ
american_scientific_journal-2140	172	6	extensions	extension	NOUN
american_scientific_journal-2140	172	7	with	with	ADP
american_scientific_journal-2140	172	8	nonlinear	nonlinear	ADJ
american_scientific_journal-2140	172	9	constraints	constraint	NOUN
american_scientific_journal-2140	172	10	by	by	ADP
american_scientific_journal-2140	172	11	invoking	invoke	VERB
american_scientific_journal-2140	172	12	extended	extended	ADJ
american_scientific_journal-2140	172	13	optical	optical	ADJ
american_scientific_journal-2140	172	14	optimization	optimization	NOUN
american_scientific_journal-2140	172	15	functions	function	NOUN
american_scientific_journal-2140	172	16	,	,	PUNCT
american_scientific_journal-2140	172	17	as	as	ADV
american_scientific_journal-2140	172	18	well	well	ADV
american_scientific_journal-2140	172	19	.	.	PUNCT
american_scientific_journal-2140	173	1	having	having	AUX
american_scientific_journal-2140	173	2	discussed	discuss	VERB
american_scientific_journal-2140	173	3	the	the	DET
american_scientific_journal-2140	173	4	construction	construction	NOUN
american_scientific_journal-2140	173	5	of	of	ADP
american_scientific_journal-2140	173	6	optical	optical	ADJ
american_scientific_journal-2140	173	7	objective	objective	ADJ
american_scientific_journal-2140	173	8	functions	function	NOUN
american_scientific_journal-2140	173	9	,	,	PUNCT
american_scientific_journal-2140	173	10	we	we	PRON
american_scientific_journal-2140	173	11	concentrate	concentrate	VERB
american_scientific_journal-2140	173	12	towards	towards	ADP
american_scientific_journal-2140	173	13	its	its	PRON
american_scientific_journal-2140	173	14	role	role	NOUN
american_scientific_journal-2140	173	15	in	in	ADP
american_scientific_journal-2140	173	16	optoengineering	optoengineering	NOUN
american_scientific_journal-2140	173	17	and	and	CCONJ
american_scientific_journal-2140	173	18	instrument	instrument	NOUN
american_scientific_journal-2140	173	19	designing	designing	NOUN
american_scientific_journal-2140	173	20	.	.	PUNCT
american_scientific_journal-2140	174	1	in	in	ADP
american_scientific_journal-2140	174	2	this	this	DET
american_scientific_journal-2140	174	3	concern	concern	NOUN
american_scientific_journal-2140	174	4	,	,	PUNCT
american_scientific_journal-2140	174	5	we	we	PRON
american_scientific_journal-2140	174	6	focus	focus	VERB
american_scientific_journal-2140	174	7	on	on	ADP
american_scientific_journal-2140	174	8	the	the	DET
american_scientific_journal-2140	174	9	stability	stability	NOUN
american_scientific_journal-2140	174	10	and	and	CCONJ
american_scientific_journal-2140	174	11	correlation	correlation	NOUN
american_scientific_journal-2140	174	12	analysis	analysis	NOUN
american_scientific_journal-2140	174	13	of	of	ADP
american_scientific_journal-2140	174	14	the	the	DET
american_scientific_journal-2140	174	15	image	image	NOUN
american_scientific_journal-2140	174	16	of	of	ADP
american_scientific_journal-2140	174	17	a	a	DET
american_scientific_journal-2140	174	18	dynamical	dynamical	ADJ
american_scientific_journal-2140	174	19	object	object	NOUN
american_scientific_journal-2140	174	20	formed	form	VERB
american_scientific_journal-2140	174	21	by	by	ADP
american_scientific_journal-2140	174	22	an	an	DET
american_scientific_journal-2140	174	23	optical	optical	ADJ
american_scientific_journal-2140	174	24	instrument	instrument	NOUN
american_scientific_journal-2140	174	25	,	,	PUNCT
american_scientific_journal-2140	174	26	viz	viz	PROPN
american_scientific_journal-2140	174	27	.	.	PUNCT
american_scientific_journal-2140	174	28	lens	lens	PROPN
american_scientific_journal-2140	174	29	and/	and/	PROPN
american_scientific_journal-2140	174	30	or	or	CCONJ
american_scientific_journal-2140	174	31	mirror	mirror	NOUN
american_scientific_journal-2140	174	32	.	.	PUNCT
american_scientific_journal-2140	175	1	from	from	ADP
american_scientific_journal-2140	175	2	the	the	DET
american_scientific_journal-2140	175	3	perspective	perspective	NOUN
american_scientific_journal-2140	175	4	of	of	ADP
american_scientific_journal-2140	175	5	the	the	DET
american_scientific_journal-2140	175	6	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	175	7	theory	theory	NOUN
american_scientific_journal-2140	175	8	,	,	PUNCT
american_scientific_journal-2140	175	9	we	we	PRON
american_scientific_journal-2140	175	10	concentrate	concentrate	VERB
american_scientific_journal-2140	175	11	on	on	ADP
american_scientific_journal-2140	175	12	the	the	DET
american_scientific_journal-2140	175	13	optimal	optimal	ADJ
american_scientific_journal-2140	175	14	designing	designing	NOUN
american_scientific_journal-2140	175	15	of	of	ADP
american_scientific_journal-2140	175	16	optical	optical	ADJ
american_scientific_journal-2140	175	17	systems	system	NOUN
american_scientific_journal-2140	175	18	at	at	ADP
american_scientific_journal-2140	175	19	a	a	DET
american_scientific_journal-2140	175	20	given	give	VERB
american_scientific_journal-2140	175	21	lateral	lateral	ADJ
american_scientific_journal-2140	175	22	magnification	magnification	NOUN
american_scientific_journal-2140	175	23	and	and	CCONJ
american_scientific_journal-2140	175	24	object	object	VERB
american_scientific_journal-2140	175	25	distance	distance	NOUN
american_scientific_journal-2140	175	26	.	.	PUNCT
american_scientific_journal-2140	176	1	in	in	ADP
american_scientific_journal-2140	176	2	the	the	DET
american_scientific_journal-2140	176	3	sequel	sequel	NOUN
american_scientific_journal-2140	176	4	,	,	PUNCT
american_scientific_journal-2140	176	5	we	we	PRON
american_scientific_journal-2140	176	6	prolong	prolong	VERB
american_scientific_journal-2140	176	7	our	our	PRON
american_scientific_journal-2140	176	8	analysis	analysis	NOUN
american_scientific_journal-2140	176	9	towards	towards	ADP
american_scientific_journal-2140	176	10	stable	stable	ADJ
american_scientific_journal-2140	176	11	image	image	NOUN
american_scientific_journal-2140	176	12	formation	formation	NOUN
american_scientific_journal-2140	176	13	by	by	ADP
american_scientific_journal-2140	176	14	an	an	DET
american_scientific_journal-2140	176	15	optical	optical	ADJ
american_scientific_journal-2140	176	16	system	system	NOUN
american_scientific_journal-2140	176	17	having	have	VERB
american_scientific_journal-2140	176	18	finitely	finitely	ADV
american_scientific_journal-2140	176	19	many	many	ADJ
american_scientific_journal-2140	176	20	components	component	NOUN
american_scientific_journal-2140	176	21	,	,	PUNCT
american_scientific_journal-2140	176	22	in	in	ADP
american_scientific_journal-2140	176	23	the	the	DET
american_scientific_journal-2140	176	24	light	light	NOUN
american_scientific_journal-2140	176	25	of	of	ADP
american_scientific_journal-2140	176	26	the	the	DET
american_scientific_journal-2140	176	27	constrained	constrain	VERB
american_scientific_journal-2140	176	28	lagrangian	lagrangian	ADJ
american_scientific_journal-2140	176	29	systems	system	NOUN
american_scientific_journal-2140	176	30	.	.	PUNCT
american_scientific_journal-2140	177	1	herewith	herewith	PROPN
american_scientific_journal-2140	177	2	,	,	PUNCT
american_scientific_journal-2140	177	3	in	in	ADP
american_scientific_journal-2140	177	4	the	the	DET
american_scientific_journal-2140	177	5	thin	thin	ADJ
american_scientific_journal-2140	177	6	approximation	approximation	NOUN
american_scientific_journal-2140	177	7	of	of	ADP
american_scientific_journal-2140	177	8	components	component	NOUN
american_scientific_journal-2140	177	9	undermining	undermine	VERB
american_scientific_journal-2140	177	10	the	the	DET
american_scientific_journal-2140	177	11	optical	optical	ADJ
american_scientific_journal-2140	177	12	instrument	instrument	NOUN
american_scientific_journal-2140	177	13	,	,	PUNCT
american_scientific_journal-2140	177	14	we	we	PRON
american_scientific_journal-2140	177	15	characterize	characterize	VERB
american_scientific_journal-2140	177	16	the	the	DET
american_scientific_journal-2140	177	17	objective	objective	ADJ
american_scientific_journal-2140	177	18	function	function	NOUN
american_scientific_journal-2140	177	19	of	of	ADP
american_scientific_journal-2140	177	20	an	an	DET
american_scientific_journal-2140	177	21	arbitrary	arbitrary	ADJ
american_scientific_journal-2140	177	22	optical	optical	ADJ
american_scientific_journal-2140	177	23	system	system	NOUN
american_scientific_journal-2140	177	24	as	as	ADP
american_scientific_journal-2140	177	25	the	the	DET
american_scientific_journal-2140	177	26	net	net	ADJ
american_scientific_journal-2140	177	27	focal	focal	ADJ
american_scientific_journal-2140	177	28	length	length	NOUN
american_scientific_journal-2140	177	29	by	by	ADP
american_scientific_journal-2140	177	30	considering	consider	VERB
american_scientific_journal-2140	177	31	it	it	PRON
american_scientific_journal-2140	177	32	as	as	ADP
american_scientific_journal-2140	177	33	a	a	DET
american_scientific_journal-2140	177	34	function	function	NOUN
american_scientific_journal-2140	177	35	of	of	ADP
american_scientific_journal-2140	177	36	the	the	DET
american_scientific_journal-2140	177	37	optimization	optimization	NOUN
american_scientific_journal-2140	177	38	variables	variable	NOUN
american_scientific_journal-2140	177	39	,	,	PUNCT
american_scientific_journal-2140	177	40	viz	viz	PROPN
american_scientific_journal-2140	177	41	.	.	PUNCT
american_scientific_journal-2140	178	1	the	the	DET
american_scientific_journal-2140	178	2	object	object	NOUN
american_scientific_journal-2140	178	3	distance	distance	NOUN
american_scientific_journal-2140	178	4	,	,	PUNCT
american_scientific_journal-2140	178	5	lateral	lateral	ADJ
american_scientific_journal-2140	178	6	magnification	magnification	NOUN
american_scientific_journal-2140	178	7	and	and	CCONJ
american_scientific_journal-2140	178	8	others	other	NOUN
american_scientific_journal-2140	178	9	,	,	PUNCT
american_scientific_journal-2140	178	10	if	if	SCONJ
american_scientific_journal-2140	178	11	any	any	PRON
american_scientific_journal-2140	178	12	.	.	PUNCT
american_scientific_journal-2140	179	1	under	under	ADP
american_scientific_journal-2140	179	2	fluctuations	fluctuation	NOUN
american_scientific_journal-2140	179	3	of	of	ADP
american_scientific_journal-2140	179	4	the	the	DET
american_scientific_journal-2140	179	5	optimization	optimization	NOUN
american_scientific_journal-2140	179	6	variables	variable	NOUN
american_scientific_journal-2140	179	7	,	,	PUNCT
american_scientific_journal-2140	179	8	we	we	PRON
american_scientific_journal-2140	179	9	offer	offer	VERB
american_scientific_journal-2140	179	10	stability	stability	NOUN
american_scientific_journal-2140	179	11	and	and	CCONJ
american_scientific_journal-2140	179	12	correlation	correlation	NOUN
american_scientific_journal-2140	179	13	analysis	analysis	NOUN
american_scientific_journal-2140	179	14	towards	towards	ADP
american_scientific_journal-2140	179	15	an	an	DET
american_scientific_journal-2140	179	16	apt	apt	ADJ
american_scientific_journal-2140	179	17	optical	optical	ADJ
american_scientific_journal-2140	179	18	instrument	instrument	NOUN
american_scientific_journal-2140	179	19	designing	designing	NOUN
american_scientific_journal-2140	179	20	.	.	PUNCT
american_scientific_journal-2140	180	1	as	as	ADP
american_scientific_journal-2140	180	2	per	per	ADP
american_scientific_journal-2140	180	3	this	this	DET
american_scientific_journal-2140	180	4	consideration	consideration	NOUN
american_scientific_journal-2140	180	5	,	,	PUNCT
american_scientific_journal-2140	180	6	we	we	PRON
american_scientific_journal-2140	180	7	find	find	VERB
american_scientific_journal-2140	180	8	that	that	SCONJ
american_scientific_journal-2140	180	9	an	an	DET
american_scientific_journal-2140	180	10	image	image	NOUN
american_scientific_journal-2140	180	11	as	as	SCONJ
american_scientific_journal-2140	180	12	formed	form	VERB
american_scientific_journal-2140	180	13	by	by	ADP
american_scientific_journal-2140	180	14	the	the	DET
american_scientific_journal-2140	180	15	concave	concave	PROPN
american_scientific_journal-2140	180	16	and	and	CCONJ
american_scientific_journal-2140	180	17	convex	convex	VERB
american_scientific_journal-2140	180	18	lens/	lens/	NUM
american_scientific_journal-2140	180	19	mirror	mirror	NOUN
american_scientific_journal-2140	180	20	appears	appear	VERB
american_scientific_journal-2140	180	21	disjoint	disjoint	NOUN
american_scientific_journal-2140	180	22	,	,	PUNCT
american_scientific_journal-2140	180	23	whose	whose	DET
american_scientific_journal-2140	180	24	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	180	25	surfaces	surface	NOUN
american_scientific_journal-2140	180	26	are	be	AUX
american_scientific_journal-2140	180	27	separated	separate	VERB
american_scientific_journal-2140	180	28	by	by	ADP
american_scientific_journal-2140	180	29	the	the	DET
american_scientific_journal-2140	180	30	line	line	NOUN
american_scientific_journal-2140	180	31	of	of	ADP
american_scientific_journal-2140	180	32	the	the	DET
american_scientific_journal-2140	180	33	unit	unit	NOUN
american_scientific_journal-2140	180	34	lateral	lateral	ADJ
american_scientific_journal-2140	180	35	magnification	magnification	NOUN
american_scientific_journal-2140	180	36	.	.	PUNCT
american_scientific_journal-2140	181	1	by	by	ADP
american_scientific_journal-2140	181	2	american	american	ADJ
american_scientific_journal-2140	181	3	scientific	scientific	PROPN
american_scientific_journal-2140	181	4	research	research	PROPN
american_scientific_journal-2140	181	5	journal	journal	NOUN
american_scientific_journal-2140	181	6	for	for	ADP
american_scientific_journal-2140	181	7	engineering	engineering	NOUN
american_scientific_journal-2140	181	8	,	,	PUNCT
american_scientific_journal-2140	181	9	technology	technology	NOUN
american_scientific_journal-2140	181	10	,	,	PUNCT
american_scientific_journal-2140	181	11	and	and	CCONJ
american_scientific_journal-2140	181	12	sciences	science	NOUN
american_scientific_journal-2140	181	13	(	(	PUNCT
american_scientific_journal-2140	181	14	asrjets	asrjet	NOUN
american_scientific_journal-2140	181	15	)	)	PUNCT
american_scientific_journal-2140	181	16	(	(	PUNCT
american_scientific_journal-2140	181	17	2016	2016	NUM
american_scientific_journal-2140	181	18	)	)	PUNCT
american_scientific_journal-2140	181	19	volume	volume	NOUN
american_scientific_journal-2140	181	20	26	26	NUM
american_scientific_journal-2140	181	21	,	,	PUNCT
american_scientific_journal-2140	181	22	no	no	DET
american_scientific_journal-2140	181	23	1	1	NUM
american_scientific_journal-2140	181	24	,	,	PUNCT
american_scientific_journal-2140	181	25	pp	pp	ADV
american_scientific_journal-2140	181	26	302	302	NUM
american_scientific_journal-2140	181	27	-	-	SYM
american_scientific_journal-2140	181	28	313	313	NUM
american_scientific_journal-2140	181	29	312	312	NUM
american_scientific_journal-2140	181	30	invoking	invoke	VERB
american_scientific_journal-2140	181	31	multivariable	multivariable	ADJ
american_scientific_journal-2140	181	32	calculus	calculus	NOUN
american_scientific_journal-2140	181	33	based	base	VERB
american_scientific_journal-2140	181	34	saddle	saddle	NOUN
american_scientific_journal-2140	181	35	point	point	NOUN
american_scientific_journal-2140	181	36	analysis	analysis	NOUN
american_scientific_journal-2140	181	37	,	,	PUNCT
american_scientific_journal-2140	181	38	the	the	DET
american_scientific_journal-2140	181	39	local	local	ADJ
american_scientific_journal-2140	181	40	stability	stability	NOUN
american_scientific_journal-2140	181	41	is	be	AUX
american_scientific_journal-2140	181	42	characterized	characterize	VERB
american_scientific_journal-2140	181	43	by	by	ADP
american_scientific_journal-2140	181	44	the	the	DET
american_scientific_journal-2140	181	45	positivity	positivity	NOUN
american_scientific_journal-2140	181	46	of	of	ADP
american_scientific_journal-2140	181	47	the	the	DET
american_scientific_journal-2140	181	48	pure	pure	ADJ
american_scientific_journal-2140	181	49	components	component	NOUN
american_scientific_journal-2140	181	50	of	of	ADP
american_scientific_journal-2140	181	51	the	the	DET
american_scientific_journal-2140	181	52	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	181	53	matrix	matrix	NOUN
american_scientific_journal-2140	181	54	of	of	ADP
american_scientific_journal-2140	181	55	the	the	DET
american_scientific_journal-2140	181	56	optical	optical	ADJ
american_scientific_journal-2140	181	57	optimization	optimization	NOUN
american_scientific_journal-2140	181	58	function	function	NOUN
american_scientific_journal-2140	181	59	,	,	PUNCT
american_scientific_journal-2140	181	60	whilst	whilst	SCONJ
american_scientific_journal-2140	181	61	the	the	DET
american_scientific_journal-2140	181	62	global	global	ADJ
american_scientific_journal-2140	181	63	stability	stability	NOUN
american_scientific_journal-2140	181	64	as	as	ADP
american_scientific_journal-2140	181	65	the	the	DET
american_scientific_journal-2140	181	66	positivity	positivity	NOUN
american_scientific_journal-2140	181	67	of	of	ADP
american_scientific_journal-2140	181	68	the	the	DET
american_scientific_journal-2140	181	69	product	product	NOUN
american_scientific_journal-2140	181	70	of	of	ADP
american_scientific_journal-2140	181	71	its	its	PRON
american_scientific_journal-2140	181	72	eigenvalues	eigenvalue	NOUN
american_scientific_journal-2140	181	73	.	.	PUNCT
american_scientific_journal-2140	182	1	it	it	PRON
american_scientific_journal-2140	182	2	is	be	AUX
american_scientific_journal-2140	182	3	worth	worth	ADJ
american_scientific_journal-2140	182	4	mentioning	mention	VERB
american_scientific_journal-2140	182	5	that	that	SCONJ
american_scientific_journal-2140	182	6	the	the	DET
american_scientific_journal-2140	182	7	corresponding	corresponding	ADJ
american_scientific_journal-2140	182	8	eigenvectors	eigenvector	NOUN
american_scientific_journal-2140	182	9	qualify	qualify	VERB
american_scientific_journal-2140	182	10	optimal	optimal	ADJ
american_scientific_journal-2140	182	11	zooming	zooming	NOUN
american_scientific_journal-2140	182	12	in	in	ADP
american_scientific_journal-2140	182	13	the	the	DET
american_scientific_journal-2140	182	14	space	space	NOUN
american_scientific_journal-2140	182	15	of	of	ADP
american_scientific_journal-2140	182	16	the	the	DET
american_scientific_journal-2140	182	17	optical	optical	ADJ
american_scientific_journal-2140	182	18	optimization	optimization	NOUN
american_scientific_journal-2140	182	19	variables	variable	NOUN
american_scientific_journal-2140	182	20	.	.	PUNCT
american_scientific_journal-2140	183	1	we	we	PRON
american_scientific_journal-2140	183	2	anticipate	anticipate	VERB
american_scientific_journal-2140	183	3	that	that	SCONJ
american_scientific_journal-2140	183	4	the	the	DET
american_scientific_journal-2140	183	5	outcomes	outcome	NOUN
american_scientific_journal-2140	183	6	emerging	emerge	VERB
american_scientific_journal-2140	183	7	from	from	ADP
american_scientific_journal-2140	183	8	an	an	DET
american_scientific_journal-2140	183	9	unconstraint	unconstraint	ADJ
american_scientific_journal-2140	183	10	optical	optical	ADJ
american_scientific_journal-2140	183	11	system	system	NOUN
american_scientific_journal-2140	183	12	hold	hold	VERB
american_scientific_journal-2140	183	13	in	in	ADP
american_scientific_journal-2140	183	14	extended	extended	ADJ
american_scientific_journal-2140	183	15	optimization	optimization	NOUN
american_scientific_journal-2140	183	16	settings	setting	NOUN
american_scientific_journal-2140	183	17	with	with	ADP
american_scientific_journal-2140	183	18	finitely	finitely	ADV
american_scientific_journal-2140	183	19	many	many	ADJ
american_scientific_journal-2140	183	20	specific	specific	ADJ
american_scientific_journal-2140	183	21	constraints	constraint	NOUN
american_scientific_journal-2140	183	22	,	,	PUNCT
american_scientific_journal-2140	183	23	as	as	ADV
american_scientific_journal-2140	183	24	well	well	ADV
american_scientific_journal-2140	183	25	.	.	PUNCT
american_scientific_journal-2140	184	1	in	in	ADP
american_scientific_journal-2140	184	2	this	this	DET
american_scientific_journal-2140	184	3	regard	regard	NOUN
american_scientific_journal-2140	184	4	,	,	PUNCT
american_scientific_journal-2140	184	5	we	we	PRON
american_scientific_journal-2140	184	6	find	find	VERB
american_scientific_journal-2140	184	7	that	that	SCONJ
american_scientific_journal-2140	184	8	a	a	DET
american_scientific_journal-2140	184	9	linearly	linearly	ADV
american_scientific_journal-2140	184	10	constraint	constraint	ADJ
american_scientific_journal-2140	184	11	optical	optical	ADJ
american_scientific_journal-2140	184	12	system	system	NOUN
american_scientific_journal-2140	184	13	has	have	VERB
american_scientific_journal-2140	184	14	the	the	DET
american_scientific_journal-2140	184	15	same	same	ADJ
american_scientific_journal-2140	184	16	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	184	17	qualifications	qualification	NOUN
american_scientific_journal-2140	184	18	as	as	ADP
american_scientific_journal-2140	184	19	that	that	PRON
american_scientific_journal-2140	184	20	of	of	ADP
american_scientific_journal-2140	184	21	the	the	DET
american_scientific_journal-2140	184	22	free	free	ADJ
american_scientific_journal-2140	184	23	system	system	NOUN
american_scientific_journal-2140	184	24	,	,	PUNCT
american_scientific_journal-2140	184	25	except	except	SCONJ
american_scientific_journal-2140	184	26	the	the	DET
american_scientific_journal-2140	184	27	fact	fact	NOUN
american_scientific_journal-2140	184	28	that	that	SCONJ
american_scientific_journal-2140	184	29	the	the	DET
american_scientific_journal-2140	184	30	corresponding	corresponding	ADJ
american_scientific_journal-2140	184	31	optical	optical	ADJ
american_scientific_journal-2140	184	32	extrema	extrema	NOUN
american_scientific_journal-2140	184	33	are	be	AUX
american_scientific_journal-2140	184	34	translated	translate	VERB
american_scientific_journal-2140	184	35	.	.	PUNCT
american_scientific_journal-2140	185	1	it	it	PRON
american_scientific_journal-2140	185	2	is	be	AUX
american_scientific_journal-2140	185	3	worth	worth	ADJ
american_scientific_journal-2140	185	4	anticipating	anticipate	VERB
american_scientific_journal-2140	185	5	that	that	SCONJ
american_scientific_journal-2140	185	6	constrained	constrain	VERB
american_scientific_journal-2140	185	7	optimizations	optimization	NOUN
american_scientific_journal-2140	185	8	of	of	ADP
american_scientific_journal-2140	185	9	nonlinear	nonlinear	ADJ
american_scientific_journal-2140	185	10	systems	system	NOUN
american_scientific_journal-2140	185	11	offer	offer	VERB
american_scientific_journal-2140	185	12	key	key	ADJ
american_scientific_journal-2140	185	13	industrial	industrial	ADJ
american_scientific_journal-2140	185	14	significances	significance	NOUN
american_scientific_journal-2140	185	15	towards	towards	ADP
american_scientific_journal-2140	185	16	the	the	DET
american_scientific_journal-2140	185	17	modern	modern	ADJ
american_scientific_journal-2140	185	18	optical	optical	ADJ
american_scientific_journal-2140	185	19	instrument	instrument	NOUN
american_scientific_journal-2140	185	20	designing	designing	NOUN
american_scientific_journal-2140	185	21	.	.	PUNCT
american_scientific_journal-2140	186	1	such	such	ADJ
american_scientific_journal-2140	186	2	innovations	innovation	NOUN
american_scientific_journal-2140	186	3	include	include	VERB
american_scientific_journal-2140	186	4	rearview	rearview	NOUN
american_scientific_journal-2140	186	5	mirrors	mirror	NOUN
american_scientific_journal-2140	186	6	[	[	X
american_scientific_journal-2140	186	7	13	13	NUM
american_scientific_journal-2140	186	8	]	]	PUNCT
american_scientific_journal-2140	186	9	,	,	PUNCT
american_scientific_journal-2140	186	10	small	small	ADJ
american_scientific_journal-2140	186	11	concave	concave	ADJ
american_scientific_journal-2140	186	12	metal	metal	NOUN
american_scientific_journal-2140	186	13	-	-	PUNCT
american_scientific_journal-2140	186	14	replica	replica	NOUN
american_scientific_journal-2140	186	15	mirrors	mirror	NOUN
american_scientific_journal-2140	187	1	[	[	X
american_scientific_journal-2140	187	2	14	14	NUM
american_scientific_journal-2140	187	3	]	]	PUNCT
american_scientific_journal-2140	187	4	and	and	CCONJ
american_scientific_journal-2140	187	5	small	small	ADJ
american_scientific_journal-2140	187	6	-	-	PUNCT
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american_scientific_journal-2140	187	9	scattering	scatter	VERB
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american_scientific_journal-2140	187	12	focusing	focus	VERB
american_scientific_journal-2140	187	13	cold	cold	ADJ
american_scientific_journal-2140	187	14	neutrons	neutron	NOUN
american_scientific_journal-2140	187	15	involving	involve	VERB
american_scientific_journal-2140	187	16	multiple	multiple	ADJ
american_scientific_journal-2140	187	17	biconcave	biconcave	ADJ
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american_scientific_journal-2140	187	22	.	.	PUNCT
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american_scientific_journal-2140	188	4	of	of	ADP
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american_scientific_journal-2140	188	10	we	we	PRON
american_scientific_journal-2140	188	11	leave	leave	VERB
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american_scientific_journal-2140	188	18	.	.	PUNCT
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american_scientific_journal-2140	189	2	the	the	DET
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american_scientific_journal-2140	189	4	would	would	AUX
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american_scientific_journal-2140	189	32	,	,	PUNCT
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american_scientific_journal-2140	189	42	.	.	PUNCT
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american_scientific_journal-2140	190	14	,	,	PUNCT
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american_scientific_journal-2140	190	18	,	,	PUNCT
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american_scientific_journal-2140	190	27	-	-	SYM
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american_scientific_journal-2140	190	31	.	.	PUNCT
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american_scientific_journal-2140	191	4	.	.	PUNCT
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american_scientific_journal-2140	192	3	,	,	PUNCT
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american_scientific_journal-2140	203	34	,	,	PUNCT
american_scientific_journal-2140	203	35	t.	t.	PROPN
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american_scientific_journal-2140	203	37	,	,	PUNCT
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american_scientific_journal-2140	203	39	laser	laser	NOUN
american_scientific_journal-2140	203	40	diode	diode	NOUN
american_scientific_journal-2140	203	41	to	to	ADP
american_scientific_journal-2140	203	42	single	single	ADJ
american_scientific_journal-2140	203	43	-	-	PUNCT
american_scientific_journal-2140	203	44	mode	mode	NOUN
american_scientific_journal-2140	203	45	fiber	fiber	NOUN
american_scientific_journal-2140	203	46	coupling	coupling	NOUN
american_scientific_journal-2140	203	47	using	use	VERB
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american_scientific_journal-2140	203	50	of	of	ADP
american_scientific_journal-2140	203	51	two	two	NUM
american_scientific_journal-2140	203	52	lenses	lense	NOUN
american_scientific_journal-2140	203	53	in	in	ADP
american_scientific_journal-2140	203	54	confocal	confocal	ADJ
american_scientific_journal-2140	203	55	condition	condition	NOUN
american_scientific_journal-2140	203	56	,	,	PUNCT
american_scientific_journal-2140	203	57	ieee	ieee	NOUN
american_scientific_journal-2140	203	58	journal	journal	NOUN
american_scientific_journal-2140	203	59	of	of	ADP
american_scientific_journal-2140	203	60	quantum	quantum	ADJ
american_scientific_journal-2140	203	61	electronics	electronic	NOUN
american_scientific_journal-2140	203	62	,	,	PUNCT
american_scientific_journal-2140	203	63	17	17	NUM
american_scientific_journal-2140	203	64	(	(	PUNCT
american_scientific_journal-2140	203	65	6	6	NUM
american_scientific_journal-2140	203	66	)	)	PUNCT
american_scientific_journal-2140	203	67	,	,	PUNCT
american_scientific_journal-2140	203	68	1021	1021	NUM
american_scientific_journal-2140	203	69	1027	1027	NUM
american_scientific_journal-2140	203	70	,	,	PUNCT
american_scientific_journal-2140	203	71	1981	1981	NUM
american_scientific_journal-2140	203	72	.	.	PUNCT
american_scientific_journal-2140	204	1	[	[	X
american_scientific_journal-2140	204	2	9	9	NUM
american_scientific_journal-2140	204	3	]	]	PUNCT
american_scientific_journal-2140	204	4	f.	f.	PROPN
american_scientific_journal-2140	204	5	m.	m.	PROPN
american_scientific_journal-2140	204	6	goldberg	goldberg	PROPN
american_scientific_journal-2140	204	7	,	,	PUNCT
american_scientific_journal-2140	204	8	l.	l.	PROPN
american_scientific_journal-2140	204	9	c.	c.	PROPN
american_scientific_journal-2140	204	10	mcdermott	mcdermott	PROPN
american_scientific_journal-2140	204	11	,	,	PUNCT
american_scientific_journal-2140	204	12	an	an	DET
american_scientific_journal-2140	204	13	investigation	investigation	NOUN
american_scientific_journal-2140	204	14	of	of	ADP
american_scientific_journal-2140	204	15	student	student	NOUN
american_scientific_journal-2140	204	16	understanding	understanding	NOUN
american_scientific_journal-2140	204	17	of	of	ADP
american_scientific_journal-2140	204	18	the	the	DET
american_scientific_journal-2140	204	19	real	real	ADJ
american_scientific_journal-2140	204	20	image	image	NOUN
american_scientific_journal-2140	204	21	formed	form	VERB
american_scientific_journal-2140	204	22	by	by	ADP
american_scientific_journal-2140	204	23	converging	converge	VERB
american_scientific_journal-2140	204	24	lens	len	NOUN
american_scientific_journal-2140	204	25	or	or	CCONJ
american_scientific_journal-2140	204	26	concave	concave	NOUN
american_scientific_journal-2140	204	27	mirror	mirror	NOUN
american_scientific_journal-2140	204	28	,	,	PUNCT
american_scientific_journal-2140	204	29	am	be	AUX
american_scientific_journal-2140	204	30	.	.	PUNCT
american_scientific_journal-2140	205	1	j.	j.	PROPN
american_scientific_journal-2140	205	2	phys	phys	PROPN
american_scientific_journal-2140	205	3	,	,	PUNCT
american_scientific_journal-2140	205	4	55	55	NUM
american_scientific_journal-2140	205	5	(	(	PUNCT
american_scientific_journal-2140	205	6	2	2	NUM
american_scientific_journal-2140	205	7	)	)	PUNCT
american_scientific_journal-2140	205	8	,	,	PUNCT
american_scientific_journal-2140	205	9	108	108	NUM
american_scientific_journal-2140	205	10	-	-	SYM
american_scientific_journal-2140	205	11	119	119	NUM
american_scientific_journal-2140	205	12	,	,	PUNCT
american_scientific_journal-2140	205	13	1987	1987	NUM
american_scientific_journal-2140	205	14	.	.	PUNCT
american_scientific_journal-2140	206	1	[	[	X
american_scientific_journal-2140	206	2	10	10	NUM
american_scientific_journal-2140	206	3	]	]	SYM
american_scientific_journal-2140	206	4	s.-m	s.-m	NOUN
american_scientific_journal-2140	206	5	.	.	PUNCT
american_scientific_journal-2140	207	1	choi	choi	PROPN
american_scientific_journal-2140	207	2	,	,	PUNCT
american_scientific_journal-2140	207	3	j.	j.	PROPN
american_scientific_journal-2140	207	4	g.	g.	PROPN
american_scientific_journal-2140	207	5	barker	barker	PROPN
american_scientific_journal-2140	207	6	,	,	PUNCT
american_scientific_journal-2140	207	7	c.	c.	PROPN
american_scientific_journal-2140	207	8	j.	j.	PROPN
american_scientific_journal-2140	207	9	glinka	glinka	PROPN
american_scientific_journal-2140	207	10	,	,	PUNCT
american_scientific_journal-2140	207	11	y.	y.	PROPN
american_scientific_journal-2140	207	12	t.	t.	PROPN
american_scientific_journal-2140	207	13	cheng	cheng	PROPN
american_scientific_journal-2140	207	14	,	,	PUNCT
american_scientific_journal-2140	207	15	p.	p.	PROPN
american_scientific_journal-2140	207	16	l.	l.	PROPN
american_scientific_journal-2140	207	17	gammel	gammel	PROPN
american_scientific_journal-2140	207	18	,	,	PUNCT
american_scientific_journal-2140	207	19	focusing	focus	VERB
american_scientific_journal-2140	207	20	cold	cold	ADJ
american_scientific_journal-2140	207	21	neutrons	neutron	NOUN
american_scientific_journal-2140	207	22	with	with	ADP
american_scientific_journal-2140	207	23	multiple	multiple	ADJ
american_scientific_journal-2140	207	24	biconcave	biconcave	ADJ
american_scientific_journal-2140	207	25	lenses	lense	NOUN
american_scientific_journal-2140	207	26	for	for	ADP
american_scientific_journal-2140	207	27	small	small	ADJ
american_scientific_journal-2140	207	28	-	-	PUNCT
american_scientific_journal-2140	207	29	angle	angle	NOUN
american_scientific_journal-2140	207	30	neutron	neutron	NOUN
american_scientific_journal-2140	207	31	scattering	scattering	NOUN
american_scientific_journal-2140	207	32	,	,	PUNCT
american_scientific_journal-2140	207	33	j.	j.	PROPN
american_scientific_journal-2140	207	34	appl	appl	PROPN
american_scientific_journal-2140	207	35	.	.	PROPN
american_scientific_journal-2140	208	1	cryst	cryst	PROPN
american_scientific_journal-2140	208	2	,	,	PUNCT
american_scientific_journal-2140	208	3	33	33	NUM
american_scientific_journal-2140	208	4	,	,	PUNCT
american_scientific_journal-2140	208	5	793	793	NUM
american_scientific_journal-2140	208	6	-	-	SYM
american_scientific_journal-2140	208	7	796	796	NUM
american_scientific_journal-2140	208	8	,	,	PUNCT
american_scientific_journal-2140	208	9	2000	2000	NUM
american_scientific_journal-2140	208	10	.	.	PUNCT
american_scientific_journal-2140	209	1	[	[	X
american_scientific_journal-2140	209	2	11	11	NUM
american_scientific_journal-2140	209	3	]	]	X
american_scientific_journal-2140	209	4	g.	g.	PROPN
american_scientific_journal-2140	209	5	ruppeiner	ruppeiner	PROPN
american_scientific_journal-2140	209	6	,	,	PUNCT
american_scientific_journal-2140	209	7	riemannian	riemannian	ADJ
american_scientific_journal-2140	209	8	geometry	geometry	NOUN
american_scientific_journal-2140	209	9	in	in	ADP
american_scientific_journal-2140	209	10	thermodynamics	thermodynamic	NOUN
american_scientific_journal-2140	209	11	fluctuation	fluctuation	NOUN
american_scientific_journal-2140	209	12	theory	theory	NOUN
american_scientific_journal-2140	209	13	,	,	PUNCT
american_scientific_journal-2140	209	14	rev	rev	PROPN
american_scientific_journal-2140	209	15	.	.	PROPN
american_scientific_journal-2140	209	16	mod	mod	PROPN
american_scientific_journal-2140	209	17	.	.	PUNCT
american_scientific_journal-2140	210	1	phys	phy	NOUN
american_scientific_journal-2140	210	2	,	,	PUNCT
american_scientific_journal-2140	210	3	67	67	NUM
american_scientific_journal-2140	210	4	,	,	PUNCT
american_scientific_journal-2140	210	5	(	(	PUNCT
american_scientific_journal-2140	210	6	1995	1995	NUM
american_scientific_journal-2140	210	7	)	)	PUNCT
american_scientific_journal-2140	210	8	605	605	NUM
american_scientific_journal-2140	210	9	,	,	PUNCT
american_scientific_journal-2140	210	10	[	[	X
american_scientific_journal-2140	210	11	erratum	erratum	PROPN
american_scientific_journal-2140	210	12	68	68	NUM
american_scientific_journal-2140	210	13	,	,	PUNCT
american_scientific_journal-2140	210	14	(	(	PUNCT
american_scientific_journal-2140	210	15	1996	1996	NUM
american_scientific_journal-2140	210	16	)	)	PUNCT
american_scientific_journal-2140	210	17	313	313	NUM
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american_scientific_journal-2140	210	19	.	.	PUNCT
american_scientific_journal-2140	211	1	[	[	X
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american_scientific_journal-2140	211	3	]	]	PUNCT
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american_scientific_journal-2140	211	7	,	,	PUNCT
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american_scientific_journal-2140	211	13	:	:	PUNCT
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american_scientific_journal-2140	211	15	,	,	PUNCT
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american_scientific_journal-2140	211	19	,	,	PUNCT
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american_scientific_journal-2140	211	24	,	,	PUNCT
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american_scientific_journal-2140	211	26	:	:	PUNCT
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american_scientific_journal-2140	211	28	-	-	SYM
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american_scientific_journal-2140	211	30	,	,	PUNCT
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american_scientific_journal-2140	211	32	.	.	PUNCT
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american_scientific_journal-2140	212	17	-	-	PUNCT
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american_scientific_journal-2140	212	20	-	-	PUNCT
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american_scientific_journal-2140	212	28	,	,	PUNCT
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american_scientific_journal-2140	212	35	,	,	PUNCT
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american_scientific_journal-2140	212	40	,	,	PUNCT
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american_scientific_journal-2140	212	42	.	.	PUNCT
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american_scientific_journal-2140	213	28	,	,	PUNCT
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american_scientific_journal-2140	213	33	-	-	SYM
american_scientific_journal-2140	213	34	851	851	NUM
american_scientific_journal-2140	213	35	,	,	PUNCT
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american_scientific_journal-2140	213	37	.	.	PUNCT
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american_scientific_journal-2140	214	4	s.	s.	PROPN
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american_scientific_journal-2140	214	7	,	,	PUNCT
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american_scientific_journal-2140	214	33	-	-	PUNCT
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american_scientific_journal-2140	214	37	,	,	PUNCT
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american_scientific_journal-2140	215	2	,	,	PUNCT
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american_scientific_journal-2140	215	4	,	,	PUNCT
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american_scientific_journal-2140	215	6	-	-	SYM
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