id	sid	tid	token	lemma	pos
cana-4523	1	1	communications	communication	NOUN
cana-4523	1	2	on	on	ADP
cana-4523	1	3	applied	apply	VERB
cana-4523	1	4	nonlinear	nonlinear	ADJ
cana-4523	1	5	analysis	analysis	NOUN
cana-4523	1	6	issn	issn	NOUN
cana-4523	1	7	:	:	PUNCT
cana-4523	1	8	1074	1074	NUM
cana-4523	1	9	-	-	PUNCT
cana-4523	1	10	133x	133x	NUM
cana-4523	1	11	vol	vol	NOUN
cana-4523	1	12	32	32	NUM
cana-4523	1	13	no	no	NOUN
cana-4523	1	14	.	.	PUNCT
cana-4523	2	1	9s	9s	NUM
cana-4523	2	2	(	(	PUNCT
cana-4523	2	3	2025	2025	NUM
cana-4523	2	4	)	)	PUNCT
cana-4523	2	5	2359	2359	NUM
cana-4523	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	2	7	optimal	optimal	ADJ
cana-4523	2	8	replacement	replacement	NOUN
cana-4523	2	9	policies	policy	NOUN
cana-4523	2	10	for	for	ADP
cana-4523	2	11	a	a	DET
cana-4523	2	12	multistate	multistate	NOUN
cana-4523	2	13	degenerative	degenerative	ADJ
cana-4523	2	14	system	system	NOUN
cana-4523	2	15	using	use	VERB
cana-4523	2	16	partial	partial	ADJ
cana-4523	2	17	sum	sum	NOUN
cana-4523	2	18	process	process	NOUN
cana-4523	2	19	i.	i.	PROPN
cana-4523	2	20	ashwini	ashwini	PROPN
cana-4523	2	21	*	*	PROPN
cana-4523	2	22	,	,	PUNCT
cana-4523	2	23	syed	syed	ADJ
cana-4523	2	24	tahir	tahir	PROPN
cana-4523	2	25	hussainy	hussainy	PROPN
cana-4523	2	26	,	,	PUNCT
cana-4523	2	27	zahiruddeen	zahiruddeen	NUM
cana-4523	2	28	,	,	PUNCT
cana-4523	2	29	u.	u.	NOUN
cana-4523	2	30	rizwan†	rizwan†	NOUN
cana-4523	2	31	department	department	NOUN
cana-4523	2	32	of	of	ADP
cana-4523	2	33	mathematics	mathematic	NOUN
cana-4523	2	34	,	,	PUNCT
cana-4523	2	35	islamiah	islamiah	PROPN
cana-4523	2	36	college	college	NOUN
cana-4523	2	37	(	(	PUNCT
cana-4523	2	38	autonomous	autonomous	ADJ
cana-4523	2	39	)	)	PUNCT
cana-4523	2	40	,	,	PUNCT
cana-4523	2	41	vaniyambadi	vaniyambadi	NOUN
cana-4523	2	42	,	,	PUNCT
cana-4523	2	43	*	*	NOUN
cana-4523	2	44	research	research	NOUN
cana-4523	2	45	scholar	scholar	NOUN
cana-4523	2	46	,	,	PUNCT
cana-4523	2	47	thiruvalluvar	thiruvalluvar	NOUN
cana-4523	2	48	university	university	NOUN
cana-4523	2	49	,	,	PUNCT
cana-4523	2	50	serkadu	serkadu	NOUN
cana-4523	2	51	,	,	PUNCT
cana-4523	2	52	vellore-632115	vellore-632115	NOUN
cana-4523	2	53	.	.	PUNCT
cana-4523	3	1	†dr.u.rizwan@gmail.com	†dr.u.rizwan@gmail.com	X
cana-4523	3	2	article	article	NOUN
cana-4523	3	3	history	history	NOUN
cana-4523	3	4	:	:	PUNCT
cana-4523	3	5	received	receive	VERB
cana-4523	3	6	:	:	PUNCT
cana-4523	3	7	12	12	NUM
cana-4523	3	8	-	-	SYM
cana-4523	3	9	01	01	NUM
cana-4523	3	10	-	-	PUNCT
cana-4523	3	11	2025	2025	NUM
cana-4523	3	12	revised	revise	VERB
cana-4523	3	13	:	:	PUNCT
cana-4523	3	14	15	15	NUM
cana-4523	3	15	-	-	NUM
cana-4523	3	16	02	02	NUM
cana-4523	3	17	-	-	PUNCT
cana-4523	3	18	2025	2025	NUM
cana-4523	3	19	accepted	accept	VERB
cana-4523	3	20	:	:	PUNCT
cana-4523	3	21	01	01	NUM
cana-4523	3	22	-	-	SYM
cana-4523	3	23	03	03	NUM
cana-4523	3	24	-	-	PUNCT
cana-4523	3	25	2025	2025	NUM
cana-4523	3	26	abstract	abstract	NOUN
cana-4523	3	27	:	:	PUNCT
cana-4523	3	28	this	this	DET
cana-4523	3	29	paper	paper	NOUN
cana-4523	3	30	investigates	investigate	VERB
cana-4523	3	31	the	the	DET
cana-4523	3	32	maintenance	maintenance	NOUN
cana-4523	3	33	problem	problem	NOUN
cana-4523	3	34	of	of	ADP
cana-4523	3	35	a	a	DET
cana-4523	3	36	multistate	multistate	NOUN
cana-4523	3	37	degenerative	degenerative	ADJ
cana-4523	3	38	system	system	NOUN
cana-4523	3	39	with	with	ADP
cana-4523	3	40	k	k	X
cana-4523	3	41	-working	-worke	VERB
cana-4523	3	42	states	state	NOUN
cana-4523	3	43	and	and	CCONJ
cana-4523	3	44	l	l	NOUN
cana-4523	3	45	-failure	-failure	NOUN
cana-4523	3	46	states	state	NOUN
cana-4523	3	47	.	.	PUNCT
cana-4523	4	1	the	the	DET
cana-4523	4	2	long	long	ADV
cana-4523	4	3	-	-	PUNCT
cana-4523	4	4	run	run	VERB
cana-4523	4	5	average	average	ADJ
cana-4523	4	6	cost	cost	NOUN
cana-4523	4	7	for	for	ADP
cana-4523	4	8	a	a	DET
cana-4523	4	9	multistate	multistate	NOUN
cana-4523	4	10	degenerative	degenerative	ADJ
cana-4523	4	11	system	system	NOUN
cana-4523	4	12	under	under	ADP
cana-4523	4	13	univariate	univariate	ADJ
cana-4523	4	14	replacement	replacement	NOUN
cana-4523	4	15	policy	policy	NOUN
cana-4523	4	16	:	:	PUNCT
cana-4523	4	17	t	t	NOUN
cana-4523	4	18	-	-	PUNCT
cana-4523	4	19	policy	policy	NOUN
cana-4523	4	20	,	,	PUNCT
cana-4523	4	21	tpolicy	tpolicy	NOUN
cana-4523	4	22	with	with	ADP
cana-4523	4	23	nonn	nonn	PROPN
cana-4523	4	24	repair	repair	NOUN
cana-4523	4	25	times	time	NOUN
cana-4523	4	26	are	be	AUX
cana-4523	4	27	derived	derive	VERB
cana-4523	4	28	.	.	PUNCT
cana-4523	5	1	additionally	additionally	ADV
cana-4523	5	2	,	,	PUNCT
cana-4523	5	3	optimality	optimality	NOUN
cana-4523	5	4	conditions	condition	NOUN
cana-4523	5	5	are	be	AUX
cana-4523	5	6	established	establish	VERB
cana-4523	5	7	to	to	PART
cana-4523	5	8	guide	guide	VERB
cana-4523	5	9	the	the	DET
cana-4523	5	10	determination	determination	NOUN
cana-4523	5	11	of	of	ADP
cana-4523	5	12	cost	cost	NOUN
cana-4523	5	13	-	-	PUNCT
cana-4523	5	14	effective	effective	ADJ
cana-4523	5	15	replacement	replacement	NOUN
cana-4523	5	16	strategies	strategy	NOUN
cana-4523	5	17	.	.	PUNCT
cana-4523	6	1	keywords	keyword	NOUN
cana-4523	6	2	:	:	PUNCT
cana-4523	6	3	partial	partial	ADJ
cana-4523	6	4	sum	sum	NOUN
cana-4523	6	5	process	process	NOUN
cana-4523	6	6	(	(	PUNCT
cana-4523	6	7	psp	psp	NOUN
cana-4523	6	8	)	)	PUNCT
cana-4523	6	9	,	,	PUNCT
cana-4523	6	10	geometric	geometric	ADJ
cana-4523	6	11	process	process	NOUN
cana-4523	6	12	(	(	PUNCT
cana-4523	6	13	gp	gp	NOUN
cana-4523	6	14	)	)	PUNCT
cana-4523	6	15	,	,	PUNCT
cana-4523	6	16	renewal	renewal	NOUN
cana-4523	6	17	process	process	NOUN
cana-4523	6	18	,	,	PUNCT
cana-4523	6	19	optimal	optimal	ADJ
cana-4523	6	20	replacement	replacement	NOUN
cana-4523	6	21	policy	policy	NOUN
cana-4523	6	22	.	.	PUNCT
cana-4523	7	1	1	1	X
cana-4523	7	2	.	.	X
cana-4523	7	3	introduction	introduction	NOUN
cana-4523	7	4	degradation	degradation	NOUN
cana-4523	7	5	and	and	CCONJ
cana-4523	7	6	failure	failure	NOUN
cana-4523	7	7	are	be	AUX
cana-4523	7	8	inherent	inherent	ADJ
cana-4523	7	9	characteristics	characteristic	NOUN
cana-4523	7	10	of	of	ADP
cana-4523	7	11	many	many	ADJ
cana-4523	7	12	real	real	ADJ
cana-4523	7	13	-	-	PUNCT
cana-4523	7	14	world	world	NOUN
cana-4523	7	15	systems	system	NOUN
cana-4523	7	16	,	,	PUNCT
cana-4523	7	17	resulting	result	VERB
cana-4523	7	18	from	from	ADP
cana-4523	7	19	the	the	DET
cana-4523	7	20	cumulative	cumulative	ADJ
cana-4523	7	21	effects	effect	NOUN
cana-4523	7	22	of	of	ADP
cana-4523	7	23	aging	aging	NOUN
cana-4523	7	24	,	,	PUNCT
cana-4523	7	25	wear	wear	NOUN
cana-4523	7	26	,	,	PUNCT
cana-4523	7	27	and	and	CCONJ
cana-4523	7	28	environmental	environmental	ADJ
cana-4523	7	29	factors	factor	NOUN
cana-4523	7	30	.	.	PUNCT
cana-4523	8	1	this	this	DET
cana-4523	8	2	deterioration	deterioration	NOUN
cana-4523	8	3	manifests	manifest	VERB
cana-4523	8	4	as	as	ADP
cana-4523	8	5	decreasing	decrease	VERB
cana-4523	8	6	operating	operating	NOUN
cana-4523	8	7	times	time	NOUN
cana-4523	8	8	between	between	ADP
cana-4523	8	9	failures	failure	NOUN
cana-4523	8	10	and	and	CCONJ
cana-4523	8	11	increasing	increase	VERB
cana-4523	8	12	repair	repair	NOUN
cana-4523	8	13	times	time	NOUN
cana-4523	8	14	after	after	ADP
cana-4523	8	15	failures	failure	NOUN
cana-4523	8	16	.	.	PUNCT
cana-4523	9	1	the	the	DET
cana-4523	9	2	operating	operating	NOUN
cana-4523	9	3	times	time	NOUN
cana-4523	9	4	may	may	AUX
cana-4523	9	5	eventually	eventually	ADV
cana-4523	9	6	become	become	VERB
cana-4523	9	7	negligible	negligible	ADJ
cana-4523	9	8	,	,	PUNCT
cana-4523	9	9	while	while	SCONJ
cana-4523	9	10	the	the	DET
cana-4523	9	11	repair	repair	NOUN
cana-4523	9	12	times	time	NOUN
cana-4523	9	13	may	may	AUX
cana-4523	9	14	tend	tend	VERB
cana-4523	9	15	towards	towards	ADP
cana-4523	9	16	infinity	infinity	NOUN
cana-4523	9	17	.	.	PUNCT
cana-4523	10	1	to	to	PART
cana-4523	10	2	capture	capture	VERB
cana-4523	10	3	this	this	DET
cana-4523	10	4	phenomenon	phenomenon	NOUN
cana-4523	10	5	,	,	PUNCT
cana-4523	10	6	lam	lam	PROPN
cana-4523	10	7	(	(	PUNCT
cana-4523	10	8	1988	1988	NUM
cana-4523	10	9	)	)	PUNCT
cana-4523	10	10	introduced	introduce	VERB
cana-4523	10	11	the	the	DET
cana-4523	10	12	geometric	geometric	ADJ
cana-4523	10	13	process	process	NOUN
cana-4523	10	14	(	(	PUNCT
cana-4523	10	15	gp	gp	NOUN
cana-4523	10	16	)	)	PUNCT
cana-4523	10	17	repair	repair	NOUN
cana-4523	10	18	model	model	NOUN
cana-4523	10	19	,	,	PUNCT
cana-4523	10	20	which	which	PRON
cana-4523	10	21	provides	provide	VERB
cana-4523	10	22	a	a	DET
cana-4523	10	23	mathematical	mathematical	ADJ
cana-4523	10	24	framework	framework	NOUN
cana-4523	10	25	for	for	ADP
cana-4523	10	26	analyzing	analyze	VERB
cana-4523	10	27	and	and	CCONJ
cana-4523	10	28	predicting	predict	VERB
cana-4523	10	29	the	the	DET
cana-4523	10	30	behaviour	behaviour	NOUN
cana-4523	10	31	of	of	ADP
cana-4523	10	32	deteriorating	deteriorate	VERB
cana-4523	10	33	systems	system	NOUN
cana-4523	10	34	.	.	PUNCT
cana-4523	11	1	in	in	ADP
cana-4523	11	2	engineering	engineering	NOUN
cana-4523	11	3	and	and	CCONJ
cana-4523	11	4	reliability	reliability	NOUN
cana-4523	11	5	applications	application	NOUN
cana-4523	11	6	,	,	PUNCT
cana-4523	11	7	system	system	NOUN
cana-4523	11	8	failures	failure	NOUN
cana-4523	11	9	can	can	AUX
cana-4523	11	10	be	be	AUX
cana-4523	11	11	categorized	categorize	VERB
cana-4523	11	12	based	base	VERB
cana-4523	11	13	on	on	ADP
cana-4523	11	14	their	their	PRON
cana-4523	11	15	severity	severity	NOUN
cana-4523	11	16	,	,	PUNCT
cana-4523	11	17	ranging	range	VERB
cana-4523	11	18	from	from	ADP
cana-4523	11	19	minor	minor	ADJ
cana-4523	11	20	,	,	PUNCT
cana-4523	11	21	correctable	correctable	ADJ
cana-4523	11	22	faults	fault	NOUN
cana-4523	11	23	to	to	ADP
cana-4523	11	24	catastrophic	catastrophic	ADJ
cana-4523	11	25	,	,	PUNCT
cana-4523	11	26	system	system	NOUN
cana-4523	11	27	-	-	PUNCT
cana-4523	11	28	critical	critical	ADJ
cana-4523	11	29	failures	failure	NOUN
cana-4523	11	30	.	.	PUNCT
cana-4523	12	1	furthermore	furthermore	ADV
cana-4523	12	2	,	,	PUNCT
cana-4523	12	3	systems	system	NOUN
cana-4523	12	4	often	often	ADV
cana-4523	12	5	exhibit	exhibit	VERB
cana-4523	12	6	multiple	multiple	ADJ
cana-4523	12	7	functional	functional	ADJ
cana-4523	12	8	states	state	NOUN
cana-4523	12	9	,	,	PUNCT
cana-4523	12	10	representing	represent	VERB
cana-4523	12	11	varying	vary	VERB
cana-4523	12	12	levels	level	NOUN
cana-4523	12	13	of	of	ADP
cana-4523	12	14	performance	performance	NOUN
cana-4523	12	15	,	,	PUNCT
cana-4523	12	16	capacity	capacity	NOUN
cana-4523	12	17	,	,	PUNCT
cana-4523	12	18	or	or	CCONJ
cana-4523	12	19	efficiency	efficiency	NOUN
cana-4523	12	20	.	.	PUNCT
cana-4523	13	1	conversely	conversely	ADV
cana-4523	13	2	,	,	PUNCT
cana-4523	13	3	systems	system	NOUN
cana-4523	13	4	can	can	AUX
cana-4523	13	5	also	also	ADV
cana-4523	13	6	exist	exist	VERB
cana-4523	13	7	in	in	ADP
cana-4523	13	8	multiple	multiple	ADJ
cana-4523	13	9	failed	fail	VERB
cana-4523	13	10	states	state	NOUN
cana-4523	13	11	,	,	PUNCT
cana-4523	13	12	characterized	characterize	VERB
cana-4523	13	13	by	by	ADP
cana-4523	13	14	distinct	distinct	ADJ
cana-4523	13	15	fault	fault	NOUN
cana-4523	13	16	modes	mode	NOUN
cana-4523	13	17	,	,	PUNCT
cana-4523	13	18	error	error	NOUN
cana-4523	13	19	conditions	condition	NOUN
cana-4523	13	20	,	,	PUNCT
cana-4523	13	21	or	or	CCONJ
cana-4523	13	22	failure	failure	NOUN
cana-4523	13	23	mechanisms	mechanism	NOUN
cana-4523	13	24	.	.	PUNCT
cana-4523	14	1	in	in	ADP
cana-4523	14	2	this	this	DET
cana-4523	14	3	paper	paper	NOUN
cana-4523	14	4	,	,	PUNCT
cana-4523	14	5	we	we	PRON
cana-4523	14	6	study	study	VERB
cana-4523	14	7	a	a	DET
cana-4523	14	8	monotone	monotone	ADJ
cana-4523	14	9	process	process	NOUN
cana-4523	14	10	model	model	NOUN
cana-4523	14	11	for	for	ADP
cana-4523	14	12	a	a	DET
cana-4523	14	13	one	one	NUM
cana-4523	14	14	-	-	PUNCT
cana-4523	14	15	component	component	NOUN
cana-4523	14	16	multistate	multistate	NOUN
cana-4523	14	17	system	system	NOUN
cana-4523	14	18	with	with	ADP
cana-4523	14	19	(	(	PUNCT
cana-4523	14	20	k	k	PROPN
cana-4523	14	21	+	+	NUM
cana-4523	14	22	l	l	NOUN
cana-4523	14	23	)	)	PUNCT
cana-4523	14	24	states	state	NOUN
cana-4523	14	25	,	,	PUNCT
cana-4523	14	26	namely	namely	ADV
cana-4523	14	27	k	k	ADV
cana-4523	14	28	-	-	ADJ
cana-4523	14	29	working	work	VERB
cana-4523	14	30	states	state	NOUN
cana-4523	14	31	and	and	CCONJ
cana-4523	14	32	l	l	NOUN
cana-4523	14	33	-	-	NOUN
cana-4523	14	34	failure	failure	NOUN
cana-4523	14	35	states	state	NOUN
cana-4523	14	36	.	.	PUNCT
cana-4523	15	1	by	by	ADP
cana-4523	15	2	making	make	VERB
cana-4523	15	3	different	different	ADJ
cana-4523	15	4	assumptions	assumption	NOUN
cana-4523	15	5	,	,	PUNCT
cana-4523	15	6	the	the	DET
cana-4523	15	7	model	model	NOUN
cana-4523	15	8	can	can	AUX
cana-4523	15	9	be	be	AUX
cana-4523	15	10	applied	apply	VERB
cana-4523	15	11	to	to	ADP
cana-4523	15	12	a	a	DET
cana-4523	15	13	multistate	multistate	NOUN
cana-4523	15	14	degenerative	degenerative	ADJ
cana-4523	15	15	system	system	NOUN
cana-4523	15	16	.	.	PUNCT
cana-4523	16	1	we	we	PRON
cana-4523	16	2	first	first	ADV
cana-4523	16	3	give	give	VERB
cana-4523	16	4	the	the	DET
cana-4523	16	5	definition	definition	NOUN
cana-4523	16	6	of	of	ADP
cana-4523	16	7	nonn	nonn	PROPN
cana-4523	16	8	repair	repair	PROPN
cana-4523	16	9	times	time	NOUN
cana-4523	16	10	.	.	PUNCT
cana-4523	17	1	definition	definition	NOUN
cana-4523	17	2	1.1	1.1	NUM
cana-4523	17	3	:	:	PUNCT
cana-4523	17	4	if	if	SCONJ
cana-4523	17	5	a	a	DET
cana-4523	17	6	repair	repair	NOUN
cana-4523	17	7	to	to	ADP
cana-4523	17	8	a	a	DET
cana-4523	17	9	system	system	NOUN
cana-4523	17	10	after	after	SCONJ
cana-4523	17	11	failure	failure	NOUN
cana-4523	17	12	is	be	AUX
cana-4523	17	13	done	do	VERB
cana-4523	17	14	in	in	ADP
cana-4523	17	15	negligible	negligible	ADJ
cana-4523	17	16	or	or	CCONJ
cana-4523	17	17	non	non	ADJ
cana-4523	17	18	-	-	ADJ
cana-4523	17	19	negligible	negligible	ADJ
cana-4523	17	20	time	time	NOUN
cana-4523	17	21	,	,	PUNCT
cana-4523	17	22	then	then	ADV
cana-4523	17	23	it	it	PRON
cana-4523	17	24	will	will	AUX
cana-4523	17	25	be	be	AUX
cana-4523	17	26	called	call	VERB
cana-4523	17	27	a	a	DET
cana-4523	17	28	model	model	NOUN
cana-4523	17	29	with	with	ADP
cana-4523	17	30	nonn	nonn	PROPN
cana-4523	17	31	repair	repair	PROPN
cana-4523	17	32	times	time	NOUN
cana-4523	17	33	.	.	PUNCT
cana-4523	18	1	upon	upon	SCONJ
cana-4523	18	2	system	system	NOUN
cana-4523	18	3	failure	failure	NOUN
cana-4523	18	4	,	,	PUNCT
cana-4523	18	5	two	two	NUM
cana-4523	18	6	repair	repair	NOUN
cana-4523	18	7	scenarios	scenario	NOUN
cana-4523	18	8	arise	arise	VERB
cana-4523	18	9	:	:	PUNCT
cana-4523	18	10	negligible	negligible	ADJ
cana-4523	18	11	repair	repair	NOUN
cana-4523	18	12	time	time	NOUN
cana-4523	18	13	with	with	ADP
cana-4523	18	14	probability	probability	NOUN
cana-4523	18	15	p	p	X
cana-4523	18	16	,	,	PUNCT
cana-4523	18	17	or	or	CCONJ
cana-4523	18	18	non	non	ADJ
cana-4523	18	19	-	-	ADJ
cana-4523	18	20	negligible	negligible	ADJ
cana-4523	18	21	repair	repair	NOUN
cana-4523	18	22	time	time	NOUN
cana-4523	18	23	with	with	ADP
cana-4523	18	24	probability	probability	NOUN
cana-4523	18	25	1	1	NUM
cana-4523	18	26	p.	p.	NOUN
cana-4523	18	27	this	this	DET
cana-4523	18	28	nonn	nonn	PROPN
cana-4523	18	29	repair	repair	PROPN
cana-4523	18	30	times	times	PROPN
cana-4523	18	31	model	model	NOUN
cana-4523	18	32	,	,	PUNCT
cana-4523	18	33	introduced	introduce	VERB
cana-4523	18	34	by	by	ADP
cana-4523	18	35	thangaraj	thangaraj	PROPN
cana-4523	18	36	and	and	CCONJ
cana-4523	18	37	rizwan	rizwan	PROPN
cana-4523	18	38	(	(	PUNCT
cana-4523	18	39	2001	2001	NUM
cana-4523	18	40	)	)	PUNCT
cana-4523	18	41	and	and	CCONJ
cana-4523	18	42	further	far	ADV
cana-4523	18	43	studied	study	VERB
cana-4523	18	44	by	by	ADP
cana-4523	18	45	govindaraju	govindaraju	NOUN
cana-4523	18	46	et	et	PROPN
cana-4523	18	47	al	al	PROPN
cana-4523	18	48	.	.	PROPN
cana-4523	19	1	(	(	PUNCT
cana-4523	19	2	2010	2010	NUM
cana-4523	19	3	)	)	PUNCT
cana-4523	19	4	,	,	PUNCT
cana-4523	19	5	accounts	account	VERB
cana-4523	19	6	for	for	ADP
cana-4523	19	7	uncertainty	uncertainty	NOUN
cana-4523	19	8	in	in	ADP
cana-4523	19	9	repair	repair	NOUN
cana-4523	19	10	durations	duration	NOUN
cana-4523	19	11	,	,	PUNCT
cana-4523	19	12	enhancing	enhance	VERB
cana-4523	19	13	maintenance	maintenance	NOUN
cana-4523	19	14	modelling	modelling	NOUN
cana-4523	19	15	accuracy	accuracy	NOUN
cana-4523	19	16	.	.	PUNCT
cana-4523	20	1	the	the	DET
cana-4523	20	2	rest	rest	NOUN
cana-4523	20	3	of	of	ADP
cana-4523	20	4	the	the	DET
cana-4523	20	5	chapter	chapter	NOUN
cana-4523	20	6	is	be	AUX
cana-4523	20	7	arranged	arrange	VERB
cana-4523	20	8	as	as	SCONJ
cana-4523	20	9	follows	follow	VERB
cana-4523	20	10	:	:	PUNCT
cana-4523	20	11	in	in	ADP
cana-4523	20	12	section	section	NOUN
cana-4523	20	13	2	2	NUM
cana-4523	20	14	,	,	PUNCT
cana-4523	20	15	explicit	explicit	ADJ
cana-4523	20	16	expression	expression	NOUN
cana-4523	20	17	for	for	ADP
cana-4523	20	18	the	the	DET
cana-4523	20	19	longrun	longrun	ADJ
cana-4523	20	20	average	average	ADJ
cana-4523	20	21	cost	cost	NOUN
cana-4523	20	22	of	of	ADP
cana-4523	20	23	the	the	DET
cana-4523	20	24	policy	policy	NOUN
cana-4523	20	25	t	t	NOUN
cana-4523	20	26	is	be	AUX
cana-4523	20	27	derived	derive	VERB
cana-4523	20	28	,	,	PUNCT
cana-4523	20	29	also	also	ADV
cana-4523	20	30	the	the	DET
cana-4523	20	31	conditions	condition	NOUN
cana-4523	20	32	for	for	ADP
cana-4523	20	33	the	the	DET
cana-4523	20	34	existence	existence	NOUN
cana-4523	20	35	of	of	ADP
cana-4523	20	36	univariate	univariate	ADJ
cana-4523	20	37	optimal	optimal	ADJ
cana-4523	20	38	replacement	replacement	NOUN
cana-4523	20	39	policy	policy	NOUN
cana-4523	20	40	t	t	PROPN
cana-4523	20	41	*	*	PUNCT
cana-4523	20	42	are	be	AUX
cana-4523	20	43	derived	derive	VERB
cana-4523	20	44	.	.	PUNCT
cana-4523	21	1	in	in	ADP
cana-4523	21	2	section	section	NOUN
cana-4523	21	3	3	3	NUM
cana-4523	21	4	,	,	PUNCT
cana-4523	21	5	using	use	VERB
cana-4523	21	6	an	an	DET
cana-4523	21	7	alternate	alternate	ADJ
cana-4523	21	8	repair	repair	NOUN
cana-4523	21	9	model	model	NOUN
cana-4523	21	10	,	,	PUNCT
cana-4523	21	11	we	we	PRON
cana-4523	21	12	derive	derive	VERB
cana-4523	21	13	an	an	DET
cana-4523	21	14	expression	expression	NOUN
cana-4523	21	15	for	for	ADP
cana-4523	21	16	the	the	DET
cana-4523	21	17	long	long	ADV
cana-4523	21	18	-	-	PUNCT
cana-4523	21	19	run	run	VERB
cana-4523	21	20	average	average	ADJ
cana-4523	21	21	cost	cost	NOUN
cana-4523	21	22	for	for	ADP
cana-4523	21	23	this	this	DET
cana-4523	21	24	model	model	NOUN
cana-4523	21	25	under	under	ADP
cana-4523	21	26	t	t	PROPN
cana-4523	21	27	-policy	-policy	PROPN
cana-4523	21	28	.	.	PUNCT
cana-4523	22	1	the	the	DET
cana-4523	22	2	communications	communication	NOUN
cana-4523	22	3	on	on	ADP
cana-4523	22	4	applied	apply	VERB
cana-4523	22	5	nonlinear	nonlinear	ADJ
cana-4523	22	6	analysis	analysis	NOUN
cana-4523	22	7	issn	issn	NOUN
cana-4523	22	8	:	:	PUNCT
cana-4523	22	9	1074	1074	NUM
cana-4523	22	10	-	-	PUNCT
cana-4523	22	11	133x	133x	NUM
cana-4523	22	12	vol	vol	NOUN
cana-4523	22	13	32	32	NUM
cana-4523	22	14	no	no	NOUN
cana-4523	22	15	.	.	PUNCT
cana-4523	23	1	9s	9s	NUM
cana-4523	23	2	(	(	PUNCT
cana-4523	23	3	2025	2025	NUM
cana-4523	23	4	)	)	PUNCT
cana-4523	23	5	2360	2360	NUM
cana-4523	24	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	24	2	necessary	necessary	ADJ
cana-4523	24	3	conditions	condition	NOUN
cana-4523	24	4	for	for	ADP
cana-4523	24	5	the	the	DET
cana-4523	24	6	existence	existence	NOUN
cana-4523	24	7	of	of	ADP
cana-4523	24	8	the	the	DET
cana-4523	24	9	optimal	optimal	ADJ
cana-4523	24	10	replacement	replacement	NOUN
cana-4523	24	11	policy	policy	NOUN
cana-4523	24	12	are	be	AUX
cana-4523	24	13	also	also	ADV
cana-4523	24	14	derived	derive	VERB
cana-4523	24	15	in	in	ADP
cana-4523	24	16	this	this	DET
cana-4523	24	17	section	section	NOUN
cana-4523	24	18	.	.	PUNCT
cana-4523	25	1	finally	finally	ADV
cana-4523	25	2	,	,	PUNCT
cana-4523	25	3	conclusion	conclusion	NOUN
cana-4523	25	4	is	be	AUX
cana-4523	25	5	given	give	VERB
cana-4523	25	6	section	section	NOUN
cana-4523	25	7	4	4	NUM
cana-4523	25	8	.	.	NOUN
cana-4523	25	9	2	2	NUM
cana-4523	25	10	.	.	X
cana-4523	26	1	the	the	DET
cana-4523	26	2	replacement	replacement	NOUN
cana-4523	26	3	policy	policy	NOUN
cana-4523	26	4	t	t	NOUN
cana-4523	26	5	this	this	DET
cana-4523	26	6	section	section	NOUN
cana-4523	26	7	examines	examine	VERB
cana-4523	26	8	a	a	DET
cana-4523	26	9	t	t	NOUN
cana-4523	26	10	-	-	PUNCT
cana-4523	26	11	policy	policy	NOUN
cana-4523	26	12	for	for	ADP
cana-4523	26	13	optimizing	optimize	VERB
cana-4523	26	14	replacement	replacement	NOUN
cana-4523	26	15	in	in	ADP
cana-4523	26	16	a	a	DET
cana-4523	26	17	multistate	multistate	NOUN
cana-4523	26	18	,	,	PUNCT
cana-4523	26	19	singlecomponent	singlecomponent	NOUN
cana-4523	26	20	deteriorating	deteriorate	VERB
cana-4523	26	21	system	system	NOUN
cana-4523	26	22	.	.	PUNCT
cana-4523	27	1	the	the	DET
cana-4523	27	2	objective	objective	NOUN
cana-4523	27	3	is	be	AUX
cana-4523	27	4	to	to	PART
cana-4523	27	5	identify	identify	VERB
cana-4523	27	6	the	the	DET
cana-4523	27	7	optimal	optimal	ADJ
cana-4523	27	8	replacement	replacement	NOUN
cana-4523	27	9	policy	policy	NOUN
cana-4523	27	10	,	,	PUNCT
cana-4523	27	11	denoted	denote	VERB
cana-4523	27	12	as	as	ADP
cana-4523	27	13	t	t	PROPN
cana-4523	27	14	*	*	NUM
cana-4523	27	15	,	,	PUNCT
cana-4523	27	16	minimizes	minimize	VERB
cana-4523	27	17	the	the	DET
cana-4523	27	18	long	long	ADV
cana-4523	27	19	-	-	PUNCT
cana-4523	27	20	run	run	VERB
cana-4523	27	21	average	average	ADJ
cana-4523	27	22	cost	cost	NOUN
cana-4523	27	23	per	per	ADP
cana-4523	27	24	unit	unit	NOUN
cana-4523	27	25	time	time	NOUN
cana-4523	27	26	.	.	PUNCT
cana-4523	28	1	consider	consider	VERB
cana-4523	28	2	a	a	DET
cana-4523	28	3	single	single	ADJ
cana-4523	28	4	-	-	PUNCT
cana-4523	28	5	component	component	NOUN
cana-4523	28	6	multistate	multistate	NOUN
cana-4523	28	7	system	system	NOUN
cana-4523	28	8	comprising	comprising	NOUN
cana-4523	28	9	(	(	PUNCT
cana-4523	28	10	k	k	PROPN
cana-4523	28	11	+	+	CCONJ
cana-4523	28	12	l	l	NOUN
cana-4523	28	13	)	)	PUNCT
cana-4523	28	14	distinct	distinct	ADJ
cana-4523	28	15	states	state	NOUN
cana-4523	28	16	,	,	PUNCT
cana-4523	28	17	where	where	SCONJ
cana-4523	28	18	k	k	PROPN
cana-4523	28	19	represents	represent	VERB
cana-4523	28	20	functional	functional	ADJ
cana-4523	28	21	working	work	VERB
cana-4523	28	22	states	state	NOUN
cana-4523	28	23	and	and	CCONJ
cana-4523	28	24	l	l	NOUN
cana-4523	28	25	denotes	denote	NOUN
cana-4523	28	26	failure	failure	NOUN
cana-4523	28	27	states	state	NOUN
cana-4523	28	28	.	.	PUNCT
cana-4523	29	1	definition	definition	NOUN
cana-4523	29	2	2.1	2.1	NUM
cana-4523	29	3	:	:	PUNCT
cana-4523	29	4	let	let	VERB
cana-4523	29	5			PROPN
cana-4523	29	6			PROPN
cana-4523	29	7	,	,	PUNCT
cana-4523	29	8	1,2,3,=nx	1,2,3,=nx	PRON
cana-4523	29	9	n	n	PRON
cana-4523	29	10	be	be	AUX
cana-4523	29	11	a	a	DET
cana-4523	29	12	sequence	sequence	NOUN
cana-4523	29	13	of	of	ADP
cana-4523	29	14	independent	independent	ADJ
cana-4523	29	15	non	non	ADJ
cana-4523	29	16	negative	negative	ADJ
cana-4523	29	17	random	random	ADJ
cana-4523	29	18	variables	variable	NOUN
cana-4523	29	19	and	and	CCONJ
cana-4523	29	20	let	let	VERB
cana-4523	29	21	(	(	PUNCT
cana-4523	29	22	)	)	PUNCT
cana-4523	29	23	f	f	X
cana-4523	29	24	x	x	AUX
cana-4523	29	25	be	be	AUX
cana-4523	29	26	the	the	DET
cana-4523	29	27	distribution	distribution	NOUN
cana-4523	29	28	of	of	ADP
cana-4523	29	29	1.x	1.x	NUM
cana-4523	29	30	then	then	ADV
cana-4523	29	31			PROPN
cana-4523	29	32			PROPN
cana-4523	29	33	,	,	PUNCT
cana-4523	29	34	1,2,3,=nx	1,2,3,=nx	NUM
cana-4523	29	35	n	n	PART
cana-4523	29	36	is	be	AUX
cana-4523	29	37	called	call	VERB
cana-4523	29	38	partial	partial	ADJ
cana-4523	29	39	sum	sum	NOUN
cana-4523	29	40	process	process	NOUN
cana-4523	29	41	,	,	PUNCT
cana-4523	29	42	if	if	SCONJ
cana-4523	29	43	the	the	DET
cana-4523	29	44	distribution	distribution	NOUN
cana-4523	29	45	of	of	ADP
cana-4523	29	46	1ix	1ix	NOUN
cana-4523	29	47	+	+	X
cana-4523	29	48	is	be	AUX
cana-4523	29	49	(	(	PUNCT
cana-4523	29	50	)	)	PUNCT
cana-4523	29	51	(	(	PUNCT
cana-4523	29	52	)	)	PUNCT
cana-4523	29	53	1,2,3	1,2,3	NUM
cana-4523	29	54	,	,	PUNCT
cana-4523	29	55	,	,	PUNCT
cana-4523	29	56			PROPN
cana-4523	29	57	=	=	NOUN
cana-4523	29	58	if	if	SCONJ
cana-4523	29	59	x	x	X
cana-4523	29	60	i	i	PRON
cana-4523	29	61	where	where	SCONJ
cana-4523	29	62	i	i	X
cana-4523	29	63	>	>	SYM
cana-4523	29	64	0	0	NUM
cana-4523	29	65	are	be	AUX
cana-4523	29	66	constants	constant	NOUN
cana-4523	29	67	with	with	ADP
cana-4523	29	68	0	0	NUM
cana-4523	29	69	1	1	NUM
cana-4523	29	70	2	2	NUM
cana-4523	29	71	1i	1i	NOUN
cana-4523	29	72	i	i	ADP
cana-4523	30	1			PROPN
cana-4523	30	2			PROPN
cana-4523	30	3			PROPN
cana-4523	30	4			PROPN
cana-4523	30	5	−=	−=	NOUN
cana-4523	30	6	+	+	PROPN
cana-4523	30	7	+	+	PUNCT
cana-4523	30	8	+	+	NOUN
cana-4523	30	9			NOUN
cana-4523	30	10	and	and	CCONJ
cana-4523	30	11	0	0	NUM
cana-4523	31	1	0	0	NOUN
cana-4523	32	1	=	=	NOUN
cana-4523	32	2			INTJ
cana-4523	32	3	.	.	PUNCT
cana-4523	33	1	assumption	assumption	NOUN
cana-4523	33	2	2.1	2.1	NUM
cana-4523	33	3	:	:	PUNCT
cana-4523	33	4	at	at	ADP
cana-4523	33	5	time	time	NOUN
cana-4523	33	6	t	t	NOUN
cana-4523	33	7	=	=	SYM
cana-4523	33	8	0	0	PROPN
cana-4523	33	9	,	,	PUNCT
cana-4523	33	10	a	a	DET
cana-4523	33	11	new	new	ADJ
cana-4523	33	12	system	system	NOUN
cana-4523	33	13	is	be	AUX
cana-4523	33	14	deployed	deploy	VERB
cana-4523	33	15	in	in	ADP
cana-4523	33	16	the	the	DET
cana-4523	33	17	field	field	NOUN
cana-4523	33	18	.	.	PUNCT
cana-4523	34	1	each	each	DET
cana-4523	34	2	time	time	NOUN
cana-4523	34	3	the	the	DET
cana-4523	34	4	system	system	NOUN
cana-4523	34	5	fails	fail	VERB
cana-4523	34	6	,	,	PUNCT
cana-4523	34	7	it	it	PRON
cana-4523	34	8	will	will	AUX
cana-4523	34	9	be	be	AUX
cana-4523	34	10	replaced	replace	VERB
cana-4523	34	11	by	by	ADP
cana-4523	34	12	an	an	DET
cana-4523	34	13	identical	identical	ADJ
cana-4523	34	14	new	new	ADJ
cana-4523	34	15	unit	unit	NOUN
cana-4523	34	16	after	after	ADP
cana-4523	34	17	a	a	DET
cana-4523	34	18	certain	certain	ADJ
cana-4523	34	19	period	period	NOUN
cana-4523	34	20	.	.	PUNCT
cana-4523	35	1	assumption	assumption	NOUN
cana-4523	35	2	2.2	2.2	NUM
cana-4523	35	3	:	:	PUNCT
cana-4523	35	4	let	let	VERB
cana-4523	35	5	𝑆(𝑡)∈	𝑆(𝑡)∈	PROPN
cana-4523	35	6	ω	ω	NOUN
cana-4523	35	7	,	,	PUNCT
cana-4523	35	8	where	where	SCONJ
cana-4523	35	9	ω	ω	PROPN
cana-4523	35	10	is	be	AUX
cana-4523	35	11	the	the	DET
cana-4523	35	12	state	state	NOUN
cana-4523	35	13	space	space	NOUN
cana-4523	35	14	,	,	PUNCT
cana-4523	35	15	represent	represent	VERB
cana-4523	35	16	the	the	DET
cana-4523	35	17	system	system	NOUN
cana-4523	35	18	state	state	NOUN
cana-4523	35	19	at	at	ADP
cana-4523	35	20	time	time	NOUN
cana-4523	35	21	t	t	PROPN
cana-4523	35	22	,	,	PUNCT
cana-4523	35	23	characterizing	characterize	VERB
cana-4523	35	24	the	the	DET
cana-4523	35	25	system	system	NOUN
cana-4523	35	26	's	's	PART
cana-4523	35	27	dynamic	dynamic	ADJ
cana-4523	35	28	behaviour	behaviour	NOUN
cana-4523	35	29	.	.	PUNCT
cana-4523	36	1	𝑆(𝑡	𝑆(𝑡	VERB
cana-4523	36	2	)	)	PUNCT
cana-4523	36	3	=	=	NOUN
cana-4523	36	4	{	{	PUNCT
cana-4523	36	5	0	0	NUM
cana-4523	36	6	,	,	PUNCT
cana-4523	36	7	𝑖𝑓	𝑖𝑓	NOUN
cana-4523	36	8	𝑡ℎ𝑒	𝑡ℎ𝑒	VERB
cana-4523	36	9	𝑠𝑡𝑎𝑡𝑒	𝑠𝑡𝑎𝑡𝑒	NOUN
cana-4523	36	10	𝑖𝑠	𝑖𝑠	PROPN
cana-4523	36	11	𝑤𝑜𝑟𝑘𝑖𝑛𝑔	𝑤𝑜𝑟𝑘𝑖𝑛𝑔	ADJ
cana-4523	36	12	𝑎𝑡	𝑎𝑡	ADP
cana-4523	36	13	𝑡𝑖𝑚𝑒	𝑡𝑖𝑚𝑒	VERB
cana-4523	36	14	𝑡	𝑡	PROPN
cana-4523	36	15	;	;	PUNCT
cana-4523	36	16	𝑖	𝑖	SYM
cana-4523	36	17	,	,	PUNCT
cana-4523	36	18	𝑖𝑓	𝑖𝑓	NOUN
cana-4523	36	19	𝑡ℎ𝑒	𝑡ℎ𝑒	NOUN
cana-4523	37	1	𝑠𝑦𝑠𝑡𝑒𝑚	𝑠𝑦𝑠𝑡𝑒𝑚	NOUN
cana-4523	37	2	𝑖𝑠	𝑖𝑠	INTJ
cana-4523	37	3	𝑖𝑛	𝑖𝑛	INTJ
cana-4523	37	4	𝑡ℎ𝑒	𝑡ℎ𝑒	PROPN
cana-4523	37	5	𝑖	𝑖	AUX
cana-4523	37	6	𝑡ℎ	𝑡ℎ	VERB
cana-4523	37	7	𝑡𝑦𝑝𝑒	𝑡𝑦𝑝𝑒	ADV
cana-4523	37	8	𝑜𝑓	𝑜𝑓	ADP
cana-4523	37	9	𝑓𝑎𝑖𝑙𝑢𝑟𝑒	𝑓𝑎𝑖𝑙𝑢𝑟𝑒	VERB
cana-4523	37	10	𝑠𝑡𝑎𝑡𝑒	𝑠𝑡𝑎𝑡𝑒	PROPN
cana-4523	37	11	𝑎𝑡	𝑎𝑡	ADP
cana-4523	37	12	𝑡𝑖𝑚𝑒	𝑡𝑖𝑚𝑒	VERB
cana-4523	37	13	𝑡	𝑡	PROPN
cana-4523	37	14	,	,	PUNCT
cana-4523	37	15	𝑖	𝑖	NOUN
cana-4523	37	16	=	=	NOUN
cana-4523	37	17	1,2,3	1,2,3	NUM
cana-4523	37	18	,	,	PUNCT
cana-4523	37	19	…	…	PUNCT
cana-4523	37	20	.	.	PUNCT
cana-4523	38	1	𝑘	𝑘	X
cana-4523	38	2	when	when	SCONJ
cana-4523	38	3	the	the	DET
cana-4523	38	4	system	system	NOUN
cana-4523	38	5	fails	fail	VERB
cana-4523	38	6	,	,	PUNCT
cana-4523	38	7	it	it	PRON
cana-4523	38	8	transitions	transition	VERB
cana-4523	38	9	to	to	ADP
cana-4523	38	10	one	one	NUM
cana-4523	38	11	of	of	ADP
cana-4523	38	12	k	k	PROPN
cana-4523	38	13	possible	possible	ADJ
cana-4523	38	14	states	state	NOUN
cana-4523	38	15	,	,	PUNCT
cana-4523	38	16	with	with	ADP
cana-4523	38	17	probabilities	probability	NOUN
cana-4523	38	18	𝑝𝑖	𝑝𝑖	NOUN
cana-4523	38	19	,	,	PUNCT
cana-4523	38	20	i	i	NOUN
cana-4523	38	21	=	=	NOUN
cana-4523	38	22	1	1	NUM
cana-4523	38	23	,	,	PUNCT
cana-4523	38	24	2	2	NUM
cana-4523	38	25	,	,	PUNCT
cana-4523	38	26	...	...	PUNCT
cana-4523	38	27	,	,	PUNCT
cana-4523	38	28	k	k	NOUN
cana-4523	38	29	,	,	PUNCT
cana-4523	38	30	representing	represent	VERB
cana-4523	38	31	the	the	DET
cana-4523	38	32	likelihood	likelihood	NOUN
cana-4523	38	33	of	of	ADP
cana-4523	38	34	entering	enter	VERB
cana-4523	38	35	each	each	DET
cana-4523	38	36	failed	fail	VERB
cana-4523	38	37	state	state	NOUN
cana-4523	38	38	and	and	CCONJ
cana-4523	38	39	∑	∑	ADV
cana-4523	38	40	𝑝𝑖	𝑝𝑖	NOUN
cana-4523	38	41	=	=	NOUN
cana-4523	38	42	1𝑘	1𝑘	NUM
cana-4523	38	43	𝑖=1	𝑖=1	PUNCT
cana-4523	38	44	.	.	PUNCT
cana-4523	39	1	assumption	assumption	NOUN
cana-4523	39	2	2.3	2.3	NUM
cana-4523	39	3	:	:	PUNCT
cana-4523	39	4	to	to	PART
cana-4523	39	5	model	model	VERB
cana-4523	39	6	system	system	NOUN
cana-4523	39	7	behaviour	behaviour	NOUN
cana-4523	39	8	,	,	PUNCT
cana-4523	39	9	we	we	PRON
cana-4523	39	10	define	define	VERB
cana-4523	39	11	four	four	NUM
cana-4523	39	12	key	key	ADJ
cana-4523	39	13	time	time	NOUN
cana-4523	39	14	variables	variable	NOUN
cana-4523	39	15	:	:	PUNCT
cana-4523	39	16	𝑋1	𝑋1	PROPN
cana-4523	39	17	be	be	AUX
cana-4523	39	18	the	the	DET
cana-4523	39	19	first	first	ADJ
cana-4523	39	20	operating	operating	NOUN
cana-4523	39	21	time	time	NOUN
cana-4523	39	22	,	,	PUNCT
cana-4523	39	23	𝑋𝑛	𝑋𝑛	PROPN
cana-4523	39	24	be	be	AUX
cana-4523	39	25	the	the	DET
cana-4523	39	26	operating	operating	NOUN
cana-4523	39	27	time	time	NOUN
cana-4523	39	28	after	after	ADP
cana-4523	39	29	(	(	PUNCT
cana-4523	39	30	𝑛	𝑛	PRON
cana-4523	39	31	−	−	PROPN
cana-4523	39	32	1	1	NUM
cana-4523	39	33	)	)	PUNCT
cana-4523	39	34	repairs	repair	NOUN
cana-4523	39	35	,	,	PUNCT
cana-4523	39	36	𝑌𝑛	𝑌𝑛	PROPN
cana-4523	39	37	be	be	VERB
cana-4523	39	38	the	the	DET
cana-4523	39	39	repair	repair	NOUN
cana-4523	39	40	time	time	NOUN
cana-4523	39	41	after	after	ADP
cana-4523	39	42	n	n	ADP
cana-4523	39	43	failures	failure	NOUN
cana-4523	39	44	,	,	PUNCT
cana-4523	39	45	and	and	CCONJ
cana-4523	39	46	z	z	NOUN
cana-4523	39	47	be	be	AUX
cana-4523	39	48	the	the	DET
cana-4523	39	49	replacement	replacement	NOUN
cana-4523	39	50	time	time	NOUN
cana-4523	39	51	,	,	PUNCT
cana-4523	39	52	which	which	PRON
cana-4523	39	53	capture	capture	VERB
cana-4523	39	54	the	the	DET
cana-4523	39	55	dynamics	dynamic	NOUN
cana-4523	39	56	of	of	ADP
cana-4523	39	57	system	system	NOUN
cana-4523	39	58	operation	operation	NOUN
cana-4523	39	59	,	,	PUNCT
cana-4523	39	60	maintenance	maintenance	NOUN
cana-4523	39	61	,	,	PUNCT
cana-4523	39	62	and	and	CCONJ
cana-4523	39	63	replacement	replacement	NOUN
cana-4523	39	64	.	.	PUNCT
cana-4523	40	1	let	let	VERB
cana-4523	40	2	𝑡𝑛	𝑡𝑛	NOUN
cana-4523	40	3	denote	denote	VERB
cana-4523	40	4	the	the	DET
cana-4523	40	5	time	time	NOUN
cana-4523	40	6	of	of	ADP
cana-4523	40	7	the	the	DET
cana-4523	40	8	n	n	CCONJ
cana-4523	40	9	-	-	PUNCT
cana-4523	40	10	th	th	NOUN
cana-4523	40	11	failure	failure	NOUN
cana-4523	40	12	,	,	PUNCT
cana-4523	40	13	representing	represent	VERB
cana-4523	40	14	the	the	DET
cana-4523	40	15	moment	moment	NOUN
cana-4523	40	16	when	when	SCONJ
cana-4523	40	17	the	the	DET
cana-4523	40	18	system	system	NOUN
cana-4523	40	19	fails	fail	VERB
cana-4523	40	20	for	for	ADP
cana-4523	40	21	the	the	DET
cana-4523	40	22	nth	nth	NOUN
cana-4523	40	23	time	time	NOUN
cana-4523	40	24	.	.	PUNCT
cana-4523	41	1	assume	assume	VERB
cana-4523	41	2	that	that	SCONJ
cana-4523	41	3	there	there	PRON
cana-4523	41	4	exist	exist	VERB
cana-4523	41	5	a	a	DET
cana-4523	41	6	life	life	NOUN
cana-4523	41	7	-	-	PUNCT
cana-4523	41	8	time	time	NOUN
cana-4523	41	9	distribution	distribution	NOUN
cana-4523	41	10	u(t	u(t	NOUN
cana-4523	41	11	)	)	PUNCT
cana-4523	41	12	and	and	CCONJ
cana-4523	41	13	𝑎𝑖	𝑎𝑖	ADP
cana-4523	41	14	>	>	X
cana-4523	41	15	0	0	PROPN
cana-4523	41	16	,	,	PUNCT
cana-4523	41	17	𝑖	𝑖	NOUN
cana-4523	41	18	=	=	NOUN
cana-4523	41	19	1,2,3	1,2,3	NUM
cana-4523	41	20	,	,	PUNCT
cana-4523	41	21	…	…	PUNCT
cana-4523	41	22	.	.	PUNCT
cana-4523	42	1	𝑘	𝑘	PRON
cana-4523	42	2	such	such	ADJ
cana-4523	42	3	that	that	PRON
cana-4523	42	4	,	,	PUNCT
cana-4523	42	5	𝑃(𝑋1	𝑃(𝑋1	PUNCT
cana-4523	42	6	≤	≤	NUM
cana-4523	42	7	𝑡	𝑡	NOUN
cana-4523	42	8	)	)	PUNCT
cana-4523	42	9	=	=	SYM
cana-4523	42	10	𝑈(𝑡	𝑈(𝑡	NUM
cana-4523	42	11	)	)	PUNCT
cana-4523	42	12	and	and	CCONJ
cana-4523	42	13	𝑃(𝑋2	𝑃(𝑋2	PUNCT
cana-4523	42	14	≤	≤	NUM
cana-4523	42	15	𝑡|𝑆(𝑡1	𝑡|𝑆(𝑡1	NUM
cana-4523	42	16	)	)	PUNCT
cana-4523	42	17	=	=	SYM
cana-4523	42	18	𝑖	𝑖	X
cana-4523	42	19	)	)	PUNCT
cana-4523	42	20	=	=	SYM
cana-4523	42	21	𝑈(𝑎𝑖𝑡	𝑈(𝑎𝑖𝑡	NOUN
cana-4523	42	22	)	)	PUNCT
cana-4523	42	23	,	,	PUNCT
cana-4523	42	24	𝑖	𝑖	X
cana-4523	42	25	=	=	NOUN
cana-4523	42	26	1,2,3	1,2,3	NUM
cana-4523	42	27	,	,	PUNCT
cana-4523	42	28	…	…	PUNCT
cana-4523	42	29	.	.	PUNCT
cana-4523	43	1	𝑘.	𝑘.	NOUN
cana-4523	43	2	in	in	ADP
cana-4523	43	3	general	general	ADJ
cana-4523	43	4	for	for	ADP
cana-4523	43	5	𝑗	𝑗	NOUN
cana-4523	43	6	=	=	SYM
cana-4523	43	7	1,2,3	1,2,3	NUM
cana-4523	43	8	,	,	PUNCT
cana-4523	43	9	…	…	PUNCT
cana-4523	43	10	.	.	PUNCT
cana-4523	44	1	𝑛	𝑛	PRON
cana-4523	44	2	−	−	NOUN
cana-4523	44	3	1	1	NUM
cana-4523	44	4	;	;	PUNCT
cana-4523	44	5	𝑖𝑗	𝑖𝑗	ADP
cana-4523	44	6	=	=	SYM
cana-4523	44	7	1,2,3	1,2,3	NUM
cana-4523	44	8	,	,	PUNCT
cana-4523	44	9	…	…	PUNCT
cana-4523	44	10	.	.	PUNCT
cana-4523	45	1	𝑘	𝑘	X
cana-4523	45	2	,	,	PUNCT
cana-4523	45	3	𝑃(𝑋𝑛	𝑃(𝑋𝑛	ADJ
cana-4523	45	4	≤	≤	NOUN
cana-4523	45	5	𝑡|𝑆(𝑡1	𝑡|𝑆(𝑡1	NUM
cana-4523	45	6	)	)	PUNCT
cana-4523	45	7	=	=	SYM
cana-4523	45	8	𝑖1	𝑖1	PROPN
cana-4523	45	9	,	,	PUNCT
cana-4523	45	10	…	…	PUNCT
cana-4523	45	11	,	,	PUNCT
cana-4523	45	12	𝑆(𝑡𝑛−1	𝑆(𝑡𝑛−1	X
cana-4523	45	13	)	)	PUNCT
cana-4523	45	14	=	=	SYM
cana-4523	45	15	𝑖𝑛−1	𝑖𝑛−1	NOUN
cana-4523	45	16	)	)	PUNCT
cana-4523	45	17	=	=	NOUN
cana-4523	45	18	𝑈(𝑎𝑖1	𝑈(𝑎𝑖1	PRON
cana-4523	45	19	𝑎𝑖2	𝑎𝑖2	NOUN
cana-4523	45	20	.	.	PUNCT
cana-4523	45	21	…	…	PUNCT
cana-4523	46	1	𝑎𝑖𝑛−1	𝑎𝑖𝑛−1	PROPN
cana-4523	46	2	𝑡	𝑡	NOUN
cana-4523	46	3	)	)	PUNCT
cana-4523	46	4	,	,	PUNCT
cana-4523	46	5	where	where	SCONJ
cana-4523	46	6	1	1	NUM
cana-4523	46	7	≤	≤	NOUN
cana-4523	46	8	𝑎1	𝑎1	X
cana-4523	46	9	≤	≤	NUM
cana-4523	46	10	𝑎2	𝑎2	NOUN
cana-4523	46	11	≤	≤	NUM
cana-4523	46	12	⋯	⋯	NOUN
cana-4523	46	13	≤	≤	NOUN
cana-4523	46	14	𝑎𝑘.	𝑎𝑘.	CCONJ
cana-4523	46	15	similarly	similarly	ADV
cana-4523	46	16	,	,	PUNCT
cana-4523	46	17	assume	assume	VERB
cana-4523	46	18	that	that	SCONJ
cana-4523	46	19	there	there	PRON
cana-4523	46	20	exist	exist	VERB
cana-4523	46	21	a	a	DET
cana-4523	46	22	life	life	NOUN
cana-4523	46	23	-	-	PUNCT
cana-4523	46	24	time	time	NOUN
cana-4523	46	25	distribution	distribution	NOUN
cana-4523	46	26	𝑉(𝑡	𝑉(𝑡	NOUN
cana-4523	46	27	)	)	PUNCT
cana-4523	46	28	and	and	CCONJ
cana-4523	46	29	𝑏𝑖	𝑏𝑖	ADP
cana-4523	46	30	>	>	X
cana-4523	46	31	0	0	NUM
cana-4523	46	32	,	,	PUNCT
cana-4523	46	33	𝑖	𝑖	NOUN
cana-4523	46	34	=	=	NOUN
cana-4523	46	35	1,2,3	1,2,3	NUM
cana-4523	46	36	,	,	PUNCT
cana-4523	46	37	…	…	PUNCT
cana-4523	46	38	.	.	PUNCT
cana-4523	47	1	𝑘.	𝑘.	NOUN
cana-4523	47	2	such	such	ADJ
cana-4523	47	3	that	that	PRON
cana-4523	47	4	,	,	PUNCT
cana-4523	47	5	𝑃(𝑌1	𝑃(𝑌1	PROPN
cana-4523	47	6	≤	≤	NUM
cana-4523	47	7	𝑡	𝑡	NOUN
cana-4523	47	8	)	)	PUNCT
cana-4523	47	9	=	=	PUNCT
cana-4523	47	10	𝑉(𝑡	𝑉(𝑡	NOUN
cana-4523	47	11	)	)	PUNCT
cana-4523	47	12	and	and	CCONJ
cana-4523	47	13	𝑃(𝑌2	𝑃(𝑌2	PROPN
cana-4523	47	14	≤	≤	PROPN
cana-4523	47	15	𝑡|𝑆(𝑡1	𝑡|𝑆(𝑡1	PROPN
cana-4523	47	16	)	)	PUNCT
cana-4523	47	17	=	=	SYM
cana-4523	48	1	𝑖	𝑖	X
cana-4523	48	2	)	)	PUNCT
cana-4523	48	3	=	=	SYM
cana-4523	48	4	𝑉(𝑏𝑖𝑡	𝑉(𝑏𝑖𝑡	X
cana-4523	48	5	)	)	PUNCT
cana-4523	48	6	,	,	PUNCT
cana-4523	48	7	𝑖	𝑖	X
cana-4523	48	8	=	=	NOUN
cana-4523	48	9	1,2,3	1,2,3	NUM
cana-4523	48	10	,	,	PUNCT
cana-4523	48	11	…	…	PUNCT
cana-4523	48	12	.	.	PUNCT
cana-4523	49	1	𝑘.	𝑘.	NOUN
cana-4523	49	2	communications	communication	NOUN
cana-4523	49	3	on	on	ADP
cana-4523	49	4	applied	apply	VERB
cana-4523	49	5	nonlinear	nonlinear	ADJ
cana-4523	49	6	analysis	analysis	NOUN
cana-4523	49	7	issn	issn	NOUN
cana-4523	49	8	:	:	PUNCT
cana-4523	49	9	1074	1074	NUM
cana-4523	49	10	-	-	PUNCT
cana-4523	49	11	133x	133x	NUM
cana-4523	49	12	vol	vol	NOUN
cana-4523	49	13	32	32	NUM
cana-4523	49	14	no	no	NOUN
cana-4523	49	15	.	.	PUNCT
cana-4523	50	1	9s	9s	NUM
cana-4523	50	2	(	(	PUNCT
cana-4523	50	3	2025	2025	NUM
cana-4523	50	4	)	)	PUNCT
cana-4523	50	5	2361	2361	NUM
cana-4523	50	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	50	7	in	in	ADP
cana-4523	50	8	general	general	ADJ
cana-4523	50	9	for	for	ADP
cana-4523	50	10	𝑗	𝑗	NOUN
cana-4523	50	11	=	=	SYM
cana-4523	50	12	1,2,3	1,2,3	NUM
cana-4523	50	13	,	,	PUNCT
cana-4523	50	14	…	…	PUNCT
cana-4523	50	15	.	.	PUNCT
cana-4523	51	1	𝑛	𝑛	NOUN
cana-4523	51	2	;	;	PUNCT
cana-4523	51	3	𝑖𝑗	𝑖𝑗	ADP
cana-4523	51	4	=	=	SYM
cana-4523	51	5	1,2,3	1,2,3	NUM
cana-4523	51	6	,	,	PUNCT
cana-4523	51	7	…	…	PUNCT
cana-4523	51	8	.	.	PUNCT
cana-4523	52	1	𝑘	𝑘	X
cana-4523	52	2	,	,	PUNCT
cana-4523	52	3	𝑃(𝑌𝑛	𝑃(𝑌𝑛	NOUN
cana-4523	52	4	≤	≤	ADJ
cana-4523	52	5	𝑡|𝑆(𝑡1	𝑡|𝑆(𝑡1	NUM
cana-4523	52	6	)	)	PUNCT
cana-4523	52	7	=	=	SYM
cana-4523	52	8	𝑖1	𝑖1	PROPN
cana-4523	52	9	,	,	PUNCT
cana-4523	52	10	…	…	PUNCT
cana-4523	52	11	,	,	PUNCT
cana-4523	52	12	𝑆(𝑡𝑛	𝑆(𝑡𝑛	ADJ
cana-4523	52	13	)	)	PUNCT
cana-4523	52	14	=	=	SYM
cana-4523	52	15	𝑖𝑛	𝑖𝑛	NOUN
cana-4523	52	16	)	)	PUNCT
cana-4523	52	17	=	=	PUNCT
cana-4523	52	18	𝑉(𝑏𝑖1	𝑉(𝑏𝑖1	X
cana-4523	52	19	𝑏𝑖2	𝑏𝑖2	PROPN
cana-4523	52	20	.	.	PUNCT
cana-4523	53	1	…	…	PUNCT
cana-4523	53	2	𝑏𝑖𝑛	𝑏𝑖𝑛	NUM
cana-4523	53	3	𝑡	𝑡	NOUN
cana-4523	53	4	)	)	PUNCT
cana-4523	53	5	,	,	PUNCT
cana-4523	53	6	where	where	SCONJ
cana-4523	53	7	1	1	NUM
cana-4523	53	8	≥	≥	NOUN
cana-4523	53	9	𝑏1	𝑏1	PROPN
cana-4523	53	10	≥	≥	NOUN
cana-4523	53	11	𝑏2	𝑏2	PROPN
cana-4523	53	12	≥	≥	PROPN
cana-4523	53	13	⋯	⋯	PROPN
cana-4523	53	14	≥	≥	PROPN
cana-4523	53	15	𝑏𝑘	𝑏𝑘	NUM
cana-4523	53	16	≥	≥	NOUN
cana-4523	53	17	0	0	NUM
cana-4523	53	18	.	.	PUNCT
cana-4523	53	19	assumption	assumption	NOUN
cana-4523	53	20	2.4	2.4	NUM
cana-4523	53	21	:	:	PUNCT
cana-4523	53	22	the	the	DET
cana-4523	53	23	working	work	VERB
cana-4523	53	24	age	age	NOUN
cana-4523	53	25	t	t	PROPN
cana-4523	53	26	of	of	ADP
cana-4523	53	27	the	the	DET
cana-4523	53	28	system	system	NOUN
cana-4523	53	29	at	at	ADP
cana-4523	53	30	time	time	NOUN
cana-4523	53	31	t	t	PROPN
cana-4523	53	32	is	be	AUX
cana-4523	53	33	the	the	DET
cana-4523	53	34	cumulative	cumulative	ADJ
cana-4523	53	35	life	life	NOUN
cana-4523	53	36	-	-	PUNCT
cana-4523	53	37	time	time	NOUN
cana-4523	53	38	given	give	VERB
cana-4523	53	39	by	by	ADP
cana-4523	53	40	𝑇(𝑡	𝑇(𝑡	NUM
cana-4523	53	41	)	)	PUNCT
cana-4523	53	42	=	=	NOUN
cana-4523	53	43	{	{	PUNCT
cana-4523	53	44	𝑡	𝑡	X
cana-4523	53	45	−	−	PROPN
cana-4523	53	46	𝑉𝑛	𝑉𝑛	PROPN
cana-4523	53	47	,	,	PUNCT
cana-4523	53	48	𝑈𝑛	𝑈𝑛	PROPN
cana-4523	53	49	+	+	CCONJ
cana-4523	53	50	𝑉𝑛	𝑉𝑛	PROPN
cana-4523	53	51	≤	≤	NUM
cana-4523	53	52	𝑡	𝑡	NOUN
cana-4523	53	53	≤	≤	ADJ
cana-4523	53	54	𝑈𝑛+1	𝑈𝑛+1	NOUN
cana-4523	54	1	+	+	CCONJ
cana-4523	54	2	𝑉𝑛	𝑉𝑛	PROPN
cana-4523	54	3	𝑈𝑛+1	𝑈𝑛+1	NOUN
cana-4523	54	4	,	,	PUNCT
cana-4523	54	5	𝑈𝑛+1	𝑈𝑛+1	X
cana-4523	55	1	+	+	CCONJ
cana-4523	55	2	𝑉𝑛	𝑉𝑛	PROPN
cana-4523	55	3	≤	≤	NUM
cana-4523	55	4	𝑡	𝑡	NOUN
cana-4523	55	5	≤	≤	NOUN
cana-4523	55	6	𝑈𝑛+1	𝑈𝑛+1	NOUN
cana-4523	55	7	+	+	X
cana-4523	55	8	𝑉𝑛+1	𝑉𝑛+1	ADP
cana-4523	55	9	where	where	SCONJ
cana-4523	55	10	,	,	PUNCT
cana-4523	55	11	𝑈𝑛	𝑈𝑛	PROPN
cana-4523	55	12	=	=	SYM
cana-4523	55	13	∑	∑	PUNCT
cana-4523	55	14	𝑋𝑘	𝑋𝑘	ADP
cana-4523	55	15	𝑛	𝑛	PRON
cana-4523	55	16	𝑘=1	𝑘=1	NOUN
cana-4523	55	17	and	and	CCONJ
cana-4523	55	18	𝑉𝑛	𝑉𝑛	PROPN
cana-4523	55	19	=	=	PUNCT
cana-4523	55	20	∑	∑	PUNCT
cana-4523	55	21	𝑌𝑘	𝑌𝑘	PROPN
cana-4523	55	22	𝑛	𝑛	PROPN
cana-4523	55	23	𝑘=1	𝑘=1	NOUN
cana-4523	55	24	and	and	CCONJ
cana-4523	55	25	𝑈0=	𝑈0=	ADJ
cana-4523	55	26	𝑉0	𝑉0	NOUN
cana-4523	55	27	=	=	SYM
cana-4523	55	28	0	0	NUM
cana-4523	55	29	.	.	PUNCT
cana-4523	55	30	assumption	assumption	NOUN
cana-4523	55	31	2.5	2.5	NUM
cana-4523	55	32	:	:	PUNCT
cana-4523	55	33	let	let	VERB
cana-4523	55	34	‘	'	PUNCT
cana-4523	55	35	𝑟	𝑟	X
cana-4523	55	36	’	'	PUNCT
cana-4523	55	37	be	be	AUX
cana-4523	55	38	the	the	DET
cana-4523	55	39	reward	reward	NOUN
cana-4523	55	40	rate	rate	NOUN
cana-4523	55	41	per	per	ADP
cana-4523	55	42	unit	unit	NOUN
cana-4523	55	43	time	time	NOUN
cana-4523	55	44	of	of	ADP
cana-4523	55	45	the	the	DET
cana-4523	55	46	system	system	NOUN
cana-4523	55	47	when	when	SCONJ
cana-4523	55	48	it	it	PRON
cana-4523	55	49	is	be	AUX
cana-4523	55	50	operating	operate	VERB
cana-4523	55	51	and	and	CCONJ
cana-4523	55	52	‘	'	PUNCT
cana-4523	55	53	𝑐	𝑐	X
cana-4523	55	54	’	'	PUNCT
cana-4523	55	55	be	be	VERB
cana-4523	55	56	the	the	DET
cana-4523	55	57	repair	repair	NOUN
cana-4523	55	58	cost	cost	NOUN
cana-4523	55	59	per	per	ADP
cana-4523	55	60	unit	unit	NOUN
cana-4523	55	61	time	time	NOUN
cana-4523	55	62	of	of	ADP
cana-4523	55	63	the	the	DET
cana-4523	55	64	system	system	NOUN
cana-4523	55	65	.	.	PUNCT
cana-4523	56	1	assume	assume	VERB
cana-4523	56	2	further	far	ADV
cana-4523	56	3	that	that	SCONJ
cana-4523	56	4	the	the	DET
cana-4523	56	5	replacement	replacement	NOUN
cana-4523	56	6	cost	cost	NOUN
cana-4523	56	7	comprises	comprise	NOUN
cana-4523	56	8	of	of	ADP
cana-4523	56	9	two	two	NUM
cana-4523	56	10	parts	part	NOUN
cana-4523	56	11	:	:	PUNCT
cana-4523	56	12	one	one	NUM
cana-4523	56	13	part	part	NOUN
cana-4523	56	14	is	be	AUX
cana-4523	56	15	the	the	DET
cana-4523	56	16	basic	basic	ADJ
cana-4523	56	17	replacement	replacement	NOUN
cana-4523	56	18	cost	cost	NOUN
cana-4523	56	19	r	r	NOUN
cana-4523	56	20	and	and	CCONJ
cana-4523	56	21	the	the	DET
cana-4523	56	22	other	other	ADJ
cana-4523	56	23	part	part	NOUN
cana-4523	56	24	is	be	AUX
cana-4523	56	25	the	the	DET
cana-4523	56	26	cost	cost	NOUN
cana-4523	56	27	.	.	PUNCT
cana-4523	57	1	assumption	assumption	NOUN
cana-4523	57	2	2.6	2.6	NUM
cana-4523	57	3	:	:	PUNCT
cana-4523	57	4	the	the	DET
cana-4523	57	5	replacement	replacement	NOUN
cana-4523	57	6	policy	policy	NOUN
cana-4523	57	7	𝑇	𝑇	PROPN
cana-4523	57	8	is	be	AUX
cana-4523	57	9	adapted	adapt	VERB
cana-4523	57	10	.	.	PUNCT
cana-4523	58	1	following	follow	VERB
cana-4523	58	2	lam	lam	PROPN
cana-4523	58	3	,	,	PUNCT
cana-4523	58	4	zhang	zhang	PROPN
cana-4523	58	5	and	and	CCONJ
cana-4523	58	6	zheng	zheng	PROPN
cana-4523	58	7	[	[	X
cana-4523	58	8	2002	2002	NUM
cana-4523	58	9	]	]	PUNCT
cana-4523	58	10	,	,	PUNCT
cana-4523	58	11	we	we	PRON
cana-4523	58	12	have	have	VERB
cana-4523	58	13	if	if	SCONJ
cana-4523	58	14			ADJ
cana-4523	58	15	1	1	NOUN
cana-4523	58	16	0e	0e	NOUN
cana-4523	58	17	x	x	PROPN
cana-4523	59	1	=	=	NOUN
cana-4523	59	2			VERB
cana-4523	59	3	the	the	DET
cana-4523	59	4	mean	mean	PROPN
cana-4523	59	5	survival	survival	NOUN
cana-4523	59	6	time	time	NOUN
cana-4523	59	7	is	be	AUX
cana-4523	59	8	𝐸[𝑋𝑛	𝐸[𝑋𝑛	NOUN
cana-4523	59	9	]	]	X
cana-4523	59	10	=	=	X
cana-4523	59	11	𝜇	𝜇	ADP
cana-4523	59	12	2𝑖−1𝛽	2𝑖−1𝛽	NUM
cana-4523	59	13	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
cana-4523	59	14	𝛽	𝛽	NOUN
cana-4523	59	15	=	=	SYM
cana-4523	59	16	(	(	PUNCT
cana-4523	59	17	∑	∑	INTJ
cana-4523	59	18	𝑝𝑖	𝑝𝑖	NOUN
cana-4523	59	19	𝑎𝑖	𝑎𝑖	ADP
cana-4523	59	20	𝑘	𝑘	PRON
cana-4523	59	21	𝑖=1	𝑖=1	PROPN
cana-4523	59	22	)	)	PUNCT
cana-4523	59	23	−1	−1	NOUN
cana-4523	59	24	and	and	CCONJ
cana-4523	59	25	if	if	SCONJ
cana-4523	59	26	𝐸[𝑌1	𝐸[𝑌1	PROPN
cana-4523	59	27	]	]	X
cana-4523	59	28	=	=	SYM
cana-4523	59	29	𝛾	𝛾	PROPN
cana-4523	59	30	,	,	PUNCT
cana-4523	59	31	then	then	ADV
cana-4523	59	32	the	the	DET
cana-4523	59	33	mean	mean	ADJ
cana-4523	59	34	repair	repair	NOUN
cana-4523	59	35	time	time	NOUN
cana-4523	59	36	is	be	AUX
cana-4523	59	37	𝐸[𝑌𝑖	𝐸[𝑌𝑖	NOUN
cana-4523	59	38	]	]	X
cana-4523	59	39	=	=	SYM
cana-4523	59	40	𝛾	𝛾	AUX
cana-4523	59	41	𝑎𝑖−1	𝑎𝑖−1	PROPN
cana-4523	59	42	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	ADJ
cana-4523	59	43	𝑎	𝑎	X
cana-4523	59	44	=	=	SYM
cana-4523	59	45	(	(	PUNCT
cana-4523	59	46	∑	∑	ADV
cana-4523	59	47	𝑞𝑗	𝑞𝑗	VERB
cana-4523	59	48	𝑏𝑗	𝑏𝑗	PRON
cana-4523	59	49	𝑘	𝑘	DET
cana-4523	59	50	𝑗=1	𝑗=1	PROPN
cana-4523	59	51	)	)	PUNCT
cana-4523	59	52	−1	−1	NOUN
cana-4523	59	53	.	.	PUNCT
cana-4523	60	1	we	we	PRON
cana-4523	60	2	consider	consider	VERB
cana-4523	60	3	a	a	DET
cana-4523	60	4	t	t	NOUN
cana-4523	60	5	-policy	-policy	PROPN
cana-4523	60	6	under	under	ADP
cana-4523	60	7	which	which	PRON
cana-4523	60	8	the	the	DET
cana-4523	60	9	system	system	NOUN
cana-4523	60	10	will	will	AUX
cana-4523	60	11	be	be	AUX
cana-4523	60	12	replaced	replace	VERB
cana-4523	60	13	whenever	whenever	SCONJ
cana-4523	60	14	its	its	PRON
cana-4523	60	15	working	work	VERB
cana-4523	60	16	age	age	NOUN
cana-4523	60	17	reaches	reach	VERB
cana-4523	60	18	t.	t.	PROPN
cana-4523	60	19	under	under	ADP
cana-4523	60	20	the	the	DET
cana-4523	60	21	replacement	replacement	NOUN
cana-4523	60	22	policy	policy	NOUN
cana-4523	60	23	t	t	PROPN
cana-4523	60	24	,	,	PUNCT
cana-4523	60	25	the	the	DET
cana-4523	60	26	problem	problem	NOUN
cana-4523	60	27	is	be	AUX
cana-4523	60	28	to	to	PART
cana-4523	60	29	determine	determine	VERB
cana-4523	60	30	an	an	DET
cana-4523	60	31	optimal	optimal	ADJ
cana-4523	60	32	t	t	NOUN
cana-4523	60	33	such	such	ADJ
cana-4523	60	34	that	that	SCONJ
cana-4523	60	35	the	the	DET
cana-4523	60	36	long	long	ADV
cana-4523	60	37	-	-	PUNCT
cana-4523	60	38	run	run	VERB
cana-4523	60	39	average	average	ADJ
cana-4523	60	40	cost	cost	NOUN
cana-4523	60	41	per	per	ADP
cana-4523	60	42	unit	unit	NOUN
cana-4523	60	43	time	time	NOUN
cana-4523	60	44	is	be	AUX
cana-4523	60	45	minimized	minimize	VERB
cana-4523	60	46	.	.	PUNCT
cana-4523	61	1	the	the	DET
cana-4523	61	2	replacement	replacement	NOUN
cana-4523	61	3	times	time	NOUN
cana-4523	61	4	are	be	AUX
cana-4523	61	5	defined	define	VERB
cana-4523	61	6	as	as	SCONJ
cana-4523	61	7	follows	follow	VERB
cana-4523	61	8	:	:	PUNCT
cana-4523	61	9	𝑇1	𝑇1	NOUN
cana-4523	61	10	represents	represent	VERB
cana-4523	61	11	the	the	DET
cana-4523	61	12	first	first	ADJ
cana-4523	61	13	replacement	replacement	NOUN
cana-4523	61	14	time	time	NOUN
cana-4523	61	15	,	,	PUNCT
cana-4523	61	16	and	and	CCONJ
cana-4523	61	17	for	for	ADP
cana-4523	61	18	n	n	NOUN
cana-4523	61	19	=	=	SYM
cana-4523	61	20	2	2	NUM
cana-4523	61	21	,	,	PUNCT
cana-4523	61	22	3	3	NUM
cana-4523	61	23	,	,	PUNCT
cana-4523	61	24	...	...	PUNCT
cana-4523	61	25	,	,	PUNCT
cana-4523	61	26	𝑇𝑛	𝑇𝑛	PROPN
cana-4523	61	27	denotes	denote	VERB
cana-4523	61	28	the	the	DET
cana-4523	61	29	time	time	NOUN
cana-4523	61	30	between	between	ADP
cana-4523	61	31	the	the	DET
cana-4523	61	32	(	(	PUNCT
cana-4523	61	33	n-1)-st	n-1)-st	NOUN
cana-4523	61	34	replacement	replacement	NOUN
cana-4523	61	35	and	and	CCONJ
cana-4523	61	36	the	the	DET
cana-4523	61	37	n	n	CCONJ
cana-4523	61	38	-	-	PUNCT
cana-4523	61	39	th	th	NUM
cana-4523	61	40	replacement	replacement	NOUN
cana-4523	61	41	.	.	PUNCT
cana-4523	62	1	consequently	consequently	ADV
cana-4523	62	2	,	,	PUNCT
cana-4523	62	3	the	the	DET
cana-4523	62	4	sequence	sequence	NOUN
cana-4523	62	5	{	{	PUNCT
cana-4523	62	6	𝑇𝑛	𝑇𝑛	PROPN
cana-4523	62	7	,	,	PUNCT
cana-4523	62	8	n	n	NOUN
cana-4523	62	9	=	=	SYM
cana-4523	62	10	1	1	NUM
cana-4523	62	11	,	,	PUNCT
cana-4523	62	12	2	2	NUM
cana-4523	62	13	,	,	PUNCT
cana-4523	62	14	...	...	PUNCT
cana-4523	62	15	}	}	PUNCT
cana-4523	62	16	constitutes	constitute	VERB
cana-4523	62	17	a	a	DET
cana-4523	62	18	renewal	renewal	NOUN
cana-4523	62	19	process	process	NOUN
cana-4523	62	20	.	.	PUNCT
cana-4523	63	1	cycle	cycle	NOUN
cana-4523	63	2	are	be	AUX
cana-4523	63	3	defined	define	VERB
cana-4523	63	4	by	by	ADP
cana-4523	63	5	the	the	DET
cana-4523	63	6	time	time	NOUN
cana-4523	63	7	between	between	ADP
cana-4523	63	8	consecutive	consecutive	ADJ
cana-4523	63	9	system	system	NOUN
cana-4523	63	10	replacements	replacement	NOUN
cana-4523	63	11	,	,	PUNCT
cana-4523	63	12	spanning	span	VERB
cana-4523	63	13	from	from	ADP
cana-4523	63	14	initial	initial	ADJ
cana-4523	63	15	installation	installation	NOUN
cana-4523	63	16	to	to	ADP
cana-4523	63	17	first	first	ADJ
cana-4523	63	18	replacement	replacement	NOUN
cana-4523	63	19	,	,	PUNCT
cana-4523	63	20	and	and	CCONJ
cana-4523	63	21	subsequent	subsequent	ADJ
cana-4523	63	22	replacement	replacement	NOUN
cana-4523	63	23	intervals	interval	NOUN
cana-4523	63	24	.	.	PUNCT
cana-4523	64	1	each	each	DET
cana-4523	64	2	replacement	replacement	NOUN
cana-4523	64	3	concludes	conclude	VERB
cana-4523	64	4	one	one	NUM
cana-4523	64	5	cycle	cycle	NOUN
cana-4523	64	6	and	and	CCONJ
cana-4523	64	7	begins	begin	VERB
cana-4523	64	8	another	another	PRON
cana-4523	64	9	.	.	PUNCT
cana-4523	65	1	by	by	ADP
cana-4523	65	2	combining	combine	VERB
cana-4523	65	3	the	the	DET
cana-4523	65	4	successive	successive	ADJ
cana-4523	65	5	cycles	cycle	NOUN
cana-4523	65	6	with	with	ADP
cana-4523	65	7	the	the	DET
cana-4523	65	8	costs	cost	NOUN
cana-4523	65	9	associated	associate	VERB
cana-4523	65	10	with	with	ADP
cana-4523	65	11	each	each	PRON
cana-4523	65	12	,	,	PUNCT
cana-4523	65	13	we	we	PRON
cana-4523	65	14	establish	establish	VERB
cana-4523	65	15	a	a	DET
cana-4523	65	16	renewal	renewal	NOUN
cana-4523	65	17	reward	reward	NOUN
cana-4523	65	18	process	process	NOUN
cana-4523	65	19	,	,	PUNCT
cana-4523	65	20	facilitating	facilitate	VERB
cana-4523	65	21	the	the	DET
cana-4523	65	22	assessment	assessment	NOUN
cana-4523	65	23	of	of	ADP
cana-4523	65	24	cumulative	cumulative	ADJ
cana-4523	65	25	costs	cost	NOUN
cana-4523	65	26	,	,	PUNCT
cana-4523	65	27	rewards	reward	NOUN
cana-4523	65	28	,	,	PUNCT
cana-4523	65	29	and	and	CCONJ
cana-4523	65	30	system	system	NOUN
cana-4523	65	31	efficiency	efficiency	NOUN
cana-4523	65	32	.	.	PUNCT
cana-4523	66	1	the	the	DET
cana-4523	66	2	cost	cost	NOUN
cana-4523	66	3	structure	structure	NOUN
cana-4523	66	4	for	for	ADP
cana-4523	66	5	this	this	DET
cana-4523	66	6	model	model	NOUN
cana-4523	66	7	is	be	AUX
cana-4523	66	8	,	,	PUNCT
cana-4523	66	9	𝐶(𝑇	𝐶(𝑇	ADJ
cana-4523	66	10	)	)	PUNCT
cana-4523	67	1	=	=	PUNCT
cana-4523	67	2	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
cana-4523	67	3	𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑	𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑	ADJ
cana-4523	67	4	𝑐𝑜𝑠𝑡	𝑐𝑜𝑠𝑡	NOUN
cana-4523	67	5	𝑖𝑛𝑐𝑢𝑟𝑟𝑒𝑑	𝑖𝑛𝑐𝑢𝑟𝑟𝑒𝑑	NOUN
cana-4523	67	6	𝑖𝑛	𝑖𝑛	X
cana-4523	67	7	𝑎	𝑎	DET
cana-4523	67	8	𝑐𝑦𝑐𝑙𝑒	𝑐𝑦𝑐𝑙𝑒	NOUN
cana-4523	67	9	𝑡ℎ𝑒	𝑡ℎ𝑒	VERB
cana-4523	67	10	𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑	𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑	ADJ
cana-4523	67	11	𝑙𝑒𝑛𝑔𝑡ℎ	𝑙𝑒𝑛𝑔𝑡ℎ	NOUN
cana-4523	67	12	𝑜𝑓	𝑜𝑓	ADP
cana-4523	67	13	𝑎	𝑎	PRON
cana-4523	67	14	𝑐𝑦𝑐𝑙𝑒	𝑐𝑦𝑐𝑙𝑒	NOUN
cana-4523	67	15	=	=	SYM
cana-4523	67	16	𝑐𝐸[∑	𝑐𝐸[∑	VERB
cana-4523	68	1	𝑌𝑘	𝑌𝑘	PROPN
cana-4523	68	2	𝜂−1	𝜂−1	VERB
cana-4523	68	3	𝑘=1	𝑘=1	X
cana-4523	68	4	]	]	PUNCT
cana-4523	69	1	−	−	PROPN
cana-4523	70	1	𝑟	𝑟	X
cana-4523	70	2	𝐸[∑	𝐸[∑	X
cana-4523	71	1	𝑋𝑘	𝑋𝑘	PROPN
cana-4523	71	2	𝜂	𝜂	NOUN
cana-4523	71	3	𝑘=1	𝑘=1	X
cana-4523	71	4	]	]	PUNCT
cana-4523	71	5	+	+	PUNCT
cana-4523	71	6	𝑅	𝑅	PROPN
cana-4523	71	7	+	+	CCONJ
cana-4523	71	8	𝑐𝑝𝐸	𝑐𝑝𝐸	NOUN
cana-4523	71	9	[	[	PUNCT
cana-4523	71	10	𝑍	𝑍	PROPN
cana-4523	71	11	]	]	PUNCT
cana-4523	71	12	𝐸[∑	𝐸[∑	NOUN
cana-4523	72	1	𝑋𝑘	𝑋𝑘	PROPN
cana-4523	72	2	𝜂	𝜂	PROPN
cana-4523	72	3	𝑘=1	𝑘=1	X
cana-4523	72	4	]	]	PUNCT
cana-4523	73	1	+	+	CCONJ
cana-4523	73	2	𝐸[∑	𝐸[∑	PROPN
cana-4523	73	3	𝑌𝑘	𝑌𝑘	PROPN
cana-4523	73	4	𝜂−1	𝜂−1	VERB
cana-4523	73	5	𝑘=1	𝑘=1	X
cana-4523	73	6	]	]	PUNCT
cana-4523	73	7	+	+	PUNCT
cana-4523	73	8	𝐸[𝑍	𝐸[𝑍	NOUN
cana-4523	73	9	]	]	PUNCT
cana-4523	73	10	,	,	PUNCT
cana-4523	73	11	(	(	PUNCT
cana-4523	73	12	2.1	2.1	NUM
cana-4523	73	13	)	)	PUNCT
cana-4523	73	14	where	where	SCONJ
cana-4523	73	15	𝜂	𝜂	NOUN
cana-4523	73	16	is	be	AUX
cana-4523	73	17	a	a	DET
cana-4523	73	18	random	random	ADJ
cana-4523	73	19	variable	variable	NOUN
cana-4523	73	20	denoting	denote	VERB
cana-4523	73	21	the	the	DET
cana-4523	73	22	number	number	NOUN
cana-4523	73	23	of	of	ADP
cana-4523	73	24	failures	failure	NOUN
cana-4523	73	25	before	before	ADP
cana-4523	73	26	the	the	DET
cana-4523	73	27	working	work	VERB
cana-4523	73	28	age	age	NOUN
cana-4523	73	29	of	of	ADP
cana-4523	73	30	the	the	DET
cana-4523	73	31	system	system	NOUN
cana-4523	73	32	reaches	reach	VERB
cana-4523	73	33	.t	.t	PROPN
cana-4523	73	34	communications	communication	NOUN
cana-4523	73	35	on	on	ADP
cana-4523	73	36	applied	apply	VERB
cana-4523	73	37	nonlinear	nonlinear	ADJ
cana-4523	73	38	analysis	analysis	NOUN
cana-4523	73	39	issn	issn	NOUN
cana-4523	73	40	:	:	PUNCT
cana-4523	73	41	1074	1074	NUM
cana-4523	73	42	-	-	PUNCT
cana-4523	73	43	133x	133x	NUM
cana-4523	73	44	vol	vol	NOUN
cana-4523	73	45	32	32	NUM
cana-4523	73	46	no	no	NOUN
cana-4523	73	47	.	.	PUNCT
cana-4523	74	1	9s	9s	NUM
cana-4523	74	2	(	(	PUNCT
cana-4523	74	3	2025	2025	NUM
cana-4523	74	4	)	)	PUNCT
cana-4523	74	5	2362	2362	NUM
cana-4523	74	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	74	7	𝐸	𝐸	PROPN
cana-4523	75	1	[	[	X
cana-4523	75	2	∑	∑	X
cana-4523	75	3	𝑋𝑘	𝑋𝑘	NOUN
cana-4523	75	4	𝜂	𝜂	NOUN
cana-4523	75	5	𝑘=1	𝑘=1	X
cana-4523	75	6	]	]	PUNCT
cana-4523	75	7	=	=	PUNCT
cana-4523	75	8	𝐸	𝐸	PROPN
cana-4523	76	1	[	[	X
cana-4523	76	2	𝐸	𝐸	ADJ
cana-4523	76	3	[	[	X
cana-4523	76	4	∑	∑	X
cana-4523	76	5	𝑋𝑘	𝑋𝑘	PROPN
cana-4523	76	6	𝑛−1	𝑛−1	PROPN
cana-4523	76	7	𝑘=1	𝑘=1	NOUN
cana-4523	76	8	|	|	NOUN
cana-4523	76	9	=	=	SYM
cana-4523	76	10	𝑛	𝑛	NOUN
cana-4523	76	11	]	]	X
cana-4523	76	12	]	]	X
cana-4523	76	13	=	=	PUNCT
cana-4523	76	14	𝜇	𝜇	ADP
cana-4523	76	15	∑	∑	PUNCT
cana-4523	76	16	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	76	17	)	)	PUNCT
cana-4523	76	18	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	76	19	∞	∞	NUM
cana-4523	76	20	𝑛=1	𝑛=1	NOUN
cana-4523	76	21	(	(	PUNCT
cana-4523	76	22	2.2	2.2	NUM
cana-4523	76	23	)	)	PUNCT
cana-4523	76	24	where	where	SCONJ
cana-4523	76	25	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	76	26	(	(	PUNCT
cana-4523	76	27	·	·	PUNCT
cana-4523	76	28	)	)	PUNCT
cana-4523	76	29	is	be	AUX
cana-4523	76	30	the	the	DET
cana-4523	76	31	n	n	NUM
cana-4523	76	32	-fold	-fold	ADJ
cana-4523	76	33	convolution	convolution	NOUN
cana-4523	76	34	of	of	ADP
cana-4523	76	35	f	f	PROPN
cana-4523	76	36	(	(	PUNCT
cana-4523	76	37	·	·	PUNCT
cana-4523	76	38	)	)	PUNCT
cana-4523	76	39	with	with	ADP
cana-4523	76	40	itself	itself	PRON
cana-4523	76	41	and	and	CCONJ
cana-4523	76	42	𝐸	𝐸	PRON
cana-4523	77	1	[	[	X
cana-4523	77	2	∑	∑	PROPN
cana-4523	77	3	𝑌𝑘	𝑌𝑘	PROPN
cana-4523	77	4	𝜂−1	𝜂−1	X
cana-4523	77	5	𝑘=1	𝑘=1	X
cana-4523	77	6	]	]	PUNCT
cana-4523	78	1	=	=	PUNCT
cana-4523	78	2	∑	∑	PUNCT
cana-4523	78	3	[	[	X
cana-4523	78	4	∑	∑	INTJ
cana-4523	78	5	𝐸[𝑌𝑘	𝐸[𝑌𝑘	ADJ
cana-4523	78	6	]	]	X
cana-4523	78	7	𝑛−1	𝑛−1	PROPN
cana-4523	78	8	𝑘=1	𝑘=1	NOUN
cana-4523	78	9	]	]	PUNCT
cana-4523	78	10	𝑃(=	𝑃(=	NOUN
cana-4523	78	11	𝑛	𝑛	PRON
cana-4523	78	12	−	−	PROPN
cana-4523	78	13	1	1	NUM
cana-4523	78	14	)	)	PUNCT
cana-4523	78	15	∞	∞	NUM
cana-4523	78	16	𝑛=1	𝑛=1	NOUN
cana-4523	78	17	=	=	SYM
cana-4523	78	18	𝛾	𝛾	NOUN
cana-4523	78	19	∑	∑	PUNCT
cana-4523	78	20	𝐺𝑛(𝑇	𝐺𝑛(𝑇	ADJ
cana-4523	78	21	)	)	PUNCT
cana-4523	78	22	𝑎𝑛−1	𝑎𝑛−1	PROPN
cana-4523	78	23	∞	∞	PROPN
cana-4523	78	24	𝑛=1	𝑛=1	NOUN
cana-4523	78	25	(	(	PUNCT
cana-4523	78	26	2.3	2.3	NUM
cana-4523	78	27	)	)	PUNCT
cana-4523	78	28	where	where	SCONJ
cana-4523	78	29	𝐺𝑛	𝐺𝑛	PROPN
cana-4523	78	30	(	(	PUNCT
cana-4523	78	31	·	·	PUNCT
cana-4523	78	32	)	)	PUNCT
cana-4523	78	33	is	be	AUX
cana-4523	78	34	the	the	DET
cana-4523	78	35	n	n	ADV
cana-4523	78	36	-fold	-fold	ADJ
cana-4523	78	37	convolution	convolution	NOUN
cana-4523	78	38	of	of	ADP
cana-4523	78	39	g	g	PROPN
cana-4523	78	40	(	(	PUNCT
cana-4523	78	41	·	·	PUNCT
cana-4523	78	42	)	)	PUNCT
cana-4523	78	43	with	with	ADP
cana-4523	78	44	itself	itself	PRON
cana-4523	78	45	.	.	PUNCT
cana-4523	79	1	using	use	VERB
cana-4523	79	2	equations	equation	NOUN
cana-4523	79	3	(	(	PUNCT
cana-4523	79	4	2.2	2.2	NUM
cana-4523	79	5	)	)	PUNCT
cana-4523	79	6	and	and	CCONJ
cana-4523	79	7	(	(	PUNCT
cana-4523	79	8	2.3	2.3	NUM
cana-4523	79	9	)	)	PUNCT
cana-4523	79	10	,	,	PUNCT
cana-4523	79	11	the	the	DET
cana-4523	79	12	equation	equation	NOUN
cana-4523	79	13	(	(	PUNCT
cana-4523	79	14	2.1	2.1	NUM
cana-4523	79	15	)	)	PUNCT
cana-4523	79	16	becomes	become	VERB
cana-4523	79	17	𝐶(𝑇	𝐶(𝑇	ADJ
cana-4523	79	18	)	)	PUNCT
cana-4523	79	19	=	=	SYM
cana-4523	79	20	𝑐𝛾	𝑐𝛾	ADP
cana-4523	79	21	∑	∑	ADV
cana-4523	79	22	𝐺𝑛(𝑇	𝐺𝑛(𝑇	ADJ
cana-4523	79	23	)	)	PUNCT
cana-4523	79	24	𝑎𝑛−1	𝑎𝑛−1	PROPN
cana-4523	79	25	∞	∞	PROPN
cana-4523	79	26	𝑛=1	𝑛=1	NOUN
cana-4523	79	27	−	−	NOUN
cana-4523	79	28	𝑟	𝑟	NOUN
cana-4523	79	29	𝜇	𝜇	X
cana-4523	79	30	∑	∑	PUNCT
cana-4523	79	31	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	79	32	)	)	PUNCT
cana-4523	79	33	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	79	34	∞	∞	NUM
cana-4523	79	35	𝑛=1	𝑛=1	NOUN
cana-4523	79	36	+	+	X
cana-4523	79	37	𝑅	𝑅	PROPN
cana-4523	79	38	+	+	NOUN
cana-4523	79	39	𝑐𝑝	𝑐𝑝	ADP
cana-4523	79	40	𝜏	𝜏	PRON
cana-4523	79	41	𝜇	𝜇	ADP
cana-4523	79	42	∑	∑	ADV
cana-4523	79	43	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	79	44	)	)	PUNCT
cana-4523	79	45	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	79	46	∞	∞	NUM
cana-4523	79	47	𝑛=1	𝑛=1	NOUN
cana-4523	79	48	+	+	CCONJ
cana-4523	79	49	𝛾	𝛾	NOUN
cana-4523	79	50	∑	∑	PUNCT
cana-4523	79	51	𝐺𝑛(𝑇	𝐺𝑛(𝑇	ADJ
cana-4523	79	52	)	)	PUNCT
cana-4523	79	53	𝑎𝑛−1	𝑎𝑛−1	PROPN
cana-4523	79	54	∞	∞	NUM
cana-4523	79	55	𝑛=1	𝑛=1	NOUN
cana-4523	79	56	+	+	X
cana-4523	79	57	𝜏	𝜏	X
cana-4523	79	58	(	(	PUNCT
cana-4523	79	59	2.4	2.4	NUM
cana-4523	79	60	)	)	PUNCT
cana-4523	79	61	further	further	ADJ
cana-4523	79	62	𝐶(𝑇	𝐶(𝑇	NUM
cana-4523	79	63	)	)	PUNCT
cana-4523	80	1	=	=	SYM
cana-4523	80	2	(	(	PUNCT
cana-4523	80	3	𝑐	𝑐	PROPN
cana-4523	80	4	+	+	NUM
cana-4523	80	5	𝑟	𝑟	NOUN
cana-4523	80	6	)	)	PUNCT
cana-4523	80	7	∑	∑	PUNCT
cana-4523	80	8	(	(	PUNCT
cana-4523	80	9	𝛾	𝛾	PART
cana-4523	80	10	𝑎𝑛−1)𝑛−1	𝑎𝑛−1)𝑛−1	VERB
cana-4523	80	11	𝑖=1	𝑖=1	PUNCT
cana-4523	80	12	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	80	13	)	)	PUNCT
cana-4523	80	14	+	+	CCONJ
cana-4523	80	15	𝑅1	𝑅1	NOUN
cana-4523	80	16	𝜇	𝜇	ADP
cana-4523	80	17	∑	∑	PUNCT
cana-4523	80	18	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	80	19	)	)	PUNCT
cana-4523	80	20	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	80	21	∞	∞	NUM
cana-4523	80	22	𝑛=1	𝑛=1	NOUN
cana-4523	80	23	+	+	CCONJ
cana-4523	80	24	𝛾	𝛾	NOUN
cana-4523	80	25	∑	∑	PUNCT
cana-4523	80	26	𝐺𝑛(𝑇	𝐺𝑛(𝑇	ADJ
cana-4523	80	27	)	)	PUNCT
cana-4523	80	28	𝑎𝑛−1	𝑎𝑛−1	PROPN
cana-4523	80	29	∞	∞	NUM
cana-4523	80	30	𝑛=1	𝑛=1	NOUN
cana-4523	80	31	+	+	CCONJ
cana-4523	80	32	𝜏	𝜏	PART
cana-4523	80	33	−	−	NOUN
cana-4523	80	34	𝑟	𝑟	NOUN
cana-4523	80	35	where	where	SCONJ
cana-4523	80	36	𝑅1	𝑅1	PROPN
cana-4523	80	37	=	=	SYM
cana-4523	80	38	𝑅	𝑅	PROPN
cana-4523	80	39	+	+	CCONJ
cana-4523	80	40	(	(	PUNCT
cana-4523	80	41	𝑐𝑝	𝑐𝑝	ADP
cana-4523	80	42	+	+	NOUN
cana-4523	80	43	𝑟)𝜏	𝑟)𝜏	NOUN
cana-4523	80	44	,	,	PUNCT
cana-4523	80	45	𝐶1(𝑇	𝐶1(𝑇	NUM
cana-4523	80	46	)	)	PUNCT
cana-4523	80	47	=	=	SYM
cana-4523	81	1	(	(	PUNCT
cana-4523	81	2	𝑐	𝑐	PROPN
cana-4523	81	3	+	+	NUM
cana-4523	81	4	𝑟	𝑟	NOUN
cana-4523	81	5	)	)	PUNCT
cana-4523	81	6	∑	∑	PUNCT
cana-4523	81	7	(	(	PUNCT
cana-4523	81	8	𝛾	𝛾	PART
cana-4523	81	9	𝑎𝑛−1)𝑛−1	𝑎𝑛−1)𝑛−1	VERB
cana-4523	81	10	𝑖=1	𝑖=1	PUNCT
cana-4523	81	11	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	81	12	)	)	PUNCT
cana-4523	82	1	+	+	CCONJ
cana-4523	82	2	𝑅1	𝑅1	NOUN
cana-4523	82	3	𝜇	𝜇	ADP
cana-4523	82	4	∑	∑	PUNCT
cana-4523	82	5	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	82	6	)	)	PUNCT
cana-4523	82	7	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	82	8	∞	∞	NUM
cana-4523	82	9	𝑛=1	𝑛=1	NOUN
cana-4523	82	10	+	+	CCONJ
cana-4523	82	11	𝛾	𝛾	NOUN
cana-4523	82	12	∑	∑	PUNCT
cana-4523	82	13	𝐺𝑛(𝑇	𝐺𝑛(𝑇	ADJ
cana-4523	82	14	)	)	PUNCT
cana-4523	82	15	𝑎𝑛−1	𝑎𝑛−1	PROPN
cana-4523	82	16	∞	∞	NUM
cana-4523	82	17	𝑛=1	𝑛=1	NOUN
cana-4523	82	18	+	+	X
cana-4523	82	19	𝜏	𝜏	X
cana-4523	82	20	(	(	PUNCT
cana-4523	82	21	2.5	2.5	NUM
cana-4523	82	22	)	)	PUNCT
cana-4523	82	23	on	on	ADP
cana-4523	82	24	differentiating	differentiate	VERB
cana-4523	82	25	(	(	PUNCT
cana-4523	82	26	2.5	2.5	NUM
cana-4523	82	27	)	)	PUNCT
cana-4523	82	28	we	we	PRON
cana-4523	82	29	get	get	VERB
cana-4523	82	30	𝐶1	𝐶1	NUM
cana-4523	82	31	′(𝑇	′(𝑇	NOUN
cana-4523	82	32	)	)	PUNCT
cana-4523	83	1	=	=	PUNCT
cana-4523	84	1	[	[	PUNCT
cana-4523	84	2	[	[	X
cana-4523	84	3	𝜇	𝜇	ADP
cana-4523	84	4	∑	∑	PUNCT
cana-4523	84	5	∞	∞	PROPN
cana-4523	84	6	𝑛=1	𝑛=1	NOUN
cana-4523	84	7	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	84	8	)	)	PUNCT
cana-4523	84	9	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	84	10	+	+	PUNCT
cana-4523	84	11	𝜏	𝜏	X
cana-4523	84	12	]	]	X
cana-4523	85	1	[	[	X
cana-4523	85	2	(	(	PUNCT
cana-4523	85	3	𝑐	𝑐	NOUN
cana-4523	85	4	+	+	NOUN
cana-4523	85	5	𝑟	𝑟	NOUN
cana-4523	85	6	)	)	PUNCT
cana-4523	85	7	∑	∑	PUNCT
cana-4523	85	8	𝑛−1	𝑛−1	PROPN
cana-4523	85	9	𝑛=1	𝑛=1	NOUN
cana-4523	85	10	(	(	PUNCT
cana-4523	85	11	𝛾	𝛾	ADP
cana-4523	85	12	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	85	13	)	)	PUNCT
cana-4523	86	1	𝐺𝑛	𝐺𝑛	ADJ
cana-4523	86	2	′(𝑇	′(𝑇	NOUN
cana-4523	86	3	)	)	PUNCT
cana-4523	86	4	]	]	PUNCT
cana-4523	87	1	−	−	PUNCT
cana-4523	88	1	[	[	X
cana-4523	88	2	(	(	PUNCT
cana-4523	88	3	𝑐	𝑐	NOUN
cana-4523	88	4	+	+	NUM
cana-4523	88	5	𝑟)𝛾	𝑟)𝛾	NOUN
cana-4523	88	6	∑	∑	ADP
cana-4523	88	7	𝑛−1	𝑛−1	PROPN
cana-4523	88	8	𝑛=1	𝑛=1	NOUN
cana-4523	88	9	(	(	PUNCT
cana-4523	88	10	𝛾	𝛾	PROPN
cana-4523	88	11	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	88	12	)	)	PUNCT
cana-4523	88	13	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	88	14	)	)	PUNCT
cana-4523	88	15	+	+	CCONJ
cana-4523	88	16	𝑅1	𝑅1	PROPN
cana-4523	88	17	]	]	X
cana-4523	89	1	[	[	X
cana-4523	89	2	(	(	PUNCT
cana-4523	89	3	𝜇	𝜇	ADP
cana-4523	89	4	∑	∑	PROPN
cana-4523	89	5	∞	∞	PROPN
cana-4523	89	6	𝑛=1	𝑛=1	NOUN
cana-4523	89	7	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	89	8	′(𝑇	′(𝑇	NOUN
cana-4523	89	9	)	)	PUNCT
cana-4523	89	10	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	89	11	)	)	PUNCT
cana-4523	89	12	]	]	PUNCT
cana-4523	89	13	]	]	PUNCT
cana-4523	89	14	(	(	PUNCT
cana-4523	89	15	μ	μ	NOUN
cana-4523	89	16	∑	∑	PROPN
cana-4523	89	17	∞	∞	PROPN
cana-4523	89	18	𝑛=1	𝑛=1	NOUN
cana-4523	89	19	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	89	20	)	)	PUNCT
cana-4523	89	21	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	89	22	+	+	CCONJ
cana-4523	89	23	∑	∑	PROPN
cana-4523	89	24	𝑛−1	𝑛−1	PROPN
cana-4523	89	25	𝑖=1	𝑖=1	PROPN
cana-4523	89	26	(	(	PUNCT
cana-4523	89	27	𝛾	𝛾	AUX
cana-4523	89	28	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	89	29	)	)	PUNCT
cana-4523	89	30	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	89	31	)	)	PUNCT
cana-4523	90	1	+	+	CCONJ
cana-4523	90	2	𝜏	𝜏	X
cana-4523	90	3	)	)	PUNCT
cana-4523	90	4	2	2	NUM
cana-4523	90	5	(	(	PUNCT
cana-4523	90	6	2.6	2.6	NUM
cana-4523	90	7	)	)	PUNCT
cana-4523	90	8	if	if	SCONJ
cana-4523	90	9	𝐶1	𝐶1	NOUN
cana-4523	90	10	′(𝑇	′(𝑇	NOUN
cana-4523	90	11	)	)	PUNCT
cana-4523	91	1	=	=	SYM
cana-4523	91	2	0	0	PUNCT
cana-4523	91	3	,	,	PUNCT
cana-4523	91	4	then	then	ADV
cana-4523	92	1	[	[	X
cana-4523	92	2	[	[	X
cana-4523	92	3	𝜇	𝜇	ADP
cana-4523	92	4	∑	∑	PROPN
cana-4523	92	5	∞	∞	PROPN
cana-4523	92	6	𝑛=1	𝑛=1	NOUN
cana-4523	92	7	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	92	8	)	)	PUNCT
cana-4523	92	9	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	92	10	+	+	PUNCT
cana-4523	92	11	𝜏	𝜏	X
cana-4523	92	12	]	]	X
cana-4523	92	13	[	[	X
cana-4523	92	14	(	(	PUNCT
cana-4523	92	15	𝑐	𝑐	NOUN
cana-4523	92	16	+	+	NOUN
cana-4523	92	17	𝑟	𝑟	NOUN
cana-4523	92	18	)	)	PUNCT
cana-4523	92	19	∑	∑	PUNCT
cana-4523	92	20	𝑛−1	𝑛−1	PROPN
cana-4523	92	21	𝑛=1	𝑛=1	NOUN
cana-4523	92	22	(	(	PUNCT
cana-4523	92	23	𝛾	𝛾	NOUN
cana-4523	92	24	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	92	25	)	)	PUNCT
cana-4523	93	1	𝐺𝑛	𝐺𝑛	ADJ
cana-4523	93	2	′(𝑇	′(𝑇	NOUN
cana-4523	93	3	)	)	PUNCT
cana-4523	93	4	]	]	PUNCT
cana-4523	94	1	−	−	PUNCT
cana-4523	95	1	[	[	X
cana-4523	95	2	(	(	PUNCT
cana-4523	95	3	𝑐	𝑐	NOUN
cana-4523	95	4	+	+	NOUN
cana-4523	95	5	𝑟	𝑟	NOUN
cana-4523	95	6	)	)	PUNCT
cana-4523	95	7	∑	∑	PUNCT
cana-4523	95	8	𝑛−1	𝑛−1	PROPN
cana-4523	95	9	𝑛=1	𝑛=1	NOUN
cana-4523	95	10	(	(	PUNCT
cana-4523	95	11	𝛾	𝛾	PROPN
cana-4523	95	12	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	95	13	)	)	PUNCT
cana-4523	95	14	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	95	15	)	)	PUNCT
cana-4523	95	16	+	+	CCONJ
cana-4523	95	17	𝑅1	𝑅1	PROPN
cana-4523	95	18	]	]	X
cana-4523	95	19	[	[	X
cana-4523	95	20	(	(	PUNCT
cana-4523	95	21	𝜇	𝜇	ADP
cana-4523	95	22	∑	∑	PROPN
cana-4523	95	23	∞	∞	PROPN
cana-4523	95	24	𝑛=1	𝑛=1	NOUN
cana-4523	95	25	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	95	26	′(𝑇	′(𝑇	NOUN
cana-4523	95	27	)	)	PUNCT
cana-4523	95	28	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	95	29	)	)	PUNCT
cana-4523	95	30	]	]	PUNCT
cana-4523	95	31	]	]	PUNCT
cana-4523	95	32	=	=	SYM
cana-4523	95	33	0	0	NUM
cana-4523	95	34	communications	communication	NOUN
cana-4523	95	35	on	on	ADP
cana-4523	95	36	applied	apply	VERB
cana-4523	95	37	nonlinear	nonlinear	ADJ
cana-4523	95	38	analysis	analysis	NOUN
cana-4523	95	39	issn	issn	NOUN
cana-4523	95	40	:	:	PUNCT
cana-4523	95	41	1074	1074	NUM
cana-4523	95	42	-	-	PUNCT
cana-4523	95	43	133x	133x	NUM
cana-4523	95	44	vol	vol	NOUN
cana-4523	95	45	32	32	NUM
cana-4523	95	46	no	no	NOUN
cana-4523	95	47	.	.	PUNCT
cana-4523	96	1	9s	9s	NUM
cana-4523	96	2	(	(	PUNCT
cana-4523	96	3	2025	2025	NUM
cana-4523	96	4	)	)	PUNCT
cana-4523	96	5	2363	2363	NUM
cana-4523	96	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	96	7	which	which	PRON
cana-4523	96	8	implies	imply	VERB
cana-4523	96	9	[	[	X
cana-4523	96	10	𝜇	𝜇	ADP
cana-4523	96	11	∑	∑	PUNCT
cana-4523	96	12	∞	∞	PROPN
cana-4523	96	13	𝑛=1	𝑛=1	NOUN
cana-4523	96	14	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	96	15	)	)	PUNCT
cana-4523	96	16	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	97	1	+	+	PUNCT
cana-4523	98	1	𝜏	𝜏	X
cana-4523	98	2	]	]	X
cana-4523	98	3	[	[	X
cana-4523	98	4	(	(	PUNCT
cana-4523	98	5	𝑐	𝑐	NOUN
cana-4523	98	6	+	+	NOUN
cana-4523	98	7	𝑟	𝑟	NOUN
cana-4523	98	8	)	)	PUNCT
cana-4523	98	9	∑	∑	PUNCT
cana-4523	98	10	𝑛−1	𝑛−1	PROPN
cana-4523	98	11	𝑛=1	𝑛=1	NOUN
cana-4523	98	12	(	(	PUNCT
cana-4523	98	13	𝛾	𝛾	NOUN
cana-4523	98	14	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	98	15	)	)	PUNCT
cana-4523	99	1	𝐺𝑛	𝐺𝑛	ADJ
cana-4523	99	2	′(𝑇	′(𝑇	NOUN
cana-4523	99	3	)	)	PUNCT
cana-4523	99	4	]	]	PUNCT
cana-4523	100	1	=	=	PUNCT
cana-4523	101	1	[	[	X
cana-4523	101	2	(	(	PUNCT
cana-4523	101	3	𝑐	𝑐	NOUN
cana-4523	101	4	+	+	NOUN
cana-4523	101	5	𝑟	𝑟	NOUN
cana-4523	101	6	)	)	PUNCT
cana-4523	101	7	∑	∑	PUNCT
cana-4523	101	8	𝑛−1	𝑛−1	PROPN
cana-4523	101	9	𝑛=1	𝑛=1	NOUN
cana-4523	101	10	(	(	PUNCT
cana-4523	101	11	𝛾	𝛾	PROPN
cana-4523	101	12	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	101	13	)	)	PUNCT
cana-4523	101	14	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	101	15	)	)	PUNCT
cana-4523	101	16	+	+	CCONJ
cana-4523	101	17	𝑅1	𝑅1	PROPN
cana-4523	101	18	]	]	X
cana-4523	102	1	[	[	X
cana-4523	102	2	(	(	PUNCT
cana-4523	102	3	𝜇	𝜇	ADP
cana-4523	102	4	∑	∑	PROPN
cana-4523	102	5	∞	∞	PROPN
cana-4523	102	6	𝑛=1	𝑛=1	NOUN
cana-4523	102	7	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	102	8	′(𝑇	′(𝑇	NOUN
cana-4523	102	9	)	)	PUNCT
cana-4523	102	10	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	102	11	)	)	PUNCT
cana-4523	102	12	]	]	PUNCT
cana-4523	102	13	(	(	PUNCT
cana-4523	102	14	2.7	2.7	NUM
cana-4523	102	15	)	)	PUNCT
cana-4523	102	16	again	again	ADV
cana-4523	102	17	differentiating	differentiate	VERB
cana-4523	102	18	equation	equation	NOUN
cana-4523	102	19	(	(	PUNCT
cana-4523	102	20	2.6	2.6	NUM
cana-4523	102	21	)	)	PUNCT
cana-4523	102	22	using	use	VERB
cana-4523	102	23	the	the	DET
cana-4523	102	24	equation	equation	NOUN
cana-4523	102	25	(	(	PUNCT
cana-4523	102	26	2.7	2.7	NUM
cana-4523	102	27	)	)	PUNCT
cana-4523	102	28	we	we	PRON
cana-4523	102	29	obtain	obtain	VERB
cana-4523	102	30	𝐶1	𝐶1	PRON
cana-4523	102	31	′′(𝑇	′′(𝑇	X
cana-4523	102	32	)	)	PUNCT
cana-4523	102	33	=	=	NOUN
cana-4523	103	1	[	[	PUNCT
cana-4523	103	2	[	[	X
cana-4523	103	3	𝜇	𝜇	ADP
cana-4523	103	4	∑	∑	PUNCT
cana-4523	103	5	∞	∞	PROPN
cana-4523	103	6	𝑛=1	𝑛=1	NOUN
cana-4523	103	7	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	103	8	)	)	PUNCT
cana-4523	103	9	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	103	10	+	+	PUNCT
cana-4523	103	11	𝜏	𝜏	X
cana-4523	103	12	]	]	X
cana-4523	104	1	[	[	X
cana-4523	104	2	(	(	PUNCT
cana-4523	104	3	𝑐	𝑐	NOUN
cana-4523	104	4	+	+	NOUN
cana-4523	104	5	𝑟	𝑟	NOUN
cana-4523	104	6	)	)	PUNCT
cana-4523	104	7	∑	∑	ADV
cana-4523	104	8	𝑛−1	𝑛−1	PROPN
cana-4523	104	9	𝑖=1	𝑖=1	PROPN
cana-4523	104	10	(	(	PUNCT
cana-4523	104	11	𝛾	𝛾	PROPN
cana-4523	104	12	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	104	13	)	)	PUNCT
cana-4523	104	14	𝐺𝑛	𝐺𝑛	NOUN
cana-4523	104	15	′′(𝑇	′′(𝑇	NOUN
cana-4523	104	16	)	)	PUNCT
cana-4523	104	17	]	]	PUNCT
cana-4523	104	18	−	−	PROPN
cana-4523	105	1	[	[	X
cana-4523	105	2	(	(	PUNCT
cana-4523	105	3	𝑐	𝑐	NOUN
cana-4523	105	4	+	+	NOUN
cana-4523	105	5	𝑟	𝑟	NOUN
cana-4523	105	6	)	)	PUNCT
cana-4523	105	7	∑	∑	ADV
cana-4523	105	8	𝑛−1	𝑛−1	PROPN
cana-4523	105	9	𝑖=1	𝑖=1	PROPN
cana-4523	105	10	(	(	PUNCT
cana-4523	105	11	𝛾	𝛾	PROPN
cana-4523	105	12	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	105	13	)	)	PUNCT
cana-4523	105	14	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	105	15	)	)	PUNCT
cana-4523	105	16	+	+	CCONJ
cana-4523	105	17	𝑅1	𝑅1	PROPN
cana-4523	105	18	]	]	X
cana-4523	105	19	[	[	X
cana-4523	105	20	(	(	PUNCT
cana-4523	105	21	𝜇	𝜇	ADP
cana-4523	105	22	∑	∑	PROPN
cana-4523	105	23	∞	∞	PROPN
cana-4523	105	24	𝑛=1	𝑛=1	NOUN
cana-4523	106	1	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	106	2	′′(𝑇	′′(𝑇	NOUN
cana-4523	106	3	)	)	PUNCT
cana-4523	106	4	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	106	5	)	)	PUNCT
cana-4523	106	6	]	]	PUNCT
cana-4523	106	7	]	]	PUNCT
cana-4523	106	8	(	(	PUNCT
cana-4523	106	9	𝜇	𝜇	ADP
cana-4523	106	10	∑	∑	PUNCT
cana-4523	106	11	∞	∞	PROPN
cana-4523	106	12	𝑛=1	𝑛=1	NOUN
cana-4523	106	13	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	106	14	)	)	PUNCT
cana-4523	106	15	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	106	16	+	+	CCONJ
cana-4523	106	17	∑	∑	PROPN
cana-4523	106	18	𝑛−1	𝑛−1	PROPN
cana-4523	106	19	𝑖=1	𝑖=1	PROPN
cana-4523	106	20	(	(	PUNCT
cana-4523	106	21	𝛾	𝛾	PROPN
cana-4523	106	22	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	106	23	)	)	PUNCT
cana-4523	106	24	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	106	25	)	)	PUNCT
cana-4523	106	26	+	+	CCONJ
cana-4523	106	27	𝜏	𝜏	X
cana-4523	106	28	)	)	PUNCT
cana-4523	106	29	2	2	NUM
cana-4523	106	30	if	if	SCONJ
cana-4523	106	31	𝐶1′′(𝑇	𝐶1′′(𝑇	ADJ
cana-4523	106	32	)	)	PUNCT
cana-4523	106	33	>	>	X
cana-4523	106	34	0	0	NUM
cana-4523	106	35	,	,	PUNCT
cana-4523	106	36	then	then	ADV
cana-4523	106	37	[	[	X
cana-4523	106	38	𝜇	𝜇	ADP
cana-4523	106	39	∑	∑	PROPN
cana-4523	106	40	∞	∞	PROPN
cana-4523	106	41	𝑛=1	𝑛=1	NOUN
cana-4523	106	42	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	106	43	)	)	PUNCT
cana-4523	106	44	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	106	45	+	+	PUNCT
cana-4523	106	46	𝜏	𝜏	X
cana-4523	106	47	]	]	X
cana-4523	106	48	[	[	X
cana-4523	106	49	(	(	PUNCT
cana-4523	106	50	𝑐	𝑐	NOUN
cana-4523	106	51	+	+	NOUN
cana-4523	106	52	𝑟	𝑟	NOUN
cana-4523	106	53	)	)	PUNCT
cana-4523	106	54	∑	∑	PUNCT
cana-4523	106	55	𝑛−1	𝑛−1	PROPN
cana-4523	106	56	𝑛=1	𝑛=1	NOUN
cana-4523	106	57	(	(	PUNCT
cana-4523	106	58	𝛾	𝛾	PROPN
cana-4523	106	59	𝑎𝑖−1	𝑎𝑖−1	NOUN
cana-4523	106	60	)	)	PUNCT
cana-4523	106	61	𝐺𝑛	𝐺𝑛	PROPN
cana-4523	106	62	′′(𝑇	′′(𝑇	NOUN
cana-4523	106	63	)	)	PUNCT
cana-4523	106	64	]	]	PUNCT
cana-4523	106	65	>	>	X
cana-4523	107	1	[	[	X
cana-4523	107	2	(	(	PUNCT
cana-4523	107	3	𝑐	𝑐	NOUN
cana-4523	107	4	+	+	NOUN
cana-4523	107	5	𝑟	𝑟	NOUN
cana-4523	107	6	)	)	PUNCT
cana-4523	107	7	∑	∑	PUNCT
cana-4523	107	8	𝑛−1	𝑛−1	PROPN
cana-4523	107	9	𝑛=1	𝑛=1	NOUN
cana-4523	107	10	(	(	PUNCT
cana-4523	107	11	𝛾	𝛾	PROPN
cana-4523	107	12	𝑎𝑖−1	𝑎𝑖−1	NOUN
cana-4523	107	13	)	)	PUNCT
cana-4523	107	14	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	107	15	)	)	PUNCT
cana-4523	107	16	+	+	CCONJ
cana-4523	107	17	𝑅1	𝑅1	PROPN
cana-4523	107	18	]	]	X
cana-4523	108	1	[	[	X
cana-4523	108	2	(	(	PUNCT
cana-4523	108	3	𝜇	𝜇	ADP
cana-4523	108	4	∑	∑	ADP
cana-4523	108	5	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	108	6	′′(𝑇	′′(𝑇	NOUN
cana-4523	108	7	)	)	PUNCT
cana-4523	108	8	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	108	9	∞	∞	NUM
cana-4523	108	10	𝑛=1	𝑛=1	NOUN
cana-4523	108	11	)	)	PUNCT
cana-4523	108	12	]	]	PUNCT
cana-4523	108	13	(	(	PUNCT
cana-4523	108	14	2.8	2.8	NUM
cana-4523	108	15	)	)	PUNCT
cana-4523	108	16	the	the	DET
cana-4523	108	17	equation	equation	NOUN
cana-4523	108	18	(	(	PUNCT
cana-4523	108	19	2.7	2.7	NUM
cana-4523	108	20	)	)	PUNCT
cana-4523	108	21	gives	give	VERB
cana-4523	108	22	t	t	PROPN
cana-4523	108	23	*	*	PUNCT
cana-4523	108	24	for	for	ADP
cana-4523	108	25	which	which	PRON
cana-4523	108	26	c(t	c(t	PROPN
cana-4523	108	27	*	*	PUNCT
cana-4523	108	28	)	)	PUNCT
cana-4523	108	29	is	be	AUX
cana-4523	108	30	minimum	minimum	ADJ
cana-4523	108	31	.	.	PUNCT
cana-4523	109	1	based	base	VERB
cana-4523	109	2	on	on	ADP
cana-4523	109	3	the	the	DET
cana-4523	109	4	preceding	precede	VERB
cana-4523	109	5	discussion	discussion	NOUN
cana-4523	109	6	,	,	PUNCT
cana-4523	109	7	we	we	PRON
cana-4523	109	8	obtain	obtain	VERB
cana-4523	109	9	the	the	DET
cana-4523	109	10	following	following	NOUN
cana-4523	109	11	.	.	PUNCT
cana-4523	110	1	theorem	theorem	VERB
cana-4523	110	2	2.1	2.1	NUM
cana-4523	110	3	:	:	PUNCT
cana-4523	110	4	for	for	ADP
cana-4523	110	5	the	the	DET
cana-4523	110	6	model	model	NOUN
cana-4523	110	7	described	describe	VERB
cana-4523	110	8	in	in	ADP
cana-4523	110	9	section	section	NOUN
cana-4523	110	10	2	2	NUM
cana-4523	110	11	,	,	PUNCT
cana-4523	110	12	under	under	ADP
cana-4523	110	13	the	the	DET
cana-4523	110	14	assumptions	assumption	NOUN
cana-4523	110	15	2.1	2.1	NUM
cana-4523	110	16	to	to	ADP
cana-4523	110	17	2.6	2.6	NUM
cana-4523	110	18	,	,	PUNCT
cana-4523	110	19	the	the	DET
cana-4523	110	20	long	long	ADV
cana-4523	110	21	-	-	PUNCT
cana-4523	110	22	run	run	VERB
cana-4523	110	23	average	average	ADJ
cana-4523	110	24	cost	cost	NOUN
cana-4523	110	25	per	per	ADP
cana-4523	110	26	unit	unit	NOUN
cana-4523	110	27	time	time	NOUN
cana-4523	110	28	𝐶(𝑇	𝐶(𝑇	PROPN
cana-4523	110	29	)	)	PUNCT
cana-4523	110	30	is	be	AUX
cana-4523	110	31	given	give	VERB
cana-4523	110	32	by	by	ADP
cana-4523	110	33	𝐶(𝑇	𝐶(𝑇	ADJ
cana-4523	110	34	)	)	PUNCT
cana-4523	110	35	=	=	SYM
cana-4523	110	36	𝑐𝛾	𝑐𝛾	ADP
cana-4523	110	37	∑	∑	ADV
cana-4523	110	38	𝐺𝑛(𝑇	𝐺𝑛(𝑇	ADJ
cana-4523	110	39	)	)	PUNCT
cana-4523	110	40	𝑎𝑛−1	𝑎𝑛−1	PROPN
cana-4523	110	41	∞	∞	PROPN
cana-4523	110	42	𝑛=1	𝑛=1	NOUN
cana-4523	110	43	−	−	NOUN
cana-4523	110	44	𝑟	𝑟	NOUN
cana-4523	110	45	𝜇	𝜇	X
cana-4523	110	46	∑	∑	PUNCT
cana-4523	110	47	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	110	48	)	)	PUNCT
cana-4523	110	49	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	110	50	∞	∞	NUM
cana-4523	110	51	𝑛=1	𝑛=1	NOUN
cana-4523	110	52	+	+	X
cana-4523	110	53	𝑅	𝑅	PROPN
cana-4523	110	54	+	+	NOUN
cana-4523	110	55	𝑐𝑝	𝑐𝑝	ADP
cana-4523	110	56	𝜏	𝜏	PRON
cana-4523	110	57	𝜇	𝜇	ADP
cana-4523	110	58	∑	∑	ADV
cana-4523	110	59	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	110	60	)	)	PUNCT
cana-4523	110	61	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	110	62	∞	∞	NUM
cana-4523	110	63	𝑛=1	𝑛=1	NOUN
cana-4523	110	64	+	+	CCONJ
cana-4523	110	65	𝛾	𝛾	NOUN
cana-4523	110	66	∑	∑	PUNCT
cana-4523	110	67	𝐺𝑛(𝑇	𝐺𝑛(𝑇	ADJ
cana-4523	110	68	)	)	PUNCT
cana-4523	110	69	𝑎𝑛−1	𝑎𝑛−1	PROPN
cana-4523	110	70	∞	∞	NUM
cana-4523	110	71	𝑛=1	𝑛=1	NOUN
cana-4523	110	72	+	+	CCONJ
cana-4523	110	73	𝜏	𝜏	NOUN
cana-4523	110	74	for	for	ADP
cana-4523	110	75	a	a	DET
cana-4523	110	76	multistate	multistate	NOUN
cana-4523	110	77	degenerative	degenerative	ADJ
cana-4523	110	78	system	system	NOUN
cana-4523	110	79	under	under	ADP
cana-4523	110	80	the	the	DET
cana-4523	110	81	replacement	replacement	NOUN
cana-4523	110	82	policy	policy	NOUN
cana-4523	110	83	t	t	PROPN
cana-4523	110	84	is	be	AUX
cana-4523	110	85	minimum	minimum	ADJ
cana-4523	110	86	,	,	PUNCT
cana-4523	110	87	if	if	SCONJ
cana-4523	110	88	[	[	X
cana-4523	110	89	𝜇	𝜇	ADP
cana-4523	110	90	∑	∑	PUNCT
cana-4523	110	91	∞	∞	PROPN
cana-4523	110	92	𝑛=1	𝑛=1	NOUN
cana-4523	110	93	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	110	94	)	)	PUNCT
cana-4523	110	95	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	111	1	+	+	PUNCT
cana-4523	112	1	𝜏	𝜏	X
cana-4523	112	2	]	]	X
cana-4523	112	3	[	[	X
cana-4523	112	4	(	(	PUNCT
cana-4523	112	5	𝑐	𝑐	NOUN
cana-4523	112	6	+	+	NOUN
cana-4523	112	7	𝑟	𝑟	NOUN
cana-4523	112	8	)	)	PUNCT
cana-4523	112	9	∑	∑	PUNCT
cana-4523	112	10	𝑛−1	𝑛−1	PROPN
cana-4523	112	11	𝑛=1	𝑛=1	NOUN
cana-4523	112	12	(	(	PUNCT
cana-4523	112	13	𝛾	𝛾	ADP
cana-4523	112	14	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	112	15	)	)	PUNCT
cana-4523	112	16	𝐺𝑛	𝐺𝑛	ADJ
cana-4523	112	17	′(𝑇	′(𝑇	NOUN
cana-4523	112	18	)	)	PUNCT
cana-4523	112	19	]	]	PUNCT
cana-4523	113	1	=	=	PUNCT
cana-4523	114	1	[	[	X
cana-4523	114	2	(	(	PUNCT
cana-4523	114	3	𝑐	𝑐	NOUN
cana-4523	114	4	+	+	NOUN
cana-4523	114	5	𝑟	𝑟	NOUN
cana-4523	114	6	)	)	PUNCT
cana-4523	114	7	∑	∑	PUNCT
cana-4523	114	8	𝑛−1	𝑛−1	PROPN
cana-4523	114	9	𝑛=1	𝑛=1	NOUN
cana-4523	114	10	(	(	PUNCT
cana-4523	114	11	𝛾	𝛾	PROPN
cana-4523	114	12	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	114	13	)	)	PUNCT
cana-4523	114	14	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	114	15	)	)	PUNCT
cana-4523	114	16	+	+	CCONJ
cana-4523	114	17	𝑅1	𝑅1	PROPN
cana-4523	114	18	]	]	X
cana-4523	115	1	[	[	X
cana-4523	115	2	(	(	PUNCT
cana-4523	115	3	𝜇	𝜇	ADP
cana-4523	115	4	∑	∑	PROPN
cana-4523	115	5	∞	∞	PROPN
cana-4523	115	6	𝑛=1	𝑛=1	NOUN
cana-4523	115	7	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	115	8	′(𝑇	′(𝑇	NOUN
cana-4523	115	9	)	)	PUNCT
cana-4523	115	10	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	115	11	)	)	PUNCT
cana-4523	115	12	]	]	PUNCT
cana-4523	115	13	and	and	CCONJ
cana-4523	116	1	[	[	X
cana-4523	116	2	𝜇	𝜇	ADP
cana-4523	116	3	∑	∑	PROPN
cana-4523	116	4	∞	∞	PROPN
cana-4523	116	5	𝑛=1	𝑛=1	NOUN
cana-4523	116	6	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	116	7	)	)	PUNCT
cana-4523	116	8	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	116	9	+	+	PUNCT
cana-4523	116	10	𝜏	𝜏	X
cana-4523	116	11	]	]	X
cana-4523	116	12	[	[	X
cana-4523	116	13	(	(	PUNCT
cana-4523	116	14	𝑐	𝑐	NOUN
cana-4523	116	15	+	+	NOUN
cana-4523	116	16	𝑟	𝑟	NOUN
cana-4523	116	17	)	)	PUNCT
cana-4523	116	18	∑	∑	PUNCT
cana-4523	116	19	𝑛−1	𝑛−1	PROPN
cana-4523	116	20	𝑛=1	𝑛=1	NOUN
cana-4523	116	21	(	(	PUNCT
cana-4523	116	22	𝛾	𝛾	PROPN
cana-4523	116	23	𝑎𝑖−1	𝑎𝑖−1	NOUN
cana-4523	116	24	)	)	PUNCT
cana-4523	116	25	𝐺𝑛	𝐺𝑛	PROPN
cana-4523	116	26	′′(𝑇	′′(𝑇	NOUN
cana-4523	116	27	)	)	PUNCT
cana-4523	116	28	]	]	PUNCT
cana-4523	116	29	>	>	X
cana-4523	117	1	[	[	X
cana-4523	117	2	(	(	PUNCT
cana-4523	117	3	𝑐	𝑐	NOUN
cana-4523	117	4	+	+	NOUN
cana-4523	117	5	𝑟	𝑟	NOUN
cana-4523	117	6	)	)	PUNCT
cana-4523	117	7	∑	∑	PUNCT
cana-4523	117	8	𝑛−1	𝑛−1	PROPN
cana-4523	117	9	𝑛=1	𝑛=1	NOUN
cana-4523	117	10	(	(	PUNCT
cana-4523	117	11	𝛾	𝛾	PROPN
cana-4523	117	12	𝑎𝑖−1	𝑎𝑖−1	NOUN
cana-4523	117	13	)	)	PUNCT
cana-4523	117	14	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	117	15	)	)	PUNCT
cana-4523	117	16	+	+	CCONJ
cana-4523	117	17	𝑅1	𝑅1	PROPN
cana-4523	117	18	]	]	X
cana-4523	118	1	[	[	X
cana-4523	118	2	(	(	PUNCT
cana-4523	118	3	𝜇	𝜇	ADP
cana-4523	118	4	∑	∑	ADP
cana-4523	118	5	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	118	6	′′(𝑇	′′(𝑇	NOUN
cana-4523	118	7	)	)	PUNCT
cana-4523	118	8	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	118	9	∞	∞	NUM
cana-4523	118	10	𝑛=1	𝑛=1	NOUN
cana-4523	118	11	)	)	PUNCT
cana-4523	118	12	]	]	PUNCT
cana-4523	118	13	hold	hold	VERB
cana-4523	118	14	.	.	PUNCT
cana-4523	119	1	communications	communication	NOUN
cana-4523	119	2	on	on	ADP
cana-4523	119	3	applied	apply	VERB
cana-4523	119	4	nonlinear	nonlinear	ADJ
cana-4523	119	5	analysis	analysis	NOUN
cana-4523	119	6	issn	issn	NOUN
cana-4523	119	7	:	:	PUNCT
cana-4523	119	8	1074	1074	NUM
cana-4523	119	9	-	-	PUNCT
cana-4523	119	10	133x	133x	NUM
cana-4523	119	11	vol	vol	NOUN
cana-4523	119	12	32	32	NUM
cana-4523	119	13	no	no	NOUN
cana-4523	119	14	.	.	PUNCT
cana-4523	120	1	9s	9s	NUM
cana-4523	120	2	(	(	PUNCT
cana-4523	120	3	2025	2025	NUM
cana-4523	120	4	)	)	PUNCT
cana-4523	120	5	2364	2364	NUM
cana-4523	120	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	120	7	3	3	X
cana-4523	120	8	.	.	PUNCT
cana-4523	121	1	the	the	DET
cana-4523	121	2	replacement	replacement	NOUN
cana-4523	121	3	policy	policy	NOUN
cana-4523	121	4	t	t	PROPN
cana-4523	121	5	with	with	ADP
cana-4523	121	6	nonn	nonn	PROPN
cana-4523	121	7	repair	repair	PROPN
cana-4523	121	8	times	time	NOUN
cana-4523	121	9	in	in	ADP
cana-4523	121	10	this	this	DET
cana-4523	121	11	section	section	NOUN
cana-4523	121	12	,	,	PUNCT
cana-4523	121	13	we	we	PRON
cana-4523	121	14	introduce	introduce	VERB
cana-4523	121	15	and	and	CCONJ
cana-4523	121	16	study	study	VERB
cana-4523	121	17	a	a	DET
cana-4523	121	18	t	t	NOUN
cana-4523	121	19	-	-	PUNCT
cana-4523	121	20	policy	policy	NOUN
cana-4523	121	21	for	for	ADP
cana-4523	121	22	a	a	DET
cana-4523	121	23	multistate	multistate	NOUN
cana-4523	121	24	one	one	NUM
cana-4523	121	25	-	-	PUNCT
cana-4523	121	26	component	component	NOUN
cana-4523	121	27	degenerative	degenerative	ADJ
cana-4523	121	28	system	system	NOUN
cana-4523	121	29	with	with	ADP
cana-4523	121	30	nonn	nonn	PROPN
cana-4523	121	31	repair	repair	PROPN
cana-4523	121	32	times	time	NOUN
cana-4523	121	33	.	.	PUNCT
cana-4523	122	1	under	under	ADP
cana-4523	122	2	the	the	DET
cana-4523	122	3	replacement	replacement	NOUN
cana-4523	122	4	policy	policy	NOUN
cana-4523	122	5	t	t	PROPN
cana-4523	122	6	,	,	PUNCT
cana-4523	122	7	the	the	DET
cana-4523	122	8	problem	problem	NOUN
cana-4523	122	9	is	be	AUX
cana-4523	122	10	to	to	PART
cana-4523	122	11	determine	determine	VERB
cana-4523	122	12	an	an	DET
cana-4523	122	13	optimal	optimal	ADJ
cana-4523	122	14	replacement	replacement	NOUN
cana-4523	122	15	policy	policy	NOUN
cana-4523	122	16	𝑇	𝑇	PROPN
cana-4523	122	17	*	*	PROPN
cana-4523	122	18	such	such	ADJ
cana-4523	122	19	that	that	SCONJ
cana-4523	122	20	the	the	DET
cana-4523	122	21	long	long	ADV
cana-4523	122	22	-	-	PUNCT
cana-4523	122	23	run	run	VERB
cana-4523	122	24	average	average	ADJ
cana-4523	122	25	cost	cost	NOUN
cana-4523	122	26	per	per	ADP
cana-4523	122	27	unit	unit	NOUN
cana-4523	122	28	time	time	NOUN
cana-4523	122	29	is	be	AUX
cana-4523	122	30	minimized	minimize	VERB
cana-4523	122	31	.	.	PUNCT
cana-4523	123	1	we	we	PRON
cana-4523	123	2	consider	consider	VERB
cana-4523	123	3	a	a	DET
cana-4523	123	4	monotone	monotone	ADJ
cana-4523	123	5	process	process	NOUN
cana-4523	123	6	model	model	NOUN
cana-4523	123	7	for	for	ADP
cana-4523	123	8	a	a	DET
cana-4523	123	9	multistate	multistate	NOUN
cana-4523	123	10	one	one	NUM
cana-4523	123	11	-	-	PUNCT
cana-4523	123	12	component	component	NOUN
cana-4523	123	13	degenerative	degenerative	ADJ
cana-4523	123	14	system	system	NOUN
cana-4523	123	15	and	and	CCONJ
cana-4523	123	16	make	make	VERB
cana-4523	123	17	the	the	DET
cana-4523	123	18	following	follow	VERB
cana-4523	123	19	assumptions	assumption	NOUN
cana-4523	123	20	:	:	PUNCT
cana-4523	123	21	assumptions	assumption	NOUN
cana-4523	123	22	3.1	3.1	NUM
cana-4523	123	23	,	,	PUNCT
cana-4523	123	24	3.2	3.2	NUM
cana-4523	123	25	,	,	PUNCT
cana-4523	123	26	3.4	3.4	NUM
cana-4523	123	27	,	,	PUNCT
cana-4523	123	28	3.5	3.5	NUM
cana-4523	123	29	are	be	AUX
cana-4523	123	30	the	the	DET
cana-4523	123	31	same	same	ADJ
cana-4523	123	32	as	as	ADP
cana-4523	123	33	assumptions	assumption	NOUN
cana-4523	123	34	2.1,2.2,2.4,2.5	2.1,2.2,2.4,2.5	NUM
cana-4523	123	35	.	.	PUNCT
cana-4523	124	1	assumption	assumption	NOUN
cana-4523	124	2	3.3	3.3	NUM
cana-4523	124	3	:	:	PUNCT
cana-4523	124	4	let	let	VERB
cana-4523	124	5	𝑋1	𝑋1	PROPN
cana-4523	124	6	be	be	AUX
cana-4523	124	7	the	the	DET
cana-4523	124	8	first	first	ADJ
cana-4523	124	9	operating	operating	NOUN
cana-4523	124	10	time	time	NOUN
cana-4523	124	11	.	.	PUNCT
cana-4523	125	1	for	for	ADP
cana-4523	125	2	n	n	PRON
cana-4523	125	3	≥	≥	NUM
cana-4523	125	4	2	2	NUM
cana-4523	125	5	,	,	PUNCT
cana-4523	125	6	let	let	VERB
cana-4523	125	7	𝑋𝑛	𝑋𝑛	PROPN
cana-4523	125	8	be	be	AUX
cana-4523	125	9	the	the	DET
cana-4523	125	10	operating	operating	NOUN
cana-4523	125	11	time	time	NOUN
cana-4523	125	12	of	of	ADP
cana-4523	125	13	the	the	DET
cana-4523	125	14	system	system	NOUN
cana-4523	125	15	after	after	ADP
cana-4523	125	16	(	(	PUNCT
cana-4523	125	17	n	n	CCONJ
cana-4523	125	18	−	−	PROPN
cana-4523	125	19	1)-st	1)-st	NUM
cana-4523	125	20	repair	repair	NOUN
cana-4523	125	21	,	,	PUNCT
cana-4523	125	22	let	let	VERB
cana-4523	125	23	𝜉𝑛	𝜉𝑛	PRON
cana-4523	125	24	be	be	AUX
cana-4523	125	25	the	the	DET
cana-4523	125	26	repair	repair	NOUN
cana-4523	125	27	time	time	NOUN
cana-4523	125	28	after	after	ADP
cana-4523	125	29	the	the	DET
cana-4523	125	30	n	n	CCONJ
cana-4523	125	31	-	-	PUNCT
cana-4523	125	32	th	th	VERB
cana-4523	125	33	failure	failure	NOUN
cana-4523	125	34	and	and	CCONJ
cana-4523	125	35	z	z	AUX
cana-4523	125	36	be	be	AUX
cana-4523	125	37	the	the	DET
cana-4523	125	38	replacement	replacement	NOUN
cana-4523	125	39	time	time	NOUN
cana-4523	125	40	.	.	PUNCT
cana-4523	126	1	now	now	ADV
cana-4523	126	2	,	,	PUNCT
cana-4523	126	3	denote	denote	VERB
cana-4523	126	4	the	the	DET
cana-4523	126	5	time	time	NOUN
cana-4523	126	6	of	of	ADP
cana-4523	126	7	the	the	DET
cana-4523	126	8	n	n	CCONJ
cana-4523	126	9	-	-	PUNCT
cana-4523	126	10	th	th	VERB
cana-4523	126	11	failure	failure	NOUN
cana-4523	126	12	by	by	ADP
cana-4523	126	13	𝑡𝑛	𝑡𝑛	ADJ
cana-4523	126	14	assumption	assumption	NOUN
cana-4523	126	15	3.6	3.6	NUM
cana-4523	126	16	:	:	PUNCT
cana-4523	126	17	.	.	PUNCT
cana-4523	127	1	the	the	DET
cana-4523	127	2	survival	survival	PROPN
cana-4523	127	3	times	times	PROPN
cana-4523	127	4	(	(	PUNCT
cana-4523	127	5	𝑋𝑖	𝑋𝑖	PROPN
cana-4523	127	6	)	)	PUNCT
cana-4523	127	7	and	and	CCONJ
cana-4523	127	8	the	the	DET
cana-4523	127	9	nonn	nonn	PROPN
cana-4523	127	10	repair	repair	PROPN
cana-4523	127	11	times	time	NOUN
cana-4523	127	12	(	(	PUNCT
cana-4523	127	13	𝜉𝑖	𝜉𝑖	PROPN
cana-4523	127	14	)	)	PUNCT
cana-4523	127	15	and	and	CCONJ
cana-4523	127	16	the	the	DET
cana-4523	127	17	replacement	replacement	NOUN
cana-4523	127	18	time	time	NOUN
cana-4523	127	19	z	z	PROPN
cana-4523	127	20	,	,	PUNCT
cana-4523	127	21	for	for	ADP
cana-4523	127	22	i	i	PROPN
cana-4523	127	23	=	=	SYM
cana-4523	127	24	1	1	NUM
cana-4523	127	25	,	,	PUNCT
cana-4523	127	26	2	2	NUM
cana-4523	127	27	,	,	PUNCT
cana-4523	127	28	...	...	PUNCT
cana-4523	127	29	are	be	AUX
cana-4523	127	30	independent	independent	ADJ
cana-4523	127	31	.	.	PUNCT
cana-4523	128	1	assumption	assumption	NOUN
cana-4523	128	2	3.7	3.7	NUM
cana-4523	128	3	:	:	PUNCT
cana-4523	128	4	the	the	DET
cana-4523	128	5	replacement	replacement	NOUN
cana-4523	128	6	policy	policy	NOUN
cana-4523	128	7	t	t	PROPN
cana-4523	128	8	with	with	ADP
cana-4523	128	9	nonn	nonn	PROPN
cana-4523	128	10	repair	repair	NOUN
cana-4523	128	11	times	time	NOUN
cana-4523	128	12	is	be	AUX
cana-4523	128	13	adapted	adapt	VERB
cana-4523	128	14	under	under	ADP
cana-4523	128	15	which	which	PRON
cana-4523	128	16	the	the	DET
cana-4523	128	17	system	system	NOUN
cana-4523	128	18	will	will	AUX
cana-4523	128	19	be	be	AUX
cana-4523	128	20	replaced	replace	VERB
cana-4523	128	21	whenever	whenever	SCONJ
cana-4523	128	22	its	its	PRON
cana-4523	128	23	working	work	VERB
cana-4523	128	24	age	age	NOUN
cana-4523	128	25	reaches	reach	VERB
cana-4523	128	26	t.	t.	NOUN
cana-4523	128	27	by	by	ADP
cana-4523	128	28	assumption	assumption	NOUN
cana-4523	128	29	𝜉𝑛	𝜉𝑛	X
cana-4523	128	30	=	=	PUNCT
cana-4523	128	31	{	{	PUNCT
cana-4523	128	32	𝑌𝑛	𝑌𝑛	INTJ
cana-4523	128	33	𝑖𝑓	𝑖𝑓	VERB
cana-4523	129	1	𝑌𝑛	𝑌𝑛	PROPN
cana-4523	129	2	>	>	X
cana-4523	129	3	0	0	NUM
cana-4523	129	4	1	1	NUM
cana-4523	129	5	𝑖𝑓	𝑖𝑓	ADP
cana-4523	129	6	𝑌𝑛	𝑌𝑛	PROPN
cana-4523	129	7	=	=	NOUN
cana-4523	129	8	0	0	NUM
cana-4523	129	9	for	for	ADP
cana-4523	129	10	n=1,2,3	n=1,2,3	NUM
cana-4523	129	11	…	…	SYM
cana-4523	129	12	.	.	PUNCT
cana-4523	130	1	therefore	therefore	ADV
cana-4523	130	2	𝐸(𝜉𝑛	𝐸(𝜉𝑛	VERB
cana-4523	130	3	)	)	PUNCT
cana-4523	131	1	=	=	SYM
cana-4523	131	2	𝐸(𝑌𝑛)𝑃(𝑌𝑛	𝐸(𝑌𝑛)𝑃(𝑌𝑛	NOUN
cana-4523	131	3	>	>	X
cana-4523	131	4	0	0	NUM
cana-4523	131	5	)	)	PUNCT
cana-4523	132	1	+	+	CCONJ
cana-4523	132	2	1	1	X
cana-4523	132	3	.	.	X
cana-4523	132	4	𝑃(𝑌𝑛	𝑃(𝑌𝑛	NOUN
cana-4523	132	5	=	=	SYM
cana-4523	132	6	0	0	NUM
cana-4523	132	7	)	)	PUNCT
cana-4523	132	8	=	=	NOUN
cana-4523	132	9	(	(	PUNCT
cana-4523	132	10	𝛾	𝛾	PROPN
cana-4523	132	11	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	132	12	)	)	PUNCT
cana-4523	132	13	(	(	PUNCT
cana-4523	132	14	1	1	NUM
cana-4523	132	15	−	−	PROPN
cana-4523	132	16	𝑝	𝑝	NOUN
cana-4523	132	17	)	)	PUNCT
cana-4523	133	1	+	+	CCONJ
cana-4523	133	2	𝑝	𝑝	ADP
cana-4523	133	3	the	the	DET
cana-4523	133	4	replacement	replacement	NOUN
cana-4523	133	5	times	time	NOUN
cana-4523	133	6	are	be	AUX
cana-4523	133	7	defined	define	VERB
cana-4523	133	8	as	as	SCONJ
cana-4523	133	9	follows	follow	VERB
cana-4523	133	10	:	:	PUNCT
cana-4523	133	11	𝑇1	𝑇1	NOUN
cana-4523	133	12	represents	represent	VERB
cana-4523	133	13	the	the	DET
cana-4523	133	14	first	first	ADJ
cana-4523	133	15	replacement	replacement	NOUN
cana-4523	133	16	time	time	NOUN
cana-4523	133	17	,	,	PUNCT
cana-4523	133	18	and	and	CCONJ
cana-4523	133	19	for	for	ADP
cana-4523	133	20	n	n	NOUN
cana-4523	133	21	=	=	SYM
cana-4523	133	22	2	2	NUM
cana-4523	133	23	,	,	PUNCT
cana-4523	133	24	3	3	NUM
cana-4523	133	25	,	,	PUNCT
cana-4523	133	26	...	...	PUNCT
cana-4523	133	27	,	,	PUNCT
cana-4523	133	28	𝑇𝑛	𝑇𝑛	PROPN
cana-4523	133	29	denotes	denote	VERB
cana-4523	133	30	the	the	DET
cana-4523	133	31	time	time	NOUN
cana-4523	133	32	between	between	ADP
cana-4523	133	33	the	the	DET
cana-4523	133	34	(	(	PUNCT
cana-4523	133	35	n-1)-st	n-1)-st	NOUN
cana-4523	133	36	replacement	replacement	NOUN
cana-4523	133	37	and	and	CCONJ
cana-4523	133	38	the	the	DET
cana-4523	133	39	n	n	CCONJ
cana-4523	133	40	-	-	PUNCT
cana-4523	133	41	th	th	NUM
cana-4523	133	42	replacement	replacement	NOUN
cana-4523	133	43	.	.	PUNCT
cana-4523	134	1	consequently	consequently	ADV
cana-4523	134	2	,	,	PUNCT
cana-4523	134	3	the	the	DET
cana-4523	134	4	sequence	sequence	NOUN
cana-4523	134	5	{	{	PUNCT
cana-4523	134	6	𝑇𝑛	𝑇𝑛	PROPN
cana-4523	134	7	,	,	PUNCT
cana-4523	134	8	n	n	NOUN
cana-4523	134	9	=	=	SYM
cana-4523	134	10	1	1	NUM
cana-4523	134	11	,	,	PUNCT
cana-4523	134	12	2	2	NUM
cana-4523	134	13	,	,	PUNCT
cana-4523	134	14	...	...	PUNCT
cana-4523	134	15	}	}	PUNCT
cana-4523	134	16	constitutes	constitute	VERB
cana-4523	134	17	a	a	DET
cana-4523	134	18	renewal	renewal	NOUN
cana-4523	134	19	process	process	NOUN
cana-4523	134	20	.	.	PUNCT
cana-4523	135	1	cycles	cycle	NOUN
cana-4523	135	2	are	be	AUX
cana-4523	135	3	defined	define	VERB
cana-4523	135	4	by	by	ADP
cana-4523	135	5	the	the	DET
cana-4523	135	6	time	time	NOUN
cana-4523	135	7	between	between	ADP
cana-4523	135	8	consecutive	consecutive	ADJ
cana-4523	135	9	system	system	NOUN
cana-4523	135	10	replacements	replacement	NOUN
cana-4523	135	11	,	,	PUNCT
cana-4523	135	12	spanning	span	VERB
cana-4523	135	13	from	from	ADP
cana-4523	135	14	initial	initial	ADJ
cana-4523	135	15	installation	installation	NOUN
cana-4523	135	16	to	to	ADP
cana-4523	135	17	first	first	ADJ
cana-4523	135	18	replacement	replacement	NOUN
cana-4523	135	19	,	,	PUNCT
cana-4523	135	20	and	and	CCONJ
cana-4523	135	21	subsequent	subsequent	ADJ
cana-4523	135	22	replacement	replacement	NOUN
cana-4523	135	23	intervals	interval	NOUN
cana-4523	135	24	.	.	PUNCT
cana-4523	136	1	each	each	DET
cana-4523	136	2	replacement	replacement	NOUN
cana-4523	136	3	concludes	conclude	VERB
cana-4523	136	4	one	one	NUM
cana-4523	136	5	cycle	cycle	NOUN
cana-4523	136	6	and	and	CCONJ
cana-4523	136	7	begins	begin	VERB
cana-4523	136	8	another	another	PRON
cana-4523	136	9	.	.	PUNCT
cana-4523	137	1	by	by	ADP
cana-4523	137	2	combining	combine	VERB
cana-4523	137	3	the	the	DET
cana-4523	137	4	successive	successive	ADJ
cana-4523	137	5	cycles	cycle	NOUN
cana-4523	137	6	with	with	ADP
cana-4523	137	7	the	the	DET
cana-4523	137	8	costs	cost	NOUN
cana-4523	137	9	associated	associate	VERB
cana-4523	137	10	with	with	ADP
cana-4523	137	11	each	each	PRON
cana-4523	137	12	,	,	PUNCT
cana-4523	137	13	we	we	PRON
cana-4523	137	14	establish	establish	VERB
cana-4523	137	15	a	a	DET
cana-4523	137	16	renewal	renewal	NOUN
cana-4523	137	17	reward	reward	NOUN
cana-4523	137	18	process	process	NOUN
cana-4523	137	19	,	,	PUNCT
cana-4523	137	20	facilitating	facilitate	VERB
cana-4523	137	21	the	the	DET
cana-4523	137	22	assessment	assessment	NOUN
cana-4523	137	23	of	of	ADP
cana-4523	137	24	cumulative	cumulative	ADJ
cana-4523	137	25	costs	cost	NOUN
cana-4523	137	26	,	,	PUNCT
cana-4523	137	27	rewards	reward	NOUN
cana-4523	137	28	,	,	PUNCT
cana-4523	137	29	and	and	CCONJ
cana-4523	137	30	system	system	NOUN
cana-4523	137	31	efficiency	efficiency	NOUN
cana-4523	137	32	.	.	PUNCT
cana-4523	138	1	𝐶(𝑇	𝐶(𝑇	ADJ
cana-4523	138	2	)	)	PUNCT
cana-4523	139	1	=	=	SYM
cana-4523	140	1	the	the	DET
cana-4523	140	2	expected	expect	VERB
cana-4523	140	3	cost	cost	NOUN
cana-4523	140	4	incured	incur	VERB
cana-4523	140	5	in	in	ADP
cana-4523	140	6	a	a	DET
cana-4523	140	7	cycle	cycle	NOUN
cana-4523	140	8	the	the	DET
cana-4523	140	9	expected	expect	VERB
cana-4523	140	10	length	length	NOUN
cana-4523	140	11	of	of	ADP
cana-4523	140	12	a	a	DET
cana-4523	140	13	cycle	cycle	NOUN
cana-4523	140	14	=	=	SYM
cana-4523	140	15	𝑐𝐸[∑	𝑐𝐸[∑	PROPN
cana-4523	140	16	𝑛−1	𝑛−1	PROPN
cana-4523	140	17	𝑘=1	𝑘=1	NOUN
cana-4523	140	18	𝜉𝑘	𝜉𝑘	PROPN
cana-4523	140	19	]	]	PUNCT
cana-4523	140	20	−	−	PROPN
cana-4523	140	21	𝑟𝐸[∑	𝑟𝐸[∑	NUM
cana-4523	141	1	𝑋𝑘	𝑋𝑘	NOUN
cana-4523	141	2	𝜂	𝜂	NOUN
cana-4523	141	3	𝑘=1	𝑘=1	X
cana-4523	141	4	]	]	PUNCT
cana-4523	141	5	+	+	PUNCT
cana-4523	141	6	𝑅	𝑅	PROPN
cana-4523	141	7	+	+	CCONJ
cana-4523	141	8	𝑐𝑝𝐸	𝑐𝑝𝐸	NOUN
cana-4523	141	9	[	[	PUNCT
cana-4523	141	10	𝑍	𝑍	PROPN
cana-4523	141	11	]	]	PUNCT
cana-4523	141	12	𝐸[∑	𝐸[∑	NOUN
cana-4523	142	1	𝑋𝑘	𝑋𝑘	PROPN
cana-4523	142	2	𝜂	𝜂	PROPN
cana-4523	142	3	𝑘=1	𝑘=1	X
cana-4523	142	4	]	]	PUNCT
cana-4523	143	1	+	+	CCONJ
cana-4523	143	2	𝐸[∑	𝐸[∑	PROPN
cana-4523	143	3	𝜉𝑘	𝜉𝑘	PROPN
cana-4523	143	4	𝑛−1	𝑛−1	PROPN
cana-4523	143	5	𝑘=1	𝑘=1	X
cana-4523	143	6	]	]	PUNCT
cana-4523	144	1	+	+	PUNCT
cana-4523	144	2	𝐸[𝑍	𝐸[𝑍	NOUN
cana-4523	144	3	]	]	X
cana-4523	144	4	(	(	PUNCT
cana-4523	144	5	3.1	3.1	NUM
cana-4523	144	6	)	)	PUNCT
cana-4523	144	7	where	where	SCONJ
cana-4523	144	8	𝜂	𝜂	NOUN
cana-4523	144	9	=	=	SYM
cana-4523	144	10	0,1,2	0,1,2	NUM
cana-4523	144	11	,	,	PUNCT
cana-4523	144	12	…	…	PUNCT
cana-4523	144	13	,	,	PUNCT
cana-4523	144	14	𝑁	𝑁	PROPN
cana-4523	144	15	−	−	NOUN
cana-4523	144	16	1	1	NUM
cana-4523	144	17	is	be	AUX
cana-4523	144	18	a	a	DET
cana-4523	144	19	random	random	ADJ
cana-4523	144	20	variable	variable	NOUN
cana-4523	144	21	denoting	denote	VERB
cana-4523	144	22	the	the	DET
cana-4523	144	23	number	number	NOUN
cana-4523	144	24	of	of	ADP
cana-4523	144	25	failures	failure	NOUN
cana-4523	144	26	in	in	ADP
cana-4523	144	27	time	time	NOUN
cana-4523	144	28	𝑇.	𝑇.	PROPN
cana-4523	144	29	𝐸(𝑋𝑛	𝐸(𝑋𝑛	NOUN
cana-4523	144	30	)	)	PUNCT
cana-4523	145	1	=	=	SYM
cana-4523	145	2	∑	∑	PUNCT
cana-4523	145	3	(	(	PUNCT
cana-4523	145	4	𝜇	𝜇	ADP
cana-4523	145	5	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	145	6	)	)	PUNCT
cana-4523	145	7	𝜂	𝜂	NOUN
cana-4523	145	8	𝑛=1	𝑛=1	NOUN
cana-4523	145	9	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	145	10	)	)	PUNCT
cana-4523	145	11	(	(	PUNCT
cana-4523	145	12	3.2	3.2	NUM
cana-4523	145	13	)	)	PUNCT
cana-4523	145	14	the	the	DET
cana-4523	145	15	n	n	ADV
cana-4523	145	16	-	-	ADJ
cana-4523	145	17	fold	fold	ADJ
cana-4523	145	18	convolution	convolution	NOUN
cana-4523	145	19	of	of	ADP
cana-4523	145	20	𝐹	𝐹	PROPN
cana-4523	145	21	(	(	PUNCT
cana-4523	145	22	.	.	PUNCT
cana-4523	145	23	)	)	PUNCT
cana-4523	146	1	with	with	ADP
cana-4523	146	2	itself	itself	PRON
cana-4523	146	3	is	be	AUX
cana-4523	146	4	denoted	denote	VERB
cana-4523	146	5	by	by	ADP
cana-4523	146	6	𝐹𝑁	𝐹𝑁	PROPN
cana-4523	146	7	(	(	PUNCT
cana-4523	146	8	.	.	PUNCT
cana-4523	146	9	)	)	PUNCT
cana-4523	147	1	communications	communication	NOUN
cana-4523	147	2	on	on	ADP
cana-4523	147	3	applied	apply	VERB
cana-4523	147	4	nonlinear	nonlinear	ADJ
cana-4523	147	5	analysis	analysis	NOUN
cana-4523	147	6	issn	issn	NOUN
cana-4523	147	7	:	:	PUNCT
cana-4523	147	8	1074	1074	NUM
cana-4523	147	9	-	-	PUNCT
cana-4523	147	10	133x	133x	NUM
cana-4523	147	11	vol	vol	NOUN
cana-4523	147	12	32	32	NUM
cana-4523	147	13	no	no	NOUN
cana-4523	147	14	.	.	PUNCT
cana-4523	148	1	9s	9s	NUM
cana-4523	148	2	(	(	PUNCT
cana-4523	148	3	2025	2025	NUM
cana-4523	148	4	)	)	PUNCT
cana-4523	148	5	2365	2365	NUM
cana-4523	148	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	148	7	consider	consider	VERB
cana-4523	148	8	𝐸(𝜉𝑛	𝐸(𝜉𝑛	NOUN
cana-4523	148	9	)	)	PUNCT
cana-4523	149	1	=	=	SYM
cana-4523	149	2	𝐸	𝐸	PROPN
cana-4523	150	1	[	[	X
cana-4523	150	2	𝐸	𝐸	ADJ
cana-4523	150	3	[	[	X
cana-4523	150	4	∑	∑	PROPN
cana-4523	150	5	𝐸	𝐸	PROPN
cana-4523	150	6	𝑛−1	𝑛−1	PROPN
cana-4523	150	7	𝑛=1	𝑛=1	NOUN
cana-4523	150	8	(	(	PUNCT
cana-4523	150	9	𝜉𝑛|	𝜉𝑛|	PROPN
cana-4523	150	10	)	)	PUNCT
cana-4523	150	11	]	]	PUNCT
cana-4523	150	12	]	]	X
cana-4523	151	1	=	=	PUNCT
cana-4523	151	2	∑	∑	PUNCT
cana-4523	151	3	(	(	PUNCT
cana-4523	151	4	(	(	PUNCT
cana-4523	151	5	𝛾	𝛾	PROPN
cana-4523	151	6	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	151	7	)	)	PUNCT
cana-4523	151	8	(	(	PUNCT
cana-4523	151	9	1	1	NUM
cana-4523	151	10	−	−	PROPN
cana-4523	151	11	𝑝	𝑝	NOUN
cana-4523	151	12	)	)	PUNCT
cana-4523	151	13	+	+	CCONJ
cana-4523	151	14	𝑝	𝑝	X
cana-4523	151	15	)	)	PUNCT
cana-4523	151	16	𝑛−1	𝑛−1	PROPN
cana-4523	151	17	𝑛=1	𝑛=1	NOUN
cana-4523	151	18	𝐺𝑛(𝑇	𝐺𝑛(𝑇	NOUN
cana-4523	151	19	)	)	PUNCT
cana-4523	151	20	(	(	PUNCT
cana-4523	151	21	3.3	3.3	NUM
cana-4523	151	22	)	)	PUNCT
cana-4523	151	23	the	the	DET
cana-4523	151	24	n	n	ADV
cana-4523	151	25	-	-	ADJ
cana-4523	151	26	fold	fold	ADJ
cana-4523	151	27	convolution	convolution	NOUN
cana-4523	151	28	of	of	ADP
cana-4523	151	29	𝐺	𝐺	PROPN
cana-4523	151	30	(	(	PUNCT
cana-4523	151	31	.	.	PUNCT
cana-4523	151	32	)	)	PUNCT
cana-4523	152	1	with	with	ADP
cana-4523	152	2	itself	itself	PRON
cana-4523	152	3	is	be	AUX
cana-4523	152	4	denoted	denote	VERB
cana-4523	152	5	by	by	ADP
cana-4523	152	6	𝐺𝑛	𝐺𝑛	PROPN
cana-4523	152	7	(	(	PUNCT
cana-4523	152	8	.	.	PUNCT
cana-4523	152	9	)	)	PUNCT
cana-4523	152	10	using	use	VERB
cana-4523	152	11	equations	equation	NOUN
cana-4523	152	12	(	(	PUNCT
cana-4523	152	13	3.2	3.2	NUM
cana-4523	152	14	)	)	PUNCT
cana-4523	152	15	and	and	CCONJ
cana-4523	152	16	(	(	PUNCT
cana-4523	152	17	3.3	3.3	NUM
cana-4523	152	18	)	)	PUNCT
cana-4523	152	19	,	,	PUNCT
cana-4523	152	20	the	the	DET
cana-4523	152	21	equation	equation	NOUN
cana-4523	152	22	(	(	PUNCT
cana-4523	152	23	3.1	3.1	NUM
cana-4523	152	24	)	)	PUNCT
cana-4523	152	25	becomes	become	VERB
cana-4523	152	26	𝐶(𝑇	𝐶(𝑇	ADJ
cana-4523	152	27	)	)	PUNCT
cana-4523	152	28	=	=	SYM
cana-4523	152	29	𝑐	𝑐	PROPN
cana-4523	152	30	∑	∑	PROPN
cana-4523	152	31	𝑛−1	𝑛−1	PROPN
cana-4523	152	32	𝑛=1	𝑛=1	NOUN
cana-4523	152	33	(	(	PUNCT
cana-4523	152	34	(	(	PUNCT
cana-4523	152	35	𝛾	𝛾	PROPN
cana-4523	152	36	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	152	37	)	)	PUNCT
cana-4523	152	38	(	(	PUNCT
cana-4523	152	39	1	1	NUM
cana-4523	152	40	−	−	PROPN
cana-4523	152	41	𝑝	𝑝	NOUN
cana-4523	152	42	)	)	PUNCT
cana-4523	152	43	+	+	NOUN
cana-4523	152	44	𝑝	𝑝	NOUN
cana-4523	152	45	)	)	PUNCT
cana-4523	152	46	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	152	47	)	)	PUNCT
cana-4523	152	48	−	−	NOUN
cana-4523	152	49	𝑟	𝑟	SYM
cana-4523	152	50	∑	∑	PUNCT
cana-4523	152	51	∞	∞	PROPN
cana-4523	152	52	𝑛=2	𝑛=2	PROPN
cana-4523	152	53	(	(	PUNCT
cana-4523	152	54	𝜇	𝜇	ADP
cana-4523	152	55	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	152	56	)	)	PUNCT
cana-4523	152	57	𝐹𝑛(𝑇	𝐹𝑛(𝑇	SYM
cana-4523	152	58	)	)	PUNCT
cana-4523	152	59	+	+	CCONJ
cana-4523	152	60	𝑅	𝑅	PROPN
cana-4523	152	61	+	+	CCONJ
cana-4523	152	62	𝑐𝑝𝜏	𝑐𝑝𝜏	NOUN
cana-4523	152	63	∑	∑	PROPN
cana-4523	152	64	∞	∞	PROPN
cana-4523	152	65	𝑛=1	𝑛=1	NOUN
cana-4523	152	66	(	(	PUNCT
cana-4523	152	67	𝜇	𝜇	ADP
cana-4523	152	68	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	152	69	)	)	PUNCT
cana-4523	152	70	𝐹𝑛(𝑇	𝐹𝑛(𝑇	PUNCT
cana-4523	152	71	)	)	PUNCT
cana-4523	153	1	+	+	CCONJ
cana-4523	153	2	∑	∑	PROPN
cana-4523	153	3	𝑛−1	𝑛−1	PROPN
cana-4523	153	4	𝑛=1	𝑛=1	NOUN
cana-4523	153	5	(	(	PUNCT
cana-4523	153	6	(	(	PUNCT
cana-4523	153	7	𝛾	𝛾	PROPN
cana-4523	153	8	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	153	9	)	)	PUNCT
cana-4523	153	10	(	(	PUNCT
cana-4523	153	11	1	1	NUM
cana-4523	153	12	−	−	PROPN
cana-4523	153	13	𝑝	𝑝	NOUN
cana-4523	153	14	)	)	PUNCT
cana-4523	153	15	+	+	NOUN
cana-4523	153	16	𝑝	𝑝	NOUN
cana-4523	153	17	)	)	PUNCT
cana-4523	153	18	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	153	19	)	)	PUNCT
cana-4523	154	1	+	+	CCONJ
cana-4523	154	2	𝜏	𝜏	X
cana-4523	154	3	(	(	PUNCT
cana-4523	154	4	3.4	3.4	NUM
cana-4523	154	5	)	)	PUNCT
cana-4523	154	6	where	where	SCONJ
cana-4523	154	7	𝐸[𝑍	𝐸[𝑍	NOUN
cana-4523	154	8	]	]	X
cana-4523	154	9	=	=	PUNCT
cana-4523	154	10	𝜏.	𝜏.	NOUN
cana-4523	154	11	further	far	ADV
cana-4523	154	12	,	,	PUNCT
cana-4523	154	13	𝐶(𝑇	𝐶(𝑇	ADJ
cana-4523	154	14	)	)	PUNCT
cana-4523	154	15	=	=	SYM
cana-4523	154	16	𝑐	𝑐	PROPN
cana-4523	154	17	∑	∑	PROPN
cana-4523	154	18	𝑛−1	𝑛−1	PROPN
cana-4523	154	19	𝑛=1	𝑛=1	NOUN
cana-4523	154	20	(	(	PUNCT
cana-4523	154	21	(	(	PUNCT
cana-4523	154	22	𝛾	𝛾	PROPN
cana-4523	154	23	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	154	24	)	)	PUNCT
cana-4523	154	25	(	(	PUNCT
cana-4523	154	26	1	1	NUM
cana-4523	154	27	−	−	PROPN
cana-4523	154	28	𝑝	𝑝	NOUN
cana-4523	154	29	)	)	PUNCT
cana-4523	154	30	+	+	NOUN
cana-4523	154	31	𝑝	𝑝	NOUN
cana-4523	154	32	)	)	PUNCT
cana-4523	154	33	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	154	34	)	)	PUNCT
cana-4523	155	1	−	−	NOUN
cana-4523	155	2	𝑟	𝑟	SYM
cana-4523	155	3	∑	∑	PUNCT
cana-4523	155	4	∞	∞	PROPN
cana-4523	155	5	𝑛=2	𝑛=2	PROPN
cana-4523	155	6	(	(	PUNCT
cana-4523	155	7	𝜇	𝜇	ADP
cana-4523	155	8	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	155	9	)	)	PUNCT
cana-4523	155	10	𝐹𝑛(𝑇	𝐹𝑛(𝑇	PUNCT
cana-4523	155	11	)	)	PUNCT
cana-4523	156	1	+	+	CCONJ
cana-4523	156	2	𝑅1	𝑅1	PROPN
cana-4523	156	3	∑	∑	SYM
cana-4523	156	4	∞	∞	NUM
cana-4523	156	5	𝑛=1	𝑛=1	NOUN
cana-4523	156	6	(	(	PUNCT
cana-4523	156	7	𝜇	𝜇	ADP
cana-4523	156	8	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	156	9	)	)	PUNCT
cana-4523	156	10	𝐹𝑛(𝑇	𝐹𝑛(𝑇	PUNCT
cana-4523	156	11	)	)	PUNCT
cana-4523	156	12	+	+	CCONJ
cana-4523	156	13	∑	∑	PROPN
cana-4523	156	14	𝑛−1	𝑛−1	PROPN
cana-4523	156	15	𝑛=1	𝑛=1	NOUN
cana-4523	156	16	(	(	PUNCT
cana-4523	156	17	(	(	PUNCT
cana-4523	156	18	𝛾	𝛾	PROPN
cana-4523	156	19	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	156	20	)	)	PUNCT
cana-4523	156	21	(	(	PUNCT
cana-4523	156	22	1	1	NUM
cana-4523	156	23	−	−	PROPN
cana-4523	156	24	𝑝	𝑝	NOUN
cana-4523	156	25	)	)	PUNCT
cana-4523	156	26	+	+	NOUN
cana-4523	156	27	𝑝	𝑝	NOUN
cana-4523	156	28	)	)	PUNCT
cana-4523	156	29	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	156	30	)	)	PUNCT
cana-4523	157	1	+	+	CCONJ
cana-4523	157	2	𝜏	𝜏	PRON
cana-4523	157	3	−	−	NOUN
cana-4523	157	4	𝑟	𝑟	NOUN
cana-4523	157	5	where	where	SCONJ
cana-4523	157	6	𝑅1	𝑅1	PROPN
cana-4523	157	7	=	=	SYM
cana-4523	157	8	𝑅	𝑅	PROPN
cana-4523	157	9	+	+	CCONJ
cana-4523	157	10	(	(	PUNCT
cana-4523	157	11	𝑐𝑝	𝑐𝑝	ADP
cana-4523	157	12	+	+	NOUN
cana-4523	157	13	𝑟)𝜏	𝑟)𝜏	NOUN
cana-4523	157	14	,	,	PUNCT
cana-4523	157	15	𝐶1(𝑇	𝐶1(𝑇	NUM
cana-4523	157	16	)	)	PUNCT
cana-4523	157	17	=	=	SYM
cana-4523	157	18	(	(	PUNCT
cana-4523	157	19	𝑐	𝑐	PROPN
cana-4523	157	20	+	+	NUM
cana-4523	157	21	𝑟	𝑟	NOUN
cana-4523	157	22	)	)	PUNCT
cana-4523	157	23	∑	∑	PUNCT
cana-4523	157	24	𝑛−1	𝑛−1	PROPN
cana-4523	157	25	𝑛=1	𝑛=1	NOUN
cana-4523	157	26	(	(	PUNCT
cana-4523	157	27	(	(	PUNCT
cana-4523	157	28	𝛾	𝛾	PROPN
cana-4523	157	29	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	157	30	)	)	PUNCT
cana-4523	157	31	(	(	PUNCT
cana-4523	157	32	1	1	NUM
cana-4523	157	33	−	−	PROPN
cana-4523	157	34	𝑝	𝑝	NOUN
cana-4523	157	35	)	)	PUNCT
cana-4523	157	36	+	+	NOUN
cana-4523	157	37	𝑝	𝑝	NOUN
cana-4523	157	38	)	)	PUNCT
cana-4523	157	39	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	157	40	)	)	PUNCT
cana-4523	157	41	+	+	CCONJ
cana-4523	157	42	𝑅1	𝑅1	PROPN
cana-4523	157	43	∑	∑	SYM
cana-4523	157	44	∞	∞	NUM
cana-4523	157	45	𝑛=1	𝑛=1	NOUN
cana-4523	157	46	(	(	PUNCT
cana-4523	157	47	𝜇	𝜇	ADP
cana-4523	157	48	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	157	49	)	)	PUNCT
cana-4523	157	50	𝐹𝑛(𝑇	𝐹𝑛(𝑇	PUNCT
cana-4523	157	51	)	)	PUNCT
cana-4523	157	52	+	+	CCONJ
cana-4523	157	53	∑	∑	PROPN
cana-4523	157	54	𝑛−1	𝑛−1	PROPN
cana-4523	157	55	𝑛=1	𝑛=1	NOUN
cana-4523	157	56	(	(	PUNCT
cana-4523	157	57	(	(	PUNCT
cana-4523	157	58	𝛾	𝛾	PROPN
cana-4523	157	59	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	157	60	)	)	PUNCT
cana-4523	157	61	(	(	PUNCT
cana-4523	157	62	1	1	NUM
cana-4523	157	63	−	−	PROPN
cana-4523	157	64	𝑝	𝑝	NOUN
cana-4523	157	65	)	)	PUNCT
cana-4523	157	66	+	+	NOUN
cana-4523	157	67	𝑝	𝑝	NOUN
cana-4523	157	68	)	)	PUNCT
cana-4523	157	69	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	157	70	)	)	PUNCT
cana-4523	157	71	+	+	CCONJ
cana-4523	157	72	𝜏	𝜏	X
cana-4523	157	73	(	(	PUNCT
cana-4523	157	74	3.5	3.5	NUM
cana-4523	157	75	)	)	PUNCT
cana-4523	157	76	on	on	ADP
cana-4523	157	77	differentiating	differentiate	VERB
cana-4523	157	78	(	(	PUNCT
cana-4523	157	79	4.5	4.5	NUM
cana-4523	157	80	)	)	PUNCT
cana-4523	157	81	we	we	PRON
cana-4523	157	82	get	get	VERB
cana-4523	157	83	𝐶1	𝐶1	NUM
cana-4523	157	84	′(𝑇	′(𝑇	NOUN
cana-4523	157	85	)	)	PUNCT
cana-4523	158	1	=	=	PUNCT
cana-4523	159	1	[	[	PUNCT
cana-4523	159	2	[	[	X
cana-4523	159	3	𝜇	𝜇	ADP
cana-4523	159	4	∑	∑	PUNCT
cana-4523	159	5	∞	∞	PROPN
cana-4523	159	6	𝑛=1	𝑛=1	NOUN
cana-4523	159	7	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	159	8	)	)	PUNCT
cana-4523	159	9	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	159	10	+	+	PUNCT
cana-4523	159	11	𝜏	𝜏	X
cana-4523	159	12	]	]	X
cana-4523	160	1	[	[	X
cana-4523	160	2	(	(	PUNCT
cana-4523	160	3	𝑐	𝑐	NOUN
cana-4523	160	4	+	+	NOUN
cana-4523	160	5	𝑟	𝑟	NOUN
cana-4523	160	6	)	)	PUNCT
cana-4523	160	7	∑	∑	PUNCT
cana-4523	160	8	𝑛−1	𝑛−1	PROPN
cana-4523	160	9	𝑛=1	𝑛=1	NOUN
cana-4523	160	10	(	(	PUNCT
cana-4523	160	11	(	(	PUNCT
cana-4523	160	12	𝛾	𝛾	PROPN
cana-4523	160	13	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	160	14	)	)	PUNCT
cana-4523	160	15	(	(	PUNCT
cana-4523	160	16	1	1	NUM
cana-4523	160	17	−	−	PROPN
cana-4523	160	18	𝑝	𝑝	NOUN
cana-4523	160	19	)	)	PUNCT
cana-4523	160	20	+	+	CCONJ
cana-4523	161	1	𝑝	𝑝	NOUN
cana-4523	161	2	)	)	PUNCT
cana-4523	161	3	𝐺𝑛	𝐺𝑛	ADJ
cana-4523	161	4	′(𝑇	′(𝑇	NOUN
cana-4523	161	5	)	)	PUNCT
cana-4523	161	6	]	]	PUNCT
cana-4523	162	1	−	−	PUNCT
cana-4523	163	1	[	[	X
cana-4523	163	2	(	(	PUNCT
cana-4523	163	3	𝑐	𝑐	NOUN
cana-4523	163	4	+	+	NOUN
cana-4523	163	5	𝑟	𝑟	NOUN
cana-4523	163	6	)	)	PUNCT
cana-4523	163	7	∑	∑	PUNCT
cana-4523	163	8	𝑛−1	𝑛−1	PROPN
cana-4523	163	9	𝑛=1	𝑛=1	NOUN
cana-4523	163	10	(	(	PUNCT
cana-4523	163	11	(	(	PUNCT
cana-4523	163	12	𝛾	𝛾	PROPN
cana-4523	163	13	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	163	14	)	)	PUNCT
cana-4523	163	15	(	(	PUNCT
cana-4523	163	16	1	1	NUM
cana-4523	163	17	−	−	PROPN
cana-4523	163	18	𝑝	𝑝	NOUN
cana-4523	163	19	)	)	PUNCT
cana-4523	163	20	+	+	NOUN
cana-4523	163	21	𝑝	𝑝	NOUN
cana-4523	163	22	)	)	PUNCT
cana-4523	163	23	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	163	24	)	)	PUNCT
cana-4523	163	25	+	+	CCONJ
cana-4523	163	26	𝑅1	𝑅1	PROPN
cana-4523	163	27	]	]	X
cana-4523	164	1	[	[	X
cana-4523	164	2	(	(	PUNCT
cana-4523	164	3	𝜇	𝜇	ADP
cana-4523	164	4	∑	∑	PROPN
cana-4523	164	5	∞	∞	PROPN
cana-4523	164	6	𝑛=1	𝑛=1	NOUN
cana-4523	164	7	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	164	8	′(𝑇	′(𝑇	NOUN
cana-4523	164	9	)	)	PUNCT
cana-4523	164	10	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	164	11	)	)	PUNCT
cana-4523	164	12	]	]	PUNCT
cana-4523	164	13	]	]	PUNCT
cana-4523	164	14	(	(	PUNCT
cana-4523	164	15	∑	∑	PROPN
cana-4523	164	16	∞	∞	NUM
cana-4523	164	17	𝑛=1	𝑛=1	NOUN
cana-4523	164	18	(	(	PUNCT
cana-4523	164	19	𝜇	𝜇	ADP
cana-4523	164	20	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	164	21	)	)	PUNCT
cana-4523	164	22	𝐹𝑛(𝑇	𝐹𝑛(𝑇	PUNCT
cana-4523	164	23	)	)	PUNCT
cana-4523	164	24	+	+	CCONJ
cana-4523	164	25	∑	∑	PROPN
cana-4523	164	26	𝑛−1	𝑛−1	PROPN
cana-4523	164	27	𝑛=1	𝑛=1	NOUN
cana-4523	164	28	(	(	PUNCT
cana-4523	164	29	(	(	PUNCT
cana-4523	164	30	𝛾	𝛾	PROPN
cana-4523	164	31	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	164	32	)	)	PUNCT
cana-4523	164	33	(	(	PUNCT
cana-4523	164	34	1	1	NUM
cana-4523	164	35	−	−	PROPN
cana-4523	164	36	𝑝	𝑝	NOUN
cana-4523	164	37	)	)	PUNCT
cana-4523	164	38	+	+	NOUN
cana-4523	164	39	𝑝	𝑝	NOUN
cana-4523	164	40	)	)	PUNCT
cana-4523	164	41	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	164	42	)	)	PUNCT
cana-4523	164	43	+	+	CCONJ
cana-4523	164	44	𝜏	𝜏	X
cana-4523	164	45	)	)	PUNCT
cana-4523	164	46	2	2	NUM
cana-4523	164	47	(	(	PUNCT
cana-4523	164	48	3.6	3.6	NUM
cana-4523	164	49	)	)	PUNCT
cana-4523	164	50	if	if	SCONJ
cana-4523	164	51	𝐶1	𝐶1	NOUN
cana-4523	164	52	′(𝑇	′(𝑇	NOUN
cana-4523	164	53	)	)	PUNCT
cana-4523	165	1	=	=	SYM
cana-4523	165	2	0	0	NUM
cana-4523	165	3	,	,	PUNCT
cana-4523	165	4	then	then	ADV
cana-4523	165	5	communications	communication	NOUN
cana-4523	165	6	on	on	ADP
cana-4523	165	7	applied	apply	VERB
cana-4523	165	8	nonlinear	nonlinear	ADJ
cana-4523	165	9	analysis	analysis	NOUN
cana-4523	165	10	issn	issn	NOUN
cana-4523	165	11	:	:	PUNCT
cana-4523	165	12	1074	1074	NUM
cana-4523	165	13	-	-	PUNCT
cana-4523	165	14	133x	133x	NUM
cana-4523	165	15	vol	vol	NOUN
cana-4523	165	16	32	32	NUM
cana-4523	165	17	no	no	NOUN
cana-4523	165	18	.	.	PUNCT
cana-4523	166	1	9s	9s	NUM
cana-4523	166	2	(	(	PUNCT
cana-4523	166	3	2025	2025	NUM
cana-4523	166	4	)	)	PUNCT
cana-4523	166	5	2366	2366	NUM
cana-4523	166	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	167	1	[	[	X
cana-4523	167	2	[	[	X
cana-4523	167	3	𝜇	𝜇	ADP
cana-4523	167	4	∑	∑	PROPN
cana-4523	167	5	∞	∞	PROPN
cana-4523	167	6	𝑛=1	𝑛=1	NOUN
cana-4523	167	7	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	167	8	)	)	PUNCT
cana-4523	167	9	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	167	10	+	+	PUNCT
cana-4523	167	11	𝜏	𝜏	X
cana-4523	167	12	]	]	X
cana-4523	167	13	[	[	X
cana-4523	167	14	(	(	PUNCT
cana-4523	167	15	𝑐	𝑐	NOUN
cana-4523	167	16	+	+	NOUN
cana-4523	167	17	𝑟	𝑟	NOUN
cana-4523	167	18	)	)	PUNCT
cana-4523	167	19	∑	∑	PUNCT
cana-4523	167	20	𝑛−1	𝑛−1	PROPN
cana-4523	167	21	𝑛=1	𝑛=1	NOUN
cana-4523	167	22	(	(	PUNCT
cana-4523	167	23	(	(	PUNCT
cana-4523	167	24	𝛾	𝛾	PROPN
cana-4523	167	25	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	167	26	)	)	PUNCT
cana-4523	167	27	(	(	PUNCT
cana-4523	167	28	1	1	NUM
cana-4523	167	29	−	−	PROPN
cana-4523	167	30	𝑝	𝑝	NOUN
cana-4523	167	31	)	)	PUNCT
cana-4523	167	32	+	+	CCONJ
cana-4523	167	33	𝑝	𝑝	NOUN
cana-4523	167	34	)	)	PUNCT
cana-4523	167	35	𝐺𝑛	𝐺𝑛	ADJ
cana-4523	167	36	′(𝑇	′(𝑇	NOUN
cana-4523	167	37	)	)	PUNCT
cana-4523	167	38	]	]	PUNCT
cana-4523	168	1	−	−	PUNCT
cana-4523	169	1	[	[	X
cana-4523	169	2	(	(	PUNCT
cana-4523	169	3	𝑐	𝑐	NOUN
cana-4523	169	4	+	+	NOUN
cana-4523	169	5	𝑟	𝑟	NOUN
cana-4523	169	6	)	)	PUNCT
cana-4523	169	7	∑	∑	PUNCT
cana-4523	169	8	𝑛−1	𝑛−1	PROPN
cana-4523	169	9	𝑛=1	𝑛=1	NOUN
cana-4523	169	10	(	(	PUNCT
cana-4523	169	11	(	(	PUNCT
cana-4523	169	12	𝛾	𝛾	PROPN
cana-4523	169	13	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	169	14	)	)	PUNCT
cana-4523	169	15	(	(	PUNCT
cana-4523	169	16	1	1	NUM
cana-4523	169	17	−	−	PROPN
cana-4523	169	18	𝑝	𝑝	NOUN
cana-4523	169	19	)	)	PUNCT
cana-4523	169	20	+	+	NOUN
cana-4523	169	21	𝑝	𝑝	NOUN
cana-4523	169	22	)	)	PUNCT
cana-4523	169	23	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	169	24	)	)	PUNCT
cana-4523	169	25	+	+	CCONJ
cana-4523	169	26	𝑅1	𝑅1	PROPN
cana-4523	169	27	]	]	X
cana-4523	170	1	[	[	X
cana-4523	170	2	(	(	PUNCT
cana-4523	170	3	𝜇	𝜇	ADP
cana-4523	170	4	∑	∑	PROPN
cana-4523	170	5	∞	∞	PROPN
cana-4523	170	6	𝑛=1	𝑛=1	NOUN
cana-4523	170	7	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	170	8	′(𝑇	′(𝑇	NOUN
cana-4523	170	9	)	)	PUNCT
cana-4523	170	10	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	170	11	)	)	PUNCT
cana-4523	170	12	]	]	PUNCT
cana-4523	170	13	]	]	PUNCT
cana-4523	171	1	=	=	SYM
cana-4523	171	2	0	0	NUM
cana-4523	171	3	which	which	PRON
cana-4523	171	4	implies	imply	VERB
cana-4523	171	5	[	[	X
cana-4523	171	6	𝜇	𝜇	ADP
cana-4523	171	7	∑	∑	PUNCT
cana-4523	171	8	∞	∞	PROPN
cana-4523	171	9	𝑛=1	𝑛=1	NOUN
cana-4523	171	10	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	171	11	)	)	PUNCT
cana-4523	171	12	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	172	1	+	+	PUNCT
cana-4523	172	2	𝜏	𝜏	X
cana-4523	172	3	]	]	X
cana-4523	172	4	[	[	X
cana-4523	172	5	(	(	PUNCT
cana-4523	172	6	𝑐	𝑐	NOUN
cana-4523	172	7	+	+	NOUN
cana-4523	172	8	𝑟	𝑟	NOUN
cana-4523	172	9	)	)	PUNCT
cana-4523	172	10	∑	∑	PUNCT
cana-4523	172	11	𝑛−1	𝑛−1	PROPN
cana-4523	172	12	𝑛=1	𝑛=1	NOUN
cana-4523	172	13	(	(	PUNCT
cana-4523	172	14	(	(	PUNCT
cana-4523	172	15	𝛾	𝛾	PROPN
cana-4523	172	16	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	172	17	)	)	PUNCT
cana-4523	172	18	(	(	PUNCT
cana-4523	172	19	1	1	NUM
cana-4523	172	20	−	−	PROPN
cana-4523	172	21	𝑝	𝑝	NOUN
cana-4523	172	22	)	)	PUNCT
cana-4523	172	23	+	+	CCONJ
cana-4523	173	1	𝑝	𝑝	NOUN
cana-4523	173	2	)	)	PUNCT
cana-4523	173	3	𝐺𝑛	𝐺𝑛	ADJ
cana-4523	173	4	′(𝑇	′(𝑇	NOUN
cana-4523	173	5	)	)	PUNCT
cana-4523	173	6	]	]	PUNCT
cana-4523	174	1	=	=	PUNCT
cana-4523	175	1	[	[	X
cana-4523	175	2	(	(	PUNCT
cana-4523	175	3	𝑐	𝑐	NOUN
cana-4523	175	4	+	+	NOUN
cana-4523	175	5	𝑟	𝑟	NOUN
cana-4523	175	6	)	)	PUNCT
cana-4523	175	7	∑	∑	PUNCT
cana-4523	175	8	𝑛−1	𝑛−1	PROPN
cana-4523	175	9	𝑛=1	𝑛=1	NOUN
cana-4523	175	10	(	(	PUNCT
cana-4523	175	11	(	(	PUNCT
cana-4523	175	12	𝛾	𝛾	PROPN
cana-4523	175	13	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	175	14	)	)	PUNCT
cana-4523	175	15	(	(	PUNCT
cana-4523	175	16	1	1	NUM
cana-4523	175	17	−	−	PROPN
cana-4523	175	18	𝑝	𝑝	NOUN
cana-4523	175	19	)	)	PUNCT
cana-4523	175	20	+	+	NOUN
cana-4523	175	21	𝑝	𝑝	NOUN
cana-4523	175	22	)	)	PUNCT
cana-4523	175	23	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	175	24	)	)	PUNCT
cana-4523	175	25	+	+	CCONJ
cana-4523	175	26	𝑅1	𝑅1	PROPN
cana-4523	175	27	]	]	X
cana-4523	176	1	[	[	X
cana-4523	176	2	(	(	PUNCT
cana-4523	176	3	𝜇	𝜇	ADP
cana-4523	176	4	∑	∑	PROPN
cana-4523	176	5	∞	∞	PROPN
cana-4523	176	6	𝑛=1	𝑛=1	NOUN
cana-4523	176	7	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	176	8	′(𝑇	′(𝑇	NOUN
cana-4523	176	9	)	)	PUNCT
cana-4523	176	10	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	176	11	)	)	PUNCT
cana-4523	176	12	]	]	PUNCT
cana-4523	176	13	(	(	PUNCT
cana-4523	176	14	3.7	3.7	NUM
cana-4523	176	15	)	)	PUNCT
cana-4523	176	16	again	again	ADV
cana-4523	176	17	differentiating	differentiate	VERB
cana-4523	176	18	equation	equation	NOUN
cana-4523	176	19	(	(	PUNCT
cana-4523	176	20	3.6	3.6	NUM
cana-4523	176	21	)	)	PUNCT
cana-4523	176	22	using	use	VERB
cana-4523	176	23	the	the	DET
cana-4523	176	24	equation	equation	NOUN
cana-4523	176	25	(	(	PUNCT
cana-4523	176	26	3.7	3.7	NUM
cana-4523	176	27	)	)	PUNCT
cana-4523	176	28	we	we	PRON
cana-4523	176	29	obtain	obtain	VERB
cana-4523	176	30	,	,	PUNCT
cana-4523	176	31	on	on	ADP
cana-4523	176	32	simplification	simplification	NOUN
cana-4523	176	33	that	that	SCONJ
cana-4523	176	34	𝐶1	𝐶1	PRON
cana-4523	176	35	′′(𝑇	′′(𝑇	X
cana-4523	176	36	)	)	PUNCT
cana-4523	176	37	=	=	NOUN
cana-4523	177	1	[	[	PUNCT
cana-4523	177	2	[	[	X
cana-4523	177	3	𝜇	𝜇	ADP
cana-4523	177	4	∑	∑	PUNCT
cana-4523	177	5	∞	∞	PROPN
cana-4523	177	6	𝑛=1	𝑛=1	NOUN
cana-4523	177	7	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	177	8	)	)	PUNCT
cana-4523	177	9	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	177	10	+	+	PUNCT
cana-4523	177	11	𝜏	𝜏	X
cana-4523	177	12	]	]	X
cana-4523	178	1	[	[	X
cana-4523	178	2	(	(	PUNCT
cana-4523	178	3	𝑐	𝑐	NOUN
cana-4523	178	4	+	+	NOUN
cana-4523	178	5	𝑟	𝑟	NOUN
cana-4523	178	6	)	)	PUNCT
cana-4523	178	7	∑	∑	PUNCT
cana-4523	178	8	𝑛−1	𝑛−1	PROPN
cana-4523	178	9	𝑛=1	𝑛=1	NOUN
cana-4523	178	10	(	(	PUNCT
cana-4523	178	11	(	(	PUNCT
cana-4523	178	12	𝛾	𝛾	PROPN
cana-4523	178	13	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	178	14	)	)	PUNCT
cana-4523	178	15	(	(	PUNCT
cana-4523	178	16	1	1	NUM
cana-4523	178	17	−	−	PROPN
cana-4523	178	18	𝑝	𝑝	NOUN
cana-4523	178	19	)	)	PUNCT
cana-4523	178	20	+	+	CCONJ
cana-4523	178	21	𝑝	𝑝	X
cana-4523	178	22	)	)	PUNCT
cana-4523	178	23	𝐺𝑛	𝐺𝑛	PROPN
cana-4523	178	24	′′(𝑇	′′(𝑇	NOUN
cana-4523	178	25	)	)	PUNCT
cana-4523	178	26	]	]	PUNCT
cana-4523	178	27	−	−	PROPN
cana-4523	179	1	[	[	X
cana-4523	179	2	(	(	PUNCT
cana-4523	179	3	𝑐	𝑐	NOUN
cana-4523	179	4	+	+	NOUN
cana-4523	179	5	𝑟	𝑟	NOUN
cana-4523	179	6	)	)	PUNCT
cana-4523	179	7	∑	∑	PUNCT
cana-4523	179	8	𝑛−1	𝑛−1	PROPN
cana-4523	179	9	𝑛=1	𝑛=1	NOUN
cana-4523	179	10	(	(	PUNCT
cana-4523	179	11	(	(	PUNCT
cana-4523	179	12	𝛾	𝛾	PROPN
cana-4523	179	13	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	179	14	)	)	PUNCT
cana-4523	179	15	(	(	PUNCT
cana-4523	179	16	1	1	NUM
cana-4523	179	17	−	−	PROPN
cana-4523	179	18	𝑝	𝑝	NOUN
cana-4523	179	19	)	)	PUNCT
cana-4523	179	20	+	+	NOUN
cana-4523	179	21	𝑝	𝑝	NOUN
cana-4523	179	22	)	)	PUNCT
cana-4523	179	23	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	179	24	)	)	PUNCT
cana-4523	179	25	+	+	CCONJ
cana-4523	179	26	𝑅1	𝑅1	PROPN
cana-4523	179	27	]	]	X
cana-4523	180	1	[	[	X
cana-4523	180	2	(	(	PUNCT
cana-4523	180	3	𝜇	𝜇	ADP
cana-4523	180	4	∑	∑	PROPN
cana-4523	180	5	∞	∞	PROPN
cana-4523	180	6	𝑛=1	𝑛=1	NOUN
cana-4523	181	1	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	181	2	′′(𝑇	′′(𝑇	NOUN
cana-4523	181	3	)	)	PUNCT
cana-4523	181	4	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	181	5	)	)	PUNCT
cana-4523	181	6	]	]	PUNCT
cana-4523	181	7	]	]	PUNCT
cana-4523	181	8	(	(	PUNCT
cana-4523	181	9	𝜇	𝜇	ADP
cana-4523	181	10	∑	∑	PUNCT
cana-4523	181	11	∞	∞	PROPN
cana-4523	181	12	𝑛=1	𝑛=1	NOUN
cana-4523	181	13	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	181	14	)	)	PUNCT
cana-4523	181	15	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	181	16	+	+	CCONJ
cana-4523	181	17	∑	∑	PROPN
cana-4523	181	18	𝑛−1	𝑛−1	PROPN
cana-4523	181	19	𝑛=1	𝑛=1	NOUN
cana-4523	181	20	(	(	PUNCT
cana-4523	181	21	(	(	PUNCT
cana-4523	181	22	𝛾	𝛾	PROPN
cana-4523	181	23	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	181	24	)	)	PUNCT
cana-4523	181	25	(	(	PUNCT
cana-4523	181	26	1	1	NUM
cana-4523	181	27	−	−	PROPN
cana-4523	181	28	𝑝	𝑝	NOUN
cana-4523	181	29	)	)	PUNCT
cana-4523	181	30	+	+	NOUN
cana-4523	181	31	𝑝	𝑝	NOUN
cana-4523	181	32	)	)	PUNCT
cana-4523	181	33	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	181	34	)	)	PUNCT
cana-4523	181	35	+	+	CCONJ
cana-4523	181	36	𝜏	𝜏	X
cana-4523	181	37	)	)	PUNCT
cana-4523	181	38	4	4	NUM
cana-4523	181	39	if	if	SCONJ
cana-4523	181	40	𝐶1′′(𝑇	𝐶1′′(𝑇	ADJ
cana-4523	181	41	)	)	PUNCT
cana-4523	181	42	>	>	X
cana-4523	181	43	0	0	NUM
cana-4523	181	44	,	,	PUNCT
cana-4523	181	45	then	then	ADV
cana-4523	181	46	[	[	X
cana-4523	181	47	𝜇	𝜇	ADP
cana-4523	181	48	∑	∑	PROPN
cana-4523	181	49	∞	∞	PROPN
cana-4523	181	50	𝑛=1	𝑛=1	NOUN
cana-4523	181	51	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	181	52	)	)	PUNCT
cana-4523	181	53	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	181	54	+	+	PUNCT
cana-4523	181	55	𝜏	𝜏	X
cana-4523	181	56	]	]	X
cana-4523	181	57	[	[	X
cana-4523	181	58	(	(	PUNCT
cana-4523	181	59	𝑐	𝑐	NOUN
cana-4523	181	60	+	+	NOUN
cana-4523	181	61	𝑟	𝑟	NOUN
cana-4523	181	62	)	)	PUNCT
cana-4523	181	63	∑	∑	PUNCT
cana-4523	181	64	𝑛−1	𝑛−1	PROPN
cana-4523	181	65	𝑛=1	𝑛=1	NOUN
cana-4523	181	66	(	(	PUNCT
cana-4523	181	67	(	(	PUNCT
cana-4523	181	68	𝛾	𝛾	PROPN
cana-4523	181	69	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	181	70	)	)	PUNCT
cana-4523	181	71	(	(	PUNCT
cana-4523	181	72	1	1	NUM
cana-4523	181	73	−	−	PROPN
cana-4523	181	74	𝑝	𝑝	NOUN
cana-4523	181	75	)	)	PUNCT
cana-4523	181	76	+	+	CCONJ
cana-4523	181	77	𝑝	𝑝	X
cana-4523	181	78	)	)	PUNCT
cana-4523	181	79	𝐺𝑛	𝐺𝑛	PROPN
cana-4523	181	80	′′(𝑇	′′(𝑇	NOUN
cana-4523	181	81	)	)	PUNCT
cana-4523	181	82	]	]	PUNCT
cana-4523	181	83	>	>	X
cana-4523	182	1	[	[	X
cana-4523	182	2	(	(	PUNCT
cana-4523	182	3	𝑐	𝑐	NOUN
cana-4523	182	4	+	+	NOUN
cana-4523	182	5	𝑟	𝑟	NOUN
cana-4523	182	6	)	)	PUNCT
cana-4523	182	7	∑	∑	PUNCT
cana-4523	182	8	𝑛−1	𝑛−1	PROPN
cana-4523	182	9	𝑛=1	𝑛=1	NOUN
cana-4523	182	10	(	(	PUNCT
cana-4523	182	11	(	(	PUNCT
cana-4523	182	12	𝛾	𝛾	PROPN
cana-4523	182	13	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	182	14	)	)	PUNCT
cana-4523	182	15	(	(	PUNCT
cana-4523	182	16	1	1	NUM
cana-4523	182	17	−	−	PROPN
cana-4523	182	18	𝑝	𝑝	NOUN
cana-4523	182	19	)	)	PUNCT
cana-4523	182	20	+	+	NOUN
cana-4523	182	21	𝑝	𝑝	NOUN
cana-4523	182	22	)	)	PUNCT
cana-4523	182	23	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	182	24	)	)	PUNCT
cana-4523	182	25	+	+	CCONJ
cana-4523	182	26	𝑅1	𝑅1	PROPN
cana-4523	182	27	]	]	X
cana-4523	182	28	[	[	X
cana-4523	182	29	(	(	PUNCT
cana-4523	182	30	𝜇	𝜇	ADP
cana-4523	182	31	∑	∑	PROPN
cana-4523	182	32	∞	∞	PROPN
cana-4523	182	33	𝑛=1	𝑛=1	NOUN
cana-4523	183	1	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	183	2	′′(𝑇	′′(𝑇	NOUN
cana-4523	183	3	)	)	PUNCT
cana-4523	183	4	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	183	5	)	)	PUNCT
cana-4523	183	6	]	]	PUNCT
cana-4523	183	7	(	(	PUNCT
cana-4523	183	8	3.8	3.8	NUM
cana-4523	183	9	)	)	PUNCT
cana-4523	183	10	for	for	ADP
cana-4523	183	11	if	if	SCONJ
cana-4523	183	12	𝐶1	𝐶1	NOUN
cana-4523	183	13	′(𝑇	′(𝑇	NOUN
cana-4523	183	14	)	)	PUNCT
cana-4523	184	1	=	=	SYM
cana-4523	184	2	0	0	NUM
cana-4523	184	3	,	,	PUNCT
cana-4523	184	4	𝐶1′′(𝑇	𝐶1′′(𝑇	PROPN
cana-4523	184	5	)	)	PUNCT
cana-4523	184	6	>	>	X
cana-4523	185	1	0	0	NUM
cana-4523	185	2	,	,	PUNCT
cana-4523	185	3	then	then	ADV
cana-4523	185	4	𝐶1(𝑇	𝐶1(𝑇	VERB
cana-4523	185	5	)	)	PUNCT
cana-4523	185	6	attain	attain	VERB
cana-4523	185	7	its	its	PRON
cana-4523	185	8	minimum	minimum	NOUN
cana-4523	185	9	.	.	PUNCT
cana-4523	186	1	remarks	remark	NOUN
cana-4523	186	2	.	.	PUNCT
cana-4523	187	1	1	1	X
cana-4523	187	2	.	.	X
cana-4523	187	3	when	when	SCONJ
cana-4523	187	4	p	p	NOUN
cana-4523	187	5	=	=	NOUN
cana-4523	187	6	0	0	NUM
cana-4523	187	7	,	,	PUNCT
cana-4523	187	8	that	that	PRON
cana-4523	187	9	is	be	AUX
cana-4523	187	10	when	when	SCONJ
cana-4523	187	11	the	the	DET
cana-4523	187	12	repair	repair	NOUN
cana-4523	187	13	times	time	NOUN
cana-4523	187	14	non	non	ADJ
cana-4523	187	15	-	-	ADJ
cana-4523	187	16	negligible	negligible	ADJ
cana-4523	187	17	,	,	PUNCT
cana-4523	187	18	equation	equation	NOUN
cana-4523	187	19	(	(	PUNCT
cana-4523	187	20	3.4	3.4	NUM
cana-4523	187	21	)	)	PUNCT
cana-4523	187	22	reduces	reduce	VERB
cana-4523	187	23	to	to	ADP
cana-4523	187	24	𝐶(𝑇	𝐶(𝑇	ADJ
cana-4523	187	25	)	)	PUNCT
cana-4523	187	26	=	=	PUNCT
cana-4523	188	1	∑	∑	PUNCT
cana-4523	188	2	𝑛−1	𝑛−1	NUM
cana-4523	188	3	𝑖=1	𝑖=1	PROPN
cana-4523	188	4	𝑐	𝑐	PROPN
cana-4523	188	5	(	(	PUNCT
cana-4523	188	6	𝛾	𝛾	PROPN
cana-4523	188	7	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	188	8	)	)	PUNCT
cana-4523	188	9	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	188	10	)	)	PUNCT
cana-4523	188	11	−	−	NOUN
cana-4523	188	12	∑	∑	PUNCT
cana-4523	188	13	∞	∞	PROPN
cana-4523	188	14	𝑛=2	𝑛=2	NOUN
cana-4523	188	15	𝑟	𝑟	NOUN
cana-4523	188	16	(	(	PUNCT
cana-4523	188	17	𝜇	𝜇	ADP
cana-4523	188	18	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	188	19	)	)	PUNCT
cana-4523	188	20	𝐹𝑛(𝑇	𝐹𝑛(𝑇	SYM
cana-4523	188	21	)	)	PUNCT
cana-4523	189	1	+	+	CCONJ
cana-4523	189	2	𝑅	𝑅	NOUN
cana-4523	189	3	+	+	NOUN
cana-4523	189	4	𝑐𝑝	𝑐𝑝	ADP
cana-4523	189	5	𝜏	𝜏	PRON
cana-4523	189	6	𝜇	𝜇	ADP
cana-4523	189	7	∑	∑	PROPN
cana-4523	189	8	∞	∞	PROPN
cana-4523	189	9	𝑛=1	𝑛=1	NOUN
cana-4523	189	10	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	189	11	)	)	PUNCT
cana-4523	189	12	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	189	13	+	+	CCONJ
cana-4523	189	14	𝛾	𝛾	PROPN
cana-4523	189	15	∑	∑	PUNCT
cana-4523	189	16	∞	∞	NUM
cana-4523	189	17	𝑛=1	𝑛=1	NOUN
cana-4523	189	18	𝐺𝑛(𝑇	𝐺𝑛(𝑇	ADJ
cana-4523	189	19	)	)	PUNCT
cana-4523	189	20	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	189	21	+	+	CCONJ
cana-4523	189	22	𝜏	𝜏	PROPN
cana-4523	189	23	2	2	NUM
cana-4523	189	24	.	.	PUNCT
cana-4523	189	25	when	when	SCONJ
cana-4523	189	26	p	p	NOUN
cana-4523	189	27	=	=	NOUN
cana-4523	189	28	1	1	NUM
cana-4523	189	29	,	,	PUNCT
cana-4523	189	30	that	that	ADV
cana-4523	189	31	is	is	ADV
cana-4523	189	32	,	,	PUNCT
cana-4523	189	33	when	when	SCONJ
cana-4523	189	34	the	the	DET
cana-4523	189	35	repair	repair	NOUN
cana-4523	189	36	times	time	NOUN
cana-4523	189	37	are	be	AUX
cana-4523	189	38	negligible	negligible	ADJ
cana-4523	189	39	,	,	PUNCT
cana-4523	189	40	equation	equation	NOUN
cana-4523	189	41	(	(	PUNCT
cana-4523	189	42	3.4	3.4	NUM
cana-4523	189	43	)	)	PUNCT
cana-4523	189	44	reduces	reduce	VERB
cana-4523	189	45	to	to	ADP
cana-4523	189	46	communications	communication	NOUN
cana-4523	189	47	on	on	ADP
cana-4523	189	48	applied	apply	VERB
cana-4523	189	49	nonlinear	nonlinear	ADJ
cana-4523	189	50	analysis	analysis	NOUN
cana-4523	189	51	issn	issn	NOUN
cana-4523	189	52	:	:	PUNCT
cana-4523	189	53	1074	1074	NUM
cana-4523	189	54	-	-	PUNCT
cana-4523	189	55	133x	133x	NUM
cana-4523	189	56	vol	vol	NOUN
cana-4523	189	57	32	32	NUM
cana-4523	189	58	no	no	NOUN
cana-4523	189	59	.	.	PUNCT
cana-4523	190	1	9s	9s	NUM
cana-4523	190	2	(	(	PUNCT
cana-4523	190	3	2025	2025	NUM
cana-4523	190	4	)	)	PUNCT
cana-4523	190	5	2367	2367	NUM
cana-4523	190	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	190	7	𝐶(𝑇	𝐶(𝑇	ADJ
cana-4523	190	8	)	)	PUNCT
cana-4523	190	9	=	=	PUNCT
cana-4523	190	10	∑	∑	PUNCT
cana-4523	190	11	𝑛−1	𝑛−1	NUM
cana-4523	190	12	𝑖=1	𝑖=1	PROPN
cana-4523	190	13	𝑐𝐺𝑛(𝑇	𝑐𝐺𝑛(𝑇	NOUN
cana-4523	190	14	)	)	PUNCT
cana-4523	190	15	−	−	NOUN
cana-4523	190	16	∑	∑	PUNCT
cana-4523	190	17	∞	∞	PROPN
cana-4523	190	18	𝑛=2	𝑛=2	NOUN
cana-4523	190	19	𝑟	𝑟	NOUN
cana-4523	190	20	(	(	PUNCT
cana-4523	190	21	𝜇	𝜇	ADP
cana-4523	190	22	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	190	23	)	)	PUNCT
cana-4523	190	24	𝐹𝑛(𝑇	𝐹𝑛(𝑇	SYM
cana-4523	190	25	)	)	PUNCT
cana-4523	191	1	+	+	CCONJ
cana-4523	191	2	𝑅	𝑅	NOUN
cana-4523	191	3	+	+	NOUN
cana-4523	191	4	𝑐𝑝	𝑐𝑝	ADP
cana-4523	191	5	𝜏	𝜏	PRON
cana-4523	191	6	𝜇	𝜇	ADP
cana-4523	191	7	∑	∑	PROPN
cana-4523	191	8	∞	∞	PROPN
cana-4523	191	9	𝑛=1	𝑛=1	NOUN
cana-4523	191	10	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	191	11	)	)	PUNCT
cana-4523	191	12	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	191	13	+	+	CCONJ
cana-4523	191	14	∑	∑	PROPN
cana-4523	191	15	𝑛−1	𝑛−1	PROPN
cana-4523	191	16	𝑖=1	𝑖=1	PUNCT
cana-4523	191	17	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	191	18	)	)	PUNCT
cana-4523	191	19	+	+	CCONJ
cana-4523	191	20	𝜏	𝜏	NOUN
cana-4523	191	21	theorem	theorem	ADJ
cana-4523	191	22	3.1	3.1	NUM
cana-4523	191	23	:	:	PUNCT
cana-4523	191	24	for	for	ADP
cana-4523	191	25	the	the	DET
cana-4523	191	26	model	model	NOUN
cana-4523	191	27	described	describe	VERB
cana-4523	191	28	in	in	ADP
cana-4523	191	29	section	section	NOUN
cana-4523	191	30	3	3	NUM
cana-4523	191	31	,	,	PUNCT
cana-4523	191	32	under	under	ADP
cana-4523	191	33	the	the	DET
cana-4523	191	34	assumptions	assumption	NOUN
cana-4523	191	35	3.1	3.1	NUM
cana-4523	191	36	to	to	ADP
cana-4523	191	37	3.7	3.7	NUM
cana-4523	191	38	,	,	PUNCT
cana-4523	191	39	the	the	DET
cana-4523	191	40	long	long	ADV
cana-4523	191	41	-	-	PUNCT
cana-4523	191	42	run	run	VERB
cana-4523	191	43	average	average	ADJ
cana-4523	191	44	cost	cost	NOUN
cana-4523	191	45	per	per	ADP
cana-4523	191	46	unit	unit	NOUN
cana-4523	191	47	time	time	NOUN
cana-4523	191	48	𝐶(𝑇)is	𝐶(𝑇)is	PROPN
cana-4523	191	49	given	give	VERB
cana-4523	191	50	by	by	ADP
cana-4523	191	51	𝐶(𝑇	𝐶(𝑇	ADJ
cana-4523	191	52	)	)	PUNCT
cana-4523	191	53	=	=	SYM
cana-4523	191	54	𝑐	𝑐	PROPN
cana-4523	191	55	∑	∑	PROPN
cana-4523	191	56	𝑛−1	𝑛−1	PROPN
cana-4523	191	57	𝑛=1	𝑛=1	NOUN
cana-4523	191	58	(	(	PUNCT
cana-4523	191	59	(	(	PUNCT
cana-4523	191	60	𝛾	𝛾	PROPN
cana-4523	191	61	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	191	62	)	)	PUNCT
cana-4523	191	63	(	(	PUNCT
cana-4523	191	64	1	1	NUM
cana-4523	191	65	−	−	PROPN
cana-4523	191	66	𝑝	𝑝	NOUN
cana-4523	191	67	)	)	PUNCT
cana-4523	191	68	+	+	NOUN
cana-4523	191	69	𝑝	𝑝	NOUN
cana-4523	191	70	)	)	PUNCT
cana-4523	191	71	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	191	72	)	)	PUNCT
cana-4523	191	73	−	−	NOUN
cana-4523	191	74	𝑟	𝑟	SYM
cana-4523	191	75	∑	∑	PUNCT
cana-4523	191	76	∞	∞	PROPN
cana-4523	191	77	𝑛=2	𝑛=2	PROPN
cana-4523	191	78	(	(	PUNCT
cana-4523	191	79	𝜇	𝜇	ADP
cana-4523	191	80	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	191	81	)	)	PUNCT
cana-4523	191	82	𝐹𝑛(𝑇	𝐹𝑛(𝑇	SYM
cana-4523	191	83	)	)	PUNCT
cana-4523	192	1	+	+	CCONJ
cana-4523	192	2	𝑅	𝑅	PROPN
cana-4523	192	3	+	+	CCONJ
cana-4523	192	4	𝑐𝑝𝜏	𝑐𝑝𝜏	NOUN
cana-4523	192	5	∑	∑	PROPN
cana-4523	192	6	∞	∞	PROPN
cana-4523	192	7	𝑛=1	𝑛=1	NOUN
cana-4523	192	8	(	(	PUNCT
cana-4523	192	9	𝜇	𝜇	ADP
cana-4523	192	10	2𝑛−1𝛽	2𝑛−1𝛽	NOUN
cana-4523	192	11	)	)	PUNCT
cana-4523	192	12	𝐹𝑛(𝑇	𝐹𝑛(𝑇	PUNCT
cana-4523	192	13	)	)	PUNCT
cana-4523	192	14	+	+	CCONJ
cana-4523	192	15	∑	∑	PROPN
cana-4523	192	16	𝑛−1	𝑛−1	PROPN
cana-4523	192	17	𝑛=1	𝑛=1	NOUN
cana-4523	192	18	(	(	PUNCT
cana-4523	192	19	(	(	PUNCT
cana-4523	192	20	𝛾	𝛾	PROPN
cana-4523	192	21	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	192	22	)	)	PUNCT
cana-4523	192	23	(	(	PUNCT
cana-4523	192	24	1	1	NUM
cana-4523	192	25	−	−	PROPN
cana-4523	192	26	𝑝	𝑝	NOUN
cana-4523	192	27	)	)	PUNCT
cana-4523	192	28	+	+	NOUN
cana-4523	192	29	𝑝	𝑝	NOUN
cana-4523	192	30	)	)	PUNCT
cana-4523	192	31	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	192	32	)	)	PUNCT
cana-4523	193	1	+	+	CCONJ
cana-4523	193	2	𝜏	𝜏	NOUN
cana-4523	193	3	for	for	ADP
cana-4523	193	4	a	a	DET
cana-4523	193	5	multistate	multistate	NOUN
cana-4523	193	6	degenerative	degenerative	ADJ
cana-4523	193	7	system	system	NOUN
cana-4523	193	8	under	under	ADP
cana-4523	193	9	the	the	DET
cana-4523	193	10	replacement	replacement	NOUN
cana-4523	193	11	policy	policy	NOUN
cana-4523	193	12	t	t	PROPN
cana-4523	193	13	is	be	AUX
cana-4523	193	14	minimum	minimum	ADJ
cana-4523	193	15	,	,	PUNCT
cana-4523	193	16	if	if	SCONJ
cana-4523	193	17	[	[	X
cana-4523	193	18	𝜇	𝜇	X
cana-4523	193	19	∑	∑	ADV
cana-4523	193	20	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	193	21	)	)	PUNCT
cana-4523	193	22	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	193	23	∞	∞	NUM
cana-4523	193	24	𝑛=1	𝑛=1	NOUN
cana-4523	193	25	+	+	X
cana-4523	193	26	𝜏	𝜏	X
cana-4523	193	27	]	]	X
cana-4523	194	1	[	[	X
cana-4523	194	2	(	(	PUNCT
cana-4523	194	3	𝑐	𝑐	NOUN
cana-4523	194	4	+	+	NOUN
cana-4523	194	5	𝑟	𝑟	NOUN
cana-4523	194	6	)	)	PUNCT
cana-4523	194	7	∑	∑	PUNCT
cana-4523	194	8	𝑛−1	𝑛−1	PROPN
cana-4523	194	9	𝑛=1	𝑛=1	NOUN
cana-4523	194	10	(	(	PUNCT
cana-4523	194	11	(	(	PUNCT
cana-4523	194	12	𝛾	𝛾	PROPN
cana-4523	194	13	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	194	14	)	)	PUNCT
cana-4523	194	15	(	(	PUNCT
cana-4523	194	16	1	1	NUM
cana-4523	194	17	−	−	PROPN
cana-4523	194	18	𝑝	𝑝	NOUN
cana-4523	194	19	)	)	PUNCT
cana-4523	194	20	+	+	CCONJ
cana-4523	195	1	𝑝	𝑝	NOUN
cana-4523	195	2	)	)	PUNCT
cana-4523	195	3	𝐺𝑛	𝐺𝑛	ADJ
cana-4523	195	4	′(𝑇	′(𝑇	NOUN
cana-4523	195	5	)	)	PUNCT
cana-4523	195	6	]	]	PUNCT
cana-4523	196	1	=	=	PUNCT
cana-4523	197	1	[	[	X
cana-4523	197	2	(	(	PUNCT
cana-4523	197	3	𝑐	𝑐	NOUN
cana-4523	197	4	+	+	NOUN
cana-4523	197	5	𝑟	𝑟	NOUN
cana-4523	197	6	)	)	PUNCT
cana-4523	197	7	∑	∑	PUNCT
cana-4523	197	8	𝑛−1	𝑛−1	PROPN
cana-4523	197	9	𝑛=1	𝑛=1	NOUN
cana-4523	197	10	(	(	PUNCT
cana-4523	197	11	(	(	PUNCT
cana-4523	197	12	𝛾	𝛾	PROPN
cana-4523	197	13	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	197	14	)	)	PUNCT
cana-4523	197	15	(	(	PUNCT
cana-4523	197	16	1	1	NUM
cana-4523	197	17	−	−	PROPN
cana-4523	197	18	𝑝	𝑝	NOUN
cana-4523	197	19	)	)	PUNCT
cana-4523	197	20	+	+	NOUN
cana-4523	197	21	𝑝	𝑝	NOUN
cana-4523	197	22	)	)	PUNCT
cana-4523	197	23	𝐺𝑛(𝑇	𝐺𝑛(𝑇	PUNCT
cana-4523	197	24	)	)	PUNCT
cana-4523	197	25	+	+	CCONJ
cana-4523	197	26	𝑅1	𝑅1	PROPN
cana-4523	197	27	]	]	X
cana-4523	198	1	[	[	X
cana-4523	198	2	(	(	PUNCT
cana-4523	198	3	𝜇	𝜇	ADP
cana-4523	198	4	∑	∑	ADP
cana-4523	198	5	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	198	6	′(𝑇	′(𝑇	NOUN
cana-4523	198	7	)	)	PUNCT
cana-4523	198	8	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	198	9	∞	∞	NUM
cana-4523	198	10	𝑛=1	𝑛=1	NOUN
cana-4523	198	11	)	)	PUNCT
cana-4523	198	12	]	]	PUNCT
cana-4523	198	13	and	and	CCONJ
cana-4523	198	14	[	[	X
cana-4523	198	15	𝜇	𝜇	X
cana-4523	198	16	∑	∑	ADV
cana-4523	198	17	𝐹𝑛(𝑇	𝐹𝑛(𝑇	NOUN
cana-4523	198	18	)	)	PUNCT
cana-4523	198	19	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	198	20	∞	∞	NUM
cana-4523	198	21	𝑛=1	𝑛=1	NOUN
cana-4523	198	22	+	+	X
cana-4523	198	23	𝜏	𝜏	X
cana-4523	198	24	]	]	X
cana-4523	198	25	[	[	X
cana-4523	198	26	(	(	PUNCT
cana-4523	198	27	𝑐	𝑐	NOUN
cana-4523	198	28	+	+	NOUN
cana-4523	198	29	𝑟	𝑟	NOUN
cana-4523	198	30	)	)	PUNCT
cana-4523	198	31	∑	∑	PUNCT
cana-4523	198	32	(	(	PUNCT
cana-4523	198	33	(	(	PUNCT
cana-4523	198	34	𝛾	𝛾	PROPN
cana-4523	198	35	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	198	36	)	)	PUNCT
cana-4523	198	37	(	(	PUNCT
cana-4523	198	38	1	1	NUM
cana-4523	198	39	−	−	PROPN
cana-4523	198	40	𝑝	𝑝	NOUN
cana-4523	198	41	)	)	PUNCT
cana-4523	198	42	+	+	CCONJ
cana-4523	198	43	𝑝	𝑝	X
cana-4523	198	44	)	)	PUNCT
cana-4523	198	45	𝑛−1	𝑛−1	PROPN
cana-4523	198	46	𝑛=1	𝑛=1	NOUN
cana-4523	198	47	𝐺𝑛	𝐺𝑛	PROPN
cana-4523	198	48	′′(𝑇	′′(𝑇	NOUN
cana-4523	198	49	)	)	PUNCT
cana-4523	198	50	]	]	PUNCT
cana-4523	198	51	>	>	X
cana-4523	199	1	[	[	X
cana-4523	199	2	(	(	PUNCT
cana-4523	199	3	𝑐	𝑐	NOUN
cana-4523	199	4	+	+	NOUN
cana-4523	199	5	𝑟	𝑟	NOUN
cana-4523	199	6	)	)	PUNCT
cana-4523	199	7	∑	∑	PUNCT
cana-4523	199	8	(	(	PUNCT
cana-4523	199	9	(	(	PUNCT
cana-4523	199	10	𝛾	𝛾	PROPN
cana-4523	199	11	𝑎𝑛−1	𝑎𝑛−1	NOUN
cana-4523	199	12	)	)	PUNCT
cana-4523	199	13	(	(	PUNCT
cana-4523	199	14	1	1	NUM
cana-4523	199	15	−	−	PROPN
cana-4523	199	16	𝑝	𝑝	NOUN
cana-4523	199	17	)	)	PUNCT
cana-4523	199	18	+	+	CCONJ
cana-4523	199	19	𝑝	𝑝	X
cana-4523	199	20	)	)	PUNCT
cana-4523	199	21	𝑛−1	𝑛−1	PROPN
cana-4523	199	22	𝑛=1	𝑛=1	NOUN
cana-4523	199	23	𝐺𝑛(𝑇	𝐺𝑛(𝑇	ADJ
cana-4523	199	24	)	)	PUNCT
cana-4523	199	25	+	+	CCONJ
cana-4523	199	26	𝑅1	𝑅1	PROPN
cana-4523	199	27	]	]	X
cana-4523	200	1	[	[	X
cana-4523	200	2	(	(	PUNCT
cana-4523	200	3	𝜇	𝜇	ADP
cana-4523	200	4	∑	∑	ADP
cana-4523	200	5	𝐹𝑛	𝐹𝑛	PROPN
cana-4523	200	6	′′(𝑇	′′(𝑇	NOUN
cana-4523	200	7	)	)	PUNCT
cana-4523	200	8	2𝑛−1𝛽	2𝑛−1𝛽	NUM
cana-4523	200	9	∞	∞	NUM
cana-4523	200	10	𝑛=1	𝑛=1	NOUN
cana-4523	200	11	)	)	PUNCT
cana-4523	200	12	]	]	PUNCT
cana-4523	200	13	hold	hold	VERB
cana-4523	200	14	.	.	PUNCT
cana-4523	201	1	4	4	X
cana-4523	201	2	.	.	X
cana-4523	201	3	conclusion	conclusion	NOUN
cana-4523	201	4	this	this	DET
cana-4523	201	5	research	research	NOUN
cana-4523	201	6	undertakes	undertake	VERB
cana-4523	201	7	a	a	DET
cana-4523	201	8	comprehensive	comprehensive	ADJ
cana-4523	201	9	analysis	analysis	NOUN
cana-4523	201	10	of	of	ADP
cana-4523	201	11	a	a	DET
cana-4523	201	12	repairable	repairable	ADJ
cana-4523	201	13	system	system	NOUN
cana-4523	201	14	within	within	ADP
cana-4523	201	15	a	a	DET
cana-4523	201	16	monotone	monotone	ADJ
cana-4523	201	17	process	process	NOUN
cana-4523	201	18	framework	framework	NOUN
cana-4523	201	19	,	,	PUNCT
cana-4523	201	20	tailored	tailor	VERB
cana-4523	201	21	to	to	ADP
cana-4523	201	22	a	a	DET
cana-4523	201	23	one	one	NUM
cana-4523	201	24	-	-	PUNCT
cana-4523	201	25	component	component	NOUN
cana-4523	201	26	multistate	multistate	NOUN
cana-4523	201	27	degenerative	degenerative	ADJ
cana-4523	201	28	system	system	NOUN
cana-4523	201	29	.	.	PUNCT
cana-4523	202	1	explicit	explicit	ADJ
cana-4523	202	2	expressions	expression	NOUN
cana-4523	202	3	for	for	ADP
cana-4523	202	4	long	long	ADV
cana-4523	202	5	-	-	PUNCT
cana-4523	202	6	run	run	VERB
cana-4523	202	7	average	average	ADJ
cana-4523	202	8	costs	cost	NOUN
cana-4523	202	9	per	per	ADP
cana-4523	202	10	unit	unit	NOUN
cana-4523	202	11	time	time	NOUN
cana-4523	202	12	under	under	ADP
cana-4523	202	13	univariate	univariate	ADJ
cana-4523	202	14	𝑇	𝑇	PROPN
cana-4523	202	15	-policy	-policy	NOUN
cana-4523	202	16	are	be	AUX
cana-4523	202	17	derived	derive	VERB
cana-4523	202	18	.	.	PUNCT
cana-4523	203	1	furthermore	furthermore	ADV
cana-4523	203	2	,	,	PUNCT
cana-4523	203	3	assuming	assume	VERB
cana-4523	203	4	an	an	DET
cana-4523	203	5	alternate	alternate	ADJ
cana-4523	203	6	repair	repair	NOUN
cana-4523	203	7	model	model	NOUN
cana-4523	203	8	with	with	ADP
cana-4523	203	9	non	non	ADJ
cana-4523	203	10	-	-	ADJ
cana-4523	203	11	negligible	negligible	ADJ
cana-4523	203	12	repair	repair	NOUN
cana-4523	203	13	times	time	NOUN
cana-4523	203	14	(	(	PUNCT
cana-4523	203	15	nonn	nonn	PROPN
cana-4523	203	16	)	)	PUNCT
cana-4523	203	17	,	,	PUNCT
cana-4523	203	18	the	the	DET
cana-4523	203	19	study	study	NOUN
cana-4523	203	20	derives	derive	VERB
cana-4523	203	21	long	long	ADV
cana-4523	203	22	-	-	PUNCT
cana-4523	203	23	run	run	VERB
cana-4523	203	24	average	average	ADJ
cana-4523	203	25	cost	cost	NOUN
cana-4523	203	26	expressions	expression	NOUN
cana-4523	203	27	for	for	ADP
cana-4523	203	28	t	t	NOUN
cana-4523	203	29	-	-	PUNCT
cana-4523	203	30	policy	policy	NOUN
cana-4523	203	31	.	.	PUNCT
cana-4523	204	1	optimality	optimality	NOUN
cana-4523	204	2	existence	existence	NOUN
cana-4523	204	3	is	be	AUX
cana-4523	204	4	established	establish	VERB
cana-4523	204	5	for	for	ADP
cana-4523	204	6	these	these	DET
cana-4523	204	7	models	model	NOUN
cana-4523	204	8	.	.	PUNCT
cana-4523	205	1	communications	communication	NOUN
cana-4523	205	2	on	on	ADP
cana-4523	205	3	applied	apply	VERB
cana-4523	205	4	nonlinear	nonlinear	ADJ
cana-4523	205	5	analysis	analysis	NOUN
cana-4523	205	6	issn	issn	NOUN
cana-4523	205	7	:	:	PUNCT
cana-4523	205	8	1074	1074	NUM
cana-4523	205	9	-	-	PUNCT
cana-4523	205	10	133x	133x	NUM
cana-4523	205	11	vol	vol	NOUN
cana-4523	205	12	32	32	NUM
cana-4523	205	13	no	no	NOUN
cana-4523	205	14	.	.	PUNCT
cana-4523	206	1	9s	9s	NUM
cana-4523	206	2	(	(	PUNCT
cana-4523	206	3	2025	2025	NUM
cana-4523	206	4	)	)	PUNCT
cana-4523	206	5	2368	2368	NUM
cana-4523	207	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	207	2	references	reference	NOUN
cana-4523	207	3	[	[	X
cana-4523	207	4	1	1	NUM
cana-4523	207	5	]	]	PUNCT
cana-4523	207	6	ashwini	ashwini	NOUN
cana-4523	207	7	.	.	PUNCT
cana-4523	208	1	i	i	PRON
cana-4523	208	2	,	,	PUNCT
cana-4523	208	3	zahiruddeen	zahiruddeen	PROPN
cana-4523	208	4	and	and	CCONJ
cana-4523	208	5	u.	u.	PROPN
cana-4523	208	6	rizwan	rizwan	PROPN
cana-4523	208	7	(	(	PUNCT
cana-4523	208	8	2024	2024	NUM
cana-4523	208	9	)	)	PUNCT
cana-4523	208	10	.	.	PUNCT
cana-4523	209	1	optimal	optimal	ADJ
cana-4523	209	2	replacement	replacement	NOUN
cana-4523	209	3	model	model	NOUN
cana-4523	209	4	for	for	ADP
cana-4523	209	5	a	a	DET
cana-4523	209	6	deteriorating	deteriorate	VERB
cana-4523	209	7	system	system	NOUN
cana-4523	209	8	under	under	ADP
cana-4523	209	9	partial	partial	ADJ
cana-4523	209	10	sum	sum	NOUN
cana-4523	209	11	process	process	NOUN
cana-4523	209	12	,	,	PUNCT
cana-4523	209	13	journal	journal	NOUN
cana-4523	209	14	of	of	ADP
cana-4523	209	15	computational	computational	ADJ
cana-4523	209	16	analysis	analysis	NOUN
cana-4523	209	17	and	and	CCONJ
cana-4523	209	18	applications	application	NOUN
cana-4523	209	19	,	,	PUNCT
cana-4523	209	20	33(4	33(4	NUM
cana-4523	209	21	)	)	PUNCT
cana-4523	209	22	,	,	PUNCT
cana-4523	209	23	404–411	404–411	NUM
cana-4523	209	24	.	.	PUNCT
cana-4523	210	1	[	[	X
cana-4523	210	2	2	2	NUM
cana-4523	210	3	]	]	PUNCT
cana-4523	210	4	ashwini	ashwini	NOUN
cana-4523	210	5	i	i	PROPN
cana-4523	210	6	,	,	PUNCT
cana-4523	210	7	zahiruddeen	zahiruddeen	NUM
cana-4523	210	8	,	,	PUNCT
cana-4523	210	9	and	and	CCONJ
cana-4523	210	10	u.	u.	PROPN
cana-4523	210	11	rizwan	rizwan	PROPN
cana-4523	210	12	u.	u.	PROPN
cana-4523	210	13	(	(	PUNCT
cana-4523	210	14	2024	2024	NUM
cana-4523	210	15	)	)	PUNCT
cana-4523	210	16	,	,	PUNCT
cana-4523	210	17	a	a	DET
cana-4523	210	18	bivariate	bivariate	ADJ
cana-4523	210	19	replacement	replacement	NOUN
cana-4523	210	20	policy	policy	NOUN
cana-4523	210	21	for	for	ADP
cana-4523	210	22	an	an	DET
cana-4523	210	23	extreme	extreme	ADJ
cana-4523	210	24	shock	shock	NOUN
cana-4523	210	25	maintenance	maintenance	NOUN
cana-4523	210	26	model	model	NOUN
cana-4523	210	27	under	under	ADP
cana-4523	210	28	partial	partial	ADJ
cana-4523	210	29	sum	sum	NOUN
cana-4523	210	30	process	process	NOUN
cana-4523	210	31	,	,	PUNCT
cana-4523	210	32	journal	journal	NOUN
cana-4523	210	33	of	of	ADP
cana-4523	210	34	computational	computational	ADJ
cana-4523	210	35	mathematica	mathematica	PROPN
cana-4523	210	36	,	,	PUNCT
cana-4523	210	37	8(2	8(2	NUM
cana-4523	210	38	)	)	PUNCT
cana-4523	210	39	,	,	PUNCT
cana-4523	210	40	31	31	NUM
cana-4523	210	41	51	51	NUM
cana-4523	210	42	.	.	PUNCT
cana-4523	211	1	[	[	X
cana-4523	211	2	3	3	X
cana-4523	211	3	]	]	X
cana-4523	211	4	babu	babu	PROPN
cana-4523	211	5	d	d	PROPN
cana-4523	211	6	,	,	PUNCT
cana-4523	211	7	manigandan	manigandan	PROPN
cana-4523	211	8	c	c	PROPN
cana-4523	211	9	,	,	PUNCT
cana-4523	211	10	and	and	CCONJ
cana-4523	211	11	parvatham	parvatham	PROPN
cana-4523	211	12	r.	r.	PROPN
cana-4523	211	13	(	(	PUNCT
cana-4523	211	14	2020	2020	NUM
cana-4523	211	15	)	)	PUNCT
cana-4523	211	16	,	,	PUNCT
cana-4523	211	17	a	a	DET
cana-4523	211	18	deteriorating	deteriorate	VERB
cana-4523	211	19	system	system	NOUN
cana-4523	211	20	maintenance	maintenance	NOUN
cana-4523	211	21	model	model	NOUN
cana-4523	211	22	with	with	ADP
cana-4523	211	23	imperfect	imperfect	ADJ
cana-4523	211	24	delay	delay	NOUN
cana-4523	211	25	repair	repair	NOUN
cana-4523	211	26	under	under	ADP
cana-4523	211	27	partial	partial	ADJ
cana-4523	211	28	sum	sum	NOUN
cana-4523	211	29	process	process	NOUN
cana-4523	211	30	,	,	PUNCT
cana-4523	211	31	stochastic	stochastic	ADJ
cana-4523	211	32	modeling	modeling	NOUN
cana-4523	211	33	and	and	CCONJ
cana-4523	211	34	applications	application	NOUN
cana-4523	211	35	,	,	PUNCT
cana-4523	211	36	24(2),111−119	24(2),111−119	NUM
cana-4523	211	37	.	.	PUNCT
cana-4523	212	1	[	[	X
cana-4523	212	2	4	4	NUM
cana-4523	212	3	]	]	X
cana-4523	212	4	barlow	barlow	PROPN
cana-4523	212	5	,	,	PUNCT
cana-4523	212	6	r.	r.	PROPN
cana-4523	212	7	e.	e.	PROPN
cana-4523	212	8	and	and	CCONJ
cana-4523	212	9	f.	f.	PROPN
cana-4523	212	10	proschan	proschan	PROPN
cana-4523	212	11	(	(	PUNCT
cana-4523	212	12	1965	1965	NUM
cana-4523	212	13	)	)	PUNCT
cana-4523	212	14	,	,	PUNCT
cana-4523	212	15	mathematical	mathematical	ADJ
cana-4523	212	16	theory	theory	NOUN
cana-4523	212	17	of	of	ADP
cana-4523	212	18	reliability	reliability	NOUN
cana-4523	212	19	,	,	PUNCT
cana-4523	212	20	john	john	PROPN
cana-4523	212	21	wiley	wiley	PROPN
cana-4523	212	22	,	,	PUNCT
cana-4523	212	23	new	new	PROPN
cana-4523	212	24	york	york	PROPN
cana-4523	212	25	.	.	PUNCT
cana-4523	213	1	[	[	X
cana-4523	213	2	5	5	NUM
cana-4523	213	3	]	]	X
cana-4523	213	4	barlow	barlow	PROPN
cana-4523	213	5	,	,	PUNCT
cana-4523	213	6	r.	r.	PROPN
cana-4523	213	7	e.	e.	PROPN
cana-4523	213	8	and	and	CCONJ
cana-4523	213	9	f.	f.	PROPN
cana-4523	213	10	proschan	proschan	PROPN
cana-4523	213	11	(	(	PUNCT
cana-4523	213	12	1975	1975	NUM
cana-4523	213	13	)	)	PUNCT
cana-4523	213	14	,	,	PUNCT
cana-4523	213	15	statistical	statistical	ADJ
cana-4523	213	16	theory	theory	NOUN
cana-4523	213	17	of	of	ADP
cana-4523	213	18	reliability	reliability	NOUN
cana-4523	213	19	and	and	CCONJ
cana-4523	213	20	life	life	NOUN
cana-4523	213	21	testing	testing	NOUN
cana-4523	213	22	,	,	PUNCT
cana-4523	213	23	john	john	PROPN
cana-4523	213	24	wiley	wiley	PROPN
cana-4523	213	25	,	,	PUNCT
cana-4523	213	26	new	new	PROPN
cana-4523	213	27	york	york	PROPN
cana-4523	213	28	.	.	PUNCT
cana-4523	214	1	[	[	X
cana-4523	214	2	6	6	NUM
cana-4523	214	3	]	]	SYM
cana-4523	214	4	block	block	NOUN
cana-4523	214	5	,	,	PUNCT
cana-4523	214	6	h.	h.	PROPN
cana-4523	214	7	w	w	PROPN
cana-4523	214	8	,	,	PUNCT
cana-4523	214	9	langberg	langberg	PROPN
cana-4523	214	10	,	,	PUNCT
cana-4523	214	11	n.	n.	NOUN
cana-4523	214	12	a.	a.	PROPN
cana-4523	214	13	and	and	CCONJ
cana-4523	214	14	t.	t.	PROPN
cana-4523	214	15	h.	h.	PROPN
cana-4523	214	16	savits	savits	PROPN
cana-4523	214	17	(	(	PUNCT
cana-4523	214	18	1993	1993	NUM
cana-4523	214	19	)	)	PUNCT
cana-4523	214	20	,	,	PUNCT
cana-4523	214	21	repair	repair	VERB
cana-4523	214	22	replacement	replacement	NOUN
cana-4523	214	23	policies	policy	NOUN
cana-4523	214	24	,	,	PUNCT
cana-4523	214	25	the	the	DET
cana-4523	214	26	journal	journal	NOUN
cana-4523	214	27	of	of	ADP
cana-4523	214	28	applied	apply	VERB
cana-4523	214	29	probability	probability	NOUN
cana-4523	214	30	.	.	PUNCT
cana-4523	215	1	,	,	PUNCT
cana-4523	215	2	30	30	NUM
cana-4523	215	3	,	,	PUNCT
cana-4523	215	4	194	194	NUM
cana-4523	215	5	-	-	SYM
cana-4523	215	6	206	206	NUM
cana-4523	215	7	.	.	PUNCT
cana-4523	216	1	[	[	X
cana-4523	216	2	7	7	NUM
cana-4523	216	3	]	]	PUNCT
cana-4523	216	4	govindaraju	govindaraju	NOUN
cana-4523	216	5	,	,	PUNCT
cana-4523	216	6	p.	p.	PROPN
cana-4523	216	7	,	,	PUNCT
cana-4523	216	8	rizwan	rizwan	PROPN
cana-4523	216	9	,	,	PUNCT
cana-4523	216	10	u.	u.	PROPN
cana-4523	216	11	and	and	CCONJ
cana-4523	216	12	v.	v.	ADP
cana-4523	216	13	thangaraj	thangaraj	NOUN
cana-4523	216	14	(	(	PUNCT
cana-4523	216	15	2010	2010	NUM
cana-4523	216	16	)	)	PUNCT
cana-4523	216	17	,	,	PUNCT
cana-4523	216	18	optimal	optimal	ADJ
cana-4523	216	19	replacement	replacement	NOUN
cana-4523	216	20	policies	policy	NOUN
cana-4523	216	21	for	for	ADP
cana-4523	216	22	a	a	DET
cana-4523	216	23	multistate	multistate	NOUN
cana-4523	216	24	degenerative	degenerative	ADJ
cana-4523	216	25	system	system	NOUN
cana-4523	216	26	with	with	ADP
cana-4523	216	27	nonn	nonn	PROPN
cana-4523	216	28	repair	repair	PROPN
cana-4523	216	29	times	time	NOUN
cana-4523	216	30	,	,	PUNCT
cana-4523	216	31	journal	journal	NOUN
cana-4523	216	32	of	of	ADP
cana-4523	216	33	mathematical	mathematical	ADJ
cana-4523	216	34	research	research	NOUN
cana-4523	216	35	,	,	PUNCT
cana-4523	216	36	2(1	2(1	NUM
cana-4523	216	37	)	)	PUNCT
cana-4523	216	38	,	,	PUNCT
cana-4523	216	39	177	177	NUM
cana-4523	216	40	-	-	SYM
cana-4523	216	41	185	185	NUM
cana-4523	216	42	.	.	PUNCT
cana-4523	217	1	[	[	X
cana-4523	217	2	8	8	NUM
cana-4523	217	3	]	]	X
cana-4523	217	4	lam	lam	PROPN
cana-4523	217	5	,	,	PUNCT
cana-4523	217	6	y.	y.	PROPN
cana-4523	217	7	(	(	PUNCT
cana-4523	217	8	1988a	1988a	NUM
cana-4523	217	9	)	)	PUNCT
cana-4523	217	10	,	,	PUNCT
cana-4523	217	11	geometric	geometric	ADJ
cana-4523	217	12	processes	process	NOUN
cana-4523	217	13	and	and	CCONJ
cana-4523	217	14	replacement	replacement	NOUN
cana-4523	217	15	problem	problem	NOUN
cana-4523	217	16	,	,	PUNCT
cana-4523	217	17	acta	acta	PROPN
cana-4523	217	18	mathematicae	mathematicae	PROPN
cana-4523	217	19	applicatae	applicatae	PROPN
cana-4523	217	20	sinica	sinica	PROPN
cana-4523	217	21	,	,	PUNCT
cana-4523	217	22	4	4	NUM
cana-4523	217	23	,	,	PUNCT
cana-4523	217	24	366	366	NUM
cana-4523	217	25	-	-	SYM
cana-4523	217	26	377	377	NUM
cana-4523	217	27	.	.	PUNCT
cana-4523	218	1	[	[	X
cana-4523	218	2	9	9	NUM
cana-4523	218	3	]	]	X
cana-4523	218	4	lam	lam	PROPN
cana-4523	218	5	,	,	PUNCT
cana-4523	218	6	y.	y.	PROPN
cana-4523	218	7	(	(	PUNCT
cana-4523	218	8	1990	1990	NUM
cana-4523	218	9	)	)	PUNCT
cana-4523	218	10	,	,	PUNCT
cana-4523	218	11	a	a	DET
cana-4523	218	12	repair	repair	NOUN
cana-4523	218	13	replacement	replacement	NOUN
cana-4523	218	14	model	model	NOUN
cana-4523	218	15	,	,	PUNCT
cana-4523	218	16	advances	advance	NOUN
cana-4523	218	17	in	in	ADP
cana-4523	218	18	applied	apply	VERB
cana-4523	218	19	probability	probability	NOUN
cana-4523	218	20	,	,	PUNCT
cana-4523	218	21	22	22	NUM
cana-4523	218	22	,	,	PUNCT
cana-4523	218	23	494	494	NUM
cana-4523	218	24	-	-	SYM
cana-4523	218	25	497	497	NUM
cana-4523	218	26	.	.	PUNCT
cana-4523	219	1	[	[	X
cana-4523	219	2	10	10	NUM
cana-4523	219	3	]	]	X
cana-4523	219	4	lam	lam	PROPN
cana-4523	219	5	,	,	PUNCT
cana-4523	219	6	y.	y.	PROPN
cana-4523	219	7	,	,	PUNCT
cana-4523	219	8	zhang	zhang	PROPN
cana-4523	219	9	,	,	PUNCT
cana-4523	219	10	y.	y.	PROPN
cana-4523	219	11	l.	l.	PROPN
cana-4523	219	12	and	and	CCONJ
cana-4523	219	13	y.	y.	PROPN
cana-4523	219	14	h.	h.	PROPN
cana-4523	219	15	zheng	zheng	PROPN
cana-4523	219	16	(	(	PUNCT
cana-4523	219	17	2002	2002	NUM
cana-4523	219	18	)	)	PUNCT
cana-4523	219	19	,	,	PUNCT
cana-4523	219	20	a	a	DET
cana-4523	219	21	geometric	geometric	ADJ
cana-4523	219	22	process	process	NOUN
cana-4523	219	23	equivalent	equivalent	ADJ
cana-4523	219	24	model	model	NOUN
cana-4523	219	25	for	for	ADP
cana-4523	219	26	a	a	DET
cana-4523	219	27	multistate	multistate	NOUN
cana-4523	219	28	degenerative	degenerative	ADJ
cana-4523	219	29	system	system	NOUN
cana-4523	219	30	,	,	PUNCT
cana-4523	219	31	the	the	DET
cana-4523	219	32	european	european	PROPN
cana-4523	219	33	journal	journal	PROPN
cana-4523	219	34	of	of	ADP
cana-4523	219	35	operational	operational	ADJ
cana-4523	219	36	research	research	NOUN
cana-4523	219	37	,	,	PUNCT
cana-4523	219	38	142	142	NUM
cana-4523	219	39	,	,	PUNCT
cana-4523	219	40	21	21	NUM
cana-4523	219	41	-	-	SYM
cana-4523	219	42	25	25	NUM
cana-4523	219	43	.	.	PUNCT
cana-4523	220	1	[	[	X
cana-4523	220	2	11	11	NUM
cana-4523	220	3	]	]	X
cana-4523	220	4	lam	lam	PROPN
cana-4523	220	5	,	,	PUNCT
cana-4523	220	6	y.	y.	PROPN
cana-4523	220	7	and	and	CCONJ
cana-4523	220	8	y.	y.	PROPN
cana-4523	220	9	l.	l.	PROPN
cana-4523	220	10	zheng	zheng	PROPN
cana-4523	220	11	(	(	PUNCT
cana-4523	220	12	2004	2004	NUM
cana-4523	220	13	)	)	PUNCT
cana-4523	220	14	,	,	PUNCT
cana-4523	220	15	a	a	DET
cana-4523	220	16	shock	shock	NOUN
cana-4523	220	17	model	model	NOUN
cana-4523	220	18	for	for	ADP
cana-4523	220	19	the	the	DET
cana-4523	220	20	maintenance	maintenance	NOUN
cana-4523	220	21	problem	problem	NOUN
cana-4523	220	22	of	of	ADP
cana-4523	220	23	a	a	DET
cana-4523	220	24	repairable	repairable	ADJ
cana-4523	220	25	system	system	NOUN
cana-4523	220	26	,	,	PUNCT
cana-4523	220	27	computer	computer	NOUN
cana-4523	220	28	and	and	CCONJ
cana-4523	220	29	operations	operation	NOUN
cana-4523	220	30	research	research	NOUN
cana-4523	220	31	,	,	PUNCT
cana-4523	220	32	31	31	NUM
cana-4523	220	33	,	,	PUNCT
cana-4523	220	34	1807	1807	NUM
cana-4523	220	35	-	-	SYM
cana-4523	220	36	1820	1820	NUM
cana-4523	220	37	.	.	PUNCT
cana-4523	221	1	[	[	X
cana-4523	221	2	12	12	NUM
cana-4523	221	3	]	]	X
cana-4523	221	4	lam	lam	PROPN
cana-4523	221	5	,	,	PUNCT
cana-4523	221	6	y.	y.	PROPN
cana-4523	221	7	(	(	PUNCT
cana-4523	221	8	2005	2005	NUM
cana-4523	221	9	)	)	PUNCT
cana-4523	221	10	,	,	PUNCT
cana-4523	221	11	a	a	DET
cana-4523	221	12	monotone	monotone	ADJ
cana-4523	221	13	process	process	NOUN
cana-4523	221	14	maintenance	maintenance	NOUN
cana-4523	221	15	model	model	NOUN
cana-4523	221	16	for	for	ADP
cana-4523	221	17	a	a	DET
cana-4523	221	18	multistate	multistate	NOUN
cana-4523	221	19	system	system	NOUN
cana-4523	221	20	,	,	PUNCT
cana-4523	221	21	journal	journal	NOUN
cana-4523	221	22	of	of	ADP
cana-4523	221	23	applied	apply	VERB
cana-4523	221	24	probability	probability	NOUN
cana-4523	221	25	,	,	PUNCT
cana-4523	221	26	42	42	NUM
cana-4523	221	27	,	,	PUNCT
cana-4523	221	28	1	1	NUM
cana-4523	221	29	14	14	NUM
cana-4523	221	30	.	.	PUNCT
cana-4523	222	1	[	[	X
cana-4523	222	2	13	13	NUM
cana-4523	222	3	]	]	X
cana-4523	222	4	mohammad	mohammad	PROPN
cana-4523	222	5	yunus	yunus	PROPN
cana-4523	222	6	.	.	PUNCT
cana-4523	222	7	m.	m.	NOUN
cana-4523	222	8	,	,	PUNCT
cana-4523	222	9	p.	p.	NOUN
cana-4523	222	10	govindaraju	govindaraju	NOUN
cana-4523	222	11	and	and	CCONJ
cana-4523	222	12	u.	u.	PROPN
cana-4523	222	13	rizwan	rizwan	PROPN
cana-4523	222	14	(	(	PUNCT
cana-4523	222	15	2012	2012	NUM
cana-4523	222	16	)	)	PUNCT
cana-4523	222	17	,	,	PUNCT
cana-4523	222	18	an	an	DET
cana-4523	222	19	extreme	extreme	ADJ
cana-4523	222	20	shock	shock	NOUN
cana-4523	222	21	maintenance	maintenance	NOUN
cana-4523	222	22	model	model	NOUN
cana-4523	222	23	for	for	ADP
cana-4523	222	24	a	a	DET
cana-4523	222	25	multistate	multistate	NOUN
cana-4523	222	26	degenerative	degenerative	ADJ
cana-4523	222	27	system	system	NOUN
cana-4523	222	28	under	under	ADP
cana-4523	222	29	a	a	DET
cana-4523	222	30	bivariate	bivariate	ADJ
cana-4523	222	31	replacement	replacement	NOUN
cana-4523	222	32	policy	policy	NOUN
cana-4523	222	33	,	,	PUNCT
cana-4523	222	34	international	international	ADJ
cana-4523	222	35	journal	journal	NOUN
cana-4523	222	36	of	of	ADP
cana-4523	222	37	scientific	scientific	ADJ
cana-4523	222	38	and	and	CCONJ
cana-4523	222	39	engineering	engineering	NOUN
cana-4523	222	40	research	research	NOUN
cana-4523	222	41	,	,	PUNCT
cana-4523	222	42	2(11	2(11	NUM
cana-4523	222	43	)	)	PUNCT
cana-4523	222	44	,	,	PUNCT
cana-4523	222	45	34	34	NUM
cana-4523	222	46	-	-	SYM
cana-4523	222	47	40	40	NUM
cana-4523	222	48	.	.	PUNCT
cana-4523	223	1	[	[	X
cana-4523	223	2	14	14	NUM
cana-4523	223	3	]	]	X
cana-4523	223	4	rizwan	rizwan	PROPN
cana-4523	223	5	,	,	PUNCT
cana-4523	223	6	u.	u.	PROPN
cana-4523	223	7	and	and	CCONJ
cana-4523	223	8	zahiruddeen	zahiruddeen	PROPN
cana-4523	223	9	(	(	PUNCT
cana-4523	223	10	2015	2015	NUM
cana-4523	223	11	)	)	PUNCT
cana-4523	223	12	,	,	PUNCT
cana-4523	223	13	extreme	extreme	ADJ
cana-4523	223	14	shock	shock	NOUN
cana-4523	223	15	maintenance	maintenance	NOUN
cana-4523	223	16	model	model	NOUN
cana-4523	223	17	under	under	ADP
cana-4523	223	18	some	some	DET
cana-4523	223	19	bivariate	bivariate	ADJ
cana-4523	223	20	replacement	replacement	NOUN
cana-4523	223	21	policy	policy	NOUN
cana-4523	223	22	in	in	ADP
cana-4523	223	23	an	an	DET
cana-4523	223	24	alternative	alternative	ADJ
cana-4523	223	25	repair	repair	NOUN
cana-4523	223	26	model	model	NOUN
cana-4523	223	27	,	,	PUNCT
cana-4523	223	28	international	international	ADJ
cana-4523	223	29	journal	journal	NOUN
cana-4523	223	30	of	of	ADP
cana-4523	223	31	science	science	NOUN
cana-4523	223	32	and	and	CCONJ
cana-4523	223	33	humanities	humanity	NOUN
cana-4523	223	34	,	,	PUNCT
cana-4523	223	35	1(1	1(1	NUM
cana-4523	223	36	)	)	PUNCT
cana-4523	223	37	,	,	PUNCT
cana-4523	223	38	1	1	NUM
cana-4523	223	39	-	-	SYM
cana-4523	223	40	18	18	NUM
cana-4523	223	41	.	.	PUNCT
cana-4523	224	1	[	[	X
cana-4523	224	2	15	15	NUM
cana-4523	224	3	]	]	X
cana-4523	224	4	rizwan	rizwan	PROPN
cana-4523	224	5	,	,	PUNCT
cana-4523	224	6	u.	u.	PROPN
cana-4523	224	7	and	and	CCONJ
cana-4523	224	8	m.	m.	PROPN
cana-4523	224	9	mohammad	mohammad	PROPN
cana-4523	224	10	yunus	yunus	PROPN
cana-4523	224	11	(	(	PUNCT
cana-4523	224	12	2014	2014	NUM
cana-4523	224	13	)	)	PUNCT
cana-4523	224	14	,	,	PUNCT
cana-4523	224	15	an	an	DET
cana-4523	224	16	extreme	extreme	ADJ
cana-4523	224	17	shock	shock	NOUN
cana-4523	224	18	maintenance	maintenance	NOUN
cana-4523	224	19	model	model	NOUN
cana-4523	224	20	for	for	ADP
cana-4523	224	21	a	a	DET
cana-4523	224	22	multistate	multistate	NOUN
cana-4523	224	23	degenerative	degenerative	NOUN
cana-4523	224	24	system	system	NOUN
cana-4523	224	25	i	i	PRON
cana-4523	224	26	,	,	PUNCT
cana-4523	224	27	research	research	NOUN
cana-4523	224	28	methods	method	NOUN
cana-4523	224	29	in	in	ADP
cana-4523	224	30	mathematical	mathematical	ADJ
cana-4523	224	31	sciences	science	NOUN
cana-4523	224	32	,	,	PUNCT
cana-4523	224	33	7	7	NUM
cana-4523	224	34	,	,	PUNCT
cana-4523	224	35	49	49	NUM
cana-4523	224	36	-	-	SYM
cana-4523	224	37	62	62	NUM
cana-4523	224	38	.	.	PUNCT
cana-4523	225	1	communications	communication	NOUN
cana-4523	225	2	on	on	ADP
cana-4523	225	3	applied	apply	VERB
cana-4523	225	4	nonlinear	nonlinear	ADJ
cana-4523	225	5	analysis	analysis	NOUN
cana-4523	225	6	issn	issn	NOUN
cana-4523	225	7	:	:	PUNCT
cana-4523	225	8	1074	1074	NUM
cana-4523	225	9	-	-	PUNCT
cana-4523	225	10	133x	133x	NUM
cana-4523	225	11	vol	vol	NOUN
cana-4523	225	12	32	32	NUM
cana-4523	225	13	no	no	NOUN
cana-4523	225	14	.	.	PUNCT
cana-4523	226	1	9s	9s	NUM
cana-4523	226	2	(	(	PUNCT
cana-4523	226	3	2025	2025	NUM
cana-4523	226	4	)	)	PUNCT
cana-4523	226	5	2369	2369	NUM
cana-4523	226	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4523	227	1	[	[	X
cana-4523	227	2	16	16	NUM
cana-4523	227	3	]	]	X
cana-4523	227	4	rizwan	rizwan	PROPN
cana-4523	227	5	,	,	PUNCT
cana-4523	227	6	u.	u.	PROPN
cana-4523	227	7	and	and	CCONJ
cana-4523	227	8	m.	m.	PROPN
cana-4523	227	9	mohammad	mohammad	PROPN
cana-4523	227	10	yunus	yunus	PROPN
cana-4523	227	11	(	(	PUNCT
cana-4523	227	12	2015	2015	NUM
cana-4523	227	13	)	)	PUNCT
cana-4523	227	14	,	,	PUNCT
cana-4523	227	15	optimal	optimal	ADJ
cana-4523	227	16	replacement	replacement	NOUN
cana-4523	227	17	policy	policy	NOUN
cana-4523	227	18	for	for	ADP
cana-4523	227	19	a	a	DET
cana-4523	227	20	multistate	multistate	NOUN
cana-4523	227	21	degenerative	degenerative	ADJ
cana-4523	227	22	system	system	NOUN
cana-4523	227	23	under	under	ADP
cana-4523	227	24	quasi	quasi	NOUN
cana-4523	227	25	renewal	renewal	NOUN
cana-4523	227	26	process	process	NOUN
cana-4523	227	27	,	,	PUNCT
cana-4523	227	28	international	international	ADJ
cana-4523	227	29	journal	journal	NOUN
cana-4523	227	30	of	of	ADP
cana-4523	227	31	science	science	NOUN
cana-4523	227	32	and	and	CCONJ
cana-4523	227	33	humanities	humanity	NOUN
cana-4523	227	34	,	,	PUNCT
cana-4523	227	35	1(1	1(1	NUM
cana-4523	227	36	)	)	PUNCT
cana-4523	227	37	,	,	PUNCT
cana-4523	227	38	59	59	NUM
cana-4523	227	39	-	-	SYM
cana-4523	227	40	70	70	NUM
cana-4523	227	41	.	.	PUNCT
cana-4523	228	1	[	[	X
cana-4523	228	2	17	17	NUM
cana-4523	228	3	]	]	X
cana-4523	228	4	rizwan	rizwan	PROPN
cana-4523	228	5	,	,	PUNCT
cana-4523	228	6	u.	u.	PROPN
cana-4523	228	7	and	and	CCONJ
cana-4523	228	8	m.	m.	PROPN
cana-4523	228	9	mohammad	mohammad	PROPN
cana-4523	228	10	yunus	yunus	PROPN
cana-4523	228	11	(	(	PUNCT
cana-4523	228	12	2015	2015	NUM
cana-4523	228	13	)	)	PUNCT
cana-4523	228	14	,	,	PUNCT
cana-4523	228	15	geometric	geometric	ADJ
cana-4523	228	16	processes	process	NOUN
cana-4523	228	17	in	in	ADP
cana-4523	228	18	two	two	NUM
cana-4523	228	19	dimensions	dimension	NOUN
cana-4523	228	20	:	:	PUNCT
cana-4523	228	21	basis	basis	NOUN
cana-4523	228	22	result	result	NOUN
cana-4523	228	23	and	and	CCONJ
cana-4523	228	24	applications	application	NOUN
cana-4523	228	25	,	,	PUNCT
cana-4523	228	26	international	international	ADJ
cana-4523	228	27	journal	journal	NOUN
cana-4523	228	28	of	of	ADP
cana-4523	228	29	science	science	NOUN
cana-4523	228	30	and	and	CCONJ
cana-4523	228	31	humanities	humanity	NOUN
cana-4523	228	32	,	,	PUNCT
cana-4523	228	33	1(2	1(2	NUM
cana-4523	228	34	)	)	PUNCT
cana-4523	228	35	,	,	PUNCT
cana-4523	228	36	747	747	NUM
cana-4523	228	37	-	-	SYM
cana-4523	228	38	774	774	NUM
cana-4523	228	39	.	.	PUNCT
cana-4523	229	1	[	[	X
cana-4523	229	2	18	18	NUM
cana-4523	229	3	]	]	X
cana-4523	229	4	zhang	zhang	PROPN
cana-4523	229	5	,	,	PUNCT
cana-4523	229	6	y.	y.	PROPN
cana-4523	229	7	l.	l.	PROPN
cana-4523	229	8	,	,	PUNCT
cana-4523	229	9	yam	yam	NOUN
cana-4523	229	10	r.c.m	r.c.m	NOUN
cana-4523	229	11	and	and	CCONJ
cana-4523	229	12	zuo	zuo	PROPN
cana-4523	229	13	,	,	PUNCT
cana-4523	229	14	m.j	m.j	PROPN
cana-4523	229	15	.	.	PROPN
cana-4523	229	16	,	,	PUNCT
cana-4523	229	17	(	(	PUNCT
cana-4523	229	18	2002	2002	NUM
cana-4523	229	19	)	)	PUNCT
cana-4523	229	20	,	,	PUNCT
cana-4523	229	21	optimal	optimal	ADJ
cana-4523	229	22	replacement	replacement	NOUN
cana-4523	229	23	policy	policy	NOUN
cana-4523	229	24	for	for	ADP
cana-4523	229	25	a	a	DET
cana-4523	229	26	multistate	multistate	NOUN
cana-4523	229	27	repairable	repairable	ADJ
cana-4523	229	28	system	system	NOUN
cana-4523	229	29	,	,	PUNCT
cana-4523	229	30	journal	journal	NOUN
cana-4523	229	31	of	of	ADP
cana-4523	229	32	operations	operation	NOUN
cana-4523	229	33	research	research	NOUN
cana-4523	229	34	society	society	NOUN
cana-4523	229	35	,	,	PUNCT
cana-4523	229	36	53	53	NUM
cana-4523	229	37	,	,	PUNCT
cana-4523	229	38	336	336	NUM
cana-4523	229	39	-	-	SYM
cana-4523	229	40	341	341	NUM
cana-4523	229	41	.	.	PUNCT
cana-4523	230	1	[	[	X
cana-4523	230	2	19	19	NUM
cana-4523	230	3	]	]	X
cana-4523	230	4	zhang	zhang	PROPN
cana-4523	230	5	,	,	PUNCT
cana-4523	230	6	y.	y.	PROPN
cana-4523	230	7	l.	l.	PROPN
cana-4523	230	8	,	,	PUNCT
cana-4523	230	9	yam	yam	NOUN
cana-4523	230	10	r.c.m	r.c.m	NOUN
cana-4523	230	11	and	and	CCONJ
cana-4523	230	12	zuo	zuo	PROPN
cana-4523	230	13	,	,	PUNCT
cana-4523	230	14	m.j	m.j	PROPN
cana-4523	230	15	.	.	PROPN
cana-4523	230	16	,	,	PUNCT
cana-4523	230	17	(	(	PUNCT
cana-4523	230	18	2007	2007	NUM
cana-4523	230	19	)	)	PUNCT
cana-4523	230	20	,	,	PUNCT
cana-4523	230	21	a	a	DET
cana-4523	230	22	bivariate	bivariate	ADJ
cana-4523	230	23	optimal	optimal	ADJ
cana-4523	230	24	replacement	replacement	NOUN
cana-4523	230	25	policy	policy	NOUN
cana-4523	230	26	for	for	ADP
cana-4523	230	27	a	a	DET
cana-4523	230	28	multistate	multistate	NOUN
cana-4523	230	29	repairable	repairable	ADJ
cana-4523	230	30	system	system	NOUN
cana-4523	230	31	,	,	PUNCT
cana-4523	230	32	reliability	reliability	NOUN
cana-4523	230	33	engineering	engineering	NOUN
cana-4523	230	34	and	and	CCONJ
cana-4523	230	35	system	system	NOUN
cana-4523	230	36	safety	safety	NOUN
cana-4523	230	37	,	,	PUNCT
cana-4523	230	38	92	92	NUM
cana-4523	230	39	,	,	PUNCT
cana-4523	230	40	535	535	NUM
cana-4523	230	41	-	-	SYM
cana-4523	230	42	542	542	NUM
cana-4523	230	43	92	92	NUM
cana-4523	230	44	,	,	PUNCT
cana-4523	230	45	121	121	NUM
cana-4523	230	46	-	-	SYM
cana-4523	230	47	132	132	NUM
cana-4523	230	48	.	.	PUNCT