id	sid	tid	token	lemma	pos
iajs-2850	1	1	120	120	NUM
iajs-2850	1	2	this	this	DET
iajs-2850	1	3	work	work	NOUN
iajs-2850	1	4	is	be	AUX
iajs-2850	1	5	licensed	license	VERB
iajs-2850	1	6	under	under	ADP
iajs-2850	1	7	a	a	DET
iajs-2850	1	8	creative	creative	ADJ
iajs-2850	1	9	commons	common	NOUN
iajs-2850	1	10	attribution	attribution	NOUN
iajs-2850	1	11	4.0	4.0	NUM
iajs-2850	1	12	international	international	ADJ
iajs-2850	1	13	license	license	NOUN
iajs-2850	1	14	.	.	PUNCT
iajs-2850	2	1	the	the	DET
iajs-2850	2	2	new	new	ADJ
iajs-2850	2	3	complex	complex	ADJ
iajs-2850	2	4	integral	integral	ADJ
iajs-2850	2	5	transform	transform	NOUN
iajs-2850	2	6	"	"	PUNCT
iajs-2850	2	7	complex	complex	ADJ
iajs-2850	2	8	sadik	sadik	ADJ
iajs-2850	2	9	transform	transform	NOUN
iajs-2850	2	10	"	"	PUNCT
iajs-2850	2	11	and	and	CCONJ
iajs-2850	2	12	it	it	PRON
iajs-2850	2	13	’s	’	VERB
iajs-2850	2	14	applications	application	NOUN
iajs-2850	2	15	abstract	abstract	ADJ
iajs-2850	2	16	in	in	ADP
iajs-2850	2	17	this	this	DET
iajs-2850	2	18	work	work	NOUN
iajs-2850	2	19	,	,	PUNCT
iajs-2850	2	20	we	we	PRON
iajs-2850	2	21	present	present	VERB
iajs-2850	2	22	a	a	DET
iajs-2850	2	23	novel	novel	ADJ
iajs-2850	2	24	complex	complex	ADJ
iajs-2850	2	25	transform	transform	NOUN
iajs-2850	2	26	namely	namely	ADV
iajs-2850	2	27	the	the	DET
iajs-2850	2	28	"	"	PUNCT
iajs-2850	2	29	complex	complex	ADJ
iajs-2850	2	30	sadik	sadik	PROPN
iajs-2850	2	31	transform	transform	NOUN
iajs-2850	2	32	"	"	PUNCT
iajs-2850	2	33	.	.	PUNCT
iajs-2850	3	1	the	the	DET
iajs-2850	3	2	propositions	proposition	NOUN
iajs-2850	3	3	of	of	ADP
iajs-2850	3	4	this	this	DET
iajs-2850	3	5	transformation	transformation	NOUN
iajs-2850	3	6	are	be	AUX
iajs-2850	3	7	investigated	investigate	VERB
iajs-2850	3	8	.	.	PUNCT
iajs-2850	4	1	the	the	DET
iajs-2850	4	2	complex	complex	ADJ
iajs-2850	4	3	transform	transform	NOUN
iajs-2850	4	4	is	be	AUX
iajs-2850	4	5	used	use	VERB
iajs-2850	4	6	to	to	PART
iajs-2850	4	7	convert	convert	VERB
iajs-2850	4	8	the	the	DET
iajs-2850	4	9	core	core	NOUN
iajs-2850	4	10	problem	problem	NOUN
iajs-2850	4	11	to	to	ADP
iajs-2850	4	12	a	a	DET
iajs-2850	4	13	simple	simple	ADJ
iajs-2850	4	14	algebraic	algebraic	ADJ
iajs-2850	4	15	equation	equation	NOUN
iajs-2850	4	16	.	.	PUNCT
iajs-2850	5	1	then	then	ADV
iajs-2850	5	2	,	,	PUNCT
iajs-2850	5	3	the	the	DET
iajs-2850	5	4	answer	answer	NOUN
iajs-2850	5	5	to	to	ADP
iajs-2850	5	6	this	this	DET
iajs-2850	5	7	primary	primary	ADJ
iajs-2850	5	8	problem	problem	NOUN
iajs-2850	5	9	can	can	AUX
iajs-2850	5	10	be	be	AUX
iajs-2850	5	11	obtained	obtain	VERB
iajs-2850	5	12	to	to	PART
iajs-2850	5	13	find	find	VERB
iajs-2850	5	14	the	the	DET
iajs-2850	5	15	solution	solution	NOUN
iajs-2850	5	16	to	to	ADP
iajs-2850	5	17	this	this	DET
iajs-2850	5	18	equation	equation	NOUN
iajs-2850	5	19	and	and	CCONJ
iajs-2850	5	20	apply	apply	VERB
iajs-2850	5	21	the	the	DET
iajs-2850	5	22	inverse	inverse	NOUN
iajs-2850	5	23	of	of	ADP
iajs-2850	5	24	the	the	DET
iajs-2850	5	25	complex	complex	ADJ
iajs-2850	5	26	sadik	sadik	PROPN
iajs-2850	5	27	transform	transform	NOUN
iajs-2850	5	28	.	.	PUNCT
iajs-2850	6	1	as	as	ADV
iajs-2850	6	2	well	well	ADV
iajs-2850	6	3	,	,	PUNCT
iajs-2850	6	4	the	the	DET
iajs-2850	6	5	complex	complex	ADJ
iajs-2850	6	6	sadik	sadik	ADJ
iajs-2850	6	7	transform	transform	NOUN
iajs-2850	6	8	is	be	AUX
iajs-2850	6	9	applied	apply	VERB
iajs-2850	6	10	and	and	CCONJ
iajs-2850	6	11	used	use	VERB
iajs-2850	6	12	to	to	PART
iajs-2850	6	13	find	find	VERB
iajs-2850	6	14	the	the	DET
iajs-2850	6	15	solution	solution	NOUN
iajs-2850	6	16	of	of	ADP
iajs-2850	6	17	linear	linear	ADJ
iajs-2850	6	18	higher	high	ADJ
iajs-2850	6	19	order	order	NOUN
iajs-2850	6	20	ordinary	ordinary	ADJ
iajs-2850	6	21	differential	differential	ADJ
iajs-2850	6	22	equations	equation	NOUN
iajs-2850	6	23	.	.	PUNCT
iajs-2850	7	1	as	as	ADV
iajs-2850	7	2	well	well	ADV
iajs-2850	7	3	,	,	PUNCT
iajs-2850	7	4	we	we	PRON
iajs-2850	7	5	present	present	VERB
iajs-2850	7	6	and	and	CCONJ
iajs-2850	7	7	discuss	discuss	VERB
iajs-2850	7	8	,	,	PUNCT
iajs-2850	7	9	some	some	DET
iajs-2850	7	10	important	important	ADJ
iajs-2850	7	11	real	real	ADJ
iajs-2850	7	12	life	life	NOUN
iajs-2850	7	13	problems	problem	NOUN
iajs-2850	7	14	such	such	ADJ
iajs-2850	7	15	as	as	ADP
iajs-2850	7	16	pharmacokinetics	pharmacokinetic	NOUN
iajs-2850	7	17	problems	problem	NOUN
iajs-2850	7	18	,	,	PUNCT
iajs-2850	7	19	nuclear	nuclear	ADJ
iajs-2850	7	20	physics	physics	NOUN
iajs-2850	7	21	problems	problem	NOUN
iajs-2850	7	22	,	,	PUNCT
iajs-2850	7	23	and	and	CCONJ
iajs-2850	7	24	beam	beam	NOUN
iajs-2850	7	25	problems	problem	NOUN
iajs-2850	7	26	.	.	PUNCT
iajs-2850	8	1	keywords	keyword	NOUN
iajs-2850	8	2	:	:	PUNCT
iajs-2850	8	3	complex	complex	ADJ
iajs-2850	8	4	integral	integral	ADJ
iajs-2850	8	5	transformation	transformation	NOUN
iajs-2850	8	6	,	,	PUNCT
iajs-2850	8	7	the	the	DET
iajs-2850	8	8	inverse	inverse	NOUN
iajs-2850	8	9	of	of	ADP
iajs-2850	8	10	complex	complex	ADJ
iajs-2850	8	11	transform	transform	NOUN
iajs-2850	8	12	,	,	PUNCT
iajs-2850	8	13	sadik	sadik	PROPN
iajs-2850	8	14	transform	transform	NOUN
iajs-2850	8	15	,	,	PUNCT
iajs-2850	8	16	ordinary	ordinary	ADJ
iajs-2850	8	17	differential	differential	ADJ
iajs-2850	8	18	equations	equation	NOUN
iajs-2850	8	19	.	.	PUNCT
iajs-2850	9	1	1	1	X
iajs-2850	9	2	.	.	X
iajs-2850	9	3	introduction	introduction	NOUN
iajs-2850	9	4	in	in	ADP
iajs-2850	9	5	(	(	PUNCT
iajs-2850	9	6	2018	2018	NUM
iajs-2850	9	7	)	)	PUNCT
iajs-2850	9	8	,	,	PUNCT
iajs-2850	9	9	researcher	researcher	NOUN
iajs-2850	9	10	sadik	sadik	PROPN
iajs-2850	9	11	l.	l.	PROPN
iajs-2850	9	12	sheikh	sheikh	PROPN
iajs-2850	10	1	[	[	X
iajs-2850	10	2	11	11	NUM
iajs-2850	10	3	]	]	PUNCT
iajs-2850	10	4	presented	present	VERB
iajs-2850	10	5	a	a	DET
iajs-2850	10	6	new	new	ADJ
iajs-2850	10	7	integral	integral	ADJ
iajs-2850	10	8	transformation	transformation	NOUN
iajs-2850	10	9	defined	define	VERB
iajs-2850	10	10	as	as	SCONJ
iajs-2850	10	11	follows	follow	VERB
iajs-2850	10	12	:	:	PUNCT
iajs-2850	10	13	the	the	DET
iajs-2850	10	14	sadik	sadik	ADJ
iajs-2850	10	15	integral	integral	ADJ
iajs-2850	10	16	transform	transform	NOUN
iajs-2850	10	17	of	of	ADP
iajs-2850	10	18	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	10	19	)	)	PUNCT
iajs-2850	10	20	is	be	AUX
iajs-2850	10	21	defined	define	VERB
iajs-2850	10	22	as	as	ADP
iajs-2850	10	23	:	:	PUNCT
iajs-2850	10	24	𝐒𝑎[𝑔(𝑡	𝐒𝑎[𝑔(𝑡	NUM
iajs-2850	10	25	)	)	PUNCT
iajs-2850	10	26	]	]	PUNCT
iajs-2850	11	1	=	=	PUNCT
iajs-2850	11	2	𝐅(𝑣𝛼	𝐅(𝑣𝛼	PROPN
iajs-2850	11	3	,	,	PUNCT
iajs-2850	11	4	𝛽	𝛽	NOUN
iajs-2850	11	5	)	)	PUNCT
iajs-2850	11	6	=	=	SYM
iajs-2850	11	7	1	1	NUM
iajs-2850	11	8	𝑣𝛽	𝑣𝛽	ADP
iajs-2850	11	9	∫	∫	PROPN
iajs-2850	11	10	  	  	SPACE
iajs-2850	11	11	∞	∞	PROPN
iajs-2850	11	12	0	0	NUM
iajs-2850	11	13	𝑔(𝑡)𝑒−𝑣𝛼𝑡𝑑𝑡	𝑔(𝑡)𝑒−𝑣𝛼𝑡𝑑𝑡	NOUN
iajs-2850	11	14	where	where	SCONJ
iajs-2850	11	15	𝑣	𝑣	DET
iajs-2850	11	16	∈	∈	PROPN
iajs-2850	11	17	ℂ	ℂ	PROPN
iajs-2850	11	18	,	,	PUNCT
iajs-2850	11	19	𝛼	𝛼	NOUN
iajs-2850	11	20	∈	∈	NOUN
iajs-2850	11	21	ℝ∗	ℝ∗	NOUN
iajs-2850	11	22	,	,	PUNCT
iajs-2850	11	23	and	and	CCONJ
iajs-2850	11	24	𝛽	𝛽	X
iajs-2850	11	25	∈	∈	NOUN
iajs-2850	11	26	ℝ	ℝ	PROPN
iajs-2850	11	27	.	.	PUNCT
iajs-2850	12	1	the	the	DET
iajs-2850	12	2	following	follow	VERB
iajs-2850	12	3	properties	property	NOUN
iajs-2850	12	4	of	of	ADP
iajs-2850	12	5	sadik	sadik	ADJ
iajs-2850	12	6	integral	integral	ADJ
iajs-2850	12	7	transform	transform	NOUN
iajs-2850	12	8	[	[	X
iajs-2850	12	9	11	11	NUM
iajs-2850	12	10	]	]	PUNCT
iajs-2850	12	11	:	:	PUNCT
iajs-2850	12	12	1	1	NUM
iajs-2850	12	13	if	if	SCONJ
iajs-2850	12	14	𝑔(𝑡	𝑔(𝑡	NUM
iajs-2850	12	15	)	)	PUNCT
iajs-2850	12	16	=	=	SYM
iajs-2850	12	17	𝑡𝑛	𝑡𝑛	NOUN
iajs-2850	12	18	,	,	PUNCT
iajs-2850	12	19	then	then	ADV
iajs-2850	12	20	𝐒𝑎[𝑡𝑛	𝐒𝑎[𝑡𝑛	VERB
iajs-2850	12	21	]	]	X
iajs-2850	12	22	=	=	SYM
iajs-2850	12	23	𝑛	𝑛	X
iajs-2850	12	24	!	!	PUNCT
iajs-2850	12	25	𝑣𝑛𝛼+(𝛼+𝛽	𝑣𝑛𝛼+(𝛼+𝛽	VERB
iajs-2850	12	26	)	)	PUNCT
iajs-2850	12	27	,	,	PUNCT
iajs-2850	12	28	𝑛	𝑛	DET
iajs-2850	12	29	≥	≥	NOUN
iajs-2850	12	30	0	0	NUM
iajs-2850	12	31	.	.	NOUN
iajs-2850	12	32	2	2	NUM
iajs-2850	12	33	if	if	SCONJ
iajs-2850	12	34	𝑔(𝑡	𝑔(𝑡	NUM
iajs-2850	12	35	)	)	PUNCT
iajs-2850	12	36	=	=	SYM
iajs-2850	12	37	𝑒𝑎𝑡	𝑒𝑎𝑡	NOUN
iajs-2850	12	38	,	,	PUNCT
iajs-2850	12	39	then	then	ADV
iajs-2850	12	40	𝐒𝑎[𝑒𝑎𝑡	𝐒𝑎[𝑒𝑎𝑡	VERB
iajs-2850	12	41	]	]	X
iajs-2850	12	42	=	=	SYM
iajs-2850	12	43	𝑣−𝛽	𝑣−𝛽	NOUN
iajs-2850	12	44	𝑣𝛼−𝑎	𝑣𝛼−𝑎	NOUN
iajs-2850	12	45	,	,	PUNCT
iajs-2850	12	46	where	where	SCONJ
iajs-2850	12	47	𝑎	𝑎	NOUN
iajs-2850	12	48	is	be	AUX
iajs-2850	12	49	a	a	DET
iajs-2850	12	50	constant	constant	ADJ
iajs-2850	12	51	.	.	PUNCT
iajs-2850	13	1	3	3	NUM
iajs-2850	13	2	if	if	SCONJ
iajs-2850	13	3	𝑔(𝑡	𝑔(𝑡	NUM
iajs-2850	13	4	)	)	PUNCT
iajs-2850	13	5	=	=	VERB
iajs-2850	13	6	sin	sin	NOUN
iajs-2850	13	7	𝑎𝑡	𝑎𝑡	ADP
iajs-2850	13	8	,	,	PUNCT
iajs-2850	13	9	then	then	ADV
iajs-2850	13	10	𝐒𝑎[sin	𝐒𝑎[sin	VERB
iajs-2850	13	11	𝑎𝑡	𝑎𝑡	X
iajs-2850	13	12	]	]	X
iajs-2850	13	13	=	=	PUNCT
iajs-2850	13	14	𝑎𝑣−𝛽	𝑎𝑣−𝛽	PROPN
iajs-2850	13	15	𝑣2𝛼+𝑎2	𝑣2𝛼+𝑎2	NOUN
iajs-2850	13	16	.	.	PUNCT
iajs-2850	14	1	doi	doi	NOUN
iajs-2850	14	2	:	:	PUNCT
iajs-2850	14	3	10.30526/35.3.2850	10.30526/35.3.2850	PROPN
iajs-2850	14	4	ibn	ibn	NOUN
iajs-2850	14	5	al	al	PROPN
iajs-2850	14	6	haitham	haitham	PROPN
iajs-2850	14	7	journal	journal	PROPN
iajs-2850	14	8	for	for	ADP
iajs-2850	14	9	pure	pure	ADJ
iajs-2850	14	10	and	and	CCONJ
iajs-2850	14	11	applied	apply	VERB
iajs-2850	14	12	science	science	NOUN
iajs-2850	14	13	journal	journal	PROPN
iajs-2850	14	14	homepage	homepage	NOUN
iajs-2850	14	15	:	:	PUNCT
iajs-2850	14	16	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2850	14	17	article	article	NOUN
iajs-2850	14	18	history	history	NOUN
iajs-2850	14	19	:	:	PUNCT
iajs-2850	14	20	received	receive	VERB
iajs-2850	14	21	12	12	NUM
iajs-2850	14	22	may	may	PROPN
iajs-2850	14	23	2022	2022	NUM
iajs-2850	14	24	,	,	PUNCT
iajs-2850	14	25	accepted	accept	VERB
iajs-2850	14	26	6	6	NUM
iajs-2850	14	27	june	june	PROPN
iajs-2850	14	28	2022	2022	NUM
iajs-2850	14	29	,	,	PUNCT
iajs-2850	14	30	published	publish	VERB
iajs-2850	14	31	in	in	ADP
iajs-2850	14	32	july	july	PROPN
iajs-2850	14	33	2022	2022	NUM
iajs-2850	14	34	.	.	PUNCT
iajs-2850	15	1	saed	saed	NOUN
iajs-2850	15	2	m.	m.	NOUN
iajs-2850	15	3	turq	turq	PROPN
iajs-2850	15	4	teacher	teacher	NOUN
iajs-2850	15	5	at	at	ADP
iajs-2850	15	6	the	the	DET
iajs-2850	15	7	ministry	ministry	PROPN
iajs-2850	15	8	of	of	ADP
iajs-2850	15	9	education	education	PROPN
iajs-2850	15	10	hebron	hebron	PROPN
iajs-2850	15	11	,	,	PUNCT
iajs-2850	15	12	palestine	palestine	PROPN
iajs-2850	15	13	saedturq@gmail.com	saedturq@gmail.com	PROPN
iajs-2850	16	1	emad	emad	PROPN
iajs-2850	16	2	a.	a.	PROPN
iajs-2850	16	3	kuffi	kuffi	PROPN
iajs-2850	16	4	college	college	PROPN
iajs-2850	16	5	of	of	ADP
iajs-2850	16	6	engineering	engineering	PROPN
iajs-2850	16	7	,	,	PUNCT
iajs-2850	16	8	al	al	PROPN
iajs-2850	16	9	-	-	PUNCT
iajs-2850	16	10	qadisiyah	qadisiyah	PROPN
iajs-2850	16	11	university	university	NOUN
iajs-2850	16	12	,	,	PUNCT
iajs-2850	16	13	al	al	PROPN
iajs-2850	16	14	-	-	PUNCT
iajs-2850	16	15	qadisiyah	qadisiyah	PROPN
iajs-2850	16	16	,	,	PUNCT
iajs-2850	16	17	iraq	iraq	PROPN
iajs-2850	16	18	.	.	PUNCT
iajs-2850	17	1	emad.abbas@qu.edu.iq	emad.abbas@qu.edu.iq	PROPN
iajs-2850	17	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2850	17	3	mailto:saedturq@gmail.com	mailto:saedturq@gmail.com	PROPN
iajs-2850	17	4	mailto:emad.abbas@qu.edu.iq	mailto:emad.abbas@qu.edu.iq	PROPN
iajs-2850	17	5	ihjpas	ihjpa	VERB
iajs-2850	17	6	.	.	PUNCT
iajs-2850	18	1	53	53	NUM
iajs-2850	18	2	(	(	PUNCT
iajs-2850	18	3	3)2022	3)2022	NOUN
iajs-2850	18	4	121	121	NUM
iajs-2850	18	5	4	4	NUM
iajs-2850	18	6	if	if	SCONJ
iajs-2850	18	7	𝑔(𝑡	𝑔(𝑡	VERB
iajs-2850	18	8	)	)	PUNCT
iajs-2850	19	1	=	=	SYM
iajs-2850	19	2	cos	cos	PROPN
iajs-2850	20	1	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	20	2	,	,	PUNCT
iajs-2850	20	3	then	then	ADV
iajs-2850	20	4	𝐒𝑎[cos	𝐒𝑎[cos	X
iajs-2850	20	5	𝑎𝑡	𝑎𝑡	X
iajs-2850	20	6	]	]	X
iajs-2850	20	7	=	=	SYM
iajs-2850	20	8	𝑣𝛼−𝛽	𝑣𝛼−𝛽	NOUN
iajs-2850	20	9	𝑣2𝛼+𝑎2	𝑣2𝛼+𝑎2	NOUN
iajs-2850	20	10	.	.	PUNCT
iajs-2850	21	1	5	5	NUM
iajs-2850	21	2	if	if	SCONJ
iajs-2850	21	3	𝑔(𝑡	𝑔(𝑡	NUM
iajs-2850	21	4	)	)	PUNCT
iajs-2850	22	1	=	=	VERB
iajs-2850	22	2	sinh	sinh	VERB
iajs-2850	22	3	𝑎𝑡	𝑎𝑡	ADP
iajs-2850	22	4	,	,	PUNCT
iajs-2850	22	5	then	then	ADV
iajs-2850	22	6	𝐒𝑎[sinh	𝐒𝑎[sinh	X
iajs-2850	23	1	𝑎𝑡	𝑎𝑡	X
iajs-2850	23	2	]	]	X
iajs-2850	23	3	=	=	SYM
iajs-2850	23	4	𝑎𝑣−𝛽	𝑎𝑣−𝛽	VERB
iajs-2850	23	5	𝑣2𝛼−𝑎2	𝑣2𝛼−𝑎2	ADJ
iajs-2850	23	6	6	6	NUM
iajs-2850	23	7	if	if	SCONJ
iajs-2850	23	8	𝑔(𝑡	𝑔(𝑡	NUM
iajs-2850	23	9	)	)	PUNCT
iajs-2850	23	10	=	=	SYM
iajs-2850	24	1	cosh	cosh	NOUN
iajs-2850	24	2	𝑎𝑡	𝑎𝑡	ADP
iajs-2850	24	3	,	,	PUNCT
iajs-2850	24	4	then	then	ADV
iajs-2850	24	5	𝐒𝑎[cosh	𝐒𝑎[cosh	PROPN
iajs-2850	25	1	𝑎𝑡	𝑎𝑡	X
iajs-2850	25	2	]	]	X
iajs-2850	25	3	=	=	SYM
iajs-2850	25	4	𝑣𝛼−𝛽	𝑣𝛼−𝛽	NOUN
iajs-2850	25	5	𝑣2𝛼−𝑎2	𝑣2𝛼−𝑎2	ADJ
iajs-2850	25	6	.	.	PUNCT
iajs-2850	25	7	7	7	NUM
iajs-2850	25	8	𝐒𝑎[𝑔(𝑛)(𝑡	𝐒𝑎[𝑔(𝑛)(𝑡	NOUN
iajs-2850	25	9	)	)	PUNCT
iajs-2850	25	10	]	]	PUNCT
iajs-2850	26	1	=	=	SYM
iajs-2850	26	2	𝑣𝑛𝛼𝐅(𝑣	𝑣𝑛𝛼𝐅(𝑣	NUM
iajs-2850	26	3	)	)	PUNCT
iajs-2850	26	4	−	−	PROPN
iajs-2850	27	1	∑𝑘=0	∑𝑘=0	PROPN
iajs-2850	27	2	𝑛−1	𝑛−1	PROPN
iajs-2850	27	3	 	 	SPACE
iajs-2850	27	4	𝑣𝑘𝛼−𝛽𝑔((𝑛−1)−𝑘)(0	𝑣𝑘𝛼−𝛽𝑔((𝑛−1)−𝑘)(0	PROPN
iajs-2850	27	5	)	)	PUNCT
iajs-2850	27	6	.	.	PUNCT
iajs-2850	28	1	now	now	ADV
iajs-2850	28	2	,	,	PUNCT
iajs-2850	28	3	the	the	DET
iajs-2850	28	4	complex	complex	ADJ
iajs-2850	28	5	sadik	sadik	ADJ
iajs-2850	28	6	transform	transform	NOUN
iajs-2850	28	7	is	be	AUX
iajs-2850	28	8	a	a	DET
iajs-2850	28	9	new	new	ADJ
iajs-2850	28	10	complex	complex	ADJ
iajs-2850	28	11	transform	transform	NOUN
iajs-2850	28	12	and	and	CCONJ
iajs-2850	28	13	it	it	PRON
iajs-2850	28	14	is	be	AUX
iajs-2850	28	15	applied	apply	VERB
iajs-2850	28	16	and	and	CCONJ
iajs-2850	28	17	used	use	VERB
iajs-2850	28	18	to	to	PART
iajs-2850	28	19	find	find	VERB
iajs-2850	28	20	the	the	DET
iajs-2850	28	21	solution	solution	NOUN
iajs-2850	28	22	of	of	ADP
iajs-2850	28	23	ordinary	ordinary	ADJ
iajs-2850	28	24	differential	differential	ADJ
iajs-2850	28	25	equation	equation	NOUN
iajs-2850	28	26	and	and	CCONJ
iajs-2850	28	27	has	have	VERB
iajs-2850	28	28	applications	application	NOUN
iajs-2850	28	29	in	in	ADP
iajs-2850	28	30	domains	domain	NOUN
iajs-2850	28	31	such	such	ADJ
iajs-2850	28	32	as	as	ADP
iajs-2850	28	33	engineering	engineering	NOUN
iajs-2850	28	34	,	,	PUNCT
iajs-2850	28	35	applied	applied	ADJ
iajs-2850	28	36	physics	physic	NOUN
iajs-2850	28	37	,	,	PUNCT
iajs-2850	28	38	and	and	CCONJ
iajs-2850	28	39	signed	sign	VERB
iajs-2850	28	40	processing	processing	NOUN
iajs-2850	28	41	[	[	X
iajs-2850	28	42	3,4,7	3,4,7	NUM
iajs-2850	28	43	]	]	PUNCT
iajs-2850	28	44	.	.	PUNCT
iajs-2850	29	1	we	we	PRON
iajs-2850	29	2	analyze	analyze	VERB
iajs-2850	29	3	functions	function	NOUN
iajs-2850	29	4	in	in	ADP
iajs-2850	29	5	the	the	DET
iajs-2850	29	6	set	set	NOUN
iajs-2850	29	7	𝐂	𝐂	PROPN
iajs-2850	29	8	defined	define	VERB
iajs-2850	29	9	by	by	ADP
iajs-2850	29	10	a	a	DET
iajs-2850	29	11	novel	novel	ADJ
iajs-2850	29	12	complex	complex	ADJ
iajs-2850	29	13	transform	transform	NOUN
iajs-2850	29	14	defined	define	VERB
iajs-2850	29	15	for	for	ADP
iajs-2850	29	16	functions	function	NOUN
iajs-2850	29	17	of	of	ADP
iajs-2850	29	18	exponential	exponential	ADJ
iajs-2850	29	19	order	order	NOUN
iajs-2850	29	20	:	:	PUNCT
iajs-2850	29	21	𝐂	𝐂	PROPN
iajs-2850	29	22	=	=	PRON
iajs-2850	29	23	{	{	PUNCT
iajs-2850	29	24	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	29	25	):	):	PUNCT
iajs-2850	29	26	there	there	PRON
iajs-2850	29	27	exists	exist	VERB
iajs-2850	29	28	𝑀	𝑀	PROPN
iajs-2850	29	29	,	,	PUNCT
iajs-2850	29	30	𝐿1	𝐿1	PROPN
iajs-2850	29	31	and	and	CCONJ
iajs-2850	29	32	𝐿2	𝐿2	NOUN
iajs-2850	29	33	are	be	AUX
iajs-2850	29	34	greater	great	ADJ
iajs-2850	29	35	than	than	ADP
iajs-2850	29	36	zero	zero	NUM
iajs-2850	30	1	such	such	ADJ
iajs-2850	30	2	that	that	DET
iajs-2850	30	3	|𝑔(𝑡)|	|𝑔(𝑡)|	PROPN
iajs-2850	30	4	<	<	X
iajs-2850	30	5	𝑀𝑒−𝑖𝐿𝑗|𝑡|	𝑀𝑒−𝑖𝐿𝑗|𝑡|	NOUN
iajs-2850	30	6	,	,	PUNCT
iajs-2850	30	7	if	if	SCONJ
iajs-2850	30	8	𝑡	𝑡	PROPN
iajs-2850	30	9	∈	∈	PROPN
iajs-2850	30	10	(	(	PUNCT
iajs-2850	30	11	−1)𝑗	−1)𝑗	PUNCT
iajs-2850	30	12	×	×	NOUN
iajs-2850	30	13	[	[	X
iajs-2850	30	14	0	0	NUM
iajs-2850	30	15	,	,	PUNCT
iajs-2850	30	16	∞	∞	PROPN
iajs-2850	30	17	)	)	PUNCT
iajs-2850	30	18	,	,	PUNCT
iajs-2850	30	19	𝑗	𝑗	NOUN
iajs-2850	30	20	=	=	SYM
iajs-2850	30	21	1,2	1,2	NUM
iajs-2850	30	22	}	}	PUNCT
iajs-2850	30	23	where	where	SCONJ
iajs-2850	30	24	𝑖	𝑖	PRON
iajs-2850	30	25	is	be	AUX
iajs-2850	30	26	a	a	DET
iajs-2850	30	27	complex	complex	ADJ
iajs-2850	30	28	number	number	NOUN
iajs-2850	30	29	.	.	PUNCT
iajs-2850	31	1	the	the	DET
iajs-2850	31	2	constant	constant	ADJ
iajs-2850	31	3	𝑀	𝑀	PROPN
iajs-2850	31	4	must	must	AUX
iajs-2850	31	5	be	be	AUX
iajs-2850	31	6	a	a	DET
iajs-2850	31	7	finite	finite	ADJ
iajs-2850	31	8	number	number	NOUN
iajs-2850	31	9	for	for	ADP
iajs-2850	31	10	a	a	DET
iajs-2850	31	11	particular	particular	ADJ
iajs-2850	31	12	function	function	NOUN
iajs-2850	31	13	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	31	14	)	)	PUNCT
iajs-2850	31	15	in	in	ADP
iajs-2850	31	16	the	the	DET
iajs-2850	31	17	set	set	PROPN
iajs-2850	31	18	𝐂	𝐂	PROPN
iajs-2850	31	19	,	,	PUNCT
iajs-2850	31	20	while	while	SCONJ
iajs-2850	31	21	𝐿1	𝐿1	PROPN
iajs-2850	31	22	and	and	CCONJ
iajs-2850	31	23	𝐿2	𝐿2	NOUN
iajs-2850	31	24	are	be	AUX
iajs-2850	31	25	may	may	AUX
iajs-2850	31	26	be	be	AUX
iajs-2850	31	27	finite	finite	ADJ
iajs-2850	31	28	or	or	CCONJ
iajs-2850	31	29	infinite	infinite	VERB
iajs-2850	31	30	.	.	PUNCT
iajs-2850	32	1	the	the	DET
iajs-2850	32	2	complex	complex	ADJ
iajs-2850	32	3	sadik	sadik	PROPN
iajs-2850	32	4	transform	transform	NOUN
iajs-2850	32	5	(	(	PUNCT
iajs-2850	32	6	cst	cst	PROPN
iajs-2850	32	7	)	)	PUNCT
iajs-2850	32	8	denoted	denote	VERB
iajs-2850	32	9	by	by	ADP
iajs-2850	32	10	the	the	DET
iajs-2850	32	11	operator	operator	NOUN
iajs-2850	32	12	𝐒𝑎	𝐒𝑎	NOUN
iajs-2850	32	13	{	{	PUNCT
iajs-2850	32	14	.	.	PUNCT
iajs-2850	32	15	}	}	PUNCT
iajs-2850	32	16	,	,	PUNCT
iajs-2850	32	17	the	the	DET
iajs-2850	32	18	transform	transform	NOUN
iajs-2850	32	19	as	as	SCONJ
iajs-2850	32	20	follows	follow	VERB
iajs-2850	32	21	:	:	PUNCT
iajs-2850	32	22	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	32	23	𝑐	𝑐	PROPN
iajs-2850	32	24	[	[	NOUN
iajs-2850	32	25	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	32	26	)	)	PUNCT
iajs-2850	32	27	]	]	PUNCT
iajs-2850	33	1	=	=	SYM
iajs-2850	33	2	𝐅𝑐(𝑠𝛼	𝐅𝑐(𝑠𝛼	PROPN
iajs-2850	33	3	,	,	PUNCT
iajs-2850	33	4	𝛽	𝛽	NOUN
iajs-2850	33	5	)	)	PUNCT
iajs-2850	33	6	=	=	SYM
iajs-2850	34	1	1	1	NUM
iajs-2850	34	2	𝑠𝛽	𝑠𝛽	NUM
iajs-2850	34	3	∫	∫	PROPN
iajs-2850	34	4	  	  	SPACE
iajs-2850	34	5	∞	∞	PROPN
iajs-2850	34	6	0	0	PROPN
iajs-2850	35	1	𝑔(𝑡)𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	𝑔(𝑡)𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	NOUN
iajs-2850	35	2	where	where	SCONJ
iajs-2850	35	3	𝑠	𝑠	PROPN
iajs-2850	35	4	∈	∈	PROPN
iajs-2850	35	5	ℂ	ℂ	PROPN
iajs-2850	35	6	,	,	PUNCT
iajs-2850	35	7	𝛼	𝛼	NOUN
iajs-2850	35	8	∈	∈	NOUN
iajs-2850	35	9	ℝ∗	ℝ∗	NOUN
iajs-2850	35	10	,	,	PUNCT
iajs-2850	35	11	and	and	CCONJ
iajs-2850	35	12	𝛽	𝛽	X
iajs-2850	35	13	∈	∈	NOUN
iajs-2850	35	14	ℝ	ℝ	PROPN
iajs-2850	35	15	.	.	PUNCT
iajs-2850	36	1	the	the	DET
iajs-2850	36	2	aim	aim	NOUN
iajs-2850	36	3	of	of	ADP
iajs-2850	36	4	this	this	DET
iajs-2850	36	5	work	work	NOUN
iajs-2850	36	6	(	(	PUNCT
iajs-2850	36	7	complex	complex	ADJ
iajs-2850	36	8	transform	transform	NOUN
iajs-2850	36	9	)	)	PUNCT
iajs-2850	36	10	to	to	PART
iajs-2850	36	11	find	find	VERB
iajs-2850	36	12	the	the	DET
iajs-2850	36	13	solution	solution	NOUN
iajs-2850	36	14	of	of	ADP
iajs-2850	36	15	higher	high	ADJ
iajs-2850	36	16	order	order	NOUN
iajs-2850	36	17	ordinary	ordinary	ADJ
iajs-2850	36	18	differential	differential	ADJ
iajs-2850	36	19	equations	equation	NOUN
iajs-2850	36	20	.	.	PUNCT
iajs-2850	37	1	many	many	ADJ
iajs-2850	37	2	researchers	researcher	NOUN
iajs-2850	37	3	have	have	AUX
iajs-2850	37	4	proposed	propose	VERB
iajs-2850	37	5	new	new	ADJ
iajs-2850	37	6	integral	integral	ADJ
iajs-2850	37	7	transformations	transformation	NOUN
iajs-2850	37	8	for	for	ADP
iajs-2850	37	9	the	the	DET
iajs-2850	37	10	purpose	purpose	NOUN
iajs-2850	37	11	of	of	ADP
iajs-2850	37	12	solving	solve	VERB
iajs-2850	37	13	ordinary	ordinary	ADJ
iajs-2850	37	14	and	and	CCONJ
iajs-2850	37	15	partial	partial	ADJ
iajs-2850	37	16	differential	differential	ADJ
iajs-2850	37	17	equations	equation	NOUN
iajs-2850	37	18	and	and	CCONJ
iajs-2850	37	19	their	their	PRON
iajs-2850	37	20	applications	application	NOUN
iajs-2850	37	21	[	[	X
iajs-2850	37	22	2,8,9,12	2,8,9,12	X
iajs-2850	37	23	]	]	X
iajs-2850	37	24	.	.	PUNCT
iajs-2850	38	1	2	2	X
iajs-2850	38	2	.	.	X
iajs-2850	38	3	a	a	DET
iajs-2850	38	4	novel	novel	ADJ
iajs-2850	38	5	complex	complex	ADJ
iajs-2850	38	6	transform	transform	NOUN
iajs-2850	38	7	"	"	PUNCT
iajs-2850	38	8	complex	complex	ADJ
iajs-2850	38	9	sadik	sadik	PROPN
iajs-2850	38	10	transform	transform	NOUN
iajs-2850	38	11	"	"	PUNCT
iajs-2850	38	12	of	of	ADP
iajs-2850	38	13	important	important	ADJ
iajs-2850	38	14	functions	function	NOUN
iajs-2850	38	15	in	in	ADP
iajs-2850	38	16	this	this	DET
iajs-2850	38	17	section	section	NOUN
iajs-2850	38	18	,	,	PUNCT
iajs-2850	38	19	we	we	PRON
iajs-2850	38	20	present	present	VERB
iajs-2850	38	21	the	the	DET
iajs-2850	38	22	complex	complex	ADJ
iajs-2850	38	23	sadik	sadik	ADJ
iajs-2850	38	24	transform	transform	NOUN
iajs-2850	38	25	of	of	ADP
iajs-2850	38	26	famous	famous	ADJ
iajs-2850	38	27	functions	function	NOUN
iajs-2850	38	28	:	:	PUNCT
iajs-2850	38	29	1	1	NUM
iajs-2850	38	30	if	if	SCONJ
iajs-2850	38	31	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-2850	38	32	)	)	PUNCT
iajs-2850	38	33	=	=	PUNCT
iajs-2850	38	34	𝑡𝑛	𝑡𝑛	NOUN
iajs-2850	38	35	,	,	PUNCT
iajs-2850	38	36	𝑛	𝑛	DET
iajs-2850	38	37	∈	∈	PROPN
iajs-2850	38	38	ℕ	ℕ	PROPN
iajs-2850	38	39	,	,	PUNCT
iajs-2850	38	40	then	then	ADV
iajs-2850	38	41	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	38	42	𝑐	𝑐	PROPN
iajs-2850	38	43	{	{	PUNCT
iajs-2850	38	44	𝑡𝑛	𝑡𝑛	PROPN
iajs-2850	38	45	}	}	PUNCT
iajs-2850	38	46	=	=	SYM
iajs-2850	38	47	(	(	PUNCT
iajs-2850	38	48	−𝑖)𝑛+1	−𝑖)𝑛+1	PROPN
iajs-2850	38	49	𝑛	𝑛	PROPN
iajs-2850	38	50	!	!	PUNCT
iajs-2850	38	51	𝑠𝑛𝛼+(𝛼+𝛽	𝑠𝑛𝛼+(𝛼+𝛽	PROPN
iajs-2850	38	52	)	)	PUNCT
iajs-2850	38	53	,	,	PUNCT
iajs-2850	38	54	𝑠	𝑠	X
iajs-2850	38	55	>	>	X
iajs-2850	38	56	0	0	X
iajs-2850	38	57	.	.	PUNCT
iajs-2850	39	1	proof	proof	NOUN
iajs-2850	39	2	.	.	PUNCT
iajs-2850	40	1	since	since	SCONJ
iajs-2850	40	2	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	40	3	𝑐	𝑐	PROPN
iajs-2850	40	4	[	[	X
iajs-2850	40	5	𝑡𝑛	𝑡𝑛	X
iajs-2850	40	6	]	]	X
iajs-2850	40	7	=	=	SYM
iajs-2850	40	8	1	1	NUM
iajs-2850	40	9	𝑠𝛽	𝑠𝛽	NUM
iajs-2850	40	10	∫	∫	PROPN
iajs-2850	40	11	  	  	SPACE
iajs-2850	40	12	∞	∞	PROPN
iajs-2850	40	13	0	0	NUM
iajs-2850	40	14	𝑡𝑛𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	𝑡𝑛𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	PROPN
iajs-2850	40	15	let	let	VERB
iajs-2850	40	16	𝑢	𝑢	X
iajs-2850	40	17	=	=	X
iajs-2850	40	18	𝑖𝑡	𝑖𝑡	X
iajs-2850	40	19	→	→	PUNCT
iajs-2850	40	20	𝑑𝑢	𝑑𝑢	X
iajs-2850	40	21	=	=	NOUN
iajs-2850	40	22	𝑖𝑑𝑡	𝑖𝑑𝑡	NOUN
iajs-2850	40	23	or	or	CCONJ
iajs-2850	40	24	𝑑𝑢	𝑑𝑢	ADJ
iajs-2850	40	25	𝑖	𝑖	SYM
iajs-2850	40	26	=	=	PUNCT
iajs-2850	40	27	𝑑𝑡	𝑑𝑡	ADP
iajs-2850	40	28	or	or	CCONJ
iajs-2850	40	29	−𝑖𝑑𝑢	−𝑖𝑑𝑢	NOUN
iajs-2850	40	30	=	=	PUNCT
iajs-2850	41	1	𝑑𝑡	𝑑𝑡	ADP
iajs-2850	42	1	and	and	CCONJ
iajs-2850	42	2	we	we	PRON
iajs-2850	42	3	know	know	VERB
iajs-2850	42	4	𝑢	𝑢	X
iajs-2850	42	5	=	=	X
iajs-2850	42	6	𝑖𝑡	𝑖𝑡	INTJ
iajs-2850	42	7	→	→	SYM
iajs-2850	42	8	−𝑖𝑢	−𝑖𝑢	NOUN
iajs-2850	42	9	=	=	SYM
iajs-2850	42	10	𝑡	𝑡	PROPN
iajs-2850	42	11	,	,	PUNCT
iajs-2850	42	12	when	when	SCONJ
iajs-2850	42	13	𝑡	𝑡	X
iajs-2850	42	14	→	→	SYM
iajs-2850	42	15	0	0	NUM
iajs-2850	42	16	then	then	ADV
iajs-2850	42	17	𝑢	𝑢	X
iajs-2850	42	18	→	→	SYM
iajs-2850	42	19	0	0	NUM
iajs-2850	42	20	and	and	CCONJ
iajs-2850	42	21	when	when	SCONJ
iajs-2850	42	22	𝑡	𝑡	X
iajs-2850	42	23	→	→	SYM
iajs-2850	42	24	∞	∞	PROPN
iajs-2850	42	25	then	then	ADV
iajs-2850	42	26	𝑢	𝑢	X
iajs-2850	42	27	→	→	SYM
iajs-2850	42	28	∞	∞	PROPN
iajs-2850	42	29	,	,	PUNCT
iajs-2850	42	30	that	that	PRON
iajs-2850	42	31	is	be	AUX
iajs-2850	42	32	:	:	PUNCT
iajs-2850	42	33	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	42	34	𝑐	𝑐	PROPN
iajs-2850	42	35	[	[	X
iajs-2850	42	36	𝑡𝑛	𝑡𝑛	X
iajs-2850	42	37	]	]	X
iajs-2850	42	38	=	=	SYM
iajs-2850	42	39	1	1	NUM
iajs-2850	42	40	𝑠𝛽	𝑠𝛽	NUM
iajs-2850	42	41	∫	∫	PROPN
iajs-2850	42	42	  	  	SPACE
iajs-2850	42	43	∞	∞	PROPN
iajs-2850	42	44	0	0	NUM
iajs-2850	42	45	  	  	SPACE
iajs-2850	42	46	𝑡𝑛𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	𝑡𝑛𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	X
iajs-2850	43	1	=	=	NOUN
iajs-2850	43	2	1	1	NUM
iajs-2850	43	3	𝑠𝛽	𝑠𝛽	NUM
iajs-2850	43	4	∫	∫	PROPN
iajs-2850	43	5	  	  	SPACE
iajs-2850	43	6	∞	∞	PROPN
iajs-2850	43	7	0	0	NUM
iajs-2850	43	8	  	  	SPACE
iajs-2850	43	9	(	(	PUNCT
iajs-2850	43	10	−𝑖𝑢)𝑛𝑒−𝑠𝛼𝑢(−𝑖)𝑑𝑢	−𝑖𝑢)𝑛𝑒−𝑠𝛼𝑢(−𝑖)𝑑𝑢	NOUN
iajs-2850	43	11	=	=	SYM
iajs-2850	43	12	1	1	NUM
iajs-2850	43	13	𝑠𝛽	𝑠𝛽	NUM
iajs-2850	43	14	∫	∫	PROPN
iajs-2850	43	15	  	  	SPACE
iajs-2850	43	16	∞	∞	PROPN
iajs-2850	43	17	0	0	NUM
iajs-2850	43	18	  	  	SPACE
iajs-2850	43	19	(	(	PUNCT
iajs-2850	43	20	−𝑖)𝑛𝑢𝑛𝑒−𝑠𝛼	−𝑖)𝑛𝑢𝑛𝑒−𝑠𝛼	PROPN
iajs-2850	43	21	𝑢(−𝑖)𝑑𝑢	𝑢(−𝑖)𝑑𝑢	NOUN
iajs-2850	43	22	=	=	SYM
iajs-2850	43	23	(	(	PUNCT
iajs-2850	43	24	−𝑖)𝑛+1	−𝑖)𝑛+1	NOUN
iajs-2850	43	25	1	1	NUM
iajs-2850	43	26	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	43	27	∫	∫	PROPN
iajs-2850	43	28	  	  	SPACE
iajs-2850	43	29	∞	∞	PROPN
iajs-2850	43	30	0	0	PUNCT
iajs-2850	43	31	 	 	SPACE
iajs-2850	43	32	𝑢𝑛𝑒−𝑠𝛼𝑢𝑑𝑢	𝑢𝑛𝑒−𝑠𝛼𝑢𝑑𝑢	PUNCT
iajs-2850	43	33	=	=	X
iajs-2850	43	34	(	(	PUNCT
iajs-2850	43	35	−𝑖)𝑛+1𝐒𝑎[𝑡𝑛	−𝑖)𝑛+1𝐒𝑎[𝑡𝑛	X
iajs-2850	43	36	]	]	X
iajs-2850	43	37	=	=	SYM
iajs-2850	43	38	(	(	PUNCT
iajs-2850	43	39	−𝑖)𝑛+1	−𝑖)𝑛+1	PROPN
iajs-2850	43	40	𝑛	𝑛	PROPN
iajs-2850	43	41	!	!	PUNCT
iajs-2850	43	42	𝑠𝑛𝛼+(𝛼+𝛽	𝑠𝑛𝛼+(𝛼+𝛽	NOUN
iajs-2850	43	43	)	)	PUNCT
iajs-2850	44	1	⋅	⋅	PROPN
iajs-2850	44	2	𝑠	𝑠	PROPN
iajs-2850	44	3	>	>	SYM
iajs-2850	44	4	0	0	NUM
iajs-2850	44	5	2	2	NUM
iajs-2850	44	6	if	if	SCONJ
iajs-2850	44	7	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-2850	44	8	)	)	PUNCT
iajs-2850	44	9	=	=	SYM
iajs-2850	44	10	𝑒𝑎𝑡	𝑒𝑎𝑡	NOUN
iajs-2850	44	11	,	,	PUNCT
iajs-2850	44	12	𝑎	𝑎	NOUN
iajs-2850	44	13	is	be	AUX
iajs-2850	44	14	a	a	DET
iajs-2850	44	15	constant	constant	ADJ
iajs-2850	44	16	number	number	NOUN
iajs-2850	44	17	,	,	PUNCT
iajs-2850	44	18	then	then	ADV
iajs-2850	44	19	:	:	PUNCT
iajs-2850	44	20	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	44	21	𝑐	𝑐	PROPN
iajs-2850	44	22	[	[	X
iajs-2850	44	23	𝑒𝑎𝑡	𝑒𝑎𝑡	X
iajs-2850	44	24	]	]	X
iajs-2850	44	25	=	=	PUNCT
iajs-2850	44	26	−1	−1	NOUN
iajs-2850	44	27	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	44	28	[	[	PUNCT
iajs-2850	44	29	𝑎	𝑎	X
iajs-2850	44	30	(	(	PUNCT
iajs-2850	44	31	𝑠2𝛼	𝑠2𝛼	NOUN
iajs-2850	44	32	+	+	CCONJ
iajs-2850	44	33	𝑎2	𝑎2	NOUN
iajs-2850	44	34	)	)	PUNCT
iajs-2850	45	1	+	+	CCONJ
iajs-2850	45	2	𝑖	𝑖	VERB
iajs-2850	45	3	𝑠𝛼	𝑠𝛼	PROPN
iajs-2850	45	4	(	(	PUNCT
iajs-2850	45	5	𝑠2𝛼	𝑠2𝛼	PROPN
iajs-2850	45	6	+	+	CCONJ
iajs-2850	45	7	𝑎2	𝑎2	PROPN
iajs-2850	45	8	)	)	PUNCT
iajs-2850	45	9	]	]	PUNCT
iajs-2850	45	10	,	,	PUNCT
iajs-2850	45	11	𝑠	𝑠	INTJ
iajs-2850	45	12	>	>	X
iajs-2850	45	13	𝑎	𝑎	PRON
iajs-2850	45	14	ihjpas	ihjpa	NOUN
iajs-2850	45	15	.	.	PUNCT
iajs-2850	46	1	53	53	NUM
iajs-2850	46	2	(	(	PUNCT
iajs-2850	46	3	3)2022	3)2022	NOUN
iajs-2850	46	4	122	122	NUM
iajs-2850	46	5	proof	proof	NOUN
iajs-2850	46	6	.	.	PUNCT
iajs-2850	47	1	since	since	SCONJ
iajs-2850	47	2	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	47	3	𝑐	𝑐	PROPN
iajs-2850	47	4	[	[	X
iajs-2850	47	5	𝑒𝑎𝑡	𝑒𝑎𝑡	X
iajs-2850	47	6	]	]	X
iajs-2850	47	7	=	=	SYM
iajs-2850	47	8	1	1	NUM
iajs-2850	47	9	𝑠𝛽	𝑠𝛽	NUM
iajs-2850	47	10	∫	∫	PROPN
iajs-2850	47	11	  	  	SPACE
iajs-2850	47	12	∞	∞	PROPN
iajs-2850	47	13	0	0	NUM
iajs-2850	47	14	  	  	SPACE
iajs-2850	47	15	𝑒𝑎𝑡𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	𝑒𝑎𝑡𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	X
iajs-2850	47	16	=	=	PROPN
iajs-2850	47	17	1	1	NUM
iajs-2850	47	18	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	47	19	∫	∫	PROPN
iajs-2850	47	20	  	  	SPACE
iajs-2850	47	21	∞	∞	PROPN
iajs-2850	47	22	0	0	NUM
iajs-2850	47	23	  	  	SPACE
iajs-2850	47	24	𝑒−𝑡(𝑖𝑠𝛼−𝑎)𝑑𝑡	𝑒−𝑡(𝑖𝑠𝛼−𝑎)𝑑𝑡	ADP
iajs-2850	47	25	=	=	SYM
iajs-2850	47	26	1	1	NUM
iajs-2850	47	27	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	47	28	1	1	NUM
iajs-2850	47	29	𝑖𝑠𝛼	𝑖𝑠𝛼	NOUN
iajs-2850	47	30	−	−	PROPN
iajs-2850	47	31	𝑎	𝑎	NOUN
iajs-2850	47	32	,	,	PUNCT
iajs-2850	47	33	=	=	SYM
iajs-2850	47	34	1	1	NUM
iajs-2850	47	35	𝑠𝛽	𝑠𝛽	NUM
iajs-2850	47	36	1	1	NUM
iajs-2850	47	37	(	(	PUNCT
iajs-2850	47	38	𝑖𝑠𝛼	𝑖𝑠𝛼	ADV
iajs-2850	47	39	−	−	NUM
iajs-2850	47	40	𝑎	𝑎	NOUN
iajs-2850	47	41	)	)	PUNCT
iajs-2850	47	42	(	(	PUNCT
iajs-2850	47	43	−𝑖𝑠𝛼	−𝑖𝑠𝛼	VERB
iajs-2850	48	1	−	−	NUM
iajs-2850	48	2	𝑎	𝑎	NOUN
iajs-2850	48	3	)	)	PUNCT
iajs-2850	48	4	(	(	PUNCT
iajs-2850	48	5	−𝑖𝑠𝛼	−𝑖𝑠𝛼	VERB
iajs-2850	49	1	−	−	NUM
iajs-2850	49	2	𝑎	𝑎	NOUN
iajs-2850	49	3	)	)	PUNCT
iajs-2850	49	4	,	,	PUNCT
iajs-2850	50	1	=	=	NOUN
iajs-2850	50	2	1	1	NUM
iajs-2850	50	3	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	50	4	[	[	PUNCT
iajs-2850	50	5	(	(	PUNCT
iajs-2850	50	6	−1)(𝑎	−1)(𝑎	X
iajs-2850	50	7	+	+	CCONJ
iajs-2850	50	8	𝑖𝑠𝛼	𝑖𝑠𝛼	ADJ
iajs-2850	50	9	)	)	PUNCT
iajs-2850	50	10	(	(	PUNCT
iajs-2850	50	11	𝑠2𝛼	𝑠2𝛼	NOUN
iajs-2850	50	12	+	+	CCONJ
iajs-2850	50	13	𝑎2	𝑎2	PROPN
iajs-2850	50	14	)	)	PUNCT
iajs-2850	50	15	]	]	PUNCT
iajs-2850	50	16	,	,	PUNCT
iajs-2850	50	17	=	=	SYM
iajs-2850	51	1	−1	−1	NOUN
iajs-2850	51	2	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	51	3	[	[	PUNCT
iajs-2850	51	4	𝑎	𝑎	X
iajs-2850	51	5	(	(	PUNCT
iajs-2850	51	6	𝑠2𝛼	𝑠2𝛼	NOUN
iajs-2850	51	7	+	+	CCONJ
iajs-2850	51	8	𝑎2	𝑎2	NOUN
iajs-2850	51	9	)	)	PUNCT
iajs-2850	52	1	+	+	CCONJ
iajs-2850	52	2	𝑖	𝑖	VERB
iajs-2850	52	3	𝑠𝛼	𝑠𝛼	PROPN
iajs-2850	52	4	(	(	PUNCT
iajs-2850	52	5	𝑠2𝛼	𝑠2𝛼	PROPN
iajs-2850	52	6	+	+	CCONJ
iajs-2850	52	7	𝑎2	𝑎2	PROPN
iajs-2850	52	8	)	)	PUNCT
iajs-2850	52	9	]	]	PUNCT
iajs-2850	52	10	,	,	PUNCT
iajs-2850	52	11	𝑠	𝑠	INTJ
iajs-2850	52	12	>	>	X
iajs-2850	52	13	𝑎	𝑎	DET
iajs-2850	52	14	3	3	NUM
iajs-2850	52	15	let	let	VERB
iajs-2850	52	16	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-2850	52	17	)	)	PUNCT
iajs-2850	52	18	=	=	SYM
iajs-2850	52	19	sin	sin	NOUN
iajs-2850	52	20	(	(	PUNCT
iajs-2850	52	21	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	52	22	)	)	PUNCT
iajs-2850	52	23	,	,	PUNCT
iajs-2850	52	24	𝑎	𝑎	NOUN
iajs-2850	52	25	is	be	AUX
iajs-2850	52	26	a	a	DET
iajs-2850	52	27	constant	constant	ADJ
iajs-2850	52	28	number	number	NOUN
iajs-2850	52	29	,	,	PUNCT
iajs-2850	52	30	then	then	ADV
iajs-2850	52	31	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	52	32	𝑐	𝑐	PROPN
iajs-2850	53	1	[	[	X
iajs-2850	53	2	sin	sin	NOUN
iajs-2850	53	3	(	(	PUNCT
iajs-2850	53	4	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	53	5	)	)	PUNCT
iajs-2850	53	6	]	]	PUNCT
iajs-2850	54	1	=	=	SYM
iajs-2850	54	2	−𝑎	−𝑎	PROPN
iajs-2850	54	3	𝑠𝛽(𝑠2𝛼	𝑠𝛽(𝑠2𝛼	PROPN
iajs-2850	54	4	−	−	PROPN
iajs-2850	54	5	𝑎2	𝑎2	PROPN
iajs-2850	54	6	)	)	PUNCT
iajs-2850	54	7	,	,	PUNCT
iajs-2850	54	8	𝑠	𝑠	INTJ
iajs-2850	54	9	>	>	X
iajs-2850	54	10	|𝑎|	|𝑎|	PROPN
iajs-2850	54	11	proof	proof	NOUN
iajs-2850	54	12	.	.	PUNCT
iajs-2850	55	1	since	since	SCONJ
iajs-2850	55	2	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	55	3	𝑐	𝑐	PROPN
iajs-2850	55	4	[	[	X
iajs-2850	55	5	sin	sin	NOUN
iajs-2850	55	6	(	(	PUNCT
iajs-2850	55	7	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	55	8	)	)	PUNCT
iajs-2850	55	9	]	]	PUNCT
iajs-2850	56	1	=	=	PUNCT
iajs-2850	56	2	1	1	NUM
iajs-2850	56	3	𝑠𝛽	𝑠𝛽	NUM
iajs-2850	56	4	∫	∫	PROPN
iajs-2850	56	5	  	  	SPACE
iajs-2850	56	6	∞	∞	PROPN
iajs-2850	56	7	0	0	NUM
iajs-2850	56	8	 	 	SPACE
iajs-2850	56	9	sin	sin	NOUN
iajs-2850	56	10	(	(	PUNCT
iajs-2850	56	11	𝑎𝑡)𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	𝑎𝑡)𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	NOUN
iajs-2850	56	12	=	=	SYM
iajs-2850	56	13	1	1	NUM
iajs-2850	56	14	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	56	15	∫	∫	PROPN
iajs-2850	56	16	  	  	SPACE
iajs-2850	56	17	∞	∞	PROPN
iajs-2850	56	18	0	0	NUM
iajs-2850	56	19	  	  	SPACE
iajs-2850	56	20	𝑒𝑖𝑎𝑡	𝑒𝑖𝑎𝑡	NOUN
iajs-2850	56	21	−	−	PROPN
iajs-2850	56	22	𝑒−𝑖𝑎𝑡	𝑒−𝑖𝑎𝑡	VERB
iajs-2850	56	23	2𝑖	2𝑖	NOUN
iajs-2850	56	24	𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	PUNCT
iajs-2850	57	1	after	after	ADP
iajs-2850	57	2	simple	simple	ADJ
iajs-2850	57	3	computations	computation	NOUN
iajs-2850	57	4	,	,	PUNCT
iajs-2850	57	5	we	we	PRON
iajs-2850	57	6	get	get	VERB
iajs-2850	57	7	:	:	PUNCT
iajs-2850	57	8	𝐒𝑎	𝐒𝑎	PART
iajs-2850	57	9	𝑐	𝑐	NOUN
iajs-2850	58	1	[	[	X
iajs-2850	58	2	sin	sin	NOUN
iajs-2850	58	3	(	(	PUNCT
iajs-2850	58	4	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	58	5	)	)	PUNCT
iajs-2850	58	6	]	]	PUNCT
iajs-2850	59	1	=	=	SYM
iajs-2850	59	2	−𝑎	−𝑎	PROPN
iajs-2850	59	3	𝑠𝛽(𝑠2𝛼	𝑠𝛽(𝑠2𝛼	PROPN
iajs-2850	59	4	−	−	PROPN
iajs-2850	59	5	𝑎2	𝑎2	PROPN
iajs-2850	59	6	)	)	PUNCT
iajs-2850	59	7	,	,	PUNCT
iajs-2850	60	1	𝑠	𝑠	INTJ
iajs-2850	60	2	>	>	X
iajs-2850	60	3	|𝑎|	|𝑎|	ADP
iajs-2850	60	4	the	the	DET
iajs-2850	60	5	result	result	NOUN
iajs-2850	60	6	will	will	AUX
iajs-2850	60	7	be	be	AUX
iajs-2850	60	8	benefit	benefit	NOUN
iajs-2850	60	9	in	in	ADP
iajs-2850	60	10	determining	determine	VERB
iajs-2850	60	11	the	the	DET
iajs-2850	60	12	complicated	complicated	ADJ
iajs-2850	60	13	transform	transform	NOUN
iajs-2850	60	14	of	of	ADP
iajs-2850	60	15	:	:	PUNCT
iajs-2850	60	16	4	4	NUM
iajs-2850	60	17	𝐒𝑎	𝐒𝑎	NOUN
iajs-2850	60	18	𝑐	𝑐	PROPN
iajs-2850	60	19	[	[	X
iajs-2850	60	20	cos	cos	X
iajs-2850	60	21	(	(	PUNCT
iajs-2850	60	22	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	60	23	)	)	PUNCT
iajs-2850	60	24	]	]	PUNCT
iajs-2850	61	1	=	=	SYM
iajs-2850	61	2	−𝑖𝑠𝛼	−𝑖𝑠𝛼	X
iajs-2850	61	3	𝑠𝛽(𝑠2𝛼−𝑎2	𝑠𝛽(𝑠2𝛼−𝑎2	ADV
iajs-2850	61	4	)	)	PUNCT
iajs-2850	61	5	,	,	PUNCT
iajs-2850	61	6	𝑠	𝑠	INTJ
iajs-2850	61	7	>	>	X
iajs-2850	61	8	|𝑎|	|𝑎|	PROPN
iajs-2850	61	9	.	.	PROPN
iajs-2850	61	10	5	5	NUM
iajs-2850	61	11	𝐒𝑎	𝐒𝑎	NOUN
iajs-2850	61	12	𝑐	𝑐	PROPN
iajs-2850	61	13	[	[	X
iajs-2850	61	14	sinh	sinh	NOUN
iajs-2850	61	15	(	(	PUNCT
iajs-2850	61	16	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	61	17	)	)	PUNCT
iajs-2850	61	18	]	]	PUNCT
iajs-2850	62	1	=	=	SYM
iajs-2850	62	2	−𝑎	−𝑎	PROPN
iajs-2850	62	3	𝑠𝛽(𝑠2𝛼+𝑎2	𝑠𝛽(𝑠2𝛼+𝑎2	PROPN
iajs-2850	62	4	)	)	PUNCT
iajs-2850	62	5	,	,	PUNCT
iajs-2850	62	6	𝑠	𝑠	X
iajs-2850	62	7	>	>	X
iajs-2850	62	8	0	0	NUM
iajs-2850	62	9	.	.	PROPN
iajs-2850	62	10	6	6	NUM
iajs-2850	62	11	𝐒𝑎	𝐒𝑎	NOUN
iajs-2850	62	12	𝑐	𝑐	NOUN
iajs-2850	62	13	[	[	X
iajs-2850	62	14	cosh	cosh	NOUN
iajs-2850	62	15	(	(	PUNCT
iajs-2850	62	16	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	62	17	)	)	PUNCT
iajs-2850	62	18	]	]	PUNCT
iajs-2850	63	1	=	=	SYM
iajs-2850	63	2	−𝑖𝑠𝛼	−𝑖𝑠𝛼	VERB
iajs-2850	63	3	𝑠𝛽(𝑠2𝛼+𝑎2	𝑠𝛽(𝑠2𝛼+𝑎2	PROPN
iajs-2850	63	4	)	)	PUNCT
iajs-2850	63	5	,	,	PUNCT
iajs-2850	63	6	𝑠	𝑠	INTJ
iajs-2850	63	7	>	>	X
iajs-2850	63	8	0	0	NUM
iajs-2850	63	9	.	.	PROPN
iajs-2850	63	10	2.1	2.1	NUM
iajs-2850	63	11	.	.	PUNCT
iajs-2850	64	1	the	the	DET
iajs-2850	64	2	sadik	sadik	ADJ
iajs-2850	64	3	and	and	CCONJ
iajs-2850	64	4	complex	complex	ADJ
iajs-2850	64	5	sadik	sadik	ADJ
iajs-2850	64	6	integral	integral	ADJ
iajs-2850	64	7	transforms	transform	NOUN
iajs-2850	64	8	for	for	ADP
iajs-2850	64	9	some	some	DET
iajs-2850	64	10	basic	basic	ADJ
iajs-2850	64	11	functions	function	NOUN
iajs-2850	64	12	in	in	ADP
iajs-2850	64	13	this	this	DET
iajs-2850	64	14	section	section	NOUN
iajs-2850	64	15	,	,	PUNCT
iajs-2850	64	16	we	we	PRON
iajs-2850	64	17	will	will	AUX
iajs-2850	64	18	present	present	VERB
iajs-2850	64	19	the	the	DET
iajs-2850	64	20	sadik	sadik	PROPN
iajs-2850	64	21	transform	transform	NOUN
iajs-2850	64	22	and	and	CCONJ
iajs-2850	64	23	the	the	DET
iajs-2850	64	24	novel	novel	ADJ
iajs-2850	64	25	complex	complex	ADJ
iajs-2850	64	26	transform	transform	NOUN
iajs-2850	64	27	for	for	ADP
iajs-2850	64	28	some	some	DET
iajs-2850	64	29	basic	basic	ADJ
iajs-2850	64	30	functions	function	NOUN
iajs-2850	64	31	in	in	ADP
iajs-2850	64	32	the	the	DET
iajs-2850	64	33	following	follow	VERB
iajs-2850	64	34	table	table	NOUN
iajs-2850	64	35	1	1	NUM
iajs-2850	64	36	:	:	PUNCT
iajs-2850	64	37	table	table	NOUN
iajs-2850	64	38	1	1	NUM
iajs-2850	64	39	:	:	PUNCT
iajs-2850	64	40	sadik	sadik	PROPN
iajs-2850	64	41	transform	transform	NOUN
iajs-2850	64	42	and	and	CCONJ
iajs-2850	64	43	the	the	DET
iajs-2850	64	44	complex	complex	ADJ
iajs-2850	64	45	sadik	sadik	ADJ
iajs-2850	64	46	integral	integral	ADJ
iajs-2850	64	47	transform	transform	NOUN
iajs-2850	64	48	for	for	ADP
iajs-2850	64	49	some	some	DET
iajs-2850	64	50	basic	basic	ADJ
iajs-2850	64	51	functions	function	NOUN
iajs-2850	64	52	functions	function	NOUN
iajs-2850	64	53	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	64	54	)	)	PUNCT
iajs-2850	64	55	𝐒𝑎[𝑔(𝑡	𝐒𝑎[𝑔(𝑡	PROPN
iajs-2850	64	56	)	)	PUNCT
iajs-2850	64	57	]	]	PUNCT
iajs-2850	65	1	=	=	PUNCT
iajs-2850	65	2	𝐅(𝑠	𝐅(𝑠	NUM
iajs-2850	65	3	)	)	PUNCT
iajs-2850	65	4	"	"	PUNCT
iajs-2850	65	5	sadik	sadik	PROPN
iajs-2850	65	6	transform	transform	NOUN
iajs-2850	65	7	"	"	PUNCT
iajs-2850	65	8	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	65	9	𝑐	𝑐	NOUN
iajs-2850	65	10	[	[	NOUN
iajs-2850	65	11	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	65	12	)	)	PUNCT
iajs-2850	65	13	]	]	PUNCT
iajs-2850	66	1	=	=	SYM
iajs-2850	66	2	𝐅𝑐(𝑠	𝐅𝑐(𝑠	NOUN
iajs-2850	66	3	)	)	PUNCT
iajs-2850	66	4	"	"	PUNCT
iajs-2850	66	5	complex	complex	ADJ
iajs-2850	66	6	sadik	sadik	PROPN
iajs-2850	66	7	transform	transform	NOUN
iajs-2850	66	8	"	"	PUNCT
iajs-2850	66	9	𝑡𝑛	𝑡𝑛	NOUN
iajs-2850	66	10	,	,	PUNCT
iajs-2850	66	11	𝑛	𝑛	PRON
iajs-2850	66	12	∈	∈	PROPN
iajs-2850	66	13	ℕ	ℕ	PROPN
iajs-2850	66	14	𝑛	𝑛	PROPN
iajs-2850	66	15	!	!	PUNCT
iajs-2850	66	16	𝑠𝑛𝛼+(𝛼+𝛽	𝑠𝑛𝛼+(𝛼+𝛽	PROPN
iajs-2850	66	17	)	)	PUNCT
iajs-2850	66	18	(	(	PUNCT
iajs-2850	66	19	−𝑖)𝑛+1	−𝑖)𝑛+1	PROPN
iajs-2850	66	20	𝑛	𝑛	PROPN
iajs-2850	66	21	!	!	PUNCT
iajs-2850	66	22	𝑠𝑛𝛼+(𝛼+𝛽	𝑠𝑛𝛼+(𝛼+𝛽	NOUN
iajs-2850	66	23	)	)	PUNCT
iajs-2850	66	24	𝑒𝑎𝑡	𝑒𝑎𝑡	NOUN
iajs-2850	66	25	,	,	PUNCT
iajs-2850	66	26	𝑎	𝑎	PRON
iajs-2850	66	27	constant	constant	ADJ
iajs-2850	66	28	1	1	NUM
iajs-2850	66	29	𝑠𝛽(𝑠𝛼	𝑠𝛽(𝑠𝛼	NOUN
iajs-2850	66	30	−	−	NUM
iajs-2850	66	31	𝑎	𝑎	NOUN
iajs-2850	66	32	)	)	PUNCT
iajs-2850	66	33	−1	−1	NOUN
iajs-2850	66	34	𝑠𝛽	𝑠𝛽	NOUN
iajs-2850	66	35	[	[	PUNCT
iajs-2850	66	36	𝑎	𝑎	X
iajs-2850	66	37	(	(	PUNCT
iajs-2850	66	38	𝑠2𝛼	𝑠2𝛼	NOUN
iajs-2850	66	39	+	+	CCONJ
iajs-2850	66	40	𝑎2	𝑎2	NOUN
iajs-2850	66	41	)	)	PUNCT
iajs-2850	67	1	+	+	CCONJ
iajs-2850	67	2	𝑖	𝑖	VERB
iajs-2850	67	3	𝑠𝛼	𝑠𝛼	PROPN
iajs-2850	67	4	(	(	PUNCT
iajs-2850	67	5	𝑠2𝛼	𝑠2𝛼	PROPN
iajs-2850	67	6	+	+	CCONJ
iajs-2850	67	7	𝑎2	𝑎2	PROPN
iajs-2850	67	8	)	)	PUNCT
iajs-2850	67	9	]	]	PUNCT
iajs-2850	67	10	sin	sin	NOUN
iajs-2850	67	11	(	(	PUNCT
iajs-2850	67	12	𝑎𝑡	𝑎𝑡	X
iajs-2850	67	13	)	)	PUNCT
iajs-2850	67	14	𝑎	𝑎	PROPN
iajs-2850	67	15	𝑠𝛽(𝑠2𝛼	𝑠𝛽(𝑠2𝛼	PROPN
iajs-2850	67	16	+	+	CCONJ
iajs-2850	67	17	𝑎2	𝑎2	PROPN
iajs-2850	67	18	)	)	PUNCT
iajs-2850	68	1	−𝑎	−𝑎	PROPN
iajs-2850	68	2	𝑠𝛽(𝑠2𝛼	𝑠𝛽(𝑠2𝛼	PROPN
iajs-2850	68	3	−	−	PROPN
iajs-2850	68	4	𝑎2	𝑎2	PROPN
iajs-2850	68	5	)	)	PUNCT
iajs-2850	68	6	cos	cos	PROPN
iajs-2850	68	7	(	(	PUNCT
iajs-2850	68	8	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	68	9	)	)	PUNCT
iajs-2850	68	10	𝑠𝛼	𝑠𝛼	PROPN
iajs-2850	68	11	𝑠𝛽(𝑠2𝛼	𝑠𝛽(𝑠2𝛼	PROPN
iajs-2850	68	12	+	+	CCONJ
iajs-2850	68	13	𝑎2	𝑎2	PROPN
iajs-2850	68	14	)	)	PUNCT
iajs-2850	68	15	−𝑖𝑠𝛼	−𝑖𝑠𝛼	PROPN
iajs-2850	68	16	𝑠𝛽(𝑠2𝛼	𝑠𝛽(𝑠2𝛼	PROPN
iajs-2850	69	1	−	−	PROPN
iajs-2850	69	2	𝑎2	𝑎2	PROPN
iajs-2850	69	3	)	)	PUNCT
iajs-2850	69	4	sinh	sinh	NOUN
iajs-2850	69	5	(	(	PUNCT
iajs-2850	69	6	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	69	7	)	)	PUNCT
iajs-2850	69	8	𝑎	𝑎	PROPN
iajs-2850	69	9	𝑠𝛽(𝑠2𝛼	𝑠𝛽(𝑠2𝛼	PROPN
iajs-2850	69	10	−	−	ADP
iajs-2850	69	11	𝑎2	𝑎2	PROPN
iajs-2850	69	12	)	)	PUNCT
iajs-2850	69	13	−𝑎	−𝑎	PROPN
iajs-2850	69	14	𝑠𝛽(𝑠2𝛼	𝑠𝛽(𝑠2𝛼	PROPN
iajs-2850	70	1	+	+	CCONJ
iajs-2850	70	2	𝑎2	𝑎2	PROPN
iajs-2850	70	3	)	)	PUNCT
iajs-2850	70	4	ihjpas	ihjpa	NOUN
iajs-2850	70	5	.	.	PUNCT
iajs-2850	71	1	53	53	NUM
iajs-2850	71	2	(	(	PUNCT
iajs-2850	71	3	3)2022	3)2022	NOUN
iajs-2850	71	4	123	123	NUM
iajs-2850	71	5	cosh	cosh	NOUN
iajs-2850	71	6	(	(	PUNCT
iajs-2850	71	7	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	71	8	)	)	PUNCT
iajs-2850	71	9	𝑠𝛼	𝑠𝛼	PROPN
iajs-2850	71	10	𝑠𝛽(𝑠2𝛼	𝑠𝛽(𝑠2𝛼	PROPN
iajs-2850	71	11	−	−	PROPN
iajs-2850	71	12	𝑎2	𝑎2	PROPN
iajs-2850	71	13	)	)	PUNCT
iajs-2850	71	14	−𝑖𝑠𝛼	−𝑖𝑠𝛼	PROPN
iajs-2850	71	15	𝑠𝛽(𝑠2𝛼	𝑠𝛽(𝑠2𝛼	PROPN
iajs-2850	72	1	+	+	CCONJ
iajs-2850	72	2	𝑎2	𝑎2	PROPN
iajs-2850	72	3	)	)	PUNCT
iajs-2850	72	4	2.2	2.2	NUM
iajs-2850	72	5	.	.	PUNCT
iajs-2850	73	1	the	the	DET
iajs-2850	73	2	inverse	inverse	NOUN
iajs-2850	73	3	of	of	ADP
iajs-2850	73	4	sadik	sadik	ADJ
iajs-2850	73	5	complex	complex	ADJ
iajs-2850	73	6	integral	integral	ADJ
iajs-2850	73	7	transform	transform	NOUN
iajs-2850	73	8	:	:	PUNCT
iajs-2850	73	9	if	if	SCONJ
iajs-2850	73	10	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	73	11	𝑐	𝑐	PROPN
iajs-2850	73	12	{	{	PUNCT
iajs-2850	73	13	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	73	14	)	)	PUNCT
iajs-2850	73	15	}	}	PUNCT
iajs-2850	73	16	=	=	SYM
iajs-2850	73	17	𝐅𝑐(𝑠	𝐅𝑐(𝑠	NOUN
iajs-2850	73	18	)	)	PUNCT
iajs-2850	73	19	is	be	AUX
iajs-2850	73	20	the	the	DET
iajs-2850	73	21	sadik	sadik	PROPN
iajs-2850	73	22	complex	complex	PROPN
iajs-2850	73	23	transform	transform	NOUN
iajs-2850	73	24	,	,	PUNCT
iajs-2850	73	25	then	then	ADV
iajs-2850	73	26	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	73	27	)	)	PUNCT
iajs-2850	74	1	=	=	PUNCT
iajs-2850	74	2	(	(	PUNCT
iajs-2850	74	3	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	74	4	𝑐	𝑐	PROPN
iajs-2850	74	5	)	)	PUNCT
iajs-2850	74	6	−1[𝐅𝑐(𝑠	−1[𝐅𝑐(𝑠	PROPN
iajs-2850	74	7	)	)	PUNCT
iajs-2850	74	8	]	]	PUNCT
iajs-2850	74	9	is	be	AUX
iajs-2850	74	10	said	say	VERB
iajs-2850	74	11	to	to	PART
iajs-2850	74	12	be	be	AUX
iajs-2850	74	13	an	an	DET
iajs-2850	74	14	inverse	inverse	NOUN
iajs-2850	74	15	of	of	ADP
iajs-2850	74	16	the	the	DET
iajs-2850	74	17	sadik	sadik	PROPN
iajs-2850	74	18	complex	complex	PROPN
iajs-2850	74	19	transform	transform	NOUN
iajs-2850	74	20	.	.	PUNCT
iajs-2850	75	1	in	in	ADP
iajs-2850	75	2	this	this	DET
iajs-2850	75	3	section	section	NOUN
iajs-2850	75	4	,	,	PUNCT
iajs-2850	75	5	we	we	PRON
iajs-2850	75	6	present	present	VERB
iajs-2850	75	7	the	the	DET
iajs-2850	75	8	inverse	inverse	NOUN
iajs-2850	75	9	of	of	ADP
iajs-2850	75	10	sadik	sadik	ADJ
iajs-2850	75	11	complex	complex	ADJ
iajs-2850	75	12	integral	integral	ADJ
iajs-2850	75	13	transform	transform	NOUN
iajs-2850	75	14	of	of	ADP
iajs-2850	75	15	simple	simple	ADJ
iajs-2850	75	16	functions	function	NOUN
iajs-2850	75	17	:	:	PUNCT
iajs-2850	75	18	1	1	NUM
iajs-2850	75	19	(	(	PUNCT
iajs-2850	75	20	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	75	21	𝑐	𝑐	NOUN
iajs-2850	75	22	)	)	PUNCT
iajs-2850	75	23	−1	−1	NOUN
iajs-2850	76	1	[	[	X
iajs-2850	76	2	(	(	PUNCT
iajs-2850	76	3	−𝑖)𝑛+1	−𝑖)𝑛+1	PROPN
iajs-2850	76	4	𝑛	𝑛	PROPN
iajs-2850	76	5	!	!	PUNCT
iajs-2850	76	6	𝑠𝑛𝛼+(𝛼+𝛽	𝑠𝑛𝛼+(𝛼+𝛽	PROPN
iajs-2850	76	7	)	)	PUNCT
iajs-2850	76	8	]	]	PUNCT
iajs-2850	76	9	=	=	SYM
iajs-2850	76	10	𝑡𝑛.	𝑡𝑛.	ADJ
iajs-2850	76	11	2	2	NUM
iajs-2850	76	12	(	(	PUNCT
iajs-2850	76	13	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	76	14	𝑐	𝑐	NOUN
iajs-2850	76	15	)	)	PUNCT
iajs-2850	76	16	−1	−1	NOUN
iajs-2850	76	17	[	[	PUNCT
iajs-2850	76	18	−1	−1	NOUN
iajs-2850	76	19	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	76	20	[	[	PUNCT
iajs-2850	76	21	𝑎	𝑎	PROPN
iajs-2850	76	22	(	(	PUNCT
iajs-2850	76	23	𝑠2𝛼+𝑎2	𝑠2𝛼+𝑎2	NOUN
iajs-2850	76	24	)	)	PUNCT
iajs-2850	76	25	+	+	CCONJ
iajs-2850	76	26	𝑖	𝑖	VERB
iajs-2850	76	27	𝑠𝛼	𝑠𝛼	PROPN
iajs-2850	76	28	(	(	PUNCT
iajs-2850	76	29	𝑠2𝛼+𝑎2	𝑠2𝛼+𝑎2	NOUN
iajs-2850	76	30	)	)	PUNCT
iajs-2850	76	31	]	]	PUNCT
iajs-2850	76	32	]	]	X
iajs-2850	76	33	=	=	SYM
iajs-2850	76	34	𝑒𝑎𝑡.	𝑒𝑎𝑡.	X
iajs-2850	76	35	3	3	NUM
iajs-2850	76	36	(	(	PUNCT
iajs-2850	76	37	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	76	38	𝑐	𝑐	NOUN
iajs-2850	76	39	)	)	PUNCT
iajs-2850	76	40	−1	−1	NOUN
iajs-2850	76	41	[	[	PUNCT
iajs-2850	76	42	−𝑎	−𝑎	NOUN
iajs-2850	76	43	𝑠𝛽(𝑠2𝛼−𝑎2	𝑠𝛽(𝑠2𝛼−𝑎2	NOUN
iajs-2850	76	44	)	)	PUNCT
iajs-2850	76	45	]	]	PUNCT
iajs-2850	76	46	=	=	PUNCT
iajs-2850	76	47	sin	sin	NOUN
iajs-2850	76	48	(	(	PUNCT
iajs-2850	76	49	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	76	50	)	)	PUNCT
iajs-2850	76	51	.	.	PUNCT
iajs-2850	77	1	4	4	NUM
iajs-2850	77	2	(	(	PUNCT
iajs-2850	77	3	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	77	4	𝑐	𝑐	NOUN
iajs-2850	77	5	)	)	PUNCT
iajs-2850	77	6	−1	−1	NOUN
iajs-2850	77	7	[	[	PUNCT
iajs-2850	77	8	−𝑖𝑠𝛼	−𝑖𝑠𝛼	X
iajs-2850	77	9	𝑠𝛽(𝑠2𝛼−𝑎2	𝑠𝛽(𝑠2𝛼−𝑎2	X
iajs-2850	77	10	)	)	PUNCT
iajs-2850	77	11	]	]	PUNCT
iajs-2850	78	1	=	=	PUNCT
iajs-2850	78	2	cos	cos	X
iajs-2850	78	3	(	(	PUNCT
iajs-2850	78	4	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	78	5	)	)	PUNCT
iajs-2850	78	6	.	.	PUNCT
iajs-2850	79	1	5	5	NUM
iajs-2850	79	2	(	(	PUNCT
iajs-2850	79	3	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	79	4	𝑐	𝑐	NOUN
iajs-2850	79	5	)	)	PUNCT
iajs-2850	79	6	−1	−1	NOUN
iajs-2850	79	7	[	[	PUNCT
iajs-2850	79	8	−𝑎	−𝑎	PROPN
iajs-2850	79	9	𝑠𝛽(𝑠2𝛼+𝑎2	𝑠𝛽(𝑠2𝛼+𝑎2	PROPN
iajs-2850	79	10	)	)	PUNCT
iajs-2850	79	11	]	]	PUNCT
iajs-2850	80	1	=	=	PUNCT
iajs-2850	80	2	sinh	sinh	NOUN
iajs-2850	80	3	(	(	PUNCT
iajs-2850	80	4	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	80	5	)	)	PUNCT
iajs-2850	80	6	6	6	NUM
iajs-2850	80	7	(	(	PUNCT
iajs-2850	80	8	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	80	9	𝑐	𝑐	NOUN
iajs-2850	80	10	)	)	PUNCT
iajs-2850	80	11	−1	−1	NOUN
iajs-2850	80	12	[	[	PUNCT
iajs-2850	80	13	−𝑖𝑠𝛼	−𝑖𝑠𝛼	NOUN
iajs-2850	80	14	𝑠𝛽(𝑠2𝛼+𝑎2	𝑠𝛽(𝑠2𝛼+𝑎2	PROPN
iajs-2850	80	15	)	)	PUNCT
iajs-2850	80	16	]	]	PUNCT
iajs-2850	81	1	=	=	PUNCT
iajs-2850	81	2	cosh	cosh	NOUN
iajs-2850	81	3	(	(	PUNCT
iajs-2850	81	4	𝑎𝑡	𝑎𝑡	PROPN
iajs-2850	81	5	)	)	PUNCT
iajs-2850	81	6	3	3	NUM
iajs-2850	81	7	.	.	PUNCT
iajs-2850	81	8	complex	complex	ADJ
iajs-2850	81	9	sadik	sadik	ADJ
iajs-2850	81	10	integral	integral	ADJ
iajs-2850	81	11	transform	transform	NOUN
iajs-2850	81	12	of	of	ADP
iajs-2850	81	13	derivatives	derivative	NOUN
iajs-2850	81	14	:	:	PUNCT
iajs-2850	81	15	let	let	VERB
iajs-2850	81	16	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-2850	81	17	)	)	PUNCT
iajs-2850	81	18	be	be	AUX
iajs-2850	81	19	a	a	DET
iajs-2850	81	20	continuous	continuous	ADJ
iajs-2850	81	21	function	function	NOUN
iajs-2850	81	22	and	and	CCONJ
iajs-2850	81	23	piecewise	piecewise	NOUN
iajs-2850	81	24	continuous	continuous	ADJ
iajs-2850	81	25	on	on	ADP
iajs-2850	81	26	any	any	DET
iajs-2850	81	27	interval	interval	NOUN
iajs-2850	81	28	,	,	PUNCT
iajs-2850	81	29	then	then	ADV
iajs-2850	81	30	the	the	DET
iajs-2850	81	31	complex	complex	ADJ
iajs-2850	81	32	sadik	sadik	ADJ
iajs-2850	81	33	transform	transform	NOUN
iajs-2850	81	34	of	of	ADP
iajs-2850	81	35	first	first	ADJ
iajs-2850	81	36	derivative	derivative	NOUN
iajs-2850	81	37	of	of	ADP
iajs-2850	81	38	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-2850	81	39	)	)	PUNCT
iajs-2850	81	40	is	be	AUX
iajs-2850	81	41	given	give	VERB
iajs-2850	81	42	by	by	ADP
iajs-2850	81	43	:	:	PUNCT
iajs-2850	81	44	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	81	45	𝑐	𝑐	PROPN
iajs-2850	81	46	[	[	NOUN
iajs-2850	81	47	𝑓′(𝑡	𝑓′(𝑡	NOUN
iajs-2850	81	48	)	)	PUNCT
iajs-2850	81	49	]	]	PUNCT
iajs-2850	82	1	=	=	PUNCT
iajs-2850	82	2	1	1	NUM
iajs-2850	82	3	𝑠𝛽	𝑠𝛽	NUM
iajs-2850	82	4	∫	∫	PROPN
iajs-2850	82	5	  	  	SPACE
iajs-2850	82	6	∞	∞	PROPN
iajs-2850	82	7	0	0	NUM
iajs-2850	83	1	𝑓′(𝑡)𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	𝑓′(𝑡)𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	PROPN
iajs-2850	83	2	,	,	PUNCT
iajs-2850	83	3	integrating	integrate	VERB
iajs-2850	83	4	by	by	ADP
iajs-2850	83	5	parts	part	NOUN
iajs-2850	83	6	.	.	PUNCT
iajs-2850	84	1	let	let	VERB
iajs-2850	84	2	𝑢	𝑢	X
iajs-2850	84	3	=	=	SYM
iajs-2850	84	4	𝑒−𝑖𝑠𝛼𝑡	𝑒−𝑖𝑠𝛼𝑡	PROPN
iajs-2850	84	5	,	,	PUNCT
iajs-2850	84	6	𝑑𝑣	𝑑𝑣	PROPN
iajs-2850	84	7	=	=	NOUN
iajs-2850	84	8	𝑓′(𝑡)𝑑𝑡	𝑓′(𝑡)𝑑𝑡	PROPN
iajs-2850	84	9	𝑑𝑢	𝑑𝑢	ADJ
iajs-2850	84	10	=	=	SYM
iajs-2850	84	11	−𝑖𝑠𝛼𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	−𝑖𝑠𝛼𝑒−𝑖𝑠𝛼𝑡𝑑𝑡	PROPN
iajs-2850	84	12	,	,	PUNCT
iajs-2850	84	13	𝑣	𝑣	X
iajs-2850	84	14	=	=	PUNCT
iajs-2850	84	15	𝑓(𝑡	𝑓(𝑡	PROPN
iajs-2850	84	16	)	)	PUNCT
iajs-2850	84	17	1	1	NUM
iajs-2850	84	18	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	84	19	[	[	X
iajs-2850	84	20	−𝑓(0	−𝑓(0	NOUN
iajs-2850	84	21	)	)	PUNCT
iajs-2850	85	1	+	+	CCONJ
iajs-2850	86	1	𝑖𝑠𝛼	𝑖𝑠𝛼	ADJ
iajs-2850	86	2	∫	∫	PROPN
iajs-2850	86	3	  	  	SPACE
iajs-2850	86	4	∞	∞	PROPN
iajs-2850	86	5	0	0	NUM
iajs-2850	86	6	  	  	SPACE
iajs-2850	86	7	𝑒−𝑖𝑠𝛼𝑡𝑓(𝑡)𝑑𝑡	𝑒−𝑖𝑠𝛼𝑡𝑓(𝑡)𝑑𝑡	PRON
iajs-2850	86	8	]	]	PUNCT
iajs-2850	86	9	−𝑓(0	−𝑓(0	NOUN
iajs-2850	86	10	)	)	PUNCT
iajs-2850	86	11	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	87	1	+	+	CCONJ
iajs-2850	87	2	𝑖𝑠𝛼	𝑖𝑠𝛼	PROPN
iajs-2850	87	3	1	1	NUM
iajs-2850	87	4	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	87	5	∫	∫	PROPN
iajs-2850	87	6	  	  	SPACE
iajs-2850	87	7	∞	∞	PROPN
iajs-2850	87	8	0	0	NUM
iajs-2850	87	9	  	  	SPACE
iajs-2850	87	10	𝑒−𝑖𝑠𝛼𝑡𝑓(𝑡)𝑑𝑡	𝑒−𝑖𝑠𝛼𝑡𝑓(𝑡)𝑑𝑡	PROPN
iajs-2850	87	11	−𝑓(0	−𝑓(0	PROPN
iajs-2850	87	12	)	)	PUNCT
iajs-2850	87	13	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	88	1	+	+	CCONJ
iajs-2850	88	2	𝑖𝑠𝛼𝐒𝑎	𝑖𝑠𝛼𝐒𝑎	PUNCT
iajs-2850	88	3	𝑐	𝑐	NOUN
iajs-2850	89	1	[	[	X
iajs-2850	89	2	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-2850	89	3	)	)	PUNCT
iajs-2850	89	4	]	]	PUNCT
iajs-2850	90	1	𝐒𝑎	𝐒𝑎	NOUN
iajs-2850	90	2	𝑐	𝑐	NOUN
iajs-2850	90	3	[	[	NOUN
iajs-2850	90	4	𝑓′(𝑡	𝑓′(𝑡	NOUN
iajs-2850	90	5	)	)	PUNCT
iajs-2850	90	6	]	]	PUNCT
iajs-2850	91	1	=	=	PUNCT
iajs-2850	91	2	1	1	NUM
iajs-2850	91	3	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	91	4	[	[	X
iajs-2850	91	5	−𝑓(0	−𝑓(0	NOUN
iajs-2850	91	6	)	)	PUNCT
iajs-2850	92	1	+	+	CCONJ
iajs-2850	92	2	𝑖𝑠𝛼	𝑖𝑠𝛼	ADJ
iajs-2850	92	3	∫	∫	PROPN
iajs-2850	92	4	  	  	SPACE
iajs-2850	92	5	∞	∞	PROPN
iajs-2850	92	6	0	0	NUM
iajs-2850	92	7	  	  	SPACE
iajs-2850	92	8	𝑒−𝑖𝑠𝛼𝑡𝑓(𝑡)𝑑𝑡	𝑒−𝑖𝑠𝛼𝑡𝑓(𝑡)𝑑𝑡	PRON
iajs-2850	92	9	]	]	PUNCT
iajs-2850	92	10	,	,	PUNCT
iajs-2850	92	11	or	or	CCONJ
iajs-2850	92	12	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	92	13	𝑐	𝑐	PROPN
iajs-2850	92	14	[	[	NOUN
iajs-2850	92	15	𝑓′(𝑡	𝑓′(𝑡	NOUN
iajs-2850	92	16	)	)	PUNCT
iajs-2850	92	17	]	]	PUNCT
iajs-2850	93	1	=	=	PUNCT
iajs-2850	93	2	𝑖𝑠𝛼𝐅𝑐(𝑠	𝑖𝑠𝛼𝐅𝑐(𝑠	ADJ
iajs-2850	93	3	)	)	PUNCT
iajs-2850	93	4	−	−	PROPN
iajs-2850	94	1	𝑓(0	𝑓(0	NOUN
iajs-2850	94	2	)	)	PUNCT
iajs-2850	94	3	𝑠𝛽	𝑠𝛽	ADP
iajs-2850	94	4	therefore	therefore	ADV
iajs-2850	94	5	,	,	PUNCT
iajs-2850	94	6	when	when	SCONJ
iajs-2850	94	7	substituted	substitute	VERB
iajs-2850	94	8	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-2850	94	9	)	)	PUNCT
iajs-2850	94	10	by	by	ADP
iajs-2850	94	11	𝑓′(𝑡	𝑓′(𝑡	NOUN
iajs-2850	94	12	)	)	PUNCT
iajs-2850	94	13	and	and	CCONJ
iajs-2850	94	14	𝑓′(𝑡	𝑓′(𝑡	VERB
iajs-2850	94	15	)	)	PUNCT
iajs-2850	94	16	by	by	ADP
iajs-2850	94	17	𝑓′′(𝑡	𝑓′′(𝑡	NOUN
iajs-2850	94	18	)	)	PUNCT
iajs-2850	94	19	,	,	PUNCT
iajs-2850	94	20	we	we	PRON
iajs-2850	94	21	get	get	VERB
iajs-2850	94	22	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	94	23	𝑐	𝑐	NOUN
iajs-2850	94	24	[	[	NOUN
iajs-2850	94	25	𝑓′′(𝑡	𝑓′′(𝑡	NOUN
iajs-2850	94	26	)	)	PUNCT
iajs-2850	94	27	]	]	PUNCT
iajs-2850	95	1	=	=	PUNCT
iajs-2850	95	2	(	(	PUNCT
iajs-2850	95	3	𝑖𝑠𝛼)2𝐅𝑐(𝑠	𝑖𝑠𝛼)2𝐅𝑐(𝑠	NUM
iajs-2850	95	4	)	)	PUNCT
iajs-2850	95	5	−	−	PROPN
iajs-2850	95	6	𝑓′(0	𝑓′(0	NOUN
iajs-2850	95	7	)	)	PUNCT
iajs-2850	95	8	𝑠𝛽	𝑠𝛽	ADP
iajs-2850	95	9	−	−	PROPN
iajs-2850	95	10	𝑖𝑠𝛼𝑓(0	𝑖𝑠𝛼𝑓(0	PROPN
iajs-2850	95	11	)	)	PUNCT
iajs-2850	95	12	𝑠𝛽	𝑠𝛽	ADP
iajs-2850	95	13	similarly	similarly	ADV
iajs-2850	95	14	,	,	PUNCT
iajs-2850	95	15	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	95	16	𝑐	𝑐	PROPN
iajs-2850	95	17	[	[	NOUN
iajs-2850	95	18	𝑓′′′(𝑡	𝑓′′′(𝑡	NOUN
iajs-2850	95	19	)	)	PUNCT
iajs-2850	95	20	]	]	PUNCT
iajs-2850	96	1	=	=	PUNCT
iajs-2850	96	2	(	(	PUNCT
iajs-2850	96	3	𝑖𝑠𝛼)3𝐅𝑐(𝑠	𝑖𝑠𝛼)3𝐅𝑐(𝑠	NUM
iajs-2850	96	4	)	)	PUNCT
iajs-2850	96	5	−	−	PROPN
iajs-2850	97	1	1	1	NUM
iajs-2850	97	2	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	97	3	[	[	X
iajs-2850	97	4	𝑓′′(0	𝑓′′(0	NOUN
iajs-2850	97	5	)	)	PUNCT
iajs-2850	98	1	+	+	NOUN
iajs-2850	98	2	𝑖𝑠𝛼𝑓′(0	𝑖𝑠𝛼𝑓′(0	NOUN
iajs-2850	98	3	)	)	PUNCT
iajs-2850	99	1	+	+	CCONJ
iajs-2850	99	2	(	(	PUNCT
iajs-2850	99	3	𝑖𝑠𝛼)2𝑓(0	𝑖𝑠𝛼)2𝑓(0	NUM
iajs-2850	99	4	)	)	PUNCT
iajs-2850	99	5	]	]	PUNCT
iajs-2850	99	6	.	.	PUNCT
iajs-2850	100	1	in	in	ADP
iajs-2850	100	2	general	general	ADJ
iajs-2850	100	3	:	:	PUNCT
iajs-2850	100	4	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	100	5	𝑐	𝑐	PROPN
iajs-2850	100	6	[	[	X
iajs-2850	100	7	𝑓(𝑛)(𝑡	𝑓(𝑛)(𝑡	NUM
iajs-2850	100	8	)	)	PUNCT
iajs-2850	100	9	]	]	PUNCT
iajs-2850	101	1	=	=	PUNCT
iajs-2850	101	2	(	(	PUNCT
iajs-2850	101	3	𝑖𝑠𝛼)𝑛𝐅𝑐(𝑠	𝑖𝑠𝛼)𝑛𝐅𝑐(𝑠	NOUN
iajs-2850	101	4	)	)	PUNCT
iajs-2850	101	5	−	−	PROPN
iajs-2850	102	1	1	1	NUM
iajs-2850	102	2	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	102	3	[	[	X
iajs-2850	102	4	𝑓(𝑛−1)(0	𝑓(𝑛−1)(0	ADV
iajs-2850	102	5	)	)	PUNCT
iajs-2850	102	6	+	+	CCONJ
iajs-2850	102	7	𝑖𝑠𝛼𝑓(𝑛−2)(0	𝑖𝑠𝛼𝑓(𝑛−2)(0	X
iajs-2850	102	8	)	)	PUNCT
iajs-2850	102	9	+	+	CCONJ
iajs-2850	102	10	(	(	PUNCT
iajs-2850	102	11	𝑖𝑠𝛼)2𝑓(𝑛−3)(0	𝑖𝑠𝛼)2𝑓(𝑛−3)(0	ADV
iajs-2850	102	12	)	)	PUNCT
iajs-2850	102	13	+	+	CCONJ
iajs-2850	102	14	⋯	⋯	VERB
iajs-2850	102	15	+	+	CCONJ
iajs-2850	102	16	(	(	PUNCT
iajs-2850	102	17	𝑖𝑠𝛼)𝑛−2𝑓′(0	𝑖𝑠𝛼)𝑛−2𝑓′(0	NOUN
iajs-2850	102	18	)	)	PUNCT
iajs-2850	102	19	+	+	CCONJ
iajs-2850	102	20	(	(	PUNCT
iajs-2850	102	21	𝑖𝑠𝛼)𝑛−1𝑓(0	𝑖𝑠𝛼)𝑛−1𝑓(0	ADJ
iajs-2850	102	22	)	)	PUNCT
iajs-2850	102	23	]	]	PUNCT
iajs-2850	102	24	ihjpas	ihjpa	VERB
iajs-2850	102	25	.	.	PUNCT
iajs-2850	103	1	53	53	NUM
iajs-2850	103	2	(	(	PUNCT
iajs-2850	103	3	3)2022	3)2022	NOUN
iajs-2850	103	4	124	124	NUM
iajs-2850	103	5	or	or	CCONJ
iajs-2850	103	6	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	103	7	𝑐	𝑐	PROPN
iajs-2850	103	8	[	[	X
iajs-2850	103	9	𝑓(𝑛(𝑡	𝑓(𝑛(𝑡	NOUN
iajs-2850	103	10	)	)	PUNCT
iajs-2850	103	11	]	]	PUNCT
iajs-2850	104	1	=	=	PUNCT
iajs-2850	104	2	(	(	PUNCT
iajs-2850	104	3	𝑖𝑠𝛼)𝑛𝐅𝑐(𝑠	𝑖𝑠𝛼)𝑛𝐅𝑐(𝑠	NOUN
iajs-2850	104	4	)	)	PUNCT
iajs-2850	104	5	−	−	PROPN
iajs-2850	105	1	1	1	NUM
iajs-2850	105	2	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	105	3	[	[	X
iajs-2850	105	4	∑𝑘=1	∑𝑘=1	NOUN
iajs-2850	105	5	𝑛	𝑛	VERB
iajs-2850	105	6	 	 	SPACE
iajs-2850	105	7	(	(	PUNCT
iajs-2850	105	8	𝑖𝑠𝛼)𝑘−1𝑓(𝑛−𝑘)(0	𝑖𝑠𝛼)𝑘−1𝑓(𝑛−𝑘)(0	PROPN
iajs-2850	105	9	)	)	PUNCT
iajs-2850	105	10	]	]	PUNCT
iajs-2850	105	11	.	.	PUNCT
iajs-2850	106	1	theorem	theorem	VERB
iajs-2850	106	2	3.1	3.1	NUM
iajs-2850	106	3	.	.	PUNCT
iajs-2850	107	1	let	let	AUX
iajs-2850	107	2	𝐅𝑐(𝑠	𝐅𝑐(𝑠	NOUN
iajs-2850	107	3	)	)	PUNCT
iajs-2850	107	4	be	be	VERB
iajs-2850	107	5	the	the	DET
iajs-2850	107	6	complex	complex	ADJ
iajs-2850	107	7	sadik	sadik	ADJ
iajs-2850	107	8	integral	integral	ADJ
iajs-2850	107	9	transform	transform	NOUN
iajs-2850	107	10	of	of	ADP
iajs-2850	107	11	𝑓(𝑡)(𝐅𝑐(𝑠	𝑓(𝑡)(𝐅𝑐(𝑠	NOUN
iajs-2850	107	12	)	)	PUNCT
iajs-2850	107	13	=	=	SYM
iajs-2850	108	1	𝐒𝑎	𝐒𝑎	NOUN
iajs-2850	108	2	𝑐	𝑐	PROPN
iajs-2850	108	3	[	[	X
iajs-2850	108	4	𝑓(𝑡	𝑓(𝑡	PROPN
iajs-2850	108	5	)	)	PUNCT
iajs-2850	108	6	]	]	PUNCT
iajs-2850	108	7	)	)	PUNCT
iajs-2850	108	8	,	,	PUNCT
iajs-2850	108	9	then	then	ADV
iajs-2850	108	10	:	:	PUNCT
iajs-2850	108	11	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	108	12	𝑐	𝑐	PROPN
iajs-2850	108	13	[	[	X
iajs-2850	108	14	𝑓(𝑛)(𝑡	𝑓(𝑛)(𝑡	NUM
iajs-2850	108	15	)	)	PUNCT
iajs-2850	108	16	]	]	PUNCT
iajs-2850	109	1	=	=	PUNCT
iajs-2850	109	2	(	(	PUNCT
iajs-2850	109	3	𝑖𝑠𝛼)𝑛𝐅𝑐(𝑠	𝑖𝑠𝛼)𝑛𝐅𝑐(𝑠	NOUN
iajs-2850	109	4	)	)	PUNCT
iajs-2850	109	5	−	−	PROPN
iajs-2850	110	1	1	1	NUM
iajs-2850	110	2	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	110	3	[	[	X
iajs-2850	110	4	∑	∑	INTJ
iajs-2850	110	5	  	  	SPACE
iajs-2850	110	6	𝑛	𝑛	PRON
iajs-2850	110	7	𝑘=1	𝑘=1	ADJ
iajs-2850	110	8	  	  	SPACE
iajs-2850	110	9	(	(	PUNCT
iajs-2850	110	10	𝑖𝑠𝛼)𝑘−1𝑓(𝑛−𝑘)(0	𝑖𝑠𝛼)𝑘−1𝑓(𝑛−𝑘)(0	PROPN
iajs-2850	110	11	)	)	PUNCT
iajs-2850	110	12	]	]	PUNCT
iajs-2850	110	13	.	.	PUNCT
iajs-2850	111	1	proof	proof	NOUN
iajs-2850	111	2	.	.	PUNCT
iajs-2850	112	1	by	by	ADP
iajs-2850	112	2	mathematical	mathematical	ADJ
iajs-2850	112	3	induction	induction	NOUN
iajs-2850	112	4	1	1	NUM
iajs-2850	112	5	for	for	ADP
iajs-2850	112	6	𝑛	𝑛	NOUN
iajs-2850	112	7	=	=	SYM
iajs-2850	112	8	1	1	NUM
iajs-2850	112	9	,	,	PUNCT
iajs-2850	112	10	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	112	11	𝑐	𝑐	NOUN
iajs-2850	112	12	[	[	NOUN
iajs-2850	112	13	𝑓′(𝑡	𝑓′(𝑡	NOUN
iajs-2850	112	14	)	)	PUNCT
iajs-2850	112	15	]	]	PUNCT
iajs-2850	113	1	=	=	PUNCT
iajs-2850	113	2	𝑖𝑠𝛼𝐅𝑐(𝑠	𝑖𝑠𝛼𝐅𝑐(𝑠	ADJ
iajs-2850	113	3	)	)	PUNCT
iajs-2850	113	4	−	−	PROPN
iajs-2850	114	1	𝑓(0	𝑓(0	NOUN
iajs-2850	114	2	)	)	PUNCT
iajs-2850	115	1	𝑠𝛽	𝑠𝛽	ADP
iajs-2850	115	2	thus	thus	ADV
iajs-2850	115	3	true	true	ADJ
iajs-2850	115	4	for	for	ADP
iajs-2850	115	5	𝑛	𝑛	NOUN
iajs-2850	115	6	=	=	SYM
iajs-2850	115	7	1	1	NUM
iajs-2850	115	8	.	.	NOUN
iajs-2850	115	9	2	2	NUM
iajs-2850	115	10	.	.	X
iajs-2850	115	11	assume	assume	VERB
iajs-2850	115	12	that	that	SCONJ
iajs-2850	115	13	,	,	PUNCT
iajs-2850	115	14	true	true	ADJ
iajs-2850	115	15	for	for	ADP
iajs-2850	115	16	𝑛	𝑛	PROPN
iajs-2850	115	17	=	=	SYM
iajs-2850	115	18	𝑚	𝑚	PROPN
iajs-2850	115	19	that	that	PRON
iajs-2850	115	20	means	mean	VERB
iajs-2850	115	21	:	:	PUNCT
iajs-2850	115	22	𝐒𝑎	𝐒𝑎	PART
iajs-2850	115	23	𝑐	𝑐	PROPN
iajs-2850	115	24	[	[	X
iajs-2850	115	25	𝑓(𝑚)(𝑡	𝑓(𝑚)(𝑡	NUM
iajs-2850	115	26	)	)	PUNCT
iajs-2850	115	27	]	]	PUNCT
iajs-2850	116	1	=	=	PUNCT
iajs-2850	116	2	(	(	PUNCT
iajs-2850	116	3	𝑖𝑠𝛼)𝑚𝐅𝑐(𝑠	𝑖𝑠𝛼)𝑚𝐅𝑐(𝑠	NOUN
iajs-2850	116	4	)	)	PUNCT
iajs-2850	116	5	−	−	PROPN
iajs-2850	117	1	1	1	NUM
iajs-2850	117	2	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	118	1	[	[	X
iajs-2850	118	2	∑	∑	INTJ
iajs-2850	118	3	  	  	SPACE
iajs-2850	118	4	𝑚	𝑚	NOUN
iajs-2850	118	5	𝑘=1	𝑘=1	NOUN
iajs-2850	118	6	  	  	SPACE
iajs-2850	118	7	(	(	PUNCT
iajs-2850	118	8	𝑖𝑠𝛼)𝑘−1𝑓(𝑚−𝑘)(0	𝑖𝑠𝛼)𝑘−1𝑓(𝑚−𝑘)(0	PROPN
iajs-2850	118	9	)	)	PUNCT
iajs-2850	118	10	]	]	PUNCT
iajs-2850	119	1	3	3	NUM
iajs-2850	119	2	we	we	PRON
iajs-2850	119	3	want	want	VERB
iajs-2850	119	4	to	to	PART
iajs-2850	119	5	prove	prove	VERB
iajs-2850	119	6	for	for	ADP
iajs-2850	119	7	𝑛	𝑛	NOUN
iajs-2850	119	8	=	=	SYM
iajs-2850	119	9	𝑚	𝑚	PROPN
iajs-2850	119	10	+	+	NOUN
iajs-2850	119	11	1	1	NUM
iajs-2850	119	12	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	119	13	𝑐	𝑐	NOUN
iajs-2850	119	14	[	[	X
iajs-2850	119	15	𝑓(𝑚+1)(𝑡	𝑓(𝑚+1)(𝑡	X
iajs-2850	119	16	)	)	PUNCT
iajs-2850	119	17	]	]	PUNCT
iajs-2850	120	1	=	=	PUNCT
iajs-2850	120	2	𝐒𝑎	𝐒𝑎	NOUN
iajs-2850	120	3	𝑐	𝑐	PROPN
iajs-2850	120	4	[	[	X
iajs-2850	120	5	(	(	PUNCT
iajs-2850	120	6	𝑓(𝑚)(𝑡	𝑓(𝑚)(𝑡	NUM
iajs-2850	120	7	)	)	PUNCT
iajs-2850	120	8	)	)	PUNCT
iajs-2850	121	1	′	′	NUM
iajs-2850	121	2	]	]	PUNCT
iajs-2850	122	1	=	=	PUNCT
iajs-2850	122	2	𝑖𝑠𝛼𝐒𝑎	𝑖𝑠𝛼𝐒𝑎	PUNCT
iajs-2850	122	3	𝑐	𝑐	PUNCT
iajs-2850	123	1	[	[	X
iajs-2850	123	2	𝑓(𝑚)(𝑡	𝑓(𝑚)(𝑡	NUM
iajs-2850	123	3	)	)	PUNCT
iajs-2850	123	4	]	]	PUNCT
iajs-2850	124	1	−	−	PROPN
iajs-2850	124	2	1	1	NUM
iajs-2850	124	3	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	124	4	[	[	X
iajs-2850	124	5	𝑓(𝑚)(0	𝑓(𝑚)(0	NUM
iajs-2850	124	6	)	)	PUNCT
iajs-2850	124	7	]	]	PUNCT
iajs-2850	124	8	,	,	PUNCT
iajs-2850	124	9	=	=	PUNCT
iajs-2850	125	1	𝑖𝑠𝛼𝐒𝑎	𝑖𝑠𝛼𝐒𝑎	PUNCT
iajs-2850	125	2	𝑐	𝑐	NOUN
iajs-2850	126	1	[	[	X
iajs-2850	126	2	𝑓(𝑚)(𝑡	𝑓(𝑚)(𝑡	NUM
iajs-2850	126	3	)	)	PUNCT
iajs-2850	126	4	]	]	PUNCT
iajs-2850	126	5	−	−	PROPN
iajs-2850	126	6	𝑓(𝑚)(0	𝑓(𝑚)(0	PROPN
iajs-2850	126	7	)	)	PUNCT
iajs-2850	126	8	𝑠𝛽	𝑠𝛽	NOUN
iajs-2850	126	9	,	,	PUNCT
iajs-2850	126	10	=	=	PUNCT
iajs-2850	126	11	𝑖𝑠𝛼	𝑖𝑠𝛼	PROPN
iajs-2850	127	1	[	[	X
iajs-2850	127	2	(	(	PUNCT
iajs-2850	127	3	𝑖𝑠𝛼)𝑚𝐅𝑐(𝑠	𝑖𝑠𝛼)𝑚𝐅𝑐(𝑠	NOUN
iajs-2850	127	4	)	)	PUNCT
iajs-2850	127	5	−	−	PROPN
iajs-2850	127	6	1	1	NUM
iajs-2850	127	7	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	128	1	[	[	X
iajs-2850	128	2	∑	∑	INTJ
iajs-2850	128	3	  	  	SPACE
iajs-2850	128	4	𝑚	𝑚	NOUN
iajs-2850	128	5	𝑘=1	𝑘=1	NOUN
iajs-2850	128	6	  	  	SPACE
iajs-2850	128	7	(	(	PUNCT
iajs-2850	128	8	𝑖𝑠𝛼)𝑘−1𝑓(𝑚−𝑘)(0	𝑖𝑠𝛼)𝑘−1𝑓(𝑚−𝑘)(0	PROPN
iajs-2850	128	9	)	)	PUNCT
iajs-2850	128	10	]	]	X
iajs-2850	128	11	]	]	X
iajs-2850	128	12	−	−	PUNCT
iajs-2850	128	13	𝑓(𝑚	𝑓(𝑚	NOUN
iajs-2850	128	14	)	)	PUNCT
iajs-2850	128	15	𝑠	𝑠	PROPN
iajs-2850	128	16	(	(	PUNCT
iajs-2850	128	17	0	0	NUM
iajs-2850	128	18	)	)	PUNCT
iajs-2850	128	19	]	]	PUNCT
iajs-2850	129	1	=	=	PUNCT
iajs-2850	129	2	(	(	PUNCT
iajs-2850	129	3	𝑖𝑠𝛼)𝑚+1𝐅𝑐(𝑠	𝑖𝑠𝛼)𝑚+1𝐅𝑐(𝑠	NOUN
iajs-2850	129	4	)	)	PUNCT
iajs-2850	129	5	−	−	PROPN
iajs-2850	129	6	1	1	NUM
iajs-2850	129	7	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	129	8	[	[	X
iajs-2850	129	9	∑	∑	INTJ
iajs-2850	129	10	  	  	SPACE
iajs-2850	129	11	𝑚	𝑚	NOUN
iajs-2850	129	12	𝑘=1	𝑘=1	NOUN
iajs-2850	129	13	  	  	SPACE
iajs-2850	129	14	(	(	PUNCT
iajs-2850	129	15	𝑖𝑠𝛼)𝑘𝑓(𝑚−𝑘)(0	𝑖𝑠𝛼)𝑘𝑓(𝑚−𝑘)(0	ADJ
iajs-2850	129	16	)	)	PUNCT
iajs-2850	129	17	]	]	PUNCT
iajs-2850	129	18	]	]	X
iajs-2850	129	19	−	−	PROPN
iajs-2850	129	20	𝑓(𝑚)(0	𝑓(𝑚)(0	NUM
iajs-2850	129	21	)	)	PUNCT
iajs-2850	129	22	𝑠𝛽	𝑠𝛽	NOUN
iajs-2850	129	23	=	=	SYM
iajs-2850	129	24	(	(	PUNCT
iajs-2850	129	25	𝑖𝑠𝛼)𝑚+1𝐅𝑐(𝑠	𝑖𝑠𝛼)𝑚+1𝐅𝑐(𝑠	NOUN
iajs-2850	129	26	)	)	PUNCT
iajs-2850	129	27	−	−	PROPN
iajs-2850	129	28	1	1	NUM
iajs-2850	129	29	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	130	1	[	[	X
iajs-2850	130	2	∑	∑	INTJ
iajs-2850	130	3	  	  	SPACE
iajs-2850	130	4	𝑚	𝑚	NOUN
iajs-2850	130	5	𝑘=1	𝑘=1	NOUN
iajs-2850	130	6	  	  	SPACE
iajs-2850	130	7	(	(	PUNCT
iajs-2850	130	8	𝑖𝑠𝛼)𝑘𝑓(𝑚−𝑘)(0	𝑖𝑠𝛼)𝑘𝑓(𝑚−𝑘)(0	ADJ
iajs-2850	130	9	)	)	PUNCT
iajs-2850	130	10	]	]	PUNCT
iajs-2850	131	1	+	+	CCONJ
iajs-2850	131	2	𝑓(𝑚)(0	𝑓(𝑚)(0	NUM
iajs-2850	131	3	)	)	PUNCT
iajs-2850	131	4	]	]	PUNCT
iajs-2850	131	5	,	,	PUNCT
iajs-2850	131	6	=	=	PRON
iajs-2850	131	7	(	(	PUNCT
iajs-2850	131	8	𝑖𝑠𝛼)𝑚+1𝐅𝑐(𝑠	𝑖𝑠𝛼)𝑚+1𝐅𝑐(𝑠	NOUN
iajs-2850	131	9	)	)	PUNCT
iajs-2850	131	10	−	−	PROPN
iajs-2850	132	1	1	1	NUM
iajs-2850	132	2	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	132	3	[	[	X
iajs-2850	132	4	∑	∑	INTJ
iajs-2850	132	5	  	  	SPACE
iajs-2850	132	6	𝑚	𝑚	NOUN
iajs-2850	132	7	𝑘=0	𝑘=0	ADP
iajs-2850	132	8	  	  	SPACE
iajs-2850	132	9	(	(	PUNCT
iajs-2850	132	10	𝑖𝑠𝛼)𝑘𝑓(𝑚−𝑘)(0	𝑖𝑠𝛼)𝑘𝑓(𝑚−𝑘)(0	ADJ
iajs-2850	132	11	)	)	PUNCT
iajs-2850	132	12	]	]	PUNCT
iajs-2850	132	13	]	]	PUNCT
iajs-2850	132	14	,	,	PUNCT
iajs-2850	132	15	=	=	SYM
iajs-2850	132	16	(	(	PUNCT
iajs-2850	132	17	𝑖𝑠𝛼)𝑚+1𝐅𝑐(𝑠	𝑖𝑠𝛼)𝑚+1𝐅𝑐(𝑠	NOUN
iajs-2850	132	18	)	)	PUNCT
iajs-2850	132	19	−	−	PROPN
iajs-2850	132	20	1	1	NUM
iajs-2850	132	21	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	132	22	[	[	PUNCT
iajs-2850	132	23	∑	∑	ADV
iajs-2850	132	24	  	  	SPACE
iajs-2850	132	25	𝑚+1	𝑚+1	CCONJ
iajs-2850	132	26	𝑘=1	𝑘=1	NOUN
iajs-2850	132	27	  	  	SPACE
iajs-2850	132	28	(	(	PUNCT
iajs-2850	132	29	𝑖𝑠𝛼)𝑘−1𝑓(𝑚−(𝑘−1))(0	𝑖𝑠𝛼)𝑘−1𝑓(𝑚−(𝑘−1))(0	ADJ
iajs-2850	132	30	)	)	PUNCT
iajs-2850	132	31	]	]	PUNCT
iajs-2850	132	32	]	]	X
iajs-2850	133	1	=	=	SYM
iajs-2850	133	2	(	(	PUNCT
iajs-2850	133	3	𝑖𝑠𝛼)𝑚+1𝐅𝑐(𝑠	𝑖𝑠𝛼)𝑚+1𝐅𝑐(𝑠	NOUN
iajs-2850	133	4	)	)	PUNCT
iajs-2850	133	5	−	−	PROPN
iajs-2850	133	6	1	1	NUM
iajs-2850	133	7	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	133	8	[	[	PUNCT
iajs-2850	133	9	∑	∑	ADV
iajs-2850	133	10	  	  	SPACE
iajs-2850	133	11	𝑚+1	𝑚+1	CCONJ
iajs-2850	133	12	𝑘=1	𝑘=1	NOUN
iajs-2850	133	13	  	  	SPACE
iajs-2850	133	14	(	(	PUNCT
iajs-2850	133	15	𝑖𝑠𝛼)𝑘−1𝑓(𝑚+1−𝑘))(0	𝑖𝑠𝛼)𝑘−1𝑓(𝑚+1−𝑘))(0	PROPN
iajs-2850	133	16	)	)	PUNCT
iajs-2850	133	17	]	]	PUNCT
iajs-2850	133	18	]	]	PUNCT
iajs-2850	133	19	,	,	PUNCT
iajs-2850	133	20	so	so	ADV
iajs-2850	133	21	theorem	theorem	ADJ
iajs-2850	133	22	is	be	AUX
iajs-2850	133	23	true	true	ADJ
iajs-2850	133	24	for	for	ADP
iajs-2850	133	25	𝑛	𝑛	DET
iajs-2850	133	26	∈	∈	PROPN
iajs-2850	133	27	ℕ.	ℕ.	PROPN
iajs-2850	133	28	4	4	NUM
iajs-2850	133	29	.	.	PUNCT
iajs-2850	133	30	applications	application	NOUN
iajs-2850	133	31	of	of	ADP
iajs-2850	133	32	complex	complex	ADJ
iajs-2850	133	33	sadik	sadik	ADJ
iajs-2850	133	34	integral	integral	ADJ
iajs-2850	133	35	transform	transform	NOUN
iajs-2850	133	36	:	:	PUNCT
iajs-2850	133	37	in	in	ADP
iajs-2850	133	38	this	this	DET
iajs-2850	133	39	section	section	NOUN
iajs-2850	133	40	,	,	PUNCT
iajs-2850	133	41	we	we	PRON
iajs-2850	133	42	introduce	introduce	VERB
iajs-2850	133	43	three	three	NUM
iajs-2850	133	44	real	real	ADJ
iajs-2850	133	45	life	life	NOUN
iajs-2850	133	46	problems	problem	NOUN
iajs-2850	133	47	:	:	PUNCT
iajs-2850	133	48	pharmacokinetics	pharmacokinetic	NOUN
iajs-2850	133	49	problem	problem	NOUN
iajs-2850	133	50	,	,	PUNCT
iajs-2850	133	51	nuclear	nuclear	ADJ
iajs-2850	133	52	physics	physics	NOUN
iajs-2850	133	53	and	and	CCONJ
iajs-2850	133	54	beam	beam	NOUN
iajs-2850	133	55	problems	problem	NOUN
iajs-2850	133	56	.	.	PUNCT
iajs-2850	134	1	example	example	NOUN
iajs-2850	134	2	4.1	4.1	NUM
iajs-2850	134	3	.	.	PUNCT
iajs-2850	135	1	for	for	ADP
iajs-2850	135	2	a	a	DET
iajs-2850	135	3	physical	physical	ADJ
iajs-2850	135	4	explanation	explanation	NOUN
iajs-2850	135	5	of	of	ADP
iajs-2850	135	6	the	the	DET
iajs-2850	135	7	present	present	ADJ
iajs-2850	135	8	scheme	scheme	NOUN
iajs-2850	135	9	,	,	PUNCT
iajs-2850	135	10	we	we	PRON
iajs-2850	135	11	consider	consider	VERB
iajs-2850	135	12	a	a	DET
iajs-2850	135	13	problem	problem	NOUN
iajs-2850	135	14	from	from	ADP
iajs-2850	135	15	the	the	DET
iajs-2850	135	16	field	field	NOUN
iajs-2850	135	17	of	of	ADP
iajs-2850	135	18	"	"	PUNCT
iajs-2850	135	19	pharmacokinetics	pharmacokinetic	NOUN
iajs-2850	135	20	"	"	PUNCT
iajs-2850	135	21	for	for	ADP
iajs-2850	135	22	solving	solve	VERB
iajs-2850	135	23	the	the	DET
iajs-2850	135	24	concentration	concentration	NOUN
iajs-2850	135	25	of	of	ADP
iajs-2850	135	26	the	the	DET
iajs-2850	135	27	drug	drug	NOUN
iajs-2850	135	28	at	at	ADP
iajs-2850	135	29	any	any	DET
iajs-2850	135	30	given	give	VERB
iajs-2850	135	31	time	time	NOUN
iajs-2850	135	32	"	"	PUNCT
iajs-2850	135	33	𝑡	𝑡	NOUN
iajs-2850	135	34	"	"	PUNCT
iajs-2850	135	35	in	in	ADP
iajs-2850	135	36	the	the	DET
iajs-2850	135	37	blood	blood	NOUN
iajs-2850	135	38	during	during	ADP
iajs-2850	135	39	continuous	continuous	ADJ
iajs-2850	135	40	intravenous	intravenous	ADJ
iajs-2850	135	41	injection	injection	NOUN
iajs-2850	135	42	of	of	ADP
iajs-2850	135	43	drug	drug	NOUN
iajs-2850	135	44	and	and	CCONJ
iajs-2850	135	45	find	find	VERB
iajs-2850	135	46	its	its	PRON
iajs-2850	135	47	solution	solution	NOUN
iajs-2850	135	48	in	in	ADP
iajs-2850	135	49	this	this	DET
iajs-2850	135	50	application	application	NOUN
iajs-2850	135	51	.	.	PUNCT
iajs-2850	136	1	this	this	PRON
iajs-2850	136	2	ihjpas	ihjpa	VERB
iajs-2850	136	3	.	.	PUNCT
iajs-2850	137	1	53	53	NUM
iajs-2850	137	2	(	(	PUNCT
iajs-2850	137	3	3)2022	3)2022	NOUN
iajs-2850	137	4	125	125	NUM
iajs-2850	137	5	application	application	NOUN
iajs-2850	137	6	can	can	AUX
iajs-2850	137	7	be	be	AUX
iajs-2850	137	8	written	write	VERB
iajs-2850	137	9	in	in	ADP
iajs-2850	137	10	terms	term	NOUN
iajs-2850	137	11	of	of	ADP
iajs-2850	137	12	1𝑠𝑡	1𝑠𝑡	ADJ
iajs-2850	137	13	order	order	NOUN
iajs-2850	137	14	linear	linear	VERB
iajs-2850	137	15	ordinary	ordinary	ADJ
iajs-2850	137	16	differential	differential	ADJ
iajs-2850	137	17	equation	equation	NOUN
iajs-2850	137	18	with	with	ADP
iajs-2850	137	19	constant	constant	ADJ
iajs-2850	137	20	coefficients	coefficient	NOUN
iajs-2850	137	21	as	as	ADP
iajs-2850	137	22	[	[	X
iajs-2850	137	23	1,5,6	1,5,6	NUM
iajs-2850	137	24	]	]	X
iajs-2850	137	25	.	.	PUNCT
iajs-2850	138	1	𝑑𝑔(𝑡	𝑑𝑔(𝑡	PROPN
iajs-2850	138	2	)	)	PUNCT
iajs-2850	139	1	𝑑𝑡	𝑑𝑡	ADP
iajs-2850	139	2	+	+	ADJ
iajs-2850	139	3	𝜆𝑔(𝑡	𝜆𝑔(𝑡	NUM
iajs-2850	139	4	)	)	PUNCT
iajs-2850	139	5	=	=	PUNCT
iajs-2850	140	1	𝛾	𝛾	ADP
iajs-2850	140	2	volume	volume	NOUN
iajs-2850	140	3	,	,	PUNCT
iajs-2850	140	4	where	where	SCONJ
iajs-2850	140	5	𝑡	𝑡	X
iajs-2850	140	6	>	>	X
iajs-2850	140	7	0	0	PUNCT
iajs-2850	140	8	(	(	PUNCT
iajs-2850	140	9	1	1	NUM
iajs-2850	140	10	)	)	PUNCT
iajs-2850	140	11	with	with	ADP
iajs-2850	140	12	initial	initial	ADJ
iajs-2850	140	13	conditions	condition	NOUN
iajs-2850	140	14	𝑔(0	𝑔(0	NOUN
iajs-2850	140	15	)	)	PUNCT
iajs-2850	140	16	=	=	SYM
iajs-2850	140	17	0	0	PUNCT
iajs-2850	140	18	(	(	PUNCT
iajs-2850	140	19	2	2	NUM
iajs-2850	140	20	)	)	PUNCT
iajs-2850	140	21	here	here	ADV
iajs-2850	140	22	:	:	PUNCT
iajs-2850	140	23	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	140	24	)	)	PUNCT
iajs-2850	140	25	:	:	PUNCT
iajs-2850	140	26	is	be	AUX
iajs-2850	140	27	the	the	DET
iajs-2850	140	28	drug	drug	NOUN
iajs-2850	140	29	concentration	concentration	NOUN
iajs-2850	140	30	in	in	ADP
iajs-2850	140	31	the	the	DET
iajs-2850	140	32	blood	blood	NOUN
iajs-2850	140	33	at	at	ADP
iajs-2850	140	34	any	any	DET
iajs-2850	140	35	time	time	NOUN
iajs-2850	140	36	"	"	PUNCT
iajs-2850	140	37	𝑡	𝑡	NOUN
iajs-2850	140	38	"	"	PUNCT
iajs-2850	140	39	.	.	PUNCT
iajs-2850	141	1	𝜆	𝜆	X
iajs-2850	141	2	:	:	PUNCT
iajs-2850	141	3	is	be	AUX
iajs-2850	141	4	the	the	DET
iajs-2850	141	5	constant	constant	ADJ
iajs-2850	141	6	velocity	velocity	NOUN
iajs-2850	141	7	of	of	ADP
iajs-2850	141	8	elimination	elimination	NOUN
iajs-2850	141	9	.	.	PUNCT
iajs-2850	142	1	𝛾	𝛾	X
iajs-2850	142	2	:	:	PUNCT
iajs-2850	142	3	the	the	DET
iajs-2850	142	4	rate	rate	NOUN
iajs-2850	142	5	of	of	ADP
iajs-2850	142	6	infusion	infusion	NOUN
iajs-2850	142	7	(	(	PUNCT
iajs-2850	142	8	in	in	ADP
iajs-2850	142	9	mg	mg	PROPN
iajs-2850	142	10	/	/	SYM
iajs-2850	142	11	min	min	NOUN
iajs-2850	142	12	.	.	PUNCT
iajs-2850	142	13	)	)	PUNCT
iajs-2850	143	1	volume	volume	NOUN
iajs-2850	143	2	:	:	PUNCT
iajs-2850	144	1	volume	volume	NOUN
iajs-2850	144	2	in	in	ADP
iajs-2850	144	3	which	which	PRON
iajs-2850	144	4	drug	drug	NOUN
iajs-2850	144	5	is	be	AUX
iajs-2850	144	6	distributed	distribute	VERB
iajs-2850	144	7	.	.	PUNCT
iajs-2850	145	1	complex	complex	ADJ
iajs-2850	145	2	sadik	sadik	ADJ
iajs-2850	145	3	transform	transform	NOUN
iajs-2850	145	4	of	of	ADP
iajs-2850	145	5	both	both	DET
iajs-2850	145	6	sides	side	NOUN
iajs-2850	145	7	of	of	ADP
iajs-2850	145	8	equation	equation	NOUN
iajs-2850	145	9	(	(	PUNCT
iajs-2850	145	10	1	1	X
iajs-2850	145	11	)	)	PUNCT
iajs-2850	145	12	gives	give	VERB
iajs-2850	145	13	:	:	PUNCT
iajs-2850	145	14	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	145	15	𝑐	𝑐	PROPN
iajs-2850	145	16	{	{	PUNCT
iajs-2850	145	17	𝑑𝑔(𝑡	𝑑𝑔(𝑡	PROPN
iajs-2850	145	18	)	)	PUNCT
iajs-2850	145	19	𝑑𝑡	𝑑𝑡	ADP
iajs-2850	145	20	}	}	PUNCT
iajs-2850	145	21	+	+	NUM
iajs-2850	145	22	𝜆𝐒𝑎	𝜆𝐒𝑎	NOUN
iajs-2850	145	23	𝑐	𝑐	PROPN
iajs-2850	145	24	{	{	PUNCT
iajs-2850	145	25	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	145	26	)	)	PUNCT
iajs-2850	145	27	}	}	PUNCT
iajs-2850	145	28	=	=	PUNCT
iajs-2850	146	1	𝛾	𝛾	PRON
iajs-2850	146	2	volume	volume	NOUN
iajs-2850	146	3	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	146	4	𝑐	𝑐	PROPN
iajs-2850	146	5	{	{	PUNCT
iajs-2850	146	6	1	1	NUM
iajs-2850	146	7	}	}	PUNCT
iajs-2850	146	8	(	(	PUNCT
iajs-2850	146	9	3	3	X
iajs-2850	146	10	)	)	PUNCT
iajs-2850	146	11	applying	apply	VERB
iajs-2850	146	12	theorem	theorem	NOUN
iajs-2850	146	13	3.1	3.1	NUM
iajs-2850	146	14	,	,	PUNCT
iajs-2850	146	15	we	we	PRON
iajs-2850	146	16	get	get	VERB
iajs-2850	146	17	:	:	PUNCT
iajs-2850	146	18	𝑖𝑠𝛼𝐅𝑐(𝑠	𝑖𝑠𝛼𝐅𝑐(𝑠	ADJ
iajs-2850	146	19	)	)	PUNCT
iajs-2850	146	20	−	−	PROPN
iajs-2850	147	1	𝑔(0	𝑔(0	NOUN
iajs-2850	147	2	)	)	PUNCT
iajs-2850	147	3	𝑠𝛽	𝑠𝛽	NOUN
iajs-2850	148	1	+	+	NOUN
iajs-2850	148	2	𝜆𝐅𝑐(𝑠	𝜆𝐅𝑐(𝑠	ADJ
iajs-2850	148	3	)	)	PUNCT
iajs-2850	148	4	=	=	PUNCT
iajs-2850	149	1	𝛾	𝛾	ADP
iajs-2850	149	2	volume	volume	NOUN
iajs-2850	149	3	−𝑖	−𝑖	PROPN
iajs-2850	149	4	𝑠𝛼+𝛽	𝑠𝛼+𝛽	PROPN
iajs-2850	149	5	(	(	PUNCT
iajs-2850	149	6	4	4	X
iajs-2850	149	7	)	)	PUNCT
iajs-2850	149	8	the	the	DET
iajs-2850	149	9	use	use	NOUN
iajs-2850	149	10	of	of	ADP
iajs-2850	149	11	the	the	DET
iajs-2850	149	12	initial	initial	ADJ
iajs-2850	149	13	condition	condition	NOUN
iajs-2850	149	14	equation	equation	NOUN
iajs-2850	149	15	(	(	PUNCT
iajs-2850	149	16	2	2	NUM
iajs-2850	149	17	)	)	PUNCT
iajs-2850	149	18	in	in	ADP
iajs-2850	149	19	(	(	PUNCT
iajs-2850	149	20	4	4	X
iajs-2850	149	21	)	)	PUNCT
iajs-2850	149	22	gives	give	VERB
iajs-2850	149	23	:	:	PUNCT
iajs-2850	149	24	𝑖𝑠𝛼𝐅𝑐(𝑠	𝑖𝑠𝛼𝐅𝑐(𝑠	X
iajs-2850	149	25	)	)	PUNCT
iajs-2850	149	26	+	+	NUM
iajs-2850	149	27	𝜆𝐅𝑐(𝑠	𝜆𝐅𝑐(𝑠	ADJ
iajs-2850	149	28	)	)	PUNCT
iajs-2850	149	29	=	=	PUNCT
iajs-2850	150	1	−𝑖𝛾	−𝑖𝛾	PROPN
iajs-2850	150	2	volume	volume	NOUN
iajs-2850	150	3	𝑠𝛼+𝛽	𝑠𝛼+𝛽	PROPN
iajs-2850	150	4	.	.	PUNCT
iajs-2850	151	1	𝐅𝑐(𝑠	𝐅𝑐(𝑠	NOUN
iajs-2850	151	2	)	)	PUNCT
iajs-2850	151	3	=	=	PUNCT
iajs-2850	152	1	𝛾	𝛾	ADP
iajs-2850	152	2	volume	volume	NOUN
iajs-2850	152	3	−𝑖𝑠−𝛽	−𝑖𝑠−𝛽	NOUN
iajs-2850	152	4	𝑠𝛼(𝜆	𝑠𝛼(𝜆	NOUN
iajs-2850	153	1	+	+	CCONJ
iajs-2850	153	2	𝑖𝑠𝛼	𝑖𝑠𝛼	X
iajs-2850	153	3	)	)	PUNCT
iajs-2850	153	4	(	(	PUNCT
iajs-2850	153	5	5	5	X
iajs-2850	153	6	)	)	PUNCT
iajs-2850	153	7	applying	apply	VERB
iajs-2850	153	8	inverse	inverse	NOUN
iajs-2850	153	9	complex	complex	NOUN
iajs-2850	153	10	sadik	sadik	PROPN
iajs-2850	153	11	transform	transform	NOUN
iajs-2850	153	12	in	in	ADP
iajs-2850	153	13	equation	equation	NOUN
iajs-2850	153	14	(	(	PUNCT
iajs-2850	153	15	5	5	NUM
iajs-2850	153	16	)	)	PUNCT
iajs-2850	153	17	,	,	PUNCT
iajs-2850	153	18	we	we	PRON
iajs-2850	153	19	get	get	VERB
iajs-2850	153	20	:	:	PUNCT
iajs-2850	153	21	𝑔(𝑡	𝑔(𝑡	X
iajs-2850	153	22	)	)	PUNCT
iajs-2850	153	23	=	=	PUNCT
iajs-2850	154	1	𝛾	𝛾	ADP
iajs-2850	154	2	volume	volume	NOUN
iajs-2850	154	3	(	(	PUNCT
iajs-2850	154	4	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	154	5	𝑐	𝑐	PROPN
iajs-2850	154	6	)	)	PUNCT
iajs-2850	154	7	−1	−1	NOUN
iajs-2850	154	8	[	[	PUNCT
iajs-2850	154	9	−𝑖𝑠−𝛽	−𝑖𝑠−𝛽	NOUN
iajs-2850	154	10	𝑠𝛼(𝜆	𝑠𝛼(𝜆	PUNCT
iajs-2850	154	11	+	+	CCONJ
iajs-2850	154	12	𝑖𝑠𝛼	𝑖𝑠𝛼	ADJ
iajs-2850	154	13	)	)	PUNCT
iajs-2850	154	14	]	]	PUNCT
iajs-2850	154	15	by	by	ADP
iajs-2850	154	16	a	a	DET
iajs-2850	154	17	fractional	fractional	ADJ
iajs-2850	154	18	fraction	fraction	NOUN
iajs-2850	154	19	,	,	PUNCT
iajs-2850	154	20	after	after	ADP
iajs-2850	154	21	simple	simple	ADJ
iajs-2850	154	22	computations	computation	NOUN
iajs-2850	154	23	,	,	PUNCT
iajs-2850	154	24	we	we	PRON
iajs-2850	154	25	get	get	VERB
iajs-2850	154	26	:	:	PUNCT
iajs-2850	154	27	𝑔(𝑡	𝑔(𝑡	X
iajs-2850	154	28	)	)	PUNCT
iajs-2850	154	29	=	=	PUNCT
iajs-2850	155	1	𝛾	𝛾	ADP
iajs-2850	155	2	𝜆	𝜆	DET
iajs-2850	155	3	volume	volume	NOUN
iajs-2850	155	4	[	[	X
iajs-2850	155	5	1	1	NUM
iajs-2850	155	6	−	−	NUM
iajs-2850	155	7	𝑒−𝜆𝑡	𝑒−𝜆𝑡	NOUN
iajs-2850	155	8	]	]	PUNCT
iajs-2850	155	9	.	.	PUNCT
iajs-2850	156	1	which	which	PRON
iajs-2850	156	2	is	be	AUX
iajs-2850	156	3	the	the	DET
iajs-2850	156	4	required	require	VERB
iajs-2850	156	5	concentration	concentration	NOUN
iajs-2850	156	6	of	of	ADP
iajs-2850	156	7	drug	drug	NOUN
iajs-2850	156	8	at	at	ADP
iajs-2850	156	9	any	any	DET
iajs-2850	156	10	given	give	VERB
iajs-2850	156	11	time	time	NOUN
iajs-2850	156	12	"	"	PUNCT
iajs-2850	156	13	𝑡	𝑡	NOUN
iajs-2850	156	14	"	"	PUNCT
iajs-2850	156	15	in	in	ADP
iajs-2850	156	16	the	the	DET
iajs-2850	156	17	blood	blood	NOUN
iajs-2850	156	18	during	during	ADP
iajs-2850	156	19	continuous	continuous	ADJ
iajs-2850	156	20	intravenous	intravenous	ADJ
iajs-2850	156	21	injection	injection	NOUN
iajs-2850	156	22	of	of	ADP
iajs-2850	156	23	a	a	DET
iajs-2850	156	24	drug	drug	NOUN
iajs-2850	156	25	.	.	PUNCT
iajs-2850	156	26	example	example	NOUN
iajs-2850	156	27	4.2	4.2	NUM
iajs-2850	156	28	.	.	PUNCT
iajs-2850	157	1	"	"	PUNCT
iajs-2850	157	2	complex	complex	ADJ
iajs-2850	157	3	sadik	sadik	ADJ
iajs-2850	157	4	transform	transform	NOUN
iajs-2850	157	5	in	in	ADP
iajs-2850	157	6	nuclear	nuclear	ADJ
iajs-2850	157	7	physics	physics	NOUN
iajs-2850	157	8	"	"	PUNCT
iajs-2850	157	9	:	:	PUNCT
iajs-2850	157	10	consider	consider	VERB
iajs-2850	157	11	the	the	DET
iajs-2850	157	12	first	first	ADJ
iajs-2850	157	13	order	order	NOUN
iajs-2850	157	14	linear	linear	PROPN
iajs-2850	157	15	differential	differential	NOUN
iajs-2850	157	16	equation	equation	NOUN
iajs-2850	157	17	:	:	PUNCT
iajs-2850	157	18	𝑑𝑔(𝑡	𝑑𝑔(𝑡	PROPN
iajs-2850	157	19	)	)	PUNCT
iajs-2850	157	20	𝑑𝑡	𝑑𝑡	ADP
iajs-2850	157	21	=	=	SYM
iajs-2850	157	22	−𝜆𝑔(𝑡	−𝜆𝑔(𝑡	PROPN
iajs-2850	157	23	)	)	PUNCT
iajs-2850	157	24	this	this	DET
iajs-2850	157	25	differential	differential	ADJ
iajs-2850	157	26	equation	equation	NOUN
iajs-2850	157	27	is	be	AUX
iajs-2850	157	28	the	the	DET
iajs-2850	157	29	fundamental	fundamental	ADJ
iajs-2850	157	30	relationship	relationship	NOUN
iajs-2850	157	31	describing	describe	VERB
iajs-2850	157	32	radioactive	radioactive	ADJ
iajs-2850	157	33	decay	decay	NOUN
iajs-2850	157	34	,	,	PUNCT
iajs-2850	157	35	where	where	SCONJ
iajs-2850	157	36	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	157	37	)	)	PUNCT
iajs-2850	157	38	represents	represent	VERB
iajs-2850	157	39	the	the	DET
iajs-2850	157	40	number	number	NOUN
iajs-2850	157	41	of	of	ADP
iajs-2850	157	42	un	un	PROPN
iajs-2850	157	43	decayed	decay	VERB
iajs-2850	157	44	atoms	atom	NOUN
iajs-2850	157	45	remaining	remain	VERB
iajs-2850	157	46	in	in	ADP
iajs-2850	157	47	a	a	DET
iajs-2850	157	48	sample	sample	NOUN
iajs-2850	157	49	of	of	ADP
iajs-2850	157	50	radioactive	radioactive	ADJ
iajs-2850	157	51	isotope	isotope	NOUN
iajs-2850	157	52	at	at	ADP
iajs-2850	157	53	the	the	DET
iajs-2850	157	54	time	time	NOUN
iajs-2850	157	55	"	"	PUNCT
iajs-2850	157	56	𝑡	𝑡	PROPN
iajs-2850	157	57	"	"	PUNCT
iajs-2850	157	58	and	and	CCONJ
iajs-2850	157	59	𝜆	𝜆	PROPN
iajs-2850	157	60	is	be	AUX
iajs-2850	157	61	the	the	DET
iajs-2850	157	62	decay	decay	NOUN
iajs-2850	157	63	constant	constant	ADJ
iajs-2850	157	64	,	,	PUNCT
iajs-2850	157	65	[	[	X
iajs-2850	157	66	7,10	7,10	X
iajs-2850	157	67	]	]	PUNCT
iajs-2850	157	68	.	.	PUNCT
iajs-2850	158	1	we	we	PRON
iajs-2850	158	2	can	can	AUX
iajs-2850	158	3	apply	apply	VERB
iajs-2850	158	4	the	the	DET
iajs-2850	158	5	complex	complex	ADJ
iajs-2850	158	6	sadik	sadik	PROPN
iajs-2850	158	7	transform	transform	NOUN
iajs-2850	158	8	to	to	PART
iajs-2850	158	9	find	find	VERB
iajs-2850	158	10	the	the	DET
iajs-2850	158	11	solution	solution	NOUN
iajs-2850	158	12	to	to	ADP
iajs-2850	158	13	this	this	DET
iajs-2850	158	14	differential	differential	ADJ
iajs-2850	158	15	equation	equation	NOUN
iajs-2850	158	16	.	.	PUNCT
iajs-2850	159	1	rearranging	rearrange	VERB
iajs-2850	159	2	the	the	DET
iajs-2850	159	3	above	above	ADJ
iajs-2850	159	4	differential	differential	ADJ
iajs-2850	159	5	equation	equation	NOUN
iajs-2850	159	6	,	,	PUNCT
iajs-2850	159	7	we	we	PRON
iajs-2850	159	8	obtain	obtain	VERB
iajs-2850	159	9	:	:	PUNCT
iajs-2850	159	10	𝑑𝑔(𝑡	𝑑𝑔(𝑡	NUM
iajs-2850	159	11	)	)	PUNCT
iajs-2850	159	12	𝑑𝑡	𝑑𝑡	ADP
iajs-2850	159	13	+	+	ADJ
iajs-2850	159	14	𝜆𝑔(𝑡	𝜆𝑔(𝑡	NUM
iajs-2850	159	15	)	)	PUNCT
iajs-2850	159	16	=	=	SYM
iajs-2850	159	17	0	0	NUM
iajs-2850	160	1	taking	take	VERB
iajs-2850	160	2	complex	complex	ADJ
iajs-2850	160	3	sadik	sadik	ADJ
iajs-2850	160	4	transform	transform	NOUN
iajs-2850	160	5	on	on	ADP
iajs-2850	160	6	both	both	DET
iajs-2850	160	7	sides	side	NOUN
iajs-2850	160	8	,	,	PUNCT
iajs-2850	160	9	we	we	PRON
iajs-2850	160	10	have	have	VERB
iajs-2850	160	11	:	:	PUNCT
iajs-2850	160	12	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	160	13	𝑐	𝑐	PROPN
iajs-2850	160	14	{	{	PUNCT
iajs-2850	160	15	𝑑𝑔(𝑡	𝑑𝑔(𝑡	PROPN
iajs-2850	160	16	)	)	PUNCT
iajs-2850	160	17	𝑑𝑡	𝑑𝑡	ADP
iajs-2850	160	18	}	}	PUNCT
iajs-2850	160	19	+	+	NUM
iajs-2850	160	20	𝜆𝐒𝑎	𝜆𝐒𝑎	NOUN
iajs-2850	160	21	𝑐	𝑐	PROPN
iajs-2850	160	22	{	{	PUNCT
iajs-2850	160	23	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	160	24	)	)	PUNCT
iajs-2850	160	25	}	}	PUNCT
iajs-2850	160	26	=	=	SYM
iajs-2850	160	27	0	0	PUNCT
iajs-2850	160	28	then	then	ADV
iajs-2850	160	29	:	:	PUNCT
iajs-2850	160	30	ihjpas	ihjpa	VERB
iajs-2850	160	31	.	.	PUNCT
iajs-2850	161	1	53	53	NUM
iajs-2850	161	2	(	(	PUNCT
iajs-2850	161	3	3)2022	3)2022	NOUN
iajs-2850	161	4	126	126	NUM
iajs-2850	161	5	𝑖𝑠𝛼𝐒𝑎	𝑖𝑠𝛼𝐒𝑎	SYM
iajs-2850	161	6	𝑐	𝑐	NOUN
iajs-2850	161	7	{	{	PUNCT
iajs-2850	161	8	𝑔(𝑥	𝑔(𝑥	PROPN
iajs-2850	161	9	)	)	PUNCT
iajs-2850	161	10	}	}	PUNCT
iajs-2850	161	11	−	−	ADP
iajs-2850	161	12	𝑔(0	𝑔(0	NOUN
iajs-2850	161	13	)	)	PUNCT
iajs-2850	161	14	𝑠𝛽	𝑠𝛽	NOUN
iajs-2850	161	15	+	+	NUM
iajs-2850	161	16	𝜆𝐒𝑎	𝜆𝐒𝑎	PROPN
iajs-2850	161	17	𝑐	𝑐	PROPN
iajs-2850	161	18	{	{	PUNCT
iajs-2850	161	19	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	161	20	)	)	PUNCT
iajs-2850	161	21	}	}	PUNCT
iajs-2850	161	22	=	=	SYM
iajs-2850	161	23	0	0	PUNCT
iajs-2850	161	24	(	(	PUNCT
iajs-2850	161	25	𝑖𝑠𝛼	𝑖𝑠𝛼	ADJ
iajs-2850	161	26	+	+	CCONJ
iajs-2850	161	27	𝜆)𝐒𝑎	𝜆)𝐒𝑎	PROPN
iajs-2850	161	28	𝑐	𝑐	PROPN
iajs-2850	161	29	{	{	PUNCT
iajs-2850	161	30	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	161	31	)	)	PUNCT
iajs-2850	161	32	}	}	PUNCT
iajs-2850	161	33	=	=	SYM
iajs-2850	161	34	𝑔(0	𝑔(0	VERB
iajs-2850	161	35	)	)	PUNCT
iajs-2850	161	36	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	161	37	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	161	38	𝑐	𝑐	PROPN
iajs-2850	161	39	{	{	PUNCT
iajs-2850	161	40	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	161	41	)	)	PUNCT
iajs-2850	161	42	}	}	PUNCT
iajs-2850	161	43	=	=	SYM
iajs-2850	161	44	𝑔(0	𝑔(0	VERB
iajs-2850	161	45	)	)	PUNCT
iajs-2850	161	46	𝑠𝛽(𝑖𝑠𝛼	𝑠𝛽(𝑖𝑠𝛼	VERB
iajs-2850	161	47	+	+	CCONJ
iajs-2850	161	48	𝜆	𝜆	X
iajs-2850	161	49	)	)	PUNCT
iajs-2850	161	50	,	,	PUNCT
iajs-2850	161	51	here	here	ADV
iajs-2850	161	52	𝑔(0	𝑔(0	PROPN
iajs-2850	161	53	)	)	PUNCT
iajs-2850	161	54	=	=	SYM
iajs-2850	161	55	𝑔0	𝑔0	NOUN
iajs-2850	161	56	then	then	ADV
iajs-2850	161	57	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	161	58	𝑐	𝑐	PROPN
iajs-2850	161	59	{	{	PUNCT
iajs-2850	161	60	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2850	161	61	)	)	PUNCT
iajs-2850	161	62	}	}	PUNCT
iajs-2850	161	63	=	=	PUNCT
iajs-2850	161	64	𝑔0	𝑔0	NOUN
iajs-2850	161	65	𝑠𝛽(𝑖𝑠𝛼	𝑠𝛽(𝑖𝑠𝛼	VERB
iajs-2850	161	66	+	+	CCONJ
iajs-2850	161	67	𝜆	𝜆	X
iajs-2850	161	68	)	)	PUNCT
iajs-2850	161	69	now	now	ADV
iajs-2850	161	70	,	,	PUNCT
iajs-2850	161	71	we	we	PRON
iajs-2850	161	72	take	take	VERB
iajs-2850	161	73	the	the	DET
iajs-2850	161	74	inverse	inverse	NOUN
iajs-2850	161	75	complex	complex	NOUN
iajs-2850	161	76	sadik	sadik	PROPN
iajs-2850	161	77	transform	transform	NOUN
iajs-2850	161	78	on	on	ADP
iajs-2850	161	79	both	both	DET
iajs-2850	161	80	sides	side	NOUN
iajs-2850	161	81	,	,	PUNCT
iajs-2850	161	82	we	we	PRON
iajs-2850	161	83	obtain	obtain	VERB
iajs-2850	161	84	:	:	PUNCT
iajs-2850	161	85	𝑔(𝑡	𝑔(𝑡	NUM
iajs-2850	161	86	)	)	PUNCT
iajs-2850	162	1	=	=	PUNCT
iajs-2850	162	2	𝑔0(𝐒𝑎	𝑔0(𝐒𝑎	PROPN
iajs-2850	162	3	𝑐	𝑐	PROPN
iajs-2850	162	4	)	)	PUNCT
iajs-2850	162	5	−1	−1	NOUN
iajs-2850	162	6	{	{	PUNCT
iajs-2850	162	7	1	1	NUM
iajs-2850	162	8	𝑠𝛽(𝑖𝑠𝛼	𝑠𝛽(𝑖𝑠𝛼	VERB
iajs-2850	162	9	+	+	CCONJ
iajs-2850	162	10	𝜆	𝜆	X
iajs-2850	162	11	)	)	PUNCT
iajs-2850	162	12	}	}	PUNCT
iajs-2850	163	1	=	=	PUNCT
iajs-2850	163	2	𝑔0(𝐒𝑎	𝑔0(𝐒𝑎	PROPN
iajs-2850	163	3	𝑐	𝑐	PROPN
iajs-2850	163	4	)	)	PUNCT
iajs-2850	163	5	−1	−1	NOUN
iajs-2850	163	6	{	{	PUNCT
iajs-2850	163	7	1	1	NUM
iajs-2850	163	8	𝑠𝛽(𝑖𝑠𝛼	𝑠𝛽(𝑖𝑠𝛼	VERB
iajs-2850	163	9	+	+	CCONJ
iajs-2850	163	10	𝜆	𝜆	X
iajs-2850	163	11	)	)	PUNCT
iajs-2850	163	12	𝜆	𝜆	ADV
iajs-2850	163	13	−	−	PROPN
iajs-2850	163	14	𝑖𝑠𝛼	𝑖𝑠𝛼	NOUN
iajs-2850	163	15	𝜆	𝜆	DET
iajs-2850	163	16	−	−	PROPN
iajs-2850	163	17	𝑖𝑠𝛼	𝑖𝑠𝛼	NOUN
iajs-2850	163	18	}	}	PUNCT
iajs-2850	163	19	=	=	PUNCT
iajs-2850	163	20	𝑔0(𝐒𝑎	𝑔0(𝐒𝑎	PROPN
iajs-2850	163	21	𝑐	𝑐	PROPN
iajs-2850	163	22	)	)	PUNCT
iajs-2850	163	23	−1	−1	NOUN
iajs-2850	163	24	{	{	PUNCT
iajs-2850	163	25	1	1	NUM
iajs-2850	163	26	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	163	27	[	[	PUNCT
iajs-2850	163	28	𝜆	𝜆	DET
iajs-2850	163	29	𝑠2𝛼	𝑠2𝛼	NOUN
iajs-2850	163	30	+	+	NUM
iajs-2850	164	1	𝜆2	𝜆2	NOUN
iajs-2850	164	2	−	−	NOUN
iajs-2850	164	3	𝑖	𝑖	SYM
iajs-2850	164	4	𝑠𝛼	𝑠𝛼	PROPN
iajs-2850	164	5	𝑠2𝛼	𝑠2𝛼	PROPN
iajs-2850	164	6	+	+	CCONJ
iajs-2850	164	7	𝜆2	𝜆2	NOUN
iajs-2850	164	8	]	]	PUNCT
iajs-2850	164	9	}	}	PUNCT
iajs-2850	164	10	=	=	PUNCT
iajs-2850	164	11	𝑔0(𝐒𝑎	𝑔0(𝐒𝑎	PROPN
iajs-2850	164	12	𝑐	𝑐	PROPN
iajs-2850	164	13	)	)	PUNCT
iajs-2850	164	14	−1	−1	NOUN
iajs-2850	164	15	{	{	PUNCT
iajs-2850	164	16	−1	−1	NOUN
iajs-2850	164	17	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	164	18	[	[	PUNCT
iajs-2850	164	19	−𝜆	−𝜆	ADJ
iajs-2850	164	20	𝑠2𝛼	𝑠2𝛼	PROPN
iajs-2850	164	21	+	+	CCONJ
iajs-2850	164	22	𝜆2	𝜆2	PROPN
iajs-2850	165	1	+	+	CCONJ
iajs-2850	165	2	𝑖	𝑖	PUNCT
iajs-2850	165	3	𝑠𝛼	𝑠𝛼	PROPN
iajs-2850	165	4	𝑠2𝛼	𝑠2𝛼	PROPN
iajs-2850	165	5	+	+	CCONJ
iajs-2850	165	6	𝜆2	𝜆2	NOUN
iajs-2850	165	7	]	]	PUNCT
iajs-2850	165	8	}	}	PUNCT
iajs-2850	165	9	=	=	PUNCT
iajs-2850	165	10	𝑔0𝑒−𝜆𝑡	𝑔0𝑒−𝜆𝑡	NOUN
iajs-2850	165	11	which	which	PRON
iajs-2850	165	12	is	be	AUX
iajs-2850	165	13	indeed	indeed	ADV
iajs-2850	165	14	the	the	DET
iajs-2850	165	15	correct	correct	ADJ
iajs-2850	165	16	formula	formula	NOUN
iajs-2850	165	17	for	for	ADP
iajs-2850	165	18	radioactive	radioactive	ADJ
iajs-2850	165	19	decay	decay	NOUN
iajs-2850	165	20	.	.	PUNCT
iajs-2850	165	21	example	example	NOUN
iajs-2850	166	1	4.3	4.3	NUM
iajs-2850	166	2	.	.	PUNCT
iajs-2850	166	3	problem	problem	NOUN
iajs-2850	166	4	to	to	AUX
iajs-2850	166	5	beams	beam	NOUN
iajs-2850	166	6	:	:	PUNCT
iajs-2850	166	7	a	a	DET
iajs-2850	166	8	beam	beam	NOUN
iajs-2850	166	9	that	that	PRON
iajs-2850	166	10	is	be	AUX
iajs-2850	166	11	hinged	hinge	VERB
iajs-2850	166	12	at	at	ADP
iajs-2850	166	13	its	its	PRON
iajs-2850	166	14	ends	end	NOUN
iajs-2850	166	15	,	,	PUNCT
iajs-2850	166	16	𝑥	𝑥	NOUN
iajs-2850	166	17	=	=	SYM
iajs-2850	166	18	0	0	NUM
iajs-2850	166	19	and	and	CCONJ
iajs-2850	166	20	𝑥	𝑥	NOUN
iajs-2850	166	21	=	=	SYM
iajs-2850	166	22	𝐿	𝐿	PROPN
iajs-2850	166	23	carries	carry	VERB
iajs-2850	166	24	a	a	DET
iajs-2850	166	25	uniform	uniform	ADJ
iajs-2850	166	26	loud	loud	ADJ
iajs-2850	166	27	𝑤0	𝑤0	PROPN
iajs-2850	166	28	per	per	ADP
iajs-2850	166	29	unit	unit	NOUN
iajs-2850	166	30	length	length	NOUN
iajs-2850	166	31	.	.	PUNCT
iajs-2850	167	1	find	find	VERB
iajs-2850	167	2	the	the	DET
iajs-2850	167	3	deflection	deflection	NOUN
iajs-2850	167	4	at	at	ADP
iajs-2850	167	5	any	any	DET
iajs-2850	167	6	point	point	NOUN
iajs-2850	167	7	𝑃.	𝑃.	PROPN
iajs-2850	167	8	solutions	solution	NOUN
iajs-2850	167	9	:	:	PUNCT
iajs-2850	167	10	the	the	DET
iajs-2850	167	11	ordinary	ordinary	ADJ
iajs-2850	167	12	differential	differential	ADJ
iajs-2850	167	13	equation	equation	NOUN
iajs-2850	167	14	and	and	CCONJ
iajs-2850	167	15	boundary	boundary	ADJ
iajs-2850	167	16	conditions	condition	NOUN
iajs-2850	167	17	are	be	AUX
iajs-2850	167	18	:	:	PUNCT
iajs-2850	167	19	𝑑4𝑦	𝑑4𝑦	X
iajs-2850	167	20	𝑑𝑥4	𝑑𝑥4	PROPN
iajs-2850	167	21	=	=	SYM
iajs-2850	167	22	𝑤0	𝑤0	PROPN
iajs-2850	167	23	𝐸1	𝐸1	NOUN
iajs-2850	167	24	,	,	PUNCT
iajs-2850	167	25	0	0	PUNCT
iajs-2850	167	26	<	<	X
iajs-2850	167	27	𝑥	𝑥	X
iajs-2850	167	28	<	<	X
iajs-2850	167	29	𝐿	𝐿	PROPN
iajs-2850	167	30	(	(	PUNCT
iajs-2850	167	31	6	6	NUM
iajs-2850	167	32	)	)	PUNCT
iajs-2850	167	33	𝑦(0	𝑦(0	PROPN
iajs-2850	167	34	)	)	PUNCT
iajs-2850	167	35	=	=	SYM
iajs-2850	167	36	𝑦′′(0	𝑦′′(0	NOUN
iajs-2850	167	37	)	)	PUNCT
iajs-2850	168	1	=	=	SYM
iajs-2850	168	2	0	0	NUM
iajs-2850	168	3	,	,	PUNCT
iajs-2850	168	4	𝑦(𝐿	𝑦(𝐿	NUM
iajs-2850	168	5	)	)	PUNCT
iajs-2850	168	6	=	=	PUNCT
iajs-2850	169	1	𝑦′′(𝐿	𝑦′′(𝐿	NOUN
iajs-2850	169	2	)	)	PUNCT
iajs-2850	169	3	=	=	SYM
iajs-2850	169	4	0	0	PUNCT
iajs-2850	169	5	(	(	PUNCT
iajs-2850	169	6	7	7	NUM
iajs-2850	169	7	)	)	PUNCT
iajs-2850	169	8	where	where	SCONJ
iajs-2850	169	9	𝐸	𝐸	PROPN
iajs-2850	169	10	is	be	AUX
iajs-2850	169	11	young	young	ADJ
iajs-2850	169	12	's	's	PART
iajs-2850	169	13	modulus	modulus	NOUN
iajs-2850	169	14	,	,	PUNCT
iajs-2850	169	15	i	i	PRON
iajs-2850	169	16	is	be	AUX
iajs-2850	169	17	the	the	DET
iajs-2850	169	18	moment	moment	NOUN
iajs-2850	169	19	of	of	ADP
iajs-2850	169	20	inertia	inertia	NOUN
iajs-2850	169	21	of	of	ADP
iajs-2850	169	22	the	the	DET
iajs-2850	169	23	cross	cross	NOUN
iajs-2850	169	24	section	section	NOUN
iajs-2850	169	25	about	about	ADP
iajs-2850	169	26	an	an	DET
iajs-2850	169	27	axis	axis	NOUN
iajs-2850	169	28	normal	normal	ADJ
iajs-2850	169	29	to	to	ADP
iajs-2850	169	30	the	the	DET
iajs-2850	169	31	plane	plane	NOUN
iajs-2850	169	32	of	of	ADP
iajs-2850	169	33	bending	bending	NOUN
iajs-2850	169	34	and	and	CCONJ
iajs-2850	169	35	𝐸𝐼	𝐸𝐼	PROPN
iajs-2850	169	36	is	be	AUX
iajs-2850	169	37	said	say	VERB
iajs-2850	169	38	to	to	PART
iajs-2850	169	39	be	be	AUX
iajs-2850	169	40	the	the	DET
iajs-2850	169	41	flexural	flexural	ADJ
iajs-2850	169	42	rigidity	rigidity	NOUN
iajs-2850	169	43	of	of	ADP
iajs-2850	169	44	the	the	DET
iajs-2850	169	45	beam	beam	NOUN
iajs-2850	169	46	.	.	PUNCT
iajs-2850	170	1	some	some	DET
iajs-2850	170	2	physical	physical	ADJ
iajs-2850	170	3	quantities	quantity	NOUN
iajs-2850	170	4	associated	associate	VERB
iajs-2850	170	5	with	with	ADP
iajs-2850	170	6	the	the	DET
iajs-2850	170	7	application	application	NOUN
iajs-2850	170	8	are	be	AUX
iajs-2850	170	9	:	:	PUNCT
iajs-2850	170	10	𝑦′(𝑥	𝑦′(𝑥	ADJ
iajs-2850	170	11	)	)	PUNCT
iajs-2850	170	12	,	,	PUNCT
iajs-2850	170	13	𝑀(𝑥	𝑀(𝑥	NUM
iajs-2850	170	14	)	)	PUNCT
iajs-2850	170	15	=	=	PUNCT
iajs-2850	170	16	𝐸𝐼𝑦′′(𝑥	𝐸𝐼𝑦′′(𝑥	NOUN
iajs-2850	170	17	)	)	PUNCT
iajs-2850	170	18	and	and	CCONJ
iajs-2850	170	19	𝑆(𝑥	𝑆(𝑥	X
iajs-2850	170	20	)	)	PUNCT
iajs-2850	170	21	=	=	PUNCT
iajs-2850	170	22	𝑀′(𝑥)𝐸𝐼𝑦′′(𝑥	𝑀′(𝑥)𝐸𝐼𝑦′′(𝑥	X
iajs-2850	170	23	)	)	PUNCT
iajs-2850	170	24	which	which	PRON
iajs-2850	170	25	respectively	respectively	ADV
iajs-2850	170	26	represent	represent	VERB
iajs-2850	170	27	the	the	DET
iajs-2850	170	28	"	"	PUNCT
iajs-2850	170	29	slope	slope	NOUN
iajs-2850	170	30	"	"	PUNCT
iajs-2850	170	31	,	,	PUNCT
iajs-2850	170	32	bending	bend	VERB
iajs-2850	170	33	moment	moment	NOUN
iajs-2850	170	34	,	,	PUNCT
iajs-2850	170	35	and	and	CCONJ
iajs-2850	170	36	shear	shear	NOUN
iajs-2850	170	37	at	at	ADP
iajs-2850	170	38	a	a	DET
iajs-2850	170	39	point	point	NOUN
iajs-2850	170	40	𝑃.	𝑃.	PROPN
iajs-2850	170	41	taking	take	VERB
iajs-2850	170	42	complex	complex	ADJ
iajs-2850	170	43	sadik	sadik	ADJ
iajs-2850	170	44	transform	transform	NOUN
iajs-2850	170	45	of	of	ADP
iajs-2850	170	46	both	both	DET
iajs-2850	170	47	sides	side	NOUN
iajs-2850	170	48	of	of	ADP
iajs-2850	170	49	equation	equation	NOUN
iajs-2850	170	50	(	(	PUNCT
iajs-2850	170	51	6	6	NUM
iajs-2850	170	52	)	)	PUNCT
iajs-2850	170	53	,	,	PUNCT
iajs-2850	170	54	we	we	PRON
iajs-2850	170	55	get	get	VERB
iajs-2850	170	56	,	,	PUNCT
iajs-2850	170	57	if	if	SCONJ
iajs-2850	170	58	𝐅𝑐(𝑠	𝐅𝑐(𝑠	NOUN
iajs-2850	170	59	)	)	PUNCT
iajs-2850	170	60	=	=	PUNCT
iajs-2850	171	1	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	171	2	𝑐	𝑐	PROPN
iajs-2850	171	3	{	{	PUNCT
iajs-2850	171	4	𝑦(𝑥	𝑦(𝑥	PROPN
iajs-2850	171	5	)	)	PUNCT
iajs-2850	171	6	}	}	PUNCT
iajs-2850	171	7	,	,	PUNCT
iajs-2850	171	8	(	(	PUNCT
iajs-2850	171	9	𝑖𝑠𝛼)4𝐅𝑐(𝑠	𝑖𝑠𝛼)4𝐅𝑐(𝑠	NUM
iajs-2850	171	10	)	)	PUNCT
iajs-2850	171	11	−	−	PROPN
iajs-2850	172	1	1	1	NUM
iajs-2850	172	2	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	172	3	[	[	X
iajs-2850	172	4	𝑦′′′(0	𝑦′′′(0	NOUN
iajs-2850	172	5	)	)	PUNCT
iajs-2850	172	6	+	+	NUM
iajs-2850	172	7	𝑖𝑠𝛼𝑦′′(0	𝑖𝑠𝛼𝑦′′(0	NOUN
iajs-2850	172	8	)	)	PUNCT
iajs-2850	173	1	+	+	CCONJ
iajs-2850	173	2	(	(	PUNCT
iajs-2850	173	3	𝑖𝑠𝛼)2𝑦′(0	𝑖𝑠𝛼)2𝑦′(0	NOUN
iajs-2850	173	4	)	)	PUNCT
iajs-2850	173	5	+	+	CCONJ
iajs-2850	173	6	(	(	PUNCT
iajs-2850	173	7	𝑖𝑠𝛼)3𝑦(0	𝑖𝑠𝛼)3𝑦(0	NOUN
iajs-2850	173	8	)	)	PUNCT
iajs-2850	173	9	]	]	PUNCT
iajs-2850	174	1	=	=	PUNCT
iajs-2850	174	2	𝑤0	𝑤0	PROPN
iajs-2850	174	3	𝐸𝐼	𝐸𝐼	PROPN
iajs-2850	174	4	(	(	PUNCT
iajs-2850	174	5	−𝑖	−𝑖	PROPN
iajs-2850	174	6	𝑠𝛼+𝛽	𝑠𝛼+𝛽	PROPN
iajs-2850	174	7	)	)	PUNCT
iajs-2850	174	8	(	(	PUNCT
iajs-2850	174	9	𝑖𝑠𝛼)4𝐅𝑐(𝑠	𝑖𝑠𝛼)4𝐅𝑐(𝑠	NUM
iajs-2850	174	10	)	)	PUNCT
iajs-2850	174	11	−	−	PROPN
iajs-2850	175	1	1	1	NUM
iajs-2850	175	2	𝑠𝛽	𝑠𝛽	PROPN
iajs-2850	175	3	[	[	X
iajs-2850	175	4	𝐶2	𝐶2	INTJ
iajs-2850	175	5	+	+	CCONJ
iajs-2850	175	6	(	(	PUNCT
iajs-2850	175	7	𝑖𝑠𝛼)2𝐶1	𝑖𝑠𝛼)2𝐶1	NUM
iajs-2850	175	8	)	)	PUNCT
iajs-2850	175	9	]	]	PUNCT
iajs-2850	176	1	=	=	PUNCT
iajs-2850	176	2	−𝑤0𝑖	−𝑤0𝑖	PUNCT
iajs-2850	176	3	𝐸𝐼𝑠𝛼+𝛽	𝐸𝐼𝑠𝛼+𝛽	X
iajs-2850	176	4	,	,	PUNCT
iajs-2850	176	5	𝑠4𝛼𝐅𝑐(𝑠	𝑠4𝛼𝐅𝑐(𝑠	PROPN
iajs-2850	176	6	)	)	PUNCT
iajs-2850	176	7	=	=	SYM
iajs-2850	176	8	−𝑤0𝑖	−𝑤0𝑖	PUNCT
iajs-2850	176	9	𝐸𝐼𝑠𝛼+𝛽	𝐸𝐼𝑠𝛼+𝛽	X
iajs-2850	177	1	+	+	CCONJ
iajs-2850	177	2	1	1	NUM
iajs-2850	177	3	𝑠𝛽	𝑠𝛽	NOUN
iajs-2850	177	4	[	[	X
iajs-2850	177	5	𝐶2	𝐶2	INTJ
iajs-2850	177	6	−	−	PROPN
iajs-2850	177	7	𝑠2𝛼𝐶1	𝑠2𝛼𝐶1	PROPN
iajs-2850	177	8	)	)	PUNCT
iajs-2850	177	9	]	]	PUNCT
iajs-2850	177	10	,	,	PUNCT
iajs-2850	177	11	𝐒𝑎	𝐒𝑎	PROPN
iajs-2850	177	12	𝑐	𝑐	PROPN
iajs-2850	177	13	{	{	PUNCT
iajs-2850	177	14	𝑦(𝑥	𝑦(𝑥	X
iajs-2850	177	15	)	)	PUNCT
iajs-2850	177	16	}	}	PUNCT
iajs-2850	177	17	=	=	SYM
iajs-2850	177	18	𝐅𝑐(𝑠	𝐅𝑐(𝑠	NOUN
iajs-2850	177	19	)	)	PUNCT
iajs-2850	177	20	=	=	SYM
iajs-2850	177	21	−𝑤0𝑖	−𝑤0𝑖	PUNCT
iajs-2850	178	1	𝐸𝐼𝑠5𝛼+𝛽	𝐸𝐼𝑠5𝛼+𝛽	VERB
iajs-2850	178	2	+	+	CCONJ
iajs-2850	178	3	𝐶2	𝐶2	INTJ
iajs-2850	178	4	𝑠4𝛼+𝛽	𝑠4𝛼+𝛽	PROPN
iajs-2850	178	5	−	−	PROPN
iajs-2850	178	6	𝐶1	𝐶1	NUM
iajs-2850	178	7	𝑠2𝛼+𝛽	𝑠2𝛼+𝛽	NOUN
iajs-2850	178	8	inverting	inverting	NOUN
iajs-2850	178	9	to	to	PART
iajs-2850	178	10	find	find	VERB
iajs-2850	178	11	the	the	DET
iajs-2850	178	12	solution	solution	NOUN
iajs-2850	178	13	:	:	PUNCT
iajs-2850	178	14	𝑦(𝑥	𝑦(𝑥	NUM
iajs-2850	178	15	)	)	PUNCT
iajs-2850	178	16	=	=	SYM
iajs-2850	179	1	𝐶1𝑥	𝐶1𝑥	PROPN
iajs-2850	179	2	+	+	CCONJ
iajs-2850	179	3	𝐶2	𝐶2	INTJ
iajs-2850	179	4	𝑥3	𝑥3	NOUN
iajs-2850	179	5	3	3	NUM
iajs-2850	179	6	!	!	PUNCT
iajs-2850	180	1	+	+	CCONJ
iajs-2850	180	2	𝑤0	𝑤0	PROPN
iajs-2850	180	3	𝐸𝐼	𝐸𝐼	PROPN
iajs-2850	180	4	𝑥4	𝑥4	NOUN
iajs-2850	180	5	4	4	NUM
iajs-2850	180	6	!	!	NUM
iajs-2850	180	7	,	,	PUNCT
iajs-2850	180	8	or	or	CCONJ
iajs-2850	180	9	ihjpas	ihjpa	VERB
iajs-2850	180	10	.	.	PUNCT
iajs-2850	181	1	53	53	NUM
iajs-2850	181	2	(	(	PUNCT
iajs-2850	181	3	3)2022	3)2022	NOUN
iajs-2850	181	4	127	127	NUM
iajs-2850	181	5	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-2850	181	6	)	)	PUNCT
iajs-2850	181	7	=	=	SYM
iajs-2850	182	1	𝐶1𝑥	𝐶1𝑥	PROPN
iajs-2850	182	2	+	+	CCONJ
iajs-2850	182	3	𝐶2	𝐶2	PROPN
iajs-2850	182	4	𝑥3	𝑥3	NOUN
iajs-2850	182	5	6	6	NUM
iajs-2850	182	6	+	+	NUM
iajs-2850	182	7	𝑤0	𝑤0	PROPN
iajs-2850	182	8	𝐸𝐼	𝐸𝐼	PROPN
iajs-2850	182	9	𝑥4	𝑥4	NOUN
iajs-2850	182	10	24	24	NUM
iajs-2850	182	11	.	.	PUNCT
iajs-2850	183	1	from	from	ADP
iajs-2850	183	2	the	the	DET
iajs-2850	183	3	last	last	ADJ
iajs-2850	183	4	two	two	NUM
iajs-2850	183	5	conditions	condition	NOUN
iajs-2850	183	6	in	in	ADP
iajs-2850	183	7	equation	equation	NOUN
iajs-2850	183	8	(	(	PUNCT
iajs-2850	183	9	7	7	NUM
iajs-2850	183	10	)	)	PUNCT
iajs-2850	183	11	,	,	PUNCT
iajs-2850	183	12	we	we	PRON
iajs-2850	183	13	find	find	VERB
iajs-2850	183	14	:	:	PUNCT
iajs-2850	183	15	𝐶1	𝐶1	PROPN
iajs-2850	183	16	=	=	SYM
iajs-2850	183	17	𝑤0𝐿3	𝑤0𝐿3	SYM
iajs-2850	183	18	24𝐸𝐼	24𝐸𝐼	NUM
iajs-2850	183	19	,	,	PUNCT
iajs-2850	183	20	𝐶2	𝐶2	ADJ
iajs-2850	183	21	=	=	NOUN
iajs-2850	183	22	𝑤0𝐿	𝑤0𝐿	X
iajs-2850	183	23	2𝐸𝐼	2𝐸𝐼	NUM
iajs-2850	183	24	.	.	PUNCT
iajs-2850	184	1	thus	thus	ADV
iajs-2850	184	2	,	,	PUNCT
iajs-2850	184	3	the	the	DET
iajs-2850	184	4	required	require	VERB
iajs-2850	184	5	deflection	deflection	NOUN
iajs-2850	184	6	is	be	AUX
iajs-2850	184	7	:	:	PUNCT
iajs-2850	184	8	𝑦(𝑥	𝑦(𝑥	X
iajs-2850	184	9	)	)	PUNCT
iajs-2850	184	10	=	=	SYM
iajs-2850	184	11	𝑤0	𝑤0	NOUN
iajs-2850	184	12	24𝐸𝐼	24𝐸𝐼	NUM
iajs-2850	184	13	𝑥(𝐿	𝑥(𝐿	NOUN
iajs-2850	184	14	−	−	PROPN
iajs-2850	185	1	𝑥)(𝐿2	𝑥)(𝐿2	VERB
iajs-2850	185	2	−	−	PROPN
iajs-2850	185	3	𝐿𝑥	𝐿𝑥	PROPN
iajs-2850	185	4	−	−	NOUN
iajs-2850	185	5	𝑥2	𝑥2	NOUN
iajs-2850	185	6	)	)	PUNCT
iajs-2850	185	7	.	.	PUNCT
iajs-2850	186	1	it	it	PRON
iajs-2850	186	2	is	be	AUX
iajs-2850	186	3	possible	possible	ADJ
iajs-2850	186	4	to	to	PART
iajs-2850	186	5	calculate	calculate	VERB
iajs-2850	186	6	the	the	DET
iajs-2850	186	7	bending	bend	VERB
iajs-2850	186	8	moment	moment	NOUN
iajs-2850	186	9	and	and	CCONJ
iajs-2850	186	10	shear	shear	NOUN
iajs-2850	186	11	at	at	ADP
iajs-2850	186	12	any	any	DET
iajs-2850	186	13	point	point	NOUN
iajs-2850	186	14	𝑃	𝑃	NOUN
iajs-2850	186	15	of	of	ADP
iajs-2850	186	16	the	the	DET
iajs-2850	186	17	beam	beam	NOUN
iajs-2850	186	18	,	,	PUNCT
iajs-2850	186	19	and	and	CCONJ
iajs-2850	186	20	in	in	ADP
iajs-2850	186	21	particular	particular	ADJ
iajs-2850	186	22	,	,	PUNCT
iajs-2850	186	23	at	at	ADP
iajs-2850	186	24	the	the	DET
iajs-2850	186	25	ends	end	NOUN
iajs-2850	186	26	.	.	PUNCT
iajs-2850	187	1	5	5	X
iajs-2850	187	2	.	.	X
iajs-2850	187	3	conclusions	conclusion	NOUN
iajs-2850	187	4	the	the	DET
iajs-2850	187	5	definition	definition	NOUN
iajs-2850	187	6	and	and	CCONJ
iajs-2850	187	7	applications	application	NOUN
iajs-2850	187	8	of	of	ADP
iajs-2850	187	9	the	the	DET
iajs-2850	187	10	novel	novel	ADJ
iajs-2850	187	11	complex	complex	ADJ
iajs-2850	187	12	sadik	sadik	PROPN
iajs-2850	187	13	transform	transform	NOUN
iajs-2850	187	14	to	to	PART
iajs-2850	187	15	solve	solve	VERB
iajs-2850	187	16	ordinary	ordinary	ADJ
iajs-2850	187	17	differential	differential	ADJ
iajs-2850	187	18	equations	equation	NOUN
iajs-2850	187	19	have	have	AUX
iajs-2850	187	20	been	be	AUX
iajs-2850	187	21	demonstrated	demonstrate	VERB
iajs-2850	187	22	.	.	PUNCT
iajs-2850	188	1	references	reference	NOUN
iajs-2850	188	2	1	1	NUM
iajs-2850	188	3	.	.	PUNCT
iajs-2850	188	4	aggarwal	aggarwal	NOUN
iajs-2850	188	5	,	,	PUNCT
iajs-2850	188	6	s.;,sharma	s.;,sharma	NOUN
iajs-2850	188	7	,	,	PUNCT
iajs-2850	188	8	n.	n.	NOUN
iajs-2850	188	9	;	;	PUNCT
iajs-2850	188	10	chauhan	chauhan	PROPN
iajs-2850	188	11	,	,	PUNCT
iajs-2850	188	12	r.	r.	PROPN
iajs-2850	188	13	duality	duality	PROPN
iajs-2850	188	14	relations	relation	NOUN
iajs-2850	188	15	of	of	ADP
iajs-2850	188	16	kamal	kamal	PROPN
iajs-2850	188	17	transform	transform	VERB
iajs-2850	188	18	with	with	ADP
iajs-2850	188	19	laplace	laplace	NOUN
iajs-2850	188	20	,	,	PUNCT
iajs-2850	188	21	laplace	laplace	NOUN
iajs-2850	188	22	–	–	PUNCT
iajs-2850	188	23	carson	carson	PROPN
iajs-2850	188	24	,	,	PUNCT
iajs-2850	188	25	aboodh	aboodh	PROPN
iajs-2850	188	26	,	,	PUNCT
iajs-2850	188	27	sumudu	sumudu	NOUN
iajs-2850	188	28	,	,	PUNCT
iajs-2850	188	29	elzaki	elzaki	NOUN
iajs-2850	188	30	,	,	PUNCT
iajs-2850	188	31	mohand	mohand	NOUN
iajs-2850	188	32	and	and	CCONJ
iajs-2850	188	33	sawi	sawi	ADJ
iajs-2850	188	34	transforms	transform	VERB
iajs-2850	188	35	.	.	PUNCT
iajs-2850	189	1	sn	sn	PROPN
iajs-2850	189	2	applied	apply	VERB
iajs-2850	189	3	sciences	science	NOUN
iajs-2850	189	4	2020	2020	NUM
iajs-2850	189	5	.	.	PUNCT
iajs-2850	190	1	2(1	2(1	NUM
iajs-2850	190	2	)	)	PUNCT
iajs-2850	190	3	,	,	PUNCT
iajs-2850	190	4	1	1	NUM
iajs-2850	190	5	-	-	SYM
iajs-2850	190	6	8	8	NUM
iajs-2850	190	7	2	2	NUM
iajs-2850	190	8	.	.	PUNCT
iajs-2850	190	9	aggarwal	aggarwal	NOUN
iajs-2850	190	10	,	,	PUNCT
iajs-2850	190	11	s.	s.	PROPN
iajs-2850	190	12	kamal	kamal	PROPN
iajs-2850	190	13	transform	transform	PROPN
iajs-2850	190	14	of	of	ADP
iajs-2850	190	15	bessel	bessel	NOUN
iajs-2850	190	16	's	's	PART
iajs-2850	190	17	functions	function	NOUN
iajs-2850	190	18	.	.	PUNCT
iajs-2850	191	1	international	international	ADJ
iajs-2850	191	2	journal	journal	PROPN
iajs-2850	191	3	of	of	ADP
iajs-2850	191	4	research	research	NOUN
iajs-2850	191	5	and	and	CCONJ
iajs-2850	191	6	innovation	innovation	NOUN
iajs-2850	191	7	in	in	ADP
iajs-2850	191	8	applied	apply	VERB
iajs-2850	191	9	science	science	NOUN
iajs-2850	191	10	(	(	PUNCT
iajs-2850	191	11	ijrias	ijrias	PROPN
iajs-2850	191	12	)	)	PUNCT
iajs-2850	191	13	,	,	PUNCT
iajs-2850	191	14	2018	2018	NUM
iajs-2850	191	15	,	,	PUNCT
iajs-2850	191	16	3(7),1	3(7),1	NUM
iajs-2850	191	17	-	-	SYM
iajs-2850	191	18	4	4	NUM
iajs-2850	191	19	.	.	NOUN
iajs-2850	191	20	3	3	NUM
iajs-2850	191	21	.	.	X
iajs-2850	192	1	mansour	mansour	PROPN
iajs-2850	192	2	,	,	PUNCT
iajs-2850	192	3	e.a	e.a	PROPN
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iajs-2850	217	8	(	(	PUNCT
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iajs-2850	218	10	:	:	PUNCT
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