id	sid	tid	token	lemma	pos
ajpdis-1851	1	1	113	113	NUM
ajpdis-1851	1	2	-	-	SYM
ajpdis-1851	1	3	118	118	NUM
ajpdis-1851	1	4	extreme	extreme	ADJ
ajpdis-1851	1	5	problems	problem	NOUN
ajpdis-1851	1	6	and	and	CCONJ
ajpdis-1851	1	7	their	their	PRON
ajpdis-1851	1	8	study	study	NOUN
ajpdis-1851	1	9	in	in	ADP
ajpdis-1851	1	10	a	a	DET
ajpdis-1851	1	11	mathematics	mathematic	NOUN
ajpdis-1851	1	12	113	113	NUM
ajpdis-1851	1	13	american	american	ADJ
ajpdis-1851	1	14	journal	journal	NOUN
ajpdis-1851	1	15	of	of	ADP
ajpdis-1851	1	16	public	public	ADJ
ajpdis-1851	1	17	diplomacy	diplomacy	NOUN
ajpdis-1851	1	18	and	and	CCONJ
ajpdis-1851	1	19	international	international	ADJ
ajpdis-1851	1	20	studies	study	NOUN
ajpdis-1851	1	21	www	www	PROPN
ajpdis-1851	1	22	.	.	PROPN
ajpdis-1851	2	1	grnjournal.us	grnjournal.us	PROPN
ajpdis-1851	2	2	american	american	PROPN
ajpdis-1851	2	3	journal	journal	PROPN
ajpdis-1851	2	4	of	of	ADP
ajpdis-1851	2	5	public	public	ADJ
ajpdis-1851	2	6	diplomacy	diplomacy	NOUN
ajpdis-1851	2	7	and	and	CCONJ
ajpdis-1851	2	8	international	international	ADJ
ajpdis-1851	2	9	studies	study	NOUN
ajpdis-1851	2	10	volume	volume	NOUN
ajpdis-1851	2	11	01	01	NUM
ajpdis-1851	2	12	,	,	PUNCT
ajpdis-1851	2	13	issue	issue	NOUN
ajpdis-1851	2	14	10	10	NUM
ajpdis-1851	2	15	,	,	PUNCT
ajpdis-1851	2	16	2023	2023	NUM
ajpdis-1851	2	17	issn	issn	X
ajpdis-1851	2	18	(	(	PUNCT
ajpdis-1851	2	19	e	e	NOUN
ajpdis-1851	2	20	):	):	PUNCT
ajpdis-1851	2	21	2993	2993	NUM
ajpdis-1851	2	22	-	-	SYM
ajpdis-1851	2	23	2157	2157	NUM
ajpdis-1851	2	24	extreme	extreme	ADJ
ajpdis-1851	2	25	problems	problem	NOUN
ajpdis-1851	2	26	and	and	CCONJ
ajpdis-1851	2	27	their	their	PRON
ajpdis-1851	2	28	study	study	NOUN
ajpdis-1851	2	29	in	in	ADP
ajpdis-1851	2	30	a	a	DET
ajpdis-1851	2	31	mathematics	mathematics	NOUN
ajpdis-1851	2	32	course	course	NOUN
ajpdis-1851	2	33	djalilova	djalilova	X
ajpdis-1851	2	34	turgunoy	turgunoy	ADV
ajpdis-1851	2	35	abdujalilovna	abdujalilovna	VERB
ajpdis-1851	2	36	candidate	candidate	NOUN
ajpdis-1851	2	37	of	of	ADP
ajpdis-1851	2	38	physical	physical	ADJ
ajpdis-1851	2	39	and	and	CCONJ
ajpdis-1851	2	40	mathematical	mathematical	ADJ
ajpdis-1851	2	41	sciences	science	NOUN
ajpdis-1851	2	42	,	,	PUNCT
ajpdis-1851	2	43	associate	associate	ADJ
ajpdis-1851	2	44	professor	professor	NOUN
ajpdis-1851	2	45	of	of	ADP
ajpdis-1851	2	46	andijan	andijan	NOUN
ajpdis-1851	2	47	machine	machine	NOUN
ajpdis-1851	2	48	-	-	PUNCT
ajpdis-1851	2	49	building	building	NOUN
ajpdis-1851	2	50	institute	institute	NOUN
ajpdis-1851	2	51	khalilov	khalilov	PROPN
ajpdis-1851	2	52	murodiljan	murodiljan	PROPN
ajpdis-1851	2	53	durbek	durbek	PROPN
ajpdis-1851	2	54	son	son	PROPN
ajpdis-1851	2	55	teacher	teacher	NOUN
ajpdis-1851	2	56	of	of	ADP
ajpdis-1851	2	57	andijan	andijan	PROPN
ajpdis-1851	2	58	mechanical	mechanical	PROPN
ajpdis-1851	2	59	,	,	PUNCT
ajpdis-1851	2	60	engineering	engineering	NOUN
ajpdis-1851	2	61	institute	institute	NOUN
ajpdis-1851	2	62	abstract	abstract	NOUN
ajpdis-1851	2	63	:	:	PUNCT
ajpdis-1851	2	64	in	in	ADP
ajpdis-1851	2	65	this	this	DET
ajpdis-1851	2	66	article	article	NOUN
ajpdis-1851	2	67	,	,	PUNCT
ajpdis-1851	2	68	the	the	DET
ajpdis-1851	2	69	methods	method	NOUN
ajpdis-1851	2	70	that	that	PRON
ajpdis-1851	2	71	can	can	AUX
ajpdis-1851	2	72	be	be	AUX
ajpdis-1851	2	73	used	use	VERB
ajpdis-1851	2	74	in	in	ADP
ajpdis-1851	2	75	solving	solve	VERB
ajpdis-1851	2	76	problems	problem	NOUN
ajpdis-1851	2	77	that	that	PRON
ajpdis-1851	2	78	lead	lead	VERB
ajpdis-1851	2	79	to	to	ADP
ajpdis-1851	2	80	finding	find	VERB
ajpdis-1851	2	81	the	the	DET
ajpdis-1851	2	82	largest	large	ADJ
ajpdis-1851	2	83	and	and	CCONJ
ajpdis-1851	2	84	smallest	small	ADJ
ajpdis-1851	2	85	values	value	NOUN
ajpdis-1851	2	86	of	of	ADP
ajpdis-1851	2	87	the	the	DET
ajpdis-1851	2	88	function	function	NOUN
ajpdis-1851	2	89	:	:	PUNCT
ajpdis-1851	2	90	the	the	DET
ajpdis-1851	2	91	method	method	NOUN
ajpdis-1851	2	92	of	of	ADP
ajpdis-1851	2	93	inequalities	inequality	NOUN
ajpdis-1851	2	94	,	,	PUNCT
ajpdis-1851	2	95	the	the	DET
ajpdis-1851	2	96	method	method	NOUN
ajpdis-1851	2	97	of	of	ADP
ajpdis-1851	2	98	using	use	VERB
ajpdis-1851	2	99	quadratic	quadratic	ADJ
ajpdis-1851	2	100	triangle	triangle	NOUN
ajpdis-1851	2	101	properties	property	NOUN
ajpdis-1851	2	102	,	,	PUNCT
ajpdis-1851	2	103	the	the	DET
ajpdis-1851	2	104	symmetry	symmetry	NOUN
ajpdis-1851	2	105	method	method	NOUN
ajpdis-1851	2	106	and	and	CCONJ
ajpdis-1851	2	107	the	the	DET
ajpdis-1851	2	108	essence	essence	NOUN
ajpdis-1851	2	109	of	of	ADP
ajpdis-1851	2	110	the	the	DET
ajpdis-1851	2	111	differential	differential	ADJ
ajpdis-1851	2	112	calculus	calculus	NOUN
ajpdis-1851	2	113	methods	method	NOUN
ajpdis-1851	2	114	are	be	AUX
ajpdis-1851	2	115	explained	explain	VERB
ajpdis-1851	2	116	with	with	ADP
ajpdis-1851	2	117	the	the	DET
ajpdis-1851	2	118	help	help	NOUN
ajpdis-1851	2	119	of	of	ADP
ajpdis-1851	2	120	problems	problem	NOUN
ajpdis-1851	2	121	.	.	PUNCT
ajpdis-1851	3	1	keywords	keyword	NOUN
ajpdis-1851	3	2	:	:	PUNCT
ajpdis-1851	3	3	maximum	maximum	ADJ
ajpdis-1851	3	4	,	,	PUNCT
ajpdis-1851	3	5	minimum	minimum	ADJ
ajpdis-1851	3	6	,	,	PUNCT
ajpdis-1851	3	7	extremum	extremum	ADJ
ajpdis-1851	3	8	,	,	PUNCT
ajpdis-1851	3	9	largest	large	ADJ
ajpdis-1851	3	10	value	value	NOUN
ajpdis-1851	3	11	,	,	PUNCT
ajpdis-1851	3	12	smallest	small	ADJ
ajpdis-1851	3	13	value	value	NOUN
ajpdis-1851	3	14	,	,	PUNCT
ajpdis-1851	3	15	arithmetic	arithmetic	ADJ
ajpdis-1851	3	16	mean	mean	NOUN
ajpdis-1851	3	17	,	,	PUNCT
ajpdis-1851	3	18	geometric	geometric	ADJ
ajpdis-1851	3	19	mean	mean	NOUN
ajpdis-1851	3	20	,	,	PUNCT
ajpdis-1851	3	21	isoperimetric	isoperimetric	ADJ
ajpdis-1851	3	22	problem	problem	NOUN
ajpdis-1851	3	23	,	,	PUNCT
ajpdis-1851	3	24	critical	critical	ADJ
ajpdis-1851	3	25	point	point	NOUN
ajpdis-1851	3	26	.	.	PUNCT
ajpdis-1851	4	1	it	it	PRON
ajpdis-1851	4	2	is	be	AUX
ajpdis-1851	4	3	known	know	VERB
ajpdis-1851	4	4	that	that	SCONJ
ajpdis-1851	4	5	in	in	ADP
ajpdis-1851	4	6	recent	recent	ADJ
ajpdis-1851	4	7	years	year	NOUN
ajpdis-1851	4	8	,	,	PUNCT
ajpdis-1851	4	9	great	great	ADJ
ajpdis-1851	4	10	importance	importance	NOUN
ajpdis-1851	4	11	has	have	AUX
ajpdis-1851	4	12	been	be	AUX
ajpdis-1851	4	13	attached	attach	VERB
ajpdis-1851	4	14	to	to	ADP
ajpdis-1851	4	15	the	the	DET
ajpdis-1851	4	16	development	development	NOUN
ajpdis-1851	4	17	of	of	ADP
ajpdis-1851	4	18	mathematical	mathematical	ADJ
ajpdis-1851	4	19	education	education	NOUN
ajpdis-1851	4	20	in	in	ADP
ajpdis-1851	4	21	our	our	PRON
ajpdis-1851	4	22	republic	republic	NOUN
ajpdis-1851	4	23	.	.	PUNCT
ajpdis-1851	5	1	as	as	ADP
ajpdis-1851	5	2	a	a	DET
ajpdis-1851	5	3	clear	clear	ADJ
ajpdis-1851	5	4	example	example	NOUN
ajpdis-1851	5	5	of	of	ADP
ajpdis-1851	5	6	this	this	PRON
ajpdis-1851	5	7	,	,	PUNCT
ajpdis-1851	5	8	on	on	ADP
ajpdis-1851	5	9	may	may	PROPN
ajpdis-1851	5	10	7	7	NUM
ajpdis-1851	5	11	,	,	PUNCT
ajpdis-1851	5	12	2020	2020	NUM
ajpdis-1851	5	13	,	,	PUNCT
ajpdis-1851	5	14	the	the	DET
ajpdis-1851	5	15	president	president	NOUN
ajpdis-1851	5	16	of	of	ADP
ajpdis-1851	5	17	the	the	DET
ajpdis-1851	5	18	republic	republic	NOUN
ajpdis-1851	5	19	of	of	ADP
ajpdis-1851	5	20	uzbekistan	uzbekistan	PROPN
ajpdis-1851	5	21	"	"	PUNCT
ajpdis-1851	5	22	measures	measure	NOUN
ajpdis-1851	5	23	to	to	PART
ajpdis-1851	5	24	improve	improve	VERB
ajpdis-1851	5	25	the	the	DET
ajpdis-1851	5	26	quality	quality	NOUN
ajpdis-1851	5	27	of	of	ADP
ajpdis-1851	5	28	education	education	NOUN
ajpdis-1851	5	29	and	and	CCONJ
ajpdis-1851	5	30	develop	develop	VERB
ajpdis-1851	5	31	scientific	scientific	ADJ
ajpdis-1851	5	32	research	research	NOUN
ajpdis-1851	5	33	in	in	ADP
ajpdis-1851	5	34	the	the	DET
ajpdis-1851	5	35	field	field	NOUN
ajpdis-1851	5	36	of	of	ADP
ajpdis-1851	5	37	mathematics	mathematic	NOUN
ajpdis-1851	5	38	pq-4708	pq-4708	NOUN
ajpdis-1851	5	39	,	,	PUNCT
ajpdis-1851	5	40	july	july	PROPN
ajpdis-1851	5	41	9	9	NUM
ajpdis-1851	5	42	,	,	PUNCT
ajpdis-1851	5	43	2019	2019	NUM
ajpdis-1851	5	44	pq-4387	pq-4387	NOUN
ajpdis-1851	5	45	"	"	PUNCT
ajpdis-1851	5	46	state	state	NOUN
ajpdis-1851	5	47	support	support	NOUN
ajpdis-1851	5	48	in	in	ADP
ajpdis-1851	5	49	the	the	DET
ajpdis-1851	5	50	further	further	ADJ
ajpdis-1851	5	51	development	development	NOUN
ajpdis-1851	5	52	of	of	ADP
ajpdis-1851	5	53	mathematics	mathematics	PROPN
ajpdis-1851	5	54	education	education	NOUN
ajpdis-1851	5	55	and	and	CCONJ
ajpdis-1851	5	56	sciences	science	NOUN
ajpdis-1851	5	57	,	,	PUNCT
ajpdis-1851	5	58	measures	measure	NOUN
ajpdis-1851	5	59	to	to	PART
ajpdis-1851	5	60	fundamentally	fundamentally	ADV
ajpdis-1851	5	61	improve	improve	VERB
ajpdis-1851	5	62	the	the	DET
ajpdis-1851	5	63	activities	activity	NOUN
ajpdis-1851	5	64	of	of	ADP
ajpdis-1851	5	65	the	the	DET
ajpdis-1851	5	66	institute	institute	NOUN
ajpdis-1851	5	67	of	of	ADP
ajpdis-1851	5	68	mathematics	mathematics	PROPN
ajpdis-1851	5	69	of	of	ADP
ajpdis-1851	5	70	the	the	DET
ajpdis-1851	5	71	academy	academy	PROPN
ajpdis-1851	5	72	of	of	ADP
ajpdis-1851	5	73	sciences	sciences	PROPN
ajpdis-1851	5	74	of	of	ADP
ajpdis-1851	5	75	the	the	DET
ajpdis-1851	5	76	republic	republic	NOUN
ajpdis-1851	5	77	of	of	ADP
ajpdis-1851	5	78	uzbekistan	uzbekistan	PROPN
ajpdis-1851	5	79	named	name	VERB
ajpdis-1851	5	80	after	after	ADP
ajpdis-1851	5	81	vi	vi	PROPN
ajpdis-1851	5	82	romanovisky	romanovisky	ADJ
ajpdis-1851	5	83	"	"	PUNCT
ajpdis-1851	5	84	decisions	decision	NOUN
ajpdis-1851	5	85	can	can	AUX
ajpdis-1851	5	86	be	be	AUX
ajpdis-1851	5	87	made	make	VERB
ajpdis-1851	5	88	.	.	PUNCT
ajpdis-1851	6	1	the	the	DET
ajpdis-1851	6	2	main	main	ADJ
ajpdis-1851	6	3	goal	goal	NOUN
ajpdis-1851	6	4	of	of	ADP
ajpdis-1851	6	5	this	this	DET
ajpdis-1851	6	6	decision	decision	NOUN
ajpdis-1851	6	7	is	be	AUX
ajpdis-1851	6	8	to	to	PART
ajpdis-1851	6	9	develop	develop	VERB
ajpdis-1851	6	10	mathematical	mathematical	ADJ
ajpdis-1851	6	11	sciences	science	NOUN
ajpdis-1851	6	12	in	in	ADP
ajpdis-1851	6	13	our	our	PRON
ajpdis-1851	6	14	republic	republic	NOUN
ajpdis-1851	6	15	and	and	CCONJ
ajpdis-1851	6	16	to	to	PART
ajpdis-1851	6	17	train	train	VERB
ajpdis-1851	6	18	qualified	qualified	ADJ
ajpdis-1851	6	19	specialists	specialist	NOUN
ajpdis-1851	6	20	who	who	PRON
ajpdis-1851	6	21	are	be	AUX
ajpdis-1851	6	22	not	not	PART
ajpdis-1851	6	23	far	far	ADV
ajpdis-1851	6	24	behind	behind	ADP
ajpdis-1851	6	25	the	the	DET
ajpdis-1851	6	26	specialists	specialist	NOUN
ajpdis-1851	6	27	trained	train	VERB
ajpdis-1851	6	28	in	in	ADP
ajpdis-1851	6	29	developed	develop	VERB
ajpdis-1851	6	30	countries	country	NOUN
ajpdis-1851	6	31	.	.	PUNCT
ajpdis-1851	7	1	among	among	ADP
ajpdis-1851	7	2	the	the	DET
ajpdis-1851	7	3	subjects	subject	NOUN
ajpdis-1851	7	4	taught	teach	VERB
ajpdis-1851	7	5	in	in	ADP
ajpdis-1851	7	6	higher	high	ADJ
ajpdis-1851	7	7	educational	educational	ADJ
ajpdis-1851	7	8	institutions	institution	NOUN
ajpdis-1851	7	9	,	,	PUNCT
ajpdis-1851	7	10	higher	high	ADJ
ajpdis-1851	7	11	mathematics	mathematic	NOUN
ajpdis-1851	7	12	takes	take	VERB
ajpdis-1851	7	13	an	an	DET
ajpdis-1851	7	14	important	important	ADJ
ajpdis-1851	7	15	place	place	NOUN
ajpdis-1851	7	16	in	in	ADP
ajpdis-1851	7	17	the	the	DET
ajpdis-1851	7	18	training	training	NOUN
ajpdis-1851	7	19	of	of	ADP
ajpdis-1851	7	20	such	such	ADJ
ajpdis-1851	7	21	specialists	specialist	NOUN
ajpdis-1851	7	22	.	.	PUNCT
ajpdis-1851	8	1	that	that	PRON
ajpdis-1851	8	2	is	be	AUX
ajpdis-1851	8	3	why	why	SCONJ
ajpdis-1851	8	4	teaching	teach	VERB
ajpdis-1851	8	5	higher	high	ADJ
ajpdis-1851	8	6	mathematics	mathematic	NOUN
ajpdis-1851	8	7	in	in	ADP
ajpdis-1851	8	8	higher	high	ADJ
ajpdis-1851	8	9	educational	educational	ADJ
ajpdis-1851	8	10	institutions	institution	NOUN
ajpdis-1851	8	11	should	should	AUX
ajpdis-1851	8	12	be	be	AUX
ajpdis-1851	8	13	given	give	VERB
ajpdis-1851	8	14	great	great	ADJ
ajpdis-1851	8	15	importance	importance	NOUN
ajpdis-1851	8	16	.	.	PUNCT
ajpdis-1851	9	1	because	because	SCONJ
ajpdis-1851	9	2	today	today	NOUN
ajpdis-1851	9	3	in	in	ADP
ajpdis-1851	9	4	the	the	DET
ajpdis-1851	9	5	day	day	NOUN
ajpdis-1851	9	6	each	each	PRON
ajpdis-1851	9	7	how	how	SCONJ
ajpdis-1851	9	8	expert	expert	NOUN
ajpdis-1851	9	9	own	own	VERB
ajpdis-1851	9	10	in	in	ADP
ajpdis-1851	9	11	the	the	DET
ajpdis-1851	9	12	activity	activity	NOUN
ajpdis-1851	9	13	mathematics	mathematic	NOUN
ajpdis-1851	9	14	and	and	CCONJ
ajpdis-1851	9	15	mathematician	mathematician	NOUN
ajpdis-1851	9	16	to	to	ADP
ajpdis-1851	9	17	methods	method	NOUN
ajpdis-1851	9	18	often	often	ADV
ajpdis-1851	9	19	appeal	appeal	VERB
ajpdis-1851	9	20	does	do	AUX
ajpdis-1851	9	21	.	.	PUNCT
ajpdis-1851	10	1	it	it	PRON
ajpdis-1851	10	2	is	be	AUX
ajpdis-1851	10	3	known	know	VERB
ajpdis-1851	10	4	that	that	SCONJ
ajpdis-1851	10	5	there	there	PRON
ajpdis-1851	10	6	are	be	VERB
ajpdis-1851	10	7	many	many	ADJ
ajpdis-1851	10	8	practical	practical	ADJ
ajpdis-1851	10	9	issues	issue	NOUN
ajpdis-1851	10	10	mathematics	mathematic	NOUN
ajpdis-1851	10	11	and	and	CCONJ
ajpdis-1851	10	12	mathematician	mathematician	ADJ
ajpdis-1851	10	13	methods	method	NOUN
ajpdis-1851	10	14	using	use	VERB
ajpdis-1851	10	15	own	own	ADJ
ajpdis-1851	10	16	the	the	DET
ajpdis-1851	10	17	solution	solution	NOUN
ajpdis-1851	10	18	easy	easy	ADJ
ajpdis-1851	10	19	finds	find	VERB
ajpdis-1851	10	20	.	.	PUNCT
ajpdis-1851	11	1	such	such	ADJ
ajpdis-1851	11	2	to	to	ADP
ajpdis-1851	11	3	issues	issue	NOUN
ajpdis-1851	11	4	example	example	NOUN
ajpdis-1851	11	5	as	as	ADP
ajpdis-1851	11	6	extreme	extreme	ADJ
ajpdis-1851	11	7	issues	issue	NOUN
ajpdis-1851	11	8	to	to	PART
ajpdis-1851	11	9	bring	bring	VERB
ajpdis-1851	11	10	can	can	AUX
ajpdis-1851	11	11	extreme	extreme	ADJ
ajpdis-1851	11	12	to	to	AUX
ajpdis-1851	11	13	issues	issue	VERB
ajpdis-1851	11	14	people	people	NOUN
ajpdis-1851	11	15	their	their	PRON
ajpdis-1851	11	16	own	own	ADJ
ajpdis-1851	11	17	practical	practical	ADJ
ajpdis-1851	11	18	activity	activity	NOUN
ajpdis-1851	11	19	during	during	ADP
ajpdis-1851	11	20	often	often	ADV
ajpdis-1851	11	21	face	face	NOUN
ajpdis-1851	11	22	they	they	PRON
ajpdis-1851	11	23	come	come	VERB
ajpdis-1851	11	24	extreme	extreme	ADJ
ajpdis-1851	11	25	matters	matter	NOUN
ajpdis-1851	11	26	of	of	ADP
ajpdis-1851	11	27	quantities	quantity	NOUN
ajpdis-1851	11	28	the	the	DET
ajpdis-1851	11	29	most	most	ADV
ajpdis-1851	11	30	big	big	ADJ
ajpdis-1851	11	31	and	and	CCONJ
ajpdis-1851	11	32	the	the	DET
ajpdis-1851	11	33	most	most	ADV
ajpdis-1851	11	34	small	small	ADJ
ajpdis-1851	11	35	values	value	NOUN
ajpdis-1851	11	36	to	to	PART
ajpdis-1851	11	37	find	find	VERB
ajpdis-1851	11	38	circle	circle	NOUN
ajpdis-1851	11	39	issues	issue	NOUN
ajpdis-1851	11	40	being	be	AUX
ajpdis-1851	11	41	such	such	ADJ
ajpdis-1851	11	42	issues	issue	NOUN
ajpdis-1851	11	43	solve	solve	VERB
ajpdis-1851	11	44	with	with	ADP
ajpdis-1851	11	45	ancient	ancient	ADJ
ajpdis-1851	11	46	time	time	NOUN
ajpdis-1851	11	47	mathematicians	mathematicians	PROPN
ajpdis-1851	11	48	euclid	euclid	PROPN
ajpdis-1851	11	49	,	,	PUNCT
ajpdis-1851	11	50	pythagoras	pythagoras	PROPN
ajpdis-1851	11	51	,	,	PUNCT
ajpdis-1851	11	52	archimedes	archimede	NOUN
ajpdis-1851	11	53	,	,	PUNCT
ajpdis-1851	11	54	apollonius	apollonius	NOUN
ajpdis-1851	11	55	,	,	PUNCT
ajpdis-1851	11	56	zenodorus	zenodorus	NOUN
ajpdis-1851	11	57	,	,	PUNCT
ajpdis-1851	11	58	geron	geron	NOUN
ajpdis-1851	11	59	and	and	CCONJ
ajpdis-1851	11	60	others	other	NOUN
ajpdis-1851	11	61	are	be	AUX
ajpdis-1851	11	62	also	also	ADV
ajpdis-1851	11	63	involved	involve	VERB
ajpdis-1851	11	64	.	.	PUNCT
ajpdis-1851	12	1	medium	medium	NOUN
ajpdis-1851	12	2	in	in	ADP
ajpdis-1851	12	3	asia	asia	PROPN
ajpdis-1851	12	4	while	while	SCONJ
ajpdis-1851	12	5	such	such	ADJ
ajpdis-1851	12	6	issues	issue	NOUN
ajpdis-1851	12	7	with	with	ADP
ajpdis-1851	12	8	abu	abu	PROPN
ajpdis-1851	12	9	rayhan	rayhan	PROPN
ajpdis-1851	12	10	beruni	beruni	PROPN
ajpdis-1851	12	11	engaged	engage	VERB
ajpdis-1851	12	12	in	in	ADP
ajpdis-1851	12	13	until	until	ADP
ajpdis-1851	12	14	the	the	DET
ajpdis-1851	12	15	17th	17th	ADJ
ajpdis-1851	12	16	century	century	NOUN
ajpdis-1851	12	17	such	such	ADJ
ajpdis-1851	12	18	matters	matter	NOUN
ajpdis-1851	12	19	basically	basically	ADV
ajpdis-1851	12	20	geometric	geometric	ADJ
ajpdis-1851	12	21	method	method	NOUN
ajpdis-1851	12	22	solved	solve	VERB
ajpdis-1851	12	23	.	.	PUNCT
ajpdis-1851	13	1	french	french	ADJ
ajpdis-1851	13	2	math	math	PROPN
ajpdis-1851	13	3	p.	p.	PROPN
ajpdis-1851	13	4	farm	farm	PROPN
ajpdis-1851	13	5	english	english	PROPN
ajpdis-1851	13	6	math	math	PROPN
ajpdis-1851	13	7	and	and	CCONJ
ajpdis-1851	13	8	physical	physical	PROPN
ajpdis-1851	13	9	i.	i.	PROPN
ajpdis-1851	13	10	newton	newton	PROPN
ajpdis-1851	13	11	and	and	CCONJ
ajpdis-1851	13	12	german	german	ADJ
ajpdis-1851	13	13	math	math	NOUN
ajpdis-1851	13	14	g.	g.	PROPN
ajpdis-1851	13	15	leibniz	leibniz	PROPN
ajpdis-1851	13	16	works	work	VERB
ajpdis-1851	13	17	using	use	VERB
ajpdis-1851	13	18	later	later	ADV
ajpdis-1851	13	19	on	on	ADP
ajpdis-1851	13	20	such	such	ADJ
ajpdis-1851	13	21	issues	issue	NOUN
ajpdis-1851	13	22	analytical	analytical	ADJ
ajpdis-1851	13	23	method	method	NOUN
ajpdis-1851	13	24	solve	solve	NOUN
ajpdis-1851	13	25	started	start	VERB
ajpdis-1851	13	26	.	.	PUNCT
ajpdis-1851	14	1	114	114	NUM
ajpdis-1851	14	2	american	american	ADJ
ajpdis-1851	14	3	journal	journal	PROPN
ajpdis-1851	14	4	of	of	ADP
ajpdis-1851	14	5	public	public	ADJ
ajpdis-1851	14	6	diplomacy	diplomacy	NOUN
ajpdis-1851	14	7	and	and	CCONJ
ajpdis-1851	14	8	international	international	ADJ
ajpdis-1851	14	9	studies	study	NOUN
ajpdis-1851	14	10	www	www	PROPN
ajpdis-1851	14	11	.	.	PUNCT
ajpdis-1851	15	1	grnjournal.us	grnjournal.us	X
ajpdis-1851	15	2	someone	someone	PRON
ajpdis-1851	15	3	of	of	ADP
ajpdis-1851	15	4	the	the	DET
ajpdis-1851	15	5	amount	amount	NOUN
ajpdis-1851	15	6	the	the	DET
ajpdis-1851	15	7	most	most	ADV
ajpdis-1851	15	8	big	big	ADJ
ajpdis-1851	15	9	and	and	CCONJ
ajpdis-1851	15	10	the	the	DET
ajpdis-1851	15	11	most	most	ADV
ajpdis-1851	15	12	small	small	ADJ
ajpdis-1851	15	13	values	value	NOUN
ajpdis-1851	15	14	to	to	PART
ajpdis-1851	15	15	find	find	VERB
ajpdis-1851	15	16	and	and	CCONJ
ajpdis-1851	15	17	such	such	ADJ
ajpdis-1851	15	18	values	value	NOUN
ajpdis-1851	15	19	there	there	PRON
ajpdis-1851	15	20	is	be	VERB
ajpdis-1851	15	21	to	to	PART
ajpdis-1851	15	22	be	be	AUX
ajpdis-1851	15	23	conditions	condition	NOUN
ajpdis-1851	15	24	determination	determination	NOUN
ajpdis-1851	15	25	demand	demand	NOUN
ajpdis-1851	15	26	done	do	VERB
ajpdis-1851	15	27	issues	issue	NOUN
ajpdis-1851	15	28	usually	usually	ADV
ajpdis-1851	15	29	to	to	ADP
ajpdis-1851	15	30	the	the	DET
ajpdis-1851	15	31	extreme	extreme	NOUN
ajpdis-1851	15	32	about	about	ADP
ajpdis-1851	15	33	issues	issue	NOUN
ajpdis-1851	15	34	called	call	VERB
ajpdis-1851	15	35	(	(	PUNCT
ajpdis-1851	15	36	latin	latin	PROPN
ajpdis-1851	15	37	extremum	extremum	ADJ
ajpdis-1851	15	38	the	the	DET
ajpdis-1851	15	39	edge	edge	NOUN
ajpdis-1851	15	40	)	)	PUNCT
ajpdis-1851	15	41	.	.	PUNCT
ajpdis-1851	16	1	they	they	PRON
ajpdis-1851	16	2	are	be	AUX
ajpdis-1851	16	3	"	"	PUNCT
ajpdis-1851	16	4	maximum	maximum	ADJ
ajpdis-1851	16	5	"	"	PUNCT
ajpdis-1851	16	6	and	and	CCONJ
ajpdis-1851	16	7	"	"	PUNCT
ajpdis-1851	16	8	minimum	minimum	NOUN
ajpdis-1851	16	9	"	"	PUNCT
ajpdis-1851	16	10	(	(	PUNCT
ajpdis-1851	16	11	latin	latin	ADJ
ajpdis-1851	16	12	maximum	maximum	ADJ
ajpdis-1851	16	13	and	and	CCONJ
ajpdis-1851	16	14	minimum	minimum	NOUN
ajpdis-1851	16	15	corresponding	corresponding	NOUN
ajpdis-1851	16	16	without	without	ADP
ajpdis-1851	16	17	"	"	PUNCT
ajpdis-1851	16	18	eng	eng	X
ajpdis-1851	16	19	big	big	ADJ
ajpdis-1851	16	20	”	"	PUNCT
ajpdis-1851	16	21	and	and	CCONJ
ajpdis-1851	16	22	“	"	PUNCT
ajpdis-1851	16	23	most	most	ADJ
ajpdis-1851	16	24	to	to	AUX
ajpdis-1851	16	25	small	small	ADJ
ajpdis-1851	16	26	"	"	PUNCT
ajpdis-1851	16	27	)	)	PUNCT
ajpdis-1851	16	28	,	,	PUNCT
ajpdis-1851	16	29	about	about	ADP
ajpdis-1851	16	30	are	be	AUX
ajpdis-1851	16	31	also	also	ADV
ajpdis-1851	16	32	called	call	VERB
ajpdis-1851	16	33	issues	issue	NOUN
ajpdis-1851	16	34	.	.	PUNCT
ajpdis-1851	17	1	to	to	ADP
ajpdis-1851	17	2	this	this	PRON
ajpdis-1851	17	3	similar	similar	ADJ
ajpdis-1851	17	4	to	to	ADP
ajpdis-1851	17	5	issues	issue	NOUN
ajpdis-1851	17	6	mathematics	mathematic	NOUN
ajpdis-1851	17	7	,	,	PUNCT
ajpdis-1851	17	8	physics	physics	NOUN
ajpdis-1851	17	9	,	,	PUNCT
ajpdis-1851	17	10	mechanics	mechanic	NOUN
ajpdis-1851	17	11	,	,	PUNCT
ajpdis-1851	17	12	technology	technology	NOUN
ajpdis-1851	17	13	,	,	PUNCT
ajpdis-1851	17	14	medicine	medicine	NOUN
ajpdis-1851	17	15	,	,	PUNCT
ajpdis-1851	17	16	economy	economy	NOUN
ajpdis-1851	17	17	and	and	CCONJ
ajpdis-1851	17	18	etc	etc	X
ajpdis-1851	17	19	in	in	ADP
ajpdis-1851	17	20	the	the	DET
ajpdis-1851	17	21	sciences	science	NOUN
ajpdis-1851	17	22	often	often	ADV
ajpdis-1851	17	23	face	face	VERB
ajpdis-1851	17	24	will	will	AUX
ajpdis-1851	17	25	come	come	VERB
ajpdis-1851	17	26	.	.	PUNCT
ajpdis-1851	18	1	for	for	ADP
ajpdis-1851	18	2	example	example	NOUN
ajpdis-1851	18	3	,	,	PUNCT
ajpdis-1851	18	4	round	round	ADV
ajpdis-1851	18	5	from	from	ADP
ajpdis-1851	18	6	wood	wood	NOUN
ajpdis-1851	18	7	how	how	SCONJ
ajpdis-1851	18	8	by	by	ADP
ajpdis-1851	18	9	doing	do	VERB
ajpdis-1851	18	10	right	right	ADJ
ajpdis-1851	18	11	rectangle	rectangle	NOUN
ajpdis-1851	18	12	sectional	sectional	ADJ
ajpdis-1851	18	13	beam	beam	NOUN
ajpdis-1851	18	14	it	it	PRON
ajpdis-1851	18	15	's	be	AUX
ajpdis-1851	18	16	waste	waste	NOUN
ajpdis-1851	18	17	the	the	DET
ajpdis-1851	18	18	most	most	ADV
ajpdis-1851	18	19	less	less	ADJ
ajpdis-1851	18	20	will	will	AUX
ajpdis-1851	18	21	be	be	AUX
ajpdis-1851	18	22	given	give	VERB
ajpdis-1851	18	23	from	from	ADP
ajpdis-1851	18	24	the	the	DET
ajpdis-1851	18	25	material	material	NOUN
ajpdis-1851	18	26	made	make	VERB
ajpdis-1851	18	27	of	of	ADP
ajpdis-1851	18	28	the	the	DET
ajpdis-1851	18	29	box	box	PROPN
ajpdis-1851	18	30	volume	volume	NOUN
ajpdis-1851	18	31	the	the	DET
ajpdis-1851	18	32	most	most	ADV
ajpdis-1851	18	33	big	big	ADJ
ajpdis-1851	18	34	to	to	PART
ajpdis-1851	18	35	be	be	AUX
ajpdis-1851	18	36	for	for	ADP
ajpdis-1851	18	37	his	his	PRON
ajpdis-1851	18	38	dimensions	dimension	NOUN
ajpdis-1851	18	39	how	how	SCONJ
ajpdis-1851	18	40	to	to	PART
ajpdis-1851	18	41	be	be	AUX
ajpdis-1851	18	42	do	do	AUX
ajpdis-1851	18	43	you	you	PRON
ajpdis-1851	18	44	need	need	VERB
ajpdis-1851	18	45	.	.	PUNCT
ajpdis-1851	19	1	two	two	NUM
ajpdis-1851	19	2	the	the	DET
ajpdis-1851	19	3	city	city	NOUN
ajpdis-1851	19	4	connector	connector	NOUN
ajpdis-1851	19	5	road	road	NOUN
ajpdis-1851	19	6	the	the	DET
ajpdis-1851	19	7	most	most	ADV
ajpdis-1851	19	8	short	short	ADJ
ajpdis-1851	19	9	to	to	PART
ajpdis-1851	19	10	be	be	AUX
ajpdis-1851	19	11	for	for	ADP
ajpdis-1851	19	12	the	the	DET
ajpdis-1851	19	13	bridge	bridge	NOUN
ajpdis-1851	19	14	of	of	ADP
ajpdis-1851	19	15	the	the	DET
ajpdis-1851	19	16	river	river	NOUN
ajpdis-1851	19	17	which	which	PRON
ajpdis-1851	19	18	to	to	ADP
ajpdis-1851	19	19	the	the	DET
ajpdis-1851	19	20	place	place	NOUN
ajpdis-1851	19	21	to	to	PART
ajpdis-1851	19	22	build	build	VERB
ajpdis-1851	19	23	do	do	AUX
ajpdis-1851	19	24	you	you	PRON
ajpdis-1851	19	25	need	need	VERB
ajpdis-1851	19	26	and	and	CCONJ
ajpdis-1851	19	27	etc	etc	X
ajpdis-1851	19	28	issues	issue	NOUN
ajpdis-1851	19	29	these	these	PRON
ajpdis-1851	19	30	are	be	AUX
ajpdis-1851	19	31	including	include	VERB
ajpdis-1851	19	32	.	.	PUNCT
ajpdis-1851	20	1	such	such	ADJ
ajpdis-1851	20	2	practical	practical	ADJ
ajpdis-1851	20	3	important	important	ADJ
ajpdis-1851	20	4	have	have	AUX
ajpdis-1851	20	5	issues	issue	NOUN
ajpdis-1851	20	6	geometric	geometric	ADJ
ajpdis-1851	20	7	to	to	ADP
ajpdis-1851	20	8	the	the	DET
ajpdis-1851	20	9	view	view	NOUN
ajpdis-1851	20	10	to	to	PART
ajpdis-1851	20	11	bring	bring	VERB
ajpdis-1851	20	12	difficulty	difficulty	NOUN
ajpdis-1851	20	13	does	do	AUX
ajpdis-1851	20	14	not	not	PART
ajpdis-1851	20	15	give	give	VERB
ajpdis-1851	20	16	birth	birth	NOUN
ajpdis-1851	20	17	.	.	PUNCT
ajpdis-1851	21	1	most	most	ADJ
ajpdis-1851	21	2	simple	simple	ADJ
ajpdis-1851	21	3	and	and	CCONJ
ajpdis-1851	21	4	ancient	ancient	ADJ
ajpdis-1851	21	5	from	from	ADP
ajpdis-1851	21	6	issues	issue	NOUN
ajpdis-1851	21	7	one	one	NUM
ajpdis-1851	21	8	:	:	PUNCT
ajpdis-1851	21	9	perimeter	perimeter	NOUN
ajpdis-1851	21	10	known	know	VERB
ajpdis-1851	21	11	right	right	ADJ
ajpdis-1851	21	12	rectangles	rectangle	NOUN
ajpdis-1851	21	13	between	between	ADP
ajpdis-1851	21	14	which	which	PRON
ajpdis-1851	21	15	one	one	NOUN
ajpdis-1851	21	16	's	's	PART
ajpdis-1851	21	17	surface	surface	NOUN
ajpdis-1851	21	18	the	the	DET
ajpdis-1851	21	19	most	most	ADV
ajpdis-1851	21	20	big	big	ADJ
ajpdis-1851	21	21	that	that	SCONJ
ajpdis-1851	21	22	determination	determination	NOUN
ajpdis-1851	21	23	issue	issue	NOUN
ajpdis-1851	22	1	and	and	CCONJ
ajpdis-1851	22	2	it	it	PRON
ajpdis-1851	22	3	is	be	AUX
ajpdis-1851	22	4	called	call	VERB
ajpdis-1851	22	5	an	an	DET
ajpdis-1851	22	6	isoperimetric	isoperimetric	ADJ
ajpdis-1851	22	7	problem	problem	NOUN
ajpdis-1851	22	8	.	.	PUNCT
ajpdis-1851	23	1	to	to	ADP
ajpdis-1851	23	2	the	the	DET
ajpdis-1851	23	3	extreme	extreme	NOUN
ajpdis-1851	23	4	about	about	ADP
ajpdis-1851	23	5	such	such	ADJ
ajpdis-1851	23	6	issues	issue	NOUN
ajpdis-1851	23	7	in	in	ADP
ajpdis-1851	23	8	solving	solve	VERB
ajpdis-1851	23	9	most	most	ADJ
ajpdis-1851	23	10	of	of	ADP
ajpdis-1851	23	11	the	the	DET
ajpdis-1851	23	12	time	time	NOUN
ajpdis-1851	23	13	of	of	ADP
ajpdis-1851	23	14	quantities	quantity	NOUN
ajpdis-1851	23	15	medium	medium	ADJ
ajpdis-1851	23	16	arithmetic	arithmetic	ADJ
ajpdis-1851	23	17	and	and	CCONJ
ajpdis-1851	23	18	medium	medium	ADJ
ajpdis-1851	23	19	geometric	geometric	ADJ
ajpdis-1851	23	20	values	value	NOUN
ajpdis-1851	23	21	conjunction	conjunction	NOUN
ajpdis-1851	23	22	from	from	ADP
ajpdis-1851	23	23	the	the	DET
ajpdis-1851	23	24	relationship	relationship	NOUN
ajpdis-1851	23	25	is	be	AUX
ajpdis-1851	23	26	used	use	VERB
ajpdis-1851	23	27	.	.	PUNCT
ajpdis-1851	24	1	this	this	PRON
ajpdis-1851	24	2	is	be	AUX
ajpdis-1851	24	3	the	the	DET
ajpdis-1851	24	4	following	follow	VERB
ajpdis-1851	24	5	theorem	theorem	VERB
ajpdis-1851	24	6	with	with	ADP
ajpdis-1851	24	7	defined	define	VERB
ajpdis-1851	24	8	as	as	ADP
ajpdis-1851	24	9	:	:	PUNCT
ajpdis-1851	24	10	theorem	theorem	ADJ
ajpdis-1851	24	11	.	.	PROPN
ajpdis-1851	24	12	minus	minus	PROPN
ajpdis-1851	24	13	did	do	AUX
ajpdis-1851	24	14	n't	not	PART
ajpdis-1851	24	15	happen	happen	VERB
ajpdis-1851	24	16	𝑛of	𝑛of	NOUN
ajpdis-1851	24	17	a	a	DET
ajpdis-1851	24	18	natural	natural	ADJ
ajpdis-1851	24	19	number	number	NOUN
ajpdis-1851	24	20	medium	medium	NOUN
ajpdis-1851	24	21	arithmetic	arithmetic	ADJ
ajpdis-1851	24	22	value	value	NOUN
ajpdis-1851	24	23	that	that	PRON
ajpdis-1851	24	24	's	be	AUX
ajpdis-1851	24	25	it	it	PRON
ajpdis-1851	24	26	of	of	ADP
ajpdis-1851	24	27	thighs	thigh	NOUN
ajpdis-1851	24	28	medium	medium	ADJ
ajpdis-1851	24	29	from	from	ADP
ajpdis-1851	24	30	geometry	geometry	NOUN
ajpdis-1851	24	31	small	small	ADJ
ajpdis-1851	24	32	not	not	PART
ajpdis-1851	24	33	,	,	PUNCT
ajpdis-1851	24	34	that	that	PRON
ajpdis-1851	24	35	is	be	AUX
ajpdis-1851	24	36	𝑥	𝑥	PRON
ajpdis-1851	24	37	!	!	PUNCT
ajpdis-1851	25	1	+	+	PUNCT
ajpdis-1851	26	1	𝑥	𝑥	X
ajpdis-1851	26	2	"	"	PUNCT
ajpdis-1851	26	3	+	+	ADJ
ajpdis-1851	26	4	⋯+	⋯+	NOUN
ajpdis-1851	26	5	𝑥	𝑥	DET
ajpdis-1851	26	6	#	#	NOUN
ajpdis-1851	26	7	𝑛	𝑛	PRON
ajpdis-1851	26	8	≥	≥	NOUN
ajpdis-1851	26	9	&	&	CCONJ
ajpdis-1851	26	10	𝑥	𝑥	NOUN
ajpdis-1851	26	11	!	!	PUNCT
ajpdis-1851	27	1	∙	∙	NOUN
ajpdis-1851	28	1	𝑥	𝑥	X
ajpdis-1851	28	2	"	"	PUNCT
ajpdis-1851	28	3	∙	∙	NOUN
ajpdis-1851	28	4	…	…	PUNCT
ajpdis-1851	28	5	𝑥	𝑥	PRON
ajpdis-1851	28	6	#	#	NOUN
ajpdis-1851	28	7	!	!	PUNCT
ajpdis-1851	28	8	.	.	PUNCT
ajpdis-1851	29	1	equality	equality	NOUN
ajpdis-1851	29	2	sign	sign	VERB
ajpdis-1851	29	3	𝑥	𝑥	X
ajpdis-1851	29	4	!	!	PUNCT
ajpdis-1851	30	1	=	=	PUNCT
ajpdis-1851	30	2	𝑥	𝑥	NOUN
ajpdis-1851	30	3	"	"	PUNCT
ajpdis-1851	30	4	=	=	SYM
ajpdis-1851	30	5	⋯	⋯	NOUN
ajpdis-1851	30	6	=	=	SYM
ajpdis-1851	30	7	𝑥	𝑥	NOUN
ajpdis-1851	30	8	#	#	NOUN
ajpdis-1851	30	9	will	will	AUX
ajpdis-1851	30	10	be	be	AUX
ajpdis-1851	30	11	executed	execute	VERB
ajpdis-1851	30	12	when	when	SCONJ
ajpdis-1851	30	13	below	below	ADP
ajpdis-1851	30	14	this	this	PRON
ajpdis-1851	30	15	of	of	ADP
ajpdis-1851	30	16	the	the	DET
ajpdis-1851	30	17	theorem	theorem	NOUN
ajpdis-1851	30	18	private	private	ADJ
ajpdis-1851	30	19	from	from	ADP
ajpdis-1851	30	20	consists	consist	NOUN
ajpdis-1851	30	21	of	of	ADP
ajpdis-1851	30	22	was	be	AUX
ajpdis-1851	30	23	𝑥	𝑥	PRON
ajpdis-1851	30	24	!	!	PUNCT
ajpdis-1851	31	1	+	+	PUNCT
ajpdis-1851	31	2	𝑥	𝑥	X
ajpdis-1851	31	3	"	"	PUNCT
ajpdis-1851	31	4	2	2	NUM
ajpdis-1851	31	5	≥	≥	NOUN
ajpdis-1851	31	6	&	&	CCONJ
ajpdis-1851	31	7	𝑥!𝑥	𝑥!𝑥	PROPN
ajpdis-1851	31	8	"	"	PUNCT
ajpdis-1851	31	9	relationship	relationship	NOUN
ajpdis-1851	31	10	using	use	VERB
ajpdis-1851	31	11	solvable	solvable	ADJ
ajpdis-1851	31	12	extreme	extreme	NOUN
ajpdis-1851	31	13	to	to	ADP
ajpdis-1851	31	14	the	the	DET
ajpdis-1851	31	15	matter	matter	NOUN
ajpdis-1851	31	16	we	we	PRON
ajpdis-1851	31	17	will	will	AUX
ajpdis-1851	31	18	stop	stop	VERB
ajpdis-1851	31	19	.	.	PUNCT
ajpdis-1851	32	1	issue	issue	NOUN
ajpdis-1851	32	2	1	1	NUM
ajpdis-1851	32	3	.	.	PUNCT
ajpdis-1851	32	4	surface	surface	NOUN
ajpdis-1851	32	5	surface	surface	NOUN
ajpdis-1851	32	6	when	when	SCONJ
ajpdis-1851	32	7	given	give	VERB
ajpdis-1851	32	8	volume	volume	NOUN
ajpdis-1851	32	9	the	the	DET
ajpdis-1851	32	10	most	most	ADV
ajpdis-1851	32	11	big	big	ADJ
ajpdis-1851	32	12	will	will	AUX
ajpdis-1851	32	13	be	be	AUX
ajpdis-1851	32	14	box	box	NOUN
ajpdis-1851	32	15	(	(	PUNCT
ajpdis-1851	32	16	true	true	ADJ
ajpdis-1851	32	17	rectangular	rectangular	ADJ
ajpdis-1851	32	18	parallelepiped	parallelepiped	NOUN
ajpdis-1851	32	19	)	)	PUNCT
ajpdis-1851	32	20	.	.	PUNCT
ajpdis-1851	33	1	dimensions	dimension	NOUN
ajpdis-1851	33	2	how	how	SCONJ
ajpdis-1851	33	3	selection	selection	NOUN
ajpdis-1851	33	4	do	do	AUX
ajpdis-1851	33	5	you	you	PRON
ajpdis-1851	33	6	need	need	VERB
ajpdis-1851	33	7	solution	solution	NOUN
ajpdis-1851	33	8	:	:	PUNCT
ajpdis-1851	33	9	get	get	AUX
ajpdis-1851	33	10	rid	rid	VERB
ajpdis-1851	33	11	of	of	ADP
ajpdis-1851	33	12	it	it	PRON
ajpdis-1851	33	13	edges	edge	VERB
ajpdis-1851	33	14	𝑎	𝑎	PROPN
ajpdis-1851	33	15	,	,	PUNCT
ajpdis-1851	33	16	𝑏	𝑏	NOUN
ajpdis-1851	33	17	,	,	PUNCT
ajpdis-1851	33	18	𝑐	𝑐	NOUN
ajpdis-1851	33	19	with	with	ADP
ajpdis-1851	33	20	s	s	PROPN
ajpdis-1851	33	21	,	,	PUNCT
ajpdis-1851	33	22	his	his	PRON
ajpdis-1851	33	23	full	full	ADJ
ajpdis-1851	33	24	the	the	DET
ajpdis-1851	33	25	surface	surface	NOUN
ajpdis-1851	33	26	while	while	SCONJ
ajpdis-1851	33	27	𝑆	𝑆	PROPN
ajpdis-1851	33	28	with	with	ADP
ajpdis-1851	33	29	and	and	CCONJ
ajpdis-1851	33	30	𝑉	𝑉	PROPN
ajpdis-1851	33	31	we	we	PRON
ajpdis-1851	33	32	define	define	VERB
ajpdis-1851	33	33	the	the	DET
ajpdis-1851	33	34	size	size	NOUN
ajpdis-1851	33	35	with	with	ADP
ajpdis-1851	33	36	.	.	PUNCT
ajpdis-1851	34	1	in	in	ADP
ajpdis-1851	34	2	that	that	DET
ajpdis-1851	34	3	case	case	NOUN
ajpdis-1851	34	4	𝑆	𝑆	PROPN
ajpdis-1851	34	5	=	=	SYM
ajpdis-1851	34	6	2(𝑎𝑏	2(𝑎𝑏	PROPN
ajpdis-1851	35	1	+	+	CCONJ
ajpdis-1851	35	2	𝑎𝑐	𝑎𝑐	PROPN
ajpdis-1851	35	3	+	+	NUM
ajpdis-1851	35	4	𝑏𝑐	𝑏𝑐	PROPN
ajpdis-1851	35	5	)	)	PUNCT
ajpdis-1851	35	6	and	and	CCONJ
ajpdis-1851	35	7	𝑉	𝑉	PROPN
ajpdis-1851	35	8	=	=	NOUN
ajpdis-1851	35	9	𝑎𝑏𝑐	𝑎𝑏𝑐	NOUN
ajpdis-1851	35	10	will	will	AUX
ajpdis-1851	35	11	be	be	AUX
ajpdis-1851	35	12	(	(	PUNCT
ajpdis-1851	35	13	fig	fig	NOUN
ajpdis-1851	35	14	.	.	NOUN
ajpdis-1851	35	15	1	1	NUM
ajpdis-1851	35	16	)	)	PUNCT
ajpdis-1851	35	17	.	.	PUNCT
ajpdis-1851	36	1	first	first	ADV
ajpdis-1851	36	2	from	from	ADP
ajpdis-1851	36	3	equality	equality	NOUN
ajpdis-1851	36	4	𝑎𝑏	𝑎𝑏	PRON
ajpdis-1851	36	5	+	+	CCONJ
ajpdis-1851	36	6	𝑎𝑐	𝑎𝑐	PROPN
ajpdis-1851	36	7	+	+	NUM
ajpdis-1851	36	8	𝑏𝑐	𝑏𝑐	PROPN
ajpdis-1851	36	9	=	=	SYM
ajpdis-1851	36	10	$	$	SYM
ajpdis-1851	36	11	"	"	PUNCT
ajpdis-1851	36	12	the	the	DET
ajpdis-1851	36	13	fact	fact	NOUN
ajpdis-1851	36	14	that	that	SCONJ
ajpdis-1851	36	15	known	know	VERB
ajpdis-1851	36	16	.	.	PUNCT
ajpdis-1851	37	1	secondly	secondly	ADV
ajpdis-1851	37	2	𝑎𝑏	𝑎𝑏	ADP
ajpdis-1851	37	3	∙	∙	PROPN
ajpdis-1851	37	4	𝑎𝑐	𝑎𝑐	PROPN
ajpdis-1851	37	5	∙	∙	PROPN
ajpdis-1851	37	6	𝑏𝑐	𝑏𝑐	PROPN
ajpdis-1851	37	7	=	=	SYM
ajpdis-1851	37	8	𝑉	𝑉	PROPN
ajpdis-1851	37	9	"	"	PUNCT
ajpdis-1851	37	10	the	the	PRON
ajpdis-1851	37	11	to	to	PART
ajpdis-1851	37	12	write	write	VERB
ajpdis-1851	37	13	can	can	AUX
ajpdis-1851	37	14	now	now	ADV
ajpdis-1851	37	15	these	these	PRON
ajpdis-1851	37	16	are	be	AUX
ajpdis-1851	37	17	for	for	ADP
ajpdis-1851	37	18	medium	medium	ADJ
ajpdis-1851	37	19	arithmetic	arithmetic	ADJ
ajpdis-1851	37	20	and	and	CCONJ
ajpdis-1851	37	21	medium	medium	NOUN
ajpdis-1851	37	22	geometric	geometric	ADJ
ajpdis-1851	37	23	about	about	ADP
ajpdis-1851	37	24	inequality	inequality	NOUN
ajpdis-1851	37	25	if	if	SCONJ
ajpdis-1851	37	26	we	we	PRON
ajpdis-1851	37	27	apply	apply	VERB
ajpdis-1851	37	28	,	,	PUNCT
ajpdis-1851	37	29	to	to	ADP
ajpdis-1851	37	30	the	the	DET
ajpdis-1851	37	31	following	following	NOUN
ajpdis-1851	37	32	have	have	AUX
ajpdis-1851	37	33	we	we	PRON
ajpdis-1851	37	34	will	will	AUX
ajpdis-1851	37	35	be	be	AUX
ajpdis-1851	37	36	:	:	PUNCT
ajpdis-1851	37	37	𝑎𝑏	𝑎𝑏	PROPN
ajpdis-1851	37	38	+	+	CCONJ
ajpdis-1851	37	39	𝑎𝑐	𝑎𝑐	PROPN
ajpdis-1851	38	1	+	+	CCONJ
ajpdis-1851	38	2	𝑏𝑐	𝑏𝑐	PROPN
ajpdis-1851	38	3	3	3	NUM
ajpdis-1851	38	4	≥	≥	NOUN
ajpdis-1851	38	5	√𝑎𝑏	√𝑎𝑏	NOUN
ajpdis-1851	38	6	∙	∙	PROPN
ajpdis-1851	38	7	𝑎𝑐	𝑎𝑐	PROPN
ajpdis-1851	38	8	∙	∙	PROPN
ajpdis-1851	38	9	𝑏𝑐	𝑏𝑐	PROPN
ajpdis-1851	38	10	"	"	PUNCT
ajpdis-1851	38	11	,	,	PUNCT
ajpdis-1851	38	12	𝑆	𝑆	PROPN
ajpdis-1851	38	13	6	6	NUM
ajpdis-1851	38	14	≥	≥	NOUN
ajpdis-1851	38	15	𝑉	𝑉	PROPN
ajpdis-1851	38	16	"	"	PUNCT
ajpdis-1851	38	17	%	%	NOUN
ajpdis-1851	38	18	𝑦𝑜𝑘𝑖	𝑦𝑜𝑘𝑖	NOUN
ajpdis-1851	38	19	𝑉	𝑉	PROPN
ajpdis-1851	38	20	≤	≤	NOUN
ajpdis-1851	38	21	=	=	PUNCT
ajpdis-1851	38	22	𝑆	𝑆	PROPN
ajpdis-1851	38	23	6	6	NUM
ajpdis-1851	38	24	>	>	SYM
ajpdis-1851	38	25	%	%	NOUN
ajpdis-1851	38	26	"	"	PUNCT
ajpdis-1851	38	27	medium	medium	ADJ
ajpdis-1851	38	28	values	value	NOUN
ajpdis-1851	38	29	about	about	ADP
ajpdis-1851	38	30	from	from	ADP
ajpdis-1851	38	31	the	the	DET
ajpdis-1851	38	32	theorem	theorem	NOUN
ajpdis-1851	38	33	only	only	ADV
ajpdis-1851	38	34	=	=	PUNCT
ajpdis-1851	38	35	𝑎𝑐	𝑎𝑐	PROPN
ajpdis-1851	38	36	=	=	PUNCT
ajpdis-1851	38	37	𝑏𝑐	𝑏𝑐	PROPN
ajpdis-1851	38	38	,	,	PUNCT
ajpdis-1851	38	39	i.e.	i.e.	X
ajpdis-1851	38	40	when	when	SCONJ
ajpdis-1851	38	41	𝑎	𝑎	PROPN
ajpdis-1851	38	42	=	=	SYM
ajpdis-1851	38	43	𝑏	𝑏	NOUN
ajpdis-1851	38	44	=	=	PUNCT
ajpdis-1851	38	45	𝑐b	𝑐b	PROPN
ajpdis-1851	38	46	dies	die	VERB
ajpdis-1851	38	47	inequality	inequality	NOUN
ajpdis-1851	38	48	it	it	PRON
ajpdis-1851	38	49	follows	follow	VERB
ajpdis-1851	38	50	that	that	SCONJ
ajpdis-1851	38	51	the	the	DET
ajpdis-1851	38	52	sign	sign	NOUN
ajpdis-1851	38	53	becomes	become	VERB
ajpdis-1851	38	54	equal	equal	ADJ
ajpdis-1851	38	55	,	,	PUNCT
ajpdis-1851	38	56	and	and	CCONJ
ajpdis-1851	38	57	in	in	ADP
ajpdis-1851	38	58	this	this	DET
ajpdis-1851	38	59	case	case	NOUN
ajpdis-1851	38	60	the	the	DET
ajpdis-1851	38	61	volume	volume	NOUN
ajpdis-1851	38	62	v	v	NOUN
ajpdis-1851	38	63	assumes	assume	VERB
ajpdis-1851	38	64	the	the	DET
ajpdis-1851	38	65	largest	large	ADJ
ajpdis-1851	38	66	value	value	NOUN
ajpdis-1851	38	67	.	.	PUNCT
ajpdis-1851	39	1	to	to	ADP
ajpdis-1851	39	2	the	the	DET
ajpdis-1851	39	3	extreme	extreme	NOUN
ajpdis-1851	39	4	about	about	ADP
ajpdis-1851	39	5	some	some	DET
ajpdis-1851	39	6	geometric	geometric	ADJ
ajpdis-1851	39	7	issues	issue	NOUN
ajpdis-1851	39	8	in	in	ADP
ajpdis-1851	39	9	solving	solve	VERB
ajpdis-1851	39	10	symmetry	symmetry	NOUN
ajpdis-1851	39	11	using	use	VERB
ajpdis-1851	39	12	the	the	DET
ajpdis-1851	39	13	method	method	NOUN
ajpdis-1851	39	14	can	can	AUX
ajpdis-1851	39	15	below	below	ADV
ajpdis-1851	39	16	to	to	ADP
ajpdis-1851	39	17	him	he	PRON
ajpdis-1851	39	18	let	let	VERB
ajpdis-1851	39	19	's	us	PRON
ajpdis-1851	39	20	look	look	VERB
ajpdis-1851	39	21	at	at	ADP
ajpdis-1851	39	22	the	the	DET
ajpdis-1851	39	23	issue	issue	NOUN
ajpdis-1851	39	24	:	:	PUNCT
ajpdis-1851	39	25	issue	issue	NOUN
ajpdis-1851	39	26	2.𝑎	2.𝑎	NUM
ajpdis-1851	39	27	given	give	VERB
ajpdis-1851	39	28	a	a	DET
ajpdis-1851	39	29	𝑎straight	𝑎straight	ADJ
ajpdis-1851	39	30	line	line	NOUN
ajpdis-1851	39	31	and	and	CCONJ
ajpdis-1851	39	32	points	point	VERB
ajpdis-1851	39	33	𝐵	𝐵	NOUN
ajpdis-1851	39	34	on	on	ADP
ajpdis-1851	39	35	one	one	NUM
ajpdis-1851	39	36	side	side	NOUN
ajpdis-1851	39	37	of	of	ADP
ajpdis-1851	39	38	it	it	PRON
ajpdis-1851	39	39	.	.	PUNCT
ajpdis-1851	40	1	𝐴	𝐴	PROPN
ajpdis-1851	40	2	find	find	VERB
ajpdis-1851	40	3	a	a	DET
ajpdis-1851	40	4	point	point	NOUN
ajpdis-1851	40	5	on	on	ADP
ajpdis-1851	40	6	the	the	DET
ajpdis-1851	40	7	𝐴	𝐴	PROPN
ajpdis-1851	40	8	straight	straight	ADJ
ajpdis-1851	40	9	line	line	NOUN
ajpdis-1851	40	10	such	such	ADJ
ajpdis-1851	40	11	𝐶	𝐶	PROPN
ajpdis-1851	40	12	that	that	SCONJ
ajpdis-1851	40	13	𝐵	𝐵	NOUN
ajpdis-1851	40	14	to	to	ADP
ajpdis-1851	40	15	the	the	DET
ajpdis-1851	40	16	points	point	NOUN
ajpdis-1851	40	17	distances	distance	NOUN
ajpdis-1851	40	18	sum	sum	VERB
ajpdis-1851	40	19	the	the	DET
ajpdis-1851	40	20	most	most	ADV
ajpdis-1851	40	21	small	small	ADJ
ajpdis-1851	40	22	to	to	PART
ajpdis-1851	40	23	value	value	VERB
ajpdis-1851	40	24	let	let	VERB
ajpdis-1851	40	25	it	it	PRON
ajpdis-1851	40	26	reach	reach	VERB
ajpdis-1851	40	27	(	(	PUNCT
ajpdis-1851	40	28	fig	fig	NOUN
ajpdis-1851	40	29	.	.	PUNCT
ajpdis-1851	40	30	2	2	NUM
ajpdis-1851	40	31	)	)	PUNCT
ajpdis-1851	40	32	.	.	PUNCT
ajpdis-1851	41	1	solution	solution	NOUN
ajpdis-1851	41	2	:	:	PUNCT
ajpdis-1851	41	3	let	let	VERB
ajpdis-1851	41	4	𝐴′	𝐴′	PROPN
ajpdis-1851	41	5	the	the	DET
ajpdis-1851	41	6	point	point	NOUN
ajpdis-1851	41	7	𝑎be	𝑎be	NOUN
ajpdis-1851	41	8	point	point	NOUN
ajpdis-1851	41	9	-	-	PUNCT
ajpdis-1851	41	10	to	to	ADP
ajpdis-1851	41	11	-	-	PUNCT
ajpdis-1851	41	12	point	point	NOUN
ajpdis-1851	41	13	symmetric	symmetric	PROPN
ajpdis-1851	41	14	𝐶	𝐶	PROPN
ajpdis-1851	41	15	with	with	ADP
ajpdis-1851	41	16	respect	respect	NOUN
ajpdis-1851	41	17	to	to	ADP
ajpdis-1851	41	18	the	the	DET
ajpdis-1851	41	19	straight	straight	ADJ
ajpdis-1851	41	20	line	line	NOUN
ajpdis-1851	41	21	,	,	PUNCT
ajpdis-1851	41	22	𝐴	𝐴	PROPN
ajpdis-1851	41	23	and	and	CCONJ
ajpdis-1851	41	24	the	the	DET
ajpdis-1851	41	25	point	point	NOUN
ajpdis-1851	41	26	and	and	CCONJ
ajpdis-1851	41	27	𝐴′𝐵	𝐴′𝐵	PUNCT
ajpdis-1851	41	28	and	and	CCONJ
ajpdis-1851	41	29	𝑎be	𝑎be	VERB
ajpdis-1851	41	30	the	the	DET
ajpdis-1851	41	31	point	point	NOUN
ajpdis-1851	41	32	of	of	ADP
ajpdis-1851	41	33	intersection	intersection	NOUN
ajpdis-1851	41	34	of	of	ADP
ajpdis-1851	41	35	straight	straight	ADJ
ajpdis-1851	41	36	lines	line	NOUN
ajpdis-1851	41	37	.	.	PUNCT
ajpdis-1851	42	1	in	in	ADP
ajpdis-1851	42	2	that	that	DET
ajpdis-1851	42	3	case	case	NOUN
ajpdis-1851	42	4	𝐶	𝐶	PROPN
ajpdis-1851	42	5	the	the	DET
ajpdis-1851	42	6	wanted	wanted	ADJ
ajpdis-1851	42	7	point	point	NOUN
ajpdis-1851	42	8	will	will	AUX
ajpdis-1851	42	9	be	be	AUX
ajpdis-1851	42	10	indeed	indeed	ADV
ajpdis-1851	42	11	too	too	ADV
ajpdis-1851	42	12	𝐶𝐴	𝐶𝐴	PRON
ajpdis-1851	42	13	+	+	CCONJ
ajpdis-1851	42	14	𝐶𝐵	𝐶𝐵	PROPN
ajpdis-1851	42	15	=	=	SYM
ajpdis-1851	42	16	𝐶𝐴	𝐶𝐴	PROPN
ajpdis-1851	42	17	&	&	CCONJ
ajpdis-1851	42	18	+	+	ADJ
ajpdis-1851	42	19	𝐶𝐵	𝐶𝐵	PROPN
ajpdis-1851	42	20	=	=	PUNCT
ajpdis-1851	42	21	𝐴′𝐵.	𝐴′𝐵.	PROPN
ajpdis-1851	42	22	if	if	SCONJ
ajpdis-1851	42	23	we	we	PRON
ajpdis-1851	42	24	𝑎choose	𝑎choose	VERB
ajpdis-1851	42	25	another	another	DET
ajpdis-1851	42	26	option	option	NOUN
ajpdis-1851	42	27	of	of	ADP
ajpdis-1851	42	28	a	a	DET
ajpdis-1851	42	29	straight	straight	ADJ
ajpdis-1851	42	30	line	line	NOUN
ajpdis-1851	42	31	𝐷	𝐷	PROPN
ajpdis-1851	42	32	the	the	DET
ajpdis-1851	42	33	point	point	NOUN
ajpdis-1851	42	34	if	if	SCONJ
ajpdis-1851	42	35	we	we	PRON
ajpdis-1851	42	36	get	get	VERB
ajpdis-1851	42	37	,	,	PUNCT
ajpdis-1851	42	38	𝐴𝐷	𝐴𝐷	PROPN
ajpdis-1851	42	39	+	+	CCONJ
ajpdis-1851	42	40	𝐷𝐵	𝐷𝐵	PROPN
ajpdis-1851	43	1	=	=	SYM
ajpdis-1851	43	2	𝐴&𝐷	𝐴&𝐷	PROPN
ajpdis-1851	43	3	+	+	CCONJ
ajpdis-1851	43	4	𝐷𝐵	𝐷𝐵	PROPN
ajpdis-1851	43	5	>	>	PUNCT
ajpdis-1851	44	1	𝐴′𝐵	𝐴′𝐵	X
ajpdis-1851	44	2	the	the	DET
ajpdis-1851	44	3	inequality	inequality	NOUN
ajpdis-1851	44	4	will	will	AUX
ajpdis-1851	44	5	be	be	AUX
ajpdis-1851	44	6	valid	valid	ADJ
ajpdis-1851	44	7	.	.	PUNCT
ajpdis-1851	45	1	115	115	NUM
ajpdis-1851	45	2	american	american	ADJ
ajpdis-1851	45	3	journal	journal	PROPN
ajpdis-1851	45	4	of	of	ADP
ajpdis-1851	45	5	public	public	ADJ
ajpdis-1851	45	6	diplomacy	diplomacy	NOUN
ajpdis-1851	45	7	and	and	CCONJ
ajpdis-1851	45	8	international	international	ADJ
ajpdis-1851	45	9	studies	study	NOUN
ajpdis-1851	45	10	www	www	PROPN
ajpdis-1851	45	11	.	.	PROPN
ajpdis-1851	46	1	grnjournal.us	grnjournal.us	X
ajpdis-1851	46	2	extreme	extreme	ADJ
ajpdis-1851	46	3	issues	issue	NOUN
ajpdis-1851	46	4	in	in	ADP
ajpdis-1851	46	5	solving	solve	VERB
ajpdis-1851	46	6	most	most	ADJ
ajpdis-1851	46	7	of	of	ADP
ajpdis-1851	46	8	the	the	DET
ajpdis-1851	46	9	time	time	NOUN
ajpdis-1851	47	1	do	do	AUX
ajpdis-1851	47	2	n’t	not	PART
ajpdis-1851	47	3	multiply	multiply	VERB
ajpdis-1851	47	4	maximum	maximum	ADV
ajpdis-1851	47	5	and	and	CCONJ
ajpdis-1851	47	6	get	get	VERB
ajpdis-1851	47	7	together	together	ADV
ajpdis-1851	47	8	minimum	minimum	NOUN
ajpdis-1851	47	9	about	about	ADP
ajpdis-1851	47	10	theorems	theorem	NOUN
ajpdis-1851	47	11	are	be	AUX
ajpdis-1851	47	12	also	also	ADV
ajpdis-1851	47	13	used	use	VERB
ajpdis-1851	47	14	.	.	PUNCT
ajpdis-1851	48	1	below	below	ADP
ajpdis-1851	48	2	them	they	PRON
ajpdis-1851	48	3	without	without	ADP
ajpdis-1851	48	4	proof	proof	NOUN
ajpdis-1851	48	5	we	we	PRON
ajpdis-1851	48	6	bring	bring	VERB
ajpdis-1851	48	7	.	.	PUNCT
ajpdis-1851	49	1	theorem	theorem	VERB
ajpdis-1851	49	2	1.𝑛	1.𝑛	NUM
ajpdis-1851	49	3	if	if	SCONJ
ajpdis-1851	49	4	the	the	DET
ajpdis-1851	49	5	sum	sum	NOUN
ajpdis-1851	49	6	of	of	ADP
ajpdis-1851	49	7	positive	positive	ADJ
ajpdis-1851	49	8	numbers	number	NOUN
ajpdis-1851	49	9	is	be	AUX
ajpdis-1851	49	10	constant	constant	ADJ
ajpdis-1851	49	11	,	,	PUNCT
ajpdis-1851	49	12	then	then	ADV
ajpdis-1851	49	13	the	the	DET
ajpdis-1851	49	14	product	product	NOUN
ajpdis-1851	49	15	of	of	ADP
ajpdis-1851	49	16	these	these	DET
ajpdis-1851	49	17	numbers	number	NOUN
ajpdis-1851	49	18	is	be	AUX
ajpdis-1851	49	19	the	the	DET
ajpdis-1851	49	20	largest	large	ADJ
ajpdis-1851	49	21	value	value	NOUN
ajpdis-1851	49	22	of	of	ADP
ajpdis-1851	49	23	these	these	DET
ajpdis-1851	49	24	numbers	number	NOUN
ajpdis-1851	49	25	mutually	mutually	ADV
ajpdis-1851	49	26	equal	equal	ADJ
ajpdis-1851	49	27	to	to	ADP
ajpdis-1851	49	28	when	when	SCONJ
ajpdis-1851	49	29	achieves	achieve	VERB
ajpdis-1851	49	30	.	.	PUNCT
ajpdis-1851	50	1	theorem	theorem	VERB
ajpdis-1851	50	2	2.𝑛	2.𝑛	NUM
ajpdis-1851	50	3	if	if	SCONJ
ajpdis-1851	50	4	the	the	DET
ajpdis-1851	50	5	product	product	NOUN
ajpdis-1851	50	6	of	of	ADP
ajpdis-1851	50	7	a	a	DET
ajpdis-1851	50	8	positive	positive	ADJ
ajpdis-1851	50	9	number	number	NOUN
ajpdis-1851	50	10	is	be	AUX
ajpdis-1851	50	11	constant	constant	ADJ
ajpdis-1851	50	12	,	,	PUNCT
ajpdis-1851	50	13	then	then	ADV
ajpdis-1851	50	14	the	the	DET
ajpdis-1851	50	15	sum	sum	NOUN
ajpdis-1851	50	16	of	of	ADP
ajpdis-1851	50	17	these	these	DET
ajpdis-1851	50	18	numbers	number	NOUN
ajpdis-1851	50	19	reaches	reach	VERB
ajpdis-1851	50	20	its	its	PRON
ajpdis-1851	50	21	smallest	small	ADJ
ajpdis-1851	50	22	value	value	NOUN
ajpdis-1851	50	23	when	when	SCONJ
ajpdis-1851	50	24	these	these	DET
ajpdis-1851	50	25	numbers	number	NOUN
ajpdis-1851	50	26	are	be	AUX
ajpdis-1851	50	27	equal	equal	ADJ
ajpdis-1851	50	28	to	to	ADP
ajpdis-1851	50	29	each	each	DET
ajpdis-1851	50	30	other	other	ADJ
ajpdis-1851	50	31	.	.	PUNCT
ajpdis-1851	51	1	below	below	ADP
ajpdis-1851	51	2	this	this	DET
ajpdis-1851	51	3	theorems	theorem	NOUN
ajpdis-1851	51	4	to	to	PART
ajpdis-1851	51	5	apply	apply	VERB
ajpdis-1851	51	6	let	let	VERB
ajpdis-1851	51	7	’s	’s	NOUN
ajpdis-1851	51	8	see	see	VERB
ajpdis-1851	51	9	the	the	DET
ajpdis-1851	51	10	issue	issue	NOUN
ajpdis-1851	51	11	:	:	PUNCT
ajpdis-1851	51	12	issue	issue	NOUN
ajpdis-1851	51	13	3	3	NUM
ajpdis-1851	51	14	.	.	PUNCT
ajpdis-1851	51	15	side	side	NOUN
ajpdis-1851	51	16	𝑎there	𝑎there	ADV
ajpdis-1851	51	17	was	be	AUX
ajpdis-1851	51	18	an	an	DET
ajpdis-1851	51	19	awning	awning	NOUN
ajpdis-1851	51	20	square	square	ADJ
ajpdis-1851	51	21	shaped	shape	VERB
ajpdis-1851	51	22	tin	tin	NOUN
ajpdis-1851	51	23	given	give	VERB
ajpdis-1851	51	24	tin	tin	NOUN
ajpdis-1851	51	25	off	off	ADP
ajpdis-1851	51	26	four	four	NUM
ajpdis-1851	51	27	from	from	ADP
ajpdis-1851	51	28	the	the	DET
ajpdis-1851	51	29	tip	tip	NOUN
ajpdis-1851	51	30	one	one	NUM
ajpdis-1851	51	31	different	different	ADJ
ajpdis-1851	51	32	square	square	NOUN
ajpdis-1851	51	33	will	will	AUX
ajpdis-1851	51	34	play	play	VERB
ajpdis-1851	51	35	cut	cut	VERB
ajpdis-1851	51	36	off	off	ADP
ajpdis-1851	51	37	taken	take	VERB
ajpdis-1851	51	38	and	and	CCONJ
ajpdis-1851	51	39	left	leave	VERB
ajpdis-1851	51	40	from	from	ADP
ajpdis-1851	51	41	the	the	DET
ajpdis-1851	51	42	part	part	NOUN
ajpdis-1851	51	43	over	over	ADP
ajpdis-1851	51	44	open	open	ADJ
ajpdis-1851	51	45	box	box	NOUN
ajpdis-1851	51	46	made	make	VERB
ajpdis-1851	51	47	cut	cut	VERB
ajpdis-1851	51	48	off	off	ADP
ajpdis-1851	51	49	received	receive	VERB
ajpdis-1851	51	50	squares	square	NOUN
ajpdis-1851	51	51	side	side	NOUN
ajpdis-1851	51	52	how	how	SCONJ
ajpdis-1851	51	53	when	when	SCONJ
ajpdis-1851	51	54	box	box	NOUN
ajpdis-1851	51	55	volume	volume	NOUN
ajpdis-1851	51	56	the	the	DET
ajpdis-1851	51	57	most	most	ADV
ajpdis-1851	51	58	big	big	ADJ
ajpdis-1851	51	59	will	will	AUX
ajpdis-1851	51	60	be	be	AUX
ajpdis-1851	51	61	.	.	PUNCT
ajpdis-1851	52	1	solution	solution	NOUN
ajpdis-1851	52	2	:	:	PUNCT
ajpdis-1851	52	3	cut	cut	NOUN
ajpdis-1851	52	4	received	receive	VERB
ajpdis-1851	52	5	squares	square	NOUN
ajpdis-1851	52	6	let	let	VERB
ajpdis-1851	52	7	the	the	DET
ajpdis-1851	52	8	side	side	NOUN
ajpdis-1851	52	9	be	be	AUX
ajpdis-1851	52	10	x	x	PUNCT
ajpdis-1851	52	11	(	(	PUNCT
ajpdis-1851	52	12	fig	fig	NOUN
ajpdis-1851	52	13	.	.	PUNCT
ajpdis-1851	53	1	3	3	NUM
ajpdis-1851	53	2	)	)	PUNCT
ajpdis-1851	53	3	.	.	PUNCT
ajpdis-1851	54	1	in	in	ADP
ajpdis-1851	54	2	that	that	DET
ajpdis-1851	54	3	case	case	NOUN
ajpdis-1851	54	4	of	of	ADP
ajpdis-1851	54	5	the	the	DET
ajpdis-1851	54	6	box	box	NOUN
ajpdis-1851	54	7	𝑉	𝑉	PROPN
ajpdis-1851	54	8	=	=	PUNCT
ajpdis-1851	54	9	(	(	PUNCT
ajpdis-1851	54	10	𝑎	𝑎	DET
ajpdis-1851	54	11	−	−	NUM
ajpdis-1851	54	12	2𝑥)"𝑥	2𝑥)"𝑥	NUM
ajpdis-1851	54	13	volume	volume	NOUN
ajpdis-1851	54	14	will	will	AUX
ajpdis-1851	54	15	be	be	AUX
ajpdis-1851	54	16	of	of	ADP
ajpdis-1851	54	17	this	this	PRON
ajpdis-1851	54	18	the	the	DET
ajpdis-1851	54	19	most	most	ADV
ajpdis-1851	54	20	big	big	ADJ
ajpdis-1851	54	21	value	value	NOUN
ajpdis-1851	54	22	to	to	PART
ajpdis-1851	54	23	find	find	VERB
ajpdis-1851	54	24	for	for	ADP
ajpdis-1851	54	25	as	as	SCONJ
ajpdis-1851	54	26	follows	follow	VERB
ajpdis-1851	54	27	form	form	NOUN
ajpdis-1851	54	28	change	change	NOUN
ajpdis-1851	54	29	we	we	PRON
ajpdis-1851	54	30	do	do	VERB
ajpdis-1851	54	31	:	:	PUNCT
ajpdis-1851	54	32	4𝑉	4𝑉	PROPN
ajpdis-1851	54	33	=	=	SYM
ajpdis-1851	54	34	4𝑥(𝑎	4𝑥(𝑎	PROPN
ajpdis-1851	54	35	−	−	NUM
ajpdis-1851	54	36	2𝑥)(𝑎	2𝑥)(𝑎	NUM
ajpdis-1851	54	37	−	−	PROPN
ajpdis-1851	54	38	2𝑥	2𝑥	NOUN
ajpdis-1851	54	39	)	)	PUNCT
ajpdis-1851	54	40	.	.	PUNCT
ajpdis-1851	55	1	multipliers	multiplier	NOUN
ajpdis-1851	55	2	sum	sum	VERB
ajpdis-1851	55	3	4𝑥	4𝑥	NOUN
ajpdis-1851	56	1	+	+	CCONJ
ajpdis-1851	56	2	𝑎	𝑎	DET
ajpdis-1851	56	3	−	−	NOUN
ajpdis-1851	56	4	2𝑥	2𝑥	NOUN
ajpdis-1851	56	5	+	+	CCONJ
ajpdis-1851	56	6	𝑎	𝑎	DET
ajpdis-1851	56	7	−	−	NOUN
ajpdis-1851	56	8	2𝑥	2𝑥	NOUN
ajpdis-1851	56	9	=	=	SYM
ajpdis-1851	56	10	2𝑎	2𝑎	NUM
ajpdis-1851	56	11	immutable	immutable	ADJ
ajpdis-1851	56	12	that	that	SCONJ
ajpdis-1851	56	13	it	it	PRON
ajpdis-1851	56	14	was	be	AUX
ajpdis-1851	56	15	for	for	ADP
ajpdis-1851	56	16	4𝑥	4𝑥	NOUN
ajpdis-1851	56	17	=	=	PUNCT
ajpdis-1851	57	1	𝑎	𝑎	PRON
ajpdis-1851	57	2	−	−	PROPN
ajpdis-1851	57	3	2𝑥reaches	2𝑥reaches	NUM
ajpdis-1851	57	4	its	its	PRON
ajpdis-1851	57	5	maximum	maximum	ADJ
ajpdis-1851	57	6	value	value	NOUN
ajpdis-1851	57	7	when	when	SCONJ
ajpdis-1851	57	8	4𝑉	4𝑉	PROPN
ajpdis-1851	57	9	4𝑥	4𝑥	NOUN
ajpdis-1851	57	10	=	=	PUNCT
ajpdis-1851	57	11	𝑎	𝑎	PRON
ajpdis-1851	57	12	−	−	NOUN
ajpdis-1851	57	13	2𝑥	2𝑥	NOUN
ajpdis-1851	57	14	;	;	PUNCT
ajpdis-1851	57	15	6𝑥	6𝑥	NUM
ajpdis-1851	57	16	=	=	SYM
ajpdis-1851	57	17	𝑎	𝑎	NOUN
ajpdis-1851	57	18	;	;	PUNCT
ajpdis-1851	57	19	𝑥	𝑥	NOUN
ajpdis-1851	57	20	=	=	SYM
ajpdis-1851	58	1	𝑎	𝑎	PRON
ajpdis-1851	58	2	6	6	NUM
ajpdis-1851	58	3	;	;	PUNCT
ajpdis-1851	58	4	𝑉	𝑉	PROPN
ajpdis-1851	58	5	'	'	PUNCT
ajpdis-1851	58	6	(	(	PUNCT
ajpdis-1851	58	7	)	)	PUNCT
ajpdis-1851	58	8	h	h	NOUN
ajpdis-1851	59	1	𝑎	𝑎	DET
ajpdis-1851	59	2	6i	6i	NUM
ajpdis-1851	59	3	=	=	SYM
ajpdis-1851	59	4	2	2	NUM
ajpdis-1851	59	5	27𝑎	27𝑎	NUM
ajpdis-1851	59	6	%	%	NOUN
ajpdis-1851	59	7	.	.	PUNCT
ajpdis-1851	60	1	so	so	ADV
ajpdis-1851	60	2	,	,	PUNCT
ajpdis-1851	60	3	cut	cut	VERB
ajpdis-1851	60	4	received	receive	VERB
ajpdis-1851	60	5	square	square	ADJ
ajpdis-1851	60	6	side	side	NOUN
ajpdis-1851	60	7	given	give	VERB
ajpdis-1851	60	8	square	square	ADJ
ajpdis-1851	60	9	side	side	NOUN
ajpdis-1851	60	10	of	of	ADP
ajpdis-1851	60	11	!	!	PUNCT
ajpdis-1851	61	1	*	*	PUNCT
ajpdis-1851	61	2	when	when	SCONJ
ajpdis-1851	61	3	forming	form	VERB
ajpdis-1851	61	4	the	the	DET
ajpdis-1851	61	5	part	part	NOUN
ajpdis-1851	61	6	box	box	NOUN
ajpdis-1851	61	7	the	the	DET
ajpdis-1851	61	8	most	most	ADV
ajpdis-1851	61	9	big	big	ADJ
ajpdis-1851	61	10	to	to	PART
ajpdis-1851	61	11	volume	volume	NOUN
ajpdis-1851	61	12	have	have	AUX
ajpdis-1851	61	13	will	will	AUX
ajpdis-1851	61	14	be	be	AUX
ajpdis-1851	61	15	.	.	PUNCT
ajpdis-1851	62	1	some	some	DET
ajpdis-1851	62	2	one	one	NUM
ajpdis-1851	62	3	extreme	extreme	ADJ
ajpdis-1851	62	4	issues	issue	NOUN
ajpdis-1851	62	5	in	in	ADP
ajpdis-1851	62	6	solving	solve	VERB
ajpdis-1851	62	7	square	square	NOUN
ajpdis-1851	62	8	of	of	ADP
ajpdis-1851	62	9	the	the	DET
ajpdis-1851	62	10	triangle	triangle	NOUN
ajpdis-1851	62	11	properties	property	NOUN
ajpdis-1851	62	12	are	be	AUX
ajpdis-1851	62	13	also	also	ADV
ajpdis-1851	62	14	used	use	VERB
ajpdis-1851	62	15	.	.	PUNCT
ajpdis-1851	63	1	in	in	ADP
ajpdis-1851	63	2	this	this	PRON
ajpdis-1851	63	3	the	the	DET
ajpdis-1851	63	4	following	following	NOUN
ajpdis-1851	63	5	from	from	ADP
ajpdis-1851	63	6	the	the	DET
ajpdis-1851	63	7	theorem	theorem	NOUN
ajpdis-1851	63	8	is	be	AUX
ajpdis-1851	63	9	used	use	VERB
ajpdis-1851	63	10	.	.	PUNCT
ajpdis-1851	64	1	theorem	theorem	VERB
ajpdis-1851	64	2	.	.	PROPN
ajpdis-1851	65	1	𝑦	𝑦	NOUN
ajpdis-1851	65	2	=	=	SYM
ajpdis-1851	65	3	𝑎𝑥	𝑎𝑥	NOUN
ajpdis-1851	65	4	"	"	PUNCT
ajpdis-1851	65	5	+	+	ADJ
ajpdis-1851	65	6	𝑏𝑥	𝑏𝑥	PROPN
ajpdis-1851	65	7	+	+	SYM
ajpdis-1851	65	8	𝑐	𝑐	PROPN
ajpdis-1851	65	9	kvadrat	kvadrat	PROPN
ajpdis-1851	65	10	triple	triple	ADV
ajpdis-1851	66	1	𝑎	𝑎	X
ajpdis-1851	66	2	>	>	X
ajpdis-1851	66	3	0	0	PUNCT
ajpdis-1851	66	4	when	when	SCONJ
ajpdis-1851	66	5	𝑥	𝑥	ADP
ajpdis-1851	66	6	=	=	SYM
ajpdis-1851	66	7	−	−	PROPN
ajpdis-1851	67	1	+	+	CCONJ
ajpdis-1851	67	2	"	"	PUNCT
ajpdis-1851	67	3	(	(	PUNCT
ajpdis-1851	67	4	at	at	ADP
ajpdis-1851	67	5	the	the	DET
ajpdis-1851	67	6	point	point	NOUN
ajpdis-1851	67	7	,	,	PUNCT
ajpdis-1851	67	8	(	(	PUNCT
ajpdis-1851	67	9	-.+	-.+	PROPN
ajpdis-1851	67	10	#	#	PROPN
ajpdis-1851	67	11	,	,	PUNCT
ajpdis-1851	67	12	(	(	PUNCT
ajpdis-1851	67	13	is	be	AUX
ajpdis-1851	67	14	equal	equal	ADJ
ajpdis-1851	67	15	to	to	ADP
ajpdis-1851	67	16	the	the	DET
ajpdis-1851	67	17	most	most	ADV
ajpdis-1851	67	18	small	small	ADJ
ajpdis-1851	67	19	to	to	ADP
ajpdis-1851	67	20	𝑎	𝑎	NOUN
ajpdis-1851	67	21	<	<	X
ajpdis-1851	67	22	0	0	NUM
ajpdis-1851	67	23	value	value	NOUN
ajpdis-1851	67	24	when	when	SCONJ
ajpdis-1851	67	25	𝑥	𝑥	PROPN
ajpdis-1851	67	26	=	=	SYM
ajpdis-1851	67	27	−	−	PROPN
ajpdis-1851	68	1	+	+	CCONJ
ajpdis-1851	68	2	"	"	PUNCT
ajpdis-1851	68	3	(	(	PUNCT
ajpdis-1851	68	4	at	at	ADP
ajpdis-1851	68	5	the	the	DET
ajpdis-1851	68	6	point	point	NOUN
ajpdis-1851	68	7	,	,	PUNCT
ajpdis-1851	68	8	(	(	PUNCT
ajpdis-1851	68	9	-.+	-.+	PROPN
ajpdis-1851	68	10	#	#	PROPN
ajpdis-1851	68	11	,	,	PUNCT
ajpdis-1851	68	12	(	(	PUNCT
ajpdis-1851	68	13	is	be	AUX
ajpdis-1851	68	14	equal	equal	ADJ
ajpdis-1851	68	15	to	to	ADP
ajpdis-1851	68	16	the	the	DET
ajpdis-1851	68	17	most	most	ADV
ajpdis-1851	68	18	big	big	ADJ
ajpdis-1851	68	19	to	to	PART
ajpdis-1851	68	20	value	value	NOUN
ajpdis-1851	68	21	have	have	AUX
ajpdis-1851	68	22	will	will	AUX
ajpdis-1851	68	23	be	be	AUX
ajpdis-1851	68	24	.	.	PUNCT
ajpdis-1851	69	1	below	below	ADP
ajpdis-1851	69	2	this	this	PRON
ajpdis-1851	69	3	the	the	DET
ajpdis-1851	69	4	theorem	theorem	NOUN
ajpdis-1851	69	5	to	to	PART
ajpdis-1851	69	6	apply	apply	VERB
ajpdis-1851	69	7	let	let	VERB
ajpdis-1851	69	8	's	us	PRON
ajpdis-1851	69	9	see	see	VERB
ajpdis-1851	69	10	the	the	DET
ajpdis-1851	69	11	issue	issue	NOUN
ajpdis-1851	69	12	:	:	PUNCT
ajpdis-1851	69	13	issue	issue	NOUN
ajpdis-1851	69	14	4	4	NUM
ajpdis-1851	69	15	.	.	PUNCT
ajpdis-1851	69	16	𝑦	𝑦	NOUN
ajpdis-1851	69	17	=	=	SYM
ajpdis-1851	69	18	−2𝑥	−2𝑥	PROPN
ajpdis-1851	69	19	"	"	PUNCT
ajpdis-1851	69	20	−	−	PROPN
ajpdis-1851	69	21	3𝑥	3𝑥	NUM
ajpdis-1851	69	22	−	−	NOUN
ajpdis-1851	69	23	1	1	NUM
ajpdis-1851	69	24	of	of	ADP
ajpdis-1851	69	25	the	the	DET
ajpdis-1851	69	26	function	function	NOUN
ajpdis-1851	69	27	extremum	extremum	ADJ
ajpdis-1851	69	28	be	be	AUX
ajpdis-1851	69	29	found	find	VERB
ajpdis-1851	69	30	.	.	PUNCT
ajpdis-1851	70	1	solution	solution	NOUN
ajpdis-1851	70	2	:	:	PUNCT
ajpdis-1851	70	3	here	here	ADV
ajpdis-1851	70	4	𝑎	𝑎	X
ajpdis-1851	70	5	=	=	VERB
ajpdis-1851	70	6	−2	−2	NOUN
ajpdis-1851	70	7	<	<	X
ajpdis-1851	70	8	0	0	NUM
ajpdis-1851	70	9	,	,	PUNCT
ajpdis-1851	70	10	that	that	PRON
ajpdis-1851	70	11	is	be	AUX
ajpdis-1851	70	12	function	function	NOUN
ajpdis-1851	70	13	to	to	ADP
ajpdis-1851	70	14	the	the	DET
ajpdis-1851	70	15	maximum	maximum	NOUN
ajpdis-1851	70	16	have	have	AUX
ajpdis-1851	70	17	will	will	AUX
ajpdis-1851	70	18	be	be	AUX
ajpdis-1851	70	19	here	here	ADV
ajpdis-1851	70	20	𝑏	𝑏	PROPN
ajpdis-1851	70	21	=	=	PUNCT
ajpdis-1851	70	22	−3	−3	PROPN
ajpdis-1851	70	23	,	,	PUNCT
ajpdis-1851	70	24	𝑐	𝑐	NOUN
ajpdis-1851	70	25	=	=	PUNCT
ajpdis-1851	70	26	−1	−1	NOUN
ajpdis-1851	70	27	that	that	SCONJ
ajpdis-1851	70	28	b	b	NOUN
ajpdis-1851	70	29	is	be	AUX
ajpdis-1851	70	30	dead	dead	ADJ
ajpdis-1851	70	31	for	for	ADP
ajpdis-1851	70	32	𝑥	𝑥	NOUN
ajpdis-1851	70	33	=	=	SYM
ajpdis-1851	70	34	−	−	PROPN
ajpdis-1851	71	1	+	+	CCONJ
ajpdis-1851	71	2	"	"	PUNCT
ajpdis-1851	71	3	(	(	PUNCT
ajpdis-1851	71	4	=	=	SYM
ajpdis-1851	71	5	−	−	PROPN
ajpdis-1851	71	6	%	%	NOUN
ajpdis-1851	71	7	,	,	PUNCT
ajpdis-1851	71	8	function	function	NOUN
ajpdis-1851	71	9	at	at	ADP
ajpdis-1851	71	10	the	the	DET
ajpdis-1851	71	11	point	point	NOUN
ajpdis-1851	71	12	to	to	ADP
ajpdis-1851	71	13	the	the	DET
ajpdis-1851	71	14	maximum	maximum	NOUN
ajpdis-1851	71	15	have	have	AUX
ajpdis-1851	71	16	will	will	AUX
ajpdis-1851	71	17	be	be	AUX
ajpdis-1851	71	18	we	we	PRON
ajpdis-1851	71	19	will	will	AUX
ajpdis-1851	71	20	find	find	VERB
ajpdis-1851	71	21	it	it	PRON
ajpdis-1851	71	22	.	.	PUNCT
ajpdis-1851	72	1	𝑦	𝑦	X
ajpdis-1851	72	2	'	'	PUNCT
ajpdis-1851	72	3	(	(	PUNCT
ajpdis-1851	72	4	)	)	PUNCT
ajpdis-1851	73	1	=	=	X
ajpdis-1851	73	2	−	−	NOUN
ajpdis-1851	73	3	3	3	NUM
ajpdis-1851	73	4	4	4	NUM
ajpdis-1851	73	5	>	>	PUNCT
ajpdis-1851	73	6	=	=	PUNCT
ajpdis-1851	73	7	4𝑎𝑐	4𝑎𝑐	ADJ
ajpdis-1851	73	8	−	−	NOUN
ajpdis-1851	74	1	𝑏	𝑏	NOUN
ajpdis-1851	74	2	"	"	PUNCT
ajpdis-1851	74	3	4𝑎	4𝑎	NOUN
ajpdis-1851	74	4	=	=	SYM
ajpdis-1851	74	5	4	4	NUM
ajpdis-1851	74	6	∙	∙	PROPN
ajpdis-1851	74	7	(	(	PUNCT
ajpdis-1851	74	8	−2	−2	NOUN
ajpdis-1851	74	9	)	)	PUNCT
ajpdis-1851	74	10	∙	∙	PROPN
ajpdis-1851	74	11	(	(	PUNCT
ajpdis-1851	74	12	−1	−1	NOUN
ajpdis-1851	74	13	)	)	PUNCT
ajpdis-1851	74	14	−	−	PROPN
ajpdis-1851	75	1	(	(	PUNCT
ajpdis-1851	75	2	−3	−3	NOUN
ajpdis-1851	75	3	)	)	PUNCT
ajpdis-1851	75	4	"	"	PUNCT
ajpdis-1851	75	5	4	4	NUM
ajpdis-1851	75	6	∙	∙	PROPN
ajpdis-1851	75	7	(	(	PUNCT
ajpdis-1851	75	8	−2	−2	NOUN
ajpdis-1851	75	9	)	)	PUNCT
ajpdis-1851	75	10	=	=	SYM
ajpdis-1851	75	11	8	8	NUM
ajpdis-1851	75	12	−	−	NUM
ajpdis-1851	75	13	9	9	NUM
ajpdis-1851	75	14	−8	−8	NOUN
ajpdis-1851	75	15	=	=	NOUN
ajpdis-1851	75	16	1	1	NUM
ajpdis-1851	75	17	8	8	NUM
ajpdis-1851	75	18	.	.	PUNCT
ajpdis-1851	76	1	some	some	DET
ajpdis-1851	76	2	one	one	NUM
ajpdis-1851	76	3	extreme	extreme	ADJ
ajpdis-1851	76	4	issues	issue	NOUN
ajpdis-1851	76	5	in	in	ADP
ajpdis-1851	76	6	solving	solve	VERB
ajpdis-1851	76	7	above	above	ADP
ajpdis-1851	76	8	seeing	see	VERB
ajpdis-1851	76	9	passed	pass	VERB
ajpdis-1851	76	10	methods	method	NOUN
ajpdis-1851	76	11	supporting	support	VERB
ajpdis-1851	76	12	it	it	PRON
ajpdis-1851	76	13	did	do	AUX
ajpdis-1851	76	14	n't	not	PART
ajpdis-1851	76	15	happen	happen	VERB
ajpdis-1851	76	16	.	.	PUNCT
ajpdis-1851	77	1	such	such	ADJ
ajpdis-1851	77	2	cases	case	NOUN
ajpdis-1851	77	3	derivative	derivative	ADJ
ajpdis-1851	77	4	from	from	ADP
ajpdis-1851	77	5	the	the	DET
ajpdis-1851	77	6	concept	concept	NOUN
ajpdis-1851	77	7	use	use	NOUN
ajpdis-1851	77	8	comfortable	comfortable	ADJ
ajpdis-1851	77	9	will	will	AUX
ajpdis-1851	77	10	be	be	AUX
ajpdis-1851	77	11	in	in	ADP
ajpdis-1851	77	12	this	this	PRON
ajpdis-1851	77	13	initially	initially	ADV
ajpdis-1851	77	14	given	give	VERB
ajpdis-1851	77	15	issue	issue	NOUN
ajpdis-1851	77	16	116	116	NUM
ajpdis-1851	77	17	american	american	ADJ
ajpdis-1851	77	18	journal	journal	NOUN
ajpdis-1851	77	19	of	of	ADP
ajpdis-1851	77	20	public	public	ADJ
ajpdis-1851	77	21	diplomacy	diplomacy	NOUN
ajpdis-1851	77	22	and	and	CCONJ
ajpdis-1851	77	23	international	international	ADJ
ajpdis-1851	77	24	studies	study	NOUN
ajpdis-1851	77	25	www	www	PROPN
ajpdis-1851	77	26	.	.	PUNCT
ajpdis-1851	78	1	grnjournal.us	grnjournal.us	PROPN
ajpdis-1851	78	2	mathematical	mathematical	ADJ
ajpdis-1851	78	3	model	model	NOUN
ajpdis-1851	78	4	has	have	AUX
ajpdis-1851	78	5	been	be	AUX
ajpdis-1851	78	6	function	function	NOUN
ajpdis-1851	78	7	is	be	AUX
ajpdis-1851	78	8	made	make	VERB
ajpdis-1851	78	9	and	and	CCONJ
ajpdis-1851	78	10	the	the	DET
ajpdis-1851	78	11	following	follow	VERB
ajpdis-1851	78	12	confirmations	confirmation	NOUN
ajpdis-1851	78	13	attention	attention	NOUN
ajpdis-1851	78	14	is	be	AUX
ajpdis-1851	78	15	taken	take	VERB
ajpdis-1851	78	16	.	.	PUNCT
ajpdis-1851	79	1	1	1	X
ajpdis-1851	79	2	.	.	X
ajpdis-1851	80	1	if	if	SCONJ
ajpdis-1851	80	2	𝑓(𝑥	𝑓(𝑥	NOUN
ajpdis-1851	80	3	)	)	PUNCT
ajpdis-1851	80	4	the	the	DET
ajpdis-1851	80	5	function	function	NOUN
ajpdis-1851	80	6	is	be	AUX
ajpdis-1851	80	7	something	something	PRON
ajpdis-1851	80	8	[	[	X
ajpdis-1851	80	9	𝑎	𝑎	X
ajpdis-1851	80	10	,	,	PUNCT
ajpdis-1851	80	11	𝑏	𝑏	NOUN
ajpdis-1851	80	12	]	]	PUNCT
ajpdis-1851	80	13	in	in	ADP
ajpdis-1851	80	14	cross	cross	NOUN
ajpdis-1851	80	15	section	section	NOUN
ajpdis-1851	80	16	continuously	continuously	ADV
ajpdis-1851	80	17	being	be	AUX
ajpdis-1851	80	18	,	,	PUNCT
ajpdis-1851	80	19	then	then	ADV
ajpdis-1851	80	20	only	only	ADV
ajpdis-1851	80	21	one	one	NUM
ajpdis-1851	80	22	to	to	ADP
ajpdis-1851	80	23	the	the	DET
ajpdis-1851	80	24	extreme	extreme	NOUN
ajpdis-1851	80	25	have	have	VERB
ajpdis-1851	80	26	if	if	SCONJ
ajpdis-1851	80	27	,	,	PUNCT
ajpdis-1851	80	28	then	then	ADV
ajpdis-1851	80	29	this	this	DET
ajpdis-1851	80	30	extremum	extremum	ADJ
ajpdis-1851	80	31	when	when	SCONJ
ajpdis-1851	80	32	the	the	DET
ajpdis-1851	80	33	maximum	maximum	ADJ
ajpdis-1851	80	34	(	(	PUNCT
ajpdis-1851	80	35	minimum	minimum	NOUN
ajpdis-1851	80	36	)	)	PUNCT
ajpdis-1851	80	37	is	be	AUX
ajpdis-1851	80	38	,	,	PUNCT
ajpdis-1851	80	39	it	it	PRON
ajpdis-1851	80	40	is	be	AUX
ajpdis-1851	80	41	a	a	DET
ajpdis-1851	80	42	function	function	NOUN
ajpdis-1851	80	43	that	that	PRON
ajpdis-1851	80	44	's	be	AUX
ajpdis-1851	80	45	it	it	PRON
ajpdis-1851	80	46	in	in	ADP
ajpdis-1851	80	47	cross	cross	NOUN
ajpdis-1851	80	48	section	section	NOUN
ajpdis-1851	80	49	the	the	DET
ajpdis-1851	80	50	most	most	ADV
ajpdis-1851	80	51	big	big	ADJ
ajpdis-1851	80	52	(	(	PUNCT
ajpdis-1851	80	53	eng	eng	NOUN
ajpdis-1851	80	54	small	small	ADJ
ajpdis-1851	80	55	)	)	PUNCT
ajpdis-1851	80	56	value	value	NOUN
ajpdis-1851	80	57	will	will	AUX
ajpdis-1851	80	58	be	be	AUX
ajpdis-1851	80	59	.	.	PUNCT
ajpdis-1851	81	1	2	2	X
ajpdis-1851	81	2	.	.	X
ajpdis-1851	81	3	if	if	SCONJ
ajpdis-1851	81	4	𝑓(𝑥	𝑓(𝑥	NOUN
ajpdis-1851	81	5	)	)	PUNCT
ajpdis-1851	81	6	the	the	DET
ajpdis-1851	81	7	function	function	NOUN
ajpdis-1851	81	8	is	be	AUX
ajpdis-1851	81	9	something	something	PRON
ajpdis-1851	81	10	[	[	X
ajpdis-1851	81	11	𝑎	𝑎	X
ajpdis-1851	81	12	,	,	PUNCT
ajpdis-1851	81	13	𝑏	𝑏	NOUN
ajpdis-1851	81	14	]	]	PUNCT
ajpdis-1851	81	15	in	in	ADP
ajpdis-1851	81	16	cross	cross	NOUN
ajpdis-1851	81	17	section	section	NOUN
ajpdis-1851	81	18	continuously	continuously	ADV
ajpdis-1851	81	19	being	be	AUX
ajpdis-1851	81	20	,	,	PUNCT
ajpdis-1851	81	21	then	then	ADV
ajpdis-1851	81	22	to	to	ADP
ajpdis-1851	81	23	the	the	DET
ajpdis-1851	81	24	extreme	extreme	NOUN
ajpdis-1851	81	25	have	have	AUX
ajpdis-1851	81	26	if	if	SCONJ
ajpdis-1851	81	27	not	not	PART
ajpdis-1851	81	28	,	,	PUNCT
ajpdis-1851	81	29	then	then	ADV
ajpdis-1851	81	30	of	of	ADP
ajpdis-1851	81	31	the	the	DET
ajpdis-1851	81	32	function	function	NOUN
ajpdis-1851	81	33	the	the	DET
ajpdis-1851	81	34	most	most	ADV
ajpdis-1851	81	35	big	big	ADJ
ajpdis-1851	81	36	and	and	CCONJ
ajpdis-1851	81	37	the	the	DET
ajpdis-1851	81	38	most	most	ADV
ajpdis-1851	81	39	small	small	ADJ
ajpdis-1851	81	40	values	value	NOUN
ajpdis-1851	81	41	do	do	AUX
ajpdis-1851	81	42	n't	not	PART
ajpdis-1851	81	43	cut	cut	VERB
ajpdis-1851	81	44	at	at	ADP
ajpdis-1851	81	45	the	the	DET
ajpdis-1851	81	46	ends	end	NOUN
ajpdis-1851	81	47	will	will	AUX
ajpdis-1851	81	48	be	be	AUX
ajpdis-1851	81	49	.	.	PUNCT
ajpdis-1851	82	1	3	3	X
ajpdis-1851	82	2	.	.	X
ajpdis-1851	82	3	if	if	SCONJ
ajpdis-1851	82	4	𝑓(𝑥	𝑓(𝑥	NOUN
ajpdis-1851	82	5	)	)	PUNCT
ajpdis-1851	82	6	the	the	DET
ajpdis-1851	82	7	function	function	NOUN
ajpdis-1851	82	8	is	be	AUX
ajpdis-1851	82	9	something	something	PRON
ajpdis-1851	82	10	[	[	X
ajpdis-1851	82	11	𝑎	𝑎	X
ajpdis-1851	82	12	,	,	PUNCT
ajpdis-1851	82	13	𝑏	𝑏	NOUN
ajpdis-1851	82	14	]	]	PUNCT
ajpdis-1851	82	15	in	in	ADP
ajpdis-1851	82	16	cross	cross	NOUN
ajpdis-1851	82	17	section	section	NOUN
ajpdis-1851	82	18	continuously	continuously	ADV
ajpdis-1851	82	19	is	be	AUX
ajpdis-1851	82	20	the	the	DET
ajpdis-1851	82	21	following	follow	VERB
ajpdis-1851	82	22	conditions	condition	NOUN
ajpdis-1851	82	23	if	if	SCONJ
ajpdis-1851	82	24	satisfied	satisfied	ADJ
ajpdis-1851	82	25	:	:	PUNCT
ajpdis-1851	82	26	a	a	X
ajpdis-1851	82	27	)	)	PUNCT
ajpdis-1851	82	28	𝑎	𝑎	X
ajpdis-1851	82	29	<	<	X
ajpdis-1851	82	30	𝑥	𝑥	X
ajpdis-1851	82	31	<	<	X
ajpdis-1851	82	32	𝑏at𝑓(𝑥	𝑏at𝑓(𝑥	PROPN
ajpdis-1851	82	33	)	)	PUNCT
ajpdis-1851	82	34	>	>	X
ajpdis-1851	82	35	0	0	PUNCT
ajpdis-1851	82	36	(	(	PUNCT
ajpdis-1851	82	37	𝑓(𝑥	𝑓(𝑥	NOUN
ajpdis-1851	82	38	)	)	PUNCT
ajpdis-1851	82	39	<	<	X
ajpdis-1851	82	40	0	0	NUM
ajpdis-1851	82	41	)	)	PUNCT
ajpdis-1851	82	42	,	,	PUNCT
ajpdis-1851	82	43	b	b	X
ajpdis-1851	82	44	)	)	PUNCT
ajpdis-1851	82	45	𝑓(𝑎	𝑓(𝑎	ADJ
ajpdis-1851	82	46	)	)	PUNCT
ajpdis-1851	82	47	=	=	SYM
ajpdis-1851	82	48	𝑓(𝑏	𝑓(𝑏	NOUN
ajpdis-1851	82	49	)	)	PUNCT
ajpdis-1851	82	50	=	=	SYM
ajpdis-1851	82	51	0	0	NUM
ajpdis-1851	82	52	,	,	PUNCT
ajpdis-1851	82	53	c	c	NOUN
ajpdis-1851	82	54	)	)	PUNCT
ajpdis-1851	82	55	only	only	ADV
ajpdis-1851	82	56	one	one	NUM
ajpdis-1851	82	57	𝑎	𝑎	PRON
ajpdis-1851	82	58	<	<	X
ajpdis-1851	82	59	𝑥/	𝑥/	NOUN
ajpdis-1851	82	60	<	<	X
ajpdis-1851	82	61	𝑏there	𝑏there	NOUN
ajpdis-1851	82	62	is	be	AUX
ajpdis-1851	82	63	a	a	DET
ajpdis-1851	82	64	critical	critical	ADJ
ajpdis-1851	82	65	point	point	NOUN
ajpdis-1851	82	66	,	,	PUNCT
ajpdis-1851	82	67	then	then	ADV
ajpdis-1851	82	68	𝑓(𝑥/	𝑓(𝑥/	PROPN
ajpdis-1851	82	69	)	)	PUNCT
ajpdis-1851	82	70	the	the	DET
ajpdis-1851	82	71	function	function	NOUN
ajpdis-1851	82	72	is	be	AUX
ajpdis-1851	82	73	the	the	DET
ajpdis-1851	82	74	largest	large	ADJ
ajpdis-1851	82	75	(	(	PUNCT
ajpdis-1851	82	76	max	max	PROPN
ajpdis-1851	82	77	small	small	ADJ
ajpdis-1851	82	78	)	)	PUNCT
ajpdis-1851	82	79	value	value	NOUN
ajpdis-1851	82	80	will	will	AUX
ajpdis-1851	82	81	be	be	AUX
ajpdis-1851	82	82	.	.	PUNCT
ajpdis-1851	83	1	4	4	X
ajpdis-1851	83	2	.	.	X
ajpdis-1851	83	3	if	if	SCONJ
ajpdis-1851	83	4	given	give	VERB
ajpdis-1851	83	5	𝑓(𝑥	𝑓(𝑥	NOUN
ajpdis-1851	83	6	)	)	PUNCT
ajpdis-1851	83	7	function	function	NOUN
ajpdis-1851	83	8	𝑥	𝑥	NOUN
ajpdis-1851	83	9	=	=	SYM
ajpdis-1851	83	10	𝑥/	𝑥/	PROPN
ajpdis-1851	83	11	at	at	ADP
ajpdis-1851	83	12	the	the	DET
ajpdis-1851	83	13	point	point	NOUN
ajpdis-1851	83	14	to	to	ADP
ajpdis-1851	83	15	zero	zero	NUM
ajpdis-1851	83	16	equal	equal	ADJ
ajpdis-1851	83	17	to	to	PART
ajpdis-1851	83	18	did	do	AUX
ajpdis-1851	83	19	n't	not	PART
ajpdis-1851	83	20	happen	happen	VERB
ajpdis-1851	83	21	to	to	ADP
ajpdis-1851	83	22	the	the	DET
ajpdis-1851	83	23	maximum	maximum	ADJ
ajpdis-1851	83	24	(	(	PUNCT
ajpdis-1851	83	25	minimum	minimum	NOUN
ajpdis-1851	83	26	)	)	PUNCT
ajpdis-1851	83	27	.	.	PUNCT
ajpdis-1851	84	1	have	have	AUX
ajpdis-1851	84	2	if	if	SCONJ
ajpdis-1851	84	3	,	,	PUNCT
ajpdis-1851	84	4	then	then	ADV
ajpdis-1851	84	5	!	!	PUNCT
ajpdis-1851	85	1	0	0	PUNCT
ajpdis-1851	85	2	(	(	PUNCT
ajpdis-1851	85	3	)	)	PUNCT
ajpdis-1851	85	4	)	)	PUNCT
ajpdis-1851	86	1	the	the	DET
ajpdis-1851	86	2	function	function	NOUN
ajpdis-1851	86	3	𝑥	𝑥	NOUN
ajpdis-1851	86	4	=	=	SYM
ajpdis-1851	86	5	𝑥/	𝑥/	NOUN
ajpdis-1851	86	6	to	to	ADP
ajpdis-1851	86	7	the	the	DET
ajpdis-1851	86	8	minimum	minimum	ADJ
ajpdis-1851	86	9	(	(	PUNCT
ajpdis-1851	86	10	maximum	maximum	ADJ
ajpdis-1851	86	11	)	)	PUNCT
ajpdis-1851	86	12	at	at	ADP
ajpdis-1851	86	13	the	the	DET
ajpdis-1851	86	14	point	point	NOUN
ajpdis-1851	86	15	have	have	AUX
ajpdis-1851	86	16	will	will	AUX
ajpdis-1851	86	17	be	be	AUX
ajpdis-1851	86	18	.	.	PUNCT
ajpdis-1851	87	1	derivative	derivative	ADJ
ajpdis-1851	87	2	using	using	NOUN
ajpdis-1851	87	3	of	of	ADP
ajpdis-1851	87	4	the	the	DET
ajpdis-1851	87	5	function	function	NOUN
ajpdis-1851	87	6	the	the	DET
ajpdis-1851	87	7	most	most	ADV
ajpdis-1851	87	8	big	big	ADJ
ajpdis-1851	87	9	and	and	CCONJ
ajpdis-1851	87	10	the	the	DET
ajpdis-1851	87	11	most	most	ADV
ajpdis-1851	87	12	small	small	ADJ
ajpdis-1851	87	13	value	value	NOUN
ajpdis-1851	87	14	to	to	PART
ajpdis-1851	87	15	find	find	VERB
ajpdis-1851	87	16	circle	circle	NOUN
ajpdis-1851	87	17	the	the	DET
ajpdis-1851	87	18	following	follow	VERB
ajpdis-1851	87	19	issue	issue	NOUN
ajpdis-1851	87	20	let	let	VERB
ajpdis-1851	87	21	's	us	PRON
ajpdis-1851	87	22	see	see	VERB
ajpdis-1851	87	23	:	:	PUNCT
ajpdis-1851	87	24	issue	issue	NOUN
ajpdis-1851	87	25	5	5	NUM
ajpdis-1851	87	26	.	.	PUNCT
ajpdis-1851	87	27	size	size	NOUN
ajpdis-1851	87	28	125𝑚%	125𝑚%	PROPN
ajpdis-1851	87	29	has	have	AUX
ajpdis-1851	87	30	been	be	AUX
ajpdis-1851	87	31	cylinder	cylinder	NOUN
ajpdis-1851	87	32	shaped	shape	VERB
ajpdis-1851	87	33	it	it	PRON
ajpdis-1851	87	34	is	be	AUX
ajpdis-1851	87	35	necessary	necessary	ADJ
ajpdis-1851	87	36	to	to	PART
ajpdis-1851	87	37	prepare	prepare	VERB
ajpdis-1851	87	38	a	a	DET
ajpdis-1851	87	39	water	water	NOUN
ajpdis-1851	87	40	container	container	NOUN
ajpdis-1851	87	41	without	without	ADP
ajpdis-1851	87	42	a	a	DET
ajpdis-1851	87	43	lid	lid	NOUN
ajpdis-1851	87	44	.	.	PUNCT
ajpdis-1851	88	1	water	water	NOUN
ajpdis-1851	88	2	of	of	ADP
ajpdis-1851	88	3	the	the	DET
ajpdis-1851	88	4	vessel	vessel	NOUN
ajpdis-1851	88	5	measurements	measurement	NOUN
ajpdis-1851	88	6	how	how	SCONJ
ajpdis-1851	88	7	when	when	SCONJ
ajpdis-1851	88	8	him	he	PRON
ajpdis-1851	88	9	preparation	preparation	NOUN
ajpdis-1851	88	10	for	for	ADP
ajpdis-1851	88	11	the	the	DET
ajpdis-1851	88	12	most	most	ADV
ajpdis-1851	88	13	less	less	ADJ
ajpdis-1851	88	14	material	material	NOUN
ajpdis-1851	88	15	is	be	AUX
ajpdis-1851	88	16	used	use	VERB
ajpdis-1851	88	17	?	?	PUNCT
ajpdis-1851	89	1	solution	solution	NOUN
ajpdis-1851	89	2	:	:	PUNCT
ajpdis-1851	89	3	water	water	NOUN
ajpdis-1851	89	4	dish	dish	NOUN
ajpdis-1851	89	5	to	to	PART
ajpdis-1851	89	6	prepare	prepare	VERB
ajpdis-1851	89	7	expendable	expendable	ADJ
ajpdis-1851	89	8	of	of	ADP
ajpdis-1851	89	9	the	the	DET
ajpdis-1851	89	10	material	material	NOUN
ajpdis-1851	89	11	quantity	quantity	NOUN
ajpdis-1851	89	12	dish	dish	NOUN
ajpdis-1851	89	13	of	of	ADP
ajpdis-1851	89	14	the	the	DET
ajpdis-1851	89	15	surface	surface	NOUN
ajpdis-1851	89	16	face	face	NOUN
ajpdis-1851	89	17	measure	measure	NOUN
ajpdis-1851	89	18	with	with	ADP
ajpdis-1851	89	19	is	be	AUX
ajpdis-1851	89	20	(	(	PUNCT
ajpdis-1851	89	21	in	in	ADP
ajpdis-1851	89	22	this	this	PRON
ajpdis-1851	89	23	to	to	ADP
ajpdis-1851	89	24	the	the	DET
ajpdis-1851	89	25	seams	seam	NOUN
ajpdis-1851	89	26	taking	take	VERB
ajpdis-1851	89	27	into	into	ADP
ajpdis-1851	89	28	account	account	NOUN
ajpdis-1851	89	29	consumables	consumable	NOUN
ajpdis-1851	89	30	not	not	PART
ajpdis-1851	89	31	available	available	ADJ
ajpdis-1851	89	32	)	)	PUNCT
ajpdis-1851	89	33	.	.	PUNCT
ajpdis-1851	90	1	so	so	ADV
ajpdis-1851	90	2	,	,	PUNCT
ajpdis-1851	90	3	a	a	DET
ajpdis-1851	90	4	cylinder	cylinder	NOUN
ajpdis-1851	90	5	of	of	ADP
ajpdis-1851	90	6	the	the	DET
ajpdis-1851	90	7	basis	basis	NOUN
ajpdis-1851	90	8	radius	radius	NOUN
ajpdis-1851	90	9	𝑅	𝑅	PROPN
ajpdis-1851	90	10	and	and	CCONJ
ajpdis-1851	90	11	the	the	DET
ajpdis-1851	90	12	height	height	NOUN
ajpdis-1851	90	13	𝐻	𝐻	PROPN
ajpdis-1851	90	14	should	should	AUX
ajpdis-1851	90	15	be	be	AUX
ajpdis-1851	90	16	chosen	choose	VERB
ajpdis-1851	90	17	such	such	ADJ
ajpdis-1851	90	18	that	that	SCONJ
ajpdis-1851	90	19	125𝑚%	125𝑚%	PROPN
ajpdis-1851	90	20	capacity	capacity	NOUN
ajpdis-1851	90	21	dish	dish	VERB
ajpdis-1851	90	22	the	the	DET
ajpdis-1851	90	23	surface	surface	NOUN
ajpdis-1851	90	24	the	the	DET
ajpdis-1851	90	25	most	most	ADV
ajpdis-1851	90	26	small	small	ADJ
ajpdis-1851	90	27	surface	surface	NOUN
ajpdis-1851	90	28	have	have	AUX
ajpdis-1851	90	29	let	let	VERB
ajpdis-1851	90	30	it	it	PRON
ajpdis-1851	90	31	be	be	AUX
ajpdis-1851	90	32	.	.	PUNCT
ajpdis-1851	91	1	cylinder	cylinder	NOUN
ajpdis-1851	91	2	of	of	ADP
ajpdis-1851	91	3	the	the	DET
ajpdis-1851	91	4	basis	basis	NOUN
ajpdis-1851	91	5	radius	radius	NOUN
ajpdis-1851	91	6	𝑅	𝑅	PROPN
ajpdis-1851	91	7	the	the	DET
ajpdis-1851	91	8	manly	manly	ADJ
ajpdis-1851	91	9	we	we	PRON
ajpdis-1851	91	10	consider	consider	VERB
ajpdis-1851	91	11	it	it	PRON
ajpdis-1851	91	12	a	a	DET
ajpdis-1851	91	13	variable	variable	NOUN
ajpdis-1851	91	14	.	.	PUNCT
ajpdis-1851	92	1	then	then	ADV
ajpdis-1851	92	2	the	the	DET
ajpdis-1851	92	3	volume	volume	NOUN
ajpdis-1851	92	4	of	of	ADP
ajpdis-1851	92	5	the	the	DET
ajpdis-1851	92	6	cylinder	cylinder	NOUN
ajpdis-1851	92	7	𝑉	𝑉	PROPN
ajpdis-1851	92	8	=	=	PUNCT
ajpdis-1851	92	9	𝜋𝑅"𝐻	𝜋𝑅"𝐻	PROPN
ajpdis-1851	92	10	or	or	CCONJ
ajpdis-1851	92	11	𝜋𝑅"𝐻	𝜋𝑅"𝐻	PROPN
ajpdis-1851	92	12	=	=	SYM
ajpdis-1851	92	13	125	125	NUM
ajpdis-1851	92	14	died	die	VERB
ajpdis-1851	92	15	from	from	ADP
ajpdis-1851	92	16	this	this	DET
ajpdis-1851	92	17	𝐻	𝐻	PROPN
ajpdis-1851	92	18	=	=	PUNCT
ajpdis-1851	92	19	!	!	PUNCT
ajpdis-1851	93	1	"	"	PUNCT
ajpdis-1851	93	2	3	3	NUM
ajpdis-1851	93	3	45	45	NUM
ajpdis-1851	93	4	#	#	NOUN
ajpdis-1851	93	5	will	will	AUX
ajpdis-1851	93	6	be	be	AUX
ajpdis-1851	93	7	.	.	PUNCT
ajpdis-1851	94	1	the	the	DET
ajpdis-1851	94	2	surface	surface	NOUN
ajpdis-1851	94	3	of	of	ADP
ajpdis-1851	94	4	the	the	DET
ajpdis-1851	94	5	cylinder	cylinder	NOUN
ajpdis-1851	94	6	surface	surface	NOUN
ajpdis-1851	94	7	(	(	PUNCT
ajpdis-1851	94	8	top	top	ADJ
ajpdis-1851	94	9	basis	basis	NOUN
ajpdis-1851	94	10	not	not	PART
ajpdis-1851	94	11	added	add	VERB
ajpdis-1851	94	12	without	without	ADP
ajpdis-1851	94	13	)	)	PUNCT
ajpdis-1851	94	14	.	.	PUNCT
ajpdis-1851	95	1	𝑆	𝑆	PROPN
ajpdis-1851	95	2	=	=	SYM
ajpdis-1851	95	3	𝜋𝑅	𝜋𝑅	NOUN
ajpdis-1851	95	4	"	"	PUNCT
ajpdis-1851	96	1	+	+	CCONJ
ajpdis-1851	96	2	2𝜋𝑅𝐻	2𝜋𝑅𝐻	X
ajpdis-1851	96	3	=	=	PUNCT
ajpdis-1851	96	4	𝜋𝑅	𝜋𝑅	NOUN
ajpdis-1851	96	5	"	"	PUNCT
ajpdis-1851	97	1	+	+	CCONJ
ajpdis-1851	97	2	250	250	NUM
ajpdis-1851	97	3	𝑅	𝑅	PROPN
ajpdis-1851	97	4	.	.	PUNCT
ajpdis-1851	97	5	will	will	AUX
ajpdis-1851	97	6	be	be	AUX
ajpdis-1851	97	7	here	here	ADV
ajpdis-1851	97	8	0	0	PUNCT
ajpdis-1851	97	9	<	<	X
ajpdis-1851	97	10	𝑅	𝑅	PROPN
ajpdis-1851	97	11	<	<	X
ajpdis-1851	97	12	∞.	∞.	PROPN
ajpdis-1851	97	13	thus	thus	ADV
ajpdis-1851	97	14	,	,	PUNCT
ajpdis-1851	97	15	the	the	DET
ajpdis-1851	97	16	surface	surface	NOUN
ajpdis-1851	97	17	area	area	NOUN
ajpdis-1851	97	18	of	of	ADP
ajpdis-1851	97	19	the	the	DET
ajpdis-1851	97	20	cylinder	cylinder	NOUN
ajpdis-1851	97	21	𝑆	𝑆	PROPN
ajpdis-1851	97	22	is	be	AUX
ajpdis-1851	97	23	a	a	DET
ajpdis-1851	97	24	function	function	NOUN
ajpdis-1851	97	25	of	of	ADP
ajpdis-1851	97	26	the	the	DET
ajpdis-1851	97	27	radius	radius	NOUN
ajpdis-1851	97	28	of	of	ADP
ajpdis-1851	97	29	the	the	DET
ajpdis-1851	97	30	base	base	NOUN
ajpdis-1851	97	31	.	.	PUNCT
ajpdis-1851	98	1	𝑅	𝑅	NOUN
ajpdis-1851	98	2	so	so	SCONJ
ajpdis-1851	98	3	the	the	DET
ajpdis-1851	98	4	question	question	NOUN
ajpdis-1851	98	5	𝑅	𝑅	PROPN
ajpdis-1851	98	6	is	be	AUX
ajpdis-1851	98	7	what	what	PRON
ajpdis-1851	98	8	is	be	AUX
ajpdis-1851	98	9	the	the	DET
ajpdis-1851	98	10	value	value	NOUN
ajpdis-1851	98	11	of	of	ADP
ajpdis-1851	98	12	𝑆(𝑅	𝑆(𝑅	NOUN
ajpdis-1851	98	13	)	)	PUNCT
ajpdis-1851	98	14	the	the	DET
ajpdis-1851	98	15	most	most	ADV
ajpdis-1851	98	16	small	small	ADJ
ajpdis-1851	98	17	to	to	PART
ajpdis-1851	98	18	be	be	AUX
ajpdis-1851	98	19	from	from	ADP
ajpdis-1851	98	20	detection	detection	NOUN
ajpdis-1851	98	21	consists	consist	VERB
ajpdis-1851	98	22	of	of	SCONJ
ajpdis-1851	98	23	will	will	AUX
ajpdis-1851	98	24	be	be	AUX
ajpdis-1851	98	25	.	.	PUNCT
ajpdis-1851	99	1	1	1	X
ajpdis-1851	99	2	)	)	PUNCT
ajpdis-1851	99	3	𝑆&(𝑅	𝑆&(𝑅	PROPN
ajpdis-1851	99	4	)	)	PUNCT
ajpdis-1851	99	5	we	we	PRON
ajpdis-1851	99	6	find	find	VERB
ajpdis-1851	99	7	:	:	PUNCT
ajpdis-1851	99	8	𝑆&(𝑅	𝑆&(𝑅	ADJ
ajpdis-1851	99	9	)	)	PUNCT
ajpdis-1851	99	10	=	=	SYM
ajpdis-1851	99	11	h𝜋𝑅	h𝜋𝑅	NOUN
ajpdis-1851	99	12	"	"	PUNCT
ajpdis-1851	99	13	+	+	CCONJ
ajpdis-1851	99	14	"	"	PUNCT
ajpdis-1851	99	15	3/	3/	NUM
ajpdis-1851	99	16	5	5	NUM
ajpdis-1851	99	17	i	i	NOUN
ajpdis-1851	99	18	&	&	CCONJ
ajpdis-1851	99	19	=	=	SYM
ajpdis-1851	99	20	2𝜋𝑅	2𝜋𝑅	NUM
ajpdis-1851	99	21	−	−	NOUN
ajpdis-1851	99	22	"	"	PUNCT
ajpdis-1851	99	23	3/	3/	NUM
ajpdis-1851	99	24	5	5	NUM
ajpdis-1851	99	25	#	#	NOUN
ajpdis-1851	99	26	;	;	PUNCT
ajpdis-1851	99	27	2	2	X
ajpdis-1851	99	28	)	)	PUNCT
ajpdis-1851	100	1	𝑆&(𝑅	𝑆&(𝑅	PROPN
ajpdis-1851	100	2	)	)	PUNCT
ajpdis-1851	100	3	we	we	PRON
ajpdis-1851	100	4	solve	solve	VERB
ajpdis-1851	100	5	for	for	ADP
ajpdis-1851	100	6	:	:	PUNCT
ajpdis-1851	100	7	2𝜋𝑅	2𝜋𝑅	NUM
ajpdis-1851	100	8	−	−	NOUN
ajpdis-1851	100	9	"	"	PUNCT
ajpdis-1851	100	10	3/	3/	NUM
ajpdis-1851	100	11	5	5	NUM
ajpdis-1851	100	12	#	#	NOUN
ajpdis-1851	100	13	=	=	SYM
ajpdis-1851	100	14	0	0	NUM
ajpdis-1851	100	15	,	,	PUNCT
ajpdis-1851	100	16	"	"	PUNCT
ajpdis-1851	100	17	45	45	NUM
ajpdis-1851	100	18	"	"	PUNCT
ajpdis-1851	100	19	."3/	."3/	PROPN
ajpdis-1851	100	20	5	5	NUM
ajpdis-1851	100	21	#	#	NOUN
ajpdis-1851	100	22	=	=	SYM
ajpdis-1851	100	23	0	0	NUM
ajpdis-1851	100	24	,	,	PUNCT
ajpdis-1851	100	25	2𝜋𝑅%	2𝜋𝑅%	VERB
ajpdis-1851	100	26	−	−	NOUN
ajpdis-1851	100	27	250	250	NUM
ajpdis-1851	100	28	=	=	SYM
ajpdis-1851	100	29	0	0	NUM
ajpdis-1851	100	30	,	,	PUNCT
ajpdis-1851	100	31	𝑅	𝑅	NOUN
ajpdis-1851	100	32	=	=	NOUN
ajpdis-1851	100	33	3	3	NUM
ajpdis-1851	100	34	√4	√4	PROPN
ajpdis-1851	100	35	"	"	PUNCT
ajpdis-1851	100	36	≈	≈	PROPN
ajpdis-1851	100	37	3,42	3,42	NUM
ajpdis-1851	100	38	;	;	PUNCT
ajpdis-1851	100	39	3	3	X
ajpdis-1851	100	40	)	)	PUNCT
ajpdis-1851	100	41	𝑆&(𝑅	𝑆&(𝑅	PROPN
ajpdis-1851	100	42	)	)	PUNCT
ajpdis-1851	101	1	=	=	SYM
ajpdis-1851	101	2	2𝜋𝑅	2𝜋𝑅	NUM
ajpdis-1851	101	3	−	−	NOUN
ajpdis-1851	101	4	"	"	PUNCT
ajpdis-1851	101	5	3/	3/	NUM
ajpdis-1851	101	6	5	5	NUM
ajpdis-1851	101	7	#	#	NOUN
ajpdis-1851	101	8	=	=	NOUN
ajpdis-1851	101	9	"	"	PUNCT
ajpdis-1851	101	10	5	5	NUM
ajpdis-1851	101	11	#	#	NOUN
ajpdis-1851	101	12	(	(	PUNCT
ajpdis-1851	101	13	𝜋𝑅%	𝜋𝑅%	X
ajpdis-1851	101	14	−	−	PROPN
ajpdis-1851	101	15	125	125	NUM
ajpdis-1851	101	16	)	)	PUNCT
ajpdis-1851	101	17	of	of	ADP
ajpdis-1851	101	18	𝑅	𝑅	PROPN
ajpdis-1851	101	19	=	=	PROPN
ajpdis-1851	101	20	3	3	NUM
ajpdis-1851	101	21	√4	√4	PROPN
ajpdis-1851	101	22	"	"	PUNCT
ajpdis-1851	101	23	we	we	PRON
ajpdis-1851	101	24	define	define	VERB
ajpdis-1851	101	25	the	the	DET
ajpdis-1851	101	26	pointer	pointer	NOUN
ajpdis-1851	101	27	around	around	ADP
ajpdis-1851	101	28	the	the	DET
ajpdis-1851	101	29	point	point	NOUN
ajpdis-1851	101	30	.	.	PUNCT
ajpdis-1851	101	31	"	"	PUNCT
ajpdis-1851	102	1	5	5	NUM
ajpdis-1851	102	2	#	#	NOUN
ajpdis-1851	102	3	>	>	X
ajpdis-1851	102	4	0	0	PUNCT
ajpdis-1851	103	1	that	that	PRON
ajpdis-1851	103	2	b	b	NOUN
ajpdis-1851	103	3	is	be	AUX
ajpdis-1851	103	4	dead	dead	ADJ
ajpdis-1851	103	5	for	for	ADP
ajpdis-1851	103	6	𝑓(𝑅	𝑓(𝑅	NOUN
ajpdis-1851	103	7	)	)	PUNCT
ajpdis-1851	104	1	=	=	PUNCT
ajpdis-1851	105	1	𝜋𝑅%	𝜋𝑅%	X
ajpdis-1851	105	2	−	−	NUM
ajpdis-1851	105	3	125	125	NUM
ajpdis-1851	105	4	we	we	PRON
ajpdis-1851	105	5	limit	limit	VERB
ajpdis-1851	105	6	ourselves	ourselves	PRON
ajpdis-1851	105	7	to	to	ADP
ajpdis-1851	105	8	checking	check	VERB
ajpdis-1851	105	9	.	.	PUNCT
ajpdis-1851	106	1	117	117	NUM
ajpdis-1851	106	2	american	american	ADJ
ajpdis-1851	106	3	journal	journal	PROPN
ajpdis-1851	106	4	of	of	ADP
ajpdis-1851	106	5	public	public	ADJ
ajpdis-1851	106	6	diplomacy	diplomacy	NOUN
ajpdis-1851	106	7	and	and	CCONJ
ajpdis-1851	106	8	international	international	ADJ
ajpdis-1851	106	9	studies	study	NOUN
ajpdis-1851	106	10	www	www	PROPN
ajpdis-1851	106	11	.	.	PUNCT
ajpdis-1851	107	1	grnjournal.us	grnjournal.us	X
ajpdis-1851	107	2	0	0	PUNCT
ajpdis-1851	107	3	<	<	X
ajpdis-1851	107	4	𝑅	𝑅	PROPN
ajpdis-1851	107	5	<	<	X
ajpdis-1851	107	6	3	3	NUM
ajpdis-1851	107	7	√4	√4	PROPN
ajpdis-1851	107	8	"	"	PUNCT
ajpdis-1851	107	9	when	when	SCONJ
ajpdis-1851	107	10	𝑓&(𝑅	𝑓&(𝑅	VERB
ajpdis-1851	107	11	)	)	PUNCT
ajpdis-1851	107	12	<	<	X
ajpdis-1851	107	13	0	0	PUNCT
ajpdis-1851	107	14	and	and	CCONJ
ajpdis-1851	107	15	when	when	SCONJ
ajpdis-1851	107	16	𝑅	𝑅	PROPN
ajpdis-1851	107	17	>	>	X
ajpdis-1851	107	18	3	3	NUM
ajpdis-1851	107	19	√4	√4	PROPN
ajpdis-1851	107	20	"	"	PUNCT
ajpdis-1851	107	21	dies	die	VERB
ajpdis-1851	107	22	𝑓&(𝑅	𝑓&(𝑅	VERB
ajpdis-1851	107	23	)	)	PUNCT
ajpdis-1851	107	24	>	>	X
ajpdis-1851	108	1	0	0	X
ajpdis-1851	108	2	.	.	PUNCT
ajpdis-1851	109	1	so	so	ADV
ajpdis-1851	109	2	,	,	PUNCT
ajpdis-1851	109	3	𝑆(𝑅	𝑆(𝑅	X
ajpdis-1851	109	4	)	)	PUNCT
ajpdis-1851	109	5	the	the	DET
ajpdis-1851	109	6	function	function	NOUN
ajpdis-1851	109	7	𝑅	𝑅	PROPN
ajpdis-1851	109	8	=	=	PROPN
ajpdis-1851	109	9	3	3	NUM
ajpdis-1851	109	10	√4	√4	PROPN
ajpdis-1851	109	11	"	"	PUNCT
ajpdis-1851	109	12	has	have	VERB
ajpdis-1851	109	13	a	a	DET
ajpdis-1851	109	14	minimum	minimum	NOUN
ajpdis-1851	109	15	at	at	ADP
ajpdis-1851	109	16	the	the	DET
ajpdis-1851	109	17	point	point	NOUN
ajpdis-1851	109	18	.	.	PUNCT
ajpdis-1851	110	1	this	this	PRON
ajpdis-1851	110	2	is	be	AUX
ajpdis-1851	110	3	the	the	DET
ajpdis-1851	110	4	only	only	ADJ
ajpdis-1851	110	5	one	one	NUM
ajpdis-1851	110	6	extremum	extremum	ADJ
ajpdis-1851	110	7	that	that	SCONJ
ajpdis-1851	110	8	it	it	PRON
ajpdis-1851	110	9	was	be	AUX
ajpdis-1851	110	10	for	for	ADP
ajpdis-1851	110	11	the	the	DET
ajpdis-1851	110	12	smallest	small	ADJ
ajpdis-1851	110	13	value	value	NOUN
ajpdis-1851	110	14	of	of	ADP
ajpdis-1851	110	15	u	u	NOUN
ajpdis-1851	110	16	𝑆(𝑅	𝑆(𝑅	X
ajpdis-1851	110	17	)	)	PUNCT
ajpdis-1851	110	18	will	will	AUX
ajpdis-1851	110	19	be	be	AUX
ajpdis-1851	110	20	b	b	NUM
ajpdis-1851	110	21	,	,	PUNCT
ajpdis-1851	110	22	i.e	i.e	PROPN
ajpdis-1851	110	23	𝑅	𝑅	PROPN
ajpdis-1851	110	24	=	=	NOUN
ajpdis-1851	110	25	𝐻	𝐻	NOUN
ajpdis-1851	110	26	=	=	SYM
ajpdis-1851	110	27	3	3	NUM
ajpdis-1851	110	28	√4	√4	PROPN
ajpdis-1851	110	29	"	"	PUNCT
ajpdis-1851	111	1	when	when	SCONJ
ajpdis-1851	111	2	𝑆'7	𝑆'7	NOUN
ajpdis-1851	111	3	#	#	NOUN
ajpdis-1851	111	4	=	=	NOUN
ajpdis-1851	111	5	3𝜋𝑅%	3𝜋𝑅%	NOUN
ajpdis-1851	111	6	=	=	SYM
ajpdis-1851	111	7	75√𝜋	75√𝜋	NUM
ajpdis-1851	111	8	"	"	PUNCT
ajpdis-1851	111	9	will	will	AUX
ajpdis-1851	111	10	die	die	VERB
ajpdis-1851	111	11	.	.	PUNCT
ajpdis-1851	112	1	this	this	DET
ajpdis-1851	112	2	issue	issue	NOUN
ajpdis-1851	112	3	is	be	AUX
ajpdis-1851	112	4	practical	practical	ADJ
ajpdis-1851	112	5	being	be	AUX
ajpdis-1851	112	6	a	a	DET
ajpdis-1851	112	7	matter	matter	NOUN
ajpdis-1851	112	8	of	of	ADP
ajpdis-1851	112	9	character	character	NOUN
ajpdis-1851	112	10	to	to	ADP
ajpdis-1851	112	11	this	this	DET
ajpdis-1851	112	12	similar	similar	ADJ
ajpdis-1851	112	13	issues	issue	NOUN
ajpdis-1851	112	14	many	many	ADJ
ajpdis-1851	112	15	to	to	PART
ajpdis-1851	112	16	bring	bring	VERB
ajpdis-1851	112	17	can	can	AUX
ajpdis-1851	112	18	.	.	PUNCT
ajpdis-1851	113	1	such	such	ADJ
ajpdis-1851	113	2	issues	issue	NOUN
ajpdis-1851	113	3	solve	solve	VERB
ajpdis-1851	113	4	in	in	ADP
ajpdis-1851	113	5	the	the	DET
ajpdis-1851	113	6	process	process	NOUN
ajpdis-1851	113	7	of	of	ADP
ajpdis-1851	113	8	students	student	NOUN
ajpdis-1851	113	9	creative	creative	ADJ
ajpdis-1851	113	10	thinking	thinking	NOUN
ajpdis-1851	113	11	abilities	ability	NOUN
ajpdis-1851	113	12	more	more	ADV
ajpdis-1851	113	13	develops	develop	NOUN
ajpdis-1851	113	14	and	and	CCONJ
ajpdis-1851	113	15	education	education	NOUN
ajpdis-1851	113	16	process	process	NOUN
ajpdis-1851	113	17	efficient	efficient	ADJ
ajpdis-1851	113	18	will	will	AUX
ajpdis-1851	113	19	be	be	AUX
ajpdis-1851	113	20	so	so	ADV
ajpdis-1851	113	21	so	so	ADV
ajpdis-1851	113	22	we	we	PRON
ajpdis-1851	113	23	do	do	VERB
ajpdis-1851	113	24	this	this	PRON
ajpdis-1851	113	25	in	in	ADP
ajpdis-1851	113	26	the	the	DET
ajpdis-1851	113	27	article	article	NOUN
ajpdis-1851	113	28	extreme	extreme	ADJ
ajpdis-1851	113	29	issues	issue	NOUN
ajpdis-1851	113	30	of	of	ADP
ajpdis-1851	113	31	solving	solve	VERB
ajpdis-1851	113	32	one	one	NUM
ajpdis-1851	113	33	how	how	SCONJ
ajpdis-1851	113	34	many	many	ADJ
ajpdis-1851	113	35	method	method	NOUN
ajpdis-1851	113	36	with	with	SCONJ
ajpdis-1851	113	37	we	we	PRON
ajpdis-1851	113	38	met	meet	VERB
ajpdis-1851	113	39	and	and	CCONJ
ajpdis-1851	113	40	this	this	DET
ajpdis-1851	113	41	methods	method	NOUN
ajpdis-1851	113	42	inside	inside	ADV
ajpdis-1851	113	43	from	from	ADP
ajpdis-1851	113	44	the	the	DET
ajpdis-1851	113	45	derivation	derivation	NOUN
ajpdis-1851	113	46	use	use	VERB
ajpdis-1851	113	47	much	much	ADV
ajpdis-1851	113	48	comfortable	comfortable	ADJ
ajpdis-1851	113	49	and	and	CCONJ
ajpdis-1851	113	50	common	common	ADJ
ajpdis-1851	113	51	method	method	NOUN
ajpdis-1851	113	52	that	that	PRON
ajpdis-1851	113	53	trust	trust	NOUN
ajpdis-1851	113	54	harvest	harvest	NOUN
ajpdis-1851	113	55	we	we	PRON
ajpdis-1851	113	56	did	do	VERB
ajpdis-1851	113	57	.	.	PUNCT
ajpdis-1851	114	1	literature	literature	PROPN
ajpdis-1851	114	2	1	1	NUM
ajpdis-1851	114	3	.	.	PUNCT
ajpdis-1851	114	4	h.	h.	PROPN
ajpdis-1851	114	5	a.	a.	PROPN
ajpdis-1851	114	6	rahmatulin	rahmatulin	PROPN
ajpdis-1851	114	7	.	.	PUNCT
ajpdis-1851	115	1	fundamentals	fundamental	NOUN
ajpdis-1851	115	2	of	of	ADP
ajpdis-1851	115	3	gas	gas	NOUN
ajpdis-1851	115	4	dynamics	dynamic	NOUN
ajpdis-1851	115	5	of	of	ADP
ajpdis-1851	115	6	interpenetrating	interpenetrate	VERB
ajpdis-1851	115	7	movements	movement	NOUN
ajpdis-1851	115	8	of	of	ADP
ajpdis-1851	115	9	a	a	DET
ajpdis-1851	115	10	compressed	compressed	ADJ
ajpdis-1851	115	11	medium	medium	NOUN
ajpdis-1851	115	12	.	.	PUNCT
ajpdis-1851	116	1	pmm	pmm	PROPN
ajpdis-1851	116	2	,	,	PUNCT
ajpdis-1851	116	3	20	20	NUM
ajpdis-1851	116	4	,	,	PUNCT
ajpdis-1851	116	5	no.2	no.2	PROPN
ajpdis-1851	116	6	,	,	PUNCT
ajpdis-1851	116	7	1956	1956	NUM
ajpdis-1851	116	8	.	.	PUNCT
ajpdis-1851	117	1	2	2	X
ajpdis-1851	117	2	.	.	PUNCT
ajpdis-1851	117	3	n.	n.	PROPN
ajpdis-1851	117	4	a.	a.	PROPN
ajpdis-1851	117	5	mamadaliyev	mamadaliyev	PROPN
ajpdis-1851	117	6	.	.	PUNCT
ajpdis-1851	118	1	about	about	ADP
ajpdis-1851	118	2	the	the	DET
ajpdis-1851	118	3	movement	movement	NOUN
ajpdis-1851	118	4	of	of	ADP
ajpdis-1851	118	5	bodies	body	NOUN
ajpdis-1851	118	6	at	at	ADP
ajpdis-1851	118	7	a	a	DET
ajpdis-1851	118	8	speed	speed	NOUN
ajpdis-1851	118	9	higher	high	ADJ
ajpdis-1851	118	10	than	than	ADP
ajpdis-1851	118	11	sound	sound	NOUN
ajpdis-1851	118	12	in	in	ADP
ajpdis-1851	118	13	a	a	DET
ajpdis-1851	118	14	twocomponent	twocomponent	NOUN
ajpdis-1851	118	15	environment	environment	NOUN
ajpdis-1851	118	16	.	.	PUNCT
ajpdis-1851	119	1	izv	izv	PROPN
ajpdis-1851	119	2	.	.	PROPN
ajpdis-1851	119	3	academy	academy	PROPN
ajpdis-1851	119	4	of	of	ADP
ajpdis-1851	119	5	sciences	sciences	PROPN
ajpdis-1851	119	6	of	of	ADP
ajpdis-1851	119	7	the	the	DET
ajpdis-1851	119	8	uzssr	uzssr	ADJ
ajpdis-1851	119	9	,	,	PUNCT
ajpdis-1851	119	10	a	a	DET
ajpdis-1851	119	11	number	number	NOUN
ajpdis-1851	119	12	of	of	ADP
ajpdis-1851	119	13	technologies	technology	NOUN
ajpdis-1851	119	14	.	.	PUNCT
ajpdis-1851	120	1	sciences	science	NOUN
ajpdis-1851	120	2	,	,	PUNCT
ajpdis-1851	120	3	1966	1966	NUM
ajpdis-1851	120	4	no	no	NOUN
ajpdis-1851	120	5	.	.	NOUN
ajpdis-1851	121	1	1	1	NUM
ajpdis-1851	121	2	.	.	X
ajpdis-1851	122	1	3	3	NUM
ajpdis-1851	122	2	.	.	X
ajpdis-1851	122	3	r.	r.	PROPN
ajpdis-1851	122	4	i.	i.	PROPN
ajpdis-1851	122	5	nigmatulin	nigmatulin	PROPN
ajpdis-1851	122	6	.	.	PUNCT
ajpdis-1851	123	1	the	the	DET
ajpdis-1851	123	2	degree	degree	NOUN
ajpdis-1851	123	3	of	of	ADP
ajpdis-1851	123	4	hydromechanics	hydromechanic	NOUN
ajpdis-1851	123	5	and	and	CCONJ
ajpdis-1851	123	6	compression	compression	NOUN
ajpdis-1851	123	7	waves	wave	NOUN
ajpdis-1851	123	8	in	in	ADP
ajpdis-1851	123	9	a	a	DET
ajpdis-1851	123	10	two	two	NUM
ajpdis-1851	123	11	-	-	PUNCT
ajpdis-1851	123	12	speed	speed	NOUN
ajpdis-1851	123	13	and	and	CCONJ
ajpdis-1851	123	14	two	two	NUM
ajpdis-1851	123	15	-	-	PUNCT
ajpdis-1851	123	16	temperature	temperature	NOUN
ajpdis-1851	123	17	constant	constant	ADJ
ajpdis-1851	123	18	medium	medium	NOUN
ajpdis-1851	123	19	in	in	ADP
ajpdis-1851	123	20	the	the	DET
ajpdis-1851	123	21	presence	presence	NOUN
ajpdis-1851	123	22	of	of	ADP
ajpdis-1851	123	23	phase	phase	NOUN
ajpdis-1851	123	24	changes	change	NOUN
ajpdis-1851	123	25	.	.	PUNCT
ajpdis-1851	124	1	izv	izv	NOUN
ajpdis-1851	124	2	1967	1967	NUM
ajpdis-1851	124	3	no	no	NOUN
ajpdis-1851	124	4	.	.	PROPN
ajpdis-1851	124	5	5	5	NUM
ajpdis-1851	124	6	.	.	X
ajpdis-1851	124	7	4	4	NUM
ajpdis-1851	124	8	.	.	PUNCT
ajpdis-1851	124	9	t.	t.	PROPN
ajpdis-1851	124	10	a.	a.	PROPN
ajpdis-1851	124	11	djalilova	djalilova	PROPN
ajpdis-1851	124	12	,	,	PUNCT
ajpdis-1851	124	13	g.	g.	PROPN
ajpdis-1851	124	14	sh	sh	PROPN
ajpdis-1851	124	15	.	.	PROPN
ajpdis-1851	124	16	komolova	komolova	PROPN
ajpdis-1851	124	17	,	,	PUNCT
ajpdis-1851	124	18	m.	m.	PROPN
ajpdis-1851	124	19	d.	d.	PROPN
ajpdis-1851	124	20	khalilov	khalilov	PROPN
ajpdis-1851	124	21	.	.	PUNCT
ajpdis-1851	125	1	on	on	ADP
ajpdis-1851	125	2	the	the	DET
ajpdis-1851	125	3	distribution	distribution	NOUN
ajpdis-1851	125	4	of	of	ADP
ajpdis-1851	125	5	the	the	DET
ajpdis-1851	125	6	spherical	spherical	ADJ
ajpdis-1851	125	7	wave	wave	NOUN
ajpdis-1851	125	8	v.	v.	ADP
ajpdis-1851	125	9	innovative	innovative	ADJ
ajpdis-1851	125	10	,	,	PUNCT
ajpdis-1851	125	11	educational	educational	ADJ
ajpdis-1851	125	12	,	,	PUNCT
ajpdis-1851	125	13	natural	natural	ADJ
ajpdis-1851	125	14	and	and	CCONJ
ajpdis-1851	125	15	social	social	ADJ
ajpdis-1851	125	16	sciences	science	NOUN
ajpdis-1851	125	17	.	.	PUNCT
ajpdis-1851	126	1	87	87	NUM
ajpdis-1851	126	2	-	-	SYM
ajpdis-1851	126	3	92	92	NUM
ajpdis-1851	126	4	page	page	NOUN
ajpdis-1851	126	5	16	16	NUM
ajpdis-1851	126	6	.	.	PUNCT
ajpdis-1851	126	7	03	03	NUM
ajpdis-1851	126	8	.	.	PUNCT
ajpdis-1851	127	1	2022	2022	NUM
ajpdis-1851	127	2	year	year	NOUN
ajpdis-1851	127	3	.	.	PUNCT
ajpdis-1851	128	1	5	5	X
ajpdis-1851	128	2	.	.	X
ajpdis-1851	128	3	ergashev	ergashev	PROPN
ajpdis-1851	128	4	sultonmurod	sultonmurod	PROPN
ajpdis-1851	128	5	,	,	PUNCT
ajpdis-1851	128	6	k.	k.	PROPN
ajpdis-1851	128	7	b.	b.	PROPN
ajpdis-1851	128	8	(	(	PUNCT
ajpdis-1851	128	9	2021/12	2021/12	NUM
ajpdis-1851	128	10	)	)	PUNCT
ajpdis-1851	128	11	.	.	PUNCT
ajpdis-1851	129	1	differensial	differensial	ADJ
ajpdis-1851	129	2	tenglamalarni	tenglamalarni	PROPN
ajpdis-1851	129	3	mehanika	mehanika	PROPN
ajpdis-1851	129	4	va	va	PROPN
ajpdis-1851	129	5	fizikaning	fizikaning	NOUN
ajpdis-1851	129	6	ba`zi	ba`zi	NOUN
ajpdis-1851	129	7	masalalarini	masalalarini	PROPN
ajpdis-1851	129	8	yechishga	yechishga	PROPN
ajpdis-1851	129	9	tadbiqlari	tadbiqlari	PROPN
ajpdis-1851	129	10	.	.	PUNCT
ajpdis-1851	130	1	наманган	наманган	PROPN
ajpdis-1851	130	2	муҳандисликтехнология	муҳандисликтехнология	PROPN
ajpdis-1851	130	3	институти	институти	PROPN
ajpdis-1851	130	4	илмий	илмий	NOUN
ajpdis-1851	130	5	-	-	PUNCT
ajpdis-1851	130	6	техника	техника	NOUN
ajpdis-1851	130	7	журнали	журнали	NOUN
ajpdis-1851	130	8	,	,	PUNCT
ajpdis-1851	130	9	430	430	NUM
ajpdis-1851	130	10	-	-	SYM
ajpdis-1851	130	11	433	433	NUM
ajpdis-1851	130	12	.	.	PUNCT
ajpdis-1851	131	1	6	6	NUM
ajpdis-1851	131	2	.	.	X
ajpdis-1851	131	3	durbek	durbek	VERB
ajpdis-1851	131	4	o‘g‘li	o‘g‘li	ADV
ajpdis-1851	131	5	,	,	PUNCT
ajpdis-1851	131	6	x.	x.	NOUN
ajpdis-1851	131	7	m.	m.	NOUN
ajpdis-1851	131	8	,	,	PUNCT
ajpdis-1851	131	9	&	&	CCONJ
ajpdis-1851	131	10	ibragimjon	ibragimjon	VERB
ajpdis-1851	131	11	o‘g‘li	o‘g‘li	NOUN
ajpdis-1851	131	12	,	,	PUNCT
ajpdis-1851	131	13	m.	m.	NOUN
ajpdis-1851	131	14	s.	s.	PROPN
ajpdis-1851	131	15	(	(	PUNCT
ajpdis-1851	131	16	2022	2022	NUM
ajpdis-1851	131	17	)	)	PUNCT
ajpdis-1851	131	18	.	.	PUNCT
ajpdis-1851	132	1	matritsa	matritsa	PROPN
ajpdis-1851	133	1	yordamida	yordamida	PROPN
ajpdis-1851	133	2	elektr	elektr	VERB
ajpdis-1851	133	3	tokini	tokini	NOUN
ajpdis-1851	133	4	aniqlash	aniqlash	NOUN
ajpdis-1851	133	5	.	.	PUNCT
ajpdis-1851	134	1	ta'lim	ta'lim	PROPN
ajpdis-1851	134	2	va	va	PROPN
ajpdis-1851	134	3	rivojlanish	rivojlanish	ADJ
ajpdis-1851	134	4	tahlili	tahlili	NOUN
ajpdis-1851	134	5	onlayn	onlayn	PROPN
ajpdis-1851	134	6	ilmiy	ilmiy	PROPN
ajpdis-1851	134	7	jurnali	jurnali	PROPN
ajpdis-1851	134	8	,	,	PUNCT
ajpdis-1851	134	9	223	223	NUM
ajpdis-1851	134	10	-	-	SYM
ajpdis-1851	134	11	226	226	NUM
ajpdis-1851	134	12	.	.	PUNCT
ajpdis-1851	135	1	7	7	X
ajpdis-1851	135	2	.	.	X
ajpdis-1851	135	3	durbek	durbek	VERB
ajpdis-1851	135	4	o‘g‘li	o‘g‘li	ADV
ajpdis-1851	135	5	,	,	PUNCT
ajpdis-1851	135	6	x.	x.	NOUN
ajpdis-1851	135	7	m.	m.	NOUN
ajpdis-1851	135	8	,	,	PUNCT
ajpdis-1851	135	9	&	&	CCONJ
ajpdis-1851	135	10	komiljon	komiljon	PROPN
ajpdis-1851	135	11	o‘g‘li	o‘g‘li	PROPN
ajpdis-1851	135	12	,	,	PUNCT
ajpdis-1851	135	13	k.	k.	PROPN
ajpdis-1851	135	14	b.	b.	PROPN
ajpdis-1851	136	1	(	(	PUNCT
ajpdis-1851	136	2	2022	2022	NUM
ajpdis-1851	136	3	)	)	PUNCT
ajpdis-1851	136	4	.	.	PUNCT
ajpdis-1851	137	1	differensial	differensial	ADJ
ajpdis-1851	137	2	tenglamaga	tenglamaga	PROPN
ajpdis-1851	137	3	olib	olib	PROPN
ajpdis-1851	137	4	keluvchi	keluvchi	PROPN
ajpdis-1851	137	5	ba’zi	ba’zi	PROPN
ajpdis-1851	137	6	masalalar	masalalar	PROPN
ajpdis-1851	137	7	.	.	PUNCT
ajpdis-1851	138	1	barqarorlik	barqarorlik	PROPN
ajpdis-1851	138	2	va	va	PROPN
ajpdis-1851	138	3	yetakchi	yetakchi	PROPN
ajpdis-1851	138	4	tadqiqotlar	tadqiqotlar	ADJ
ajpdis-1851	138	5	onlayn	onlayn	PROPN
ajpdis-1851	138	6	ilmiy	ilmiy	PROPN
ajpdis-1851	138	7	jurnali	jurnali	PROPN
ajpdis-1851	138	8	,	,	PUNCT
ajpdis-1851	138	9	15	15	NUM
ajpdis-1851	138	10	-	-	SYM
ajpdis-1851	138	11	19	19	NUM
ajpdis-1851	138	12	.	.	NOUN
ajpdis-1851	138	13	8	8	NUM
ajpdis-1851	138	14	.	.	X
ajpdis-1851	139	1	durbek	durbek	VERB
ajpdis-1851	139	2	o‘g‘li	o‘g‘li	ADV
ajpdis-1851	139	3	,	,	PUNCT
ajpdis-1851	139	4	x.	x.	NOUN
ajpdis-1851	139	5	m.	m.	NOUN
ajpdis-1851	139	6	,	,	PUNCT
ajpdis-1851	139	7	&	&	CCONJ
ajpdis-1851	139	8	tulqinovna	tulqinovna	PROPN
ajpdis-1851	139	9	,	,	PUNCT
ajpdis-1851	140	1	s.	s.	PROPN
ajpdis-1851	140	2	m.	m.	PROPN
ajpdis-1851	140	3	(	(	PUNCT
ajpdis-1851	140	4	2023/1/1	2023/1/1	PROPN
ajpdis-1851	140	5	)	)	PUNCT
ajpdis-1851	140	6	.	.	PUNCT
ajpdis-1851	141	1	oddiy	oddiy	PROPN
ajpdis-1851	141	2	differensial	differensial	ADJ
ajpdis-1851	141	3	tenglamalarni	tenglamalarni	PROPN
ajpdis-1851	141	4	mehanika	mehanika	PROPN
ajpdis-1851	141	5	va	va	PROPN
ajpdis-1851	141	6	fizikaning	fizikaning	NOUN
ajpdis-1851	141	7	bazi	bazi	PROPN
ajpdis-1851	141	8	masalalarini	masalalarini	PROPN
ajpdis-1851	141	9	yechishga	yechishga	PROPN
ajpdis-1851	141	10	tadbiqlari	tadbiqlari	PROPN
ajpdis-1851	141	11	.	.	PUNCT
ajpdis-1851	142	1	новости	новости	PROPN
ajpdis-1851	142	2	образования	образования	PROPN
ajpdis-1851	142	3	:	:	PUNCT
ajpdis-1851	142	4	исследование	исследование	PROPN
ajpdis-1851	142	5	в	в	PROPN
ajpdis-1851	142	6	xxi	xxi	PROPN
ajpdis-1851	142	7	веке	веке	PROPN
ajpdis-1851	142	8	(	(	PUNCT
ajpdis-1851	142	9	стр	стр	NOUN
ajpdis-1851	142	10	.	.	NOUN
ajpdis-1851	142	11	763773	763773	NUM
ajpdis-1851	142	12	)	)	PUNCT
ajpdis-1851	142	13	.	.	PUNCT
ajpdis-1851	143	1	rossiya	rossiya	NOUN
ajpdis-1851	143	2	:	:	PUNCT
ajpdis-1851	143	3	международный	международный	NOUN
ajpdis-1851	143	4	научный	научный	NOUN
ajpdis-1851	143	5	журнал	журнал	NOUN
ajpdis-1851	143	6	.	.	PUNCT
ajpdis-1851	144	1	9	9	X
ajpdis-1851	144	2	.	.	X
ajpdis-1851	144	3	o‘g‘li	o‘g‘li	NUM
ajpdis-1851	144	4	,	,	PUNCT
ajpdis-1851	144	5	x.	x.	NOUN
ajpdis-1851	144	6	m.	m.	NOUN
ajpdis-1851	144	7	(	(	PUNCT
ajpdis-1851	144	8	2021/12	2021/12	NUM
ajpdis-1851	144	9	)	)	PUNCT
ajpdis-1851	144	10	.	.	PUNCT
ajpdis-1851	145	1	irratsional	irratsional	ADJ
ajpdis-1851	145	2	tenglama	tenglama	PROPN
ajpdis-1851	145	3	va	va	PROPN
ajpdis-1851	145	4	tengsizliklarni	tengsizliklarni	PROPN
ajpdis-1851	145	5	yechishda	yechishda	PROPN
ajpdis-1851	145	6	o‘quvchilarning	o‘quvchilarne	VERB
ajpdis-1851	145	7	qobiliyatlarini	qobiliyatlarini	PROPN
ajpdis-1851	145	8	rivojlantirish	rivojlantirish	PROPN
ajpdis-1851	145	9	.	.	PUNCT
ajpdis-1851	146	1	наманган	наманган	PROPN
ajpdis-1851	146	2	муҳандислик	муҳандислик	PROPN
ajpdis-1851	146	3	технология	технология	PROPN
ajpdis-1851	146	4	институти	институти	NOUN
ajpdis-1851	146	5	илмий	илмий	NOUN
ajpdis-1851	146	6	-	-	PUNCT
ajpdis-1851	146	7	техника	техника	NOUN
ajpdis-1851	146	8	журнали	журнали	NOUN
ajpdis-1851	146	9	,	,	PUNCT
ajpdis-1851	146	10	476	476	NUM
ajpdis-1851	146	11	-	-	SYM
ajpdis-1851	146	12	481	481	NUM
ajpdis-1851	146	13	.	.	PUNCT
ajpdis-1851	146	14	10	10	NUM
ajpdis-1851	146	15	.	.	PUNCT
ajpdis-1851	147	1	komiljonov	komiljonov	NOUN
ajpdis-1851	147	2	boburjon	boburjon	NOUN
ajpdis-1851	147	3	,	,	PUNCT
ajpdis-1851	147	4	x.	x.	NOUN
ajpdis-1851	147	5	m.	m.	NOUN
ajpdis-1851	147	6	(	(	PUNCT
ajpdis-1851	147	7	2021/4/9	2021/4/9	NUM
ajpdis-1851	147	8	)	)	PUNCT
ajpdis-1851	147	9	.	.	PUNCT
ajpdis-1851	148	1	o’quvchilarda	o’quvchilarda	PROPN
ajpdis-1851	148	2	funksiya	funksiya	NOUN
ajpdis-1851	148	3	tushunchasini	tushunchasini	PROPN
ajpdis-1851	148	4	shakllantirish	shakllantirish	NOUN
ajpdis-1851	148	5	.	.	PUNCT
ajpdis-1851	149	1	matematikani	matematikani	PROPN
ajpdis-1851	149	2	iqtisodiy	iqtisodiy	NOUN
ajpdis-1851	149	3	-	-	PUNCT
ajpdis-1851	149	4	texnik	texnik	NOUN
ajpdis-1851	149	5	masalalarga	masalalarga	PROPN
ajpdis-1851	149	6	tadbiqlari	tadbiqlari	PROPN
ajpdis-1851	149	7	va	va	PROPN
ajpdis-1851	149	8	o`qitish	o`qitish	PROPN
ajpdis-1851	149	9	muammolari	muammolari	NOUN
ajpdis-1851	149	10	,	,	PUNCT
ajpdis-1851	149	11	(	(	PUNCT
ajpdis-1851	149	12	стр	стр	NOUN
ajpdis-1851	149	13	.	.	NOUN
ajpdis-1851	149	14	297	297	NUM
ajpdis-1851	149	15	-	-	SYM
ajpdis-1851	149	16	303	303	NUM
ajpdis-1851	149	17	)	)	PUNCT
ajpdis-1851	149	18	.	.	PUNCT
ajpdis-1851	150	1	узбекистан	узбекистан	NOUN
ajpdis-1851	150	2	.	.	PUNCT
ajpdis-1851	151	1	11	11	NUM
ajpdis-1851	151	2	.	.	X
ajpdis-1851	151	3	tillayev	tillayev	PROPN
ajpdis-1851	151	4	donyorbek	donyorbek	PROPN
ajpdis-1851	151	5	,	,	PUNCT
ajpdis-1851	151	6	x.	x.	NOUN
ajpdis-1851	151	7	m.	m.	NOUN
ajpdis-1851	151	8	(	(	PUNCT
ajpdis-1851	151	9	2021/11/15	2021/11/15	NOUN
ajpdis-1851	151	10	)	)	PUNCT
ajpdis-1851	151	11	.	.	PUNCT
ajpdis-1851	152	1	fazoda	fazoda	PROPN
ajpdis-1851	152	2	urinma	urinma	PROPN
ajpdis-1851	152	3	akslantirish	akslantirish	PROPN
ajpdis-1851	152	4	va	va	PROPN
ajpdis-1851	152	5	uning	une	VERB
ajpdis-1851	152	6	formalizmga	formalizmga	PROPN
ajpdis-1851	152	7	bog‘liqligi	bog‘liqligi	PROPN
ajpdis-1851	152	8	.	.	PUNCT
ajpdis-1851	153	1	uzacademia	uzacademia	PROPN
ajpdis-1851	153	2	ilmiy	ilmiy	PROPN
ajpdis-1851	153	3	-	-	PUNCT
ajpdis-1851	153	4	uslubiy	uslubiy	PROPN
ajpdis-1851	153	5	jurnali	jurnali	PROPN
ajpdis-1851	153	6	,	,	PUNCT
ajpdis-1851	153	7	86	86	NUM
ajpdis-1851	153	8	-	-	SYM
ajpdis-1851	153	9	92	92	NUM
ajpdis-1851	153	10	.	.	PUNCT
ajpdis-1851	154	1	12	12	NUM
ajpdis-1851	154	2	.	.	PUNCT
ajpdis-1851	154	3	sultanmurad	sultanmurad	PROPN
ajpdis-1851	154	4	,	,	PUNCT
ajpdis-1851	154	5	e.	e.	PROPN
ajpdis-1851	154	6	(	(	PUNCT
ajpdis-1851	154	7	2022	2022	NUM
ajpdis-1851	154	8	)	)	PUNCT
ajpdis-1851	154	9	.	.	PUNCT
ajpdis-1851	155	1	vektorning	vektorne	VERB
ajpdis-1851	155	2	hosilasi	hosilasi	PROPN
ajpdis-1851	155	3	va	va	PROPN
ajpdis-1851	155	4	uning	une	VERB
ajpdis-1851	155	5	tatbiqlari	tatbiqlari	NOUN
ajpdis-1851	155	6	.	.	PUNCT
ajpdis-1851	156	1	машинасозлик	машинасозлик	X
ajpdis-1851	156	2	илмий	илмий	NOUN
ajpdis-1851	156	3	-	-	PUNCT
ajpdis-1851	156	4	техника	техника	NOUN
ajpdis-1851	156	5	журнали	журнали	NOUN
ajpdis-1851	156	6	,	,	PUNCT
ajpdis-1851	156	7	241	241	NUM
ajpdis-1851	156	8	-	-	SYM
ajpdis-1851	156	9	246	246	NUM
ajpdis-1851	156	10	.	.	PUNCT
ajpdis-1851	156	11	118	118	NUM
ajpdis-1851	156	12	american	american	ADJ
ajpdis-1851	156	13	journal	journal	PROPN
ajpdis-1851	156	14	of	of	ADP
ajpdis-1851	156	15	public	public	ADJ
ajpdis-1851	156	16	diplomacy	diplomacy	NOUN
ajpdis-1851	156	17	and	and	CCONJ
ajpdis-1851	156	18	international	international	ADJ
ajpdis-1851	156	19	studies	study	NOUN
ajpdis-1851	156	20	www	www	PROPN
ajpdis-1851	156	21	.	.	PROPN
ajpdis-1851	157	1	grnjournal.us	grnjournal.us	X
ajpdis-1851	157	2	13	13	NUM
ajpdis-1851	157	3	.	.	PUNCT
ajpdis-1851	157	4	ergashov	ergashov	PROPN
ajpdis-1851	157	5	s.	s.	PROPN
ajpdis-1851	157	6	,	,	PUNCT
ajpdis-1851	157	7	komiljonov	komiljonov	PROPN
ajpdis-1851	157	8	b.	b.	PROPN
ajpdis-1851	157	9	,	,	PUNCT
ajpdis-1851	157	10	xalilov	xalilov	PROPN
ajpdis-1851	157	11	m.	m.	PROPN
ajpdis-1851	157	12	differensial	differensial	PROPN
ajpdis-1851	157	13	tenglamalarni	tenglamalarni	PROPN
ajpdis-1851	157	14	mexanika	mexanika	PROPN
ajpdis-1851	157	15	va	va	PROPN
ajpdis-1851	157	16	fizikaning	fizikaning	PROPN
ajpdis-1851	157	17	baʼzi	baʼzi	ADJ
ajpdis-1851	157	18	masalalarini	masalalarini	PROPN
ajpdis-1851	157	19	yechishga	yechishga	PROPN
ajpdis-1851	157	20	tadbiqlari	tadbiqlari	PROPN
ajpdis-1851	157	21	//	//	PROPN
ajpdis-1851	157	22	namangan	namangan	PROPN
ajpdis-1851	157	23	muhandislik	muhandislik	PROPN
ajpdis-1851	157	24	texnologiyalari	texnologiyalari	PROPN
ajpdis-1851	157	25	instituti	instituti	PROPN
ajpdis-1851	157	26	ilmiy	ilmiy	NOUN
ajpdis-1851	157	27	-	-	PUNCT
ajpdis-1851	157	28	texnika	texnika	NOUN
ajpdis-1851	157	29	jurnali	jurnali	PROPN
ajpdis-1851	157	30	430	430	NUM
ajpdis-1851	157	31	-	-	SYM
ajpdis-1851	157	32	433	433	NUM
ajpdis-1851	157	33	b.	b.	PROPN
ajpdis-1851	157	34	14	14	NUM
ajpdis-1851	157	35	.	.	PUNCT
ajpdis-1851	158	1	xalilov	xalilov	PROPN
ajpdis-1851	158	2	murodiljon	murodiljon	PROPN
ajpdis-1851	158	3	,	,	PUNCT
ajpdis-1851	158	4	tillayev	tillayev	ADJ
ajpdis-1851	158	5	donyorbek	donyorbek	PROPN
ajpdis-1851	158	6	experience	experience	NOUN
ajpdis-1851	158	7	in	in	ADP
ajpdis-1851	158	8	using	use	VERB
ajpdis-1851	158	9	the	the	DET
ajpdis-1851	158	10	relationship	relationship	NOUN
ajpdis-1851	158	11	between	between	ADP
ajpdis-1851	158	12	mathematics	mathematic	NOUN
ajpdis-1851	158	13	and	and	CCONJ
ajpdis-1851	158	14	physics	physics	NOUN
ajpdis-1851	158	15	in	in	ADP
ajpdis-1851	158	16	shaping	shape	VERB
ajpdis-1851	158	17	the	the	DET
ajpdis-1851	158	18	concept	concept	NOUN
ajpdis-1851	158	19	of	of	ADP
ajpdis-1851	158	20	limit	limit	NOUN
ajpdis-1851	158	21	//	//	NUM
ajpdis-1851	158	22	analytical	analytical	ADJ
ajpdis-1851	158	23	journal	journal	NOUN
ajpdis-1851	158	24	of	of	ADP
ajpdis-1851	158	25	education	education	NOUN
ajpdis-1851	158	26	and	and	CCONJ
ajpdis-1851	158	27	development	development	NOUN
ajpdis-1851	158	28	2021	2021	NUM
ajpdis-1851	158	29	yil	yil	PROPN
ajpdis-1851	158	30	,	,	PUNCT
ajpdis-1851	158	31	212	212	NUM
ajpdis-1851	158	32	-	-	SYM
ajpdis-1851	158	33	215	215	NUM
ajpdis-1851	158	34	b	b	PROPN
ajpdis-1851	158	35	..	..	PROPN
ajpdis-1851	158	36	15	15	NUM
ajpdis-1851	158	37	.	.	PUNCT
ajpdis-1851	159	1	xalilov	xalilov	PROPN
ajpdis-1851	159	2	m.	m.	PROPN
ajpdis-1851	159	3	,	,	PUNCT
ajpdis-1851	159	4	komolova	komolova	X
ajpdis-1851	159	5	g.	g.	PROPN
ajpdis-1851	159	6	,	,	PUNCT
ajpdis-1851	159	7	komiljonov	komiljonov	PROPN
ajpdis-1851	159	8	b.	b.	PROPN
ajpdis-1851	159	9	solve	solve	VERB
ajpdis-1851	159	10	some	some	DET
ajpdis-1851	159	11	chemical	chemical	ADJ
ajpdis-1851	159	12	reactions	reaction	NOUN
ajpdis-1851	159	13	using	use	VERB
ajpdis-1851	159	14	equations	equation	NOUN
ajpdis-1851	159	15	//	//	PROPN
ajpdis-1851	159	16	european	european	PROPN
ajpdis-1851	159	17	journal	journal	PROPN
ajpdis-1851	159	18	of	of	ADP
ajpdis-1851	159	19	business	business	NOUN
ajpdis-1851	159	20	startups	startup	NOUN
ajpdis-1851	159	21	and	and	CCONJ
ajpdis-1851	159	22	open	open	ADJ
ajpdis-1851	159	23	society	society	NOUN
ajpdis-1851	159	24	.	.	PUNCT
ajpdis-1851	160	1	vol	vol	NOUN
ajpdis-1851	160	2	.	.	PROPN
ajpdis-1851	161	1	2	2	NUM
ajpdis-1851	161	2	no	no	NOUN
ajpdis-1851	161	3	.	.	NOUN
ajpdis-1851	161	4	1	1	NUM
ajpdis-1851	161	5	(	(	PUNCT
ajpdis-1851	161	6	2022	2022	NUM
ajpdis-1851	161	7	):	):	PUNCT
ajpdis-1851	161	8	ejbsos	ejbsos	PROPN
ajpdis-1851	161	9	issn	issn	PROPN
ajpdis-1851	161	10	:	:	PUNCT
ajpdis-1851	161	11	2795	2795	NUM
ajpdis-1851	161	12	-	-	SYM
ajpdis-1851	161	13	9228	9228	NUM
ajpdis-1851	161	14	.	.	PUNCT
ajpdis-1851	162	1	45	45	NUM
ajpdis-1851	162	2	-	-	SYM
ajpdis-1851	162	3	48	48	NUM
ajpdis-1851	162	4	p.	p.	NOUN
ajpdis-1851	162	5	16	16	NUM
ajpdis-1851	162	6	.	.	PUNCT
ajpdis-1851	163	1	м	м	X
ajpdis-1851	163	2	.	.	PUNCT
ajpdis-1851	164	1	д	д	X
ajpdis-1851	164	2	.	.	PROPN
ajpdis-1851	164	3	халилов	халилов	PROPN
ajpdis-1851	164	4	,	,	PUNCT
ajpdis-1851	164	5	б	б	NOUN
ajpdis-1851	164	6	.	.	PUNCT
ajpdis-1851	165	1	к	к	X
ajpdis-1851	165	2	.	.	PUNCT
ajpdis-1851	165	3	комилжонов	комилжонов	PROPN
ajpdis-1851	165	4	.	.	PUNCT
ajpdis-1851	166	1	differensial	differensial	ADJ
ajpdis-1851	166	2	tenglamaga	tenglamaga	PROPN
ajpdis-1851	166	3	olib	olib	PROPN
ajpdis-1851	166	4	keluvchi	keluvchi	PROPN
ajpdis-1851	166	5	ba’zi	ba’zi	PROPN
ajpdis-1851	166	6	masalalar	masalalar	PROPN
ajpdis-1851	166	7	.	.	PUNCT
ajpdis-1851	167	1	journal	journal	PROPN
ajpdis-1851	167	2	of	of	ADP
ajpdis-1851	167	3	advanced	advanced	ADJ
ajpdis-1851	167	4	research	research	NOUN
ajpdis-1851	167	5	and	and	CCONJ
ajpdis-1851	167	6	stability	stability	NOUN
ajpdis-1851	167	7	issn	issn	VERB
ajpdis-1851	167	8	:	:	PUNCT
ajpdis-1851	167	9	2181	2181	NUM
ajpdis-1851	167	10	-	-	SYM
ajpdis-1851	167	11	2608	2608	NUM
ajpdis-1851	167	12	15	15	NUM
ajpdis-1851	167	13	-	-	SYM
ajpdis-1851	167	14	19	19	NUM
ajpdis-1851	167	15	b.	b.	NOUN
ajpdis-1851	167	16	17	17	NUM
ajpdis-1851	167	17	.	.	PUNCT
ajpdis-1851	168	1	m.d	m.d	PROPN
ajpdis-1851	168	2	.	.	PROPN
ajpdis-1851	168	3	xalilov	xalilov	PROPN
ajpdis-1851	168	4	,	,	PUNCT
ajpdis-1851	168	5	b.k	b.k	PROPN
ajpdis-1851	168	6	.	.	PUNCT
ajpdis-1851	168	7	komiljonov	komiljonov	PROPN
ajpdis-1851	168	8	,	,	PUNCT
ajpdis-1851	168	9	g.sh	g.sh	PROPN
ajpdis-1851	168	10	.	.	PUNCT
ajpdis-1851	169	1	komolova	komolova	X
ajpdis-1851	169	2	.	.	PUNCT
ajpdis-1851	170	1	garmonik	garmonik	PROPN
ajpdis-1851	170	2	skalyar	skalyar	PROPN
ajpdis-1851	170	3	tebranishlarning	tebranishlarne	VERB
ajpdis-1851	170	4	kompleks	kompleks	PROPN
ajpdis-1851	170	5	va	va	PROPN
ajpdis-1851	170	6	vektor	vektor	PROPN
ajpdis-1851	170	7	ifodalanishi	ifodalanishi	PROPN
ajpdis-1851	170	8	.	.	PUNCT
ajpdis-1851	171	1	miasto	miasto	PROPN
ajpdis-1851	171	2	przyszłości	przyszłości	PROPN
ajpdis-1851	171	3	.	.	PUNCT
ajpdis-1851	172	1	issn	issn	PROPN
ajpdis-1851	172	2	-	-	PUNCT
ajpdis-1851	172	3	l:2544980x	l:2544980x	PROPN
ajpdis-1851	172	4	.	.	NOUN
ajpdis-1851	172	5	table	table	NOUN
ajpdis-1851	172	6	of	of	ADP
ajpdis-1851	172	7	content	content	NOUN
ajpdis-1851	172	8	volume	volume	NOUN
ajpdis-1851	172	9	24	24	NUM
ajpdis-1851	172	10	(	(	PUNCT
ajpdis-1851	172	11	jun	jun	PROPN
ajpdis-1851	172	12	2022	2022	NUM
ajpdis-1851	172	13	)	)	PUNCT
ajpdis-1851	172	14	.	.	PUNCT
ajpdis-1851	173	1	18	18	NUM
ajpdis-1851	173	2	.	.	PUNCT
ajpdis-1851	173	3	джалилова	джалилова	NOUN
ajpdis-1851	173	4	,	,	PUNCT
ajpdis-1851	173	5	т	т	PROPN
ajpdis-1851	173	6	.	.	PUNCT
ajpdis-1851	173	7	а	а	PROPN
ajpdis-1851	173	8	.	.	PROPN
ajpdis-1851	173	9	,	,	PUNCT
ajpdis-1851	173	10	комолова	комолова	VERB
ajpdis-1851	173	11	,	,	PUNCT
ajpdis-1851	173	12	г	г	PROPN
ajpdis-1851	173	13	.	.	PUNCT
ajpdis-1851	174	1	ш	ш	X
ajpdis-1851	174	2	.	.	PUNCT
ajpdis-1851	175	1	к	к	X
ajpdis-1851	175	2	.	.	PROPN
ajpdis-1851	175	3	,	,	PUNCT
ajpdis-1851	175	4	&	&	CCONJ
ajpdis-1851	175	5	халилов	халилов	PROPN
ajpdis-1851	175	6	,	,	PUNCT
ajpdis-1851	175	7	м	м	X
ajpdis-1851	175	8	.	.	PUNCT
ajpdis-1851	176	1	д	д	NOUN
ajpdis-1851	176	2	.	.	NOUN
ajpdis-1851	177	1	у	у	X
ajpdis-1851	177	2	.	.	PUNCT
ajpdis-1851	177	3	(	(	PUNCT
ajpdis-1851	177	4	2022	2022	NUM
ajpdis-1851	177	5	)	)	PUNCT
ajpdis-1851	177	6	.	.	PUNCT
ajpdis-1851	178	1	о	о	PROPN
ajpdis-1851	178	2	распространении	распространении	PROPN
ajpdis-1851	178	3	сферической	сферической	PROPN
ajpdis-1851	178	4	волны	волны	VERB
ajpdis-1851	178	5	в	в	PROPN
ajpdis-1851	178	6	нелинейно	нелинейно	PROPN
ajpdis-1851	178	7	-	-	PUNCT
ajpdis-1851	178	8	сжимаемой	сжимаемой	PROPN
ajpdis-1851	178	9	и	и	NOUN
ajpdis-1851	178	10	упругопластической	упругопластической	ADJ
ajpdis-1851	178	11	средах	средах	NOUN
ajpdis-1851	178	12	.	.	PUNCT
ajpdis-1851	179	1	oriental	oriental	ADJ
ajpdis-1851	179	2	renaissance	renaissance	NOUN
ajpdis-1851	179	3	:	:	PUNCT
ajpdis-1851	179	4	innovative	innovative	ADJ
ajpdis-1851	179	5	,	,	PUNCT
ajpdis-1851	179	6	educational	educational	ADJ
ajpdis-1851	179	7	,	,	PUNCT
ajpdis-1851	179	8	natural	natural	ADJ
ajpdis-1851	179	9	and	and	CCONJ
ajpdis-1851	179	10	social	social	ADJ
ajpdis-1851	179	11	sciences	science	NOUN
ajpdis-1851	179	12	,	,	PUNCT
ajpdis-1851	179	13	2(3	2(3	NUM
ajpdis-1851	179	14	)	)	PUNCT
ajpdis-1851	179	15	,	,	PUNCT
ajpdis-1851	179	16	87	87	NUM
ajpdis-1851	179	17	-	-	SYM
ajpdis-1851	179	18	92	92	NUM
ajpdis-1851	179	19	..	..	SYM
ajpdis-1851	179	20	19	19	NUM
ajpdis-1851	179	21	.	.	PUNCT
ajpdis-1851	179	22	комолова	комолова	NOUN
ajpdis-1851	179	23	,	,	PUNCT
ajpdis-1851	179	24	г	г	PROPN
ajpdis-1851	179	25	.	.	PROPN
ajpdis-1851	179	26	,	,	PUNCT
ajpdis-1851	179	27	&	&	CCONJ
ajpdis-1851	179	28	халилов	халилов	PROPN
ajpdis-1851	179	29	,	,	PUNCT
ajpdis-1851	179	30	м	м	X
ajpdis-1851	179	31	.	.	PUNCT
ajpdis-1851	180	1	stages	stage	NOUN
ajpdis-1851	180	2	of	of	ADP
ajpdis-1851	180	3	drawing	draw	VERB
ajpdis-1851	180	4	up	up	ADP
ajpdis-1851	180	5	a	a	DET
ajpdis-1851	180	6	mathematical	mathematical	ADJ
ajpdis-1851	180	7	model	model	NOUN
ajpdis-1851	180	8	of	of	ADP
ajpdis-1851	180	9	the	the	DET
ajpdis-1851	180	10	economic	economic	ADJ
ajpdis-1851	180	11	issue	issue	NOUN
ajpdis-1851	180	12	.	.	PUNCT
ajpdis-1851	181	1	journal	journal	PROPN
ajpdis-1851	181	2	of	of	ADP
ajpdis-1851	181	3	ethics	ethic	NOUN
ajpdis-1851	181	4	anddiversity	anddiversity	NOUN
ajpdis-1851	181	5	in	in	ADP
ajpdis-1851	181	6	international	international	ADJ
ajpdis-1851	181	7	communication	communication	NOUN
ajpdis-1851	181	8	.	.	PUNCT
ajpdis-1851	182	1	испания-2022	испания-2022	NOUN
ajpdis-1851	182	2	,	,	PUNCT
ajpdis-1851	182	3	60	60	NUM
ajpdis-1851	182	4	,	,	PUNCT
ajpdis-1851	182	5	4548	4548	NUM
ajpdis-1851	182	6	.	.	PUNCT
ajpdis-1851	183	1	20	20	NUM
ajpdis-1851	183	2	.	.	PUNCT
ajpdis-1851	184	1	дурбекович	дурбекович	PROPN
ajpdis-1851	184	2	,	,	PUNCT
ajpdis-1851	184	3	m.	m.	NOUN
ajpdis-1851	184	4	x.	x.	PROPN
ajpdis-1851	184	5	,	,	PUNCT
ajpdis-1851	184	6	&	&	CCONJ
ajpdis-1851	184	7	жавлонбек	жавлонбек	PROPN
ajpdis-1851	184	8	,	,	PUNCT
ajpdis-1851	184	9	и	и	PROPN
ajpdis-1851	184	10	.	.	PUNCT
ajpdis-1851	184	11	р	р	ADP
ajpdis-1851	184	12	.	.	PROPN
ajpdis-1851	184	13	(	(	PUNCT
ajpdis-1851	184	14	2023	2023	NUM
ajpdis-1851	184	15	,	,	PUNCT
ajpdis-1851	184	16	january	january	PROPN
ajpdis-1851	184	17	)	)	PUNCT
ajpdis-1851	184	18	.	.	PUNCT
ajpdis-1851	185	1	об	об	PROPN
ajpdis-1851	185	2	особых	особых	PROPN
ajpdis-1851	185	3	точках	точках	PROPN
ajpdis-1851	185	4	решений	решений	PROPN
ajpdis-1851	185	5	многомерной	многомерной	PROPN
ajpdis-1851	185	6	системы	системы	PROPN
ajpdis-1851	185	7	в	в	PROPN
ajpdis-1851	185	8	комплексной	комплексной	PROPN
ajpdis-1851	185	9	области	области	PROPN
ajpdis-1851	185	10	.	.	PUNCT
ajpdis-1851	186	1	in	in	ADP
ajpdis-1851	186	2	"	"	PUNCT
ajpdis-1851	186	3	canada	canada	PROPN
ajpdis-1851	186	4	"	"	PUNCT
ajpdis-1851	186	5	internati̇onal	internati̇onal	PROPN
ajpdis-1851	186	6	conference	conference	NOUN
ajpdis-1851	186	7	on	on	ADP
ajpdis-1851	186	8	developments	development	NOUN
ajpdis-1851	186	9	i̇n	i̇n	PROPN
ajpdis-1851	186	10	educati̇on	educati̇on	PROPN
ajpdis-1851	186	11	,	,	PUNCT
ajpdis-1851	186	12	sci̇encesand	sci̇encesand	PROPN
ajpdis-1851	186	13	humani̇ti̇es	humani̇ti̇es	PROPN
ajpdis-1851	186	14	(	(	PUNCT
ajpdis-1851	186	15	vol	vol	NOUN
ajpdis-1851	186	16	.	.	NOUN
ajpdis-1851	186	17	9	9	NUM
ajpdis-1851	186	18	,	,	PUNCT
ajpdis-1851	186	19	no	no	INTJ
ajpdis-1851	186	20	.	.	NOUN
ajpdis-1851	186	21	1	1	NUM
ajpdis-1851	186	22	)	)	PUNCT
ajpdis-1851	186	23	.	.	PUNCT
ajpdis-1851	187	1	21	21	NUM
ajpdis-1851	187	2	.	.	X
ajpdis-1851	187	3	durbek	durbek	VERB
ajpdis-1851	187	4	o‘g‘li	o‘g‘li	ADV
ajpdis-1851	187	5	,	,	PUNCT
ajpdis-1851	187	6	x.	x.	NOUN
ajpdis-1851	187	7	m.	m.	NOUN
ajpdis-1851	187	8	,	,	PUNCT
ajpdis-1851	187	9	&	&	CCONJ
ajpdis-1851	187	10	tulqinovna	tulqinovna	PROPN
ajpdis-1851	187	11	,	,	PUNCT
ajpdis-1851	187	12	s.	s.	PROPN
ajpdis-1851	187	13	m.	m.	PROPN
ajpdis-1851	187	14	(	(	PUNCT
ajpdis-1851	187	15	2023	2023	NUM
ajpdis-1851	187	16	,	,	PUNCT
ajpdis-1851	187	17	january	january	PROPN
ajpdis-1851	187	18	)	)	PUNCT
ajpdis-1851	187	19	.	.	PUNCT
ajpdis-1851	188	1	matritsalarning	matritsalarne	VERB
ajpdis-1851	188	2	iqtisodiyotdagi	iqtisodiyotdagi	PROPN
ajpdis-1851	188	3	tadbiqlari	tadbiqlari	PROPN
ajpdis-1851	188	4	.	.	PUNCT
ajpdis-1851	189	1	in	in	ADP
ajpdis-1851	189	2	"	"	PUNCT
ajpdis-1851	189	3	usa	usa	PROPN
ajpdis-1851	189	4	"	"	PUNCT
ajpdis-1851	189	5	international	international	ADJ
ajpdis-1851	189	6	scientific	scientific	ADJ
ajpdis-1851	189	7	and	and	CCONJ
ajpdis-1851	189	8	practical	practical	ADJ
ajpdis-1851	189	9	conference	conference	NOUN
ajpdis-1851	189	10	topical	topical	ADJ
ajpdis-1851	189	11	issues	issue	NOUN
ajpdis-1851	189	12	of	of	ADP
ajpdis-1851	189	13	science	science	NOUN
ajpdis-1851	189	14	(	(	PUNCT
ajpdis-1851	189	15	vol	vol	NOUN
ajpdis-1851	189	16	.	.	PROPN
ajpdis-1851	189	17	11	11	NUM
ajpdis-1851	189	18	,	,	PUNCT
ajpdis-1851	189	19	no	no	INTJ
ajpdis-1851	189	20	.	.	NOUN
ajpdis-1851	189	21	1	1	NUM
ajpdis-1851	189	22	,	,	PUNCT
ajpdis-1851	189	23	pp	pp	ADJ
ajpdis-1851	189	24	.	.	PUNCT
ajpdis-1851	189	25	15	15	NUM
ajpdis-1851	189	26	-	-	SYM
ajpdis-1851	189	27	19	19	NUM
ajpdis-1851	189	28	)	)	PUNCT
ajpdis-1851	189	29	.	.	PUNCT
ajpdis-1851	190	1	22	22	NUM
ajpdis-1851	190	2	.	.	PUNCT
ajpdis-1851	191	1	xalilov	xalilov	PROPN
ajpdis-1851	191	2	,	,	PUNCT
ajpdis-1851	191	3	m.	m.	PROPN
ajpdis-1851	191	4	d.	d.	PROPN
ajpdis-1851	191	5	,	,	PUNCT
ajpdis-1851	191	6	komiljonov	komiljonov	PROPN
ajpdis-1851	191	7	,	,	PUNCT
ajpdis-1851	191	8	b.	b.	PROPN
ajpdis-1851	191	9	k.	k.	PROPN
ajpdis-1851	191	10	,	,	PUNCT
ajpdis-1851	191	11	&	&	CCONJ
ajpdis-1851	191	12	komolova	komolova	PROPN
ajpdis-1851	191	13	,	,	PUNCT
ajpdis-1851	191	14	g.	g.	PROPN
ajpdis-1851	191	15	s.	s.	PROPN
ajpdis-1851	191	16	(	(	PUNCT
ajpdis-1851	191	17	2022	2022	NUM
ajpdis-1851	191	18	)	)	PUNCT
ajpdis-1851	191	19	.	.	PUNCT
ajpdis-1851	192	1	complex	complex	ADJ
ajpdis-1851	192	2	and	and	CCONJ
ajpdis-1851	192	3	vector	vector	NOUN
ajpdis-1851	192	4	expression	expression	NOUN
ajpdis-1851	192	5	of	of	ADP
ajpdis-1851	192	6	harmonic	harmonic	ADJ
ajpdis-1851	192	7	scaliar	scaliar	ADJ
ajpdis-1851	192	8	vibrations	vibration	NOUN
ajpdis-1851	192	9	.	.	PUNCT
ajpdis-1851	193	1	miasto	miasto	PROPN
ajpdis-1851	193	2	przyszłości	przyszłości	PROPN
ajpdis-1851	193	3	,	,	PUNCT
ajpdis-1851	193	4	24	24	NUM
ajpdis-1851	193	5	,	,	PUNCT
ajpdis-1851	193	6	341344	341344	NUM
ajpdis-1851	193	7	.	.	PUNCT
ajpdis-1851	194	1	23	23	NUM
ajpdis-1851	194	2	.	.	X
ajpdis-1851	195	1	djalilova	djalilova	PROPN
ajpdis-1851	195	2	,	,	PUNCT
ajpdis-1851	195	3	t.	t.	PROPN
ajpdis-1851	195	4	,	,	PUNCT
ajpdis-1851	195	5	komolova	komolova	X
ajpdis-1851	195	6	,	,	PUNCT
ajpdis-1851	195	7	g.	g.	PROPN
ajpdis-1851	195	8	,	,	PUNCT
ajpdis-1851	195	9	&	&	CCONJ
ajpdis-1851	195	10	xalilov	xalilov	PROPN
ajpdis-1851	195	11	,	,	PUNCT
ajpdis-1851	195	12	m.	m.	NOUN
ajpdis-1851	195	13	(	(	PUNCT
ajpdis-1851	195	14	2022	2022	NUM
ajpdis-1851	195	15	)	)	PUNCT
ajpdis-1851	195	16	.	.	PUNCT
ajpdis-1851	196	1	о	о	PROPN
ajpdis-1851	196	2	распространении	распространении	PROPN
ajpdis-1851	196	3	сферической	сферической	PROPN
ajpdis-1851	196	4	волны	волны	VERB
ajpdis-1851	196	5	в	в	PROPN
ajpdis-1851	196	6	нелинейно	нелинейно	PROPN
ajpdis-1851	196	7	-	-	PUNCT
ajpdis-1851	196	8	сжимаемой	сжимаемой	PROPN
ajpdis-1851	196	9	и	и	NOUN
ajpdis-1851	196	10	упругопластической	упругопластической	ADJ
ajpdis-1851	196	11	средах	средах	NOUN
ajpdis-1851	196	12	.	.	PUNCT
ajpdis-1851	197	1	oriental	oriental	ADJ
ajpdis-1851	197	2	renaissance	renaissance	NOUN
ajpdis-1851	197	3	:	:	PUNCT
ajpdis-1851	197	4	innovative	innovative	ADJ
ajpdis-1851	197	5	,	,	PUNCT
ajpdis-1851	197	6	educational	educational	ADJ
ajpdis-1851	197	7	,	,	PUNCT
ajpdis-1851	197	8	natural	natural	ADJ
ajpdis-1851	197	9	and	and	CCONJ
ajpdis-1851	197	10	social	social	ADJ
ajpdis-1851	197	11	sciences	science	NOUN
ajpdis-1851	197	12	jurnali	jurnali	PROPN
ajpdis-1851	197	13	,	,	PUNCT
ajpdis-1851	197	14	2181	2181	NUM
ajpdis-1851	197	15	-	-	SYM
ajpdis-1851	197	16	1784	1784	NUM
ajpdis-1851	197	17	.	.	PUNCT
ajpdis-1851	198	1	24	24	NUM
ajpdis-1851	198	2	.	.	PUNCT
ajpdis-1851	198	3	акбарова	акбарова	NOUN
ajpdis-1851	198	4	,	,	PUNCT
ajpdis-1851	198	5	с	с	PROPN
ajpdis-1851	198	6	.	.	PUNCT
ajpdis-1851	199	1	х	х	PROPN
ajpdis-1851	199	2	.	.	PROPN
ajpdis-1851	199	3	,	,	PUNCT
ajpdis-1851	199	4	&	&	CCONJ
ajpdis-1851	199	5	халилов	халилов	PROPN
ajpdis-1851	199	6	,	,	PUNCT
ajpdis-1851	199	7	м	м	X
ajpdis-1851	199	8	.	.	PUNCT
ajpdis-1851	200	1	д	д	X
ajpdis-1851	200	2	.	.	PUNCT
ajpdis-1851	201	1	(	(	PUNCT
ajpdis-1851	201	2	2019	2019	NUM
ajpdis-1851	201	3	)	)	PUNCT
ajpdis-1851	201	4	.	.	PUNCT
ajpdis-1851	202	1	о	о	PROPN
ajpdis-1851	202	2	краевой	краевой	NOUN
ajpdis-1851	202	3	задаче	задаче	NOUN
ajpdis-1851	202	4	для	для	PROPN
ajpdis-1851	202	5	смешаннопараболического	смешаннопараболического	PROPN
ajpdis-1851	202	6	уравнения	уравнения	PROPN
ajpdis-1851	202	7	.	.	PUNCT
ajpdis-1851	203	1	in	in	ADP
ajpdis-1851	203	2	andijan	andijan	NOUN
ajpdis-1851	203	3	state	state	PROPN
ajpdis-1851	203	4	university	university	NOUN
ajpdis-1851	203	5	named	name	VERB
ajpdis-1851	203	6	after	after	ADP
ajpdis-1851	203	7	zm	zm	PROPN
ajpdis-1851	203	8	babur	babur	PROPN
ajpdis-1851	203	9	institute	institute	PROPN
ajpdis-1851	203	10	of	of	ADP
ajpdis-1851	203	11	mathematics	mathematics	PROPN
ajpdis-1851	203	12	of	of	ADP
ajpdis-1851	203	13	uzbekistan	uzbekistan	PROPN
ajpdis-1851	203	14	academy	academy	PROPN
ajpdis-1851	203	15	of	of	ADP
ajpdis-1851	203	16	science	science	PROPN
ajpdis-1851	203	17	national	national	PROPN
ajpdis-1851	203	18	university	university	PROPN
ajpdis-1851	203	19	of	of	ADP
ajpdis-1851	203	20	uzbekistan	uzbekistan	PROPN
ajpdis-1851	203	21	named	name	VERB
ajpdis-1851	203	22	after	after	ADP
ajpdis-1851	203	23	mirzo	mirzo	PROPN
ajpdis-1851	203	24	ulugbek	ulugbek	PROPN
ajpdis-1851	203	25	scientific	scientific	ADJ
ajpdis-1851	203	26	conference	conference	NOUN
ajpdis-1851	203	27	(	(	PUNCT
ajpdis-1851	203	28	pp	pp	ADJ
ajpdis-1851	203	29	.	.	PUNCT
ajpdis-1851	204	1	88	88	NUM
ajpdis-1851	204	2	-	-	SYM
ajpdis-1851	204	3	89	89	NUM
ajpdis-1851	204	4	)	)	PUNCT
ajpdis-1851	204	5	.	.	PUNCT
ajpdis-1851	205	1	25	25	NUM
ajpdis-1851	205	2	.	.	PUNCT
ajpdis-1851	205	3	акбарова	акбарова	NOUN
ajpdis-1851	205	4	,	,	PUNCT
ajpdis-1851	205	5	с	с	PROPN
ajpdis-1851	205	6	.	.	PUNCT
ajpdis-1851	206	1	х	х	PROPN
ajpdis-1851	206	2	.	.	PROPN
ajpdis-1851	206	3	,	,	PUNCT
ajpdis-1851	206	4	акбарова	акбарова	NOUN
ajpdis-1851	206	5	,	,	PUNCT
ajpdis-1851	206	6	м	м	X
ajpdis-1851	206	7	.	.	PUNCT
ajpdis-1851	207	1	х	х	PROPN
ajpdis-1851	207	2	.	.	PROPN
ajpdis-1851	207	3	,	,	PUNCT
ajpdis-1851	207	4	&	&	CCONJ
ajpdis-1851	207	5	халилов	халилов	PROPN
ajpdis-1851	207	6	,	,	PUNCT
ajpdis-1851	207	7	м	м	X
ajpdis-1851	207	8	.	.	PUNCT
ajpdis-1851	208	1	д	д	X
ajpdis-1851	208	2	.	.	PUNCT
ajpdis-1851	209	1	(	(	PUNCT
ajpdis-1851	209	2	2019	2019	NUM
ajpdis-1851	209	3	)	)	PUNCT
ajpdis-1851	209	4	.	.	PUNCT
ajpdis-1851	210	1	о	о	PROPN
ajpdis-1851	210	2	разрешимости	разрешимости	PROPN
ajpdis-1851	210	3	нелокальной	нелокальной	PROPN
ajpdis-1851	210	4	краевой	краевой	PROPN
ajpdis-1851	210	5	задачи	задачи	PROPN
ajpdis-1851	210	6	для	для	PROPN
ajpdis-1851	210	7	смешанно	смешанно	PROPN
ajpdis-1851	210	8	–	–	PUNCT
ajpdis-1851	210	9	параболического	параболического	ADJ
ajpdis-1851	210	10	уравнения	уравнения	NOUN
ajpdis-1851	210	11	.	.	PUNCT
ajpdis-1851	211	1	international	international	ADJ
ajpdis-1851	211	2	scientific	scientific	ADJ
ajpdis-1851	211	3	journal	journal	NOUN
ajpdis-1851	211	4	«	«	PUNCT
ajpdis-1851	211	5	global	global	ADJ
ajpdis-1851	211	6	science	science	NOUN
ajpdis-1851	211	7	and	and	CCONJ
ajpdis-1851	211	8	innovations	innovation	NOUN
ajpdis-1851	211	9	,	,	PUNCT
ajpdis-1851	211	10	130	130	NUM
ajpdis-1851	211	11	-	-	SYM
ajpdis-1851	211	12	131	131	NUM
ajpdis-1851	211	13	.	.	NOUN
ajpdis-1851	211	14	26	26	NUM
ajpdis-1851	211	15	.	.	PUNCT
ajpdis-1851	211	16	muradiljon	muradiljon	NOUN
ajpdis-1851	211	17	,	,	PUNCT
ajpdis-1851	211	18	khalilov	khalilov	PROPN
ajpdis-1851	211	19	;	;	PUNCT
ajpdis-1851	211	20	mashxuraxon	mashxuraxon	PROPN
ajpdis-1851	211	21	,	,	PUNCT
ajpdis-1851	211	22	sayidjonova	sayidjonova	PROPN
ajpdis-1851	211	23	.	.	PUNCT
ajpdis-1851	211	24	(	(	PUNCT
ajpdis-1851	211	25	2023	2023	NUM
ajpdis-1851	211	26	)	)	PUNCT
ajpdis-1851	211	27	.	.	PUNCT
ajpdis-1851	212	1	application	application	NOUN
ajpdis-1851	212	2	of	of	ADP
ajpdis-1851	212	3	the	the	DET
ajpdis-1851	212	4	theory	theory	NOUN
ajpdis-1851	212	5	of	of	ADP
ajpdis-1851	212	6	linear	linear	PROPN
ajpdis-1851	212	7	differential	differential	ADJ
ajpdis-1851	212	8	equations	equation	NOUN
ajpdis-1851	212	9	to	to	ADP
ajpdis-1851	212	10	the	the	DET
ajpdis-1851	212	11	study	study	NOUN
ajpdis-1851	212	12	of	of	ADP
ajpdis-1851	212	13	some	some	DET
ajpdis-1851	212	14	oscillations	oscillation	NOUN
ajpdis-1851	212	15	.	.	PUNCT
ajpdis-1851	213	1	web	web	NOUN
ajpdis-1851	213	2	of	of	ADP
ajpdis-1851	213	3	synergy	synergy	NOUN
ajpdis-1851	213	4	:	:	PUNCT
ajpdis-1851	213	5	international	international	ADJ
ajpdis-1851	213	6	interdisciplinary	interdisciplinary	ADJ
ajpdis-1851	213	7	research	research	NOUN
ajpdis-1851	213	8	journal	journal	NOUN
ajpdis-1851	213	9	.	.	PUNCT
ajpdis-1851	214	1	60	60	NUM
ajpdis-1851	214	2	-	-	SYM
ajpdis-1851	214	3	65	65	NUM
ajpdis-1851	214	4	.	.	PUNCT