id	sid	tid	token	lemma	pos
ajset-590	1	1	academic	academic	ADJ
ajset-590	1	2	journal	journal	NOUN
ajset-590	1	3	of	of	ADP
ajset-590	1	4	science	science	NOUN
ajset-590	1	5	,	,	PUNCT
ajset-590	1	6	engineering	engineering	NOUN
ajset-590	1	7	and	and	CCONJ
ajset-590	1	8	technology	technology	NOUN
ajset-590	1	9	vol.8	vol.8	PROPN
ajset-590	1	10	,	,	PUNCT
ajset-590	1	11	issue	issue	NOUN
ajset-590	1	12	5	5	NUM
ajset-590	1	13	;	;	PUNCT
ajset-590	1	14	september	september	PROPN
ajset-590	1	15	october	october	PROPN
ajset-590	1	16	2023	2023	NUM
ajset-590	1	17	;	;	PUNCT
ajset-590	1	18	issn	issn	PROPN
ajset-590	1	19	:	:	PUNCT
ajset-590	1	20	2837	2837	NUM
ajset-590	1	21	-	-	SYM
ajset-590	1	22	2964	2964	NUM
ajset-590	1	23	impact	impact	NOUN
ajset-590	1	24	factor	factor	NOUN
ajset-590	1	25	:	:	PUNCT
ajset-590	1	26	6.67	6.67	NUM
ajset-590	1	27	1252	1252	NUM
ajset-590	1	28	columbia	columbia	PROPN
ajset-590	1	29	rd	rd	PROPN
ajset-590	1	30	nw	nw	PROPN
ajset-590	1	31	,	,	PUNCT
ajset-590	1	32	washington	washington	PROPN
ajset-590	1	33	dc	dc	PROPN
ajset-590	1	34	,	,	PUNCT
ajset-590	1	35	united	united	PROPN
ajset-590	1	36	states	states	PROPN
ajset-590	1	37	https://topjournals.org/index.php/ajset/index	https://topjournals.org/index.php/ajset/index	PROPN
ajset-590	1	38	;	;	PUNCT
ajset-590	1	39	mail	mail	NOUN
ajset-590	1	40	:	:	PUNCT
ajset-590	2	1	topacademicjournals@gmail.com	topacademicjournals@gmail.com	X
ajset-590	2	2	9	9	NUM
ajset-590	3	1	|	|	ADV
ajset-590	3	2	a	a	DET
ajset-590	3	3	c	c	NOUN
ajset-590	3	4	a	a	PRON
ajset-590	3	5	d	d	X
ajset-590	3	6	e	e	NOUN
ajset-590	3	7	m	m	NOUN
ajset-590	3	8	i	i	NOUN
ajset-590	3	9	c	c	NOUN
ajset-590	3	10	j	j	NOUN
ajset-590	3	11	o	o	X
ajset-590	3	12	u	u	NOUN
ajset-590	3	13	r	r	NOUN
ajset-590	3	14	n	n	NOUN
ajset-590	3	15	a	a	DET
ajset-590	3	16	l	l	NOUN
ajset-590	4	1	o	o	X
ajset-590	4	2	f	f	X
ajset-590	4	3	s	s	X
ajset-590	4	4	c	c	NOUN
ajset-590	5	1	i	i	NOUN
ajset-590	5	2	e	e	PROPN
ajset-590	5	3	n	n	PROPN
ajset-590	5	4	c	c	NOUN
ajset-590	5	5	e	e	X
ajset-590	5	6	,	,	PUNCT
ajset-590	5	7	e	e	PROPN
ajset-590	5	8	n	n	PRON
ajset-590	5	9	g	g	NOUN
ajset-590	5	10	i	i	PRON
ajset-590	5	11	n	n	VERB
ajset-590	5	12	e	e	NOUN
ajset-590	5	13	e	e	NOUN
ajset-590	5	14	r	r	VERB
ajset-590	5	15	i	i	PRON
ajset-590	5	16	n	n	CCONJ
ajset-590	5	17	g	g	PROPN
ajset-590	5	18	a	a	DET
ajset-590	5	19	n	n	NOUN
ajset-590	5	20	d	d	NOUN
ajset-590	5	21	t	t	NOUN
ajset-590	5	22	e	e	X
ajset-590	5	23	c	c	NOUN
ajset-590	5	24	h	h	NOUN
ajset-590	5	25	n	n	ADV
ajset-590	5	26	o	o	NOUN
ajset-590	5	27	l	l	NOUN
ajset-590	6	1	o	o	X
ajset-590	6	2	g	g	NOUN
ajset-590	6	3	y	y	PROPN
ajset-590	6	4	|	|	ADV
ajset-590	6	5	https://topjournals.org/index.php/ajset	https://topjournals.org/index.php/ajset	VERB
ajset-590	6	6	a	a	DET
ajset-590	6	7	critical	critical	ADJ
ajset-590	6	8	examination	examination	NOUN
ajset-590	6	9	of	of	ADP
ajset-590	6	10	vector	vector	NOUN
ajset-590	6	11	calculus	calculus	NOUN
ajset-590	6	12	:	:	PUNCT
ajset-590	6	13	a	a	DET
ajset-590	6	14	logical	logical	ADJ
ajset-590	6	15	approach	approach	NOUN
ajset-590	6	16	akmal	akmal	PROPN
ajset-590	6	17	khurshidov	khurshidov	PROPN
ajset-590	6	18	home	home	ADV
ajset-590	6	19	of	of	ADP
ajset-590	6	20	physical	physical	ADJ
ajset-590	6	21	problems	problem	NOUN
ajset-590	6	22	,	,	PUNCT
ajset-590	6	23	pisatelskaya	pisatelskaya	PROPN
ajset-590	6	24	tashkent	tashkent	PROPN
ajset-590	6	25	,	,	PUNCT
ajset-590	6	26	uzbekistan	uzbekistan	PROPN
ajset-590	6	27	abstract	abstract	NOUN
ajset-590	6	28	:	:	PUNCT
ajset-590	6	29	this	this	DET
ajset-590	6	30	study	study	NOUN
ajset-590	6	31	addresses	address	VERB
ajset-590	6	32	the	the	DET
ajset-590	6	33	foundational	foundational	ADJ
ajset-590	6	34	aspects	aspect	NOUN
ajset-590	6	35	of	of	ADP
ajset-590	6	36	vector	vector	NOUN
ajset-590	6	37	calculus	calculus	NOUN
ajset-590	6	38	,	,	PUNCT
ajset-590	6	39	acknowledging	acknowledge	VERB
ajset-590	6	40	its	its	PRON
ajset-590	6	41	widespread	widespread	ADJ
ajset-590	6	42	use	use	NOUN
ajset-590	6	43	in	in	ADP
ajset-590	6	44	the	the	DET
ajset-590	6	45	natural	natural	ADJ
ajset-590	6	46	sciences	science	NOUN
ajset-590	6	47	.	.	PUNCT
ajset-590	7	1	while	while	SCONJ
ajset-590	7	2	vector	vector	NOUN
ajset-590	7	3	calculus	calculus	NOUN
ajset-590	7	4	has	have	AUX
ajset-590	7	5	proven	prove	VERB
ajset-590	7	6	highly	highly	ADV
ajset-590	7	7	effective	effective	ADJ
ajset-590	7	8	in	in	ADP
ajset-590	7	9	various	various	ADJ
ajset-590	7	10	scientific	scientific	ADJ
ajset-590	7	11	applications	application	NOUN
ajset-590	7	12	,	,	PUNCT
ajset-590	7	13	its	its	PRON
ajset-590	7	14	validity	validity	NOUN
ajset-590	7	15	and	and	CCONJ
ajset-590	7	16	foundational	foundational	ADJ
ajset-590	7	17	underpinnings	underpinning	NOUN
ajset-590	7	18	warrant	warrant	VERB
ajset-590	7	19	formal	formal	ADJ
ajset-590	7	20	-	-	PUNCT
ajset-590	7	21	logical	logical	ADJ
ajset-590	7	22	scrutiny	scrutiny	NOUN
ajset-590	7	23	.	.	PUNCT
ajset-590	8	1	the	the	DET
ajset-590	8	2	absence	absence	NOUN
ajset-590	8	3	of	of	ADP
ajset-590	8	4	a	a	DET
ajset-590	8	5	comprehensive	comprehensive	ADJ
ajset-590	8	6	formal	formal	ADJ
ajset-590	8	7	-	-	PUNCT
ajset-590	8	8	logical	logical	ADJ
ajset-590	8	9	basis	basis	NOUN
ajset-590	8	10	challenges	challenge	VERB
ajset-590	8	11	the	the	DET
ajset-590	8	12	assertion	assertion	NOUN
ajset-590	8	13	of	of	ADP
ajset-590	8	14	vector	vector	NOUN
ajset-590	8	15	calculus	calculus	NOUN
ajset-590	8	16	as	as	ADP
ajset-590	8	17	absolute	absolute	ADJ
ajset-590	8	18	truth	truth	NOUN
ajset-590	8	19	.	.	PUNCT
ajset-590	9	1	this	this	DET
ajset-590	9	2	paper	paper	NOUN
ajset-590	9	3	endeavors	endeavor	NOUN
ajset-590	9	4	to	to	PART
ajset-590	9	5	fill	fill	VERB
ajset-590	9	6	this	this	DET
ajset-590	9	7	gap	gap	NOUN
ajset-590	9	8	by	by	ADP
ajset-590	9	9	conducting	conduct	VERB
ajset-590	9	10	a	a	DET
ajset-590	9	11	critical	critical	ADJ
ajset-590	9	12	analysis	analysis	NOUN
ajset-590	9	13	of	of	ADP
ajset-590	9	14	vector	vector	NOUN
ajset-590	9	15	calculus	calculus	NOUN
ajset-590	9	16	,	,	PUNCT
ajset-590	9	17	employing	employ	VERB
ajset-590	9	18	the	the	DET
ajset-590	9	19	unity	unity	NOUN
ajset-590	9	20	of	of	ADP
ajset-590	9	21	formal	formal	ADJ
ajset-590	9	22	logic	logic	NOUN
ajset-590	9	23	and	and	CCONJ
ajset-590	9	24	rational	rational	ADJ
ajset-590	9	25	dialectics	dialectic	NOUN
ajset-590	9	26	as	as	ADP
ajset-590	9	27	the	the	DET
ajset-590	9	28	methodological	methodological	ADJ
ajset-590	9	29	framework	framework	NOUN
ajset-590	9	30	.	.	PUNCT
ajset-590	10	1	by	by	ADP
ajset-590	10	2	subjecting	subject	VERB
ajset-590	10	3	vector	vector	NOUN
ajset-590	10	4	calculus	calculus	NOUN
ajset-590	10	5	to	to	ADP
ajset-590	10	6	this	this	DET
ajset-590	10	7	rigorous	rigorous	ADJ
ajset-590	10	8	analysis	analysis	NOUN
ajset-590	10	9	,	,	PUNCT
ajset-590	10	10	we	we	PRON
ajset-590	10	11	aim	aim	VERB
ajset-590	10	12	to	to	PART
ajset-590	10	13	establish	establish	VERB
ajset-590	10	14	a	a	DET
ajset-590	10	15	solid	solid	ADJ
ajset-590	10	16	foundation	foundation	NOUN
ajset-590	10	17	for	for	ADP
ajset-590	10	18	this	this	DET
ajset-590	10	19	mathematical	mathematical	ADJ
ajset-590	10	20	formalism	formalism	NOUN
ajset-590	10	21	.	.	PUNCT
ajset-590	11	1	keywords	keyword	NOUN
ajset-590	11	2	:	:	PUNCT
ajset-590	11	3	vector	vector	NOUN
ajset-590	11	4	calculus	calculus	NOUN
ajset-590	11	5	,	,	PUNCT
ajset-590	11	6	formal	formal	ADJ
ajset-590	11	7	logic	logic	NOUN
ajset-590	11	8	,	,	PUNCT
ajset-590	11	9	rational	rational	ADJ
ajset-590	11	10	dialectics	dialectic	NOUN
ajset-590	11	11	,	,	PUNCT
ajset-590	11	12	foundational	foundational	ADJ
ajset-590	11	13	analysis	analysis	NOUN
ajset-590	11	14	,	,	PUNCT
ajset-590	11	15	mathematical	mathematical	ADJ
ajset-590	11	16	formalism	formalism	NOUN
ajset-590	11	17	.	.	PUNCT
ajset-590	12	1	introduction	introduction	NOUN
ajset-590	12	2	as	as	SCONJ
ajset-590	12	3	is	be	AUX
ajset-590	12	4	well	well	ADV
ajset-590	12	5	known	know	VERB
ajset-590	12	6	,	,	PUNCT
ajset-590	12	7	the	the	DET
ajset-590	12	8	mathematical	mathematical	ADJ
ajset-590	12	9	formalism	formalism	NOUN
ajset-590	12	10	of	of	ADP
ajset-590	12	11	vector	vector	NOUN
ajset-590	12	12	calculus	calculus	NOUN
ajset-590	12	13	is	be	AUX
ajset-590	12	14	widely	widely	ADV
ajset-590	12	15	and	and	CCONJ
ajset-590	12	16	successfully	successfully	ADV
ajset-590	12	17	used	use	VERB
ajset-590	12	18	in	in	ADP
ajset-590	12	19	natural	natural	ADJ
ajset-590	12	20	sciences	science	NOUN
ajset-590	13	1	[	[	X
ajset-590	13	2	1	1	NUM
ajset-590	13	3	-	-	SYM
ajset-590	13	4	7	7	NUM
ajset-590	13	5	]	]	PUNCT
ajset-590	13	6	.	.	PUNCT
ajset-590	14	1	however	however	ADV
ajset-590	14	2	,	,	PUNCT
ajset-590	14	3	this	this	PRON
ajset-590	14	4	does	do	AUX
ajset-590	14	5	not	not	PART
ajset-590	14	6	mean	mean	VERB
ajset-590	14	7	that	that	SCONJ
ajset-590	14	8	the	the	DET
ajset-590	14	9	problem	problem	NOUN
ajset-590	14	10	of	of	ADP
ajset-590	14	11	validity	validity	NOUN
ajset-590	14	12	of	of	ADP
ajset-590	14	13	vector	vector	NOUN
ajset-590	14	14	calculus	calculus	NOUN
ajset-590	14	15	is	be	AUX
ajset-590	14	16	now	now	ADV
ajset-590	14	17	completely	completely	ADV
ajset-590	14	18	solved	solve	VERB
ajset-590	14	19	,	,	PUNCT
ajset-590	14	20	or	or	CCONJ
ajset-590	14	21	that	that	SCONJ
ajset-590	14	22	the	the	DET
ajset-590	14	23	foundations	foundation	NOUN
ajset-590	14	24	of	of	ADP
ajset-590	14	25	vector	vector	NOUN
ajset-590	14	26	calculus	calculus	NOUN
ajset-590	14	27	are	be	AUX
ajset-590	14	28	not	not	PART
ajset-590	14	29	in	in	ADP
ajset-590	14	30	need	need	NOUN
ajset-590	14	31	of	of	ADP
ajset-590	14	32	formal	formal	ADJ
ajset-590	14	33	-	-	PUNCT
ajset-590	14	34	logical	logical	ADJ
ajset-590	14	35	analysis	analysis	NOUN
ajset-590	14	36	.	.	PUNCT
ajset-590	15	1	in	in	ADP
ajset-590	15	2	my	my	PRON
ajset-590	15	3	view	view	NOUN
ajset-590	15	4	,	,	PUNCT
ajset-590	15	5	standard	standard	ADJ
ajset-590	15	6	vector	vector	NOUN
ajset-590	15	7	calculus	calculus	NOUN
ajset-590	15	8	can	can	AUX
ajset-590	15	9	not	not	PART
ajset-590	15	10	be	be	AUX
ajset-590	15	11	considered	consider	VERB
ajset-590	15	12	as	as	ADP
ajset-590	15	13	absolute	absolute	ADJ
ajset-590	15	14	truth	truth	NOUN
ajset-590	15	15	if	if	SCONJ
ajset-590	15	16	there	there	PRON
ajset-590	15	17	is	be	VERB
ajset-590	15	18	no	no	DET
ajset-590	15	19	formal	formal	ADJ
ajset-590	15	20	-	-	PUNCT
ajset-590	15	21	logical	logical	ADJ
ajset-590	15	22	substantiation	substantiation	NOUN
ajset-590	15	23	of	of	ADP
ajset-590	15	24	this	this	DET
ajset-590	15	25	calculus	calculus	NOUN
ajset-590	15	26	.	.	PUNCT
ajset-590	16	1	recently	recently	ADV
ajset-590	16	2	,	,	PUNCT
ajset-590	16	3	there	there	PRON
ajset-590	16	4	has	have	AUX
ajset-590	16	5	arisen	arise	VERB
ajset-590	16	6	a	a	DET
ajset-590	16	7	necessity	necessity	NOUN
ajset-590	16	8	for	for	ADP
ajset-590	16	9	critical	critical	ADJ
ajset-590	16	10	analysis	analysis	NOUN
ajset-590	16	11	of	of	ADP
ajset-590	16	12	the	the	DET
ajset-590	16	13	foundations	foundation	NOUN
ajset-590	16	14	of	of	ADP
ajset-590	16	15	vector	vector	NOUN
ajset-590	16	16	calculus	calculus	NOUN
ajset-590	16	17	.	.	PUNCT
ajset-590	17	1	but	but	CCONJ
ajset-590	17	2	there	there	PRON
ajset-590	17	3	are	be	VERB
ajset-590	17	4	no	no	DET
ajset-590	17	5	works	work	NOUN
ajset-590	17	6	devoted	devote	VERB
ajset-590	17	7	the	the	DET
ajset-590	17	8	analysis	analysis	NOUN
ajset-590	17	9	of	of	ADP
ajset-590	17	10	vector	vector	NOUN
ajset-590	17	11	calculus	calculus	NOUN
ajset-590	17	12	within	within	ADP
ajset-590	17	13	the	the	DET
ajset-590	17	14	framework	framework	NOUN
ajset-590	17	15	of	of	ADP
ajset-590	17	16	the	the	DET
ajset-590	17	17	unity	unity	NOUN
ajset-590	17	18	of	of	ADP
ajset-590	17	19	formal	formal	ADJ
ajset-590	17	20	logic	logic	NOUN
ajset-590	17	21	and	and	CCONJ
ajset-590	17	22	of	of	ADP
ajset-590	17	23	rational	rational	ADJ
ajset-590	17	24	dialectics	dialectic	NOUN
ajset-590	17	25	.	.	PUNCT
ajset-590	18	1	the	the	DET
ajset-590	18	2	purpose	purpose	NOUN
ajset-590	18	3	of	of	ADP
ajset-590	18	4	the	the	DET
ajset-590	18	5	present	present	ADJ
ajset-590	18	6	work	work	NOUN
ajset-590	18	7	is	be	AUX
ajset-590	18	8	to	to	PART
ajset-590	18	9	propose	propose	VERB
ajset-590	18	10	the	the	DET
ajset-590	18	11	correct	correct	ADJ
ajset-590	18	12	analysis	analysis	NOUN
ajset-590	18	13	of	of	ADP
ajset-590	18	14	the	the	DET
ajset-590	18	15	foundations	foundation	NOUN
ajset-590	18	16	of	of	ADP
ajset-590	18	17	vector	vector	NOUN
ajset-590	18	18	calculus	calculus	NOUN
ajset-590	18	19	.	.	PUNCT
ajset-590	19	1	the	the	DET
ajset-590	19	2	analysis	analysis	NOUN
ajset-590	19	3	is	be	AUX
ajset-590	19	4	carried	carry	VERB
ajset-590	19	5	out	out	ADP
ajset-590	19	6	within	within	ADP
ajset-590	19	7	the	the	DET
ajset-590	19	8	framework	framework	NOUN
ajset-590	19	9	of	of	ADP
ajset-590	19	10	the	the	DET
ajset-590	19	11	correct	correct	ADJ
ajset-590	19	12	methodological	methodological	ADJ
ajset-590	19	13	basis	basis	NOUN
ajset-590	19	14	:	:	PUNCT
ajset-590	19	15	the	the	DET
ajset-590	19	16	unity	unity	NOUN
ajset-590	19	17	of	of	ADP
ajset-590	19	18	formal	formal	ADJ
ajset-590	19	19	logic	logic	NOUN
ajset-590	19	20	and	and	CCONJ
ajset-590	19	21	of	of	ADP
ajset-590	19	22	rational	rational	ADJ
ajset-590	19	23	dialectics	dialectic	NOUN
ajset-590	19	24	.	.	PUNCT
ajset-590	20	1	1	1	X
ajset-590	20	2	.	.	X
ajset-590	20	3	analysis	analysis	NOUN
ajset-590	20	4	of	of	ADP
ajset-590	20	5	the	the	DET
ajset-590	20	6	concepts	concept	NOUN
ajset-590	20	7	of	of	ADP
ajset-590	20	8	“	"	PUNCT
ajset-590	20	9	direction	direction	NOUN
ajset-590	20	10	”	"	PUNCT
ajset-590	20	11	and	and	CCONJ
ajset-590	20	12	“	"	PUNCT
ajset-590	20	13	vector	vector	NOUN
ajset-590	20	14	"	"	PUNCT
ajset-590	20	15	as	as	SCONJ
ajset-590	20	16	is	be	AUX
ajset-590	20	17	well	well	ADV
ajset-590	20	18	known	know	VERB
ajset-590	20	19	,	,	PUNCT
ajset-590	20	20	in	in	ADP
ajset-590	20	21	mathematics	mathematic	NOUN
ajset-590	20	22	,	,	PUNCT
ajset-590	20	23	physics	physics	NOUN
ajset-590	20	24	,	,	PUNCT
ajset-590	20	25	and	and	CCONJ
ajset-590	20	26	engineering	engineering	NOUN
ajset-590	20	27	,	,	PUNCT
ajset-590	20	28	a	a	DET
ajset-590	20	29	vector	vector	NOUN
ajset-590	20	30	(	(	PUNCT
ajset-590	20	31	or	or	CCONJ
ajset-590	20	32	euclidean	euclidean	ADJ
ajset-590	20	33	vector	vector	NOUN
ajset-590	20	34	,	,	PUNCT
ajset-590	20	35	or	or	CCONJ
ajset-590	20	36	geometric	geometric	ADJ
ajset-590	20	37	vector	vector	NOUN
ajset-590	20	38	,	,	PUNCT
ajset-590	20	39	or	or	CCONJ
ajset-590	20	40	spatial	spatial	ADJ
ajset-590	20	41	vector	vector	NOUN
ajset-590	20	42	)	)	PUNCT
ajset-590	20	43	is	be	AUX
ajset-590	20	44	called	call	VERB
ajset-590	20	45	quantitative	quantitative	ADJ
ajset-590	20	46	characteristics	characteristic	NOUN
ajset-590	20	47	which	which	PRON
ajset-590	20	48	has	have	VERB
ajset-590	20	49	not	not	PART
ajset-590	20	50	only	only	ADV
ajset-590	20	51	a	a	DET
ajset-590	20	52	numerical	numerical	ADJ
ajset-590	20	53	value	value	NOUN
ajset-590	20	54	,	,	PUNCT
ajset-590	20	55	but	but	CCONJ
ajset-590	20	56	also	also	ADV
ajset-590	20	57	the	the	DET
ajset-590	20	58	direction	direction	NOUN
ajset-590	20	59	[	[	X
ajset-590	20	60	7	7	NUM
ajset-590	20	61	,	,	PUNCT
ajset-590	20	62	8	8	NUM
ajset-590	20	63	]	]	PUNCT
ajset-590	20	64	.	.	PUNCT
ajset-590	21	1	in	in	ADP
ajset-590	21	2	other	other	ADJ
ajset-590	21	3	words	word	NOUN
ajset-590	21	4	,	,	PUNCT
ajset-590	21	5	vector	vector	NOUN
ajset-590	21	6	is	be	AUX
ajset-590	21	7	a	a	DET
ajset-590	21	8	line	line	NOUN
ajset-590	21	9	segment	segment	NOUN
ajset-590	21	10	with	with	ADP
ajset-590	21	11	a	a	DET
ajset-590	21	12	definite	definite	ADJ
ajset-590	21	13	direction	direction	NOUN
ajset-590	21	14	(	(	PUNCT
ajset-590	21	15	or	or	CCONJ
ajset-590	21	16	graphically	graphically	ADV
ajset-590	21	17	is	be	AUX
ajset-590	21	18	an	an	DET
ajset-590	21	19	arrow	arrow	NOUN
ajset-590	21	20	)	)	PUNCT
ajset-590	21	21	,	,	PUNCT
ajset-590	21	22	connecting	connect	VERB
ajset-590	21	23	an	an	DET
ajset-590	21	24	initial	initial	ADJ
ajset-590	21	25	point	point	NOUN
ajset-590	21	26	with	with	ADP
ajset-590	21	27	a	a	DET
ajset-590	21	28	terminal	terminal	ADJ
ajset-590	21	29	point	point	NOUN
ajset-590	21	30	.	.	PUNCT
ajset-590	22	1	i.e.	i.e.	X
ajset-590	22	2	,	,	PUNCT
ajset-590	22	3	vector	vector	NOUN
ajset-590	22	4	is	be	AUX
ajset-590	22	5	a	a	DET
ajset-590	22	6	geometric	geometric	ADJ
ajset-590	22	7	object	object	NOUN
ajset-590	22	8	that	that	PRON
ajset-590	22	9	has	have	VERB
ajset-590	22	10	magnitude	magnitude	NOUN
ajset-590	22	11	(	(	PUNCT
ajset-590	22	12	or	or	CCONJ
ajset-590	22	13	length	length	NOUN
ajset-590	22	14	)	)	PUNCT
ajset-590	22	15	and	and	CCONJ
ajset-590	22	16	direction	direction	NOUN
ajset-590	22	17	and	and	CCONJ
ajset-590	22	18	can	can	AUX
ajset-590	22	19	be	be	AUX
ajset-590	22	20	added	add	VERB
ajset-590	22	21	to	to	ADP
ajset-590	22	22	other	other	ADJ
ajset-590	22	23	vectors	vector	NOUN
ajset-590	22	24	according	accord	VERB
ajset-590	22	25	to	to	ADP
ajset-590	22	26	vector	vector	NOUN
ajset-590	22	27	algebra	algebra	NOUN
ajset-590	22	28	.	.	PUNCT
ajset-590	23	1	physical	physical	ADJ
ajset-590	23	2	examples	example	NOUN
ajset-590	23	3	of	of	ADP
ajset-590	23	4	vector	vector	NOUN
ajset-590	23	5	quantities	quantity	NOUN
ajset-590	23	6	are	be	AUX
ajset-590	23	7	material	material	NOUN
ajset-590	23	8	point	point	NOUN
ajset-590	23	9	displacement	displacement	NOUN
ajset-590	23	10	,	,	PUNCT
ajset-590	23	11	velocity	velocity	NOUN
ajset-590	23	12	and	and	CCONJ
ajset-590	23	13	acceleration	acceleration	NOUN
ajset-590	23	14	of	of	ADP
ajset-590	23	15	a	a	DET
ajset-590	23	16	material	material	NOUN
ajset-590	23	17	point	point	NOUN
ajset-590	23	18	,	,	PUNCT
ajset-590	23	19	as	as	ADV
ajset-590	23	20	well	well	ADV
ajset-590	23	21	as	as	ADP
ajset-590	23	22	a	a	DET
ajset-590	23	23	force	force	NOUN
ajset-590	23	24	.	.	PUNCT
ajset-590	24	1	therefore	therefore	ADV
ajset-590	24	2	,	,	PUNCT
ajset-590	24	3	analysis	analysis	NOUN
ajset-590	24	4	of	of	ADP
ajset-590	24	5	the	the	DET
ajset-590	24	6	concept	concept	NOUN
ajset-590	24	7	of	of	ADP
ajset-590	24	8	“	"	PUNCT
ajset-590	24	9	vector	vector	NOUN
ajset-590	24	10	”	"	PUNCT
ajset-590	24	11	is	be	AUX
ajset-590	24	12	not	not	PART
ajset-590	24	13	possible	possible	ADJ
ajset-590	24	14	without	without	ADP
ajset-590	24	15	the	the	DET
ajset-590	24	16	definitions	definition	NOUN
ajset-590	24	17	of	of	ADP
ajset-590	24	18	concepts	concept	NOUN
ajset-590	24	19	of	of	ADP
ajset-590	24	20	“	"	PUNCT
ajset-590	24	21	movement	movement	NOUN
ajset-590	24	22	”	"	PUNCT
ajset-590	24	23	and	and	CCONJ
ajset-590	24	24	“	"	PUNCT
ajset-590	24	25	direction	direction	NOUN
ajset-590	24	26	”	"	PUNCT
ajset-590	24	27	.	.	PUNCT
ajset-590	25	1	1	1	X
ajset-590	25	2	.	.	X
ajset-590	25	3	movement	movement	NOUN
ajset-590	25	4	is	be	AUX
ajset-590	25	5	a	a	DET
ajset-590	25	6	change	change	NOUN
ajset-590	25	7	in	in	ADP
ajset-590	25	8	general	general	ADJ
ajset-590	25	9	,	,	PUNCT
ajset-590	25	10	any	any	DET
ajset-590	25	11	interaction	interaction	NOUN
ajset-590	25	12	of	of	ADP
ajset-590	25	13	material	material	ADJ
ajset-590	25	14	objects	object	NOUN
ajset-590	25	15	.	.	PUNCT
ajset-590	26	1	category	category	NOUN
ajset-590	26	2	of	of	ADP
ajset-590	26	3	mailto:topacademicjournals@gmail.com	mailto:topacademicjournals@gmail.com	PROPN
ajset-590	26	4	academic	academic	ADJ
ajset-590	26	5	journal	journal	NOUN
ajset-590	26	6	of	of	ADP
ajset-590	26	7	science	science	NOUN
ajset-590	26	8	,	,	PUNCT
ajset-590	26	9	engineering	engineering	NOUN
ajset-590	26	10	and	and	CCONJ
ajset-590	26	11	technology	technology	NOUN
ajset-590	26	12	vol.8	vol.8	PROPN
ajset-590	26	13	,	,	PUNCT
ajset-590	26	14	issue	issue	NOUN
ajset-590	26	15	5	5	NUM
ajset-590	26	16	;	;	PUNCT
ajset-590	26	17	september	september	PROPN
ajset-590	26	18	october	october	PROPN
ajset-590	26	19	2023	2023	NUM
ajset-590	26	20	;	;	PUNCT
ajset-590	26	21	issn	issn	PROPN
ajset-590	26	22	:	:	PUNCT
ajset-590	26	23	2837	2837	NUM
ajset-590	26	24	-	-	SYM
ajset-590	26	25	2964	2964	NUM
ajset-590	26	26	impact	impact	NOUN
ajset-590	26	27	factor	factor	NOUN
ajset-590	26	28	:	:	PUNCT
ajset-590	26	29	6.67	6.67	NUM
ajset-590	26	30	1252	1252	NUM
ajset-590	26	31	columbia	columbia	PROPN
ajset-590	26	32	rd	rd	PROPN
ajset-590	26	33	nw	nw	PROPN
ajset-590	26	34	,	,	PUNCT
ajset-590	26	35	washington	washington	PROPN
ajset-590	26	36	dc	dc	PROPN
ajset-590	26	37	,	,	PUNCT
ajset-590	26	38	united	united	PROPN
ajset-590	26	39	states	states	PROPN
ajset-590	26	40	https://topjournals.org/index.php/ajset/index	https://topjournals.org/index.php/ajset/index	PROPN
ajset-590	26	41	;	;	PUNCT
ajset-590	26	42	mail	mail	NOUN
ajset-590	26	43	:	:	PUNCT
ajset-590	27	1	topacademicjournals@gmail.com	topacademicjournals@gmail.com	X
ajset-590	28	1	10	10	NUM
ajset-590	28	2	|	|	ADV
ajset-590	28	3	a	a	DET
ajset-590	28	4	c	c	NOUN
ajset-590	28	5	a	a	PRON
ajset-590	28	6	d	d	X
ajset-590	28	7	e	e	NOUN
ajset-590	28	8	m	m	NOUN
ajset-590	28	9	i	i	NOUN
ajset-590	28	10	c	c	NOUN
ajset-590	28	11	j	j	NOUN
ajset-590	28	12	o	o	X
ajset-590	28	13	u	u	NOUN
ajset-590	28	14	r	r	NOUN
ajset-590	28	15	n	n	NOUN
ajset-590	28	16	a	a	DET
ajset-590	28	17	l	l	NOUN
ajset-590	29	1	o	o	X
ajset-590	29	2	f	f	X
ajset-590	29	3	s	s	X
ajset-590	29	4	c	c	NOUN
ajset-590	30	1	i	i	NOUN
ajset-590	30	2	e	e	PROPN
ajset-590	30	3	n	n	PROPN
ajset-590	30	4	c	c	NOUN
ajset-590	30	5	e	e	X
ajset-590	30	6	,	,	PUNCT
ajset-590	30	7	e	e	PROPN
ajset-590	30	8	n	n	PRON
ajset-590	30	9	g	g	NOUN
ajset-590	30	10	i	i	PRON
ajset-590	30	11	n	n	VERB
ajset-590	30	12	e	e	NOUN
ajset-590	30	13	e	e	NOUN
ajset-590	30	14	r	r	VERB
ajset-590	30	15	i	i	PRON
ajset-590	30	16	n	n	CCONJ
ajset-590	30	17	g	g	PROPN
ajset-590	30	18	a	a	DET
ajset-590	30	19	n	n	NOUN
ajset-590	30	20	d	d	NOUN
ajset-590	30	21	t	t	NOUN
ajset-590	30	22	e	e	X
ajset-590	30	23	c	c	NOUN
ajset-590	30	24	h	h	NOUN
ajset-590	30	25	n	n	ADV
ajset-590	30	26	o	o	NOUN
ajset-590	30	27	l	l	NOUN
ajset-590	31	1	o	o	X
ajset-590	31	2	g	g	NOUN
ajset-590	31	3	y	y	PROPN
ajset-590	31	4	|	|	ADV
ajset-590	31	5	https://topjournals.org/index.php/ajset	https://topjournals.org/index.php/ajset	VERB
ajset-590	31	6	“	"	PUNCT
ajset-590	31	7	movement	movement	NOUN
ajset-590	31	8	”	"	PUNCT
ajset-590	31	9	is	be	AUX
ajset-590	31	10	a	a	DET
ajset-590	31	11	scientific	scientific	ADJ
ajset-590	31	12	concept	concept	NOUN
ajset-590	31	13	that	that	PRON
ajset-590	31	14	reflects	reflect	VERB
ajset-590	31	15	the	the	DET
ajset-590	31	16	most	most	ADV
ajset-590	31	17	common	common	ADJ
ajset-590	31	18	and	and	CCONJ
ajset-590	31	19	essential	essential	ADJ
ajset-590	31	20	property	property	NOUN
ajset-590	31	21	of	of	ADP
ajset-590	31	22	phenomena	phenomenon	NOUN
ajset-590	31	23	(	(	PUNCT
ajset-590	31	24	processes	process	NOUN
ajset-590	31	25	)	)	PUNCT
ajset-590	31	26	,	,	PUNCT
ajset-590	31	27	the	the	DET
ajset-590	31	28	most	most	ADV
ajset-590	31	29	common	common	ADJ
ajset-590	31	30	and	and	CCONJ
ajset-590	31	31	essential	essential	ADJ
ajset-590	31	32	relations	relation	NOUN
ajset-590	31	33	and	and	CCONJ
ajset-590	31	34	connections	connection	NOUN
ajset-590	31	35	in	in	ADP
ajset-590	31	36	reality	reality	NOUN
ajset-590	31	37	.	.	PUNCT
ajset-590	32	1	movement	movement	NOUN
ajset-590	32	2	is	be	AUX
ajset-590	32	3	an	an	DET
ajset-590	32	4	attribute	attribute	NOUN
ajset-590	32	5	of	of	ADP
ajset-590	32	6	matter	matter	NOUN
ajset-590	32	7	.	.	PUNCT
ajset-590	33	1	in	in	ADP
ajset-590	33	2	accordance	accordance	NOUN
ajset-590	33	3	with	with	ADP
ajset-590	33	4	the	the	DET
ajset-590	33	5	dialectical	dialectical	ADJ
ajset-590	33	6	principle	principle	NOUN
ajset-590	33	7	of	of	ADP
ajset-590	33	8	the	the	DET
ajset-590	33	9	unity	unity	NOUN
ajset-590	33	10	of	of	ADP
ajset-590	33	11	matter	matter	NOUN
ajset-590	33	12	and	and	CCONJ
ajset-590	33	13	movement	movement	NOUN
ajset-590	33	14	,	,	PUNCT
ajset-590	33	15	the	the	DET
ajset-590	33	16	movement	movement	NOUN
ajset-590	33	17	does	do	AUX
ajset-590	33	18	not	not	PART
ajset-590	33	19	exist	exist	VERB
ajset-590	33	20	without	without	ADP
ajset-590	33	21	material	material	NOUN
ajset-590	33	22	objects	object	NOUN
ajset-590	33	23	.	.	PUNCT
ajset-590	34	1	but	but	CCONJ
ajset-590	34	2	the	the	DET
ajset-590	34	3	movement	movement	NOUN
ajset-590	34	4	is	be	AUX
ajset-590	34	5	not	not	PART
ajset-590	34	6	a	a	DET
ajset-590	34	7	material	material	ADJ
ajset-590	34	8	object	object	NOUN
ajset-590	34	9	.	.	PUNCT
ajset-590	35	1	the	the	DET
ajset-590	35	2	movement	movement	NOUN
ajset-590	35	3	is	be	AUX
ajset-590	35	4	manifested	manifest	VERB
ajset-590	35	5	as	as	ADP
ajset-590	35	6	the	the	DET
ajset-590	35	7	unity	unity	NOUN
ajset-590	35	8	of	of	ADP
ajset-590	35	9	opposites	opposite	NOUN
ajset-590	35	10	:	:	PUNCT
ajset-590	35	11	changeableness	changeableness	NOUN
ajset-590	35	12	and	and	CCONJ
ajset-590	35	13	stability	stability	NOUN
ajset-590	35	14	,	,	PUNCT
ajset-590	35	15	continuity	continuity	NOUN
ajset-590	35	16	and	and	CCONJ
ajset-590	35	17	discontinuity	discontinuity	NOUN
ajset-590	35	18	.	.	PUNCT
ajset-590	36	1	concretization	concretization	NOUN
ajset-590	36	2	of	of	ADP
ajset-590	36	3	the	the	DET
ajset-590	36	4	movement	movement	NOUN
ajset-590	36	5	is	be	AUX
ajset-590	36	6	the	the	DET
ajset-590	36	7	main	main	ADJ
ajset-590	36	8	forms	form	NOUN
ajset-590	36	9	of	of	ADP
ajset-590	36	10	movement	movement	NOUN
ajset-590	36	11	:	:	PUNCT
ajset-590	36	12	mechanical	mechanical	ADJ
ajset-590	36	13	,	,	PUNCT
ajset-590	36	14	physical	physical	ADJ
ajset-590	36	15	(	(	PUNCT
ajset-590	36	16	thermal	thermal	ADJ
ajset-590	36	17	,	,	PUNCT
ajset-590	36	18	electromagnetic	electromagnetic	ADJ
ajset-590	36	19	,	,	PUNCT
ajset-590	36	20	gravitational	gravitational	ADJ
ajset-590	36	21	,	,	PUNCT
ajset-590	36	22	atomic	atomic	ADJ
ajset-590	36	23	,	,	PUNCT
ajset-590	36	24	and	and	CCONJ
ajset-590	36	25	nuclear	nuclear	ADJ
ajset-590	36	26	)	)	PUNCT
ajset-590	36	27	,	,	PUNCT
ajset-590	36	28	chemical	chemical	NOUN
ajset-590	36	29	,	,	PUNCT
ajset-590	36	30	biological	biological	ADJ
ajset-590	36	31	,	,	PUNCT
ajset-590	36	32	informational	informational	ADJ
ajset-590	36	33	,	,	PUNCT
ajset-590	36	34	and	and	CCONJ
ajset-590	36	35	social	social	ADJ
ajset-590	36	36	ones	one	NOUN
ajset-590	36	37	.	.	PUNCT
ajset-590	37	1	2	2	X
ajset-590	37	2	.	.	X
ajset-590	37	3	change	change	NOUN
ajset-590	37	4	as	as	ADP
ajset-590	37	5	a	a	DET
ajset-590	37	6	process	process	NOUN
ajset-590	37	7	can	can	AUX
ajset-590	37	8	be	be	AUX
ajset-590	37	9	of	of	ADP
ajset-590	37	10	two	two	NUM
ajset-590	37	11	types	type	NOUN
ajset-590	37	12	:	:	PUNCT
ajset-590	37	13	a	a	DET
ajset-590	37	14	qualitative	qualitative	ADJ
ajset-590	37	15	change	change	NOUN
ajset-590	37	16	and	and	CCONJ
ajset-590	37	17	quantitative	quantitative	ADJ
ajset-590	37	18	change	change	NOUN
ajset-590	37	19	.	.	PUNCT
ajset-590	38	1	the	the	DET
ajset-590	38	2	qualitative	qualitative	ADJ
ajset-590	38	3	change	change	NOUN
ajset-590	38	4	(	(	PUNCT
ajset-590	38	5	i.e.	i.e.	X
ajset-590	38	6	a	a	DET
ajset-590	38	7	change	change	NOUN
ajset-590	38	8	of	of	ADP
ajset-590	38	9	qualitative	qualitative	ADJ
ajset-590	38	10	determinacy	determinacy	NOUN
ajset-590	38	11	)	)	PUNCT
ajset-590	38	12	is	be	AUX
ajset-590	38	13	studied	study	VERB
ajset-590	38	14	by	by	ADP
ajset-590	38	15	dialectical	dialectical	ADJ
ajset-590	38	16	logic	logic	NOUN
ajset-590	38	17	and	and	CCONJ
ajset-590	38	18	natural	natural	ADJ
ajset-590	38	19	sciences	science	NOUN
ajset-590	38	20	.	.	PUNCT
ajset-590	39	1	the	the	DET
ajset-590	39	2	quantitative	quantitative	ADJ
ajset-590	39	3	change	change	NOUN
ajset-590	39	4	(	(	PUNCT
ajset-590	39	5	i.e.	i.e.	X
ajset-590	39	6	a	a	DET
ajset-590	39	7	change	change	NOUN
ajset-590	39	8	of	of	ADP
ajset-590	39	9	quantitative	quantitative	ADJ
ajset-590	39	10	determinacy	determinacy	NOUN
ajset-590	39	11	)	)	PUNCT
ajset-590	39	12	within	within	ADP
ajset-590	39	13	the	the	DET
ajset-590	39	14	limits	limit	NOUN
ajset-590	39	15	of	of	ADP
ajset-590	39	16	certain	certain	ADJ
ajset-590	39	17	qualitative	qualitative	ADJ
ajset-590	39	18	determinacy	determinacy	NOUN
ajset-590	39	19	is	be	AUX
ajset-590	39	20	studied	study	VERB
ajset-590	39	21	by	by	ADP
ajset-590	39	22	formal	formal	ADJ
ajset-590	39	23	logic	logic	NOUN
ajset-590	39	24	and	and	CCONJ
ajset-590	39	25	mathematics	mathematic	NOUN
ajset-590	39	26	.	.	PUNCT
ajset-590	40	1	the	the	DET
ajset-590	40	2	quantitative	quantitative	ADJ
ajset-590	40	3	change	change	NOUN
ajset-590	40	4	can	can	AUX
ajset-590	40	5	be	be	AUX
ajset-590	40	6	studied	study	VERB
ajset-590	40	7	only	only	ADV
ajset-590	40	8	within	within	ADP
ajset-590	40	9	a	a	DET
ajset-590	40	10	reference	reference	NOUN
ajset-590	40	11	system	system	NOUN
ajset-590	40	12	which	which	PRON
ajset-590	40	13	contains	contain	VERB
ajset-590	40	14	a	a	DET
ajset-590	40	15	clock	clock	NOUN
ajset-590	40	16	as	as	ADP
ajset-590	40	17	component	component	NOUN
ajset-590	40	18	part	part	NOUN
ajset-590	40	19	.	.	PUNCT
ajset-590	41	1	3	3	X
ajset-590	41	2	.	.	X
ajset-590	41	3	a	a	DET
ajset-590	41	4	clock	clock	NOUN
ajset-590	41	5	(	(	PUNCT
ajset-590	41	6	i.e.	i.e.	X
ajset-590	41	7	,	,	PUNCT
ajset-590	41	8	a	a	DET
ajset-590	41	9	device	device	NOUN
ajset-590	41	10	containing	contain	VERB
ajset-590	41	11	a	a	DET
ajset-590	41	12	working	work	VERB
ajset-590	41	13	clock	clock	NOUN
ajset-590	41	14	mechanism	mechanism	NOUN
ajset-590	41	15	,	,	PUNCT
ajset-590	41	16	moving	move	VERB
ajset-590	41	17	the	the	DET
ajset-590	41	18	arrow	arrow	NOUN
ajset-590	41	19	and	and	CCONJ
ajset-590	41	20	the	the	DET
ajset-590	41	21	fixed	fix	VERB
ajset-590	41	22	dial	dial	NOUN
ajset-590	41	23	)	)	PUNCT
ajset-590	41	24	determines	determine	VERB
ajset-590	41	25	the	the	DET
ajset-590	41	26	time	time	NOUN
ajset-590	41	27	and	and	CCONJ
ajset-590	41	28	time	time	NOUN
ajset-590	41	29	characterizes	characterize	VERB
ajset-590	41	30	the	the	DET
ajset-590	41	31	clock	clock	NOUN
ajset-590	41	32	.	.	PUNCT
ajset-590	42	1	time	time	NOUN
ajset-590	42	2	is	be	AUX
ajset-590	42	3	a	a	DET
ajset-590	42	4	concrete	concrete	ADJ
ajset-590	42	5	concept	concept	NOUN
ajset-590	42	6	because	because	SCONJ
ajset-590	42	7	it	it	PRON
ajset-590	42	8	expresses	express	VERB
ajset-590	42	9	the	the	DET
ajset-590	42	10	property	property	NOUN
ajset-590	42	11	of	of	ADP
ajset-590	42	12	the	the	DET
ajset-590	42	13	clock	clock	NOUN
ajset-590	42	14	mechanism	mechanism	NOUN
ajset-590	42	15	(	(	PUNCT
ajset-590	42	16	clock	clock	NOUN
ajset-590	42	17	process	process	NOUN
ajset-590	42	18	)	)	PUNCT
ajset-590	42	19	.	.	PUNCT
ajset-590	43	1	time	time	NOUN
ajset-590	43	2	t	t	PROPN
ajset-590	43	3	is	be	AUX
ajset-590	43	4	a	a	DET
ajset-590	43	5	universal	universal	ADJ
ajset-590	43	6	variable	variable	NOUN
ajset-590	43	7	(	(	PUNCT
ajset-590	43	8	with	with	ADP
ajset-590	43	9	the	the	DET
ajset-590	43	10	dimension	dimension	NOUN
ajset-590	43	11	of	of	ADP
ajset-590	43	12	“	"	PUNCT
ajset-590	43	13	second	second	ADJ
ajset-590	43	14	”	"	PUNCT
ajset-590	43	15	)	)	PUNCT
ajset-590	43	16	,	,	PUNCT
ajset-590	43	17	an	an	DET
ajset-590	43	18	information	information	NOUN
ajset-590	43	19	basis	basis	NOUN
ajset-590	43	20	that	that	PRON
ajset-590	43	21	is	be	AUX
ajset-590	43	22	used	use	VERB
ajset-590	43	23	to	to	PART
ajset-590	43	24	put	put	VERB
ajset-590	43	25	in	in	ADP
ajset-590	43	26	order	order	NOUN
ajset-590	43	27	of	of	ADP
ajset-590	43	28	information	information	NOUN
ajset-590	43	29	about	about	ADP
ajset-590	43	30	events	event	NOUN
ajset-590	43	31	and	and	CCONJ
ajset-590	43	32	processes	process	NOUN
ajset-590	43	33	in	in	ADP
ajset-590	43	34	the	the	DET
ajset-590	43	35	world	world	NOUN
ajset-590	43	36	.	.	PUNCT
ajset-590	44	1	time	time	NOUN
ajset-590	44	2	t	t	PROPN
ajset-590	44	3	is	be	AUX
ajset-590	44	4	defined	define	VERB
ajset-590	44	5	by	by	ADP
ajset-590	44	6	the	the	DET
ajset-590	44	7	following	follow	VERB
ajset-590	44	8	mathematical	mathematical	ADJ
ajset-590	44	9	expression	expression	NOUN
ajset-590	44	10	[	[	X
ajset-590	44	11	9	9	NUM
ajset-590	44	12	]	]	SYM
ajset-590	44	13	:	:	PUNCT
ajset-590	44	14	tn	tn	PROPN
ajset-590	44	15	n	n	PRON
ajset-590	44	16	where	where	SCONJ
ajset-590	44	17	n	n	ADV
ajset-590	44	18	0	0	NUM
ajset-590	44	19	,	,	PUNCT
ajset-590	44	20	1	1	NUM
ajset-590	44	21	,	,	PUNCT
ajset-590	44	22	2	2	NUM
ajset-590	44	23	,	,	PUNCT
ajset-590	44	24	...	...	PUNCT
ajset-590	44	25	;	;	PUNCT
ajset-590	44	26	is	be	AUX
ajset-590	44	27	elementary	elementary	ADJ
ajset-590	44	28	(	(	PUNCT
ajset-590	44	29	unit	unit	NOUN
ajset-590	44	30	)	)	PUNCT
ajset-590	44	31	duration	duration	NOUN
ajset-590	44	32	which	which	PRON
ajset-590	44	33	can	can	AUX
ajset-590	44	34	be	be	AUX
ajset-590	44	35	made	make	VERB
ajset-590	44	36	as	as	ADV
ajset-590	44	37	small	small	ADJ
ajset-590	44	38	as	as	SCONJ
ajset-590	44	39	desired	desire	VERB
ajset-590	44	40	.	.	PUNCT
ajset-590	45	1	concrete	concrete	ADJ
ajset-590	45	2	numbers	number	NOUN
ajset-590	45	3	(	(	PUNCT
ajset-590	45	4	denominate	denominate	NOUN
ajset-590	45	5	numbers	number	NOUN
ajset-590	45	6	)	)	PUNCT
ajset-590	45	7	tn	tn	PROPN
ajset-590	45	8	have	have	VERB
ajset-590	45	9	one	one	NUM
ajset-590	45	10	and	and	CCONJ
ajset-590	45	11	the	the	DET
ajset-590	45	12	same	same	ADJ
ajset-590	45	13	qualitative	qualitative	ADJ
ajset-590	45	14	determinacy	determinacy	NOUN
ajset-590	45	15	(	(	PUNCT
ajset-590	45	16	i.e.	i.e.	X
ajset-590	45	17	,	,	PUNCT
ajset-590	45	18	dimension	dimension	NOUN
ajset-590	45	19	of	of	ADP
ajset-590	45	20	“	"	PUNCT
ajset-590	45	21	time	time	NOUN
ajset-590	45	22	”	"	PUNCT
ajset-590	45	23	)	)	PUNCT
ajset-590	45	24	.	.	PUNCT
ajset-590	46	1	the	the	DET
ajset-590	46	2	set	set	NOUN
ajset-590	46	3	of	of	ADP
ajset-590	46	4	numbers	number	NOUN
ajset-590	46	5	tn	tn	NOUN
ajset-590	46	6	forms	form	VERB
ajset-590	46	7	an	an	DET
ajset-590	46	8	ordered	order	VERB
ajset-590	46	9	sequence	sequence	NOUN
ajset-590	46	10	.	.	PUNCT
ajset-590	47	1	a	a	DET
ajset-590	47	2	member	member	NOUN
ajset-590	47	3	of	of	ADP
ajset-590	47	4	the	the	DET
ajset-590	47	5	sequence	sequence	NOUN
ajset-590	47	6	is	be	AUX
ajset-590	47	7	called	call	VERB
ajset-590	47	8	a	a	DET
ajset-590	47	9	moment	moment	NOUN
ajset-590	47	10	of	of	ADP
ajset-590	47	11	time	time	NOUN
ajset-590	47	12	.	.	PUNCT
ajset-590	48	1	numerical	numerical	ADJ
ajset-590	48	2	values	value	NOUN
ajset-590	48	3	of	of	ADP
ajset-590	48	4	quantity	quantity	NOUN
ajset-590	48	5	tn	tn	PROPN
ajset-590	48	6	is	be	AUX
ajset-590	48	7	changed	change	VERB
ajset-590	48	8	due	due	ADP
ajset-590	48	9	to	to	ADP
ajset-590	48	10	clock	clock	NOUN
ajset-590	48	11	mechanism	mechanism	NOUN
ajset-590	48	12	which	which	PRON
ajset-590	48	13	continuously	continuously	ADV
ajset-590	48	14	changes	change	VERB
ajset-590	48	15	numerical	numerical	ADJ
ajset-590	48	16	values	value	NOUN
ajset-590	48	17	of	of	ADP
ajset-590	48	18	the	the	DET
ajset-590	48	19	quantity	quantity	NOUN
ajset-590	48	20	n	n	NOUN
ajset-590	48	21	.	.	PUNCT
ajset-590	49	1	4	4	X
ajset-590	49	2	.	.	X
ajset-590	49	3	the	the	DET
ajset-590	49	4	mechanical	mechanical	ADJ
ajset-590	49	5	form	form	NOUN
ajset-590	49	6	of	of	ADP
ajset-590	49	7	movement	movement	NOUN
ajset-590	49	8	(	(	PUNCT
ajset-590	49	9	in	in	ADP
ajset-590	49	10	particular	particular	ADJ
ajset-590	49	11	,	,	PUNCT
ajset-590	49	12	the	the	DET
ajset-590	49	13	motion	motion	NOUN
ajset-590	49	14	of	of	ADP
ajset-590	49	15	a	a	DET
ajset-590	49	16	material	material	NOUN
ajset-590	49	17	point	point	NOUN
ajset-590	49	18	m	m	PROPN
ajset-590	49	19	)	)	PUNCT
ajset-590	49	20	is	be	AUX
ajset-590	49	21	studied	study	VERB
ajset-590	49	22	in	in	ADP
ajset-590	49	23	a	a	DET
ajset-590	49	24	reference	reference	NOUN
ajset-590	49	25	system	system	NOUN
ajset-590	49	26	which	which	PRON
ajset-590	49	27	represents	represent	VERB
ajset-590	49	28	the	the	DET
ajset-590	49	29	unity	unity	NOUN
ajset-590	49	30	of	of	ADP
ajset-590	49	31	the	the	DET
ajset-590	49	32	system	system	NOUN
ajset-590	49	33	of	of	ADP
ajset-590	49	34	coordinates	coordinate	NOUN
ajset-590	49	35	and	and	CCONJ
ajset-590	49	36	clock	clock	NOUN
ajset-590	49	37	.	.	PUNCT
ajset-590	50	1	the	the	DET
ajset-590	50	2	system	system	NOUN
ajset-590	50	3	of	of	ADP
ajset-590	50	4	coordinates	coordinate	NOUN
ajset-590	50	5	is	be	AUX
ajset-590	50	6	a	a	DET
ajset-590	50	7	system	system	NOUN
ajset-590	50	8	of	of	ADP
ajset-590	50	9	measuring	measure	VERB
ajset-590	50	10	devices	device	NOUN
ajset-590	50	11	which	which	PRON
ajset-590	50	12	determines	determine	VERB
ajset-590	50	13	the	the	DET
ajset-590	50	14	position	position	NOUN
ajset-590	50	15	(	(	PUNCT
ajset-590	50	16	i.e.	i.e.	X
ajset-590	50	17	,	,	PUNCT
ajset-590	50	18	the	the	DET
ajset-590	50	19	set	set	NOUN
ajset-590	50	20	of	of	ADP
ajset-590	50	21	coordinates	coordinate	NOUN
ajset-590	50	22	)	)	PUNCT
ajset-590	50	23	of	of	ADP
ajset-590	50	24	a	a	DET
ajset-590	50	25	material	material	NOUN
ajset-590	50	26	point	point	NOUN
ajset-590	50	27	m	m	VERB
ajset-590	50	28	in	in	ADP
ajset-590	50	29	space	space	NOUN
ajset-590	50	30	.	.	PUNCT
ajset-590	51	1	(	(	PUNCT
ajset-590	51	2	for	for	ADP
ajset-590	51	3	example	example	NOUN
ajset-590	51	4	,	,	PUNCT
ajset-590	51	5	the	the	DET
ajset-590	51	6	cartesian	cartesian	ADJ
ajset-590	51	7	coordinate	coordinate	NOUN
ajset-590	51	8	system	system	NOUN
ajset-590	51	9	represents	represent	VERB
ajset-590	51	10	the	the	DET
ajset-590	51	11	system	system	NOUN
ajset-590	51	12	of	of	ADP
ajset-590	51	13	three	three	NUM
ajset-590	51	14	connected	connected	ADJ
ajset-590	51	15	measuring	measuring	NOUN
ajset-590	51	16	scales	scale	NOUN
ajset-590	51	17	(	(	PUNCT
ajset-590	51	18	drawing	draw	VERB
ajset-590	51	19	scales	scale	NOUN
ajset-590	51	20	):	):	PUNCT
ajset-590	51	21	straight	straight	ADJ
ajset-590	51	22	linesox	linesox	NOUN
ajset-590	51	23	,	,	PUNCT
ajset-590	51	24	oy	oy	X
ajset-590	51	25	,	,	PUNCT
ajset-590	51	26	oz	oz	X
ajset-590	51	27	with	with	ADP
ajset-590	51	28	printed	print	VERB
ajset-590	51	29	concrete	concrete	ADJ
ajset-590	51	30	numbers	number	NOUN
ajset-590	51	31	(	(	PUNCT
ajset-590	51	32	denominate	denominate	NOUN
ajset-590	51	33	numbers	number	NOUN
ajset-590	51	34	)	)	PUNCT
ajset-590	51	35	having	have	VERB
ajset-590	51	36	the	the	DET
ajset-590	51	37	identical	identical	ADJ
ajset-590	51	38	dimension	dimension	NOUN
ajset-590	51	39	of	of	ADP
ajset-590	51	40	“	"	PUNCT
ajset-590	51	41	meter	meter	NOUN
ajset-590	51	42	”	"	PUNCT
ajset-590	51	43	)	)	PUNCT
ajset-590	51	44	.	.	PUNCT
ajset-590	52	1	the	the	DET
ajset-590	52	2	space	space	NOUN
ajset-590	52	3	of	of	ADP
ajset-590	52	4	the	the	DET
ajset-590	52	5	object	object	NOUN
ajset-590	52	6	(	(	PUNCT
ajset-590	52	7	for	for	ADP
ajset-590	52	8	example	example	NOUN
ajset-590	52	9	,	,	PUNCT
ajset-590	52	10	geometric	geometric	ADJ
ajset-590	52	11	space	space	NOUN
ajset-590	52	12	,	,	PUNCT
ajset-590	52	13	and	and	CCONJ
ajset-590	52	14	energy	energy	NOUN
ajset-590	52	15	space	space	NOUN
ajset-590	52	16	)	)	PUNCT
ajset-590	52	17	is	be	AUX
ajset-590	52	18	the	the	DET
ajset-590	52	19	set	set	NOUN
ajset-590	52	20	of	of	ADP
ajset-590	52	21	possible	possible	ADJ
ajset-590	52	22	(	(	PUNCT
ajset-590	52	23	available	available	ADJ
ajset-590	52	24	)	)	PUNCT
ajset-590	52	25	states	state	NOUN
ajset-590	52	26	of	of	ADP
ajset-590	52	27	the	the	DET
ajset-590	52	28	material	material	ADJ
ajset-590	52	29	object	object	NOUN
ajset-590	52	30	(	(	PUNCT
ajset-590	52	31	in	in	ADP
ajset-590	52	32	particular	particular	ADJ
ajset-590	52	33	,	,	PUNCT
ajset-590	52	34	the	the	DET
ajset-590	52	35	set	set	NOUN
ajset-590	52	36	of	of	ADP
ajset-590	52	37	positions	position	NOUN
ajset-590	52	38	of	of	ADP
ajset-590	52	39	the	the	DET
ajset-590	52	40	material	material	NOUN
ajset-590	52	41	point	point	NOUN
ajset-590	52	42	m	m	PROPN
ajset-590	52	43	)	)	PUNCT
ajset-590	52	44	.	.	PUNCT
ajset-590	53	1	each	each	DET
ajset-590	53	2	state	state	NOUN
ajset-590	53	3	is	be	AUX
ajset-590	53	4	characterized	characterize	VERB
ajset-590	53	5	by	by	ADP
ajset-590	53	6	a	a	DET
ajset-590	53	7	certain	certain	ADJ
ajset-590	53	8	concrete	concrete	ADJ
ajset-590	53	9	number	number	NOUN
ajset-590	53	10	(	(	PUNCT
ajset-590	53	11	denominate	denominate	NOUN
ajset-590	53	12	number	number	NOUN
ajset-590	53	13	)	)	PUNCT
ajset-590	53	14	having	have	VERB
ajset-590	53	15	a	a	DET
ajset-590	53	16	dimension	dimension	NOUN
ajset-590	53	17	.	.	PUNCT
ajset-590	54	1	movement	movement	NOUN
ajset-590	54	2	of	of	ADP
ajset-590	54	3	an	an	DET
ajset-590	54	4	object	object	NOUN
ajset-590	54	5	in	in	ADP
ajset-590	54	6	space	space	NOUN
ajset-590	54	7	is	be	AUX
ajset-590	54	8	a	a	DET
ajset-590	54	9	process	process	NOUN
ajset-590	54	10	of	of	ADP
ajset-590	54	11	transition	transition	NOUN
ajset-590	54	12	from	from	ADP
ajset-590	54	13	some	some	DET
ajset-590	54	14	states	state	NOUN
ajset-590	54	15	to	to	ADP
ajset-590	54	16	other	other	ADJ
ajset-590	54	17	states	state	NOUN
ajset-590	54	18	,	,	PUNCT
ajset-590	54	19	i.e.	i.e.	X
ajset-590	54	20	the	the	DET
ajset-590	54	21	process	process	NOUN
ajset-590	54	22	of	of	ADP
ajset-590	54	23	transition	transition	NOUN
ajset-590	54	24	from	from	ADP
ajset-590	54	25	some	some	DET
ajset-590	54	26	concrete	concrete	ADJ
ajset-590	54	27	(	(	PUNCT
ajset-590	54	28	denominate	denominate	NOUN
ajset-590	54	29	)	)	PUNCT
ajset-590	54	30	numbers	number	NOUN
ajset-590	54	31	to	to	ADP
ajset-590	54	32	other	other	ADJ
ajset-590	54	33	concrete	concrete	ADJ
ajset-590	54	34	(	(	PUNCT
ajset-590	54	35	denominate	denominate	NOUN
ajset-590	54	36	)	)	PUNCT
ajset-590	54	37	numbers	number	NOUN
ajset-590	54	38	.	.	PUNCT
ajset-590	55	1	5	5	X
ajset-590	55	2	.	.	X
ajset-590	55	3	a	a	DET
ajset-590	55	4	process	process	NOUN
ajset-590	55	5	has	have	VERB
ajset-590	55	6	the	the	DET
ajset-590	55	7	beginning	beginning	NOUN
ajset-590	55	8	(	(	PUNCT
ajset-590	55	9	i.e.	i.e.	X
ajset-590	55	10	,	,	PUNCT
ajset-590	55	11	the	the	DET
ajset-590	55	12	beginning	beginning	NOUN
ajset-590	55	13	of	of	ADP
ajset-590	55	14	the	the	DET
ajset-590	55	15	changes	change	NOUN
ajset-590	55	16	)	)	PUNCT
ajset-590	55	17	and	and	CCONJ
ajset-590	55	18	the	the	DET
ajset-590	55	19	end	end	NOUN
ajset-590	55	20	(	(	PUNCT
ajset-590	55	21	i.e.	i.e.	X
ajset-590	55	22	,	,	PUNCT
ajset-590	55	23	the	the	DET
ajset-590	55	24	end	end	NOUN
ajset-590	55	25	of	of	ADP
ajset-590	55	26	the	the	DET
ajset-590	55	27	changes	change	NOUN
ajset-590	55	28	)	)	PUNCT
ajset-590	55	29	.	.	PUNCT
ajset-590	56	1	the	the	DET
ajset-590	56	2	transition	transition	NOUN
ajset-590	56	3	from	from	ADP
ajset-590	56	4	the	the	DET
ajset-590	56	5	initial	initial	ADJ
ajset-590	56	6	state	state	NOUN
ajset-590	56	7	to	to	ADP
ajset-590	56	8	the	the	DET
ajset-590	56	9	final	final	ADJ
ajset-590	56	10	state	state	NOUN
ajset-590	56	11	represents	represent	VERB
ajset-590	56	12	the	the	DET
ajset-590	56	13	sum	sum	NOUN
ajset-590	56	14	of	of	ADP
ajset-590	56	15	elementary	elementary	ADJ
ajset-590	56	16	transitions	transition	NOUN
ajset-590	56	17	and	and	CCONJ
ajset-590	56	18	,	,	PUNCT
ajset-590	56	19	therefore	therefore	ADV
ajset-590	56	20	,	,	PUNCT
ajset-590	56	21	is	be	AUX
ajset-590	56	22	characterized	characterize	VERB
ajset-590	56	23	by	by	ADP
ajset-590	56	24	an	an	DET
ajset-590	56	25	increase	increase	NOUN
ajset-590	56	26	of	of	ADP
ajset-590	56	27	the	the	DET
ajset-590	56	28	changes	change	NOUN
ajset-590	56	29	.	.	PUNCT
ajset-590	57	1	in	in	ADP
ajset-590	57	2	other	other	ADJ
ajset-590	57	3	words	word	NOUN
ajset-590	57	4	,	,	PUNCT
ajset-590	57	5	the	the	DET
ajset-590	57	6	total	total	ADJ
ajset-590	57	7	change	change	NOUN
ajset-590	57	8	is	be	AUX
ajset-590	57	9	the	the	DET
ajset-590	57	10	sum	sum	NOUN
ajset-590	57	11	of	of	ADP
ajset-590	57	12	elementary	elementary	ADJ
ajset-590	57	13	changes	change	NOUN
ajset-590	57	14	.	.	PUNCT
ajset-590	58	1	since	since	SCONJ
ajset-590	58	2	elementary	elementary	ADJ
ajset-590	58	3	change	change	NOUN
ajset-590	58	4	is	be	AUX
ajset-590	58	5	characterized	characterize	VERB
ajset-590	58	6	by	by	ADP
ajset-590	58	7	the	the	DET
ajset-590	58	8	concrete	concrete	ADJ
ajset-590	58	9	(	(	PUNCT
ajset-590	58	10	denominate	denominate	NOUN
ajset-590	58	11	)	)	PUNCT
ajset-590	58	12	number	number	NOUN
ajset-590	58	13	having	have	VERB
ajset-590	58	14	a	a	DET
ajset-590	58	15	dimension	dimension	NOUN
ajset-590	58	16	,	,	PUNCT
ajset-590	58	17	the	the	DET
ajset-590	58	18	total	total	ADJ
ajset-590	58	19	change	change	NOUN
ajset-590	58	20	has	have	VERB
ajset-590	58	21	dimension	dimension	NOUN
ajset-590	58	22	as	as	ADV
ajset-590	58	23	well	well	ADV
ajset-590	58	24	and	and	CCONJ
ajset-590	58	25	is	be	AUX
ajset-590	58	26	expressed	express	VERB
ajset-590	58	27	by	by	ADP
ajset-590	58	28	the	the	DET
ajset-590	58	29	following	following	ADJ
ajset-590	58	30	mathematical	mathematical	ADJ
ajset-590	58	31	formula	formula	NOUN
ajset-590	58	32	:	:	PUNCT
ajset-590	58	33	sn	sn	PROPN
ajset-590	58	34	n	n	CCONJ
ajset-590	58	35	,	,	PUNCT
ajset-590	58	36	where	where	SCONJ
ajset-590	58	37	n	n	ADV
ajset-590	58	38	0	0	NUM
ajset-590	58	39	,	,	PUNCT
ajset-590	58	40	1	1	NUM
ajset-590	58	41	,	,	PUNCT
ajset-590	58	42	2	2	NUM
ajset-590	58	43	,	,	PUNCT
ajset-590	58	44	3	3	NUM
ajset-590	58	45	,	,	PUNCT
ajset-590	58	46	...	...	PUNCT
ajset-590	58	47	,	,	PUNCT
ajset-590	58	48	is	be	AUX
ajset-590	58	49	elementary	elementary	ADJ
ajset-590	58	50	(	(	PUNCT
ajset-590	58	51	single	single	ADJ
ajset-590	58	52	)	)	PUNCT
ajset-590	58	53	change	change	NOUN
ajset-590	58	54	which	which	PRON
ajset-590	58	55	has	have	VERB
ajset-590	58	56	the	the	DET
ajset-590	58	57	dimension	dimension	NOUN
ajset-590	58	58	and	and	CCONJ
ajset-590	58	59	is	be	AUX
ajset-590	58	60	mailto:topacademicjournals@gmail.com	mailto:topacademicjournals@gmail.com	PROPN
ajset-590	58	61	academic	academic	ADJ
ajset-590	58	62	journal	journal	NOUN
ajset-590	58	63	of	of	ADP
ajset-590	58	64	science	science	NOUN
ajset-590	58	65	,	,	PUNCT
ajset-590	58	66	engineering	engineering	NOUN
ajset-590	58	67	and	and	CCONJ
ajset-590	58	68	technology	technology	NOUN
ajset-590	58	69	vol.8	vol.8	PROPN
ajset-590	58	70	,	,	PUNCT
ajset-590	58	71	issue	issue	NOUN
ajset-590	58	72	5	5	NUM
ajset-590	58	73	;	;	PUNCT
ajset-590	58	74	september	september	PROPN
ajset-590	58	75	october	october	PROPN
ajset-590	58	76	2023	2023	NUM
ajset-590	58	77	;	;	PUNCT
ajset-590	58	78	issn	issn	PROPN
ajset-590	58	79	:	:	PUNCT
ajset-590	58	80	2837	2837	NUM
ajset-590	58	81	-	-	SYM
ajset-590	58	82	2964	2964	NUM
ajset-590	58	83	impact	impact	NOUN
ajset-590	58	84	factor	factor	NOUN
ajset-590	58	85	:	:	PUNCT
ajset-590	58	86	6.67	6.67	NUM
ajset-590	58	87	1252	1252	NUM
ajset-590	58	88	columbia	columbia	PROPN
ajset-590	58	89	rd	rd	PROPN
ajset-590	58	90	nw	nw	PROPN
ajset-590	58	91	,	,	PUNCT
ajset-590	58	92	washington	washington	PROPN
ajset-590	58	93	dc	dc	PROPN
ajset-590	58	94	,	,	PUNCT
ajset-590	58	95	united	united	PROPN
ajset-590	58	96	states	states	PROPN
ajset-590	58	97	https://topjournals.org/index.php/ajset/index	https://topjournals.org/index.php/ajset/index	PROPN
ajset-590	58	98	;	;	PUNCT
ajset-590	58	99	mail	mail	NOUN
ajset-590	58	100	:	:	PUNCT
ajset-590	58	101	topacademicjournals@gmail.com	topacademicjournals@gmail.com	X
ajset-590	59	1	11	11	NUM
ajset-590	60	1	|	|	ADV
ajset-590	60	2	a	a	DET
ajset-590	60	3	c	c	NOUN
ajset-590	60	4	a	a	PRON
ajset-590	60	5	d	d	X
ajset-590	60	6	e	e	NOUN
ajset-590	60	7	m	m	NOUN
ajset-590	60	8	i	i	NOUN
ajset-590	60	9	c	c	NOUN
ajset-590	60	10	j	j	NOUN
ajset-590	60	11	o	o	X
ajset-590	60	12	u	u	NOUN
ajset-590	60	13	r	r	NOUN
ajset-590	60	14	n	n	NOUN
ajset-590	60	15	a	a	DET
ajset-590	60	16	l	l	NOUN
ajset-590	61	1	o	o	X
ajset-590	61	2	f	f	X
ajset-590	61	3	s	s	X
ajset-590	61	4	c	c	NOUN
ajset-590	62	1	i	i	NOUN
ajset-590	62	2	e	e	PROPN
ajset-590	62	3	n	n	PROPN
ajset-590	62	4	c	c	NOUN
ajset-590	62	5	e	e	X
ajset-590	62	6	,	,	PUNCT
ajset-590	62	7	e	e	PROPN
ajset-590	62	8	n	n	PRON
ajset-590	62	9	g	g	NOUN
ajset-590	62	10	i	i	PRON
ajset-590	62	11	n	n	VERB
ajset-590	62	12	e	e	NOUN
ajset-590	62	13	e	e	NOUN
ajset-590	62	14	r	r	VERB
ajset-590	62	15	i	i	PRON
ajset-590	62	16	n	n	CCONJ
ajset-590	62	17	g	g	PROPN
ajset-590	62	18	a	a	DET
ajset-590	62	19	n	n	NOUN
ajset-590	62	20	d	d	NOUN
ajset-590	62	21	t	t	NOUN
ajset-590	62	22	e	e	X
ajset-590	62	23	c	c	NOUN
ajset-590	62	24	h	h	NOUN
ajset-590	62	25	n	n	ADV
ajset-590	62	26	o	o	NOUN
ajset-590	62	27	l	l	NOUN
ajset-590	63	1	o	o	X
ajset-590	63	2	g	g	NOUN
ajset-590	63	3	y	y	PROPN
ajset-590	63	4	|	|	ADV
ajset-590	63	5	https://topjournals.org/index.php/ajset	https://topjournals.org/index.php/ajset	NOUN
ajset-590	63	6	assumed	assume	VERB
ajset-590	63	7	to	to	PART
ajset-590	63	8	be	be	AUX
ajset-590	63	9	constant	constant	ADJ
ajset-590	63	10	.	.	PUNCT
ajset-590	64	1	the	the	DET
ajset-590	64	2	set	set	NOUN
ajset-590	64	3	of	of	ADP
ajset-590	64	4	denominate	denominate	NOUN
ajset-590	64	5	numbers	number	NOUN
ajset-590	64	6	sn	sn	PROPN
ajset-590	64	7	forms	form	VERB
ajset-590	64	8	an	an	DET
ajset-590	64	9	ordered	order	VERB
ajset-590	64	10	sequence	sequence	NOUN
ajset-590	64	11	.	.	PUNCT
ajset-590	65	1	the	the	DET
ajset-590	65	2	numerical	numerical	ADJ
ajset-590	65	3	values	value	NOUN
ajset-590	65	4	of	of	ADP
ajset-590	65	5	the	the	DET
ajset-590	65	6	denominate	denominate	NOUN
ajset-590	65	7	quantity	quantity	NOUN
ajset-590	65	8	sn	sn	PROPN
ajset-590	65	9	are	be	AUX
ajset-590	65	10	changed	change	VERB
ajset-590	65	11	if	if	SCONJ
ajset-590	65	12	the	the	DET
ajset-590	65	13	numerical	numerical	ADJ
ajset-590	65	14	values	value	NOUN
ajset-590	65	15	of	of	ADP
ajset-590	65	16	the	the	DET
ajset-590	65	17	quantity	quantity	NOUN
ajset-590	65	18	n	n	PRON
ajset-590	65	19	are	be	AUX
ajset-590	65	20	changed	change	VERB
ajset-590	65	21	.	.	PUNCT
ajset-590	66	1	if	if	SCONJ
ajset-590	66	2	the	the	DET
ajset-590	66	3	numerical	numerical	ADJ
ajset-590	66	4	values	value	NOUN
ajset-590	66	5	of	of	ADP
ajset-590	66	6	the	the	DET
ajset-590	66	7	quantity	quantity	NOUN
ajset-590	66	8	n	n	PRON
ajset-590	66	9	are	be	AUX
ajset-590	66	10	not	not	PART
ajset-590	66	11	changed	change	VERB
ajset-590	66	12	with	with	ADP
ajset-590	66	13	time	time	NOUN
ajset-590	66	14	,	,	PUNCT
ajset-590	66	15	the	the	DET
ajset-590	66	16	process	process	NOUN
ajset-590	66	17	is	be	AUX
ajset-590	66	18	not	not	PART
ajset-590	66	19	realized	realize	VERB
ajset-590	66	20	.	.	PUNCT
ajset-590	67	1	6	6	X
ajset-590	67	2	.	.	X
ajset-590	67	3	a	a	DET
ajset-590	67	4	process	process	NOUN
ajset-590	67	5	is	be	AUX
ajset-590	67	6	characterized	characterize	VERB
ajset-590	67	7	by	by	ADP
ajset-590	67	8	the	the	DET
ajset-590	67	9	direction	direction	NOUN
ajset-590	67	10	(	(	PUNCT
ajset-590	67	11	directivity	directivity	NOUN
ajset-590	67	12	)	)	PUNCT
ajset-590	67	13	of	of	ADP
ajset-590	67	14	change	change	NOUN
ajset-590	67	15	,	,	PUNCT
ajset-590	67	16	the	the	DET
ajset-590	67	17	rate	rate	NOUN
ajset-590	67	18	of	of	ADP
ajset-590	67	19	change	change	NOUN
ajset-590	67	20	,	,	PUNCT
ajset-590	67	21	and	and	CCONJ
ajset-590	67	22	acceleration	acceleration	NOUN
ajset-590	67	23	of	of	ADP
ajset-590	67	24	change	change	NOUN
ajset-590	67	25	.	.	PUNCT
ajset-590	68	1	if	if	SCONJ
ajset-590	68	2	the	the	DET
ajset-590	68	3	process	process	NOUN
ajset-590	68	4	is	be	AUX
ajset-590	68	5	not	not	PART
ajset-590	68	6	realized	realize	VERB
ajset-590	68	7	,	,	PUNCT
ajset-590	68	8	the	the	DET
ajset-590	68	9	direction	direction	NOUN
ajset-590	68	10	(	(	PUNCT
ajset-590	68	11	directivity	directivity	PROPN
ajset-590	68	12	)	)	PUNCT
ajset-590	68	13	,	,	PUNCT
ajset-590	68	14	the	the	DET
ajset-590	68	15	rate	rate	NOUN
ajset-590	68	16	,	,	PUNCT
ajset-590	68	17	and	and	CCONJ
ajset-590	68	18	acceleration	acceleration	NOUN
ajset-590	68	19	do	do	AUX
ajset-590	68	20	not	not	PART
ajset-590	68	21	exist	exist	VERB
ajset-590	68	22	.	.	PUNCT
ajset-590	69	1	explanation	explanation	NOUN
ajset-590	69	2	is	be	AUX
ajset-590	69	3	that	that	SCONJ
ajset-590	69	4	the	the	DET
ajset-590	69	5	direction	direction	NOUN
ajset-590	69	6	(	(	PUNCT
ajset-590	69	7	directivity	directivity	NOUN
ajset-590	69	8	)	)	PUNCT
ajset-590	69	9	,	,	PUNCT
ajset-590	69	10	rate	rate	NOUN
ajset-590	69	11	,	,	PUNCT
ajset-590	69	12	and	and	CCONJ
ajset-590	69	13	acceleration	acceleration	NOUN
ajset-590	69	14	are	be	AUX
ajset-590	69	15	the	the	DET
ajset-590	69	16	properties	property	NOUN
ajset-590	69	17	of	of	ADP
ajset-590	69	18	the	the	DET
ajset-590	69	19	process	process	NOUN
ajset-590	69	20	and	and	CCONJ
ajset-590	69	21	not	not	PART
ajset-590	69	22	the	the	DET
ajset-590	69	23	properties	property	NOUN
ajset-590	69	24	of	of	ADP
ajset-590	69	25	the	the	DET
ajset-590	69	26	material	material	ADJ
ajset-590	69	27	object	object	NOUN
ajset-590	69	28	.	.	PUNCT
ajset-590	70	1	therefore	therefore	ADV
ajset-590	70	2	,	,	PUNCT
ajset-590	70	3	the	the	DET
ajset-590	70	4	direction	direction	NOUN
ajset-590	70	5	of	of	ADP
ajset-590	70	6	change	change	NOUN
ajset-590	70	7	determines	determine	VERB
ajset-590	70	8	the	the	DET
ajset-590	70	9	order	order	NOUN
ajset-590	70	10	of	of	ADP
ajset-590	70	11	the	the	DET
ajset-590	70	12	number	number	NOUN
ajset-590	70	13	set	set	VERB
ajset-590	70	14	but	but	CCONJ
ajset-590	70	15	an	an	DET
ajset-590	70	16	ordered	order	VERB
ajset-590	70	17	number	number	NOUN
ajset-590	70	18	set	set	NOUN
ajset-590	70	19	does	do	AUX
ajset-590	70	20	not	not	PART
ajset-590	70	21	determine	determine	VERB
ajset-590	70	22	the	the	DET
ajset-590	70	23	direction	direction	NOUN
ajset-590	70	24	.	.	PUNCT
ajset-590	71	1	neither	neither	CCONJ
ajset-590	71	2	pure	pure	ADJ
ajset-590	71	3	mathematics	mathematic	NOUN
ajset-590	71	4	nor	nor	CCONJ
ajset-590	71	5	applied	apply	VERB
ajset-590	71	6	mathematics	mathematic	NOUN
ajset-590	71	7	(	(	PUNCT
ajset-590	71	8	i.e.	i.e.	X
ajset-590	71	9	,	,	PUNCT
ajset-590	71	10	the	the	DET
ajset-590	71	11	mathematical	mathematical	ADJ
ajset-590	71	12	formalism	formalism	NOUN
ajset-590	71	13	of	of	ADP
ajset-590	71	14	the	the	DET
ajset-590	71	15	natural	natural	ADJ
ajset-590	71	16	sciences	science	NOUN
ajset-590	71	17	)	)	PUNCT
ajset-590	71	18	does	do	AUX
ajset-590	71	19	not	not	PART
ajset-590	71	20	contain	contain	VERB
ajset-590	71	21	a	a	DET
ajset-590	71	22	mathematical	mathematical	ADJ
ajset-590	71	23	(	(	PUNCT
ajset-590	71	24	calculation	calculation	NOUN
ajset-590	71	25	)	)	PUNCT
ajset-590	71	26	process	process	NOUN
ajset-590	71	27	because	because	SCONJ
ajset-590	71	28	the	the	DET
ajset-590	71	29	mathematics	mathematic	NOUN
ajset-590	71	30	does	do	AUX
ajset-590	71	31	not	not	PART
ajset-590	71	32	represent	represent	VERB
ajset-590	71	33	a	a	DET
ajset-590	71	34	computer	computer	NOUN
ajset-590	71	35	or	or	CCONJ
ajset-590	71	36	some	some	DET
ajset-590	71	37	other	other	ADJ
ajset-590	71	38	material	material	NOUN
ajset-590	71	39	device	device	NOUN
ajset-590	71	40	that	that	PRON
ajset-590	71	41	realizes	realize	VERB
ajset-590	71	42	the	the	DET
ajset-590	71	43	process	process	NOUN
ajset-590	71	44	of	of	ADP
ajset-590	71	45	change	change	NOUN
ajset-590	71	46	of	of	ADP
ajset-590	71	47	the	the	DET
ajset-590	71	48	values	value	NOUN
ajset-590	71	49	of	of	ADP
ajset-590	71	50	the	the	DET
ajset-590	71	51	quantitysn	quantitysn	NOUN
ajset-590	71	52	.	.	PUNCT
ajset-590	72	1	change	change	NOUN
ajset-590	72	2	of	of	ADP
ajset-590	72	3	the	the	DET
ajset-590	72	4	valuesof	valuesof	NOUN
ajset-590	72	5	the	the	DET
ajset-590	72	6	quantity	quantity	NOUN
ajset-590	72	7	n	n	PRON
ajset-590	72	8	is	be	AUX
ajset-590	72	9	carried	carry	VERB
ajset-590	72	10	out	out	ADP
ajset-590	72	11	by	by	ADP
ajset-590	72	12	an	an	DET
ajset-590	72	13	operator	operator	NOUN
ajset-590	72	14	(	(	PUNCT
ajset-590	72	15	person	person	NOUN
ajset-590	72	16	)	)	PUNCT
ajset-590	72	17	.	.	PUNCT
ajset-590	73	1	therefore	therefore	ADV
ajset-590	73	2	,	,	PUNCT
ajset-590	73	3	the	the	DET
ajset-590	73	4	correct	correct	ADJ
ajset-590	73	5	mathematical	mathematical	ADJ
ajset-590	73	6	formalism	formalism	NOUN
ajset-590	73	7	can	can	AUX
ajset-590	73	8	not	not	PART
ajset-590	73	9	contain	contain	VERB
ajset-590	73	10	the	the	DET
ajset-590	73	11	concepts	concept	NOUN
ajset-590	73	12	of	of	ADP
ajset-590	73	13	“	"	PUNCT
ajset-590	73	14	direction	direction	NOUN
ajset-590	73	15	(	(	PUNCT
ajset-590	73	16	directivity	directivity	NOUN
ajset-590	73	17	)	)	PUNCT
ajset-590	73	18	”	"	PUNCT
ajset-590	73	19	and	and	CCONJ
ajset-590	73	20	“	"	PUNCT
ajset-590	73	21	vector	vector	NOUN
ajset-590	73	22	”	"	PUNCT
ajset-590	73	23	.	.	PUNCT
ajset-590	74	1	7	7	X
ajset-590	74	2	.	.	X
ajset-590	74	3	if	if	SCONJ
ajset-590	74	4	one	one	PRON
ajset-590	74	5	assumes	assume	VERB
ajset-590	74	6	that	that	SCONJ
ajset-590	74	7	the	the	DET
ajset-590	74	8	mathematical	mathematical	ADJ
ajset-590	74	9	formalism	formalism	NOUN
ajset-590	74	10	contains	contain	VERB
ajset-590	74	11	the	the	DET
ajset-590	74	12	concepts	concept	NOUN
ajset-590	74	13	“	"	PUNCT
ajset-590	74	14	direction	direction	NOUN
ajset-590	74	15	(	(	PUNCT
ajset-590	74	16	directivity	directivity	NOUN
ajset-590	74	17	)	)	PUNCT
ajset-590	74	18	”	"	PUNCT
ajset-590	74	19	and	and	CCONJ
ajset-590	74	20	“	"	PUNCT
ajset-590	74	21	vector	vector	NOUN
ajset-590	74	22	”	"	PUNCT
ajset-590	74	23	,	,	PUNCT
ajset-590	74	24	then	then	ADV
ajset-590	74	25	the	the	DET
ajset-590	74	26	formula	formula	NOUN
ajset-590	74	27	for	for	ADP
ajset-590	74	28	the	the	DET
ajset-590	74	29	quantity	quantity	NOUN
ajset-590	74	30	sn	sn	NOUN
ajset-590	74	31	to	to	PART
ajset-590	74	32	be	be	AUX
ajset-590	74	33	written	write	VERB
ajset-590	74	34	in	in	ADP
ajset-590	74	35	the	the	DET
ajset-590	74	36	following	follow	VERB
ajset-590	74	37	vector	vector	NOUN
ajset-590	74	38	form	form	NOUN
ajset-590	74	39	:	:	PUNCT
ajset-590	74	40	sn	sn	PROPN
ajset-590	74	41	n	n	CCONJ
ajset-590	74	42	where	where	SCONJ
ajset-590	74	43	is	be	AUX
ajset-590	74	44	elementary	elementary	ADJ
ajset-590	74	45	(	(	PUNCT
ajset-590	74	46	unit	unit	NOUN
ajset-590	74	47	)	)	PUNCT
ajset-590	74	48	vector	vector	NOUN
ajset-590	74	49	.	.	PUNCT
ajset-590	75	1	but	but	CCONJ
ajset-590	75	2	since	since	SCONJ
ajset-590	75	3	the	the	DET
ajset-590	75	4	numerical	numerical	ADJ
ajset-590	75	5	values	value	NOUN
ajset-590	75	6	of	of	ADP
ajset-590	75	7	quantity	quantity	NOUN
ajset-590	75	8	n	n	CCONJ
ajset-590	75	9	in	in	ADP
ajset-590	75	10	this	this	DET
ajset-590	75	11	formula	formula	NOUN
ajset-590	75	12	are	be	AUX
ajset-590	75	13	not	not	PART
ajset-590	75	14	changed	change	VERB
ajset-590	75	15	with	with	ADP
ajset-590	75	16	time	time	NOUN
ajset-590	75	17	,	,	PUNCT
ajset-590	75	18	the	the	DET
ajset-590	75	19	process	process	NOUN
ajset-590	75	20	of	of	ADP
ajset-590	75	21	change	change	NOUN
ajset-590	75	22	of	of	ADP
ajset-590	75	23	the	the	DET
ajset-590	75	24	numerical	numerical	ADJ
ajset-590	75	25	values	value	NOUN
ajset-590	75	26	of	of	ADP
ajset-590	75	27	the	the	DET
ajset-590	75	28	quantity	quantity	NOUN
ajset-590	75	29	sn	sn	INTJ
ajset-590	75	30	in	in	ADP
ajset-590	75	31	mathematical	mathematical	ADJ
ajset-590	75	32	formalism	formalism	NOUN
ajset-590	75	33	is	be	AUX
ajset-590	75	34	not	not	PART
ajset-590	75	35	realized	realize	VERB
ajset-590	75	36	.	.	PUNCT
ajset-590	76	1	therefore	therefore	ADV
ajset-590	76	2	,	,	PUNCT
ajset-590	76	3	this	this	DET
ajset-590	76	4	formula	formula	NOUN
ajset-590	76	5	does	do	AUX
ajset-590	76	6	not	not	PART
ajset-590	76	7	describe	describe	VERB
ajset-590	76	8	direction	direction	NOUN
ajset-590	76	9	,	,	PUNCT
ajset-590	76	10	and	and	CCONJ
ajset-590	76	11	the	the	DET
ajset-590	76	12	mathematical	mathematical	ADJ
ajset-590	76	13	formalism	formalism	NOUN
ajset-590	76	14	does	do	AUX
ajset-590	76	15	not	not	PART
ajset-590	76	16	contain	contain	VERB
ajset-590	76	17	the	the	DET
ajset-590	76	18	concepts	concept	NOUN
ajset-590	76	19	of	of	ADP
ajset-590	76	20	“	"	PUNCT
ajset-590	76	21	direction	direction	NOUN
ajset-590	76	22	(	(	PUNCT
ajset-590	76	23	directivity	directivity	NOUN
ajset-590	76	24	)	)	PUNCT
ajset-590	76	25	”	"	PUNCT
ajset-590	76	26	,	,	PUNCT
ajset-590	76	27	“	"	PUNCT
ajset-590	76	28	vector	vector	NOUN
ajset-590	76	29	”	"	PUNCT
ajset-590	76	30	,	,	PUNCT
ajset-590	76	31	and	and	CCONJ
ajset-590	76	32	“	"	PUNCT
ajset-590	76	33	unit	unit	NOUN
ajset-590	76	34	vector	vector	NOUN
ajset-590	76	35	”	"	PUNCT
ajset-590	76	36	.	.	PUNCT
ajset-590	77	1	thus	thus	ADV
ajset-590	77	2	,	,	PUNCT
ajset-590	77	3	the	the	DET
ajset-590	77	4	“	"	PUNCT
ajset-590	77	5	direction	direction	NOUN
ajset-590	77	6	(	(	PUNCT
ajset-590	77	7	directivity	directivity	NOUN
ajset-590	77	8	)	)	PUNCT
ajset-590	77	9	”	"	PUNCT
ajset-590	77	10	and	and	CCONJ
ajset-590	77	11	“	"	PUNCT
ajset-590	77	12	vector	vector	NOUN
ajset-590	77	13	”	"	PUNCT
ajset-590	77	14	are	be	AUX
ajset-590	77	15	not	not	PART
ajset-590	77	16	mathematical	mathematical	ADJ
ajset-590	77	17	objects	object	NOUN
ajset-590	77	18	(	(	PUNCT
ajset-590	77	19	concepts	concept	NOUN
ajset-590	77	20	)	)	PUNCT
ajset-590	77	21	.	.	PUNCT
ajset-590	78	1	the	the	DET
ajset-590	78	2	concepts	concept	NOUN
ajset-590	78	3	of	of	ADP
ajset-590	78	4	“	"	PUNCT
ajset-590	78	5	direction	direction	NOUN
ajset-590	78	6	”	"	PUNCT
ajset-590	78	7	and	and	CCONJ
ajset-590	78	8	“	"	PUNCT
ajset-590	78	9	vector	vector	NOUN
ajset-590	78	10	”	"	PUNCT
ajset-590	78	11	do	do	AUX
ajset-590	78	12	not	not	PART
ajset-590	78	13	correspond	correspond	VERB
ajset-590	78	14	to	to	ADP
ajset-590	78	15	any	any	DET
ajset-590	78	16	geometric	geometric	ADJ
ajset-590	78	17	object	object	NOUN
ajset-590	78	18	(	(	PUNCT
ajset-590	78	19	for	for	ADP
ajset-590	78	20	example	example	NOUN
ajset-590	78	21	,	,	PUNCT
ajset-590	78	22	a	a	DET
ajset-590	78	23	line	line	NOUN
ajset-590	78	24	segment	segment	NOUN
ajset-590	78	25	)	)	PUNCT
ajset-590	78	26	.	.	PUNCT
ajset-590	79	1	indication	indication	NOUN
ajset-590	79	2	of	of	ADP
ajset-590	79	3	the	the	DET
ajset-590	79	4	boundary	boundary	ADJ
ajset-590	79	5	points	point	NOUN
ajset-590	79	6	of	of	ADP
ajset-590	79	7	the	the	DET
ajset-590	79	8	line	line	NOUN
ajset-590	79	9	segment	segment	NOUN
ajset-590	79	10	and	and	CCONJ
ajset-590	79	11	designation	designation	NOUN
ajset-590	79	12	of	of	ADP
ajset-590	79	13	these	these	DET
ajset-590	79	14	points	point	NOUN
ajset-590	79	15	with	with	ADP
ajset-590	79	16	the	the	DET
ajset-590	79	17	help	help	NOUN
ajset-590	79	18	of	of	ADP
ajset-590	79	19	terms	term	NOUN
ajset-590	79	20	(	(	PUNCT
ajset-590	79	21	words	word	NOUN
ajset-590	79	22	)	)	PUNCT
ajset-590	79	23	”	"	PUNCT
ajset-590	79	24	beginning	begin	VERB
ajset-590	79	25	”	"	PUNCT
ajset-590	79	26	(	(	PUNCT
ajset-590	79	27	“	"	PUNCT
ajset-590	79	28	initial	initial	ADJ
ajset-590	79	29	point	point	NOUN
ajset-590	79	30	”	"	PUNCT
ajset-590	79	31	)	)	PUNCT
ajset-590	79	32	and	and	CCONJ
ajset-590	79	33	“	"	PUNCT
ajset-590	79	34	end	end	NOUN
ajset-590	79	35	”	"	PUNCT
ajset-590	79	36	(	(	PUNCT
ajset-590	79	37	“	"	PUNCT
ajset-590	79	38	terminal	terminal	ADJ
ajset-590	79	39	point	point	NOUN
ajset-590	79	40	”	"	PUNCT
ajset-590	79	41	)	)	PUNCT
ajset-590	79	42	do	do	AUX
ajset-590	79	43	not	not	PART
ajset-590	79	44	define	define	VERB
ajset-590	79	45	mathematically	mathematically	ADV
ajset-590	79	46	a	a	DET
ajset-590	79	47	geometric	geometric	ADJ
ajset-590	79	48	vector	vector	NOUN
ajset-590	79	49	(	(	PUNCT
ajset-590	79	50	because	because	SCONJ
ajset-590	79	51	the	the	DET
ajset-590	79	52	order	order	NOUN
ajset-590	79	53	of	of	ADP
ajset-590	79	54	points	point	NOUN
ajset-590	79	55	do	do	AUX
ajset-590	79	56	not	not	PART
ajset-590	79	57	define	define	VERB
ajset-590	79	58	the	the	DET
ajset-590	79	59	direction	direction	NOUN
ajset-590	79	60	of	of	ADP
ajset-590	79	61	movement	movement	NOUN
ajset-590	79	62	)	)	PUNCT
ajset-590	79	63	.	.	PUNCT
ajset-590	80	1	all	all	DET
ajset-590	80	2	points	point	NOUN
ajset-590	80	3	of	of	ADP
ajset-590	80	4	the	the	DET
ajset-590	80	5	line	line	NOUN
ajset-590	80	6	segment	segment	NOUN
ajset-590	80	7	have	have	VERB
ajset-590	80	8	one	one	NUM
ajset-590	80	9	and	and	CCONJ
ajset-590	80	10	the	the	DET
ajset-590	80	11	same	same	ADJ
ajset-590	80	12	qualitative	qualitative	ADJ
ajset-590	80	13	determinacy	determinacy	NOUN
ajset-590	80	14	:	:	PUNCT
ajset-590	80	15	concept	concept	NOUN
ajset-590	80	16	of	of	ADP
ajset-590	80	17	“	"	PUNCT
ajset-590	80	18	initial	initial	ADJ
ajset-590	80	19	point	point	NOUN
ajset-590	80	20	”	"	PUNCT
ajset-590	80	21	and	and	CCONJ
ajset-590	80	22	concept	concept	NOUN
ajset-590	80	23	of	of	ADP
ajset-590	80	24	“	"	PUNCT
ajset-590	80	25	terminal	terminal	ADJ
ajset-590	80	26	point	point	NOUN
ajset-590	80	27	”	"	PUNCT
ajset-590	80	28	are	be	AUX
ajset-590	80	29	identical	identical	ADJ
ajset-590	80	30	ones	one	NOUN
ajset-590	80	31	.	.	PUNCT
ajset-590	81	1	therefore	therefore	ADV
ajset-590	81	2	,	,	PUNCT
ajset-590	81	3	the	the	DET
ajset-590	81	4	terms	term	NOUN
ajset-590	81	5	“	"	PUNCT
ajset-590	81	6	beginning	begin	VERB
ajset-590	81	7	”	"	PUNCT
ajset-590	81	8	and	and	CCONJ
ajset-590	81	9	“	"	PUNCT
ajset-590	81	10	end	end	NOUN
ajset-590	81	11	”	"	PUNCT
ajset-590	81	12	of	of	ADP
ajset-590	81	13	the	the	DET
ajset-590	81	14	segment	segment	NOUN
ajset-590	81	15	are	be	AUX
ajset-590	81	16	not	not	PART
ajset-590	81	17	mathematical	mathematical	ADJ
ajset-590	81	18	definitions	definition	NOUN
ajset-590	81	19	of	of	ADP
ajset-590	81	20	the	the	DET
ajset-590	81	21	concept	concept	NOUN
ajset-590	81	22	of	of	ADP
ajset-590	81	23	“	"	PUNCT
ajset-590	81	24	direction	direction	NOUN
ajset-590	81	25	(	(	PUNCT
ajset-590	81	26	directivity	directivity	NOUN
ajset-590	81	27	)	)	PUNCT
ajset-590	81	28	”	"	PUNCT
ajset-590	81	29	.	.	PUNCT
ajset-590	82	1	an	an	DET
ajset-590	82	2	arrow	arrow	NOUN
ajset-590	82	3	is	be	AUX
ajset-590	82	4	a	a	DET
ajset-590	82	5	visual	visual	ADJ
ajset-590	82	6	(	(	PUNCT
ajset-590	82	7	graphic	graphic	ADJ
ajset-590	82	8	)	)	PUNCT
ajset-590	82	9	image	image	NOUN
ajset-590	82	10	of	of	ADP
ajset-590	82	11	course	course	NOUN
ajset-590	82	12	.	.	PUNCT
ajset-590	83	1	in	in	ADP
ajset-590	83	2	other	other	ADJ
ajset-590	83	3	words	word	NOUN
ajset-590	83	4	,	,	PUNCT
ajset-590	83	5	verbal	verbal	ADJ
ajset-590	83	6	,	,	PUNCT
ajset-590	83	7	literal	literal	ADJ
ajset-590	83	8	,	,	PUNCT
ajset-590	83	9	symbolic	symbolic	ADJ
ajset-590	83	10	,	,	PUNCT
ajset-590	83	11	numerical	numerical	ADJ
ajset-590	83	12	,	,	PUNCT
ajset-590	83	13	and	and	CCONJ
ajset-590	83	14	graphical	graphical	ADJ
ajset-590	83	15	representations	representation	NOUN
ajset-590	83	16	(	(	PUNCT
ajset-590	83	17	display	display	NOUN
ajset-590	83	18	)	)	PUNCT
ajset-590	83	19	of	of	ADP
ajset-590	83	20	the	the	DET
ajset-590	83	21	beginning	beginning	NOUN
ajset-590	83	22	and	and	CCONJ
ajset-590	83	23	the	the	DET
ajset-590	83	24	end	end	NOUN
ajset-590	83	25	of	of	ADP
ajset-590	83	26	the	the	DET
ajset-590	83	27	segment	segment	NOUN
ajset-590	83	28	are	be	AUX
ajset-590	83	29	not	not	PART
ajset-590	83	30	a	a	DET
ajset-590	83	31	mathematical	mathematical	ADJ
ajset-590	83	32	definition	definition	NOUN
ajset-590	83	33	of	of	ADP
ajset-590	83	34	the	the	DET
ajset-590	83	35	concept	concept	NOUN
ajset-590	83	36	of	of	ADP
ajset-590	83	37	“	"	PUNCT
ajset-590	83	38	direction	direction	NOUN
ajset-590	83	39	(	(	PUNCT
ajset-590	83	40	directivity	directivity	NOUN
ajset-590	83	41	)	)	PUNCT
ajset-590	83	42	”	"	PUNCT
ajset-590	83	43	.	.	PUNCT
ajset-590	84	1	therefore	therefore	ADV
ajset-590	84	2	,	,	PUNCT
ajset-590	84	3	the	the	DET
ajset-590	84	4	correct	correct	ADJ
ajset-590	84	5	mathematical	mathematical	ADJ
ajset-590	84	6	formalism	formalism	NOUN
ajset-590	84	7	can	can	AUX
ajset-590	84	8	not	not	PART
ajset-590	84	9	and	and	CCONJ
ajset-590	84	10	must	must	AUX
ajset-590	84	11	not	not	PART
ajset-590	84	12	contain	contain	VERB
ajset-590	84	13	the	the	DET
ajset-590	84	14	concepts	concept	NOUN
ajset-590	84	15	of	of	ADP
ajset-590	84	16	“	"	PUNCT
ajset-590	84	17	direction	direction	NOUN
ajset-590	84	18	(	(	PUNCT
ajset-590	84	19	directivity	directivity	NOUN
ajset-590	84	20	)	)	PUNCT
ajset-590	84	21	”	"	PUNCT
ajset-590	84	22	and	and	CCONJ
ajset-590	84	23	“	"	PUNCT
ajset-590	84	24	vector	vector	NOUN
ajset-590	84	25	”	"	PUNCT
ajset-590	84	26	.	.	PUNCT
ajset-590	85	1	the	the	DET
ajset-590	85	2	coordinate	coordinate	NOUN
ajset-590	85	3	system	system	NOUN
ajset-590	85	4	represents	represent	VERB
ajset-590	85	5	a	a	DET
ajset-590	85	6	system	system	NOUN
ajset-590	85	7	of	of	ADP
ajset-590	85	8	three	three	NUM
ajset-590	85	9	connected	connected	ADJ
ajset-590	85	10	drawing	drawing	NOUN
ajset-590	85	11	scales	scale	NOUN
ajset-590	85	12	:	:	PUNCT
ajset-590	85	13	straight	straight	ADJ
ajset-590	85	14	lines	line	NOUN
ajset-590	85	15	ox	ox	NOUN
ajset-590	85	16	,	,	PUNCT
ajset-590	85	17	oy	oy	INTJ
ajset-590	85	18	,	,	PUNCT
ajset-590	85	19	oz	oz	NOUN
ajset-590	85	20	,	,	PUNCT
ajset-590	85	21	which	which	PRON
ajset-590	85	22	can	can	AUX
ajset-590	85	23	not	not	PART
ajset-590	85	24	be	be	AUX
ajset-590	85	25	attributed	attribute	VERB
ajset-590	85	26	to	to	ADP
ajset-590	85	27	the	the	DET
ajset-590	85	28	direction	direction	NOUN
ajset-590	85	29	.	.	PUNCT
ajset-590	86	1	also	also	ADV
ajset-590	86	2	,	,	PUNCT
ajset-590	86	3	straight	straight	ADJ
ajset-590	86	4	linesox	linesox	NOUN
ajset-590	86	5	,	,	PUNCT
ajset-590	86	6	oy	oy	INTJ
ajset-590	86	7	,	,	PUNCT
ajset-590	86	8	oz	oz	X
ajset-590	86	9	can	can	AUX
ajset-590	86	10	not	not	PART
ajset-590	86	11	contain	contain	VERB
ajset-590	86	12	the	the	DET
ajset-590	86	13	unit	unit	NOUN
ajset-590	86	14	vectors	vector	NOUN
ajset-590	86	15	.	.	PUNCT
ajset-590	87	1	from	from	ADP
ajset-590	87	2	the	the	DET
ajset-590	87	3	point	point	NOUN
ajset-590	87	4	of	of	ADP
ajset-590	87	5	view	view	NOUN
ajset-590	87	6	of	of	ADP
ajset-590	87	7	formal	formal	ADJ
ajset-590	87	8	logic	logic	NOUN
ajset-590	87	9	,	,	PUNCT
ajset-590	87	10	the	the	DET
ajset-590	87	11	terms	term	NOUN
ajset-590	87	12	“	"	PUNCT
ajset-590	87	13	direction	direction	NOUN
ajset-590	87	14	(	(	PUNCT
ajset-590	87	15	directivity	directivity	NOUN
ajset-590	87	16	)	)	PUNCT
ajset-590	87	17	”	"	PUNCT
ajset-590	87	18	and	and	CCONJ
ajset-590	87	19	“	"	PUNCT
ajset-590	87	20	vector	vector	NOUN
ajset-590	87	21	”	"	PUNCT
ajset-590	87	22	in	in	ADP
ajset-590	87	23	mathematics	mathematic	NOUN
ajset-590	87	24	and	and	CCONJ
ajset-590	87	25	theoretical	theoretical	ADJ
ajset-590	87	26	physics	physics	NOUN
ajset-590	87	27	mean	mean	NOUN
ajset-590	87	28	representation	representation	NOUN
ajset-590	87	29	,	,	PUNCT
ajset-590	87	30	i.e.	i.e.	X
ajset-590	87	31	imaginary	imaginary	ADJ
ajset-590	87	32	image	image	NOUN
ajset-590	87	33	of	of	ADP
ajset-590	87	34	the	the	DET
ajset-590	87	35	process	process	NOUN
ajset-590	87	36	,	,	PUNCT
ajset-590	87	37	which	which	PRON
ajset-590	87	38	is	be	AUX
ajset-590	87	39	depicted	depict	VERB
ajset-590	87	40	with	with	ADP
ajset-590	87	41	the	the	DET
ajset-590	87	42	help	help	NOUN
ajset-590	87	43	of	of	ADP
ajset-590	87	44	an	an	DET
ajset-590	87	45	arrow	arrow	NOUN
ajset-590	87	46	.	.	PUNCT
ajset-590	88	1	mailto:topacademicjournals@gmail.com	mailto:topacademicjournals@gmail.com	PROPN
ajset-590	88	2	academic	academic	ADJ
ajset-590	88	3	journal	journal	NOUN
ajset-590	88	4	of	of	ADP
ajset-590	88	5	science	science	NOUN
ajset-590	88	6	,	,	PUNCT
ajset-590	88	7	engineering	engineering	NOUN
ajset-590	88	8	and	and	CCONJ
ajset-590	88	9	technology	technology	NOUN
ajset-590	88	10	vol.8	vol.8	PROPN
ajset-590	88	11	,	,	PUNCT
ajset-590	88	12	issue	issue	NOUN
ajset-590	88	13	5	5	NUM
ajset-590	88	14	;	;	PUNCT
ajset-590	88	15	september	september	PROPN
ajset-590	88	16	october	october	PROPN
ajset-590	88	17	2023	2023	NUM
ajset-590	88	18	;	;	PUNCT
ajset-590	88	19	issn	issn	PROPN
ajset-590	88	20	:	:	PUNCT
ajset-590	88	21	2837	2837	NUM
ajset-590	88	22	-	-	SYM
ajset-590	88	23	2964	2964	NUM
ajset-590	88	24	impact	impact	NOUN
ajset-590	88	25	factor	factor	NOUN
ajset-590	88	26	:	:	PUNCT
ajset-590	88	27	6.67	6.67	NUM
ajset-590	88	28	1252	1252	NUM
ajset-590	88	29	columbia	columbia	PROPN
ajset-590	88	30	rd	rd	PROPN
ajset-590	88	31	nw	nw	PROPN
ajset-590	88	32	,	,	PUNCT
ajset-590	88	33	washington	washington	PROPN
ajset-590	88	34	dc	dc	PROPN
ajset-590	88	35	,	,	PUNCT
ajset-590	88	36	united	united	PROPN
ajset-590	88	37	states	states	PROPN
ajset-590	88	38	https://topjournals.org/index.php/ajset/index	https://topjournals.org/index.php/ajset/index	PROPN
ajset-590	88	39	;	;	PUNCT
ajset-590	88	40	mail	mail	NOUN
ajset-590	88	41	:	:	PUNCT
ajset-590	89	1	topacademicjournals@gmail.com	topacademicjournals@gmail.com	X
ajset-590	89	2	12	12	NUM
ajset-590	90	1	|	|	ADV
ajset-590	90	2	a	a	DET
ajset-590	90	3	c	c	NOUN
ajset-590	90	4	a	a	PRON
ajset-590	90	5	d	d	X
ajset-590	90	6	e	e	NOUN
ajset-590	90	7	m	m	NOUN
ajset-590	90	8	i	i	NOUN
ajset-590	90	9	c	c	NOUN
ajset-590	90	10	j	j	NOUN
ajset-590	90	11	o	o	X
ajset-590	90	12	u	u	NOUN
ajset-590	90	13	r	r	NOUN
ajset-590	90	14	n	n	NOUN
ajset-590	90	15	a	a	DET
ajset-590	90	16	l	l	NOUN
ajset-590	91	1	o	o	X
ajset-590	91	2	f	f	X
ajset-590	91	3	s	s	X
ajset-590	91	4	c	c	NOUN
ajset-590	92	1	i	i	NOUN
ajset-590	92	2	e	e	PROPN
ajset-590	92	3	n	n	PROPN
ajset-590	92	4	c	c	NOUN
ajset-590	92	5	e	e	X
ajset-590	92	6	,	,	PUNCT
ajset-590	92	7	e	e	PROPN
ajset-590	92	8	n	n	PRON
ajset-590	92	9	g	g	NOUN
ajset-590	92	10	i	i	PRON
ajset-590	92	11	n	n	VERB
ajset-590	92	12	e	e	NOUN
ajset-590	92	13	e	e	NOUN
ajset-590	92	14	r	r	VERB
ajset-590	92	15	i	i	PRON
ajset-590	92	16	n	n	CCONJ
ajset-590	92	17	g	g	PROPN
ajset-590	92	18	a	a	DET
ajset-590	92	19	n	n	NOUN
ajset-590	92	20	d	d	NOUN
ajset-590	92	21	t	t	NOUN
ajset-590	92	22	e	e	X
ajset-590	92	23	c	c	NOUN
ajset-590	92	24	h	h	NOUN
ajset-590	92	25	n	n	ADV
ajset-590	92	26	o	o	NOUN
ajset-590	92	27	l	l	NOUN
ajset-590	93	1	o	o	X
ajset-590	93	2	g	g	NOUN
ajset-590	93	3	y	y	PROPN
ajset-590	93	4	|	|	ADV
ajset-590	93	5	https://topjournals.org/index.php/ajset	https://topjournals.org/index.php/ajset	VERB
ajset-590	93	6	x	x	PUNCT
ajset-590	94	1	cos	cos	ADP
ajset-590	94	2	v	v	PRON
ajset-590	94	3	v	v	NOUN
ajset-590	94	4	x	x	NOUN
ajset-590	94	5			NOUN
ajset-590	94	6	2	2	NUM
ajset-590	94	7	.	.	PUNCT
ajset-590	94	8	analysis	analysis	NOUN
ajset-590	94	9	of	of	ADP
ajset-590	94	10	the	the	DET
ajset-590	94	11	standard	standard	ADJ
ajset-590	94	12	propositions	proposition	NOUN
ajset-590	94	13	of	of	ADP
ajset-590	94	14	vector	vector	NOUN
ajset-590	94	15	algebra	algebra	NOUN
ajset-590	94	16	the	the	DET
ajset-590	94	17	mathematical	mathematical	ADJ
ajset-590	94	18	concept	concept	NOUN
ajset-590	94	19	of	of	ADP
ajset-590	94	20	“	"	PUNCT
ajset-590	94	21	vector	vector	NOUN
ajset-590	94	22	in	in	ADP
ajset-590	94	23	generall	generall	NOUN
ajset-590	94	24	”	"	PUNCT
ajset-590	94	25	can	can	AUX
ajset-590	94	26	not	not	PART
ajset-590	94	27	be	be	AUX
ajset-590	94	28	used	use	VERB
ajset-590	94	29	in	in	ADP
ajset-590	94	30	the	the	DET
ajset-590	94	31	natural	natural	ADJ
ajset-590	94	32	sciences	science	NOUN
ajset-590	94	33	:	:	PUNCT
ajset-590	94	34	this	this	DET
ajset-590	94	35	concept	concept	NOUN
ajset-590	94	36	does	do	AUX
ajset-590	94	37	not	not	PART
ajset-590	94	38	make	make	VERB
ajset-590	94	39	sense	sense	NOUN
ajset-590	94	40	in	in	ADP
ajset-590	94	41	the	the	DET
ajset-590	94	42	natural	natural	ADJ
ajset-590	94	43	sciences	science	NOUN
ajset-590	94	44	.	.	PUNCT
ajset-590	95	1	the	the	DET
ajset-590	95	2	concept	concept	NOUN
ajset-590	95	3	of	of	ADP
ajset-590	95	4	“	"	PUNCT
ajset-590	95	5	vector	vector	NOUN
ajset-590	95	6	”	"	PUNCT
ajset-590	95	7	as	as	SCONJ
ajset-590	95	8	used	use	VERB
ajset-590	95	9	in	in	ADP
ajset-590	95	10	the	the	DET
ajset-590	95	11	natural	natural	ADJ
ajset-590	95	12	sciences	science	NOUN
ajset-590	95	13	is	be	AUX
ajset-590	95	14	characterized	characterize	VERB
ajset-590	95	15	by	by	ADP
ajset-590	95	16	the	the	DET
ajset-590	95	17	concepts	concept	NOUN
ajset-590	95	18	of	of	ADP
ajset-590	95	19	“	"	PUNCT
ajset-590	95	20	denominate	denominate	NOUN
ajset-590	95	21	quantity	quantity	NOUN
ajset-590	95	22	”	"	PUNCT
ajset-590	95	23	and	and	CCONJ
ajset-590	95	24	“	"	PUNCT
ajset-590	95	25	dimension	dimension	NOUN
ajset-590	95	26	of	of	ADP
ajset-590	95	27	quantity	quantity	NOUN
ajset-590	95	28	”	"	PUNCT
ajset-590	95	29	.	.	PUNCT
ajset-590	96	1	therefore	therefore	ADV
ajset-590	96	2	,	,	PUNCT
ajset-590	96	3	analysis	analysis	NOUN
ajset-590	96	4	of	of	ADP
ajset-590	96	5	the	the	DET
ajset-590	96	6	standard	standard	ADJ
ajset-590	96	7	propositions	proposition	NOUN
ajset-590	96	8	of	of	ADP
ajset-590	96	9	vector	vector	NOUN
ajset-590	96	10	algebra	algebra	NOUN
ajset-590	96	11	must	must	AUX
ajset-590	96	12	be	be	AUX
ajset-590	96	13	done	do	VERB
ajset-590	96	14	from	from	ADP
ajset-590	96	15	this	this	DET
ajset-590	96	16	viewpoint	viewpoint	NOUN
ajset-590	96	17	.	.	PUNCT
ajset-590	97	1	1	1	X
ajset-590	97	2	.	.	X
ajset-590	97	3	as	as	SCONJ
ajset-590	97	4	is	be	AUX
ajset-590	97	5	known	know	VERB
ajset-590	97	6	,	,	PUNCT
ajset-590	97	7	the	the	DET
ajset-590	97	8	position	position	NOUN
ajset-590	97	9	of	of	ADP
ajset-590	97	10	a	a	DET
ajset-590	97	11	vector	vector	NOUN
ajset-590	97	12	in	in	ADP
ajset-590	97	13	the	the	DET
ajset-590	97	14	cartesian	cartesian	ADJ
ajset-590	97	15	coordinate	coordinate	NOUN
ajset-590	97	16	system	system	NOUN
ajset-590	97	17	oxyz	oxyz	NOUN
ajset-590	97	18	is	be	AUX
ajset-590	97	19	determined	determine	VERB
ajset-590	97	20	by	by	ADP
ajset-590	97	21	its	its	PRON
ajset-590	97	22	projections	projection	NOUN
ajset-590	97	23	.	.	PUNCT
ajset-590	98	1	the	the	DET
ajset-590	98	2	projection	projection	NOUN
ajset-590	98	3	of	of	ADP
ajset-590	98	4	the	the	DET
ajset-590	98	5	vector	vector	NOUN
ajset-590	98	6	on	on	ADP
ajset-590	98	7	the	the	DET
ajset-590	98	8	axis	axis	NOUN
ajset-590	98	9	is	be	AUX
ajset-590	98	10	defined	define	VERB
ajset-590	98	11	as	as	SCONJ
ajset-590	98	12	follows	follow	VERB
ajset-590	98	13	.	.	PUNCT
ajset-590	99	1	there	there	PRON
ajset-590	99	2	are	be	VERB
ajset-590	99	3	vector	vector	NOUN
ajset-590	99	4	v	v	NOUN
ajset-590	99	5	whose	whose	DET
ajset-590	99	6	module	module	NOUN
ajset-590	99	7	has	have	VERB
ajset-590	99	8	the	the	DET
ajset-590	99	9	dimension	dimension	NOUN
ajset-590	99	10	(	(	PUNCT
ajset-590	99	11	for	for	ADP
ajset-590	99	12	example	example	NOUN
ajset-590	99	13	,	,	PUNCT
ajset-590	99	14	the	the	DET
ajset-590	99	15	dimension	dimension	NOUN
ajset-590	99	16	of	of	ADP
ajset-590	99	17	speed	speed	NOUN
ajset-590	99	18	,	,	PUNCT
ajset-590	99	19	acceleration	acceleration	NOUN
ajset-590	99	20	dimension	dimension	NOUN
ajset-590	99	21	,	,	PUNCT
ajset-590	99	22	the	the	DET
ajset-590	99	23	dimension	dimension	NOUN
ajset-590	99	24	of	of	ADP
ajset-590	99	25	power	power	NOUN
ajset-590	99	26	)	)	PUNCT
ajset-590	99	27	and	and	CCONJ
ajset-590	99	28	the	the	DET
ajset-590	99	29	axis	axis	ADJ
ajset-590	99	30	ox	ox	NOUN
ajset-590	99	31	with	with	ADP
ajset-590	99	32	the	the	DET
ajset-590	99	33	denominate	denominate	NOUN
ajset-590	99	34	numbers	number	NOUN
ajset-590	99	35	which	which	PRON
ajset-590	99	36	have	have	VERB
ajset-590	99	37	dimension	dimension	NOUN
ajset-590	99	38	of	of	ADP
ajset-590	99	39	length	length	NOUN
ajset-590	99	40	.	.	PUNCT
ajset-590	100	1	the	the	DET
ajset-590	100	2	projection	projection	NOUN
ajset-590	100	3	of	of	ADP
ajset-590	100	4	the	the	DET
ajset-590	100	5	vector	vector	NOUN
ajset-590	100	6	v	v	NOUN
ajset-590	100	7	on	on	ADP
ajset-590	100	8	the	the	DET
ajset-590	100	9	axis	axis	NOUN
ajset-590	100	10	ox	ox	NOUN
ajset-590	100	11	is	be	AUX
ajset-590	100	12	called	call	VERB
ajset-590	100	13	the	the	DET
ajset-590	100	14	quantity	quantity	NOUN
ajset-590	100	15	(	(	PUNCT
ajset-590	100	16	module	module	NOUN
ajset-590	100	17	,	,	PUNCT
ajset-590	100	18	length	length	NOUN
ajset-590	100	19	)	)	PUNCT
ajset-590	100	20	v	v	NOUN
ajset-590	100	21	of	of	ADP
ajset-590	100	22	directed	direct	VERB
ajset-590	100	23	segment	segment	NOUN
ajset-590	100	24	vx	vx	PROPN
ajset-590	100	25	located	locate	VERB
ajset-590	100	26	(	(	PUNCT
ajset-590	100	27	placed	place	VERB
ajset-590	100	28	,	,	PUNCT
ajset-590	100	29	putted	putt	VERB
ajset-590	100	30	)	)	PUNCT
ajset-590	100	31	on	on	ADP
ajset-590	100	32	the	the	DET
ajset-590	100	33	axis	axis	ADJ
ajset-590	100	34	ox	ox	NOUN
ajset-590	100	35	:	:	PUNCT
ajset-590	100	36	where	where	SCONJ
ajset-590	100	37	is	be	AUX
ajset-590	100	38	the	the	DET
ajset-590	100	39	angle	angle	NOUN
ajset-590	100	40	between	between	ADP
ajset-590	100	41	the	the	DET
ajset-590	100	42	vector	vector	NOUN
ajset-590	100	43	v	v	NOUN
ajset-590	100	44	and	and	CCONJ
ajset-590	100	45	the	the	DET
ajset-590	100	46	axis	axis	ADJ
ajset-590	100	47	ox	ox	NOUN
ajset-590	100	48	.	.	PUNCT
ajset-590	101	1	in	in	ADP
ajset-590	101	2	general	general	ADJ
ajset-590	101	3	case	case	NOUN
ajset-590	101	4	,	,	PUNCT
ajset-590	101	5	the	the	DET
ajset-590	101	6	vector	vector	NOUN
ajset-590	101	7	v	v	NOUN
ajset-590	101	8	is	be	AUX
ajset-590	101	9	decomposed	decompose	VERB
ajset-590	101	10	into	into	ADP
ajset-590	101	11	components	component	NOUN
ajset-590	101	12	under	under	ADP
ajset-590	101	13	the	the	DET
ajset-590	101	14	cartesian	cartesian	ADJ
ajset-590	101	15	orthonormal	orthonormal	ADJ
ajset-590	101	16	basis	basis	NOUN
ajset-590	101	17	i	i	PRON
ajset-590	101	18	,	,	PUNCT
ajset-590	101	19	j	j	PROPN
ajset-590	101	20	,	,	PUNCT
ajset-590	101	21	k	k	PROPN
ajset-590	101	22	as	as	SCONJ
ajset-590	101	23	follows	follow	VERB
ajset-590	101	24	:	:	PUNCT
ajset-590	102	1	v	v	X
ajset-590	102	2	vx	vx	INTJ
ajset-590	103	1	i	i	PROPN
ajset-590	103	2	vy	vy	PROPN
ajset-590	103	3	j	j	PROPN
ajset-590	103	4	vz	vz	PROPN
ajset-590	103	5	k	k	PROPN
ajset-590	103	6	where	where	SCONJ
ajset-590	103	7	i	i	PRON
ajset-590	103	8	,	,	PUNCT
ajset-590	103	9	j	j	PROPN
ajset-590	103	10	,	,	PUNCT
ajset-590	103	11	k	k	PROPN
ajset-590	103	12	are	be	AUX
ajset-590	103	13	the	the	DET
ajset-590	103	14	unit	unit	NOUN
ajset-590	103	15	vectors	vector	NOUN
ajset-590	103	16	of	of	ADP
ajset-590	103	17	the	the	DET
ajset-590	103	18	cartesian	cartesian	ADJ
ajset-590	103	19	coordinate	coordinate	NOUN
ajset-590	103	20	system	system	NOUN
ajset-590	103	21	;	;	PUNCT
ajset-590	103	22	vx	vx	X
ajset-590	103	23	,	,	PUNCT
ajset-590	103	24	vy	vy	PROPN
ajset-590	103	25	,	,	PUNCT
ajset-590	103	26	vz	vz	PROPN
ajset-590	103	27	are	be	AUX
ajset-590	103	28	the	the	DET
ajset-590	103	29	projections	projection	NOUN
ajset-590	103	30	of	of	ADP
ajset-590	103	31	the	the	DET
ajset-590	103	32	vector	vector	NOUN
ajset-590	103	33	on	on	ADP
ajset-590	103	34	the	the	DET
ajset-590	103	35	corresponding	corresponding	ADJ
ajset-590	103	36	axes	axis	NOUN
ajset-590	103	37	.	.	PUNCT
ajset-590	104	1	the	the	DET
ajset-590	104	2	principal	principal	ADJ
ajset-590	104	3	importance	importance	NOUN
ajset-590	104	4	of	of	ADP
ajset-590	104	5	the	the	DET
ajset-590	104	6	basis	basis	NOUN
ajset-590	104	7	i	i	PRON
ajset-590	104	8	,	,	PUNCT
ajset-590	104	9	j	j	PROPN
ajset-590	104	10	,	,	PUNCT
ajset-590	104	11	k	k	PROPN
ajset-590	104	12	is	be	AUX
ajset-590	104	13	that	that	SCONJ
ajset-590	104	14	the	the	DET
ajset-590	104	15	linear	linear	ADJ
ajset-590	104	16	operations	operation	NOUN
ajset-590	104	17	on	on	ADP
ajset-590	104	18	vectors	vector	NOUN
ajset-590	104	19	under	under	ADP
ajset-590	104	20	the	the	DET
ajset-590	104	21	given	give	VERB
ajset-590	104	22	basis	basis	NOUN
ajset-590	104	23	become	become	VERB
ajset-590	104	24	the	the	DET
ajset-590	104	25	usual	usual	ADJ
ajset-590	104	26	linear	linear	ADJ
ajset-590	104	27	operations	operation	NOUN
ajset-590	104	28	on	on	ADP
ajset-590	104	29	numbers	number	NOUN
ajset-590	104	30	–	–	PUNCT
ajset-590	104	31	the	the	DET
ajset-590	104	32	coordinates	coordinate	NOUN
ajset-590	104	33	of	of	ADP
ajset-590	104	34	these	these	DET
ajset-590	104	35	vectors	vector	NOUN
ajset-590	104	36	.	.	PUNCT
ajset-590	105	1	in	in	ADP
ajset-590	105	2	my	my	PRON
ajset-590	105	3	opinion	opinion	NOUN
ajset-590	105	4	,	,	PUNCT
ajset-590	105	5	these	these	DET
ajset-590	105	6	standard	standard	ADJ
ajset-590	105	7	expressions	expression	NOUN
ajset-590	105	8	are	be	AUX
ajset-590	105	9	not	not	PART
ajset-590	105	10	free	free	ADJ
ajset-590	105	11	from	from	ADP
ajset-590	105	12	objection	objection	NOUN
ajset-590	105	13	.	.	PUNCT
ajset-590	106	1	the	the	DET
ajset-590	106	2	objection	objection	NOUN
ajset-590	106	3	is	be	AUX
ajset-590	106	4	that	that	SCONJ
ajset-590	106	5	the	the	DET
ajset-590	106	6	standard	standard	ADJ
ajset-590	106	7	expressions	expression	NOUN
ajset-590	106	8	are	be	AUX
ajset-590	106	9	contrary	contrary	ADJ
ajset-590	106	10	to	to	ADP
ajset-590	106	11	the	the	DET
ajset-590	106	12	formal	formal	ADJ
ajset-590	106	13	-	-	PUNCT
ajset-590	106	14	logical	logical	ADJ
ajset-590	106	15	laws	law	NOUN
ajset-590	106	16	.	.	PUNCT
ajset-590	107	1	really	really	ADV
ajset-590	107	2	,	,	PUNCT
ajset-590	107	3	the	the	DET
ajset-590	107	4	standard	standard	ADJ
ajset-590	107	5	expressions	expression	NOUN
ajset-590	107	6	assert	assert	VERB
ajset-590	107	7	that	that	DET
ajset-590	107	8	segment	segment	NOUN
ajset-590	107	9	vx	vx	PROPN
ajset-590	107	10	lies	lie	NOUN
ajset-590	107	11	on	on	ADP
ajset-590	107	12	the	the	DET
ajset-590	107	13	axis	axis	NOUN
ajset-590	107	14	ox	ox	NOUN
ajset-590	107	15	(	(	PUNCT
ajset-590	107	16	i.e.	i.e.	X
ajset-590	107	17	,	,	PUNCT
ajset-590	107	18	segment	segment	NOUN
ajset-590	107	19	vx	vx	PROPN
ajset-590	107	20	coincides	coincide	VERB
ajset-590	107	21	with	with	ADP
ajset-590	107	22	the	the	DET
ajset-590	107	23	segment	segment	NOUN
ajset-590	107	24	of	of	ADP
ajset-590	107	25	axis	axis	NOUN
ajset-590	107	26	ox	ox	NOUN
ajset-590	107	27	)	)	PUNCT
ajset-590	107	28	.	.	PUNCT
ajset-590	108	1	from	from	ADP
ajset-590	108	2	the	the	DET
ajset-590	108	3	point	point	NOUN
ajset-590	108	4	of	of	ADP
ajset-590	108	5	view	view	NOUN
ajset-590	108	6	of	of	ADP
ajset-590	108	7	formal	formal	ADJ
ajset-590	108	8	-	-	PUNCT
ajset-590	108	9	logical	logical	ADJ
ajset-590	108	10	law	law	NOUN
ajset-590	108	11	of	of	ADP
ajset-590	108	12	identity	identity	NOUN
ajset-590	108	13	,	,	PUNCT
ajset-590	108	14	this	this	PRON
ajset-590	108	15	implies	imply	VERB
ajset-590	108	16	that	that	SCONJ
ajset-590	108	17	these	these	DET
ajset-590	108	18	segments	segment	NOUN
ajset-590	108	19	have	have	VERB
ajset-590	108	20	the	the	DET
ajset-590	108	21	same	same	ADJ
ajset-590	108	22	qualitative	qualitative	ADJ
ajset-590	108	23	determinacy	determinacy	NOUN
ajset-590	108	24	(	(	PUNCT
ajset-590	108	25	i.e.	i.e.	X
ajset-590	108	26	,	,	PUNCT
ajset-590	108	27	the	the	DET
ajset-590	108	28	same	same	ADJ
ajset-590	108	29	sense	sense	NOUN
ajset-590	108	30	,	,	PUNCT
ajset-590	108	31	the	the	DET
ajset-590	108	32	same	same	ADJ
ajset-590	108	33	dimensions	dimension	NOUN
ajset-590	108	34	):	):	PUNCT
ajset-590	108	35	(	(	PUNCT
ajset-590	108	36	qualitative	qualitative	ADJ
ajset-590	108	37	determinacy	determinacy	NOUN
ajset-590	108	38	of	of	ADP
ajset-590	108	39	the	the	DET
ajset-590	108	40	segment	segment	NOUN
ajset-590	108	41	vx	vx	PROPN
ajset-590	108	42	)	)	PUNCT
ajset-590	108	43	=	=	SYM
ajset-590	108	44	(	(	PUNCT
ajset-590	108	45	qualitative	qualitative	ADJ
ajset-590	108	46	determinacy	determinacy	NOUN
ajset-590	108	47	of	of	ADP
ajset-590	108	48	the	the	DET
ajset-590	108	49	segment	segment	NOUN
ajset-590	108	50	of	of	ADP
ajset-590	108	51	the	the	DET
ajset-590	108	52	axis	axis	NOUN
ajset-590	108	53	ox	ox	NOUN
ajset-590	108	54	)	)	PUNCT
ajset-590	108	55	.	.	PUNCT
ajset-590	109	1	but	but	CCONJ
ajset-590	109	2	the	the	DET
ajset-590	109	3	segment	segment	NOUN
ajset-590	109	4	vx	vx	AUX
ajset-590	109	5	can	can	AUX
ajset-590	109	6	not	not	PART
ajset-590	109	7	lie	lie	VERB
ajset-590	109	8	on	on	ADP
ajset-590	109	9	the	the	DET
ajset-590	109	10	axis	axis	NOUN
ajset-590	109	11	ox	ox	NOUN
ajset-590	109	12	(	(	PUNCT
ajset-590	109	13	i.e.	i.e.	X
ajset-590	109	14	,	,	PUNCT
ajset-590	109	15	the	the	DET
ajset-590	109	16	segment	segment	NOUN
ajset-590	109	17	vx	vx	AUX
ajset-590	109	18	can	can	AUX
ajset-590	109	19	not	not	PART
ajset-590	109	20	be	be	AUX
ajset-590	109	21	coincided	coincide	VERB
ajset-590	109	22	with	with	ADP
ajset-590	109	23	a	a	DET
ajset-590	109	24	segment	segment	NOUN
ajset-590	109	25	of	of	ADP
ajset-590	109	26	the	the	DET
ajset-590	109	27	axisox	axisox	NOUN
ajset-590	109	28	)	)	PUNCT
ajset-590	109	29	because	because	SCONJ
ajset-590	109	30	these	these	DET
ajset-590	109	31	segments	segment	NOUN
ajset-590	109	32	have	have	VERB
ajset-590	109	33	different	different	ADJ
ajset-590	109	34	dimensions	dimension	NOUN
ajset-590	109	35	and	and	CCONJ
ajset-590	109	36	,	,	PUNCT
ajset-590	109	37	therefore	therefore	ADV
ajset-590	109	38	,	,	PUNCT
ajset-590	109	39	different	different	ADJ
ajset-590	109	40	qualitative	qualitative	ADJ
ajset-590	109	41	determinacy	determinacy	NOUN
ajset-590	109	42	(	(	PUNCT
ajset-590	109	43	i.e.	i.e.	X
ajset-590	109	44	,	,	PUNCT
ajset-590	109	45	different	different	ADJ
ajset-590	109	46	senses	sense	NOUN
ajset-590	109	47	)	)	PUNCT
ajset-590	109	48	.	.	PUNCT
ajset-590	110	1	this	this	DET
ajset-590	110	2	statement	statement	NOUN
ajset-590	110	3	is	be	AUX
ajset-590	110	4	expressed	express	VERB
ajset-590	110	5	by	by	ADP
ajset-590	110	6	formal	formal	ADJ
ajset-590	110	7	-	-	PUNCT
ajset-590	110	8	logical	logical	ADJ
ajset-590	110	9	law	law	NOUN
ajset-590	110	10	of	of	ADP
ajset-590	110	11	absence	absence	NOUN
ajset-590	110	12	of	of	ADP
ajset-590	110	13	contradiction	contradiction	NOUN
ajset-590	110	14	:	:	PUNCT
ajset-590	110	15	(	(	PUNCT
ajset-590	110	16	qualitative	qualitative	ADJ
ajset-590	110	17	determinacy	determinacy	NOUN
ajset-590	110	18	of	of	ADP
ajset-590	110	19	the	the	DET
ajset-590	110	20	segment	segment	NOUN
ajset-590	110	21	vx	vx	PROPN
ajset-590	110	22	)	)	PUNCT
ajset-590	110	23	(	(	PUNCT
ajset-590	110	24	qualitative	qualitative	ADJ
ajset-590	110	25	determinacy	determinacy	NOUN
ajset-590	110	26	of	of	ADP
ajset-590	110	27	the	the	DET
ajset-590	110	28	segment	segment	NOUN
ajset-590	110	29	of	of	ADP
ajset-590	110	30	the	the	DET
ajset-590	110	31	axis	axis	NOUN
ajset-590	110	32	ox	ox	NOUN
ajset-590	110	33	)	)	PUNCT
ajset-590	110	34	.	.	PUNCT
ajset-590	111	1	mailto:topacademicjournals@gmail.com	mailto:topacademicjournals@gmail.com	PROPN
ajset-590	111	2	academic	academic	ADJ
ajset-590	111	3	journal	journal	NOUN
ajset-590	111	4	of	of	ADP
ajset-590	111	5	science	science	NOUN
ajset-590	111	6	,	,	PUNCT
ajset-590	111	7	engineering	engineering	NOUN
ajset-590	111	8	and	and	CCONJ
ajset-590	111	9	technology	technology	NOUN
ajset-590	111	10	vol.8	vol.8	PROPN
ajset-590	111	11	,	,	PUNCT
ajset-590	111	12	issue	issue	NOUN
ajset-590	111	13	5	5	NUM
ajset-590	111	14	;	;	PUNCT
ajset-590	111	15	september	september	PROPN
ajset-590	111	16	october	october	PROPN
ajset-590	111	17	2023	2023	NUM
ajset-590	111	18	;	;	PUNCT
ajset-590	111	19	issn	issn	PROPN
ajset-590	111	20	:	:	PUNCT
ajset-590	111	21	2837	2837	NUM
ajset-590	111	22	-	-	SYM
ajset-590	111	23	2964	2964	NUM
ajset-590	111	24	impact	impact	NOUN
ajset-590	111	25	factor	factor	NOUN
ajset-590	111	26	:	:	PUNCT
ajset-590	111	27	6.67	6.67	NUM
ajset-590	111	28	1252	1252	NUM
ajset-590	111	29	columbia	columbia	PROPN
ajset-590	111	30	rd	rd	PROPN
ajset-590	111	31	nw	nw	PROPN
ajset-590	111	32	,	,	PUNCT
ajset-590	111	33	washington	washington	PROPN
ajset-590	111	34	dc	dc	PROPN
ajset-590	111	35	,	,	PUNCT
ajset-590	111	36	united	united	PROPN
ajset-590	111	37	states	states	PROPN
ajset-590	111	38	https://topjournals.org/index.php/ajset/index	https://topjournals.org/index.php/ajset/index	PROPN
ajset-590	111	39	;	;	PUNCT
ajset-590	111	40	mail	mail	NOUN
ajset-590	111	41	:	:	PUNCT
ajset-590	111	42	topacademicjournals@gmail.com	topacademicjournals@gmail.com	X
ajset-590	112	1	13	13	NUM
ajset-590	113	1	|	|	ADV
ajset-590	113	2	a	a	DET
ajset-590	113	3	c	c	NOUN
ajset-590	113	4	a	a	PRON
ajset-590	113	5	d	d	X
ajset-590	113	6	e	e	NOUN
ajset-590	113	7	m	m	NOUN
ajset-590	113	8	i	i	NOUN
ajset-590	113	9	c	c	NOUN
ajset-590	113	10	j	j	NOUN
ajset-590	113	11	o	o	X
ajset-590	113	12	u	u	NOUN
ajset-590	113	13	r	r	NOUN
ajset-590	113	14	n	n	NOUN
ajset-590	113	15	a	a	DET
ajset-590	113	16	l	l	NOUN
ajset-590	114	1	o	o	X
ajset-590	114	2	f	f	X
ajset-590	114	3	s	s	X
ajset-590	114	4	c	c	NOUN
ajset-590	115	1	i	i	NOUN
ajset-590	115	2	e	e	PROPN
ajset-590	115	3	n	n	PROPN
ajset-590	115	4	c	c	NOUN
ajset-590	115	5	e	e	X
ajset-590	115	6	,	,	PUNCT
ajset-590	115	7	e	e	PROPN
ajset-590	115	8	n	n	PRON
ajset-590	115	9	g	g	NOUN
ajset-590	115	10	i	i	PRON
ajset-590	115	11	n	n	VERB
ajset-590	115	12	e	e	NOUN
ajset-590	115	13	e	e	NOUN
ajset-590	115	14	r	r	VERB
ajset-590	115	15	i	i	PRON
ajset-590	115	16	n	n	CCONJ
ajset-590	115	17	g	g	PROPN
ajset-590	115	18	a	a	DET
ajset-590	115	19	n	n	NOUN
ajset-590	115	20	d	d	NOUN
ajset-590	115	21	t	t	NOUN
ajset-590	115	22	e	e	X
ajset-590	115	23	c	c	NOUN
ajset-590	115	24	h	h	NOUN
ajset-590	115	25	n	n	ADV
ajset-590	115	26	o	o	NOUN
ajset-590	115	27	l	l	NOUN
ajset-590	116	1	o	o	X
ajset-590	116	2	g	g	NOUN
ajset-590	116	3	y	y	PROPN
ajset-590	116	4	|	|	ADV
ajset-590	116	5	https://topjournals.org/index.php/ajset	https://topjournals.org/index.php/ajset	VERB
ajset-590	116	6	consequently	consequently	ADV
ajset-590	116	7	,	,	PUNCT
ajset-590	116	8	the	the	DET
ajset-590	116	9	mathematical	mathematical	ADJ
ajset-590	116	10	operation	operation	NOUN
ajset-590	116	11	of	of	ADP
ajset-590	116	12	finding	find	VERB
ajset-590	116	13	the	the	DET
ajset-590	116	14	projection	projection	NOUN
ajset-590	116	15	of	of	ADP
ajset-590	116	16	the	the	DET
ajset-590	116	17	vector	vector	NOUN
ajset-590	116	18	v	v	NOUN
ajset-590	116	19	on	on	ADP
ajset-590	116	20	the	the	DET
ajset-590	116	21	coordinate	coordinate	NOUN
ajset-590	116	22	axes	axis	NOUN
ajset-590	116	23	represents	represent	VERB
ajset-590	116	24	the	the	DET
ajset-590	116	25	formal	formal	ADJ
ajset-590	116	26	-	-	PUNCT
ajset-590	116	27	logical	logical	ADJ
ajset-590	116	28	error	error	NOUN
ajset-590	116	29	:	:	PUNCT
ajset-590	116	30	violation	violation	NOUN
ajset-590	116	31	of	of	ADP
ajset-590	116	32	the	the	DET
ajset-590	116	33	law	law	NOUN
ajset-590	116	34	of	of	ADP
ajset-590	116	35	absence	absence	NOUN
ajset-590	116	36	of	of	ADP
ajset-590	116	37	contradiction	contradiction	NOUN
ajset-590	116	38	.	.	PUNCT
ajset-590	117	1	2	2	X
ajset-590	117	2	.	.	AUX
ajset-590	117	3	as	as	SCONJ
ajset-590	117	4	is	be	AUX
ajset-590	117	5	known	know	VERB
ajset-590	117	6	,	,	PUNCT
ajset-590	117	7	the	the	DET
ajset-590	117	8	rule	rule	NOUN
ajset-590	117	9	of	of	ADP
ajset-590	117	10	addition	addition	NOUN
ajset-590	117	11	of	of	ADP
ajset-590	117	12	vectors	vector	NOUN
ajset-590	117	13	having	have	VERB
ajset-590	117	14	the	the	DET
ajset-590	117	15	same	same	ADJ
ajset-590	117	16	qualitative	qualitative	ADJ
ajset-590	117	17	determinacy	determinacy	NOUN
ajset-590	117	18	is	be	AUX
ajset-590	117	19	called	call	VERB
ajset-590	117	20	the	the	DET
ajset-590	117	21	“	"	PUNCT
ajset-590	117	22	triangle	triangle	NOUN
ajset-590	117	23	rule	rule	NOUN
ajset-590	117	24	”	"	PUNCT
ajset-590	117	25	or	or	CCONJ
ajset-590	117	26	“	"	PUNCT
ajset-590	117	27	parallelogram	parallelogram	NOUN
ajset-590	117	28	rule	rule	NOUN
ajset-590	117	29	”	"	PUNCT
ajset-590	117	30	.	.	PUNCT
ajset-590	118	1	standard	standard	ADJ
ajset-590	118	2	operation	operation	NOUN
ajset-590	118	3	of	of	ADP
ajset-590	118	4	addition	addition	NOUN
ajset-590	118	5	of	of	ADP
ajset-590	118	6	two	two	NUM
ajset-590	118	7	vectors	vector	NOUN
ajset-590	118	8	is	be	AUX
ajset-590	118	9	defined	define	VERB
ajset-590	118	10	as	as	SCONJ
ajset-590	118	11	follows	follow	VERB
ajset-590	118	12	:	:	PUNCT
ajset-590	118	13	the	the	DET
ajset-590	118	14	sum	sum	NOUN
ajset-590	118	15	v1	v1	NOUN
ajset-590	118	16	v2	v2	PROPN
ajset-590	118	17	of	of	ADP
ajset-590	118	18	two	two	NUM
ajset-590	118	19	vectors	vector	NOUN
ajset-590	118	20	v1	v1	VERB
ajset-590	118	21	and	and	CCONJ
ajset-590	118	22	v2	v2	PROPN
ajset-590	118	23	is	be	AUX
ajset-590	118	24	called	call	VERB
ajset-590	118	25	the	the	DET
ajset-590	118	26	vector	vector	NOUN
ajset-590	118	27	running	run	VERB
ajset-590	118	28	from	from	ADP
ajset-590	118	29	the	the	DET
ajset-590	118	30	beginning	beginning	NOUN
ajset-590	118	31	of	of	ADP
ajset-590	118	32	the	the	DET
ajset-590	118	33	vector	vector	NOUN
ajset-590	118	34	v1	v1	NOUN
ajset-590	118	35	to	to	ADP
ajset-590	118	36	the	the	DET
ajset-590	118	37	end	end	NOUN
ajset-590	118	38	of	of	ADP
ajset-590	118	39	the	the	DET
ajset-590	118	40	vector	vector	NOUN
ajset-590	118	41	v2	v2	NOUN
ajset-590	118	42	under	under	ADP
ajset-590	118	43	the	the	DET
ajset-590	118	44	condition	condition	NOUN
ajset-590	118	45	that	that	SCONJ
ajset-590	118	46	the	the	DET
ajset-590	118	47	vector	vector	NOUN
ajset-590	118	48	v2	v2	PROPN
ajset-590	118	49	is	be	AUX
ajset-590	118	50	applied	apply	VERB
ajset-590	118	51	to	to	ADP
ajset-590	118	52	the	the	DET
ajset-590	118	53	end	end	NOUN
ajset-590	118	54	of	of	ADP
ajset-590	118	55	the	the	DET
ajset-590	118	56	vector	vector	NOUN
ajset-590	118	57	v1	v1	NOUN
ajset-590	118	58	.	.	PUNCT
ajset-590	119	1	under	under	ADP
ajset-590	119	2	the	the	DET
ajset-590	119	3	addition	addition	NOUN
ajset-590	119	4	of	of	ADP
ajset-590	119	5	two	two	NUM
ajset-590	119	6	vectors	vector	NOUN
ajset-590	119	7	,	,	PUNCT
ajset-590	119	8	their	their	PRON
ajset-590	119	9	projections	projection	NOUN
ajset-590	119	10	on	on	ADP
ajset-590	119	11	an	an	DET
ajset-590	119	12	arbitrary	arbitrary	ADJ
ajset-590	119	13	axis	axis	NOUN
ajset-590	119	14	are	be	AUX
ajset-590	119	15	added	add	VERB
ajset-590	119	16	,	,	PUNCT
ajset-590	119	17	and	and	CCONJ
ajset-590	119	18	under	under	ADP
ajset-590	119	19	the	the	DET
ajset-590	119	20	multiplication	multiplication	NOUN
ajset-590	119	21	of	of	ADP
ajset-590	119	22	a	a	DET
ajset-590	119	23	vector	vector	NOUN
ajset-590	119	24	by	by	ADP
ajset-590	119	25	any	any	DET
ajset-590	119	26	number	number	NOUN
ajset-590	119	27	,	,	PUNCT
ajset-590	119	28	its	its	PRON
ajset-590	119	29	projection	projection	NOUN
ajset-590	119	30	on	on	ADP
ajset-590	119	31	an	an	DET
ajset-590	119	32	arbitrary	arbitrary	ADJ
ajset-590	119	33	axis	axis	NOUN
ajset-590	119	34	is	be	AUX
ajset-590	119	35	multiplied	multiply	VERB
ajset-590	119	36	by	by	ADP
ajset-590	119	37	this	this	DET
ajset-590	119	38	number	number	NOUN
ajset-590	119	39	.	.	PUNCT
ajset-590	120	1	in	in	ADP
ajset-590	120	2	my	my	PRON
ajset-590	120	3	view	view	NOUN
ajset-590	120	4	,	,	PUNCT
ajset-590	120	5	these	these	DET
ajset-590	120	6	standard	standard	ADJ
ajset-590	120	7	assertions	assertion	NOUN
ajset-590	120	8	are	be	AUX
ajset-590	120	9	not	not	PART
ajset-590	120	10	free	free	ADJ
ajset-590	120	11	from	from	ADP
ajset-590	120	12	objection	objection	NOUN
ajset-590	120	13	.	.	PUNCT
ajset-590	121	1	the	the	DET
ajset-590	121	2	objection	objection	NOUN
ajset-590	121	3	is	be	AUX
ajset-590	121	4	that	that	SCONJ
ajset-590	121	5	the	the	DET
ajset-590	121	6	standard	standard	ADJ
ajset-590	121	7	assertions	assertion	NOUN
ajset-590	121	8	are	be	AUX
ajset-590	121	9	contrary	contrary	ADJ
ajset-590	121	10	to	to	ADP
ajset-590	121	11	the	the	DET
ajset-590	121	12	formal	formal	ADJ
ajset-590	121	13	-	-	PUNCT
ajset-590	121	14	logical	logical	ADJ
ajset-590	121	15	laws	law	NOUN
ajset-590	121	16	.	.	PUNCT
ajset-590	122	1	really	really	ADV
ajset-590	122	2	,	,	PUNCT
ajset-590	122	3	segments	segment	NOUN
ajset-590	122	4	of	of	ADP
ajset-590	122	5	vectors	vector	NOUN
ajset-590	122	6	and	and	CCONJ
ajset-590	122	7	segments	segment	NOUN
ajset-590	122	8	of	of	ADP
ajset-590	122	9	arbitrary	arbitrary	ADJ
ajset-590	122	10	axis	axis	NOUN
ajset-590	122	11	have	have	VERB
ajset-590	122	12	different	different	ADJ
ajset-590	122	13	qualitative	qualitative	ADJ
ajset-590	122	14	determinacy	determinacy	NOUN
ajset-590	122	15	(	(	PUNCT
ajset-590	122	16	i.e.	i.e.	X
ajset-590	122	17	,	,	PUNCT
ajset-590	122	18	different	different	ADJ
ajset-590	122	19	senses	sense	NOUN
ajset-590	122	20	)	)	PUNCT
ajset-590	122	21	.	.	PUNCT
ajset-590	123	1	this	this	PRON
ajset-590	123	2	implies	imply	VERB
ajset-590	123	3	that	that	SCONJ
ajset-590	123	4	the	the	DET
ajset-590	123	5	segments	segment	NOUN
ajset-590	123	6	of	of	ADP
ajset-590	123	7	the	the	DET
ajset-590	123	8	vectors	vector	NOUN
ajset-590	123	9	v1	v1	VERB
ajset-590	123	10	and	and	CCONJ
ajset-590	123	11	v2	v2	NOUN
ajset-590	123	12	can	can	AUX
ajset-590	123	13	not	not	PART
ajset-590	123	14	lie	lie	VERB
ajset-590	123	15	on	on	ADP
ajset-590	123	16	a	a	DET
ajset-590	123	17	segment	segment	NOUN
ajset-590	123	18	of	of	ADP
ajset-590	123	19	an	an	DET
ajset-590	123	20	arbitrary	arbitrary	ADJ
ajset-590	123	21	axis	axis	NOUN
ajset-590	123	22	(	(	PUNCT
ajset-590	123	23	i.e.	i.e.	X
ajset-590	123	24	,	,	PUNCT
ajset-590	123	25	the	the	DET
ajset-590	123	26	segments	segment	NOUN
ajset-590	123	27	of	of	ADP
ajset-590	123	28	the	the	DET
ajset-590	123	29	vectors	vector	NOUN
ajset-590	123	30	can	can	AUX
ajset-590	123	31	not	not	PART
ajset-590	123	32	coincide	coincide	VERB
ajset-590	123	33	with	with	ADP
ajset-590	123	34	a	a	DET
ajset-590	123	35	segment	segment	NOUN
ajset-590	123	36	of	of	ADP
ajset-590	123	37	an	an	DET
ajset-590	123	38	arbitrary	arbitrary	ADJ
ajset-590	123	39	axis	axis	NOUN
ajset-590	123	40	)	)	PUNCT
ajset-590	123	41	.	.	PUNCT
ajset-590	124	1	from	from	ADP
ajset-590	124	2	the	the	DET
ajset-590	124	3	point	point	NOUN
ajset-590	124	4	of	of	ADP
ajset-590	124	5	view	view	NOUN
ajset-590	124	6	of	of	ADP
ajset-590	124	7	formal	formal	ADJ
ajset-590	124	8	-	-	PUNCT
ajset-590	124	9	logical	logical	ADJ
ajset-590	124	10	law	law	NOUN
ajset-590	124	11	of	of	ADP
ajset-590	124	12	identity	identity	NOUN
ajset-590	124	13	,	,	PUNCT
ajset-590	124	14	these	these	DET
ajset-590	124	15	segments	segment	NOUN
ajset-590	124	16	can	can	AUX
ajset-590	124	17	be	be	AUX
ajset-590	124	18	coincided	coincide	VERB
ajset-590	124	19	if	if	SCONJ
ajset-590	124	20	only	only	ADV
ajset-590	124	21	they	they	PRON
ajset-590	124	22	have	have	VERB
ajset-590	124	23	identical	identical	ADJ
ajset-590	124	24	qualitative	qualitative	ADJ
ajset-590	124	25	determinacy	determinacy	NOUN
ajset-590	124	26	(	(	PUNCT
ajset-590	124	27	i.e.	i.e.	X
ajset-590	124	28	,	,	PUNCT
ajset-590	124	29	the	the	DET
ajset-590	124	30	same	same	ADJ
ajset-590	124	31	dimension	dimension	NOUN
ajset-590	124	32	,	,	PUNCT
ajset-590	124	33	the	the	DET
ajset-590	124	34	same	same	ADJ
ajset-590	124	35	meaning	meaning	NOUN
ajset-590	124	36	)	)	PUNCT
ajset-590	124	37	.	.	PUNCT
ajset-590	125	1	3	3	X
ajset-590	125	2	.	.	X
ajset-590	125	3	as	as	SCONJ
ajset-590	125	4	is	be	AUX
ajset-590	125	5	known	know	VERB
ajset-590	125	6	,	,	PUNCT
ajset-590	125	7	the	the	DET
ajset-590	125	8	scalar	scalar	ADJ
ajset-590	125	9	product	product	NOUN
ajset-590	125	10	of	of	ADP
ajset-590	125	11	two	two	NUM
ajset-590	125	12	vectors	vector	NOUN
ajset-590	125	13	v	v	NOUN
ajset-590	125	14	and	and	CCONJ
ajset-590	125	15	f	f	PROPN
ajset-590	125	16	is	be	AUX
ajset-590	125	17	defined	define	VERB
ajset-590	125	18	as	as	SCONJ
ajset-590	125	19	follows	follow	VERB
ajset-590	125	20	:	:	PUNCT
ajset-590	125	21	(	(	PUNCT
ajset-590	125	22	a	a	X
ajset-590	125	23	)	)	PUNCT
ajset-590	125	24	one	one	NOUN
ajset-590	125	25	brings	bring	VERB
ajset-590	125	26	the	the	DET
ajset-590	125	27	initial	initial	ADJ
ajset-590	125	28	points	point	NOUN
ajset-590	125	29	of	of	ADP
ajset-590	125	30	vectors	vector	NOUN
ajset-590	125	31	in	in	ADP
ajset-590	125	32	coincidence	coincidence	NOUN
ajset-590	125	33	with	with	ADP
ajset-590	125	34	each	each	DET
ajset-590	125	35	other	other	ADJ
ajset-590	125	36	(	(	PUNCT
ajset-590	125	37	i.e.	i.e.	X
ajset-590	125	38	,	,	PUNCT
ajset-590	125	39	the	the	DET
ajset-590	125	40	initial	initial	ADJ
ajset-590	125	41	points	point	NOUN
ajset-590	125	42	are	be	AUX
ajset-590	125	43	connected	connect	VERB
ajset-590	125	44	)	)	PUNCT
ajset-590	125	45	;	;	PUNCT
ajset-590	125	46	(	(	PUNCT
ajset-590	125	47	b	b	X
ajset-590	125	48	)	)	PUNCT
ajset-590	125	49	one	one	NOUN
ajset-590	125	50	postulates	postulate	VERB
ajset-590	125	51	the	the	DET
ajset-590	125	52	relation	relation	NOUN
ajset-590	125	53	v	v	ADP
ajset-590	125	54	f	f	PROPN
ajset-590	125	55	v	v	X
ajset-590	125	56	f	f	PROPN
ajset-590	125	57	cos	cos	PROPN
ajset-590	125	58	where	where	SCONJ
ajset-590	125	59	the	the	DET
ajset-590	125	60	point	point	NOUN
ajset-590	125	61	between	between	ADP
ajset-590	125	62	symbols	symbol	NOUN
ajset-590	125	63	of	of	ADP
ajset-590	125	64	vectors	vector	NOUN
ajset-590	125	65	denotes	denote	VERB
ajset-590	125	66	the	the	DET
ajset-590	125	67	operation	operation	NOUN
ajset-590	125	68	of	of	ADP
ajset-590	125	69	scalar	scalar	ADJ
ajset-590	125	70	multiplication	multiplication	NOUN
ajset-590	125	71	of	of	ADP
ajset-590	125	72	vectors	vector	NOUN
ajset-590	125	73	,	,	PUNCT
ajset-590	125	74	is	be	AUX
ajset-590	125	75	angle	angle	NOUN
ajset-590	125	76	between	between	ADP
ajset-590	125	77	the	the	DET
ajset-590	125	78	vectors	vector	NOUN
ajset-590	125	79	.	.	PUNCT
ajset-590	126	1	the	the	DET
ajset-590	126	2	expression	expression	NOUN
ajset-590	126	3	v	v	NOUN
ajset-590	126	4	cos	cos	PROPN
ajset-590	126	5	represents	represent	VERB
ajset-590	126	6	a	a	DET
ajset-590	126	7	denominate	denominate	NOUN
ajset-590	126	8	number	number	NOUN
ajset-590	126	9	:	:	PUNCT
ajset-590	126	10	the	the	DET
ajset-590	126	11	projection	projection	NOUN
ajset-590	126	12	of	of	ADP
ajset-590	126	13	the	the	DET
ajset-590	126	14	vector	vector	NOUN
ajset-590	126	15	v	v	NOUN
ajset-590	126	16	on	on	ADP
ajset-590	126	17	the	the	DET
ajset-590	126	18	vector	vector	NOUN
ajset-590	126	19	f	f	PROPN
ajset-590	126	20	.	.	PUNCT
ajset-590	127	1	also	also	ADV
ajset-590	127	2	,	,	PUNCT
ajset-590	127	3	the	the	DET
ajset-590	127	4	expression	expression	NOUN
ajset-590	127	5	f	f	PROPN
ajset-590	127	6	cos	cos	PROPN
ajset-590	127	7	represents	represent	VERB
ajset-590	127	8	a	a	DET
ajset-590	127	9	denominate	denominate	NOUN
ajset-590	127	10	number	number	NOUN
ajset-590	127	11	:	:	PUNCT
ajset-590	127	12	the	the	DET
ajset-590	127	13	projection	projection	NOUN
ajset-590	127	14	of	of	ADP
ajset-590	127	15	the	the	DET
ajset-590	127	16	vector	vector	NOUN
ajset-590	127	17	f	f	PROPN
ajset-590	127	18	on	on	ADP
ajset-590	127	19	the	the	DET
ajset-590	127	20	vector	vector	NOUN
ajset-590	127	21	v	v	NOUN
ajset-590	127	22	.	.	PUNCT
ajset-590	128	1	in	in	ADP
ajset-590	128	2	my	my	PRON
ajset-590	128	3	opinion	opinion	NOUN
ajset-590	128	4	,	,	PUNCT
ajset-590	128	5	the	the	DET
ajset-590	128	6	standard	standard	ADJ
ajset-590	128	7	definition	definition	NOUN
ajset-590	128	8	of	of	ADP
ajset-590	128	9	the	the	DET
ajset-590	128	10	scalar	scalar	ADJ
ajset-590	128	11	product	product	NOUN
ajset-590	128	12	of	of	ADP
ajset-590	128	13	vectors	vector	NOUN
ajset-590	128	14	is	be	AUX
ajset-590	128	15	not	not	PART
ajset-590	128	16	free	free	ADJ
ajset-590	128	17	from	from	ADP
ajset-590	128	18	objection	objection	NOUN
ajset-590	128	19	.	.	PUNCT
ajset-590	129	1	the	the	DET
ajset-590	129	2	objection	objection	NOUN
ajset-590	129	3	is	be	AUX
ajset-590	129	4	that	that	SCONJ
ajset-590	129	5	the	the	DET
ajset-590	129	6	standard	standard	ADJ
ajset-590	129	7	definition	definition	NOUN
ajset-590	129	8	is	be	AUX
ajset-590	129	9	contrary	contrary	ADJ
ajset-590	129	10	to	to	ADP
ajset-590	129	11	the	the	DET
ajset-590	129	12	formal	formal	ADJ
ajset-590	129	13	-	-	PUNCT
ajset-590	129	14	logical	logical	ADJ
ajset-590	129	15	laws	law	NOUN
ajset-590	129	16	.	.	PUNCT
ajset-590	130	1	really	really	ADV
ajset-590	130	2	,	,	PUNCT
ajset-590	130	3	the	the	DET
ajset-590	130	4	coincidence	coincidence	NOUN
ajset-590	130	5	(	(	PUNCT
ajset-590	130	6	connection	connection	NOUN
ajset-590	130	7	)	)	PUNCT
ajset-590	130	8	of	of	ADP
ajset-590	130	9	initial	initial	ADJ
ajset-590	130	10	points	point	NOUN
ajset-590	130	11	of	of	ADP
ajset-590	130	12	vectors	vector	NOUN
ajset-590	130	13	and	and	CCONJ
ajset-590	130	14	the	the	DET
ajset-590	130	15	formation	formation	NOUN
ajset-590	130	16	of	of	ADP
ajset-590	130	17	the	the	DET
ajset-590	130	18	projections	projection	NOUN
ajset-590	130	19	imply	imply	VERB
ajset-590	130	20	that	that	SCONJ
ajset-590	130	21	the	the	DET
ajset-590	130	22	dimension	dimension	NOUN
ajset-590	130	23	of	of	ADP
ajset-590	130	24	length	length	NOUN
ajset-590	130	25	(	(	PUNCT
ajset-590	130	26	i.e.	i.e.	X
ajset-590	130	27	,	,	PUNCT
ajset-590	130	28	the	the	DET
ajset-590	130	29	qualitative	qualitative	ADJ
ajset-590	130	30	determinacy	determinacy	NOUN
ajset-590	130	31	)	)	PUNCT
ajset-590	130	32	of	of	ADP
ajset-590	130	33	the	the	DET
ajset-590	130	34	vector	vector	NOUN
ajset-590	130	35	v	v	NOUN
ajset-590	130	36	is	be	AUX
ajset-590	130	37	identical	identical	ADJ
ajset-590	130	38	to	to	ADP
ajset-590	130	39	the	the	DET
ajset-590	130	40	dimension	dimension	NOUN
ajset-590	130	41	of	of	ADP
ajset-590	130	42	length	length	NOUN
ajset-590	130	43	(	(	PUNCT
ajset-590	130	44	i.e.	i.e.	X
ajset-590	130	45	,	,	PUNCT
ajset-590	130	46	the	the	DET
ajset-590	130	47	qualitative	qualitative	ADJ
ajset-590	130	48	determinacy	determinacy	NOUN
ajset-590	130	49	)	)	PUNCT
ajset-590	130	50	of	of	ADP
ajset-590	130	51	the	the	DET
ajset-590	130	52	vector	vector	NOUN
ajset-590	131	1	f	f	NOUN
ajset-590	131	2	:	:	PUNCT
ajset-590	131	3	mailto:topacademicjournals@gmail.com	mailto:topacademicjournals@gmail.com	PROPN
ajset-590	131	4	academic	academic	ADJ
ajset-590	131	5	journal	journal	NOUN
ajset-590	131	6	of	of	ADP
ajset-590	131	7	science	science	NOUN
ajset-590	131	8	,	,	PUNCT
ajset-590	131	9	engineering	engineering	NOUN
ajset-590	131	10	and	and	CCONJ
ajset-590	131	11	technology	technology	NOUN
ajset-590	131	12	vol.8	vol.8	PROPN
ajset-590	131	13	,	,	PUNCT
ajset-590	131	14	issue	issue	NOUN
ajset-590	131	15	5	5	NUM
ajset-590	131	16	;	;	PUNCT
ajset-590	131	17	september	september	PROPN
ajset-590	131	18	october	october	PROPN
ajset-590	131	19	2023	2023	NUM
ajset-590	131	20	;	;	PUNCT
ajset-590	131	21	issn	issn	PROPN
ajset-590	131	22	:	:	PUNCT
ajset-590	131	23	2837	2837	NUM
ajset-590	131	24	-	-	SYM
ajset-590	131	25	2964	2964	NUM
ajset-590	131	26	impact	impact	NOUN
ajset-590	131	27	factor	factor	NOUN
ajset-590	131	28	:	:	PUNCT
ajset-590	131	29	6.67	6.67	NUM
ajset-590	131	30	1252	1252	NUM
ajset-590	131	31	columbia	columbia	PROPN
ajset-590	131	32	rd	rd	PROPN
ajset-590	131	33	nw	nw	PROPN
ajset-590	131	34	,	,	PUNCT
ajset-590	131	35	washington	washington	PROPN
ajset-590	131	36	dc	dc	PROPN
ajset-590	131	37	,	,	PUNCT
ajset-590	131	38	united	united	PROPN
ajset-590	131	39	states	states	PROPN
ajset-590	131	40	https://topjournals.org/index.php/ajset/index	https://topjournals.org/index.php/ajset/index	PROPN
ajset-590	131	41	;	;	PUNCT
ajset-590	131	42	mail	mail	NOUN
ajset-590	131	43	:	:	PUNCT
ajset-590	131	44	topacademicjournals@gmail.com	topacademicjournals@gmail.com	X
ajset-590	132	1	14	14	NUM
ajset-590	133	1	|	|	ADV
ajset-590	133	2	a	a	DET
ajset-590	133	3	c	c	NOUN
ajset-590	133	4	a	a	PRON
ajset-590	133	5	d	d	X
ajset-590	133	6	e	e	NOUN
ajset-590	133	7	m	m	NOUN
ajset-590	133	8	i	i	NOUN
ajset-590	133	9	c	c	NOUN
ajset-590	133	10	j	j	NOUN
ajset-590	133	11	o	o	X
ajset-590	133	12	u	u	NOUN
ajset-590	133	13	r	r	NOUN
ajset-590	133	14	n	n	NOUN
ajset-590	133	15	a	a	DET
ajset-590	133	16	l	l	NOUN
ajset-590	134	1	o	o	X
ajset-590	134	2	f	f	X
ajset-590	134	3	s	s	X
ajset-590	134	4	c	c	NOUN
ajset-590	135	1	i	i	NOUN
ajset-590	135	2	e	e	PROPN
ajset-590	135	3	n	n	PROPN
ajset-590	135	4	c	c	NOUN
ajset-590	135	5	e	e	X
ajset-590	135	6	,	,	PUNCT
ajset-590	135	7	e	e	PROPN
ajset-590	135	8	n	n	PRON
ajset-590	135	9	g	g	NOUN
ajset-590	135	10	i	i	PRON
ajset-590	135	11	n	n	VERB
ajset-590	135	12	e	e	NOUN
ajset-590	135	13	e	e	NOUN
ajset-590	135	14	r	r	VERB
ajset-590	135	15	i	i	PRON
ajset-590	135	16	n	n	CCONJ
ajset-590	135	17	g	g	PROPN
ajset-590	135	18	a	a	DET
ajset-590	135	19	n	n	NOUN
ajset-590	135	20	d	d	NOUN
ajset-590	135	21	t	t	NOUN
ajset-590	135	22	e	e	X
ajset-590	135	23	c	c	NOUN
ajset-590	135	24	h	h	NOUN
ajset-590	135	25	n	n	ADV
ajset-590	135	26	o	o	NOUN
ajset-590	135	27	l	l	NOUN
ajset-590	136	1	o	o	X
ajset-590	136	2	g	g	NOUN
ajset-590	136	3	y	y	PROPN
ajset-590	136	4	|	|	ADV
ajset-590	136	5	https://topjournals.org/index.php/ajset	https://topjournals.org/index.php/ajset	VERB
ajset-590	136	6	(	(	PUNCT
ajset-590	136	7	qualitative	qualitative	ADJ
ajset-590	136	8	determinacy	determinacy	NOUN
ajset-590	136	9	of	of	ADP
ajset-590	136	10	the	the	DET
ajset-590	136	11	vector	vector	NOUN
ajset-590	136	12	v	v	NOUN
ajset-590	136	13	)	)	PUNCT
ajset-590	136	14	=	=	SYM
ajset-590	136	15	(	(	PUNCT
ajset-590	136	16	qualitative	qualitative	ADJ
ajset-590	136	17	determinacy	determinacy	NOUN
ajset-590	136	18	of	of	ADP
ajset-590	136	19	the	the	DET
ajset-590	136	20	vector	vector	NOUN
ajset-590	136	21	f	f	PROPN
ajset-590	136	22	)	)	PUNCT
ajset-590	136	23	.	.	PUNCT
ajset-590	137	1	in	in	ADP
ajset-590	137	2	general	general	ADJ
ajset-590	137	3	case	case	NOUN
ajset-590	137	4	,	,	PUNCT
ajset-590	137	5	however	however	ADV
ajset-590	137	6	,	,	PUNCT
ajset-590	137	7	the	the	DET
ajset-590	137	8	dimensions	dimension	NOUN
ajset-590	137	9	of	of	ADP
ajset-590	137	10	vector	vector	NOUN
ajset-590	137	11	lengths	length	NOUN
ajset-590	137	12	are	be	AUX
ajset-590	137	13	different	different	ADJ
ajset-590	137	14	.	.	PUNCT
ajset-590	138	1	therefore	therefore	ADV
ajset-590	138	2	,	,	PUNCT
ajset-590	138	3	these	these	DET
ajset-590	138	4	vectors	vector	NOUN
ajset-590	138	5	can	can	AUX
ajset-590	138	6	not	not	PART
ajset-590	138	7	have	have	VERB
ajset-590	138	8	a	a	DET
ajset-590	138	9	common	common	ADJ
ajset-590	138	10	point	point	NOUN
ajset-590	138	11	,	,	PUNCT
ajset-590	138	12	and	and	CCONJ
ajset-590	138	13	the	the	DET
ajset-590	138	14	multiplication	multiplication	NOUN
ajset-590	138	15	can	can	AUX
ajset-590	138	16	not	not	PART
ajset-590	138	17	be	be	AUX
ajset-590	138	18	performed	perform	VERB
ajset-590	138	19	(	(	PUNCT
ajset-590	138	20	i.e.	i.e.	X
ajset-590	138	21	the	the	DET
ajset-590	138	22	multiplication	multiplication	NOUN
ajset-590	138	23	has	have	AUX
ajset-590	138	24	no	no	DET
ajset-590	138	25	sense	sense	NOUN
ajset-590	138	26	)	)	PUNCT
ajset-590	138	27	.	.	PUNCT
ajset-590	139	1	this	this	DET
ajset-590	139	2	fact	fact	NOUN
ajset-590	139	3	is	be	AUX
ajset-590	139	4	expressed	express	VERB
ajset-590	139	5	formal	formal	ADJ
ajset-590	139	6	-	-	PUNCT
ajset-590	139	7	logical	logical	ADJ
ajset-590	139	8	law	law	NOUN
ajset-590	139	9	of	of	ADP
ajset-590	139	10	absence	absence	NOUN
ajset-590	139	11	of	of	ADP
ajset-590	139	12	contradiction	contradiction	NOUN
ajset-590	139	13	:	:	PUNCT
ajset-590	139	14	(	(	PUNCT
ajset-590	139	15	qualitative	qualitative	ADJ
ajset-590	139	16	determinacy	determinacy	NOUN
ajset-590	139	17	of	of	ADP
ajset-590	139	18	the	the	DET
ajset-590	139	19	vectorv	vectorv	NOUN
ajset-590	139	20	)	)	PUNCT
ajset-590	139	21	(	(	PUNCT
ajset-590	139	22	qualitative	qualitative	ADJ
ajset-590	139	23	determinacy	determinacy	NOUN
ajset-590	139	24	of	of	ADP
ajset-590	139	25	the	the	DET
ajset-590	139	26	vector	vector	NOUN
ajset-590	139	27	f	f	PROPN
ajset-590	139	28	)	)	PUNCT
ajset-590	139	29	.	.	PUNCT
ajset-590	140	1	consequently	consequently	ADV
ajset-590	140	2	,	,	PUNCT
ajset-590	140	3	the	the	DET
ajset-590	140	4	mathematical	mathematical	ADJ
ajset-590	140	5	operation	operation	NOUN
ajset-590	140	6	of	of	ADP
ajset-590	140	7	scalar	scalar	ADJ
ajset-590	140	8	product	product	NOUN
ajset-590	140	9	of	of	ADP
ajset-590	140	10	two	two	NUM
ajset-590	140	11	vectors	vector	NOUN
ajset-590	140	12	represents	represent	VERB
ajset-590	140	13	a	a	DET
ajset-590	140	14	formal	formal	ADJ
ajset-590	140	15	-	-	PUNCT
ajset-590	140	16	logical	logical	ADJ
ajset-590	140	17	error	error	NOUN
ajset-590	140	18	:	:	PUNCT
ajset-590	140	19	a	a	DET
ajset-590	140	20	violation	violation	NOUN
ajset-590	140	21	of	of	ADP
ajset-590	140	22	the	the	DET
ajset-590	140	23	law	law	NOUN
ajset-590	140	24	of	of	ADP
ajset-590	140	25	absence	absence	NOUN
ajset-590	140	26	of	of	ADP
ajset-590	140	27	contradiction	contradiction	NOUN
ajset-590	140	28	.	.	PUNCT
ajset-590	141	1	4	4	X
ajset-590	141	2	.	.	X
ajset-590	141	3	as	as	SCONJ
ajset-590	141	4	is	be	AUX
ajset-590	141	5	known	know	VERB
ajset-590	141	6	,	,	PUNCT
ajset-590	141	7	the	the	DET
ajset-590	141	8	cross	cross	NOUN
ajset-590	141	9	-	-	NOUN
ajset-590	141	10	product	product	NOUN
ajset-590	141	11	of	of	ADP
ajset-590	141	12	two	two	NUM
ajset-590	141	13	vectors	vector	NOUN
ajset-590	141	14	v	v	NOUN
ajset-590	141	15	and	and	CCONJ
ajset-590	141	16	f	f	PROPN
ajset-590	141	17	is	be	AUX
ajset-590	141	18	defined	define	VERB
ajset-590	141	19	as	as	SCONJ
ajset-590	141	20	follows	follow	VERB
ajset-590	141	21	:	:	PUNCT
ajset-590	141	22	(	(	PUNCT
ajset-590	141	23	a	a	X
ajset-590	141	24	)	)	PUNCT
ajset-590	141	25	one	one	NOUN
ajset-590	141	26	brings	bring	VERB
ajset-590	141	27	the	the	DET
ajset-590	141	28	initial	initial	ADJ
ajset-590	141	29	points	point	NOUN
ajset-590	141	30	of	of	ADP
ajset-590	141	31	vectors	vector	NOUN
ajset-590	141	32	in	in	ADP
ajset-590	141	33	coincidence	coincidence	NOUN
ajset-590	141	34	with	with	ADP
ajset-590	141	35	each	each	DET
ajset-590	141	36	other	other	ADJ
ajset-590	141	37	(	(	PUNCT
ajset-590	141	38	i.e.	i.e.	X
ajset-590	141	39	,	,	PUNCT
ajset-590	141	40	the	the	DET
ajset-590	141	41	initial	initial	ADJ
ajset-590	141	42	points	point	NOUN
ajset-590	141	43	are	be	AUX
ajset-590	141	44	connected	connect	VERB
ajset-590	141	45	)	)	PUNCT
ajset-590	141	46	;	;	PUNCT
ajset-590	141	47	(	(	PUNCT
ajset-590	141	48	b	b	X
ajset-590	141	49	)	)	PUNCT
ajset-590	141	50	one	one	NOUN
ajset-590	141	51	postulates	postulate	VERB
ajset-590	141	52	the	the	DET
ajset-590	141	53	relation	relation	NOUN
ajset-590	141	54	h	h	NOUN
ajset-590	142	1	v	v	NOUN
ajset-590	142	2	f	f	PROPN
ajset-590	142	3	h	h	NOUN
ajset-590	142	4	v	v	PROPN
ajset-590	142	5	f	f	PROPN
ajset-590	142	6	sin	sin	NOUN
ajset-590	142	7	where	where	SCONJ
ajset-590	142	8	the	the	DET
ajset-590	142	9	cross	cross	NOUN
ajset-590	142	10	between	between	ADP
ajset-590	142	11	the	the	DET
ajset-590	142	12	symbols	symbol	NOUN
ajset-590	142	13	of	of	ADP
ajset-590	142	14	vectors	vector	NOUN
ajset-590	142	15	denotes	denote	VERB
ajset-590	142	16	the	the	DET
ajset-590	142	17	operation	operation	NOUN
ajset-590	142	18	of	of	ADP
ajset-590	142	19	vector	vector	NOUN
ajset-590	142	20	multiplication	multiplication	NOUN
ajset-590	142	21	of	of	ADP
ajset-590	142	22	vectors	vector	NOUN
ajset-590	142	23	,	,	PUNCT
ajset-590	142	24	is	be	AUX
ajset-590	142	25	angle	angle	NOUN
ajset-590	142	26	between	between	ADP
ajset-590	142	27	the	the	DET
ajset-590	142	28	vectors	vector	NOUN
ajset-590	142	29	,	,	PUNCT
ajset-590	142	30	h	h	NOUN
ajset-590	142	31	is	be	AUX
ajset-590	142	32	vector	vector	NOUN
ajset-590	142	33	which	which	PRON
ajset-590	142	34	is	be	AUX
ajset-590	142	35	normal	normal	ADJ
ajset-590	142	36	to	to	ADP
ajset-590	142	37	the	the	DET
ajset-590	142	38	plane	plane	NOUN
ajset-590	142	39	formed	form	VERB
ajset-590	142	40	by	by	ADP
ajset-590	142	41	the	the	DET
ajset-590	142	42	vectors	vector	NOUN
ajset-590	142	43	v	v	NOUN
ajset-590	142	44	and	and	CCONJ
ajset-590	142	45	f	f	PROPN
ajset-590	142	46	;	;	PUNCT
ajset-590	142	47	h	h	PROPN
ajset-590	142	48	is	be	AUX
ajset-590	142	49	unit	unit	NOUN
ajset-590	142	50	vector	vector	NOUN
ajset-590	142	51	which	which	PRON
ajset-590	142	52	is	be	AUX
ajset-590	142	53	normal	normal	ADJ
ajset-590	142	54	to	to	ADP
ajset-590	142	55	the	the	DET
ajset-590	142	56	plane	plane	NOUN
ajset-590	142	57	.	.	PUNCT
ajset-590	143	1	under	under	ADP
ajset-590	143	2	the	the	DET
ajset-590	143	3	established	establish	VERB
ajset-590	143	4	agreement	agreement	NOUN
ajset-590	143	5	,	,	PUNCT
ajset-590	143	6	the	the	DET
ajset-590	143	7	direction	direction	NOUN
ajset-590	143	8	of	of	ADP
ajset-590	143	9	vectors	vector	NOUN
ajset-590	143	10	h	h	NOUN
ajset-590	143	11	and	and	CCONJ
ajset-590	143	12	h	h	NOUN
ajset-590	143	13	is	be	AUX
ajset-590	143	14	determined	determine	VERB
ajset-590	143	15	by	by	ADP
ajset-590	143	16	the	the	DET
ajset-590	143	17	“	"	PUNCT
ajset-590	143	18	right	right	ADJ
ajset-590	143	19	-	-	PUNCT
ajset-590	143	20	hand	hand	NOUN
ajset-590	143	21	screw	screw	NOUN
ajset-590	143	22	rule	rule	NOUN
ajset-590	143	23	”	"	PUNCT
ajset-590	143	24	.	.	PUNCT
ajset-590	144	1	in	in	ADP
ajset-590	144	2	my	my	PRON
ajset-590	144	3	opinion	opinion	NOUN
ajset-590	144	4	,	,	PUNCT
ajset-590	144	5	the	the	DET
ajset-590	144	6	standard	standard	ADJ
ajset-590	144	7	definition	definition	NOUN
ajset-590	144	8	of	of	ADP
ajset-590	144	9	the	the	DET
ajset-590	144	10	cross	cross	NOUN
ajset-590	144	11	-	-	NOUN
ajset-590	144	12	product	product	NOUN
ajset-590	144	13	of	of	ADP
ajset-590	144	14	vectors	vector	NOUN
ajset-590	144	15	is	be	AUX
ajset-590	144	16	not	not	PART
ajset-590	144	17	free	free	ADJ
ajset-590	144	18	from	from	ADP
ajset-590	144	19	objection	objection	NOUN
ajset-590	144	20	.	.	PUNCT
ajset-590	145	1	the	the	DET
ajset-590	145	2	objection	objection	NOUN
ajset-590	145	3	is	be	AUX
ajset-590	145	4	that	that	SCONJ
ajset-590	145	5	the	the	DET
ajset-590	145	6	standard	standard	ADJ
ajset-590	145	7	definition	definition	NOUN
ajset-590	145	8	is	be	AUX
ajset-590	145	9	contrary	contrary	ADJ
ajset-590	145	10	to	to	ADP
ajset-590	145	11	the	the	DET
ajset-590	145	12	formal	formal	ADJ
ajset-590	145	13	-	-	PUNCT
ajset-590	145	14	logical	logical	ADJ
ajset-590	145	15	laws	law	NOUN
ajset-590	145	16	.	.	PUNCT
ajset-590	146	1	really	really	ADV
ajset-590	146	2	,	,	PUNCT
ajset-590	146	3	the	the	DET
ajset-590	146	4	coincidence	coincidence	NOUN
ajset-590	146	5	of	of	ADP
ajset-590	146	6	the	the	DET
ajset-590	146	7	initial	initial	ADJ
ajset-590	146	8	points	point	NOUN
ajset-590	146	9	of	of	ADP
ajset-590	146	10	the	the	DET
ajset-590	146	11	three	three	NUM
ajset-590	146	12	vectors	vector	NOUN
ajset-590	146	13	means	mean	VERB
ajset-590	146	14	that	that	SCONJ
ajset-590	146	15	the	the	DET
ajset-590	146	16	dimensions	dimension	NOUN
ajset-590	146	17	of	of	ADP
ajset-590	146	18	lengths	length	NOUN
ajset-590	146	19	(	(	PUNCT
ajset-590	146	20	i.e.	i.e.	X
ajset-590	146	21	,	,	PUNCT
ajset-590	146	22	the	the	DET
ajset-590	146	23	qualitative	qualitative	ADJ
ajset-590	146	24	determinacy	determinacy	NOUN
ajset-590	146	25	)	)	PUNCT
ajset-590	146	26	of	of	ADP
ajset-590	146	27	the	the	DET
ajset-590	146	28	vectors	vector	NOUN
ajset-590	146	29	v	v	NOUN
ajset-590	146	30	,	,	PUNCT
ajset-590	146	31	f	f	X
ajset-590	146	32	,	,	PUNCT
ajset-590	146	33	and	and	CCONJ
ajset-590	146	34	h	h	NOUN
ajset-590	146	35	are	be	AUX
ajset-590	146	36	identical	identical	ADJ
ajset-590	146	37	:	:	PUNCT
ajset-590	146	38	(	(	PUNCT
ajset-590	146	39	qualitative	qualitative	ADJ
ajset-590	146	40	determination	determination	NOUN
ajset-590	146	41	of	of	ADP
ajset-590	146	42	the	the	DET
ajset-590	146	43	vector	vector	NOUN
ajset-590	146	44	v	v	NOUN
ajset-590	146	45	)	)	PUNCT
ajset-590	146	46	=	=	PUNCT
ajset-590	146	47	(	(	PUNCT
ajset-590	146	48	qualitative	qualitative	ADJ
ajset-590	146	49	determination	determination	NOUN
ajset-590	146	50	of	of	ADP
ajset-590	146	51	the	the	DET
ajset-590	146	52	vector	vector	NOUN
ajset-590	146	53	f	f	PROPN
ajset-590	146	54	)	)	PUNCT
ajset-590	147	1	=	=	PUNCT
ajset-590	147	2	(	(	PUNCT
ajset-590	147	3	qualitative	qualitative	ADJ
ajset-590	147	4	determination	determination	NOUN
ajset-590	147	5	of	of	ADP
ajset-590	147	6	the	the	DET
ajset-590	147	7	vector	vector	NOUN
ajset-590	147	8	h	h	NOUN
ajset-590	147	9	)	)	PUNCT
ajset-590	147	10	.	.	PUNCT
ajset-590	148	1	in	in	ADP
ajset-590	148	2	general	general	ADJ
ajset-590	148	3	case	case	NOUN
ajset-590	148	4	,	,	PUNCT
ajset-590	148	5	however	however	ADV
ajset-590	148	6	,	,	PUNCT
ajset-590	148	7	the	the	DET
ajset-590	148	8	dimensions	dimension	NOUN
ajset-590	148	9	of	of	ADP
ajset-590	148	10	the	the	DET
ajset-590	148	11	lengths	length	NOUN
ajset-590	148	12	of	of	ADP
ajset-590	148	13	the	the	DET
ajset-590	148	14	vectors	vector	NOUN
ajset-590	148	15	are	be	AUX
ajset-590	148	16	different	different	ADJ
ajset-590	148	17	.	.	PUNCT
ajset-590	149	1	therefore	therefore	ADV
ajset-590	149	2	,	,	PUNCT
ajset-590	149	3	these	these	DET
ajset-590	149	4	vectors	vector	NOUN
ajset-590	149	5	can	can	AUX
ajset-590	149	6	not	not	PART
ajset-590	149	7	have	have	VERB
ajset-590	149	8	a	a	DET
ajset-590	149	9	common	common	ADJ
ajset-590	149	10	point	point	NOUN
ajset-590	149	11	,	,	PUNCT
ajset-590	149	12	and	and	CCONJ
ajset-590	149	13	the	the	DET
ajset-590	149	14	operation	operation	NOUN
ajset-590	149	15	of	of	ADP
ajset-590	149	16	vector	vector	NOUN
ajset-590	149	17	multiplication	multiplication	NOUN
ajset-590	149	18	can	can	AUX
ajset-590	149	19	not	not	PART
ajset-590	149	20	be	be	AUX
ajset-590	149	21	performed	perform	VERB
ajset-590	149	22	(	(	PUNCT
ajset-590	149	23	i.e.	i.e.	X
ajset-590	149	24	,	,	PUNCT
ajset-590	149	25	the	the	DET
ajset-590	149	26	operation	operation	NOUN
ajset-590	149	27	of	of	ADP
ajset-590	149	28	multiplication	multiplication	NOUN
ajset-590	149	29	has	have	VERB
ajset-590	149	30	no	no	DET
ajset-590	149	31	sense	sense	NOUN
ajset-590	149	32	)	)	PUNCT
ajset-590	149	33	.	.	PUNCT
ajset-590	150	1	this	this	DET
ajset-590	150	2	fact	fact	NOUN
ajset-590	150	3	is	be	AUX
ajset-590	150	4	expressed	express	VERB
ajset-590	150	5	formal	formal	ADJ
ajset-590	150	6	-	-	PUNCT
ajset-590	150	7	logical	logical	ADJ
ajset-590	150	8	law	law	NOUN
ajset-590	150	9	of	of	ADP
ajset-590	150	10	absence	absence	NOUN
ajset-590	150	11	of	of	ADP
ajset-590	150	12	contradiction	contradiction	NOUN
ajset-590	150	13	:	:	PUNCT
ajset-590	150	14	(	(	PUNCT
ajset-590	150	15	qualitative	qualitative	ADJ
ajset-590	150	16	determinacy	determinacy	NOUN
ajset-590	150	17	of	of	ADP
ajset-590	150	18	the	the	DET
ajset-590	150	19	vectorv	vectorv	NOUN
ajset-590	150	20	)	)	PUNCT
ajset-590	150	21	mailto:topacademicjournals@gmail.com	mailto:topacademicjournals@gmail.com	PROPN
ajset-590	150	22	academic	academic	ADJ
ajset-590	150	23	journal	journal	NOUN
ajset-590	150	24	of	of	ADP
ajset-590	150	25	science	science	NOUN
ajset-590	150	26	,	,	PUNCT
ajset-590	150	27	engineering	engineering	NOUN
ajset-590	150	28	and	and	CCONJ
ajset-590	150	29	technology	technology	NOUN
ajset-590	150	30	vol.8	vol.8	PROPN
ajset-590	150	31	,	,	PUNCT
ajset-590	150	32	issue	issue	NOUN
ajset-590	150	33	5	5	NUM
ajset-590	150	34	;	;	PUNCT
ajset-590	150	35	september	september	PROPN
ajset-590	150	36	october	october	PROPN
ajset-590	150	37	2023	2023	NUM
ajset-590	150	38	;	;	PUNCT
ajset-590	150	39	issn	issn	PROPN
ajset-590	150	40	:	:	PUNCT
ajset-590	150	41	2837	2837	NUM
ajset-590	150	42	-	-	SYM
ajset-590	150	43	2964	2964	NUM
ajset-590	150	44	impact	impact	NOUN
ajset-590	150	45	factor	factor	NOUN
ajset-590	150	46	:	:	PUNCT
ajset-590	150	47	6.67	6.67	NUM
ajset-590	150	48	1252	1252	NUM
ajset-590	150	49	columbia	columbia	PROPN
ajset-590	150	50	rd	rd	PROPN
ajset-590	150	51	nw	nw	PROPN
ajset-590	150	52	,	,	PUNCT
ajset-590	150	53	washington	washington	PROPN
ajset-590	150	54	dc	dc	PROPN
ajset-590	150	55	,	,	PUNCT
ajset-590	150	56	united	united	PROPN
ajset-590	150	57	states	states	PROPN
ajset-590	150	58	https://topjournals.org/index.php/ajset/index	https://topjournals.org/index.php/ajset/index	PROPN
ajset-590	150	59	;	;	PUNCT
ajset-590	150	60	mail	mail	NOUN
ajset-590	150	61	:	:	PUNCT
ajset-590	150	62	topacademicjournals@gmail.com	topacademicjournals@gmail.com	X
ajset-590	151	1	15	15	NUM
ajset-590	152	1	|	|	ADV
ajset-590	152	2	a	a	DET
ajset-590	152	3	c	c	NOUN
ajset-590	152	4	a	a	PRON
ajset-590	152	5	d	d	X
ajset-590	152	6	e	e	NOUN
ajset-590	152	7	m	m	NOUN
ajset-590	152	8	i	i	NOUN
ajset-590	152	9	c	c	NOUN
ajset-590	152	10	j	j	NOUN
ajset-590	152	11	o	o	X
ajset-590	152	12	u	u	NOUN
ajset-590	152	13	r	r	NOUN
ajset-590	152	14	n	n	NOUN
ajset-590	152	15	a	a	DET
ajset-590	152	16	l	l	NOUN
ajset-590	153	1	o	o	X
ajset-590	153	2	f	f	X
ajset-590	153	3	s	s	X
ajset-590	153	4	c	c	NOUN
ajset-590	154	1	i	i	NOUN
ajset-590	154	2	e	e	PROPN
ajset-590	154	3	n	n	PROPN
ajset-590	154	4	c	c	NOUN
ajset-590	154	5	e	e	X
ajset-590	154	6	,	,	PUNCT
ajset-590	154	7	e	e	PROPN
ajset-590	154	8	n	n	PRON
ajset-590	154	9	g	g	NOUN
ajset-590	154	10	i	i	PRON
ajset-590	154	11	n	n	VERB
ajset-590	154	12	e	e	NOUN
ajset-590	154	13	e	e	NOUN
ajset-590	154	14	r	r	VERB
ajset-590	154	15	i	i	PRON
ajset-590	154	16	n	n	CCONJ
ajset-590	154	17	g	g	PROPN
ajset-590	154	18	a	a	DET
ajset-590	154	19	n	n	NOUN
ajset-590	154	20	d	d	NOUN
ajset-590	154	21	t	t	NOUN
ajset-590	154	22	e	e	X
ajset-590	154	23	c	c	NOUN
ajset-590	154	24	h	h	NOUN
ajset-590	154	25	n	n	ADV
ajset-590	154	26	o	o	NOUN
ajset-590	154	27	l	l	NOUN
ajset-590	155	1	o	o	X
ajset-590	155	2	g	g	NOUN
ajset-590	155	3	y	y	PROPN
ajset-590	155	4	|	|	ADV
ajset-590	155	5	https://topjournals.org/index.php/ajset	https://topjournals.org/index.php/ajset	VERB
ajset-590	155	6	(	(	PUNCT
ajset-590	155	7	qualitative	qualitative	ADJ
ajset-590	155	8	determinacy	determinacy	NOUN
ajset-590	155	9	of	of	ADP
ajset-590	155	10	the	the	DET
ajset-590	155	11	vector	vector	NOUN
ajset-590	155	12	f	f	PROPN
ajset-590	155	13	)	)	PUNCT
ajset-590	155	14	(	(	PUNCT
ajset-590	155	15	qualitative	qualitative	ADJ
ajset-590	155	16	determinacy	determinacy	NOUN
ajset-590	155	17	of	of	ADP
ajset-590	155	18	the	the	DET
ajset-590	155	19	vector	vector	NOUN
ajset-590	155	20	h	h	NOUN
ajset-590	155	21	)	)	PUNCT
ajset-590	155	22	.	.	PUNCT
ajset-590	156	1	consequently	consequently	ADV
ajset-590	156	2	,	,	PUNCT
ajset-590	156	3	the	the	DET
ajset-590	156	4	mathematical	mathematical	ADJ
ajset-590	156	5	operation	operation	NOUN
ajset-590	156	6	of	of	ADP
ajset-590	156	7	the	the	DET
ajset-590	156	8	cross	cross	NOUN
ajset-590	156	9	-	-	NOUN
ajset-590	156	10	product	product	NOUN
ajset-590	156	11	of	of	ADP
ajset-590	156	12	vectors	vector	NOUN
ajset-590	156	13	is	be	AUX
ajset-590	156	14	a	a	DET
ajset-590	156	15	formal	formal	ADJ
ajset-590	156	16	-	-	PUNCT
ajset-590	156	17	logical	logical	ADJ
ajset-590	156	18	error	error	NOUN
ajset-590	156	19	:	:	PUNCT
ajset-590	156	20	a	a	DET
ajset-590	156	21	violation	violation	NOUN
ajset-590	156	22	of	of	ADP
ajset-590	156	23	the	the	DET
ajset-590	156	24	law	law	NOUN
ajset-590	156	25	of	of	ADP
ajset-590	156	26	absence	absence	NOUN
ajset-590	156	27	of	of	ADP
ajset-590	156	28	contradiction	contradiction	NOUN
ajset-590	156	29	.	.	PUNCT
ajset-590	157	1	discussion	discussion	NOUN
ajset-590	157	2	1	1	NUM
ajset-590	157	3	.	.	PUNCT
ajset-590	158	1	as	as	SCONJ
ajset-590	158	2	is	be	AUX
ajset-590	158	3	known	know	VERB
ajset-590	158	4	,	,	PUNCT
ajset-590	158	5	the	the	DET
ajset-590	158	6	confidence	confidence	NOUN
ajset-590	158	7	in	in	ADP
ajset-590	158	8	the	the	DET
ajset-590	158	9	scientific	scientific	ADJ
ajset-590	158	10	method	method	NOUN
ajset-590	158	11	of	of	ADP
ajset-590	158	12	research	research	NOUN
ajset-590	158	13	and	and	CCONJ
ajset-590	158	14	in	in	ADP
ajset-590	158	15	rational	rational	ADJ
ajset-590	158	16	thinking	thinking	NOUN
ajset-590	158	17	replaced	replace	VERB
ajset-590	158	18	all	all	DET
ajset-590	158	19	other	other	ADJ
ajset-590	158	20	ways	way	NOUN
ajset-590	158	21	of	of	ADP
ajset-590	158	22	cognition	cognition	NOUN
ajset-590	158	23	in	in	ADP
ajset-590	158	24	the	the	DET
ajset-590	158	25	20th	20th	ADJ
ajset-590	158	26	century	century	NOUN
ajset-590	158	27	.	.	PUNCT
ajset-590	159	1	rational	rational	ADJ
ajset-590	159	2	thinking	thinking	NOUN
ajset-590	159	3	represents	represent	VERB
ajset-590	159	4	the	the	DET
ajset-590	159	5	greatest	great	ADJ
ajset-590	159	6	achievement	achievement	NOUN
ajset-590	159	7	of	of	ADP
ajset-590	159	8	mankind	mankind	NOUN
ajset-590	159	9	.	.	PUNCT
ajset-590	160	1	rationalization	rationalization	NOUN
ajset-590	160	2	of	of	ADP
ajset-590	160	3	thinking	thinking	NOUN
ajset-590	160	4	and	and	CCONJ
ajset-590	160	5	of	of	ADP
ajset-590	160	6	science	science	NOUN
ajset-590	160	7	is	be	AUX
ajset-590	160	8	dialectical	dialectical	ADJ
ajset-590	160	9	imperative	imperative	NOUN
ajset-590	160	10	of	of	ADP
ajset-590	160	11	our	our	PRON
ajset-590	160	12	time	time	NOUN
ajset-590	160	13	.	.	PUNCT
ajset-590	161	1	the	the	DET
ajset-590	161	2	development	development	NOUN
ajset-590	161	3	of	of	ADP
ajset-590	161	4	rational	rational	ADJ
ajset-590	161	5	thinking	thinking	NOUN
ajset-590	161	6	in	in	ADP
ajset-590	161	7	the	the	DET
ajset-590	161	8	21st	21st	ADJ
ajset-590	161	9	century	century	NOUN
ajset-590	161	10	leads	lead	VERB
ajset-590	161	11	to	to	ADP
ajset-590	161	12	critical	critical	ADJ
ajset-590	161	13	analysis	analysis	NOUN
ajset-590	161	14	,	,	PUNCT
ajset-590	161	15	reconsideration	reconsideration	NOUN
ajset-590	161	16	,	,	PUNCT
ajset-590	161	17	and	and	CCONJ
ajset-590	161	18	rationalization	rationalization	NOUN
ajset-590	161	19	of	of	ADP
ajset-590	161	20	the	the	DET
ajset-590	161	21	generally	generally	ADV
ajset-590	161	22	accepted	accept	VERB
ajset-590	161	23	theories	theory	NOUN
ajset-590	161	24	created	create	VERB
ajset-590	161	25	by	by	ADP
ajset-590	161	26	the	the	DET
ajset-590	161	27	classics	classic	NOUN
ajset-590	161	28	of	of	ADP
ajset-590	161	29	science	science	NOUN
ajset-590	161	30	(	(	PUNCT
ajset-590	161	31	for	for	ADP
ajset-590	161	32	example	example	NOUN
ajset-590	161	33	,	,	PUNCT
ajset-590	161	34	n.	n.	PROPN
ajset-590	161	35	bohr	bohr	PROPN
ajset-590	161	36	,	,	PUNCT
ajset-590	161	37	e.	e.	PROPN
ajset-590	161	38	schrödinger	schrödinger	PROPN
ajset-590	161	39	,	,	PUNCT
ajset-590	161	40	w.	w.	PROPN
ajset-590	161	41	heisenberg	heisenberg	PROPN
ajset-590	161	42	,	,	PUNCT
ajset-590	161	43	a.	a.	PROPN
ajset-590	161	44	einstein	einstein	PROPN
ajset-590	161	45	,	,	PUNCT
ajset-590	161	46	i.	i.	PROPN
ajset-590	161	47	newton	newton	PROPN
ajset-590	161	48	,	,	PUNCT
ajset-590	161	49	g.	g.	PROPN
ajset-590	161	50	leibniz	leibniz	PROPN
ajset-590	161	51	,	,	PUNCT
ajset-590	161	52	l.	l.	PROPN
ajset-590	161	53	euler	euler	PROPN
ajset-590	161	54	,	,	PUNCT
ajset-590	161	55	j.	j.	PROPN
ajset-590	161	56	lagrange	lagrange	PROPN
ajset-590	161	57	,	,	PUNCT
ajset-590	161	58	a.	a.	NOUN
ajset-590	161	59	cauchy	cauchy	PROPN
ajset-590	161	60	,	,	PUNCT
ajset-590	161	61	w.r	w.r	PROPN
ajset-590	161	62	.	.	PROPN
ajset-590	161	63	hamilton	hamilton	PROPN
ajset-590	161	64	,	,	PUNCT
ajset-590	161	65	j.w	j.w	PROPN
ajset-590	161	66	.	.	PROPN
ajset-590	161	67	gibbs	gibbs	PROPN
ajset-590	161	68	,	,	PUNCT
ajset-590	161	69	o.	o.	PROPN
ajset-590	161	70	heaviside	heaviside	PROPN
ajset-590	161	71	,	,	PUNCT
ajset-590	161	72	etc	etc	X
ajset-590	161	73	.	.	X
ajset-590	161	74	)	)	PUNCT
ajset-590	161	75	.	.	PUNCT
ajset-590	162	1	rationalization	rationalization	NOUN
ajset-590	162	2	and	and	CCONJ
ajset-590	162	3	critical	critical	ADJ
ajset-590	162	4	analysis	analysis	NOUN
ajset-590	162	5	of	of	ADP
ajset-590	162	6	science	science	NOUN
ajset-590	162	7	are	be	AUX
ajset-590	162	8	two	two	NUM
ajset-590	162	9	side	side	NOUN
ajset-590	162	10	pieces	piece	NOUN
ajset-590	162	11	(	(	PUNCT
ajset-590	162	12	component	component	NOUN
ajset-590	162	13	factors	factor	NOUN
ajset-590	162	14	)	)	PUNCT
ajset-590	162	15	in	in	ADP
ajset-590	162	16	progress	progress	NOUN
ajset-590	162	17	of	of	ADP
ajset-590	162	18	science	science	NOUN
ajset-590	162	19	.	.	PUNCT
ajset-590	163	1	critical	critical	ADJ
ajset-590	163	2	analysis	analysis	NOUN
ajset-590	163	3	and	and	CCONJ
ajset-590	163	4	rationalization	rationalization	NOUN
ajset-590	163	5	of	of	ADP
ajset-590	163	6	theories	theory	NOUN
ajset-590	163	7	are	be	AUX
ajset-590	163	8	based	base	VERB
ajset-590	163	9	on	on	ADP
ajset-590	163	10	formal	formal	ADJ
ajset-590	163	11	-	-	PUNCT
ajset-590	163	12	logical	logical	ADJ
ajset-590	163	13	analysis	analysis	NOUN
ajset-590	163	14	of	of	ADP
ajset-590	163	15	scientific	scientific	ADJ
ajset-590	163	16	concepts	concept	NOUN
ajset-590	163	17	,	,	PUNCT
ajset-590	163	18	of	of	ADP
ajset-590	163	19	the	the	DET
ajset-590	163	20	completeness	completeness	NOUN
ajset-590	163	21	of	of	ADP
ajset-590	163	22	concepts	concept	NOUN
ajset-590	163	23	,	,	PUNCT
ajset-590	163	24	of	of	ADP
ajset-590	163	25	the	the	DET
ajset-590	163	26	completeness	completeness	NOUN
ajset-590	163	27	of	of	ADP
ajset-590	163	28	a	a	DET
ajset-590	163	29	system	system	NOUN
ajset-590	163	30	of	of	ADP
ajset-590	163	31	concepts	concept	NOUN
ajset-590	163	32	because	because	SCONJ
ajset-590	163	33	“	"	PUNCT
ajset-590	163	34	only	only	ADV
ajset-590	163	35	the	the	DET
ajset-590	163	36	completeness	completeness	NOUN
ajset-590	163	37	leads	lead	VERB
ajset-590	163	38	to	to	ADP
ajset-590	163	39	clarity	clarity	NOUN
ajset-590	163	40	”	"	PUNCT
ajset-590	163	41	(	(	PUNCT
ajset-590	163	42	confucius	confucius	NOUN
ajset-590	163	43	)	)	PUNCT
ajset-590	163	44	.	.	PUNCT
ajset-590	164	1	recently	recently	ADV
ajset-590	164	2	,	,	PUNCT
ajset-590	164	3	independent	independent	ADJ
ajset-590	164	4	researchers	researcher	NOUN
ajset-590	164	5	give	give	VERB
ajset-590	164	6	attention	attention	NOUN
ajset-590	164	7	to	to	ADP
ajset-590	164	8	critical	critical	ADJ
ajset-590	164	9	analysis	analysis	NOUN
ajset-590	164	10	of	of	ADP
ajset-590	164	11	theoretical	theoretical	ADJ
ajset-590	164	12	physics	physics	NOUN
ajset-590	164	13	,	,	PUNCT
ajset-590	164	14	mathematics	mathematic	NOUN
ajset-590	164	15	,	,	PUNCT
ajset-590	164	16	biology	biology	NOUN
ajset-590	164	17	,	,	PUNCT
ajset-590	164	18	etc	etc	X
ajset-590	164	19	.	.	X
ajset-590	164	20	(	(	PUNCT
ajset-590	164	21	see	see	VERB
ajset-590	164	22	,	,	PUNCT
ajset-590	164	23	for	for	ADP
ajset-590	164	24	example	example	NOUN
ajset-590	164	25	,	,	PUNCT
ajset-590	164	26	www.gsjournal.net	www.gsjournal.net	NOUN
ajset-590	164	27	)	)	PUNCT
ajset-590	164	28	.	.	PUNCT
ajset-590	165	1	in	in	ADP
ajset-590	165	2	the	the	DET
ajset-590	165	3	process	process	NOUN
ajset-590	165	4	of	of	ADP
ajset-590	165	5	critical	critical	ADJ
ajset-590	165	6	analysis	analysis	NOUN
ajset-590	165	7	and	and	CCONJ
ajset-590	165	8	of	of	ADP
ajset-590	165	9	interpretation	interpretation	NOUN
ajset-590	165	10	of	of	ADP
ajset-590	165	11	scientific	scientific	ADJ
ajset-590	165	12	theories	theory	NOUN
ajset-590	165	13	,	,	PUNCT
ajset-590	165	14	“	"	PUNCT
ajset-590	165	15	...	...	PUNCT
ajset-590	165	16	we	we	PRON
ajset-590	165	17	can	can	AUX
ajset-590	165	18	hardly	hardly	ADV
ajset-590	165	19	rely	rely	VERB
ajset-590	165	20	on	on	ADP
ajset-590	165	21	any	any	PRON
ajset-590	165	22	of	of	ADP
ajset-590	165	23	the	the	DET
ajset-590	165	24	old	old	ADJ
ajset-590	165	25	principles	principle	NOUN
ajset-590	165	26	even	even	ADV
ajset-590	165	27	if	if	SCONJ
ajset-590	165	28	they	they	PRON
ajset-590	165	29	are	be	AUX
ajset-590	165	30	very	very	ADV
ajset-590	165	31	common	common	ADJ
ajset-590	165	32	.	.	PUNCT
ajset-590	166	1	the	the	DET
ajset-590	166	2	only	only	ADJ
ajset-590	166	3	mandatory	mandatory	ADJ
ajset-590	166	4	requirement	requirement	NOUN
ajset-590	166	5	is	be	AUX
ajset-590	166	6	the	the	DET
ajset-590	166	7	absence	absence	NOUN
ajset-590	166	8	of	of	ADP
ajset-590	166	9	logical	logical	ADJ
ajset-590	166	10	contradictions	contradiction	NOUN
ajset-590	166	11	.	.	PUNCT
ajset-590	166	12	”	"	PUNCT
ajset-590	167	1	(	(	PUNCT
ajset-590	167	2	n.	n.	PROPN
ajset-590	167	3	bohr	bohr	PROPN
ajset-590	167	4	)	)	PUNCT
ajset-590	167	5	.	.	PUNCT
ajset-590	168	1	logical	logical	ADJ
ajset-590	168	2	consistency	consistency	NOUN
ajset-590	168	3	of	of	ADP
ajset-590	168	4	theories	theory	NOUN
ajset-590	168	5	is	be	AUX
ajset-590	168	6	achieved	achieve	VERB
ajset-590	168	7	with	with	ADP
ajset-590	168	8	use	use	NOUN
ajset-590	168	9	of	of	ADP
ajset-590	168	10	the	the	DET
ajset-590	168	11	formal	formal	ADJ
ajset-590	168	12	-	-	PUNCT
ajset-590	168	13	logical	logical	ADJ
ajset-590	168	14	laws	law	NOUN
ajset-590	168	15	.	.	PUNCT
ajset-590	169	1	and	and	CCONJ
ajset-590	169	2	a	a	DET
ajset-590	169	3	natural	natural	ADJ
ajset-590	169	4	-	-	PUNCT
ajset-590	169	5	scientific	scientific	ADJ
ajset-590	169	6	interpretation	interpretation	NOUN
ajset-590	169	7	of	of	ADP
ajset-590	169	8	theories	theory	NOUN
ajset-590	169	9	is	be	AUX
ajset-590	169	10	based	base	VERB
ajset-590	169	11	on	on	ADP
ajset-590	169	12	the	the	DET
ajset-590	169	13	use	use	NOUN
ajset-590	169	14	of	of	ADP
ajset-590	169	15	rational	rational	ADJ
ajset-590	169	16	dialectics	dialectic	NOUN
ajset-590	169	17	.	.	PUNCT
ajset-590	170	1	the	the	DET
ajset-590	170	2	system	system	NOUN
ajset-590	170	3	of	of	ADP
ajset-590	170	4	universal	universal	ADJ
ajset-590	170	5	(	(	PUNCT
ajset-590	170	6	general	general	ADJ
ajset-590	170	7	-	-	PUNCT
ajset-590	170	8	scientific	scientific	ADJ
ajset-590	170	9	)	)	PUNCT
ajset-590	170	10	concepts	concept	NOUN
ajset-590	170	11	and	and	CCONJ
ajset-590	170	12	laws	law	NOUN
ajset-590	170	13	–	–	PUNCT
ajset-590	170	14	i.e.	i.e.	X
ajset-590	170	15	,	,	PUNCT
ajset-590	170	16	science	science	NOUN
ajset-590	170	17	of	of	ADP
ajset-590	170	18	the	the	DET
ajset-590	170	19	general	general	ADJ
ajset-590	170	20	laws	law	NOUN
ajset-590	170	21	of	of	ADP
ajset-590	170	22	development	development	NOUN
ajset-590	170	23	of	of	ADP
ajset-590	170	24	the	the	DET
ajset-590	170	25	nature	nature	NOUN
ajset-590	170	26	,	,	PUNCT
ajset-590	170	27	human	human	ADJ
ajset-590	170	28	society	society	NOUN
ajset-590	170	29	,	,	PUNCT
ajset-590	170	30	and	and	CCONJ
ajset-590	170	31	correct	correct	ADJ
ajset-590	170	32	thinking	thinking	NOUN
ajset-590	170	33	–	–	PUNCT
ajset-590	170	34	is	be	AUX
ajset-590	170	35	the	the	DET
ajset-590	170	36	unity	unity	NOUN
ajset-590	170	37	of	of	ADP
ajset-590	170	38	formal	formal	ADJ
ajset-590	170	39	logic	logic	NOUN
ajset-590	170	40	and	and	CCONJ
ajset-590	170	41	rational	rational	ADJ
ajset-590	170	42	dialectics	dialectic	NOUN
ajset-590	170	43	.	.	PUNCT
ajset-590	171	1	this	this	DET
ajset-590	171	2	unity	unity	NOUN
ajset-590	171	3	is	be	AUX
ajset-590	171	4	not	not	PART
ajset-590	171	5	only	only	ADV
ajset-590	171	6	correct	correct	ADJ
ajset-590	171	7	methodological	methodological	ADJ
ajset-590	171	8	basis	basis	NOUN
ajset-590	171	9	of	of	ADP
ajset-590	171	10	science	science	NOUN
ajset-590	171	11	but	but	CCONJ
ajset-590	171	12	also	also	ADV
ajset-590	171	13	the	the	DET
ajset-590	171	14	correct	correct	ADJ
ajset-590	171	15	methodological	methodological	ADJ
ajset-590	171	16	basis	basis	NOUN
ajset-590	171	17	for	for	ADP
ajset-590	171	18	a	a	DET
ajset-590	171	19	critical	critical	ADJ
ajset-590	171	20	analysis	analysis	NOUN
ajset-590	171	21	of	of	ADP
ajset-590	171	22	theories	theory	NOUN
ajset-590	171	23	.	.	PUNCT
ajset-590	172	1	2	2	X
ajset-590	172	2	.	.	X
ajset-590	172	3	the	the	DET
ajset-590	172	4	origin	origin	NOUN
ajset-590	172	5	of	of	ADP
ajset-590	172	6	vector	vector	NOUN
ajset-590	172	7	calculus	calculus	NOUN
ajset-590	172	8	is	be	AUX
ajset-590	172	9	closely	closely	ADV
ajset-590	172	10	related	relate	VERB
ajset-590	172	11	to	to	ADP
ajset-590	172	12	the	the	DET
ajset-590	172	13	needs	need	NOUN
ajset-590	172	14	of	of	ADP
ajset-590	172	15	mechanics	mechanic	NOUN
ajset-590	172	16	and	and	CCONJ
ajset-590	172	17	physics	physics	PROPN
ajset-590	172	18	:	:	PUNCT
ajset-590	172	19	the	the	DET
ajset-590	172	20	idea	idea	NOUN
ajset-590	172	21	of	of	ADP
ajset-590	172	22	motion	motion	NOUN
ajset-590	172	23	,	,	PUNCT
ajset-590	172	24	the	the	DET
ajset-590	172	25	concepts	concept	NOUN
ajset-590	172	26	of	of	ADP
ajset-590	172	27	process	process	NOUN
ajset-590	172	28	,	,	PUNCT
ajset-590	172	29	velocity	velocity	NOUN
ajset-590	172	30	,	,	PUNCT
ajset-590	172	31	acceleration	acceleration	NOUN
ajset-590	172	32	,	,	PUNCT
ajset-590	172	33	displacement	displacement	NOUN
ajset-590	172	34	,	,	PUNCT
ajset-590	172	35	force	force	NOUN
ajset-590	172	36	,	,	PUNCT
ajset-590	172	37	and	and	CCONJ
ajset-590	172	38	vector	vector	NOUN
ajset-590	172	39	were	be	AUX
ajset-590	172	40	introduced	introduce	VERB
ajset-590	172	41	into	into	ADP
ajset-590	172	42	mathematics	mathematic	NOUN
ajset-590	172	43	in	in	ADP
ajset-590	172	44	the	the	DET
ajset-590	172	45	17	17	NUM
ajset-590	172	46	-	-	PUNCT
ajset-590	172	47	18th	18th	NOUN
ajset-590	172	48	centuries	century	NOUN
ajset-590	172	49	.	.	PUNCT
ajset-590	173	1	the	the	DET
ajset-590	173	2	modern	modern	ADJ
ajset-590	173	3	meaning	meaning	NOUN
ajset-590	173	4	of	of	ADP
ajset-590	173	5	the	the	DET
ajset-590	173	6	word	word	NOUN
ajset-590	173	7	“	"	PUNCT
ajset-590	173	8	vector	vector	NOUN
ajset-590	173	9	”	"	PUNCT
ajset-590	173	10	represents	represent	VERB
ajset-590	173	11	generalization	generalization	NOUN
ajset-590	173	12	of	of	ADP
ajset-590	173	13	its	its	PRON
ajset-590	173	14	previous	previous	ADJ
ajset-590	173	15	(	(	PUNCT
ajset-590	173	16	out	out	NOUN
ajset-590	173	17	-	-	PUNCT
ajset-590	173	18	of	of	ADP
ajset-590	173	19	-	-	PUNCT
ajset-590	173	20	date	date	NOUN
ajset-590	173	21	)	)	PUNCT
ajset-590	173	22	meaning	meaning	NOUN
ajset-590	173	23	in	in	ADP
ajset-590	173	24	astronomy	astronomy	NOUN
ajset-590	173	25	,	,	PUNCT
ajset-590	173	26	where	where	SCONJ
ajset-590	173	27	,	,	PUNCT
ajset-590	173	28	in	in	ADP
ajset-590	173	29	18th	18th	ADJ
ajset-590	173	30	century	century	NOUN
ajset-590	173	31	,	,	PUNCT
ajset-590	173	32	a	a	DET
ajset-590	173	33	vector	vector	NOUN
ajset-590	173	34	is	be	AUX
ajset-590	173	35	called	call	VERB
ajset-590	173	36	an	an	DET
ajset-590	173	37	imaginary	imaginary	ADJ
ajset-590	173	38	straight	straight	ADJ
ajset-590	173	39	line	line	NOUN
ajset-590	173	40	segment	segment	NOUN
ajset-590	173	41	connecting	connect	VERB
ajset-590	173	42	the	the	DET
ajset-590	173	43	planet	planet	NOUN
ajset-590	173	44	to	to	ADP
ajset-590	173	45	the	the	DET
ajset-590	173	46	center	center	NOUN
ajset-590	173	47	(	(	PUNCT
ajset-590	173	48	focus	focus	NOUN
ajset-590	173	49	)	)	PUNCT
ajset-590	173	50	of	of	ADP
ajset-590	173	51	the	the	DET
ajset-590	173	52	motion	motion	NOUN
ajset-590	173	53	.	.	PUNCT
ajset-590	174	1	at	at	ADP
ajset-590	174	2	present	present	ADJ
ajset-590	174	3	,	,	PUNCT
ajset-590	174	4	vector	vector	NOUN
ajset-590	174	5	calculus	calculus	NOUN
ajset-590	174	6	is	be	AUX
ajset-590	174	7	a	a	DET
ajset-590	174	8	branch	branch	NOUN
ajset-590	174	9	of	of	ADP
ajset-590	174	10	mathematics	mathematic	NOUN
ajset-590	174	11	in	in	ADP
ajset-590	174	12	which	which	PRON
ajset-590	174	13	one	one	NUM
ajset-590	174	14	studies	study	VERB
ajset-590	174	15	the	the	DET
ajset-590	174	16	properties	property	NOUN
ajset-590	174	17	of	of	ADP
ajset-590	174	18	operations	operation	NOUN
ajset-590	174	19	on	on	ADP
ajset-590	174	20	vectors	vector	NOUN
ajset-590	174	21	.	.	PUNCT
ajset-590	175	1	but	but	CCONJ
ajset-590	175	2	the	the	DET
ajset-590	175	3	mathematical	mathematical	ADJ
ajset-590	175	4	formalism	formalism	NOUN
ajset-590	175	5	does	do	AUX
ajset-590	175	6	not	not	PART
ajset-590	175	7	contain	contain	VERB
ajset-590	175	8	motion	motion	NOUN
ajset-590	175	9	,	,	PUNCT
ajset-590	175	10	mathematical	mathematical	ADJ
ajset-590	175	11	process	process	NOUN
ajset-590	175	12	.	.	PUNCT
ajset-590	176	1	a	a	DET
ajset-590	176	2	mathematical	mathematical	ADJ
ajset-590	176	3	process	process	NOUN
ajset-590	176	4	is	be	AUX
ajset-590	176	5	carried	carry	VERB
ajset-590	176	6	out	out	ADP
ajset-590	176	7	only	only	ADV
ajset-590	176	8	in	in	ADP
ajset-590	176	9	computers	computer	NOUN
ajset-590	176	10	.	.	PUNCT
ajset-590	177	1	(	(	PUNCT
ajset-590	177	2	this	this	PRON
ajset-590	177	3	is	be	AUX
ajset-590	177	4	why	why	SCONJ
ajset-590	177	5	continual	continual	ADJ
ajset-590	177	6	mathematics	mathematic	NOUN
ajset-590	177	7	must	must	AUX
ajset-590	177	8	be	be	AUX
ajset-590	177	9	replaced	replace	VERB
ajset-590	177	10	by	by	ADP
ajset-590	177	11	discrete	discrete	ADJ
ajset-590	177	12	mathematics	mathematic	NOUN
ajset-590	177	13	–	–	PUNCT
ajset-590	177	14	computer	computer	NOUN
ajset-590	177	15	mathematics	mathematic	NOUN
ajset-590	177	16	)	)	PUNCT
ajset-590	177	17	.	.	PUNCT
ajset-590	178	1	in	in	ADP
ajset-590	178	2	specific	specific	ADJ
ajset-590	178	3	scientific	scientific	ADJ
ajset-590	178	4	problem	problem	NOUN
ajset-590	178	5	,	,	PUNCT
ajset-590	178	6	one	one	PRON
ajset-590	178	7	considers	consider	VERB
ajset-590	178	8	the	the	DET
ajset-590	178	9	quantities	quantity	NOUN
ajset-590	178	10	of	of	ADP
ajset-590	178	11	the	the	DET
ajset-590	178	12	various	various	ADJ
ajset-590	178	13	natures	nature	NOUN
ajset-590	178	14	.	.	PUNCT
ajset-590	179	1	these	these	DET
ajset-590	179	2	quantities	quantity	NOUN
ajset-590	179	3	have	have	VERB
ajset-590	179	4	different	different	ADJ
ajset-590	179	5	dimensions	dimension	NOUN
ajset-590	179	6	:	:	PUNCT
ajset-590	179	7	length	length	NOUN
ajset-590	179	8	,	,	PUNCT
ajset-590	179	9	area	area	NOUN
ajset-590	179	10	,	,	PUNCT
ajset-590	179	11	volume	volume	NOUN
ajset-590	179	12	,	,	PUNCT
ajset-590	179	13	weight	weight	NOUN
ajset-590	179	14	,	,	PUNCT
ajset-590	179	15	temperature	temperature	NOUN
ajset-590	179	16	,	,	PUNCT
ajset-590	179	17	speed	speed	NOUN
ajset-590	179	18	,	,	PUNCT
ajset-590	179	19	strength	strength	NOUN
ajset-590	179	20	,	,	PUNCT
ajset-590	179	21	etc	etc	X
ajset-590	179	22	.	.	X
ajset-590	179	23	)	)	PUNCT
ajset-590	179	24	.	.	PUNCT
ajset-590	180	1	if	if	SCONJ
ajset-590	180	2	one	one	NUM
ajset-590	180	3	selects	select	VERB
ajset-590	180	4	a	a	DET
ajset-590	180	5	(	(	PUNCT
ajset-590	180	6	define	define	NOUN
ajset-590	180	7	,	,	PUNCT
ajset-590	180	8	explicit	explicit	ADJ
ajset-590	180	9	,	,	PUNCT
ajset-590	180	10	appointed	appoint	VERB
ajset-590	180	11	)	)	PUNCT
ajset-590	180	12	determined	determined	ADJ
ajset-590	180	13	unit	unit	NOUN
ajset-590	180	14	,	,	PUNCT
ajset-590	180	15	then	then	ADV
ajset-590	180	16	each	each	DET
ajset-590	180	17	value	value	NOUN
ajset-590	180	18	of	of	ADP
ajset-590	180	19	the	the	DET
ajset-590	180	20	quantity	quantity	NOUN
ajset-590	180	21	must	must	AUX
ajset-590	180	22	be	be	AUX
ajset-590	180	23	expressed	express	VERB
ajset-590	180	24	by	by	ADP
ajset-590	180	25	denominate	denominate	NOUN
ajset-590	180	26	number	number	NOUN
ajset-590	180	27	.	.	PUNCT
ajset-590	181	1	but	but	CCONJ
ajset-590	181	2	mathematics	mathematic	NOUN
ajset-590	181	3	does	do	AUX
ajset-590	181	4	not	not	PART
ajset-590	181	5	consider	consider	VERB
ajset-590	181	6	the	the	DET
ajset-590	181	7	specific	specific	ADJ
ajset-590	181	8	quantities	quantity	NOUN
ajset-590	181	9	:	:	PUNCT
ajset-590	181	10	the	the	DET
ajset-590	181	11	mathematical	mathematical	ADJ
ajset-590	181	12	propositions	proposition	NOUN
ajset-590	181	13	and	and	CCONJ
ajset-590	181	14	laws	law	NOUN
ajset-590	181	15	are	be	AUX
ajset-590	181	16	formulated	formulate	VERB
ajset-590	181	17	,	,	PUNCT
ajset-590	181	18	abstracting	abstract	VERB
ajset-590	181	19	from	from	ADP
ajset-590	181	20	the	the	DET
ajset-590	181	21	specific	specific	ADJ
ajset-590	181	22	nature	nature	NOUN
ajset-590	181	23	of	of	ADP
ajset-590	181	24	the	the	DET
ajset-590	181	25	quantities	quantity	NOUN
ajset-590	181	26	,	,	PUNCT
ajset-590	181	27	taking	take	VERB
ajset-590	181	28	into	into	ADP
ajset-590	181	29	consideration	consideration	NOUN
ajset-590	181	30	only	only	ADV
ajset-590	181	31	their	their	PRON
ajset-590	181	32	mailto:topacademicjournals@gmail.com	mailto:topacademicjournals@gmail.com	PROPN
ajset-590	181	33	academic	academic	ADJ
ajset-590	181	34	journal	journal	NOUN
ajset-590	181	35	of	of	ADP
ajset-590	181	36	science	science	NOUN
ajset-590	181	37	,	,	PUNCT
ajset-590	181	38	engineering	engineering	NOUN
ajset-590	181	39	and	and	CCONJ
ajset-590	181	40	technology	technology	NOUN
ajset-590	181	41	vol.8	vol.8	PROPN
ajset-590	181	42	,	,	PUNCT
ajset-590	181	43	issue	issue	NOUN
ajset-590	181	44	5	5	NUM
ajset-590	181	45	;	;	PUNCT
ajset-590	181	46	september	september	PROPN
ajset-590	181	47	october	october	PROPN
ajset-590	181	48	2023	2023	NUM
ajset-590	181	49	;	;	PUNCT
ajset-590	181	50	issn	issn	PROPN
ajset-590	181	51	:	:	PUNCT
ajset-590	181	52	2837	2837	NUM
ajset-590	181	53	-	-	SYM
ajset-590	181	54	2964	2964	NUM
ajset-590	181	55	impact	impact	NOUN
ajset-590	181	56	factor	factor	NOUN
ajset-590	181	57	:	:	PUNCT
ajset-590	181	58	6.67	6.67	NUM
ajset-590	181	59	1252	1252	NUM
ajset-590	181	60	columbia	columbia	PROPN
ajset-590	181	61	rd	rd	PROPN
ajset-590	181	62	nw	nw	PROPN
ajset-590	181	63	,	,	PUNCT
ajset-590	181	64	washington	washington	PROPN
ajset-590	181	65	dc	dc	PROPN
ajset-590	181	66	,	,	PUNCT
ajset-590	181	67	united	united	PROPN
ajset-590	181	68	states	states	PROPN
ajset-590	181	69	https://topjournals.org/index.php/ajset/index	https://topjournals.org/index.php/ajset/index	PROPN
ajset-590	181	70	;	;	PUNCT
ajset-590	181	71	mail	mail	NOUN
ajset-590	181	72	:	:	PUNCT
ajset-590	181	73	topacademicjournals@gmail.com	topacademicjournals@gmail.com	X
ajset-590	182	1	16	16	NUM
ajset-590	183	1	|	|	ADV
ajset-590	183	2	a	a	DET
ajset-590	183	3	c	c	NOUN
ajset-590	183	4	a	a	PRON
ajset-590	183	5	d	d	X
ajset-590	183	6	e	e	NOUN
ajset-590	183	7	m	m	NOUN
ajset-590	183	8	i	i	NOUN
ajset-590	183	9	c	c	NOUN
ajset-590	183	10	j	j	NOUN
ajset-590	183	11	o	o	X
ajset-590	183	12	u	u	NOUN
ajset-590	183	13	r	r	NOUN
ajset-590	183	14	n	n	NOUN
ajset-590	183	15	a	a	DET
ajset-590	183	16	l	l	NOUN
ajset-590	184	1	o	o	X
ajset-590	184	2	f	f	X
ajset-590	184	3	s	s	X
ajset-590	184	4	c	c	NOUN
ajset-590	185	1	i	i	NOUN
ajset-590	185	2	e	e	PROPN
ajset-590	185	3	n	n	PROPN
ajset-590	185	4	c	c	NOUN
ajset-590	185	5	e	e	X
ajset-590	185	6	,	,	PUNCT
ajset-590	185	7	e	e	PROPN
ajset-590	185	8	n	n	PRON
ajset-590	185	9	g	g	NOUN
ajset-590	185	10	i	i	PRON
ajset-590	185	11	n	n	VERB
ajset-590	185	12	e	e	NOUN
ajset-590	185	13	e	e	NOUN
ajset-590	185	14	r	r	VERB
ajset-590	185	15	i	i	PRON
ajset-590	185	16	n	n	CCONJ
ajset-590	185	17	g	g	PROPN
ajset-590	185	18	a	a	DET
ajset-590	185	19	n	n	NOUN
ajset-590	185	20	d	d	NOUN
ajset-590	185	21	t	t	NOUN
ajset-590	185	22	e	e	X
ajset-590	185	23	c	c	NOUN
ajset-590	185	24	h	h	NOUN
ajset-590	185	25	n	n	ADV
ajset-590	185	26	o	o	NOUN
ajset-590	185	27	l	l	NOUN
ajset-590	186	1	o	o	X
ajset-590	186	2	g	g	NOUN
ajset-590	186	3	y	y	PROPN
ajset-590	186	4	|	|	ADV
ajset-590	186	5	https://topjournals.org/index.php/ajset	https://topjournals.org/index.php/ajset	VERB
ajset-590	186	6	numerical	numerical	ADJ
ajset-590	186	7	values	value	NOUN
ajset-590	186	8	.	.	PUNCT
ajset-590	187	1	in	in	ADP
ajset-590	187	2	line	line	NOUN
ajset-590	187	3	with	with	ADP
ajset-590	187	4	this	this	PRON
ajset-590	187	5	,	,	PUNCT
ajset-590	187	6	mathematics	mathematic	NOUN
ajset-590	187	7	considers	consider	VERB
ajset-590	187	8	the	the	DET
ajset-590	187	9	quantity	quantity	NOUN
ajset-590	187	10	in	in	ADP
ajset-590	187	11	general	general	ADJ
ajset-590	187	12	,	,	PUNCT
ajset-590	187	13	the	the	DET
ajset-590	187	14	vector	vector	NOUN
ajset-590	187	15	in	in	ADP
ajset-590	187	16	general	general	ADJ
ajset-590	187	17	,	,	PUNCT
ajset-590	187	18	and	and	CCONJ
ajset-590	187	19	so	so	ADV
ajset-590	187	20	on	on	ADV
ajset-590	187	21	,	,	PUNCT
ajset-590	187	22	neglecting	neglect	VERB
ajset-590	187	23	the	the	DET
ajset-590	187	24	natural	natural	ADJ
ajset-590	187	25	-	-	PUNCT
ajset-590	187	26	scientific	scientific	ADJ
ajset-590	187	27	meaning	meaning	NOUN
ajset-590	187	28	of	of	ADP
ajset-590	187	29	the	the	DET
ajset-590	187	30	quantity	quantity	NOUN
ajset-590	187	31	.	.	PUNCT
ajset-590	188	1	abstract	abstract	ADJ
ajset-590	188	2	mathematical	mathematical	ADJ
ajset-590	188	3	propositions	proposition	NOUN
ajset-590	188	4	,	,	PUNCT
ajset-590	188	5	theories	theory	NOUN
ajset-590	188	6	,	,	PUNCT
ajset-590	188	7	and	and	CCONJ
ajset-590	188	8	models	model	NOUN
ajset-590	188	9	can	can	AUX
ajset-590	188	10	not	not	PART
ajset-590	188	11	be	be	AUX
ajset-590	188	12	tested	test	VERB
ajset-590	188	13	and	and	CCONJ
ajset-590	188	14	used	use	VERB
ajset-590	188	15	in	in	ADP
ajset-590	188	16	the	the	DET
ajset-590	188	17	natural	natural	ADJ
ajset-590	188	18	sciences	science	NOUN
ajset-590	188	19	.	.	PUNCT
ajset-590	189	1	from	from	ADP
ajset-590	189	2	the	the	DET
ajset-590	189	3	point	point	NOUN
ajset-590	189	4	of	of	ADP
ajset-590	189	5	view	view	NOUN
ajset-590	189	6	of	of	ADP
ajset-590	189	7	formal	formal	ADJ
ajset-590	189	8	logic	logic	NOUN
ajset-590	189	9	and	and	CCONJ
ajset-590	189	10	of	of	ADP
ajset-590	189	11	rational	rational	ADJ
ajset-590	189	12	dialectics	dialectic	NOUN
ajset-590	189	13	,	,	PUNCT
ajset-590	189	14	in	in	ADP
ajset-590	189	15	order	order	NOUN
ajset-590	189	16	to	to	PART
ajset-590	189	17	test	test	VERB
ajset-590	189	18	and	and	CCONJ
ajset-590	189	19	use	use	VERB
ajset-590	189	20	mathematical	mathematical	ADJ
ajset-590	189	21	propositions	proposition	NOUN
ajset-590	189	22	,	,	PUNCT
ajset-590	189	23	theories	theory	NOUN
ajset-590	189	24	,	,	PUNCT
ajset-590	189	25	and	and	CCONJ
ajset-590	189	26	models	model	NOUN
ajset-590	189	27	in	in	ADP
ajset-590	189	28	practice	practice	NOUN
ajset-590	189	29	,	,	PUNCT
ajset-590	189	30	it	it	PRON
ajset-590	189	31	is	be	AUX
ajset-590	189	32	necessary	necessary	ADJ
ajset-590	189	33	to	to	PART
ajset-590	189	34	define	define	VERB
ajset-590	189	35	the	the	DET
ajset-590	189	36	natural	natural	ADJ
ajset-590	189	37	-	-	PUNCT
ajset-590	189	38	scientific	scientific	ADJ
ajset-590	189	39	(	(	PUNCT
ajset-590	189	40	practical	practical	ADJ
ajset-590	189	41	)	)	PUNCT
ajset-590	189	42	meaning	meaning	NOUN
ajset-590	189	43	of	of	ADP
ajset-590	189	44	mathematical	mathematical	ADJ
ajset-590	189	45	concepts	concept	NOUN
ajset-590	189	46	(	(	PUNCT
ajset-590	189	47	objects	object	NOUN
ajset-590	189	48	)	)	PUNCT
ajset-590	189	49	and	and	CCONJ
ajset-590	189	50	relations	relation	NOUN
ajset-590	189	51	,	,	PUNCT
ajset-590	189	52	i.e.	i.e.	X
ajset-590	189	53	,	,	PUNCT
ajset-590	189	54	to	to	PART
ajset-590	189	55	consider	consider	VERB
ajset-590	189	56	not	not	PART
ajset-590	189	57	a	a	DET
ajset-590	189	58	“	"	PUNCT
ajset-590	189	59	quantity	quantity	NOUN
ajset-590	189	60	in	in	ADP
ajset-590	189	61	general	general	ADJ
ajset-590	189	62	”	"	PUNCT
ajset-590	189	63	,	,	PUNCT
ajset-590	189	64	a	a	DET
ajset-590	189	65	“	"	PUNCT
ajset-590	189	66	number	number	NOUN
ajset-590	189	67	in	in	ADP
ajset-590	189	68	general	general	NOUN
ajset-590	189	69	”	"	PUNCT
ajset-590	189	70	,	,	PUNCT
ajset-590	189	71	“	"	PUNCT
ajset-590	189	72	vector	vector	NOUN
ajset-590	189	73	in	in	ADP
ajset-590	189	74	general	general	NOUN
ajset-590	189	75	”	"	PUNCT
ajset-590	189	76	,	,	PUNCT
ajset-590	189	77	but	but	CCONJ
ajset-590	189	78	to	to	PART
ajset-590	189	79	consider	consider	VERB
ajset-590	189	80	the	the	DET
ajset-590	189	81	nature	nature	NOUN
ajset-590	189	82	(	(	PUNCT
ajset-590	189	83	i.e.	i.e.	X
ajset-590	189	84	,	,	PUNCT
ajset-590	189	85	dimensions	dimension	NOUN
ajset-590	189	86	)	)	PUNCT
ajset-590	189	87	of	of	ADP
ajset-590	189	88	quantities	quantity	NOUN
ajset-590	189	89	(	(	PUNCT
ajset-590	189	90	length	length	NOUN
ajset-590	189	91	,	,	PUNCT
ajset-590	189	92	area	area	NOUN
ajset-590	189	93	,	,	PUNCT
ajset-590	189	94	volume	volume	NOUN
ajset-590	189	95	,	,	PUNCT
ajset-590	189	96	weight	weight	NOUN
ajset-590	189	97	,	,	PUNCT
ajset-590	189	98	temperature	temperature	NOUN
ajset-590	189	99	,	,	PUNCT
ajset-590	189	100	speed	speed	NOUN
ajset-590	189	101	,	,	PUNCT
ajset-590	189	102	acceleration	acceleration	NOUN
ajset-590	189	103	,	,	PUNCT
ajset-590	189	104	displacement	displacement	NOUN
ajset-590	189	105	,	,	PUNCT
ajset-590	189	106	force	force	NOUN
ajset-590	189	107	,	,	PUNCT
ajset-590	189	108	etc	etc	X
ajset-590	189	109	.	.	X
ajset-590	189	110	)	)	PUNCT
ajset-590	189	111	.	.	PUNCT
ajset-590	190	1	from	from	ADP
ajset-590	190	2	this	this	DET
ajset-590	190	3	point	point	NOUN
ajset-590	190	4	of	of	ADP
ajset-590	190	5	view	view	NOUN
ajset-590	190	6	,	,	PUNCT
ajset-590	190	7	the	the	DET
ajset-590	190	8	standard	standard	ADJ
ajset-590	190	9	vector	vector	NOUN
ajset-590	190	10	calculus	calculus	NOUN
ajset-590	190	11	does	do	AUX
ajset-590	190	12	not	not	PART
ajset-590	190	13	have	have	VERB
ajset-590	190	14	a	a	DET
ajset-590	190	15	natural	natural	ADJ
ajset-590	190	16	-	-	PUNCT
ajset-590	190	17	scientific	scientific	ADJ
ajset-590	190	18	meaning	meaning	NOUN
ajset-590	190	19	because	because	SCONJ
ajset-590	190	20	the	the	DET
ajset-590	190	21	standard	standard	ADJ
ajset-590	190	22	vector	vector	NOUN
ajset-590	190	23	calculus	calculus	NOUN
ajset-590	190	24	is	be	AUX
ajset-590	190	25	based	base	VERB
ajset-590	190	26	on	on	ADP
ajset-590	190	27	the	the	DET
ajset-590	190	28	concept	concept	NOUN
ajset-590	190	29	of	of	ADP
ajset-590	190	30	“	"	PUNCT
ajset-590	190	31	vector	vector	NOUN
ajset-590	190	32	in	in	ADP
ajset-590	190	33	general	general	NOUN
ajset-590	190	34	”	"	PUNCT
ajset-590	190	35	.	.	PUNCT
ajset-590	191	1	clarification	clarification	NOUN
ajset-590	191	2	of	of	ADP
ajset-590	191	3	naturalscientific	naturalscientific	ADJ
ajset-590	191	4	meaning	meaning	NOUN
ajset-590	191	5	of	of	ADP
ajset-590	191	6	concept	concept	NOUN
ajset-590	191	7	of	of	ADP
ajset-590	191	8	“	"	PUNCT
ajset-590	191	9	vector	vector	NOUN
ajset-590	191	10	”	"	PUNCT
ajset-590	191	11	and	and	CCONJ
ajset-590	191	12	a	a	DET
ajset-590	191	13	logical	logical	ADJ
ajset-590	191	14	analysis	analysis	NOUN
ajset-590	191	15	of	of	ADP
ajset-590	191	16	operations	operation	NOUN
ajset-590	191	17	on	on	ADP
ajset-590	191	18	the	the	DET
ajset-590	191	19	“	"	PUNCT
ajset-590	191	20	physical	physical	ADJ
ajset-590	191	21	vectors	vector	NOUN
ajset-590	191	22	”	"	PUNCT
ajset-590	191	23	show	show	VERB
ajset-590	191	24	that	that	SCONJ
ajset-590	191	25	the	the	DET
ajset-590	191	26	standard	standard	ADJ
ajset-590	191	27	propositions	proposition	NOUN
ajset-590	191	28	of	of	ADP
ajset-590	191	29	vector	vector	NOUN
ajset-590	191	30	calculus	calculus	NOUN
ajset-590	191	31	,	,	PUNCT
ajset-590	191	32	relating	relate	VERB
ajset-590	191	33	to	to	ADP
ajset-590	191	34	the	the	DET
ajset-590	191	35	“	"	PUNCT
ajset-590	191	36	physical	physical	ADJ
ajset-590	191	37	vectors	vector	NOUN
ajset-590	191	38	”	"	PUNCT
ajset-590	191	39	,	,	PUNCT
ajset-590	191	40	are	be	AUX
ajset-590	191	41	contrary	contrary	ADJ
ajset-590	191	42	to	to	ADP
ajset-590	191	43	formal	formal	ADJ
ajset-590	191	44	logic	logic	NOUN
ajset-590	191	45	.	.	PUNCT
ajset-590	192	1	3	3	X
ajset-590	192	2	.	.	X
ajset-590	192	3	there	there	PRON
ajset-590	192	4	are	be	VERB
ajset-590	192	5	two	two	NUM
ajset-590	192	6	opinions	opinion	NOUN
ajset-590	192	7	about	about	ADP
ajset-590	192	8	the	the	DET
ajset-590	192	9	existence	existence	NOUN
ajset-590	192	10	of	of	ADP
ajset-590	192	11	logical	logical	ADJ
ajset-590	192	12	errors	error	NOUN
ajset-590	192	13	in	in	ADP
ajset-590	192	14	generally	generally	ADV
ajset-590	192	15	accepted	accept	VERB
ajset-590	192	16	theories	theory	NOUN
ajset-590	192	17	(	(	PUNCT
ajset-590	192	18	for	for	ADP
ajset-590	192	19	example	example	NOUN
ajset-590	192	20	,	,	PUNCT
ajset-590	192	21	in	in	ADP
ajset-590	192	22	physics	physics	NOUN
ajset-590	192	23	and	and	CCONJ
ajset-590	192	24	mathematics	mathematic	NOUN
ajset-590	192	25	)	)	PUNCT
ajset-590	192	26	.	.	PUNCT
ajset-590	193	1	the	the	DET
ajset-590	193	2	first	first	ADJ
ajset-590	193	3	opinion	opinion	NOUN
ajset-590	193	4	is	be	AUX
ajset-590	193	5	that	that	SCONJ
ajset-590	193	6	,	,	PUNCT
ajset-590	193	7	although	although	SCONJ
ajset-590	193	8	a	a	DET
ajset-590	193	9	theory	theory	NOUN
ajset-590	193	10	(	(	PUNCT
ajset-590	193	11	for	for	ADP
ajset-590	193	12	example	example	NOUN
ajset-590	193	13	,	,	PUNCT
ajset-590	193	14	the	the	DET
ajset-590	193	15	special	special	ADJ
ajset-590	193	16	theory	theory	NOUN
ajset-590	193	17	of	of	ADP
ajset-590	193	18	relativity	relativity	NOUN
ajset-590	193	19	)	)	PUNCT
ajset-590	193	20	contains	contain	VERB
ajset-590	193	21	logical	logical	ADJ
ajset-590	193	22	errors	error	NOUN
ajset-590	193	23	,	,	PUNCT
ajset-590	193	24	“	"	PUNCT
ajset-590	193	25	it	it	PRON
ajset-590	193	26	works	work	VERB
ajset-590	193	27	well	well	ADV
ajset-590	193	28	”	"	PUNCT
ajset-590	193	29	(	(	PUNCT
ajset-590	193	30	gerard’t	gerard’t	PROPN
ajset-590	193	31	hooft	hooft	NOUN
ajset-590	193	32	)	)	PUNCT
ajset-590	193	33	.	.	PUNCT
ajset-590	194	1	the	the	DET
ajset-590	194	2	second	second	ADJ
ajset-590	194	3	opinion	opinion	NOUN
ajset-590	194	4	is	be	AUX
ajset-590	194	5	that	that	SCONJ
ajset-590	194	6	the	the	DET
ajset-590	194	7	system	system	NOUN
ajset-590	194	8	of	of	ADP
ajset-590	194	9	four	four	NUM
ajset-590	194	10	fundamental	fundamental	ADJ
ajset-590	194	11	formal	formal	ADJ
ajset-590	194	12	-	-	PUNCT
ajset-590	194	13	logical	logical	ADJ
ajset-590	194	14	laws	law	NOUN
ajset-590	194	15	is	be	AUX
ajset-590	194	16	incomplete	incomplete	ADJ
ajset-590	194	17	and	and	CCONJ
ajset-590	194	18	insufficient	insufficient	ADJ
ajset-590	194	19	for	for	ADP
ajset-590	194	20	a	a	DET
ajset-590	194	21	panchreston	panchreston	NOUN
ajset-590	194	22	(	(	PUNCT
ajset-590	194	23	i.e.	i.e.	X
ajset-590	194	24	,	,	PUNCT
ajset-590	194	25	for	for	ADP
ajset-590	194	26	complete	complete	ADJ
ajset-590	194	27	explanation	explanation	NOUN
ajset-590	194	28	)	)	PUNCT
ajset-590	194	29	and	and	CCONJ
ajset-590	194	30	mathematical	mathematical	ADJ
ajset-590	194	31	description	description	NOUN
ajset-590	194	32	of	of	ADP
ajset-590	194	33	reality	reality	NOUN
ajset-590	194	34	.	.	PUNCT
ajset-590	195	1	in	in	ADP
ajset-590	195	2	essence	essence	NOUN
ajset-590	195	3	,	,	PUNCT
ajset-590	195	4	these	these	DET
ajset-590	195	5	opinions	opinion	NOUN
ajset-590	195	6	are	be	AUX
ajset-590	195	7	identical	identical	ADJ
ajset-590	195	8	.	.	PUNCT
ajset-590	196	1	however	however	ADV
ajset-590	196	2	,	,	PUNCT
ajset-590	196	3	in	in	ADP
ajset-590	196	4	my	my	PRON
ajset-590	196	5	opinion	opinion	NOUN
ajset-590	196	6	,	,	PUNCT
ajset-590	196	7	these	these	DET
ajset-590	196	8	views	view	NOUN
ajset-590	196	9	are	be	AUX
ajset-590	196	10	not	not	PART
ajset-590	196	11	free	free	ADJ
ajset-590	196	12	from	from	ADP
ajset-590	196	13	objection	objection	NOUN
ajset-590	196	14	.	.	PUNCT
ajset-590	197	1	the	the	DET
ajset-590	197	2	objection	objection	NOUN
ajset-590	197	3	is	be	AUX
ajset-590	197	4	as	as	SCONJ
ajset-590	197	5	follows	follow	VERB
ajset-590	197	6	.	.	PUNCT
ajset-590	198	1	if	if	SCONJ
ajset-590	198	2	one	one	PRON
ajset-590	198	3	will	will	AUX
ajset-590	198	4	discover	discover	VERB
ajset-590	198	5	additional	additional	ADJ
ajset-590	198	6	formal	formal	ADJ
ajset-590	198	7	logic	logic	NOUN
ajset-590	198	8	laws	law	NOUN
ajset-590	198	9	,	,	PUNCT
ajset-590	198	10	then	then	ADV
ajset-590	198	11	the	the	DET
ajset-590	198	12	complete	complete	ADJ
ajset-590	198	13	system	system	NOUN
ajset-590	198	14	of	of	ADP
ajset-590	198	15	laws	law	NOUN
ajset-590	198	16	should	should	AUX
ajset-590	198	17	not	not	PART
ajset-590	198	18	be	be	AUX
ajset-590	198	19	contradictory	contradictory	ADJ
ajset-590	198	20	:	:	PUNCT
ajset-590	198	21	the	the	DET
ajset-590	198	22	four	four	NUM
ajset-590	198	23	basic	basic	ADJ
ajset-590	198	24	laws	law	NOUN
ajset-590	198	25	will	will	AUX
ajset-590	198	26	retain	retain	VERB
ajset-590	198	27	its	its	PRON
ajset-590	198	28	place	place	NOUN
ajset-590	198	29	and	and	CCONJ
ajset-590	198	30	importance	importance	NOUN
ajset-590	198	31	in	in	ADP
ajset-590	198	32	a	a	DET
ajset-590	198	33	new	new	ADJ
ajset-590	198	34	,	,	PUNCT
ajset-590	198	35	complete	complete	ADJ
ajset-590	198	36	system	system	NOUN
ajset-590	198	37	(	(	PUNCT
ajset-590	198	38	in	in	ADP
ajset-590	198	39	other	other	ADJ
ajset-590	198	40	words	word	NOUN
ajset-590	198	41	,	,	PUNCT
ajset-590	198	42	the	the	DET
ajset-590	198	43	four	four	NUM
ajset-590	198	44	basic	basic	ADJ
ajset-590	198	45	laws	law	NOUN
ajset-590	198	46	will	will	AUX
ajset-590	198	47	not	not	PART
ajset-590	198	48	be	be	AUX
ajset-590	198	49	refuted	refute	VERB
ajset-590	198	50	)	)	PUNCT
ajset-590	198	51	.	.	PUNCT
ajset-590	199	1	in	in	ADP
ajset-590	199	2	this	this	DET
ajset-590	199	3	case	case	NOUN
ajset-590	199	4	,	,	PUNCT
ajset-590	199	5	the	the	DET
ajset-590	199	6	theories	theory	NOUN
ajset-590	199	7	that	that	PRON
ajset-590	199	8	are	be	AUX
ajset-590	199	9	erroneous	erroneous	ADJ
ajset-590	199	10	in	in	ADP
ajset-590	199	11	“	"	PUNCT
ajset-590	199	12	incomplete	incomplete	ADJ
ajset-590	199	13	”	"	PUNCT
ajset-590	199	14	logical	logical	ADJ
ajset-590	199	15	system	system	NOUN
ajset-590	199	16	will	will	AUX
ajset-590	199	17	also	also	ADV
ajset-590	199	18	be	be	AUX
ajset-590	199	19	erroneous	erroneous	ADJ
ajset-590	199	20	in	in	ADP
ajset-590	199	21	the	the	DET
ajset-590	199	22	“	"	PUNCT
ajset-590	199	23	complete	complete	ADJ
ajset-590	199	24	”	"	PUNCT
ajset-590	199	25	logical	logical	ADJ
ajset-590	199	26	system	system	NOUN
ajset-590	199	27	.	.	PUNCT
ajset-590	200	1	and	and	CCONJ
ajset-590	200	2	the	the	DET
ajset-590	200	3	theories	theory	NOUN
ajset-590	200	4	that	that	PRON
ajset-590	200	5	contain	contain	VERB
ajset-590	200	6	logical	logical	ADJ
ajset-590	200	7	errors	error	NOUN
ajset-590	200	8	are	be	AUX
ajset-590	200	9	false	false	ADJ
ajset-590	200	10	in	in	ADP
ajset-590	200	11	essence	essence	NOUN
ajset-590	200	12	.	.	PUNCT
ajset-590	201	1	but	but	CCONJ
ajset-590	201	2	the	the	DET
ajset-590	201	3	following	follow	VERB
ajset-590	201	4	questions	question	NOUN
ajset-590	201	5	will	will	AUX
ajset-590	201	6	always	always	ADV
ajset-590	201	7	remain	remain	VERB
ajset-590	201	8	open	open	ADJ
ajset-590	201	9	:	:	PUNCT
ajset-590	201	10	why	why	SCONJ
ajset-590	201	11	devices	device	NOUN
ajset-590	201	12	that	that	PRON
ajset-590	201	13	are	be	AUX
ajset-590	201	14	based	base	VERB
ajset-590	201	15	on	on	ADP
ajset-590	201	16	false	false	ADJ
ajset-590	201	17	scientific	scientific	ADJ
ajset-590	201	18	theories	theory	NOUN
ajset-590	201	19	(	(	PUNCT
ajset-590	201	20	ideas	idea	NOUN
ajset-590	201	21	)	)	PUNCT
ajset-590	201	22	work	work	NOUN
ajset-590	201	23	?	?	PUNCT
ajset-590	202	1	why	why	SCONJ
ajset-590	202	2	do	do	AUX
ajset-590	202	3	the	the	DET
ajset-590	202	4	false	false	ADJ
ajset-590	202	5	scientific	scientific	ADJ
ajset-590	202	6	theories	theory	NOUN
ajset-590	202	7	contribute	contribute	VERB
ajset-590	202	8	to	to	ADP
ajset-590	202	9	the	the	DET
ajset-590	202	10	development	development	NOUN
ajset-590	202	11	of	of	ADP
ajset-590	202	12	mankind	mankind	NOUN
ajset-590	202	13	?	?	PUNCT
ajset-590	203	1	where	where	SCONJ
ajset-590	203	2	is	be	AUX
ajset-590	203	3	the	the	DET
ajset-590	203	4	limit	limit	NOUN
ajset-590	203	5	of	of	ADP
ajset-590	203	6	development	development	NOUN
ajset-590	203	7	based	base	VERB
ajset-590	203	8	on	on	ADP
ajset-590	203	9	false	false	ADJ
ajset-590	203	10	theories	theory	NOUN
ajset-590	203	11	?	?	PUNCT
ajset-590	204	1	what	what	PRON
ajset-590	204	2	is	be	AUX
ajset-590	204	3	the	the	DET
ajset-590	204	4	danger	danger	NOUN
ajset-590	204	5	of	of	ADP
ajset-590	204	6	development	development	NOUN
ajset-590	204	7	based	base	VERB
ajset-590	204	8	on	on	ADP
ajset-590	204	9	false	false	ADJ
ajset-590	204	10	theories	theory	NOUN
ajset-590	204	11	?	?	PUNCT
ajset-590	205	1	what	what	PRON
ajset-590	205	2	are	be	AUX
ajset-590	205	3	the	the	DET
ajset-590	205	4	essence	essence	NOUN
ajset-590	205	5	and	and	CCONJ
ajset-590	205	6	predestination	predestination	NOUN
ajset-590	205	7	of	of	ADP
ajset-590	205	8	development	development	NOUN
ajset-590	205	9	?	?	PUNCT
ajset-590	206	1	conclusion	conclusion	NOUN
ajset-590	206	2	thus	thus	ADV
ajset-590	206	3	,	,	PUNCT
ajset-590	206	4	the	the	DET
ajset-590	206	5	formal	formal	ADJ
ajset-590	206	6	-	-	PUNCT
ajset-590	206	7	logical	logical	ADJ
ajset-590	206	8	and	and	CCONJ
ajset-590	206	9	dialectical	dialectical	ADJ
ajset-590	206	10	analysis	analysis	NOUN
ajset-590	206	11	of	of	ADP
ajset-590	206	12	the	the	DET
ajset-590	206	13	foundations	foundation	NOUN
ajset-590	206	14	of	of	ADP
ajset-590	206	15	vector	vector	NOUN
ajset-590	206	16	calculus	calculus	NOUN
ajset-590	206	17	leads	lead	VERB
ajset-590	206	18	to	to	ADP
ajset-590	206	19	the	the	DET
ajset-590	206	20	following	follow	VERB
ajset-590	206	21	main	main	ADJ
ajset-590	206	22	results	result	NOUN
ajset-590	206	23	:	:	PUNCT
ajset-590	206	24	the	the	DET
ajset-590	206	25	standard	standard	ADJ
ajset-590	206	26	vector	vector	NOUN
ajset-590	206	27	calculus	calculus	NOUN
ajset-590	206	28	is	be	AUX
ajset-590	206	29	incorrect	incorrect	ADJ
ajset-590	206	30	theory	theory	NOUN
ajset-590	206	31	because	because	SCONJ
ajset-590	206	32	a.	a.	NOUN
ajset-590	206	33	it	it	PRON
ajset-590	206	34	is	be	AUX
ajset-590	206	35	not	not	PART
ajset-590	206	36	based	base	VERB
ajset-590	206	37	on	on	ADP
ajset-590	206	38	the	the	DET
ajset-590	206	39	correct	correct	ADJ
ajset-590	206	40	methodological	methodological	ADJ
ajset-590	206	41	basis	basis	NOUN
ajset-590	206	42	:	:	PUNCT
ajset-590	206	43	the	the	DET
ajset-590	206	44	unity	unity	NOUN
ajset-590	206	45	of	of	ADP
ajset-590	206	46	formal	formal	ADJ
ajset-590	206	47	logic	logic	NOUN
ajset-590	206	48	and	and	CCONJ
ajset-590	206	49	of	of	ADP
ajset-590	206	50	rational	rational	ADJ
ajset-590	206	51	dialectics	dialectic	NOUN
ajset-590	206	52	;	;	PUNCT
ajset-590	206	53	b.	b.	PROPN
ajset-590	206	54	it	it	PRON
ajset-590	206	55	does	do	AUX
ajset-590	206	56	not	not	PART
ajset-590	206	57	contain	contain	VERB
ajset-590	206	58	the	the	DET
ajset-590	206	59	correct	correct	ADJ
ajset-590	206	60	definitions	definition	NOUN
ajset-590	206	61	of	of	ADP
ajset-590	206	62	concepts	concept	NOUN
ajset-590	206	63	of	of	ADP
ajset-590	206	64	“	"	PUNCT
ajset-590	206	65	movement	movement	NOUN
ajset-590	206	66	”	"	PUNCT
ajset-590	206	67	,	,	PUNCT
ajset-590	206	68	“	"	PUNCT
ajset-590	206	69	direction	direction	NOUN
ajset-590	206	70	”	"	PUNCT
ajset-590	206	71	,	,	PUNCT
ajset-590	206	72	and	and	CCONJ
ajset-590	206	73	“	"	PUNCT
ajset-590	206	74	vector	vector	NOUN
ajset-590	206	75	”	"	PUNCT
ajset-590	206	76	;	;	PUNCT
ajset-590	206	77	c.	c.	PROPN
ajset-590	206	78	it	it	PRON
ajset-590	206	79	does	do	AUX
ajset-590	206	80	not	not	PART
ajset-590	206	81	take	take	VERB
ajset-590	206	82	into	into	ADP
ajset-590	206	83	consideration	consideration	NOUN
ajset-590	206	84	the	the	DET
ajset-590	206	85	dimensions	dimension	NOUN
ajset-590	206	86	of	of	ADP
ajset-590	206	87	physical	physical	ADJ
ajset-590	206	88	quantities	quantity	NOUN
ajset-590	206	89	(	(	PUNCT
ajset-590	206	90	i.e.	i.e.	X
ajset-590	206	91	,	,	PUNCT
ajset-590	206	92	number	number	NOUN
ajset-590	206	93	names	name	NOUN
ajset-590	206	94	,	,	PUNCT
ajset-590	206	95	denominate	denominate	NOUN
ajset-590	206	96	numbers	number	NOUN
ajset-590	206	97	,	,	PUNCT
ajset-590	206	98	concrete	concrete	ADJ
ajset-590	206	99	numbers	number	NOUN
ajset-590	206	100	)	)	PUNCT
ajset-590	206	101	,	,	PUNCT
ajset-590	206	102	characterizing	characterize	VERB
ajset-590	206	103	the	the	DET
ajset-590	206	104	concept	concept	NOUN
ajset-590	206	105	of	of	ADP
ajset-590	206	106	“	"	PUNCT
ajset-590	206	107	physical	physical	ADJ
ajset-590	206	108	vector	vector	NOUN
ajset-590	206	109	”	"	PUNCT
ajset-590	206	110	,	,	PUNCT
ajset-590	206	111	and	and	CCONJ
ajset-590	206	112	,	,	PUNCT
ajset-590	206	113	therefore	therefore	ADV
ajset-590	206	114	,	,	PUNCT
ajset-590	206	115	it	it	PRON
ajset-590	206	116	has	have	VERB
ajset-590	206	117	no	no	DET
ajset-590	206	118	natural	natural	ADJ
ajset-590	206	119	-	-	PUNCT
ajset-590	206	120	scientific	scientific	ADJ
ajset-590	206	121	meaning	meaning	NOUN
ajset-590	206	122	;	;	PUNCT
ajset-590	206	123	d.	d.	PROPN
ajset-590	206	124	operations	operation	NOUN
ajset-590	206	125	on	on	ADP
ajset-590	206	126	“	"	PUNCT
ajset-590	206	127	physical	physical	ADJ
ajset-590	206	128	vectors	vector	NOUN
ajset-590	206	129	”	"	PUNCT
ajset-590	206	130	and	and	CCONJ
ajset-590	206	131	the	the	DET
ajset-590	206	132	theoretical	theoretical	ADJ
ajset-590	206	133	propositions	proposition	NOUN
ajset-590	206	134	of	of	ADP
ajset-590	206	135	the	the	DET
ajset-590	206	136	standard	standard	ADJ
ajset-590	206	137	vector	vector	NOUN
ajset-590	206	138	calculus	calculus	NOUN
ajset-590	206	139	,	,	PUNCT
ajset-590	206	140	relating	relate	VERB
ajset-590	206	141	to	to	ADP
ajset-590	206	142	the	the	DET
ajset-590	206	143	“	"	PUNCT
ajset-590	206	144	physical	physical	ADJ
ajset-590	206	145	vectors	vector	NOUN
ajset-590	206	146	”	"	PUNCT
ajset-590	206	147	,	,	PUNCT
ajset-590	206	148	are	be	AUX
ajset-590	206	149	contrary	contrary	ADJ
ajset-590	206	150	to	to	ADP
ajset-590	206	151	formal	formal	ADJ
ajset-590	206	152	logic	logic	NOUN
ajset-590	206	153	.	.	PUNCT
ajset-590	207	1	mailto:topacademicjournals@gmail.com	mailto:topacademicjournals@gmail.com	PROPN
ajset-590	207	2	academic	academic	ADJ
ajset-590	207	3	journal	journal	NOUN
ajset-590	207	4	of	of	ADP
ajset-590	207	5	science	science	NOUN
ajset-590	207	6	,	,	PUNCT
ajset-590	207	7	engineering	engineering	NOUN
ajset-590	207	8	and	and	CCONJ
ajset-590	207	9	technology	technology	NOUN
ajset-590	207	10	vol.8	vol.8	PROPN
ajset-590	207	11	,	,	PUNCT
ajset-590	207	12	issue	issue	NOUN
ajset-590	207	13	5	5	NUM
ajset-590	207	14	;	;	PUNCT
ajset-590	207	15	september	september	PROPN
ajset-590	207	16	october	october	PROPN
ajset-590	207	17	2023	2023	NUM
ajset-590	207	18	;	;	PUNCT
ajset-590	207	19	issn	issn	PROPN
ajset-590	207	20	:	:	PUNCT
ajset-590	207	21	2837	2837	NUM
ajset-590	207	22	-	-	SYM
ajset-590	207	23	2964	2964	NUM
ajset-590	207	24	impact	impact	NOUN
ajset-590	207	25	factor	factor	NOUN
ajset-590	207	26	:	:	PUNCT
ajset-590	207	27	6.67	6.67	NUM
ajset-590	207	28	1252	1252	NUM
ajset-590	207	29	columbia	columbia	PROPN
ajset-590	207	30	rd	rd	PROPN
ajset-590	207	31	nw	nw	PROPN
ajset-590	207	32	,	,	PUNCT
ajset-590	207	33	washington	washington	PROPN
ajset-590	207	34	dc	dc	PROPN
ajset-590	207	35	,	,	PUNCT
ajset-590	207	36	united	united	PROPN
ajset-590	207	37	states	states	PROPN
ajset-590	207	38	https://topjournals.org/index.php/ajset/index	https://topjournals.org/index.php/ajset/index	PROPN
ajset-590	207	39	;	;	PUNCT
ajset-590	207	40	mail	mail	NOUN
ajset-590	207	41	:	:	PUNCT
ajset-590	207	42	topacademicjournals@gmail.com	topacademicjournals@gmail.com	X
ajset-590	208	1	17	17	NUM
ajset-590	209	1	|	|	ADV
ajset-590	209	2	a	a	DET
ajset-590	209	3	c	c	NOUN
ajset-590	209	4	a	a	PRON
ajset-590	209	5	d	d	X
ajset-590	209	6	e	e	NOUN
ajset-590	209	7	m	m	NOUN
ajset-590	209	8	i	i	NOUN
ajset-590	209	9	c	c	NOUN
ajset-590	209	10	j	j	NOUN
ajset-590	209	11	o	o	X
ajset-590	209	12	u	u	NOUN
ajset-590	209	13	r	r	NOUN
ajset-590	209	14	n	n	NOUN
ajset-590	209	15	a	a	DET
ajset-590	209	16	l	l	NOUN
ajset-590	210	1	o	o	X
ajset-590	210	2	f	f	X
ajset-590	210	3	s	s	X
ajset-590	210	4	c	c	NOUN
ajset-590	211	1	i	i	NOUN
ajset-590	211	2	e	e	PROPN
ajset-590	211	3	n	n	PROPN
ajset-590	211	4	c	c	NOUN
ajset-590	211	5	e	e	X
ajset-590	211	6	,	,	PUNCT
ajset-590	211	7	e	e	PROPN
ajset-590	211	8	n	n	PRON
ajset-590	211	9	g	g	NOUN
ajset-590	211	10	i	i	PRON
ajset-590	211	11	n	n	VERB
ajset-590	211	12	e	e	NOUN
ajset-590	211	13	e	e	NOUN
ajset-590	211	14	r	r	VERB
ajset-590	211	15	i	i	PRON
ajset-590	211	16	n	n	CCONJ
ajset-590	211	17	g	g	PROPN
ajset-590	211	18	a	a	DET
ajset-590	211	19	n	n	NOUN
ajset-590	211	20	d	d	NOUN
ajset-590	211	21	t	t	NOUN
ajset-590	211	22	e	e	X
ajset-590	211	23	c	c	NOUN
ajset-590	211	24	h	h	NOUN
ajset-590	211	25	n	n	ADV
ajset-590	211	26	o	o	NOUN
ajset-590	211	27	l	l	NOUN
ajset-590	212	1	o	o	X
ajset-590	212	2	g	g	NOUN
ajset-590	212	3	y	y	PROPN
ajset-590	212	4	|	|	ADV
ajset-590	212	5	https://topjournals.org/index.php/ajset	https://topjournals.org/index.php/ajset	VERB
ajset-590	212	6	references	reference	NOUN
ajset-590	212	7	t.	t.	PROPN
ajset-590	212	8	apostol	apostol	PROPN
ajset-590	212	9	.	.	PUNCT
ajset-590	213	1	calculus	calculus	NOUN
ajset-590	213	2	,	,	PUNCT
ajset-590	213	3	vol	vol	NOUN
ajset-590	213	4	.	.	PROPN
ajset-590	214	1	1	1	NUM
ajset-590	214	2	:	:	PUNCT
ajset-590	214	3	one	one	NUM
ajset-590	214	4	-	-	PUNCT
ajset-590	214	5	variable	variable	NOUN
ajset-590	214	6	calculus	calculus	NOUN
ajset-590	214	7	with	with	ADP
ajset-590	214	8	an	an	DET
ajset-590	214	9	introduction	introduction	NOUN
ajset-590	214	10	to	to	ADP
ajset-590	214	11	linear	linear	PROPN
ajset-590	214	12	algebra	algebra	PROPN
ajset-590	214	13	.	.	PUNCT
ajset-590	215	1	john	john	PROPN
ajset-590	215	2	wiley	wiley	PROPN
ajset-590	215	3	and	and	CCONJ
ajset-590	215	4	sons	son	NOUN
ajset-590	215	5	.	.	PUNCT
ajset-590	216	1	isbn	isbn	ADJ
ajset-590	216	2	978	978	NUM
ajset-590	216	3	-	-	SYM
ajset-590	216	4	0	0	NUM
ajset-590	216	5	-	-	PUNCT
ajset-590	216	6	471	471	NUM
ajset-590	216	7	-	-	PUNCT
ajset-590	216	8	00005	00005	NUM
ajset-590	216	9	-	-	SYM
ajset-590	216	10	1	1	NUM
ajset-590	216	11	,	,	PUNCT
ajset-590	216	12	(	(	PUNCT
ajset-590	216	13	1967	1967	NUM
ajset-590	216	14	)	)	PUNCT
ajset-590	216	15	.	.	PUNCT
ajset-590	217	1	t.	t.	PROPN
ajset-590	217	2	apostol	apostol	PROPN
ajset-590	217	3	.	.	PUNCT
ajset-590	218	1	calculus	calculus	NOUN
ajset-590	218	2	,	,	PUNCT
ajset-590	218	3	vol	vol	NOUN
ajset-590	218	4	.	.	PROPN
ajset-590	219	1	2	2	NUM
ajset-590	219	2	:	:	PUNCT
ajset-590	219	3	multi	multi	ADJ
ajset-590	219	4	-	-	ADJ
ajset-590	219	5	variable	variable	ADJ
ajset-590	219	6	calculus	calculus	NOUN
ajset-590	219	7	and	and	CCONJ
ajset-590	219	8	linear	linear	PROPN
ajset-590	219	9	algebra	algebra	PROPN
ajset-590	219	10	with	with	ADP
ajset-590	219	11	applications	application	NOUN
ajset-590	219	12	.	.	PUNCT
ajset-590	220	1	john	john	PROPN
ajset-590	220	2	wiley	wiley	PROPN
ajset-590	220	3	and	and	CCONJ
ajset-590	220	4	sons	son	NOUN
ajset-590	220	5	.	.	PUNCT
ajset-590	221	1	isbn	isbn	ADJ
ajset-590	221	2	978	978	NUM
ajset-590	221	3	-	-	SYM
ajset-590	221	4	0	0	NUM
ajset-590	221	5	-	-	PUNCT
ajset-590	221	6	471	471	NUM
ajset-590	221	7	-	-	PUNCT
ajset-590	221	8	00007	00007	NUM
ajset-590	221	9	-	-	PUNCT
ajset-590	221	10	5	5	NUM
ajset-590	221	11	,	,	PUNCT
ajset-590	221	12	(	(	PUNCT
ajset-590	221	13	1969	1969	NUM
ajset-590	221	14	)	)	PUNCT
ajset-590	221	15	.	.	PUNCT
ajset-590	222	1	kiyosi	kiyosi	PROPN
ajset-590	222	2	ito	ito	PROPN
ajset-590	222	3	.	.	PROPN
ajset-590	222	4	encyclopedic	encyclopedic	ADJ
ajset-590	222	5	dictionary	dictionary	NOUN
ajset-590	222	6	of	of	ADP
ajset-590	222	7	mathematics	mathematics	PROPN
ajset-590	222	8	(	(	PUNCT
ajset-590	222	9	2nd	2nd	ADJ
ajset-590	222	10	ed	ed	NOUN
ajset-590	222	11	.	.	PUNCT
ajset-590	222	12	)	)	PUNCT
ajset-590	222	13	,	,	PUNCT
ajset-590	222	14	mit	mit	PROPN
ajset-590	222	15	press	press	NOUN
ajset-590	222	16	,	,	PUNCT
ajset-590	222	17	isbn	isbn	ADJ
ajset-590	222	18	978	978	NUM
ajset-590	222	19	-	-	SYM
ajset-590	222	20	0262	0262	NUM
ajset-590	222	21	-	-	PUNCT
ajset-590	222	22	59020	59020	NUM
ajset-590	222	23	-	-	PUNCT
ajset-590	222	24	4	4	NUM
ajset-590	222	25	,	,	PUNCT
ajset-590	222	26	(	(	PUNCT
ajset-590	222	27	1993	1993	NUM
ajset-590	222	28	)	)	PUNCT
ajset-590	222	29	.	.	PUNCT
ajset-590	223	1	a.b	a.b	PROPN
ajset-590	223	2	.	.	PROPN
ajset-590	223	3	ivanov	ivanov	PROPN
ajset-590	223	4	.	.	PUNCT
ajset-590	224	1	"	"	PUNCT
ajset-590	224	2	vector	vector	NOUN
ajset-590	224	3	,	,	PUNCT
ajset-590	224	4	geometric	geometric	ADJ
ajset-590	224	5	"	"	PUNCT
ajset-590	224	6	,	,	PUNCT
ajset-590	224	7	in	in	ADP
ajset-590	224	8	hazewinkel	hazewinkel	PROPN
ajset-590	224	9	,	,	PUNCT
ajset-590	224	10	michiel	michiel	PROPN
ajset-590	224	11	,	,	PUNCT
ajset-590	224	12	encyclopedia	encyclopedia	NOUN
ajset-590	224	13	of	of	ADP
ajset-590	224	14	mathematics	mathematic	NOUN
ajset-590	224	15	,	,	PUNCT
ajset-590	224	16	springer	springer	NOUN
ajset-590	224	17	,	,	PUNCT
ajset-590	224	18	isbn	isbn	ADJ
ajset-590	224	19	978	978	NUM
ajset-590	224	20	-	-	SYM
ajset-590	224	21	1	1	NUM
ajset-590	224	22	-	-	PUNCT
ajset-590	224	23	55608	55608	NUM
ajset-590	224	24	-	-	PUNCT
ajset-590	224	25	010	010	NUM
ajset-590	224	26	-	-	SYM
ajset-590	224	27	4	4	NUM
ajset-590	224	28	,	,	PUNCT
ajset-590	224	29	(	(	PUNCT
ajset-590	224	30	2001	2001	NUM
ajset-590	224	31	)	)	PUNCT
ajset-590	224	32	.	.	PUNCT
ajset-590	225	1	d.	d.	PROPN
ajset-590	225	2	pedoe	pedoe	PROPN
ajset-590	225	3	.	.	PUNCT
ajset-590	226	1	geometry	geometry	NOUN
ajset-590	226	2	:	:	PUNCT
ajset-590	226	3	a	a	DET
ajset-590	226	4	comprehensive	comprehensive	ADJ
ajset-590	226	5	course	course	NOUN
ajset-590	226	6	.	.	PUNCT
ajset-590	227	1	dover	dover	PROPN
ajset-590	227	2	.	.	PUNCT
ajset-590	228	1	isbn	isbn	PROPN
ajset-590	228	2	0	0	NUM
ajset-590	228	3	-	-	SYM
ajset-590	228	4	486	486	NUM
ajset-590	228	5	-	-	PUNCT
ajset-590	228	6	65812	65812	NUM
ajset-590	228	7	-	-	SYM
ajset-590	228	8	0	0	NUM
ajset-590	228	9	,	,	PUNCT
ajset-590	228	10	(	(	PUNCT
ajset-590	228	11	1988	1988	NUM
ajset-590	228	12	)	)	PUNCT
ajset-590	228	13	.	.	PUNCT
ajset-590	229	1	[	[	X
ajset-590	229	2	6	6	NUM
ajset-590	229	3	]	]	X
ajset-590	229	4	r.	r.	PROPN
ajset-590	229	5	aris	aris	PROPN
ajset-590	229	6	.	.	PUNCT
ajset-590	230	1	vectors	vector	NOUN
ajset-590	230	2	,	,	PUNCT
ajset-590	230	3	tensors	tensor	NOUN
ajset-590	230	4	and	and	CCONJ
ajset-590	230	5	the	the	DET
ajset-590	230	6	basic	basic	ADJ
ajset-590	230	7	equations	equation	NOUN
ajset-590	230	8	of	of	ADP
ajset-590	230	9	fluid	fluid	ADJ
ajset-590	230	10	mechanics	mechanic	NOUN
ajset-590	230	11	.	.	PUNCT
ajset-590	231	1	dover	dover	PROPN
ajset-590	231	2	.	.	PUNCT
ajset-590	232	1	isbn	isbn	PROPN
ajset-590	232	2	9780	9780	NUM
ajset-590	232	3	-	-	PUNCT
ajset-590	232	4	486	486	NUM
ajset-590	232	5	-	-	PUNCT
ajset-590	232	6	66110	66110	NUM
ajset-590	232	7	-	-	SYM
ajset-590	232	8	0	0	NUM
ajset-590	232	9	,	,	PUNCT
ajset-590	232	10	(	(	PUNCT
ajset-590	232	11	1990	1990	NUM
ajset-590	232	12	)	)	PUNCT
ajset-590	232	13	.	.	PUNCT
ajset-590	233	1	r.	r.	PROPN
ajset-590	233	2	feynman	feynman	PROPN
ajset-590	233	3	,	,	PUNCT
ajset-590	233	4	r.	r.	PROPN
ajset-590	233	5	leighton	leighton	PROPN
ajset-590	233	6	,	,	PUNCT
ajset-590	233	7	and	and	CCONJ
ajset-590	233	8	m.	m.	NOUN
ajset-590	233	9	sands	sand	NOUN
ajset-590	233	10	.	.	PUNCT
ajset-590	234	1	"	"	PUNCT
ajset-590	234	2	chapter	chapter	NOUN
ajset-590	234	3	11	11	NUM
ajset-590	234	4	"	"	PUNCT
ajset-590	234	5	.	.	PUNCT
ajset-590	235	1	the	the	DET
ajset-590	235	2	feynman	feynman	PROPN
ajset-590	235	3	lectures	lecture	VERB
ajset-590	235	4	on	on	ADP
ajset-590	235	5	physics	physics	NOUN
ajset-590	235	6	,	,	PUNCT
ajset-590	235	7	volume	volume	NOUN
ajset-590	235	8	i	i	PRON
ajset-590	235	9	(	(	PUNCT
ajset-590	235	10	2nd	2nd	ADJ
ajset-590	235	11	ed	ed	NOUN
ajset-590	235	12	ed	ed	NOUN
ajset-590	235	13	.	.	PUNCT
ajset-590	235	14	)	)	PUNCT
ajset-590	235	15	.	.	PUNCT
ajset-590	236	1	addison	addison	PROPN
ajset-590	236	2	wesley	wesley	PROPN
ajset-590	236	3	.	.	PUNCT
ajset-590	237	1	isbn	isbn	ADJ
ajset-590	237	2	978	978	NUM
ajset-590	237	3	-	-	SYM
ajset-590	237	4	0	0	NUM
ajset-590	237	5	-	-	PUNCT
ajset-590	237	6	8053	8053	NUM
ajset-590	237	7	-	-	PUNCT
ajset-590	237	8	9046	9046	NUM
ajset-590	237	9	-	-	SYM
ajset-590	237	10	9	9	NUM
ajset-590	237	11	,	,	PUNCT
ajset-590	237	12	(	(	PUNCT
ajset-590	237	13	2005	2005	NUM
ajset-590	237	14	)	)	PUNCT
ajset-590	237	15	.	.	PUNCT
ajset-590	238	1	mechanics	mechanic	NOUN
ajset-590	238	2	.	.	PUNCT
ajset-590	239	1	berkeley	berkeley	PROPN
ajset-590	239	2	physics	physics	PROPN
ajset-590	239	3	course	course	NOUN
ajset-590	239	4	.	.	PUNCT
ajset-590	240	1	v.	v.	ADP
ajset-590	240	2	1	1	X
ajset-590	240	3	.	.	PUNCT
ajset-590	241	1	mcgraw	mcgraw	PROPN
ajset-590	241	2	-	-	PUNCT
ajset-590	241	3	hill	hill	NOUN
ajset-590	241	4	book	book	NOUN
ajset-590	241	5	company	company	NOUN
ajset-590	241	6	,	,	PUNCT
ajset-590	241	7	(	(	PUNCT
ajset-590	241	8	1964	1964	NUM
ajset-590	241	9	)	)	PUNCT
ajset-590	241	10	.	.	PUNCT
ajset-590	242	1	t.z	t.z	PROPN
ajset-590	242	2	.	.	PROPN
ajset-590	242	3	kalanov	kalanov	PROPN
ajset-590	242	4	.	.	PUNCT
ajset-590	243	1	the	the	DET
ajset-590	243	2	critical	critical	ADJ
ajset-590	243	3	analysis	analysis	NOUN
ajset-590	243	4	of	of	ADP
ajset-590	243	5	the	the	DET
ajset-590	243	6	foundations	foundation	NOUN
ajset-590	243	7	of	of	ADP
ajset-590	243	8	theoretical	theoretical	ADJ
ajset-590	243	9	physics.crisis	physics.crisis	NOUN
ajset-590	243	10	in	in	ADP
ajset-590	243	11	theoretical	theoretical	ADJ
ajset-590	243	12	physics	physics	NOUN
ajset-590	243	13	:	:	PUNCT
ajset-590	243	14	the	the	DET
ajset-590	243	15	problem	problem	NOUN
ajset-590	243	16	of	of	ADP
ajset-590	243	17	scientific	scientific	ADJ
ajset-590	243	18	truth	truth	NOUN
ajset-590	243	19	.	.	PUNCT
ajset-590	244	1	lap	lap	NOUN
ajset-590	244	2	lambert	lambert	PROPN
ajset-590	244	3	academic	academic	ADJ
ajset-590	244	4	publishing	publishing	NOUN
ajset-590	244	5	.	.	PUNCT
ajset-590	245	1	isbn	isbn	ADJ
ajset-590	245	2	978	978	NUM
ajset-590	245	3	-	-	SYM
ajset-590	245	4	3	3	NUM
ajset-590	245	5	-	-	PUNCT
ajset-590	245	6	8433	8433	NUM
ajset-590	245	7	-	-	SYM
ajset-590	245	8	6367	6367	NUM
ajset-590	245	9	-	-	SYM
ajset-590	245	10	9	9	NUM
ajset-590	245	11	,	,	PUNCT
ajset-590	245	12	(	(	PUNCT
ajset-590	245	13	2010	2010	NUM
ajset-590	245	14	)	)	PUNCT
ajset-590	245	15	.	.	PUNCT
ajset-590	246	1	mailto:topacademicjournals@gmail.com	mailto:topacademicjournals@gmail.com	X