id	sid	tid	token	lemma	pos
ejpam-1173	1	1	5_xxx_salim.dvi	5_xxx_salim.dvi	NUM
ejpam-1173	1	2	european	european	ADJ
ejpam-1173	1	3	journal	journal	NOUN
ejpam-1173	1	4	of	of	ADP
ejpam-1173	1	5	pure	pure	ADJ
ejpam-1173	1	6	and	and	CCONJ
ejpam-1173	1	7	applied	apply	VERB
ejpam-1173	1	8	mathematics	mathematic	NOUN
ejpam-1173	1	9	vol	vol	NOUN
ejpam-1173	1	10	.	.	PROPN
ejpam-1173	1	11	4	4	NUM
ejpam-1173	1	12	,	,	PUNCT
ejpam-1173	1	13	no	no	INTJ
ejpam-1173	1	14	.	.	NOUN
ejpam-1173	1	15	2	2	NUM
ejpam-1173	1	16	,	,	PUNCT
ejpam-1173	1	17	2011	2011	NUM
ejpam-1173	1	18	,	,	PUNCT
ejpam-1173	1	19	142	142	NUM
ejpam-1173	1	20	-	-	SYM
ejpam-1173	1	21	146	146	NUM
ejpam-1173	1	22	issn	issn	PROPN
ejpam-1173	1	23	1307	1307	NUM
ejpam-1173	1	24	-	-	SYM
ejpam-1173	1	25	5543	5543	NUM
ejpam-1173	1	26	–	–	PUNCT
ejpam-1173	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1173	1	28	on	on	ADP
ejpam-1173	1	29	properties	property	NOUN
ejpam-1173	1	30	of	of	ADP
ejpam-1173	1	31	the	the	DET
ejpam-1173	1	32	dual	dual	ADJ
ejpam-1173	1	33	quaternions	quaternions	ADJ
ejpam-1173	1	34	zeynep	zeynep	NOUN
ejpam-1173	1	35	ercan1	ercan1	PROPN
ejpam-1173	1	36	,	,	PUNCT
ejpam-1173	1	37	salim	salim	PROPN
ejpam-1173	1	38	yüce2,∗	yüce2,∗	PROPN
ejpam-1173	1	39	1	1	NUM
ejpam-1173	1	40	koç	koç	PROPN
ejpam-1173	1	41	university	university	PROPN
ejpam-1173	1	42	,	,	PUNCT
ejpam-1173	1	43	department	department	NOUN
ejpam-1173	1	44	of	of	ADP
ejpam-1173	1	45	mathematics	mathematic	NOUN
ejpam-1173	1	46	,	,	PUNCT
ejpam-1173	1	47	rumelifeneri	rumelifeneri	PROPN
ejpam-1173	1	48	yolu	yolu	PROPN
ejpam-1173	1	49	,	,	PUNCT
ejpam-1173	1	50	34450	34450	NUM
ejpam-1173	1	51	,	,	PUNCT
ejpam-1173	1	52	sarıyer	sarıyer	NOUN
ejpam-1173	1	53	,	,	PUNCT
ejpam-1173	1	54	i̇stanbul	i̇stanbul	ADV
ejpam-1173	1	55	,	,	PUNCT
ejpam-1173	1	56	turkey	turkey	PROPN
ejpam-1173	1	57	2	2	NUM
ejpam-1173	1	58	yıldız	yıldız	PROPN
ejpam-1173	1	59	technical	technical	PROPN
ejpam-1173	1	60	university	university	PROPN
ejpam-1173	1	61	,	,	PUNCT
ejpam-1173	1	62	faculty	faculty	NOUN
ejpam-1173	1	63	of	of	ADP
ejpam-1173	1	64	arts	art	NOUN
ejpam-1173	1	65	and	and	CCONJ
ejpam-1173	1	66	sciences	science	NOUN
ejpam-1173	1	67	,	,	PUNCT
ejpam-1173	1	68	department	department	NOUN
ejpam-1173	1	69	of	of	ADP
ejpam-1173	1	70	mathematics	mathematic	NOUN
ejpam-1173	1	71	,	,	PUNCT
ejpam-1173	1	72	34210	34210	NUM
ejpam-1173	1	73	,	,	PUNCT
ejpam-1173	1	74	esenler	esenler	NOUN
ejpam-1173	1	75	,	,	PUNCT
ejpam-1173	1	76	i̇stanbul	i̇stanbul	INTJ
ejpam-1173	1	77	,	,	PUNCT
ejpam-1173	1	78	turkey	turkey	PROPN
ejpam-1173	1	79	abstract	abstract	NOUN
ejpam-1173	1	80	.	.	PUNCT
ejpam-1173	2	1	in	in	ADP
ejpam-1173	2	2	this	this	DET
ejpam-1173	2	3	paper	paper	NOUN
ejpam-1173	2	4	,	,	PUNCT
ejpam-1173	2	5	euler	euler	VERB
ejpam-1173	2	6	’s	’s	PROPN
ejpam-1173	2	7	and	and	CCONJ
ejpam-1173	2	8	de	de	ADP
ejpam-1173	2	9	moivre	moivre	NOUN
ejpam-1173	2	10	’s	’s	PART
ejpam-1173	2	11	formulas	formula	NOUN
ejpam-1173	2	12	for	for	ADP
ejpam-1173	2	13	complex	complex	ADJ
ejpam-1173	2	14	numbers	number	NOUN
ejpam-1173	2	15	and	and	CCONJ
ejpam-1173	2	16	quaternions	quaternion	NOUN
ejpam-1173	2	17	are	be	AUX
ejpam-1173	2	18	generalized	generalize	VERB
ejpam-1173	2	19	for	for	ADP
ejpam-1173	2	20	the	the	DET
ejpam-1173	2	21	dual	dual	ADJ
ejpam-1173	2	22	quaternions	quaternion	NOUN
ejpam-1173	2	23	.	.	PUNCT
ejpam-1173	3	1	also	also	ADV
ejpam-1173	3	2	,	,	PUNCT
ejpam-1173	3	3	the	the	DET
ejpam-1173	3	4	matrix	matrix	NOUN
ejpam-1173	3	5	representation	representation	NOUN
ejpam-1173	3	6	of	of	ADP
ejpam-1173	3	7	dual	dual	ADJ
ejpam-1173	3	8	quaternions	quaternion	NOUN
ejpam-1173	3	9	is	be	AUX
ejpam-1173	3	10	expressed	express	VERB
ejpam-1173	3	11	.	.	PUNCT
ejpam-1173	4	1	2000	2000	NUM
ejpam-1173	4	2	mathematics	mathematic	NOUN
ejpam-1173	4	3	subject	subject	NOUN
ejpam-1173	4	4	classifications	classification	NOUN
ejpam-1173	4	5	:	:	PUNCT
ejpam-1173	4	6	11r52	11r52	NUM
ejpam-1173	4	7	key	key	ADJ
ejpam-1173	4	8	words	word	NOUN
ejpam-1173	4	9	and	and	CCONJ
ejpam-1173	4	10	phrases	phrase	NOUN
ejpam-1173	4	11	:	:	PUNCT
ejpam-1173	4	12	dual	dual	ADJ
ejpam-1173	4	13	number	number	NOUN
ejpam-1173	4	14	,	,	PUNCT
ejpam-1173	4	15	dual	dual	ADJ
ejpam-1173	4	16	quaternion	quaternion	NOUN
ejpam-1173	4	17	,	,	PUNCT
ejpam-1173	4	18	euler	euler	NOUN
ejpam-1173	4	19	’s	’s	PART
ejpam-1173	4	20	formula	formula	NOUN
ejpam-1173	4	21	,	,	PUNCT
ejpam-1173	4	22	de	de	ADP
ejpam-1173	4	23	moivre	moivre	NOUN
ejpam-1173	4	24	’s	’s	PART
ejpam-1173	4	25	formula	formula	NOUN
ejpam-1173	4	26	1	1	NUM
ejpam-1173	4	27	.	.	PUNCT
ejpam-1173	5	1	introduction	introduction	NOUN
ejpam-1173	5	2	a	a	DET
ejpam-1173	5	3	dual	dual	ADJ
ejpam-1173	5	4	number	number	NOUN
ejpam-1173	5	5	z	z	NOUN
ejpam-1173	5	6	is	be	AUX
ejpam-1173	5	7	an	an	DET
ejpam-1173	5	8	ordered	order	VERB
ejpam-1173	5	9	pair	pair	NOUN
ejpam-1173	5	10	of	of	ADP
ejpam-1173	5	11	real	real	ADJ
ejpam-1173	5	12	numbers	number	NOUN
ejpam-1173	5	13	(	(	PUNCT
ejpam-1173	5	14	x	x	X
ejpam-1173	5	15	,	,	PUNCT
ejpam-1173	5	16	y	y	PROPN
ejpam-1173	5	17	)	)	PUNCT
ejpam-1173	5	18	associated	associate	VERB
ejpam-1173	5	19	with	with	ADP
ejpam-1173	5	20	a	a	DET
ejpam-1173	5	21	real	real	ADJ
ejpam-1173	5	22	unit	unit	NOUN
ejpam-1173	5	23	+1	+1	PROPN
ejpam-1173	5	24	and	and	CCONJ
ejpam-1173	5	25	the	the	DET
ejpam-1173	5	26	dual	dual	ADJ
ejpam-1173	5	27	unit	unit	NOUN
ejpam-1173	5	28	,	,	PUNCT
ejpam-1173	5	29	or	or	CCONJ
ejpam-1173	5	30	operator	operator	NOUN
ejpam-1173	5	31	ǫ	ǫ	NOUN
ejpam-1173	5	32	,	,	PUNCT
ejpam-1173	5	33	where	where	SCONJ
ejpam-1173	5	34	ǫ2	ǫ2	NOUN
ejpam-1173	5	35	=	=	SYM
ejpam-1173	5	36	ǫ3	ǫ3	PROPN
ejpam-1173	5	37	=	=	PUNCT
ejpam-1173	5	38	.	.	PUNCT
ejpam-1173	5	39	.	.	PUNCT
ejpam-1173	5	40	.	.	PUNCT
ejpam-1173	6	1	=	=	PUNCT
ejpam-1173	6	2	0	0	NUM
ejpam-1173	6	3	.	.	PUNCT
ejpam-1173	7	1	a	a	DET
ejpam-1173	7	2	dual	dual	ADJ
ejpam-1173	7	3	number	number	NOUN
ejpam-1173	7	4	is	be	AUX
ejpam-1173	7	5	usually	usually	ADV
ejpam-1173	7	6	denoted	denote	VERB
ejpam-1173	7	7	in	in	ADP
ejpam-1173	7	8	the	the	DET
ejpam-1173	7	9	form	form	NOUN
ejpam-1173	7	10	z	z	NOUN
ejpam-1173	7	11	=	=	PUNCT
ejpam-1173	8	1	x	x	PUNCT
ejpam-1173	8	2	+	+	SYM
ejpam-1173	8	3	ǫ	ǫ	X
ejpam-1173	8	4	y.	y.	NOUN
ejpam-1173	8	5	(	(	PUNCT
ejpam-1173	8	6	1	1	NUM
ejpam-1173	8	7	)	)	PUNCT
ejpam-1173	8	8	thus	thus	ADV
ejpam-1173	8	9	,	,	PUNCT
ejpam-1173	8	10	the	the	DET
ejpam-1173	8	11	dual	dual	ADJ
ejpam-1173	8	12	numbers	number	NOUN
ejpam-1173	8	13	are	be	AUX
ejpam-1173	8	14	elements	element	NOUN
ejpam-1173	8	15	of	of	ADP
ejpam-1173	8	16	the	the	DET
ejpam-1173	8	17	2	2	NUM
ejpam-1173	8	18	-	-	PUNCT
ejpam-1173	8	19	dimensional	dimensional	ADJ
ejpam-1173	8	20	real	real	ADJ
ejpam-1173	8	21	algebra	algebra	NOUN
ejpam-1173	9	1	d	d	NOUN
ejpam-1173	9	2	=	=	SYM
ejpam-1173	9	3	r[ǫ	r[ǫ	X
ejpam-1173	9	4	]	]	X
ejpam-1173	9	5	=	=	PUNCT
ejpam-1173	9	6	{	{	PUNCT
ejpam-1173	9	7	z	z	NOUN
ejpam-1173	9	8	=	=	PUNCT
ejpam-1173	9	9	x	x	PROPN
ejpam-1173	10	1	+	+	PUNCT
ejpam-1173	10	2	ǫ	ǫ	VERB
ejpam-1173	10	3	y|x	y|x	NOUN
ejpam-1173	10	4	,	,	PUNCT
ejpam-1173	10	5	y	y	PROPN
ejpam-1173	10	6	∈	∈	PROPN
ejpam-1173	10	7	r	r	NOUN
ejpam-1173	10	8	,	,	PUNCT
ejpam-1173	10	9	ǫ2	ǫ2	NOUN
ejpam-1173	10	10	=	=	PUNCT
ejpam-1173	10	11	0,ǫ	0,ǫ	PROPN
ejpam-1173	10	12	6=	6=	ADP
ejpam-1173	10	13	0	0	NUM
ejpam-1173	10	14	}	}	PUNCT
ejpam-1173	10	15	generated	generate	VERB
ejpam-1173	10	16	by	by	ADP
ejpam-1173	10	17	1	1	NUM
ejpam-1173	10	18	and	and	CCONJ
ejpam-1173	10	19	ǫ	ǫ	PRON
ejpam-1173	10	20	,	,	PUNCT
ejpam-1173	10	21	[	[	X
ejpam-1173	10	22	7	7	NUM
ejpam-1173	10	23	]	]	PUNCT
ejpam-1173	10	24	.	.	PUNCT
ejpam-1173	11	1	addition	addition	NOUN
ejpam-1173	11	2	and	and	CCONJ
ejpam-1173	11	3	multiplication	multiplication	NOUN
ejpam-1173	11	4	of	of	ADP
ejpam-1173	11	5	the	the	DET
ejpam-1173	11	6	dual	dual	ADJ
ejpam-1173	11	7	numbers	number	NOUN
ejpam-1173	11	8	are	be	AUX
ejpam-1173	11	9	defined	define	VERB
ejpam-1173	11	10	by	by	ADP
ejpam-1173	11	11	(	(	PUNCT
ejpam-1173	11	12	x	x	PROPN
ejpam-1173	11	13	+	+	PUNCT
ejpam-1173	11	14	ǫ	ǫ	PROPN
ejpam-1173	11	15	y	y	NOUN
ejpam-1173	11	16	)	)	PUNCT
ejpam-1173	12	1	+	+	CCONJ
ejpam-1173	12	2	(	(	PUNCT
ejpam-1173	12	3	a+	a+	X
ejpam-1173	12	4	ǫb	ǫb	PROPN
ejpam-1173	12	5	)	)	PUNCT
ejpam-1173	12	6	=	=	SYM
ejpam-1173	13	1	(	(	PUNCT
ejpam-1173	13	2	x	x	X
ejpam-1173	13	3	+	+	X
ejpam-1173	13	4	a	a	X
ejpam-1173	13	5	)	)	PUNCT
ejpam-1173	14	1	+	+	PROPN
ejpam-1173	14	2	ǫ(y	ǫ(y	PROPN
ejpam-1173	14	3	+	+	NUM
ejpam-1173	14	4	b	b	NOUN
ejpam-1173	14	5	)	)	PUNCT
ejpam-1173	14	6	,	,	PUNCT
ejpam-1173	14	7	(	(	PUNCT
ejpam-1173	14	8	2	2	X
ejpam-1173	14	9	)	)	PUNCT
ejpam-1173	14	10	(	(	PUNCT
ejpam-1173	14	11	x	x	X
ejpam-1173	15	1	+	+	PUNCT
ejpam-1173	15	2	ǫ	ǫ	PRON
ejpam-1173	15	3	y).(a+	y).(a+	NOUN
ejpam-1173	15	4	ǫb	ǫb	NUM
ejpam-1173	15	5	)	)	PUNCT
ejpam-1173	15	6	=	=	PUNCT
ejpam-1173	16	1	(	(	PUNCT
ejpam-1173	16	2	xa)+	xa)+	NOUN
ejpam-1173	16	3	ǫ(x	ǫ(x	PROPN
ejpam-1173	16	4	b+	b+	NUM
ejpam-1173	16	5	ya	ya	NOUN
ejpam-1173	16	6	)	)	PUNCT
ejpam-1173	16	7	.	.	PUNCT
ejpam-1173	17	1	(	(	PUNCT
ejpam-1173	17	2	3	3	X
ejpam-1173	17	3	)	)	PUNCT
ejpam-1173	17	4	this	this	DET
ejpam-1173	17	5	multiplication	multiplication	NOUN
ejpam-1173	17	6	is	be	AUX
ejpam-1173	17	7	commutative	commutative	ADJ
ejpam-1173	17	8	,	,	PUNCT
ejpam-1173	17	9	associative	associative	ADJ
ejpam-1173	17	10	and	and	CCONJ
ejpam-1173	17	11	distributes	distribute	VERB
ejpam-1173	17	12	over	over	ADP
ejpam-1173	17	13	addition	addition	NOUN
ejpam-1173	17	14	.	.	PUNCT
ejpam-1173	18	1	the	the	DET
ejpam-1173	18	2	conjugate	conjugate	ADJ
ejpam-1173	18	3	dual	dual	ADJ
ejpam-1173	18	4	number	number	NOUN
ejpam-1173	18	5	z̄	z̄	NOUN
ejpam-1173	18	6	of	of	ADP
ejpam-1173	18	7	z	z	NOUN
ejpam-1173	18	8	=	=	PUNCT
ejpam-1173	19	1	x	x	PUNCT
ejpam-1173	20	1	+	+	CCONJ
ejpam-1173	20	2	ǫ	ǫ	NOUN
ejpam-1173	20	3	y	y	NOUN
ejpam-1173	20	4	is	be	AUX
ejpam-1173	20	5	defined	define	VERB
ejpam-1173	20	6	by	by	ADP
ejpam-1173	20	7	z̄	z̄	NOUN
ejpam-1173	20	8	=	=	PUNCT
ejpam-1173	20	9	x	x	PUNCT
ejpam-1173	21	1	−	−	NOUN
ejpam-1173	21	2	ǫ	ǫ	NOUN
ejpam-1173	21	3	y	y	PROPN
ejpam-1173	22	1	and	and	CCONJ
ejpam-1173	22	2	we	we	PRON
ejpam-1173	22	3	obtain	obtain	VERB
ejpam-1173	22	4	zz̄	zz̄	NOUN
ejpam-1173	22	5	=	=	SYM
ejpam-1173	22	6	x2	x2	PROPN
ejpam-1173	22	7	.	.	PUNCT
ejpam-1173	23	1	(	(	PUNCT
ejpam-1173	23	2	4	4	X
ejpam-1173	23	3	)	)	PUNCT
ejpam-1173	23	4	∗corresponding	∗corresponde	VERB
ejpam-1173	23	5	author	author	NOUN
ejpam-1173	23	6	.	.	PUNCT
ejpam-1173	24	1	email	email	NOUN
ejpam-1173	24	2	addresses	address	NOUN
ejpam-1173	24	3	:	:	PUNCT
ejpam-1173	24	4	zer	zer	PROPN
ejpam-1173	24	5	an�ku.edu.tr	an�ku.edu.tr	PROPN
ejpam-1173	24	6	(	(	PUNCT
ejpam-1173	24	7	z.	z.	PROPN
ejpam-1173	24	8	ercan	ercan	PROPN
ejpam-1173	24	9	)	)	PUNCT
ejpam-1173	24	10	,	,	PUNCT
ejpam-1173	24	11	sayu	sayu	PROPN
ejpam-1173	24	12	e�yildiz.edu.tr	e�yildiz.edu.tr	PROPN
ejpam-1173	24	13	(	(	PUNCT
ejpam-1173	24	14	s.	s.	PROPN
ejpam-1173	24	15	yuce	yuce	PROPN
ejpam-1173	24	16	)	)	PUNCT
ejpam-1173	24	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1173	25	1	142	142	NUM
ejpam-1173	25	2	c	c	X
ejpam-1173	25	3	©	©	NOUN
ejpam-1173	25	4	2011	2011	NUM
ejpam-1173	25	5	ejpam	ejpam	VERB
ejpam-1173	25	6	all	all	DET
ejpam-1173	25	7	rights	right	NOUN
ejpam-1173	25	8	reserved	reserve	VERB
ejpam-1173	25	9	.	.	PUNCT
ejpam-1173	26	1	z.	z.	PROPN
ejpam-1173	26	2	ercan	ercan	PROPN
ejpam-1173	26	3	,	,	PUNCT
ejpam-1173	26	4	s.	s.	PROPN
ejpam-1173	26	5	yuce	yuce	PROPN
ejpam-1173	26	6	/	/	SYM
ejpam-1173	26	7	eur	eur	PROPN
ejpam-1173	26	8	.	.	PUNCT
ejpam-1173	27	1	j.	j.	PROPN
ejpam-1173	27	2	pure	pure	PROPN
ejpam-1173	27	3	appl	appl	PROPN
ejpam-1173	27	4	.	.	PROPN
ejpam-1173	27	5	math	math	PROPN
ejpam-1173	27	6	,	,	PUNCT
ejpam-1173	27	7	4	4	NUM
ejpam-1173	27	8	(	(	PUNCT
ejpam-1173	27	9	2011	2011	NUM
ejpam-1173	27	10	)	)	PUNCT
ejpam-1173	27	11	,	,	PUNCT
ejpam-1173	27	12	142	142	NUM
ejpam-1173	27	13	-	-	SYM
ejpam-1173	27	14	146	146	NUM
ejpam-1173	27	15	143	143	NUM
ejpam-1173	27	16	the	the	DET
ejpam-1173	27	17	algebra	algebra	NOUN
ejpam-1173	27	18	of	of	ADP
ejpam-1173	27	19	dual	dual	ADJ
ejpam-1173	27	20	numbers	number	NOUN
ejpam-1173	27	21	has	have	AUX
ejpam-1173	27	22	been	be	AUX
ejpam-1173	27	23	originally	originally	ADV
ejpam-1173	27	24	conceived	conceive	VERB
ejpam-1173	27	25	by	by	ADP
ejpam-1173	27	26	w.k	w.k	PROPN
ejpam-1173	27	27	clifford	clifford	PROPN
ejpam-1173	28	1	[	[	X
ejpam-1173	28	2	4	4	NUM
ejpam-1173	28	3	]	]	PUNCT
ejpam-1173	28	4	,	,	PUNCT
ejpam-1173	28	5	but	but	CCONJ
ejpam-1173	28	6	its	its	PRON
ejpam-1173	28	7	first	first	ADJ
ejpam-1173	28	8	application	application	NOUN
ejpam-1173	28	9	to	to	ADP
ejpam-1173	28	10	mechanics	mechanic	NOUN
ejpam-1173	28	11	are	be	AUX
ejpam-1173	28	12	due	due	ADJ
ejpam-1173	28	13	to	to	ADP
ejpam-1173	28	14	e.	e.	PROPN
ejpam-1173	28	15	study	study	PROPN
ejpam-1173	28	16	[	[	X
ejpam-1173	28	17	8	8	NUM
ejpam-1173	28	18	]	]	PUNCT
ejpam-1173	28	19	.	.	PUNCT
ejpam-1173	29	1	because	because	SCONJ
ejpam-1173	29	2	of	of	ADP
ejpam-1173	29	3	conciseness	conciseness	NOUN
ejpam-1173	29	4	of	of	ADP
ejpam-1173	29	5	notation	notation	NOUN
ejpam-1173	29	6	,	,	PUNCT
ejpam-1173	29	7	dual	dual	ADJ
ejpam-1173	29	8	algebra	algebra	NOUN
ejpam-1173	29	9	has	have	AUX
ejpam-1173	29	10	been	be	AUX
ejpam-1173	29	11	often	often	ADV
ejpam-1173	29	12	used	use	VERB
ejpam-1173	29	13	for	for	ADP
ejpam-1173	29	14	the	the	DET
ejpam-1173	29	15	search	search	NOUN
ejpam-1173	29	16	of	of	ADP
ejpam-1173	29	17	closed	closed	ADJ
ejpam-1173	29	18	form	form	NOUN
ejpam-1173	29	19	solutions	solution	NOUN
ejpam-1173	29	20	in	in	ADP
ejpam-1173	29	21	the	the	DET
ejpam-1173	29	22	field	field	NOUN
ejpam-1173	29	23	of	of	ADP
ejpam-1173	29	24	displacement	displacement	ADJ
ejpam-1173	29	25	analysis	analysis	NOUN
ejpam-1173	29	26	,	,	PUNCT
ejpam-1173	29	27	kinematic	kinematic	ADJ
ejpam-1173	29	28	synthesis	synthesis	NOUN
ejpam-1173	29	29	and	and	CCONJ
ejpam-1173	29	30	dynamic	dynamic	ADJ
ejpam-1173	29	31	analysis	analysis	NOUN
ejpam-1173	29	32	of	of	ADP
ejpam-1173	29	33	spatial	spatial	ADJ
ejpam-1173	29	34	mechanisms	mechanism	NOUN
ejpam-1173	29	35	.	.	PUNCT
ejpam-1173	30	1	dual	dual	ADJ
ejpam-1173	30	2	numbers	number	NOUN
ejpam-1173	30	3	can	can	AUX
ejpam-1173	30	4	be	be	AUX
ejpam-1173	30	5	represented	represent	VERB
ejpam-1173	30	6	as	as	SCONJ
ejpam-1173	30	7	follows	follow	VERB
ejpam-1173	30	8	:	:	PUNCT
ejpam-1173	30	9	1	1	X
ejpam-1173	30	10	.	.	PUNCT
ejpam-1173	30	11	gaussian	gaussian	ADJ
ejpam-1173	30	12	representation	representation	NOUN
ejpam-1173	30	13	:	:	PUNCT
ejpam-1173	30	14	z	z	NOUN
ejpam-1173	30	15	=	=	PUNCT
ejpam-1173	31	1	x	x	PUNCT
ejpam-1173	32	1	+	+	PUNCT
ejpam-1173	32	2	ǫ	ǫ	VERB
ejpam-1173	32	3	y	y	PROPN
ejpam-1173	32	4	2	2	NUM
ejpam-1173	32	5	.	.	PUNCT
ejpam-1173	32	6	polar	polar	ADJ
ejpam-1173	32	7	representation	representation	NOUN
ejpam-1173	32	8	:	:	PUNCT
ejpam-1173	32	9	z	z	NOUN
ejpam-1173	32	10	=	=	PUNCT
ejpam-1173	32	11	ρ(1	ρ(1	PROPN
ejpam-1173	32	12	+	+	NOUN
ejpam-1173	32	13	ǫϕ	ǫϕ	NOUN
ejpam-1173	32	14	)	)	PUNCT
ejpam-1173	32	15	3	3	NUM
ejpam-1173	32	16	.	.	PUNCT
ejpam-1173	32	17	exponential	exponential	ADJ
ejpam-1173	32	18	representation	representation	NOUN
ejpam-1173	32	19	:	:	PUNCT
ejpam-1173	32	20	z	z	NOUN
ejpam-1173	32	21	=	=	PUNCT
ejpam-1173	32	22	ρeǫϕ	ρeǫϕ	X
ejpam-1173	32	23	,	,	PUNCT
ejpam-1173	32	24	where	where	SCONJ
ejpam-1173	33	1	ρ	ρ	PROPN
ejpam-1173	33	2	=	=	SYM
ejpam-1173	33	3	x(x	x(x	PROPN
ejpam-1173	33	4	6=	6=	ADP
ejpam-1173	33	5	0),ϕ	0),ϕ	NOUN
ejpam-1173	33	6	=	=	SYM
ejpam-1173	33	7	y	y	PROPN
ejpam-1173	33	8	/	/	SYM
ejpam-1173	33	9	x	x	PROPN
ejpam-1173	33	10	and	and	CCONJ
ejpam-1173	33	11	eǫϕ	eǫϕ	VERB
ejpam-1173	33	12	=	=	SYM
ejpam-1173	33	13	1+ǫϕ.	1+ǫϕ.	NUM
ejpam-1173	33	14	as	as	ADP
ejpam-1173	33	15	the	the	DET
ejpam-1173	33	16	complex	complex	NOUN
ejpam-1173	33	17	number,|z|	number,|z|	NOUN
ejpam-1173	33	18	=	=	SYM
ejpam-1173	33	19	|x	|x	NOUN
ejpam-1173	33	20	|=	|=	PUNCT
ejpam-1173	33	21	ρ	ρ	PROPN
ejpam-1173	33	22	is	be	AUX
ejpam-1173	33	23	called	call	VERB
ejpam-1173	33	24	the	the	DET
ejpam-1173	33	25	modulus	modulus	NOUN
ejpam-1173	33	26	of	of	ADP
ejpam-1173	33	27	the	the	DET
ejpam-1173	33	28	dual	dual	ADJ
ejpam-1173	33	29	number	number	NOUN
ejpam-1173	33	30	z	z	NOUN
ejpam-1173	33	31	and	and	CCONJ
ejpam-1173	33	32	ϕ	ϕ	X
ejpam-1173	33	33	=	=	PUNCT
ejpam-1173	33	34	y	y	PROPN
ejpam-1173	33	35	/	/	SYM
ejpam-1173	33	36	x	x	PUNCT
ejpam-1173	33	37	is	be	AUX
ejpam-1173	33	38	called	call	VERB
ejpam-1173	33	39	the	the	DET
ejpam-1173	33	40	parameter	parameter	NOUN
ejpam-1173	33	41	,	,	PUNCT
ejpam-1173	33	42	[	[	X
ejpam-1173	33	43	2,9	2,9	NUM
ejpam-1173	33	44	]	]	PUNCT
ejpam-1173	33	45	.	.	PUNCT
ejpam-1173	34	1	if	if	SCONJ
ejpam-1173	34	2	|z|	|z|	NOUN
ejpam-1173	34	3	=	=	SYM
ejpam-1173	34	4	1	1	NUM
ejpam-1173	34	5	,	,	PUNCT
ejpam-1173	34	6	then	then	ADV
ejpam-1173	34	7	z	z	PROPN
ejpam-1173	34	8	=	=	SYM
ejpam-1173	34	9	x+ǫ	x+ǫ	PUNCT
ejpam-1173	35	1	y	y	PROPN
ejpam-1173	35	2	is	be	AUX
ejpam-1173	35	3	called	call	VERB
ejpam-1173	35	4	unit	unit	NOUN
ejpam-1173	35	5	dual	dual	ADJ
ejpam-1173	35	6	number	number	NOUN
ejpam-1173	35	7	and	and	CCONJ
ejpam-1173	35	8	the	the	DET
ejpam-1173	35	9	set	set	NOUN
ejpam-1173	35	10	that	that	PRON
ejpam-1173	35	11	satisfy	satisfy	VERB
ejpam-1173	35	12	|z|	|z|	NOUN
ejpam-1173	35	13	=	=	SYM
ejpam-1173	35	14	1	1	NUM
ejpam-1173	35	15	(	(	PUNCT
ejpam-1173	35	16	or	or	CCONJ
ejpam-1173	35	17	x	x	SYM
ejpam-1173	35	18	=	=	NOUN
ejpam-1173	35	19	∓1	∓1	X
ejpam-1173	35	20	)	)	PUNCT
ejpam-1173	35	21	is	be	AUX
ejpam-1173	35	22	called	call	VERB
ejpam-1173	35	23	galilean	galilean	PROPN
ejpam-1173	35	24	unit	unit	NOUN
ejpam-1173	35	25	circle	circle	NOUN
ejpam-1173	35	26	on	on	ADP
ejpam-1173	35	27	the	the	DET
ejpam-1173	35	28	dual	dual	ADJ
ejpam-1173	35	29	plane	plane	NOUN
ejpam-1173	35	30	.	.	PUNCT
ejpam-1173	36	1	for	for	ADP
ejpam-1173	36	2	any	any	DET
ejpam-1173	36	3	real	real	ADJ
ejpam-1173	36	4	ϕ	ϕ	NOUN
ejpam-1173	36	5	,	,	PUNCT
ejpam-1173	36	6	the	the	DET
ejpam-1173	36	7	galilean	galilean	PROPN
ejpam-1173	36	8	cosine	cosine	NOUN
ejpam-1173	36	9	of	of	ADP
ejpam-1173	36	10	ϕ	ϕ	PROPN
ejpam-1173	36	11	(	(	PUNCT
ejpam-1173	36	12	abbreviated	abbreviate	VERB
ejpam-1173	36	13	cosg	cosg	NOUN
ejpam-1173	36	14	)	)	PUNCT
ejpam-1173	36	15	and	and	CCONJ
ejpam-1173	36	16	the	the	DET
ejpam-1173	36	17	galilean	galilean	PROPN
ejpam-1173	36	18	sine	sine	NOUN
ejpam-1173	36	19	of	of	ADP
ejpam-1173	36	20	ϕ	ϕ	PROPN
ejpam-1173	36	21	(	(	PUNCT
ejpam-1173	36	22	abbreviated	abbreviate	VERB
ejpam-1173	36	23	sing	sing	NOUN
ejpam-1173	36	24	)	)	PUNCT
ejpam-1173	36	25	are	be	AUX
ejpam-1173	36	26	the	the	DET
ejpam-1173	36	27	x−	x−	PROPN
ejpam-1173	36	28	and	and	CCONJ
ejpam-1173	36	29	y−	y−	PROPN
ejpam-1173	36	30	coordinates	coordinate	NOUN
ejpam-1173	36	31	of	of	ADP
ejpam-1173	36	32	the	the	DET
ejpam-1173	36	33	point	point	NOUN
ejpam-1173	36	34	p	p	X
ejpam-1173	36	35	=	=	SYM
ejpam-1173	36	36	(	(	PUNCT
ejpam-1173	36	37	x	x	PROPN
ejpam-1173	36	38	,	,	PUNCT
ejpam-1173	36	39	y	y	PROPN
ejpam-1173	36	40	)	)	PUNCT
ejpam-1173	36	41	on	on	ADP
ejpam-1173	36	42	the	the	DET
ejpam-1173	36	43	galilean	galilean	PROPN
ejpam-1173	36	44	unit	unit	NOUN
ejpam-1173	36	45	circle	circle	PROPN
ejpam-1173	36	46	,	,	PUNCT
ejpam-1173	36	47	respectively	respectively	ADV
ejpam-1173	36	48	.	.	PUNCT
ejpam-1173	37	1	furthermore	furthermore	ADV
ejpam-1173	37	2	,	,	PUNCT
ejpam-1173	37	3	the	the	DET
ejpam-1173	37	4	galilean	galilean	PROPN
ejpam-1173	37	5	cosine	cosine	PROPN
ejpam-1173	37	6	,	,	PUNCT
ejpam-1173	37	7	cosgϕ	cosgϕ	NOUN
ejpam-1173	37	8	,	,	PUNCT
ejpam-1173	37	9	and	and	CCONJ
ejpam-1173	37	10	the	the	DET
ejpam-1173	37	11	galilean	galilean	PROPN
ejpam-1173	37	12	sine	sine	NOUN
ejpam-1173	37	13	,	,	PUNCT
ejpam-1173	37	14	singϕ	singϕ	PROPN
ejpam-1173	37	15	,	,	PUNCT
ejpam-1173	37	16	are	be	AUX
ejpam-1173	37	17	defined	define	VERB
ejpam-1173	37	18	by	by	ADP
ejpam-1173	37	19	cosgϕ	cosgϕ	X
ejpam-1173	37	20	=	=	PUNCT
ejpam-1173	37	21	x	x	PROPN
ejpam-1173	37	22	/	/	SYM
ejpam-1173	37	23	x	x	SYM
ejpam-1173	37	24	=	=	SYM
ejpam-1173	37	25	1	1	NUM
ejpam-1173	37	26	,	,	PUNCT
ejpam-1173	37	27	singϕ	singϕ	PROPN
ejpam-1173	37	28	=	=	SYM
ejpam-1173	37	29	y	y	PROPN
ejpam-1173	37	30	/	/	SYM
ejpam-1173	37	31	x	x	SYM
ejpam-1173	37	32	=	=	SYM
ejpam-1173	37	33	ϕ	ϕ	X
ejpam-1173	37	34	(	(	PUNCT
ejpam-1173	37	35	5	5	NUM
ejpam-1173	37	36	)	)	PUNCT
ejpam-1173	37	37	for	for	ADP
ejpam-1173	37	38	all	all	DET
ejpam-1173	37	39	real	real	ADJ
ejpam-1173	37	40	ϕ	ϕ	NOUN
ejpam-1173	37	41	,	,	PUNCT
ejpam-1173	37	42	(	(	PUNCT
ejpam-1173	37	43	see	see	VERB
ejpam-1173	37	44	,	,	PUNCT
ejpam-1173	37	45	[	[	X
ejpam-1173	37	46	5	5	NUM
ejpam-1173	37	47	]	]	NUM
ejpam-1173	37	48	)	)	PUNCT
ejpam-1173	37	49	.	.	PUNCT
ejpam-1173	38	1	the	the	DET
ejpam-1173	38	2	following	follow	VERB
ejpam-1173	38	3	formulas	formula	NOUN
ejpam-1173	38	4	can	can	AUX
ejpam-1173	38	5	be	be	AUX
ejpam-1173	38	6	checked	check	VERB
ejpam-1173	38	7	algebraically	algebraically	ADV
ejpam-1173	38	8	by	by	ADP
ejpam-1173	38	9	using	use	VERB
ejpam-1173	38	10	the	the	DET
ejpam-1173	38	11	definition	definition	NOUN
ejpam-1173	38	12	of	of	ADP
ejpam-1173	38	13	cosg	cosg	NOUN
ejpam-1173	38	14	and	and	CCONJ
ejpam-1173	38	15	sing	sing	VERB
ejpam-1173	38	16	and	and	CCONJ
ejpam-1173	38	17	the	the	DET
ejpam-1173	38	18	laws	law	NOUN
ejpam-1173	38	19	of	of	ADP
ejpam-1173	38	20	exponents	exponent	NOUN
ejpam-1173	38	21	:	:	PUNCT
ejpam-1173	38	22	cosg(x	cosg(x	VERB
ejpam-1173	38	23	+	+	NOUN
ejpam-1173	38	24	y	y	X
ejpam-1173	38	25	)	)	PUNCT
ejpam-1173	39	1	=	=	NOUN
ejpam-1173	39	2	cosg	cosg	NOUN
ejpam-1173	39	3	x	x	PUNCT
ejpam-1173	39	4	cosg	cosg	VERB
ejpam-1173	39	5	y	y	PROPN
ejpam-1173	39	6	−	−	PROPN
ejpam-1173	39	7	ǫ2sing	ǫ2se	VERB
ejpam-1173	39	8	x	x	SYM
ejpam-1173	39	9	sing	sing	VERB
ejpam-1173	39	10	y	y	PRON
ejpam-1173	39	11	,	,	PUNCT
ejpam-1173	39	12	sing(x	sing(x	NOUN
ejpam-1173	39	13	+	+	CCONJ
ejpam-1173	39	14	y	y	NOUN
ejpam-1173	39	15	)	)	PUNCT
ejpam-1173	39	16	=	=	PUNCT
ejpam-1173	40	1	sing	sing	NOUN
ejpam-1173	40	2	x	x	PUNCT
ejpam-1173	40	3	cosg	cosg	VERB
ejpam-1173	40	4	y	y	PROPN
ejpam-1173	40	5	+	+	NUM
ejpam-1173	40	6	cosg	cosg	ADJ
ejpam-1173	40	7	x	x	SYM
ejpam-1173	40	8	sing	sing	VERB
ejpam-1173	40	9	y	y	PROPN
ejpam-1173	40	10	(	(	PUNCT
ejpam-1173	40	11	6	6	NUM
ejpam-1173	40	12	)	)	PUNCT
ejpam-1173	40	13	cosg2	cosg2	NOUN
ejpam-1173	40	14	x	x	X
ejpam-1173	41	1	+	+	CCONJ
ejpam-1173	41	2	ǫ2sing2	ǫ2sing2	ADJ
ejpam-1173	41	3	x	x	SYM
ejpam-1173	41	4	=	=	NOUN
ejpam-1173	41	5	1	1	X
ejpam-1173	41	6	.	.	PUNCT
ejpam-1173	42	1	the	the	DET
ejpam-1173	42	2	dual	dual	ADJ
ejpam-1173	42	3	number	number	NOUN
ejpam-1173	42	4	has	have	VERB
ejpam-1173	42	5	a	a	DET
ejpam-1173	42	6	geometrical	geometrical	ADJ
ejpam-1173	42	7	meaning	meaning	NOUN
ejpam-1173	42	8	which	which	PRON
ejpam-1173	42	9	is	be	AUX
ejpam-1173	42	10	discussed	discuss	VERB
ejpam-1173	42	11	detail	detail	NOUN
ejpam-1173	42	12	in	in	ADP
ejpam-1173	42	13	[	[	X
ejpam-1173	42	14	5,7	5,7	NUM
ejpam-1173	42	15	]	]	PUNCT
ejpam-1173	42	16	.	.	PUNCT
ejpam-1173	43	1	2	2	X
ejpam-1173	43	2	.	.	X
ejpam-1173	43	3	dual	dual	ADJ
ejpam-1173	43	4	quaternions	quaternion	NOUN
ejpam-1173	43	5	a	a	DET
ejpam-1173	43	6	dual	dual	ADJ
ejpam-1173	43	7	quaternion	quaternion	NOUN
ejpam-1173	43	8	q	q	NOUN
ejpam-1173	43	9	is	be	AUX
ejpam-1173	43	10	a	a	DET
ejpam-1173	43	11	linear	linear	ADJ
ejpam-1173	43	12	combination	combination	NOUN
ejpam-1173	43	13	q	q	NOUN
ejpam-1173	43	14	=	=	SYM
ejpam-1173	43	15	a1	a1	PROPN
ejpam-1173	43	16	+	+	CCONJ
ejpam-1173	43	17	bi+	bi+	ADJ
ejpam-1173	43	18	c	c	NOUN
ejpam-1173	43	19	j+dk	j+dk	NOUN
ejpam-1173	43	20	,	,	PUNCT
ejpam-1173	43	21	where	where	SCONJ
ejpam-1173	43	22	a	a	DET
ejpam-1173	43	23	,	,	PUNCT
ejpam-1173	43	24	b	b	NOUN
ejpam-1173	43	25	,	,	PUNCT
ejpam-1173	43	26	c	c	NOUN
ejpam-1173	43	27	,	,	PUNCT
ejpam-1173	43	28	d	d	X
ejpam-1173	43	29	are	be	AUX
ejpam-1173	43	30	real	real	ADJ
ejpam-1173	43	31	numbers	number	NOUN
ejpam-1173	43	32	and	and	CCONJ
ejpam-1173	43	33	1	1	NUM
ejpam-1173	43	34	=	=	SYM
ejpam-1173	43	35	(	(	PUNCT
ejpam-1173	43	36	1,0,0,0	1,0,0,0	NUM
ejpam-1173	43	37	)	)	PUNCT
ejpam-1173	43	38	,	,	PUNCT
ejpam-1173	43	39	i	i	PRON
ejpam-1173	43	40	=	=	PUNCT
ejpam-1173	43	41	(	(	PUNCT
ejpam-1173	43	42	0,1,0,0	0,1,0,0	NUM
ejpam-1173	43	43	)	)	PUNCT
ejpam-1173	43	44	,	,	PUNCT
ejpam-1173	44	1	j	j	X
ejpam-1173	44	2	=	=	PUNCT
ejpam-1173	44	3	(	(	PUNCT
ejpam-1173	44	4	0,0,1,0	0,0,1,0	NUM
ejpam-1173	44	5	)	)	PUNCT
ejpam-1173	44	6	,	,	PUNCT
ejpam-1173	44	7	k	k	PROPN
ejpam-1173	44	8	=	=	PUNCT
ejpam-1173	44	9	(	(	PUNCT
ejpam-1173	44	10	0,0,0,1	0,0,0,1	NOUN
ejpam-1173	44	11	)	)	PUNCT
ejpam-1173	44	12	.	.	PUNCT
ejpam-1173	45	1	the	the	DET
ejpam-1173	45	2	sum	sum	NOUN
ejpam-1173	45	3	of	of	ADP
ejpam-1173	45	4	quaternions	quaternion	NOUN
ejpam-1173	45	5	is	be	AUX
ejpam-1173	45	6	the	the	DET
ejpam-1173	45	7	usual	usual	ADJ
ejpam-1173	45	8	componentwise	componentwise	NOUN
ejpam-1173	45	9	sum	sum	NOUN
ejpam-1173	45	10	and	and	CCONJ
ejpam-1173	45	11	the	the	DET
ejpam-1173	45	12	multiplication	multiplication	NOUN
ejpam-1173	45	13	is	be	AUX
ejpam-1173	45	14	defined	define	VERB
ejpam-1173	45	15	so	so	SCONJ
ejpam-1173	45	16	that	that	SCONJ
ejpam-1173	45	17	(	(	PUNCT
ejpam-1173	45	18	1,0,0,0	1,0,0,0	NUM
ejpam-1173	45	19	)	)	PUNCT
ejpam-1173	45	20	is	be	AUX
ejpam-1173	45	21	the	the	DET
ejpam-1173	45	22	identity	identity	NOUN
ejpam-1173	45	23	and	and	CCONJ
ejpam-1173	45	24	i	i	PRON
ejpam-1173	45	25	,	,	PUNCT
ejpam-1173	45	26	j	j	PROPN
ejpam-1173	45	27	and	and	CCONJ
ejpam-1173	45	28	k	k	PROPN
ejpam-1173	45	29	satisfy	satisfy	PROPN
ejpam-1173	45	30	i2	i2	PROPN
ejpam-1173	45	31	=	=	PROPN
ejpam-1173	45	32	j2	j2	PROPN
ejpam-1173	45	33	=	=	SYM
ejpam-1173	45	34	k2	k2	PROPN
ejpam-1173	46	1	=	=	PROPN
ejpam-1173	47	1	i	i	NOUN
ejpam-1173	47	2	jk	jk	NOUN
ejpam-1173	47	3	=	=	PUNCT
ejpam-1173	47	4	0	0	X
ejpam-1173	47	5	.	.	PUNCT
ejpam-1173	48	1	(	(	PUNCT
ejpam-1173	48	2	7	7	X
ejpam-1173	48	3	)	)	PUNCT
ejpam-1173	48	4	it	it	PRON
ejpam-1173	48	5	follows	follow	VERB
ejpam-1173	48	6	from	from	ADP
ejpam-1173	48	7	(	(	PUNCT
ejpam-1173	48	8	7	7	NUM
ejpam-1173	48	9	)	)	PUNCT
ejpam-1173	48	10	that	that	PRON
ejpam-1173	49	1	i	i	PRON
ejpam-1173	49	2	j	j	NOUN
ejpam-1173	50	1	=	=	PUNCT
ejpam-1173	51	1	−	−	PROPN
ejpam-1173	52	1	ji	ji	X
ejpam-1173	52	2	=	=	PUNCT
ejpam-1173	52	3	jk	jk	PROPN
ejpam-1173	52	4	=	=	PUNCT
ejpam-1173	53	1	−k	−k	PROPN
ejpam-1173	53	2	j	j	PROPN
ejpam-1173	54	1	=	=	PUNCT
ejpam-1173	54	2	ki	ki	PROPN
ejpam-1173	54	3	=	=	SYM
ejpam-1173	54	4	−ik	−ik	NOUN
ejpam-1173	54	5	=	=	SYM
ejpam-1173	54	6	0	0	NUM
ejpam-1173	54	7	.	.	PUNCT
ejpam-1173	55	1	the	the	DET
ejpam-1173	55	2	set	set	NOUN
ejpam-1173	55	3	of	of	ADP
ejpam-1173	55	4	dual	dual	ADJ
ejpam-1173	55	5	quaternions	quaternion	NOUN
ejpam-1173	55	6	denoted	denote	VERB
ejpam-1173	55	7	by	by	ADP
ejpam-1173	55	8	hd	hd	NOUN
ejpam-1173	55	9	=	=	SYM
ejpam-1173	55	10	{	{	PUNCT
ejpam-1173	55	11	q	q	NOUN
ejpam-1173	55	12	=	=	X
ejpam-1173	55	13	a+	a+	PUNCT
ejpam-1173	55	14	bi	bi	NOUN
ejpam-1173	55	15	+	+	PROPN
ejpam-1173	55	16	c	c	PROPN
ejpam-1173	55	17	j	j	PROPN
ejpam-1173	56	1	+	+	PUNCT
ejpam-1173	56	2	dk|	dk|	VERB
ejpam-1173	56	3	a	a	DET
ejpam-1173	56	4	,	,	PUNCT
ejpam-1173	56	5	b	b	NOUN
ejpam-1173	56	6	,	,	PUNCT
ejpam-1173	56	7	c	c	NOUN
ejpam-1173	56	8	,	,	PUNCT
ejpam-1173	56	9	d	d	PROPN
ejpam-1173	56	10	∈	∈	PROPN
ejpam-1173	56	11	r	r	NOUN
ejpam-1173	56	12	,	,	PUNCT
ejpam-1173	56	13	i2	i2	NOUN
ejpam-1173	56	14	=	=	PROPN
ejpam-1173	56	15	j2	j2	PROPN
ejpam-1173	56	16	=	=	SYM
ejpam-1173	56	17	k2	k2	PROPN
ejpam-1173	57	1	=	=	PROPN
ejpam-1173	57	2	i	i	NOUN
ejpam-1173	57	3	jk	jk	NOUN
ejpam-1173	57	4	=	=	PUNCT
ejpam-1173	57	5	0	0	NUM
ejpam-1173	57	6	}	}	PUNCT
ejpam-1173	57	7	.	.	PUNCT
ejpam-1173	58	1	z.	z.	PROPN
ejpam-1173	58	2	ercan	ercan	PROPN
ejpam-1173	58	3	,	,	PUNCT
ejpam-1173	58	4	s.	s.	PROPN
ejpam-1173	58	5	yuce	yuce	PROPN
ejpam-1173	58	6	/	/	SYM
ejpam-1173	58	7	eur	eur	PROPN
ejpam-1173	58	8	.	.	PUNCT
ejpam-1173	59	1	j.	j.	PROPN
ejpam-1173	59	2	pure	pure	PROPN
ejpam-1173	59	3	appl	appl	PROPN
ejpam-1173	59	4	.	.	PROPN
ejpam-1173	59	5	math	math	PROPN
ejpam-1173	59	6	,	,	PUNCT
ejpam-1173	59	7	4	4	NUM
ejpam-1173	59	8	(	(	PUNCT
ejpam-1173	59	9	2011	2011	NUM
ejpam-1173	59	10	)	)	PUNCT
ejpam-1173	59	11	,	,	PUNCT
ejpam-1173	59	12	142	142	NUM
ejpam-1173	59	13	-	-	SYM
ejpam-1173	59	14	146	146	NUM
ejpam-1173	59	15	144	144	NUM
ejpam-1173	59	16	we	we	PRON
ejpam-1173	59	17	can	can	AUX
ejpam-1173	59	18	also	also	ADV
ejpam-1173	59	19	write	write	VERB
ejpam-1173	59	20	q	q	PROPN
ejpam-1173	59	21	=	=	SYM
ejpam-1173	59	22	a+w	a+w	PROPN
ejpam-1173	59	23	,	,	PUNCT
ejpam-1173	59	24	where	where	SCONJ
ejpam-1173	59	25	a	a	PRON
ejpam-1173	59	26	is	be	AUX
ejpam-1173	59	27	the	the	DET
ejpam-1173	59	28	real	real	ADJ
ejpam-1173	59	29	part	part	NOUN
ejpam-1173	59	30	of	of	ADP
ejpam-1173	59	31	q	q	PROPN
ejpam-1173	59	32	and	and	CCONJ
ejpam-1173	59	33	w	w	NOUN
ejpam-1173	59	34	=	=	SYM
ejpam-1173	59	35	bi	bi	PROPN
ejpam-1173	60	1	+	+	NOUN
ejpam-1173	60	2	c	c	PROPN
ejpam-1173	60	3	j	j	PROPN
ejpam-1173	61	1	+	+	CCONJ
ejpam-1173	61	2	dk	dk	PROPN
ejpam-1173	61	3	∈	∈	PROPN
ejpam-1173	61	4	r3	r3	PROPN
ejpam-1173	61	5	,	,	PUNCT
ejpam-1173	61	6	called	call	VERB
ejpam-1173	61	7	the	the	DET
ejpam-1173	61	8	pure	pure	ADJ
ejpam-1173	61	9	dual	dual	ADJ
ejpam-1173	61	10	quaternion	quaternion	ADJ
ejpam-1173	61	11	part	part	NOUN
ejpam-1173	61	12	of	of	ADP
ejpam-1173	61	13	q	q	PROPN
ejpam-1173	61	14	.	.	PUNCT
ejpam-1173	62	1	the	the	DET
ejpam-1173	62	2	conjugate	conjugate	NOUN
ejpam-1173	62	3	of	of	ADP
ejpam-1173	62	4	q	q	NOUN
ejpam-1173	62	5	is	be	AUX
ejpam-1173	62	6	q̄	q̄	ADJ
ejpam-1173	62	7	=	=	NOUN
ejpam-1173	62	8	a	a	DET
ejpam-1173	62	9	−w	−w	NOUN
ejpam-1173	62	10	.	.	PUNCT
ejpam-1173	63	1	a	a	DET
ejpam-1173	63	2	simple	simple	ADJ
ejpam-1173	63	3	computation	computation	NOUN
ejpam-1173	63	4	shows	show	VERB
ejpam-1173	63	5	w1w2	w1w2	PUNCT
ejpam-1173	63	6	=	=	SYM
ejpam-1173	63	7	0	0	PUNCT
ejpam-1173	63	8	(	(	PUNCT
ejpam-1173	63	9	8)	8)	NUM
ejpam-1173	63	10	where	where	SCONJ
ejpam-1173	63	11	w1	w1	NOUN
ejpam-1173	63	12	and	and	CCONJ
ejpam-1173	63	13	w2	w2	NOUN
ejpam-1173	63	14	are	be	AUX
ejpam-1173	63	15	the	the	DET
ejpam-1173	63	16	pure	pure	ADJ
ejpam-1173	63	17	dual	dual	ADJ
ejpam-1173	63	18	quaternions	quaternion	NOUN
ejpam-1173	63	19	.	.	PUNCT
ejpam-1173	64	1	let	let	VERB
ejpam-1173	64	2	a1	a1	NOUN
ejpam-1173	64	3	,	,	PUNCT
ejpam-1173	64	4	a2	a2	PROPN
ejpam-1173	64	5	be	be	VERB
ejpam-1173	64	6	real	real	ADJ
ejpam-1173	64	7	numbers	number	NOUN
ejpam-1173	64	8	.	.	PUNCT
ejpam-1173	65	1	then	then	ADV
ejpam-1173	65	2	,	,	PUNCT
ejpam-1173	65	3	q1q2	q1q2	X
ejpam-1173	65	4	=	=	X
ejpam-1173	65	5	(	(	PUNCT
ejpam-1173	65	6	a1+w1)(a2	a1+w1)(a2	VERB
ejpam-1173	65	7	+	+	NOUN
ejpam-1173	65	8	w2	w2	NOUN
ejpam-1173	65	9	)	)	PUNCT
ejpam-1173	65	10	=	=	PUNCT
ejpam-1173	66	1	a1a2	a1a2	PROPN
ejpam-1173	66	2	+	+	NOUN
ejpam-1173	66	3	a1w2	a1w2	X
ejpam-1173	66	4	+	+	X
ejpam-1173	66	5	a2w1	a2w1	X
ejpam-1173	66	6	=	=	SYM
ejpam-1173	66	7	q2q1	q2q1	PROPN
ejpam-1173	66	8	.	.	PUNCT
ejpam-1173	67	1	(	(	PUNCT
ejpam-1173	67	2	9	9	X
ejpam-1173	67	3	)	)	PUNCT
ejpam-1173	67	4	it	it	PRON
ejpam-1173	67	5	follows	follow	VERB
ejpam-1173	67	6	form	form	NOUN
ejpam-1173	67	7	(	(	PUNCT
ejpam-1173	67	8	8)	8)	NUM
ejpam-1173	67	9	that	that	DET
ejpam-1173	67	10	q1q2	q1q2	ADJ
ejpam-1173	67	11	=	=	SYM
ejpam-1173	67	12	q1	q1	PROPN
ejpam-1173	67	13	q2	q2	NOUN
ejpam-1173	67	14	=	=	SYM
ejpam-1173	67	15	q2	q2	PROPN
ejpam-1173	67	16	q1	q1	PROPN
ejpam-1173	67	17	for	for	ADP
ejpam-1173	67	18	two	two	NUM
ejpam-1173	67	19	dual	dual	ADJ
ejpam-1173	67	20	quaternions	quaternion	NOUN
ejpam-1173	67	21	.	.	PUNCT
ejpam-1173	68	1	the	the	DET
ejpam-1173	68	2	norm	norm	NOUN
ejpam-1173	68	3	of	of	ADP
ejpam-1173	68	4	a	a	DET
ejpam-1173	68	5	dual	dual	ADJ
ejpam-1173	68	6	quaternion	quaternion	NOUN
ejpam-1173	68	7	q	q	NOUN
ejpam-1173	68	8	=	=	PUNCT
ejpam-1173	68	9	a	a	DET
ejpam-1173	68	10	+	+	NOUN
ejpam-1173	68	11	bi	bi	NOUN
ejpam-1173	68	12	+	+	NOUN
ejpam-1173	68	13	c	c	PROPN
ejpam-1173	68	14	j	j	PROPN
ejpam-1173	69	1	+	+	CCONJ
ejpam-1173	69	2	dk	dk	X
ejpam-1173	69	3	=	=	PUNCT
ejpam-1173	69	4	a	a	PRON
ejpam-1173	69	5	+	+	NOUN
ejpam-1173	69	6	w	w	NOUN
ejpam-1173	69	7	is	be	AUX
ejpam-1173	69	8	defined	define	VERB
ejpam-1173	69	9	as	as	ADP
ejpam-1173	69	10	||q||	||q||	PROPN
ejpam-1173	69	11	=	=	PROPN
ejpam-1173	69	12	p	p	NOUN
ejpam-1173	69	13	qq̄	qq̄	NOUN
ejpam-1173	69	14	=	=	PROPN
ejpam-1173	69	15	p	p	NOUN
ejpam-1173	69	16	a2	a2	PROPN
ejpam-1173	69	17	=	=	SYM
ejpam-1173	69	18	|a|	|a|	PROPN
ejpam-1173	69	19	.	.	NOUN
ejpam-1173	70	1	if	if	SCONJ
ejpam-1173	70	2	||q||=	||q||=	ADV
ejpam-1173	70	3	1	1	NUM
ejpam-1173	70	4	,	,	PUNCT
ejpam-1173	70	5	then	then	ADV
ejpam-1173	70	6	q	q	X
ejpam-1173	70	7	is	be	AUX
ejpam-1173	70	8	called	call	VERB
ejpam-1173	70	9	unit	unit	NOUN
ejpam-1173	70	10	dual	dual	ADJ
ejpam-1173	70	11	quaternion	quaternion	NOUN
ejpam-1173	70	12	.	.	PUNCT
ejpam-1173	71	1	the	the	DET
ejpam-1173	71	2	set	set	PROPN
ejpam-1173	71	3	hd	hd	NOUN
ejpam-1173	71	4	forms	form	VERB
ejpam-1173	71	5	a	a	DET
ejpam-1173	71	6	commutative	commutative	ADJ
ejpam-1173	71	7	ring	ring	NOUN
ejpam-1173	71	8	under	under	ADP
ejpam-1173	71	9	the	the	DET
ejpam-1173	71	10	dual	dual	ADJ
ejpam-1173	71	11	quaternion	quaternion	NOUN
ejpam-1173	71	12	multiplication	multiplication	NOUN
ejpam-1173	71	13	and	and	CCONJ
ejpam-1173	71	14	also	also	ADV
ejpam-1173	71	15	it	it	PRON
ejpam-1173	71	16	is	be	AUX
ejpam-1173	71	17	a	a	DET
ejpam-1173	71	18	vector	vector	NOUN
ejpam-1173	71	19	space	space	NOUN
ejpam-1173	71	20	of	of	ADP
ejpam-1173	71	21	dimensions	dimension	NOUN
ejpam-1173	71	22	four	four	NUM
ejpam-1173	71	23	on	on	ADP
ejpam-1173	71	24	r	r	NOUN
ejpam-1173	71	25	and	and	CCONJ
ejpam-1173	71	26	its	its	PRON
ejpam-1173	71	27	basis	basis	NOUN
ejpam-1173	71	28	is	be	AUX
ejpam-1173	71	29	the	the	DET
ejpam-1173	71	30	set	set	NOUN
ejpam-1173	71	31	{	{	PUNCT
ejpam-1173	71	32	1	1	NUM
ejpam-1173	71	33	,	,	PUNCT
ejpam-1173	71	34	i	i	PRON
ejpam-1173	71	35	,	,	PUNCT
ejpam-1173	71	36	j	j	PROPN
ejpam-1173	71	37	,	,	PUNCT
ejpam-1173	71	38	k	k	NOUN
ejpam-1173	71	39	}	}	PUNCT
ejpam-1173	71	40	.	.	PUNCT
ejpam-1173	72	1	the	the	DET
ejpam-1173	72	2	interesting	interesting	ADJ
ejpam-1173	72	3	property	property	NOUN
ejpam-1173	72	4	of	of	ADP
ejpam-1173	72	5	dual	dual	ADJ
ejpam-1173	72	6	quaternions	quaternion	NOUN
ejpam-1173	72	7	is	be	AUX
ejpam-1173	72	8	that	that	SCONJ
ejpam-1173	72	9	by	by	ADP
ejpam-1173	72	10	their	their	PRON
ejpam-1173	72	11	means	mean	NOUN
ejpam-1173	72	12	one	one	PRON
ejpam-1173	72	13	can	can	AUX
ejpam-1173	72	14	express	express	VERB
ejpam-1173	72	15	the	the	DET
ejpam-1173	72	16	galilean	galilean	PROPN
ejpam-1173	72	17	transformation	transformation	NOUN
ejpam-1173	72	18	in	in	ADP
ejpam-1173	72	19	one	one	NUM
ejpam-1173	72	20	quaternion	quaternion	NOUN
ejpam-1173	72	21	equation	equation	NOUN
ejpam-1173	72	22	.	.	PUNCT
ejpam-1173	73	1	since	since	SCONJ
ejpam-1173	73	2	the	the	DET
ejpam-1173	73	3	multiplication	multiplication	NOUN
ejpam-1173	73	4	and	and	CCONJ
ejpam-1173	73	5	ratio	ratio	NOUN
ejpam-1173	73	6	of	of	ADP
ejpam-1173	73	7	two	two	NUM
ejpam-1173	73	8	dual	dual	ADJ
ejpam-1173	73	9	quaternions	quaternions	ADJ
ejpam-1173	73	10	q1	q1	PROPN
ejpam-1173	73	11	and	and	CCONJ
ejpam-1173	73	12	q2	q2	NOUN
ejpam-1173	73	13	is	be	AUX
ejpam-1173	73	14	again	again	ADV
ejpam-1173	73	15	a	a	DET
ejpam-1173	73	16	dual	dual	ADJ
ejpam-1173	73	17	quaternion	quaternion	NOUN
ejpam-1173	73	18	,	,	PUNCT
ejpam-1173	73	19	the	the	DET
ejpam-1173	73	20	set	set	NOUN
ejpam-1173	73	21	of	of	ADP
ejpam-1173	73	22	dual	dual	ADJ
ejpam-1173	73	23	quaternions	quaternion	NOUN
ejpam-1173	73	24	form	form	VERB
ejpam-1173	73	25	a	a	DET
ejpam-1173	73	26	division	division	NOUN
ejpam-1173	73	27	algebra	algebra	NOUN
ejpam-1173	73	28	under	under	ADP
ejpam-1173	73	29	addition	addition	NOUN
ejpam-1173	73	30	and	and	CCONJ
ejpam-1173	73	31	multiplication	multiplication	NOUN
ejpam-1173	73	32	.	.	PUNCT
ejpam-1173	74	1	for	for	ADP
ejpam-1173	74	2	more	more	ADJ
ejpam-1173	74	3	details	detail	NOUN
ejpam-1173	74	4	on	on	ADP
ejpam-1173	74	5	dual	dual	ADJ
ejpam-1173	74	6	quaternions	quaternion	NOUN
ejpam-1173	74	7	,	,	PUNCT
ejpam-1173	74	8	we	we	PRON
ejpam-1173	74	9	refer	refer	VERB
ejpam-1173	74	10	the	the	DET
ejpam-1173	74	11	reader	reader	NOUN
ejpam-1173	74	12	to	to	ADP
ejpam-1173	74	13	[	[	X
ejpam-1173	74	14	1	1	NUM
ejpam-1173	74	15	]	]	PUNCT
ejpam-1173	74	16	,	,	PUNCT
ejpam-1173	74	17	[	[	X
ejpam-1173	74	18	6	6	NUM
ejpam-1173	74	19	]	]	PUNCT
ejpam-1173	74	20	.	.	PUNCT
ejpam-1173	75	1	3	3	X
ejpam-1173	75	2	.	.	X
ejpam-1173	75	3	euler	euler	PROPN
ejpam-1173	75	4	’s	’s	PART
ejpam-1173	75	5	formula	formula	NOUN
ejpam-1173	75	6	and	and	CCONJ
ejpam-1173	75	7	de	de	ADP
ejpam-1173	75	8	moivre	moivre	NOUN
ejpam-1173	75	9	’s	’s	PART
ejpam-1173	75	10	formula	formula	NOUN
ejpam-1173	75	11	for	for	ADP
ejpam-1173	75	12	dual	dual	ADJ
ejpam-1173	75	13	quaternions	quaternion	NOUN
ejpam-1173	75	14	let	let	VERB
ejpam-1173	75	15	q	q	NOUN
ejpam-1173	75	16	=	=	SYM
ejpam-1173	75	17	a+bi+c	a+bi+c	ADJ
ejpam-1173	75	18	j+dk	j+dk	NOUN
ejpam-1173	75	19	be	be	VERB
ejpam-1173	75	20	a	a	DET
ejpam-1173	75	21	unit	unit	NOUN
ejpam-1173	75	22	dual	dual	ADV
ejpam-1173	75	23	quaternion	quaternion	NOUN
ejpam-1173	75	24	.	.	PUNCT
ejpam-1173	76	1	we	we	PRON
ejpam-1173	76	2	can	can	AUX
ejpam-1173	76	3	express	express	VERB
ejpam-1173	76	4	any	any	DET
ejpam-1173	76	5	unit	unit	NOUN
ejpam-1173	76	6	dual	dual	ADV
ejpam-1173	76	7	quaternion	quaternion	NOUN
ejpam-1173	76	8	q	q	PUNCT
ejpam-1173	76	9	as	as	ADP
ejpam-1173	76	10	q	q	NOUN
ejpam-1173	76	11	=	=	PUNCT
ejpam-1173	76	12	cosgθ	cosgθ	NOUN
ejpam-1173	76	13	+	+	NOUN
ejpam-1173	76	14	wsingθ	wsingθ	NOUN
ejpam-1173	76	15	(	(	PUNCT
ejpam-1173	76	16	10	10	NUM
ejpam-1173	76	17	)	)	PUNCT
ejpam-1173	76	18	where	where	SCONJ
ejpam-1173	76	19	w	w	NOUN
ejpam-1173	76	20	=	=	SYM
ejpam-1173	76	21	bi+c	bi+c	PROPN
ejpam-1173	76	22	j+dkp	j+dkp	NOUN
ejpam-1173	76	23	b2+c2+d2	b2+c2+d2	PROPN
ejpam-1173	76	24	and	and	CCONJ
ejpam-1173	76	25	singθ	singθ	PROPN
ejpam-1173	76	26	=	=	SYM
ejpam-1173	76	27	θ	θ	X
ejpam-1173	76	28	=	=	SYM
ejpam-1173	76	29	p	p	NOUN
ejpam-1173	76	30	b2	b2	NOUN
ejpam-1173	76	31	+	+	CCONJ
ejpam-1173	76	32	c2	c2	PROPN
ejpam-1173	76	33	+	+	CCONJ
ejpam-1173	76	34	d2	d2	PROPN
ejpam-1173	76	35	.	.	PUNCT
ejpam-1173	77	1	this	this	PRON
ejpam-1173	77	2	is	be	AUX
ejpam-1173	77	3	similar	similar	ADJ
ejpam-1173	77	4	to	to	ADP
ejpam-1173	77	5	the	the	DET
ejpam-1173	77	6	polar	polar	ADJ
ejpam-1173	77	7	coordinated	coordinated	ADJ
ejpam-1173	77	8	expression	expression	NOUN
ejpam-1173	77	9	of	of	ADP
ejpam-1173	77	10	a	a	DET
ejpam-1173	77	11	complex	complex	ADJ
ejpam-1173	77	12	number	number	NOUN
ejpam-1173	77	13	z	z	NOUN
ejpam-1173	77	14	=	=	SYM
ejpam-1173	77	15	cosϕ	cosϕ	NOUN
ejpam-1173	78	1	+	+	CCONJ
ejpam-1173	78	2	i	i	PRON
ejpam-1173	78	3	sinϕ.	sinϕ.	VERB
ejpam-1173	78	4	since	since	SCONJ
ejpam-1173	78	5	w2	w2	NOUN
ejpam-1173	78	6	=	=	PROPN
ejpam-1173	78	7	0	0	NUM
ejpam-1173	78	8	for	for	ADP
ejpam-1173	78	9	any	any	DET
ejpam-1173	78	10	pure	pure	ADJ
ejpam-1173	78	11	dual	dual	ADJ
ejpam-1173	78	12	quaternion	quaternion	NOUN
ejpam-1173	78	13	w	w	NOUN
ejpam-1173	78	14	,	,	PUNCT
ejpam-1173	78	15	we	we	PRON
ejpam-1173	78	16	have	have	VERB
ejpam-1173	78	17	a	a	DET
ejpam-1173	78	18	natural	natural	ADJ
ejpam-1173	78	19	generalization	generalization	NOUN
ejpam-1173	78	20	of	of	ADP
ejpam-1173	78	21	euler	euler	PROPN
ejpam-1173	78	22	’s	’s	PART
ejpam-1173	78	23	formula	formula	NOUN
ejpam-1173	78	24	for	for	ADP
ejpam-1173	78	25	dual	dual	ADJ
ejpam-1173	78	26	quaternion	quaternion	NOUN
ejpam-1173	78	27	ewθ	ewθ	NOUN
ejpam-1173	78	28	=	=	SYM
ejpam-1173	79	1	1+wθ	1+wθ	PROPN
ejpam-1173	79	2	+	+	CCONJ
ejpam-1173	79	3	(	(	PUNCT
ejpam-1173	79	4	wθ)2	wθ)2	PROPN
ejpam-1173	79	5	2	2	NUM
ejpam-1173	79	6	!	!	PUNCT
ejpam-1173	80	1	+	+	CCONJ
ejpam-1173	80	2	(	(	PUNCT
ejpam-1173	80	3	wθ)3	wθ)3	NOUN
ejpam-1173	80	4	3	3	NUM
ejpam-1173	80	5	!	!	PUNCT
ejpam-1173	81	1	+	+	CCONJ
ejpam-1173	81	2	.	.	PUNCT
ejpam-1173	81	3	.	.	PUNCT
ejpam-1173	81	4	.	.	PUNCT
ejpam-1173	82	1	=	=	PUNCT
ejpam-1173	83	1	1+wθ	1+wθ	NUM
ejpam-1173	83	2	=	=	SYM
ejpam-1173	83	3	cosgθ	cosgθ	PROPN
ejpam-1173	83	4	+	+	PROPN
ejpam-1173	83	5	w	w	PROPN
ejpam-1173	83	6	singθ	singθ	NOUN
ejpam-1173	83	7	=	=	SYM
ejpam-1173	83	8	q	q	PROPN
ejpam-1173	83	9	for	for	ADP
ejpam-1173	83	10	any	any	DET
ejpam-1173	83	11	real	real	ADJ
ejpam-1173	83	12	q	q	NOUN
ejpam-1173	83	13	.	.	PUNCT
ejpam-1173	84	1	for	for	ADP
ejpam-1173	84	2	more	more	ADJ
ejpam-1173	84	3	on	on	ADP
ejpam-1173	84	4	euler	euler	NOUN
ejpam-1173	84	5	’s	’s	PART
ejpam-1173	84	6	formula	formula	NOUN
ejpam-1173	84	7	for	for	ADP
ejpam-1173	84	8	complex	complex	ADJ
ejpam-1173	84	9	numbers	number	NOUN
ejpam-1173	84	10	and	and	CCONJ
ejpam-1173	84	11	real	real	ADJ
ejpam-1173	84	12	quaternion	quaternion	NOUN
ejpam-1173	84	13	,	,	PUNCT
ejpam-1173	84	14	we	we	PRON
ejpam-1173	84	15	refer	refer	VERB
ejpam-1173	84	16	the	the	DET
ejpam-1173	84	17	reader	reader	NOUN
ejpam-1173	84	18	to	to	ADP
ejpam-1173	84	19	[	[	X
ejpam-1173	84	20	2,3	2,3	NUM
ejpam-1173	84	21	]	]	PUNCT
ejpam-1173	84	22	.	.	PUNCT
ejpam-1173	85	1	we	we	PRON
ejpam-1173	85	2	can	can	AUX
ejpam-1173	85	3	give	give	VERB
ejpam-1173	85	4	the	the	DET
ejpam-1173	85	5	following	follow	VERB
ejpam-1173	85	6	lemma	lemma	PROPN
ejpam-1173	85	7	using	use	VERB
ejpam-1173	85	8	equation	equation	NOUN
ejpam-1173	85	9	(	(	PUNCT
ejpam-1173	85	10	6	6	NUM
ejpam-1173	85	11	)	)	PUNCT
ejpam-1173	85	12	according	accord	VERB
ejpam-1173	85	13	to	to	ADP
ejpam-1173	85	14	the	the	DET
ejpam-1173	85	15	addition	addition	NOUN
ejpam-1173	85	16	formula	formula	NOUN
ejpam-1173	85	17	for	for	ADP
ejpam-1173	85	18	galilean	galilean	PROPN
ejpam-1173	85	19	cosine	cosine	PROPN
ejpam-1173	85	20	and	and	CCONJ
ejpam-1173	85	21	galilean	galilean	PROPN
ejpam-1173	85	22	sine	sine	NOUN
ejpam-1173	85	23	:	:	PUNCT
ejpam-1173	85	24	lemma	lemma	PROPN
ejpam-1173	85	25	1	1	NUM
ejpam-1173	85	26	.	.	PUNCT
ejpam-1173	86	1	for	for	ADP
ejpam-1173	86	2	any	any	DET
ejpam-1173	86	3	pure	pure	ADJ
ejpam-1173	86	4	dual	dual	ADJ
ejpam-1173	86	5	quaternion	quaternion	NOUN
ejpam-1173	86	6	w	w	NOUN
ejpam-1173	86	7	,	,	PUNCT
ejpam-1173	86	8	we	we	PRON
ejpam-1173	86	9	have	have	VERB
ejpam-1173	86	10	,	,	PUNCT
ejpam-1173	86	11	1	1	X
ejpam-1173	86	12	.	.	PUNCT
ejpam-1173	87	1	ewθ1	ewθ1	PROPN
ejpam-1173	87	2	ewθ2	ewθ2	PROPN
ejpam-1173	87	3	=	=	SYM
ejpam-1173	87	4	ew(θ1+θ2	ew(θ1+θ2	X
ejpam-1173	87	5	)	)	PUNCT
ejpam-1173	87	6	2	2	NUM
ejpam-1173	87	7	.	.	NOUN
ejpam-1173	87	8	1	1	NUM
ejpam-1173	87	9	ewθ	ewθ	NOUN
ejpam-1173	87	10	=	=	SYM
ejpam-1173	87	11	ew(−θ	ew(−θ	NOUN
ejpam-1173	87	12	)	)	PUNCT
ejpam-1173	87	13	3	3	X
ejpam-1173	87	14	.	.	PUNCT
ejpam-1173	87	15	ewθ1	ewθ1	PROPN
ejpam-1173	87	16	ewθ2	ewθ2	PROPN
ejpam-1173	87	17	=	=	SYM
ejpam-1173	87	18	ew(θ1−θ2	ew(θ1−θ2	PROPN
ejpam-1173	87	19	)	)	PUNCT
ejpam-1173	87	20	z.	z.	PROPN
ejpam-1173	87	21	ercan	ercan	PROPN
ejpam-1173	87	22	,	,	PUNCT
ejpam-1173	87	23	s.	s.	PROPN
ejpam-1173	87	24	yuce	yuce	PROPN
ejpam-1173	87	25	/	/	SYM
ejpam-1173	87	26	eur	eur	PROPN
ejpam-1173	87	27	.	.	PUNCT
ejpam-1173	88	1	j.	j.	PROPN
ejpam-1173	88	2	pure	pure	PROPN
ejpam-1173	88	3	appl	appl	PROPN
ejpam-1173	88	4	.	.	PROPN
ejpam-1173	88	5	math	math	PROPN
ejpam-1173	88	6	,	,	PUNCT
ejpam-1173	88	7	4	4	NUM
ejpam-1173	88	8	(	(	PUNCT
ejpam-1173	88	9	2011	2011	NUM
ejpam-1173	88	10	)	)	PUNCT
ejpam-1173	88	11	,	,	PUNCT
ejpam-1173	88	12	142	142	NUM
ejpam-1173	88	13	-	-	SYM
ejpam-1173	88	14	146	146	NUM
ejpam-1173	88	15	145	145	NUM
ejpam-1173	88	16	proposition	proposition	NOUN
ejpam-1173	88	17	1	1	NUM
ejpam-1173	88	18	(	(	PUNCT
ejpam-1173	88	19	de	de	X
ejpam-1173	88	20	moivre	moivre	NOUN
ejpam-1173	88	21	’s	’s	PART
ejpam-1173	88	22	formula	formula	NOUN
ejpam-1173	88	23	)	)	PUNCT
ejpam-1173	88	24	.	.	PUNCT
ejpam-1173	89	1	let	let	VERB
ejpam-1173	89	2	q	q	NOUN
ejpam-1173	89	3	=	=	PUNCT
ejpam-1173	89	4	ewθ	ewθ	NOUN
ejpam-1173	89	5	=	=	PUNCT
ejpam-1173	89	6	cosgθ	cosgθ	NOUN
ejpam-1173	89	7	+	+	NOUN
ejpam-1173	89	8	wsingθ	wsingθ	AUX
ejpam-1173	89	9	be	be	AUX
ejpam-1173	89	10	a	a	DET
ejpam-1173	89	11	unit	unit	NOUN
ejpam-1173	89	12	dual	dual	ADJ
ejpam-1173	89	13	quaternion	quaternion	NOUN
ejpam-1173	89	14	.	.	PUNCT
ejpam-1173	90	1	then	then	ADV
ejpam-1173	90	2	,	,	PUNCT
ejpam-1173	90	3	qn	qn	NOUN
ejpam-1173	90	4	=	=	X
ejpam-1173	90	5	(	(	PUNCT
ejpam-1173	90	6	ewθ	ewθ	NOUN
ejpam-1173	90	7	)	)	PUNCT
ejpam-1173	90	8	n	n	NOUN
ejpam-1173	90	9	=	=	SYM
ejpam-1173	90	10	(	(	PUNCT
ejpam-1173	90	11	cosgθ	cosgθ	NOUN
ejpam-1173	90	12	+	+	PROPN
ejpam-1173	90	13	wsingθ)n	wsingθ)n	NOUN
ejpam-1173	90	14	=	=	SYM
ejpam-1173	90	15	cosg(nθ	cosg(nθ	NOUN
ejpam-1173	90	16	)	)	PUNCT
ejpam-1173	90	17	+	+	NOUN
ejpam-1173	90	18	wsing(nθ	wsing(nθ	NOUN
ejpam-1173	90	19	)	)	PUNCT
ejpam-1173	90	20	for	for	ADP
ejpam-1173	90	21	every	every	DET
ejpam-1173	90	22	integer	integer	NOUN
ejpam-1173	90	23	.	.	PUNCT
ejpam-1173	91	1	proof	proof	NOUN
ejpam-1173	91	2	.	.	PUNCT
ejpam-1173	92	1	the	the	DET
ejpam-1173	92	2	proof	proof	NOUN
ejpam-1173	92	3	will	will	AUX
ejpam-1173	92	4	be	be	AUX
ejpam-1173	92	5	a	a	DET
ejpam-1173	92	6	induction	induction	NOUN
ejpam-1173	92	7	on	on	ADP
ejpam-1173	92	8	nonnegative	nonnegative	ADJ
ejpam-1173	92	9	integers	integer	NOUN
ejpam-1173	92	10	n	n	ADP
ejpam-1173	92	11	using	use	VERB
ejpam-1173	92	12	equation	equation	NOUN
ejpam-1173	92	13	(	(	PUNCT
ejpam-1173	92	14	6	6	NUM
ejpam-1173	92	15	):	):	PUNCT
ejpam-1173	92	16	qn+1	qn+1	NUM
ejpam-1173	92	17	=	=	SYM
ejpam-1173	92	18	(	(	PUNCT
ejpam-1173	92	19	cosgθ	cosgθ	PROPN
ejpam-1173	92	20	+	+	NOUN
ejpam-1173	92	21	wsingθ)n+1	wsingθ)n+1	X
ejpam-1173	92	22	=	=	SYM
ejpam-1173	92	23	(	(	PUNCT
ejpam-1173	92	24	cosg(nθ	cosg(nθ	NOUN
ejpam-1173	92	25	)	)	PUNCT
ejpam-1173	92	26	+	+	NOUN
ejpam-1173	92	27	wsing(nθ	wsing(nθ	NOUN
ejpam-1173	92	28	)	)	PUNCT
ejpam-1173	92	29	)	)	PUNCT
ejpam-1173	92	30	(	(	PUNCT
ejpam-1173	92	31	cosgθ	cosgθ	NOUN
ejpam-1173	92	32	+	+	NOUN
ejpam-1173	92	33	wsingθ	wsingθ	NOUN
ejpam-1173	92	34	)	)	PUNCT
ejpam-1173	92	35	=	=	PUNCT
ejpam-1173	92	36	cosg(n+	cosg(n+	X
ejpam-1173	92	37	1)θ	1)θ	NUM
ejpam-1173	92	38	+	+	ADJ
ejpam-1173	92	39	wsing(n+	wsing(n+	ADP
ejpam-1173	92	40	1)θ	1)θ	NUM
ejpam-1173	92	41	.	.	PUNCT
ejpam-1173	93	1	the	the	DET
ejpam-1173	93	2	formulas	formula	NOUN
ejpam-1173	93	3	holds	hold	VERB
ejpam-1173	93	4	for	for	ADP
ejpam-1173	93	5	all	all	DET
ejpam-1173	93	6	integers	integer	NOUN
ejpam-1173	93	7	n	n	ADV
ejpam-1173	93	8	since	since	SCONJ
ejpam-1173	93	9	q−1	q−1	PROPN
ejpam-1173	93	10	=	=	PROPN
ejpam-1173	93	11	cosgθ	cosgθ	PROPN
ejpam-1173	93	12	−wsingθ	−wsingθ	PROPN
ejpam-1173	93	13	and	and	CCONJ
ejpam-1173	93	14	q−n	q−n	PROPN
ejpam-1173	93	15	=	=	SYM
ejpam-1173	93	16	cosg(nθ)−wsing(nθ	cosg(nθ)−wsing(nθ	PROPN
ejpam-1173	93	17	)	)	PUNCT
ejpam-1173	93	18	=	=	SYM
ejpam-1173	93	19	cosg(−nθ	cosg(−nθ	X
ejpam-1173	93	20	)	)	PUNCT
ejpam-1173	93	21	+	+	NOUN
ejpam-1173	93	22	wsing(−nθ	wsing(−nθ	NOUN
ejpam-1173	93	23	)	)	PUNCT
ejpam-1173	93	24	.	.	PUNCT
ejpam-1173	94	1	4	4	X
ejpam-1173	94	2	.	.	X
ejpam-1173	94	3	the	the	DET
ejpam-1173	94	4	matrix	matrix	NOUN
ejpam-1173	94	5	representation	representation	NOUN
ejpam-1173	94	6	of	of	ADP
ejpam-1173	94	7	the	the	DET
ejpam-1173	94	8	dual	dual	ADJ
ejpam-1173	94	9	quaternions	quaternion	NOUN
ejpam-1173	94	10	let	let	VERB
ejpam-1173	94	11	q	q	NOUN
ejpam-1173	94	12	=	=	PUNCT
ejpam-1173	94	13	a	a	DET
ejpam-1173	94	14	+	+	NOUN
ejpam-1173	94	15	bi	bi	NOUN
ejpam-1173	94	16	+	+	NOUN
ejpam-1173	94	17	c	c	PROPN
ejpam-1173	94	18	j	j	PROPN
ejpam-1173	95	1	+	+	CCONJ
ejpam-1173	95	2	dk	dk	AUX
ejpam-1173	95	3	be	be	VERB
ejpam-1173	95	4	a	a	DET
ejpam-1173	95	5	dual	dual	ADJ
ejpam-1173	95	6	quaternion	quaternion	NOUN
ejpam-1173	95	7	.	.	PUNCT
ejpam-1173	96	1	we	we	PRON
ejpam-1173	96	2	will	will	AUX
ejpam-1173	96	3	define	define	VERB
ejpam-1173	96	4	the	the	DET
ejpam-1173	96	5	linear	linear	ADJ
ejpam-1173	96	6	map	map	NOUN
ejpam-1173	96	7	lq	lq	VERB
ejpam-1173	96	8	as	as	ADP
ejpam-1173	96	9	lq	lq	ADV
ejpam-1173	96	10	:	:	PUNCT
ejpam-1173	96	11	hd	hd	PROPN
ejpam-1173	96	12	→	→	SYM
ejpam-1173	96	13	hd	hd	VERB
ejpam-1173	96	14	such	such	DET
ejpam-1173	96	15	that	that	DET
ejpam-1173	96	16	lq(q1	lq(q1	NOUN
ejpam-1173	96	17	)	)	PUNCT
ejpam-1173	96	18	=	=	SYM
ejpam-1173	96	19	qq1	qq1	PROPN
ejpam-1173	96	20	.	.	PUNCT
ejpam-1173	97	1	using	use	VERB
ejpam-1173	97	2	our	our	PRON
ejpam-1173	97	3	newly	newly	ADV
ejpam-1173	97	4	defined	define	VERB
ejpam-1173	97	5	operator	operator	NOUN
ejpam-1173	97	6	and	and	CCONJ
ejpam-1173	97	7	the	the	DET
ejpam-1173	97	8	basis	basis	NOUN
ejpam-1173	97	9	{	{	PUNCT
ejpam-1173	97	10	1	1	NUM
ejpam-1173	97	11	,	,	PUNCT
ejpam-1173	97	12	i	i	PRON
ejpam-1173	97	13	,	,	PUNCT
ejpam-1173	97	14	j	j	PROPN
ejpam-1173	97	15	,	,	PUNCT
ejpam-1173	97	16	k	k	NOUN
ejpam-1173	97	17	}	}	PUNCT
ejpam-1173	97	18	of	of	ADP
ejpam-1173	97	19	the	the	DET
ejpam-1173	97	20	vector	vector	NOUN
ejpam-1173	97	21	space	space	NOUN
ejpam-1173	97	22	hd	hd	NOUN
ejpam-1173	97	23	,	,	PUNCT
ejpam-1173	97	24	we	we	PRON
ejpam-1173	97	25	can	can	AUX
ejpam-1173	97	26	write	write	VERB
ejpam-1173	97	27	lq(1	lq(1	NOUN
ejpam-1173	97	28	)	)	PUNCT
ejpam-1173	97	29	=	=	SYM
ejpam-1173	98	1	q×	q×	X
ejpam-1173	98	2	1=	1=	X
ejpam-1173	98	3	a1	a1	NOUN
ejpam-1173	98	4	+	+	NOUN
ejpam-1173	98	5	bi	bi	NOUN
ejpam-1173	98	6	+	+	NOUN
ejpam-1173	98	7	c	c	PROPN
ejpam-1173	98	8	j	j	PROPN
ejpam-1173	99	1	+	+	CCONJ
ejpam-1173	99	2	dk	dk	PROPN
ejpam-1173	99	3	lq(i	lq(i	X
ejpam-1173	99	4	)	)	PUNCT
ejpam-1173	99	5	=	=	VERB
ejpam-1173	100	1	q×	q×	PUNCT
ejpam-1173	100	2	i	i	PRON
ejpam-1173	100	3	=	=	NOUN
ejpam-1173	100	4	01	01	PROPN
ejpam-1173	100	5	+	+	CCONJ
ejpam-1173	100	6	ai	ai	VERB
ejpam-1173	100	7	+	+	ADJ
ejpam-1173	100	8	0	0	NUM
ejpam-1173	100	9	j+	j+	NUM
ejpam-1173	100	10	0k	0k	NOUN
ejpam-1173	100	11	lq	lq	X
ejpam-1173	100	12	(	(	PUNCT
ejpam-1173	100	13	j	j	NOUN
ejpam-1173	100	14	)	)	PUNCT
ejpam-1173	100	15	=	=	PUNCT
ejpam-1173	101	1	q×	q×	PROPN
ejpam-1173	101	2	j	j	X
ejpam-1173	101	3	=	=	SYM
ejpam-1173	101	4	01	01	PROPN
ejpam-1173	102	1	+	+	NUM
ejpam-1173	102	2	0i	0i	NOUN
ejpam-1173	102	3	+	+	CCONJ
ejpam-1173	102	4	a	a	DET
ejpam-1173	102	5	j	j	NOUN
ejpam-1173	102	6	+	+	NUM
ejpam-1173	102	7	0k	0k	NOUN
ejpam-1173	102	8	lq(k	lq(k	PUNCT
ejpam-1173	102	9	)	)	PUNCT
ejpam-1173	103	1	=	=	PUNCT
ejpam-1173	104	1	q×	q×	PUNCT
ejpam-1173	104	2	k	k	X
ejpam-1173	104	3	=	=	SYM
ejpam-1173	104	4	01	01	PROPN
ejpam-1173	104	5	+	+	NUM
ejpam-1173	104	6	0i+	0i+	NUM
ejpam-1173	104	7	0	0	NUM
ejpam-1173	104	8	j+	j+	NUM
ejpam-1173	104	9	ak	ak	PROPN
ejpam-1173	104	10	.	.	PROPN
ejpam-1173	105	1	then	then	ADV
ejpam-1173	105	2	,	,	PUNCT
ejpam-1173	105	3	we	we	PRON
ejpam-1173	105	4	find	find	VERB
ejpam-1173	105	5	the	the	DET
ejpam-1173	105	6	following	follow	VERB
ejpam-1173	105	7	real	real	ADJ
ejpam-1173	105	8	matrix	matrix	NOUN
ejpam-1173	105	9	representation	representation	NOUN
ejpam-1173	105	10	lq	lq	VERB
ejpam-1173	105	11	=	=	NOUN
ejpam-1173	105	12			PROPN
ejpam-1173	105	13			NOUN
ejpam-1173	105	14			NOUN
ejpam-1173	105	15			NOUN
ejpam-1173	105	16			NOUN
ejpam-1173	105	17	a	a	DET
ejpam-1173	105	18	0	0	NUM
ejpam-1173	105	19	0	0	NUM
ejpam-1173	105	20	0	0	NUM
ejpam-1173	105	21	b	b	X
ejpam-1173	105	22	a	a	DET
ejpam-1173	105	23	0	0	NUM
ejpam-1173	105	24	0	0	NUM
ejpam-1173	105	25	c	c	NOUN
ejpam-1173	105	26	0	0	NUM
ejpam-1173	106	1	a	a	DET
ejpam-1173	106	2	0	0	NUM
ejpam-1173	106	3	d	d	NOUN
ejpam-1173	106	4	0	0	NUM
ejpam-1173	106	5	0	0	NUM
ejpam-1173	107	1	a	a	DET
ejpam-1173	107	2			NOUN
ejpam-1173	107	3			NOUN
ejpam-1173	107	4			VERB
ejpam-1173	107	5			NOUN
ejpam-1173	107	6			PUNCT
ejpam-1173	107	7	.	.	PUNCT
ejpam-1173	108	1	it	it	PRON
ejpam-1173	108	2	is	be	AUX
ejpam-1173	108	3	interesting	interesting	ADJ
ejpam-1173	108	4	to	to	PART
ejpam-1173	108	5	note	note	VERB
ejpam-1173	108	6	that	that	SCONJ
ejpam-1173	108	7	p	p	PROPN
ejpam-1173	108	8	det	det	PROPN
ejpam-1173	108	9	lq	lq	PROPN
ejpam-1173	108	10	=	=	PROPN
ejpam-1173	108	11	a2	a2	PROPN
ejpam-1173	108	12	=	=	SYM
ejpam-1173	108	13	||q||2	||q||2	PROPN
ejpam-1173	108	14	.	.	PUNCT
ejpam-1173	109	1	references	reference	VERB
ejpam-1173	109	2	146	146	NUM
ejpam-1173	109	3	references	reference	NOUN
ejpam-1173	109	4	[	[	X
ejpam-1173	109	5	1	1	NUM
ejpam-1173	109	6	]	]	X
ejpam-1173	109	7	b.	b.	PROPN
ejpam-1173	109	8	artmann	artmann	PROPN
ejpam-1173	109	9	.	.	PUNCT
ejpam-1173	110	1	the	the	DET
ejpam-1173	110	2	concept	concept	NOUN
ejpam-1173	110	3	of	of	ADP
ejpam-1173	110	4	number	number	NOUN
ejpam-1173	110	5	:	:	PUNCT
ejpam-1173	110	6	from	from	ADP
ejpam-1173	110	7	quaternions	quaternion	NOUN
ejpam-1173	110	8	to	to	ADP
ejpam-1173	110	9	modads	modad	NOUN
ejpam-1173	110	10	and	and	CCONJ
ejpam-1173	110	11	topological	topological	ADJ
ejpam-1173	110	12	fields	field	NOUN
ejpam-1173	110	13	,	,	PUNCT
ejpam-1173	110	14	ellis	ellis	PROPN
ejpam-1173	110	15	horwood	horwood	PROPN
ejpam-1173	110	16	,	,	PUNCT
ejpam-1173	110	17	chicherster	chicherster	NOUN
ejpam-1173	110	18	,	,	PUNCT
ejpam-1173	110	19	1988	1988	NUM
ejpam-1173	110	20	.	.	PUNCT
ejpam-1173	111	1	[	[	X
ejpam-1173	111	2	2	2	X
ejpam-1173	111	3	]	]	PUNCT
ejpam-1173	111	4	p.	p.	NOUN
ejpam-1173	111	5	p.	p.	NOUN
ejpam-1173	111	6	boas	boas	NOUN
ejpam-1173	111	7	.	.	PUNCT
ejpam-1173	112	1	invitation	invitation	NOUN
ejpam-1173	112	2	to	to	ADP
ejpam-1173	112	3	complex	complex	ADJ
ejpam-1173	112	4	analysis	analysis	NOUN
ejpam-1173	112	5	,	,	PUNCT
ejpam-1173	112	6	random	random	ADJ
ejpam-1173	112	7	house	house	NOUN
ejpam-1173	112	8	,	,	PUNCT
ejpam-1173	112	9	new	new	PROPN
ejpam-1173	112	10	york	york	PROPN
ejpam-1173	112	11	,	,	PUNCT
ejpam-1173	112	12	1987	1987	NUM
ejpam-1173	112	13	.	.	PUNCT
ejpam-1173	113	1	[	[	X
ejpam-1173	113	2	3	3	X
ejpam-1173	113	3	]	]	X
ejpam-1173	113	4	e.	e.	PROPN
ejpam-1173	113	5	cho	cho	PROPN
ejpam-1173	113	6	.	.	PUNCT
ejpam-1173	114	1	de	de	PROPN
ejpam-1173	114	2	moivre	moivre	NOUN
ejpam-1173	114	3	’s	’s	PART
ejpam-1173	114	4	formula	formula	NOUN
ejpam-1173	114	5	for	for	ADP
ejpam-1173	114	6	quaternions	quaternion	NOUN
ejpam-1173	114	7	.	.	PUNCT
ejpam-1173	115	1	appl	appl	PROPN
ejpam-1173	115	2	.	.	PROPN
ejpam-1173	115	3	math	math	PROPN
ejpam-1173	115	4	.	.	PUNCT
ejpam-1173	116	1	lett	lett	PROPN
ejpam-1173	116	2	.	.	PROPN
ejpam-1173	116	3	,	,	PUNCT
ejpam-1173	116	4	11.6	11.6	NUM
ejpam-1173	116	5	:	:	SYM
ejpam-1173	116	6	33	33	NUM
ejpam-1173	116	7	-	-	SYM
ejpam-1173	116	8	35	35	NUM
ejpam-1173	116	9	.	.	PUNCT
ejpam-1173	116	10	1998	1998	NUM
ejpam-1173	116	11	.	.	PUNCT
ejpam-1173	117	1	[	[	X
ejpam-1173	117	2	4	4	X
ejpam-1173	117	3	]	]	PUNCT
ejpam-1173	117	4	w.	w.	PROPN
ejpam-1173	117	5	k.	k.	PROPN
ejpam-1173	117	6	clifford	clifford	PROPN
ejpam-1173	117	7	.	.	PUNCT
ejpam-1173	118	1	preliminary	preliminary	ADJ
ejpam-1173	118	2	sketch	sketch	NOUN
ejpam-1173	118	3	of	of	ADP
ejpam-1173	118	4	bi	bi	NOUN
ejpam-1173	118	5	-	-	NOUN
ejpam-1173	118	6	quaternions	quaternion	NOUN
ejpam-1173	118	7	.	.	PUNCT
ejpam-1173	119	1	proc	proc	NOUN
ejpam-1173	119	2	.	.	PUNCT
ejpam-1173	120	1	london	london	PROPN
ejpam-1173	120	2	math	math	PROPN
ejpam-1173	120	3	.	.	PUNCT
ejpam-1173	121	1	soc	soc	PROPN
ejpam-1173	121	2	.	.	PUNCT
ejpam-1173	122	1	4	4	NUM
ejpam-1173	122	2	.	.	X
ejpam-1173	122	3	381	381	NUM
ejpam-1173	122	4	-	-	SYM
ejpam-1173	122	5	395	395	NUM
ejpam-1173	122	6	.	.	PUNCT
ejpam-1173	122	7	1873	1873	NUM
ejpam-1173	122	8	.	.	PUNCT
ejpam-1173	123	1	[	[	X
ejpam-1173	123	2	5	5	X
ejpam-1173	123	3	]	]	PUNCT
ejpam-1173	123	4	g.	g.	PROPN
ejpam-1173	123	5	helzer	helzer	PROPN
ejpam-1173	123	6	.	.	PUNCT
ejpam-1173	124	1	special	special	ADJ
ejpam-1173	124	2	relativity	relativity	NOUN
ejpam-1173	124	3	with	with	ADP
ejpam-1173	124	4	acceleration	acceleration	NOUN
ejpam-1173	124	5	.	.	PUNCT
ejpam-1173	125	1	amer	amer	PROPN
ejpam-1173	125	2	.	.	PUNCT
ejpam-1173	125	3	math	math	PROPN
ejpam-1173	125	4	.	.	PUNCT
ejpam-1173	126	1	monthy	monthy	ADJ
ejpam-1173	126	2	,	,	PUNCT
ejpam-1173	126	3	107.3	107.3	NUM
ejpam-1173	126	4	:	:	PUNCT
ejpam-1173	126	5	215	215	NUM
ejpam-1173	126	6	-	-	SYM
ejpam-1173	126	7	237	237	NUM
ejpam-1173	126	8	.	.	PUNCT
ejpam-1173	127	1	2000	2000	NUM
ejpam-1173	127	2	.	.	PUNCT
ejpam-1173	128	1	[	[	X
ejpam-1173	128	2	6	6	NUM
ejpam-1173	128	3	]	]	PUNCT
ejpam-1173	128	4	v.	v.	X
ejpam-1173	128	5	majernik	majernik	VERB
ejpam-1173	128	6	.	.	PUNCT
ejpam-1173	129	1	quaternion	quaternion	ADJ
ejpam-1173	129	2	formulation	formulation	NOUN
ejpam-1173	129	3	of	of	ADP
ejpam-1173	129	4	the	the	DET
ejpam-1173	129	5	galilean	galilean	PROPN
ejpam-1173	129	6	space	space	NOUN
ejpam-1173	129	7	-	-	PUNCT
ejpam-1173	129	8	time	time	NOUN
ejpam-1173	129	9	transformation	transformation	NOUN
ejpam-1173	129	10	.	.	PUNCT
ejpam-1173	130	1	acta	acta	PROPN
ejpam-1173	130	2	phy	phy	PROPN
ejpam-1173	130	3	.	.	PUNCT
ejpam-1173	131	1	slovaca	slovaca	PROPN
ejpam-1173	131	2	,	,	PUNCT
ejpam-1173	131	3	56.1	56.1	NUM
ejpam-1173	131	4	:	:	SYM
ejpam-1173	131	5	9	9	NUM
ejpam-1173	131	6	-	-	SYM
ejpam-1173	131	7	14	14	NUM
ejpam-1173	131	8	.	.	PUNCT
ejpam-1173	132	1	2006	2006	NUM
ejpam-1173	132	2	.	.	PUNCT
ejpam-1173	133	1	[	[	X
ejpam-1173	133	2	7	7	X
ejpam-1173	133	3	]	]	X
ejpam-1173	133	4	e.	e.	PROPN
ejpam-1173	133	5	pennestrì	pennestrì	PROPN
ejpam-1173	133	6	and	and	CCONJ
ejpam-1173	133	7	r.	r.	PROPN
ejpam-1173	133	8	stefanelli	stefanelli	PROPN
ejpam-1173	133	9	.	.	PUNCT
ejpam-1173	134	1	linear	linear	PROPN
ejpam-1173	134	2	algebra	algebra	PROPN
ejpam-1173	134	3	and	and	CCONJ
ejpam-1173	134	4	numerical	numerical	ADJ
ejpam-1173	134	5	algorithms	algorithm	NOUN
ejpam-1173	134	6	using	use	VERB
ejpam-1173	134	7	dual	dual	ADJ
ejpam-1173	134	8	numbers	number	NOUN
ejpam-1173	134	9	.	.	PUNCT
ejpam-1173	135	1	multibody	multibody	ADJ
ejpam-1173	135	2	syst	syst	PROPN
ejpam-1173	135	3	.	.	PUNCT
ejpam-1173	136	1	dyn	dyn	PROPN
ejpam-1173	136	2	.	.	PUNCT
ejpam-1173	137	1	18.3	18.3	NUM
ejpam-1173	137	2	:	:	PUNCT
ejpam-1173	137	3	323	323	NUM
ejpam-1173	137	4	-	-	SYM
ejpam-1173	137	5	344	344	NUM
ejpam-1173	137	6	.	.	PUNCT
ejpam-1173	137	7	2007	2007	NUM
ejpam-1173	137	8	.	.	PUNCT
ejpam-1173	138	1	[	[	X
ejpam-1173	138	2	8	8	NUM
ejpam-1173	138	3	]	]	X
ejpam-1173	138	4	e.	e.	PROPN
ejpam-1173	138	5	study	study	PROPN
ejpam-1173	138	6	.	.	PUNCT
ejpam-1173	139	1	geometrie	geometrie	PROPN
ejpam-1173	139	2	der	der	PROPN
ejpam-1173	139	3	dynamen	dynamen	PROPN
ejpam-1173	139	4	,	,	PUNCT
ejpam-1173	139	5	leipzig	leipzig	PROPN
ejpam-1173	139	6	,	,	PUNCT
ejpam-1173	139	7	germany	germany	PROPN
ejpam-1173	139	8	,	,	PUNCT
ejpam-1173	139	9	1903	1903	NUM
ejpam-1173	139	10	.	.	PUNCT
ejpam-1173	140	1	[	[	X
ejpam-1173	140	2	9	9	NUM
ejpam-1173	140	3	]	]	PUNCT
ejpam-1173	140	4	i.	i.	NOUN
ejpam-1173	140	5	m.	m.	PROPN
ejpam-1173	140	6	yaglom	yaglom	PROPN
ejpam-1173	140	7	.	.	PUNCT
ejpam-1173	141	1	complex	complex	ADJ
ejpam-1173	141	2	numbers	number	NOUN
ejpam-1173	141	3	in	in	ADP
ejpam-1173	141	4	geometry	geometry	NOUN
ejpam-1173	141	5	,	,	PUNCT
ejpam-1173	141	6	new	new	PROPN
ejpam-1173	141	7	york	york	PROPN
ejpam-1173	141	8	,	,	PUNCT
ejpam-1173	141	9	academic	academic	NOUN
ejpam-1173	141	10	,	,	PUNCT
ejpam-1173	141	11	1968	1968	NUM
ejpam-1173	141	12	.	.	PUNCT