id	sid	eid	entity	type
ejpam-3074	1	1	european journal	ORG
ejpam-3074	2	1	10	CARDINAL
ejpam-3074	2	2	4	CARDINAL
ejpam-3074	2	3	2017	DATE
ejpam-3074	2	4	602	CARDINAL
ejpam-3074	2	5	new york	GPE
ejpam-3074	2	6	thomas l. saaty1	PERSON
ejpam-3074	2	7	luis g. vargas1,∗	PERSON
ejpam-3074	2	8	1	CARDINAL
ejpam-3074	2	9	joseph m. katz	PERSON
ejpam-3074	2	10	university of pittsburgh	ORG
ejpam-3074	5	1	bohr	PERSON
ejpam-3074	9	1	g2-manifolds	ORG
ejpam-3074	10	1	2010	DATE
ejpam-3074	10	2	16w20	CARDINAL
ejpam-3074	10	3	20g20	DATE
ejpam-3074	12	1	the past century or so	DATE
ejpam-3074	14	1	t. l. saaty	PERSON
ejpam-3074	15	1	l. g. vargas	PERSON
ejpam-3074	16	1	602	CARDINAL
ejpam-3074	17	1	2017	CARDINAL
ejpam-3074	18	1	t. l. saaty	PERSON
ejpam-3074	18	2	l. g. vargas	PERSON
ejpam-3074	19	1	j. pure	PERSON
ejpam-3074	19	2	10	CARDINAL
ejpam-3074	19	3	4	CARDINAL
ejpam-3074	19	4	2017	CARDINAL
ejpam-3074	19	5	602	CARDINAL
ejpam-3074	19	6	613 603	CARDINAL
ejpam-3074	22	1	arthur schopenhauer	PERSON
ejpam-3074	27	1	13	CARDINAL
ejpam-3074	27	2	14	CARDINAL
ejpam-3074	32	1	9	CARDINAL
ejpam-3074	42	1	ten	CARDINAL
ejpam-3074	42	2	eleventh	ORDINAL
ejpam-3074	42	3	approximately 3.5	CARDINAL
ejpam-3074	47	1	t. l. saaty	PERSON
ejpam-3074	47	2	l. g. vargas	PERSON
ejpam-3074	48	1	j. pure	PERSON
ejpam-3074	48	2	10	CARDINAL
ejpam-3074	48	3	4	CARDINAL
ejpam-3074	48	4	2017	CARDINAL
ejpam-3074	48	5	602	CARDINAL
ejpam-3074	51	1	adolf hurwitz	PERSON
ejpam-3074	52	1	8	CARDINAL
ejpam-3074	52	2	four	CARDINAL
ejpam-3074	52	3	normed	ORG
ejpam-3074	53	1	john t. graves	PERSON
ejpam-3074	53	2	1844	DATE
ejpam-3074	54	1	john graves	PERSON
ejpam-3074	54	2	arthur cayley	PERSON
ejpam-3074	54	3	1845	DATE
ejpam-3074	54	4	4	CARDINAL
ejpam-3074	56	1	2	CARDINAL
ejpam-3074	56	2	11	CARDINAL
ejpam-3074	57	1	conway	GPE
ejpam-3074	58	1	5	CARDINAL
ejpam-3074	58	2	octonions	CARDINAL
ejpam-3074	59	1	four	CARDINAL
ejpam-3074	60	1	2n	CARDINAL
ejpam-3074	60	2	3	CARDINAL
ejpam-3074	60	3	0	CARDINAL
ejpam-3074	61	1	mark robert waldman	PERSON
ejpam-3074	61	2	eight	CARDINAL
ejpam-3074	61	3	three	CARDINAL
ejpam-3074	61	4	seven	CARDINAL
ejpam-3074	61	5	plato nuomena	PERSON
ejpam-3074	62	1	waldmans	GPE
ejpam-3074	62	2	more than 31,000	CARDINAL
ejpam-3074	63	1	first	ORDINAL
ejpam-3074	63	2	four	CARDINAL
ejpam-3074	64	1	6	CARDINAL
ejpam-3074	67	1	6	CARDINAL
ejpam-3074	69	1	eight	CARDINAL
ejpam-3074	70	1	octonions	ORG
ejpam-3074	70	2	7	CARDINAL
ejpam-3074	70	3	t. l. saaty	PERSON
ejpam-3074	70	4	l. g. vargas	PERSON
ejpam-3074	71	1	j. pure	PERSON
ejpam-3074	71	2	10	CARDINAL
ejpam-3074	71	3	4	CARDINAL
ejpam-3074	71	4	2017	CARDINAL
ejpam-3074	71	5	602	CARDINAL
ejpam-3074	73	1	automorphisms	ORG
ejpam-3074	78	1	three	CARDINAL
ejpam-3074	78	2	octonions	CARDINAL
ejpam-3074	85	1	2	CARDINAL
ejpam-3074	86	1	two	CARDINAL
ejpam-3074	86	2	one	CARDINAL
ejpam-3074	86	3	five	CARDINAL
ejpam-3074	86	4	one	CARDINAL
ejpam-3074	86	5	fifth	ORDINAL
ejpam-3074	86	6	first	ORDINAL
ejpam-3074	87	1	one	CARDINAL
ejpam-3074	92	1	five	CARDINAL
ejpam-3074	92	2	three	CARDINAL
ejpam-3074	92	3	fifteen	CARDINAL
ejpam-3074	95	1	aij ajk	PRODUCT
ejpam-3074	95	2	t. l. saaty	PERSON
ejpam-3074	95	3	l. g. vargas	PERSON
ejpam-3074	96	1	j. pure	PERSON
ejpam-3074	96	2	10	CARDINAL
ejpam-3074	96	3	4	CARDINAL
ejpam-3074	96	4	2017	CARDINAL
ejpam-3074	96	5	602	CARDINAL
ejpam-3074	96	6	1	CARDINAL
ejpam-3074	96	7	2	DATE
ejpam-3074	99	1	1	CARDINAL
ejpam-3074	100	1	2	CARDINAL
ejpam-3074	101	1	= nw.	PERSON
ejpam-3074	101	2	1	CARDINAL
ejpam-3074	101	3	2	CARDINAL
ejpam-3074	102	1	w1 wn	PERSON
ejpam-3074	104	1	w1 wn	PERSON
ejpam-3074	106	1		ORG
ejpam-3074	110	1	a− ni vanishes	FAC
ejpam-3074	110	2	w	ORG
ejpam-3074	111	1	w	ORG
ejpam-3074	112	1	wi/wj	ORG
ejpam-3074	114	1	1	CARDINAL
ejpam-3074	114	2	2	CARDINAL
ejpam-3074	114	3	3	CARDINAL
ejpam-3074	114	4	3	CARDINAL
ejpam-3074	114	5	a′	ORG
ejpam-3074	114	6	1 a12	DATE
ejpam-3074	115	1	1/a12 1 ·	DATE
ejpam-3074	115	2	a2n	PERSON
ejpam-3074	116	1	1/a1n 1	CARDINAL
ejpam-3074	116	2	1	CARDINAL
ejpam-3074	116	3	4	CARDINAL
ejpam-3074	116	4	1 a12	DATE
ejpam-3074	117	1	1/a12 1 ·	DATE
ejpam-3074	117	2	a2n	PERSON
ejpam-3074	118	1	1/a1n 1	CARDINAL
ejpam-3074	118	2	1	CARDINAL
ejpam-3074	120	1	t. l. saaty	PERSON
ejpam-3074	120	2	l. g. vargas	PERSON
ejpam-3074	121	1	j. pure	PERSON
ejpam-3074	121	2	10	CARDINAL
ejpam-3074	121	3	4	CARDINAL
ejpam-3074	121	4	2017	CARDINAL
ejpam-3074	121	5	602	CARDINAL
ejpam-3074	123	1	second	ORDINAL
ejpam-3074	126	1	k(s	GPE
ejpam-3074	126	2	k(s	GPE
ejpam-3074	126	3	w(s)ds	EVENT
ejpam-3074	126	4	1	CARDINAL
ejpam-3074	126	5	k(s	PERSON
ejpam-3074	126	6	0	CARDINAL
ejpam-3074	126	7	w	PERSON
ejpam-3074	127	1	two	CARDINAL
ejpam-3074	128	1	two	CARDINAL
ejpam-3074	130	1	first	ORDINAL
ejpam-3074	132	1	w(s)ds	EVENT
ejpam-3074	132	2	1	CARDINAL
ejpam-3074	133	1	k(s	PERSON
ejpam-3074	133	2	1	CARDINAL
ejpam-3074	133	3	2	CARDINAL
ejpam-3074	133	4	k(s	PERSON
ejpam-3074	133	5	1	CARDINAL
ejpam-3074	133	6	w(t	PERSON
ejpam-3074	135	1	w(t	PERSON
ejpam-3074	136	1	w(t	PERSON
ejpam-3074	139	1	3.1	CARDINAL
ejpam-3074	141	1	0	CARDINAL
ejpam-3074	142	1	tn−1	PERSON
ejpam-3074	142	2	0	CARDINAL
ejpam-3074	142	3	1	CARDINAL
ejpam-3074	142	4	2	DATE
ejpam-3074	142	5	w(t	PERSON
ejpam-3074	143	1	0	CARDINAL
ejpam-3074	143	2	t. l. saaty	PERSON
ejpam-3074	143	3	l. g. vargas	PERSON
ejpam-3074	144	1	j. pure	PERSON
ejpam-3074	144	2	10	CARDINAL
ejpam-3074	144	3	4	CARDINAL
ejpam-3074	144	4	2017	CARDINAL
ejpam-3074	144	5	602	CARDINAL
ejpam-3074	145	1	g(t	NORP
ejpam-3074	146	1	0	CARDINAL
ejpam-3074	148	1	g(t	PERSON
ejpam-3074	148	2	w(t	PERSON
ejpam-3074	151	1	1	CARDINAL
ejpam-3074	152	1	1	CARDINAL
ejpam-3074	152	2	2	DATE
ejpam-3074	152	3	1	CARDINAL
ejpam-3074	152	4	g(t	PERSON
ejpam-3074	152	5	c1(0	PRODUCT
ejpam-3074	152	6	∆tk	GPE
ejpam-3074	152	7	k(ii	GPE
ejpam-3074	152	8	ij)→ k(s	PERSON
ejpam-3074	152	9	w(t	PERSON
ejpam-3074	152	10	0	CARDINAL
ejpam-3074	153	1	1	CARDINAL
ejpam-3074	153	2	∆tk	GPE
ejpam-3074	153	3	0	DATE
ejpam-3074	153	4	n→∞	CARDINAL
ejpam-3074	153	5	1	CARDINAL
ejpam-3074	153	6	k(s	PERSON
ejpam-3074	154	1	k(s	PERSON
ejpam-3074	154	2	w(s	PERSON
ejpam-3074	155	1	ω k(s	PERSON
ejpam-3074	155	2	t)w(t)dt	GPE
ejpam-3074	156	1	2	CARDINAL
ejpam-3074	156	2	w(s	PERSON
ejpam-3074	157	1	k(s	PERSON
ejpam-3074	157	2	k(s	GPE
ejpam-3074	157	3	w(s	PERSON
ejpam-3074	159	1	saaty	PERSON
ejpam-3074	159	2	12	CARDINAL
ejpam-3074	159	3	second	ORDINAL
ejpam-3074	159	4	2	CARDINAL
ejpam-3074	159	5	3	CARDINAL
ejpam-3074	159	6	t. l. saaty	PERSON
ejpam-3074	159	7	l. g. vargas	PERSON
ejpam-3074	160	1	j. pure	PERSON
ejpam-3074	160	2	10	CARDINAL
ejpam-3074	160	3	4	CARDINAL
ejpam-3074	160	4	2017	CARDINAL
ejpam-3074	160	5	602	CARDINAL
ejpam-3074	161	1	12	CARDINAL
ejpam-3074	162	1	113-121	CARDINAL
ejpam-3074	162	2	3	CARDINAL
ejpam-3074	163	1	normed	ORG
ejpam-3074	163	2	algebras	ORG
ejpam-3074	166	1	hurwitz	PERSON
ejpam-3074	167	1	8	CARDINAL
ejpam-3074	168	1	r.	NORP
ejpam-3074	169	1	⊕ ir	PERSON
ejpam-3074	170	1	1	CARDINAL
ejpam-3074	170	2	⊕ jc	PERSON
ejpam-3074	171	1	1	CARDINAL
ejpam-3074	173	1	two	CARDINAL
ejpam-3074	174	1	octonions	DATE
ejpam-3074	174	2	three	CARDINAL
ejpam-3074	175	1	4	CARDINAL
ejpam-3074	175	2	1	CARDINAL
ejpam-3074	176	1	o	DATE
ejpam-3074	183	1	w̃g(u)⊕ w̃d(u	PERSON
ejpam-3074	183	2	5	CARDINAL
ejpam-3074	184	1	5	CARDINAL
ejpam-3074	186	1	6=	CARDINAL
ejpam-3074	186	2	∩	PERSON
ejpam-3074	187	1	the octonions g2	ORG
ejpam-3074	188	1	automorphisms	ORG
ejpam-3074	192	1	1	CARDINAL
ejpam-3074	193	1	1	CARDINAL
ejpam-3074	198	1	t. l. saaty	PERSON
ejpam-3074	198	2	l. g. vargas	PERSON
ejpam-3074	199	1	j. pure	PERSON
ejpam-3074	199	2	10	CARDINAL
ejpam-3074	199	3	4	CARDINAL
ejpam-3074	199	4	2017	CARDINAL
ejpam-3074	199	5	602	CARDINAL
ejpam-3074	205	1	3	CARDINAL
ejpam-3074	207	1	6	CARDINAL
ejpam-3074	210	1	1	CARDINAL
ejpam-3074	210	2	1u	CARDINAL
ejpam-3074	212	1	1	CARDINAL
ejpam-3074	216	1	9	CARDINAL
ejpam-3074	216	2	octonions	CARDINAL
ejpam-3074	216	3	π/3	NORP
ejpam-3074	216	4	sixth	ORDINAL
ejpam-3074	216	5	3	CARDINAL
ejpam-3074	216	6	5	CARDINAL
ejpam-3074	217	1	2nπ +	DATE
ejpam-3074	218	1	3	CARDINAL
ejpam-3074	218	2	3	CARDINAL
ejpam-3074	219	1	5	CARDINAL
ejpam-3074	222	1	3	CARDINAL
ejpam-3074	223	1	7	CARDINAL
ejpam-3074	223	2	normed	ORG
ejpam-3074	224	1	t. l. saaty	PERSON
ejpam-3074	224	2	l. g. vargas	PERSON
ejpam-3074	225	1	j. pure	PERSON
ejpam-3074	225	2	10	CARDINAL
ejpam-3074	225	3	4	CARDINAL
ejpam-3074	225	4	2017	CARDINAL
ejpam-3074	225	5	602	CARDINAL
ejpam-3074	225	6	1	CARDINAL
ejpam-3074	225	7	1	CARDINAL
ejpam-3074	225	8	0.1	CARDINAL
ejpam-3074	225	9	1	CARDINAL
ejpam-3074	225	10	7	CARDINAL
ejpam-3074	225	11	xq	ORG
ejpam-3074	226	1	1 xn2 2	QUANTITY
ejpam-3074	226	2	jn	ORG
ejpam-3074	226	3	6	CARDINAL
ejpam-3074	227	1	6	CARDINAL
ejpam-3074	228	1	the octonions g2	ORG
ejpam-3074	228	2	xq	ORG
ejpam-3074	229	1	w̃i(u)εxi	PERSON
ejpam-3074	229	2	1	CARDINAL
ejpam-3074	229	3	2	DATE
ejpam-3074	229	4	w	GPE
ejpam-3074	229	5	9	CARDINAL
ejpam-3074	230	1	9	CARDINAL
ejpam-3074	230	2	o	DATE
ejpam-3074	230	3	martinez et al	PERSON
ejpam-3074	231	1	10	CARDINAL
ejpam-3074	232	1	1	CARDINAL
ejpam-3074	232	2	p̃	ORG
ejpam-3074	232	3	+ 1 7	DATE
ejpam-3074	232	4	7∑ k=1	PRODUCT
ejpam-3074	232	5	1 2 +1/2∫	CARDINAL
ejpam-3074	233	1	1	CARDINAL
ejpam-3074	233	2	o	DATE
ejpam-3074	235	1	2	CARDINAL
ejpam-3074	236	1	∈	ORG
ejpam-3074	237	1	3	CARDINAL
ejpam-3074	238	1	∈	ORG
ejpam-3074	238	2	t. l. saaty	PERSON
ejpam-3074	238	3	l. g. vargas	PERSON
ejpam-3074	239	1	j. pure	PERSON
ejpam-3074	239	2	10	CARDINAL
ejpam-3074	239	3	4	CARDINAL
ejpam-3074	239	4	2017	CARDINAL
ejpam-3074	239	5	602	CARDINAL
ejpam-3074	240	1	octonions	CARDINAL
ejpam-3074	243	1	b. s. acharya	PERSON
ejpam-3074	243	2	1	CARDINAL
ejpam-3074	244	1	1	CARDINAL
ejpam-3074	244	2	maxwell	ORG
ejpam-3074	244	3	2	CARDINAL
ejpam-3074	244	4	3	CARDINAL
ejpam-3074	244	5	4	CARDINAL
ejpam-3074	244	6	5	CARDINAL
ejpam-3074	245	1	2	CARDINAL
ejpam-3074	246	1	five	CARDINAL
ejpam-3074	247	1	five	CARDINAL
ejpam-3074	247	2	ten	CARDINAL
ejpam-3074	247	3	three	CARDINAL
ejpam-3074	247	4	six	CARDINAL
ejpam-3074	248	1	eleven	CARDINAL
ejpam-3074	250	1	g2	PERSON
ejpam-3074	252	1	seven	CARDINAL
ejpam-3074	252	2	one	CARDINAL
ejpam-3074	252	3	five	CARDINAL
ejpam-3074	255	1	613	CARDINAL
ejpam-3074	255	2	1	CARDINAL
ejpam-3074	255	3	acharya	PERSON
ejpam-3074	255	4	2014	DATE
ejpam-3074	256	1	october 7, 2014	DATE
ejpam-3074	256	2	kings college	ORG
ejpam-3074	256	3	london	GPE
ejpam-3074	257	1	2	CARDINAL
ejpam-3074	257	2	j.c.	PERSON
ejpam-3074	257	3	2001	DATE
ejpam-3074	258	1	octonions	EVENT
ejpam-3074	258	2	american	NORP
ejpam-3074	258	3	39	CARDINAL
ejpam-3074	258	4	2,145	CARDINAL
ejpam-3074	259	1	3	CARDINAL
ejpam-3074	259	2	1999	DATE
ejpam-3074	260	1	normed linear spaces	ORG
ejpam-3074	260	2	ecole centrale de nantes	ORG
ejpam-3074	261	1	03	CARDINAL
ejpam-3074	261	2	france	GPE
ejpam-3074	261	3	october	DATE
ejpam-3074	262	1	4	CARDINAL
ejpam-3074	262	2	a.	PERSON
ejpam-3074	262	3	1963	DATE
ejpam-3074	263	1	jacobi	PERSON
ejpam-3074	263	2	b. bronwin	PERSON
ejpam-3074	263	3	quaternions(appendix	PERSON
ejpam-3074	263	4	johnson reprint co.	ORG
ejpam-3074	263	5	newyork	ORG
ejpam-3074	263	6	127	CARDINAL
ejpam-3074	264	1	5	CARDINAL
ejpam-3074	264	2	conway j.h.	PERSON
ejpam-3074	264	3	d.a. smith	PERSON
ejpam-3074	264	4	2003	DATE
ejpam-3074	265	1	octonions	GPE
ejpam-3074	265	2	a.k. peters	ORG
ejpam-3074	265	3	natick	GPE
ejpam-3074	265	4	ma	GPE
ejpam-3074	266	1	6	CARDINAL
ejpam-3074	266	2	1996	DATE
ejpam-3074	267	1	hamilton	PERSON
ejpam-3074	267	2	w.r.	GPE
ejpam-3074	267	3	1967	DATE
ejpam-3074	268	1	four	CARDINAL
ejpam-3074	268	2	3	CARDINAL
ejpam-3074	268	3	william rowan hamilton	PERSON
ejpam-3074	269	1	3	CARDINAL
ejpam-3074	270	1	h. halberstam	PERSON
ejpam-3074	270	2	r. e. ingram	PERSON
ejpam-3074	270	3	cambridge university press	ORG
ejpam-3074	270	4	cambridge	GPE
ejpam-3074	270	5	648-656	CARDINAL
ejpam-3074	271	1	8	CARDINAL
ejpam-3074	271	2	hurwitz, a. (1898	ORG
ejpam-3074	272	1	formen von beliebig vielen variabeln	PERSON
ejpam-3074	273	1	ges	ORG
ejpam-3074	273	2	wiss	PERSON
ejpam-3074	274	1	309	CARDINAL
ejpam-3074	275	1	9	CARDINAL
ejpam-3074	275	2	c.a.	GPE
ejpam-3074	275	3	j. schray	PERSON
ejpam-3074	275	4	1993	DATE
ejpam-3074	276	1	lorentz transformations	PERSON
ejpam-3074	276	2	automorphisms	ORG
ejpam-3074	276	3	j. math	PERSON
ejpam-3074	277	1	3746-3767	CARDINAL
ejpam-3074	278	1	10	CARDINAL
ejpam-3074	278	2	c.a.p.	GPE
ejpam-3074	279	1	martinez	PERSON
ejpam-3074	279	2	m.f. borges	PERSON
ejpam-3074	279	3	castelani	PERSON
ejpam-3074	279	4	2013	DATE
ejpam-3074	280	1	hypercomplex	FAC
ejpam-3074	280	2	tendencias	PERSON
ejpam-3074	280	3	matematica aplicada e computacional	ORG
ejpam-3074	280	4	14, 3	DATE
ejpam-3074	280	5	483	CARDINAL
ejpam-3074	281	1	11	CARDINAL
ejpam-3074	281	2	j.p.	GPE
ejpam-3074	281	3	s. georgiev	PERSON
ejpam-3074	281	4	w. spröβig	PERSON
ejpam-3074	281	5	2014	DATE
ejpam-3074	283	1	12	CARDINAL
ejpam-3074	283	2	2015	CARDINAL
ejpam-3074	284	1	anp	PRODUCT
ejpam-3074	285	1	13	CARDINAL
ejpam-3074	286	1	86	CARDINAL
ejpam-3074	286	2	102-114	CARDINAL
ejpam-3074	287	1	14	CARDINAL
ejpam-3074	287	2	2017b	CARDINAL
ejpam-3074	288	1	86	CARDINAL
ejpam-3074	288	2	115	CARDINAL
ejpam-3074	289	1	15	CARDINAL
ejpam-3074	289	2	waldman	ORG
ejpam-3074	289	3	m.r.	GPE
ejpam-3074	289	4	2014	DATE
ejpam-3074	290	1	101	CARDINAL
ejpam-3074	292	1	robert waldman	PERSON