id	sid	eid	entity	type
ejpam-6041	1	1	european journal	ORG
ejpam-6041	1	2	2025	DATE
ejpam-6041	1	3	18	CARDINAL
ejpam-6041	1	4	2	CARDINAL
ejpam-6041	1	5	1307-5543	DATE
ejpam-6041	1	6	new york	GPE
ejpam-6041	1	7	maungchang1	DATE
ejpam-6041	1	8	atiponrat2	ORG
ejpam-6041	1	9	suwansri1	GPE
ejpam-6041	2	1	teerapong	PERSON
ejpam-6041	2	2	1	CARDINAL
ejpam-6041	2	3	nakhon si thammarat	ORG
ejpam-6041	2	4	80160	DATE
ejpam-6041	2	5	thailand 2	ORG
ejpam-6041	2	6	chiang mai university	ORG
ejpam-6041	2	7	mai 50200	DATE
ejpam-6041	2	8	thailand 3	ORG
ejpam-6041	2	9	chiang mai university	ORG
ejpam-6041	2	10	mai 50200	DATE
ejpam-6041	2	11	thailand	GPE
ejpam-6041	3	1	1	CARDINAL
ejpam-6041	3	2	1 +	CARDINAL
ejpam-6041	3	3	l(a	PERSON
ejpam-6041	5	1	91	CARDINAL
ejpam-6041	5	2	2017	CARDINAL
ejpam-6041	6	1	491–503	CARDINAL
ejpam-6041	8	1	2020	DATE
ejpam-6041	8	2	39b32	CARDINAL
ejpam-6041	8	3	30d05	CARDINAL
ejpam-6041	8	4	20n05	CARDINAL
ejpam-6041	8	5	1	CARDINAL
ejpam-6041	9	1	1	CARDINAL
ejpam-6041	9	2	2	CARDINAL
ejpam-6041	11	1	multiplicative	NORP
ejpam-6041	14	1	r. maungchang	PERSON
ejpam-6041	14	2	w. atiponrat	PERSON
ejpam-6041	15	1	j. wattanapan	PERSON
ejpam-6041	16	1	1	CARDINAL
ejpam-6041	16	2	2025	CARDINAL
ejpam-6041	17	1	r. maungchang	PERSON
ejpam-6041	18	1	j. pure	PERSON
ejpam-6041	18	2	18	CARDINAL
ejpam-6041	18	3	2	CARDINAL
ejpam-6041	18	4	2025	CARDINAL
ejpam-6041	18	5	6041 2	DATE
ejpam-6041	18	6	8	CARDINAL
ejpam-6041	18	7	1	CARDINAL
ejpam-6041	18	8	1 + ab	CARDINAL
ejpam-6041	18	9	1	CARDINAL
ejpam-6041	18	10	∈	ORG
ejpam-6041	18	11	d.	NORP
ejpam-6041	18	12	d,⊕m	GPE
ejpam-6041	19	1	∈	ORG
ejpam-6041	19	2	3	CARDINAL
ejpam-6041	19	3	schur	ORG
ejpam-6041	19	4	l(a⊕m	ORG
ejpam-6041	19	5	1	CARDINAL
ejpam-6041	19	6	1.3	CARDINAL
ejpam-6041	19	7	3	CARDINAL
ejpam-6041	20	1	one	CARDINAL
ejpam-6041	20	2	section 3.2	LAW
ejpam-6041	20	3	3	CARDINAL
ejpam-6041	21	1	4	CARDINAL
ejpam-6041	22	1	2	CARDINAL
ejpam-6041	22	2	492	CARDINAL
ejpam-6041	22	3	3	CARDINAL
ejpam-6041	22	4	zero	CARDINAL
ejpam-6041	23	1	zero	CARDINAL
ejpam-6041	23	2	l(r	PERSON
ejpam-6041	24	1	∈	ORG
ejpam-6041	24	2	−1	CARDINAL
ejpam-6041	24	3	1	CARDINAL
ejpam-6041	24	4	1.2	CARDINAL
ejpam-6041	24	5	3	CARDINAL
ejpam-6041	25	1	3	CARDINAL
ejpam-6041	26	1	1	CARDINAL
ejpam-6041	28	1	∈	ORG
ejpam-6041	28	2	1	CARDINAL
ejpam-6041	28	3	3	CARDINAL
ejpam-6041	29	1	3	CARDINAL
ejpam-6041	30	1	1	CARDINAL
ejpam-6041	31	1	r. maungchang	PERSON
ejpam-6041	32	1	j. pure	PERSON
ejpam-6041	32	2	18	CARDINAL
ejpam-6041	32	3	2	CARDINAL
ejpam-6041	32	4	2025	CARDINAL
ejpam-6041	32	5	6041 3	DATE
ejpam-6041	33	1	d,⊕m	GPE
ejpam-6041	35	1	∈	ORG
ejpam-6041	35	2	section 2	LAW
ejpam-6041	35	3	l(z	PERSON
ejpam-6041	35	4	∈	ORG
ejpam-6041	35	5	multiplicative	ORG
ejpam-6041	36	1	l(z	PERSON
ejpam-6041	36	2	l(z	PERSON
ejpam-6041	36	3	1	CARDINAL
ejpam-6041	39	1	2	CARDINAL
ejpam-6041	39	2	4	DATE
ejpam-6041	39	3	5	CARDINAL
ejpam-6041	40	1	4	CARDINAL
ejpam-6041	40	2	∈	ORG
ejpam-6041	40	3	2	CARDINAL
ejpam-6041	40	4	⊖ma = −a	PERSON
ejpam-6041	42	1	3	CARDINAL
ejpam-6041	42	2	∈	ORG
ejpam-6041	42	3	d.	NORP
ejpam-6041	44	1	3	CARDINAL
ejpam-6041	45	1	1	CARDINAL
ejpam-6041	47	1	+ ab+	NORP
ejpam-6041	47	2	bc	ORG
ejpam-6041	47	3	1 +	CARDINAL
ejpam-6041	47	4	bc	ORG
ejpam-6041	47	5	4	CARDINAL
ejpam-6041	47	6	∈	ORG
ejpam-6041	47	7	d.	NORP
ejpam-6041	48	1	1	CARDINAL
ejpam-6041	48	2	2	CARDINAL
ejpam-6041	48	3	3	CARDINAL
ejpam-6041	49	1	1	CARDINAL
ejpam-6041	49	2	2	CARDINAL
ejpam-6041	49	3	1	CARDINAL
ejpam-6041	49	4	three	CARDINAL
ejpam-6041	49	5	1	CARDINAL
ejpam-6041	50	1	first	ORDINAL
ejpam-6041	50	2	zero	CARDINAL
ejpam-6041	52	1	2	CARDINAL
ejpam-6041	52	2	∈	ORG
ejpam-6041	54	1	0 or a	CARDINAL
ejpam-6041	54	2	c. r. maungchang	PERSON
ejpam-6041	55	1	j. pure	PERSON
ejpam-6041	55	2	18	CARDINAL
ejpam-6041	55	3	2	CARDINAL
ejpam-6041	55	4	2025	CARDINAL
ejpam-6041	55	5	6041 4	DATE
ejpam-6041	55	6	8	CARDINAL
ejpam-6041	55	7	1	CARDINAL
ejpam-6041	55	8	0	CARDINAL
ejpam-6041	55	9	1	CARDINAL
ejpam-6041	55	10	0.5	CARDINAL
ejpam-6041	57	1	0	CARDINAL
ejpam-6041	58	1	4	CARDINAL
ejpam-6041	60	1	1 + ab	QUANTITY
ejpam-6041	61	1	∈	ORG
ejpam-6041	61	2	1	CARDINAL
ejpam-6041	62	1	1 +	QUANTITY
ejpam-6041	63	1	1 +	CARDINAL
ejpam-6041	63	2	ac	ORG
ejpam-6041	63	3	1 +	CARDINAL
ejpam-6041	63	4	1 +	CARDINAL
ejpam-6041	63	5	bc	ORG
ejpam-6041	63	6	1 + bc	DATE
ejpam-6041	64	1	1 + ab	QUANTITY
ejpam-6041	64	2	1 +	CARDINAL
ejpam-6041	64	3	bc ̸= 0	ORG
ejpam-6041	65	1	0	CARDINAL
ejpam-6041	65	2	ab − ab	ORG
ejpam-6041	65	3	0	CARDINAL
ejpam-6041	67	1	zero	CARDINAL
ejpam-6041	69	1	ab − ab	ORG
ejpam-6041	69	2	0	CARDINAL
ejpam-6041	70	1	0	CARDINAL
ejpam-6041	71	1	− a2b	PERSON
ejpam-6041	72	1	0	CARDINAL
ejpam-6041	72	2	zero	CARDINAL
ejpam-6041	73	1	0	CARDINAL
ejpam-6041	75	1	0 or a	CARDINAL
ejpam-6041	76	1	0	CARDINAL
ejpam-6041	78	1	zero	CARDINAL
ejpam-6041	78	2	0	CARDINAL
ejpam-6041	79	1	0	CARDINAL
ejpam-6041	79	2	0	CARDINAL
ejpam-6041	79	3	0	CARDINAL
ejpam-6041	81	1	r.	NORP
ejpam-6041	81	2	0	CARDINAL
ejpam-6041	82	1	0	CARDINAL
ejpam-6041	82	2	0	CARDINAL
ejpam-6041	83	1	0	CARDINAL
ejpam-6041	84	1	0	CARDINAL
ejpam-6041	85	1	∈	ORG
ejpam-6041	87	1	0 or a	CARDINAL
ejpam-6041	89	1	r. maungchang	PERSON
ejpam-6041	90	1	j. pure	PERSON
ejpam-6041	90	2	18	CARDINAL
ejpam-6041	90	3	2	CARDINAL
ejpam-6041	90	4	2025	CARDINAL
ejpam-6041	90	5	6041 5	DATE
ejpam-6041	90	6	8	CARDINAL
ejpam-6041	90	7	2	CARDINAL
ejpam-6041	90	8	0.5	CARDINAL
ejpam-6041	91	1	∈	ORG
ejpam-6041	93	1	1	CARDINAL
ejpam-6041	94	1	ω	ORG
ejpam-6041	94	2	1	CARDINAL
ejpam-6041	94	3	∈	ORG
ejpam-6041	94	4	d.	NORP
ejpam-6041	95	1	1	CARDINAL
ejpam-6041	97	1	lemma	ORG
ejpam-6041	97	2	4	CARDINAL
ejpam-6041	100	1	3	CARDINAL
ejpam-6041	101	1	d.	NORP
ejpam-6041	102	1	∈	ORG
ejpam-6041	102	2	first	ORDINAL
ejpam-6041	102	3	1 + ab	QUANTITY
ejpam-6041	103	1	1+ab	CARDINAL
ejpam-6041	103	2	|a||b|	CARDINAL
ejpam-6041	104	1	1	CARDINAL
ejpam-6041	106	1	1 + ab	QUANTITY
ejpam-6041	106	2	1 + ab	QUANTITY
ejpam-6041	107	1	r. maungchang	PERSON
ejpam-6041	108	1	j. pure	PERSON
ejpam-6041	108	2	18	CARDINAL
ejpam-6041	108	3	2	CARDINAL
ejpam-6041	108	4	2025	CARDINAL
ejpam-6041	108	5	6041 6	DATE
ejpam-6041	108	6	8	CARDINAL
ejpam-6041	108	7	1 + ab	QUANTITY
ejpam-6041	109	1	0	CARDINAL
ejpam-6041	109	2	1 + ab	QUANTITY
ejpam-6041	109	3	0	CARDINAL
ejpam-6041	109	4	|c|2	ORG
ejpam-6041	109	5	1 +	CARDINAL
ejpam-6041	109	6	1	CARDINAL
ejpam-6041	110	1	1	CARDINAL
ejpam-6041	110	2	bc ̸= 0	ORG
ejpam-6041	110	3	2	CARDINAL
ejpam-6041	111	1	fa	ORG
ejpam-6041	111	2	0	CARDINAL
ejpam-6041	111	3	1	CARDINAL
ejpam-6041	111	4	fa	ORG
ejpam-6041	112	1	aλ+ bλ	PERSON
ejpam-6041	112	2	1 +	CARDINAL
ejpam-6041	112	3	aλ+ bλ	PERSON
ejpam-6041	112	4	5	CARDINAL
ejpam-6041	113	1	0	CARDINAL
ejpam-6041	113	2	1	CARDINAL
ejpam-6041	114	1	1 +	CARDINAL
ejpam-6041	114	2	aλ+ bλ	PERSON
ejpam-6041	115	1	1	CARDINAL
ejpam-6041	115	2	1 +	CARDINAL
ejpam-6041	115	3	aλ+ bλ	PERSON
ejpam-6041	115	4	a+ b	PERSON
ejpam-6041	115	5	zero	CARDINAL
ejpam-6041	115	6	1 +	CARDINAL
ejpam-6041	115	7	1 + ab	QUANTITY
ejpam-6041	115	8	1 + ab	QUANTITY
ejpam-6041	116	1	1 +	CARDINAL
ejpam-6041	116	2	1 + ab	QUANTITY
ejpam-6041	116	3	1 + ab	QUANTITY
ejpam-6041	117	1	fa	ORG
ejpam-6041	118	1	fa	ORG
ejpam-6041	118	2	fa	ORG
ejpam-6041	119	1	ab−ab ̸= 0	ORG
ejpam-6041	119	2	ga	ORG
ejpam-6041	119	3	ga	ORG
ejpam-6041	119	4	|fa	ORG
ejpam-6041	120	1	0	CARDINAL
ejpam-6041	120	2	1	CARDINAL
ejpam-6041	121	1	ga	ORG
ejpam-6041	121	2	0	CARDINAL
ejpam-6041	121	3	1	CARDINAL
ejpam-6041	121	4	0	CARDINAL
ejpam-6041	121	5	1	CARDINAL
ejpam-6041	122	1	ga	ORG
ejpam-6041	122	2	ga	ORG
ejpam-6041	122	3	1	CARDINAL
ejpam-6041	122	4	fa	ORG
ejpam-6041	122	5	b(1	PERSON
ejpam-6041	123	1	1 +	CARDINAL
ejpam-6041	124	1	|fa	ORG
ejpam-6041	124	2	b(1)|	ORG
ejpam-6041	124	3	1	CARDINAL
ejpam-6041	124	4	26	CARDINAL
ejpam-6041	124	5	6	CARDINAL
ejpam-6041	124	6	1	CARDINAL
ejpam-6041	124	7	ga	ORG
ejpam-6041	124	8	∈	ORG
ejpam-6041	124	9	0	CARDINAL
ejpam-6041	124	10	1	CARDINAL
ejpam-6041	126	1	w ∈	PERSON
ejpam-6041	126	2	0	CARDINAL
ejpam-6041	126	3	0	CARDINAL
ejpam-6041	126	4	0	DATE
ejpam-6041	127	1	0	CARDINAL
ejpam-6041	129	1	r.	NORP
ejpam-6041	130	1	ab − ab ̸= 0	ORG
ejpam-6041	130	2	0.5	CARDINAL
ejpam-6041	131	1	ga	ORG
ejpam-6041	131	2	|w|	WORK_OF_ART
ejpam-6041	131	3	∈	ORG
ejpam-6041	131	4	0	CARDINAL
ejpam-6041	131	5	1	CARDINAL
ejpam-6041	132	1	|w|	FAC
ejpam-6041	132	2	ga	ORG
ejpam-6041	133	1	fa	ORG
ejpam-6041	133	2	fa	ORG
ejpam-6041	133	3	b(λ0	PERSON
ejpam-6041	133	4	fa	ORG
ejpam-6041	135	1	∈	ORG
ejpam-6041	135	2	fa	ORG
ejpam-6041	137	1	ω = cos	ORG
ejpam-6041	139	1	1	CARDINAL
ejpam-6041	139	2	1	CARDINAL
ejpam-6041	139	3	r. maungchang	PERSON
ejpam-6041	140	1	j. pure	PERSON
ejpam-6041	140	2	18	CARDINAL
ejpam-6041	140	3	2	CARDINAL
ejpam-6041	140	4	2025	CARDINAL
ejpam-6041	140	5	6041 7	DATE
ejpam-6041	140	6	8	CARDINAL
ejpam-6041	146	1	w.	PERSON
ejpam-6041	148	1	4	CARDINAL
ejpam-6041	148	2	d.	NORP
ejpam-6041	148	3	3.4	CARDINAL
ejpam-6041	148	4	4	CARDINAL
ejpam-6041	148	5	φ	ORG
ejpam-6041	148	6	φ	ORG
ejpam-6041	150	1	3	CARDINAL
ejpam-6041	152	1	2	CARDINAL
ejpam-6041	155	1	4	CARDINAL
ejpam-6041	158	1	φ	ORG
ejpam-6041	158	2	3.4	CARDINAL
ejpam-6041	158	3	4	CARDINAL
ejpam-6041	160	1	φ	ORG
ejpam-6041	161	1	4	CARDINAL
ejpam-6041	161	2	multiplicative	ORG
ejpam-6041	162	1	1	CARDINAL
ejpam-6041	162	2	1.3	CARDINAL
ejpam-6041	162	3	3	CARDINAL
ejpam-6041	171	1	r. maungchang	PERSON
ejpam-6041	172	1	j. pure	PERSON
ejpam-6041	172	2	18	CARDINAL
ejpam-6041	172	3	2	CARDINAL
ejpam-6041	172	4	2025	CARDINAL
ejpam-6041	172	5	6041 8	DATE
ejpam-6041	172	6	8	CARDINAL
ejpam-6041	172	7	chiang mai university	ORG
ejpam-6041	175	1	r. maungchang	PERSON
ejpam-6041	175	2	w. atiponrat	PERSON
ejpam-6041	175	3	t. suwansri	ORG
ejpam-6041	175	4	j. wattanapan	PERSON
ejpam-6041	177	1	1	CARDINAL
ejpam-6041	177	2	t. scarr	PERSON
ejpam-6041	178	1	40	CARDINAL
ejpam-6041	179	1	birkhäuser, boston	ORG
ejpam-6041	179	2	2005	DATE
ejpam-6041	180	1	2	CARDINAL
ejpam-6041	180	2	a. ungar	PERSON
ejpam-6041	181	1	analytic hyperbolic	ORG
ejpam-6041	181	2	albert einstein’s	PERSON
ejpam-6041	182	1	hackensack	GPE
ejpam-6041	182	2	nj	GPE
ejpam-6041	182	3	2008	DATE
ejpam-6041	183	1	3	CARDINAL
ejpam-6041	183	2	k. wiboonton	PERSON
ejpam-6041	184	1	schur	ORG
ejpam-6041	185	1	91(3):491–503	DATE
ejpam-6041	185	2	2017	DATE
ejpam-6041	186	1	4	CARDINAL
ejpam-6041	188	1	asian	NORP
ejpam-6041	189	1	j. math.	PERSON
ejpam-6041	189	2	17(11):article 2450066	CARDINAL
ejpam-6041	189	3	16	CARDINAL
ejpam-6041	189	4	2024	DATE
ejpam-6041	190	1	5	CARDINAL
ejpam-6041	191	1	cayley	ORG
ejpam-6041	191	2	lagrange	GPE
ejpam-6041	192	1	m. rassias	PERSON
ejpam-6041	192	2	p. m. pardalos	PERSON
ejpam-6041	192	3	369–437	CARDINAL
ejpam-6041	192	4	2016	DATE
ejpam-6041	193	1	6	CARDINAL
ejpam-6041	193	2	fitzpatrick	PERSON
ejpam-6041	195	1	prentice hall, hoboken	ORG
ejpam-6041	195	2	nj	GPE
ejpam-6041	195	3	4th	ORDINAL
ejpam-6041	195	4	2010	DATE