id	sid	eid	entity	type
ejpam-4983	1	1	european journal	ORG
ejpam-4983	2	1	17	CARDINAL
ejpam-4983	2	2	1	CARDINAL
ejpam-4983	2	3	2024	DATE
ejpam-4983	2	4	11	CARDINAL
ejpam-4983	3	1	new york	GPE
ejpam-4983	3	2	jitman1,∗	GPE
ejpam-4983	3	3	modjam1 1	FAC
ejpam-4983	3	4	silpakorn university	ORG
ejpam-4983	3	5	nakhon	ORG
ejpam-4983	3	6	73000	CARDINAL
ejpam-4983	3	7	thailand	GPE
ejpam-4983	6	1	n × n	LOC
ejpam-4983	6	2	r.	NORP
ejpam-4983	6	3	n × n	ORG
ejpam-4983	8	1	2020	DATE
ejpam-4983	8	2	11c20	CARDINAL
ejpam-4983	8	3	15b33	CARDINAL
ejpam-4983	8	4	1	CARDINAL
ejpam-4983	10	1	2	CARDINAL
ejpam-4983	10	2	9	CARDINAL
ejpam-4983	10	3	10	CARDINAL
ejpam-4983	11	1	2	CARDINAL
ejpam-4983	11	2	11	CARDINAL
ejpam-4983	12	1	n × n	ORG
ejpam-4983	12	2	13	CARDINAL
ejpam-4983	13	1	zp	ORG
ejpam-4983	13	2	n × n	ORG
ejpam-4983	13	3	zm	ORG
ejpam-4983	13	4	first	ORDINAL
ejpam-4983	13	5	1	CARDINAL
ejpam-4983	14	1	1	CARDINAL
ejpam-4983	14	2	10	CARDINAL
ejpam-4983	15	1	zm	ORG
ejpam-4983	16	1	3	CARDINAL
ejpam-4983	16	2	10	CARDINAL
ejpam-4983	17	1	n × n	ORG
ejpam-4983	20	1	s. jitman	PERSON
ejpam-4983	20	2	pornrudee.ole@gmail.com	ORG
ejpam-4983	21	1	11	CARDINAL
ejpam-4983	21	2	2024	CARDINAL
ejpam-4983	22	1	s. jitman	PERSON
ejpam-4983	23	1	j. pure	PERSON
ejpam-4983	23	2	17	CARDINAL
ejpam-4983	23	3	1	CARDINAL
ejpam-4983	23	4	2024	CARDINAL
ejpam-4983	23	5	11-29 12	PERCENT
ejpam-4983	23	6	3	CARDINAL
ejpam-4983	24	1	8	CARDINAL
ejpam-4983	25	1	zeros	CARDINAL
ejpam-4983	25	2	the first row	DATE
ejpam-4983	25	3	first	ORDINAL
ejpam-4983	28	1	0	CARDINAL
ejpam-4983	32	1	∗ 	PERSON
ejpam-4983	34	1	r.	NORP
ejpam-4983	34	2	1	CARDINAL
ejpam-4983	34	3	2	CARDINAL
ejpam-4983	34	4	n × n	PRODUCT
ejpam-4983	34	5	14	CARDINAL
ejpam-4983	35	1	15	CARDINAL
ejpam-4983	35	2	16	CARDINAL
ejpam-4983	36	1	15	CARDINAL
ejpam-4983	36	2	16	CARDINAL
ejpam-4983	36	3	quantum	ORG
ejpam-4983	36	4	4	CARDINAL
ejpam-4983	37	1	8	CARDINAL
ejpam-4983	38	1	z(r	DATE
ejpam-4983	38	2	zero	CARDINAL
ejpam-4983	38	3	r.	NORP
ejpam-4983	38	4	r.	NORP
ejpam-4983	39	1	1	CARDINAL
ejpam-4983	41	1	∈	ORG
ejpam-4983	41	2	∈	ORG
ejpam-4983	42	1	∈	ORG
ejpam-4983	43	1	a. clearly	PERSON
ejpam-4983	43	2	⋃	DATE
ejpam-4983	44	1	s. jitman	PERSON
ejpam-4983	45	1	j. pure	PERSON
ejpam-4983	45	2	17	CARDINAL
ejpam-4983	45	3	1	CARDINAL
ejpam-4983	45	4	2024	CARDINAL
ejpam-4983	45	5	11-29 13	DATE
ejpam-4983	46	1	n × n	ORG
ejpam-4983	46	2	section 2	LAW
ejpam-4983	47	1	section 3	LAW
ejpam-4983	48	1	n × n	PRODUCT
ejpam-4983	48	2	3.1	CARDINAL
ejpam-4983	49	1	n × n	ORG
ejpam-4983	49	2	3.2	CARDINAL
ejpam-4983	50	1	section 4. 2	DATE
ejpam-4983	50	2	n × n	PRODUCT
ejpam-4983	50	3	1	CARDINAL
ejpam-4983	51	1	1	CARDINAL
ejpam-4983	51	2	1	CARDINAL
ejpam-4983	54	1	|ia1(fq)|	ORG
ejpam-4983	56	1	1)|ian−1(fq)|	CARDINAL
ejpam-4983	56	2	2	CARDINAL
ejpam-4983	58	1	|ia1(fq)|	ORG
ejpam-4983	58	2	0}|	CARDINAL
ejpam-4983	59	1	1	CARDINAL
ejpam-4983	60	1	2	CARDINAL
ejpam-4983	60	2	a11 a12	ORG
ejpam-4983	61	1	0	CARDINAL
ejpam-4983	61	2	0 a33	QUANTITY
ejpam-4983	65	1	1	CARDINAL
ejpam-4983	65	2	2	DATE
ejpam-4983	65	3	ri	GPE
ejpam-4983	65	4	ci	PERSON
ejpam-4983	65	5	two	CARDINAL
ejpam-4983	66	1	1	CARDINAL
ejpam-4983	70	1	s. jitman	PERSON
ejpam-4983	71	1	j. pure	PERSON
ejpam-4983	71	2	17	CARDINAL
ejpam-4983	71	3	1	CARDINAL
ejpam-4983	71	4	2024	CARDINAL
ejpam-4983	71	5	11	CARDINAL
ejpam-4983	71	6	a11 − a1nan1ann	PERSON
ejpam-4983	72	1	0	CARDINAL
ejpam-4983	72	2	0	CARDINAL
ejpam-4983	73	1	0 a33	QUANTITY
ejpam-4983	77	1	ann det(c	PERSON
ejpam-4983	78	1	s12 s13 ·	PERSON
ejpam-4983	78	2	0	CARDINAL
ejpam-4983	78	3	0	CARDINAL
ejpam-4983	78	4	0	CARDINAL
ejpam-4983	80	1	det	PERSON
ejpam-4983	80	2	− a1nan1ann	PERSON
ejpam-4983	80	3	0	CARDINAL
ejpam-4983	80	4	0	CARDINAL
ejpam-4983	81	1	0	CARDINAL
ejpam-4983	83	1	  ̸= 0	PRODUCT
ejpam-4983	84	1	s12 s13 ·	PERSON
ejpam-4983	84	2	0	CARDINAL
ejpam-4983	84	3	0	CARDINAL
ejpam-4983	84	4	0	CARDINAL
ejpam-4983	86	1	− a1nan1ann	PERSON
ejpam-4983	86	2	0	CARDINAL
ejpam-4983	86	3	0	CARDINAL
ejpam-4983	87	1	0	CARDINAL
ejpam-4983	90	1	|ian−1(fq)|	PERSON
ejpam-4983	91	1	ann det(c	PERSON
ejpam-4983	91	2	a11 a12	ORG
ejpam-4983	91	3	0	CARDINAL
ejpam-4983	91	4	0	CARDINAL
ejpam-4983	92	1	0 a33	QUANTITY
ejpam-4983	94	1	s. s. jitman	PERSON
ejpam-4983	95	1	j. pure	PERSON
ejpam-4983	95	2	17	CARDINAL
ejpam-4983	95	3	1	CARDINAL
ejpam-4983	95	4	2024	CARDINAL
ejpam-4983	95	5	11	CARDINAL
ejpam-4983	96	1	an1	NORP
ejpam-4983	96	2	ann	PERSON
ejpam-4983	96	3	1	CARDINAL
ejpam-4983	97	1	1)|ian−1(fq)|	CARDINAL
ejpam-4983	97	2	2	CARDINAL
ejpam-4983	98	1	an1 ̸= 0	ORG
ejpam-4983	100	1	1	CARDINAL
ejpam-4983	100	2	2	DATE
ejpam-4983	103	1	c1 ↔	PERSON
ejpam-4983	105	1	0	CARDINAL
ejpam-4983	105	2	0	CARDINAL
ejpam-4983	105	3	0	CARDINAL
ejpam-4983	107	1	0	CARDINAL
ejpam-4983	109	1	det(a′	PERSON
ejpam-4983	114	1	an−1,n−1	NORP
ejpam-4983	114	2	an1	NORP
ejpam-4983	116	1	an−1,n−1,	ORG
ejpam-4983	116	2	q−1)n	GPE
ejpam-4983	119	1	q2n−3(q − 1)n	ORG
ejpam-4983	120	1	two	CARDINAL
ejpam-4983	121	1	1)|ian−1(fq)|	CARDINAL
ejpam-4983	122	1	1	CARDINAL
ejpam-4983	123	1	1	CARDINAL
ejpam-4983	125	1	1	CARDINAL
ejpam-4983	126	1	|ia1(fq)|	ORG
ejpam-4983	126	2	1	CARDINAL
ejpam-4983	126	3	1− 1	DATE
ejpam-4983	127	1	2	CARDINAL
ejpam-4983	130	1	1	CARDINAL
ejpam-4983	131	1	1	CARDINAL
ejpam-4983	132	1	1)|iak−1(fq)|	CARDINAL
ejpam-4983	133	1	1)(q2(k−1)−3(q	CARDINAL
ejpam-4983	135	1	s. jitman	PERSON
ejpam-4983	136	1	j. pure	PERSON
ejpam-4983	136	2	17	CARDINAL
ejpam-4983	136	3	1	CARDINAL
ejpam-4983	136	4	2024	CARDINAL
ejpam-4983	136	5	11	CARDINAL
ejpam-4983	138	1	1)k(q +	DATE
ejpam-4983	141	1	1	CARDINAL
ejpam-4983	141	2	0	CARDINAL
ejpam-4983	141	3	1	CARDINAL
ejpam-4983	141	4	2	CARDINAL
ejpam-4983	143	1	1)|	CARDINAL
ejpam-4983	143	2	0	CARDINAL
ejpam-4983	145	1	0	CARDINAL
ejpam-4983	145	2	1	CARDINAL
ejpam-4983	145	3	f(a	ORG
ejpam-4983	146	1	1	CARDINAL
ejpam-4983	146	2	1	CARDINAL
ejpam-4983	147	1	1)a	DATE
ejpam-4983	148	1	a11 a12	PERSON
ejpam-4983	149	1	0	CARDINAL
ejpam-4983	149	2	0	CARDINAL
ejpam-4983	150	1	0 a33	QUANTITY
ejpam-4983	152	1	ann  ∈ an(fq	PERSON
ejpam-4983	152	2	1	CARDINAL
ejpam-4983	153	1	1	CARDINAL
ejpam-4983	154	1	1	CARDINAL
ejpam-4983	154	2	1	CARDINAL
ejpam-4983	155	1	1)a	CARDINAL
ejpam-4983	155	2	aa11 aa12 aa13	PERSON
ejpam-4983	155	3	0	CARDINAL
ejpam-4983	155	4	0	CARDINAL
ejpam-4983	155	5	0 a33	QUANTITY
ejpam-4983	157	1	ann  ∈ an(fq	PERSON
ejpam-4983	157	2	2	CARDINAL
ejpam-4983	158	1	det(diag(a	DATE
ejpam-4983	158	2	1	DATE
ejpam-4983	158	3	1	CARDINAL
ejpam-4983	159	1	1)a	CARDINAL
ejpam-4983	159	2	det(diag(a	DATE
ejpam-4983	159	3	1	DATE
ejpam-4983	159	4	1	CARDINAL
ejpam-4983	160	1	1	CARDINAL
ejpam-4983	161	1	1	CARDINAL
ejpam-4983	161	2	a. hence	PERSON
ejpam-4983	162	1	1	CARDINAL
ejpam-4983	162	2	1	CARDINAL
ejpam-4983	163	1	1	CARDINAL
ejpam-4983	164	1	1	DATE
ejpam-4983	164	2	1	CARDINAL
ejpam-4983	166	1	1)x	DATE
ejpam-4983	167	1	1	CARDINAL
ejpam-4983	167	2	1	CARDINAL
ejpam-4983	168	1	1)x	DATE
ejpam-4983	168	2	1	CARDINAL
ejpam-4983	169	1	∈	ORG
ejpam-4983	169	2	1	CARDINAL
ejpam-4983	169	3	f(diag(a−1	PERSON
ejpam-4983	169	4	1	DATE
ejpam-4983	169	5	1	CARDINAL
ejpam-4983	170	1	1)x	DATE
ejpam-4983	170	2	1	CARDINAL
ejpam-4983	170	3	1	CARDINAL
ejpam-4983	171	1	1)diag(a−1	CARDINAL
ejpam-4983	171	2	1	CARDINAL
ejpam-4983	171	3	1	CARDINAL
ejpam-4983	172	1	1)x	CARDINAL
ejpam-4983	173	1	s. jitman	PERSON
ejpam-4983	174	1	j. pure	PERSON
ejpam-4983	174	2	17	CARDINAL
ejpam-4983	174	3	1	CARDINAL
ejpam-4983	174	4	2024	CARDINAL
ejpam-4983	174	5	11	CARDINAL
ejpam-4983	174	6	1	CARDINAL
ejpam-4983	174	7	1)|	CARDINAL
ejpam-4983	175	1	2	CARDINAL
ejpam-4983	176	1	1)|	CARDINAL
ejpam-4983	176	2	0	CARDINAL
ejpam-4983	177	1	1	CARDINAL
ejpam-4983	177	2	2	CARDINAL
ejpam-4983	178	1	1	CARDINAL
ejpam-4983	183	1	1	CARDINAL
ejpam-4983	183	2	0	CARDINAL
ejpam-4983	185	1	2	CARDINAL
ejpam-4983	186	1	1)|	CARDINAL
ejpam-4983	186	2	0	CARDINAL
ejpam-4983	187	1	⋃	DATE
ejpam-4983	187	2	0}|	CARDINAL
ejpam-4983	187	3	1	CARDINAL
ejpam-4983	187	4	0}||an(fq	CARDINAL
ejpam-4983	187	5	1)|	CARDINAL
ejpam-4983	187	6	1)|an(fq	ORDINAL
ejpam-4983	187	7	1)|	CARDINAL
ejpam-4983	188	1	1	CARDINAL
ejpam-4983	188	2	2	CARDINAL
ejpam-4983	189	1	1)|	CARDINAL
ejpam-4983	189	2	1	CARDINAL
ejpam-4983	189	3	1	CARDINAL
ejpam-4983	191	1	1	CARDINAL
ejpam-4983	192	1	1	CARDINAL
ejpam-4983	194	1	1	CARDINAL
ejpam-4983	194	2	1	CARDINAL
ejpam-4983	194	3	1	CARDINAL
ejpam-4983	195	1	0)|	CARDINAL
ejpam-4983	196	1	2	CARDINAL
ejpam-4983	198	1	1	CARDINAL
ejpam-4983	198	2	n. s. jitman	PERSON
ejpam-4983	199	1	j. pure	PERSON
ejpam-4983	199	2	17	CARDINAL
ejpam-4983	199	3	1	CARDINAL
ejpam-4983	199	4	2024	CARDINAL
ejpam-4983	199	5	11	CARDINAL
ejpam-4983	201	1	n × n	PRODUCT
ejpam-4983	203	1	n × n	PRODUCT
ejpam-4983	205	1	5	CARDINAL
ejpam-4983	205	2	6	CARDINAL
ejpam-4983	206	1	1	CARDINAL
ejpam-4983	207	1	γ.	GPE
ejpam-4983	207	2	⊋	DATE
ejpam-4983	207	3	⊋	DATE
ejpam-4983	207	4	⊋	DATE
ejpam-4983	208	1	γe−1r ⊋	DATE
ejpam-4983	208	2	0	CARDINAL
ejpam-4983	208	3	integer e.	PERSON
ejpam-4983	208	4	r.	NORP
ejpam-4983	208	5	r.	NORP
ejpam-4983	208	6	6	CARDINAL
ejpam-4983	209	1	3	CARDINAL
ejpam-4983	210	1	1	CARDINAL
ejpam-4983	212	1	⊆	CARDINAL
ejpam-4983	212	2	modulo γ	ORG
ejpam-4983	213	1	1	CARDINAL
ejpam-4983	213	2	∈	ORG
ejpam-4983	213	3	a1	PRODUCT
ejpam-4983	216	1	2	CARDINAL
ejpam-4983	216	2	3	CARDINAL
ejpam-4983	217	1	0 ≤	QUANTITY
ejpam-4983	218	1	∈	ORG
ejpam-4983	218	2	0	CARDINAL
ejpam-4983	219	1	∈	ORG
ejpam-4983	220	1	5	CARDINAL
ejpam-4983	220	2	1)qe−1	CARDINAL
ejpam-4983	220	3	6	CARDINAL
ejpam-4983	220	4	0 ≤	MONEY
ejpam-4983	220	5	3.1	CARDINAL
ejpam-4983	221	1	first	ORDINAL
ejpam-4983	221	2	n × n	PRODUCT
ejpam-4983	222	1	n × n	PRODUCT
ejpam-4983	223	1	n × n	PRODUCT
ejpam-4983	224	1	s. jitman	PERSON
ejpam-4983	225	1	j. pure	PERSON
ejpam-4983	225	2	17	CARDINAL
ejpam-4983	225	3	1	CARDINAL
ejpam-4983	225	4	2024	CARDINAL
ejpam-4983	225	5	11	CARDINAL
ejpam-4983	225	6	2	CARDINAL
ejpam-4983	230	1	1	CARDINAL
ejpam-4983	231	1	7→	CARDINAL
ejpam-4983	234	1	first	ORDINAL
ejpam-4983	237	1	∈	ORG
ejpam-4983	241	1	ϕ(a	PRODUCT
ejpam-4983	241	2	fq	PRODUCT
ejpam-4983	242	1	one	CARDINAL
ejpam-4983	243	1	1	CARDINAL
ejpam-4983	243	2	1	CARDINAL
ejpam-4983	246	1	1	CARDINAL
ejpam-4983	250	1	1	CARDINAL
ejpam-4983	251	1	|an(r	PERSON
ejpam-4983	251	2	1)|	CARDINAL
ejpam-4983	251	3	|an(r	PERSON
ejpam-4983	251	4	3	CARDINAL
ejpam-4983	253	1	|an(r	PERSON
ejpam-4983	253	2	|an(r	PERSON
ejpam-4983	253	3	1)|	CARDINAL
ejpam-4983	255	1	1	CARDINAL
ejpam-4983	255	2	θ(a	ORG
ejpam-4983	256	1	1	CARDINAL
ejpam-4983	256	2	1	CARDINAL
ejpam-4983	257	1	1)a	DATE
ejpam-4983	258	1	s. jitman	PERSON
ejpam-4983	259	1	j. pure	PERSON
ejpam-4983	259	2	17	CARDINAL
ejpam-4983	259	3	1	CARDINAL
ejpam-4983	259	4	2024	CARDINAL
ejpam-4983	259	5	11	CARDINAL
ejpam-4983	259	6	2	CARDINAL
ejpam-4983	259	7	1	CARDINAL
ejpam-4983	260	1	|an(r	PERSON
ejpam-4983	260	2	|an(r	PERSON
ejpam-4983	260	3	1)|	CARDINAL
ejpam-4983	261	1	3	CARDINAL
ejpam-4983	261	2	|an(r	PERSON
ejpam-4983	261	3	|an(r	PERSON
ejpam-4983	261	4	1)|	CARDINAL
ejpam-4983	262	1	∈	ORG
ejpam-4983	262	2	n × n	PRODUCT
ejpam-4983	262	3	3	CARDINAL
ejpam-4983	262	4	3	CARDINAL
ejpam-4983	264	1	|an(r	PERSON
ejpam-4983	266	1	1	CARDINAL
ejpam-4983	268	1	first	ORDINAL
ejpam-4983	269	1	⋃	DATE
ejpam-4983	270	1	3	CARDINAL
ejpam-4983	270	2	1	CARDINAL
ejpam-4983	270	3	⋃	DATE
ejpam-4983	271	1	∑ a∈u(r	PERSON
ejpam-4983	271	2	|an(r	PERSON
ejpam-4983	272	1	|an(r	PERSON
ejpam-4983	272	2	1)|	CARDINAL
ejpam-4983	272	3	1)|	CARDINAL
ejpam-4983	273	1	lemma 1	ORG
ejpam-4983	273	2	1)qe−1	CARDINAL
ejpam-4983	274	1	|an(r	PERSON
ejpam-4983	274	2	|an(r	PERSON
ejpam-4983	274	3	1)|	CARDINAL
ejpam-4983	274	4	1)n(q +	DATE
ejpam-4983	274	5	1	CARDINAL
ejpam-4983	275	1	1)qe−1	CARDINAL
ejpam-4983	277	1	1	CARDINAL
ejpam-4983	279	1	3.2	CARDINAL
ejpam-4983	280	1	s. jitman	PERSON
ejpam-4983	281	1	j. pure	PERSON
ejpam-4983	281	2	17	CARDINAL
ejpam-4983	281	3	1	CARDINAL
ejpam-4983	281	4	2024	CARDINAL
ejpam-4983	281	5	11-29 21	DATE
ejpam-4983	282	1	n × n	PRODUCT
ejpam-4983	282	2	2	CARDINAL
ejpam-4983	286	1	1	CARDINAL
ejpam-4983	287	1	3.2.1	CARDINAL
ejpam-4983	287	2	zero	CARDINAL
ejpam-4983	287	3	zero	CARDINAL
ejpam-4983	288	1	2	CARDINAL
ejpam-4983	288	2	5	CARDINAL
ejpam-4983	291	1	|a1(r	LOC
ejpam-4983	291	2	0)|	CARDINAL
ejpam-4983	291	3	1	CARDINAL
ejpam-4983	291	4	0)|	CARDINAL
ejpam-4983	291	5	1)q2(e−1)(qe+1 + 1)|an−1(r	DATE
ejpam-4983	291	6	q3n−4|an(r/γ e−1r	ORG
ejpam-4983	291	7	0	CARDINAL
ejpam-4983	292	1	2	CARDINAL
ejpam-4983	294	1	0)|	CARDINAL
ejpam-4983	294	2	1	CARDINAL
ejpam-4983	295	1	2	CARDINAL
ejpam-4983	295	2	a11 a12	ORG
ejpam-4983	296	1	0	CARDINAL
ejpam-4983	296	2	0 a33	QUANTITY
ejpam-4983	299	1	ann  ∈	PERSON
ejpam-4983	299	2	0	CARDINAL
ejpam-4983	300	1	1	CARDINAL
ejpam-4983	300	2	2	DATE
ejpam-4983	303	1	ri	GPE
ejpam-4983	303	2	ci	PERSON
ejpam-4983	303	3	two	CARDINAL
ejpam-4983	304	1	1	CARDINAL
ejpam-4983	304	2	ann ∈ u(r	ORG
ejpam-4983	305	1	1.1	CARDINAL
ejpam-4983	305	2	ann ∈ u(r	ORG
ejpam-4983	306	1	−1	CARDINAL
ejpam-4983	308	1	s. jitman	PERSON
ejpam-4983	309	1	j. pure	PERSON
ejpam-4983	309	2	17	CARDINAL
ejpam-4983	309	3	1	CARDINAL
ejpam-4983	309	4	2024	CARDINAL
ejpam-4983	309	5	11-29 22	TIME
ejpam-4983	309	6	a11 − a1nan1ann	PERSON
ejpam-4983	310	1	0	CARDINAL
ejpam-4983	310	2	0	CARDINAL
ejpam-4983	311	1	0 a33	QUANTITY
ejpam-4983	315	1	ann det(c	PERSON
ejpam-4983	316	1	3	CARDINAL
ejpam-4983	316	2	t11 t12 t13	PERSON
ejpam-4983	316	3	t1,n−1 t21	PERSON
ejpam-4983	316	4	0	CARDINAL
ejpam-4983	316	5	0	CARDINAL
ejpam-4983	317	1	0 t33	PERCENT
ejpam-4983	319	1	− a1nan1a	PERSON
ejpam-4983	320	1	t1,n−1 t21	PERSON
ejpam-4983	320	2	0	CARDINAL
ejpam-4983	320	3	0	CARDINAL
ejpam-4983	320	4	0 t33	PERCENT
ejpam-4983	322	1	0	CARDINAL
ejpam-4983	323	1	t11 t12	PERSON
ejpam-4983	323	2	t1,n−1 t21	PERSON
ejpam-4983	323	3	0	CARDINAL
ejpam-4983	323	4	0	CARDINAL
ejpam-4983	324	1	0 t33	PERCENT
ejpam-4983	327	1	− a1nan1a	PERSON
ejpam-4983	328	1	t1,n−1 t21	PERSON
ejpam-4983	328	2	0	CARDINAL
ejpam-4983	328	3	0	CARDINAL
ejpam-4983	328	4	0 t33	PERCENT
ejpam-4983	330	1	0	DATE
ejpam-4983	331	1	0)|	CARDINAL
ejpam-4983	332	1	3	CARDINAL
ejpam-4983	332	2	0	CARDINAL
ejpam-4983	333	1	0	CARDINAL
ejpam-4983	334	1	0	DATE
ejpam-4983	334	2	0)|	CARDINAL
ejpam-4983	335	1	ann	PERSON
ejpam-4983	335	2	1)qe−1	CARDINAL
ejpam-4983	337	1	s. jitman	PERSON
ejpam-4983	338	1	j. pure	PERSON
ejpam-4983	338	2	17	CARDINAL
ejpam-4983	338	3	1	CARDINAL
ejpam-4983	338	4	2024	CARDINAL
ejpam-4983	338	5	11	CARDINAL
ejpam-4983	338	6	1.2	CARDINAL
ejpam-4983	338	7	ann /∈	ORG
ejpam-4983	340	1	a11 a12	PERSON
ejpam-4983	340	2	0	CARDINAL
ejpam-4983	340	3	0	CARDINAL
ejpam-4983	341	1	0 a33	QUANTITY
ejpam-4983	344	1	+1a1nan1diag(a22	DATE
ejpam-4983	348	1	+ ann det(d	PERSON
ejpam-4983	349	1	4	CARDINAL
ejpam-4983	350	1	0	CARDINAL
ejpam-4983	351	1	an1	ORG
ejpam-4983	352	1	1)qe−1	CARDINAL
ejpam-4983	352	2	qe−1	ORG
ejpam-4983	352	3	0)|	CARDINAL
ejpam-4983	353	1	0)|	CARDINAL
ejpam-4983	354	1	2	CARDINAL
ejpam-4983	354	2	ann /∈	ORG
ejpam-4983	358	1	bij	ORG
ejpam-4983	358	2	wij	ORG
ejpam-4983	358	3	1	CARDINAL
ejpam-4983	358	4	aij	ORG
ejpam-4983	358	5	γw1n	PERSON
ejpam-4983	358	6	ann = γwnn	PERSON
ejpam-4983	358	7	wnn ∈ e−2∑ j=0	ORG
ejpam-4983	358	8	1	CARDINAL
ejpam-4983	360	1	γ e−1r	GPE
ejpam-4983	360	2	bij + γe−1r	ORG
ejpam-4983	361	1	γ det(b	PERSON
ejpam-4983	361	2	r.	NORP
ejpam-4983	362	1	det(b	PERSON
ejpam-4983	362	2	γe−1r	CARDINAL
ejpam-4983	364	1	∈	ORG
ejpam-4983	364	2	γ e−1r	GPE
ejpam-4983	364	3	0 + γe−1r	QUANTITY
ejpam-4983	364	4	0	CARDINAL
ejpam-4983	365	1	γ e−1r	GPE
ejpam-4983	366	1	0	CARDINAL
ejpam-4983	368	1	|an(r	PERSON
ejpam-4983	368	2	0)|	CARDINAL
ejpam-4983	368	3	1	CARDINAL
ejpam-4983	369	1	q3n−4|an(r/γ e−1r	ORG
ejpam-4983	369	2	0	CARDINAL
ejpam-4983	371	1	2	CARDINAL
ejpam-4983	372	1	s. jitman	PERSON
ejpam-4983	373	1	j. pure	PERSON
ejpam-4983	373	2	17	CARDINAL
ejpam-4983	373	3	1	CARDINAL
ejpam-4983	373	4	2024	CARDINAL
ejpam-4983	373	5	11	CARDINAL
ejpam-4983	373	6	5	CARDINAL
ejpam-4983	374	1	2	CARDINAL
ejpam-4983	375	1	|a1(r	LOC
ejpam-4983	375	2	0)|	CARDINAL
ejpam-4983	375	3	1	CARDINAL
ejpam-4983	375	4	0)|	CARDINAL
ejpam-4983	378	1	1	CARDINAL
ejpam-4983	379	1	2	CARDINAL
ejpam-4983	381	1	0)|	CARDINAL
ejpam-4983	381	2	1	CARDINAL
ejpam-4983	382	1	2	CARDINAL
ejpam-4983	383	1	4	CARDINAL
ejpam-4983	383	2	2	CARDINAL
ejpam-4983	383	3	|an(r	PERSON
ejpam-4983	383	4	0)|	CARDINAL
ejpam-4983	384	1	0)|	CARDINAL
ejpam-4983	386	1	1	CARDINAL
ejpam-4983	387	1	3.2.2	CARDINAL
ejpam-4983	387	2	n × n	ORG
ejpam-4983	388	1	first	ORDINAL
ejpam-4983	388	2	|an(r	PERSON
ejpam-4983	388	3	γ	GPE
ejpam-4983	388	4	|an(r	PERSON
ejpam-4983	388	5	∈	ORG
ejpam-4983	390	1	γ	GPE
ejpam-4983	390	2	∈	ORG
ejpam-4983	394	1	ψ(a	PERSON
ejpam-4983	394	2	1	CARDINAL
ejpam-4983	394	3	1	CARDINAL
ejpam-4983	396	1	1)a	DATE
ejpam-4983	397	1	2	CARDINAL
ejpam-4983	398	1	|an(r	PERSON
ejpam-4983	398	2	γ	GPE
ejpam-4983	399	1	2	CARDINAL
ejpam-4983	399	2	3	CARDINAL
ejpam-4983	400	1	|an(r	PERSON
ejpam-4983	400	2	+ γe−1r)|	GPE
ejpam-4983	400	3	1	CARDINAL
ejpam-4983	402	1	1 ≤	QUANTITY
ejpam-4983	402	2	1	CARDINAL
ejpam-4983	402	3	γ e−1r	GPE
ejpam-4983	402	4	β(a	ORG
ejpam-4983	403	1	s. jitman	PERSON
ejpam-4983	404	1	j. pure	PERSON
ejpam-4983	404	2	17	CARDINAL
ejpam-4983	404	3	1	CARDINAL
ejpam-4983	404	4	2024	CARDINAL
ejpam-4983	404	5	11-29 25	TIME
ejpam-4983	407	1	∈	ORG
ejpam-4983	407	2	det(β(a	PERSON
ejpam-4983	407	3	+ γe−1r	CARDINAL
ejpam-4983	408	1	1	CARDINAL
ejpam-4983	409	1	1 ≤	QUANTITY
ejpam-4983	410	1	1	CARDINAL
ejpam-4983	410	2	1 +	CARDINAL
ejpam-4983	411	1	|{a	CARDINAL
ejpam-4983	411	2	∈	ORG
ejpam-4983	415	1	γ s)|	GPE
ejpam-4983	416	1	|{a	CARDINAL
ejpam-4983	417	1	||an(r, γ	PERSON
ejpam-4983	417	2	γ s)|	GPE
ejpam-4983	418	1	5	CARDINAL
ejpam-4983	418	2	|{a	CARDINAL
ejpam-4983	422	1	ker(β)||{b ∈	ORG
ejpam-4983	422	2	+ γe−1r)|	GPE
ejpam-4983	423	1	6	CARDINAL
ejpam-4983	423	2	5	CARDINAL
ejpam-4983	423	3	6	CARDINAL
ejpam-4983	423	4	+ γe−1r)|	GPE
ejpam-4983	424	1	|an(r	PERSON
ejpam-4983	424	2	γ	GPE
ejpam-4983	424	3	+ γe−1r)|	GPE
ejpam-4983	425	1	2	CARDINAL
ejpam-4983	426	1	6	CARDINAL
ejpam-4983	427	1	2 ≤	QUANTITY
ejpam-4983	427	2	1 ≤	QUANTITY
ejpam-4983	428	1	|an(r	PERSON
ejpam-4983	428	2	γ s	ORG
ejpam-4983	428	3	1	CARDINAL
ejpam-4983	429	1	3	CARDINAL
ejpam-4983	431	1	|an(r	PERSON
ejpam-4983	431	2	γ	GPE
ejpam-4983	435	1	1 ≤	QUANTITY
ejpam-4983	435	2	e. s. jitman	PERSON
ejpam-4983	436	1	j. pure	PERSON
ejpam-4983	436	2	17	CARDINAL
ejpam-4983	436	3	1	CARDINAL
ejpam-4983	436	4	2024	CARDINAL
ejpam-4983	436	5	11	CARDINAL
ejpam-4983	437	1	1 ≤	QUANTITY
ejpam-4983	437	2	µ(a	PERSON
ejpam-4983	440	1	∈	ORG
ejpam-4983	442	1	1	CARDINAL
ejpam-4983	445	1	ker(µ)||an(r/γ sr	ORG
ejpam-4983	448	1	+ γs+1r)|	DATE
ejpam-4983	449	1	|an(r	PERSON
ejpam-4983	449	2	+ γs+1r)|	DATE
ejpam-4983	449	3	1	CARDINAL
ejpam-4983	452	1	7	CARDINAL
ejpam-4983	452	2	6	CARDINAL
ejpam-4983	452	3	|an(r	PERSON
ejpam-4983	452	4	q3(e−s−1)(n−1)|an(r/γ	ORG
ejpam-4983	452	5	+ γs+1r)|	DATE
ejpam-4983	453	1	8)	CARDINAL
ejpam-4983	453	2	7	CARDINAL
ejpam-4983	453	3	|an(r	PERSON
ejpam-4983	453	4	γ	GPE
ejpam-4983	457	1	2	CARDINAL
ejpam-4983	457	2	|an(r	PERSON
ejpam-4983	457	3	∈	ORG
ejpam-4983	458	1	2	CARDINAL
ejpam-4983	459	1	|a1(r	LOC
ejpam-4983	460	1	1	CARDINAL
ejpam-4983	461	1	+ 1)q5n−7	DATE
ejpam-4983	461	2	1)n(q +	DATE
ejpam-4983	461	3	1	CARDINAL
ejpam-4983	464	1	0)|	CARDINAL
ejpam-4983	464	2	∈	ORG
ejpam-4983	464	3	2	CARDINAL
ejpam-4983	467	1	1	CARDINAL
ejpam-4983	468	1	2	CARDINAL
ejpam-4983	469	1	1	CARDINAL
ejpam-4983	469	2	7	CARDINAL
ejpam-4983	469	3	|an(r	PERSON
ejpam-4983	470	1	s. jitman	PERSON
ejpam-4983	471	1	j. pure	PERSON
ejpam-4983	471	2	17	CARDINAL
ejpam-4983	471	3	1	CARDINAL
ejpam-4983	471	4	2024	CARDINAL
ejpam-4983	471	5	11	CARDINAL
ejpam-4983	471	6	1	CARDINAL
ejpam-4983	473	1	0)|	CARDINAL
ejpam-4983	474	1	1	CARDINAL
ejpam-4983	474	2	0)|	CARDINAL
ejpam-4983	474	3	0)|	CARDINAL
ejpam-4983	475	1	5	CARDINAL
ejpam-4983	475	2	|an(r	PERSON
ejpam-4983	475	3	0)|	CARDINAL
ejpam-4983	476	1	0)|	CARDINAL
ejpam-4983	476	2	|an(r	PERSON
ejpam-4983	476	3	0)|	CARDINAL
ejpam-4983	477	1	0)|	CARDINAL
ejpam-4983	479	1	1	CARDINAL
ejpam-4983	479	2	0)|	CARDINAL
ejpam-4983	481	1	0)|	CARDINAL
ejpam-4983	483	1	1	CARDINAL
ejpam-4983	483	2	1)q3n−4|an(fq	CARDINAL
ejpam-4983	483	3	1)q2(q3 + 1)|an−1(r	DATE
ejpam-4983	485	1	+ 1)q3n−4|an(fq	DATE
ejpam-4983	486	1	0)|	CARDINAL
ejpam-4983	487	1	2	CARDINAL
ejpam-4983	488	1	1	CARDINAL
ejpam-4983	488	2	|an(r	PERSON
ejpam-4983	488	3	1	CARDINAL
ejpam-4983	491	1	0)|	CARDINAL
ejpam-4983	491	2	+ 1)q5n−7	DATE
ejpam-4983	492	1	1)n(q +	DATE
ejpam-4983	492	2	1	CARDINAL
ejpam-4983	495	1	0)|	CARDINAL
ejpam-4983	496	1	2	CARDINAL
ejpam-4983	496	2	0)|	CARDINAL
ejpam-4983	496	3	5	CARDINAL
ejpam-4983	496	4	4	CARDINAL
ejpam-4983	496	5	r.	NORP
ejpam-4983	496	6	n × n	ORG
ejpam-4983	497	1	n × n	ORG
ejpam-4983	497	2	zero	CARDINAL
ejpam-4983	497	3	n × n	ORG
ejpam-4983	497	4	zero	CARDINAL
ejpam-4983	498	1	2	CARDINAL
ejpam-4983	499	1	28	CARDINAL
ejpam-4983	499	2	r.	NORP
ejpam-4983	499	3	n × n	ORG
ejpam-4983	501	1	s. jitman	PERSON
ejpam-4983	501	2	national research council of thailand	ORG
ejpam-4983	501	3	silpakorn university	ORG
ejpam-4983	502	1	1	CARDINAL
ejpam-4983	503	1	zm	ORG
ejpam-4983	504	1	66:35–49	CARDINAL
ejpam-4983	504	2	1987	DATE
ejpam-4983	505	1	2	CARDINAL
ejpam-4983	505	2	w cheney	PERSON
ejpam-4983	506	1	2nd	ORDINAL
ejpam-4983	507	1	jones	PERSON
ejpam-4983	507	2	bartlett publishers	PERSON
ejpam-4983	507	3	2010	DATE
ejpam-4983	508	1	3	CARDINAL
ejpam-4983	510	1	2017:126	CARDINAL
ejpam-4983	510	2	140	CARDINAL
ejpam-4983	510	3	48	DATE
ejpam-4983	511	1	4	CARDINAL
ejpam-4983	511	2	j. dubail	PERSON
ejpam-4983	511	3	t. botzung	PERSON
ejpam-4983	511	4	j. schachenmayer	PERSON
ejpam-4983	511	5	g. pupillo	PERSON
ejpam-4983	511	6	d.	NORP
ejpam-4983	512	1	quantum	ORG
ejpam-4983	515	1	105:023714	CARDINAL
ejpam-4983	515	2	feb 2022	DATE
ejpam-4983	516	1	5	CARDINAL
ejpam-4983	518	1	springer, 2002	DATE
ejpam-4983	519	1	6	CARDINAL
ejpam-4983	520	1	7:382	CARDINAL
ejpam-4983	520	2	396	CARDINAL
ejpam-4983	520	3	2001	DATE
ejpam-4983	521	1	k h leung	PERSON
ejpam-4983	523	1	9:20–38, 2003	DATE
ejpam-4983	524	1	8	CARDINAL
ejpam-4983	526	1	8:242–256	CARDINAL
ejpam-4983	526	2	2020	DATE
ejpam-4983	527	1	9	CARDINAL
ejpam-4983	529	1	american	NORP
ejpam-4983	529	2	monthly	DATE
ejpam-4983	529	3	2004	DATE
ejpam-4983	530	1	10	CARDINAL
ejpam-4983	530	2	j m lockhart	PERSON
ejpam-4983	530	3	w	GPE
ejpam-4983	531	1	m. mathematics magazine	ORG
ejpam-4983	531	2	80:207–214, 2007	DATE
ejpam-4983	532	1	29	CARDINAL
ejpam-4983	532	2	11	CARDINAL
ejpam-4983	534	1	20:87–99, 1989	DATE
ejpam-4983	535	1	12	CARDINAL
ejpam-4983	535	2	j n valdés	PERSON
ejpam-4983	537	1	41(6):2360–2369, 2018	ORG
ejpam-4983	538	1	13	CARDINAL
ejpam-4983	540	1	51:311–315	CARDINAL
ejpam-4983	540	2	1984	DATE
ejpam-4983	541	1	14	CARDINAL
ejpam-4983	543	1	33:1–5	CARDINAL
ejpam-4983	543	2	2014	DATE
ejpam-4983	544	1	15	CARDINAL
ejpam-4983	546	1	2009(1):379402	CARDINAL
ejpam-4983	546	2	2009	DATE
ejpam-4983	547	1	16	CARDINAL
ejpam-4983	547	2	j l barlow	PERSON
ejpam-4983	549	1	464:62–89	CARDINAL
ejpam-4983	549	2	2015	DATE