id	sid	eid	entity	type
ejpam-5757	1	1	european journal	ORG
ejpam-5757	1	2	2025	DATE
ejpam-5757	1	3	18	CARDINAL
ejpam-5757	1	4	1	CARDINAL
ejpam-5757	1	5	5757	CARDINAL
ejpam-5757	1	6	1307-5543	DATE
ejpam-5757	1	7	new york	GPE
ejpam-5757	1	8	karthikeyan1	PERSON
ejpam-5757	1	9	siriluk donganont2,∗	PERSON
ejpam-5757	1	10	park3	EVENT
ejpam-5757	1	11	tamilvanan1	GPE
ejpam-5757	1	12	wang4 1	ORG
ejpam-5757	2	1	kavaraipettai	PERSON
ejpam-5757	2	2	601 206	CARDINAL
ejpam-5757	2	3	india	GPE
ejpam-5757	2	4	2	CARDINAL
ejpam-5757	2	5	university of phayao	ORG
ejpam-5757	2	6	56000	CARDINAL
ejpam-5757	2	7	thailand 3	ORG
ejpam-5757	2	8	hanyang university	ORG
ejpam-5757	2	9	04763	DATE
ejpam-5757	2	10	korea 4 school of science	ORG
ejpam-5757	2	11	dalian maritime university	ORG
ejpam-5757	3	1	china	GPE
ejpam-5757	6	1	5ϕ(u+	CARDINAL
ejpam-5757	6	2	2v	CARDINAL
ejpam-5757	8	1	0	CARDINAL
ejpam-5757	8	2	brzdȩk	PERSON
ejpam-5757	8	3	2020	DATE
ejpam-5757	8	4	39b52	CARDINAL
ejpam-5757	8	5	39b72,	DATE
ejpam-5757	8	6	39b82	DATE
ejpam-5757	8	7	47h10	CARDINAL
ejpam-5757	8	8	1	CARDINAL
ejpam-5757	11	1	28	CARDINAL
ejpam-5757	11	2	first	ORDINAL
ejpam-5757	13	1	0	CARDINAL
ejpam-5757	13	2	0	CARDINAL
ejpam-5757	15	1	φ	PERSON
ejpam-5757	15	2	∗corresponding	PERSON
ejpam-5757	16	1	s. karthikeyan	PERSON
ejpam-5757	16	2	siriluk.pa@up.ac.th	PERSON
ejpam-5757	16	3	s. donganont	PERSON
ejpam-5757	16	4	baak@hanyang.ac.kr	ORG
ejpam-5757	16	5	c. park	GPE
ejpam-5757	16	6	k. tamilvanan	PERSON
ejpam-5757	16	7	y. wang	PERSON
ejpam-5757	17	1	1	CARDINAL
ejpam-5757	17	2	2025	CARDINAL
ejpam-5757	18	1	s. karthikeyan et al	PERSON
ejpam-5757	19	1	j. pure	PERSON
ejpam-5757	19	2	18	CARDINAL
ejpam-5757	19	3	1	CARDINAL
ejpam-5757	19	4	2025	CARDINAL
ejpam-5757	19	5	5757 2	DATE
ejpam-5757	19	6	18	DATE
ejpam-5757	19	7	∈	ORG
ejpam-5757	20	1	first	ORDINAL
ejpam-5757	20	2	19	CARDINAL
ejpam-5757	21	1	aoki	PERSON
ejpam-5757	21	2	first	ORDINAL
ejpam-5757	21	3	24	CARDINAL
ejpam-5757	21	4	18	CARDINAL
ejpam-5757	22	1	7	CARDINAL
ejpam-5757	22	2	8	DATE
ejpam-5757	22	3	20	DATE
ejpam-5757	22	4	25	DATE
ejpam-5757	24	1	first	ORDINAL
ejpam-5757	24	2	6	CARDINAL
ejpam-5757	25	1	first	ORDINAL
ejpam-5757	25	2	21	CARDINAL
ejpam-5757	26	1	brzdȩk	PERSON
ejpam-5757	26	2	9–11	CARDINAL
ejpam-5757	27	1	gselmann	ORG
ejpam-5757	27	2	17	CARDINAL
ejpam-5757	28	1	bahyrycz	PERSON
ejpam-5757	28	2	4	CARDINAL
ejpam-5757	29	1	brzdȩk	PERSON
ejpam-5757	29	2	13	CARDINAL
ejpam-5757	29	3	non-archimedean	NORP
ejpam-5757	31	1	12	CARDINAL
ejpam-5757	31	2	1	CARDINAL
ejpam-5757	31	3	2	CARDINAL
ejpam-5757	32	1	15	CARDINAL
ejpam-5757	32	2	2017	DATE
ejpam-5757	32	3	2	CARDINAL
ejpam-5757	33	1	5	CARDINAL
ejpam-5757	34	1	2	CARDINAL
ejpam-5757	35	1	2020	DATE
ejpam-5757	36	1	27	CARDINAL
ejpam-5757	36	2	2	CARDINAL
ejpam-5757	37	1	5ϕ(u+	CARDINAL
ejpam-5757	37	2	ϕ(u−	ORG
ejpam-5757	37	3	2v	CARDINAL
ejpam-5757	39	1	0	CARDINAL
ejpam-5757	39	2	brzdȩk	PERSON
ejpam-5757	40	1	brzdȩk	PERSON
ejpam-5757	40	2	9–11	CARDINAL
ejpam-5757	40	3	23	CARDINAL
ejpam-5757	41	1	brzdȩk	PERSON
ejpam-5757	41	2	12	CARDINAL
ejpam-5757	43	1	1	CARDINAL
ejpam-5757	43	2	3	DATE
ejpam-5757	43	3	4	DATE
ejpam-5757	43	4	14	DATE
ejpam-5757	43	5	16	DATE
ejpam-5757	43	6	17	DATE
ejpam-5757	43	7	21	DATE
ejpam-5757	43	8	22	DATE
ejpam-5757	43	9	26	DATE
ejpam-5757	43	10	29	CARDINAL
ejpam-5757	44	1	n0 = n	NORP
ejpam-5757	44	2	0	CARDINAL
ejpam-5757	44	3	∈	ORG
ejpam-5757	46	1	s. karthikeyan et al	PERSON
ejpam-5757	47	1	j. pure	PERSON
ejpam-5757	47	2	18	CARDINAL
ejpam-5757	47	3	1	CARDINAL
ejpam-5757	47	4	2025	CARDINAL
ejpam-5757	47	5	5757 3	DATE
ejpam-5757	47	6	18	CARDINAL
ejpam-5757	47	7	1	CARDINAL
ejpam-5757	48	1	13	CARDINAL
ejpam-5757	49	1	lim	PERSON
ejpam-5757	49	2	0	CARDINAL
ejpam-5757	49	3	lim	PERSON
ejpam-5757	49	4	0	CARDINAL
ejpam-5757	49	5	φ	PERSON
ejpam-5757	49	6	∈	ORG
ejpam-5757	49	7	ς(u	PERSON
ejpam-5757	49	8	∈	ORG
ejpam-5757	50	1	m∈n0	TIME
ejpam-5757	50	2	lim	PERSON
ejpam-5757	50	3	φmζ	ORG
ejpam-5757	50	4	∈	ORG
ejpam-5757	51	1	∈	ORG
ejpam-5757	51	2	χ(u	ORG
ejpam-5757	51	3	lim	PERSON
ejpam-5757	51	4	φmζ	ORG
ejpam-5757	51	5	φ	ORG
ejpam-5757	51	6	ζ(u	PERSON
ejpam-5757	51	7	χ(u	ORG
ejpam-5757	51	8	∈	ORG
ejpam-5757	52	1	1	CARDINAL
ejpam-5757	54	1	2	CARDINAL
ejpam-5757	55	1	u → u	ORG
ejpam-5757	56	1	two	CARDINAL
ejpam-5757	56	2	ru×u +	ORG
ejpam-5757	56	3	ru×u	GPE
ejpam-5757	56	4	φς(u)∥	ORG
ejpam-5757	56	5	i=1 li(u	GPE
ejpam-5757	58	1	j. pure	PERSON
ejpam-5757	58	2	18	CARDINAL
ejpam-5757	58	3	1	CARDINAL
ejpam-5757	58	4	2025	CARDINAL
ejpam-5757	58	5	5757 4	DATE
ejpam-5757	58	6	18	DATE
ejpam-5757	58	7	∈	ORG
ejpam-5757	58	8	∈	ORG
ejpam-5757	59	1	i=1 li(u)δ	GPE
ejpam-5757	60	1	u × u	ORG
ejpam-5757	60	2	ϑ(u	PERSON
ejpam-5757	61	1	lim	PERSON
ejpam-5757	61	2	φmζ	ORG
ejpam-5757	61	3	1	CARDINAL
ejpam-5757	61	4	∈	ORG
ejpam-5757	62	1	φmζ	ORG
ejpam-5757	62	2	φ	ORG
ejpam-5757	62	3	∈	ORG
ejpam-5757	65	1	3v)−	CARDINAL
ejpam-5757	65	2	2v	CARDINAL
ejpam-5757	66	1	+5ϕ(u− v)− 10ϕ(u)−	PERCENT
ejpam-5757	67	1	2	CARDINAL
ejpam-5757	67	2	2	CARDINAL
ejpam-5757	67	3	2	CARDINAL
ejpam-5757	67	4	2	CARDINAL
ejpam-5757	68	1	3	CARDINAL
ejpam-5757	69	1	two	CARDINAL
ejpam-5757	69	2	1	CARDINAL
ejpam-5757	70	1	1 120	CARDINAL
ejpam-5757	70	2	3)η2(m+ 3	DATE
ejpam-5757	70	3	2)η2(m+ 2	DATE
ejpam-5757	70	4	1)η2(m+ 1	DATE
ejpam-5757	70	5	s. karthikeyan et al	PERSON
ejpam-5757	71	1	j. pure	PERSON
ejpam-5757	71	2	18	CARDINAL
ejpam-5757	71	3	1	CARDINAL
ejpam-5757	71	4	2025	CARDINAL
ejpam-5757	71	5	5757 5	DATE
ejpam-5757	72	1	∈	ORG
ejpam-5757	72	2	1	CARDINAL
ejpam-5757	72	3	2	CARDINAL
ejpam-5757	72	4	∈	ORG
ejpam-5757	72	5	3	CARDINAL
ejpam-5757	72	6	2v+	CARDINAL
ejpam-5757	72	7	2v	PRODUCT
ejpam-5757	72	8	u− v ̸= 0	ORG
ejpam-5757	74	1	only one	CARDINAL
ejpam-5757	74	2	120(1−	CARDINAL
ejpam-5757	76	1	3	CARDINAL
ejpam-5757	76	2	1 120	CARDINAL
ejpam-5757	77	1	1 24	CARDINAL
ejpam-5757	77	2	ϕ((2	ORG
ejpam-5757	77	3	1 120	CARDINAL
ejpam-5757	77	4	2)u	CARDINAL
ejpam-5757	79	1	1)u)− 1 12	DATE
ejpam-5757	80	1	1 120 τ1(nu)τ2(u	TIME
ejpam-5757	80	2	4	CARDINAL
ejpam-5757	80	3	n ∈ n	ORG
ejpam-5757	81	1	1 120	CARDINAL
ejpam-5757	81	2	1 24	CARDINAL
ejpam-5757	81	3	1 120	CARDINAL
ejpam-5757	81	4	2)u	CARDINAL
ejpam-5757	81	5	ψ((1	ORG
ejpam-5757	81	6	1)u)−	CARDINAL
ejpam-5757	81	7	5	CARDINAL
ejpam-5757	81	8	∈	ORG
ejpam-5757	81	9	∈	ORG
ejpam-5757	83	1	1 120 τ1(nu)τ2(u	TIME
ejpam-5757	83	2	6	CARDINAL
ejpam-5757	83	3	1 120 τ1(nu)τ2(u	TIME
ejpam-5757	83	4	7	CARDINAL
ejpam-5757	83	5	5	CARDINAL
ejpam-5757	83	6	7	CARDINAL
ejpam-5757	83	7	4	CARDINAL
ejpam-5757	83	8	∈	ORG
ejpam-5757	84	1	∈	ORG
ejpam-5757	84	2	1 120	CARDINAL
ejpam-5757	84	3	1 24	CARDINAL
ejpam-5757	84	4	1 120	CARDINAL
ejpam-5757	84	5	2)u	CARDINAL
ejpam-5757	84	6	s. karthikeyan et al	PERSON
ejpam-5757	85	1	j. pure	PERSON
ejpam-5757	85	2	18	CARDINAL
ejpam-5757	85	3	1	CARDINAL
ejpam-5757	85	4	2025	CARDINAL
ejpam-5757	85	5	5757 6	DATE
ejpam-5757	85	6	ψ((1	ORG
ejpam-5757	86	1	1)u)−	CARDINAL
ejpam-5757	86	2	2)u	CARDINAL
ejpam-5757	86	3	1 12	CARDINAL
ejpam-5757	87	1	1 24	DATE
ejpam-5757	87	2	1)u	CARDINAL
ejpam-5757	88	1	1 120	CARDINAL
ejpam-5757	89	1	1 24	CARDINAL
ejpam-5757	89	2	− ς)((2	ORG
ejpam-5757	89	3	+ n)u) ∥∥∥∥	DATE
ejpam-5757	91	1	1 12	CARDINAL
ejpam-5757	92	1	1 12	CARDINAL
ejpam-5757	93	1	1 120	CARDINAL
ejpam-5757	93	2	+ n)u	DATE
ejpam-5757	93	3	δ((2	ORG
ejpam-5757	93	4	2)u	CARDINAL
ejpam-5757	95	1	1)u	CARDINAL
ejpam-5757	95	2	+ 1 12	CARDINAL
ejpam-5757	96	1	1	CARDINAL
ejpam-5757	96	2	3 + n)u	DATE
ejpam-5757	96	3	1 120	CARDINAL
ejpam-5757	97	1	2 + n)u	DATE
ejpam-5757	97	2	1 24	DATE
ejpam-5757	97	3	n−2)u	GPE
ejpam-5757	97	4	1 120	CARDINAL
ejpam-5757	97	5	1+n)u	CARDINAL
ejpam-5757	97	6	1 12	CARDINAL
ejpam-5757	97	7	1 24	DATE
ejpam-5757	97	8	= nu	PERSON
ejpam-5757	97	9	1 12	CARDINAL
ejpam-5757	97	10	∈	ORG
ejpam-5757	98	1	∈ n0	ORG
ejpam-5757	98	2	n ∈w	LOC
ejpam-5757	99	1	1 120	CARDINAL
ejpam-5757	99	2	n τ1(u)τ2(u	PERSON
ejpam-5757	100	1	0	CARDINAL
ejpam-5757	100	2	6	CARDINAL
ejpam-5757	100	3	7	CARDINAL
ejpam-5757	101	1	= k	PERSON
ejpam-5757	101	2	k ∈ n.	PERSON
ejpam-5757	103	1	1 120	CARDINAL
ejpam-5757	103	2	3 + n)x	DATE
ejpam-5757	103	3	+ 1 24	DATE
ejpam-5757	103	4	2 + n)u	DATE
ejpam-5757	103	5	2)u	CARDINAL
ejpam-5757	103	6	1 + n)u	DATE
ejpam-5757	103	7	+ 1 24	DATE
ejpam-5757	103	8	1)u	CARDINAL
ejpam-5757	103	9	≤ 1 120	CARDINAL
ejpam-5757	103	10	1 120	CARDINAL
ejpam-5757	105	1	+ 1 24	DATE
ejpam-5757	105	2	1 120	CARDINAL
ejpam-5757	107	1	+ n)u	DATE
ejpam-5757	108	1	+ 1 120	CARDINAL
ejpam-5757	108	2	1 120	CARDINAL
ejpam-5757	109	1	2)u)τ2((n− 2)u	PRODUCT
ejpam-5757	110	1	s. karthikeyan et al	PERSON
ejpam-5757	111	1	j. pure	PERSON
ejpam-5757	111	2	18	CARDINAL
ejpam-5757	111	3	1	CARDINAL
ejpam-5757	111	4	2025	CARDINAL
ejpam-5757	111	5	5757 7	DATE
ejpam-5757	111	6	1 120	CARDINAL
ejpam-5757	113	1	+ 1 24	DATE
ejpam-5757	113	2	1 120	CARDINAL
ejpam-5757	114	1	1)u)τ2((n− 1)u	DATE
ejpam-5757	116	1	1 120	CARDINAL
ejpam-5757	116	2	1 120	CARDINAL
ejpam-5757	116	3	n ∈ w	ORG
ejpam-5757	118	1	+ 1	DATE
ejpam-5757	119	1	∈	ORG
ejpam-5757	121	1	1 120	CARDINAL
ejpam-5757	121	2	n τ1(u)τ2(u	PERSON
ejpam-5757	121	3	120(1−	CARDINAL
ejpam-5757	122	1	n ∈w	ORG
ejpam-5757	123	1	2	CARDINAL
ejpam-5757	123	2	lim	PERSON
ejpam-5757	123	3	120(1−	CARDINAL
ejpam-5757	123	4	9	CARDINAL
ejpam-5757	123	5	n ∈w	LOC
ejpam-5757	124	1	2	CARDINAL
ejpam-5757	125	1	10	CARDINAL
ejpam-5757	125	2	n ∈ w	ORG
ejpam-5757	126	1	k ∈ n	PERSON
ejpam-5757	126	2	10	CARDINAL
ejpam-5757	126	3	= k.	PERSON
ejpam-5757	126	4	nτ1((3	ORG
ejpam-5757	127	1	+ 1 24	DATE
ejpam-5757	128	1	2)u)τ2((n− 2)v	DATE
ejpam-5757	129	1	+ 1 24	DATE
ejpam-5757	129	2	1)u)τ2((n− 1)v	DATE
ejpam-5757	130	1	+ 1 12	DATE
ejpam-5757	131	1	s. karthikeyan et al	PERSON
ejpam-5757	132	1	j. pure	PERSON
ejpam-5757	132	2	18	CARDINAL
ejpam-5757	132	3	1	CARDINAL
ejpam-5757	132	4	2025	CARDINAL
ejpam-5757	132	5	5757 8	DATE
ejpam-5757	132	6	18	CARDINAL
ejpam-5757	132	7	10	CARDINAL
ejpam-5757	132	8	∈ n0	ORG
ejpam-5757	132	9	n ∈ w	ORG
ejpam-5757	133	1	10	CARDINAL
ejpam-5757	133	2	3v)−	CARDINAL
ejpam-5757	133	3	5hn(u+ 2v)−hn(u− 2v	QUANTITY
ejpam-5757	134	1	+ 10hn(u+	DATE
ejpam-5757	135	1	+5hn(u− v)− 10hn(u)− 120hn(v	DATE
ejpam-5757	135	2	∈	ORG
ejpam-5757	135	3	∈ n0	ORG
ejpam-5757	135	4	n ∈w	LOC
ejpam-5757	137	1	1 120	CARDINAL
ejpam-5757	137	2	3)u)−	CARDINAL
ejpam-5757	137	3	2)u)−	CARDINAL
ejpam-5757	137	4	1 24	TIME
ejpam-5757	137	5	2)u	CARDINAL
ejpam-5757	137	6	+ 1 12	DATE
ejpam-5757	137	7	1)u)− 1 12	DATE
ejpam-5757	137	8	1)u	CARDINAL
ejpam-5757	137	9	11	CARDINAL
ejpam-5757	138	1	12	CARDINAL
ejpam-5757	138	2	0	CARDINAL
ejpam-5757	139	1	n0 ∈ w	ORG
ejpam-5757	139	2	12	CARDINAL
ejpam-5757	140	1	9	CARDINAL
ejpam-5757	143	1	m=0 αm n0	ORG
ejpam-5757	143	2	13	CARDINAL
ejpam-5757	143	3	1−αn0)l+ 1 120η1(n0	DATE
ejpam-5757	144	1	0 or τ2(u	TIME
ejpam-5757	144	2	0	CARDINAL
ejpam-5757	145	1	11	CARDINAL
ejpam-5757	147	1	14	CARDINAL
ejpam-5757	147	2	∈	ORG
ejpam-5757	148	1	13	CARDINAL
ejpam-5757	149	1	k ∈ n	ORG
ejpam-5757	149	2	14	CARDINAL
ejpam-5757	149	3	j = k.	PERSON
ejpam-5757	149	4	13	CARDINAL
ejpam-5757	151	1	n0 s. karthikeyan et al	PERSON
ejpam-5757	152	1	j. pure	PERSON
ejpam-5757	152	2	18	CARDINAL
ejpam-5757	152	3	1	CARDINAL
ejpam-5757	152	4	2025	CARDINAL
ejpam-5757	152	5	5757 9	DATE
ejpam-5757	152	6	120	CARDINAL
ejpam-5757	154	1	+ n0)u)τ2((−1 + n0)u	PERSON
ejpam-5757	157	1	n0	GPE
ejpam-5757	158	1	14	CARDINAL
ejpam-5757	158	2	1+ k.	DATE
ejpam-5757	158	3	14	CARDINAL
ejpam-5757	159	1	14	CARDINAL
ejpam-5757	160	1	15	CARDINAL
ejpam-5757	160	2	9	CARDINAL
ejpam-5757	160	3	120(1−	CARDINAL
ejpam-5757	162	1	3	CARDINAL
ejpam-5757	162	2	hn0	DATE
ejpam-5757	162	3	15	CARDINAL
ejpam-5757	164	1	1	CARDINAL
ejpam-5757	164	2	1 120	CARDINAL
ejpam-5757	165	1	+ 1 24 η(2	QUANTITY
ejpam-5757	168	1	+ 1 24	DATE
ejpam-5757	169	1	η(m	GPE
ejpam-5757	169	2	η(m	GPE
ejpam-5757	169	3	16	CARDINAL
ejpam-5757	170	1	17	CARDINAL
ejpam-5757	170	2	s. karthikeyan et al	PERSON
ejpam-5757	171	1	j. pure	PERSON
ejpam-5757	171	2	18	CARDINAL
ejpam-5757	171	3	1	CARDINAL
ejpam-5757	171	4	2025	CARDINAL
ejpam-5757	171	5	5757 10	DATE
ejpam-5757	171	6	18	DATE
ejpam-5757	171	7	∈	ORG
ejpam-5757	171	8	3v	CARDINAL
ejpam-5757	171	9	2v	CARDINAL
ejpam-5757	171	10	2v	PRODUCT
ejpam-5757	171	11	u− v ̸= 0	ORG
ejpam-5757	172	1	only one	CARDINAL
ejpam-5757	172	2	18	CARDINAL
ejpam-5757	172	3	120(1−	CARDINAL
ejpam-5757	174	1	17	CARDINAL
ejpam-5757	174	2	1 120	CARDINAL
ejpam-5757	176	1	1 24	CARDINAL
ejpam-5757	176	2	ϕ((2	ORG
ejpam-5757	176	3	1 120	DATE
ejpam-5757	177	1	1 12	DATE
ejpam-5757	178	1	1 120	CARDINAL
ejpam-5757	178	2	19	CARDINAL
ejpam-5757	178	3	n ∈ n	ORG
ejpam-5757	178	4	1 120	CARDINAL
ejpam-5757	178	5	3)u)− 1 24	DATE
ejpam-5757	178	6	2)u)−	CARDINAL
ejpam-5757	178	7	1 120 ψ((n−	TIME
ejpam-5757	178	8	2)u	CARDINAL
ejpam-5757	178	9	1)u	CARDINAL
ejpam-5757	178	10	+ 1 24	DATE
ejpam-5757	178	11	1)u)−	CARDINAL
ejpam-5757	178	12	∈	ORG
ejpam-5757	178	13	∈	ORG
ejpam-5757	180	1	1 120	CARDINAL
ejpam-5757	180	2	20	CARDINAL
ejpam-5757	180	3	1 120	CARDINAL
ejpam-5757	180	4	1 120	CARDINAL
ejpam-5757	180	5	21	CARDINAL
ejpam-5757	180	6	19	CARDINAL
ejpam-5757	180	7	∈	ORG
ejpam-5757	181	1	∈	ORG
ejpam-5757	181	2	≤ 1 120	CARDINAL
ejpam-5757	181	3	1 24	CARDINAL
ejpam-5757	183	1	1 12	CARDINAL
ejpam-5757	184	1	1 12	CARDINAL
ejpam-5757	185	1	1 120	CARDINAL
ejpam-5757	186	1	2)u	CARDINAL
ejpam-5757	187	1	2)u	CARDINAL
ejpam-5757	188	1	s. karthikeyan et al	PERSON
ejpam-5757	189	1	j. pure	PERSON
ejpam-5757	189	2	18	CARDINAL
ejpam-5757	189	3	1	CARDINAL
ejpam-5757	189	4	2025	CARDINAL
ejpam-5757	189	5	5757 11	DATE
ejpam-5757	190	1	+ 1 24 δ((n− 1)u	QUANTITY
ejpam-5757	190	2	+ 1 12	CARDINAL
ejpam-5757	191	1	1	CARDINAL
ejpam-5757	192	1	1 120 , ϕ2(u	DATE
ejpam-5757	192	2	2)u	CARDINAL
ejpam-5757	192	3	1 24	DATE
ejpam-5757	192	4	2)u	CARDINAL
ejpam-5757	192	5	1 120	CARDINAL
ejpam-5757	193	1	1)u	CARDINAL
ejpam-5757	193	2	1 12	DATE
ejpam-5757	194	1	1)u	CARDINAL
ejpam-5757	194	2	1 24	DATE
ejpam-5757	194	3	= nu	PERSON
ejpam-5757	194	4	1 12	CARDINAL
ejpam-5757	194	5	∈	ORG
ejpam-5757	195	1	∈ n0	ORG
ejpam-5757	195	2	n ∈w	LOC
ejpam-5757	195	3	1 120	CARDINAL
ejpam-5757	196	1	22	CARDINAL
ejpam-5757	196	2	22	CARDINAL
ejpam-5757	196	3	20	CARDINAL
ejpam-5757	196	4	21	CARDINAL
ejpam-5757	197	1	22	CARDINAL
ejpam-5757	197	2	= k.	PERSON
ejpam-5757	199	1	1 120	CARDINAL
ejpam-5757	199	2	3)x	CARDINAL
ejpam-5757	199	3	+ 1 24	DATE
ejpam-5757	199	4	2)u	CARDINAL
ejpam-5757	199	5	+ 1 120	DATE
ejpam-5757	199	6	2)u	CARDINAL
ejpam-5757	200	1	1)u	CARDINAL
ejpam-5757	200	2	+ 1 24	DATE
ejpam-5757	200	3	1)u	CARDINAL
ejpam-5757	200	4	1 120	CARDINAL
ejpam-5757	201	1	22	CARDINAL
ejpam-5757	202	1	22	CARDINAL
ejpam-5757	202	2	∈ n0.	ORG
ejpam-5757	204	1	1 120	CARDINAL
ejpam-5757	204	2	120(1−	CARDINAL
ejpam-5757	205	1	∞ s. karthikeyan et al	PERSON
ejpam-5757	206	1	j. pure	PERSON
ejpam-5757	206	2	18	CARDINAL
ejpam-5757	206	3	1	CARDINAL
ejpam-5757	206	4	2025	CARDINAL
ejpam-5757	206	5	5757 12	DATE
ejpam-5757	206	6	18	DATE
ejpam-5757	206	7	n ∈w	ORG
ejpam-5757	207	1	2	CARDINAL
ejpam-5757	207	2	lim	PERSON
ejpam-5757	207	3	120(1−	CARDINAL
ejpam-5757	207	4	23	CARDINAL
ejpam-5757	207	5	n ∈w	LOC
ejpam-5757	208	1	2	CARDINAL
ejpam-5757	210	1	24	CARDINAL
ejpam-5757	210	2	∈ n0	ORG
ejpam-5757	210	3	n ∈ w	ORG
ejpam-5757	211	1	17	CARDINAL
ejpam-5757	211	2	k ∈ n	ORG
ejpam-5757	211	3	24	CARDINAL
ejpam-5757	211	4	= k	PERSON
ejpam-5757	211	5	n ∈w	ORG
ejpam-5757	213	1	24	CARDINAL
ejpam-5757	213	2	∈	ORG
ejpam-5757	213	3	∈ n0	ORG
ejpam-5757	213	4	n ∈ w	ORG
ejpam-5757	214	1	24	CARDINAL
ejpam-5757	214	2	dhn(u	PRODUCT
ejpam-5757	215	1	∈ n0	ORG
ejpam-5757	215	2	n ∈w	LOC
ejpam-5757	217	1	1 120	CARDINAL
ejpam-5757	217	2	3)u)− 1 24	DATE
ejpam-5757	217	3	2)u)−	CARDINAL
ejpam-5757	217	4	1 120	QUANTITY
ejpam-5757	217	5	2)u	CARDINAL
ejpam-5757	217	6	+ 1 12	DATE
ejpam-5757	217	7	1)u	CARDINAL
ejpam-5757	217	8	1)u)−	CARDINAL
ejpam-5757	217	9	1 12	CARDINAL
ejpam-5757	217	10	25	CARDINAL
ejpam-5757	218	1	26	CARDINAL
ejpam-5757	219	1	n0 ∈w	GPE
ejpam-5757	219	2	26	CARDINAL
ejpam-5757	220	1	16	CARDINAL
ejpam-5757	221	1	m=0 αm n0	ORG
ejpam-5757	221	2	27	CARDINAL
ejpam-5757	221	3	s. karthikeyan et al	PERSON
ejpam-5757	222	1	j. pure	PERSON
ejpam-5757	222	2	18	CARDINAL
ejpam-5757	222	3	1	CARDINAL
ejpam-5757	222	4	2025	CARDINAL
ejpam-5757	222	5	5757 13	DATE
ejpam-5757	222	6	18	CARDINAL
ejpam-5757	222	7	1	CARDINAL
ejpam-5757	222	8	+ 1 120η(n0	DATE
ejpam-5757	223	1	τ(u	PERSON
ejpam-5757	223	2	0	CARDINAL
ejpam-5757	224	1	25	CARDINAL
ejpam-5757	226	1	n0	GPE
ejpam-5757	226	2	28	CARDINAL
ejpam-5757	226	3	∈	ORG
ejpam-5757	227	1	27	CARDINAL
ejpam-5757	229	1	k ∈ n	ORG
ejpam-5757	229	2	28	CARDINAL
ejpam-5757	229	3	j = k.	PERSON
ejpam-5757	230	1	27	CARDINAL
ejpam-5757	231	1	2)u	CARDINAL
ejpam-5757	232	1	1)u	CARDINAL
ejpam-5757	233	1	n0 .	GPE
ejpam-5757	235	1	n0	GPE
ejpam-5757	236	1	28	CARDINAL
ejpam-5757	237	1	j ∈ n0	ORG
ejpam-5757	237	2	28	CARDINAL
ejpam-5757	238	1	28	CARDINAL
ejpam-5757	239	1	29	CARDINAL
ejpam-5757	239	2	23	CARDINAL
ejpam-5757	240	1	120(1−	CARDINAL
ejpam-5757	240	2	n ∈ w	ORG
ejpam-5757	241	1	18	CARDINAL
ejpam-5757	241	2	hn0	DATE
ejpam-5757	241	3	29	CARDINAL
ejpam-5757	241	4	3	CARDINAL
ejpam-5757	241	5	φ	ORG
ejpam-5757	241	6	2	CARDINAL
ejpam-5757	242	1	2	CARDINAL
ejpam-5757	242	2	s. karthikeyan et al	PERSON
ejpam-5757	243	1	j. pure	PERSON
ejpam-5757	243	2	18	CARDINAL
ejpam-5757	243	3	1	CARDINAL
ejpam-5757	243	4	2025	CARDINAL
ejpam-5757	243	5	5757 14	DATE
ejpam-5757	243	6	18	DATE
ejpam-5757	243	7	∈	ORG
ejpam-5757	243	8	3v	CARDINAL
ejpam-5757	243	9	2v ̸= 0	PRODUCT
ejpam-5757	243	10	2v	PRODUCT
ejpam-5757	243	11	u− v ̸= 0	ORG
ejpam-5757	243	12	φ	ORG
ejpam-5757	244	1	φ	ORG
ejpam-5757	244	2	2	CARDINAL
ejpam-5757	245	1	5	CARDINAL
ejpam-5757	246	1	w	ORG
ejpam-5757	246	2	3	CARDINAL
ejpam-5757	247	1	that limm→+∞ η1(m	ORG
ejpam-5757	248	1	0	CARDINAL
ejpam-5757	248	2	0	CARDINAL
ejpam-5757	250	1	0	CARDINAL
ejpam-5757	251	1	3	CARDINAL
ejpam-5757	251	2	2	CARDINAL
ejpam-5757	253	1	3	CARDINAL
ejpam-5757	254	1	3	CARDINAL
ejpam-5757	254	2	2	CARDINAL
ejpam-5757	254	3	120(1−	CARDINAL
ejpam-5757	255	1	5	CARDINAL
ejpam-5757	257	1	∈	ORG
ejpam-5757	259	1	∈	ORG
ejpam-5757	259	2	3v	CARDINAL
ejpam-5757	259	3	2v ̸= 0	PRODUCT
ejpam-5757	259	4	2v	PRODUCT
ejpam-5757	259	5	u− v ̸= 0	ORG
ejpam-5757	259	6	2	CARDINAL
ejpam-5757	260	1	1	CARDINAL
ejpam-5757	261	1	∈	ORG
ejpam-5757	261	2	30	CARDINAL
ejpam-5757	261	3	∈	ORG
ejpam-5757	261	4	2v	PRODUCT
ejpam-5757	261	5	u− v ̸= 0	ORG
ejpam-5757	264	1	3	CARDINAL
ejpam-5757	265	1	∈	ORG
ejpam-5757	265	2	∈	ORG
ejpam-5757	266	1	∈	ORG
ejpam-5757	266	2	∈	ORG
ejpam-5757	266	3	∈	ORG
ejpam-5757	266	4	s. karthikeyan et al	PERSON
ejpam-5757	267	1	j. pure	PERSON
ejpam-5757	267	2	18	CARDINAL
ejpam-5757	267	3	1	CARDINAL
ejpam-5757	267	4	2025	CARDINAL
ejpam-5757	267	5	5757 15	DATE
ejpam-5757	267	6	18	CARDINAL
ejpam-5757	267	7	mc1	ORG
ejpam-5757	268	1	mc2	PERSON
ejpam-5757	268	2	1 120	CARDINAL
ejpam-5757	268	3	m+	CARDINAL
ejpam-5757	268	4	m+	CARDINAL
ejpam-5757	269	1	m−	NORP
ejpam-5757	269	2	2)c1+c2 + 1 12	MONEY
ejpam-5757	269	3	m−	NORP
ejpam-5757	269	4	m)c1+c2	ORG
ejpam-5757	270	1	3	CARDINAL
ejpam-5757	270	2	only one	CARDINAL
ejpam-5757	270	3	∈	ORG
ejpam-5757	271	1	c1 + c2	PERSON
ejpam-5757	271	2	one	CARDINAL
ejpam-5757	273	1	0	CARDINAL
ejpam-5757	274	1	η1(m− 2)η2(m− 2	DATE
ejpam-5757	275	1	2)c1+c2	CARDINAL
ejpam-5757	275	2	0	CARDINAL
ejpam-5757	276	1	5	CARDINAL
ejpam-5757	277	1	1	CARDINAL
ejpam-5757	279	1	∈	ORG
ejpam-5757	279	2	u + 3v	ORG
ejpam-5757	279	3	2v	CARDINAL
ejpam-5757	279	4	u − v ̸= 0	ORG
ejpam-5757	281	1	5ϕ(u+	CARDINAL
ejpam-5757	281	2	ϕ(u−	ORG
ejpam-5757	281	3	2v	CARDINAL
ejpam-5757	283	1	0	CARDINAL
ejpam-5757	283	2	∀u	ORG
ejpam-5757	283	3	∈	ORG
ejpam-5757	283	4	31	CARDINAL
ejpam-5757	284	1	31	CARDINAL
ejpam-5757	285	1	30	CARDINAL
ejpam-5757	285	2	1	CARDINAL
ejpam-5757	286	1	0	CARDINAL
ejpam-5757	288	1	2	CARDINAL
ejpam-5757	289	1	∈	ORG
ejpam-5757	290	1	32	CARDINAL
ejpam-5757	290	2	∈	ORG
ejpam-5757	290	3	2v	PRODUCT
ejpam-5757	290	4	u− v ̸= 0	ORG
ejpam-5757	292	1	s. karthikeyan et al	PERSON
ejpam-5757	293	1	j. pure	PERSON
ejpam-5757	293	2	18	CARDINAL
ejpam-5757	293	3	1	CARDINAL
ejpam-5757	293	4	2025	CARDINAL
ejpam-5757	293	5	5757 16	DATE
ejpam-5757	293	6	18	CARDINAL
ejpam-5757	293	7	2	CARDINAL
ejpam-5757	295	1	∈	ORG
ejpam-5757	295	2	2v	PRODUCT
ejpam-5757	295	3	u− v ̸= 0	ORG
ejpam-5757	295	4	∈	ORG
ejpam-5757	297	1	5ϕ(u+	CARDINAL
ejpam-5757	297	2	ϕ(u−	ORG
ejpam-5757	297	3	2v	CARDINAL
ejpam-5757	299	1	0	CARDINAL
ejpam-5757	299	2	∀u	ORG
ejpam-5757	299	3	∈	ORG
ejpam-5757	299	4	33	CARDINAL
ejpam-5757	300	1	33	CARDINAL
ejpam-5757	301	1	32	CARDINAL
ejpam-5757	301	2	2	CARDINAL
ejpam-5757	302	1	0	CARDINAL
ejpam-5757	305	1	3	CARDINAL
ejpam-5757	306	1	∈	ORG
ejpam-5757	307	1	34	CARDINAL
ejpam-5757	307	2	u + 3v	ORG
ejpam-5757	307	3	2v	CARDINAL
ejpam-5757	307	4	u − v ̸= 0	ORG
ejpam-5757	308	1	34	CARDINAL
ejpam-5757	310	1	34	CARDINAL
ejpam-5757	310	2	32	CARDINAL
ejpam-5757	311	1	2	CARDINAL
ejpam-5757	311	2	1	CARDINAL
ejpam-5757	312	1	∈	ORG
ejpam-5757	312	2	3v	CARDINAL
ejpam-5757	312	3	2v ̸= 0	PRODUCT
ejpam-5757	312	4	2v	PRODUCT
ejpam-5757	312	5	u− v ̸= 0	ORG
ejpam-5757	312	6	3	CARDINAL
ejpam-5757	312	7	4.	CARDINAL
ejpam-5757	316	1	0	CARDINAL
ejpam-5757	316	2	brzdȩk	PERSON
ejpam-5757	317	1	s. karthikeyan et al	PERSON
ejpam-5757	318	1	j. pure	PERSON
ejpam-5757	318	2	18	CARDINAL
ejpam-5757	318	3	1	CARDINAL
ejpam-5757	318	4	2025	CARDINAL
ejpam-5757	318	5	5757 17	DATE
ejpam-5757	318	6	18	CARDINAL
ejpam-5757	319	1	s. donganont	PERSON
ejpam-5757	319	2	the university of phayao	ORG
ejpam-5757	319	3	thailand science	ORG
ejpam-5757	319	4	2025	CARDINAL
ejpam-5757	320	1	5020/2567	PERSON
ejpam-5757	324	1	1	CARDINAL
ejpam-5757	324	2	w	ORG
ejpam-5757	325	1	brzdȩk	PERSON
ejpam-5757	325	2	2	CARDINAL
ejpam-5757	328	1	sci.	ORG
ejpam-5757	328	2	40(3):824–834	DATE
ejpam-5757	328	3	2020	DATE
ejpam-5757	329	1	2	CARDINAL
ejpam-5757	329	2	ultrametric spaces	ORG
ejpam-5757	331	1	14(2):105–120	DATE
ejpam-5757	331	2	2019	DATE
ejpam-5757	332	1	3	CARDINAL
ejpam-5757	334	1	ann	PERSON
ejpam-5757	334	2	univ.	ORG
ejpam-5757	335	1	vii sci	PERSON
ejpam-5757	335	2	69(2):317–328	DATE
ejpam-5757	335	3	2023	CARDINAL
ejpam-5757	336	1	4	CARDINAL
ejpam-5757	339	1	hungar	PERSON
ejpam-5757	339	2	2014	DATE
ejpam-5757	340	1	5	CARDINAL
ejpam-5757	342	1	36(1):29–44	CARDINAL
ejpam-5757	342	2	2017	DATE
ejpam-5757	343	1	6	CARDINAL
ejpam-5757	346	1	j.	PERSON
ejpam-5757	346	2	16:383–397	DATE
ejpam-5757	346	3	2019	DATE
ejpam-5757	347	1	7	CARDINAL
ejpam-5757	347	2	g balasubramanian	PERSON
ejpam-5757	348	1	generalized linear	PERSON
ejpam-5757	350	1	j. pure	PERSON
ejpam-5757	350	2	17(4):3415–3435	DATE
ejpam-5757	350	3	2024	DATE
ejpam-5757	351	1	8	CARDINAL
ejpam-5757	351	2	g balasubramanian	PERSON
ejpam-5757	352	1	fifth	ORDINAL
ejpam-5757	354	1	j. pure	PERSON
ejpam-5757	354	2	17(4):3585–3609	DATE
ejpam-5757	354	3	2024	DATE
ejpam-5757	355	1	9	CARDINAL
ejpam-5757	355	2	j brzdȩk	PERSON
ejpam-5757	357	1	hungar	PERSON
ejpam-5757	357	2	14:58–67,	DATE
ejpam-5757	357	3	2013	DATE
ejpam-5757	358	1	s. karthikeyan et al	PERSON
ejpam-5757	359	1	j. pure	PERSON
ejpam-5757	359	2	18	CARDINAL
ejpam-5757	359	3	1	CARDINAL
ejpam-5757	359	4	2025	CARDINAL
ejpam-5757	359	5	5757 18	DATE
ejpam-5757	359	6	10	CARDINAL
ejpam-5757	359	7	j brzdȩk	PERSON
ejpam-5757	362	1	86:255–267	GPE
ejpam-5757	362	2	2013	DATE
ejpam-5757	363	1	11	CARDINAL
ejpam-5757	363	2	j brzdȩk	PERSON
ejpam-5757	365	1	bull	PERSON
ejpam-5757	366	1	aust	GPE
ejpam-5757	367	1	2014	DATE
ejpam-5757	368	1	12	CARDINAL
ejpam-5757	368	2	j brzdȩk	PERSON
ejpam-5757	368	3	j chudziak	PERSON
ejpam-5757	370	1	74:6728–6732, 2011	DATE
ejpam-5757	371	1	13	CARDINAL
ejpam-5757	371	2	j brzdȩk	PERSON
ejpam-5757	371	3	k ciepliński	PERSON
ejpam-5757	372	1	non-archimedean	NORP
ejpam-5757	373	1	74:6861–6867, 2011	DATE
ejpam-5757	374	1	14	CARDINAL
ejpam-5757	374	2	j brzdȩk	PERSON
ejpam-5757	374	3	k ciepliński	PERSON
ejpam-5757	376	1	2017(401756):1–7	DATE
ejpam-5757	376	2	2017	DATE
ejpam-5757	377	1	15	CARDINAL
ejpam-5757	378	1	2	CARDINAL
ejpam-5757	379	1	j. math	PERSON
ejpam-5757	381	1	455:2001–2013, 2017	DATE
ejpam-5757	382	1	16	CARDINAL
ejpam-5757	383	1	abelian	NORP
ejpam-5757	384	1	bull	PERSON
ejpam-5757	385	1	sci.	ORG
ejpam-5757	385	2	197(103532):1–30	CARDINAL
ejpam-5757	385	3	2024	DATE
ejpam-5757	386	1	17	CARDINAL
ejpam-5757	389	1	hungar	PERSON
ejpam-5757	390	1	124:179	CARDINAL
ejpam-5757	390	2	188	CARDINAL
ejpam-5757	390	3	2009	DATE
ejpam-5757	391	1	18	CARDINAL
ejpam-5757	391	2	2	CARDINAL
ejpam-5757	392	1	j. math	PERSON
ejpam-5757	394	1	184:431–436, 1994	DATE
ejpam-5757	395	1	19	CARDINAL
ejpam-5757	399	1	acad	ORG
ejpam-5757	400	1	sci. u.s.a.	ORG
ejpam-5757	400	2	27:222–224	CARDINAL
ejpam-5757	400	3	1941	DATE
ejpam-5757	401	1	20	CARDINAL
ejpam-5757	401	2	senthil kumar	PERSON
ejpam-5757	402	1	second	ORDINAL
ejpam-5757	404	1	j. pure	PERSON
ejpam-5757	405	1	13(5):1162–1175	DATE
ejpam-5757	405	2	2020	DATE
ejpam-5757	406	1	21	CARDINAL
ejpam-5757	412	1	n.s.	GPE
ejpam-5757	412	2	17(2):107–224, 2001	DATE
ejpam-5757	413	1	22	CARDINAL
ejpam-5757	416	1	j. math	PERSON
ejpam-5757	416	2	13(3):738–745	DATE
ejpam-5757	416	3	2024	DATE
ejpam-5757	417	1	23	CARDINAL
ejpam-5757	418	1	linear	ORG
ejpam-5757	420	1	88:163–168	CARDINAL
ejpam-5757	420	2	2014	DATE
ejpam-5757	421	1	24	CARDINAL
ejpam-5757	424	1	amer	PERSON
ejpam-5757	425	1	72:297–300, 1978	DATE
ejpam-5757	426	1	25	CARDINAL
ejpam-5757	426	2	senthil kumar	PERSON
ejpam-5757	427	1	generalized hyers-ulam-rassias	PERSON
ejpam-5757	429	1	j. pure	PERSON
ejpam-5757	429	2	2015	DATE
ejpam-5757	430	1	26	CARDINAL
ejpam-5757	431	1	2	CARDINAL
ejpam-5757	432	1	j.	PERSON
ejpam-5757	432	2	22(9):1–15, 2020	DATE
ejpam-5757	433	1	27	CARDINAL
ejpam-5757	433	2	k y n	PERSON
ejpam-5757	434	1	2	CARDINAL
ejpam-5757	435	1	j.	PERSON
ejpam-5757	435	2	22(3):1	CARDINAL
ejpam-5757	435	3	16	CARDINAL
ejpam-5757	435	4	2020	DATE
ejpam-5757	436	1	28	CARDINAL
ejpam-5757	438	1	john wiley & sons, inc.	ORG
ejpam-5757	438	2	new york	GPE
ejpam-5757	438	3	1964	DATE
ejpam-5757	439	1	29	CARDINAL
ejpam-5757	439	2	k yadav	PERSON
ejpam-5757	442	1	24:212–227	CARDINAL
ejpam-5757	442	2	2024	DATE