id	sid	eid	entity	type
ap-4607	1	1	acta polytechnica doi:10.14311/ap.2017.57.0404	PERSON
ap-4607	1	2	57(6):404–411	CARDINAL
ap-4607	1	3	2017	DATE
ap-4607	1	4	czech technical university	ORG
ap-4607	1	5	prague	GPE
ap-4607	1	6	2017	CARDINAL
ap-4607	1	7	http://ojs.cvut.cz/ojs/index.php/ap	ORG
ap-4607	1	8	albert t. kotvytskiya	PERSON
ap-4607	1	9	b,∗	GPE
ap-4607	1	10	volodymyr yu	ORG
ap-4607	2	1	karazin kharkov national university	ORG
ap-4607	2	2	kharkiv	GPE
ap-4607	2	3	61022	DATE
ap-4607	2	4	ukraine	GPE
ap-4607	2	5	7, 61050	DATE
ap-4607	2	6	kharkiv	GPE
ap-4607	6	1	1	CARDINAL
ap-4607	10	1	algebraic geometry	ORG
ap-4607	13	1	1	CARDINAL
ap-4607	13	2	0	CARDINAL
ap-4607	15	1	1	CARDINAL
ap-4607	19	1	1	CARDINAL
ap-4607	19	2	2	CARDINAL
ap-4607	20	1	2	CARDINAL
ap-4607	20	2	3	CARDINAL
ap-4607	20	3	4	CARDINAL
ap-4607	23	1	9	CARDINAL
ap-4607	23	2	10	CARDINAL
ap-4607	26	1	2	CARDINAL
ap-4607	26	2	9	CARDINAL
ap-4607	26	3	10	CARDINAL
ap-4607	26	4	1	CARDINAL
ap-4607	28	1	i=1 mi	PERSON
ap-4607	28	2	2	CARDINAL
ap-4607	30	1	1	CARDINAL
ap-4607	30	2	1	CARDINAL
ap-4607	30	3	2	CARDINAL
ap-4607	37	1	i=1 mi	PERSON
ap-4607	40	1	0	CARDINAL
ap-4607	40	2	3	CARDINAL
ap-4607	41	1	3	CARDINAL
ap-4607	41	2	two	CARDINAL
ap-4607	41	3	two	CARDINAL
ap-4607	41	4	cartesian	NORP
ap-4607	42	1	3	CARDINAL
ap-4607	42	2	3a	CARDINAL
ap-4607	43	1	3	CARDINAL
ap-4607	43	2	3a	CARDINAL
ap-4607	44	1	3a	CARDINAL
ap-4607	45	1	404	CARDINAL
ap-4607	45	2	http://ojs.cvut.cz/ojs/index.php/ap	PRODUCT
ap-4607	46	1	57	CARDINAL
ap-4607	47	1	6/2017	CARDINAL
ap-4607	47	2	algebraic geometry	PERSON
ap-4607	48	1	3a	CARDINAL
ap-4607	50	1	3	CARDINAL
ap-4607	51	1	3a	CARDINAL
ap-4607	55	1	aj	PERSON
ap-4607	55	2	i=1,i6=j	PERSON
ap-4607	60	1	4	CARDINAL
ap-4607	62	1	1	CARDINAL
ap-4607	62	2	2	DATE
ap-4607	65	1	4	CARDINAL
ap-4607	66	1	4	CARDINAL
ap-4607	66	2	affine	ORG
ap-4607	67	1	4	CARDINAL
ap-4607	67	2	3a	CARDINAL
ap-4607	68	1	3a	CARDINAL
ap-4607	68	2	4	CARDINAL
ap-4607	69	1	3a	CARDINAL
ap-4607	71	1	1	CARDINAL
ap-4607	71	2	4	CARDINAL
ap-4607	71	3	3a	CARDINAL
ap-4607	72	1	f1	PERSON
ap-4607	72	2	first	ORDINAL
ap-4607	72	3	second	ORDINAL
ap-4607	72	4	3a	CARDINAL
ap-4607	72	5	f2	ORG
ap-4607	72	6	3a	CARDINAL
ap-4607	72	7	f1	PERSON
ap-4607	72	8	4	CARDINAL
ap-4607	72	9	f1	PERSON
ap-4607	72	10	f2	ORG
ap-4607	72	11	⊂	GPE
ap-4607	72	12	f1	PERSON
ap-4607	72	13	f2	ORG
ap-4607	72	14	f2	ORG
ap-4607	73	1	f1	PERSON
ap-4607	73	2	f2)/{∪(ai	NORP
ap-4607	74	1	5	CARDINAL
ap-4607	74	2	11	CARDINAL
ap-4607	74	3	f1	PERSON
ap-4607	74	4	f1	PERSON
ap-4607	75	1	0(f1	CARDINAL
ap-4607	75	2	f2	ORG
ap-4607	76	1	1(f1	CARDINAL
ap-4607	76	2	f2	ORG
ap-4607	76	3	6	CARDINAL
ap-4607	76	4	1(f1	CARDINAL
ap-4607	76	5	f2	ORG
ap-4607	77	1	0(f1	CARDINAL
ap-4607	77	2	f2	ORG
ap-4607	77	3	3a	CARDINAL
ap-4607	78	1	0(f1	CARDINAL
ap-4607	78	2	f2	ORG
ap-4607	79	1	0(f1	CARDINAL
ap-4607	79	2	f2	ORG
ap-4607	79	3	f2	ORG
ap-4607	80	1	1	CARDINAL
ap-4607	80	2	4	CARDINAL
ap-4607	80	3	1(f1	CARDINAL
ap-4607	80	4	f2	ORG
ap-4607	80	5	1(f1	CARDINAL
ap-4607	80	6	f2	ORG
ap-4607	80	7	12	CARDINAL
ap-4607	80	8	13	CARDINAL
ap-4607	81	1	5	CARDINAL
ap-4607	82	1	1(f1	CARDINAL
ap-4607	82	2	f2	ORG
ap-4607	82	3	3	CARDINAL
ap-4607	83	1	1(f1	CARDINAL
ap-4607	83	2	f2	ORG
ap-4607	84	1	4.1	CARDINAL
ap-4607	84	2	1	CARDINAL
ap-4607	84	3	1(f1	CARDINAL
ap-4607	84	4	f2	ORG
ap-4607	85	1	1	CARDINAL
ap-4607	85	2	0	CARDINAL
ap-4607	93	1	7	CARDINAL
ap-4607	93	2	1 +x2 2	QUANTITY
ap-4607	93	3	0	CARDINAL
ap-4607	95	1	7	CARDINAL
ap-4607	97	1	0	CARDINAL
ap-4607	97	2	1 + x2 2)(x2	QUANTITY
ap-4607	98	1	− y1)− x2 =	PERSON
ap-4607	99	1	2 2	CARDINAL
ap-4607	100	1	1y1	CARDINAL
ap-4607	104	1	0	CARDINAL
ap-4607	107	1	2y2	CARDINAL
ap-4607	111	1	0	CARDINAL
ap-4607	112	1	9	CARDINAL
ap-4607	112	2	1	CARDINAL
ap-4607	112	3	− y1x	PERSON
ap-4607	113	1	2	CARDINAL
ap-4607	113	2	1)x1	CARDINAL
ap-4607	114	1	0	CARDINAL
ap-4607	115	1	− x2	PERSON
ap-4607	116	1	2y2	CARDINAL
ap-4607	117	1	0	CARDINAL
ap-4607	118	1	10	CARDINAL
ap-4607	118	2	1	CARDINAL
ap-4607	118	3	0	CARDINAL
ap-4607	118	4	0	CARDINAL
ap-4607	118	5	0	CARDINAL
ap-4607	118	6	0	CARDINAL
ap-4607	118	7	11	CARDINAL
ap-4607	119	1	2	CARDINAL
ap-4607	119	2	1	CARDINAL
ap-4607	119	3	2	CARDINAL
ap-4607	120	1	2y2	CARDINAL
ap-4607	122	1	405	CARDINAL
ap-4607	122	2	a. t. kotvytskiy	PERSON
ap-4607	122	3	s. d. bronza	PERSON
ap-4607	122	4	v. yu	PERSON
ap-4607	124	1	1y	CARDINAL
ap-4607	124	2	2y	CARDINAL
ap-4607	124	3	2 1	CARDINAL
ap-4607	124	4	2y	CARDINAL
ap-4607	124	5	2y	CARDINAL
ap-4607	125	1	12	CARDINAL
ap-4607	125	2	7	CARDINAL
ap-4607	125	3	0	CARDINAL
ap-4607	126	1	5a	CARDINAL
ap-4607	128	1	2 + y2(y2	DATE
ap-4607	128	2	0	CARDINAL
ap-4607	129	1	13	CARDINAL
ap-4607	129	2	two	CARDINAL
ap-4607	129	3	0	CARDINAL
ap-4607	130	1	2 + y2(y2	DATE
ap-4607	131	1	0	CARDINAL
ap-4607	132	1	14	CARDINAL
ap-4607	133	1	zero	CARDINAL
ap-4607	133	2	zero	CARDINAL
ap-4607	135	1	0	CARDINAL
ap-4607	135	2	0	CARDINAL
ap-4607	136	1	15	CARDINAL
ap-4607	136	2	0	CARDINAL
ap-4607	137	1	7	CARDINAL
ap-4607	139	1	1 + x22	QUANTITY
ap-4607	139	2	0	CARDINAL
ap-4607	142	1	0	CARDINAL
ap-4607	143	1	0	CARDINAL
ap-4607	144	1	16	CARDINAL
ap-4607	144	2	16	CARDINAL
ap-4607	144	3	three	CARDINAL
ap-4607	144	4	one	CARDINAL
ap-4607	144	5	0	CARDINAL
ap-4607	144	6	17a)	CARDINAL
ap-4607	144	7	0	CARDINAL
ap-4607	144	8	1− 1 x2 1	QUANTITY
ap-4607	145	1	0	CARDINAL
ap-4607	145	2	17b	CARDINAL
ap-4607	145	3	0	CARDINAL
ap-4607	145	4	0	CARDINAL
ap-4607	145	5	1− 1 x2 1 + x22	QUANTITY
ap-4607	145	6	0	CARDINAL
ap-4607	146	1	18	CARDINAL
ap-4607	146	2	17a	CARDINAL
ap-4607	147	1	7	CARDINAL
ap-4607	148	1	17b	CARDINAL
ap-4607	148	2	two	CARDINAL
ap-4607	149	1	two	CARDINAL
ap-4607	150	1	18	CARDINAL
ap-4607	151	1	2	CARDINAL
ap-4607	151	2	1	CARDINAL
ap-4607	151	3	0	CARDINAL
ap-4607	151	4	19	CARDINAL
ap-4607	151	5	19	CARDINAL
ap-4607	152	1	17b	CARDINAL
ap-4607	152	2	19	CARDINAL
ap-4607	154	1	19	CARDINAL
ap-4607	154	2	1(f1	CARDINAL
ap-4607	154	3	f2	ORG
ap-4607	157	1	2	CARDINAL
ap-4607	157	2	1	CARDINAL
ap-4607	157	3	0	CARDINAL
ap-4607	158	1	20	CARDINAL
ap-4607	160	1	4.2	CARDINAL
ap-4607	160	2	2	CARDINAL
ap-4607	160	3	two	CARDINAL
ap-4607	160	4	m1 = m2	PERSON
ap-4607	160	5	1 2	CARDINAL
ap-4607	162	1	3	CARDINAL
ap-4607	164	1	2	CARDINAL
ap-4607	164	2	1 2	CARDINAL
ap-4607	165	1	1 2 x2	QUANTITY
ap-4607	166	1	2	CARDINAL
ap-4607	166	2	1 2 x2	QUANTITY
ap-4607	166	3	2	CARDINAL
ap-4607	167	1	21	CARDINAL
ap-4607	167	2	21	CARDINAL
ap-4607	167	3	f1	PERSON
ap-4607	167	4	f2	ORG
ap-4607	167	5	x1:	GPE
ap-4607	168	1	+ 2x2 2y1	PERCENT
ap-4607	169	1	2 +	CARDINAL
ap-4607	173	1	2)x2 1 +	DATE
ap-4607	173	2	2x2 2	CARDINAL
ap-4607	173	3	1−	ORDINAL
ap-4607	178	1	1	CARDINAL
ap-4607	178	2	22	CARDINAL
ap-4607	178	3	f2	ORG
ap-4607	179	1	sylvester matrix s1 = s(f1	PERSON
ap-4607	179	2	f2	ORG
ap-4607	180	1	9	CARDINAL
ap-4607	180	2	r1 = dets1	PERSON
ap-4607	183	1	2 +	DATE
ap-4607	183	2	2	CARDINAL
ap-4607	183	3	4a4y2 2	CARDINAL
ap-4607	183	4	4a2y4	CARDINAL
ap-4607	184	1	4a6y2	CARDINAL
ap-4607	185	1	1y 2	CARDINAL
ap-4607	185	2	4a2y2	CARDINAL
ap-4607	185	3	4a2y2 1y2	CARDINAL
ap-4607	185	4	5y3 2 + 4a2y3	DATE
ap-4607	185	5	8a4y3 2	CARDINAL
ap-4607	185	6	4a2y5	CARDINAL
ap-4607	185	7	2 + (−4a4 + 4a6	DATE
ap-4607	188	1	12a2y2	CARDINAL
ap-4607	189	1	2	CARDINAL
ap-4607	189	2	2a2y2	CARDINAL
ap-4607	191	1	2 + 2y2	DATE
ap-4607	191	2	2 + 4(a4	DATE
ap-4607	191	3	2a2y2 1 + y4	DATE
ap-4607	191	4	2 + y4 2)x5 2	DATE
ap-4607	192	1	23	CARDINAL
ap-4607	192	2	406	CARDINAL
ap-4607	192	3	57	CARDINAL
ap-4607	193	1	6/2017	CARDINAL
ap-4607	193	2	r1 ≡ 0	ORG
ap-4607	194	1	three	CARDINAL
ap-4607	194	2	one	CARDINAL
ap-4607	195	1	0	CARDINAL
ap-4607	195	2	2	CARDINAL
ap-4607	195	3	0	CARDINAL
ap-4607	195	4	2	CARDINAL
ap-4607	196	1	1	CARDINAL
ap-4607	197	1	2 +	DATE
ap-4607	197	2	2	CARDINAL
ap-4607	198	1	4a4y2 2	CARDINAL
ap-4607	198	2	4a2y4	CARDINAL
ap-4607	199	1	1y	CARDINAL
ap-4607	199	2	1y2	CARDINAL
ap-4607	199	3	4a2y2 1y2	CARDINAL
ap-4607	199	4	5y3 2 + 4a2y3	DATE
ap-4607	199	5	8a4y3 2	CARDINAL
ap-4607	199	6	4a2y5	CARDINAL
ap-4607	199	7	2 + (−4a4 + 4a6	DATE
ap-4607	202	1	12a2y2	CARDINAL
ap-4607	203	1	2	CARDINAL
ap-4607	203	2	2a2y2	CARDINAL
ap-4607	205	1	2 + 2y2	DATE
ap-4607	205	2	2 + 4(a4	DATE
ap-4607	205	3	2a2y2 1 + y4	DATE
ap-4607	205	4	2 + y4	DATE
ap-4607	205	5	0	CARDINAL
ap-4607	206	1	24	CARDINAL
ap-4607	206	2	zero	CARDINAL
ap-4607	206	3	2	CARDINAL
ap-4607	206	4	0	CARDINAL
ap-4607	207	1	2	CARDINAL
ap-4607	207	2	4a4y2 2	CARDINAL
ap-4607	207	3	4a2y4 2	CARDINAL
ap-4607	207	4	0	CARDINAL
ap-4607	207	5	4a6y2	CARDINAL
ap-4607	208	1	1y 2 2	QUANTITY
ap-4607	208	2	1y2	CARDINAL
ap-4607	208	3	4a2y5 2	CARDINAL
ap-4607	208	4	4a2y2 1y2	CARDINAL
ap-4607	208	5	5y3 2 + 4a2y3	DATE
ap-4607	208	6	8a4y3 2 + 8a4y2	DATE
ap-4607	208	7	0	CARDINAL
ap-4607	211	1	12a2y2	CARDINAL
ap-4607	211	2	0	CARDINAL
ap-4607	211	3	2a2y2	CARDINAL
ap-4607	213	1	2 + 2y2	DATE
ap-4607	213	2	2	CARDINAL
ap-4607	213	3	0	CARDINAL
ap-4607	213	4	2a2y2 1 + y4 1 + 2a2y2	DATE
ap-4607	213	5	2 + y4 2	DATE
ap-4607	213	6	0	CARDINAL
ap-4607	214	1	25	CARDINAL
ap-4607	214	2	0	CARDINAL
ap-4607	214	3	5y3 2	DATE
ap-4607	214	4	0	CARDINAL
ap-4607	215	1	2 + 2y2	CARDINAL
ap-4607	215	2	2	CARDINAL
ap-4607	215	3	0	CARDINAL
ap-4607	215	4	1 + 2y2	CARDINAL
ap-4607	215	5	2 + y4 2	DATE
ap-4607	215	6	0	CARDINAL
ap-4607	216	1	26	CARDINAL
ap-4607	216	2	one	CARDINAL
ap-4607	217	1	0	CARDINAL
ap-4607	218	1	2	CARDINAL
ap-4607	218	2	1	CARDINAL
ap-4607	220	1	4a4(a−	CARDINAL
ap-4607	222	1	1+ +	DATE
ap-4607	222	2	4a2y2 1	CARDINAL
ap-4607	222	3	4a2y2 2)y2	CARDINAL
ap-4607	222	4	−4a2 + 4a4	ORG
ap-4607	223	1	4a2y4	CARDINAL
ap-4607	224	1	4a2y2 2	CARDINAL
ap-4607	224	2	2	CARDINAL
ap-4607	224	3	8a2y2	CARDINAL
ap-4607	224	4	1y 2 2	QUANTITY
ap-4607	225	1	4a2y4	CARDINAL
ap-4607	226	1	2 1 + ( 4a4	DATE
ap-4607	227	1	12a2	CARDINAL
ap-4607	227	2	8a4	CARDINAL
ap-4607	227	3	1 + 4a2y2	DATE
ap-4607	227	4	4a2y2 1 +	CARDINAL
ap-4607	227	5	2a2y3	CARDINAL
ap-4607	227	6	1	CARDINAL
ap-4607	227	7	2 2 +	DATE
ap-4607	227	8	4	CARDINAL
ap-4607	227	9	1	CARDINAL
ap-4607	227	10	4(a4	CARDINAL
ap-4607	228	1	2a2y2 1	DATE
ap-4607	229	1	2 + y4 2)x5 1	DATE
ap-4607	230	1	27	CARDINAL
ap-4607	230	2	21	CARDINAL
ap-4607	230	3	2	CARDINAL
ap-4607	230	4	1	CARDINAL
ap-4607	231	1	•	CARDINAL
ap-4607	231	2	1	CARDINAL
ap-4607	231	3	1(f1	CARDINAL
ap-4607	231	4	f2	ORG
ap-4607	234	1	2	CARDINAL
ap-4607	234	2	1	CARDINAL
ap-4607	234	3	0	CARDINAL
ap-4607	234	4	•	CARDINAL
ap-4607	234	5	2	CARDINAL
ap-4607	234	6	1(f1	CARDINAL
ap-4607	234	7	f2	ORG
ap-4607	234	8	1(f1	CARDINAL
ap-4607	234	9	f2	ORG
ap-4607	234	10	f2	ORG
ap-4607	234	11	28	CARDINAL
ap-4607	234	12	f2	ORG
ap-4607	234	13	0(f1	CARDINAL
ap-4607	234	14	f2)/{∪(ai	NORP
ap-4607	235	1	1(f1	ORDINAL
ap-4607	235	2	f2)/{∪(ai	NORP
ap-4607	236	1	1	CARDINAL
ap-4607	237	1	9	CARDINAL
ap-4607	237	2	10	DATE
ap-4607	237	3	14	CARDINAL
ap-4607	237	4	1(f1	CARDINAL
ap-4607	237	5	f2	ORG
ap-4607	237	6	5	CARDINAL
ap-4607	238	1	2	CARDINAL
ap-4607	238	2	5	CARDINAL
ap-4607	238	3	f2	ORG
ap-4607	238	4	1	CARDINAL
ap-4607	238	5	5	CARDINAL
ap-4607	239	1	0(f1	CARDINAL
ap-4607	239	2	f2	ORG
ap-4607	239	3	0(f1	CARDINAL
ap-4607	239	4	f2	ORG
ap-4607	239	5	3	CARDINAL
ap-4607	239	6	11	CARDINAL
ap-4607	239	7	13	CARDINAL
ap-4607	239	8	15	CARDINAL
ap-4607	240	1	11	CARDINAL
ap-4607	240	2	12	DATE
ap-4607	240	3	15	CARDINAL
ap-4607	241	1	one	CARDINAL
ap-4607	242	1	13	CARDINAL
ap-4607	242	2	affine	ORG
ap-4607	245	1	1	CARDINAL
ap-4607	247	1	g2(x0	PERSON
ap-4607	249	1	degg2(x0	NORP
ap-4607	251	1	zero	CARDINAL
ap-4607	252	1	x0	ORG
ap-4607	252	2	degr1(g1	GPE
ap-4607	252	3	m. proof	PERSON
ap-4607	253	1	the variablesx0 andx2	ORG
ap-4607	254	1	a. t. kotvytskiy	PERSON
ap-4607	254	2	s. d. bronza	PERSON
ap-4607	254	3	v. yu	PERSON
ap-4607	257	1	x0	ORG
ap-4607	257	2	m. really	PERSON
ap-4607	259	1	29	CARDINAL
ap-4607	259	2	1a	CARDINAL
ap-4607	261	1	det sul	PERSON
ap-4607	262	1	30	CARDINAL
ap-4607	262	2	30	CARDINAL
ap-4607	263	1	n+m	DATE
ap-4607	265	1	n∑ i=0	PERSON
ap-4607	265	2	aix n−i 1	PRODUCT
ap-4607	265	3	1	CARDINAL
ap-4607	272	1	tjbj(x0	ORDINAL
ap-4607	274	1	1	CARDINAL
ap-4607	274	2	2	DATE
ap-4607	275	1	j-th row	PERSON
ap-4607	276	1	+ 2	DATE
ap-4607	277	1	1	CARDINAL
ap-4607	277	2	2	DATE
ap-4607	279	1	s.	PERSON
ap-4607	280	1	i=1 i− m∑	PERSON
ap-4607	281	1	1	CARDINAL
ap-4607	281	2	2	CARDINAL
ap-4607	281	3	1	CARDINAL
ap-4607	281	4	2	CARDINAL
ap-4607	281	5	2	CARDINAL
ap-4607	282	1	31	CARDINAL
ap-4607	282	2	det sul	PERSON
ap-4607	283	1	tnm det sul	PERSON
ap-4607	283	2	g2(x0	ORG
ap-4607	284	1	32	CARDINAL
ap-4607	284	2	32	CARDINAL
ap-4607	284	3	30	CARDINAL
ap-4607	284	4	29	CARDINAL
ap-4607	284	5	x0	ORG
ap-4607	285	1	33	CARDINAL
ap-4607	286	1	1	CARDINAL
ap-4607	287	1	7	CARDINAL
ap-4607	287	2	16	CARDINAL
ap-4607	288	1	3	CARDINAL
ap-4607	289	1	3	CARDINAL
ap-4607	292	1	34	CARDINAL
ap-4607	292	2	x2n+1 0 f1	EVENT
ap-4607	292	3	x1 x0	PERSON
ap-4607	292	4	x2 x0	PERSON
ap-4607	294	1	x1 x0	PERSON
ap-4607	294	2	x2 x0	PERSON
ap-4607	295	1	0	CARDINAL
ap-4607	296	1	35	CARDINAL
ap-4607	296	2	coordinatesx0	PERSON
ap-4607	297	1	34	CARDINAL
ap-4607	297	2	c2 → cp 2	ORG
ap-4607	299	1	2	CARDINAL
ap-4607	299	2	2	CARDINAL
ap-4607	300	1	λx1	PERSON
ap-4607	302	1	2	CARDINAL
ap-4607	303	1	0	CARDINAL
ap-4607	303	2	0	CARDINAL
ap-4607	303	3	36	CARDINAL
ap-4607	303	4	2	CARDINAL
ap-4607	305	1	2n	CARDINAL
ap-4607	307	1	at least one	CARDINAL
ap-4607	307	2	zero	CARDINAL
ap-4607	310	1	2	CARDINAL
ap-4607	310	2	three	CARDINAL
ap-4607	311	1	0	CARDINAL
ap-4607	312	1	37	CARDINAL
ap-4607	312	2	2 one	CARDINAL
ap-4607	312	3	0	CARDINAL
ap-4607	312	4	affine	PRODUCT
ap-4607	312	5	2	CARDINAL
ap-4607	313	1	2\a2(h	CARDINAL
ap-4607	313	2	one	CARDINAL
ap-4607	313	3	11	CARDINAL
ap-4607	313	4	15	CARDINAL
ap-4607	315	1	1	CARDINAL
ap-4607	315	2	2	CARDINAL
ap-4607	315	3	1	CARDINAL
ap-4607	316	1	408	CARDINAL
ap-4607	317	1	57	CARDINAL
ap-4607	319	1	6/2017	CARDINAL
ap-4607	320	1	0	CARDINAL
ap-4607	321	1	jacobian	NORP
ap-4607	321	2	zero	CARDINAL
ap-4607	322	1	3	CARDINAL
ap-4607	323	1	jacobian	NORP
ap-4607	323	2	zero	CARDINAL
ap-4607	324	1	3	CARDINAL
ap-4607	325	1	1	CARDINAL
ap-4607	326	1	37	CARDINAL
ap-4607	326	2	0	CARDINAL
ap-4607	326	3	2n	CARDINAL
ap-4607	328	1	37	CARDINAL
ap-4607	328	2	form	ORG
ap-4607	328	3	−x0y1	GPE
ap-4607	330	1	−x0aj	CARDINAL
ap-4607	331	1	0	CARDINAL
ap-4607	332	1	−x0bj	CARDINAL
ap-4607	332	2	38	CARDINAL
ap-4607	338	1	1 +x2 2	QUANTITY
ap-4607	338	2	0	CARDINAL
ap-4607	339	1	1 +x2 2	QUANTITY
ap-4607	339	2	1 +x2 2	QUANTITY
ap-4607	342	1	39	CARDINAL
ap-4607	342	2	two	CARDINAL
ap-4607	343	1	−ic	PRODUCT
ap-4607	344	1	2	CARDINAL
ap-4607	344	2	3	CARDINAL
ap-4607	344	3	5	CARDINAL
ap-4607	344	4	degf1	PERSON
ap-4607	345	1	2n	CARDINAL
ap-4607	346	1	36	CARDINAL
ap-4607	346	2	2n + 1)2	CARDINAL
ap-4607	346	3	2q	CARDINAL
ap-4607	346	4	2n	CARDINAL
ap-4607	347	1	36	CARDINAL
ap-4607	347	2	f2	ORG
ap-4607	348	1	2n + 1)2	QUANTITY
ap-4607	348	2	2q	CARDINAL
ap-4607	349	1	2n + 1)2	QUANTITY
ap-4607	349	2	2q	CARDINAL
ap-4607	349	3	2n	CARDINAL
ap-4607	351	1	40	CARDINAL
ap-4607	351	2	−1	DATE
ap-4607	351	3	2	CARDINAL
ap-4607	351	4	x0	CARDINAL
ap-4607	352	1	1	CARDINAL
ap-4607	353	1	f2	ORG
ap-4607	354	1	0(f1	CARDINAL
ap-4607	354	2	f2	ORG
ap-4607	355	1	4n2	CARDINAL
ap-4607	357	1	41	CARDINAL
ap-4607	357	2	f1	PERSON
ap-4607	357	3	f2	ORG
ap-4607	358	1	f1	PERSON
ap-4607	358	2	f2	ORG
ap-4607	359	1	9	CARDINAL
ap-4607	360	1	3	CARDINAL
ap-4607	360	2	9	CARDINAL
ap-4607	360	3	10	CARDINAL
ap-4607	362	1	1	CARDINAL
ap-4607	362	2	1	CARDINAL
ap-4607	362	3	2	CARDINAL
ap-4607	362	4	9	CARDINAL
ap-4607	362	5	10	DATE
ap-4607	362	6	14	CARDINAL
ap-4607	363	1	2	CARDINAL
ap-4607	363	2	2	CARDINAL
ap-4607	363	3	3	CARDINAL
ap-4607	363	4	17	CARDINAL
ap-4607	364	1	6	CARDINAL
ap-4607	364	2	1	CARDINAL
ap-4607	364	3	0	CARDINAL
ap-4607	365	1	1	CARDINAL
ap-4607	365	2	1	CARDINAL
ap-4607	365	3	1	CARDINAL
ap-4607	365	4	1	CARDINAL
ap-4607	367	1	18	CARDINAL
ap-4607	368	1	18	CARDINAL
ap-4607	368	2	newton	ORG
ap-4607	371	1	a. appendix let	PERSON
ap-4607	371	2	f(x	PRODUCT
ap-4607	371	3	two	CARDINAL
ap-4607	371	4	f(x	ORG
ap-4607	371	5	x0	ORG
ap-4607	372	1	taylor	PERSON
ap-4607	374	1	k)(x− x0	PERSON
ap-4607	374	2	y − y0	PERSON
ap-4607	374	3	42	CARDINAL
ap-4607	374	4	409	CARDINAL
ap-4607	374	5	a. t. kotvytskiy	PERSON
ap-4607	374	6	s. d. bronza	PERSON
ap-4607	374	7	v. yu	PERSON
ap-4607	375	1	acta polytechnica	PERSON
ap-4607	375	2	k)(x− x0	PERSON
ap-4607	375	3	y − y0	PERSON
ap-4607	376	1	n∑ k=1 ci	PERSON
ap-4607	377	1	k ∂kf(x0	PERSON
ap-4607	378	1	− y0)i	PERSON
ap-4607	378	2	43	CARDINAL
ap-4607	378	3	f(x	ORG
ap-4607	379	1	f(x	ORG
ap-4607	379	2	andm = deg f(x	PERSON
ap-4607	379	3	1a	CARDINAL
ap-4607	380	1	f(x	ORG
ap-4607	380	2	0	CARDINAL
ap-4607	381	1	•	CARDINAL
ap-4607	381	2	0	CARDINAL
ap-4607	381	3	•	CARDINAL
ap-4607	381	4	x0	ORG
ap-4607	381	5	y − y0	PERSON
ap-4607	381	6	1	CARDINAL
ap-4607	381	7	2	DATE
ap-4607	382	1	1	CARDINAL
ap-4607	382	2	•	CARDINAL
ap-4607	382	3	− x0	PERSON
ap-4607	382	4	y − y0	PERSON
ap-4607	382	5	x0	ORG
ap-4607	382	6	mult(f(x0	GPE
ap-4607	383	1	= s.	PERSON
ap-4607	383	2	0	CARDINAL
ap-4607	383	3	0	DATE
ap-4607	383	4	f(x	ORG
ap-4607	385	1	• f(0	PERSON
ap-4607	385	2	0	CARDINAL
ap-4607	385	3	•	CARDINAL
ap-4607	385	4	i)(x	ORG
ap-4607	385	5	1	CARDINAL
ap-4607	385	6	2	DATE
ap-4607	385	7	1	CARDINAL
ap-4607	385	8	•	CARDINAL
ap-4607	385	9	s)(x	PERSON
ap-4607	385	10	0	CARDINAL
ap-4607	386	1	zero	CARDINAL
ap-4607	387	1	2a	CARDINAL
ap-4607	388	1	f(x	ORG
ap-4607	389	1	44	DATE
ap-4607	389	2	y0	GPE
ap-4607	390	1	x0	ORG
ap-4607	390	2	44	CARDINAL
ap-4607	390	3	g)(x0, y0	ORG
ap-4607	393	1	12	CARDINAL
ap-4607	393	2	19	DATE
ap-4607	393	3	20	CARDINAL
ap-4607	394	1	3a	CARDINAL
ap-4607	395	1	f(x	ORG
ap-4607	396	1	f(x	ORG
ap-4607	397	1	0	CARDINAL
ap-4607	397	2	0	CARDINAL
ap-4607	397	3	i=0 m∏ j=0	GPE
ap-4607	397	4	45	CARDINAL
ap-4607	397	5	f(x	ORG
ap-4607	398	1	∑n i=0	PERSON
ap-4607	398	2	aix n−i	PERSON
ap-4607	399	1	6=	CARDINAL
ap-4607	399	2	0	CARDINAL
ap-4607	400	1	f(x	ORG
ap-4607	401	1	45	CARDINAL
ap-4607	403	1	two	CARDINAL
ap-4607	404	1	one	CARDINAL
ap-4607	406	1	4a	CARDINAL
ap-4607	407	1	f(x	ORG
ap-4607	409	1	∑n i=0	PERSON
ap-4607	409	2	aix n−i	PERSON
ap-4607	410	1	s(f	ORG
ap-4607	410	2	aj−i	PERSON
ap-4607	410	3	0 ≤	QUANTITY
ap-4607	413	1	1	CARDINAL
ap-4607	414	1	j = 1	PERSON
ap-4607	416	1	n+m	DATE
ap-4607	417	1	0 ≤ j −	QUANTITY
ap-4607	418	1	1	CARDINAL
ap-4607	418	2	n+m	DATE
ap-4607	418	3	0	DATE
ap-4607	418	4	46) i.e.	DATE
ap-4607	418	5	s(f	ORG
ap-4607	419	1	a1	PERSON
ap-4607	420	1	0 · ·	PERCENT
ap-4607	421	1	0 0	DATE
ap-4607	421	2	0 a0 a1	PERSON
ap-4607	422	1	0 0	DATE
ap-4607	425	1	0 b0	MONEY
ap-4607	425	2	bm 	PERSON
ap-4607	426	1	47	CARDINAL
ap-4607	426	2	sul(f	ORG
ap-4607	427	1	1a	CARDINAL
ap-4607	428	1	r(f	PERSON
ap-4607	429	1	s(f	ORG
ap-4607	430	1	19	CARDINAL
ap-4607	430	2	20	CARDINAL
ap-4607	431	1	2a	CARDINAL
ap-4607	434	1	0	CARDINAL
ap-4607	435	1	48	CARDINAL
ap-4607	435	2	13	CARDINAL
ap-4607	436	1	3a	CARDINAL
ap-4607	437	1	φ2	GPE
ap-4607	437	2	•	CARDINAL
ap-4607	437	3	•	CARDINAL
ap-4607	437	4	•	CARDINAL
ap-4607	438	1	12	CARDINAL
ap-4607	439	1	410	CARDINAL
ap-4607	439	2	57	CARDINAL
ap-4607	440	1	6/2017	CARDINAL
ap-4607	440	2	4a	CARDINAL
ap-4607	443	1	j=0	GPE
ap-4607	444	1	1x	CARDINAL
ap-4607	444	2	j 2	PERSON
ap-4607	446	1	1x	CARDINAL
ap-4607	446	2	2	CARDINAL
ap-4607	447	1	6=	DATE
ap-4607	447	2	g0m	ORG
ap-4607	447	3	6= 0	DATE
ap-4607	448	1	degr1	PERSON
ap-4607	449	1	deg g(x1	PERSON
ap-4607	449	2	49	CARDINAL
ap-4607	449	3	12	CARDINAL
ap-4607	450	1	5a	CARDINAL
ap-4607	452	1	12	CARDINAL
ap-4607	453	1	5a	CARDINAL
ap-4607	455	1	1x	CARDINAL
ap-4607	455	2	j 2	PERSON
ap-4607	455	3	k.	PERSON
ap-4607	458	1	6a	CARDINAL
ap-4607	462	1	∂xi 1 r1	ORG
ap-4607	463	1	0	CARDINAL
ap-4607	463	2	∂xi 2 r2	PERSON
ap-4607	464	1	0	CARDINAL
ap-4607	464	2	50	CARDINAL
ap-4607	464	3	1	CARDINAL
ap-4607	464	4	only zero	CARDINAL
ap-4607	465	1	50	CARDINAL
ap-4607	466	1	7	CARDINAL
ap-4607	467	1	7	CARDINAL
ap-4607	467	2	16	CARDINAL
ap-4607	468	1	7	CARDINAL
ap-4607	469	1	1	CARDINAL
ap-4607	469	2	e. y. bannikova	PERSON
ap-4607	469	3	a. t. kotvytskiy	PERSON
ap-4607	470	1	three	CARDINAL
ap-4607	471	1	445(4):4435–4442, 2014	DATE
ap-4607	473	1	2	CARDINAL
ap-4607	473	2	a. t. kotvytskiy	PERSON
ap-4607	475	1	184(1):160–174,	DATE
ap-4607	475	2	2015	DATE
ap-4607	477	1	3	CARDINAL
ap-4607	477	2	a. cassan	PERSON
ap-4607	479	1	491(2):587–595, 2008	DATE
ap-4607	481	1	4	CARDINAL
ap-4607	481	2	a. weiss	PERSON
ap-4607	482	1	two	CARDINAL
ap-4607	483	1	164(2):237–259, 1986	DATE
ap-4607	484	1	5	CARDINAL
ap-4607	484	2	a. t. kotvytskiy	PERSON
ap-4607	484	3	s. d. bronza	PERSON
ap-4607	484	4	k. d. nerushenko	PERSON
ap-4607	485	1	yogo	NORP
ap-4607	486	1	doslidzhennya	PERSON
ap-4607	487	1	naukovyx prac	PERSON
ap-4607	488	1	198–213	CARDINAL
ap-4607	488	2	vinnytsia	GPE
ap-4607	488	3	2017	DATE
ap-4607	489	1	6	CARDINAL
ap-4607	489	2	a. t. kotvytskiy	PERSON
ap-4607	489	3	s. d. bronza	PERSON
ap-4607	489	4	s. r. vovk	PERSON
ap-4607	491	1	visnyk khnu	PERSON
ap-4607	491	2	serija	PERSON
ap-4607	491	3	2016	DATE
ap-4607	492	1	7	CARDINAL
ap-4607	492	2	s. d. bronza	PERSON
ap-4607	492	3	a. t. kotvytskiy	PERSON
ap-4607	494	1	1	CARDINAL
ap-4607	496	1	visnyk khnu	PERSON
ap-4607	496	2	seriya	PERSON
ap-4607	496	3	2017	DATE
ap-4607	497	1	8	CARDINAL
ap-4607	497	2	a. t. kotvytskiy	PERSON
ap-4607	497	3	s. d. bronza	PERSON
ap-4607	499	1	odessa	ORG
ap-4607	499	2	29:31–33	CARDINAL
ap-4607	499	3	2016	DATE
ap-4607	500	1	doi:0.18524/1810-4215.2016.29.84958	ORG
ap-4607	501	1	9	CARDINAL
ap-4607	501	2	a. f. zakharov.	PERSON
ap-4607	504	1	russian	NORP
ap-4607	505	1	janus-k	PERSON
ap-4607	505	2	moscow	GPE
ap-4607	505	3	1997	DATE
ap-4607	506	1	10	CARDINAL
ap-4607	506	2	j. ehlers	PERSON
ap-4607	506	3	e. falco	PERSON
ap-4607	508	1	second	ORDINAL
ap-4607	508	2	springer-verlag	PERSON
ap-4607	508	3	berlin	GPE
ap-4607	508	4	heidelberg	GPE
ap-4607	508	5	1999	DATE
ap-4607	509	1	11	CARDINAL
ap-4607	509	2	i. v. arzhantcev	PERSON
ap-4607	510	1	bazisy grebnera	PERSON
ap-4607	512	1	russian	NORP
ap-4607	513	1	moscow	GPE
ap-4607	513	2	2003	DATE
ap-4607	514	1	12	CARDINAL
ap-4607	514	2	r. j. walker	PERSON
ap-4607	515	1	algebraic curves	PERSON
ap-4607	516	1	new york	GPE
ap-4607	516	2	1978	DATE
ap-4607	517	1	13	CARDINAL
ap-4607	517	2	e. kalinina	PERSON
ap-4607	517	3	a. j. uteshev	PERSON
ap-4607	518	1	teoria iskluchenij	PERSON
ap-4607	518	2	russian	NORP
ap-4607	519	1	nii chimii spbgu saint petersburg	ORG
ap-4607	519	2	2002	DATE
ap-4607	520	1	14	CARDINAL
ap-4607	521	1	a. a. minakov	PERSON
ap-4607	522	1	russian	NORP
ap-4607	523	1	naukova dumka	PERSON
ap-4607	523	2	kiev	GPE
ap-4607	523	3	1989	DATE
ap-4607	524	1	15	CARDINAL
ap-4607	524	2	m. reid	PERSON
ap-4607	525	1	algebraic geometry	PERSON
ap-4607	526	1	university of warwick	ORG
ap-4607	526	2	2013	DATE
ap-4607	527	1	16	CARDINAL
ap-4607	527	2	s. d. bronza	PERSON
ap-4607	528	1	kriteriy neprivodimosti	ORG
ap-4607	528	2	mnogochlenov ot dvuh	GPE
ap-4607	528	3	nad	NORP
ap-4607	528	4	polem kompleksnih	PERSON
ap-4607	528	5	russian	LANGUAGE
ap-4607	529	1	naukovyx prac’	PERSON
ap-4607	530	1	114–115	CARDINAL
ap-4607	531	1	ukrduzt	ORG
ap-4607	531	2	2016	DATE
ap-4607	532	1	17	CARDINAL
ap-4607	532	2	s. h. phie	PERSON
ap-4607	534	1	484(1):63–69, 1997	DATE
ap-4607	536	1	18	CARDINAL
ap-4607	536	2	a. t. kotvytskiy	PERSON
ap-4607	536	3	s. d. bronza	PERSON
ap-4607	538	1	astroparticle physics	ORG
ap-4607	538	2	12	CARDINAL
ap-4607	539	1	odessa international	ORG
ap-4607	539	2	2017	DATE
ap-4607	540	1	19	CARDINAL
ap-4607	540	2	b. l. van der waerden	PERSON
ap-4607	542	1	new york	GPE
ap-4607	542	2	frederic ungar publishing co.	ORG
ap-4607	542	3	1950	DATE
ap-4607	543	1	20	CARDINAL
ap-4607	543	2	s. lang	PERSON
ap-4607	545	1	third	ORDINAL
ap-4607	546	1	columbia university	ORG
ap-4607	547	1	new york	GPE
ap-4607	547	2	1965	DATE
ap-4607	548	1	411	CARDINAL
ap-4607	549	1	57(6):404–411	CARDINAL
ap-4607	549	2	2017 1	DATE
ap-4607	549	3	2	CARDINAL
ap-4607	549	4	3	CARDINAL
ap-4607	549	5	4	CARDINAL
ap-4607	549	6	4.1 1	CARDINAL
ap-4607	549	7	4.2 2	CARDINAL
ap-4607	549	8	5	CARDINAL
ap-4607	549	9	6	CARDINAL