id sid eid entity type cana-3900 1 1 1074 CARDINAL cana-3900 1 2 32 CARDINAL cana-3900 2 1 9s CARDINAL cana-3900 2 2 2025 CARDINAL cana-3900 2 3 345 CARDINAL cana-3900 3 1 2g.sugantha DATE cana-3900 3 2 3 CARDINAL cana-3900 3 3 1research CARDINAL cana-3900 3 4 21122102092007 DATE cana-3900 4 1 kamaraj college ORG cana-3900 4 2 628003 DATE cana-3900 4 3 manonmaniam sundaranar university ORG cana-3900 4 4 tirunelveli NORP cana-3900 4 5 627012 DATE cana-3900 5 1 2assistant CARDINAL cana-3900 5 2 pope PERSON cana-3900 5 3 tamil NORP cana-3900 5 4 india GPE cana-3900 7 1 manonmaniam sundaranar university ORG cana-3900 7 2 tirunelveli NORP cana-3900 7 3 627012 DATE cana-3900 8 1 kamaraj college ORG cana-3900 8 2 628003 DATE cana-3900 9 1 manonmaniam sundaranar university ORG cana-3900 9 2 tirunelveli NORP cana-3900 9 3 627012 DATE cana-3900 9 4 14-11-2024 CARDINAL cana-3900 9 5 25 CARDINAL cana-3900 12 1 xny= PERSON cana-3900 14 1 16y30 CARDINAL cana-3900 15 1 1 CARDINAL cana-3900 15 2 two CARDINAL cana-3900 15 3 abelian NORP cana-3900 15 4 0 CARDINAL cana-3900 16 1 0n CARDINAL cana-3900 17 1 0 CARDINAL cana-3900 17 2 zero CARDINAL cana-3900 17 3 0 CARDINAL cana-3900 17 4 ∈ 𝑁π‘₯ ORG cana-3900 17 5 ∈ ORG cana-3900 17 6 ∈ ORG cana-3900 17 7 𝑁𝑀 βŠ‚ 𝑀 ORG cana-3900 17 8 𝑀𝑁 βŠ‚ ORG cana-3900 17 9 j of n. 𝐽2 PERSON cana-3900 18 1 𝐼 β‡’ 𝐽 βŠ‚ 𝐼 ORG cana-3900 20 1 ∈ ORG cana-3900 20 2 0 CARDINAL cana-3900 20 3 0 CARDINAL cana-3900 20 4 0 CARDINAL cana-3900 21 1 ∈ 𝐼 β‡’ ORG cana-3900 22 1 3 CARDINAL cana-3900 22 2 4 CARDINAL cana-3900 23 1 n. 𝑓(π‘₯ PERSON cana-3900 24 1 n. mailto:sssivanthi@gmail.com ORG cana-3900 24 2 1074 CARDINAL cana-3900 24 3 32 CARDINAL cana-3900 26 1 9s CARDINAL cana-3900 26 2 2025 CARDINAL cana-3900 26 3 346 CARDINAL cana-3900 26 4 pilz GPE cana-3900 26 5 3 CARDINAL cana-3900 27 1 at least two CARDINAL cana-3900 28 1 p.249 pilz ORG cana-3900 28 2 3 CARDINAL cana-3900 28 3 1.15 CARDINAL cana-3900 28 4 pilz ORG cana-3900 29 1 3 CARDINAL cana-3900 30 1 𝑀𝑐 PERSON cana-3900 30 2 2 CARDINAL cana-3900 30 3 zero CARDINAL cana-3900 31 1 zero CARDINAL cana-3900 31 2 2 CARDINAL cana-3900 31 3 integer k. PERSON cana-3900 32 1 zero CARDINAL cana-3900 33 1 4 CARDINAL cana-3900 33 2 3 CARDINAL cana-3900 33 3 2 CARDINAL cana-3900 33 4 2 CARDINAL cana-3900 35 1 3.2 CARDINAL cana-3900 35 2 4 CARDINAL cana-3900 36 1 k(2 PERSON cana-3900 36 2 n= n0 ORG cana-3900 37 1 ifp ORG cana-3900 37 2 ifp ORG cana-3900 38 1 2.3 CARDINAL cana-3900 38 2 4 CARDINAL cana-3900 39 1 k PERSON cana-3900 39 2 3 CARDINAL cana-3900 39 3 zero CARDINAL cana-3900 39 4 ifp ORG cana-3900 39 5 9.3 CARDINAL cana-3900 39 6 3 CARDINAL cana-3900 40 1 k PERSON cana-3900 40 2 4 DATE cana-3900 40 3 14 CARDINAL cana-3900 40 4 2 CARDINAL cana-3900 41 1 3.1 CARDINAL cana-3900 43 1 3.1.1 CARDINAL cana-3900 45 1 klein GPE cana-3900 45 2 four CARDINAL cana-3900 45 3 0 CARDINAL cana-3900 46 1 12 CARDINAL cana-3900 46 2 33 CARDINAL cana-3900 48 1 1074 CARDINAL cana-3900 48 2 32 CARDINAL cana-3900 49 1 9s CARDINAL cana-3900 49 2 2025 CARDINAL cana-3900 49 3 347 CARDINAL cana-3900 49 4 0 CARDINAL cana-3900 50 1 0 CARDINAL cana-3900 50 2 0 CARDINAL cana-3900 50 3 0 CARDINAL cana-3900 51 1 0 CARDINAL cana-3900 52 1 0 CARDINAL cana-3900 53 1 klein GPE cana-3900 53 2 four CARDINAL cana-3900 53 3 0 CARDINAL cana-3900 54 1 11 CARDINAL cana-3900 54 2 33 CARDINAL cana-3900 56 1 0 CARDINAL cana-3900 56 2 0 CARDINAL cana-3900 56 3 0 CARDINAL cana-3900 56 4 0 CARDINAL cana-3900 58 1 β‰  π‘π‘Ž2𝑏2 3.2 PERSON cana-3900 59 1 3.2.1 CARDINAL cana-3900 60 1 zero CARDINAL cana-3900 64 1 1 CARDINAL cana-3900 65 1 1 CARDINAL cana-3900 65 2 n. β‡’ PERSON cana-3900 65 3 0 CARDINAL cana-3900 65 4 0 CARDINAL cana-3900 66 1 zero CARDINAL cana-3900 67 1 1 CARDINAL cana-3900 67 2 2 CARDINAL cana-3900 68 1 ∈ ORG cana-3900 68 2 ∈ ORG cana-3900 69 1 2 CARDINAL cana-3900 70 1 𝑧π‘₯2 TIME cana-3900 70 2 0 CARDINAL cana-3900 71 1 k (2) ORG cana-3900 71 2 π‘₯(π‘₯ βˆ’ PERSON cana-3900 72 1 0 CARDINAL cana-3900 73 1 2 CARDINAL cana-3900 73 2 0 CARDINAL cana-3900 74 1 0 CARDINAL cana-3900 75 1 ∈ ORG cana-3900 78 1 k (4 ORG cana-3900 80 1 1074 CARDINAL cana-3900 80 2 32 CARDINAL cana-3900 81 1 9s CARDINAL cana-3900 81 2 2025 CARDINAL cana-3900 81 3 348 CARDINAL cana-3900 82 1 2 CARDINAL cana-3900 82 2 ifp ORG cana-3900 84 1 3.2.3 CARDINAL cana-3900 90 1 𝑛π‘₯2𝑦2 NORP cana-3900 90 2 3 CARDINAL cana-3900 91 1 𝑓(𝑛)𝑓(π‘₯2)𝑓(𝑦2 ORDINAL cana-3900 91 2 ∈ ORG cana-3900 91 3 ′𝑁 ORG cana-3900 91 4 βŠ† CARDINAL cana-3900 92 1 4 CARDINAL cana-3900 92 2 βŠ† CARDINAL cana-3900 92 3 5 CARDINAL cana-3900 92 4 4 CARDINAL cana-3900 92 5 5 CARDINAL cana-3900 92 6 n β€² ORG cana-3900 94 1 3.2.3we CARDINAL cana-3900 94 2 3.2.4 DATE cana-3900 96 1 1.62 CARDINAL cana-3900 96 2 p.26 ORG cana-3900 96 3 pilz ORG cana-3900 96 4 3 CARDINAL cana-3900 96 5 3.2.3 CARDINAL cana-3900 98 1 3.2.5 CARDINAL cana-3900 103 1 7 CARDINAL cana-3900 104 1 𝑁π‘₯𝑁 ORG cana-3900 104 2 𝑁𝑁π‘₯21 CARDINAL cana-3900 105 1 6 CARDINAL cana-3900 106 1 βŠ† CARDINAL cana-3900 106 2 𝑁π‘₯𝑁 ORG cana-3900 106 3 ………… PRODUCT cana-3900 108 1 7 CARDINAL cana-3900 109 1 βŠ† CARDINAL cana-3900 109 2 βŠ†οƒ₯ CARDINAL cana-3900 110 1 οƒŽax ORG cana-3900 111 1 βŠ† CARDINAL cana-3900 112 1 1074 CARDINAL cana-3900 112 2 32 CARDINAL cana-3900 113 1 9s CARDINAL cana-3900 113 2 2025 CARDINAL cana-3900 113 3 349 CARDINAL cana-3900 118 1 zero CARDINAL cana-3900 118 2 βŠ† CARDINAL cana-3900 118 3 3.2.5 CARDINAL cana-3900 119 1 3.2.7 CARDINAL cana-3900 120 1 3.2.8 CARDINAL cana-3900 121 1 ifp ORG cana-3900 124 1 9.2 pilz PERSON cana-3900 125 1 3 CARDINAL cana-3900 125 2 n in n PRODUCT cana-3900 125 3 𝐼𝑁 βŠ† 𝐼 ORG cana-3900 125 4 zero CARDINAL cana-3900 125 5 n. ORG cana-3900 125 6 𝑁𝐼 ORG cana-3900 125 7 βŠ† PRODUCT cana-3900 125 8 ∈ ORG cana-3900 126 1 9 CARDINAL cana-3900 126 2 𝑁𝐼 ORG cana-3900 126 3 3.2.9 CARDINAL cana-3900 127 1 3.2.10 CARDINAL cana-3900 127 2 ∈ ORG cana-3900 127 3 k (4 ORG cana-3900 127 4 0 CARDINAL cana-3900 128 1 3.2.11 DATE cana-3900 129 1 βŠ† CARDINAL cana-3900 131 1 2 CARDINAL cana-3900 132 1 10).also ORDINAL cana-3900 132 2 0 CARDINAL cana-3900 133 1 0 CARDINAL cana-3900 133 2 0 CARDINAL cana-3900 136 1 0 CARDINAL cana-3900 137 1 zero CARDINAL cana-3900 138 1 0 CARDINAL cana-3900 139 1 4 CARDINAL cana-3900 140 1 11).from CARDINAL cana-3900 140 2 10 CARDINAL cana-3900 140 3 11 CARDINAL cana-3900 140 4 βŠ† CARDINAL cana-3900 141 1 3.2.12 CARDINAL cana-3900 142 1 1074 CARDINAL cana-3900 142 2 32 CARDINAL cana-3900 143 1 9s CARDINAL cana-3900 143 2 2025 CARDINAL cana-3900 143 3 350 CARDINAL cana-3900 149 1 ∈ ORG cana-3900 151 1 ∈ ORG cana-3900 151 2 3.2.1(iii PRODUCT cana-3900 151 3 3.2.2 CARDINAL cana-3900 151 4 π‘₯(π‘₯ βˆ’ PERSON cana-3900 152 1 0 CARDINAL cana-3900 153 1 0 CARDINAL cana-3900 153 2 0i.e CARDINAL cana-3900 155 1 3.2.14 CARDINAL cana-3900 156 1 𝑆’-𝛿1near DATE cana-3900 160 1 3.2.12 CARDINAL cana-3900 161 1 ifp ORG cana-3900 164 1 0 CARDINAL cana-3900 164 2 ifp ORG cana-3900 166 1 3.2.16 CARDINAL cana-3900 167 1 zero CARDINAL cana-3900 168 1 βŠ† CARDINAL cana-3900 169 1 βŠ† CARDINAL cana-3900 174 1 1)].i.e ORG cana-3900 179 1 3.2.16 CARDINAL cana-3900 180 1 3.2.18 CARDINAL cana-3900 183 1 k (2 ORG cana-3900 183 2 ifp ORG cana-3900 184 1 βŠ† CARDINAL cana-3900 184 2 k(3 PERSON cana-3900 186 1 first ORDINAL cana-3900 186 2 𝑁π‘₯ ORG cana-3900 187 1 0 ∢ 𝑁π‘₯ PRODUCT cana-3900 188 1 𝑁π‘₯ ORG cana-3900 190 1 βŠ‚ GPE cana-3900 190 2 12 CARDINAL cana-3900 190 3 ∈ ORG cana-3900 190 4 0 CARDINAL cana-3900 191 1 13 CARDINAL cana-3900 191 2 𝑦𝑓(π‘₯)π‘₯)𝑁𝑓(π‘₯)π‘₯ NORP cana-3900 191 3 0 CARDINAL cana-3900 192 1 0 ∢ 𝑁π‘₯ ORG cana-3900 192 2 0 CARDINAL cana-3900 192 3 …… PRODUCT cana-3900 192 4 14 CARDINAL cana-3900 192 5 ifp ORG cana-3900 192 6 1074 CARDINAL cana-3900 192 7 32 CARDINAL cana-3900 193 1 9s CARDINAL cana-3900 193 2 2025 CARDINAL cana-3900 193 3 351 CARDINAL cana-3900 193 4 13 CARDINAL cana-3900 193 5 14 CARDINAL cana-3900 194 1 0 CARDINAL cana-3900 195 1 0 CARDINAL cana-3900 195 2 0 CARDINAL cana-3900 196 1 ∈ 𝑁π‘₯ ORG cana-3900 197 1 ………… PRODUCT cana-3900 198 1 15 CARDINAL cana-3900 198 2 12 CARDINAL cana-3900 198 3 15 CARDINAL cana-3900 198 4 𝑁π‘₯ ORG cana-3900 200 1 3.2.19 CARDINAL cana-3900 202 1 0 CARDINAL cana-3900 202 2 0 CARDINAL cana-3900 203 1 3.2.20 CARDINAL cana-3900 206 1 3.2.18 CARDINAL cana-3900 207 1 ifp ORG cana-3900 207 2 ∈ 𝐼 i.e. ORG cana-3900 209 1 3.2.21 CARDINAL cana-3900 210 1 𝑦π‘₯)2 ORG cana-3900 211 1 𝑦(π‘₯𝑦)π‘₯ CARDINAL cana-3900 212 1 3.2.19 CARDINAL cana-3900 212 2 𝑦π‘₯)2 ORG cana-3900 212 3 ∈ PRODUCT cana-3900 214 1 3.3 CARDINAL cana-3900 215 1 3.3.1 CARDINAL cana-3900 219 1 first ORDINAL cana-3900 220 1 zero CARDINAL cana-3900 221 1 0 ∢ 𝑒)π‘’βˆˆπ½ ORG cana-3900 222 1 𝐼 β‰  PERSON cana-3900 222 2 0 CARDINAL cana-3900 224 1 16 CARDINAL cana-3900 224 2 0 CARDINAL cana-3900 226 1 2 CARDINAL cana-3900 227 1 16 CARDINAL cana-3900 227 2 0 CARDINAL cana-3900 228 1 17 CARDINAL cana-3900 229 1 zero CARDINAL cana-3900 232 1 1 CARDINAL cana-3900 232 2 1 CARDINAL cana-3900 233 1 1 CARDINAL cana-3900 234 1 0 β‡’ PERCENT cana-3900 234 2 ∈ ORG cana-3900 234 3 βŠ† CARDINAL cana-3900 235 1 0 CARDINAL cana-3900 235 2 nn ORG cana-3900 237 1 18 CARDINAL cana-3900 237 2 .also ORG cana-3900 237 3 𝑁𝑑 β‰  PERSON cana-3900 237 4 βŠ† CARDINAL cana-3900 238 1 18 CARDINAL cana-3900 239 1 8.3 CARDINAL cana-3900 240 1 3 CARDINAL cana-3900 241 1 3.1 CARDINAL cana-3900 241 2 3.3.2 CARDINAL cana-3900 242 1 zero CARDINAL cana-3900 243 1 1074 CARDINAL cana-3900 243 2 32 CARDINAL cana-3900 245 1 9s CARDINAL cana-3900 245 2 352 CARDINAL cana-3900 246 1 3.3.3 PRODUCT cana-3900 249 1 3.2.4 DATE cana-3900 252 1 3.3.1 CARDINAL cana-3900 253 1 3.3.4 CARDINAL cana-3900 254 1 8.11 CARDINAL cana-3900 254 2 3 CARDINAL cana-3900 254 3 abelian NORP cana-3900 255 1 abelian NORP cana-3900 260 1 3.2.16 CARDINAL cana-3900 260 2 3.3.4 CARDINAL cana-3900 260 3 abelian NORP cana-3900 262 1 n,π‘₯𝑛 ORG cana-3900 262 2 𝑁π‘₯2𝑦2hence ORG cana-3900 263 1 3.3.6 CARDINAL cana-3900 264 1 zero CARDINAL cana-3900 266 1 3.3.2 CARDINAL cana-3900 267 1 abelian NORP cana-3900 268 1 1 CARDINAL cana-3900 269 1 z. 104 PERSON cana-3900 269 2 1968 DATE cana-3900 269 3 364 CARDINAL cana-3900 270 1 2 CARDINAL cana-3900 270 2 mccoy PERSON cana-3900 270 3 macmillan & co. ORG cana-3900 270 4 1970 DATE cana-3900 271 1 3 CARDINAL cana-3900 271 2 g. pilz PERSON cana-3900 271 3 north holland ORG cana-3900 271 4 american elsevier ORG cana-3900 271 5 amsterdam GPE cana-3900 271 6 1983 DATE cana-3900 272 1 4 CARDINAL cana-3900 272 2 s. suryanarayanan PERSON cana-3900 272 3 n. ganesan PERSON cana-3900 272 4 indian NORP cana-3900 273 1 19 CARDINAL cana-3900 273 2 december, 1988 DATE cana-3900 273 3 1206-1216 DATE cana-3900 274 1 5 CARDINAL cana-3900 274 2 s. suryanarayanan PERSON cana-3900 275 1 malaysian NORP cana-3900 277 1 second ORDINAL cana-3900 277 2 19 (1996 DATE cana-3900 277 3 17 CARDINAL