id sid eid entity type american_scientific_journal-7479 1 1 332 CARDINAL american_scientific_journal-7479 1 2 american NORP american_scientific_journal-7479 1 3 sciences issn ORG american_scientific_journal-7479 1 4 2313 CARDINAL american_scientific_journal-7479 1 5 2313 CARDINAL american_scientific_journal-7479 1 6 mesallata ORG american_scientific_journal-7479 1 7 libya GPE american_scientific_journal-7479 1 8 adm ORG american_scientific_journal-7479 1 9 the euler bernoulli hypothesis ORG american_scientific_journal-7479 2 1 two CARDINAL american_scientific_journal-7479 2 2 spring DATE american_scientific_journal-7479 3 1 adm ORG american_scientific_journal-7479 4 1 adm PERSON american_scientific_journal-7479 4 2 first ORDINAL american_scientific_journal-7479 5 1 adm ORG american_scientific_journal-7479 6 1 adm PERSON american_scientific_journal-7479 7 1 euler-bernoulli beam ORG american_scientific_journal-7479 8 1 1 CARDINAL american_scientific_journal-7479 13 1 the last century 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CARDINAL american_scientific_journal-7479 34 2 adm ORG american_scientific_journal-7479 34 3 adm ORG american_scientific_journal-7479 36 1 adm ORG american_scientific_journal-7479 39 1 adm ORG american_scientific_journal-7479 40 1 18,19 CARDINAL american_scientific_journal-7479 41 1 adm ORG american_scientific_journal-7479 41 2 euler PERSON american_scientific_journal-7479 41 3 bernoulli PERSON american_scientific_journal-7479 43 1 # MONEY american_scientific_journal-7479 45 1 american NORP american_scientific_journal-7479 45 2 2022 CARDINAL american_scientific_journal-7479 45 3 88 CARDINAL american_scientific_journal-7479 45 4 332-348 334 QUANTITY american_scientific_journal-7479 45 5 1 CARDINAL american_scientific_journal-7479 45 6 two CARDINAL american_scientific_journal-7479 46 1 this spring DATE american_scientific_journal-7479 47 1 euler-bernoulli PERSON american_scientific_journal-7479 47 2 1,2 CARDINAL american_scientific_journal-7479 47 3 1 CARDINAL american_scientific_journal-7479 47 4 1 CARDINAL american_scientific_journal-7479 47 5 2 CARDINAL american_scientific_journal-7479 47 6 the dirac delta function ORG american_scientific_journal-7479 49 1 0 CARDINAL american_scientific_journal-7479 49 2 𝑑2𝑀2(𝐿 ORG american_scientific_journal-7479 49 3 0 CARDINAL american_scientific_journal-7479 49 4 2 CARDINAL american_scientific_journal-7479 50 1 𝑑π‘₯3 PERSON american_scientific_journal-7479 50 2 3 CARDINAL american_scientific_journal-7479 50 3 𝐿𝑐+ ORG american_scientific_journal-7479 53 1 4 CARDINAL american_scientific_journal-7479 54 1 american NORP american_scientific_journal-7479 54 2 2022 CARDINAL american_scientific_journal-7479 54 3 88 CARDINAL american_scientific_journal-7479 54 4 332 CARDINAL american_scientific_journal-7479 54 5 335 CARDINAL american_scientific_journal-7479 55 1 𝐸𝐼 𝑄(𝛼,cross PERSON american_scientific_journal-7479 55 2 5 CARDINAL american_scientific_journal-7479 55 3 6 CARDINAL 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american_scientific_journal-7479 65 1 10 CARDINAL american_scientific_journal-7479 66 1 first ORDINAL american_scientific_journal-7479 67 1 10 CARDINAL american_scientific_journal-7479 68 1 βˆ’ ψ4πœ‘π‘Ÿ(π‘₯ PERSON american_scientific_journal-7479 69 1 1,2 CARDINAL american_scientific_journal-7479 69 2 12 CARDINAL american_scientific_journal-7479 69 3 american NORP american_scientific_journal-7479 69 4 2022 CARDINAL american_scientific_journal-7479 69 5 88 CARDINAL american_scientific_journal-7479 69 6 332-348 336 QUANTITY american_scientific_journal-7479 69 7 4-fold CARDINAL american_scientific_journal-7479 69 8 𝐻π‘₯ βˆ’1 ORG american_scientific_journal-7479 70 1 ∫ ∫ ∫ ∫ ORG american_scientific_journal-7479 70 2 0 CARDINAL american_scientific_journal-7479 70 3 0 CARDINAL american_scientific_journal-7479 71 1 0 CARDINAL american_scientific_journal-7479 71 2 0 CARDINAL american_scientific_journal-7479 71 3 13 CARDINAL american_scientific_journal-7479 71 4 appling 𝐻π‘₯ PERSON american_scientific_journal-7479 72 1 12 CARDINAL american_scientific_journal-7479 74 1 1 CARDINAL american_scientific_journal-7479 74 2 1)(0 CARDINAL american_scientific_journal-7479 74 3 2 CARDINAL american_scientific_journal-7479 74 4 2)(0 TIME american_scientific_journal-7479 74 5 3 CARDINAL american_scientific_journal-7479 74 6 3)(0 CARDINAL american_scientific_journal-7479 74 7 14 CARDINAL american_scientific_journal-7479 76 1 π‘₯π‘Ÿβˆ’1 GPE american_scientific_journal-7479 76 2 1,2 CARDINAL american_scientific_journal-7479 76 3 15 CARDINAL american_scientific_journal-7479 77 1 15 CARDINAL american_scientific_journal-7479 78 1 14 CARDINAL american_scientific_journal-7479 78 2 0](π‘₯ CARDINAL american_scientific_journal-7479 79 1 1)(0)π‘₯ + π‘₯2 CARDINAL american_scientific_journal-7479 79 2 2 CARDINAL american_scientific_journal-7479 79 3 2)(0 TIME american_scientific_journal-7479 79 4 3 CARDINAL american_scientific_journal-7479 79 5 3)(0 CARDINAL american_scientific_journal-7479 85 1 π‘₯π‘Ÿβˆ’1 GPE american_scientific_journal-7479 85 2 1,2 CARDINAL american_scientific_journal-7479 85 3 16 CARDINAL american_scientific_journal-7479 85 4 0](π‘₯ CARDINAL american_scientific_journal-7479 87 1 3 CARDINAL american_scientific_journal-7479 87 2 17 CARDINAL american_scientific_journal-7479 89 1 1 CARDINAL american_scientific_journal-7479 89 2 1,2 CARDINAL american_scientific_journal-7479 89 3 18 CARDINAL american_scientific_journal-7479 91 1 18 CARDINAL american_scientific_journal-7479 93 1 17 CARDINAL american_scientific_journal-7479 94 1 18 CARDINAL american_scientific_journal-7479 95 1 1](π‘₯ CARDINAL american_scientific_journal-7479 99 1 3 CARDINAL american_scientific_journal-7479 99 2 19 CARDINAL american_scientific_journal-7479 100 1 2](π‘₯ CARDINAL american_scientific_journal-7479 102 1 1](π‘₯ CARDINAL american_scientific_journal-7479 102 2 8 + QUANTITY american_scientific_journal-7479 103 1 3 CARDINAL american_scientific_journal-7479 103 2 20 CARDINAL american_scientific_journal-7479 103 3 american NORP american_scientific_journal-7479 103 4 2022 CARDINAL american_scientific_journal-7479 103 5 88 CARDINAL american_scientific_journal-7479 103 6 332-348 337 QUANTITY american_scientific_journal-7479 107 1 π‘₯4𝑗+𝑒 CARDINAL american_scientific_journal-7479 107 2 4𝑗 + QUANTITY american_scientific_journal-7479 108 1 3 CARDINAL american_scientific_journal-7479 108 2 𝑛(π‘₯ ORG american_scientific_journal-7479 112 1 𝑗=0 ORG american_scientific_journal-7479 113 1 𝑗=0 ORG american_scientific_journal-7479 114 1 4𝑗 + 𝑛 CARDINAL american_scientific_journal-7479 115 1 3 CARDINAL american_scientific_journal-7479 115 2 22 CARDINAL american_scientific_journal-7479 116 1 = lim PERSON american_scientific_journal-7479 117 1 23 CARDINAL american_scientific_journal-7479 117 2 1)(0 CARDINAL american_scientific_journal-7479 117 3 2)(0 TIME american_scientific_journal-7479 117 4 3)(0 CARDINAL american_scientific_journal-7479 117 5 1,2 CARDINAL american_scientific_journal-7479 119 1 23 CARDINAL american_scientific_journal-7479 121 1 four CARDINAL american_scientific_journal-7479 121 2 eight CARDINAL american_scientific_journal-7479 121 3 0 CARDINAL american_scientific_journal-7479 121 4 24 CARDINAL american_scientific_journal-7479 121 5 𝑇𝑠1 𝑛 MONEY american_scientific_journal-7479 122 1 one to CARDINAL american_scientific_journal-7479 122 2 four CARDINAL american_scientific_journal-7479 123 1 second ORDINAL american_scientific_journal-7479 123 2 𝑏2 GPE american_scientific_journal-7479 123 3 first ORDINAL american_scientific_journal-7479 123 4 eqs CARDINAL american_scientific_journal-7479 124 1 3 CARDINAL american_scientific_journal-7479 124 2 4 CARDINAL american_scientific_journal-7479 124 3 𝑏2 𝑐2 GPE american_scientific_journal-7479 125 1 4 CARDINAL american_scientific_journal-7479 125 2 american NORP american_scientific_journal-7479 125 3 2022 CARDINAL american_scientific_journal-7479 125 4 88 CARDINAL american_scientific_journal-7479 125 5 332 CARDINAL american_scientific_journal-7479 125 6 348 338 CARDINAL american_scientific_journal-7479 125 7 0 CARDINAL american_scientific_journal-7479 125 8 𝑏2 𝑐2 GPE american_scientific_journal-7479 127 1 25𝑏 TIME american_scientific_journal-7479 127 2 𝑇22 ORG american_scientific_journal-7479 127 3 25𝑐 DATE american_scientific_journal-7479 127 4 25𝑑 CARDINAL american_scientific_journal-7479 128 1 0 CARDINAL american_scientific_journal-7479 129 1 26 CARDINAL american_scientific_journal-7479 129 2 26 CARDINAL american_scientific_journal-7479 131 1 26 CARDINAL american_scientific_journal-7479 131 2 three CARDINAL american_scientific_journal-7479 133 1 23 CARDINAL american_scientific_journal-7479 134 1 2 CARDINAL american_scientific_journal-7479 135 1 1 CARDINAL american_scientific_journal-7479 135 2 𝐸𝐼 πœ•2π‘€π‘Ÿ(π‘₯ PERSON american_scientific_journal-7479 136 1 1,2 CARDINAL american_scientific_journal-7479 136 2 27 CARDINAL american_scientific_journal-7479 136 3 𝑛(π‘₯ PERSON american_scientific_journal-7479 137 1 𝑛(𝑑 LOC american_scientific_journal-7479 137 2 1,2 CARDINAL american_scientific_journal-7479 137 3 28 CARDINAL american_scientific_journal-7479 137 4 𝑛(π‘₯ PERSON american_scientific_journal-7479 137 5 section 2),πœ‚π‘Ÿ 𝑛(𝑑 LAW american_scientific_journal-7479 139 1 28 CARDINAL american_scientific_journal-7479 140 1 27 CARDINAL american_scientific_journal-7479 141 1 1,2 CARDINAL american_scientific_journal-7479 141 2 29 CARDINAL american_scientific_journal-7479 141 3 american NORP american_scientific_journal-7479 141 4 2022 CARDINAL american_scientific_journal-7479 141 5 88 CARDINAL american_scientific_journal-7479 141 6 332-348 339 QUANTITY american_scientific_journal-7479 141 7 adm ORG american_scientific_journal-7479 142 1 29 CARDINAL american_scientific_journal-7479 143 1 first ORDINAL american_scientific_journal-7479 144 1 29 CARDINAL american_scientific_journal-7479 146 1 + πœ”2πœ‚π‘Ÿ(𝑑 DATE american_scientific_journal-7479 146 2 1,2 CARDINAL american_scientific_journal-7479 146 3 30 CARDINAL american_scientific_journal-7479 147 1 𝐺𝑑 = 𝑑4 𝑑𝑑4 PERSON american_scientific_journal-7479 147 2 2-fold CARDINAL american_scientific_journal-7479 151 1 0 CARDINAL american_scientific_journal-7479 151 2 31 CARDINAL american_scientific_journal-7479 151 3 appling 𝐺𝑑 PERSON american_scientific_journal-7479 152 1 30 CARDINAL american_scientific_journal-7479 153 1 1)(0 CARDINAL american_scientific_journal-7479 154 1 32 CARDINAL american_scientific_journal-7479 154 2 adm ORG american_scientific_journal-7479 154 3 𝑛(𝑑 ORG american_scientific_journal-7479 156 1 33 CARDINAL american_scientific_journal-7479 158 1 1 CARDINAL american_scientific_journal-7479 158 2 34 CARDINAL american_scientific_journal-7479 159 1 22 CARDINAL american_scientific_journal-7479 160 1 34 CARDINAL american_scientific_journal-7479 161 1 1 CARDINAL american_scientific_journal-7479 163 1 4𝑗 + 𝑛 CARDINAL american_scientific_journal-7479 164 1 3 CARDINAL american_scientific_journal-7479 164 2 𝑗=0 ORG american_scientific_journal-7479 165 1 1 CARDINAL american_scientific_journal-7479 165 2 𝑗=0 ORG american_scientific_journal-7479 165 3 4𝑗 + 𝑛 + 2 DATE american_scientific_journal-7479 166 1 3 CARDINAL american_scientific_journal-7479 166 2 35 CARDINAL american_scientific_journal-7479 168 1 1 CARDINAL american_scientific_journal-7479 168 2 1,2 CARDINAL american_scientific_journal-7479 168 3 36 CARDINAL american_scientific_journal-7479 169 1 american NORP american_scientific_journal-7479 169 2 2022 CARDINAL american_scientific_journal-7479 169 3 88 CARDINAL american_scientific_journal-7479 169 4 332 CARDINAL american_scientific_journal-7479 169 5 348 340 CARDINAL american_scientific_journal-7479 170 1 36 CARDINAL american_scientific_journal-7479 172 1 35 CARDINAL american_scientific_journal-7479 173 1 36 CARDINAL american_scientific_journal-7479 174 1 1](𝑑 CARDINAL american_scientific_journal-7479 179 1 1 CARDINAL american_scientific_journal-7479 179 2 𝑗=0 ORG american_scientific_journal-7479 179 3 𝑑4𝑗+𝑛+4 ORG american_scientific_journal-7479 179 4 4𝑗 + 𝑛 + 4 DATE american_scientific_journal-7479 180 1 3 CARDINAL american_scientific_journal-7479 180 2 37 CARDINAL american_scientific_journal-7479 181 1 2](𝑑 CARDINAL american_scientific_journal-7479 183 1 1](𝑑 CARDINAL american_scientific_journal-7479 186 1 1 CARDINAL american_scientific_journal-7479 186 2 𝑗=0 ORG american_scientific_journal-7479 186 3 βˆ‘ v4𝑗+𝑛. 𝑑4𝑗+𝑛+6 PERSON american_scientific_journal-7479 186 4 4𝑗 + 𝑛 + 6 DATE american_scientific_journal-7479 187 1 3 CARDINAL american_scientific_journal-7479 187 2 38 CARDINAL american_scientific_journal-7479 188 1 3](𝑑 CARDINAL american_scientific_journal-7479 190 1 2](𝑑 CARDINAL american_scientific_journal-7479 193 1 1 CARDINAL american_scientific_journal-7479 193 2 𝑗=0 ORG american_scientific_journal-7479 193 3 βˆ‘ v4𝑗+𝑛. PERSON american_scientific_journal-7479 193 4 4𝑗 + 𝑛 + 8) DATE american_scientific_journal-7479 193 5 3 CARDINAL american_scientific_journal-7479 193 6 39 CARDINAL american_scientific_journal-7479 196 1 1 CARDINAL american_scientific_journal-7479 196 2 𝑗=0 ORG american_scientific_journal-7479 196 3 βˆ‘ v4𝑗+𝑛 . PERSON american_scientific_journal-7479 197 1 4𝑗 + 𝑛 + 2π‘š DATE american_scientific_journal-7479 198 1 3 CARDINAL american_scientific_journal-7479 198 2 βˆ’πœ”2π‘š PRODUCT american_scientific_journal-7479 199 1 1 CARDINAL american_scientific_journal-7479 199 2 𝑗=0 ORG american_scientific_journal-7479 199 3 βˆ‘ v4𝑗+𝑛. 𝑑4𝑗+𝑛+2π‘š+2 PERSON american_scientific_journal-7479 199 4 4𝑗 + 𝑛 + 2π‘š DATE american_scientific_journal-7479 200 1 3 CARDINAL american_scientific_journal-7479 201 1 1 CARDINAL american_scientific_journal-7479 201 2 41 CARDINAL american_scientific_journal-7479 201 3 american NORP american_scientific_journal-7479 201 4 2022 CARDINAL american_scientific_journal-7479 201 5 88 CARDINAL american_scientific_journal-7479 201 6 332-348 341 QUANTITY american_scientific_journal-7479 201 7 adm ORG american_scientific_journal-7479 202 1 𝑛(𝑑 ORG american_scientific_journal-7479 204 1 1,2 CARDINAL american_scientific_journal-7479 204 2 42 CARDINAL american_scientific_journal-7479 204 3 two CARDINAL american_scientific_journal-7479 205 1 42 CARDINAL american_scientific_journal-7479 207 1 four CARDINAL american_scientific_journal-7479 209 1 23 CARDINAL american_scientific_journal-7479 210 1 42 CARDINAL american_scientific_journal-7479 211 1 28 CARDINAL american_scientific_journal-7479 212 1 4 CARDINAL american_scientific_journal-7479 212 2 4.1 CARDINAL american_scientific_journal-7479 213 1 adm ORG american_scientific_journal-7479 214 1 adm PERSON american_scientific_journal-7479 215 1 the euler bernoulli beam ORG american_scientific_journal-7479 215 2 2.1Γ—1011(gpa CARDINAL american_scientific_journal-7479 215 3 second ORDINAL american_scientific_journal-7479 216 1 12 CARDINAL american_scientific_journal-7479 216 2 mahmoud PERSON american_scientific_journal-7479 216 3 2001 DATE american_scientific_journal-7479 217 1 23 CARDINAL american_scientific_journal-7479 217 2 28 CARDINAL american_scientific_journal-7479 217 3 42 CARDINAL american_scientific_journal-7479 217 4 adm ORG american_scientific_journal-7479 217 5 adm ORG american_scientific_journal-7479 219 1 mid-span DATE american_scientific_journal-7479 219 2 f. 4.2 PERSON american_scientific_journal-7479 219 3 2000(n TIME american_scientific_journal-7479 219 4 zero CARDINAL american_scientific_journal-7479 219 5 0 CARDINAL american_scientific_journal-7479 222 1 fig ORG american_scientific_journal-7479 223 1 2 CARDINAL american_scientific_journal-7479 223 2 adm ORG american_scientific_journal-7479 223 3 100 CARDINAL american_scientific_journal-7479 225 1 2 CARDINAL american_scientific_journal-7479 225 2 adm ORG american_scientific_journal-7479 226 1 adm ORG american_scientific_journal-7479 227 1 ppe ORG american_scientific_journal-7479 228 1 43 CARDINAL american_scientific_journal-7479 229 1 adm PERSON american_scientific_journal-7479 229 2 1 CARDINAL american_scientific_journal-7479 229 3 american NORP american_scientific_journal-7479 229 4 2022 CARDINAL american_scientific_journal-7479 229 5 88 CARDINAL american_scientific_journal-7479 229 6 332 CARDINAL american_scientific_journal-7479 229 7 348 342 CARDINAL american_scientific_journal-7479 231 1 βˆ’ adm PERSON american_scientific_journal-7479 231 2 adm PERSON american_scientific_journal-7479 232 1 section 4 LAW american_scientific_journal-7479 232 2 zero CARDINAL american_scientific_journal-7479 232 3 euler bernoulli PERSON american_scientific_journal-7479 233 1 dirac delta LOC american_scientific_journal-7479 234 1 fig.3 ORDINAL american_scientific_journal-7479 234 2 adm ORG american_scientific_journal-7479 234 3 100 CARDINAL american_scientific_journal-7479 234 4 mid-span DATE american_scientific_journal-7479 236 1 70 CARDINAL american_scientific_journal-7479 237 1 1000 CARDINAL american_scientific_journal-7479 237 2 2000 DATE american_scientific_journal-7479 239 1 mid-span DATE american_scientific_journal-7479 240 1 mid-span DATE american_scientific_journal-7479 242 1 adm ORG american_scientific_journal-7479 242 2 1992 DATE american_scientific_journal-7479 242 3 adm ORG american_scientific_journal-7479 244 1 44 CARDINAL american_scientific_journal-7479 245 1 adm PERSON american_scientific_journal-7479 246 1 2 CARDINAL american_scientific_journal-7479 247 1 adm PERSON american_scientific_journal-7479 248 1 βˆ’ adm PERSON american_scientific_journal-7479 249 1 6 CARDINAL american_scientific_journal-7479 252 1 45 CARDINAL american_scientific_journal-7479 252 2 70 CARDINAL american_scientific_journal-7479 253 1 3 CARDINAL american_scientific_journal-7479 253 2 adm ORG american_scientific_journal-7479 254 1 american NORP american_scientific_journal-7479 254 2 2022 CARDINAL american_scientific_journal-7479 254 3 88 CARDINAL american_scientific_journal-7479 254 4 332 CARDINAL american_scientific_journal-7479 254 5 45 CARDINAL american_scientific_journal-7479 254 6 70 CARDINAL american_scientific_journal-7479 254 7 adm ORG american_scientific_journal-7479 255 1 two CARDINAL american_scientific_journal-7479 256 1 2 CARDINAL american_scientific_journal-7479 256 2 mid-span DATE american_scientific_journal-7479 256 3 adm PERSON american_scientific_journal-7479 256 4 80 CARDINAL american_scientific_journal-7479 256 5 100 CARDINAL american_scientific_journal-7479 256 6 three CARDINAL american_scientific_journal-7479 256 7 1 CARDINAL american_scientific_journal-7479 256 8 adm ORG american_scientific_journal-7479 256 9 80 CARDINAL american_scientific_journal-7479 256 10 mid-span DATE american_scientific_journal-7479 256 11 ppe ORG american_scientific_journal-7479 257 1 american NORP american_scientific_journal-7479 257 2 2022 CARDINAL american_scientific_journal-7479 257 3 88 CARDINAL american_scientific_journal-7479 257 4 332 CARDINAL american_scientific_journal-7479 257 5 adm ORG american_scientific_journal-7479 257 6 80 CARDINAL american_scientific_journal-7479 257 7 100 CARDINAL american_scientific_journal-7479 258 1 0.0092 0.2302 0.1657 MONEY american_scientific_journal-7479 258 2 3 CARDINAL american_scientific_journal-7479 258 3 70, 80 DATE american_scientific_journal-7479 258 4 mid-span DATE american_scientific_journal-7479 258 5 adm PERSON american_scientific_journal-7479 258 6 100 CARDINAL american_scientific_journal-7479 258 7 two CARDINAL american_scientific_journal-7479 258 8 american NORP american_scientific_journal-7479 258 9 2022 CARDINAL american_scientific_journal-7479 258 10 88 CARDINAL american_scientific_journal-7479 258 11 332 CARDINAL american_scientific_journal-7479 258 12 4 CARDINAL american_scientific_journal-7479 258 13 mid-span DATE american_scientific_journal-7479 258 14 adm ORG american_scientific_journal-7479 258 15 5 CARDINAL american_scientific_journal-7479 258 16 mid-span DATE american_scientific_journal-7479 258 17 adm PERSON american_scientific_journal-7479 258 18 60 CARDINAL american_scientific_journal-7479 258 19 100 CARDINAL american_scientific_journal-7479 258 20 three CARDINAL 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