id sid eid entity type iajs-3638 1 1 445 CARDINAL iajs-3638 2 1 2025 CARDINAL iajs-3638 3 1 al-haitham ORG iajs-3638 3 2 university of baghdad ORG iajs-3638 4 1 4.0 CARDINAL iajs-3638 4 2 covid-19 PRODUCT iajs-3638 4 3 rami raad PERSON iajs-3638 4 4 1 CARDINAL iajs-3638 4 5 hassan f. al-husseiny PERSON iajs-3638 4 6 2 1department DATE iajs-3638 4 7 baghdad GPE iajs-3638 4 8 iraq GPE iajs-3638 5 1 1,2department TIME iajs-3638 5 2 university of baghdad ORG iajs-3638 5 3 baghdad GPE iajs-3638 5 4 iraq GPE iajs-3638 7 1 july 2023 DATE iajs-3638 7 2 2023 CARDINAL iajs-3638 7 3 january 2025 DATE iajs-3638 7 4 covid-19 PERSON iajs-3638 7 5 covid-19 PERSON iajs-3638 8 1 five CARDINAL iajs-3638 10 1 first ORDINAL iajs-3638 14 1 t.d. GPE iajs-3638 14 2 e.ps. PERSON iajs-3638 14 3 covid-19 DATE iajs-3638 14 4 n.s. GPE iajs-3638 15 1 1 CARDINAL iajs-3638 17 1 ferguson PERSON iajs-3638 18 1 1 CARDINAL iajs-3638 18 2 great britain GPE iajs-3638 19 1 donnelly et al ORG iajs-3638 20 1 2 CARDINAL iajs-3638 21 1 cauchemez et al PERSON iajs-3638 22 1 3 CARDINAL iajs-3638 22 2 the middle east LOC iajs-3638 23 1 https://orcid.org/0009-0007-7883-5875 mailto PERSON iajs-3638 23 2 ihjpas PERSON iajs-3638 24 1 2025 CARDINAL iajs-3638 24 2 38 CARDINAL iajs-3638 24 3 1 CARDINAL iajs-3638 24 4 446 CARDINAL iajs-3638 25 1 mohsen et al PERSON iajs-3638 26 1 4 CARDINAL iajs-3638 26 2 covid-19 PRODUCT iajs-3638 28 1 5 CARDINAL iajs-3638 28 2 covid-19 PRODUCT iajs-3638 30 1 6 CARDINAL iajs-3638 30 2 covid-19 DATE iajs-3638 31 1 7 CARDINAL iajs-3638 31 2 covid-19 PRODUCT iajs-3638 38 1 m. yaseen et al PERSON iajs-3638 39 1 10 CARDINAL iajs-3638 40 1 zhe yin et al PERSON iajs-3638 41 1 11 CARDINAL iajs-3638 42 1 mohsen et al PERSON iajs-3638 43 1 12 CARDINAL iajs-3638 44 1 zizhen et al PERSON iajs-3638 45 1 13 CARDINAL iajs-3638 46 1 dehingia et al PERSON iajs-3638 47 1 14 CARDINAL iajs-3638 49 1 15 CARDINAL iajs-3638 49 2 covid-19 PRODUCT iajs-3638 50 1 naji PERSON iajs-3638 50 2 hussien PERSON iajs-3638 50 3 16 CARDINAL iajs-3638 51 1 ahmed et al PERSON iajs-3638 52 1 17 CARDINAL iajs-3638 52 2 covid-19 GPE iajs-3638 53 1 naji PERSON iajs-3638 53 2 mohsen PERSON iajs-3638 54 1 18 CARDINAL iajs-3638 55 1 ahmed PERSON iajs-3638 55 2 19 CARDINAL iajs-3638 56 1 mohsen PERSON iajs-3638 56 2 20 CARDINAL iajs-3638 56 3 covid-19 DATE iajs-3638 57 1 covid-19 PRODUCT iajs-3638 57 2 two CARDINAL iajs-3638 58 1 section 2 LAW iajs-3638 58 2 two CARDINAL iajs-3638 59 1 section 3 LAW iajs-3638 60 1 section 4 LAW iajs-3638 61 1 ihjpas PERSON iajs-3638 62 1 2025 CARDINAL iajs-3638 62 2 38 CARDINAL iajs-3638 62 3 1 CARDINAL iajs-3638 62 4 447 2 CARDINAL iajs-3638 62 5 in(21 GPE iajs-3638 62 6 1+𝑛𝑉1 CARDINAL iajs-3638 62 7 𝑑𝑉1 ORG iajs-3638 63 1 1+𝑛𝑉1 CARDINAL iajs-3638 63 2 βˆ’ πœ‡π‘‰1 𝑑𝑉2 PERSON iajs-3638 64 1 πœ‡π‘‰2 PERSON iajs-3638 64 2 1 CARDINAL iajs-3638 64 3 2 CARDINAL iajs-3638 64 4 1 CARDINAL iajs-3638 64 5 1+𝑛𝑉1 CARDINAL iajs-3638 64 6 𝑑𝑉1 ORG iajs-3638 64 7 1+𝑛𝑉1 CARDINAL iajs-3638 64 8 βˆ’ πœ‡π‘‰1 𝑑𝑉2 PERSON iajs-3638 64 9 βˆ’ πœ‡π‘‰2 PERSON iajs-3638 64 10 3 CARDINAL iajs-3638 64 11 3 CARDINAL iajs-3638 64 12 h.b PERSON iajs-3638 64 13 3 CARDINAL iajs-3638 66 1 21 CARDINAL iajs-3638 66 2 3 CARDINAL iajs-3638 66 3 six CARDINAL iajs-3638 66 4 0 CARDINAL iajs-3638 66 5 𝐸1 CARDINAL iajs-3638 66 6 0 CARDINAL iajs-3638 66 7 𝐸3 CARDINAL iajs-3638 66 8 1 CARDINAL iajs-3638 66 9 2 CARDINAL iajs-3638 66 10 0 DATE iajs-3638 66 11 𝐸4 CARDINAL iajs-3638 66 12 1 CARDINAL iajs-3638 66 13 0 DATE iajs-3638 66 14 βˆ— CARDINAL iajs-3638 66 15 𝑉2 ORG iajs-3638 67 1 3 CARDINAL iajs-3638 67 2 𝑉1 CARDINAL iajs-3638 67 3 𝑉2 LOC iajs-3638 67 4 𝐽(𝐸 GPE iajs-3638 67 5 π‘Žπ‘–π‘—)4Γ—4 PERSON iajs-3638 67 6 1,2,3,4 DATE iajs-3638 68 1 1+𝑛𝑉1 + DATE iajs-3638 68 2 1+𝑛𝑉1)2 CARDINAL iajs-3638 69 1 βˆ’πœ†πœ GPE iajs-3638 69 2 1+𝑛𝑉1 CARDINAL iajs-3638 69 3 1+𝑛𝑉1)2 + 𝛾 + DATE iajs-3638 69 4 βˆ’π›½2𝑉1 ORG iajs-3638 69 5 βˆ’π›½3𝑉2 ORG iajs-3638 69 6 βˆ’πœ†πœ GPE iajs-3638 69 7 𝛽3𝐼 GPE iajs-3638 69 8 0 CARDINAL iajs-3638 69 9 βˆ’πœ†πœ GPE iajs-3638 69 10 4 CARDINAL iajs-3638 72 1 2025 CARDINAL iajs-3638 72 2 38 CARDINAL iajs-3638 72 3 1 CARDINAL iajs-3638 72 4 448 CARDINAL iajs-3638 73 1 0 CARDINAL iajs-3638 73 2 5 CARDINAL iajs-3638 73 3 l.s. GPE iajs-3638 73 4 3 CARDINAL iajs-3638 73 5 0 CARDINAL iajs-3638 73 6 0 CARDINAL iajs-3638 73 7 4 CARDINAL iajs-3638 74 1 βˆ’πœ‡ PERSON iajs-3638 74 2 0 CARDINAL iajs-3638 75 1 6 CARDINAL iajs-3638 75 2 c.e. GPE iajs-3638 75 3 βˆ’ πœ†)(βˆ’πœ‡ ORG iajs-3638 76 1 0 CARDINAL iajs-3638 76 2 6a CARDINAL iajs-3638 76 3 6a CARDINAL iajs-3638 76 4 4 CARDINAL iajs-3638 77 1 6b CARDINAL iajs-3638 78 1 𝛽1𝑆̅ GPE iajs-3638 78 2 7 CARDINAL iajs-3638 78 3 0 CARDINAL iajs-3638 79 1 6b CARDINAL iajs-3638 79 2 two CARDINAL iajs-3638 79 3 namely= CARDINAL iajs-3638 80 1 6b CARDINAL iajs-3638 81 1 + πœ‡1 + DATE iajs-3638 82 1 + πœ‡1 + DATE iajs-3638 83 1 6a CARDINAL iajs-3638 85 1 7 CARDINAL iajs-3638 86 1 β€’ CARDINAL iajs-3638 86 2 0 CARDINAL iajs-3638 86 3 4 CARDINAL iajs-3638 86 4 𝐽(𝐸1 GPE iajs-3638 87 1 ΜΏ PERSON iajs-3638 87 2 ΜΏ PERSON iajs-3638 87 3 1 CARDINAL iajs-3638 87 4 2 CARDINAL iajs-3638 87 5 βˆ’πœ†πœ GPE iajs-3638 87 6 1 + 𝑛 QUANTITY iajs-3638 87 7 ΜΏ PERSON iajs-3638 87 8 ΜΏ PERSON iajs-3638 87 9 2 + DATE iajs-3638 88 1 ΜΏ PERSON iajs-3638 88 2 1 CARDINAL iajs-3638 88 3 0 CARDINAL iajs-3638 89 1 0 CARDINAL iajs-3638 89 2 ΜΏ PERSON iajs-3638 89 3 9 CARDINAL iajs-3638 89 4 𝐽(𝐸1 GPE iajs-3638 90 1 βˆ’ πœ†][𝛽1𝑆̿𝑒 βˆ’πœ†πœ + PERSON iajs-3638 90 2 ΜΏ PERSON iajs-3638 91 1 10a DATE iajs-3638 91 2 ihjpas PERSON iajs-3638 92 1 2025 CARDINAL iajs-3638 92 2 38 CARDINAL iajs-3638 92 3 1 CARDINAL iajs-3638 92 4 449 CARDINAL iajs-3638 92 5 1+𝑛 CARDINAL iajs-3638 92 6 ΜΏ PERSON iajs-3638 92 7 ΜΏ PERSON iajs-3638 92 8 1+𝑛𝑉1 CARDINAL iajs-3638 92 9 2 CARDINAL iajs-3638 93 1 ΜΏ PERSON iajs-3638 93 2 1+𝑛 CARDINAL iajs-3638 93 3 2 CARDINAL iajs-3638 94 1 1+𝑛 CARDINAL iajs-3638 94 2 ΜΏ PERSON iajs-3638 94 3 10a DATE iajs-3638 94 4 𝐽(𝐸1 GPE iajs-3638 94 5 4 CARDINAL iajs-3638 96 1 1 2 CARDINAL iajs-3638 96 2 2 CARDINAL iajs-3638 96 3 4𝐴2 CARDINAL iajs-3638 96 4 ΜΏ PERSON iajs-3638 96 5 10b CARDINAL iajs-3638 97 1 11 CARDINAL iajs-3638 97 2 0 CARDINAL iajs-3638 98 1 10b CARDINAL iajs-3638 98 2 two CARDINAL iajs-3638 98 3 namely= CARDINAL iajs-3638 99 1 10b CARDINAL iajs-3638 99 2 βˆ’ π‘–π‘ π‘–π‘›πœ”πœ PERSON iajs-3638 100 1 ΜΏ PERSON iajs-3638 100 2 12 CARDINAL iajs-3638 100 3 βˆ“βˆšπ›½1 2(𝑆̅̅ PERSON iajs-3638 100 4 2 CARDINAL iajs-3638 100 5 1 CARDINAL iajs-3638 100 6 2 CARDINAL iajs-3638 101 1 10a DATE iajs-3638 101 2 sep CARDINAL iajs-3638 103 1 11 CARDINAL iajs-3638 104 1 0 CARDINAL iajs-3638 104 2 4 CARDINAL iajs-3638 104 3 𝐽(𝐸2 GPE iajs-3638 105 1 0 CARDINAL iajs-3638 107 1 0 CARDINAL iajs-3638 108 1 𝛽3𝐼 GPE iajs-3638 108 2 βˆ’πœ†πœ GPE iajs-3638 108 3 13 CARDINAL iajs-3638 108 4 𝑅1 CARDINAL iajs-3638 108 5 𝑅2 CARDINAL iajs-3638 108 6 𝑅3 CARDINAL iajs-3638 109 1 𝐽(𝐸2 GPE iajs-3638 111 1 14 CARDINAL iajs-3638 111 2 𝐡1 CARDINAL iajs-3638 111 3 𝑅2 CARDINAL iajs-3638 111 4 𝑅4 CARDINAL iajs-3638 111 5 𝐡3 ORG iajs-3638 111 6 𝐡4 PERSON iajs-3638 112 1 0 CARDINAL iajs-3638 112 2 14 CARDINAL iajs-3638 113 1 𝐡1 CARDINAL iajs-3638 115 1 0 CARDINAL iajs-3638 115 2 15 CARDINAL iajs-3638 117 1 ihjpas PERSON iajs-3638 118 1 2025 CARDINAL iajs-3638 118 2 38 CARDINAL iajs-3638 118 3 1 CARDINAL iajs-3638 118 4 450 CARDINAL iajs-3638 119 1 𝐡1 CARDINAL iajs-3638 119 2 0 CARDINAL iajs-3638 119 3 16b CARDINAL iajs-3638 120 1 + DATE iajs-3638 121 1 𝐡1 CARDINAL iajs-3638 121 2 0 CARDINAL iajs-3638 122 1 0 CARDINAL iajs-3638 123 1 17a CARDINAL iajs-3638 125 1 17b CARDINAL iajs-3638 125 2 16b CARDINAL iajs-3638 125 3 13 CARDINAL iajs-3638 126 1 17a-17b ORDINAL iajs-3638 127 1 3 CARDINAL iajs-3638 127 2 0 CARDINAL iajs-3638 128 1 0 CARDINAL iajs-3638 130 1 0 CARDINAL iajs-3638 130 2 18 CARDINAL iajs-3638 130 3 18 CARDINAL iajs-3638 130 4 two CARDINAL iajs-3638 130 5 namely= CARDINAL iajs-3638 131 1 18 CARDINAL iajs-3638 131 2 𝐡4π‘π‘œπ‘ πœ”πœ GPE iajs-3638 131 3 2 CARDINAL iajs-3638 131 4 𝐡2 DATE iajs-3638 131 5 19 CARDINAL iajs-3638 131 6 19 CARDINAL iajs-3638 131 7 2 + DATE iajs-3638 131 8 0 CARDINAL iajs-3638 131 9 20 CARDINAL iajs-3638 131 10 20 CARDINAL iajs-3638 133 1 0 CARDINAL iajs-3638 133 2 𝑅2 CARDINAL iajs-3638 133 3 2 DATE iajs-3638 133 4 𝑅2 CARDINAL iajs-3638 133 5 2 CARDINAL iajs-3638 134 1 descartes GPE iajs-3638 134 2 2 CARDINAL iajs-3638 134 3 21a CARDINAL iajs-3638 135 1 20 CARDINAL iajs-3638 136 1 18 CARDINAL iajs-3638 136 2 at least two CARDINAL iajs-3638 136 3 19 CARDINAL iajs-3638 136 4 1 πœ”0 π‘π‘œπ‘ βˆ’1 MONEY iajs-3638 136 5 2+𝐡3 GPE iajs-3638 136 6 2πœ”0 DATE iajs-3638 136 7 2 + 2π‘˜πœ‹ DATE iajs-3638 136 8 22 CARDINAL iajs-3638 136 9 0,1,2 DATE iajs-3638 137 1 0 CARDINAL iajs-3638 137 2 3 CARDINAL iajs-3638 137 3 two CARDINAL iajs-3638 137 4 Β±πœ”0 DATE iajs-3638 138 1 πœ†(𝜏 NORP iajs-3638 140 1 18 CARDINAL iajs-3638 142 1 theorem1 PERSON iajs-3638 143 1 18 CARDINAL iajs-3638 144 1 0 CARDINAL iajs-3638 144 2 23a CARDINAL iajs-3638 145 1 2025 CARDINAL iajs-3638 145 2 38 CARDINAL iajs-3638 145 3 1 CARDINAL iajs-3638 145 4 451 CARDINAL iajs-3638 146 1 πœ†(𝜏 PRODUCT iajs-3638 146 2 18 CARDINAL iajs-3638 146 3 2πœ† + 𝐡1 CARDINAL iajs-3638 149 1 24 CARDINAL iajs-3638 149 2 βˆ’1 DATE iajs-3638 150 1 πœ†(𝐡3πœ†+𝐡4)π‘’βˆ’πœ†πœ + 𝐡3 πœ†(𝐡3πœ†+𝐡4 ORG iajs-3638 151 1 25 CARDINAL iajs-3638 151 2 𝜏=𝜏0 NORP iajs-3638 151 3 𝐡1 CARDINAL iajs-3638 151 4 2+π‘–πœ”0(πœ”0 CARDINAL iajs-3638 152 1 26 CARDINAL iajs-3638 154 1 27 CARDINAL iajs-3638 154 2 𝑅𝑒 PERSON iajs-3638 154 3 𝐡1 CARDINAL iajs-3638 154 4 2+π‘–πœ”0(πœ”0 CARDINAL iajs-3638 155 1 𝐡1 CARDINAL iajs-3638 155 2 𝐡1 CARDINAL iajs-3638 155 3 2+(πœ”0 CARDINAL iajs-3638 155 4 2 DATE iajs-3638 155 5 𝐡3 CARDINAL iajs-3638 155 6 𝐡3 2 ORG iajs-3638 155 7 𝐡3 ORG iajs-3638 156 1 𝑅𝑒 [ π‘‘πœ† π‘‘πœ PERSON iajs-3638 156 2 𝜏=𝜏0 NORP iajs-3638 156 3 𝐡1 CARDINAL iajs-3638 157 1 𝐡1 CARDINAL iajs-3638 157 2 2 CARDINAL iajs-3638 157 3 2 CARDINAL iajs-3638 157 4 2 CARDINAL iajs-3638 157 5 0 CARDINAL iajs-3638 157 6 0 CARDINAL iajs-3638 159 1 0 CARDINAL iajs-3638 161 1 c.e. GPE iajs-3638 162 1 18 CARDINAL iajs-3638 163 1 3 CARDINAL iajs-3638 165 1 5 CARDINAL iajs-3638 166 1 1 + DATE iajs-3638 166 2 1 CARDINAL iajs-3638 166 3 2 CARDINAL iajs-3638 166 4 1 + 𝑛�̆ QUANTITY iajs-3638 167 1 1 CARDINAL iajs-3638 168 1 1 0 CARDINAL iajs-3638 168 2 2 CARDINAL iajs-3638 168 3 2 CARDINAL iajs-3638 168 4 28 CARDINAL iajs-3638 168 5 𝐽(𝐸3 NORP iajs-3638 169 1 2 CARDINAL iajs-3638 170 1 29a CARDINAL iajs-3638 171 1 2025 CARDINAL iajs-3638 171 2 38 CARDINAL iajs-3638 171 3 1 CARDINAL iajs-3638 171 4 452 CARDINAL iajs-3638 171 5 𝐢1 CARDINAL iajs-3638 171 6 1+𝑛𝑉1 CARDINAL iajs-3638 171 7 1+𝑛𝑉1 CARDINAL iajs-3638 173 1 1+𝑛𝑉1 CARDINAL iajs-3638 173 2 1+𝑛𝑉1 + DATE iajs-3638 173 3 29a CARDINAL iajs-3638 173 4 4 CARDINAL iajs-3638 174 1 2 CARDINAL iajs-3638 174 2 1 2 CARDINAL iajs-3638 174 3 4𝐢2 CARDINAL iajs-3638 174 4 2 CARDINAL iajs-3638 174 5 29b ORDINAL iajs-3638 175 1 2 CARDINAL iajs-3638 175 2 30 CARDINAL iajs-3638 175 3 0 CARDINAL iajs-3638 175 4 29b ORDINAL iajs-3638 175 5 two CARDINAL iajs-3638 177 1 2 + CARDINAL iajs-3638 177 2 2 CARDINAL iajs-3638 177 3 31 CARDINAL iajs-3638 177 4 2( CARDINAL iajs-3638 178 1 2 CARDINAL iajs-3638 178 2 2 CARDINAL iajs-3638 178 3 2 CARDINAL iajs-3638 178 4 30),πœ”(𝜏 CARDINAL iajs-3638 179 1 29a CARDINAL iajs-3638 179 2 𝐸1 DATE iajs-3638 181 1 30 CARDINAL iajs-3638 182 1 0 CARDINAL iajs-3638 182 2 4 CARDINAL iajs-3638 183 1 𝑑𝑖𝑗)4Γ—4 NORP iajs-3638 183 2 1 CARDINAL iajs-3638 183 3 2 CARDINAL iajs-3638 183 4 βˆ’π‘…3𝑒 βˆ’πœ†πœ PERSON iajs-3638 184 1 1 + 𝑛 QUANTITY iajs-3638 184 2 1 CARDINAL iajs-3638 185 1 + DATE iajs-3638 185 2 βˆ’πœ†πœ GPE iajs-3638 185 3 𝛽3𝐼 GPE iajs-3638 185 4 βˆ’πœ†πœ GPE iajs-3638 186 1 0 CARDINAL iajs-3638 187 1 32 CARDINAL iajs-3638 187 2 𝑅1 GPE iajs-3638 187 3 1+𝑛 CARDINAL iajs-3638 187 4 1 + DATE iajs-3638 187 5 𝑅2 CARDINAL iajs-3638 187 6 𝑅3 CARDINAL iajs-3638 188 1 the c.e of 𝐽(𝐸4 ORG iajs-3638 190 1 3 + DATE iajs-3638 190 2 2 + QUANTITY iajs-3638 190 3 + 𝐷3 DATE iajs-3638 190 4 0 CARDINAL iajs-3638 190 5 33 CARDINAL iajs-3638 191 1 2025 CARDINAL iajs-3638 191 2 38 CARDINAL iajs-3638 191 3 1 CARDINAL iajs-3638 191 4 453 CARDINAL iajs-3638 192 1 𝐷2 CARDINAL iajs-3638 192 2 𝐷3 CARDINAL iajs-3638 192 3 βˆ’ 𝑅1𝑑23𝑑32 PERSON iajs-3638 192 4 𝑅2 CARDINAL iajs-3638 192 5 𝐷6 CARDINAL iajs-3638 194 1 0 CARDINAL iajs-3638 194 2 33 CARDINAL iajs-3638 195 1 3 + (𝐷1 + 𝐷4)πœ† DATE iajs-3638 195 2 2 + DATE iajs-3638 195 3 0 CARDINAL iajs-3638 195 4 34 CARDINAL iajs-3638 197 1 2 + DATE iajs-3638 199 1 𝐷1 + 𝐷4 ORG iajs-3638 199 2 0 CARDINAL iajs-3638 200 1 𝐷3 CARDINAL iajs-3638 200 2 0 CARDINAL iajs-3638 201 1 1+𝑛 CARDINAL iajs-3638 201 2 1 CARDINAL iajs-3638 201 3 1+𝑛 CARDINAL iajs-3638 201 4 1+𝑛 CARDINAL iajs-3638 201 5 36b CARDINAL iajs-3638 204 1 0 CARDINAL iajs-3638 205 1 𝑛𝛽1𝛼 PERSON iajs-3638 205 2 1+𝑛 CARDINAL iajs-3638 205 3 1 CARDINAL iajs-3638 205 4 1+𝑛 CARDINAL iajs-3638 205 5 36c CARDINAL iajs-3638 205 6 1 CARDINAL iajs-3638 205 7 1(πœ‡ + πœ‡1 + DATE iajs-3638 205 8 routh-hurwitz criterion ORG iajs-3638 205 9 32 CARDINAL iajs-3638 206 1 36a)-(36d CARDINAL iajs-3638 206 2 𝐸4 CARDINAL iajs-3638 206 3 3 CARDINAL iajs-3638 206 4 0 CARDINAL iajs-3638 207 1 0 CARDINAL iajs-3638 209 1 + 𝐷3 DATE iajs-3638 209 2 37 CARDINAL iajs-3638 209 3 37 CARDINAL iajs-3638 209 4 two CARDINAL iajs-3638 209 5 namely= CARDINAL iajs-3638 210 1 37 CARDINAL iajs-3638 210 2 𝐷6 CARDINAL iajs-3638 210 3 𝐷1πœ” ORDINAL iajs-3638 210 4 2)π‘π‘œπ‘ πœ”πœ + 𝐷5πœ”π‘ π‘–π‘›πœ”πœ DATE iajs-3638 210 5 𝐷1πœ” ORDINAL iajs-3638 210 6 2 CARDINAL iajs-3638 210 7 3 CARDINAL iajs-3638 210 8 38 CARDINAL iajs-3638 210 9 38 CARDINAL iajs-3638 210 10 0 CARDINAL iajs-3638 210 11 39 CARDINAL iajs-3638 211 1 39 CARDINAL iajs-3638 211 2 2 CARDINAL iajs-3638 211 3 0 CARDINAL iajs-3638 212 1 2025 CARDINAL iajs-3638 212 2 38 CARDINAL iajs-3638 212 3 1 CARDINAL iajs-3638 212 4 454 CARDINAL iajs-3638 212 5 2 CARDINAL iajs-3638 212 6 2𝐷2 CARDINAL iajs-3638 212 7 2𝐷4𝐷6 CARDINAL iajs-3638 212 8 βˆ’ 𝐷5 2 βˆ’ 2𝐷1𝐷3 ORG iajs-3638 212 9 𝐷3 CARDINAL iajs-3638 213 1 2 CARDINAL iajs-3638 213 2 𝐷3 CARDINAL iajs-3638 214 1 descartes GPE iajs-3638 214 2 2 CARDINAL iajs-3638 215 1 39 CARDINAL iajs-3638 216 1 37 CARDINAL iajs-3638 216 2 at least two CARDINAL iajs-3638 216 3 38 CARDINAL iajs-3638 216 4 1 πœ”0 π‘π‘œπ‘ βˆ’1 MONEY iajs-3638 216 5 2πœ”0 4+(𝐷5 DATE iajs-3638 216 6 2 + 2π‘˜πœ‹ DATE iajs-3638 216 7 41 CARDINAL iajs-3638 216 8 0,1,2 DATE iajs-3638 217 1 0 CARDINAL iajs-3638 217 2 3 CARDINAL iajs-3638 217 3 two CARDINAL iajs-3638 217 4 Β±πœ”0 DATE iajs-3638 218 1 πœ†(𝜏 NORP iajs-3638 220 1 37 CARDINAL iajs-3638 222 1 theorem2 PERSON iajs-3638 223 1 37 CARDINAL iajs-3638 224 1 0 CARDINAL iajs-3638 224 2 42a CARDINAL iajs-3638 224 3 2𝐷2 CARDINAL iajs-3638 224 4 𝐷1 2 ( DATE iajs-3638 224 5 𝐷2 2 > 2𝐷1𝐷3 QUANTITY iajs-3638 224 6 2𝐷4𝐷6 CARDINAL iajs-3638 224 7 2𝐷4 CARDINAL iajs-3638 224 8 2πœ”0 CARDINAL iajs-3638 225 1 πœ†(𝜏 PRODUCT iajs-3638 225 2 37 CARDINAL iajs-3638 225 3 3πœ†2 + 2𝐷1πœ† DATE iajs-3638 225 4 2𝐷4πœ† + 𝐷5)𝑒 βˆ’πœ†πœ βˆ’ QUANTITY iajs-3638 225 5 2 + CARDINAL iajs-3638 225 6 2 CARDINAL iajs-3638 225 7 43 CARDINAL iajs-3638 225 8 βˆ’1 DATE iajs-3638 226 1 3πœ†2+2𝐷1πœ†+𝐷2 DATE iajs-3638 228 1 44 CARDINAL iajs-3638 228 2 𝜏=𝜏0 NORP iajs-3638 228 3 𝐷2 CARDINAL iajs-3638 228 4 3πœ”0 CARDINAL iajs-3638 229 1 2(πœ”0 2 CARDINAL iajs-3638 230 1 2 CARDINAL iajs-3638 230 2 𝐷3 CARDINAL iajs-3638 232 1 2 + CARDINAL iajs-3638 232 2 2 CARDINAL iajs-3638 235 1 45 CARDINAL iajs-3638 235 2 ihjpas PERSON iajs-3638 236 1 2025 CARDINAL iajs-3638 236 2 38 CARDINAL iajs-3638 236 3 1 CARDINAL iajs-3638 236 4 455 CARDINAL iajs-3638 237 1 2(πœ”0 MONEY iajs-3638 238 1 2𝐷1(𝐷1πœ”0 CARDINAL iajs-3638 238 2 2βˆ’π·3)βˆ’(πœ”0 CARDINAL iajs-3638 238 3 2 CARDINAL iajs-3638 238 4 2(πœ”0 2βˆ’π·2 DATE iajs-3638 238 5 2 CARDINAL iajs-3638 239 1 2βˆ’π·3 CARDINAL iajs-3638 239 2 2 CARDINAL iajs-3638 239 3 2 CARDINAL iajs-3638 240 1 2 CARDINAL iajs-3638 240 2 𝑅𝑒 [ π‘‘πœ† π‘‘πœ PERSON iajs-3638 240 3 𝜏=𝜏0 NORP iajs-3638 240 4 2𝐷1(𝐷1πœ”0 CARDINAL iajs-3638 240 5 2βˆ’π·3)βˆ’(πœ”0 CARDINAL iajs-3638 240 6 2 CARDINAL iajs-3638 240 7 2(πœ”0 2 CARDINAL iajs-3638 240 8 𝐷2 CARDINAL iajs-3638 240 9 2 CARDINAL iajs-3638 241 1 2 CARDINAL iajs-3638 241 2 𝐷3 CARDINAL iajs-3638 241 3 2 CARDINAL iajs-3638 241 4 0 CARDINAL iajs-3638 241 5 2πœ”0 2 DATE iajs-3638 242 1 𝐷6 CARDINAL iajs-3638 242 2 0 CARDINAL iajs-3638 244 1 0 CARDINAL iajs-3638 245 1 42b42d CARDINAL iajs-3638 246 1 c.e. GPE iajs-3638 247 1 37 CARDINAL iajs-3638 248 1 3 CARDINAL iajs-3638 250 1 4 CARDINAL iajs-3638 251 1 βˆ’π‘…3𝑒 βˆ’πœ†πœ PERSON iajs-3638 251 2 1 + CARDINAL iajs-3638 251 3 βˆ— CARDINAL iajs-3638 251 4 βˆ’π›½2𝑉1 βˆ— ORG iajs-3638 251 5 βˆ— + DATE iajs-3638 251 6 βˆ’π›½3𝑉2 βˆ— ORG iajs-3638 251 7 𝛽3𝐼 PERSON iajs-3638 251 8 βˆ’πœ†πœ GPE iajs-3638 251 9 0 CARDINAL iajs-3638 252 1 46 DATE iajs-3638 252 2 𝑅1 GPE iajs-3638 252 3 1 + CARDINAL iajs-3638 252 4 βˆ— + DATE iajs-3638 252 5 𝑅2 CARDINAL iajs-3638 252 6 βˆ— CARDINAL iajs-3638 253 1 3 + 𝐢2πœ† QUANTITY iajs-3638 253 2 0 CARDINAL iajs-3638 253 3 47 CARDINAL iajs-3638 254 1 2025 CARDINAL iajs-3638 254 2 38 CARDINAL iajs-3638 254 3 1 CARDINAL iajs-3638 254 4 456 CARDINAL iajs-3638 254 5 𝐢1 CARDINAL iajs-3638 254 6 𝑅1 CARDINAL iajs-3638 255 1 𝐢2 CARDINAL iajs-3638 255 2 𝐢3 ORG iajs-3638 255 3 𝑐22𝑐33 + 𝑅4𝑐22 + LOC iajs-3638 257 1 𝑅4𝑐22𝑐33 CARDINAL iajs-3638 258 1 𝑅2 CARDINAL iajs-3638 258 2 𝑅3 CARDINAL iajs-3638 258 3 𝐢6 DATE iajs-3638 259 1 𝑅2 CARDINAL iajs-3638 266 1 0 CARDINAL iajs-3638 266 2 47 CARDINAL iajs-3638 266 3 0 CARDINAL iajs-3638 266 4 48 DATE iajs-3638 266 5 48 CARDINAL iajs-3638 266 6 half CARDINAL iajs-3638 266 7 3 CARDINAL iajs-3638 266 8 2(𝛽1𝑆 βˆ— + MONEY iajs-3638 266 9 βˆ— + 𝛽3𝑉2 βˆ— PRODUCT iajs-3638 266 10 49 DATE iajs-3638 266 11 0 CARDINAL iajs-3638 266 12 47 CARDINAL iajs-3638 266 13 two CARDINAL iajs-3638 267 1 47 CARDINAL iajs-3638 267 2 3)π‘ π‘–π‘›πœ”πœ CARDINAL iajs-3638 267 3 2 CARDINAL iajs-3638 267 4 βˆ’ 𝐢4 PERSON iajs-3638 267 5 3)π‘π‘œπ‘ πœ”πœ + QUANTITY iajs-3638 268 1 2 CARDINAL iajs-3638 269 1 3 CARDINAL iajs-3638 269 2 βˆ’ 𝐢3πœ”. ORG iajs-3638 269 3 50 CARDINAL iajs-3638 269 4 50 CARDINAL iajs-3638 270 1 0 CARDINAL iajs-3638 270 2 51 CARDINAL iajs-3638 270 3 51 CARDINAL iajs-3638 270 4 0 CARDINAL iajs-3638 270 5 2 CARDINAL iajs-3638 270 6 2𝐢2 CARDINAL iajs-3638 271 1 2 CARDINAL iajs-3638 271 2 2𝐢5𝐢7 + 𝐢2 MONEY iajs-3638 271 3 2 + 2𝐢4 DATE iajs-3638 271 4 2𝐢1𝐢3 CARDINAL iajs-3638 271 5 2𝐢6𝐢8 + 𝐢3 2 MONEY iajs-3638 271 6 2𝐢1𝐢4 CARDINAL iajs-3638 271 7 2 CARDINAL iajs-3638 271 8 52b CARDINAL iajs-3638 272 1 descartes GPE iajs-3638 272 2 2 CARDINAL iajs-3638 272 3 52a CARDINAL iajs-3638 273 1 51 CARDINAL iajs-3638 274 1 47 CARDINAL iajs-3638 274 2 at least two CARDINAL iajs-3638 274 3 50 CARDINAL iajs-3638 274 4 1 πœ”0 π‘π‘œπ‘ βˆ’1 MONEY iajs-3638 274 5 𝐢6βˆ’πΆ1𝐢5)πœ”0 ORG iajs-3638 274 6 2πœ”0 CARDINAL iajs-3638 275 1 4+(𝐢7 NORP iajs-3638 275 2 53 CARDINAL iajs-3638 276 1 2025 CARDINAL iajs-3638 276 2 38 CARDINAL iajs-3638 276 3 1 CARDINAL iajs-3638 276 4 457 CARDINAL iajs-3638 276 5 k=0,1,2 ORG iajs-3638 277 1 0 CARDINAL iajs-3638 277 2 3 CARDINAL iajs-3638 277 3 two CARDINAL iajs-3638 277 4 Β±πœ”0 DATE iajs-3638 278 1 πœ†(𝜏 NORP iajs-3638 283 1 theorem3 DATE iajs-3638 284 1 47 CARDINAL iajs-3638 285 1 0 CARDINAL iajs-3638 285 2 54a CARDINAL iajs-3638 285 3 6 + 2𝐢1 DATE iajs-3638 285 4 2πœ”0 CARDINAL iajs-3638 285 5 2 + 2𝐢4)πœ”0 DATE iajs-3638 285 6 2 + 2𝐢2𝐢3πœ”0 QUANTITY iajs-3638 286 1 4 + 𝐢3(𝐢1 + 4 DATE iajs-3638 286 2 54b CARDINAL iajs-3638 286 3 2𝐢5 CARDINAL iajs-3638 286 4 3 + 2𝐢6(𝐢7 + 𝐢8 DATE iajs-3638 287 1 54c CARDINAL iajs-3638 288 1 πœ†(𝜏 PRODUCT iajs-3638 288 2 47 CARDINAL iajs-3638 288 3 3𝐢5πœ† CARDINAL iajs-3638 290 1 55 CARDINAL iajs-3638 290 2 βˆ’1 DATE iajs-3638 290 3 4πœ†3+3𝐢1πœ† CARDINAL iajs-3638 290 4 2+2𝐢2πœ†+𝐢3 πœ†(𝐢5πœ†3+𝐢6πœ†2+𝐢7πœ†+𝐢8)π‘’βˆ’πœ†πœ + DATE iajs-3638 290 5 56 CARDINAL iajs-3638 290 6 𝜏=𝜏0 NORP iajs-3638 290 7 𝐢3 βˆ’ ORG iajs-3638 291 1 2 + DATE iajs-3638 291 2 4 + CARDINAL iajs-3638 291 3 4 + 𝐢4 QUANTITY iajs-3638 291 4 2 CARDINAL iajs-3638 293 1 2 + 𝐢7 + 2𝑖𝐢6πœ”0 DATE iajs-3638 293 2 4 + DATE iajs-3638 296 1 57 CARDINAL iajs-3638 296 2 𝑅𝑒 PERSON iajs-3638 296 3 2+π‘–πœ”0(2𝐢2βˆ’4πœ”0 CARDINAL iajs-3638 296 4 4+π‘–πœ”0(πœ”0 CARDINAL iajs-3638 296 5 2βˆ’πΆ3πœ”0 CARDINAL iajs-3638 298 1 2πœ”0 CARDINAL iajs-3638 298 2 2)(πœ”0 CARDINAL iajs-3638 298 3 2βˆ’πΆ3πœ”0 CARDINAL iajs-3638 298 4 2πœ”0 6+(πœ”0 CARDINAL iajs-3638 298 5 2βˆ’πΆ3πœ”0 CARDINAL iajs-3638 298 6 2 CARDINAL iajs-3638 299 1 𝑅𝑒 PERSON iajs-3638 299 2 2+𝐢7+2𝑖𝐢6πœ”0 𝐢5πœ”0 4+π‘–πœ”0(𝐢7+𝐢8βˆ’πΆ6πœ”0 2 DATE iajs-3638 300 1 2 CARDINAL iajs-3638 300 2 2πœ”0 6+(𝐢6+𝐢7βˆ’πΆ8πœ”0 DATE iajs-3638 300 3 2 CARDINAL iajs-3638 300 4 2 DATE iajs-3638 300 5 𝑅𝑒 PERSON iajs-3638 300 6 π‘§π‘’π‘Ÿπ‘œ. DATE iajs-3638 300 7 𝑅𝑒 [ π‘‘πœ† π‘‘πœ PERSON iajs-3638 300 8 𝜏=𝜏0 NORP iajs-3638 300 9 2πœ”0 CARDINAL iajs-3638 300 10 2)(πœ”0 CARDINAL iajs-3638 300 11 2βˆ’πΆ3πœ”0 CARDINAL iajs-3638 301 1 2πœ”0 CARDINAL iajs-3638 302 1 4 + 𝐢4 QUANTITY iajs-3638 302 2 2 CARDINAL iajs-3638 302 3 0 CARDINAL iajs-3638 302 4 2πœ”0 CARDINAL iajs-3638 303 1 0 CARDINAL iajs-3638 304 1 ihjpas PERSON iajs-3638 305 1 2025 CARDINAL iajs-3638 305 2 38 CARDINAL iajs-3638 305 3 1 CARDINAL iajs-3638 305 4 458 CARDINAL iajs-3638 306 1 0 CARDINAL iajs-3638 308 1 c.e. GPE iajs-3638 309 1 47 CARDINAL iajs-3638 310 1 3 CARDINAL iajs-3638 312 1 4 CARDINAL iajs-3638 313 1 0.042 CARDINAL iajs-3638 313 2 0.03 CARDINAL iajs-3638 313 3 0.02 CARDINAL iajs-3638 313 4 0.01 CARDINAL iajs-3638 313 5 0.3 CARDINAL iajs-3638 313 6 50 CARDINAL iajs-3638 313 7 0.1 CARDINAL iajs-3638 313 8 0.01 CARDINAL iajs-3638 313 9 0.03 CARDINAL iajs-3638 313 10 0.00015 CARDINAL iajs-3638 313 11 25.2225 CARDINAL iajs-3638 314 1 58 CARDINAL iajs-3638 314 2 3 CARDINAL iajs-3638 314 3 t.d. 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