From 20fc727d4f954eb2109b71a7686c3107fdfa4bbf Mon Sep 17 00:00:00 2001 From: Anhgelus Morhtuuzh Date: Fri, 21 Nov 2025 18:37:48 +0100 Subject: Cours du 3 au 21 novembre ce qui fait 3 semaines en philo et une semaine en info --- .../.gitignore" | 1 + .../4- Automates finis.pdf" | 4100 ++++++++++++-------- .../4- Automates finis.typ" | 36 +- 3 files changed, 2597 insertions(+), 1540 deletions(-) (limited to 'semestre 3/mathématiques discrètes') diff --git "a/semestre 3/math\303\251matiques discr\303\250tes/.gitignore" "b/semestre 3/math\303\251matiques discr\303\250tes/.gitignore" index 98f05f7..90f2441 100644 --- "a/semestre 3/math\303\251matiques discr\303\250tes/.gitignore" +++ "b/semestre 3/math\303\251matiques discr\303\250tes/.gitignore" @@ -315,3 +315,4 @@ TSWLatexianTemp* TD*.pdf *Recettes.pdf +projet diff --git "a/semestre 3/math\303\251matiques discr\303\250tes/4- Automates finis.pdf" "b/semestre 3/math\303\251matiques discr\303\250tes/4- Automates finis.pdf" index d3d22a0..8362275 100644 --- "a/semestre 3/math\303\251matiques discr\303\250tes/4- Automates finis.pdf" +++ "b/semestre 3/math\303\251matiques discr\303\250tes/4- Automates finis.pdf" @@ -5,7 +5,7 @@ << /Type /Pages /Count 5 - /Kids [244 0 R 246 0 R 249 0 R 252 0 R 254 0 R] + /Kids [319 0 R 321 0 R 324 0 R 327 0 R 329 0 R] >> endobj @@ -26,7 +26,7 @@ endobj /Last 5 0 R /Count -2 /Title (1. Langages et automates) - /Dest 236 0 R + /Dest 310 0 R >> endobj @@ -35,7 +35,7 @@ endobj /Parent 3 0 R /Next 5 0 R /Title - /Dest 234 0 R + /Dest 308 0 R >> endobj @@ -44,7 +44,7 @@ endobj /Parent 3 0 R /Prev 4 0 R /Title - /Dest 235 0 R + /Dest 309 0 R >> endobj @@ -57,7 +57,7 @@ endobj /Last 10 0 R /Count -2 /Title - /Dest 241 0 R + /Dest 315 0 R >> endobj @@ -69,7 +69,7 @@ endobj /Last 9 0 R /Count -2 /Title - /Dest 239 0 R + /Dest 313 0 R >> endobj @@ -78,7 +78,7 @@ endobj /Parent 7 0 R /Next 9 0 R /Title - /Dest 237 0 R + /Dest 311 0 R >> endobj @@ -87,7 +87,7 @@ endobj /Parent 7 0 R /Prev 8 0 R /Title - /Dest 238 0 R + /Dest 312 0 R >> endobj @@ -96,7 +96,7 @@ endobj /Parent 6 0 R /Prev 7 0 R /Title - /Dest 240 0 R + /Dest 314 0 R >> endobj @@ -105,13 +105,13 @@ endobj /Parent 2 0 R /Prev 6 0 R /Title - /Dest 242 0 R + /Dest 316 0 R >> endobj 12 0 obj << - /Nums [0 207 0 R 1 208 0 R 2 209 0 R 3 210 0 R 4 211 0 R] + /Nums [0 265 0 R 1 266 0 R 2 267 0 R 3 268 0 R 4 269 0 R] >> endobj @@ -127,30 +127,30 @@ endobj >> /K [19 0 R] /ParentTree << - /Nums [0 14 0 R 1 15 0 R 2 59 0 R 3 16 0 R 4 41 0 R 5 17 0 R 6 18 0 R] + /Nums [0 14 0 R 1 15 0 R 2 117 0 R 3 16 0 R 4 70 0 R 5 17 0 R 6 18 0 R] >> /ParentTreeNextKey 7 >> endobj 14 0 obj -[206 0 R 205 0 R 205 0 R 204 0 R 204 0 R 200 0 R 203 0 R 203 0 R 200 0 R 202 0 R 202 0 R 200 0 R 201 0 R 200 0 R 197 0 R 199 0 R 197 0 R 198 0 R 197 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 196 0 R 193 0 R 195 0 R 195 0 R 193 0 R 194 0 R 194 0 R 194 0 R 193 0 R 188 0 R 192 0 R 192 0 R 188 0 R 191 0 R 191 0 R 191 0 R 191 0 R 188 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 188 0 R 189 0 R 189 0 R 189 0 R 183 0 R 187 0 R 183 0 R 186 0 R 183 0 R 185 0 R 183 0 R 184 0 R 183 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 182 0 R 178 0 R 181 0 R 181 0 R 178 0 R 180 0 R 178 0 R 179 0 R 179 0 R 178 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 174 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 174 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 174 0 R 173 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 172 0 R 169 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 158 0 R 164 0 R 158 0 R 163 0 R 158 0 R 158 0 R 162 0 R 158 0 R 158 0 R 161 0 R 158 0 R 160 0 R 160 0 R 158 0 R 159 0 R 158 0 R 157 0 R 157 0 R 151 0 R 156 0 R 156 0 R 156 0 R 156 0 R 151 0 R 155 0 R 151 0 R 154 0 R 154 0 R 151 0 R 153 0 R 151 0 R 152 0 R 151 0 R 148 0 R 150 0 R 148 0 R 148 0 R 149 0 R 148 0 R 148 0 R 145 0 R 147 0 R 145 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 145 0 R 144 0 R 143 0 R 142 0 R 140 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 138 0 R 136 0 R 135 0 R 135 0 R 135 0 R 134 0 R 132 0 R 131 0 R 131 0 R 131 0 R 130 0 R] +[264 0 R 263 0 R 263 0 R 262 0 R 262 0 R 258 0 R 261 0 R 261 0 R 258 0 R 260 0 R 260 0 R 258 0 R 259 0 R 258 0 R 255 0 R 257 0 R 255 0 R 256 0 R 255 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 251 0 R 253 0 R 253 0 R 251 0 R 252 0 R 252 0 R 252 0 R 251 0 R 246 0 R 250 0 R 250 0 R 246 0 R 249 0 R 249 0 R 249 0 R 249 0 R 246 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 246 0 R 247 0 R 247 0 R 247 0 R 241 0 R 245 0 R 241 0 R 244 0 R 241 0 R 243 0 R 241 0 R 242 0 R 241 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 236 0 R 239 0 R 239 0 R 236 0 R 238 0 R 236 0 R 237 0 R 237 0 R 236 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 232 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 232 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 232 0 R 231 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 230 0 R 227 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 226 0 R 216 0 R 222 0 R 216 0 R 221 0 R 216 0 R 216 0 R 220 0 R 216 0 R 216 0 R 219 0 R 216 0 R 218 0 R 218 0 R 216 0 R 217 0 R 216 0 R 215 0 R 215 0 R 209 0 R 214 0 R 214 0 R 214 0 R 214 0 R 209 0 R 213 0 R 209 0 R 212 0 R 212 0 R 209 0 R 211 0 R 209 0 R 210 0 R 209 0 R 206 0 R 208 0 R 206 0 R 206 0 R 207 0 R 206 0 R 206 0 R 203 0 R 205 0 R 203 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 203 0 R 202 0 R 201 0 R 200 0 R 198 0 R 197 0 R 197 0 R 197 0 R 197 0 R 197 0 R 197 0 R 197 0 R 196 0 R 194 0 R 193 0 R 193 0 R 193 0 R 192 0 R 190 0 R 189 0 R 189 0 R 189 0 R 188 0 R] endobj 15 0 obj -[123 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 123 0 R 123 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 123 0 R 125 0 R 125 0 R 123 0 R 123 0 R 124 0 R 123 0 R 118 0 R 122 0 R 121 0 R 121 0 R 120 0 R 114 0 R 116 0 R 114 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 114 0 R 113 0 R 112 0 R 112 0 R 112 0 R 112 0 R 111 0 R 109 0 R 106 0 R 108 0 R 108 0 R 108 0 R 108 0 R 108 0 R 106 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 106 0 R 106 0 R 97 0 R 103 0 R 103 0 R 103 0 R 103 0 R 103 0 R 97 0 R 102 0 R 97 0 R 101 0 R 97 0 R 100 0 R 100 0 R 100 0 R 100 0 R 97 0 R 99 0 R 97 0 R 98 0 R 97 0 R 97 0 R 94 0 R 96 0 R 94 0 R 95 0 R 95 0 R 95 0 R 95 0 R 94 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 88 0 R 92 0 R 88 0 R 91 0 R 88 0 R 90 0 R 88 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 88 0 R 83 0 R 87 0 R 87 0 R 87 0 R 87 0 R 83 0 R 86 0 R 83 0 R 85 0 R 83 0 R 84 0 R 83 0 R 82 0 R 82 0 R 82 0 R 82 0 R 82 0 R 82 0 R] +[181 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 181 0 R 181 0 R 184 0 R 184 0 R 184 0 R 184 0 R 184 0 R 184 0 R 181 0 R 183 0 R 183 0 R 181 0 R 181 0 R 182 0 R 181 0 R 176 0 R 180 0 R 179 0 R 179 0 R 178 0 R 172 0 R 174 0 R 172 0 R 173 0 R 173 0 R 173 0 R 173 0 R 173 0 R 173 0 R 173 0 R 173 0 R 173 0 R 173 0 R 173 0 R 172 0 R 171 0 R 170 0 R 170 0 R 170 0 R 170 0 R 169 0 R 167 0 R 164 0 R 166 0 R 166 0 R 166 0 R 166 0 R 166 0 R 164 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 164 0 R 164 0 R 155 0 R 161 0 R 161 0 R 161 0 R 161 0 R 161 0 R 155 0 R 160 0 R 155 0 R 159 0 R 155 0 R 158 0 R 158 0 R 158 0 R 158 0 R 155 0 R 157 0 R 155 0 R 156 0 R 155 0 R 155 0 R 152 0 R 154 0 R 152 0 R 153 0 R 153 0 R 153 0 R 153 0 R 152 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 146 0 R 150 0 R 146 0 R 149 0 R 146 0 R 148 0 R 146 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 146 0 R 141 0 R 145 0 R 145 0 R 145 0 R 145 0 R 141 0 R 144 0 R 141 0 R 143 0 R 141 0 R 142 0 R 141 0 R 140 0 R 140 0 R 140 0 R 140 0 R 140 0 R 140 0 R] endobj 16 0 obj -[81 0 R 81 0 R 81 0 R 81 0 R 80 0 R 80 0 R 79 0 R 79 0 R 78 0 R 78 0 R 77 0 R 76 0 R 74 0 R 72 0 R 73 0 R 72 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 64 0 R 68 0 R 64 0 R 67 0 R 64 0 R 66 0 R 66 0 R 66 0 R 64 0 R 65 0 R 64 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 61 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 61 0 R 60 0 R 59 0 R 58 0 R 57 0 R 54 0 R 56 0 R 52 0 R 52 0 R 51 0 R 50 0 R 50 0 R 46 0 R 49 0 R 49 0 R 49 0 R 49 0 R 49 0 R 49 0 R 49 0 R 49 0 R 49 0 R 49 0 R 49 0 R 46 0 R 48 0 R 46 0 R 47 0 R 46 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 44 0 R 43 0 R] +[139 0 R 139 0 R 138 0 R 138 0 R 137 0 R 137 0 R 136 0 R 136 0 R 135 0 R 134 0 R 132 0 R 130 0 R 131 0 R 130 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 122 0 R 126 0 R 122 0 R 125 0 R 122 0 R 124 0 R 124 0 R 124 0 R 122 0 R 123 0 R 122 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 119 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 119 0 R 118 0 R 117 0 R 116 0 R 115 0 R 112 0 R 114 0 R 110 0 R 110 0 R 109 0 R 108 0 R 108 0 R 104 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 107 0 R 104 0 R 106 0 R 104 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 104 0 R 103 0 R 98 0 R 102 0 R 98 0 R 101 0 R 101 0 R 101 0 R 101 0 R 98 0 R 100 0 R 100 0 R 100 0 R 98 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 99 0 R 96 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 92 0 R 91 0 R 91 0 R 91 0 R 91 0 R 90 0 R 88 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 84 0 R 83 0 R 79 0 R 79 0 R 75 0 R 78 0 R 78 0 R 78 0 R 78 0 R 78 0 R 78 0 R 78 0 R 78 0 R 78 0 R 78 0 R 78 0 R 75 0 R 77 0 R 75 0 R 76 0 R 75 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R] endobj 17 0 obj -[38 0 R 42 0 R 41 0 R 40 0 R 34 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 34 0 R 35 0 R 34 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 32 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 30 0 R 29 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 25 0 R 24 0 R 24 0 R 24 0 R 24 0 R 23 0 R] +[73 0 R 72 0 R 67 0 R 71 0 R 70 0 R 69 0 R 63 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 63 0 R 64 0 R 63 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 61 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 59 0 R 58 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 54 0 R 53 0 R 53 0 R 53 0 R 53 0 R 52 0 R] endobj 18 0 obj -[20 0 R 20 0 R] +[49 0 R 49 0 R 46 0 R 48 0 R 48 0 R 48 0 R 48 0 R 46 0 R 47 0 R 46 0 R 42 0 R 45 0 R 42 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 42 0 R 43 0 R 42 0 R 42 0 R 42 0 R 38 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 38 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 38 0 R 39 0 R 39 0 R 39 0 R 39 0 R 39 0 R 39 0 R 38 0 R 37 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 33 0 R 31 0 R 32 0 R 31 0 R 28 0 R 28 0 R 22 0 R 27 0 R 27 0 R 22 0 R 26 0 R 26 0 R 22 0 R 25 0 R 22 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 22 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 22 0 R 22 0 R 21 0 R] endobj 19 0 obj @@ -158,50 +158,46 @@ endobj /Type /StructElem /S /Document /P 13 0 R - /K [206 0 R 205 0 R 204 0 R 200 0 R 197 0 R 196 0 R 193 0 R 188 0 R 183 0 R 182 0 R 178 0 R 177 0 R 174 0 R 165 0 R 158 0 R 157 0 R 151 0 R 148 0 R 145 0 R 128 0 R 123 0 R 117 0 R 114 0 R 104 0 R 97 0 R 94 0 R 93 0 R 88 0 R 83 0 R 82 0 R 81 0 R 80 0 R 79 0 R 78 0 R 70 0 R 69 0 R 64 0 R 63 0 R 61 0 R 60 0 R 58 0 R 57 0 R 53 0 R 52 0 R 51 0 R 50 0 R 46 0 R 45 0 R 44 0 R 43 0 R 37 0 R 34 0 R 33 0 R 32 0 R 31 0 R 30 0 R 21 0 R 20 0 R] + /K [264 0 R 263 0 R 262 0 R 258 0 R 255 0 R 254 0 R 251 0 R 246 0 R 241 0 R 240 0 R 236 0 R 235 0 R 232 0 R 223 0 R 216 0 R 215 0 R 209 0 R 206 0 R 203 0 R 186 0 R 181 0 R 175 0 R 172 0 R 162 0 R 155 0 R 152 0 R 151 0 R 146 0 R 141 0 R 140 0 R 139 0 R 138 0 R 137 0 R 136 0 R 128 0 R 127 0 R 122 0 R 121 0 R 119 0 R 118 0 R 116 0 R 115 0 R 111 0 R 110 0 R 109 0 R 108 0 R 104 0 R 80 0 R 79 0 R 75 0 R 74 0 R 73 0 R 72 0 R 66 0 R 63 0 R 62 0 R 61 0 R 60 0 R 59 0 R 50 0 R 49 0 R 46 0 R 42 0 R 38 0 R 29 0 R 28 0 R 22 0 R 20 0 R] >> endobj 20 0 obj << /Type /StructElem - /S /H1 + /S /P /P 19 0 R - /T - /K [0 1] - /Pg 254 0 R + /K [21 0 R] >> endobj 21 0 obj << /Type /StructElem - /S /L - /P 19 0 R - /A [<< - /O /List - /ListNumbering /Circle - >>] - /K [26 0 R 22 0 R] + /S /Em + /P 20 0 R + /K [92] + /Pg 329 0 R >> endobj 22 0 obj << /Type /StructElem - /S /LI - /P 21 0 R - /K [25 0 R 23 0 R] + /S /P + /P 19 0 R + /K [70 27 0 R 73 26 0 R 76 25 0 R 78 24 0 R 84 23 0 R 90 91] + /Pg 329 0 R >> endobj 23 0 obj << /Type /StructElem - /S /LBody + /S /Formula /P 22 0 R - /K [24 0 R 101] - /Pg 252 0 R + /K [85 86 87 88 89] + /Pg 329 0 R >> endobj @@ -209,125 +205,119 @@ endobj << /Type /StructElem /S /Formula - /P 23 0 R - /K [97 98 99 100] - /Pg 252 0 R + /P 22 0 R + /K [79 80 81 82 83] + /Pg 329 0 R >> endobj 25 0 obj << /Type /StructElem - /S /Lbl + /S /Formula /P 22 0 R - /K [96] - /Pg 252 0 R + /K [77] + /Pg 329 0 R >> endobj 26 0 obj << /Type /StructElem - /S /LI - /P 21 0 R - /K [29 0 R 27 0 R] + /S /Formula + /P 22 0 R + /K [74 75] + /Pg 329 0 R >> endobj 27 0 obj << /Type /StructElem - /S /LBody - /P 26 0 R - /K [28 0 R] + /S /Formula + /P 22 0 R + /K [71 72] + /Pg 329 0 R >> endobj 28 0 obj << /Type /StructElem - /S /Formula - /P 27 0 R - /K [84 85 86 87 88 89 90 91 92 93 94 95] - /Pg 252 0 R + /S /P + /P 19 0 R + /K [68 69] + /Pg 329 0 R >> endobj 29 0 obj << /Type /StructElem - /S /Lbl - /P 26 0 R - /K [83] - /Pg 252 0 R + /S /L + /P 19 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [34 0 R 30 0 R] >> endobj 30 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [82] - /Pg 252 0 R + /S /LI + /P 29 0 R + /K [33 0 R 31 0 R] >> endobj 31 0 obj << /Type /StructElem - /S /Formula - /P 19 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81] - /Pg 252 0 R + /S /LBody + /P 30 0 R + /K [65 32 0 R 67] + /Pg 329 0 R >> endobj 32 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [38] - /Pg 252 0 R + /S /Formula + /P 31 0 R + /K [66] + /Pg 329 0 R >> endobj 33 0 obj << /Type /StructElem - /S /Formula - /P 19 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37] - /Pg 252 0 R + /S /Lbl + /P 30 0 R + /K [64] + /Pg 329 0 R >> endobj 34 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [4 36 0 R 16 35 0 R 18] - /Pg 252 0 R + /S /LI + /P 29 0 R + /K [37 0 R 35 0 R] >> endobj 35 0 obj << /Type /StructElem - /S /Formula + /S /LBody /P 34 0 R - /K [17] - /Pg 252 0 R + /K [36 0 R] >> endobj @@ -335,107 +325,89 @@ endobj << /Type /StructElem /S /Formula - /P 34 0 R - /K [5 6 7 8 9 10 11 12 13 14 15] - /Pg 252 0 R + /P 35 0 R + /K [58 59 60 61 62 63] + /Pg 329 0 R >> endobj 37 0 obj << /Type /StructElem - /S /Div - /P 19 0 R - /K [39 0 R 38 0 R] + /S /Lbl + /P 34 0 R + /K [57] + /Pg 329 0 R >> endobj 38 0 obj << /Type /StructElem - /S /Figure - /P 37 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0] - /Pg 252 0 R + /S /P + /P 19 0 R + /K [24 41 0 R 36 40 0 R 49 39 0 R 56] + /Pg 329 0 R >> endobj 39 0 obj << /Type /StructElem - /S /Caption - /P 37 0 R - /K [42 0 R 41 0 R 40 0 R] + /S /Formula + /P 38 0 R + /K [50 51 52 53 54 55] + /Pg 329 0 R >> endobj 40 0 obj << /Type /StructElem - /S /Span - /P 39 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [3] - /Pg 252 0 R + /S /Formula + /P 38 0 R + /K [37 38 39 40 41 42 43 44 45 46 47 48] + /Pg 329 0 R >> endobj 41 0 obj << /Type /StructElem - /S /Link - /P 39 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [2 << - /Type /OBJR - /Pg 252 0 R - /Obj 251 0 R - >>] - /Pg 252 0 R + /S /Formula + /P 38 0 R + /K [25 26 27 28 29 30 31 32 33 34 35] + /Pg 329 0 R >> endobj 42 0 obj << /Type /StructElem - /S /Span - /P 39 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [1] - /Pg 252 0 R + /S /P + /P 19 0 R + /K [10 45 0 R 12 44 0 R 19 43 0 R 21 22 23] + /Pg 329 0 R >> endobj 43 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [128] - /Pg 249 0 R + /S /Formula + /P 42 0 R + /K [20] + /Pg 329 0 R >> endobj 44 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [127] - /Pg 249 0 R + /S /Formula + /P 42 0 R + /K [13 14 15 16 17 18] + /Pg 329 0 R >> endobj @@ -443,13 +415,9 @@ endobj << /Type /StructElem /S /Formula - /P 19 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126] - /Pg 249 0 R + /P 42 0 R + /K [11] + /Pg 329 0 R >> endobj @@ -458,18 +426,18 @@ endobj /Type /StructElem /S /P /P 19 0 R - /K [84 49 0 R 96 48 0 R 98 47 0 R 100] - /Pg 249 0 R + /K [2 48 0 R 7 47 0 R 9] + /Pg 329 0 R >> endobj 47 0 obj << /Type /StructElem - /S /Em + /S /Formula /P 46 0 R - /K [99] - /Pg 249 0 R + /K [8] + /Pg 329 0 R >> endobj @@ -478,140 +446,133 @@ endobj /Type /StructElem /S /Formula /P 46 0 R - /K [97] - /Pg 249 0 R + /K [3 4 5 6] + /Pg 329 0 R >> endobj 49 0 obj << /Type /StructElem - /S /Formula - /P 46 0 R - /K [85 86 87 88 89 90 91 92 93 94 95] - /Pg 249 0 R + /S /H1 + /P 19 0 R + /T + /K [0 1] + /Pg 329 0 R >> endobj 50 0 obj << /Type /StructElem - /S /H2 + /S /L /P 19 0 R - /T - /K [82 83] - /Pg 249 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [55 0 R 51 0 R] >> endobj 51 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [81] - /Pg 249 0 R + /S /LI + /P 50 0 R + /K [54 0 R 52 0 R] >> endobj 52 0 obj << /Type /StructElem - /S /H3 - /P 19 0 R - /T - /K [79 80] - /Pg 249 0 R + /S /LBody + /P 51 0 R + /K [53 0 R 103] + /Pg 327 0 R >> endobj 53 0 obj << /Type /StructElem - /S /Div - /P 19 0 R - /K [55 0 R 54 0 R] + /S /Formula + /P 52 0 R + /K [99 100 101 102] + /Pg 327 0 R >> endobj 54 0 obj << /Type /StructElem - /S /Figure - /P 53 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [77] - /Pg 249 0 R + /S /Lbl + /P 51 0 R + /K [98] + /Pg 327 0 R >> endobj 55 0 obj << /Type /StructElem - /S /Caption - /P 53 0 R - /K [56 0 R] + /S /LI + /P 50 0 R + /K [58 0 R 56 0 R] >> endobj 56 0 obj << /Type /StructElem - /S /Span + /S /LBody /P 55 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [78] - /Pg 249 0 R + /K [57 0 R] >> endobj 57 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [76] - /Pg 249 0 R + /S /Formula + /P 56 0 R + /K [86 87 88 89 90 91 92 93 94 95 96 97] + /Pg 327 0 R >> endobj 58 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [59 0 R 75] - /Pg 249 0 R + /S /Lbl + /P 55 0 R + /K [85] + /Pg 327 0 R >> endobj 59 0 obj << /Type /StructElem - /S /Link - /P 58 0 R - /K [74 << - /Type /OBJR - /Pg 249 0 R - /Obj 248 0 R - >>] - /Pg 249 0 R + /S /P + /P 19 0 R + /K [84] + /Pg 327 0 R >> endobj 60 0 obj << /Type /StructElem - /S /P + /S /Formula /P 19 0 R - /K [73] - /Pg 249 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83] + /Pg 327 0 R >> endobj @@ -620,8 +581,8 @@ endobj /Type /StructElem /S /P /P 19 0 R - /K [61 62 0 R 72] - /Pg 249 0 R + /K [40] + /Pg 327 0 R >> endobj @@ -629,33 +590,33 @@ endobj << /Type /StructElem /S /Formula - /P 61 0 R - /K [62 63 64 65 66 67 68 69 70 71] - /Pg 249 0 R + /P 19 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39] + /Pg 327 0 R >> endobj 63 0 obj << /Type /StructElem - /S /Formula + /S /P /P 19 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [52 53 54 55 56 57 58 59 60] - /Pg 249 0 R + /K [6 65 0 R 18 64 0 R 20] + /Pg 327 0 R >> endobj 64 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [41 68 0 R 43 67 0 R 45 66 0 R 49 65 0 R 51] - /Pg 249 0 R + /S /Formula + /P 63 0 R + /K [19] + /Pg 327 0 R >> endobj @@ -663,231 +624,241 @@ endobj << /Type /StructElem /S /Formula - /P 64 0 R - /K [50] - /Pg 249 0 R + /P 63 0 R + /K [7 8 9 10 11 12 13 14 15 16 17] + /Pg 327 0 R >> endobj 66 0 obj << /Type /StructElem - /S /Formula - /P 64 0 R - /K [46 47 48] - /Pg 249 0 R + /S /Div + /P 19 0 R + /K [68 0 R 67 0 R] >> endobj 67 0 obj << /Type /StructElem - /S /Em - /P 64 0 R - /K [44] - /Pg 249 0 R + /S /Figure + /P 66 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [2] + /Pg 327 0 R >> endobj 68 0 obj << /Type /StructElem - /S /Formula - /P 64 0 R - /K [42] - /Pg 249 0 R + /S /Caption + /P 66 0 R + /K [71 0 R 70 0 R 69 0 R] >> endobj 69 0 obj << /Type /StructElem - /S /Formula - /P 19 0 R + /S /Span + /P 68 0 R /A [<< /O /Layout /Placement /Block >>] - /K [16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40] - /Pg 249 0 R + /K [5] + /Pg 327 0 R >> endobj 70 0 obj << /Type /StructElem - /S /L - /P 19 0 R + /S /Link + /P 68 0 R /A [<< - /O /List - /ListNumbering /Circle + /O /Layout + /Placement /Block >>] - /K [75 0 R 71 0 R] + /K [4 << + /Type /OBJR + /Pg 327 0 R + /Obj 326 0 R + >>] + /Pg 327 0 R >> endobj 71 0 obj << /Type /StructElem - /S /LI - /P 70 0 R - /K [74 0 R 72 0 R] + /S /Span + /P 68 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [3] + /Pg 327 0 R >> endobj 72 0 obj << /Type /StructElem - /S /LBody - /P 71 0 R - /K [13 73 0 R 15] - /Pg 249 0 R + /S /P + /P 19 0 R + /K [1] + /Pg 327 0 R >> endobj 73 0 obj << /Type /StructElem - /S /Formula - /P 72 0 R - /K [14] - /Pg 249 0 R + /S /P + /P 19 0 R + /K [0] + /Pg 327 0 R >> endobj 74 0 obj << /Type /StructElem - /S /Lbl - /P 71 0 R - /K [12] - /Pg 249 0 R + /S /Formula + /P 19 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240] + /Pg 324 0 R >> endobj 75 0 obj << /Type /StructElem - /S /LI - /P 70 0 R - /K [77 0 R 76 0 R] + /S /P + /P 19 0 R + /K [198 78 0 R 210 77 0 R 212 76 0 R 214] + /Pg 324 0 R >> endobj 76 0 obj << /Type /StructElem - /S /LBody + /S /Em /P 75 0 R - /K [11] - /Pg 249 0 R + /K [213] + /Pg 324 0 R >> endobj 77 0 obj << /Type /StructElem - /S /Lbl + /S /Formula /P 75 0 R - /K [10] - /Pg 249 0 R + /K [211] + /Pg 324 0 R >> endobj 78 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [8 9] - /Pg 249 0 R + /S /Formula + /P 75 0 R + /K [199 200 201 202 203 204 205 206 207 208 209] + /Pg 324 0 R >> endobj 79 0 obj << /Type /StructElem - /S /H3 + /S /H2 /P 19 0 R - /T - /K [6 7] - /Pg 249 0 R + /T + /K [196 197] + /Pg 324 0 R >> endobj 80 0 obj << /Type /StructElem - /S /H2 + /S /L /P 19 0 R - /T - /K [4 5] - /Pg 249 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [97 0 R 93 0 R 89 0 R 85 0 R 81 0 R] >> endobj 81 0 obj << /Type /StructElem - /S /H1 - /P 19 0 R - /T - /K [0 1 2 3] - /Pg 249 0 R + /S /LI + /P 80 0 R + /K [84 0 R 82 0 R] >> endobj 82 0 obj << /Type /StructElem - /S /Formula - /P 19 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [148 149 150 151 152 153] - /Pg 246 0 R + /S /LBody + /P 81 0 R + /K [83 0 R] >> endobj 83 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [136 87 0 R 141 86 0 R 143 85 0 R 145 84 0 R 147] - /Pg 246 0 R + /S /Em + /P 82 0 R + /K [195] + /Pg 324 0 R >> endobj 84 0 obj << /Type /StructElem - /S /Formula - /P 83 0 R - /K [146] - /Pg 246 0 R + /S /Lbl + /P 81 0 R + /K [194] + /Pg 324 0 R >> endobj 85 0 obj << /Type /StructElem - /S /Formula - /P 83 0 R - /K [144] - /Pg 246 0 R + /S /LI + /P 80 0 R + /K [88 0 R 86 0 R] >> endobj 86 0 obj << /Type /StructElem - /S /Em - /P 83 0 R - /K [142] - /Pg 246 0 R + /S /LBody + /P 85 0 R + /K [87 0 R] >> endobj @@ -895,39 +866,38 @@ endobj << /Type /StructElem /S /Formula - /P 83 0 R - /K [137 138 139 140] - /Pg 246 0 R + /P 86 0 R + /K [182 183 184 185 186 187 188 189 190 191 192 193] + /Pg 324 0 R >> endobj 88 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [119 92 0 R 121 91 0 R 123 90 0 R 125 89 0 R 135] - /Pg 246 0 R + /S /Lbl + /P 85 0 R + /K [181] + /Pg 324 0 R >> endobj 89 0 obj << /Type /StructElem - /S /Formula - /P 88 0 R - /K [126 127 128 129 130 131 132 133 134] - /Pg 246 0 R + /S /LI + /P 80 0 R + /K [92 0 R 90 0 R] >> endobj 90 0 obj << /Type /StructElem - /S /Em - /P 88 0 R - /K [124] - /Pg 246 0 R + /S /LBody + /P 89 0 R + /K [91 0 R 180] + /Pg 324 0 R >> endobj @@ -935,43 +905,37 @@ endobj << /Type /StructElem /S /Formula - /P 88 0 R - /K [122] - /Pg 246 0 R + /P 90 0 R + /K [176 177 178 179] + /Pg 324 0 R >> endobj 92 0 obj << /Type /StructElem - /S /Formula - /P 88 0 R - /K [120] - /Pg 246 0 R + /S /Lbl + /P 89 0 R + /K [175] + /Pg 324 0 R >> endobj 93 0 obj << /Type /StructElem - /S /Formula - /P 19 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [104 105 106 107 108 109 110 111 112 113 114 115 116 117 118] - /Pg 246 0 R + /S /LI + /P 80 0 R + /K [96 0 R 94 0 R] >> endobj 94 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [96 96 0 R 98 95 0 R 103] - /Pg 246 0 R + /S /LBody + /P 93 0 R + /K [95 0 R] >> endobj @@ -980,48 +944,47 @@ endobj /Type /StructElem /S /Formula /P 94 0 R - /K [99 100 101 102] - /Pg 246 0 R + /K [161 162 163 164 165 166 167 168 169 170 171 172 173 174] + /Pg 324 0 R >> endobj 96 0 obj << /Type /StructElem - /S /Formula - /P 94 0 R - /K [97] - /Pg 246 0 R + /S /Lbl + /P 93 0 R + /K [160] + /Pg 324 0 R >> endobj 97 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [75 103 0 R 81 102 0 R 83 101 0 R 85 100 0 R 90 99 0 R 92 98 0 R 94 95] - /Pg 246 0 R + /S /LI + /P 80 0 R + /K [103 0 R 98 0 R] >> endobj 98 0 obj << /Type /StructElem - /S /Formula + /S /LBody /P 97 0 R - /K [93] - /Pg 246 0 R + /K [118 102 0 R 120 101 0 R 125 100 0 R 129 99 0 R] + /Pg 324 0 R >> endobj 99 0 obj << /Type /StructElem - /S /Em - /P 97 0 R - /K [91] - /Pg 246 0 R + /S /Formula + /P 98 0 R + /K [130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159] + /Pg 324 0 R >> endobj @@ -1029,19 +992,19 @@ endobj << /Type /StructElem /S /Formula - /P 97 0 R - /K [86 87 88 89] - /Pg 246 0 R + /P 98 0 R + /K [126 127 128] + /Pg 324 0 R >> endobj 101 0 obj << /Type /StructElem - /S /Em - /P 97 0 R - /K [84] - /Pg 246 0 R + /S /Formula + /P 98 0 R + /K [121 122 123 124] + /Pg 324 0 R >> endobj @@ -1049,51 +1012,49 @@ endobj << /Type /StructElem /S /Formula - /P 97 0 R - /K [82] - /Pg 246 0 R + /P 98 0 R + /K [119] + /Pg 324 0 R >> endobj 103 0 obj << /Type /StructElem - /S /Formula + /S /Lbl /P 97 0 R - /K [76 77 78 79 80] - /Pg 246 0 R + /K [117] + /Pg 324 0 R >> endobj 104 0 obj << /Type /StructElem - /S /L + /S /P /P 19 0 R - /A [<< - /O /List - /ListNumbering /Circle - >>] - /K [110 0 R 105 0 R] + /K [82 107 0 R 94 106 0 R 96 105 0 R 116] + /Pg 324 0 R >> endobj 105 0 obj << /Type /StructElem - /S /LI + /S /Formula /P 104 0 R - /K [109 0 R 106 0 R] + /K [97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115] + /Pg 324 0 R >> endobj 106 0 obj << /Type /StructElem - /S /LBody - /P 105 0 R - /K [50 108 0 R 56 107 0 R 73 74] - /Pg 246 0 R + /S /Formula + /P 104 0 R + /K [95] + /Pg 324 0 R >> endobj @@ -1101,144 +1062,150 @@ endobj << /Type /StructElem /S /Formula - /P 106 0 R - /K [57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72] - /Pg 246 0 R + /P 104 0 R + /K [83 84 85 86 87 88 89 90 91 92 93] + /Pg 324 0 R >> endobj 108 0 obj << /Type /StructElem - /S /Formula - /P 106 0 R - /K [51 52 53 54 55] - /Pg 246 0 R + /S /P + /P 19 0 R + /K [80 81] + /Pg 324 0 R >> endobj 109 0 obj << /Type /StructElem - /S /Lbl - /P 105 0 R - /K [49] - /Pg 246 0 R + /S /P + /P 19 0 R + /K [79] + /Pg 324 0 R >> endobj 110 0 obj << /Type /StructElem - /S /LI - /P 104 0 R - /K [113 0 R 111 0 R] + /S /H3 + /P 19 0 R + /T + /K [77 78] + /Pg 324 0 R >> endobj 111 0 obj << /Type /StructElem - /S /LBody - /P 110 0 R - /K [112 0 R 48] - /Pg 246 0 R + /S /Div + /P 19 0 R + /K [113 0 R 112 0 R] >> endobj 112 0 obj << /Type /StructElem - /S /Formula + /S /Figure /P 111 0 R - /K [44 45 46 47] - /Pg 246 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [75] + /Pg 324 0 R >> endobj 113 0 obj << /Type /StructElem - /S /Lbl - /P 110 0 R - /K [43] - /Pg 246 0 R + /S /Caption + /P 111 0 R + /K [114 0 R] >> endobj 114 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [28 116 0 R 30 115 0 R 42] - /Pg 246 0 R + /S /Span + /P 113 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [76] + /Pg 324 0 R >> endobj 115 0 obj << /Type /StructElem - /S /Formula - /P 114 0 R - /K [31 32 33 34 35 36 37 38 39 40 41] - /Pg 246 0 R + /S /P + /P 19 0 R + /K [74] + /Pg 324 0 R >> endobj 116 0 obj << /Type /StructElem - /S /Formula - /P 114 0 R - /K [29] - /Pg 246 0 R + /S /P + /P 19 0 R + /K [117 0 R 73] + /Pg 324 0 R >> endobj 117 0 obj << /Type /StructElem - /S /Div - /P 19 0 R - /K [119 0 R 118 0 R] + /S /Link + /P 116 0 R + /K [72 << + /Type /OBJR + /Pg 324 0 R + /Obj 323 0 R + >>] + /Pg 324 0 R >> endobj 118 0 obj << /Type /StructElem - /S /Figure - /P 117 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [23] - /Pg 246 0 R + /S /P + /P 19 0 R + /K [71] + /Pg 324 0 R >> endobj 119 0 obj << /Type /StructElem - /S /Caption - /P 117 0 R - /K [122 0 R 121 0 R 120 0 R] + /S /P + /P 19 0 R + /K [59 120 0 R 70] + /Pg 324 0 R >> endobj 120 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 119 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [27] - /Pg 246 0 R + /K [60 61 62 63 64 65 66 67 68 69] + /Pg 324 0 R >> endobj @@ -1246,37 +1213,33 @@ endobj << /Type /StructElem /S /Formula - /P 119 0 R + /P 19 0 R /A [<< /O /Layout /Placement /Block >>] - /K [25 26] - /Pg 246 0 R + /K [50 51 52 53 54 55 56 57 58] + /Pg 324 0 R >> endobj 122 0 obj << /Type /StructElem - /S /Span - /P 119 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [24] - /Pg 246 0 R + /S /P + /P 19 0 R + /K [39 126 0 R 41 125 0 R 43 124 0 R 47 123 0 R 49] + /Pg 324 0 R >> endobj 123 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [0 127 0 R 8 9 126 0 R 16 125 0 R 19 20 124 0 R 22] - /Pg 246 0 R + /S /Formula + /P 122 0 R + /K [48] + /Pg 324 0 R >> endobj @@ -1284,19 +1247,19 @@ endobj << /Type /StructElem /S /Formula - /P 123 0 R - /K [21] - /Pg 246 0 R + /P 122 0 R + /K [44 45 46] + /Pg 324 0 R >> endobj 125 0 obj << /Type /StructElem - /S /Formula - /P 123 0 R - /K [17 18] - /Pg 246 0 R + /S /Em + /P 122 0 R + /K [42] + /Pg 324 0 R >> endobj @@ -1304,9 +1267,9 @@ endobj << /Type /StructElem /S /Formula - /P 123 0 R - /K [10 11 12 13 14 15] - /Pg 246 0 R + /P 122 0 R + /K [40] + /Pg 324 0 R >> endobj @@ -1314,9 +1277,13 @@ endobj << /Type /StructElem /S /Formula - /P 123 0 R - /K [1 2 3 4 5 6 7] - /Pg 246 0 R + /P 19 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38] + /Pg 324 0 R >> endobj @@ -1329,7 +1296,7 @@ endobj /O /List /ListNumbering /Circle >>] - /K [141 0 R 137 0 R 133 0 R 129 0 R] + /K [133 0 R 129 0 R] >> endobj @@ -1347,8 +1314,8 @@ endobj /Type /StructElem /S /LBody /P 129 0 R - /K [131 0 R 254] - /Pg 244 0 R + /K [11 131 0 R 13] + /Pg 324 0 R >> endobj @@ -1357,8 +1324,8 @@ endobj /Type /StructElem /S /Formula /P 130 0 R - /K [251 252 253] - /Pg 244 0 R + /K [12] + /Pg 324 0 R >> endobj @@ -1367,8 +1334,8 @@ endobj /Type /StructElem /S /Lbl /P 129 0 R - /K [250] - /Pg 244 0 R + /K [10] + /Pg 324 0 R >> endobj @@ -1377,7 +1344,7 @@ endobj /Type /StructElem /S /LI /P 128 0 R - /K [136 0 R 134 0 R] + /K [135 0 R 134 0 R] >> endobj @@ -1386,86 +1353,95 @@ endobj /Type /StructElem /S /LBody /P 133 0 R - /K [135 0 R 249] - /Pg 244 0 R + /K [9] + /Pg 324 0 R >> endobj 135 0 obj << /Type /StructElem - /S /Formula - /P 134 0 R - /K [246 247 248] - /Pg 244 0 R + /S /Lbl + /P 133 0 R + /K [8] + /Pg 324 0 R >> endobj 136 0 obj << /Type /StructElem - /S /Lbl - /P 133 0 R - /K [245] - /Pg 244 0 R + /S /P + /P 19 0 R + /K [6 7] + /Pg 324 0 R >> endobj 137 0 obj << /Type /StructElem - /S /LI - /P 128 0 R - /K [140 0 R 138 0 R] + /S /H3 + /P 19 0 R + /T + /K [4 5] + /Pg 324 0 R >> endobj 138 0 obj << /Type /StructElem - /S /LBody - /P 137 0 R - /K [139 0 R 244] - /Pg 244 0 R + /S /H2 + /P 19 0 R + /T + /K [2 3] + /Pg 324 0 R >> endobj 139 0 obj << /Type /StructElem - /S /Formula - /P 138 0 R - /K [237 238 239 240 241 242 243] - /Pg 244 0 R + /S /H1 + /P 19 0 R + /T + /K [0 1] + /Pg 324 0 R >> endobj 140 0 obj << /Type /StructElem - /S /Lbl - /P 137 0 R - /K [236] - /Pg 244 0 R + /S /Formula + /P 19 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [148 149 150 151 152 153] + /Pg 321 0 R >> endobj 141 0 obj << /Type /StructElem - /S /LI - /P 128 0 R - /K [144 0 R 142 0 R] + /S /P + /P 19 0 R + /K [136 145 0 R 141 144 0 R 143 143 0 R 145 142 0 R 147] + /Pg 321 0 R >> endobj 142 0 obj << /Type /StructElem - /S /LBody + /S /Formula /P 141 0 R - /K [143 0 R 235] - /Pg 244 0 R + /K [146] + /Pg 321 0 R >> endobj @@ -1473,39 +1449,39 @@ endobj << /Type /StructElem /S /Formula - /P 142 0 R - /K [234] - /Pg 244 0 R + /P 141 0 R + /K [144] + /Pg 321 0 R >> endobj 144 0 obj << /Type /StructElem - /S /Lbl + /S /Em /P 141 0 R - /K [233] - /Pg 244 0 R + /K [142] + /Pg 321 0 R >> endobj 145 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [218 147 0 R 220 146 0 R 232] - /Pg 244 0 R + /S /Formula + /P 141 0 R + /K [137 138 139 140] + /Pg 321 0 R >> endobj 146 0 obj << /Type /StructElem - /S /Formula - /P 145 0 R - /K [221 222 223 224 225 226 227 228 229 230 231] - /Pg 244 0 R + /S /P + /P 19 0 R + /K [119 150 0 R 121 149 0 R 123 148 0 R 125 147 0 R 135] + /Pg 321 0 R >> endobj @@ -1513,59 +1489,63 @@ endobj << /Type /StructElem /S /Formula - /P 145 0 R - /K [219] - /Pg 244 0 R + /P 146 0 R + /K [126 127 128 129 130 131 132 133 134] + /Pg 321 0 R >> endobj 148 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [211 150 0 R 213 214 149 0 R 216 217] - /Pg 244 0 R ->> + /S /Em + /P 146 0 R + /K [124] + /Pg 321 0 R +>> endobj 149 0 obj << /Type /StructElem - /S /Em - /P 148 0 R - /K [215] - /Pg 244 0 R + /S /Formula + /P 146 0 R + /K [122] + /Pg 321 0 R >> endobj 150 0 obj << /Type /StructElem - /S /Strong - /P 148 0 R - /K [212] - /Pg 244 0 R + /S /Formula + /P 146 0 R + /K [120] + /Pg 321 0 R >> endobj 151 0 obj << /Type /StructElem - /S /P + /S /Formula /P 19 0 R - /K [196 156 0 R 201 155 0 R 203 154 0 R 206 153 0 R 208 152 0 R 210] - /Pg 244 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [104 105 106 107 108 109 110 111 112 113 114 115 116 117 118] + /Pg 321 0 R >> endobj 152 0 obj << /Type /StructElem - /S /Formula - /P 151 0 R - /K [209] - /Pg 244 0 R + /S /P + /P 19 0 R + /K [96 154 0 R 98 153 0 R 103] + /Pg 321 0 R >> endobj @@ -1573,9 +1553,9 @@ endobj << /Type /StructElem /S /Formula - /P 151 0 R - /K [207] - /Pg 244 0 R + /P 152 0 R + /K [99 100 101 102] + /Pg 321 0 R >> endobj @@ -1583,19 +1563,19 @@ endobj << /Type /StructElem /S /Formula - /P 151 0 R - /K [204 205] - /Pg 244 0 R + /P 152 0 R + /K [97] + /Pg 321 0 R >> endobj 155 0 obj << /Type /StructElem - /S /Formula - /P 151 0 R - /K [202] - /Pg 244 0 R + /S /P + /P 19 0 R + /K [75 161 0 R 81 160 0 R 83 159 0 R 85 158 0 R 90 157 0 R 92 156 0 R 94 95] + /Pg 321 0 R >> endobj @@ -1603,40 +1583,39 @@ endobj << /Type /StructElem /S /Formula - /P 151 0 R - /K [197 198 199 200] - /Pg 244 0 R + /P 155 0 R + /K [93] + /Pg 321 0 R >> endobj 157 0 obj << /Type /StructElem - /S /H2 - /P 19 0 R - /T - /K [194 195] - /Pg 244 0 R + /S /Em + /P 155 0 R + /K [91] + /Pg 321 0 R >> endobj 158 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [178 164 0 R 180 163 0 R 182 183 162 0 R 185 186 161 0 R 188 160 0 R 191 159 0 R 193] - /Pg 244 0 R + /S /Formula + /P 155 0 R + /K [86 87 88 89] + /Pg 321 0 R >> endobj 159 0 obj << /Type /StructElem - /S /Formula - /P 158 0 R - /K [192] - /Pg 244 0 R + /S /Em + /P 155 0 R + /K [84] + /Pg 321 0 R >> endobj @@ -1644,9 +1623,9 @@ endobj << /Type /StructElem /S /Formula - /P 158 0 R - /K [189 190] - /Pg 244 0 R + /P 155 0 R + /K [82] + /Pg 321 0 R >> endobj @@ -1654,182 +1633,186 @@ endobj << /Type /StructElem /S /Formula - /P 158 0 R - /K [187] - /Pg 244 0 R + /P 155 0 R + /K [76 77 78 79 80] + /Pg 321 0 R >> endobj 162 0 obj << /Type /StructElem - /S /Em - /P 158 0 R - /K [184] - /Pg 244 0 R + /S /L + /P 19 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [168 0 R 163 0 R] >> endobj 163 0 obj << /Type /StructElem - /S /Em - /P 158 0 R - /K [181] - /Pg 244 0 R + /S /LI + /P 162 0 R + /K [167 0 R 164 0 R] >> endobj 164 0 obj << /Type /StructElem - /S /Em - /P 158 0 R - /K [179] - /Pg 244 0 R + /S /LBody + /P 163 0 R + /K [50 166 0 R 56 165 0 R 73 74] + /Pg 321 0 R >> endobj 165 0 obj << /Type /StructElem - /S /L - /P 19 0 R - /A [<< - /O /List - /ListNumbering /Circle - >>] - /K [170 0 R 166 0 R] + /S /Formula + /P 164 0 R + /K [57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72] + /Pg 321 0 R >> endobj 166 0 obj << /Type /StructElem - /S /LI - /P 165 0 R - /K [169 0 R 167 0 R] + /S /Formula + /P 164 0 R + /K [51 52 53 54 55] + /Pg 321 0 R >> endobj 167 0 obj << /Type /StructElem - /S /LBody - /P 166 0 R - /K [168 0 R] + /S /Lbl + /P 163 0 R + /K [49] + /Pg 321 0 R >> endobj 168 0 obj << /Type /StructElem - /S /Formula - /P 167 0 R - /K [157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177] - /Pg 244 0 R + /S /LI + /P 162 0 R + /K [171 0 R 169 0 R] >> endobj 169 0 obj << /Type /StructElem - /S /Lbl - /P 166 0 R - /K [156] - /Pg 244 0 R + /S /LBody + /P 168 0 R + /K [170 0 R 48] + /Pg 321 0 R >> endobj 170 0 obj << /Type /StructElem - /S /LI - /P 165 0 R - /K [173 0 R 171 0 R] + /S /Formula + /P 169 0 R + /K [44 45 46 47] + /Pg 321 0 R >> endobj 171 0 obj << /Type /StructElem - /S /LBody - /P 170 0 R - /K [172 0 R] + /S /Lbl + /P 168 0 R + /K [43] + /Pg 321 0 R >> endobj 172 0 obj << /Type /StructElem - /S /Formula - /P 171 0 R - /K [137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155] - /Pg 244 0 R + /S /P + /P 19 0 R + /K [28 174 0 R 30 173 0 R 42] + /Pg 321 0 R >> endobj 173 0 obj << /Type /StructElem - /S /Lbl - /P 170 0 R - /K [136] - /Pg 244 0 R + /S /Formula + /P 172 0 R + /K [31 32 33 34 35 36 37 38 39 40 41] + /Pg 321 0 R >> endobj 174 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [115 176 0 R 125 175 0 R 135] - /Pg 244 0 R + /S /Formula + /P 172 0 R + /K [29] + /Pg 321 0 R >> endobj 175 0 obj << /Type /StructElem - /S /Formula - /P 174 0 R - /K [126 127 128 129 130 131 132 133 134] - /Pg 244 0 R + /S /Div + /P 19 0 R + /K [177 0 R 176 0 R] >> endobj 176 0 obj << /Type /StructElem - /S /Formula - /P 174 0 R - /K [116 117 118 119 120 121 122 123 124] - /Pg 244 0 R + /S /Figure + /P 175 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [23] + /Pg 321 0 R >> endobj 177 0 obj << /Type /StructElem - /S /Formula - /P 19 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [105 106 107 108 109 110 111 112 113 114] - /Pg 244 0 R + /S /Caption + /P 175 0 R + /K [180 0 R 179 0 R 178 0 R] >> endobj 178 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [96 181 0 R 99 180 0 R 101 179 0 R 104] - /Pg 244 0 R + /S /Span + /P 177 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [27] + /Pg 321 0 R >> endobj @@ -1837,29 +1820,37 @@ endobj << /Type /StructElem /S /Formula - /P 178 0 R - /K [102 103] - /Pg 244 0 R + /P 177 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [25 26] + /Pg 321 0 R >> endobj 180 0 obj << /Type /StructElem - /S /Formula - /P 178 0 R - /K [100] - /Pg 244 0 R + /S /Span + /P 177 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [24] + /Pg 321 0 R >> endobj 181 0 obj << /Type /StructElem - /S /Formula - /P 178 0 R - /K [97 98] - /Pg 244 0 R + /S /P + /P 19 0 R + /K [0 185 0 R 8 9 184 0 R 16 183 0 R 19 20 182 0 R 22] + /Pg 321 0 R >> endobj @@ -1867,23 +1858,19 @@ endobj << /Type /StructElem /S /Formula - /P 19 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [86 87 88 89 90 91 92 93 94 95] - /Pg 244 0 R + /P 181 0 R + /K [21] + /Pg 321 0 R >> endobj 183 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [77 187 0 R 79 186 0 R 81 185 0 R 83 184 0 R 85] - /Pg 244 0 R + /S /Formula + /P 181 0 R + /K [17 18] + /Pg 321 0 R >> endobj @@ -1891,9 +1878,9 @@ endobj << /Type /StructElem /S /Formula - /P 183 0 R - /K [84] - /Pg 244 0 R + /P 181 0 R + /K [10 11 12 13 14 15] + /Pg 321 0 R >> endobj @@ -1901,39 +1888,41 @@ endobj << /Type /StructElem /S /Formula - /P 183 0 R - /K [82] - /Pg 244 0 R + /P 181 0 R + /K [1 2 3 4 5 6 7] + /Pg 321 0 R >> endobj 186 0 obj << /Type /StructElem - /S /Formula - /P 183 0 R - /K [80] - /Pg 244 0 R + /S /L + /P 19 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [199 0 R 195 0 R 191 0 R 187 0 R] >> endobj 187 0 obj << /Type /StructElem - /S /Em - /P 183 0 R - /K [78] - /Pg 244 0 R + /S /LI + /P 186 0 R + /K [190 0 R 188 0 R] >> endobj 188 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [55 192 0 R 58 191 0 R 63 190 0 R 73 189 0 R] - /Pg 244 0 R + /S /LBody + /P 187 0 R + /K [189 0 R 254] + /Pg 319 0 R >> endobj @@ -1942,122 +1931,115 @@ endobj /Type /StructElem /S /Formula /P 188 0 R - /K [74 75 76] - /Pg 244 0 R + /K [251 252 253] + /Pg 319 0 R >> endobj 190 0 obj << /Type /StructElem - /S /Formula - /P 188 0 R - /K [64 65 66 67 68 69 70 71 72] - /Pg 244 0 R + /S /Lbl + /P 187 0 R + /K [250] + /Pg 319 0 R >> endobj 191 0 obj << /Type /StructElem - /S /Formula - /P 188 0 R - /K [59 60 61 62] - /Pg 244 0 R + /S /LI + /P 186 0 R + /K [194 0 R 192 0 R] >> endobj 192 0 obj << /Type /StructElem - /S /Formula - /P 188 0 R - /K [56 57] - /Pg 244 0 R + /S /LBody + /P 191 0 R + /K [193 0 R 249] + /Pg 319 0 R >> endobj 193 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [47 195 0 R 50 194 0 R 54] - /Pg 244 0 R + /S /Formula + /P 192 0 R + /K [246 247 248] + /Pg 319 0 R >> endobj 194 0 obj << /Type /StructElem - /S /Formula - /P 193 0 R - /K [51 52 53] - /Pg 244 0 R + /S /Lbl + /P 191 0 R + /K [245] + /Pg 319 0 R >> endobj 195 0 obj << /Type /StructElem - /S /Formula - /P 193 0 R - /K [48 49] - /Pg 244 0 R + /S /LI + /P 186 0 R + /K [198 0 R 196 0 R] >> endobj 196 0 obj << /Type /StructElem - /S /Formula - /P 19 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46] - /Pg 244 0 R + /S /LBody + /P 195 0 R + /K [197 0 R 244] + /Pg 319 0 R >> endobj 197 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [14 199 0 R 16 198 0 R 18] - /Pg 244 0 R + /S /Formula + /P 196 0 R + /K [237 238 239 240 241 242 243] + /Pg 319 0 R >> endobj 198 0 obj << /Type /StructElem - /S /Em - /P 197 0 R - /K [17] - /Pg 244 0 R + /S /Lbl + /P 195 0 R + /K [236] + /Pg 319 0 R >> endobj 199 0 obj << /Type /StructElem - /S /Em - /P 197 0 R - /K [15] - /Pg 244 0 R + /S /LI + /P 186 0 R + /K [202 0 R 200 0 R] >> endobj 200 0 obj << /Type /StructElem - /S /P - /P 19 0 R - /K [5 203 0 R 8 202 0 R 11 201 0 R 13] - /Pg 244 0 R + /S /LBody + /P 199 0 R + /K [201 0 R 235] + /Pg 319 0 R >> endobj @@ -2066,72 +2048,664 @@ endobj /Type /StructElem /S /Formula /P 200 0 R - /K [12] - /Pg 244 0 R + /K [234] + /Pg 319 0 R >> endobj 202 0 obj << /Type /StructElem - /S /Formula - /P 200 0 R - /K [9 10] - /Pg 244 0 R + /S /Lbl + /P 199 0 R + /K [233] + /Pg 319 0 R >> endobj 203 0 obj << /Type /StructElem - /S /Formula - /P 200 0 R - /K [6 7] - /Pg 244 0 R + /S /P + /P 19 0 R + /K [218 205 0 R 220 204 0 R 232] + /Pg 319 0 R >> endobj 204 0 obj << /Type /StructElem - /S /H2 - /P 19 0 R - /T - /K [3 4] - /Pg 244 0 R + /S /Formula + /P 203 0 R + /K [221 222 223 224 225 226 227 228 229 230 231] + /Pg 319 0 R >> endobj 205 0 obj << /Type /StructElem - /S /H1 - /P 19 0 R - /T (Langages et automates) - /K [1 2] - /Pg 244 0 R + /S /Formula + /P 203 0 R + /K [219] + /Pg 319 0 R >> endobj 206 0 obj << /Type /StructElem - /S /Title + /S /P /P 19 0 R - /K [0] - /Pg 244 0 R + /K [211 208 0 R 213 214 207 0 R 216 217] + /Pg 319 0 R >> endobj 207 0 obj << - /Type /PageLabel - /S /D - /St 1 ->> + /Type /StructElem + /S /Em + /P 206 0 R + /K [215] + /Pg 319 0 R +>> +endobj + +208 0 obj +<< + /Type /StructElem + /S /Strong + /P 206 0 R + /K [212] + /Pg 319 0 R +>> +endobj + +209 0 obj +<< + /Type /StructElem + /S /P + /P 19 0 R + /K [196 214 0 R 201 213 0 R 203 212 0 R 206 211 0 R 208 210 0 R 210] + /Pg 319 0 R +>> +endobj + +210 0 obj +<< + /Type /StructElem + /S /Formula + /P 209 0 R + /K [209] + /Pg 319 0 R +>> +endobj + +211 0 obj +<< + /Type /StructElem + /S /Formula + /P 209 0 R + /K [207] + /Pg 319 0 R +>> +endobj + +212 0 obj +<< + /Type /StructElem + /S /Formula + /P 209 0 R + /K [204 205] + /Pg 319 0 R +>> +endobj + +213 0 obj +<< + /Type /StructElem + /S /Formula + /P 209 0 R + /K [202] + /Pg 319 0 R +>> +endobj + +214 0 obj +<< + /Type /StructElem + /S /Formula + /P 209 0 R + /K [197 198 199 200] + /Pg 319 0 R +>> +endobj + +215 0 obj +<< + /Type /StructElem + /S /H2 + /P 19 0 R + /T + /K [194 195] + /Pg 319 0 R +>> +endobj + +216 0 obj +<< + /Type /StructElem + /S /P + /P 19 0 R + /K [178 222 0 R 180 221 0 R 182 183 220 0 R 185 186 219 0 R 188 218 0 R 191 217 0 R 193] + /Pg 319 0 R +>> +endobj + +217 0 obj +<< + /Type /StructElem + /S /Formula + /P 216 0 R + /K [192] + /Pg 319 0 R +>> +endobj + +218 0 obj +<< + /Type /StructElem + /S /Formula + /P 216 0 R + /K [189 190] + /Pg 319 0 R +>> +endobj + +219 0 obj +<< + /Type /StructElem + /S /Formula + /P 216 0 R + /K [187] + /Pg 319 0 R +>> +endobj + +220 0 obj +<< + /Type /StructElem + /S /Em + /P 216 0 R + /K [184] + /Pg 319 0 R +>> +endobj + +221 0 obj +<< + /Type /StructElem + /S /Em + /P 216 0 R + /K [181] + /Pg 319 0 R +>> +endobj + +222 0 obj +<< + /Type /StructElem + /S /Em + /P 216 0 R + /K [179] + /Pg 319 0 R +>> +endobj + +223 0 obj +<< + /Type /StructElem + /S /L + /P 19 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [228 0 R 224 0 R] +>> +endobj + +224 0 obj +<< + /Type /StructElem + /S /LI + /P 223 0 R + /K [227 0 R 225 0 R] +>> +endobj + +225 0 obj +<< + /Type /StructElem + /S /LBody + /P 224 0 R + /K [226 0 R] +>> +endobj + +226 0 obj +<< + /Type /StructElem + /S /Formula + /P 225 0 R + /K [157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177] + /Pg 319 0 R +>> +endobj + +227 0 obj +<< + /Type /StructElem + /S /Lbl + /P 224 0 R + /K [156] + /Pg 319 0 R +>> +endobj + +228 0 obj +<< + /Type /StructElem + /S /LI + /P 223 0 R + /K [231 0 R 229 0 R] +>> +endobj + +229 0 obj +<< + /Type /StructElem + /S /LBody + /P 228 0 R + /K [230 0 R] +>> +endobj + +230 0 obj +<< + /Type /StructElem + /S /Formula + /P 229 0 R + /K [137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155] + /Pg 319 0 R +>> +endobj + +231 0 obj +<< + /Type /StructElem + /S /Lbl + /P 228 0 R + /K [136] + /Pg 319 0 R +>> +endobj + +232 0 obj +<< + /Type /StructElem + /S /P + /P 19 0 R + /K [115 234 0 R 125 233 0 R 135] + /Pg 319 0 R +>> +endobj + +233 0 obj +<< + /Type /StructElem + /S /Formula + /P 232 0 R + /K [126 127 128 129 130 131 132 133 134] + /Pg 319 0 R +>> +endobj + +234 0 obj +<< + /Type /StructElem + /S /Formula + /P 232 0 R + /K [116 117 118 119 120 121 122 123 124] + /Pg 319 0 R +>> +endobj + +235 0 obj +<< + /Type /StructElem + /S /Formula + /P 19 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [105 106 107 108 109 110 111 112 113 114] + /Pg 319 0 R +>> +endobj + +236 0 obj +<< + /Type /StructElem + /S /P + /P 19 0 R + /K [96 239 0 R 99 238 0 R 101 237 0 R 104] + /Pg 319 0 R +>> +endobj + +237 0 obj +<< + /Type /StructElem + /S /Formula + /P 236 0 R + /K [102 103] + /Pg 319 0 R +>> +endobj + +238 0 obj +<< + /Type /StructElem + /S /Formula + /P 236 0 R + /K [100] + /Pg 319 0 R +>> +endobj + +239 0 obj +<< + /Type /StructElem + /S /Formula + /P 236 0 R + /K [97 98] + /Pg 319 0 R +>> +endobj + +240 0 obj +<< + /Type /StructElem + /S /Formula + /P 19 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [86 87 88 89 90 91 92 93 94 95] + /Pg 319 0 R +>> +endobj + +241 0 obj +<< + /Type /StructElem + /S /P + /P 19 0 R + /K [77 245 0 R 79 244 0 R 81 243 0 R 83 242 0 R 85] + /Pg 319 0 R +>> +endobj + +242 0 obj +<< + /Type /StructElem + /S /Formula + /P 241 0 R + /K [84] + /Pg 319 0 R +>> +endobj + +243 0 obj +<< + /Type /StructElem + /S /Formula + /P 241 0 R + /K [82] + /Pg 319 0 R +>> +endobj + +244 0 obj +<< + /Type /StructElem + /S /Formula + /P 241 0 R + /K [80] + /Pg 319 0 R +>> +endobj + +245 0 obj +<< + /Type /StructElem + /S /Em + /P 241 0 R + /K [78] + /Pg 319 0 R +>> +endobj + +246 0 obj +<< + /Type /StructElem + /S /P 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discr\303\250tes/4- Automates finis.typ" +++ "b/semestre 3/math\303\251matiques discr\303\250tes/4- Automates finis.typ" @@ -9,13 +9,13 @@ #set par(justify: true) #set text( size: 12pt, - font: "Times New Roman" + font: "PT Astra Serif" ) #set heading(numbering: "1.") #show heading: set block(above: 1.4em, below: 1em) -#show heading: set text(font: "Raveo") +#show heading: set text(font: "PT Astra Serif") -#show title: set text(size: 24pt, font: "Raveo") +#show title: set text(size: 24pt, font: "Inter") #show title: set align(center) #title[ @@ -82,7 +82,7 @@ Le langage $L_("pair")={"nombres pairs"}$ est donc constitué de l'ensemble des Une exécution de $cal(A)$ est une séquence finie $s_0a_1s_1 dots a_n s_n$ telle que~: - $s_0 in I$ est un état initial -- pour tout $O <= i < n$, alors $(s_i, a_(i+1), s_(i+1)) in T$ est une transition autorisée par la relation de transition +- pour tout $0 <= i < n$, alors $(s_i, a_(i+1), s_(i+1)) in T$ est une transition autorisée par la relation de transition La séquence $a_1 dots a_n$ est un mot de $A$ qui étiquette l'exécution. On dit qu'une exécution est _acceptante_ si $s_n in F$. @@ -108,7 +108,8 @@ D'une manière formelle, un automate est déterministre si~: - la relation $R$ (les transitions de l'automate) est fonctionnelle au sens suivant~: $ (p,a,q) in R and (p,a,q') in R ==> q=q' $ -Dans un automate fini déterministe, $T$ est une _fonction_ allant de $S times A$ vers $S$. On note parfois $ T(s,a) = s' $ pour $(s,a,s') in T$ dans un automate déterministe. +Dans un automate fini déterministe, $T$ est une _fonction_ allant de $S times A$ vers $S$. +On note parfois $ T(s,a) = s' $ pour $(s,a,s') in T$ dans un automate déterministe. Dans un automate fini déterministe, tout mot est étiquette d'au plus une exécution. @@ -127,6 +128,15 @@ Un automate dit non déterministe s'il n'est pas déterministe. Tout automate fini est équivalent à un automate fini déterministe. +#emoji.warning Un automate déterministe ne possède qu'un unique état d'entrée~! + +Soit $cal(A)=(S,T,I,F)$ un automate fini sur un alphabet $A$. On définit $op(det)(cal(A))=(cal(P)(S),T',I,F')$ avec +- pour $X$ dans $cal(P)(S)$, pour $a in E$, on a $T'(X,a)={ s' in S | exists s in X, (s,a,s') in T }$ +- $F'={X subset.eq S | X inter F eq.not emptyset}$ +- $op(det)(cal(A))$ set déterministe +- $L(cal(A)) = L(op(det)(cal(A)))$ +- _il manque un point_ + == Complétude Un automate $cal(A)=(S,T,I,F)$ sur un alphabet $A$ est _complet_ si~: @@ -153,3 +163,19 @@ On a que~: - $op("comp")(cal(A))$ est complet = Propriétés de clôture + +Si $L subset.eq A^*$ est un langage reconnaissable, alors $overline(L)$ est reconnaissable. + +Soit $cal(A)$ tel que $L(cal(A)) = L$. Sans perte de généraliste, on suppose que $cal(A)$ est complet et déterministe +(sinon on le complète et on le déterminise). + +Si $cal(A) = (S,T,i,F)$, alors on construit $cal(B) = (S,T,i,F')$ avec $F'=S backslash F$. +- $L(cal(B)) = overline(L)$ +- L'approche n'est correcte que si $A$ est déterministe et complet~! +Il s'agit du même automate où les états normaux deviennent finaux et les états finaux deviennent normaux. +On les inverse. + +Si $L_1$ et $L_2$ sont deux langages reconnaissable de $A$, alors $L_1 union L_2$ et $L_1 inter L_2$ sont aussi +reconnaissables. + +_compléter avec la diapo 26_ -- cgit v1.2.3