{VERSION 2 3 "IBM INTEL NT" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 }
{CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "2
D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 256 "
" 1 24 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 128 0 1 
1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 
0 }{CSTYLE "" -1 259 "Courier" 1 18 255 0 0 1 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 260 "Courier" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE 
"" -1 261 "Courier" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
262 "" 0 1 0 0 255 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 
0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 266 "" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 
128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 1 14 255 0 255 1 1 1 
0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 255 0 255 1 1 1 0 0 0 0 0 0 0 
}{CSTYLE "" -1 270 "" 1 14 255 0 255 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 271 "" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 
128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 128 0 1 1 1 0 0 
0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 275 "" 0 1 128 0 128 1 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 
276 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "Courier" 1 
14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 1 1 
0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 280 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
281 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 1 14 0 0 
0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 19 283 "" 1 14 0 0 0 0 0 1 0 0 0 0 
0 0 0 }{CSTYLE "" -1 284 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "
" 19 285 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 286 "" 1 14 
0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 19 287 "" 1 14 0 0 0 0 0 1 0 0 
0 0 0 0 0 }{CSTYLE "" -1 288 "Courier" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 
0 }{CSTYLE "" -1 289 "" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 290 "Courier" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 291 "
" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 292 "" 1 14 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{CSTYLE "" 19 293 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 294 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 
"" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 296 "" 1 14 0 0 0 0 
0 1 0 0 0 0 0 0 0 }{CSTYLE "" 19 297 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 
0 }{CSTYLE "" -1 298 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
299 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 300 "" 0 1 0 0 0 
0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 301 "Courier" 1 18 255 0 0 1 0 1 0 
0 0 0 0 0 0 }{CSTYLE "" -1 302 "Times" 1 18 0 0 255 1 1 0 0 0 0 0 0 0 
0 }{CSTYLE "" -1 303 "Times" 1 18 0 0 255 1 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 304 "" 1 18 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
305 "" 1 18 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 306 "Courier" 
1 18 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 307 "Courier" 1 18 
255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 308 "Courier" 1 18 255 0 0 
1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 309 "Courier" 1 18 255 0 0 1 0 1 0 
0 0 0 0 0 0 }{CSTYLE "" -1 310 "Courier" 1 18 255 0 0 1 0 1 0 0 0 0 0 
0 0 }{CSTYLE "" -1 311 "Courier" 1 18 255 0 0 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 312 "" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
313 "" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 314 "" 1 18 255 
0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 315 "" 1 14 0 0 0 0 0 1 0 0 0 
0 0 0 0 }{CSTYLE "" -1 316 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE 
"" 19 317 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 318 "" 1 
14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 319 "Times" 1 14 0 0 0 
0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 320 "Times" 1 14 0 0 0 0 0 0 0 0 0 
0 0 0 0 }{CSTYLE "" -1 321 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "
" -1 322 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 323 "" 1 18 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 324 "" 1 18 0 0 0 0 0 1 0 0 
0 0 0 0 0 }{CSTYLE "" -1 325 "" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 326 "Times" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 327 "Times" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 328 "" 0 
1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 329 "" 1 14 0 0 0 0 0 1 0 
0 0 0 0 0 0 }{CSTYLE "" -1 330 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" 19 331 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
332 "" 1 14 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 333 "Times" 1 
14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 334 "Times" 1 14 0 0 0 0 
0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 335 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 
}{CSTYLE "" -1 336 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
337 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 19 338 "" 1 18 0 0 
0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 339 "" 1 14 255 0 0 1 0 1 0 0 0 
0 0 0 0 }{CSTYLE "" -1 340 "Times" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 341 "Times" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 342 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 343 "" 1 14 0 
0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 19 344 "" 1 18 0 0 0 0 0 1 0 0 0 
0 0 0 0 }{CSTYLE "" -1 345 "Times" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 346 "Times" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 347 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 19 348 "" 1 18 0 
0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 349 "" 1 14 0 0 0 0 0 1 0 0 0 
0 0 0 0 }{CSTYLE "" 19 350 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE 
"" -1 351 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 19 352 "" 1 
18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 19 353 "" 1 14 0 0 0 0 0 1 0 
0 0 0 0 0 0 }{CSTYLE "" -1 354 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 355 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
356 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 19 357 "" 1 14 0 0 
0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 358 "" 1 14 0 0 0 0 0 1 0 0 0 0 
0 0 0 }{CSTYLE "" 19 359 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "
" -1 360 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 361 "" 1 14 
0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 362 "" 1 14 0 0 0 0 0 1 0 0 
0 0 0 0 0 }{CSTYLE "" 19 363 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 364 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
365 "" 0 1 128 0 128 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 366 "" 0 1 
128 0 128 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 
-1 "Helvetica" 1 12 0 0 0 0 0 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 
0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 
0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 
3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 4 
4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "
" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 
-1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 
0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "R3 Font 0" -1 
256 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 
0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "
" -1 -1 "Courier" 1 12 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 18 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 
0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 3 259 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 
0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 
0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 263 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 0 264 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 
0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 265 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 0 266 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 
0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 267 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 0 268 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 
0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 
-1 269 1 {CSTYLE "" -1 -1 "Helvetica" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 }
1 1 0 0 6 6 1 0 1 0 2 2 0 1 }{PSTYLE "" 0 270 1 {CSTYLE "" -1 -1 "" 0 
1 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE 
"" 0 271 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 258 18 "Laplace transforms" }}
{PARA 258 "" 0 "" {TEXT 256 4 "HW 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 260 "Click on a [+]  sign to expan
d a section. Click on a [-] sign to collapse a section. To do these ex
ercises you will have to insert execution groups. That can be done by \+
clicking on the toolbar icon that looks like \"[>\". It can also be do
ne via the Insert menu." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 279 22 "Student Name and ID
:  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 280 21 "S
tudent Name and ID: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Introduction" 
}}{PARA 0 "" 0 "" {TEXT -1 9 "In this  " }{TEXT 257 5 "MAPLE" }{TEXT 
-1 3 "   " }{HYPERLNK 17 "worksheet" 2 "worksheet" "" }{TEXT -1 60 ", \+
 you will be asked to compute several Laplace transforms. " }}}{SECT 
1 {PARA 3 "" 0 "" {TEXT -1 7 "Reports" }}{PARA 0 "" 0 "" {TEXT -1 30 "
Reports that you prepare with " }{TEXT 266 5 "MAPLE" }{TEXT -1 112 "  \+
 should be prepared with the same care that you would devote to labora
tory reports in biology and chemistry.  " }{TEXT 268 46 "A report shou
ld not be a diary or history of a" }{TEXT -1 1 " " }{TEXT 267 6 " MAPL
E" }{TEXT -1 2 "  " }{TEXT 269 1 " " }{TEXT 270 51 "session.  Delete w
hat is not needed for the report." }{TEXT -1 25 "  All lines of the fo
rm  " }{TEXT 259 6 "?topic" }{TEXT -1 82 "  (that arise from help quer
ies) should be erased.  All errors should be erased.  " }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "When you are printin
g a " }{TEXT 271 5 "MAPLE" }{TEXT -1 165 "  report, think about the to
ner and paper resources that you are using. All commands must be termi
nated - either with the standard terminator, the semicolon, or the " }
{TEXT 275 17 "silent terminator" }{TEXT -1 57 ", the colon. When you a
ssign a variable, for example  \n \"" }{TEXT 277 7 "x := 5;" }{TEXT 
-1 30 " \",  there is no need to have " }{TEXT 272 5 "MAPLE" }{TEXT 
-1 12 " echo back  " }{TEXT 260 6 "x := 5" }{TEXT -1 89 ".  When this \+
is printed, it simply wastes paper and ink.  Choose the silent termina
tor  \"" }{TEXT 261 7 "x := 5:" }{TEXT -1 70 " \"  instead.  When you \+
load a package (without the silent terminator)," }{TEXT 262 1 " " }
{TEXT -1 2 "  " }{TEXT 273 5 "MAPLE" }{TEXT -1 123 " will list the com
mands that become available with the package. This is fine - it will h
elp you become familiar with what  " }{TEXT 274 5 "MAPLE" }{TEXT -1 
125 " makes available. However, these commands should not be part of a
 lab report. Reload the package with the silent terminator. " }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "Much of the tex
t in this worksheet should be deleted.  For example, delete the " }
{TEXT 263 12 "Introduction" }{TEXT -1 5 " and " }{TEXT 264 8 "Keywords
" }{TEXT -1 34 " sections. Delete this section on " }{TEXT 265 7 "Repo
rts" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 235 "Remember that your worksheet should execute in the ord
er that it has been written.  In particular, remember that the ditto r
efers to the result of the last executed command - not the result of t
he command that physically precedes it.  " }}}{SECT 0 {PARA 3 "" 0 "" 
{TEXT -1 8 "Keywords" }}{PARA 0 "" 0 "" {TEXT -1 3 "   " }{HYPERLNK 
17 "DEplot" 2 "DEtools[DEplot]" "" }{TEXT -1 4 " ,  " }{HYPERLNK 17 "D
Etools" 2 "DEtools" "" }{TEXT -1 5 " ,   " }{HYPERLNK 17 "Dirac" 2 "Di
rac" "" }{TEXT -1 6 ",     " }{HYPERLNK 17 "floor" 2 "floor" "" }
{TEXT -1 7 " ,     " }{HYPERLNK 17 "Heaviside" 2 "Heaviside" "" }
{TEXT -1 6 " ,    " }{HYPERLNK 17 "inttrans" 2 "inttrans" "" }{TEXT 
-1 6 " ,    " }{HYPERLNK 17 "invlaplace" 2 "invlaplace" "" }{TEXT -1 
4 " ,  " }{HYPERLNK 17 "isolate" 2 "isolate" "" }{TEXT -1 3 ",  " }
{HYPERLNK 17 "laplace" 2 "laplace" "" }{TEXT -1 5 " ,   " }{HYPERLNK 
17 "map" 2 "map" "" }{TEXT -1 3 ",  " }{HYPERLNK 17 "rhs" 2 "rhs" "" }
{TEXT -1 4 ",   " }{HYPERLNK 17 "sum" 2 "sum" "" }{TEXT -1 5 " ,   " }
{HYPERLNK 17 "unapply" 2 "unapply" "" }{TEXT -1 2 " ," }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 21 "Background Worksheets" }}{PARA 0 "" 0 "" 
{TEXT -1 420 "The following worksheets, available for download from  t
he syllabus web page, have examples or discussions that will help you \+
do this homework.  If they are in the same directory as this worksheet
, and if you have retained the filename under which they were posted, \+
then clicking on the hyperlink below will automatically open them. Use
 the Window menu to control the view when multiple files are opened si
multaneously. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 2 "  " }{HYPERLNK 17 "4.1-4.6epR4.mws" 1 "4.1-4.6epR4.mws" "
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 
83 "Exercise 1   The Laplace Transform of Several Important Piecewise \+
Defined Functions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 300 18 "Backgroud Reading:" }{TEXT -1 4 "    " }{HYPERLNK 17 "4.
1-4.3epR4.mws   " 1 "" "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 
{PARA 4 "" 0 "" {TEXT -1 78 "a) Greatest Integer Function   or   Floor
 Function    or    Staircase Function" }}{PARA 4 "" 0 "" {TEXT -1 61 "
\n    (Must be a great function if it has three names, right?)" }}
{PARA 0 "" 0 "" {TEXT -1 50 "\n\n\nRestart and load the packages that \+
are needed:\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "restart; wi
th(inttrans): with(plots):  with(DEtools):   #Execute this line!" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 34 "The greatest integer function of  " }{TEXT 302 
1 "x" }{TEXT -1 65 "  is defined to be the greatest integer that is no
t larger than  " }{TEXT 303 1 "x" }{TEXT -1 18 ".  It is denoted  " }
{TEXT 301 5 "floor" }{TEXT -1 5 "  in " }{TEXT 312 6 " MAPLE" }{TEXT 
-1 58 ", as it often is in math, science, and engineering texts. " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 197 " #Execute. \n #The left sid
es are not evaluated because of the single quotes.\n\n'floor( Pi )' = \+
floor( Pi );\n'floor( - Pi )' = floor( - Pi );\n'floor(- 7 )' = floor(
- 7 );\n'floor( 13 )' = floor( 13 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#/-%&floorG6#%#PiG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&floorG
6#,$%#PiG!\"\"!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&floorG6#!\"(
F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&floorG6#\"#8F'" }}}{PARA 0 "
" 0 "" {TEXT -1 17 "\n\n\nThe plot of   " }{TEXT 310 9 " floor(t)" }
{TEXT 311 1 " " }{TEXT -1 61 "  explains why it is sometimes called th
e staircase function:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 52 "plot( floor(t),  t = 0 .. 5.5, color = aq
uamarine );" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6#7dq7$\"\"!F(7$
$\"1nm;zM%))>\"!#;F(7$$\"1L$3-y]>C#F,F(7$$\"1mmTNS.:MF,F(7$$\"1nm\"zC$
*ef%F,F(7$$\"1L$3F/S6x&F,F(7$$\"1m;ajUugoF,F(7$$\"1+](=Km*))zF,F(7$$\"
1L$3_vqBd)F,F(7$$\"1m;a)=vd:*F,F(7$$\"1****\\7>aY%*F,F(7$$\"1L$ekj3tt*
F,F(7$$\"1;zW<.+5)*F,F(7$$\"1*\\P%)*>p#))*F,F(7$$\"1#HK*Qy.>**F,F(7$$
\"1$3F%zOQb**F,F(7$$\"1v=#*>&H<***F,F(7$$\"1n;/Ov!G+\"!#:$\"\"\"F(7$$
\"1$eRA(eM<5FgnFhn7$$\"1+vV3U)=.\"FgnFhn7$$\"1</^r?q\"4\"FgnFhn7$$\"1L
LeM*>::\"FgnFhn7$$\"1n;HZ^*oD\"FgnFhn7$$\"1++vyE_v8FgnFhn7$$\"1++D1tj%
\\\"FgnFhn7$$\"1++D@jU4;FgnFhn7$$\"1mT&QulOr\"FgnFhn7$$\"1LLe*\\;w$=Fg
nFhn7$$\"1L$eRx<,*=FgnFhn7$$\"1LLL[!>E%>FgnFhn7$$\"1/w79p)y&>FgnFhn7$$
\"1v=#*zZ:t>FgnFhn7$$\"15!>Gr)y!)>FgnFhn7$$\"1YhrXEU))>FgnFhn7$$\"18Z;
7'RA*>FgnFhn7$$\"1\"G8'yl0'*>FgnFhn7$$\"1\\=1XN()**>FgnFhn7$$\"1;/^60p
.?Fgn$\"\"#F(7$$\"1e*)4ViAM?FgnFfr7$$\"1+vou>wk?FgnFfr7$$\"1;/wn0#)=@F
gnFfr7$$\"1LL$3;zG<#FgnFfr7$$\"1+vo\\3]\"H#FgnFfr7$$\"1+D1\\nX/CFgnFfr
7$$\"1L$3-Q9B_#FgnFfr7$$\"1L3xwWaIEFgnFfr7$$\"1m;Hd_GZFFgnFfr7$$\"1mT&
)=haoGFgnFfr7$$\"1LL3(3D8#HFgnFfr7$$\"1+DJbS5uHFgnFfr7$$\"1BVw'RH7)HFg
nFfr7$$\"1Yh@QZN))HFgnFfr7$$\"1d?%*3u\">*HFgnFfr7$$\"1pzmz+[&*HFgnFfr7
$$\"1!)QR]F/**HFgnFfr7$$\"1\"z>6U0E+$Fgn$\"\"$F(7$$\"1QM-/h&o,$FgnF^v7
$$\"1$3Fpy16.$FgnF^v7$$\"1vVt_\"3'fIFgnF^v7$$\"1n;a=&4\")3$FgnF^v7$$\"
1L3-=*)*p9$FgnF^v7$$\"1****\\<$))e?$FgnF^v7$$\"1+]P%*=6@LFgnF^v7$$\"1+
voHmfKMFgnF^v7$$\"1+]i?9QcNFgnF^v7$$\"1LL$3c2wm$FgnF^v7$$\"1++D1_O'y$F
gnF^v7$$\"1$3_]Cr,%QFgnF^v7$$\"1mT&QGxR*QFgnF^v7$$\"1D\"y+R*QBRFgnF^v7
$$\"1$3-j\\,G&RFgnF^v7$$\"1iST\\v]nRFgnF^v7$$\"1Tg_-O@#)RFgnF^v7$$\"1J
?3Hmc*)RFgnF^v7$$\"1?!Qcl>p*RFgnF^v7$$\"1:g\"*ohf+SFgn$\"\"%F(7$$\"15S
>#osU+%FgnF\\z7$$\"10?Z&>\\z+%FgnF\\z7$$\"1++v3di6SFgnF\\z7$$\"1;aQ3Z(
p1%FgnF\\z7$$\"1L3-3PKATFgnF\\z7$$\"1+vV8].QUFgnF\\z7$$\"1LLekR;^VFgnF
\\z7$$\"1*\\(=#\\*fpWFgnF\\z7$$\"1nmm\")pm$e%FgnF\\z7$$\"1n;zkuJ+ZFgnF
\\z7$$\"1L3-B?+;[FgnF\\z7$$\"1</EqI:p[FgnF\\z7$$\"1++]<TIA\\FgnF\\z7$$
\"1%e9mmiF&\\FgnF\\z7$$\"1m\"Hd@@K)\\FgnF\\z7$$\"18y+`e$3*\\FgnF\\z7$$
\"1fkG!\\]%)*\\FgnF\\z7$$\"1#yD*3yD-]Fgn$\"\"&F(7$$\"10^cF^11]FgnFd]l7
$$\"1GW?YC()4]FgnFd]l7$$\"1]P%[wzO,&FgnFd]l7$$\"1T5SR!4*G]FgnFd]l7$$\"
1L$eRJQT/&FgnFd]l7$$\"1+D\"GHB')4&FgnFd]l7$$\"1nmmr#3J:&FgnFd]l7$$\"1+
vouHHp_FgnFd]l7$$\"1+DJgl\\!Q&FgnFd]l7$$\"1+++++++bFgnFd]l-%+AXESLABEL
SG6$%\"tG%!G-%'COLOURG6&%$RGBG$\")p:#R%!\")$\")`B)e)F_`l$\")fqkdF_`l-%
%VIEWG6$;F($\"#b!\"\"%(DEFAULTG" 2 373 373 373 2 0 1 0 2 6 0 4 2 
1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 107 "\nIn fact, a more
 accurate plot is obtained by instructing Maple not to make the joins \+
at discontinuities.\n\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 " \+
plot( floor(t),  t = 0 .. 5.5, discont = true, color = maroon); " }}
{PARA 13 "" 1 "" {INLPLOT "6*-%'CURVESG6$7S7$\"\"!F(7$$\"1OsI7arz@!#<F
(7$$\"1&y!oPTFwSF,F(7$$\"1h$[#zF:4iF,F(7$$\"1GV&\\_phN)F,F(7$$\"1PZ[(=
)H\\5!#;F(7$$\"1]=UX!3uC\"F9F(7$$\"1@\\MG$RDX\"F9F(7$$\"1%H(e%R'ok;F9F
(7$$\"1%p(\\-J:w=F9F(7$$\"1))f9/En$4#F9F(7$$\"1Rhf**QE&G#F9F(7$$\"1*4)
**>.&4]#F9F(7$$\"1b\\cpB_<FF9F(7$$\"1Tv9p'Hi#HF9F(7$$\"1b^o\"*ev:JF9F(
7$$\"1\"4^;!47TLF9F(7$$\"1k#piiM?`$F9F(7$$\"1v<utE6aPF9F(7$$\"1a>Vv$*o
]RF9F(7$$\"1qs\"H<lj;%F9F(7$$\"1@l+N&R<P%F9F(7$$\"1\"Ghm8Ege%F9F(7$$\"
1<x,I\"3Gy%F9F(7$$\"1Ql<%4k]*\\F9F(7$$\"1!f&[(QQb@&F9F(7$$\"1w]$z!>Y2a
F9F(7$$\"1yr$zcWZh&F9F(7$$\"1CAMQy))GeF9F(7$$\"1HKU]_QQgF9F(7$$\"1Jywo
Z3TiF9F(7$$\"1/xcC![hY'F9F(7$$\"1yl**ptPomF9F(7$$\"1*RJ7O+V)oF9F(7$$\"
1\\nv$oe*zqF9F(7$$\"1qAT5\\'QH(F9F(7$$\"1kIf**R8&\\(F9F(7$$\"1k*Q3>=bq
(F9F(7$$\"1=4^#>27\"zF9F(7$$\"15p*\\^Wl7)F9F(7$$\"1(y)**\\*RRL)F9F(7$$
\"1.Y2P<.Y&)F9F(7$$\"1*fqqHnjv)F9F(7$$\"1725KQk\\*)F9F(7$$\"175\\_0;r
\"*F9F(7$$\"1\"4Gzu(Gp$*F9F(7$$\"1M*)3iE`!e*F9F(7$$\"1eX=**4s#y*F9F(7$
$\"0+++)********!#:F(-%'COLOURG6&%$RGBG$\")viob!\")$\")!\\DP\"F\\u$\")
%yg>%F\\u-F$6$7S7$$\"1+++/+++5Fet$\"\"\"F(7$$\"1!H#*z:(z@5FetFgu7$$\"1
JA8XFwS5FetFgu7$$\"1N*>9`\"4i5FetFgu7$$\"1t\"[()phN3\"FetFgu7$$\"1&*)=
@#)H\\5\"FetFgu7$$\"1SPz23uC6FetFgu7$$\"1pH'f$RDX6FetFgu7$$\"1=*fCkok;
\"FetFgu7$$\"1yS78`h(=\"FetFgu7$$\"1&ReJEn$47FetFgu7$$\"1c%)e#RE&G7Fet
Fgu7$$\"1S#*\\M]4]7FetFgu7$$\"1#)fKRAvr7FetFgu7$$\"1;!f\"pHi#H\"FetFgu
7$$\"1i!*H\"fv:J\"FetFgu7$$\"1P/;#47TL\"FetFgu7$$\"11x]kM?`8FetFgu7$$
\"15<7p7Tv8FetFgu7$$\"1#ys\"R*o]R\"FetFgu7$$\"13>z=lj;9FetFgu7$$\"13w(
[&R<P9FetFgu7$$\"17X\"\\h-'e9FetFgu7$$\"1(3KT\"3Gy9FetFgu7$$\"1:1U5k]*
\\\"FetFgu7$$\"1O#>'RQb@:FetFgu7$$\"1I!\\:>Y2a\"FetFgu7$$\"1r[UdWZh:Fe
tFgu7$$\"1!*oL%y))Ge\"FetFgu7$$\"1#H>a_QQg\"FetFgu7$$\"1K@8x%3Ti\"FetF
gu7$$\"1\"3xD![hY;FetFgu7$$\"1J')*ptPom\"FetFgu7$$\"1gD*f.I%)o\"FetFgu
7$$\"1+x7oe*zq\"FetFgu7$$\"13\\m!\\'QH<FetFgu7$$\"1EAY*R8&\\<FetFgu7$$
\"1&eg%==bq<FetFgu7$$\"1nV]=27\"z\"FetFgu7$$\"1kPi]Wl7=FetFgu7$$\"1:&*
*R*RRL=FetFgu7$$\"1T)zD<.Y&=FetFgu7$$\"1SKXGnjv=FetFgu7$$\"1&GS=Qk\\*=
FetFgu7$$\"10ku`g6<>FetFgu7$$\"1O7<t(Gp$>FetFgu7$$\"1u0YkK0e>FetFgu7$$
\"1B)[!)4s#y>FetFgu7$$\"1+++'*******>FetFguFft-F$6$7S7$$\"1+++1+++?Fet
$\"\"#F(7$$\"1,^!*frz@?FetF__l7$$\"1\"=ppui2/#FetF__l7$$\"1o:<L:4i?Fet
F__l7$$\"1ERT+<c$3#FetF__l7$$\"1v\"*pB)H\\5#FetF__l7$$\"1xZH43uC@FetF_
_l7$$\"1`>QPRDX@FetF__l7$$\"1VSzV'ok;#FetF__l7$$\"1;OP9`h(=#FetF__l7$$
\"1E4KksO4AFetF__l7$$\"1]Vn$RE&GAFetF__l7$$\"1g))\\N]4]AFetF__l7$$\"1t
*Q-C_<F#FetF__l7$$\"1C&))*pHi#H#FetF__l7$$\"1gF0#fv:J#FetF__l7$$\"1))R
#G47TL#FetF__l7$$\"1#*[4lM?`BFetF__l7$$\"1l+ip7TvBFetF__l7$$\"11DfR*o]
R#FetF__l7$$\"1i`7>lj;CFetF__l7$$\"17*G^&R<PCFetF__l7$$\"1-,3:EgeCFetF
__l7$$\"1k*=U\"3GyCFetF__l7$$\"1!fA/T1&*\\#FetF__l7$$\"1@I`RQb@DFetF__
l7$$\"1YgQ\">Y2a#FetF__l7$$\"1t*yrXu9c#FetF__l7$$\"1N`+%y))Ge#FetF__l7
$$\"1QR+D&QQg#FetF__l7$$\"1)pNmZ3Ti#FetF__l7$$\"1A1*>![hYEFetF__l7$$\"
1\"GJjtPom#FetF__l7$$\"1S)Q_.I%)o#FetF__l7$$\"1;dHne*zq#FetF__l7$$\"1i
tu*['QHFFetF__l7$$\"1sTY)R8&\\FFetF__l7$$\"1y$yt\"=bqFFetF__l7$$\"1&))
Rtr?6z#FetF__l7$$\"1YJP\\Wl7GFetF__l7$$\"1Rfm#*RRLGFetF__l7$$\"1H9;rJg
aGFetF__l7$$\"1$p]psOc(GFetF__l7$$\"1F/E!Qk\\*GFetF__l7$$\"1Tz2_g6<HFe
tF__l7$$\"1@NUr(Gp$HFetF__l7$$\"1h$GEE`!eHFetF__l7$$\"1Nd8'4s#yHFetF__
l7$$\"1+++%*******HFetF__lFft-F$6$7S7$$\"1+++3+++IFet$\"\"$F(7$$\"17z
\"=;(z@IFetFghl7$$\"1Ih!)[FwSIFetFghl7$$\"1-K#\\`\"4iIFetFghl7$$\"1!oz
?qhN3$FetFghl7$$\"1d%z_#)H\\5$FetFghl7$$\"19ez53uCJFetFghl7$$\"1P4!)QR
DXJFetFghl7$$\"1p\"G^kok;$FetFghl7$$\"1bJi:`h(=$FetFghl7$$\"1dM[lsO4KF
etFghl7$$\"1X-w%RE&GKFetFghl7$$\"1![)\\O]4]KFetFghl7$$\"1k>:TAvrKFetFg
hl7$$\"1L!=3(Hi#H$FetFghl7$$\"1dk!Gfv:J$FetFghl7$$\"1Sv[$47TL$FetFghl7
$$\"1y?olM?`LFetFghl7$$\"1?%=,F6aP$FetFghl7$$\"1IA,S*o]R$FetFghl7$$\"1
;)e%>lj;MFetFghl7$$\"1<-QbR<PMFetFghl7$$\"1#pX_h-'eMFetFghl7$$\"1SeI93
GyMFetFghl7$$\"1kXU5k]*\\$FetFghl7$$\"10oWRQb@NFetFghl7$$\"1hIA\">Y2a$
FetFghl7$$\"1vI$pXu9c$FetFghl7$$\"1zPn$y))Ge$FetFghl7$$\"1%e)eC&QQg$Fe
tFghl7$$\"1l#RhZ3Ti$FetFghl7$$\"1jTS,[hYOFetFghl7$$\"1HRmNx$om$FetFghl
7$$\"1?^[M+V)o$FetFghl7$$\"1LPYme*zq$FetFghl7$$\"1;)H))['QHPFetFghl7$$
\"1>hY(R8&\\PFetFghl7$$\"1rhH;=bqPFetFghl7$$\"1-a<;27\"z$FetFghl7$$\"1
HD7[Wl7QFetFghl7$$\"1jBL\"*RRLQFetFghl7$$\"1;IupJgaQFetFghl7$$\"1Y\"[a
sOc(QFetFghl7$$\"1q0oyV'\\*QFetFghl7$$\"1w%4/0;r\"RFetFghl7$$\"11enp(G
p$RFetFghl7$$\"1[hzgK0eRFetFghl7$$\"1YEA%4s#yRFetFghl7$$\"1+++#*******
RFetFghlFft-F$6$7S7$$\"1+++5+++SFet$\"\"%F(7$$\"1B2tjrz@SFetF_bm7$$\"1
yIk]FwSSFetF_bm7$$\"1O[nO:4iSFetF_bm7$$\"1Lau.<c$3%FetF_bm7$$\"1P(fo#)
H\\5%FetF_bm7$$\"1]oH73uCTFetF_bm7$$\"1@*>-%RDXTFetF_bm7$$\"1%Hikkok;%
FetF_bm7$$\"1%psoJ:w=%FetF_bm7$$\"1))fkmsO4UFetF_bm7$$\"1Rh%eRE&GUFetF
_bm7$$\"1+\")\\P]4]UFetF_bm7$$\"1b\\1UAvrUFetF_bm7$$\"1TvkrHi#H%FetF_b
m7$$\"1b,c$fv:J%FetF_bm7$$\"1#4^T47TL%FetF_bm7$$\"1k#piY.KN%FetF_bm7$$
\"1vnhq7TvVFetF_bm7$$\"1b>VS*o]R%FetF_bm7$$\"1pAz>lj;WFetF_bm7$$\"1@:j
bR<PWFetF_bm7$$\"1\"G6ah-'eWFetF_bm7$$\"1<FR93GyWFetF_bm7$$\"1QlU5k]*
\\%FetF_bm7$$\"1!fg$RQb@XFetF_bm7$$\"1x+1\">Y2a%FetF_bm7$$\"1xrocWZhXF
etF_bm7$$\"1CAM$y))Ge%FetF_bm7$$\"1IK<C&QQg%FetF_bm7$$\"1JGkv%3Ti%FetF
_bm7$$\"1/x\"3![hYYFetF_bm7$$\"1yl*\\tPom%FetF_bm7$$\"1*RJP.I%)o%FetF_
bm7$$\"1\\<jle*zq%FetF_bm7$$\"1qA\"z['QHZFetF_bm7$$\"1l!okR8&\\ZFetF_b
m7$$\"1jR@:=bqZFetF_bm7$$\"1>4,:27\"z%FetF_bm7$$\"16>(oWaE\"[FetF_bm7$
$\"1(y)***)RRL[FetF_bm7$$\"1.YKoJga[FetF_bm7$$\"1*fXRsOc([FetF_bm7$$\"
1725xV'\\*[FetF_bm7$$\"175u[g6<\\FetF_bm7$$\"1\"4GzwGp$\\FetF_bm7$$\"1
MR'*eK0e\\FetF_bm7$$\"1e&4B4s#y\\FetF_bm7$$\"1+++!*******\\FetF_bmFft-
F$6$7S7$$\"1+++6+++]Fet$\"\"&F(7$$\"1lN%ye)*3,&FetFg[n7$$\"1w2G\"Q\"Q?
]FetFg[n7$$\"1E`Fud/J]FetFg[n7$$\"1b\"*yd3yT]FetFg[n7$$\"1Q\\K>\\Y_]Fe
tFg[n7$$\"1%oB?TqB1&FetFg[n7$$\"12Z'f(pis]FetFg[n7$$\"1zY1HVB$3&FetFg[
n7$$\"1K([Um2Q4&FetFg[n7$$\"1FO6ROo/^FetFg[n7$$\"1VXp.KE9^FetFg[n7$$\"
1b*)\\Cv/D^FetFg[n7$$\"1D2wEh(e8&FetFg[n7$$\"1Z6`\"\\6j9&FetFg[n7$$\"1
-&oC!yyb^FetFg[n7$$\"1M9u_g0n^FetFg[n7$$\"1H9yQ<gw^FetFg[n7$$\"1wH$4k0
x=&FetFg[n7$$\"134#eZMv>&FetFg[n7$$\"1)\\zaE=$3_FetFg[n7$$\"1(eyL)pe=_
FetFg[n7$$\"1QqC88IH_FetFg[n7$$\"1x!=FTS\"R_FetFg[n7$$\"1jPr5Kv\\_FetF
g[n7$$\"1U(e^#pxg_FetFg[n7$$\"1#H*)45t.F&FetFg[n7$$\"19@yLst!G&FetFg[n
7$$\"1B#)3(RW9H&FetFg[n7$$\"1wF[n#>>I&FetFg[n7$$\"12t>VU07`FetFg[n7$$
\"1PAw0uIB`FetFg[n7$$\"1_9$G()=ML&FetFg[n7$$\"1qs<A]@W`FetFg[n7$$\"1zy
5Qz*RN&FetFg[n7$$\"1\\nA\\Kpk`FetFg[n7$$\"1>X[.nvu`FetFg[n7$$\"1Ik$G\"
fF&Q&FetFg[n7$$\"1QVri.c&R&FetFg[n7$$\"1,LiGsK1aFetFg[n7$$\"1+g;+qp;aF
etFg[n7$$\"1*p2$*e,tU&FetFg[n7$$\"1ir4n$=yV&FetFg[n7$$\"1#RbO>#[ZaFetF
g[n7$$\"1!R`%H!e&eaFetFg[n7$$\"1<r-*Qk%oaFetFg[n7$$\"19R_Mm-zaFetFg[n7
$$\"12l<^g8*[&FetFg[n7$$\"1+++++++bFetFg[nFft-%+AXESLABELSG6$%\"tG%!G-
%%VIEWG6$;F($\"#b!\"\"%(DEFAULTG" 2 373 373 373 2 0 1 0 2 9 0 4 2 
1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 3 "\n\n\n" }}{PARA 0 "" 0 "" {TEXT -1 38 "We will use the L
aplace Transform of  " }{TEXT 307 12 "Heaviside(t)" }{TEXT -1 38 "  to
 derive the Laplace Transform of  " }{TEXT 308 8 "floor(t)" }{TEXT -1 
1 "." }}{PARA 0 "" 0 "" {TEXT -1 16 "First, express  " }{TEXT 304 8 "f
loor(t)" }{TEXT -1 7 "  for  " }{TEXT 314 6 " t > 0" }{TEXT -1 62 "   \+
as an infinite sum of translates of the Heaviside function " }{TEXT 
305 1 " " }{TEXT 309 12 "Heaviside(t)" }{TEXT -1 69 " .  Use this repr
esentation to calculate the Laplace transform of    " }{TEXT 306 8 "fl
oor(t)" }{TEXT -1 59 ".  (Use your own name, one that has no a priori \+
meaning to " }{TEXT 313 5 "MAPLE" }{TEXT -1 21 ",  on the left side.)
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 111 "staircase := t -> sum( Heaviside(t-j) , j = 0 .. infinity ); \+
# This is not a Maple question! The text can help." }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%*staircaseG:6#%\"tG6\"6$%)operatorG%&arrowGF(-%$sum
G6$-%*HeavisideG6#,&9$\"\"\"%\"jG!\"\"/F5;\"\"!%)infinityGF(F(" }}}
{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 105 "Apply th
e Laplace transform to compute the Laplace transform of the floor func
tion.  Name the expression." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "Staircase  := s -> laplace( stairca
se(t) , t , s );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*StaircaseG:6#%
\"sG6\"6$%)operatorG%&arrowGF(-%(laplaceG6%-%*staircaseG6#%\"tGF29$F(F
(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 64 "Evaluate this last Laplace transform to s
ee what the formula is:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Stairca
se(s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"sG!\"\",&\"\"\"F'-%$exp
G6#,$F$F%F%F%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 3 "   " }{TEXT 319 28 "In the
 next line we will use" }{TEXT -1 2 "  " }{TEXT 318 6 "DEplot" }{TEXT 
-1 1 " " }{TEXT 321 1 " " }{TEXT 320 49 "to plot the solution to the i
nitial value problem" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT 315 10 "  \n       " }{XPPEDIT 317 1 "diff(diff(x(t),t),t)+2*d
iff(x(t),t)+x(t) = 5*floor(t)*``, `    `*x(0) = `0.0`*``, `   `*D(x)(0
) = 0" "6%/,(-%%diffG6$-F&6$-%\"xG6#%\"tGF-F-\"\"\"*&\"\"#F.-F&6$-F+6#
F-F-F.F.-F+6#F-F.*(\"\"&F.-%&floorG6#F-F.%!GF./*&%%~~~~GF.-F+6#\"\"!F.
*&%$0.0GF.F<F./*&%$~~~GF.--%\"DG6#F+6#FBF.FB" }{TEXT 316 1 ":" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 6 "\nfor  " }
{TEXT 343 1 " " }{XPPEDIT 344 1 "t = 0 .. 10" "/%\"tG;\"\"!\"#5" }
{TEXT -1 2 " :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 169 " ode := diff(x(t),t$2) + 2*diff(x(t),t)+ x(t) =
 2*floor(t):  # Execute!\nDEplot(\{ode\}, [x(t)], t=0.. 10, [[x(0)=0.0
,D(x)(0)=0]], stepsize= 0.01, linecolor = aquamarine); " }}{PARA 13 "
" 1 "" {INLPLOT "6&-%'CURVESG6%7ein7$\"\"!F(7$$\"\"\"!\"#F(7$$\"\"#F,F
(7$$\"\"$F,F(7$$\"\"%F,F(7$$\"\"&F,F(7$$\"\"'F,F(7$$\"\"(F,F(7$$\"\")F
,F(7$$\"\"*F,F(7$$\"#5F,F(7$$\"#6F,F(7$$\"#7F,F(7$$\"#8F,F(7$$\"#9F,F(
7$$\"#:F,F(7$$\"#;F,F(7$$\"#<F,F(7$$\"#=F,F(7$$\"#>F,F(7$$\"#?F,F(7$$
\"#@F,F(7$$\"#AF,F(7$$\"#BF,F(7$$\"#CF,F(7$$\"#DF,F(7$$\"#EF,F(7$$\"#F
F,F(7$$\"#GF,F(7$$\"#HF,F(7$$\"#IF,F(7$$\"#JF,F(7$$\"#KF,F(7$$\"#LF,F(
7$$\"#MF,F(7$$\"#NF,F(7$$\"#OF,F(7$$\"#PF,F(7$$\"#QF,F(7$$\"#RF,F(7$$
\"#SF,F(7$$\"#TF,F(7$$\"#UF,F(7$$\"#VF,F(7$$\"#WF,F(7$$\"#XF,F(7$$\"#Y
F,F(7$$\"#ZF,F(7$$\"#[F,F(7$$\"#\\F,F(7$$\"#]F,F(7$$\"#^F,F(7$$\"#_F,F
(7$$\"#`F,F(7$$\"#aF,F(7$$\"#bF,F(7$$\"#cF,F(7$$\"#dF,F(7$$\"#eF,F(7$$
\"#fF,F(7$$\"#gF,F(7$$\"#hF,F(7$$\"#iF,F(7$$\"#jF,F(7$$\"#kF,F(7$$\"#l
F,F(7$$\"#mF,F(7$$\"#nF,F(7$$\"#oF,F(7$$\"#pF,F(7$$\"#qF,F(7$$\"#rF,F(
7$$\"#sF,F(7$$\"#tF,F(7$$\"#uF,F(7$$\"#vF,F(7$$\"#wF,F(7$$\"#xF,F(7$$
\"#yF,F(7$$\"#zF,F(7$$\"#!)F,F(7$$\"#\")F,F(7$$\"##)F,F(7$$\"#$)F,F(7$
$\"#%)F,F(7$$\"#&)F,F(7$$\"#')F,F(7$$\"#()F,F(7$$\"#))F,F(7$$\"#*)F,F(
7$$\"#!*F,F(7$$\"#\"*F,F(7$$\"##*F,F(7$$\"#$*F,F(7$$\"#%*F,F(7$$\"#&*F
,F(7$$\"#'*F,F(7$$\"#(*F,F(7$$\"#)*F,F(7$$\"#**F,F(7$$\"$+\"F,F(7$$\"$
,\"F,$\"1WWWW\\PB8!#>7$$\"$-\"F,$\"1d]_b/`+YFe^l7$$\"$.\"F,$\"1Vv_GYX#
z*Fe^l7$$\"$/\"F,$\"1W))HZ=2'o\"!#=7$$\"$0\"F,$\"1)G\"\\<ouwDFe_l7$$\"
$1\"F,$\"1'[EbuTvk$Fe_l7$$\"$2\"F,$\"1L!eB+%y%*[Fe_l7$$\"$3\"F,$\"1jmb
7i&[J'Fe_l7$$\"$4\"F,$\"1*\\c$=b>/zFe_l7$$\"$5\"F,$\"13m(G&GHf'*Fe_l7$
$\"$6\"F,$\"163CA#pw:\"!#<7$$\"$7\"F,$\"1Vew***)Hl8Fial7$$\"$8\"F,$\"1
QXQ@M[)e\"Fial7$$\"$9\"F,$\"1]N&zQ#*o#=Fial7$$\"$:\"F,$\"1<@TH3?!3#Fia
l7$$\"$;\"F,$\"1&R$QP')3[BFial7$$\"$<\"F,$\"1@\">')fS-j#Fial7$$\"$=\"F
,$\"16vFHjMEHFial7$$\"$>\"F,$\"17W-5-5OKFial7$$\"$?\"F,$\"1;y%>K,#fNFi
al7$$\"$@\"F,$\"1')fF$Q``*QFial7$$\"$A\"F,$\"1Y&*)ookUC%Fial7$$\"$B\"F
,$\"1\"*zhQ![cg%Fial7$$\"$C\"F,$\"1.7J'p?#z\\Fial7$$\"$D\"F,$\"1emn4Vq
k`Fial7$$\"$E\"F,$\"17J(3'[#=w&Fial7$$\"$F\"F,$\"1\"o^eg7.<'Fial7$$\"$
G\"F,$\"10`V;?!**e'Fial7$$\"$H\"F,$\"1Bx7B<L?qFial7$$\"$I\"F,$\"1#=V'e
WMhuFial7$$\"$J\"F,$\"1t\"[@+(o7zFial7$$\"$K\"F,$\"1\\m?C,6u$)Fial7$$
\"$L\"F,$\"1;-UK&o`%))Fial7$$\"$M\"F,$\"1R\\v<3AE$*Fial7$$\"$N\"F,$\"1
uka,%Hk\")*Fial7$$\"$O\"F,$\"1LvJ[gdJ5!#;7$$\"$P\"F,$\"1=/%))R)R#3\"Fg
il7$$\"$Q\"F,$\"1Ep$=N(3M6Fgil7$$\"$R\"F,$\"1*y@*H1i'=\"Fgil7$$\"$S\"F
,$\"1L%QKJw*R7Fgil7$$\"$T\"F,$\"1K'\\X$G8%H\"Fgil7$$\"$U\"F,$\"1b/Ru*o
!\\8Fgil7$$\"$V\"F,$\"1nFGcQw/9Fgil7$$\"$W\"F,$\"1E0,Up>h9Fgil7$$\"$X
\"F,$\"1[^&p-[$=:Fgil7$$\"$Y\"F,$\"15-\\Ns>w:Fgil7$$\"$Z\"F,$\"1qZV;]s
M;Fgil7$$\"$[\"F,$\"1(fk&Q@\"Rp\"Fgil7$$\"$\\\"F,$\"121='oRPv\"Fgil7$$
\"$]\"F,$\"15Qta!*=9=Fgil7$$\"$^\"F,$\"1%31l%>Cv=Fgil7$$\"$_\"F,$\"1(4
YjO!)o$>Fgil7$$\"$`\"F,$\"12(fuh'3**>Fgil7$$\"$a\"F,$\"1\"=asHV=1#Fgil
7$$\"$b\"F,$\"1ubB$HL^7#Fgil7$$\"$c\"F,$\"1A'e*y(R*)=#Fgil7$$\"$d\"F,$
\"1<&G+@YKD#Fgil7$$\"$e\"F,$\"1ER:?j.=BFgil7$$\"$f\"F,$\"1E1D<TH$Q#Fgi
l7$$\"$g\"F,$\"1a^fzQ+\\CFgil7$$\"$h\"F,$\"1Uy-_,::DFgil7$$\"$i\"F,$\"
1dY?Uxr\"e#Fgil7$$\"$j\"F,$\"1Ds*or\"p[EFgil7$$\"$k\"F,$\"1&[S$)Rdgr#F
gil7$$\"$l\"F,$\"1Ytig.!Qy#Fgil7$$\"$m\"F,$\"1E)\\hU1>&GFgil7$$\"$n\"F
,$\"1fg3i;O?HFgil7$$\"$o\"F,$\"1QE$pP_\"*)HFgil7$$\"$p\"F,$\"1F<3<^EeI
Fgil7$$\"$q\"F,$\"1*RUMm'oFJFgil7$$\"$r\"F,$\"1cc5GSS(>$Fgil7$$\"$s\"F
,$\"1*f_5X/uE$Fgil7$$\"$t\"F,$\"1=_!pRvwL$Fgil7$$\"$u\"F,$\"1y#><b/#3M
Fgil7$$\"$v\"F,$\"1\"z=)>)z*yMFgil7$$\"$w\"F,$\"1b:n?$*)*\\NFgil7$$\"$
x\"F,$\"1m_!eQ@7i$Fgil7$$\"$y\"F,$\"1$pjdbkEp$Fgil7$$\"$z\"F,$\"1RC5xv
IkPFgil7$$\"$!=F,$\"1!zB%*RRh$QFgil7$$\"$\"=F,$\"1q,Xs\"\\\"3RFgil7$$
\"$#=F,$\"1Vd8ViK!)RFgil7$$\"$$=F,$\"1uc\"G:gE0%Fgil7$$\"$%=F,$\"1%f#R
M19DTFgil7$$\"$&=F,$\"1:)f&4wv(>%Fgil7$$\"$'=F,$\"1M31'=,0F%Fgil7$$\"$
(=F,$\"1%o%)\\lhLM%Fgil7$$\"$)=F,$\"1%o'4)[HjT%Fgil7$$\"$*=F,$\"1oT?N`
R*[%Fgil7$$\"$!>F,$\"1Jnb@+biXFgil7$$\"$\">F,$\"1'f!GXXyNYFgil7$$\"$#>
F,$\"1pm%[2!44ZFgil7$$\"$$>F,$\"1b=dYzX#y%Fgil7$$\"$%>F,$\"1WK:i'ze&[F
gil7$$\"$&>F,$\"1WZB')oMH\\Fgil7$$\"$'>F,$\"1ld+W9&G+&Fgil7$$\"$(>F,$
\"1h:$)=`Qw]Fgil7$$\"$)>F,$\"1J[\"*\\1%*\\^Fgil7$$\"$*>F,$\"1'>))*H(4N
A&Fgil7$$\"$+#F,$\"1kr..]3(H&Fgil7$$\"$,#F,$\"1ew*pV#)>P&Fgil7$$\"$-#F
,$\"1\\@Fx^#)[aFgil7$$\"$.#F,$\"1nrL'4nv_&Fgil7$$\"$/#F,$\"1$pD?zi\"3c
Fgil7$$\"$0#F,$\"1w\"fwdn0p&Fgil7$$\"$1#F,$\"1%>/BZPZx&Fgil7$$\"$2#F,$
\"1\"4_6>H1'eFgil7$$\"$3#F,$\"1s--O,?[fFgil7$$\"$4#F,$\"1=N(fQ3u.'Fgil
7$$\"$5#F,$\"1cS1)o7#GhFgil7$$\"$6#F,$\"1^()=[Cd?iFgil7$$\"$7#F,$\"16A
1AxW9jFgil7$$\"$8#F,$\"1+UI1#*z4kFgil7$$\"$9#F,$\"1y,kH#)e1lFgil7$$\"$
:#F,$\"1+M@Wnx/mFgil7$$\"$;#F,$\"1Fu+<tK/nFgil7$$\"$<#F,$\"12vP@J?0oFg
il7$$\"$=#F,$\"18(*oGzO2pFgil7$$\"$>#F,$\"1Jj1+hy5qFgil7$$\"$?#F,$\"15
kByDU:rFgil7$$\"$@#F,$\"1++\\zGC@sFgil7$$\"$A#F,$\"1>]t&38#GtFgil7$$\"
$B#F,$\"18`lO)*HOuFgil7$$\"$C#F,$\"1h)o>Kqaa(Fgil7$$\"$D#F,$\"1HZytApb
wFgil7$$\"$E#F,$\"1ix0fR$pw(Fgil7$$\"$F#F,$\"1p'R@<k\"zyFgil7$$\"$G#F,
$\"1q`UFAN#*zFgil7$$\"$H#F,$\"1rN4_zY1\")Fgil7$$\"$I#F,$\"1z,%*y;[@#)F
gil7$$\"$J#F,$\"1-PIRUOP$)Fgil7$$\"$K#F,$\"1Y73cp3a%)Fgil7$$\"$L#F,$\"
1oU$oj@;d)Fgil7$$\"$M#F,$\"1GF)pcS**o)Fgil7$$\"$N#F,$\"1Eo3.l,4))Fgil7
$$\"$O#F,$\"1(*\\@mE#)G*)Fgil7$$\"$P#F,$\"1itRNFL\\!*Fgil7$$\"$Q#F,$\"
1WL;T3_q\"*Fgil7$$\"$R#F,$\"1!oi\"f:O#H*Fgil7$$\"$S#F,$\"1N&oQ!*H[T*Fg
il7$$\"$T#F,$\"1)*>OA8!z`*Fgil7$$\"$U#F,$\"1'o'>)o^:m*Fgil7$$\"$V#F,$
\"1XFM&Hddy*Fgil7$$\"$W#F,$\"1<!4A&[\\5**Fgil7$$\"$X#F,$\"1nUdZTd.5!#:
7$$\"$Y#F,$\"140cou9;5Fi[o7$$\"$Z#F,$\"1MB%)RswG5Fi[o7$$\"$[#F,$\"10;@
#HJ9/\"Fi[o7$$\"$\\#F,$\"1.$H]\\PT0\"Fi[o7$$\"$]#F,$\"1XFnbP)o1\"Fi[o7
$$\"$^#F,$\"1)***)*=!o'z5Fi[o7$$\"$_#F,$\"1!QhnE)[#4\"Fi[o7$$\"$`#F,$
\"1iz;<DM06Fi[o7$$\"$a#F,$\"10qEC)G#=6Fi[o7$$\"$b#F,$\"1;UZx_9J6Fi[o7$
$\"$c#F,$\"1oF0,+4W6Fi[o7$$\"$d#F,$\"1z*3O:hq:\"Fi[o7$$\"$e#F,$\"1&e%f
Fp0q6Fi[o7$$\"$f#F,$\"13b\")[b2$=\"Fi[o7$$\"$g#F,$\"1hq%fF:h>\"Fi[o7$$
\"$h#F,$\"1%[b+Su\"47Fi[o7$$\"$i#F,$\"1ld7W7DA7Fi[o7$$\"$j#F,$\"1HcfiT
MN7Fi[o7$$\"$k#F,$\"1jc*3a^%[7Fi[o7$$\"$l#F,$\"1fa*\\zr:E\"Fi[o7$$\"$m
#F,$\"1Qd&4P.ZF\"Fi[o7$$\"$n#F,$\"1Zj[WZ%yG\"Fi[o7$$\"$o#F,$\"1(350U%*
4I\"Fi[o7$$\"$p#F,$\"1sAtK4:98Fi[o7$$\"$q#F,$\"1wf@VGJF8Fi[o7$$\"$r#F,
$\"1rG'>uy/M\"Fi[o7$$\"$s#F,$\"12'*\\Ysk`8Fi[o7$$\"$t#F,$\"1\\'p9+<oO
\"Fi[o7$$\"$u#F,$\"1C0Bym)*z8Fi[o7$$\"$v#F,$\"1!QcW(\\:$R\"Fi[o7$$\"$w
#F,$\"1Jeu81K19Fi[o7$$\"$x#F,$\"1#)\\BXB[>9Fi[o7$$\"$y#F,$\"1&f:K%*QEV
\"Fi[o7$$\"$z#F,$\"1M$en?*yX9Fi[o7$$\"$!GF,$\"1(*4Mf>$*e9Fi[o7$$\"$\"G
F,$\"1<<[[g1s9Fi[o7$$\"$#GF,$\"1AqPX.>&[\"Fi[o7$$\"$$GF,$\"1TZaWPI)\\
\"Fi[o7$$\"$%GF,$\"1^;Zj^S6:Fi[o7$$\"$&GF,$\"1WeEUN\\C:Fi[o7$$\"$'GF,$
\"1BPJVycP:Fi[o7$$\"$(GF,$\"1*fT40F1b\"Fi[o7$$\"$)GF,$\"1-=3r,nj:Fi[o7
$$\"$*GF,$\"1zK%4B'pw:Fi[o7$$\"$!HF,$\"1&f'oyUq*e\"Fi[o7$$\"$\"HF,$\"1
/L5$Q$p-;Fi[o7$$\"$#HF,$\"1@'*HLEm:;Fi[o7$$\"$$HF,$\"1^VQQ6hG;Fi[o7$$
\"$%HF,$\"165;F!Q:k\"Fi[o7$$\"$&HF,$\"12T#yWUWl\"Fi[o7$$\"$'HF,$\"1&\\
fwcBtm\"Fi[o7$$\"$(HF,$\"1&z[Fd!=!o\"Fi[o7$$\"$)HF,$\"1*yxwm7Ip\"Fi[o7
$$\"$*HF,$\"1o([_2>eq\"Fi[o7$$\"$+$F,$\"1kn>O!*f=<Fi[o7$$\"$,$F,$\"1!3
/k9%[J<Fi[o7$$\"$-$F,$\"1*[(>An`W<Fi[o7$$\"$.$F,$\"1\"Rb_:_xv\"Fi[o7$$
\"$/$F,$\"1dKQ7f7r<Fi[o7$$\"$0$F,$\"1<[ZMNl%y\"Fi[o7$$\"$1$F,$\"1*\\'[
N1L)z\"Fi[o7$$\"$2$F,$\"1G\\U,H:7=Fi[o7$$\"$3$F,$\"1atM*3;h#=Fi[o7$$\"
$4$F,$\"1C[PEg@S=Fi[o7$$\"$5$F,$\"1szr3'[W&=Fi[o7$$\"$6$F,$\"1Y_r+)4)o
=Fi[o7$$\"$7$F,$\"1ZM)Qj&H$)=Fi[o7$$\"$8$F,$\"11/)f?-z*=Fi[o7$$\"$9$F,
$\"1t'z+oDE\">Fi[o7$$\"$:$F,$\"1_ql$Giu#>Fi[o7$$\"$;$F,$\"1g))o2$3C%>F
i[o7$$\"$<$F,$\"1Q<w0,Yd>Fi[o7$$\"$=$F,$\"13R>$49E(>Fi[o7$$\"$>$F,$\"1
0x;Yn'y)>Fi[o7$$\"$?$F,$\"1rK(3g9K+#Fi[o7$$\"$@$F,$\"1[Km_Ul=?Fi[o7$$
\"$A$F,$\"1t$=_N#=M?Fi[o7$$\"$B$F,$\"1-Qs>cz\\?Fi[o7$$\"$C$F,$\"1jg093
\\l?Fi[o7$$\"$D$F,$\"1$[!)>wk73#Fi[o7$$\"$E$F,$\"1#**eBM9r4#Fi[o7$$\"$
F$F,$\"1S\"o$)[OI6#Fi[o7$$\"$G$F,$\"1Hss'=G!H@Fi[o7$$\"$H$F,$\"1Mk$pZ'
3X@Fi[o7$$\"$I$F,$\"1qZ_]%37;#Fi[o7$$\"$J$F,$\"1<yI]7Rx@Fi[o7$$\"$K$F,
$\"1W]lp?j$>#Fi[o7$$\"$L$F,$\"1gmw^\"G*4AFi[o7$$\"$M$F,$\"1G)f*)ywiA#F
i[o7$$\"$N$F,$\"1qT'>KvEC#Fi[o7$$\"$O$F,$\"14kAR67fAFi[o7$$\"$P$F,$\"1
wSAw;hvAFi[o7$$\"$Q$F,$\"1K\")y9W9#H#Fi[o7$$\"$R$F,$\"1IWV#)or3BFi[o7$
$\"$S$F,$\"1uQq^mKDBFi[o7$$\"$T$F,$\"127^R8(>M#Fi[o7$$\"$U$F,$\"1yA]1'
['eBFi[o7$$\"$V$F,$\"1G(>k:c`P#Fi[o7$$\"$W$F,$\"1]pZN<4#R#Fi[o7$$\"$X$
F,$\"1h-uJJ&)3CFi[o7$$\"$Y$F,$\"1Q\">X<QcU#Fi[o7$$\"$Z$F,$\"1uWwLZWUCF
i[o7$$\"$[$F,$\"1,ZZ>2FfCFi[o7$$\"$\\$F,$\"1E(4639hZ#Fi[o7$$\"$]$F,$\"
1[D,2G(H\\#Fi[o7$$\"$^$F,$\"1'\\QQ#\\%)4DFi[o7$$\"$_$F,$\"1i>*f\\Gn_#F
i[o7$$\"$`$F,$\"1^02D;iVDFi[o7$$\"$a$F,$\"1olJ\\C_gDFi[o7$$\"$b$F,$\"1
?d2V\"Hud#Fi[o7$$\"$c$F,$\"1yHE;*RVf#Fi[o7$$\"$d$F,$\"1#[NQ,`7h#Fi[o7$
$\"$e$F,$\"1CCF:n;GEFi[o7$$\"$f$F,$\"1,=1M$z]k#Fi[o7$$\"$g$F,$\"1yR><#
*)>m#Fi[o7$$\"$h$F,$\"1Y>mWZ*)yEFi[o7$$\"$i$F,$\"1B#o*GVz&p#Fi[o7$$\"$
j$F,$\"1(GQYT'o7FFi[o7$$\"$k$F,$\"1)[SxZp&HFFi[o7$$\"$l$F,$\"1GBTD?WYF
Fi[o7$$\"$m$F,$\"1eIR&f-Lw#Fi[o7$$\"$n$F,$\"1!\\ibv\\,y#Fi[o7$$\"$o$F,
$\"1pf[.@)pz#Fi[o7$$\"$p$F,$\"1*RlfE)z8GFi[o7$$\"$q$F,$\"1)G'f)*ofIGFi
[o7$$\"$r$F,$\"1)oI`owt%GFi[o7$$\"$s$F,$\"1/g/Qj8kGFi[o7$$\"$t$F,$\"1d
&>hfu3)GFi[o7$$\"$u$F,$\"1p)3gA!f(*GFi[o7$$\"$v$F,$\"1cv$3-#G9HFi[o7$$
\"$w$F,$\"1,o)**z[4$HFi[o7$$\"$x$F,$\"1-Bp3%*eZHFi[o7$$\"$y$F,$\"1Zmk<
F?kHFi[o7$$\"$z$F,$\"1XqgAwy!)HFi[o7$$\"$!QF,$\"1N$3S/Vt*HFi[o7$$\"$\"
QF,$\"1E7eEz'Q,$Fi[o7$$\"$#QF,$\"1wc(*Q7OIIFi[o7$$\"$$QF,$\"1x$*Qt>#o/
$Fi[o7$$\"$%QF,$\"1\\7?X\"\\K1$Fi[o7$$\"$&QF,$\"18*4EzT'zIFi[o7$$\"$'Q
F,$\"1WqFw*)*f4$Fi[o7$$\"$(QF,$\"1&ev*y(>B6$Fi[o7$$\"$)QF,$\"18FC0LgGJ
Fi[o7$$\"$*QF,$\"1Wv.\"o[[9$Fi[o7$$\"$!RF,$\"1zMS`]0hJFi[o7$$\"$\"RF,$
\"1g^8!f@s<$Fi[o7$$\"$#RF,$\"1a*\\%zuM$>$Fi[o7$$\"$$RF,$\"1PRmH>V4KFi[
o7$$\"$%RF,$\"1$Gs)oTZDKFi[o7$$\"$&RF,$\"1YSjWMZTKFi[o7$$\"$'RF,$\"1M7
mB!HuD$Fi[o7$$\"$(RF,$\"1m@^\">SLF$Fi[o7$$\"$)RF,$\"19!*G_i?*G$Fi[o7$$
\"$*RF,$\"1=&R$Gl-0LFi[o7$$\"$+%F,$\"1yF'*f.!3K$Fi[o7$$\"$,%F,$\"1mNhU
%fmL$Fi[o7$$\"$-%F,$\"1)\\*=#>mEN$Fi[o7$$\"$.%F,$\"1n$G**4;)oLFi[o7$$
\"$/%F,$\"1YR<KZ5&Q$Fi[o7$$\"$0%F,$\"1cxKHx_,MFi[o7$$\"$1%F,$\"1VU\"[!
33=MFi[o7$$\"$2%F,$\"1G#fSufZV$Fi[o7$$\"$3%F,$\"1W9[./c^MFi[o7$$\"$4%F
,$\"1Iq\\4(y%oMFi[o7$$\"$5%F,$\"1$zOvl5b[$Fi[o7$$\"$6%F,$\"1/h26Bl-NFi
[o7$$\"$7%F,$\"1csn+)**)>NFi[o7$$\"$8%F,$\"1lT/B$\\s`$Fi[o7$$\"$9%F,$
\"1:#*3SrpaNFi[o7$$\"$:%F,$\"1V@,y&RAd$Fi[o7$$\"$;%F,$\"1#y!REI()*e$Fi
[o7$$\"$<%F,$\"1dNGPRf2OFi[o7$$\"$=%F,$\"1VNMC))RDOFi[o7$$\"$>%F,$\"1%
)R%>E%GVOFi[o7$$\"$?%F,$\"1,^J%)oChOFi[o7$$\"$@%F,$\"1)3#p%Q$GzOFi[o7$
$\"$A%F,$\"19TZ90R(p$Fi[o7$$\"$B%F,$\"1PUR#3lbr$Fi[o7$$\"$C%F,$\"1f+q`
R!Qt$Fi[o7$$\"$D%F,$\"1O]M\\S5_PFi[o7$$\"$E%F,$\"1l->XBYqPFi[o7$$\"$F%
F,$\"1Xm@re())y$Fi[o7$$\"$G%F,$\"1*GZ2rTt!QFi[o7$$\"$H%F,$\"1L+o**p&e#
QFi[o7$$\"$I%F,$\"1l*Hd#*=W%QFi[o7$$\"$J%F,$\"1)z\"oFZ-jQFi[o7$$\"$K%F
,$\"1/?l%pr;)QFi[o7$$\"$L%F,$\"1h0OlrN+RFi[o7$$\"$M%F,$\"1PATF&y!>RFi[
o7$$\"$N%F,$\"1Qse;K$y$RFi[o7$$\"$O%F,$\"1X69;(=m&RFi[o7$$\"$P%F,$\"12
S6cDVvRFi[o7$$\"$Q%F,$\"1'\\[EJsU*RFi[o7$$\"$R%F,$\"1$)pJ2c88SFi[o7$$
\"$S%F,$\"1]uX1,-KSFi[o7$$\"$T%F,$\"18\"=0_B40%Fi[o7$$\"$U%F,$\"1q1T.O
%)pSFi[o7$$\"$V%F,$\"1L?(=:y()3%Fi[o7$$\"$W%F,$\"1sW$[+Dx5%Fi[o7$$\"$X
%F,$\"1WS!G/#oETFi[o7$$\"$Y%F,$\"1FsC(=Zc9%Fi[o7$$\"$Z%F,$\"1Lc)**R=Y;
%Fi[o7$$\"$[%F,$\"1:()f#o$f$=%Fi[o7$$\"$\\%F,$\"1bV$e2rD?%Fi[o7$$\"$]%
F,$\"1qs-f'[:A%Fi[o7$$\"$^%F,$\"1)3D&\\X_SUFi[o7$$\"$_%F,$\"1R?7-p\\fU
Fi[o7$$\"$`%F,$\"1\\,]3RYyUFi[o7$$\"$a%F,$\"1Tyn'zBuH%Fi[o7$$\"$b%F,$
\"1teYI[P;VFi[o7$$\"$c%F,$\"1'[I*3`JNVFi[o7$$\"$d%F,$\"14P'ecVUN%Fi[o7
$$\"$e%F,$\"1$pg#pz:tVFi[o7$$\"$f%F,$\"1RS!3#p0#R%Fi[o7$$\"$g%F,$\"1t
\\Nb)Q4T%Fi[o7$$\"$h%F,$\"1H8XSA!)HWFi[o7$$\"$i%F,$\"1@A\"edX'[WFi[o7$
$\"$j%F,$\"1k$\\GRnuY%Fi[o7$$\"$k%F,$\"10\\=aiE'[%Fi[o7$$\"$l%F,$\"1Hd
<`2/0XFi[o7$$\"$m%F,$\"1HTW8&*yBXFi[o7$$\"$n%F,$\"1\"z9%)=6Da%Fi[o7$$
\"$o%F,$\"1yz&3Y/7c%Fi[o7$$\"$p%F,$\"1q)QC/o)zXFi[o7$$\"$q%F,$\"1VHFt1
])f%Fi[o7$$\"$r%F,$\"1qt[@65<YFi[o7$$\"$s%F,$\"10$)y#=ocj%Fi[o7$$\"$t%
F,$\"1<S.!o+Ul%Fi[o7$$\"$u%F,$\"1!y8GY(psYFi[o7$$\"$v%F,$\"1rC.2u:\"p%
Fi[o7$$\"$w%F,$\"1t2]9%z&4ZFi[o7$$\"$x%F,$\"1K4`7C'zs%Fi[o7$$\"$y%F,$
\"1)*z```IYZFi[o7$$\"$z%F,$\"1mkk9sgkZFi[o7$$\"$![F,$\"1uAI(*p'Gy%Fi[o
7$$\"$\"[F,$\"1n+*os$3,[Fi[o7$$\"$#[F,$\"1ucN_kD>[Fi[o7$$\"$$[F,$\"19P
$eC%QP[Fi[o7$$\"$%[F,$\"11.G-iYb[Fi[o7$$\"$&[F,$\"1o26R9]t[Fi[o7$$\"$'
[F,$\"1$GUe4*[\"*[Fi[o7$$\"$([F,$\"1L9uL$G%4\\Fi[o7$$\"$)[F,$\"1(ewaL=
t#\\Fi[o7$$\"$*[F,$\"1I]x/$e^%\\Fi[o7$$\"$!\\F,$\"12[3mu%H'\\Fi[o7$$\"
$\"\\F,$\"1*>TU1&o!)\\Fi[o7$$\"$#\\F,$\"14y8k.P)*\\Fi[o7$$\"$$\\F,$\"1
^@S]E+;]Fi[o7$$\"$%\\F,$\"1Bd2F7eL]Fi[o7$$\"$&\\F,$\"1#[)H<a5^]Fi[o7$$
\"$'\\F,$\"1(o(*Hcu&o]Fi[o7$$\"$(\\F,$\"1U5eC!))f3&Fi[o7$$\"$)\\F,$\"1
xSj!=XL5&Fi[o7$$\"$*\\F,$\"1@<iFak?^Fi[o7$$\"$+&F,$\"1MSfz\"))y8&Fi[o7
$$\"$,&F,$\"1W/R0_?b^Fi[o7$$\"$-&F,$\"1<p#R**eE<&Fi[o7$$\"$.&F,$\"1<L4
4^C!>&Fi[o7$$\"$/&F,$\"1h#>&*=fz?&Fi[o7$$\"$0&F,$\"1\"*f_ZpzD_Fi[o7$$
\"$1&F,$\"1s;4oTvV_Fi[o7$$\"$2&F,$\"16+$yqE=E&Fi[o7$$\"$3&F,$\"1&)>)R
\\5+G&Fi[o7$$\"$4&F,$\"1p0UB:I)H&Fi[o7$$\"$5&F,$\"1_#o;'ep;`Fi[o7$$\"$
6&F,$\"1Js#>k*=N`Fi[o7$$\"$7&F,$\"1$3AT1zPN&Fi[o7$$\"$8&F,$\"1@[&RRgCP
&Fi[o7$$\"$9&F,$\"1>@(>'*H7R&Fi[o7$$\"$:&F,$\"11YkiT35aFi[o7$$\"$;&F,$
\"1V!eMX>!HaFi[o7$$\"$<&F,$\"1'G;SNK![aFi[o7$$\"$=&F,$\"1Le:X%>rY&Fi[o
7$$\"$>&F,$\"1h=2otF'[&Fi[o7$$\"$?&F,$\"1ubXBG]0bFi[o7$$\"$@&F,$\"1mFk
qDzCbFi[o7$$\"$A&F,$\"1=MxEM9WbFi[o7$$\"$B&F,$\"1FA'fE_Nc&Fi[o7$$\"$C&
F,$\"1'*)z%=g,$e&Fi[o7$$\"$D&F,$\"14^%*p;`-cFi[o7$$\"$E&F,$\"1.q_gi4Ac
Fi[o7$$\"$F&F,$\"1K!eT)oqTcFi[o7$$\"$G&F,$\"15rv(og8m&Fi[o7$$\"$H&F,$
\"1kGYq[0\"o&Fi[o7$$\"$I&F,$\"1Mp(Go'y+dFi[o7$$\"$J&F,$\"1KrJEMb?dFi[o
7$$\"$K&F,$\"1(Q!3_CNSdFi[o7$$\"$L&F,$\"1>`rg6=gdFi[o7$$\"$M&F,$\"1iVI
,q.!y&Fi[o7$$\"$N&F,$\"1\"Gb2Z<**z&Fi[o7$$\"$O&F,$\"1()>58,#)>eFi[o7$$
\"$P&F,$\"1HX\")=DuReFi[o7$$\"$Q&F,$\"1j\"=TK#ofeFi[o7$$\"$R&F,$\"1d8K
5sjzeFi[o7$$\"$S&F,$\"1aE:.\\g**eFi[o7$$\"$T&F,$\"1_i5sJe>fFi[o7$$\"$U
&F,$\"1LizH)p&RfFi[o7$$\"$V&F,$\"1&G>8ti&ffFi[o7$$\"$W&F,$\"1aeit(f&zf
Fi[o7$$\"$X&F,$\"1*e**[*)e&**fFi[o7$$\"$Y&F,$\"1:]%R2e&>gFi[o7$$\"$Z&F
,$\"1*G$eH`bRgFi[o7$$\"$[&F,$\"1lf0?([&fgFi[o7$$\"$\\&F,$\"1emVUj`zgFi
[o7$$\"$]&F,$\"1L00Kj^*4'Fi[o7$$\"$^&F,$\"1w9!>'o[>hFi[o7$$\"$_&F,$\"1
!*o5UhWRhFi[o7$$\"$`&F,$\"18+M>CRfhFi[o7$$\"$a&F,$\"1R'zi(RKzhFi[o7$$
\"$b&F,$\"10s1J\"R#*>'Fi[o7$$\"$c&F,$\"1$3rnBO\">iFi[o7$$\"$d&F,$\"1U!
e3o8!RiFi[o7$$\"$e&F,$\"1c<n%))p)eiFi[o7$$\"$f&F,$\"13$=HI.(yiFi[o7$$
\"$g&F,$\"1]&eJU7&)H'Fi[o7$$\"$h&F,$\"1\"G2`w&H=jFi[o7$$\"$i&F,$\"1E\"
R6)=0QjFi[o7$$\"$j&F,$\"1l5!QNzxN'Fi[o7$$\"$k&F,$\"1#[JtzwuP'Fi[o7$$\"
$l&F,$\"1/d=cG9(R'Fi[o7$$\"$m&F,$\"1)*yw/ix;kFi[o7$$\"$n&F,$\"1+$ppavj
V'Fi[o7$$\"$o&F,$\"1[Er:'RfX'Fi[o7$$\"$p&F,$\"1oF]srYvkFi[o7$$\"$q&F,$
\"1BK)p+d\\\\'Fi[o7$$\"$r&F,$\"1w*)\\OzS9lFi[o7$$\"$s&F,$\"1T\\m0)=Q`'
Fi[o7$$\"$t&F,$\"1+/%f[)=`lFi[o7$$\"$u&F,$\"1s\"4_(e^slFi[o7$$\"$v&F,$
\"1*\\lt*)*z\"f'Fi[o7$$\"$w&F,$\"1Sb!>]R5h'Fi[o7$$\"$x&F,$\"1DW_jOBImF
i[o7$$\"$y&F,$\"1'z=<Q\"Q\\mFi[o7$$\"$z&F,$\"1_ZR!o\"[omFi[o7$$\"$!eF,
$\"1f6[2O`(o'Fi[o7$$\"$\"eF,$\"1@#[XBOlq'Fi[o7$$\"$#eF,$\"1v7Vc')[DnFi
[o7$$\"$$eF,$\"1<(f3***QWnFi[o7$$\"$%eF,$\"1L54y$RKw'Fi[o7$$\"$&eF,$\"
1B)\\0)f.#y'Fi[o7$$\"$'eF,$\"1$zrC)*y2!oFi[o7$$\"$(eF,$\"1AEb*en%>oFi[
o7$$\"$)eF,$\"1!o,'G55QoFi[o7$$\"$*eF,$\"1!\\+saym&oFi[o7$$\"$!fF,$\"1
7fO8%*>voFi[o7$$\"$\"fF,$\"1bz@:Hm$*oFi[o7$$\"$#fF,$\"10Alg$o?\"pFi[o7
$$\"$$fF,$\"1`n,x]TIpFi[o7$$\"$%fF,$\"17Oz5Cq[pFi[o7$$\"$&fF,$\"1JXGF(
Hp'pFi[o7$$\"$'fF,$\"1$>,.T'4&)pFi[o7$$\"$(fF,$\"1&pf='=?.qFi[o7$$\"$)
fF,$\"1w#z=]X7-(Fi[o7$$\"$*fF,$\"1T_)ywE#RqFi[o7$$\"$+'F,$\"1Ogr9^9dqF
i[o7$$\"$,'F,$\"1M)G<NK^2(Fi[o7$$\"$-'F,$\"1b!)335D$4(Fi[o7$$\"$.'F,$
\"1qSm(o'\\6rFi[o7$$\"$/'F,$\"11/!)o]')HrFi[o7$$\"$0'F,$\"1epE.>N[rFi[
o7$$\"$1'F,$\"1ZmA:I&p;(Fi[o7$$\"$2'F,$\"1t`@+Vm&=(Fi[o7$$\"$3'F,$\"1%
4NTs\"[/sFi[o7$$\"$4'F,$\"1)*)fAK,MA(Fi[o7$$\"$5'F,$\"1j[D)>>CC(Fi[o7$
$\"$6'F,$\"1#f2K_J:E(Fi[o7$$\"$7'F,$\"1GAnMXt!G(Fi[o7$$\"$8'F,$\"1`esN
X-+tFi[o7$$\"$9'F,$\"1Zq.%*yR>tFi[o7$$\"$:'F,$\"1Al%4/^)QtFi[o7$$\"$;'
F,$\"1O'f0Z!QetFi[o7$$\"$<'F,$\"1!p])QF)zP(Fi[o7$$\"$='F,$\"12)yFYawR(
Fi[o7$$\"$>'F,$\"1+`T>BR<uFi[o7$$\"$?'F,$\"1[B3XI>PuFi[o7$$\"$@'F,$\"1
*)G]MM0duFi[o7$$\"$A'F,$\"1R:'*R.(pZ(Fi[o7$$\"$B'F,$\"1RkZq1%p\\(Fi[o7
$$\"$C'F,$\"1x=)4Rhp^(Fi[o7$$\"$D'F,$\"1s:_@&Hq`(Fi[o7$$\"$E'F,$\"1gCX
O@9dvFi[o7$$\"$F'F,$\"1y)eOO'HxvFi[o7$$\"$G'F,$\"13qx$Q*[(f(Fi[o7$$\"$
H'F,$\"1Z%H%H%=xh(Fi[o7$$\"$I'F,$\"10)pWy!)zj(Fi[o7$$\"$J'F,$\"1qrB$yt
#ewFi[o7$$\"$K'F,$\"1X.#)4[fywFi[o7$$\"$L'F,$\"1E<L(HT*)p(Fi[o7$$\"$M'
F,$\"162>F2J>xFi[o7$$\"$N'F,$\"18lTG1qRxFi[o7$$\"$O'F,$\"1b-$pd3,w(Fi[
o7$$\"$P'F,$\"1]i'[>K0y(Fi[o7$$\"$Q'F,$\"1ZB*)\\\"p4!yFi[o7$$\"$R'F,$
\"18#RX:<9#yFi[o7$$\"$S'F,$\"1p%Qb'R(=%yFi[o7$$\"$T'F,$\"1T&pJQPB'yFi[
o7$$\"$U'F,$\"1\\^h]_!G)yFi[o7$$\"$V'F,$\"1-`K`aF.zFi[o7$$\"$W'F,$\"1&
p*Q=fuBzFi[o7$$\"$X'F,$\"1A%=Rh9U%zFi[o7$$\"$Y'F,$\"1!*3V[&zY'zFi[o7$$
\"$Z'F,$\"1EGDq(Q^)zFi[o7$$\"$['F,$\"1)G@pO!f0!)Fi[o7$$\"$\\'F,$\"1lvf
kC.E!)Fi[o7$$\"$]'F,$\"1+z[FKYY!)Fi[o7$$\"$^'F,$\"1(*=Fd3)o1)Fi[o7$$\"
$_'F,$\"1W&QDf$G(3)Fi[o7$$\"$`'F,$\"1Y(H#3(pw5)Fi[o7$$\"$a'F,$\"1z74:v
.G\")Fi[o7$$\"$b'F,$\"1y58f`Q[\")Fi[o7$$\"$c'F,$\"1]Z3@;ro\")Fi[o7$$\"
$d'F,$\"1S#))er9!*=)Fi[o7$$\"$e'F,$\"1Ov:#4$H4#)Fi[o7$$\"$f'F,$\"1x`nJ
_aH#)Fi[o7$$\"$g'F,$\"11[))['p(\\#)Fi[o7$$\"$h'F,$\"1M&*Q!*['*p#)Fi[o7
$$\"$i'F,$\"125YM&H,H)Fi[o7$$\"$j'F,$\"16@b!>i-J)Fi[o7$$\"$k'F,$\"1-u
\"))\\h.L)Fi[o7$$\"$l'F,$\"19)R'HhU]$)Fi[o7$$\"$m'F,$\"1DP;$ya/P)Fi[o7
$$\"$n'F,$\"1TV$))=Y/R)Fi[o7$$\"$o'F,$\"1(HV\\5*R5%)Fi[o7$$\"$p'F,$\"1
*Q!==BJI%)Fi[o7$$\"$q'F,$\"1w8>VY=]%)Fi[o7$$\"$r'F,$\"1z<9A\\,q%)Fi[o7
$$\"$s'F,$\"1$e'GC?!)*[)Fi[o7$$\"$t'F,$\"1xdaX[a4&)Fi[o7$$\"$u'F,$\"1k
c33BCH&)Fi[o7$$\"$v'F,$\"1fe!*fL*)[&)Fi[o7$$\"$w'F,$\"1;>Vup\\o&)Fi[o7
$$\"$x'F,$\"1*[8,:_!)e)Fi[o7$$\"$y'F,$\"1()z-5zb2')Fi[o7$$\"$z'F,$\"1C
'*[,L,F')Fi[o7$$\"$!oF,$\"1NQm&R<kk)Fi[o7$$\"$\"oF,$\"1Np=(Gpdm)Fi[o7$
$\"$#oF,$\"155z$4o]o)Fi[o7$$\"$$oF,$\"1LR$f&HJ/()Fi[o7$$\"$%oF,$\"1pWV
OI]B()Fi[o7$$\"$&oF,$\"1#Q7,_PEu)Fi[o7$$\"$'oF,$\"1(\\LMh:<w)Fi[o7$$\"
$(oF,$\"1O'fTaO2y)Fi[o7$$\"$)oF,$\"1$R.5c*p*z)Fi[o7$$\"$*oF,$\"1lwGLRg
=))Fi[o7$$\"$!pF,$\"1s)41&*[u$))Fi[o7$$\"$\"pF,$\"1I3^ARBc))Fi[o7$$\"$
#pF,$\"1;#[\"y\"e\\())Fi[o7$$\"$$pF,$\"1KX(f1@O*))Fi[o7$$\"$%pF,$\"1j&
>M&>A7*)Fi[o7$$\"$&pF,$\"13sdE-wI*)Fi[o7$$\"$'pF,$\"14n*)*GN#\\*)Fi[o7
$$\"$(pF,$\"1V\"yecYw'*)Fi[o7$$\"$)pF,$\"1p@x%\\$*f)*)Fi[o7$$\"$*pF,$
\"1cRGMbF/!*Fi[o7$$\"$+(F,$\"1g7Gf@\\A!*Fi[o7$$\"$,(F,$\"1:5+*>v2/*Fi[
o7$$\"$-(F,$\"1P)QB?(=f!*Fi[o7$$\"$.(F,$\"1@([FzBx2*Fi[o7$$\"$/(F,$\"1
G7,o1Q'4*Fi[o7$$\"$0(F,$\"1!o(=*f`^6*Fi[o7$$\"$1(F,$\"1%y(eH%QS8*Fi[o7
$$\"$2(F,$\"1e0vt5.`\"*Fi[o7$$\"$3(F,$\"1r$Qk^F@<*Fi[o7$$\"$4(F,$\"1uR
k6QK\">*Fi[o7$$\"$5(F,$\"1<.h\"3;1@*Fi[o7$$\"$6(F,$\"1FI'e^++B*Fi[o7$$
\"$7(F,$\"1t`DqLZ\\#*Fi[o7$$\"$8(F,$\"1&fDg'4.p#*Fi[o7$$\"$9(F,$\"1/k'
))op')G*Fi[o7$$\"$:(F,$\"1Xl+))fQ3$*Fi[o7$$\"$;(F,$\"1JUIvj<G$*Fi[o7$$
\"$<(F,$\"1fBNCu.[$*Fi[o7$$\"$=(F,$\"13`fpd'zO*Fi[o7$$\"$>(F,$\"17sX0
\"ezQ*Fi[o7$$\"$?(F,$\"1S:[&=6!3%*Fi[o7$$\"$@(F,$\"1!*=[@=7G%*Fi[o7$$
\"$A(F,$\"1.Qq#)oG[%*Fi[o7$$\"$B(F,$\"1-v*\\H.&o%*Fi[o7$$\"$C(F,$\"1$R
,+/o()[*Fi[o7$$\"$D(F,$\"1JiLa\"y!4&*Fi[o7$$\"$E(F,$\"1&y4)G2VH&*Fi[o7
$$\"$F(F,$\"1()=j2H#)\\&*Fi[o7$$\"$G(F,$\"1Y(Rw)=Dq&*Fi[o7$$\"$H(F,$\"
1uL`<\\r!f*Fi[o7$$\"$I(F,$\"1Z57(H47h*Fi[o7$$\"$J(F,$\"16YdwBtJ'*Fi[o7
$$\"$K(F,$\"1vXpb:G_'*Fi[o7$$\"$L(F,$\"1C[=$GaGn*Fi[o7$$\"$M(F,$\"1ro$
f0[Mp*Fi[o7$$\"$N(F,$\"1$\\B$=/19(*Fi[o7$$\"$O(F,$\"1j;]h*)oM(*Fi[o7$$
\"$P(F,$\"1UYsA8Lb(*Fi[o7$$\"$Q(F,$\"1aJm%=&)fx*Fi[o7$$\"$R(F,$\"1watu
#[mz*Fi[o7$$\"$S(F,$\"1\"QYWO=t\")*Fi[o7$$\"$T(F,$\"1#zM(oK*z$)*Fi[o7$
$\"$U(F,$\"1w+LX3ne)*Fi[o7$$\"$V(F,$\"1Eo6%**[$z)*Fi[o7$$\"$W(F,$\"1e!
3llD+!**Fi[o7$$\"$X(F,$\"1&pE[\"))p?**Fi[o7$$\"$Y(F,$\"1t_p\"\\m8%**Fi
[o7$$\"$Z(F,$\"1?PV\\n-i**Fi[o7$$\"$[(F,$\"1Q^Y*oxE)**Fi[o7$$\"$\\(F,$
\"1ZH<X<L+5!#97$$\"$](F,$\"1*\\59U%R-5Fbix7$$\"$^(F,$\"1YP=>cX/5Fbix7$
$\"$_(F,$\"1\"p(pj^^15Fbix7$$\"$`(F,$\"1#>#y$)Gd35Fbix7$$\"$a(F,$\"1Jr
$=hG1,\"Fbix7$$\"$b(F,$\"1>$yP=#o75Fbix7$$\"$c(F,$\"1>T)*QMt95Fbix7$$
\"$d(F,$\"1&yU-A#y;5Fbix7$$\"$e(F,$\"130qt$G)=5Fbix7$$\"$f(F,$\"1b,\")
[<(3-\"Fbix7$$\"$g(F,$\"1+2G)>7H-\"Fbix7$$\"$h(F,$\"1Ht-y&\\\\-\"Fbix7
$$\"$i(F,$\"1>A7ZP)p-\"Fbix7$$\"$j(F,$\"1zfunX,H5Fbix7$$\"$k(F,$\"1U(R
^!>/J5Fbix7$$\"$l(F,$\"10zbFc1L5Fbix7$$\"$m(F,$\"12:A1c3N5Fbix7$$\"$n(
F,$\"1NAF:<5P5Fbix7$$\"$o(F,$\"1^qsJQ6R5Fbix7$$\"$p(F,$\"1NMVN=7T5Fbix
7$$\"$q(F,$\"1K_-4c7V5Fbix7$$\"$r(F,$\"1)4zy.D^/\"Fbix7$$\"$s(F,$\"1R:
25+7Z5Fbix7$$\"$t(F,$\"1HlL;/6\\5Fbix7$$\"$u(F,$\"12P-]h4^5Fbix7$$\"$v
(F,$\"1Xr02r2`5Fbix7$$\"$w(F,$\"1rY*e=`]0\"Fbix7$$\"$x(F,$\"1`x[(GCq0
\"Fbix7$$\"$y(F,$\"1G>C:.**e5Fbix7$$\"$z(F,$\"1qx(\\<^41\"Fbix7$$\"$!y
F,$\"1'R#*[x1H1\"Fbix7$$\"$\"yF,$\"1$\\@b-d[1\"Fbix7$$\"$#yF,$\"1r=qR=
!o1\"Fbix7$$\"$$yF,$\"1GX`K6uo5Fbix7$$\"$%yF,$\"1>#[8#[nq5Fbix7$$\"$&y
F,$\"1INmDGgs5Fbix7$$\"$'yF,$\"1Wu:n]_u5Fbix7$$\"$(yF,$\"1)RG'p9Ww5Fbi
x7$$\"$)yF,$\"1<='*e>Ny5Fbix7$$\"$*yF,$\"1Gh4jkD!3\"Fbix7$$\"$!zF,$\"1
V#*)>\"\\:#3\"Fbix7$$\"$\"zF,$\"1.bePs/%3\"Fbix7$$\"$#zF,$\"1&3$ytL$f3
\"Fbix7$$\"$$zF,$\"1b=ScK\"y3\"Fbix7$$\"$%zF,$\"1r;:Boo*3\"Fbix7$$\"$&
zF,$\"1F6g8Sb\"4\"Fbix7$$\"$'zF,$\"1In9pZT$4\"Fbix7$$\"$(zF,$\"11D)H.p
_4\"Fbix7$$\"$)zF,$\"1L+2]n6(4\"Fbix7$$\"$*zF,$\"1())3r'y&*)4\"Fbix7$$
\"$+)F,$\"12v]KBz+6Fbix7$$\"$,)F,$\"15R5ILj-6Fbix7$$\"$-)F,$\"1$p%p:r[
/6Fbix7$$\"$.)F,$\"1h]__KN16Fbix7$$\"$/)F,$\"1*pl7JJ#36Fbix7$$\"$0)F,$
\"1W#3*p3756Fbix7$$\"$1)F,$\"1)4iO^@?6\"Fbix7$$\"$2)F,$\"1\"e_[$G$R6\"
Fbix7$$\"$3)F,$\"1#Q?GVae6\"Fbix7$$\"$4)F,$\"1;B#Q\"fy<6Fbix7$$\"$5)F,
$\"1dL$4*os>6Fbix7$$\"$6)F,$\"1R*\\R)pn@6Fbix7$$\"$7)F,$\"1-XH>ejB6Fbi
x7$$\"$8)F,$\"1x7#*HIgD6Fbix7$$\"$9)F,$\"1(GB_Dyv7\"Fbix7$$\"$:)F,$\"1
^0%49h&H6Fbix7$$\"$;)F,$\"1![p!R8bJ6Fbix7$$\"$<)F,$\"1[Mx2&[N8\"Fbix7$
$\"$=)F,$\"1>XH6BbN6Fbix7$$\"$>)F,$\"1Cj')>CcP6Fbix7$$\"$?)F,$\"1q!G'4
&y&R6Fbix7$$\"$@)F,$\"1l'RDE+;9\"Fbix7$$\"$A)F,$\"1YzHmtiV6Fbix7$$\"$B
)F,$\"1/SD9&fc9\"Fbix7$$\"$C)F,$\"1!eJ`S'pZ6Fbix7$$\"$D)F,$\"1Fl%RuP(
\\6Fbix7$$\"$E)F,$\"1Dt#*RKy^6Fbix7$$\"$F)F,$\"1KmV3E$Q:\"Fbix7$$\"$G)
F,$\"1fQ*)pb)e:\"Fbix7$$\"$H)F,$\"1i()*)\\=%z:\"Fbix7$$\"$I)F,$\"1Jg:z
6+g6Fbix7$$\"$J)F,$\"1l3S$Hj?;\"Fbix7$$\"$K)F,$\"1FbKLz7k6Fbix7$$\"$L)
F,$\"1io]W[>m6Fbix7$$\"$M)F,$\"1iZLxPEo6Fbix7$$\"$N)F,$\"1v:%p[M.<\"Fb
ix7$$\"$O)F,$\"1VC8LnSs6Fbix7$$\"$P)F,$\"1alJ!G![u6Fbix7$$\"$Q)F,$\"1,
$Ru*[bw6Fbix7$$\"$R)F,$\"1L`\"zNI'y6Fbix7$$\"$S)F,$\"1&\\i&Rkq!=\"Fbix
7$$\"$T)F,$\"1Km`CHy#=\"Fbix7$$\"$U)F,$\"1isE*ff[=\"Fbix7$$\"$V)F,$\"1
$4%Rai$p=\"Fbix7$$\"$W)F,$\"1)Q/Zo7!*=\"Fbix7$$\"$X)F,$\"1]62*o)3\">\"
Fbix7$$\"$Y)F,$\"1P@RqS;$>\"Fbix7$$\"$Z)F,$\"1v'HbjQ_>\"Fbix7$$\"$[)F,
$\"1\"G^_>7t>\"Fbix7$$\"$\\)F,$\"1o5<kXQ*>\"Fbix7$$\"$])F,$\"1K>pgbX,7
Fbix7$$\"$^)F,$\"12&[p+DN?\"Fbix7$$\"$_)F,$\"1$)3vGFf07Fbix7$$\"$`)F,$
\"1t!Hbbew?\"Fbix7$$\"$a)F,$\"1?#y-KA(47Fbix7$$\"$b)F,$\"1PX]fQy67Fbix
7$$\"$c)F,$\"1q><8I%Q@\"Fbix7$$\"$d)F,$\"1y&\\Yi**e@\"Fbix7$$\"$e)F,$
\"14'f1a`z@\"Fbix7$$\"$f)F,$\"1$GE7h/+A\"Fbix7$$\"$g)F,$\"1`_i*o_?A\"F
bix7$$\"$h)F,$\"1_PLKw4C7Fbix7$$\"$i)F,$\"119)*)HRhA\"Fbix7$$\"$j)F,$
\"14<I_v<G7Fbix7$$\"$k)F,$\"1`T3eA@I7Fbix7$$\"$l)F,$\"1.q7&GVAB\"Fbix7
$$\"$m)F,$\"152>00FM7Fbix7$$\"$n)F,$\"1]>&Hz$HO7Fbix7$$\"$o)F,$\"1)Gef
-8$Q7Fbix7$$\"$p)F,$\"1bMe%3G.C\"Fbix7$$\"$q)F,$\"1GK)>&)QBC\"Fbix7$$
\"$r)F,$\"16>09_MW7Fbix7$$\"$s)F,$\"10%z$fqMY7Fbix7$$\"$t)F,$\"1k)3#zU
M[7Fbix7$$\"$u)F,$\"1@\\RnnL]7Fbix7$$\"$v)F,$\"1*[i.UCBD\"Fbix7$$\"$w)
F,$\"1@h1PrIa7Fbix7$$\"$x)F,$\"1@*\\*=[Gc7Fbix7$$\"$y)F,$\"13!3*ptDe7F
bix7$$\"$z)F,$\"1;bC'pC-E\"Fbix7$$\"$!))F,$\"1I,k1n=i7Fbix7$$\"$\"))F,
$\"1YT57L9k7Fbix7$$\"$#))F,$\"1bq%fU%4m7Fbix7$$\"$$))F,$\"1P'QP'*R!o7F
bix7$$\"$%))F,$\"1lDFV)z*p7Fbix7$$\"$&))F,$\"100`%)R\">F\"Fbix7$$\"$')
)F,$\"1;nk4B%QF\"Fbix7$$\"$())F,$\"1MJ(GukdF\"Fbix7$$\"$)))F,$\"1P\\a5
7ox7Fbix7$$\"$*))F,$\"1!fY5k\"fz7Fbix7$$\"$!*)F,$\"1b$yZ'f\\\"G\"Fbix7
$$\"$\"*)F,$\"1oK79TR$G\"Fbix7$$\"$#*)F,$\"1pXTBgG&G\"Fbix7$$\"$$*)F,$
\"1*e.*G;<(G\"Fbix7$$\"$%*)F,$\"1\"3G(o30*G\"Fbix7$$\"$&*)F,$\"1\"*4)G
oB4H\"Fbix7$$\"$'*)F,$\"1h'zJ,!z#H\"Fbix7$$\"$(*)F,$\"1naB.)\\YH\"Fbix
7$$\"$)*)F,$\"1wQU)*H]'H\"Fbix7$$\"$**)F,$\"1D\\&ea\\$)H\"Fbix7$$\"$+*
F,$\"13TM%R*=+8Fbix7$$\"$,*F,$\"1>J8Gd.-8Fbix7$$\"$-*F,$\"1%))=M![*QI
\"Fbix7$$\"$.*F,$\"16O%Q=mdI\"Fbix7$$\"$/*F,$\"1$pr/W\\wI\"Fbix7$$\"$0
*F,$\"1-_o^Ta48Fbix7$$\"$1*F,$\"1M23.*\\9J\"Fbix7$$\"$2*F,$\"1!entGmLJ
\"Fbix7$$\"$3*F,$\"16sE/HH:8Fbix7$$\"$4*F,$\"1bSTg$HsJ\"Fbix7$$\"$5*F,
$\"1cvDp_<>8Fbix7$$\"$6*F,$\"1-b'4DI6K\"Fbix7$$\"$7*F,$\"1'fGB$R4B8Fbi
x7$$\"$8*F,$\"1jimYf1D8Fbix7$$\"$9*F,$\"1xOtLf/F8Fbix7$$\"$:*F,$\"1$**
H'RN.H8Fbix7$$\"$;*F,$\"1hxq;%G5L\"Fbix7$$\"$<*F,$\"1CN[B-.L8Fbix7$$\"
$=*F,$\"1q&\\XiQ]L\"Fbix7$$\"$>*F,$\"1Ko[!H`qL\"Fbix7$$\"$?*F,$\"1>*yx
*Q2R8Fbix7$$\"$@*F,$\"1lssG,5T8Fbix7$$\"$A*F,$\"1\"Qn8nJJM\"Fbix7$$\"$
B*F,$\"1,iQ>#o^M\"Fbix7$$\"$C*F,$\"100/s%4sM\"Fbix7$$\"$D*F,$\"1)RwS8b
#\\8Fbix7$$\"$E*F,$\"1_)\\c\"\\I^8Fbix7$$\"$F*F,$\"1w#[A`eLN\"Fbix7$$
\"$G*F,$\"1;Jh/dTb8Fbix7$$\"$H*F,$\"1nMmehZd8Fbix7$$\"$I*F,$\"1$o?aiR&
f8Fbix7$$\"$J*F,$\"1xR$4%egh8Fbix7$$\"$K*F,$\"1%*p?YXnj8Fbix7$$\"$L*F,
$\"1^`7([XdO\"Fbix7$$\"$M*F,$\"1C^Q9%=yO\"Fbix7$$\"$N*F,$\"1zAU$3$*)p8
Fbix7$$\"$O*F,$\"1GIMa#p>P\"Fbix7$$\"$P*F,$\"1-^&=pYSP\"Fbix7$$\"$Q*F,
$\"1L**>l^7w8Fbix7$$\"$R*F,$\"1Cd3[W?y8Fbix7$$\"$S*F,$\"129i=VG!Q\"Fbi
x7$$\"$T*F,$\"1r9DfXO#Q\"Fbix7$$\"$U*F,$\"1^;pc\\W%Q\"Fbix7$$\"$V*F,$
\"1oa'=IDlQ\"Fbix7$$\"$W*F,$\"15;%)*Q0')Q\"Fbix7$$\"$X*F,$\"1S@x>]o!R
\"Fbix7$$\"$Y*F,$\"1F:$[*Rw#R\"Fbix7$$\"$Z*F,$\"1#[c@7U[R\"Fbix7$$\"$[
*F,$\"1&f'y7#>pR\"Fbix7$$\"$\\*F,$\"1jdg\"3&**)R\"Fbix7$$\"$]*F,$\"1$R
%GZ&p5S\"Fbix7$$\"$^*F,$\"1xBAKC9.9Fbix7$$\"$_*F,$\"1HG\\iN@09Fbix7$$
\"$`*F,$\"1mlynFG29Fbix7$$\"$a*F,$\"1RtN\"))\\$49Fbix7$$\"$b*F,$\"1)yn
*RZT69Fbix7$$\"$c*F,$\"1Ah$Q=xMT\"Fbix7$$\"$d*F,$\"1;Necq`:9Fbix7$$\"$
e*F,$\"15A=0Uf<9Fbix7$$\"$f*F,$\"1,V!*z%['>9Fbix7$$\"$g*F,$\"1I7FM(*p@
9Fbix7$$\"$h*F,$\"1SR+DyuB9Fbix7$$\"$i*F,$\"11P(>h#zD9Fbix7$$\"$j*F,$
\"1JO:eR$yU\"Fbix7$$\"$k*F,$\"1*yq&H<()H9Fbix7$$\"$l*F,$\"1?!f_z0>V\"F
bix7$$\"$m*F,$\"1bB@Fg$RV\"Fbix7$$\"$n*F,$\"1v!R.IifV\"Fbix7$$\"$o*F,$
\"1!R;C\\%)zV\"Fbix7$$\"$p*F,$\"1Kd/%[-+W\"Fbix7$$\"$q*F,$\"1]'3'eh,U9
Fbix7$$\"$r*F,$\"15LA-a-W9Fbix7$$\"$s*F,$\"1w:q.,.Y9Fbix7$$\"$t*F,$\"1
&o1X:I![9Fbix7$$\"$u*F,$\"1*[6([a-]9Fbix7$$\"$v*F,$\"1os&H)e,_9Fbix7$$
\"$w*F,$\"13JTc8+a9Fbix7$$\"$x*F,$\"1Eetq<)fX\"Fbix7$$\"$y*F,$\"1[/.Iq
&zX\"Fbix7$$\"$z*F,$\"1F7\"3/F*f9Fbix7$$\"$!)*F,$\"1\">j>r\"*=Y\"Fbix7
$$\"$\")*F,$\"1<Uqa4&QY\"Fbix7$$\"$#)*F,$\"1Mwa#o/eY\"Fbix7$$\"$$)*F,$
\"1D`E6Gvn9Fbix7$$\"$%)*F,$\"1]8&)e_pp9Fbix7$$\"$&)*F,$\"1gg[X>jr9Fbix
7$$\"$')*F,$\"122]$ziNZ\"Fbix7$$\"$()*F,$\"1ZDMFx[v9Fbix7$$\"$))*F,$\"
1;/atmSx9Fbix7$$\"$*)*F,$\"1)yq1c>$z9Fbix7$$\"$!**F,$\"1-VK>jA\"[\"Fbi
x7$$\"$\"**F,$\"1\\F2#)o7$[\"Fbix7$$\"$#**F,$\"1=lV$=@][\"Fbix7$$\"$$*
*F,$\"1%\\_)f\"4p[\"Fbix7$$\"$%**F,$\"1.Ck\\2z)[\"Fbix7$$\"$&**F,$\"1(
f\")H*em!\\\"Fbix7$$\"$'**F,$\"1q#o=`MD\\\"Fbix7$$\"$(**F,$\"12J45mR%
\\\"Fbix7$$\"$)**F,$\"1d$4K2_i\\\"Fbix7$$\"$***F,$\"1@L]o35)\\\"Fbix7$
$\"%+5F,$\"1`_'\\%H%**\\\"Fbix-%&STYLEG6#%%LINEG-%*THICKNESSG6#F2-%'CO
LOURG6&%$RGBG$\")p:#R%!\")$\")`B)e)Fgh]l$\")fqkdFgh]l-%%VIEWG6$;$!++++
+]!#5$\"++++]5Fgh]l;$!+DZr*\\(Fbi]l$\"+#4S\\d\"Fgh]l-%+AXESLABELSG6$%
\"tG%%x(t)G" 2 373 373 373 2 0 1 0 2 6 0 4 2 1.000000 45.000000 
45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 
}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 21 "
b) Saw Tooth Function" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 38 "The saw-tooth function is defined by:\n" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "saw_tooth := t -> 2*t-2*floor(t)-1;
  # Execute!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*saw_toothG:6#%\"tG6
\"6$%)operatorG%&arrowGF(,(9$\"\"#-%&floorG6#F-!\"#!\"\"\"\"\"F(F(" }}
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "Here is t
he plot of the saw-tooth function  for  " }{MPLTEXT 1 0 10 "t = 0 .. 6
" }{TEXT -1 27 ",   as typically rendered:\n" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 43 "plot( saw_tooth(t), t = 0 .. 6); # Execute!" }}
{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6$7]t7$\"\"!$!\"\"F(7$$\"1+++]i
9Rl!#<$!1+++]2<#p)!#;7$$\"1+++]#HyI\"F1$!1++++:M%Q(F17$$\"1++voozw=F1$
!1****\\iiSYiF17$$\"1++]([kdW#F1$!1+++D5Z3^F17$$\"1++D\"3Gc3$F1$!1****
\\PQuGQF17$$\"1+++v;\\DPF1$!1+++]m,\\DF17$$\"1++++nfpVF1$!1++++m!3E\"F
17$$\"1+++D<q8]F1$\"1)3+++X.u#!#=7$$\"1++DJauacF1$\"1++]i3\\48F17$$\"1
++]P\"*y&H'F1$\"1*****\\Fy:f#F17$$\"1++]7(=,*oF1$\"1*****\\UP-y$F17$$
\"1++](G[W[(F1$\"1*****\\d'*)o\\F17$$\"1++]P@%)*4)F1$\"1*****\\F%o*>'F
17$$\"1++]()fB:()F1$\"1*****\\(>ZIuF17$$\"1++](=x;N*F1$\"1,++vVN.()F17
$$\"1++](Q=\"))**F1$\"1+++vnBw**F17$$\"1]7`Rox-5!#:$!1,]P4KYW**F17$$\"
1+DJS=u15F[q$!1-+v$>j^')*F17$$\"1]P4Toq55F[q$!1)*\\7yJ'ey*F17$$\"1+](=
%=n95F[q$!1****\\iJc1(*F17$$\"1+vVV=gA5F[q$!1(**\\78jza*F17$$\"1+++X=`
I5F[q$!1*******4j$*Q*F17$$\"1+]7[=RY5F[q$!1)***\\PI;s!*F17$$\"1++D^=Di
5F[q$!1)****\\(H'\\v)F17$$\"1++]d=(R4\"F[q$!1(*****\\Gc?\")F17$$\"1++v
j=pD6F[q$!1,++DF;'[(F17$$\"1+]P9x%4>\"F[q$!1++]7d/\"='F17$$\"1+++lN?c7
F[q$!1)******pGf([F17$$\"1++v`4o88F[q$!1*****\\#4QEPF17$$\"1++]U$e6P\"
F[q$!1+++]J$od#F17$$\"1++voU'eV\"F[q$!1*****\\i9FG\"F17$$\"1+++&>q0]\"
F[q$\"18-+++RS6FU7$$\"1+++5=al:F[q$\"1,+++i$3J\"F17$$\"1+++DM^I;F[q$\"
1*******\\o-h#F17$$\"1+++:c7$p\"F[q$\"1,+++B^iQF17$$\"1+++0ytb<F[q$\"1
-+++hv9^F17$$\"1+](=n&f7=F[q$\"1,+]PM\">D'F17$$\"1++vQNXp=F[q$\"1+++v2
2*Q(F17$$\"1+DJ!HeK!>F[q$\"1***\\i!e;l!)F17$$\"1+](=/jq$>F[q$\"1-+]P3E
T()F17$$\"1]il<a'R&>F[q$\"1/]7`$3$z!*F17$$\"1+vV$zn3(>F[q$\"1,+voeN<%*
F17$$\"1D\"G8)*=$z>F[q$\"1-DcE'zje*F17$$\"1](=#p,x()>F[q$\"1**\\P%Q.av
*F17$$\"1iS;jd*>*>F[q$\"1Z7Gj_\"*R)*F17$$\"1v$4rN@i*>F[q$\"1+v=UrUC**F
17$$\"1)oa5&pW+?F[q$!1[i!*y41\"***F17$$\"1+++XDn/?F[q$!1*******4\\l!**
F17$$\"1++]im%>1#F[q$!1******\\n1h()F17$$\"1+++!y?#>@F[q$!1*******R%e:
wF17$$\"1+]P%>We=#F[q$!1++]7h6$G'F17$$\"1++v3wY_AF[q$!1,++Dyk]\\F17$$
\"1+]P>1W6BF[q$!1-+]7w=rPF17$$\"1+++IOTqBF[q$!1.+++us\"f#F17$$\"1+]Ppj
6NCF[q$!10+]7En(H\"F17$$\"1++v3\">)*\\#F[q$!15u****\\#yh$!#>7$$\"1++]<
9VhDF[q$\"1.++]$G'G7F17$$\"1++DEP/BEF[q$\"1.++DX(3Y#F17$$\"1+](oqHto#F
[q$\"13+]PTfYPF17$$\"1++](o:;v#F[q$\"1/++]PJK]F17$$\"1+]i&G]1\"GF[q$\"
1****\\7d+8iF17$$\"1++v$)[opGF[q$\"1/++vwp$R(F17$$\"1+]7t;OLHF[q$\"1(*
**\\iMBn')F17$$\"1++]i%Qq*HF[q$\"1******\\#p2%**F17$$\"17y]bB<,IF[q$!1
^P%)*)Gbw**F17$$\"1Dc^[iI0IF[q$!1+voH](Q*)*F17$$\"1QM_T,W4IF[q$!1\\7`p
r>6)*F17$$\"1]7`MSd8IF[q$!1**\\P4$>&G(*F17$$\"1voa?=%=-$F[q$!1)\\i!*ej
Jc*F17$$\"1+Dc1'4,.$F[q$!1(**\\(oy!yR*F17$$\"1]Pfy^kYIF[q$!1%*\\7Gk4n!
*F17$$\"1+]i]2=jIF[q$!1,+]()\\QO()F17$$\"1+vo%*=D'4$F[q$!10+D1@'\\2)F1
7$$\"1++vQIKHJF[q$!1,++D#RNT(F17$$\"1+++&4+p=$F[q$!1,+++\")*>E'F17$$\"
1++D^rZWKF[q$!1-++vpX5^F17$$\"1+]P\\>m1LF[q$!1++]75wmQF17$$\"1++]Zn%)o
LF[q$!1(*****\\]1BEF17$$\"1++vG(*3LMF[q$!10++Da?Q8F17$$\"1+++5FL(\\$F[
q$!1A/+++eM`FU7$$\"1++vL>=gNF[q$\"1,++v'QO?\"F17$$\"1++]d6.BOF[q$\"1'*
****\\JigCF17$$\"1+]785%Qo$F[q$\"1)***\\i-#on$F17$$\"1++vo3lWPF[q$\"1*
****\\P<I*[F17$$\"1+]iX)p@\"QF[q$\"1.+]7pRViF17$$\"1++]A))ozQF[q$\"1)*
****\\kx$f(F17$$\"1+]PCK-5RF[q$\"1.+]([k/?)F17$$\"1++DEwNSRF[q$\"1****
*\\__r!))F17$$\"1+v=F[_bRF[q$\"1(**\\Pa'\\5\"*F17$$\"1+]7G?pqRF[q$\"1&
***\\i0%QT*F17$$\"1]PfGcFyRF[q$\"1!*\\(=d7bc*F17$$\"1+D1H#fe)RF[q$\"1%
**\\7e%=<(*F17$$\"1voHH5l*)RF[q$\"1\"\\Pfe?Iz*F17$$\"1]7`HGW$*RF[q$\"1
(*\\i!fc)o)*F17$$\"1DcwHYB(*RF[q$\"1%\\7`f#pW**F17$$\"1+++Ik-,SF[q$!13
+++9Zz**F17$$\"1****\\FL!e1%F[q$!17++]M$Ro)F17$$\"1+++D-eITF[q$!1)****
**\\&R)Q(F17$$\"1**\\(=sx#*=%F[q$!16+]ibW9iF17$$\"1++v=_(zC%F[q$!10++D
c\\S]F17$$\"1+](o3Z@J%F[q$!1****\\i#eqv$F17$$\"1+++b*=jP%F[q$!1$******
*3itCF17$$\"1+](=o*pOWF[q$!1,+]ij+m7F17$$\"1++v3/3(\\%F[q$!1<3++D=ReFU
7$$\"1***\\im&>gXF[q$\"1))***\\K8R?\"F17$$\"1++vB4JBYF[q$\"1-++v%=iY#F
17$$\"1+]PCw,&o%F[q$\"1)***\\([_.q$F17$$\"1+++DVsYZF[q$\"1&******\\'[M
\\F17$$\"1+](=_D8\"[F[q$\"1/+]P/^EiF17$$\"1++v=n#f([F[q$\"1%****\\PM&=
vF17$$\"1+D1Mg.2\\F[q$\"1-+D\"o?29)F17$$\"1+]P\\`9Q\\F[q$\"15+]()p!Hw)
F17$$\"1^7.2+q`\\F[q$\"19]iS,+u!*F17$$\"1,vokYDp\\F[q$\"1=+v$H$4&Q*F17
$$\"1Ec^$*>.x\\F[q$\"16DJq)R1a*F17$$\"1]PMA$4[)\\F[q$\"1/](oW'='p*F17$
$\"18yv')zp))\\F[q$\"1]i:N(fRx*F17$$\"1v=<^me#*\\F[q$\"1(\\PM-L<&)*F17
$$\"1Qfe:`Z'*\\F[q$\"1h(=<J1&H**F17$$\"1+++!)RO+]F[q$!1$******R?F***F1
7$$\"1,+D;:*R1&F[q$!1()***\\np,s)F17$$\"1++]_!>w7&F[q$!1******\\*=wW(F
17$$\"1+]i?(>2>&F[q$!1'***\\(e0c='F17$$\"1++v)Q?QD&F[q$!1$****\\A#fB\\
F17$$\"1+]P\\L!=J&F[q$!1%***\\7I$Rw$F17$$\"1+++5jyp`F[q$!1%******ztUg#
F17$$\"1++DE8COaF[q$!1&****\\Zt^F\"F17$$\"1++]Ujp-bF[q$\"1T.++]o#R&FU7
$$\"1++D,X8ibF[q$\"1-++D+pU7F17$$\"1+++gEd@cF[q$\"1++++KXJCF17$$\"1+]P
Mh%\\o&F[q$\"1,+](oA*)p$F17$$\"1++v3'>$[dF[q$\"1.++v@Rm\\F17$$\"1+++5h
(*3eF[q$\"1%******>A&zhF17$$\"1++D6EjpeF[q$\"1.++DAl#R(F17$$\"1+vVeWA-
fF[q$\"1)**\\(o\"*[W!)F17$$\"1,]i0j\"[$fF[q$\"15+]7hK'p)F17$$\"1^(=#HA
6^fF[q$\"1<]P%eWA-*F17$$\"1+D\"G:3u'fF[q$\"10+DcI;[$*F17$$\"1v$4Y6cb(f
F[q$\"13v=#HA6^*F17$$\"1]iSwSq$)fF[q$\"1%*\\7G:3u'*F17$$\"1)o/t0yx)fF[
q$\"1aP4Y6cb(*F17$$\"1DJ?Q?&=*fF[q$\"1(\\iSwSq$)*F17$$\"1i:5>g#f*fF[q$
\"1S7.#Q?&=**F17$$\"\"'F(F)-%'COLOURG6&%$RGBG$\"#5F*F(F(-%+AXESLABELSG
6$%\"tG%!G-%%VIEWG6$;F(Ffhm%(DEFAULTG" 2 780 368 368 2 0 1 0 2 9 0 4 
2 1.000000 45.000000 45.000000 10030 10061 10056 10074 0 0 0 20030 0 
12020 0 0 0 0 0 0 0 1 1 0 0 0 54 123 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 61 "\n\n\nCalculate the Lapla
ce Transform of the Saw Tooth Function." }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "laplace( saw_tooth(t), \+
t , s ); # Execute!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$%\"sG!\"#\"
\"#-%(laplaceG6%-%&floorG6#%\"tGF.F%F&*$F%!\"\"F0" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 54 "Early releases of Maple did not know how to simplify  " }{TEXT 
345 21 "laplace(floor(t),t,s)" }{TEXT -1 86 ".   If needed, use the re
sult of part (a) together with the subs command to replace   " }{TEXT 
346 21 "laplace(floor(t),t,s)" }{TEXT -1 20 "   with its value: \n" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "subs( laplace(floor(t),t,s) \+
= Staircase(s), \" );    # Fill in and executed if needed." }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,(*$%\"sG!\"#\"\"#*&F%!\"\",&\"\"\"F+-%$expG
6#,$F%F)F)F)F&*$F%F)F)" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 37 "For the record,  let us write it out!" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "`laplac
e( saw_tooth(t), t , s )` =  \" ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/
%?laplace(~saw_tooth(t),~t~,~s~)G,(*$%\"sG!\"#\"\"#*&F'!\"\",&\"\"\"F-
-%$expG6#,$F'F+F+F+F(*$F'F+F+" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 326 3 "Use" }
{TEXT -1 2 "  " }{TEXT 325 6 "DEplot" }{TEXT -1 1 " " }{TEXT 328 1 " \+
" }{TEXT 327 51 "to plot the solution to the initial value problem f" 
}{TEXT -1 4 "or  " }{TEXT 347 1 " " }{XPPEDIT 348 1 "t = 0 .. 10" "/%
\"tG;\"\"!\"#5" }{TEXT -1 2 " :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 322 10 "  \n       " }{XPPEDIT 324 1 "diff(diff(
x(t),t),t)+2*diff(x(t),t)+ x(t) = 5*saw_tooth(t)*``, `    `*x(0) = `0.
0`*``, `   `*D(x)(0) = 0" "6%/,(-%%diffG6$-F&6$-%\"xG6#%\"tGF-F-\"\"\"
*&\"\"#F.-F&6$-F+6#F-F-F.F.-F+6#F-F.*(\"\"&F.-%*saw_toothG6#F-F.%!GF./
*&%%~~~~GF.-F+6#\"\"!F.*&%$0.0GF.F<F./*&%$~~~GF.--%\"DG6#F+6#FBF.FB" }
{TEXT 323 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 173 "ode := diff(x(t),t$2) + 2*diff(x(t),t)+ x(t) = 5*
saw_tooth(t):  # Execute!\nDEplot(\{ode\}, [x(t)], t=0.. 10, [[x(0)=0.
0,D(x)(0)=0]], stepsize= 0.01, linecolor = aquamarine);  " }}{PARA 13 
"" 1 "" {INLPLOT "6&-%'CURVESG6%7ein7$\"\"!F(7$$\"\"\"!\"#$!1++++D\"oY
#!#>7$$\"\"#F,$!14Yp6UlN(*F/7$$\"\"$F,$!1,G*>Jr6;#!#=7$$\"\"%F,$!1\"pj
/'yN!z$F:7$$\"\"&F,$!1Gy%RI>B%eF:7$$\"\"'F,$!1h-p,/e)H)F:7$$\"\"(F,$!1
$)*>><*496!#<7$$\"\")F,$!1K_P(\\s^V\"FO7$$\"\"*F,$!1(HES%oK\"z\"FO7$$
\"#5F,$!1t(y;CU3=#FO7$$\"#6F,$!1[@*[ZH?g#FO7$$\"#7F,$!1?qBT'HK0$FO7$$
\"#8F,$!1K#)H:P\"G`$FO7$$\"#9F,$!1KLN=@=RSFO7$$\"#:F,$!1xll$Hk2d%FO7$$
\"#;F,$!1I&fsG=g7&FO7$$\"#<F,$!1A,IM.V.dFO7$$\"#=F,$!1eGp]W^,jFO7$$\"#
>F,$!1WO:I?\")=pFO7$$\"#?F,$!1([$\\Y9*Qb(FO7$$\"#@F,$!1Bh6hwM0#)FO7$$
\"#AF,$!10alN=!=())FO7$$\"#BF,$!1q*)o\\4!>b*FO7$$\"#CF,$!1glMU<VC5!#;7
$$\"#DF,$!1G%eX([x%4\"F_s7$$\"#EF,$!1\"Qc0r\"4m6F_s7$$\"#FF,$!1YU7.pDQ
7F_s7$$\"#GF,$!1+[4.v968F_s7$$\"#HF,$!1**y.CHk%Q\"F_s7$$\"#IF,$!16RT2
\\ie9F_s7$$\"#JF,$!1qm=)[xH`\"F_s7$$\"#KF,$!1%G!*3'pe2;F_s7$$\"#LF,$!1
WT9Y=M#o\"F_s7$$\"#MF,$!1(e5w&G8d<F_s7$$\"#NF,$!1A(*QpG&=$=F_s7$$\"#OF
,$!1!)f%Q)oR1>F_s7$$\"#PF,$!1K5')**>m!)>F_s7$$\"#QF,$!1xx]\"QZX0#F_s7$
$\"#RF,$!1c,9FU&z7#F_s7$$\"#SF,$!1EO*)Qdy+AF_s7$$\"#TF,$!1z6f#4ZHF#F_s
7$$\"#UF,$!1b)\\!3aMWBF_s7$$\"#VF,$!1dFy>(*)[T#F_s7$$\"#WF,$!1T;4[4\\%
[#F_s7$$\"#XF,$!10_aq=1`DF_s7$$\"#YF,$!1q#QQ4<0i#F_s7$$\"#ZF,$!1(3Fg-t
no#F_s7$$\"#[F,$!1!3O\"\\yu^FF_s7$$\"#\\F,$!1u88#\\h`\"GF_s7$$\"#]F,$!
1NlD/c`xGF_s7$$\"#^F,$!1pfsGN>QHF_s7$$\"#_F,$!1B:xw-E(*HF_s7$$\"#`F,$!
1Zy.-DmaIF_s7$$\"#aF,$!1e@Kv%G.6$F_s7$$\"#bF,$!1$3a'f!)=kJF_s7$$\"#cF,
$!178r&osh@$F_s7$$\"#dF,$!1WocF`@mKF_s7$$\"#eF,$!1tOwy/D9LF_s7$$\"#fF,
$!1&y7(GT@gLF_s7$$\"#gF,$!1./TRP//MF_s7$$\"#hF,$!1y/ZA#ycW$F_s7$$\"#iF
,$!1N%ok\"z0&[$F_s7$$\"#jF,$!1sAfkX7ANF_s7$$\"#kF,$!1Jrf#H@ob$F_s7$$\"
#lF,$!17&fqe#4*e$F_s7$$\"#mF,$!1gt#RF%))=OF_s7$$\"#nF,$!1wAO(\\Vhk$F_s
7$$\"#oF,$!1v,())p=3n$F_s7$$\"#pF,$!1Pnr'ffGp$F_s7$$\"#qF,$!1aSilr@7PF
_s7$$\"#rF,$!15\\u;O%)GPF_s7$$\"#sF,$!1$>6zP#pUPF_s7$$\"#tF,$!1VH:u!=P
v$F_s7$$\"#uF,$!1JY[3l(=w$F_s7$$\"#vF,$!1f_&HkCrw$F_s7$$\"#wF,$!1[*e*z
0UpPF_s7$$\"#xF,$!1(p-QaB(oPF_s7$$\"#yF,$!1]!GD'Q*\\w$F_s7$$\"#zF,$!1W
M)*\\H>ePF_s7$$\"#!)F,$!1US9)G$G[PF_s7$$\"#\")F,$!17fn4%G_t$F_s7$$\"##
)F,$!1H9u!)G**=PF_s7$$\"#$)F,$!1LG/%GU&*p$F_s7$$\"#%)F,$!1045-K%on$F_s
7$$\"#&)F,$!1bdw+K'3l$F_s7$$\"#')F,$!1pn&H\"3d@OF_s7$$\"#()F,$!1x(GE_N
*)e$F_s7$$\"#))F,$!1b:'*[x#Hb$F_s7$$\"#*)F,$!1.)p2$)=N^$F_s7$$\"#!*F,$
!1x2865oqMF_s7$$\"#\"*F,$!1*yEAU(QCMF_s7$$\"##*F,$!1<)*Rq?huLF_s7$$\"#
$*F,$!10bT@)H8K$F_s7$$\"#%*F,$!1qQ$fQ;XE$F_s7$$\"#&*F,$!1gS=0$[T?$F_s7
$$\"#'*F,$!1P0%o$H?SJF_s7$$\"#(*F,$!1(4)4T%eE2$F_s7$$\"#)*F,$!1sJ%pw$
\\,IF_s7$$\"#**F,$!1#))='Q')oEHF_s7$$\"$+\"F,$!1S8GUNA[GF_s7$$\"$,\"F,
$!1rpc(e'psFF_s7$$\"$-\"F,$!1w/Ht<C.FF_s7$$\"$.\"F,$!1epjLnkREF_s7$$\"
$/\"F,$!1yYwFFq\"e#F_s7$$\"$0\"F,$!1HBp)e/#HDF_s7$$\"$1\"F,$!1$eWGn]>[
#F_s7$$\"$2\"F,$!1hyC5GuRCF_s7$$\"$3\"F,$!1#Ro`D'Q-CF_s7$$\"$4\"F,$!1(
p%eQ'*opBF_s7$$\"$5\"F,$!1`nG=\\YTBF_s7$$\"$6\"F,$!1iTfLt_<BF_s7$$\"$7
\"F,$!1`dod`p(H#F_s7$$\"$8\"F,$!1EJt^1z\"G#F_s7$$\"$9\"F,$!1[2V>!Q'pAF
_s7$$\"$:\"F,$!1$G:@Ol5E#F_s7$$\"$;\"F,$!1KpYMO!fD#F_s7$$\"$<\"F,$!1]c
y+o)RD#F_s7$$\"$=\"F,$!1#=N=z^^D#F_s7$$\"$>\"F,$!1VzCi%Q#fAF_s7$$\"$?
\"F,$!1jQ[[&*3mAF_s7$$\"$@\"F,$!1#QOti]bF#F_s7$$\"$A\"F,$!1u)y\\2quG#F
_s7$$\"$B\"F,$!1[[aE!*p,BF_s7$$\"$C\"F,$!1k`BO84=BF_s7$$\"$D\"F,$!1sr%
z`.lL#F_s7$$\"$E\"F,$!1g^T1[zcBF_s7$$\"$F\"F,$!1sF')=p#)yBF_s7$$\"$G\"
F,$!1UT:<UY-CF_s7$$\"$H\"F,$!1[<WqNdFCF_s7$$\"$I\"F,$!1zMIQV-aCF_s7$$
\"$J\"F,$!1mIOM$)o\"[#F_s7$$\"$K\"F,$!1;zQ!zR/^#F_s7$$\"$L\"F,$!1V%e3K
b,a#F_s7$$\"$M\"F,$!1uI+))QrqDF_s7$$\"$N\"F,$!1nJHnn*>g#F_s7$$\"$O\"F,
$!1Y@R8v)Qj#F_s7$$\"$P\"F,$!1UKbE>FmEF_s7$$\"$Q\"F,$!1u-Y>!Q!*p#F_s7$$
\"$R\"F,$!1%)f]%)f2KFF_s7$$\"$S\"F,$!1%\\-:;y_w#F_s7$$\"$T\"F,$!1V&=e+
R&)z#F_s7$$\"$U\"F,$!1)=Qp0b<$GF_s7$$\"$V\"F,$!1\\dV2\\#['GF_s7$$\"$W
\"F,$!1B=Os\"\\w*GF_s7$$\"$X\"F,$!1`_.f/8IHF_s7$$\"$Y\"F,$!1?gBPL<iHF_
s7$$\"$Z\"F,$!1aSz4Vo$*HF_s7$$\"$[\"F,$!1U!pNyrX-$F_s7$$\"$\\\"F,$!1lj
\"3/YZ0$F_s7$$\"$]\"F,$!1bV$4@>T3$F_s7$$\"$^\"F,$!17\")eU_g7JF_s7$$\"$
_\"F,$!1#>0i()>,9$F_s7$$\"$`\"F,$!1@&Qoh!emJF_s7$$\"$a\"F,$!1\\>R2n!>>
$F_s7$$\"$b\"F,$!1;R?-\">g@$F_s7$$\"$c\"F,$!1gZ)4WS)QKF_s7$$\"$d\"F,$!
1KK5B]HgKF_s7$$\"$e\"F,$!1jy@#y3.G$F_s7$$\"$f\"F,$!1a)[7E4))H$F_s7$$\"
$g\"F,$!1Kio(eDdJ$F_s7$$\"$h\"F,$!1c+B\\%))4L$F_s7$$\"$i\"F,$!13&e(p+`
WLF_s7$$\"$j\"F,$!1d(>c=%GcLF_s7$$\"$k\"F,$!1PNCAg=mLF_s7$$\"$l\"F,$!1
5%o5FsTP$F_s7$$\"$m\"F,$!1m2ym5=!Q$F_s7$$\"$n\"F,$!1A;'['>:%Q$F_s7$$\"
$o\"F,$!1ntV>f-'Q$F_s7$$\"$p\"F,$!141Vh_u&Q$F_s7$$\"$q\"F,$!1ft+xOD$Q$
F_s7$$\"$r\"F,$!13oJ'='\\yLF_s7$$\"$s\"F,$!1;+_A\">9P$F_s7$$\"$t\"F,$!
1lQ56,(>O$F_s7$$\"$u\"F,$!1smZ\\!)4]LF_s7$$\"$v\"F,$!17>%o3`dL$F_s7$$
\"$w\"F,$!1LlM/m))=LF_s7$$\"$x\"F,$!1%Q+b>^%*H$F_s7$$\"$y\"F,$!1ZL'ok+
uF$F_s7$$\"$z\"F,$!1bn**=**o_KF_s7$$\"$!=F,$!1xdnF^FDKF_s7$$\"$\"=F,$!
1U%f`_8^>$F_s7$$\"$#=F,$!1Z]\"H[j@;$F_s7$$\"$$=F,$!19PfrWQEJF_s7$$\"$%
=F,$!18RDXqt(3$F_s7$$\"$&=F,$!1(zHG#G=YIF_s7$$\"$'=F,$!1Q7/rWo,IF_s7$$
\"$(=F,$!1#\\Uto0U&HF_s7$$\"$)=F,$!1bk5$=6P!HF_s7$$\"$*=F,$!1/:/nm;]GF
_s7$$\"$!>F,$!1tz$)G)QNz#F_s7$$\"$\">F,$!1@8/B`zLFF_s7$$\"$#>F,$!12\"
\\Jv/4n#F_s7$$\"$$>F,$!1<*GflO[g#F_s7$$\"$%>F,$!1;W&f[hb`#F_s7$$\"$&>F
,$!1RnN+10jCF_s7$$\"$'>F,$!1m%)yViF(Q#F_s7$$\"$(>F,$!1fufL:@3BF_s7$$\"
$)>F,$!1zy?X/$eA#F_s7$$\"$*>F,$!1>dq(z2,9#F_s7$$\"$+#F,$!1QiiR#>50#F_s
7$$\"$,#F,$!1EHm4\"e^'>F_s7$$\"$-#F,$!1'\\<:q`c)=F_s7$$\"$.#F,$!1_VD4!
*G7=F_s7$$\"$/#F,$!1od2;2&[u\"F_s7$$\"$0#F,$!12<RU\"HJo\"F_s7$$\"$1#F,
$!1Sxb%>=pi\"F_s7$$\"$2#F,$!1rIF9`,w:F_s7$$\"$3#F,$!1e/jG9AI:F_s7$$\"$
4#F,$!1+-\"3!4M*[\"F_s7$$\"$5#F,$!1+-T\"[\"=`9F_s7$$\"$6#F,$!1LWSgUb@9
F_s7$$\"$7#F,$!1T?s>OF%R\"F_s7$$\"$8#F,$!1M&Rk=d6P\"F_s7$$\"$9#F,$!1N&
ylyD?N\"F_s7$$\"$:#F,$!1(p,&*R.nL\"F_s7$$\"$;#F,$!1A%**G6<]K\"F_s7$$\"
$<#F,$!1\"=g$yqz;8F_s7$$\"$=#F,$!1Ss^nk(=J\"F_s7$$\"$>#F,$!1ZZwG9458F_
s7$$\"$?#F,$!1vh`W5G68F_s7$$\"$@#F,$!1G#Q\"*G(G:8F_s7$$\"$A#F,$!1tL8()
\\&>K\"F_s7$$\"$B#F,$!1nUEs<8J8F_s7$$\"$C#F,$!1/M\"p/oEM\"F_s7$$\"$D#F
,$!1294UpTc8F_s7$$\"$E#F,$!1bu%zFMAP\"F_s7$$\"$F#F,$!1;azC&y**Q\"F_s7$
$\"$G#F,$!1C$\\Yw5&49F_s7$$\"$H#F,$!1]>E`YpI9F_s7$$\"$I#F,$!1?-m#Q'R`9
F_s7$$\"$J#F,$!1+9<WY[x9F_s7$$\"$K#F,$!1XR$>fIG]\"F_s7$$\"$L#F,$!1pq)o
!yIH:F_s7$$\"$M#F,$!1zIBhAzc:F_s7$$\"$N#F,$!1zmO$Gi^e\"F_s7$$\"$O#F,$!
1=aEB&)H9;F_s7$$\"$P#F,$!1GcL=R3W;F_s7$$\"$Q#F,$!1g\"3(fOSu;F_s7$$\"$R
#F,$!18%y*e^90<F_s7$$\"$S#F,$!1v]Q:!)>O<F_s7$$\"$T#F,$!1?AU$)RXn<F_s7$
$\"$U#F,$!13$z3%p!))z\"F_s7$$\"$V#F,$!1_QIdG:I=F_s7$$\"$W#F,$!1N9)Gw*Q
h=F_s7$$\"$X#F,$!1kzs<xT#*=F_s7$$\"$Y#F,$!1n*)e\"yQJ#>F_s7$$\"$Z#F,$!1
Y4%R)pX`>F_s7$$\"$[#F,$!18(*[%HyK)>F_s7$$\"$\\#F,$!1P31%f5D,#F_s7$$\"$
]#F,$!1as(ekj5/#F_s7$$\"$^#F,$!1\"G>s1\\)o?F_s7$$\"$_#F,$!1<AY,.y&4#F_
s7$$\"$`#F,$!1Wo[!fs<7#F_s7$$\"$a#F,$!1)=eu%HuY@F_s7$$\"$b#F,$!15z'*H,
hq@F_s7$$\"$c#F,$!1Be`8YH$>#F_s7$$\"$d#F,$!17gYl&=Z@#F_s7$$\"$e#F,$!1h
J0>e![B#F_s7$$\"$f#F,$!1kY8[=[`AF_s7$$\"$g#F,$!1NU)>ut1F#F_s7$$\"$h#F,
$!1-Fa!=5jG#F_s7$$\"$i#F,$!1*z\")*49K+BF_s7$$\"$j#F,$!1Qnf=#REJ#F_s7$$
\"$k#F,$!1%[BI\"p>BBF_s7$$\"$l#F,$!1<mx%HH>L#F_s7$$\"$m#F,$!1%y.rjs(QB
F_s7$$\"$n#F,$!1]F:iYmVBF_s7$$\"$o#F,$!1ArW=XaYBF_s7$$\"$p#F,$!1momeFN
ZBF_s7$$\"$q#F,$!1w(HxJJgM#F_s7$$\"$r#F,$!18,<\"\\BDM#F_s7$$\"$s#F,$!1
k1\"Q\"RxOBF_s7$$\"$t#F,$!1IXsQ&G(GBF_s7$$\"$u#F,$!1vH[;YL=BF_s7$$\"$v
#F,$!1[dou1a0BF_s7$$\"$w#F,$!1$Gqx\\'H!H#F_s7$$\"$x#F,$!1$G'42JbsAF_s7
$$\"$y#F,$!1!>-8uiAD#F_s7$$\"$z#F,$!1&4Ip$)y$HAF_s7$$\"$!GF,$!1?dJ4g&Q
?#F_s7$$\"$\"GF,$!1v+uL+lv@F_s7$$\"$#GF,$!1=&Ro#yrW@F_s7$$\"$$GF,$!1$*
3FGu,6@F_s7$$\"$%GF,$!1q&GE)z]u?F_s7$$\"$&GF,$!1?,h@(\\^.#F_s7$$\"$'GF
,$!1TvUYR!H*>F_s7$$\"$(GF,$!1S3Y5ItZ>F_s7$$\"$)GF,$!1k4:-.g**=F_s7$$\"
$*GF,$!1`*G\"G-Z[=F_s7$$\"$!HF,$!1/%yl>3Vz\"F_s7$$\"$\"HF,$!1k\"G3g!3P
<F_s7$$\"$#HF,$!1HC<.[vw;F_s7$$\"$$HF,$!1T_\"*=\"*H8;F_s7$$\"$%HF,$!1E
mj+GoY:F_s7$$\"$&HF,$!1GunAg(oZ\"F_s7$$\"$'HF,$!1p,%e')\\QS\"F_s7$$\"$
(HF,$!1PII-jdF8F_s7$$\"$)HF,$!1@Wu!=G![7F_s7$$\"$*HF,$!1X^n6#z^;\"F_s7
$$\"$+$F,$!1#*e(H&R+z5F_s7$$\"$,$F,$!1FEf.n%4'**FO7$$\"$-$F,$!1;1w>gz&
>*FO7$$\"$.$F,$!1S7HNqS#\\)FO7$$\"$/$F,$!1+$4\"ojj[yFO7$$\"$0$F,$!1w()
QvrPisFO7$$\"$1$F,$!1YlhQ'e:t'FO7$$\"$2$F,$!1rlGba9aiFO7$$\"$3$F,$!1JB
9Pt8GeFO7$$\"$4$F,$!1L'))[^o:X&FO7$$\"$5$F,$!1OFH\\s]A^FO7$$\"$6$F,$!1
qvf[`0R[FO7$$\"$7$F,$!1[!p@pZ$*f%FO7$$\"$8$F,$!1y=Ig<b,WFO7$$\"$9$F,$!
1&*y5qr'QC%FO7$$\"$:$F,$!13HT<__CTFO7$$\"$;$F,$!1W!)eC%)yTSFO7$$\"$<$F
,$!1dJC%4]R*RFO7$$\"$=$F,$!1%=5(oQLzRFO7$$\"$>$F,$!1hbC&H$H'*RFO7$$\"$
?$F,$!1C9)oR6K/%FO7$$\"$@$F,$!1\\i&)[-]=TFO7$$\"$A$F,$!1;kbg0g?UFO7$$
\"$B$F,$!1))3!HE\")zM%FO7$$\"$C$F,$!11A5,\"R\"*\\%FO7$$\"$D$F,$!1kutK#
)fsYFO7$$\"$E$F,$!1iT1J)4p'[FO7$$\"$F$F,$!1Jh^$p^13&FO7$$\"$G$F,$!1(y:
`&yU7`FO7$$\"$H$F,$!1G)R\"3#o3c&FO7$$\"$I$F,$!1*pvP7GY#eFO7$$\"$J$F,$!
1Gxq#3)Q-hFO7$$\"$K$F,$!1r:d2L&GR'FO7$$\"$L$F,$!1@uT,Mv%p'FO7$$\"$M$F,
$!1v>s!*>%o+(FO7$$\"$N$F,$!1'4\"4tj*yK(FO7$$\"$O$F,$!1HXfprrcwFO7$$\"$
P$F,$!1;gn\")z7#*zFO7$$\"$Q$F,$!1D:e_](HL)FO7$$\"$R$F,$!1C.DLp7y')FO7$
$\"$S$F,$!12Hh_TZE!*FO7$$\"$T$F,$!1o=C#*)GpP*FO7$$\"$U$F,$!1D5IlYUG(*F
O7$$\"$V$F,$!1>S(**f\"*z+\"F_s7$$\"$W$F,$!19#oD\"y.V5F_s7$$\"$X$F,$!1
\\]pm1)y2\"F_s7$$\"$Y$F,$!1C'oOt@C6\"F_s7$$\"$Z$F,$!1'H+Pckl9\"F_s7$$
\"$[$F,$!1cHEcY@!=\"F_s7$$\"$\\$F,$!1(=\\3VzK@\"F_s7$$\"$]$F,$!18$=\")
>ocC\"F_s7$$\"$^$F,$!1!eF98#Hx7F_s7$$\"$_$F,$!13EuQU138F_s7$$\"$`$F,$!
1EC#\\L**yL\"F_s7$$\"$a$F,$!1@WP9Srm8F_s7$$\"$b$F,$!1VX2CmU%R\"F_s7$$
\"$c$F,$!1h#[pBd4U\"F_s7$$\"$d$F,$!1,xgDwAY9F_s7$$\"$e$F,$!1y0WO7;q9F_
s7$$\"$f$F,$!1ck/kJo#\\\"F_s7$$\"$g$F,$!1[g,E,s8:F_s7$$\"$h$F,$!17#\\!
Q/?L:F_s7$$\"$i$F,$!1VuS*)R0^:F_s7$$\"$j$F,$!1Dmp=A@n:F_s7$$\"$k$F,$!1
Tf(**33;e\"F_s7$$\"$l$F,$!18))=pg<%f\"F_s7$$\"$m$F,$!1k=\"45_[g\"F_s7$
$\"$n$F,$!1nyT&etNh\"F_s7$$\"$o$F,$!1v([gNz-i\"F_s7$$\"$p$F,$!1+\\*ol4
\\i\"F_s7$$\"$q$F,$!14kx?hSF;F_s7$$\"$r$F,$!1<L_Z<rF;F_s7$$\"$s$F,$!1H
-b#)3xD;F_s7$$\"$t$F,$!11@s&>H:i\"F_s7$$\"$u$F,$!1)Q20mL\\h\"F_s7$$\"$
v$F,$!1b[TLD$fg\"F_s7$$\"$w$F,$!1G1rL`Z%f\"F_s7$$\"$x$F,$!1%y6M#G^!e\"
F_s7$$\"$y$F,$!1!4`v)p*Rc\"F_s7$$\"$z$F,$!1#QBZ,\")[a\"F_s7$$\"$!QF,$!
14#oyF>J_\"F_s7$$\"$\"QF,$!1L`N:tm)\\\"F_s7$$\"$#QF,$!1#z*H7=[r9F_s7$$
\"$$QF,$!1'>X@e?:W\"F_s7$$\"$%QF,$!1b!)\\[Du39F_s7$$\"$&QF,$!1i=@Fx5t8
F_s7$$\"$'QF,$!1Qyr3sdM8F_s7$$\"$(QF,$!1=\"*fSJ6$H\"F_s7$$\"$)QF,$!1u`
S5(y'[7F_s7$$\"$*QF,$!1?ZqG\"Q7?\"F_s7$$\"$!RF,$!1u*pBhc2:\"F_s7$$\"$
\"RF,$!1*>'4o.?(4\"F_s7$$\"$#RF,$!1mm9wl`S5F_s7$$\"$$RF,$!1DBCVPL2)*FO
7$$\"$%RF,$!1qNl@%)fx\"*FO7$$\"$&RF,$!1,!QN&)fe^)FO7$$\"$'RF,$!1OK^.s#
=#yFO7$$\"$(RF,$!1>[U#f=_4(FO7$$\"$)RF,$!1o!4z%4wNjFO7$$\"$*RF,$!1(HUq
&)*=VbFO7$$\"$+%F,$!1L70@%\\sr%FO7$$\"$,%F,$!1m)y#f3'Q#RFO7$$\"$-%F,$!
1$p,Y:0V>$FO7$$\"$.%F,$!1M4$R]+k_#FO7$$\"$/%F,$!1@8'H?-!=>FO7$$\"$0%F,
$!19P!R7-qO\"FO7$$\"$1%F,$!1vuQ**>G8()F:7$$\"$2%F,$!1iJ3j\"R%*G%F:7$$
\"$3%F,$!1xtX'z!y%y$F/7$$\"$4%F,$\"1YX/j.FRIF:7$$\"$5%F,$\"1G$3NjMJ)fF
:7$$\"$6%F,$\"1GCB)Q2@Z)F:7$$\"$7%F,$\"1H43C][_5FO7$$\"$8%F,$\"1)*=%p%
)pf@\"FO7$$\"$9%F,$\"14.MmlYR8FO7$$\"$:%F,$\"1(4o4$[uC9FO7$$\"$;%F,$\"
1.V(>.VNZ\"FO7$$\"$<%F,$\"1E^z\\(ov[\"FO7$$\"$=%F,$\"1$\\'=&>*\\o9FO7$
$\"$>%F,$\"1:/`W;)zT\"FO7$$\"$?%F,$\"1.a[pQjP8FO7$$\"$@%F,$\"16.0hX/H7
FO7$$\"$A%F,$\"1e.6[Px$4\"FO7$$\"$B%F,$\"1W1L0@`L$*F:7$$\"$C%F,$\"1lC
\")o)oG\\(F:7$$\"$D%F,$\"1)G!4oF^IaF:7$$\"$E%F,$\"1Sm1#Qe4;$F:7$$\"$F%
F,$\"17o&e\"zL%)pF/7$$\"$G%F,$!1IY@_b4V>F:7$$\"$H%F,$!1Eb95I#*\\ZF:7$$
\"$I%F,$!1)4'=()pf3xF:7$$\"$J%F,$!1JbS@<f!3\"FO7$$\"$K%F,$!1!H`x5$*GS
\"FO7$$\"$L%F,$!1JB*)**H\\O<FO7$$\"$M%F,$!1et+'eW,3#FO7$$\"$N%F,$!1I]j
ZZiKCFO7$$\"$O%F,$!1m+g6Pt#z#FO7$$\"$P%F,$!1A>`1ZHfJFO7$$\"$Q%F,$!1!)f
!Ri`6`$FO7$$\"$R%F,$!1BCb$oyr!RFO7$$\"$S%F,$!1x!yN5giG%FO7$$\"$T%F,$!1
Pgku(4tm%FO7$$\"$U%F,$!1#pf&Q4E\\]FO7$$\"$V%F,$!1:p4ry1JaFO7$$\"$W%F,$
!1;B/pbq6eFO7$$\"$X%F,$!1A\\OT%p,>'FO7$$\"$Y%F,$!1X/\\/]ZllFO7$$\"$Z%F
,$!1!R;;edm$pFO7$$\"$[%F,$!1y.-1?x-tFO7$$\"$\\%F,$!1>:JGB*Gm(FO7$$\"$]
%F,$!1`jdF:6;!)FO7$$\"$^%F,$!1r+PE7ah$)FO7$$\"$_%F,$!1kc]49J)p)FO7$$\"
$`%F,$!1_MfY,dD!*FO7$$\"$a%F,$!1;SG=L[U$*FO7$$\"$b%F,$!1\\)ohMM#['*FO7
$$\"$c%F,$!1;BHER-U**FO7$$\"$d%F,$!1PIiwpIA5F_s7$$\"$e%F,$!1-\"pDjg!\\
5F_s7$$\"$f%F,$!1.$fgX)Qu5F_s7$$\"$g%F,$!1jy0nr@)4\"F_s7$$\"$h%F,$!1#y
\"*\\3v/7\"F_s7$$\"$i%F,$!1Jh</@4T6F_s7$$\"$j%F,$!1m+dp'***f6F_s7$$\"$
k%F,$!1d$fGvIr<\"F_s7$$\"$l%F,$!1p8')G)>C>\"F_s7$$\"$m%F,$!1H%[A&G!e?
\"F_s7$$\"$n%F,$!13ceMs@<7F_s7$$\"$o%F,$!1?*y;#=gE7F_s7$$\"$p%F,$!1s+B
ro*QB\"F_s7$$\"$q%F,$!1))QzIS/R7F_s7$$\"$r%F,$!14Y.;j)>C\"F_s7$$\"$s%F
,$!1!Hx#*3oEC\"F_s7$$\"$t%F,$!1!e]$Q].T7F_s7$$\"$u%F,$!1;srbT.P7F_s7$$
\"$v%F,$!1*e))yr81B\"F_s7$$\"$w%F,$!1.)>^EB<A\"F_s7$$\"$x%F,$!1$o\"Q\"
e8.@\"F_s7$$\"$y%F,$!1@igumL'>\"F_s7$$\"$z%F,$!1D??dduz6F_s7$$\"$![F,$
!1;j$oA&\\g6F_s7$$\"$\"[F,$!1N,[Z1aQ6F_s7$$\"$#[F,$!11MrI(QQ6\"F_s7$$
\"$$[F,$!1nlG<tM'3\"F_s7$$\"$%[F,$!1(\\N*e`-c5F_s7$$\"$&[F,$!1^lW+H$G-
\"F_s7$$\"$'[F,$!1k]o>1Jn)*FO7$$\"$([F,$!1gIo:-#oZ*FO7$$\"$)[F,$!1AWF!
)**[c!*FO7$$\"$*[F,$!1$)*f(QB'fg)FO7$$\"$!\\F,$!1cDh'y*)[7)FO7$$\"$\"
\\F,$!1c$zWsMHh(FO7$$\"$#\\F,$!1%QqaHp(pqFO7$$\"$$\\F,$!1zYqC_2&\\'FO7
$$\"$%\\F,$!1uZ3hOa))eFO7$$\"$&\\F,$!1,;F@]()\\_FO7$$\"$'\\F,$!1r1$e$)
y(yXFO7$$\"$(\\F,$!1'4Bvft\\(QFO7$$\"$)\\F,$!1HHr6m=QJFO7$$\"$*\\F,$!1
7Y')[Q:oBFO7$$\"$+&F,$!1sC5*z>Yc\"FO7$$\"$,&F,$!1$['Hg21NzF:7$$\"$-&F,
$!1!*G)**>1%4')F/7$$\"$.&F,$\"16LC:k(zf&F:7$$\"$/&F,$\"1gHOHLJY6FO7$$
\"$0&F,$\"1xX-:2cv;FO7$$\"$1&F,$\"1E%)QY9h\\@FO7$$\"$2&F,$\"1Fnu9;]qDF
O7$$\"$3&F,$\"1IsGdABSHFO7$$\"$4&F,$\"1fp4`)p2E$FO7$$\"$5&F,$\"1:aw7o/
MNFO7$$\"$6&F,$\"1Bimh>'>w$FO7$$\"$7&F,$\"1GT*p,\"QYRFO7$$\"$8&F,$\"1r
Tjeq8*3%FO7$$\"$9&F,$\"1i!QR*4.#>%FO7$$\"$:&F,$\"1lF[;?$oD%FO7$$\"$;&F
,$\"1\\[))e!y_G%FO7$$\"$<&F,$\"1'fV(Ri2zUFO7$$\"$=&F,$\"1NZy/L!*RUFO7$
$\"$>&F,$\"1ngFigSpTFO7$$\"$?&F,$\"1+`y7=?pSFO7$$\"$@&F,$\"1j%\\Lxy3%R
FO7$$\"$A&F,$\"17Z7'\\'*fy$FO7$$\"$B&F,$\"1bUe\"G'31OFO7$$\"$C&F,$\"1%
fJje^ES$FO7$$\"$D&F,$\"1H]fD%or<$FO7$$\"$E&F,$\"1#Hp/x&3JHFO7$$\"$F&F,
$\"1'po*Rf#em#FO7$$\"$G&F,$\"14e&z)\\y#Q#FO7$$\"$H&F,$\"1%**3]3LL3#FO7
$$\"$I&F,$\"1Q2H&*[\")o<FO7$$\"$J&F,$\"1)3z%[*\\0W\"FO7$$\"$K&F,$\"1>E
#o+L)*4\"FO7$$\"$L&F,$\"1+cztUMzuF:7$$\"$M&F,$\"1Z***\\>05'QF:7$$\"$N&
F,$\"1(fm5w*Qb:F/7$$\"$O&F,$!1J6S1<1DOF:7$$\"$P&F,$!1*o&>3U.puF:7$$\"$
Q&F,$!1SNn_U[O6FO7$$\"$R&F,$!1M'ebR<,`\"FO7$$\"$S&F,$!1h()GyNpE>FO7$$
\"$T&F,$!103M._7DBFO7$$\"$U&F,$!1xgODgMCFFO7$$\"$V&F,$!1WK&R$3JBJFO7$$
\"$W&F,$!1^1fS^*4_$FO7$$\"$X&F,$!1``xp[R;RFO7$$\"$Y&F,$!1I!=U0E&3VFO7$
$\"$Z&F,$!1$)>4MXU'p%FO7$$\"$[&F,$!1.mFgc9z]FO7$$\"$\\&F,$!1\"4X:+kdX&
FO7$$\"$]&F,$!1yzkbIPDeFO7$$\"$^&F,$!1&3VU'\\3(='FO7$$\"$_&F,$!1(fC;BI
+a'FO7$$\"$`&F,$!1kO?ZuN$)oFO7$$\"$a&F,$!1ONp6IB;sFO7$$\"$b&F,$!1\\N&p
'3%y`(FO7$$\"$c&F,$!1/bWHAQZyFO7$$\"$d&F,$!1.zDF`2W\")FO7$$\"$e&F,$!1'
*HlS^:F%)FO7$$\"$f&F,$!1:J4YJ(ep)FO7$$\"$g&F,$!1s?qjq\\\\*)FO7$$\"$h&F
,$!1H\">\"31J(=*FO7$$\"$i&F,$!1#o-FC8'3%*FO7$$\"$j&F,$!1#3Uq$*>Fh*FO7$
$\"$k&F,$!1tbtF4'*)z*FO7$$\"$l&F,$!1sPR#[\"om**FO7$$\"$m&F,$!1#z#omT_6
5F_s7$$\"$n&F,$!1?$Q:h,W-\"F_s7$$\"$o&F,$!1<xV!QR_.\"F_s7$$\"$p&F,$!1i
/'GyxR/\"F_s7$$\"$q&F,$!1/q3=&e00\"F_s7$$\"$r&F,$!1v4X`Y#\\0\"F_s7$$\"
$s&F,$!1\"e')Gg?q0\"F_s7$$\"$t&F,$!1ouw0@zc5F_s7$$\"$u&F,$!1%QLg?'=a5F
_s7$$\"$v&F,$!1#*4gJ7:\\5F_s7$$\"$w&F,$!1j_0unjT5F_s7$$\"$x&F,$!1#*yho
OfJ5F_s7$$\"$y&F,$!1P#*QuR(*=5F_s7$$\"$z&F,$!1M.'[&4t.5F_s7$$\"$!eF,$!
1!R:pe!>e)*FO7$$\"$\"eF,$!1^Xa2!R>l*FO7$$\"$#eF,$!1dyLMC7=%*FO7$$\"$$e
F,$!1x$e=y>j:*FO7$$\"$%eF,$!14Q]t57m))FO7$$\"$&eF,$!1!)p7is7Z&)FO7$$\"
$'eF,$!1dg7`+&*)>)FO7$$\"$(eF,$!1eM(*H<@@yFO7$$\"$)eF,$!1d=:#)\\a8uFO7
$$\"$*eF,$!1(Qnat#fvpFO7$$\"$!fF,$!1(>4Z)z+2lFO7$$\"$\"fF,$!1hfiGOX2gF
O7$$\"$#fF,$!1@!*=2BgwaFO7$$\"$$fF,$!1%*R6Ti89\\FO7$$\"$%fF,$!137htqu>
VFO7$$\"$&fF,$!1\"=PVrNJp$FO7$$\"$'fF,$!1&)z^&=7S.$FO7$$\"$(fF,$!1=!=-
Z&4UBFO7$$\"$)fF,$!1\"oDFO8rh\"FO7$$\"$*fF,$!1LsH5K-)e)F:7$$\"$+'F,$!1
I%>e8K2p'F/7$$\"$,'F,$\"1$HE-Q&\\EpF:7$$\"$-'F,$\"1ifb\"R'e)Q\"FO7$$\"
$.'F,$\"1C]0cT3B?FO7$$\"$/'F,$\"1,K6YmG)f#FO7$$\"$0'F,$\"1Rv_'4,j6$FO7
$$\"$1'F,$\"1x%)*zn)>zNFO7$$\"$2'F,$\"1))*)=1],*)RFO7$$\"$3'F,$\"1YNAW
1vZVFO7$$\"$4'F,$\"1)y2()frtl%FO7$$\"$5'F,$\"1wrM4)4)>\\FO7$$\"$6'F,$
\"1POCKO'p8&FO7$$\"$7'F,$\"1$4ZpJ)p5`FO7$$\"$8'F,$\"1;(QtZYGW&FO7$$\"$
9'F,$\"1_4Uc&3_`&FO7$$\"$:'F,$\"16$*3&G`&*e&FO7$$\"$;'F,$\"12&f\\8=wg&
FO7$$\"$<'F,$\"1BHKl(46f&FO7$$\"$='F,$\"1,BIkWqTbFO7$$\"$>'F,$\"15*yUe
[5Y&FO7$$\"$?'F,$\"1M:mr*e2N&FO7$$\"$@'F,$\"1Km1\"RBC@&FO7$$\"$A'F,$\"
1B&yR%4gZ]FO7$$\"$B'F,$\"1)Hd>[Ay&[FO7$$\"$C'F,$\"1&ohW,\"fWYFO7$$\"$D
'F,$\"10GN6@Q4WFO7$$\"$E'F,$\"1-Z9+Vk`TFO7$$\"$F'F,$\"1Ng1e%*zyQFO7$$
\"$G'F,$\"1Zp**)>Vie$FO7$$\"$H'F,$\"1eWMb_MxKFO7$$\"$I'F,$\"1<$=\\&)\\
M&HFO7$$\"$J'F,$\"1D'pG4weh#FO7$$\"$K'F,$\"1rEv)H=fE#FO7$$\"$L'F,$\"18
1x)RY[!>FO7$$\"$M'F,$\"15REti!R`\"FO7$$\"$N'F,$\"1j5]4,Ka6FO7$$\"$O'F,
$\"1\\:H)\\nGn(F:7$$\"$P'F,$\"163U_.#)RPF:7$$\"$Q'F,$!1/$[xb&3WCF/7$$
\"$R'F,$!1ZZ&or5&oUF:7$$\"$S'F,$!1_\\=(f(R@$)F:7$$\"$T'F,$!1v_4Q(>#R7F
O7$$\"$U'F,$!1\">Cb<Dqk\"FO7$$\"$V'F,$!1?Dwt7^a?FO7$$\"$W'F,$!1^`daRlg
CFO7$$\"$X'F,$!1_9%3b\\W'GFO7$$\"$Y'F,$!1(Gb<]9\\E$FO7$$\"$Z'F,$!1TL2_
]3hOFO7$$\"$['F,$!1s^Nbp,_SFO7$$\"$\\'F,$!1S*[6=&yOWFO7$$\"$]'F,$!1#)H
2EO[9[FO7$$\"$^'F,$!1RSuG[A%=&FO7$$\"$_'F,$!1I[])oR^a&FO7$$\"$`'F,$!1p
L!z=xj*eFO7$$\"$a'F,$!1Iq()=T5PiFO7$$\"$b'F,$!1vcf7[]mlFO7$$\"$c'F,$!1
\"Q<H(3y$)oFO7$$\"$d'F,$!1AAT84:)=(FO7$$\"$e'F,$!1v!4zH])yuFO7$$\"$f'F
,$!1()=_%)38bxFO7$$\"$g'F,$!1376t2E;!)FO7$$\"$h'F,$!1#\\Qh0C:E)FO7$$\"
$i'F,$!1q-(Gd?-\\)FO7$$\"$j'F,$!1m1*oml;q)FO7$$\"$k'F,$!1\">!)o%**=&*)
)FO7$$\"$l'F,$!1d-i]!R,2*FO7$$\"$m'F,$!1@E=7M(eA*FO7$$\"$n'F,$!1rSEK!o
<O*FO7$$\"$o'F,$!1-ki^A@x%*FO7$$\"$p'F,$!1YHgF&4;d*FO7$$\"$q'F,$!1\")G
j8sPW'*FO7$$\"$r'F,$!1Y`yTj%\\p*FO7$$\"$s'F,$!1=bB39wA(*FO7$$\"$t'F,$!
1fblh,GF(*FO7$$\"$u'F,$!1AO[%Rtzq*FO7$$\"$v'F,$!1;Y.PZKk'*FO7$$\"$w'F,
$!1(z;WXIef*FO7$$\"$x'F,$!1&y=iC**>]*FO7$$\"$y'F,$!1O>$*[?N#Q*FO7$$\"$
z'F,$!1`N2T=UO#*FO7$$\"$!oF,$!1il(4X`P1*FO7$$\"$\"oF,$!1M@@nL!R'))FO7$
$\"$#oF,$!1b;h^&Rkj)FO7$$\"$$oF,$!1b`&[DT4Q)FO7$$\"$%oF,$!1'f%fM))*p4)
FO7$$\"$&oF,$!1xh2wN@%y(FO7$$\"$'oF,$!1hkB:v>UuFO7$$\"$(oF,$!14VBkKdqq
FO7$$\"$)oF,$!1/7RRQ(*omFO7$$\"$*oF,$!1%p3:\\UqB'FO7$$\"$!pF,$!1eA`QDV
udFO7$$\"$\"pF,$!1[A`+s!3G&FO7$$\"$#pF,$!1W:(pVRev%FO7$$\"$$pF,$!1p<B'
y6#*>%FO7$$\"$%pF,$!1C%ot?;1h$FO7$$\"$&pF,$!1Yr1CRv*)HFO7$$\"$'pF,$!1
\\>xq_LOBFO7$$\"$(pF,$!1W*e4az+l\"FO7$$\"$)pF,$!1-0Fv$[rI*F:7$$\"$*pF,
$!1*[%z_#z(z<F:7$$\"$+(F,$\"1/FKX\"fQ3'F:7$$\"$,(F,$\"1CRS!GaCO\"FO7$$
\"$-(F,$\"1;6K0]%H0#FO7$$\"$.(F,$\"1VVT1(Q?o#FO7$$\"$/(F,$\"1)oj.!*y=D
$FO7$$\"$0(F,$\"1kn\"e_sXw$FO7$$\"$1(F,$\"1XG3f/>AUFO7$$\"$2(F,$\"1Qj=
B!oni%FO7$$\"$3(F,$\"1;+O!\\0.)\\FO7$$\"$4(F,$\"1#*)e!y&oZG&FO7$$\"$5(
F,$\"1MIdQ*)3UbFO7$$\"$6(F,$\"1&H=BkkTv&FO7$$\"$7(F,$\"1%*=)[lgG#fFO7$
$\"$8(F,$\"1`'**yI4+0'FO7$$\"$9(F,$\"1f*RQw5u8'FO7$$\"$:(F,$\"1Z%pZZLo
='FO7$$\"$;(F,$\"1!)R<NY,+iFO7$$\"$<(F,$\"10z!*G1myhFO7$$\"$=(F,$\"1&
\\V.ZZW7'FO7$$\"$>(F,$\"1A=zR7-RgFO7$$\"$?(F,$\"19aE8&)*R#fFO7$$\"$@(F
,$\"1P?l'ym4y&FO7$$\"$A(F,$\"1l%oV*[[6cFO7$$\"$B(F,$\"1R>cAM3<aFO7$$\"
$C(F,$\"1]l#p6l#*>&FO7$$\"$D(F,$\"1m/?&G0&f\\FO7$$\"$E(F,$\"17*4W>_#*p
%FO7$$\"$F(F,$\"1nU#HYF*>WFO7$$\"$G(F,$\"1>jQZk#H7%FO7$$\"$H(F,$\"195e
C'='4QFO7$$\"$I(F,$\"1>YIozM\"[$FO7$$\"$J(F,$\"1amH@LVRJFO7$$\"$K(F,$
\"1*)\\Hi(o^y#FO7$$\"$L(F,$\"1\"yu#oR#)>CFO7$$\"$M(F,$\"1<,$>dWY/#FO7$
$\"$N(F,$\"1lzX9D&3m\"FO7$$\"$O(F,$\"1%)=q$RY'p7FO7$$\"$P(F,$\"15U8x!=
?s)F:7$$\"$Q(F,$\"1A@(y$pr'p%F:7$$\"$R(F,$\"119n-jm=jF/7$$\"$S(F,$!1Yu
/&pY9Y$F:7$$\"$T(F,$!1mL#**e`Bd(F:7$$\"$U(F,$!1%=%Q4)>!p6FO7$$\"$V(F,$
!1_v:cMX!e\"FO7$$\"$W(F,$!15ZG`C^!*>FO7$$\"$X(F,$!1pdMkL>)R#FO7$$\"$Y(
F,$!1uwtdG^-GFO7$$\"$Z(F,$!1:v#fS2D?$FO7$$\"$[(F,$!1z0q))HB(f$FO7$$\"$
\\(F,$!1yGN+[w&)RFO7$$\"$](F,$!1T(z2'p>nVFO7$$\"$^(F,$!1f5TIAkSZFO7$$
\"$_(F,$!1&)e%*G<B0^FO7$$\"$`(F,$!1\"yQyl9,Y&FO7$$\"$a(F,$!194\\E!eW!e
FO7$$\"$b(F,$!1G-5#QYu8'FO7$$\"$c(F,$!14U7V:GekFO7$$\"$d(F,$!192JOB=mn
FO7$$\"$e(F,$!16=DPVQgqFO7$$\"$f(F,$!1.rT9'R,M(FO7$$\"$g(F,$!1+Biwkr/w
FO7$$\"$h(F,$!1h0*QA*R`yFO7$$\"$i(F,$!1=Pm,z[&3)FO7$$\"$j(F,$!1@=Ke!)H
+$)FO7$$\"$k(F,$!1!)*of]gr\\)FO7$$\"$l(F,$!1/\\W%3@an)FO7$$\"$m(F,$!1$
Q@&G/WM))FO7$$\"$n(F,$!1\"*RCQPft*)FO7$$\"$o(F,$!1#4zBbqA4*FO7$$\"$p(F
,$!1st#\\_u)*=*FO7$$\"$q(F,$!1e^m/K#eE*FO7$$\"$r(F,$!1Wbn<ya>$*FO7$$\"
$s(F,$!1[9$G0$\\]$*FO7$$\"$t(F,$!1YN>]o6e$*FO7$$\"$u(F,$!1jiG#>!*=M*FO
7$$\"$v(F,$!1\"\\:#)*oH,$*FO7$$\"$w(F,$!1\\@f?M$eB*FO7$$\"$x(F,$!1NhAX
'3]9*FO7$$\"$y(F,$!1Xcb$pV$G!*FO7$$\"$z(F,$!1,txF<P&)))FO7$$\"$!yF,$!1
[Fkexj:()FO7$$\"$\"yF,$!1m\"))eX)p=&)FO7$$\"$#yF,$!1SJEh>7%H)FO7$$\"$$
yF,$!1dh7/x[T!)FO7$$\"$%yF,$!1gPd>iQgxFO7$$\"$&yF,$!1,<2p*=/X(FO7$$\"$
'yF,$!1,fbj\")>6rFO7$$\"$(yF,$!1.A(*)eYBu'FO7$$\"$)yF,$!10LAMu\\VjFO7$
$\"$*yF,$!1')H\\@TH9fFO7$$\"$!zF,$!1]n\"*Q,RaaFO7$$\"$\"zF,$!1D&pb()[M
'\\FO7$$\"$#zF,$!1c+ueM9TWFO7$$\"$$zF,$!1_QY$fcr)QFO7$$\"$%zF,$!1<]G//
=,LFO7$$\"$&zF,$!12#>#zi\"Ho#FO7$$\"$'zF,$!1P&))eru?.#FO7$$\"$(zF,$!1f
>!)p^P[8FO7$$\"$)zF,$!1rg_Z!faJ'F:7$$\"$*zF,$\"1O8%pahn=\"F:7$$\"$+)F,
$\"1&z)\\'oba-*F:7$$\"$,)F,$\"1'[#4y(RTl\"FO7$$\"$-)F,$\"1q=gfk<UBFO7$
$\"$.)F,$\"16&3]2O)oHFO7$$\"$/)F,$\"1!*=z')>EONFO7$$\"$0)F,$\"1C;\\!)4
cYSFO7$$\"$1)F,$\"1'*\\R!y.=]%FO7$$\"$2)F,$\"1sWeeb-/\\FO7$$\"$3)F,$\"
1^UUPkAb_FO7$$\"$4)F,$\"1hvc&)>PdbFO7$$\"$5)F,$\"1jKc2PR7eFO7$$\"$6)F,
$\"1X,9F&*=AgFO7$$\"$7)F,$\"1LiCkUi)='FO7$$\"$8)F,$\"1&e>f5INJ'FO7$$\"
$9)F,$\"1df1rqq)R'FO7$$\"$:)F,$\"16$=#pM#fW'FO7$$\"$;)F,$\"1^9N`j\"pX'
FO7$$\"$<)F,$\"1O]#o'>RLkFO7$$\"$=)F,$\"1Ho_%=EqP'FO7$$\"$>)F,$\"1'Q(G
[\\Y*G'FO7$$\"$?)F,$\"1$\\OmpCB<'FO7$$\"$@)F,$\"1M3(*)y#>FgFO7$$\"$A)F
,$\"1C<?CzibeFO7$$\"$B)F,$\"1D.&Rbg\"fcFO7$$\"$C)F,$\"1szN!H$HRaFO7$$
\"$D)F,$\"1fud38](>&FO7$$\"$E)F,$\"1(*3,WFBN\\FO7$$\"$F)F,$\"1T)eV34Rl
%FO7$$\"$G)F,$\"1\"fWlbD\\N%FO7$$\"$H)F,$\"1aod3:lRSFO7$$\"$I)F,$\"17J
T'yI%4PFO7$$\"$J)F,$\"1yd)e5#elLFO7$$\"$K)F,$\"1(4^(>%*R4IFO7$$\"$L)F,
$\"1@B#*zA:UEFO7$$\"$M)F,$\"1,d%\\>'3lAFO7$$\"$N)F,$\"1m%yF)HUz=FO7$$
\"$O)F,$\"1Xo#*=6O'[\"FO7$$\"$P)F,$\"1F:+!3wq3\"FO7$$\"$Q)F,$\"1?@ZFo?
FoF:7$$\"$R)F,$\"1'*y-'=aUu#F:7$$\"$S)F,$!1lo`h@,n8F:7$$\"$T)F,$!1f))=
YRs&\\&F:7$$\"$U)F,$!1!)3%yPE7j*F:7$$\"$V)F,$!1drI(\\2jP\"FO7$$\"$W)F,
$!1'*Q[UK5)y\"FO7$$\"$X)F,$!19mO^l](>#FO7$$\"$Y)F,$!1`%yf?MNg#FO7$$\"$
Z)F,$!1j?d\"zA_+$FO7$$\"$[)F,$!1AN))*RG;S$FO7$$\"$\\)F,$!1m,LOj#=z$FO7
$$\"$])F,$!1BW5J3\"\\<%FO7$$\"$^)F,$!1KY6aZ**\\XFO7$$\"$_)F,$!1q\\sL$4
i\"\\FO7$$\"$`)F,$!12rCzQqs_FO7$$\"$a)F,$!1\"yOr]X'=cFO7$$\"$b)F,$!1\"
4\\3()=K&fFO7$$\"$c)F,$!1FkI%*eiviFO7$$\"$d)F,$!1o[$*3b3&e'FO7$$\"$e)F
,$!1.JA%RL3)oFO7$$\"$f)F,$!163w@<7irFO7$$\"$g)F,$!1QDr-*=#GuFO7$$\"$h)
F,$!19ToQ$4%ywFO7$$\"$i)F,$!1'4Rf<$*>\"zFO7$$\"$j)F,$!1%GBH1'GG\")FO7$
$\"$k)F,$!1hb06*=mK)FO7$$\"$l)F,$!1\"oW(ewL1&)FO7$$\"$m)F,$!1j1fQI!om)
FO7$$\"$n)F,$!1/9tZ.R2))FO7$$\"$o)F,$!1?ZH@#*[F*)FO7$$\"$p)F,$!1&y;*3M
]E!*FO7$$\"$q)F,$!1)R)Ga0&Q5*FO7$$\"$r)F,$!1G4px>'*e\"*FO7$$\"$s)F,$!1
LU[hCG\">*FO7$$\"$t)F,$!1&[4&Q+F+#*FO7$$\"$u)F,$!12*pLy&R&=*FO7$$\"$v)
F,$!1%G`lgVh9*FO7$$\"$w)F,$!1u-O^+,#3*FO7$$\"$x)F,$!1+Jg$4/D**)FO7$$\"
$y)F,$!1h&RS%p9x))FO7$$\"$z)F,$!10y]`=ZN()FO7$$\"$!))F,$!1)fF2#R-n&)FO
7$$\"$\"))F,$!1lXt-*f8P)FO7$$\"$#))F,$!1!\\8z-[![\")FO7$$\"$$))F,$!1:%
)f6ym'*yFO7$$\"$%))F,$!1fk?u)4oh(FO7$$\"$&))F,$!1-M(=wv!3tFO7$$\"$'))F
,$!1-#f&px2qpFO7$$\"$())F,$!1r?fm(QCg'FO7$$\"$)))F,$!1(**>Y-#z/iFO7$$
\"$*))F,$!1r&Rz/\"ywdFO7$$\"$!*)F,$!1X1<1%f!=`FO7$$\"$\"*)F,$!1+&[#p0H
G[FO7$$\"$#*)F,$!1FGqWx92VFO7$$\"$$*)F,$!1)y%><PJaPFO7$$\"$%*)F,$!1qKG
!p![pJFO7$$\"$&*)F,$!1^=RI,N_DFO7$$\"$'*)F,$!15#[HhKE!>FO7$$\"$(*)F,$!
1-!p1nZ+A\"FO7$$\"$)*)F,$!15xgRkBV]F:7$$\"$**)F,$\"1Bh(emC![CF:7$$\"$+
*F,$\"10(\\c9&eF5FO7$$\"$,*F,$\"16pMf<5y<FO7$$\"$-*F,$\"1E,)*4*p]Y#FO7
$$\"$.*F,$\"1bTn&)*p14$FO7$$\"$/*F,$\"1)4sdFXql$FO7$$\"$0*F,$\"1]CC$\\
-j;%FO7$$\"$1*F,$\"1HEO!H70i%FO7$$\"$2*F,$\"1.Dwn(4<-&FO7$$\"$3*F,$\"1
yp!p(\\*=P&FO7$$\"$4*F,$\"1l$*4;M.tcFO7$$\"$5*F,$\"1lS3?l0FfFO7$$\"$6*
F,$\"1tpKV@'e8'FO7$$\"$7*F,$\"1D40P]J,jFO7$$\"$8*F,$\"1_E5?tCDkFO7$$\"
$9*F,$\"1:msV*e%4lFO7$$\"$:*F,$\"1I2K]\"=db'FO7$$\"$;*F,$\"1AsCE>wllFO
7$$\"$<*F,$\"1))=x[kHTlFO7$$\"$=*F,$\"1BO?Fv*R['FO7$$\"$>*F,$\"1*R0$Q5
^&R'FO7$$\"$?*F,$\"1Bq/cLXxiFO7$$\"$@*F,$\"1Z\"pdx698'FO7$$\"$A*F,$\"1
et#G$\\%*efFO7$$\"$B*F,$\"1%y$y:KehdFO7$$\"$C*F,$\"1JQ@u\"H3a&FO7$$\"$
D*F,$\"1\"*Q>@z:)H&FO7$$\"$E*F,$\"1jc`Iv,N]FO7$$\"$F*F,$\"1W<$)G%HGv%F
O7$$\"$G*F,$\"1LkP#y))HX%FO7$$\"$H*F,$\"17\\-z['o8%FO7$$\"$I*F,$\"1_J0
0:!e!QFO7$$\"$J*F,$\"1L13<t6hMFO7$$\"$K*F,$\"1Fe64i5/JFO7$$\"$L*F,$\"1
\")fyuw.OFFO7$$\"$M*F,$\"1L(4[;d\"eBFO7$$\"$N*F,$\"1V<xRkor>FO7$$\"$O*
F,$\"1$Qd#=R#yd\"FO7$$\"$P*F,$\"1))[S?]ux6FO7$$\"$Q*F,$\"1%=;$p]-ExF:7
$$\"$R*F,$\"1H(4p8o_j$F:7$$\"$S*F,$!1'G)e==OP[F/7$$\"$T*F,$!1$Hr];?,i%
F:7$$\"$U*F,$!1MQVl&HKw)F:7$$\"$V*F,$!1eG!Q/i-H\"FO7$$\"$W*F,$!1xe+,c!
Gq\"FO7$$\"$X*F,$!1)e1#f.&H6#FO7$$\"$Y*F,$!15/,`Jr>DFO7$$\"$Z*F,$!15e$
)>18AHFO7$$\"$[*F,$!1.8<.*e#>LFO7$$\"$\\*F,$!1[jxfL<5PFO7$$\"$]*F,$!1@
#y2FoR4%FO7$$\"$^*F,$!1behclvpWFO7$$\"$_*F,$!1qFy&\\pm$[FO7$$\"$`*F,$!
17<KZk&Q>&FO7$$\"$a*F,$!1(=Cqd%[SbFO7$$\"$b*F,$!1,()G(eQd(eFO7$$\"$c*F
,$!13;f]/#))>'FO7$$\"$d*F,$!1<k_Y\"\\*3lFO7$$\"$e*F,$!1)flBSg`!oFO7$$
\"$f*F,$!1H=5PkI(3(FO7$$\"$g*F,$!15Z#*3d0atFO7$$\"$h*F,$!1B+4mE*[g(FO7
$$\"$i*F,$!1s*Q6]<\"RyFO7$$\"$j*F,$!1)\\D%3f/c!)FO7$$\"$k*F,$!1\"))4\\
%)3]D)FO7$$\"$l*F,$!1#HyTH_`V)FO7$$\"$m*F,$!18pkLqV'f)FO7$$\"$n*F,$!1p
7\"\\SQwt)FO7$$\"$o*F,$!1m4?(3Y$e))FO7$$\"$p*F,$!1;3!R(Q'z&*)FO7$$\"$q
*F,$!1d(*4_%4f.*FO7$$\"$r*F,$!1V%H^=9;4*FO7$$\"$s*F,$!1$za!)*G_C\"*FO7
$$\"$t*F,$!1C%zgm$4M\"*FO7$$\"$u*F,$!1s*Geg(z>\"*FO7$$\"$v*F,$!1\"=w%p
'=63*FO7$$\"$w*F,$!1o<nTMb<!*FO7$$\"$x*F,$!1\\cCR4hG*)FO7$$\"$y*F,$!1y
Mk8C\"Q\"))FO7$$\"$z*F,$!1:R1c6ps')FO7$$\"$!)*F,$!1'Qi_I#z/&)FO7$$\"$
\")*F,$!1'y()zls'4$)FO7$$\"$#)*F,$!1V#=?[+p3)FO7$$\"$$)*F,$!1POwJ`0OyF
O7$$\"$%)*F,$!1_=SmyscvFO7$$\"$&)*F,$!1[n^q'>&[sFO7$$\"$')*F,$!1ug?xI/
6pFO7$$\"$()*F,$!1-zi$*4#Ra'FO7$$\"$))*F,$!18X&*GnyYhFO7$$\"$*)*F,$!1Z
NqCQG>dFO7$$\"$!**F,$!1*)\\T()e1h_FO7$$\"$\"**F,$!1QckBkzrZFO7$$\"$#**
F,$!1w.Dx'[6D%FO7$$\"$$**F,$!1)\\@*oa!))p$FO7$$\"$%**F,$!1@s&z.fW6$FO7
$$\"$&**F,$!1#*3B')3\"y\\#FO7$$\"$'**F,$!1BELC;d[=FO7$$\"$(**F,$!1sj&)
>3Ym6FO7$$\"$)**F,$!1*[I!y%o?^%F:7$$\"$***F,$\"1x'[#pD`uHF:7$$\"%+5F,$
\"1Cf'\\%Rxz5FO-%&STYLEG6#%%LINEG-%*THICKNESSG6#F7-%'COLOURG6&%$RGBG$
\")p:#R%!\")$\")`B)e)F]e^l$\")fqkdF]e^l-%%VIEWG6$;$!+++++]!#5$\"++++]5
F]e^l;$!+>/s!*RFhe^l$\"+8.wy()!#6-%+AXESLABELSG6$%\"tG%%x(t)G" 2 373 
373 373 2 0 1 0 2 6 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 18 "c) Triangular Wave" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 42 "The trian
gular wave function is defined by" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "triangular_wave := t -> abs(
2*t+1-4*floor(1/2*t+3/4))-1;  # Execute!" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%0triangular_waveG:6#%\"tG6\"6$%)operatorG%&arrowGF(,&-%$absG6#
,(9$\"\"#\"\"\"F3-%&floorG6#,&F1#F3F2#\"\"$\"\"%F3!\"%F3!\"\"F3F(F(" }
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "Here is t
he plot of the triangular wave function  for  " }{MPLTEXT 1 0 10 "t = \+
0 .. 6" }{TEXT -1 27 ",   as typically rendered:\n" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "plot( triang
ular_wave(t), t = 0 .. 6); # Execute!" }}{PARA 13 "" 1 "" {INLPLOT "6%
-%'CURVESG6$7]q7$\"\"!F(7$$\"1+++]i9Rl!#<$\"1,++]#HyI\"!#;7$$\"1+++]#H
yI\"F/$\"1++++&ech#F/7$$\"1++voozw=F/$\"1,+]PPf`PF/7$$\"1++]([kdW#F/$
\"1*****\\(*G:*[F/7$$\"1++D\"3Gc3$F/$\"1,+]ihDrhF/7$$\"1+++v;\\DPF/$\"
1+++]L)4X(F/7$$\"1++++nfpVF/$\"1++++M>R()F/7$$\"1+++D<q8]F/$\"1(*****
\\lfs**F/7$$\"1++DJauacF/$\"1)***\\P\"40p)F/7$$\"1++]P\"*y&H'F/$\"1)**
**\\s@%3uF/7$$\"1++]7(=,*oF/$\"1,++vDw>iF/7$$\"1++](G[W[(F/$\"1.++DM5J
]F/7$$\"1++]P@%)*4)F/$\"1,++DdJ+QF/7$$\"1++]()fB:()F/$\"1*****\\-G&pDF
/7$$\"1++](=x;N*F/$\"1*****\\iXmH\"F/7$$\"1++](Q=\"))**F/$\"1s*****\\A
jP#!#=7$$\"1++D^=Di5!#:$!1-++Dq.X7F/7$$\"1++vj=pD6Fip$!1*****\\FPQ^#F/
7$$\"1+]P9x%4>\"Fip$!1++](Ga*=QF/7$$\"1+++lN?c7Fip$!1-+++82C^F/7$$\"1+
+v`4o88Fip$!1,++v!>OF'F/7$$\"1++]U$e6P\"Fip$!1+++]o;BuF/7$$\"1++voU'eV
\"Fip$!1,++v`G<()F/7$$\"1+++&>q0]\"Fip$!1-+++hf))**F/7$$\"1+++5=al:Fip
$!1*******zj\"*o)F/7$$\"1+++DM^I;Fip$!1'******\\J(*Q(F/7$$\"1+++:c7$p
\"Fip$!1*******p([PhF/7$$\"1+++0ytb<Fip$!1.+++RC&)[F/7$$\"1+](=n&f7=Fi
p$!1****\\il3[PF/7$$\"1++vQNXp=Fip$!1'****\\AH4h#F/7$$\"1+](=/jq$>Fip$
!1)***\\i\"R(e7F/7$$\"1+++XDn/?Fip$\"1c++++4X$*Fep7$$\"1++]im%>1#Fip$
\"1,++]K$*Q7F/7$$\"1+++!y?#>@Fip$\"1,+++cT%Q#F/7$$\"1+]P%>We=#Fip$\"1+
+]()Q)or$F/7$$\"1++v3wY_AFip$\"1*****\\<_$\\]F/7$$\"1+]P>1W6BFip$\"1)*
**\\(Q7)GiF/7$$\"1+++IOTqBFip$\"1(******fs#3uF/7$$\"1+]Ppj6NCFip$\"1&*
**\\(QFBq)F/7$$\"1++v3\">)*\\#Fip$\"1.++v@Q'***F/7$$\"1++]<9VhDFip$\"1
(*****\\;Pr()F/7$$\"1++DEP/BEFip$\"1(****\\ZD\"RvF/7$$\"1+](oqHto#Fip$
\"1#***\\ieS`iF/7$$\"1++](o:;v#Fip$\"1'*****\\ion\\F/7$$\"1+]i&G]1\"GF
ip$\"1,+](G%*py$F/7$$\"1++v$)[opGFip$\"1'****\\K-jg#F/7$$\"1+]7t;OLHFi
p$\"1.+]PlwK8F/7$$\"1++]i%Qq*HFip$\"16,++]2BfFep7$$\"1+]i]2=jIFip$!1**
**\\7]hj7F/7$$\"1++vQIKHJFip$!1*****\\xgke#F/7$$\"1+++&4+p=$Fip$!1****
****=+QPF/7$$\"1++D^rZWKFip$!1)****\\-V&*)[F/7$$\"1+]P\\>m1LFip$!1++](
)*QK8'F/7$$\"1++]Zn%)oLFip$!1.++]\\$pP(F/7$$\"1++vG(*3LMFip$!1&****\\d
%zh')F/7$$\"1+++5FL(\\$Fip$!1'******>am%**F/7$$\"1++vL>=gNFip$!1*****
\\Khjz)F/7$$\"1++]d6.BOFip$!1/++]oPRvF/7$$\"1+]785%Qo$Fip$!1-+]P(zJK'F
/7$$\"1++vo3lWPFip$!1,++DE)p5&F/7$$\"1+]iX)p@\"QFip$!1(***\\(3.mv$F/7$
$\"1++]A))ozQFip$!1$*****\\NA1CF/7$$\"1++DEwNSRFip$!1,++vu%G>\"F/7$$\"
1+++Ik-,SFip$\"1d\"******fG0#Fep7$$\"1****\\FL!e1%Fip$\"1))****\\l1;8F
/7$$\"1+++D-eITFip$\"1-+++Xg6EF/7$$\"1**\\(=sx#*=%Fip$\"1*)**\\PWb&y$F
/7$$\"1++v=_(zC%Fip$\"1&****\\P/&f\\F/7$$\"1+](o3Z@J%Fip$\"1,+]P<%HC'F
/7$$\"1+++b*=jP%Fip$\"12+++\"zj_(F/7$$\"1+](=o*pOWFip$\"1****\\PO*Rt)F
/7$$\"1++v3/3(\\%Fip$\"1#****\\<3;%**F/7$$\"1***\\im&>gXFip$\"17++vm3'
z)F/7$$\"1++vB4JBYFip$\"1)****\\_\"yLvF/7$$\"1+]PCw,&o%Fip$\"1-+]7vk*H
'F/7$$\"1+++DVsYZFip$\"10+++N^l]F/7$$\"1+](=_D8\"[Fip$\"1'***\\i&*[tPF
/7$$\"1++v=n#f([Fip$\"11++DcY\"[#F/7$$\"1+]P\\`9Q\\Fip$\"1!***\\7I4P7F
/7$$\"1+++!)RO+]Fip$!1\"\\2+++'zs!#>7$$\"1,+D;:*R1&Fip$!18++D.$)z7F/7$
$\"1++]_!>w7&Fip$!1,++]5Q_DF/7$$\"1+]i?(>2>&Fip$!1/+]7WR9QF/7$$\"1++v)
Q?QD&Fip$!12++vxSw]F/7$$\"1+]P\\L!=J&Fip$!11+]()p1OiF/7$$\"1+++5jyp`Fi
p$!11+++is&R(F/7$$\"1++DE8COaFip$!10++Dl#[s)F/7$$\"1++]Ujp-bFip$!1(***
**\\J2Y**F/7$$\"1++D,X8ibFip$!1)****\\(*4tv)F/7$$\"1+++gEd@cFip$!1++++
oaovF/7$$\"1+]PMh%\\o&Fip$!1****\\7t2,jF/7$$\"1++v3'>$[dFip$!1(****\\#
ygL]F/7$$\"1+++5h(*3eFip$!11+++yZ?QF/7$$\"1++D6EjpeFip$!1(****\\xZtg#F
/7$$\"1,]i0j\"[$fFip$!1!***\\()Qn.8F/7$$\"\"'F(F(-%'COLOURG6&%$RGBG$\"
#5!\"\"F(F(-%+AXESLABELSG6$%\"tG%!G-%%VIEWG6$;F(Fdil%(DEFAULTG" 2 772 
286 286 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10030 10061 
10056 10074 0 0 0 20030 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 166 173 0 0 0 
0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 4 "" 0 "" {TEXT -1 64 "Calculate the Laplace Transform of th
e Triangular Wave Function." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 182 "The triangular wave is periodic. Its Laplace t
ransform can therefore be reduced to integrating over its period. That
 integral should be broken into three integrals over subintervals." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
163 "`laplace(triangular_wave(t),t,s)` = (int(2*t*exp(-s*t),t=0..1/2) \+
+ int((-2*(t-1/2)+1)*exp(-s*t),t=1/2..3/2) + int((2*(t-3/2)-1)*exp(-s*
t),t=3/2..2))/(1-exp(-2*s));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%@lap
lace(triangular_wave(t),t,s)G*&,.*(,&%\"sG!\"\"!\"#\"\"\"F,F)F+-%$expG
6#,$F)#F*\"\"#F,F,*$F)F+F2*(-F.6#,$F)#!\"$F2F,,&F)F,F2F,F,F)F+F,*(F-F,
,&F)F,F+F,F,F)F+F,*&-F.6#,$F)F+F,F)F+F+*(,&F)F*F2F,F,F)F+F5F,F,F,,&F,F
,F>F*F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 333 3 "Us
e" }{TEXT -1 2 "  " }{TEXT 332 6 "DEplot" }{TEXT -1 1 " " }{TEXT 335 
1 " " }{TEXT 334 51 "to plot the solution to the initial value problem
 f" }{TEXT -1 4 "or  " }{TEXT 349 1 " " }{XPPEDIT 350 1 "t = 0 .. 6" "
/%\"tG;\"\"!\"\"'" }{TEXT -1 2 " :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 329 10 "  \n       " }{XPPEDIT 331 1 "diff(diff(
x(t),t),t)+2*diff(x(t),t)+ x(t) = 5*triangular_wave(t)*``, `    `*x(0)
 = `0.0`*``, `   `*D(x)(0) = 0" "6%/,(-%%diffG6$-F&6$-%\"xG6#%\"tGF-F-
\"\"\"*&\"\"#F.-F&6$-F+6#F-F-F.F.-F+6#F-F.*(\"\"&F.-%0triangular_waveG
6#F-F.%!GF./*&%%~~~~GF.-F+6#\"\"!F.*&%$0.0GF.F<F./*&%$~~~GF.--%\"DG6#F
+6#FBF.FB" }{TEXT 330 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 177 "ode := diff(x(t),t$2) + 2*diff(x(t),t)+ \+
x(t) = 5*triangular_wave(t):  # Execute!\nDEplot(\{ode\}, [x(t)], t=0.
. 10, [[x(0)=0.0,D(x)(0)=0]], stepsize= 0.01, linecolor = aquamarine);
" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6%7ein7$\"\"!F(7$$\"\"\"!\"
#$\"1KLLLLLe;!#@7$$\"\"#F,$\"1Dc\"Hsu+K\"!#?7$$\"\"$F,$\"13]M&='4LWF57
$$\"\"%F,$\"1(>I`6'eX5!#>7$$\"\"&F,$\"1tc.k9-K?F@7$$\"\"'F,$\"1)H'Hbp
\"R\\$F@7$$\"\"(F,$\"1M#e(>*=2_&F@7$$\"\")F,$\"1\"4JIgY+?)F@7$$\"\"*F,
$\"1T\"ep'>xh6!#=7$$\"#5F,$\"1_\"=S`yde\"FZ7$$\"#6F,$\"15$[n^a-5#FZ7$$
\"#7F,$\"1CIUX\"eKr#FZ7$$\"#8F,$\"1Ws&=LyEV$FZ7$$\"#9F,$\"1/&)3TsBmUFZ
7$$\"#:F,$\"1T^kGG\\@_FZ7$$\"#;F,$\"1T4$QMTeI'FZ7$$\"#<F,$\"1r7X*z>l_(
FZ7$$\"#=F,$\"1.2S3%31*))FZ7$$\"#>F,$\"13Fv)H.0/\"!#<7$$\"#?F,$\"1)>=H
tcw?\"Fgq7$$\"#@F,$\"1ii3aN=\"R\"Fgq7$$\"#AF,$\"1[XLN9t\"f\"Fgq7$$\"#B
F,$\"1!pq(RN$*4=Fgq7$$\"#CF,$\"1S@;X(3k/#Fgq7$$\"#DF,$\"1jB`l=w,BFgq7$
$\"#EF,$\"1D:wpQewDFgq7$$\"#FF,$\"1W$Hs4_9(GFgq7$$\"#GF,$\"1Lt`q/$p=$F
gq7$$\"#HF,$\"1\">Z`qpN_$Fgq7$$\"#IF,$\"1\"prt^2>)QFgq7$$\"#JF,$\"1FRb
E)oCE%Fgq7$$\"#KF,$\"19/ZefwlYFgq7$$\"#LF,$\"1UI*H%))H#4&Fgq7$$\"#MF,$
\"1;XC5_bUbFgq7$$\"#NF,$\"1b9)Qy5q,'Fgq7$$\"#OF,$\"1c*Q<ZHh^'Fgq7$$\"#
PF,$\"1\\*pQbj./(Fgq7$$\"#QF,$\"1qB,oQ:!f(Fgq7$$\"#RF,$\"1vm^#**Hf;)Fg
q7$$\"#SF,$\"11fwE/6o()Fgq7$$\"#TF,$\"1h+7pF5(R*Fgq7$$\"#UF,$\"1B;C*QI
`+\"!#;7$$\"#VF,$\"1Wbq6+rt5F[y7$$\"#WF,$\"1$pq\"Qn)[9\"F[y7$$\"#XF,$
\"15g;Tr*)=7F[y7$$\"#YF,$\"13a[)ywdH\"F[y7$$\"#ZF,$\"1P9cf-cv8F[y7$$\"
#[F,$\"1*e7;;\"Ge9F[y7$$\"#\\F,$\"1:rcX@(Ra\"F[y7$$\"#]F,$\"14iw@\\mK;
F[y7$$\"#^F,$\"10Fy3rNC<F[y7$$\"#_F,$\"1],3nS\"*==F[y7$$\"#`F,$\"1:+*G
qqh\">F[y7$$\"#aF,$\"1gcBC\\'f,#F[y7$$\"#bF,$\"1B4a(fP\"=@F[y7$$\"#cF,
$\"16]![]KDA#F[y7$$\"#dF,$\"1InL,j**GBF[y7$$\"#eF,$\"1h6/u%ytV#F[y7$$
\"#fF,$\"1i>D+8`ZDF[y7$$\"#gF,$\"1'e-r!)4$fEF[y7$$\"#hF,$\"1`(H9trDx#F
[y7$$\"#iF,$\"13E?![xr)GF[y7$$\"#jF,$\"1y5Z\"4!*H+$F[y7$$\"#kF,$\"15q#
e>v)>JF[y7$$\"#lF,$\"1c<Py4qPKF[y7$$\"#mF,$\"1MR=T\"QjN$F[y7$$\"#nF,$
\"1$=\"Gm)fcZ$F[y7$$\"#oF,$\"1,)p!z<a&f$F[y7$$\"#pF,$\"14iF7>'er$F[y7$
$\"#qF,$\"1'Ha.n+l$QF[y7$$\"#rF,$\"1:FO%zSt&RF[y7$$\"#sF,$\"1EjIFtEySF
[y7$$\"#tF,$\"1@g$*zv;*>%F[y7$$\"#uF,$\"1J7+(4J*>VF[y7$$\"#vF,$\"1.&\\
Ri\\/W%F[y7$$\"#wF,$\"1)enS2<1c%F[y7$$\"#xF,$\"1]&eg\\H.o%F[y7$$\"#yF,
$\"1p%\\?/&[*z%F[y7$$\"#zF,$\"1!RCg$R)z\"\\F[y7$$\"#!)F,$\"15snU%Gd.&F
[y7$$\"#\")F,$\"1w#zm$Gi_^F[y7$$\"##)F,$\"1JlNsLdo_F[y7$$\"#$)F,$\"1&4
rPD)[$Q&F[y7$$\"#%)F,$\"1GA?0wF(\\&F[y7$$\"#&)F,$\"1/<-UM&)4cF[y7$$\"#
')F,$\"1g'e>kH6s&F[y7$$\"#()F,$\"1a!\\n\">-JeF[y7$$\"#))F,$\"1C\\;%yZ%
RfF[y7$$\"#*)F,$\"1)p=/aEj/'F[y7$$\"#!*F,$\"1ey$HBz::'F[y7$$\"#\"*F,$
\"1C`]L'G^D'F[y7$$\"##*F,$\"1l4w6#**oN'F[y7$$\"#$*F,$\"1I(f!4r\"oX'F[y
7$$\"#%*F,$\"1/>o7,\"[b'F[y7$$\"#&*F,$\"1y5RIw!3l'F[y7$$\"#'*F,$\"1xaL
l1uWnF[y7$$\"#(*F,$\"17$)G\"zTl$oF[y7$$\"#)*F,$\"18HAG^9EpF[y7$$\"#**F
,$\"1;%=#=j[8qF[y7$$\"$+\"F,$\"1i=p,D])4(F[y7$$\"$,\"F,$\"1!e_RHK6=(F[
y7$$\"$-\"F,$\"1/[2idJhsF[y7$$\"$.\"F,$\"13X3-W**QtF[y7$$\"$/\"F,$\"1-
lX;669uF[y7$$\"$0\"F,$\"1ly\">>5m[(F[y7$$\"$1\"F,$\"1]QbxsVcvF[y7$$\"$
2\"F,$\"1UC@j$RNi(F[y7$$\"$3\"F,$\"1(y.#eZ'yo(F[y7$$\"$4\"F,$\"1x2HqIO
\\xF[y7$$\"$5\"F,$\"1xq'\\=&)z!yF[y7$$\"$6\"F,$\"1!**=]C$ojyF[y7$$\"$7
\"F,$\"1LvOI1T;zF[y7$$\"$8\"F,$\"1(=(=Q>7mzF[y7$$\"$9\"F,$\"16yHjHx7!)
F[y7$$\"$:\"F,$\"1Ni#)y1Kc!)F[y7$$\"$;\"F,$\"1UT8<Ks'4)F[y7$$\"$<\"F,$
\"13)35&)RR8)F[y7$$\"$=\"F,$\"1)R8^(4$z;)F[y7$$\"$>\"F,$\"1$\\$p(3e')>
)F[y7$$\"$?\"F,$\"1#fODx$3E#)F[y7$$\"$@\"F,$\"1i8=\"or,D)F[y7$$\"$A\"F
,$\"1eMP:l)3F)F[y7$$\"$B\"F,$\"1mZw4S>)G)F[y7$$\"$C\"F,$\"1`H&[\"41-$)
F[y7$$\"$D\"F,$\"1t#e,)\\X7$)F[y7$$\"$E\"F,$\"1rXjP\\M>$)F[y7$$\"$F\"F
,$\"1@:J&[+FK)F[y7$$\"$G\"F,$\"12^;rA\\A$)F[y7$$\"$H\"F,$\"1aM@x=p=$)F
[y7$$\"$I\"F,$\"1$4NQ!=F6$)F[y7$$\"$J\"F,$\"1IoIaa?+$)F[y7$$\"$K\"F,$
\"1(Re&>rY&G)F[y7$$\"$L\"F,$\"1)3TJ'>.n#)F[y7$$\"$M\"F,$\"1_wS1g([C)F[
y7$$\"$N\"F,$\"112!R6w*=#)F[y7$$\"$O\"F,$\"11q%*y*4$*=)F[y7$$\"$P\"F,$
\"17\\X4h&e:)F[y7$$\"$Q\"F,$\"1IC\"R\"Qf=\")F[y7$$\"$R\"F,$\"1bKe(=.v2
)F[y7$$\"$S\"F,$\"1^#)*))4lD.)F[y7$$\"$T\"F,$\"1c)Rg<hP)zF[y7$$\"$U\"F
,$\"12pr$zt5$zF[y7$$\"$V\"F,$\"1Ku7gg[uyF[y7$$\"$W\"F,$\"1zp5/=)R\"yF[
y7$$\"$X\"F,$\"1t+Yiba\\xF[y7$$\"$Y\"F,$\"1VCZnD;\"o(F[y7$$\"$Z\"F,$\"
1d;gM(=)3wF[y7$$\"$[\"F,$\"1mQM]1]KvF[y7$$\"$\\\"F,$\"1kVFgb>_uF[y7$$
\"$]\"F,$\"13(fsN\"*yO(F[y7$$\"$^\"F,$\"1Pe]O(4'zsF[y7$$\"$_\"F,$\"1)*
yrlV](=(F[y7$$\"$`\"F,$\"1+Y*\\3f<4(F[y7$$\"$a\"F,$\"1@!HXXaD*pF[y7$$
\"$b\"F,$\"1)ey;!y1!*oF[y7$$\"$c\"F,$\"1rIUnKZ%y'F[y7$$\"$d\"F,$\"1@\"
=A&=%fn'F[y7$$\"$e\"F,$\"1v<Dh9kklF[y7$$\"$f\"F,$\"1p76\\pt]kF[y7$$\"$
g\"F,$\"1Eu'Q;!RMjF[y7$$\"$h\"F,$\"1nPe!**fd@'F[y7$$\"$i\"F,$\"1RuD%R-
]4'F[y7$$\"$j\"F,$\"1u*)>i/FsfF[y7$$\"$k\"F,$\"1]x&eW9x%eF[y7$$\"$l\"F
,$\"1d+5-=[@dF[y7$$\"$m\"F,$\"1ak%RB<Pf&F[y7$$\"$n\"F,$\"1G^xIFckaF[y7
$$\"$o\"F,$\"1Vy*zgdTL&F[y7$$\"$p\"F,$\"1()\\@Y&QE?&F[y7$$\"$q\"F,$\"1
gh&)H'R,2&F[y7$$\"$r\"F,$\"1eEJ&Q#zO\\F[y7$$\"$s\"F,$\"1b\"o&=es-[F[y7
$$\"$t\"F,$\"1tPL_k1oYF[y7$$\"$u\"F,$\"1*o$pi$QH`%F[y7$$\"$v\"F,$\"1Wt
E:KY(R%F[y7$$\"$w\"F,$\"1NU*3Ig<E%F[y7$$\"$x\"F,$\"1Gs%3dYf7%F[y7$$\"$
y\"F,$\"1A-erm8!*RF[y7$$\"$z\"F,$\"1gf,zHWaQF[y7$$\"$!=F,$\"1'ozBjv*=P
F[y7$$\"$\"=F,$\"1/VenD%Qe$F[y7$$\"$#=F,$\"1+E<]&\\\"\\MF[y7$$\"$$=F,$
\"1[?#y?+]J$F[y7$$\"$%=F,$\"1PwTig\\\"=$F[y7$$\"$&=F,$\"1*4)phlt[IF[y7
$$\"$'=F,$\"1a3[5\">o\"HF[y7$$\"$(=F,$\"1?4Z,\"Rey#F[y7$$\"$)=F,$\"1x*
ec%**)el#F[y7$$\"$*=F,$\"1+PJ-J1FDF[y7$$\"$!>F,$\"1iMd3\"[%*R#F[y7$$\"
$\">F,$\"1aBk3E8tAF[y7$$\"$#>F,$\"1:bf#Q-#[@F[y7$$\"$$>F,$\"1K')zu8uC?
F[y7$$\"$%>F,$\"1Uk%>sJG!>F[y7$$\"$&>F,$\"11]s!y`Dy\"F[y7$$\"$'>F,$\"1
jC5bh)Rm\"F[y7$$\"$(>F,$\"1@HDBd?Z:F[y7$$\"$)>F,$\"1$3=Tm(GK9F[y7$$\"$
*>F,$\"1^6h$[0$>8F[y7$$\"$+#F,$\"1)\\n//J$37F[y7$$\"$,#F,$\"1VlurXV*4
\"F[y7$$\"$-#F,$\"1m>*)zr%o#**Fgq7$$\"$.#F,$\"1\"o_.[&[\")))Fgq7$$\"$/
#F,$\"1m(\\]$e\"*eyFgq7$$\"$0#F,$\"1b)*[H#y(foFgq7$$\"$1#F,$\"1%=4nl(p
%)eFgq7$$\"$2#F,$\"1%)pE_VGM\\Fgq7$$\"$3#F,$\"1>d/ES84SFgq7$$\"$4#F,$
\"1A0!44G)4JFgq7$$\"$5#F,$\"1qb>))Q$pB#Fgq7$$\"$6#F,$\"1_'o-\"\\+\"R\"
Fgq7$$\"$7#F,$\"1I&3')>5es&FZ7$$\"$8#F,$!1bX[ML6y@FZ7$$\"$9#F,$!1-@l(*
*)e'z*FZ7$$\"$:#F,$!1%oB$=9Y7<Fgq7$$\"$;#F,$!1JO\")49t:CFgq7$$\"$<#F,$
!19MbrR**)3$Fgq7$$\"$=#F,$!1fXZvlyJPFgq7$$\"$>#F,$!1;1))o)eOM%Fgq7$$\"
$?#F,$!11l%zZsT#\\Fgq7$$\"$@#F,$!15A#R\"3!HZ&Fgq7$$\"$A#F,$!1<x+#))G%*
)fFgq7$$\"$B#F,$!1SS'G4`LZ'Fgq7$$\"$C#F,$!1;zsw5GCpFgq7$$\"$D#F,$!1af4
+:$=M(Fgq7$$\"$E#F,$!1!\\Y\\)QjDxFgq7$$\"$F#F,$!1EgYI%G`2)Fgq7$$\"$G#F
,$!1b'[s$ec!R)Fgq7$$\"$H#F,$!1!3PR825n)Fgq7$$\"$I#F,$!1BNF1NK;*)Fgq7$$
\"$J#F,$!1W.`Gh>E\"*Fgq7$$\"$K#F,$!1j$*G(*fJ+$*Fgq7$$\"$L#F,$!1W.anPQQ
%*Fgq7$$\"$M#F,$!15&o5f4,a*Fgq7$$\"$N#F,$!1A@5dH@0'*Fgq7$$\"$O#F,$!1e3
>NDUL'*Fgq7$$\"$P#F,$!1,mG?gZC'*Fgq7$$\"$Q#F,$!1/#)**z*>\"y&*Fgq7$$\"$
R#F,$!1'Q#*Rq4T\\*Fgq7$$\"$S#F,$!1%=8b04AP*Fgq7$$\"$T#F,$!19E*\\K!>7#*
Fgq7$$\"$U#F,$!10es&3MQ,*Fgq7$$\"$V#F,$!1`Pe^!Hpx)Fgq7$$\"$W#F,$!1rxtO
>F,&)Fgq7$$\"$X#F,$!1%HptJnm=)Fgq7$$\"$Y#F,$!1v)R`\\FH$yFgq7$$\"$Z#F,$
!1?bzjB()RuFgq7$$\"$[#F,$!1$)4ou#Ht+(Fgq7$$\"$\\#F,$!1>'Q\"3H8NlFgq7$$
\"$]#F,$!1*>oP9DJ-'Fgq7$$\"$^#F,$!1(R*Q+m[raFgq7$$\"$_#F,$!1VI1F$=<)[F
gq7$$\"$`#F,$!1msf\"zBcD%Fgq7$$\"$a#F,$!1SdDZV(\\f$Fgq7$$\"$b#F,$!1IVH
$p4:!HFgq7$$\"$c#F,$!1t<^H$Qp<#Fgq7$$\"$d#F,$!1w#*)[+QHU\"Fgq7$$\"$e#F
,$!1#H-Rgh:T'FZ7$$\"$f#F,$\"1hm1Sj*ym\"FZ7$$\"$g#F,$\"1!*\\rzC6$***FZ7
$$\"$h#F,$\"1`F6l&\\[&=Fgq7$$\"$i#F,$\"1X[#G1u=t#Fgq7$$\"$j#F,$\"17Mi(
R#))GOFgq7$$\"$k#F,$\"17D!f***RWXFgq7$$\"$l#F,$\"1x]/]'zpZ&Fgq7$$\"$m#
F,$\"1iC#)>6?DkFgq7$$\"$n#F,$\"1?f,R2n(Q(Fgq7$$\"$o#F,$\"1*\\(>F5-j$)F
gq7$$\"$p#F,$\"1`Yg1.\"*\\$*Fgq7$$\"$q#F,$\"1iZSKAqM5F[y7$$\"$r#F,$\"1
O&yxe1`8\"F[y7$$\"$s#F,$\"1i5$\\WxmB\"F[y7$$\"$t#F,$\"1L\")*Re!pQ8F[y7
$$\"$u#F,$\"1SSC\"=C7W\"F[y7$$\"$v#F,$\"1bint(eTa\"F[y7$$\"$w#F,$\"1gr
7CsPZ;F[y7$$\"$x#F,$\"1ooz'ok2v\"F[y7$$\"$y#F,$\"1$[^Kd3U&=F[y7$$\"$z#
F,$\"1:7()=&)fd>F[y7$$\"$!GF,$\"1&fU(\\j#31#F[y7$$\"$\"GF,$\"1\"[*)*\\
gyj@F[y7$$\"$#GF,$\"1%>P&HPPmAF[y7$$\"$$GF,$\"1+YI#f([oBF[y7$$\"$%GF,$
\"13'=[!z-qCF[y7$$\"$&GF,$\"1XgClp*3d#F[y7$$\"$'GF,$\"1$[PG2**4n#F[y7$
$\"$(GF,$\"16\"yx\\S-x#F[y7$$\"$)GF,$\"1c.W^%H&oGF[y7$$\"$*GF,$\"1hM.d
gxlHF[y7$$\"$!HF,$\"1a[k?B*=1$F[y7$$\"$\"HF,$\"1='oE5#zcJF[y7$$\"$#HF,
$\"1Kgh*3\"R]KF[y7$$\"$$HF,$\"1.OImngULF[y7$$\"$%HF,$\"1qOT)QeLV$F[y7$
$\"$&HF,$\"19JUbpcANF[y7$$\"$'HF,$\"1z`*Q=b,h$F[y7$$\"$(HF,$\"1K98\"[Z
gp$F[y7$$\"$)HF,$\"1\"*\\<>*p,y$F[y7$$\"$*HF,$\"1]x;4-XiQF[y7$$\"$+$F,
$\"1P+0ww\"G%RF[y7$$\"$,$F,$\"1TFgLK?@SF[y7$$\"$-$F,$\"1zg#)f$Rv4%F[y7
$$\"$.$F,$\"1P5ls+wrTF[y7$$\"$/$F,$\"1P$zf!4!QC%F[y7$$\"$0$F,$\"1)oZg)
))f8VF[y7$$\"$1$F,$\"1vB63D4\"Q%F[y7$$\"$2$F,$\"1>+X8<AYWF[y7$$\"$3$F,
$\"1Y1nmy#*3XF[y7$$\"$4$F,$\"1:!RLt`\"pXF[y7$$\"$5$F,$\"1C/!zXVoi%F[y7
$$\"$6$F,$\"1Vq!>aU>o%F[y7$$\"$7$F,$\"1)3TD#yRMZF[y7$$\"$8$F,$\"1u4V^u
:%y%F[y7$$\"$9$F,$\"1`ovt3<J[F[y7$$\"$:$F,$\"1q<k2))Qv[F[y7$$\"$;$F,$
\"1?\\#QAjn\"\\F[y7$$\"$<$F,$\"1SLhDtCb\\F[y7$$\"$=$F,$\"1&f3\"Hbz!*\\
F[y7$$\"$>$F,$\"1!*[qVMOB]F[y7$$\"$?$F,$\"1Q_&G&y!H0&F[y7$$\"$@$F,$\"1
5A5&p'Qz]F[y7$$\"$A$F,$\"1t*p`/fF5&F[y7$$\"$B$F,$\"1LU^'4&)H7&F[y7$$\"
$C$F,$\"1ho7Th-S^F[y7$$\"$D$F,$\"1,>f`X%Q:&F[y7$$\"$E$F,$\"1;)*QsPSk^F
[y7$$\"$F$F,$\"1lnk#Go;<&F[y7$$\"$G$F,$\"11e#*)f.c<&F[y7$$\"$H$F,$\"1X
pD[i<w^F[y7$$\"$I$F,$\"1fHS`PNt^F[y7$$\"$J$F,$\"11!ejh/r;&F[y7$$\"$K$F
,$\"1Dg2-$)Rd^F[y7$$\"$L$F,$\"11gUA_?W^F[y7$$\"$M$F,$\"197P?n\\F^F[y7$
$\"$N$F,$\"1%\\pV0Xs5&F[y7$$\"$O$F,$\"1W=*HQBM3&F[y7$$\"$P$F,$\"1Ikv\\
d+c]F[y7$$\"$Q$F,$\"18`<oq'\\-&F[y7$$\"$R$F,$\"126,2JG!*\\F[y7$$\"$S$F
,$\"1M4uv/$>&\\F[y7$$\"$T$F,$\"1U\\A5m))4\\F[y7$$\"$U$F,$\"1Dode(HT'[F
[y7$$\"$V$F,$\"1kOBn*QY\"[F[y7$$\"$W$F,$\"1<EAnSRhZF[y7$$\"$X$F,$\"16=
igcP/ZF[y7$$\"$Y$F,$\"1[I@2^cVYF[y7$$\"$Z$F,$\"1CPK6X%*yXF[y7$$\"$[$F,
$\"1Zc&)3n\\5XF[y7$$\"$\\$F,$\"1.#)\\a_?QWF[y7$$\"$]$F,$\"1HO74W0iVF[y
7$$\"$^$F,$\"1_&GSHi?G%F[y7$$\"$_$F,$\"14vHg!z$)>%F[y7$$\"$`$F,$\"1'36
z3&=6TF[y7$$\"$a$F,$\"1W/nKvl?SF[y7$$\"$b$F,$\"1N4]s.(p#RF[y7$$\"$c$F,
$\"1\"R`JX%HIQF[y7$$\"$d$F,$\"1k1JLvzIPF[y7$$\"$e$F,$\"1Gl5HVkGOF[y7$$
\"$f$F,$\"1)Qk!el*R_$F[y7$$\"$g$F,$\"1:FY#)H,<MF[y7$$\"$h$F,$\"1([M@X
\\yI$F[y7$$\"$i$F,$\"1ttqY*em>$F[y7$$\"$j$F,$\"1&z\"H<;f$3$F[y7$$\"$k$
F,$\"1KMiF[zoHF[y7$$\"$l$F,$\"1Jrm%>8C&GF[y7$$\"$m$F,$\"1K')oG')eMFF[y
7$$\"$n$F,$\"1D4!GPgah#F[y7$$\"$o$F,$\"1r9*>/l^\\#F[y7$$\"$p$F,$\"1hpj
hm$QP#F[y7$$\"$q$F,$\"1\"p6bq1;D#F[y7$$\"$r$F,$\"1sgHLTgG@F[y7$$\"$s$F
,$\"1+7fFa&\\+#F[y7$$\"$t$F,$\"1neWIYy!)=F[y7$$\"$u$F,$\"1'y,%zL@c<F[y
7$$\"$v$F,$\"1kK1V4OJ;F[y7$$\"$w$F,$\"1ip>cUM1:F[y7$$\"$x$F,$\"1#ynV&z
F\"Q\"F[y7$$\"$y$F,$\"1Zl63WFc7F[y7$$\"$z$F,$\"1$4&ocPWJ6F[y7$$\"$!QF,
$\"1)e%HTR*o+\"F[y7$$\"$\"QF,$\"1MQ#)ztIF))Fgq7$$\"$#QF,$\"12:.+zd!f(F
gq7$$\"$$QF,$\"1#e%*zRm(fjFgq7$$\"$%QF,$\"11TZ0w'e8&Fgq7$$\"$&QF,$\"1W
Q#G(e&)>RFgq7$$\"$'QF,$\"1tM5wao7FFgq7$$\"$(QF,$\"1Kn4?4H::Fgq7$$\"$)Q
F,$\"1-9)GPseG$FZ7$$\"$*QF,$!1Sz`rrHl%)FZ7$$\"$!RF,$!1CXLuH=4?Fgq7$$\"
$\"RF,$!14e[kT^eJFgq7$$\"$#RF,$!1F8mLKo$H%Fgq7$$\"$$RF,$!1?*HU;oQT&Fgq
7$$\"$%RF,$!1_l6*pk#=lFgq7$$\"$&RF,$!1Tkupg31wFgq7$$\"$'RF,$!1POkFFcw'
)Fgq7$$\"$(RF,$!1a0kz?%*G(*Fgq7$$\"$)RF,$!1\"4lE#)[i2\"F[y7$$\"$*RF,$!
1fjfq\"[w<\"F[y7$$\"$+%F,$!136qB>-x7F[y7$$\"$,%F,$!1'3dqM,VP\"F[y7$$\"
$-%F,$!1'\\NTF>%p9F[y7$$\"$.%F,$!1;YR#35Bc\"F[y7$$\"$/%F,$!1!y.#p'4Hl
\"F[y7$$\"$0%F,$!1;P4Ga:T<F[y7$$\"$1%F,$!1G*G`A')p#=F[y7$$\"$2%F,$!1I#
)zwBM5>F[y7$$\"$3%F,$!1(H>_il6*>F[y7$$\"$4%F,$!1BMl<\"*Rp?F[y7$$\"$5%F
,$!1#RELQ()\\9#F[y7$$\"$6%F,$!1J<v6j(y@#F[y7$$\"$7%F,$!1KC:JJ,)G#F[y7$
$\"$8%F,$!1$[xrQY`N#F[y7$$\"$9%F,$!1Q$4>#f#)>CF[y7$$\"$:%F,$!1`(eJ&GS
\"[#F[y7$$\"$;%F,$!1nK/a&H+a#F[y7$$\"$<%F,$!1Se%Gjfcf#F[y7$$\"$=%F,$!1
i*\\J\"zC[EF[y7$$\"$>%F,$!1HyC9/v(p#F[y7$$\"$?%F,$!1]!==LCTu#F[y7$$\"$
@%F,$!1V&p)=!Gty#F[y7$$\"$A%F,$!1J\"[p'4KFGF[y7$$\"$B%F,$!1&e-wyjS'GF[
y7$$\"$C%F,$!1Yn5%>=v*GF[y7$$\"$D%F,$!1WXV$)pkFHF[y7$$\"$E%F,$!1#f%[=S
TaHF[y7$$\"$F%F,$!1a7b5UyxHF[y7$$\"$G%F,$!11!R?]Bx*HF[y7$$\"$H%F,$!1xp
T\\))>9IF[y7$$\"$I%F,$!1T1T1#yr-$F[y7$$\"$J%F,$!1tvU20jOIF[y7$$\"$K%F,
$!1BV@^c_UIF[y7$$\"$L%F,$!1=9u%[M[/$F[y7$$\"$M%F,$!1'f8tyGN/$F[y7$$\"$
N%F,$!1fB!\\D\"eQIF[y7$$\"$O%F,$!17!)p%[l*HIF[y7$$\"$P%F,$!1t$y)ffl<IF
[y7$$\"$Q%F,$!1^8fM!G;+$F[y7$$\"$R%F,$!1n'[\">z&=)HF[y7$$\"$S%F,$!1#*z
UlEKeHF[y7$$\"$T%F,$!1I3[_,+JHF[y7$$\"$U%F,$!1oMMs!p)**GF[y7$$\"$V%F,$
!1>%[g\"*3\\'GF[y7$$\"$W%F,$!1PP$)f**4EGF[y7$$\"$X%F,$!1\"pZ:DBMy#F[y7
$$\"$Y%F,$!1/iC(fgot#F[y7$$\"$Z%F,$!1i1)za%R'o#F[y7$$\"$[%F,$!1^Nx'Q3?
j#F[y7$$\"$\\%F,$!1e&zd6'otDF[y7$$\"$]%F,$!1['HOW79^#F[y7$$\"$^%F,$!1:
DiRf?XCF[y7$$\"$_%F,$!17*QI?<_P#F[y7$$\"$`%F,$!1\\:?iqi,BF[y7$$\"$a%F,
$!11CN@JhCAF[y7$$\"$b%F,$!15*4p!)\\V9#F[y7$$\"$c%F,$!1g[78%351#F[y7$$
\"$d%F,$!1fB9Zrvu>F[y7$$\"$e%F,$!1brZt6w&)=F[y7$$\"$f%F,$!1d%4zl#=%z\"
F[y7$$\"$g%F,$!1S&33\"3=+<F[y7$$\"$h%F,$!1I5*)H>\"Rg\"F[y7$$\"$i%F,$!1
a4UU%Hb]\"F[y7$$\"$j%F,$!1`#eo%R=09F[y7$$\"$k%F,$!1yF'RDBII\"F[y7$$\"$
l%F,$!1/.OFC>*>\"F[y7$$\"$m%F,$!1JtdBQ$Q4\"F[y7$$\"$n%F,$!1S0^:8(3()*F
gq7$$\"$o%F,$!1k>@;T*3z)Fgq7$$\"$p%F,$!1\\$*4S8v*p(Fgq7$$\"$q%F,$!1'yj
z;i()f'Fgq7$$\"$r%F,$!1*f;Rj?#*[&Fgq7$$\"$s%F,$!1Y0@&*fRsVFgq7$$\"$t%F
,$!12/>(4L&\\KFgq7$$\"$u%F,$!1EZVLF&=7#Fgq7$$\"$v%F,$!1`HY6+_0**FZ7$$
\"$w%F,$\"11DZ\"[`>V\"FZ7$$\"$x%F,$\"1Pk_i&Q#y7Fgq7$$\"$y%F,$\"1U%)=[&
\\MT#Fgq7$$\"$z%F,$\"1oOZKDsZNFgq7$$\"$![F,$\"1_hNJP(*zYFgq7$$\"$\"[F,
$\"1n)R8-T\"4eFgq7$$\"$#[F,$\"1P\"3dh$=MpFgq7$$\"$$[F,$\"1H02X<3a!)Fgq
7$$\"$%[F,$\"1]d:Uj$y;*Fgq7$$\"$&[F,$\"1>&zI(oWF5F[y7$$\"$'[F,$\"1*o/>
.-t8\"F[y7$$\"$([F,$\"1%pS'H_DY7F[y7$$\"$)[F,$\"17f]LX@a8F[y7$$\"$*[F,
$\"1>5^H**3h9F[y7$$\"$!\\F,$\"1'GwLH$zm:F[y7$$\"$\"\\F,$\"1\"fP=OQ7n\"
F[y7$$\"$#\\F,$\"1ukL/2Mu<F[y7$$\"$$\\F,$\"10#*3&p<g(=F[y7$$\"$%\\F,$
\"1-.`&[)=w>F[y7$$\"$&\\F,$\"1*oDr(Rxu?F[y7$$\"$'\\F,$\"1I5b%z'pr@F[y7
$$\"$(\\F,$\"1`/Bf7)oE#F[y7$$\"$)\\F,$\"1?8BjLDgBF[y7$$\"$*\\F,$\"1Z/^
V2u^CF[y7$$\"$+&F,$\"1Pv]cEFTDF[y7$$\"$,&F,$\"1]73`*z(GEF[y7$$\"$-&F,$
\"1oPy`]>9FF[y7$$\"$.&F,$\"1_&pW#>X(z#F[y7$$\"$/&F,$\"1JSB_g[yGF[y7$$
\"$0&F,$\"1>#y;UMs&HF[y7$$\"$1&F,$\"1w\\\\\"\\NO.$F[y7$$\"$2&F,$\"1\"*
HPr\"Hw5$F[y7$$\"$3&F,$\"10W@*zc\"zJF[y7$$\"$4&F,$\"1@Am=6;[KF[y7$$\"$
5&F,$\"1^M$pD'e9LF[y7$$\"$6&F,$\"1hU&Hqx$yLF[y7$$\"$7&F,$\"12Kz&G#[RMF
[y7$$\"$8&F,$\"18*)Q`\"[y\\$F[y7$$\"$9&F,$\"1=$o:vCMb$F[y7$$\"$:&F,$\"
1P>N.G;1OF[y7$$\"$;&F,$\"1=Ca)G9gl$F[y7$$\"$<&F,$\"1,HfBC$Hq$F[y7$$\"$
=&F,$\"1;:vT;(ou$F[y7$$\"$>&F,$\"19'yMd(y(y$F[y7$$\"$?&F,$\"1*>Lr-Pc#Q
F[y7$$\"$@&F,$\"1A_#*pzPgQF[y7$$\"$A&F,$\"1p-84&p>*QF[y7$$\"$B&F,$\"1s
Lct=P?RF[y7$$\"$C&F,$\"12'3`RYb%RF[y7$$\"$D&F,$\"1p7q\"\\bu'RF[y7$$\"$
E&F,$\"1]$fvkig)RF[y7$$\"$F&F,$\"1\"=hwRK8+%F[y7$$\"$G&F,$\"1*3m%4.B8S
F[y7$$\"$H&F,$\"1g\\2mHs@SF[y7$$\"$I&F,$\"1mwU\\zxESF[y7$$\"$J&F,$\"1&
HMP#QOGSF[y7$$\"$K&F,$\"1Ds8>,XESF[y7$$\"$L&F,$\"1#3,cJ25-%F[y7$$\"$M&
F,$\"1Yw-Fo+7SF[y7$$\"$N&F,$\"1]Gf&)4U**RF[y7$$\"$O&F,$\"13IIEIA$)RF[y
7$$\"$P&F,$\"1suwrqQjRF[y7$$\"$Q&F,$\"19\\=<\")))RRF[y7$$\"$R&F,$\"1H0
a:?q7RF[y7$$\"$S&F,$\"179,ja!=)QF[y7$$\"$T&F,$\"1pud%)f<ZQF[y7$$\"$U&F
,$\"1e^$)>>z3QF[y7$$\"$V&F,$\"1?:,4CjmPF[y7$$\"$W&F,$\"1he<ztn?PF[y7$$
\"$X&F,$\"1*eY1`24n$F[y7$$\"$Y&F,$\"101fBVI<OF[y7$$\"$Z&F,$\"1nG\"['*
\\)fNF[y7$$\"$[&F,$\"1&eLZRF&)\\$F[y7$$\"$\\&F,$\"1(o]XF?LV$F[y7$$\"$]
&F,$\"1j]etH@kLF[y7$$\"$^&F,$\"16IZBPA\"H$F[y7$$\"$_&F,$\"1m8[(y-X@$F[
y7$$\"$`&F,$\"1C!o&f1BMJF[y7$$\"$a&F,$\"12(f7h%e]IF[y7$$\"$b&F,$\"19%4
ztQP'HF[y7$$\"$c&F,$\"1dCN/S'Q(GF[y7$$\"$d&F,$\"1N$o**GG6y#F[y7$$\"$e&
F,$\"1ee:Lkp&o#F[y7$$\"$f&F,$\"1\"eG_FIxe#F[y7$$\"$g&F,$\"1xyt.()Q([#F
[y7$$\"$h&F,$\"1O0B&pF[Q#F[y7$$\"$i&F,$\"1zzWd.?!G#F[y7$$\"$j&F,$\"1(y
t4(plt@F[y7$$\"$k&F,$\"1rlLI]Ml?F[y7$$\"$l&F,$\"1;Zd%G4a&>F[y7$$\"$m&F
,$\"1)ypsx\"*R%=F[y7$$\"$n&F,$\"1_\\0')=BJ<F[y7$$\"$o&F,$\"1T^ghjE<;F[
y7$$\"$p&F,$\"1z^6m$HA]\"F[y7$$\"$q&F,$\"1OBF6DD'Q\"F[y7$$\"$r&F,$\"1h
$Hd*[Yp7F[y7$$\"$s&F,$\"1QW3UJ*>:\"F[y7$$\"$t&F,$\"1\\RPL9'R.\"F[y7$$
\"$u&F,$\"1pC%3\\:\\:*Fgq7$$\"$v&F,$\"1\"z\")o+Hq'zFgq7$$\"$w&F,$\"1%>
DrmDrx'Fgq7$$\"$x&F,$\"1%G>MF`je&Fgq7$$\"$y&F,$\"1!e_c)p$eR%Fgq7$$\"$z
&F,$\"1'[*pe'zm?$Fgq7$$\"$!eF,$\"1S$**[<i*>?Fgq7$$\"$\"eF,$\"17lG@xVn$
)FZ7$$\"$#eF,$!1cy![Kw$>MFZ7$$\"$$eF,$!1l@7B^1::Fgq7$$\"$%eF,$!1<49qCk
\"o#Fgq7$$\"$&eF,$!1cM0>QpSQFgq7$$\"$'eF,$!1(G2PQj7*\\Fgq7$$\"$(eF,$!1
#HHN9:C8'Fgq7$$\"$)eF,$!1sK\"[aKKE(Fgq7$$\"$*eF,$!1#z$*f?=GQ)Fgq7$$\"$
!fF,$!1'eeoi$H!\\*Fgq7$$\"$\"fF,$!1')[;!*)z%e5F[y7$$\"$#fF,$!1&3+OC\\l
;\"F[y7$$\"$$fF,$!16ywm]:t7F[y7$$\"$%fF,$!1>\\5zn@y8F[y7$$\"$&fF,$!1Fi
_[bl\"[\"F[y7$$\"$'fF,$!1NsgkUR$e\"F[y7$$\"$(fF,$!1#HF@^dLo\"F[y7$$\"$
)fF,$!1#))o\\ar9y\"F[y7$$\"$*fF,$!1:%o.Ekw(=F[y7$$\"$+'F,$!1'H9N<l=(>F
[y7$$\"$,'F,$!1&p([#R0S1#F[y7$$\"$-'F,$!1j=a$f<S:#F[y7$$\"$.'F,$!1,dr'
*f$=C#F[y7$$\"$/'F,$!16txTjRFBF[y7$$\"$0'F,$!1RN\\kej5CF[y7$$\"$1'F,$!
1*>@KF$\\\"\\#F[y7$$\"$2'F,$!1&3;es3*pDF[y7$$\"$3'F,$!1`c&o!Q#ek#F[y7$
$\"$4'F,$!1e:<0:=>FF[y7$$\"$5'F,$!1gzo\">E**y#F[y7$$\"$6'F,$!1w=c(f.!e
GF[y7$$\"$7'F,$!1m;i#zgL#HF[y7$$\"$8'F,$!1.+5kh%f)HF[y7$$\"$9'F,$!1bul
&R4d/$F[y7$$\"$:'F,$!1;JpY9g-JF[y7$$\"$;'F,$!1p&Q>`ul:$F[y7$$\"$<'F,$!
1%pJ85#e2KF[y7$$\"$='F,$!1Ym;?)ybD$F[y7$$\"$>'F,$!1,m^\\0_+LF[y7$$\"$?
'F,$!1Md#pKkBM$F[y7$$\"$@'F,$!1$4ntMo5Q$F[y7$$\"$A'F,$!1$*GYW>f;MF[y7$
$\"$B'F,$!1rR'>d&*)[MF[y7$$\"$C'F,$!1W][&ySzZ$F[y7$$\"$D'F,$!1$e#\\C-p
.NF[y7$$\"$E'F,$!10?a%f2h_$F[y7$$\"$F'F,$!1i5w\\w:XNF[y7$$\"$G'F,$!1ki
dvh!3c$F[y7$$\"$H'F,$!1M#z;(*>Id$F[y7$$\"$I'F,$!1W*H_$ow\"e$F[y7$$\"$J
'F,$!1!y$HWb,(e$F[y7$$\"$K'F,$!1m%4:%et)e$F[y7$$\"$L'F,$!1#*[)zT)*oe$F
[y7$$\"$M'F,$!16zT(*[Z\"e$F[y7$$\"$N'F,$!1W#R/#yVsNF[y7$$\"$O'F,$!1CY<
H1wfNF[y7$$\"$P'F,$!1$RB?l<Ma$F[y7$$\"$Q'F,$!1K2l)3%QBNF[y7$$\"$R'F,$!
1J3>&*fj*\\$F[y7$$\"$S'F,$!1P#e'p-:sMF[y7$$\"$T'F,$!1bZcPY!4W$F[y7$$\"
$U'F,$!1&=RxjxeS$F[y7$$\"$V'F,$!1jtM3'[qO$F[y7$$\"$W'F,$!1e)4Jn(RCLF[y
7$$\"$X'F,$!1M[rFd!zF$F[y7$$\"$Y'F,$!1wMUEWbFKF[y7$$\"$Z'F,$!1$fl)ohKt
JF[y7$$\"$['F,$!1cG-(3/_6$F[y7$$\"$\\'F,$!1=tRK?<`IF[y7$$\"$]'F,$!18FO
jX@()HF[y7$$\"$^'F,$!1gHO*4]t\"HF[y7$$\"$_'F,$!1fLB!4HP%GF[y7$$\"$`'F,
$!1wrE:A`mFF[y7$$\"$a'F,$!1y%*4Ip$fo#F[y7$$\"$b'F,$!1a1(H^<@g#F[y7$$\"
$c'F,$!1=&)Q5^C:DF[y7$$\"$d'F,$!1`i>#y([DCF[y7$$\"$e'F,$!12O0Y0,LBF[y7
$$\"$f'F,$!1#RQ8UvzB#F[y7$$\"$g'F,$!1FcZs9aS@F[y7$$\"$h'F,$!1(>,<&['3/
#F[y7$$\"$i'F,$!1IrET))4R>F[y7$$\"$j'F,$!1'=&4&*QRN=F[y7$$\"$k'F,$!1xd
))zw*)H<F[y7$$\"$l'F,$!1p()o:^vA;F[y7$$\"$m'F,$!1AH%fT3T^\"F[y7$$\"$n'
F,$!1c.*p7(4/9F[y7$$\"$o'F,$!1`F2n\"eGH\"F[y7$$\"$p'F,$!1/b\"['e_!=\"F
[y7$$\"$q'F,$!1$G1s*>Bn5F[y7$$\"$r'F,$!145uq#e5`*Fgq7$$\"$s'F,$!1vDv+9
u#Q)Fgq7$$\"$t'F,$!1q5#>\"GhGsFgq7$$\"$u'F,$!1l\"3v!>*)pgFgq7$$\"$v'F,
$!19(Q'*Rux!\\Fgq7$$\"$w'F,$!1`Z.gEVVPFgq7$$\"$x'F,$!13Z6mg,yDFgq7$$\"
$y'F,$!1Vf^U8l79Fgq7$$\"$z'F,$!1V5)4)*GW[#FZ7$$\"$!oF,$\"1l_=:%o_8*FZ7
$$\"$\"oF,$\"1[;#e5(>s?Fgq7$$\"$#oF,$\"1l(HcXGlA$Fgq7$$\"$$oF,$\"1\\Nh
jC]vVFgq7$$\"$%oF,$\"1mU1*R@\"=bFgq7$$\"$&oF,$\"1nQ&o\"zS`mFgq7$$\"$'o
F,$\"1Nl`]ZS!y(Fgq7$$\"$(oF,$\"1\"eQ&4W<)*))Fgq7$$\"$)oF,$\"1q(Q!)))z0
+\"F[y7$$\"$*oF,$\"1oG>LzB56F[y7$$\"$!pF,$\"1%yZCe.(=7F[y7$$\"$\"pF,$
\"1\\lG-2*eK\"F[y7$$\"$#pF,$\"1w>L\"*\\rJ9F[y7$$\"$$pF,$\"1TTT_R4O:F[y
7$$\"$%pF,$\"13C,lo%*Q;F[y7$$\"$&pF,$\"1qr1eZ>S<F[y7$$\"$'pF,$\"1io:$Q
g(R=F[y7$$\"$(pF,$\"1Ra.)=ov$>F[y7$$\"$)pF,$\"1%)f_!HWN.#F[y7$$\"$*pF,
$\"1Zew_khF@F[y7$$\"$+(F,$\"1q!*zbSr>AF[y7$$\"$,(F,$\"1K:^u!o(4BF[y7$$
\"$-(F,$\"1mY!H06xR#F[y7$$\"$.(F,$\"1JMqzqZ$[#F[y7$$\"$/(F,$\"1-VHk<+n
DF[y7$$\"$0(F,$\"1^#*)H@A#[EF[y7$$\"$1(F,$\"1W9h0q2FFF[y7$$\"$2(F,$\"1
L()Rsh].GF[y7$$\"$3(F,$\"1V3Ar6XxGF[y7$$\"$4(F,$\"1Jk5l[&)[HF[y7$$\"$5
(F,$\"1Gf2+:m<IF[y7$$\"$6(F,$\"1bkF$o;Q3$F[y7$$\"$7(F,$\"1()[ThtEZJF[y
7$$\"$8(F,$\"1>a[*zhz?$F[y7$$\"$9(F,$\"1nxyf&\\eE$F[y7$$\"$:(F,$\"1NCB
\"[\")3K$F[y7$$\"$;(F,$\"1P$H*e'4IP$F[y7$$\"$<(F,$\"1\"GcSU(=AMF[y7$$
\"$=(F,$\"1XO+C$p$oMF[y7$$\"$>(F,$\"1R=z-6^6NF[y7$$\"$?(F,$\"1>!e<op:b
$F[y7$$\"$@(F,$\"1E(309.&)e$F[y7$$\"$A(F,$\"1`\\8)pqAi$F[y7$$\"$B(F,$
\"1+ko%pKGl$F[y7$$\"$C(F,$\"1a:!Hd],o$F[y7$$\"$D(F,$\"1-/>go=/PF[y7$$
\"$E(F,$\"1)[m3:0\\s$F[y7$$\"$F(F,$\"1#=D')3qAu$F[y7$$\"$G(F,$\"17]E\\
tCcPF[y7$$\"$H(F,$\"1T*[Oi.ow$F[y7$$\"$I(F,$\"1ZD!4g1Rx$F[y7$$\"$J(F,$
\"1lg%=&\\_xPF[y7$$\"$K(F,$\"1'HdEJGwx$F[y7$$\"$L(F,$\"1VCwos=uPF[y7$$
\"$M(F,$\"1\\>&*QL<nPF[y7$$\"$N(F,$\"1\\%=(f*elv$F[y7$$\"$O(F,$\"1(*R
\")puJUPF[y7$$\"$P(F,$\"1dP-&4BWs$F[y7$$\"$Q(F,$\"1eL:L4&Gq$F[y7$$\"$R
(F,$\"1(>F#RpdxOF[y7$$\"$S(F,$\"1i\\*3\"zd[OF[y7$$\"$T(F,$\"18P/u9$eh$
F[y7$$\"$U(F,$\"1GGhogJzNF[y7$$\"$V(F,$\"1v#4Y$4,RNF[y7$$\"$W(F,$\"1g0
K)4'*[\\$F[y7$$\"$X(F,$\"1mGseB&pW$F[y7$$\"$Y(F,$\"1u<3u7;&R$F[y7$$\"$
Z(F,$\"1%=V([^]RLF[y7$$\"$[(F,$\"1&*=6?q'*zKF[y7$$\"$\\(F,$\"1\"\\:ekI
l@$F[y7$$\"$](F,$\"1@50\"\\!=\\JF[y7$$\"$^(F,$\"1:*yF)[$z2$F[y7$$\"$_(
F,$\"12'R!zT%H+$F[y7$$\"$`(F,$\"1ub,o*)QCHF[y7$$\"$a(F,$\"1Y1\"\\hYC%G
F[y7$$\"$b(F,$\"1E!4#38HdFF[y7$$\"$c(F,$\"13HL0T4pEF[y7$$\"$d(F,$\"1nf
qxH-yDF[y7$$\"$e(F,$\"1<,BbGC%[#F[y7$$\"$f(F,$\"1(f#=qc\"zQ#F[y7$$\"$g
(F,$\"1B2a+/?*G#F[y7$$\"$h(F,$\"1y6u7JD)=#F[y7$$\"$i(F,$\"1W4)Q+F_3#F[
y7$$\"$j(F,$\"1jlOVCF!)>F[y7$$\"$k(F,$\"1f(=S,PN(=F[y7$$\"$l(F,$\"1c*Q
Ebl^w\"F[y7$$\"$m(F,$\"1mW/!>+`l\"F[y7$$\"$n(F,$\"1;(y0R!3W:F[y7$$\"$o
(F,$\"1OK5\"*HkJ9F[y7$$\"$p(F,$\"1=wZRA7=8F[y7$$\"$q(F,$\"1@R`K)\\O?\"
F[y7$$\"$r(F,$\"1x:b`\\N)3\"F[y7$$\"$s(F,$\"1\"=#R#4VOs*Fgq7$$\"$t(F,$
\"1>MHi;-e&)Fgq7$$\"$u(F,$\"1w)>4(Q!zQ(Fgq7$$\"$v(F,$\"1T=teY[9iFgq7$$
\"$w(F,$\"1IJkJc$*Q]Fgq7$$\"$x(F,$\"1b,32aSiQFgq7$$\"$y(F,$\"1UXYb*>go
#Fgq7$$\"$z(F,$\"1yn<PH)3^\"Fgq7$$\"$!yF,$\"1W1b].w!Q$FZ7$$\"$\"yF,$!1
4c7vrS8$)FZ7$$\"$#yF,$!11,&GhGj*>Fgq7$$\"$$yF,$!1;Qb\\*pe:$Fgq7$$\"$%y
F,$!1H#*H<x'*3VFgq7$$\"$&yF,$!1d'ReGXYX&Fgq7$$\"$'yF,$!1Kf9)4Y>f'Fgq7$
$\"$(yF,$!1pUjnL$*>xFgq7$$\"$)yF,$!1tKVz(*oP))Fgq7$$\"$*yF,$!1;sj&><V%
**Fgq7$$\"$!zF,$!1y(\\kj$*Q5\"F[y7$$\"$\"zF,$!1i.Nj'o?@\"F[y7$$\"$#zF,
$!1:,jmD()=8F[y7$$\"$$zF,$!1+1M;HAC9F[y7$$\"$%zF,$!1wfme!R!G:F[y7$$\"$
&zF,$!1n$Q()3U-j\"F[y7$$\"$'zF,$!1![=Q#[vI<F[y7$$\"$(zF,$!1om$ox,&H=F[
y7$$\"$)zF,$!1-,HI\"4k#>F[y7$$\"$*zF,$!1`9\\5ZS@?F[y7$$\"$+)F,$!1T[;iz
T9@F[y7$$\"$,)F,$!1#[%QB*z`?#F[y7$$\"$-)F,$!1$)=&3?BUH#F[y7$$\"$.)F,$!
1ps]X>)3Q#F[y7$$\"$/)F,$!1Y5ZG=HlCF[y7$$\"$0)F,$!1n6J<+RZDF[y7$$\"$1)F
,$!1(>KE::ri#F[y7$$\"$2)F,$!1lA)\\K2Wq#F[y7$$\"$3)F,$!1yN2_!3#zFF[y7$$
\"$4)F,$!1#y7jDg9&GF[y7$$\"$5)F,$!1grjU#36#HF[y7$$\"$6)F,$!1FGlww4))HF
[y7$$\"$7)F,$!1/62jbP_IF[y7$$\"$8)F,$!12$RWA!*Q6$F[y7$$\"$9)F,$!1r@;!G
\"fsJF[y7$$\"$:)F,$!1&R5eiH%GKF[y7$$\"$;)F,$!1PCr7uN\"G$F[y7$$\"$<)F,$
!1`h#y-G8L$F[y7$$\"$=)F,$!1fm)Q2'HyLF[y7$$\"$>)F,$!1>p#)\\t@AMF[y7$$\"
$?)F,$!11wYJ)[IY$F[y7$$\"$@)F,$!17GZ_'[2]$F[y7$$\"$A)F,$!1%>ob3w_`$F[y
7$$\"$B)F,$!1E$=S_\"fmNF[y7$$\"$C)F,$!14)fLYcYf$F[y7$$\"$D)F,$!1$*pQ$[
L%>OF[y7$$\"$E)F,$!1dqQIi)3k$F[y7$$\"$F)F,$!1i7i*Rz*eOF[y7$$\"$G)F,$!1
X#\\!=(yOn$F[y7$$\"$H)F,$!1cKHF4&\\o$F[y7$$\"$I)F,$!1l#RowjFp$F[y7$$\"
$J)F,$!13>Zdf3(p$F[y7$$\"$K)F,$!11.%\\=()yp$F[y7$$\"$L)F,$!1n<&Q3Q^p$F
[y7$$\"$M)F,$!1$[!z@-\"))o$F[y7$$\"$N)F,$!1A$eO3w)yOF[y7$$\"$O)F,$!1y[
Bc!4`m$F[y7$$\"$P)F,$!1dR&HT$3[OF[y7$$\"$Q)F,$!1BP*))Huri$F[y7$$\"$R)F
,$!1$yxfrdDg$F[y7$$\"$S)F,$!1KWQ30@uNF[y7$$\"$T)F,$!1u9;[.6UNF[y7$$\"$
U)F,$!1%*Q/@dB1NF[y7$$\"$V)F,$!1;=Z7fcmMF[y7$$\"$W)F,$!1Rh!Q*43BMF[y7$
$\"$X)F,$!18$R(3=wvLF[y7$$\"$Y)F,$!1G()*)f**eCLF[y7$$\"$Z)F,$!1!GSczZ&
pKF[y7$$\"$[)F,$!19&HqR=1@$F[y7$$\"$\\)F,$!18\"3]c&yZJF[y7$$\"$])F,$!1
'=Vx!Q.\"3$F[y7$$\"$^)F,$!18P#[\\\"Q5IF[y7$$\"$_)F,$!1@(zl-zf$HF[y7$$
\"$`)F,$!1`o9Lq+eGF[y7$$\"$a)F,$!1`\"[8#HkwFF[y7$$\"$b)F,$!13c&4#41#p#
F[y7$$\"$c)F,$!1%G].8KWg#F[y7$$\"$d)F,$!1$=)ehX#R^#F[y7$$\"$e)F,$!1w%z
[=.2U#F[y7$$\"$f)F,$!1c!)[s*H\\K#F[y7$$\"$g)F,$!1e'e?%RwEAF[y7$$\"$h)F
,$!1o&y$*>hj7#F[y7$$\"$i)F,$!1&)3e!)\\(Q-#F[y7$$\"$j)F,$!1#>'z$pb%>>F[
y7$$\"$k)F,$!1h&f-'4D8=F[y7$$\"$l)F,$!1+$z[l0aq\"F[y7$$\"$m)F,$!1\"\\u
i%>1'f\"F[y7$$\"$n)F,$!1kvGO$f`[\"F[y7$$\"$o)F,$!1E&y*)pMMP\"F[y7$$\"$
p)F,$!13s5>BUg7F[y7$$\"$q)F,$!1t)4,$RXY6F[y7$$\"$r)F,$!14kd^(e;.\"F[y7
$$\"$s)F,$!1mUMi_jh\"*Fgq7$$\"$t)F,$!1B,Ykb#4+)Fgq7$$\"$u)F,$!1&ROASxc
$oFgq7$$\"$v)F,$!1k%3x1'3ncFgq7$$\"$w)F,$!10r`:NK'\\%Fgq7$$\"$x)F,$!1Z
\"*34(QXK$Fgq7$$\"$y)F,$!1X:%>'z&G:#Fgq7$$\"$z)F,$!1Yol[F&Q#)*FZ7$$\"$
!))F,$\"1c=_;L(z&=FZ7$$\"$\"))F,$\"1QvH*[H1N\"Fgq7$$\"$#))F,$\"1T)p\"e
@26DFgq7$$\"$$))F,$\"1Q<K2t5mOFgq7$$\"$%))F,$\"1,^a*fPZ\"[Fgq7$$\"$&))
F,$\"1@(\\.3')f&fFgq7$$\"$'))F,$\"1>E3re*))3(Fgq7$$\"$())F,$\"1\"QOh')
HD@)Fgq7$$\"$)))F,$\"1Rd>M/(fK*Fgq7$$\"$*))F,$\"1qqM7>$G/\"F[y7$$\"$!*
)F,$\"1xp3P'p=:\"F[y7$$\"$\"*)F,$\"1jf]@Tif7F[y7$$\"$#*)F,$\"11mL,6,m8
F[y7$$\"$$*)F,$\"1mmC;\"[4Z\"F[y7$$\"$%*)F,$\"1LGG#[aVd\"F[y7$$\"$&*)F
,$\"1UUok7:w;F[y7$$\"$'*)F,$\"1m61^7Ew<F[y7$$\"$(*)F,$\"1vT$\\#*3Y(=F[
y7$$\"$)*)F,$\"1_&H'R/7r>F[y7$$\"$**)F,$\"1'4EDfBd1#F[y7$$\"$+*F,$\"1*
>\\'*zZ$e@F[y7$$\"$,*F,$\"1?xgqS#*[AF[y7$$\"$-*F,$\"1m$pQ)\\QPBF[y7$$
\"$.*F,$\"1I.PiYmBCF[y7$$\"$/*F,$\"1y\\X\\()p2DF[y7$$\"$0*F,$\"1[99&QC
%*e#F[y7$$\"$1*F,$\"1l*3F=!yoEF[y7$$\"$2*F,$\"1_Ig0iqXFF[y7$$\"$3*F,$
\"1=VlWR9?GF[y7$$\"$4*F,$\"1.rg&HO?*GF[y7$$\"$5*F,$\"1vR&p`F8'HF[y7$$
\"$6*F,$\"1NA23L'z-$F[y7$$\"$7*F,$\"13'ewe!*=4$F[y7$$\"$8*F,$\"1t$eCnd
I:$F[y7$$\"$9*F,$\"1G^GcTT6KF[y7$$\"$:*F,$\"1!pF$44\"pE$F[y7$$\"$;*F,$
\"1o-ud+]>LF[y7$$\"$<*F,$\"1vC^j\\8pLF[y7$$\"$=*F,$\"1&e:Y?qdT$F[y7$$
\"$>*F,$\"1G:Ub:OfMF[y7$$\"$?*F,$\"1k6Rnf')*\\$F[y7$$\"$@*F,$\"1?%G+bT
s`$F[y7$$\"$A*F,$\"1zo4_vWrNF[y7$$\"$B*F,$\"1xb4VVW-OF[y7$$\"$C*F,$\"1
v0*\\R$>IOF[y7$$\"$D*F,$\"1c\"*>kslaOF[y7$$\"$E*F,$\"1&QBQd*zvOF[y7$$
\"$F*F,$\"1f)Hh*\\e$p$F[y7$$\"$G*F,$\"13DFN#zzq$F[y7$$\"$H*F,$\"1X`D5!
\\*=PF[y7$$\"$I*F,$\"1,@8Q?YEPF[y7$$\"$J*F,$\"13(Ru,([IPF[y7$$\"$K*F,$
\"1qE'=h$*4t$F[y7$$\"$L*F,$\"1A`7MC&zs$F[y7$$\"$M*F,$\"1%44,.N8s$F[y7$
$\"$N*F,$\"1!*=>jQ66PF[y7$$\"$O*F,$\"1@n!))Hisp$F[y7$$\"$P*F,$\"1)z;#*
ea(zOF[y7$$\"$Q*F,$\"1(G/&eeceOF[y7$$\"$R*F,$\"18+x(3sOj$F[y7$$\"$S*F,
$\"1U8a+,00OF[y7$$\"$T*F,$\"1QcQ[vnsNF[y7$$\"$U*F,$\"1#fEn*G`ONF[y7$$
\"$V*F,$\"1Q3'3T&f'\\$F[y7$$\"$W*F,$\"1hA<U^%GX$F[y7$$\"$X*F,$\"1c9a9H
E0MF[y7$$\"$Y*F,$\"11y%4JIQN$F[y7$$\"$Z*F,$\"1^<Eg'H&)H$F[y7$$\"$[*F,$
\"1TYACSMRKF[y7$$\"$\\*F,$\"1VRh%=di<$F[y7$$\"$]*F,$\"1h7fIOD4JF[y7$$
\"$^*F,$\"1?v*Gr^$QIF[y7$$\"$_*F,$\"1()3<8=qjHF[y7$$\"$`*F,$\"1-,,VX[&
)GF[y7$$\"$a*F,$\"1F]&3HxQ!GF[y7$$\"$b*F,$\"1mpCoU0>FF[y7$$\"$c*F,$\"1
&e([bl=JEF[y7$$\"$d*F,$\"1lNqY@WSDF[y7$$\"$e*F,$\"1NYK%*f)pW#F[y7$$\"$
f*F,$\"1T>)H0!)4N#F[y7$$\"$g*F,$\"1')R$GK$e_AF[y7$$\"$h*F,$\"1orK#*=&>
:#F[y7$$\"$i*F,$\"1#)yR!)*Q#\\?F[y7$$\"$j*F,$\"1OI7y\\fW>F[y7$$\"$k*F,
$\"1=f#)*[n\"Q=F[y7$$\"$l*F,$\"1.Qkt85I<F[y7$$\"$m*F,$\"1jVc\"yQ0i\"F[
y7$$\"$n*F,$\"1Ir$*)>>'4:F[y7$$\"$o*F,$\"11mY$[zuR\"F[y7$$\"$p*F,$\"1:
Mp.RD%G\"F[y7$$\"$q*F,$\"1<)pp<u+<\"F[y7$$\"$r*F,$\"1;e$p]p]0\"F[y7$$
\"$s*F,$\"1w<-0im$R*Fgq7$$\"$t*F,$\"1\">hM/)*3B)Fgq7$$\"$u*F,$\"1l:E4%
4O1(Fgq7$$\"$v*F,$\"1?t@Sa*H*eFgq7$$\"$w*F,$\"1Jk.QzA?ZFgq7$$\"$x*F,$
\"1G2T9dXYNFgq7$$\"$y*F,$\"1z'4D$\\!GP#Fgq7$$\"$z*F,$\"1\"\\aRWz.?\"Fg
q7$$\"$!)*F,$\"1v5%G87h-$F@7$$\"$\")*F,$!16*>P\")*[O6Fgq7$$\"$#)*F,$!1
q'GnYM))H#Fgq7$$\"$$)*F,$!1))>(4&\\vbMFgq7$$\"$%)*F,$!1%zbA2aig%Fgq7$$
\"$&)*F,$!1gi!z,b$\\dFgq7$$\"$')*F,$!1'y)*)\\55%)oFgq7$$\"$()*F,$!1Pf2
-_b4!)Fgq7$$\"$))*F,$!1aNS\")**zC\"*Fgq7$$\"$*)*F,$!1M8K2P*G-\"F[y7$$
\"$!**F,$!1X&Q]q3@8\"F[y7$$\"$\"**F,$!1]<k3*Q+C\"F[y7$$\"$#**F,$!1rMBn
+gY8F[y7$$\"$$**F,$!1#=RPt4<X\"F[y7$$\"$%**F,$!1j>NPsGb:F[y7$$\"$&**F,
$!1@pMcODd;F[y7$$\"$'**F,$!1w2E\"zJvv\"F[y7$$\"$(**F,$!17>VQh/c=F[y7$$
\"$)**F,$!1tm*Q'Gs_>F[y7$$\"$***F,$!1Uqjx(*[Z?F[y7$$\"%+5F,$!1'ev\"3jF
S@F[y-%&STYLEG6#%%LINEG-%*THICKNESSG6#F8-%'COLOURG6&%$RGBG$\")p:#R%!\"
)$\")`B)e)F_e^l$\")fqkdF_e^l-%%VIEWG6$;$!+++++]!#5$\"++++]5F_e^l;$!+pl
\"*)H%Fje^l$\"+p)HP#*)Fje^l-%+AXESLABELSG6$%\"tG%%x(t)G" 2 373 373 
373 2 0 1 0 2 6 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 1 0 0 0 0 -25744 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 14 "d) Square Wave" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "The square wave fu
nction is defined by\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "sq
uare_wave := t ->  signum(abs(2*t+1-4*floor(1/2*t+3/4))-1);  # Execute
!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,square_waveG:6#%\"tG6\"6$%)ope
ratorG%&arrowGF(-%'signumG6#,&-%$absG6#,(9$\"\"#\"\"\"F6-%&floorG6#,&F
4#F6F5#\"\"$\"\"%F6!\"%F6!\"\"F6F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "Here \+
is the plot of this function for  " }{MPLTEXT 1 0 10 "t = 0 .. 6" }
{TEXT -1 26 ",   as typically rendered:" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot( square_wave(t)  ,
 t = 0 .. 6);  # Execute!" }}{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6$
7hr7$\"\"!F(7$$\"1++D1k'p3%!#=$\"\"\"F(7$$\"1++]7G$R<)F,F-7$$\"1+](=#*
*3E7!#<F-7$$\"1++]ilyM;F5F-7$$\"1++vV)z@X#F5F-7$$\"1+++DJdpKF5F-7$$\"1
++](ofV!\\F5F-7$$\"1+++]i9RlF5F-7$$\"1+++v$>(3)*F5F-7$$\"1+++]#HyI\"!#
;F-7$$\"1++voozw=FKF-7$$\"1++]([kdW#FKF-7$$\"1+++v;\\DPFKF-7$$\"1+++D<
q8]FKF-7$$\"1++]P\"*y&H'FKF-7$$\"1++](G[W[(FKF-7$$\"1++]()fB:()FKF-7$$
\"1++](=x;N*FKF-7$$\"1++](Q=\"))**FKF-7$$\"1]7`Rox-5!#:$!\"\"F(7$$\"1+
DJS=u15FdoFeo7$$\"1]P4Toq55FdoFeo7$$\"1+](=%=n95FdoFeo7$$\"1+vVV=gA5Fd
oFeo7$$\"1+++X=`I5FdoFeo7$$\"1+]7[=RY5FdoFeo7$$\"1++D^=Di5FdoFeo7$$\"1
++]d=(R4\"FdoFeo7$$\"1++vj=pD6FdoFeo7$$\"1+]P9x%4>\"FdoFeo7$$\"1+++lN?
c7FdoFeo7$$\"1++]U$e6P\"FdoFeo7$$\"1+++&>q0]\"FdoFeo7$$\"1+++DM^I;FdoF
eo7$$\"1+++0ytb<FdoFeo7$$\"1+](=n&f7=FdoFeo7$$\"1++vQNXp=FdoFeo7$$\"1+
DJ!HeK!>FdoFeo7$$\"1+](=/jq$>FdoFeo7$$\"1]il<a'R&>FdoFeo7$$\"1+vV$zn3(
>FdoFeo7$$\"1D\"G8)*=$z>FdoFeo7$$\"1](=#p,x()>FdoFeo7$$\"1iS;jd*>*>Fdo
Feo7$$\"1v$4rN@i*>FdoFeo7$$\"1)oa5&pW+?FdoF-7$$\"1+++XDn/?FdoF-7$$\"1+
+]im%>1#FdoF-7$$\"1+++!y?#>@FdoF-7$$\"1++v3wY_AFdoF-7$$\"1+++IOTqBFdoF
-7$$\"1++v3\">)*\\#FdoF-7$$\"1++DEP/BEFdoF-7$$\"1++](o:;v#FdoF-7$$\"1+
+v$)[opGFdoF-7$$\"1+]7t;OLHFdoF-7$$\"1++]i%Qq*HFdoF-7$$\"17y]bB<,IFdoF
eo7$$\"1Dc^[iI0IFdoFeo7$$\"1QM_T,W4IFdoFeo7$$\"1]7`MSd8IFdoFeo7$$\"1vo
a?=%=-$FdoFeo7$$\"1+Dc1'4,.$FdoFeo7$$\"1]Pfy^kYIFdoFeo7$$\"1+]i]2=jIFd
oFeo7$$\"1+vo%*=D'4$FdoFeo7$$\"1++vQIKHJFdoFeo7$$\"1+++&4+p=$FdoFeo7$$
\"1++D^rZWKFdoFeo7$$\"1++]Zn%)oLFdoFeo7$$\"1+++5FL(\\$FdoFeo7$$\"1++]d
6.BOFdoFeo7$$\"1++vo3lWPFdoFeo7$$\"1+]iX)p@\"QFdoFeo7$$\"1++]A))ozQFdo
Feo7$$\"1+]PCK-5RFdoFeo7$$\"1++DEwNSRFdoFeo7$$\"1+v=F[_bRFdoFeo7$$\"1+
]7G?pqRFdoFeo7$$\"1]PfGcFyRFdoFeo7$$\"1+D1H#fe)RFdoFeo7$$\"1voHH5l*)RF
doFeo7$$\"1]7`HGW$*RFdoFeo7$$\"1DcwHYB(*RFdoFeo7$$\"1+++Ik-,SFdoF-7$$
\"1****\\FL!e1%FdoF-7$$\"1+++D-eITFdoF-7$$\"1++v=_(zC%FdoF-7$$\"1+++b*
=jP%FdoF-7$$\"1++v3/3(\\%FdoF-7$$\"1++vB4JBYFdoF-7$$\"1+++DVsYZFdoF-7$
$\"1+](=_D8\"[FdoF-7$$\"1++v=n#f([FdoF-7$$\"1+D1Mg.2\\FdoF-7$$\"1+]P\\
`9Q\\FdoF-7$$\"1^7.2+q`\\FdoF-7$$\"1,vokYDp\\FdoF-7$$\"1Ec^$*>.x\\FdoF
-7$$\"1]PMA$4[)\\FdoF-7$$\"18yv')zp))\\FdoF-7$$\"1v=<^me#*\\FdoF-7$$\"
1Qfe:`Z'*\\FdoF-7$$\"1+++!)RO+]FdoFeo7$$\"1,+D;:*R1&FdoFeo7$$\"1++]_!>
w7&FdoFeo7$$\"1++v)Q?QD&FdoFeo7$$\"1+++5jyp`FdoFeo7$$\"1++]Ujp-bFdoFeo
7$$\"1+++gEd@cFdoFeo7$$\"1++v3'>$[dFdoFeo7$$\"1+++5h(*3eFdoFeo7$$\"1++
D6EjpeFdoFeo7$$\"1+vVeWA-fFdoFeo7$$\"1,]i0j\"[$fFdoFeo7$$\"1^(=#HA6^fF
doFeo7$$\"1+D\"G:3u'fFdoFeo7$$\"1v$4Y6cb(fFdoFeo7$$\"1]iSwSq$)fFdoFeo7
$$\"1)o/t0yx)fFdoFeo7$$\"1DJ?Q?&=*fFdoFeo7$$\"1i:5>g#f*fFdoFeo7$$\"\"'
F(F(-%'COLOURG6&%$RGBG$\"#5FfoF(F(-%+AXESLABELSG6$%\"tG%!G-%%VIEWG6$;F
(Fjbl%(DEFAULTG" 2 373 373 373 2 0 1 0 2 9 0 4 2 1.000000 45.000000 
45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 257 -28088 0 0 
0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 180 "The triangular wave is periodic. Its Lap
lace transform can therefore be reduced to integrating over its period
. That integral should be broken into two integrals over subintervals.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 99 "`laplace(square_wave(t),t,s)` = (int(1*exp(-s*t),t=0..1) + int
(-1*exp(-s*t),t=1..2))/(1-exp(-2*s));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#/%<laplace(square_wave(t),t,s)G*&,(*&%\"sG!\"\"-%$expG6#,$F(F)\"\"
\"!\"#*$F(F)F.*&-F+6#,$F(F/F.F(F)F.F.,&F.F.F2F)F)" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 340 3 "Use" }{TEXT -1 2 "  " }{TEXT 
339 6 "DEplot" }{TEXT -1 1 " " }{TEXT 342 1 " " }{TEXT 341 51 "to plot
 the solution to the initial value problem f" }{TEXT -1 4 "or  " }
{TEXT 351 1 " " }{XPPEDIT 352 1 "t = 0 .. 10" "/%\"tG;\"\"!\"#5" }
{TEXT -1 2 " :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 336 10 "  \n       " }{XPPEDIT 338 1 "diff(diff(x(t),t),t)+2*dif
f(x(t),t)+ x(t) = 5*square_wave(t)*``, `    `*x(0) = `0.0`*``, `   `*D
(x)(0) = 0" "6%/,(-%%diffG6$-F&6$-%\"xG6#%\"tGF-F-\"\"\"*&\"\"#F.-F&6$
-F+6#F-F-F.F.-F+6#F-F.*(\"\"&F.-%,square_waveG6#F-F.%!GF./*&%%~~~~GF.-
F+6#\"\"!F.*&%$0.0GF.F<F./*&%$~~~GF.--%\"DG6#F+6#FBF.FB" }{TEXT 337 1 
":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
161 "ode := diff(x(t),t$2) + 2*diff(x(t),t)+ x(t) = 5*square_wave(t):
\nDEplot(\{ode\}, [x(t)], t=0.. 10, [[x(0)=0.0,D(x)(0)=0]], stepsize= \+
0.01, linecolor = aquamarine);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURV
ESG6%7ein7$\"\"!F(7$$\"\"\"!\"#$\"1LLLLLLe;!#>7$$\"\"#F,$\"1/=rMl(RB)F
/7$$\"\"$F,$\"1;\"[&[)))G'>!#=7$$\"\"%F,$\"1w]#3J^Yd$F:7$$\"\"&F,$\"1Y
w!)oQ<\\cF:7$$\"\"'F,$\"1>!y)oy3x\")F:7$$\"\"(F,$\"15.3Gl\"\\6\"!#<7$$
\"\")F,$\"1[Lo#oJcX\"FO7$$\"\"*F,$\"1_6T8!f*Q=FO7$$\"#5F,$\"1w4,\"z;SE
#FO7$$\"#6F,$\"1HC39m$*HFFO7$$\"#7F,$\"12^9JK'eB$FO7$$\"#8F,$\"1#fF\\O
a4y$FO7$$\"#9F,$\"1V7&)Q0QkVFO7$$\"#:F,$\"1'\\#o0\\K&)\\FO7$$\"#;F,$\"
1*pF$yI)Hk&FO7$$\"#<F,$\"1.[uiHcOjFO7$$\"#=F,$\"1Tl%Hf%GlqFO7$$\"#>F,$
\"1B+2o*z$GyFO7$$\"#?F,$\"1Oz[\"*G4D')FO7$$\"#@F,$\"1\")o$>\")yYX*FO7$
$\"#AF,$\"1iQmm/kJ5!#;7$$\"#BF,$\"1J!RE([&47\"Fer7$$\"#CF,$\"1.+EW+M87
Fer7$$\"#DF,$\"1KWiHgs38Fer7$$\"#EF,$\"1^C(['R/29Fer7$$\"#FF,$\"17*f%f
gA3:Fer7$$\"#GF,$\"1oph\"e0Ah\"Fer7$$\"#HF,$\"1o(*)R%o\"*=<Fer7$$\"#IF
,$\"1oIY*=&HG=Fer7$$\"#JF,$\"1l:;xpFS>Fer7$$\"#KF,$\"1=yio&*za?Fer7$$
\"#LF,$\"19Y<98!=<#Fer7$$\"#MF,$\"1$o4%R:A\"H#Fer7$$\"#NF,$\"1\"oI>`+I
T#Fer7$$\"#OF,$\"1!R)=G&zq`#Fer7$$\"#PF,$\"1'4;0q+Mm#Fer7$$\"#QF,$\"1`
JKWr!>z#Fer7$$\"#RF,$\"1N2XlGaAHFer7$$\"#SF,$\"1ByonFDbIFer7$$\"#TF,$
\"1'\\X/k#)**=$Fer7$$\"#UF,$\"1.weY\"zmK$Fer7$$\"#VF,$\"1<fT5)*GlMFer7
$$\"#WF,$\"1Iz!e+jdg$Fer7$$\"#XF,$\"12a]Wz/[PFer7$$\"#YF,$\"1'*=bkY4#*
QFer7$$\"#ZF,$\"1zt()=S&y.%Fer7$$\"#[F,$\"1)GGSmx_=%Fer7$$\"#\\F,$\"18
6/\\!=VL%Fer7$$\"#]F,$\"1ryX/%G\\[%Fer7$$\"#^F,$\"1/<[JF1PYFer7$$\"#_F
,$\"1?4F\"zv1z%Fer7$$\"#`F,$\"1x(pV4Bd%\\Fer7$$\"#aF,$\"1gVF!*3;-^Fer7
$$\"#bF,$\"18>8dh%*f_Fer7$$\"#cF,$\"1!*>d\"fO!>aFer7$$\"#dF,$\"1Gym)f!
RzbFer7$$\"#eF,$\"1uj-#Gn4u&Fer7$$\"#fF,$\"1``+Mks.fFer7$$\"#gF,$\"1&*
e0E&Gw1'Fer7$$\"#hF,$\"1I\"*=*pMEB'Fer7$$\"#iF,$\"1&GlXv1()R'Fer7$$\"#
jF,$\"1dP?Wr!ec'Fer7$$\"#kF,$\"13F\"='*)*Qt'Fer7$$\"#lF,$\"1:ntLf%H!pF
er7$$\"#mF,$\"1L5-5C\"H2(Fer7$$\"#nF,$\"1U5fbLwVsFer7$$\"#oF,$\"1'[X:M
kaT(Fer7$$\"#pF,$\"1\"4il`\")ze(Fer7$$\"#qF,$\"1:UT)p\"GhxFer7$$