In this paper, we derive sharp upper and lower bounds on the sum <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="51.388pt" style="vertical-align:-4.679399pt" id="M1" height="16.5775pt" version="1.1" viewBox="-0.0498162 -11.8981 51.388 16.5775"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-225" d="M478 372C478 418 458 448 431 448C409 448 389 431 389 410C389 404 391 400 394 395C398 388 406 371 406 348C406 253 308 122 251 51H249C254 122 249 257 231 336C212 421 189 448 159 448C126 448 75 412 23 327L48 306C83 354 103 371 115 371C125 371 134 360 144 334C185 224 192 64 183 -19C146 -100 116 -202 110 -244L125 -261C154 -259 208 -234 222 -220C222 -194 225 -84 235 -23C247 -3 273 36 308 79C379 165 478 288 478 372Z"/></g><g transform="matrix(.0091,0,0,-0.0091,5.668,3.132)"><path id="g50-92" d="M297 -163V-131C189 -122 187 -119 187 -41V582C187 660 190 663 297 672V704H122V-163H297Z"/></g><g transform="matrix(.0091,0,0,-0.0091,8.926,3.132)"><path id="g50-52" d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"/></g><g transform="matrix(.0091,0,0,-0.0091,13.358,3.132)"><path id="g50-83" d="M636 22C611 29 589 38 560 74C536 104 518 134 495 173L430 300C518 328 592 392 592 492C592 555 563 594 528 618C491 643 435 650 377 650H140L131 618C222 610 223 601 208 518L137 136C121 43 116 40 27 32L18 0H295L300 32C212 40 206 42 223 138L248 279H296C334 279 350 272 369 230C393 174 413 140 441 94C482 24 523 1 626 -8L636 22ZM497 480C497 422 468 374 417 343C387 324 353 315 304 315H255L298 556C303 583 309 598 319 603C331 610 348 613 367 613C448 613 497 573 497 480Z"/></g><g transform="matrix(.0091,0,0,-0.0091,19.145,3.132)"><path id="g50-94" d="M237 -163V704H62V672C170 663 172 660 172 582V-40C172 -118 170 -122 62 -131V-163H237Z"/></g><g transform="matrix(.013,0,0,-0.013,22.964,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.013,0,0,-0.013,27.462,0)"><path id="g113-72" d="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z"/></g><g transform="matrix(.013,0,0,-0.013,36.354,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g><g transform="matrix(.013,0,0,-0.013,43.757,0)"><path id="g117-36" d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"/></g></svg><span class="ibiop"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="41.156pt" style="vertical-align:-4.679399pt" height="16.5775pt" version="1.1" viewBox="54.244183799999995 -11.8981 41.156 16.5775"><g transform="matrix(.013,0,0,-0.013,54.294,0)"><use xlink:href="#g113-225"/></g><g transform="matrix(.0091,0,0,-0.0091,59.962,3.132)"><use xlink:href="#g50-92"/></g><g transform="matrix(.0091,0,0,-0.0091,63.22,3.132)"><use xlink:href="#g50-52"/></g><g transform="matrix(.0091,0,0,-0.0091,67.652,3.132)"><use xlink:href="#g50-83"/></g><g transform="matrix(.0091,0,0,-0.0091,73.439,3.132)"><use xlink:href="#g50-94"/></g><g transform="matrix(.013,0,0,-0.013,77.258,0)"><use xlink:href="#g113-41"/></g><rect height="0.65243" width="8.92533" x="81.7556" y="-11.1958"/><g transform="matrix(.013,0,0,-0.013,81.756,0)"><use xlink:href="#g113-72"/></g><g transform="matrix(.013,0,0,-0.013,90.681,0)"><use xlink:href="#g113-42"/></g></svg></span> and product <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.679399pt" id="M2" height="16.5775pt" version="1.1" viewBox="-0.0498162 -11.8981 81.9797 16.5775" width="81.9797pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-225"/></g><g transform="matrix(.0091,0,0,-0.0091,5.668,3.132)"><use xlink:href="#g50-92"/></g><g transform="matrix(.0091,0,0,-0.0091,8.926,3.132)"><use xlink:href="#g50-52"/></g><g transform="matrix(.0091,0,0,-0.0091,13.358,3.132)"><use xlink:href="#g50-83"/></g><g transform="matrix(.0091,0,0,-0.0091,19.145,3.132)"><use xlink:href="#g50-94"/></g><g transform="matrix(.013,0,0,-0.013,22.964,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,27.462,0)"><use xlink:href="#g113-72"/></g><g transform="matrix(.013,0,0,-0.013,36.354,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,40.852,0)"><use xlink:href="#g113-225"/></g><g transform="matrix(.0091,0,0,-0.0091,46.52,3.132)"><use xlink:href="#g50-92"/></g><g transform="matrix(.0091,0,0,-0.0091,49.778,3.132)"><use xlink:href="#g50-52"/></g><g transform="matrix(.0091,0,0,-0.0091,54.21,3.132)"><use xlink:href="#g50-83"/></g><g transform="matrix(.0091,0,0,-0.0091,59.997,3.132)"><use xlink:href="#g50-94"/></g><g transform="matrix(.013,0,0,-0.013,63.816,0)"><use xlink:href="#g113-41"/></g><rect height="0.65243" width="8.92533" x="68.3136" y="-11.1958"/><g transform="matrix(.013,0,0,-0.013,68.314,0)"><use xlink:href="#g113-72"/></g><g transform="matrix(.013,0,0,-0.013,77.239,0)"><use xlink:href="#g113-42"/></g></svg>,</span> where <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2062998pt" id="M3" height="12.1044pt" version="1.1" viewBox="-0.0498162 -11.8981 9.02496 12.1044" width="9.02496pt"><rect height="0.65243" width="8.92533" x="0" y="-11.1958"/><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-72"/></g></svg> is the complement of graph <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2064009pt" id="M4" height="8.8423pt" version="1.1" viewBox="-0.0498162 -8.6359 9.02496 8.8423" width="9.02496pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-72"/></g></svg>.</span> We also show that for each tree <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.04981995pt" id="M5" height="9.01194pt" version="1.1" viewBox="-0.0498162 -8.96212 8.41168 9.01194" width="8.41168pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-85" d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"/></g></svg> of order <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="17.789pt" style="vertical-align:-1.11981pt" id="M6" height="9.46863pt" version="1.1" viewBox="-0.0498162 -8.34882 17.789 9.46863"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-111" d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"/></g><g transform="matrix(.013,0,0,-0.013,10.158,0)"><path id="g117-94" d="M531 285V335L57 550V494L473 310L57 127V71L531 285ZM531 -40V10H57V-40H531Z"/></g></svg><span class="irelop"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="6.416pt" style="vertical-align:-1.11981pt" height="9.46863pt" version="1.1" viewBox="21.3711838 -8.34882 6.416 9.46863"><g transform="matrix(.013,0,0,-0.013,21.421,0)"><path id="g113-51" d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"/></g></svg>,</span></span> <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="51.508pt" style="vertical-align:-4.67947pt" id="M7" height="13.9678pt" version="1.1" viewBox="-0.0498162 -9.28833 51.508 13.9678"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-225"/></g><g transform="matrix(.0091,0,0,-0.0091,5.668,3.132)"><use xlink:href="#g50-92"/></g><g transform="matrix(.0091,0,0,-0.0091,8.926,3.132)"><use xlink:href="#g50-52"/></g><g transform="matrix(.0091,0,0,-0.0091,13.358,3.132)"><use xlink:href="#g50-83"/></g><g transform="matrix(.0091,0,0,-0.0091,19.145,3.132)"><use xlink:href="#g50-94"/></g><g transform="matrix(.013,0,0,-0.013,22.964,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,27.462,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.013,0,0,-0.013,35.747,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,43.877,0)"><path id="g117-93" d="M531 71V127L115 310L531 494V550L57 335V285L531 71ZM531 -40V10H57V-40H531Z"/></g></svg><span class="irelop"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="53.72pt" style="vertical-align:-4.67947pt" height="13.9678pt" version="1.1" viewBox="55.0901838 -9.28833 53.72 13.9678"><g transform="matrix(.013,0,0,-0.013,55.14,0)"><path id="g113-52" d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z"/></g><g transform="matrix(.013,0,0,-0.013,61.38,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.013,0,0,-0.013,70.812,0)"><use xlink:href="#g117-36"/></g><g transform="matrix(.013,0,0,-0.013,81.348,0)"><path id="g113-116" d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"/></g><g transform="matrix(.013,0,0,-0.013,86.223,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,90.721,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.013,0,0,-0.013,99.006,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,103.504,0)"><path id="g113-48" d="M368 703H309L44 -163H104L368 703Z"/></g></svg><span class="isep"/><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="6.643pt" style="vertical-align:-4.67947pt" height="13.9678pt" version="1.1" viewBox="108.8161838 -9.28833 6.643 13.9678"><g transform="matrix(.013,0,0,-0.013,108.866,0)"><use xlink:href="#g113-51"/></g></svg></span> and <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="51.508pt" style="vertical-align:-4.67947pt" id="M8" height="13.9678pt" version="1.1" viewBox="-0.0498162 -9.28833 51.508 13.9678"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-225"/></g><g transform="matrix(.0091,0,0,-0.0091,5.668,3.132)"><use xlink:href="#g50-92"/></g><g transform="matrix(.0091,0,0,-0.0091,8.926,3.132)"><use xlink:href="#g50-52"/></g><g transform="matrix(.0091,0,0,-0.0091,13.358,3.132)"><use xlink:href="#g50-83"/></g><g transform="matrix(.0091,0,0,-0.0091,19.145,3.132)"><use xlink:href="#g50-94"/></g><g transform="matrix(.013,0,0,-0.013,22.964,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,27.462,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.013,0,0,-0.013,35.747,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,43.877,0)"><use xlink:href="#g117-94"/></g></svg><span class="irelop"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="50.321pt" style="vertical-align:-4.67947pt" height="13.9678pt" version="1.1" viewBox="55.0901838 -9.28833 50.321 13.9678"><g transform="matrix(.013,0,0,-0.013,55.14,0)"><path id="g113-3" d="M348 662V703H120V-163H181V570C181 649 184 662 290 662H348Z"/></g><g transform="matrix(.013,0,0,-0.013,60.379,0)"><path id="g113-53" d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"/></g><g transform="matrix(.013,0,0,-0.013,66.619,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,71.117,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.013,0,0,-0.013,77.643,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,82.141,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.013,0,0,-0.013,90.426,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,97.83,0)"><use xlink:href="#g117-36"/></g></svg><span class="ibiop"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="64.94pt" style="vertical-align:-4.67947pt" height="13.9678pt" version="1.1" viewBox="108.3161838 -9.28833 64.94 13.9678"><g transform="matrix(.013,0,0,-0.013,108.366,0)"><use xlink:href="#g113-51"/></g><g transform="matrix(.013,0,0,-0.013,117.512,0)"><path id="g117-33" d="M535 230V280H52V230H535Z"/></g><g transform="matrix(.013,0,0,-0.013,128.048,0)"><path id="g113-127" d="M442 569C442 628 407 660 362 660C328 660 292 648 255 616C200 568 165 508 123 334L106 264C80 242 52 222 23 202L30 176C54 191 76 205 100 222L87 166C73 103 79 43 95 19C108 0 139 -12 169 -12C242 -12 318 38 369 106L354 129C322 93 260 49 215 49C173 49 147 81 170 187L189 274C293 344 442 452 442 569ZM380 565C380 478 267 377 196 322L216 406C254 556 282 623 332 623C364 623 380 596 380 565Z"/></g><g transform="matrix(.013,0,0,-0.013,134.095,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,138.593,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.013,0,0,-0.013,146.879,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,151.377,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,155.875,0)"><use xlink:href="#g113-48"/></g><g transform="matrix(.013,0,0,-0.013,161.236,0)"><use xlink:href="#g113-52"/></g><g transform="matrix(.013,0,0,-0.013,167.476,0)"><path id="g113-4" d="M284 -163V703H56V663H114C220 663 223 649 223 571V-163H284Z"/></g></svg>,</span></span> where <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.26807pt" id="M9" height="11.5564pt" version="1.1" viewBox="-0.0498162 -9.28833 22.3347 11.5564" width="22.3347pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-116"/></g><g transform="matrix(.013,0,0,-0.013,4.875,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,9.373,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.013,0,0,-0.013,17.658,0)"><use xlink:href="#g113-42"/></g></svg> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.26807pt" id="M10" height="11.5564pt" version="1.1" viewBox="-0.0498162 -9.28833 23.5091 11.5564" width="23.5091pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-127"/></g><g transform="matrix(.013,0,0,-0.013,6.047,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,10.545,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.013,0,0,-0.013,18.83,0)"><use xlink:href="#g113-42"/></g></svg> are the number of support vertices and leaves of <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.04981995pt" id="M11" height="9.01194pt" version="1.1" viewBox="-0.0498162 -8.96212 8.41168 9.01194" width="8.41168pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-85"/></g></svg>.</span>

M. Hajjari

H. Abdollahzadeh Ahangar

R. Khoeilar

Z. Shao

S. M. Sheikholeslami

New Bounds on the Triple Roman Domination Number of Graphs

This paper provides an in-depth study and analysis of the characterization of the digital economy ecosystem and the mechanism of eye-flowering through the method of interspecies competition. The evolutionary game model of symbiotic decision-making in the entrepreneurial ecosystem is constructed, the evolutionary process of symbiotic decision-making of subjects is analyzed through mathematical derivation, and the symbiotic decision-making process of subjects is simulated through computer simulation to answer how the subjects of the entrepreneurial ecosystem make symbiotic decisions and explore the mechanism of symbiotic formation of the entrepreneurial ecosystem. Then, based on the ecological perspective, the symbiotic evolution model of entrepreneurial ecosystem subjects is constructed from the subject level, the equilibrium point of the evolution of entrepreneurial ecosystem subjects, the stability conditions, and the relationship between the equilibrium point and the symbiosis model are analyzed, and the symbiotic evolution paths of entrepreneurial ecosystem subjects under different symbiosis modes, initial population size, maximum size, and natural growth rate are presented with simulation experiments, respectively. The main characteristics and manifestations of the dynamic evolution of the platform ecosystem are analyzed, and the key competitive factors that determine the dynamic evolution of the platform ecosystem are depicted. Then, according to the inherent characteristic laws of the platform ecosystem, the complex network approach is applied to construct a dynamic evolution model with originality and wide applicability for the change of bilateral user scale. Based on the dynamic evolution process, the relationship between model parameters and business performance is explored, and the trajectory of bilateral user size change over time and the range of parameters are derived by numerical calculation. Finally, using Monte Carlo simulation methods, the dynamic evolution model is used to predict the future operating conditions of platform enterprises, providing a valuation basis for investors to make investment decisions and helping platform managers to formulate business strategies.

Han Zhou

Xiaorui Han

Le Wang

Characterization and Evolution of a Digital Economy Ecosystem Based on an Interspecies Competition Model

Moving target detection (MTD) is one of the emphases and difficulties in the field of computer vision and image processing. It is the basis of moving target tracking and behavior recognition. We propose two methods are improved and fused, respectively, and the fusion algorithm is applied to the complex scene for MTD, so as to improve the accuracy of MTD in complex and hybrid scenes. Using the main idea of the three-frame difference image method, the background difference method and the interframe difference method are combined to make their advantages complementary to overcome each other’s weaknesses. The experimental results show that the method can be well adapted to the situation of periodic motion interference in the background, and it can adapt to the situation of sudden background changes.

Zhichao Xiong

[Retracted] Design of Sports Image Contour Feature Acquisition System Based on the Background Subtraction Method

For different premodular, which is a generalization of modular, defined by weighted Orlicz sequence space and its prequasi operator ideal, we have examined the existence of a fixed point for both Kannan contraction and nonexpansive mappings acting on these spaces. Some numerous numerical experiments and practical applications are presented to support our results.

Awad A. Bakery

OM Kalthum S. K. Mohamed

Nonexpansive Mappings on New Premodular Special Space of Sequences

In this paper, RNN (Recurrent Neural Network) algorithm is used to conduct an in-depth analysis of HR strategic decision-making and an HR strategic decision model is constructed for simulation. The four evaluation dimensions of index screening are extracted, the generalized gray correlation analysis is applied to screen the initial selection indexes of HR strategic decision-making, and then the HR strategic decision-making index system of power supply enterprises is constructed. On this basis, the applicability of the BP neural network in HR strategic decision-making is analysed and demonstrated, a BP neural network-based HR strategic decision-making model for power supply enterprises is constructed, and the rationality of the model is illustrated through the model training and testing. Finally, an empirical study is conducted with S power supply company as an example to illustrate the operability of the BP network model for HR strategic decision-making. The results of this paper provide a scientific basis for human resource decision-making in power supply enterprises and provide theoretical support for promoting the healthy development of power supply enterprises. Improving the level of human resource management can make fuller use of human resources and realize the strategic goals of the enterprise. A strategy for optimizing the training of hybrid convolutional neural networks is proposed, using an exponential linear unit activation function to solve the problem of neuron dead zones, a hybrid pooling strategy is used to improve the problem of feature information loss in maximum pooling processing, and an improved cross-entropy loss function is used to solve the problem of insufficient learning of difficult classification samples. The optimization of the model training process is finally completed, and the recommendation quality is improved. The Bayesian probability distribution table is learned to be filled in the expert data set; finally, the accuracy and effectiveness of the model are tested on the experimental platform. The results of the experiments show that the established Bayesian model beats the platform&#x2019;s built-in intelligent method with a 78.2&#x0025; win rate. That is, the model can make intelligent recommendations for strategies in staffed and unmanned platform decision-making and command-and-control combat units to execute tactical actions to achieve the best operational effectiveness.

Xiaorong Li

Lijun Zhang

Dongchen Li

Dan Guo

Construction and Simulation of a Strategic HR Decision Model Based on Recurrent Neural Network

Since the exhibition is an exhibition industry, it has got so much importance by many countries. In China, the development of the said industry is wonderful. Therefore, we use the grey relational model to study the impact of convention. Moreover, the exhibition industry on regional economic development is proposed, and the concept and characteristics of exhibition industry, exhibition economy, and the research results of exhibition industry at home and abroad are expounded in detail. Then, according to the influence mechanism of exhibition industry on regional economy, the grey relational model is used to analyze the economic development of Changsha from 2012 to 2016. The analysis disclosed that the exhibition industry remained the main driving force of Changsha’s economic development in these five years, which effectively promoted the economic development and the benign growth of various industries in Changsha.

Xiaoning Yang

[Retracted] The Impact of Convention and Exhibition Industry on Regional Economic Development Based on Grey Relational Model

With the development of the country’s economy, there is a flourishing situation in the field of culture and art. However, the diversification of artistic expressions has not brought development to folk music. On the contrary, it brought a huge impact, and some national music even fell into the dilemma of being lost. This article is mainly aimed at the recognition and classification of folk music emotions and finds the model that can make the classification accuracy rate as high as possible. The classification model used in this article is mainly after determining the use of Support Vector Machine (SVM) classification method, a variety of attempts have been made to feature extraction, and good results have been achieved. Explore the Deep Belief Network (DBN) pretraining and reverse fine-tuning process, using DBN to learn the fusion characteristics of music. According to the abstract characteristics learned by them, the recognition and classification of folk music emotions are carried out. The DBN is improved by adding “Dropout” to each Restricted Boltzmann Machine (RBM) and adjusting the increase standard of weight and bias. The improved network can avoid the overfitting problem and speed up the training of the network. Through experiments, it is found that using the fusion features proposed in this paper, through classification, the classification accuracy has been improved.

Zijin Wu

[Retracted] Research on Automatic Classification Method of Ethnic Music Emotion Based on Machine Learning

In the paper, we study the upper bound estimation of the Lebesgue constant of the bivariate Lagrange interpolation polynomial based on the common zeros of product Chebyshev polynomials of the second kind on the square <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.1507pt" id="M1" height="13.7421pt" version="1.1" viewBox="-0.0498162 -11.5914 39.3903 13.7421" width="39.3903pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-92" d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z"/></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><path id="g117-33" d="M535 230V280H52V230H535Z"/></g><g transform="matrix(.013,0,0,-0.013,12.116,0)"><path id="g113-50" d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"/></g><g transform="matrix(.013,0,0,-0.013,18.356,0)"><path id="g113-45" d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"/></g><g transform="matrix(.013,0,0,-0.013,23.499,0)"><use xlink:href="#g113-50"/></g><g transform="matrix(.013,0,0,-0.013,29.739,0)"><path id="g113-94" d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z"/></g><g transform="matrix(.0091,0,0,-0.0091,34.224,-5.741)"><path id="g50-51" d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"/></g></svg>.</span> And, we prove that the growth order of the Lebesgue constant is <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.2681pt" id="M2" height="13.8595pt" version="1.1" viewBox="-0.0498162 -11.5914 58.8112 13.8595" width="58.8112pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-80" d="M699 369C699 549 575 666 407 666C186 666 23 488 23 278C23 101 145 -16 312 -16C535 -16 699 153 699 369ZM600 373C600 210 500 19 321 19C186 19 120 129 120 272C120 450 232 631 399 631C541 631 600 522 600 373Z"/></g><g transform="matrix(.013,0,0,-0.013,9.387,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.013,0,0,-0.013,13.885,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,18.383,0)"><path id="g113-111" d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"/></g><g transform="matrix(.013,0,0,-0.013,27.815,0)"><path id="g117-36" d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"/></g><g transform="matrix(.013,0,0,-0.013,38.351,0)"><path id="g113-51" d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"/></g><g transform="matrix(.013,0,0,-0.013,44.591,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g><g transform="matrix(.0091,0,0,-0.0091,49.089,-5.741)"><use xlink:href="#g50-51"/></g><g transform="matrix(.013,0,0,-0.013,54.036,0)"><use xlink:href="#g113-42"/></g></svg>.</span> This result is different from the Lebesgue constant of Lagrange interpolation polynomial on the unit disk, the growth order of which is <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.636801pt" id="M3" height="13.1484pt" version="1.1" viewBox="-0.0498162 -10.5116 35.0703 13.1484" width="35.0703pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-80"/></g><g transform="matrix(.013,0,0,-0.013,9.387,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,13.885,-.271)"><path id="g119-37" d="M782 731H740L476 -79H474L280 352L133 274L151 239L242 286L473 -219L782 731Z"/></g><rect height="0.65243" width="6.55046" x="23.8545" y="-9.80939"/><g transform="matrix(.013,0,0,-0.013,23.854,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.013,0,0,-0.013,30.405,0)"><use xlink:href="#g113-42"/></g></svg>.</span> And, it is different from the Lebesgue constant of the Lagrange interpolation polynomial based on the common zeros of product Chebyshev polynomials of the first kind on the square <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.1507pt" id="M4" height="13.7421pt" version="1.1" viewBox="-0.0498162 -11.5914 39.3903 13.7421" width="39.3903pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-92"/></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><use xlink:href="#g117-33"/></g><g transform="matrix(.013,0,0,-0.013,12.116,0)"><use xlink:href="#g113-50"/></g><g transform="matrix(.013,0,0,-0.013,18.356,0)"><use xlink:href="#g113-45"/></g><g transform="matrix(.013,0,0,-0.013,23.499,0)"><use xlink:href="#g113-50"/></g><g transform="matrix(.013,0,0,-0.013,29.739,0)"><use xlink:href="#g113-94"/></g><g transform="matrix(.0091,0,0,-0.0091,34.224,-5.741)"><use xlink:href="#g50-51"/></g></svg>,</span> the growth order of which is <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.2681pt" id="M5" height="13.8595pt" version="1.1" viewBox="-0.0498162 -11.5914 49.5162 13.8595" width="49.5162pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-80"/></g><g transform="matrix(.013,0,0,-0.013,9.387,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,13.885,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,18.383,0)"><path id="g190-109" d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z"/></g><g transform="matrix(.013,0,0,-0.013,21.672,0)"><path id="g190-111" d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 331 449C302 449 276 437 248 419C223 402 201 387 181 372V451C137 432 90 420 42 411V388C96 378 102 374 102 310V104C102 38 97 33 29 26V0H246V26C187 32 181 36 181 104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z"/></g><g transform="matrix(.013,0,0,-0.013,28.822,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.013,0,0,-0.013,35.348,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.0091,0,0,-0.0091,39.846,-5.741)"><use xlink:href="#g50-51"/></g><g transform="matrix(.013,0,0,-0.013,44.793,0)"><use xlink:href="#g113-42"/></g></svg>.</span>

Juan Liu

Laiyi Zhu

Upper Bound for Lebesgue Constant of Bivariate Lagrange Interpolation Polynomial on the Second Kind Chebyshev Points

In this article, some algebraic properties of the Wilson loop have been investigated in a broad manner. These properties include identities, autotopisms, and implications. We use some equivalent conditions to study the behavior of holomorphism of this loop. Under the shadow of this holomorphism, we are able to observe coincident loops.

Han Li

M. Nadeem

M. A. Ali

H. Mutee ur Rehman

Some Algebraic Properties of the Wilson Loop

About this journal

<p><em>Journal of Mathematics</em> is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics.</p>


Journal profile

Meet the editorial board

<p>Chief Editor, Professor Jen-Chih Yao, is currently based at Zhejiang Normal University in China. His current research includes dynamic programming, mathematical programming, and operations research.</p>


Editor spotlight

Submit to Special Issue

We currently have a number of Special Issues open for submission. Special Issues highlight emerging areas of research within a field, or provide a venue for a deeper investigation into an existing research area.

Special Issues

Author guidelines

Editorial board

Databases and indexing

Journal of Mathematics - Table of contents 2022

title

Journal of Mathematics is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics.

Journal of Mathematics