The QiTai Radio Telescope (QTT) will be equipped with the active surface adjustment system (ASAS) to correct the main reflector deformation caused by environmental loading. In order to guarantee the stability and performance of the active surface system under fault conditions, it is necessary to adopt the fault-tolerant method when actuator faults have occurred. In this paper, a fault control method based on actuator faults weighting is proposed to solve the active surface fault control problem. According to the coordinates of the adjustable points of the panels corresponding to the faulty actuators, a new paraboloid is fitted by a weighted health matrix, and the fitting surface is taken as the target to adjust the surface shape.

Danqing Zhang

Binbin Xiang

Aili Yusup

Na Wang

Guljaina Kazezkhan

Fault Tolerance for Active Surface System with Actuator Faults

This work aims to study the stability of certain motions of a rigid body rotating about its fixed point and carrying a rotor that rotates with constant angular velocity about an axis parallel to one of the principal axes. This motion is presumed to take place due to the combined influence of the magnetic field and the Newtonian force field. The equations of motion are deduced, and moreover, they are expressed as a Lie&#x2013;Poisson Hamilton system. The permanent rotations are calculated and interpreted mechanically. The sufficient conditions for instability are presented employing the linear approximation method. The energy-Casimir method is applied to gain sufficient conditions for stability. The regions of linear stability and Lyapunov stability are illustrated graphically for certain values of the parameters.

A. A. Elmandouh

Fatimah H. Alsaad

The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field

Using an analytical and numerical study, this paper investigates the equilibrium state of the triangular equilibrium points <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.3507pt" id="M1" height="12.9866pt" version="1.1" viewBox="-0.0498162 -8.6359 23.0296 12.9866" width="23.0296pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-77" d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"/></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path id="g50-53" d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z"/></g><g transform="matrix(.0091,0,0,-0.0091,12.726,3.132)"><path id="g50-45" d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"/></g><g transform="matrix(.0091,0,0,-0.0091,17.928,3.132)"><path id="g50-54" d="M158 548H390L417 615L410 623H122L83 318C105 326 143 337 185 337C296 337 350 275 350 188C350 116 308 42 225 42C164 42 122 74 100 93C90 101 82 99 72 92C60 82 51 68 50 59C48 46 52 38 66 24C82 9 125 -12 172 -12C225 -11 292 15 346 59C408 108 437 166 437 226C437 309 371 397 242 397C214 397 170 382 133 369L158 548Z"/></g></svg> of the Sun-Earth system in the frame of the elliptic restricted problem of three bodies subject to the radial component of Poynting–Robertson (P–R) drag and radiation pressure factor of the bigger primary as well as dynamical flattening parameters of both primary bodies (i.e., Sun and Earth). The equations of motion are presented in a dimensionless-pulsating coordinate system <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.429399pt" id="M2" height="13.1353pt" version="1.1" viewBox="-0.0498162 -9.7059 34.8918 13.1353" width="34.8918pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><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,-0.013,4.498,0)"><path id="g113-236" d="M425 682C425 693 422 699 407 699C369 699 308 677 260 646C213 651 191 674 191 701C191 715 195 726 200 734L183 740C153 730 118 709 118 681C118 644 163 619 218 615C168 582 115 534 115 463C115 418 147 382 180 369C102 329 23 261 23 163C23 74 74 38 158 14C183 7 201 2 221 -2C279 -15 290 -33 290 -58C290 -94 251 -145 230 -169L252 -189C280 -171 367 -103 367 -25C367 20 333 51 266 68C245 73 218 80 191 89C139 106 107 135 107 192C107 261 161 329 221 355C248 350 281 347 314 347C330 347 370 388 370 406C370 418 366 422 352 422C321 422 280 413 255 407C218 413 192 448 192 493C192 544 229 588 266 610C309 610 354 615 376 623C397 631 425 651 425 682Z"/></g><g transform="matrix(.013,0,0,-0.013,13.229,0)"><path id="g117-33" d="M535 230V280H52V230H535Z"/></g><g transform="matrix(.013,0,0,-0.013,23.765,0)"><path id="g113-229" d="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z"/></g><g transform="matrix(.013,0,0,-0.013,30.188,0)"><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></svg>,</span> and the positions of the triangular equilibrium points are found to depend on the mass ratio <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.42947pt" id="M3" height="12.7178pt" version="1.1" viewBox="-0.0498162 -9.28833 16.3714 12.7178" width="16.3714pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path id="g113-234" d="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z"/></g><g transform="matrix(.013,0,0,-0.013,11.714,0)"><use xlink:href="#g113-42"/></g></svg> and the perturbing forces involved in the equations of motion. A numerical analysis of the positions and stability of the triangular equilibrium points of the Sun-Earth system shows that the perturbing forces have no significant effect on the positions of the triangular equilibrium points and their stability. Hence, this research work concludes that the motion of an infinitesimal mass near the triangular equilibrium points of the Sun-Earth system remains linearly stable in the presence of the perturbing forces.

Aishetu Umar

Aminu Abubakar Hussain

Impacts of Poynting&#x2013;Robertson Drag and Dynamical Flattening Parameters on Motion around the Triangular Equilibrium Points of the Photogravitational ER3BP

This study presents the chaotic oscillation of the satellite around the Earth due to aerodynamic torque. The orbital plane of the satellite concurs is same as the tropical plane of Earth. The half-width of riotous separatrix is assessed utilizing Chirikov&#x2019;s measure. Variety of boundary techniques shows that streamlined force boundary (<i>&#x25b;</i>), unpredictability of circle (<i>e</i>), and mass-proportion (<i>&#x3c9;</i><sub>0</sub>) convert normal wavering to the disorganized one. We studied the behavior of trajectories due to change in parameters with Lyapunov exponents and time series plots. The theory is applied to Resourcesat-1, an artificial satellite of the Earth.

Rashmi Bhardwaj

Mohammad Sajid

Chaotic Oscillation of Satellite due to Aerodynamic Torque

In the present work, we investigate the existence of compact star model in the background of <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="28.086pt" style="vertical-align:-3.42947pt" id="M2" height="12.7178pt" version="1.1" viewBox="-0.0498162 -9.28833 28.086 12.7178"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-103"/></g><g transform="matrix(.013,0,0,-0.013,8.352,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,12.85,0)"><use xlink:href="#g198-19"/></g><g transform="matrix(.013,0,0,-0.013,25.122,0)"><use xlink:href="#g113-45"/></g></svg><span class="ipunc"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="12.83pt" style="vertical-align:-3.42947pt" height="12.7178pt" version="1.1" viewBox="30.215183800000002 -9.28833 12.83 12.7178"><g transform="matrix(.013,0,0,-0.013,30.265,0)"><use xlink:href="#g197-31"/></g><g transform="matrix(.013,0,0,-0.013,38.356,0)"><use xlink:href="#g113-42"/></g></svg></span> gravity theory, where <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2455397pt" id="M3" height="9.25986pt" version="1.1" viewBox="-0.0498162 -9.01432 12.4177 9.25986" width="12.4177pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g198-19"/></g></svg> represents the Ricci scalar and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.04981995pt" id="M4" height="8.73791pt" version="1.1" viewBox="-0.0498162 -8.68809 8.21596 8.73791" width="8.21596pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g197-31"/></g></svg> refers to the energy-momentum tensor trace. Here, we use Karmarkar condition for the interior stellar setup so that a complete and precise model following the embedding class-I strategy can be obtained. For this purpose, we assume anisotropic matter contents along with static and spherically symmetric geometry of compact star. As Karmarkar embedding condition yields a relationship of metric potentials, therefore we assume a suitable form for one of the metric components as <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="22.404pt" style="vertical-align:-0.3499994pt" id="M5" height="12.3798pt" version="1.1" viewBox="-0.0498162 -12.0298 22.404 12.3798"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-102" d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z"/></g><g transform="matrix(.0091,0,0,-0.0091,5.382,-5.741)"><path id="g50-243" d="M552 243C552 372 474 431 385 468C378 471 378 492 382 510L419 675L401 683L345 637L224 54C173 71 118 128 118 218C118 323 174 382 270 423L255 458C130 420 24 339 24 204C24 97 93 14 213 -8L188 -131C170 -220 197 -250 217 -257L224 -254L278 -7C427 -3 552 98 552 243ZM478 228C478 124 408 37 287 40L363 405C401 395 478 336 478 228Z"/></g><g transform="matrix(.013,0,0,-0.013,14.773,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></g></svg><span class="irelop"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="27.552pt" style="vertical-align:-0.3499994pt" height="12.3798pt" version="1.1" viewBox="25.986183800000003 -12.0298 27.552 12.3798"><g transform="matrix(.013,0,0,-0.013,26.036,0)"><path id="g113-98" d="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z"/></g><g transform="matrix(.013,0,0,-0.013,32.616,0)"><path id="g113-115" d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z"/></g><g transform="matrix(.0091,0,0,-0.0091,38.105,-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><g transform="matrix(.013,0,0,-0.013,45.957,0)"><path id="g117-36" d="M535 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451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"/></g><g transform="matrix(.0091,0,0,-0.0091,67.254,-5.741)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g><g transform="matrix(.0091,0,0,-0.0091,72.814,-5.741)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g><g transform="matrix(.013,0,0,-0.013,77.798,0)"><use xlink:href="#g113-115"/></g><g transform="matrix(.0091,0,0,-0.0091,83.286,-5.741)"><use xlink:href="#g50-111"/></g><g transform="matrix(.013,0,0,-0.013,91.367,0)"><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="6.547pt" style="vertical-align:-0.3499994pt" height="12.3798pt" version="1.1" viewBox="101.85318380000001 -12.0298 6.547 12.3798"><g transform="matrix(.013,0,0,-0.013,101.903,0)"><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></svg>,</span></span> where <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063904pt" id="M6" height="6.1673pt" version="1.1" viewBox="-0.0498162 -5.96091 6.7023 6.1673" width="6.7023pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-98"/></g></svg> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M7" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-99"/></g></svg> represent constants and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063904pt" id="M8" height="6.1673pt" version="1.1" viewBox="-0.0498162 -5.96091 6.6501 6.1673" width="6.6501pt"><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></svg> is a free parameter, and evaluate the other. We approximate the values of physical parameters like <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="9.544pt" style="vertical-align:-1.576501pt" id="M9" height="10.2124pt" version="1.1" viewBox="-0.0498162 -8.6359 9.544 10.2124"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-98"/></g><g transform="matrix(.013,0,0,-0.013,6.58,0)"><use xlink:href="#g113-45"/></g></svg><span class="ipunc"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="9.307pt" style="vertical-align:-1.576501pt" height="10.2124pt" version="1.1" viewBox="11.6731838 -8.6359 9.307 10.2124"><g transform="matrix(.013,0,0,-0.013,11.723,0)"><path id="g113-66" d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z"/></g></svg>,</span></span> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0498209pt" id="M10" height="8.68572pt" version="1.1" viewBox="-0.0498162 -8.6359 7.94191 8.68572" width="7.94191pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-67" d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"/></g></svg> by utilizing the known values of mass and radius for the compact star Vela X-1. The validity of the acquired model is then explored for different values of coupling parameter <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M11" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 7.30254 9.49473" width="7.30254pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-233" d="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"/></g></svg> graphically. It is found that the resulting solution is physically interesting and well-behaved.

M. Zubair

Saira Waheed

Hina Javaid

A Generic Embedding Class-I Model via Karmarkar Condition in <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"   style="vertical-align:-3.42947pt" height="12.7178pt" version="1.1" viewBox="-0.0498162 -9.28833 43.0952 12.7178" width="43.0952pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-103" d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" /></g><g transform="matrix(.013,0,0,-0.013,8.352,0)"><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,-0.013,12.85,0)"><path id="g198-19" d="M852 669C820 657 792 643 768 628C705 667 627 687 547 687C310 687 154 548 154 412C154 332 212 282 296 282C434 282 515 426 523 557H503C474 402 410 312 298 312C241 312 195 352 195 408C195 535 341 657 546 657C613 657 683 644 738 609C640 538 574 431 486 271C374 71 314 16 189 16C118 16 69 60 69 95H71C78 84 93 83 101 83C129 83 144 106 144 131C144 160 121 179 93 179C60 179 34 151 34 108C34 42 100 -15 207 -15C364 -15 491 73 603 304C614 297 639 293 650 293C681 293 683 254 683 245C683 181 599 150 599 70C599 21 645 -12 692 -12C747 -12 804 30 868 103L851 119C789 52 741 18 706 18C685 18 674 29 674 52C674 92 750 157 750 226C750 257 727 287 696 310V312C812 315 876 394 876 473C876 525 849 577 793 612C812 627 832 639 859 650L852 669ZM814 486C814 417 765 345 686 337C669 348 649 354 626 354C673 451 708 533 766 588C799 561 814 525 814 486Z" /></g><g transform="matrix(.013,0,0,-0.013,25.122,0)"><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,-0.013,30.265,0)"><path id="g197-31" d="M622 618V662H20V618H238V0H404V618H622ZM360 44H282V618H360V44Z" /></g><g transform="matrix(.013,0,0,-0.013,38.356,0)"><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></svg> Gravity

We present a new statistical analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey (data release 7). A set of volume-limited samples shows that the stellar mass of galaxies is concentrated in a range of galaxy luminosities that is very different from the range selected by the usual analysis of galaxy positions. Nevertheless, the two-point correlation function is a power-law with the usual exponent <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="17.779pt" style="vertical-align:-3.42938pt" id="M1" height="11.7782pt" version="1.1" viewBox="-0.0498162 -8.34882 17.779 11.7782"><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(.013,0,0,-0.013,10.148,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></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="57.15pt" style="vertical-align:-3.42938pt" height="11.7782pt" version="1.1" viewBox="21.361183800000003 -8.34882 57.15 11.7782"><g transform="matrix(.013,0,0,-0.013,21.411,0)"><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,-0.013,27.651,0)"><path id="g113-47" d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"/></g><g transform="matrix(.013,0,0,-0.013,30.615,0)"><path id="g113-56" d="M447 623H65C61 580 56 530 47 475H76C100 541 106 550 172 550H388C308 376 196 170 91 -1L98 -12L172 -2C268 204 360 408 455 611L447 623Z"/></g><g transform="matrix(.013,0,0,-0.013,36.857,0)"><use xlink:href="#g113-50"/></g><g transform="matrix(.013,0,0,-0.013,46.003,0)"><path id="g117-33" d="M535 230V280H52V230H535Z"/></g><g transform="matrix(.013,0,0,-0.013,56.539,0)"><use xlink:href="#g113-50"/></g><g transform="matrix(.013,0,0,-0.013,62.779,0)"><use xlink:href="#g113-47"/></g><g transform="matrix(.013,0,0,-0.013,65.743,0)"><path id="g113-57" d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z"/></g><g transform="matrix(.013,0,0,-0.013,71.983,0)"><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> which varies with luminosity. The mass concentration property allows us to make a meaningful analysis of the angular distribution of the full flux-limited sample. With this analysis, after suppressing the shot noise, we extend further the scaling range and thus obtain <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="17.779pt" style="vertical-align:-3.42938pt" id="M2" height="11.7782pt" version="1.1" viewBox="-0.0498162 -8.34882 17.779 11.7782"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-225"/></g><g transform="matrix(.013,0,0,-0.013,10.148,0)"><use xlink:href="#g117-34"/></g></svg><span class="irelop"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="21.915pt" style="vertical-align:-3.42938pt" height="11.7782pt" version="1.1" viewBox="21.361183800000003 -8.34882 21.915 11.7782"><g transform="matrix(.013,0,0,-0.013,21.411,0)"><use xlink:href="#g113-50"/></g><g transform="matrix(.013,0,0,-0.013,27.651,0)"><use xlink:href="#g113-47"/></g><g transform="matrix(.013,0,0,-0.013,30.615,0)"><use 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transform="matrix(.013,0,0,-0.013,97.722,0)"><path id="g190-113" d="M169 380V459C122 440 66 423 24 416V392C86 384 90 382 90 317V-135C90 -201 81 -207 17 -213V-240H253V-213C176 -207 169 -201 169 -125V6C182 -1 208 -11 238 -12C368 12 487 109 487 260C487 358 421 449 310 449C298 449 279 444 261 433L169 380ZM169 346C196 367 237 389 269 389C341 389 403 329 403 221C403 109 347 37 263 37C228 37 191 53 169 76V346Z"/></g><g transform="matrix(.013,0,0,-0.013,104.652,0)"><path id="g190-100" d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z"/></g></svg>.</span></span> Fractional statistical moments of the coarse-grained stellar mass density exhibit multifractal scaling. Our results support a multifractal model with a transition to homogeneity at about <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.1684pt" id="M4" height="15.0339pt" version="1.1" viewBox="-0.0498162 -11.8655 53.7923 15.0339" width="53.7923pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-50"/></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><use xlink:href="#g113-49"/></g><g transform="matrix(.013,0,0,-0.013,12.48,0)"><use xlink:href="#g190-105"/></g><g transform="matrix(.0091,0,0,-0.0091,19.448,-6.016)"><use xlink:href="#g54-33"/></g><g transform="matrix(.0091,0,0,-0.0091,25.008,-6.016)"><use xlink:href="#g50-50"/></g><g transform="matrix(.013,0,0,-0.013,29.975,0)"><use xlink:href="#g190-78"/></g><g transform="matrix(.013,0,0,-0.013,41.128,0)"><use xlink:href="#g190-113"/></g><g transform="matrix(.013,0,0,-0.013,48.057,0)"><use xlink:href="#g190-100"/></g></svg>.</span>

Jos&#xe9; Gaite

Scaling Laws in the Stellar Mass Distribution and the Transition to Homogeneity

A shooting method has been introduced for determining the numerical solution of the ordinary differential equations which describe the Newtonian magnetohydrodynamic laminar fluid flow due to an unsteady stretching sheet together with the presence of thermal radiation and variable heat flux. The variable viscosity and variable conductivity are taken into consideration. Absence of magnetic field in some studies restricts the development of the energy-efficient heat transfer mechanism as is desired in numerous applications. The present study encompasses parameters such as unsteadiness parameter, porous parameter, viscosity parameter, magnetic number, radiation parameter, and conductivity parameter. It has been consummated that the proposed model is superior to other existing models for the industrial fluid.

Ahmed M. Megahed

Nourhan I. Ghoneim

M. Gnaneswara Reddy

Mostafa El-Khatib

Magnetohydrodynamic Fluid Flow due to an Unsteady Stretching Sheet with Thermal Radiation, Porous Medium, and Variable Heat Flux

This paper investigates the geometry of compact stellar objects through the Noether symmetry approach in the energy-momentum squared gravity. This newly developed theory overcomes the problems of big bang singularity and provides the viable cosmological consequences in the early time universe. Moreover, its implications occur in high curvature regime where the deviations of energy-momentum squared gravity from general relativity is confirmed. We consider the minimal coupling model of this modified theory and formulate symmetry generators as well as corresponding conserved quantities. We use conservation relation and apply some suitable initial conditions to evaluate the metric potentials. Finally, we explore some interesting features of the compact objects for appropriate values of the model parameters through numeric analysis. It is found that compact stellar objects in this particular framework depend on the model parameters as well as conserved quantities. We conclude that Noether symmetries generate solutions that are consistent with the astrophysical observational data and hence confirm the viability of this procedure.

M. Sharif

M. Zeeshan Gul

Compact Stars Admitting Noether Symmetries in Energy-Momentum Squared Gravity

H. Nazar

G. Abbas

Model of Charged Anisotropic Strange Stars in Minimally Coupled <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"   style="vertical-align:-3.42947pt" height="12.7178pt" version="1.1" viewBox="-0.0498162 -9.28833 25.6882 12.7178" width="25.6882pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-103" d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" /></g><g transform="matrix(.013,0,0,-0.013,8.352,0)"><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,-0.013,12.85,0)"><path id="g113-83" d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" /></g><g transform="matrix(.013,0,0,-0.013,21.001,0)"><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></svg> Gravity

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<p><em>Advances in Astronomy</em> publishes in all areas of astronomy, astrophysics, and cosmology, and accepts observational and theoretical investigations into celestial objects and the wider universe.</p>


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<p>Chief Editor, Professor Trigo-Rodríguez (ICE, IEEC-CSIC), has a background in the formation of primitive solar system minor bodies, the study of their fragments in space and the analysis of their surviving rocks that arrived on the Earth.</p>


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