The present paper has enormous applications including fields of crystal growth, material processing, spacecraft, underground spread of chemical contaminants, petroleum reservoirs, waste dispersal and fertilizer migration in saturated soil, alloy solidification, and many more. The importance of double-diffusive convection has been recognized in various engineering applications, and it has thoroughly been investigated theoretically. In the presence of a constant heat source/sink on both layers, the double component-magneto-Marangoni-convection in a composite layer is examined. Due to heat, this combined layer is enclosed by adiabatic boundaries and exposed to basic temperature gradients. For the system of ordinary differential equations, the thermal surface-tension-driven (Marangoni) number, which also happens to be the Eigenvalue, is solved in closed form. For basic temperature gradients, the eigenvalues, or thermal Marangoni numbers are determined in closed form for lower rigid and higher free boundaries with surface tension, depending on both temperature and concentration. The effect of several parameters on the eigenvalue against depth ratio was studied. It is observed that the inverted parabolic temperature gradient on double component magneto-Marangoni-convection in a combined layer is the most stable of the three temperature gradients and for larger values of depth ratios, all physical parameters are nominal for the porous region dominant combined system.

N. Manjunatha

R. Sumithra

Nazek Alessa

K. Loganathan

C. Selvamani

Sonam Gyeltshen

Influence of Temperature Gradients and Heat Source in a Combined Layer on Double Component-Magneto-Marangoni-Convection

In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties. Then, we introduce a quaternion-type Catalan transform, which is a generalization of the Catalan transform, and its inverse. Moreover, we apply the quaternion-type Catalan transforms to <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.42943pt" id="M1" height="9.39034pt" version="1.1" viewBox="-0.0498162 -5.96091 7.13289 9.39034" width="7.13289pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-239" d="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 259Z"/></g></svg>-</span>Fibonacci and <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.42943pt" id="M2" height="9.39034pt" version="1.1" viewBox="-0.0498162 -5.96091 7.13289 9.39034" width="7.13289pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-239"/></g></svg>-</span>Lucas sequences and derive some new sequences by using these quaternion-type Catalan transforms.

Kübra Gül

Quaternion-Type Catalan Transforms of the <i>ρ</i>-Fibonacci and <i>ρ</i>-Lucas Numbers

Journal of Mathematics

Retracted: A Survey of Multimedia-Assisted English Classroom Teaching Based on Statistical Analysis

The author studies the minimax optimal control problem for an extensible beam equation that takes into account rotational inertia effects. A velocity term multiplied by the bilinear control and disturbance functions to construct a minimax optimal control strategy is added. The existence of an optimal pair, meaning optimal control and perturbation, is proved by assuming some conditions on the considered quadratic cost function. The optimal conditions for optimal pairs are provided by the adjoint systems that correspond to some physically meaningful observation cases.

Jinsoo Hwang

Bilinear Minimax Optimal Control Problems of the Velocity Term in an Extensible Beam Equation with Rotational Inertia

Multigranulation rough set theory is one of the most effective tools for data analysis and mining in multicriteria information systems. Six types of covering-based multigranulation fuzzy rough set (CMFRS) models have been constructed through fuzzy <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.42947pt" id="M1" height="12.7178pt" version="1.1" viewBox="-0.0498162 -9.28833 7.68094 12.7178" width="7.68094pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-224" d="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z"/></g></svg>-</span>neighborhoods or multigranulation fuzzy measures. However, it is often time-consuming to compute these CMFRS models with a large fuzzy covering using set representation approaches. Hence, presenting novel methods to compute them quickly is our motivation for this paper. In this article, we study the matrix representations of CMFRS models to save time in data processing. Firstly, some new matrices and matrix operations are proposed. Then, matrix representations of optimistic CMFRSs are presented. Moreover, matrix approaches for computing pessimistic CMFRSs are also proposed. Finally, some experiments are proposed to illustrate the effectiveness of our approaches.

Zaibin Chang

Junchao Wei

Matrix Approaches for Covering-Based Multigranulation Fuzzy Rough Set Models

The consistency problem of multiagent systems with the output feedback and state delay was considered in this paper. First, the reduced-order observer based on the consensus protocol of state delay is designed, and the consensus protocol is proposed by the output information of neighboring agents. Then, by constructing the Lyapunov–Krasovskii functional and combining matrix inequality and the Schur complement lemma, the asymptotic stability of the system can be obtained, and the consistency of state-delay multiagent systems is derived. Finally, the theoretical results are verified by a simulation example.

Xingmei Li

Shasha Deng

Yanhong Wang

Hongyong Deng

Stability Analysis of State Delay Multiagent Systems with Observer-Based Control Protocols

Predator interference refers to the competition effect on individuals of the same species through preventing or limiting access to a resource. In this paper, a novel predator–prey model that includes predator interference is considered. In the novel model, a high prey density is taken into consideration by investigating Crowley–Martin as a numerical response, while the growth rate of prey is logistically described and Holling type II is used as a functional response. In contrast to literature, this model has distinct and notable features: predator and prey species have an intraspecific competition, and this model has a numerical response that generalizes several of the commonly utilized depictions of predator interference. The boundedness of the model is proved. Predator interference effects are theoretically and numerically studied in terms of stability, coexistence, and extinction. Theoretical results show that the system has no effect on coexistence or extinction in these types of models. Numerical simulations present two different dynamics with identical results on the theoretical side of model stabilization for both dynamics. Moreover, the numerical simulations show that there is a change from periodic to steady state dynamics as the value of predator interference increases. This means that the coexistence probability of the model increases. The attained results are explained from both a mathematical and an ecological points of view.

Jawdat Alebraheem

Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

This article aims to propose an efficient Fibonacci wavelet-based collocation method for solving the nonlinear reaction-diffusion equation of Fisher-type. The underlying numerical scheme starts by formulating operational matrices of integration corresponding to the Fibonacci wavelets. Besides, we study the error analysis and convergence theorem of the proposed technique. Subsequently, a set of algebraic equations are formed corresponding to the given problem, which could be handled via any conventional method, for instance, the Newton iteration technique. To demonstrate the efficiency of the proposed wavelet-based numerical method, we compare the obtained absolute, <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.291101pt" id="M1" height="11.927pt" version="1.1" viewBox="-0.0498162 -8.6359 18.4041 11.927" width="18.4041pt"><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="g50-30" d="M1000 227C1000 351 905 451 780 451C658 451 590 380 530 279C465 385 388 451 261 451C168 451 38 376 38 210C38 98 121 -12 261 -12C381 -12 448 59 508 160C573 53 652 -12 780 -12C879 -12 1000 64 1000 227ZM485 199C434 109 370 25 271 25C188 25 133 117 133 241C133 355 189 414 249 414C357 414 426 302 485 199ZM903 204C903 70 852 25 790 25C681 25 611 136 552 240C603 330 669 414 768 414C855 414 903 321 903 204Z"/></g></svg>,</span> <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.1815pt" id="M2" height="11.8174pt" version="1.1" viewBox="-0.0498162 -8.6359 13.3712 11.8174" width="13.3712pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-77"/></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><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 root mean square (RMS) error norms with the existing Lie symmetry method and cubic trigonometric <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0498209pt" id="M3" 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>-</span>spline (CTB) differential quadrature method in tabular form. From the numerical outcomes, it is ascertained that the proposed numerical technique is computationally more effective and yields precise outcomes in comparison to the existing ones.

Naied A. Nayied

Firdous A. Shah

M. A. Khanday

Fibonacci Wavelet Method for the Numerical Solution of Nonlinear Reaction-Diffusion Equations of Fisher-Type

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<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>


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<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>


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Journal of Mathematics - Table of contents 2023

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