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In this paper, we study the existence and nonexistence of the global solutions to nonlinear reaction‐diffusion equations ut(x,t)=Δu(x,t)+ψ(t)f(u(x,t)),(x,t)∈Ω×(0,∞),u(·,0)=u0(x),x∈Ω,u(x,t)=0,(x,t)∈∂Ω×(0,∞),$$ \left\{\begin{array}{ll}{u}_t\left(x,t\right)=\Delta u\left(x,t\right)+\psi (t)f\left(u\left(x,t\right)\right),& \left(x,t\right)\in \Omega \times \left(0,\infty \right),\\ {}u\left(\cdotp, 0\right)={u}_0(x),& x\in \Omega, \\ {}u\left(x,t\right)=0,& \left(x,t\right)\in \mathrm{\partial \Omega}\times \left(0,\infty \right),\end{array}\right. $$where Ω$$ \Omega $$ is the half‐space ℝKN$$ {\mathrm{\mathbb{R}}}_K^N $$, ψ$$ \psi $$ is a nonnegative continuous function, and f$$ f $$ is a locally Lipschitz function with some additional properties. The purpose of this paper is to give a necessary and sufficient condition for the existence of global solutions as follows: There is no global solution for any nonnegative and nontrivial initial data u0∈C0(Ω)$$ {u}_0\in {C}_0\left(\Omega \right) $$ if and only if ∫1∞ψ(t)tN+K2fϵt−N+K2dt=∞$$ {\int}_1^{\infty}\psi (t){t}^{\frac{N+K}{2}}f\left(\epsilon \kern0.1em {t}^{-\frac{N+K}{2}}\right) dt=\infty $$ for every ϵ>0$$ \epsilon >0 $$. In fact, we introduce a very special curve in ℝKN$$ {\mathrm{\mathbb{R}}}_K^N $$x^(t):=t,⋯,t⏟K‐times,xK+1,⋯,xN,t>0,$$ \hat{x}(t):= \left(\underset{K\hbox{-} \mathrm{times}}{\underbrace{\sqrt{t},\cdots, \sqrt{t}}},{x}_{K+1},\cdots, {x}_N\right),t>0, $$to obtain the lower bound of decay of the heat semigroup, which is essential to prove the main result. [ABSTRACT FROM AUTHOR]

This document is an editorial summarizing the Applied Geometric Algebras in Computer Science and Engineering (AGACSE) conference held in Brno, Czech Republic in September 2021. The conference aimed to promote the use of geometric algebra in fields such as image processing, robotics, and quantum computing. The conference proceedings were published in the journal Mathematical Methods in the Applied Sciences. The editorial provides a list of accepted papers, covering topics such as applied geometry, technological applications, algebra, and quantum phenomena. One specific paper explores the use of geometric algebra in teaching rotations through neural networks. The document is a compilation of research papers showcasing the applications of geometric algebra in various fields, including robotics, control systems, image processing, cryptography, and physics. Each paper presents a specific problem or application and proposes a unique approach or solution using geometric algebra. The authors compare their methods with existing techniques and provide mathematical analysis to support their claims. Overall, the papers demonstrate the versatility and effectiveness of geometric algebra in different domains. [Extracted from the article]

As the evolution of species relies on not only the current state but also the past information, it is more reasonable and realistic to take delay into an ecological model. This paper deals with a stochastic predator–prey model that considers the distribution delay and assume that the intrinsic growth rate and the death rate in the model are governed by Ornstein–Uhlenbeck process to simulate the random factors in the environment. Based on the existence and uniqueness of the global solution to the model and the boundedness of the p$$ p $$ order moments of the solution, several conditions are established to analyze the survival of the species. Specifically, a criteria for the existence of the stationary distribution to the stochastic system is established by constructing some suitable Lyapunov functions. And the analytical expression of the probability density function of the model around the quasi‐equilibrium is obtained. Furthermore, the extinction of species in the model is also explored. Finally, numerical simulations are carried out to illustrate the theoretical results obtained in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider the asymptotic behavior of the solutions of the quadratic wave equations with perturbed oscillating coefficients which are very important mathematical models in describing the oscillation of particles imposed with time‐dependent electromagnetic fields. By the application of microlocal analysis and stochastic analysis, this paper makes a delicate classification of various types of time‐dependent oscillating coefficients on the principal quantum harmonic oscillator part and explores the corresponding regularity behavior and L2$$ {L}^2 $$‐estimates of the solution of the equation. It is interesting to find out that weak or mild oscillations will not cause any energy growth, while regular and strong oscillations will lead to polynomial or exponential growth of the energy. This is meaningful to help us explore the energy conversion mechanism in the electromagnetic field. Furthermore, in order to demonstrate the optimality of the L2$$ {L}^2 $$‐estimates, typical counterexamples with periodic coefficients will be constructed to show the lower bound of growth rate by the application of harmonic analysis and instability arguments. Compared with formal literatures focusing on the constant coefficients, current results in this paper reveal the essential relation between oscillation types and energy growth. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove the existence of weak solutions to thermo‐visco‐elastic system of equations. In considered problem, the temperature term is included in the elastic constitutive equations (generalized Hooke's law) as well as in describing the evolution of visco‐elastic strain. The main idea of presented proof is to analyze reformulated model, in which visco‐elastic strain (internal variable) is eliminated. For such system of equations, we propose a two‐level Galerkin approximation, which allows us to show a non‐negativity of temperature during the entire deformation process. In order to characterize the weak limits in the nonlinearities occurring in the system at different levels of approximation, the following tools are used: Truncation methods for heat equation proposed in the paper of D. Blanchard [Nonlinear Analysis, 21(10):725‐743, 1993], modified Boccardo‐Gallouët's approach, and Minty‐Browder trick. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cauchy problem of the d‐dimensional magneto‐micropolar equations (d=2$$ d=2 $$ or d=3$$ d=3 $$) with general fractional dissipation. The aim of this paper is to obtain the existence and uniqueness of solutions in the weakest possible inhomogeneous Besov spaces. Using the technical tools of Litttlewood–Paley decomposition and Besov spaces theory, we obtain the local existence in the functional setting of inhomogeneous Besov spaces. Furthermore, such solutions are unique only in 2D case. [ABSTRACT FROM AUTHOR]

In this paper, using the Faà di Bruno formula and some properties of the Bell polynomials of the second kind, we obtain a new explicit formula for the generalized Humbert–Hermite polynomials. We provide determinantal representations for the ratio of two differentiable functions. We obtain a recursive relation for the generalized Humbert–Hermite polynomials. As a practice, we derive an alternative recursive relation for generalized Humbert–Hermite polynomials via the Hessenberg determinant. Finally, we derive several families of multilinear and multilateral generating functions for the generalized Humbert–Hermite‐type polynomials and other polynomials which are mentioned in this paper. Our results also include many well‐known polynomials in the literature. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the influence of time delay effect and steady flow control strategy on traffic flow. Consider that the time delay in sensing flux information during the operation of traffic system is inevitable. Meanwhile, a new method is applied to model and analyse traffic system. A novel discrete‐time lattice hydrodynamic model considering time delay is introduced in this paper. Based on the proposed model with constant and varying time‐delay, the asymptotic stabilities are investigated and corresponding stable conditions are derived. The traffic flow evolution trend with and without time delay is conducted and compared by numerical simulations. Also, under the influence of different control gain conditions, density wave characteristics for traffic flow system with time delay are intuitively shown. The results indicate that time delay effect in sensing density and flux information can aggravate traffic congestion, and traffic congestion will be effectively relieved by considering steady flow control signal. [ABSTRACT FROM AUTHOR]

This paper concerns the mixed H∞$$ {H}_{\infty } $$ and passivity‐based filtering problem for networked nonlinear systems with randomly occurring parameter uncertainties, multipath data packet dropouts, time‐varying delay, and quantization effects. The discrete‐time nonlinear plant considered in this paper is modeled as a Takagi–Sugeno fuzzy system with plant rules. The data missing phenomenon is considered in both measurement and performance output signals due to the unreliable nature of communication links. Further, to reduce the network bandwidth utilization, the measurement quantization is also employed for both the outputs before transmitting through the communication channel. Also, additive filter gain fluctuation is taken into account to reflect the imprecision in filter implementation. Stochastic variables obeying the Bernoulli distribution are incorporated in the model description to characterize the random occurrence of parameter uncertainties and data packet dropouts. A set of sufficient conditions assuring the stochastic stability of the filtering error system with mixed H∞$$ {H}_{\infty } $$ and passivity performance is derived according to Lyapunov stability theory. Finally, three numerical examples including mass–spring–damper and tunnel diode circuit model are established to establish the validity of the developed filter design algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we aim to establish the uniform stability criteria for fractional‐order time‐delayed gene regulatory networks with leakage delays (FOTDGRNL). First, we establish the existence and uniqueness of the considered systems by using the Banach fixed point theorem. Second, the delay‐dependent uniform stability and robust uniform stability of FOFGRNLT are investigated with the help of certain analysis techniques depending on equivalent norm techniques. Finally, the paper comes up with two numerical examples to justify the applicability of our theoretical results. [ABSTRACT FROM AUTHOR]

During past decades, the study of the interaction between predator and prey species has become one of the most exciting topics in computational biology and mathematical ecology. In this paper, we aim to investigate the stability of a diseased model of susceptible, infected prey and predators around an internal steady state. To this end, the fractional derivatives based on the Mittag‐Leffler kernels in the Liouville‐Caputo concept has been taken into consideration. The existence and uniqueness of the acquired solutions to the model are also studied in this paper. In order to investigate the effects of the fractional‐order along with other existing parameters in the model, several possible scenarios have been examined. As it is seen in the proposed graphical simulations, the employed fractional operator is capable of capturing all anticipated theoretical features of the model. The numerical technique employed in this contribution is precise and efficient and can be easily adopted to investigate many fractional‐order models in biology. It is found that new proposed operators of fractional‐order can describe the real‐world phenomena even better than integer‐order differential equations because of their memory‐related properties. [ABSTRACT FROM AUTHOR]

This paper provides a new robust control approach to uncertain mechanical manipulators in the computed torque framework. With respect to the fact that model uncertainties occurring from the framework could make the overall system unstable although the resulting nominal plant is stabilized, this paper develops a readily applicable method for estimating such uncertain elements. More precisely, we propose a time‐delay compensation method, by which prior values relevant to the model uncertainties in a sufficiently small time instant are used for such an estimation. The theoretical effectiveness of the proposed method is validated by establishing the two different arguments on operator‐theoretic exponential stability and Lypaunov‐based disturbance input‐to‐state stability. Finally, some simulation and experiment results are provided to demonstrate the overall arguments developed in this paper for both the theoretical and practical aspects. [ABSTRACT FROM AUTHOR]

In the paper mentioned in the title, we studied the semi‐Markovian random walk processes with jumps and delaying screen in zero. More precisely, we obtained a mathematical modeling of the semi‐Markov random walk processes with a delaying screen in zero, given in general form by means of fractional differential equation. In this note, we provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the multiplicity results to a class of p$$ p $$‐Kirchhoff type elliptic equation with the homogeneous Neumann boundary conditions by the abstract linking lemma due to Brézis and Nirenberg. We obtain the twofold results in subcritical and critical cases, which is a meaningful addition and completeness to the known results about Kirchhoff equation. At the same time, this paper also gives a method to deal with p$$ p $$‐Laplacian, Kirchhoff equation, and some Kirchhoff type equation in a unified variational framework. [ABSTRACT FROM AUTHOR]

We consider the following fractional NLS with focusing inhomogeneous power‐type nonlinearity: i∂tu−(−Δ)su+|x|−b|u|p−1u=0,(t,x)∈ℝ×ℝN,$$ i{\partial}_tu-{\left(-\Delta \right)}^su+{\left|x\right|}^{-b}{\left|u\right|}^{p-1}u=0,\kern0.30em \left(t,x\right)\in \mathrm{\mathbb{R}}\times {\mathrm{\mathbb{R}}}^N, $$where N≥2$$ N\ge 2 $$, 1/2

Let μ$$ \mu $$ be a finite Borel measure on [0,1)$$ \left[0,1\right) $$. In this paper, we consider the generalized integral type Hilbert operator Iμα+1(f)(z)=∫01f(t)(1−tz)α+1dμ(t)(α>−1).$$ {\mathcal{I}}_{\mu_{\alpha +1}}(f)(z)={\int}_0^1\frac{f(t)}{{\left(1- tz\right)}^{\alpha +1}} d\mu (t)\kern0.30em \left(\alpha >-1\right). $$The operator Iμ1$$ {\mathcal{I}}_{\mu_1} $$ has been extensively studied recently. The aim of this paper is to study the boundedness (resp. compactness) of Iμα+1$$ {\mathcal{I}}_{\mu_{\alpha +1}} $$ acting from the normal weight Bloch space into another of the same kind. As consequences of our study, we get completely results for the boundedness of Iμα+1$$ {\mathcal{I}}_{\mu_{\alpha +1}} $$ acting between Bloch type spaces, and between logarithmic Bloch spaces. [ABSTRACT FROM AUTHOR]

In this paper, we devise a novel method to solve Kawahara‐type equations numerically. In this novel method, for spatial discretization, we use delta‐shaped basis functions and generate differentiation matrices for spatial derivatives of the Kawahara‐type equations. For discretization of temporal variable, we utilize a high‐order geometric numerical integrator based on Lie group methods. For illustration of efficiency of the suggested method, we consider some test problems. We calculate errors and make some comparisons with other results that exist in literature. We also report changes in conservation laws during numerical simulations, and we indicate that the suggested method can preserve the conservation laws pretty good. Outcomes of numerical simulations indicate that the suggested method in this paper is reliable and effective for nonlinear partial differential equations (PDEs). [ABSTRACT FROM AUTHOR]

Many challenges are still faced in bridging the gap between mathematical modeling and biological sciences. Measuring population immunity to assess the epidemiology of health and disease is a challenging task and is currently an active area of research. However, to meet these challenges, mathematical modeling is an effective technique in shaping the population dynamics that can help disease control. In this paper, we introduce a susceptible–infected–recovered (SIR) model and a susceptible–exposed–infected–recovered–deceased (SEIRD) model based on conformable space‐time partial differential equations (PDEs) for the coronavirus disease 2019 (COVID‐19) pandemic. As efficient analytical tools, we present new modifications based on the fractional exponential rational function method (ERFM) and an analytical technique based on the Adomian decomposition method for obtaining the solutions for the proposed models. These analytical approaches are more efficacious for obtaining analytical solutions for nonlinear systems of PDEs with conformable derivatives. The interesting result of this paper is that it yields new exact and approximate solutions to the proposed COVID‐19 pandemic models with conformable space‐time partial derivatives. [ABSTRACT FROM AUTHOR]

Nonstationary Gabor (NSG) frames for L2(ℝ)$$ {L}^2\left(\mathrm{\mathbb{R}}\right) $$ allow for flexible sampling and varying window functions and have found applications in adaptive signal analysis. Recently, the first author of this paper generalized the notion of NSG frames for L2(ℝ)$$ {L}^2\left(\mathrm{\mathbb{R}}\right) $$ to the space L2(ℝ,ℂK)$$ {L}^2\left(\mathrm{\mathbb{R}},{\mathrm{\mathbb{C}}}^K\right) $$ of vector‐valued signals and investigated the existence of vector‐valued NSG (VVNSG) frames. In this paper, we consider the reconstruction of any functions in L2(ℝ,ℂK)$$ {L}^2\left(\mathrm{\mathbb{R}},{\mathrm{\mathbb{C}}}^K\right) $$ from coefficients obtained from VVNSG frames. We provide different approximately dual frames of VVNSG frames and give the corresponding reconstruction error bounds. In particular, for a special class of VVNSG frames that are related to painless VVNSG frames, we show that the approximately dual frames carry the VVNSG structure, which is very important since there exist fast analysis and reconstruction algorithms for VVNSG frames. We also provide a method to construct the special class of VVNSG Bessel sequences. Finally, a constructive example is given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

We consider the incremental subgradient algorithm employing dynamic step sizes for minimizing the sum of a large number of component convex functions. The dynamic step size rule was firstly introduced by Goffin and Kiwiel [Math. Program., 1999, 85(1): 207‐211] for the subgradient algorithm, soon later, for the incremental subgradient algorithm by Nedic and Bertsekas in [SIAM J. Optim., 2001, 12(1): 109‐138]. It was observed experimentally that the incremental approach has been very successful in solving large separable optimizations and that the dynamic step sizes generally have better computational performance than others in the literature. In the present paper, we propose two modified dynamic step size rules for the incremental subgradient algorithm and analyse the convergence and complexity properties of them. At last, the assignment problem is considered and the incremental subgradient algorithms employing different kinds of dynamic step sizes are applied to solve the problem. The computational experiments show that the two modified ones converges dramatically faster and more stable than the corresponding one in [SIAM J. Optim., 2001, 12(1): 109‐138]. Particularly, for solving large separable convex optimizations, we strongly recommend the second one (see Algorithm 3.3 in the paper) since it has interesting computational performance and is the simplest one. [ABSTRACT FROM AUTHOR]

In this paper, a class of fractional stochastic differential equations (SFDEs) with impulses is considered. By virtue of Mönch's fixed point theorem and Banach contraction principle, we explore the existence and uniqueness of solutions to the addressed system. Furthermore, with the aid of the Jensen inequality, Hölder inequality, Burkholder–Davis–Gundy inequality, Grönwall–Bellman inequality, and some novel assumptions, the averaging principle of our considered system is obtained. At the end of this paper, an example is provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper numerically investigates the effect of pulsating flow on the settling dynamics of rigid circular particles. This is an interdisciplinary subject and spans several areas ranging from mathematical and numerical modeling to fluid mechanics. For this purpose, pulsatile flow characteristics are embedded in the combination of the direct‐forcing immersed boundary method and the split‐forcing lattice Boltzmann method. Inter‐collision forces between the solid boundaries (particles and boundaries) and the added mass force due to acceleration are considered. Adequate verification tests are done to ensure the credibility of the findings. The critical parameters of pulsating flow, such as amplitude and frequency of pulsation, are investigated in detail. The paper especially puts emphasis on the interaction between particles and studies the well‐known drafting, kissing, and tumbling (DKT) phenomena. Two different scenarios are taken into account and also compared with the stationary flow. The first case is when the pulsating flow is in the direction of gravity (co‐flow), while in the latter, there is an opposing flow (counterflow). The sedimentation manners of 12 particles in a vertical channel are also presented. The findings shed light on the importance of pulsating flow and the extension of the proposed computational method for such problems. It is also revealed that pulsation and its variables can alter DKT by either postponing or speeding up the process. Also, in some cases, the cycle of DKT can be maintained incompletely, and particles would just stick together. The results can be useful for various engineering problems like filtration and particle sorting. [ABSTRACT FROM AUTHOR]

This paper is concerned with a mixed type differential operator Lu=kyuxx−uyy+byux+qyu,$$ Lu=k(y){u}_{xx}-{u}_{yy}+b(y){u}_x+q(y)u, $$which is initially defined with C0,π∞Ω‾$$ {C}_{0,\pi}^{\infty}\left(\overline{\Omega}\right) $$, where Ω‾={x,y:−π≤x≤π,−∞

In this paper, we study a predator–prey system with the simplified Holling IV functional response and antipredator behavior such that the adult prey can attack vulnerable predators. The model has been investigated by Tang and Xiao, and the existence and stability of all possible equilibria are determined. In addition, they performed a bifurcation analysis and showed that the system undergoes a Codimension 2 Bogdanov–Takens bifurcation. In this paper, for the same model, we further show that the cusp‐type Bogdanov–Takens bifurcation can be of Codimension 3, which acts as an organizing center for the whole bifurcation set. In addition, we propose the existence of Hopf bifurcation of Codimension 2 and the coexistence of stable limit cycle and unstable limit cycle. In particular, we show that the antipredator behavior has great effect on the dynamics of the model, it may cause the predator population to extinct while the prey population will increase up to the carrying capacity. Numerical simulations including bifurcation diagrams and phase portraits are performed to illustrate and confirm the theoretical results. These results may enrich the dynamics of predator–prey systems. [ABSTRACT FROM AUTHOR]

This paper proposed a new class of stochastic cellular neural networks (SCNNs) with distributed time delays. It is driven by time‐varying Brownian motion. By constructing the Lyapunov functions with a more concise form and using the time‐varying Itô formula, combining some inequality techniques, this paper proved the almost surely exponential stability and the p$$ p $$‐th moment exponential stability of the solution of the SCNNs. The numerical example verifies the theoretical results of this paper. [ABSTRACT FROM AUTHOR]

The paper focuses on applying the octonions to explore the influence of the external torque on the angular momentum of fluid elements, revealing the interconnection of the external torque and the vortices of vortex streets. J. C. Maxwell was the first to introduce the quaternions to study the physical properties of electromagnetic fields. The contemporary scholars utilize the quaternions and octonions to investigate the electromagnetic theory, gravitational theory, quantum mechanics, special relativity, general relativity, curved spaces, and so forth. The paper adopts the octonions to describe the electromagnetic and gravitational theories, including the octonionic field potential, field strength, linear momentum, angular momentum, torque, and force. In case the octonion force is equal to zero, it is able to deduce eight independent equations, including the fluid continuity equation, current continuity equation, and force equilibrium equation. Especially, one of the eight independent equations will uncover the interrelation of the external torque and angular momentums of fluid elements. One of its inferences is that the direction, magnitude, and frequency of the external torque must impact the direction and curl of the angular momentum of fluid elements, altering the frequencies of Karman vortex streets within the fluids. It means that the external torque is interrelated with the velocity circulation, by means of the liquid viscosity. The external torque is able to exert an influence on the direction of downwash flows, improving the lift and drag characteristics generated by the fluids. [ABSTRACT FROM AUTHOR]

This paper is dedicated to obtaining closed‐form solutions of linear difference equations which are asymptotically close to the self‐adjoint Euler‐type difference equation. In this sense, the equation is related to the Euler–Cauchy differential equation y′′+λ/t2y=0$$ {y}^{\prime \prime }+\lambda /{t}^2y=0 $$. Throughout the paper, we consider a system of sequences which behave asymptotically as an iterated logarithm. [ABSTRACT FROM AUTHOR]

The paper deals with a new type of inverse spectral problems for second‐order quadratic differential pencils when one of the boundary conditions involves arbitrary entire functions of the spectral parameter. Although various aspects of the inverse spectral theory for the pencils have been of a special interest during the last decades, such settings were considered before only in the particular case of a Sturm–Liouville equation. We develop an approach covering also the quadratic dependence on the spectral parameter in the differential equation, which is based on the completeness and basisness of certain functional systems. By this approach, we obtain a uniqueness theorem and an algorithm for solving the inverse problem along with sufficient properties of the mentioned systems. The presented results give a universal tool for studying a number of important specific situations, including various Hochstadt–Lieberman‐type inverse problems both on an interval and on geometrical graphs, which is illustrated as well. [ABSTRACT FROM AUTHOR]

Acupuncture is an important part of traditional Chinese medicine (TCM). Although the efficacy of acupuncture has been widely accepted, the scientific basis behind it is still lack of exploration. Some experimental studies have shown that acupuncture can lead to changes in cell membrane potential, thus affecting the transmission of nerve signals to a certain extent. The change of cell membrane potential mainly depends on a large number of voltage dependent ion channels on the cell membrane. Relevant studies have proved that such voltage dependent ion channels have certain mechanical sensitivity, but the principle is not clear. Based on the theoretical model of cell action potential excitability proposed by Hodgkin–Huxley, taking rat skeletal muscle cell fibers as an example, this paper makes a rough stability analysis of the nonlinear system, explores the conditions of repeated discharge of cell membrane, and simulates the law of cell membrane potential frequency variation under different stimulating currents by numerical calculation. Based on the results of numerical simulation, we propose a hypothesis: Mechanical stimulation will produce a certain amount of stimulating current on the cell membrane, making the cell membrane potential in the state of repeated discharge, so as to block or interfere with the transmission of nerve signals and achieve the analgesic effect and so forth. [ABSTRACT FROM AUTHOR]

This paper deals with a fourth‐order parabolic equation involving variable exponents, subject to Navier boundary conditions. We firstly give an optimal classification on the initial energy for blow‐up or global solutions, which is characterized by the sign of the Nehari energy and the difference between the initial energy and the depth of the potential well. Then, large time estimates of solutions are obtained. The results of the paper extend and complete the ones in "Applied Mathematics Letters 78(2018)141–146." [ABSTRACT FROM AUTHOR]

This paper is dedicated to solving the model reconstruction problem of Boolean networks (BNs) based on incomplete information. By resorting to semi‐tensor product, the issue of finding logical functions is converted into designing corresponding structure matrices. In line with desired attractors, two circumstances, standard BNs and delayed BNs, are taken into consideration, and several new results are presented. For the model reconstruction of standard BNs, an algebraic condition is put forward and an algorithm is developed for reconstructing unknown logical functions. For the model reconstruction of delayed BNs, an augmented system is deduced, based on which, several criteria and the corresponding algorithm are proposed. Finally, as an application to gene regulatory networks, the results obtained in this paper are used to analyze the WNT5A network and the apoptosis network. [ABSTRACT FROM AUTHOR]

In this paper, the problem of attractivity of solutions for functional hereditary integral equations is initiated. A hereditary integral equation is converted into a second kind Volterra integral equation of convolution type by use of the property of convolution. Sufficient conditions for the existence of attractive solutions are established according to the fixed point theorem. The conclusions presented in this paper extend some published results. The effectiveness of the proposed results is illustrated by three numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we study the stabilization of a laminated beam system under the action of a new thermal coupling. Motivated by the work of Almeida Júnior et al. in the context of the Timoshenko system, we consider a thermoelastic coupling acting on the shear force. The present work constitutes a generalization of Almeida Júnior's paper because our study model considers an interfacial slip. More precisely, if we make the parameter γ$$ \gamma $$ of our system go to infinity, we obtain the Timoshenko beam system studied by the authors. We show that the weakly dissipative system of our manuscript is exponentially stable if, and only if, the wave propagation speeds are equal. Otherwise, we show that the system is polynomially stable and that the associated semigroup decays with rate t−1/2$$ {t}^{-1/2} $$. Furthermore, we show that this decay rate is optimal. [ABSTRACT FROM AUTHOR]

In this paper, we study the full parabolic attraction–repulsion Keller–Segel model with a fractional diffusion in ℝn$$ {\mathbb{R}}^n $$ for n=2$$ n=2 $$ or 3. We are more interested in the question that whether the solutions exist globally or blow up in finite time, which was studied in the classical attraction‐repulsion Keller‐Segel model by Jin and Wang (J. Differential Equations, 2016) through constructing a suitable energy functional. However, for the fractional attraction–repulsion Keller–Segel model, it is challenging to find a similar energy functional to study the existence of the solutions. In the present paper, under the condition of ξγ=χα$$ \xi \gamma =\chi \alpha $$, we introduce the Lp$$ {L}_p $$‐ Lq$$ {L}_q $$ estimates of the fractional derivative modulus of the solution to carry out the first step of the problem. Armed with a priori estimate, it is sufficient for us to obtain the global existence of the solutions by the Moser–Alikakos iterative method and finally arrive at the decay estimates of the solutions. [ABSTRACT FROM AUTHOR]

In this paper, we continue to study an initial boundary value problems to a model describing the evolution in time of diffusive phase interfaces in sea ice growth. In a previous paper, the global existence and the large‐time behavior of weak solutions in one space was studied under Dirichlet boundary conditions. Here, we show that the global existence of weak solutions and the large‐time behavior are also studied under Neumann boundary condition. In this paper, we study in space dimension lower than or equal to 3. [ABSTRACT FROM AUTHOR]

In this paper, we consider the effects of singular convection term and lower order term on the existence and regularity of solutions to the following elliptic Dirichlet problem: −divM(x)∇u=−divuE(x)+f(x)uγ,x∈Ω,u(x)=0,x∈∂Ω,$$ \left\{\begin{array}{rl}-\operatorname{div}\left(M(x)\nabla u\right)=-\operatorname{div}\left(uE(x)\right)+\frac{f(x)}{u^{\gamma }},& x\in \Omega, \\ {}\kern45pt u(x)=0,& x\in \mathrm{\partial \Omega },\end{array}\right. $$where γ>0,Ω⊂ℝN(N>2)$$ \gamma >0,\Omega \subset {\mathbb{R}}^N\left(N>2\right) $$ is a bounded smooth domain with 0∈Ω,f∈Lm(Ω)$$ 0\in \Omega, f\in {L}^m\left(\Omega \right) $$ with m≥1$$ m\ge 1 $$ is a non‐negative function. The main results of this paper show the combined effects of singular convection term and lower order term on the existence and regularity of solution to this problem. [ABSTRACT FROM AUTHOR]

The previous published work by Othmani et al. invites a further useful discussion on how the viscoelastic rheological model affects the second harmonic and single modes of guided waves. However, this paper has two main objectives. The first objective is to establish a simple relationship between the Rayleigh waves velocity (VR), fundamental Lamb modes (A0 and S0), and the shear wave velocity (VS) in unidirectional viscoelastic carbon–epoxy at high frequency. The second objective is to study the second harmonic Lamb modes. Numerical codes based on Legendre polynomial and Newton–Raphson methods are developed and implemented to predict dispersion and attenuation curves. The second harmonic generation was investigated with the hysteretic and Kelvin–Voigt viscoelastic models. Results showed that rheological models have a much larger effect on the attenuation curves than the ones on the dispersion trajectories. Additionally, the optimal angles of Lamb and SH modes in unidirectional carbon–epoxy under Snell‐Descartes law was investigated. The present numerical results may render as a useful message for the rheological community. [ABSTRACT FROM AUTHOR]

In this paper, we study the long‐time dynamical behavior of the non‐autonomous velocity–vorticity–Voigt model of the 3D Navier–Stokes equations with damping and memory. We first investigate the existence and uniqueness of weak solutions to the initial boundary value problem for above‐mentioned model. Next, we prove the existence of uniform attractor of this problem, where the time‐dependent forcing term f∈Lb2(ℝ;H−1(Ω))$$ f\in {L}_b^2\left(\mathbb{R};{H}^{-1}\left(\Omega \right)\right) $$ is only translation bounded instead of translation compact. The results in this paper will extend and improve some results in Yue and Wang (Comput. Math. Appl., 2020) in the case of non‐autonomous and contain memory kernels which have not been studied before. [ABSTRACT FROM AUTHOR]

This paper presents a two‐warehouse inventory model for non‐instantaneous deteriorating items with a price‐dependent stochastic demand under advance sales discount and available capacity. In this model, the retailer offers a price discount to customers if they can commit their orders prior to the sales period. It encourages the retailer to order a large quantity that can be stored in an owned warehouse and then in a rented warehouse if there are excess items. Shortages are allowed and partially backlogged. The objective of this paper is to simultaneously determine the optimal price discount, the optimal order quantity, and the optimal replenishment schedule in such a way that the expected total profit is maximized. Two theorems are proved in order to verify that the expected total profit function is concave and to identify that an optimal replenishment decision exists. We further propose an algorithm to find the optimal replenishment policy by the retailer. Finally, we use numerical examples to illustrate the results presented herein. Moreover, based upon the sensitivity analysis, some important managerial implications are also discussed. [ABSTRACT FROM AUTHOR]

In this paper a thorough analysis is carried out of the type of order reduction that Lawson methods exhibit when used to integrate nonlinear initial boundary value problems. In particular, we focus on nonlinear reaction‐diffusion problems, and therefore, this study is important in a large number of practical applications modeled by this type of nonlinear equations. A theoretical study of the local and global error of the total discretization of the problem is carried out, taking into account both, the error coming from the space discretization and that due to the integration in time. These results are also corroborated by the numerical experiments performed in this paper. [ABSTRACT FROM AUTHOR]

It is well‐known that discrete‐time Kolmogorov systems play important role in studying predator‐prey models with interactions. A topic of this paper deals with stochastic discrete‐time Kolmogorov systems which are called Lotka–Volterra operators. In the present paper, we provide a new class of LV operators, and establish that each of operator from this class has historical behavior, that is, their time averages diverge. [ABSTRACT FROM AUTHOR]

In this paper, using the Gromov–Hausdorff distances between two global attractors (which may be in disjoint phase spaces) and two semi‐dynamical systems introduced by Lee et al. (2020), we consider the continuous dependence of the global attractors and the stability of the semi‐dynamical systems on global attractors induced by the Brinkman–Forchheimer equation under variation of the domain. The results of this paper improve on previous results, which can compare any two systems in different phase spaces without the process of "pull‐backing" the perturbed systems to the original domain. [ABSTRACT FROM AUTHOR]

The aim of this study is to explore the global stability of Cohen–Grossberg Clifford‐valued neutral‐type neural network models with time delays. In order to achieve the aim of this paper, and to solve the non‐commutativity problem caused by Clifford numbers multiplication, the original Clifford‐valued system is first decomposed into 2mn$$ {2}^mn $$‐dimensional real‐valued systems. Some sufficient criteria for the global stability of the addressed network models are established by constructing an appropriate Lyapunov functional. The established stability conditions have not been affected by the neutral delay and time delay values. The proposed method and results of this paper are new. The feasibility of the stability criteria obtained are verified using two numerical examples. [ABSTRACT FROM AUTHOR]

In this work, we consider the one‐dimensional Dirac operator DQ+Qsu(x)=1iσ2ddx+Q(x)+Qs(x)u(x),$$ {\mathfrak{D}}_{\mathrm{Q}+{\mathrm{Q}}_s}u(x)=\left(\frac{1}{\mathrm{i}}{\sigma}_2\frac{d}{dx}+\mathrm{Q}(x)+{\mathrm{Q}}_s(x)\right)u(x), $$where σ2$$ {\sigma}_2 $$ is Pauli's matrix, Q$$ \mathrm{Q} $$ is a 2×2$$ 2\times 2 $$‐matrix representing a regular potential that includes the electrostatic and scalar interactions as well as the anomalous magnetic momentum, Qs$$ {\mathrm{Q}}_s $$ is a singular potential consisting of N$$ N $$ delta distributions Qs(x)=∑j=1NAjδx−xj,$$ {\mathrm{Q}}_s(x)=\sum \limits_{j=1}^N{\mathrm{A}}_j\delta \left(x-{x}_j\right), $$Aj$$ {\mathrm{A}}_j $$ (j=1,⋯,N$$ j=1,\cdots, N $$) are 2×2$$ 2\times 2 $$‐matrices representing the strengths of Dirac deltas, and u=u1u2⊤$$ u={\left({u}^1\kern0.5em {u}^2\right)}^{\top } $$ is a two‐spinor. We associate to the operator DQ+Qs$$ {\mathfrak{D}}_{\mathrm{Q}+{\mathrm{Q}}_s} $$ an unbounded in L2ℝ,ℂ2$$ {L}^2\left(\mathbb{R},{\mathbb{C}}^2\right) $$ symmetric operator denoted by DQ,Ω$$ {\mathcal{D}}_{\mathrm{Q},\Omega} $$, where Ω=xjj=1N$$ \Omega ={\left\{{x}_j\right\}}_{j=1}^N $$ is the support of singular potential Qs$$ {\mathrm{Q}}_s $$. The operator DQ,Ω$$ {\mathcal{D}}_{\mathrm{Q},\Omega} $$ includes only the regular potential Q$$ \mathrm{Q} $$ together with certain interaction conditions at each point xj∈Ω$$ {x}_j\in \Omega $$. The paper presents a method for determining the discrete spectrum of the operator DQ,Ω$$ {\mathcal{D}}_{\mathrm{Q},\Omega} $$ for arbitrary potential Q$$ \mathrm{Q} $$ whose entries are given by L∞(ℝ)$$ {L}^{\infty}\left(\mathbb{R}\right) $$‐functions. The eigenvalues λn$$ {\lambda}_n $$ of the operator DQ,Ω$$ {\mathcal{D}}_{\mathrm{Q},\Omega} $$ are the zeros of a dispersion equation ηΩ(λ)=0$$ {\eta}_{\Omega}\left(\lambda \right)=0 $$, where the characteristic function ηΩ$$ {\eta}_{\Omega} $$ is determined explicitly in terms of power series involving the spectral parameter λ$$ \lambda $$. The construction of the characteristic function ηΩ$$ {\eta}_{\Omega} $$ from a set of monodromy matrices and the interaction conditions is presented in the paper. Moreover, its power series representation leads to an efficient numerical method for calculating the eigenvalues of the Dirac operator DQ,Ω$$ {\mathcal{D}}_{\mathrm{Q},\Omega} $$ from the zeros of certain approximate function η˜Ω$$ {\tilde{\eta}}_{\Omega} $$ which is obtained by truncating the series up to a finite number of terms. Several examples show the applicability and accuracy of the numerical method. [ABSTRACT FROM AUTHOR]

The dynamic transitions of the Brusselator model has been recently analyzed in Choi et al. (2021) and Ma and Wang (2011). Our aim in this paper is to address the relation between the pattern formation and dynamic transition results left open in those papers. We consider the problem in the setting of a 2D rectangular box where an instability of the homogeneous steady state occurs due to the perturbations in the direction of several modes becoming critical simultaneously. Our main results are twofold: (1) a rigorous characterization of the types and structure of the dynamic transitions of the model from basic homogeneous states and (2) the relation between the dynamic transitions and the pattern formations. We observe that the Brusselator model exhibits different transition types and patterns depending on the nonlinear interactions of the pattern of the critical modes. [ABSTRACT FROM AUTHOR]

This paper focuses on a class of exponential stability control problem for the stochastic neural networks (SNNs) with time‐varying delays and Markov jump (TVDMJ). As a prerequisite to the main theorem, the existence and uniqueness of the solution for the main system are proved via contraction map principle. For the stability control of the system, we design a controller Ct,xtδδ,m(t)$$ C\left(t,x\left(\left[\frac{t}{\delta}\right]\delta \right),m(t)\right) $$ which can be adjusted the parameters δ$$ \delta $$ to make the system stabilization. We use this controller to actively control the stability behavior of the system, rather than the papers by setting the appropriate parameters to make the system achieve a stable state. Based on the intermittent control, we design a novel trajectory similarity process control and obtain exponential stability results, which are less conservative than the existing theoretical results. Two examples based on some numerical calculation and simulation diagrams are presented to validate the effectiveness for the utilized techniques. [ABSTRACT FROM AUTHOR]

In this paper, the H∞$$ {H}_{\infty } $$ synchronization issue of discrete‐time Markov jump neural networks under DoS attacks is studied, in which the transition probability of the Markov chain is considered as time‐varying governed by a mode‐dependent persistent dwell‐time switching rule. The purpose of this paper is to design a suitable controller such that mean‐square exponentially stable of the synchronization error system can be accomplished, and an H∞$$ {H}_{\infty } $$ performance is satisfied under denial of service (DoS) attacks. In order to reduce the conservatism of obtained results, some synchronization analysis criteria are obtained by adopting an activation function division method. Based on these criteria, an effective security synchronization controller design method is presented. Conclusively, an example is given to verify the validity of the results. [ABSTRACT FROM AUTHOR]

This paper studies the monic semi‐classical Laguerre polynomials based on previous work by Boelen and Van Assche, Filipuk et al., and Clarkson and Jordaan. Filipuk et al. proved that the diagonal recurrence coefficient αn(t)$$ {\alpha}_n(t) $$ satisfies the fourth Painlevé equation. In this paper, we show that the off‐diagonal recurrence coefficient βn(t)$$ {\beta}_n(t) $$ fulfills the first member of Chazy II system. We also prove that the sub‐leading coefficient of the monic semi‐classical Laguerre polynomials satisfies both the continuous and discrete Jimbo–Miwa–Okamoto σ$$ \sigma $$‐form of Painlevé IV. By using Dyson's Coulomb fluid approach together with the discrete system for αn(t)$$ {\alpha}_n(t) $$ and βn(t)$$ {\beta}_n(t) $$, we obtain the large n$$ n $$ asymptotic expansions of the recurrence coefficients and the sub‐leading coefficient. The large n$$ n $$ asymptotics of the associated Hankel determinant (including the constant term) is derived from its integral representation in terms of the sub‐leading coefficient. [ABSTRACT FROM AUTHOR]

This research focuses on the fractional complex order plant (FCOP). The significant contribution is the role of complex plant models in system stability and robustness and associated physical phenomena. A general transfer function is studied in the paper. Other plant models may be built with this structure since the FCOP is a general mathematical form covering integer order plant (IOP) and fractional order plant (FOP). Using the equations produced with the proposed technique and the recommended integer order proportional derivative (IOPD controller, physical changes in integer, fractional and complex coefficients, and orders are observed within this paper. Analysis of the plant controlled with an IOPD controller is done by applying an integrator to reveal the differences. The effects of the parameters are discussed together with the visuals, supported by simulations. The aim is to tune the controller parameters to achieve the phase and specifications as the researcher desired. It is observed that the integrator greatly takes part in reducing the steady‐state error. The IOP with the integrator showed the lowest steady‐state error, and also, the settling and overshoot time were enhanced. Increase in the phase margin also caused an increase in the phase crossover frequency. It is also observed that the fractional order affected the phase crossover frequency comparing with the IOP, and the complex order modification also had an effect comparing to the fractional order version. The complex order of the system is considered with its conjugate components in the imaginary part thus, the results are found separately for each case. [ABSTRACT FROM AUTHOR]