In this paper, we mainly study the local energy equation of the weak solutions of the compressible isentropic MHD equation defined on 𝕋 3 . We prove that the regularity of the solution is sufficient to guarantee the balance of the total energy in the B 3 α , ∞ ( ( 0 , T ) × 𝕋 3 ) space. We adopt a variant of the method of Feireisl et al.

In this paper, we develop two fast implicit difference schemes for solving a class of variable‐coefficient time–space fractional diffusion equations with integral fractional Laplacian (IFL). The proposed schemes utilize the graded L1 formula for the Caputo fractional derivative and a special finite difference discretization for IFL, where the graded mesh can capture the model problem with a weak singularity

In this paper, we consider a class of chemotaxis models with two arbitrary constitutive functions g(u) and f(v). After having performed a complete symmetry group classification with respect to them the reduced systems are derived. By considering g(u) of the logistic form, wide classes of exact solutions are found.

The paper is concerned with a class of nonlinear reaction–diffusion equations with a dissipating parameter. The problem is singularly perturbed from a mathematical perspective. Solutions of these problems are known to exhibit multiscale character. There are narrow regions in which the solution has a steep gradient. To approximate the multiscale solution, we present and analyze an iterative analytic

In this paper, we notice a property of the extension operator from the space of tangential traces of H(curl; Ω) in the context of the linear relaxed micromorphic model, a theory that is recently used to describe the behavior of some metamaterials showing unorthodox behaviors with respect to elastic wave propagation. We show that the new property is important for existence results of strong solution

In this paper, we deal with the randomized generalized diffusion equation with delay: ut(t, x) = a2uxx(t, x) + b2uxx(t − τ, x), t > τ, 0 ≤ x ≤ l; u ( t , 0 ) = u ( t , l ) = 0 , t ≥ 0; u ( t , x ) = φ ( t , x ) , 0 ≤ t ≤ τ, 0 ≤ x ≤ l. Here, τ > 0 and l > 0 are constant. The coefficients a2 and b2 are nonnegative random variables, and the initial condition φ(t, x) and the solution u(t, x) are random

Two different phase‐field crystal (PFC) free excess energy expansions have been analyzed with respect to the order of a truncation term and to the accuracy of a pair correlation functions fitting. The coefficients of the correlation function in PFC model was found for the aluminum crystal based on the molecular dynamics data. A machine learning (ML) approach has been utilized to construct a neural

Historically, the Poincaré disk model has taken a pioneering role in the development of non‐Euclidean geometry. But still today, this model is critical as a playground for simulations and new theories. In this paper, we discuss how to implement and simulate acoustic wave phenomena on the Poincaré disk with the help of so‐called metamaterials. After formally developing a theory based on the acoustic

Estimating the quadratic variation (QV) using high‐frequency financial data is studied in this article, and this work makes two major contributions: first, the fundamental Itô isometry E ∫ b a f ( t , ω ) d B t 2 = E ∫ b a f 2 ( t , ω ) d t is generalized to some extent, and as an application example, the widely known convergence property of realized volatility (RV) estimator of QV is analyzed by alternatively

In this paper, we characterize a new generalization of Perov fixed point result via Λ‐admissibility and Ψ‐contractivity on vector‐valued metric space and provide a comparative example. Then we investigate the existence of solution of a complex partial differential equation of the form, ∂ z ¯ w = F z , w , ∂ z w , via obtained new fixed point results under suitable conditions.

Hosoya polynomial is a vertex‐distance based polynomial highly consigned with Wiener and hyper‐Wiener index. Nanotubes are the nano scale material which can be used to explain novel attributes like highlights contrasted and expanded quality conductivity of material. In this paper, we presented the Hosoya polynomial and Harary polynomial for zigzag polyhex nanotube TUHC6. Moreover, some distance‐dependent

Anomalous diffusion problems are used to describe the evolution of particle's motion in crowded environments with many applications, such as modeling the intracellular transport and disordered media. In the present paper, we develop a Petrov–Galerkin spectral method for the fourth‐order anomalous fractional diffusion equations. For the dimension reduction, we use a discretization in time by the convolution

A nonlinear oscillator describing dynamics of parallel plate capacitor is considered with zero initial conditions. This case of initial conditions makes some effective methods, for example, the variational iteration method and the homotopy perturbation method, inapplicable. To overcome the shortcoming of classical methods, a simple transform is proposed to convert the problem into a traditional case

The knapsack problem is a problem in combinatorial optimization, and in many such problems, exhaustive search is not tractable. In this paper, we describe and analyze the randomized time‐varying knapsack problem (RTVKP) as a time‐varying integer linear programming (TV‐ILP) problem. In this way, we present the on‐line solution to the RTVKP combinatorial optimization problem and highlight the restrictions

In this paper, we focus on designing a well‐conditioned Galerkin spectral methods for solving a two‐sided fractional diffusion equations with drift in which the fractional operators are defined neither in Riemann–Liouville nor Caputo sense, and its physical meaning is clear. Based on the image spaces of Riemann–Liouville fractional integral operators on Lp([a, b]) space discussed in our previous work

A graph is said to be regular if all its vertices have the same degree, otherwise, it is irregular. Irregularity indices are usually used for quantitative characterization of the topological structure of nonregular graphs. In numerous applications and problems in material engineering and chemistry, it is useful to be aware that how irregular a molecular structure is. Furthermore, evaluations of the

In this article, we study the blow‐up of the damped wave equation in the scale‐invariant case and in the presence of two nonlinearities. More precisely, we consider the following equation: u t t − Δ u + μ 1 + t u t = | u t | p + | u | q , in ℝ N × [ 0 , ∞ ) , with small initial data.

The higher order mixture nonlocal gradient theory of elasticity is conceived via consistent unification of the higher order stress‐ and strain‐driven mixture nonlocal elasticity and the higher order strain gradient theory. The integro‐differential constitutive law is established applying an abstract variational approach and appropriately replaced with the equivalent differential condition subject to

This paper concerns the global existence and large time behavior of classical, strong, and weak solutions to the two‐dimensional compressible micropolar equations with large initial data and vacuum. We assume that the shear and angular viscosity coefficients are positive constants and the bulk coefficient is λ = ρ β , where ρ is the density and β > 3/2. It is crucial to derive an upper bound of the

A mathematical model for the dynamics of prion proliferation in the presence of chaperone involving a coupled system consisting of an ordinary differential equation and a partial integro‐differential equation is analyzed. For bounded reaction rates, we prove the existence and uniqueness of positive classical solutions with the help of the theory of evolution system. In the case of unbounded reaction

A ℂ ‐linear problem is considered for the Moisil‐Theodorescu system written in a complex form. The Fredholm theorem for this problem is proved, and the index formula obtained.

We propose a new numerical method for pricing options in the Black–Scholes model with jumps. Specifically, we consider the partial integro‐differential problem that yields the option price, and we solve it by means of a finite difference scheme that combines a fixed‐point iteration technique and a repeated space‐time Richardson extrapolation procedure. Such an approach turns out to be not only extremely

Programmed to retain active responsivity to environmental stimuli, diverse types of synthetic gels have been attracting interests regarding various applications, such as elastomer biodevices. In a different approach, when the gels are made of tissue‐derived biopolymers, they can act as an artificial extracellular matrix (ECM) for use as soft implants in medicine. To explore the physical properties

A nonlinear oscillator arising in a microelectromechanical system (MEMS) is difficult to be solved analytically due to the zero conditions. So the main objective of this work is to analyze the mathematical model of this system, and its approximate analytical solution is solved via the coupling variational iteration method and Laplace transform (LVIM). This method provides an efficient way to obtain

In this article, the variable‐order (VO) time fractional 2D Kuramoto‐Sivashinsky equation is introduced, and a semidiscrete approach is presented through 2D Chebyshev cardinal functions (CCFs) for solving this equation. In the proposed method, we obtain a recurrent algorithm by using the finite difference method to approximate the VO fractional differentiation, the weighted finite difference method

Studying the spread of epidemics and diseases is a worldwide problem especially during the current time where the whole world is suffering from COVID‐19 pandemic. Antimicrobial resistance (AMR) and waning vaccination are classified as worldwide problems. Both depend on the exposure time to antibiotic and vaccination. Here, a simple model for competition between drug‐resistant and drug‐sensitive bacteria

In this paper, the authors obtain some new blow‐up criteria for the smooth solutions to the three‐dimensional magnetic Bénard equations without thermal diffusion in terms of pressure. We prove that if π ∈ L 2 0 , T ; L 3 r ( R 3 ) with 0 < r ≤ 1, then the strong solutions (u, b, θ) to the magnetic Bénard equations can be extended beyond time t = T . Meanwhile, we also show that provided that ∇ π ∈

In this paper, a spatially extended stochastic reaction–diffusion model is studied. Due to Turing instability, stable nonhomogeneous stationary patterns are generated in such models. A theoretical approach to estimating the mean‐square deviation of random solutions from the stable deterministic pattern–attractor is demonstrated. Stochastic sensitivity functions for stable stationary patterns are introduced

This paper aims to identify the topological structures of multi‐weighted complex networks (MWCN) with and without time delay based on adaptive synchronization. First, by using the concept of drive‐response synchronization, one takes the MWCN as a drive system and introduces the adaptive controller and white noise in the response system to get stochastic MWCN. Then, drive system and response system

An efficient multiscale‐like multigrid (MSLMG) method combined with a high‐order compact (HOC) difference scheme on nonuniform grids is presented to solve the two‐dimensional (2D) convection‐diffusion equations. The discrete systems with given appropriate initial solutions on two finest grids are solved to obtain the MSLMG solutions with discretization‐level accuracy by performing fewer multigrid cycles;

In this paper, we obtain the existence of solutions for a nonlocal Sturm–Liouville problem with composite fractional derivatives under some initial value conditions. Furthermore, applying above results and operator theory, we specifically research the geometric multiplicity of eigenvalues for the nonlocal Sturm–Liouville eigenvalue problem.

Zika is a flavivirus that is transmitted to humans either through the bites of infected Aedes mosquitoes or through sexual transmission. Zika has been associated with congenital anomalies, like microcephalus. We developed and analyzed the fractional‐order Zika virus model in this paper, considering the vector transmission route with human influence. The model consists of four compartments: susceptible

Every now and then, there has been natural or man‐made calamities. Such adversities instigate various institutions to find solutions for them. The current study attempts to explore the disaster caused by the micro enemy called coronavirus for the past few months and aims at finding the solution for the system of nonlinear ordinary differential equations to which q−homotopy analysis transform method

In this work, two new number‐ and volume‐consistent finite volume methods for the numerical solution of binary and multifragmentation problems are introduced. The new number‐consistency is achieved by introducing a single weight function. Several benchmark problems of different complexity are solved to assess the accuracy. Mathematical convergence analysis suggests that both of the new methods are

From many fewer acquired measurements than that suggested by the Nyquist sampling theory, compressive sensing (CS) theory demonstrates that a signal can be reconstructed with high probability when it exhibits sparsity in a certain domain. Recent CS methods have employed analytical sparsifying transforms such as wavelets, curvelets, and finite differences. In this paper, we propose a novel algorithm

In this paper, using the localization method of compact invariant sets, we examine the ultimate dynamics of the 3D prey–predator model containing two subpopulations of susceptible and infected predators. Our attention is focused to finding ultimate sizes of interacting populations, and, in addition, we show the existence of a global attracting set. Then, we derive various global conditions of ultimate

In the present paper, initial problem for the integro‐differential diffusion system with nonlocal nonlinear sources is considered. The results on existence of local mild solutions and nonexistence of global weak solution to the nonlinear integro‐differential diffusion system are presented.

Irregularities indices are commonly utilized for quantitative portrayal of topological structure of graphs which are not regular. As indicated by a broadly acknowledged bias, utilizing a topological descriptor (known as irregularity index of a graph) for that reason, the consequences of graph irregularity grouping ought to be predictable with our abstract decisions (instinctive inclination). In the

The higher order two‐phase local/nonlocal elasticity model and the higher order strain gradient theory are unified via an abstract variational scheme. The higher order constitutive integral convolution is established in a consistent variational framework governed by ad hoc functional space of test fields. Equivalent differential constitutive law equipped with nonclassical boundary conditions of constitutive

A phase‐field crystal model (PFC model) which takes into account exponential relaxation of the atomic flux and its fluctuations is developed. The model corresponds to a system undergoing phase transformation described with a partial differential equation of hyperbolic type. Such a model covers slow and rapid regimes of interface propagation at small and large driving forces during melting and solidification

The aim of this paper is to show the existence of R ‐bounded solution operator families for a generalized resolvent problem on the half‐space arising from a compressible fluid model of Korteweg type. Our main result covers not only the large resolvent parameter λ ∈ C + : = { z ∈ C | ℜ z > 0 } so that |λ|≥δ for some δ > 0, but also small λ satisfying |λ|≤δ.

We establish the existence of nonnegative weak solutions to time fractional Keller–Segel system with Dirichlet boundary condition in a bounded domain with smooth boundary. Since the considered system has a cross‐diffusion term and the corresponding diffusion matrix is not positive definite, we first regularize the system. Then under suitable assumptions on the initial conditions, we establish the existence

The objective of this article is to present the analysis of stochastic functional differential equations in the G‐framework (G‐SFDEs) with monotone type conditions. The existence–uniqueness theorem has been proved. The exponential and L G 2 estimates have been obtained. We have derived that the Lyapunov exponent of the solution is less than K ( 1 + 2 c 1 + 4 c 2 2 ) .

The universal approximation property of feedforward neural networks (FNNs) is the basis for all FNNs applications. In almost all existing FNN approximation studies, it is always assumed that the activation function of the network satisfies certain conditions, such as sigmoid or bounded continuity. This paper focuses on building simple architecture FNNs with approximation ability by constructing an

Quantum Fisher information (QFI) and geometric phase have recently performed different tasks in quantum information technology. We investigate the statistical quantities as the QFI and entanglement of a three‐level atom in Λ configuration interacting with a quantized field mode by using linear entropy. We study the dynamical behavior of the geometric phase based on the engineering of a three‐level

This paper presents an estimation method for the random effect parameters and the variance components in linear mixed models. These models may be orthogonal or nonorthogonal. In particular, least squares estimators and the corresponding confidence regions, based on the estimation of quantiles, are considered. As to the random effects parameters, it is only assumed that they have null mean vectors and

In this paper, we first obtain the existence of positive ground state solutions for the following critical fractional Laplacian system: ( − Δ ) s u = μ 1 | u | 2 s ∗ − 2 u + α γ 2 s ∗ | u | α − 2 u | v | β in ℝ n , ( − Δ ) s v = μ 2 | v | 2 s ∗ − 2 v + β γ 2 s ∗ | u | α | v | β − 2 v in ℝ n , then we give a complete classification of positive ground state solutions with different Morse index. More

In this work, we develop a numerical scheme for a class of singularly perturbed quasilinear problems with integral boundary conditions. The quasilinear equation is discretized using a hybrid scheme, and the composite trapezoidal rule is used to discretize the boundary condition. We construct a general error analysis framework for the discrete scheme. Within this framework, the discrete scheme is shown

In this paper, we prove several Jensen‐Grüss type inequalities under various conditions. Some applications in information theory are also given.

This paper is devoted by developing sufficient condition required for the existence of solution to a nonlinear fractional order boundary value problem D γ u ( ℓ ) = ψ ( ℓ , u ( λ ℓ ) ) , ℓ ∈ Z = [ 0 , 1 ] , with fractional integral boundary conditions p 1 u ( 0 ) + q 1 u ( 1 ) = 1 Γ ( γ ) ∫ 0 1 ( 1 − ρ ) γ − 1 g 1 ( ρ , u ( ρ ) ) d ρ , and p 2 u ′ ( 0 ) + q 2 u ′ ( 1 ) = 1 Γ ( γ ) ∫ 0 1 ( 1 − ρ ) γ

In this paper, we use power series method to study the propagation of cylindrical shock waves produced on account of a strong explosion in a non‐ideal gas under the influence of azimuthal magnetic field. Here, the density is assumed to be uniform and magnetic pressure is assumed to vary according to power law with distance from the symmetry axis in the undisturbed medium. Using power series method

This paper investigates the equivalence between p‐mean Poisson μ‐pseudo almost automorphic and Poisson asymptotically almost automorphic stochastic processes outside one μ‐ergodic zero set and then obtains the completeness of the space of Poisson μ‐pseudo almost automorphic stochastic processes without the Lipschitz condition. These properties established enrich the knowledge of Poisson μ‐pseudo almost

With every passing day, one comes to know that cases of the corona virus disease are increasing. This is an alarming situation in many countries of the globe. So far, the virus has attacked as many as 188 countries of the world and 5 549 131 (27 May 2020) human population is affected with 348 224 deaths. In this regard, public and private health authorities are looking for manpower with modeling skills

We deal with Euler‐type half‐linear second‐order differential equations, and our intention is to derive conditions in order their non‐trivial solutions are non‐oscillatory. This paper connects to the article P. Hasil, J. Šišoláková, M. Veselý: Averaging technique and oscillation criterion for linear and half‐linear equations, Appl. Math. Lett. 92 (2019), 62–69, where the corresponding oscillatory counterpart

We study the stochastic aggregation of linearly coupled Cucker–Smale (CS) particles on several asymmetric networks. Our proposed first‐order stochastic CS model was motivated as a stochastic dynamics modeling on the rates of multiasset return. In this study, we consider three asymmetric networks and study sufficient conditions toward stochastic aggregation for each proposed network. We also provide

This paper deals with the blow‐up phenomenon to the following quasi‐linear pseudo‐parabolic equation with nonlocal source: u t − Δ u t − ∇ · ( | ∇ u | 2 q ∇ u ) = u p ( x , t ) ∫ Ω K ( x , y ) u p + 1 ( y , t ) d y , x , y ∈ Ω , t > 0 , where Ω ⊆ ℝ n , n ≥ 3 , is a bounded domain with smooth boundary. Here, 0 < q ≤ p and K(x,y) is an integrable real‐valued function. We show that for q < p, the blow‐up

The Hirota bilinear method is prepared for searching the diverse soliton solutions for the fractional generalized Calogero‐Bogoyavlenskii‐Schiff‐Bogoyavlensky‐Konopelchenko (CBS‐BK) equation. Also, the Hirota bilinear method is used to finding the lump and interaction with two stripe soliton solutions. Interaction among lumps, periodic waves, and multi‐kink soliton solutions will be investigated. Also

A time fractional initial boundary value problem of mixed parabolic–elliptic type is considered. The domain of such problem is divided into two subdomains. A reaction–diffusion parabolic problem is considered on the first domain, and on the second, a convection–diffusion elliptic type problem is considered. Such problem has a mild singularity at the initial time t = 0. The classical L1 scheme is introduced

This work is motivated by a longstanding interest in the long time behavior of flow‐structure interaction (FSI) PDE dynamics. We consider a linearized compressible flow structure interaction (FSI) PDE model with a view of analyzing the stability properties of both the compressible flow and plate solution components. In our earlier work, we gave an answer in the affirmative to question of uniform stability

This paper studies resilient coordinated control over networks with hybrid dynamics and malicious agents. In a hybrid multi‐agent system, continuous‐time and discrete‐time agents concurrently exist and communicate through local interaction. We introduce the notion of heterogeneous robustness to capture the topological structure and facilitate convergence analysis of hybrid agents over multiple subnetworks