The knowledge of the principal refractive indices and their dependence on the applied stress is the starting point for any experimental analysis of transparent crystals. Because for strongly anisotropic crystals and a general state of stress an explicit analytical solution can be difficult to obtain, then we need some approximated solutions. Here, we propose a coherent approximation procedure that

We establish the local (in time) solvability in the classical sense for the Cauchy problem and first and second boundary‐value problems on the half‐line for a nonlinear equation similar to Benjamin‐Bona‐Mahony‐Bürgers‐type equation. We also derive an a priori estimate that implies sufficient blow‐up conditions for the second boundary‐value problem. We obtain analytically an upper bound of the blow‐up

In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a logarithmic weight. We give necessary conditions when the symbol is of the form ψ + φ ‾ , where ψ and φ are analytic on the annulus z ∈ ℂ , 1 / 2 < | z | < 1 .

No abstract is available for this article.

We study the global well‐posedness and existence of uniform attractor for magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier–Stokes equations for the fluid velocity and pressure coupled with a reduced from of the Maxwell equations for the magnetic field. The fluid velocity is assumed to satisfy a no‐slip boundary condition, while the magnetic field is subject to a time‐dependent

We present the reconstruction formula for the solenoidal part of a vector field compactly supported in a unit ball of R 3 by using a new type of transform called the first integral moment transverse transform. In contrast to the first integral moment transform, this transform is an integral over line components perpendicular to the rays weighted according to the length of the rays. The solenoidal part

We study the constraint minimization problem related to the Gross–Pitaevskii functional with a higher order interaction I a δ : = inf E a δ ( ϕ ) : ϕ ∈ H ( R 2 ) , ‖ ϕ ‖ L 2 2 = 1 , where δ >0,a >0, E a δ ( ϕ ) : = ∫ R 2 | ∇ ϕ | 2 d x + ∫ R 2 V | ϕ | 2 d x + δ 2 ∫ R 2 | ∇ ( | ϕ | 2 ) | 2 d x − a 2 ∫ R 2 | ϕ | 4 d x and V is a continuous periodic potential. Thanks to the concentration‐compactness principle

In this paper, we explore a pricing model for corporate bond accompanied with multiple credit rating migration risk and stochastic interest rate. The bond price volatility strongly depends on potentially multiple credit rating migration and stochastic change of interest rate. A free boundary problem of partial differential equation is presented, which is the equivalent transformation of the pricing

In this paper, multiple lump solutions of the (2+1)‐dimensional Konopelchenko–Dubrovsky equation are obtained by means of the Hirota bilinear method. With the aid of positive quartic‐quadratic‐functions, we can get the 1‐lump solutions, 3‐lump solutions, and 6‐lump solutions. Via the density plots and three‐dimensional plots, the dynamic properties of multiple lump solutions are discussed by choosing

In this paper, we present an improved wheelset motion model with two degrees of freedom and study the dynamic behaviors of the system including the symmetry, the existence and uniqueness of the solution, continuous dependence on initial conditions, and Hopf bifurcation. The dynamic characteristics of the wheelset motion system under a nonholonomic constraint are investigated. These results generalize

This work presents an iterative scheme for the numerical solution of the space‐time fractional two‐dimensional advection–reaction–diffusion equation applying homotopy perturbation with Laplace transform using Caputo fractional‐order derivatives. The solution obtained is beneficial and significant to analyze the modeling of superdiffusive systems and subdiffusive system, anomalous diffusion, transport

This paper studies partial differential equation model with the new general fractional derivatives involving the kernels of the extended Mittag–Leffler type functions. An initial boundary value problem for the anomalous diffusion of fractional order is analyzed and considered. The fractional derivative with Mittag–Leffler kernel or also called Atangana and Baleanu fractional derivative in time is taken

In this paper, we introduce 8×8 real matrix representations of complex split quaternions. Then, the relations between real matrix representations of split and complex split quaternions are stated. Moreover, we investigate some linear split and complex split quaternionic equations with split Fibonacci and complex split Fibonacci quaternion coefficients. Finally, we also give some numerical examples

The theory of operator‐valued Fourier multipliers is used to obtain characterizations for well‐posedness of a large class of degenerate integro‐differential equations of second order in time in Banach spaces. Specifically, we treat the case of vector‐valued Besov spaces on the real line. It is important to note that in particular, the results are applicable to the more familiar scale of vector‐valued

This paper investigates the Lagrange global exponential stability of the quaternion‐valued memristive neural networks (QVMNNs). Two kinds of activation functions based on different assumptions are considered. Then, based on the Lyapunov function approach, decomposition method, and some inequality skills, two novel sufficient conditions for lagrange stability of QVMNNs are provided corresponding to

In this paper, we study one‐dimensional linear degenerate wave equations with a distributed controller. We establish observability inequalities for degenerate wave equation by multiplier method. We also deduce the exact controllability for degenerate wave equation by Hilbert uniqueness method when the control acts on the nondegenerate boundary. Moreover, an explicit expression for the controllability

Inspired by Cooke and York's work, we concentrate on the delay dynamic equation x Δ ( t ) = g t , x ( t ) − g t , x δ ( t ) on a nonempty, arbitrary, closed set of real numbers, so‐called a time scale. The utilization of an abstract delay function δ in the above‐given equation relaxes the condition that each individual has a fixed constant life span when it fits a growth process.

This paper presents necessary and sufficient conditions for uniform exponential stabilization of a class of nonlinear systems in Banach state spaces. The stabilization assumptions are formulated in terms of integral estimates involving the control operator and the state of the uncontrolled version of the system at hand. An explicit estimate of the convergence speed is given. Applications to feedback

This manuscript mainly deals with quaternion‐valued neural networks (QVNNs) with delays and inertial term. Using Wirtinger inequality and coincidence degree theory, a new sufficient criterion to ensure the existence of antiperiodic solution of involved quaternion‐valued neural networks is derived. With the aid of Lyapunov function, we discuss the exponential stability of antiperiodic solutions to quaternion‐valued

This paper first puts forward the concept of global polynomial stabilization (GPS) of coupled neural networks (CNNs) with multi‐proportional delays. First, the existence and uniqueness of the equilibrium point of the proposed CNNs are proved by using homeomorphic mapping theorem. Second, by taking discrete controller, based on Lyapunov functionals and linear matrix inequality (LMI) skills, we gain

This work is concerned with the Neumann initial boundary value problem and Cauchy problem of a parabolic p ‐Laplacian equation with nonlocal Fisher–KPP type reaction terms. We establish a uniform boundedness and global existence of solutions to the equation by applying the method of multipliers and modified Moser's iteration technique for some ranges of parameters. The ranges of parameters have similar

This paper deals with the parabolic–elliptic Keller–Segel system with density‐dependent sublinear sensitivity and logistic source, u t = Δ u − χ ∇ · ( u ( u + 1 ) α − 1 ∇ v ) + λ u − μ u κ , x ∈ Ω , t > 0 , 0 = Δ v − v + u , x ∈ Ω , t > 0 , where Ω : = B R ( 0 ) ⊂ R n ( n ≥ 3 ) is a ball with some R >0 and χ >0, 0<α <1, λ ∈ R , μ >0, and κ >1. In the case α =1, Winkler (Z. Angew. Math. Phys.; 2018;

In this article, a nutrient‐autotroph‐herbivore model with nutrient recycling is constructed. Holling type‐II functional response for the relation between nutrient and autotroph while Beddington‐DeAngelis‐type functional response for autotroph and herbivore relation are considered here. It is plausible that the conversion of nutrient from dead biomass (autotroph and herbivore) by decomposers (i.e.

In this paper, we consider a class of nonlocal stochastic functional differential equations driven by G‐Brownian motion (GNSFDEs) at phase space B C ( ( − ∞ , 0 ] ; R n ) whose coefficients are dependent on the p ‐th moment. Existence and uniqueness of solutions for GNSFDEs are investigated by virtue of theory of nonlinear expectation. Furthermore, we show that the solution map of GNSFDEs can generate

In this present investigation, we proposed a reliable and new algorithm for solving time‐fractional differential models arising from physics and engineering. This algorithm employs the Shehu transform method, and then nonlinearity term is decomposed. We apply the algorithm to solve many models of practical importance and the outcomes show that the method is efficient, precise, and easy to use. Closed

We study the free boundary problem for a plasma–vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div‐curl system of pre‐Maxwell dynamics, to better understand the influence of the electric field in vacuum, we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric

In this paper, we study mean‐field backward stochastic differential equations driven by G ‐Brownian motion (G ‐BSDEs). We first obtain the existence and uniqueness theorem of these equations. In fact, we can obtain local solutions by constructing Picard contraction mapping for Y term on small interval, and the global solution can be obtained through backward iteration of local solutions. Then, a comparison

We show the existence of infinitely many weak solutions to a class of quasilinear elliptic p (x )‐polyharmonic Kirchhoff equations via the mountain pass principle without the (AR) condition. Furthermore, we obtain infinitely many solutions to this equation based on the genus theory, introduced by Krasnoselskii and the abstract critical point theorem (a variant of Ljusternik‐Schnirelman theory) under

Very recently, the concept of fractal differentiation and fractional differentiation has been combined to produce new differentiation operators. The new operators were constructed using three different kernels, namely, power law, exponential decay, and the generalized Mittag‐Leffler function. The new operators have two parameters: the first is considered as fractional order and the second as fractal

In this paper, synchronization for stochastic hybrid‐delayed coupled systems with Lévy noise on a network (SHDCLN) is investigated via aperiodically intermittent control. Here time delays, Markovian switching and Lévy noise are considered on a network simultaneously for the first time. After that, by means of Lyapunov method, graph theory, and some techniques of inequality, some sufficient conditions

This paper studies the Hankel determinant generated by a perturbed Jacobi weight, which is closely related to the largest and smallest eigenvalue distribution of the degenerate Jacobi unitary ensemble. By using the ladder operator approach for the orthogonal polynomials, we find that the logarithmic derivative of the Hankel determinant satisfies a nonlinear second‐order differential equation, which

The boundary integral equation is solved analytically in the case of two‐ and three‐dimensional growth of angled dendrites and arbitrary parabolic/paraboloidal solid/liquid interfaces. The undercooling of a binary melt and the solute concentration at the phase transition boundary are found. The theory under consideration has a potential impact in describing more complex growth shapes and interfaces

We propose a novel Markov chain Monte‐Carlo (MCMC) method for reverse engineering the topological structure of stochastic reaction networks, a notoriously challenging problem that is relevant in many modern areas of research, like discovering gene regulatory networks or analyzing epidemic spread. The method relies on projecting the original time series trajectories, from the stochastic data generating

The motivation of the current article is to explore a numerical investigation on steady triply diffusive convection in a vertical channel. Heat is exchanged from the external fluid with the plates. The reference temperature is taken as equal and also as different for the external fluid. Solutions in the absence of viscous dissipation and buoyancy forces are also obtained as special cases. General solutions

This paper starts with the derivation of the most general equations of motion for the infinitesimal rotators moving on arbitrary two‐dimensional surfaces of revolution. Both geodesic and geodetic (i.e., without any external potential) equations of motion on surfaces with nontrivial curvatures that are embedded into the three‐dimensional Euclidean space are discussed. The Mylar balloon as a concrete

For the speed control of direct current motor, a fractional complex‐order controller (FCOC) is proposed in this paper. The FCOC is an extension of the fractional‐order controller. It is known that fractional‐order controllers exhibit strong robustness to open‐loop gain variations. However, in actual situations, due to external interference, the phase angle and gain of the system may change at the same

Based on the nonlocal strain gradient theory, the coupling nonlinear dynamic equations of a rotating double‐tapered cantilever Timoshenko nano‐beam are derived using the Hamilton principle. The equation of motion is discretized via the differential quadrature method. The effects of the angular velocity, nonlocal parameter, slenderness ratio, cross‐section parameter, and taper ratios are examined and

In this paper, based on the pathogenesis of Alzheimer's disease, we investigate a stochastic mathematical model, focusing on the dynamics of β‐amyloid (Aβ) plaques, Aβ oligomers, PrPC proteins, and the Aβ‐x‐PrP C complex. Within the framework of the Lyapunov method, we first show existence and uniqueness of global positive solution of the model and then establish the sufficient conditions for existence

In the present research manuscript, we introduce a novel general fractional boundary value inclusion problem and investigate the necessary and sufficient conditions for desired existence results. Indeed, more precisely, we formulate a class of fractional multiterm Caputo–Hadamard differential inclusion problem with two‐point sum boundary value conditions. In two separate theorems, we prove the existence

We introduce a neural field equation with a neuron‐dependent Heaviside‐type activation function and spatial‐dependent delay. The basic object of the study is represented by a Volterra–Hammerstein integral equation involving a discontinuous nonlinearity with respect to the state variable that is both time and space dependent. We replace the discontinuous nonlinearity by its multivalued convexification

Parameters in mathematical models for glioblastoma multiforme (GBM) tumour growth are highly patient specific. Here, we aim to estimate parameters in a Cahn–Hilliard type diffuse interface model in an optimised way using model order reduction (MOR) based on proper orthogonal decomposition (POD). Based on snapshots derived from finite element simulations for the full‐order model (FOM), we use POD for

In some circumstances, sound waves in a rarefied gas can be studied using a linearised form of the regularised 13‐moment equations of Struchtrup and Torrilhon. We build solutions of those equations in spherical polar coordinates using vector spherical harmonics. We first solve a reduced system of equations (with 11 unknowns) after introduction of a force vector (divergence of the stress). We then show

In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a general radial weight. We give necessary conditions when the symbol is of the form g 1 + g 2 ‾ , where g 1 and g 2 are analytic on the annulus z ∈ ℂ , 1 / 2 < | z | < 1 .

In this paper, we study the stability problem for the transmission plate equation with moment feedback control that contains a delay term and that acts on the exterior boundary. We prove under some assumptions that the closed‐loop system is exponentially stable. To establish this result, we introduce a suitable energy function and use multipliers method and compactness–uniqueness argument.

In the current investigation, the thermoelasticity with a model of fractional order is used to discuss a problem of thermoelastic half‐space. Such theory depends on the time‐fractional derivative of Caputo of order α . The thermal conductivity is considered to be a variable, and the medium surface is subjected to a free from traction and a thermal shock. Then, the transform of Laplace has been utilized

The aim of this paper is to study parabolic integro‐differential equations of Kirchhoff type. We prove the existence and uniqueness of the solution for this problem via Galerkin method. Semidiscrete formulation for this problem is presented using conforming finite element method. As a consequence of the Ritz–Volterra projection, we derive error estimates for both semidiscrete solution and its time

This paper suggests a fractal mathematical model for Fangzhu 's water collection by taking into account its nanoscale surface morphology. A fractal variational principle is established by the semi‐inverse method, which elucidates the conservation laws in the fractal space. Additionally, the variational formulation can also reveal the structure of the solution. An approximate analytical solution is

Using monotonicity methods, the Lagrange multiplier rule, and some variational arguments, we consider a type of localization results pertaining to the existence of critical points to action functionals on a closed ball. A variant of the Schechter critical point theorem on a ball in Hilbert and Banach spaces is obtained. Applications to nonlinear Dirichlet problem and to partial difference equations

We consider the Timoshenko model with partial dissipative boundary condition with delay, and we prove that the solution decays exponentially to zero, provided the wave speed are equal; this improve earlier result due to Bassam et al and Muñoz Rivera and Naso. Moreover, consider the exponential stability to the corresponding semilinear problems.

In this paper, we discuss the structure of the solutions for linear interval‐valued Volterra integro‐differential equations (VIDEs) based on gH‐difference. The considered VIDEs consist of six forms. Among those six forms, three forms are obtained by using the definition of generalized Hukuhara difference (or gH‐difference). We obtain solutions of that linear interval‐valued VIDEs and discuss their

We give necessary conditions to get oscillatory solutions of a class of fractional order neutral differential equations with continuously distributed delay by means of the fractional derivative with respect to a given function. In particular, oscillatory solutions of the considered fractional equations with Caputo and Hadamard type of fractional derivatives are established. Some explicit examples are

We establish the existence and qualitative behavior of positive continuous solutions to some nonlinear singular fractional differential equation in the frame of conformable fractional derivative. To this end, we combine estimates on the Green's function and a fixed point argument. Some examples are given to illustrate the applicability of our main result.

The main purpose of this paper is to study the following semi‐linear structurally damped wave equation with nonlinearity of derivative type: u t t − Δ u + μ ( − Δ ) σ / 2 u t = | u t | p , u ( 0 , x ) = u 0 ( x ) , u t ( 0 , x ) = u 1 ( x ) , with μ >0, n  ≥ 1, σ ∈(0,2], and p >1. In particular, we would like to prove the nonexistence of global weak solutions by using a new test function and suitable

In this paper, we extend Lyapunov‐ and Hartman–Wintner‐type inequalities for fractional differential equation with Dirichlet‐type boundary conditions and generalized Hilfer fractional derivative. An upper bound of eigenvalues of the corresponding problem is obtained; finally, a Hartman–Wintner‐type inequality is presented.

We investigate the plane problem of an edge dislocation inside a bilayer elastic film in which an elastic film of infinite thickness is perfectly bonded to one of finite thickness fixed on a rigid substrate. The two elastic films have identical shear moduli but distinct Poisson's ratios. Under this assumption, analytical expressions of the two pairs of analytic functions (characterizing the corresponding

Using the general method of Owe Axelsson given in 1986 for incomplete factorization of M ‐matrices in block‐matrix form, we give a recursive approach to construct incomplete block‐matrix factorization of M ‐matrices by proposing a two‐step iterative method for the approximation of the inverse of diagonal pivoting block matrices at each stage of the recursion. For various predescribed tolerances in

In this paper, we find the solution and analyse the behaviour of the obtained results for the nonlinear Schrödinger‐Boussinesq equations using q ‐homotopy analysis transform method (q ‐HATM) within the frame of fractional order. The considered system describes the interfaces between intermediate long and short waves. The projected fractional operator is proposed with the help of Mittag‐Leffler function

In this study, the forced vibration of cylinders reinforced by carbon nanotubes (CNTs) under a moving load is estimated based on the theory of oscillations. The composite cylinders reinforced with CNTs of infinite length subjected to combined action of the internal pressure and ring‐shaped compressive pressure with constant velocity. Here, we consider uniform and nonuniform reinforcement distributions

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl . 2006;7:235–247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and

We provide a new perturbation theorem for substochastic semigroups on abstract AL spaces extending Kato's perturbation theorem to nondensely defined operators. We show how it can be applied to piecewise deterministic Markov processes and transport equations with abstract boundary conditions. We give particular examples to illustrate our results.