In this article, we study the exhaustive analysis of nonlinear wave interactions for a 2 × 2 homogeneous system of quasilinear hyperbolic partial differential equations (PDEs) governing the macroscopic production. We use the hodograph transformation and differential constraints technique to obtain the exact solution of governing equations. Furthermore, we study the interaction between simple waves

In this article, we present the existence, uniqueness, Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales, with the help of a fixed point approach. We use Grönwall’s inequality on time scales, an abstract Gröwall’s lemma and a Picard operator as basic tools to develop our main results. To

We prove that, as in the finite dimensional case, the space of Bloch functions on the unit ball of a Hilbert space contains, under very mild conditions, any semi-Banach space of analytic functions invariant under automorphisms. The multipliers for such Bloch space are characterized and some of their spectral properties are described.

In this paper, we consider a class of left invariant Riemannian metrics on Sp(n), which is invariant under the adjoint action of the subgroup Sp(n − 3) × Sp(1) × Sp(1) × Sp(1). Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gröbner basis

In this paper, dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated. The model involves the concentrations of uninfected cells, infected cells, free virus, CTL response cells, and antibody antibody response cells. There are three delays in the model: the intracellular delay, virus replication delay and the antibody delay. The basic

In this paper, we establish the global existence and uniqueness of the solution of the Cauchy problem of a one-dimensional compressible isentropic Euler system for a Chaplygin gas with large initial data in the space L 1loc . The hypotheses on the initial data may be the least requirement to ensure the existence of a weak solution in the Lebesgue measurable sense. The novelty and also the essence of

We consider Toeplitz operators Tu with symbol u on the Bergman space of the unit ball, and then study the convergences and summability for the sequences of powers of Toeplitz operators. We first charactreize analytic symbols φ for which the sequence \(T_\varphi ^{*k}\) f or \(T_\varphi ^k\) f converges to 0 or ∞ as k → ∞ in norm for every nonzero Bergman function f. Also, we characterize analytic symbols

Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality ∣Δf(z)∣ ≤ B · ∣Df (z)∣2 for some B > 0 and f(0) = 0. In this note, we show that f does not always satisfy the Schwarz-Pick type inequality $$\frac{1-\vert z\vert^{2}}{1-\vert f(z)\vert^{2}}\leq\ C(B),$$ where C(B) is a constant depending only on B. Moreover, a more general Schwarz-Pick

In the article, we prove that the double inequalities $$\begin{array}{*{20}{c}} {{G^p}\left[ {{\lambda _1}a + \left( {1 - {\lambda _1}} \right)b,{\lambda _1}b + \left( {1 - {\lambda _1}} \right)a} \right]{A^{1 - p}}\left( {a,b} \right) < T\left[ {A\left( {a,b} \right),G\left( {a,b} \right)} \right]} \\ { < {G^p}\left[ {\mu _1^{}a + \left( {1 - {\mu _1}} \right)a} \right]{A^{1 - p}}\left( {a,b} \right)

For n ≥ 3, we construct a class \(\left\{{{W_{n,{\pi _1},{\pi _2}}}} \right\}\) of n2 × n2 hermitian matrices by the permutation pairs and show that, for a pair {π1, π2} of permutations on (1, 2, …, n), \({{W_{n,{\pi _1},{\pi _2}}}}\) is an entanglement witness of the n ⊗ n system if {π1, π2} has the property (C). Recall that a pair {π1, π2} of permutations of (1, 2, …, n) has the property (C) if,

We are concerned with the nonlinear Schrödinger-Poisson equation $$\begin{cases}-\Delta u+(V(x)-\lambda)u+\phi(x)u=f(u),\\-\Delta\phi=u^{2},\lim\limits_{\vert x\vert\rightarrow+\infty}\phi(x)=0,x\in \mathbb{R}^{3},\end{cases}\ {\mathrm{(P)}}$$ where λ is a parameter, V (x) is an unbounded potential and f (u) is a general nonlinearity. We prove the existence of a ground state solution and multiple solutions

This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation. First, we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives. Second, based on the piecewise-quadratic polynomials, we construct the nodal basis functions, and then discretize the multi-term fractional equation by the

Denote a finite dimensional Hopf C*-algebra by H, and a Hopf *-subalgebra of H by H1. In this paper, we study the construction of the field algebra in Hopf spin models determined by H1 together with its symmetry. More precisely, we consider the quantum double D(H, H1) as the bicrossed product of the opposite dual \(\widehat{{H^{op}}}\) of H and H1 with respect to the coadjoint representation, the latter

The severe acute respiratory syndrome COVID-19 was discovered on December 31, 2019 in China. Subsequently, many COVID-19 cases were reported in many other countries. However, some positive COVID-19 samples had been reported earlier than those officially accepted by health authorities in other countries, such as France and Italy. Thus, it is of great importance to determine the place where SARS-CoV-2

In this paper, we give a characterization for the general complex (α, β) metrics to be strongly convex. As an application, we show that the well-known complex Randers metrics are strongly convex complex Finsler metrics, whereas the complex Kropina metrics are only strongly pseudoconvex.

The reflection of a weak shock wave is considered using a shock polar. We present a sufficient condition under which the von Neumann paradox appears for the Euler equations. In an attempt to resolve the von Neumann paradox for the Euler equations, two new types of reflection configuration, one called the von Neumann reflection (vNR) and the other called the Guderley reflection (GR), are observed in

In this paper, we study the proximal relation, regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions. A useful tool is the support of a topological dynamical system which is used to study the structure of the Banach proximal relation, and we prove that above three relations all coincide on a Banach mean equicontinuous system generated

This paper is concerned with the Fisher-KPP equation with diffusion and nonlocal delay. Firstly, we establish the global existence and uniform boundedness of solutions to the Cauchy problem. Then, we establish the spreading speed for the solutions with compactly supported initial data. Finally, we investigate the long time behavior of solutions by numerical simulations.

As we know, thus far, there has appeared no definition of bilinear spectral multipliers on Heisenberg groups. In this article, we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and investigate its boundedness. We find some restrained conditions to separately ensure its boundedness from \({{\cal C}_0}\left({{\mathbb{H}^n}} \right) \times {L^2}\left({{\mathbb{H}^n}}

In this paper, we consider the measure determined by a fractional Ornstein-Uhlenbeck process. For such a measure, we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality. To this end, we also present the integration by parts formula for such a measure, which is obtained via its pull back formula and the Bismut

In this paper, for any local area-minimizing closed hypersurface Σ with \(R{c_{\rm{\Sigma }}} = {{{R_{\rm{\Sigma }}}} \over n}{g_{\rm{\Sigma }}}\) immersed in a (n + 1)-dimension Riemannian manifold M which has positive scalar curvature and nonnegative Ricci curvature, we obtain an upper bound for the area of Σ. In particular, when Σ saturates the corresponding upper bound, Σ is isometric to \({\mathbb{S}^n}\)

In this paper we prove the existence and uniqueness of time global mild solutions to the Navier-Stokes-Oseen equations, which describes dynamics of incompressible viscous fluid flows passing a translating and rotating obstacle, in the solenoidal Lorentz space L 3σ, w . Besides, boundedness and polynomial stability of these solutions are also shown.

In this paper, we study the generalized complete (p, q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters, and establish the monotonicity, generalized convexity and concavity of these functions. In particular, some Turán type inequalities are given. Finally, we also show some new series representations of these functions by

In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations (BDSDEs), that is, BDSDEs whose coefficients depend not only on the solution processes but also on their law. The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions. With the help of the comparison result for the Lipschitz

Let Ta,ϕ be a Fourier integral operator defined by the oscillatory integral $${T_{a,\varphi }}u(x) = {1 \over {{{(2\pi )}^n}}}\int_{{^n}} {{e^{{\rm{i}}\varphi (x,\xi )}}} a(x,\xi )\hat u(\xi ){\rm{d}}\xi,$$ where\(a \in S_{\varrho,\delta }^m\) and ϕ ∈ Φ2, satisfying the strong non-degenerate condition. It is shown that if 0 < ϱ ≤ 1, 0 ≤ δ < 1 and \( \le {{{\varrho ^2} - n} \over 2}\), then Ta,ϕ is

In this paper, we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function. It is proved that the Riemann zeta function and the Euler gamma function cannot satisfy a class of nontrivial algebraic differential equations and algebraic difference equations.

We prove the reducibility of analytic multipliers Mϕ with a class of finite Blaschke products symbol ϕ on the Sobolev disk algebra R(ⅅ). We also describe their nontrivial minimal reducing subspaces.

Let M be a C2-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov. Let u: M → X be a Sobolev mapping in the sense of Korevaar and Schoen. In this short note, we introduce a notion of p-energy for u which is slightly different from the original definition of Korevaar and Schoen. We show that each minimizing p-harmonic mapping (p ≥ 2)

This article sets forth results on the existence and boundedness of solutions for quasilinear elliptic systems involving p-Laplacian and q-Laplacian operators. The approach combines Schaefer’s fixed point as well as Moser’s iteration procedure.

Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world. It is caused by various species of the genus Aphthovirus of the family Picornavirus, and it always brings a large number of infections and heavy financial losses. The disease has become a major public health concern. In this paper, we propose a nonlocal foot-and-mouth disease model in a spatially heterogeneous environment

We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes $$d{Y_s} = \left( {\sum\limits_{j = 1}^k {{\mu _j}{\phi _j}\left( s \right) - \beta {Y_s}} } \right){\rm{d}}s + {\rm{dZ}}_s^{q,H},$$ driven by the Hermite process Z q,Hs with order q ≥ 1 and a Hurst index H ∈ (½, 1), where the periodic functions φj(s),j = 1,⌦, k are bounded, and the real numbers μj, j = 1, …,

The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper. Obtained via the Symmetric Mountain Pass Lemma, two results about infinitely many periodic solutions of the systems extend some previously known results.

The first aim of this paper is to investigate the growth of the entire function defined by the Laplace-Stieltjes transform converges on the whole complex plane. By introducing the concept of generalized order, we obtain two equivalence theorems of Laplace-Stieltjes transforms related to the generalized order, A *n and λn. The second purpose of this paper is to study the problem on the approximation

This paper is concerned with a Pontryagin’s maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables. By virtue of the duality method and the generalized anticipated backward stochastic differential equations, we establish a necessary maximum principle and a sufficient verification theorem

In this paper, we prove that (X, p) is separable if and only if there exists a w*-lower semicontinuous norm sequence \(\left\{ {{p_n}} \right\}_{n = 1}^\infty \) of (X*, p) such that (1) there exists a dense subset Gn of X* such that pn is Gâteaux differentiable on Gn and dpn (Gn) ⊂ X for all n ∊ N; (2) pn ≤ p and pn → p uniformly on each bounded subset of X*; (3) for any α ∈ (0, 1), there exists a

This paper is mainly concerned with the S-asymptotically Bloch type periodicity. Firstly, we introduce a new notion of S-asymptotically Bloch type periodic functions, which can be seen as a generalization of concepts of S-asymptotically ω-periodic functions and S-asymptotically ω-anti-periodic functions. Secondly, we establish some fundamental properties on S-asymptotically Bloch type periodic functions

In this paper, we construct sign-changing radial solutions for a class of Schrödinger equations with saturable nonlinearity which arises from several models in mathematical physics. More precisely, for any given nonnegative integer k, by using a minimization argument, we first obtain a sign-changing minimizer with k nodes of a constrained minimization problem, and show, by a deformation lemma and Miranda’s

Let 0 < β < 1 and Ω be a proper open and non-empty subset of Rn. In this paper, the object of our investigation is the multilinear local maximal operator \({{\cal M}_\beta }\), defined by $${{\cal M}_\beta }\left( {\overrightarrow f } \right)\left( x \right) = \mathop {\sup }\limits_{\matrix{{Q \ni x} \cr {Q \in {{\cal F}_\beta }} \cr } } \prod\limits_{i = 1}^m {{1 \over {\left| Q \right|}}\int_Q {\left|

In this paper, we consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process (Gt)t≥0. The second order mixed partial derivative of the covariance function \(R(t,s) = \mathbb{E}\left[ {{G_t}{G_s}} \right]\) can be decomposed into two parts, one of which coincides with that of fractional Brownian motion and the other of which is bounded

In this paper, we study the martingale inequalities under G-expectation and their applications. To this end, we introduce a new kind of random time, called G-stopping time, and then investigate the properties of a G-martingale (supermartingale) such as the optional sampling theorem and upcrossing inequalities. With the help of these properties, we can show the martingale convergence property under

The existence of global BV solutions for the Aw-Rascle system with linear damping is considered. In order to get approximate solutions we consider the system in Lagrangian coordinates, then by using the wave front tracking method coupling with and suitable splitting algorithm and the ideas of [1] we get a sequence of approximate solutions. Finally we show the convergence of this approximate sequence

In this paper we prove the local well-posedness of strong solutions to a chemotaxis-shallow water system with initial vacuum in a bounded domain Ω ų ℝ2 without the standard compatibility condition for the initial data. This improves some results obtained in [J. Differential Equations 261(2016), 6758–6789].

In this article, we solve completely Gleason’s problem on Fock-Sobolev spaces Fp,m for any non-negative integer m and 0 < p ≤ ∞.

For high-dimensional models with a focus on classification performance, the ℓ1-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data. We propose two types of weighted Lasso estimates, depending upon covariates determined by the McDiarmid inequality. Given

This article explores the characteristics of the average abundance function with mutation on the basis of the multi-player snowdrift evolutionary game model by analytical analysis and numerical simulation. The specific field of this research concerns the approximate expressions of the average abundance function with mutation on the basis of different levels of selection intensity and an analysis of

In this article, we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities. Firstly, we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality, the Poincaré inequality, and the Hardy inequality. Then, by using the potential well method and the inequality

Let L:= −Δ + V be the Schrödinger operator on ℝn with n ≥ 3, where V is a non-negative potential satisfying Δ−1 (V) ∈ L∞(ℝn). Let w be an L-harmonic function, determined by V, satisfying that there exists a positive constant ö such that, for any x ∈ ℝn, 0 < δ ≤ w(x) ≤ 1. Assume that p(·): ℝn → (0, 1] is a variable exponent satisfying the globally log-Hölder continuous condition. In this article, the

Most results on the polynomial-like iterative equation are given under the condition that the given function is monotone, while a work by L. Liu and X. Gong gets non-monotone PM solutions with height 1 when the given function is of the same case. Removing the condition on height for the given function, we first give a method to assert the nonexistence of C0 solutions, then present equivalent conditions

Hilbert Problem 15 required an understanding of Schubert’s book [1], both its methods and its results. In this paper, following his idea, we prove that the formulas in §6, §7, §10, about the incidence of points, lines and planes, are all correct. As an application, we prove formulas 8 and 9 in §12, which are frequently used in his book.

In this article, we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation. Based on defining a Finsler-type norm on the tangent space for solutions, we first establish the Lipschitz metric for smooth solutions, then by proving the generic regularity result, we extend this metric to general weak solutions.

In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space \({\cal F}\dot {\cal N}_{p\left( \cdot \right),h\left( \cdot \right),q}^{s\left( \cdot \right)}\left( {{\mathbb{R}^3}} \right)\) with \(s\left( \cdot \right) = 4 - 2\alpha - {3 \over {p\left( \cdot \right)}}\). We prove global well-posedness result

In this paper we deal with the martingales in variable Lebesgue space over a probability space. We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space. The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue

In this article, we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities. Furthermore, we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.

This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space. Utilizing the KKM theorem, a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established. By using a fixed point theorem for a condensing set-valued map, the nonemptiness and compactness of the set

In this article, we are concerned with analytical solutions for a model of inviscid liquid-gas two-phase flow. On the basis of Yuen’s works [25, 27–29] on self-similar solutions for compressible Euler equations, we present some special self-similar solutions for a model of inviscid liquid-gas two-phase flow in radial symmetry with and without rotation, and in elliptic symmetry without rotation. Some

This paper studies the mixed radial-angular integrability of parametric Marcinkiewicz integrals along “polynomial curves”. Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness, the authors prove that such operators are bounded on the mixed radial-angular spaces. Meanwhile, corresponding vector-valued versions are also obtained.

In this paper, we consider an inflow problem for the non-isentropic Navier-Stokes-Poisson system in a half line (0, ∞). For the general gas including ideal polytropic gas, we first give some results for the existence of the stationary solution with the aid of center manifold theory on a 4 × 4 system of autonomous ordinary differential equations. We also show the time asymptotic stability of the stationary

In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate. The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models. We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that, via

The aim of this article is twofold. One aim is to establish the precise forms of Landau-Bloch type theorems for certain polyharmonic mappings in the unit disk by applying a geometric method. The other is to obtain the precise values of Bloch constants for certain log-p-harmonic mappings. These results improve upon the corresponding results given in Bai et al. (Complex Anal. Oper. Theory, 13(2): 321–340

Let A be an infinite dimensional stably finite unital simple separable C*-algebra. Let B ⊂ A be a stably (centrally) large subalgebra in A such that B is m-almost divisible (m-almost divisible, weakly (m, n)-divisible). Then A is 2(m + 1)-almost divisible (weakly m-almost divisible, secondly weakly (m, n)-divisible).