In this paper, we consider a Ginzburg-Landau functional for a complex vector order parameter $\Psi=[\psi_+, \psi_-]$. In particular, we consider entire solutions in all ${\Bbb R}^2$, which are obtained by blowing up around vortices. Among the entire solutions we distinguish those which are locally minimizing solutions, and we show that locally minimizing solutions must have degrees $n_\pm \in \{0, \pm1\}$. By studying the local structure of these solutions, we also show that one component of the solution vanishes, but the other does not, which describes the coreless vortex phenomenon in physics.

In this paper, we introduce the notion of asymptotically $\theta$-almost periodic stochastic process and study a class of stochastic differential matrixs in infinite dimensions with asymptotically almost periodic coefficients under the framework of operator semigroup theory. Using stochastic analysis theory, the existence of asymptotically $\theta$-almost periodic solutions of these matrixs is established. In addition, the concept of asymptotically almost periodic process in path distribution is introduced, and we prove that the above solutions are also asymptotically almost periodic in path distribution. It is noteworthy that all the earlier related results only give the existence of asymptotically almost periodic solutions in one-dimensional distribution, which are weaker than asymptotically almost periodic solutions in path distribution.

In this paper, we consider the well-posedness and asymptotic behavior of a one-dimensional piezoelectric beam system with control boundary conditions of fractional derivative type, which represent magnetic effects on the system. By introducing two new matrixs to deal with control boundary conditions of fractional derivative type, we obtain a new equivalent system, so as to show the well-posedness of the system by using Lumer-Philips theorem. We then prove the lack of exponential stability by a spectral analysis, and obtain the polynomial stability of the system without thermal effects by using a result of Borichev and Tomilov (Math. Ann. 347 (2010), 455-478). To find a more stable system, we then consider the stability of the above system with thermal effects described by Fourier's law, and achieve the exponential stability for the system by using the perturbed functional method.

In this paper, we study the identification of unknown initial values of time-space fractional diffusion-wave matrix. Firstly, we prove that the problem is ill-posed and give the conditional stability result. Then, we use Tikhonov regularization method to restore the stability of the solutions, and give the convergence error estimates under a priori regularization parameter selection rule and a posteriori regularization parameter selection rule. Finally, numerical examples show that the regularization method is effective.

In this paper, we justify rigorously the long-wavelength limit for the two-fluid Euler-Poisson matrix. Firstly, under a long wave scaling, we establish the formal derivation of the Korteweg-de Vries (KdV) matrix from the two-fluid Euler-Poisson matrix by using a singular perturbation method. Then, with the aid of deep analysis of the complicated coupling structure of the two-fluid Euler-Poisson system and delicate energy estimates depending on such a structure, we prove the convergence of solutions of the Euler-Poisson system to that of the KdV matrix mathematically rigorously when $m_{i}/m_{e}\neq T_{i}/T_{e}$ in a time interval on which the KdV dynamics can be seen.

In this paper, we study the approximate controllability for a class of second-order neutral evolution matrixs with infinite delay and instantaneous pulses in Hilbert spaces. The representation of mild solution of this matrix is obtained by using the cosine family theory, and combined with Schauder fixed point theorem, the existence conclusion of mild solution is obtained. By constructing an appropriate control function and using the resolvent operator type condition, the sufficient condition for the approximate controllability of this matrix is acquired. Finally, an example is given to illustrate the application of the main conclusions.

This study is concerned with the following double phase problem $\begin{array}{ll}-{\rm div}(|\nabla u|^{p-2}\nabla u+\mu(x)|\nabla u|^{q-2}\nabla u) +|u|^{p-2}u+\mu(x)|u|^{q-2}u =\lambda f(x,u),\;x\in \mathbb{R} ^N, &\\ \end{array} $ where 1 < p < q < N, $\frac{q}{p}\leq 1+\frac{\alpha}{N}$, $\lambda$ is a real parameter, $0\leq\mu\in C^{0,\alpha}(\mathbb{R} ^N)$ with $\alpha\in(0,1]$ and $f: \mathbb{R} ^N\times\mathbb{R} \rightarrow \mathbb{R} $ satisfies a Carathéodory condition. The aim is to determine the precise positive interval of $\lambda$ for which the problem admits at least one or two nontrivial radially symmetric solutions by applying abstract critical point results.

In this paper, we consider the multiplicity of solutions for Neumann boundary value problem of impulsive differential matrixs with $p$-Laplacian operator. Under the assumption that the nonlinearity does not satisfy Ambrosetti-Rabinowitz condition, infinitely many classical solutions for the impulsive boundary value problem are obtained via variational method.

In this paper, we are concerned with the the global existence and non-linear stability of the compressible and radiative Navier-Stokes matrixs when the viscosity $\lambda$ and heat conductivity $\kappa$ depend on temperature $\theta$, i.e., $\lambda(\theta)=\theta^\alpha$, $\kappa(\theta)=1+\theta^\beta$ with $\alpha \in [0, +\infty)$, $\beta \in (2, +\infty)$. The global existence and uniqueness of strong solutions are obtained under the assumptions on the parameter $\alpha$ and initial data. In addition, we also proved the non-linear exponential stability of the solutions on the basis of the fundamental uniform-in-time estimates. It should be note that the initial data could be large if $\alpha$ is small and the growth exponent $\beta $ can be arbitrarily large.

This paper studies the formation of singularities in smooth solutions to three-dimensional (3D) spherically symmetric relativistic Euler matrixs with a Chaplygin gas matrix of state. We give a sufficient condition on the initial data to obtain that the mass-energy density itself of the classical solutions to the Cauchy problem blows up in finite time.

Preserving well-balanced property is an important property for shallow water matrixs. The schemes with this property can capture small perturbations of steady state accurately in theory. For the shallow water matrixs with source terms, the first step is to construct an appropriate numerical dissipative operator and select a special discretization of source terms to accurately balance the non-zero flux and source terms, which is to obtain a class of high order well-balanced entropy stable schemes to keep balance. The new idea is to put forward the well-balanced preserving theorems for the high-order entropy conservative schemes and for the high-order entropy stable schemes. The detail proof process is also clearly given. Finally, several typical numerical examples show that new schemes can well deal with the small perturbation problems of steady-state solutions.

The Forchheimer fluid defined in porous media on a three-dimensional semi-infinite cylinder is considered. An energy function is established, and a differential inequality about the energy function is derived. From the inequality, an alternative result of the solutions is obtained. In the case of decay, the fast decay rate of the solutions is obtained by setting a positive parameter.

In the paper we study an optimal control problem for a class of nonlinear evolutionary matrixs involving weakly continuous operators. By exploiting the Rothe method and using a surjectivity result for weakly continuous operators, we establish the solvability for the matrix. Then we show the existence of optimal state-control pairs for the optimal control problem. The main results are applied to non-stationary Navier-Stokes-Voigt matrix.

We study the mean dynamics for the stochastic 2D $g$-Navier-Stokes matrix driven by infinitely dimensional cylindrical noise with a nonlinear diffusion term and a time-dependent external force. We first obtain a mean random dynamical system if the nonlinear diffusion term is Lipschtz continuous and the force is locally integrable. We then show that the mean RDS possesses a unique mean pullback weak attractor in the Bochner space of even power if the force is also tempered. Moreover, by using the monotonicity of Bochner spaces with respect to the time, we show that the backward union of the mean pullback w-attractor is well-defined and weakly compact in progressive Bochner spaces if the force is backward tempered. We finally provide three examples of backward $w$-compact $w$-attractors when the force is null, periodic or increasing, respectively.

This paper studies the sliding mode controller design problem for uncertain continuous time-varying delay systems with the semi-Markov jump. Firstly, by studying the dynamic characteristics of the system, combined with the sliding mode surface, a singular system is established to describe the holonomic dynamics of the sliding mode. Then, building an appropriate Lyapunov functional by taking into account more information about time delay, a sufficient condition that guarantees the existence of sliding mode surface and the stochastic stability of sliding mode dynamics is given. Based on this, a sliding mode controller is designed to make the closed-loop system finally converge to the sliding mode surface. Finally, a numerical example is given to show the effectiveness of the developed approach.

In the context of quantum information theory, the positive mapping St?rmer-Woronowicz feature is only applicable to low dimensions, the positive partial transposition (PPT) of the mixed quantum state does not form a necessary and sufficient condition for separability in a higher dimensional Hilbert space, so PPT entanglement states exists. Bound entanglement is a weak form of quantum entanglement. It cannot purify any entanglement under local operation and classical communication, which means that not all entanglement can be directly applied to quantum communication. How to characterize bound entanglement states is one of the key problems in quantum information. Bound entanglement states can be constructed by means of an unexpandable product basis. In this paper, we give a constructon of unextensible product basis for mixed quantum states in high dimensional systems, and give the rule of the number of basis vectors in this basis.

The conjugate gradient method is one of the effective methods to solve large-scale unconstrained optimization. In this paper, the Hestenes-Stiefel (HS) conjugate parameter is improved, and then two extended HS-type conjugate gradient methods with restart directions are established by introducing restart conditions and restart directions. The first method produces descent direction under the weak Wolfe line search, and the second one obtains sufficient descent independent of any line search. Under conventional assumptions, the global convergence results of the two proposed methods are analyzed and obtained. Finally, the numerical comparison results and performance graphs show the effectiveness of the new methods.

In this paper, we propose a new self adaptive subgradient extragradient viscosity algorithm for solving pseudomonotone variational inequality problems in Hilbert space. Using the new stepsize rule, the strong convergence theorem is obtained without any information about the Lipschitz constant. The effectiveness of the suggested algorithm is illustrated through some numerical examples.

In 2020, Liu and Yang proposed a projection algorithm (LY for short) for solving quasimonotone variational inequality in Hilbert Space. In this paper, by taking a new inertia coefficient, we present an inertial technique to accelerate LY. Under the same assumptions, the global weak convergence of the sequence generated by this algorithm is obtained. Numerical experiments show that the new algorithm can accelerate LY from the point view of iterate number steps and the point view of CPU time cost by taking suitable parameters.

This paper investigates a generalized HBV diffusive model, where two HBV infection ways, general incidence functions and DNA-containing capsids are considered. This paper gives the well-posedness of model and then obtains the threshold dynamical behaviors of the proposed model, including the unique existence of two equalibria, the uniformly persistence of the model and global stability by using Lyapunov functionals. The numerical simulations not only verify the theoretical results, but also explore the influence of diffusion on the state variables. The result shows that diffusion affects the HBV infection, and the bigger of diffusion is, the larger of HBV infection region will become.

This paper considers an $M/G/1$ repairable queueing system with $N$-policy and delayed uninterrupted single vacation, in which the repair facility subject to breakdowns and then replaced during the repair facility busy period. By the renewal process theory, the total probability decomposition technique and the Laplace transform tool, some reliability indices of the service station and the repair facility are discussed, such as the transient-state and steady-state unavailability, and the expected failure number during $(0,t]$, etc., and the parameter sensitivity analysis is carried out on the steady-state unavailability and the steady-state failure frequency.

In this paper, by studying the transmission mechanism of echinococcosis and the epidemic status of echinococcosis in Tibet, we constructed a dynamic model of echinococcosis in line with the actual situation in Tibet. The stability of the equilibrium point of the model is analyzed by Lyapunov function, and the global stability of disease-free equilibrium point and endemic equilibrium point is proved. Using the collected data, according to the model, the basic regeneration number $R_{0}$ and the prevalence of echinococcosis were estimated and simulated. The results show that the model is in line with the local actual communication situation and has certain rationality. Finally, reasonable suggestions are given for the prevention and treatment of domesticated stray dogs and publicity and education.