GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE

In this paper,we consider the weak solutions of compressible Navier-StokesLandau-Lifshitz-Maxwell(CNSLLM)system for quantum fluids with a linear density dependent viscosity in a 3D torus.By introducing the cold pressure Pc,we prove the global existence of weak solutions with the pressure P+Pc,where P=Aργwithγ≥1.Our main result extends the one in[13]on the quantum Navier-Stokes equations to the CNSLLM system.

Parameterized monogamy and polygamy relations of multipartite entanglement

Monogamy and polygamy relations are important properties of entanglement,which characterize the entanglement distribution of multipartite systems.We explore monogamy and polygamy relations of entanglement in multipartite systems by using two newly derived parameterized mathematical inequalities,and establish classes of parameterized monogamy and polygamy relations of multiqubit entanglement in terms of concurrence and entanglement of formation.We show that these new parameterized monogamy and poelygamy inequalities are tighter than the existing ones by detailed examples.

Bounds on positive operator-valued measure based coherence of superposition

Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing.By generalizing the resource theory of coherence from von Neumann measurements to positive operatorvalued measures(POVMs),POVM-based coherence measures have been proposed with respect to the relative entropy of coherence,the l_(1) norm of coherence,the robustness of coherence and the Tsallis relative entropy of coherence.We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition.Our results can be used to estimate range of quantum coherence of superposed states.Detailed examples are presented to verify our analytical bounds.

LARGE DEVIATIONS FOR TOP EIGENVALUES OFβ-JACOBI ENSEMBLES AT SCALING TEMPERATURES

Letλ=(λ_(1),…,λ_(n))beβ-Jacobi ensembles with parameters p_(1),p_(2),n andβ,withβvarying with n.Set■.Suppose that■and 0≤σγ<1.We offer the large deviation for p_(1)+p_(2)/p_(1)■λ_(i)whenγ>0 via the large deviation of the corresponding empirical measure and via a direct estimate,respectively,whenγ=0.

ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL

This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal(convolution)dispersals:{u_(t)=k*u-u+u(1-u-av),x∈R,t∈R,vt=d(k*v-v)+rv(1-v-bu),c∈R,t∈R.(0.1)Here a≠1,b≠1,d,and r are positive constants.By studying the eigenvalue problem of(0.1)linearized at(ϕc(ξ),0),we construct a pair of super-and sub-solutions for(0.1),and then establish the existence of entire solutions originating from(ϕc(ξ),0)as t→−∞,whereϕc denotes the traveling wave solution of the nonlocal Fisher-KPP equation ut=k*u−u+u(1−u).Moreover,we give a detailed description on the long-time behavior of such entire solutions as t→∞.Compared to the known works on the Lotka-Volterra competition system with classical diffusions,this paper overcomes many difficulties due to the appearance of nonlocal dispersal operators.

MATHEMATICAL RESULTS RELATED TO A TWO-DIMENSIONAL MAGNETOHYDRODYNAMIC EQUATIONS

The two-dimensional magneto-hydrodynamic （MHD） equations are considered in this article. Viscous approximations are used to obtain the local existence and uniqueness of the classical solution. When the viscous term vanishes, the convergence rates, a main problem in turbulence, are also discussed. Moreover, a blow-up criterion for our classical solution is established in terms of the magnetic fields.

Zeroes of the Bergman Kernels on Some New Hartogs Domains

We obtain the Bergman kernel for a new type of Hartogs domain.The corresponding LU Qi-Keng's problem is considered.

AN IMPROVEMENT OF THE OCTONIONIC TAYLOR TYPE THEOREM

We prove that the octonionic polynomials Vl 1k……lk. are independent of the associative orders k. This improves the oetonionic Taylor type theorem.

EXISTENCE OF SOLITARY WAVES TO A GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION

In this article, we study the existence of nontrivial solitary waves of a gener- alized Kadomtsev-Petviashvili equation via variational methods.

Covariant Prolongation Structure of Konno-Asai-Kakuhata Equation

Based upon the covariant prolongation structures theory, we construct the sl（2, R）×R（p） prolongation structure for Konno-Asai-Kakuhata equation. By taking two and one-dimensional prolongation spaces, we obtain the inverse scattering equations given by Konno et al. and the corresponding Riccati equation. The Baecklund transformations are also presented.

Comparative analysis of phase extraction methods based on phase-stepping and shifting curve in grating interferometry

Two phase extraction methods which are based separately on phase-stepping and shifting curve are mainly used in phase-sensitive imaging in gating interferometry to determine the x-ray phase shift induced by an object in the beam. In this paper, the authors perform a full comparative analysis and present the main virtues and limitations of these two methods according to the theoretical analysis of the grating interferometry.

Quasideterminant Solutions of a Noncommutative Nonisospectral Kadomtsev-Petviashvili Equation

Solutions of a noncommutative nonisospectral Kadomtsev-Petviashvili equation are given in terms of quasiwronskian and quasigrammian respectively. These solutions are verified by direct substitutions. Dynamics of some obtained solutions are illustrated.

LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ（ρ） = ρ^β with β≥0. Note that the initial data can be arbitrarily large to contain vacuum states.

A BLOW-UP CRITERION OF SPHERICALLY SYMMETRIC STRONG SOLUTIONS TO 3D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spherically symmetric strong solution in terms of the regularity estimates near the symmetric center and the free boundary respectively.

Coset Structure of Spin Group

This article considers One example is also given to take a the coset structure closer look at what of spin group via analyzing the expression of its representation. the coset and the subgroup are.

Energy Spectra of the Harmonic Oscillator in a Generalized Noncommutative Phase Space of Arbitrary Dimension

We use the invariant eigen-operator method to study the higher-dimensional harmonic oscillator in a type of generalized noncommutative phase space,and obtain the explicit expression of the energy spectra of the noncommutative harmonic oscillator in arbitrary dimension.It is found that the energy spectra of the higher-dimensional noncommutative harmonic oscillator are equal to the sum of the energy spectra of some 1D harmonic oscillators and some 2D noncommutative harmonic oscillators.We believe that the properties of the harmonic oscillator may reflect some essence of the noncommutative phase space.

GLOBAL WELL-POSEDNESS OF THE 2D BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION

In this paper,we prove the global well-posedness of the 2 D Boussinesq equations with three kinds of partial dissipation;among these the initial data(u_(0),θ_(0))is required such that its own and the derivative of one of its directions(x,y)are assumed to be L^(2)(R^(2)).Our results only need the lower regularity of the initial data,which ensures the uniqueness of the solutions.

STRONG EQUIVALENCES OF APPROXIMATION NUMBERS AND TRACTABILITY OF WEIGHTED ANISOTROPIC SOBOLEV EMBEDDINGS

In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the approximation numbers,and necessary and sufficient conditions on a,b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.

A Categorification of the Boson Oscillator

In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product of these states.We find that there are two different categorical definitions of the inner product of the Fock states.These two definitions are consistent with each other,and the decategorification results also coincide with those in conventional quantum mechanics.We also find that there are some interesting properties of the 2-morphisms which relate to the inner product of the states.

Covariant Prolongation Structure of Coupled Inhomogeneous Nonlinear Schrodinger Equation

We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations, Backlundtransformation, and one-soliton solution.