A Note on Normal Forms of Quantum States and Separability

We study the normal form of multipartite density matrices.It is shown that the correlation matrix(CM)separability criterion can be improved from the normal form we obtained under filtering transformations.Based on CMcriterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite andmultipartite systems.

TIME ASYMPTOTIC BEHAVIOR OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM

The bipolar Navier-Stokes-Poisson system （BNSP） has been used to simulate the transport of charged particles （ions and electrons for instance） under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate （1 ＋ t）^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate （1 ＋ t）^-1/4 which is slower than the rate （1 ＋ t）^-3/4 for the compressible Navier-Stokes equations （NS）. In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate （1 ＋ t）^-3/4＋ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.

LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.

The Equivalence between Bergman Metric and Einstein-Kahler Metric on the Cartan-Hartogs Domain of the Fourth Type

In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly,we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new metric; Secondly, the Ricci curvature of the new metric has the super bound and lower bound; Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound; Finally, we obtain the equivalence between Bergman metric and Einstein-Khler metric on the Cartan-Hartogs domain of the fourth type.

THE WELL-POSEDNESS AND ASYMPTOTICS OF MULTI-DIMENSIONAL QUANTUM HYDRODYNAMICS

The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up in quantum wells） take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.

LOCAL EXISTENCE OF SOLUTION TO FREE BOUNDARY VALUE PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS

This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local （in time） existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.

Genus Distributions of M(o|¨)bius Ladders

The genus distribution of a graph is a polynomial whose coefficients are the partition of the number of embeddings with respect to the genera. In this paper, the genus distribution of Mobius ladders is provided which is an infinite class of 3-connected simple graphs.

On Polynomial Representations of Lie Algebras

We study polynomial representations of finite dimensional （R or C） Lie algebras. As a total classification, we show that there are altogether three types of such nontrivial representations and give their subtle structures.

Entanglement of Formation for Quantum States

我们调查形成的纠纷因为 high-dimensionalquantum 的一个班混合了状态。我们在场为 high-dimensionalquantum 的一个类的一种概括同时发生纯状态以便形成的纠纷是 monotonically 增加概括同时发生的凸的功能。从单音的强健和凸状，为高度维的混合状态的一个班的形成的纠纷被计算了经分解。

Capacity of a Simultaneous Quantum Secure Direct Communication Scheme between the Central Party and Other M Parties

我们分析在经由 M +1 粒子 GHZ 的中央聚会和另外的 M 聚会之间的安全直接通讯计划说的同时的量和交换量纠纷的能力。如果另外的 M 聚会想要播送 1 位古典的 M + ，编码计划应该是秘密的，这被显示出到中心的消息秘密地狂欢。然而，当编码计划公开被宣布时，我们证明在播送秘密的计划的能力在 2 位中发送消息，不管 M 怎么大。

Incidence Colorings of Powers of Circuits

发生 G 的色彩的数字是颜色的最少的数字以便 G 有发生着色。这被证明发生 Cpn 的色彩的数字，电路图的 p-th 力量，是 2p+1 如果并且仅当 n=k (2p+1 ) ，为另外的盒子。它色彩的数字是的发生至多 2p+[r/k ]+2 n=k (p+1 )+r， k 是一个积极整数。这上面的界限为一些盒子是紧张的。

Local Invariants for a Class of Tripartite Quantum Mixed States

我们在本地单一的转变下面学习分成三部分的混合状态的等价。为在 C~K 直接 X C~MdirectX C~N 合成系统的分成三部分的量状态的一个类的非局部的性质被调查，在为这些状态的本地单一的转变下面的 invariants 的一个完全的集合被介绍。如果并且仅当，二个这些状态是局部地相等的，这被显示出所有这些 invariants 有一样的价值。

Inverse Theorem of Approximation in L_p for the Stancu Integral-type Operators on a Simplex

在这份报纸，不可分类型的 Stancu 操作员在上一单一被考虑，它在 Lp (1 p +) 的近似的反的定理被获得了。

Matrix Tensor Product Approach to the Equivalence of Multipartite States under Local Unitary Transformations

混合的多国参加的量的等价在本地人下面声明单一的转变被学习。为在本地单一的转变下面的非退化的混合的多国参加的量状态的等价的一个标准被介绍。

LARGE TIME BEHAVIOR OF THE 1D ISENTROPIC NAVIER-STOKES-POISSON SYSTEM

The initial value problem(IVP)for the one-dimensional isentropic compressible Navier-Stokes-Poisson(CNSP)system is considered in this paper.For the variables,the electric field and the velocity,under the Lagrange coordinate,we establish the global existence and uniqueness of the classical solutions to this IVP problem.Then we prove by the method of complex analysis,that the solutions to this system converge to those of the corresponding linearized system in the L^(2) norm as time tends to infinity.In addition,we show,using Green’s function,that the solutions to this system are close to a diffusion profile,pointwisely,as time goes to infinity.

CONVERGENCE OF SIMPLIFIED AND STABILIZED MIXED ELEMENT FORMATS BASED ON BUBBLE FUNCTION FOR THE STOKES PROBLEM

Two simplifled and stabilized mixed element formats for the Stokes problem are derived by bubble function, and their convergence, i.e., error analysis, are proved. These formats can save more freedom degrees than other usual formats.

Invariants for a Class of Nongeneric Three-Qubit States

我们在本地单一的转变下面调查量状态的等价。在本地单一的转变下面的 invariants 的一个完全的集合是混合的非通用的 three-qubit 的班说的介绍论坛。如果并且仅当，在这个班上的二个如此的状态是局部地相等的，这被显示出所有这些 invariants 为他们有相等的价值。

List Extremal Number of Union of Short Cycles

The list extremal number f（G） is defined for a graph G as the smallest integer k such that the join of G with a stable set of size k is not ｜V（G）｜-choosable. In this paper, we find the exact value of f（G）, where G is the union of edge-disjoint cycles of length three, four, five and six. Our results confirm two conjectures posed by S. Gravier, F. Maffray and B. Mohar.

Homological Dimension of Crossed Products of Hopf Algebras

Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.