Efficient remote preparation of arbitrary twoand three-qubit states via the χ state

The application of χ state are investigated in remote state preparation （RSP）. By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and three-qubit states via the χ state as the entangled resource. It is shown that the original state can be successfully prepared with the probability 100% and 50% for real coefficients and complex coefficients, respectively. For the latter case, the special ensembles with unit success probability are discussed by the permutation group. It is worth mentioning that the novel measurement bases have no restrictions on the coefficients of the prepared state, which means that the proposed schemes are more applicable.

Existence and Nonexistence of Global Solutions of a Fully Nonlinear Parabolic Equation

In the paper, we study the global existence of weak solution of the fully nonlinear parabolic problem (1.1)-(1.3) with nonlinear boundary conditions for the situation without strong absorption terms. Also, we consider the blow up of global solution of the problem (1.1)-(1.3) by using the convexity method.

Joint Invariants and Joint Differential Invariants of Some Transformation Groups

The theory of moving frames developed by Peter J Olver and M Fels has impor-tant applications to geometry, classical invariant theory. We will use this theory to classify joint invariants and joint differential invariants of some transformation groups.

规范场论中自对偶磁单极子解的存在唯一性

Magnetic monopoles stand for the static solution arising from a(1 + 3)–dimensional theory describing the interaction between a real scalar triplet and non–Abelian gauge field. In this paper, we obtain a two–point boundary value problem of a first–order ordinary differential equations from the self–dual monopole model. Then we establish the existence and uniqueness theorem for the problem by using a dynamical shooting method, we also obtain sharp asymptotic estimates for the solutions at infinity.

LORENTZ MARTINGALE SPACES AND INTERPOLATION

In this article, the authors introduce some new Lorentz spaces for martingales, which are extensions of Hardy spaces of martingales. Then they discuss their basic properties, embedding relationships, and interpolation spaces between them, during which the use of rearrangement good-λ-inequality plays an important role.

UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL B^n

In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.

Directional Filter for SAR Images Based on Nonsubsampled Contourlet Transform and Immune Clonal Selection

A directional filter algorithm for intensity synthetic aperture radar （SAR） image based on nonsubsampled contourlet transform （NSCT） and immune clonal selection （ICS） is presented. The proposed filter mainly focuses on exploiting different features of edges and noises by NSCT. Furthermore, ICS strategy is introduced to optimize threshold parameter and amplify parameter adaptively. Numerical experiments on real SAR images show that there are improvements in both visual effects and objective indexes.

A New Scheme to Projective Synchronization of Fractional-Order Chaotic Systems

我们证明射影的同步能在联合部分顺序的混乱系统被观察。一个新系统、强大的联合计划被开发经由 open-plus-closed-loop 控制调查射影的同步，它允许我们任意地操作射影的同步的可伸缩的因素。建议计划根据部分微分方程的稳定性定理被证明经分解。部分顺序上的数字模拟混乱的陈系统被介绍认为理论分析正当。

QUANTIZATION OF LIE ALGEBRAS OF BLOCK TYPE

In this article, we use the general method of quantization by Drinfeld’s twist to quantize explicitly the Lie bialgebra structures on Lie algebras of Block type.

Deterministic assisted clone of an unknown four-particle entangled cluster-type state

Two deterministic schemes are proposed to realize the assisted clone of an unknown four-particle entangled cluster- type state. The schemes include two stages. The first stage requires teleportation via maximal entanglement as the quantum channel. In the second stages of the protocols, two novel sets of mutually orthogonal basis vectors are constructed, With the assistance of the preparer through a four-particle or two-step two-particle projective measurement under these bases, the perfect copy of an original state can be produced. Comparing with the previous protocols which produce the unknown state and its orthogonal complement state at the site of the sender, the proposed schemes generate the unknown state deterministically.

Hochschild Homology of Tame Hecke Algebras

Let A be a tame Hecke algebra of type A. A new minimal projective bimodule resolution for A is constructed and the dimensions of all the Hochschild homology groups and cyclic homology groups are calculated explicitly.

One Kind of Mappings with Parametric Representation in Cn

In this paper, a kind of mappings with parametric representation is introduced,the growth theorem is set up.

Competitive and exclusion and oscillation phenomena of an eco-epidemiological model: An invasive approach

Eco-epidemiological model plays a crucial role in maintaining ecological balance and biological invasions.In this paper,we propose a predator-prey model where the predator population is infected by the disease.The non-negativity and boundedness of the solution are addressed.The existence and stability of equilibrium are discussed by an invasive approach.Numerical simulations are used to demonstrate the competitive and exclusion,and oscillation behaviors of the model.Interestingly,the predation rate of the infected predator is shown to have far-reaching implications for the structure and stability of ecological communities.

A New Periodic Solution to Jacobi Elliptic Functions of MKdV Equation and BBM Equation

Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations. New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney （BBM） equations are obtained with the aid of computer algebraic system Maple. The method is also valid for other （l＋l）-dimensional and higher dimensional systems.

Scheme for Cloing a Three-Particle GHZ Class State with Assistance

我们的担心与高可能性是设计能生产一个三粒子的 GreenbergerHorneZeilinger (GHZ ) 班的一个完美的拷贝的一个帮助克隆的计划州的。在协议的第一个阶段，到由使用三 EPR 的接收装置的输入状态作为量隧道配对的发送者 teleports。在协议的第二个阶段，互相直角的基础向量的一个新奇集合被构造。与通过在这个基础下面的三粒子的射影的大小的 preparer 的帮助，一个原来的状态的完美的拷贝能被发送者与概率 1/2 重建。而且，计划的古典通讯费用也被计算。

ROPER-SUFFRIDGE EXTENSION OPERATOR ON A REINHARDT DOMAIN

Let pj ∈ N and pj≥ 1, j = 2, …, k, k ≥ 2 be a fixed positive integer. We introduce a Roper-Suffridge extension operator on the following Reinhardt domain ΩN ={z =（z1, z′2,…, z′k）′∈ C × C^n2×…× Cnk： ｜z1｜^2＋ ｜｜z2｜｜2^p2＋ … ＋ ｜｜zk ｜｜k^pk〈 1} given〈1} give by F（z）=（f（z1）＋f＇（z1）∑j=2 kPj（zj,（f＇（z1））1/p2 z2＇,…,（f＇（z1））1/pkzk＇）＇, where f is a normaljized biholomorphic function k（z） =（f（z1） ＋ f′（z1）=2 on the unit disc D, and for 2 ≤ j ≤ k, Pj ： C^nj→ C is a homogeneous polynomial of degree pj and zj =（zj1, …, zjnj）′∈ C^nj, nj ≥ 1, pj ≥ 1,｜｜zj｜｜j =（∑l=1 nj｜zjl｜^pj）1/pj. In this paper, some conditions for Pjare found under which the loperator p ｜zjl｜pj=1reserves the properties of almost starlikeness of order α, starlikeness of order αand strongly starlikeness of order α on ΩN, respectively.

A unified result for variable-rate linear network coding

Fong et al.analyzed variable-rate linear network coding for linear broadcast.However,the authors didn't investigate it for the other three types of linear network codes.In this paper,by simple and clear proofs,it is found that there are similar results for variable-rate linear generic and linear dispersion if the field size is large enough.It means that linear generics and linear dispersions of different dimensions can be implemented on the same network,while each non-source node is required to store only one copy of the local encoding kernel within a session.Moreover,an example is given to show that there isn't a similar result for linear multicast.

An Economical Scheme for Cloning an Unknown M-Qudit Equatorial-Like State with Assistance

我们建议认识到量克隆未知 M-qudit 象赤道一样的一个计划纠缠了状态。协议的第一个阶段要求远距传物。在远距传物被完成以后，接收装置能重建原来的状态。在协议的第二个阶段，与帮助(通过单个粒子的射影的大小) preparer，一个原来的状态的完美的拷贝能在发送者的地点被生产。我们的计划作为量隧道和三摩尔斯讯号的短音要求单个最大地纠缠的 qudit 对古典通讯。计划在损坏消费包括 M 的本地资源的情况下是可行的 ? 1 辅助 qudits 由接收装置和另外的 bi-qudit 操作介绍了。而且，我们构造保证辅助 qudits 被发送者未必介绍的一种单一的转变。比作以前的协议，建议协议是节俭的由于量的费用非局部的资源和古典通讯最低。

Bipartite quasi-synchronization of multiple neural networks with generalized cooperative-competitive topology

This study examines the bipartite quasi-synchronization(B-Q synchronization)issue of coupled networks with general cooperative-competitive topology and the event-triggered communications between nodes to curb the communication cost.In the existing literature concerning bipartite synchronization,the network topology is required to be structurally balanced,which necessitates that competitive interactions exist only between two distinct subgroups.In this study,we aim to lengthen the network’s topology to a more general signed network in which antagonistic interactions can exist in the same or different subgroups.According to signed graph theory and the markovian stochastic event-triggering mechanism,the dynamical model of multiple neural networks(MNNs)with structurally unbalanced and markovian event-triggered communication is established.By utilizing the stochastic Lyapunov stability analysis,some adequate criteria for B-Q synchronization of MNNs with the structurally unbalanced graph are obtained;also,a bound for the B-Q synchronization error is provided.As a special case,the bipartite synchronization criteria for MNNs with the structurally balanced graph are also obtained.Finally,two simulations are performed to verify the theoretical result.