BOUNDARY INTEGRAL FORMULAS FOR ELASTIC PLANE PROBLEM OF EXTERIOR CIRCULAR DOMAIN

After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.

NUMERICAL SOLUTIONS OF AN EIGENVALUE PROBLEM IN UNBOUNDED DOMAINS

A coupling method of finite element and infinite large element is proposed for the numerical solution of an eigenvalue problem in unbounded domains in this paper. With some conditions satisfied, the considered problem is proved to have discrete spectra. Several numerical experiments are presented. The results demonstrate the feasibility of the proposed method.

A New Analytical Approach for Solving Nonlinear Boundary Value Problems in Finite Domains

Based on the homotopy analysis method (HAM), we propose an analytical approach for solving the following type of nonlinear boundary value problems in finite domain. In framework of HAM a convenient way to adjust and control the convergence region and rate of convergence of the obtained series solutions, by defining the so-called control parameter h , is provided. This paper aims to propose an efficient way of finding the proper values of h.Such values of parameter can be determined at the any order of approximations of HAM series solutions by solving of a nonlinear polynomial equation. Some examples of nonlinear initial value problems in finite domain are used to illustrate the validity of the proposed approach. Numerical results confirm that obtained series solutions agree very well with the exact solutions.

THE ANALYTICAL SOLUTION FOR HELMHOLTZ BOUNDARY PROBLEM IN NON-HORIZONTALLY STRATIFIED DOMAINS

There are N domains Dj(j=0,1,...,N-1) of different physical parameters in the whole space and their interfaces S,are non-horizontally smooth curved surfaces. The following boundary problem is called Hclinholiz boundary problem:The analytical solution of the above problem is given in this paper.

Goldbach's Problem in the Matrix Ring over a Principal Ideal Domain

In this paper, we consider the Goldbach＇s problem for matrix rings, namely, we decompose an n × n （n 〉 1） matrix over a principal ideal domain R into a sum of two matrices in Mn,（R） with given determinants. We prove the following result： Let n 〉 1 be a natural number and A = （aij） be a matrix in Mn（R）. Define d（A） ：= g.c.d{aij}. Suppose that p and q are two elements in R. Then （1） If n 〉 1 is even, then A can be written as a sum of two matrices X, Y in Mn（R） with det（X） = p and det（Y） = q if and only if d（A） [ p - q; （2） If n 〉 1 is odd, then A can be written as a sum of two matrices X, Y in Mn（R） with det（X） = p and det（Y） = q if and only if d（A） ｜ p ＋ q. We apply the result to the matrices in Mn（Z） and Mn（Q[x]） and prove that if R = 7. or Q[x], then any nonzero matrix A in Mn（R） can be written as a sum of two matrices in Mn（R） with prime determinants.

Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions

Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.

PoincaréProblem for Nonlinear Elliptic Equations of Second Order in Unbounded Domains

In [1], I. N. Vekua propose the Poincaré problem for some second order elliptic equations, but it can not be solved. In [2], the authors discussed the boundary value problem for nonlinear elliptic equations of second order in some bounded domains. In this article, the Poincaré boundary value problem for general nonlinear elliptic equations of second order in unbounded multiply connected domains have been completely investigated. We first provide the formulation of the above boundary value problem and corresponding modified well posed-ness. Next we obtain the representation theorem and a priori estimates of solutions for the modified problem. Finally by the above estimates of solutions and the Schauder fixed-point theorem, the solvability results of the above Poincaré problem for the nonlinear elliptic equations of second order can be obtained. The above problem possesses many applications in mechanics and physics and so on.

Boundary Value Problems for Nonlinear Elliptic Equations of Second Order in High Dimensional Domains

This paper mainly concerns oblique derivative problems for nonlinear nondivergent elliptic equations of second order with measurable coefficients in a multiply connected domain. Under certain condition, we derive a priori estimates of solutions. By using these estimates and the fixed-point theorem, we prove the existence of solutions.

ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

In this paper analytic boundary value problems for some classical domains in Cn are developed by using the harmonic analysis due to L.K. Hua. First it is discussed for the version of one variable in order to induce the relation between the analytic boundary value problem and the decomposition of function space L2 on the boundary manifold. Then an easy example of several variables, the version of torus in C2, is stated. For the noncommutative classical group L1, the characteristic boundary of a kind of bounded symmetric domain in C4, the boundary behaviors of the Cauchy integral are obtained by using both the harmonic expansion and polar coordinate transformation. At last we obtain the conditions of solvability of Schwarz problem on L1, if so, the solution is given explicitly.

CHEBYSHEV PSEUDOSPECTRAL DOMAIN DECOMPOSITION METHOD OF ONE－DIMENSIONAL ELLIPTIC PROBLEMS

This paper is devoted to the Chebyshev pseudospectral domain decomposition method of one-dimensional elliptic problems,it is easily applied to complex geometry.The approximate accuracy can be increased by increasing the order of approximation in fixed number of subdomains,rather than by resorting to a further partitioning.The stability and the convergence of this method are proved.

Shape Identification for Stokes-Oseen Problem Based on Domain Derivative Method

In this paper, we consider the shape identification problem of a body immersed in the incompressible fluid governed by Stokes-Oseen equations. Based on the domain derivative method, we derive the explicit representation of the derivative of solution with respect to the boundary. Then, according to the boundary parametrization technique, we propose a regularized Gauss-Newton algorithm for the shape inverse problem. Finally, numerical examples indicate that the iterative algorithm is feasible and effective for the practical purpose.

THE CONVERGENCE OF A DOMAIN DECOMPOSITION ALGORITHM FOR PARABOLIC PROBLEMS

At recent, Hourgat et gave a domain decomposition algorithm for elliptic problems which can be implemented in parallel. Many numerical experiments have illustrated its efficiency. In the present paper, we apply this algorithm to solve the discrete parabolic problems, analyse its convergence and show that its convergence rale is about (1 - 2p + σp2 ) which is nearly optimal and independent of the parameter τ, where σ τ O((1 +H )(1 + ln(H / h))2 ). 0 【 p 【 1 / σ,τ,h,H are the time step size, finite element parameter and subdomain diameter, respectively.

General Boundary Value Problems for Nonlinear Uniformly Elliptic Equations in Multiply Connected Infinite Domains

This article discusses the general boundary value problem for the nonlinear uniformly elliptic equation of second order in D (0.1) and the boundary condition,(0.2) in a multiply connected infinite domain D with the boundary T. The above boundary value problem is called Problem G. Problem G extends the work [8] in which the equation (0.1) includes a nonlinear lower term and the boundary condition (0.2) is more general. If the complex equation (0.1) and the boundary condition (0.2) meet certain assumptions, some solvability results for Problem G can be obtained. By using reduction to absurdity, we first discuss a priori estimates of solutions and solvability for a modified problem. Then we present results on solvability of Problem G.

思想史、问题域与当代性——《资本论》政治哲学阐释的三条路径

《资本论》政治哲学思想的当代阐释不仅是马克思政治哲学基础理论研究的重要内容,而且是当代中国马克思主义政治哲学研究的重要课题。从政治哲学角度阐释《资本论》的哲学思想,既需要在西方政治哲学的理论谱系中界定《资本论》的政治哲学意义,也需要在马克思政治经济学批判对于政治与经济辩证关系的理论自觉中解读《资本论》的政治哲学思想的理论特质,更需要立足当代中国马克思主义政治建构的理论语境,激活《资本论》政治哲学思想的当代价值。思想史、问题域和当代性分别在“纵向”“横向”和“坐标系”的意义上,构成推进《资本论》政治哲学思想当代阐释的三条路径。

Approximate Method of Riemann-Hilbert Problem for Elliptic Complex Equations of First Order in Multiply Connected Unbounded Domains

In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.

城乡传播的问题域、内涵及意义

城乡传播是城乡关系在传播学领域的反映,是城乡研究与传播学研究的创新交叉前沿领域,也是建筑学、城乡规划等与传播学、社会学等学科交叉的创新前沿方向,可提供一个全新的视角来看待城乡发展、互动及转型的问题。文章一方面对城市传播、乡村传播与城乡传播之间的关系进行辨析,并基于与大众传播等传播学概念的比较,明确城乡传播的问题域;另一方面,探索城乡传播独特内涵,阐明城乡传播的独特意义及其时代语境,力图为城乡传播创新型交叉领域的研究搭建一个初步框架。

A Dual Discriminator Method for Generalized Zero-Shot Learning

Zero-shot learning enables the recognition of new class samples by migrating models learned from semanticfeatures and existing sample features to things that have never been seen before. The problems of consistencyof different types of features and domain shift problems are two of the critical issues in zero-shot learning. Toaddress both of these issues, this paper proposes a new modeling structure. The traditional approach mappedsemantic features and visual features into the same feature space;based on this, a dual discriminator approachis used in the proposed model. This dual discriminator approach can further enhance the consistency betweensemantic and visual features. At the same time, this approach can also align unseen class semantic features andtraining set samples, providing a portion of information about the unseen classes. In addition, a new feature fusionmethod is proposed in the model. This method is equivalent to adding perturbation to the seen class features,which can reduce the degree to which the classification results in the model are biased towards the seen classes.At the same time, this feature fusion method can provide part of the information of the unseen classes, improvingits classification accuracy in generalized zero-shot learning and reducing domain bias. The proposed method isvalidated and compared with othermethods on four datasets, and fromthe experimental results, it can be seen thatthe method proposed in this paper achieves promising results.

二维水下声辐射问题的改进径向基点插值法研究

径向基点插值法是一种典型的无网格数值计算方法,在分析声学问题时,相比于传统有限元法能更好地抑制频散误差,且在相同的节点分布下通常可以得到更精确的数值解。本文提出一种改进的节点选取方案用于构造插值形函数,即改进径向基点插值法。该方案采取一个简单而直接的格式,可确保在进行数值积分时同一背景积分单元中的被积函数是连续可微的,从而减小数值积分误差,得到比原始径向基点插值法更精确的数值解。同时,为了处理外声场问题,本文采用DtN映射技术将无限域截断为有界计算域,满足索默菲尔德辐射条件。数值试验表明,相比于传统有限元法和原始径向基点插值法,本文改进方法具有更高的计算精度和计算效率,在研究水下声辐射问题时具有良好的应用前景。

源域数据增强与多兴趣细化迁移的跨域推荐模型

针对跨域推荐任务中源域用户交互数据不丰富所导致的兴趣偏好建模困难问题,以及多个兴趣之间的关联被忽略问题,提出源域数据增强与多兴趣细化迁移的跨域推荐模型.该模型引入源域数据增强策略,为每个用户在源域中生成经过去噪处理的辅助序列,缓解用户在源域中的交互数据稀疏问题,获得更丰富的用户兴趣偏好.使用双序列多兴趣提取模块和多兴趣细化迁移模块,完成兴趣提取与多个兴趣的细化迁移.在基于3个公开跨域推荐评测任务的对比实验中,与最优的基线相比,提出方法的平均MAE降低了22.86%,平均RMSE降低了19.65%,取得了最优的性能表现,证明了提出方法的有效性.

各向异性问题的多子域区域分解算法

在自然边界归化原理的基础上,构造了一种无界凹角区域上各向异性问题的多子域非重叠区域分解算法,这是两子域的非重叠区域分解法的推广.本文给出了多子域区域分解算法的离散和变分形式,利用等价性理论,通过详细的理论证明说明此算法是收敛的,且与网格参数h无关.