本文继续[Ⅰ]的讨论,建立了亚正定阵的行列式理论。给出了许多新的结果:例如广义Minkowski不等式、广义凸性不等式等等,对某些种类的亚正定阵,还将关于任意阵的行列式的Hadamard不等式作了改进。最后,将Open-heim关于正定阵的Hadamavd乘积的著名结果推广到亚正定阵上。

In this paper, some simple determinate conditions for nonsingular H-matrices areobtained, and some results include and generalize the related results in [1, 2, 3].

In this paper a finite element method based on cubic B-spline is presented to obtainnig approximate solution for the equilibrium problems of elastic composite structures on regular regions.A computational scheme well suited for various types of boundary conditions is derived.It is easily carried out by a computer.In comparison with the usual nodal finite element method, the main features of the present method are higher accuracy and more economy in computing storage and time requirements.The effect of imposing natural boundary condition as constraints is considered and it is shown by a plate bending problem that this effect is quite superficial.Several numerical results are presented.

Investor sentiment can help people to correctly understand the mechanism of stock market, which further can be used to market regulation and investment strategy. On the basis of a comprehensive definition of investor sentiment, a theoretical analysis about the relationship between investor sentiment and spot return is given, and five hypotheses of investor sentiment are concluded. With the available proxies, the principal component analysis is used to build an investor sentiment index for China's stock market. EGARCH models are used to evaluate how movement of sentiment affects spot return and the different effects towards different types of stocks. These empirical results provide a good support for the theoretical analysis.

1.Consider an analytic function (s) defined by a Dirichlet series whose axis of convergence is σ = 0, where 0 ≤λ_n< + ∞ and lim (log n/λ_n) = 0. We define the Ritt order and proximate order of f(s) in σ > 0 and have obtained some relations between the growth of f(s) and the coefficients, which extend some of G. Valiron's results.2. Let (Ω, P) be a probability space. Consider a random Dirichlet series whose abscissa of convergence is σ(ω), where a_n(ω) are random variables in (Ω,P) and λ_n satisfy the same conditions as in 1(n = 0,1,2,…). To σ(ω) we extend L. Arnold's results on the radius of a.s. convergence of random Taylor series and have solved some of his problems.In the case σ(ω) = 0 a.s. the results mentioned in 1 is applied to studying the a.s. growth of f(s, ω) in σ> 0. As a special case we find that if |a_n(ω)| are independent and have the same non-degenerate distribution function F(x) and if the radius of a.s. convergence of g(s, ω)is 1, then the a.s. growth of g(s, ω |z|<1 ean be determined by the convergence or divergence of(logx)~k dF(x) (k≥1).3. Let the probability space in 2 be such that Ω = [0, 1], is composed of all Lebesgue measurable sets E on Ω and P[E] is the Lebesgue measure of E. Let a_n(ω)= b_nε_n(ω) or b_nγ_n(ω), where {ε_n(ω)} or {γ_n(ω)}is a Rademaeher or Steinhaus sequenee and b_n are constants such that the abscissa of convergence of f(s, ω) is zero. Then, under certain conditions every point on σ = 0 is a Pieard or Borel (R) point of f(s, ω) a.S.

<正> §1 引言设 P_1,P_2,…,P_N 是正 N 边形 S_N 的顶点,所有线段 P_iP_j 之长的平方和∑r_(ij)~2记为 N_1;所有三角形△P_iP_jP_k 的面积平方和∑△_(ijk)~2记为 N_2.对 N=3,4,…进行计算表明,总有

A=(a_ij) ∈R~(n×n ) is termed bisymmetric matrix if We denote the set of all n × n bisymmetric matrices by BSR~(n×n ) In this paper, we discuss the following two problems: Problem I. Given X, Find such that Problem Ⅱ. Gived . Find such that where ||·|| is Frobenius norm, and S_E is the solution set of Problem I. The general form of S_E has been given. The necessary and sufficient conditions have been studied for the special cases AX = B and AX = XA of problem I. For problem Ⅱ the expression of the solution has been provided.

关于矩阵的迹,[5,6]推广了Bellman不等式,在A_1,A_2,…,A_m为n阶两两可换的正定Hermite矩阵的条件下,证明了本文中的不等式(2).本文对半正定Hermite矩阵乘积的迹证明了一个新的更强的不等式(1).从而不等式(1)和(2)成立的条件只要求A_1,A_2,…,A_m是半正定的Hermite矩阵.

The piece-wise smoothy Lyapunov function is used for the error analysis of the second order ESO. It is indicated that the nonlinear ESO has ability to get better estimation precision. For the better estimation precision the conditions that should be satisfied by the parameters of ESO are obtained.

A three-species ratio-dependent predator-prey food chain model with time delays is investigated.It is shown that the system is uniformly persistent under some appropriate conditions,and sufficient conditions are obtained for the global stability of the positive equilibrium of the system.

本文给出了S-闭空间的另一等价定义,建立了刻划S-闭空间特征的定理1,在应用上比[1]中的特征定理2方便得多.以此为依据我们得出了S-闭空间的若干性质,包括:(1)为使Hausdorff空间x是S-闭空间,必须且只须X是极不连通的H-闭空间.(2)为使正则空间是S-闭空间,必须且只须X是极不连通的紧空间.(3)为使拓扑空间X是S-闭空间,必须且只须X的半正则化是S-闭空间.(4)满足第一可数公理的S-闭的Hausdorff空间是有限的.此外,我们指出了[2]的主要结论的证明是错误的.

This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vries equation posed on a finite interval with general nonhomogeneous boundary conditions. Using the strong Kato smoothing property of the associated linear problem, the IBVP is shown to be locally well-posed in the space $H^s (0,1)$ for any $s\geq0$ via the contraction mapping principle.

<正> 本文是作者工作[1]的继续. 关于增算子的不动点定理,在数学的许多领域,特别是在非线性微分方程和非线性积分方程中,有着广泛的应用(见[2][3]L4][5][6]).设E是Banach空间,P是E中的锥,D=[u_o,ν_o]是E中的序区间,A:D→E是增算子,满足u_o≤Au_o,Au_o≤ν_o.关于增算子的三个有代表性的结论是:

In this paper, several practical sufficient conditions for nonsingular H-matrices are obtained by comparing the elements of a matrix. Advantage of results obtained is illustrated by a numerical example.

The following two kinds of inverse eigenvalue problems arising from structuraldesign are discussed. Problem SIELS: Given a real n×k matrix X_1 (1≤k

This paper, considers the following two problems: Problem Ⅰ. Given X, B R~(n×m),find A∈P_u such that AX = B,where P_u = {A∈R~(n×m)|A=A~x, x~TAx≥0,?x∈R~u}. Problem Ⅱ. Given A∈R~n×n, find A∈S_E such that‖A-A‖ - inf‖A - A‖,where ‖·‖ is Frobenius norm, and S_E denotes the solution set of problem Ⅰ. The necessary and sufficient condition, under which S_E is nonempty, is studied.The general form of S_E is given. For problem Ⅱ, the expression of the solution isprovided.

The Delaunay triangulation, in both classic and more generalized sense, is studied in this paper for minimizing the linear interpolation error (measure in $L^p$-norm) for a given function. The classic Delaunay triangulation can then be characterized as an optimal triangulation that minimizes the interpolation error for the isotropic function $||x||^2$ among all the triangulations with a given set of vertices. For a more general function, a function- dependent Delaunay triangulation is then defined to be an optimal triangulation that minimizes the interpolation error for this function and its construction can be obtained by a simple lifting and projection procedure. The optimal Delaunay triangulation is the one that minimizes the interpolation error among all triangulations with the same number of vertices, i.e. the distribution of vertices are optimized in order to minimize the interpolation error. Such a function- dependent optimal Delaunay triangulation is proved to exist for any given convex continuous function. On an optimal Delaunay triangulation associated with f, it is proved that $\nabla f$ at the interior vertices can be exactly recovered by the function values on its neighboring vertices. Since the optimal Delaunay triangulation is difficult to obtain in practice, the concept of nearly optimal triangulation is introduced and two sufficient conditions are presented for a triangulation to be nearly optimal.

<正> 关于丢番图方程x~4-Dy~2=1,D>0且不是平方数,(1)有过一系列工作,其主要结果如下:Nagell 证明了 D≡3(mod 8)是素数,(1)无正整数解.Ljunggren 证明了(1)最多只有两组正整数解.Cohn 证明了 D 使得 x~2-Dy~2=-4有解 x≡y≡1(mod 2),则(1)除开有限个D 的值外,仅有整数解 x=1.

A clustering dynamic state method of maximal tree of fuzzy graph theory has been develo-ped to improve the application of a method of maximal tree of fuzzy graph theory to the clu-stering method. An application to the environmental quality assessment is giwen.

In this paper, we study the uncertain multi-attribute group decision-making problems in which attribute assessments are given in the forms of fuzzy linguistic assessments, and define a scale of the fuzzy linguistic assessments and give the corresponding representation of triangular fuzzy numbers. We also utilize a generalized induced ordered weighted averaging (GIOWA) operator to aggregate the fuzzy linguistic assessment information. A method based on the fuzzy linguistic assessments and the GIOWA operator for multi-attribute group decision-making problems is proposed. Finally, an illustrative example is also given.