可合对称张量相等的条件

本文讨论了由一般对称化算子诱导的两非零可合对称张量相等的必要充分条件与可合对称张量为零的必要充分条件。     

Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor

Third order three-dimensional symmetric and traceless tensors play an important role in physics and tensor representation theory. A minimal integrity basis of a third order three-dimensional symmetric and traceless tensor has four invariants with degrees two, four, six, and ten, respectively. In this paper, we show that any minimal integrity basis of a third order three-dimensional symmetric and traceless tensor is also an irreducible function basis of that tensor, and there is no syzygy relation among the four invariants of that basis, i.e., these four invariants are algebraically independent.     

The young diagrams of a pair of irreducible characters of S n with the same zero set on S n ?

In studying the pairs of irreducible characters of the symmetric group S _n with the same zero set on A _n or S _n ∖ A _n (as well as the pairs of irreducible characters with the same zero set on the alternating group A _n ), the results are important on the connection between the Young diagrams of the characters of these pairs. We prove a theorem that considerably generalizes two previous results of frequent use in this direction. Original Russian Text Copyright ? 2008 Belonogov V. A. The author was supported by the Russian Foundation for Basic Research (Grant 07-01-00148) and the RFBR-NSFC (Grant 05-01-39000). __________ Ekaterinburg. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 5, pp. 992–1006, September–October, 2008.     

Generators for decompositions of tensor products of modules associated with standard Jordan partitions

If K is a field of finite characteristic p, G is a cyclic group of order q = p^α, U and W are indecomposable KG-modules with dim U = m and dim W = n, and λ(m,n,p) is a standard Jordan partition of mn, we describe how to find a generator for each of the indecomposable components of the KG-module U ? W.     

A New Plethysm Formula for Symmetric Functions

This paper gives a new formula for the plethysm of power-sum symmetric functions and Schur symmetric functions with one part. The form of the main result is that for b,

有限可解群的若干充分条件

运用有限群的弱c-正规性,得到了有限可解群的若干充分条件,推广了相关文献的一些结果.     

关于可解群的若干充分条件

本文在［１］的基础上，利用半正规子群的概念考查了有限群的可解性，得到了若干充分条件．     

Asymptotic expansion of the solution to the convective diffusion problem in the wake of a spherical particle

The exterior boundary value problem of steady-state diffusion around a spherical particle placed in a Stokes flow is considered at high Peclet numbers. A complete asymptotic expansion of the solution in the wake of the particle is constructed by the method of matched asymptotic expansions.     

获得参数最短置信区间长度的条件

寻找统计分布中参数的最短置信区间长度往往不容易,一些文献往往讨论具体分布中参数的最短置信区间长度.本文从常用枢轴变量的形式即参数的线性函数形式和反比例函数形式出发,可以获得得到参数最短置信区间长度的两个条件,并且枢轴变量的密度函数满足一定条件时,最短置信区间长度是存在且唯一的,结论具有一般性.     

对两点关于圆周对称定义的讨论

本文给出了两点关于圆周对称的一种新定义，克服了［１］，［２］所给定义的不严密性。     

A Criterion for the Second Real Continuous Bounded Cohomology of a Locally Compact Group to be Finite-Dimensional

We present a brief review of the theory of quasi-characters and quasi-representations and prove a necessary and sufficient condition that the second real continuous bounded cohomology of a locally compact group to be finite-dimensional. This criterion is established by using the properties of continuous pseudocharacters on a locally compact group.     

Necessary conditions for reversed Dickson polynomials of the second kind to be permutational

In this paper, we present several necessary conditions for the reversed Dickson polynomial $E_n(1,x)$ of the second kind to be a permutation of ${\mathbb{F}}_q$. In particular, we give explicit evaluation of the sum ${\sum }_{a\in {\mathbb{F}}_q}{E}_n(1,a)$.     

The fekete-szegö problem for close-to-convex functions with respect to the koebe function

An analytic function f   in the unit disk D :={z ∈ ? : |z| < 1}$\mathbb{D}\hspace{0.17em}:=\left\{z\hspace{0.17em}\in \hspace{0.17em}?\hspace{0.17em}:\hspace{0.17em}\left|z\right|\hspace{0.17em}<\hspace{0.17em}1\right\}$, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1−z)², z ∈ D$k\left(z\right)\hspace{0.17em}:=\hspace{0.17em}z/{\left(1-z\right)}^2,\hspace{0.17em}z\hspace{0.17em}\in \hspace{0.17em}\mathbb{D}$ if there exists δ∈(-π/2,π/2) such that Re{eiδ(1−z)²f^′(z)} > 0, ∈ D$\text{Re}\left\{{\text{e}}^{\text{i}\delta }{\left(1-z\right)}^2{f}^{\prime }\left(z\right)\right\}\hspace{0.17em}>\hspace{0.17em}0,\hspace{0.17em}\in \hspace{0.17em}\mathbb{D}$. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szegö problem is studied.     

On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers

The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 10³. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ～ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ～ 5 × 10³.     

The core of an economy with a common pool resource: A partition function form approach

In this paper we consider a model of an economy with a common pool resource. Under decreasing returns to scale, it is well-known that no Nash equilibrium attains Pareto efficiency. We examine whether it is possible to achieve Pareto efficiency and avoid the tragedy of the commons through cooperation among players. For that purpose, we use the notion of a game in partition function form. Whether or not the core exists depends crucially on the expectations of each coalition regarding the coalition formation of the outsiders. If each coalition has pessimistic expectations, then the core always exists, while if it has optimistic expectations, the core may be empty. Received: January 1998/Final version: November 1998     

群体多目标决策联合有效解类的不变凸充分条件

对于群体多目标决策问题，文[1]引进它的联合有效解类的概念，并给出这类解的最优性必要条件，在对于问题的目标函数和约束函数附加凸性的条件下，文[2]又给出了联合有效解类的最优性充分条件，本文进一步在目标函数和约束函数具不变凸和不变广义 凸的情况下，分别给出了联合有效解类的若干最优性充分条件。     

Quadratic Hermite–Padé polynomials associated with the exponential function

The asymptotic behavior of quadratic Hermite–Padé polynomials associated with the exponential function is studied for n→∞. These polynomials are defined by the relation

(*)

p_n(z)+q_n(z)e^z+r_n(z)e^2z=O(z³ⁿ⁺²) as z→0,

where O(·) denotes Landau's symbol. In the investigation analytic expressions are proved for the asymptotics of the polynomials, for the asymptotics of the remainder term in (*), and also for the arcs on which the zeros of the polynomials and of the remainder term cluster if the independent variable z is rescaled in an appropriate way. The asymptotic expressions are defined with the help of an algebraic function of third degree and its associated Riemann surface. Among other possible applications, the results form the basis for the investigation of the convergence of quadratic Hermite–Padé approximants, which will be done in a follow-up paper.     

乘积Banach空间中等式约束向量极值问题的最优性必要条件

本文利用Banach空间中的隐函数定理和序线性拓扑空间中对于次似凸向量值映射的择一定理,得出了乘积Banach空间中具有等式约束向量极值问题的若干最优性必要条件.     

One-step smoothing Newton method for solving the mixed complementarity problem with a function

The mixed complementarity problem (denote by MCP(F)) can be reformulated as the solution of a smooth system of equations. In the paper, based on a perturbed mid function, we propose a new smoothing function, which has an important property, not satisfied by many other smoothing function. The existence and continuity of a smooth path for solving the mixed complementarity problem with a P₀ function are discussed. Then we presented a one-step smoothing Newton algorithm to solve the MCP with a P₀ function. The global convergence of the proposed algorithm is verified under mild conditions. And by using the smooth and semismooth technique, the rate of convergence of the method is proved under some suitable assumptions.