正态变差系数的经典限

本文推导了正态变差系数的经典精确限.为了满足工程实践的需要,利用Odeh和Owen的计算方法及Brent算法,给出了高精度的可手算的近似限.对不同的置信度γ及样本大小n=1(1)30,40,60,120,样本变差系数ε=0.01(0.01)0.20,计算了正态变差系数的经典精确限表.本文指出,当n≤8,ε≤0.20时,经典精确限C_u略大于Fiducial精确限C_u,F.当n>8.ε≤0.20时.C_u-C_u,F<5×10-6.     

Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms

A set of matrices is said to have the finiteness property if the maximal rate of exponential growth of long products of matrices drawn from that set is realised by a periodic product. The extent to which the finiteness property is prevalent among finite sets of matrices is the subject of ongoing research. In this article, we give a condition on a finite irreducible set of matrices which guarantees that the finiteness property holds not only for that set, but also for all sufficiently nearby sets of equal cardinality. We also prove a theorem giving conditions under which the Barabanov norm associated to a finite irreducible set of matrices is unique up to multiplication by a scalar, and show that in certain cases these conditions are also persistent under small perturbations.     

Criterion for the strong solvability of the mixed Cauchy problem for the Laplace equation

In the present paper, we prove a necessary and sufficient condition for the well-posedness of the problem indicated in the title in the space L ₂(Ω). To this end, we use expansions in the eigenfunctions of the mixed Cauchy problem for the Laplace equation with a deviating argument.     

Estimates for the classical parametrix for the Laplacian

We consider the integral operators which were used classically to give a parametrix and remainder for the Laplacian on a Riemannian manifold. Their kernels are defined in terms of the distance function. These operators are shown to be bounded operators on the L₂ Hilbert spaces of differential forms, under the hypotheses that the manifold be complete and of finite volume, and that it satisfy curvature bounds. Furthermore, the remainder is shown to be compact.     

Implicit algorithms for solving the Cauchy problem for the equations of the dynamics of mechanical systems

It is shown that in the numerical solution of the Cauchy problem for systems of second-order ordinary differential equations, when solved for the highest-order derivative, it is possible to construct simple and economical implicit computational algorithms for step-by-step integration without using laborious iterative procedures based on processes of the Newton-Raphson iterative type. The initial problem must first be transformed to a new argument — the length of its integral curve. Such a transformation is carried out using an equation relating the initial parameter of the problem to the length of the integral curve. The linear acceleration method is used as an example to demonstrate the procedure of constructing an implicit algorithm using simple iterations for the numerical solution of the transformed Cauchy problem. Propositions concerning the computational properties of the iterative process are formulated and proved. Explicit estimates are given for an integration stepsize that guarantees the convergence of the simple iterations. The efficacy of the proposed procedure is demonstrated by the numerical solution of three problems. A comparative analysis is carried out of the numerical solutions obtained with and without parametrization of the initial problems in these three settings. As a qualitative test the problem of the celestial mechanics of the “Pleiades” is considered. The second example is devoted to modelling the non-linear dynamics of an elastic flexible rod fixed at one end as a cantilever and coiled in its initial (static) state into a ring by a bending moment. The third example demonstrates the numerical solution of the problem of the “unfolding” of a mechanical system consisting of three flexible rods with given control input.     

A modification of the uniqueness criterion for the solution of the Watson problem for a half-plane

It is proved that a known theorem yielding the solution of the Watson problem for a half-plane in terms of the Ostrovskii function remains valid if the Ostrovskii function is replaced by the function 0} r^x /m (x)$$ " align="middle" border="0"> , where for x [n, n+1) the function m(x)=m_n, or by the function .Translated from Matematicheskie Zametki, Vol. 14, No. 5, pp. 609–614, November, 1973.     

行业对电子商务综合规范需求分析研究

通过对中国各大城市不同类型的企业调查分析,运用多变量统计分析模型,对各行业的电子商务综合规范需求及差异进行了对比分析,利用统计分析结果剖析其原因与关键问题,最后提出若干合理化建议.     

A Posteriori Estimators for the FEM: Analysis of the Robustness of the Estimators for the Poisson Equation

This paper is a summary of our study on estimators for the error in the finite element solution given in [4,5,7,9,10]. We will persent the analysis of estimators for finite element solutions of the Poisson equation in the interior of meshes of triangles with straight edges, as well as the analysis at the boundary.     

Estimates for the Fourier transform of the indicator function for nonconvex domains

Tashkent State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 3, pp. 16–24, July–September, 1995.     

A new approach for the derivation of bounds for the Jensen difference

There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory.     

Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation

The surface integral equation for a spatial mixed boundary value problem for the Helmholtz equation is considered. At a set of chosen points, the equation is replaced with a system of algebraic equations, and the existence and uniqueness of the solution of this system is established. The convergence of the solutions of this system to the exact solution of the integral equation is proven, and the convergence rate of the method is determined.     

Estimates for the Rate of Convergence of the Galerkin Method for Abstract Hyperbolic Equations

We study the rate of convergence of the semidiscrete Galerkin method for linear hyperbolic equations in a Hilbert space. We establish asymptotic estimates for the error arising as a result of the arbitrariness in the choice of subspaces in which the approximation problems are solved.     

Results on the dynamics for models for the sexual transmission of the human immunodeficiency virus

In this note, we report on the formulation and mathematical analysis of single and multiple group models for the spread of the human immuno-deficiency virus (HIV), which is the etiological agent for the acquired immunodeficiency syndrome (AIDS). Results on the robustness of a single group model are stated for specific and arbitrary survivorship functions. In addition, we provide results that show that multiple group models can have multiple endemic equilibria.