Analysis of a nonlinear beam in contact with a foundation

The paper investigates the contact between a nonlinear dynamic Gao beam and a rigid or reactive foundation. The contact is modeled with the normal compliance condition for the deformable foundation and with the Signorini condition for the rigid foundation. The existence and uniqueness of the weak solution for the problem with normal compliance are obtained. The solution of the Signorini condition for the rigid foundation is obtained by passing to the limit when the normal compliance approaches infinity.     

On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem

For standard eigenvalue problems, closed-form expressions for the condition numbers of a multiple eigenvalue are known. In particular, they are uniformly 1 in the Hermitian case and generally take different values in the non-Hermitian case. We consider the generalized eigenvalue problem and identify the condition numbers. Our main result is that a multiple eigenvalue generally has multiple condition numbers, even in the Hermitian definite case. The condition numbers are characterized in terms of the singular values of the outer product of the corresponding left and right eigenvectors.     

Semilocal convergence for a family of Chebyshev-Halley like iterations under a mild differentiability condition

The semilocal convergence of a family of Chebyshev-Halley like iterations for nonlinear operator equations is studied under the hypothesis that the first derivative satisfies a mild differentiability condition. This condition includes the usual Lipschitz condition and the H?lder condition as special cases. The method employed in the present paper is based on a family of recurrence relations. The R-order of convergence of the methods is also analyzed. As well, an application to a nonlinear Hammerstein integral equation of the second kind is provided. Furthermore, two numerical examples are presented to demonstrate the applicability and efficiency of the convergence results.     

A criterion for checking if a convex set belongs to the union of a finite number of convex sets

A necessary and sufficient condition for the inclusion of a convex compact set in the union of a finite number of convex sets is proved. This condition obtained using the convex analysis techniques is a condition on the maximin of a given function. Using the dynamic programming, checking this condition is reduced to evaluating a set of functions and checking a condition for their values. The reduced form of the criterion is more convenient from the computational point of view.     

On condition numbers of a nondefective multiple eigenvalue of a nonsymmetric matrix pencil

This paper considers the condition numbers of a nondefective multiple eigenvalue of a nonsymmetric matrix pencil. Based on the directional derivatives of a nondefective multiple eigenvalue of a nonsymmetric matrix pencil analytically dependent on several parameters, different condition numbers of a nondefective multiple eigenvalue are introduced. The computable expressions and bounds of introduced condition numbers are derived. Moreover, some results on the perturbation of a nondefective multiple eigenvalue of a nonsymmetric matrix pencil are given.     

一类非线性离散系统基于有界反馈的奇异H_∞控制问题

主要研究基于有界控制律的一类非线性离散系统的奇异H∞控制问题.在系统不满足正则条件的情况下,分离出正则部分与非正则部分,给出基于有界反馈与二次Lyapunov函数的离散系统奇异H∞问题可解性的必要条件以及充分条件,求出的有界控制律能使得闭环系统在保证内稳定的条件下达到干扰衰减.     

一类拟线性椭圆方程组非平凡解的存在性

首先证明了一个抽象的紧性定理,然后借此定理证明了对应于一类拟线性椭圆方程组的泛函在比Boccardo和De．Figueiredo(2002)的条件更弱的条件(文中记为弱类(AR)条件)下满足(C)条件,并利用山路引理证明了这类拟线性椭圆方程组非平凡解的存在性,最后举出两个例子验证了文中所给条件(即弱类(AR)条件)的确比Boccardo和De．Figueiredo(2002)的条件弱．     

Diffraction of a plane wave by a narrow cone

The problem of diffraction of a plane scalar wave by a narrow cone is considered. The shape of the cone is arbitrary. The boundary condition is the Dirichlet or Neumann one. The wave scattered by the cone vertex arises as a result of the diffraction process. The subject of this paper is to calculate the wave amplitude. If the cone is narrow, it is possible to obtain simpler approximate formulas in comparison with Smyshlayev's one. The exactness of the approximate formulas is checked numerically. The etalon is a solution in explicit form in the axially symmetric case. The calculation shows that our formula is more exact in the case of the Dirichlet boundary condition than Felsen's formula. The approximate formula is a generalization of Felsen's one for circular cone to an arbitrary narrow cone in the case of the Neumann boundary condition. Bibliography: 6 titles. Dedicated to N. N. Uraltseva on her jubilee Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 67–74. Translated by D. B. Dement'ev.     

Towards a general condition based maintenance model for a stochastic dynamic system

This paper considers a stochastic dynamic system subject to random deterioration, with regular condition monitoring and preventive maintenance. A model is presented to advise at a monitoring check what maintenance action to take based upon the condition monitoring and preventive maintenance information obtained to date. A general assumption adopted in the paper is that the performance of the system concerned can not be described directly by the monitored information, but is correlated with it stochastically. The model is relevant to a large class of condition monitoring techniques currently employed in industry including vibration and oil analysis. The model is constructed under fairly general conditions and includes two novel developments. Firstly, the concept of the conditional residual time is used to measure the condition of the monitored system at the time of a monitoring check, and secondly, contrary to previous practice, the monitored observation is now assumed to be a function of the system condition. Relationships between the observed history of condition monitoring, preventive maintenance actions, and the condition of the system are established. Methods for estimating model parameters are discussed. Since the model presented is generally beyond the scope for an analytical solution, a numerical approximation method is also proposed. Finally, a case example is presented to illustrate the modelling concepts in the case of non-maintained plant.     

Banach空间上一个定理的推广

针对Banach空间上一个定理,指出其命题条件过强,并在减弱后的条件下,运用Zorn引理给出证明,从而对该定理进行了推广.     

Closedness of a Convex Cone and Application by Means of the End Set of a Convex Set

This article presents new conditions that ensure the closedness of a convex cone in terms of the end set and the extent of its generator. The results significantly extend the classic condition. The new closedness conditions are utilized to obtain a simple formula of the least global error bound and a suitable regularity condition of the set containment problem for sublinear functions.     

Closedness of a Convex Cone and Application by Means of the End Set of a Convex Set

This article presents new conditions that ensure the closedness of a convex cone in terms of the end set and the extent of its generator. The results significantly extend the classic condition. The new closedness conditions are utilized to obtain a simple formula of the least global error bound and a suitable regularity condition of the set containment problem for sublinear functions.     

一类具有保护区域的Leslie-Gower捕食-食饵模型的分歧分析

研究了一类Neumann边界条件下带有保护区域的Leslie-Gower捕食-食饵模型,分析稳态系统从半平凡解处发生分歧的条件,得到了分歧方向及分歧值的唯一性,得到了在确定参数范围内,从半平凡解出发的分支解曲线的稳定性.     

Effect of slip on the linear stability of flow through a tube

A theoretical investigation of the linear stability of the flow of a Newtonian fluid through a tube is presented using an alternative boundary condition to the standard no-slip condition. The linear stability analysis is based on the classical method of infinitesimal axially symmetric harmonic perturbations super-imposed on the steady state solution. In this analysis the standard no-slip boundary condition is replaced with the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter, which may be regarded as a positive slip length. The aim of this analysis is to assess the effect of a nonzero slip length on the behavior of infinitesimal disturbances in the flow through a tube. It is demonstrated that for positive slip the rate of decay of the least damped disturbance is reduced, although the flow still remains stable to all infinitesimal disturbances of the type considered, as it does for the no-slip boundary condition.     

Boundary element solution of a scattering problem involving a generalized impedance boundary condition

A boundary element method is introduced to approximate the solution of a scattering problem for the Helmholtz equation with a generalized Fourier–Robin‐type boundary condition given by a second‐order elliptic differential operator. The formulation involves three unknown fields, but is free from any hypersingular integral. Existence and uniqueness of the solution are established using a Babuška inf–sup condition. When implementing the method, a lumping process allows to remove two fields from the formulation. The numerical solution has thus the same cost as the one of a problem relative to a usual Neumann boundary condition. Numerical tests confirm the ability of the method for solving this type of non‐standard boundary value problems. Copyright © 1999 John Wiley & Sons, Ltd.     

A study of a numerical algorithm for a nonlinear transport model

For a nonlinear transport model, we propose a simple and economical two-step algorithm that decreases the dimension of the system of nonlinear equations, as compared with implicit difference schemes. We prove theorems on necessary conditions for stability with respect to the initial data for the nonlinear problem and theorems on sufficient conditions for stability in the case of the linearized model. We also obtain theorems on approximation of the integral conservation law on a grid. The necessary condition obtained is a condition on the coefficients of the differential equation (which singles out an admissible class of equations) but not a condition on the ratio of the grid steps. Bibliography: 3 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 25–32.     

Effect of slip on the linear stability of flow through a tube

A theoretical investigation of the linear stability of the flow of a Newtonian fluid through a tube is presented using an alternative boundary condition to the standard no-slip condition. The linear stability analysis is based on the classical method of infinitesimal axially symmetric harmonic perturbations super-imposed on the steady state solution. In this analysis the standard no-slip boundary condition is replaced with the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter, which may be regarded as a positive slip length. The aim of this analysis is to assess the effect of a nonzero slip length on the behavior of infinitesimal disturbances in the flow through a tube. It is demonstrated that for positive slip the rate of decay of the least damped disturbance is reduced, although the flow still remains stable to all infinitesimal disturbances of the type considered, as it does for the no-slip boundary condition.     

On a sufficient condition for the existence of a common stabilizer for a family of dynamical systems

We consider the problem on the existence of a common stabilizing controller for a finite family of linear vector dynamical systems. A sufficient condition, obtained on the basis of topological methods, is presented for the existence of a common stabilizer. Constructive approaches to the development of an algorithm for verifying this condition are indicated.     

The Convexity of Families of Adjoint Patches for a Bezier Triangular Surface

A necessary and sufficient condition for the convexity of adjoint patches for a Bezier triangular surface is presented. Furthermore, it is proved that this condition is equivalent to the fact that the adjoint patches form a decreasing sequence as the corresponding degree decreases. The condition can be easily computationally verified.     

The condition of almost everywhere convergence for a functional series with a weak analogue of the orthonormality property

The almost everywhere convergence condition similar to the Menchoff-Rademacher condition is obtained for functional series with some weak analogue of the orthogonality property. As a corollary, results related to almost everywhere convergence of series with respect to Riesz systems, Hilbert and Bessel systems, and frames are obtained.