Finite element analysis for general elastic multi-structures

A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.     

Scale and time effects on mathematical models for transport in the environment

The purpose of this paper is to analyse mathematical models used in environmental modelling.Following a brief survey of the development in modelling scale-and time-dependent dispersion processes in the environment,this paper compares three similarity solutions,one of which is a solution of the generalized Feller equation(GF)with fractal parameters,and the other two for the newly-developed generalized Fokker-Planck equation(GFP).The three solutions are derived with parameters having physical significance.Data from field experiments are used to verify the solutions.The analyses indicate that the solutions of both GF and GFP represent the physically meaningful natural processes,and simulate the realistic shapes of tracer breakthrough curves.     

Justification of the Kirchhoff hypotheses and error estimation for two-dimensional models of anisotropic and inhomogeneous plates, including laminated plates

Asymptotic analysis of the problem describing deformation ofa thin cylindrical plate with clamped lateral side is performed.The problem is considered under the most general statement withthe plate being laminated and consisting of an arbitrary numberof nonhomogeneous and anisotropic (21 elastic moduli) layers.Explicit integral representations of the differential operatorswhich form the two-dimensional model of the plate are derived.In the case when the elastic moduli of each of the layers areconstant, these integral representations turn into algebraicones. The asymptotic procedure is justified with the help ofa weighted inequality of Korn's type. The error estimates obtainedgive a rigorous mathematical proof of both of Kirchhoff's hypotheses(kinematic and static) and shed light on the well-known intrinsicinconsistency of two of the hypotheses.     

求解含平衡约束数学规划的熵函数法

提出求解含平衡约束数学规划问题(简记为MPEC问题)的熵函数法，在将原问题等价改写为单层非光滑优化问题的基础上，通过熵函数逼近，给出求解MPEC问题的序列光滑优化方法，证明了熵函数逼近问题解的存在性和算法的全局收敛性，数值算例表明了算法的有效性。     

Some inequalities for the generalized linear distortion function

In this paper,we establish several inequalities for the the generalized linear distortion function λ(a,K) by using the monotonicity and convexity of certain combinations λ(a,K).     

Some remarks on solvability and various indices for implicit differential equations

It has been shown [17,18,21] that the notion of index for DAEs (Differential Algebraic Equations), or more generally implicit differential equations, could be interpreted in the framework of the formal theory of PDEs. Such an approach has at least two decisive advantages: on the one hand, its definition is not restricted to a “state-space” formulation (order one systems), so that it may be computed on “natural” model equations coming from physics (which can be, for example, second or fourth order in mechanics, second order in electricity, etc.) and there is no need to destroy this natural way through a first order rewriting. On the other hand, this formal framework allows for a straightforward generalization of the index to the case of PDEs (either “ordinary” or “algebraic”). In the present work, we analyze several notions of index that appeared in the literature and give a simple interpretation of each of them in the same general framework and exhibit the links they have with each other, from the formal point of view. Namely, we shall revisit the notions of differential, perturbation, local, global indices and try to give some clarification on the solvability of DAEs, with examples on time-varying implicit linear DAEs. No algorithmic results will be given here (see [34,35] for computational issues) but it has to be said that the complexity of computing the index, whatever approach is taken, is that of differential elimination, which makes it a difficult problem. We show that in fact one essential concept for our approach is that of formal integrability for usual DAEs and that of involution for PDEs. We concentrate here on the first, for the sake of simplicity. Last, because of the huge amount of work on DAEs in the past two decades, we shall mainly mention the most recent results. This revised version was published online in June 2006 with corrections to the Cover Date.     

均衡约束数学规划问题的一类广义Mond-Weir型对偶理论

针对均衡约束数学规划模型难以满足约束规范及难于求解的问题,基于Mond和Weir提出的标准非线性规划的对偶形式,利用其S稳定性,建立了均衡约束数学规划问题的一类广义Mond-Weir型对偶,从而为求解均衡约束优化问题提供了一种新的方法.在Hanson-Mond广义凸性条件下,利用次线性函数,分别提出了弱对偶性、强对偶性和严格逆对偶性定理,并给出了相应证明.该对偶化方法的推广为研究均衡约束数学规划问题的解提供了理论依据.     

Explicit models for elastic and piezoelastic surface waves

^** Email: julius.kaplunov{at}brunel.ac.uk Explicit models for the Rayleigh and Bleustein–Gulyaevsurface waves are extracted from the original 2D formulationswithin the general framework of linear elasticity and electroelasticity.The derivations are based on perturbing in slow time the self-similarsolutions for homogeneous surface wave. Both the proposed modelsinvolve hyperbolic equations on the surface along with ellipticequations over the interior, emphasizing the dual nature ofa surface wave. Comparisons with exact solutions are presented,including that for the plane Lamb problem.     

A note on stability of stationary points in mathematical programs with generalized complementarity constraints

We consider parameter-dependent mathematical programs with constraints governed by the generalized non-linear complementarity problem and with additional non-equilibrial constraints. We study a local behaviour of stationarity maps that assign the respective C- or M-stationarity points of the problem to the parameter. Using generalized differential calculus rules, we provide criteria for the isolated calmness and the Aubin properties of stationarity maps considered. To this end, we derive and apply formulas of some particular objects of the third-order variational analysis.     

An operator model for the oscillation problem of liquids on an elastic bottom

This paper deals with the problem of small oscillations in a liquid layer of finite depth under the assumption that the bottom is an elastic medium. The system of equations corresponding to the problem is written out and explained. The main aim of the paper is to recast these equations in the form

A stable approach to Newton's method for general mathematical programming problems inR n

The usual approach to Newton's method for mathematical programming problems with equality constraints leads to the solution of linear systems ofn +m equations inn +m unknowns, wheren is the dimension of the space andm is the number of constraints. Moreover, these linear systems are never positive definite. It is our feeling that this approach is somewhat artificial, since in the unconstrained case the linear systems are very often positive definite. With this in mind, we present an alternate Newton-like approach for the constrained problem in which all the linear systems are of order less than or equal ton. Furthermore, when the Hessian of the Lagrangian at the solution is positive definite (a situation frequently occurring), all our systems will be positive definite. Hence, in all cases, our Newton-like method offers greater numerical stability. We demonstrate that the convergence properties of this Newton-like method are superior to those of the standard approach to Newton's method. The operation count for the new method using Gaussian elimination is of the same order as the operation count for the standard method. However, if the Hessian of the Lagrangian at the solution is positive definite and we use Cholesky decomposition, then the order of the operation count for the new method is half that for the standard approach to Newton's method. This theory is generalized to problems with both equality and inequality constraints.     

Strong convergence analysis of a hybrid algorithm for nonlinear operators in a Banach space

In this paper, a hybrid algorithm is investigated for an asymptotically quasi-$\phi$-nonexpansive mapping in the intermediate sense and a bifunction. Strong convergence of the algorithm is obtained in a strictly convex, smooth and reflexive Banach space.     

广义平衡问题与非扩张映象不动点问题公解的一个新迭代方法

In this paper,we introduce a new iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems and the set of fixed points for nonexpansive mappings in Hilbert space.Under suitable conditions,some strong convergence theorems are proved.Our results extend and improve some recent results.     

A finite-element analysis of critical-state models for type-II superconductivity in 3D

^** Email: c.m.elliott{at}sussex.ac.uk^*** Corresponding author. Email: y.kashima{at}sussex.ac.uk We consider the numerical analysis of evolution variationalinequalities which are derived from Maxwell's equations coupledwith a nonlinear constitutive relation between the electricfield and the current density and governing the magnetic fieldaround a type-II bulk superconductor located in 3D space. Thenonlinear Ohm's law is formulated using the subdifferentialof a convex energy so the theory is applied to the Bean critical-statemodel, a power law model and an extended Bean critical-statemodel. The magnetic field in the nonconducting region is expressedas a gradient of a magnetic scalar potential in order to handlethe curl-free constraint. The variational inequalities are discretizedin time implicitly and in space by Nédélec's curl-conformingfinite element of lowest order. The nonsmooth energies are smoothedwith a regularization parameter so that the fully discrete problemis a system of nonlinear algebraic equations at each time step.We prove various convergence results. Some numerical simulationsunder a uniform external magnetic field are presented.     

均衡约束数学规划的约束规格和最优性条件综述

约束规格在约束优化问题的最优性条件中起着重要的作用,介绍了近几年国际上关于均衡约束数学规划(简记为MPEC)的约束规格以及最优性条件的研究成果, 包括以下主要内容: (1) MPEC常用的约束规格(如线性无关约束规格 (MPEC-LICQ)、Mangasarian-Fromovitz约束规格 (MPEC-MFCQ)等)和新的约束规格(如恒秩约束规格、常数正线性相关约束规格等), 以及它们之间的关系; (2) MPEC常用的稳定点; (3) MPEC的最优性条件. 最后还对MPEC的约束规格和最优性条件的研究前景进行了探讨.     

Some remarks on the genericity of unique range sets for meromorphic functions

In this paper we relate the study of unique range sets for meromorphic functions (URSM) with the hyperbolic hypersurfaces and give some remarks on the genericity of unique range sets for meromorphic functions.     

The blow-up rate for semilinear parabolic problems on general domains

We derive results on blow-up rates for parabolic equations and systems from Fujita-type theorems. We complement a previous study by allowing (possibly unbounded) domains with boundary. Received May 2000     

Some Improvements on Hermite-Hadamard's Inequalities for $s$-Convex Functions

Using an integral identity for a once differentiable mapping, this paper establishes Hadamard's integral inequalities for $s$-convex and $s$-concave mappings. In particular, our results improve and extend some known ones in the literature. Finally, these inequalities are applied to special means.     

Variable selection of generalized regression models based on maximum rank correlation

In this paper, we investigate the variable selection problem of the generalized regression models. To estimate the regression parameter, a procedure combining the rank correlation method and the adaptive lasso technique is developed, which is proved to have oracle properties. A modified IMO （iterative marginal optimization） algorithm which directly aims to maximize the penalized rank correlation function is proposed. The effects of the estimating procedure are illustrated by simulation studies.     

A general regularized gradient-projection method for solving equilibrium and constrained convex minimization problems

In this article, we provide a general iterative method for solving an equilibrium and a constrained convex minimization problem. By using the idea of regularized gradient-projection algorithm (RGPA), we find a common element, which is also a solution of a variational inequality problem. Then the strong convergence theorems are obtained under suitable conditions.