A semilinear elliptic PDE not in divergence form via variational methods

In this paper we consider a semilinear equation driven by an operator not in divergence form. Precisely, the principal part of the operator is in divergence form, but it has also a lower order term depending on Du. While the right-hand side of the equation satisfies superlinear and subcritical growth conditions at zero and at infinity. The problem has not a variational structure, but, despite that, we use variational techniques in order to prove an existence and regularity result for the equation.     

Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.     

Regularity for obstacle problems without structure conditions

This paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurrence of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed functional and Lavrentiev gap is needed. The main tool used here is a crucial Lemma which reveals to be needed because it allows us to move from the variational obstacle problem to the relaxed-functional-related one. This is fundamental in order to find the solutions’ regularity that we intended to study. We assume the same Sobolev regularity both for the gradient of the obstacle and for the coefficients.     

Worms,gaps, and hydras

We define a direct translation from finite rooted trees to finite natural functions which shows that the Worm Principle introduced by Lev Beklemishev is equivalent to a very slight variant of the well‐known Kirby‐Paris' Hydra Game. We further show that the elements in a reduction sequence of the Worm Principle determine a bad sequence in the well‐quasi‐ordering of finite sequences of natural numbers with respect to Friedman's gapembeddability. A characterization of gap‐embeddability in terms of provability logic due to Lev Beklemishev is also presented. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于s估计σ引出的无偏修正

用s去估计总体分布的标准差σ不是无偏估计,在特定总体分布下,可以通过简单的修正达到无偏估计.修正系数的确定与样本容量有关.     

运用因子分析法综合评价广东烟草工业经济效益

正确运用因子分析与SPSS统计软件,对广东省内7所卷烟工业企业的经济效益进行定量定性综合评价.其结论有一定的参考价值.     

主成分分析法在企业经济效益综合评价中的有效应用

运用主成分分析法,结合SPSS统计软件,对广东省内8所卷烟工业企业的经济效益进行定量定性综合评价.其结论有一定的参考价值     

Boolos‐style proofs of limitative theorems

Boolos's proof of incompleteness is extended straightforwardly to yield simple “diagonalization‐free” proofs of some classical limitative theorems of logic. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study of the HP version of mixed discontinuous finite element methods for reaction‐diffusion problems: The 1D case

This article studies the stability and convergence of the hp version of the three families of mixed discontinuous finite element (MDFE) methods for the numerical solution of reaction‐diffusion problems. The focus of this article is on these problems for one space dimension. Error estimates are obtained explicitly in the grid size h, the polynomial degree p, and the solution regularity; arbitrary space grids and polynomial degree are allowed. These estimates are asymptotically optimal in both h and p for some of these methods. Extensive numerical results to show convergence rates in h and p of the MDFE methods are presented. Theoretical and numerical comparisons between the three families of MDFE methods are described. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 525–553, 2003     

Gross–Pitaevskii dynamics of Bose–Einstein condensates and superfluid turbulence

The Gross–Pitaevskii equation, also called the nonlinear Schrödinger equation (NLSE), describes the dynamics of low-temperature superflows and Bose–Einstein Condensates (BEC). We review some of our recent NLSE-based numerical studies of superfluid turbulence and BEC stability. The relations with experiments are discussed.