A capacitary weak type inequality for Sobolev functions and its applications

In this paper a capacitary weak type inequality for Sobolev functions is established and is applied to reprove some well-known results concerning Lebesgue points, Taylor expansions in the -sense, and the Lusin type approximation of Sobolev functions.

     

Semi-infinite programming,duality, discretization and optimality conditions†

The aim of this article is to give a survey of some basic theory of semi-infinite programming. In particular, we discuss various approaches to derivations of duality, discretization, and first- and second-order optimality conditions. Some of the surveyed results are well known while others seem to be less noticed in that area of research.     

Bounded sets of Lagrange multipliers for vector optimization problems in infinite dimension

The aim of this paper is to point out some sufficient constraint qualification conditions ensuring the boundedness of a set of Lagrange multipliers for vectorial optimization problems in infinite dimension. In some (smooth) cases these conditions turn out to be necessary for the existence of multipliers as well.     

Abstract Hardy-Sobolev spaces and interpolation

The purpose of this work is to describe an abstract theory of Hardy-Sobolev spaces on doubling Riemannian manifolds via an atomic decomposition. We study the real interpolation of these spaces with Sobolev spaces and finally give applications to Riesz inequalities.     

Optimality Conditions and Stability Analysis via the Mordukhovich Subdifferential

This article shows that finite-dimensional multiplier rules, which are based on the limiting subdifferential, can be proved by Ekeland's variational principle and some basic calculus tools of the generalized differentiation theory introduced by B. S. Mordukhovich. Consequences of a limiting constraint qualification, which yields the normal form of the multiplier rules, stability and calmness of optimization problems, are investigated in detail.     

Riesz transforms for a non-symmetric Ornstein-Uhlenbeck semigroup

Let (ℋ _t ) _t≥0 be the Ornstein-Uhlenbeck semigroup on ℝ ^d with covariance matrix I and drift matrix −λ(I+R), where λ>0 and R is a skew-adjoint matrix and denote by γ _∞ the invariant measure for (ℋ _t ) _t≥0. Semigroups of this form are the basic building blocks of Ornstein-Uhlenbeck semigroups which are normal on L ²(γ _∞). We investigate the weak type 1 estimate of the Riesz transforms for (ℋ _t ) _t≥0. We prove that if the matrix R generates a one-parameter group of periodic rotations then the first order Riesz transforms are of weak type 1 with respect to the invariant measure γ _∞. We also prove that the Riesz transforms of any order associated to a general Ornstein-Uhlenbeck semigroup are bounded on L ^p (γ _∞) if 1<p<∞. The authors have received support by the Italian MIUR-PRIN 2005 project “Harmonic Analysis” and by the EU IHP 2002-2006 project “HARP”.     

Angle criteria for frame sequences and frames containing a Riesz basis

We obtain a condition implying that the union of two frame sequences is also a frame sequence. Christensen found a condition for this in terms of orthogonal projections. We phrase our condition by use of the angle between closed subspaces. Also a lower bound formula is obtained. We then apply the results to find conditions for a frame containing a Riesz basis to be a Riesz frame.     

Analyticity and Dynamic Behavior of a Damped Three-Layer Sandwich Beam

Using the Riesz basis approach, we study a sandwich beam that is composed of an outer stiff layer and a compliant middle layer. The dynamic behavior and analyticity of the system are obtained based on a detailed spectral analysis and Riesz basis generation. As a consequence, the analyticity of the solution and the exponential stability of the system are concluded. This work was supported by the National Natural Science Foundation of China, Program for New Century Excellent Talents in the Universities of China and by the National Research Foundation of South Africa.     

抢渡长江最优路径的讨论

给出了2003年全国大学生数学建模竞赛D题的一种求解方法.运用拉格朗日乘数法与变分法建立了水速变化时最优路径适合的方程.特别针对问题4,当水流速度线性变化时,导出了求解最优解的函数方程.     

二阶线性微分方程的乘子可积性

在偏微分方程Riemann解法和微分方程裂变思想的启发下,引入了微分方程乘子函数(解)和乘子解法的概念,系统地讨论了二阶线性微分方程的乘子可积性.得到了二阶线性微分方程乘子可积的条件以及Riceati方程可积的充分必要条件,并分别给出了二阶线性微分方程和Riccati方程在乘子解下的通积分.