Testing for the Mean of Random Curves: A Penalization Approach

Let X ₁,...,X _n be an i.i.d. sample of random curves, viewed as Hilbert space valued random elements, with mean curve m. An asymptotic test of m = m ₀ vs m ≠ m ₀ is proposed, when m ₀ is a fixed known function. The test statistics converges under very mild assumptions and relies on the pseudo-inversion of the covariance operator (leading to a non standard inverse problem). The power against local alternatives is investigated. In final form November 2004     

On a non-abelian invariant on complex surfaces of general type Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper, we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S. Cheung, Bun Wong and Stephen S. T. Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.     

Topological methods for the global controllability of nonlinear systems

Sufficient conditions for the local and global controllability of general nonlinear systems, by means of controls belonging to a fixed finite-dimensional subspace of the space of all admissible controls, are established with the aid of topological methods, such as homotopy invariance principles. Some applications to certain classes of nonlinear control processes are given, and various known results on the controllability of perturbed linear systems are also derived as particular cases.     

局域功函数图像及其在Cu(111)-Au/Pd表面的应用

用扫描隧道显微镜（STM）对Cu(111)-Au和Cu(111)-Pd表面的局域功函数进行了研究.通过 测量隧道电流对针尖样品间距的响应，得到了与STM形貌图一一对应的表面局域功函数图像. 实验发现，Au/Pd覆盖层和Cu衬底间的功函数有明显的不同.Pd薄膜的功函数甚至超过了其体 本征值，且功函数在台阶处变小.用偶极子的形成解释了台阶处功函数的降低.这一工作表明 ，用测量局域功函数的方法容易区分表面上不同的元素，并具有纳米尺度的空间分辨率. 关键词： 扫描隧道显微镜 局域功函数 台阶     

Determination of a Homogeneous Strictly Pseudoconvex Surface from the Coefficients of Its Normal Equation

Mathematical Notes -     

Local Search Algorithms for the Bin Packing Problem and Their Relationships to Various Construction Heuristics

The tradeoff between the speed and quality of the solutions obtained by various construction and local search algorithms for the elementary bin packing problem (BPP) are analyzed to obtain useful information for designing algorithms for real-world problems that can be modeled as BPPs. On the basis of intensive computational experiments, we observe that the framework of a solution (i.e., a part of a solution consisting of large items or items with tight constraints) should be constructed in the early stages of a local search. New local search algorithms are proposed as empirical support for the observation.     

Constrained second order optimization on non-archimedean fields

Constrained optimization on non-Archimedean fields is presented. We formalize the notion of a tangent plane to the surface defined by the constraints making use of an implicit function Theorem similar to its real counterpart. Then we derive necessary and sufficient conditions of second order for the existence of a local minimizer of a function subject to a set of equality and inequality constraints, based on a concept of continuity and differentiability that is stronger than the conventional one.     

Predictor-Corrector Smoothing Newton Method,Based on a New Smoothing Function,for Solving the Nonlinear Complementarity Problem with a P 0 Function

By smoothing a perturbed minimum function, we propose in this paper a new smoothing function. The existence and continuity of a smooth path for solving the nonlinear complementarity problem (NCP) with a P ₀ function are discussed. We investigate the boundedness of the iteration sequence generated by noninterior continuation/smoothing methods under the assumption that the solution set of the NCP is nonempty and bounded. Based on the new smoothing function, we present a predictor-corrector smoothing Newton algorithm for solving the NCP with a P ₀ function, which is shown to be globally linearly and locally superlinearly convergent under suitable assumptions. Some preliminary computational results are reported.     

Exact local behavior of positive solutions for a semilinear elliptic equation with Hardy term

We characterize an exact growth order near zero for positive solutions of a semilinear elliptic equation with Hardy term. This result strengthens an existence result due to E. Jannelli [The role played by space dimension in elliptic critical problems, JDE 156 (1999), 407-426].