用三个关系式与Mathematica软件求第二类自然数幂和公式

首先介绍三个第二类自然数幂和关系式并对其中的两式给出证明,接着利用这些关系式与数学软件M athem atica4.0,给出求解第二类自然数幂和公式的若干机械计算方法.     

Semiconvergence in distribution of random closed sets with application to random optimization problems

The paper considers upper semicontinuous behavior in distribution of sequences of random closed sets. Semiconvergence in distribution will be described via convergence in distribution of random variables with values in a suitable topological space. Convergence statements for suitable functions of random sets are proved and the results are employed to derive stability statements for random optimization problems where the objective function and the constraint set are approximated simultaneously. The author is grateful to two anonymous referees for helpful suggestions.     

Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets

Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation.     

The Frontier Movement and The American Values and Beliefs

This paper briefly accounts the background of American values and beliefs. It analyses the essence of the American ideals and points out that the American values are exaggerated and glamorized by the American upper class. They are in a sense, a dose of anaesthetic and a kind of hypocrisy.     

强伪凸函数的某些性质

强伪凸函数是凸函数的重要推广函数之一。文中在给出强伪凸函数定义的基础上讨论了它的一些性质,另外还给出了它与强凸函数之间的关系。     

Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.     

桥头跳车的成因及处理方法

桥头跳车会增加行车风险并且会大大增加每年的养护费用．本文作者根据多年的养护管理及施工经验，对桥头跳车的成因从设计、施工及运营使用几方面进行了分析并提出了几种处理方法，尤其是对桥头搭板和土工格栅网两种目前工程界常用方法从设计机理到施工实践进行了比较详细的论述，同时对设计机理方面引入了相应的数学模型．     

Proximality and Chebyshev sets

This paper is a companion to a lecture given at the Prague Spring School in Analysis in April 2006. It highlights four distinct variational methods of proving that a finite dimensional Chebyshev set is convex and hopes to inspire renewed work on the open question of whether every Chebyshev set in Hilbert space is convex.     

On‐line Determination of Particle Size Distributions in Flowing Dispersions

Emulsions are of great importance to industry. They are involved in many engineering operations, including chemical reactions, extraction, emulsification and suspension polymerization, etc. However, an important problem for these processes is how to control the size distribution of the dispersed phase. Indeed, off‐line analysis of the emulsion may generate uncertainties due to sampling and dilution of the product, which are likely to change the dispersion state and physico‐chemical properties. In this work, an on‐line optical method is proposed to characterize dispersed media in real flowing conditions. This method is based on the time‐analysis of back‐scattered light fluctuations. The present paper deals with the development of this method and its application to dispersions of alumina in water. The results obtained with the on‐line optical method are compared with those acquired by classical laser light scattering and microscopy.     

On an approach to the study of the Jaynes–Cummings sum in quantum optics

A new approach to the study of the Jaynes–Cummings sum, which determines the atomic inversion in quantum model of a single two-level atom interacting with a single mode of the quantized radiation field, based on the number theory theorems on approximation of trigonometric sums is presented.