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 Hopf Property for Subgroups of Hyperbolic Groups

A group is said to be Hopfian if every surjective endomorphism of the group is injective. We show that finitely generated subgroups of torsion-free hyperbolic groups are Hopfian. Our proof generalizes a theorem of Sela (Topology 35 (2) 1999, 301–321).     

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.     

用电磁打点计时器进行受迫振动实验--介绍我校的一个自学物理实验

介绍一种用简单的方法进行的受迫振动实验。     

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．     

甘南藏族自治州特色旅游业发展研究

从甘南藏族自治州特色旅游业比较优势的评价入手,对制约因子和外部环境进行了深入的剖析,进而对甘南州特色旅游业的发展模式进行了现实而又独特的构想,最后提出了特色旅游业发展的战略对策与建议.     

连铸板坯外形的在线检测方法

介绍了板坯外形在线检测的测量原理，计算方法，并给出了实验测量方法，过程及计算机图像处理系统的处理结果，该方法简单，实用，精度较高。     

省级旅游市场供给环境及其评价方法研究--以山东省为例

旅游市场供给的内容十分丰富，其质量和效益的高低可通过对旅游市场的供给环境分析加以确定。本文在对旅游市场供给环境做简要分析的基础上，主要采用层次分析法对山东省旅游市场供给环境做出综合评价，为供给方充分利用和认识市场环境，发挥优势，寻找市场机会提供参考依据。     

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.