一类拟线性退化抛物方程Dirichlet问题粘性解的正则性

本文考虑下面的Ｄｉｒｉｃｈｌｅｔ问题利用粘性解理论证明了；当Ｈ，Г满足一定条件时，（ＤＰ）的粘性解ｕ（ｘ，ｔ）满足：如果ψ∈Ｃａ，ａ／２，则ｕ（ｘ，ｔ）∈Ｃａ，ａ／２，若ψ＝０，则ｕ（ｘ，ｔ）是Ｌｉｐｓｃｈｉｔｚ连续的．     

非线性波动方程整体解存在的一个必要条件

该文给出了非线性波动方程ｕｎ＝△ｕ＋ｆ（ｕ），（ｆ（ｕ）＝ｕ＾ｐ，ｐ〉１）的Ｃａｕｃｈｙ问题在函数空间Ｃ＾ｋ０（Ｒ＾ｎ）的原点领域有古典整体解的一个必要条件：１／２（ｕ（０）＾２Ｌ２＋ｕｔ（０）＾２Ｌ２）－∫Ｒ＾ｎ∫＾ｕ００ｆ（ｓ）ｄｓｄｘ≤０，并且证明了１〈ｐ〈＾ｎ＾２＋ｎ＋２／ｎ（ｎ－１），ｎ≠１（ｎ＝１，１〈ｐ〈＋∞）古典解与广义解有相同的生命跨度，同时给出了生命跨度的上界估计。     

双非线性抛物型方程非负解的一个性质

在Ｅ＾ｎ（０，∞）上讨论双非线性抛物型方程ａ／ａｔ（｜ｕ｜＾λ－２ｕ）－ｄｉｖ（｜△ｕ｜＾ｐ－２△ｕ）＝０在ｐ＞λ＞２的条件下，证明它的齐次Ｃａｕｃｈｙ问题非负整体解必是零解。     

关于Fibonacci数的两个表达式

关于Ｆｉｂｏｎａｃｃｉ数的两个表达式胡久稔（南开大学数学研究所，天津３０００７１）关键词Ｆｉｂｏｎａｃｉ数，表达式．分类号ＡＭＳ（１９９１）０５Ａ／ＣＣＬＯ１５７．１｛ｕｎ｝（ｎ＝１，２，…）表示Ｆｉｂｏｎａｃｃｉ数列：ｕ１＝ｕ２＝１，ｕｎ＋２＝ｕｎ...     

一个反应扩散过程的门槛结果

本文讨论反应扩散方程Ｃａｕｃｈｙ问题（ｕｔ－△ｕ＝ｕ＾ｐ－ｕ＾ｐ－ｕ，Ｘ∈Ｒ＾ｎ，ｔ∈（０，Ｔ），ｕ（ｘ，０）＝ｕ０（ｘ）≥０，Ｘ∈Ｒ＾ｎ，解的整体存在性，渐近性质和Ｂｌｏｗ－ｕｐ问题，其中１＜ｑ＜ｐ＜ｎ＋２／ｎ－２，ｎ≥３或者１＜ｑ＜ｐ＋∞，ｎ＝２．得到门槛结果。     

非线性波动与社会传播混合型方程的整体紧吸引子

本文研究非一波动与神经传播混合型方程ｕｔｔ＝ｕｘｘｔ＋σ（ｕｘ）ｘ－ｈ（ｕ）ｕｔ－ｆ（ｕ）＋ｇ（ｘ）初边值问题的整体吸引子，在σ∈Ｃ＾２，σ（ｓ）〉σ０〉０及ｈ（ｓ）∈Ｃ＾１，－Ｃｏ〈ｈ（ｓ）（０〈Ｃｏ〈λ１／２）且∫ｏ＾ｕｈ（ｓ）ｓｄｓ〈Ｃｕ＾２条件下我们得到了与该方程相应的动力系统整体紧吸引子的存在性，并证明了它具有有限的Ｈａｕｓｄｏｒｆｆｘ维数和ｆｒａｃｔａｌ维数。     

三维椭球的光线障碍问题

对任给的正实数ｕ，令Ｃ＿ｕ＝｛（ｘ，ｙ，ｚ）：ｕ￣２ｘ￣２＋ｙ￣２＋ｚ￣２≤１｝．α为一正实数，使得对于任给的射线ｘ＿ｉ＝α＿ｉｔ（α＿ｉ＞０，ｉ＝１，２，３，ｔ≥０）都和相交。关于Ｃ＿ｕ的光线障碍问题就是要确定Ｋ（Ｃ＿ｕ）＝ｉｎｆα．本文对所有的实数ｕ，确定了Ｋ（Ｃ＿ｕ）的值。     

椭球等高分布族中T^20的精确分布

设Ｘ～ＥＣｐ（ｕ１，Σ，φ），即Ｘ服从椭球等高布分；Ｘ１，Ｘ２，…，Ｘｎ是来自Ｘ的样本，作：Ｔ＾２０＝（Ｘ－ｕ）′Σ＾－１（Ｘ－ｕ），（Ｘ＝１／ｎΣ＾ｎｉ＝１Ｘｉ）本文将在一定条件下，给出Ｔ＾２０的密度函数。     

均匀设计法在优化青霉素1~＃、2~＃菌种培养基配方中的应用

我们将均匀设计法与传统正交设计法相结合，通过实验成功地优化青霉素菌种配方，筛选培养基。（仅ｕ／ｍｌ这一项就比对照１＃配方高２０．７５％，比２＃配方高３１．８４％）。     

一类抛物型偏泛函微分方程解的强迫振动性

本文研究抛物型偏泛函微分方程γ／γｔ［ｕ－ｍΣｔ－１Ｃｔ（ｔ）ｕ（ｘ，ｔ－τｔ）］＝ａ（ｔ）Δｕ－Ｐ（ｘ，ｔ）ｕ－Ｑ（ｘ，ｔ）Ｇ［ｕ（ｘ，ｐ（ｔ）］＋Ｆ（ｘ，ｔ），（ｘ，ｔ）包含Ｄ×［０，＋∞］解的强近振动性，其中Ｄ为Ｒ＾ｎ中具有逐片光滑边办γＤ的有界区域，ｕ＝ｕ（ｘ，ｔ），Δ是Ｒ＾ｎ中的Ｌａｐｌａｃｅ算子。     

二次回归正交设计在天然橡胶复合材料制备工艺中的应用

本文通过二次回归正交设计,对天然橡胶复合材料制备工艺中有机土浓度、分散剂浓度、胶乳浓度和土填充量四个因子进行研究。结果表明,当有机土浓度取6.4%,分散剂浓度取50.7%,胶乳浓度取22.9%,土填充量取7.0%时,可以使天然橡胶复合材料的硬度达到最佳值。     

Design and Fabrication of Composite Smart Structures with High Electric and Mechanical Performances for Future Mobile Communication

In this paper, we have developed a load-bearing outer skin for antennas, which is termed a composite smart structure (CSS). The CSS is a multilayer composite sandwich structure in which antenna layers are inserted. A direct-feed stacked patch antenna is considered. A design procedure including the structure design, material selection, and design of antenna elements in order to obtain high electric and mechanical performances is presented. An optimized honeycomb thickness is selected for efficient radiation and impedance characteristics. High gain conditions can be obtained by placing the outer facesheet in the resonance position, which is at about a half wavelength distance from the ground plane. The measured electrical performances show that the CSS has a great bandwidth (over 10%) and a higher gain than an antenna without a facesheet and has excellent mechanical performances, owing to the composite laminates and honeycomb cores. The CSS concept can be extended to give a useful guide for manufacturers of structural body panels and for antenna designers.     

Coupled Thermo-Mechanical and Wear Effects on the Analysis of High Speed Railway Brake Systems

The high speed railway brakes transfer a large amount of kinetic energy into heat. The temperature during a brake operation could reach values higher than 90 °C. The dynamics of the brake system is rather complicated with respect to the multiphysical phenomena. In this paper, the thermo-mechanical coupling are investigated combined with the loos of brake material due to wear. The coupled model is discretized by conventional finite element method. Different coupled algorithms have been tested. Various scenarios have been simulated and shown reasonable results. The temperature and deformation on pad and disc, especially the thermal deformation of disc the so–called coning effect can also be prescribed with this coupled multiphysics model. Furthermore, the tapered wear on brake pads is also discussed as a requirement of railway brake design in terms of durability. Thereby, the Ehlers's model is normally used to minimize tapered wear by selecting an adequate point of applied braking force. An extended Ehlers's model is also presented here, which concerns wear effect based on Archard's model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Particle Learning of Gaussian Process Models for Sequential Design and Optimization

We develop a simulation-based method for the online updating of Gaussian process regression and classification models. Our method exploits sequential Monte Carlo to produce a fast sequential design algorithm for these models relative to the established MCMC alternative. The latter is less ideal for sequential design since it must be restarted and iterated to convergence with the inclusion of each new design point. We illustrate some attractive ensemble aspects of our SMC approach, and show how active learning heuristics may be implemented via particles to optimize a noisy function or to explore classification boundaries online. Supplemental material, including an R package, is available online.     

Formulação numérica de estruturas compósitas amortecidas utilizando as teorias da Deformação Cisalhante de Primeira Ordem e de Alta Ordem

Composite materials have been used in the design of the aircrafts structures because their low weight and high mechanical strength. However, structures made in composite material are exposed to dynamical and/or static loading environments. Therefore, a major research effort is undertaken in the development of tools numerical for analysis and design of composite structures. This paper presents a numerical formulation of the composite structures using the Finite Element Method (FEM). The damped composite structures, using inserted viscoelastic devices, and undamped composite structures are formulated by FEM. Viscoelastic materials are applied as continuous layers inserted on composite structures. The intrinsic damping of the composite material is included in the studies, too. The First‐order (FSDT) and Higher‐order Shear Deformation (HSDT) theories are formulated. They are distinguished by order of the approximation functions used in the mechanical displacements field. Both theories are computationally implemented using the Serendipity finite element. This is a rectangular finite element with 8 nodes, 5 or 11 degrees of freedom per node. The results are compared with papers predictions. The advantages and disadvantages of using each theory in the modeling of composite (thin or thick) and thick sandwiches structures, including the intrinsic and the viscoelastic damping, are discusses.     

Structure and Properties of Teflon Composites with Natural Diamond Powders

The results of experimental investigations of the structure and properties of composites based on polytetrafluorethylene (PTFE) containing natural diamond powders (NDP) of different dispersity are presented. To obtain diamond-containing compositions for antifrictional applications, we used a preliminary mechanical treatment of NDP (40 m) in a planetary mill. It was stated that the formation of the maximum ordered small-spherulite structure of PTFE after injection of NDP significantly increased the wear resistance and deformational and strength characteristics of the polymer composite materials. To produce abrasive materials, PTFE was filled with NDP having a larger graininess (from 40 to 125 m). It was found that the injection of NDP did not cause evident morphological changes in the binder — the bonds between diamond grains and the polymer are created by physicomechanical forces. To strengthen the adhesion interaction at the interface between the binder and diamond grains and to raise the wear resistance of the material, a complex modification of the polymer with inorganic and organic fillers was carried out. It is shown that the injection of the complex filler significantly improves the tribotechnical and operational properties of the diamond-containing composite material. The general laws of the influence of NDP on the formation of the supermolecular structure of PTFE are revealed. It is shown that, by varying the degree of dispersity and the content of NDP in PTFE, and by applying different methods of their injection into the polymer matrix, it is possible to control the operational properties of the composites and to produce materials of different functional application, from antifrictional to abrasive ones.     

Design of two-way glass-reinforced plastics with high compressive strength

The conditions determining the design of two-way glass-reinforced plastics with high compressive strength are investigated. The relations between the physicomechanical and geometric parameters of the composite are obtained in the form of a system of inequalities, satisfaction of which ensures the obtaining of a high-strength material with a given utilization factor. It has been shown experimentally that these inequalities can be used as a first approximation for the optimal design of a two-way reinforced composite with high compressive strength.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow. Moscow Institute of Electronic Machine Building. Translated from Mekhanika Polimerov, No. 4, pp. 655–660, July–August, 1973.     

基于特征正交分解的材料微结构参数化表征模型及等效性能优化设计

随着计算能力的不断发展,近年来基于材料微结构图像的材料等效性能数值模拟越来越受到学者们的重视.在此背景下,提出了一种针对材料微结构图像的高效参数化表征模型.通过特征正交分解(proper orthogonal decomposition,POD)对已有材料微结构图像数据进行特征分析,得到近似描述该类材料微结构的特征缩减基.应用移动最小二乘(moving least squares,MLS)法建立特征缩减基映射系数的响应面模型,拟合得到任意给定参量相应的缩减基映射系数.利用拟合缩减基系数可获得任意给定参量对应的微结构图像矩阵.该参数化表征模型被用于表征含椭球夹杂的两相材料(2-phase composite)的二维情形, 并进一步应用于这类复合材料宏观等效力学性能的优化设计.     

Nonparametric Regression with Singular Design

Theories of nonparametric regression are usually based on the assumption that the design density exists. However, in some applications such as those involving high-dimensional or chaotic time series data, the design measure may be singular and may be likely to have a fractal (nonintegral) dimension. In this paper, the popular Nadaraya–Watson estimator is studied under the general setup that the continuity of the design measure is governed by the local or pointwise dimension. It will be shown in the iid setup that the nonparametric regression estimator achieves a convergence rate which is dependent only on the pointwise dimension. The case of time series data is also studied. For the latter case, a new mixing condition is introduced, and an assumption of marginal or joint density is completely avoided. Three examples, a fractal regression and two applications for predicting chaotic time series, are used to illustrate the implications of the obtained results.     

A cellular automaton model for boundary friction of PEEK and PEEK6

Nowadays a common material for journal bearings is PEEK (Polyetheretherketon) which is increasingly used under boundary friction. A Cellular Automaton model is developed to describe the boundary layer dynamics of PEEK and its composite PEEK6 sliding against a steel surface. Whereas PEEK is a homogeneous synthetic material, PEEK6 contains also carbon fibres for stability and fillers working as solid lubricants. The automaton shows a representative area of the real surface. The processes in the interface are described by a set of rules based on physical assumptions and measurements. Based on these rules the simulations show the dependency of friction and wear on the load spectrum. The discrete simulation allows to observe the topographic development of the PEEK and PEEK6 surface as well as the build-up of a transfer film on the steel surface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)