On the non-classical mathematical models of coupled problems of thermo-elasticity for multi-layer shallow shells with initial imperfections

Mathematical modeling of evolutionary states of non-homogeneous multi-layer shallow shells with orthotropic initial imperfections belongs to one of the most important and necessary steps while constructing numerous technical devices, as well as aviation and ship structural members. In first part of the paper fundamental hypotheses are formulated which allow us to derive Hamilton–Ostrogradsky equations. The latter yield equations governing shell behavior within the applied hypotheses and modified Pelekh–Sheremetev conditions. The aim of second part of the paper is to formulate fundamental hypotheses in order to construct coupled boundary problems of thermo-elasticity which are used in non-classical mathematical models for multi-layer shallow shells with initial imperfections. In addition, a coupled problem for multi-layer shell taking into account a 3D heat transfer equation is formulated. Third part of the paper introduces necessary phase spaces for the second boundary value problem for evolutionary equations, defining the coupled problem of thermo-elasticity for a simply supported shallow shell. The theorem regarding uniqueness of the mentioned boundary value problem is proved. It is also proved that the approximate solution regarding the second boundary value problem defining condition for the thermo-mechanical evolution for rectangular shallow homogeneous and isotropic shells can be found using the Bubnov–Galerkin method.     

Frozen 1-RSB structure of the symmetric Ising perceptron

We prove, under an assumption on the critical points of a real-valued function, that the symmetric Ising perceptron exhibits the ‘frozen 1-RSB’ structure conjectured by Krauth and Mézard in the physics literature; that is, typical solutions of the model lie in clusters of vanishing entropy density. Moreover, we prove this in a very strong form conjectured by Huang, Wong, and Kabashima: a typical solution of the model is isolated with high probability and the Hamming distance to all other solutions is linear in the dimension. The frozen 1-RSB scenario is part of a recent and intriguing explanation of the performance of learning algorithms by Baldassi, Ingrosso, Lucibello, Saglietti, and Zecchina. We prove this structural result by comparing the symmetric Ising perceptron model to a planted model and proving a comparison result between the two models. Our main technical tool towards this comparison is an inductive argument for the concentration of the logarithm of number of solutions in the model.     

竖向载荷作用下框架结构力学模型的简化与计算

针对结构力学与工程结构设计中力学模型和载荷作用方式的简化,分别采用一次性加载法、模拟施工三加载法和分层法,研究了竖向载荷作用下框架结构力学模型的简化与计算,分析了三种方法的计算假定和计算结果,给出了合理适用范围。一次性加载法更适用于抗连续性倒塌分析和建筑结构改造设计计算,模拟施工三加载法更适用于新建工程的设计计算,分层法作为一种简化的手算方法可作为理解结构力学原理的基本方法。     

多层介质膜脉宽压缩光栅的严格矢量分析

用于展宽和压缩激光脉冲的多层膜脉宽压缩光栅是由多层介质高反膜和位于其顶层的浮雕光栅构成。以设计的高反射多层膜为基础,利用傅里叶模式理论分析了其衍射场分布,给出了TE波自准直角入射的使用条件下,多层介质膜脉宽压缩光栅衍射效率的表达式。以-1级衍射效率为评价函数,分别讨论了HfO2和SiO2为顶层材料时,多层膜脉宽压缩光栅-1级衍射效率高于0.95的光栅结构参量范围。结果表明,在该条件下,选择HfO2为顶层材料时,光栅结构参量有较大的取值范围。给出了优化的光栅结构参量,并分析了光栅制作误差及其使用条件的宽容度,对光栅制作工艺和使用具有一定的指导意义。     

多层神经网络的一个快速算法

本文对文[4]提出的前馈式多层神经网络的单参数动态搜索（SPDS）算法进行了深入的分析，给出了实现快速一维搜索的两个方案，从而实现了多层神经网络更为快速的学习训练．     

在一种扩展多层感知器模型中实现命题知识的语义推演

§ 1.　Introduction　　Artificialintelligentisbasedonknowledgeexpression ,atthesametimeitisdependedonusingknowledge .Wecangetanalysisanddecisionandforecastbyusingknowledge .Inlogicsystem ,usingknowledgemeanslogicinferenceordeduction .Now ,manylogicsystemshavebeenproposedasformalmodelsforknowledgeexpressionandreasoning [1 ] ,[2 ] ,[6]— [9] .Althoughpropositionalcalculus(P(X) )isthesimplestlogicsystem ,itprovideswithuniversalmethodforotherlogicsystems.Asweknow ,reasoninginpropositionalcalculu…     

Modified optimization layer by layer algorithm for learning multilayer perceptrons

1. IntroductionThe feedforward Multilayer Perceptron (MLP) is one of the most widely used artificial neural networks among other network models. Its field of application includes patternrecognition, identification and control of dynamic systems, system modeling and nonlinearprediction of time series, etc. [1--41 founded on its nonlinear function approximation capability. Research of this type of networks has been stimulated since the discovery andpopularization of the Backpropagation learnin…     

Void fraction prediction in two-phase flows independent of the liquid phase density changes

Gamma-ray densitometry is a frequently used non-invasive method to determine void fraction in two-phase gas liquid pipe flows. Performance of flow meters using gamma-ray attenuation depends strongly on the fluid properties. Variations of the fluid properties such as density in situations where temperature and pressure fluctuate would cause significant errors in determination of the void fraction in two-phase flows. A conventional solution overcoming such an obstacle is periodical recalibration which is a difficult task. This paper presents a method based on dual modality densitometry using Artificial Neural Network (ANN), which offers the advantage of measuring the void fraction independent of the liquid phase changes. An experimental setup was implemented to generate the required input data for training the network.ANNs were trained on the registered counts of the transmission and scattering detectors in different liquid phase densities and void fractions. Void fractions were predicted by ANNs with mean relative error of less than 0.45% in density variations range of 0.735 up to 0.98 gcm⁻³. Applying this method would improve the performance of two-phase flow meters and eliminates the necessity of periodical recalibration.     

层状压电陶瓷致动器中力电耦合场奇异性的数值分析

首先推导了不同压电材料界面裂纹尖端处的扇形区域内包含基本方程、裂纹面D-P边界条件和交界面处边界条件的弱形式。通过假设力电耦合位移场(位移和电势)与到裂纹尖端距离的(λ 1)次方成正比,可以得到一个分析压电材料裂纹尖端处力电耦合场奇异性的特殊的一维有限元列式。该一维有限元列式只需对扇形区域在角度方向上离散,最后的总体方程为一个关于λ的二次特征根方程。探讨了层状压电陶瓷致动器中可能出现奇异力电耦合场的部位的裂纹面边界条件及交界面处边界条件,进而将该一维有限元法进行推广,用于研究了这些部位的力电耦合场的奇异性。通过数值算例与相应的精确解的比较表明该方法是正确的,而且仅用很少单元就可以得到非常精确的结果。     

Electrohydrodynamic direct-writing of conductor–insulator–conductor multi-layer interconnection

A multi-layer interconnection structure is a basic component of electronic devices, and printing of the multi-layer interconnection structure is the key process in printed electronics. In this work, electrohydrodynamic direct-writing （EDW） is utilized to print the conductor-insulator--conductor multi-layer ~nterconne~ction structure. Silver ink is chosen to print the conductor pattern, and a polyvinylpyrrolidone （PVP） solution is util~zed to f~bricate the insulator layer between the bottom and top conductor patterns. The influences of EDW process parameters on the line width of the printed conductor and insulator patterns are studied systematically. The obtained ~es~l~s show that the line width of the printed structure increases with the increase of the flow rate, but decreases with the increase of applied voltage and PVP content in the solution. The average resistivity values of the bottom and top silver conductor tracks are determined to be 1.34 × 10-7 Ω.m and 1.39×10-7 Ω.m, respectively. The printed PVP layer between the two conductor tracks is well insulated, which can meet the insulation requirement of the electronic devices. This study offers an alternative, fast, and cost-effective method of fabricating conductor-insulator-conductor multi-layer interconnections in the electronic industry.