关于三角形旁切圆半径的一个有趣性质

文[1]曾老师给出了三角形中关于角平分线的一个优美不等式,即定理1 a,b,c是△ABC的三边,wa,wb,wc为△ABC的角平分线,那么有1/(wa4)+1/(wb4)+1/(wc4)≥1/(a4+b4+c4) (1)文[2]安老师把不等式(1)加强为定理2 a,b,c是△ABC的三边,ma,mb,mc为△ABC的中线,那么有1/(ma4)+1/(mb4)+1/(mc4)≥16/(a4+b4+c4) (2)经笔者探究发现三角形旁切圆半径也有以上有趣性质.     

动态调整出水温度的高效制冷方法研究

通过数学方法较为精确地建立了吸收式制冷机需满足负荷要求的数学模型,确立了蒸发器冷冻水出口温度与室外温度之间的关系式。进而建立了吸收式出水温度控制系统的动态特性模型,并采用并联程序法对水温控制系统进行仿真。     

面向客户需求的企业集群知识传播模型与仿真

本文从市场中客户对企业提出的各种需求出发,建立了一个面向客户需求的知识传播网络,并通过计算机仿真模拟了企业集群在此网络中的知识传播过程,考察了集群的平均知识水平和知识方差在传播过程中的动态变化。通过仿真发现:随着时间的推移和对客户需求的满足,集群的平均知识水平呈单调递增趋势,知识传播效率呈现先增后减规律;集群知识方差在传播前期会出现剧烈震荡现象,而后期则会逐渐收敛;此外本文对市场规模以及知识维度对知识水平的影响也做了简单的考察,发现小规模市场有利于企业集群的初期发展,而过高或过低的知识维度都不利于企业集群平均知识水平的提高。     

Integral Self-affiine Tiles of Bandt＇s Model

Integral self-affine tiling of Bandt＇s model is a generalization of the integral self-affine tiling. Using ergodic theory, we show that the Lebesgue measure of the tile is a rational number where the denominator equals to the order of the associate symmetry group. We apply the result to the study of the Levy Dragon.     

ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.     

NODAL O（h^4）-SUPERCONVERGENCE IN 3D BY AVERAGING PIECEWISE LINEAR,BILINEAR, AND TRILINEAR FE APPROXIMATIONS

We construct and analyse a nodal O（h^4）-superconvergent FE scheme for approximating the Poisson equation with homogeneous boundary conditions in three-dimensional domains by means of piecewise trilinear functions. The scheme is based on averaging the equations that arise from FE approximations on uniform cubic, tetrahedral, and prismatic partitions. This approach presents a three-dimensional generalization of a two-dimensional averaging of linear and bilinear elements which also exhibits nodal O（h^4）-superconvergence （ultracon- vergence）. The obtained superconvergence result is illustrated by two numerical examples.     

物价、利率与收入对居民消费需求影响研究——基于时变参数状态空间模型

运用时变参数状态空间模型对我国改革开放三十年来物价、利率与收入对农村和城镇居民消费需求影响的动态特征进行了研究。发现物价、收入对农村和城镇居民的消费需求弹性不同,农村消费需求受收入影响较大,而城市居民消费需求受物价影响较大;利率对农村和城镇居民消费需求影响不显著,利率机制目前还不是调解中国消费需求的理想工具。在此基础上给出了相应的政策建议。     

Double-image sharing encryption based on associated fractional Fourier transform and gyrator transform

<正>We present a novel method for realizing double-image encryption algorithm by combining the images in different transform domains.Two original images are encrypted into two interim images by fractional Fourier transform and gyrator transform,respectively.The two encrypted images can be obtained by means of the addition and subtraction of the two interim images.This is defined as a double-image sharing scheme,in which the original images are encrypted into two parts.The original images cannot be recovered only with any one of the two interim images.Numerical simulation experiments demonstrate the validity of the algorithm.     

The simulation of ultrasonic beams with a Gaussian beam equivalent point source model

Point Sources and Gaussian beams are used frequently as fundamental building blocks for developing ultrasonic beam models. Both these models have different weaknesses that limit their effectiveness. Here, we will show that one can develop a Gaussian Beam Equivalent Point Source （GBEPS） model that removes those weaknesses and combines the accuracy and versatility of the point source models with much of the speed and well-behaved nature of Gaussian beam models. We will demonstrate the efficiency and versatility of this new GBEPS model in simulating the beams generated from ultrasonic phased arrays, using as few as one Gaussian beam per element of the array. A single element GBEPS model will be shown to be as accurate as a point source model even when substantial beam focusing or steering is present in the array or where the array beam is transmitted through an interface. At the same time the GBEPS model will be shown to be several orders of magnitude faster than the point source model.     

基于Bootstrap-DEA的工业能源效率分析

传统DEA方法存在小样本估计有偏、无法进行统计检验等缺点.而Bootstrap-DEA方法能够通过数值模拟技术产生大量的模拟样本,通过对新生成的样本进行估计来修正DEA效率估计偏差,进而计算出效率值的置信区间.作者利用Bootstrap-DEA方法首次对我国36个工业行业1995-2008年的能源利用效率进行分析.研究结果表明,我国工业行业的能源效率呈现出U字型变动趋势,行业间的能源效率差异不断减小.