一类线性约束凸规划的内椭球算法

1引言自从1984年Karmarkar的著名算法——梯度投影算法发表以来,由其理论上的多项式收敛性及实际计算的有效性,使得内点算法成为近十几年来优化界研究的热点（［1］）．通过中外学者的深入研究,线性规划与凸二次规划的内点算法研究已取得了不少成果（［2」、［3〕）．这些算法大致可分为四种类型：梯度投影算法、仿射尺度算法、路径跟踪法和势函数减少法吸3］、〔9〕）．近来,人们开始着手将这些方法推广到非线性规划中的凸规划问题、线性互补问题和非线性互补问题（【6」、［7」、〔sj、［10」、Ill〕）．例如：文［8」对一类凸可分规…     

基于属性识别准则大学生思想品德量化的数学模型

依据一定的社会评价标准,建立大学生思想品德评价的指标体系,利用现代数学方法——属性识别理论和层次分析方法,建立定量研究模型.     

旋转对称椭球颗粒沿轴脉冲光声波波形的几何计算

针对旋转对称椭球颗粒脉冲光声波的产生,推导沿其对称轴方向的波形的解析表达式.结果表明,无论是长椭球还是扁椭球颗粒,沿轴波形相对于球形颗粒所产生的N形波都有一定的形变,并且在近场条件下显示出能反映椭球颗粒形状与大小的明显特征.因此通过对脉冲光声波的测量和分析,能对旋转对称椭球颗粒进行形貌判定.     

Large Deviation Probabilities for Square-Gaussian Stochastic Processes

We investigate properties of square-Gaussian stochastic processes. These processes are formed by quadratic forms of Gaussian processes or by limits in the mean square of quadratic forms of Gaussian processes. Special classes of these processes are determined and investigated. For processes from these classes estimates of large deviation probability are obtained. These estimates we use to estimate the probability that Gaussian vector-valued process leave some region on some interval of time. We construct asymptotic confidence regions for estimates of covariance functions of vector-valued Gaussian processes. Criterion of hypothesis testing on covariance functions of these processes is constructed.     

Complexity of linear programming

The complexity of linear programming is discussed in the “integer” and “real number” models of computation. Even though the integer model is widely used in theoretical computer science, the real number model is more useful for estimating an algorithm's running time in actual computation.Although the ellipsoid algorithm is a polynomial-time algorithm in the integer model, we prove that it has unbounded complexity in the real number model. We conjecture that there exists no polynomial-time algorithm for the linear inequalities problem in the real number model. We also conjecture that linear inequalities are strictly harder than linear equalities in all “reasonable” models of computation.     

Second-Order Properties of a Two-Stage Fixed-Size Confidence Region for the Mean Vector of a Multivariate Normal Distribution

We consider the classical fixed-size confidence region estimation problem for the mean vectorμin theN_p(μ, Σ) population where Σ is unknown but positive definite. We writeλ₁for the largest characteristic root of Σ and assume thatλ₁is simple. Moreover, we suppose that, in many practical applications, we will often have available a numberλ*(>0) and that we can assumeλ₁>λ*. Given this addi- tional, and yet very minimal, knowledge regardingλ₁, the two-stage procedure of Chatterjee (Calcutta Statist. Assoc. Bull.8(1959a), 121–148;9(1959b), 20–28;11(1962), 144–159) is revised appropriately. The highlight in this paper involves the verification ofsecond-order propertiesassociated with such revised two-stage estimation techniques, along with the maintenance of the nominal confidence coefficient.     

太阳模拟器中椭球面聚光镜参数的确定

椭球面聚光镜是太阳模拟器设备的重要组成部分,其能量收集的效率决定着太阳模拟系统的能量传递效率,而太阳模拟器光学系统中的椭球面聚光镜参数一直没有理论上的设计依据,结合氙灯的发光特性并通过对MATLAB 中建立的椭球面聚光镜聚光过程数值分析模型给出了椭球面聚光镜包括第一焦距、最大成像放大倍率、包容角范围及前后开口直径的确定依据,并通过在Lighttools 中建立的4种仿真模型验证了理论分析的正确性。第一焦距由光源光中心高确定,最大成像放大倍率由光学积分器相对孔径及椭球镜包容角范围共同确定,椭球镜包容角范围不小于30°～120°,前开直径口由椭球镜的最大孔径角确定,后开口直径由最小孔径角和光源的径向调节量共同确定。该结论给椭球面聚光镜的设计提供了理论支撑,有利于设计完成高能量收集效率的椭球面聚光镜。     

液体中光击穿阈值的研究

从等离子体中自由电子密度速率方程出发,考虑到脉冲激光在聚焦区域的特征以及液体中光击穿的实验情况,提出了等离子体椭球模型.通过该模型的建立,对自由电子密度速率方程中电子扩散速率进行了修正,在理论上得到了光击穿的阈值.结果表明,等离子体椭球模型计算出水的击穿阈值更符合实验情况.     

氦同位素原子与钠分子碰撞转动激发积分散射截面的理论计算

多体刚性椭球模型是一种比较精确的描述氦原子与钠分子碰撞的理论模型.本文用多体刚性椭球模型计算了不同能量下He的同位素原子3He,4He,7He,10He与Na2分子碰撞的转动激发积分散射截面,表明增加椭球等势面个数可以得到更准确的转动激发积分散射截面;总结出3He,4He,7He,10He-Na2碰撞体系转动激发积分散射截面随相对入射能量和体系约化质量变化的规律;讨论了相对入射能量为100meV时,相互作用势的不同区域对4He-Na2碰撞体系转动激发积分散射截面的影响情况.     

微波效应实验最小样本量估计分析

 为规范微波效应实验最小样本量,采用区间估计的统计推断方法,开展了样本作用概率与总体作用概率对应关系的分析和研究工作,对满足一定置信度和一定总体作用概率下所需要的最小样本量进行估计。研究结果表明,实验最小样本量确定为10是较为合理的。在80％的置信度下,当10支样本量样本作用概率达到70％时,总体作用概率置信下限约为51.6％。通过该方法能够将所获取的微波效应数据通过同一指标“总体作用概率置信下限”进行有效整理。