Introducing Undergraduates to the Spirit of OR whilst Imparting Substantive Skills

This paper presents analytical expressions for the moments of job flow time in a job shop by computing the moments of a random number of random variables assuming that the job shop satisfies the sufficient conditions of the Jackson decomposition principle. The mathematical equivalence of the proposed method to the Laplace transform method is shown and then demonstrated in a simple example. Then, expressions for the moments of job flow time in more realistic (and more complex) job shop settings are derived by computing the moments of a random number of random variables, provided that expressions for the moments of job flow time are available for the corresponding single stage shop. It is shown that the analytical expressions developed are exact as long as the assumptions of the Jackson decomposition principle hold. Any violation of these assumptions makes the derived expressions approximations, and their accuracy should be tested by simulation.     

Exact penalty functions method for mathematical programming problems involving invex functions

In this paper, some new results on the exact penalty function method are presented. Simple optimality characterizations are given for the differentiable nonconvex optimization problems with both inequality and equality constraints via exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable invexity assumption. Furthermore, the equivalence between a saddle point in the invex mathematical programming problem and an optimal point in its exact penalized optimization problem is also proved.     

Mathematical analysis of the Miller-Modigliani theory

This paper provides a rigorous mathematical treatment of the problem of valuation of a firm in a deterministic, partial equilibrium framework. It is shown that the dividend and arbitrage approaches to valuation are not equivalent in general. A necessary and sufficient condition for their equivalence is also obtained.     

Mathematical programs with multiobjective generalized Nash equilibrium problems in the constraints

This paper considers a class of mathematical programs that include multiobjective generalized Nash equilibrium problems in the constraints. Little research can be found in the literature although it has some interesting applications. We present a single level reformulation for this kind of problems and show their equivalence in terms of global and local minimizers. We find that the reformulation is a special case of the so-called mathematical program with equilibrium constraints which is extensively studied in the literature.     

A simple direct method to find equivalence transformations of a generalized nonlinear Schrödinger equation and a generalized KdV equation

A simple direct method is presented to find equivalence transformations of nonlinear mathematical physics equations. By using the direct method, we obtain the continuous equivalence transformations of a class of nonlinear Schröequations with variable coefficients and a family of nonlinear KdV equations with variable coefficients. For the nonlinear Schrödinger equations with variable coefficients, the equivalence transformations obtained by the direct method coincide, in nature, with those obtained via the infinitesimal Lie criterion, but our computation is much simpler.     

Application of a delta-method for random operators to testing equality of two covariance operators

In this paper some useful mathematical tools for the analysis of functional data are applied to the problem of testing the equality of two covariance operators. The test to be used is derived from a univariate likelihood ratio test in conjunction with Roy’s union-intersection principle. The asymptotic distribution and asymptotic power against rather general local alternatives are calculated. Perturbation theory of operators, in particular, a delta-method for smooth functions of operators, is exploited to obtain these theoretical results that are corroborated by some simulations.     

The shrinking principle and the axiom of choice

The axiom of choice is equivalent to the shrinking principle: every indexed cover of a set has a refinement with the same index set which is a partition. A simple and direct proof of this equivalence is given within an elementary fragment of constructive Zermelo–Fraenkel set theory. Variants of the shrinking principle are discussed, and it is related to a similar but different principle formulated by Vaught.     

The shrinking principle and the axiom of choice

The axiom of choice is equivalent to the shrinking principle: every indexed cover of a set has a refinement with the same index set which is a partition. A simple and direct proof of this equivalence is given within an elementary fragment of constructive Zermelo–Fraenkel set theory. Variants of the shrinking principle are discussed, and it is related to a similar but different principle formulated by Vaught.     

Statistical Inferences of Risk Premium under the Generalized Exponential Premium Theory

The principle of exponential premium is an important premium principle in non-life actuarial science. This paper proposes an improved exponential premium principle. This premium principle can not only include the principle of exponential premium as a special case, but also the generalizations of Esscher premium principle and net premium principle, which has many excellent properties as a premium principle. We study the maximal likelihood estimates, nonparametric estimates and Bayesian estimation of risk premium, and discuss the statistical properties including asymptotic unbiased, coincidence, and asymptotic normality. In addition, the asymptotic confidence interval for this risk premium is given. Finally, the convergence rate of maximum likelihood estimation and nonparametric estimation is compared by numerical simulation method. The results show that the nonparametric estimation has a small mean square error when the sample size is small.     

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??The principle of exponential premium is an important premium principle in non-life actuarial science. This paper proposes an improved exponential premium principle. This premium principle can not only include the principle of exponential premium as a special case, but also the generalizations of Esscher premium principle and net premium principle, which has many excellent properties as a premium principle. We study the maximal likelihood estimates, nonparametric estimates and Bayesian estimation of risk premium, and discuss the statistical properties including asymptotic unbiased, coincidence, and asymptotic normality. In addition, the asymptotic confidence interval for this risk premium is given. Finally, the convergence rate of maximum likelihood estimation and nonparametric estimation is compared by numerical simulation method. The results show that the nonparametric estimation has a small mean square error when the sample size is small.     

Banach压缩映象原理与空间完备性

本文进一步揭示了Ｂａｎａｃｈ压缩映象原理与完备性的关系，指出：一般地，Ｂａｎａｃｈ压缩映象原理等价于道路完备性，在一定条件下才等价于完备性，进一步给出了这一等价性成立的充要条件     

Graded quaternion symbol equivalence of function fields

We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group.     

On the comparison of distribution functions of random variables

We prove a rather general comparison principle for the distribution functions of random variables. As a consequence, we obtain a criterion for the equivalence in distribution in the vector sense of an arbitrary sequence of random variables to the Rademacher system; we study the applications of this principle to special cases.     

弹性动力学的等效内含物法和两椭球异质体的散射场

用Gurtin变分原理推导了一般线弹性动力学的多异质体问题的等效性方程.用“等效内含物法”求得两椭球异质体对入射弹性波的散射场和散射横截面的近似表达式,并给出了计算实例.     

A note on seemingly unrelated regression equations with residual vectors as explanatory variables

This paper demonstrates the equivalence of two SURE models. In the first, the explanatory variables of the first equation form a subset of those in the second equation. The second model is identical except that its second equation is augmented with the OLS residual vector from the first equation. There is a computational advantage in obtaining maximum likelihood estimates from the second model.     

Channel metrization

We present an algorithm that, given a channel, determines if there is a distance for it such that the maximum likelihood decoder coincides with the minimum distance decoder.We also show that any metric, up to a decoding equivalence, can be isometrically embedded into the hypercube with the Hamming metric, and thus, in terms of decoding, the Hamming metric is universal.     

Safe density ratio modeling

An important problem in logistic regression modeling is the existence of the maximum likelihood estimators. In particular, when the sample size is small, the maximum likelihood estimator of the regression parameters does not exist if the data are completely, or quasicompletely separated. Recognizing that this phenomenon has a serious impact on the fitting of the density ratio model–which is a semiparametric model whose profile empirical log-likelihood has the logistic form because of the equivalence between prospective and retrospective sampling–we suggest a linear programming methodology for examining whether the maximum likelihood estimators of the finite dimensional parameter vector of the model exist. It is shown that the methodology can be effectively utilized in the analysis of case–control gene expression data by identifying cases where the density ratio model cannot be applied. It is demonstrated that naive application of the density ratio model yields erroneous conclusions.     

线性规划的教学

作者给出了线性规划的一个更为一般的表现形式 ,明确定义了具有标准型形式的线性规划的等价变换 ,使得单纯形法的讲解更清晰简洁 ,便于学生掌握 ,且兼顾了数学形式美和逻辑美的学科特点 ;文中也体现了重视实例式教学的想法 .     

组合型扁壳的一种广义变分原理及对幕壳的应用

本文提出一个带边梁的组合型扁壳弹性动力学广义变分原理,对它与相应的基本方程、脊线条件及边界条件的等价性作了论证.然后将这一变分原理应用于幕壳结构,利用多重级数给出幕壳在常见的边界条件下的静动力学近似解析解,将本文解析解同有限元计算及试验值作了比较,结果表明我们的解析解收敛性好,精确性令人满意.     

关于二元函数非负定性的一个注记

非负定性是数学中一个重要概念,本文提出了二元函数非负定性的两个定义,并且证明了它们的等价性.此外本文还给出了严格非负定条件下实正态过程存在的一个充要条件.