Note on Multiple Objective Dynamic Programming

A technique for finding MINSUM and MINMAX solutions to multi-criteria decision problems, called Multi Objective Dynamic Programming, capable of handling a wide range of linear, nonlinear, deterministic and stochastic multi-criteria decision problems, is presented and illustrated. Multiple objectives are considered by defining an adjoint state space and solving a (N + 1) terminal optimisation problem. The method efficiently generates both individual (criterion) optima and multiple criteria solutions in a single pass. Sensitivity analysis on weights over the various objectives is easily performed.     

A Cautionary Note on Likelihood Ratio Tests in Mixture Models

We show that iterative methods for maximizing the likelihood in a mixture of exponentials model depend strongly on their particular implementation. Different starting strategies and stopping rules yield completely different estimators of the parameters. This is demonstrated for the likelihood ratio test of homogeneity against two-component exponential mixtures, when the test statistic is calculated by the EM algorithm.     

论假设检验中的两类错误

蔡越江．论假设检验中的两类错误．本文从假设检验的两个例子谈起,指出备择假设也是影响接区域的。接着论述了假设检验中的两类错误之间的关系。最后讨论如何同时控制两类错误。     

A Note on Ranking in the Plackett-Luce Model for Multiple Comparisons

Acta Mathematicae Applicatae Sinica, English Series - Ranking and rating individuals is a fundamental problem in multiple comparisons. One of the most well-known approaches is the Plackett-Luce...     

A Note on the Bendixson-Dulac Theorem for Refracted Systems with Multiple Zones

This note extends the Bendixson-Dulac theorem to refracted systems with multiple zones. As an application, we prove that piecewise linear Duffing-type system has neither crossing limit cycles nor sliding limit cycles Therefore, it gives a positive answer to the Conjecture of \cite{TA2007}.     

需求不确定的多周期的容量决策问题

研究每个周期的需求随机增加的情形下的容量扩充问题,建立起切合实际的有限周期随机动态规划模型及在期现值准则下的无限周期随机动态规划模型,进而探索生产单一产品的公司在面对随机增加的市场需求时,风险中立的管理者该如何扩充其生产容量,才能使得其公司在折扣意义下的总期望利润最大.研究无限阶段的容量扩充问题,得出某种约束条件下的优化策略解,给公司管理者提供了其长期可持续发展的优化策略和依据.     

A Note on Random Perturbations of a Multiple Eigenvalue of a Hermitian Operator

The problem of a random Hermitian perturbation of a multiple isolated eigenvalue of a Hermitian operator is considered. It is shown that the combined multiplicities of the perturbed eigenvalues converge in probability to the multiplicity of the eigenvalue of the target operator. Also the asymptotic distribution of a certain average of these eigenvalues, centered at the target, is obtained. As a tool differentiation of analytic functions of operators is employed in conjunction with an ensuing “delta-method”. The result is of a probabilistic rather than statistical nature.     

A Note on a Generalization of the Multiple Cover Formula and the Simple Flop

We prove a closed formula for an excess integral over the moduli space of stable maps from genus one, unmarked curves to the projective space ? ^r of degree d for any positive integers r and d. The result generalizes the multiple cover formula for ?¹. We also show that any simple ? ^r flop preserves the theory of arbitrary-genus Gromov-Witten invariants in exceptional curve classes.     

A Note on the Characterization of Optimal Allocations in OLG Models with Multiple Goods

We consider a pure exchange overlapping generations economy with a varying number of commodities and consumers per period having possibly non-complete non transitive preferences. We provide a geometric and direct proof of the Balasko-Shell characterization of Pareto optimal allocations. As a by-product, we compute an explicit Pareto improving transfer when the criterion is not satisfied, which is minimal for some suitable distance.     

多元协方差分析用于艾滋病疗法的选择

目的:优化HAART药物治疗方案,提高治疗效果,为广大患者和医生选择艾滋病的疗法提供科学的依据.方法:以CD4细胞数的增加值作为体现治疗效果的因变量,治疗时间和初始治疗CD4细胞数为协变量,通过四组疗法分组进行多元协方差分析。结果:患者治疗效果的差异主要是由于治疗方法和治疗时间以及初始治疗cd4值的差异所致;四种疗法的疗效总体上差异显著,满足完备性条件和显著性条件的疗法疗效优劣顺序是:M4>M2≈M3≈M1.结论:多元协方差分析用于艾滋病疗法的选择对实际工作有积极的指导意义.     

Paracompactness of Metric Spaces and the Axiom of Multiple Choice

The axiom of multiple choice implies that metric spaces are paracompact but the reverse implication cannot be proved in set theory without the axiom of choice.     

Generating Cuts from Surrogate Constraint Analysis for Zero-One and Multiple Choice Programming

This paper presents a new surrogate constraint analysis that givesrise to a family of strong valid inequalities calledsurrogate-knapsack (S-K) cuts. The analytical procedure presentedprovides a strong S-K cut subject to constraining the values ofselected cut coefficients, including the right-hand side. Ourapproach is applicable to both zero-one integer problems and problemshaving multiple choice (generalized upper bound) constraints. We alsodevelop a strengthening process that further tightens the S-K cutobtained via the surrogate analysis. Building on this, we develop apolynomial-time separation procedure that successfully generates anS-K cut that renders a given non-integer extreme point infeasible. Weshow how sequential lifting processes can be viewed in our framework,and demonstrate that our approach can obtain facets that are notavailable to standard lifting methods. We also provide a relatedanalysis for generating fast cuts. Finally, we presentcomputational results of the new S-K cuts for solving 0-1 integerprogramming problems. Our outcomes disclose that the new cuts arecapable of reducing the duality gap between optimal continuous andinteger feasible solutions more effectively than standard liftedcover inequalities, as used in modern codes such as the CPLEX mixed0-1 integer programming solver.     

Note on models

The first part of this note deals with the importance of the polytechnical tradition for mathematical models.¹ In the second part I discuss the question of the “semantic shift” in the mathematical usage of the word “model” (M. Epple),² that means, the passage from concrete material objects to models in the modern sense of the word – abstract entities satisfying a certain system of axioms. My aim is to provide some new information on the theme and to open a new and in my opinion essential aspect – the polytechnical tradition – to look at it. The two parts are only in a loose connection.     

一种基于决策者风险态度的区间数多指标方法的注记

本对基于决策风险态度的区间数多指标方法的映射函数的可区分性、理想点的存在性进行了论证，确保了区间数多指标决策方法的正确性，并对决策风险态度因子进行随机化，使此方法更合理，更有深度。     

Note on non-D-rings

Abstract

Recall that an integral domain R is said to be a non-D-ring if there exists a non-constant polynomial f (X) in R[X] (called a uv-polynomial) such that f (a) is a unit of R for every a in R. In this note we generalize this notion to commutative rings (that are not necessarily integral domains) as follows: for a positive integer n, we say that R is an n-non-D-ring if there exists a polynomial f of degree n in R[X] such that f (a) is a unit of R for every a in R. We then investigate the properties of this notion in di?erent contexts of commutative rings.