Assumptions and methodologies in OR

This paper argues that the subject of methodology is importnat for OR practitioners and academics. It isolates four common assumptions about OR from the normal literature of OR, and shows how they lead to identifiable methodological positions. It is argued that the future of OR depends, in part at least, on methodological debate. If it is to be successful, this debate requires some understanding of the assumptions of other people.     

Implicit perturbations

Equations of the form $\text{X}\text{(}\text{x, u}\text{; ?)}\text{du}\text{dx}\text{=}\text{U}\text{(}\text{x, u}\text{; ?)}\text{with}\text{| ? | ? 1}$ are considered to have asymptotic approximations in implicit form. This allows the dependent and independent variables to be related in non-analytic as well as analytic ways. A weakly-interacting predator-prey model containing a nodal point singularity is analyzed and the relationships of the perturbation solutions on various branches is shown.     

Implicit proof

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

Communications in Mathematics and Statistics

<正>Aims and Scope Communications in Mathematics and Statistics(Commun Math Stat)is an international journal published by Springcr-Veriag in collaboration with the School of Mathematical Sciences in University of Science and Technology of China(USTC).The journal is committed to publish high level original research papers in various areas of mathematical sciences,including pure mathematics,applied mathematics,     

Communications in Mathematics and Statistics

Aims and Scope Communications in Mathenatics and Statistics (Commun Math Stat) is an international journal published by Springer-Verlag in collaboration with the School of Mathenatics and Sciences in University of Sciences and Technology of China     

Communications in Mathematics and Statistics

<正>ISSN:2194-6701(print version)ISSN:2194-671X(electronic version)Aims and Scope Communications in Mathematics and Statistics(Commun Math Stat)is an international journal published by Springer-Vcrlag in collaboration with the School of Mathematical Sciences in University of Science and Technology of China(USTC).The journal is committed to publish high level original research papers in various     

Communications in Mathematics and Statistics

<正>ISSN:2194-6701(print version)ISSN:2194-671X(electronic version)Aims and Scope Communications in Mathematics and Statistics(Commun Math Stat)is an international journal published by Springer-Vcrlag in collaboration with the School of Mathematical Sciences in University of Science and Technology of China(USTC).The journal is committed to publish high level original research papers in various areas of mathematical sciences,including pure mathematics,applied mathematics,computational mathematics,and probability and statistics.Typically one volume is published each year,and each volume consists of four issues.     

Communications in Mathematics and Statistics

<正>ISSN:2194-6701(print version)ISSN:2194-671X(electronic version)Aims and Scope Communications in Mathematics and Statistics(Commun Math Stat)is an international journal published by Springer-Verlag in collaboration with the School of Mathematical Sciences in University of Science and Technology of China(USTC).     

Implicit functionals and eigenvalue problems

An approach to nonlinear, positively homogeneous eigenvalue problems based on the use of the spectral parameter as a functional of Euler type is suggested. It allows one to present the spectral-parameter domain as a bifurcation diagram of the problem. Fučik spectrum problems (classical and for p-Laplacians) and the problem with a nonlinear dependence of the weight function on the spectral parameter are considered. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 169–186, 2005.     

Lightenings of Assumptions for Pontryagin Principles in Infinite Horizon and Discrete Time

In the infinite-horizon and discrete-time framework, we establish maximum principles of Pontryagin under assumptions, which are weaker than those of existing results. We avoid several assumptions of continuity and of Fréchet differentiability and of linear independence.     

Implicit Convex Polygons

Convex polygons in the plane can be defined explicitly as an ordered list of vertices, or given implicitly, for example by a list of linear constraints. The latter representation has been considered in several fields such as facility location, robotics and computer graphics. In this paper, we investigate many fundamental geometric problems for implicitly represented polygons and give simple and fast algorithms that are easy to implement. We uncover an interesting partition of the problems into two classes: those that exhibit an (nlogn) lower bound on their complexity, and those that yield O(n) time algorithms via prune-and-search methods.     

Analysis of Simulation Experiments Under Normality Assumptions

The use of control variables in computer simulations to improve the performance of estimators of model parameters is widely advocated. The technique that usually seems to be suggested is a distribution free approach based on least squares. In this note it is suggested that, frequently, normality assumptions apply which allow a more detailed, as well as simpler, statistical analysis. It is also pointed out that though the analysis is similar in many ways to an ordinary regression analysis, there are certain important differences, especially when variances are to be estimated.     

Statistics and schools

This paper considers the place of statistics in school, putting forward the view that it should be seen as an interdisciplinary subject, relevant to all pupils, rather than solely as a separate specialism for a minority of children.     

Implicit Multifunction Theorems

We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest.     

Introducing Young Children to the Role of Assumptions in Proving

The notion of assumptions permeates school mathematics, but instruction tends to highlight this notion only in the advanced grades. In this article, I argue that it is important for even young children to develop a sense of the role of assumptions in proving, and I investigate what it might mean and look like for instruction to promote this goal. Toward this end, I study an episode from third grade that describes the first time that the students in the class were introduced in a deliberate and explicit way to the role of assumptions in proving. The central role of the mathematical task in the episode is identified, and features of mathematical tasks that can generate rich mathematical activity in the intersection of assumptions and proving are discussed. In addition, issues of the role of teachers in fostering productive interactions between students and mathematical tasks that have those features are considered.