摘要:

The problems of validation of an input‐output model for forecasting the effects of clothing imports on the textile and other industries in the Australian economy are described. These relate to incomplete data requiring estimators to complete a fundamental matrix and allowance for technological change from one previous time period to another. Although reasonable reconciliation was achieved between computed results and industry observations and data over the most recent historical periods for which data is available, the use of the method for forecasting requires allowance to be made for the inclusion of forecasted technological changes via endogenous variables or other means. The method described for the Australian study throws light on some important economic issues which required qualification during the period used for validation. It is operated on a desk top computer.

ISSN:0020-739X    

DOI:10.1080/0020739820130601

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

A simple, well‐known, model of ferromagnetic materials which accounts for the transition, at the Curie temperature, between paramagnetic behaviour and spontaneous magnetization is presented. As the same equations can reasonably describe certain properties of an economic system, it is suggested that a magnet may be a working model of the economy. The magnetic model, which incorporates the process of symmetry breaking, accounts for the transition from a simple market economy to the oligopolistic stage and suggests that government intervention is needed to achieve economic coordination between different sectors of the economy.

ISSN:0020-739X    

DOI:10.1080/0020739820130602

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

This paper develops the solution of a ‘real’ problem which involves simple numerical techniques. The numerical solution is interesting because of possible divergence and round‐off error growth. The problem makes an ideal case study for undergraduates following a course in numerical mathematics.

ISSN:0020-739X    

DOI:10.1080/0020739820130603

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The Entropy‐Maximization Principle has been examined from both the statistical‐mechanics and information‐theoretic points of view and has been applied to obtain solutions for some population‐density and transportation models. For the former, the well‐known negative exponential and quadratic gamma distributions have been obtained and the problem of simultaneous determination of population density and rent has been solved. The transportation models considered include production‐constrained model, attraction‐constrained model, production‐attraction‐constrained model, a model for transportation by different modes, and models for transportation via intermediate points. Both continuous and discrete models are considered. In the usual models, entropy is maximized subject to cost of travel being fixed and known. This cost is however not known so the models are conceptually weak. Here a new point of view is given drawing its inspiration from optimal portfolio selection theory and Pareto optimality. An attempt at maximizing the entropy and minimizing the cost is made to obtain a cost‐efficient entropy‐maximizing function. Some interesting results are obtained for both types of models and the existing models are reestablished on a logically sounder foundation.

ISSN:0020-739X    

DOI:10.1080/0020739820130604

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739820130605

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

This article is intended to aid mathematicians involved in designing and/or teaching courses involving mathematical modelling. It consists of a description of a methodology for model formulation which is well suited to classroom use, followed by a critique of current methods of including modelling in the curriculum with suggestions for alternate methods.

ISSN:0020-739X    

DOI:10.1080/0020739820130606

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

In this article the authors describe their course in mathematical modelling, and give a list of major do's and don'ts. They stress the difference between models and modelling and show how modelling examples can be introduced into existing undergraduate courses.

ISSN:0020-739X    

DOI:10.1080/0020739820130607

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The development of an undergraduate mathematical modelling course currently in its fifth iteration at the United States Military Academy is described. The principal purpose of the course designed for sophomores is to provide students the opportunity to practice model construction in an artistic fashion while demonstrating the utility and universality of elementary mathematics. The resolution of issues such as the determination of course prerequisites, choice of model construction or model selection, number and type of student projects, choice of disciplines in which to model, instructor preparation, text selection and development of supporting textual materials is discussed. After a detailed description of the course, the authors discuss lessons learned and evaluate the course.

ISSN:0020-739X    

DOI:10.1080/0020739820130608

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The motivation for developing some easy‐to‐use interactive simulation packages is described. The underlying development philosophy for the software is also highlighted together with brief outlines of the structure of the packages. Some informal conclusions on the utility of the packages in courses on mathematical modelling are summarized.

ISSN:0020-739X    

DOI:10.1080/0020739820130609

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

After a theoretical discussion of the necessity and possibilities for mathematical modelling qualifications, an experiment to teach these qualifications is presented. The aim of the experiment was to confront graduate mathematics students with a realistic working situation which is similar to the expected professional praxis. The basic principles of the concept presented are:arabicThe starting point is a real problem which should be presented to the students by representatives of a company where the problem has come up.arabicThe problem should already be solved in practice to get criteria for the success of the mathematical model to be built by the students.arabicThe existing solution should be known neither to the teachers nor to the students.

ISSN:0020-739X    

DOI:10.1080/0020739820130610

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor