摘要:

This paper consists of two parts, the first of which appeared in the previous issue of the journal. It deals with some of the many aspects of modelling physical systems in terms of differential equations (DE), ordinary and partial. Among the issues touched upon are (a) the important role played by the assumptions underlying a DE based mathematical model (Part I), and (b) the interplay between modelling and simulation when using differential equation models (Part II). In a more philosophical vein, there is a section on determinism as well as one on model validation; while fairly general in scope, the concepts examined therein are introduced in direct relation to DE models.

ISSN:0020-739X    

DOI:10.1080/0020739890200601

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The paper outlines a method for introducing undergraduates (especially computer science majors) to abstract Boolean algebra and to the process of mathematical abstraction itself. The method is based on the use of a common hardware representation (the bit vector representation) for sets and truth tables as a pedagogical device to motivate the study of partially ordered sets, lattices, and Boolean algebras.

ISSN:0020-739X    

DOI:10.1080/0020739890200602

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The necessary and sufficient conditions for a set of points to form a rotatable design of order four have been given by Patel and Arap Koske [1], In this paper, a set of 98 points for three factors which satisfies these conditions is given.

ISSN:0020-739X    

DOI:10.1080/0020739890200603

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The methods for the anlaysis of simple electrical circuits and of structural trusses can be based on matrix formulations. These are derived from the graph theoretical structure of the inter‐connectivity of the components involved and results about the inter‐relationships of the associated physical parameters. This paper looks at the analogies between the two situations and shows that with a good choice of notation the matrix formulations are identical. These ideas can be used in a teaching environment to illustrate that widely different engineering applications are susceptible of similar means of analysis and produce analogous mathematical models.

ISSN:0020-739X    

DOI:10.1080/0020739890200604

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This paper is an overview of the classic travelling salesman problem, and selected algorithms and heuristics that solve the problem. Four algorithms or heuristics are presented. They were chosen because of their diverse modes of attack and their implications for efficiency. Two of the algorithms are exact: an exhaustive approach and a dynamic programming approach. The other two are heuristics (approximate algorithms): the nearest neighbour approach and the nearest addition approach. The nearest insertion algorithm, which is similar to the nearest addition algorithm, is also discussed. Examples are given for each algorithm, and its worst case behaviour is analysed. Finally, there is discussion of guaranteed bounds on the costs of tours produced by the heuristics.

ISSN:0020-739X    

DOI:10.1080/0020739890200605

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Because of their graphics capabilities, it is possible to use personal computers to analyse the behaviour of dynamical systems. We therefore require a way to introduce pedagogically both this technique and the important aspects of the study of non‐linear systems. This paper considers first the formal points of the phase plane method, and then presents three relevant examples: (a) second order linear systems; (b) the Van der Pol oscillator; and (c) the forced pendulum. In each case programs in Turbo‐Pascal are given for plotting the trajectories.

ISSN:0020-739X    

DOI:10.1080/0020739890200606

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Middle school dropouts and stayins were compared on mathematical creativity, some personality and biographical factors. Verbal and non‐verbal mathematical creativity tests, a Hindi adaptation of the Thorndike dimensions of temperament test and a biographical inventory were used on 70 dropouts and 100 stayins male students, aged 11+ to 13+ years, randomly selected, from Sultanpur District, India. The results showed that: (1) mathematical creativity of dropouts was found to be lower than stayins; (2) dropouts were found to be sociable, accepting, reflective, lethargic and casual in nature whereas stayins were found to be solitary, critical, practical, premeditated, active and responsible in nature; and (3) the level of family income, professional background of the family, parents’ education, standard of living, interest‐patterns, attitude and level of aspiration of the stayins were found to be higher than of the dropouts.

ISSN:0020-739X    

DOI:10.1080/0020739890200607

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Various methods of fitting angular distributions of y‐rays, resulting from neutron inelastic scattering, have been introduced and discussed. Sample cases are calculated and different methods are compared. The comparison is instructive and gives deep insight to those various methods.

ISSN:0020-739X    

DOI:10.1080/0020739890200608

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

If A, B are linear operators on a finite‐dimensional space it is known that AB and BA have the same characteristic polynomial. We show that this result can be proved very simply by the use of exterior algebra.

ISSN:0020-739X    

DOI:10.1080/0020739890200609

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Some of the misconceptions in the minds of calculus students are due to faulty arguments used by teachers and authors of textbooks. An incoherent presentation of certain topics is almost universal in introductory calculus texts.

ISSN:0020-739X    

DOI:10.1080/0020739890200610

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor