摘要:

Integer linear programming is an important technique because of its potential applicability to a wide range of decision problems. Despite many algorithmic developments, the solution of integer linear programs may still carry a substantial computational cost. Recent research has made it apparent that the user of ILP software may be able to reduce this cost by paying careful attention to the formulation of the ILP model. Here we present illustrative computational results for several ILP formulations of a simple graph partitioning problem which may be useful pedagogically.

ISSN:0020-739X    

DOI:10.1080/0020739890200311

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The initial value problem y’ = x2+y2with y(0) = l is solved using both numerical and analytical methods namely (i) a fourth order Runge‐Kutta numerical scheme, (ii) the Taylor‐Maclaurin series solution, (iii) Picard's successive integration, (iv) a transformation method, and (v) an ad hoc successive approximation. It is found that both the Taylor‐Maclaurin and Picard solutions are unsatisfactory for values of x larger than a half. The transformation method shows that the solution should tend to infinity as x tends to one. This is confirmed by the ad hoc successive approximation method. The numerical scheme is found to be satisfactory even for values of x fairly close to one.

ISSN:0020-739X    

DOI:10.1080/0020739890200312

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Methods of scoring in multiple choice examinations are outlined in which the examinee's expected change in score because of random guessing must be negative for all situations of partial knowledge. Thus, it can be argued that the guessing component in multiple choice examinations can be completely removed. The examinee is instructed to tick the correct box or, if the correct box is unknown, to cross boxes known to be incorrect, or to leave the question blank. Under the proposed scoring system, it is argued that an examinee will not attempt to demonstrate more knowledge on any particular question than the examinee in fact has. Also, the examiner has quite a degree of freedom as to the size of the rewards for correctly crossed boxes; rewards which need not be equal. There is also quite a range in the possible values of the penalties for incorrect responses and appropriate recommendations are made.

ISSN:0020-739X    

DOI:10.1080/0020739890200313

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This paper formed the basis of a talk given by the author at the CTISS conference in September 1986 at the University of Kent. At the present time, a great deal of the development work of software for the interactive teaching of mathematics to honours degree students is concentrated on packages for use at first year level. The aim of this paper is to discuss the value of microcomputers in the teaching of applied mathematics at higher levels in the normal university course.

ISSN:0020-739X    

DOI:10.1080/0020739890200314

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

‘Two‐arrowheaded’ or ‘senseless’ vectors are introduced as a new kind of entity in plane. By means of heuristic transformation W that duplicates the phases in the plane of ‘senseless’ vectors, they become ordinary vectors. In this way, the set of ‘senseless’ vectors in plane acquires the structure of an Euclidean vectorial space provided with adequate operations: addition, product by scalar and. scalar product. Uniaxial magnetic anisotropies are proposed as a physical example of these singular entities.

ISSN:0020-739X    

DOI:10.1080/0020739890200315

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A general method is described of deducing the stresses induced in a semi‐infinite body by axi‐symmetric contact pressure applied over part of the boundary. The technique is illustrated by re‐evaluating the solution to the Hertz problem, and by deducing the stresses induced in a fourth‐order contacting pair.

ISSN:0020-739X    

DOI:10.1080/0020739890200316

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

After a discussion about objectivity in measurement, this paper describes some linear and logistic models for the implementation of latent trait theory. The aim is to consider those mathematical and educational issues pertinent to learning more about the topic and using those standardized tests which utilize the Rasch and similar models of assessment.

ISSN:0020-739X    

DOI:10.1080/0020739890200317

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

In this paper we describe a modular first year course which provides considerable flexibility in its content, both as a service course and as a preparation for a mathematics degree, while making efficient use of staff time. The structure of the course also makes it easily adaptable to any new requirements resulting, for example, from changes in school syllabi.

ISSN:0020-739X    

DOI:10.1080/0020739890200318

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739890200319

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor