摘要:

The theory of probability is viewed from the perspective of the Greek developers of Euclidean geometry. It is observed that much of probability theory was accessible to the Greeks, but that the concept of independence might have been a troublesome one. Analogies are drawn between the difficulties posed by parallelism and independence in the formal development of geometry and probability.

ISSN:0020-739X    

DOI:10.1080/0020739890200301

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

With the use of two non‐dimensional parameters, it is shown how a variable computational mesh may be obtained in a methodological and simple manner. The mesh refinement is achieved by means of an arithmetic or geometric progression of mesh spacings once their number and ultimate (non‐dimensional) thickness are specified.

ISSN:0020-739X    

DOI:10.1080/0020739890200302

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We consider the problem of finding those points of a certain subset A of Rn for which a real function defined on A cannot have two different differentials. Our approach is elementary and can be part of a rigorous course in advanced calculus, thus helping the understanding of the concept of the differential at a point.

ISSN:0020-739X    

DOI:10.1080/0020739890200303

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This paper is derived from lecture notes from a course in ‘object oriented programming’. They formed part of the section comparing and contrasting Smalltalk with FP systems. The work is an extension of separate published work by Knuth [1] and Turner [2]. Three types of series are considered: (a) binomial series; (b) exponential series; and (c) recurring fractions.

ISSN:0020-739X    

DOI:10.1080/0020739890200304

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Computer graphics may support the understanding of statistical inference. This paper presents examples of problems whose solutions are most easily achieved through analysis of computer graphics showing the results of repeated simulations. The quality of estimators and the risk related to statistical decision‐making is made obvious through the use of such graphics.

ISSN:0020-739X    

DOI:10.1080/0020739890200305

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Euclidean geometry is axiomatic in classical mechanics. In our paper, we have reversed the traditional roles of geometry and mechanics to obtain elegant results in Euclidean geometry.

ISSN:0020-739X    

DOI:10.1080/0020739890200306

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The ideas behind this paper were generated as a result of the problems encountered by an HND Engineering student at Trent Polytechnic. The student was studying on the second year of a Production Engineering course, a course which contains only very little formal mathematics. He had been given by a member of the Production Engineering staff a mini‐project on a real computer‐controlled drilling machine, and unfortunately the engineer who had given the project did not appreciate the problems the student would have. The project required the writing and verifying of a program which would move the drilling‐bit along a two dimensional curve which was defined by a few points only.

ISSN:0020-739X    

DOI:10.1080/0020739890200307

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Peters [1] discussed some theoretical aspects of the ‘ringing’ sound associated with barbershop quartet singing. These combination tones were first investigated theoretically by Helmholtz [2] who showed that the transient displacement of the ear membrane is governed by the anharmonic motion equation. Rayleigh [3] modelled the situation as an initial value problem and this is now referred to as the Rayleigh problem. Following [1] there has been a renewed interest in the problem (see [4‐8]). The intention of the present paper is to:alfaillustrate the qualitative behaviour of the solutions of the Rayleigh problem by a phase plane analysis;alfadescribe how the method of multiple scales provides a framework within which previous analyses can be seen;alfadescribe an improvement to the method of multiple scales, which may also prove useful in other applications.

ISSN:0020-739X    

DOI:10.1080/0020739890200308

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

In many areas of research and development the final product is assessed by means of a panel response. This response will only be meaningful when it is supported by a strong consensus within the panel. At present there does not appear to be a simple standard definition of consensus measure. This paper suggests a definition based on the interquartile range of the panel response and structured in such a way as to permit the resulting measure to be subjected to the conventional statistical procedures of estimation and hypothesis testing by utilizing Snedecor's F distribution.

ISSN:0020-739X    

DOI:10.1080/0020739890200309

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We present an algebraic technique for solving integral equations. This technique is based on first differentiating both sides of the integral equation n times and then substituting the Taylor series for the unknown function in the resulting equation. This results in a linear algebraic system which can be solved approximately by a suitable truncation scheme. An interesting feature of this method is that we get exact solutions in many cases. We present four simple examples to illustrate this feature.

ISSN:0020-739X    

DOI:10.1080/0020739890200310

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor