摘要:

Rayleigh and Buckingham's methods of dimensional analysis are reviewed and formulated in terms of matrices. The authors suggest that this formulation is easier to use in complex problems with a large number of variables.

ISSN:0020-739X    

DOI:10.1080/0020739830140401

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The purpose of this article is to motivate the study of permutation groups by discussing card shuffles on a deck of cards.

ISSN:0020-739X    

DOI:10.1080/0020739830140402

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A case is made for restoring the idea of proof to a fundamental position in school mathematics, thereby giving a truer picture of what mathematics is really about, and closing the gap which exists between sixth form and early undergraduate versions of the subject.

ISSN:0020-739X    

DOI:10.1080/0020739830140403

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Euler's criterion is the usual procedure used for assessing the solvability of the equation x2= b(mod m). This criterion is applicable only when b and m are relatively prime and must be applied to each b (0≤ b < m). Described in this paper is an alternative criterion which characterizes and counts, for a general modulus m, all numbers b for which x2= b(mod m) is solvable.

ISSN:0020-739X    

DOI:10.1080/0020739830140404

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The simplicity of the BASIC interpreter, available to desk‐top computers, has afforded instructors of all disciplines in schools and colleges the opportunity to write useful demonstration programs. For those programs which demand changing function statements, it is usually necessary to edit these statements between runs. The algorithms here outlined provide for the input of functions as strings at run‐time, and demand only simple programming techniques without recourse to sophisticated software.

ISSN:0020-739X    

DOI:10.1080/0020739830140405

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The interpretation as well as derivation of the multi‐dimensional wave functions for spherically symmetric potentials is an uphill task in quantum mechanics. The wave functions for spherical harmonics are obtained in the context of hydrogen‐like atoms using the theory of Green's functions. The process of obtaining the Green's functions is new and is being reported for the first time. The process elucidates all the relevant features whatsoever required by the system. One of the salient features of the technique used is that it reduces all the hierarchies and higher‐order Green's functions to Green's functions of the lowest order.

ISSN:0020-739X    

DOI:10.1080/0020739830140406

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Repeated integration by parts is used as a matter of course by sixth‐form and undergraduate students. Here the final result from such a process is given together with analysis of its two most common applications.

ISSN:0020-739X    

DOI:10.1080/0020739830140407

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The derivation of Maximum Likelihood estimators for highly correlated probability density functions is treated abstractly in advanced texts in statistics. Stripped of its mathematical complexity, we illustrate here a simple and useful Maximum Likelihood procedure for estimating the statistical parameters associated with a correlated multivariate normal distribution. We first convert a correlated real continuous stationary stochastic series of finite length into an equally spaced discrete set of n random variables. On the assumption (1) that the points of the set are jointly normally distributed each having the same mean and variance and (2) that the correlation between the set members can adequately be described by an exponentially decaying function of the absolute distance between them, the coupled nonlinear system of algebraic equations for the estimation of the mean, variance and correlation parameter are derived using the Maximum Likelihood algorithm. In the limit, when the correlation parameter approaches zero (i.e., statistical independence), the solution of the system reduces to the well known result that the estimators of the mean and variance are respectively the sample mean and sample variance.

ISSN:0020-739X    

DOI:10.1080/0020739830140408

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739830140409

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

In this paper a number of interesting results are defined and explained that are related to the notions of piecewise congruence by addition or subtraction. Two polygons are piecewise congruent by addition if either polygon can be cut into a finite number of polygonal pieces that can be rearranged to cover the other polygon.

ISSN:0020-739X    

DOI:10.1080/0020739830140410

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor