摘要:

This paper considers a deterministic model in the theory of contagious disease. The major assumption made is that all infected individuals remain in the population to spread the disease. For this particular case an exact solution can be obtained for the differential equation arising from the mathematical model. However, a more generally useful numerical method using the Runge ‐‐ Kutta ‐‐ Fehlberg algorithm is applied and is found to give highly accurate results. This work could well form the basis of useful mathematical modelling projects in the classroom.

ISSN:0020-739X    

DOI:10.1080/0020739950260501

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In this presentation, we attempt further investigation into the interval of uncertainty #opIu#cp on the particular integral for a geophysical problem of the form:

ISSN:0020-739X    

DOI:10.1080/0020739950260502

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We consider the problem of determining the periodicity of a binary sequence, a problem of some importance in cryptography. A program for the solution of this problem is specified using a functional notation. Results on the likely period of a random binary sequence are developed. We discuss the benefits of using a functional specification both for the case study and in general.

ISSN:0020-739X    

DOI:10.1080/0020739950260503

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The construction of polynomials with maximum turning points lower than minimum turning points is investigated. As well as providing cautionary examples for students, the solution requires the application of quadratic inequalities and could provide an interesting topic for coursework at A level. The problem also provides an opportunity for practice in the use of graph plotting software.

ISSN:0020-739X    

DOI:10.1080/0020739950260504

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

This paper is concerned with solving a problem from the literature, namely to solve non‐linear systems of equations involving non‐negative variables. Based on previously published computer programs, the complete computer program listed here incorporates an additional way of moving from a current point to another point. A larger variety of moves for leaving a current point for another point results in an algorithm suitable for more problems. This additional move is due to specification in the listed computer program that a variable's new value is equal to its current value plus or minus a varying proper fraction of one per cent of the current value. The computational results presented here are comparable to those presented in a substantial article published in 1986, which are repeated here for convenient comparisons. The new results suggest that the listed computer program can be used as a model to obtain solutions to the problem.

ISSN:0020-739X    

DOI:10.1080/0020739950260505

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In the past decade there have been significant developments in computer technology and solution techniques for analysing business and industrial decision problems. In recent years good modelling systems have become available to ease the burden of model communication. Currently the single most important barrier to increased use of structured approaches to decision modelling is the acquisition of the necessary skills to initially develop models of complex decision systems. This paper examines the modelling process with reference to linear programming. Two related production planning problems are presented and their associated models developed. The relationship between the two problems is such that student modellers are forced to become involved in the important details of the problems and, by examining the nature of solution spaces in constrained optimisation, students are able to rapidly gain confidence and skills in modelling.

ISSN:0020-739X    

DOI:10.1080/0020739950260506

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We criticize the traditional way of defining a matrix as being an array of elements #opwhich satisfies certain definitions of addition and multiplication#cp: this way, we argue, involves conceptual difficulties. We introduce a method of presenting matrices which avoids these difficulties.

ISSN:0020-739X    

DOI:10.1080/0020739950260507

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Genetic algorithms and their hybrids are increasingly being applied to produce near‐optimal solutions to difficult optimization problems. Simple genetic algorithms encode a problem's parameters using concatentated, fixed‐length, unsigned‐integer bit‐strings, but the precision obtainable using this coding scheme is inherently limited. For this reason, genetic algorithms which employ real‐valued parameters are of interest. A new hybrid algorithm is described which improves obtainable precision by combining a simple genetic algorithm with a systematic reduction of the search region, real‐valued parameter encodings, and redefined genetic operators. The resulting multistage genetic algorithm is used to obtain approximate solutions to a pair of 20‐segment brachistochrone problems. The results obtained using this new algorithm are compared to those obtained using a multistage Monte Carlo method.

ISSN:0020-739X    

DOI:10.1080/0020739950260508

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

There are three main aspects in mathematical problem solving, especially when the problem includes a real situation: #opa#cp formulating the problem in mathematical terms; #opb#cp operating within the mathematical world; #opc#cp translating the mathematical results into the original situation. In research on problem solving, researchers’ attentions have been mainly paid to the first aspect #opa#cp, and the third aspect #opc#cp has not been deliberated. The purpose of this paper is making this aspect clearer by applying the theory of mathematical modelling to problem solving. Taking problem solving as a kind of mathematical modelling, the mathematical results can be seen as a basis for forecasts, decisions, or actions, and the third aspect of problem solving can be seen as the process in which solvers would make forecasts or decisions and take an action on the problem situation. The example, the case of augmented‐quotient division problems, is presented to illustrate this aspect in detail, and it shows the advantage of the analysis in this paper.

ISSN:0020-739X    

DOI:10.1080/0020739950260509

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We present an interesting new procedure for computing the mean first passage times #opMFPTs#cp in an irreducible,N#pl1 state Markov chain. To compute the MFPTs to a given state we embed the submatrix of transition probabilities for theNremaining states in an augmented matrix. We perform successive repetitions of matrix reduction to reduce the augmented matrix to a column vector ofNelements which represent the MFPTs. The new procedure has a higher operation count than Gaussian elimination. We use matrix reduction to solve a numerical example problem for the MFPTs in a four‐state Markov chain.

ISSN:0020-739X    

DOI:10.1080/0020739950260510

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor