David C. Blest

University of Tasmania

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Tariq Jamil

Nishtar Medical College and Hospital

Ahmad Kamal Zulkifle

University of Strathclyde

B. R. Duffy

University of Strathclyde

S. McKee

University of Strathclyde

Tariq Jamil

Sultan Qaboos University

B. L. Robinson

University of Edinburgh

M. F. Tomé

Universidade de São Paulo

S. McKee

University of Strathclyde

P. Marshall

Washington State University Vancouver

Amer H. Alhabsi

Sultan Qaboos University

Cooperative Institutions

University of Strathclyde

University of Tasmania

University of Oxford

Sultan Qaboos University

Florida Institute of Technology

Unilever (United Kingdom)

Manchester College

Mehran University of Engineering and Technology

University of Edinburgh

Launceston General Hospital

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Two studies in process modelling: injection moulding and resin film infusion

IMA Journal of Management Mathematics (1996)

David C. Blest B. R. Duffy S. McKee M. F. Tomé

This paper discusses two problems from important areas of process modelling, namely injection moulding and resin film infusion. The first comes from the food-processing sector, and involves the filling of tubs with liquid foodstuffs. The approach taken here is computational, with the foodstuffs modelled as incompressible viscous (Newtonian or non-Newtonian) fluids. In practice, the liquids have multiple free surfaces; the correct treatment of these surfaces is a crucial element of the modelling herein. Resin film infusion is one of the preferred processes for the manufacture of composite materials. In essence it involves squeezing a viscous incompressible fluid into a woven carbon-fibre matrix. With the matrix treated as a porous medium, and with exothermic reactions (and consequent thermal effects) neglected, simple analytical results are obtainable which can be verified by straightforward engineering experiments.

Exothermic reaction

Injection moulding

Matrix (chemical analysis)

10.1093/imaman/7.1.23

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84.58 Optimising sums of cubes of integer differences

The Mathematical Gazette (2000)

David C. Blest

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

Content (measure theory)

10.2307/3620788

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Division in a binary representation for complex numbers

International Journal of Mathematical Education in Science and Technology (2003)

David C. Blest Tariq Jamil

Computer operations involving complex numbers, essential in such applications as Fourier transforms or image processing, are normally performed in a 'divide-and-conquer' approach dealing separately with real and imaginary parts. A number of proposals have treated complex numbers as a single unit but all have foundered on the problem of the division process without which it is impossible to carry out all but the most basic arithmetic. This paper resurrects an early proposal to express complex numbers in a single 'binary' representation, reviews basic complex arithmetic and is able to provide a fail-safe procedure for obtaining the quotient of two complex numbers expressed in the representation. Thus, while an outstanding problem is solved, recourse is made only to readily accessible methods. A variety of extensions to the work requiring similar basic techniques are also identified. An interesting side-line is the occurrence of fractal structures, and the power of the 'binary' representation in analysing the structure is briefly discussed.

Representation

Binary operation

Carry (investment)

10.1080/0020739031000108592

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Citations (9)

Towards Formulation of a Complex Binary Number System

Maǧallaẗ ǧāmiʿaẗ al-Sulṭān Qābūs li-l-ʿulūm/Sultan Qaboos University journal for science (2002)

Tariq Jamil David C. Blest Amer H. Alhabsi

For years complex numbers have been treated as distant relatives of real numbers despite their widespread applications in the fields of electrical and computer engineering. These days computer operations involving complex numbers are most commonly performed by applying divide-and-conquer technique whereby each complex number is separated into its real and imaginary parts, operations are carried out on each group of real and imaginary components, and then the final result of the operation is obtained by accumulating the individual results of the real and imaginary components. This technique forsakes the advantages of using complex numbers in computer arithmetic and there exists a need, at least for some problems, to treat a complex number as one unit and to carry out all operations in this form. In this paper, we have analyzed and proposed a (–1–j)-base binary number system for complex numbers. We have discussed the arithmetic operations of two such binary numbers and outlined work which is currently underway in this area of computer arithmetic.

Base (topology)

Real number

Carry (investment)

The Imaginary

10.24200/squjs.vol7iss1pp199-209

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Lower Bounds for Athletic Performance

Journal of the Royal Statistical Society Series D (The Statistician) (1996)

David C. Blest

This paper analyses a set of world records in athletic running events to extract long-term bounds for those events. The approach adopted is to identify a single parameter to represent the achieved standard of athletic performance at a series of fixed intervals. The long-term behaviour of this single parameter is then investigated by fitting a variety of non-linear models and restrictions on the accuracy of the fits are discussed. The paper concludes with a range of estimates for each of the events considered in the original data set.

10.2307/2988413

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Citations (34)

Theory & Methods: Rank Correlation — an Alternative Measure

Australian & New Zealand Journal of Statistics (2000)

David C. Blest

Within the bounds of a general theory of rank correlation two particular measures have been adopted widely: Spearman7apos;s rank correlation coefficient, ρ in which ranks replace variates in Pearson's product‐moment correlation calculation; and Kendall's τ in which the disarray of x ‐ordered data due to a y ‐ordering is measured by counting the minimum number, s ; of transpositions (interchanges between adjacent ranks) of the y ‐ordering sufficient to recover the x‐ordering. Based on insights from the calculation of Kendall's coefficient, this paper develops a graphical approach which leads to a new rank correlation coefficient akin to that of Spearman. This measure appears to stand outside general theorybut has greater power of discrimination amongst differing reorderings of the data whilst simultaneously being strongly correlated with both ρ and τ. The development is focused on situations where agreement over ordering is more important for top place getters than for those lower down the order as, for example, in subjectively judged Olympic events such as ice skating. The basic properties of the proposed coefficient are identified.

Rank correlation

Rank (graph theory)

Partial correlation

10.1111/1467-842x.00110

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Citations (74)

Efficient division in the binary representation of complex numbers

David C. Blest Tariq Jamil

Computer operations involving complex numbers, essential in such applications as digital signal processing and image processing, are usually performed in a "divide-and-conquer" approach dealing separately with the real and imaginary parts and then accumulating the results. There have been several proposals to treat complex numbers as a single unit but all seem to have floundered on the basic problem of the division process without which, of course, it is impossible to carry out all but the most basic arithmetic. This paper resurrects an early proposal to express complex numbers in a single "binary" representation and provides a fail-safe procedure for obtaining the quotient of two complex numbers expressed in this representation.

Representation

Carry (investment)

Arithmetic logic unit

Division algorithm

10.1109/secon.2001.923114

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Citations (11)

A New Measure of Kurtosis Adjusted for Skewness

Australian & New Zealand Journal of Statistics (2003)

David C. Blest

Abstract Studies of kurtosis often concentrate on only symmetric distributions. This paper identifies a process through which the standardized measure of kurtosis based on the fourth moment about the mean can be written in terms of two parts: (i) an irreducible component, about L 4 , which can be seen to occur naturally in the analysis of fourth moments; (ii) terms that depend only on moments of lower order, in particular including the effects of asymmetry attached to the third moment about the mean. This separation of the effect of skewness allows definition of an improved measure of kurtosis. This paper calculates and discusses examples of the new measure of kurtosis for a range of standard distributions.

Kurtosis

Central moment

10.1111/1467-842x.00273

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Citations (39)

THE COMPOUND EYE

Elsevier eBooks (1980)

Adrian Horridge David C. Blest

10.1016/b978-0-12-454340-9.50038-0

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Citations (22)

Reduction of order as a neglected method for the solution of inhomogeneous linear ordinary differential equations

International Journal of Mathematical Education in Science and Technology (1990)

David C. Blest

This paper shows that the method of ‘reduction of order’ is both a simpler way of teaching and of obtaining solutions for inhomogeneous linear ordinary differential equations than is the normally espoused method of ‘variation of parameters’. Details are given of the results of the method for the general nth order equation and the two methods are compared for n = 2, 3. It will be noted that the proposed method takes a particularly simple form when the right‐hand side of the equation is a multiple of one of the solutions to the related homogeneous equation.

Reduction of order

Homogeneous differential equation

Variation of parameters

Integrating factor

Linear equation

10.1080/0020739900210307

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Citations (2)