Showing papers in "The Mathematical Gazette in 1998"
297 citations
TL;DR: Partial table of contents: Modelling Cardiac Excitation and Excitability (M. Boyett, et al.) and Finite Element Methods for Modelling Impulse Propagation in the Heart.
Abstract: Partial table of contents: Modelling Cardiac Excitation and Excitability (M. Boyett, et al.). Modelling Propagation in Excitable Media (A. Holden & A. Panfilov). Rotors, Fibrillation and Dimensionality (A. Winfree). A Mathematical Model of Cardiac Anatomy (P. Hunter, et al.). Finite Element Methods for Modelling Impulse Propagation in the Heart (J. Rogers, et al.). The Effects of Geometry and Fibre Orientation on Propagation and Extracellular Potentials in Myocardium (J. Keener & A. Panfilov). Forward and Inverse Problems in Electrocardiography (A. van Oosterom). Computational Electromechanics of the Heart (P. Hunter, et al.). Index.
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TL;DR: Ollerenshaw and Brée as mentioned in this paper gave a method of construction and enumeration of all pandiagonal magic squares of a class known as "most-perfect" which has the integers in all rows, all columns and all diagonals adding to the same sum.
Abstract: Their construction and enumeration by Kathleen Ollerenshaw and David Brée. This book gives a method of construction and enumeration of all pandiagonal magic squares of a class known as ‘most-perfect’. Pandiagonal magic squares have the integers in all rows, all columns and all diagonals adding to the same sum. Characteristically, all integers come in complementary pairs along the diagonals and the integers in any 2 x 2 block of four add to the same sum. This is the first time, in thousands of years of mathematical experience that a method of construction has been found for a whole class. Formulas are given for the enumeration of all mostperfect squares, however large. Published by the IMA. Please contact publications@ima.org.uk to order.
31 citations
TL;DR: In this article, a mathematical model to represent the effects of the forces which operate during the rowing of racing shells is presented, and the analysis is conducted in terms of eights, but could apply equally well to fours, pairs and double or quad sculls.
Abstract: In this article we set up a mathematical model to represent the effects of the forces which operate during the rowing of racing shells. The analysis is conducted in terms of eights, but could apply equally well to fours, pairs and double or quad sculls, and even (with obvious verbal changes) to single sculls. McMahon as well as McMahon and Bonner have previously considered various numbers of rowers in racing shells, and reached conclusions suggesting that consideration of an eight is representative of all possible combinations of rowers.
27 citations
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TL;DR: Weierstrass and some members of his circle: Kovalevskaia, Fuchs, Schwarz, Schottky, Frobenius, Schur, and the Berlin Algebraic Tradition.
Abstract: Mathematics at the Prussian Academy of Sciences 1700-1810.- Mathematics in Berlin, 1810-1933.- Augustus Leopold Crelle.- Gustav Peter Lejeune Dirichlet.- Carl Gustav Jacob Jacobi.- Jacob Steiner and Synthetic Geometry.- Gotthold Eisenstein.- Kummer and Kronecker.- Weierstrass and some members of his circle: Kovalevskaia, Fuchs, Schwarz, Schottky.- Frobenius, Schur, and the Berlin Algebraic Tradition.- Erhard Schmidt, John von Neumann.- Constantin Caratheodory.- Richard von Mises.- Einstein in Berlin.- The Nazi era: the Berlin way of politicizing mathematics.- The University of Berlin from Reopening until 1953.- Helmut Hasse, Hermann Ludwig Schmid and their students in Berlin.- Freie Universitat Berlin, a summary of its history.- Mathematics at the Berlin Technische Hochschule/Technische Universitat.- Mathematics in Berlin at the Humboldt University: from 1953 until now.- The Mathematical Institute of the Academy of Sciences of the GDR.- Fast Algorithms, Fast Computers: The Konrad-Zuse-Zentrum Berlin (ZIB).- Weierstrass Institute for Applied Analysis and Stochastics (WIAS).- Zentralblatt fur Mathematik und ihre Grenzgebiete.- Sources of photographs.- Addresses of authors and editors.
14 citations
TL;DR: In Euclidean plane geometry there exists an interesting, although limited, duality between the concepts angle and side, similar to the general dualities between points and lines in projective geometry.
Abstract: In Euclidean plane geometry there exists an interesting, although limited, duality between the concepts angle and side, similar to the general duality between points and lines in projective geometry. Perhaps surprisingly, this duality occurs quite frequently and is explored fairly extensively in [2]. The square is self-dual regarding these concepts as it has all angles, as well as all sides equal. Similarly, the rectangle and rhombus are each other's duals as shown in the table below: Rectangle Rhombus All angles equal All sides equal Center equidistant from vertices, hence has circum circle Center equidistant from sides, hence has in circle Axes of symmetry bisect opposite sides Axes of symmetry bisect opposite angles
TL;DR: The Roth's removal rule as discussed by the authors, which is known as Roth's Removal Rule, is a generalization of the removal rule of the invertible matrix R such that RMR -1 = N.
Abstract: In 1952 W. E. Roth published two theorems, one of which has come to be known as Roth’s removal rule and (slightly generalised) goes as follows. [Recall that square matrices M , N are similar when there is an invertible matrix R such that RMR -1 = N . The matrix entries can be elements from any field, although for simplicity we shall call them ‘numbers’.]
TL;DR: Dehaene's seminal work The Number Sense as discussed by the authors explores how the human brain performs simple mathematical calculations and reveals that human infants also have a rudimentary number sense, which is as basic to the way the brain understands the world as our perception of color or object in space.
Abstract: Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eyeopening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. These are but a few of the wealth of fascinating observations contained here. We also discover, for example, that because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--Englishspeaking people can only remember seven. The book also explores the unique abilities of idiot savants and mathematical geniuses, and we meet people whose minute brain lesions render their mathematical ability useless. This new and completely updated edition includes all of the most recent scientific data on how numbers are encoded by single neurons, and which brain areas activate when we perform calculations. Perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in learning, mathematics, or the mind. "A delight." --Ian Stewart, New Scientist "Read The Number Sense for its rich insights into matters as varying as the cuneiform depiction of numbers, why Jean Piaget's theory of stages in infant learning is wrong, and to discover the brain regions involved in the number sense." --The New York Times Book Review "Dehaene weaves the latest technical research into a remarkably lucid and engrossing investigation. Even readers normally indifferent to mathematics will find themselves marveling at the wonder of minds making numbers." --Booklist
TL;DR: In this article, the Riemann Integral and the Fourier series of functions are used to define a sequence of functions and a series of Functions of Functions, respectively, for probability theory.
Abstract: Preliminaries. Sequences. The Riemann Integral. Differentiation. Sequences of Functions. Series of Functions. Differential Equations. Complex Analysis. Fourier Series. Probability Theory. Bibliography. Indexes.
TL;DR: The Fibonacci series 0, 1,1,2,3,5,8,13, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 44, 81,149 is well known because so many properties have been found for it.
Abstract: The Fibonacci series 0,1,1,2,3,5,8,13,.... is well known because so many properties have been found for it and because there are many instances of it occurring both in nature and mathematics. It is of course formed from the recurrence relationship
The Tribonacci series 0,1,1,2,4,7,13,24,44,81,149,... is formed in a similar way but from the recurrence
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TL;DR: The early development of quaternions in the hands of Hamilton's successor, Peter Guthrie Tait, Professor of Natural Philosophy in the University of Edinburgh from 1860 to 1900, was traced in this paper.
Abstract: In the first part of this paper we traced the early development of quaternions in the hands of Hamilton’s successor, Peter Guthrie Tait, Professor of Natural Philosophy in the University of Edinburgh from 1860 to 1900. Tait had neither the intuitive feel for physical concepts that Maxwell possessed nor the entrepreneurial talent of Thomson (Lord Kelvin) and yet he fulfilled a pivotal role in nineteenth century British physics through his correspondence with the former, with whom he went to school, and his collaboration with the latter. Though ambivalent towards quaternions, Maxwell was chivvied by Tait into drafting his 1873 Treatise on Electricity and Magnetism in both Cartesian and quaternion form.
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