An analytical model for close combat dynamics

A coherent dynamic combat model is developed from basic principles. The governing set of equations has a striking resemblance to the continuity equation in fluid dynamics with an additional term for the losses of combat units. The salient features of the model are a moving battle front, the replenishment of losses, and the withdrawal of combat units while others are still engaged. A basic example shows that the often used force ratio of three can produce a frontline movement up to 90% of the speed of the attacker. Another example simulates a well documented battle from the American Civil War. It is shown that terrain influences and the absence of reconnaissance had a large adverse effect on the outcome of the battle for the Confederate forces.     

The history and ideas of pragmatism

This paper examines the origins of philosophical pragmatism in the USA in the second half of the 19th-century and its development and use up to the Second World War. The story is told through the lives and ideas of some of the main originators, Oliver Wendell Holmes Jr, Charles Saunders Peirce, William James and John Dewey. The core idea of pragmatism, that beliefs are guides to actions and should be judged against the outcomes rather than abstract principles, dominated American thinking during the period of economic and political growth from which the USA emerged as a world power. The paper suggests that the practical, commonsense, scientific approach embedded in pragmatism resonates with OR as practised and that much of pragmatism could be attractive to practitioners and academics alike.     

Problem solving: a personal perspective from Brazil

In this paper, I do a historical review of the concept of Problem Solving, and make some considerations about the State of the Art nowadays. A very brief notice of the art of Problem Solving in Latin America is also presented. Finally, I present some reflections on the future of the Art of Problem Solving.     

雅各布·伯努利的《猜度术》研究

《猜度术》是概率论的第一部奠基性著作,其出版是概率论成为独立数学分支的标志．本文详细分析了雅各布·伯努利的概率新思想,尤其对伯努利数及伯努利大数定律进行了较为深刻地探讨．另外,还澄清了长期以来对《猜度术》整理出版者的—个误传．     

Art,mathematics & cultural industry: new trends in the digital era

In view of modern technologies proper of the Digital Era we shortly discuss some recent activities of our research groups in the broad field of Cultural Industry, where Art, Mathematics and Physics are gaining new interrelationships concerning the use of Digital Art and Web Technologies in the domain of Scientific Communication and Visualization. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aspekte der Stirlingschen Zahlen zweiter Art

Zusammenfassung. Die Stirlingschen Zahlen zweiter Art spielen in der Differenzenrechnung (und damit auch in der Numerischen Mathematik) sowie in der Kombinatorik eine bedeutende Rolle. Verwiesen sei hierbei auf Jordan [2], der sie in seinem Buch über Differenzenrechnung als mindestens so bedeutend wie die Bernoullischen Zahlen erachtet, sowie im zweiten Fall u.a. auf die Bücher über Kombinatorik von Aigner [1] bzw. Riordan [3]. über eine Anwendung der Stirlingschen Zahlen zweiter Art in der Wahrscheinlichkeitsrechnung sollen in der vorliegenden Arbeit neue Aspekte bezüglich der Darstellung gewisser Potenzsummen gewonnen werden. Ferner wollen wir herausarbeiten, da? diese Zahlen unter mehreren Gesichtspunkten als komplement?r zu den Binomialkoeffizienten betrachtet werden k?nnen. Dies wird an den entsprechenden Stellen durch „Argumente” hervorgehoben. Wie die folgenden Herleitungen zeigen werden, erweist sich die Einführung der Stirlingschen Zahlen zweiter Art über die Rekursionsformel als der einfachste Weg. Eingegangen am 5.5.1995 / Angenommen am 10.1.1996     

Ein algorithmischer Zugang zu Polynomen und Splines

Zusammenfassung. Um polynomiale Kurven auf dem Computer modellieren zu k?nnen, verwendet man in der CAD-Praxis zumeist sogenannte Bézier-Kurven. Verallgemeinert man den zugeh?rigen Auswertungsalgorithmus, so kann man, auf ganz konstruktive Art auch Splinekurven definieren und ihre wesentlichen Eigenschaften auf sehr elementare Art und Weise herleiten. Der Zusammenhang wird dabei durch das sogenannte “Blossoming principle” hergestellt. Eingegangen am: 12.3.1996 / Angenommen am: 7.5.1996     

Der Algorithmus von Marti für inkorrekt gestellte Gleichungen mit gestörtem Operator und beliebiger rechter Seite

Zusammenfassung Das Verfahren von Marti zur Lösung Fredholmscher Integralgleichungen erster Art wird modifiziert, so daß die Näherungen stabil gegen kleine Störungen des Operators sind. Das Verfahren wird an zwei-dimensionalen Integralgleichungen erster Art getestet.

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Summary For Marti's algorithm for solving Fredholm integral equations of the first kind a modification is presented. For this algorithm stability for small perturbations of the operator is shown. An application to two-dimensional integral equations of the first kind shows the numerical efficiency.

     

Mathematicians and World War I: The international diplomacy of G. H. Hardy and Gösta Mittag-Leffler as reflected in their personal correspondence

Gösta Mittag-Leffler was the founding editor of the journal Acta Mathematica. In the early 1870's it was meant, in part, to bring the mathematicians of Germany and France together in the aftermath of the Franco-Prussian War, and the political neutrality of Sweden made it possible for Mittag-Leffler to realize this goal by publishing articles in German and French, side by side. Even before the end of the First World War, Mittag-Leffler again saw his role as mediator, and began to work for a reconciliation between German and Allied mathematicians through the auspices of his journal. Similarly, G. H. Hardy was particularly concerned about the reluctance of many scientists in England to attempt any sort of rapprochement with the Central European countries and he sought to do all he could to bring English and German mathematicians together after the War. His correspondence with Mittag-Leffler survives in the Archives of the Institut Mittag-Leffler, Djursholm, Sweden, and serves as the basis for this article, which focuses upon the attempts of Mittag-Leffler to reconcile mathematicians after the War, and to renew international cooperation.     

On the propagation of stress waves in a rate sensitive plastic medium

Zusammenfassung Es wird für gewisse elastisch-viskoplastische Materalien, deren Stoffgleichungen der Verfasser in früheren Arbeiten diskutiert hat, die Ausbreitung von Kompressions- und Distorsionswellen verschiedener Art untersucht.     

Gambling your way to New York: A story of expectation

Scenarios 1 and 2 assume the player only plays the one game to turn over the required 10,000. If a player had a good run in the first10,000. If a player had a good run in the first 5,000 turnover in Casino War, he or she may be inclined to switch to 3 Card Stud Poker. Likewise, if a player had a bad run in the first $5,000 turnover in 3 Card Stud Poker, he or she may be inclined to switch to Casino War. A player’s choice to switch between 3 Card Stud Poker and Casino War is dependent on his or her current bankroll and how many hands are left to play to wager the required $5,000 turnover in 3 Card Stud Poker, he or she may be inclined to switch to Casino War. A player’s choice to switch between 3 Card Stud Poker and Casino War is dependent on his or her current bankroll and how many hands are left to play to wager the required 10,000. The minimum bet for both games has always been applied. A player may choose to speed up the process by betting higher than the minimum. This may again depend on the player’s current bankroll and how many hands are left to play. In general, increasing the size of the bankroll in any casino game increases the variance and skewness. This would amount to increasing the probability of losing the initial 200 before wagering the initial200 before wagering the initial 5,000 (i.e., a greater chance of having to deposit more money into the casino account).     

The ‘invisible science’: operational research for the British Armed Forces after 1945

This paper presents an original account of the contribution of operational research (OR) to the formulation of tactics and strategy on behalf of the British Armed Forces in the four decades after 1945. The main focus is on the Cold War in the European theatre, where OR analysts devoted considerable time and effort to the modelling of warfare on behalf of the British Army of the Rhine. In the absence of combat data for nuclear weapons, OR analysts devised a sequence of war games which evolved in conformity with the development of NATO strategy in relation to the Warsaw Pact. Again in the context of the Cold War, the paper analyses the role of OR in relation to the early V bomber force and the introduction of ‘global war studies’ on behalf of the Royal Navy. The paper also comments on the organisational structure of British military OR following on the creation of a centralised OR facility within the Ministry of Defence in 1965. In conclusion, the paper notes the sea-change in military OR following the end of the Cold War in 1990 and the onset of a period of sustained ‘asymmetric’ military operations in the former Yugoslavia, the Middle East and Afghanistan.     

BOOK REVIEWS

Book reviewed in this article: Fractals: A User's Guide For the Natural Sciences, Harold M. Hastings and George Sugihara How Amazing, Charles Snape and Heather How Puzzling, Charles Snape and Heather Scott Classic Math: History Topics for the Classroom, Art Johnson     

Book Vignettes

Book reviewed in this article: Jargocki, Christopher P., Science Brain-Twisters, Paradoxes, and Fallacies Bello, Ignacio, Contemporary Basic Mathematical Skills Ghyka, Matila, The Geometry of Art and Life     

Statistische Qualitätskontrolle

Zusammenfassung Die statistischen Methoden als zusätzliche Regelungseinrichtung in der Materialbeschaffung, Lagerhaltung, Fertigung und Absatzwirtschaft. Zusätzliche Kosten werden durch Regelungsfehler erster Art (blinder Alarm) und zweiter Art (Alarmversager) verursacht. Das Regelungs-system ist optimal, wenn die erwarteten Kosten ein Minimum sind. Beispiele über die Anwendung des Fehlerfortpflanzungsgesetzes, Abstimmung der Kontrollkarten auf die Abnahmebedingungen und die Reaktionsfähigkeit des Kontrollsystems ergänzen die Ausführungen.

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Summary Statistical techniques as additional control mechanism in the procurement of materials, stock-keeping, production and marketing. Additional costs may be due to control errors of the first kind (erroneous alarm) and of the second kind (failure to alarm). The control-system is optimal when the expected costs are minimised. Examples concerning the application of the Law of Propagation of Errors, installment of control charts according to the conditions for acceptance and the effeciency of response of the control system terminate the paper.

     

Zen and the art of finite element design

The paper reviews Robert M. Pirsig's ideas concerning the concept of quality as expressed in his book Zen and the Art of Motorcycle Maintenance and applies them to the problem of designing finite elements. Using quadrilateral membrane elements as a typical example, it is conclude that finite elements differ remarkably in the quality of their performance and that improvements in quality occur in response to the dedication and insight which finite element designers brings to their task.     

Longitudinal vibrations of a composite bar

Zusammenfassung Mathematische Untersuchung von Längsschwingungen in zusammengesetzten Stäben ist ein verhältnismässig kompliziertes, jedoch industriell wichtiges Problem. Die vorliegende Arbeit zeigt an einem typischen Beispiel die Art der dabei vorkommenden Schwierigkeiten. Sie kann auch bei rechnerischer Behandlung anderer Fragen aus der Schwingungstheorie zur Orientierung dienen.     

Alice Bache Gould: mathematician in search of war work, 1918

Alliances between American mathematics and the military were not well defined when the United States entered World War I in April of 1917. Although academic mathematicians – like other American faculty members and students – were among the strongest supporters of the cause, it took time to identify how and where to utilize their technical training in the war effort. This paper investigates the case of Alice Bach Gould, one of E H Moore's mathematics graduate students at the University of Chicago, and her efforts to support US military endeavors with her scientific expertise. Although Gould's substantial research accomplishments in Spanish archives eventually surpassed her mathematical achievements, her quest for war work in 1917 nonetheless illustrates the difficulty of contributing mathematical training to patriotic service in the United States during World War I.     

The beginnings of mathematics in a howling wilderness

This paper analyzes factors that influenced the development of mathematics in Anglo-America, particularly New England, before the Revolutionary War. It discusses the effects on the emerging nation of the development of mathematics in Europe.