The groundbreaking work of Russian mathematician A. M. Liapunov (1857–1918) on the stability of dynamical systems was overlooked for decades because of political turmoil. During the Cold War, when it was discovered that his method was applicable to the stability of aerospace guidance systems, interest in his research was rekindled. It has remained high ever since. This monograph on both the theory and applications of Liapunov's direct method reflects the work of a period when the theory had been studied seriously for some time and reached a degree of completeness and sophistication. It remains of interest to applied mathematicians in many areas. Topics include applications of the stability theorems to concrete problems, the converse of the main theorems, Liapunov functions with certain properties of rate of change, the sensitivity of the stability behavior to perturbations, the critical cases, and generalizations of the concept of stability.

Theory and Application of Liapunov's Direct Method (Dover Books on Mathematics)

Science & Math

Hahn, Wolfgang

Astronomy & Space Science

Dover Publications

While the Roman and Byzantine gold coinage has been the focus of a great deal of study, it is still not possible to produce a synthetic monograph on all aspects of the subject. A number of contributions brought together to try to demonstrate how progress has been made possible through new or refined methods as well as evidence from new finds. Contents: The Joint Reign Gold of Justin I and Justinian I byu William E. Metcalf, The Monte Judica Hoard and the Sicilian Moneta Auri under Justinian I and Justin II by Niall Fairhead and Wolfgang Hahn, Carthage: The Moneta Auri under Justinian I and Justin II 537-578 by Cecile Morrisson, The Minting of Gold Coinage at Thessalonica in the Fifth and Sixth Centuries and the Gold Currency of Illyricum and Dalmatia by D.M. Metcalf, Seventh-Century Byzantine Coins in Southern Russia and the Problems of Light Weight Solidi by John Smedley, Microchemical Analysis of the Metal Content of Some Eighth-Century Coins of Rome and Ravenna by Wolfgang Hahn, and The Debasement of the Provincial Byzantine Gold Coinage from the Seventh to Ninth Centuries by W.A. Oddy.

Studies on Early Byzantine Gold Coinage (Numismatic Studies)

Arts & Photography

History & Criticism

American Numismatic Society

•No other book approaches this level of academic expertise on significant Aksumite coinage•The Ashmolean museum's coins are of considerably higher quality and interest than even the similar collection at the British MuseumThese essays by Hahn and West will deal respectively with the formation of the collection and the figure of Bent Juel-Jensen, the seminal Aksumite coin collector in Oxford (as well as a medical doctor, academic, and traveler). They will also discuss recent problems that have emerged regarding the study of this coinage. In its entirety, this publication will make a fundamental contribution to this area of research and be an indispensible acquisition for many institutions and individuals.Contents: Introduction; History of Aksumite Coins; History of the Collection; Bibliography; Catalogue.

Sylloge of Aksumite Coins in the Ashmolean Museum, Oxford

West, Vincent

Ashmolean Museum

The theory of the stability of motion has gained increasing signifi cance in the last decades as is apparent from the large number of publi cations on the subject. A considerable part of this work is concerned with practical problems, especially problems from the area of controls and servo-mechanisms, and concrete problems from engineering were the ones which first gave the decisin' impetus for the expansion and modern development of stability theory. In comparison with the many single publications, which are num bered in the thousands, the number of books on stability theory, and especially books not \\Titten in Russian, is extraordinarily small. Books which giw the student a complete introduction into the topic and which simultaneously familiarize him with the newer results of the theory and their applications to practical questions are completely lacking. I hope that the book which I hereby present will to some extent do justice to this double task. I haw endeavored to treat stability theory as a mathe matical discipline, to characterize its methods, and to prove its theorems rigorollsly and completely as mathematical theorems. Still I always strove to make reference to applications, to illustrate the arguments with examples, and to stress the interaction between theory and practice. The mathematical preparation of the reader should consist of about two to three years of university mathematics.

Stability of Motion (Grundlehren der mathematischen Wissenschaften)

Mathematics

Springer

Die grundlegende Arbeit von A. M. LJAPUNOV (1857 bis 1918) über die Stabilität der Bewegung, die 1892 in russischer Sprache, 1907 in französischer Übersetzung! erschien, hat ursprünglich nur wenig Beach tung gefunden und war lange Zeit hindurch nahezu vergessen. Erst vor etwa 25 Jahren wurden diese Untersuchungen von einigen sowjetischen Mathematikern wieder aufgegriffen. Man bemerkte dabei, daß sich die Ljapunovschen Ansätze zur Bewältigung konkreter Probleme der Physik und Technik eigneten, und seitdem befaßt man sich, wie die wachsende Zahl der Veröffentlichungen erkennen läßt, in steigendem Maße mit der von LJAPUNOV begründeten Stabilitätstheorie. Vor allem gilt das für die sogenannte zweite oder direkte Methode. LJAPUNOV hat sie eigentlich nur zur Ableitung von Stabilitätskriterien der theoretischen Mechanik benutzt. Jetzt verwendet man sie einerseits bei praktischen Aufgaben aus dem Bereich der mechanischen und elektrischen Schwin gungen, insbesondere in der Regelungstechnik; andererseits hat man erkannt, daß die direkte Methode als leitendes Prinzip einer allgemeinen Stabilitätstheorie dienen kann, die erheblich mehr umfaßt als die bei gewöhnlichen Differentialgleichungen auftretenden Probleme. Die Theorie der direkten Methode ist in den letzten Jahren sehr gefördert und zu einem gewissen Abschluß gebracht worden. Sie kann daher jetzt in einem zusammenfassenden Ergebnisbericht dargestellt werden. Eine Übersicht, die diese Dinge einem größeren Kreise näher bringen kann, erscheint um so mehr angezeigt, als fast die gesamte Literatur in russischer Sprache und an teilweise schwer zugänglichen Stellen erschienen isP.

Theorie und Anwendung der direkten Methode von Ljapunov (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge) (German Edition)