107 In this way the absolute values of the structure factors may be found, not the phases (6. 8). The problem to find these phases is the phase problem. The present article will treat the following topics. At first the description of the ideal crystal will be given in Chap. B. The underlying principles of this description are the concepts of reciprocal lattice, FOURIER synthesis and sym metry. The evaluation of the intensity will then follow in Chap. C and D. Chap. E is concerned with the phase problem and related topics. Though this article treats the analysis of crystal structures, the fundamental concepts for other structures will here be found too. But these topics, and the experimental methods, will l find their place elsewhere . B. Description of the crystalline state. I. Lattice theory. a) The direct lattice. 8. Introduction. In Sect. 3, a description of the ideal crystal was given: The space, occupied by a crystal, is divided into congruent parallelepipeds, each with the same orientation. This parallelepiped is defined by the three basic vectors, a, band c, drawn from an origin 0 (Fig. 2), and is called the primitive cell. This cell is filled with atoms (or ions), and the...
Session LXIX. 7 - 31 July 1998
This book constitutes the strictly refereed proceedings of the 9th International Conference on Computer Aided Verification, CAV '97, held in Haifa, Israel, in June 1997. The volume presents 34 revised full papers selected from a total of 84 submissions. Also included are 7 invited contributions as well as 12 tool descriptions. The volume is dedicated to the theory and practice of computer aided formal methods for software and hardware verification, with an emphasis on verification tools and algorithms and the techniques needed for their implementation. The book is a unique record documenting the recent progress in the area.
Collected papers of Salomon Bochner, American mathematician, known for work in mathematical analysis, probability theory and differential geometry.
In the past thirty years, differential geometry has undergone an enormous change with infusion of topology, Lie theory, complex analysis, algebraic geometry and partial differential equations. Professor Matsushima played a leading role in this transformation by bringing new techniques of Lie groups and Lie algebras into the study of real and complex manifolds. This volume is a collection of all the 46 papers written by him.
One of the greatest mathematicians in the world, Michael Atiyah has earned numerous honors, including a Fields Medal, the mathematical equivalent of the Nobel Prize. While the focus of his work has been in the areas of algebraic geometry and topology, he has also participated in research with theoretical physicists. For the first time, these volumes bring together Atiyah's collected papers--both monographs and collaborative works-- including those dealing with mathematical education and current topics of research such as K-theory and gauge theory. The volumes are organized thematically. They will be of great interest to research mathematicians, theoretical physicists, and graduate students in these areas.
X 1 O S R Cher lecteur, J'entre bien tard dans la sphere etroite des ecrivains au double alphabet, moi qui, il y a plus de quarante ans deja, avais accueilli sur mes terres un general epris de mathematiques. JI m'avait parle de ses projets grandioses en promettant d'ailleurs de m'envoyer ses ouvrages de geometrie. Je suis entiche de geometrie et c'est d'elle dontje voudrais vous parler, oh! certes pas de toute la geometrie, mais de celle que fait l'artisan qui taille, burine, amene, gauchit, peaufine les formes. Mon interet pour le probleme dont je veux vous entretenir ici, je le dois a un ami ebeniste. En effet comme je rendais un jour visite il cet ami, je le trouvai dans son atelier affaire a un tour. Il se retourna bientot, puis, rayonnant, me tendit une sorte de toupie et me dit: {laquo}Monsieur Besse, vous qui calculez les formes avec vos grimoires, que pensez-vous de ceci?)) Je le regardai interloque. Il poursuivit: {laquo}Regardez! Si vous prenez ce collier de laine et si vous le maintenez fermement avec un doigt place n'importe ou sur la toupie, eh bien! la toupie passera toujours juste en son interieur, sans laisser le moindre espace.)) Je rentrai chez moi, fort etonne,...
This collection of scholarly articles asks the question How useful is translation technology? Pointing to the need for a widely used and reliable way to test the efficiency of language translation programs, the presenters show that commercial tools such as translation memories and translation workbenches are popular, and their developers find them useful in terms of productivity, consistency, or quality. However, these claims are rarely proven using objective comparative studies, and this group describes several new statistical approaches to more rigorous evaluation methods. -- Product Description.
CONTENTS: L. Boutet de Monvel: Indice de systemes differentiels.- C. De Concini, C. Procesi: Quantum groups.- P. Schapira, J.P. Schneiders: Index theorems for R-constructible sheaves and for D-modules.- N. Berline, M. Vergne: The equivariant Chern character and index of G-invariant operators.
It is fitting that Professor Dirk Jan Struik be greeted with this melange of mathematical, scientific, historical, sociological and political essays. The authors are also appropriately varied: different countries, outlooks, religions, generations, and we suppose - of course we did not as- different politics too. Many more would have joined us, we know, but the good friends in this book make a fine and representative assembly of the intersection of two (mathematical!) classes: affectionately respect ful admirers of Dirk Struik, and the best thinkers of this troubled century. Struik has been among the most steadfast supporters of the Boston Colloquium for the Philosophy of Science, that discussion group which we have been holding at Boston University since 1960, but his luminous collaboration has been welcome, in Boston and Cambridge, for nearly five decades among mathematicians, physicists, philosophical and political thinkers, and especially among the students. It has not mattered whether they have been his own students or not, whether at M.LT. or elsewhere, whether scholars or dropouts, nature-lovers or book worms, anarchists or Republicans, Catholics or Unitarians, Communists or ...
A ring theory conference took place at the University of Waterloo, 12-16 June 1978, and these are its proceedings. This conference was held as a part of the Summer Research Institute in Ring Theory, at Waterloo, sponsored by the Canadian Mathematical Society. In soliciting speakers, and contributors to the Proceedings, we attempted to represent those portions of ring theory which seemed to us interesting. There was thus considerable emphasis on lower K-theory and related topics, Artinian and Noetherian rings, as well as actions and representations of groups on rings. Regrettably, we could only obtain one paper in the mainstream of commutative ring theory, but we believe that the lack of quantity is more than made up for by the quality. We also took the liberty of including a survey of results in a field which we feel deserves more attention by ring theorists, C* algebras from an algebraic point of view.
For a long period Soil Mechanics has remained at the semi-empirica stage, and only a few decades ago it has shown a tendency to become a fundamental science. However, this evolution is taking place slowly; in spite of the efforts of numerous research scientists, the very complex rheological laws of soils are still not well known. Even if these laws were elucidated, it would take a long time still to deduce simple rules from them for reliable and convenient use in current practical engineer ing. In the pursuit of these distant aims - and of others more imme diate - fundamental research and applied research are very active, both in Rheology and Soil Mechanics. The complexity of the problems to be solved should incite the laboratory researchers and the engineers to a continuous collaboration. Everyone acknowledges the advantage of these connections although aware of the difficulty of realizing this wish. However, contacts are being made little by little between the repre sentatives of the different branches of Rheology and Soil Mechanics, to the great benefit of science. The bureau of the International Union of Theoretical and Applied Mechanics (IUTAM), aware of the importance of...
Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.
Depuis Ie lancement de SPOUTNIK I par l'Union Sovietique Ie 4 Octobre 1957, des experiences humaines de Mecanique celeste de cette sorte ont ete repetees it de nombreuses reprises en U.R.S.S. et aux U.S.A. En 1961, sur ma proposition, l'Union Internationale de Mecanique tMorique et appliquee retint l'idee de consacrer en 1962 un Symposium special it la confrontation des resultats des experiences sovietiques et americaines en vue d'en tirer Ie maximum d'enseignements sur la question fondamentale suivante concernant la {laquo} Dynamique des satellites artificiels) de la Terre: quelles sont la nature et les lois des forces reelles qui agissent sur ces mobiles au voisinage de notre planete, et qui determinent par consequent leur mouvement~ En d'autres termes, il s'agissait de faire Ie point de nos connaissances sur Ie probleme du mouvement des Astres, magistralement resolu par NEWTON il Y a plus de trois siecles pour des astres quasi-ponctuels et assez eloignes. Les moyens d'observation utilises pour connaitre avec la meilleure precision possible Ie mouvement des satellites artificiels lances depuis 1957, et Ie fait de. la proximite relative de ces satellites par rapport it la Terre...
A. Blaquière: Quelques aspects géométriques des processus optimaux.- C. Castaing: Quelques problèmes de mesurabilité liés à la théorie des commandes.- L. Cesari: Existence theorems for Lagrange and Pontryagin problems of the calculus of variations and optimal control of more-dimensional extensions in Sobolev space.- H. Halkin: Optimal control as programming in infinite dimensional spaces.- C. Olech: The range of integrals of a certain class vector-valued functions.- E. Rothe: Weak topology and calculus of variations.- E.O. Roxin: Problems about the set of attainability.
This is a collection of the works of Michael Atiyah, a well-established mathematician and winner of the Fields Medal. It is thematically divided into volumes; this one discusses gauge theory, a current topic of research.
Proceedings of the Second Workshop held at Montpellier, France, 1989
This book contains three lectures each of 10 sessions; the first on Potential Theory on graphs and manifolds, the second on annealing and another algorithms for image reconstruction, the third on Malliavin Calculus.
Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.
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A. Dynin: Pseudo-differential operators on Heisenberg groups.- A. Dynin: An index formula for elliptic boundary problems.- G.I. Eskin: General mixed boundary problems for elliptic differential equations.- B. Helffer: Hypoellipticité pour des opérateurs différentiels sur des groupes de Lie nilpotents.- J.J. Kohn: Lectures on degenerate elliptic problems.- K. Taira: Conditions nécessaires et suffisantes pour l’existence et l’unicité des solutions du problème de la dérivée oblique.- F. Treves: Boundary value problems for elliptic equations.