Theory Of Incomplete Cylindrical Functions And Their Applications

Author : Matest M. Agrest,Michail S. Maksimov
Publisher : Springer
Page : 332 pages
File Size : 51,5 Mb
Release : 2011-11-22
Category : Mathematics
ISBN : 3642650228

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Theory of Incomplete Cylindrical Functions and their Applications by Matest M. Agrest,Michail S. Maksimov Pdf

In preparing the English edition of this unique work, every effort has been made to obtain an easily read and lueid exposition of the material. This has frequently been done at the expense of a literal translation of the original text and it is felt that such liberties as have been taken with the author's language are justified in the interest of ease in readingo None of us pretends to be an authority in the Russian language, and we trust that the original intent of the authors has not been lost. The equations, whieh were for the most part taken verbatim from the original work, were eheeked only eursorily; obvious and previously noted errors have been eorreeted. Fortunately, the Russian and English mathematieal notations are generally in good agreement. An exeeption is the shortened abbreviations for the hyperbolie functions (e.g. sh for sinh), and the symbol Jm rather that Im to denote the imaginary part. As near as possible, these diserepaneies have been correeted. In preparing the Bibliography, works having an English equivalent have been translated into the English title, but in the text the referenee to the Russian work was retained, as it was impraetieal to attempt to find in eaeh ease the eorresponding eitation in the English edition. Authors' names and titles associated with purely Russian works have been transliterated as nearly as possible to the English equivalent, along with the equivalent English title of the work cited.

Author : Matest Mendeleevich Agrest,Michail S. Maksimov,Mikhail Zakharovich Maksimov
Publisher : Springer
Page : 0 pages
File Size : 55,8 Mb
Release : 1971
Category : Bessel functions
ISBN : 0387051112

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Theory of Incomplete Cylindrical Functions and Their Applications by Matest Mendeleevich Agrest,Michail S. Maksimov,Mikhail Zakharovich Maksimov Pdf

Author : Matest M. Agrest,Michail S. Maksimov
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 52,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783642650215

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Theory of Incomplete Cylindrical Functions and their Applications by Matest M. Agrest,Michail S. Maksimov Pdf

In preparing the English edition of this unique work, every effort has been made to obtain an easily read and lueid exposition of the material. This has frequently been done at the expense of a literal translation of the original text and it is felt that such liberties as have been taken with the author's language are justified in the interest of ease in readingo None of us pretends to be an authority in the Russian language, and we trust that the original intent of the authors has not been lost. The equations, whieh were for the most part taken verbatim from the original work, were eheeked only eursorily; obvious and previously noted errors have been eorreeted. Fortunately, the Russian and English mathematieal notations are generally in good agreement. An exeeption is the shortened abbreviations for the hyperbolie functions (e.g. sh for sinh), and the symbol Jm rather that Im to denote the imaginary part. As near as possible, these diserepaneies have been correeted. In preparing the Bibliography, works having an English equivalent have been translated into the English title, but in the text the referenee to the Russian work was retained, as it was impraetieal to attempt to find in eaeh ease the eorresponding eitation in the English edition. Authors' names and titles associated with purely Russian works have been transliterated as nearly as possible to the English equivalent, along with the equivalent English title of the work cited.

Author : B G Korenev
Publisher : CRC Press
Page : 290 pages
File Size : 53,9 Mb
Release : 2002-07-25
Category : Mathematics
ISBN : 020321692X

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Bessel Functions and Their Applications by B G Korenev Pdf

Bessel functions are associated with a wide range of problems in important areas of mathematical physics. Bessel function theory is applied to problems of acoustics, radio physics, hydrodynamics, and atomic and nuclear physics. Bessel Functions and Their Applications consists of two parts. In Part One, the author presents a clear and rigorous intro

Author : M. Aslam Chaudhry,Syed M. Zubair
Publisher : CRC Press
Page : 515 pages
File Size : 45,7 Mb
Release : 2001-08-21
Category : Mathematics
ISBN : 9781420036046

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On a Class of Incomplete Gamma Functions with Applications by M. Aslam Chaudhry,Syed M. Zubair Pdf

The subject of special functions is rich and expanding continuously with the emergence of new problems encountered in engineering and applied science applications. The development of computational techniques and the rapid growth in computing power have increased the importance of the special functions and their formulae for analytic representations

Author : Anonim
Publisher : Unknown
Page : 542 pages
File Size : 50,5 Mb
Release : 1972
Category : Mechanics, Applied
ISBN : UCAL:C2682437

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Applied Mechanics Reviews by Anonim Pdf

Author : W. Rudin
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461380986

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Function Theory in the Unit Ball of Cn by W. Rudin Pdf

Around 1970, an abrupt change occurred in the study of holomorphic functions of several complex variables. Sheaves vanished into the back ground, and attention was focused on integral formulas and on the "hard analysis" problems that could be attacked with them: boundary behavior, complex-tangential phenomena, solutions of the J-problem with control over growth and smoothness, quantitative theorems about zero-varieties, and so on. The present book describes some of these developments in the simple setting of the unit ball of en. There are several reasons for choosing the ball for our principal stage. The ball is the prototype of two important classes of regions that have been studied in depth, namely the strictly pseudoconvex domains and the bounded symmetric ones. The presence of the second structure (i.e., the existence of a transitive group of automorphisms) makes it possible to develop the basic machinery with a minimum of fuss and bother. The principal ideas can be presented quite concretely and explicitly in the ball, and one can quickly arrive at specific theorems of obvious interest. Once one has seen these in this simple context, it should be much easier to learn the more complicated machinery (developed largely by Henkin and his co-workers) that extends them to arbitrary strictly pseudoconvex domains. In some parts of the book (for instance, in Chapters 14-16) it would, however, have been unnatural to confine our attention exclusively to the ball, and no significant simplifications would have resulted from such a restriction.

Author : Jun-ichi Igusa
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642653155

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Theta Functions by Jun-ichi Igusa Pdf

The theory of theta functions has a long history; for this, we refer A. Krazer and W. Wirtinger the reader to an encyclopedia article by ("Sources" [9]). We shall restrict ourselves to postwar, i. e., after 1945, periods. Around 1948/49, F. Conforto, c. L. Siegel, A. Well reconsidered the main existence theorems of theta functions and found natural proofs for them. These are contained in Conforto: Abelsche Funktionen und algebraische Geometrie, Springer (1956); Siegel: Analytic functions of several complex variables, Lect. Notes, I.A.S. (1948/49); Well: Theoremes fondamentaux de la theorie des fonctions theta, Sem. Bourbaki, No. 16 (1949). The complete account of Weil's method appeared in his book of 1958 [20]. The next important achievement was the theory of compacti fication of the quotient variety of Siegel's upper-half space by a modular group. There are many ways to compactify the quotient variety; we are talking about what might be called a standard compactification. Such a compactification was obtained first as a Hausdorff space by I. Satake in "On the compactification of the Siegel space", J. Ind. Math. Soc. 20, 259-281 (1956), and as a normal projective variety by W.L. Baily in 1958 [1]. In 1957/58, H. Cartan took up this theory in his seminar [3]; it was shown that the graded ring of modular forms relative to the given modular group is a normal integral domain which is finitely generated over C

Author : Jacques Louis Lions,Enrico Magenes
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642653933

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Non-Homogeneous Boundary Value Problems and Applications by Jacques Louis Lions,Enrico Magenes Pdf

1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN, (2) fQjtl = gj on am (boundary of m), lor on a subset of the boundm"J am 1

Author : Anonim
Publisher : Academic Press
Page : 398 pages
File Size : 53,9 Mb
Release : 2015-08-06
Category : Science
ISBN : 9780128028681

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Concepts of Mathematical Physics in Chemistry: A Tribute to Frank E. Harris - Part A by Anonim Pdf

This volume presents a series of articles concerning current important topics in quantum chemistry. Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology Features detailed reviews written by leading international researchers

Author : J.-P. Aubin,A. Cellina
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642695124

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Differential Inclusions by J.-P. Aubin,A. Cellina Pdf

A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the set-valued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen tial inclusion" (**) x'(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x'(t)=A(x(t)) dt (B(x(t))+ C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x'(t)) = 0 which can be regarded as a differential inclusion (**), where the right-hand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E - A(x(t)), x (0) =xo where A is a "maximal monotone" map. This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = -VV(x(t)), x(O)=xo when V is a differentiable "potential". 2 Introduction There are many instances when potential functions are not differentiable

Author : Sterling K. Berberian
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 54,6 Mb
Release : 2010-10-27
Category : Mathematics
ISBN : 9783642150715

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Baer *-Rings by Sterling K. Berberian Pdf

A systematic exposition of Baer *-Rings, with emphasis on the ring-theoretic and lattice-theoretic foundations of von Neumann algebras. Equivalence of projections, decompositio into types; connections with AW*-algebras, *-regular rings, continuous geometries. Special topics include the theory of finite Baer *-rings (dimension theory, reduction theory, embedding in *-regular rings) and matrix rings over Baer *-rings. Written to be used as a textbook as well as a reference, the book includes more than 400 exercises, accompanied by notes, hints, and references to the literature. Errata and comments from the author have been added at the end of the present reprint (2nd printing 2010).

Author : D. Kubert,S. Lang
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 51,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475717419

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Modular Units by D. Kubert,S. Lang Pdf

In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Let i) be the upper half plane, and N a positive integer. Let r(N) be the subgroup of SL (Z) consisting of those matrices == 1 mod N. Then r(N)\i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N). The affine ring of regular functions on yeN) over C is the integral closure of C[j] in the function field of X(N) over C. Here j is the classical modular function. However, for arithmetic applications, one considers the curve as defined over the cyclotomic field Q(JlN) of N-th roots of unity, and one takes the integral closure either of Q[j] or Z[j], depending on how much arithmetic one wants to throw in. The units in these rings consist of those modular functions which have no zeros or poles in the upper half plane. The points of X(N) which lie at infinity, that is which do not correspond to points on the above affine set, are called the cusps, because of the way they look in a fundamental domain in the upper half plane. They generate a subgroup of the divisor class group, which turns out to be finite, and is called the cuspidal divisor class group.

Author : Felix Klein
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 43,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783642678882

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Vorlesungen über die hypergeometrische Funktion by Felix Klein Pdf

Bei der Herausgabe der KLEINschen Vorlesung über die hyper geometrische Funktion erschienen nur zwei Wege gangbar: Entweder eine durchgreifende Umarbeitung, auch im großen, oder eine möglichst weitgehende Erhaltung der ursprünglichen Form. Vor allem auch aus historischen Gründen wurde der letztere Weg beschritten. Daher ist die Anordnung des Stoffes erhalten geblieben; e, s ist nur, von kleinen Änderungen abgesehen, ein Exkurs über homogene Schreibweise aus der KLEINschen Vorlesung über lineare Differentialgleichungen ein gefügt, ferner sind die Schlußbemerkungen zur geometrischen Theorie im Falle komplexer Exponenten als durch die Arbeiten von F. SCHILLING überholt, weggelassen. Aus dem obengenannten Grunde sind beispiels weise auch Entwicklungen beibehalten worden, die heute schon dem Anfänger geläufig sind (etwa die Ausführungen über stereographische Projektion). In Rücksicht auf möglichste Erhaltung der KLEINschen Darstellung sind ferner Hinweise des Herausgebers auf inzwischen ge machte Fortschritte der Wissenschaft vom Texte getrennt als Anmerkun gen am Schluß zusammengestellt. Diese Hinweise erheben aber in keiner Weise den Anspruch auf Vollständigkeit. Bei der nicht zu um gehenden Revision des Textes im einzelnen ist, dem oben angegebenen Gesichtspunkt entsprechend, möglichste Wahrung des persönlichen KLEINschen Stils angestrebt. übrigens habe ich darauf Bedacht genommen, auch dem A nlänger die Lektüre durch Anmerkungen und durch Nachweise der KLEINschen Zitate zu erleichtern. Denn zweifellos bieten gerade diese Vorlesungen eine treffliche Ergänzung und Weiterführung dessen, was der Studierende mittleren Semesters an Geometrie und Funktionentheorie kennen gelernt hat.

Author : Kai Lai Chung
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 55,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475717761

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Lectures from Markov Processes to Brownian Motion by Kai Lai Chung Pdf

This book evolved from several stacks of lecture notes written over a decade and given in classes at slightly varying levels. In transforming the over lapping material into a book, I aimed at presenting some of the best features of the subject with a minimum of prerequisities and technicalities. (Needless to say, one man's technicality is another's professionalism. ) But a text frozen in print does not allow for the latitude of the classroom; and the tendency to expand becomes harder to curb without the constraints of time and audience. The result is that this volume contains more topics and details than I had intended, but I hope the forest is still visible with the trees. The book begins at the beginning with the Markov property, followed quickly by the introduction of option al times and martingales. These three topics in the discrete parameter setting are fully discussed in my book A Course In Probability Theory (second edition, Academic Press, 1974). The latter will be referred to throughout this book as the Course, and may be considered as a general background; its specific use is limited to the mate rial on discrete parameter martingale theory cited in § 1. 4. Apart from this and some dispensable references to Markov chains as examples, the book is self-contained.