Format: Book ISBN: 0-486-49508-6 Page Count: 256 Dimensions: 5 5/8 x 8 1/2
Originally evolved in the 19th century from an attempt by Galton and Watson (earlier work of Bienaym・has been found recently) to show how probability related to the extinction of family names, the theory of branching processes has become widely used as a theoretical basis for the study of populations of such objects as genes, neutrons, or cosmic rays. The present hardcover volume, originally sponsored by The RAND Corporation, was the first systematic and comprehensive treatment of a theory of mathematical models for the development of populations whose members reproduce and die, subject to laws of change. Beginning with the classical Galton-Watson model for the propagation of a family of objects all of one type, the author then extends the theory of objects of several types and to objects described by continuous variables. He next applies the theory to one of the simpler mathematical models for neutron chain reactions. Succeeding chapters treat Markov branching processes with a continuous time parameter and age-dependent branching processes. The last chapter gives the mathematical theory of electron-photo cascades, one of the components of cosmic radiation. Unabridged, corrected Dover republication of the edition co-published by Springer-Verlag, Berlin, and Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. Prefaces. Appendixes. Bibliography. Additional References. Index. 6 illustrations.
Format: Book ISBN: 0-486-49510-8 Page Count: 144 Dimensions: 5 5/8 x 8 1/2
"A rigorous and lively introduction . . . careful and lucid . . ."--The American Mathematical Monthly. Excellent hardcover edition. This concise and idea-rich introduction to a topic of perennial interest in mathematics is written so clearly and lucidly, it is well within the reach of senior mathematics students. It covers mainly existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Throughout, the emphasis is on geometric methods. Witold Hurewicz was a world-class mathematician whose untimely death in 1956 deprived the mathematics community of one of its leading lights. His contributions to dimension theory, homotopy and other topics are outlined by Professor Solomon Lefschetz in a prefatory article "Witold Hurewicz in Memoriam" included in this volume. Also included is a list of books on differential equations for those interested in further reading, and a bibliography of Hurewicz's published works. Unabridged Dover republication of the work originally published by MIT Press, 1958. Prefatory article "Witold Hurewicz in Memoriam" by Solomon Lefschetz. List of References. Index. 26 figures.
Format: Book ISBN: 0-486-49512-4 Page Count: 832 Dimensions: 5 5/8 x 8 1/2
Any geologist can now afford to sharpen his thinking and improve the reliability of his conclusions through the statistical methods that are explained in this excellent hardcover volume. No previous knowledge of statistics is necessary, and only those statistical methods are introduced that pertain to geological data and geological problems. Illustrating the methods are many numerical examples, all using a minimum of mathematical terminology and most based on real geological data. The text begins with an extensive discussion of univariate statistical methods: distribution, sampling, inference, analysis of variances, and distributions and transformations. Geological sampling and variability in geological data are then considered. Upon this foundation the authors present a masterful exposition of multivariate statistical methods and some problems in applied geology. Covered here are such topics as geological trend analysis; analysis of multivariate data by methods that include multiple regression, the generalized analysis of variance, and factor analysis; ratios and variables of constant sum; exploration for natural resources; statistical methods for markedly improving estimates of grade and amount of ore; some methods of operations research for making decisions in the natural resources field; specialized geological sampling--sampling of broken rock, placer sampling, and sampling in exploration geochemistry; and gold and the lognormal distribution. Concluding the volume is a brief evaluation of electronic computers and geology. Unabridged, corrected republication in one volume of the original, two-volume (1970, 1971) edition. 197 figures. References. Appendixes. Indexes.
Format: Book ISBN: 0-486-49514-0 Page Count: 224 Dimensions: 5 5/8 x 8 1/2
This hardcover edition of A Survey of Minimal Surfaces is divided into twelve sections discussing parametric surfaces, non-parametric surfaces, surfaces that minimize area, isothermal parameters on surfaces, Bernstein's theorem, minimal surfaces with boundary, the Gauss map of parametric surfaces in E3, non-parametric minimal surfaces in E3, application of parametric surfaces to non-parametric problems, and parametric surfaces in En. For this edition, Robert Osserman, Professor of Mathematics at Stanford University, has substantially expanded his original work, including the uses of minimal surfaces to settle important conjectures in relativity and topology. He also discusses new work on Plateau's problem and on isoperimetric inequalities. With a new appendix, supplementary references and expanded index, this Dover edition offers a clear, modern and comprehensive examination of minimal surfaces, providing serious students with fundamental insights into an increasingly active and important area of mathematics. Corrected and enlarged Dover republication of the work first published in book form by the Van Nostrand Reinhold Company, New York, 1969. Preface to Dover edition. Appendixes. New appendix updating original edition. References. Supplementary references. Expanded indexes.
Format: Book ISBN: 0-486-49518-3 Page Count: 384 Dimensions: 5 5/8 x 8 1/2
"A book of great value . . . it should have a profound influence upon future research."--Mathematical Reviews. Hardcover edition. The foundations of the study of asymptotic series in the theory of differential equations were laid by Poincar・in the late 19th century, but it was not until the middle of this century that it became apparent how essential asymptotic series are to understanding the solutions of ordinary differential equations. Moreover, they have come to be seen as crucial to such areas of applied mathematics as quantum mechanics, viscous flows, elasticity, electromagnetic theory, electronics, and astrophysics. In this outstanding text, the first book devoted exclusively to the subject, the author concentrates on the mathematical ideas underlying the various asymptotic methods; however, asymptotic methods for differential equations are included only if they lead to full, infinite expansions. Unabridged Dover republication of the edition published by Robert E. Krieger Publishing Company, Huntington, N.Y., 1976, a corrected, slightly enlarged reprint of the original edition published by Interscience Publishers, New York, 1965. 12 illustrations. Preface. 2 bibliographies. Appendix. Index.
Description
This monograph presents original material in the theory of Riemann surfaces. A compact Riemann surface X is symmetric if it admits an anti-analytic involution tau: Xrightarrow X. Such an involution is called a real structure. Two real structures are isomorphic if they are conjugate in the full group mathrm{Aut}^{pm}X of analytic and anti-analytic automorphisms of X. In this memoir, the authors classify the real structures of all symmetric hyperelliptic Riemann surfaces of genus ggeq 2 up to isomorphism. The topological invariants of each isomorphism class are also computed. They also give the list of groups which act as the full group of analytic and anti-analytic automorphisms of such surfaces. Moreover, the complex algebraic curve associated to any such Riemann surface is described in terms of polynomial equations. They also find an explicit formula for a real structure in each isomorphism class.
The book is suitable for advanced graduate students and researchers interested in algebraic geometry and Riemann surfaces.
Contents
・Introduction ・Preliminaries ・Automorphism groups of symmetric hyperelliptic Riemann surfaces ・Symmetry types of hyperelliptic Riemann surfaces ・Bibliography
Details:
Series: Memoires de la Societe Mathematique de France, Number: 86 Publication Year: 2001 ISBN: 2-85629-112-0 Paging: 122 pp. Binding: Softcover
Description
This volume gives a nice summary of current work in the theory of 1-motives. The authors present the following: Let X be an n-dimensional algebraic variety over a field of characteristic zero. They describe algebraically defined Deligne 1-motives mathrm{Alb}^{+} (X), mathrm{Alb}^{-} (X), mathrm{Pic}^{+} (X) and mathrm{Pic}^{-} (X) which generalize the classical Albanese and Picard varieties of a smooth projective variety. Computed are Hodge, ell-adic, and De Rham realizations, proving Deligne's conjecture for H^{2n-1}, H_{2n-1}, H^1 and H_1.
Investigated are functoriality, universality, homotopical invariance and invariance under formation of projective bundles. The authors compare the cohomological and homological 1-motives for normal schemes. For proper schemes, they obtain an Abel-Jacobi map from Albanese 1-motive, which is the universal regular homomorphism to semi-abelian varieties. By using this universal property, they obtain "motivic" Gysin maps for projective local complete intersection morphisms.
The volume is suitable for advanced graduate students and researchers interested in algebraic geometry.
Contents
・Introduction ・Preliminaries on 1-motives ・Homological Picard 1-motive: mathrm{Pic}^- ・Cohomological Albanese 1-motive: mathrm{Alb}^+ ・Cohomological Picard 1-motive: mathrm{Pic}^+ ・Homological Albanese 1-motive: mathrm{Alb}^- ・Motivic Abel-Jacobi and Gysin maps ・Rationality questions ・Appendix. Picard functors ・Bibliography
Details:
Series: Memoires de la Societe Mathematique de France, Number: 87 Publication Year: 2001 ISBN: 2-85629-113-9 Paging: 104 pp. Binding: Softcover