Series: Universitext
2011, 2012, XIV, 258 p. 50 illus.
Softcover, ISBN 978-1-4614-1498-8
About this textbook
This book is an enhanced version of an earlier Russian edition. Besides thorough revisions, more emphasis was put on reordering the topics according to a category-theoretical view. This allows the mathematical results to be stated, proved, and understood in a much easier and elegant way.
Preface.- 1 Basic Notions of Calculus on Manifolds.- 2 Relations.- 3 Symplectic Relations on Symplectic Manifolds.- 4 Symplectic Relations on Cotangent Bundles.- 5 Canonical Lift on Cotangent Bundles.- 6 The Geometry of the Hamilton-Jacobi Equation.- 7 Hamiltonian Optics in Euclidean Spaces.- 8 Control of Static Systems.- 9 Supplementary Topics.- 10 Global Hamilton Principal Functions on S2 and H2.- References.- Index.
Series: Universitext
2011, XVII, 399 p. 8 illus., 1 in color.
Softcover, ISBN 978-1-4614-1098-0
Updated and revised edition
Includes a new chapter on matrix inequalities, and a new chapter with updated material on numerical ranges and radii and matrix norms
Includes more than 1000 exercises
Aids the reader in mastering basic matrix results and techniques that are useful for applications in various fields such as mathematics, statistics, physics, computer science, and engineering
The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems.
Major changes in this revised and expanded second edition:
-Expansion on topics such as matrix functions, nonnegative matrices, and (unitarily invariant) matrix norms
-The inclusion of more than 1000 exercises
-A new chapter, Chapter 4, with updated material on numerical ranges and radii, matrix norms, and special operations such as the Kronecker and Hadamard products and compound matrices
-A new chapter, Chapter 10, on matrix inequalities, which presents a variety of inequalities on the eigenvalues and singular values of matrices and unitarily invariant norms.
Preface to the Second Edition.- Preface.- Frequently Used Notation and Terminology.- Frequently Used Terms.- 1 Elementary Linear Algebra Review.- 2 Partitioned Matrices, Rank, and Eigenvalues.- 3 Matrix Polynomials and Canonical Forms.- 4 Numerical Ranges, Matrix Norms, and Special Operations.- 5 Special Types of Matrices.- 6 Unitary Matrices and Contractions.- 7 Positive Semidefinite Matrices.- 8 Hermitian Matrices.- 9 Normal Matrices.- 10 Majorization and Matrix Inequalities.- References.- Notation.- Index.
Downloads
Series: SpringerBriefs in Mathematics
1st Edition., 2012, X, 122 p.
Softcover, ISBN 978-1-4614-1520-6
Due: November 28, 2011
The main aim of this book is to present recent results concerning inequalities
of the Jensen, Cebysev and Gruss type for continuous functions of bounded
selfadjoint operators on complex Hilbert spaces.
In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive selfadjoint operators as well as some results for the spectrum of this class of operators are presented. This text introduces the reader to the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators as well as the step functions of selfadjoint operators. The spectral decomposition for this class of operators, which play a central role in the rest of the book and its consequences are introduced. At the end of the chapter, some classical operator inequalities are presented as well.
Recent new results that deal with different aspects of the famous Jensen operator inequality are explored through the second chapter. These include but are not limited to the operator version of the Dragomir-Ionescu inequality, the Slater type inequalities for operators and its inverses, Jensen’s inequality for twice differentiable functions whose second derivatives satisfy some upper and lower bound conditions and Jensen’s type inequalities for log-convex functions. Hermite-Hadamard’s type inequalities for convex functions and the corresponding results for operator convex functions are also presented.
-1. Functions of Selfadjoint Operators in Hilbert Spaces (Introduction,
Bounded Selfadjoint Operators, Continuous Functions of Selfadjoint Operators,
Step Functions of Selfadjoint Operators, The Spectral Decomposition of
Selfadjoint Operators, References). -2. Inequalities of the Jensen Type
( Introduction, Reverses of the Jensen Inequality, Some Slater Type Inequalities,
Other Inequalities for Convex Functions, Some Jensen Type Inequalities
for Twice Differentiable Functions, Some Jensen’s Type Inequalities for
Log-convex Functions, Hermite-Hadamard’s Type Inequalities, Hermite-Hadamard’s
Type Inequalities for Operator Convex Functions, References). -3. Inequalities
of the Cebysev and Gruss Type (Introduction, Cebysev’s Inequality, Gruss
Inequality, More Inequalities of Gruss Type, More Inequalities for the
Cebysev Functional, Bounds for the Cebysev Functional of Lipschitzian Functions,
Quasi Gruss Type Inequalities, Two Operator Gruss Type Inequalities, References).
Series: Stochastic Modelling and Applied Probability, Vol. 67
1st Edition., 2012, XIV, 586 p.
Hardcover, ISBN 978-3-642-24126-0
Due: November 30, 2011
In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made about the structure of such processes, and serious researchers will want to justify those assumptions through the use of data. As statisticians are wont to say, “In God we trust; all others must bring data.”
This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. For the first time in book form, the authors present these latest techniques, based on research from the last 10 years. They include new findings.
Part I Introduction and Preliminary Material.- 1.Introduction .- 2.Some Prerequisites.- Part II The Basic Results.- 3.Laws of Large Numbers: the Basic Results.- 4.Central Limit Theorems: Technical Tools.- 5.Central Limit Theorems: the Basic Results.- 6.Integrated Discretization Error.- Part III More Laws of Large Numbers.- 7.First Extension: Random Weights.- 8.Second Extension: Functions of Several Increments.- 9.Third Extension: Truncated Functionals.- Part IV Extensions of the Central Limit Theorems.- 10.The Central Limit Theorem for Random Weights.- 11.The Central Limit Theorem for Functions of a Finite Number of Increments.- 12.The Central Limit Theorem for Functions of an Increasing Number of Increments.- 13.The Central Limit Theorem for Truncated Functionals.- Part V Various Extensions.- 14.Irregular Discretization Schemes. 15.Higher Order Limit Theorems.- 16.Semimartingales Contaminated by Noise.- Appendix.- References.- Assumptions.- Index of Functionals.- Index.
Series: Applied Mathematical Sciences, Vol. 156
2012, VIII, 396 p. 48 illus.
Hardcover, ISBN 978-1-4614-0501-6
Due: November 28, 2011
Gives a unified presentation in an abstract setting
Two new sections along with many revisions
More references included
In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.
The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.
Introduction.- Global Theory.- Applications.
Series: Lecture Notes in Mathematics, Vol. 2041
1st Edition., 2011, VIII, 140 p.
Softcover, ISBN 978-3-642-23978-6
Due: November 30, 2011
This monograph treats one case of a series of conjectures by S. Kudla, whose goal is to show that Fourier of Eisenstein series encode information about the Arakelov intersection theory of special cycles on Shimura varieties of orthogonal and unitary type. Here, the Eisenstein series is a Hilbert modular form of weight one over a real quadratic field, the Shimura variety is a classical Hilbert modular surface, and the special cycles are complex multiplication points and the Hirzebruch?Zagier divisors. By developing new techniques in deformation theory, the authors successfully compute the Arakelov intersection multiplicities of these divisors, and show that they agree with the Fourier coefficients of derivatives of Eisenstein series.
1. Introduction.- 2. Linear Algebra.- 3. Moduli Spaces of Abelian Surfaces.- 4. Eisenstein Series.- 5. The Main Results.- 6. Local Calculations.