Series: Lecture Notes in Mathematics, Vol. 2031
2011, X, 360 p. 153 illus.
Softcover, ISBN 978-3-642-21918-4
Due: July 31, 2011
This book chronicles the development of graph factors and factorizations. It pursues a comprehensive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observation that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.
Content Level ≫ Graduate
Keywords ≫ 05C; 05CXX; 05C75 - Factorizations of Graphs - Factors of Graphs - Matchings in Graphs - Proof Technique
Related subjects ≫ Mathematics - Software Engineering
1 Basic Terminology.- 2 Matchings and 1-Factors.- 3 Regular Factors and f-Factors.- 4 (g, f)-Factors and [a, b]-Factors.- 5 [a, b]-Factorizations.- 6 Parity Factors.- 7 Component Factors.- 8 Spanning Trees.
2011, XIV, 346 p. 92 illus.
Hardcover, ISBN 978-1-4614-0194-0
Due: August 28, 2011
This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner.
An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.
-Preface. -Complex Numbers I. - Complex Numbers II. - Complex Numbers III. - Set Theory in the Complex Plane. - Complex Functions. -Analytic Functions I. - Analytic Functions II. - Elementary Functions I. - Elementary Functions II. - Mappings by Functions I. - Mappings by Functions II. - Curves, Contours, and Simply Connected Domains. - Complex Integration. -Independence of Path. - Cauchy-Goursat Theorem. - Deformation Theorem. - Cauchy’s Integral Formula. - Cauchy’s Integral Formula for Derivatives. - The Fundamental Theorem of Algebra. - Maximum Modulus Principle. - Sequences and Series of Numbers. - Sequences and Series of Functions. - Power Series. -Taylor’s Series. -Laurent’s Series. - Zeros of Analytic Functions. -Analytic Continuation. -Symmetry and Reflection. -Singularities and Poles I. -Singularities and Poles II. - Cauchy’s Residue Theorem. - Evaluation of Real Integrals by Contour Integration I. - Evaluation of Real Integrals by Contour Integration II. -Indented Contour Integrals. -Contour Integrals Involving Multi-valued Functions. -Summation of Series. -Argument Principle and Rouch´e and Hurwitz Theorems. -Behavior of Analytic Mappings. - Conformal Mappings. -Harmonic Functions. -The Schwarz-Christoffel Transformation. -Infinite Products. - Weierstrass’s Factorization Theorem. - Mittag-Leffler Theorem. -Periodic Functions. -The Riemann Zeta Function. -Bieberbach’s Conjecture. -Riemann Surfaces. -Julia and Mandelbrot Sets. -History of Complex Numbers. -References for Further Reading. -Index
Series: SpringerBriefs in Mathematics
2011, X, 127 p.
Softcover, ISBN 978-1-4614-0702-7
Due: September 28, 2011
Content Level ≫ Research
Keywords ≫ Caputo fractional derivative - Fractional Calculus - Fractional differentiation inequalities - Opial type - Ostrowski inequalities
Related subjects ≫ Analysis - Dynamical Systems & Differential Equations - Mathematics
-1. Opial-type inequalities for balanced fractional derivatives(Introduction, Background, Main Results, References). -2. Univariate right Caputo fractional Ostrowski inequalities (Introduction, Main Results, References). -3. Multivariate right Caputo fractional Ostrowski inequalities (Introduction, Main Results, References).-4. Univariate mixed fractional Ostrowski inequalities (Introduction, Main Results, References).-5. Multivariate radical mixed fractional Ostrowski inequalities(Introduction, Main Results, References).-6. Shell mixed Caputo fractional Ostrowski inequalities(Introduction, Main Results, References).-7. Left Caputo fractional uniform Landau inequalities (Introduction, Main Results, References).-8. Left Caputo Fractional Landau type Inequalities(Introduction, Main Results, References).-9. Right Caputo Fractional Landau type Inequalities(Introduction, Main Results, References).-10. Mixed Caputo Fractional Landau type Inequalities(Introduction, Main Results, References).-11. Multivariate Caputo Fractional Landau type Inequalities(Introduction, Main Results, References).
Series: Modern Birkhauser Classics
2011, VIII, 247 p.
Softcover, ISBN 978-0-8176-8246-0
Due: August 22, 2011
Interest in the spin-c Dirac operator originally came about from the study of complex analytic manifolds, where in the non-Kahler case the Dolbeault operator is no longer suitable for getting local formulas fot the Riemann-Roch number or the holomorphic Lefschetz number. However, every symplectic manifold (phase space in classical mechanics) also carries an almost complex structure and hence a corresponding spin-c Dirac operator. Using the heat kernels theory of Berline, Getzler, and Vergne, this work revisits some fundamental concepts of the theory, and presents the application to symplectic geometry.
1 Introduction.- 2 The Dolbeault-Dirac Operator.- 3 Clifford Modules.- 4 The Spin Group and the Spin-c Group.- 5 The Spin-c Dirac Operator.- 6 Its Square.- 7 The Heat Kernel Method.- 8 The Heat Kernel Expansion.- 9 The Heat Kernel on a Principal Bundle.- 10 The Automorphism.- 11 The Hirzebruch-Riemann-Roch Integrand.- 12 The Local Lefschetz Fixed Point Formula.- 13 Characteristic Case.- 14 The Orbifold Version.- 15 Application to Symplectic Geometry.- 16 Appendix: Equivariant Forms.
Series: Problem Books in Mathematics
2011, VI, 146 p.
Hardcover, ISBN 978-1-4614-0429-3
Due: October 28, 2011
A Sequence of Problems on Semigroups consists of an arrangement of problems which are designed to develop a variety of aspects to understanding the area of one-parameter semigroups of operators. Written in the Socratic/Moore method, this is a problem book with neither the proofs nor the answers presented. To get the most out of the content requires high motivation to work out the exercises. However, the reader is given the opportunity to discover important developments of the subject and to quickly arrive at the point of independent research.
Many of the problems are not found easily in other books and they vary in level of difficulty. A few open research questions are also presented. The compactness of the volume and the reputation of the author lends this concise set of problems to be a 'classic' in the making. This text is highly recommended for use as supplementary material for three graduate level courses.
-Preface.-1. Introduction.-2. The idea of a semigroup.-3. Translation semigroups.-4. Linear continuous semigroups.-5.Strongly continuous linear semigroups.-6. An Application to the Heat Equation.-7. Some Problems in Analysis.-8.Semigroups of steepest descent.-9. Numerics of semigroups of steepest descent.-10. Nonlinear semigroups studied by linear methods.-11. Measures and linear extension of nonlinear semigroups.-12. Local semigroups and Lie generators.-13. Quasi-analyticity of semigroups.-14. Continuous Newton's method and semigroups-15. Generalized semigroups without forward uniqueness.-16. Semigroups of nonlinear contractions and monotone operators.-17. Notes.-18. References.