ISBN: 978-1-84265-586-3
Publication Year: 2010
Pages: 150 Binding: Hard Back
Dimension: 160mm x 240mm
Applied Differential Equations discusses the Legendre and Bessel Differential equations and its solutions. Various properties of Legendre Polynomials as well as Legendre function and Bessel functions in part one. The second order Partial Differential equation of three types is studied and the technique to solve with the Separation of Variables technique called Fourierfs Method have been discussed in the second part. In the Appendix some applications of the Heat Equation are discussed to Model the Environment.
* MATLAB solutions of First Order as well as Second Order ODE
* At the end of each Chapter a set of problems is also there
Table of Contents
Preface / PART-A: Power Series Solution of Ordinary Differential Equation / Legendre Differential Equation and its Properties / Bessel and Euler-Cauchy Differential Equation / PART-B: Partial Differential Equations / Laplace Equation / Heat Conduction Diffusion Equation / Appendixes / Index.
Undergraduate and Postgraduate Students in Mathematics
ISBN: 978-1-84265-609-9
Publication Year: 2010
Pages: 252 Binding: Hard Back
Dimension: 185mm x 240mm
The concept of a differentiable manifold is introduced in a simple manner without going into its topological structure. Subsequently the reader is led to the same conceptual details as are found in other texts on the subjects. Since calculus on a differentiable manifold is done via the calculus on Rn, a preliminary chapter on the calculus on Rn is added. While introducing concepts such as tangent and cotangent bundles, tensor algebra and calculus, Riemannian geometry etc., enough care is taken to provide many details which enable the reader to grasp them easily. The material of the book has been tried in class-room successfully. Queries raised by the students have helped us to improve the presentation.
Preface / Differential Calculus on Rn and Related Topics / Differentiable Manifolds / Tangent, Cotangent Spaces and Bundles / One Parameter Group and Lie Derivatives / Tensor Algebra and Calculus / Connections / Riemannian Manifolds / Submanifolds / Bibliography / Index.
Postgraduate Students and Researchers
ISBN: 978-1-84265-580-1
Publication Year: 2010
Pages: 208 Binding: Hard Back
Dimension: 160mm x 240mm
Fuzzy Mathematical Concepts deals with the theory and applications of Fuzzy sets, Fuzzy relations, Fuzzy logic and Rough sets including the theory and applications to Algebra, Topology, Analysis, probability, and Measure Theory. While the first two chapters deal with basic theory and the prerequisite for the rest of the book, readers interested in Algebra and Logic may go through chapters 3 and 4, those interested in Topology may proceed to chapters 5 to 8 and for Analysis one may read chapters 8 and 9. Readers interested in Rough Set Theory may directly proceed to chapter 10 after completing chapters 1 and 2. A part of the book can be covered in one semester depending on the requirement and the whole book in two semesters.
* Contains applications of Fuzzy Set Theory to Algebra and Topology
* Includes Rough Set Theory and its comparison to Fuzzy Sets
Preface / Fuzzy Subsets and Fuzzy Mappings / Fuzzy Relations and Fuzzy Logic / Fuzzy Groups and Fuzzy Rings / Fuzzy Fields and Fuzzy Linear Spaces / Fuzzy Topological Spaces / Ordered Fuzzy Topological Spaces/ Fuzzy Topological Vector Spaces / Fuzzy Metric Space / Possibility and Fuzzy Measure / Fuzzy Sets and Rough Sets/ Bibliography / Index.
Undergraduate and Graduate Students of Mathematics, Statistics, Engineering, Computer Science, Science and Management
Clay Mathematics Proceedings, Volume: 12
2010; 349 pp; softcover
ISBN-13: 978-0-8218-5199-9
Expected publication date is January 15, 2011.
This volume contains articles related to the conference "Motives, Quantum Field Theory, and Pseudodifferntial Operators" held at Boston University in June 2008, with partial support from the Clay Mathematics Institute, Boston University, and the National Science Foundation. There are deep but only partially understood connections between the three conference fields, so this book is intended both to explain the known connections and to offer directions for further research.
In keeping with the organization of the conference, this book contains introductory lectures on each of the conference themes and research articles on current topics in these fields. The introductory lectures are suitable for graduate students and new Ph.D.'s in both mathematics and theoretical physics, as well as for senior researchers, since few mathematicians are expert in any two of the conference areas.
Among the topics discussed in the introductory lectures are the appearance of multiple zeta values both as periods of motives and in Feynman integral calculations in perturbative QFT, the use of Hopf algebra techniques for renormalization in QFT, and regularized traces of pseudodifferential operators. The motivic interpretation of multiple zeta values points to a fundamental link between motives and QFT, and there are strong parallels between regularized traces and Feynman integral techniques.
The research articles cover a range of topics in areas related to the conference themes, including geometric, Hopf algebraic, analytic, motivic and computational aspects of quantum field theory and mirror symmetry. There is no unifying theory of the conference areas at present, so the research articles present the current state of the art pointing towards such a unification.
Graduate students and research mathematicians interested in algebraic geometry, quantum field theory, and pseudodifferential operators, and the connections between these areas in mathematics.
Introductory articles
Y. Andre -- An introduction to motivic zeta functions of motives
D. Kreimer -- Algebra for quantum fields
M. Lesch -- Pseudodifferential operators and regularized traces
D. Manchon -- Renormalization in connected graded Hopf algebras: An introduction
Research articles
P. Albin and R. Melrose -- Fredholm realizations of elliptic symbols on manifolds with boundary II: Fibered boundary
J. Bergstrom and F. Brown -- Inversion of series and the cohomology of the moduli spaces $\mathcal{M}^{\delta}_{0,n}$
P. Bouwknegt, K. C. Hannabuss, and V. Mathai -- C*-algebras in tensor categories
J. Blumlein -- Structural relations of harmonic sums and Mellin transforms at weight $w=6$
L. Foissy -- Hopf subalgebras of rooted trees from Dyson-Schwinger equations
J. Mickelsson -- From gauge anomalies to Gerbes and Gerbal actions
R. Ponge -- A microlocal approach to Fefferman's program in conformal and CR geometry
M. Roth and N. Yui -- Mirror symmetry for elliptic curves: The A-model (fermionic) counting
C. Schneider -- A symbolic summation approach to find optimal nested sum representations
S. Scott -- Logarithmic structures and TQFT
W. D. van Suijlekom -- Renormalization Hopf algebras for gauge theories and BRST-symmetries
Fields Institute Communications,
2011; 213 pp; hardcover
ISBN-13: 978-0-8218-5237-8
Expected publication date is February 24, 2011.
Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas.
This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero.
This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.
Graduate students and research mathematicians interested in Lie algebras and algebraic combinatorics.
J. Kamnitzer -- Geometric constructions of the irreducible representations of $GL_n$
S.-J. Kang -- Introduction to crystal bases
A. Savage -- Geometric realizations of crystals
W. Wang -- Nilpotent orbits and finite $W$-algebras
E. Neher -- Extended affine Lie algebras--An introduction to their structure theory
V. Chari -- Representations of affine and toroidal Lie algebras
Bibliography
Index