This book, which is split into two parts, is about Prof. Zhidong Bai's life and his contributions to statistics and probability. The first part contains an interview with Zhidong Bai conducted by Dr Atanu Biswas from the Indian Statistical Institute, and seven short articles detailing Bai's contributions. The second part is a collection of his selected seminal papers in the areas of random matrix theory, Edgeworth expansion, M-estimation, model selection, adaptive design in clinical trials, applied probability in algorithms, small area estimation, and time series, among others. This book provides an easy access to Zhidong Bai's important works, and serves as a useful reference for researchers who are working in the relevant areas.
Professor Bai’s Life and His Contributions:
A Conversation with Zhidong Bai (A Biswas)
Professor Z D Bai: My Friend, Philosopher and Guide (D Kundu)
Collaboration with a Dear Friend and Colleague (J W Silverstein)
Edgeworth Expansions: A Brief Review of Zhidong Bai’s Contributions (G J Babu)
Bai’s Contribution to M-Estimation and Relevant Tests in Linear Models (L Zhao)
Professor Bai’s Main Contributions on Randomized URN Models (F Hu)
Professor Bai’s Contributions to M-Estimation (Y Wu)
On Professor Bai’s Main Contributions to the Spectral Theory of Random Matrices (J F Yao)
Selected Papers of Professor Bai:
Edgeworth Expansions of a Function of Sample Means Under Minimal Moment Conditions and Partial Cramer’s Condition (G J Babu & Z D Bai)
Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part II. Sample Covariance Matrices (Z D Bai)
Circular Law (Z D Bai)
and other papers
396pp Pub. date: Feb 2008
ISBN 978-981-279-308-9
This book is ideal for a one-semester course for advanced undergraduate students and first-year graduate students in mathematics. It is a straightforward and coherent account of a body of knowledge in complex analysis, from complex numbers to Cauchy’s integral theorems and formulas to more advanced topics such as automorphism groups, the Schwarz problem in partial differential equations, and boundary behavior of harmonic functions.
The book covers a wide range of topics, from the most basic complex numbers to those that underpin current research on some aspects of analysis and partial differential equations. The novelty of this book lies in its choice of topics, genesis of presentation, and lucidity of exposition.
Complex Numbers
Arguments and Polar Forms of Complex Numbers
Exponentials, Powers and Roots
Functions of a Complex Variable
Holomorphic Functions and Cauchy?Riemann Equations
The Exponential, Trigonometric and Hyperbolic Functions
Logarithms, Complex Powers, Branches and Cuts
Contour Integrals and Path Independence
Cauchy’s Integral Theorems
Cauchy’s Integral Formulas
Taylor Series and Power Series
Laurent Series and Isolated Singularities
Residues
Trigonometric Integrals: Cauchy Principal Values of Improper Integrals on (?∞, ∞)
Fourier Transforms of Rational Functions
Singular Integrals on (?∞, ∞)
Integrals on Branch Cuts
Biholomorphisms
Zeros, Maximum Modulus Principle and Schwarz’s Lemma
Aut(??) and SU(1,1)
Aut(?), SL(2, ?) and the Iwasawa Decomposition
Harmonic Functions and the Schwarz Problem on ??
Readership: Advanced undergraduate and graduate students in mathematics, physics and engineering.
160pp Pub. date: Mar 2008
ISBN 978-981-281-107-3
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providing a mathematical construction of models at low dimensions and discussing the removal of the ultraviolet and infrared cut-off, the verification of the axioms and the validity of Ward Identities with the relative anomalies. The second part is devoted to lattice 2D Statistical Physics, analyzing in particular the theory of universality in perturbed Ising models and the computation of the non-universal critical indices in Vertex or Ashkin-Teller models. Finally the third part is devoted to the analysis of complex quantum fluids showing Luttinger of Fermi liquid behavior, like the 1D or 2D Hubbard model.
Introduction to Renormalization:
Basic Notions
Fermionic Functional Integrals
Quantum Field Theory:
The Ultraviolet Problem in Massive QED2
Infrared Problem and Anomalous Behavior
Ward Identities and Vanishing of the Beta Function
Thirring and Gross-Neveu Models
Axioms Verification and Wilson Fermions
Infrared QED4 with Large Photon Mass
Lattice Statistical Mechanics:
Universality in Generalized Ising Models
Nonuniversality in Vertex or Isotropic Ashkin-Teller Models
Universality-Nonuniversality Crossover in the Ashkin-Teller Model
Quantum Liquids:
Spinless Luttinger Liquids
The 1d Hubbard Model
Fermi Liquids in Two Dimensions
BCS Model with Long Range Interaction
Readership: Mathematical and theoretical physicists; mathematicians interested in the rigorous theory of renormalization.
304pp Pub. date: Apr 2008
ISBN 978-981-279-239-6
Differential-algebraic equations (DAEs) provide an essential tool for system modeling and analysis within different fields of applied sciences and engineering. This book addresses modeling issues and analytical properties of DAEs, together with some applications in electrical circuit theory.
Beginning with elementary aspects, the author succeeds in providing a self-contained and comprehensive presentation of several advanced topics in DAE theory, such as the full characterization of linear time-varying equations via projector methods or the geometric reduction of nonlinear systems. Recent results on singularities are extensively discussed. The book also addresses in detail differential-algebraic models of electrical and electronic circuits, including index characterizations and qualitative aspects of circuit dynamics. In particular, the reader will find a thorough discussion of the state/semistate dichotomy in circuit modeling. The state formulation problem, which has attracted much attention in the engineering literature, is cleverly tackled here as a reduction problem on semistate models.
Introduction to Differential-Algebraic Equations
Linear DAEs and Projector-Based Methods
Nonlinear DAEs and Reduction Methods
Singularities
Semistate Models of Electrical Circuits
Nodal Analysis
Branch-Oriented Methods
Readers with general background in differential calculus, linear algebra and ordinary differential equations; experts and graduate students in applied mathematics, dynamical systems and mathematical analysis; researchers from other fields interested in getting an introduction to DAEs; electrical and electronic engineers.
320pp (approx.) Pub. date: Scheduled Summer 2008
ISBN 978-981-279-180-1
The book comprises a collection of published papers which form a coherent treatment of Markov random walks and Markov additive processes together with their applications. Part I provides the foundations of these stochastic processes underpinned by a solid theoretical framework based on Semiregenerative phenomena. Part II presents some applications to queueing and storage systems.
Foundations of Markov Random Walks and Markov Additive Processes:
Theory of Semiregenerative Phenomena
Markov Random Walk-Fluctuation Theory and Wiener?Hopf Factorization
Further Results for Semiregenerative Phenomena
Limits Theorems for Markov Random Walks
Markov Renewal and Markov-Additive Processes ? A Review and Some New Results
Markov-Additive Processes of Arrivals
Application Examples:
Markov-Modulated Single-Server Queueing Systems
A Storage Model for Data Communications Systems
A Markovian Storage Model
Readership: Academics, researchers and graduate students who are interested in queueing theory and stochastic processes.
220pp (approx.) Pub. date: Scheduled Fall 2008
ISBN 978-981-279-318-8
Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions form renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory.
Basic Algebraic Geometry for Coding Theory
Algebraic Geometry Codes: General Theory
Decoding Algebraic Geometry Codes
The Key Equation for One-Point Codes and Its Solution with Koetter's Algorithm
Evaluation Codes
Asymptotically Good Codes
Algebraic Curves with Many Points over Finite Fields
Algebraic Geometry Codes from Higher-Dimensional Varieties
Generalized Toric Codes
Algebraic Geometry Codes over Rings
Trellis and Generalized Weights of AG Codes
Algebraic-Geometric Constructions of Convolutional Codes
Quantum Error-Correcting Codes from Algebraic Curves
Readership: Mathematicians, computer scientists, engineers in information theory.
380pp (approx.) Pub. date: Scheduled Fall 2008
ISBN 978-981-279-400-0
This textbook presents a classical approach to some techniques of multivariate analysis in a simple and transparent manner. It offers clear and concise development of the concepts; interpretation of the output of the analysis; and criteria for selection of the methods, taking into account the strengths and weaknesses of each. With its roots in matrix algebra, for which a separate chapter has been added as an appendix, the book includes both data-oriented techniques and a reasonable coverage of classical methods supplemented by comments about robustness and general practical applicability. It also illustrates the methods of numerical calculations at various stages.
This self-contained book is ideal as an advanced textbook for graduate students in statistics and other disciplines like social, biological and physical sciences. It will also be of benefit to professional statisticians.
Organization of the Multivariate Data, Measures of Distance, Treatment of Missing Observations
Multivariate Normal Distribution and Related Distributions (Wishart, Hotelling’s T2, Wilks’)
Tests for Multivariate Normality, Robust Estimation of Location and Scale Parameters
Testing of Multivariate Hypotheses, Simultaneous Confidence Intervals
Multivariate Regression Analysis
Analysis of Variance and Covariance
Principal Component Analysis
Factor Analysis
Canonical Correlation
Classification and Discrimination
Undergraduate and graduate students in probability & statistics, economists, sociologists and related scientists.
550pp (approx.) Pub. date: Scheduled Fall 2008
ISBN 978-981-279-175-7