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Siu Yum-Tong: Introduction to Several
Complex Variables

Introduction to Several Complex Variables

Contemporary Mathematics And Its Applications: Monographs, Expositions And Lecture Notes

In this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions.

The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series.

Brownian Motion And Potential Theory, Modern And Classical

This book provides a comprehensive exploration of generalization in deep learning, focusing on both theoretical foundations and practical strategies. It delves deeply into how machine learning models, particularly deep neural networks, achieve robust performance on unseen data.

Theoretical Foundations and Practical Strategies

Deep Learning Generalization

The Handbook of Complex Analysis will be an entree for advanced undergraduates and beginning graduate students in the subject of complex analysis. The subject of complex analysis of increasing importance. Even the function theory of several complex variables has seen applications in cosmology, geophysics, and engineering.

The Handbook of Complex Analysis will be an entree for advanced undergraduates and beginning graduate students in the subject of complex analysis. The subject of complex analysis of increasing importance. Even the function theory of several complex variables has seen applications in cosmology, geophysics, and engineering.

Handbook of Complex Analysis

Fibonacci Cubes have been an extremely popular area of research since the 1990s.


This unique compendium features the state of research into Fibonacci Cubes. It expands the knowledge in graph theoretic and combinatorial properties of Fibonacci Cubes and their variants.


By highlighting various approaches with numerous examples, it provides a fundamental source for further research in the field. This useful reference text surely benefits advanced students in computer science and mathematics and serves as an archival record of the current state of the field.

Fibonacci Cubes With Applications And Variations

Textbooks in Mathematics

The textbook is designed for university students studying science and engineering. I have aimed for a comparatively short book that would give a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications.

The textbook is designed for university students studying science and engineering.&nbsp;I have aimed for a comparatively short book that would give a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications.

An Introduction to Complex Analysis and the Laplace Transform

"Economic Bifurcation and Chaos provides a unified presentation of the contributions to the literature on economic bifurcation, nonlinear dynamics, and chaos by William A Barnett and his coauthors. The span of the research begins in 1988 with Barnett's initial finding of chaos in economic data. The book continues with subsequent findings of bifurcation in all dynamical macroeconomic models so far tested by Barnett and his coauthors. The research covered extends over 3 decades to his recent findings of Shilnikov chaos in New Keynesian models of the UK and US economies. While methodology for testing for bifurcation, nonlinear dynamics, and chaos are fundamental to the research, the book's ultimate objectives focus on implications for robustness of dynamical inferences and implications for policy. Bifurcation subsets are found stratifying the parameter space of all tested macroeconomic models, with confidence regions of parameter estimates crossing the boundaries between those subsets. A robustness problem results from policy simulations conducted only at point estimates of model parameters. Such simulations should be conducted at various locations throughout the confidence region to explore the dynamical implications of such models. A more dramatic result is acquired in the special case of New Keynesian models during periods of active Taylor rule setting of short-term interest rates. That policy, without the imposition of a long run transversality condition, bifurcates the economy's dynamics to Shilnikov chaos, implying unintended long run downward drift of interest rates within the Shilnikov fractal attractor set. To control the drift, there needs to be a second policy instrument focused on the long run"--

Economic Bifurcation And Chaos

"This rigorous introduction to the fundamental ideas of convexity and their use in optimization offers a unifying approach for both discrete and continuous applications. Students and researchers in optimization, operations research, computer science, and applied mathematics will appreciate the book's 300+ exercises and coverage of new developments"--

This rigorous introduction to the fundamental ideas of convexity and their use in optimization offers a unifying approach for both discrete and continuous applications. Students and researchers in optimization, operations research, computer science, and applied mathematics will appreciate the book's 300+ exercises and coverage of new developments.

Convexity and its Applications in Discrete and Continuous Optimization

This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space).

This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space).

Normal Families and Normal Functions

The book comprises six chapters, each meticulously structured to build a comprehensive understanding of complex analysis. Chapter 1 covers the most fundamental concepts, providing the essential groundwork that permeates the entire text. Chapter 2 delves into normal families, the Riemann mapping theorem, and conformal mapping. Chapter 3 focuses on the zeros of analytic functions, while Chapter 4 explores the essential properties of harmonic and subharmonic functions. Chapter 5 introduces H^p spaces and the Fourier transform, highlighting their interconnections. The final chapter discusses uniform approximation by rational functions.

Emphasizing foundational theories, modern methods, and key ideas in complex analysis, this book also presents some cutting-edge research problems and recent advancements. The topics are thoughtfully selected, and the exposition is clear and rigorous. This book is an excellent resource for graduate students and independent learners alike. It features many new and concise proofs of classical theorems, and offers numerous challenging exercises to deepen understanding.

Complex Analysis

One of the central highlights of this work is the exploration of the Yoneda lemma and its profound implications, during which intuitive explanations are provided, as well as detailed proofs, and specific examples. This book covers aspects of category theory often considered advanced in a clear and intuitive way, with rigorous mathematical proofs. It investigates universal properties, coherence, the relationship between categories and graphs, and treats monads and comonads on an equal footing, providing theorems, interpretations and concrete examples. Finally, this text contains an introduction to monoidal categories and to strong and commutative monads, which are essential tools in current research but seldom found in other textbooks.


Starting Category Theory serves as an accessible and comprehensive introduction to the fundamental concepts of category theory. Originally crafted as lecture notes for an undergraduate course, it has been developed to be equally well-suited for individuals pursuing self-study. Most crucially, it deliberately caters to those who are new to category theory, not requiring readers to have a background in pure mathematics, but only a basic understanding of linear algebra.

Starting Category Theory

Oxford Graduate Texts in Mathematics

Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory, and covers twenty examples of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator.

Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory, and covers twenty examples of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator.

Operator Theory by Example

Nankai Tracts in Mathematics

Finsler geometry is just Riemannian geometry without a quadratic restriction. It has applications in many fields of natural sciences, including physics, psychology, and ecology. The book is intended to provide basic materials on Finsler geometry for readers and to bring them to the frontiers of active research on related topics.

This book is comprised of three parts. In Part I (Chapters 1-4), the author introduces the basics, such as Finsler metrics, the Chern connection, geometric invariant quantities, etc., and gives some rigidity results on Finsler manifolds with certain curvature properties. Part II (Chapters 5-6) covers the theory of geodesics, using which the author establishes some comparison theorems, which are fundamental tools to study global Finsler geometry. In Part III (Chapters 7-9), the author presents recent developments in nonlinear geometric analysis on Finsler spaces, partly based on the author's recent works on Finsler harmonic functions, the eigenvalue problem, and heat flow. The author has made efforts to ensure that the contents are accessible to advanced undergraduates, graduate students, and researchers who are interested in Finsler geometry.

Geometry And Analysis On Finsler Spaces

Introduction to Several Complex Variables

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Bibliografische Angaben

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