Kompleks analyse, komplekse variabler

This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and PohangThe conferences were focused on the following two related problems:¿ existence of Kähler¿Einstein metrics on Fano varieties¿ degenerations of Fano varietieson which two famous conjectures were recently proved. The first is the famous Borisov¿Alexeev¿Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian¿YaüDonaldson Conjecture on the existence of Kähler¿Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide.These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow¿Shanghai¿Pohang conferences, while the others helped to expand the research breadth of the volume¿the diversity of their contributions reflects the vitality of modern Algebraic Geometry.

This book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem.The book aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text.This second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.

Denna bok är en nyutgåva av ett kompendium om analytiska funktioner i en komplex variabel som Lars Hörmander gav 1979.

Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Your government warns that 10% of your neighbors have a deadly contagious virus. The producer of a diagnostic test advertises that 90% of its tests are correct for any population. The test indicates that you have the virus. This book's author claims your test has a 50% chance of being false, given your test's result. Who do you believe? This book gives you insights necessary to interpret metrics that make a difference in life's decisions.This book gives methods and software that are essential to analyze change and error. Change describes a phenomenon across time points. Error compares diagnoses with the truth. Other texts give insufficient attention to these topics. This book's novel ideas dispel popular misconceptions and replace previous methods. The author uses carefully designed graphics and high school mathematics to communicate easily with college students and advanced scientists. Applications include but are not limited to Remote Sensing, Land Change Science, and Geographic Information Science."e;A wide range of tools to aid understanding of land cover and its change has been used but scientific progress has sometimes been limited through misuse and misunderstanding. Professor Pontius seeks to rectify this situation by providing a book to accompany the researcher's toolbox. Metrics That Make a Difference addresses basic issues of relevance to a broad community in a mathematically friendly way and should greatly enhance the ability to elicit correct information. I wish this book existed while I was a grad student."e; - Giles Foody, Professor of Geographical Information Science, The University of Nottingham"e;Metrics That Make a Difference provides a comprehensive synthesis of over two decades of work during which Dr. Pontius researched, developed, and applied these metrics. The book meticulously and successfully guides the reader through the conceptual basis, computations, and proper interpretation of the many metrics derived for different types of variables. The book is not just a mathematical treatise but includes practical guidance to good data analysis and good science. Data scientists from many fields of endeavor will benefit substantially from Dr. Pontius' articulate review of traditionally used metrics and his presentation of the innovative and novel metrics he has developed. While reading this book, I had multiple 'aha' moments about metrics that I shouldn't be using and metrics that I should be using instead."e; - Stephen Stehman, Distinguished Teaching Professor, State University of New York

This textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles.The book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier¿Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained.This book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.

This book collects papers related to the session ¿Harmonic Analysis and Partial Differential Equations¿ held at the 13th International ISAAC Congress in Ghent and provides an overview on recent trends and advances in the interplay between harmonic analysis and partial differential equations. The book can serve as useful source of information for mathematicians, scientists and engineers.The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.

Integrals and sums are not generally considered for evaluation using complex integration. This book proposes techniques that mainly use complex integration and are quite different from those in the existing texts. Such techniques, ostensibly taught in Complex Analysis courses to undergraduate students who have had two semesters of calculus, are usually limited to a very small set of problems.Few practitioners consider complex integration as a tool for computing difficult integrals. While there are a number of books on the market that provide tutorials on this subject, the existing texts in this field focus on real methods. Accordingly, this book offers an eye-opening experience for computation enthusiasts used to relying on clever substitutions and transformations to evaluate integrals and sums.The book is the result of nine years of providing solutions to difficult calculus problems on forums such as Math Stack Exchange or the author's website, residuetheorem.com.It serves to detail to the enthusiastic mathematics undergraduate, or the physics or engineering graduate student, the art and science of evaluating difficult integrals, sums, and products.

This book is an introductory guide for data scientists to learn the mathematical principles behind the most well-known AI algorithms. The author proposes two original theoretical concepts: the accordion theory and the recurrent third iteration theory. He then applies them to real cases. This work covers topics of higher mathematics from algebraic topology and spectral theory to functional analysis and ergodic theory. These concepts are fundamental to understanding AI concepts and algorithms. This deepens both practitioners' and managers' knowledge of mathematical modeling and assists them to engage with specialized literature. More importantly this book will help them to formally write their own ideas and research.

The theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or ¿donut¿) is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric ¿chord-and-tangent¿ method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.