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Books in Several complex variables and analytic spaces

Artificial Intelligence Modeling for Dynamical Problems
1st Edition
Snehashish Chakraverty + 2 more
English
Artificial Intelligence Modeling for Dynamical Problems provides a comprehensive exploration of AI-driven methodologies tailored to address the intricate challenges posed by dynamical systems. The chapters in this book delve into cutting-edge techniques, including scientific machine learning, operator learning, fuzzy logic, and optimization algorithms, highlighting their applications in structural dynamics, fluid dynamics, robotics, and wave dynamics. Readers will gain insights into innovative state-of-the-art approaches such as Physics-Informed Neural Networks (PINNs) for precise navigation and control in autonomous vehicles, convolutional neural networks (CNNs) for frequency dynamics recognition, and data-driven models for market sentiment analysis. Additionally, the book explores the role of uncertainty modeling, statistical inference, and hybrid AI techniques, such as Type-2 fuzzy fractional modeling, in advancing the field of dynamical system analysis. Each chapter combines foundational principles with practical applications, including recent investigations, making it a valuable resource for researchers, practitioners, students of STEM seeking to apply theoretical AI models to real-world dynamical problems.
Theory and Computation of Tensors
Multi-Dimensional Arrays
1st Edition
Yimin Wei + 1 more
English
Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships.
Handbook of Complex Analysis
Geometric Function Theory
1st Edition
Reiner Kuhnau
English
Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane).
Multivariate Polysplines
Applications to Numerical and Wavelet Analysis
1st Edition
Ognyan Kounchev
English
Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and "smoothing" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature.
A Matlab Companion for Multivariable Calculus
1st Edition
Jeffery Cooper
English
Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton's method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-...
Mathematical Tools for Applied Multivariate Analysis
1st Edition
J. Douglas Carroll + 1 more
Anil Chaturvedi
English
This revised edition presents the relevant aspects of transformational geometry, matrix algebra, and calculus to those who may be lacking the necessary mathematical foundations of applied multivariate analysis. It brings up-to-date many definitions of mathematical concepts and their operations. It also clearly defines the relevance of the exercises to concerns within the business community and the social and behavioral sciences. Readers gain a technical background for tackling applications-oriente... multivariate texts and receive a geometric perspective for understanding multivariate methods."Mathematica... Tools for Applied Multivariate Analysis, Revised Edition illustrates major concepts in matrix algebra, linear structures, and eigenstructures geometrically, numerically, and algebraically. The authors emphasize the applications of these techniques by discussing potential solutions to problems outlined early in the book. They also present small numerical examples of the various concepts.
Exploratory and Multivariate Data Analysis
1st Edition
Michel Jambu
English
With a useful index of notations at the beginning, this book explains and illustrates the theory and application of data analysis methods from univariate to multidimensional and how to learn and use them efficiently. This book is well illustrated and is a useful and well-documented review of the most important data analysis techniques.
An Introduction to Complex Analysis in Several Variables
3rd Edition
Volume 7
L. Hormander
English
A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based on the solution of the Neumann Problem as the main tool. The additions made in this third, revised edition place additional stress on results where these methods are particularly important. Thus, a section has been added presenting Ehrenpreis' ``fundamental principle'' in full. The local arguments in this section are closely related to the proof of the coherence of the sheaf of germs of functions vanishing on an analytic set. Also added is a discussion of the theorem of Siu on the Lelong numbers of plurisubharmonic functions. Since the L2 techniques are essential in the proof and plurisubharmonic functions play such an important role in this book, it seems natural to discuss their main singularities.
Multivariate Analysis
1st Edition
Kanti V. Mardia + 2 more
English
Multivariate Analysis deals with observations on more than one variable where there is some inherent interdependence between the variables. With several texts already available in this area, one may very well enquire of the authors as to the need for yet another book. Most of the available books fall into two categories, either theoretical or data analytic. The present book not only combines the two approaches but it also has been guided by the need to give suitable matter for the beginner as well as illustrating some deeper aspects of the subject for the research worker. Practical examples are kept to the forefront and, wherever feasible, each technique is motivated by such an example.
An Introduction to Complex Analysis in Several Variables
2nd Edition
Volume 7
L. Hormander
English