الصفحة 1
الصفحة 1
Numerical Mathematics
Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis.
Hierarchical Matrices : A Means to Efficiently Solve Elliptic Boundary Value Problems
Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients.
Harmonic Analysis and Rational Approximation : Their Rôles in Signals, Control and Dynamical Systems
This book - an outgrowth of a topical summer school - sets out to introduce non-specialists from physics and engineering to the basic mathematical concepts of approximation and Fourier theory. After a general introduction, Part II of this volume contains basic material on the complex and harmonic analysis underlying the further developments presented. Part III deals with the essentials of approximation theory while Part IV completes the foundations by a tour of probability theory. Part V reviews some major applications in signal and control theory. In Part VI mathematical aspects of dynamical systems theory are discussed. Part VII, finally, is devoted to a modern approach to two physics problems: turbulence and the control and noise analysis in gravitational waves measurements.
Graph-theoretic concepts in computer science ; 46th International Workshop, WG 2020, Leeds, UK, June 24–26, 2020, Revised Selected Papers
This book constitutes the revised papers of the 46th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2020, held in Leeds, UK, in June 2020. The workshop was held virtually due to the COVID-19 pandemic. The 32 full papers presented in this volume were carefully reviewed and selected from 94 submissions. They cover a wide range of areas, aiming to present emerging research results and to identify and explore directions of future research of concepts on graph theory and how they can be applied to various areas in computer science.
Frontiers in Algorithmics ; 14th International Workshop, FAW 2020, Haikou, China, October 19-21, 2020, Proceedings
This book constitutes the proceedings of the 14th International Workshop on Frontiers in Algorithmics, FAW 2020, held in Haikou, China, in May 2020. The conference was held virtually due to the COVID-19 pandemic. The 12 full papers presented in this volume were carefully reviewed and selected from 15 submissions. The workshop provides a focused forum on current trends of research on algorithms, discrete structures, and their applications, and brings together international experts at the research frontiers in these areas to exchange ideas and to present significant new results. The papers detail graph theory, scheduling and algorithm and complexity.
Computational Methods for Algebraic Spline Surfaces : ESF Exploratory Workshop
The papers included in this volume provide an overview about the state-of-the-art in approximative implicitization and various related topics, including both the theoretical basis and the existing computational techniques. The novel idea of approximate implicitization has strengthened the existing link between Computer Aided Geometric Design and classical algebraic geometry. There is a growing interest from researchers and professionals both in CAGD and Algebraic Geometry, to meet and combine knowledge and ideas, in order to better solve industrial--type challenges, as well as to initiate new directions for basic research. This volume will support this exchange of ideas between the various communities.
Combinatorial optimization and applications ; 14th International Conference, COCOA 2020, Dallas, TX, USA, December 11–13, 2020, Proceedings
This volume constitutes the proceedings of the 14th International Conference on Combinatorial Optimization and Applications, COCOA 2020, held in Dallas, TX, USA, in December 2020. The 55 full papers presented in this volume were carefully reviewed and selected from 104 submissions. The papers are grouped into the following topics: Approximation Algorithms; Scheduling; Network Optimization; Complexity and Logic; Search, Facility and Graphs; Geometric Problem; Sensors, Vehicles and Graphs; and Graph Problems.
Complex Systems in Biomedicine
Features contributions from several Italian research groups that are working on the field of biomedicine. Each chapter in this book deals with a specific subfield, with the aim of providing an overview of the subject and an account of the research results.
Applied Proof Theory : Proof Interpretations and Their Use in Mathematics
Ulrich Kohlenbach presents an applied form of proof theory that has led in recent years to new results in number theory, approximation theory, nonlinear analysis, geodesic geometry and ergodic theory (among others). This applied approach is based on logical transformations (so-called proof interpretations) and concerns the extraction of effective data (such as bounds) from prima facie ineffective proofs as well as new qualitative results such as independence of solutions from certain parameters, generalizations of proofs by elimination of premises. The book first develops the necessary logical machinery emphasizing novel forms of Gödel's famous functional ('Dialectica') interpretation. It then establishes general logical metatheorems that connect these techniques with concrete mathematics. Finally, two extended case studies (one in approximation theory and one in fixed point theory) show in detail how this machinery can be applied to concrete proofs in different areas of mathematics.
Applicazioni ed esercizi di modellistica numerica per problemi differenziali = Applications and exercises in numerical modeling for differential problems
Contains a collection of exercises related to typical topics in a course on analytical and numerical methods offered in a degree program in Engineering or Mathematics. Starting with exercises in functional analysis and approximation theory, the text develops problems related to the numerical resolution of elliptic, parabolic, and hyperbolic partial differential equations, scalar or vector, in one or more spatial dimensions. Pure diffusion and pure convection problems are therefore addressed, alongside diffusion-transport problems and problems in compressible and incompressible fluid dynamics. Particular emphasis is given to the finite element method for the spatial discretization of the problems considered, although exercises on the finite difference and finite volume methods are also included.
Algorithms and data structures ; 17th International Symposium, WADS 2021, Virtual Event, August 9–11, 2021, Proceedings
This book constitutes the refereed proceedings of the 17th International Symposium on Algorithms and Data Structures, WADS 2021, held in virtually in August 2021. The 47 full papers, presented together with two invited lectures, were carefully reviewed and selected from a total of 123 submissions. They present original research on the theory, design and application of algorithms and data structures.
Algorithmic Aspects in Information and Management ; 14th International Conference, AAIM 2020, Jinhua, China, August 10–12, 2020, Proceedings
This volume constitutes the proceedings of the 14th International Conference on Algorithmic Aspects in Information and Management, AAIM 2020, held in Jinhua, China in August 2020. The 39 full papers and 17 short papers presented were carefully reviewed and selected from 76 submissions. The papers deal with emerging important algorithmic problems with a focus on the fundamental background, theoretical technology development, and real-world applications associated with information and management analysis, modeling and data mining. Special considerations are given to algorithmic research that was motivated by real-world applications.
