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SISSA Springer Series

Vidossich G: Topological Degree with
Applications

Topological Degree with Applications

The book is made up by several worked out problems concerning the application of reduced order modeling to different parametric partial differential equations problems with an increasing degree of complexity.This work is based on some experience acquired during lectures and exercises in classes taught at SISSA Mathematics Area in the Doctoral Programme “Mathematical Analysis, Modelling and Applications”, especially in computational mechanics classes, as well as regular courses previously taught at EPF Lausanne and during several summer and winter schools. The book is a companion for master and doctoral degree classes by allowing to go more deeply inside some partial differential equations worked out problems, examples and even exercises, but it is also addressed for researchers who are newcomers in computational mechanics with reduced order modeling.In order to discuss computational results for the worked out problems presented in this booklet, we will rely on the RBniCS Project. The RBniCS Project contains an implementation in FEniCS of the reduced order modeling techniques (such as certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods) for parametric problems that will be introduced in this booklet.

Parametric PDEs Worked Out Problems

Real Time Reduced Order Computational Mechanics

De Gruyter Textbook

A Multi-scale Approach with Mathematica®

Applied Linear Analysis for Chemical Engineers

The book focuses on &nbsp;the mathematical foundations of boundary integro-differential equation method, with a primary focus on reducing the hypersingular integrals in traditional boundary integral equations into boundary integro-differential equations with weak singularities. It briefly introduces the theory of distributions, while the boundary integral equations method is grounded in the fundamental solutions of linear partial differential equations, hence a relatively detailed exposition of the fundamental solutions of differential equations is also provided. In the subsequent chapters, the authors sequentially discuss the boundary integro-differential equation methods and theories for Laplace equation, Helmholtz equation, Navier equations, Stokes equations, among others. Furthermore, the book addresses the boundary integro-differential equation method for certain nonlinear problems, such as thermal radiation, variational inequalities, and Steklov eigenvalue problems. Lastly, it explores the symmetric coupling issues between finite element and boundary element methods.

Mathematical Foundation of the Boundary Integro-Differential Equation Method

De Gruyter Series in Nonlinear Analysis and Applications

Dynamics, Coexistence and Persistence

Cross-Diffusion Systems

Data-Directed Mathematical Modeling

An accessible resource to help you puzzle out logic concepts Logic For Dummies, 2nd Edition explains all the varied ways we use logic in philosophy, science, and everyday life. College students taking a logic course and lifelong learners alike can benefit from this accessible guide to logic concepts--such as syllogisms, constructing proofs and refutations, propositional and predicate logic, symbolic logic, modal and fuzzy logic, deductive and inductive reasoning, and beyond. With real-world examples, fun logic problems, and fully worked out proofs, you have plenty of opportunities to follow along and apply what you've learned. Logic For Dummies, 2nd Edition helps you connect the logical dots! Inside: <ul> <li>Grasp formal and informal logic with clear explanations and practice problems</li> <li>See how logic shows up in everyday life and discover how to spot logical fallacies</li> <li>Work through logical proofs and refutations, with answer explanations to strengthen your understanding</li> <li>Sharpen your ability to reason through complex issues with truth tables</li> </ul> Logic For Dummies, 2nd Edition is the logical choice for anyone who wants or needs to learn the concepts, theories, and formulas of logical reasoning.

Logic For Dummies

Microsoft Power BI For Dummies

This book provides a comprehensive study of structural design and optimization of different truss structures for size, shape, and topology of structure. It describes truss optimization based on into three categories: size optimization, shape optimization, and topology optimization.It also studies the performance of metaheuristic algorithms developed after 2011 for truss optimization problems. The results highlight the best approach to achieve the best performance of the structural design. Pseudo codes of all the methods are provided at the end of the book so that it can be used by the researchers, practitioners, and students to test it for different real-world systems.This book ideal for structural design engineers to realize the appropriate systems with properly optimized parameters as well as designers, practitioners, consultants involved in structural designs, researchers, academics, and graduate students in mechanical, civil, and architectural engineering.

A Metaheuristic Optimization Approach

Truss Optimization

Math Survival Guide: Tips for Science Student, 3E

Springer Asia Pacific Mathematics Series

A variety of theorems named the Liouville property play fundamental roles in modern theory of mathematical analysis. Understanding each of them individually is not so difficult nowadays. What are they pointing toward in their totality, however? This monograph asserts that self-organization may be an answer, searching recent studies on linear and nonlinear partial differential equations. Critical breakthroughs have emerged in accordance with the widely spread classical ideas of J. Liouville in various forms, that is, the spectral, elliptic, surface, and transport theories, in turn. A fusion of them is seen in recently developing research fields—mathematical oncology, non-equilibrium statistical mechanics, dynamical theory, and shape optimization—which taken together may be called the potential for self-organization.

A variety of theorems named the Liouville property play fundamental roles in modern theory of mathematical analysis. Understanding each of them individually is not so difficult nowadays. What are they pointing toward in their totality, however? This monograph asserts that self-organization may be an answer, searching recent studies on linear and nonlinear partial differential equations. Critical breakthroughs have emerged in accordance with the widely spread classical ideas of J. Liouville in various forms, that is, the spectral, elliptic, surface, and transport theories, in turn. A fusion of them is seen in recently developing research fields—mathematical oncology, non-equilibrium statistical mechanics, dynamical theory, and shape optimization—which taken together may be called the potential for self-organization.&nbsp;
&nbsp;

Liouville’s Theory in Linear and Nonlinear Partial Differential Equations

SpringerBriefs in Optimization

This book delves into the intricate world of fixed point theory, focusing on the Krasnoselskii-Mann method to tackle common fixed point problems within a finite family of quasi-nonexpansive mappings in hyperbolic metric spaces. By exploring various iterative algorithms, including the Cimmino algorithm and dynamic string-averaging methods, this volume offers a comprehensive study of convergence and approximate solutions amidst computational errors.


Key concepts such as W-hyperbolic spaces, convex combinations, and set-valued inclusions are meticulously examined. The author presents a detailed analysis of iterative methods, highlighting their effectiveness in solving complex fixed-point problems. Readers will encounter critical discussions on the behavior of exact and inexact iterates, the role of computational errors, and innovative approaches like remotest set control. This book invites readers to engage with challenging questions about convergence and solution accuracy in mathematical spaces.


Ideal for researchers and scholars in mathematics and related fields, this book provides valuable insights into advanced iterative methods for solving fixed-point problems. Whether you are a mathematician specializing in nonlinear analysis or an academic exploring optimization theory, this volume is an essential resource for understanding the latest developments in fixed point theory.

The Krasnoselskii-Mann Method for Common Fixed Point Problems

Essentials

Dieses Buch erklärt kurz und prägnant die Forschung zum faszinierenden mengentheoretischen Unabhängigkeitsphänomen: Zahlreiche mengentheoretische Sätze sind gemäß den Standardaxiomen weder beweisbar noch widerlegbar. Um das zu zeigen, baut man zwei verschiedene mengentheoretische Modelle, meist mit Hilfe der bahnbrechenden Beweistechnik Forcing. Am Beispiel des berühmtesten unabhängigen Satzes – der Kontinuumshypothese – erläutert dieses Buch die Grundstruktur und die wesentlichen Argumente eines Unabhängigkeitsbeweises. Anschließend bietet es Einblicke in Themen, die Mengentheoretiker:innen aktuell beschäftigen und diskutiert verschiedene philosophische Sichtweisen auf das mysteriöse Phänomen.Der Inhalt<ul><li>Beschreibung des Unabhängigkeitsbeweises der Kontinuumshypothese, inklusive Forcing</li><li>Einblick in aktuelle mengentheoretische Forschung</li><li>Erläuterung verschiedener philosophischer Sichtweisen</li></ul>Die Zielgruppen<ul><li>An den Grundlagen interessierte Mathematikstudierende</li><li>An Mathematik interessierte Philosophiestudierende</li></ul>Die Autorin Nach ihrem Mathematikstudium mit Schwerpunkt Mengenlehre hat Deborah Kant in ihrer Doktorarbeit das Unabhängigkeitsphänomen philosophisch untersucht und in einer Interviewstudie herausgefunden, dass sich Mengentheoretiker:innen sehr uneinig über ihre philosophischen Ansichten sind und dennoch hervorragend miteinander arbeiten können. Aktuell forscht sie an der Universität Hamburg weiter zur mathematischen Forschungspraxis.

Eine Welt jenseits der mathematischen Beweiskraft

Das mengentheoretische Unabhängigkeitsphänomen

Storytelling with Data Box Set

Topological Degree with Applications

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