SISSA Springer Series – serie
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11 produkter
11 produkter
Del 1 - SISSA Springer Series
Continuum Thermodynamics
Inbunden, Engelska, 2019
972 kr
Skickas inom 10-15 vardagar
This book deals with an important topic in rational continuum physics, thermodynamics.Although slim, it is fairly well self-contained; some basic notions in continuum mechanics, which a well-intentioned reader should but may not be familiar with, are collected in a final appendix.Modern continuum thermodynamics is a field theory devised to handle a large class of processes that typically are neither spatially homogeneous nor sequences of equilibrium states. The most basic chapter addresses the continuum theory of heat conduction, in which the constitutive laws furnish a mathematical characterization of the macroscopic manifestations of those fluctuations in position and velocity of the microscopic matter constituents that statistical thermodynamics considers collectively. In addition to a nonstandard exposition of the conceptual steps leading to the classical heat equation, the crucial assumption that energy and entropy inflows should be proportional is discussed and a hyperbolic version of that prototypical parabolic PDE is presented. Thermomechanics comes next, a slightly more complex paradigmatic example of a field theory where microscopic and macroscopic manifestations of motion become intertwined. Finally, a virtual power format for thermomechanics is proposed, whose formulation requires that temperature is regarded formally as the time derivative of thermal displacement. It is shown that this format permits an alternative formulation of the theory of heat conduction, and a physical interpretation of the notion of thermal displacement is given.It is addressed to mathematical modelers – or mathematical modelers to be – of continuous material bodies, be they mathematicians, physicists, or mathematically versed engineers.
Del 2 - SISSA Springer Series
Lectures on Nonsmooth Differential Geometry
Inbunden, Engelska, 2020
648 kr
Skickas inom 5-8 vardagar
This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis. In particular, a quite detailed account of the first-order structure of general metric measure spaces is presented, and the reader is introduced to the second-order calculus on spaces – known as RCD spaces – satisfying a synthetic lower Ricci curvature bound. Examples of the main topics covered include notions of Sobolev space on abstract metric measure spaces; normed modules, which constitute a convenient technical tool for the introduction of a robust differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow and its regularizing properties, within the general framework of “infinitesimally Hilbertian” metric measure spaces; the RCD condition and its effects on the behavior of heat flow; and second-order calculus on RCD spaces. The book is mainly intended for young researchers seeking acomprehensive and fairly self-contained introduction to this active research field. The only prerequisites are a basic knowledge of functional analysis, measure theory, and Riemannian geometry.
Del 2 - SISSA Springer Series
Lectures on Nonsmooth Differential Geometry
Häftad, Engelska, 2021
474 kr
Skickas inom 5-8 vardagar
This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis. In particular, a quite detailed account of the first-order structure of general metric measure spaces is presented, and the reader is introduced to the second-order calculus on spaces – known as RCD spaces – satisfying a synthetic lower Ricci curvature bound. Examples of the main topics covered include notions of Sobolev space on abstract metric measure spaces; normed modules, which constitute a convenient technical tool for the introduction of a robust differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow and its regularizing properties, within the general framework of “infinitesimally Hilbertian” metric measure spaces; the RCD condition and its effects on the behavior of heat flow; and second-order calculus on RCD spaces. The book is mainly intended for young researchers seeking acomprehensive and fairly self-contained introduction to this active research field. The only prerequisites are a basic knowledge of functional analysis, measure theory, and Riemannian geometry.
Del 3 - SISSA Springer Series
Invitation to Modern Enumerative Geometry
Inbunden, Engelska, 2022
1 508 kr
Skickas inom 10-15 vardagar
This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD courses Techniques in enumerative geometry (2019) and Localisation in enumerative geometry (2021). The goal of this book is to provide a gentle introduction, aimed mainly at graduate students, to the fast-growing subject of enumerative geometry and, more specifically, counting invariants in algebraic geometry. In addition to the more advanced techniques explained and applied in full detail to concrete calculations, the book contains the proofs of several background results, important for the foundations of the theory. In this respect, this text is conceived for PhD students or research “beginners” in the field of enumerative geometry or related areas. This book can be read as an introduction to Hilbert schemes and Quot schemes on 3-folds but also as an introduction to localisation formulae in enumerative geometry. It is meant to be accessible without a strong background in algebraic geometry; however, three appendices (one on deformation theory, one on intersection theory, one on virtual fundamental classes) are meant to help the reader dive deeper into the main material of the book and to make the text itself as self-contained as possible.
Del 3 - SISSA Springer Series
Invitation to Modern Enumerative Geometry
Häftad, Engelska, 2023
1 508 kr
Skickas inom 10-15 vardagar
This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD courses Techniques in enumerative geometry (2019) and Localisation in enumerative geometry (2021). The goal of this book is to provide a gentle introduction, aimed mainly at graduate students, to the fast-growing subject of enumerative geometry and, more specifically, counting invariants in algebraic geometry. In addition to the more advanced techniques explained and applied in full detail to concrete calculations, the book contains the proofs of several background results, important for the foundations of the theory. In this respect, this text is conceived for PhD students or research “beginners” in the field of enumerative geometry or related areas. This book can be read as an introduction to Hilbert schemes and Quot schemes on 3-folds but also as an introduction to localisation formulae in enumerative geometry. It is meant to be accessible without a strong background in algebraic geometry; however, three appendices (one on deformation theory, one on intersection theory, one on virtual fundamental classes) are meant to help the reader dive deeper into the main material of the book and to make the text itself as self-contained as possible.
Del 4 - SISSA Springer Series
Algebraic Curves and Surfaces
A History of Shapes
Inbunden, Engelska, 2023
1 401 kr
Skickas inom 10-15 vardagar
This volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces and the classification theorem of algebraic surfaces by Castelnuovo and Enriques; the use of such a classical geometric approach, as the one introduced by Castelnuovo, to study linear systems of hypersurfaces; and the algebraic methods used to find implicit equations of parametrized algebraic curves and surfaces, ranging from classical elimination theory to more modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Since our subject has a long and venerable history, this book cannot cover all the details of this broad topic, theory and applications, but it is meant to serve as a guide for both young mathematicians to approach the subject from a classical and yet computational perspective, and for experienced researchers as a valuable source for recent applications.
Del 4 - SISSA Springer Series
Algebraic Curves and Surfaces
A History of Shapes
Häftad, Engelska, 2024
1 079 kr
Skickas inom 10-15 vardagar
This volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces and the classification theorem of algebraic surfaces by Castelnuovo and Enriques; the use of such a classical geometric approach, as the one introduced by Castelnuovo, to study linear systems of hypersurfaces; and the algebraic methods used to find implicit equations of parametrized algebraic curves and surfaces, ranging from classical elimination theory to more modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Since our subject has a long and venerable history, this book cannot cover all the details of this broad topic, theory and applications, but it is meant to serve as a guide for both young mathematicians to approach the subject from a classical and yet computational perspective, and for experienced researchers as a valuable source for recent applications.
Del 5 - SISSA Springer Series
Real Time Reduced Order Computational Mechanics
Parametric PDEs Worked Out Problems
Inbunden, Engelska, 2024
1 294 kr
Skickas inom 5-8 vardagar
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.
Del 5 - SISSA Springer Series
Real Time Reduced Order Computational Mechanics
Parametric PDEs Worked Out Problems
Häftad, Engelska, 2025
1 294 kr
Skickas inom 10-15 vardagar
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.
- Nyhet
Del 6 - SISSA Springer Series
Topological Degree with Applications
Inbunden, Engelska, 2026
2 152 kr
Skickas inom 10-15 vardagar
This book is unique in the current scenario because it provides a complete treatment of modern Brouwer and of Leray-Schauder degree theories, including detailed proofs and selected applications to differential equations. In addition, new results and open problems appear throughout. It aims to introduce Ph.D. students to research on nonlinear boundary value problems for ordinary, elliptic, and evolution equations using the topological methods of nonlinear functional analysis. It is suitable for self-study, as all proofs are detailed, with prerequisites provided when necessary. It is based on personal notes compiled over more than forty years of teaching.GV studied Mathematics in Pisa during the 1960s with G.Stampacchia as supervisor. He has been professor at the Universities of Brasilia and Trieste, ending his career at SISSA (the research institute he co-founded together with P.Budinich, L.Fonda and L.Stasi). He has held visiting positions in Brazil, Peru, Somalia, South Africa and USA. After an initial activity in General Topology, his main research topic has become BVPs of ODEs in connection with the topological methods of Nonlinear Functional Analysis.
- Nyhet
Inbunden, Engelska, 2026
543 kr
Skickas inom 10-15 vardagar
Functional Analysis is based on the lecture notes of a Functional Analysis course taught for many years by Sandro Zagatti at SISSA (the International School for Advanced Studies, Trieste). Faithfully transcribed and typeset after his passing, the book preserves the clarity, structure, and pedagogical precision that defined his teaching. The text provides a rigorous and complete introduction to the fundamental concepts and methods of functional analysis, guiding readers from the study of metric and normed spaces to the more advanced theory of Banach and Hilbert spaces. It develops systematically the key results that underlie modern analysis—the Hahn–Banach theorem, the Baire category theorem, compact and weak topologies, dual spaces, compact operators, and reflexivity—together with the classical spaces of continuous functions, sequence spaces, and Lp spaces. Each topic is presented with careful attention to logical structure and with numerous worked examples that illustrate both abstract results and their applications. The exposition emphasizes conceptual understanding and the ability to reason independently, following a style that makes abstract notions accessible without compromising mathematical rigor. The volume also includes a rich collection of exercises, many drawn from Zagatti’s original written exams, offering readers a way to consolidate and test their understanding. The problems often require combining ideas from different chapters, encouraging synthesis rather than rote application.Intended primarily for graduate and advanced undergraduate students in mathematics and physics, the book is also a valuable reference for researchers and instructors seeking a compact and elegant presentation of the core principles of functional analysis. It can serve as both a self-contained text for a first course and a preparatory reference for further study in analysis, partial differential equations, or mathematical physics. By preserving the depth and lucidity of Zagatti’s lectures, Functional Analysis stands as both a pedagogical tool and a tribute to his contribution to the SISSA mathematics community.