Provides a genuinely compressible convex integration approach
Surveys most results achieved by convex integration
Explains the essentials of hyperbolic conservation laws
This book applies the convex integration method to multi-dimensional compressible Euler
equations in the barotropic case as well as the full system with temperature. The convex
integration technique, originally developed in the context of differential inclusions, was applied
in the groundbreaking work of De Lellis and Szekelyhidi to the incompressible Euler equations,
leading to infinitely many solutions. This theory was later refined to prove non-uniqueness of
solutions of the compressible Euler system, too. These non-uniqueness results all use an
ansatz which reduces the equations to a kind of incompressible system to which a slight
modification of the incompressible theory can be applied. This book presents, for the first time,
a generalization of the De Lellis?Szekelyhidi approach to the setting of compressible Euler
equations. The structure of this book is as follows: after providing an accessible introduction to
the subject, including the essentials of hyperbolic conservation laws, the idea of convex
integration in the compressible framework is developed. The main result proves that under a
certain assumption there exist infinitely many solutions to an abstract initial boundary value
problem for the Euler system. Next some applications of this theorem are discussed, in
particular concerning the Riemann problem. Finally there is a survey of some related results.
This self-contained book is suitable for both beginners in the field of hyperbolic conservation
laws as well as for advanced readers who already know about convex integration in the
incompressible framework
Due 2021-11-06
1st ed. 2021, X, 200 p. 17 illus., 9 illus. in color.
Softcover
ISBN 978-3-030-83784-6
Product category : Monograph
Series :Lecture Notes in Mathematics
Mathematics : Analysis
An introduction to near-rings with many new contributions
Includes the first detailed English-language account of the theory of nearfields
Presents new ideas and problems for further research
This book offers an original account of the theory of near-rings, with a considerable amount of
material which has not previously been available in book form, some of it completely new. The
book begins with an introduction to the subject and goes on to consider the theory of nearfields,
transformation near-rings and near-rings hosted by a group. The bulk of the chapter on
near-fields has not previously been available in English. The transformation near-rings chapters
considerably augment existing knowledge and the chapters on product hosting are essentially
new. Other chapters contain original material on new classes of near-rings and non-abelian
group cohomology. The Theory of Near-Ringswill be of interest to researchers in the subject
and, more broadly, ring and representation theorists. The presentation is elementary and selfcontained,
with the necessary background in group and ring theory available in standard references.
Due 2021-11-04
1st ed. 2021, X, 560 p.
Softcover
ISBN 978-3-030-81754-1
Product category : Monograph
Series : Lecture Notes in Mathematics
Mathematics : Associative Rings and Algebras
Contains new, original presentations at the forefront of current international
research
Includes different interconnected subjects with different applications
Provides contributions to advanced subjects which offer a useful reference for
young researchers
This book includes four courses on geometric measure theory, the calculus of variations, partial
differential equations, and differential geometry. Authored by leading experts in their fields, the
lectures present different approaches to research topics with the common background of a
relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics
covered concern differentiation and functions of bounded variation in metric spaces, Sobolev
spaces, and differential geometry in the so-called Carnot?Caratheodory spaces. The text is
based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces"
held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione
Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and
researchers.
Due 2021-11-22
1st ed. 2021, X, 250 p.
Softcover
ISBN 978-3-030-84140-9
Product category : Proceedings
Series : C.I.M.E. Foundation Subseries
Mathematics : Optimization
Brings to light the axioms and fundamental postulates of science, revitalising
the conventions and clarifying the conceptual schemes that have allowed the
evolution of scientific disciplines as they are currently practised
Targets researchers and graduate students in engineering and physical
sciences, as well as researchers interested in a clarification of the
methodology, of dimensional analysis and theory of similarity aims and
purposes
Includes a chapter-end glossary listing the meaning of specific terms typical
of dimensional
The book provides a summary of the historical evolution of dimensional analysis, and frames
the problem of dimensions, systems of units and similarity in a vision dominated by the
conventions that formalise even the exact sciences. The first four chapters address the
definitions, with few dimensional analysis theorems and similarity criteria. There is also the
analysis of self-similarity, both of first and second kind, with a couple of completely solved
problems, framed within the group theory. From chapter 5 onward, the focus is on applications
in some of the engineering sectors. The number of topics is necessarily limited, but, almost
always, there are details, calculations and treatment of assumptions. The book contains
descriptions of some of the experimental apparatuses currently used for the realisation of
physical models, such as the wind tunnel, the shaking table, the centrifuge, and with the
exclusion of many others, which can be found in specialist monographies. Measurement
techniques and instrumentation and statistical data processing is also available in other books.
Due 2021-09-30
1st ed. 2021, XXXI, 429 p. 119 illus., 106 illus. in color.
Hardcover
ISBN 978-3-030-79216-9
Product category : Graduate/advanced undergraduate textbook
Series : Mathematical Engineering
Mathematics : Analysis
https://doi.org/10.1142/12358 | September 2021
Pages: 500
The aim of this book is to provide a complete synthetic exposition of plane isometries, similarities and inversions to readers who are interested in studying, teaching, and using this material.
The topics developed in this book can provide new proofs and solutions to many results and problems of classical geometry, which are presented with different proofs in the literature. Their applications are numerous and some, such as the Steiner Chains and Point, are useful to engineers.
The book contains many good examples, important applications and numerous exercises of various level and difficulty, which are classified in the three groups of: general exercises, geometrical constructions, and geometrical loci. Some lengthy exercises or groups of related exercises can be viewed as projects. On the basis of the above, this book, besides Classical Geometry, is an important addition to Mathematics Education.
Some Preliminaries
Isometries
Exercises on Isometries
Similarities
Exercises on Similarities
The Transformation of Inversion
Exercises on Circles
Exercises on Radical Axis
Exercises on Inversion
Bibliography
Index
College and high school students in mathematics, computational geometry, computational sciences.