Makes an extended version of the ojasiewicz?Simon inequality more available
to certain concrete problems
Offers a unified method to show asymptotic convergence of solutions for
nonlinear parabolic equations and systems
Covers a range of applications of concrete nonlinear parabolic equations,
including the famous Keller?Segel equations
The classical ojasiewicz gradient inequality (1963) was extended by Simon (1983) to the
infinite-dimensional setting, now called the ojasiewicz?Simon gradient inequality. This book
presents a unified method to show asymptotic convergence of solutions to a stationary solution
for abstract parabolic evolution equations of the gradient form by utilizing this ojasiewicz?
Simon gradient inequality. In order to apply the abstract results to a wider class of concrete
nonlinear parabolic equations, the usual ojasiewicz?Simon inequality is extended, which is
published here for the first time. In the second version, these abstract results are applied to
reaction?diffusion equations with discontinuous coefficients, reaction?diffusion systems, and
epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e.,
the Keller?Segel equations even for higher-dimensional ones.
Due 2021-07-09
1st ed. 2021, X, 61 p. 1 illus.
Softcover
ISBN 978-981-16-1895-6
Product category : Brief
Series : SpringerBriefs in Mathematics
Mathematics : Partial Differential Equations
Updated contributions in the areas covered by the workshop
The book contains papers of distinguished researchers
Geometric properties of solutions to elliptic and parabolic pdes are an
intriguing subject of research
This book contains the contributions resulting from the 6th Italian-Japanese workshop on
Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during
the week of May 20?24, 2019. This book will be of great interest for the mathematical
community and in particular for researchers studying parabolic and elliptic PDEs. It covers
many different fields of current research as follows: convexity of solutions to PDEs, qualitative
properties of solutions to parabolic equations, overdetermined problems, inverse problems,
Brunn-Minkowski inequalities, Sobolev inequalities, and isoperimetric inequalities.
Due 2021-07-11
1st ed. 2021, IX, 305 p. 27 illus., 18 illus. in color.
Hardcover
ISBN 978-3-030-73362-9
Product category : Contributed volume
Series : Springer INdAM Series
Mathematics : Analysis
Offers a unique exploration of analytic number theory that focuses on proving
explicit bounds in cases suited to versatile tools
Emphasizes a methodological approach to the material with several different
pathways to proceed
Promotes an active learning style with nearly 300 exercises appearing
throughout
This textbook offers a unique exploration of analytic number theory that is focused on explicit
and realistic numerical bounds. By giving precise proofs in simplified settings, the author
strategically builds practical tools and insights for exploring the behavior of arithmetical
functions. An active learning style is encouraged across nearly three hundred exercises, making
this an indispensable resource for both students and instructors. Designed to allow readers
several different pathways to progress from basic notions to active areas of research, the book
begins with a study of arithmetic functions and notions of arithmetical interest. From here,
several guided gwalksh invite readers to continue, offering explorations along three broad
themes: the convolution method, the Levin?Fanleb theorem, and the Mellin transform. Having
followed any one of the walks, readers will arrive at ghigher groundh, where they will find
opportunities for extensions and applications, such as the Selberg formula, Brunfs sieve, and
the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities
to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in
Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate
students who are familiar with the fundamentals of analytic number theory. It will also appeal
to researchers in mathematics and engineering interested in experimental techniques in this
active area.
Due 2021-07-12
XXII, 336 p.
Hardcover
ISBN 978-3-030-73168-7
Product category : Graduate/advanced undergraduate textbook
Series : Birkhauser Advanced Texts Basler Lehrbuche
Mathematics : Number Theory
Presents the summability of higher dimensional Fourier series, and
generalizes the concept of Lebesgue points
Introduces readers to multiple methods of summability, focusing particularly
on Fejer and Cesaro summability, as well as theta-summation
Includes multiple real-world applications, recent results, and a presentation
that prioritizes clarity throughout
This monograph presents the summability of higher dimensional Fourier series, and
generalizes the concept of Lebesgue points. Focusing on Fejer and Cesaro summability, as well
as theta-summation, readers will become more familiar with a wide variety of summability
methods. Within the theory of higher dimensional summability of Fourier series, the book also
provides a much-needed simple proof of Lebesguefs theorem, filling a gap in the literature.
Recent results and real-world applications are highlighted as well, making this a timely
resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One
covers basic results from the one-dimensional Fourier series, and offers a clear proof of the
Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lqsummability are
presented. The restricted and unrestricted rectangular summability are
provided in Chapter Three, as well as the sufficient and necessary condition for the norm
convergence of the rectangular theta-means. Chapter Four then introduces six types of
Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher
Dimensional Fourier Series will appeal to researchers working in mathematical analysis,
particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will
also find this useful.
Due 2021-07-22
1st ed. 2021, XIII, 290 p. 24 illus., 1 illus. in color.
Hardcover
ISBN 978-3-030-74635-3
Product category : Monograph
Mathematics : Fourier Analysis
Explores additional important decidability results in this thoroughly updated
new edition
Introduces mathematical logic by analyzing foundational questions on proofs
and provability in mathematics
Highlights the capabilities and limitations of algorithms and proof methods
both in mathematics and computer science
Examines advanced topics, such as linking logic with computability and
automata theory, as well as the unique role first-order logic plays in logical
systems
This textbook introduces first-order logic and its role in the foundations of mathematics by
examining fundamental questions. What is a mathematical proof? How can mathematical
proofs be justified? Are there limitations to provability? To what extent can machines carry out
mathematical proofs? In answering these questions, this textbook explores the capabilities and
limitations of algorithms and proof methods in mathematics and computer science. The
chapters are carefully organized, featuring complete proofs and numerous examples
throughout. Beginning with motivating examples, the book goes on to present the syntax and
semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type
proof of the completeness theorem is given. These introductory chapters prepare the reader for
the advanced topics that follow, such as Godel's Incompleteness Theorems, Trakhtenbrot's
undecidability theorem, Lindstrom's theorems on the maximality of first-order logic, and results
linking logic with automata theory. This new edition features many modernizations, as well as
two additional important results: The decidability of Presburger arithmetic, and the decidability
of the weak monadic theory of the successor function. Mathematical Logic is ideal for students
beginning their studies in logic and the foundations of mathematics. Although the primary
audience for this textbook will be graduate students or advanced undergraduates in
mathematics or computer science, in fact the book has few formal prerequisites.
Due 2021-06-29
3rd ed. 2021, IX, 304 p. 17 illus.
Hardcover
ISBN 978-3-030-73838-9
Product category : Graduate/advanced undergraduate textbook
Series : Graduate Texts in Mathematics
Mathematics : Mathematical Logic and Foundations
Introduces readers to the mathematical tools and principles of highdimensional statistics
Includes numerous exercises, many of them with detailed solutions
Features computer labs in R that convey valuable practical insights
Offers suggestions for further reading
This textbook provides a step-by-step introduction to the tools and principles of highdimensional statistics.
Each chapter is complemented by numerous exercises, many of them
with detailed solutions, and computer labs in R that convey valuable practical insights. The
book covers the theory and practice of high-dimensional linear regression, graphical models,
and inference, ensuring readers have a smooth start in the field. It also offers suggestions for
further reading. Given its scope, the textbook is intended for beginning graduate and advanced
undergraduate students in statistics, biostatistics, and bioinformatics, though it will be equally
useful to a broader audience
Due 2021-08-02
1st ed. 2021, X, 427 p. 34 illus., 21 illus. in color.
Hardcover
ISBN 978-3-030-73791-7
Product category :Graduate/advanced undergraduate textbook
Series : Springer Texts in Statistics
Statistics : Statistical Theory and Methods