Bøger i SpringerBriefs in Mathematics serien

This book offers a gentle introduction to key elements of Geometric Algebra, along with their applications in Physics, Robotics and Molecular Geometry. robotics, including formulations for the forward and inverse kinematics and an overview of the singularity problem for serial robots;

This book introduces random currents by presenting underlying mathematical methods necessary for applications. Beginning with an overview of mathematical aspects of the theory of currents, this book moves on to examine applications in medicine, material science, and image analysis.

This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry.After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index.Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.

Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory.

This book provides a direct and comprehensive introduction to theoretical and numerical concepts in the emerging field of optimal control of partial differential equations (PDEs) under uncertainty.

This book depicts graph labelings that have led to thought-provoking problems and conjectures. Problems and conjectures in graceful labelings, harmonious labelings, prime labelings, additive labelings, and zonal labelings are introduced with fundamentals, examples, and illustrations.

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The aim of this book is to present results related to Kato's famous inequality for bounded linear operators on complex Hilbert spaces obtained by the author in a sequence of recent research papers. As Linear Operator Theory in Hilbert spaces plays a central role in contemporary mathematics, with numerous applications in fields including Partial Differential Equations, Approximation Theory, Optimization Theory, and Numerical Analysis, the volume is intended for use by both researchers in various fields and postgraduate students and scientists applying inequalities in their specific areas. For the sake of completeness, all the results presented are completely proved and the original references where they have been firstly obtained are mentioned.

This book in the BCAM SpringerBriefs series is a treatise on the p-Laplace equation. The p-Laplace equation is a far-reaching generalization of the ordinary Laplace equation, but it is non-linear and degenerate (p>2) or singular (p

This book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory.

These notes give a beautiful and completely detailed account of the adelic approach to Hecke's L-functions attached to any number field, including the proof of analytic continuation, the functional equation of these L-functions, and the class number formula arising from the Dedekind zeta function for a general number field.

However, L (X,L, )* cannot be similarly described, and is instead represented as a class of finitely additive measures.This book provides a reasonably elementary account of the representation theory of L (X,L, )*, examining pathologies and paradoxes, and uncovering some surprising consequences.

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The purpose of this book is to provide background and principal results on these topics, along with same related problems and conjectures, for researchers in these areas.

In particular, the topological derivative is used here in numerical methods of shape optimization, with applications in the context of compliance structural topology optimization and topology design of compliant mechanisms.

This book explores topics in Gallai-Ramsey theory, which looks into whether rainbow colored subgraphs or monochromatic subgraphs exist in a sufficiently large edge-colored complete graphs.

It serves as an almost self-contained introduction to the theory of complex algebraic surfaces, including concise proofs of Gorenstein's theorem for curves on a surface and Noether's formula for the arithmetic genus.

This book aims to establish a foundation for fractional derivatives and fractional differential equations.

The Iitaka conjecture for fiber spaces whose base space is of general type is also proved as an easy application of Viehweg's weak positivity theorem, and the Viehweg conjecture for fiber spaces whose general fibers are elliptic curves is explained.

The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.

The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. In this book, the unsolved cases of the conjecture will be discussed.It will be shown that the problem is closely related to the geometry of moduli spaces of test configurations for polarized algebraic manifolds.

In this book, the optimal transportation problem (OT) is described as a variational problem for absolutely continuous stochastic processes with fixed initial and terminal distributions.

The classical Lojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Lojasiewicz-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 Lojasiewicz-Simon gradient inequality.In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Lojasiewicz-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.

Die Theorie der regularen Graphen (The Theory of Regular Graphs), written by the Danish Mathematician Julius Petersen in 1891, is often considered the first strictly theoretical paper dealing with graphs.

This book collects some basic results on the null controllability for degenerate and singular parabolic problems. For these reasons, the authors will not give all the detailed proofs of the given theorems, but just some of them, in order to show the underlying strategy in this area.

This brief studies recent work conducted on certain exponential type operators and other integral type operators. It consists of three chapters: the first on exponential type operators, the second a study of some modifications of linear positive operators, and the third on difference estimates between two operators.

Lyapunov methods have been and are still one of the main tools to analyze the stability properties of dynamical systems. As a final result, ideas combining control Lyapunov and control Chetaev functions to simultaneously guarantee stability, i.e., convergence, and instability, i.e., avoidance, are outlined.