Books in the SpringerBriefs in Mathematics series

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.

This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Lojasiewicz-Simon gradient inequality.

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.

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 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.

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

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 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.

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.

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.

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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 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.

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 gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control.

Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations.

Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation.

The methodology is applied to solve mathematical functions considering test cases from the literature and various engineering systems design, such as cantilevered beam design, biochemical reactor, crystallization process, machine tool spindle design, rotary dryer design, among others.

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This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control.

This book explains the notion of Brakke's mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory.

This book is devoted to control of finite and infinite dimensional processes with continuous-time and discrete time control, focusing on suppression problems and new methods of adaptation applicable for systems with sliding motions only.

This book offers a concise and practical survey of the principles governing compressible flows, along with selected applications. It starts with derivation of the time-dependent, three-dimensional equation of compressible potential flows, and a study of weak waves, including evaluation of the sound speed in gases.

This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems.