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This book explains the notion of Brakke’s mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory. The focus of study is a time-parameterized family of k-dimensional surfaces in the n-dimensional Euclidean...
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...
This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools. Many of the techniques extend to the...
This book offers an organized and systematic approach to poset metrics and codes. Poset metrics, or metrics on a vector field determined by a partial order over a finite set, were first introduced in the mid-1990s by the mathematicians Richard A. Brualdi, Janine S....
This book presents properties, examples, rigidity theorems and classification results of such Finsler metrics. In particular, this book introduces how to investigate spherically symmetric Finsler geometry using ODE or PDE methods. Spherically symmetric Finsler...
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. The main objective of the book is to offer graduate students and...
This book introduces random currents by presenting underlying mathematical methods necessary for applications. The theory of currents is an advanced topic in geometric measure theory that extends distribution to linear functionals within the space of differential forms...
This book explores two of the most striking features of quantum theory – contextuality and nonlocality – using a formulation based on graph theory. Quantum theory provides a set of rules to predict probabilities of different outcomes in different experimental settings,...
This book introduces readers to techniques of geometric optimal control as well as the exposure and applicability of adapted numerical schemes. It is based on two real-world applications, which have been the subject of two current academic research programs and...
The purpose of this Brief is to give a quick practical introduction into the subject of Toeplitz operators on Kähler manifolds, via examples, worked out carefully and in detail. Necessary background is included. Several theorems on asymptotics of Toeplitz...
This book provides a concise introduction to convex duality in financial mathematics. Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex...
This book offers a gentle introduction to key elements of Geometric Algebra, along with their applications in Physics, Robotics and Molecular Geometry. Major applications covered are the physics of space-time, including Maxwell electromagnetism and the Dirac equation;...
This book proposes a semi-discrete version of the theory of Petitot and Citti-Sarti, leading to a left-invariant structure over the group SE(2,N), restricted to a finite number of rotations.This apparently very simple group is in fact quite atypical: it is maximally...
This book focuses on maximum principle and verification theorem for incomplete information forward-backward stochastic differential equations (FBSDEs) and their applications in linear-quadratic optimal controls and mathematical finance. ?Lots of interesting...
A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to...
This book gives a comprehensive overview of the relationship between admissibility and hyperbolicity. Essential theories and selected developments are discussed with highlights to applications. The dedicated readership includes researchers and graduate students...
This book gathers the revised lecture notes from a seminar course offered at the Federal University of Rio de Janeiro in 1986, then in Tokyo in 1987. An additional chapter has been added to reflect more recent advances in the field.
This work reviews the most important results regarding the use of the a-point in Scheduling Theory. It provides a number of different LP-relaxations for scheduling problems and seeks to explain their polyhedral consequences. It also explains the concept of the a-point...
This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing...
This book provides a first course on lattices – mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory...
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