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This book presents the topological derivative method through selected examples, using a direct approach based on calculus of variations combined with compound asymptotic analysis.This new concept in shape optimization has applications in many different fields such as...
In measure theory, a familiar representation theorem due to F. Riesz identifies the dual space Lp(X,L,?)* with Lq(X,L,?), where 1/p+1/q=1, as long as 1 = p<8. However, L8(X,L,?)* cannot be similarly described, and is instead represented as a class of finitely...
This book offers an introduction to a classical problem in ergodic theory and smooth dynamics, namely, the Kolmogorov–Bernoulli (non)equivalence problem, and presents recent results in this field. Starting with a crash course on ergodic theory, it uses the class of...
This book is aimed toward graduate students and researchers in mathematics, physics and engineering interested in the latest developments in analytic inequalities, Hilbert-Type and Hardy-Type integral inequalities, and their applications. Theories, methods, and...
Gödel's true-but-unprovable sentence from the first incompleteness theorem is purely logical in nature, i.e. not mathematically natural or interesting. An interesting problem is to find mathematically natural and interesting statements that are similarly unprovable. A...
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...
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...
This book offers a broad survey of all information made public - from 1993 until today - on keystream sequence generators based on irregular decimation, which are referred to as shrinking generators. Starting with an overview of cryptography, it describes each type of...
This book in the BCAM SpringerBriefs series is a treatise on the p-Laplace equation. It is based on lectures by the author that were originally delivered at the Summer School in Jyväskylä, Finland, in August 2005 and have since been updated and extended to cover various...
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...
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