Series: Progress in Mathematics, Vol. 299
2012, 2012, XII, 230 p.
Hardcover, ISBN 978-3-0348-0375-5
Due: June 29, 2012
Up-to-date results on the subject not yet available in book form
A number of new results and techniques as well as new proofs of known results
Clear account of a number of key methods from geometric analysis accessible to non-specialists in the field
Self-contained treatment, detailed description of both the geometric and the main analytic tools exploited
The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem, and to describe in a way accessible to non-specialists a range of methods and techniques that can be successfully applied to nonlinear differential equations in situations where the lack of compactness and of symmetry and homogeneity prevents the use of more standard tools typical of compact situations or of the Euclidean setting.
After providing a self-contained treatment of the geometric tools used in the book, the reader is introduced to the main subject through a concise but clear study of some aspects of the Yamabe problem on compact manifolds, which provides motivation and geometrical feeling for the subsequent study. In the main body of the book it is shown how the geometry and the analysis of nonlinear partial differential equations blend together to give up to date results on existence, nonexistence, uniqueness and a priori estimates for solutions of general Yamabe-type equations and inequalities on complete, non-compact Riemannian manifolds.
Introduction.- 1 Some Riemannian Geometry.- 2 Pointwise conformal metrics.- 3 General nonexistence results.- 4 A priori estimates.- 5 Uniqueness.- 6 Existence.- 7 Some special cases.- References.- Index.
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Published 6th July 2011 419 pages
Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science
Hardback: 978-1-43-983455-8:
Modeling and Control in Vibrational and Structural Dynamics: A Differential Geometric Approach describes the control behavior of mechanical objects, such as wave equations, plates, and shells. It shows how the differential geometric approach is used when the coefficients of partial differential equations (PDEs) are variable in space (waves/plates), when the PDEs themselves are defined on curved surfaces (shells), and when the systems have quasilinear principal parts.
To make the book self-contained, the author starts with the necessary background on Riemannian geometry. He then describes differential geometric energy methods that are generalizations of the classical energy methods of the 1980s. He illustrates how a basic computational technique can enable multiplier schemes for controls and provide mathematical models for shells in the form of free coordinates. The author also examines the quasilinearity of models for nonlinear materials, the dependence of controllability/stabilization on variable coefficients and equilibria, and the use of curvature theory to check assumptions.
With numerous examples and exercises throughout, this book presents a complete and up-to-date account of many important advances in the modeling and control of vibrational and structural dynamics.
Mathematical Olympiad Series - Vol. 8
Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education.
This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well.
In each lecture, the concepts, theories and methods are taken as the core. The examples serve to explain and enrich their intentions and to indicate their applications. Besides, appropriate number of test questions is available for the readers' practice and testing purpose. Their detailed solutions are also conveniently provided.
The examples are not very complicated so readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions originate from many countries all over the world.
This book will serve as a useful textbook of mathematical Olympiad courses, a self-study lecture notes for students, or as a reference book for related teachers and researchers.
Fractional Equations
Higher Degree Polynomial Equations
Irrational Equations
Indicial Functions and Logarithmic Functions
Trigonometric Functions
Law of Sines and Law of Cosines
Manipulations of Trigonometric Expressions
Extreme Values of Functions and Mean Inequality
Extreme Value Problems in Trigonometry
Fundamental Properties of Circles
Relation of Line and Circle and Relation of Circles
Cyclic Polygons
Power of a Point with Respect to a Circle
Some Important Theorems in Geometry
Five Centers of a Triangle
Mathematical Induction
Arithmetic Progression and Geometric Progression
Recursive Sequence
Summation of Series
Some Fundamental Theorems on Congruence
Chinese Remainder Theorem and Order of Integer
Diophantine Equation (III)
Cauchy?Schwartz Inequality
Rearrangement Inequality and Jensen' Inequality
Schur Inequality
Fractional Inequality
Variable?Freezing Method
Some Methods in Counting Numbers (I)
Some Methods in Counting Numbers (II)
Introduction to Functional Equations
Set
500pp (approx.) Pub. date: Scheduled Spring 2012
ISBN: 978-981-4368-94-0(pbk)
Vol. 1 :ISBN: 978-981-4368-95-7(pbk)
Vol. 2 :ISBN: 978-981-4368-96-4(pbk)