Topics in Geometric Inequalities, Titu Andreescu, Oleg Mushkarov

Автор: Leng Gangsong
Название: Geometric Inequalities
ISBN: 981470413X ISBN-13(EAN): 9789814704137
Издательство: World Scientific Publishing
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Цена: 42240.00 T
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Описание:

In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results -- they won the first place almost every year.

The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.

This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on Geometric Inequality problems such as inequality for the inscribed quadrilateral, the area inequality for special polygons, linear geometric inequalities, etc.

Автор: Leng Gangsong
Название: Geometric Inequalities
ISBN: 981469648X ISBN-13(EAN): 9789814696487
Издательство: World Scientific Publishing
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Цена: 22170.00 T
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Описание:

In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results -- they won the first place almost every year.

The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.

This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on Geometric Inequality problems such as inequality for the inscribed quadrilateral, the area inequality for special polygons, linear geometric inequalities, etc.

Автор: Yurii D. Burago; A.B. Sossinsky; Viktor A. Zalgall
Название: Geometric Inequalities
ISBN: 3642057241 ISBN-13(EAN): 9783642057243
Издательство: Springer
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Цена: 111760.00 T
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Описание: A 1988 classic, covering Two-dimensional Surfaces; Domains on the Plane and on Surfaces; Brunn-Minkowski Inequality and Classical Isoperimetric Inequality; Isoperimetric Inequalities for Various Definitions of Area; and Inequalities Involving Mean Curvature.

Автор: Adrian Andreescu, Titu Andreescu, Oleg Mushkarov
Название: 113 Geometric Inequalities from the AwesomeMath Summer Program
ISBN: 097992698X ISBN-13(EAN): 9780979926983
Издательство: Mare Nostrum (Eurospan)
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Цена: 61910.00 T
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Описание: For the curious reader looking to sharpen their arsenal of mathematical strategies on the Olympiad level, 113 Geometric Inequalities from the AwesomeMath Summer Program is a valuable addition. This problem-solving methodology prompts key ideas in other domains such as calculus or complex numbers as the solutions are usually nonstandard in a geometric sense.

Автор: Ruzhansky Michael, Suragan Durvudkhan
Название: Hardy Inequalities on Homogeneous Groups: 100 Years of Hardy Inequalities
ISBN: 3030028941 ISBN-13(EAN): 9783030028947
Издательство: Springer
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Цена: 46570.00 T
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Описание: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general H?rmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Автор: Damir Gainanov
Название: Graphs for Pattern Recognition: Infeasible Systems of Linear Inequalities
ISBN: 3110480131 ISBN-13(EAN): 9783110480139
Издательство: Walter de Gruyter
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Цена: 123910.00 T
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Описание: This monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition.Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important special subclass of infeasible systems of constraints with a monotonicity property - systems whose multi-indices of feasible subsystems form abstract simplicial complexes (independence systems), which are fundamental objects of combinatorial topology.The methods of data mining and machine learning discussed in this monograph form the foundation of technologies like big data and deep learning, which play a growing role in many areas of human-technology interaction and help to find solutions, better solutions and excellent solutions. Contents: PrefacePattern recognition, infeasible systems of linear inequalities, and graphsInfeasible monotone systems of constraintsComplexes, (hyper)graphs, and inequality systemsPolytopes, positive bases, and inequality systemsMonotone Boolean functions, complexes, graphs, and inequality systemsInequality systems, committees, (hyper)graphs, and alternative coversBibliographyList of notationIndex

Автор: Chavel
Название: Isoperimetric Inequalities
ISBN: 1107402271 ISBN-13(EAN): 9781107402270
Издательство: Cambridge Academ
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Цена: 57030.00 T
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Описание: This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject. It discusses inequalities in Euclidean and Riemannian geometry, methods of classical differential geometry and elementary modern geometric measure theory, discretization of smooth spaces, and the influence of isoperimetric inequalities on heat diffusion on Riemannian manifolds.

Автор: Yang Bicheng Et Al
Название: Half-Discrete Hilbert-Type Inequalities
ISBN: 9814504971 ISBN-13(EAN): 9789814504973
Издательство: World Scientific Publishing
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Цена: 116160.00 T
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Описание: In 1934, G. H. Hardy et al. published a book entitled "Inequalities," in which a few theorems about Hilbert-type inequalities with homogeneous kernels of degree-one were considered. Since then, the theory of Hilbert-type discrete and integral inequalities is almost built by Prof. Bicheng Yang in their four published books.This monograph deals with half-discrete Hilbert-type inequalities. By means of building the theory of discrete and integral Hilbert-type inequalities, and applying the technique of Real Analysis and Summation Theory, some kinds of half-discrete Hilbert-type inequalities with the general homogeneous kernels and non-homogeneous kernels are built. The relating best possible constant factors are all obtained and proved. The equivalent forms, operator expressions and some kinds of reverses with the best constant factors are given. We also consider some multi-dimensional extensions and two kinds of multiple inequalities with parameters and variables, which are some extensions of the two-dimensional cases. As applications, a large number of examples with particular kernels are also discussed.The authors have been successful in applying Hilbert-type discrete and integral inequalities to the topic of half-discrete inequalities. The lemmas and theorems in this book provide an extensive account of these kinds of inequalities and operators. This book can help many readers make good progress in research on Hilbert-type inequalities and their applications.

Автор: Ravi P. Agarwal; Shusen Ding; Craig Nolder
Название: Inequalities for Differential Forms
ISBN: 1489983511 ISBN-13(EAN): 9781489983510
Издательство: Springer
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Цена: 135090.00 T
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Описание: This volume systematically presents a series of local and global estimates and inequalities for differential forms satisfying the A-harmonic equations. Integral homotopy, the Laplace-Beltrami, and gradient operator estimates are also included.

Автор: Anca Capatina
Название: Variational Inequalities and Frictional Contact Problems
ISBN: 3319101625 ISBN-13(EAN): 9783319101620
Издательство: Springer
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Цена: 93160.00 T
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Описание: Variational Inequalities and Frictional Contact Problems contains a carefully selected collection of results on elliptic and evolutionary quasi-variational inequalities including existence, uniqueness, regularity, dual formulations, numerical approximations and error estimates ones.