Inequalities In Geometry And Applications

Author : Gabriel-Eduard Vîlcu
Publisher : MDPI
Page : 208 pages
File Size : 40,8 Mb
Release : 2021-03-09
Category : Mathematics
ISBN : 9783036502984

Get Book

Inequalities in Geometry and Applications by Gabriel-Eduard Vîlcu Pdf

This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.

Author : Michael J. Cloud,Byron C. Drachman,Leonid P. Lebedev
Publisher : Springer
Page : 239 pages
File Size : 48,7 Mb
Release : 2014-05-06
Category : Mathematics
ISBN : 9783319053110

Get Book

Inequalities by Michael J. Cloud,Byron C. Drachman,Leonid P. Lebedev Pdf

This book offers a concise introduction to mathematical inequalities for graduate students and researchers in the fields of engineering and applied mathematics. It begins by reviewing essential facts from algebra and calculus and proceeds with a presentation of the central inequalities of applied analysis, illustrating a wide variety of practical applications. The text provides a gentle introduction to abstract spaces, such as metric, normed and inner product spaces. It also provides full coverage of the central inequalities of applied analysis, such as Young's inequality, the inequality of the means, Hölder's inequality, Minkowski's inequality, the Cauchy–Schwarz inequality, Chebyshev's inequality, Jensen's inequality and the triangle inequality. The second edition features extended coverage of applications, including continuum mechanics and interval analysis. It also includes many additional examples and exercises with hints and full solutions that may appeal to upper-level undergraduate and graduate students, as well as researchers in engineering, mathematics, physics, chemistry or any other quantitative science.

Author : Gabriel Eduard Vilcu
Publisher : Unknown
Page : 208 pages
File Size : 47,8 Mb
Release : 2021
Category : Electronic
ISBN : 3036502998

Get Book

Inequalities in Geometry and Applications by Gabriel Eduard Vilcu Pdf

This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös-Mordell inequality, Barrow's inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.

Author : Dragoslav S. Mitrinovic,J. Pecaric,V. Volenec
Publisher : Springer Science & Business Media
Page : 728 pages
File Size : 55,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401578424

Get Book

Recent Advances in Geometric Inequalities by Dragoslav S. Mitrinovic,J. Pecaric,V. Volenec Pdf

Author : Catherine Bandle
Publisher : Pitman Publishing
Page : 248 pages
File Size : 46,5 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39015015622353

Get Book

Isoperimetric Inequalities and Applications by Catherine Bandle Pdf

Author : D.D. Bainov,P.S Simeonov
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 51,9 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401580342

Get Book

Integral Inequalities and Applications by D.D. Bainov,P.S Simeonov Pdf

This volume is devoted to integral inequalities of the Gronwall-Bellman-Bihari type. Following a systematic exposition of linear and nonlinear inequalities, attention is paid to analogues including integro-differential inequalities, functional differential inequalities, and discrete and abstract analogues. Applications to the investigation of the properties of solutions of various classes of equations such as uniqueness, stability, dichotomy, asymptotic equivalence and behaviour is also discussed. The book comprises three chapters. Chapter I and II consider classical linear and nonlinear integral inequalities. Chapter III is devoted to various classes of integral inequalities of Gronwall type, and their analogues, which find applications in the theory of integro-differential equations, partial differential equations, differential equations with deviating argument, impube differential equations, etc. Each chapter concludes with a section illustrating the manner of application. The book also contains an extensive bibliography. For researchers whose work involves the theory and application of integral inequalities in mathematics, engineering and physics.

Author : Michael Kapovich,Bernhard Leeb,John James Millson
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 41,8 Mb
Release : 2008
Category : Geometric group theory
ISBN : 9780821840542

Get Book

The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra by Michael Kapovich,Bernhard Leeb,John James Millson Pdf

In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $\mathbb{Q}$ and its complex Langlands' dual. The authors give a new proof of the Saturation Conjecture for $GL(\ell)$ as a consequence of their solution of the corresponding saturation problem for the Hecke structure constants for all split reductive algebraic groups over $\mathbb{Q}$.

Author : Nassif Ghoussoub,Amir Moradifam
Publisher : American Mathematical Soc.
Page : 331 pages
File Size : 48,5 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780821891520

Get Book

Functional Inequalities: New Perspectives and New Applications by Nassif Ghoussoub,Amir Moradifam Pdf

"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.

Author : Michael J. Cloud,Bryon C. Drachman
Publisher : Springer Science & Business Media
Page : 150 pages
File Size : 47,9 Mb
Release : 2006-05-10
Category : Mathematics
ISBN : 9780387226262

Get Book

Inequalities by Michael J. Cloud,Bryon C. Drachman Pdf

A working knowledge of inequalities can be beneficial to the practicing engineer, and inequalities are central to the definitions of all limiting processes, including differentiation and integration. When exact solutions are unavailable, inconvenient, or unnecessary, inequalities can be used to obtain error bounds for numerical approximation. They can also lead to an understanding of the qualitative behavior of solutions. This guide to inequalities was written specifically with engineers and other applied scientists in mind, and helps fill the gap between college algebra-level treatments, and the formidable treatise on the subject that exist in the mathematics literature. To consolidate the learning process, every chapter ends with a rich collection of exercises.

Author : Hayk Sedrakyan,Nairi Sedrakyan
Publisher : Springer
Page : 452 pages
File Size : 54,8 Mb
Release : 2017-05-27
Category : Mathematics
ISBN : 9783319550800

Get Book

Geometric Inequalities by Hayk Sedrakyan,Nairi Sedrakyan Pdf

This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities.

Author : Themistocles RASSIAS,Hari M. Srivastava
Publisher : Springer Science & Business Media
Page : 377 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401145770

Get Book

Analytic and Geometric Inequalities and Applications by Themistocles RASSIAS,Hari M. Srivastava Pdf

Analytic and Geometric Inequalities and Applications is devoted to recent advances in a variety of inequalities of Mathematical Analysis and Geo metry. Subjects dealt with in this volume include: Fractional order inequalities of Hardy type, differential and integral inequalities with initial time differ ence, multi-dimensional integral inequalities, Opial type inequalities, Gruss' inequality, Furuta inequality, Laguerre-Samuelson inequality with extensions and applications in statistics and matrix theory, distortion inequalities for ana lytic and univalent functions associated with certain fractional calculus and other linear operators, problem of infimum in the positive cone, alpha-quasi convex functions defined by convolution with incomplete beta functions, Chebyshev polynomials with integer coefficients, extremal problems for poly nomials, Bernstein's inequality and Gauss-Lucas theorem, numerical radii of some companion matrices and bounds for the zeros of polynomials, degree of convergence for a class of linear operators, open problems on eigenvalues of the Laplacian, fourth order obstacle boundary value problems, bounds on entropy measures for mixed populations as well as controlling the velocity of Brownian motion by its terminal value. A wealth of applications of the above is also included. We wish to express our appreciation to the distinguished mathematicians who contributed to this volume. Finally, it is our pleasure to acknowledge the fine cooperation and assistance provided by the staff of Kluwer Academic Publishers. June 1999 Themistocles M. Rassias Hari M.

Author : Ravi P. Agarwal
Publisher : CRC Press
Page : 1010 pages
File Size : 44,8 Mb
Release : 2000-01-27
Category : Mathematics
ISBN : 1420027026

Get Book

Difference Equations and Inequalities by Ravi P. Agarwal Pdf

A study of difference equations and inequalities. This second edition offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, sociology, and

Author : B.G. Pachpatte
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 54,6 Mb
Release : 2012-01-05
Category : Mathematics
ISBN : 9789491216442

Get Book

Analytic Inequalities by B.G. Pachpatte Pdf

For more than a century, the study of various types of inequalities has been the focus of great attention by many researchers, interested both in the theory and its applications. In particular, there exists a very rich literature related to the well known Cebysev, Gruss, Trapezoid, Ostrowski, Hadamard and Jensen type inequalities. The present monograph is an attempt to organize recent progress related to the above inequalities, which we hope will widen the scope of their applications. The field to be covered is extremely wide and it is impossible to treat all of these here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with a reasonable background in real analysis and an acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be invaluable reading for mathematicians and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.

Author : Michael Kapovich
Publisher : American Mathematical Society(RI)
Page : 98 pages
File Size : 48,9 Mb
Release : 2014-09-11
Category : Geometric group theory
ISBN : 1470405024

Get Book

The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra by Michael Kapovich Pdf

In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $\mathbb{Q}$ and its complex Langlands' dual. The authors give a new proof of the Saturation Conjecture for $GL(\ell)$ as a consequence of their solution of the corresponding saturation problem for the Hecke structure constants for all split reductive algebraic groups over $\mathbb{Q}$.

Author : Huan-nan Shi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 256 pages
File Size : 47,7 Mb
Release : 2019-07-08
Category : Mathematics
ISBN : 9783110607864

Get Book

Schur-Convex Functions and Inequalities by Huan-nan Shi Pdf

This two-volume work introduces the theory and applications of Schur-convex functions. The second volume mainly focuses on the application of Schur-convex functions in sequences inequalities, integral inequalities, mean value inequalities for two variables, mean value inequalities for multi-variables, and in geometric inequalities.