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Advances in Inequalities for Special Functions (Advances in Mathematical Inequalities)

17 October 2010

**Advances in Inequalities for Special Functions (Advances in Mathematical Inequalities)** by Pietro Cerone

Publisher: Nova Science Publishers | 2007-09 | ISBN: 1600219195 | PDF | 170 pages | 12 MB

This book is the first in a collection of research monographs that are devoted to presenting recent research, development and use of Mathematical Inequalities for Special Functions. All the papers incorporated in the book have peen peer-reviewed and cover a range of topics that include both survey material of previously published works as well as new results. In his presentation on special functions approximations and bounds via integral representation, Pietro Cerone utilises the classical Stevensen inequality and bounds for the Ceby sev functional to obtain bounds for some classical special functions. The methodology relies on determining bounds on integrals of products of functions. The techniques are used to obtain novel and useful bounds for the Bessel function of the first kind, the Beta function, the Zeta function and Mathieu series.

17 October 2010

Publisher: Nova Science Publishers | 2007-09 | ISBN: 1600219195 | PDF | 170 pages | 12 MB

This book is the first in a collection of research monographs that are devoted to presenting recent research, development and use of Mathematical Inequalities for Special Functions. All the papers incorporated in the book have peen peer-reviewed and cover a range of topics that include both survey material of previously published works as well as new results. In his presentation on special functions approximations and bounds via integral representation, Pietro Cerone utilises the classical Stevensen inequality and bounds for the Ceby sev functional to obtain bounds for some classical special functions. The methodology relies on determining bounds on integrals of products of functions. The techniques are used to obtain novel and useful bounds for the Bessel function of the first kind, the Beta function, the Zeta function and Mathieu series.

Advances on Fractional Inequalities

8 February 2012

**Advances on Fractional Inequalities**

2011-07-25 | ISBN: 1461407028 | 132 pages | PDF | 1,7 MB

Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate and multivariate cases. Next the right and left, as well as mixed, Landau fractional differentiation inequalities in the univariate and multivariate cases are illustrated. Throughout the book many applications are given.

8 February 2012

2011-07-25 | ISBN: 1461407028 | 132 pages | PDF | 1,7 MB

Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate and multivariate cases. Next the right and left, as well as mixed, Landau fractional differentiation inequalities in the univariate and multivariate cases are illustrated. Throughout the book many applications are given.

Improved Bonferroni Inequalities via Abstract Tubes: Inequalities and Identities of Inclusion-Exclusion Type

22 November 2010

**Improved Bonferroni Inequalities via Abstract Tubes: Inequalities and Identities of Inclusion-Exclusion Type**

This introduction to the recent theory of abstract tubes describes the framework for establishing improved inclusion-exclusion identities and Bonferroni inequalities, which are provably at least as sharp as their classical counterparts while involving fewer terms. All necessary definitions from graph theory, lattice theory and topology are provided. The role of closure and kernel operators is emphasized, and examples are provided throughout to demonstrate the applicability of this new theory. Applications are given to system and network reliability, reliability covering problems and chromatic graph theory. Topics also covered include Zeilberger's abstract lace expansion, matroid polynomials and Mobius functions. ...

22 November 2010

2003 | 113 | ISBN: 3540200258 | PDF | 1 Mb

This introduction to the recent theory of abstract tubes describes the framework for establishing improved inclusion-exclusion identities and Bonferroni inequalities, which are provably at least as sharp as their classical counterparts while involving fewer terms. All necessary definitions from graph theory, lattice theory and topology are provided. The role of closure and kernel operators is emphasized, and examples are provided throughout to demonstrate the applicability of this new theory. Applications are given to system and network reliability, reliability covering problems and chromatic graph theory. Topics also covered include Zeilberger's abstract lace expansion, matroid polynomials and Mobius functions. ...

An Introduction to Variational Inequalities and Their Applications

19 June 2011

**An Introduction to Variational Inequalities and Their Applications**

This unabridged republication of the 1980 text, an established classic in the field, is a resource for many important topics in elliptic equations and systems and is the first modern treatment of free boundary problems. Variational inequalities (equilibrium or evolution problems typically with convex constraints) are carefully explained in An Introduction to Variational Inequalities and Their Applications. They are shown to be extremely useful across a wide variety of subjects, ranging from linear programming to free boundary problems in partial differential equations. Exciting new areas like finance and phase transformations along with more historical ones like contact problems have begun to rely on variational inequalities, making this book a necessity once again. ...

19 June 2011

1980 | 313 | ISBN: 0124073506 | DJVU | 2 Mb

This unabridged republication of the 1980 text, an established classic in the field, is a resource for many important topics in elliptic equations and systems and is the first modern treatment of free boundary problems. Variational inequalities (equilibrium or evolution problems typically with convex constraints) are carefully explained in An Introduction to Variational Inequalities and Their Applications. They are shown to be extremely useful across a wide variety of subjects, ranging from linear programming to free boundary problems in partial differential equations. Exciting new areas like finance and phase transformations along with more historical ones like contact problems have begun to rely on variational inequalities, making this book a necessity once again. ...

Geometric Inequalities

21 April 2013

**Geometric Inequalities**

Nicholas D. Kazarinoff,

English | 1975 | ISBN: 0883856042 | PDF | 139 pages | 11 mb

21 April 2013

Nicholas D. Kazarinoff,

English | 1975 | ISBN: 0883856042 | PDF | 139 pages | 11 mb

Probabilistic Inequalities

24 September 2010

**Probabilistic Inequalities**

World Scientific Publishing Company | 2009-08-11 | ISBN: 981428078X, 9814280798 | 428 pages | PDF | 12 MB

In this monograph, the author presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment generating function and covariance. These are built on the recent classical form of real analysis inequalities which are also discussed in full details. This treatise is the culmination and crystallization of the author's last two decades of research work in related discipline. Each of the chapters is self-contained and a few advanced courses can be taught out of this book. Extensive background and motivations for specific topics are given in each chapter. A very extensive list of references is also provided at the end.

24 September 2010

World Scientific Publishing Company | 2009-08-11 | ISBN: 981428078X, 9814280798 | 428 pages | PDF | 12 MB

In this monograph, the author presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment generating function and covariance. These are built on the recent classical form of real analysis inequalities which are also discussed in full details. This treatise is the culmination and crystallization of the author's last two decades of research work in related discipline. Each of the chapters is self-contained and a few advanced courses can be taught out of this book. Extensive background and motivations for specific topics are given in each chapter. A very extensive list of references is also provided at the end.

Optimal Control of Variational Inequalities

29 May 2011

**Optimal Control of Variational Inequalities**

0273086294Variational inequalities represent an important class of nonlinear problems and occur in the mathematical description of a large variety of physical problems. The most recent method in the study of free boundary value problems arising in filtration, heat conduction and diffusion theory uses a reformulation of these problems as variational inequalities. Quite often these problems arise as controlled systems with specified objectives. Roughly speaking, optimal control is concerned with finding the optimal input controls, within prescribed restrictions, in order to achieve the desired objectives. ...

29 May 2011

1984 | 300 | ISBN: 0470203927 | DJVU | 2 Mb

0273086294Variational inequalities represent an important class of nonlinear problems and occur in the mathematical description of a large variety of physical problems. The most recent method in the study of free boundary value problems arising in filtration, heat conduction and diffusion theory uses a reformulation of these problems as variational inequalities. Quite often these problems arise as controlled systems with specified objectives. Roughly speaking, optimal control is concerned with finding the optimal input controls, within prescribed restrictions, in order to achieve the desired objectives. ...

Inequalities

3 July 2010

**Inequalities**

Publisher: Springer | English | July 4, 2002 | ISBN: 3540430210 | PDF | 610 pages | 12.4Mb

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. Lieb has discovered a host of inequalities that are enormeously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.

3 July 2010

Publisher: Springer | English | July 4, 2002 | ISBN: 3540430210 | PDF | 610 pages | 12.4Mb

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. Lieb has discovered a host of inequalities that are enormeously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.

Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture

29 July 2011

**Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture**

Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows, especially with surgeries. The author explains key ideas, difficult proofs, and important applications in a succinct, accessible, and unified manner....

29 July 2011

2011 | 432 | ISBN: 1439834598 | PDF | 2 Mb

Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows, especially with surgeries. The author explains key ideas, difficult proofs, and important applications in a succinct, accessible, and unified manner....

Operator Inequalities

16 August 2011

**Operator Inequalities**

This book is concerned with inequalities that are described by operators or, briefly, with operator inequalities. These operators may be matrices, differential operators, integral operators, etc. Special emphasis is given to differential operators related to boundary value problems. ...

16 August 2011

1980 | 384 | ISBN: 0126297509 | DJVU | 3 Mb

This book is concerned with inequalities that are described by operators or, briefly, with operator inequalities. These operators may be matrices, differential operators, integral operators, etc. Special emphasis is given to differential operators related to boundary value problems. ...