Gradient Inequalities

Gradient Inequalities PDF

Author: Sen-Zhong Huang

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 194

ISBN-13: 0821840703

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This book presents a survey of the relatively new research field of gradient inequalities and their applications. The exposition emphasizes the powerful applications of gradient inequalities in studying asymptotic behavior and stability of gradient-like dynamical systems. It explains in-depth how gradient inequalities are established and how they can be used to prove convergence and stability of solutions to gradient-like systems. This book will serve as an introduction for furtherstudies of gradient inequalities and their applications in other fields, such as geometry and computer sciences. This book is written for advanced graduate students, researchers and applied mathematicians interested in dynamical systems and mathematical modeling.

Sobolev Gradients and Differential Equations

Sobolev Gradients and Differential Equations PDF

Author: John Neuberger

Publisher: Springer Science & Business Media

Published: 2009-12-01

Total Pages: 287

ISBN-13: 3642040403

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A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair portion of the material have in the past been able to use the theory on their own applications and also gain an appreciation of the possibility of a rather comprehensive point of view on the subject of partial differential equations.

Harnack Inequalities for Stochastic Partial Differential Equations

Harnack Inequalities for Stochastic Partial Differential Equations PDF

Author: Feng-Yu Wang

Publisher: Springer Science & Business Media

Published: 2013-08-13

Total Pages: 135

ISBN-13: 1461479347

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​In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

Health Inequalities

Health Inequalities PDF

Author: Katherine E. Smith

Publisher: Oxford University Press

Published: 2016

Total Pages: 351

ISBN-13: 019870335X

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This edited volume provides wide-ranging anaylses and reviews of the UK's experiences of health inequalities research and policy to date, and reflects on the lessons that have been learnt from these experiences, both within the UK and internationally

Key Maths

Key Maths PDF

Author: David Baker

Publisher: Nelson Thornes

Published: 2001

Total Pages: 576

ISBN-13: 0748759956

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Planned, developed and written by practising classroom teachers with a wide variety of experience in schools, this maths course has been designed to be enjoyable and motivating for pupils and teachers. The course is open and accessible to pupils of all abilities and backgrounds, and is differentiated to provide material which is appropriate for all pupils. It provides spiral coverage of the curriculum which involves regular revisiting of key concepts to promote familiarity through practice. This teacher's file is designed for stage three of Year 9.

Health inequalities

Health inequalities PDF

Author: Johan P. Mackenbach

Publisher: Oxford University Press

Published: 2019-08-29

Total Pages: 252

ISBN-13: 0192567179

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The world we live in is hugely unequal. People in a better socioeconomic position do not only lead more comfortable lives, but also longer and healthier lives. This is true not only in the poorer parts of the world but also in the richest countries, including the advanced welfare states of Western Europe which have successfully pushed back poverty and other forms of material disadvantage. Why are health inequalities - systematically higher rates of disease, disability, and premature death among people with a lower level of education, occupation or income - so persistent? How can we expect to reduce this when it persists even in the most advanced states? Written by a leading figure in public health, this book looks to answer these questions by taking a broad, critical look at the scientific evidence surrounding the explanation of health inequalities, including recent findings from the fields of epidemiology, sociology, psychology, economics, and genetics. It concludes that a simplistic view, in which health inequalities are a direct consequence of social inequality, does not tell us the full story. Drawing upon a unique series of studies covering 30 European countries and more than three decades of observations, it shows that health inequalities are partly driven by autonomous forces that are difficult to counteract, such as educational expansion, increased social mobility, and rapid but differential health improvements. Finally, the book explores how we might use these new findings to continue our efforts to build a healthier and more equal future. Offering a truly multidisciplinary perspective and an accessible writing style, Health Inequalities is an indispensable resource for health researchers, professionals, and policy-makers, as well as for social scientists interested in inequality.

Inequalities in the UK

Inequalities in the UK PDF

Author: David Fee

Publisher: Emerald Group Publishing

Published: 2017-11-17

Total Pages: 392

ISBN-13: 1787144798

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This book addresses the question of the extent of and responses to inequalities in the UK in 2017 in the wake of the 2008 Great Recession and provides an up-to-date account of the distribution of inequalities, the evolving ways they are measured/addressed as well as the changing perception of inequalities by the general public and policy-makers.

Health Inequalities

Health Inequalities PDF

Author: Great Britain. Parliament. House of Commons. Health Committee

Publisher: The Stationery Office

Published: 2008

Total Pages: 370

ISBN-13: 9780215514516

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Uncertainty Quantification in Variational Inequalities

Uncertainty Quantification in Variational Inequalities PDF

Author: Joachim Gwinner

Publisher: CRC Press

Published: 2021-12-24

Total Pages: 405

ISBN-13: 1351857673

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Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature