Multiplying Inequalities

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Carleman Inequalities

Nicolas Lerner
Carleman Inequalities Book PDF

Author : Nicolas Lerner
Publisher : Springer
Page : 557 pages
File Size : 54,5 Mb
Release : 2019-05-18
Category : Mathematics
ISBN : 9783030159931

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Carleman Inequalities by Nicolas Lerner Pdf

Over the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inverse problems, or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman Inequalities, driven by applications to various questions of unique continuation. Beginning with an elementary introduction to the topic, including examples accessible to readers without prior knowledge of advanced mathematics, the book's first five chapters contain a thorough exposition of the most classical results, such as Calderón's and Hörmander's theorems. Later chapters explore a selection of results of the last four decades around the themes of continuation for elliptic equations, with the Jerison-Kenig estimates for strong unique continuation, counterexamples to Cauchy uniqueness of Cohen and Alinhac & Baouendi, operators with partially analytic coefficients with intermediate results between Holmgren's and Hörmander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more. With examples and special cases motivating the general theory, as well as appendices on mathematical background, this monograph provides an accessible, self-contained basic reference on the subject, including a selection of the developments of the past thirty years in unique continuation.

Interpretation of Algebraic Inequalities

Michael Todinov
Interpretation of Algebraic Inequalities Book PDF

Author : Michael Todinov
Publisher : CRC Press
Page : 154 pages
File Size : 41,8 Mb
Release : 2021-10-13
Category : Technology & Engineering
ISBN : 9781000468953

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Interpretation of Algebraic Inequalities by Michael Todinov Pdf

This book introduces a new method based on algebraic inequalities for optimising engineering systems and processes, with applications in mechanical engineering, materials science, electrical engineering, reliability engineering, risk management and operational research. This book shows that the application potential of algebraic inequalities in engineering and technology is far-reaching and certainly not restricted to specifying design constraints. Algebraic inequalities can handle deep uncertainty associated with design variables and control parameters. With the method presented in this book, powerful new knowledge about systems and processes can be generated through meaningful interpretation of algebraic inequalities. This book demonstrates how the generated knowledge can be put into practice through covering the algebraic inequalities suitable for interpretation in different contexts and describing how to apply this knowledge to enhance system and process performance. Depending on the specific interpretation, knowledge, applicable to different systems from different application domains, can be generated from the same algebraic inequality. Furthermore, an important class of algebraic inequalities has been introduced that can be used for optimising systems and processes in any area of science and technology provided that the variables and the separate terms of the inequalities are additive quantities. With the presented various examples and solutions, this book will be of interest to engineers, students and researchers in the field of optimisation, engineering design, reliability engineering, risk management and operational research.

Equations and Inequalities

Jiri Herman,Radan Kucera,Jaromir Simsa
Equations and Inequalities Book PDF

Author : Jiri Herman,Radan Kucera,Jaromir Simsa
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461212706

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Equations and Inequalities by Jiri Herman,Radan Kucera,Jaromir Simsa Pdf

A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.

Advances in Mathematical Inequalities and Applications

Praveen Agarwal,Silvestru Sever Dragomir,Mohamed Jleli,Bessem Samet
Advances in Mathematical Inequalities and Applications Book PDF

Author : Praveen Agarwal,Silvestru Sever Dragomir,Mohamed Jleli,Bessem Samet
Publisher : Springer
Page : 349 pages
File Size : 50,8 Mb
Release : 2018-12-31
Category : Mathematics
ISBN : 9789811330131

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Advances in Mathematical Inequalities and Applications by Praveen Agarwal,Silvestru Sever Dragomir,Mohamed Jleli,Bessem Samet Pdf

This book is a collection of original research and survey articles on mathematical inequalities and their numerous applications in diverse areas of mathematics and engineering. It includes chapters on convexity and related concepts; inequalities for mean values, sums, functions, operators, functionals, integrals and their applications in various branches of mathematics and related sciences; fractional integral inequalities; and weighted type integral inequalities. It also presents their wide applications in biomathematics, boundary value problems, mechanics, queuing models, scattering, and geomechanics in a concise, but easily understandable way that makes the further ramifications and future directions clear. The broad scope and high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers. All the contributing authors are leading international academics, scientists, researchers and scholars.

Opial Inequalities with Applications in Differential and Difference Equations

R.P. Agarwal,P.Y. Pang
Opial Inequalities with Applications in Differential and Difference Equations Book PDF

Author : R.P. Agarwal,P.Y. Pang
Publisher : Springer Science & Business Media
Page : 407 pages
File Size : 55,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401584265

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Opial Inequalities with Applications in Differential and Difference Equations by R.P. Agarwal,P.Y. Pang Pdf

In 1960 the Polish mathematician Zdzidlaw Opial (1930--1974) published an inequality involving integrals of a function and its derivative. This volume offers a systematic and up-to-date account of developments in Opial-type inequalities. The book presents a complete survey of results in the field, starting with Opial's landmark paper, traversing through its generalizations, extensions and discretizations. Some of the important applications of these inequalities in the theory of differential and difference equations, such as uniqueness of solutions of boundary value problems, and upper bounds of solutions are also presented. This book is suitable for graduate students and researchers in mathematical analysis and applications.

Inequalities

Anonim
Inequalities Book PDF

Author : Anonim
Publisher : Rumi Michael Leigh
Page : 71 pages
File Size : 54,8 Mb
Release : 2023-05-24
Category : Mathematics
ISBN : 8210379456XXX

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Inequalities by Anonim Pdf

Unlock the power of mathematical inequalities with "Inequalities, things you should know, questions and answers," an essential resource designed to equip students, educators, and mathematics enthusiasts with the tools to conquer this challenging branch of mathematics. Whether you are aiming to ace exams, deepen your understanding, or simply enhance your problem-solving abilities, this book offers a comprehensive collection of exercises that will sharpen your skills and boost your confidence. This book takes a structured approach, starting with fundamental concepts and gradually progressing to more advanced topics. Through a carefully curated selection of exercises, ranging from basic inequalities to complex systems of inequalities, readers will be guided through a step-by-step journey, enabling them to build a solid foundation and grasp the intricacies of this important mathematical field. Key features of "Inequalities Math Exercises" include: 1. Wide-ranging Exercise Selection: The book presents a vast array of exercises, encompassing various types of inequalities, such as linear, quadratic, absolute value, rational, and logarithmic inequalities. Each exercise is accompanied by detailed solutions, providing valuable insights and strategies. 2. Problem-Solving Techniques: In addition to solving individual exercises, readers will learn valuable problem-solving techniques and strategies that can be applied to a wide range of mathematical problems. These techniques include algebraic manipulation, graphing, substitution, and logical reasoning. 3. Self-Assessment and Progress Tracking: Self-assessment exercises allow readers to evaluate their progress, identify areas for improvement, and reinforce their understanding of the material. "Inequalities Math Exercises" is an invaluable companion for students preparing for standardized tests, such as the SAT, ACT, or GRE, as well as for teachers seeking to enrich their curriculum and provide additional practice material. This book also serves as a handy reference guide for mathematics enthusiasts who wish to deepen their knowledge and explore the captivating world of inequalities. Embark on a journey of mathematical discovery and develop the skills needed to conquer inequalities with confidence. Whether you're a student, an educator, or a curious mind, "Inequalities, things you should know, questions and answers" is your ultimate guide to mastering this vital branch of mathematics.

Risk and Uncertainty Reduction by Using Algebraic Inequalities

Michael T. Todinov
Risk and Uncertainty Reduction by Using Algebraic Inequalities Book PDF

Author : Michael T. Todinov
Publisher : CRC Press
Page : 142 pages
File Size : 46,8 Mb
Release : 2020-06-02
Category : Technology & Engineering
ISBN : 9781000076448

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Risk and Uncertainty Reduction by Using Algebraic Inequalities by Michael T. Todinov Pdf

This book covers the application of algebraic inequalities for reliability improvement and for uncertainty and risk reduction. It equips readers with powerful domain-independent methods for reducing risk based on algebraic inequalities and demonstrates the significant benefits derived from the application for risk and uncertainty reduction. Algebraic inequalities: • Provide a powerful reliability improvement, risk and uncertainty reduction method that transcends engineering and can be applied in various domains of human activity • Present an effective tool for dealing with deep uncertainty related to key reliability-critical parameters of systems and processes • Permit meaningful interpretations which link abstract inequalities with the real world • Offer a tool for determining tight bounds for the variation of risk-critical parameters and complying the design with these bounds to avoid failure • Allow optimising designs and processes by minimising the deviation of critical output parameters from their specified values and maximising their performance This book is primarily for engineering professionals and academic researchers in virtually all existing engineering disciplines.

Algebraic Inequalities

Hayk Sedrakyan,Nairi Sedrakyan
Algebraic Inequalities Book PDF

Author : Hayk Sedrakyan,Nairi Sedrakyan
Publisher : Springer
Page : 243 pages
File Size : 40,5 Mb
Release : 2018-07-05
Category : Mathematics
ISBN : 9783319778365

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Algebraic Inequalities by Hayk Sedrakyan,Nairi Sedrakyan Pdf

This unique collection of new and classical problems provides full coverage of algebraic inequalities. Many of the exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. Algebraic Inequalities can be considered a continuation of the book Geometric Inequalities: Methods of Proving by the authors. 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 algebraic inequalities.

Analytic Inequalities

Dragoslav S. Mitrinovic
Analytic Inequalities Book PDF

Author : Dragoslav S. Mitrinovic
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642999703

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Analytic Inequalities by Dragoslav S. Mitrinovic Pdf

The Theory of Inequalities began its development from the time when C. F. GACSS, A. L. CATCHY and P. L. CEBYSEY, to mention only the most important, laid the theoretical foundation for approximative meth ods. Around the end of the 19th and the beginning of the 20th century, numerous inequalities were proyed, some of which became classic, while most remained as isolated and unconnected results. It is almost generally acknowledged that the classic work "Inequali ties" by G. H. HARDY, J. E. LITTLEWOOD and G. POLYA, which appeared in 1934, transformed the field of inequalities from a collection of isolated formulas into a systematic discipline. The modern Theory of Inequalities, as well as the continuing and growing interest in this field, undoubtedly stem from this work. The second English edition of this book, published in 1952, was unchanged except for three appendices, totalling 10 pages, added at the end of the book. Today inequalities playa significant role in all fields of mathematics, and they present a very active and attractive field of research. J. DIEUDONNE, in his book "Calcullnfinitesimal" (Paris 1968), attri buted special significance to inequalities, adopting the method of exposi tion characterized by "majorer, minorer, approcher". Since 1934 a multitude of papers devoted to inequalities have been published: in some of them new inequalities were discovered, in others classical inequalities ,vere sharpened or extended, various inequalities ,vere linked by finding their common source, while some other papers gave a large number of miscellaneous applications.

Algebra I Essentials For Dummies

Mary Jane Sterling
Algebra I Essentials For Dummies Book PDF

Author : Mary Jane Sterling
Publisher : John Wiley & Sons
Page : 192 pages
File Size : 52,8 Mb
Release : 2019-04-15
Category : Mathematics
ISBN : 9781119590989

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Algebra I Essentials For Dummies by Mary Jane Sterling Pdf

Algebra I Essentials For Dummies (9781119590965) was previously published as Algebra I Essentials For Dummies (9780470618349). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, Algebra I Essentials For Dummies provides content focused on key topics only, with discrete explanations of critical concepts taught in a typical Algebra I course, from functions and FOILs to quadratic and linear equations. This guide is also a perfect reference for parents who need to review critical algebra concepts as they help students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts. The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Analytic Inequalities

B.G. Pachpatte
Analytic Inequalities Book PDF

Author : B.G. Pachpatte
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 50,8 Mb
Release : 2012-01-05
Category : Mathematics
ISBN : 9789491216442

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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.

Continuous Optimization and Variational Inequalities

Anurag Jayswal,Tadeusz Antczak
Continuous Optimization and Variational Inequalities Book PDF

Author : Anurag Jayswal,Tadeusz Antczak
Publisher : CRC Press
Page : 379 pages
File Size : 43,5 Mb
Release : 2022-09-13
Category : Technology & Engineering
ISBN : 9781000648935

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Continuous Optimization and Variational Inequalities by Anurag Jayswal,Tadeusz Antczak Pdf

The proposed book provides a comprehensive coverage of theory and methods in the areas of continuous optimization and variational inequality. It describes theory and solution methods for optimization with smooth and non-smooth functions, for variational inequalities with single-valued and multivalued mappings, and for related classes such as mixed variational inequalities, complementarity problems, and general equilibrium problems. The emphasis is made on revealing generic properties of these problems that allow creation of efficient solution methods. Salient Features The book presents a deep, wide-ranging introduction to the theory of the optimal control of processes governed by optimization techniques and variational inequality Several solution methods are provided which will help the reader to develop various optimization tools for real-life problems which can be modeled by optimization techniques involving linear and nonlinear functions. The book focuses on most recent contributions in the nonlinear phenomena, which can appear in various areas of human activities. This book also presents relevant mathematics clearly and simply to help solve real life problems in diverse fields such as mechanical engineering, management, control behavior, traffic signal, industry, etc. This book is aimed primarily at advanced undergraduates and graduate students pursuing computer engineering and electrical engineering courses. Researchers, academicians and industry people will also find this book useful.

General Inequalities 6

Wolfgang Walter
General Inequalities 6 Book PDF

Author : Wolfgang Walter
Publisher : Birkhäuser
Page : 507 pages
File Size : 50,8 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783034875653

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General Inequalities 6 by Wolfgang Walter Pdf

The sixthInternational Conference on General Inequalities was held from Dec. 9 to Dec. 15, 1990, at the Mathematisches Forschungsinstitut Oberwolfach (Black Fa rest, Germany). The organizing committee was composed of W.N. Everitt (Birm ingham), L. Losonczi (Debrecen) and W. Walter (Karlsruhe). Dr. A. Kovacec ( Coimbra) served cheerfully and efficiently as secretary of the meeting. The con ference was attended by 44 participants from 20 countries. Yet again the importance of inequalities in both pure and applied mathematics was made evident from the wide range of interests of the individual participants, and from the wealth of new results announced. New inequalities were presented in the usual spread of the subject areas now expected for these meetings: Classical and functional analysis, existence and boundary value problems for both ordinary and partial differential equations, with special contributions to computer science, quantum holography and error analysis. More strongly than ever, the role played by modern electronic computers was made clear in testing out and prohing into the validity and structure of certain inequalities. Here the computer acts not only for numerical calculations of great complexity, but also in symbolic manipulation of complex finite structures. Prob lems in inequalities which even a few years ago were intractable, now fall to solution or receive direct and positive guidance as a result of computer applications. The interface between finite and infinite structures in mathematics and the versatility of modern computers is weil developed in the subject of general inequalities.

Integral and Discrete Inequalities and Their Applications

Yuming Qin
Integral and Discrete Inequalities and Their Applications Book PDF

Author : Yuming Qin
Publisher : Birkhäuser
Page : 1072 pages
File Size : 41,7 Mb
Release : 2016-10-06
Category : Mathematics
ISBN : 9783319333045

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Integral and Discrete Inequalities and Their Applications by Yuming Qin Pdf

This book concentrates on one- and multi-dimensional nonlinear integral and discrete Gronwall-Bellman type inequalities. It complements the author’s book on linear inequalities and serves as an essential tool for researchers interested in differential (ODE and PDE), difference, and integral equations. The present volume is part 2 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization

Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta
Generalized Convexity Nonsmooth Variational Inequalities and Nonsmooth Optimization Book PDF

Author : Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta
Publisher : CRC Press
Page : 294 pages
File Size : 46,9 Mb
Release : 2013-07-18
Category : Business & Economics
ISBN : 9781439868218

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Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization by Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta Pdf

Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction.The first part of the book focuses on generalized convexity and generalized