Multiplying Inequalities

Author : Nicolas Lerner
Publisher : Springer
ISBN 13 : 3030159930
Total Pages : 557 pages
Book Rating : 4.31/5 ( download)

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Download or read book Carleman Inequalities written by Nicolas Lerner and published by Springer. This book was released on 2019-05-18 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michael Todinov
Publisher : CRC Press
ISBN 13 : 100046895X
Total Pages : 154 pages
Book Rating : 4.53/5 ( download)

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Download or read book Interpretation of Algebraic Inequalities written by Michael Todinov and published by CRC Press. This book was released on 2021-10-13 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jiri Herman
Publisher : Springer Science & Business Media
ISBN 13 : 1461212707
Total Pages : 353 pages
Book Rating : 4.06/5 ( download)

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Download or read book Equations and Inequalities written by Jiri Herman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Praveen Agarwal
Publisher : Springer
ISBN 13 : 9811330131
Total Pages : 349 pages
Book Rating : 4.31/5 ( download)

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Download or read book Advances in Mathematical Inequalities and Applications written by Praveen Agarwal and published by Springer. This book was released on 2018-12-31 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : R.P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 9401584265
Total Pages : 407 pages
Book Rating : 4.65/5 ( download)

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Download or read book Opial Inequalities with Applications in Differential and Difference Equations written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author :
Publisher : Rumi Michael Leigh
ISBN 13 :
Total Pages : 71 pages
Book Rating : 4./5 ( download)

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Download or read book Inequalities written by and published by Rumi Michael Leigh. This book was released on 2023-05-24 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michael T. Todinov
Publisher : CRC Press
ISBN 13 : 100007644X
Total Pages : 142 pages
Book Rating : 4.48/5 ( download)

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Download or read book Risk and Uncertainty Reduction by Using Algebraic Inequalities written by Michael T. Todinov and published by CRC Press. This book was released on 2020-06-02 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Hayk Sedrakyan
Publisher : Springer
ISBN 13 : 3319778366
Total Pages : 243 pages
Book Rating : 4.65/5 ( download)

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Download or read book Algebraic Inequalities written by Hayk Sedrakyan and published by Springer. This book was released on 2018-07-05 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Dragoslav S. Mitrinovic
Publisher : Springer Science & Business Media
ISBN 13 : 3642999700
Total Pages : 416 pages
Book Rating : 4.03/5 ( download)

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Download or read book Analytic Inequalities written by Dragoslav S. Mitrinovic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Mary Jane Sterling
Publisher : John Wiley & Sons
ISBN 13 : 1119590981
Total Pages : 192 pages
Book Rating : 4.89/5 ( download)

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Download or read book Algebra I Essentials For Dummies written by Mary Jane Sterling and published by John Wiley & Sons. This book was released on 2019-04-15 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.