Interpretation Of Algebraic Inequalities
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Interpretation Of Algebraic Inequalities
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Author : Michael T. Todinov
language : en
Publisher: CRC Press
Release Date : 2021-10-13
Interpretation Of Algebraic Inequalities written by Michael T. Todinov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-13 with Technology & Engineering categories.
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.
Reverse Engineering Of Algebraic Inequalities
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Author : Michael T. Todinov
language : en
Publisher: CRC Press
Release Date : 2024-12-30
Reverse Engineering Of Algebraic Inequalities written by Michael T. Todinov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-30 with Technology & Engineering categories.
The second edition of Reverse Engineering of Algebraic Inequalities is a comprehensively updated new edition demonstrating the exploration of new physical realities in various unrelated domains of human activity through reverse engineering of algebraic inequalities. This book introduces a groundbreaking method for generating new knowledge in science and technology that relies on reverse engineering of algebraic inequalities. By using this knowledge, the purpose is to optimize systems and processes in diverse fields such as mechanical engineering, structural engineering, physics, electrical engineering, reliability engineering, risk management and economics. This book will provide the reader with methods to enhance the reliability of systems in total absence of knowledge about the reliabilities of the components building the systems; to develop light-weight structures with very big materials savings; to develop structures with very big load-bearing capacity; to enhance process performance and decision-making; to obtain new useful physical properties; and to correct serious flaws in the current practice for predicting system reliability. This book will greatly benefit professionals and mathematical modelling researchers working on optimising processes and systems in diverse disciplines. It will also benefit undergraduate students introduced to mathematical modelling, post-graduate students and post-doctoral researchers working in the area of mathematical modelling, mechanical engineering, reliability engineering, structural engineering, risk management, and engineering design. .
Early Algebraization
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Author : Jinfa Cai
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-24
Early Algebraization written by Jinfa Cai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-24 with Education categories.
In this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.
Inequalities
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Author : Radmila Bulajich Manfrino
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-01
Inequalities written by Radmila Bulajich Manfrino and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.
This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.
College Algebra
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Author : OpenStax
language : en
Publisher:
Release Date : 2016-10-11
College Algebra written by OpenStax and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-11 with Mathematics categories.
College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. The text and images in this textbook are grayscale.
Inequalities
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Author : Zdravko Cvetkovski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-06
Inequalities written by Zdravko Cvetkovski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-06 with Mathematics categories.
This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.
Risk And Uncertainty Reduction By Using Algebraic Inequalities
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Author : Michael T. Todinov
language : en
Publisher: CRC Press
Release Date : 2020-06-02
Risk And Uncertainty Reduction By Using Algebraic Inequalities written by Michael T. Todinov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-02 with Technology & Engineering categories.
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.
Intermediate Algebra 2e
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Author : Lynn Marecek
language : en
Publisher:
Release Date : 2020
Intermediate Algebra 2e written by Lynn Marecek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Algebra categories.
Intermediate Algebra 2e is designed to meet the scope and sequence requirements of a one-semester Intermediate algebra course. The book's organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. The material is presented as a sequence of clear steps, building on concepts presented in prealgebra and elementary algebra courses. The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty.
Standards Driven Math Combo Book 7th Grade Math Algebra I Geometry I Algebra Ii Math Analysis Calculus
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Author : Nathaniel Max Rock
language : en
Publisher: Team Rock Press
Release Date : 2007-08
Standards Driven Math Combo Book 7th Grade Math Algebra I Geometry I Algebra Ii Math Analysis Calculus written by Nathaniel Max Rock and has been published by Team Rock Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08 with categories.
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Inequalities For The Numerical Radius Of Linear Operators In Hilbert Spaces
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Author : Silvestru Sever Dragomir
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-14
Inequalities For The Numerical Radius Of Linear Operators In Hilbert Spaces written by Silvestru Sever Dragomir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-14 with Mathematics categories.
Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, and quantum computation, to name several. Chapter 1 presents fundamental facts about the numerical range and the numerical radius of bounded linear operators in Hilbert spaces. Chapter 2 illustrates recent results obtained concerning numerical radius and norm inequalities for one operator on a complex Hilbert space, as well as some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse Schwarz inequalities and Grüss type inequalities obtained by the author. Chapter 3 presents recent results regarding the norms and the numerical radii of two bounded linear operators. The techniques shown in this chapter are elementary but elegant and may be accessible to undergraduate students with a working knowledge of operator theory. A number of vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are also employed in this chapter. All the results presented are completely proved and the original references are mentioned.