Interpretation of Algebraic Inequalities PDF Download

Author: Michael Todinov
Publisher: CRC Press
ISBN: 100046895X
Category : Technology & Engineering
Languages : en
Pages : 154

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Book Description
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: Michael T. Todinov
Publisher: CRC Press
ISBN: 1040261531
Category : Technology & Engineering
Languages : en
Pages : 214

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Book Description
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. .

Author: Jiri Herman
Publisher: Springer Science & Business Media
ISBN: 1461212707
Category : Mathematics
Languages : en
Pages : 353

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Book Description
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: Hayk Sedrakyan
Publisher: Springer
ISBN: 3319778366
Category : Mathematics
Languages : en
Pages : 244

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Book Description
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: Nicolas Lerner
Publisher: Springer
ISBN: 3030159930
Category : Mathematics
Languages : en
Pages : 576

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Book Description
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:
Publisher: Rumi Michael Leigh
ISBN:
Category : Mathematics
Languages : en
Pages : 71

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Book Description
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: Praveen Agarwal
Publisher: Springer
ISBN: 9811330131
Category : Mathematics
Languages : en
Pages : 351

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Book Description
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: B.G. Pachpatte
Publisher: Springer Science & Business Media
ISBN: 9491216449
Category : Mathematics
Languages : en
Pages : 310

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Book Description
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.

Author: Tony Croft
Publisher: Pearson UK
ISBN: 129225369X
Category : Engineering mathematics
Languages : en
Pages : 2342

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Book Description

Author: Yuming Qin
Publisher: Birkhäuser
ISBN: 3319008315
Category : Mathematics
Languages : en
Pages : 570

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Book Description
This book presents a number of analytic inequalities and their applications in partial differential equations. These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations. Summarizing results from a vast number of literature sources such as published papers, preprints and books, it categorizes inequalities in terms of their different properties.