Svetlin G. Georgiev's Books

Differential Geometry

Frenet Equations and Differentiable Maps

By: Muhittin E. Aydin,Svetlin G. Georgiev

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Differential Geometry

Frenet Equations and Differentiable Maps

By: Muhittin E. Aydin,Svetlin G. Georgiev

This textbook offers a different approach to classical textbooks in Differential Geometry. It includes practical examples and over 300 advanced problems designed for graduate students in various fields, such as fluid mechanics, gravitational fields, nuclear physics, electromagnetism, solid-state physics, and thermodynamics. Additionally, it contains problems tailored for students specializing in chemical, civil, and electrical engineering and electronics. The book provides fully detailed solutions to each problem and includes many illustrations to help visualize theoretical concepts. The book introduces Frenet equations for plane and space curves, presents the basic theory of surfaces, and introduces differentiable maps and differentials on the surface. It also provides the first and second fundamental forms of surfaces, minimal surfaces, and geodesics. Furthermore, it contains a detailed analysis of covariant derivatives and manifolds. The book covers many classical results, such as the Lancret Theorem, Shell Theorem, Joachimsthal Theorem, and Meusnier Theorem, as well as the fundamental theorems of plane curves, space curves, surfaces, and manifolds.

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290

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

311150185X

ISBN 13

9783111501857

Differential Equations

Projector Analysis on Time Scales

By: Svetlin G. Georgiev,Khaled Zennir

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Differential Equations

Projector Analysis on Time Scales

By: Svetlin G. Georgiev,Khaled Zennir

This book presents a projector analysis of dynamic systems on time scales. The dynamic systems are classified as first, second, third and fourth kinds. For each classes of dynamic systems the basic matrix chains are constructed. The proposed theory is applied for decoupling of dynamic equations on time scales. Properly involved derivatives, constraints and consistent initial values for the considered equations are defined. A linearization for nonlinear dynamic systems is introduced and the total derivative for regular linearized equations with tractability index one is investigated.

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553

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3111377717

ISBN 13

9783111377711

An Excursion Through Partial Differential Equations

By: Svetlin G. Georgiev

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An Excursion Through Partial Differential Equations

By: Svetlin G. Georgiev

Presenting a rich collection of exercises on partial differential equations, this textbook equips readers with 96 examples, 222 exercises, and 289 problems complete with detailed solutions or hints. It explores a broad spectrum of partial differential equations, fundamental to mathematically oriented scientific fields, from physics and engineering to differential geometry and variational calculus. Organized thoughtfully into seven chapters, the journey begins with fundamental problems in the realm of PDEs. Readers progress through first and second-order equations, wave and heat equations, and finally, the Laplace equation. The text adopts a highly readable and mathematically solid format, ensuring concepts are introduced with clarity and organization. Designed to cater to upper undergraduate and graduate students, this book offers a comprehensive understanding of partial differential equations. Researchers and practitioners seeking to strengthen their problem-solving skills will also find this exercise collection both challenging and beneficial.

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424

Publisher

Springer Nature

Published Date

ISBN 10

3031487842

ISBN 13

9783031487842

General Quantum Numerical Analysis

By: Svetlin G. Georgiev,Khaled Zennir

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General Quantum Numerical Analysis

By: Svetlin G. Georgiev,Khaled Zennir

This book is focused on the qualitative theory of general quantum calculus, the modern name for the investigation of calculus without limits. It centers on designing, analysing and applying computational techniques for general quantum differential equations. The quantum calculus or q-calculus began with F.H. Jackson in the early twentieth century, but this kind of calculus had already been worked out by Euler and Jacobi. Recently, it has aroused interest due to high demand of mathematics that models quantum computing and the connection between mathematics and physics. Quantum calculus has many applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hyper-geometric functions and other sciences such as quantum theory, mechanics and the theory of relativity. The authors summarize the most recent contributions in this area. General Quantum Numerical Analysis is intended for senior undergraduate students and beginning graduate students of engineering and science courses. The twelve chapters in this book are pedagogically organized, each concluding with a section of practical problems.

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371

Publisher

CRC Press

Published Date

ISBN 10

1040023339

ISBN 13

9781040023334

Numerical Analysis on Time Scales

By: Svetlin G. Georgiev,Inci M. Erhan

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Numerical Analysis on Time Scales

By: Svetlin G. Georgiev,Inci M. Erhan

Mathematical models cannot be solved using the traditional analytical methods for dynamic equations on time scales. These models must be dealt with using computational methods. This textbook introduces numerical methods for initial value problems for dynamic equations on time scales. Hands-on examples utilizing MATLAB and practical problems illustrate a wide variety of solution techniques.

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267

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110787342

ISBN 13

9783110787344

Multivariable Dynamic Calculus on Time Scales

By: Martin Bohner,Svetlin G. Georgiev

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Multivariable Dynamic Calculus on Time Scales

By: Martin Bohner,Svetlin G. Georgiev

This book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales, taking readers beyond the traditional calculus texts. Covering topics from parameter-dependent integrals to partial differentiation on time scales, the book’s nine pedagogically oriented chapters provide a pathway to this active area of research that will appeal to students and researchers in mathematics and the physical sciences. The authors present a clear and well-organized treatment of the concept behind the mathematics and solution techniques, including many practical examples and exercises.

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608

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Springer

Published Date

ISBN 10

3319476203

ISBN 13

9783319476209

Functional Dynamic Equations on Time Scales

By: Svetlin G. Georgiev

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Functional Dynamic Equations on Time Scales

By: Svetlin G. Georgiev

This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.

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886

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Springer

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ISBN 10

3030154203

ISBN 13

9783030154202

Advances On Fractional Dynamic Inequalities On Time Scales

By: Svetlin G Georgiev,Khaled Zennir

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Advances On Fractional Dynamic Inequalities On Time Scales

By: Svetlin G Georgiev,Khaled Zennir

This book is devoted on recent developments of linear and nonlinear fractional Riemann-Liouville and Caputo integral inequalities on time scales. The book is intended for the use in the field of fractional dynamic calculus on time scales and fractional dynamic equations on time scales. It is also suitable for graduate courses in the above fields, and contains ten chapters. The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques. The text material of this book is presented in a readable and mathematically solid format.

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337

Publisher

World Scientific

Published Date

ISBN 10

9811275483

ISBN 13

9789811275487

Boundary Value Problems on Time Scales, Volume I

By: Svetlin G. Georgiev,Khaled Zennir

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Boundary Value Problems on Time Scales, Volume I

By: Svetlin G. Georgiev,Khaled Zennir

Boundary Value Problems on Time Scales, Volume I is devoted to the qualitative theory of boundary value problems on time scales. Summarizing the most recent contributions in this area, it addresses a wide audience of specialists such as mathematicians, physicists, engineers and biologists. It can be used as a textbook at the graduate level and as a reference book for several disciplines. The text contains two volumes, both published by Chapman & Hall/CRC Press. Volume I presents boundary value problems for first- and second-order dynamic equations on time scales. Volume II investigates boundary value problems for three, four, and higher-order dynamic equations on time scales. Many results to differential equations carry over easily to corresponding results for difference equations, while other results seem to be totally different in nature. Because of these reasons, the theory of dynamic equations is an active area of research. The time-scale calculus can be applied to any field in which dynamic processes are described by discrete or continuous time models. The calculus of time scales has various applications involving noncontinuous domains such as certain bug populations, phytoremediation of metals, wound healing, maximization problems in economics, and traffic problems. Boundary value problems on time scales have been extensively investigated in simulating processes and the phenomena subject to short-time perturbations during their evolution. The material in this book is presented in highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques. AUTHORS Svetlin G. Georgiev is a mathematician who has worked in various areas of the study. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. Khaled Zennir earned his PhD in mathematics in 2013 from Sidi Bel Abbès University, Algeria. In 2015, he received his highest diploma in Habilitation in mathematics from Constantine University, Algeria. He is currently assistant professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and long-time behavior.

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324

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CRC Press

Published Date

ISBN 10

100042989X

ISBN 13

9781000429893

Integral Inequalities on Time Scales

By: Svetlin G. Georgiev

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Integral Inequalities on Time Scales

By: Svetlin G. Georgiev

This book is devoted to recent developments of linear and nonlinear integral inequalities on time scales. The book is intended for the use in the field of dynamic calculus on time scales, dynamic equation and integral equations on time scales. It is also suitable for graduate courses in the above fields. The book is designed for those who have mathematical background on time scales calculus.

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186

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110705664

ISBN 13

9783110705669

Conformable Dynamic Equations on Time Scales

By: Douglas R. Anderson,Svetlin G. Georgiev

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Conformable Dynamic Equations on Time Scales

By: Douglas R. Anderson,Svetlin G. Georgiev

The concept of derivatives of non-integer order, known as fractional derivatives, first appeared in the letter between L’Hopital and Leibniz in which the question of a half-order derivative was posed. Since then, many formulations of fractional derivatives have appeared. Recently, a new definition of fractional derivative, called the "fractional conformable derivative," has been introduced. This new fractional derivative is compatible with the classical derivative and it has attracted attention in areas as diverse as mechanics, electronics, and anomalous diffusion. Conformable Dynamic Equations on Time Scales is devoted to the qualitative theory of conformable dynamic equations on time scales. This book summarizes the most recent contributions in this area, and vastly expands on them to conceive of a comprehensive theory developed exclusively for this book. Except for a few sections in Chapter 1, the results here are presented for the first time. As a result, the book is intended for researchers who work on dynamic calculus on time scales and its applications. Features Can be used as a textbook at the graduate level as well as a reference book for several disciplines Suitable for an audience of specialists such as mathematicians, physicists, engineers, and biologists Contains a new definition of fractional derivative About the Authors Douglas R. Anderson is professor and chair of the mathematics department at Concordia College, Moorhead. His research areas of interest include dynamic equations on time scales and Ulam-type stability of difference and dynamic equations. He is also active in investigating the existence of solutions for boundary value problems. Svetlin G. Georgiev is currently professor at Sorbonne University, Paris, France and works in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, dynamic calculus on time scales, and integral equations.

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347

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CRC Press

Published Date

ISBN 10

100009393X

ISBN 13

9781000093933

Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

By: Svetlin G. Georgiev

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Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

By: Svetlin G. Georgiev

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations. Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales.

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364

Publisher

Springer

Published Date

ISBN 10

3319739549

ISBN 13

9783319739540

Functional Analysis with Applications

By: Svetlin G. Georgiev,Khaled Zennir

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Functional Analysis with Applications

By: Svetlin G. Georgiev,Khaled Zennir

This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study.

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404

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110657724

ISBN 13

9783110657722

Multiplicative Differential Calculus

By: Svetlin G. Georgiev,Khaled Zennir

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Multiplicative Differential Calculus

By: Svetlin G. Georgiev,Khaled Zennir

This book is devoted to the multiplicative differential calculus. Its seven pedagogically organized chapters summarize the most recent contributions in this area, concluding with a section of practical problems to be assigned or for self-study. Two operations, differentiation and integration, are basic in calculus and analysis. In fact, they are the infinitesimal versions of the subtraction and addition operations on numbers, respectively. From 1967 till 1970, Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, moving the roles of subtraction and addition to division and multiplication, and thus established a new calculus, called multiplicative calculus. It is also called an alternative or non-Newtonian calculus. Multiplicative calculus can especially be useful as a mathematical tool for economics, finance, biology, and engineering. Multiplicative Differential Calculus is written to be of interest to a wide audience of specialists such as mathematicians, physicists, engineers, and biologists. It is primarily a textbook at the senior undergraduate and beginning graduate level and may be used for a course on differential calculus. It is also for students studying engineering and science. Authors Svetlin G. Georgiev is a mathematician who has worked in various areas of the study. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. He is also the author of Dynamic Geometry of Time Scales (CRC Press). He is a co-author of Conformable Dynamic Equations on Time Scales, with Douglas R. Anderson (CRC Press). Khaled Zennir earned his PhD in mathematics from Sidi Bel Abbès University, Algeria. He earned his highest diploma in Habilitation in Mathematics from Constantine University, Algeria. He is currently Assistant Professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and long-time behavior. The authors have also published: Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDE; Boundary Value Problems on Time Scales, Volume 1 and Volume II, all with CRC Press.

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232

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CRC Press

Published Date

ISBN 10

1000605507

ISBN 13

9781000605501

Boundary Value Problems on Time Scales, Volume II

By: Svetlin G. Georgiev,Khaled Zennir

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Boundary Value Problems on Time Scales, Volume II

By: Svetlin G. Georgiev,Khaled Zennir

Boundary Value Problems on Time Scales, Volume II is devoted to the qualitative theory of boundary value problems on time scales. Summarizing the most recent contributions in this area, it addresses a wide audience of specialists such as mathematicians, physicists, engineers and biologists. It can be used as a textbook at the graduate level and as a reference book for several disciplines. The text contains two volumes, both published by Chapman & Hall/CRC Press. Volume I presents boundary value problems for first- and second-order dynamic equations on time scales. Volume II investigates boundary value problems for three, four, and higher-order dynamic equations on time scales. Many results to differential equations carry over easily to corresponding results for difference equations, while other results seem to be totally different in nature. Because of these reasons, the theory of dynamic equations is an active area of research. The time-scale calculus can be applied to any field in which dynamic processes are described by discrete or continuous time models. The calculus of time scales has various applications involving noncontinuous domains such as certain bug populations, phytoremediation of metals, wound healing, maximization problems in economics, and traffic problems. Boundary value problems on time scales have been extensively investigated in simulating processes and the phenomena subject to short-time perturbations during their evolution. The material in this book is presented in highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques. AUTHORS Svetlin G. Georgiev is a mathematician who has worked in various areas of the study. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. Khaled Zennir earned his PhD in mathematics in 2013 from Sidi Bel Abbès University, Algeria. In 2015, he received his highest diploma in Habilitation in mathematics from Constantine University, Algeria. He is currently assistant professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and long-time behavior.

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213

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CRC Press

Published Date

ISBN 10

1000429903

ISBN 13

9781000429909

Integral Equations on Time Scales

By: Svetlin G. Georgiev

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Integral Equations on Time Scales

By: Svetlin G. Georgiev

This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background.

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403

Publisher

Springer

Published Date

ISBN 10

9462392285

ISBN 13

9789462392281

Dynamic Geometry on Time Scales

By: Svetlin G. Georgiev

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Dynamic Geometry on Time Scales

By: Svetlin G. Georgiev

This book introduces plane curves on time scales. They are deducted the Frenet equations for plane and space curves. In the book is presented the basic theory of surfaces on time scales. They are defined tangent plane, \sigma_1 and \sigma_2 tangent planes, normal, \sigma_1 and \sigma_2 normals to a surface. They are introduced differentiable maps and differentials on surface. This book provides the first and second fundamental forms of surfaces on time scales. They are introduced minimal surfaces and geodesics on time scales. In the book are studied the covaraint derivatives on time scales, pseudo-spherical surfaces and \sigma_1, \sigma_2 manifolds on time scales.

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Page Count

397

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CRC Press

Published Date

ISBN 10

1000471144

ISBN 13

9781000471144

Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales

By: Svetlin G. Georgiev

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Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales

By: Svetlin G. Georgiev

The theory of dynamic equations has many interesting applications in control theory, mathematical economics, mathematical biology, engineering and technology. In some cases, there exists uncertainty, ambiguity, or vague factors in such problems, and fuzzy theory and interval analysis are powerful tools for modeling these equations on time scales. The aim of this book is to present a systematic account of recent developments; describe the current state of the useful theory; show the essential unity achieved in the theory fuzzy dynamic equations, dynamic inclusions and optimal control problems on time scales; and initiate several new extensions to other types of fuzzy dynamic systems and dynamic inclusions. The material is presented in a highly readable, mathematically solid format. Many practical problems are illustrated, displaying a wide variety of solution techniques. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. Students in mathematical and physical sciences will find many sections of direct relevance.

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882

Publisher

Springer Nature

Published Date

ISBN 10

3030761320

ISBN 13

9783030761325

Multiplicative Partial Differential Equations

By: Svetlin G. Georgiev,Khaled Zennir

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Multiplicative Partial Differential Equations

By: Svetlin G. Georgiev,Khaled Zennir

The book includes new classification and canonical forms of Second order MPDEs Proposes a new technique to solve the multiplicative wave equation such as method of separation of variables, energy method. The proposed technique in the book can be used to give the basic properties of multiplicative elliptic problems, the fundamental solutions, multiplicative integral representation of multiplicative harmonic functions, mean-value formulas, strong principle of maximum, the multiplicative Poisson equation, multiplicative Green functions, method of separation of variables, theorems of Liouville and Harnack.

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269

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CRC Press

Published Date

ISBN 10

1000970051

ISBN 13

9781000970050

Multiplicative Differential Geometry

By: Svetlin G. Georgiev

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Multiplicative Differential Geometry

By: Svetlin G. Georgiev

This book introduces multiplicative Frenet curves. We define multiplicative tangent, multiplicative normal, and multiplicative normal plane for a multiplicative Frenet curve. We investigate the local behaviours of a multiplicative parameterized curve around multiplicative biregular points, define multiplicative Bertrand curves and investigate some of their properties. A multiplicative rigid motion is introduced. The book is addressed to instructors and graduate students, and also specialists in geometry, mathematical physics, differential equations, engineering, and specialists in applied sciences. The book is suitable as a textbook for graduate and under-graduate level courses in geometry and analysis. Many examples and problems are included. The author introduces the main conceptions for multiplicative surfaces: multiplicative first fundamental form, the main multiplicative rules for differentiations on multiplicative surfaces, and the main multiplicative regularity conditions for multiplicative surfaces. An investigation of the main classes of multiplicative surfaces and second fundamental forms for multiplicative surfaces is also employed. Multiplicative differential forms and their properties, multiplicative manifolds, multiplicative Einstein manifolds and their properties, are investigated as well. Many unique applications in mathematical physics, classical geometry, economic theory, and theory of time scale calculus are offered.

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373

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CRC Press

Published Date

ISBN 10

1000606945

ISBN 13

9781000606942

Theory of Distributions

By: Svetlin G. Georgiev

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Theory of Distributions

By: Svetlin G. Georgiev

This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This second edition, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.

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270

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Springer Nature

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ISBN 10

3030812650

ISBN 13

9783030812652

Theory of Distributions

By: Svetlin G. Georgiev

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Theory of Distributions

By: Svetlin G. Georgiev

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270

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Springer Nature

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3030812650

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9783030812652

Multiplicative Differential Geometry

By: Svetlin G. Georgiev

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Multiplicative Differential Geometry

By: Svetlin G. Georgiev

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373

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CRC Press

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1000606945

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9781000606942

P(x)-bi-laplacian: Application On Time-pdes In Viscoelasticity

By: Khaled Zennir,Svetlin G Georgiev

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P(x)-bi-laplacian: Application On Time-pdes In Viscoelasticity

By: Khaled Zennir,Svetlin G Georgiev

The main subject of our book is to use the (p, p(x) and p(x))-bi-Laplacian operator in some partial differential systems, where we developed and obtained many results in quantitative and qualitative point of view.

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439

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World Scientific

Published Date

ISBN 10

9811291578

ISBN 13

9789811291579

Dynamic Geometry on Time Scales

By: Svetlin G. Georgiev

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Dynamic Geometry on Time Scales

By: Svetlin G. Georgiev

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397

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CRC Press

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1000471144

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9781000471144

Multiplicative Differential Calculus

By: Svetlin G. Georgiev,Khaled Zennir

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Multiplicative Differential Calculus

By: Svetlin G. Georgiev,Khaled Zennir

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232

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CRC Press

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1000605507

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9781000605501

Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs

By: Svetlin G. Georgiev,Khaled Zennir

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Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs

By: Svetlin G. Georgiev,Khaled Zennir

Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs covers all the basics of the subject of fixed-point theory and its applications with a strong focus on examples, proofs and practical problems, thus making it ideal as course material but also as a reference for self-study. Many problems in science lead to nonlinear equations T x + F x = x posed in some closed convex subset of a Banach space. In particular, ordinary, fractional, partial differential equations and integral equations can be formulated like these abstract equations. It is desirable to develop fixed-point theorems for such equations. In this book, the authors investigate the existence of multiple fixed points for some operators that are of the form T + F, where T is an expansive operator and F is a k-set contraction. This book offers the reader an overview of recent developments of multiple fixed-point theorems and their applications. About the Authors Svetlin G. Georgiev is a mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations and dynamic calculus on time scales. Khaled Zennir is assistant professor at Qassim University, KSA. He received his PhD in mathematics in 2013 from Sidi Bel Abbès University, Algeria. He obtained his Habilitation in mathematics from Constantine University, Algeria in 2015. His research interests lie in nonlinear hyperbolic partial differential equations: global existence, blow up and long-time behavior.

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154

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CRC Press

Published Date

ISBN 10

1000079015

ISBN 13

9781000079012

An Excursion Through Partial Differential Equations

By: Svetlin G. Georgiev

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An Excursion Through Partial Differential Equations

By: Svetlin G. Georgiev

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424

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Springer Nature

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ISBN 10

3031487842

ISBN 13

9783031487842

Boundary Value Problems on Time Scales, Volume II

By: Svetlin G. Georgiev,Khaled Zennir

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Boundary Value Problems on Time Scales, Volume II

By: Svetlin G. Georgiev,Khaled Zennir

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213

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CRC Press

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ISBN 10

1000429903

ISBN 13

9781000429909

Boundary Value Problems on Time Scales, Volume I

By: Svetlin Georgiev,Khaled Zennir

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Boundary Value Problems on Time Scales, Volume I

By: Svetlin Georgiev,Khaled Zennir

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Page Count

693

Publisher

CRC Press

Published Date

ISBN 10

1000429849

ISBN 13

9781000429848

Multiplicative Euclidean and Non-Euclidean Geometry

By: Svetlin G. Georgiev

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Multiplicative Euclidean and Non-Euclidean Geometry

By: Svetlin G. Georgiev

Differential and integral calculus, the most applicable mathematical theory, was created independently by Isaac Newton and Gottfried Wilhelm Leibnitz in the second half of the 17th century. Later, Leonard Euler redirected calculus by giving a central place to the concept of function, and thus founded analysis. Two operations, differentiation and integration, are basic in calculus and analysis. In fact, they are the infinitesimal versions of the subtraction and addition operations on numbers, respectively. From 1967 until 1970, Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, moving the roles of subtraction and addition to division and multiplication, and thus established a new calculus, called multiplicative calculus. Multiplicative calculus can especially be useful as a mathematical tool for economics and finance. This book is devoted to multiplicative Euclidean and non-Euclidean geometry, summarizing the most recent contributions in this area. It will appeal to a wide audience of specialists such as mathematicians, physicists, engineers and biologists, and can be used as a textbook at the graduate level or as a reference book for several disciplines.

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