Volume 12 in the series De Gruyter Series in Logic and Its Applications
Automatic Complexity discusses a treatment of a computable form of Kolmogorov complexity, in which Turing machines are replaced by finite automata. The complexities of many types of words are studied, including random words, normal words, Fibonacci words, Thue words, and words produced by linear feedback shift registers.
Automatic Complexity discusses the treatment of a computable form of Kolmogorov complexity, in which Turing machines are replaced by finite automata. It covers the Combinatorics on words most likely to be encountered
Frontmatter
Publicly Available I
Preface
Publicly Available VII
Acknowledgments
Publicly Available IX
Publicly Available XI
1 First steps in automatic complexity
Requires Authentication 1
2 Nondeterminism and overlap-free words
Requires Authentication 33
3 Edge complexity and digraphs
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4 The many variants
Requires Authentication 77
5 The incompressibility theorem
Requires Authentication 103
6 Conditional automatic complexity
Requires Authentication 111
7 Logical depth and automatic complexity
Requires Authentication 122
Bibliography
Requires Authentication 137
Index
Volume 43 in the series De Gruyter Series in Nonlinear Analysis and Applications
The book is focused on physical interpretation and visualization of the obtained invariant solutions for nonlinear mathematical modeling of atmospheric and ocean waves. This volume represents a unique blend of analytical and numerical methods complemented by the author's developments in ocean and atmospheric sciences and it is meant for researchers and graduate students interested in applied mathematics and mathematical modeling.
Presents an introduction to Lie Group Analysis of Differential Equations with detailed solutions.
Provides examples of Invariant solutions for nonlinear physical models.
Includes visualization and physical interpretation of invariant solutions.
Analysis
Applied Mathematics
Differential Equations and Dynamical Systems
Mathematics
In the series De Gruyter Proceedings in Mathematics
The present collection of essays are published in honor of the distinguished historian of mathematics Professor Emeritus Jesper Lutzen. In a career that spans more than four decades, Professor Lutzen's scholarly contributions have enhanced our understanding of the history, development, and organization of mathematics. The essays cover a broad range of areas connected to Professor Lutzen's work. In addition to this noteworthy scholarship, Professor Lutzen has always been an exemplary colleague, providing support to peers as well as new faculty and graduate students. We dedicate this Festschrift to Professor Lutzen?as a scholarly role model, mentor, colleague, and friend.
This book presents current research on specialized topics in the history of mathematics and physical sciences with contributions from academic scholars also discussed are research methods and how scholars investigate the history of mathematics.
Engineering
General Mathematics
History
History and Philosophy
History of Engineering
Introductions and Overviews
Mathematics
Miscellaneous
In the series De Gruyter Textbook
This book covers the basic ideas of quantum mechanics, with emphasis on concepts, calculations, and their applications in many areas of modern science and technology. As opposed to other available introductions to quantum mechanics, this book was developed in close collaboration with students in order to guarantee that the explanations and exercises are clear and effective.
Concise and accessible introduction to quantum mechanics.
With plenty of exercises and questions, including a sample exam at the end of each chapter.
Includes applications to chemical reactions, ultrafast lasers, and quantum computing.
Applied Mathematics
Condensed Matter Physics
Materials Sciences
Mathematics
Modeling and Simulations
Physics
Quantum Physics
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.
The first book devoted on projector analysis of dynamic equations on time scales
Provides decoupling of all classes of linear time-varying dynamic equations.
Provides with many examples illustrated the main theory.
Svetlin G. Georgiev works on various aspects of mathematics. His current research focuses on harmonic analysis, ordinary differential equations, partial differential equations, fractional calculus, time scale calculus, integral equations, numerical analysis, differential geometry, and dynamic geometry.
Khaled Zennir: was born in Algeria 1982. He received his PhD in Mathematics in 2013 from Sidi Bel Abbes University, Algeria (Assist. professor). He is now associate Professor at Qassim University, KSA. His research interests lie in Nonlinear Hyperbolic Partial Differential Equations: Global Existence, Blow-Up, and Long Time Behavior.
Applied Mathematics
Differential Equations and Dynamical Systems
Mathematics
*
Volume 97 in the series De Gruyter Studies in Mathematics
This book aims to be a comprehensive treatise on the interactions between Coding Theory and Commutative Algebra. With the help of a multitude of examples, it expands and systematizes the known and versatile commutative algebraic framework used, since the early 90fs, to study linear codes. The book provides the necessary background for the reader to advance with similar research on coding theory topics from commutative algebraic perspectives.
Gathers as many results as possible which can lead to developing new approaches and coding.
Presents the natural connections between commutative algebra and coding theory topics and concepts.
Algebra and Number Theory
Geometry and Topology
Mathematics
Volume 10 in the series Advances in Analysis and Geometry
Provides the first systematic study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups. In addition to geometry and topology, this study involves several other areas of Mathematics ? from algebra of varieties of groups representations and geometric group theory, to geometric analysis including classical questions from function theory.
This must-have reference provides the first comprehensive study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups.
Boris N. Apanasov, University of Oklahoma, USA.
Applied Mathematics
Geometry and Topology
Mathematics
In the series De Gruyter Textbook
The second editions covers the introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. The new edition includes new topics on Banach Spaces of Functions and Measures and Nonlinear Analysis.
A detailed presentation of nonlinear functional analysis now in its second edition
Updates include advanced material for semigroups of Operators and Generalized Orlicz Spaces
Now covers the parts of Nonlinear Operators, Identities, inequalities
Patrick Winkert, TU Berlin, Germany; Nikolaos S. Papageorgiou, National Technical University of Athens, Greece
Analysis
Mathematics
In the series De Gruyter Textbook
The book concerns with solving about 650 ordinary and partial differential equations. Each equation has at least one solution and each solution has at least one coloured graph. The coloured graphs reveal different features of the solutions. Some graphs are dynamical as for Clairaut differential equations. Thus, one can study the general and the singular solutions. All the equations are solved by Mathematica. The first chapter contains mathematical notions and results that are used later through the book. Thus, the book is self-contained that is an advantage for the reader. The ordinary differential equations are treated in Chapters 2 to 4, while the partial differential equations are discussed in Chapters 5 to 10. The book is useful for undergraduate and graduate students, for researchers in engineering, physics, chemistry, and others. Chapter 9 treats parabolic partial differential equations while Chapter 10 treats third and higher order nonlinear partial differential equations, both with modern methods. Chapter 10 discusses the Korteweg-de Vries, Dodd-Bullough-Mikhailov, Tzitzeica-Dodd-Bullough, Benjamin, Kadomtsev-Petviashvili, Sawada-Kotera, and Kaup-Kupershmidt equations.
All the equations are completely solved by Mathematica (analytically, numerically, and/or graphically)
All solutions are accompanied by full codes
The equations are gradually introduced according to the degree of difficulty
Marian Mure?an, G. DIMA street, 15, ap. 25, Cluj-Napoca, 400335, ROMANIA
E-mail: mmarianus24@yahoo.com, marian.muresan@ubbcluj.ro
Work address:
Faculty of Mathematics and Computer Science, Babe?-Bolyai University
M. Kog?lniceanu st. 1, 400084 Cluj-Napoca, ROMANIA
Phone:(+40-)264-405300 ext. 5244, Mobil:(+40-)743-130380
Basics and Tools
Computer Sciences
Differential Equations and Dynamical Systems
Engineering
Introductions and Overviews
Mathematics
Physics
Programming and Languages
Theoretical and Mathematical Physics