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Orbital Integrals on Reductive Lie Groups and Their Algebras

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ISBN: 9789535110071 Year: Pages: 196 DOI: 10.5772/55875 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:49

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The purpose is to present a complete course on global analysis topics and establish some orbital applications of the integration on topological groups and their algebras to harmonic analysis and induced representations in representation theory.

Differential Equations - Theory and Current Research

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ISBN: 9781789231564 9781789231571 Year: Pages: 182 DOI: 10.5772/intechopen.71745 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:51

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The editor has incorporated contributions from a diverse group of leading researchers in the field of differential equations. This book aims to provide an overview of the current knowledge in the field of differential equations. The main subject areas are divided into general theory and applications. These include fixed point approach to solution existence of differential equations, existence theory of differential equations of arbitrary order, topological methods in the theory of ordinary differential equations, impulsive fractional differential equations with finite delay and integral boundary conditions, an extension of Massera's theorem for n-dimensional stochastic differential equations, phase portraits of cubic dynamic systems in a Poincare circle, differential equations arising from the three-variable Hermite polynomials and computation of their zeros and reproducing kernel method for differential equations. Applications include local discontinuous Galerkin method for nonlinear Ginzburg-Landau equation, general function method in transport boundary value problems of theory of elasticity and solution of nonlinear partial differential equations by new Laplace variational iteration method. Existence/uniqueness theory of differential equations is presented in this book with applications that will be of benefit to mathematicians, applied mathematicians and researchers in the field. The book is written primarily for those who have some knowledge of differential equations and mathematical analysis. The authors of each section bring a strong emphasis on theoretical foundations to the book.

The Craft of Fractional Modelling in Science and Engineering

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ISBN: 9783038429838 9783038429845 Year: Pages: X, 128 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics --- Physics (General)
Added to DOAB on : 2018-06-22 14:41:30
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This book is a result of the contributions of scientists involved in a Special Issue entitled “The Craft of Fractional Modelling in Science and Engineering” published by the journal Fractal and Fractional (MDPI). Most of the articles were published at the end of 2017 and the beginning 2018. In accordance with the initial aim of the Special Issue, the best published have now been consolidated into this book. The articles included span a broad area of applications of fractional calculus and demonstrate the feasibility of the non-integer differentiation and integration approach in modeling, directly related to pertinent problems in science and engineering.This a good beginning and it would be beneficial to continue with this collection under the same title and potentially provide a second volume of this book in the future.

Advanced Problems in Mathematics

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Book Series: OBP Series in Mathematics ISBN: 9781783741441 Year: Pages: 186 DOI: 10.11647/OBP.0075 Language: English
Publisher: Open Book Publishers
Subject: Mathematics
Added to DOAB on : 2017-08-22 11:01:03
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" This book is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge colleges as the basis for conditional offers. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.&#xD;This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.&#xD;"

Special Functions: Fractional Calculus and the Pathway for Entropy

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ISBN: 9783038426653 9783038426646 Year: Pages: 304 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General)
Added to DOAB on : 2018-01-24 13:53:41
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Historically, the notion of entropy emerged in conceptually very distinct contexts. This book deals with the connection between entropy, probability, and fractional dynamics as they appeared, for example, in solar neutrino astrophysics since the 1970's (Mathai and Rathie 1975, Mathai and Pederzoli 1977, Mathai and Saxena 1978, Mathai, Saxena, and Haubold 2010).The original solar neutrino problem, experimentally and theoretically, was resolved through the discovery of neutrino oscillations and was recently enriched by neutrino entanglement entropy. To reconsider possible new physics of solar neutrinos, diffusion entropy analysis, utilizing Boltzmann entropy, and standard deviation analysis was undertaken with Super-Kamiokande solar neutrino data. This analysis revealed a non-Gaussian signal with harmonic content. The Hurst exponent is different from the scaling exponent of the probability density function and both Hurst exponent and scaling exponent of the Super-Kamiokande data deviate considerably from the value of ½, which indicates that the statistics of the underlying phenomenon is anomalous. Here experiment may provide guidance about the generalization of theory of Boltzmann statistical mechanics. Arguments in the so-called Boltzmann-Planck-Einstein discussion related to Planck's discovery of the black-body radiation law are recapitulated mathematically and statistically and emphasize from this discussion is pursued that a meaningful implementation of the complex ‘entropy-probability-dynamics’ may offer two ways for explaining the results of diffusion entropy analysis and standard deviation analysis. One way is to consider an anomalous diffusion process that needs to use the fractional space-time diffusion equation (Gorenflo and Mainardi) and the other way is to consider a generalized Boltzmann entropy by assuming a power law probability density function. Here new mathematical framework, invented by sheer thought, may provide guidance for the generalization of Boltzmann statistical mechanics. In this book Boltzmann entropy, generalized by Tsallis and Mathai, is considered. The second one contains a varying parameter that is used to construct an entropic pathway covering generalized type-1 beta, type-2 beta, and gamma families of densities. Similarly, pathways for respective distributions and differential equations can be developed. Mathai's entropy is optimized under various conditions reproducing the well-known Boltzmann distribution, Raleigh distribution, and other distributions used in physics. Properties of the entropy measure for the generalized entropy are examined. In this process the role of special functions of mathematical physics, particularly the H-function, is highlighted.

Fractional Calculus: Theory and Applications

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ISBN: 9783038972068 9783038972075 Year: Pages: 208 DOI: 10.3390/books978-3-03897-207-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Mathematics
Added to DOAB on : 2018-09-20 11:39:19
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Fractional calculus is allowing integrals and derivatives of any positive order (the term fractional is kept only for historical reasons). It can be considered a branch of mathematical physics that deals with integro-differential equations, where integrals are of convolution type and exhibit mainly singular kernels of power law or logarithm type.It is a subject that has gained considerably popularity and importance in the past few decades in diverse fields of science and engineering. Efficient analytical and numerical methods have been developed but still need particular attention.The purpose of this Special Issue is to establish a collection of articles that reflect the latest mathematical and conceptual developments in the field of fractional calculus and explore the scope for applications in applied sciences.

Dynamical Systems

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ISBN: 9783906980478 9783906980522 Year: Pages: 551 DOI: 10.3390/books978-3-906980-52-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Added to DOAB on : 2015-01-12 10:53:34
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Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...]

Advanced Problems in Mathematics: Preparing for University

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Book Series: OBP Series in Mathematics ISSN: 2397-1126 / 2397-1134 ISBN: 9781783747764 / 9781783747771 Pages: 186 DOI: 10.11647/OBP.0181 Language: English
Publisher: Open Book Publishers
Added to DOAB on : 2019-10-29 12:26:38
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This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Fractional Order Systems

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ISBN: 9783039216086 / 9783039216093 Year: Pages: 114 DOI: 10.3390/books978-3-03921-609-3 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:16
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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.

Sémantique formelle: Volume 1

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Book Series: Textbooks in Language Sciences ISBN: 9783961100170 9781977891549 Year: Pages: 498 DOI: 10.5281/zenodo.1000504 Language: French
Publisher: Language Science Press
Subject: Linguistics
Added to DOAB on : 2018-01-13 11:02:32
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"For nearly half a century formal semantics has been a prominent area in linguistic theory, developed in a fruitful collaboration among linguists, logicians and philosophers. Formal semantics is sometimes regarded with reluctance (even dreaded) due to its mathematical precision and the apparent complexity of its symbolism. This textbook —the first one of this scope in French— provides a relaxed self-contained introduction to the domain, allowing the reader autonomous progressive study from the basic central concepts to significant innovations that have shaped the domain since Montague’s seminal work. Through its chapters, the book provides acquaintance with elements of scientific methodology generally used in formal semantics. The six chapters, completed with solved exercises, gradually move from basic notions in logic and model-theoretic semantics, to quantification, temporal and modal logic, intensionality, and typed λ-calculus, culminating in compositional semantic analysis at the syntax-semantics interface. This introduction will be supplemented with a second volume that would focus on applications and advances in the field which extend the scope of the formalism.&#xD;The book is intended for linguistics undergraduate and postgraduate students and researchers wishing to improve their skills in formal semantics, as well as for students and researchers of other domains, such as philosophy, logic, or computational science."

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