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Dynamic Geometry On Time Scales
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Book Synopsis Dynamic Geometry on Time Scales by : Svetlin G. Georgiev
Download or read book Dynamic Geometry on Time Scales written by Svetlin G. Georgiev and published by CRC Press. This book was released on 2021-12-22 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Difference Equations, Discrete Dynamical Systems and Applications by : Sorin Olaru
Download or read book Difference Equations, Discrete Dynamical Systems and Applications written by Sorin Olaru and published by Springer Nature. This book was released on with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiplicative Differential Geometry by : Svetlin G. Georgiev
Download or read book Multiplicative Differential Geometry written by Svetlin G. Georgiev and published by CRC Press. This book was released on 2022-07-20 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Multiple Scales of Suspended Sediment Dynamics in a Complex Geometry Estuary by : Fernanda Achete
Download or read book Multiple Scales of Suspended Sediment Dynamics in a Complex Geometry Estuary written by Fernanda Achete and published by CRC Press. This book was released on 2020-04-22 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many estuaries are located in urbanized, highly engineered environments. Cohesive sediment plays an important role due to its link with estuarine health and ecology. An important ecological parameter is the suspended sediment concentration (SSC) translated into turbidity levels and sediment budget. This study contributes to investigate and forecast turbidity levels and sediment budget variability at San Francisco Bay-Delta system at a variety of spatial and temporal scales applying a flexible mesh process-based model (Delft3D FM). It is possible to have a robust sediment model, which reproduces 90% of the yearly data derived sediment budget, with simple model settings, like applying one mud fraction and a simple bottom sediment distribution. This finding opens the horizon for modeling less monitored estuaries. Comparing two case studies, i.e. the Sacramento-San Joaquin Delta and Alviso Slough, a classification for estuaries regarding the main sediment dynamic forcing is proposed: event-driven estuary (Delta) and tide-driven estuary (Alviso Slough). In the event-driven estuaries, the rivers are the main sediment source and the tides have minor impact in the net sediment transport. In the tide-driven estuaries, the main sediment source is the bottom sediment and the tide asymmetry defines the net sediment transport. This research also makes advances in connecting different scientific fields and developing a managerial tool to support decision making. It provides the basis to a chain of models, which goes from the hydrodynamics, to suspended sediment, to phytoplankton, to fish, clams and marshes.
Book Synopsis Multiplicative Differential Calculus by : Svetlin G. Georgiev
Download or read book Multiplicative Differential Calculus written by Svetlin G. Georgiev and published by CRC Press. This book was released on 2022-07-04 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamic Equations on Time Scales by : Martin Bohner
Download or read book Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.
Book Synopsis A Holistic Story of Space and Time by : David Pearcey
Download or read book A Holistic Story of Space and Time written by David Pearcey and published by Troubador Publishing Ltd. This book was released on 2023-06-28 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Have you ever wondered how the space and time of our everyday lives works - and why? David Pearcey is here to help, with A Holistic Story of Space and Time, a thorough exploration through our world of space and time. Explaining how space and time works as a complete system, the book is helped by brief accounts of the contributions of some of the great scientists and philosophers who helped us understand its components. Intended for the general reader who has no previous technical understanding, A Holistic Story of Space and Time delves into several areas - the types of geometries of space, the motion of matter in space, and how the force fields of matter pervade space, as well as how we perceive space and time by treating the brain as an information management system. It shows how the process of perception allows us to determine the true nature of the geometry of the space and time of the real world. Much more is also looked into in detail such as Einstein's special and general theories of relativity including his unified field theory, electromagnetism, and quantum physics, including charts and diagrams to explain some of the concepts involved. The final part of the book investigates the relationship between us who perceive the real world and the space and time of the real world, using the ideas developed by the philosophers Kant and Schopenhauer. This all combines to give the reader a uniquely broad look into our world and explains how it works as a total entity, from the cosmic world of the curved geometry of general relativity to the mysterious quantum world and then the philosophical aspects of how we are part of it. Anyone with an interest in the way things work will be well-suited to this extraordinary book that answers the why as well as the what and how.
Author :Christopher K.R.T. Jones Publisher :Springer Science & Business Media ISBN 13 :1461301173 Total Pages :278 pages Book Rating :4.4/5 (613 download)
Book Synopsis Multiple-Time-Scale Dynamical Systems by : Christopher K.R.T. Jones
Download or read book Multiple-Time-Scale Dynamical Systems written by Christopher K.R.T. Jones and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.
Book Synopsis Dynamic Equations on Time Scales and Applications by : Ravi P Agarwal
Download or read book Dynamic Equations on Time Scales and Applications written by Ravi P Agarwal and published by CRC Press. This book was released on 2024-10-18 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. Presents cutting-edge research trends of dynamic equations and recent advances in contemporary research on the topic of time scales Connects several new areas of dynamic equations on time scales with applications in different fields Includes mathematical explanation from the perspective of existing knowledge of dynamic equations on time scales Offers several new recently developed results, which are useful for the mathematical modeling of various phenomena Useful for several interdisciplinary fields like economics, biology, and population dynamics from the perspective of new trends The text is for postgraduate students, professionals, and academic researchers working in the fields of Applied Mathematics
Book Synopsis The Fractal Geometry of the Brain by : Antonio Di Ieva
Download or read book The Fractal Geometry of the Brain written by Antonio Di Ieva and published by Springer Nature. This book was released on with total page 999 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics by : Panos Macheras
Download or read book Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics written by Panos Macheras and published by Springer. This book was released on 2016-03-30 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: The state of the art in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics Modeling is presented in this new second edition book. It shows how advanced physical and mathematical methods can expand classical models in order to cover heterogeneous drug-biological processes and therapeutic effects in the body. The book is divided into four parts; the first deals with the fundamental principles of fractals, diffusion and nonlinear dynamics; the second with drug dissolution, release, and absorption; the third with epirical, compartmental, and stochastic pharmacokinetic models, with two new chapters, one on fractional pharmacokinetics and one on bioequivalence; and the fourth mainly with classical and nonclassical aspects of pharmacodynamics. The classical models that have relevance and application to these sciences are also considered throughout. This second edition has new information on reaction limited models of dissolution, non binary biopharmaceutic classification system, time varying models, and interface models. Many examples are used to illustrate the intrinsic complexity of drug administration related phenomena in the human, justifying the use of advanced modeling methods. This book will appeal to graduate students and researchers in pharmacology, pharmaceutical sciences, bioengineering, and physiology. Reviews of the first edition: "This book presents a novel modelling approach to biopharmaceutics, pharmacokinetics and pharmacodynamic phenomena. This state-of-the-art volume will be helpful to students and researchers in pharmacology, bioengineering, and physiology. This book is a must for pharmaceutical researchers to keep up with recent developments in this field." (P. R. Parthasarathy, Zentralblatt MATH, Vol. 1103 (5), 2007) "These authors are the unique (or sole) contributors in this area that are working on these questions and bring a special expertise to the field that is now being recognized as essential to understanding biological system and kinetic/dynamic characteristics in drug development...This text is an essential primer for those who would envision the incorporation of heterogeneous approaches to systems where homogeneous approaches are not sufficient to describe the system." (Robert R. Bies, Journal of Clinical Pharmacology, Vol. 46, 2006)
Book Synopsis Combined Measure and Shift Invariance Theory of Time Scales and Applications by : Chao Wang
Download or read book Combined Measure and Shift Invariance Theory of Time Scales and Applications written by Chao Wang and published by Springer Nature. This book was released on 2022-09-22 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales. First proposed by S. Hilger, the time scale theory—a unified view of continuous and discrete analysis—has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains. As a new and exciting type of mathematics—and more comprehensive and versatile than the traditional theories of differential and difference equations—, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences. Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.
Book Synopsis Eddy Bar Responses to the Sediment Dynamics of Pool-riffle Environments by : Brian L. Cluer
Download or read book Eddy Bar Responses to the Sediment Dynamics of Pool-riffle Environments written by Brian L. Cluer and published by . This book was released on 1997 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Concise Encyclopedia of Magnetic and Superconducting Materials by : K.H.J. Buschow
Download or read book Concise Encyclopedia of Magnetic and Superconducting Materials written by K.H.J. Buschow and published by Elsevier. This book was released on 2005-12-28 with total page 1361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magnetic and superconducting materials pervade every avenue of the technological world – from microelectronics and mass-data storage to medicine and heavy engineering. Both areas have experienced a recent revitalisation of interest due to the discovery of new materials, and the re-evaluation of a wide range of basic mechanisms and phenomena.This Concise Encyclopedia draws its material from the award-winning Encyclopedia of Materials and Engineering, and includes updates and revisions not available in the original set -- making it the ideal reference companion for materials scientists and engineers with an interest in magnetic and superconducting materials. - Contains in excess of 130 articles, taken from the award-winning Encyclopedia of Materials: Science and Technology, including ScienceDirect updates not available in the original set - Each article discusses one aspect of magnetic and superconducting materials and includes photographs, line drawings and tables to aid the understanding of the topic at hand - Cross-referencing guides readers to articles covering subjects of related interest
Book Synopsis Solid State Physics by : S. L. Chaplot
Download or read book Solid State Physics written by S. L. Chaplot and published by Alpha Science Int'l Ltd.. This book was released on 2002 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the proceedings of the 44th Department of Atomic Engineering (DAE) Solid State Physics Symposium.With contributions of papers from institutions from around the world. Contains 316 research articles, including 28 invited papers, on a wide range of topics of current interest in solid state physics comprising the following categories: Phase Transitions Phonons Soft-condensed Matter Electronic Structure Novel Materials Superconductivity Experimental Techniques and Instrumentation Magnetism Liquids, Glasses and Amorphous Systems Transport Properties Relaxation Studies Semiconductor Physics Surface Science Key Features: Recent developments in Synchrotron Research Photo-electron Spectroscopy Newly emerging superconductors
Book Synopsis Frontiers of Computational Fluid Dynamics 2006 by : David A. Caughey
Download or read book Frontiers of Computational Fluid Dynamics 2006 written by David A. Caughey and published by World Scientific. This book was released on 2005 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series of volumes to which this book belongs honors contributors who have made a major impact in computational fluid dynamics. This fourth volume in the series is dedicated to David Caughey on the occasion of his 60th birthday. The first volume was published in 1994 and was dedicated to Prof Antony Jameson. The second, dedicated to Earl Murman, was published in 1998. The third volume was dedicated to Robert MacCormack in 2002. Written by leading researchers from academia, government laboratories, and industry, the contributions in this volume present descriptions of the latest developments in techniques for numerical analysis of fluid flow problems, as well as applications to important problems in industry.
Download or read book Abrupt Climate Change written by and published by . This book was released on 2008 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
