Dynamic Geometry on Time Scales

T , = T2 = N. = = - 6.4 Minimal Surfaces Suppose that T , T1 , T2 , T3 , T ( 1 ) , T ( 2 ) , T3 ) are time scales with forward jump operators and ... 01 CA1 T1 , ft f 1 be 01f4201 320 Dynamic Geometry on Time Scales 6.4 Minimal Surfaces.

Author: Svetlin G. Georgiev

Publisher: CRC Press

ISBN: 9781000471144

Category: Mathematics

Page: 396

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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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Multiple Scales of Suspended Sediment Dynamics in a Complex Geometry Estuary

The models were calibrated for intertidal dynamics, and the two applications give the confidence to reproduce spatial maps of fine sediment dynamics ranging from hourly time scale to yearly budgets. Sediment budgets are often derived ...

Author: Fernanda Minikowski Achete

Publisher: CRC Press

ISBN: 9780429611506

Category: Science

Page: 138

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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.
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Multiplicative Differential Calculus

He is also the author of Dynamic Geometry of Time Scales, CRC Press/Taylor & Francis Group. He is a coauthor of Conformable Dynamic Equations on Time Scales, with Douglas R. Anderson, CRC Press/Taylor & Francis Group.

Author: Svetlin G. Georgiev

Publisher: CRC Press

ISBN: 9781000605501

Category: Mathematics

Page: 216

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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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Multiplicative Differential Geometry

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 ...

Author: Svetlin G. Georgiev

Publisher: CRC Press

ISBN: 1032290609

Category:

Page: 176

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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. Many examples and problems are included.
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Modeling in Biopharmaceutics Pharmacokinetics and Pharmacodynamics

The concept of fractals may be used for modeling certain aspects of dynamics, i.e., temporal evolution of spatially extended dynamic systems in nature. Such systems exhibit fractal geometry and may ...

Author: Panos Macheras

Publisher: Springer

ISBN: 9783319275987

Category: Mathematics

Page: 483

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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)
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Concise Encyclopedia of Magnetic and Superconducting Materials

Moreover, the mutual orientation of molecular moieties before and after the move can be read from the off-diagonal exchange patterns (geometry of dynamics). This experiment provides information on slow dynamic processes on time scales ...

Author: K.H.J. Buschow

Publisher: Elsevier

ISBN: 0080457657

Category: Technology & Engineering

Page: 1360

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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.
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Eddy Bar Responses to the Sediment Dynamics of Pool riffle Environments

The sand grains that constitute sand bars have time scales of residence , transport or deposition depending not only on the time scale of changes in channel geometry but on the time scale of individual changes in discharge and sand ...

Author: Brian L. Cluer

Publisher:

ISBN: UCR:31210024756395

Category: Colorado River (Colo.-Mexico)

Page: 128

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Abrupt Climate Change

The present state of the art in these simulations is termed as static-geometry simulations, as the actual shape of the ... The dynamic response has two different time scales: an instantaneous mechanical response through longitudinal ...

Author: Peter U. Clark

Publisher: DIANE Publishing

ISBN: 9781437915693

Category:

Page: 459

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This report is part of a series of 21 Synthesis and Assessments (SAP) aimed at providing current assessments of climate change science to inform public debate, policy, and operational decisions. These reports are also intended to help develop future program research priorities. The guiding vision is to provide the Nation and the global community with the science-based knowledge needed to manage the risks and capture the opportunities associated with climate and related environmental changes. This SAP assesses abrupt climate change events where key aspects of the climate system change faster than the responsible forces would suggest and/or faster than society can respond to those changes. Illustrations.
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Rheology of Complex Fluids

The other is a dynamic time scale associated with the motion of the fluid packets themselves. Examples are the time it takes for a fluid packet to transverse a geometry or a section, pulsatile flow, etc. We denote this time scale by td.

Author: Abhijit P. Deshpande

Publisher: Springer Science & Business Media

ISBN: 9781441964946

Category: Technology & Engineering

Page: 258

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The aim of the School on Rheology of Complex fluids is to bring together young researchers and teachers from educational and R&D institutions, and expose them to the basic concepts and research techniques used in the study of rheological behavior of complex fluids. The lectures will be delivered by well-recognized experts. The book contents will be based on the lecture notes of the school.
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Dynamics of Biological Macromolecules by Neutron Scattering

Mark T.F. Telling* ISIS Facility, Rutherford Appleton Laboratory, OX11 OQX, UK Abstract: The spatial and temporal ranges ... allowing access to length and time scales inaccessible using, for example, light scattering techniques alone.

Author: Salvatore Magazù

Publisher: Bentham Science Publishers

ISBN: 9781608052196

Category: Science

Page: 111

View: 991

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Dynamics of Biological Macromolecules by Neutron Scattering provides insight into the study of the dynamics of biological macromolecules by neutron scattering techniques. The applicability of neutron scattering to expanding fields of biological studies is
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