Vladimir Rovenski's Books

Extrinsic Geometry of Foliations

By: Vladimir Rovenski,Paweł Walczak

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Extrinsic Geometry of Foliations

By: Vladimir Rovenski,Paweł Walczak

This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics. The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.

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319

Publisher

Springer Nature

Published Date

ISBN 10

3030700674

ISBN 13

9783030700676

Modeling of Curves and Surfaces with MATLAB®

By: Vladimir Rovenski

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Modeling of Curves and Surfaces with MATLAB®

By: Vladimir Rovenski

This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors and transformations using matrices. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines.

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463

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Springer Science & Business Media

Published Date

ISBN 10

0387712771

ISBN 13

9780387712772

Foliations on Riemannian Manifolds and Submanifolds

By: Vladimir Rovenski

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Foliations on Riemannian Manifolds and Submanifolds

By: Vladimir Rovenski

This monograph is based on the author's results on the Riemannian ge ometry of foliations with nonnegative mixed curvature and on the geometry of sub manifolds with generators (rulings) in a Riemannian space of nonnegative curvature. The main idea is that such foliated (sub) manifolds can be decom posed when the dimension of the leaves (generators) is large. The methods of investigation are mostly synthetic. The work is divided into two parts, consisting of seven chapters and three appendices. Appendix A was written jointly with V. Toponogov. Part 1 is devoted to the Riemannian geometry of foliations. In the first few sections of Chapter I we give a survey of the basic results on foliated smooth manifolds (Sections 1.1-1.3), and finish in Section 1.4 with a discussion of the key problem of this work: the role of Riemannian curvature in the study of foliations on manifolds and submanifolds.

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296

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Springer Science & Business Media

Published Date

ISBN 10

1461242703

ISBN 13

9781461242703

Analytical Methods in Anisotropic Elasticity

with Symbolic Computational Tools

By: Omri Rand,Vladimir Rovenski

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Analytical Methods in Anisotropic Elasticity

with Symbolic Computational Tools

By: Omri Rand,Vladimir Rovenski

* Comprehensive textbook/reference applies mathematical methods and modern symbolic computational tools to anisotropic elasticity * Presents unified approach to a vast diversity of structural models * State-of-the-art solutions are provided for a wide range of composite material configurations, including: 3-D anisotropic bodies, 2-D anisotropic plates, laminated and thin-walled structures

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Page Count

466

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Springer Science & Business Media

Published Date

ISBN 10

0817644202

ISBN 13

9780817644208

Geometry of Curves and Surfaces with MAPLE

By: Vladimir Y. Rovenskii

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Geometry of Curves and Surfaces with MAPLE

By: Vladimir Y. Rovenskii

This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, {\it Geometry of Curves and Surfaces with Maple} will integrate traditional differential and non- Euclidean geometries with more current computer algebra systems in a practical and user-friendly format.

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396

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Springer Science & Business Media

Published Date

ISBN 10

0817640746

ISBN 13

9780817640743

Information Technologies for Remote Monitoring of the Environment

By: Vladimir Krapivin,Anatolij M. Shutko

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Information Technologies for Remote Monitoring of the Environment

By: Vladimir Krapivin,Anatolij M. Shutko

The key novelty of this book is first of all in the successful attempt to conduct jointly modeling of environment in terms of physical environment related parameters and measuring similar parameters by means of multispectral remote sensing, primarily by means of passive microwave remote sensing technology. Another new step is in the development and utilization of a multilevel approach which includes remote sensing of the land and water parameters like soil moisture, depth to water table, biomass of vegetation, temperature and salinity of water, in situ measurements of similar parameters and incorporation of GIS and data sets into the models of typical environments. The part of book, which contains remote sensing is focused on multipurpose observations from aircraft obtained in many soil-climatic zones in different countries and is reach of the examples of practical application. Applied mathematicians, geophysics, hydrologists, socio-economists, statesmans and other researchers of environmental changes will find a wealth of information and ideas in this book.

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528

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Springer Science & Business Media

Published Date

ISBN 10

3642205674

ISBN 13

9783642205675

Constructive Processing of Microwave and Optical Data for Hydrogeochemical Applications

By: Costas A. Varotsos,Vladimir F. Krapivin,Ferdenant A. Mkrtchyan,Yong Xue

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Constructive Processing of Microwave and Optical Data for Hydrogeochemical Applications

By: Costas A. Varotsos,Vladimir F. Krapivin,Ferdenant A. Mkrtchyan,Yong Xue

This book presents results of the combined use of microwave remote sensing, optical tools, and ecoinformatics methods under solution-applied tasks at both regional and global scales. Ecoinformatics methods are used to assess links between global climate change and the level of ocean pollution, with specific focus on the Arctic Ocean, the Sea of Okhotsk, and the South-China Sea. The theoretical and applied aspects of instrumental tools are considered in this book as a basis for the monitoring of water quality in various watersheds, with particular attention to microwave remote sensing monitoring data to determine the ecotoxicological status of hydro-ecosystems affected by climate change. The book develops new information technologies that provide solutions for hydrochemical tasks using algorithms and models based on computer technologies for big data processing. This will help to synthesize effective computer-based systems for the solution of problems arising due to anthropogenic impacts on hydrological processes and objects at various spatial scales. This book is intended for specialists in the fields of environmental monitoring, climate change, human-nature interactions, and geopolitics. The book will be useful for undergraduate and postgraduate students studying these fields of science as well.

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531

Publisher

Springer Nature

Published Date

ISBN 10

3031288777

ISBN 13

9783031288777

Microwave Remote Sensing Tools in Environmental Science

By: Costas A. Varotsos,Vladimir F. Krapivin

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Microwave Remote Sensing Tools in Environmental Science

By: Costas A. Varotsos,Vladimir F. Krapivin

This book gives new insight to the study of the global environmental changes using the ecoinformatics and microwave remote sensing tools together with the adaptive-evolutionary technology of geoinformation monitoring. The main advantage of this book consists in the accumulation of the interdisciplinary scientific knowledge for the parameterization of the global biogeochemical cycles and other environmental processes in the context of globalization and sustainable development. In this regard, the crucial global problems of the dynamics of the climate-nature-society system have been considered and the key problems of ensuring its sustainable development have been addressed. An analysis of the present trend in changing ecological systems has been discussed, including different types of forest ecosystems and ocean aquatories. The emphasis has been given to the accomplishment of the global geoinformation monitoring, which could provide a reliable control of the environmental processes development with reliable prognostic estimates of the consequences of human activities. A new approach to the numerical modelling of the climate-nature-society system has been presented and demonstrative results have been given about the modelling of the dynamics of this system‟s characteristics, in cases of realization of some scenarios of the anthropogenic impacts to the biogeochemical cycles, the land ecosystems and oceans. Methods and algorithms for the big data manipulation and processing in the remote sensing environmental monitoring systems have been described.

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484

Publisher

Springer Nature

Published Date

ISBN 10

3030457672

ISBN 13

9783030457679

Analytical Methods in Anisotropic Elasticity

with Symbolic Computational Tools

By: Omri Rand,Vladimir Rovenski

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Analytical Methods in Anisotropic Elasticity

with Symbolic Computational Tools

By: Omri Rand,Vladimir Rovenski

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466

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Springer Science & Business Media

Published Date

ISBN 10

0817644202

ISBN 13

9780817644208

Extrinsic Geometry of Foliations

By: Vladimir Rovenski,Paweł Walczak

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Extrinsic Geometry of Foliations

By: Vladimir Rovenski,Paweł Walczak

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319

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Springer Nature

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ISBN 10

3030700674

ISBN 13

9783030700676

Foliations on Riemannian Manifolds and Submanifolds

By: Vladimir Rovenski

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Foliations on Riemannian Manifolds and Submanifolds

By: Vladimir Rovenski

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296

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Springer Science & Business Media

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ISBN 10

1461242703

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9781461242703

Topics in Extrinsic Geometry of Codimension-One Foliations

By: Vladimir Rovenski,Paweł Walczak

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Topics in Extrinsic Geometry of Codimension-One Foliations

By: Vladimir Rovenski,Paweł Walczak

Extrinsic geometry describes properties of foliations on Riemannian manifolds which can be expressed in terms of the second fundamental form of the leaves. The authors of Topics in Extrinsic Geometry of Codimension-One Foliations achieve a technical tour de force, which will lead to important geometric results. The Integral Formulae, introduced in chapter 1, is a useful for problems such as: prescribing higher mean curvatures of foliations, minimizing volume and energy defined for vector or plane fields on manifolds, and existence of foliations whose leaves enjoy given geometric properties. The Integral Formulae steams from a Reeb formula, for foliations on space forms which generalize the classical ones. For a special auxiliary functions the formulae involve the Newton transformations of the Weingarten operator. The central topic of this book is Extrinsic Geometric Flow (EGF) on foliated manifolds, which may be a tool for prescribing extrinsic geometric properties of foliations. To develop EGF, one needs Variational Formulae, revealed in chapter 2, which expresses a change in different extrinsic geometric quantities of a fixed foliation under leaf-wise variation of the Riemannian Structure of the ambient manifold. Chapter 3 defines a general notion of EGF and studies the evolution of Riemannian metrics along the trajectories of this flow(e.g., describes the short-time existence and uniqueness theory and estimate the maximal existence time).Some special solutions (called Extrinsic Geometric Solutions) of EGF are presented and are of great interest, since they provide Riemannian Structures with very particular geometry of the leaves. This work is aimed at those who have an interest in the differential geometry of submanifolds and foliations of Riemannian manifolds.

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129

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441999086

ISBN 13

9781441999085

Geometry of Curves and Surfaces with MAPLE

By: Vladimir Rovenski

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Geometry of Curves and Surfaces with MAPLE

By: Vladimir Rovenski

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310

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Springer Science & Business Media

Published Date

ISBN 10

1461221285

ISBN 13

9781461221289

Modeling of Curves and Surfaces with MATLAB®

By: Vladimir Rovenski

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Modeling of Curves and Surfaces with MATLAB®

By: Vladimir Rovenski

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463

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Springer Science & Business Media

Published Date

ISBN 10

038771278X

ISBN 13

9780387712789

Modeling in Fluid Mechanics

Instabilities and Turbulence

By: Igor Gaissinski,Vladimir Rovenski

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Modeling in Fluid Mechanics

Instabilities and Turbulence

By: Igor Gaissinski,Vladimir Rovenski

This volume is dedicated to modeling in fluid mechanics and is divided into four chapters, which contain a significant number of useful exercises with solutions. The authors provide relatively complete references on relevant topics in the bibliography at the end of each chapter.

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Page Count

658

Publisher

CRC Press

Published Date

ISBN 10

1351029045

ISBN 13

9781351029049

Book's by Vladimir Rovenski

Extrinsic Geometry of Foliations

Extrinsic Geometry of Foliations

Modeling of Curves and Surfaces with MATLAB®

Modeling of Curves and Surfaces with MATLAB®

Foliations on Riemannian Manifolds and Submanifolds

Foliations on Riemannian Manifolds and Submanifolds

Analytical Methods in Anisotropic Elasticity

Analytical Methods in Anisotropic Elasticity

Geometry of Curves and Surfaces with MAPLE

Geometry of Curves and Surfaces with MAPLE

Information Technologies for Remote Monitoring of the Environment

Information Technologies for Remote Monitoring of the Environment

Constructive Processing of Microwave and Optical Data for Hydrogeochemical Applications

Constructive Processing of Microwave and Optical Data for Hydrogeochemical Applications

Microwave Remote Sensing Tools in Environmental Science

Microwave Remote Sensing Tools in Environmental Science

Analytical Methods in Anisotropic Elasticity

Analytical Methods in Anisotropic Elasticity

Extrinsic Geometry of Foliations

Extrinsic Geometry of Foliations

Foliations on Riemannian Manifolds and Submanifolds

Foliations on Riemannian Manifolds and Submanifolds

Topics in Extrinsic Geometry of Codimension-One Foliations

Topics in Extrinsic Geometry of Codimension-One Foliations

Geometry of Curves and Surfaces with MAPLE

Geometry of Curves and Surfaces with MAPLE

Modeling of Curves and Surfaces with MATLAB®

Modeling of Curves and Surfaces with MATLAB®

Modeling in Fluid Mechanics

Modeling in Fluid Mechanics

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