Alexey Postnikov's Books

Exploring and Mapping Alaska

The Russian America Era, 1741-1867

By: Alexey Postnikov,Marvin Falk

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Exploring and Mapping Alaska

The Russian America Era, 1741-1867

By: Alexey Postnikov,Marvin Falk

Russia first encountered Alaska in 1741 as part of the most ambitious and expensive expedition of the entire eighteenth century. For centuries since, cartographers have struggled to define and develop the enormous region comprising northeastern Asia, the North Pacific, and Alaska. The forces of nature and the follies of human error conspired to make the area incredibly difficult to map. Exploring and Mapping Alaska focuses on this foundational period in Arctic cartography. Russia spurred a golden era of cartographic exploration, while shrouding their efforts in a veil of secrecy. They drew both on old systems developed by early fur traders and new methodologies created in Europe. With Great Britain, France, and Spain following close behind, their expeditions led to an astounding increase in the world’s knowledge of North America. Through engrossing descriptions of the explorations and expert navigators, aided by informative illustrations, readers can clearly trace the evolution of the maps of the era, watching as a once-mysterious region came into sharper focus. The result of years of cross-continental research, Exploring and Mapping Alaska is a fascinating study of the trials and triumphs of one of the last great eras of historic mapmaking.

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545

Publisher

University of Alaska Press

Published Date

ISBN 10

1602232520

ISBN 13

9781602232525

Wavelets in Neuroscience

By: Alexander E. Hramov,Alexey A. Koronovskii,Valeri A. Makarov,Vladimir A. Maksimenko,Alexey N. Pavlov,Evgenia Sitnikova

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Wavelets in Neuroscience

By: Alexander E. Hramov,Alexey A. Koronovskii,Valeri A. Makarov,Vladimir A. Maksimenko,Alexey N. Pavlov,Evgenia Sitnikova

This book illustrates how modern mathematical wavelet transform techniques offer fresh insights into the complex behavior of neural systems at different levels: from the microscopic dynamics of individual cells to the macroscopic behavior of large neural networks. It also demonstrates how and where wavelet-based mathematical tools can provide an advantage over classical approaches used in neuroscience. The authors well describe single neuron and populational neural recordings. This 2nd edition discusses novel areas and significant advances resulting from experimental techniques and computational approaches developed since 2015, and includes three new topics: • Detection of fEPSPs in multielectrode LFPs recordings. • Analysis of Visual Sensory Processing in the Brain and BCI for Human Attention Control; • Analysis and Real-time Classification of Motor-related EEG Patterns; The book is a valuable resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in these and related areas.

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Page Count

384

Publisher

Springer Nature

Published Date

ISBN 10

303075992X

ISBN 13

9783030759926

Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

By: Alexey V. Shchepetilov

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Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

By: Alexey V. Shchepetilov

This is an introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, empahsizing spaces with constant curvature. Chapters 1-4 provide basic notations for studying two-body dynamics. Chapter 5 deals with the problem of finding explicitly invariant expressions for the two-body quantum Hamiltonian. Chapter 6 addresses one-body problems in a central potential. Chapter 7 investigates the classical counterpart of the quantum system introduced in Chapter 5. Chapter 8 discusses applications in the quantum realm.

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Page Count

267

Publisher

Springer

Published Date

ISBN 10

3540353860

ISBN 13

9783540353867

Connectedness and Necessary Conditions for an Extremum

By: Alexey Abramov

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Connectedness and Necessary Conditions for an Extremum

By: Alexey Abramov

The present book is the outcome of efforts to introduce topological connectedness as one of the basic tools for the study of necessary conditions for an extremum. Apparently this monograph is the first book in the theory of maxima and minima where topological connectedness is used so widely for this purpose. Its application permits us to obtain new results in this sphere and to consider the classical results from a nonstandard point of view. Regarding the style of the present book it should be remarked that it is comparatively elementary. The author has made constant efforts to make the book as self-contained as possible. Certainly, familiarity with the basic facts of topology, functional analysis, and the theory of optimization is assumed. The book is written for applied mathematicians and graduate students interested in the theory of optimization and its applications. We present the synthesis of the well known Dybovitskii'-Milyutin ap proach for the study of necessary conditions for an extremum, based on functional analysis, and topological methods. This synthesis allows us to show that in some cases we have the following important result: if the Euler equation has no non trivial solution at a point of an extremum, then some inclusion is valid for the functionals belonging to the dual space. This general result is obtained for an optimization problem considered in a lin ear topological space. We also show an application of our result to some problems of nonlinear programming and optimal control.

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Page Count

213

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401591199

ISBN 13

9789401591195

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

By: Alexey P Isaev,Valery A Rubakov

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Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

By: Alexey P Isaev,Valery A Rubakov

The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence.The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles — the Standard Model — is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics.

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Page Count

475

Publisher

World Scientific

Published Date

ISBN 10

9813236876

ISBN 13

9789813236875

Linear Algebra and Geometry

By: Igor R. Shafarevich,Alexey O. Remizov

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Linear Algebra and Geometry

By: Igor R. Shafarevich,Alexey O. Remizov

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.

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Page Count

536

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642309941

ISBN 13

9783642309946

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

By: Alexey P Isaev,Valery A Rubakov

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Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

By: Alexey P Isaev,Valery A Rubakov

This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.

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Page Count

615

Publisher

World Scientific

Published Date

ISBN 10

9811217424

ISBN 13

9789811217425

Blow-up in Nonlinear Sobolev Type Equations

By: Alexander B. Al'shin,Maxim O. Korpusov,Alexey G. Sveshnikov

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Blow-up in Nonlinear Sobolev Type Equations

By: Alexander B. Al'shin,Maxim O. Korpusov,Alexey G. Sveshnikov

The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) differential equations with nonlinear operator coefficients with respect to spatial variables. The main aim of the monograph is to obtain sufficient conditions for global (in time) solvability, to obtain sufficient conditions for blow-up of solutions at finite time, and to derive upper and lower estimates for the blow-up time. The abstract results apply to a large variety of problems. Thus, the well-known Benjamin-Bona-Mahony-Burgers equation and Rosenau-Burgers equations with sources and many other physical problems are considered as examples. Moreover, the method proposed for studying blow-up phenomena for nonlinear Sobolev-type equations is applied to equations which play an important role in physics. For instance, several examples describe different electrical breakdown mechanisms in crystal semiconductors, as well as the breakdown in the presence of sources of free charges in a self-consistent electric field. The monograph contains a vast list of references (440 items) and gives an overall view of the contemporary state-of-the-art of the mathematical modeling of various important problems arising in physics. Since the list of references contains many papers which have been published previously only in Russian research journals, it may also serve as a guide to the Russian literature.

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Page Count

661

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110255294

ISBN 13

9783110255294

Exploring and Mapping Alaska

The Russian America Era, 1741-1867

By: Alexey Postnikov,Marvin Falk

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Exploring and Mapping Alaska

The Russian America Era, 1741-1867

By: Alexey Postnikov,Marvin Falk

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

545

Publisher

University of Alaska Press

Published Date

ISBN 10

1602232520

ISBN 13

9781602232525

Book's by Alexey Postnikov

Exploring and Mapping Alaska

Exploring and Mapping Alaska

Wavelets in Neuroscience

Wavelets in Neuroscience

Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

Connectedness and Necessary Conditions for an Extremum

Connectedness and Necessary Conditions for an Extremum

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

Linear Algebra and Geometry

Linear Algebra and Geometry

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

Blow-up in Nonlinear Sobolev Type Equations

Blow-up in Nonlinear Sobolev Type Equations

Exploring and Mapping Alaska

Exploring and Mapping Alaska

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