Fractal Geometry, Complex Dimensions and Zeta Functions

Fractal Geometry, Complex Dimensions and Zeta Functions

Author: Michel L. Lapidus

Publisher: Springer Science & Business Media

Published: 2007-08-08

Total Pages: 472

ISBN-13: 0387352082

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Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.


Fractal Geometry, Complex Dimensions and Zeta Functions

Fractal Geometry, Complex Dimensions and Zeta Functions

Author: Michel Lapidus

Publisher: Springer Science & Business Media

Published: 2012-09-20

Total Pages: 583

ISBN-13: 1461421756

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Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.


Higher-dimensional Geometry Over Finite Fields

Higher-dimensional Geometry Over Finite Fields

Author: Dmitri Kaledin

Publisher: IOS Press

Published: 2008

Total Pages: 356

ISBN-13: 1586038559

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"Proceedings of the NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields, Geottingen, Germany, 25 June-6 July 2007."--T.p. verso.


21st Century Challenges in Chemical Crystallography II

21st Century Challenges in Chemical Crystallography II

Author: D. Michael P. Mingos

Publisher: Springer Nature

Published: 2021-01-20

Total Pages: 240

ISBN-13: 3030647471

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This volume summarises recent developments and highlights new techniques which will define possible future directions for small molecule X-ray crystallography. It provides an insight into how specific aspects of crystallography are developing and shows how they may interact or integrate with other areas of science. The development of more sophisticated equipment and the massive rise in computing power has made it possible to solve the three-dimensional structure of an organic molecule within hours if not minutes. This successful trajectory has resulted in the ability to study ever more complex molecules and use smaller and smaller crystals. The structural parameters for over a million organic and organometallic compounds are now archived in the most commonly used database and this wealth of information creates a new set of problems for future generations of scientists. The volume provides some insight into how users of crystallographic structural data banks can navigate their way through a world where “big data” has become the norm. The coupling of crystallography to quantum chemical calculations provides detailed information about electron distributions in crystals affording a much more detailed analysis of bonding than has been possible previously. In quantum crystallography, quantum mechanical wavefunctions are used to extract information about bonding and properties from the measured X-ray structure factors. The advent of quantum crystallography has resulted in form and structure factors derived from quantum mechanics which have been used in advanced refinement and wavefunction fitting. This volume describes how quantum mechanically derived atomic form factors and structure factors are constructed to allow the improved description of the diffraction experiment. It further discusses recent developments in this field and illustrates their applications with a wide range of examples. This volume will be of interest to chemists and crystallographers with an interest in the synthesis, characterisation and physical and catalytic properties of solid-state materials. It will also be relevant for the community of computational chemists who study chemical systems. Postgraduate students entering the field will benefit from a historical introduction to the way in which scientists have used the data derived from crystallography to develop new structural and bonding models.


Experimental Aerodynamic Derivatives of a Sinusoidally Oscillating Airfoil in Two-dimensional Flow

Experimental Aerodynamic Derivatives of a Sinusoidally Oscillating Airfoil in Two-dimensional Flow

Author: Robert L. Halfman

Publisher:

Published: 1951

Total Pages: 752

ISBN-13:

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Experimental measurements of the aerodynamic reactions on a symmetrical airfoil oscillating harmonically in a two-dimensional flow are presented and analyzed in this paper. Harmonic motions include pure pitch and pure translation, for several amplitudes and superimposed on an initial angle of attack, as well as combined pitch and translation. Considerable consistent data for pure pitch were obtained from a search of available reference material, and several definite Reynolds number effects are evident.


Introduction to Complex Analysis

Introduction to Complex Analysis

Author: Boris Vladimirovich Shabat

Publisher: American Mathematical Soc.

Published: 1992-11-04

Total Pages: 384

ISBN-13: 0821819755

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Since the 1960s, there has been a flowering in higher-dimensional complex analysis. Both classical and new results in this area have found numerous applications in analysis, differential and algebraic geometry, and, in particular, contemporary mathematical physics. In many areas of modern mathematics, the mastery of the foundations of higher-dimensional complex analysis has become necessary for any specialist. Intended as a first study of higher-dimensional complex analysis, this book covers the theory of holomorphic functions of several complex variables, holomorphic mappings, and submanifolds of complex Euclidean space.


Zero-Dimensional Schemes

Zero-Dimensional Schemes

Author: Ferruccio Orecchia

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2016-11-21

Total Pages: 348

ISBN-13: 3110889269

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The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.


Holomorphic Functions in the Plane and n-dimensional Space

Holomorphic Functions in the Plane and n-dimensional Space

Author: Klaus Gürlebeck

Publisher: Springer Science & Business Media

Published: 2007-12-23

Total Pages: 407

ISBN-13: 3764382724

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Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.