Kooperativer Bibliotheksverbund

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Format: 1 Online-Ressource (XLIII, 689 p. 429 illus).

ISBN: 978-981-10-3908-9

Series Statement: Springer Proceedings in Physics volume 194

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-981-10-3907-2

Language: English

Subjects: Physics

Keywords: Konferenzschrift ; Konferenzschrift

DOI: 10.1007/978-981-10-3908-9

URL: Volltext  (URL des Erstveröffentlichers)

URL: lizenzpflichtig

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URL: Cover

UID:

Format: 1 Online-Ressource (XVI, 118 S.) , Ill., graph. Darst.

ISBN: 9781461455615 , 9781461455622

Series Statement: Lecture notes in statistics 206

Language: English

Subjects: Mathematics

DOI: 10.1007/978-1-4614-5562-2

URL: Volltext

URL: Inhaltsverzeichnis

URL: Abstract

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Format: 1 Online-Ressource (X, 227 p)

ISBN: 9781461517115 , 9780792375821

Note: Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Many features oflight propagation can be analyzed in terms ofrays,ofcourse, subtle effects near foci, caustics or turning points would need an analysis based on the wave natureoflight. Allofgeometric optics can be derived from Fermat's principle which is an extremum principle. The counterpart in classical mechanics is of course Hamilton's principle. There is a very close analogy between mechanics ofparticles and optics oflight rays. Much insight (and useful results) can be obtained by analyzing these analogies. Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, 1956), classical mechanics is only a geometrical optics approximation to a wave theory! In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of ray propagation through various media. Given the current interest and activity in optical fibers and optical communication, analysis of light propagation in inhomogeneous media is dealt with in great detail. The past decade has witnessed great advances in adaptive optics and compensation for optical aberrations. The formalism described herein can be used to calculate aberrations ofoptical systems. Toward the end of the book, we present application of the formalism to current research problems. Of particular interest is the use of dynamic programming techniques which can be used to handle variational/extremum problems. This method has only recently been applied to opticalproblems

Language: English

Keywords: Geometrische Optik

DOI: 10.1007/978-1-4615-1711-5

URL: Volltext

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UID:

Format: 1 online resource (various pagings).

ISBN: 0-7503-1495-8 , 0-7503-1496-6

Series Statement: [IOP release 5]

Content: In 1813, Gauss first outlined his studies of the hypergeometric series which has been of great significance in the mathematical modelling of physical phenomena. This detailed monograph outlines the fundamental relationships between the hypergeometric function and special functions. In nine comprehensive chapters, Dr. Rao and Dr. Lakshminarayanan present a unified approach to the study of special functions of mathematics using Group theory. The book offers fresh insight into various aspects of special functions and their relationship, utilizing transformations and group theory and their applications. It will lay the foundation for deeper understanding by both experienced researchers and novice students.

Note: "Version: 20181001"--Title page verso. , 1. Hypergeometric series -- 1.1. Introduction -- 1.2. The Gauss differential equation -- 1.3. Special functions -- 1.4. Properties of the hypergeometric functions -- 1.5. A conjecture , 2. Group theory: basics -- 2.1. Introduction -- 2.2. Invariances, symmetries, and physics -- 2.3. Discrete groups -- 2.4. The symmetric group Sn -- 2.5. An interesting property of Sn -- 2.6. Representations of a group -- 2.7. Lie groups and Lie algebras -- 2.8. Angular momentum and the rotation group -- 2.9. Compact Lie groups -- 2.10. Subgroups, cosets, invariant subgroups -- 2.11. Simple and semi-simple groups -- 2.12. Compact groups , 3. Group theory of the Kummer solutions of the Gauss differential equation -- 3.1. Introduction -- 3.2. The 24 solutions of the Gauss ODE -- 3.3. The Riemann equation , 4. Group theory of terminating and non-terminating 3F2(a, b, c; d, e; 1) transformations -- 4.1. Introduction -- 4.2. The Whipple notation -- 4.3. Terminating 3F2(1) series -- 4.4. Structure of GT and its irreps -- 4.5. Scaling the WE transformation -- 4.6. Non-terminating 3F2(a, b, c; d, e; 1) series -- 4.7. Concluding remarks , 5. Angular momentum and the rotation group -- 5.1. Introduction: historical -- 5.2. Angular momentum algebra -- 5.3. Representations of angular momentum operators -- 5.4. The rotation group -- 5.5. The 3F2(1) sets -- 5.6. Symmetries of the 3-j coefficient -- 5.7. Inter-relationship between the sets of 3F2(1)s , 6. Angular momentum recoupling and sets of 4F3(1)s -- 6.1. Introduction: historical -- 6.2. Addition of three angular momenta -- 6.3. Symmetries of the Racah coefficient -- 6.4. Two sets of 4F3(1)s -- 6.5. Inter-relationship of the two sets of 4F3(1)s -- 6.6. Bargmann-Shelepin arrays -- 6.7. The set of Bailey transformations -- 6.8. Basis states and symmetries of the 6-j coefficient , 7. Double and triple hypergeometric series -- 7.1. Introduction: a history -- 7.2. Multiple hypergeometric series -- 7.3. Definitions of the 9-j coefficient -- 7.4. Symmetries of the 9-j coefficient -- 7.5. The Jucys-Bandzaitis triple sum series -- 7.6. Stretched 9-j coefficients -- 7.7. A general transformation formula -- 7.8. Transformation formulas for F⁰:3;4 ₁:1;2 -- 7.9. Transformation formulas for F¹:2;2 ₀:2;2 -- 7.10. Some summation formulas , 8. Beta integral method and hypergeometric transformations -- 8.1. Introduction -- 8.2. Extensions of Euler's integral for 2F1(a, b; c; z) -- 8.3. The beta integral method -- 8.4. The algorithm -- 8.5. New single sum hypergeometric identities from old ones , 9. Gauss, hypergeometric series, and Ramanujan -- 9.1. Introduction -- 9.2. On some entries of Ramanujan on hypergeomtric series in his notebooks -- 9.3. Entry 43, in chapter XII of Ramanujan's Notebook 1 -- 9.4. The theorem of Rao, Berghe, and Krattenthaler -- 9.5. Observations and concluding remarks -- 9.6. Epilogue. , Also available in print. , Mode of access: World Wide Web. , System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Additional Edition: ISBN 0-7503-1494-X

Language: English

DOI: 10.1088/978-0-7503-1496-1

URL: http://iopscience.iop.org/book/978-0-7503-1496-1

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Format: XIX, 609 S. , Ill., graph. Darst.

ISBN: 9781439869604

Language: English

Subjects: Physics

Keywords: Geometrische Optik ; Quantenoptik

URL: Inhaltsverzeichnis

URL: Klappentext

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Format: Abb.; Diagr.; Foto; Lit.

ISSN: 1079-5006

Note: Band: 54A; Heft: 8; Seiten: B336-351

In: The journals of gerontology / A, Cary, NC : Oxford University Press, 1995, 54(1999), 8, Seite 336-351, 1079-5006

In: volume:54

In: year:1999

In: number:8

In: pages:336-351

Language: English

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Format: xv, 192 Seiten : , Illustrationen, Diagramme (überwiegend farbig).

ISBN: 978-1-4665-8397-9 , 1-4665-8397-5

Series Statement: Multidisciplinary and applied optics

Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-0-42910239-4

Language: English

Subjects: Physics

UID:

Format: Online-Ressource (XXXIX, 644 p. 399 illus, online resource)

ISBN: 9788132223672

Series Statement: Springer Proceedings in Physics 166

Content: The Proceedings of First International Conference on Opto-Electronics and Applied Optics 2014, IEM OPTRONIX 2014 presents the research contributions presented in the conference by researchers from both India and abroad. Contributions from established scientists as well as students are included. The book is organized to enable easy access to various topics of interest. The first part includes the Keynote addresses by Phillip Russell, Max Planck Institute of the Light Sciences, Erlangen, Germany and Lorenzo Pavesi, University of Trento, Italy. The second part focuses on the Plenary Talks given by eminent scientists, namely, Azizur Rahman, City University London, London; Bishnu Pal, President, The Optical Society of India; Kamakhya Ghatak, National Institute of Technology, Agartala; Kehar Singh, Former Professor, India Institute of Technology Delhi; Mourad Zghal, SUPCOM, University of Carthage, Tunisia; Partha Roy Chaudhuri, IIT Kharagpur; S K. Bhadra, CSIR-Central Glass and Ceramic Research Institute, Kolkata; Sanjib Chatterjee, Raja Ramanna Centre for Advanced Technology, Indore; Takeo Sasaki, Tokyo University, Japan; Lakshminarayan Hazra, Emeritus Professor, University of Calcutta, Kolkata; Shyam Akashe, ITM University, Gwalior and Vasudevan Lakshminarayanan, University of Waterloo, Canada. The subsequent parts focus on topic-wise contributory papers in Application of Solar Energy; Diffraction Tomography; E.M. Radiation Theory and Antenna; Fibre Optics and Devices; Photonics for Space Applications; Micro-Electronics and VLSI; Nano-Photonics, Bio-Photonics and Bio-Medical Optics; Non-linear Phenomena and Chaos; Optical and Digital Data and Image Processing; Optical Communications and Networks; Optical Design; Opto-Electronic Devices; Opto-Electronic Materials and Quantum Optics and Information Processing

Note: Description based upon print version of record , Application of Solar EnergyDiffraction Tomography -- E.M. Radiation Theory and Antenna -- Fibre optics and Devices -- Photonics for Space Applications -- Micro-electronics and VLSI -- Nano-Photonics, Bio-Photonics and Bio-Medical Optics -- Non-linear Phenomena and Chaos -- Optical and Digital Data & Image Processing -- Optical Communications and Networks -- Optical Design -- Opto-Electronic Devices -- Opto-Electronic Materials -- Quantum Optics and Information Processing.

Additional Edition: ISBN 9788132223665

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-813-2223-66-5

Language: English

DOI: 10.1007/978-81-322-2367-2

URL: Volltext

URL: Volltext  (lizenzpflichtig)

URL: Cover

UID:

Format: Online-Ressource (XVI, 118 p. 48 illus., 46 illus. in color, digital)

ISBN: 9781461455622

Series Statement: SpringerLink

Content: Symmetry and Experimental Data -- Algebraic and Data-Analytic Aspects -- Curvature and Refraction Data -- Symbolic Sequences -- Symmetry Preference and Perception -- Other Applications -- Glossary -- Index.

Content: Dihedral Fourier Analysis introduces the theory and applications necessary to study experimental data indexed by, or associated with, the points in a dihedral symmetry orbit. This book looks at experimental data and analytical models indexed by certain dihedral rotations and reversals realized as vector fields. Its particular relevance as a research tool in areas such as optical and molecular biology statistics appears when formulated within the context of symmetry studies, which formally connects algebraic and statistical reasoning together in one methodology for data summary and inference. Chapter 1 presents an overview of the theory and methods of dihedral analysis. It introduces data sets and examples defining and connecting the algebraic notions of symmetry with those of statistical summaries and inference. Chapter 2 includes the required algebraic aspects and data-analytic results. Chapters 3-6 offer applications of the methods presented in the text. This book is intended for data analysts of both theoretical and applied statistics.

Note: Description based upon print version of record , Symmetry and Experimental Data -- Algebraic and Data-Analytic Aspects -- Curvature and Refraction Data -- Symbolic Sequences -- Symmetry Preference and Perception -- Other Applications -- Glossary -- Index.

Additional Edition: ISBN 9781461455615

Additional Edition: Buchausg. u.d.T. Viana, Marlos A. G., 1946 - Dihedral Fourier analysis New York : Springer, 2013 ISBN 9781461455615

Language: English

Subjects: Mathematics

Keywords: Diedergruppe ; Fourier-Transformation ; Harmonische Analyse ; Harmonische Analyse ; Multivariate Analyse

DOI: 10.1007/978-1-4614-5562-2

URL: Volltext  (lizenzpflichtig)

URL: Volltext  (lizenzpflichtig)

URL: Cover

URL: Inhaltstext

UID:

Format: 1 Online-Ressource (XLIII, 689 p. 429 illus).

ISBN: 978-981-10-3908-9

Series Statement: Springer Proceedings in Physics volume 194

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-981-10-3907-2

Language: English

Subjects: Physics

Keywords: Konferenzschrift

DOI: 10.1007/978-981-10-3908-9

URL: Volltext  (URL des Erstveröffentlichers)