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Author  Title  Accn#  Year  Item Type  Claims 
1 
Yoshida, Kentaroh 
Yang???Baxter Deformation of 2D NonLinear Sigma Models 
I11819 
2021 
eBook 

2 
Schweizer, Wolfgang 
Special Functions in Physics with MATLAB 
I11728 
2021 
eBook 

3 
Nagao, Hidehito 
Pad?? Methods for Painlev?? Equations 
I11676 
2021 
eBook 

4 
Akhmedova, Valeriya 
Selected Special Functions for Fundamental Physics 
I09479 
2019 
eBook 

5 
Pastras, Georgios 
The Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics 
I09024 
2020 
eBook 

6 
Mathai, A.M 
The HFunction 
I05634 
2010 
eBook 

7 
Araki, Huzihiro 
Quantum and NonCommutative Analysis 
I04479 
1993 
eBook 

8 
Terziogammalu, T 
Advances in the Theory of Fr??chet Spaces 
I03867 
1989 
eBook 

9 
Avery, John S 
Hyperspherical Harmonics 
I03066 
1989 
eBook 

10 
Nevai, Paul 
Orthogonal Polynomials 
I02652 
1990 
eBook 


1.


Title  Yang???Baxter Deformation of 2D NonLinear Sigma Models : Towards Applications to AdS/CFT 
Author(s)  Yoshida, Kentaroh 
Publication  Singapore, Springer Nature Singapore, 2021. 
Description  XII, 70 p. 2 illus : online resource 
Abstract Note  In mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, nonperturbative techniques that have been developed have triggered significant insight for real physics. There are basically two notions of integrability: classical integrability and quantum integrability. In this book, the focus is on the former, classical integrability. When the system has a finite number of degrees of freedom, it has been well captured by the Arnold???Liouville theorem. However, when the number of degrees of freedom is infinite, as in classical field theories, the integrable structure is enriched profoundly. In fact, the study of classically integrable field theories has a long history and various kinds of techniques, including the classical inverse scattering method, which have been developed so far. In previously published books, these techniques have been collected and well described and are easy to find in traditional, standard textbooks. One of the intriguing subjects in classically integrable systems is the investigation of deformations preserving integrability. Usually, it is not considered systematic to perform such a deformation, and one must study systems case by case and show the integrability of the deformed systems by constructing the associated Lax pair or actionangle variables. Recently, a new, systematic method to perform integrable deformations of 2D nonlinear sigma models was developed. It was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was shown in 2008. The original work was done for 2D principal chiral models, but it has been generalized in various directions nowadays. In this book, the recent progress on this Yang???Baxter deformation is described in a pedagogical manner, including some simple examples. Applications of Yang???Baxter deformation to string theory are also described briefly. 
ISBN,Price  9789811617034 
Keyword(s)  1. DIFFERENTIAL EQUATIONS
2. EBOOK
3. EBOOK  SPRINGER
4. MATHEMATICAL PHYSICS
5. SPECIAL FUNCTIONS

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I11819 


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2.


Title  Special Functions in Physics with MATLAB 
Author(s)  Schweizer, Wolfgang 
Publication  Cham, Springer International Publishing, 2021. 
Description  XVII, 282 p. 49 illus., 17 illus. in color : online resource 
Abstract Note  This handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLABbased programs for each of these functions and a detailed htmlbased documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book???s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering 
ISBN,Price  9783030642327 
Keyword(s)  1. Computational Mathematics and Numerical Analysis
2. Computational Physics and Simulations
3. COMPUTER SIMULATION
4. EBOOK
5. EBOOK  SPRINGER
6. MATHEMATICAL PHYSICS
7. Mathematics???Data processing
8. SPECIAL FUNCTIONS
9. Theoretical, Mathematical and Computational Physics

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Call#  Status  Issued To  Return Due On  Physical Location 
I11728 


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3.


Title  Pad?? Methods for Painlev?? Equations 
Author(s)  Nagao, Hidehito;Yamada, Yasuhiko 
Publication  Singapore, Springer Nature Singapore, 2021. 
Description  VIII, 90 p. 2 illus., 1 illus. in color : online resource 
Abstract Note  The isomonodromic deformation equations such as the Painlev?? and Garnier systems are an important class of nonlinear differential equations in mathematics and mathematical physics. For discrete analogs of these equations in particular, much progress has been made in recent decades. Various approaches to such isomonodromic equations are known: the Painlev?? test/Painlev?? property, reduction of integrable hierarchy, the Lax formulation, algebrogeometric methods, and others. Among them, the Pad?? method explained in this book provides a simple approach to those equations in both continuous and discrete cases. For a given function f(x), the Pad?? approximation/interpolation supplies the rational functions P(x), Q(x) as approximants such as f(x)~P(x)/Q(x). The basic idea of the Pad?? method is to consider the linear differential (or difference) equations satisfied by P(x) and f(x)Q(x). In choosing the suitable approximation problem, the linear differential equations give the Lax pair for some isomonodromic equations. Although this relation between the isomonodromic equations and Pad?? approximations has been known classically, a systematic study including discrete cases has been conducted only recently. By this simple and easy procedure, one can simultaneously obtain various results such as the nonlinear evolution equation, its Lax pair, and their special solutions. In this way, the method is a convenient means of approaching the isomonodromic deformation equations 
ISBN,Price  9789811629983 
Keyword(s)  1. ANALYSIS
2. EBOOK
3. EBOOK  SPRINGER
4. MATHEMATICAL ANALYSIS
5. MATHEMATICAL PHYSICS
6. SPECIAL FUNCTIONS

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Call#  Status  Issued To  Return Due On  Physical Location 
I11676 


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4.


Title  Selected Special Functions for Fundamental Physics 
Author(s)  Akhmedova, Valeriya;Akhmedov, Emil T 
Publication  Cham, Springer International Publishing, 2019. 
Description  XI, 116 p. 20 illus : online resource 
Abstract Note  This book presents calculation methods that are used in both mathematical and theoretical physics. These methods will allow readers to work with selected special functions and more generally with differential equations, which are the most frequently used in quantum mechanics, theory of relativity and quantum field theory. The authors explain various approximation methods used to solve differential equations and to estimate integrals. They also address the basics of the relations between differential equations, special functions and representation theory of some of the simplest algebras on the one hand, and fundamental physics on the other. Based on a seminar for graduate physics students, the book offers a compact and quick way to learn about special functions. To gain the most from it, readers should be familiar with the basics of calculus, linear algebra, and complex analysis, as well as the basic methods used to solve differential equations and calculate integrals. 
ISBN,Price  9783030350895 
Keyword(s)  1. EBOOK
2. EBOOK  SPRINGER
3. Mathematical Applications in the Physical Sciences
4. Mathematical Methods in Physics
5. MATHEMATICAL PHYSICS
6. PHYSICS
7. SPECIAL FUNCTIONS

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Call#  Status  Issued To  Return Due On  Physical Location 
I09479 


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5.


Title  The Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics : A Primer for Advanced Undergraduates 
Author(s)  Pastras, Georgios 
Publication  Cham, Springer International Publishing, 2020. 
Description  XIII, 111 p. 14 illus., 13 illus. in color : online resource 
Abstract Note  The field of elliptic functions, apart from its own mathematical beauty, has many applications in physics in a variety of topics, such as string theory or integrable systems. This book, which focuses on the Weierstrass theory of elliptic functions, aims at senior undergraduate and junior graduate students in physics or applied mathematics. Supplemented by problems and solutions, it provides a fast, but thorough introduction to the mathematical theory and presents some important applications in classical and quantum mechanics. Elementary applications, such as the simple pendulum, help the readers develop physical intuition on the behavior of the Weierstrass elliptic and related functions, whereas more Interesting and advanced examples, like the n=1 Lam?? problema periodic potential with an exactly solvable band structure, are also presented 
ISBN,Price  9783030593858 
Keyword(s)  1. Applications of Mathematics
2. APPLIED MATHEMATICS
3. CLASSICAL MECHANICS
4. EBOOK
5. EBOOK  SPRINGER
6. ENGINEERING MATHEMATICS
7. MATHEMATICAL PHYSICS
8. MECHANICS
9. NUCLEAR PHYSICS
10. Particle and Nuclear Physics
11. SPECIAL FUNCTIONS
12. Theoretical, Mathematical and Computational Physics

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Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
I09024 


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6.


Title  The HFunction : Theory and Applications 
Author(s)  Mathai, A.M;Saxena, Ram Kishore;Haubold, Hans J 
Publication  New York, NY, Springer New York, 2010. 
Description  XIV, 268 p : online resource 
Abstract Note  The topics of special Hfunction and fractional calculus are currently undergoing rapid changes both in theory and application. Taking into account the latest research results, the authors delve into these topics as they relate to applications to problems in statistics, physics, and engineering, particularly in condensed matter physics, plasma physics, and astrophysics. The book sets forth the definitions, contours, existence conditions, and particular cases for the Hfunction, then explores the properties and relationships among the Laplace, Fourier, Hankel, and other transforms. From here, the Hfunctions are utilized for applications in statistical distribution theory, structures of random variables, generalized distributions, Mathai???s pathway models, and versatile integrals. Functions of matrix argument are introduced with a focus on realvalued scalar functions when the matrices are real or Hermitian positivedefinite. The text concludes with important recent applications to physical problems in reaction, diffusion, reactiondiffusion theory and statistics, and superstatistics. Generalized entropies as well as applications in astrophysics are dealt with. Over the last few years, material in this book has been added to various courses and developed to meet the needs of scholars at the PhD level. All exercises in the book have been used to probe the knowledge and ability of mathematics, statistics, and physics to students and researchers. 
ISBN,Price  9781441909169 
Keyword(s)  1. APPLIED MATHEMATICS
2. EBOOK
3. EBOOK  SPRINGER
4. ENGINEERING MATHEMATICS
5. FUNCTIONAL ANALYSIS
6. Mathematical and Computational Engineering
7. Mathematical Methods in Physics
8. MATHEMATICAL PHYSICS
9. PHYSICS
10. SPECIAL FUNCTIONS
11. Statistical Theory and Methods
12. Statistics??
13. Theoretical, Mathematical and Computational Physics

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Call#  Status  Issued To  Return Due On  Physical Location 
I05634 


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7.


Title  Quantum and NonCommutative Analysis : Past, Present and Future Perspectives 
Author(s)  Araki, Huzihiro;Ito, Keiichi R;Kishimoto, Akitaka;Ojima, Izumi 
Publication  Dordrecht, Springer Netherlands, 1993. 
Description  XII, 464 p : online resource 
Abstract Note  In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 2529, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two keynote addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap?? proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held 
ISBN,Price  9789401728232 
Keyword(s)  1. Associative rings
2. Associative Rings and Algebras
3. EBOOK
4. EBOOK  SPRINGER
5. Elementary particles (Physics)
6. Elementary Particles, Quantum Field Theory
7. GROUP THEORY
8. Group Theory and Generalizations
9. QUANTUM FIELD THEORY
10. Rings (Algebra)
11. SPECIAL FUNCTIONS

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Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
I04479 


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9.


Title  Hyperspherical Harmonics : Applications in Quantum Theory 
Author(s)  Avery, John S 
Publication  Dordrecht, Springer Netherlands, 1989. 
Description  XVI, 256 p : online resource 
Abstract Note  where d 3 3)2 ( L x   i3x j3x j i i>j Thus the Gegenbauer polynomials play a role in the theory of hyper spherical harmonics which is analogous to the role played by Legendre polynomials in the familiar theory of 3dimensional spherical harmonics; and when d = 3, the Gegenbauer polynomials reduce to Legendre polynomials. The familiar sum rule, in 'lrlhich a sum of spherical harmonics is expressed as a Legendre polynomial, also has a ddimensional generalization, in which a sum of hyper spherical harmonics is expressed as a Gegenbauer polynomial (equation (327??: The hyper spherical harmonics which appear in this sum rule are eigenfunctions of the generalized angular monentum 2 operator A , chosen in such a way as to fulfil the orthonormality relation: VIe are all familiar with the fact that a plane wave can be expanded in terms of spherical Bessel functions and either Legendre polynomials or spherical harmonics in a 3dimensional space. Similarly, one finds that a ddimensional plane wave can be expanded in terms of HYPERSPHERICAL HARMONICS xii "hyperspherical Bessel functions" and either Gegenbauer polynomials or else hyperspherical harmonics (equations ( 4  27) and ( 4  30) ) : 00 ik??x e = (d4)!!A~oiA(d+2A2)j~(kr)C~(~k'~) 00 (d2)!!I(0) 2: iAj~(kr) 2:Y~ (["2k)Y (["2) A A=O ). l). l)J where I(O) is the total solid angle. This expansion of a ddimensional plane wave is useful when we wish to calculate Fourier transforms in a ddimensional space 
ISBN,Price  9789400923232 
Keyword(s)  1. Atomic, Molecular, Optical and Plasma Physics
2. ATOMS
3. EBOOK
4. EBOOK  SPRINGER
5. PHYSICAL CHEMISTRY
6. PHYSICS
7. QUANTUM PHYSICS
8. SPECIAL FUNCTIONS

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Call#  Status  Issued To  Return Due On  Physical Location 
I03066 


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10.
 
Title  Orthogonal Polynomials : Theory and Practice 
Author(s)  Nevai, Paul 
Publication  Dordrecht, Springer Netherlands, 1990. 
Description  488 p : online resource 
Abstract Note  This volume contains the Proceedings of the NATO Advanced Study Institute on "Orthogonal Polynomials and Their Applications" held at The Ohio State University in Columbus, Ohio, U.S.A. between May 22,1989 and June 3,1989. The Advanced Study Institute primarily concentrated on those aspects of the theory and practice of orthogonal polynomials which surfaced in the past decade when the theory of orthogonal polynomials started to experience an unparalleled growth. This progress started with Richard Askey's Regional Confer?? ence Lectures on "Orthogonal Polynomials and Special Functions" in 1975, and subsequent discoveries led to a substantial revaluation of one's perceptions as to the nature of orthogonal polynomials and their applicability. The recent popularity of orthogonal polynomials is only partially due to Louis de Branges's solution of the Bieberbach conjecture which uses an inequality of Askey and Gasper on Jacobi polynomials. The main reason lies in their wide applicability in areas such as Pade approximations, continued fractions, Tauberian theorems, numerical analysis, probability theory, mathematical statistics, scattering theory, nuclear physics, solid state physics, digital signal processing, electrical engineering, theoretical chemistry and so forth. This was emphasized and convincingly demonstrated during the presentations by both the principal speakers and the invited special lecturers. The main subjects of our Advanced Study Institute included complex orthogonal polynomials, signal processing, the recursion method, combinatorial interpretations of orthogonal polynomials, computational problems, potential theory, Pade approximations, Julia sets, special functions, quantum groups, weighted approximations, orthogonal polynomials associated with root systems, matrix orthogonal polynomials, operator theory and group representations 
ISBN,Price  9789400905016 
Keyword(s)  1. Computational Mathematics and Numerical Analysis
2. Computer mathematics
3. EBOOK
4. EBOOK  SPRINGER
5. FOURIER ANALYSIS
6. SPECIAL FUNCTIONS

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Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
I02652 


On Shelf 



 