Orthogonal polynomials, special functions and mathematical physics

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics.Editorial policyThe Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki.The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutationscluster structure on Poisson varietiescluster algebras and soliton interactionscluster positivity conjectureY-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjectureT-system of transfer matrices of integrable lattice modelsdilogarithm identities in conformal field theorywall crossing in 4d N = 2 supersymmetric gauge theories4d N = 1 quiver gauge theories described by networksscattering amplitudes of 4d N = 4 theories3d N = 2 gauge theories described by flat connections on 3-manifoldsintegrability of dimer/Ising models on graphs.All contributions will be refereed and processed according to the usual procedure of the journal.Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014.There is no strict regulation on article size, but as a guide the preferable size is 15–30 pages for contributed papers and 40–60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa.Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting ‘JPhysA special issue on cluster algebras in mathematical physics’. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions.All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address.The special issue will be published in the print and online versions of the journal.

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics.Editorial policyThe Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki.The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutationscluster structure on Poisson varietiescluster algebras and soliton interactionscluster positivity conjectureY-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjectureT-system of transfer matrices of integrable lattice modelsdilogarithm identities in conformal field theorywall crossing in 4d N = 2 supersymmetric gauge theories4d N = 1 quiver gauge theories described by networksscattering amplitudes of 4d N = 4 theories3d N = 2 gauge theories described by flat connections on 3-manifoldsintegrability of dimer/Ising models on graphs.All contributions will be refereed and processed according to the usual procedure of the journal.Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014.There is no strict regulation on article size, but as a guide the preferable size is 15–30 pages for contributed papers and 40–60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa.Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting ‘JPhysA special issue on cluster algebras in mathematical physics’. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions.All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address.The special issue will be published in the print and online versions of the journal.

At present there can be no doubt to say that the quantum group theory has been one of the most important, modern and rapidly developing directions of mathematics and mathematical physics in the end of the twentieth century. Although initially (in the early 1980’s) the quantum group theory was formulated for solving problems in the theory of integrable systems and statistical physics, later the surprising connection of this theory with many branches of mathematics, and the theoretical and mathematical physics was discovered. Today the quantum group theory is connected with such mathematical fields as special functions (especially, with (q-orthogonal polynomials and basic hypergeometric series), the theory of difference and differential equations, combinatorial analysis and representation theory, matrix and operator algebras, noncommutative geometry, knot theory, topology, category theory and so on. From point of view of the mathematical physics there exists interconnection of the quantum group theory with the quantum inverse scattering method, conformai and quantum fields theory and so on. It is expected that the quantum groups will provide deeper understanding of concept of symmetry in physics.KeywordsQuantum GroupSimple RootBasic Hypergeometric SeriesReduction ChainGeneral Projection OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The effectiveness of dual integral equations for handling mixed boundary value problems has established them as an important tool for applied mathematicians. Their many applications in mathematical physics have prompted extensive research over the last 25 years, and many researchers have made significant contributions to the methodology of solving and to the applications of dual integral equations. However, until now, much of this work has been available only in the form of research papers scattered throughout different journals.In Advances in Dual Integral Equations, the authors systematically present some of the recent developments in dual integral equations involving various special functions as kernel. They examine dual integral equations with Bessel, Legendre, and trigonometric functions as kernel plus dual integral equations involving inverse Mellin transforms. These can be particularly useful in studying certain mixed boundary value problems involving homogeneous media in continuum mechanics. However, when dealing with problems involving non-homogenous media, the corresponding equations may have different kernels. This application prompts the authors to conclude with a discussion of hybrid dual integral equations-mixed kernels with generalized associated Legendre functions and mixed kernels involving Bessel functions.Researchers in the theory of elasticity, fluid dynamics, and mathematical physics will find Advances in Dual Integral Equations a concise, one-stop resource for recent work addressing special functions as kernel.

The preface is given to report the recent results on the special calculus operators containing the fractional calculus, general fractional calculus, fractal scaling-law calculus, power-law calculus, conformable calculus, and local fractional calculus. The inequalities for them are considered. The soliton solutions for the PDEs in the real-world problems are solved. We give the interesting results on number theory, elliptic curves, and special functions in mathematical physics.

Orthogonal Laurent polynomials and strong moment theory: a survey

This annual conference was established at the National Nuclear Research University – Moscow Engineering Institute in the year 2012. The scope was initially on mathematical physics and mathematical modelling, while since this year theoretical physics was also included. The Conference was organized by three leading departments of the MEPhI in the field of theoretical and mathematical physics.Each year, more than 100 participants from different countries including Belorussia, Czech Republic, France, Great Britain, Japan, Moldova, Russia, Slovakia, Spain, Sweden and the USA take part in the Conference with oral talks.The aim of this conference is to bring together researchers with interests in: Analytical Theory of Differential Equations, Interaction of Radiation With Matter and Physics of Extreme Light, Nuclear Physics and Theory of Elementary Particles, Optimization Problems, Solid Mechanics, Soft Matter and Interdisciplinary Physics, Fluid Mechanics, Mathematical Modelling, Time Series.Nikolay A. KudryashovOleg V. NagornovSergey V. Popruzhenko

Dedicated to the memory of Professor Richard Askey (1933–2019) and to pay tribute to the Bateman Project. Harry Bateman planned his “shoe-boxes” project (accomplished after his death as Higher Transcendental Functions, Vols. 1–3, 1953–1955, under the editorship by A. Erdélyi) as a “Guide to the Functions”. This inspired the author to use the modified title of the present survey. Most of the standard (classical) Special Functions are representable in terms of the Meijer G-function and, specially, of the generalized hypergeometric functions pFq. These appeared as solutions of differential equations in mathematical physics and other applied sciences that are of integer order, usually of second order. However, recently, mathematical models of fractional order are preferred because they reflect more adequately the nature and various social events, and these needs attracted attention to “new” classes of special functions as their solutions, the so-called Special Functions of Fractional Calculus (SF of FC). Generally, under this notion, we have in mind the Fox H-functions, their most widely used cases of the Wright generalized hypergeometric functions pΨq and, in particular, the Mittag–Leffler type functions, among them the “Queen function of fractional calculus”, the Mittag–Leffler function. These fractional indices/parameters extensions of the classical special functions became an unavoidable tool when fractalized models of phenomena and events are treated. Here, we try to review some of the basic results on the theory of the SF of FC, obtained in the author’s works for more than 30 years, and support the wide spreading and important role of these functions by several examples.

<b>Fannes, M.; Verbeure, A.</b> (eds.), Mathematical Methods in Statistical Mechanics. Conference Proceedings, Leuven, 23–24 June 1988. Leuven, Leuven University Press 1989. III, 196 pp., Bef 600.‐. ISBN 90–6186–306‐6 (Leuven Notes in Mathematical and Theoretical Physics. Vol. 1. Ser. A: Mathematical Physics)

On December 10th, 1947, John von Neumann wrote to the Spanish translator of his Mathematical Foundations of Quantum Mechanics: 1 Your questions on the nature of mathematical physics and theoretical physics are interesting but a little difficult to answer with precision in my own mind. I have always drawn a somewhat vague line of demarcation between the two subjects, but it was really more a difference in distribution of emphases. I think that in theoretical physics the main emphasis is on the connection with experimental physics and those methodological processes which lead to new theories and new formulations, whereas mathematical physics deals with the actual solution and mathematical execution of a theory which is assumed to be correct per se, or assumed to be correct for the sake of the discussion. In other words, I would say that theoretical physics deals rather with the formation and mathematical physics rather with the exploitation of physical theories. However, when a new theory has to be evaluated and compared with experience, both aspects mix.

The special matrix functions have received significant attention in many fields, such as theoretical physics, number theory, probability theory, and the theory of group representations. In 2017, Dwivedi and Sahai introduced the generalized hypergeometric matrix function using matrix parameters and proved the convergence on | z | = 1 {|z|=1} . Recently, hypergeometric matrix functions and their potential applications have played a major role in mathematical physics and engineering. Motivated by aforesaid works and in order to enrich this flourishing field, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and determine various transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have been provided for several particular cases.

This book brings together the essential ideas and methods behind applications of variational theory in theoretical physics and chemistry. The emphasis is on understanding physical and computational applications of variational methodology rather than on rigorous mathematical formalism. The text begins with an historical survey of familiar variational principles in classical mechanics and optimization theory, then proceeds to develop the variational principles and formalism behind current computational methodology for bound and continuum quantum states of interacting electrons in atoms, molecules, and condensed matter. It covers multiple-scattering theory, including a detailed presentation of contemporary methodology for electron-impact rotational and vibrational excitation of molecules. The book ends with an introduction to the variational theory of relativistic fields. Ideal for graduate students and researchers in any field that uses variational methodology, this book is particularly suitable as a backup reference for lecture courses in mathematical methods in physics and theoretical chemistry.

Coxeter energy of graphs

"Michell, John Henry, (26 Oct. 1863–3 Feb. 1940), late Assistant Professor of Mathematics in the University of Melbourne; formerly Fellow of Trinity College, Cambridge; distinguished for researches in Mathematical Physics" published on by Oxford University Press.

The aim of this paper is to derive the dependence of the nature of a solution of a class of differential equations of n-th order with polynomial coefficients on the solutions of the corresponding characteristic algebraic equation of n-th degree.