Applications :: Math
Topology :: Math

JMP: Statistical Physics

Generalized log-likelihood functions and Bregman divergences
Tatsuaki Wada Based on a two-parameter generalization of Gauss' law of error, a generalized log-likelihood is related to a Bregman divergence. This relation is a two-parameter generalization of the well-known relation between log-likelihood and KullbackLeibler divergence. ... [J. Math. Phys. 50, 113301 (2009)] published Tue Nov 10, 2009.
Quantum hypothesis testing with group symmetry
Fumio Hiai, Milan Mosonyi, and Masahito Hayashi The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with the problems of the Chernoff bound, the Hoeffding bound, an ... [J. Math. Phys. 50, 103304 (2009)] published Thu Oct 22, 2009.
Nonlinear stability of boundary layer solution to the Boltzmann equation with diffusive effect at the boundary
Qianzhu Tian and Jie Sun In this paper, the stability of boundary layer solutions to the Boltzmann equation with diffusive effect at the boundary for hard sphere model is considered. When the Mach number of the far field is less than 1, the exponential decay in time is proven for linearized operator first. At last, based on ... [J. Math. Phys. 50, 103303 (2009)] published Thu Oct 8, 2009.

JMP: Methods of Mathematical Physics

HyersUlam stability on a generalized quadratic functional equation in distributions and hyperfunctions
Jae-Young Chung, Dohan Kim, and John Michael Rassias We consider the HyersUlam stability of a generalized quadratic functional equation in the spaces of distributions of Schwartz and hyperfunctions of Gelfand modulo bounded distributions and hyperfunctions. ... [J. Math. Phys. 50, 113519 (2009)] published Wed Nov 25, 2009.
Painleve singularity structure analysis of three component GrossPitaevskii type equations
T. Kanna, K. Sakkaravarthi, C. Senthil Kumar, M. Lakshmanan, and M. Wadati In this paper, we have studied the integrability nature of a system of three-coupled GrossPitaevskii type nonlinear evolution equations arising in the context of spinor BoseEinstein condensates by applying the Painleve singularity structure analysis. We show that only for two sets of parametric choi ... [J. Math. Phys. 50, 113520 (2009)] published Wed Nov 25, 2009.
Asymptotic behavior for logarithmic diffusion
F. Salvarani In this paper we prove, via the entropy dissipation method, that the solutions of the d-dimensional logarithmic diffusion equation, with nonhomogeneous Dirichlet boundary data, decay exponentially in time toward its own steady state. The result is valid not only in L-norm (as customary when applying ... [J. Math. Phys. 50, 113518 (2009)] published Fri Nov 20, 2009.

 

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An Introduction to Noncommutative Geometry - A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics.

404 Celestial Mechanics Research - Links, animations, references, and a brief description of research into n-body problems.
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404 Clyde Davenport's Commutative Hypercomplex Mathematics - Summary and application as it relates to electromagnetic theory and special relativity.
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Complex Geometry of Nature and General Relativity - A paper by Giampiero Esposito attempting to give a self-contained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.

Differential Equations and Oscillations - Many problems in physics are described by differential equations. As a complete discussion of differential equations is beyond the scope of this chapter we will deal only with linear first and second order ordinary differential equations.

Dimensional Analysis - A simple review of the powerful technique of dimensional analysis.

Discrete Self-trapping Equation - A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.

Doing Physics with Quaternions - A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra.

Euclidean Geometric Transforms for Physics - A new method of correlating physics formulas to derive one formula from a related formula using Euclidean geometry to represent the inter-relationship of physics formulas.

Five Lectures on Soliton Equations - A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.

Geometry and Duality - Lecture notes from the ITP miniprogram on Geometry and Duality

his Week's Finds in Mathematical Physics - This is a column written about modern topics in mathematical physics.

Holomorphic Methods in Mathematical Physics - This set of lecture notes by Brian C. Hall gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations.

Homological Methods in Mathematical Physics - These lecture notes by Joseph Krasil'shchik and Alexander Verbovetsky are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations.

500 Hyperreal World - Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.
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Inexplicable Secrets of Creation - Relationships between number theory and physics.

Intrinsic Localized Modes - Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell.

Journal on Applied Clifford Algebra - Journal devoted to the development of Geometric Analysis in particular through the use of Clifford Algebras, Quaternions, Hypercomplex Analysis and Multivector Techniques. Main emphasis en the applications to Physics.

Kinetic Theory and its Applications. - This resource is devoted to mathematical aspects of kinetic theory and its applications in physics and chemistry.

Klaus Brauer's Soliton Page - Presents a history of J.S.Russell's discovery of solitary waves, and animations of one-, two- and three-soliton solutions to the Korteweg-de Vries equation. Includes an article in PDF format on finding exact solutions to the KdV equation using the method of Backlund transform with the help of Mathematica.

Lectures on Orientifolds and Duality - Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.

Local Quantum Physics Crossroads - An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP).

Mathematical Methods I - This site contains the complete lecture notes and homework sets for PHYCS498MMA, a course of mathematical methods for physics given to entering graduate students, and senior undergraduates, at the University of Illinois at Urbana-Champaign.

Non Commutative Geometry - Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.

On the Origins of Twister Theory - A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity.

Open Problems in Mathematics and Physics - Links to open problems in mathematics, physics and other subjects.

404 Period and energy in one degree of freedom systems - An article by Jorge Rezende, University of Lisbon (PDF).

404 Radial Symmetric Fourier Transforms - Fourier transforms of radially-symmetric functions can be performed efficiently using the Hankel transform of order zero. Illustrations of the method are presented, and of the Gibbs' phenomenon.

Recent Developments in Skyrme Models - An introduction by T. Gisiger and M.B. Paranjape to recent, more mathematical developments in the Skyrme model. The aim is to render these advances accessible to mainstream nuclear and particle physicists.

Solitons - An overview of the classical and quantum theory related to solitons

Solitons - Resources at Heriot-Watt University. Meetings, local and other links.

Symplectic Geometries in Quantum Physics and Optics - A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics

The Dirac Delta Function - A brief introduction to the properties and uses of the Dirac delta function.
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Topology and Physics - An essay by C. Nash on the historical connection between topology and physics.

Twistors- What are they? - A set of notes introducing spinors and twistors.

500 Visual Mathematical Physics - Collection of animated gif pictures describing the solutions of the main partial differential equations such as Laplace, Poisson, string and membrane oscillations and heat conduction.