JMP: Methods of Mathematical Physics

Do ultradiscrete systems with parity variables satisfy the singularity confinement criterion?

N. Mimura, S. Isojima, M. Murata, J. Satsuma, A. Ramani et al.
Ultradiscrete singularity confinement test, which is an integrability detector for ultradiscrete equations with parity variables, is applied to various ultradiscrete equations. The ultradiscrete equations exhibit singularity structures analogous to those of the discrete counterparts. Exact solutions ... [J. Math. Phys. 53, 023510 (2012)] published Mon Feb 13, 2012.

Symmetry groups and fundamental solutions for systems of parabolic equations

Jing Kang and Changzheng Qu
In this paper, the relationship between Lie point symmetry and fundamental solution for systems of parabolic equations is explored. It is shown that the fundamental solutions of the systems of parabolic equations admitting certain symmetries can be obtained by inverting the Laplace transformation of ... [J. Math. Phys. 53, 023509 (2012)] published Mon Feb 13, 2012.

On convergent series representations of Mellin-Barnes integrals

Samuel Friot and David Greynat
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple power series and logarithms of the parameters involved in the p ... [J. Math. Phys. 53, 023508 (2012)] published Mon Feb 13, 2012.

Stability of multi-Jensen mappings in non-Archimedean normed spaces

Tian Zhou Xu
In this paper, we study the stability of the multi-Jensen mappings in non-Archimedean normed spaces. The results improve and extend some recent results. ... [J. Math. Phys. 53, 023507 (2012)] published Mon Feb 13, 2012.

Discretising the Painleve equations a la Hirota-Mickens

B. Grammaticos, A. Ramani, J. Satsuma, and R. Willox
We present a systematic method for discretising the Painleve equations inspired by the method of Hirota (while extending it) and by that of Mickens (by specifying it to the case at hand). We derive various discrete analogues of Painleve I and II. We obtain forms that have been previously derived as ... [J. Math. Phys. 53, 023506 (2012)] published Thu Feb 9, 2012.

A note on the first integrals of the ABC system

Jaume Llibre and Claudia Valls
Without loss of generality the ABC systems reduce to two cases: either A = 0 and B, C >= 0, or A = 1 and 0 < B, C <= 1. In the first case it is known that the ABC system is completely integrable, here we provide its explicit first integrals. In the second case Ziglin [Dichotomy of the separatrices a ... [J. Math. Phys. 53, 023505 (2012)] published Wed Feb 8, 2012.

Rational solutions of the Noumi and Yamada system of type A

Kazuhide Matsuda
We completely classify the rational solutions of the Noumi and Yamada system of type A, which is a generalization of the fourth Painleve equation. The rational solutions are classified to three by the Backlund transformation group. ... [J. Math. Phys. 53, 023504 (2012)] published Wed Feb 8, 2012.

Planar waveguide with twisted boundary conditions: Small width

Denis Borisov and Giuseppe Cardone
We consider a planar waveguide with twisted boundary conditions. By twisting we mean a special combination of Dirichlet and Neumann boundary conditions. Assuming that the width of the waveguide goes to zero, we identify the effective (limiting) operator as the width of the waveguide tends to zero, e ... [J. Math. Phys. 53, 023503 (2012)] published Tue Feb 7, 2012.

Quasi-periodic functions on the torus and sl(n)-elliptic Lie algebra

T. Skrypnyk
We investigate properties of the sl(n) automorphic elliptic algebra [fraktur E](sl(n)). We prove it to be [openface Z] quasi-graded Lie algebra which could be viewed as a deformation of a graded loop algebra. We show that it admits the decomposition into the direct sum of two subalgebras: [fraktur E ... [J. Math. Phys. 53, 023502 (2012)] published Wed Feb 1, 2012.

Block type symmetry of bigraded Toda hierarchy

Chuanzhong Li, Jingsong He, and Yucai Su
In this paper, we define Orlov-Schulman's operators M, M, and then use them to construct the additional symmetries of the bigraded Toda hierarchy. We further show that these additional symmetries form an interesting infinite-dimensional Lie algebra known as a Block type Lie algebra, whose structure ... [J. Math. Phys. 53, 013517 (2012)] published Mon Jan 30, 2012.

Affine reflection groups for tiling applications: Knot theory and DNA

M. Bodner, J. Patera, and M. Peterson
We present in this paper some non-conventional applications of affine Weyl groups W of rank 2, the symmetry group of the tiling/lattice. We first develop and present the tools for applications requiring tilings of a real Euclidean plane [openface R]. We then elucidate the equivalence of these tiling ... [J. Math. Phys. 53, 013516 (2012)] published Thu Jan 26, 2012.

Free field realization of quantum affine superalgebra U(sl-hat(N|1))

Takeo Kojima
We construct a free field realization of the quantum affine superalgebra U(sl-hat(N|1)) for an arbitrary level k[is-an-element-of][openface C]. ... [J. Math. Phys. 53, 013515 (2012)] published Wed Jan 25, 2012.

Fractional Brownian sheets run with nonlinear clocks

Dongsheng Wu
Let X={X(t), t[is-an-element-of][openface R]} be an (N, d)-fractional Brownian sheet run with nonlinear clocks, that is, X(t) = B(F(t), …, F(t)) for all t=(t,...,t)[is-an-element-of][openface R], where B is an (N, d)-fractional Brownian sheet with Hurst indices H = (H, …, H) [is-an-el ... [J. Math. Phys. 53, 013514 (2012)] published Fri Jan 20, 2012.

On the transition from microscopic to macroscopic electrodynamics

O. L. de Lange, R. E. Raab, and A. Welter
Implicit in the change from microscopic electrodynamics to a macroscopic, multipole theory is a set of molecule-fixed coordinate systems and hence an arbitrary set of molecular origins {O} relative to which the positions of molecular constituents are specified. We examine the extent to which this ... [J. Math. Phys. 53, 013513 (2012)] published Fri Jan 20, 2012.

Global existence and asymptotic behavior of solutions to a nonlinear wave equation of fourth-order

Yu-Zhu Wang and Yin-Xia Wang
In this paper we focus on the Cauchy problem for a nonlinear wave equation of fourth-order in n-dimensional space (n >= 1), the decay structure of which is of regularity-loss property. Based on the decay estimate of solutions to the linear problem, we introduce a set of time-weighted Sobolev spaces. ... [J. Math. Phys. 53, 013512 (2012)] published Thu Jan 19, 2012.

New symbolic tools for differential geometry, gravitation, and field theory

I. M. Anderson and C. G. Torre
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combin ... [J. Math. Phys. 53, 013511 (2012)] published Wed Jan 18, 2012.

Soliton cellular automaton associated with G crystal base

Kailash C. Misra, Masato Okado, and Evan A. Wilson
We calculate the combinatorial R matrix for all elements of [script B][direct-product][script B] where [script B] denotes the G-perfect crystal of level l, and then study the soliton cellular automaton constructed from it. The solitons of length l are identified with elements of the A-crystal [scrip ... [J. Math. Phys. 53, 013510 (2012)] published Wed Jan 18, 2012.

Fourier, Gauss, Fraunhofer, Porod and the shape from moments problem

Gregg M. Gallatin
We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra in three dimensions, etc. We also show how this combination of Fourier and Gauss can be related to numerous classical proble ... [J. Math. Phys. 53, 013509 (2012)] published Tue Jan 17, 2012.

Quantum field theory on quantized Bergman domain

H. Grosse, P. Presnajder, and Zhituo Wang
We present an oscillator realization of discrete series representations of group SU(2, 2). We give formulas for the coherent state star-product quantization of a Bergman domain D. A formulation of a (regularized) noncommutative scalar field on a quantized D is given. ... [J. Math. Phys. 53, 013508 (2012)] published Fri Jan 13, 2012.

Linear differential equations and multiple zeta-values. III. Zeta(3)

Michal Zakrzewski and Henryk Zoladek
We consider the hypergeometric equation (1 t)[partial-derivative]t[partial-derivative]t[partial-derivative]g + xg = 0, whose unique analytic solution [cursive phi](t; x) = 1 + O(t) near t = 0 for t = 1 becomes a generating function for multiple zeta values [cursive phi](1; x) = f(x) = 1 zeta(3)x + ... [J. Math. Phys. 53, 013507 (2012)] published Thu Jan 12, 2012.

Interaction of a weak discontinuity with elementary waves of Riemann problem

R. Radha and V. D. Sharma
We study the interaction of a weak discontinuity wave with the elementary waves of the Riemann problem for the one-dimensional Euler equations governing the flow of ideal polytropic gases, and investigate the effects of initial states, and the shock strength on the jumps in shock acceleration and th ... [J. Math. Phys. 53, 013506 (2012)] published Wed Jan 11, 2012.