The Lie-group formalism is applied to investigate the symmetries of the Dullin-Gottwald-Holm equation φt −αφxxt +2wφx +3φφx + γφxxx = α(2φxφxx +φφxxx), which describes the unidirectional propagation of two dimensional waves in shallow water over a flat bottom. We derived the infinitesimals that admit the classical symmetry group. The reduced ordinary differential equation is further studied and...

We prove that there is a unique folding tessellation of the sphere and an infinite family of folding tessellations of the plane with prototiles a kite and an equilateral triangle. Each tiling of this family is obtained by successive gluing of two patterns composed of triangles and kites, respectively. The combinatorial structure and the symmetry group is achieved.

We consider the one-loop two-point function for multi-trace operators in the U(2) sector of N = 4 supersymmetric Yang-Mills at finite N . We derive an expression for it in terms of U(N) and Sn+1 group theory data, where n is the length of the operators. The Clebsch-Gordan operators constructed in [1], which are diagonal at tree level, only mix at one loop if you can reach the same (n + 1)-box Y...

We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang–Mills equations on R discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the symmetry algebra generates the tangent space to the instanton moduli space at each point. We explicitly find the subgroup of the symmetry group that preserves the one-ins...

M P = {A(x) ∈ M : det(A(x)− yIr) = P (x, y)}. The system (1) has an obvious symmetry group G = IPGLr(I C; J) which is the subgroup of the projective group IPGLr(I C) formed by matrices which commute with J . The group G acts on M by conjugation, the action is Poisson, and the reduced Hamiltonian system is completely integrable too. As the symmetry group G acts freely and properly on the general...

1.1. This article surveys some developments in pure mathematics which have, to varying degrees, grown out of the ideas of gauge theory in Mathematical Physics. The realisation that the gauge fields of particle physics and the connections of differential geometry are one and the same has had wide-ranging consequences, at different levels. Most directly, it has lead mathematicians to work on new ...

Nucleon-nucleon scattering at large momentum transfer is analyzed within the framework of quantum chromodynamic quark and gluon interactions. The spin dependence of the hadronic amplitude is found to be particularly sensitive to the underlying dynamical mechanisms. Detailed discussions of the quark interchange and Landshoff pinch singularity contributions are given for large angle pp, np and pi...

All complete, axially symmetric surfaces of constant mean curvature in R lie in the one-parameter family Dτ of Delaunay surfaces. The elements of this family which are embedded are called unduloids; all other elements, which correspond to parameter value τ ∈ R, are immersed and are called nodoids. The unduloids are stable in the sense that the only global constant mean curvature deformations of...

The Birkhoff polytope Bn is the convex hull of all n× n permutation matrices in Rn×n. We compute the combinatorial symmetry group of the Birkhoff polytope. A representation polytope is the convex hull of some finite matrix group G 6 GL(d,R). We show that the group of permutation matrices is essentially the only finite matrix group which yields a representation polytope with the face lattice of ...

In many examples of repeating patterns in the art of various cultures, the use of symmetries to analyze those patterns does a good job of capturing the repetition intended by the artist. In other cases, however, the artist uses precise forms of repetition that are not well modeled by mathematical symmetries. The analysis of the orbits of motifs under the action of the symmetry group both reveal...