The requirements of conformal invariance for the two point function of the energy momentum tensor in the neighbourhood of a plane boundary are investigated, restricting the conformal group to those transformations leaving the boundary invariant. It is shown that the general solution may contain an arbitrary function of a single conformally invariant variable v, except in dimension 2. The functi...

Aperiodic point sets (or tilings) which can be obtained by the method of cut and projection from higher dimensional periodic sets play an important role for the description of quasicrystals. Their topological invariants can be computed using the higher dimensional periodic structure. We report on the results obtained for the cohomology groups of projection point patterns supplemented by explici...

Let K be a finite simplicial complex and f:K—>K be a "skeletal" map. A digraph D is defined whose vertices correspond to the Simplexes of K and whose arcs give information about the behavior of / on the Simplexes. For every walk in D there exists a point of K whose iterates under / mimic the walk. Periodic walks are mimicked by a periodic point. Digraphs with uncountably many infinite walks are...

By using the critical point theory, the existence of periodic solutions for a 2nth-order nonlinear difference equation containing both advance and retardation involving p-Laplacian is obtained. The main approaches used in our paper are variational techniques and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions for a 2nth-order p-Laplacian difference equation...

An example of a homeomorphism without periodic points is constructed on a tree-like continuum.

This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will prove Needham’s theorem in a more general version. 1. Fixed point indices of holomorphic mappings Let C be the complex vector space of dimension n, let U be a...

We report a study of the thermodynamic properties of indium clusters on a SiN (x) surface during the early stages of thin film growth using a sensitive nanocalorimetry technique. The measurements reveal the presence of abnormal discontinuities in the heat of melting below 100 degrees C. These discontinuities, for which temperature separation corresponds to a spatial periodicity equal to the thi...

We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific N -point functions is also presented.

A statistical approach to a problem of assemblies of point vortices (PVs) goes back to Onsager (1949). A state of negative temperature is considered to be related to clustering of vortices rotating in the same direction and the inverse energy cascade predicted in the two-dimensional Navier-Stokes (2D NS) turbulence. In many numerical simulations, PVs are bounded in a circular wall, since a velo...

Spectrum of the second-order differential operator with periodic point interactions in L2 R is investigated. Classes of unitary equivalent operators of this type are described. Spectral asymptotics for the whole family of periodic operators are calculated. It is proven that the first several terms in the asymptotics determine the class of equivalent operators uniquely. It is proven that the spe...