Lie symmetry group method is applied to study the Fisher-Kolmogorov equation. The symmetry group is given, and travelling wave solutions are obtained. Finally the conservation laws are determined.

Let L be a lattice in R. We upper bound the number of points of L contained in a small sphere, centered anywhere in R. One way to do this is based on the observation that if the radius of the sphere is sufficiently small then the lattice points contained in that sphere give rise to a spherical code with a certain minimum angle. Another method involves Gaussian measures on L in the sense of [2]....

We discuss implications of the fundamental plane parameters of clusters of galaxies derived from combined optical and X–ray data of a sample of 78 nearby clusters. In particular, we investigate the dependence of these parameters on the dynamical state of the cluster. We introduce a new concept of allocation of the fundamental plane of clusters derived from their intrinsic morphological properti...

In this paper, three SIAM-Review problems selected from Vol. 34 (1992) are reconsidered and treated using methods according to my own vision on them. 1 Consider the functions S(v) and C(v) defined as the sums of two infinite double series : S(v) = +∞ m=0 +∞ n=1 (−1) m+n sin(2v √ m 2 + n 2) √ m 2 + n 2 , (1.1) C(v) = +∞ m=0 +∞ n=1 (−1) m+n cos(2v √ m 2 + n 2) √ m 2 + n 2 , (1.2) whereby it is in...

By use of Green 's functions f o r the diffusional motion a very concise formulation and computation of correlation functions is possible. For an axially symmetric overall diffusion with internal rotation about one and two axes correlation functions of a second rank spherical tensor are calculated. The results comprise all the solutions of the pertinent problem as given so far and allow the ext...

We give formulas for the multiplicities of eigenvalues of generalized rotation operators in terms of generalized Frobenius-Schur indicators in a semi-simple spherical tensor category C. In particular, this implies for a finite depth planar algebra, the entire collection of rotation eigenvalues can be computed from the fusion rules and the traces of rotation at finitely many depths. If C is also...

A method for the determination of the progress rate and the probability of success for thèEvolution Strategy' (short ES) is presented. The new method is based on the asymptotical behavior of the-distribution and yields exact results in case of innnite-dimensional parameter spaces. The technique is demonstrated for the (1; +) ES using a spherical model including noisy quality functions. The resu...

We study the properties of a model system that exhibits a transition between ferromagnetic and helical order at a Lifshitz point, as interaction parameters R and S compete.neighbour and next-nearest-neighbour spin pairs respectively in the z direction, and J,, is a nearest-neighbour interaction between spin pairs in each xy plane. We calculate the high-temperature susceptibility series to order...