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...

Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in various fields. The simplest of such maps is the spherical proximity map which maps a point from the class of interest to a disk centered at the same point with ...

We develop coarse-grained, distance- and orientation-dependent statistical potentials from the growing protein structural databases. For protein structural classes (alpha, beta, and alpha/beta), a substantial number of backbone-backbone and backbone-side-chain contacts stabilize the native folds. By taking into account the importance of backbone interactions with a virtual backbone interaction ...

Abstract We discuss meromorphic functions on the complex plane which are Brody curves regarded as holomorphic maps to $${{\mathbb {P}}}_1$$ P 1 , i.e., have bounded spherical derivative. For some special classes we gave explicit criteria Brody. also divisors of very slo...

At a macroscopic level, concepts such as top spin, back spin and rolling are commonly used to describe the collision of balls surfaces. Each term refers an aspect coupling rotational motion during spherical particle with planar surface. In this paper we explore mechanisms energy transfer involving rotating sphere surface using model frictional interactions developed for granular material. We pr...