Noncommutative parameters of quantum symmetries and star products

The star product technique translates the framework of local fields on noncommutative spacetime into nonlocal fields on standard spacetime. We consider the example of fields on κ-deformed Minkowski space, transforming under κ-deformed Poincaré group, with noncommutative parameters. By extending the star product to the tensor product of functions on κ-deformed Minkowski space and κ-deformed Poincaré group we represent the algebra of noncommutative parameters of deformed relativistic symmetries by functions on classical Poincaré group.     

Van der Pauw method on a sample with an isolated hole

Explicit results of the van der Pauw method for a sample containing an isolated hole are presented together with experimental confirmation. Results of measurements and numerical analysis strongly suggest that four probe resistivities obey inequality similar in the form to the famous van der Pauw equation. The inequality seems to be valid for any sample with an isolated hole and contacts located on the same edge, however rigorous proof is not given. The inequality can be used for experimental detection of the sample quality.     

On a subclass of close-to-convex functions

We consider a subclass of the class of close-to-convex functions. We show the relationship between our class and the appropriate subordination. Moreover, we give the coefficient estimates and a sufficient condition for functions to belong to the class investigated. Finally, we obtain the distortion and the growth theorems. The results presented are a generalization of the results obtained by Gao and Zhou.     

Gluon cascades and amplitudes in light-front perturbation theory

We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.     

A note on Srivastava and Hui’s tests of multivariate normality

The aim of the paper is to point out some imprecision in Srivastava and Hui’s tests for multivariate normality. A correction for their tests is proposed.     

Global stability and the Hopf bifurcation for some class of delay differential equation

In this paper, we present an analysis for the class of delay differential equations with one discrete delay and the right‐hand side depending only on the past. We extend the results from paper by U. Fory? (Appl. Math. Lett. 2004; 17 (5):581–584), where the right‐hand side is a unimodal function. In the performed analysis, we state more general conditions for global stability of the positive steady state and propose some conditions for the stable Hopf bifurcation occurring when this steady state looses stability. We illustrate the analysis by biological examples coming from the population dynamics. Copyright © 2007 John Wiley & Sons, Ltd.     

KIDs are Non-Generic

We prove that the space-time developments of generic solutions of the vacuum constraint Einstein equations do not possess any global or local Killing vectors, when Cauchy data are prescribed on an asymptotically flat Cauchy surface, or on a compact Cauchy surface with mean curvature close to a constant, or for CMC asymptotically hyperbolic initial data sets. More generally, we show that nonexistence of global symmetries implies, generically, non-existence of local ones. As part of the argument, we prove that generic metrics do not possess any local or global conformal Killing vectors.submitted 22/02/04, accepted 28/07/04     

Some remarks on the Hook formula

Summary Without the Frame-Robinson-Thral hook formula we establish some divisibility properties of degrees of irreducible representations of the symmetric group.

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Riassunto Senza utilizzare una nota formula di Frame-Robinson-Thrall stabiliamo alcune proprietà di divisibilità di gradi di rappresentazioni irriducibili del grupposimmetrico.