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.     

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.

     

Simultaneous confidence bands for the integrated hazard function

The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson–Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Four methods of construction of such confidence bands are proposed. The weird and conditional bootstrap methods are used for resampling. Simulations are made to compare the actual coverage probability of the bootstrap and the asymptotic simultaneous confidence bands. It is shown that the equal-tailed bootstrap confidence band has the coverage probability closest to the nominal one. We also present application of our confidence bands to the data regarding survival after heart transplant. This research was partly supported by AGH grant No. 10.420.03.     

Application of arc-plasma discharges to coating of screw taps

The paper reports on results of technological research on the coating of standard screw taps with TiN layers deposited by means of arc-plasma discharges, which were carried out within a BULAT-type device equipped with three identical metal-plasma sources. Particular attention is paid to morphology of the coated surfaces. Some data about thickness and microhardness of the coating layers, as well as results of laboratory wear tests of the coated tools, are also presented.     

On photovoltaic effect in hybrid heterojunction formed from palladium phthalocyanine and titanium dioxide layers

The results of the research on the photovoltaic properties of a system formed from tin oxide, titanium dioxide, palladium phthalocyanine and gold (SnO₂:F/TiO₂/PdPc/Au) are presented. Films of TiO₂ were deposited using a sol–gel method, then PdPc and Au layers were subsequently evaporated under a high vacuum. The system exhibits a strong rectification effect in the dark, while an effective photogeneration of charge carriers within the TiO₂/PdPc junction is observed under illumination. The experimental relations of a short-circuit current and an open-circuit voltage against the light intensity suggest that trapping states participate in recombination processes.