How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Comparison of Algorithms for the Degree Constrained Minimum Spanning Tree

The Degree Constrained Minimum Spanning Tree (DCMST) on a graph is the problem of generating a minimum spanning tree with constraints on the number of arcs that can be incident to vertices of the graph. In this paper we develop three heuristics for the DCMST, including simulated annealing, a genetic algorithm and a method based on problem space search. We propose alternative tree representations to facilitate the neighbourhood searches for the genetic algorithm. The tree representation that we use for the genetic algorithm can be generalised to other tree optimisation problems as well. We compare the computational performance of all of these approaches against the performance of an exact solution approach in the literature. In addition, we also develop a new exact solution approach based on the combinatorial structure of the problem. We test all of these approaches using standard problems taken from the literature and some new test problems that we generate.     

Path Integral for an Effective Two Level Atom in a Kerr-Like Medium and Stark Shift with a Pseudo Hermitian Hamiltonian

We use the coherent state path integral and a angular model for the spin to solve the generalized Jaynes-Cummings model with a pseudo-hermitian Hamiltonian and nonlinear Kerr cavity. The propagators are given explicitly as perturbation series. These are summed up exactly. The energy spectrum and the bi-orthonormal basis of states are deduced.     

Optical properties of electron beam- and UV-cured polypropyleneglycoldiacrylate/liquid crystal E7 systems

This contribution focuses on a detailed investigation of the relationship between the method of polymerisation/cross-linking, such as slow and rapid UV radiation, and high voltage accelerated electron beam (EB), and the obtained physical properties including phase diagrams, polymerisation and phase separation kinetics, morphologies and electro-optic responses of polypropyleneglycoldiacrylate (PPGDA) monomers, in the presence of the nematic liquid crystal E7. The longer the spacing between double bonds, the more rapid was the photopolymerisation under both UV systems; however, the reverse was proved under EB. More homogenous and regular morphologies were obtained under EB curing.

The electro-optical responses of various polymer dispersed liquid crystals (PDLCs) systems exhibited remarkable differences between the UV-cured samples and those cured by the EB technique. It was found that the threshold and saturation voltages considerably increased in the case of the UV-cured systems. Other results involving the contrast ratio, which is higher for EB-cured systems, confirm their higher quality, although the rapid photopolymerisation UV source was employed, which slightly improved the electro-optical responses. Moreover, EB curing leads to high enough conversions without a photoinitiator, which may act as an impurity that might have a strong impact on the electro-optical performance of the obtained PDLCs.     

Search for isovector giant monopole resonances via the Pb(3He,tp) reaction

The (nat)Pb(3He,tp) reaction at E(3He) = 177 MeV was studied to identify 2Planck's over 2piomega isovector monopole strength in Bi isotopes. Monopole strength was found in the region -45相似文献