A generalization of the cosine-sine functional equation on groups

The functional equation f(xy)=f(x)g(y)+g(x)f(y)+h(x)h(y) is solved where f, g, h are complex functions defined on a group.     

Crystallographic report: Crystal structure of a two‐dimensional coordination polymer: dizinc diterephthalate pyrazine dihydrate

A two‐dimensional coordination polymer [Zn₂(tp)₂(pz)(H₂O)₂]_n (tp = terephthalate, pz = pyrazine) has been synthesized by the hydrothermal reaction of zinc terephthalate and pyrazine. The Zinc(II) centre is in a distorted pyramidal geometry, being coordinated by one water molecule, one nitrogen atom from a bridging pz and two different bridging tp ligands, one chelating and the other monodentate. Copyright © 2003 John Wiley & Sons, Ltd.     

µ2‐Diiodotetrakis(2‐hydroxymethyl‐1‐methyl‐1‐imidazole‐N3)dicadmium(II) bis[triiodo(2‐hydroxymethyl‐1‐methyl‐1‐imidazole‐N3)cadmate(II)] dihydrate

There are two types of Cd in the title compound, the six‐coordinated Cd atom in the cation is in a distorted octahedral geometry while the four‐coordinated Cd in the anion shows a distorted tetrahedral geometry. Copyright © 2005 John Wiley & Sons, Ltd.     

Further experimental study of fast fission with the Cl + Au system

The onset of fast fission was investigated with the Cl + Au system. The mass distribution of the fragments and the fusion cross sections were determined at six different bombarding energies. It turns out that the width of the symmetric component of the mass distribution increases strongly with the critical angular momentum. This could be related with the disappearance of the fission barrier due to centrifugal effects. A semi-static model is developed and the results are compared with the experimental data. In this framework, the observed broadening of the mass distribution can be attributed to the presence of the fast fission phenomenon.     

A multivariate Markov chain model for categorical data sequences and its applications in demand predictions

Markov models are commonly used in modelling many practicalsystems such as telecommunication systems, manufacturing systemsand inventory systems. In this paper we propose a multivariateMarkov chain model for modelling multiple categorical data sequences.We develop efficient estimation methods for the model parameters.We then apply the model and method to demand predictions fora soft-drink company in Hong Kong.     

Strain interactions and defect formation in stacked InGaAs quantum dot and dot-in-well structures

The growth of high-quality stacked quantum dot (QD) structures represents one of the key challenges for future device applications. Electronic coupling between QDs requires closely separated electronic levels and thin barrier layers, requiring near identical composition and shape, despite strong strain interactions. This paper presents a detailed characterization study of stacked InGaAs QD and InAs/InGaAs dot-in-well (DWELL) structures using cross-sectional transmission electron microscopy. For In_.5Ga_.5As/GaAs QD structures we have observed optimized stacking using a barrier thickness 12 nm.We also report studies of stacking in DWELL laser structures. Despite reports of very low threshold currents in such lasers, designed for 1.3 μm emission, performance is limited by gain saturation and thermal excitation effects. We have explored solutions to these problems by stacking multiple DWELL layers of three, five and 10 repeats. Initial attempts at stacked multilayer structures, particularly samples with a large number of repeats, produced variable results, with a number of the final devices characterized by poor emission and electrical characteristics. Analysis by transmission electron microscopy has identified the presence of large defective regions arising from the complex interaction of dots on several planes and propagating threading dislocations into the cladding layers. The origin of this defect is identified as the coalescence of QDs at very high density and the resulting dislocation propagating to higher dot planes. An effective modified method to reduce the defect density by growing the barrier layer at higher temperature will be discussed. Finally, we report the growth of a stacked 10-layer structure using relatively thin barriers, grown using this technique.     

Multifragmentation of excited nuclei within a schematic hydrodynamical and percolation picture

We present a simple model to describe the evolution of hot and compressed nuclei. It is based on irrotational hydrodynamics and a 3-dimensional site-bond percolation model. Hydrodynamics is used if the evolution of the system is dominated by the mean field. This situation occurs when the fluctuations of the mean field are small. These latter are evaluated using the percolation model. In some cases it turns out that these fluctuations become very large and the system breaks up into several pieces (multifragmentation). The results of this process are described by the percolation model. We have obtained analytical or fitted expressions for all the results which compare well with those obtained in a previous and more involved model based on the same physical ideas. In particular we found that a noncompressed nucleus undergoes multifragmentation if the thermal excitation energy is larger than 70% of its binding energy. If the nucleus is compressed this value is notably decreased.