Beurling algebra analogues of the classical theorems of Wiener and Levy on absolutely convergent Fourier series

Let $f$ be a continuous function on the unit circle $\Gamma$, whose Fourier series is $\omega$-absolutely convergent for some weight $\omega$ on the set of integers $\mathcal{Z}$. If $f$ is nowhere vanishing on $\Gamma$, then there exists a weight $\nu$ on $\mathcal{Z}$ such that $1/f$ had $\nu$-absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary, it follows that if $\phi$ is holomorphic on a neighbourhood of the range of $f$, then there exists a weight $\chi$ on $\mathcal{Z}$ such that \hbox{$\phi\circ f$} has $\chi$-absolutely convergent Fourier series. This is a weighted analogue of L\'{e}vy's generalization of Wiener's theorem. In the theorems, $\nu$ and $\chi$ are non-constant if and only if $\omega$ is non-constant. In general, the results fail if $\nu$ or $\chi$ is required to be the same weight $\omega$.Comment: 4 page

Porous silicon & titanium dioxide coatings prepared by atmospheric pressure plasma jet chemical vapour deposition technique-a novel coating technology for photovoltaic modules

Atmospheric Pressure Plasma Jet (APPJ) is an alternative for wet processes used to make anti reflection coatings and smooth substrate surface for the PV module. It is also an attractive technique because of it’s high growth rate, low power consumption, lower cost and absence of high cost vacuum systems. This work deals with the deposition of silicon oxide from hexamethyldisiloxane (HMDSO) thin films and titanium dioxide from tetraisopropyl ortho titanate using an atmospheric pressure plasma jet (APPJ) system in open air conditions. A sinusoidal high voltage with a frequency between 19-23 kHz at power up to 1000 W was applied between two tubular electrodes separated by a dielectric material. The jet, characterized by Tg ~ 600-800 K, was mostly laminar (Re ~ 1200) at the nozzle exit and became partially turbulent along the jet axis (Re ~ 3300). The spatially resolved emission spectra showed OH, N2, N2+ and CN molecular bands and O, H, N, Cu and Cr lines as well as the NO2 chemiluminescence continuum (450-800 nm). Thin films with good uniformity on the substrate were obtained at high deposition rate, between 800 -1000 nm.s-1, and AFM results revealed that coatings are relatively smooth (Ra ~ 2 nm). The FTIR and SEM analyses were better used to monitor the chemical composition and the morphology of the films in function of the different experimental conditions. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2790

Laparoscopic cholecystectomy at the Aga Khan Hospital, Nairobi

Objective: To evaluate our experience of laparoscopic cholecystectomies at the Aga Khan Hospital, Nairobi over a three-year period from the inception of the technique, and to assess its value and advantages to the patients. Design: A prospective case series study. Setting: The Aga Khan Hospital, Nairobi. Patients: One hundred and thirty five cases operated from February 1996 to April 1999. All patients were subjected to the American method of laparoscopic cholecystectomy, which is described in detail in this paper. Main outcome measures: Clinical presentation, age and sex demographics, average hospital stay, intraoperative and postoperative complications and outcome. Results: There was a female preponderance with a female to male ratio of 5:1. Mean age was forty nine years. Majority of patients suffered from chronic cholecystitis. The conversion rate to an open procedure was five per cent. There were two cases of significant bile leakage which required laparotomy. No mortality was reported in this series. Conclusion: This technique was found to have distinct advantages such as shorter hospital stay, lesser postoperative pain and very good cosmesis. It is a safe procedure if performed by a well trained surgeon

Tripartite phase separation of two signal effectors with vesicles priming B cell responsiveness.

Antibody-mediated immune responses rely on antigen recognition by the B cell antigen receptor (BCR) and the proper engagement of its intracellular signal effector proteins. Src homology (SH) 2 domain-containing leukocyte protein of 65 kDa (SLP65) is the key scaffold protein mediating BCR signaling. In resting B cells, SLP65 colocalizes with Cbl-interacting protein of 85 kDa (CIN85) in cytoplasmic granules whose formation is not fully understood. Here we show that effective B cell activation requires tripartite phase separation of SLP65, CIN85, and lipid vesicles into droplets via vesicle binding of SLP65 and promiscuous interactions between nine SH3 domains of the trimeric CIN85 and the proline-rich motifs (PRMs) of SLP65. Vesicles are clustered and the dynamical structure of SLP65 persists in the droplet phase in vitro. Our results demonstrate that phase separation driven by concerted transient interactions between scaffold proteins and vesicles is a cellular mechanism to concentrate and organize signal transducers

A note on generalized characters

For a compactly generated LCA group G, it is shown that the set H(G) of all generalized characters on G equipped with the compact-open topology is a LCA group and H(G) = G^ (the dual group of G) if and only if G is compact. Both results fail for arbitrary LCA groups. Further, if G is second countable, then the Gel'fand space of the commutative convolution algebra Cc (G) equipped with the inductive limit topology is topologically homeomorphic to H(G)

Long-range order versus random-singlet phases in quantum antiferromagnetic systems with quenched disorder

The stability of antiferromagnetic long-range order against quenched disorder is considered. A simple model of an antiferromagnet with a spatially varying Neel temperature is shown to possess a nontrivial fixed point corresponding to long-range order that is stable unless either the order parameter or the spatial dimensionality exceeds a critical value. The instability of this fixed point corresponds to the system entering a random-singlet phase. The stabilization of long-range order is due to quantum fluctuations, whose role in determining the phase diagram is discussed.Comment: 5 pp., REVTeX, epsf, 3 eps figs, final version as published, including erratu

Spin Waves in Disordered III-V Diluted Magnetic Semiconductors

We propose a new scheme for numerically computing collective-mode spectra for large-size systems, using a reformulation of the Random Phase Approximation. In this study, we apply this method to investigate the spectrum and nature of the spin-waves of a (III,Mn)V Diluted Magnetic Semiconductor. We use an impurity band picture to describe the interaction of the charge carriers with the local Mn spins. The spin-wave spectrum is shown to depend sensitively on the positional disorder of the Mn atoms inside the host semiconductor. Both localized and extended spin-wave modes are found. Unusual spin and charge transport is implied.Comment: 14 pages, including 11 figure

Monte Carlo simulations of an impurity band model for III-V diluted magnetic semiconductors

We report the results of a Monte Carlo study of a model of (III,Mn)V diluted magnetic semiconductors which uses an impurity band description of carriers coupled to localized Mn spins and is applicable for carrier densities below and around the metal-insulator transition. In agreement with mean field studies, we find a transition to a ferromagnetic phase at low temperatures. We compare our results for the magnetic properties with the mean field approximation, as well as with experiments, and find favorable qualitative agreement with the latter. The local Mn magnetization below the Curie temperature is found to be spatially inhomogeneous, and strongly correlated with the local carrier charge density at the Mn sites. The model contains fermions and classical spins and hence we introduce a perturbative Monte Carlo scheme to increase the speed of our simulations.Comment: 17 pages, 24 figures, 2 table

Renormalization group study of the two-dimensional random transverse-field Ising model

The infinite disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to $L=2048$. We have calculated sample dependent pseudo-critical points and studied their distribution, which is found to be characterized by the same shift and width exponent: $\nu=1.24(2)$. For different types of disorder the infinite disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: $x=0.982(15)$ and $\psi=0.48(2)$. We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases