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

Understanding and Improving the Wang-Landau Algorithm

We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuation after a stage of initial accumulation, and the statistical error is found to scale as $\sqrt{\ln f}$ with the modification factor $f$. This has implications for strategies for obtaining fast convergence.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

Answer Set Programming Modulo `Space-Time'

We present ASP Modulo `Space-Time', a declarative representational and computational framework to perform commonsense reasoning about regions with both spatial and temporal components. Supported are capabilities for mixed qualitative-quantitative reasoning, consistency checking, and inferring compositions of space-time relations; these capabilities combine and synergise for applications in a range of AI application areas where the processing and interpretation of spatio-temporal data is crucial. The framework and resulting system is the only general KR-based method for declaratively reasoning about the dynamics of `space-time' regions as first-class objects. We present an empirical evaluation (with scalability and robustness results), and include diverse application examples involving interpretation and control tasks

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