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Beurling algebra analogues of the classical theorems of Wiener and Levy on absolutely convergent Fourier series
Let be a continuous function on the unit circle , whose Fourier
series is -absolutely convergent for some weight on the set of
integers . If is nowhere vanishing on , then there
exists a weight on such that had -absolutely
convergent Fourier series. This includes Wiener's classical theorem. As a
corollary, it follows that if is holomorphic on a neighbourhood of the
range of , then there exists a weight on such that
\hbox{} has -absolutely convergent Fourier series. This is a
weighted analogue of L\'{e}vy's generalization of Wiener's theorem. In the
theorems, and are non-constant if and only if is
non-constant. In general, the results fail if or is required to be
the same weight .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 with the modification factor . This has implications
for strategies for obtaining fast convergence.Comment: 4 pages, 2 figures, to appear in Phys. Rev.
"ધ્યાન કરતા અને ધ્યાન ન કરતા સ્ત્રી-પુરુષોમાં સ્વ-નિયંત્રણ, મનોવૈજ્ઞાનિક સુખાકારી અને માનસિક સ્વાસ્થ્યનો તુલનાત્મક અભ્યાસ"
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