We examine the Kosterlitz–Thouless universality class and show that essential scaling at this type of phase transition is not self– consistent unless multiplicative logarithmic corrections are included. In the case of specific heat these logarithmic corrections are identified analytically. To identify those corresponding to the susceptibility we set up a numerical method involving the finite–si...

Microwave image reconstruction is typically based on a regularized least-square minimization of either the complex-valued field difference between recorded and modeled data or the logarithmic transformation of these field differences. Prior work has shown anecdotally that the latter outperforms the former in limited surveys of simulated and experimental phantom results. In this paper, we provid...

This paper addresses the implementation of a filterbank for digital hearing aids using a multi-dimensional logarithmic number system (MDLNS). The MDLNS, which has similar properties to the classical logarithmic number system (LNS), provides more degrees of freedom than the LNS by virtue of having two, or more, orthogonal bases and the ability to use multiple MDLNS components or digits. The loga...

Yu.A. Litvinov1,2, F. Bosch1, H. Geissel1,2, J. Kurcewicz3, N. Winckler1,2, L. Batist4, K. Beckert1, P. Beller1, D. Boutin1,2, C. Brandau1,2, L. Chen2, C. Dimopoulou1, T. Faestermann5, L. Grigorenko6, P. Kienle5,7, R. Knöbel1,2, C. Kozhuharov1, S.A. Litvinov1,2, L. Maier5, M. Mazzocco1, G. Münzenberg1, A. Musumarra8, C. Nociforo1, F. Nolden1, Z. Patyk9, M. Pfützner3, W.R. Plass2, C. Scheidenber...

We consider the semilinear problem Δu=λ+(− log u+)1{u>0}−λ−(− u−)1{u<0} in B1, where B1 is unit ball Rn and assume λ+,λ−>0. Using a monotonicity formula argument, we prove an optimal regularity result for solutions: ∇u log-Lipschitz function. This introduces two main difficulties. The first lack of invariance scaling blow-up problem. other (more serious) issue term Weiss energy which potentiall...

In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.