Within the Hartree-Fock approximation the ground state of the composite fermion metal is found. We observe that the single-particle energy spectrum is dominated by the logarithmic interaction exchange term which leads to an infinite jump of the singleparticle energy at the Fermi momentum. It is shown that the Hartree-Fock result brings no corrections to the RPA Fermi velocity.

A single parameter model of the mean Solar limbdarkening is presented. This empirical law has the advantage to represent the limb darkening over a large spectrum at least as well as a quadratic or logarithmic law. Since it is less sensitive than high degree polynomial laws, it is recommended for subsequent analysis of average limb-darkening variations and comparisons.

Numerical results for the first gap of the Lyapunov spectrum of the selfdual random-bond Ising model on strips are analysed. It is shown that finite-width corrections can be fitted very well by an inverse logarithmic form, predicted to hold when the Hamiltonian contains a marginal operator. PACS numbers: 05.50.+q, 05.70.Jk, 64.60.Fr, 75.10.Nr Short title: LETTER TO THE EDITOR

Running of gauge couplings on a slice of AdS 5 is examined using the decon-struction setup. Logarithmic running instead of (linear) power law is justified when the cutoff is lower than the curvature scale. Most of interesting features including the localization of Kaluza-Klein modes and the widening of higher Kaluza-Klein spectrum spacing are well captured within the framework of deconstruction.

We consider the spectrum of a two-dimensional Pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value. The rate of accumulation of eigenvalues to zero is described in terms of the logarithmic capacity of the support of the electric potential. A connection between these eigenvalues and orthogonal polynomials in complex domains is esta...

We find logarithmic asymptotics of L2-small deviation probabilities for weighted stationary Gaussian processes (both for real and complex-valued) having power-type discrete or continuous spectrum. As in [12], our results are based on the spectral theory of pseudodifferential operators developed by Birman and Solomyak.

The evolution equation for high twist operators is solved in the Double Logarithmic Approximation for cylinder-type diagrams which dominate in the limit of large number of colors. The asymptotic behaviour of the parton correlation function is shown to be determined by the spectrum of the Ising model for a one-dimensional chain of spin-1/2 magnets.

Results of experiments investigating air showers in the energy region of the knee are summarized. The all-particle energy spectrum, the mean logarithmic mass, and the average depth of the shower maximum will be discussed. Spectra for groups of elements from air shower data are compared to results from direct measurements.

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...