Weighted Radon transforms for which the Chang approximate inversion formula is precise

We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given

Aspects of the stochastic Burgers equation and their connection with turbulence

We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless state to a structured state dominated by shocks. This transition takes place through an intermediate region where the system exhibits rich multifractal behavior. This is mainly the region of interest to us. We only mention in passing the hydrodynamic limit of forcing confined to large scales, where much work has taken place since that of Polyakov. In order to make the general framework clear, we give an introduction to aspects of isotropic, homogeneous turbulence, a description of Kolmogorov scaling, and, with the help of a simple model, an introduction to the language of multifractality which is used to discuss intermittency corrections to scaling. We continue with a general discussion of the Burgers equation and forcing, and some aspects of three dimensional turbulence where - because of the mathematical analogy between equations derived from the Navier-Stokes and Burgers equations - one can gain insight from the study of the simpler stochastic Burgers equation. These aspects concern the connection of dissipation rate intermittency exponents with those characterizing the structure functions of the velocity field, and the dynamical behavior, characterized by different time constants, of velocity structure functions. We also show how the exponents characterizing the multifractal behavior of velocity structure functions in the above mentioned transition region can effectively be calculated in the case of the stochastic Burgers equation.Comment: 25 pages, 4 figure

Power corrections and perturbative coupling from lattice gauge thoeries

From the analysis of the perturbative expansion of the lattice regularized gluon condensate, toghether with MC data, we present evidence of OPE-unexpected dim-2 power corrections in the scaling behaviour of the Wilson loop. These can be interpreted as an indication that in lattice gauge theories the running coupling at large momentum contains contributions of order Q^2.Comment: 3 pages, 2 figures. Talk given at the Lattice97 conference, Edinburgh, U

Homogeneous singularities inside collapsing wormholes

We analyze analytically and numerically the origin of the singularity in the course of the collapse of a wormhole with the exotic scalar field Psi with negative energy density, and with this field Psi together with the ordered magnetic field H. We do this under the simplifying assumptions of the spherical symmetry and that in the vicinity of the singularity the solution of the Einstein equations depends only on one coordinate (the homogeneous approximation). In the framework of these assumptions we found the principal difference between the case of the collapse of the ordinary scalar field Phi with the positive energy density together with an ordered magnetic field H and the collapse of the exotic scalar field Psi together with the magnetic field H. The later case is important for the possible astrophysical manifestation of the wormholes.Comment: 10 pages, 5 figures each of which has a),b),c),and d) sub-figures. To be published in "Physical review. D, Particles, fields, gravitation, and cosmology

Constraints on Mass Spectrum of Fourth Generation Fermions and Higgs Bosons

We reanalyze constraints on the mass spectrum of the chiral fourth generation fermions and the Higgs bosons for the standard model (SM4) and the two Higgs doublet model (THDM). We find that the Higgs mass in the SM4 should be larger than roughly the fourth generation up-type quark mass, while the light CP even Higgs mass in the THDM can be smaller. Various mass spectra of the fourth generation fermions and the Higgs bosons are allowed. The phenomenology of the fourth generation models is still rich.Comment: 15 pages, 16 figures; some points clarified, references added, to appear in Phys.Rev.