Conjugacy problem in groups of oriented geometrizable 3-manifolds

The aim of this paper is to show that the fundamental group of an oriented 3-manifold which satisfies Thurston's geometrization conjecture has a solvable conjugacy problem. In other words, for any such 3-manifold M, there exists an algorithm which can decide for any couple of elements u,v of π₁(M) whether u and v are in the same conjugacy class of π₁(M) or not. More topologically, the algorithm decides for any two loops in M, whether they are freely homotopic or not.     

Statistical study of the radiation losses due to surface roughness for a dilectric slab deposited on a metal substrate

This paper presents an original method of analyzing radiation loss from dielectric slab with random wall imperfections. The method is based on Maxwell’s equations under their covariant form written in a non-orthogonal coordinate system. The solution is found by using a perturbation method applied to the smooth surface problem. The statistical characteristics of the radiation intensity, the average value and the probability density function, are analytically determined.