There are an increasing number of older installations in use on the Norwegian Continental shelf. Inspections are a key issue in ensuring the safety of an older installation, and the inspection intervals, inspection methods and its reliability are clearly influencing the safety of the installations. Different approaches for updating inspection plans for older installations are considered in orde...

Budapest In this note I will mainly discuss the joint work of Turán and mvself and some of my own results and I do not claim to give a survey of the whole subject. Let-1 c xl <. .. < xn < 1 be n points in (-1, +1). Denote bv_ l k (x) the fundamental functions of Lagrange interpolation, we have n 1, (x) = 0(x)-w(x) = L((x-xk). ~~'(xk)(x-xk~ k=1 n It is well known that the sum 1lk (x) I plays a f...

Abstract. We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very la...

The underlying problem confronting us in this paper is the determination of precise upper bounds for the moduli of the coefficients in these normalized expansions at » for functions in the classes S and T. This problem for the first two coefficients in each class has already been solved. We note first that since 4> and / are inverse, ai= —bx and a2= —b2, so for these two cases, discussion of on...

Abstract: In this article we have elaborated the numerical schemes of reduction methods for approximate solution of system of singular integro-differential equations when the kernel has a weak singularity. The equations are defined on the arbitrary smooth closed contour of complex plane. We suggest the numerical schemes of the reduction method over the system of Faber-Laurent polynomials for th...

Abstract We consider the conductivity problem with a simply connected or multi-coated inclusion in two dimensions. The potential perturbation due to an admits classical multipole expansion whose coefficients are so-called generalized polarization tensors (GPTs). GPTs have been fundamental building blocks problems. In this paper, we present new concept of geometric and its coefficients, named Fa...