We compare the Chen-Ruan cohomology ring of the weighted projective spaces P(1, 3, 4, 4) and P(1, ..., 1, n) with the cohomology ring of their crepant resolutions. In both cases, we prove that the Chen-Ruan cohomology ring is isomorphic to the quantum corrected cohomology ring of the crepant resolution after suitable evaluation of the quantum parameters. For this, we prove a formula for the Gro...

We begin by shortly recalling a generalized mean value inequality for subharmonic functions, and two applications of it: first a weighted boundary behavior result (with some new references and remarks), and then a borderline case result to Suzuki’s nonintegrability results for superharmonic and subharmonic funtions. The main part of the talk consists, however, of partial improvements to Blanche...

A weighted-norm least-squares method is considered for the numerical approximation of solutions that have singularities at the boundary. While many methods suffer from a global loss of accuracy due to boundary singularities, the least-squares method can be particularly sensitive to a loss of regularity. The method we describe here requires only a rough lower bound on the power of the singularit...

Many types of point singularity have a topological index, or ‘charge’, associated with them. For example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple zero, enabling the zeros to be assigned charges of ±1. In random fields we can define a correlation function for the charge-weighted density of singularities....

We recall L-shapes, which are minimal distance diagrams, related to weighted 2-Cayley digraphs, and we give the number and the relation between minimal distance diagrams related to the same digraph. On the other hand, we consider some classes of numerical semigroups useful in the study of curve singularity. Then, we associate L-shapes to each numerical 3-semigroup and we describe some main inva...

An initial startupmethod for a spacecraft actuated by a pyramidal arrangement of variable-speed controlmoment gyroscopes is developed. The method provides closed-loop internal momentum tracking control to enable the flywheels to start from rest and reach desired wheel speeds. The proposed controller functioning as a variable-speed control moment gyroscope steering law is developed in terms of t...

We associate to a regular system of weights a weighted projective line over an algebraically closed field of characteristic zero in two different ways. One is defined as a quotient stack via a hypersurface singularity for a regular system of weights and the other is defined via the signature of the same regular system of weights. The main result in this paper is that if a regular system of weig...

In this paper, we consider a convex function defined as 1D-regularized total variation with nonhomogeneous coefficients, and prove the Main Theorem concerned decomposition of subdifferential to weighted singular diffusion linear regular diffusion. The will be enhance previous regularity result for quasilinear equation singularity, moreover, it provide some useful information in advanced mathema...