A bstract We present new asymptotic formulas for the distribution of OPE coefficients in conformal field theories. These involve products four or more and include light-light-heavy as well heavy-heavy-heavy contributions. They are derived from crossing symmetry six higher point functions on plane should be interpreted non-Gaussianities statistical coefficients. begin with a formula arbitrary op...

To nd a global and smooth curve tting, cubic B-Spline method and gathering-line methods are investigated. When segmenting and recognizing a contour curve of character shape, some global method is required. If we want to connect contour curves around a singular point like crossing points, merging separated contours together which lies apart crossing the singular point is necessary. For this purp...

We study the level crossing in the energy spectrum due to Rashba-Dresselhaus spinorbit coupling in nanowires modulated by longitudinal potential. By implementing both an analytical methodology and a numerical technique based on the finite element method (FEM), we show that the level crossing point can be manipulated with the application of spin-orbit coupling in parabolic nanowires. In particul...

The proton spectrum of single crystals of Cu(NOs)2-2 ) Hz0 is studied between 0.3 and 1 OK. Fields up to 47 kOe were applied along the b axis. The field and temperature dependence of the magnetization obtained from these measurements can be described by an interpair exchange coupling zJ'/k = 1.9 OK that generates a transverse ordering below a critical temperature of 0.45 OK. Introduction. Low f...

We focus on the energy landscape of a simple mean-field model glasses and analyze activated barrier-crossing by combining Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in pure spherical p-spin model. select as initial condition one many unstable index-1 saddles vicinity reference local minimu...

The planarization method is the strongest known method to heuristically find good solutions to the general crossing number problem in graphs: starting from a planar subgraph, one iteratively inserts edges, representing crossings via dummy nodes. In the recent years, several improvements both from the practical and the theoretical point of view have been made. We review these advances and conduc...