Contour dynamics is a classical subject both in physics and in complex analysis. We show that the dynamics provided by the Löwner-Kufarev ODE and PDE possesses a rigid algebraic structure given by the Virasoro algebra. Namely, the ‘positive’ Virasoro generators span the holomorphic part of the complexified vector bundle over the space of univalent functions, smooth on the boundary. In the covar...

To suitably complete an image without seams, block effects, and artifacts, a novel exemplar-based image completion model employing partial differential equation (PDE) is proposed. Firstly, the novel model determines the processing order of exemplar according to a composite function, which is the product of the colour property and structure property in exemplar. Then the exemplar along a geometr...

This study determined whether phosphodiesterase (PDE) was activated by protein kinase C (PKC) upon kappa-receptor stimulation, and if so, to identify the isozyme. We first studied the effects of trans-(+/-)-3,4-dichloro-N-methyl-N-(2-[1-pyrrolidinyl] cyclohexyl) benzeneacetamide methanesulphonate (U50,488H), a selective kappa-opioid receptor (OR) agonist, and phorbol-12-myristate-13-acetate (PM...

The level of phosphodiesterase (PDE) activity is lower in collagenase-isolated human fat cells than in adipose tissue fragments. The inhibition is not species-specific since collagenase also inhibits PDE in rat adipose tissue and bovine heart. In subcellular fractions from isolated fat cells, the PDE activities were lowest in the plasma membrane-enriched fractions and highest in the cytosolic f...

The presented paper is devoted to the study of well-known Hilbert boundary-value problem for semi-linear Beltrami equations with arbitrary boundary data that are measurable respect logarithmic capacity. Namely, we prove here corresponding results on existence, regularity, and representation its nonclassical solutions a geometric interpretation values as angular (along nontangential paths) limit...

We present performance analyses of a fast three-dimensional elliptic orthogonal spline collocation (OSC) method on the Connection Machine CM-5, and various network clusters using the Parallel Virtual Machine (PVM) software package. While the OSC method is an eecient approach for solving Poisson, Helmholtz, and other separable PDE problems, it poses serious challenges for parallel architec-tures...

It is known that one can improve the accuracy of the finite element solution of partial differential equation (PDE) by uniformly refining a triangulation. Similarly, one can uniformly refine a quadrangulation. Recently a refinement scheme of pentagonal partition was introduced in [4]. It is demonstrated that the numerical solution of Poisson equation based on the pentagonal refinement scheme ou...

A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It proved that the has first order of weak convergence. Together with Monte Carlo technique, it can be used numerically solve linear parabolic elliptic PDEs Robin boundary condition. One key results this paper use for computing ergodic limits, i.e. expec...