相关论文: One Parameter Families of Conformal Mappings of Bo…

In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…

We derive a representation formula for harmonic polynomials and Laurent polynomials in terms of densities of the double-layer potential on bounded piecewise smooth and simply connected domains. From this result, we obtain a method for the…

Let $\gamma_1,\gamma_2:[0,T]\to \overline{\mathbb{D}}\setminus\{0\}$ be parametrizations of two slits $\Gamma_1:=\gamma(0,T], \Gamma_2=\gamma_2(0,T]$ such that $\Gamma_1$ and $\Gamma_2$ are disjoint. \\ Let $g_t$ to be the unique normalized…

Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be…

In conformal field theory (CFT) on simply connected domains of the Riemann sphere, the natural conformal symmetries under self-maps are extended, in a certain way, to local symmetries under general conformal maps, and this is at the basis…

The generation of smoother and shorter spiral complete coverage paths in multi-connected domains is a crucial research topic in path planning for robotic cavity machining and other related fields. Traditional methods for spiral path…

We present a new efficient analytical approximation scheme to two-point boundary value problems of ordinary differential equations (ODEs) adapted to the study of the derivative expansion of the exact renormalization group equations. It is…

Inspired by recent advances in the chromosome capture techniques, a method is proposed to study the structural organization of systems of polymers rings with topological constraints.To this purpose, the system is divided into compartments…

The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times…

We implement a version of conformal field theory in a doubly connected domain to connect it to the theory of annulus SLE of various types, including the standard annulus SLE, the reversible annulus SLE, and the annulus SLE with several…

We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has a continuous or homeomorphic extension to the closures of the domains. Our conditions involve the…

We study conformal mappings from the unit disk (or a rectangle) to one-tooth gear-shaped planar domains from the point of view of the Schwarzian derivative, with emphasis on numerical considerations. Applications are given to evaluation of…

We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via…

Parametrized families of PDEs arise in various contexts such as inverse problems, control and optimization, risk assessment, and uncertainty quantification. In most of these applications, the number of parameters is large or perhaps even…

Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization.…

This paper presents a MATLAB toolbox for computing the conformal mapping from a given polygonal multiply connected domain onto a circular multiply connected domain and its inverse. The toolbox can be used for multiply connected domains with…

Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal…

We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by…

A classic result of Brooks, Smith, Stone and Tutte associates to any finite planar network with distinguished source and sink vertices, a tiling of a rectangle by smaller subrectangles whose aspect ratios are given by the conductances of…

This paper works on the structure of infinitely connected Fatou damains of rational maps in terms of Koebe uniformization. Due to the complicated boundary behavior, the existing uniformization results are failed to apply in general. We…