Classical function theory, operator dilation theory, and machine computation on multiply-connected domains

2008 ◽  
Vol 191 (892) ◽  
pp. 0-0 ◽  
Author(s):  
Jim Agler ◽  
John Harland ◽  
Benjamin J. Raphael
Keyword(s):  
Function Theory ◽  
Multiply Connected Domains ◽  
Machine Computation ◽  
Multiply Connected ◽  
Dilation Theory ◽  
Classical Function ◽  
Theory Operator

scholarly journals CONFORMAL SLIT MAPS IN APPLIED MATHEMATICS

2012 ◽  
Vol 53 (3) ◽  
pp. 171-189 ◽  
Author(s):  
DARREN CROWDY
Keyword(s):  
Special Function ◽  
Function Theory ◽  
Applied Mathematics ◽  
Building Blocks ◽  
Review Article ◽  
Multiply Connected Domains ◽  
Multiply Connected ◽  
Mathematical Problems ◽  
Explicit Formulae ◽  
Prime Function

AbstractConformal slit maps play a fundamental theoretical role in analytic function theory and potential theory. A lesser-known fact is that they also have a key role to play in applied mathematics. This review article discusses several canonical conformal slit maps for multiply connected domains and gives explicit formulae for them in terms of a classical special function known as the Schottky–Klein prime function associated with a circular preimage domain. It is shown, by a series of examples, that these slit mapping functions can be used as basic building blocks to construct more complicated functions relevant to a variety of applied mathematical problems.

Conformal and Quasiconformal Mappings of Close Multiply-Connected Domains

2002 ◽  
Vol 9 (2) ◽  
pp. 367-382
Author(s):  
Z. Samsonia ◽  
L. Zivzivadze
Keyword(s):  
Integral Equations ◽  
Quasiconformal Mappings ◽  
Multiply Connected Domains ◽  
Multiply Connected

Abstract Doubly-connected and triply-connected domains close to each other in a certain sense are considered. Some questions connected with conformal and quasiconformal mappings of such domains are studied using integral equations.

scholarly journals Eigenvalues of the negative Laplacian for arbitrary multiply connected domains

1996 ◽  
Vol 19 (3) ◽  
pp. 581-586
Author(s):  
E. M. E. Zayed
Keyword(s):  
Boundary Conditions ◽  
Spectral Function ◽  
Three Dimensions ◽  
Bounded Domains ◽  
Multiply Connected Domains ◽  
Multiply Connected ◽  
Asymptotic Formulae ◽  
Negative Laplacian

The purpose of this paper is to derive some interesting asymptotic formulae for spectra of arbitrary multiply connected bounded domains in two or three dimensions, linked with variation of positive distinct functions entering the boundary conditions, using the spectral function∑k=1∞{μk(σ1,…,σn)+P}−2asP→∞. Further results may be obtained.

Conformal parameterization for multiply connected domains: combining finite elements and complex analysis

2013 ◽  
Vol 30 (4) ◽  
pp. 441-455 ◽  
Author(s):  
Everett Kropf ◽  
Xiaotian Yin ◽  
Shing-Tung Yau ◽  
Xianfeng David Gu
Keyword(s):  
Finite Elements ◽  
Complex Analysis ◽  
Multiply Connected Domains ◽  
Multiply Connected

Shape Interrogation by Medial Axis Transform

1990 ◽  
Author(s):  
N. M. Patrikalakis ◽  
H. N. Gursoy
Keyword(s):  
Finite Element ◽  
Medial Axis ◽  
Multiply Connected Domains ◽  
Medial Axis Transform ◽  
Curved Boundaries ◽  
Multiply Connected ◽  
Maximum Thickness ◽  
Surface Patches ◽  
Geometric Representations ◽  
Shape Characteristics

Abstract In this paper we develop a new interrogation method based on the medial axis transform to extract some important global shape characteristics from geometric representations. These shape characteristics include constrictions, maximum thickness points, and associated length scales; isolation of holes and their proximity information; and a set of topologically simple subdomains decomposing a complex domain. The algorithm we develop to compute the medial axis transform of planar multiply connected shapes with curved boundaries can automatically identify these characteristics. Higher level algorithms for generation of finite element meshes of planar multiply connected domains, adaptive triangulation and approximation of trimmed curved surface patches and other engineering applications using the medial axis transform are also discussed.

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