319 research outputs found
A domain decomposition method for conformal mapping onto a rectangle
No full textLet g be the function which maps conformally a simply-connected domain G onto a rectangle R so that four specified points z1, z2, z3, z4,o n ∂G are mapped respectively onto the four vertices
of R. This paper is concerned with the study of a domain decomposition method for computing approximations to g and to an associated domain functional in cases where: (i) G is bounded by two
parallel straight lines and two Jordan arcs. (ii) The four points z1, z2, z3, z4, are the corners where the two straight lines meet the two arcs
Numerical conformal mapping onto a rectangle with applications to the solution of Laplacian problems
No full textLet F be the function which maps conformally a simple-connected domain onto a rectangle R, so that four specified points on are mapped Ω∂respectively onto the four vertices of R. In this paper we consider the problem of approximating the conformal map F, and present a survey of the available numerical methods. We also illustrate the practical significance of the conformal map, by presenting a number of applications involving the solution of Laplacian boundary value problems
Papamichael Anna J. — Birth and Plant symbolism
No full textHaudricourt André-Georges. Papamichael Anna J. — Birth and Plant symbolism. In: Journal d'agriculture traditionnelle et de botanique appliquée, 30ᵉ année, bulletin n°2, Avril-juin 1983. p. 177
Contribution à l'analyse du comportement professionnel de l'enseignante de maternelle en activité de dessin et peinture
No full textPapamichael Yannis. Contribution à l'analyse du comportement professionnel de l'enseignante de maternelle en activité de dessin et peinture. In: Bulletin de psychologie, tome 36 n°362, 1983. Psychologie projective II. pp. 961-964
The use of singular functions for the approximate conformal mapping of doubly-connected domains
No full textLet f be the function which maps conformally a given doubly- connected domain onto a circular annulus. We consider the use of two closely related methods for determining approximations to f of the form
fn (z) = z exp, ⎪⎩⎪⎨⎧⎭⎬⎫Σ−(z)uan1jjj
where {uj} is a set of basis functions. The two methods are respectively a variational method, based on an extremum property of the function
H(z) = f′(z)/f(z) - 1/z,
and an orthononnalization method, based on approximating the function H by a finite Fourier series sum.
The main purpose of the paper is to consider the use of the two methods for the mapping of domains having sharp corners, where corner singularities occur. We show, by means of numerical examples, that both methods are capable of producing approximations of high accuracy for the mapping of such "difficult" doubly-connected domains. The essential requirement for this is that the basis set {uj} contains singular functions that reflect the asymptotic behaviour of the function H in the neighbourhood of each "singular" corner
A domain decomposition method for approximating the conformal modules of long quadrilaterals
No full textThis paper is concerned with the study of a domain decomposition method for
approximating the conformal modules of long quadrilaterals. The method has been studied already by us and also by D Gaier and W K Hayman, but only in connection with a special class of quadrilaterals, viz. quadrilaterals where: (a) the defining domain is bounded by two parallel straight lines and two Jordan arcs, and (b) the four specified boundary points are the four corners where the arcs meet the straight lines.
Our main purpose here is to explain how the method may be extended to a wider class of qua-drilaterals than that indicated above
Asymptotic behaviour of zeros of bieberbach polynomials
No full textAbstractLet Ω be a simply-connected domain in the complex plane and let πn denote the nth-degree Bieberbach polynomial approximation to the conformal map f of Ω onto a disc. In this paper we investigate the asymptotic behaviour (as n→σ) of the zeros of πn, πn′ and also of the zeroes of certain closely related rational approximants to f. Our result show that, in each case, the distribution of the zeros is governed by the location of the singularities of the mapping function f in C⧹ω, and we present numerical examples illustrating this
End conditions for improved cubic spline derivative approximations
No full textAbstractWe consider the problem of deriving accurate end conditions for cubic spline interpolation at equally spaced knots. In particular we derive a number of end conditions which lead to derivative approximations of high accuracy
Pole type singularities and the numerical conformal mapping of doubly-connected domains
No full textLet f be the function which maps conformally a given doubly-connected domain onto a circular annulus, and let Ω
H(z) = f '(z) / f(z) - 1/z .
In this paper we consider the problem of determining the main singularities of the function H in compl)(Ω∂∪Ω. Our purpose is to provide information regarding the location and nature of such singularities, and to explain how this information can be used to improve the efficiency of certain expansion methods for numerical conformal mapping
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