Conformal mapping of the unit circle or of the upper half plane onto a polygon

Computing ◽  
1983 ◽  
Vol 31 (2) ◽  
pp. 155-172 ◽  
Author(s):  
W. Prochazka
Keyword(s):  
Conformal Mapping ◽  
Unit Circle ◽  
Half Plane ◽  
Upper Half Plane

A Point Dislocation Interacting with an Elliptical Hole Located at a Bi-Material Interface

2012 ◽  
Vol 151 ◽  
pp. 75-79 ◽  
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe ◽  
P.B.N. Prasad
Keyword(s):  
Conformal Mapping ◽  
Unit Circle ◽  
Half Plane ◽  
Elliptical Hole ◽  
Mapping Function ◽  
Complex Stress ◽  
Complex Variables ◽  
Material Interface ◽  
Rational Mapping ◽  
Point Dislocation

The problem of a point dislocation interacting with an elliptical hole at the interface of two bonded half-planes is studied. Complex stress potentials are obtained by applying the methods of complex variables and conformal mapping. A rational mapping function that maps a half plane with a semi-elliptical notch onto a unit circle is used for mapping the bonded half-planes. The solution derived can serve as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

scholarly journals On Tangential Principal Cluster Sets of Normal Meromorphic Functions

1970 ◽  
Vol 40 ◽  
pp. 133-137 ◽  
Author(s):  
Theodore A. Vessey
Keyword(s):  
Meromorphic Function ◽  
Conformal Mapping ◽  
Finite Order ◽  
Real Axis ◽  
Half Plane ◽  
Meromorphic Functions ◽  
The Family ◽  
Normal Meromorphic Function ◽  
Upper Half Plane ◽  
Principal Cluster

Let w = f(z) be a normal meromorphic function defined in the upper half plane U = {Im(z) >0}. We recall that a meromorphic function f(z) is normal in U if the family {f(S(z))}, where z′ = S(z) is an arbitrary one-one conformal mapping of U onto U, is normal in the sense of Montel. It is the purpose of this paper to state some results on the behavior of f(z) on curves which approach a point x0 on the real axis R with a fixed (finite) order of contact q at x0.

scholarly journals On Complex Explicit Formulae Connected with the Möbius Function of an Elliptic Curve

2014 ◽  
Vol 57 (2) ◽  
pp. 381-389
Author(s):  
Adrian Łydka
Keyword(s):  
Functional Equation ◽  
Meromorphic Function ◽  
Elliptic Curve ◽  
Explicit Formula ◽  
Half Plane ◽  
Complex Plane ◽  
Möbius Function ◽  
Mobius Function ◽  
Upper Half Plane ◽  
Explicit Formulae

AbstractWe study analytic properties function m(z, E), which is defined on the upper half-plane as an integral from the shifted L-function of an elliptic curve. We show that m(z, E) analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for m(z, E) in the strip |ℑz| < 2π.

Exact determination of gravity stresses in finite elastic slopes: Part I. Theoretical considerations

1983 ◽  
Vol 20 (1) ◽  
pp. 47-54 ◽  
Author(s):  
V. Silvestri ◽  
C. Tabib
Keyword(s):  
Plane Strain ◽  
Half Plane ◽  
Inclination Angle ◽  
Complex Variable ◽  
Earth Pressure ◽  
Exact Distributions ◽  
Exact Determination ◽  
Upper Half Plane ◽  
Theoretical Considerations

The exact distributions of gravity stresses are obtained within slopes of finite height inclined at various angles, −β (β = π/2, π/3, π/4, π/6, and π/8), to the horizontal. The solutions are obtained by application of the theory of a complex variable. In homogeneous, isotropic, and linearly elastic slopes under plane strain conditions, the gravity stresses are independent of Young's modulus and are a function of (a) the coordinates, (b) the height, (c) the inclination angle, (d) Poisson's ratio or the coefficient of earth pressure at rest, and (e) the volumetric weight. Conformal applications that transform the planes of the various slopes studied onto the upper half-plane are analytically obtained. These solutions are also represented graphically.

scholarly journals Revisiting the Siegel upper half plane II

2004 ◽  
Vol 376 ◽  
pp. 45-67 ◽  
Author(s):  
Pedro J. Freitas ◽  
Shmuel Friedland
Keyword(s):  
Half Plane ◽  
Upper Half Plane
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