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The Kadomtsev-Petviashvili I Equation on the Half-Plane
Kadomtsev-Petviashvili Half-Plane Analysis of PDEs
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2011/9/22
Abstract: A new method for the solution of initial-boundary value problems for \textit{linear} and \textit{integrable nonlinear} evolution PDEs in one spatial dimension was introduced by one of the au...
Travelling Randomly on the Poincaré Half-Plane with a Pythagorean Compass
Random motions Poisson process telegraph process hyperbolic and spherical trigonometry
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2011/9/20
Abstract: A random motion on the Poincar\'e half-plane is studied. A particle runs on the geodesic lines changing direction at Poisson-paced times. The hyperbolic distance is analyzed, also in the cas...
Laplacian growth in the half plane
Laplacian growth half plane
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2010/4/7
We investigate a version of the Laplacian growth problem with zero surface tension in the half plane and find families of self-similar exact solutions.
Convex Functions in a Half-plane
Univalent function Convex function Half-plane
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2008/7/1
The class of convex hydrodynamically normalized functions in a half-plane was introduced by J. Stankiewicz. In this paper we introduce the general class of convex functions in the upper half-plane D (...
Convex Functions in a Half-plane, II
Univalent function Convex function Half-plane
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2008/7/1
In the present paper we obtain new sufficient conditions for the univalence and convexity of an analytic function defined in the upper half-plane. In particular, in the case of hydrodynamically normal...