We give explicit representation of Neumann boundary value problem for Bitsadze equation on the upper half plane. will also solution inhomogeneous polyanalytic arising from and (n-1) Dirichlet conditions plane H.

Abstract We consider a class of weighted harmonic functions in the open upper half-plane known as α -harmonic functions. Of particular interest is uniqueness problem for such subject to vanishing Dirichlet boundary value on real line and an appropriate condition at infinity. find that non-classical case ( ≠ 0) allows considerably more relaxed infinity compared classical = usual half-plane. The ...

In this paper we study the vertex operator algebra Dch(H,Γ) constructed from fixed points of chiral differential operators on upper half plane which is holomorphic at all cusps, under action a congruence subgroup Γ. To end, introduce an SL(2,R)-invariant filtration labeled by partition pairs and its successive quotient. We show that quotient cuspidal condition isomorphic to space modular forms....

We show that it is possible to extend, in a homomorphic fashion, each quasisymmetric homeomorphism of the real line to a quasi-isometry of the upper-half plane. Epstein and Markovic have recently shown that a homomorphic extension to quasiconformal homeomorphisms of the upper-half plane is not possible.

In this research we have implemented the Random Vortex Method to calculate velocity fields of fluids inside open cavities in both turbulent and laminar flows. the Random Vortex Method is a CFD method (in both turbulent and laminar fields) which needs the Schwarz-Christoffel transformation formula to map the physical geometry into the upper half plane. In some complex geometries like the flow in...

A “fat slit” is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit parameterized by harmonic moments of the latter and show that they obey an infinite set of Lax equations for the dispersionless KP hierarchy. Deformation of a fat ...