In 1986 A. Ancona showed, using the Koebe one-quarter Theorem, that for a simply-connected planar domain the constant in the Hardy inequality with the distance to the boundary is greater than or equal to 1/16. In this paper we consider classes of domains for which there is a stronger version of the Koebe Theorem. This implies better estimates for the constant appearing in the Hardy inequality. ...

Using Mazur’s theorem on torsions of elliptic curves, an upper bound 24 for the order finite Galois group ℋ associated with weighted walks in quarter plane ℤ + 2 is obtained. The explicit criterion to have 4 or 6 rederived by simple geometric arguments. division polynomials, a recursive 4m 4m+2 also As corollary, 8 given through method simpler than existing one.

The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop tools that address the question: does a quantum version of the PCP theorem hold? The story of this study starts with classical complexity and takes unexpecte...

This paper utilizes the method of extremal length to study several diameter problems for functions conformal outside of a disc centered at the origin, with a standard normalization, which possess a quasiconformal extension to a ring subdomain of this disc. Known results on the diameter of a complementary component of the image domain of a univalent function are extended. Applications to the tra...

This essay relates to a recent article of Koblitz&Menezes that “criticizes several typical ‘provable security’ results” and argues that the “theorem-proof paradigm of theoretical mathematics is often of limited relevance” to cryptography. Although it should be obvious that these claims are utterly wrong, we undertake articulating this triviality. In particular, we point out some of the fundamen...

introduction after the rapid population growth in the iranian cities, these cities have experienced great changes. the physical structures of the cities are eroded and the managers have no attention to them. many immigrants entered the cities  have dwelled in the inefficient urban textures like in the marginal areas and old textures. thus, the environmental quality of place has been weak. undes...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...