We present a short elementary proof of the following Twelve Points Theorem: Let M be a convex polygon with vertices at the lattice points, containing a single lattice point in its interior. Denote by m (resp. m) the number of lattice points in the boundary of M (resp. in the boundary of the dual polygon). Then

We give an elementary proof of Sarason’s solvability criterion for the Nevanlinna-Pick problem with boundary interpolation nodes and boundary target values. We also give a concrete parametrization of all solutions of such a problem. The proofs are based on a reduction method due to Nevanlinna and the fact that reduction of functions corresponds to Schur complementation of the corresponding Pick...

We present a short elementary proof of the following Twelve Points Theorem: Let M be a convex polygon with vertices at the lattice points, containing a single lattice point in its interior. Denote by m (resp. m) the number of lattice points in the boundary of M (resp. in the boundary of the dual polygon). Then

For all affine Toda field theories we propose a new type of generic boundary bootstrap equations, which can be viewed as a very specific combination of elementary boundary bootstrap equations. These equations allow to construct generic solutions for the boundary reflection amplitudes, which are valid for theories related to all simple Lie algebras, that is simply laced and non-simply laced. We ...

Let M be a compact, oriented, irreducible, and boundary incompressible 3–manifold. Assume that its fundamental group is without rank two abelian subgroups and ∂M 6= ∅. We will show that every homomorphism θ: π1(M )→ PSL(2,C) which is not “boundary elementary” is induced by a possibly branched complex projective structure on the boundary of a hyperbolic manifold homeomorphic to M . AMS Classific...

A Planar antenna with Microstrip feed Sierpinski carpet fractal geometry for multiband applications is presented. The multiband behavior is analyzed through two fractal iterations. Self similarity property of fractal technology is applied in the antenna design to reduce the physical size, increase bandwidth and gain. The proposed antenna covers multi bands such as 1.8/5.59/5.78/6.4/6.63/7.84 GH...

In this talk we consider a free boundary problem describing a change of the length of a one-dimensional elastic material. By elementary calculation the free boundary problem is given as the initial boundary value problem for the hyperbolic equation with dynamic boundary condition. Moreover, as the practical example for the elastic material we deal with a new mathematical model for a valve made ...

This paper is second one in the series devoted to the calculation of particle masses in the framework of p-adic conformal field theory limit of Topological GeometroDynamics. The concept of topological condensate generalizes the concept of 3-space in radical manner. The various hierarchically ordered levels of the condensate obey effective p-adic topology and fractal considerations motivate the ...