A novel method for designing a signature based on the conformal mapping is proposed. Conformal mapping function preserves the local angles of the shape of the object. Schwarz Christoffel mapping transformation is effectively implemented. A conformal transformation of the upper half plane onto the interior of a simple polygon is carried out. The widely used in 2-D potential flow for the computat...

In this article, we extend the definition of Christoffel words to directed subgraphs of the hypercubic lattice in arbitrary dimension that we call Christoffel graphs. Christoffel graphs when d = 2 correspond to well-known Christoffel words. Due to periodicity, the d-dimensional Christoffel graph can be embedded in a (d−1)-torus (a parallelogram when d = 3). We show that Christoffel graphs have ...

A monic Jacobi matrix is a tridiagonal matrix which contains the parameters of the three-term recurrence relation satisfied by the sequence of monic polynomials orthogonal with respect to a measure. The basic Christoffel transformation with shift α transforms the monic Jacobi matrix associated with a measure dμ into the monic Jacobi matrix associated with (x − α)dμ. This transformation is known...

An inversion procedure, based on the methods used in proving Btirmasm’s theorem, is used to provide an integral expression which exhibits the form of the electrostatic field explicitly in terms of the field coordinates. The method is illustrated with an example of a stepped-guide junction. The form of the field and the expression for the mode expansion coefficients are examined. The results are...