On the other hand, whether the Christoffel symbol is the only connection which can be constructed from a symmetric second–rank tensor gμν remains an open question. In this note we exhibit a constructive demonstration of the uniqueness of the Christoffel symbol. Let us start by reviewing some simple results of tensor calculus. Let M be an n–dimensional differentiable manifold. Several geometric ...

We present analytical physics-based compact models for the Schottky barriers at interfaces between organic semiconductor and source drain contacts in thin-film transistors (TFTs) fabricated coplanar staggered device architecture, we illustrate effect of these on current-voltage characteristics TFTs. The model barrier explicitly considers field-dependent lowering due to image charges. Potential ...

We propose Möbius transformations as the natural rotation and scaling tools for editing spherical images. As an application we produce spherical Droste images. We obtain other self-similar visual effects using rational functions, elliptic functions, and Schwarz-Christoffel maps.

We define Markoff words as certain factors appearing in bi-infinite words satisfying the Markoff condition. We prove that these words coincide with central words, yielding a new characterization of Christoffel words.

in this paper, the lorentzian version of beltrami-euler formula is investigated in 1n . initially,the first fundamental form and the metric coefficients of generalized timelike ruled surface are calculated and by the help of the christoffel symbols, riemann-christoffel curvatures are obtained. thus, the curvatures of spacelike and timelike tangential sections of generalized timelike ruled surf...

for transforming Legendre polynomial expansions, but it appears not to generalize to the spherical case. This paper introduces a fast algorithm for obtaining a uniform resolution representation of a function known at a latitude– Swarztrauber [12] has reviewed other transformation algolongitude grid on the surface of a sphere, equivalent to a triangular, rithms. isotropic truncation of the spher...

We present a generalization of multiple orthogonal polynomials of type I and type II, which we call multiple orthogonal polynomials of mixed type. Some basic properties are formulated, and a Riemann-Hilbert problem for the multiple orthogonal polynomials of mixed type is given. We derive a Christoffel-Darboux formula for these polynomials using the solution of the Riemann-Hilbert problem. The m...