Related papers: An Introduction to Inversion in an Ellipse
An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian…
We introduce a class of iterated integrals that generalize multiple polylogarithms to elliptic curves. These elliptic multiple polylogarithms are closely related to similar functions defined in pure math- ematics and string theory. We then…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
We study monotonicity and convexity properties of functions arising in the theory of elliptic integrals, and in particular in the case of a Schwarz-Christoffel conformal mapping from a half-plane to a trapezoid. We obtain sharp monotonicity…
We present a detailed error analysis of Ramanujan's most accurate approximation to the perimeter of an ellipse.
Envelopes of parameterized families of plane curves is an important topic, both for the mathematics involved and for its applications. Nowadays, it is generally studied in a technology-rich environment, and automated methods are developed…
We reconsider the Euclidean version of the photon number integral introduced in ref 1. This integral is well defined for any smooth non-self-intersecting curve in $\R^N$. Besides studying general features of this integral (including it s…
The recent literature shows a renewed interest, with various independent approaches, in the classical models for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore…
In this paper we consider the plane elliptic motion which occurs if the moving centrode is a circle of radius $r$ and the fixed centrode a circle of radius $2r$. Every point of the moving plane generates an ellipse in the fixed plane. Let a…
Abelian integrals arise in the mathematical description of various physical processes. According to Abel's theorem these integrals are related to motion of a set of points along a plane curve around fixed points, which are relatively little…
We introduce a class of functions which constitutes an obvious elliptic generalization of multiple polylogarithms. A subset of these functions appears naturally in the \epsilon-expansion of the imaginary part of the two-loop massive sunrise…
The main objective of this article is to study several generalizations of the reverse order law for the Moore-Penrose inverse in ring with involution.
We discuss elliptic Pl\"ucker transformations of three-dimensional elliptic spaces. These are permutations on the set of lines such that any two related (orthogonally intersecting or identical) lines go over to related lines in both…
We investigate the subclass of reversible functions that are self-inverse and relate them to reversible circuits that are equal to their reverse circuit, which are called palindromic circuits. We precisely determine which self-inverse…
The description of many dynamical problems like the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of a holomorphic hyperelliptic integral. The result of the inversion is…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
Consider the scenario, in which human civilization undergoes periodic eras of progression and regression, and consequently, changes in cosmological knowledge are cyclic. There exist solutions of general theory of relativity, such as the…
The $n$ integrals in involution for the motion on the $n$-dimensional ellipsoid under the influence of a harmonic force are explicitly found. The classical separation of variables is given by the inverse momentum map. In the quantum case…
Following a recent paper by N. Mandache (Inverse Problems 17 (2001), pp. 1435-1444), we establish a general procedure for determining the instability character of inverse problems. We apply this procedure to many elliptic inverse problems…
Based on the distinction between the covariant and contravariant metric tensor components in the framework of the affine geometry approach and also on the choice of the contravariant components, it was shown that a wide variety of third,…