Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order ≤ 4 are a superset of Dupin cyclides and quadrics, and they carry up to six real families of circles. Revisiting the classical approach to these surfaces based on the spherical model of 3D Möbius geometry, we provide computational tools for the identificiation of circle families on ...

In this short note we propose a new method for construction new nice arrangement on the sphere Sd using the spaces of spherical harmonic.

Consider a sequence of point sets on S, where each set X is a spherical ndesign with m points, where m = O(n), and where the spherical distance between points of X is at least λ/ √ m, for some λ common to all sets of the sequence. For each X of such a sequence, the Coulomb energy E(X) is bounded by E(X) 6 1 2 m2 + O(m). The first term and the order of the second term are the same as for the bou...

An L-spherical code is a set of Euclidean unit vectors whose pairwise inner products belong to the set L. We show, for a fixed α, β > 0, that the size of any [−1,−β] ∪ {α}-spherical code is at most linear in the dimension. In particular, this bound applies to sets of lines such that every two are at a fixed angle to each another.

In the context of the p-spin spherical model we show how saddle points of the

We present the results of an empirical study, which investigated the effects of the amount of information and the type of information refuted in refutation texts. The study compared the effects of three refutation texts on elementary school children’s understanding of the scientific concept of the Earth. One text refuted only the belief that the Earth is flat, the second refuted in addition the...

We give a simple lower bound for the dimensions of the families of polynomially constructible spherical codes of given minimal angle ~o, deduced from the analog of the Katsman-Tsfasman-Vl~du!i bound for linear codes. In particulax the supremum rpol of the numbers log 2 CardX/dim X, where X ranges over all polynomially constructible families of spherical codes with ~ _> Ir/3, is such th~.t rpot ...

This paper describes an approach of representing 3D shape by using a set of invariant Spherical Harmonic (SH) coefficients after conformal mapping. Specifically, a genus-zero 3D mesh object is first conformally mapped onto the unit sphere by using a modified discrete conformal mapping, where the modification is based on Möbius Factorization and is aimed at obtaining a canonical conformal mappin...

Two disordered models are considered: spherical model and non-interacting electron gas on lattice. The supersymmetry representation for correlation functions of these models is obtained. Using this representation the conngura-tional averaging can be performed before thermodynamical one and the problem of calculation of conngurationally averaged correlation functions of disordered spherical mode...

A set C of unit vectors in R is called an L-spherical code if x ·y ∈ L for any distinct x, y in C. Spherical codes have been extensively studied since their introduction in the 1970’s by Delsarte, Goethals and Seidel. In this note we prove a conjecture of Bukh on the maximum size of spherical codes. In particular, we show that for any set of k fixed angles, one can choose at most O(d) lines in ...