A packing of spherical caps on the surface of a sphere (that is, a spherical code) is called rigid or jammed if it is isolated within the space of packings. In other words, aside from applying a global isometry, the packing cannot be deformed. In this paper, we systematically study the rigidity of spherical codes, particularly kissing configurations. One surprise is that the kissing configurati...

This article reviews the popular reasons for the belief that dwarf elliptical galaxies and (ordinary) elliptical galaxies are distinct and separate species. They include: light–profile shape (or similarly image concentration); the magnitude–central surface brightness diagram; the magnitude–effective surface brightness diagram (or similarly the magnitude–effective radius diagram); and the Fundam...

Commutative algebra of symmetries is not a sufficient condition for the separation of variables. It is necessary for the solvability of system (2) that operators Yμ must meet additional requirements [2]. Let linear differential equation (1) allow a non-Abelian symmetry group G. We shall now investigate the most efficient way how the non-Abelian symmetry group can be used for the integration of ...

Whiteley, W., Weavings, sections and projections of spherical polyhedra, Discrete Applied Mathematics 32 (1991) 275-294. In this paper we give simultaneous answers to three questions: (a) When does a plane picture of lines, weaving over and under in the plane, lift and separate into a configuration of disjoint lines in 3-space? (b) When is a configuration of lines in the plane the cross-section...

Consider the d-dimensional euclidean space E d. Two main results are presented: First, for any N 2 N, the number of types of periodic equivariant tilings (T ; ?) that have precisely N orbits of (2; 4; 6 : : :)-ags with respect to the symmetry group ?, is nite. Second, for any N 2 N, the number of types of convex, periodic equivariant tilings (T ; ?) that have precisely N orbits of tiles with re...

Mariner 6 and 7 ultraviolet spectrometers that flew by Mars in 1969 observed the Lyman-, dayglow of atomic hydrogen. Data in the altitude range 200 to 24,000 km are analyzed to determine the structure of the Martian exosphere. The classical evaporative theory is applied to calculate a hydrogen density distribution. A spherical model of the dayglow Lyman-a emission, using radiative transfer theo...

Algebra Interview 1 The first interview began with Edwards asking “What is mathematics?” By asking follow-up questions as needed, Edwards made sure each student said something about the nature and role of definitions in mathematics. After that introductory discussion, each student was handed the following definition. Binary operations were being studied in class, but the definition of group had...