We use techniques of Bannai and Sloane to give a new proof that there is a unique (22, 891, 1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a minor error in the uniqueness proof given by Bannai and Sloane for the (23, 4600, 1/3) spherical code.

Observational consequences of a jet-driven supernova (SN) explosion model are presented. The results are compared in detail with optical observations of SN 1998bw associated with a Gamma-Ray Burst. It is shown that the jet model is able to reproduce virtually all the optical observations available for this SN, although a spherical model fails to explain some of observed features. Because of the...

in this work, two parametric l-systems have been introduced to generate the figures of two series of nanostructures. these series consist of different spherical fullerenes with various number of carbon atoms. by specifying a parameter in each series a spherical fullerene can be determined. the members of the first series are c60 , c240 , c540 , c940 ,… which can be produced by applying paramete...

We prove that the D4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S, based on numerical computations suggesting that every 5-design consisting of 24 points in S is in a 3-parameter family (which we describe explicitly, based on a constr...

We use techniques of Bannai and Sloane to give a new proof that there is a unique (22, 891, 1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a minor error in the uniqueness proof given by Bannai and Sloane for the (23, 4600, 1/3) spherical code.

From the view of differential geometry, a straight line is a geometric curve with the curvature κ(s) = 0. A plane curve is a family of geometric curves with torsion τ(s) = 0. Helix is a geometric curve with non-vanishing constant curvature κ and non-vanishing constant torsion τ [4]. The helix may be called a circular helix or W -curve [9]. It is known that straight line (κ(s) = 0) and circle (κ...