An algorithm for motion estimation of articulated 3D objects for object–based analysis–synthesis coding (OBASC) is presented. For motion estimation an articulated object is first decomposed automatically into flexibly connected object– components. Each rigid 3D object–component is assumed to be connected to the object by spherical joints. Then, the 3D motion of the largest object–component is e...

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 ...

We show a numerical evidence that a tethered surface model with extrinsic curvature undergoes a first-order crumpling transition between the smooth phase and a nonsmooth phase on triangulated tori. The results obtained in this Letter together with the previous ones on spherical surfaces lead us to conclude that the tethered surface model undergoes a first-order transition on compact surfaces.

We strengthen previously applied polynomial techniques for investigation of spherical designs to obtain new bounds on inner products in some class of designs. This allows further improvements on the best known lower bounds for the minimum possible odd cardinality of designs of odd strength either in small dimensions and in certain asymptotic process.

We consider the period of a simple pendulum in the gravitational field of the spherical Earth. Effectively, gravity is enhanced compared with the often used flat Earth approximation, such that the period of the pendulum is shortened. We discuss the flat Earth approximation, and show when the corrections due to the spherical Earth may be of interest.

Let N(n, t) be the minimal number of points in a spherical t-design on the unit sphere Sn in Rn+1. For each n ≥ 3, we prove a new asymptotic upper bound N(n, t) ≤ C(n)tn , where C(n) is a constant depending only on n, a3 ≤ 4, a4 ≤ 7, a5 ≤ 9, a6 ≤ 11, a7 ≤ 12, a8 ≤ 16, a9 ≤ 19, a10 ≤ 22, and an < n 2 log2 2n, n > 10.

The Milky Way galaxy contains a large, spherical component which is believed to harbor a substantial amount of unseen matter. Recent observations indirectly suggest that as much as half of this "dark matter" may be in the form of old, very cool white dwarfs, the remnants of an ancient population of stars as old as the galaxy itself. We conducted a survey to find faint, cool white dwarfs with la...

Thermodynamics of the multi-component dimerizing hard-sphere Yukawa mixture in the associative mean spherical approximation. Abstract Explicit analytical expressions for Helmholtz free energy, chemical potential , entropy and pressure of the multi-component dimerizing Yukawa hard-sphere fluid are presented. These expressions are written in terms of the Blum's scaling parameter Γ, which follows ...

Penrose’s identification with warp provides the general framework for constructing the continuous form of impulsive gravitational wave metrics. We present the 2-component spinor formalism for the derivation of the full family of impulsive spherical gravitational wave metrics which brings out the power in identification with warp and leads to the simplest derivation of exact solutions. These sol...