In this paper we investigate the approximation of a class of parabolic partial differential equations on the unit spheres S n ⊂ R n+1 using spherical basis functions. Error estimates in the Sobolev norm are derived.

Traditionally, optimality and uniqueness of an (n, N, t) spherical code is proved using linear programming bounds. However, this approach does not apply to the parameter (4, 10, 1/6). We use semidefinite programming bounds instead to show that the Petersen code (which are the vertices of the 4dimensional second hypersimplex or the midpoints of the edges of the regular simplex in dimension 4) is...

We developed an open source software for crustal strain analysis using the least-squares collocation method based on the spherical model of the earth. The software is able to simultaneously determine the signal and noise of the velocities at the observation points with the best possible removal of the observational errors, or at any other position with no velocity observation. Furthermore, the ...

In this paper we describe a new approach to programming which generalizes object-oriented programming. It is based on using a new programming construct, called concept, which generalizes classes. Concept is defined as a pair of two classes: one reference class and one object class. Each concept has a parent concept which is specified using inclusion relation generalizing inheritance. We describ...

In this column, the author outlines some of the results of the Listening to Mothers Survey, conducted by the Maternity Center Association, and the implications of the results on childbirth education.

We consider the problem of identifying the worst case dependence structure of a portfolio X1, . . . ,Xn of d-dimensional risks, which yields the largest risk of the joint portfolio. Based on a recent characterization result of law invariant convex risk measures the worst case portfolio structure is identified as a μ-comonotone risk vector for some worst case scenario measure μ. It turns out tha...

New spherical codes called laminated spherical codes are constructed in dimensions 2–49 using a technique similar to the construction of laminated lattices. Each spherical code is recursively constructed from existing spherical codes in one lower dimension. Laminated spherical codes outperform the best known spherical codes in the minimum distance sense for many code sizes. The density of a lam...

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...

in this research, the effect of the first order magnetic field on the ground-state of a centered hydrogenic donor impurity in a gaas/alas spherical quantum dot has been calculated. the perturbation method has been used within the framework of effective mass approximation for these calculations. overall, the analysis shows that a proper choice of quantum dot radius and magnetic field can signifi...

In this paper we construct the supersymmetric tensor hierarchy of N=1, d=4 supergravity. We find some differences with the general bosonic construction of 4dimensional gauged supergravities. The global symmetry group of N = 1, d = 4 supergravity consists of three factors: the scalar manifold isometry group, the invariance group of the complex vector kinetic matrix and the U(1) R-symmetry group....