Weak and Norm Convergence on the Unit Sphere

LAGO on the unit sphere

LAGO is an efficient kernel algorithm designed specifically for the rare target detection problem. However, unlike other kernel algorithms, LAGO cannot be easily used with many domain-specific kernels. We solve this problem by first providing a unified framework for LAGO and clarifying its basic principle, and then applying that principle on the unit sphere instead of in the Euclidean space.

On Weak Statistical Convergence

The main object of this paper is to introduce a new concept of weak statistically Cauchy sequence in a normed space. It is shown that in a reflexive space, weak statistically Cauchy sequences are the same as weakly statistically convergent sequences. Finally, weak statistical convergence has been discussed in l p spaces. under the Creative Commons Attribution License, which permits unrestricted...

Interpolation on the Unit Sphere Ii

The problem of interpolation at (n + 1) 2 points on the unit sphere S 2 by spherical polynomials of degree at most n is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials.

Polynomial Interpolation on the Unit Sphere

Rational Points on the Unit Sphere

The unit sphere, centered at the origin in R, has a dense set of points with rational coordinates. We give an elementary proof of this fact that includes explicit bounds on the complexity of the coordinates: for every point v on the unit sphere in R, and every > 0, there is a point r = (r1, r2, . . . , rn) such that: • ||r− v||∞ < . • r is also a point on the unit sphere; P r i = 1. • r has rat...