In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be used for solving a scattered data interpolation problem on spheres. Since positive definite functions on the sphere were already characterized by Schoenberg some fifty years ago, the issue here is to determine what kind of positive definite functions are act...

In this paper, we show that under a mild condition, principal submodule of the Bergman module on bounded strongly pseudoconvex domain with smooth boundary in Cn is p-essentially normal for all p>n. This improves previous result by first author and K. Wang, which it was shown any polynomial-generated unit ball Bn As consequence, La2(Bn) consisting functions vanishing an analytic subset pure codi...

We use a payment pattern of the type {1k,2k,3k,…} to generalize standard level and increasing annuity polynomial patterns. derive explicit formulas for present value an n-year annuity, m-monthly continuous annuity. also idea extend annuities patterns derived from analytic functions, as well {1r,2r,3r,…}, with r being arbitrary real number. In process, we develop possible approximations k! gamma...

We establish q-analogues of Taylor series expansions in special polynomial bases for functions analytic in bounded domains and for entire functions whose maximum modulus Mðr; f Þ satisfies jln Mðr; f ÞjpA ln r: This solves the problem of constructing such entire functions from their values at 1⁄2aq þ q =a =2; for 0oqo1: Our technique is constructive and gives an explicit representation of the s...

Level-restricted paths play an important rôle in crystal theory. They correspond to certain highest weight vectors of modules of quantum affine algebras. We show that the recently established bijection between Littlewood–Richardson tableaux and rigged configurations is well-behaved with respect to level-restriction and give an explicit characterization of level-restricted rigged configurations....

In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be used for solving a scattered data interpolation problem on spheres. Since positive definite functions on the sphere were already characterized by Schoenberg some fifty years ago, the issue here is to determine what kind of positive definite functions are act...

Smale’s α-theory certifies that Newton iterations will converge quadratically to a solution of a square system of analytic functions based on the Newton residual and all higher order derivatives at the given point. Shub and Smale presented a bound for the higher order derivatives of a system of polynomial equations based in part on the degrees of the equations. For a given system of polynomial-...