On certain generalized Gaussian sums

Random Gaussian sums on trees

Let T be a tree with induced partial order . We investigate centered Gaussian processes X = (X t)t∈T represented as X t = σ(t) ∑ v t α(v)ξv for given weight functions α and σ on T and with (ξv)v∈T i.i.d. standard normal. In a first part we treat general trees and weights and derive necessary and sufficient conditions for the a.s. boundedness of X in terms of compactness properties of (T, d). He...

A Note on Artinianess of Certain Generalized

Let ?: R0?R be a ring homomorphism and suppose that a and a0, respectively, are ideals of R and R0 such that is an Artinian ring. Let M and N be two finitely generated R-modules and suppose that (R0,m0) is a local ring. In this note we prove that the R-modules and are Artinian for all integers i and j, whenever and . Also we will show that if a is principal, then the R-modules and ...

On Certain Character Sums over Smooth Numbers

On the Integrity of Certain Fibonacci Sums

[n is an arbitrary natural number, r is an arbitrary (nonzero) real quantity) gives & positive integer k. Since both r and k turn out to be Fibonacci number ratios, the results established in this paper can be viewed as a particular kind of Fibonacci identities that are believed to be new [see (4.7) and (4.8)]. Throughout the paper we shall make use of the following properties of the Fibonacci ...

On the Asymptotic Distribution of Certain Sums