It is known that the so-called Bercovici-Pata bijection can be explained in terms of certain Hermitian random matrix ensembles (Md)d≥1 whose asymptotic spectral distributions are free infinitely divisible. We investigate Hermitian Lévy processes with jumps of rank one associated to these random matrix ensembles introduced in [6] and [10]. A sample path approximation by covariation processes for...

Let G be a locally compact Abelian topological group having a countable basis of its topology. We also suppose that G has the T0–property, that is, ⋂ U∈Ne U = {e}, where e denotes the identity element of G and Ne is the collection of all Borel neighbourhoods of e. (By a Borel neighbourhood U of e we mean a Borel subset of G for which there exists an open subset Ũ of G such that e ∈ Ũ ⊂ U.) Let ...

What is the set of p~, ib le s'aines ~d" a n~asnremem error? In the majority of practical applications, an error is caused m~ 1~, a single cause; it is camaL.d by. a large mtmber of inclependent causes, each of which adds a small O.nlxment to the t(aal error. This fact is widely used in v, atistics: Namely, since it is known that the distlilxltitm ~d" the snm o( many independent stnali random v...

Knowledge to execute wild conceptual mathematical computations helped immensely even out of the park. Knowing these quick calculations has been great interest ever since. Divisibility tests were required know whether a number (large enough) was divisible by given integer or not? Let 0,m  and be any integer. The symbol, mod , am used represent residue when divided m. In this piece treatised wor...

Directed Acyclic Graph(DAG) could be used for modeling subsumption hierarchies. Several labeling schemes have been proposed or tailored for indexing DAG in order to efficiently explore relationships in such hierarchy. However few of them can satisfy all the requirements in response time, space, and effect of updates simultaneously. In this paper, the prime number labeling scheme is extended for...