Lacunary systems and generalized linear processes

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

On Generalized Difference Lacunary Statistical Convergence

A lacunary sequence is an increasing integer sequence θ = (kr) such that k0 =0, kr−kr−1 →∞ as r →∞. A sequence x is called Sθ(∆)− convergent to L provided that for each ε > 0, limr(kr − kr−1) {the number of kr−1 < k ≤ kr : |∆xk−L| ≥ ε} = 0, where ∆xk = ∆xk− ∆xk+1. The purpose of this paper is to introduce the concept of ∆ − lacunary statistical convergence and ∆-lacunary strongly convergence an...

Generalized Determinantal Point Processes: The Linear Case

A determinantal point process (DPP) over a universe {1, . . . ,m} with respect to an m×m positive semidefinite matrix L is a probability distribution where the probability of a subset S ⊆ {1, . . . ,m} is proportional to the determinant of the principal minor of L corresponding to S. DPPs encapsulate a wide variety of known distributions and appear naturally (and surprisingly) in a wide variety...

on solving linear diophantine systems using generalized rosser's algorithm

Generalized Iterative Methods for augmented linear systems ∗

In this paper we study the solution of large sparse augmented linear systems. The generalized modified extrapolated SOR (GMESOR) method is considered. We find sufficient conditions for GMESOR to converge and determine its optimal iteration parameters and the corresponding minimum value of its convergence factor. Under the assumption that the eigenvalues of a key matrix are real it is shown that...