Sentence examples for variables which generalize from inspiring English sources

We study the addition problem for strongly matricially free random variables which generalize free random variables.

Some nonlinear weakly singular integral inequalities in two variables which generalize some known results are discussed.

The main purpose of this paper is to study strong convergence results for weighted sums of pairwise NQD random variables, which generalize the previous known results for negatively associated random variables and negatively orthant dependent random variables, such as those of Wang et al. [10, 11].

The concept of NSD random variables, which generalizes the concept of NA, was proposed by Hu [1].

In addition, we will study the strong stability for weighted sums of ψ-mixing random variables, which generalizes the corresponding one of independent random variables.

We will further study the strong stability for weighted sums of ψ-mixing random variables, which generalizes corresponding one of independent sequences.

By introducing an auxiliary function of two variables and using Riccati transformation, several Kamenev type interval oscillation criteria are established, which generalize and extend some known ones, such as those of Huang and Feng.

In addition, the strong stability for weighted sums of ψ-mixing random variables is studied, which generalizes the corresponding one of independent random variables.

The main purpose of this work is to further study the complete convergence for weighted sums of arrays of rowwise NSD random variables without identical distribution, which generalizes and improves some known results of random variables.

The purpose of the present paper is to establish a recurring mean inequality, which generalizes the mean inequality of two random variables to random variables.

To our knowledge, the current state-of-the-art MDR-related method that can accommodate nuclear families of any size and different types of outcome variables is the recently proposed Pedigree-based Generalized MDR method [35] (PGMDR) which generalizes the Generalized MDR method [36] (GMDR) to family data.