A basic task of exploratory data analysis is the characterisation of “structure” in multivariate datasets. For bivariate Gaussian distributions, natural measures of dependence (the predictive relationship between individual variables) and compactness (the degree of concentration of the probability density function (pdf) around a low-dimensional axis) are respectively provided by ordinary least-...

We establish the consistency of the failure of the diamond principle on a cardinal κ which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of κ in a Radin generic extension.

In this paper, we will use the notion of α-admissible mappings in Banach spaces, to introduce concept Tβ-contractive and establish a fixed point theorem for type contractions. Our theorems generalize improve many results literature. Moreover, apply main result prove existence solution Volterra-integral equation, under more general assumptions than previously made.