Let M be a finite von Neumann algebra with a faithful normal trace τ. Denote by Lp(M)sh the skew-Hermitian part of the non-commutative Lp space associated with (M, τ). Let 1 < p < ∞, z ∈ Lp(M)sh and S be a real closed ...

Based on a fundamental work of R. B. Holmes from 1973, we study differentiability properties of the metric projection onto prox-regular sets. We show that if the set is a nonconvex body with a Cp+1-smooth boundary, then ...

Left invariant metrics induced by the p-norms of the trace in the matrix algebra are studied on the general linear group. By means of the Euler–Lagrange equations, existence and uniqueness of extremal paths for the length ...

Machine Learning is an increasing area over the last few years and it is one of the highlights in Artificial Intelligence area. Nowadays, one of the most studied areas is Semi-supervised learning, mainly due to its ...

For a given Hilbert space H, consider the space of self-adjoint projections P(H). In this paper we study the differentiable structure of a canonical sphere bundle over P(H) given by R={(P,f)∈P(H)×H:Pf=f,‖f‖=1}.We establish ...

As the number and complexity of visualization techniques have grown, it has be come progressively more difficult to make a decision as to which technique to employ for any given situation or application. A particular case ...

Coupling is an interdependence relationship between the modules of object-oriented software. It is a property with the most influence on quality attributes of the object-oriented software. Coupling with high values results ...