The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results.

We calculate the van der Waals friction between two semi-infinite solids in normal relative motion and find a drastic difference in comparison with the parallel relative motion. The case of the good conductors is investigated in details both within the local optic approximation , and using a non-local optic dielectric approach. We show that the friction may increase by many order of magnitude w...

We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are asymtotically free with amalgamation over a subalgebra. Therefore we can define a “rectangular free convolution”, linearized by cumulants and by an analytic integral...

We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically free with amalgamation over a subalgebra. Therefore we can define a “rectangular free convolution”, linearized by cumulants and by an analytic integral...

Susceptibility-weighted imaging (SWI) has continued to develop into a powerful clinical tool to visualize venous structures and iron in the brain and to study diverse pathologic conditions. It is a new art which evaluates and exploits the properties of blood, iron and other tissues. It is a magnitude or filtered phase images or combination of both, obtained with high-resolution 3D fully velocit...

Susceptibility-weighted imaging (SWI) has continued to develop into a powerful clinical tool to visualize venous structures and iron in the brain and to study diverse pathologic conditions. It is a new art which evaluates and exploits the properties of blood, iron and other tissues. It is a magnitude or filtered phase images or combination of both, obtained with high-resolution 3D fully velocit...

Susceptibility-weighted imaging (SWI) has continued to develop into a powerful clinical tool to visualize venous structures and iron in the brain and to study diverse pathologic conditions. It is a new art which evaluates and exploits the properties of blood, iron and other tissues. It is a magnitude or filtered phase images or combination of both, obtained with high-resolution 3D fully velocit...