In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that any positive map Λ : Md(C) → Md(C) can be written as the difference between two completely positive maps Λ = Λ1 − Λ2, we propose a possible way to generalize...

We introduce a transport-majorization argument that establishes majorization in the convex order between two densities, based on control of gradient transportation map them. As applications, we give elementary derivations some delicate Fourier analytic inequalities, which turn yield geometric “slicing-inequalities” both continuous and discrete settings. further consequence our investigation pro...

would finally overrule Miranda v. Arizona. After all, beginning in the 1970s, the Justices had gradually narrowed Miranda's reach, and Berkemer seemed to present an enticing opportunity to remove it from the books altogether! That step the Justices did not take. Writing for a unanimous Court,4 Justice Marshall may have held against the defendant, but his opinion reaffirmed a "central principle"...

Miranda and Persson classified all extremal rational elliptic surfaces in characteristic zero. We show that each surface in Miranda and Persson’s classification has an integral model with good reduction everywhere (except for those of type X11( j), which is an exceptional case), and that every extremal rational elliptic surface over an algebraically closed field of characteristic p > 0 can be o...