In this paper, we investigate po-purity using finitely presented S-posets, and give some equivalent conditions under which an S-poset is absolutely po-pure. We also introduce strongly finitely presented S-posets to characterize absolutely pure S-posets. Similar to the acts, every finitely presented cyclic S-posets is isomorphic to a factor S-poset of a pomonoid S by a finitely generated right con...

A set of quantum states is said to be absolutely entangled when at least one state in the remains for any definition subsystems, i.e., choice global reference frame. In this work we investigate properties sets (AESs) pure states. For case a two-qubit system, present sufficient condition detect an AES, and use it construct families $N$ such that $N\ensuremath{-}3$ (the maximal possible number) r...

Eu(3+)-doped mixed rare earth orthophosphates (rare earth = La, Y, Gd) have been prepared by hydrothermal technology, whose crystal phase and microstructure both vary with the molar ratio of the mixed rare earth ions. For La(x)Y(1-x)PO(4): Eu(3+), the ion radius distinction between the La(3+) and Y(3+) is so large that only La(0.9)Y(0.1)PO(4): Eu(3+) shows the pure monoclinic phase. For La(x)Gd...

We introduce a class of real analytic “peaky” potentials for which the corresponding quasiperiodic 1D-Schrödinger operators exhibit, frequencies in set positive Lebesgue measure, both absolutely continuous and pure point spectrum.

Let   a family of monomorphisms in the category A ‎To study mathematical notions in a category  A‎, ‎such as injectivity‎, ‎tensor products‎, ‎flatness‎, ‎with respect to a class M of its (mono)morphisms‎, ‎one should know some of the categorical properties of the pair (A ‎,M ‎)‎. ‎In this paper we take A to be the‎‎category  Pos-S  of S-partially ordered sets  and   to be a particular‎ class o...

We consider the discrete Schrödinger operator H = − Δ + V $$ H=-\Delta +V with a sparse potential and find conditions guaranteeing either existence of wave operators for pair 0 {H}_0=-\Delta or presence dense purely point spectrum on some interval [ λ , ] \left[{\lambda}_0,0\right] < {\lambda}_0<0 .