A sharp base B is a base such that whenever (Bi)i<ω is an injective sequence from B with x ∈ i<ω Bi, then { ⋂ i<n Bi : n < ω} is a base at x. Alleche, Arhangel’skĭı and Calbrix asked: if X has a sharp base, must X × [0, 1] have a sharp base? Good, Knight and Mohamad claimed to construct an example of a Tychonoff space P with a sharp base such that P × [0, 1] does not have a sharp base. However,...

Experimental studies have shown that some proteins exist in two alternative native-state conformations. It has been proposed that such bi-stable proteins can potentially function as evolutionary bridges at the interface between two neutral networks of protein sequences that fold uniquely into the two different native conformations. Under adaptive conflict scenarios, bi-stable proteins may be of...

We describe all possible ways of bi-ordering Thompson group F: its space of bi-orderings is made up of eight isolated points and four canonical copies of the Cantor set.

We describe all possible ways of bi-ordering Thompson group F: its space of bi-orderings is made up of eight isolated points and four canonical copies of the Cantor set.

For Ω a Polish space we consider operator semigroups on the space Cb(Ω) of bounded, continuous functions and on the space M (Ω) of bounded Borel measures. The important fact here is that the dual of Cb(Ω) with the strict topology is M (Ω). We pursue the approach via bi-continuous semigroups, but we also show that the class of bi-continuous semigroups on Cb(Ω) with respect to the compact-open to...

Dicaesium bis-muth(III) phosphate(V) tungstate(VI), Cs(2)Bi(PO(4))(WO(4)), has been synthesized during complex investigation in a molten pseudo-quaternary Cs(2)O-Bi(2)O(3)-P(2)O(5)-WO(3) system. It is isotypic with K(2)Bi(PO(4))(WO(4)). The three-dimensional framework is built up from [Bi(PO(4))(WO(4))] nets, which are organized by adhesion of [BiPO(4)] layers and [WO(4)] tetra-hedra above and ...

Definition of bi-supra topological space via graph theory was introduced in this study. We also studied some concepts related bi supra-topological theory. "At least many theorems were proofed as a characterization and examples to explain the subject".

Abstract. We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time transformations, we combine these one-dimensional spinors into bi-dimensional column vectors. From the transformation properties of the two-component ...