A two-parameter quantum algebra U qp (u 2) is briefly investigated in this paper. The basic ingredients of a model based on the U qp (u 2) symmetry, the qp-rotator model, are presented in detail. Some general tendencies arising from the application of this model to the description of rotational bands of various atomic nuclei are summarized.

The establishment and maintenance of Epstein-Barr Virus (EBV) latent infection requires distinct viral gene expression programs. These gene expression programs, termed latency types, are determined largely by promoter selection, and controlled through the interplay between cell-type specific transcription factors, chromatin structure, and epigenetic modifications. We used a genome-wide chromati...

Let p be a prime number. Let w2 and w ∗ 2 denote the exponents of approximation defined by Mahler and Koksma, respectively, in their classifications of p-adic numbers. It is well-known that every p-adic number ξ satisfies w∗ 2(ξ) ≤ w2(ξ) ≤ w∗ 2(ξ) + 1, with w∗ 2(ξ) = w2(ξ) = 2 for almost all ξ. By means of Schneider’s continued fractions, we give explicit examples of p-adic numbers ξ for which ...

Exercise 1 (Maximal compact subgroups of G). A lattice in Qp is a finitelygenerated Zp-submodule of Qp that generates Qp as vector space. In particular, it’s free of rank n. Note that G acts transitively on the set of lattices in Qp . (i) Show that K = StabG(Zp ). (ii) Suppose that K ′ is a compact subgroup of G. Show that K ′ stabilises a lattice. (Hint: show that the K ′-orbit of Zp is finite...

For a fairly general reductive group G/Qp , we explicitly compute the space of locally algebraic vectors in the Breuil-Herzig construction Π(ρ)ord, for a potentially semistable Borel-valued representation ρ of Gal(Q̄p/Qp). The point being we deal with the whole representation, not just its socle – and we go beyond GLn(Qp). In the case of GL2(Qp), this relation is one of the key properties of the...