A direct application of Zorn’s lemma gives that every Lipschitz map f : X ⊂ Qp → Qp has an extension to a Lipschitz map f̃ : Qp → Qp . This is analogous to, but easier than, Kirszbraun’s theorem about the existence of Lipschitz extensions of Lipschitz maps S ⊂ Rn → R`. Recently, Fischer and Aschenbrenner obtained a definable version of Kirszbraun’s theorem. In this paper, we prove in the p-adic ...

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of infinite families of QP codes which includes all binary, ternary and quaternary codes known to is. We continue further with a list of sporadic examples of binary ...

Let Qp be an algebraic closure of Qp and C its p-adic completion. Let K be a finite extension of Qp contained in Qp and set GK = Gal(Qp/K). A Qp-representation (resp. a C-representation) of GK is a finite dimensional Qp-vector space (resp. C-vector space) equipped with a linear (resp. semi-linear) continuous action of GK . A banach representation of GK is a topological Qp-vector space, whose to...

For a linear group G acting on an absolutely irreducible variety X over Q, we describe the orbits of X(Qp) under G(Qp) and of X(Fp((t))) under G(Fp((t))) for p big enough. This allows us to show that the degree of a wide class of orbital integrals over Qp or Fp((t)) is ≤ 0 for p big enough, and similarly for all finite field extensions of Qp and Fp((t)).

For a linear group G acting on an absolutely irreducible variety X over Q, we describe the orbits of X(Qp) under G(Qp) and of X(Fp((t))) under G(Fp((t))) for p big enough. This allows us to show that the degree of a wide class of orbital integrals over Qp or Fp((t)) is ≤ 0 for p big enough, and similarly for all finite field extensions of Qp and Fp((t)).

The ideals of the ring Zp are {0} and pZp, n ≥ 0. From this it follows that Zp is a discrete valuation ring, a principal ideal domain with exactly one maximal ideal, namely pZp; Zp is the valuation ring of Qp with the valuation vp. For n ≥ 1, Zp/pZp is isomorphic as a ring with Z/pZ. |x|p = p−vp(x), dp(x, y) = |x− y|p. With the topology induced by the metric dp, Qp is a locally compact abelian ...

This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very “varied” class of problems, comprising sub-classes of problems ranging from trivial to undecidable. Solution methods for QP are very diverse, ranging from entirely co...

A nonrigid rotor model is developed from the two-parameter quantum algebra U qp (u 2). [This model presents the U qp (u 2) symmetry and shall be referred to as the qp-rotor model.] A ro-tational energy formula as well as a qp-deformation of E2 reduced transition probabilities are derived. The qp-rotor model is applied (through fitting procedures) to twenty rotational bands of superdeformed nucl...

Like most photosynthetic organisms, cyanobacteria are vulnerable to fluctuations in light intensity, which can damage their machinery. To protect against this, they use a photoprotective mechanism called non-photochemical quenching (NPQ), where excess absorbed photo-energy is dissipated as heat. In cyanobacteria, activation of Orange Carotenoid Protein (OCP) the critical first step NPQ response...