We present a necessary and sufficient condition for a graph of odd-girth 2k + 1 to bound the class of K4-minor-free graphs of odd-girth (at least) 2k + 1, that is, to admit a homomorphism from any such K4-minor-free graph. This yields a polynomial-time algorithm to recognize such bounds. Using this condition, we first prove that every K4-minor free graph of odd-girth 2k+1 admits a homomorphism ...

Since its initial identification in St. Petersburg, Russia, the recombinant hepatitis C virus (HCV) 2k/1b has been isolated from several countries throughout Eurasia. The 2k/1b strain is the only recombinant HCV to have spread widely, raising questions about the epidemiological background in which it first appeared. In order to further understand the circumstances by which HCV recombinants migh...

A k-digraph is a digraph in which every vertex has outdegree at most k. A (k ∨ l)digraph is a digraph in which a vertex has either outdegree at most k or indegree at most l. Motivated by function theory, we study the maximum value Φ(k) (resp. Φ(k, l)) of the arc-chromatic number over the k-digraphs (resp. (k ∨ l)-digraphs). El-Sahili [3] showed that Φ(k, k) ≤ 2k+1. After giving a simple proof o...

We compute certain (2K + 4)–point, one–loop couplings in the type IIA string compactified on K3 × T 2 , which are related to the topologi-cal index Tr(−1) J L +J R J L J R 2K+1 q L 0 q L 0 on this manifold. Their special feature is that they are sensitive to only short and intermediate BPS mul-tiplets. The couplings derive from underlying prepotentials of the form G [2K+4] (T, U) ∼ (∂ V) 2K ln ...

Serological cross-reactivity between the products of the H-2K and H-2D genes has been demonstrated by a design in which antibody was produced against determinants controlled by one locus (e .g . H-2K(k)), and then tested against the product of the opposite locus (e .g . H-2D(d)). A total of 13 out of 18 such test combinations exhibited H-2K-H-2D cross-reactivity. The presence or absence of cros...

In this paper, we characterize the computational power of dynamical systems with piecewise constant derivatives (PCD) considered as computational machines working on a continuous real space with a continuous real time: we prove that piecewise constant derivative systems recognize precisely the languages of the ω th (respectively: ω + 1 th ) level of the hyper-arithmetical hierarchy in dimension...

In this paper, we consider the nonlinear difference equation xn 1 f xn−l 1, xn−2k 1 , n 0, 1, . . . , where k, l ∈ {1, 2, . . . } with 2k / l and gcd 2k, l 1 and the initial values x−α, x−α 1, . . . , x0 ∈ 0, ∞ with α max{l − 1, 2k − 1}. We give sufficient conditions under which every positive solution of this equation converges to a not necessarily prime 2-periodic solution, which extends and ...

We show that if the cardinality of a subset of the (2k− 1)-dimensional vector space over a finite field with q elements is q2k−1− 1 2k , then it contains a positive proportional of all k-simplexes up to congruence. Résumé. Nous montrons que si la cardinalité d’un sous-ensemble de l’espace vectoriel à (2k − 1) dimensions sur un corps fini à q éléments est q2k−1− 1 2k , alors il contient une prop...

We prove that the Duflo-Serganova functor DSx attached to an odd nilpotent element x of osp(m|2n) is semisimple, i.e. sends a semisimple representation M osp(m−2k|2n−2k) where k rank x. closed formula for DSx(L(λ)) in terms arc diagram λ.