Vertex Covering by Paths on Trees with applications in machine translation is the task to cover all vertices of a tree T = (V,E) by choosing a minimum-weight subset of given paths in the tree. The problem is NP-hard and has recently been solved by an exact algorithm running in O(4 · |V |2) time, where C denotes the maximum number of paths covering a tree vertex. We improve this running time to ...

Given five positive integers v,m, k, λ and t where v > k > t and v > m > t, a t-(v, k,m, λ) general covering design is a pair (X,B) where X is a set of v elements (called points) and B a multiset of k-subsets of X (called blocks) such that every m-subset of X intersects (is covered by) at least λ members of B in at least t points. In this article we present new constructions for general coverin...

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

List homomorphisms generalize list colourings in the following way: Given graphs G; H , and lists L(v) V (H); v 2 V (G), a list homomorphism of G to H with respect to the lists L is a mapping f : V (G) ! V (H) such that uv 2 E (G) implies f (u)f(v) 2 E (H), and f (v) 2 L(v) for all v 2 V (G). The list homomorphism problem for a xed graph H asks whether or not an input graph G together with list...

We present V and I CCD photometry of suspected low-surface brightness dwarf galaxies detected in a survey covering ∼ 2.4 deg2 around the central region of the Dorado group of galaxies. The low-surface brightness galaxies were chosen based on their sizes and magnitudes at the limiting isophote of 26.0Vμ. The selected galaxies have magnitudes brighter than V ≈ 20 (MV ≈ −11 for an assumed distance...

this study is aimed to evaluate the effect of covering exposed root surface by collagen membrane and to compare this method with coronoally advanced flap covering. 26 teeth in 20 patients (12m/8f) with miller1 gingival recession were selected. 14 teeth were allocated into test group and 12 teeth in control group. following first phase of treatment, clinical parameters including the height and w...

Let V be a standard subspace in the complex Hilbert space H and U : G \to U(H) unitary representation of finite dimensional Lie group. We assume existence an element h algebra such that U(exp th) is modular group involution J_V normalizes U(G). want to determine semigroup $S_V = \{ g\in U(g)V \subseteq V\}.$ In previous work we have seen its infinitesimal generators span on which ad defines 3-g...

Elven, E., Bachmann, L. & Gusarov V. I. (2012) Molecular phylogeny of the Athetini-Lomechusini-Ecitocharini clade of aleocharine rove beetles (Insecta). -Zoologica Scripta, 41, 617-636.It has previously been shown that the Aleocharinae tribes Athetini and Lomechusini form a well-supported clade, which also includes the small Neotropical tribe Ecitocharini. However, neither Athetini nor Lomechus...

A covering array CA(N; t, k, v) is an N × k array such that every N × t sub-array contains all t-tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used in experiments to screen for interactions among t-subsets of k components. Strength two covering arrays have been studied from numerous viewpoints, resulting in a variety of computational, direct, and...