This paper is concerned with the discrete spectra of Schrödinger operators H = −∆ + V, where V (r) is an attractive potential in N spatial dimensions. Two principal results are reported for the bottom of the spectrum of H in each angular-momentum subspace Hl : (i) an optimized lower bound when the potential is a sum of terms V (r) = V (r) + V (r) , and the bottoms of the spectra of −∆+V (r) and...

A graph G is claw-free if no induced subgraph of it is isomorphic to the complete bipartite graph K1,3, and it is prime if |V (G)| ≥ 4 and there is no X ⊆ V (G) with 1 < |X| < |V (G)| such that every vertex of V (G) \X with a neighbour in X is adjacent to every x ∈ X. A simplicial clique in G is a non-empty clique K, such that for every k ∈ K the set of neighbours of k in V (G) \K is a clique. ...

economics has hit the mainstream in the last decade with popular books like freakonomics and the undercover economist reaching the masses. these authors have used their toolkits far beyond the narrow scope of money and finance and answered questions pertaining to anything from social policy to demographics to crime. their appeal has largely been their ability to explain that small underlying fo...

A bicolorable STS(v) is a Steiner triple system whose vertices are colored in such way that every block receives precisely two colors. A k-bicoloring of a STS is a vertex coloring using each of k colors, and the feasible set Ω is a set of integers k for which k-bicolorings exist. In this paper, we study feasible sets of STS(v)s of all orders v < 50.

When we are learning people’s preferences the training material can be expressed as in regression problems: the description of each object is then followed by a number that assesses the degree of satisfaction. Alternatively, training examples can be represented by preference judgments: pairs of vectors (v, u) where someone expresses that he or she prefers v to u. Usually, obtaining preference i...

Given two disjoint groups U and V each containing 2n−1 people. Suppose an experiment (or a game) requires pairwise comparisons between u ∈ U and v ∈ V in such a way that u ∈ U (v ∈ V ) is compared exactly with n people v ∈ V (u ∈ U). Only one comparison can be done at a time, and the comparisons are made along the n2n−1 edges of the n−cube graph Qn with vertex classes U and V . The paper deals ...

This study was an attempt to investigate what metacognitive strategies are specifically employed by English learners when it comes to different speaking task types.60 students at advanced level (female) were randomly selected and given an OPT as a test of homogeneity. They were assigned to experimental and control groups. The MS questionnaire (Oxford, 1990) was also administered to see what MS ...

Given a left module U and a right modules V over an algebra D and a bilinear form β : U × V → D, we may define an associative algebra structure on the tensor product V ⊗D U . This algebra is called a near-matrix algebra. In this paper, we shall investigate algebras filtered by near-matrix algebras in some nice way and give a unified treatment for quasi-hereditary algebras, cellular algebras, an...

In this paper, we consider the following problem: given an undirected graph G = (V , E) and an integer k, find I ⊆ V 2 with |I| ≤ k in such a way that G = (V , E ∪ I) has the maximum number of triangles (a cycle of length 3). We first prove that this problem is NP-hard and then give an approximation algorithm for it. © 2015 Elsevier B.V. All rights reserved.