Let M and N be a compact differentiable manifolds of dimension d and d + 1 respectively. Given a compact interval I ⊂ R, we suppose that we have a (fixed) embedding I ×M ⊂ N . See figure 1. Let N denote the complement of {0} ×M . Let h be a Riemannian metric on M , and let ρ be a positive function on R that is positively homogeneous of degree 1 and smooth away from (0, 0). Given (a, b) ∈ R, we ...

It is known that if (A,A∗) is a Leonard pair, then the linear transformations A, A∗ satisfy the Askey-Wilson relations A 2 A ∗ − βAA ∗ A + A∗A2 − γ (AA∗+A∗A) − ̺A∗ = γ∗A2 + ωA + η I, A ∗2 A− βA ∗ AA ∗+ AA∗2− γ∗(A∗A+AA∗) − ̺∗A = γA∗2+ ωA∗+ η∗I, for some scalars β, γ, γ∗, ̺, ̺∗, ω, η, η∗. The problem of this paper is the following: given a pair of Askey-Wilson relations as above, how many Leonard pai...

A transitive (infinite) permutation group which has m orbits on ordered pairs of distinct points has at least mn−1 orbits on ordered n-tuples. This is best possible, and groups attaining the bound can be characterised.

We report results from a search for production of a neutral Higgs boson in association with a b quark. We look for Higgs decays to tau pairs with one tau subsequently decaying to a muon and the other to hadrons. The data come from 2.7 fb−1 of pp collisions recorded by the D0 detector at √ s = 1.96 TeV. The data are found to be consistent with background predictions. The result is used to exclud...

For a nonempty nite set V let 3 V be the set of all the ordered pairs of disjoint subsets of

Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. If the second square is the (3, 2, 1)-conjugate of the first one, we say that the first square is (3, 2, 1)conjugate r-orthogonal, denoted by (3, 2, 1)-r-COLS(v). The nonexistence of (3, 2, 1)-r-COLS(v) for r ∈ {v + 2, v + 3, v + 5} has been proved by Zhang and Xu [Int. J. Combin. Gra...

In this paper, the effects of socioeconomic characteristics (gender, age, education level, marital status, income, occupational and health status, household size and social relationships) on individuals ́ health status in Spain from 1994 to 2001 are analysed. The estimations are carried out using ordered probit models and new data from the whole waves of the European Community Household Panel (E...

For a pair of positive parameters D,χ, a partition P of the vertex set V of an n-vertex graph G = (V,E) into disjoint clusters of diameter at most D each is called a (D,χ) network decomposition, if the supergraph G(P), obtained by contracting each of the clusters of P , can be properly χ-colored. The decompositionP is said to be strong (resp., weak) if each of the clusters has strong (resp., we...

An edge-ordered graph is an ordered pair (G, f), where G = G(V,E) is a graph and f is a bijective function, f : E(G) → {1, 2, ..., |E(G)|}. f is called an edge ordering of G. A monotone path of length k in (G, f) is a simple path Pk+1 : v1, v2..., vk+1 in G such that either, f((vi, vi+1)) < f((vi+1, vi+2)) or f((vi, vi+1)) > f((vi+1, vi+2)) for i = 1, 2, ..., k − 1. Given an undirected graph G,...

We report the direct soft chemical synthesis and characterization of a family of face centered cubic (fcc) and partially ordered face centered tetragonal (fct) FePt nanoparticles (NPs) suitable for biomedical applications. Both fcc and partially ordered fct-FePt NPs are synthesized by employing a simple polyol method. By using polyvinyl pyrolidone (PVP) as a stabilizer in various ratios during ...