Let the bicoloring cover number χ(G) for a hypergraph G(V,E) be the minimum number of bicolorings of vertices of G such that every hyperedge e ∈ E of G is properly bicolored in at least one of the χ(G) bicolorings. We establish a tight bound for χ(K n), where K n is the complete k-uniform hypergraph on n vertices. We investigate the relationship between χ(G), matchings, hitting sets, α(G)(indep...

Let K be a totally imaginary quadratic extension of a totally real number field F , and assume that F has narrow ideal class number 1. Let χ be a character of the ideal class group CL(K) of K, and let LK(χ, s) be its associated L–function. In this paper we prove that for all > 0, #{χ ∈ CL(K)∧ : LK(χ, 1 2 ) 6= 0} ,F d 1 100− K as the absolute discriminant dK →∞.

PURPOSE To identify the critical success factors (CSF) associated with coverage of low vision services. METHODS Data were collected from a survey distributed to Vision 2020 contacts, government, and non-government organizations (NGOs) in 195 countries. The Classification and Regression Tree Analysis (CART) was used to identify the critical success factors of low vision service coverage. Indep...

Given elliptic modular forms f and g satisfying certain conditions on their weights and levels, we prove (a quantitative version of the statement) that there exist infinitely many imaginary quadratic fields K and characters χ of the ideal class group ClK such that L( 1 2 , fK × χ) 6= 0 and L( 1 2 , gK × χ) 6= 0. The proof is based on a non-vanishing result for Fourier coefficients of Siegel mod...

In the present study, we examined whether the ARNTL (BMAL1) rs2278749 T/C polymorphism was associated with the susceptibility to Alzheimer disease (AD). This case-control study examined the genotypes of apolipoprotein E (APOE e4) and BMAL1 rs2278749 T/C using restriction fragment length polymorphism and the TaqMan assay, respectively. A total of 296 unrelated AD patients and 423 control subject...