Let R and B be two disjoint sets of red points and blue points, respectively, in the plane such that no three points of R ∪ B are co-linear. Suppose ag ≤ |R| ≤ (a + 1)g, bg ≤ |B| ≤ (b + 1)g. Then without loss of generality, we can express |R| = a(g1 + g2) + (a + 1)g3, |B| = bg1 + (b + 1)(g2 + g3), where g = g1 + g2 + g3, g1 ≥ 0, g2 ≥ 0, g3 ≥ 0 and g1+g2+g3 ≥ 1. We show that the plane can be sub...

In [2], Brousek characterizes all triples of graphs, G1, G2, G3, with Gi = K1,3 for some i = 1, 2, or 3, such that all G1G2G3-free graphs contain a hamiltonian cycle. In [6], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G1, G2, G3, none of which is a K1,s, s ≥ 3 such that G1, G2, G3-free graphs of sufficiently large order contain a hamiltonian cycle. In...

Peptides containing the asparagines-glycine-arginine (NGR) motif have been identified as specific ligands binding to CD13/aminopeptidase N (APN) receptor, a tumor neovascular biomarker. In this study, we synthesized a novel NGR-containing peptide (NOTA-G3-NGR), and labeled NOTA-G3-NGR with (68)Ga (t1/2 = 67.7 min). The resulting (68)Ga-NOTA-G3-NGR peptide was subject to in vitro and in vivo cha...

The concomitant influence of grandparental (Generation 1; G1) and parental (G2) substance use disorder (SUD) on grandchild (G3) emotional disorder (EmD) across three generations is unclear. The present study addressed this in a sample of 284 families participating in the Oregon Adolescent Depression Project. Structured clinical interviews were used to collect psychiatric history data on a commu...

Aim: the aim is to determine immunopathological modifications in rectal mucosa from rabbit after local challenge in sensitized animals with ovalbumin (OVA). Experimental design: thirty rabbits divided into three groups: G1: normal, G2: subcutaneously OVA sensitized, G3: sensitized, locally OVA challenged and sampled 4 hours after challenge. Specific anti-OVA IgE levels were evaluated by passive...

Low-grade prostate cancers (Gleason pattern 3, G3) detected on needle biopsies are generally viewed as indolent and suitable for conservative management with only interval repeat biopsies to monitor by watchful waiting. Higher grade tumors eventually emerge in 20% to 30% of these cases, but this process may only reflect incomplete sampling on the initial biopsy, such that it remains unknown whe...

BACKGROUND Although ginsenosides such as Rg1, Rb1 and Rg3 have shown promise as potential nutraceuticals for cognitive impairment, their use has been limited due to high production cost and low potency. In particular, the process of extracting pure Rg3 from ginseng is laborious and expensive. METHODS We described the methods in preparing ginseol k-g3, an Rg3-enriched fraction, and evaluated i...