An entanglement measure for pure-state continuous-variable bi-partite problem, the Schmidt number, is analytically calculated for one simple model of atom-field scattering.

For all integers k with k≥2, if G is a balanced k-partite graph on n≥3 vertices minimum degree at least⌈n2⌉+⌊n+22⌈k+12⌉⌋−nk={⌈n2⌉+⌊n+2k+1⌋−nk:k odd n2+⌊n+2k+2⌋−nk:k even , then has Hamiltonian cycle unless 4 divides n and k∈{2,n2}. In the case where k∈{2,n2}, we can characterize graphs which do not have see that ⌈n2⌉+⌊n+22⌈k+12⌉⌋−nk+1 suffices. This result tight for k≥2 divisible by k.

in this paper we study the coprime graph of a group $g$. the coprime graph of a group $g$, is a graph whose vertices are elements of $g$ and two distinct vertices $x$ and $y$ are adjacent iff $(|x|,|y|)=1$. in this paper we classify all the groups which the coprime graph is a complete r-partite graph or a planar graph. also we study the automorphism group of the coprime graph.

The effectiveness of recombinant vaccines encoding full-length M2 protein of influenza virus or its ectodomain (M2e) have previously been tested in a number of models with varying degrees of success. Recently, we reported a strong cytotoxic effect exhibited by M2 on mammalian cells in vitro. Here we demonstrated a decrease in protection when M2 was added to a DNA vaccination regimen that includ...

We present a novel approach for robust localization of multiple people observed using a set of static cameras. We use this location information to generate a visualization of the virtual offside line in soccer games. To compute the position of the offside line, we need to localize players′ positions, and identify their team roles. We solve the problem of fusing corresponding players′ positional...