1 Macrodiversity against Shadowing So far, the diversity techniques that are discussed are used to mitigate the eeects of small scale fading. These techniques are often called microscopic diversity. Similar diversity techniques exist in literature with the objective to combat shadow fading, which is known as macroscopic diversity. With macroscopic diversity, signals that are received from a mob...

let $m$ be an $r$-module and $0 neq fin m^*={rm hom}(m,r)$. we associate an undirected graph $gf$ to $m$ in which non-zero elements $x$ and $y$ of $m$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. weobserve that over a commutative ring $r$, $gf$ is connected anddiam$(gf)leq 3$. moreover, if $gamma (m)$ contains a cycle,then $mbox{gr}(gf)leq 4$. furthermore if $|gf|geq 1$, then$gf$ is finit...

graph Trevor Fenner S hool of Computer S ien e Birkbe k College, University of London Malet Street, London WC1E 7HX email trevor d s.bbk.a .uk Abraham Flaxman Department of Mathemati al S ien es Carnegie Mellon University Pittsburgh, PA, 15213, USA email abie mu.edu Alan Frieze y Department of Mathemati al S ien es Carnegie Mellon University Pittsburgh, PA, 15213, USA email alan random.math. mu...

In this paper, we present a new method for creating shadow texture atlas with which we can represent the self-shadow. Shadow texture atlas is a texture atlas with shadow information in each texel. Shadow texture is effective to represent high-quality shadow using the graphics hardware because it stores shadow information as color unlike shadow map which stores depth. However, it cannot represen...