let $g$ be a $p$-group of order $p^n$ and $phi$=$phi(g)$ be the frattini subgroup of $g$. it is shown that the nilpotency class of $autf(g)$, the group of all automorphisms of $g$ centralizing $g/ fr(g)$, takes the maximum value $n-2$ if and only if $g$ is of maximal class. we also determine the nilpotency class of $autf(g)$ when $g$ is a finite abelian $p$-group.

Universal source coding at short blocklengths is considered for an exponential family of distributions. The Type Size code has previously been shown to be optimal up to the third-order rate for universal compression of all memoryless sources over finite alphabets. The Type Size code assigns sequences ordered based on their type class sizes to binary strings ordered lexicographically. To general...

Many patients prefer to use the best hospitals even if there are one or more other hospitals closer to their homes; this behavior is called “hospital bypass behavior”. Because this behavior can be problematic in urban areas, it is important that it be reduced. In this paper, the taxi GPS data of Beijing and Suzhou were used to measure hospital bypass behavior. The “bypass behavior index” (BBI) ...

We consider a time-dependent brane configuration that corresponds to the Q-ball in the effective Lagrangian. We discuss the brane Q-balls, branonium and brane Q-ball inflation, which might have the same origin. We show the allowed parameter regions for these configurations. It is shown that the brane Q-ball looks similar to a conventional Q-ball when it is large, but its decay is dominated by t...

let $g$ be a $p$-group of order $p^n$ and $phi$=$phi(g)$ be the frattini subgroup of $g$. it is shown that the nilpotency class of $autf(g)$, the group of all automorphisms of $g$ centralizing $g/ fr(g)$, takes the maximum value $n-2$ if and only if $g$ is of maximal class. we also determine the nilpotency class of $autf(g)$ when $g$ is a finite abelian $p$-group.