introductionpopulation data is easily accessible and shows the relationship between city size and other socio-economic factors in the city indirectly, so many geographers using this type of data to gain an understanding of the structure of the cities network and distribution of the people in the different levels of urban hierarchy. in fact, urban hierarchy is the best way of space organization ...

‎let $g$ be a finite group‎. ‎in [ghasemabadi et al.‎, ‎characterizations of the simple group ${}^2d_n(3)$ by prime graph‎ ‎and spectrum‎, ‎monatsh math.‎, ‎2011] it is‎ ‎proved that if $n$ is odd‎, ‎then ${}^2d _n(3)$ is recognizable by‎ ‎prime graph and also by element orders‎. ‎in this paper we prove‎ ‎that if $n$ is even‎, ‎then $d={}^2d_{n}(3)$ is quasirecognizable by‎ ‎prime graph‎, ‎i.e‎...

We consider applications where an untrusted aggregator would like to collect privacy sensitive data from users, and compute aggregate statistics periodically. For example, imagine a smart grid operator who wishes to aggregate the total power consumption of a neighborhood every ten minutes; or a market researcher who wishes to track the fraction of population watching ESPN on an hourly basis. We...

let $g $ be a finite group and let $gamma(g)$ be the prime graph‎ ‎of g‎. ‎assume $2 < q = p^{alpha} < 100$‎. ‎we determine finite groups‎ ‎g such that $gamma(g) = gamma(u_3(q))$ and prove that if $q neq‎ ‎3‎, ‎5‎, ‎9‎, ‎17$‎, ‎then $u_3(q)$ is quasirecognizable by prime graph‎, ‎i.e‎. ‎if $g$ is a finite group with the same prime graph as the‎ ‎finite simple group $u_3(q)$‎, ‎then $g$ has a un...

The prime graph of a finite group $G$ is denoted by$ga(G)$. A nonabelian simple group $G$ is called quasirecognizable by primegraph, if for every finite group $H$, where $ga(H)=ga(G)$, thereexists a nonabelian composition factor of $H$ which is isomorphic to$G$. Until now, it is proved that some finite linear simple groups arequasirecognizable by prime graph, for instance, the linear groups $L_...

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.