let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

in some quality control applications, the quality of a process or a product is described by the relationship between a response variable and one or more explanatory variables, called a profile. moreover, in most practical applications, the qualitative characteristic of a product/service is vague, uncertain and linguistic and cannot be precisely stated. the purpose of this paper is to propose a ...

Assuming a first-order auto-regressive model for the auto-correlation structure between observations, in this paper, a transformation method is first employed to eliminate the effect of auto-correlation. Then, a maximum likelihood estimator (MLE) of a step change in the parameters of the transformed model is derived and three separate EWMA control charts are used to monitor the parameters of th...

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...

let l := u3(11). in this article, we classify groups with the same order and degree pattern as an almost simple group related to l. in fact, we prove that l, l:2 and l:3 are od-characterizable, and l:s3 is 5-fold od-characterizable.