Abstract This paper proposes a fractional-order reset element whose architecture allows for the suppression of nonlinear effects range frequencies. Suppressing desired frequency while maintaining it rest is beneficial, especially when used in framework “Constant gain, Lead phase” (CgLp) filter. CgLp newly introduced filter, bound to circumvent well-known linear control limitation—the waterbed e...

‎let $g$ be a finite group and $pi_{e}(g)$ be the set of element‎ ‎orders of $g$‎. ‎let $k in pi_{e}(g)$ and $m_{k}$ be the number of‎ ‎elements of order $k$ in $g$‎. ‎set nse($g$):=${ m_{k} | k in‎ ‎pi_{e}(g)}$‎. ‎in this paper‎, ‎we prove that if $g$ is a group such‎ ‎that nse($g$)=nse($psl(2‎, ‎25)$)‎, ‎then $g cong psl(2‎, ‎25) $‎.

‎let $g$ be a finite group and $pi_{e}(g)$ be the set of element‎ ‎orders of $g$‎. ‎let $k in pi_{e}(g)$ and $m_{k}$ be the number of‎ ‎elements of order $k$ in $g$‎. ‎set nse($g$):=${ m_{k} | k in‎ ‎pi_{e}(g)}$‎. ‎in this paper‎, ‎we prove that if $g$ is a group such‎ ‎that nse($g$)=nse($psl(2‎, ‎25)$)‎, ‎then $g cong psl(2‎, ‎25) $‎.

A subset S of a finite Abelian group G is said to be a sum cover of G if every element of G can be expressed as the sum of two not necessarily distinct elements in S, a strict sum cover of G if every element of G can be expressed as the sum of two distinct elements in S, and a difference cover of G if every element of G can be expressed as the difference of two elements in S. For each type of c...

suppose that  is a finite group. then the set of all prime divisors of  is denoted by  and the set of element orders of  is denoted by . suppose that . then the number of elements of order  in  is denoted by  and the sizes of the set of elements with the same order is denoted by ; that is, . in this paper, we prove that if  is a group such that , where , then . here  denotes the family of suzuk...

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...

Let F be a family of subsets of an n-element set not containing four distinct members such that A∪B ⊆ C∩D. It is proved that the maximum size of F under this condition is equal to the sum of the two largest binomial coefficients of order n. The maximum families are also characterized. A LYM-type inequality for such families is given, too.