biharmonic surfaces in euclidean space $mathbb{e}^3$ are firstly studied from a differential geometric point of view by bang-yen chen, who showed that the only biharmonic surfaces are minimal ones. a surface $x : m^2rightarrowmathbb{e}^{3}$ is called biharmonic if $delta^2x=0$, where $delta$ is the laplace operator of $m^2$. we study the $l_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

‎Let $G$ be a finite group‎. ‎By $MT(G)=(m_1,cdots,m_k)$ we denote the type of‎ ‎conjugacy classes of maximal subgroups of $G$‎, ‎which implies that $G$ has exactly $k$ conjugacy classes of‎ ‎maximal subgroups and $m_1,ldots,m_k$ are the numbers of conjugates‎ ‎of maximal subgroups of $G$‎, ‎where $m_1leqcdotsleq m_k$‎. ‎In this paper‎, ‎we‎ ‎give some new characterizations of finite groups by ...

We present a collection of new structural, algorithmic, and complexity results for two types of matching problems. The first problem involves the computation of k-maximal matchings, where a matching is k-maximal if it admits no augmenting path with ≤ 2k vertices. The second involves finding a maximal set of vertices that is matchable — comprising one side of the edges in some matching. Among ou...

Let k > 0 be an integer and let D be a simple digraph on n > k vertices. We prove that If |A(D)| > k(2n − k − 1)+ ( n − k 2 )