the aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von neumann algebra on a hilbert space with a normal faithful semi-finite trace $tau$. the submajorization inequalities generalize some results due to zhang, furuichi and lin, etc..

in this paper, a finite-time control scheme is presented for stabilization ofthe satellite chaotic attitude around its equilibrium point whenits attitude is confused by a disturbed torque. controllers and settling timeof stabilizaton are obtained, based on the lyapunov stability theoremand finite-time control scheme. this method is satisfied for any initial condition.numerical simulations are ...

‎in this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional heisenberg group $rm nil_3$‎. ‎in particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm nil_3$‎ ‎whose position vector $x$ satisfies the equation $delta x = ax$‎, ‎where $delta$ is the laplacian operator of the surface and $a$‎ ‎is a $3 times 3$-real matrix‎.

‎let $g$ be a finite group which is not a cyclic $p$-group‎, ‎$p$ a prime number‎. ‎we define an undirected simple graph $delta(g)$ whose‎ ‎vertices are the proper subgroups of $g$, which are not contained in the‎ ‎frattini subgroup of $g$ and two vertices $h$ and $k$ are joined by an edge‎ ‎if and only if $g=langle h‎ , ‎krangle$‎. ‎in this paper we classify finite groups with planar graph‎. ‎...