Invariant times *

Translation invariant surfaces in the 3-dimensional Heisenberg‎ ‎group

‎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.

Topologically Left Invariant Mean on Dual Semigroup Algebras

Generalized Baer-Invariant of a Pair of Groups and Marginal Extension

In this paper, we give connection between the order of the generalized Baer-invariant of a pair of finite groups and its factor groups, when ? is considered to be the specific variety. Moreover, we give a necessary and sufficient condition in which the generalized Baer-invariant of a pair of groups can be embedded into the generalized Baer-invariant of pair of its factor groups.

Global existence‎, ‎stability results and compact invariant sets‎ ‎for a quasilinear nonlocal wave equation on $mathbb{R}^{N}$

We discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of Kirchhoff Type [ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+delta u_{t}=|u|^{a}u,, x in mathbb{R}^{N} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$  is a positive function lying in $L^{N/2}(mathb...

Coordinate finite type invariant surfaces in Sol spaces

In the present paper, we study surfaces invariant under the 1-parameter subgroup in Sol space $rm Sol_3$. Also, we characterize the surfaces in $rm Sol_3$ whose coordinate functions of an immersion of the surface are eigenfunctions of the Laplacian $Delta$ of the surface.