Three new heteroleptic copper(II) complexes, [(tmen)Cu(dike)H2O]X where tmen = N,N,N',N'-tetramethylethylenediamine, dike = 2-acetylcyclopentanone anion and X= ClO4- (1), Cl- (2) and Br- (3) are prepared and characterized by elemental analyses, molar conductance measurements and IR and UV-Vis spectroscopy techniques. The complex 1 is fairly soluble in various organic solvents and demonstrates d...

The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...

Let $R$ be a commutative ring with identity. A proper submodule $N$ of an $R$-module $M$ is an n-submodule if $rmin N~(rin R, min M)$ with $rnotinsqrt{Ann_R(M)}$, then $min N$. A number of results concerning n-submodules are given. For example, we give other characterizations of n-submodules. Also various properties of n-submodules are considered.