Global Attractivity of the Equilibrium of a Nonlinear Difference Equation

The authors consider the nonlinear difference equation x_n+1=x_n+x_n-kf(x_n-k),n=0,1,(0.1) where (0,1), k 0,1, and f C¹[[0,), [0,)] with f(x) < 0.They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.     

Behavior of Solutions of Second-Order Differential Equations with Sublinear Damping

We investigate the asymptotic behavior of solutions of the damped nonlinear oscillator equation

Structure models for β-MnGa2S4 as derived from electron diffraction and high-resolution electron microscopy

A study by high-resolution electron microscopy and electron diffraction on the tetrahedrally coordinated compound β-MnGa₂S₄ is reported. The structure-imaging technique enabled a new structure model to be proposed for the accommodation of deviations from stoichiometry in compounds of the type $\text{x}\text{MnS}\text{y}\text{Ga}{}_2\text{S}{}_3$. The model is based on the Ga₂S₃ structure wherein by the substitution of MnS layers chemical twin planes are formed. Depending on the spacing of the periodic twin planes a homologous series of compounds is expected and a number of members of this series was identified mainly by electron diffraction. In the β-MnGa₂S₄ compound, two structure modifications are observed mainly differing in the orientation of the twin planes (coherent or incoherent). This conclusion is substantiated by structure image calculations for the interpretation of the high-resolution results.