On the positive nonoscillatory solutions of the difference equation x_(n+1)= α +(x_(n-K)/x_(n-m))~p

The aim of this paper is to show that the following difference equation:xn+1=α+(xn-k/xn-m)p,n=0,1,2…,where α＞-1,p＞0,k,m ∈ N are fixed, 0≤m＜k,x-k,x-k+1,…,x-m,…,x-1,x0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium x=α+1.It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.     

ON THE CONTRACTION AND DEFORMATION OF DEUTERON CLUSTER IN 6Li

The ground state of ⁶Li is investigated by means of the projected variational method for double well-cluster shell model. The results of the variational calculation show that the root-mean-square radius of d-cluster in the ground state of ⁶Li is smaller than that of free deuteron and as the mean distance between the α-cluster and the d-cluster decreases there are two effects on the d-cluster, namely contraction effect in which the d-cluster contracts first and then makes a bit extension and deformation effect in which the d-cluster makes oblation first and then streteches.It is also demonstrated by the calculation that the repulsive component of the odd sytate of N-N force and the pauli exchange of the nucleons between the clusters play an important role not only on the cluster structure in the ground state of ⁶Li but also on the contraction and the deformation of d-cluster in ⁶Li.     

Constrained controllability of linear infinite-dimensional systems: a set-valued analysis approach

This paper presents necessary and sufficient conditions forcontrollability of linear discrete-time and continuous-timesystems with constrained controls in Banach spaces. The proofsof the main results are based on extenosions of the Banach theoremof categories and the surjectivity theorem for convex set-valuedfunctions.