A meet semilattice with a partial join operation satisfying certain axioms is a JP-semilattice. A PJP-semilattice is a pseudocomplemented JP-semilattice. In this paper we describe the smallest PJP-congruence containing a kernel ideal as a class. Also we describe the largest PJP-congruence containing a filter as a class. Then we give several characterizations of congruence kernels and cokernels for distributive PJP-semilattices.
The main objective of this paper is to study the boundedness character, the periodic character, the convergence and the global stability of positive solutions of the difference equation xn+1 = ( A + ∑ k i=0 αixn−i)
⁄ ∑ k i=0 βixn−i , n = 0, 1, 2, . . . where the coefficients A, αi , βi and the initial conditions x−k, x−k+1, . . . , x−1, x0 are positive real numbers, while k is a positive integer number.