The generating functional of correlation functions for theXXZ spin chain is considered in the thermodynamic limit. We derive a system of integro-difference equations that prescribe this functional. On the basis of this system we establish the operator-valued Riemann–Hilbert problem for correlation functions of the XXZ spin chain.

Sufficient conditions are established for the oscillation of the linear two-dimensional difference system ∆xn = pn yn, ∆yn−1 = −qnxn, n ∈ N (n0) = {n0, n0 + 1, . . .}, where {pn}, {qn} are nonnegative real sequences. Our results extend the results in the literature. c © 2007 Elsevier Ltd. All rights reserved.

In this study we, give some new explicit expressions and recurrence relations satisfied by marginal and joint moment generating functions of k−th upper record values from extended type II generalized logistic distribution. Next we show that results for upper record values of this distribution can be derived from our result as special cases. Further, a characterizing result of this distribution ...