We interpret divided power structures on the homotopy groups of simplicial commutative rings as having a counterpart in divided power structures on chain complexes coming from a non-standard symmetric monoidal structure.

By a result of H. Cartan (cf. 5]), the homotopy of a simplicial commutative algebra is equipped with divided power operations. In this paper, we provide a general approach to the construction of Cartan operations in the context of simplicial algebras over an operad.

The object of this paper is to identify the divided power series corresponding to the zeta measure associated to f f ,,[ r]. The first section introduces the zeta function for JF4[ T] and describes some of its interesting properties. In the second section, we describe results on interpolations and measures and state our main result (Theorem VII). The third section summarizes various results abo...

In this paper, a function involving the divided difference of the psi function is proved to be completely monotonic, a class of inequalities involving sums is found, and an equivalent relation between complete monotonicity and one of the class of inequalities is established. 2000 Mathematics subject classification: primary 33B15, 26D15; secondary 26A48, 26A51.

A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of two gamma functions and originating from establishment of the best upper and lower bounds in Kershaw’s doubl...