We show that the nth derivative of Riemann zeta function, when summed over non-trivial zeros zeta, is real and positive/negative in mean for n odd/even, respectively. this by giving a full asymptotic expansion these sums.

We introduce a boundedness condition on the Malliavin derivative of a random variable to study subGaussian and other non-Gaussian properties of functionals of random …elds, with particular attention to the estimation of suprema. We relate the boundedness of nth Malliavin derivatives to a new class of “sub-nth Gaussian chaos” processes. An expected supremum estimation, extending the DudleyFerniq...

Let denote by Fk,n the nth k-Fibonacci number where Fk,n = kFk,n−1+Fk,n−2 for n 2 with initial conditions Fk,0 = 0, Fk,1 = 1, we may derive a functionalequation f(k, x) = kf(k, x − 1) + f(k, x − 2). In this paper, we solve thisequation and prove its Hyere-Ulam stability in the class of functions f : N×R ! X,where X is a real Banach space.

In this paper, we consider the finitely 2-generated groups $K(s,l)$ and $G_m$ as follows:$$K(s,l)=langle a,b|ab^s=b^la, ba^s=a^lbrangle,\G_m=langle a,b|a^m=b^m=1, {[a,b]}^a=[a,b], {[a,b]}^b=[a,b]rangle$$ and find the explicit formulas for the probability of having nth-roots for them. Also, we investigate integers n for which, these groups are n-central.

Sánchez, J.A. & S.D. Cairns. An unusual new gorgonian coral (Anthozoa: Octocorallia) from the Aleutian Islands, Alaska. Zool. Med. Leiden 78 (15), 27.viii.2004: 265-274, figs 1-8.— ISSN 0024-0672. Juan A. Sánchez & Stephen Cairns, Department of Systematic Biology, National Museum of Natural History, Smithsonian Institution, P.O. Box 37012, MRC-0163, Washington, D.C. 20013-7012, U.S.A. (email: c...

Hofmann, K. & Tausig, F. (1955). J. biol. Chem. 213, 425. Lapworth, A. & Mottram, E. N. (1925). J. chem. Soc. 127, 1628. Longenecker, H. E. (1939). J. biol. Chem. 128, 645. Moir, R. J., Somers, M., Sharman, G. & Waring, H. (1954). Nature, Lond., 173, 269. Reiser, R. (1951). Fed. Proc. 10, 236. Society of Public Analysts (1933). Analyst, 58, 203. Sperry, W. M. (1928). J. biol. Chem. 78, xliv. Sw...