m at h . C A ] 1 6 Ju n 20 04 Markov ’ s Transformation of Series and the WZ Method

3 1 M ay 2 00 4 Markov ’ s Transformation of Series and the WZ Method

In a well forgotten memoir of 1890, Andrei Markov devised a convergence acceleration technique based on a series transformation which is very similar to what is now known as the WilfZeilberger (WZ) method. We review Markov’s work, put it in the context of modern computeraided WZ machinery, and speculate about possible reasons of the memoir being shelved for so long.

un 2 00 4 Markov ’ s Transformation of Series and the WZ Method

In a well forgotten memoir of 1890, Andrei Markov devised a convergence acceleration technique based on a series transformation which is very similar to what is now known as the WilfZeilberger (WZ) method. We review Markov’s work, put it in the context of modern computeraided WZ machinery, and speculate about possible reasons of the memoir being shelved for so long.

ar X iv : m at h / 03 04 41 7 v 2 [ m at h . C A ] 1 6 Ju n 20 03 BMO is the intersection of two translates of dyadic

Let T be the unit circle on R. Denote by BMO(T) the classical BMO space and denote by BMOD(T) the usual dyadic BMO space on T. Then, for suitably chosen δ ∈ R, we have ‖φ‖BMO(T) ⋍ ‖φ‖BMOD(T) + ‖φ(· − 2δπ)‖BMOD(T) ,∀φ ∈ BMO(T) To cite this article: C. R. Acad. Sci. Paris, Ser. I 336 (2003).

m at h . A G ] 1 5 Ju n 20 04 NESTED SETS AND JEFFREY KIRWAN CYCLES

Transformation and gene expression study of recombinant fish GnRH in E. coli BL21 in order to produce recombinant hormone

Gonadotropin releasing hormone (GnRH) is a neuropeptide known to regulate reproduction in vertebrates. Different analogues of synthetic GnRH are used to induce final sexual maturation in fish breeders. The purpose of this research was to evaluate the expression of recombinant GnRH (rGnRH) in Escherichia coli BL21 to produce recombinant hormone. In the present research, the sequence of DNA relat...