Construction of the Paths of Brownian Motions on Star Graphs

Pathwise constructions of Brownian motions which satisfy all possible boundary conditions at the vertex of star graphs are given.Comment: 36 pages. The material of our previous articles 1012.0733, 1012.0737, 1012.0739 has been re-organized. The present article is a self contained version of 1012.073

Pell and associated Pell braid sequences as GCDs of sums of kk consecutive Pell, balancing, and related numbers

We consider the greatest common divisor (GCD) of all sums of $k$ consecutive terms of a sequence $(S_n)_{n\geq 0}$ where the terms $S_n$ come from exactly one of following six well-known sequences' terms: Pell $P_n$, associated Pell $Q_n$, balancing $B_n$, Lucas-balancing $C_n$, cobalancing $b_n$, and Lucas-cobalancing $c_n$ numbers. For each of the six GCDs, we provide closed forms dependent on $k$. Moreover, each of these closed forms can be realized as braid sequences of Pell and associated Pell numbers in an intriguing manner. We end with partial results on GCDs of sums of squared terms and open questions.Comment: 24 pages, Version 3 is the published version in the Journal of Integer Sequence

Insulin Induces the Release of Vasodilator Compounds From Platelets by a Nitric Oxide–G Kinase–VAMP-3–dependent Pathway

Insulin-induced vasodilatation is sensitive to nitric oxide (NO) synthase (NOS) inhibitors. However, insulin is unable to relax isolated arteries or to activate endothelial NOS in endothelial cells. Since insulin can enhance platelet endothelial NOS activity, we determined whether insulin-induced vasodilatation can be attributed to a NO-dependent, platelet-mediated process