Relaxation induced by nitric oxide (NO) donors is impaired in renal hypertensive two kidney-one clip (2K-1C) rat aortas. It has been proposed that caveolae are important in signal transduction and Ca2+ homeostasis. Therefore, in the present study we investigate the integrity of caveolae in vascular smooth muscle cells (VSMCs), as well as their influence on the effects produced by NO released fr...

A discretized rotation is the composition of an Euclidean rotation with the rounding operation. For 0 < α < π/4, we prove that the discretized rotation [rα] is bijective if and only if there exists a positive integer k such as {cosα, sinα} = { 2k + 1 2k2 + 2k + 1 , 2k + 2k 2k2 + 2k + 1 } The proof uses a particular subgroup of the torus (R/Z).

Let E be the ellipse with major and minor radii a and b respectively, and Pbe its perimeter, then P = lim 4 tan(p/n)(a + b + 2) Σ a2 cos2 (2k-2)Pi/n+ sin2 (2k-2)Pi/n; where n = 2m. So without considering the limit, it gives a reasonable approxi-mation for P, it means that we can choose n large enough such that the amountof error be less than any given small number. On the other hand, the form...

BACKGROUND Labdane-type diterpenes induce lower blood pressure via relaxation of vascular smooth muscle; however, there are no studies describing the effects of labdanes in hypertensive rats. OBJECTIVE The present study was designed to investigate the cardiovascular actions of the labdane-type diterpene ent-3-acetoxy-labda-8(17), 13-dien-15-oic acid (labda-15-oic acid) in two-kidney 1 clip (2...

We obtain q-analogues of several series for powers $$\pi $$ . For example, the identity $$\begin{aligned} \mathop {\sum }\limits _{k=0}^\infty \frac{(-1)^k}{(2k+1)^3}=\frac{\pi ^3}{32} \end{aligned}$$ has following q-analogue: (-1)^k\frac{q^{2k}(1+q^{2k+1})}{(1-q^{2k+1})^3}=\frac{(q^2;q^4)_{\infty }^2(q^4;q^4)_{\infty }^6}{(q;q^2)_{\infty }^4}, where q is any complex number with $$|q|<1$$ al...

The aim of this note is to call attention to a peculiar odd–even regularity regarding the number of walks in a finite graph G: Let Wk denote the number of walks of length k (≥ 0) in G and put ∆k := Wk+1Wk−1−W 2 k (k ≥ 1) . Then • ∆2k−1 ≥ 0 holds for all k ≥ 1, • one has either ∆1 ≥ 0 and ∆k = 0 for all k ≥ 2 which holds if and only if G is harmonic (i.e. if and only if the degree map which asso...

A Dyck path with 2k steps and e flaws is a path in the integer lattice that starts at the origin and consists of k many ↗-steps and k many ↘-steps that change the current coordinate by (1, 1) or (1,−1), respectively, and that has exactly e many ↘-steps below the line y = 0. Denoting by D 2k the set of Dyck paths with 2k steps and e flaws, the Chung-Feller theorem asserts that the sets D 2k, D 1...

The Kneser graph K (n, k) is the graph whose vertices are the k-element subsets of an n elements set, with two vertices adjacent if they are disjoint. The square G2 of a graph G is the graph defined on V (G) such that two vertices u and v are adjacent in G2 if the distance between u and v in G is at most 2. Determining the chromatic number of the square of the Kneser graph K (n, k) is an intere...