The infinite series Rp = P ∞ k=1 (2k − 1) −p x 2k−1 , 0 < 1 − x 1, p = 2 or 3 , and the related series C(x, b, 2) = ∞ X k=1 (2k − 1) −2 cosh(2k − 1)x/ cosh(2k − 1)b, 0 < 1 − x/b 1, S(x, b, 3) = ∞ X k=1 (2k − 1) −3 sinh(2k − 1)x/ cosh(2k − 1)b, are of interest in problems concerning contact between plates and unilateral supports. This article will reexamine a previously published result of Barat...

A 2k-dicycle is a 2k-cycle of a directed bipartite graph and a 2k-dicycle system of order (m,n) is a triple (X, Y,D), where D is a collection of edge disjoint 2k-dicycles which partitions the edge set of the complete directed bipartite graph Dm,n with parts X and Y . A partial 2k-dicycle system of order (s, t) is a triple (S, T, P ), where P is a collection of edge disjoint 2k-dicycles of Ds,t ...

We study the solutions and attractivity of the difference equation xn+1 = axn−(2k+2) −a + 2k+2 ∏ i=0 xn−i for n = 0, 1, 2, ... where a, x−(2k+2),x−(2k+1),..., x0 are the real numbers, x−(2k+2)x−(2k+1)... x0 = a, and k ∈ Z. Mathematics Subject Classification: 39A10, 39A12

Abstract Purpose 8K Ultra-high-definition (UHD) imaging has been developed in accordance with the progression of technologies. We evaluated laparoscopic procedures performed by novice medical students using 2K/two-dimensional (2D), 2K/three-dimensional (3D) and 8K/2D monitors, a particular focus on depth perception. Methods Nine were enrolled. They two tasks 2K/2D, 2K/3D monitors. In Task 1, th...

Modern video cameras often only capture a single color per pixel in a single pass operation. This process is called ltering, where pixels are ltered through a color lter array, and the Bayer lter is perhaps the most common lter used today. This means that the missing color channels must be restored in the image or the video frame in a post-processing step, i.e., a process referred to as debayer...

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 formul...

A classical result of Rothschild and van Lint asserts that if every non-zero Fourier coefficient a Boolean function f over F2n has the same absolute value, namely |fˆ(α)|=1/2k for α in support f, then must be indicator some affine subspace dimension n−k. In this paper we slightly generalize their result. Our main shows that, roughly speaking, functions whose coefficients take values set {−2/2k,...

Fn−k+1H 2n−2k+1(X)∼= F n−k+1A2n−2k+1(X)c dFn−k+1A2n−2k(X) . If (Zt )t∈C is a flat family of codimension k algebraic cycles on X parametrized by a smooth irreducible curve C, the map t → kX(Zt − Z0) factors through a homomorphism from the Jacobian J (C) to J 2k−1(X), and one can show that the image of this morphism is a complex subtorus of J 2k−1(X) whose tangent space is contained in Hk−1,k(X) ...

We tested the hypothesis that an abnormal function of K(+) channels in vascular smooth muscle cells plays a key role in the impaired acetylcholine (ACh) vasodilation in aortas from two kidney-one clip (2K-1C) hypertensive rats and further investigated the K(+) channel subtype involved in this altered response. ACh-induced endothelium-dependent relaxation was assessed in aortic rings from 2K-1C ...