Lattices that can be represented in a kagomé-like form are shown to satisfy a universal percolation criticality condition, expressed as a relation between P3 , the probability that all three vertices in the triangle connect, and P0 , the probability that none connect. A linear approximation for P3(P0) is derived and appears to provide a rigorous upper bound for critical thresholds. A numericall...

was first discovered by M. Petrovich in 1917, [5] (see [4, p. 492]) and subsequently was rediscovered by other authors, including J. Karamata [2, p. 300 – 301], H.S. Wilf [6], and in an equivalent form by M. Marden [3]. The first to consider the problem of obtaining reverses for the triangle inequality in the more general case of Hilbert and Banach spaces were J.B. Diaz and F.T. Metcalf [1] who...

We use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and two nonstandard finite difference variational integrators for the nonlinear Klein-Gordon equation with a triangle discretization and a square ...

We look at the four-fold symmetry given by the Incenter quadrangle of a triangle, and the relation with the cirumcircle, which in this case is the nine-point conic of the quadrangle. By investigating Euler lines of Incenter triangles, we show that the classical Schiffler point extends to a set of four Schiffler points, all of which lie on the Euler line. We discover also an additional quadrangl...

Synthetic nanostructures consisting of biomacromolecules such as nucleic acids have been constructed using bottom-up approaches. In particular, Watson-Crick base pairing has been used to construct a variety of two- and three-dimensional DNA nanostructures. Here, we show that RNA and the ribosomal protein L7Ae can form a nanostructure shaped like an equilateral triangle that consists of three pr...

Studies of the linguistic landscape (LL) are concerned with language in its written form, in the public sphere; language that is visible to all through texts such as billboards and other public signs. The LL is such a taken-for-granted part of our everyday experience that its importance as a form of social practice is often overlooked. Taking a mixed methods approach to the case of the linguist...

DStrips is a simple and efficient method to dynamically manage and generate triangle strips for real-time viewdependent multiresolution meshing and rendering. Progressive view-dependent triangle mesh simplification and rendering is an important concept for interactive visualization environments. To minimize the rendering cost, triangle meshes are simplified to the maximal tolerated perceptual e...

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...