Several formulas for crossing functions arising in the continuum limit of critical two-dimensional percolation models are studied. These include Watts’s formula for the horizontal-vertical crossing probability and Cardy’s new formula for the expected number of crossing clusters. It is shown that for lattices where conformal invariance holds, they simplify when the spatial domain is taken to be ...

A graph G = (V,E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if (x, y) ∈ E. A triangular grid graph is a subgraph of a tiling of the plane with equilateral triangles defined by a finite number of triangles, called cells. A face subdivision of a triangular grid graph is replacing some of its cells by plane copies of the...

We present exact results for the contact forces in a three dimensional static piling of identical, sti and frictionless spheres. The pile studied is a pyramid of equilateral triangular base (“stack of cannonballs”) with a FCC (face centered cubic) structure. We show in particular that, as for the two dimensional case, the pressure on the base of such a pile is uniform. c © 1999 Elsevier Science...

This paper reports the design of a Ka-band Equilateral triangular patch antenna (ETPA) fabricated using postCMOS and post-MMIC compatible process technology. The antenna uses an air-cavity underneath the patch radiator that is supported on thin dielectric membrane. The antenna structure was analysed and optimised using the finite element method (FEM) based Agilent High Frequency Structure Simul...

In this contribution, we propose a DOA (Direction Of Arrival) estimation method of speech signal whose angular resolution is almost uniform with respect to DOA. Our previous DOA estimation method[1] achieves high precision with only two microphones, however its resolution degrades as the propagating direction apart from the array broadside. In the proposed method, the equilateral-triangular mic...

What is the smallest circular or square wall hole that a regular tetrahedron can pass? This problem was solved by Itoh–Tanoue– Zamfirescu [8]. Then, we settled the case of equilateral triangular hole in [1]. Motivated by these results, we consider the corresponding problems in higher dimensions. Among other results, we determine the minimum (n−1)-dimensional ball hole that a unit regular n-simp...

We explore periodic orbits on an equilateral triangular billiard table. We prove that there is exactly one periodic orbit with odd period. For any positive integer n, there exist P d|n μ(d)P ¡ n d ¢ periodic orbits of period 2n, where μ(d) is the Möbius transformation function and P (n) = bn+2 2 c− bn+2 3 c. We count periodic orbits by introducing a new type of integer partition.

A very simple and more efficient CAD model is proposed to demonstrate the effect on input impedance characteristics based on cavity model analysis for wide range of superstrate parameters and feed locations of an equilateral triangular microstrip patch antenna having different side lengths. The computed values are compared with different theoretical and experimental values available in open lit...

w w w . i j e c t . o r g 106 InternatIonal Journal of electronIcs & communIcatIon technology Abstract This paper presents a novel technique for miniaturization of equilateral triangular Microstrip patch antenna by reducing its resonant frequency. Parallel slotting technique is applied in both radiating patch and ground plane to achieve the size reduction of about 84%. Ansoft Designer V2 is emp...