Isoperimetric estimates stretch back for thousands of years in geometry, and for more than a hundred years in harmonic analysis and mathematical physics. We will touch on some of these highlights before describing recent progress that uses rotational symmetry to prove sharp upper bounds on sums of eigenvalues of the Laplacian. For example, we prove in 2 dimensions that the scale-normalized eige...

In this paper, we study different variations of minimum width color-spanning annulus problem among a set of points P = {p1, p2, . . . , pn} in IR, where each point is assigned with a color in {1, 2, . . . , k}. We present algorithms for finding a minimum width color-spanning axis parallel square annulus (CSSA), minimum width color spanning axis parallel rectangular annulus (CSRA), and minimum w...

A decrease in physical size and multiband ability are essential requirements for antenna incoming wireless devices.The antenna based on Sierpinski fractal antenna theory. Design & simulation of fractal triangle microstrip patch antenna done by using IE3D software of Zeland. In this paper, a special technique is proposed to design a new patch antenna, shapes is equilateral triangular fed by a 50...

Original scientific paper This study proposes an artificial neural network (ANN) model in order to approximate the resonant frequencies of equilateral triangular patch antennas. The neural network structure applied here is trained and tested for both single-layer and double-layer antennas. It is shown upon experiment that the resonant frequencies obtained from the neural network are both more a...

A model of monomer adsorption on infinitely long, finite-width M equilateral triangular lattices with nonperiodic boundaries is presented. The study includes adsorbate-adsorbate first- and second-neighbor interactions with results obtained for repulsive first neighbors. The matrix method and numerical algorithms presented here allow determination of the occupational characteristics of the adsor...

The dual band equilateral triangular microstrip antennas are realized by cutting the slots of either quarter wave or half wave in length, inside the patch. In this design, however these simpler approximations of slot length against the frequency do not give closer results for different slot lengths and there positions inside the patch. In this paper, the modal variations of slot cut patch anten...

The resonant optical modes of a high permittivity dielectric prism with an equilateral triangular cross section are discussed. Eigenmode solutions of the scalar Helmholtz equation with Dirichlet boundary conditions, appropriate to a conducting boundary, are applied for this purpose. The particular plane wave components present in these modes are analyzed for their total internal reflection beha...

The geometric percolation thresholds for circular, elliptical, square, and triangular plates in the three-dimensional space are determined precisely by Monte Carlo simulations. These geometries represent oblate particles in the limit of zero thickness. The normalized percolation points, which are estimated by extrapolating the data to zero radius, are etac=0.961 4+/-0.000 5, 0.864 7+/-0.000 6, ...

Two-dimensional lattices provide the arena for many physics problems of essential importance, a scale symmetry, which rarely exists as noticed by Galileo, in such lattices can help reveal the underlying physics. Here we report the discovery and proof of directional scaling symmetry for high symmetry 2D lattices, i.e., the square lattice, the equilateral triangular lattice and thus the honeycomb...

1 Eric Swanson, MD Swanson Center Leawood, Kans. Sir: C et al1 conclude that radiofrequency-assisted liposuction provides greater skin contraction of the arms than aggressive superficial liposuction. Unfortunately, no measurement data are presented, only the percentage changes in 10 patients. Two patients underwent skin excisions. The authors do not report the inclusion rate or whether their st...