to start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ode. then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. it is required to state that the infinite series method is a well-organized method for obtaining exact s...

The isophote curvature times the gradient magnitude to some power has been studied in the literature as a measure of cornerness in images. Stability in terms of sampling noise has been proposed by selecting corners at high scale and locating them at fine scale. We will examine the problem of tracking extrema of these measures in the Linear Scale-Space using catastrophe theory. This enables us t...

Contour integration refers to the ability of the visual system to bind disjoint local elements into coherent global shapes. In cluttered images containing randomly oriented elements a contour becomes salient when its elements are coaligned with a smooth global trajectory, as described by the Gestalt law of good continuation. Abrupt changes of curvature strongly diminish contour salience. Here w...

In this paper, a dual-polarized frequency-reconfigurable mm-wave patch antenna array is described. The design incorporates varactor diodes symmetrically loaded onto the four corners of square patch. Parallel plate series capacitors are constructed to achieve required low total capacitance by moving an inner layer. Additionally, novel dual-function shorting vias implemented into structure, which...

A two-dimensional, time-harmonic eddy-current problem is examined in which a uniform field is perturbed by a long, surface-breaking crack in a non-magnetic, conducting half-space. The crack is assumed to be ideal in the sense that it has infinitesimal opening and yet forms a perfect barrier to the passage of electric current. A solution is sought which is accurate both at high frequencies, at w...

It is known that given a directed graph E and a subset X of vertices, the sum Σ v∈X P v of vertex projections in the C *-algebra of E converges strictly in the multiplier algebra to a projection P X. Here we give a construction which, in certain cases, produces a directed graph F such that C * (F) is isomorphic to the corner P X C * (E)P X. Corners of this type arise naturally as the fixed poin...

This note is an illustration of the density-increment method used in the proof of the density Hales-Jewett theorem for k = 3. (Polymath project [2]) I will repeat the argument applying it to a problem which is easier than DHJ. In the last section I will describe the proof of the density Hales-Jewett theorem for k = 3. The results stated here are direct interpretations of the project’s results, ...

We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard’s corner point. We prove that smooth Hamiltonian flows which limit to this billiard have a nearby periodic orbit if and only if the polygon angles at the corner are ‘‘acceptable.’’ The criterion for...

The simplest modeling of planar quantum waveguides is the Dirichlet eigenproblem for the Laplace operator in unbounded open sets which are uniformly thin in one direction. Here we consider V-shaped guides. Their spectral properties depend essentially on a sole parameter, the opening of the V. The free energy band is a semi-infinite interval bounded from below. As soon as the V is not flat, ther...

Gaseous oxidized mercury (GOM) dry deposition measurements using aerodynamic surrogate surface passive samplers were collected in central and eastern Texas and eastern Oklahoma, from September 2011 to September 2012. The purpose of this study was to provide an initial characterization of the magnitude and spatial extent of ambient GOM dry deposition in central and eastern Texas for a 12-month p...