The function W (a, b) = 2π 0 dx 2π 0 dy ln[1−a cos x−b cos y−(1−a−b) cos(x+y)] which expresses the spanning-tree entropy for various two dimensional lattices, for example, is evaluated directly in terms of standard functions. It is applied to derive several limiting values of the Triangular lattice Green function.

Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not hold but in which we may still like to perform analysis. This paper investigates what happens if the triangle inequality is removed all together, leaving wha...

We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal bloc...

In the present study, the nonlinear Boussinesq type equation describe the bi-directional propagation of small amplitude long capillary–gravity waves on the surface of shallow water. By using the extended auxiliary equation method, we obtained some new soliton like solutions for the two-dimensional fourth-order nonlinear Boussinesq equation with constant coefficient. These solutions include symm...

We show that there are n! matchings on 2n points without socalled left (neighbor) nestings. We also define a set of naturally labeled (2+2)free posets and show that there are n! such posets on n elements. Our work was inspired by Bousquet-Mélou, Claesson, Dukes and Kitaev [J. Combin. Theory Ser. A. 117 (2010) 884–909]. They gave bijections between four classes of combinatorial objects: matching...

Airborne LiDAR bathymetry (ALB) has been shown to have the ability to retrieve water turbidity using the waveform parameters (i.e., slopes and amplitudes) of volume backscatter returns. However, directly and accurately extracting the parameters of volume backscatter returns from raw green-pulse waveforms in shallow waters is difficult because of the short waveform. This study proposes a new acc...

The mexican hat function is used to model a compensated (in density) gravitational lens. First we discuss the need for compensation. Then we integrate photon orbits to construct wavefronts. One consequence of underdensities is an o -axis caustic. We report the structure of the critical curves and caustics using the thin lens approximation, both for the mexican hat and for a perturbed mexican ha...

Let H,,(q) be the Iwahori-Hecke algebra of the symmetric group S,,. Let F, be a finite field with y elements and let B be the Bore1 subgroup of upper triangular matrices in the general linear group G = GL,(F,). Let 1: denote the trivial representation of B induced to G. Then H,,(q) has a natural action on 1; that commutes with the G-action, and we define the bitrace btr(g, a) to be the trace of...

ABSTRACT The Tesler matrices with hook sums (a1, a2, . . . , an) are non-negative integral upper triangular matrices, whose i diagonal element plus the sum of the entries in the arm of its (french) hook minus the sum of the entries in its leg is equal to ai for all i. In a recent paper [6], the second author expressed the Hilbert series of the Diagonal Harmonic modules as a weighted sum of the ...

In this paper, as an application of our recent results to appear elsewhere [5], we compare digital (0, 1)-sequences generated by nonsingular upper triangular matrices in arbitrary prime bases to van der Corput sequences and show these last ones are the worst distributed with respect to the star discrepancy, the extreme discrepancy, the L2-discrepancy and the diaphony. Moreover, we obtain digita...