the present study has been conducted on shemiranat county landscape, using lattice hexagon approach, for the first time, in order to achieve homogeneous units in degradation model. to this aim, with respect to the extent of the studied area, a lattice hexagon composed of 36 units (cells) was created and each grid cell was considered as a sub landscape. next, ecological vulnerability, degradatio...

We review recent computational results for hexagon patterns in nonBoussinesq convection. For sufficiently strong dependence of the fluid parameters on the temperature we find reentrance of steady hexagons, i.e. while near onset the hexagon patterns become unstable to rolls as usually, they become again stable in the strongly nonlinear regime. If the convection apparatus is rotated about a verti...

A classical theorem of MacMahon states that the number of lozenge tilings of any centrally symmetric hexagon drawn on the triangular lattice is given by a beautifully simple product formula. In this paper, we present a counterpart of this formula, corresponding to the exterior of a concave hexagon obtained by turning 120° after drawing each side (MacMahon’s hexagon is obtained by turning 60° af...

We first show that the tilings of a domain D form a lattice (using the same kind of arguments as in [Rém99]) which we then undertake to decompose and generate without any redundance. To this end, we study extensively the relatively simple case of hexagons and their deformations. We show that general domains can be broken up into hexagon-like parts. Finally we give an algorithm to generate exact...

We first show that the tilings of a domain D form a lattice (using the same kind of arguments as in [Rém99]) which we then undertake to decompose and generate without any redundance. To this end, we study extensively the relatively simple case of hexagons and their deformations. We show that general domains can be broken up into hexagon-like parts. Finally we give an algorithm to generate exact...

Some new finite lattices (for example, A/4 , M7, and the hexagon lattice) are shown to be isomorphic to the lattice of elementary substructures of a model of Peano Arithmetic. The set of elementary substructures of a model JV of Peano Arithmetic forms a lattice Lt(yf), the substructure lattice of jV. It is unknown whether there are finite lattices that are not isomorphic to any substructure lat...

In this paper, we will describe and use a novel technique called “squishing”, which one applies to the dimer model on the regular honeycomb lattice. We developed this technique as an attempt to verify a conjectured generating function which arises in algebraic geometry (specifically, in the Donaldson-Thomas theory of the orbifold C/Z2 × Z2 [1]). Our attempt was only partially successful, and we...