Mathematical and scientific computing problems are often approached using a divide and conquer paradigm in which a large problem domain is solved by combining results from smaller subdomains. In this very broad context, we focus on nested spatial decompositions of regularly sampled domains obtained by the regular simplex bisection scheme. Specifically, we utilize clusters of such simplices, ref...

We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This recurrence was studied by Propp and by Fomin and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and conjectured that the coefficients were 1. Our proof establishes a bijection between the terms of the L...

Abstract We use the octahedron recurrence, which generalizes quadratic recurrence found by Kuo for standard Aztec diamonds, in order to compute boundary one-refined and two-refined partition functions two-periodic diamonds. In a first approach, geometric tangent method allows derive parametric form of arctic curve, separating solid liquid phases. This is done using recent reformulation without ...

We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This recurrence was studied by Propp and by Fomin and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and conjectured that the coefficients were 1. Our proof establishes a bijection between the terms of the L...

We say that two graphs are similar if their adjacency matrices are similar matrices. We show that the square grid Gn of order n is similar to the disjoint union of two copies of the quartered Aztec diamond QADn−1 of order n− 1 with the path P (2) n on n vertices having edge weights equal to 2. Our proof is based on an explicit change of basis in the vector space on which the adjacency matrix ac...

The origin of diamond in ureilites is still debating. There are two the most popular explanations: (1) as a result of shock transformation from graphite caused by meteorite impact in the parent bodies [1-4], and (2) in a CVD process in the solar nebula [5-7]. We isolated a sample strongly enriched with diamond from the Novo-Urei ureilite and separated it into two density fractions in a heavy li...

INTRODUCTION A variety of mantle-derived igneous rocks comprise the primary sources of diamond, with the principal hosts being kimberlite and lamproite. Primary diamonds or graphite pseudomorphs after diamond are also known to occur in some lamprophyres (Jaques, Kerr et al., 1989), alkali basalts and alpine type peridotites (Kaminskii, 1984). Significant quantities of diamond have not yet been ...

We construct some +-Souslin trees which cannot be specialised by any forcing which preserves cardinals and coonalities. For a regular cardinal we use the principle, for singular we use squares and diamonds.

We present the results of study structure and composition microcrystalline diamonds obtained by high-pressure high temperature sintering detonation nanodiamond particles. Using optical detected magnetic resonance method, photoluminescence spectroscopy Raman we found significantly differ from initial nanodiamonds can be compared to quality diamonds. Monocrystals method oriented attachment have d...