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...

We provide simple, faster algorithms for the detection of cliques and dominating sets of fixed order. Our algorithms are based on reductions to rectangular matrix multiplication. We also describe an improved algorithm for diamonds detection.

Hydrogen-related infrared absorption bands in natural diamonds have been extensively investigated and widely used to identify natural, treated, synthetic grown by high pressure temperature (HPHT) chemical vapor deposition (CVD) techniques. However, the evolutional behavior of hydrogen-related defects relationship between nitrogen-related HPHT-treated Ib are unclear. In this article, defects, pa...