We introduce a recurrence which we term the multidimensional cube recurrence, generalizing the octahedron recurrence studied by Propp, Fomin and Zelevinsky, Speyer, and Fock and Goncharov and the three-dimensional cube recurrence studied by Fomin and Zelevinsky, and Carroll and Speyer. The states of this recurrence are indexed by tilings of a polygon with rhombi, and the variables in the recurr...

• Published 1. Rectilinear equilateral sets in Rn, Geombinatorics, 20 (2011) 151–167. Kusner (1983) conjectured that the maximum size of a set whose elements are pairwise equidistant under the `1-norm in Rn is 2n. If true, this would be sharp. The conjecture has been proved for n = 3 (in 1998) and n = 4 (in 2000). Recently, Alon and Pudlak gave an upper bound of O(n lnn). These proofs are very ...

dft and qtaim computations have been performed on numbers of pure nitrogen cluster speciesi.e. nn (n = 4, 6) for investigating the structure and bonding. this study is critical since thesemolecules have been nominated as the good synthetic targets of high energy materials (hem).0nthe other hand the decomposition mechanism is closely depends on the bonding pattern. thislatter concept was searche...

Carbothermal reduction to recover lithium-ion batteries is an environmentally friendly recycling method. This work provides a theoretical analysis of the thermodynamics and experimental verification process for carbon thermal recovery lithium cobaltate (LiCoO 2 ), as well explanation microstructural changes. The reaction conditions are controlled obtain ideal product. A thermodynamic graph poss...

This paper reports the construction of cubature formulas for a finite element in form bipyramid, which have second algebraic order accuracy. The proposed explicitly take into consideration parameter bipyramid deformation, is important when using irregular grids. were constructed by applying two schemes location interpolation nodes along polyhedron axes: symmetrical and asymmetrical. intervals c...

T he first annual International Bio-Molecular Design Competition (BIOMOD2011) was held on November 5, 2011, at the Wyss Institute for Biologically Inspired Engineering at Harvard University (Cambridge, MA, USA). BioMod is a design competition for undergraduate students that was founded by Wyss Institute Technology Development Fellow Shawn Douglas. Teams of students engineer novel nanoscale stru...

Using the spin unrestricted Becke-3-Lee-Yang-Parr density functional, we computed the electronic structure of explicitly doped La22xSrxCuO4 (x50.125, 0.25, and 0.5!. At each doping level, an impurity hole band is formed within the undoped insulating gap. This band is well localized to CuO6 octahedra adjacent to the Sr impurities. The nature of the impurity hole is A1g in symmetry, formed primar...

The Ta(6)Br(12)(2+) cluster compound is known to be a powerful reagent for derivatization of crystals of large macromolecules at low resolution. The cluster is a regular octahedron of six Ta atoms with 12 bridging Br atoms at the edges of the octahedron. The cluster is compact, of approximately spherical shape, with a radius of about 6 A. Both tantalum and bromine display a significant anomalou...

Cerium oxide nanoparticles (nano-CeO₂) have been reported to cause damage and apoptosis in human primary hepatocytes. Here, we compared the toxicity of three types of nano-CeO₂ with different nanocrystal morphologies (cube-, octahedron-, and rod-like crystals) in human hepatocellular carcinoma cells (HepG2). The cells were treated with the nano-CeO₂ at various concentrations (6.25, 12.5, 25, 50...

In recent years a method of recursive subdivisions of the triangular faces of the octahedron or icosahedron has been developed for approximating to the surface of the earth. But the triangle-based discrete grids produced by this method are complicated in geometry structure, and is difficult to make such geographical operations as neighbor-finding, spatial searches and so on. In this paper we co...