In an Euclidean d-space, the container problem asks to pack n equally sized spheres into a minimal dilate of a fixed container. If the container is a smooth convex body and d ≥ 2 we show that solutions to the container problem can not have a “simple structure” for large n. By this we in particular find that there exist arbitrary small r > 0, such that packings in a smooth, 3-dimensional convex ...

The superprism behavior of Photonic Crystal (PC) due to different geometrical shapes, e.g., circular, hexagonal and square of air holes arranged in triangular lattice has been studied. Structures rely on phase velocity sensitivity in a 2D photonic crystal slab to observe and compare the angular magnification in the uniform medium outside the PC. The observation of superprism behavior has been m...

The structure of a crystalline material may be described by a crystal lattice structure and the locations of atoms in this lattice. The crystal lattice is a 3-dimensional periodic array that defines the symmetries, i.e. shape, of the crystal. There are seven possible crystal lattices: cubic, hexagonal, tetragonal, rombohedral, orthorhombic, monoclinic and triclinic. When we define the possible ...

T he topic of the “credit crunch” received considerable attention during the early 1990s. As a result, several initiatives aimed at eliminating regulatory disincentives to lending were put in place. For example, documentation requirements recently were reduced to the legal minimum for loans to small and medium-sized businesses. Also, examiners and bankers were encouraged to emphasize the charac...

Hexagonal phase (β) sodium rare earth tetrafluorides (NaREF4, RE = Y, Gd, Lu, et al.) are considered the ideal matrices for lanthanide (Ln) ions doped upconversion (UC) luminescence materials, because they can provide favorable crystal lattice structures for the doped luminescent Ln ions to make intensive emissions. However, the cubic phase (α) NaREF4 always preferentially forms at low reaction...

We performed a constrained search for the geometries of low-lying neutral germanium clusters Ge(N) in the size range of 21 < or = N < or = 29. The basin-hopping global optimization method is employed for the search. The potential-energy surface is computed based on the plane-wave pseudopotential density functional theory. A new series of low-lying clusters is found on the basis of several gener...

The study describes the synthesis and characterization of zinc(II) minoxidil nanocomposite (1). The reaction between zinc(II) acetate, minoxidil, {C9H15N5O=minoxidil=(2,4-diamino-6-piperidine-1-yl) pyrimidine N-oxide)} as a ligand and KI as bridging agent, in methanol at 60°C leads to the formation of nano-sized Zn(II) minoxidil nanocomposite, 1. Characterization of (1) was carried out by eleme...

Two-dimensional (2-D) spatially varying convolutional filters for three-dimensional (3-D) depth extrapolation are efficiently designed and implemented by using McClellan transformations. Although efficient, McClellan transformations only approximate circularly symmetric depth extrapolation filters. The accuracy of the extrapolation filters can be increased only at an increase in the computation...

Graphene, a single layer of carbon atoms bonded in a hexagonal lattice, is the thinnest, strongest, and stiffest known material and an excellent conductor of heat and electricity. However, these superior properties have yet to be realized for graphene-derived macroscopic structures such as graphene fibers. We report the fabrication of graphene fibers with high thermal and electrical conductivit...

In this paper, ZnO thin film is deposited on slide glass substrate using the sol-gel process. Presenting well-defined orientation of ZnO thin films Nanostructure were obtained by dip coating of zinc acetate dihydrate, monoethanolamine (MEA), de-ionized water and isopropanol alcohol. The annealed ZnO thin films were transparent ca 85-90% in visible range with an absorption edges at about 375 nm....