Given a line arrangement A with n lines, we show that there exists a path of length n/3−O(n) in the dual graph of A formed by its faces. This bound is tight up to lower order terms. For the bicolored version, we describe an example of a line arrangement with 3k blue and 2k red lines with no alternating path longer than 14k. Further, we show that any line arrangement with n lines has a coloring ...

The realizability problem for rank 3 oriented matroids (see [1]) is equivalent to the pseudoline stretchability problem (see [4]). This paper uses an example to illustrate a new approach to this problem. The main theorem of this paper, like the trigonometric form of Ceva’s theorem, shows a non-trivial relationship amongst the angles in a specific line arrangement figure (c). We work in polar co...

In the title mercury complex, catena-poly[[di-chlorido-mercury(II)]-μ-2,2'-(2-bromo-5-tert-butyl-1,3-phenyl-ene)bis-(1-methyl-1H-benzimidazole)-κ2N3:N3'], [HgCl2(C26H25BrN4)] n , the HgII atom is coordinated by two Cl atoms and by two N atoms from two 2,2'-(2-bromo-5-tert-butyl-1,3-phenyl-ene)bis-(1-methyl-1H-benzimidazole) ligands. The metal cation adopts a distorted tetrahedral coordination g...

We consider generalizations of the honeycomb problem to the sphere S and seek the perimeter-minimizing partition into n regions of equal area. We provide a new proof of Masters’ result that three great semicircles meeting at the poles at 120 degrees minimize perimeter among partitions into three equal areas. We also treat the case of four equal areas, and we prove under various hypotheses that ...

Making an initial tetrahedral grid for complex geometry can be a tedious and time consuming task. This paper describes a novel procedure for generation of starting tetrahedral cells using hexahedral block topology. Hexahedral blocks are arranged around an aerodynamic body to form a flow domain. Each of the hexahedral blocks is then decomposed into six tetrahedral elements to obtain an initial t...

Analyses of the x-ray diffraction intensity data by the Patterson synthesis and rotation function techniques show that the true space group of the monoclinic crystals of L-asparaginase (L-asparagine amidohydrolase, EC 3.5.1.1) from Proteus vulgaris is P21, that the molecular centers lie at x = 0.054, y = 0, z = 0.256, and its symmetry related positions, and that the tetramer molecules possess t...

A method has been developed for analyzing the X-ray diffraction patterns of amorphous solids, and the atomic arrangement in two simple glasses has been completely worked out. In SO2, for example, each silicon is tetrahedrally surrounded by 4 oxygens at a distance 1.60 A, and each oxygen is shared between two such tetrahedral groups. The mutual orientation of the two groups about their common di...

We report results from a molecular simulation study of the structure and dynamics of water near single carbohydrate molecules (glucose, trehalose, and sucrose) at 0 and 30 degrees C. The presence of a carbohydrate molecule has a number of significant effects on the microscopic water structure and dynamics. All three carbohydrates disrupt the tetrahedral arrangement of proximal water molecules a...

Near-field vector intensity measurements have been made of a 12.7-cm diameter nozzle solid rocket motor. The measurements utilized a test rig comprised of four probes each with four low-sensitivity 6.35-mm pressure microphones in a tetrahedral arrangement. Measurements were made with the rig at nine positions (36 probe locations) within six nozzle diameters of the plume shear layer. Overall lev...

low stacking fault energy face centered cubic (fcc) materials contain characteristic defect structures. stackingfault tetrahedral are one of those rare structures that occur under special experimental conditions. for the first time,stacking fault tetrahedral were observed in fe-30mn-3al-3si twinning induced plasticity (twip) steel. theirpresence resulted from a quenching heat treatment.