We study two kinds of segment orders, using definitions first proposed by Farhad Shahrokhi. Although the two kinds of segment orders appear to be quite different, we prove several results suggesting that the are very much the same. For example, we show that the following classes belong to both kinds of segment orders: (1) all posets having dimension at most 3; (2) interval orders; and for n ≥ 3...

We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline arrangements, proved in this paper. Counting results derived from an implementation of our algorithm are also reported.

Let GH(S; H) be the bipartite graph with partition sets S and H , the set of simplices and hyperplanes of H, where simplex s∈ S is adjacent to hyperplane h∈H if one facet of s lies on h. In this paper, we give a complete characterization of GH(S; H) when H is a -arrangement. We also study GH(S; H) when H is a pseudoline arrangement. c © 2001 Elsevier Science B.V. All rights reserved.

X-ray data on single crystals of the quaternary metal hydride near the composition LiB(0.33)N(0.67)H(2.67), previously identified as "Li3BN2H8", reveal that its true composition is Li4BN3H10. The structure has body-centered-cubic symmetry [space group I2(1)3, cell parameter a = 10.679(1)-10.672(1) Angstroms] and contains an ordered arrangement of BH4- and NH2- anions in the molar ratio 1:3. The...

The arrangement of the centers of the molecules in the crystal is that corresponding to the diamond structure. Each molecule is surrounded tetrahedrally by four molecules. If we consider a molecule as roughly tetrahedral in shape with similar orientation to the tetrahedron formed by the four beryllium atoms, then the adjacent molecules are so oriented as to present tetrahedral faces to one anot...

X-ray absorption spectroscopy and x-ray Raman scattering were used to probe the molecular arrangement in the first coordination shell of liquid water. The local structure is characterized by comparison with bulk and surface of ordinary hexagonal ice Ih and with calculated spectra. Most molecules in liquid water are in two hydrogen-bonded configurations with one strong donor and one strong accep...

The transformation of SiO2 from low pressure tetrahedral phases into denser octahedral phases takes place via the collapse of the oxygen sublattice into a close-packed arrangement. The transition paths and the resulting products are known to be affected by the presence of anisotropic stresses, which are difficult to control, so interpretation of the experimental results is problematic. Based on...

Any finite set of lines in the real projective plane determines a cell complex; these complexes and their combinatorial properties have been a subject of study at least since 1826 [9]. More recently, Levi [6] considered a topological generalization of this notion, defined as follows: Consider a simple closed curve in RP2 which does not separate RP2; this is called a pseudoline. (It is clear tha...

The polysaccharides, such as κ-carrageenan, ι-carrageenan, agarose (agar), gellan gum, amylose, curdlan, alginate, and deacetylated rhamsan gum, in water changed into an ice-like structure with hydrogen bonding between polymer and water molecules, and between water-water molecules even at a concentration range of 0.1% 1.0% (W/V) at room temperature, resulting in gelation. Such dramatic changes ...