The Central Curve in Linear Programming

The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over any region in the associated hyperplane arrangement. We determine the degree, arithmetic genus and defining prime ideal of the central curve, thereby answering a question of Bayer and Lagarias. These invariants, along with the degree of the Gauss image of the curve, are expressed in terms of the matroid of the input matrix. Extending work of Dedieu, Malajovich and Shub, this yields an instance-specific bound on the total curvature of the central path, a quantity relevant for interior-point methods. The global geometry of central curves is studied in detail.     

On semiprojectivity of -algebras of directed graphs

It is shown that if is a countable, transitive directed graph with finitely many vertices, then is semiprojective.

     

Liquid secondary ion mass spectrometric investigation of ion-pair precipitates of some ethoxylates with barium tetraphenylborate

Liquid secondary ion mass spectrometry seems to be useful technique for the qualitative characterization of ion-pair precipitates of ethoxylates with barium tetraphenylborate. In the positive mode, barium complexes of ethoxylates were examined. In the negative mode, the ion signal of tetraphenylborate had 100% intensity relative to the matrix peaks. The low-resolution mass spectra were found to be suitable for checking the purity of ion-pair precipitates of ethoxylates with barium tetraphenylborate. On the basis of B/E mass spectra, the fragmentation routes of [M - H + Ba](+) ions are proposed. Copyright 2000 John Wiley & Sons, Ltd.     

A synthesis of some novel 4,5-dihydroazepines by the reaction of oxazolium 5-oxides with 1,2-dicyanocyclobutene

Heating primary or secondary α-amino acids in acetic anhydride in the presence of 1,2-dicyanocyclobutene leads to 4,5-dihydroazepines via the intermediacy of mesoionic oxazolium 5-oxides.     

Efficient stream distributions in radiative transfer theory

This paper discusses a new, computationally-efficient method for approximating the integro-differential equation of radiative transfer with a finite set of coupled differential equations for discrete streams. The method uses recommended spatial distributions of streams that are quite different from those typically used in that they are based on the symmetry of several regular Platonic solids. To facilitate the use of such distributions, an explicit, one- parameter relationship between the physical radiance and the abstract stream is formulated. The parameter is used to determine the minimum number of streams required in the radiative transfer model. Accuracy and computational efficiency are shown to be served best by choosing a stream distribution that is invariant to a large number of three space rotations. For various values of the above-mentioned parameter, the resulting recommended stream distribution is shown to be more computationally efficient than more conventional stream distributions. Finally, the incorporation of polarization in the stream definition is described.     

Synthesis and characterization of seven-coordinate tripodal imidazole complexes of iron(II) and manganese(II)

The iron(II) and manganese(II) complexes of the N(7) Schiff-base condensate of tris(3-aminopropyl)amine with 1-methyl-2-imidazolecarbaldehyde and the manganese(II) complex of the N(7) Schiff-base condensate of tris(3-aminopropyl)amine with 4-imidazolecarbaldehyde are high-spin mono capped octahedral seven-coordinate complexes with a short, approximately 2.44 è, metal to apical nitrogen bond.     

Nuclear magnetic shielding and chirality IV. The odd and even character of the shielding response to a chiral potential

We investigate the odd and even character of the shielding response in a chiral molecule (modeled by a Ne8 helix) when subjected to a chiral potential. We establish that the diastereomeric splittings are a measure of odd powers of Vodd. Implications for diastereomeric, splittings of Xe in handed cages with handed tethers are discussed.     

Spermine participates in oxidative damage of guanosine and 8-oxoguanosine leading to deoxyribosylurea formation

Oxidation of single- or double-stranded DNA containing a 7,8-dihydro-8-oxoguanosine lesion with the one-electron oxidant Na2IrCl6 in the presence of spermine led to formation of a covalent adduct that was analyzed by gel electrophoresis, HPLC, ESI-MS, and UV-vis. The adduct was labile to heat, exhibiting a t1/2 of 12 h at 37 degrees C, and the ultimate hydrolysis product was characterized as a deoxyribosylurea lesion. Data from model studies with 1,3-diaminopropane vs 1,4-diaminobutane are consistent with initial formation of a C5 spermine adduct from a dehydro-8-oxoguanosine intermediate, followed by rearrangement to a spiroaminal subject to slow hydrolysis at C4 of the purine. Spermine adducts could also be formed from oxidation of the analogous G-containing oligomer from reaction with singlet oxygen, albeit in lower yield. These results are surprising in light of the traditional view that spermine is radioprotective against DNA oxidation.