Essential domains and two conjectures in dimension theory

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.

     

Etude théorique par la méthode DFT des structures non-classiques des systèmes X2H2F2 (X=Si, Ge, Sn)

The structure and the relative stability of isomers of molecules X₂H₂F₂ (X=Si, Ge, Sn) have been studied using the density functional theory (DFT). We have determined the optimised structures of the substituted isomers. The XX bond have been studied and compared to that of the parent molecules: X₂H₄. It appears that, for the planar and trans ethylenic systems, the double bond character of the XX decreases when the hydrogen atoms are substituted by fluorine atoms. The most stable structure is shown to be the one where the two fluorine atoms are fixed on the same atom. The bridged structures are also studied.     

Cohomology Rings of Aspherical Groups

It is shown by construction that the only restriction on theintegral cohomology ring of a finitely presented asphericalgroup is that it has dimension at most 2.     

Two-dimensional electrophoresis of plasma proteins and high density lipoproteins during inflammation

Plasma protein and lipoprotein fractions of five patients were analyzed on day 1, 5, and 15 after severe head injury by combining three types of two-dimensional electrophoresis (2-DE) to obtain information on lipoprotein and apolipoprotein composition. On analysis under nondenaturing conditions in both dimensions on day 5, the samples show modifications of isoelectric point (pI) and molecular weight (Mr) properties of the high density lipoprotein (HDL) fraction in addition to an increase in inflammatory proteins and a return to a normal pattern on day 15. In the second type of 2-DE the samples were analyzed employing isoelectric focusing without denaturant in the first dimension, followed by sodium dodecyl sulfate (SDS) in the second dimension in order to study the protein composition of lipoprotein fractions. On day 5, a decrease of the apolipoproteins apo A-I, apo A-II, and apo C were noted, with simultaneous appearance of an unidentified protein with Mr 12,000 and pI 6.0. In the third type of 2-DE, employing urea and Nonidet P-40 in the first and SDS in the second dimension, the plasma polypeptide composition was studied. The presence of an unidentified polypeptide could be confirmed on day 5, tending to disappear thereafter. This Mr 12,000 component consists of two major spots at pI 5.7 and 6.0 and four minor ones between pI 6.0 and 8.0. These properties suggest that this protein corresponds to serum amyloid A apolipoprotein.     

Variational approach to serial multilevel production/inventory systems

We discuss stochastic, continuous-time models of serial multilevel production/inventory systems using quasi-variational inequalities. The value functions are characterized as maximum solutions of suitable equivalent problems. Then, we show how to construct optimal centralized policies and, if possible, decentralized policies. Finally, we present some numerical examples for the deterministic case.The work of the second author was supported by the National Science Foundation under Grant No. DMS-87-02236.     

Molecular geometry and vibrational studies of 3,5-diamino-1,2,4-triazole using quantum chemical calculations and FT-IR and FT-Raman spectroscopies

The 3,5-diamino-1,2,4-triazole (guanazole) was investigated by vibrational spectroscopy and quantum methods. The solid phase FT-IR and FT-Raman spectra were recorded in the region 4000-400 cm(-1) and 3600-50 cm(-1) respectively, and the band assignments were supported by deuteration effects. The results of energy calculations have shown that the most stable form is 1H-3,5-diamino-1,2,4-triazole under C1 symmetry. For this form, the molecular structure, harmonic vibrational wave numbers, infrared intensities and Raman activities were calculated by the ab initio/HF and DFT/B3LYP methods using 6-31G* basis set. The calculated geometrical parameters of the guanazole molecule using B3LYP methodology are in good agreement with the previously reported X-ray data, and the scaled vibrational wave number values are in good agreement with the experimental data. The normal vibrations were characterized in terms of potential energy distribution (PEDs) using VEDA 4 program.