Gauss-Manin connections for arrangements, III Formal connections

We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a complex rank one local system. We define formal Gauss-Manin connection matrices in the Aomoto complex and prove that, for all arrangements and all local systems, these formal connection matrices specialize to Gauss-Manin connection matrices.

     

The exponential characteristic of the Volterra integral operator with kernel depending on 2<Emphasis Type="Italic">N</Emphasis> variables

Exponential growth is estimated for integral operators with continuous periodic kernels of exponential type. The result is applied to the boundary-value problem for a general hyperbolic differential equation having periodic coefficients with Goursat boundary conditions. It is proved that the exponential characteristic for such a boundary-value problem has canonical form. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal Conference-2004, Part 3, 2006.     

Resonance multiplicities in a hadron transport approach

In this article we focus on the multiplicities of resonances, ratios of resonant over non-resonant states and rescattering processes in heavy ion collisions. Therefore we utilize a hadron transport model (UrQMD v1.3). We find that rescattering of decay particles is of great importance when studying resonances in a hadronic medium.     

Effect of the composition of nickel-containing composites based on stabilised zirconia on catalytic activity in methane steam conversion

A study was carried out on the composition and nature of the stabilizing additive on the activity of nickel-containing composites based on zirconia in the methane steam conversion. The methane conversions were 91–99% on Ni/ZrO₂(Y, Sc, Ce) at 700–800 °C.     

Reduction of NO by C1-C4 hydrocarbons on cation-exchanged zeolites

New data are presented for the reduction of nitric oxide by C₁-C₄ hydrocarbons (alkanes and olefins) on active copper, cerium, and cobalt zeolite catalysts both with and without oxygen in the reaction mixture. The following hydrocarbon reactivity series were obtained. Olefins: C₄H₈ > C₃H₆ > C₂H₄. Alkanes: C₄H₁₀ > C₃H₈ > CH₄.L. V. Pisarzhevskii Institute of Physical Chemistry, National Academy of Sciences of Ukraine, 31 Prospekt Nauki, 252039 Kiev, Ukraine. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 32, No. 4, pp. 238–242, July–August, 1996. Original article submitted September 14, 1995.     

Microsolvation of the [Ni(acac)(tmen)]+ complex

Microsolvation of the [Ni(acac)(tmen)]⁺ complex by a series of aliphatic n-alcohols (Solv) has been studied in ClCH₂CH₂Cl solutions by spectrophotometry. Based on the changes in the electronic spectrum of the afore-mentioned complex, observed under the influence of any alcohol, the equilibrium constants for the formation of the [Ni(acac)(tmen)Solv]⁺ and [Ni(acac)(tmen)Solv₂]⁺ species have been computed according to the algorithm presented in this work. It was found that, in all the systems studied, the stability of five-coordinated [Ni(acac)(tmen)Solv]⁺ is higher than that of octahedral [Ni(acac)(tmen)Solv₂]⁺. The resulting values are discussed in terms of the Lewis basicity of alcohols.     

Enantioselective Preparation of 2‐Aminomethyl Carboxylic Acid Derivatives: Solving the β2‐Amino Acid Problem with the Chiral Auxiliary 4‐Isopropyl‐5,5‐diphenyloxazolidin‐2‐one (DIOZ). Preliminary Communication

Multigram amounts of suitably protected β²‐amino acids with 17 of the 20 proteinogenic side chains are prepared by diastereoselective reactions of Li, B, or Ti enolates of the corresponding 3‐acyl‐4‐isopropyl‐5,5‐diphenyloxazolidin‐2‐ones (acyl‐DIOZ; 1 ) with appropriate electrophiles (amidomethylation, hydroxyalkylation, (benzyloxycarbonyl)methylation) in yields of 55–90% and with diastereoselectivities of 80 to >97% (Scheme). The primary products 2 – 8 thus obtained are converted to protected β²‐amino acids by standard procedures (Table 1). Many of the DIOZ derivatives are highly crystalline compounds (31 X‐ray crystal structures in Table 2). The chiral auxiliary DIOZ, readily prepared in either enantiomeric form, is recovered with high yield.     

Optical sensor systems for bioprocess monitoring

Bioreactors are closed systems in which microorganisms can be cultivated under defined, controllable conditions that can be optimized with regard to viability, reproducibility, and product-oriented productivity. To drive the biochemical reaction network of the biological system through the desired reaction optimally, the complex interactions of the overall system must be understood and controlled. Optical sensors which encompass all analytical methods based on interactions of light with matter are efficient tools to obtain this information. Optical sensors generally offer the advantages of noninvasive, nondestructive, continuous, and simultaneous multianalyte monitoring. However, at this time, no general optical detection system has been developed. Since modern bioprocesses are extremely complex and differ from process to process (e.g., fungal antibiotic production versus mammalian cell cultivation), appropriate analytical systems must be set up from different basic modules, designed to meet the special demands of each particular process. In this minireview, some new applications in bioprocess monitoring of the following optical sensing principles will be discussed: UV spectroscopy, IR spectroscopy, Raman spectroscopy, fluorescence spectroscopy, pulsed terahertz spectroscopy (PTS), optical biosensors, in situ microscope, surface plasmon resonance (SPR), and reflectometric interference spectroscopy (RIF).     

Heterogeneous Catalytic Partial Oxidation of C3-C4 Alkanes with Nitrogen Monoxide

The possibility of making products of partial oxidation, alcohols and acids in particular, by the reaction of C₃-C₄ alkanes with nitrogen monoxide over oxide and zeolite catalysts is demonstrated. The most effective catalysts are CeO₂ and Fe-TsVK. The dependence of the rate and selectivity of the process on the reaction conditions has been established.