Fully closed mappings and their applications

This survey is devoted to the theory of fully closed mappings and their applications. The theoretical part includes a systematic study of relations between fully closed mappings and fiber products, inverse systems, and resolutions. The projective properties of fully closed mappings are studied. The applications are largely related to dimension and cardinal functions. The results are mainly due to the author and his students. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 4, pp. 105–235, 2003.     

Use of Voltammetry for Determining Antibiotics Streptomycin and Azitromycin

Conditions were selected for the voltammetric determination of streptomycin and azitromycin using electrodes of different types. The interfering effects of cations, anions, and organic substances, food proteins among them, on the analytical signals from antibiotics were estimated. Procedures for determining streptomycin and azitromycin in pharmaceuticals and for determining streptomycin in milk at nano levels were developed.__________Translated from Zhurnal Analiticheskoi Khimii, Vol. 60, No. 6, 2005, pp. 586–591.Original Russian Text Copyright © 2005 by Fedorchuk, Puchkovskaya, Anisimova, Slepchenko.Presented at the VI All-Russian Conference (with international participation) on Electrochemical Methods of Analysis (EMA-2004, Ufa, May 23–27, 2004).     

An asymmetrically substituted borazine

The B₃N₃ ring in the title compound, 1,3,5‐tri‐tert‐butyl‐2,4‐difluoro‐6‐phenyl­cyclo­triborazane, [PhF₂B₃N₃^tBu₃] or C₁₈H₃₂B₃F₂N₃, an asymmetrically substituted borazine, is distorted from planarity. The molecule resides on a twofold axis. The N atoms of the N—B(Ph)—N group lie on opposite sides of the least‐squares plane formed by the four remaining ring atoms, due to steric accommodation of the tert‐butyl groups, a conformation not previously observed for a borazine. The B—N bond lengths are in the range 1.4283 (14)–1.4493 (12) Å, due to the F substituents residing on two of the B atoms, which also produce a large deviation from 120° in one of the B—N—B angles [ca 113.6 (1)°]. The phenyl group is twisted with respect to the B₃N₃ ring, the interplanar angle being 62.87 (5)°.     

Symmetry reduction and some exact solutions of a nonlinear five-dimensional wave equation

By using decomposable subgroups of the generalized Poincaré group P(1,4), we perform a symmetry reduction of a nonlinear five-dimensional wave equation to differential equations with a smaller number of independent variables. On the basis of solutions of the reduced equations, we construct some classes of exact solutions of the equation under consideration.     

Ordered proximity spaces

We shall investigate proximities in ordered sets corresponding to ordered bicompact extensions.Translated from Matematicheskie Zametki, Vol. 4, No. 6, pp. 659–667, December, 1968.     

Finite Hilbert stability of (bi)canonical curves

We prove that a generic canonically or bicanonically embedded smooth curve has semistable mth Hilbert points for all m≥2. We also prove that a generic bicanonically embedded smooth curve has stable mth Hilbert points for all m≥3. In the canonical case, this is accomplished by proving finite Hilbert semistability of special singular curves with $\mathbb{G}_{m}$ -action, namely the canonically embedded balanced ribbon and the canonically embedded balanced double A _2k+1-curve. In the bicanonical case, we prove finite Hilbert stability of special hyperelliptic curves, namely Wiman curves. Finally, we give examples of canonically embedded smooth curves whose mth Hilbert points are non-semistable for low values of m, but become semistable past a definite threshold.     

Rational Design of Practically Important Enzymes

Majority of native enzymes are poorly applicable for practical usage: that is why different methods of enzyme modification are used to obtain the biocatalysts with appropriate characteristics. Development of genome sequencing and various modern approaches in protein engineering allow one to identify protein of interest and to improve the enzyme properties for a particular process. This review describes the results on development of novel biocatalysts based on bioinformatics and rational design. New genes encoding formate dehydrogenase (FDH) from bacterium Staphylococcus aureus, yeasts Ogataea parapolymorpha and Saccharomyces cerevisiae and moss Physcomitrella patens (SauFDH, OpaFDH, SceFDH and PpaFDH, respectively), have been cloned. New FDHs were produced in the active form and characterized. SauFDH was shown to have at least 2-fold higher catalytic constant than other known FDHs. OpaFDH has catalytic parameters as good as those for soy FDH mutant forms, and in addition, is more thermostable. Apo- and holo-forms of SauFDH have been crystallized. Mutation of two Cys residues in Pseudomonas sp.101 enzyme (PseFDH) yields enzyme preparations with improved kinetic parameters and enhanced thermal and chemical stability. New generation of PseFDH preparations with the coenzyme specificity changed from NAD⁺ to NADP⁺ have been obtained. The effect of ionic liquids on the catalytic properties and thermal stability of six wild-type recombinant FDHs, and a number of their mutants, have been studied. In case of D-amino acid oxidase (DAAO), single-point mutations have been combined to create multi-point mutants. The introduced amino acid replacements have been shown to exert an additive effect, improving both kinetic parameters and increasing thermal and chemical stability. DAAO genes from Hansenula polymorpha yeast have been cloned. α-Amino acid ester hydrolase (AEH) gene has been cloned and expressed in the active form in E. coli. Structural modeling has been performed and the effectiveness in amino beta-lactams synthesis studied. The structure of a single-chain penicillin acylase from Alcaligenes faecalis (scAfPA) has been modeled and two variants of scAfPA gene was generated by PCR. Both variants have been expressed in E. coli, isolated and characterized. Catalytic properties of scAfPA were slightly better than those of its natural heterodimer.     

Partial Sn‐atom ordering in Sm3Ga0.80–2.48Sn4.20–2.52

Trisamarium digallide tristannide crystallizes with a partially ordered Pu₃Pd₅‐type structure in space group Cmcm. In a single crystal of Sm₃Ga_1.89(4)Sn_3.11(4), the 8g position is mostly occupied by Sn atoms (93% Sn and 7% Ga), while the 4c and 8f positions are occupied by a Ga/Sn statistical mixture. The evolution of the structure as a function of the Ga content has been studied by X‐ray powder diffraction on ten Sm₃Ga_5−xSn_x samples. It is shown that the 8g position remains occupied essentially exclusively by Sn atoms within the whole homogeneity range, with x ranging from 2.52 to 4.20.