Total synthesis of the marine cytotoxic caulibugulones A-D

We report the first total synthesis of the cytotoxic marine alkaloids caulibugulone A-D. This synthesis confirmed the assigned structures and provided sufficient material for further biological testing.     

Non-Steady-State Natural Convection in a Model Electrochemical System with Vertical and Horizontal Plane Electrodes

Non-steady-state mass-transfer processes in the electrochemical cells of rectangular cross-section with vertical and horizontal electrodes under the conditions of natural convection are simulated numerically taking into account the diffusion and convection of solely ions discharging at the electrode under limiting-current conditions. The interrelated time variations of the limiting current density at various ratios of the electrode height (length) to the interelectrode distance and the distributions of ion concentration and hydrodynamic velocity over the cell are determined.     

Absorption of cnoidal electromagnetic waves by superlattice electrons in the process of impurity ionization

Absorption of cnoidal electromagnetic waves, which are the most general periodic solution to the sine-Gordon equation, by electrons of a one-dimensional quantum semiconductor superlattice in the process of impurity ionization is studied in terms of the semiclassical approximation. The dependence of the absorption coefficient on the electric field of an electromagnetic wave is found to be nonmonotone with a pronounced peak.     

Condensation of Isatoic Anhydride with Hetarylguanidines

Condensation of isatoic anhydride with 4-methylquinazolin-2-yl-, 2-benzoxazolyl-, 2-benzothiazolyl-, and 4,6-dimethylpyrimidin-2-ylguanidines leads to the corresponding 2-hetarylamino-4-hydroxyquinazolines as a result of cyclization of intermediate anthranilic acid hetarylguanidides. These intermediates can be isolated as individual compounds.     

Dispersion analysis of the least‐squares finite‐element shallow‐water system

The frequency or dispersion relation for the least‐squares mixed formulation of the shallow‐water equations is analysed. We consider the use of different approximation spaces corresponding to co‐located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd.     

On simultaneous linear extensions of partial (pseudo)metrics

We consider the question of simultaneous extension of (pseudo) metrics defined on nonempty closed subsets of a compact metrizable space. The main result is a counterpart of the result due to Künzi and Shapiro for the case of extension operators of partial continuous functions and includes, as a special case, Banakh's theorem on linear regular operators extending (pseudo)metrics.

     

Noncommutative differential geometry related to the Young-Baxter equation

An analogue of the differential calculus associated with a unitary solution of the quantum Young-Baxter equation is constructed. An example of a ring sheaf is considered in which local solutions of the Young-Baxter quantum equation are defined but there is no global section. Bibliography: 13 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 199, 1992, pp. 51–70. Translated by I. A. Izergina.