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.     

A bicontinuous structure in some systems with cubic mesophases

A cubic structure of polymer colloid complexes is studied. The technique of the research includes i) an analysis of well-known literature SAXS data; on this basis, ii) constructing a simple model to estimate geometric structure parameters and to obtain a simulated scattering curve; and iii) comparing the model with the real structure obtained from the SAXS data, using the reconstruction of electron density distribution. A bicontinuous structure in cubic mesophases is formed. Dedicated to the memory of Alexander T. Dembo     

Fundamental solutions of the acoustic and diffusion equations in nonhomogeneous medium

A fundamental solution of the acoustical equation with a variable refraction coefficient is constructed. The solution satisfies the limiting absorption and radiation conditions. The optimal high frequency estimate is proved for square means of the solution. The source function for the diffusion equation is a by-product of this construction. Partially supported by a stipend of the Mathematical Scientific Research Institute at Berkeley, 2001.     

Target Level Method in Linear Multi-Criterion Problems

We consider the target level method for solving linear multi-criterion maximization problems. The method finds an efficient (Pareto-optimal) vector estimate that is closest in the Chebyshev metric to the target level point specified by the decision maker. The proposed method describes (parametrizes and approximates) the efficient set. In the linear case the number of scalar optimization problems needed to describe the set of efficient vector estimates is substantially reduced. A formula is derived which, under certain conditions, can be used to compute efficient vector estimates without solving any optimization problems. An algorithm based on these results is proposed for two-criterion problems.     

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.     

Covering group and graph of discretized volumes

We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L _V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ _v associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.     

On an Inverse Problem for a Parabolic Equation

In this paper, we study the inverse problem of the reconstruction of the right-hand side of special form for a parabolic equation in u in which the coefficients of u _t and u depend on u _(x,t) , with overdetermination given by the integral of the solution over time. The Fredholm property for this problem and the existence and uniqueness theorems in Sobolev spaces are established.     

On the structure of hyperbolic manifolds

Forn≥2, we quantify the Margulis constant ε(n) giving rise to a thick and thin decomposition of hyperbolicn-manifolds of finite volume. As a consequence, we obtain new universal lower bounds for the volume and Gromov's invariant as well as a geometrical inequality between injectivity radius and diameter for compact manifolds. Finally, we concretise the upper bound for the counting function of hyperbolic manifolds of dimension >4 as described by Burger, Gelander, Lubotzky and Mozes. Partially supported by Schweizerischer Nationalfonds No. 20-61379.00 and 20-67619.02.