Volume comparison and the σk-Yamabe problem

In this paper we study the problem of finding a conformal metric with the property that the kth elementary symmetric polynomial of the eigenvalues of its Weyl-Schouten tensor is constant. A new conformal invariant involving maximal volumes is defined, and this invariant is then used in several cases to prove existence of a solution, and compactness of the space of solutions (provided the conformal class admits an admissible metric). In particular, the problem is completely solved in dimension four, and in dimension three if the manifold is not simply connected.     

Conformational analysis of 3-borabicyclo[3.3.1]nonane derivatives

Conformations of 3-borabicyclo[3.3.1]nonane derivatives have been studied by means of ¹H and ¹³C NMR spectroscopy. With the aid of the coupling constants ³J(HH) and ¹³C chemical shifts it has been shown that all the derivatives of 3-borabicyclo[3.3.1]nonane with the trigonal boron atom studied are in a flattened double-chair conformation. In 3-borabicyclo[3.3.1]nonane derivatives with the tetra-coordinated boron atom and substituents at the 7α-position, the chair-boat conformation predominates, the boat conformation being characteristic of the cyclohexane ring; exceptions are the compounds with the internal donor—acceptor bond between the boron atom an 7α-substituent.     

How gap genes make their domains: An analytical study based on data driven approximations

We consider a mathematical formulation of the problem of protein production during segment determination in the Drosophila blastoderm, together with some preliminary results of its analytical study. We reformulate the spatial difference equations as a set of nonlinear partial differential equations and obtain their dimensionless form in the continuum limit. Using previous results obtained by the gene circuit method, we find an asymptotic statement of the problem with a small parameter. Some results of the comparison method applied to the model are obtained, and exact stationary upper solutions are derived. They exhibit distinctive features of localized bell-shaped structures. (c) 2001 American Institute of Physics.     

Existence of complete conformal metrics of negative Ricci curvature on manifolds with boundary

We show that on a compact Riemannian manifold with boundary there exists ${u \in C^{\infty}(M)}$ such that, u _|?M ?? 0 and u solves the ?? _k -Ricci problem. In the case k = n the metric has negative Ricci curvature. Furthermore, we show the existence of a complete conformally related metric on the interior solving the ?? _k -Ricci problem. By adopting results of (Mazzeo and Pacard, Pacific J. Math. 212(1), 169?C185 (2003)), we show an interesting relationship between the complete metrics we construct and the existence of Poincaré?CEinstein metrics. Finally we give a brief discussion of the corresponding questions in the case of positive curvature.     

Application of Chemical Kinetics Methods to the Study of Iodonitrotetrazolium Chloride Reduction in the Presence of Bacillus subtilis Cells

It is demonstrated that the reduction of iodonitrotetrazolum chloride in the presence of a Bacillus subtilis suspension in a physiological solution can be described using chemical kinetics equations. The effective kinetic parameters are determined and the role of the diffusion of iodonitrotetrazolium chloride in the process of its reduction involving bacterial cell components is described.

     

Inhibition of Intracellular Succinate Dehydrogenase of the Bacillus subtilis Bacterium as a Criterion for the Involvement of an Enzyme in the Reduction of Chloride Iodonitrotetrazolium,an Indicator of Cell Viability

Moscow University Chemistry Bulletin - After diffusion of the tetrazolium salt to membrane reducing agents of the Bacillus subtilis cells, the reduction rate is shown to be affected by the state of...