S-matrices

A new class of so called S-matrices is introduced which allows investigating links between various known classes of matrices such as Vandermonde matrices, Hankel matrices, companion matrices, etc. For complex S-matrices, the problem of decomposition into a quasidirect sum (a sum for which the sum of the ranks of the summands equals the rank of the given matrix) of indecomposable complex S-matrices is completely solved, and the uniqueness of such a decomposition is proved.     

Application of NMR spectroscopy of chiral association complexes. 8—Rotation about the C(sp2)–C(aryl) Bond in 2,6–disubstituted benzamides

The barrier to rotation about the C(sp²)? C(aryl) single bond in non-planar benzoyl compounds was investigated using N,N-dimethyl, N,N-tetramethylene and N,N-diisopropyl derivatives of 2,4,6-trimethylbenzamide and 2,6-dimethoxybenzamide and N,N-dimethyl derivatives of the corresponding thiobenzamides. Their ¹H and ¹³C NMR spectra were determined and assigned and the splittings in the ¹H spectra due to the addition of the optically active shift reagent (+)-Eu(hfbc)₃, are discussed. The free enthalpy of activation was calculated from the coalescence temperature of the ortho-methyl or -methoxyl signals and from a line-shape analysis. An exact equation for the determination of the rate constant at coalescence and a valid approximation which includes the line-width are presented. A distinct effect of the size of the N-substituent on the barrier to rotation in 2,6-dimethoxybenzamides was observed, while the π values for the 2,4,6-trimethylbenzamides studied are practically identical.     

Long range substituent effects relfected in the 13C NMR spectra of allyl alcohols and their derivatives

Acylation of allyl alcohols induces strong carbon shifts, shielding γ and deshielding δ effects. These shifts are a consequence of through-bond polarization of the olefinic carbons. Allyl ethers show similar, but milder perturbations. The olefinic carbon shifts reveal a strong concentration dependence. This effect, in greatly reduced form, is also observed in non-oxygenated alkenes. Hydrogen bonding by alcohols enhances the chemical shift difference in olefinic carbon pairs by increased polarization.     

Generalized reflective cum coreflective classes in Top and Unif

The Herrlich's problem from [8] whether there are nontrivial classes of topological spaces that are both almost reflective or injective and almost coreflective or projective, is investigated in a more general setting using cone and cocone modifications of the classes used in the problem. We look also at the problem for uniform spaces. Typical results: There is no nontrivial multiprojective and orthogonal class of topological spaces; There is a reflective class of uniform spaces that is almost coreflective in Unif.Work on this paper was initiated while the first author was a C.N.R. visitor of the University of L'Aquila. Partial financial assistence by Charles University Grant 349/1994 is also acknowledged.     

Numerical experiments with two approximate inverse preconditioners

We present the results of numerical experiments aimed at comparing two recently proposed sparse approximate inverse preconditioners from the point of view of robustness, cost, and effectiveness. Results for a standard ILU preconditioner are also included. The numerical experiments were carried out on a Cray C98 vector processor. This work was partially supported by the GA AS CR under grant 2030706 and by the grant GA CR 205/96/0921.     

Topological characterizations of linearly uniformizable spaces

The spaces having uniformities with a totally ordered base are characterized in bigger classes of non-archimedean spaces and suborderable spaces. Consequently, several new metrization results are obtained. By examples, we show that the conditions used in our main theorem cannot be weakened essentially. Our examples may be interesting elsewhere, too.     

Sesquiterpene lactones of new stereostructural types from laser trilobum

The newly established structures of sesquiterpene lactones from Laser trilobum showed that these lactones belong among the stereostructural types of germacranolides, guaianolides, eudesmanolides and elemanolides.