Structural trends of 77Se?1H spin–spin coupling constants and conformational behavior of 2‐substituted selenophenes

Experimental measurements and second‐order polarization propagator approach (SOPPA) calculations of ⁷⁷Se? ¹H spin–spin coupling constants together with theoretical energy‐based conformational analysis in the series of 2‐substituted selenophenes have been carried out. A new basis set optimized for the calculation of ⁷⁷Se? ¹H spin–spin coupling constants has been introduced by extending the aug‐cc‐pVTZ‐J basis for selenium. Most of the spin–spin coupling constants under study, especially vicinal ⁷⁷Se? ¹H couplings, demonstrated a remarkable stereochemical behavior with respect to the internal rotation of the substituent in the 2‐position of the selenophene ring, which is of major importance in the stereochemical studies of the related organoselenium compounds. Copyright © 2009 John Wiley & Sons, Ltd.     

Mechanistic study of palladium catalyzed S-S and Se-Se bonds addition to alkynes

The mechanistic study of palladium catalyzed S-S and Se-Se bonds addition to alkynes revealed the involvement of dinuclear transition metal complexes in the catalytic cycle. Coordination of alkyne to dinuclear transition metal complex was found to be the rate determining step of the reaction. An unusual phosphine ligand effect increasing the yield of addition reaction was found in the studied system. A new synthetic procedure was developed to perform the catalytic reaction using easily available Pd(II) complex. The scope of the reaction and the reactivity of S-S and Se-Se bonds toward alkynes were investigated. The X-ray structure of the product of S-S bond addition reaction showed favorable geometry for the possible application as a chelate ligand.     

Investigation of dielectric after-effects in poly- and single crystalline BaTiO3

Dielectric relaxation occurring in single- and polycrystalline BaTiO₃, following different polarization treatments of the specimens has been investigated in the temperature range 10 K<T<450 K. The observed relaxation phenomena are discussed in terms of polarization induced growth of extra-domains which, via corresponding enhancement of the total domain wall area, may account for the time dependence of the dielectric constant. On the basis of this relaxation model the activation parameters of the different processes are determined and discussed in terms of variations of the wall mobility within the different crystallographic phases occurring in BaTiO₃.     

On the Total Domination Number of Cartesian Products of Graphs

The most famous open problem involving domination in graphs is Vizings conjecture which states the domination number of the Cartesian product of any two graphs is at least as large as the product of their domination numbers. In this paper, we investigate a similar problem for total domination. In particular, we prove that the product of the total domination numbers of any nontrivial tree and any graph without isolated vertices is at most twice the total domination number of their Cartesian product, and we characterize the extremal graphs.Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal     

Malliavin's theorem for weak synthesis on nonabelian groups

Malliavin's celebrated theorem on the failure of spectral synthesis for the Fourier algebra A(G) on nondiscrete abelian groups was strengthened to give failure of weak synthesis by Parthasarathy and Varma. We extend this to nonabelian groups by proving that weak synthesis holds for A(G) if and only if G is discrete. We give the injection theorem and the inverse projection theorem for weak X-spectral synthesis, as well as a condition for the union of two weak X-spectral sets to be weak X-spectral for an A(G)-submodule X of VN(G). Relations between weak X-synthesis in A(G) and A(G×G) and the Varopoulos algebra V(G) are explored. The concept of operator synthesis was introduced by Arveson. We extend several recent investigations on operator synthesis by defining and studying, for a V^∞(G)-submodule M of B(L²(G)), sets of weak M-operator synthesis. Relations between X-Ditkin sets and M-operator Ditkin sets and between weak X-spectral synthesis and weak M-operator synthesis are explored.     

On k-networks and weak bases for spaces

In this paper, we answer some problems on k-networks and weak bases posed by Liu and Tanaka (2007) [19].     

The central limit theorem for stationary Markov processes with normal generator—with applications to hypergroups

We extend the central limit theorem for additive functionals of a stationary, ergodic Markov chain with normal transition operator due to Gordin and Lif?ic, 1981 [A remark about a Markov process with normal transition operator, In: Third Vilnius Conference on Probability and Statistics 1, pp. 147–48] to continuous-time Markov processes with normal generators. As examples, we discuss random walks on compact commutative hypergroups as well as certain random walks on non-commutative, compact groups.