Exterior algebras related to the quantum group O(O q(3))

For the 9-dimensional bicovariant differential calculi on the quantum group O(O _q(3)) several kinds of exterior algebras are examined. The corresponding dimensions, bicovariant subbimodules and eigenvalues of the antisymmetrizer are given. Exactly one of the exterior algebras studied by the authors has a unique left invariant form with maximal degree.     

Modeling rate-controlling solvent effects. The pericyclic meisenheimer rearrangement of N-propargylmorpholine N-oxide

The activation parameters of the pericyclic Meisenheimer rearrangement and a competitive rearrangement of N-propargylmorpholine N-oxide were determined by experimental and computational methods. A number of aprotic and protic solvents of different polarities and hydrogen bond-forming abilities and the roles of electron-pair acceptor additives were investigated. The reaction kinetics were followed by means of NMR. In protic solvents, isotope-labeling experiments revealed a novel inverse secondary kinetic isotope effect (k(H)/k(D) about 0.8) for the rate-determining cyclization step, probably occurring because of a C(sp) --> C(sp(2)) change in hybridization at the reaction center. In molecular computations at the B3LYP/6-31++G(d,p) level of theory, implicit, explicit, and joint explicit-implicit solvent models were used. The explicit-implicit model and molecular dynamic simulations gave the most accurate results. The components of the rate-controlling solvent effect are discussed, and general equations are proposed for accurate prediction of the solvent-dependent activation parameters.     

A Solution of a Problem of A. E. Brouwer

Let q=p^e 1(mod 4) be a prime power, and let ^(q) be the Paley graph over the finite field . Denote by ^(q) the subgraph of ^(q) induced on the set of non-zero squares of . In this paper the full automorphism group of ^(q) is determined affirming the conjecture of Brouwer [Des. Codes Cryptograph. 21, 69–76 (2000)]. The proof combines spectral and Schur ring techniques.     

Equilibrium and NMR studies on GdIII, YIII, CuII and ZnII complexes of various DTPA-N,N'-bis(amide) ligands. Kinetic stabilities of the gadolinium(III) complexes

Three DTPA-derivative ligands, the non-substituted DTPA-bis(amide) (L(0)), the mono-substituted DTPA-bis(n-butylamide) (L(1)) and the di-substituted DTPA-bis[bis(n-butylamide)] (L(2)) were synthesized. The stability constants of their Gd3+ complexes (GdL) have been determined by pH-potentiometry with the use of EDTA or DTPA as competing ligands. The endogenous Cu2+ and Zn2+ ions form ML, MHL and M(2)L species. For the complexes CuL(0) and CuL(1) the dissociation of the amide hydrogens (CuLH(-1)) has also been detected. The stability constants of complexes formed with Gd3+, Cu2+ and Zn2+ increase with an increase in the number of butyl substituents in the order ML(0) < ML(1) < ML(2). NMR studies of the diamagnetic YL(0) show the presence of four diastereomers formed by changing the chirality of the terminal nitrogens of their enantiomers. At 323 K, the enantiomerization process, involving the racemization of central nitrogen, falls into the fast exchange range. By the assignment and interpretation of 1H and 13C NMR spectra, the fractions of the diastereomers were found to be equal at pH = 5.8 for YL(0). The kinetic stabilities of GdL(0), GdL(1) and GdL(2) have been characterized by the rates of the exchange reactions occurring between the complexes and Eu3+, Cu2+ or Zn2+. The rates of reaction with Eu3+ are independent of the [Eu3+] and increase with increasing [H+], indicating the rate determining role of the proton assisted dissociation of complexes. The rates of reaction with Cu2+ and Zn2+ increase with rising metal ion concentration, which shows that the exchange can take place with direct attack of Cu2+ or Zn2+ on the complex, via the formation of a dinuclear intermediate. The rates of the proton, Cu2+ and Zn2+ assisted dissociation of Gd3+ complexes decrease with increasing number of the n-butyl substituents, which is presumably the result of steric hindrance hampering the formation or dissociation of the intermediates. The kinetic stabilities of GdL(0) and GdL(1) at pH = 7.4, [Cu2+] = 1 x 10(-6) M and [Zn(2+)] = 1 x 10(-5) M are similar to that of Gd(DTPA)2-, while the complex GdL2 possesses a much higher kinetic stability.     

Tandem radical rearrangement/Pd-catalysed translocation of bicyclo[2.2.2]lactones. An efficient access to the oxa-triquinane core structure

The skeletal rearrangement of bicyclo[2.2.2]lactones, involving a mild and chemoselective palladium-catalysed translocation key-step, provides an efficient and diastereoselective access to synthetically useful bicyclo[3.3.0]lactones.     

Solute-solvent contact by intermolecular cross-relaxation. 2. The water-micelle interface and the micellar interior

The intermolecular dipole-dipole cross-relaxation is measured between 19F nuclei of sodium perfluorooctanoate in micelles and 1H nuclei of the water solvent. The cross-relaxation rates for fluorines in the different moieties along the surfactant vary strongly by the resonance frequency in the investigated range of 188-470 MHz. This frequency dependence indicates that the cross-relaxation between water and amphiphilic aggregates is not controlled solely by the fast local water dynamics but significantly contributed to by the long-range translational diffusion of water. The cross-relaxation rates, analyzed in the framework of a model (Nordstierna, L.; Yushmanov, P. V.; Furó, I. J. Chem. Phys. 2006, 125, 074704), provide information about the dynamic retardation of water molecules by the micellar headgroup region and the location of the various moieties along the hydrophobic tail with respect to the water-micelle interface. Both intermolecular cross-relaxation and aggregation-induced 19F chemical shift changes indicate no direct water contact to fluorines except for those closest to the head group.     

Uncatalyzed reactions in the classical Belousov-Zhabotinsky system. 2. The malonic acid-bromate reaction in acidic media

The title reaction was studied with various techniques in 1 M sulfuric acid, a usual medium for the oscillatory Belousov-Zhabotinsky (BZ) reaction. It was found to be a more complex process than the bromomalonic acid (BrMA)-BrO3- reaction studied previously in the first part of this work. Malonic acid (MA) can react with acidic bromate by two parallel mechanisms. The main aim of the present research was to determine the mechanisms, the rate laws, and the rate constants for these parallel channels. In one reaction channel the first molecular products are glyoxalic acid (GOA) and CO2 while in the other channel mesoxalic acid (MOA) is the first molecular intermediate, that is, no CO2 is formed in this step. To prove these two independent routes specific colorimetric techniques were developed to determine GOA and MOA selectively. The rate of the GOA channel was determined by following the rate of the carbon dioxide evolution characteristic for this reaction route. In this step, regarding it as an overall process, one MA is oxidized to GOA and CO2 and one BrO3- is reduced to HOBr, which forms BrMA with another MA. The initial rate of the GOA channel is a bilinear function of the initial MA and BrO3- concentrations with a second-order rate constant k(GOA)= 2.4 x 10(-7) M(-1) s(-1). The rate of the other channel was calculated from the rate of the BrO3- consumption measured in separate experiments, assuming that the measured depletion is a sum of two separate terms reflecting the consumptions due to the two independent channels. In the MOA channel one MA is oxidized to MOA and one BrO3- is consumed while another MA is brominated as in the GOA channel. It was found that the initial rate of the MOA channel is also a bilinear function of the MA and BrO3- concentrations with a second-order rate constant k(MOA)= 2.46 x 10(-6) M(-1) s(-1). Separate chemical mechanisms are suggested for both channels. In all of the various bromate-substrate reactions of these mechanisms oxygen atom transfer from the bromate to the substrate occurs generating bromous acid intermediate. This can be of high importance in BZ systems as bromous acid is the autocatalytic intermediate there. GOA and MOA also can be oxidized by acidic bromate but a study of these reactions will be published later.