Multiplication Modules and a Theorem of P. F. Smith

P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith"s theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules. This revised version was published online in June 2006 with corrections to the Cover Date.     

Towards a synthetic glycoconjugate vaccine against Neisseria meningitidis A

Albumin conjugates of synthetic fragments of the capsular polysaccharide of the Gram-negative bacterium Neisseria meningitidis serogroup A were prepared. The fragments include monosaccharides 1 [alpha-D-ManpNAc-(1-->O)-(CH(2))(2)NH(2)] and 2 [6-O-P(O)(O(-))(2)-alpha-D-ManpNAc-(1-->O)-(CH(2))(2)NH(2)], disaccharide 3 [alpha-D-ManpNAc-[1-->O-P(O)(O(-))-->6]-alpha-D-ManpNAc-(1-->O)-(CH(2))(2)NH(2)], and trisaccharide 4 [alpha-D-ManpNAc-[1-->O-P(O)(O(-))-->6]-alpha-D-ManpNAc-[1-->O-P(O)(O(-))-->6]-alpha-D-ManpNAc-(1-->O)-(CH(2))(2)NH(2)]. Two monosaccharide blocks were employed as key intermediates. The reducing-end mannose unit featured the NHAc group at C-2, and contained the aminoethyl spacer as the aglycon for the final bioconjugation. The interresidual phosphodiester linkages were fashioned from an anomerically positioned H-phosphonate group in a 2-azido-mannose building block. The spacer-linked saccharides 1-4 were N-acylated with hepta-4,6-dienoic acid and the resulting conjugated diene-equipped saccharides were subjected to Diels-Alder-type addition with maleimidobutyryl-group functionalized human serum albumin to form covalent conjugates containing up to 26 saccharide haptens per albumin molecule. Complete (1)H, (13)C, and (31)P NMR assignments for 1-4 are given. Antigenicity of the neoglycoconjugates containing 1-4 was demonstrated by a double immunodiffusion assay which indicated that a fragment as small as a monosaccharide is recognized by a polyclonal meningococcus group A antiserum and that the O-acetyl group(s) present in the natural capsular material is not essential for antigenicity.     

Isoflavonoid glycosides from the rhizomes of Iris germanica

Four isoflavone glycosides were isolated from the rhizomes of Iris germanica. Compounds 1 and 2 are new, while compounds 3 and 4 are known isoflavone glycosides. These compounds were identified as iriskashmirianin 4'-O-beta-D-glucoside (1), nigricin 4'-O-beta-D-glucoside (2), irilone 4'-O-beta-D-glucoside (3) and iridin (4). Their structures were determined with the help of spectroscopic methods.     

Adsorption characteristics and the kinetics of the cation exchange of rhodamine-6G with Na+-montmorillonite

The adsorption and the kinetics of the cation exchange of rhodamine-6G (Rh-6G) with Na(+)-montmorillonite (Na(+)-MMT) have been studied. The binding parameters of Rh-6G have been determined by applying Freundlich and D-R isotherms. The enthalpy and the entropy of adsorption have been determined. The isosteric heat of adsorption has also been determined and decreases with increasing the concentration of Rh-6G. Increasing the concentration of Rh-6G led to a decrease in the adsorption capacity, which attributed to the formation of Rh-6G aggregates. Kinetic measurements of the cation exchange were followed up using a stopped-flow electrical conductivity detection unit. The cation-exchange process exhibited first-order kinetics with respect to the dye concentration and inversely proportional to the clay concentration. The measurements were accomplished at different temperatures and the activation parameters were determined. Increasing the Na(+)-MMT concentration led to a decrease in the rate constant. The latter is also affected by changing the exchangeable cation.     

Implications of $B \to \rho \gamma$ measurements in the standard model and supersymmetric theories

We study the implications of the recently improved upper limits on the branching ratios for the decays , expressed as . We work out the constraints that the current bound on implies on the parameters of the quark mixing matrix in the standard model (SM). Using the present profile of the unitarity triangle, we predict this ratio to lie in the range (at 95% C.L.), with the central value . We also work out the correlations involving , the isospin-violating ratio , and the direct CP-violating asymmetry in decays in the SM, in the minimal supersymmetric extension of the SM (MSSM), and in an extension of the MSSM involving an additional flavor-changing structure in transitions. Received: 19 August 2002 / Published online: 18 October 2002 RID="a" ID="a" e-mail: ali@mail.desy.de RID="b" ID="b" e-mail: lunghi@mail.desy.de     

Novel cycloartane saponins from Corchorus depressus L

Two novel bidesmosidic cycloartane-type glycosides, depressosides C and D were isolated from Corchorus depressus L. Their structures were elucidated as (22R)-16beta,22-epoxy-3beta,26-dihydroxy-9,19-cyclolanost-++ +24E-ene 3, 26-di-O-beta-D-glucopyranoside and (22R,24S)-22,25-epoxy-3beta,16beta,24-trihydroxy-9,19-cyclolano stane 3, 24-di-O-beta-glucopyranoside, respectively on the basis of chemical evidence and detailed spectroscopic studies.     

On the local stability of limit cycles

Orbital stability of limit cycles is the result of the competing local tendencies of perturbations from the cycle to decay (during phases of local stability) and to grow (during phases of local instability), averaged over a cycle. We examine this coexistence of attractive and repulsive phases on limit cycles, including the local rates of expansion and contraction of phase space volumes. This is done in a frame of reference that moves along the orbit, to partially decouple motions tangential and perpendicular to the cycle. Dynamical systems used for illustration are the generalized Bonhoeffer-van-der-Pol and Rossler models, both far from and near to different types of bifurcations. Finally, it is shown that the nonuniformity of local stability in phase space affects the response of limit cycle oscillators to perturbations and gives rise to their phase-dependent response. (c) 1999 American Institute of Physics.     

Study of the kinetics and activation parameters of reduction of Mn(III) to Mn(II) by SO3 2− ion in (MnSiW11O40H2)5- heteropoly ion

In order to gain an insight into the mechanism of reduction of Mn(III) heteropoly ions, and also to establish the conditions for use of some of these ions as oxidizing agent, following measurements have been made. The pseudo-first order rate constants, k_obs, have been determined and specific rate constants, k, were calculated from the plots of k_obs against SO₃ ^2? concentrations. A plot of ln(k₂/T) against inverse temperature gives enthalpy of activation as 10.67 kJ mol^?1 and entropy of activation as ?237.90 J K^?1 mol^?1. Effects of ionic strength and pH have also been studied over a limited range.     

Kinetic studies on the reduction of a nickel (III) oxime-imine complex by sulphur(IV) and selenium(IV)

The kinetics of the reduction of [Ni^III(L¹)]²⁺ (where HL¹ = 15-amino-3-methyl-4,7,10,13-tetraazapentadec-3-en-2-one oxime) by sulphur(IV) and selenium (IV) over the regions pH 2.50–8.02 and 2.01–4.00 respectively have been investigated at 30°C. Attempts were made to evaluate the reactivity of all the reacting species, of sulphur(IV) and selenium(IV) by considering suitable pH ranges. The oxidation of SC₂·H₂O and HSO ₃ ⁻ is proposed to proceed through the formation of a hydrogen-bonded adduct. The reaction with SO ₃ ²⁻ seems to follow a direct outer-sphere route which is well supported by Marcus crossrelation calculation. The oxidation of HSeO _l3 ⁻ is ≈ 10³ times slower than that of H₂SeO₃. The kinetic data indicate that the oxidation of sulphur(IV) by [Ni^IIIL¹)]²⁺ is much more favourable as compared to the corresponding oxidation of selenium(IV).