On block preconditioners for saddle point problems with singular or indefinite (1, 1) block

We discuss a class of preconditioning methods for the iterative solution of symmetric algebraic saddle point problems, where the (1, 1) block matrix may be indefinite or singular. Such problems may arise, e.g. from discrete approximations of certain partial differential equations, such as the Maxwell time harmonic equations. We prove that, under mild assumptions on the underlying problem, a class of block preconditioners (including block diagonal, triangular and symmetric indefinite preconditioners) can be chosen in a way which guarantees that the convergence rate of the preconditioned conjugate residuals method is independent of the discretization mesh parameter. We provide examples of such preconditioners that do not require additional scaling. Copyright © 2010 John Wiley & Sons, Ltd.     

On the implicit bond-dependency origins of bridge interactions

The indirect (through-bridge) components of chemical interactions between atomic orbitals (AO) are shown to originate from the indirect dependencies between AO due to the orbital intermediaries in the bond system of the molecule. They are expressed in terms of the bridge-coupling elements of the density matrix via the chain rule transformation of the implicit derivatives between the indirectly bonded AO in the molecular bond system. The elements of the charge-and-bond-order (CBO) matrix are interpreted as the canonical derivatives between the AO-projections onto the bond subspace combining the occupied Molecular Orbitals (MO). The chain-rule manipulations are then used to express the scattering amplitudes via AO intermediaries in terms of the relevant elements of the CBO matrix. The squares of such amplitudes are related to the Wiberg-type indirect bond components, which complement the familiar direct Wiberg bond-order contributions. The interference implications of the probability scatterings via the multiple cascades involving all basis functions are examined. These probability propagations are shown to preserve the stationary conditional probabilities of the underlying molecular communication channel in AO resolution.     

Highly enantioselective addition of phenylethynylzinc to aldehydes using aziridine-functionalized tridentate sulfinyl ligands

Diastereomerically pure tridentate heteroorganic ligands containing hydroxyl, sulfinyl and aziridine moieties as nucleophilic centers, capable of binding to various organometallic reagents, have been proven to be highly efficient catalysts in the enantioselective addition of phenylethynylzinc to aldehydes to give the desired products in very high yields (up to 95%) and with ee’s up to 90%. The influence of the stereogenic centers located on the sulfinyl sulfur atom and in the aziridine moiety on the stereochemical course of the reaction is also discussed.     

Synthesis and characterisation of coating polyurethane cationomers containing fluorine built-in hard urethane segments

Polyurethane cationomers were synthesised in the reaction of 4,4’-methylenebis(phenyl isocyanate) with polyoxyethylene glycol (M?= 2,000) or poly(tetrafluoroethyleneoxide-co-difluoromethylene oxide) α,ω-diisocyanate and N-methyl diethanolamine. Amine segments were built-in to the urethane-isocyanate prepolymer in the reaction with 1-bromobutane or formic acid, and then they were converted to alkylammonium cations. The obtained isocyanate prepolymers were then extended in the aqueous medium that yielded stable aqueous dispersions which were applied on the surfaces of test poly(tetrafluoroethylene) plates. After evaporation of water, the dispersions formed thin polymer coatings. ¹H, ¹³C NMR and IR spectral methods were employed to confirm chemical structures of synthesised cationomers. Based on ¹H NMR and IR spectra, the factors κ and α were calculated, which represented the polarity level of the obtained cationomers. The DSC, wide angle X-ray scattering and atom force microscopy methods were employed for the microstructural assessment of the obtained materials. Changes were discussed in the surface free energy and its components, as calculated independently according to the method suggested by van Oss–Good, in relation to chemical and physical structures of cationomers as well as morphology of coating surfaces obtained from those cationomers. Fluorine incorporated into cationomers (about 30%) contributed to lower surface free energy values, down to about 15 mJ/m². That was caused by gradual weakening of long-range interactions within which the highest share is taken by dispersion interactions.     

Empirical wavelet analysis of tail and memory properties of LARCH and FIGARCH models

Using computationally efficient wavelet methods, we study two nonlinear models of financial returns {r _t }: linear ARCH (LARCH) and fractionally integrated GARCH (FIGARCH). We estimate the tail index α and the long memory parameter d of the squared returns X_t = r_t²{X_t= r_t^2} of LARCH, and of the powers X _t = |r _t | ^p of FIGARCH. We find that the X _t have infinite variance and long memory, and show how the estimates of α and d depend on the model parameters. These relationships are determined empirically, as the setting is quite complex, and no suitable theory has been developed so far. In particular, we provide empirical relationships between the estimates [^(d)]{\hat d} and the difference parameters in LARCH and FIGARCH. Our computational work uncovers tail and memory properties of LARCH and FIGARCH for practically relevant parameter ranges, and provides some guidance on modeling returns on speculative assets including FX rates, stocks and market indices.     

Retention of configuration in the action of human plasma 3'-exonuclease on oligo(deoxynucleoside phosphorothioate). A new method for assignment of absolute configuration at phosphorus in isotopomeric deoxyadenosine 5'-O-[(18)O]phosphorothioate

A new method of analysis has allowed the exonucleolytic cleavage by human 3'-exonuclease to be determined. Hydrolysis by human plasma 3'-exonuclease proceeds with retention of configuration at phosphorus. The new method determines the sense of chirality at phosphorus in isotopomeric adenosine 5'-O-[(18)O]phosphorothioates. This is based on stereospecific two-step conversion of the mono-thionucleotide into the corresponding deoxyadenosine 5'-O-alpha-[(18)O]thiotriphosphate, followed by the use of terminal deoxyribonucleotidyl transferase and MALDI TOF mass spectrometry of the resulting elongated primer. Retention of configuration in the reaction of plasma 3'-exonuclease implies a two-step mechanism with two displacements on phosphorus. Inversion at each step leads to overall retention.     

Wave properties of a methyl group under ambient conditions

Liquid-phase NMR studies on hindered rotation of methyl group in a 9-methyltriptycene derivative are reported where the standard, classical jump model of the methyl dynamics proves inadequate. On the other hand, accurate reproduction of the observed NMR line shape effects is afforded by the use of a recent quantum mechanical model in which the relevant methyl dynamics are described in terms of two quantum rate (coherence-damping) processes, characterized by two different rate constants. For ambient temperatures, such a direct evidence of the quantum nature of a rate process generally believed to be classical seems to have no precedence in the literature.