The construction of good extensible rank-1 lattices

It has been shown by Hickernell and Niederreiter that there exist generating vectors for integration lattices which yield small integration errors for for all integers . This paper provides algorithms for the construction of generating vectors which are finitely extensible for for all integers . The proofs which show that our algorithms yield good extensible rank-1 lattices are based on a sieve principle. Particularly fast algorithms are obtained by using the fast component-by-component construction of Nuyens and Cools. Analogous results are presented for generating vectors with small weighted star discrepancy.

     

Synthesis, characterization, antibacterial and cytotoxic activity of new palladium(II) complexes with dithiocarbamate ligands: X-ray structure of bis(dibenzyl-1-S:S′-dithiocarbamato)Pd(II)

Six palladium(II) dithiocarbamates of general formula Pd(AmDTC)₂, where HAmDTC = aminedithiocarbamic acid, [Pd(II) piperidinedithiocarbamate (1), Pd(II) 4-methylpiperidinedithiocarbamate (2), Pd(II) N-methylbenzyldithiocarbamate (3), Pd(II) dibenzyldithiocarbamate (4), Pd(II) dicyclohexyldithiocarbamate (5), Pd(II) N-cyclohexyl-N-methyldithiocarbamate (6)] have been synthesized and characterized by elemental analyses, FT-IR, ¹H and ¹³C NMR. The X-ray structure of Pd(II), compounds 3 and 4, showed that the ligands are chelated by both sulfur atoms with bond angles S1-Pd-S4 = 179.24(2)° and S2-Pd-S3 = 179.09(5)°, with a distorted square planar geometry around Pd. All these complexes were screened for cytotoxic and antibacterial effects and showed significant antibacterial activity and no substantial in vitro cytotoxicity indicating specificity of the compounds.     

The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets

In this paper we investigate multivariate integration in reproducing kernel Sobolev spaces for which the second partial derivatives are square integrable. As quadrature points for our quasi-Monte Carlo algorithm we use digital (t,m,s)-nets over which are randomly digitally shifted and then folded using the tent transformation. For this QMC algorithm we show that the root mean square worst-case error converges with order for any ɛ > 0, where 2 ^m is the number of points. A similar result for lattice rules has previously been shown by Hickernell. Ligia L. Cristea is supported by the Austrian Research Fund (FWF), Project P 17022-N 12 and Project S 9609. Josef Dick is supported by the Australian Research Council under its Center of Excellence Program. Gunther Leobacher is supported by the Austrian Research Fund (FWF), Project S 8305. Friedrich Pillichshammer is supported by the Austrian Research Fund (FWF), Project P 17022-N 12, Project S 8305 and Project S 9609.     

Synthesis of enantiopure chloroalcohols by enzymatic kinetic resolution

3-Alkenyl and heteroaryl chloroalcohols have been obtained in excellent enantiomeric excess (>99%) by enzymatic kinetic resolution using the haloalcohol dehalogenase HheC. Yields were close to the theoretical maximum for all substrates employed. Furthermore, the applicability of this methodology on multigram scale has been established.     

Near limit behavior of the detonation velocity

The behavior of the detonation velocity near the limits is investigated. Circular tubes of diameters 65, 44 and 13 mm are used. To simulate a quasi two-dimensional rectangular geometry thin annular channels are also used. The annular channels are formed by a 1.5 m long insert of a smaller diameter tube into the larger outer diameter detonation tube. Premixed mixtures of C₂H₂ + 2.5O₂ + 70%Ar, CH₄ + 2O₂ and C₂H₂ + 5N₂O + 50%Ar are used in the present study. The high argon dilution stoichiometric C₂H₂ + 2.5O₂ mixture has a regular cell size and piecewise laminar reaction zone and thus referred to as “stable”. The other two mixtures give highly irregular cell pattern and a turbulent reaction zone and are hence, referred to as “unstable” mixtures. Pressure transducers and optical fibers spaced 10 cm apart along the tube are used for pressure and velocity measurements. Cell size of the three mixtures studied is also determined using smoked foils in both the circular tubes and annular channels. The ratio d/λ (representing the number of cells across the tube diameter) is found to be an appropriate sensitivity parameter to characterize the mixture. The present results indicate that well within the limit, the detonation velocity is generally a few percent below the theoretical Chapman–Jouguet (CJ) value. As the limit is approached, the velocity decreases rapidly to a minimum value before the detonation fails. The narrow range of values of d/λ of the mixture where the velocity drops rapidly is found to correspond to the range of values for the onset of single headed spinning detonations. Thus we may conclude that the onset of single headed spin can be used as a criterion for defining the limits. Spinning detonations are also observed near the limits in annular channels.     

A construction of polynomial lattice rules with small gain coefficients

In this paper we construct polynomial lattice rules which have, in some sense, small gain coefficients using a component-by-component approach. The gain coefficients, as introduced by Owen, indicate to what degree the method improves upon Monte Carlo. We show that the variance of an estimator based on a scrambled polynomial lattice rule constructed component-by-component decays at a rate of N ^{−(2α+1)+δ} , for all δ > 0, assuming that the function under consideration has bounded variation of order α for some 0 < α ≤ 1, and where N denotes the number of quadrature points. An analogous result is obtained for Korobov polynomial lattice rules. It is also established that these rules are almost optimal for the function space considered in this paper. Furthermore, we discuss the implementation of the component-by-component approach and show how to reduce the computational cost associated with it. Finally, we present numerical results comparing scrambled polynomial lattice rules and scrambled digital nets.     

Electron transfer within self-assembling cyclic tetramers using chlorophyll-based donor-acceptor building blocks

The synthesis and photoinduced charge transfer properties of a series of Chl-based donor-acceptor triad building blocks that self-assemble into cyclic tetramers are reported. Chlorophyll a was converted into zinc methyl 3-ethylpyrochlorophyllide a (Chl) and then further modified at its 20-position to covalently attach a pyromellitimide (PI) acceptor bearing a pyridine ligand and one or two naphthalene-1,8:4,5-bis(dicarboximide) (NDI) secondary electron acceptors to give Chl-PI-NDI and Chl-PI-NDI(2). The pyridine ligand within each ambident triad enables intermolecular Chl metal-ligand coordination in dry toluene, which results in the formation of cyclic tetramers in solution, as determined using small- and wide-angle X-ray scattering at a synchrotron source. Femtosecond and nanosecond transient absorption spectroscopy of the monomers in toluene-1% pyridine and the cyclic tetramers in toluene shows that the selective photoexcitation of Chl results in intramolecular electron transfer from (1*)Chl to PI to form Chl(+?)-PI(-?)-NDI and Chl(+?)-PI(-?)-NDI(2). This initial charge separation is followed by a rapid charge shift from PI(-?) to NDI and subsequent charge recombination of Chl(+?)-PI-NDI(-?) and Chl(+?)-PI-(NDI)NDI(-?) on a 5-30 ns time scale. Charge recombination in the Chl-PI-NDI(2) cyclic tetramer (τ(CR) = 30 ± 1 ns in toluene) is slower by a factor of 3 relative to the monomeric building blocks (τ(CR) = 10 ± 1 ns in toluene-1% pyridine). This indicates that the self-assembly of these building blocks into the cyclic tetramers alters their structures in a way that lengthens their charge separation lifetimes, which is an advantageous strategy for artificial photosynthetic systems.     

Improving riverbed sediment classification using backscatter and depth residual features of multi-beam echo-sounder systems

Riverbed and seafloor sediment classification using acoustic remote sensing techniques is of high interest due to their high coverage capabilities at limited cost. This contribution presents the results of riverbed sediment classification using multi-beam echo-sounder data based on an empirical method. Two data sets are considered, both taken at the Waal River, namely Sint Andries and Nijmegen. This work is a follow-up to the work carried out by Amiri-Simkooei et al. [J. Acoust. Soc. Am. 126(4), 1724-1738 (2009)]. The empirical method bases the classification on features of the backscatter strength and depth residuals. A principal component analysis is used to identify the most appropriate and informative features. Clustering is then applied to the principal components resulting from this set of features to assign a sediment class to each measurement. The results show that the backscatter strength features discriminate between different classes based on the sediment properties, whereas the depth residual features discriminate classes based on riverbed forms such as the "fixed layer" (stone having riprap structure) and riverbed ripples. Combination of these two sets of features is highly recommended because they provide complementary information on both the composition and the structure of the riverbed.     

Spectrophotometric system for measuring the characteristics of light scattered by biological tissues and humoral media

The structure, assembly, and physical capabilities of a spectrophotometric system intended for studying biotissues and humoral fluids are described. It can be used to investigate all the characteristics of scattered light at wavelengths of 400–1000 nm that are of interest for various problems in biomedical optics. Examples of these problems include noninvasive diagnostics of the structural and biophysical parameters of human skin tissue, analysis of the hemoglobin composition, sizes and degree of aggregation of erythrocytes, and evaluating the depth of penetration of light into biotissue. Pilot experiments on measuring the characteristics of scattered light are conducted in order to select an optimum operating mode for the system, estimate its errors, and develop ways of minimizing these errors.     

Quasi–Monte Carlo rules for numerical integration over the unit sphere {\mathbb{S}^2}

We study numerical integration on the unit sphere ${\mathbb{S}^2 \subseteq\mathbb{R}^3}$ using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly. The quadrature points are constructed by lifting a (0, m, 2)-net given in the unit square [0, 1]² to the sphere ${\mathbb{S}^2}$ by means of an area preserving map. A similar approach has previously been suggested by Cui and Freeden [SIAM J Sci Comput 18(2):595–609, 1997]. We prove three results. The first one is that the construction is (almost) optimal with respect to discrepancies based on spherical rectangles. Further we prove that the point set is asymptotically uniformly distributed on ${\mathbb{S}^2}$ . And finally, we prove an upper bound on the spherical cap L ₂-discrepancy of order N ^?1/2(log N)^1/2 (where N denotes the number of points). This improves upon the bound on the spherical cap L ₂-discrepancy of the construction by Lubotzky, Phillips and Sarnak [Commun Pure Appl Math 39(S, suppl):S149–S186, 1986] by a factor of ${\sqrt{\log N}}$ . Numerical results suggest that the (0, m, 2)-nets lifted to the sphere ${\mathbb{S}^2}$ have spherical cap L ₂-discrepancy converging with the optimal order of N ^?3/4.