Searching for extensible Korobov rules

Extensible lattice sequences have been proposed and studied in [F.J. Hickernell, H.S. Hong, Computing multivariate normal probabilities using rank-1 lattice sequences, in: G.H. Golub, S.H. Lui, F.T. Luk, R.J. Plemmons (Eds.), Proceedings of the Workshop on Scientific Computing (Hong Kong), Singapore, Springer, Berlin, 1997, pp. 209–215; F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138; F.J. Hickernell, H.Niederreiter, The existence of good extensible rank-1 lattices, J. Complexity 19 (2003) 286–300]. For the special case of extensible Korobov sequences, parameters can be found in [F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C.Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138]. The searches made to obtain these parameters were based on quality measures that look at several projections of the lattice. Because it is often the case in practice that low-dimensional projections are very important, it is of interest to find parameters for these sequences based on measures that look more closely at these projections. In this paper, we prove the existence of “good” extensible Korobov rules with respect to a quality measure that considers two-dimensional projections. We also report results of experiments made on different problems where the newly obtained parameters compare favorably with those given in [F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138].     

Banach spaces which are somewhat uniformly noncreasy

We consider a family of spaces wider than r-UNC spaces and we give some fixed point results in the setting of these spaces.     

Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac

We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.Preprint Université de Bourgogne-mai 1990     

Two Other Interpretations of the Entringer Numbers

The Entringer's integers were introduced to enumerate the down-up (or up-down) permutations according to the first term. In a previous paper these integers are shown to enumerate André's trees according to two parameters. In this paper we prove that they enumerate the direct alternative permutations according to the absolute value of the first two terms and also according to a specified term.     

Wavelength independence of Eu quantum yields

A quantitative comparison between the excitation and absorption spectra of Eu³⁺ in aqueous solution is given which leads to the conclusion that fluorescence quantum yields are independent of the excitation wavelength. Use is made therefore of the series of homologous lines ⁵D₃, ⁵D₂, ⁵D₁, ⁵D₀ → ⁷F₁.     

Electrochemical synthesis of nanostructured ZnO films utilizing self-assembly of surfactant molecules at solid-liquid interfaces

An electrochemical synthesis strategy for the production of nanostructured films was developed by combining self-assembly of surfactant-inorganic aggregates at solid-liquid interfaces and an electrodeposition process. Through this approach high quality nanostructured ZnO films were cathodically deposited from a plating solution containing 0.1 wt % of sodium dodecyl sulfate (SDS). The resulting ZnO films possess lamellar structures with two different repeat distances, d001 = 31.7 A and d001* = 27.5 A, both of which feature well-defined long range order. Due to kinetically controlled surfactant-inorganic assembly during the deposition process, the film exhibits a wide distribution of the stacking directions of the ZnO layers, which will allow facile access of the guest molecules and analytes to the interlayers. The synthetic mechanism used here can be generalized to generate nanostructured films of other semiconducting and metallic materials with architectures that cannot be assembled by other means.     

Indications for the Occurrence of Nitric Oxide Synthases in Fungi and Plants and the Involvement in Photoconidiation of Neurospora crassa*

Indications for the occurrence of nitric oxide synthases in Dictyostelium, Neurospora, Phycomyces and the leguminous plant Mucuna hassjoo as well as a physiological role of nitric oxide in Neurospora crassa are demonstrated. An exogenous nitric oxide donor, sodium nitroprus-side, inhibited light-stimulated conidiation in N. crassa. Specific inhibitors of nitric oxide synthase, like the arginine derivatives N^G-nitro-L-arginine (L-NA) and N^G-nitro-L-arginine-methyl ester (L-NAME), enhanced conidiation in darkness and in the light, whereas the stereo-isomer D-NAME was inactive. This communication reports to our knowledge the first time the presence of enzymatic activity of nitric oxide synthase in fungi and a higher plant and an effect of nitric oxide in fungal photophysiology.     

Carbonylation of (+)-2-carene induced by iron-pentacarbonyl.

(+)-2-carene heated neat with iron pentacarbonyl leads to α-phellandrene-Fe(CO)₃ complex ( ～15 % ), p. cymene ( ～15 % ), (-)-(1S)-3,8,8-trimethylbicyclo (4.1.1) oct-3-ene-7-one ( ～50 % ) and (+)-(1S,7S)-3,8,8-trimethylbicyclo (4.1.1.) oct-3-ene-7-ol ( ～20 % ).