Distances between oriented curves in geometric modeling

We consider the choice of a functional to measure the distance between two parametric curves. We identify properties of such a distance functional that are important for geometric design. Several popular definitions of distance are examined, and new functionals are presented which satisfy the desired properties. This revised version was published online in August 2006 with corrections to the Cover Date.     

Standardization of Methods for Characterizing the Surface Geometry of Solids

Since a comprehensive survey published in 1999 [1] much work was done in standardizing measuring methods to characterize the surface geometry of dispersed and/or porous solids and to certify reference materials. The present paper is an extension of a short communication [2]. It gives a survey on existing standards and reports on new drafts and proposals.     

On the concentration and determination of plutonium in natural waters by adsorption on MnO2 filters

A new method of analysis of the efficiency of four filters of MnO₂ in series which takes into account the reactions induced in plutonium by the sorbent is described. The system of differential equations describing the behaviour of plutonium in water as it passes through the filters is solved and the parameters of the filters are determined for a best fitting of the solutions corresponding to the experimental uncertainties. The method is checked by numerical simulation and then applied to water solutions with a known plutonium concentration and to some experimental results given by other authors. In all occassions the results are consistent with the possibility of determining the contents of plutonium in sea and continental waters with uncertainties of the order of 10%.     

Quasi-genericity of bifurcations to high dimensional invariant tori for maps

We consider a family of maps in a Banach spaceE near the situation when the derivative at the fixed point has two pairs of complex eigenvalues lying on the unit circle, the other part of the spectrum being strictly inside the unit disc. We focus our attention on the region of the parameter space where the truncated normal form of the maps shows a bifurcation of a family of invariantT ¹-circles into a family of invariantT ²-tori. We show that this problem needs a 3 dimensional parameter unfolding and that, for the complete maps, bifurcation occurs at points _,, where is the rotation number on the non-normally hyperbolicT ¹-circle, ande ^±2i are the eigenvalues of the constant matrix conjugated to the non-contracting part of the linearization on the normal fiber bundle overT ¹. Making some non-resonance and diophantine assumptions on (, ) leading to a positive measure Cantor set inT ², we show that in paraboloïdal regions of the 3 dim. parameter space we have clean bifurcations as for the truncated normal form. The complement of these regions forms a set of bubbles such as the ones obtained by Chenciner in [Chen] for a codimension 2 problem for maps in ². The main tool here is a generalization for a matrix function onT ¹, close to a constant, of the quasi-conjugacy to a constant, modulo a minimum of additional parameters (moved quasi-conjugacy). For the infinite dimensional case we use aC decoupling result on the angular dependent linear parts into a contraction, still angular dependent, and another part quasi-conjugated to a constant matrix. This type of analysis applies for a wide range of problems, where truncated normal forms of the maps give bifurcations fromT ⁿ toT ⁿ⁺¹ tori, and this needs a (n+1)-dimensional parameter unfolding.We gratefully acknowledge the DRET (contrat 86/1445) who supported one of the authors (J.L.) during this work. This research has been also supported by the E.E.C. contract No. ST 2J-0316-C (EDB) on Mathematical problems in nonlinear Mechanics     

Large-scale synthesis of globotriose derivatives through recombinant E. coli

The carbohydrate chains decorating cell membranes and secreted proteins participate in a range of important biological processes. However, their ultimate significance and possible therapeutic potential have not been fully explored due to the lack of economical methods for their production. This study is an example of the use of a genetically engineered bacterial strain in the preparation of diverse oligosaccharides. Based on an ex vivo biosynthetic pathway, an artificial gene cluster was constructed by linking the genes of five associated enzymes on a plasmid vector. This plasmid was inserted into the E. coli NM522 strain to form globotriose-producing cells ('superbug' pLDR20-CKTUF). The specific strain was conveniently applied to the synthesis of globotriose trisaccharide and its derivatives, as potential neutralizers for Shiga toxin. This work demonstrates a novel and economical method for generating ligand diversity for carbohydrate drug development.     

Impedance studies of porous lanthanum-phosphate-bonded nickel electrodes in concentrated sodium hydroxide solution

The hydrogen evolution reaction (HER) was investigated on a lanthanum-phosphate-bonded nickel (LPBN) powder electrode in 30 wt.% NaOH at 70°C using ac impedance and steady-state polarization techniques. Circuits containing one or two constant-phase elements (CPEs) in parallel with a resistance and corresponding to fractal and porous electrode models were tested in order to interpret the ac impedance data. The experimental impedance spectra were well described by the porous electrode model and the circuit containing two CPEs. The results obtained from the ac impedance and steady-state measurements allowed the mechanism and kinetics of the HER to be evaluated. Comparison of these parameters with those obtained on the polycrystalline nickel electrode in 1 M alkaline solution at 25°C indicates that an increase in activity is principally due to an increase in the real surface area.     

Sulfoxides as ‘traceless’ resolving agents for the synthesis of atropisomers by dynamic or classical resolution

Reacting (−)-menthyl sulfinate with an atropisomeric but racemic aryllithium gives two atropdiastereoisomeric sulfoxides. Separation (by chromatography or crystallisation) and sulfoxide-lithium exchange of each diastereoisomer regenerates the aryllithium in enantiomerically pure form which can be quenched with a range of electrophiles with retention of stereochemical integrity. Overall the reaction sequence is a resolution but without the need for an acidic or basic substituent—a ‘traceless’ method. In certain instances, for example when the nucleophile is an ortholithiated peri-substituted 1-naphthamide, the diastereoisomeric sulfoxides may be interconverted thermally. This allows a dynamic resolution, under thermodynamic control, and hence in principle can give yields of the final products of greater than 50%. The utility of the method is demonstrated by the synthesis of a known atropisomeric phosphine ligand.     

Identification of a light-regulated protein kinase activity from seedlings of Arabidopsis thaliana

Protein kinase transduction pathways are thought to be involved in light signaling in plants, but other than the photoreceptors, no protein kinase activity has been shown to be light-regulated in vivo. Using an in-gel protein kinase assay technique with histone H III SS as an exogenous substrate, we identified a light-regulated protein kinase activity with an apparent molecular weight ca 50 kDa. The kinase activity increased transiently after irradiation of dark-grown seedlings with continuous far red light (FR) and blue light (B) and decreased after irradiation with red light (R). The maximal activation was achieved after 30 min to 1 h with FR or B. After irradiation times longer than 2 h, the kinase activity decreased to below the sensitivity level of the assay. In Arabidopsis mutants lacking either the photoreceptors phytochrome A, phytochrome B or the blue-light receptor cryptochrome 1, kinase activity was undetectable, whereas in the photomorphogenic mutants cop1 and det1 the kinase activity was also observed in the absence of light signals, though still stimulated by B and FR. Interestingly, the R inhibition of the kinase activity was lost in the mutant hy5. Pretreatment with cycloheximide blocked the kinase activity.