Chiral stationary phases for LC and SFC obtained by “Polymer coating”

Summary Chirally substituted Si–H-containing polysiloxanes were synthesized, which can be immobilized on small particle silica gel as well as on the smooth surfaces of fused silica capillaries. Immobilization is achieved either by crosslinking or by chemical bonding to the surfaces via silanol groups; both reactions can only be performed by addition of H₂PtCl₆, which acts as catalyst for hydrosilylation and as stoichiometric reagent for crosslinking. Chiral substituents of systematically varied chemical structure were introduced into the polysiloxanes by hydrosilylation. The mechanism of immobilization was investigated by spectroscopic methods, notably²⁹Si-NMR. Homogenous stationary-phase coatings of variable film thickness and corresponding retentivity can easily be achieved. The enantioselectivity of the phase systems was characterized in dependency on the chemical structure of the chiral selectors attached to the polysiloxane chain of the chiral stationary phases and also in terms of the functional groups introduced into the solutes by derivatisation.     

Manipulation of the Electroosmotic Flow in Glass und PMMA Microchips with Respect to Specific Enzymatic Glucose Determinations

The determination of glucose in microfluidic chips made of glass or PMMA was used as a model for the combination of an enzymatic reaction with the separation of compounds. It was based on the enzymatic oxidation of glucose and the amperometric detection of hydrogen peroxide. Real samples frequently contain compounds, such as ascorbic acid, which may interfere with quantitative glucose determinations. Thus, electrophoretic separation of specific from unspecific signals was envisaged by applying electric fields which are also used to control the flow of liquid via electroosmotic effects. Surface charge densities of the capillaries influence the electroosmotic flow (EOF). They are dependent on the chip material and on the adsorption of components from the background electrolyte. Reversal of the EOF after addition of cetyltrimethylammonium bromide (CTAB) and an increase in EOF after addition of sodium dodecylsulfate (SDS) were observed at lower surfactant concentrations with the PMMA chips rather than with the glass chips. For both chip materials these concentrations were below the critical micelle concentration. Effective separation of H₂O₂ and ascorbic acid was achieved with low CTAB concentrations, which lead to a reduction, but not to a reversal of the EOF. Reversal of the EOF by higher CTAB concentrations or the increase in cathodic EOF by SDS accelerated ascorbic acid transportation and reduced the differences in migration times. Thus, for the specific determination of glucose, glucose oxidase was added together with low CTAB concentrations to the background electrolyte. This avoided interference from ascorbic acid, and data obtained from the analysis of fruit juices showed a good correlation to data obtained from a reference method.     

A new quantum group associated with a ‘nonstandard’ braid group representation

A new quantum group is derived from a nonstandard braid group representation by employing the Faddeev-Reshetikhin-Takhtajan constructive method. The classical limit is not a Lie superalgebra, despite relations like x ²–y ²=0. We classify all finite-dimensional irreducible representations of the new Hopf algebra and find only one- and two-dimensional ones.     

On coherent states for the simplest quantum groups

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU _q (2) and the discrete series of representations of SU _q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed.     

Cocycles d'Euler et de Maslov

Conclusion Nous espérons avoir convaincu le lecteur qu'il peut être utile de considérer la classe de Maslov comme une classe bornée. Dans [Gh], nous avons montré que la classe d'Euler bornée pour un groupe d'homéomorphismes directs du cercle rend compte de la dynamique topologique de ce groupe. Existe-t-il un résultat analogue pour Sp(2n,)? En d'autres termes, soit un groupe discret et ₁, ₂ deux représentations de dans Sp(2n,). On suppose que les cocycles ₁ ^* et ₂ ^* définissent la même classe bornée. Que peut-on en conclure sur ₁ et ₂?Par ailleurs, l'article [At l] traite aussi d'invariants sur SL(2,) différents de ceux que nous avons considérés, comme par exemple les fonctionsL de Shimizu. Est-il possible de les faire rentrer naturellement dans notre cadre?

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Convergence to equilibrium of critical branching particle systems and superprocesses,and related nonlinear partial differential equations

We consider a class of multitype particle systems in ^d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).     

Smoothness of Brownian local times and related functionals

In this paper we show that the local time of the Brownian motion belongs to the Sobolev space for any p2 and 0<<1/p. In order to prove this result we first discuss the smoothness and integrability properties of the composition of the Dirac function with a Wiener integral W(h), and we show that this composition belongs to , for any >0 and p>1 such that +1/p>1.     

Chern forms,chern numbers and curvature conditions on a Kähler-Einstein surface

In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL ²-norm of (3C ₂ ?C ₁ ² )/C ₁ ² is sufficiently small, whereC ₁ andC ₂ are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C ₂ ?C ₁ ² = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature.     

Countable Fréchetα 1-spaces may be first countable

It is shown to be consistent that countable, Fréchet, ₁-spaces are first countable. The result is obtained by using a countable support iteration of proper partial orders of length ₂.The research of both authors is partially supported by NSERC     

Convex hull of powers of a complex number,trinomial equations and the Farey sequence

The color of a complex number is defined as the number of vertices of the convex hull of powers of that number. This induces a coloring of the unit disk. The structure of the set of points where the color changes is investigated here. It is observed that there is a connection between this fractal set and some family of trinomial equations. Three algorithms for coloring the unit disk are described, the last one (related to the Farey sequence) arising out of a conjecture. This conjecture is formulated and proved in this presentation.