Dynamics on the Virasoro group, 2D gravity and hidden symmetries

We derive the action of 2D gravity from the two-cocycle of the Virasoro group by using a previously introduced method for constructing a dynamical system from a Lie group. A natural construction and explanation of the hidden SL(2, )-Kac-Moody symmetry, of general applicability, is provided. We also show how the proper quantization goes beyond the ordinary co-adjoint orbit method, and the possible connection with the Poisson-Lie groups.     

Group algebras of Kleinian type and groups of units

The algebras of Kleinian type are finite-dimensional semisimple rational algebras A such that the group of units of an order in A is commensurable with a direct product of Kleinian groups. We classify the Schur algebras of Kleinian type and the group algebras of Kleinian type. As an application, we characterize the group rings RG, with R an order in a number field and G a finite group, such that the group of units of RG is virtually a direct product of free-by-free groups.     

Coupling leads to chaos

The main goal of this paper is to prove analytically the existence of strange attractors in a family of vector fields consisting of two Brusselators linearly coupled by diffusion. We will show that such a family contains a generic unfolding of a 4-dimensional nilpotent singularity of codimension 4. On the other hand, we will prove that in any generic unfolding Xμ of an n-dimensional nilpotent singularity of codimension n there are bifurcation curves of (n−1)-dimensional nilpotent singularities of codimension n−1 which are in turn generically unfolded by Xμ. Arguments conclude recalling that any generic unfolding of the 3-dimensional nilpotent singularity of codimension 3 exhibits strange attractors.     

On the power of the zeros of Bessel functions

For ν≥0 let c_νk be the k-th positive zero of the cylinder functionC _v(t)=J _v(t)cosα-Y _v(t)sinα, 0≤α>π whereJ _ν(t) andY _ν(t) denote the Bessel functions of the first and the second kind, respectively. We prove thatC _v,k ^1+H(x) is convex as a function of ν, ifc _νk≥x>0 and ν≥0, whereH(x) is specified in Theorem 1.1.     

Indirect spectrophotometric determination of cyanide

A spectrophotometric method for cyanide based on its inhibition of the colour formation reaction between nickel(II) and 3-(4,5-dimethyl-2-thiazolylazo)-2,6-dihydroxybenzoic acid has been developed, and allows the determination of down to 0.1 g of cyanide. Most of the interferences can be avoided by displacement of the hydrogen cyanide using an arsine generator.     

Degradation of ²-O-4 lignin model and related compounds by the ascomyceteChrysonilia sitophila (TFB 27441 strain)

Growth of the ascomyceteChrysonilia sitophila during degradation of lignin model dimers and monomers was compared to a glucose control. An inhibition of growth by Cα-carbonyl monomers and stimulation by β-O-4 lignin model and vanillyl alcohol were observed. A comparison of the degradation by this ascomycete with the basidiomycetePhanerochaete chrysosoporium showed similarities in relation to the type of degradation caused.     

Rapid determination of aliphatic amines in water samples by pressure-assisted monolithic octadecylsilica capillary electrochromatography-mass spectrometry

A pressure-assisted capillary chromatography-mass spectrometry method based on the use of a monolithic octadecylsilica (ODS) capillary is proposed for the determination of aliphatic amines. A 25 mM citric acid buffer containing 10% methanol is used as running electrolyte. Separation is achieved by simultaneously applying a capillary electrophoresis (CE) voltage of 13 kV and an overimposed pressure of 8 bar. The use of pressure is required to ensure stable electrospray conditions. Analysis times are reduced by using a capillary column consisting of a 30 cm long monolithic silica capillary column bound with ODS and a fused-silica capillary column also 30 cm long. The proposed method was successfully applied to the determination of low-molecular-weight aliphatic amines in tap and river water. The analysis of real samples requires cleanup and preconcentration, which can be performed automatically by inserting a minicolumn in the replenishment system of the commercial instrument.     

Polarographic determination of pilocarpine using the catalysed pre-wave of nickel(II)

On the basis of a detailed study of the pilocarpine-induced nickel(II) pre-wave using various polarographic techniques, an electrode process mechanism is proposed in which the formation of a catalytic complex between aquo-nickel(II) and veronalate-nickel(II) on the one hand and unprotonated pilocarpine adsorbed on the electrode surface on the other is followed by the reduction of nickel(II) in the complex and the release of the catalytic ligand. The pre-peak recorded by differential-pulse polarography in the system 1 × 10^?3 M Ni(II)-1 × 10^?2 M sodium veronal, nitric acid (pH 8.5) (with ionic strength maintained at 0.2 with sodium nitrate) can be used for quantitative determination of pilocarpine at concentrations in the range 2.5 × 10^?7-8 × 10^?6 M.