On toric face rings

Following a construction of Stanley we consider toric face rings associated to rational pointed fans. This class of rings is a common generalization of the concepts of Stanley-Reisner and affine monoid algebras. The main goal of this article is to unify parts of the theories of Stanley-Reisner and affine monoid algebras. We consider (non-pure) shellable fan’s and the Cohen-Macaulay property. Moreover, we study the local cohomology, the canonical module and the Gorenstein property of a toric face ring.     

Cramér-Rao bound for estimates of frequencies and damping factors of real superimposed signals with multiple poles in noise

The problem of estimating frequencies and damping factors of real superimposed signals with multiple poles in white Gaussian noise is considered. Such signals are described by real quasipolynomials, i.e. by linear combinations of real damped sinusoids multiplied by power functions. In a particular case when poles are simple, a real quasipolynomial becomes a real damped sinusoid. An explicit expression of the Cramér-Rao bound (CRB) for the estimation of frequencies and damping factors of the signals is obtained. To derive the CRB, we use the expression for the Fisher information matrix (FIM) which we obtained in a previous paper for the model of complex quasipolynomials (i.e. complex exponentials multiplied by complex polynomials). We rewrite the model of real quasipolynomials as a model of complex quasipolynomials with constraints imposed on the parameter set. Then we make use of the formula presented by Gorman and Hero that allows us to obtain the CRB for the model with constraints from the FIM for the model without constraints. The results of numerical simulations are presented and discussed.     

2-Ketogluconic acid production by acetobacter pasteurianus

Production of 2-ketogluconic acid in batch fermentation was investigated.Acetobacter pasteurianus ATCC 6438, which produces selectively 2-ketogluconic acid only, was used. The optimal pH for glucose dehydrogenation to gluconate by resting cells was 5.0 and for gluconate dehydrogenation to 2-ketogluconate 4.25. When glucose medium was used, the 89% yield was achieved after 90 h. For the optimal productivity, medium containing glucose and gluconate with the molar glucose:gluconate ratio 7.4 was proposed, and the yield of 92% after 56 h was achieved. This composition of medium led to the elevation of dissolved oxygen concentration during fermentation. It consequently resulted in elevated gluconate dehydrogenase activity being discussed as the rate-limiting activity of the batch production.     

Membrane extraction for preconcentration of radionuclides

Membrane extraction is treated as an analogue of solvent extraction in three-phase distribution systems. Its advantages and drawbacks are discussed with respect to separation and preconcentration of radionuclides, fission products of uranium and uranium itself.     

Vitamin a derivatives labelled with 131I — Potential agents for liver scientigraphy

Two retinol derivatives, 4-[(¹³¹I)-4-iodobenzoyloxy]retinol propionate and 4-[(¹³¹I)-3-iodobenzylcarbamoyl]retinol propionate, were synthesized and their biodistribution in rats was studied in vivo by the whole body scintigraphy.     

Asymptotic aspects of Schreier graphs and Hanoi Towers groups

We present relations between growth, growth of diameters and the rate of vanishing of the spectral gap in Schreier graphs of automaton groups. In particular, we introduce a series of examples, called Hanoi Towers groups since they model the well known Hanoi Towers Problem, that illustrate some of the possible types of behavior. To cite this article: R. Grigorchuk, Z. ?unik´, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

In-situ study of Ag nanoparticle hydrosol optical spectra evolution during laser ablation/fragmentation

The results of in-situ monitoring of a laser fragmentation process of a largely polydisperse and morphologically heterogeneous citrate-reduced Ag hydrosol containing a fraction of Ag nanowires are presented. The laser fragmentation was performed using several wavelengths of the incident laser pulses (1064, 532 and 355 nm). Surface plasmon extinction spectra monitoring the nanoparticle fragmentation process were acquired pulse by pulse and related to transmission electron microscopy (TEM) images and statistical TEM image analysis of Ag nanoparticles collected in selected stages of the fragmentation. It was found that, due to different interactions of the laser pulses of various wavelengths with a specific fraction of the Ag nanoparticles in the hydrosol, the course of the fragmentation process depends on the wavelength, leading to different size distributions of the nanoparticles in the resulting hydrosol. The laser pulses of 532 nm wavelength are the most effective for the fragmentation process of the citrate-reduced Ag hydrosol, yielding the narrowest size distribution and the smallest mean radius of the Ag nanoparticles. PACS 81.07.-b; 73.21.-b; 81.16.-c     

Light trapping effect in silicon wafers with anodically etched surfaces

Received: 10 May 1996/Accepted: 19 November 1996     

Electrical properties of Au–polystyrene–Au submicron structures

Received: 25 January 1998/Accepted: 28 May 1998     

Silylation of silanols with vinylsilanes catalyzed by a ruthenium complex

A new ruthenium complex-catalyzed O-silylation of silanols with vinylsilanes leading to siloxane bond formation with the evolution of ethylene is described. A maximum conversion of silanol is reached using an excess of vinylsilane to also yield the product of the homo-coupling of the latter. Under the optimum conditions, when vinylsilane with at least one ethoxy substituent is used, the reaction gives exclusively unsymmetrical siloxanes.