Spectral analysis of the finite Hankel transform and circular prolate spheroidal wave functions

In this paper, we develop two practical methods for the computation of the eigenvalues as well as the eigenfunctions of the finite Hankel transform operator. These different eigenfunctions are called circular prolate spheroidal wave functions (CPSWFs). This work is motivated by the potential applications of the CPSWFs as well as the development of practical methods for computing their values. Also, in this work, we should prove that the CPSWFs form an orthonormal basis of the space of Hankel band-limited functions, an orthogonal basis of L²([0,1]) and an orthonormal system of L²([0,+∞[). Our computation of the CPSWFs and their associated eigenvalues is done by the use of two different methods. The first method is based on a suitable matrix representation of the finite Hankel transform operator. The second method is based on the use of an efficient quadrature method based on a special family of orthogonal polynomials. Also, we give two Maple programs that implement the previous two methods. Finally, we present some numerical results that illustrate the results of this work.     

Production of γ-Decalactone by a Psychrophilic and a Mesophilic Strain of the Yeast <Emphasis Type="Italic">Rhodotorula aurantiaca</Emphasis>

Among 18 psychrophilic strains isolated near the Antarctic Station, the psychrophilic strain Rhodotorula aurantiaca A19 was selected for its ability of growth and γ-decalactone production at low temperatures. The effects of temperature, initial pH, and castor oil concentration on the growth and γ-decalactone production by a psychrophilic and a mesophilic strain of R. aurantiaca were investigated. The highest γ-decalactone production in flasks (5.8 g/l) was obtained with the strain A19 at 14 °C and initial pH 7.0 in medium containing 20 g/l castor oil. On the other hand, these factors did not affect the production of γ-decalactone by the mesophilic strain. In fermentor, a γ-decalactone concentration of 6.6 g/l was reached with the strain A19, whereas a maximum of 0.1 g/l was obtained with the mesophilic strain. Our results suggest that the ability to synthesize γ-decalactone is a particularity of the strain A19, since the mesophilic strain (no. 30645) produced small amounts, and the other (no. 31354) did not exhibit this property. It is, to our knowledge, the first report of γ-decalactone production by R. aurantiaca and furthermore by a psychrophilic yeast strain. Moreover, the amount of γ-decalactone obtained in fermentor with the strain 19 was on the order of concentrations usually described in patents.     

The band spectrum of the periodic Airy–Schrödinger operator on the real line

We introduce the periodic Airy–Schrödinger operator and we describe its band spectrum. This is an example of solvable model with a periodic potential which is not differentiable at its extrema. We prove that there exists a sequence of explicit constants giving upper bounds of the semiclassical parameter for which explicit estimates are valid. We completely determine the behaviour of the edges of the first spectral band with respect to the semiclassical parameter. Then, we investigate the spectral bands and gaps situated in the range of the potential. We prove precise estimates on the widths of these spectral bands and these spectral gaps and we determine an upper bound on the integrated spectral density in this range. Finally, we get estimates of the edges of spectral bands and thus of the widths of spectral bands and spectral gaps which are stated for values of the semiclassical parameter in fixed intervals.     

Une preuve alternative de l'existence d'un équilibre de Nash dans les jeux discontinus

This Note presents a theorem of the existence of the Nash equilibrium for discontinuous games in a topological vector space. We will use an assumption of better reply secure which is stronger then that of Reny. If the payoff function is upper semi-continuous, the two assumptions coincide. Our proof is simple, independent and based on a version of Fan–Browder theorem of existence of maximal element due to Deguire and Lassonde, which is extended to the non-Hausdorf case. To cite this article: J.-M. Bonnisseau et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Monitoring of dynamic processes by rectangular hybrid automata

In this paper we develop a method of monitoring dynamic processes based on rectangular hybrid automats. This method takes into account the behavior of the system and the evolution of its parameters. A failure during the execution of the process can lead to a dysfunctional state in the system.The monitoring system, we propose, makes it possible to detect this state of dysfunction as soon as possible thanks to the reachability analysis.     

Effect of disorder on two-dimensional wetting

For the problem of the 2D wetting transition near a 1D random wall, we show by a renormalization calculation that the effect of disorder is marginally relevant. It is therefore expected that the nature of the wetting transition and the location of the critical point are modified by any amount of disorder. This is supported by numerical simulations based on transfer matrix calculations. We investigate also the problem of wetting near a random wall on hierarchical lattices and find similar results.     

A simple technique for the pyrosol process and deposition of tin oxide films

A very simple and low-cost device for the deposition of thin films by the pyrosol process has been designed Doped and undoped transparent conducting SnO₂ films have been prepared on glass substrates The films obtained were nonstoichiometric but homogeneous and polycrystalline in nature It is found that an activation energy of about 0 2 eV is associated with the film growth process The logarithm of the film thickness varies approximately linearly with the deposition time, and the sheet resistance shows a size effect below a thickness of about 0 3 micro m Doping increases the conductivity but at the cost of transparency The best compromise between transparency and conductivity was obtained at a substrate temperature of about 380°C and with 1 6 mole percent of Sb or 13 mole percent of F as dopants in the as-deposited condition The figure of ment of these films is compared to those of films obtained earlier by the spray pyrolysis method F doping produces better results than Sb doping.     

Mass spectrometric study of randomly methylated beta-cyclodextrins using ionspray, atmospheric pressure chemical ionization and matrix-assisted laser desorption/ionization

Mixtures of methylated beta-cyclodextrins were characterized using three different methods of mass spectrometry: ionspray, atmospheric pressure chemical ionization (APCI) and matrix-assisted laser desorption/ionization (MALDI). Each of these methods allows a fast and simple determination of the degree of substitution, and can provide evidence for differences in the methylation of batches which have very similar global degrees of substitution. The three methods are in good qualitative agreement, but there are systematic differences in the quantitative results for the percentages of the various methylated molecules present in a batch. This is attributed to ionization yields which increase with the number of methyl groups, with different slopes for the different methods.     

Strong coupling series for glueball masses in (2+1) dimensional PQED

We compute glueball masses to high order in strong coupling perturbation theory, and find no evidence for pathologies of the kind observed for the tension of the string (roughening). Results suggest a smooth extrapolation of the mass gap to the weak coupling regime.     

Analysis of Chemical Composition and In Vitro and In Vivo Antifungal Activity of Raphanus raphanistrum Extracts against Fusarium and Pythiaceae,Affecting Apple and Peach Seedlings

The goal of this investigation was to evaluate the in vitro and in vivo efficiency of Raphanus raphanistrum extracts against Fusarium and Pythiaceae species associated with apple and peach seedling decline in Tunisian nurseries. A chemical composition of organic extracts was accomplished using liquid chromatography, thin layer chromatography, and gas chromatography analysis. The in vitro test of three aqueous extract doses of R. raphanistrum against some apple and peach decline agents showed its efficacy in reducing mycelia growth. The in vivo assay of fine powder of this plant on peach seedlings revealed that treatment 8-weeks before the inoculation and planting was more efficient than the treatment before one week. This experiment revealed that the root weight of peach seedlings inoculated by F. oxysporum was improved to 207.29%. For apple seedlings, the treatment 8 weeks before the inoculation and plantation was more efficient than the treatment one week before; it reduced the root browning index. The study of R. raphanistrum chemical composition and its efficiency showed that the glucosinolates products: nitrile (4-Hydroxy-3-(4-methylphenylthio) butane nitrile, benzene acetonitrile, 4-fluoro,butane nitrile, 4-hydroxy-3-[(4-methylphenyl) thio] nitrile), and thiocyanate molecules (thiocyanic acid, ethyle) are responsible for the anti-fungal activities.