Self-broadening coefficients in the ν2 and ν5 bands of CH3F at 183 and 298 K

The self-broadening coefficients of 33 rovibrational lines in the ν₂ and ν₅ bands of ¹²CH₃F were measured at a sample temperature of 183 K using a diode-laser spectrometer. We have also realized the measurement of these coefficients at room temperature for 10 of these lines in order to determine their temperature dependence. These results were obtained by fitting to the experimental profile the Voigt lineshape and the Rautian and Galatry models taking into account the collisional narrowing. Calculations of the self-broadening coefficients were also performed for the same temperatures from a semiclassical model involving only electrostatic interactions in the intermolecular potential. The calculated values are significantly larger than the experimental data for both temperatures but the J-dependences of the self-broadenings are well reproduced. Moreover, the theoretical temperature dependence of these coefficients is in good agreement with that derived from the measurements.     

CO2-broadening coefficients in the ν4 + ν5 band of acetylene

The CO₂-broadening coefficients of 24 P- and R-branch transitions in the ν₄ + ν₅ band of acetylene were measured at room temperature using a diode-laser spectrometer. These lines with J values up to 26, were located in the spectral range 1270 to 1400 cm⁻¹. The collisional broadening coefficients were retrieved by fitting the experimental profiles to the Voigt, Rautian, and Galatry lineshape models. Two experimental values for the narrowing coefficient were determined from the spectra and compared with the theoretical narrowing coefficient. The calculations of these broadenings were also performed in the frame of a semiclassical formalism involving a simple intermolecular potential with an adjustable parameter. The theoretical results are in good agreement with the experimental results and reproduce well the J dependence of the broadening coefficients.     

High resolution infrared spectra of carbon disulfide: 13CS2

By using a “dual-grille” spectrometer, twelve transitions of ¹³CS₂ have been observed between 1400 and 3000 cm^?1. The position of eleven vibration levels have been fixed accurately. The molecular constants of ¹³CS₂ determined by vibrational and vibrorotational analysis are in good agreement with the constants issued from the ¹²CS₂ analysis.     

Some remarks on generalized roundness

By using the links between generalized roundness, negative type inequalities and equivariant Hilbert space compressions, we obtain that the generalized roundness of the usual Cayley graph of finitely generated free groups and free abelian groups of rank  ≥ 2 equals 1. This answers a question of J-F. Lafont and S. Prassidis.      

The Distribution of Discounted Compound PH–Renewal Processes

We continue and extend the work in Léveillé et al. (2010) Scand Actuar J 3:165–184 that gives analytical formulas for the moment generating function (mgf) of some discounted compound renewal processes. Here these mgf’s are used to derive and study the distribution of discounted compound Phase-type (PH) renewal sums. The approach consists in first deriving a differential equation, in the time variable, for the mgf of discounted compound sums when the inter–arrival times are PH–distributed. Then the corresponding distribution of the discounted compound PH sum is obtained by inversion of its mgf (or the equivalent Laplace transform). Analytical expressions for the asymptotic distribution of these discounted compound renewal sums are also given, to test general expressions in some limiting cases. Despite the technical difficulty, several new examples are provided where the inversion is possible, through symbolic computation in MAPLE. When the inversion is too complex, a truncated series solution method is proposed, which is not new but turns out to be very fast and accurate here, much more than other methods (such as rational approximations). The article concludes with some applications where the mgf and the distribution are used to calculate risk measures such as VaR, CTE, Esscher’s, Wang’s Proportional Hazard transforms and evaluate their evolution in time.     

A fluorogenic assay for transketolase from Saccharomyces cerevisiae

In order to generate transketolase (TK) with new or improved properties by in vitro evolution, an efficient screening system is an absolute prerequisite for identifying the evolved enzyme variants. We report here an assay allowing us to detect wild type TK activity in vitro by fluorescence. We examined the use of the fluorogenic compound 1 as donor substrate of TK, which is itself non fluorescent but releases a fluorescent product: umbelliferone.     

5,5-Dimethyl-1,4,2-dioxazoles as versatile aprotic hydroxamic acid protecting groups

5,5-Dimethyl-1,4,2-dioxazoles are readily installed by transketalization of 2,2-diethoxypropane, where both the NH and OH moieties are protected in a nonprotic form. The dioxazoles are stable to a wide variety of reaction conditions and readily revert back to the hydroxamic acid by treatment with Nafion-H in 2-propanol. The method is applicable to primary, secondary, tertiary, and aromatic hydroxamic acids, and the acidity of the protons adjacent to the dioxazole allows alpha-functionalization.     

On a class of stably finite nuclear C*-algebras

In this note we show that a separable C^*-algebra is nuclear and has a quasidiagonal extension by (the ideal of compact operators on an infinite-dimensional separable Hilbert space) if and only if it is anuclear finite algebra (NF-algebra) in the sense of Blackadar and Kirchberg, and deduce that every nuclear C^*-subalgebra of aNF-algebra isNF. We show that strongNF-algebras satisfy a Følner type condition.     

An extension of the TV-HLL scheme for multi-dimensional compressible flows

This paper investigates a very simple method to numerically approximate the solution of the multi-dimensional Riemann problem for gas dynamics, using the literal extension of the Toro Vazquez-Harten Lax Leer (TV-HLL) scheme as its basis. Indeed, the present scheme is obtained by following the Toro–Vazquez splitting, and using the HLL algorithm with modified wave speeds for the pressure system. An essential feature of the TV-HLL scheme is its simplicity and its accuracy in computing multi-dimensional flows. The proposed scheme is carefully designed to simplify its eventual numerical implementation. It has been applied to numerical tests and its performances are demonstrated for some two-dimensional and three-dimensional test problems.