Bounds on the Range of Multivariate Rational Functions

By utilising the expansion of a polynomial into Bernstein polynomials, we construct bounds for the range of a multivariate rational function over a box. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kristallstruktur und spektroskopische Daten von Rb2[VOF4(H2O)]

Crystal Structure and Spectroscopic Data of Rb₂[VOF₄(H₂O)] Blue crystals of Rb₂[VOF₄(H₂O)] have been obtained from hydrofluoric acid. The crystal structure (space group Cmcm, a = 969.6(4), b = 780.6(2), c = 835.4(4) pm, Z = 4, d_c = 3.486 gcm^?3, d_m = 3.41 gcm^?3, R_w = 0.032 for 411 independent reflections) shows isolated [VOF₄(H₂O)]^2? anions — with H₂O in trans-position to the relatively long V? O bond (d(V? O) = 166.8(7) pm) — which are connected with each other by hydrogen bonds forming infinite chains. The blue colour of the compound despite of the isotypism to the “green” modification of Cs₂[VOF₄(H₂O)] is discussed on the basis of the structural data, i.r./Raman and u.v./vis reflection spectra. The magnetic moment is 1.72 B.M. at 295 K.     

Dependence on light amplitude of the dynamic stark splitting of an optical line

The dynamic Stark splitting of an optical line is found proportional to the intensity of the resonant light. At high intensity, the results are compatible with asymptotic proportionality to the field amplitude, as predicted by non-perturbative theory.     

Interaction of laser light waves by dynamic stark splitting

The internal stresses of condensed films are measured during both, condensation and annealing. Especially, materials are studied which can be stabilized in amorphous phases by quenching condensation technique. All amorphous films of Bi, Bi + Pb, Bi+Sb, Pb+Bi and Sn+Cu grow without any noticeable stress. In contrary, amorphous Sb-films arise with remarkable tensil stresses. The probably important difference between Sb and the other materials consists in the composition of the vapor. At normal evaporation conditions Sb-vapor contains almost only Sb₄-molecules, whereas the other materials evaporate monoatomically. The results are discussed with regard to a modell for the origin of the stresses based on the socalled Ostwald's rule for crystal growth.     

Dynamic stark effect of an optical line observed by cross-saturated absorption

Cross-saturated absorption at the neon line 2s ₂–2p ₄ caused by the saturating line 3s ₂–2p ₄ has been applied to the observation of the dynamic Stark effect by 1) power broadening, due to triple-quantum and higher multiple-quantum transitions, of the light shift contribution to the susceptibility, and 2) a direct splitting in the electronic Raman-Stokes contribution which occurs because of the partial compensation of the Doppler broadening. Work supported by the “Deutsche Forschungsgemeinschaft”.     

New Crystalline Salts of Nicotinamide Riboside as Food Additives

NR⁺ is a highly effective vitamin B₃ type supplement due to its unique ability to replenish NAD⁺ levels. While NR⁺ chloride is already on the market as a nutritional supplement, its synthesis is challenging, expensive, and low yielding, making it cumbersome for large-scale industrial production. Here we report the novel crystalline NR⁺ salts, d/l/dl-hydrogen tartrate and d/l/dl-hydrogen malate. Their high-yielding, one-pot manufacture does not require specific equipment and is suitable for multi-ton scale production. These new NR⁺ salts seem ideal for nutritional applications due to their bio-equivalence compared to the approved NR⁺ chloride. In addition, the crystal structures of all stereoisomers of NR⁺ hydrogen tartrate and NR⁺ hydrogen malate and a comparison to the known NR⁺ halogenides are presented.     

Collisional broadening of saturated absorption in neon

Saturation spectroscopy involving laser light fields of two different frequencies has been applied to the investigation of Ne*-Ne collisions in an absorptive neon discharge. The pressure broadening of the saturation signals is interpreted in terms of “weak” collisions. Half the signal width results from velocity shifts of 2p ₄ atoms rather than from oscillator dephasing. The mean velocity shift is considerably larger than in collisions with helium atoms.