General Coorbit Space Theory for Quasi-Banach Spaces and Inhomogeneous Function Spaces with Variable Smoothness and Integrability

In this paper we propose a general coorbit space theory suitable to define coorbits of quasi-Banach spaces using an abstract continuous frame, indexed by a locally compact Hausdorff space, and an associated generalized voice transform. The proposed theory realizes a further step in the development of a universal abstract theory towards various function spaces and their atomic decompositions which has been initiated by Feichtinger and Gröchenig in the late 1980s. We combine the recent approaches in Rauhut and Ullrich (J Funct Anal 260(11):3299–3362, 2011) and Rauhut (Stud Math 180(3):237–253, 2007) to identify, in particular, various inhomogeneous (quasi-Banach) spaces of Besov–Lizorkin–Triebel type. To prove the potential of our new theory we apply it to spaces with variable smoothness and integrability which have attracted significant interest in the last 10 years. From the abstract discretization machinery we obtain atomic decompositions as well as wavelet frame isomorphisms for these spaces.     

Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G

We developed a gravity-gradiometer based on atom interferometry for the determination of the Newtonian gravitational constant G. The apparatus, combining a Rb fountain, Raman interferometry and a juggling scheme for fast launch of two atomic clouds, was specifically designed to reduce possible systematic effects. We present instrument performances and preliminary results for the measurement of G with a relative uncertainty of 1%. A discussion of projected accuracy for G measurement using this new scheme shows that the results of the experiment will be significant to discriminate between previous inconsistent values.     

Cooling mechanisms in potassium magneto-optical traps

We report on a theoretical and experimental investigation of ³⁹K magneto-optical trapping. The small hyperfine splitting characterizing the upper level of the cooling transition affects the cooling mechanism. In order to model the atom-laser interaction, the whole level structure of the D₂ line has to be taken into account. Two different regimes have been recognized, one optimizing the loading of the trap, the second minimizing the temperature of the atoms. We investigated these two regimes experimentally and found results in agreement with the theoretical predictions. Received: 6 March 1998 / Received in final form: 13 May 1998 / Accepted: 13 May 1998     

The Chemical Ionization of Organic Compounds. 1st Communication. Linear alkenes with six to nine carbon atoms

The chemical ionization spectra of linear alkenes have been measured using H₂O, CH₄ or CD₃OD as ionizing gas. In the case of 1-heptene the dependence of spectra on pressure, temperature and repeller field strength has been measured and is discussed.     

Physico-chemical properties of deuteriated compounds 3rd communication. The viscosity of n-heptane

The kinematic viscosity of mixtures of perdeuteriated and protiated heptane has been measured between 15° and 35° and is given in polynomial form as a function of concentration and temperature. Using the McAllister equation to describe viscosity [4], it can be shown that the interactions between molecules containing the same or different isotopic species differ slightly.     

Disproportionation-to-combination ratios for cyclohexyl-h11 and -d11 radicals in the gas phase as determined by the radiolysis of water vapor–cyclohexane mixtures

In the radiolysis of water vapor containing small concentrations of cyclohexane, the principal products which account for about 98% of all end products are found to be hydrogen, cyclohexene, and bicyclohexyl. Cyclohexene and bicyclohexyl yields were determined over a range of temperatures (70–200°C), total pressures (50–2400 torr), and total doses (0.15–2.0 Mrad). The disproportionation–combination ratio k/k for c-C₆H₁₁ radicals could be determined as 0.56 ± 0.01 from the ratio of cyclohexene to bicyclohexyl yield. By using c-C₆D₁₂, the ratio k/k for c-C₆D₁₁ radicals is found to be 0.38 ± 0.01. Comparison of the reactivity pattern of C₆H₁₁ and C₆D₁₁ radicals leads to (k)/(k)/(k/k) = 1.47 ± 0.02. The corresponding values for the reactions of c-C₆H₁₁ with c-C₆D₁₁ were also determined.     

Physikalisch-chemische Eigenschaften deuterierter Verbindungen. 4. Mitteilung. Deuterierung von Kohlenwasserstoffen durch heterogen katalysierten Isotopenaustausch im Gegenstrom

The Deuteration of Hydrocarbons by Heterogeneous Catalysis in a Counter-current Column A counter-current method for the perdeuteration of liquid hydrocarbons by heterogeneously catalysed isotope exchange with deuterium gas is described. The efficiency of the column which was developed for this purpose has been investigated and optimised as a function of the experimental variables. The limits of the applicability of this method are discussed.     

Polarization spectroscopy of atomic oxygen by dye and semiconductor diode lasers

Summary We used polarization spectroscopy to perform a high-resolution investigation of atomic oxygen in the visible and near-infrared spectral region by means of dye and semiconductor diode lasers. We measured the fine structure of the highly excited 4d ⁵ D level and resolved the hyperfine structure of the metastable 3s ⁵ S ₂ level of¹⁷O. Isotope shift values are also reported for several transitions of the three stable oxygen isotopes (¹⁶O,¹⁷O,¹⁸O). Polarization lineshapes are discussed and compared with those obtained in saturation techniques.     

Physicochemical Properties of Deuterated Compounds. 7th Communication. The H/D exchange between hydrogen and methane over Ni Catalyst

The isotopic exchange between hydrogen and methane over Ni catalyst has been studied as a function of temperature, isotopic substitution, and ratio of hydrogen to methane. The experimental results can be described by means of a model in which methane is adsorbed either as methyl or as methylene. The adsorbed species undergo one or several exchanges. The four required parameters are adjusted to the experimental results. The exchange of partially deuterated methane with H₂ or D₂ allowed us to study the isotopic effect on the adsorption and the exchange processes.