光学偶极阱中铷原子5S_(1/2)及5P_(3/2)态的AC Stark频移

基于二能级模型和多能级模型,分析计算了由强聚焦高斯光束形成的光学偶极阱中87Rb原子5S1/2态和5P3/2态的AC Stark频移。基于多能级模型,针对在852 nm高斯激光束强聚焦所形成的87Rb原子远失谐光学偶极阱中进行偏振梯度冷却的情形,计算了冷却循环跃迁(5S1/2F=2-5P3/2F′=3)的频移量,结果显示频移对molasses冷却过程产生了重要的影响。同时,计算了5S1/2|F=2,mF=±2〉态和5P3/2|F′=3,mF=±3〉态的AC Stark频移随光学偶极阱激光波长的变化情况,发现在红失谐情况下,对于87Rb原子5S1/2-5P3/2态跃迁不存在魔数波长。     

Understanding the polarization signal of spherical particles for microwave limb radiances

This paper presents a simple conceptual model to explain that even spherical scatterers lead to a polarization difference signal for microwave limb radiances. The conceptual model relates the polarization difference measured by a limb-looking sensor situated inside a cloud with the anisotropy of the radiation. In the simulations, it was assumed that the cloud consists of spherical ice particles with a radius of which were situated between 10.6 and 12.3 km altitude. The frequencies 318 and 500 GHz were considered.The results of the conceptual model were compared to the results of the fully polarized scattering model ARTS-1-1. The comparison showed a good qualitative agreement. The polarization difference decreases inside the cloud with increasing height and changes sign. This behavior can be related to a different amount of radiation coming from the atmosphere above and below the cloud, compared to the amount of radiation coming from the sides. The sign of polarization difference of the scattered radiation is opposite for these two radiation sources.     

Random Latin squares and 2-dimensional expanders

Expander graphs have been playing an important role in combinatorics and computer science over the last four decades. In recent years a theory of high dimensional expanders is emerging, but as of now all known examples of expanders (random and explicit) have unbounded degrees. The question of existence of bounded degree high dimensional expanders was raised by Gromov and by Dotterrer and Kahle. In this paper we present a new model, based on Latin squares, of 2-dimensional complexes of bounded edge degrees that are expanders with probability tending to 1.     

Addition-type polynorbornene with Si(CH3)3 side groups: Detailed study of gas permeation and thermodynamic properties

Polymerization of norbornene bearing Si(CH₃)₃ groups in the five position with the opening of double bonds was performed. By accurate selection of the ratios catalyst/co-catalyst and monomer/catalyst the samples with increased molecular mass (about 400,000) were obtained. Transport parameters of this, addition type poly(trimethylsilyl norbornene) (PTMSN) were measured using the gas chromatographic and mass spectrometric methods for different gases (H₂, He, O₂, N₂, CO₂, CH₄, C₂H₆, C₃H₈ and n-C₄H₁₀). Temperature dependence of the permeability coefficients (P) indicated that low activation energies of permeation (E_P) and diffusion (E_D) are characteristic for PTMSN. In some cases (CO₂, C₂H₆) negative E_P values were observed. Thermodynamics of vapor sorption in this polymer was studied using the inverse gas chromatography method. It was shown that PTMSN is characterized by very large solubility coefficients S similar to those of poly(trimethylsilyl propyne) (PTMSP). The comparison of the P, D, and S values of these highly permeable polymers showed that the greater permeability of PTMSP is determined by the larger D values. Application of different approaches for the determination of the size of microcavities in PTMSN indicated that this polymer is characterized by large size of microcavity (800–1200 ?³).     

On holomorphic functions of slow growth on coverings of strongly pseudoconvex manifolds

In this paper we extend some results of the paper [M. Gromov, G. Henkin, M. Shubin, Holomorphic L²-functions on coverings of pseudoconvex manifolds, Geom. Funct. Anal. 8 (1998) 552-585].     

Solid-State Rb NMR Study in Powdered RbMnCl3

Structural phase transition at 290 K and the implication on the intermediate phase above 290 K in powdered RbMnCl₃ are observed by using a solid-state ⁸⁷Rb NMR spectroscopy. Quadrupole coupling constants (e²qQ/h), the asymmetry parameters (η), and the relative peak intensities for two physically nonequivalent Rb sites, Rb(I) and Rb(II), are determined from nonlinear least-squares fits to the ⁸⁷Rb NMR powder patterns in the temperature range from 260 to 330 K. Quadrupole coupling constants and the asymmetry parameters are examined for the detection of the phase transition resulting in a significant structural change in the Rb(II) site. In addition, changes in the relative peak intensity between the Rb(I) and Rb(II) sites seem to suggest the existence of an anomalous intermediate phase, which is complemented by the differential scanning calorimetry and X-ray diffraction studies.     

Specificity and Origin of the Stability of the Sr Isotopic Ratio in Champagne Wines

The ⁸⁷Sr/⁸⁶Sr ratio of 39 Champagnes from six different brands, originating from the whole “Appellation d’Origine Contrôlée” (AOC) Champagne was analyzed to establish a possible relation with the geographical origin. Musts (i.e., grape juice) and base wines were also analyzed to study the evolution of the Sr isotopic ratio during the elaboration process of sparkling wine. The results demonstrate that there is a very homogeneous Sr isotopic ratio (⁸⁷Sr/⁸⁶Sr = 0.70812, n = 37) and a narrow span of variability (2σ = 0.00007, n = 37). Moreover, the Sr concentrations in Champagnes have also low variability, which can be in part explained by the homogeneity of the bedrock in the AOC Champagne. Measurements of the ⁸⁷Sr/⁸⁶Sr ratio from musts and base wines show that blending during Champagne production plays a major role in the limited variability observed. Further, the ⁸⁷Sr/⁸⁶Sr of the musts were closely linked to the ⁸⁷Sr/⁸⁶Sr ratio of the vineyard soil. It appears that the ⁸⁷Sr/⁸⁶Sr of the product does not change during the elaboration process, but its variability decreases throughout the process due to blending. Both the homogeneity of the soil composition in the Champagne AOC and the blending process during the wine making process with several blending steps at different stages account for the unique and stable Sr isotopic signature of the Champagne wines.     

Solvability of the -Laplacian with nonlocal boundary conditions

Rather mild sufficient conditions are provided for the existence of positive solutions of a boundary value problem of the form

which unify several cases discussed in the literature. In order to formulate these conditions one needs to know only properties of the homeomorphism and have information about the level of growth of the response operator F. No metric information concerning the linear operators L₀,L₁ in the boundary conditions is used, except that they are positive and continuous and such that L_j(1)<1 j{0,1}.     

Generalized Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers-Ulam stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces.