Integration on then th power of a hyperbolic space in terms of invariants under diagonal action of isometries (Lorentz transformations)

The integral of a function over then'th power of hyperbolicd-dimensional spaceH is decomposed into integration along each orbit under diagonal action onH ⁿ of the isometry groupG onH, followed by integration over the orbit space, parametrized in terms of a complete set of invariants. The Jacobian entering in this last integral is expressed explicitly in terms of certain determinants. When viewingH as a half-hyperboloid in _d+1 ,G is induced by the homogeneous Lorentz groupO (1,d) acting on _d+1 .     

Competition and selectivity of organic reactions on semiconductor surfaces: reaction of unsaturated ketones on Si(100)-2 x 1 and Ge(100)-2 x 1

A combined experimental and theoretical study of a model system of multifunctional unsaturated ketones, including ethyl vinyl ketone (EVK), 2-cyclohexen-1-one, and 5-hexen-2-one, on the Si(100)-2 x 1 and Ge(100)-2 x 1 surfaces was performed in order to probe the factors controlling the competition and selectivity of organic reactions on clean semiconductor surfaces. Multiple internal reflection infrared spectroscopy data and density functional theory calculations indicate that EVK and 2-cyclohexen-1-one undergo selective [4 + 2] hetero-Diels-Alder and [4 + 2] trans cycloaddition reactions on the Ge(100)-2 x 1 surface at room temperature. In contrast, on the Si(100)-2 x 1 surface, evidence is seen for significant ene and possibly [2 + 2] C=O cycloaddition side products. The greater selectivity of these compounds on Ge(100) versus Si(100) is explained by differences between the two surfaces in both thermodynamic factors and kinetic factors. With 5-hexen-2-one, for which [4 + 2] cycloaddition is not possible, a small [2 + 2] C=C cycloaddition product is observed on Ge(100) and possibly Si(100), even though the [2 + 2] C=C transition state is calculated to be the highest barrier reaction by several kilocalories per mole. The results suggest that, due to the high reactivity of clean semiconductor surfaces, thermodynamic selectivity and control will play important roles in their selective functionalization, favoring the use of Ge for selective attachment of multifunctional organics.     

Simultaneous extraction of tetracycline, macrolide and sulfonamide antibiotics from agricultural soils using pressurised liquid extraction, followed by solid-phase extraction and liquid chromatography-tandem mass spectrometry

The veterinary antibacterial agents chlortetracycline (CTC), oxytetracycline (OTC), sulfadiazine (SDZ), erythromycin (ERY) and tylosin (TYL A, B, C and D) were extracted from soil using pressurized liquid extraction (PLE). Citric acid (pH 4.7) and methanol was used as extraction buffer, followed by tandem-solid-phase extraction (SPE) clean-up (SAX + HLB) for all compounds. For quantification two slightly different methods were employed using LC-MS-MS with MRM detection. The soil extraction method was validated using a loamy sand soil and a sandy soil, representing two typical Danish agricultural soils. Recoveries were 50-80% for the tetracyclines (CTC and OTC) and sulfadiazine (SDZ) and 60-100% for the macrolides (TYL and ERY). Limits of detection for the soil extraction method (LOD(soil)) were 0.6-5.6 microg kg(-1) soil for CTC and OTC, 0.9-2.9 microg kg(-1) soil for SDZ and 2.4-5.5 microg kg(-1) soil for TYL A and ERY. Furthermore, the method was applied to field samples taken from two agricultural fields fertilised with liquid manure containing CTC and TYL A. These results showed a decline in the content of antibacterial agents throughout the sampling period of 155 days from 10 to 15 microg CTC kg(-1) soil and 20-55 microg TYL A kg(-1) soil to below or near the LOD(soil) listed above. Finally, the method was applied to barley grains harvested from the fields. None of the antibacterial agents were measured in grain samples, but recoveries for spiked grain samples were similar to soil recoveries.     

Some properties of the riesz charge associated with a δ-subharmonic function

The first property is a refinement of earlier results of Ch. de la Vallée Poussin, M. Brelot, and A. F. Grishin. Let w=u–v with u, v superharmonic on a suitable harmonic space (for example an open subset of R ⁿ ), and let [w]=[u]–[v] denote the associated Riesz charge. If w0, and if E denotes the set of those points of at which the lim inf of w in thefine topology is 0, then the restriction of [w] to E is 0. Another property states that, if e denotes a polar subset of such that the fine lim inf of |w| at each point of e is finite, then the restriction of [w] to e is 0.     

Simulations of full multivariate Tweedie with flexible dependence structure

We employ a variables-in-common method for constructing multivariate Tweedie distributions, based on linear combinations of independent univariate Tweedie variables. The method lies on the convolution and scaling properties of the Tweedie laws, using the cumulant generating function for characterization of the distributions and correlation structure. The routine allows the equivalence between independence and zero correlation and gives a parametrization through given values of the mean vector and dispersion matrix, similarly to the Gaussian vector. Our approach leads to a matrix representation of multivariate Tweedie models, which permits the simulations of many known distributions, including Gaussian, Poisson, non-central gamma, gamma, and inverse Gaussian, both positively or negatively correlated.     

SILYL- AND GERMYL-DIAZADIPHOSPHETIDINES

Abstract

Reaction of the 1,3,2,4-diazadiphosphetidine, trans-[C₆H₅N(H)P(S)NC₆H₅]₂ with LiR (R = Me, n-Bu) followed by treatment of the resulting dianions with Me₃SiCl and Me₃GeBr produced trans-[C₆H₅N(R)P(S)NC₆H₅]₂(R = Me₃Si, 2; Me₃Ge, 3). Substitution occurs without cis-trans isomerization or significant cleavage of the 1,3,2,4-diazadiphosphetidine ring. 2 and 3 have been characterized by spectral (¹H and ³¹P NMR, IR, and MS) and elemental analytical data. Analogous reactions involving Me₃SnCl yield mixtures containing [C₆H₅N(SnMe₃)P(S)NC₆H₅]₂ which could not be isolated or completely characterized.     

Analytic continuation of Flensted-Jensen representations

LetX=G/H be an affine symmetric space of Hermitian type. For modules in the analytic continuation of the scalar holomorphic discrete series forG, we show existence and uniqueness (that is, a multiplicity one result) of imbeddings into functions onX. The corresponding intertwining operators are analyzed using our previous methods for discrete series. In a slightly less explicit way, we also give the analogous results for the continuation of the general discrete series.     

AB initio calculations of the electronic properties of N4− in KN3

The energies of the ground state and low-lying excited states of the N₄^? defect in KN₃ have been calculated using ab initio techniques. A rectangular equilibrium geometry with dimensions X = 2.76 and Z = 2.47 a.u. and ground state symmetry of Γ₄⁺ was determined by calculating N₄^? as a free radical. For this ground state the unpaired electron is in a π orbital which is consistent with the experimental hyperfine tensor only if one edge of the N₄^? radical is parallel to the c axis in KN₃. These results were used to calculate the X²Γ₄⁺ state of N₄^? in the crystal field of KN₃, yielding an energy of ?217.899 Hartrees. The isotropic hyperfine constant was calculated to be a = 2.1 G and the components of the anisotropic hyperfine tensor as B_xx = ?3.4 G, B_yy = 7.0 G and B_zz = ?3.6 G, in good agreement with experimental and INDO results. Several excited states were calculated for the N₄^? defect in KN₃. When an estimate was made of the correlation energy, the transition energy of the X²Γ₄⁺→A²Γ₃^? transition agreed well with the peak energy of the 780 nm absorption band which has been attributed to N₄^?.     

Hesseltin A, a novel antiviral metabolite from Penicillium hesseltinei

[structure: see text] Hesseltin A 1, a novel compound of mixed polyketide-terpenoid origins was isolated from the filamentous fungus Penicillium hesseltinei. The structure and stereochemistry were determined from extensive one- and two-dimensional NMR and mass spectral data.     

Development and validation of a high-precision capillary electrophoresis method for main component assay of ragaglitazar

The ability of a developed capillary electrophoresis (CE) method for fast, efficient and reliable main component assay of ragaglitazar [NNC 61-0029/DRF(-)2725] has been demonstrated through documentation of the analytical performance and the results of a successful validation. The fast analysis time of around 1.2 min ensures a high analytical capacity, and the validation results show that the CE method is robust and gives reliable and precise results. The results from the validation of the CE method meet the acceptance criteria that are normally set for other main component assays such as high-performance liquid chromatography assays.