On the geometry of reduced cotangent bundles at zero momentum

We consider the problem of cotangent bundle reduction for proper non-free group actions at zero momentum. We show that in this context the symplectic stratification obtained by Sjamaar and Lerman refines in two ways: (i) each symplectic stratum admits a stratification which we call the secondary stratification with two distinct types of pieces, one of which is open and dense and symplectomorphic to a cotangent bundle; (ii) the reduced space at zero momentum admits a finer stratification than the symplectic one into pieces that are coisotropic in their respective symplectic strata.     

Simulation of outdoor sound propagation with a transmission line matrix method

The present paper focusses on the application of the transmission line matrix method (TLM) for outdoor sound propagation simulations. It is shown how the reflection at the ground and vertical sound speed gradients can be taken into account. The comparison with calculations using finite differences in the time domain (FDTD), with calculations using parabolic equation and with analytical solutions showed all very good agreement. Thereby the computational effort of TLM is significantly lower compared to common FDTD calculation schemes.     

Optical absorption and photoluminescence studies of Eu-doped phosphate and fluorophosphate glasses

Phosphate (P₂O₅+K₂O+BaO+Al₂O₃+Eu₂O₃) and fluorophosphate (P₂O₅+K₂O+BaO+BaF₂+Al₂O₃+Eu₂O₃) glasses with different Eu³⁺ ion concentrations have been prepared and characterized through optical absorption, photoluminescence and decay times. An intense red luminescence is observed from the ⁵D₀ emitting level of Eu³⁺ ions in these glasses. The relative luminescence intensity ratio of ⁵D₀→⁷F₂→⁵D₀→⁷F₁ transitions has been evaluated to estimate the local site symmetry around the Eu³⁺ ions. The emission spectra of these glasses show a complete removal of degeneracy for the ⁵D₀→⁷F₁ and ⁵D₀→⁷F₂ transitions. Second and fourth rank crystal-field (CF) parameters have been calculated together with the CF strength parameter by assuming the C_2v symmetry for the Eu³⁺ ions in both the phosphate and fluorophosphate glasses. Judd-Ofelt parameters have been evaluated from the luminescence intensity ratios of ⁵D₀→⁷F_J (J=2, 4 and 6) to ⁵D₀→⁷F₁ transitions. These parameters have been used to derive radiative properties such as transition probabilities, branching ratios, radiative lifetimes and peak stimulated emission cross-sections for the ⁵D₀→⁷F_J transitions. Decay curves of the ⁵D₀ level of Eu³⁺ ions in these two Eu³⁺:glass systems have been measured by monitoring the ⁵D₀→⁷F₂ transition (611 nm) at room temperature. The experimental lifetime of the ⁵D₀ level in the title glasses is found to be higher than Eu³⁺-doped niobium phosphate glasses. The analysis indicates that the lifetime of the ⁵D₀ level is found to be less sensitive to the Eu³⁺ ion concentration and addition of BaF₂ has no significant effect on the optical properties of Eu³⁺-doped phosphate glasses.     

1H, 13C and 15N NMR spectral analysis of substituted 1,2,3,4‐tetrahydro‐pyrido[1,2‐a]pyrimidines

The NMR spectroscopic data of a series of thirty‐four 3‐acylpyrido[1,2‐a]pyrimidinium salts are analyzed, which were prepared as either perchlorates or chlorides. Methyl group substituted 3‐aroyltetrahydropyrido[1,2‐a]pyrimidines with the methyl substituent in positions 6, 8 and 9 as well as both in positions 6 and 8 were investigated bearing various aroyl substituents. Unequivocal assignment of all resonances was achieved via two‐dimensional ¹H,¹H‐COSY measurements, ¹H,¹³C and ¹H,¹⁵N HSQC as well as HMBC experiments, and important diagnostic CH and NH couplings in the heteroaromatic ring system are evaluated. The influence of the methyl substituents was analyzed on the proton, carbon and nitrogen shifts. A significant effect of the counter ion on some chemical shifts of the nuclei under discussion of the pyridopyrimidines is found, allowing the indirect detection of the anion, which is confirmed by direct measurement of the ³⁵Cl nucleus of the perchlorates. Copyright © 2013 John Wiley & Sons, Ltd.     

Vanishing structure set of 3-manifolds

In this short note we update a result proved in Roushon (2007) [17]. This will complete our program of Roushon (2000) [13] showing that the structure set vanishes for compact aspherical 3-manifolds.     

Correlation between proton transfer and 35Cl NQR frequency as well as molecular geometry of chloranilic acid in co‐crystals with some organic bases

Proton transfer in hydrogen‐bonded organic co‐crystals of chloranilic acid with some organic bases was investigated by nuclear quadrupole resonance (NQR) spectroscopy. The ³⁵Cl NQR frequencies of chloranilic acid molecule as well as ¹⁴N NQR frequencies of the organic base molecule were measured with the conventional pulse methods as well as double‐resonance methods, respectively. The extent of proton transfer in the O···H···N hydrogen bond was estimated from Townes–Dailey analysis of the ¹⁴N NQR parameters. The ³⁵Cl NQR frequency and molecular geometry of chloranilic acid are correlated to the extent of proton transfer in the protonation process of the organic base molecule. It is shown that the hydrogen bond affects the π‐electron system of chloranilic acid. Geometry dependence of the O···H···N hydrogen bond, i.e. the H? N valence bond order versus the hydrogen‐bond geometry correlation is also discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Approach theory meets probability theory

In this paper we reconsider the basic topological and metric structures on spaces of probability measures and random variables, such as e.g. the weak topology and the total variation metric, replacing them with more intrinsic and richer approach structures. We comprehensibly investigate the relationships among, and basic facts about these structures, and prove that fundamental results, such as e.g. the portmanteau theorem and Prokhorov?s theorem, can be recaptured in a considerably stronger form in the new setting.     

Stitching pairs of Lévy processes into harnesses

We consider natural exponential families of Lévy processes with randomized parameter. Such processes are Markov, and under suitable assumptions, pairs of such processes with shared randomization can be “stitched together” into a single harness. The stitching consists of deterministic reparametrization of the time for both processes, so that they run on adjacent time intervals, and of the choice of the appropriate law at the boundary.     

NON-EXISTENCE OF A COGENERATOR FOR ORDERED VECTOR SPACES

Abstract

See title.     

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH₂O, H₂O, HF, F₂, HCN, SiH₄ and H₂S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS‐2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization‐consistent pcS‐n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS‐2 and aug‐cc‐pVTZ‐J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS‐2, MP2/pcS‐2 and DFT/CBS calculations with pcS‐n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.