Sur les fonctions méromorphes limites de fonctions rationnelles

Sans résumé     

Über die Nullstellen einiger Klassen von Polynomen

Ohne Zusammenfassung     

Three-dimensional numerical studies on the effect of the particle charge to mass ratio distribution in the electrostatic coating process

Charge to mass ratio is a crucial parameter that governs the behavior of particle trajectories in a charged cloud of particles. The complex nature of the charging process limits our ability to accurately determine the charging level when particles of varying size are present. Using a numerical approach, it is possible, however, to take into account predefined values for this parameter. In this paper, the average charge to mass ratio and the distribution of the charge to mass ratio in the coating of a flat target were systematically varied to demonstrate their effect on the motion of the charged particles. The results show that the transfer efficiency increases as the average charge to mass ratio increases. It was found that the transfer efficiency is a weak function of the average particle size in the range tested and that it increases as the width of the size distribution increases.     

Electron emission from photo-excited testosterone in water–ethanol solution

Testosterone (TES; 4-androstene-17β-ol-3-on) is found for the first time to eject electrons from its singlet excited state in water–ethanol solvent mixture. This ability was very recently also observed for 17β-estradiol (17βE2) and progesterone (PRG)/1/. With increasing TES-concentration, the yield of solvated electrons (${\text{e}}_{\text{s}}^{-}$) is decreasing, because of “associate” formation. At higher absorbed UV-doses (λ = 254 nm) the ${\text{e}}_{\text{s}}^{-}$ yield is passing a sharp maximum by formation of TES–ethanol adducts, which are able likewise to emit electrons when excited. At prolonged irradiation the resulting photolytic products of TES–ethanol adducts are also able to emit electrons.The capability of the hormones: 17βE2, PRG and TES to eject electrons and the resulting metabolites, some of which can induce cancer, is discussed.     

Investigation of the chemical composition–antibacterial activity relationship of essential oils by chemometric methods

The antibacterial effects of Thymus vulgaris (Lamiaceae), Lavandula angustifolia (Lamiaceae), and Calamintha nepeta (Lamiaceae) Savi subsp. nepeta var. subisodonda (Borb.) Hayek essential oils on five different bacteria were estimated. Laboratory control strain and clinical isolates from different pathogenic media were researched by broth microdilution method, with an emphasis on a chemical composition–antibacterial activity relationship. The main constituents of thyme oil were thymol (59.95%) and p-cymene (18.34%). Linalool acetate (38.23%) and β-linalool (35.01%) were main compounds in lavender oil. C. nepeta essential oil was characterized by a high percentage of piperitone oxide (59.07%) and limonene (9.05%). Essential oils have been found to have antimicrobial activity against all tested microorganisms. Classification and comparison of essential oils on the basis of their chemical composition and antibacterial activity were made by utilization of appropriate chemometric methods. The chemical principal component analysis (PCA) and hierachical cluster analysis (HCA) separated essential oils into two groups and two sub-groups. Thyme essential oil forms separate chemical HCA group and exhibits highest antibacterial activity, similar to tetracycline. Essential oils of lavender and C. nepeta in the same chemical HCA group were classified in different groups, within antibacterial PCA and HCA analyses. Lavender oil exhibits higher antibacterial ability in comparison with C. nepeta essential oil, probably based on the concept of synergistic activity of essential oil components.     

Very Efficient Generation of Quinone Methides through Excited State Intramolecular Proton Transfer to a Carbon Atom

Irradiation of 2-phenyl-1-naphthol (6) in CH(3) CN/D(2) O (3:1) leads to very efficient incorporation of deuterium at the ortho-positions of the adjacent phenyl ring (overall Φ=0.73±0.07), along with minor incorporation at the naphthalene positions 5 and 8. These finding are explained by excited state intramolecular proton transfer (ESIPT) from the phenolic OH group to the corresponding carbon atoms, the main pathway giving rise to quinone methide (QM) 7, which has been characterized by LFP (τ≈20?ns; 460?nm). The ESIPT reaction paths have been explored with the second order approximate coupled cluster (CC2) method. In nonprotic solvents the ESIPT from the naphthol O-H to the ortho-position of the phenyl ring proceeds in a barrierless manner along the (1) L(a) energy surface via a conical intersection with the S(0) state, delivering 7. In aqueous solvent, clusters with H(2) O are formed wherein proton transfer (PT) to solvent and a H(2) O-mediated relay mechanism gives rise to naphtholates and QMs. The results are compared with 2-phenylphenol (3) that also undergoes barrierless ESIPT giving a QM via a conical intersection. However, due to an unfavorable conformation in the ground state, the quantum efficiency for ESIPT of 3 is significantly lower (Φ for D-exchange=0.041). These results show that ESIPT from phenol to carbon need not be an intrinsically inefficient process.     

Dynamical time versus system time in quantum mechanics

Properties of an operator representing the dynamical time in the extended parameterization invariant formulation of quantum mechanics are studied. It is shown that this time operator is given by a positive operator measure analogously to the quantities that are known to represent various measurable time operators. The relation between the dynamical time of the extended formulation and the best known example of the system time operator, i.e., for the free one-dimensional particle, is obtained.     

On the Domain Dependence of Solutions to the Compressible Navier-Stokes Equations of an Isothermal Fluid

The aim of this paper is to study the behaviour of the variational solutions to the Navier-Stokes equations describing viscous compressible isothermal fluids with nonlinear stress tensors in a sequence of domains $\{\varOmega_{n}\} _{n=1}^{\infty}$ . The sequence converges in sense of the Sobolev-Orlicz capacity to domain Ω. We prove that the solutions of the equations in Ω _n converge to a solution of the respective equations in Ω. Moreover, The result can be applied to generalization of the existence result.     

Long-time behavior of stable-like processes

In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol p(x,ξ)=−iβ(x)ξ+γ(x)|ξ|^α(x)$p(x,\xi )=-i\beta \left(x\right)\xi +\gamma \left(x\right){\left|\xi \right|}^{\alpha \left(x\right)}$, where α(x)∈(0,2)$\alpha \left(x\right)\in (0,2)$, β(x)∈R$\beta \left(x\right)\in \mathbb{R}$ and γ(x)∈(0,∞)$\gamma \left(x\right)\in (0,\infty )$. More precisely, we give sufficient conditions for recurrence, transience and ergodicity of stable-like processes in terms of the stability function α(x)$\alpha \left(x\right)$, the drift function β(x)$\beta \left(x\right)$ and the scaling function γ(x)$\gamma \left(x\right)$. Further, as a special case of these results we give a new proof for the recurrence and transience property of one-dimensional symmetric stable Lévy processes with the index of stability α≠1$\alpha \ne 1$.