Cauchy problem for effectively hyperbolic operators with triple characteristics

We study a class of third-order effectively hyperbolic operators P   in G={(t,x):0?t?T,x∈U?Rⁿ}$G=\{(t,x):0?t?T,x\in U?{\mathbb{R}}^n\}$ with triple characteristics at ρ=(0,x₀,ξ),ξ∈Rⁿ?{0}$\rho =(0,x_0,\xi ),\xi \in {\mathbb{R}}^n?\{0\}$. V. Ivrii introduced the conjecture that every effectively hyperbolic operator is strongly hyperbolic  , that is the Cauchy problem for P+Q$P+Q$ is locally well posed for any lower-order terms Q. For operators with triple characteristics, this conjecture was established [3] in the case when the principal symbol of P admits a factorization as a product of two symbols of principal type. A strongly hyperbolic operator in G could have triple characteristics in G   only for t=0$t=0$ or for t=T$t=T$. The operators that we investigate have a principal symbol which in general is not factorizable and we prove that these operators are strongly hyperbolic if T is small enough.     

IR-spectral investigation of the structure of glasses in the Fe2O3-V2O5 system

The structure of glasses in the Fe₂O₃-V₂O₅ system in the 0–50 mol% Fe₂O₃ range is studied by IR-spectroscopy. It is found that the introduction of Fe₂O₃ favours the transformation of the VO₅-groups into VO₄ ones. This effect may be shown with the aid of IR-spectra, owing to the fact that these glasses are characterized by two high-frequency bands at 1020 and 930 cm^–1. The first is determined by the vibrations of the short V=O nonbridging bonds in the VO₅-groups, while the second is assigned to the vibrations of the V—O-bonds in deformed VO₄-tetrahedra.

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IR-spektroskopische Strukturuntersuchung von Gläsern des Systems Fe₂O₃-V₂O₅

Zusammenfassung Die Struktur von Gläsern des Systems Fe₂O₃-V₂O₅ in dem Bereich von 0–50 Molprozent Fe₂O₃ wurde mit Hilfe der IR-Spektroskopie untersucht. Zusatz von Fe₂O₃ begünstigt die Umwandlung der VO₅- in VO₄-Gruppen. Das kann in den IR-Spektren durch zwei Banden bei 1020 und 930 cm^–1 festgestellt werden. Die erste wird durch Schwingungen der kurzen V=O-Nichtbrücken-bindungen in den VO₅-Gruppen verursacht, die zweite wird auf Schwingungen der V—O-Bindungen in dem deformierten VO₄-Tetraeder zurückgeführt.

     

High-power pulsed diode-pumped Er:ZBLAN fiber laser

We report on the operation and performance of a gain-switched Er:ZBLAN fiber laser based on an active pulsed diode pump system. The produced laser pulses offer high peak powers while retaining the high average powers and efficiency of the cw regime. The measured pulse duration was about 300 ns and nearly independent of the pump repetition frequency. The maximum obtained 68 W of peak power is the highest reported, to our knowledge, for diode-pumped Er:ZBLAN fiber lasers, and the 2 W of average power at the repetition frequency of 100 kHz is 2 orders of magnitude higher than previously reported average power in a pulsed regime. The obtained slope efficiency was 34%.     

Photophysical properties of novel fluorescent poly(oxyethylene phosphate) tris(β-diketonate) europium (III) complexes

In the present study, photophysical properties of fluorescent poly(oxyethylene phosphate) tris(β-diketonate) europium (III) complexes have been studied by means of stationary and time-resolved fluorescence spectroscopy (in ethanol at room temperature). The luminescent quantum yields and efficiency for the energy transfer from β-diketonate ligands to Eu(III) ion have been determined for the studied complexes by using diffusion-enhanced fluorescence resonance energy transfer. Obtained results show effect of the polymer ligands upon photophysical properties of the complexes and a relation has been established with length of the oxyethylene spacer between two phosphonate groups. The Förster radiuses of the synthesized compounds with SulfoRhodamine 101 as acceptor have been calculated. Measured distances between molecules of the donors and acceptor at identical acceptor/donor molar ratios have been illustrated the difference in structure of the ternary and polymer complexes in solution even at low concentration.     

Approach to thermal properties and electronic polarizability from average single bond strength in ZnOBi2O3B2O3 glasses

The glass transition temperature (T_g), density, refractive index, Raman scattering spectra, and X-ray photoelectron spectra (XPS) for xZnO-yBi₂O₃-zB₂O₃ glasses (x=10-65, y=10-50, z=25-60 mol%) are measured to clarify the bonding and structure features of the glasses with large amounts of ZnO. The average electronic polarizability of oxide ions (α_O2−) and optical basicity (Λ) of the glasses estimated using Lorentz-Lorenz equation increase with increasing ZnO or Bi₂O₃ content, giving the values of α_O2−=1.963 Å³ and Λ=0.819 for 60ZnO-10Bi₂O₃-30B₂O₃ glass. The formation of BOBi and BOZn bridging bonds in the glass structure is suggested from Raman and XPS spectra. The average single bond strength (B_MO) proposed by Dimitrov and Komatsu is applied to the glasses and is calculated using single bond strengths of 150.6 kJ/mol for ZnO bonds in ZnO₄ groups, 102.5 kJ/mol for BiO bonds in BiO₆ groups, 498 kJ/mol for BO bonds in BO₃ groups, and 373 kJ/mol for BO bonds in BO₄ groups. Good correlations are observed between T_g and B_MO, Λ and B_MO, and T_g and Λ, proposing that the average single bond strength is a good parameter for understanding thermal and optical properties of ZnOBi₂O₃B₂O₃ glasses.     

On the tautomerism of 1-phenyl-3-substituted-pyrazol-5-ones and their photoinduced products — experimental and theoretical UV spectral analysis

A detailed experimental and theoretical UV-spectral analysis of the tautomeric forms of 3-methyl-1-phenyl pyrazol-5-one and 1,3-diphenyl pyrazol-5-one as well as of the UV-irradiated photoinduced products of the latter compound were carried out. The experimental UV-spectra were compared with the theoretical ones obtained by CIS/6-31G**. Selected geometrical parameters of the different tautomers were estimated by ab initio calculations using the RHF/6-31G** level of theory and basis set, which have also been discussed with a view to the corresponding UV-results.     

Carbon Nanotube Fiber Ionization Mass Spectrometry: A Fundamental Study of a Multi-Walled Carbon Nanotube Functionalized Corona Discharge Pin for Polycyclic Aromatic Hydrocarbons Analysis

Mass spectrometry continues to tackle many complicated tasks, and ongoing research seeks to simplify its instrumentation as well as sampling. The desorption electrospray ionization (DESI) source was the first ambient ionization source to function without extensive gas requirements and chromatography. Electrospray techniques generally have low efficiency for ionization of nonpolar analytes and some researchers have resorted to methods such as direct analysis in real time (DART) or desorption atmospheric pressure chemical ionization (DAPCI) for their analysis. In this work, a carbon nanotube fiber ionization (nanoCFI) source was developed and was found to be capable of solid phase microextraction (SPME) of nonpolar analytes as well as ionization and sampling similar to that of direct probe atmospheric pressure chemical ionization (DP-APCI). Conductivity and adsorption were maintained by utilizing a corona pin functionalized with a multi-walled carbon nanotube (MWCNT) thread. Quantitative work with the nanoCFI source with a designed corona discharge pin insert demonstrated linearity up to 0.97 (R²) of three target PAHs with phenanthrene internal standard.

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Influence of the retardation of the multiplexing element in a dual channel Q-switched laser

We present an experimental and numerical analysis, how deviations of the multiplexer-retardation influence the output power of a time-multiplexed dual channel laser. The laser has two different channels, each one with its own gain medium. The channels are time-multiplexed by a single crystal photo-elastic modulator. It enables to double the repetition rate and output power of the laser. However, as multiplexing is based on polarization-switching, the retardation of the modulator should be kept within certain limits. By experimental measurement and theoretical analysis, we determine the operational window within which the retardation should be kept to avoid additional losses into the resonator. The analysis was done for two configurations of the laser setup, namely with and without a quarter-wave plate.