Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

Synthesis and fluorescent properties of some new unsymmetricbis-benzothiazolyl furans and thiophenes

Summary Some newmono- andbis-benzothiazolyl compounds with furan or thiophene nuclei were synthesized by multistep reactions from the corresponding furan and thiophene aldehydes. The data obtained from emission spectra show a large influence of the benzothiazole rings on the relative quantum efficiency of the compounds under investigation.

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Synthese und Fluoreszenzeigenschaften von neuen unsymmetrischenbis-Benzothiazolylfuranen und thiophenen

Zusammenfassung Einige neuebis-Benzothiazolylverbindungen mit einem Furan- bzw. Thiophenenring wurden in einer mehrstufigen Reaktion dargestellt. Die Fluoreszenzdaten der untersuchten Verbindungen zeigen einen großen Einfluß der Benzothiazolringe auf die relative Fluoreszenzquantenausbeute.

     

Photochemistry of condensed isoxazolines

Summary The condensed bridged isoxazolines4 are rearranged on irradiation with a low-pressure mercury lamp exclusively into condensed derivatives of tetrahydropyridine5. The selectivity of the rearrangement is due to a stabilization of the biradical8 by the overlap of the radical-electrons with -electrons of the C=C double bond and the heterocyclic ring. Quantum yields of the photorearrangement, established from the consumption of the starting materials4, were determined.

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Photochemie kondensierter Isoxazoline

Zusammenfassung Die kondensierten überbrückten Isoxazoline4 werden durch Bestrahlen mit einer Niederdruckquecksilberlampe ausschließlich zu kondensierten Tetrahydropyridinderivaten (5) umgelagert. Die Selektivität der Umlagerung beruht auf der Stabilisierung des Diradikals8 durch Überlappung der ungepaarten Elektronen mit -Elektronen der C=C-Doppelbindung und des Heterocyclus. Aus dem Verbrauch an Ausgangsmaterial (4) wurden Quantenausbeuten der Photoumlagerung bestimmt.

     

Preparation and stereoselectivity of 1,3-dipolar cycloaddition ofD-glucose-derived nitrones to N-arylmaleimides

Summary Nitrones2 derived fromD-glucose oxime and benzaldehydes without employing any protection of hydroxyl group were isolated in pure state. The 1,3-dipolar cycloaddition of2 to N-arylmaleimides gave predominantly theanti isoxazolidines3 and was rationalized byZ/E isomerization of N-glycosylnitrones2. The structure and steric configuration of the products have been assigned on the basis of¹H- and¹³C-NMR spectroscopy. AM1 calculations of the nitrones and MM2 calculations of the adducts were performed.

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Darstellung und Stereoselektivität der 1,3-dipolaren Cycloaddition vonD-Glucose-abgeleiteten Nitronen an N-Arylmaleimiden

Zusammenfassung Die Nitrone2 wurden ausD-Glucoseoxim und Benzaldehyden ohne Schutz von Hydroxylgruppen in reinem Zustand erhalten. Die 1,3-dipolare Cycloaddition von2 an N-Arylmaleimiden ergab bevorzugt dieanti-Isoxazolidine3; dies wurde über eineZ/E-Isomerisierung der N-Glycosylnitrone2 rationalisiert. Struktur und Stereochemie wurden auf Basis von¹H- und¹³C-NMR-Spektroskopie ermittelt. Außerdem wurden AM1-Berechnungen an den Nitronen und MM2-Rechnungen an den Addukten ausgeführt.

     

Bianchi type V perfect fluid cosmologies

Bianchi type V solutions of the Einstein equations are studied using the Hamiltonian approach. Explicit expressions depending on a single quadrature are given for the metric components in the general orthogonal perfect fluid case. It is shown that the quadrature can be evaluated in terms of elementary or elliptic integrals when the parameter in the equation of statep=(–1) takes the values 1, 10/9, 4/3, 14/9, 5/3, 2.     

Nuclear structure and chemical effects in internal conversion of the 35 keVM1+E2 transition in125Te

The relative conversion line intensities of the 35 keV transition in¹²⁵Te were measured using the 50 cm π√2 iron-yoke magnetic spectrometer. The transition was proved to be ofM1+(8.7±1.5)×10^?4 E2 multipolarity, the magnetic component being affected by the nuclear structure with λ=2.4±1.4. The conversion intensity ratio,0/N ₁ , was determined to be 0.115+0.005 for both Ag¹²⁵ I and Cu¹²⁵ I sources. It is in accordance with previous measurements for the Zn^125m Te and Pb^125m Te sources and differs from those for the^125mTeO₂ and Na₂H ₄ ^125m TeO₆ ones. The conversion coefficients were calculated for 32 configurations of the valence shell of free tellurium atom and ions and were compared with the experimental results.     

Mean fluorescence lifetime and its error

Mean excited-state lifetime is one of the fundamental fluorescence characteristics and enters as an important parameter into numerous calculations characterizing molecular interactions, such as e.g. FRET or fluorescence quenching. Our experiments demonstrated that the intensity-weighted mean fluorescence lifetime is very robust characteristic, in contrast to the amplitude-weighted one, which value is dependent on the data quality and particularly on the used fitting model. For the first time, we also report the procedure for the error estimation for both the intensity- and amplitude-weighted mean fluorescence lifetimes. Furthermore, we present a method for estimation of the mean fluorescence lifetime directly from the fluorescence-decay curve recorded by TCSPC (Time-Correlated Single-Photon Counting) method. For its simplicity and low computational demands, it could be a useful tool in the high-throughput applications, such as FACS, FLIM-FRET or HPLC detectors.     

A mass conservative well‐balanced reconstruction at wet/dry interfaces for the Godunov‐type shallow water model

This paper presents a novel mass conservative, positivity preserving wetting and drying treatment for Godunov‐type shallow water models with second‐order bed elevation discretization. The novel method allows to compute water depths equal to machine accuracy without any restrictions on the time step or any threshold that defines whether the finite volume cell is considered to be wet or dry. The resulting scheme is second‐order accurate in space and keeps the C‐property condition at fully flooded area and also at the wet/dry interface. For the time integration, a second‐order accurate Runge–Kutta method is used. The method is tested in two well‐known computational benchmarks for which an analytical solution can be derived, a C‐property benchmark and in an additional example where the experimental results are reproduced. Overall, the presented scheme shows very good agreement with the reference solutions. The method can also be used in the discontinuous Galerkin method. Copyright © 2016 John Wiley & Sons, Ltd.