Pyrene fluorescence quenching by aromatic azides

Pyrene fluorescence quenching by phenylazide derivatives with donor and acceptor substituents has been studied by fluorescence spectroscopy and flash photolysis. The rate constants of quenching (k _q) in acetonitrile ((0.2–1.2) × 10¹⁰ l mol^?1 s^?1) are found to be close to a diffusion limit; the rate constants were somewhat higher for perfluoro-substituted arylazides. It is found that k _q does not depend on solvent polarity; the formation of the pyrene cation in the course of pyrene fluorescence quenching by tolylazide was not detected. Pyrene fluorescence quenching occurred by an energy-transfer mechanism; this is supported by the coincidence of the quantum yields of the direct and sensitized photodecomposition of tolylazide. As estimated, energy transfer in rigid media occurs at characteristic distances of about 10 Å.     

A bound of the exterior arcs for a univalent mapping

In this paper we consider the intersection of the circle ¦w|=x with the image of the disc ¦z|&#x2264;r, 0f(z)=z+c₂z²+... which is univalent analytic in ¦z|<1. Earlier I. E. Bazilevich proved that for xc^/er the measure of the above intersection does not exceed the measure of the intersection produced by the functionf ^*(z)=z/(1–z)², ¦=1. In this paper I. E. Bazilevich's ideas are used to strengthen some of his results.Translated from Matematicheskie Zametki, Vol. 18, No. 3, pp. 367–378, September, 1975.     

Investigation of the quantitative properties of the quadrupole orthogonal acceleration time-of-flight mass spectrometer with electrospray ionisation using 3,4-methylenedioxymethamphetamine

This paper describes the investigation of the potential of a quadrupole orthogonal acceleration time-of-flight mass spectrometer (Q-TOF) equipped with an atmospheric pressure ionisation interface for quantitative measurements of small molecules separated by reversed phase liquid chromatography. To this end, the detection limits and linear dynamic range in particular were studied in an LC/MS/MS experiment using 3,4-methylenedioxymethamphetamine standards and 3,4-methylenedioxyethylamphetamine for internal standardisation. In a second phase, the experiment was repeated with real biological extracts (whole blood, serum, and vitreous humour). A calibration for 3,4-methylenedioxymethamphetamine and its metabolite 3,4-methylenedioxyamphetamine was prepared in each of these matrices again using 3,4-methylenedioxyethylamphetamine as internal standard. The resulting quantitative data were compared with those obtained by liquid chromatography with fluorescence detection for the same extracts. The Q-TOF results revealed excellent sensitivity and a linear dynamic range of nearly four decades (2-10 000 pg on-column, r(2) = 0.9998, 1/x weighting). Furthermore, all the calibration curves prepared in biological material were superimposable, LC/MS/MS and LC-fluorescence, and the quantitative results for actual samples compared very favourably. It was concluded that the Q-TOF achieves a linear dynamic range for quantitative LC/MS/MS work exceeding that of fluorescence detection and at much better absolute sensitivity. Copyright 1999 John Wiley & Sons, Ltd.     

Calculation of the Defect Numbers of the Generalized Hilbert and Carleman Boundary Value Problems with Linear Fractional Carleman Shift

The defect numbers of the generalized Hilbert and Carleman boundary value problems with a direct or an inverse linear fractional Carleman shift of order 2 (α (α (t)) ≡ t) on the unit circle are computed. The approach followed consists of the reduction of the mentioned problems to singular integral equations with linear fractional Carleman shift and of the factorization of Hermitian matrix functions with negative determinant.     

Numerical-analytic investigation of the dynamics of viscoelastic and porous elastic bodies

This paper presents the results of mathematical and discrete modeling of linear dynamics problems for three-dimensional viscoelastic and porous elastic bodies. The employed methods and approaches are based on formulating boundary integral equations solved using boundary elements. The model of a standard viscoelastic body is employed as the viscoelastic model. The properties of porous elastic materials are described using the full Biot model with four basic functions. Examples of numerical solutions of the problems are compared with known results of solutions.     

Spectrum Problems for Singular Integral Operators with Carleman Shift

In this paper we are concerned with the complete spectral analysis for the operator 𝒯 = 𝒳𝒮𝒰 in the space L_p(𝕋) (𝕋 denoting the unit circle), where 𝒳 is the characteristic function of some arc of 𝕋, 𝒮 is the singular integral operator with Cauchy kernel and 𝒰 is a Carleman shift operator which satisfies the relations 𝒰² = I and 𝒮𝒰 = ±𝒰𝒮, where the sign + or — is taken in dependence on whether 𝒰 is a shift operator on L_p(𝕋) preserving or changing the orientation of 𝕋. This includes the identification of the Fredholm and essential parts of the spectrum of the operator 𝒯, the determination of the defect numbers of 𝒯 — λI, for λ in the Fredholm part of the spectrum, as well as a formula for the resolvent operator.     

Thermodynamic and kinetic stability of synthetic multifunctional rigid-rod beta-barrel pores: evidence for supramolecular catalysis

The lessons learned from p-octiphenyl beta-barrel pores are applied to the rational design of synthetic multifunctional pore 1 that is unstable but inert, two characteristics proposed to be ideal for practical applications. Nonlinear dependence on monomer concentration provided direct evidence that pore 1 is tetrameric (n = 4.0), unstable, and "invisible," i.e., incompatible with structural studies by conventional methods. The long lifetime of high-conductance single pores in planar bilayers demonstrated that rigid-rod beta-barrel 1 is inert and large (d approximately 12 A). Multifunctionality of rigid-rod beta-barrel 1 was confirmed by adaptable blockage of pore host 1 with representative guests in planar (8-hydroxy-1,3,6-pyrenetrisulfonate, KD = 190 microM, n = 4.9) and spherical bilayers (poly-L-glutamate, KD < or = 105 nM, n = 1.0; adenosine triphosphate, KD = 240 microM, n = 2.0) and saturation kinetics for the esterolysis of a representative substrate (8-acetoxy-1,3,6-pyrenetrisulfonate, KM = 0.6 microM). The thermodynamic instability of rigid-rod beta-barrel 1 provided unprecedented access to experimental evidence for supramolecular catalysis (n = 3.7). Comparison of the obtained kcat = 0.03 min(-1) with the kcat approximately 0.18 min(-1) for stable analogues gave a global KD approximately 39 microM3 for supramolecular catalyst 1 with a monomer/barrel ratio approximately 20 under experimental conditions. The demonstrated "invisibility" of supramolecular multifunctionality identified molecular modeling as an attractive method to secure otherwise elusive insights into structure. The first molecular mechanics modeling (MacroModel, MMFF94) of multifunctional rigid-rod beta-barrel pore hosts 1 with internal 1,3,6-pyrenetrisulfonate guests is reported.