On higher order Bessel potentials

The solutions of the equation in , where are investigated, Bessel potentials of higher order are defined, and recurrence relations between these solutions and these Bessel potentials are obtained. It is also proved that these solutions and the solutions of , under certain conditions, are identical. Received: 6 November 2002     

Transmission problems and spectral theory for singular integral operators on Lipschitz domains

We prove the well-posedness of the transmission problem for the Laplacian across a Lipschitz interface, with optimal non-tangential maximal function estimates, for data in Lebesgue and Hardy spaces on the boundary. As a corollary, we show that the spectral radius of the (adjoint) harmonic double layer potential K∗ in is less than , whenever is a bounded convex domain and 1<p?2.     

Capillary Coated with Layer-by-Layer Assembly of γ-Zirconium Phosphate/ Lysozyme Nanocomposite Film for Open Tubular Capillary Electrochromatography Chiral Separation

A new capillary coating of alternate 31n/xxlarge947.gif" alt="gamma" align="MIDDLE" BORDER="0">-zirconium phosphate lysozyme fabricated for open-tubular electrochromatography enantioseparation. The chiral compounds D, L-tryptophan tested were enantiomerically resolved. The influences brought by experimental parameters, such as organic modifier, temperature, applied voltage and pH of running buffer on the performance of the column, were investigated.     

Are the Elements Elementary? Nineteenth-Century Chemical and Spectroscopical Answers

We analyze the role and influence of a tradition of research linked to the concept of 31dee30v5t/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0">primary matter31dee30v5t/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> in nineteenth-century studies on the nature of the elements.The suggestion of William Prout (1785-1850) in 1816 that the atomic weights of pure chemical elements are whole numbers and multiples of the atomic weight of hydrogen, taken as unity, was met with serious confutations,which in turn prompted several attempts to save Prout31dee30v5t/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s hypothesis.We discuss these attempts in detail and the objections raised against them, for instance by Dmitry Ivanovich Mendeleev (1834-1907). We pay particular attention to the use of spectroscopy as a method for proving the existence of elementary forms of matter inside atoms. Leaders in this field of research were two English scientists, the astrophysicist Norman Lockyer (1836-1920) and the chemist William Crookes (1832- 1919). Both of their approaches involved the idea of primary matter. However, while Crookes31dee30v5t/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s approach proved to be incorrect, Lockyer31dee30v5t/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s ideas survived for several years and supported the discovery of the electron by J.J.Thomson (1856-1940).     

The distribution of patterns of inverses modulo a prime

We investigate the distribution of the numbers x∈[1,p] for which 314X03000593-si1.gif"> all lie in a subset 314X03000593-si2.gif"> of the set of multiplicative inverses modulo a prime p. Here the a_i are integers coprime to p and the numbers 314X03000593-si3.gif"> are distinct 314X03000593-si4.gif">.     

Dirichlet and Neumann boundary conditions: What is in between?

Given an admissible measure μ on where is an open set, we define a realization of the Laplacian in with general Robin boundary conditions and we show that generates a holomorphic C ₀ -semigroup on which is sandwiched by the Dirichlet Laplacian and the Neumann Laplacian semigroups. Moreover, under a locality and a regularity assumption, the generator of each sandwiched semigroup is of the form . We also show that if contains smooth functions, then μ is of the form (where σ is the (n-1)-dimensional Hausdorff measure and β a positive measurable bounded function on ); i.e. we have the classical Robin boundary conditions. RID="h1" ID="h1"Dédié à Philippe Bénilan RID="*" ID="h1"This work is part of the DGF-Project: "Regularit?t und Asymptotik für elliptische und parabolische Probleme".     

Dirichlet operators and the positive maximum principle

Let (A, D(A)) denote the infinitesimal generator of some strongly continuous sub-Markovian contraction semigroup onL ^p (m), p1 andm not necessarily -finite. We show under mild regularity conditions thatA is a Dirichlet operator in all spacesL ^q (m), qp. It turns out that, in the limitq,A satisfies the positive maximum principle. If the test functionsC _c D(A), then the positive maximum principle implies thatA is a pseudo-differential operator associated with a negative definite symbol, i.e., a Lévy-type operator. Conversely, we provide sufficient criteria for an operator (A, D(A)) onL ^p(m) satisfying the positive maximum principle to be a Dirichlet operator. If, in particular,A onL ² (m) is a symmetric integro-differential operator associated with a negative definite symbol, thenA extends to a generator of a regular (symmetric) Dirichlet form onL ² (m) with explicitly given Beurling-Deny formula.     

Structural characterization of silver dialkylphosphite salts using solid‐state 109Ag and 31P NMR spectroscopy,IR spectroscopy and DFT calculations

High‐resolution solid‐state ¹⁰⁹Ag and ³¹P NMR spectroscopy was used to investigate a series of silver dialkylphosphite salts, Ag(O)P(OR)₂ (R = CH₃, C₂H₅, C₄H₉ and C₈H₁₇), and determine whether they adopt keto, enol or dimer structures in the solid state. The silver chemical shift, CS, tensors and |J(¹⁰⁹Ag, ³¹P)| values for these salts were determined using ¹⁰⁹Ag (Ξ = 4.652%) NMR spectroscopy. The magnitudes of J(¹⁰⁹Ag, ³¹P) range from 1250 ± 10 to 1318 ± 10 Hz and are the largest reported so far. These values indicate that phosphorus is directly bonded to silver for all these salts and thus exclude the enol structure. All ³¹P NMR spectra exhibit splittings due to indirect spin–spin coupling to ¹⁰⁷Ag (I = 1/2, NA = 51.8%) and ¹⁰⁹Ag (I = 1/2, NA = 48.2%). The ¹J(¹⁰⁹Ag, ³¹P) values measured by both ¹⁰⁹Ag and ³¹P NMR spectroscopy agree within experimental error. Analysis of ³¹P NMR spectra of stationary samples for these salts allowed the determination of the phosphorus CS tensors. The absence of characteristic P?O stretching absorption bands near 1250 cm^?1 in the IR spectra for these salts exclude the simple keto tautomer. Thus, the combination of solid‐state NMR and IR results indicate that these silver dialkylphosphite salts probably have a dimer structure. Values of silver and phosphorus CS tensors as well as ¹J(¹⁰⁹Ag, ³¹P) values for a dimer model calculated using the density functional theory (DFT) method are in agreement with the experimental observations. Copyright © 2010 John Wiley & Sons, Ltd.     

大鼠肝细胞膜胰岛素受体与胰岛素的相互作用

采用125I-胰岛素标记法研究大鼠肝细胞膜中胰岛素受体与胰岛素的结合性质,用31P-核磁共振法(31P-NMR)研究大鼠肝细胞膜中胰岛素刺激下的胰岛素受体体外自磷酸化,实验结果表明大鼠肝细胞膜胰岛素受体与胰岛素结合的最佳酸度大约为pH=7.5,并且表明大鼠肝细胞膜上的胰岛素受体为高亲和、低容量和低亲和、高容量两型受体.非放射性的31P-NMR波谱法检测到胰岛素刺激下的大鼠肝细胞膜胰岛素受体的体外自磷酸说明所提取纯化的胰岛素受体具有生物活性.