The limiting absorption principle for the two-dimensional inhomogeneous anisotropic elasticity system

In this work we establish the limiting absorption principle for the two-dimensional steady-state elasticity system in an inhomogeneous aniso- tropic medium. We then use the limiting absorption principle to prove the existence of a radiation solution to the exterior Dirichlet or Neumann boundary value problems for such a system. In order to define the radiation solution, we need to impose certain appropriate radiation conditions at infinity. It should be remarked that even though in this paper we assume that the medium is homogeneous outside of a large domain, it still preserves anisotropy. Thus the classical Kupradze's radiation conditions for the isotropic system are not suitable in our problem and new radiation conditions are required. The uniqueness of the radiation solution plays a key role in establishing the limiting absorption principle. To prove the uniqueness of the radiation solution, we make use of the unique continuation property, which was recently obtained by the authors. The study of this work is motivated by related inverse problems in the anisotropic elasticity system. The existence and uniqueness of the radiation solution are fundamental questions in the investigation of inverse problems.

     

A light scattering and fluorescence emission coupled ratiometry using the interaction of functional CdS quantum dots with aminoglycoside antibiotics as a model system

Any signals, if their intensities have simple functional relationship with analyte concentration, can be applied to analytical purposes. Rayleigh light scattering signals and fluorescence signals are twins in flurospectroscopy, so the light scattering signals are the major interference when the Stokes shift is small. Herein, we propose a light scattering and fluorescence emission (LS-FL) coupled ratiometry using CdS quantum dots (QDs) as a fluorescence probe to detect aminoglycoside antibiotics (AGs). As model analytes, AGs, when attached to the surface of CdS-QDs via electrostatic interaction in aqueous medium, result in strong enhanced light scattering (LS) emission characterized at 376 nm and fluorescence quenching of CdS-QDs at 500 nm. Thus, a ratiometry using the coexistent light scattering and fluorescent emission signals has been proposed. Based on the linear relationship between logarithm of light scattering and fluorescence emission ratio (R) and logarithm of AGs concentration, a novel assay of AGs is established with the limits of detection (3σ) being 58-190 nmol l⁻¹, and applied successfully to detect AGs injection and serum samples.     

Synthesis,characterization and in vitro cytotoxicity screening of some triarylbismuth(V) di(N‐salicylidene)amino carboxylates and the crystal structure of (2‐HOC6H4CHNCH2CO2)2Bi(C6H5)3

Four novel triarylbismuth(V) di(N‐salicylidene)amino carboxylates were synthesized. Their structures were confirmed by IR, ¹H NMR, ¹³C NMR and elemental analysis. The crystal structure of (2‐HOC₆H₄CH?NCH₂CO₂)₂BiPh₃ was determined by X‐ray diffraction. The in vitro cytotoxicity of all compounds against three human cancer cells (HL‐60, BGC‐823 and MDA‐MB‐435) at 10 µM are reported. Copyright © 2005 John Wiley & Sons, Ltd.     

Crystallographic report: A two‐dimensional homochiral coordination polymer: [cadmium(II) bis(S‐(−)‐lactate)]n

In the two‐dimensional (2D) homochiral structure of [cadmium(II) bis(S‐(?)‐lactate)]_n, the lactate ligand adopts a µ₃‐bridging mode to connect two cadmium atoms, leading to the formation of a 2D network. Copyright © 2004 John Wiley & Sons, Ltd.     

Theoretical analysis of atom formation-time curves for HGA-74

A simplified mathematical analysis of atom formation was developed. For this purpose, the atomization process was considered as first order kinetics. Experimental studies were carried out. From the initial portion of experimental curves the Arrhenius-type rate constants, activation energies and frequency factors for atom formation reactions were calculated. The values obtained for activation energy could be attributed to the heat of vaporization of the test element nickel. The rate constants proportionality factors relating absorbance to the amount of metal vapour in the graphite furnace were found to be considerably dependent upon the temperature.     

The Relation of the Morse Index of Closed Geodesics with the Maslov-type Index of Symplectic Paths

In this paper, we consider the relation of the Morse index of a closed geodesic with the Maslov–type index of a path in a symplectic group. More precisely, for a closed geodesic c on a Riemannian manifold M with its linear Poincaré map P (a symplectic matrix), we construct a symplectic path γ(t) starting from identity I and ending at P, such that the Morse index of the closed geodesic c equals the Maslov–type index of γ. As an application of this result, we study the parity of the Morse index of any closed geodesic. Project 10071040 supported by NNSF, 200014 supported by Excellent. Ph.D. Funds of ME of China, and PMC Key Lab. of ME of China     

Integral Formulas for the Minimal Representation of O(p,2)

The minimal representation of O(p,q) (p+q: even) is realized on the Hilbert space of square integrable functions on the conical subvariety of R^p+q–2. This model presents a close resemblance of the Schrödinger model of the Segal–Shale–Weil representation of the metaplectic group. We shall give explicit integral formulas for the inversion together with the analytic continuation to a certain semigroup of O(p+2,C) of the minimal representation of O(p,2) by using Bessel functions.Mathematics Subject Classifications (2000) primary 22E30; secondary 22E46, 20M20, 43A80.     

Evidence of coupled rotational tunnel states of methyl groups of hexamethylbenzene by nuclear magnetic resonance

Two tunneling frequencies were identified for methyl groups in hexamethylbenzene from 4.2 up to 30.9 K by means of the N.M.R. field cycling method. The frequencies were 9.6 ±- 0.4 MHz (A) and 7.9 ±- 0.4 MHz (B) at 4.2 K. The frequency A was almost independent of the temperature whereas the frequency B decreased as the temperature increased, the decrease being a linear function of T³. These facts indicate that the six methyl groups in hexamethylbenzene molecule are not independent but are coupled to one another rather strongly.     

Ethyl 4-diphenylphosphinoyl-2-oxobutanoate: A convenient reagent for the synthesis of γ,δ-unsaturated β-ketoesters

Aldehydes and ketones can be converted into γ,δ-unsaturated-β-ketoesters by reaction with the dianion from phosphine oxide $\text{1}$.