Complete Asymptotic Expansions of Solutions of the System of Elastostatics in the Presence of an Inclusion of Small Diameter and Detection of an Inclusion

We consider the system of elastostatics for an elastic medium consisting of an imperfection of small diameter, embedded in a homogeneous reference medium. The Lamé constants of the imperfection are different from those of the background medium. We establish a complete asymptotic formula for the displacement vector in terms of the reference Lamé constants, the location of the imperfection and its geometry. Our derivation is rigorous, and based on layer potential techniques. The asymptotic expansions in this paper are valid for an elastic imperfection with Lipschitz boundaries. In the course of derivation of the asymptotic formula, we introduce the concept of (generalized) elastic moment tensors (Pólya–Szegö tensor) and prove that the first order elastic moment tensor is symmetric and positive (negative)-definite. We also obtain estimation of its eigenvalue. We then apply these asymptotic formulas for the purpose of identifying with high precision the order of magnitude of the diameter of the elastic inclusion, its location, and its elastic moment tensors.     

Green synthesis of gold nanoparticles using glycerol-incorporated nanosized liposomes

There has been enormous interest in the last decade in development methods for the inorganic synthesis of metallic nanoparticles of desired sizes and shapes because of their unique properties and extensive applications in catalysis, electronics, plasmonics, and sensing. Here we report on an environmentally friendly, one-pot synthesis of metallic nanoparticles, which avoids the use of organic solvents and requires mild experimental conditions. The developed method uses liposomes as nanoreactors, where the liposomes were prepared by encapsulating chloroauric acid and exploited the use of glycerol, incorporated within the lipid bilayer as well as in its hydrophilic core, as a reducing agent for the controlled preparation of highly homogeneous populations of gold nanoparticles. The effects of temperature, the presence of a capping agent, and the concentration of glycerol on the size and homogeneity of the nanoparticles formed were investigated and compared with solution-based glycerol-mediated nanoparticle synthesis. Well-distributed gold nanoparticle populations in the range of 2-8 nm were prepared in the designed liposomal nanoreactor with a clear dependence of the size on the concentration of glycerol, the temperature, and the presence of a capping agent whereas large, heterogeneous populations of nanoparticles with amorphous shapes were obtained in the absence of liposomes. The particle morphology and sizes were analyzed using transmission electron microscopy imaging, and the liposome size was measured using photon correlation spectroscopy.     

A novel ion‐imprinted hydrogel for recognition of potassium ions with rapid response

A novel ion‐imprinted strategy is developed for synthesizing responsive hydrogels with rapid response to potassium ions. With potassium ions as templates, ion‐imprinted poly(N‐isopropylacrylamide‐co‐benzo‐15‐crown‐5‐acrylamide) (P(NIPAM‐co‐B15C5Am)) hydrogels are synthesized with 15‐crown‐5 crown ethers mounted on the polymer networks in pairs; therefore, it is very easy and fast for the crown ethers to capture potassium ions again by their Venus flytrap action and form stable 2:1 “host–guest” complexes with potassium ions in the ion‐recognition process. As a result, the response rate of the ion‐imprinted hydrogels to potassium ions is significantly faster than that of normal P(NIPAM‐co‐B15C5Am) hydrogels in which 15‐crown‐5 crown ethers are randomly pendent on the polymeric networks. Copyright © 2010 John Wiley & Sons, Ltd.     

Trigonometric Widths and Best N-Term Approximations of the Generalized Periodic Besov Classes BΩp,θ

In this paper,we determine the estimates exact in order for the trigonometric widths and the best n-term trigonometric approximations of the generalized classes of periodic functions BΩp,θ in the space Lq for some values of parameters p,q.     

A transformation of certain infinite series based on the non-local derangement identity

The aim of the paper is a new transformation of certain infinite series based on an identity from Sylvester also known as the non-local derangement identity. Surprisingly, the result found can be applied to evaluate certain types of the generalized hypergeometric function _p F _q (z) or infinite series involving the combination of hyperbolic functions, irrational functions and polynomials like

Special functions associated with a certain fourth-order differential equation

We develop a theory of “special functions” associated with a certain fourth-order differential operator D_m,n\mathcal{D}_{\mu,\nu} on ℝ depending on two parameters μ,ν. For integers μ,ν≥−1 with μ+ν∈2ℕ₀, this operator extends to a self-adjoint operator on L ²(ℝ₊,x ^μ+ν+1 dx) with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, L ²-norms, integral representations, and various recurrence relations.     

Synthesis and NHE1 inhibitory activity of ligustrazine derivatives

A series of novel derivatives of ligustrazine linked with substituted benzoyl guanidine were synthesized. These compounds have not been reported in literature, and their chemical structures were confirmed by IR, 1H NMR and MS. The results of NHE1 inhibitory activity test showed that compounds I2, I3, I4, I6, and I7 possess more potent NHE1 inhibitory activity than cariporide.     

Mechanism of crystallization of enzyme protein thermolysin

The mechanism of crystallization of enzyme protein thermolysin was investigated. The size distribution of thermolysin precipitates was measured by dynamic light scattering during precipitation, and the surface and cross section of the finally obtained precipitate were observed by scanning electron microscopy. The thermolysin precipitates obtained at the initial supersaturation ratio of 8.9 to 164 and pH 7.0 were hexagonal rods having an average size of 9.2×1.5 μm, and were composed of a number of small particles of 15 to 200 nm in diameter. The average size of the small particles was 60 nm in diameter, and the formation of the particles was found to be completed in the early stage of precipitation. Observation of the finally recovered thermolysin precipitate by polarizing microscopy revealed that the precipitate is a crystalline solid. From these data, a possible mechanism of thermolysin crystallization was proposed. The crystallization proceeds through two steps: the first step is the formation of primary particles, and the second step is crystal growth by highly ordered aggregation of the primary particles.     

22Na(p,γ)23Mg反应的实验研究

讨论了目前有关²²Na(p,γ)²³Mg反应的实验研究工作,结合兰州放射性束流线上的放射性束流²³Al的β⁺延发质子衰变实验的测量结果,给出了²³Al延发衰变的质子能谱,并比较了近期实验给出的相关能级的自旋、宇称值,正是由于这种自旋、宇称和能级部分宽度的不确定性,导致了反应率计算的不确定性.计算了同位旋相似态的共振强度.对于测量到的新的延发衰变能级E_d=8.916MeV,由于没有相应的能级宽度值,实验仅给出其相对共振强度值.