Analytical formula for a decentered elliptical Gaussian beam propagating in a turbulent atmosphere

Analytical formulas for the average intensity and decentered parameter of a decentered elliptical Gaussian beam (DEGB) propagating in a turbulent atmosphere are derived in a tensor form. The propagation properties of a DEGB in a turbulent atmosphere are investigated in detail, and found to be different from that in free space. Furthermore, as an application example, we investigate the propagation of a decentered elliptical flat-topped beam (DEFB) by expressing its electric field as a finite sum of DEGBs in a turbulent atmosphere. The properties of a DEGB or a DEFB in a turbulent atmosphere are closely related with the beam’s parameters and the structure constant of the turbulent atmosphere.     

测地距离的基本解方法求解各向异性热传导方程

基本解方法属于径向基函数类方法,它使用微分算子的基本解作为基于欧氏距离的径向基函数．借助测地距离,给出了求解各向异性材料中的热传导方程的基本解方法．该方法无需对时间进行离散或Laplace变换,也无需进行变量变换,而是直接在整个时间空间区域上进行求解．文中给出了数值例子,来验证基于测地距离的基本解方法在求解该各向异性问题时的稳定性和有效性．     

Lag synchronization for fuzzy chaotic system based on fuzzy observer

A new fuzzy observer for lag synchronization is given in this paper. By investi- gating synchronization of chaotic systems, the structure of drive-response lag synchronization for fuzzy chaos system based on fuzzy observer is proposed. A new lag synchronization criterion is derived using the Lyapunov stability theorem, in which control gains are obtained under the LMI condition. The proposed approach is applied to the well-known Chen＇s systems. A simulation example is presented to illustrate its effectiveness.     

CuI-catalyzed direct synthesis of diaryl thioethers from aryl boronic acids and arylsulfonyl chlorides

A CuI-catalyzed direct coupling of aryl boronic acids with arylsulfonyl chlorides for the preparation of diaryl thioethers was developed. The reaction is initiated by a PPh₃ reduction of the arylsulfonyl chloride, followed by a CuI-catalyzed C–S coupling with an aryl boronic acid. Various arylsulfonyl chlorides can directly serve as a sulfur source in this mild and efficient reaction giving the desired products in moderate to good yields. Moreover, this practical method has also been applied to the thioetherification of aryl iodides and acetylacetones.     

Pseudo almost periodic solutions for a Lasota–Wazewska model with an oscillating death rate

This paper is concerned with a Lasota–Wazewska model with an oscillating death rate. Under proper conditions, we employ a novel argument to establish a criterion on the existence and stability of positive pseudo almost periodic solutions. The obtained result complements with some existing ones.     

Using polyethyleneimine (PEI) as a scaffold to construct mimicking systems of [FeFe]‐hydrogenase: preparation,characterization of PEI‐based materials,and their catalysis on proton reduction

Ten branched polymeric materials (PEI‐P‐Fe₂s) derived from polyethyleneimine (PEI) functionalized with [Fe₂(CO)₅]‐units to mimic [FeFe]‐hydrogenase were prepared. Before the functionalization, PEI was first premodified using diphenylphosphinamine (NPPh₂) group. In the premodification, three approaches were employed: (i) using PEI with an average molecular weight of 1800 and 600, respectively; (ii) grafting NPPh₂ group by either direct reaction of chlorodiphenylphosphine with PEI or Br(CH₂)₁₁OPPh₂; and (iii) further premodification with BrCH₂COOH after immobilization of the NPPh₂ group. Reaction of the premodified PEI with diiron hexacarbonyl complexes, [Fe₂(μ‐S)₂(CO)₆] (1), or [Fe₂(μ‐S₂C₂H₄)(CO)₆] (3) produced 10 functionalized materials, PEI‐P‐Fe₂s. These materials were characterized using a variety of spectroscopic techniques, FTIR, NMR, TGA, and cyclic voltammetry. Spectral comparison with two control complexes, [Fe₂(μ‐S)₂(CO)₅PPh₃] (2) and [Fe₂(μ‐S₂C₂H₄)(CO)₅PPh₃] (4), suggested that the immobilized diiron units of PEI‐P‐Fe₂s were dominantly pentacarbonyl analogous to complexes 2 and 4, although tetracarbonyl units may also exist because the amine groups of PEI could also be involved in substituting CO, as was the NPPh₂ group. The catalysis of these materials on proton reduction was examined in 0.1 mol l^?1 [NBut₄]BF₄/DMF containing acetic acid by using cyclic voltammetry. Our results indicated that both the presence of carboxylic acid and dangling the diiron units at the end of a long aliphatic chain improved catalytic efficiency by one‐fold. The improvement was attributed to the increase in flexibility of the catalytic center and enhancement of proton transfer during the catalysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Boundedness of Iterated Spherical Average on α-Modulation Spaces*

For the iteration of spherical average (A₁)^N and the Laplace operator ?, we consider the boundedness of the operator ?(A₁)^N on the α-modulation spaces M_p,q ^s,α. The authors obtain some sufficient and necessary conditions to ensure the boundedness on the α-modulation spaces. The main theorems significantly improve some known results.     

The synthesis of Cu/plate-like ZnO nanostructures and their self-assembly mechanism

A composite Cu/ZnO nanostructure with Cu nanoparticles supported on ZnO hexagonal nanoplates has been successfully fabricated by a heating approach, using their metal oleate salts as the precursors without any additives. Combined Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), transmission electron microscopy (TEM) and other examination technologies, the structural properties and formation mechanism of as-synthesized Cu/ZnO nanocomposites are studied in detail. The results reveal that the nanostructures are plate-like with uniform shape and size, and Cu nanoparticles exhibit specific (111) plane matching with the (002) facet of ZnO, indicating a surface-induced interaction mechanism. Further characterization demonstrates that copper nanoparticles can be generated by a decomposition/self-reduction route of copper salts, and the oleate ions act as dual roles in the process: reducing and protecting agents. The difference of decomposition temperature between metal oleates also plays important roles in the formation of Cu/ZnO nanostructure. In addition, the catalytic performance of these nanocomposites is evaluated and it can be found that compared with Cu/rod-like ZnO, as-synthesized samples are highly selective for methanol.     

Permanence for Nicholson-type delay systems with nonlinear density-dependent mortality terms

In this paper, we study the generalized Nicholson-type delay systems with nonlinear density-dependent mortality terms. Under proper conditions, we establish some criteria to guarantee the permanence of this model. Moreover, we give two examples to illustrate our main results.     

Modeling of optical spectroscopy for the crystalline silicon

The paper is aimed at modeling optical spectra of silicon. Optical spectra of silicon are described with the Logistic function. A satisfactory agreement between the measured and the modeled optical spectra are obtained. The minimum magnitude of the correlation coefficient between experiment and theoretical results is 0.994, and the maximum average relative error is 4.21%. Meanwhile, it is found that the band gap of semiconductor may be determined by fitting absorption coefficient as a function of wavelength. Lastly, the mathematical relationships between the parameters, which are used to link the reflectance of silicon and wavelength, and radiation fluency, are obtained. Consequently, the change of reflectance for silicon can be predicted by both wavelength and dose radiation fluency only one function. All results in this paper are of interest from both optics and materials point of view.