THE FRACTIONAL QUADRATIC-FORM IDENTITY AND BI-HAMILTONIAN STRUCTURES OF AN INTEGRABLE COUPLING OF THE FRACTIONAL COUPLED BURGERS HIERARCHY

Based on a general isospectral problem of fractional order and the fractional quadratic-form identity by Yue and Xia, the new integrable coupling of fractional coupled Burgers hierarchy and its fractional bi-Hamiltonian structures are obtained.     

向量优化中改进集的一些拓扑性质

主要研究改进集的一些拓扑运算性质。首先在改进集条件下给出了拓扑向量空间中两个非空集之和的拓扑内部的一些运算性质。进一步,利用改进集获得了 Flores-Baz′an 和 Hern′andez 提出的假定 B 的一个加强形式。此外,给出了一些例子对主要结果进行了解释。     

A projection subgradient method for solving optimization with variational inequality constraints

In this paper, we propose a projection subgradient method for solving some classical variational inequality problem over the set of solutions of mixed variational inequalities. Under the conditions that $T$ is a $\Theta $ -pseudomonotone mapping and $A$ is a $\rho $ -strongly pseudomonotone mapping, we prove the convergence of the algorithm constructed by projection subgradient method. Our algorithm can be applied for instance to some mathematical programs with complementarity constraints.     

Crystal growth and spectroscopic properties of Yb:CaYAlO4 single crystal

A Yb³⁺-doped CaYAlO₄ laser crystal has been grown by the Czochralski technique. The segregation coefficient was measured by Inductively Coupled Plasma Atomic Emission Spectrometry (ICP-AES). The cell parameters were analyzed with X-ray diffraction experiments. Color defects in Yb:CaYAlO₄ have been evidenced to be similar to those in undoped CaYAlO₄. The polarized absorption spectra and the fluorescence spectrum of the Yb:CaYAlO₄ crystal were measured at room temperature. The fluorescence decay time of the Yb³⁺ ion was investigated. The results show that Yb:CaYAlO₄ has potential as a laser gain medium for an ultrashort laser system.     

Polypropylene/poly(butyl methacrylate) blends prepared by diffusion and subsequent polymerization of butyl methacrylate in isotactic polypropylene pellets

Polypropylene/poly(butyl methacrylate)(PP/PBMA) blends were prepared by diffusion and subsequent polymerization of butyl methacrylate(BMA) in commercial isotactic polypropylene(iPP) pellets.The diffusion kinetics,diametrical distribution of PBMA in a pellet and phase morphology of a typical PP/PBMA blend were investigated.     

Three-dimensional simulations of air–water bubbly flows

Interfacial area transport equation (IATE) is considered promising to evaluate dynamic changes of the interfacial area concentration in gas–liquid two-phase flows, which is of significance in characterizing the interfacial structure of the flows. Efforts were made by the authors in the past on the implementation of the IATE into computational fluid dynamics codes, such as Fluent. However, it remained unclear whether the IATE model coefficients derived from one-dimensional IATE model calibrations can be applied to three-dimensional simulations. The current study aimed to examine, primarily by investigating the lateral profiles of phase distributions, the applicability of the coefficients obtained from the one-dimensional IATE model calibration to a three-dimensional simulation of bubbly flow in a pipe. In addition, effects of the lift force on the lateral phase distributions were studied. A new set of the IATE model coefficients was suggested for a three-dimensional bubbly flow simulation. Good agreement was obtained with the updated coefficients between the predicted and measured flow parameters.     

The effect of water molecule on the thermal stability of lanthanide compounds with 1,3-benzeneditetrazol-5-yl

Six lanthanide compounds [Ln(H₂O)₉](m-BDTH)₃·9(H₂O) where Ln = La (1), and [Ln(H₂O)₈](m-BDTH)₃·9(H₂O) (m-BDTH₂ = 1,3-benzeneditetrazol-5-yl) where Ln = Lu (2), Yb (3), Er (4), Ho (5) and Y (6) were hydrothermally synthesized and characterized by elemental analyses, infrared spectra, powder X-ray diffraction (PXRD) and X-ray single crystal diffraction. PXRD indicates that 2–6 are isomorphous. Structural analyses reveal that 1 is coordinated by nine water molecules forming a capped-square antiprism, while 2–6 are coordinated by eight water molecules forming a simple square antiprismatic geometry. Effects of water molecules on thermal stability were also discussed by thermogravimetric (TG), DSC, and PXRD under different temperatures. TG analyses suggest that 1 loses lattice and coordinated water molecules with no diacritical boundary, and 6 removes lattice water molecules first and then coordinated water molecules. DSC and PXRD further confirm the consequence.     

Intermolecular cyclocondensation reaction of 3,4-dihydropyrimidine-2-thione under the Mitsunobu reaction conditions

A self-intermolecular cyclocondensation reaction of 3,4-dihydropyrimidine-2-thione(DHPM) to give a novel tricyclic structure containing DHPM core in the presence of diethyl azodicarboxylate(DEAD) and triphenylphosphine(TPP) at room temperature is reported.     

Synthesis of cyclicβ-silylenones via oxidative rearrangement of tertiaryα-hydroxy allylsilanes with PCC

An oxidative rearrangement of cyclic tertiary a-hydroxy allylsilanes has been carried out in refluxing ClCH₂CH₂Cl with pyridinium chlorochromate（PCC）.The reaction provides a convenient method to synthesize cyclicβ-silylenones in modest to excellent yields.     

An efficient and convenient method for preparation of disulfides from thiols using air as oxidant catalyzed by Co-Salophen

Disulfides have been synthesized by oxidation of thiols using air as oxidant catalyzed by Co-Salophen with high yields,mild and neutral conditions,and easy procedures of the catalyst.The products were confirmed by ~1H NMR and IR.