ON THE ERROR-SUM FUNCTION OF ALTERNATING LüROTH SERIES

The error-sum function of alternating Luroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.     

Conservative schemes for the symmetric Regularized Long Wave equations

In this paper, we study the Symmetric Regularized Long Wave (SRLW) equations by finite difference method. We design some numerical schemes which preserve the original conservative properties for the equations. The first scheme is two-level and nonlinear-implicit. Existence of its difference solutions are proved by Brouwer fixed point theorem. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable and second-order convergent for U in L_∞ norm, and for N in L₂ norm on the basis of the priori estimates. The second scheme is three-level and linear-implicit. Its stability and second-order convergence are proved. Both of the two schemes are conservative so can be used for long time computation. However, they are coupled in computing so need more CPU time. Thus we propose another three-level linear scheme which is not only conservative but also uncoupled in computation, and give the numerical analysis on it. Numerical experiments demonstrate that the schemes are accurate and efficient.     

Iron oxide and alumina nanocomposites applied to Fischer-Tropsch synthesis

Nanocomposites composed of nanoparticles of iron oxide and aluminium oxide (Fe(2)O(3)-Al(2)O(3)) with a unique structure show a remarkable catalytic performance in Fischer-Tropsch synthesis (FTS), compared with the traditional iron-based catalyst.     

Nanocrystals of CeVO4 doped by metallic heteroions

CeVO(4) nanocrystals doped by heteroions were prepared via a hydrothermal method without the presence of surfactants or templates. Transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), X-ray diffraction (XRD), solid state (51)V NMR, and inductively coupled plasma (ICP) were used to characterize the morphology, structure, and compositions of the materials. X-ray photoelectron spectroscopy (XPS) results confirmed that there is a valence change from Ce(3+) to Ce(4+) for a fraction of cerium atoms whereas the vanadium atoms remain in the pentavalent state V(5+) upon the substitution of Ca(2+) into CeVO(4). Raman spectroscopy was used to monitor the effects of the doping ion on the CeVO(4) lattice contraction and distortion. The appearance of the shifted and broadened Raman peaks for the doped CeVO(4) was interpreted by theoretical calculations performed with Vienna ab initio simulation package. The redox properties and photocatalytic activities of the obtained nanocrystals were also investigated and discussed in detail.     

On finite difference methods for fourth-order fractional diffusion-wave and subdiffusion systems

In this paper, firstly, the finite difference method is explored for the fourth-order fractional diffusion-wave system. The method is proved to be uniquely solvable, stable and convergent in l_∞-norm by the energy method. Then we examine a subdiffusion system and present the numerical analysis using a different method. Numerical experiments are provided to demonstrate the accuracy and efficiency of the proposed schemes.     

High resolution O MAS and triple-quantum MAS NMR studies of gallosilicate glasses

Gallosilicate (or ‘galliosilicate’) glasses have been widely studied as analogs of aluminosilicates, and the variations with composition in properties are known to be similar in both systems. We have applied ¹⁷O MAS and triple-quantum MAS (3QMAS) NMR spectroscopy to investigate the oxygen local environments in Na-, Li-, Ca- and Y-gallosilicate glasses. Signals due to several different oxygen species can be resolved and their concentrations quantified and NMR parameters determined. The NMR spectra generally resemble those of aluminosilicate glasses, indicating that the current model of gallium ions occupying the same types of sites as aluminum ions is a good first approximation. Quadrupolar coupling constants for the various oxygen sites tend to be larger than those for aluminosilicates, however, and vary less among different types of sites. Broader ¹⁷O spectra at low to medium external magnetic fields result. In detail, several types of differences between the observed oxygen species populations for gallosilicate and aluminosilicate are consistent with the larger radius of Ga³⁺ in comparison to Al³⁺, and possibly with a somewhat greater tendency for the former to form groups with oxygen coordination numbers greater than four. These include more Si-Ga disorder than Si-Al disorder in corresponding sodium gallo- vs. aluminosilicates, and more ‘non-stoichiometric’ non-bridging oxygen in a calcium gallosilicate than in a calcium aluminosilicate glass.     

ON THE ERROR-SUM FUNCTION OF ALTERNATING L(U)ROTH SERIES

The error-sum function of alternating Lüroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.     

阿硅正传

Silicon is the second most abundant element in the earth's crust, and its compounds are indispensable in our production and life. The application and prospect of Silicon and its compounds are described in this paper from the perspective of Silicon's past life, present life and future.     

Hydrophobic Functionalization of ZnO Nanosheets by In Situ Center‐Substituted Synthesis for Selective Photocatalysis under Visible Irradiation

The selective degradation of specific substances in mixed contaminants is quite challenging. And a general approach for sensitized oxide semiconductor relies on dip‐coating method with sensitizer. Here, hydrophilic 2D, nest‐like architecture ZnO (ZnO NA) was hydrophobicly functioned by monomolecular–layer tetraphenylporphyrin zinc (ZnTPP), where ZnTPP was synthesized by means of an in situ center‐substituted (ISCS) process., i.e., the hydrogen atoms in the core of metal‐free tetraphenylporphyrin (H₂TPP) are substituted by the unsaturated zinc ions in ZnO NAs. ZnTPP/ZnO NA was exhibited with significant hydrophobicity, benefitting to absorb hydrophobic phenol (PL). Further, it is realized to selectively photodegradate PL in the mixture by ZnTPP/ZnO NAs under visible irradiation. Note that the rate of degradation to hydrophobic PL by ZnTPP/ZnO NA is 9.17 times of that for ZnO NA within 150 min; on the contrary, the degradation rate of hydrophilic rhodamine B (RhB) by ZnTPP/ZnO is reduced by 40%. Radiative lifetime of photogenerated charges is obviously increased by ZnTPP/ZnO NA compared with that of ZnTPP, indicating the effective charge separation for ZnTPP/ZnO NAs. In addition, ZnTPP/ZnO NA produced more superoxide radicals (·O₂^?) in comparison to ZnO NA. With surface functionalization, the feasibility of selective photocatalysis under visible irradiation is demonstrated.     

一种单摄像机虚拟鼠标的标定方法

建立单摄像机虚拟鼠标的数学模型,提出一种虚拟鼠标的现场标定方法.以二维实体靶标为中介.利用计算机屏幕生成的虚拟靶标,确定摄像机坐标系到屏幕坐标系的变换.建立空间三维控制点图像坐标到鼠标指针的映射,实现了单摄像机虚拟鼠标的现场标定.提出的方法无需高成本的辅助设备,现场操作简单.在30 cm作用距离内采用640 pixel×480 pixel图像中50个特征点,当图像噪声方差达到1 pixel时,试验中控制点映射为屏幕坐标的均方根(RMS)误差小于3 pixel.该方法应用于研发的虚拟鼠标演示程序.表明切实可行,适用于虚拟鼻尖鼠标的现场标定.